diff --git a/lean/OAI/Analysis/OInfinity/ProjectionCorner.lean b/lean/OAI/Analysis/OInfinity/ProjectionCorner.lean new file mode 100644 index 0000000000000000000000000000000000000000..b74b2d4b030ddff6517e9733b81e7d103b9c27ee --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ProjectionCorner.lean @@ -0,0 +1,166 @@ +import OAI.Analysis.OInfinity.RowCocycleDefect + +namespace OAI + +/-! # Unital C⋆ structure and unitary paths in a projection corner + +The corner has unit `q`; its inclusion in the ambient algebra is nonunital. +A corner unitary becomes an ambient unitary by adding `1-q`, preserving +norm differences and therefore the quantitative path estimates. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +def projectionCornerAlgebra (q : E) (hq : star q = q) : NonUnitalStarSubalgebra ℂ E where + carrier := {x | q * x = x ∧ x * q = x} + zero_mem' := by simp + add_mem' hx hy := by + exact ⟨by rw [mul_add, hx.1, hy.1], by rw [add_mul, hx.2, hy.2]⟩ + mul_mem' hx hy := ⟨by rw [← mul_assoc, hx.1], by rw [mul_assoc, hy.2]⟩ + smul_mem' c x hx := + ⟨by rw [mul_smul_comm, hx.1], by rw [smul_mul_assoc, hx.2]⟩ + star_mem' hx := ⟨by simpa only [star_mul, hq] using congrArg star hx.2, + by simpa only [star_mul, hq] using congrArg star hx.1⟩ + +lemma projectionCornerAlgebra_closed (q : E) (hq : star q = q) : + IsClosed (projectionCornerAlgebra q hq : Set E) := + (isClosed_eq (by fun_prop) continuous_id).inter + (isClosed_eq (by fun_prop) continuous_id) + +/-- The closed supported corner, equipped below with unit `q`. -/ +abbrev ProjectionCorner (q : E) (hq : star q = q) (_hqq : q * q = q) : Type _ := + projectionCornerAlgebra q hq + +instance projectionCornerClosed (q : E) (hq : star q = q) : + IsClosed (projectionCornerAlgebra q hq : Set E) := projectionCornerAlgebra_closed q hq + +instance projectionCornerSemiring (q : E) (hq : star q = q) (hqq : q * q = q) : + Semiring (ProjectionCorner q hq hqq) where + __ : NonUnitalSemiring (ProjectionCorner q hq hqq) := + inferInstanceAs (NonUnitalSemiring (projectionCornerAlgebra q hq)) + one := ⟨q, hqq, hqq⟩ + one_mul x := Subtype.ext x.property.1 + mul_one x := Subtype.ext x.property.2 + +instance projectionCornerRing (q : E) (hq : star q = q) (hqq : q * q = q) : + Ring (ProjectionCorner q hq hqq) where + __ : Semiring (ProjectionCorner q hq hqq) := projectionCornerSemiring q hq hqq + __ : NonUnitalRing (ProjectionCorner q hq hqq) := + inferInstanceAs (NonUnitalRing (projectionCornerAlgebra q hq)) + +instance projectionCornerNormedRing (q : E) (hq : star q = q) (hqq : q * q = q) : + NormedRing (ProjectionCorner q hq hqq) where + __ : Ring (ProjectionCorner q hq hqq) := projectionCornerRing q hq hqq + __ : NonUnitalNormedRing (ProjectionCorner q hq hqq) := + inferInstanceAs (NonUnitalNormedRing (projectionCornerAlgebra q hq)) + +instance projectionCornerAlgebraStructure (q : E) (hq : star q = q) (hqq : q * q = q) : + Algebra ℂ (ProjectionCorner q hq hqq) := + Algebra.ofModule (fun _ _ _ => Subtype.ext (smul_mul_assoc _ _ _)) + (fun _ _ _ => Subtype.ext (mul_smul_comm _ _ _)) + +instance projectionCornerNormedAlgebra (q : E) (hq : star q = q) (hqq : q * q = q) : + NormedAlgebra ℂ (ProjectionCorner q hq hqq) where + __ := projectionCornerAlgebraStructure q hq hqq + norm_smul_le c x := by exact norm_smul_le c (x : E) + +instance projectionCornerCStarAlgebra (q : E) (hq : star q = q) (hqq : q * q = q) : + CStarAlgebra (ProjectionCorner q hq hqq) where + __ : NormedRing (ProjectionCorner q hq hqq) := projectionCornerNormedRing q hq hqq + __ : NormedAlgebra ℂ (ProjectionCorner q hq hqq) := projectionCornerNormedAlgebra q hq hqq + __ : StarRing (ProjectionCorner q hq hqq) := + inferInstanceAs (StarRing (projectionCornerAlgebra q hq)) + __ : CompleteSpace (ProjectionCorner q hq hqq) := + inferInstanceAs (CompleteSpace (projectionCornerAlgebra q hq)) + __ : StarModule ℂ (ProjectionCorner q hq hqq) := + inferInstanceAs (StarModule ℂ (projectionCornerAlgebra q hq)) + norm_mul_self_le x := (CStarRing.norm_star_mul_self (x := (x : E))).symm.le + +instance projectionCornerNontrivial (q : E) (hq : star q = q) (hqq : q * q = q) + [NeZero q] : Nontrivial (ProjectionCorner q hq hqq) := by + apply nontrivial_of_ne (0 : ProjectionCorner q hq hqq) 1 + intro h + have he := congrArg (fun x : ProjectionCorner q hq hqq => (x : E)) h + exact (NeZero.ne q) he.symm + +/-- The algebra inclusion sends the corner unit to `q`. -/ +def projectionCornerInclusion (q : E) (hq : star q = q) (hqq : q * q = q) : + ProjectionCorner q hq hqq →⋆ₙₐ[ℂ] E where + toFun x := x + map_zero' := rfl + map_add' _ _ := rfl + map_mul' _ _ := rfl + map_smul' _ _ := rfl + map_star' _ := rfl + +lemma projectionCornerInclusion_one (q : E) (hq : star q = q) (hqq : q * q = q) : + projectionCornerInclusion q hq hqq 1 = q := rfl + +/-- Extending by the complementary identity gives an ambient unitary. -/ +def projectionCornerUnitary (q : E) (hq : star q = q) (hqq : q * q = q) + (u : unitary (ProjectionCorner q hq hqq)) : unitary E := by + let x : E := (u : ProjectionCorner q hq hqq) + have hl : q * x = x := (u : ProjectionCorner q hq hqq).property.1 + have hr : x * q = x := (u : ProjectionCorner q hq hqq).property.2 + have hxs : star x * x = q := congrArg + (fun y : ProjectionCorner q hq hqq => (y : E)) u.property.1 + have hsx : x * star x = q := congrArg + (fun y : ProjectionCorner q hq hqq => (y : E)) u.property.2 + have hls : q * star x = star x := by + simpa only [star_mul, hq] using congrArg star hr + have hrs : star x * q = star x := by + simpa only [star_mul, hq] using congrArg star hl + refine ⟨x + (1 - q), ?_, ?_⟩ + · change star (x + (1 - q)) * (x + (1 - q)) = 1 + simp only [star_add, star_sub, star_one, hq, add_mul, mul_add, mul_sub, + sub_mul, one_mul, mul_one, hxs, hqq, hl, hrs] + abel + · change (x + (1 - q)) * star (x + (1 - q)) = 1 + simp only [star_add, star_sub, star_one, hq, add_mul, mul_add, mul_sub, + sub_mul, one_mul, mul_one, hsx, hqq, hr, hls] + abel + +lemma projectionCornerUnitary_one (q : E) (hq : star q = q) (hqq : q * q = q) : + projectionCornerUnitary q hq hqq 1 = 1 := by + apply Subtype.ext + change q + (1 - q) = 1 + abel + +lemma projectionCornerUnitary_continuous (q : E) (hq : star q = q) (hqq : q * q = q) : + Continuous (projectionCornerUnitary q hq hqq) := by + apply Continuous.subtype_mk + change Continuous (fun u : unitary (ProjectionCorner q hq hqq) => + ((u : ProjectionCorner q hq hqq) : E) + (1 - q)) + exact (continuous_subtype_val.comp continuous_subtype_val).add continuous_const + +lemma projectionCornerUnitary_sub_norm (q : E) (hq : star q = q) (hqq : q * q = q) + (u v : unitary (ProjectionCorner q hq hqq)) : + ‖(projectionCornerUnitary q hq hqq u : E) - projectionCornerUnitary q hq hqq v‖ = + ‖(u : ProjectionCorner q hq hqq) - v‖ := by + change ‖(((u : ProjectionCorner q hq hqq) : E) + (1 - q)) - + (((v : ProjectionCorner q hq hqq) : E) + (1 - q))‖ = + ‖((u : ProjectionCorner q hq hqq) : E) - ((v : ProjectionCorner q hq hqq) : E)‖ + congr 1 + abel + +/-- Quantitative paths lift to the ambient algebra with no loss. -/ +lemma projectionCornerPath_controlled (q : E) (hq : star q = q) (hqq : q * q = q) + {u v : unitary (ProjectionCorner q hq hqq)} + (p : Path u v) (L : ℝ) + (hp : ∀ a b, ‖(p a : ProjectionCorner q hq hqq) - p b‖ ≤ L * |(a : ℝ) - b|) : + ∃ r : Path (projectionCornerUnitary q hq hqq u) (projectionCornerUnitary q hq hqq v), + ∀ a b, ‖(r a : E) - r b‖ ≤ L * |(a : ℝ) - b| := by + refine ⟨p.map (projectionCornerUnitary_continuous q hq hqq), ?_⟩ + intro a b + exact (projectionCornerUnitary_sub_norm q hq hqq (p a) (p b)).trans_le (hp a b) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ProperBufferAbsorption.lean b/lean/OAI/Analysis/OInfinity/ProperBufferAbsorption.lean new file mode 100644 index 0000000000000000000000000000000000000000..19fe04180d83769108896394ff41d19d2520ce38 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ProperBufferAbsorption.lean @@ -0,0 +1,261 @@ +import OAI.Analysis.OInfinity.BufferAnchor +import OAI.Analysis.OInfinity.ZeroUnitRows + +namespace OAI + +/-! # Connected absorption of an arbitrary finite proper row + +The target row is completed inside the zero-unit buffer corner. Only the +prescribed original entries must commute with the binary buffer; the +auxiliary completing entry is never included in that requirement. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +section Selected +variable {I : Type*} [Fintype I] [DecidableEq I] + +/-- The finite Fock estimate only needs coefficient commutation at the +indices at which an intertwining estimate is requested. -/ +lemma BufferAbsorptionCorner.exists_finite_absorption_on [Nontrivial E] + (D : BufferAbsorptionCorner E) (s t : I → E) (r : E) (P : I → Prop) + (hrr : star r * r = 1) (hr : ∀ i, star r * s i = 0) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hqr : Commute D.q r) (hqs : ∀ i, Commute D.q (s i)) + (htq : ∀ i, t i * D.q = t i) (ht : ∑ i, t i * star (t i) = D.q) + (htt : ∀ i j, star (t i) * t j = if i = j then D.q else 0) + (hat : ∀ i, P i → Commute (star D.a) (t i)) + (hbt : ∀ i, P i → Commute (star D.b) (t i)) + (ε : ℝ) (hε : 0 < ε) : + ∃ W : unitary E, Joined D.anchor W ∧ + ∀ i, P i → ‖(W : E) * s i - (t i + D.w * s i * star D.w) * (W : E)‖ < ε := by + let δ := ε / 6 + have hδ : 0 < δ := by dsimp only [δ]; positivity + obtain ⟨m, hm⟩ := exists_nat_gt (2 / δ ^ 2) + have hsmall : 2 / ((m : ℝ) + 1) < δ ^ 2 := by + have hδsq : 0 < δ ^ 2 := sq_pos_of_pos hδ + have hm' : 2 < (m : ℝ) * δ ^ 2 := (div_lt_iff₀ hδsq).mp hm + apply (div_lt_iff₀ (by positivity : 0 < (m : ℝ) + 1)).mpr + nlinarith + let v := finiteRowIsometry s t r D.q m + have hvg : star v * v = D.q := finiteRowIsometry_gram s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq hrr hr hs htq ht m + have hvq : v * D.q = v := relativeIsometry_mul_support v D.q hvg + D.projection.isSelfAdjoint.star_eq D.projection.isIdempotentElem.eq + have hqv : D.q * v = v := finiteRowIsometry_left_of_commute s t r D.q + D.projection.isIdempotentElem.eq hqr hqs m + have hvstarq : star v * D.q = star v := by + simpa only [star_mul, D.projection.isSelfAdjoint.star_eq] using congrArg star hqv + have hvw : star v * D.w = 0 := by + rw [← hvstarq, mul_assoc, D.w_orthogonal, mul_zero] + obtain ⟨u, hu, _, huv⟩ := exists_explicit_connected_unitary_extension v D.w + (by rw [mul_assoc, hvg, hvq]) D.w_gram (by rw [hvg]; exact D.w_orthogonal) + (by rw [mul_assoc, hvw, mul_zero]) + have huq : (u : E) * D.q = v := by simpa only [hvg] using huv + have hvn : ‖v‖ ≤ 1 := finiteRowIsometry_norm_le s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq hrr hr hs htq ht m + refine ⟨D.absorption u, D.absorption_joined_anchor u hu, ?_⟩ + intro i hi + have hf : ‖s i * v - v * t i‖ < δ := by + have h := finiteRowIsometry_forward_norm_sq s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq + hrr hr hs htq ht htt m i + change ‖s i * v - v * t i‖ ^ 2 ≤ _ at h + nlinarith [norm_nonneg (s i * v - v * t i)] + have hb : ‖star v * s i - t i * star v‖ < δ := by + have h := finiteRowIsometry_backward_norm_sq s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq + hrr hr hs htq ht htt m i + have he : star v * s i - t i * star v = + star (star (s i) * v - v * star (t i)) := by + simp only [star_sub, star_mul, star_star] + rw [he, norm_star] + have hone : ((m : ℝ) + 1)⁻¹ ≤ 2 / ((m : ℝ) + 1) := by + rw [← one_div] + exact div_le_div_of_nonneg_right (by norm_num) (by positivity) + change ‖star (s i) * v - v * star (t i)‖ ^ 2 ≤ _ at h + nlinarith [norm_nonneg (star (s i) * v - v * star (t i))] + calc + _ ≤ 2 * ‖s i * v - v * t i‖ + 3 * ‖star v * s i - t i * star v‖ := + D.absorption_error_bound u v (s i) (t i) huq (htq i) (hat i hi) (hbt i hi) hvn + _ < ε := by dsimp only [δ] at hf hb; linarith + +end Selected + +lemma BufferAbsorptionCorner.extend_finite_proper_row + (D : BufferAbsorptionCorner E) (n : ℕ) (x : Fin (n + 1) → E) + (hxs : ∀ i, D.q * x i = x i ∧ x i * D.q = x i) + (hx : ∀ i j, star (x i) * x j = if i = j then D.q else 0) : + ∃ t : Fin (n + 1) → E, + (∀ i : Fin n, t i.succ = x i.castSucc) ∧ + (∀ i, D.q * t i = t i ∧ t i * D.q = t i) ∧ + (∀ i j, star (t i) * t j = if i = j then D.q else 0) ∧ + (∑ i, t i * star (t i)) = D.q := by + let C := ProjectionCorner D.q D.projection.isSelfAdjoint.star_eq + D.projection.isIdempotentElem.eq + let x' : Fin (n + 1) → C := fun i => ⟨x i, hxs i⟩ + let a' : C := ⟨D.a, D.a_left, D.a_right⟩ + let b' : C := ⟨D.b, D.b_left, D.b_right⟩ + have hx' (i j : Fin (n + 1)) : star (x' i) * x' j = if i = j then 1 else 0 := by + apply Subtype.ext + change star (x i) * x j = ↑(if i = j then (1 : C) else 0) + split_ifs with h + · change star (x i) * x j = D.q + simpa only [h, ite_true] using hx i j + · change star (x i) * x j = 0 + simpa only [h, ite_false] using hx i j + have hlast (i : Fin n) : star (x' (Fin.last n)) * x' i.castSucc = 0 := by + rw [hx'] + have hne : Fin.last n ≠ i.castSucc := by + intro h + have hh := congrArg Fin.val h + change n = (i : ℕ) at hh + omega + rw [ite_eq_right hne] + obtain ⟨t, htx, ht, hts⟩ := finite_zero_unit_full_row + (fun i : Fin n => x' i.castSucc) (x' (Fin.last n)) a' b' + (fun i j => by simpa only [Fin.castSucc_inj] using hx' i.castSucc j.castSucc) + (by simpa only [ite_true] using hx' (Fin.last n) (Fin.last n)) hlast + (Subtype.ext D.a_gram) (Subtype.ext D.b_gram) + (Subtype.ext D.orthogonal) (Subtype.ext D.ranges) + refine ⟨fun i => (t i : E), fun i => congrArg (fun y : C => (y : E)) (htx i), + fun i => (t i).property, ?_, ?_⟩ + · intro i j + by_cases hij : i = j + · subst j + simp only [ite_true] + have h := ht i i + simp only [ite_true] at h + have he := congrArg (fun y : C => (y : E)) h + change star (t i : E) * (t i : E) = D.q at he + exact he + · rw [ite_eq_right hij] + have h := ht i j + rw [ite_eq_right hij] at h + have he := congrArg (fun y : C => (y : E)) h + change star (t i : E) * (t j : E) = 0 at he + exact he + + · have h := congrArg (projectionCornerInclusion D.q D.projection.isSelfAdjoint.star_eq + D.projection.isIdempotentElem.eq) hts + simp only [map_sum, map_mul, map_star, projectionCornerInclusion_one] at h + exact h + +/-- Connected absorption of any finite original proper-row prefix. The +complementary source row remains as an explicit summand. -/ +lemma exists_connected_proper_buffer_absorption [Nontrivial E] + (s t r : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (hrs : bergRowsCommute r s) (hrt : bergRowsCommute r t) + (n : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ U : unitary E, Joined (1 : unitary E) U ∧ + ∀ i : Fin n, + ‖(U : E) * s i * star (U : E) - + (t i * (1 - r 0 * star (r 0)) + s i * (r 0 * star (r 0)))‖ < ε := by + have rc (i j : ℕ) : Commute (r i) (s j) ∧ Commute (star (r i)) (s j) := + ⟨(hrs i j).1, by simpa only [star_star] using (hrs i j).2.star_star⟩ + have tc (i j : ℕ) : Commute (r i) (t j) ∧ Commute (star (r i)) (t j) := + ⟨(hrt i j).1, by simpa only [star_star] using (hrt i j).2.star_star⟩ + obtain ⟨D, hDq, hDw, _, hDjoin, hDc⟩ := exists_connected_buffer_corner (r 0) (r 1) (r 2) + (by simpa only [ite_true] using hr 0 0) + (by simpa only [ite_true] using hr 1 1) + (by simpa only [ite_true] using hr 2 2) + (by simpa using hr 0 1) (by simpa using hr 0 2) (by simpa using hr 1 2) + have hqs (i : ℕ) : Commute D.q (s i) := by + rw [hDq] + exact (Commute.one_left _).sub_left ((rc 0 i).1.mul_left (rc 0 i).2) + have hqt (i : ℕ) : Commute D.q (t i) := by + rw [hDq] + exact (Commute.one_left _).sub_left ((tc 0 i).1.mul_left (tc 0 i).2) + let x : Fin (n + 1) → E := fun i => t i * D.q + have hxs (i : Fin (n + 1)) : D.q * x i = x i ∧ x i * D.q = x i := by + constructor + · change D.q * (t i * D.q) = t i * D.q + rw [← mul_assoc, (hqt i).eq, mul_assoc, D.projection.isIdempotentElem.eq] + · change (t i * D.q) * D.q = t i * D.q + rw [mul_assoc, D.projection.isIdempotentElem.eq] + have hx (i j : Fin (n + 1)) : star (x i) * x j = if i = j then D.q else 0 := by + change star (t i * D.q) * (t j * D.q) = _ + rw [star_mul, D.projection.isSelfAdjoint.star_eq] + calc + _ = D.q * (star (t i) * t j) * D.q := by noncomm_ring + _ = _ := by + by_cases hij : i = j + · subst j + simp only [ht, ite_true, mul_one, D.projection.isIdempotentElem.eq] + · rw [ht, ite_eq_right (fun h => hij (Fin.ext h)), + ite_eq_right hij, mul_zero, zero_mul] + obtain ⟨T, hTx, hTq, hT, hTs⟩ := D.extend_finite_proper_row n x hxs hx + let S : Fin (n + 1) → E := Fin.cons (s n) (fun i : Fin n => s i) + have hS (i j : Fin (n + 1)) : star (S i) * S j = if i = j then 1 else 0 := by + refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j + · simpa only [S, Fin.cons_zero, ite_true] using hs n n + · have hne : n ≠ (j : ℕ) := by omega + simpa only [S, Fin.cons_zero, Fin.cons_succ, hne, ite_false, + (Fin.succ_ne_zero j).symm] using hs n j + · have hne : (i : ℕ) ≠ n := by omega + simpa only [S, Fin.cons_zero, Fin.cons_succ, hne, ite_false, + Fin.succ_ne_zero] using hs i n + · simpa only [S, Fin.cons_succ, Fin.succ_inj, Fin.ext_iff, Fin.val_succ, Nat.succ.injEq] using hs i j + have hroot (i : Fin (n + 1)) : star (s (n + 1)) * S i = 0 := by + refine Fin.cases ?_ (fun j => ?_) i + · simpa only [S, Fin.cons_zero, Nat.add_one_ne_self, ite_false] using hs (n + 1) n + · have hne : n + 1 ≠ (j : ℕ) := by omega + simpa only [S, Fin.cons_succ, hne, ite_false] using hs (n + 1) j + have hqS (i : Fin (n + 1)) : Commute D.q (S i) := by + refine Fin.cases (hqs n) (fun j => hqs j) i + have haT (i : Fin (n + 1)) (hi : 0 < (i : ℕ)) : Commute (star D.a) (T i) := by + revert hi + refine Fin.cases ?_ (fun j => ?_) i + · intro h; exact (Nat.lt_irrefl 0 h).elim + · intro _ + rw [hTx] + change Commute (star D.a) (t j * D.q) + exact ((hDc (t j) (tc 0 j).1 (tc 0 j).2 (tc 1 j).1 (tc 1 j).2 + (tc 2 j).1 (tc 2 j).2).2.1).mul_right + (D.a_star_right.trans D.a_star_left.symm) + have hbT (i : Fin (n + 1)) (hi : 0 < (i : ℕ)) : Commute (star D.b) (T i) := by + revert hi + refine Fin.cases ?_ (fun j => ?_) i + · intro h; exact (Nat.lt_irrefl 0 h).elim + · intro _ + rw [hTx] + change Commute (star D.b) (t j * D.q) + exact ((hDc (t j) (tc 0 j).1 (tc 0 j).2 (tc 1 j).1 (tc 1 j).2 + (tc 2 j).1 (tc 2 j).2).2.2.2).mul_right + (D.b_star_right.trans D.b_star_left.symm) + obtain ⟨U, hU, hUi⟩ := D.exists_finite_absorption_on S T (s (n + 1)) + (fun i => 0 < (i : ℕ)) (by simpa only [ite_true] using hs (n + 1) (n + 1)) + hroot hS (hqs (n + 1)) hqS (fun i => (hTq i).2) hTs hT haT hbT ε hε + refine ⟨U, hDjoin.trans hU, fun i => ?_⟩ + have hi := hUi i.succ (by simp) + rw [hTx] at hi + have he : D.w * s i * star D.w = s i * (r 0 * star (r 0)) := by + rw [hDw, (rc 0 i).1.eq, mul_assoc] + change ‖(U : E) * s i - (x i.castSucc + D.w * s i * star D.w) * (U : E)‖ < ε at hi + have hmul : ((U : E) * s i - (x i.castSucc + D.w * s i * star D.w) * (U : E)) * + star (U : E) = (U : E) * s i * star (U : E) - + (x i.castSucc + D.w * s i * star D.w) := by + rw [sub_mul, mul_assoc _ (U : E), Unitary.mul_star_self_of_mem U.property, mul_one] + have hnorm := CStarRing.norm_mul_mem_unitary + ((U : E) * s i - (x i.castSucc + D.w * s i * star D.w) * (U : E)) + (Unitary.star_mem U.property) + rw [hmul] at hnorm + have hc : ‖(U : E) * s i * star (U : E) - + (x i.castSucc + D.w * s i * star D.w)‖ < ε := by + rw [hnorm] + exact hi + simpa only [x, Fin.val_castSucc, hDq, he] using hc + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RelativeCocycle.lean b/lean/OAI/Analysis/OInfinity/RelativeCocycle.lean new file mode 100644 index 0000000000000000000000000000000000000000..636e3522ef7acb79efcf78d903e40c6589d64a67 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RelativeCocycle.lean @@ -0,0 +1,152 @@ +import OAI.Analysis.OInfinity.ProjectionCorner + +namespace OAI + +/-! # Actual binary row cocycles in a proper projection corner + +The corner unitary is extended by the identity on the complementary +projection. The complement is retained explicitly; this is not yet an +ambient approximate intertwining statement for the canonical O∞ rows. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- A supported element, regarded as an element of the unital corner. -/ +def projectionCornerElement (q : E) (hq : star q = q) (hqq : q * q = q) + (x : E) (hx : q * x = x ∧ x * q = x) : ProjectionCorner q hq hqq := ⟨x, hx⟩ + +lemma projectionCornerElement_gram {I : Type*} [DecidableEq I] + (q : E) (hq : star q = q) (hqq : q * q = q) (s : I → E) + (hsp : ∀ i, q * s i = s i ∧ s i * q = s i) + (hs : ∀ i j, star (s i) * s j = if i = j then q else 0) (i j : I) : + star (projectionCornerElement q hq hqq (s i) (hsp i)) * + projectionCornerElement q hq hqq (s j) (hsp j) = if i = j then 1 else 0 := by + apply Subtype.ext + split_ifs with hij + · change star (s i) * s j = q + simpa only [hij, ite_true] using hs i j + · change star (s i) * s j = 0 + simpa only [hij, ite_false] using hs i j + +lemma projectionCornerElement_range_sum {I : Type*} [Fintype I] + (q : E) (hq : star q = q) (hqq : q * q = q) (s : I → E) + (hsp : ∀ i, q * s i = s i ∧ s i * q = s i) + (hsum : (∑ i, s i * star (s i)) = q) : + (∑ i, projectionCornerElement q hq hqq (s i) (hsp i) * + star (projectionCornerElement q hq hqq (s i) (hsp i))) = 1 := by + apply Subtype.ext + change projectionCornerInclusion q hq hqq (∑ i, + projectionCornerElement q hq hqq (s i) (hsp i) * + star (projectionCornerElement q hq hqq (s i) (hsp i))) = q + rw [map_sum] + exact hsum + +lemma projectionCornerInclusion_rowCocycle {I : Type*} [Fintype I] + (q : E) (hq : star q = q) (hqq : q * q = q) + (s t : I → ProjectionCorner q hq hqq) : + projectionCornerInclusion q hq hqq (finiteRowCocycle s t) = + finiteRowCocycle (fun i => (s i : E)) (fun i => (t i : E)) := by + simp only [finiteRowCocycle, map_sum, map_mul, map_star] + rfl + +lemma projectionCornerInclusion_rowShift {I : Type*} [Fintype I] + (q : E) (hq : star q = q) (hqq : q * q = q) + (s : I → ProjectionCorner q hq hqq) (x : ProjectionCorner q hq hqq) : + projectionCornerInclusion q hq hqq (finiteRowShift s x) = + finiteRowShift (fun i => (s i : E)) (x : E) := by + simp only [finiteRowShift, map_sum, map_mul, map_star] + rfl + +/-- The actual product cocycle, with the corner unit as its zeroth term. -/ +def relativeRowProduct {I : Type*} [Fintype I] (q : E) (s t : I → E) : ℕ → E + | 0 => q + | n + 1 => finiteRowCocycle s t * finiteRowShift s (relativeRowProduct q s t n) + +lemma projectionCorner_rowProduct (q : E) (hq : star q = q) (hqq : q * q = q) + (s t : Fin 2 → ProjectionCorner q hq hqq) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) + (htsum : (∑ i, t i * star (t i)) = 1) (n : ℕ) : + ((binaryRowCocycleUnitary s t hs ht hsum htsum n : ProjectionCorner q hq hqq) : E) = + relativeRowProduct q (fun i => (s i : E)) (fun i => (t i : E)) n := by + induction n with + | zero => rfl + | succ n ih => + change projectionCornerInclusion q hq hqq + (finiteRowCocycle s t * + (binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1) + (binaryRowCocycleUnitary s t hs ht hsum htsum n) : ProjectionCorner q hq hqq)) = _ + rw [map_mul, binarySplitHom_coe s hs hsum, + projectionCornerInclusion_rowCocycle, projectionCornerInclusion_rowShift, ih] + rfl + +lemma projectionCornerUnitary_complement (q : E) (hq : star q = q) (hqq : q * q = q) + (u : unitary (ProjectionCorner q hq hqq)) : + (projectionCornerUnitary q hq hqq u : E) * (1 - q) = 1 - q ∧ + (1 - q) * (projectionCornerUnitary q hq hqq u : E) = 1 - q := by + have hl := (u : ProjectionCorner q hq hqq).property.1 + have hr := (u : ProjectionCorner q hq hqq).property.2 + change (((u : ProjectionCorner q hq hqq) : E) + (1 - q)) * (1 - q) = 1 - q ∧ + (1 - q) * (((u : ProjectionCorner q hq hqq) : E) + (1 - q)) = 1 - q + constructor + · simp only [add_mul, mul_sub, sub_mul, one_mul, mul_one, hqq, hr] + abel + · simp only [mul_add, mul_sub, sub_mul, one_mul, mul_one, hqq, hl] + abel + +/-- The uniform `192π` contraction survives proper-corner transport. +The constructed ambient unitary is exactly the product cocycle plus `1-q` +and fixes the complementary corner on both sides. -/ +lemma exists_relative_binaryRowCocycle_path + (q : E) (hq : star q = q) (hqq : q * q = q) (hqne : q ≠ 0) + (s t : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then q else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then q else 0) + (hsum : (∑ i, s i * star (s i)) = q) + (htsum : (∑ i, t i * star (t i)) = q) + (hc : ∀ i j, Commute (s i) (t j)) (n : ℕ) : + ∃ u : unitary E, (u : E) = relativeRowProduct q s t n + (1 - q) ∧ + (u : E) * (1 - q) = 1 - q ∧ (1 - q) * (u : E) = 1 - q ∧ + ∃ p : Path u 1, ∀ a b, ‖(p a : E) - p b‖ ≤ (192 * Real.pi) * |(a : ℝ) - b| := by + have : NeZero q := ⟨hqne⟩ + have hsp (i : Fin 2) : q * s i = s i ∧ s i * q = s i := + ⟨finiteRow_left_support q s hq hqq hs hsum i, + finiteRow_right_support q s hq hqq hs i⟩ + have htp (i : Fin 2) : q * t i = t i ∧ t i * q = t i := + ⟨finiteRow_left_support q t hq hqq ht htsum i, + finiteRow_right_support q t hq hqq ht i⟩ + let S : Fin 2 → ProjectionCorner q hq hqq := fun i => + projectionCornerElement q hq hqq (s i) (hsp i) + let T : Fin 2 → ProjectionCorner q hq hqq := fun i => + projectionCornerElement q hq hqq (t i) (htp i) + have hS := projectionCornerElement_gram q hq hqq s hsp hs + have hT := projectionCornerElement_gram q hq hqq t htp ht + have hSsum := projectionCornerElement_range_sum q hq hqq s hsp hsum + have hTsum := projectionCornerElement_range_sum q hq hqq t htp htsum + have hST (i j : Fin 2) : Commute (S i) (T j) := by + change S i * T j = T j * S i + apply Subtype.ext + exact (hc i j).eq + obtain ⟨p, hp⟩ := exists_uniform_binaryRowCocycle_path S T hS hT hSsum hTsum hST n + let v := binaryRowCocycleUnitary S T hS hT hSsum hTsum n + let u := projectionCornerUnitary q hq hqq v + obtain ⟨r, hr⟩ := projectionCornerPath_controlled q hq hqq p (192 * Real.pi) hp + refine ⟨u, ?_, (projectionCornerUnitary_complement q hq hqq v).1, + (projectionCornerUnitary_complement q hq hqq v).2, ?_⟩ + · change ((v : ProjectionCorner q hq hqq) : E) + (1 - q) = _ + rw [projectionCorner_rowProduct q hq hqq S T hS hT hSsum hTsum n] + rfl + · exact ⟨r.cast rfl (projectionCornerUnitary_one q hq hqq).symm, hr⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RelativeCompletedComparison.lean b/lean/OAI/Analysis/OInfinity/RelativeCompletedComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a58d4de04c52d49db8ebdad2fc44e4d78761028 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RelativeCompletedComparison.lean @@ -0,0 +1,147 @@ +import OAI.Analysis.OInfinity.BufferedProperComparison + +namespace OAI + +/-! # Relative comparison with the prescribed complementary action + +The corner path below is constructed from the pointwise complementary +identity, rather than inferred from ambient connectedness. It allows the +completed-row comparison to keep the external corner fixed exactly. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +lemma exists_projectionCorner_unitary_path + (q : E) (hq : star q = q) (hqq : q * q = q) + (u : unitary E) (P : Path (1 : unitary E) u) + (hP : ∀ t, (P t : E) * (1 - q) = 1 - q ∧ + (1 - q) * (P t : E) = 1 - q) : + ∃ v : unitary (ProjectionCorner q hq hqq), Joined 1 v ∧ + ((v : ProjectionCorner q hq hqq) : E) = (u : E) * q := by + let H := ProjectionCorner q hq hqq + have hcomm (t : unitInterval) : Commute (P t : E) q := + unitary_commutes_projection_of_fixed_complement q (P t) (hP t) + have hs (t : unitInterval) : q * ((P t : E) * q) = (P t : E) * q ∧ + ((P t : E) * q) * q = (P t : E) * q := by + constructor + · rw [← mul_assoc, ← (hcomm t).eq, mul_assoc, hqq] + · rw [mul_assoc, hqq] + let F : unitInterval → H := fun t => projectionCornerElement q hq hqq ((P t : E) * q) (hs t) + have hFunit (t : unitInterval) : F t ∈ unitary H := by + constructor + · apply Subtype.ext + change star ((P t : E) * q) * ((P t : E) * q) = q + rw [star_mul, hq] + calc + _ = q * (star (P t : E) * (P t : E)) * q := by noncomm_ring + _ = q := by rw [(P t).property.1, mul_one, hqq] + · apply Subtype.ext + change ((P t : E) * q) * star ((P t : E) * q) = q + rw [star_mul, hq] + calc + _ = (P t : E) * (q * q) * star (P t : E) := by noncomm_ring + _ = (P t : E) * q * star (P t : E) := by rw [hqq] + _ = q * ((P t : E) * star (P t : E)) := by rw [(hcomm t).eq, mul_assoc] + _ = q := by rw [(P t).property.2, mul_one] + let V : unitInterval → unitary H := fun t => ⟨F t, hFunit t⟩ + have hF : Continuous F := Continuous.subtype_mk + ((continuous_subtype_val.comp P.continuous).mul continuous_const) _ + have hV : Continuous V := Continuous.subtype_mk hF _ + have hV0 : V 0 = 1 := by + apply Subtype.ext + apply Subtype.ext + change (P 0 : E) * q = q + rw [P.source, OneMemClass.coe_one, one_mul] + refine ⟨V 1, ?_, ?_⟩ + · exact ⟨{ toFun := V + continuous_toFun := hV + source' := hV0 + target' := rfl }⟩ + · change (P 1 : E) * q = (u : E) * q + rw [P.target] + +/-- Both actual completion records are used in the same corner. The +three-buffer row constructs the intermediate binary pair; the final +ambient unitary fixes the complement exactly. -/ +lemma exists_relative_completed_row_comparison {n : ℕ} + (q : E) (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (b : Fin 2 → E) + (hb : ∀ i j, star (b i) * b j = if i = j then q else 0) + (hbs : (∑ i, b i * star (b i)) = q) + (x y : Fin (n + 1) → E) + (A : RelativeBinaryCompletion q b x) (B : RelativeBinaryCompletion q b y) + (R : Fin 3 → E) + (hRs : ∀ i, q * R i = R i ∧ R i * q = R i) + (hR : ∀ i j, star (R i) * R j = if i = j then q else 0) + (hAR : bergRowsCommute A.row R) (hBR : bergRowsCommute B.row R) + (ε : ℝ) (hε : 0 < ε) : + ∃ w : unitary E, Joined (1 : unitary E) w ∧ + (w : E) * (1 - q) = 1 - q ∧ (1 - q) * (w : E) = 1 - q ∧ + ∀ i : Fin (n + 1), ‖(w : E) * x i * star (w : E) - y i‖ < ε := by + let : NeZero q := ⟨hq0⟩ + let H := ProjectionCorner q hq hqq + let f := projectionCornerInclusion q hq hqq + have hbsup (i : Fin 2) : q * b i = b i ∧ b i * q = b i := + ⟨finiteRow_left_support q b hq hqq hb hbs i, + finiteRow_right_support q b hq hqq hb i⟩ + let a : Fin 2 → H := fun i => projectionCornerElement q hq hqq (A.row i) (A.support i) + let c : Fin 2 → H := fun i => projectionCornerElement q hq hqq (B.row i) (B.support i) + let d : Fin 2 → H := fun i => projectionCornerElement q hq hqq (b i) (hbsup i) + let r : Fin 3 → H := fun i => projectionCornerElement q hq hqq (R i) (hRs i) + have ha := projectionCornerElement_gram q hq hqq A.row A.support A.gram + have hc := projectionCornerElement_gram q hq hqq B.row B.support B.gram + have hd := projectionCornerElement_gram q hq hqq b hbsup hb + have has := projectionCornerElement_range_sum q hq hqq A.row A.support A.range_sum + have hcs := projectionCornerElement_range_sum q hq hqq B.row B.support B.range_sum + have hds := projectionCornerElement_range_sum q hq hqq b hbsup hbs + have hr := projectionCornerElement_gram q hq hqq R hRs hR + obtain ⟨u, hu, hue⟩ := exists_projectionCorner_unitary_path q hq hqq + A.implementer A.deformation A.fixes_complement + obtain ⟨v, hv, hve⟩ := exists_projectionCorner_unitary_path q hq hqq + B.implementer B.deformation B.fixes_complement + have hua (j : Fin 2) : (u : H) * a j = d j := by + apply Subtype.ext + change (((u : H) : E) * A.row j) = b j + rw [hue, mul_assoc, (A.support j).1, A.cocycle] + have hvc (j : Fin 2) : (v : H) * c j = d j := by + apply Subtype.ext + change (((v : H) : E) * B.row j) = b j + rw [hve, mul_assoc, (B.support j).1, B.cocycle] + have har : bergRowsCommute a r := fun i j => + ⟨Subtype.ext (hAR i j).1.eq, Subtype.ext (hAR i j).2.eq⟩ + have hcr : bergRowsCommute c r := fun i j => + ⟨Subtype.ext (hBR i j).1.eq, Subtype.ext (hBR i j).2.eq⟩ + obtain ⟨w, hw, he⟩ := exists_connected_encoded_comparison_of_buffer r hr d a c + hd hds ha has hc hcs har hcr u v hu hv hua hvc n ε hε + let W := projectionCornerUnitary q hq hqq w + have hW : Joined (1 : unitary E) W := by + simpa only [projectionCornerUnitary_one] using + hw.map (projectionCornerUnitary_continuous q hq hqq) + refine ⟨W, hW, (projectionCornerUnitary_complement q hq hqq w).1, + (projectionCornerUnitary_complement q hq hqq w).2, fun i => ?_⟩ + have hh := he (i : ℕ) (by omega) + change ‖f ((w : H) * (a 0 ^ (i : ℕ) * a 1) * star (w : H) - + (c 0 ^ (i : ℕ) * c 1))‖ < ε at hh + have hax : f (a 0 ^ (i : ℕ) * a 1) = x i := by + rw [nonunital_map_pow_mul] + exact A.encoded_prefix i + have hcy : f (c 0 ^ (i : ℕ) * c 1) = y i := by + rw [nonunital_map_pow_mul] + exact B.encoded_prefix i + rw [map_sub] at hh + have hconj := projectionCornerUnitary_conjugate q hq hqq w (a 0 ^ (i : ℕ) * a 1) + change (W : E) * f (a 0 ^ (i : ℕ) * a 1) * star (W : E) = + f ((w : H) * (a 0 ^ (i : ℕ) * a 1) * star (w : H)) at hconj + rw [← hconj, hax, hcy] at hh + exact hh + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RelativeGramCorrection.lean b/lean/OAI/Analysis/OInfinity/RelativeGramCorrection.lean new file mode 100644 index 0000000000000000000000000000000000000000..dda51cde25c877a9193adc004896ed5d009a107a --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RelativeGramCorrection.lean @@ -0,0 +1,291 @@ +import OAI.Analysis.WeakInfiniteness.CuntzPairCorrection +import OAI.Analysis.OInfinity.MaskedBandRows + +namespace OAI + +/-! # Gram correction with a common initial projection + +The removed cyclic cell is not filled. Adding its complementary projection +only to the square Gram matrix permits inverse-square-root normalization; +the corrected rectangular row still has the original initial projection. +-/ + +noncomputable section +open scoped CStarAlgebra ComplexOrder + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] [PartialOrder E] [StarOrderedRing E] + +local instance relativeGramRealModule (n : Type*) [Fintype n] : + Module ℝ (CStarMatrix n n E) := Module.complexToReal _ +local instance relativeGramRealAlgebra (n : Type*) [Fintype n] [DecidableEq n] : + Algebra ℝ (CStarMatrix n n E) := Algebra.complexToReal + +/-- Rectangular normalization preserves an exact right support. -/ +lemma exists_relative_rectangular_isometry_near + {m n : Type*} [Fintype m] [Fintype n] [DecidableEq n] + (M ε : ℝ) (hM : 0 ≤ M) (hε : 0 < ε) : + ∃ δ : ℝ, 0 < δ ∧ ∀ (u : CStarMatrix m n E) (q : CStarMatrix n n E), + IsStarProjection q → u * q = u → ‖u‖ ≤ M → + ‖u.conjTranspose * u - q‖ < δ → + ∃ v : CStarMatrix m n E, + v * q = v ∧ v.conjTranspose * v = q ∧ ‖v - u‖ < ε := by + obtain ⟨δ, hδ, hcorr⟩ := exists_inverse_sqrt_tolerance + (A := CStarMatrix n n E) (ε / (M + 1)) (div_pos hε (by linarith)) + refine ⟨δ, hδ, ?_⟩ + intro u q hq huq hu hgram + let h := u.conjTranspose * u + let g := h + (1 - q) + have hhq : h * q = h := by + change (u.conjTranspose * u) * q = u.conjTranspose * u + rw [rectangular_mul_assoc, huq] + have hqh : q * h = h := by + have hqu : q * u.conjTranspose = u.conjTranspose := by + have hz := congrArg (fun a : CStarMatrix m n E => a.conjTranspose) huq + rw [rectangular_star_mul] at hz + change star q * u.conjTranspose = u.conjTranspose at hz + rwa [hq.isSelfAdjoint.star_eq] at hz + change q * (u.conjTranspose * u) = u.conjTranspose * u + rw [← rectangular_mul_assoc, hqu] + have hgq : g * q = h := by + change (h + (1 - q)) * q = h + rw [add_mul, hhq, hq.one_sub_mul_self, add_zero] + have hqg : q * g = h := by + change q * (h + (1 - q)) = h + rw [mul_add, hqh, hq.mul_one_sub_self, add_zero] + have hg0 : 0 ≤ g := add_nonneg (rectangular_initial_nonneg u) hq.one_sub.nonneg + have hgn : ‖g - 1‖ < δ := by + have he : g - 1 = h - q := by dsimp only [g]; noncomm_ring + rw [he] + exact hgram + obtain ⟨hgp, hkn⟩ := hcorr g hg0 hgn + let k : CStarMatrix n n E := g ^ (-(1 / 2) : ℝ) + have hk : star k = k := (CFC.rpow_nonneg (a := g)).star_eq + have hkg : k * g * k = 1 := CFC.conjugate_rpow_neg_one_half g hgp + have hkq : k * q = q * k := by + have hcomm : Commute g q := hgq.trans hqg.symm + exact (hcomm.cfc_nnreal (fun t => t ^ (-(1 / 2) : ℝ))).eq + have hkh : k * h * k = q := by + calc + k * h * k = k * (q * g * q) * k := by rw [hqg, hhq] + _ = q * (k * g * k) * q := by + calc + _ = (k * q) * g * (q * k) := by noncomm_ring + _ = (q * k) * g * (k * q) := by rw [hkq] + _ = _ := by noncomm_ring + _ = q := by rw [hkg, mul_one, hq.isIdempotentElem.eq] + refine ⟨u * k, ?_, ?_, ?_⟩ + · calc + (u * k) * q = u * (k * q) := rectangular_mul_assoc _ _ _ + _ = u * (q * k) := by rw [hkq] + _ = u * k := by rw [← rectangular_mul_assoc, huq] + · rw [rectangular_initial_mul, hk] + exact hkh + · have hu1 : u * (1 : CStarMatrix n n E) = u := by + ext i j + change (∑ l, u i l * (if l = j then 1 else 0)) = u i j + simp + have hsub : u * (k - 1) = u * k - u * (1 : CStarMatrix n n E) := by + ext i j + change (∑ l, u i l * (k l j - (1 : CStarMatrix n n E) l j)) = + (∑ l, u i l * k l j) - ∑ l, u i l * (1 : CStarMatrix n n E) l j + simp only [mul_sub, Finset.sum_sub_distrib] + have he : u * k - u = u * (k - 1) := by rw [hsub, hu1] + rw [he] + calc + _ ≤ ‖u‖ * ‖k - 1‖ := rectangular_norm_mul_le _ _ + _ ≤ M * ‖k - 1‖ := mul_le_mul_of_nonneg_right hu (norm_nonneg _) + _ < (M + 1) * (ε / (M + 1)) := by + change ‖k - 1‖ < ε / (M + 1) at hkn + have hp : 0 < ε / (M + 1) := div_pos hε (by linarith) + nlinarith [norm_nonneg (k - 1)] + _ = ε := mul_div_cancel₀ _ (by linarith : M + 1 ≠ 0) + +/-- The common initial projection of a two-column row. -/ +def relativePairProjection (p : E) : CStarMatrix (Fin 2) (Fin 2) E := + CStarMatrix.ofMatrix (fun i j => if i = j then p else 0) + +omit [PartialOrder E] [StarOrderedRing E] in +lemma relativePairProjection_apply (p : E) (i j : Fin 2) : + relativePairProjection p i j = if i = j then p else 0 := rfl + +omit [PartialOrder E] [StarOrderedRing E] in +lemma relativePairProjection_isStarProjection (p : E) (hp : IsStarProjection p) : + IsStarProjection (relativePairProjection p) := by + apply isStarProjection_iff'.mpr + constructor + · ext i j + change (∑ k : Fin 2, (if i = k then p else 0) * (if k = j then p else 0)) = + (if i = j then p else 0) + fin_cases i <;> fin_cases j <;> + simp [hp.isIdempotentElem.eq] + · ext i j + change star (if j = i then p else 0) = if i = j then p else 0 + fin_cases i <;> fin_cases j <;> simp [hp.isSelfAdjoint.star_eq] + +omit [PartialOrder E] [StarOrderedRing E] in +lemma cuntzPairRow_relative_support (a b p : E) (ha : a * p = a) (hb : b * p = b) : + cuntzPairRow a b * relativePairProjection p = cuntzPairRow a b := by + ext i j + change (∑ k : Fin 2, ![a, b] k * (if k = j then p else 0)) = ![a, b] j + fin_cases j <;> simp [ha, hb] + +lemma cuntzPairRow_relative_gram_bound (a b p : E) : + ‖(cuntzPairRow a b).conjTranspose * cuntzPairRow a b - relativePairProjection p‖ ≤ + ‖star a * a - p‖ + ‖star b * b - p‖ + 2 * ‖star a * b‖ := by + have h := rectangular_norm_le_sum_entries + ((cuntzPairRow a b).conjTranspose * cuntzPairRow a b - relativePairProjection p) + have hnorm : ‖star b * a‖ = ‖star a * b‖ := by + rw [← norm_star (star a * b), star_mul, star_star] + simp only [Fin.sum_univ_two, CStarMatrix.sub_apply, cuntzPairRow_initial_entry, + Matrix.cons_val_zero, Matrix.cons_val_one, relativePairProjection_apply, + ite_true, show ¬ (0 : Fin 2) = 1 by decide, show ¬ (1 : Fin 2) = 0 by decide, + ite_false, sub_zero, hnorm] at h + linarith + +/-- Two approximately orthogonal supported columns can be corrected without +filling the removed projection. -/ +lemma exists_relative_cuntzPair_near (ε : ℝ) (hε : 0 < ε) : + ∃ δ : ℝ, 0 < δ ∧ ∀ a b p : E, + IsStarProjection p → a * p = a → b * p = b → ‖a‖ ≤ 1 → ‖b‖ ≤ 1 → + ‖star a * a - p‖ < δ → ‖star b * b - p‖ < δ → ‖star a * b‖ < δ → + ∃ r t : E, r * p = r ∧ t * p = t ∧ + star r * r = p ∧ star t * t = p ∧ star r * t = 0 ∧ + ‖r - a‖ < ε ∧ ‖t - b‖ < ε := by + obtain ⟨δ, hδ, hcorr⟩ := exists_relative_rectangular_isometry_near (E := E) + (m := Fin 1) (n := Fin 2) 2 ε (by norm_num) hε + refine ⟨δ / 4, by positivity, ?_⟩ + intro a b p hp ha hb han hbn haa hbb hab + have hu : ‖cuntzPairRow a b‖ ≤ 2 := + (norm_cuntzPairRow_le a b).trans (by linarith) + have hg : ‖(cuntzPairRow a b).conjTranspose * cuntzPairRow a b - + relativePairProjection p‖ < δ := by + have hh := cuntzPairRow_relative_gram_bound a b p + linarith + obtain ⟨v, hvp, hvg, hvn⟩ := hcorr (cuntzPairRow a b) (relativePairProjection p) + (relativePairProjection_isStarProjection p hp) (cuntzPairRow_relative_support a b p ha hb) hu hg + have hsup (j : Fin 2) : v 0 j * p = v 0 j := by + have hh := congrArg (fun w : CStarMatrix (Fin 1) (Fin 2) E => w 0 j) hvp + change (∑ k : Fin 2, v 0 k * (if k = j then p else 0)) = v 0 j at hh + fin_cases j <;> simpa [Fin.sum_univ_two] using hh + have hgr (i j : Fin 2) : star (v 0 i) * v 0 j = if i = j then p else 0 := by + have hh := congrArg (fun w : CStarMatrix (Fin 2) (Fin 2) E => w i j) hvg + change (∑ _k : Fin 1, star (v 0 i) * v 0 j) = (if i = j then p else 0) at hh + simpa only [Fin.sum_univ_one] using hh + refine ⟨v 0 0, v 0 1, hsup 0, hsup 1, ?_, ?_, ?_, ?_, ?_⟩ + · simpa using hgr 0 0 + · simpa using hgr 1 1 + · simpa using hgr 0 1 + · exact (CStarMatrix.norm_entry_le_norm (M := v - cuntzPairRow a b) (i := 0) (j := 0)).trans_lt hvn + · exact (CStarMatrix.norm_entry_le_norm (M := v - cuntzPairRow a b) (i := 0) (j := 1)).trans_lt hvn + +omit [PartialOrder E] [StarOrderedRing E] in +private lemma relativeGram_word_isometry (s : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) : + star (s 0 * s 0) * (s 0 * s 0) = 1 := by + rw [star_mul] + calc + _ = star (s 0) * (star (s 0) * s 0) * s 0 := by noncomm_ring + _ = 1 := by simp only [hs, ite_true, mul_one] + +omit [PartialOrder E] [StarOrderedRing E] in +private lemma relativeGram_iterate_isometry (s : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) (x : E) (hx : star x * x = 1) (n : ℕ) : + star (finiteRowShiftIterate s n x) * finiteRowShiftIterate s n x = 1 := by + have h1 : finiteRowShiftIterate s n 1 = 1 := by + induction n with + | zero => rfl + | succ n ih => simpa only [finiteRowShiftIterate, ih, finiteRowShift, mul_one] using hsum + rw [finiteRowShiftIterate_star, ← binaryRowIterate_mul s hs, hx, h1] + +omit [PartialOrder E] [StarOrderedRing E] in +private lemma relativeGram_isometry_norm (x : E) (hx : star x * x = 1) : ‖x‖ ≤ 1 := by + have h := congrArg norm hx + rw [CStarRing.norm_star_mul_self] at h + have h1 : ‖(1 : E)‖ ≤ 1 := (IsStarProjection.one E).norm_le + nlinarith [norm_nonneg x] + +/-- The actual iterated two-letter and one-letter bands admit exact relative +orthogonalization, with arbitrarily small correction. The cell zero stays +removed from both initial projections. -/ +lemma exists_corrected_masked_binary_rows {N : ℕ} [NeZero N] (hN : 1 < N) + (ε : ℝ) (hε : 0 < ε) : + ∃ η : ℝ, 0 < η ∧ ∀ (s : Fin 2 → E), + (∀ i j, star (s i) * s j = if i = j then 1 else 0) → + (∑ i, s i * star (s i)) = 1 → + ∀ e : ZMod N → E, (∀ j, IsStarProjection (e j)) → + (∀ j k, j ≠ k → e j * e k = 0) → (∑ j, e j) = 1 → + (∀ j, ‖finiteRowShift s (e j) - e (j + 1)‖ ≤ η) → + let a := maskedTowerBand e (Equiv.addRight 2) + (fun j => finiteRowShiftIterate s j.val (s 0 * s 0)) 0 + let b := maskedTowerBand e (Equiv.addRight 1) + (fun j => finiteRowShiftIterate s j.val (s 1)) 0 + ∃ r t : E, r * (1 - e 0) = r ∧ t * (1 - e 0) = t ∧ + star r * r = 1 - e 0 ∧ star t * t = 1 - e 0 ∧ star r * t = 0 ∧ + ‖r - a‖ < ε ∧ ‖t - b‖ < ε := by + obtain ⟨δ, hδ, hcorr⟩ := exists_relative_cuntzPair_near (E := E) ε hε + let η := δ / (2 * (N : ℝ) + 3) + have hη : 0 < η := by dsimp [η]; positivity + refine ⟨η, hη, ?_⟩ + intro s hs hsum e he ho hesum hshift + dsimp only + have hword := relativeGram_word_isometry s hs + have hsingle : star (s 1) * s 1 = 1 := by simpa only [ite_true] using hs 1 1 + have hbound (x : E) (hx : star x * x = 1) (d : ZMod N) : + ‖maskedTowerBand e (Equiv.addRight d) + (fun j => finiteRowShiftIterate s j.val x) 0‖ ≤ 1 := by + apply towerBand_norm_le e (Equiv.addRight d) _ he ho 1 zero_le_one + intro j + by_cases hj : j = 0 + · simp only [maskedBandCoefficients, ite_eq_left hj, norm_zero, zero_le_one] + · simp only [maskedBandCoefficients, ite_eq_right hj] + exact relativeGram_isometry_norm _ (relativeGram_iterate_isometry s hs hsum x hx j.val) + have hless : (2 * (N : ℝ) + 2) * η < δ := by + have heq : (2 * (N : ℝ) + 3) * η = δ := by + dsimp only [η] + exact mul_div_cancel₀ _ (by positivity) + nlinarith + apply hcorr _ _ _ (he 0).one_sub + (maskedTowerBand_right_support e _ _ 0 ho) + (maskedTowerBand_right_support e _ _ 0 ho) + (hbound _ hword _) (hbound _ hsingle _) + · exact (maskedIteratedWord_gram_bound s hs hsum e he ho hesum η hη.le hshift + (s 0 * s 0) hword 2 (cyclic_row_two_letter_transport s hs e η hshift 0 0)).trans_lt hless + · apply (maskedIteratedWord_gram_bound s hs hsum e he ho hesum η hη.le hshift + (s 1) hsingle 1 ?_).trans_lt hless + intro j + exact (cyclic_row_generator_transport s hs e η hshift 1 j).trans (by linarith) + · apply (maskedIteratedRows_cross_bound hN s hs e he ho η hη.le hshift 0 0 1 (by decide)).trans_lt + exact lt_of_le_of_lt (by nlinarith) hless + +/-- An actual cyclic partition supplies the small Gram errors; no tower +or exact orthogonal-row premise is retained in this conclusion. -/ +lemma exists_masked_binary_rotation_rows (s : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) + (m : ℕ) (hm : 1 < 2 ^ m) (ε : ℝ) (hε : 0 < ε) : + ∃ (e : ZMod (2 ^ m) → E) (r t : E), + (∀ j, IsStarProjection (e j)) ∧ + (∀ j k, j ≠ k → e j * e k = 0) ∧ (∑ j, e j) = 1 ∧ + r * (1 - e 0) = r ∧ t * (1 - e 0) = t ∧ + star r * r = 1 - e 0 ∧ star t * t = 1 - e 0 ∧ star r * t = 0 ∧ + ‖r - maskedTowerBand e (Equiv.addRight 2) + (fun j => finiteRowShiftIterate s j.val (s 0 * s 0)) 0‖ < ε ∧ + ‖t - maskedTowerBand e (Equiv.addRight 1) + (fun j => finiteRowShiftIterate s j.val (s 1)) 0‖ < ε := by + have : IsClosed ((⊤ : StarSubalgebra ℂ E) : Set E) := isClosed_univ + obtain ⟨η, hη, hcorr⟩ := exists_corrected_masked_binary_rows (E := E) hm ε hε + obtain ⟨e, _hem, he, hesum, ho, hshift⟩ := + exists_binary_cyclic_partition_in (⊤ : StarSubalgebra ℂ E) s hs hsum + (fun _ => by simp) m η hη + obtain ⟨r, t, hr, ht, hrr, htt, hrt, hra, htb⟩ := + hcorr s hs hsum e he ho hesum (fun j => (hshift j).le) + exact ⟨e, r, t, he, ho, hesum, hr, ht, hrr, htt, hrt, hra, htb⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RelativeUnitaryPath.lean b/lean/OAI/Analysis/OInfinity/RelativeUnitaryPath.lean new file mode 100644 index 0000000000000000000000000000000000000000..5d6b0d9b6f0388678e2412daa95ecaf3fe47afa7 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RelativeUnitaryPath.lean @@ -0,0 +1,140 @@ +import OAI.Analysis.OInfinity.CornerShortPath + +namespace OAI + +/-! # Uniform paths for relative unitaries + +In a fixed corner carrying a coisometric pair, a relative unitary that almost +commutes with that pair admits an explicit uniform path bound. The endpoint +is extended by the identity on the ambient complement. The existence of such +a pair in a prescribed corner is an input, not a consequence asserted here. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- Extend a relative unitary by the identity on the complementary corner. -/ +def relativeUnitaryExtension (q z : E) : E := z + (1 - q) + +lemma relativeUnitaryExtension_mem (q z : E) (hqstar : star q = q) + (hqq : q * q = q) (hqz : q * z = z) (hzq : z * q = z) + (hzz : star z * z = q) (hzz' : z * star z = q) : + relativeUnitaryExtension q z ∈ unitary E := by + have hsq : star z * q = star z := by + simpa only [star_mul, hqstar] using congrArg star hqz + have hqs : q * star z = star z := by + simpa only [star_mul, hqstar] using congrArg star hzq + constructor + · simp only [relativeUnitaryExtension, star_add, star_sub, star_one, hqstar] + noncomm_ring [hqq, hqz, hsq, hzz] + · simp only [relativeUnitaryExtension, star_add, star_sub, star_one, hqstar] + noncomm_ring [hqq, hzq, hqs, hzz'] + +lemma relativeUnitaryExtension_decomposition_error (q a b z : E) + (hsum : a * star a + b * star b = q) (hzq : z * q = z) + (hab : star a * b = 0) (ha : ‖a‖ ≤ 1) (hb : ‖b‖ ≤ 1) + (δ : ℝ) (hδ : 0 ≤ δ) + (haz : ‖z * a - a * z‖ ≤ δ) (hbz : ‖z * b - b * z‖ ≤ δ) : + ‖relativeUnitaryExtension q z - cornerCompression a z * cornerCompression b z‖ ≤ 2 * δ := by + have he : relativeUnitaryExtension q z - cornerCompression a z * cornerCompression b z = + (z * a - a * z) * star a + (z * b - b * z) * star b := by + rw [cornerCompression_pair_product a b z z hab] + unfold relativeUnitaryExtension + calc + _ = z - (a * z * star a + b * z * star b) := by rw [← hsum]; abel + _ = z * (a * star a + b * star b) - (a * z * star a + b * z * star b) := by + rw [hsum, hzq] + _ = _ := by noncomm_ring + rw [he] + calc + _ ≤ ‖(z * a - a * z) * star a‖ + ‖(z * b - b * z) * star b‖ := norm_add_le _ _ + _ ≤ ‖z * a - a * z‖ * ‖a‖ + ‖z * b - b * z‖ * ‖b‖ := by + simpa only [norm_star] using add_le_add + (norm_mul_le (z * a - a * z) (star a)) + (norm_mul_le (z * b - b * z) (star b)) + _ ≤ δ * 1 + δ * 1 := by gcongr + _ = 2 * δ := by ring + +lemma unitaryPath_mul_sub_norm_le {a b c d : unitary E} + (p : Path a b) (q : Path c d) (L K : ℝ) + (hp : ∀ t s, ‖(p t : E) - p s‖ ≤ L * |(t : ℝ) - s|) + (hq : ∀ t s, ‖(q t : E) - q s‖ ≤ K * |(t : ℝ) - s|) : + ∀ t s, ‖((p.mul q) t : E) - (p.mul q) s‖ ≤ (L + K) * |(t : ℝ) - s| := by + intro t s + have he : ((p.mul q) t : E) - (p.mul q) s = + (p t : E) * ((q t : E) - q s) + ((p t : E) - p s) * (q s : E) := by + change (p t : E) * (q t : E) - (p s : E) * (q s : E) = _ + noncomm_ring + rw [he] + calc + _ ≤ ‖(p t : E) * ((q t : E) - q s)‖ + ‖((p t : E) - p s) * (q s : E)‖ := norm_add_le _ _ + _ = ‖(q t : E) - q s‖ + ‖(p t : E) - p s‖ := by + rw [CStarRing.norm_coe_unitary_mul, CStarRing.norm_mul_coe_unitary] + _ ≤ K * |(t : ℝ) - s| + L * |(t : ℝ) - s| := add_le_add (hq t s) (hp t s) + _ = _ := by ring + +/-- The fixed-pair hypotheses give a numerical bound independent of the +relative unitary. The ambient complement is present in the initial point. -/ +lemma exists_uniform_relativeUnitary_path (q a b z : E) + (hqstar : star q = q) (hqq : q * q = q) + (haa : star a * a = q) (hbb : star b * b = q) (hab : star a * b = 0) + (hsum : a * star a + b * star b = q) + (hqz : q * z = z) (hzq : z * q = z) + (hzz : star z * z = q) (hzz' : z * star z = q) + (δ : ℝ) (hδ : 0 ≤ δ) (hsmall : 4 * δ < 2) + (haz : ‖z * a - a * z‖ ≤ δ) (hbz : ‖z * b - b * z‖ ≤ δ) : + ∃ u : unitary E, (u : E) = relativeUnitaryExtension q z ∧ + ∃ p : Path u 1, ∀ t s, ‖(p t : E) - p s‖ ≤ (32 * Real.pi) * |(t : ℝ) - s| := by + obtain ⟨u, hu, p, hp⟩ := exists_uniform_compressed_unitary_path q a b z hqstar hqq + haa hbb hab hsum hqz hzq hzz hzz' δ hδ hsmall haz hbz + have hba : star b * a = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hab + have hsum' : b * star b + a * star a = q := by rw [add_comm]; exact hsum + obtain ⟨v, hv, r, hr⟩ := exists_uniform_compressed_unitary_path q b a z hqstar hqq + hbb haa hba hsum' hqz hzq hzz hzz' δ hδ hsmall hbz haz + let w : unitary E := ⟨relativeUnitaryExtension q z, + relativeUnitaryExtension_mem q z hqstar hqq hqz hzq hzz hzz'⟩ + have hnq : ‖q‖ ≤ 1 := by + have h := congrArg norm hqq + have hs : IsSelfAdjoint q := hqstar + rw [hs.norm_mul_self] at h + nlinarith [norm_nonneg q] + have hna : ‖a‖ ≤ 1 := by + have h := congrArg norm haa + rw [CStarRing.norm_star_mul_self] at h + nlinarith [norm_nonneg a] + have hnb : ‖b‖ ≤ 1 := by + have h := congrArg norm hbb + rw [CStarRing.norm_star_mul_self] at h + nlinarith [norm_nonneg b] + have hclose : ‖((u * v : unitary E) : E) - w‖ < 2 := by + change ‖(u : E) * (v : E) - relativeUnitaryExtension q z‖ < 2 + rw [hu, hv, norm_sub_rev] + exact (relativeUnitaryExtension_decomposition_error q a b z hsum hzq hab + hna hnb δ hδ haz hbz).trans_lt (by linarith) + let middle := Unitary.path w (u * v) hclose + let productPath : Path (u * v) 1 := (p.mul r).cast rfl (by simp) + have hm : ∀ t s, ‖(middle t : E) - middle s‖ ≤ (16 * Real.pi) * |(t : ℝ) - s| := by + intro t s + exact (unitary_shortPath_sub_norm_le w (u * v) hclose t s).trans (by + nlinarith [Real.pi_pos, abs_nonneg ((t : ℝ) - s)]) + have hpr : ∀ t s, ‖(productPath t : E) - productPath s‖ ≤ + (16 * Real.pi) * |(t : ℝ) - s| := by + intro t s + change ‖((p.mul r) t : E) - (p.mul r) s‖ ≤ _ + simpa only [show 8 * Real.pi + 8 * Real.pi = 16 * Real.pi by ring] using + unitaryPath_mul_sub_norm_le p r (8 * Real.pi) (8 * Real.pi) hp hr t s + refine ⟨w, rfl, middle.trans productPath, ?_⟩ + intro t s + simpa only [show 2 * (16 * Real.pi) = 32 * Real.pi by ring] using + unitaryPath_trans_sub_norm_le middle productPath (16 * Real.pi) hm hpr t s + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RohlinGluing.lean b/lean/OAI/Analysis/OInfinity/RohlinGluing.lean new file mode 100644 index 0000000000000000000000000000000000000000..31e26ca0ca06127fe86825166085fd9b76770ea6 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RohlinGluing.lean @@ -0,0 +1,166 @@ +import OAI.Analysis.OInfinity.CocycleCentrality + +namespace OAI + +/-! # Weighted finite Rohlin sums + +Orthogonal projection domains give a square-sum norm bound. Hence N +coefficient errors of size L/N contribute at most L/√N, even before +commutation with the projections is imposed. The shift and unitarity +errors are tracked separately. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E I : Type*} [CStarAlgebra E] [Fintype I] [DecidableEq I] + +lemma weightedProjection_norm_le_one (e : E) (he : star e = e) (hee : e * e = e) : + ‖e‖ ≤ 1 := by + have h := CStarRing.norm_star_mul_self (x := e) + rw [he, hee] at h + nlinarith [norm_nonneg e] + +lemma orthogonalWeighted_square (e x : I → E) + (he : ∀ i, star (e i) = e i) (hee : ∀ i, e i * e i = e i) + (horth : ∀ i j, i ≠ j → e i * e j = 0) : + (∑ i, x i * e i) * star (∑ i, x i * e i) = + ∑ i, x i * e i * star (x i) := by + have hterm (i j : I) : (x i * e i) * star (x j * e j) = + if i = j then x i * e i * star (x i) else 0 := by + rw [star_mul, he] + calc + _ = x i * (e i * e j) * star (x j) := by noncomm_ring + _ = _ := by + split_ifs with hij + · subst j + rw [hee] + · rw [horth i j hij, mul_zero, zero_mul] + rw [star_sum, Finset.sum_mul] + simp only [Finset.mul_sum, hterm, Finset.sum_ite_eq, Finset.mem_univ, ite_true] + +lemma orthogonalWeighted_norm_sq_le (e x : I → E) + (he : ∀ i, star (e i) = e i) (hee : ∀ i, e i * e i = e i) + (horth : ∀ i j, i ≠ j → e i * e j = 0) : + ‖∑ i, x i * e i‖ ^ 2 ≤ ∑ i, ‖x i‖ ^ 2 := by + calc + _ = ‖(∑ i, x i * e i) * star (∑ i, x i * e i)‖ := by + rw [CStarRing.norm_self_mul_star, pow_two] + _ = ‖∑ i, x i * e i * star (x i)‖ := by rw [orthogonalWeighted_square e x he hee horth] + _ ≤ ∑ i, ‖x i * e i * star (x i)‖ := norm_sum_le _ _ + _ ≤ _ := by + apply Finset.sum_le_sum + intro i hi + calc + _ ≤ ‖x i‖ * ‖e i‖ * ‖x i‖ := by + simpa only [norm_star] using + (norm_mul_le (x i * e i) (star (x i))).trans + (mul_le_mul_of_nonneg_right (norm_mul_le _ _) (norm_nonneg _)) + _ ≤ ‖x i‖ * 1 * ‖x i‖ := by + gcongr + exact weightedProjection_norm_le_one (e i) (he i) (hee i) + _ = ‖x i‖ ^ 2 := by ring + +lemma orthogonalWeighted_norm_le (e x : I → E) + (he : ∀ i, star (e i) = e i) (hee : ∀ i, e i * e i = e i) + (horth : ∀ i j, i ≠ j → e i * e j = 0) + (δ : ℝ) (hδ : 0 ≤ δ) (hx : ∀ i, ‖x i‖ ≤ δ) : + ‖∑ i, x i * e i‖ ≤ Real.sqrt (Fintype.card I) * δ := by + have h := orthogonalWeighted_norm_sq_le e x he hee horth + have hb : (∑ i, ‖x i‖ ^ 2) ≤ (Fintype.card I : ℝ) * δ ^ 2 := by + calc + _ ≤ ∑ _ : I, δ ^ 2 := Finset.sum_le_sum fun i _ => by + nlinarith [norm_nonneg (x i), hx i] + _ = _ := by simp + have hs := Real.sq_sqrt (show (0 : ℝ) ≤ Fintype.card I by positivity) + have hn := Real.sqrt_nonneg (Fintype.card I : ℝ) + have hp : 0 ≤ Real.sqrt (Fintype.card I : ℝ) * δ := mul_nonneg hn hδ + nlinarith [norm_nonneg (∑ i, x i * e i)] + +def finiteRohlinSum (v : I → unitary E) (e : I → E) : E := ∑ i, (v i : E) * e i + +omit [DecidableEq I] in +lemma finiteRohlinSum_defect_identity (φ : E →⋆ₙₐ[ℂ] E) (w : unitary E) + (σ : Equiv.Perm I) (v : I → unitary E) (e : I → E) : + (w : E) * φ (finiteRohlinSum v e) - finiteRohlinSum v e = + (∑ i, ((w : E) * φ (v i) - (v (σ i) : E)) * e (σ i)) + + ∑ i, ((w : E) * φ (v i)) * (φ (e i) - e (σ i)) := by + have hreindex : (∑ i, (v (σ i) : E) * e (σ i)) = finiteRohlinSum v e := by + apply Fintype.sum_equiv σ + intro i + rfl + symm + rw [← Finset.sum_add_distrib] + calc + _ = (∑ i, (w : E) * φ ((v i : E) * e i)) - + ∑ i, (v (σ i) : E) * e (σ i) := by + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro i hi + rw [map_mul] + noncomm_ring + _ = _ := by rw [hreindex, ← Finset.mul_sum, ← map_sum]; rfl + +lemma finiteRohlinSum_defect_le [Nontrivial E] (φ : E →⋆ₙₐ[ℂ] E) (w : unitary E) + (σ : Equiv.Perm I) (v : I → unitary E) (e : I → E) + (he : ∀ i, star (e i) = e i) (hee : ∀ i, e i * e i = e i) + (horth : ∀ i j, i ≠ j → e i * e j = 0) + (δ η : ℝ) (hδ : 0 ≤ δ) + (hv : ∀ i, ‖(w : E) * φ (v i) - (v (σ i) : E)‖ ≤ δ) + (hshift : ∀ i, ‖φ (e i) - e (σ i)‖ ≤ η) : + ‖(w : E) * φ (finiteRohlinSum v e) - finiteRohlinSum v e‖ ≤ + Real.sqrt (Fintype.card I) * δ + (Fintype.card I : ℝ) * η := by + rw [finiteRohlinSum_defect_identity φ w σ v e] + apply (norm_add_le _ _).trans + apply add_le_add + · exact orthogonalWeighted_norm_le (fun i => e (σ i)) + (fun i => (w : E) * φ (v i) - (v (σ i) : E)) (fun i => he (σ i)) + (fun i => hee (σ i)) (fun i j hij => horth (σ i) (σ j) (σ.injective.ne hij)) δ hδ hv + · calc + _ ≤ ∑ i, ‖((w : E) * φ (v i)) * (φ (e i) - e (σ i))‖ := norm_sum_le _ _ + _ ≤ ∑ _ : I, η := by + apply Finset.sum_le_sum + intro i hi + rw [mul_assoc, CStarRing.norm_coe_unitary_mul] + calc + _ ≤ ‖φ (v i)‖ * ‖φ (e i) - e (σ i)‖ := norm_mul_le _ _ + _ ≤ 1 * η := by + apply mul_le_mul + · exact (NonUnitalStarAlgHom.norm_apply_le φ _).trans (CStarRing.norm_coe_unitary (v i)).le + · exact hshift i + · exact norm_nonneg _ + · norm_num + _ = η := one_mul η + _ = _ := by simp + +/-- One of the two unitary defects only needs the diagonal commutators. -/ +lemma finiteRohlinSum_coisometry_defect_le (v : I → unitary E) (e : I → E) + (he : ∀ i, star (e i) = e i) (hee : ∀ i, e i * e i = e i) + (horth : ∀ i j, i ≠ j → e i * e j = 0) + (hsum : (∑ i, e i) = 1) (δ : ℝ) + (hc : ∀ i, ‖(v i : E) * e i - e i * (v i : E)‖ ≤ δ) : + ‖finiteRohlinSum v e * star (finiteRohlinSum v e) - 1‖ ≤ (Fintype.card I : ℝ) * δ := by + change ‖(∑ i, (v i : E) * e i) * star (∑ i, (v i : E) * e i) - 1‖ ≤ _ + rw [orthogonalWeighted_square e (fun i => (v i : E)) he hee horth, ← hsum, + ← Finset.sum_sub_distrib] + calc + _ ≤ ∑ i, ‖(v i : E) * e i * star (v i : E) - e i‖ := norm_sum_le _ _ + _ ≤ ∑ _ : I, δ := by + apply Finset.sum_le_sum + intro i hi + have hid : (v i : E) * e i * star (v i : E) - e i = + ((v i : E) * e i - e i * (v i : E)) * star (v i : E) := by + rw [sub_mul, mul_assoc (e i), (v i).property.2, mul_one] + rw [hid] + change ‖((v i : E) * e i - e i * (v i : E)) * (star (v i) : unitary E)‖ ≤ δ + rw [CStarRing.norm_mul_coe_unitary] + exact hc i + _ = _ := by simp + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RohlinPartitions.lean b/lean/OAI/Analysis/OInfinity/RohlinPartitions.lean new file mode 100644 index 0000000000000000000000000000000000000000..d5ac0a3d74e3b2aa9ddf0f5079c26c39f1b039cc --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RohlinPartitions.lean @@ -0,0 +1,101 @@ +import OAI.Analysis.OInfinity.DyadicProjections + +namespace OAI + +/-! # Concrete dyadic partitions for an even Cuntz row + +The phases are explicit roots of unity. The finite partitions below use the +actual geometric CAR modes of the supplied even row, followed by the proved +Jordan–Wigner construction. Quantitative cyclic shift control is separate +from the exact partition identities. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +/-- The phase with half-period `2^i`. -/ +def carDyadicPhase (i : ℕ) : ℂ := Complex.exp (((Real.pi / (2 : ℝ) ^ i : ℝ) : ℂ) * Complex.I) + +lemma carDyadicPhase_norm (i : ℕ) : ‖carDyadicPhase i‖ = 1 := + Complex.norm_exp_ofReal_mul_I _ + +lemma carDyadicPhase_half (i : ℕ) : carDyadicPhase i ^ (2 ^ i) = -1 := by + rw [carDyadicPhase, ← Complex.exp_nat_mul] + have hp : (2 : ℂ) ^ i ≠ 0 := pow_ne_zero _ (by norm_num) + have he : ((2 ^ i : ℕ) : ℂ) * (((Real.pi / (2 : ℝ) ^ i : ℝ) : ℂ) * Complex.I) = + (Real.pi : ℂ) * Complex.I := by + push_cast + field_simp + rw [he, Complex.exp_pi_mul_I] + +variable {E : Type*} [CStarAlgebra E] {n : ℕ} + +/-- Commuting two-level coordinates of the actual even row. -/ +def evenRohlinCoordinate (q : E) (r : Fin 2 × Fin n → E) (L i : ℕ) : E := + carJordanWigner q (evenBlockFamily r L carDyadicPhase) i + +/-- The `k`th cell at dyadic level `m`. -/ +def evenRohlinProjection (q : E) (r : Fin 2 × Fin n → E) (L m k : ℕ) : E := + dyadicSpinProjection q (evenRohlinCoordinate q r L) carDyadicPhase m k + +variable (q : E) (r : Fin 2 × Fin n → E) + (hqstar : star q = q) (hqq : q * q = q) + (hrow : ∀ i j, star (r i) * r j = if i = j then q else 0) + (hsum : (∑ i, r i * star (r i)) = q) + +include hqstar hqq hrow hsum in +lemma evenRohlinCoordinate_properties (L : ℕ) (hL : 0 < L) : + (∀ i, q * evenRohlinCoordinate q r L i = evenRohlinCoordinate q r L i) ∧ + (∀ i, evenRohlinCoordinate q r L i * q = evenRohlinCoordinate q r L i) ∧ + (∀ i, evenRohlinCoordinate q r L i * evenRohlinCoordinate q r L i = 0) ∧ + (∀ i, star (evenRohlinCoordinate q r L i) * evenRohlinCoordinate q r L i + + evenRohlinCoordinate q r L i * star (evenRohlinCoordinate q r L i) = q) ∧ + (∀ i j, Commute (evenRohlinCoordinate q r L i) (evenRohlinCoordinate q r L j)) ∧ + (∀ i j, i ≠ j → Commute (star (evenRohlinCoordinate q r L i)) + (evenRohlinCoordinate q r L j)) := by + obtain ⟨hl, hr, ha, hg⟩ := evenBlockFamily_CAR q r hqstar hqq hrow hsum L hL + carDyadicPhase carDyadicPhase_norm + refine ⟨?_, ?_, ?_, ?_, ?_, ?_⟩ + · intro i + exact (carJordanWigner_support q _ hqstar hqq hl hr ha hg i).1 + · intro i + exact (carJordanWigner_support q _ hqstar hqq hl hr ha hg i).2 + · exact carJordanWigner_square_zero q _ hqstar hqq hl hr ha hg + · exact carJordanWigner_gram q _ hqstar hqq hl hr ha hg + · exact carJordanWigner_commute q _ hqstar hqq hl hr ha hg + · exact carJordanWigner_star_commute q _ hqstar hqq hl hr ha hg + +include hqstar hqq hrow hsum in +lemma evenRohlinProjection_partition (L : ℕ) (hL : 0 < L) (m : ℕ) : + (∀ k, IsStarProjection (evenRohlinProjection q r L m k)) ∧ + (∑ k ∈ Finset.range (2 ^ m), evenRohlinProjection q r L m k) = q ∧ + (∀ k l, k < 2 ^ m → l < 2 ^ m → k ≠ l → + evenRohlinProjection q r L m k * evenRohlinProjection q r L m l = 0) := by + obtain ⟨hl, hr, hz, hg, hc, hsc⟩ := evenRohlinCoordinate_properties q r hqstar hqq hrow hsum L hL + refine ⟨?_, ?_, ?_⟩ + · exact dyadicSpinProjection_isStarProjection q _ _ hqstar hqq hl hr hz hg hc hsc + carDyadicPhase_norm m + · exact dyadicSpinProjection_sum q _ _ hqstar hqq hl hr carDyadicPhase_half m + · exact dyadicSpinProjection_orthogonal q _ _ hqstar hqq hl hr hz hg hc hsc + carDyadicPhase_norm carDyadicPhase_half m + +include hqstar hqq hrow hsum in +lemma evenRohlinProjection_support (L : ℕ) (hL : 0 < L) (m k : ℕ) : + q * evenRohlinProjection q r L m k = evenRohlinProjection q r L m k ∧ + evenRohlinProjection q r L m k * q = evenRohlinProjection q r L m k := by + obtain ⟨hl, hr, _, _, _, _⟩ := evenRohlinCoordinate_properties q r hqstar hqq hrow hsum L hL + exact dyadicSpinProjection_support q _ _ hqstar hqq hl hr m k + +include hqstar hqq hrow hsum in +lemma evenRohlinBlock_shift_error (L : ℕ) (hL : 0 < L) (i : ℕ) : + ‖evenRowShift r (evenBlockFamily r L carDyadicPhase i) - + carDyadicPhase i • evenBlockFamily r L carDyadicPhase i‖ ^ 2 ≤ 18 / (L : ℝ) := + evenEigenMode_shift_error q r hqstar hqq hrow hsum _ _ L hL _ (carDyadicPhase_norm i) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RohlinPolar.lean b/lean/OAI/Analysis/OInfinity/RohlinPolar.lean new file mode 100644 index 0000000000000000000000000000000000000000..5de387f2634d221e82190d33ab477d5d0c03d26c --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RohlinPolar.lean @@ -0,0 +1,109 @@ +import OAI.Analysis.OInfinity.RohlinUnitarity + +namespace OAI + +/-! # Polar correction of the finite Rohlin sum + +Both Gram defects are used. An element with small initial and final Gram +defects is invertible; continuous functional calculus then corrects it to a +nearby unitary. This step does not supply the tower commutator estimates. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +lemma isUnit_of_two_gram_units (x : E) + (hi : IsUnit (star x * x)) (hf : IsUnit (x * star x)) : IsUnit x := by + obtain ⟨a, ha⟩ := hi + obtain ⟨b, hb⟩ := hf + apply isUnit_iff_exists_and_exists.mpr + constructor + · refine ⟨star x * (↑b⁻¹ : E), ?_⟩ + calc + x * (star x * (↑b⁻¹ : E)) = (x * star x) * (↑b⁻¹ : E) := by rw [mul_assoc] + _ = (b : E) * (↑b⁻¹ : E) := by rw [hb] + _ = 1 := b.val_inv + · refine ⟨(↑a⁻¹ : E) * star x, ?_⟩ + calc + ((↑a⁻¹ : E) * star x) * x = (↑a⁻¹ : E) * (star x * x) := by rw [mul_assoc] + _ = (↑a⁻¹ : E) * (a : E) := by rw [ha] + _ = 1 := a.inv_val + +lemma isUnit_of_norm_sub_one_lt (a : E) (ha : ‖a - 1‖ < 1) : IsUnit a := by + have h : ‖1 - a‖ < 1 := by rwa [norm_sub_rev] + convert isUnit_one_sub_of_norm_lt_one h using 1 + noncomm_ring + +local instance rohlinPolarOrder : PartialOrder E := CStarAlgebra.spectralOrder E +local instance rohlinPolarStarOrder : StarOrderedRing E := CStarAlgebra.spectralOrderedRing E + +lemma exists_polar_unitary_of_two_gram_units (x : E) + (hi : IsUnit (star x * x)) (hf : IsUnit (x * star x)) : + ∃ u : unitary E, (u : E) = x * CFC.rpow (star x * x) (-1 / 2 : ℝ) := by + let a := star x * x + let b := CFC.rpow a (-1 / 2 : ℝ) + have ha : 0 ≤ a := star_mul_self_nonneg x + have hai : IsUnit a := hi + have hb : IsSelfAdjoint b := (CFC.rpow_nonneg (a := a) (y := (-1 / 2 : ℝ))).isSelfAdjoint + have hbi : IsUnit b := hi.cfcRpow (-1 / 2 : ℝ) ha + have hx : IsUnit x := isUnit_of_two_gram_units x hi hf + have hpow : (b * a) * b = 1 := by + change (CFC.rpow a (-1 / 2 : ℝ) * a) * CFC.rpow a (-1 / 2 : ℝ) = 1 + conv_lhs => lhs; rhs; rw [← CFC.rpow_one a ha] + simp only [CFC.rpow_eq_pow] + rw [← CFC.rpow_add hai, ← CFC.rpow_add hai] + norm_num [CFC.rpow_zero a ha] + have hp : star (x * b) * (x * b) = 1 := by + rw [star_mul, hb.star_eq] + calc + _ = (b * a) * b := by dsimp [a]; noncomm_ring + _ = 1 := hpow + exact ⟨⟨x * b, (hx.mul hbi).mem_unitary_of_star_mul_self hp⟩, rfl⟩ + +/-- An arbitrarily small polar correction follows from a sufficiently small +initial Gram defect and a final Gram defect less than one. -/ +lemma exists_near_unitary_of_two_gram_errors [Nontrivial E] (ε : ℝ) (hε : 0 < ε) : + ∃ δ : ℝ, 0 < δ ∧ ∀ x : E, + ‖star x * x - 1‖ < δ → ‖x * star x - 1‖ < 1 → + ∃ u : unitary E, ‖(u : E) - x‖ < ε := by + have hcont : ContinuousWithinAt (fun a : E => CFC.rpow a (-1 / 2 : ℝ)) + {a | IsStrictlyPositive a} 1 := + CFC.continuousOn_rpow (-1 / 2 : ℝ) 1 (by exact isStrictlyPositive_one) + obtain ⟨δ, hδ, hb⟩ := Metric.continuousWithinAt_iff.mp hcont (ε / 2) (half_pos hε) + refine ⟨min δ 1, lt_min hδ zero_lt_one, ?_⟩ + intro x hix hfx + have hi1 : ‖star x * x - 1‖ < 1 := hix.trans_le (min_le_right _ _) + have hi : IsUnit (star x * x) := isUnit_of_norm_sub_one_lt _ hi1 + have hf : IsUnit (x * star x) := isUnit_of_norm_sub_one_lt _ hfx + have ha : IsStrictlyPositive (star x * x) := hi.isStrictlyPositive (star_mul_self_nonneg x) + have hbsmall : ‖CFC.rpow (star x * x) (-1 / 2 : ℝ) - 1‖ < ε / 2 := by + simpa only [dist_eq_norm, CFC.rpow_eq_pow, CFC.one_rpow] using hb ha (show dist (star x * x) 1 < δ from + by rw [dist_eq_norm]; exact hix.trans_le (min_le_left _ _)) + have hxnorm : ‖x‖ < 2 := by + have hh : ‖star x * x‖ < 2 := by + calc + _ ≤ ‖star x * x - 1‖ + ‖(1 : E)‖ := norm_le_norm_sub_add _ _ + _ = ‖star x * x - 1‖ + 1 := by rw [norm_one] + _ < 2 := by linarith + rw [CStarRing.norm_star_mul_self] at hh + nlinarith [norm_nonneg x] + obtain ⟨u, hu⟩ := exists_polar_unitary_of_two_gram_units x hi hf + refine ⟨u, ?_⟩ + rw [hu] + calc + _ = ‖x * (CFC.rpow (star x * x) (-1 / 2 : ℝ) - 1)‖ := by rw [mul_sub, mul_one] + _ ≤ ‖x‖ * ‖CFC.rpow (star x * x) (-1 / 2 : ℝ) - 1‖ := norm_mul_le _ _ + _ ≤ 2 * ‖CFC.rpow (star x * x) (-1 / 2 : ℝ) - 1‖ := + mul_le_mul_of_nonneg_right hxnorm.le (norm_nonneg _) + _ < 2 * (ε / 2) := mul_lt_mul_of_pos_left hbsmall (by norm_num) + _ = ε := by ring + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RohlinShift.lean b/lean/OAI/Analysis/OInfinity/RohlinShift.lean new file mode 100644 index 0000000000000000000000000000000000000000..9ee9bd09badcbd7b67d300ffb1d43a5a81244a8f --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RohlinShift.lean @@ -0,0 +1,180 @@ +import OAI.Analysis.OInfinity.JordanWignerEstimates + +namespace OAI + +/-! # Quantitative cyclic partitions for the finite even-row shift + +The exact dyadic projection partition is approximately cycled by the actual +row endomorphism, with an explicit error tending to zero as the geometric +blocks lengthen. No centrality for additional elements or cocycle unitary is +asserted here. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] {n : ℕ} + +lemma carSpinProjection_sub_norm_le (q a b : E) (ζ : ℂ) (hζ : ‖ζ‖ = 1) : + ‖carSpinProjection q a ζ - carSpinProjection q b ζ‖ ≤ ‖a - b‖ := by + have he : carSpinProjection q a ζ - carSpinProjection q b ζ = + (2 : ℂ)⁻¹ • (ζ • (a - b) + star ζ • star (a - b)) := by + simp only [carSpinProjection, carSpinAxis, smul_sub, smul_add, star_sub] + abel + rw [he, norm_smul] + have hhalf : ‖(2 : ℂ)⁻¹‖ = (1 / 2 : ℝ) := by norm_num + rw [hhalf] + calc + _ ≤ (1 / 2 : ℝ) * (‖ζ • (a - b)‖ + ‖star ζ • star (a - b)‖) := by + gcongr + exact norm_add_le _ _ + _ = ‖a - b‖ := by rw [norm_smul, norm_smul, norm_star, norm_star, hζ]; ring + +lemma carSpinProjection_smul (q a : E) (μ ζ : ℂ) : + carSpinProjection q (μ • a) ζ = carSpinProjection q a (ζ * μ) := by + simp only [carSpinProjection, carSpinAxis, star_smul, smul_smul, star_mul] + rw [mul_comm (star μ) (star ζ)] + +lemma evenRowShift_carSpinProjection (q : E) (r : Fin 2 × Fin n → E) + (hqstar : star q = q) (hqq : q * q = q) + (hrow : ∀ i j, star (r i) * r j = if i = j then q else 0) + (hsum : (∑ i, r i * star (r i)) = q) (a : E) (ζ : ℂ) : + evenRowShift r (carSpinProjection q a ζ) = carSpinProjection q (evenRowShift r a) ζ := by + simp only [carSpinProjection, carSpinAxis, evenRowShift_smul, evenRowShift_add, + evenRowShift_unit q r hqstar hqq hrow hsum, ← evenRowShift_star] + +lemma evenRowShift_isStarProjection (q : E) (r : Fin 2 × Fin n → E) + (hrow : ∀ i j, star (r i) * r j = if i = j then q else 0) + (p : E) (hp : IsStarProjection p) (hqp : q * p = p) : + IsStarProjection (evenRowShift r p) := by + refine ⟨?_, ?_⟩ + · change evenRowShift r p * evenRowShift r p = evenRowShift r p + rw [evenRowShift_mul q r hrow p p hqp, hp.isIdempotentElem.eq] + · change star (evenRowShift r p) = evenRowShift r p + rw [evenRowShift_star, hp.isSelfAdjoint.star_eq] + +variable (q : E) (r : Fin 2 × Fin n → E) + (hqstar : star q = q) (hqq : q * q = q) + (hrow : ∀ i j, star (r i) * r j = if i = j then q else 0) + (hsum : (∑ i, r i * star (r i)) = q) + +include hqstar hqq hrow hsum in +lemma evenRohlin_factor_shift_error (L : ℕ) (hL : 0 < L) (i k : ℕ) : + ‖evenRowShift r (carSpinProjection q (evenRohlinCoordinate q r L i) (carDyadicPhase i ^ k)) - + carSpinProjection q (evenRohlinCoordinate q r L i) (carDyadicPhase i ^ (k + 1))‖ ≤ + (4 * (i : ℝ) + 1) * Real.sqrt (18 / (L : ℝ)) := by + rw [evenRowShift_carSpinProjection q r hqstar hqq hrow hsum, pow_succ, + ← carSpinProjection_smul] + exact (carSpinProjection_sub_norm_le q _ _ _ + (by rw [norm_pow, carDyadicPhase_norm, one_pow])).trans + (evenRohlinCoordinate_shift_error q r hqstar hqq hrow hsum L hL i) + +include hqstar hqq hrow hsum in +lemma evenRohlin_factor_properties (L : ℕ) (hL : 0 < L) (i k : ℕ) : + IsStarProjection (carSpinProjection q (evenRohlinCoordinate q r L i) (carDyadicPhase i ^ k)) ∧ + q * carSpinProjection q (evenRohlinCoordinate q r L i) (carDyadicPhase i ^ k) = + carSpinProjection q (evenRohlinCoordinate q r L i) (carDyadicPhase i ^ k) := by + obtain ⟨hl, hr, hz, hg, _, _⟩ := evenRohlinCoordinate_properties q r hqstar hqq hrow hsum L hL + exact ⟨carSpinProjection_isStarProjection q _ hqstar hqq (hl i) (hr i) (hz i) (hg i) _ + (by rw [norm_pow, carDyadicPhase_norm, one_pow]), + (carSpinProjection_support q _ hqstar hqq (hl i) (hr i) _).1⟩ + +include hqstar hqq hrow hsum in +lemma evenRohlinProjection_shift_error (L : ℕ) (hL : 0 < L) (m k : ℕ) : + ‖evenRowShift r (evenRohlinProjection q r L m k) - + evenRohlinProjection q r L m (k + 1)‖ ≤ + (m : ℝ) * (4 * (m : ℝ) + 1) * Real.sqrt (18 / (L : ℝ)) := by + induction m with + | zero => + change ‖evenRowShift r q - q‖ ≤ _ + rw [evenRowShift_unit q r hqstar hqq hrow hsum, sub_self, norm_zero] + simp + | succ m ih => + let P := evenRohlinProjection q r L m k + let P' := evenRohlinProjection q r L m (k + 1) + let e := carSpinProjection q (evenRohlinCoordinate q r L m) (carDyadicPhase m ^ k) + let e' := carSpinProjection q (evenRohlinCoordinate q r L m) (carDyadicPhase m ^ (k + 1)) + let δ := Real.sqrt (18 / (L : ℝ)) + have heprops := evenRohlin_factor_properties q r hqstar hqq hrow hsum L hL m k + have henorm : ‖evenRowShift r e‖ ≤ 1 := IsStarProjection.norm_le _ + (evenRowShift_isStarProjection q r hrow e heprops.1 heprops.2) + have hPnorm : ‖P'‖ ≤ 1 := IsStarProjection.norm_le _ + ((evenRohlinProjection_partition q r hqstar hqq hrow hsum L hL m).1 (k + 1)) + have herr : ‖evenRowShift r e - e'‖ ≤ (4 * (m : ℝ) + 1) * δ := + evenRohlin_factor_shift_error q r hqstar hqq hrow hsum L hL m k + have hdecomp : evenRowShift r (evenRohlinProjection q r L (m + 1) k) - + evenRohlinProjection q r L (m + 1) (k + 1) = + (evenRowShift r P - P') * evenRowShift r e + P' * (evenRowShift r e - e') := by + change evenRowShift r (P * e) - P' * e' = _ + rw [← evenRowShift_mul q r hrow P e heprops.2] + noncomm_ring + rw [hdecomp] + calc + _ ≤ ‖(evenRowShift r P - P') * evenRowShift r e‖ + + ‖P' * (evenRowShift r e - e')‖ := norm_add_le _ _ + _ ≤ ‖evenRowShift r P - P'‖ * ‖evenRowShift r e‖ + ‖P'‖ * ‖evenRowShift r e - e'‖ := + add_le_add (norm_mul_le _ _) (norm_mul_le _ _) + _ ≤ ((m : ℝ) * (4 * (m : ℝ) + 1) * δ) * 1 + 1 * ((4 * (m : ℝ) + 1) * δ) := by + gcongr + _ ≤ (↑(m + 1) : ℝ) * (4 * (↑(m + 1) : ℝ) + 1) * δ := by + push_cast + nlinarith [Real.sqrt_nonneg (18 / (L : ℝ))] + +lemma evenRohlinProjection_period (L : ℕ) (m k : ℕ) : + evenRohlinProjection q r L m (k + 2 ^ m) = evenRohlinProjection q r L m k := + dyadicSpinProjection_period q _ carDyadicPhase carDyadicPhase_half m k + +include hqstar hqq hrow hsum in +lemma evenRohlinProjection_cyclic_error (L : ℕ) (hL : 0 < L) (m k : ℕ) (hk : k < 2 ^ m) : + ‖evenRowShift r (evenRohlinProjection q r L m k) - + evenRohlinProjection q r L m ((k + 1) % (2 ^ m))‖ ≤ + (m : ℝ) * (4 * (m : ℝ) + 1) * Real.sqrt (18 / (L : ℝ)) := by + have he : evenRohlinProjection q r L m ((k + 1) % (2 ^ m)) = + evenRohlinProjection q r L m (k + 1) := by + by_cases hlt : k + 1 < 2 ^ m + · rw [Nat.mod_eq_of_lt hlt] + · have heq : k + 1 = 2 ^ m := by omega + rw [heq, Nat.mod_self] + simpa only [zero_add] using (evenRohlinProjection_period q r L m 0).symm + rw [he] + exact evenRohlinProjection_shift_error q r hqstar hqq hrow hsum L hL m k + +include hqstar hqq hrow hsum in +lemma exists_evenRohlin_cyclic_partition (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ L : ℕ, 0 < L ∧ + (∀ k, IsStarProjection (evenRohlinProjection q r L m k)) ∧ + (∑ k ∈ Finset.range (2 ^ m), evenRohlinProjection q r L m k) = q ∧ + (∀ k l, k < 2 ^ m → l < 2 ^ m → k ≠ l → + evenRohlinProjection q r L m k * evenRohlinProjection q r L m l = 0) ∧ + (∀ k, k < 2 ^ m → ‖evenRowShift r (evenRohlinProjection q r L m k) - + evenRohlinProjection q r L m ((k + 1) % (2 ^ m))‖ < ε) := by + let C : ℝ := (m : ℝ) * (4 * (m : ℝ) + 1) + have hC : 0 ≤ C := by dsimp [C]; positivity + have hεsq : 0 < ε ^ 2 := sq_pos_of_pos hε + obtain ⟨L, hL⟩ := exists_nat_gt (18 * C ^ 2 / ε ^ 2 + 1) + have hLpos : 0 < L := by + have hnonneg : 0 ≤ 18 * C ^ 2 / ε ^ 2 := by positivity + exact_mod_cast (show (0 : ℝ) < (L : ℝ) by linarith) + have hLreal : (0 : ℝ) < (L : ℝ) := by exact_mod_cast hLpos + have hbound : 18 * C ^ 2 < (L : ℝ) * ε ^ 2 := by + apply (div_lt_iff₀ hεsq).mp + linarith + have hbound' : 18 * C ^ 2 / (L : ℝ) < ε ^ 2 := (div_lt_iff₀ hLreal).mpr (by nlinarith) + have hsqrt := Real.sq_sqrt (show 0 ≤ 18 / (L : ℝ) by positivity) + have hnorm : C * Real.sqrt (18 / (L : ℝ)) < ε := by + have he : (C * Real.sqrt (18 / (L : ℝ))) ^ 2 = 18 * C ^ 2 / (L : ℝ) := by + rw [mul_pow, hsqrt] + ring + nlinarith [mul_nonneg hC (Real.sqrt_nonneg (18 / (L : ℝ)))] + obtain ⟨hp, hsum', horth⟩ := evenRohlinProjection_partition q r hqstar hqq hrow hsum L hLpos m + refine ⟨L, hLpos, hp, hsum', horth, ?_⟩ + intro k hk + exact (evenRohlinProjection_cyclic_error q r hqstar hqq hrow hsum L hLpos m k hk).trans_lt hnorm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RohlinUnitarity.lean b/lean/OAI/Analysis/OInfinity/RohlinUnitarity.lean new file mode 100644 index 0000000000000000000000000000000000000000..49fbf724b295d4d9d17885baa664913559e736e1 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RohlinUnitarity.lean @@ -0,0 +1,115 @@ +import OAI.Analysis.OInfinity.RohlinGluing + +namespace OAI + +/-! # Both unitary defects of a weighted Rohlin sum + +The diagonal coefficient/projection commutators control both defects. The +second estimate compares the adjoint weighted sum with the weighted adjoints; +it does not require pairwise commutation of all coefficients and projections. +The hypotheses still have to be supplied by the actual tower construction. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E I : Type*} [CStarAlgebra E] [Fintype I] [DecidableEq I] + +lemma adjoint_unitary_commutator_norm (u : unitary E) (e : E) + (he : star e = e) : + ‖(star u : unitary E) * e - e * (star u : unitary E)‖ = + ‖(u : E) * e - e * (u : E)‖ := by + calc + _ = ‖star ((star u : unitary E) * e - e * (star u : unitary E))‖ := + (norm_star _).symm + _ = ‖e * (u : E) - (u : E) * e‖ := by + simp only [star_sub, star_mul, he, Unitary.coe_star, star_star] + _ = _ := norm_sub_rev _ _ + +lemma star_mul_self_sub_norm_le (x y : E) : + ‖star x * x - star y * y‖ ≤ (‖x‖ + ‖y‖) * ‖x - y‖ := by + have hid : star x * x - star y * y = + star x * (x - y) + star (x - y) * y := by + rw [star_sub] + noncomm_ring + rw [hid] + calc + _ ≤ ‖star x * (x - y)‖ + ‖star (x - y) * y‖ := norm_add_le _ _ + _ ≤ ‖x‖ * ‖x - y‖ + ‖x - y‖ * ‖y‖ := by + simpa only [norm_star] using add_le_add + (norm_mul_le (star x) (x - y)) (norm_mul_le (star (x - y)) y) + _ = _ := by ring + +lemma finiteRohlinSum_norm_le [Nontrivial E] (v : I → unitary E) (e : I → E) + (he : ∀ i, star (e i) = e i) (hee : ∀ i, e i * e i = e i) + (horth : ∀ i j, i ≠ j → e i * e j = 0) : + ‖finiteRohlinSum v e‖ ≤ Real.sqrt (Fintype.card I) := by + change ‖∑ i, (v i : E) * e i‖ ≤ _ + simpa only [mul_one] using orthogonalWeighted_norm_le e (fun i => (v i : E)) + he hee horth 1 (by norm_num) (fun i => (CStarRing.norm_coe_unitary (v i)).le) + +omit [DecidableEq I] in +lemma finiteRohlinSum_star_commutator_le (v : I → unitary E) (e : I → E) + (he : ∀ i, star (e i) = e i) (δ : ℝ) + (hc : ∀ i, ‖(v i : E) * e i - e i * (v i : E)‖ ≤ δ) : + ‖star (finiteRohlinSum v e) - finiteRohlinSum (fun i => star (v i)) e‖ ≤ + (Fintype.card I : ℝ) * δ := by + change ‖star (∑ i, (v i : E) * e i) - ∑ i, (star (v i) : unitary E) * e i‖ ≤ _ + rw [star_sum, ← Finset.sum_sub_distrib] + calc + _ ≤ ∑ i, ‖star ((v i : E) * e i) - (star (v i) : unitary E) * e i‖ := + norm_sum_le _ _ + _ ≤ ∑ _ : I, δ := by + apply Finset.sum_le_sum + intro i hi + rw [star_mul, he i, Unitary.coe_star, norm_sub_rev] + exact (adjoint_unitary_commutator_norm (v i) (e i) (he i)).le.trans (hc i) + _ = _ := by simp + +/-- The second defect has a dimension-dependent bound, sufficient when the +commutator accuracy is chosen after the finite tower size. -/ +lemma finiteRohlinSum_isometry_defect_le [Nontrivial E] (v : I → unitary E) (e : I → E) + (he : ∀ i, star (e i) = e i) (hee : ∀ i, e i * e i = e i) + (horth : ∀ i j, i ≠ j → e i * e j = 0) + (hsum : (∑ i, e i) = 1) (δ : ℝ) + (hc : ∀ i, ‖(v i : E) * e i - e i * (v i : E)‖ ≤ δ) : + ‖star (finiteRohlinSum v e) * finiteRohlinSum v e - 1‖ ≤ + (Fintype.card I : ℝ) * (2 * Real.sqrt (Fintype.card I) + 1) * δ := by + let z := finiteRohlinSum v e + let y := finiteRohlinSum (fun i => star (v i)) e + have hz : ‖z‖ ≤ Real.sqrt (Fintype.card I) := finiteRohlinSum_norm_le v e he hee horth + have hy : ‖y‖ ≤ Real.sqrt (Fintype.card I) := + finiteRohlinSum_norm_le (fun i => star (v i)) e he hee horth + have hc' (i : I) : ‖(star (v i) : unitary E) * e i - + e i * (star (v i) : unitary E)‖ ≤ δ := + (adjoint_unitary_commutator_norm (v i) (e i) (he i)).le.trans (hc i) + have hydef : ‖y * star y - 1‖ ≤ (Fintype.card I : ℝ) * δ := + finiteRohlinSum_coisometry_defect_le (fun i => star (v i)) e he hee horth hsum δ hc' + have hdist : ‖z - star y‖ ≤ (Fintype.card I : ℝ) * δ := by + calc + _ = ‖star z - y‖ := by rw [← norm_star (star z - y), star_sub, star_star] + _ ≤ _ := finiteRohlinSum_star_commutator_le v e he δ hc + have hdiff : ‖star z * z - y * star y‖ ≤ + (2 * Real.sqrt (Fintype.card I)) * ((Fintype.card I : ℝ) * δ) := by + calc + _ = ‖star z * z - star (star y) * star y‖ := by rw [star_star] + _ ≤ (‖z‖ + ‖star y‖) * ‖z - star y‖ := star_mul_self_sub_norm_le z (star y) + _ ≤ (2 * Real.sqrt (Fintype.card I)) * ((Fintype.card I : ℝ) * δ) := by + rw [norm_star] + exact mul_le_mul (by linarith) hdist (norm_nonneg _) + (by positivity) + change ‖star z * z - 1‖ ≤ _ + calc + _ ≤ ‖star z * z - y * star y‖ + ‖y * star y - 1‖ := + norm_sub_le_norm_sub_add_norm_sub _ _ _ + _ ≤ (2 * Real.sqrt (Fintype.card I)) * ((Fintype.card I : ℝ) * δ) + + (Fintype.card I : ℝ) * δ := add_le_add hdiff hydef + _ = _ := by ring + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RowCocycleDefect.lean b/lean/OAI/Analysis/OInfinity/RowCocycleDefect.lean new file mode 100644 index 0000000000000000000000000000000000000000..0d865e59b807770dcd8ef14399623f10502be995 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RowCocycleDefect.lean @@ -0,0 +1,223 @@ +import OAI.Analysis.OInfinity.BinaryFragmentation + +namespace OAI + +/-! # The actual row cocycle and its finite splitting defect + +The product cocycle `V_n = W φ(W) ... φ^[n-1](W)` is not a finite +permutation. Its splitting defect is: `V_n φ(V_n*) = ψ^[n](W*) W`, +where `ψ = Ad(W) φ`. For commuting binary Cuntz rows the right side is +the adjoint of the joint-word cycle already constructed. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +section Group + +variable {G : Type*} [Group G] + +def finiteGroupCocycle (φ : G →* G) (u : G) : ℕ → G + | 0 => 1 + | n + 1 => u * φ (finiteGroupCocycle φ u n) + +lemma finiteGroupCocycle_splitting_defect (φ ψ : G →* G) (u : G) + (hψ : ∀ x, ψ x = u * φ x * u⁻¹) (n : ℕ) : + finiteGroupCocycle φ u n * φ ((finiteGroupCocycle φ u n)⁻¹) = + (ψ^[n]) (u⁻¹) * u := by + induction n with + | zero => simp [finiteGroupCocycle] + | succ n ih => + change (u * φ (finiteGroupCocycle φ u n)) * + φ ((u * φ (finiteGroupCocycle φ u n))⁻¹) = _ + calc + _ = u * φ (finiteGroupCocycle φ u n * + φ ((finiteGroupCocycle φ u n)⁻¹)) * φ (u⁻¹) := by + simp only [map_mul, map_inv, mul_inv_rev] + group + _ = u * (φ ((ψ^[n]) (u⁻¹)) * φ u) * φ (u⁻¹) := by rw [ih, map_mul] + _ = ψ ((ψ^[n]) (u⁻¹)) * u := by + rw [hψ] + simp only [map_inv] + group + _ = _ := by rw [Function.iterate_succ_apply'] + +end Group + +variable {E : Type*} [CStarAlgebra E] + +def binarySplitHom (a b : E) (ha : star a * a = 1) (hb : star b * b = 1) + (hab : star a * b = 0) : unitary E →* unitary E where + toFun u := binaryCornerUnitary a ha u * binaryCornerUnitary b hb u + map_one' := by rw [binaryCornerUnitary_one, binaryCornerUnitary_one, one_mul] + map_mul' u v := by + change binaryCornerUnitary a ha (u * v) * binaryCornerUnitary b hb (u * v) = _ + rw [binaryCornerUnitary_mul, binaryCornerUnitary_mul] + calc + _ = binaryCornerUnitary a ha u * + (binaryCornerUnitary a ha v * binaryCornerUnitary b hb u) * + binaryCornerUnitary b hb v := by simp only [mul_assoc] + _ = binaryCornerUnitary a ha u * + (binaryCornerUnitary b hb u * binaryCornerUnitary a ha v) * + binaryCornerUnitary b hb v := by + rw [(binaryCornerUnitary_commute a b ha hb hab v u).eq] + _ = _ := by simp only [mul_assoc] + +lemma binarySplitHom_coe (s : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) (u : unitary E) : + (binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1) u : E) = finiteRowShift s u := by + change cornerCompression (s 0) u * cornerCompression (s 1) u = _ + have hsum' : s 0 * star (s 0) + s 1 * star (s 1) = 1 := by + simpa only [Fin.sum_univ_two] using hsum + rw [cornerCompression_pair_product _ _ _ _ (by simpa using hs 0 1)] + simp only [finiteRowShift, Fin.sum_univ_two] + rw [← hsum'] + noncomm_ring + +def binaryRowUnitary (s t : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) + (htsum : (∑ i, t i * star (t i)) = 1) : unitary E := + ⟨finiteRowCocycle s t, + finiteRowCocycle_gram 1 s t (by simp) (by simp) hs ht hsum htsum⟩ + +lemma finiteRowCocycle_conjugate_shift (s t : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) (x : E) : + finiteRowCocycle s t * finiteRowShift s x * star (finiteRowCocycle s t) = + finiteRowShift t x := by + simp only [finiteRowShift, Finset.mul_sum, Finset.sum_mul] + apply Finset.sum_congr rfl + intro i hi + have he : star (s i) * star (finiteRowCocycle s t) = star (t i) := by + simpa only [star_mul] using congrArg star + (finiteRowCocycle_mul_row 1 s t (by simp) (by simp) hs ht i) + calc + _ = (finiteRowCocycle s t * s i) * x * + (star (s i) * star (finiteRowCocycle s t)) := by noncomm_ring + _ = _ := by rw [finiteRowCocycle_mul_row 1 s t (by simp) (by simp) hs ht, he] + +lemma binarySplitHom_conjugacy (s t : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) + (htsum : (∑ i, t i * star (t i)) = 1) (x : unitary E) : + binarySplitHom (t 0) (t 1) (by simpa using ht 0 0) + (by simpa using ht 1 1) (by simpa using ht 0 1) x = + binaryRowUnitary s t hs ht hsum htsum * + binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1) x * + (binaryRowUnitary s t hs ht hsum htsum)⁻¹ := by + apply Subtype.ext + rw [binarySplitHom_coe t ht htsum] + change finiteRowShift t x = finiteRowCocycle s t * + (binarySplitHom (s 0) (s 1) _ _ _ x : E) * star (finiteRowCocycle s t) + rw [binarySplitHom_coe s hs hsum] + exact (finiteRowCocycle_conjugate_shift s t hs ht x).symm + +lemma binarySplitHom_iterate_coe (s : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) (x : unitary E) (n : ℕ) : + (((binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1))^[n]) x : E) = + finiteRowShiftIterate s n x := by + induction n with + | zero => rfl + | succ n ih => + rw [Function.iterate_succ_apply', binarySplitHom_coe s hs hsum, finiteRowShiftIterate, ih] + +lemma finiteRowShift_star (s : Fin 2 → E) (x : E) : + star (finiteRowShift s x) = finiteRowShift s (star x) := by + simp only [finiteRowShift, star_sum, star_mul, star_star, mul_assoc] + +lemma finiteRowShiftIterate_star (s : Fin 2 → E) (n : ℕ) (x : E) : + star (finiteRowShiftIterate s n x) = finiteRowShiftIterate s n (star x) := by + induction n with + | zero => rfl + | succ n ih => rw [finiteRowShiftIterate, finiteRowShift_star, ih]; rfl + +def binaryRowCocycleUnitary (s t : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) + (htsum : (∑ i, t i * star (t i)) = 1) (n : ℕ) : unitary E := + finiteGroupCocycle (binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1)) + (binaryRowUnitary s t hs ht hsum htsum) n + +/-- The splitting defect of the actual product cocycle, not the product +itself, is the adjoint joint-word permutation. -/ +lemma binaryRowCocycleUnitary_defect (s t : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) + (htsum : (∑ i, t i * star (t i)) = 1) (n : ℕ) : + ((binaryRowCocycleUnitary s t hs ht hsum htsum n : E) * + star (binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1) + (binaryRowCocycleUnitary s t hs ht hsum htsum n) : E)) = + star (finiteJointCycleCoboundary t s n) := by + let α := binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1) + let β := binarySplitHom (t 0) (t 1) (by simpa using ht 0 0) + (by simpa using ht 1 1) (by simpa using ht 0 1) + let w := binaryRowUnitary s t hs ht hsum htsum + have h := finiteGroupCocycle_splitting_defect α β w + (binarySplitHom_conjugacy s t hs ht hsum htsum) n + rw [map_inv] at h + have he := congrArg (fun v : unitary E => (v : E)) h + change (↑(finiteGroupCocycle α w n) : E) * star (↑(α (finiteGroupCocycle α w n)) : E) = + ((β^[n]) (w⁻¹) : E) * (w : E) at he + rw [binarySplitHom_iterate_coe t ht htsum] at he + change (binaryRowCocycleUnitary s t hs ht hsum htsum n : E) * + star (α (binaryRowCocycleUnitary s t hs ht hsum htsum n) : E) = + finiteRowShiftIterate t n (star (finiteRowCocycle s t)) * finiteRowCocycle s t at he + simpa only [finiteJointCycleCoboundary, star_mul, finiteRowShiftIterate_star, + star_star, finiteRowCocycle_star] using he + +/-- Uniform paths for the genuine binary product cocycles. The bound is +independent of the number of factors. These are coisometric rows in the +ambient unit; applying this in a proper corner requires corner transport. -/ +lemma exists_uniform_binaryRowCocycle_path [Nontrivial E] (s t : Fin 2 → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hsum : (∑ i, s i * star (s i)) = 1) + (htsum : (∑ i, t i * star (t i)) = 1) + (hc : ∀ i j, Commute (s i) (t j)) (n : ℕ) : + ∃ p : Path (binaryRowCocycleUnitary s t hs ht hsum htsum n) 1, + ∀ a b, ‖(p a : E) - p b‖ ≤ (192 * Real.pi) * |(a : ℝ) - b| := by + let v := binaryRowCocycleUnitary s t hs ht hsum htsum n + let α := binarySplitHom (s 0) (s 1) (by simpa using hs 0 0) + (by simpa using hs 1 1) (by simpa using hs 0 1) + obtain ⟨c, hcoe, p, hp⟩ := exists_controlled_jointCycleCoboundary_path + 1 t s (by simp) (by simp) ht hs htsum hsum (fun i j => (hc j i).symm) n + simp only [sub_self, add_zero] at hcoe + have hd : v * star (α v) = star c := by + apply Subtype.ext + change (v : E) * star (α v : E) = star (c : E) + rw [hcoe] + exact binaryRowCocycleUnitary_defect s t hs ht hsum htsum n + let q : Path (1 : unitary E) (v * star (α v)) := + (p.map (continuous_star : Continuous (star : unitary E → unitary E))).cast (by simp) hd + have hq : ∀ a b, ‖(q a : E) - q b‖ ≤ (4 * Real.pi) * |(a : ℝ) - b| := by + intro a b + change ‖star (p a : E) - star (p b : E)‖ ≤ _ + rw [← star_sub, norm_star] + exact hp a b + obtain ⟨r, hr⟩ := exists_binaryFragmentation_of_defect_path (s 0) (s 1) + (by simpa using hs 0 0) (by simpa using hs 1 1) (by simpa using hs 0 1) + v (4 * Real.pi) (by positivity) q hq + refine ⟨r, ?_⟩ + intro a b + simpa only [show 32 * (4 * Real.pi + 2 * Real.pi) = 192 * Real.pi by ring] using hr a b + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RowCompletionBase.lean b/lean/OAI/Analysis/OInfinity/RowCompletionBase.lean new file mode 100644 index 0000000000000000000000000000000000000000..a8c321f61323e1cb35022c4dd388461b273aab61 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RowCompletionBase.lean @@ -0,0 +1,145 @@ +import OAI.Analysis.OInfinity.ConnectedRowCompletion + +namespace OAI + +/-! # The actual base path of the common-corner shrink + +Binary completions chosen with connected left cocycles have a connected +base comparison. The proof identifies that base with compression of the +literal cocycle product by one fixed isometry. No general claim about a +corner stabilizer or about the ambient unitary group is used. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- The cross product of two fillers with the same initial projection is +the standard compression of their middle unitary product. -/ +lemma coisometry_filler_cross (A y : E) (hA : A * star A = 1) + (hy : star y * y = 1) (hpy : (star A * A) * y = y) (u v : unitary E) : + star (1 - star A * A + y * (star (v : E) * A)) * + (1 - star A * A + y * (star (u : E) * A)) = + (binaryCornerUnitary (star A) (by simpa only [star_star] using hA) (v * star u) : E) := by + let p := star A * A + let e := 1 - p + have hp : star p = p := by simp only [p, star_mul, star_star] + have hpp : p * p = p := by + change (star A * A) * (star A * A) = star A * A + calc + _ = star A * (A * star A) * A := by noncomm_ring + _ = _ := by rw [hA, mul_one] + have he : star e = e := by simp only [e, star_sub, star_one, hp] + have hee : e * e = e := by dsimp only [e]; noncomm_ring [hpp] + have hey : e * y = 0 := by + change (1 - star A * A) * y = 0 + rw [sub_mul, one_mul, hpy, sub_self] + have hleft (w : unitary E) : e * (y * (star (w : E) * A)) = 0 := by + rw [← mul_assoc, hey, zero_mul] + have hright : star (y * (star (v : E) * A)) * e = 0 := by + simpa only [star_mul, he, star_zero] using congrArg star (hleft v) + have hmiddle : star (y * (star (v : E) * A)) * (y * (star (u : E) * A)) = + star A * ((v : E) * star (u : E)) * A := by + simp only [star_mul, star_star] + calc + _ = star A * (v : E) * (star y * y) * star (u : E) * A := by noncomm_ring + _ = _ := by rw [hy, mul_one]; noncomm_ring + change _ = cornerCompression (star A) ((v * star u : unitary E) : E) + unfold cornerCompression + rw [star_star] + change star (e + y * (star (v : E) * A)) * (e + y * (star (u : E) * A)) = + star A * ((v : E) * star (u : E)) * A + e + rw [star_add, he, add_mul, mul_add, mul_add, hee, hleft, hright, hmiddle] + abel + +/-- Factoring the reference row out of the finite transfer keeps the +initial projection independent of the chosen completion cocycle. -/ +lemma binaryShrinkValue_reference (r b : Fin 2 → E) (u : unitary E) : + binaryShrinkValue r (fun i => star (u : E) * b i) 1 = + 1 - star (finiteCuntzTransfer r b 1) * finiteCuntzTransfer r b 1 + + r 1 * (star (u : E) * finiteCuntzTransfer r b 1) := by + let A := finiteCuntzTransfer r b 1 + have htransfer : finiteCuntzTransfer r (fun i => star (u : E) * b i) 1 = + star (u : E) * A := by + simp only [A, finiteCuntzTransfer, Finset.mul_sum, mul_one, mul_assoc] + rw [binaryShrinkValue_one, htransfer] + change 1 - star (star (u : E) * A) * (star (u : E) * A) + + r 1 * (star (u : E) * A) = _ + have hg : star (star (u : E) * A) * (star (u : E) * A) = star A * A := by + rw [star_mul, star_star] + calc + _ = star A * ((u : E) * star (u : E)) * A := by noncomm_ring + _ = _ := by rw [u.property.2, mul_one] + rw [hg] + +/-- The fixed isometry and the full reference row give the exact base +identity used in the two common-corner comparisons. -/ +lemma finiteCuntzTransfer_reference_coisometry (r b : Fin 2 → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (hbs : (∑ i, b i * star (b i)) = 1) : + finiteCuntzTransfer r b 1 * star (finiteCuntzTransfer r b 1) = 1 := by + have hs : star (finiteCuntzTransfer r b 1) = finiteCuntzTransfer b r 1 := by + simpa only [star_one] using finiteCuntzTransfer_star r b 1 + have hh := finiteCuntzTransfer_star_mul b r hr 1 + rw [← hs, star_star] at hh + simpa only [star_one, one_mul, mul_one, hbs] using hh + +lemma binaryShrinkValue_reference_cross (r b : Fin 2 → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (hb : ∀ i j, star (b i) * b j = if i = j then 1 else 0) + (hbs : (∑ i, b i * star (b i)) = 1) (u v : unitary E) : + ∃ K : unitary E, + (K : E) = star (binaryShrinkValue r (fun i => star (v : E) * b i) 1) * + binaryShrinkValue r (fun i => star (u : E) * b i) 1 ∧ + K = binaryCornerUnitary (star (finiteCuntzTransfer r b 1)) + (by simpa only [star_star] using + finiteCuntzTransfer_reference_coisometry r b hr hbs) (v * star u) := by + let A := finiteCuntzTransfer r b 1 + have hAst : star A = finiteCuntzTransfer b r 1 := by + simpa only [A, star_one] using finiteCuntzTransfer_star r b 1 + have hAA : A * star A = 1 := by + have hh := finiteCuntzTransfer_star_mul b r hr 1 + rw [← hAst, star_star] at hh + simpa only [star_one, one_mul, mul_one, hbs] using hh + have hAp : star A * A = ∑ i, r i * star (r i) := by + simpa only [A, star_one, one_mul, mul_one] using finiteCuntzTransfer_star_mul r b hb 1 + have hr1 : star (r 1) * r 1 = 1 := by simpa only [ite_true] using hr 1 1 + have hpy : (star A * A) * r 1 = r 1 := by + rw [hAp] + simpa only [finiteRowPermutation, Equiv.Perm.one_apply] using + finiteRowPermutation_mul_row 1 r (by simp) (by simp) hr 1 1 + let K := binaryCornerUnitary (star A) (by simpa only [star_star] using hAA) (v * star u) + refine ⟨K, ?_, rfl⟩ + rw [binaryShrinkValue_reference, binaryShrinkValue_reference] + exact (coisometry_filler_cross A (r 1) hAA hr1 hpy u v).symm + +/-- The base product is connected because its two prescribed cocycles +are connected. This is the concrete path, rather than an ambient K1 claim. -/ +lemma binaryShrinkValue_reference_cross_joined (r b : Fin 2 → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (hb : ∀ i j, star (b i) * b j = if i = j then 1 else 0) + (hbs : (∑ i, b i * star (b i)) = 1) + (u v : unitary E) (hu : Joined (1 : unitary E) u) (hv : Joined (1 : unitary E) v) : + ∃ K : unitary E, Joined (1 : unitary E) K ∧ + (K : E) = star (binaryShrinkValue r (fun i => star (v : E) * b i) 1) * + binaryShrinkValue r (fun i => star (u : E) * b i) 1 := by + obtain ⟨K, hK, hKe⟩ := binaryShrinkValue_reference_cross r b hr hb hbs u v + have hu' : Joined (1 : unitary E) (star u) := by + simpa only [star_one] using hu.map (continuous_star : Continuous (star : unitary E → unitary E)) + have huv : Joined (1 : unitary E) (v * star u) := by + simpa only [one_mul] using hv.mul hu' + refine ⟨K, ?_, hK⟩ + rw [hKe] + have hA : star (star (finiteCuntzTransfer r b 1)) * star (finiteCuntzTransfer r b 1) = 1 := by + simpa only [star_star] using finiteCuntzTransfer_reference_coisometry r b hr hbs + simpa only [binaryCornerUnitary_one] using + huv.map (binaryCornerUnitary_continuous (star (finiteCuntzTransfer r b 1)) hA) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/RowCompletionBuffer.lean b/lean/OAI/Analysis/OInfinity/RowCompletionBuffer.lean new file mode 100644 index 0000000000000000000000000000000000000000..7ac2aba44dee29e467b5077ba9fccfd3db696fb1 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/RowCompletionBuffer.lean @@ -0,0 +1,314 @@ +import OAI.Analysis.OInfinity.RowCompletionBase + +namespace OAI + +/-! # Completions in the first buffer commutant + +The relative path data records the fixed complement at every time. The +second buffer is constructed by the explicit central-row theorem inside +the norm ultrapower; its target family consists of elements of the first +buffer commutant. No commuting-row existence is assumed. +-/ + +noncomputable section +open Filter Topology +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +local instance rowCompletionCentralizerClosed (R : ℕ → E) : + IsClosed (StarSubalgebra.centralizer ℂ (Set.range R) : Set E) := + Set.isClosed_centralizer _ + +structure RelativeBinaryCompletion {n : ℕ} (q : E) (b : Fin 2 → E) + (x : Fin (n + 1) → E) where + row : Fin 2 → E + implementer : unitary E + deformation : Path (1 : unitary E) implementer + fixes_complement : ∀ t, (deformation t : E) * (1 - q) = 1 - q ∧ + (1 - q) * (deformation t : E) = 1 - q + support : ∀ i, q * row i = row i ∧ row i * q = row i + gram : ∀ i j, star (row i) * row j = if i = j then q else 0 + range_sum : (∑ i, row i * star (row i)) = q + encoded_prefix : ∀ i : Fin (n + 1), row 0 ^ (i : ℕ) * row 1 = x i + cocycle : ∀ j, (implementer : E) * row j = b j + +/-- A relative completion whose whole connecting path fixes the external +complement, obtained by doing the three connected moves in the corner. -/ +lemma exists_relative_connected_binary_completion {n : ℕ} + (q : E) (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (x : Fin (n + 2) → E) + (hxs : ∀ i, q * x i = x i ∧ x i * q = x i) + (hx : ∀ i j, star (x i) * x j = if i = j then q else 0) + (b : Fin 2 → E) + (hb : ∀ i j, star (b i) * b j = if i = j then q else 0) + (hbs : (∑ i, b i * star (b i)) = q) + (r : Fin 3 → E) + (hrs : ∀ i, q * r i = r i ∧ r i * q = r i) + (hr : ∀ i j, star (r i) * r j = if i = j then q else 0) + (her : Commute (star (r 0)) (x (Fin.last (n + 1)))) + (hfr : Commute (star (r 1)) (b 0 * x (Fin.last (n + 1)))) : + Nonempty (RelativeBinaryCompletion q b (fun i : Fin (n + 1) => x i.castSucc)) := by + let : NeZero q := ⟨hq0⟩ + let H := ProjectionCorner q hq hqq + let f := projectionCornerInclusion q hq hqq + have hf1 : f 1 = q := rfl + have hfa (a : H) : f a = (a : E) := rfl + have hbsup (i : Fin 2) : q * b i = b i ∧ b i * q = b i := + ⟨finiteRow_left_support q b hq hqq hb hbs i, + finiteRow_right_support q b hq hqq hb i⟩ + let X : Fin (n + 2) → H := fun i => projectionCornerElement q hq hqq (x i) (hxs i) + let B : Fin 2 → H := fun i => projectionCornerElement q hq hqq (b i) (hbsup i) + let R : Fin 3 → H := fun i => projectionCornerElement q hq hqq (r i) (hrs i) + have hX := projectionCornerElement_gram q hq hqq x hxs hx + have hB := projectionCornerElement_gram q hq hqq b hbsup hb + have hBs := projectionCornerElement_range_sum q hq hqq b hbsup hbs + have hR := projectionCornerElement_gram q hq hqq r hrs hr + have he : star (X (Fin.last (n + 1))) * X (Fin.last (n + 1)) = 1 := by + simpa only [ite_true] using hX (Fin.last (n + 1)) (Fin.last (n + 1)) + have hxe (i : Fin (n + 1)) : star (X i.castSucc) * X (Fin.last (n + 1)) = 0 := by + have hne : i.castSucc ≠ Fin.last (n + 1) := by + intro h + have hh := congrArg Fin.val h + change (i : ℕ) = n + 1 at hh + omega + simpa only [hne, ite_false] using hX i.castSucc (Fin.last (n + 1)) + obtain ⟨a, u, hu, hag, has, ha, huc⟩ := exists_connected_binary_row_completion + (fun i : Fin (n + 1) => X i.castSucc) + (fun i j => by simpa only [Fin.castSucc_inj] using hX i.castSucc j.castSucc) + (X (Fin.last (n + 1))) he hxe B hB hBs R hR + (show Commute (star (R 0)) (X (Fin.last (n + 1))) from Subtype.ext her.eq) + (show Commute (star (R 1)) (B 0 * X (Fin.last (n + 1))) from Subtype.ext hfr.eq) + let p := hu.somePath + let U := projectionCornerUnitary q hq hqq u + let P : Path (1 : unitary E) U := + { toFun := fun t => projectionCornerUnitary q hq hqq (p t) + continuous_toFun := (projectionCornerUnitary_continuous q hq hqq).comp p.continuous + source' := by rw [p.source, projectionCornerUnitary_one] + target' := by rw [p.target] } + refine ⟨{ + row := fun i => f (a i) + implementer := U + deformation := P + fixes_complement := fun t => projectionCornerUnitary_complement q hq hqq (p t) + support := fun i => (a i).property + gram := ?_ + range_sum := ?_ + encoded_prefix := ?_ + cocycle := ?_ }⟩ + · intro i j + have h := congrArg f (hag i j) + by_cases hij : i = j + · simpa only [hij, ite_true, map_mul, map_star, hf1] using h + · simpa only [hij, ite_false, map_mul, map_star, map_zero] using h + · have h := congrArg f has + simpa only [map_sum, map_mul, map_star, hf1] using h + · intro i + have h := congrArg f (ha i) + rw [nonunital_map_pow_mul] at h + exact h + · intro j + change ((((u : H) : E) + (1 - q)) * f (a j)) = b j + rw [add_mul, sub_mul, one_mul, hfa, (a j).property.1, sub_self, add_zero] + exact congrArg f (huc j) + +/-- Diagonalizing an element of the first row commutant preserves that +membership in the next norm ultrapower. -/ +def rowCentralizerDiagonalHom (U : Ultrafilter ℕ) (R : ℕ → E) : + StarSubalgebra.centralizer ℂ (Set.range R) →⋆ₐ[ℂ] + StarSubalgebra.centralizer ℂ + (Set.range (fun i => NormUltra.QuotientAlgebra.diagonalHom U (R i))) := by + let C := StarSubalgebra.centralizer ℂ (Set.range R) + let D := StarSubalgebra.centralizer ℂ + (Set.range (fun i => NormUltra.QuotientAlgebra.diagonalHom U (R i))) + let d := NormUltra.QuotientAlgebra.diagonalHom (A := E) U + refine (d.comp C.subtype).codRestrict D ?_ + intro x + apply (StarSubalgebra.mem_centralizer_iff ℂ).mpr + rintro _ ⟨i, rfl⟩ + obtain ⟨h₁, h₂⟩ := (StarSubalgebra.mem_centralizer_iff ℂ).mp x.property (R i) ⟨i, rfl⟩ + constructor + · change d (R i) * d (x : E) = d (x : E) * d (R i) + simpa only [map_mul] using congrArg d h₁ + · change star (d (R i)) * d (x : E) = d (x : E) * star (d (R i)) + simpa only [map_mul, map_star] using congrArg d h₂ + +/-- The second proper row is actually built. Its entries remain in the +first row's commutant and commute with every member of the chosen target +family and its adjoint. -/ +lemma exists_normUltrapower_row_in_commutant [Nontrivial E] + (U : Ultrafilter ℕ) [Fact ((U : Filter ℕ) ≤ atTop)] (R : ℕ → E) + (hR : ∀ i j, star (R i) * R j = if i = j then 1 else 0) + (t : ℕ → StarSubalgebra.centralizer ℂ (Set.range R)) : + ∃ z : ℕ → StarSubalgebra.centralizer ℂ + (Set.range (fun i => NormUltra.QuotientAlgebra.diagonalHom U (R i))), + (∀ i j, star (z i) * z j = if i = j then 1 else 0) ∧ + ∀ i j, Commute (z i) (rowCentralizerDiagonalHom U R (t j)) ∧ + Commute (z i) (star (rowCentralizerDiagonalHom U R (t j))) := by + let T : ℕ → E := fun i => t i + have hRT : bergRowsCommute R T := by + intro i j + obtain ⟨h₁, h₂⟩ := (StarSubalgebra.mem_centralizer_iff ℂ).mp (t j).property (R i) ⟨i, rfl⟩ + refine ⟨h₁, ?_⟩ + change R i * star (t j : E) = star (t j : E) * R i + simpa only [star_mul, star_star] using (congrArg star h₂).symm + obtain ⟨Z, hZ, hZR, hZT⟩ := exists_normUltrapower_central_cuntz_row U R T hR hRT + have hmem (i : ℕ) : Z i ∈ StarSubalgebra.centralizer ℂ + (Set.range (fun j => NormUltra.QuotientAlgebra.diagonalHom U (R j))) := by + apply (StarSubalgebra.mem_centralizer_iff ℂ).mpr + rintro _ ⟨j, rfl⟩ + exact ⟨(hZR i j).1.symm, (hZR i j).2.symm⟩ + let z i := (⟨Z i, hmem i⟩ : StarSubalgebra.centralizer ℂ + (Set.range (fun j => NormUltra.QuotientAlgebra.diagonalHom U (R j)))) + refine ⟨z, ?_, fun i j => ?_⟩ + · intro i j + apply Subtype.ext + change star (Z i) * Z j = ↑(if i = j then (1 : StarSubalgebra.centralizer ℂ + (Set.range (fun j => NormUltra.QuotientAlgebra.diagonalHom U (R j)))) else 0) + split_ifs with hij + · change star (Z i) * Z j = 1 + simpa only [hij, ite_true] using hZ i j + · change star (Z i) * Z j = 0 + simpa only [hij, ite_false] using hZ i j + · constructor + · exact Subtype.ext (hZT i j).1.eq + · exact Subtype.ext (hZT i j).2.eq + +private lemma rowCentralizerDiagonal_norm (U : Ultrafilter ℕ) (R : ℕ → E) + (x : StarSubalgebra.centralizer ℂ (Set.range R)) : + ‖rowCentralizerDiagonalHom U R x‖ = ‖x‖ := by + change ‖NormUltra.QuotientAlgebra.mk U (DirectComparison.boundedDiagonal (x : E))‖ = ‖(x : E)‖ + rw [NormUltra.QuotientAlgebra.norm_mk_eq_limsup] + change Filter.limsup (fun _ : ℕ => ‖(x : E)‖) (U : Filter ℕ) = ‖(x : E)‖ + rw [Filter.limsup_const] + +/-- The same reference completion is available for both proper finite +rows after the second, explicitly constructed buffer. All resulting data +belong to the first buffer commutant. -/ +lemma exists_buffer_preserving_pair_completions [Nontrivial E] + (U : Ultrafilter ℕ) [Fact ((U : Filter ℕ) ≤ atTop)] + (R : ℕ → E) (hR : ∀ i j, star (R i) * R j = if i = j then 1 else 0) + (q : StarSubalgebra.centralizer ℂ (Set.range R)) + (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (n : ℕ) (x y : Fin (n + 2) → StarSubalgebra.centralizer ℂ (Set.range R)) + (hxs : ∀ i, q * x i = x i ∧ x i * q = x i) + (hys : ∀ i, q * y i = y i ∧ y i * q = y i) + (hx : ∀ i j, star (x i) * x j = if i = j then q else 0) + (hy : ∀ i j, star (y i) * y j = if i = j then q else 0) + (b : Fin 2 → StarSubalgebra.centralizer ℂ (Set.range R)) + (hb : ∀ i j, star (b i) * b j = if i = j then q else 0) + (hbs : (∑ i, b i * star (b i)) = q) : + let θ := rowCentralizerDiagonalHom U R + Nonempty (RelativeBinaryCompletion (θ q) (fun j => θ (b j)) + (fun i : Fin (n + 1) => θ (x i.castSucc))) ∧ + Nonempty (RelativeBinaryCompletion (θ q) (fun j => θ (b j)) + (fun i : Fin (n + 1) => θ (y i.castSucc))) := by + intro θ + let C := StarSubalgebra.centralizer ℂ (Set.range R) + let D := StarSubalgebra.centralizer ℂ + (Set.range (fun i => NormUltra.QuotientAlgebra.diagonalHom U (R i))) + let ex := x (Fin.last (n + 1)) + let ey := y (Fin.last (n + 1)) + let t : ℕ → C := fun i => if i = 0 then q else if i = 1 then ex else + if i = 2 then b 0 * ex else if i = 3 then ey else b 0 * ey + obtain ⟨z, hz, hzt⟩ := exists_normUltrapower_row_in_commutant U R hR t + have hzq (j : ℕ) : Commute (z j) (θ q) := by + simpa only [t, ite_true] using (hzt j 0).1 + have hzex (j : ℕ) : Commute (star (z j)) (θ ex) := by + have h := (hzt j 1).2.star_star + simpa only [t, show (1 : ℕ) ≠ 0 by decide, ite_false, ite_true, star_star] using h + have hzfx (j : ℕ) : Commute (star (z j)) (θ (b 0 * ex)) := by + have h := (hzt j 2).2.star_star + simpa only [t, show (2 : ℕ) ≠ 0 by decide, show (2 : ℕ) ≠ 1 by decide, + ite_false, ite_true, star_star] using h + have hzey (j : ℕ) : Commute (star (z j)) (θ ey) := by + have h := (hzt j 3).2.star_star + simpa only [t, show (3 : ℕ) ≠ 0 by decide, show (3 : ℕ) ≠ 1 by decide, + show (3 : ℕ) ≠ 2 by decide, ite_false, ite_true, star_star] using h + have hzfy (j : ℕ) : Commute (star (z j)) (θ (b 0 * ey)) := by + have h := (hzt j 4).2.star_star + simpa only [t, show (4 : ℕ) ≠ 0 by decide, show (4 : ℕ) ≠ 1 by decide, + show (4 : ℕ) ≠ 2 by decide, show (4 : ℕ) ≠ 3 by decide, ite_false, star_star] using h + have hqD : star (θ q) = θ q := by rw [← map_star, hq] + have hqqD : θ q * θ q = θ q := by rw [← map_mul, hqq] + have hqD0 : θ q ≠ 0 := by + intro hzero + have hn := rowCentralizerDiagonal_norm U R q + change ‖θ q‖ = ‖q‖ at hn + rw [hzero, norm_zero] at hn + exact hq0 (norm_eq_zero.mp hn.symm) + have map_support (a : Fin (n + 2) → C) (hs : ∀ i, q * a i = a i ∧ a i * q = a i) : + ∀ i, θ q * θ (a i) = θ (a i) ∧ θ (a i) * θ q = θ (a i) := by + intro i + constructor + · simpa only [map_mul] using congrArg θ (hs i).1 + · simpa only [map_mul] using congrArg θ (hs i).2 + have map_gram {I : Type} [DecidableEq I] (a : I → C) + (h : ∀ i j, star (a i) * a j = if i = j then q else 0) : + ∀ i j, star (θ (a i)) * θ (a j) = if i = j then θ q else 0 := by + intro i j + rw [← map_star, ← map_mul, h] + split_ifs <;> simp only [map_zero] + have hbsD : (∑ i, θ (b i) * star (θ (b i))) = θ q := by + simpa only [map_sum, map_mul, map_star] using congrArg θ hbs + let r : Fin 3 → D := fun i => z i * θ q + have hrs (i : Fin 3) : θ q * r i = r i ∧ r i * θ q = r i := by + constructor + · change θ q * (z i * θ q) = z i * θ q + rw [← mul_assoc, ← (hzq i).eq, mul_assoc, hqqD] + · change (z i * θ q) * θ q = z i * θ q + rw [mul_assoc, hqqD] + have hrg (i j : Fin 3) : star (r i) * r j = if i = j then θ q else 0 := by + change star (z i * θ q) * (z j * θ q) = _ + rw [star_mul, hqD] + calc + _ = θ q * (star (z i) * z j) * θ q := by noncomm_ring + _ = _ := by + rw [hz] + by_cases hij : i = j + · simpa only [hij, ite_true, mul_one] using hqqD + · have hne : (i : ℕ) ≠ (j : ℕ) := fun h => hij (Fin.ext h) + simp only [hne, hij, ite_false, mul_zero, zero_mul] + have q_commutes (a : C) (ha : q * a = a ∧ a * q = a) : Commute (θ q) (θ a) := by + change θ q * θ a = θ a * θ q + rw [← map_mul, ← map_mul, ha.1, ha.2] + have q_bex : q * (b 0 * ex) = b 0 * ex ∧ (b 0 * ex) * q = b 0 * ex := by + constructor + · rw [← mul_assoc, finiteRow_left_support q b hq hqq hb hbs 0] + · rw [mul_assoc, (hxs (Fin.last (n + 1))).2] + have q_bey : q * (b 0 * ey) = b 0 * ey ∧ (b 0 * ey) * q = b 0 * ey := by + constructor + · rw [← mul_assoc, finiteRow_left_support q b hq hqq hb hbs 0] + · rw [mul_assoc, (hys (Fin.last (n + 1))).2] + have hrex : Commute (star (r 0)) (θ ex) := by + change Commute (star (z 0 * θ q)) (θ ex) + rw [star_mul, hqD] + exact (q_commutes ex (hxs _)).mul_left (hzex 0) + have hrfx : Commute (star (r 1)) (θ (b 0) * θ ex) := by + rw [← map_mul] + change Commute (star (z 1 * θ q)) (θ (b 0 * ex)) + rw [star_mul, hqD] + exact (q_commutes (b 0 * ex) q_bex).mul_left (hzfx 1) + have hrey : Commute (star (r 0)) (θ ey) := by + change Commute (star (z 0 * θ q)) (θ ey) + rw [star_mul, hqD] + exact (q_commutes ey (hys _)).mul_left (hzey 0) + have hrfy : Commute (star (r 1)) (θ (b 0) * θ ey) := by + rw [← map_mul] + change Commute (star (z 1 * θ q)) (θ (b 0 * ey)) + rw [star_mul, hqD] + exact (q_commutes (b 0 * ey) q_bey).mul_left (hzfy 1) + exact ⟨exists_relative_connected_binary_completion (θ q) hqD hqqD hqD0 + (fun i => θ (x i)) (map_support x hxs) (map_gram (I := Fin (n + 2)) x hx) + (fun j => θ (b j)) (map_gram (I := Fin 2) b hb) hbsD r hrs hrg hrex hrfx, + exists_relative_connected_binary_completion (θ q) hqD hqqD hqD0 + (fun i => θ (y i)) (map_support y hys) (map_gram (I := Fin (n + 2)) y hy) + (fun j => θ (b j)) (map_gram (I := Fin 2) b hb) hbsD r hrs hrg hrey hrfy⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ShrinkPaths.lean b/lean/OAI/Analysis/OInfinity/ShrinkPaths.lean new file mode 100644 index 0000000000000000000000000000000000000000..8eb089ad53d5f9d51a876e0fda87ea533897007e --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ShrinkPaths.lean @@ -0,0 +1,174 @@ +import OAI.Analysis.OInfinity.MixedComplement + +namespace OAI + +/-! # Paths of the actual inserted-unitary shrinks + +The inverse canonical-shift implementer can be chosen in the identity +component. Varying that implementer to one preserves both support +projections of the shrink. This supplies a path to the literal base +formula; the base fixed-complement extension is not asserted connected. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- Retain the connectedness supplied by the canonical-shift construction +when passing to inverse conjugation and a finite encoded prefix. -/ +lemma exists_connected_canonicalShift_prefix_inverse [Nontrivial E] + (a : Fin 2 → E) + (ha : ∀ i j, star (a i) * a j = if i = j then 1 else 0) + (has : (∑ i, a i * star (a i)) = 1) (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ u : unitary E, Joined 1 u ∧ ∀ i ≤ m, + ‖(u : E) * finiteRowShift a (a 0 ^ i * a 1) * star (u : E) - + (a 0 ^ i * a 1)‖ < ε := by + let δ := ε / ((m : ℝ) + 2) + have hδ : 0 < δ := by dsimp only [δ]; positivity + obtain ⟨u, hu, huclose⟩ := exists_connected_canonicalShift_conjugacy a ha has δ hδ + let φ := finiteCuntzDiagonalHom a ha + have han (j : Fin 2) : ‖a j‖ ≤ 1 := by + have h := congrArg norm (show star (a j) * a j = 1 by simpa only [ite_true] using ha j j) + rw [CStarRing.norm_star_mul_self, norm_one] at h + nlinarith [norm_nonneg (a j)] + have hun (j : Fin 2) : ‖(u : E) * a j * star (u : E)‖ ≤ 1 := by + rw [mul_assoc, CStarRing.norm_coe_unitary_mul] + change ‖a j * (star u : unitary E)‖ ≤ 1 + rw [CStarRing.norm_mul_coe_unitary] + exact han j + have hφn (j : Fin 2) : ‖φ (a j)‖ ≤ 1 := + (NonUnitalStarAlgHom.norm_apply_le φ _).trans (han j) + have hclose (i : ℕ) (hi : i ≤ m) : + ‖(u : E) * (a 0 ^ i * a 1) * star (u : E) - φ (a 0 ^ i * a 1)‖ < ε := by + let j : Fin (m + 1) := ⟨i, by omega⟩ + have hp := zeroCornerRow_perturbation 1 + ((u : E) * a 0 * star (u : E)) ((u : E) * a 1 * star (u : E)) + (φ (a 0)) (φ (a 1)) δ hδ.le (by simp) (hun 0) (hun 1) (hφn 0) + (huclose 0).le (huclose 1).le (m + 1) j.castSucc + rw [← zeroCornerRow_conjugate] at hp + simp only [zeroCornerRow_castSucc] at hp + rw [← nonunital_map_pow_mul] at hp + apply hp.trans_lt + have he : ((m : ℝ) + 2) * δ = ε := by dsimp only [δ]; field_simp + push_cast + nlinarith + refine ⟨star u, ?_, fun i hi => ?_⟩ + · simpa only [star_one] using hu.map (continuous_star : Continuous (star : unitary E → unitary E)) + · let x := a 0 ^ i * a 1 + have hid : (star (u : E)) * φ x * (u : E) - x = + star (u : E) * (φ x - (u : E) * x * star (u : E)) * (u : E) := by + rw [mul_sub, sub_mul] + have hcan : star (u : E) * ((u : E) * x * star (u : E)) * (u : E) = x := by + calc + _ = (star (u : E) * (u : E)) * x * (star (u : E) * (u : E)) := by noncomm_ring + _ = x := by rw [u.property.1, one_mul, mul_one] + rw [hcan] + change ‖star (u : E) * φ x * star (star (u : E)) - x‖ < ε + rw [star_star, hid, CStarRing.norm_mul_coe_unitary] + change ‖(star u : unitary E) * (φ x - (u : E) * x * star (u : E))‖ < ε + rw [CStarRing.norm_coe_unitary_mul, norm_sub_rev] + exact hclose i hi + +def binaryShrinkValue (r a : Fin 2 → E) (u : unitary E) : E := + let v := (u : E) * finiteCuntzTransfer r a 1 + 1 - star v * v + r 1 * v + +lemma binaryShrinkValue_continuous (r a : Fin 2 → E) : Continuous (binaryShrinkValue r a) := by + unfold binaryShrinkValue + fun_prop + +lemma binaryShrinkValue_one (r a : Fin 2 → E) : + binaryShrinkValue r a 1 = 1 - star (finiteCuntzTransfer r a 1) * + finiteCuntzTransfer r a 1 + r 1 * finiteCuntzTransfer r a 1 := by + simp only [binaryShrinkValue, OneMemClass.coe_one, one_mul] + +/-- The actual shrink follows a continuous path with constant initial and +final projections from its explicit base formula to the required estimate. -/ +lemma exists_binary_shrink_path [Nontrivial E] + (r a : Fin 2 → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (ha : ∀ i j, star (a i) * a j = if i = j then 1 else 0) + (has : (∑ i, a i * star (a i)) = 1) + (hc : bergRowsCommute a r) (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ C : unitInterval → E, Continuous C ∧ + C 0 = binaryShrinkValue r a 1 ∧ + (∀ t, star (C t) * C t = 1 ∧ C t * star (C t) = 1 - r 0 * star (r 0)) ∧ + ∀ i ≤ m, ‖C 1 * (a 0 ^ i * a 1) * star (C 1) - + (a 0 ^ i * a 1) * (1 - r 0 * star (r 0))‖ < ε := by + obtain ⟨u, hu, he⟩ := exists_connected_canonicalShift_prefix_inverse a ha has m ε hε + let p : Path (1 : unitary E) u := hu.somePath + let C : unitInterval → E := fun t => binaryShrinkValue r a (p t) + refine ⟨C, (binaryShrinkValue_continuous r a).comp p.continuous, ?_, ?_, ?_⟩ + · change binaryShrinkValue r a (p 0) = _ + rw [p.source] + · intro t + exact binary_shift_shrink_products r a hr ha has (p t) + · intro i hi + have hx (j : Fin 2) : Commute (a 0 ^ i * a 1) (r j) ∧ + Commute (a 0 ^ i * a 1) (star (r j)) := + ⟨((hc 0 j).1.pow_left i).mul_left (hc 1 j).1, + ((hc 0 j).2.pow_left i).mul_left (hc 1 j).2⟩ + change ‖binaryShrinkValue r a (p 1) * _ * star (binaryShrinkValue r a (p 1)) - _‖ < ε + rw [p.target] + exact (binary_shift_shrink_error r a hr ha has u _ hx).trans_lt (he i hi) + +/-- The same actual deformation inside a projection corner, including both +support equations at every time. -/ +lemma exists_relative_binary_shrink_path + (q : E) (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (r a : Fin 2 → E) + (hrs : ∀ i, q * r i = r i ∧ r i * q = r i) + (hasp : ∀ i, q * a i = a i ∧ a i * q = a i) + (hr : ∀ i j, star (r i) * r j = if i = j then q else 0) + (ha : ∀ i j, star (a i) * a j = if i = j then q else 0) + (has : (∑ i, a i * star (a i)) = q) + (hc : bergRowsCommute a r) (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ C : unitInterval → E, Continuous C ∧ + C 0 = q - star (finiteCuntzTransfer r a q) * finiteCuntzTransfer r a q + + r 1 * finiteCuntzTransfer r a q ∧ + (∀ t, q * C t = C t ∧ C t * q = C t ∧ star (C t) * C t = q ∧ + C t * star (C t) = q - r 0 * star (r 0)) ∧ + ∀ i ≤ m, ‖C 1 * (a 0 ^ i * a 1) * star (C 1) - + (a 0 ^ i * a 1) * (q - r 0 * star (r 0))‖ < ε := by + let : NeZero q := ⟨hq0⟩ + let H := ProjectionCorner q hq hqq + let R : Fin 2 → H := fun i => projectionCornerElement q hq hqq (r i) (hrs i) + let A : Fin 2 → H := fun i => projectionCornerElement q hq hqq (a i) (hasp i) + have hR := projectionCornerElement_gram q hq hqq r hrs hr + have hA := projectionCornerElement_gram q hq hqq a hasp ha + have hAs := projectionCornerElement_range_sum q hq hqq a hasp has + have hAR : bergRowsCommute A R := by + intro i j + exact ⟨Subtype.ext (hc i j).1.eq, Subtype.ext (hc i j).2.eq⟩ + obtain ⟨C, hC, hC0, hgram, he⟩ := exists_binary_shrink_path R A hR hA hAs hAR m ε hε + let f := projectionCornerInclusion q hq hqq + have hf1 : f 1 = q := rfl + have hfR (i : Fin 2) : f (R i) = r i := rfl + have htransfer : f (finiteCuntzTransfer R A 1) = finiteCuntzTransfer r a q := by + simp only [finiteCuntzTransfer, map_sum, map_mul, map_star] + rfl + have hfc : Continuous (fun x : H => f x) := continuous_subtype_val + refine ⟨fun t => f (C t), hfc.comp hC, ?_, ?_, fun i hi => ?_⟩ + · change f (C 0) = _ + rw [hC0, binaryShrinkValue_one, map_add, map_sub, map_mul, map_star, map_mul, + hf1, htransfer] + rfl + · intro t + exact ⟨(C t).property.1, (C t).property.2, + congrArg f (hgram t).1, congrArg f (hgram t).2⟩ + · have hpow : f (A 0 ^ i * A 1) = a 0 ^ i * a 1 := by + rw [nonunital_map_pow_mul] + rfl + have hh := he i hi + change ‖f (C 1 * (A 0 ^ i * A 1) * star (C 1) - + (A 0 ^ i * A 1) * (1 - R 0 * star (R 0)))‖ < ε at hh + simpa only [map_sub, map_mul, map_star, hpow, hf1, hfR] using hh + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/Simple.lean b/lean/OAI/Analysis/OInfinity/Simple.lean new file mode 100644 index 0000000000000000000000000000000000000000..d6d28efa50453e54d7a176d519198e0d63627405 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/Simple.lean @@ -0,0 +1,192 @@ +import OAI.Analysis.OInfinity.TensorApproximation +import OAI.Analysis.OInfinity.VacuumCorner + +namespace OAI + +/-! # Simplicity of O∞ from finite vacuum corners + +A nonzero Fock coefficient becomes a nonzero vacuum coefficient after a word +sandwich. Compressing a polynomial by an unused generator gives exactly that +vacuum coefficient times the unit. Polynomial approximation therefore puts an +invertible element in every nonzero two-sided ideal. +-/ + +noncomputable section +open scoped CStarAlgebra InnerProductSpace +open Filter Topology + +namespace WeakPureInfiniteness + +local instance : SMulWithZero ℂ OInfinity := + @MulActionWithZero.toSMulWithZero ℂ OInfinity _ _ + (@Module.toMulActionWithZero ℂ OInfinity _ _ inferInstance) +local instance : DistribSMul ℂ OInfinity := + @DistribMulAction.toDistribSMul ℂ OInfinity _ _ + (@Module.toDistribMulAction ℂ OInfinity _ _ inferInstance) + +private lemma norm_complex_smul_one {A : Type*} [CStarAlgebra A] [Nontrivial A] + (c : ℂ) : ‖c • (1 : A)‖ = ‖c‖ := by + rw [norm_smul, norm_one, mul_one] + +private lemma norm_contraction_sandwich {A : Type*} [NonUnitalCStarAlgebra A] + (s a : A) (hs : ‖s‖ ≤ 1) : ‖star s * a * s‖ ≤ ‖a‖ := by + have hleft : ‖star s * a‖ ≤ ‖s‖ * ‖a‖ := by + simpa only [norm_star] using norm_mul_le (star s) a + calc + _ ≤ (‖s‖ * ‖a‖) * ‖s‖ := + (norm_mul_le _ _).trans (mul_le_mul_of_nonneg_right hleft (norm_nonneg _)) + _ ≤ (1 * ‖a‖) * 1 := mul_le_mul + (mul_le_mul_of_nonneg_right hs (norm_nonneg _)) hs + (norm_nonneg _) (by positivity) + _ = ‖a‖ := by rw [one_mul, mul_one] + +def fockVacuumCoefficient (a : OInfinity) : ℂ := + inner ℂ fockVacuum (fockOperatorRepresentation a fockVacuum) + +lemma fockVacuumCoefficient_sub (a b : OInfinity) : + fockVacuumCoefficient (a - b) = fockVacuumCoefficient a - fockVacuumCoefficient b := by + simp only [fockVacuumCoefficient, map_sub, sub_apply, inner_sub_right] + +lemma fockVacuumCoefficient_norm_le (a : OInfinity) : ‖fockVacuumCoefficient a‖ ≤ ‖a‖ := by + calc + _ ≤ ‖fockVacuum‖ * ‖fockOperatorRepresentation a fockVacuum‖ := norm_inner_le_norm _ _ + _ ≤ ‖fockVacuum‖ * (‖fockOperatorRepresentation a‖ * ‖fockVacuum‖) := + mul_le_mul_of_nonneg_left ((fockOperatorRepresentation a).le_opNorm _) (norm_nonneg _) + _ ≤ ‖fockVacuum‖ * (‖a‖ * ‖fockVacuum‖) := by + gcongr + exact NonUnitalStarAlgHom.norm_apply_le fockOperatorRepresentation.toNonUnitalStarAlgHom a + _ = ‖a‖ := by rw [fockVacuum_norm, one_mul, mul_one] + +lemma finiteFockAlgebraWord_fock {N m : ℕ} (i : FiniteFockIndex N m) : + fockOperatorRepresentation (finiteFockAlgebraWord i) fockVacuum = finiteFockVector i := + oInfinityPositiveWord_fock N i.1.val i.2 + +lemma fockVacuumCoefficient_word_sandwich {N m : ℕ} (a : OInfinity) + (i j : FiniteFockIndex N m) : + fockVacuumCoefficient (star (finiteFockAlgebraWord i) * a * finiteFockAlgebraWord j) = + oInfinityFockCompression N m a i j := by + unfold fockVacuumCoefficient + rw [map_mul, map_mul, map_star] + change inner ℂ fockVacuum + ((fockOperatorRepresentation (finiteFockAlgebraWord i)).adjoint + (fockOperatorRepresentation a + (fockOperatorRepresentation (finiteFockAlgebraWord j) fockVacuum))) = _ + rw [ContinuousLinearMap.adjoint_inner_right, finiteFockAlgebraWord_fock, + finiteFockAlgebraWord_fock, oInfinityFockCompression_apply] + +lemma exists_fock_coefficient_ne_zero {a : OInfinity} (ha : a ≠ 0) : + ∃ n : ℕ, ∃ i j : FiniteFockIndex n (n + 1), + oInfinityFockCompression n (n + 1) a i j ≠ 0 := by + by_contra! h + have hc (n : ℕ) : oInfinityFockCompression n (n + 1) a = 0 := by + ext i j + exact h n i j + have happ (n : ℕ) : oInfinityApproximationSequence n a = 0 := by + change oInfinityFockReturn n (n + 1) (oInfinityFockCompression n (n + 1) a) = 0 + rw [hc, map_zero] + have ht := tendsto_iff_norm_sub_tendsto_zero.mp (oInfinityApproximationSequence_tendsto a) + simp only [happ, zero_sub, norm_neg] at ht + have hn : ‖a‖ = 0 := tendsto_nhds_unique tendsto_const_nhds ht + exact ha (norm_eq_zero.mp hn) + +lemma unusedGenerator_polynomial (c : List (ℕ × Bool) →₀ ℂ) {N : ℕ} + (hc : ∀ w ∈ c.support, ∀ p ∈ w, p.1 < N) : + star (oInfinityIsometry N) * cuntzPolynomial oInfinityIsometry c * oInfinityIsometry N = + fockVacuumCoefficient (cuntzPolynomial oInfinityIsometry c) • 1 := by + let i : FiniteFockIndex N 0 := ⟨0, fun j => Fin.elim0 j⟩ + have hw : finiteVacuumCorner N 0 i = oInfinityIsometry N := by + change oInfinityPositiveWord N (fun j : Fin 0 => Fin.elim0 j) * oInfinityIsometry N = _ + rw [oInfinityPositiveWord_zero, one_mul] + have hv : finiteFockVector i = fockVacuum := rfl + have h := finiteVacuumCorner_polynomial c hc i i + rw [hw, oInfinityFockCompression_apply, hv] at h + exact h + +lemma oInfinityIsometry_norm_le_one (N : ℕ) : ‖oInfinityIsometry N‖ ≤ 1 := by + have h := congrArg norm (oInfinityIsometry_relations N N) + simp only [ite_true, CStarRing.norm_star_mul_self] at h + nlinarith [norm_nonneg (oInfinityIsometry N), cstar_norm_one_le_one (A := OInfinity)] + +lemma unusedGenerator_error (a : OInfinity) (c : List (ℕ × Bool) →₀ ℂ) {N : ℕ} + (hc : ∀ w ∈ c.support, ∀ p ∈ w, p.1 < N) : + ‖star (oInfinityIsometry N) * a * oInfinityIsometry N - fockVacuumCoefficient a • 1‖ ≤ + 2 * ‖a - cuntzPolynomial oInfinityIsometry c‖ := by + let p := cuntzPolynomial oInfinityIsometry c + let s := oInfinityIsometry N + have hs : ‖s‖ ≤ 1 := oInfinityIsometry_norm_le_one N + have he : star s * a * s - fockVacuumCoefficient a • 1 = + star s * (a - p) * s + (fockVacuumCoefficient p - fockVacuumCoefficient a) • 1 := by + dsimp [s, p] + rw [mul_sub, sub_mul, unusedGenerator_polynomial c hc, sub_smul] + abel + have hfirst : ‖star s * (a - p) * s‖ ≤ ‖a - p‖ := + norm_contraction_sandwich s (a - p) hs + have hsecond : ‖(fockVacuumCoefficient p - fockVacuumCoefficient a) • (1 : OInfinity)‖ ≤ + ‖a - p‖ := by + calc + _ = ‖fockVacuumCoefficient p - fockVacuumCoefficient a‖ := norm_complex_smul_one _ + _ = ‖fockVacuumCoefficient (p - a)‖ := + congrArg norm (fockVacuumCoefficient_sub p a).symm + _ ≤ ‖p - a‖ := fockVacuumCoefficient_norm_le _ + _ = ‖a - p‖ := norm_sub_rev _ _ + exact (congrArg norm he).trans_le + ((norm_add_le _ _).trans ((add_le_add hfirst hsecond).trans_eq (by ring))) + +lemma twoSidedIdeal_eq_top_of_vacuumCoefficient_ne_zero (I : TwoSidedIdeal OInfinity) + {a : OInfinity} (ha : a ∈ I) (hv : fockVacuumCoefficient a ≠ 0) : I = ⊤ := by + let coeff := fockVacuumCoefficient a + have hcoeff : 0 < ‖coeff‖ := norm_pos_iff.mpr hv + obtain ⟨c, hc⟩ := Metric.denseRange_iff.mp oInfinityPolynomial_denseRange a + (‖coeff‖ / 4) (by positivity) + have hac : ‖a - cuntzPolynomial oInfinityIsometry c‖ < ‖coeff‖ / 4 := by + simpa only [dist_eq_norm, norm_sub_rev] using hc + obtain ⟨N, hN⟩ := exists_polynomial_alphabet_bound c + let z := star (oInfinityIsometry N) * a * oInfinityIsometry N + have hz : z ∈ I := I.mul_mem_right _ _ (I.mul_mem_left _ _ ha) + have he : ‖z - coeff • 1‖ < ‖coeff‖ := by + exact (unusedGenerator_error a c hN).trans_lt (by dsimp [coeff] at *; linarith) + let y := coeff⁻¹ • z + have hy : y ∈ I := by + change coeff⁻¹ • z ∈ I + rw [Algebra.smul_def] + exact I.mul_mem_left _ _ hz + have hsmall : ‖1 - y‖ < 1 := by + have hid : (1 : OInfinity) - y = coeff⁻¹ • (coeff • 1 - z) := by + dsimp [y] + rw [smul_sub, smul_smul, inv_mul_cancel₀ hv, one_smul] + rw [hid, norm_smul, norm_inv, norm_sub_rev] + exact (inv_mul_lt_one₀ hcoeff).mpr he + have hu : IsUnit y := by + simpa only [Units.val_oneSub, sub_sub_cancel] using (Units.oneSub (1 - y) hsmall).isUnit + obtain ⟨u, hu⟩ := hu + have hone := I.mul_mem_left (↑u⁻¹) y hy + rw [← hu, Units.inv_mul] at hone + exact I.eq_top hone + +/-- Every nonzero two-sided ideal of O∞ contains a unit. -/ +theorem oInfinity_twoSidedIdeal_trivial (I : TwoSidedIdeal OInfinity) : I = ⊥ ∨ I = ⊤ := by + by_cases hI : I = ⊥ + · exact Or.inl hI + right + have hex : ∃ a : OInfinity, a ∈ I ∧ a ≠ 0 := by + by_contra! h + apply hI + ext a + change (a ∈ I ↔ a = 0) + exact ⟨h a, fun he => by subst a; exact I.zero_mem⟩ + obtain ⟨a, ha, ha0⟩ := hex + obtain ⟨n, i, j, hij⟩ := exists_fock_coefficient_ne_zero ha0 + let b := star (finiteFockAlgebraWord i) * a * finiteFockAlgebraWord j + have hb : b ∈ I := I.mul_mem_right _ _ (I.mul_mem_left _ _ ha) + apply twoSidedIdeal_eq_top_of_vacuumCoefficient_ne_zero I hb + simpa only [b, fockVacuumCoefficient_word_sandwich] using hij + +theorem oInfinity_topologicallySimple : Pureness.TopologicallySimple OInfinity := by + intro I _ + exact oInfinity_twoSidedIdeal_trivial I + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/TailCancellationWitness.lean b/lean/OAI/Analysis/OInfinity/TailCancellationWitness.lean new file mode 100644 index 0000000000000000000000000000000000000000..aea994952e50e073f5f71c55513124e389cf36e0 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/TailCancellationWitness.lean @@ -0,0 +1,240 @@ +import OAI.Analysis.OInfinity.BufferedRelativeWitness +import OAI.Analysis.OInfinity.CanonicalBufferAbsorption +import OAI.Analysis.PureInfiniteness.TailCancellationRows + +namespace OAI + +/-! # The zero corner containing the entire remaining source copy + +The internal isometry `z` has range inside the absorption corner. Its +complement contains both the full residual source copy and a negative +part of the target copy. All data below are constructed in the first +buffer's commutant before applying the second-buffer comparison. +-/ + +noncomputable section +open Filter Topology +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +def BufferAbsorptionCorner.map {F : Type*} [CStarAlgebra F] + (D : BufferAbsorptionCorner E) (φ : E →⋆ₐ[ℂ] F) : BufferAbsorptionCorner F where + q := φ D.q + w := φ D.w + a := φ D.a + b := φ D.b + projection := D.projection.map φ + w_gram := by simpa only [map_mul, map_star, map_one] using congrArg φ D.w_gram + w_range := by simpa only [map_mul, map_star, map_sub, map_one] using congrArg φ D.w_range + w_orthogonal := by simpa only [map_mul, map_zero] using congrArg φ D.w_orthogonal + a_gram := by simpa only [map_mul, map_star] using congrArg φ D.a_gram + b_gram := by simpa only [map_mul, map_star] using congrArg φ D.b_gram + orthogonal := by simpa only [map_mul, map_star, map_zero] using congrArg φ D.orthogonal + ranges := by simpa only [map_add, map_mul, map_star] using congrArg φ D.ranges + +local instance tailWitnessCentralizerClosed (R : ℕ → E) : + IsClosed (StarSubalgebra.centralizer ℂ (Set.range R) : Set E) := + Set.isClosed_centralizer _ + +/-- The new comparison corner is genuinely a zero corner: its full +binary row comes from the internal isometry and two orthogonal copies +inside the original residual range. -/ +lemma exists_tail_cancellation_reference [Nontrivial E] + (D : BufferAbsorptionCorner E) (s : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (z : E) (hz : star z * z = 1) (hqz : D.q * z = z) : + (1 - z * star z) ≠ 0 ∧ ∃ b : Fin 2 → E, + (∀ i j, star (b i) * b j = if i = j then 1 - z * star z else 0) ∧ + (∑ i, b i * star (b i)) = 1 - z * star z := by + let r : Fin 3 → E := ![z, D.w * s 0, D.w * s 1] + have hzw : star z * D.w = 0 := by + have hsq : star z * D.q = star z := by + simpa only [star_mul, D.projection.isSelfAdjoint.star_eq] using congrArg star hqz + calc + _ = (star z * D.q) * D.w := by rw [hsq] + _ = 0 := by rw [mul_assoc, D.w_orthogonal, mul_zero] + have hwz : star D.w * z = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hzw + have hsg (i j : ℕ) : star (D.w * s i) * (D.w * s j) = if i = j then 1 else 0 := by + rw [star_mul] + calc + _ = star (s i) * (star D.w * D.w) * s j := by noncomm_ring + _ = _ := by rw [D.w_gram, mul_one, hs] + have hzws (j : ℕ) : star z * (D.w * s j) = 0 := by rw [← mul_assoc, hzw, zero_mul] + have hwsz (j : ℕ) : star (D.w * s j) * z = 0 := by + rw [star_mul, mul_assoc, hwz, mul_zero] + have hr (i j : Fin 3) : star (r i) * r j = if i = j then 1 else 0 := by + fin_cases i <;> fin_cases j + · exact hz + · exact hzws 0 + · exact hzws 1 + · exact hwsz 0 + · exact hsg 0 0 + · exact hsg 0 1 + · exact hwsz 1 + · exact hsg 1 0 + · exact hsg 1 1 + obtain ⟨hq0, b, hb, hbs, _⟩ := exists_buffer_shrink_range_pair r hr + exact ⟨hq0, b, hb, hbs⟩ + +/-- The second buffer compares the entire residual source representation +with the complementary target corner, while fixing the retained full +subcorner pointwise. -/ +lemma exists_buffered_tail_cancellation [Nontrivial E] + (U : Ultrafilter ℕ) [Fact ((U : Filter ℕ) ≤ atTop)] + (R : ℕ → E) (hR : ∀ i j, star (R i) * R j = if i = j then 1 else 0) + (D : BufferAbsorptionCorner (StarSubalgebra.centralizer ℂ (Set.range R))) + (s t : ℕ → StarSubalgebra.centralizer ℂ (Set.range R)) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (z : StarSubalgebra.centralizer ℂ (Set.range R)) + (hz : star z * z = 1) (hqz : D.q * z = z) + (hqt : ∀ i, Commute D.q (t i)) + (hzt : ∀ i, Commute z (t i) ∧ Commute (star z) (t i)) + (n : ℕ) (ε : ℝ) (hε : 0 < ε) : + let d := NormUltra.QuotientAlgebra.diagonalHom (A := E) U + ∃ v : unitary (NormUltra.QuotientAlgebra (fun _ : ℕ => E) U), Joined 1 v ∧ + ∀ i : Fin (n + 1), + ‖(v : NormUltra.QuotientAlgebra (fun _ : ℕ => E) U) * + d (t i * D.q + D.w * s i * star D.w) * + star (v : NormUltra.QuotientAlgebra (fun _ : ℕ => E) U) - d (t i)‖ < ε := by + intro d + let C := StarSubalgebra.centralizer ℂ (Set.range R) + let F := NormUltra.QuotientAlgebra (fun _ : ℕ => E) U + let φ : C →⋆ₐ[ℂ] F := d.comp C.subtype + let G := TailCancellation.geometry D z hz hqz + have hpt (i : ℕ) : Commute (TailCancellation.full z) (t i) := + (hzt i).1.mul_left (hzt i).2 + let x : Fin (n + 2) → C := fun i => TailCancellation.sourceRow D z s t i + let y : Fin (n + 2) → C := fun i => TailCancellation.targetRow z t i + have hx (i j : Fin (n + 2)) : star (x i) * x j = + if i = j then TailCancellation.support z else 0 := by + simpa only [x, Fin.ext_iff] using TailCancellation.source_gram D z G s t hs ht hqt hpt i j + have hy (i j : Fin (n + 2)) : star (y i) * y j = + if i = j then TailCancellation.support z else 0 := by + simpa only [y, Fin.ext_iff] using TailCancellation.target_gram z G.Q_proj t ht i j + obtain ⟨hQ0, b, hb, hbs⟩ := exists_tail_cancellation_reference D s hs z hz hqz + obtain ⟨v, hv, hvp, _, hvi⟩ := exists_buffered_relative_witness U R hR + (TailCancellation.support z) G.Q_proj.isSelfAdjoint.star_eq G.Q_proj.isIdempotentElem.eq + hQ0 n x y (fun i => TailCancellation.source_support D z G s t hpt i) + (fun i => TailCancellation.target_support z G.Q_proj t hpt i) hx hy b hb hbs ε hε + let D' := D.map φ + have hz' : star (φ z) * φ z = 1 := by + simpa only [map_mul, map_star, map_one] using congrArg φ hz + have hqz' : D'.q * φ z = φ z := by + simpa only [D', BufferAbsorptionCorner.map, map_mul] using congrArg φ hqz + let G' := TailCancellation.geometry D' (φ z) hz' hqz' + have hvp' : (v : F) * TailCancellation.full (φ z) = TailCancellation.full (φ z) := by + change (v : F) * (1 - φ (TailCancellation.support z)) = + 1 - φ (TailCancellation.support z) at hvp + simpa only [TailCancellation.support, TailCancellation.full, map_sub, map_mul, + map_star, map_one, sub_sub_cancel] using hvp + have hpt' (i : ℕ) : Commute (TailCancellation.full (φ z)) (φ (t i)) := by + have h := congrArg φ (hpt i).eq + change TailCancellation.full (φ z) * φ (t i) = φ (t i) * TailCancellation.full (φ z) + simpa only [TailCancellation.full, map_mul, map_star] using h + refine ⟨v, hv, fun i => ?_⟩ + have hi := hvi i + have he := TailCancellation.recombination_norm D' (φ z) G' + (fun j => φ (s j)) (fun j => φ (t j)) v hvp' hpt' i + have hsource : TailCancellation.sourceRow D' (φ z) (fun j => φ (s j)) + (fun j => φ (t j)) i = φ (x i.castSucc) := by + simp only [TailCancellation.sourceRow, TailCancellation.rest, TailCancellation.full, + D', BufferAbsorptionCorner.map, x, map_add, map_mul, map_sub, map_star, Fin.val_castSucc] + have htarget : TailCancellation.targetRow (φ z) (fun j => φ (t j)) i = φ (y i.castSucc) := by + simp only [TailCancellation.targetRow, TailCancellation.support, TailCancellation.full, + y, map_mul, map_sub, map_one, map_star, Fin.val_castSucc] + rw [hsource, htarget] at he + change ‖(v : F) * φ (t i * D.q + D.w * s i * star D.w) * star (v : F) - φ (t i)‖ < ε + rw [show φ (t i * D.q + D.w * s i * star D.w) = + φ (t i) * D'.q + D'.w * φ (s i) * star D'.w by + simp only [map_add, map_mul, map_star, D', BufferAbsorptionCorner.map]] + rw [he] + exact hi + +/-- Two commuting proper rows in the first buffer's commutant admit +actual connected finite conjugacy in the next norm ultrapower. -/ +lemma exists_buffered_commuting_rows_conjugacy [Nontrivial E] + (U : Ultrafilter ℕ) [Fact ((U : Filter ℕ) ≤ atTop)] + (R : ℕ → E) (hR : ∀ i j, star (R i) * R j = if i = j then 1 else 0) + (s t : ℕ → StarSubalgebra.centralizer ℂ (Set.range R)) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (ht : ∀ i j, star (t i) * t j = if i = j then 1 else 0) + (hst : bergRowsCommute s t) (n : ℕ) (ε : ℝ) (hε : 0 < ε) : + let d := NormUltra.QuotientAlgebra.diagonalHom (A := E) U + ∃ v : unitary (NormUltra.QuotientAlgebra (fun _ : ℕ => E) U), Joined 1 v ∧ + ∀ i : Fin (n + 1), + ‖(v : NormUltra.QuotientAlgebra (fun _ : ℕ => E) U) * d (s i) * + star (v : NormUltra.QuotientAlgebra (fun _ : ℕ => E) U) - d (t i)‖ < ε := by + intro d + let C := StarSubalgebra.centralizer ℂ (Set.range R) + let F := NormUltra.QuotientAlgebra (fun _ : ℕ => E) U + let φ : C →⋆ₐ[ℂ] F := d.comp C.subtype + obtain ⟨D, hanchor, _, hspare, _, _, ⟨z, hz, hqz, hzcomm⟩, hcomm⟩ := + exists_canonical_connected_absorption_corner_with_commuting_isometry s hs (n + 1) 1 + (by norm_num) + have htc (i : ℕ) : ∀ j, Commute (s j) (t i) ∧ Commute (star (s j)) (t i) := by + intro j + exact ⟨(hst j i).1, by simpa only [star_star] using (hst j i).2.star_star⟩ + have htcs (i : ℕ) : ∀ j, Commute (s j) (star (t i)) ∧ + Commute (star (s j)) (star (t i)) := by + intro j + exact ⟨(hst j i).2, (hst j i).1.star_star⟩ + have hqt (i : ℕ) := (hcomm (t i) (htc i)).1 + have hat (i : ℕ) : Commute (star D.a) (t i) := by + simpa only [star_star] using (hcomm (star (t i)) (htcs i)).2.2.1.star_star + have hbt (i : ℕ) : Commute (star D.b) (t i) := by + simpa only [star_star] using (hcomm (star (t i)) (htcs i)).2.2.2.star_star + have hzt (i : ℕ) : Commute z (t i) ∧ Commute (star z) (t i) := by + exact ⟨hzcomm (t i) (htc i), by + simpa only [star_star] using (hzcomm (star (t i)) (htcs i)).star_star⟩ + have heps : 0 < ε / 2 := by positivity + obtain ⟨a, ha, hai⟩ := D.exists_proper_vacuum_absorption s t hs ht (n + 1) + hspare hqt hat hbt (ε / 2) heps + obtain ⟨v, hv, hvi⟩ := exists_buffered_tail_cancellation U R hR D s t hs ht + z hz hqz hqt hzt n (ε / 2) heps + let A : unitary F := Unitary.map (CStarConnectedLift.starMonoidHom φ) a + have hA : Joined (1 : unitary F) A := by + have h := (hanchor.trans ha).map (CStarAbsorption.continuous_unitaryMap φ) + simpa only [map_one] using h + refine ⟨v * A, by simpa only [one_mul] using hv.mul hA, fun i => ?_⟩ + let c := φ (t i * D.q + D.w * s i * star D.w) + have hfirst : ‖(A : F) * φ (s i) * star (A : F) - c‖ < ε / 2 := by + have hn := NonUnitalStarAlgHom.norm_apply_le φ.toNonUnitalStarAlgHom + ((a : C) * s i * star (a : C) - (t i * D.q + D.w * s i * star D.w)) + have he : φ ((a : C) * s i * star (a : C) - + (t i * D.q + D.w * s i * star D.w)) = + (A : F) * φ (s i) * star (A : F) - c := by + change φ ((a : C) * s i * star (a : C) - _) = + φ (a : C) * φ (s i) * star (φ (a : C)) - φ _ + simp only [map_sub, map_mul, map_star] + change ‖φ ((a : C) * s i * star (a : C) - + (t i * D.q + D.w * s i * star D.w))‖ ≤ _ at hn + rw [he] at hn + exact hn.trans_lt (hai i) + have hsecond : ‖(v : F) * c * star (v : F) - φ (t i)‖ < ε / 2 := hvi i + have hnorm : ‖(v : F) * ((A : F) * φ (s i) * star (A : F) - c) * + star (v : F)‖ = ‖(A : F) * φ (s i) * star (A : F) - c‖ := by + rw [mul_assoc, CStarRing.norm_coe_unitary_mul] + exact CStarRing.norm_mul_mem_unitary _ (Unitary.star_mem v.property) + have hsum := norm_add_le + ((v : F) * ((A : F) * φ (s i) * star (A : F) - c) * star (v : F)) + ((v : F) * c * star (v : F) - φ (t i)) + rw [hnorm] at hsum + have hid : ((v * A : unitary F) : F) * φ (s i) * star ((v * A : unitary F) : F) - φ (t i) = + (v : F) * ((A : F) * φ (s i) * star (A : F) - c) * star (v : F) + + ((v : F) * c * star (v : F) - φ (t i)) := by + simp only [Submonoid.coe_mul, star_mul] + noncomm_ring + change ‖((v * A : unitary F) : F) * φ (s i) * star ((v * A : unitary F) : F) - φ (t i)‖ < ε + rw [hid] + exact hsum.trans_lt (by linarith) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/TensorApproximation.lean b/lean/OAI/Analysis/OInfinity/TensorApproximation.lean new file mode 100644 index 0000000000000000000000000000000000000000..c3c36106fcf3c6a3cdb8e33394814fad818fba89 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/TensorApproximation.lean @@ -0,0 +1,142 @@ +import OAI.Analysis.OInfinity.CPAP +import OAI.Analysis.OInfinity.TensorGram +import OAI.Analysis.JiangSu.TensorProducts.FaithfulTensorCrossNorm + +namespace OAI + +/-! # The finite Fock approximations in arbitrary tensor completions + +Pointwise convergence is independent of the C*-norm on the algebraic tensor +product. The uniform compression bound is a separate step in proving +uniqueness of that norm. +-/ + +noncomputable section +open scoped CStarAlgebra TensorProduct +open Filter Topology + +namespace WeakPureInfiniteness + +private lemma linearMap_error_add {V : Type*} [AddCommGroup V] [Module ℂ V] + (T : V →ₗ[ℂ] V) (x y : V) : + T (x + y) - (x + y) = (T x - x) + (T y - y) := by + rw [T.map_add, add_sub_add_comm] + +local instance : PartialOrder OInfinity := CStarAlgebra.spectralOrder _ +local instance : StarOrderedRing OInfinity := CStarAlgebra.spectralOrderedRing _ + +lemma finiteFockCoefficient_norm_le (N m : ℕ) : + ‖∑ i : FiniteFockIndex N m, + star (finiteFockUnweightedCoefficient i) * finiteFockUnweightedCoefficient i‖ ≤ (m : ℝ) + 1 ∧ + ‖∑ i : FiniteFockIndex N m, + star (finiteFockWeightedCoefficient i) * finiteFockWeightedCoefficient i‖ ≤ (m : ℝ) + 1 := by + let x : OInfinity := ∑ i : FiniteFockIndex N m, + star (finiteFockUnweightedCoefficient i) * finiteFockUnweightedCoefficient i + let y : OInfinity := ∑ i : FiniteFockIndex N m, + star (finiteFockWeightedCoefficient i) * finiteFockWeightedCoefficient i + have hx : 0 ≤ x := Finset.sum_nonneg (fun _ _ => star_mul_self_nonneg _) + have hy : 0 ≤ y := Finset.sum_nonneg (fun _ _ => star_mul_self_nonneg _) + have he : x + y = ((m : ℝ) + 1) • (1 : OInfinity) := finiteFockCoefficient_normalization N m + have hn : ‖x + y‖ = (m : ℝ) + 1 := by + rw [he] + change ‖(((((m : ℝ) + 1) : ℝ) : ℂ)) • (1 : OInfinity)‖ = _ + rw [norm_smul, norm_one, mul_one, Complex.norm_real, Real.norm_of_nonneg (by positivity)] + constructor + · exact (CStarAlgebra.norm_le_norm_of_le_of_nonneg (le_add_of_nonneg_right hy) hx).trans_eq hn + · exact (CStarAlgebra.norm_le_norm_of_le_of_nonneg (le_add_of_nonneg_left hx) hy).trans_eq hn + +lemma oInfinityFockReturn_mem_adjoin (N m : ℕ) + (M : CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) ℂ) : + oInfinityFockReturn N m M ∈ StarAlgebra.adjoin ℂ (Set.range oInfinityIsometry) := by + let S := StarAlgebra.adjoin ℂ (Set.range oInfinityIsometry) + have hgen (i : ℕ) : oInfinityIsometry i ∈ S := StarAlgebra.subset_adjoin ℂ _ ⟨i, rfl⟩ + have hword (k : ℕ) (w : Fin k → Fin N) : oInfinityPositiveWord N w ∈ S := by + induction k with + | zero => exact S.one_mem + | succ k ih => exact S.mul_mem (hgen _) (ih (Fin.tail w)) + have hlevel (k : ℕ) : oInfinityLevel N k ∈ S := by + induction k with + | zero => exact S.one_mem + | succ k ih => + change (∑ i : Fin N, oInfinityIsometry i * oInfinityLevel N k * + star (oInfinityIsometry i)) ∈ S + exact S.sum_mem (fun i _ => S.mul_mem (S.mul_mem (hgen _) ih) (S.star_mem' (hgen _))) + have hvac : oInfinityFiniteVacuum N ∈ S := S.sub_mem S.one_mem (hlevel 1) + have hu (i : FiniteFockIndex N m) : finiteFockUnweightedCoefficient i ∈ S := + S.star_mem' (hword _ i.2) + have hw (i : FiniteFockIndex N m) : finiteFockWeightedCoefficient i ∈ S := + S.smul_mem (S.mul_mem hvac (S.star_mem' (hword _ i.2))) _ + have hgram (c : FiniteFockIndex N m → OInfinity) (hc : ∀ i, c i ∈ S) : + cuntzGramMap (finiteFockCuntzFamily N m) (finiteFockCuntzFamily_relations N m) c M ∈ S := by + rw [cuntzGramMap_apply] + exact S.sum_mem (fun i _ => S.sum_mem (fun j _ => + S.smul_mem (S.mul_mem (S.star_mem' (hc i)) (hc j)) _)) + change (((((m : ℝ) + 1)⁻¹ : ℝ) : ℂ) • + (cuntzGramMap (finiteFockCuntzFamily N m) (finiteFockCuntzFamily_relations N m) + finiteFockUnweightedCoefficient M + + cuntzGramMap (finiteFockCuntzFamily N m) (finiteFockCuntzFamily_relations N m) + finiteFockWeightedCoefficient M)) ∈ S + exact S.smul_mem (S.add_mem (hgram _ hu) (hgram _ hw)) _ + +lemma exists_oInfinityApproximation_polynomial (n : ℕ) (a : OInfinity) : + ∃ c : List (ℕ × Bool) →₀ ℂ, + cuntzPolynomial oInfinityIsometry c = oInfinityApproximationSequence n a := by + apply exists_cuntzPolynomial_of_mem_adjoin + exact oInfinityFockReturn_mem_adjoin n (n + 1) (oInfinityFockCompression n (n + 1) a) + +theorem fockOperatorRepresentation_injective : Function.Injective fockOperatorRepresentation := by + apply (injective_iff_map_eq_zero _).mpr + intro a ha + have hcompression (N m : ℕ) : oInfinityFockCompression N m a = 0 := by + ext i j + rw [oInfinityFockCompression_apply, ha] + simp + have happ (n : ℕ) : oInfinityApproximationSequence n a = 0 := by + change oInfinityFockReturn n (n + 1) (oInfinityFockCompression n (n + 1) a) = 0 + rw [hcompression, map_zero] + have ht := tendsto_iff_norm_sub_tendsto_zero.mp (oInfinityApproximationSequence_tendsto a) + simp only [happ, zero_sub, norm_neg] at ht + apply norm_eq_zero.mp + exact tendsto_nhds_unique tendsto_const_nhds ht + +variable {B : Type*} [CStarAlgebra B] + +def oInfinityTensorApproximation (n : ℕ) : + OInfinity ⊗[ℂ] B →ₗ[ℂ] OInfinity ⊗[ℂ] B := + TensorProduct.map (oInfinityApproximationSequence n).toLinearMap LinearMap.id + +@[simp] lemma oInfinityTensorApproximation_tmul (n : ℕ) (a : OInfinity) (b : B) : + oInfinityTensorApproximation n (a ⊗ₜ[ℂ] b) = + oInfinityApproximationSequence n a ⊗ₜ[ℂ] b := + TensorProduct.map_tmul _ _ _ _ + +lemma oInfinityTensorApproximation_tmul_error + (p : Pureness.CStarAlgebraNorm (OInfinity ⊗[ℂ] B)) (n : ℕ) (a : OInfinity) (b : B) : + p.toAlgebraNorm (oInfinityTensorApproximation n (a ⊗ₜ[ℂ] b) - a ⊗ₜ[ℂ] b) = + ‖oInfinityApproximationSequence n a - a‖ * ‖b‖ := by + rw [oInfinityTensorApproximation_tmul, ← TensorProduct.sub_tmul, + NuclearUnitization.cstar_norm_tmul] + +theorem oInfinityTensorApproximation_error_tendsto + (p : Pureness.CStarAlgebraNorm (OInfinity ⊗[ℂ] B)) (x : OInfinity ⊗[ℂ] B) : + Tendsto (fun n => p.toAlgebraNorm (oInfinityTensorApproximation n x - x)) atTop + (𝓝 0) := by + induction x using TensorProduct.inductionOn with + | tmul a b => + simpa only [oInfinityTensorApproximation_tmul_error, zero_mul] using + (tendsto_iff_norm_sub_tendsto_zero.mp (oInfinityApproximationSequence_tendsto a)).mul_const ‖b‖ + | add x y hx hy => + refine squeeze_zero + (g := fun n => p.toAlgebraNorm (oInfinityTensorApproximation n x - x) + + p.toAlgebraNorm (oInfinityTensorApproximation n y - y)) + (fun n => apply_nonneg p.toAlgebraNorm _) ?_ ?_ + · intro n + have he := linearMap_error_add (oInfinityTensorApproximation n) x y + exact (congrArg p.toAlgebraNorm he).trans_le (map_add_le_add p.toAlgebraNorm _ _) + · simpa only [zero_add] using hx.add hy + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/TensorGram.lean b/lean/OAI/Analysis/OInfinity/TensorGram.lean new file mode 100644 index 0000000000000000000000000000000000000000..8e31e3c39bff8e54c5efe269b391c332fd82570a --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/TensorGram.lean @@ -0,0 +1,223 @@ +import OAI.Analysis.PureInfiniteness.CuntzGramMap + +namespace OAI + +/-! # Matrix-valued Gram return maps for the O∞ tensor approximation + +The corner formulation also works in a nonunital tensor completion: the common +initial projection need only act identically on the matrix coefficients. +-/ + +noncomputable section +open scoped CStarAlgebra ComplexOrder + +namespace WeakPureInfiniteness + +variable {B E I : Type*} [NonUnitalCStarAlgebra B] [NonUnitalCStarAlgebra E] + [Fintype I] [DecidableEq I] + +local instance oInfinityTensorGramLocal1 : PartialOrder B := CStarAlgebra.spectralOrder _ +local instance oInfinityTensorGramLocal2 : StarOrderedRing B := CStarAlgebra.spectralOrderedRing _ + +def supportedCuntzMatrixLinear (r : I → E) (σ : B →⋆ₙₐ[ℂ] E) : + CStarMatrix I I B →ₗ[ℂ] E where + toFun M := ∑ i, ∑ j, r i * σ (M i j) * star (r j) + map_add' M N := by + simp only [CStarMatrix.add_apply, map_add, mul_add, add_mul, Finset.sum_add_distrib] + map_smul' c M := by + simp only [CStarMatrix.smul_apply, map_smul, mul_smul_comm, smul_mul_assoc, + Finset.smul_sum, RingHom.id_apply] + +omit [Fintype I] in +lemma supportedCuntzMatrix_term_mul (r : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (M N : CStarMatrix I I B) (i j k l : I) : + (r i * σ (M i j) * star (r j)) * (r k * σ (N k l) * star (r l)) = + if j = k then r i * σ (M i j * N k l) * star (r l) else 0 := by + calc + _ = r i * σ (M i j) * (star (r j) * r k) * σ (N k l) * star (r l) := by + noncomm_ring + _ = _ := by + rw [hr] + split_ifs with h + · rw [mul_assoc (r i * σ (M i j)) e, he, map_mul] + simp only [mul_assoc] + · simp + +def supportedCuntzMatrixHom (r : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) : CStarMatrix I I B →⋆ₙₐ[ℂ] E where + toFun := supportedCuntzMatrixLinear r σ + map_zero' := by simp [supportedCuntzMatrixLinear] + map_add' := map_add _ + map_smul' := map_smul _ + map_mul' M N := by + change (∑ i, ∑ j, r i * σ ((M * N) i j) * star (r j)) = + (∑ i, ∑ j, r i * σ (M i j) * star (r j)) * + (∑ i, ∑ j, r i * σ (N i j) * star (r j)) + simp only [CStarMatrix.mul_apply, map_sum, Finset.mul_sum, Finset.sum_mul] + simp only [supportedCuntzMatrix_term_mul r e σ hr he, Finset.sum_ite_eq', + Finset.mem_univ, ite_true] + calc + _ = ∑ i, ∑ k, ∑ j, r i * σ (M i k * N k j) * star (r j) := by + apply Finset.sum_congr rfl + intro i _ + exact Finset.sum_comm + _ = ∑ k, ∑ i, ∑ j, r i * σ (M i k * N k j) * star (r j) := Finset.sum_comm + _ = _ := by + apply Finset.sum_congr rfl + intro k _ + exact Finset.sum_comm + map_star' M := by + change (∑ i, ∑ j, r i * σ ((star M) i j) * star (r j)) = + star (∑ i, ∑ j, r i * σ (M i j) * star (r j)) + simp only [CStarMatrix.star_apply, map_star, star_sum, star_mul, star_star, mul_assoc] + exact Finset.sum_comm + +lemma supportedCuntzMatrixHom_apply (r : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (M : CStarMatrix I I B) : + supportedCuntzMatrixHom r e σ hr he M = + ∑ i, ∑ j, r i * σ (M i j) * star (r j) := rfl + +lemma supportedCuntzMatrixHom_entry (r : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (heStar : star e = e) + (M : CStarMatrix I I B) (i j : I) : + star (r i) * supportedCuntzMatrixHom r e σ hr he M * r j = σ (M i j) := by + have he' (b : B) : σ b * e = σ b := by + simpa only [star_mul, map_star, star_star, heStar] using congrArg star (he (star b)) + have hterm (k l : I) : + star (r i) * (r k * σ (M k l) * star (r l)) * r j = + if i = k then (if l = j then σ (M k l) else 0) else 0 := by + calc + _ = (star (r i) * r k) * σ (M k l) * (star (r l) * r j) := by noncomm_ring + _ = _ := by + rw [hr, hr] + split_ifs <;> simp [he, he'] + rw [supportedCuntzMatrixHom_apply] + simp only [Finset.mul_sum, Finset.sum_mul, hterm, Finset.sum_ite_irrel, + Finset.sum_const_zero, Finset.sum_ite_eq', Finset.sum_ite_eq, Finset.mem_univ, ite_true] + +lemma supportedCuntzMatrixHom_injective (r : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (heStar : star e = e) + (hσ : Function.Injective σ) : + Function.Injective (supportedCuntzMatrixHom r e σ hr he) := by + apply (injective_iff_map_eq_zero _).mpr + intro M hM + ext i j + apply hσ + have h := supportedCuntzMatrixHom_entry r e σ hr he heStar M i j + rw [hM, mul_zero, zero_mul] at h + simpa only [CStarMatrix.zero_apply, map_zero] using h.symm + +lemma supportedCuntz_rangeProjection (r : I → E) (e : E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (hre : ∀ i, r i * e = r i) : IsStarProjection (∑ i, r i * star (r i)) := by + apply isStarProjection_iff'.mpr + constructor + · have hterm (i j : I) : (r i * star (r i)) * (r j * star (r j)) = + if i = j then r i * star (r i) else 0 := by + calc + _ = r i * (star (r i) * r j) * star (r j) := by noncomm_ring + _ = _ := by + rw [hr] + split_ifs with hij + · subst j; rw [hre] + · simp + simp only [Finset.sum_mul, Finset.mul_sum, hterm, Finset.sum_ite_eq', + Finset.mem_univ, ite_true] + · simp only [star_sum, star_mul, star_star] + +lemma supportedCuntzMatrixHom_of_entries (r : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (x : E) (M : CStarMatrix I I B) + (hentry : ∀ i j, star (r i) * x * r j = σ (M i j)) : + supportedCuntzMatrixHom r e σ hr he M = + (∑ i, r i * star (r i)) * x * (∑ i, r i * star (r i)) := by + rw [supportedCuntzMatrixHom_apply] + simp only [Finset.sum_mul, Finset.mul_sum] + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [← hentry] + simp only [mul_assoc] + +lemma supportedCuntz_compression_norm_le (r : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (heStar : star e = e) + (hre : ∀ i, r i * e = r i) (hσ : Function.Injective σ) + (x : E) (M : CStarMatrix I I B) + (hentry : ∀ i j, star (r i) * x * r j = σ (M i j)) : ‖M‖ ≤ ‖x‖ := by + let P := ∑ i, r i * star (r i) + have hP : ‖P‖ ≤ 1 := IsStarProjection.norm_le _ (supportedCuntz_rangeProjection r e hr hre) + have hnorm := NonUnitalStarAlgHom.norm_map (supportedCuntzMatrixHom r e σ hr he) + (supportedCuntzMatrixHom_injective r e σ hr he heStar hσ) M + rw [← hnorm, supportedCuntzMatrixHom_of_entries r e σ hr he x M hentry] + calc + ‖P * x * P‖ ≤ ‖P‖ * ‖x‖ * ‖P‖ := norm_mul₃_le + _ ≤ 1 * ‖x‖ * 1 := mul_le_mul (mul_le_mul_of_nonneg_right hP (norm_nonneg _)) hP + (norm_nonneg _) (by positivity) + _ = ‖x‖ := by ring + +lemma supportedCuntz_gram_apply (r v : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (heStar : star e = e) + (hv : ∀ i, e * v i = v i) (M : CStarMatrix I I B) : + star (∑ i, r i * v i) * supportedCuntzMatrixHom r e σ hr he M * + (∑ i, r i * v i) = ∑ i, ∑ j, star (v i) * σ (M i j) * v j := by + have hv' (i : I) : star (v i) * e = star (v i) := by + simpa only [star_mul, heStar] using congrArg star (hv i) + have hl (i : I) : star (∑ j, r j * v j) * r i = star (v i) := by + simp only [star_sum, Finset.sum_mul, star_mul, mul_assoc, hr] + simp only [mul_ite, mul_zero, Finset.sum_ite_eq', Finset.mem_univ, ite_true, hv'] + have hh (j : I) : star (r j) * (∑ i, r i * v i) = v j := by + simp only [Finset.mul_sum, ← mul_assoc, hr] + simp [hv] + rw [supportedCuntzMatrixHom_apply] + conv_lhs => arg 1; rw [Finset.mul_sum] + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro i _ + conv_lhs => arg 1; rw [Finset.mul_sum] + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro j _ + calc + _ = (star (∑ k, r k * v k) * r i) * σ (M i j) * + (star (r j) * (∑ k, r k * v k)) := by noncomm_ring + _ = _ := by rw [hl, hh] + +lemma supportedCuntz_gram_norm_le (r v : I → E) (e : E) (σ : B →⋆ₙₐ[ℂ] E) + (hr : ∀ i j, star (r i) * r j = if i = j then e else 0) + (he : ∀ b, e * σ b = σ b) (hv : ∀ i, e * v i = v i) + (M : CStarMatrix I I B) : + ‖star (∑ i, r i * v i) * supportedCuntzMatrixHom r e σ hr he M * + (∑ i, r i * v i)‖ ≤ ‖∑ i, star (v i) * v i‖ * ‖M‖ := by + let t := ∑ i, r i * v i + have ht : star t * t = ∑ i, star (v i) * v i := by + simp only [t, star_sum, Finset.sum_mul, Finset.mul_sum, star_mul] + have hh (i j : I) : (star (v i) * star (r i)) * (r j * v j) = + if i = j then star (v i) * v i else 0 := by + rw [mul_assoc, ← mul_assoc (star (r i)), hr] + split_ifs with hij + · subst j + rw [hv] + · simp + simp only [hh, Finset.sum_ite_eq', Finset.mem_univ, ite_true] + calc + _ ≤ (‖t‖ * ‖t‖) * ‖supportedCuntzMatrixHom r e σ hr he M‖ := by + exact norm_mul₃_le.trans_eq (by rw [norm_star]; ring) + _ = ‖∑ i, star (v i) * v i‖ * ‖supportedCuntzMatrixHom r e σ hr he M‖ := by + rw [← CStarRing.norm_star_mul_self, ht] + _ ≤ _ := mul_le_mul_of_nonneg_left + (NonUnitalStarAlgHom.norm_apply_le _ M) (norm_nonneg _) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/TensorNorm.lean b/lean/OAI/Analysis/OInfinity/TensorNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..af283ad9ebe58de0fd80f6878f21d6208d6dbf44 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/TensorNorm.lean @@ -0,0 +1,487 @@ +import OAI.Analysis.OInfinity.TensorApproximation +import OAI.Analysis.OInfinity.VacuumCorner + +namespace OAI + +/-! # Tensor-norm nuclearity of O∞ + +Finite unused-generator corners control the Fock matrix in every C*-completion +of the algebraic tensor product. The two Gram summands of the return map give +a uniform factor-two norm comparison, and the C*-identity removes that factor. +This proves the tensor-norm nuclearity input used by the absorption criterion. +-/ + +noncomputable section +open scoped CStarAlgebra TensorProduct +open Filter Topology + +namespace WeakPureInfiniteness + +private lemma algebraNorm_le_sub_add {R : Type*} [Ring R] [Algebra ℂ R] + (p : AlgebraNorm ℂ R) (x y : R) : p x ≤ p (x - y) + p y := by + simpa only [sub_add_cancel] using map_add_le_add p (x - y) y + +private lemma algebraNorm_le_rev_sub_add {R : Type*} [Ring R] [Algebra ℂ R] + (p : AlgebraNorm ℂ R) (x y : R) : p x ≤ p (y - x) + p y := by + simpa only [map_sub_rev p] using algebraNorm_le_sub_add p x y + +private lemma algebraNorm_le_of_approximation {R : Type*} [Ring R] [Algebra ℂ R] + (p : AlgebraNorm ℂ R) (x : R) (y : ℕ → R) (C : ℝ) + (ht : Tendsto (fun n => p (y n - x)) atTop (𝓝 0)) + (hb : ∀ᶠ n : ℕ in atTop, p (y n) ≤ C) : p x ≤ C := by + have hupper : ∀ᶠ n : ℕ in atTop, p x ≤ p (y n - x) + C := by + filter_upwards [hb] with n hn + exact (algebraNorm_le_rev_sub_add p x (y n)).trans (add_le_add_right hn _) + simpa only [zero_add] using ge_of_tendsto (ht.add_const C) hupper + +private lemma map_smul_mul {A E : Type*} [NonUnitalCStarAlgebra A] + [NonUnitalCStarAlgebra E] (R : A →⋆ₙₐ[ℂ] E) (c : ℂ) (a : A) (z : E) : + R (c • a) * z = c • (R a * z) := by + calc + R (c • a) * z = (c • R a) * z := congrArg (fun x : E => x * z) (map_smul R c a) + _ = _ := smul_mul_assoc c (R a) z + +private lemma map_scaled_sum_mul {A E : Type*} [NonUnitalCStarAlgebra A] + [NonUnitalCStarAlgebra E] (R : A →⋆ₙₐ[ℂ] E) (c : ℂ) (a b : A) (z : E) : + R (c • (a + b)) * z = c • (R a * z + R b * z) := by + rw [map_smul_mul] + exact congrArg (fun x : E => c • x) + ((congrArg (fun x : E => x * z) (map_add R a b)).trans (add_mul (R a) (R b) z)) + +private lemma map_star_sandwich {A E : Type*} [NonUnitalCStarAlgebra A] + [NonUnitalCStarAlgebra E] (R : A →⋆ₙₐ[ℂ] E) (x a y : A) : + star (R x) * R a * R y = R (star x * a * y) := by + rw [map_mul, map_mul, map_star] + +private lemma map_scalar_unit_mul {A B E : Type*} [CStarAlgebra A] [CStarAlgebra B] + [NonUnitalCStarAlgebra E] (R : A →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hsupport : ∀ b, R 1 * S b = S b) (c : ℂ) (b : B) : + R (c • (1 : A)) * S b = S (c • b) := by + calc + _ = c • (R 1 * S b) := map_smul_mul R c 1 (S b) + _ = c • S b := congrArg (fun x : E => c • x) (hsupport b) + _ = S (c • b) := (map_smul S c b).symm + +variable {B E : Type*} [CStarAlgebra B] [NonUnitalCStarAlgebra E] + +local instance oInfinityTensorNormLocal1 : PartialOrder B := CStarAlgebra.spectralOrder _ +local instance oInfinityTensorNormLocal2 : StarOrderedRing B := CStarAlgebra.spectralOrderedRing _ +local instance oInfinityTensorNormLocal3 : PartialOrder OInfinity := CStarAlgebra.spectralOrder _ +local instance oInfinityTensorNormLocal4 : StarOrderedRing OInfinity := CStarAlgebra.spectralOrderedRing _ + +def fockTensorCoefficient (N m : ℕ) (a : OInfinity) : + B →ₗ[ℂ] CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B where + toFun b := CStarMatrix.ofMatrix (fun i j => oInfinityFockCompression N m a i j • b) + map_add' b c := by + ext i j + change oInfinityFockCompression N m a i j • (b + c) = + oInfinityFockCompression N m a i j • b + oInfinityFockCompression N m a i j • c + exact smul_add _ _ _ + map_smul' c b := by + ext i j + exact smul_comm _ _ _ + +def fockTensorBilinear (N m : ℕ) : + OInfinity →ₗ[ℂ] B →ₗ[ℂ] CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B where + toFun := fockTensorCoefficient N m + map_add' a b := by + ext c i j + change oInfinityFockCompression N m (a + b) i j • c = _ + rw [map_add, CStarMatrix.add_apply, add_smul] + rfl + map_smul' c a := by + ext b i j + change oInfinityFockCompression N m (c • a) i j • b = _ + rw [map_smul, CStarMatrix.smul_apply] + exact mul_smul _ _ _ + +def fockTensorMatrix (N m : ℕ) : + OInfinity ⊗[ℂ] B →ₗ[ℂ] CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B := + TensorProduct.lift (fockTensorBilinear N m) + +@[simp] lemma fockTensorMatrix_tmul (N m : ℕ) (a : OInfinity) (b : B) + (i j : FiniteFockIndex N m) : + fockTensorMatrix N m (a ⊗ₜ[ℂ] b) i j = oInfinityFockCompression N m a i j • b := rfl + +def tensorCommutingBilinear {A : Type*} [NonUnitalCStarAlgebra A] + (R : A →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) : A →ₗ[ℂ] B →ₗ[ℂ] E where + toFun a := + { toFun b := R a * S b + map_add' b c := by rw [map_add, mul_add] + map_smul' c b := by rw [map_smul, mul_smul_comm]; rfl } + map_add' a b := by + ext c + change R (a + b) * S c = R a * S c + R b * S c + exact (congrArg (fun x : E => x * S c) (map_add R a b)).trans (add_mul _ _ _) + map_smul' c a := by + ext b + change R (c • a) * S b = c • (R a * S b) + exact map_smul_mul R c a (S b) + +def tensorCommutingEval {A : Type*} [NonUnitalCStarAlgebra A] + (R : A →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) : A ⊗[ℂ] B →ₗ[ℂ] E := TensorProduct.lift (tensorCommutingBilinear R S) + +@[simp] lemma tensorCommutingEval_tmul {A : Type*} [NonUnitalCStarAlgebra A] + (R : A →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) (a : A) (b : B) : tensorCommutingEval R S (a ⊗ₜ[ℂ] b) = R a * S b := rfl + +lemma commuting_vacuum_compression (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hcomm : ∀ a b, Commute (R a) (S b)) (hsupport : ∀ b, R 1 * S b = S b) + {N m : ℕ} (c : List (ℕ × Bool) →₀ ℂ) + (hc : ∀ w ∈ c.support, ∀ p ∈ w, p.1 < N) (b : B) + (i j : FiniteFockIndex N m) : + star (R (finiteVacuumCorner N m i)) * + tensorCommutingEval R S (cuntzPolynomial oInfinityIsometry c ⊗ₜ[ℂ] b) * + R (finiteVacuumCorner N m j) = + S (fockTensorMatrix N m (cuntzPolynomial oInfinityIsometry c ⊗ₜ[ℂ] b) i j) := by + rw [tensorCommutingEval_tmul, fockTensorMatrix_tmul] + calc + _ = (star (R (finiteVacuumCorner N m i)) * R (cuntzPolynomial oInfinityIsometry c)) * + (S b * R (finiteVacuumCorner N m j)) := by noncomm_ring + _ = (star (R (finiteVacuumCorner N m i)) * R (cuntzPolynomial oInfinityIsometry c) * + R (finiteVacuumCorner N m j)) * S b := by + rw [(hcomm _ b).symm.eq] + simp only [mul_assoc] + _ = R (star (finiteVacuumCorner N m i) * cuntzPolynomial oInfinityIsometry c * + finiteVacuumCorner N m j) * S b := + congrArg (fun z : E => z * S b) (map_star_sandwich R _ _ _) + _ = R (oInfinityFockCompression N m (cuntzPolynomial oInfinityIsometry c) i j • 1) * S b := + congrArg (fun z : OInfinity => R z * S b) (finiteVacuumCorner_polynomial c hc i j) + _ = _ := map_scalar_unit_mul R S hsupport _ b + +def polynomialTensorSum (l : List ((List (ℕ × Bool) →₀ ℂ) × B)) : OInfinity ⊗[ℂ] B := + (l.map fun t => cuntzPolynomial oInfinityIsometry t.1 ⊗ₜ[ℂ] t.2).sum + +lemma exists_tensorApproximation_polynomialSum (n : ℕ) (x : OInfinity ⊗[ℂ] B) : + ∃ l : List ((List (ℕ × Bool) →₀ ℂ) × B), + oInfinityTensorApproximation n x = polynomialTensorSum l := by + induction x using TensorProduct.inductionOn with + | tmul a b => + obtain ⟨c, hc⟩ := exists_oInfinityApproximation_polynomial n a + refine ⟨[(c, b)], ?_⟩ + simp only [oInfinityTensorApproximation_tmul, polynomialTensorSum, List.map_cons, + List.map_nil, List.sum_cons, List.sum_nil, add_zero, hc] + | add x y hx hy => + obtain ⟨l, hl⟩ := hx + obtain ⟨k, hk⟩ := hy + refine ⟨l ++ k, ?_⟩ + simp only [map_add, hl, hk, polynomialTensorSum, List.map_append, List.sum_append] + +omit [CStarAlgebra B] in +lemma exists_polynomialTensor_alphabet_bound (l : List ((List (ℕ × Bool) →₀ ℂ) × B)) : + ∃ N : ℕ, ∀ t ∈ l, ∀ w ∈ t.1.support, ∀ p ∈ w, p.1 < N := by + induction l with + | nil => exact ⟨0, by simp⟩ + | cons t l ih => + obtain ⟨N, hN⟩ := exists_polynomial_alphabet_bound t.1 + obtain ⟨M, hM⟩ := ih + refine ⟨max N M, ?_⟩ + intro u hu w hw p hp + rcases List.mem_cons.mp hu with rfl | hu + · exact (hN w hw p hp).trans_le (le_max_left _ _) + · exact (hM u hu w hw p hp).trans_le (le_max_right _ _) + +lemma commuting_vacuum_compression_list (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hcomm : ∀ a b, Commute (R a) (S b)) (hsupport : ∀ b, R 1 * S b = S b) + {N m : ℕ} (l : List ((List (ℕ × Bool) →₀ ℂ) × B)) + (hl : ∀ t ∈ l, ∀ w ∈ t.1.support, ∀ p ∈ w, p.1 < N) + (i j : FiniteFockIndex N m) : + star (R (finiteVacuumCorner N m i)) * tensorCommutingEval R S (polynomialTensorSum l) * + R (finiteVacuumCorner N m j) = S (fockTensorMatrix N m (polynomialTensorSum l) i j) := by + induction l with + | nil => simp [polynomialTensorSum] + | cons t l ih => + have ht := commuting_vacuum_compression R S hcomm hsupport t.1 + (hl t (List.mem_cons_self ..)) t.2 i j + have htail := ih (fun u hu => hl u (List.mem_cons_of_mem _ hu)) + simpa only [polynomialTensorSum, List.map_cons, List.sum_cons, map_add, mul_add, + add_mul, CStarMatrix.add_apply] using congrArg₂ (· + ·) ht htail + +lemma fockTensorMatrix_polynomial_norm_le (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hcomm : ∀ a b, Commute (R a) (S b)) (hsupport : ∀ b, R 1 * S b = S b) + (hS : Function.Injective S) {N m : ℕ} (l : List ((List (ℕ × Bool) →₀ ℂ) × B)) + (hl : ∀ t ∈ l, ∀ w ∈ t.1.support, ∀ p ∈ w, p.1 < N) : + ‖fockTensorMatrix N m (polynomialTensorSum l)‖ ≤ + ‖tensorCommutingEval R S (polynomialTensorSum l)‖ := by + let r (i : FiniteFockIndex N m) := R (finiteVacuumCorner N m i) + have hr (i j : FiniteFockIndex N m) : star (r i) * r j = if i = j then R 1 else 0 := by + dsimp [r] + rw [← map_star, ← map_mul, finiteVacuumCorner_relations] + split_ifs <;> simp only [map_zero] + have heStar : star (R 1) = R 1 := by rw [← map_star, star_one] + have hre (i : FiniteFockIndex N m) : r i * R 1 = r i := by + dsimp [r] + rw [← map_mul, mul_one] + exact supportedCuntz_compression_norm_le r (R 1) S hr hsupport heStar hre hS _ _ + (commuting_vacuum_compression_list R S hcomm hsupport l hl) + +lemma mappedFockCuntz_relations (R : OInfinity →⋆ₙₐ[ℂ] E) (N m : ℕ) + (i j : FiniteFockIndex N m) : + star (R (finiteFockCuntzFamily N m i)) * R (finiteFockCuntzFamily N m j) = + if i = j then R 1 else 0 := by + rw [← map_star, ← map_mul, finiteFockCuntzFamily_relations] + split_ifs <;> simp only [map_zero] + +def representedFockGram (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hsupport : ∀ b, R 1 * S b = S b) (N m : ℕ) + (c : FiniteFockIndex N m → OInfinity) : + CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B →L[ℂ] E := + (ContinuousLinearMap.mulLeftRight ℂ E + (star (∑ i, R (finiteFockCuntzFamily N m i) * R (c i))) + (∑ i, R (finiteFockCuntzFamily N m i) * R (c i))).comp + (starHomContinuousLinear (supportedCuntzMatrixHom + (fun i => R (finiteFockCuntzFamily N m i)) (R 1) S + (mappedFockCuntz_relations R N m) hsupport)) + +lemma representedFockGram_apply (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hsupport : ∀ b, R 1 * S b = S b) (N m : ℕ) + (c : FiniteFockIndex N m → OInfinity) + (M : CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B) : + representedFockGram R S hsupport N m c M = + ∑ i, ∑ j, star (R (c i)) * S (M i j) * R (c j) := by + have heStar : star (R 1) = R 1 := by rw [← map_star, star_one] + have hv (i : FiniteFockIndex N m) : R 1 * R (c i) = R (c i) := by + rw [← map_mul, one_mul] + exact supportedCuntz_gram_apply _ _ _ _ (mappedFockCuntz_relations R N m) + hsupport heStar hv M + +lemma representedFockGram_norm_le (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hsupport : ∀ b, R 1 * S b = S b) (N m : ℕ) + (c : FiniteFockIndex N m → OInfinity) + (M : CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B) : + ‖representedFockGram R S hsupport N m c M‖ ≤ + ‖∑ i, star (c i) * c i‖ * ‖M‖ := by + have hv (i : FiniteFockIndex N m) : R 1 * R (c i) = R (c i) := by + rw [← map_mul, one_mul] + have h := supportedCuntz_gram_norm_le (fun i => R (finiteFockCuntzFamily N m i)) + (fun i => R (c i)) (R 1) S (mappedFockCuntz_relations R N m) hsupport hv M + have he : (∑ i, star (R (c i)) * R (c i)) = R (∑ i, star (c i) * c i) := by + simp only [map_sum, map_mul, map_star] + have hR : ‖∑ i, star (R (c i)) * R (c i)‖ ≤ ‖∑ i, star (c i) * c i‖ := by + rw [he] + exact NonUnitalStarAlgHom.norm_apply_le R _ + exact h.trans (mul_le_mul_of_nonneg_right hR (norm_nonneg _)) + +lemma representedFockGram_tmul (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hcomm : ∀ a b, Commute (R a) (S b)) (hsupport : ∀ b, R 1 * S b = S b) + (N m : ℕ) (c : FiniteFockIndex N m → OInfinity) (a : OInfinity) (b : B) : + representedFockGram R S hsupport N m c (fockTensorMatrix N m (a ⊗ₜ[ℂ] b)) = + R (cuntzGramMap (finiteFockCuntzFamily N m) (finiteFockCuntzFamily_relations N m) + c (oInfinityFockCompression N m a)) * S b := by + rw [representedFockGram_apply, cuntzGramMap_apply] + simp only [fockTensorMatrix_tmul, map_sum, map_smul, Finset.sum_mul, smul_mul_assoc] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [mul_smul_comm, smul_mul_assoc, map_mul, map_star] + congr 1 + calc + _ = star (R (c i)) * (S b * R (c j)) := mul_assoc _ _ _ + _ = _ := by rw [(hcomm (c j) b).symm.eq]; simp only [mul_assoc] + +def representedFockReturn (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hsupport : ∀ b, R 1 * S b = S b) (N m : ℕ) : + CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B →L[ℂ] E := + (((((m : ℝ) + 1)⁻¹ : ℝ) : ℂ)) • + (representedFockGram R S hsupport N m finiteFockUnweightedCoefficient + + representedFockGram R S hsupport N m finiteFockWeightedCoefficient) + +lemma representedFockReturn_norm_le (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hsupport : ∀ b, R 1 * S b = S b) (N m : ℕ) + (M : CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) B) : + ‖representedFockReturn R S hsupport N m M‖ ≤ 2 * ‖M‖ := by + have hK : 0 < (m : ℝ) + 1 := by positivity + have hu := (representedFockGram_norm_le R S hsupport N m finiteFockUnweightedCoefficient M).trans + (mul_le_mul_of_nonneg_right (finiteFockCoefficient_norm_le N m).1 (norm_nonneg M)) + have hw := (representedFockGram_norm_le R S hsupport N m finiteFockWeightedCoefficient M).trans + (mul_le_mul_of_nonneg_right (finiteFockCoefficient_norm_le N m).2 (norm_nonneg M)) + change ‖(((((m : ℝ) + 1)⁻¹ : ℝ) : ℂ)) • + (representedFockGram R S hsupport N m finiteFockUnweightedCoefficient M + + representedFockGram R S hsupport N m finiteFockWeightedCoefficient M)‖ ≤ _ + rw [norm_smul, Complex.norm_real, Real.norm_of_nonneg (inv_nonneg.mpr hK.le)] + calc + _ ≤ ((m : ℝ) + 1)⁻¹ * (((m : ℝ) + 1) * ‖M‖ + ((m : ℝ) + 1) * ‖M‖) := + mul_le_mul_of_nonneg_left ((norm_add_le _ _).trans (add_le_add hu hw)) (inv_nonneg.mpr hK.le) + _ = _ := by field_simp [hK.ne']; ring + +lemma representedFockReturn_tmul (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hcomm : ∀ a b, Commute (R a) (S b)) (hsupport : ∀ b, R 1 * S b = S b) + (N m : ℕ) (a : OInfinity) (b : B) : + representedFockReturn R S hsupport N m (fockTensorMatrix N m (a ⊗ₜ[ℂ] b)) = + R (oInfinityFockApproximation N m a) * S b := by + change (((((m : ℝ) + 1)⁻¹ : ℝ) : ℂ)) • + (representedFockGram R S hsupport N m finiteFockUnweightedCoefficient + (fockTensorMatrix N m (a ⊗ₜ[ℂ] b)) + + representedFockGram R S hsupport N m finiteFockWeightedCoefficient + (fockTensorMatrix N m (a ⊗ₜ[ℂ] b))) = _ + rw [representedFockGram_tmul R S hcomm, representedFockGram_tmul R S hcomm] + change _ = R ((((((m : ℝ) + 1)⁻¹ : ℝ) : ℂ)) • + (cuntzGramMap (finiteFockCuntzFamily N m) (finiteFockCuntzFamily_relations N m) + finiteFockUnweightedCoefficient (oInfinityFockCompression N m a) + + cuntzGramMap (finiteFockCuntzFamily N m) (finiteFockCuntzFamily_relations N m) + finiteFockWeightedCoefficient (oInfinityFockCompression N m a))) * S b + exact (map_scaled_sum_mul R _ _ _ (S b)).symm + +lemma representedFockReturn_approximation (R : OInfinity →⋆ₙₐ[ℂ] E) (S : B →⋆ₙₐ[ℂ] E) + (hcomm : ∀ a b, Commute (R a) (S b)) (hsupport : ∀ b, R 1 * S b = S b) + (n : ℕ) (x : OInfinity ⊗[ℂ] B) : + representedFockReturn R S hsupport n (n + 1) (fockTensorMatrix n (n + 1) x) = + tensorCommutingEval R S (oInfinityTensorApproximation n x) := by + induction x using TensorProduct.inductionOn with + | tmul a b => + simpa only [oInfinityTensorApproximation_tmul, tensorCommutingEval_tmul, + oInfinityApproximationSequence] using + representedFockReturn_tmul R S hcomm hsupport n (n + 1) a b + | add x y hx hy => simp only [map_add, hx, hy] + +lemma tensor_norm_bound_of_approximation + (p q : Pureness.CStarAlgebraNorm (OInfinity ⊗[ℂ] B)) (x : OInfinity ⊗[ℂ] B) + {C : ℝ} (hC : 0 ≤ C) + (hb : ∀ n, q.toAlgebraNorm (oInfinityTensorApproximation n x) ≤ + C * p.toAlgebraNorm (oInfinityTensorApproximation n x)) : + q.toAlgebraNorm x ≤ C * p.toAlgebraNorm x := by + have hupper (n : ℕ) : q.toAlgebraNorm x ≤ + q.toAlgebraNorm (oInfinityTensorApproximation n x - x) + + C * (p.toAlgebraNorm (oInfinityTensorApproximation n x - x) + p.toAlgebraNorm x) := by + have hq := algebraNorm_le_rev_sub_add q.toAlgebraNorm x (oInfinityTensorApproximation n x) + have hp := algebraNorm_le_sub_add p.toAlgebraNorm (oInfinityTensorApproximation n x) x + exact hq.trans (add_le_add_right ((hb n).trans (mul_le_mul_of_nonneg_left hp hC)) _) + have ht := (oInfinityTensorApproximation_error_tendsto q x).add + (((oInfinityTensorApproximation_error_tendsto p x).add_const (p.toAlgebraNorm x)).const_mul C) + simpa only [zero_add] using ge_of_tendsto ht (Filter.Eventually.of_forall hupper) + +local instance (priority := 2000) tensorNormFastNonAssoc + {A : Type*} [CStarAlgebra A] (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : + NonUnitalNonAssocSemiring p.Completion := + (Pureness.CStarAlgebraNorm.completionCStarAlgebra p).toNonUnitalNonAssocSemiring + +local instance (priority := 2000) tensorNormFastAddMonoid + {A : Type*} [CStarAlgebra A] (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : AddMonoid p.Completion := + (Pureness.CStarAlgebraNorm.completionCStarAlgebra p).toAddMonoid + +local instance (priority := 2000) tensorNormFastAddCommGroup + {A : Type*} [CStarAlgebra A] (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : + AddCommGroup p.Completion := + (Pureness.CStarAlgebraNorm.completionCStarAlgebra p).toAddCommGroup + +local instance (priority := 2000) tensorNormFastModule + {A : Type*} [CStarAlgebra A] (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : Module ℂ p.Completion := + (Pureness.CStarAlgebraNorm.completionCStarAlgebra p).toNormedSpace.toModule + +local instance (priority := 2000) tensorNormFastDistribMulAction + {A : Type*} [CStarAlgebra A] (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : DistribMulAction ℂ p.Completion := + (tensorNormFastModule p).toDistribMulAction + +local instance (priority := 2000) tensorNormFastNorm + {A : Type*} [CStarAlgebra A] (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : Norm p.Completion := + (Pureness.CStarAlgebraNorm.completionCStarAlgebra p).toNorm + +def tensorNormLeft {A : Type*} [CStarAlgebra A] + (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : + A →⋆ₙₐ[ℂ] p.Completion where + toFun a := p.completionMap (a ⊗ₜ[ℂ] (1 : B)) + map_zero' := by simp + map_add' a b := by simp [TensorProduct.add_tmul] + map_smul' z a := by + rw [← TensorProduct.smul_tmul'] + exact p.completionMap.map_smul z _ + map_mul' a b := by rw [← map_mul]; simp + map_star' a := by rw [← map_star]; simp + +def tensorNormRight {A : Type*} [CStarAlgebra A] + (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : + B →⋆ₙₐ[ℂ] p.Completion where + toFun b := p.completionMap ((1 : A) ⊗ₜ[ℂ] b) + map_zero' := by simp + map_add' a b := by simp [TensorProduct.tmul_add] + map_smul' z a := by + rw [TensorProduct.tmul_smul] + exact p.completionMap.map_smul z _ + map_mul' a b := by rw [← map_mul]; simp + map_star' a := by rw [← map_star]; simp + +lemma tensorNorm_commute {A : Type*} [CStarAlgebra A] + (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) (a : A) (b : B) : Commute (tensorNormLeft p a) (tensorNormRight p b) := by + exact ((Commute.one_right a).tmul (Commute.one_left b)).map p.completionMap + +lemma tensorNorm_support {A : Type*} [CStarAlgebra A] + (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) + (b : B) : tensorNormLeft p 1 * tensorNormRight p b = tensorNormRight p b := by + change p.completionMap (1 ⊗ₜ[ℂ] 1) * p.completionMap (1 ⊗ₜ[ℂ] b) = _ + rw [← map_mul] + simp only [Algebra.TensorProduct.tmul_mul_tmul, one_mul] + rfl + +lemma tensorNormRight_injective {A : Type*} [CStarAlgebra A] [Nontrivial A] + (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) : + Function.Injective (tensorNormRight p) := by + apply (injective_iff_map_eq_zero _).mpr + intro b hb + have hn : ‖b‖ = 0 := by + have he := congrArg norm hb + change ‖p.completionMap ((1 : A) ⊗ₜ[ℂ] b)‖ = ‖(0 : p.Completion)‖ at he + rw [p.completionMap_norm, NuclearUnitization.cstar_norm_tmul, norm_one, + one_mul, norm_zero] at he + exact he + exact norm_eq_zero.mp hn + +lemma tensorNorm_eval {A : Type*} [CStarAlgebra A] + (p : Pureness.CStarAlgebraNorm (A ⊗[ℂ] B)) (x : A ⊗[ℂ] B) : + tensorCommutingEval (tensorNormLeft p) (tensorNormRight p) x = p.completionMap x := by + induction x using TensorProduct.inductionOn with + | tmul a b => + change p.completionMap (a ⊗ₜ[ℂ] 1) * p.completionMap (1 ⊗ₜ[ℂ] b) = _ + rw [← map_mul] + simp only [Algebra.TensorProduct.tmul_mul_tmul, mul_one, one_mul] + | add x y hx hy => simp only [map_add, hx, hy] + +lemma tensorNorm_fock_return_bound + (q : Pureness.CStarAlgebraNorm (OInfinity ⊗[ℂ] B)) (n : ℕ) (x : OInfinity ⊗[ℂ] B) : + q.toAlgebraNorm (oInfinityTensorApproximation n x) ≤ + 2 * ‖fockTensorMatrix n (n + 1) x‖ := by + rw [← q.completionMap_norm, ← tensorNorm_eval, ← representedFockReturn_approximation + _ _ (tensorNorm_commute q) (tensorNorm_support q)] + exact representedFockReturn_norm_le _ _ _ _ _ _ + +lemma tensorNorm_polynomial_bound + (p q : Pureness.CStarAlgebraNorm (OInfinity ⊗[ℂ] B)) + (l : List ((List (ℕ × Bool) →₀ ℂ) × B)) : + q.toAlgebraNorm (polynomialTensorSum l) ≤ 2 * p.toAlgebraNorm (polynomialTensorSum l) := by + obtain ⟨N, hN⟩ := exists_polynomialTensor_alphabet_bound l + have hb : ∀ᶠ n : ℕ in atTop, + q.toAlgebraNorm (oInfinityTensorApproximation n (polynomialTensorSum l)) ≤ + 2 * p.toAlgebraNorm (polynomialTensorSum l) := by + filter_upwards [eventually_ge_atTop N] with n hn + have hc := fockTensorMatrix_polynomial_norm_le (tensorNormLeft p) (tensorNormRight p) + (tensorNorm_commute p) (tensorNorm_support p) (tensorNormRight_injective p) + (m := n + 1) l (fun t ht w hw a ha => (hN t ht w hw a ha).trans_le hn) + rw [tensorNorm_eval, p.completionMap_norm] at hc + exact (tensorNorm_fock_return_bound q n _).trans (mul_le_mul_of_nonneg_left hc (by norm_num)) + exact algebraNorm_le_of_approximation q.toAlgebraNorm (polynomialTensorSum l) + (fun n => oInfinityTensorApproximation n (polynomialTensorSum l)) + (2 * p.toAlgebraNorm (polynomialTensorSum l)) + (oInfinityTensorApproximation_error_tendsto q (polynomialTensorSum l)) hb + +lemma tensorNorm_uniform_bound + (p q : Pureness.CStarAlgebraNorm (OInfinity ⊗[ℂ] B)) (x : OInfinity ⊗[ℂ] B) : + q.toAlgebraNorm x ≤ 2 * p.toAlgebraNorm x := by + apply tensor_norm_bound_of_approximation p q x (by norm_num) + intro n + obtain ⟨l, hl⟩ := exists_tensorApproximation_polynomialSum n x + rw [hl] + exact tensorNorm_polynomial_bound p q l + +/-- The Fock approximation and unused-generator corners give uniqueness of every +C*-norm on the algebraic tensor product with `OInfinity`. -/ +theorem oInfinity_isNuclear : Pureness.IsNuclear OInfinity := by + intro B _ + constructor + intro p q + exact Pureness.CStarAlgebraNorm.eq_of_mutual_bound p q + ⟨2, tensorNorm_uniform_bound q p⟩ ⟨2, tensorNorm_uniform_bound p q⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ToeplitzCompression.lean b/lean/OAI/Analysis/OInfinity/ToeplitzCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..b946de2ae4103820108e78dfb92f82213c039053 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ToeplitzCompression.lean @@ -0,0 +1,157 @@ +import Mathlib + +namespace OAI + +/-! # Finite Toeplitz rows compressed by an almost central projection + +These are the quantitative estimates in the projection-splitting step for a +finite row of canonical O∞ isometries. In addition to almost centrality, a +coisometric compression needs small compression of the original vacuum +projection. No projection with these properties is assumed to exist here. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E I : Type*} [CStarAlgebra E] [Fintype I] [DecidableEq I] + +/-- Compression in the ambient algebra, with relative unit `q`. -/ +def toeplitzRowCompression (q : E) (s : I → E) (i : I) : E := q * s i * q + +/-- The defect of the finite isometry row before compression. -/ +def toeplitzRowVacuum (s : I → E) : E := 1 - ∑ i, s i * star (s i) + +private lemma compression_projection_norm (q : E) (hq : q * q = q) + (hqs : star q = q) : ‖q‖ ≤ 1 := + IsStarProjection.norm_le q (isStarProjection_iff'.mpr ⟨hq, hqs⟩) + +private lemma compression_contract_mul_left (q x : E) (hq : ‖q‖ ≤ 1) : + ‖q * x‖ ≤ ‖x‖ := + (norm_mul_le q x).trans (mul_le_of_le_one_left (norm_nonneg x) hq) + +private lemma compression_contract_mul_right (q x : E) (hq : ‖q‖ ≤ 1) : + ‖x * q‖ ≤ ‖x‖ := + (norm_mul_le x q).trans (mul_le_of_le_one_right (norm_nonneg x) hq) + +/-- The adjoint has the same commutator error. -/ +lemma toeplitz_star_commutator_norm (q x : E) (hqs : star q = q) : + ‖q * star x - star x * q‖ = ‖q * x - x * q‖ := by + have h : q * star x - star x * q = -star (q * x - x * q) := by + rw [star_sub, star_mul, star_mul, hqs] + abel + rw [h, norm_neg, norm_star] + +omit [Fintype I] in +/-- Exact defect formula for the compressed Gram matrix. -/ +lemma toeplitzRowCompression_gram (q : E) (s : I → E) + (hq : q * q = q) (hqs : star q = q) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) (i j : I) : + star (toeplitzRowCompression q s i) * toeplitzRowCompression q s j - + (if i = j then q else 0) = + q * star (s i) * (q * s j - s j * q) * q := by + have hij : q * (star (s i) * s j) * q = if i = j then q else 0 := by + rw [hs] + split_ifs + · simpa only [mul_one] using hq + · simp only [mul_zero, zero_mul] + rw [← hij] + simp only [toeplitzRowCompression, star_mul, hqs] + noncomm_ring + simp only [← mul_assoc q q, hq] + +omit [Fintype I] in +/-- Every Gram entry is controlled by one generator commutator. -/ +lemma toeplitzRowCompression_gram_bound (q : E) (s : I → E) + (hq : q * q = q) (hqs : star q = q) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hns : ∀ i, ‖s i‖ ≤ 1) (δ : ℝ) + (hcomm : ∀ i, ‖q * s i - s i * q‖ ≤ δ) (i j : I) : + ‖star (toeplitzRowCompression q s i) * toeplitzRowCompression q s j - + (if i = j then q else 0)‖ ≤ δ := by + rw [toeplitzRowCompression_gram q s hq hqs hs] + have hnq := compression_projection_norm q hq hqs + calc + _ ≤ ‖q * star (s i) * (q * s j - s j * q)‖ := + compression_contract_mul_right _ _ hnq + _ ≤ ‖star (s i) * (q * s j - s j * q)‖ := by + rw [mul_assoc] + exact compression_contract_mul_left _ _ hnq + _ ≤ ‖q * s j - s j * q‖ := + compression_contract_mul_left _ _ (by simpa only [norm_star] using hns i) + _ ≤ δ := hcomm j + +omit [DecidableEq I] in +/-- The coisometry defect contains the compressed original vacuum explicitly. -/ +lemma toeplitzRowCompression_coisometry (q : E) (s : I → E) + (hq : q * q = q) (hqs : star q = q) : + (∑ i, toeplitzRowCompression q s i * star (toeplitzRowCompression q s i)) - q = + (∑ i, q * s i * (q * star (s i) - star (s i) * q) * q) - + q * toeplitzRowVacuum s * q := by + have hterm (i : I) : + toeplitzRowCompression q s i * star (toeplitzRowCompression q s i) = + q * s i * (q * star (s i) - star (s i) * q) * q + + q * (s i * star (s i)) * q := by + simp only [toeplitzRowCompression, star_mul, hqs] + noncomm_ring + simp only [← mul_assoc q q, hq] + abel + simp_rw [hterm] + rw [Finset.sum_add_distrib] + unfold toeplitzRowVacuum + rw [mul_sub, sub_mul, mul_one, hq, Finset.mul_sum, Finset.sum_mul] + abel + +omit [DecidableEq I] in +/-- Approximate centrality and small vacuum compression give the finite +coisometry estimate used before perturbing a Toeplitz row to a Cuntz row. -/ +lemma toeplitzRowCompression_coisometry_bound (q : E) (s : I → E) + (hq : q * q = q) (hqs : star q = q) (hns : ∀ i, ‖s i‖ ≤ 1) + (δ : ℝ) (hcomm : ∀ i, ‖q * s i - s i * q‖ ≤ δ) : + ‖(∑ i, toeplitzRowCompression q s i * star (toeplitzRowCompression q s i)) - q‖ ≤ + (Fintype.card I : ℝ) * δ + ‖q * toeplitzRowVacuum s * q‖ := by + rw [toeplitzRowCompression_coisometry q s hq hqs] + apply (norm_sub_le _ _).trans + apply add_le_add _ le_rfl + calc + _ ≤ ∑ i, ‖q * s i * (q * star (s i) - star (s i) * q) * q‖ := + norm_sum_le _ _ + _ ≤ ∑ _i : I, δ := by + apply Finset.sum_le_sum + intro i _ + calc + _ ≤ ‖q * s i * (q * star (s i) - star (s i) * q)‖ := + compression_contract_mul_right _ _ (compression_projection_norm q hq hqs) + _ ≤ ‖s i * (q * star (s i) - star (s i) * q)‖ := by + rw [mul_assoc] + exact compression_contract_mul_left _ _ (compression_projection_norm q hq hqs) + _ ≤ ‖q * star (s i) - star (s i) * q‖ := + compression_contract_mul_left _ _ (hns i) + _ = ‖q * s i - s i * q‖ := toeplitz_star_commutator_norm q (s i) hqs + _ ≤ δ := hcomm i + _ = (Fintype.card I : ℝ) * δ := by simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul] + +/-- The two relative compressions recover each generator up to twice its +commutator error. No smallness is asserted for either complementary projection. -/ +lemma toeplitz_complementary_compression_bound (q x : E) + (hq : q * q = q) (hqs : star q = q) : + ‖q * x * q + (1 - q) * x * (1 - q) - x‖ ≤ 2 * ‖q * x - x * q‖ := by + have hnq := compression_projection_norm q hq hqs + have hnp : ‖1 - q‖ ≤ 1 := compression_projection_norm (1 - q) + (by noncomm_ring [hq]) (by rw [star_sub, star_one, hqs]) + have he : q * x * q + (1 - q) * x * (1 - q) - x = + (q * x - x * q) * q - (q * x - x * q) * (1 - q) := by + noncomm_ring [hq] + rw [he] + calc + _ ≤ ‖(q * x - x * q) * q‖ + ‖(q * x - x * q) * (1 - q)‖ := norm_sub_le _ _ + _ ≤ ‖q * x - x * q‖ + ‖q * x - x * q‖ := + add_le_add (compression_contract_mul_right _ _ hnq) (compression_contract_mul_right _ _ hnp) + _ = 2 * ‖q * x - x * q‖ := by ring + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/TransportedBuffer.lean b/lean/OAI/Analysis/OInfinity/TransportedBuffer.lean new file mode 100644 index 0000000000000000000000000000000000000000..f7641d9036e5225873b3152a831a7fb4ee91462b --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/TransportedBuffer.lean @@ -0,0 +1,118 @@ +import OAI.Analysis.OInfinity.BufferAnchor +import Mathlib.Algebra.Star.UnitaryStarAlgAut + +namespace OAI + +/-! # Transporting the explicit absorption anchor + +The canonical Fock split transports its corner by a connected unitary, +but transports its complementary isometry by left multiplication. This +asymmetric transport still preserves connectedness of the absorption +anchor: its anchor is conjugate to a value of the original rotation path. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +namespace BufferAbsorptionCorner + +/-- Corner coefficients are conjugated, whereas the complementary +isometry is moved by left multiplication, as in the finite Fock split. -/ +def transported (D : BufferAbsorptionCorner E) (u : unitary E) : BufferAbsorptionCorner E := by + let F := Unitary.conjStarAlgAut ℂ E u + refine { + q := F D.q + w := (u : E) * D.w + a := F D.a + b := F D.b + projection := isStarProjection_iff'.mpr ⟨?_, ?_⟩ + w_gram := ?_ + w_range := ?_ + w_orthogonal := ?_ + a_gram := ?_ + b_gram := ?_ + orthogonal := ?_ + ranges := ?_ + } + · rw [← map_mul, D.projection.isIdempotentElem.eq] + · rw [← map_star, D.projection.isSelfAdjoint.star_eq] + · rw [star_mul] + calc + _ = star D.w * (star (u : E) * (u : E)) * D.w := by noncomm_ring + _ = 1 := by rw [Unitary.star_mul_self_of_mem u.property, mul_one, D.w_gram] + · calc + _ = (u : E) * (D.w * star D.w) * star (u : E) := by rw [star_mul]; noncomm_ring + _ = F (1 - D.q) := by rw [D.w_range]; rfl + _ = 1 - F D.q := by rw [map_sub, map_one] + · change ((u : E) * D.q * star (u : E)) * ((u : E) * D.w) = 0 + calc + _ = (u : E) * D.q * (star (u : E) * (u : E)) * D.w := by noncomm_ring + _ = 0 := by rw [Unitary.star_mul_self_of_mem u.property, mul_one, + mul_assoc, D.w_orthogonal, mul_zero] + · rw [← map_star, ← map_mul, D.a_gram] + · rw [← map_star, ← map_mul, D.b_gram] + · rw [← map_star, ← map_mul, D.orthogonal, map_zero] + · rw [← map_star, ← map_star, ← map_mul, ← map_mul, ← map_add, D.ranges] + +lemma transported_q (D : BufferAbsorptionCorner E) (u : unitary E) : + (D.transported u).q = (u : E) * D.q * star (u : E) := rfl + +lemma transported_w (D : BufferAbsorptionCorner E) (u : unitary E) : + (D.transported u).w = (u : E) * D.w := rfl + +lemma transported_a (D : BufferAbsorptionCorner E) (u : unitary E) : + (D.transported u).a = (u : E) * D.a * star (u : E) := rfl + +lemma transported_b (D : BufferAbsorptionCorner E) (u : unitary E) : + (D.transported u).b = (u : E) * D.b * star (u : E) := rfl + +/-- Exact asymmetric transport identity for the anchor. -/ +lemma transported_anchor (D : BufferAbsorptionCorner E) (u : unitary E) : + (D.transported u).anchor = u * D.rotation u * star u := by + apply Subtype.ext + change star ((u : E) * D.a * star (u : E)) + + ((u : E) * D.w) * 1 * + (star ((u : E) * D.b * star (u : E)) + + (1 - (u : E) * D.q * star (u : E))) = + ((u : E) * (star D.a + D.w * (u : E) * (star D.b + (1 - D.q)))) * star (u : E) + simp only [star_mul, star_star, mul_one] + calc + _ = (u : E) * star D.a * star (u : E) + + (u : E) * D.w * (u : E) * star D.b * star (u : E) + + (u : E) * D.w - (u : E) * D.w * (u : E) * D.q * star (u : E) := by + noncomm_ring + _ = (u : E) * star D.a * star (u : E) + + (u : E) * D.w * (u : E) * star D.b * star (u : E) + + (u : E) * D.w * ((u : E) * star (u : E)) - + (u : E) * D.w * (u : E) * D.q * star (u : E) := by + rw [Unitary.mul_star_self_of_mem u.property, mul_one] + _ = _ := by noncomm_ring + +/-- The anchor remains connected for the actual transported Fock corner; +no path in a corner stabilizer is inferred from an ambient endpoint. -/ +lemma transported_anchor_joined (D : BufferAbsorptionCorner E) (u : unitary E) + (hD : Joined (1 : unitary E) D.anchor) (hu : Joined (1 : unitary E) u) : + Joined (1 : unitary E) (D.transported u).anchor := by + have hrot : Joined (1 : unitary E) (D.rotation u) := by + have h := (hD.trans (D.absorption_joined_anchor u hu)).mul hu + have he : D.absorption u * u = D.rotation u := by + apply Subtype.ext + change ((D.rotation u : E) * star (u : E)) * (u : E) = (D.rotation u : E) + rw [mul_assoc, Unitary.star_mul_self_of_mem u.property, mul_one] + simpa only [one_mul, he] using h + have hus : Joined (1 : unitary E) (star u) := by + simpa only [star_one] using + hu.map (continuous_star : Continuous (star : unitary E → unitary E)) + simpa only [one_mul, D.transported_anchor u] using (hu.mul hrot).mul hus + +end BufferAbsorptionCorner + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/VacuumBufferAbsorption.lean b/lean/OAI/Analysis/OInfinity/VacuumBufferAbsorption.lean new file mode 100644 index 0000000000000000000000000000000000000000..830479d62840821a5aaa2e3ac55094d988d0d1c2 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/VacuumBufferAbsorption.lean @@ -0,0 +1,121 @@ +import OAI.Analysis.OInfinity.ProperBufferAbsorption +import OAI.Analysis.OInfinity.FiniteRowCompletion + +namespace OAI + +/-! # Absorption with a canonical vacuum spare + +A second unused source isometry is orthogonal to every word in the finite +Fock sum. It therefore completes that sum to a connected ambient unitary +without requiring the target corner to commute with the source row. The +commutation requirements on the tested target entries remain explicit. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E I : Type*} [CStarAlgebra E] [Fintype I] [DecidableEq I] + +/-- The second source spare replaces source-corner commutation in the +connected Fock completion. Only the selected target entries must commute +with the fixed binary coefficients. -/ +lemma BufferAbsorptionCorner.exists_vacuum_absorption_on [Nontrivial E] + (D : BufferAbsorptionCorner E) (s t : I → E) (r z : E) (P : I → Prop) + (hrr : star r * r = 1) (hr : ∀ i, star r * s i = 0) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hzz : star z * z = 1) (hqz : D.q * z = 0) + (hzr : star z * r = 0) (hzs : ∀ i, star z * s i = 0) + (htq : ∀ i, t i * D.q = t i) (ht : ∑ i, t i * star (t i) = D.q) + (htt : ∀ i j, star (t i) * t j = if i = j then D.q else 0) + (hat : ∀ i, P i → Commute (star D.a) (t i)) + (hbt : ∀ i, P i → Commute (star D.b) (t i)) + (ε : ℝ) (hε : 0 < ε) : + ∃ W : unitary E, Joined D.anchor W ∧ + ∀ i, P i → ‖(W : E) * s i - (t i + D.w * s i * star D.w) * (W : E)‖ < ε := by + let δ := ε / 6 + have hδ : 0 < δ := by dsimp only [δ]; positivity + obtain ⟨m, hm⟩ := exists_nat_gt (2 / δ ^ 2) + have hsmall : 2 / ((m : ℝ) + 1) < δ ^ 2 := by + have hδsq : 0 < δ ^ 2 := sq_pos_of_pos hδ + have hm' : 2 < (m : ℝ) * δ ^ 2 := (div_lt_iff₀ hδsq).mp hm + apply (div_lt_iff₀ (by positivity : 0 < (m : ℝ) + 1)).mpr + nlinarith + let v := finiteRowIsometry s t r D.q m + have hvg : star v * v = D.q := finiteRowIsometry_gram s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq hrr hr hs htq ht m + have hvq : v * D.q = v := relativeIsometry_mul_support v D.q hvg + D.projection.isSelfAdjoint.star_eq D.projection.isIdempotentElem.eq + have hvz : star v * z = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star + (finiteRowIsometry_unused s t r D.q z hzr hzs m) + obtain ⟨u, hu, _, huv⟩ := exists_explicit_connected_unitary_extension v z + (by rw [mul_assoc, hvg, hvq]) hzz (by rw [hvg]; exact hqz) + (by rw [mul_assoc, hvz, mul_zero]) + have huq : (u : E) * D.q = v := by simpa only [hvg] using huv + have hvn : ‖v‖ ≤ 1 := finiteRowIsometry_norm_le s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq hrr hr hs htq ht m + refine ⟨D.absorption u, D.absorption_joined_anchor u hu, ?_⟩ + intro i hi + have hf : ‖s i * v - v * t i‖ < δ := by + have h := finiteRowIsometry_forward_norm_sq s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq + hrr hr hs htq ht htt m i + change ‖s i * v - v * t i‖ ^ 2 ≤ _ at h + nlinarith [norm_nonneg (s i * v - v * t i)] + have hb : ‖star v * s i - t i * star v‖ < δ := by + have h := finiteRowIsometry_backward_norm_sq s t r D.q + D.projection.isIdempotentElem.eq D.projection.isSelfAdjoint.star_eq + hrr hr hs htq ht htt m i + have he : star v * s i - t i * star v = + star (star (s i) * v - v * star (t i)) := by + simp only [star_sub, star_mul, star_star] + rw [he, norm_star] + have hone : ((m : ℝ) + 1)⁻¹ ≤ 2 / ((m : ℝ) + 1) := by + rw [← one_div] + exact div_le_div_of_nonneg_right (by norm_num) (by positivity) + change ‖star (s i) * v - v * star (t i)‖ ^ 2 ≤ _ at h + nlinarith [norm_nonneg (star (s i) * v - v * star (t i))] + calc + _ ≤ 2 * ‖s i * v - v * t i‖ + 3 * ‖star v * s i - t i * star v‖ := + D.absorption_error_bound u v (s i) (t i) huq (htq i) (hat i hi) (hbt i hi) hvn + _ < ε := by dsimp only [δ] at hf hb; linarith + + +/-- Canonical source rows supply both required spare isometries. The +only geometric condition on the target corner is its annihilation of the +second unused generator, as provided by the canonical vacuum split. -/ +lemma BufferAbsorptionCorner.exists_canonical_vacuum_absorption [Nontrivial E] + (D : BufferAbsorptionCorner E) (s : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (n : ℕ) (t : Fin n → E) + (hqz : D.q * s (n + 1) = 0) + (htq : ∀ i, t i * D.q = t i) (ht : ∑ i, t i * star (t i) = D.q) + (htt : ∀ i j, star (t i) * t j = if i = j then D.q else 0) + (hat : ∀ i, Commute (star D.a) (t i)) + (hbt : ∀ i, Commute (star D.b) (t i)) + (ε : ℝ) (hε : 0 < ε) : + ∃ W : unitary E, Joined D.anchor W ∧ + ∀ i : Fin n, + ‖(W : E) * s i - (t i + D.w * s i * star D.w) * (W : E)‖ < ε := by + have hsource (i j : Fin n) : star (s i) * s j = if i = j then 1 else 0 := by + simpa only [Fin.ext_iff] using hs i j + have hroot (i : Fin n) : star (s n) * s i = 0 := by + rw [hs, ite_eq_right (by omega)] + have hspare (i : Fin n) : star (s (n + 1)) * s i = 0 := by + rw [hs, ite_eq_right (by omega)] + obtain ⟨W, hW, hWi⟩ := D.exists_vacuum_absorption_on (fun i : Fin n => s i) t + (s n) (s (n + 1)) (fun _ => True) + (by simpa only [ite_true] using hs n n) hroot hsource + (by simpa only [ite_true] using hs (n + 1) (n + 1)) hqz + (by rw [hs, ite_eq_right (by omega)]) hspare htq ht htt + (fun i _ => hat i) (fun i _ => hbt i) ε hε + exact ⟨W, hW, fun i => hWi i True.intro⟩ + + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/VacuumCorner.lean b/lean/OAI/Analysis/OInfinity/VacuumCorner.lean new file mode 100644 index 0000000000000000000000000000000000000000..6f1cf330aa104b2d98f1331f9dc9162d453c7f32 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/VacuumCorner.lean @@ -0,0 +1,282 @@ +import OAI.Analysis.OInfinity.FockRangeProjection + +namespace OAI + +/-! # Finite Fock coefficients from an unused Cuntz generator + +For words in the first `N` generators, the next generator has exactly the +vacuum annihilation relations. This realizes every finite Fock compression +of such a word as a corner in the Cuntz algebra itself. +-/ + +noncomputable section +open scoped CStarAlgebra InnerProductSpace + +namespace WeakPureInfiniteness + +local instance : SMulWithZero ℂ OInfinity := + @MulActionWithZero.toSMulWithZero ℂ OInfinity _ _ + (@Module.toMulActionWithZero ℂ OInfinity _ _ inferInstance) +local instance : DistribSMul ℂ OInfinity := + @DistribMulAction.toDistribSMul ℂ OInfinity _ _ + (@Module.toDistribMulAction ℂ OInfinity _ _ inferInstance) + +def oInfinityVacuumWord (N : ℕ) : List (Fin N) → OInfinity + | [] => oInfinityIsometry N + | p :: w => oInfinityIsometry p * oInfinityVacuumWord N w + +lemma oInfinityVacuumWord_relations (N : ℕ) (v w : List (Fin N)) : + star (oInfinityVacuumWord N v) * oInfinityVacuumWord N w = + if v = w then 1 else 0 := by + induction v generalizing w with + | nil => + cases w with + | nil => simp [oInfinityVacuumWord, oInfinityIsometry_relations] + | cons q w => + simp only [oInfinityVacuumWord, (List.cons_ne_nil q w).symm, ite_false] + rw [← mul_assoc, oInfinityIsometry_relations, + ite_eq_right (ne_of_gt q.isLt), zero_mul] + | cons p v ih => + cases w with + | nil => + simp only [oInfinityVacuumWord, star_mul, List.cons_ne_nil, ite_false] + rw [mul_assoc, oInfinityIsometry_relations, ite_eq_right (ne_of_lt p.isLt), mul_zero] + | cons q w => + change star (oInfinityIsometry p * oInfinityVacuumWord N v) * + (oInfinityIsometry q * oInfinityVacuumWord N w) = _ + rw [star_mul] + calc + _ = star (oInfinityVacuumWord N v) * + (star (oInfinityIsometry p) * oInfinityIsometry q) * oInfinityVacuumWord N w := by + noncomm_ring + _ = _ := by + rw [oInfinityIsometry_relations] + by_cases hpq : p = q + · subst q + simp only [ite_true, mul_one, ih, List.cons.injEq, true_and] + · have hpq' : p.val ≠ q.val := fun h => hpq (Fin.ext h) + simp [hpq', hpq] + +def finiteAlphabetWord (N : ℕ) (z : List (Fin N × Bool)) : OInfinity := + cuntzWord oInfinityIsometry (z.map fun p => (p.1.val, p.2)) + +@[simp] lemma finiteAlphabetWord_nil (N : ℕ) : finiteAlphabetWord N [] = 1 := rfl + +@[simp] lemma finiteAlphabetWord_cons (N : ℕ) (p : Fin N) (b : Bool) + (z : List (Fin N × Bool)) : + finiteAlphabetWord N ((p, b) :: z) = + (if b then oInfinityIsometry p else star (oInfinityIsometry p)) * finiteAlphabetWord N z := rfl + +def finiteAlphabetPop {N : ℕ} (p : Fin N) : List (Fin N) → Option (List (Fin N)) + | [] => none + | q :: w => if p = q then some w else none + +def finiteAlphabetRun (N : ℕ) : List (Fin N × Bool) → List (Fin N) → Option (List (Fin N)) + | [], w => some w + | (p, true) :: z, w => (finiteAlphabetRun N z w).map (List.cons p) + | (p, false) :: z, w => (finiteAlphabetRun N z w).bind (finiteAlphabetPop p) + +def vacuumRunValue {N : ℕ} (v : Option (List (Fin N))) : OInfinity := + v.elim 0 (oInfinityVacuumWord N) + +lemma oInfinityVacuumWord_annihilate {N : ℕ} (p : Fin N) (w : List (Fin N)) : + star (oInfinityIsometry p) * oInfinityVacuumWord N w = + vacuumRunValue (finiteAlphabetPop p w) := by + cases w with + | nil => + simp only [oInfinityVacuumWord, oInfinityIsometry_relations, + ite_eq_right (ne_of_lt p.isLt), finiteAlphabetPop, vacuumRunValue, Option.elim_none] + | cons q w => + rw [oInfinityVacuumWord, ← mul_assoc, oInfinityIsometry_relations] + by_cases hpq : p = q + · subst q + simp [finiteAlphabetPop, vacuumRunValue] + · have hpq' : p.val ≠ q.val := fun h => hpq (Fin.ext h) + simp [hpq', hpq, finiteAlphabetPop, vacuumRunValue] + +lemma finiteAlphabetWord_vacuum_action {N : ℕ} (z : List (Fin N × Bool)) + (w : List (Fin N)) : + finiteAlphabetWord N z * oInfinityVacuumWord N w = + vacuumRunValue (finiteAlphabetRun N z w) := by + induction z with + | nil => simp [finiteAlphabetRun, vacuumRunValue] + | cons pb z ih => + rcases pb with ⟨p, b⟩ + cases b with + | false => + change (star (oInfinityIsometry p) * finiteAlphabetWord N z) * + oInfinityVacuumWord N w = _ + rw [mul_assoc, ih] + cases hrun : finiteAlphabetRun N z w with + | none => simp [finiteAlphabetRun, hrun, vacuumRunValue] + | some v => + simpa only [finiteAlphabetRun, hrun, Option.bind_some, vacuumRunValue, + Option.elim_some] using oInfinityVacuumWord_annihilate p v + | true => + change (oInfinityIsometry p * finiteAlphabetWord N z) * + oInfinityVacuumWord N w = _ + rw [mul_assoc, ih] + cases hrun : finiteAlphabetRun N z w with + | none => simp [finiteAlphabetRun, hrun, vacuumRunValue] + | some v => simp [finiteAlphabetRun, hrun, vacuumRunValue, oInfinityVacuumWord] + +def finiteAlphabetBasis {N : ℕ} (w : List (Fin N)) : FockSpace := + lp.single 2 (w.map Fin.val) 1 + +def fockRunValue {N : ℕ} (v : Option (List (Fin N))) : FockSpace := + v.elim 0 finiteAlphabetBasis + +lemma finiteAlphabetBasis_create {N : ℕ} (p : Fin N) (w : List (Fin N)) : + fockShift p (finiteAlphabetBasis w) = finiteAlphabetBasis (p :: w) := by + simp only [finiteAlphabetBasis, fockShift_single, List.map_cons] + +lemma finiteAlphabetBasis_annihilate {N : ℕ} (p : Fin N) (w : List (Fin N)) : + (fockShift p).toContinuousLinearMap.adjoint (finiteAlphabetBasis w) = + fockRunValue (finiteAlphabetPop p w) := by + cases w with + | nil => simp [finiteAlphabetBasis, fockShift_adjoint_single_nil, finiteAlphabetPop, fockRunValue] + | cons q w => + simp only [finiteAlphabetBasis, List.map_cons, fockShift_adjoint_single_cons, + finiteAlphabetPop] + by_cases hpq : p = q + · subst q; simp [fockRunValue, finiteAlphabetBasis] + · have hpq' : p.val ≠ q.val := fun h => hpq (Fin.ext h) + simp [hpq', hpq, fockRunValue] + +lemma finiteAlphabetWord_fock_action {N : ℕ} (z : List (Fin N × Bool)) + (w : List (Fin N)) : + fockOperatorRepresentation (finiteAlphabetWord N z) (finiteAlphabetBasis w) = + fockRunValue (finiteAlphabetRun N z w) := by + induction z with + | nil => simp [finiteAlphabetRun, fockRunValue] + | cons pb z ih => + rcases pb with ⟨p, b⟩ + cases b with + | false => + change (fockOperatorRepresentation (star (oInfinityIsometry p) * finiteAlphabetWord N z)) + (finiteAlphabetBasis w) = _ + rw [map_mul, mul_apply_eq_comp, ih] + change (fockShift p).toContinuousLinearMap.adjoint (fockRunValue (finiteAlphabetRun N z w)) = _ + cases hrun : finiteAlphabetRun N z w with + | none => simp [finiteAlphabetRun, hrun, fockRunValue] + | some v => + simpa only [finiteAlphabetRun, hrun, Option.bind_some, fockRunValue, + Option.elim_some] using finiteAlphabetBasis_annihilate p v + | true => + change (fockOperatorRepresentation (oInfinityIsometry p * finiteAlphabetWord N z)) + (finiteAlphabetBasis w) = _ + rw [map_mul, mul_apply_eq_comp, ih] + change fockShift p (fockRunValue (finiteAlphabetRun N z w)) = _ + cases hrun : finiteAlphabetRun N z w with + | none => simp [finiteAlphabetRun, hrun, fockRunValue] + | some v => + simpa only [finiteAlphabetRun, hrun, Option.map_some, fockRunValue, + Option.elim_some] using finiteAlphabetBasis_create p v + +lemma finiteAlphabetBasis_inner {N : ℕ} (v w : List (Fin N)) : + inner ℂ (finiteAlphabetBasis v) (finiteAlphabetBasis w) = if v = w then 1 else 0 := by + have he : v.map Fin.val = w.map Fin.val ↔ v = w := + (List.map_injective_iff.mpr Fin.val_injective).eq_iff + simp [finiteAlphabetBasis, lp.inner_single_left, lp.single_apply, Pi.single_apply, he] + +lemma finiteAlphabetWord_coefficient {N : ℕ} (z : List (Fin N × Bool)) + (v w : List (Fin N)) : + star (oInfinityVacuumWord N v) * finiteAlphabetWord N z * oInfinityVacuumWord N w = + (inner ℂ (finiteAlphabetBasis v) + (fockOperatorRepresentation (finiteAlphabetWord N z) (finiteAlphabetBasis w))) • + (1 : OInfinity) := by + rw [mul_assoc, finiteAlphabetWord_vacuum_action, finiteAlphabetWord_fock_action] + cases hrun : finiteAlphabetRun N z w with + | none => simp [vacuumRunValue, fockRunValue] + | some t => + simp only [vacuumRunValue, fockRunValue, Option.elim_some, + oInfinityVacuumWord_relations, finiteAlphabetBasis_inner] + split_ifs <;> simp + +lemma oInfinityVacuumWord_ofFn (N k : ℕ) (w : Fin k → Fin N) : + oInfinityVacuumWord N (List.ofFn w) = + oInfinityPositiveWord N w * oInfinityIsometry N := by + induction k with + | zero => simp [oInfinityVacuumWord] + | succ k ih => + rw [List.ofFn_succ] + change oInfinityIsometry (w 0) * oInfinityVacuumWord N (List.ofFn (Fin.tail w)) = + (oInfinityIsometry (w 0) * oInfinityPositiveWord N (Fin.tail w)) * oInfinityIsometry N + rw [ih, mul_assoc] + +def finiteVacuumCorner (N m : ℕ) (i : FiniteFockIndex N m) : OInfinity := + finiteFockAlgebraWord i * oInfinityIsometry N + +lemma finiteVacuumCorner_relations (N m : ℕ) (i j : FiniteFockIndex N m) : + star (finiteVacuumCorner N m i) * finiteVacuumCorner N m j = + if i = j then 1 else 0 := by + have he : List.ofFn i.2 = List.ofFn j.2 ↔ i = j := by + constructor + · intro h + apply finiteFockWord_injective N m + have hh := congrArg (List.map Fin.val) h + simpa only [List.map_ofFn, Function.comp_def, finiteFockWord] using hh + · rintro rfl; rfl + change star (oInfinityPositiveWord N i.2 * oInfinityIsometry N) * + (oInfinityPositiveWord N j.2 * oInfinityIsometry N) = _ + rw [← oInfinityVacuumWord_ofFn, ← oInfinityVacuumWord_ofFn, oInfinityVacuumWord_relations] + simp only [he] + +lemma finiteVacuumCorner_compression {N m : ℕ} (z : List (Fin N × Bool)) + (i j : FiniteFockIndex N m) : + star (finiteVacuumCorner N m i) * finiteAlphabetWord N z * finiteVacuumCorner N m j = + oInfinityFockCompression N m (finiteAlphabetWord N z) i j • (1 : OInfinity) := by + have hi : finiteVacuumCorner N m i = oInfinityVacuumWord N (List.ofFn i.2) := + (oInfinityVacuumWord_ofFn N i.1.val i.2).symm + have hj : finiteVacuumCorner N m j = oInfinityVacuumWord N (List.ofFn j.2) := + (oInfinityVacuumWord_ofFn N j.1.val j.2).symm + rw [hi, hj, finiteAlphabetWord_coefficient, oInfinityFockCompression_apply] + simp only [finiteAlphabetBasis, finiteFockVector, finiteFockWord, List.map_ofFn, Function.comp_def] + +lemma exists_finiteAlphabet_lift {N : ℕ} (w : List (ℕ × Bool)) + (hw : ∀ p ∈ w, p.1 < N) : + ∃ z : List (Fin N × Bool), z.map (fun p => (p.1.val, p.2)) = w := by + induction w with + | nil => exact ⟨[], rfl⟩ + | cons p w ih => + obtain ⟨z, hz⟩ := ih (fun q hq => hw q (List.mem_cons_of_mem _ hq)) + refine ⟨(⟨p.1, hw p (List.mem_cons_self ..)⟩, p.2) :: z, ?_⟩ + simp only [List.map_cons, hz, Prod.mk.eta] + +lemma finiteVacuumCorner_cuntzWord {N m : ℕ} (w : List (ℕ × Bool)) + (hw : ∀ p ∈ w, p.1 < N) (i j : FiniteFockIndex N m) : + star (finiteVacuumCorner N m i) * cuntzWord oInfinityIsometry w * finiteVacuumCorner N m j = + oInfinityFockCompression N m (cuntzWord oInfinityIsometry w) i j • (1 : OInfinity) := by + obtain ⟨z, rfl⟩ := exists_finiteAlphabet_lift w hw + exact finiteVacuumCorner_compression z i j + +lemma finiteVacuumCorner_polynomial {N m : ℕ} (c : List (ℕ × Bool) →₀ ℂ) + (hc : ∀ w ∈ c.support, ∀ p ∈ w, p.1 < N) (i j : FiniteFockIndex N m) : + star (finiteVacuumCorner N m i) * cuntzPolynomial oInfinityIsometry c * + finiteVacuumCorner N m j = + oInfinityFockCompression N m (cuntzPolynomial oInfinityIsometry c) i j • (1 : OInfinity) := by + have hentry (f : List (ℕ × Bool) → CStarMatrix (FiniteFockIndex N m) (FiniteFockIndex N m) ℂ) : + (∑ w ∈ c.support, f w) i j = ∑ w ∈ c.support, f w i j := + map_sum (matrixEntryLinear i j) f c.support + simp only [cuntzPolynomial, Finsupp.sum, Finset.mul_sum, Finset.sum_mul, + mul_smul_comm, smul_mul_assoc, map_sum, map_smul, hentry, + CStarMatrix.smul_apply, Finset.sum_smul] + apply Finset.sum_congr rfl + intro w hw + rw [finiteVacuumCorner_cuntzWord w (hc w hw), smul_smul, smul_eq_mul] + +lemma exists_polynomial_alphabet_bound (c : List (ℕ × Bool) →₀ ℂ) : + ∃ N : ℕ, ∀ w ∈ c.support, ∀ p ∈ w, p.1 < N := by + let s := c.support.biUnion (fun w => w.toFinset.image Prod.fst) + refine ⟨s.sup id + 1, ?_⟩ + intro w hw p hp + apply Nat.lt_succ_of_le + apply Finset.le_sup (f := id) + exact Finset.mem_biUnion.mpr ⟨w, hw, + Finset.mem_image.mpr ⟨p, List.mem_toFinset.mpr hp, rfl⟩⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/VacuumSplit.lean b/lean/OAI/Analysis/OInfinity/VacuumSplit.lean new file mode 100644 index 0000000000000000000000000000000000000000..5d6f7846e146c1073190d96c28bb5c14ee3e0e59 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/VacuumSplit.lean @@ -0,0 +1,271 @@ +import OAI.Analysis.OInfinity.FiniteRowCompletion + +namespace OAI + +/-! # A concrete almost central split of a canonical finite O∞ row + +The corner and its coisometric row are constructed from unused canonical +isometries and the finite word sum. Its complement is the range of an actual +isometry. Thus the vacuum compression and the complement are both controlled +without assuming a projection-classification theorem. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +private lemma transported_row {J : Type*} [Fintype J] [DecidableEq J] + (v q : E) (t : J → E) (hv : star v * v = q) (hvq : v * q = v) + (htl : ∀ i, q * t i = t i) (htr : ∀ i, t i * q = t i) + (htt : ∀ i j, star (t i) * t j = if i = j then q else 0) + (ht : ∑ i, t i * star (t i) = q) : + (∀ i j, star (v * t i * star v) * (v * t j * star v) = + if i = j then v * star v else 0) ∧ + (∑ i, (v * t i * star v) * star (v * t i * star v)) = v * star v := by + constructor + · intro i j + calc + _ = v * star (t i) * (star v * v) * t j * star v := by + simp only [star_mul, star_star] + noncomm_ring + _ = v * (star (t i) * t j) * star v := by rw [hv, mul_assoc (v * star (t i)), htl]; noncomm_ring + _ = _ := by rw [htt]; split_ifs <;> simp only [hvq, mul_zero, zero_mul] + · have he (i : J) : (v * t i * star v) * star (v * t i * star v) = + v * (t i * star (t i)) * star v := by + simp only [star_mul, star_star] + calc + _ = v * (t i * q) * star (t i) * star v := by + rw [← hv]; noncomm_ring + _ = _ := by rw [htr]; noncomm_ring + simp only [he, ← Finset.mul_sum, ← Finset.sum_mul, ht, hvq] + +private lemma transported_zeroCornerRow (q a b v : E) + (hqq : q * q = q) (hqa : q * a = a) (hqb : q * b = b) (hbq : b * q = b) + (hvg : star v * v = q) (hvq : v * q = v) : + ∀ n i, v * zeroCornerRow q a b n i * star v = + zeroCornerRow (v * star v) (v * a * star v) (v * b * star v) n i := by + intro n + induction n with + | zero => intro i; change v * q * star v = v * star v; rw [hvq] + | succ n ih => + intro i + refine Fin.cases rfl (fun j => ?_) i + change v * (a * zeroCornerRow q a b n j) * star v = + (v * a * star v) * zeroCornerRow (v * star v) (v * a * star v) (v * b * star v) n j + rw [← ih j] + calc + _ = v * a * (q * zeroCornerRow q a b n j) * star v := by + rw [(zeroCornerRow_support q a b hqq hqa hqb hbq n j).1] + noncomm_ring + _ = _ := by rw [← hvg]; noncomm_ring + +/-- The explicit finite split, retaining its transported binary generators. -/ +lemma exists_canonical_vacuum_split_with_pair_and_isometry [Nontrivial E] (s : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (n : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ (f w : E) (g : Fin (n + 1) → E), + f ≠ 0 ∧ star f = f ∧ f * f = f ∧ + star w * w = 1 ∧ w * star w = 1 - f ∧ + (∀ i j, star (g i) * g j = if i = j then f else 0) ∧ + (∑ i, g i * star (g i)) = f ∧ + (∀ i : Fin (n + 1), ‖s i * f - f * s i‖ < ε) ∧ + (∀ i : Fin (n + 1), ‖f * s i * f - g i‖ < ε) ∧ + ‖f * (1 - ∑ i : Fin (n + 1), s i * star (s i)) * f‖ < ε ∧ + f * s (n + 2) = 0 ∧ + ∃ A B : E, star A * A = f ∧ star B * B = f ∧ star A * B = 0 ∧ + A * star A + B * star B = f ∧ + (∀ i, g i = zeroCornerRow f A B n i) ∧ + ∃ z : E, star z * z = 1 ∧ f * z = z := by + let z := s (n + 2) + let r := s (n + 1) + let q := 1 - z * star z + have hz : star z * z = 1 := by simpa only [z, ite_true] using hs (n + 2) (n + 2) + have hrr : star r * r = 1 := by simpa only [r, ite_true] using hs (n + 1) (n + 1) + have hqstar : star q = q := by simp only [q, star_sub, star_one, star_mul, star_star] + have hqq : q * q = q := by + have hzz : (z * star z) * (z * star z) = z * star z := by + calc + _ = z * (star z * z) * star z := by noncomm_ring + _ = _ := by rw [hz, mul_one] + dsimp only [q] + noncomm_ring [hzz] + have hz₁ : star z * s (n + 3) = 0 := by simp only [z, hs, show n + 2 ≠ n + 3 by omega, ite_false] + have hz₂ : star z * s (n + 4) = 0 := by simp only [z, hs, show n + 2 ≠ n + 4 by omega, ite_false] + have h₁₂ : star (s (n + 3)) * s (n + 4) = 0 := by simp only [hs, show n + 3 ≠ n + 4 by omega, ite_false] + obtain ⟨a, b, u₀, _hu₀, _ha, _hb, _hu₀eq, haa, hbb, hab, habsum⟩ := + exists_zero_corner_cuntz_pair z (s (n + 3)) (s (n + 4)) hz + (by simpa using hs (n + 3) (n + 3)) (by simpa using hs (n + 4) (n + 4)) + hz₁ hz₂ h₁₂ + change star a * a = q at haa + change star b * b = q at hbb + change a * star a + b * star b = q at habsum + obtain ⟨hqa, haq, hqb, hbq⟩ := relativeCuntzPair_support q a b hqstar hqq haa hbb hab habsum + let t := zeroCornerRow q a b n + have htl (i : Fin (n + 1)) : q * t i = t i := (zeroCornerRow_support q a b hqq hqa hqb hbq n i).1 + have htr (i : Fin (n + 1)) : t i * q = t i := (zeroCornerRow_support q a b hqq hqa hqb hbq n i).2 + have htt : ∀ i j, star (t i) * t j = if i = j then q else 0 := + zeroCornerRow_gram q a b hqstar hqq haa hbb hab hqa hqb hbq n + have ht : ∑ i, t i * star (t i) = q := zeroCornerRow_range_sum q a b hqstar hqq haq habsum n + let s' (i : Fin (n + 1)) := s i + have hs' (i j : Fin (n + 1)) : star (s' i) * s' j = if i = j then 1 else 0 := by + simpa only [s', Fin.ext_iff] using hs i j + have hri (i : Fin (n + 1)) : star r * s' i = 0 := by + change star (s (n + 1)) * s i = 0 + rw [hs, ite_eq_right (by omega)] + have hzi (i : Fin (n + 1)) : star z * s' i = 0 := by + change star (s (n + 2)) * s i = 0 + rw [hs, ite_eq_right (by omega)] + have hzr : star z * r = 0 := by simp only [z, r, hs, show n + 2 ≠ n + 1 by omega, ite_false] + obtain ⟨m, hm⟩ := exists_nat_one_div_lt (show (0 : ℝ) < min ε ((ε / 4) ^ 2) by positivity) + have hmε : ((m : ℝ) + 1)⁻¹ < ε := by simpa only [one_div] using hm.trans_le (min_le_left _ _) + have hmSq : ((m : ℝ) + 1)⁻¹ < (ε / 4) ^ 2 := by simpa only [one_div] using hm.trans_le (min_le_right _ _) + let v := finiteRowIsometry s' t r q m + let f := finiteRowRange s' t r q m + have hvg : star v * v = q := finiteRowIsometry_gram s' t r q hqq hqstar hrr hri hs' htr ht m + have hvq : v * q = v := relativeIsometry_mul_support v q hvg hqstar hqq + have hfv : f * v = v := by change (v * star v) * v = v; rw [mul_assoc, hvg, hvq] + obtain ⟨u, _hu, _hueq, _huq, huw, hwrange⟩ := + exists_connected_finiteRowCompletion s' t r q z hqq hqstar hrr hri hs' htr ht hz hzr hzi rfl m + let g (i : Fin (n + 1)) := v * t i * star v + have hg := transported_row v q t hvg hvq htl htr htt ht + have hqne : q ≠ 0 := by + intro hq0 + have hqa₁ : q * s (n + 3) = s (n + 3) := by + dsimp only [q] + rw [sub_mul, one_mul, mul_assoc, hz₁, mul_zero, sub_zero] + rw [hq0, zero_mul] at hqa₁ + have hx := hs (n + 3) (n + 3) + rw [← hqa₁, star_zero, zero_mul, ite_eq_left rfl] at hx + exact zero_ne_one hx + refine ⟨f, (u : E) * z, g, ?_, finiteRowRange_star s' t r q m, + finiteRowRange_sq s' t r q hqq hqstar hrr hri hs' htr ht m, huw, hwrange, + hg.1, hg.2, ?_, ?_, ?_, ?_⟩ + · intro hf + have hv0 : v = 0 := by rw [← hfv, hf, zero_mul] + have hq0 : q = 0 := by rw [← hvg, hv0, star_zero, zero_mul] + exact hqne hq0 + · intro i + have hbound := finiteRowRange_commutator_bound s' t r q hqq hqstar hrr hri hs' htr ht htt m i + have hsqrt₁ := Real.sq_sqrt (show 0 ≤ ((m : ℝ) + 1)⁻¹ by positivity) + have hsqrt₂ := Real.sq_sqrt (show 0 ≤ 2 / ((m : ℝ) + 1) by positivity) + have hc : 2 / ((m : ℝ) + 1) = 2 * ((m : ℝ) + 1)⁻¹ := by rw [div_eq_mul_inv] + have h₁ : Real.sqrt (((m : ℝ) + 1)⁻¹) < ε / 4 := by nlinarith [Real.sqrt_nonneg (((m : ℝ) + 1)⁻¹)] + have h₂ : Real.sqrt (2 / ((m : ℝ) + 1)) < ε / 2 := by + have hsqrt₂' := hsqrt₂.trans hc + nlinarith [Real.sqrt_nonneg (2 / ((m : ℝ) + 1))] + exact hbound.trans_lt (by linarith) + · intro i + have hcomp : f * s i * f = (((m : ℝ) / ((m : ℝ) + 1) : ℝ) : ℂ) • g i := by + calc + _ = v * (star v * s' i * v) * star v := by change (v * star v) * s' i * (v * star v) = _; noncomm_ring + _ = _ := by + rw [finiteRowIsometry_compression s' t r q hqq hqstar hrr hri hs' htr ht m i, + mul_smul_comm, smul_mul_assoc] + have hgn : ‖g i‖ ≤ 1 := by + have he := congrArg norm (hg.1 i i) + simp only [ite_true, CStarRing.norm_star_mul_self] at he + change ‖g i‖ * ‖g i‖ = ‖f‖ at he + have hfn : ‖f‖ ≤ 1 := IsStarProjection.norm_le _ (isStarProjection_iff'.mpr + ⟨finiteRowRange_sq s' t r q hqq hqstar hrr hri hs' htr ht m, finiteRowRange_star s' t r q m⟩) + nlinarith [norm_nonneg (g i)] + have he : f * s i * f - g i = -(((((m : ℝ) + 1)⁻¹ : ℝ) : ℂ) • g i) := by + rw [hcomp] + have hc : ((m : ℝ) / ((m : ℝ) + 1)) - 1 = -((m : ℝ) + 1)⁻¹ := by + have hn : (m : ℝ) + 1 ≠ 0 := by positivity + field_simp + ring + calc + _ = (((m : ℝ) / ((m : ℝ) + 1) - 1 : ℝ) : ℂ) • g i := by push_cast; module + _ = _ := by rw [hc, Complex.ofReal_neg, neg_smul] + rw [he, norm_neg, norm_smul, Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg (by positivity : 0 ≤ ((m : ℝ) + 1)⁻¹)] + exact (mul_le_of_le_one_right (by positivity) hgn).trans_lt hmε + · exact (finiteRowRange_vacuum_norm s' t r q hqq hqstar hrr hri hs' htr ht m).trans_lt hmε + · refine ⟨finiteRowRange_unused s' t r q z hzr hzi m, ?_⟩ + let pair : Fin 2 → E := ![a, b] + have hba : star b * a = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hab + have hpl (i : Fin 2) : q * pair i = pair i := by + fin_cases i + · exact hqa + · exact hqb + have hpr (i : Fin 2) : pair i * q = pair i := by + fin_cases i + · exact haq + · exact hbq + have hpg (i j : Fin 2) : star (pair i) * pair j = if i = j then q else 0 := by + fin_cases i <;> fin_cases j <;> simp [pair, haa, hbb, hab, hba] + have hps : ∑ i, pair i * star (pair i) = q := by + simpa only [Fin.sum_univ_two, pair, Matrix.cons_val_zero, Matrix.cons_val_one, + Matrix.cons_val_fin_one] using habsum + have hpair := transported_row v q pair hvg hvq hpl hpr hpg hps + have hvf : v * star v = f := rfl + refine ⟨v * a * star v, v * b * star v, ?_, ?_, ?_, ?_, ?_, ?_⟩ + · simpa only [pair, Matrix.cons_val_zero, ite_true, hvf] using hpair.1 0 0 + · simpa only [pair, Matrix.cons_val_one, Matrix.cons_val_fin_one, ite_true, hvf] using hpair.1 1 1 + · simpa only [pair, Matrix.cons_val_zero, Matrix.cons_val_one, + Matrix.cons_val_fin_one, Fin.zero_ne_one, ite_false] using hpair.1 0 1 + · simpa only [Fin.sum_univ_two, pair, Matrix.cons_val_zero, Matrix.cons_val_one, + Matrix.cons_val_fin_one, hvf] using hpair.2 + · intro i + exact transported_zeroCornerRow q a b v hqq hqa hqb hbq hvg hvq n i + · have hqz : q * s (n + 3) = s (n + 3) := by + dsimp only [q] + rw [sub_mul, one_mul, mul_assoc, hz₁, mul_zero, sub_zero] + refine ⟨v * s (n + 3), ?_, ?_⟩ + · rw [star_mul] + calc + _ = star (s (n + 3)) * (star v * v) * s (n + 3) := by noncomm_ring + _ = 1 := by + rw [hvg, mul_assoc, hqz] + simpa only [ite_true] using hs (n + 3) (n + 3) + · rw [← mul_assoc, hfv] + +/-- The explicit finite split, retaining its transported binary generators. -/ +lemma exists_canonical_vacuum_split_with_pair [Nontrivial E] (s : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (n : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ (f w : E) (g : Fin (n + 1) → E), + f ≠ 0 ∧ star f = f ∧ f * f = f ∧ + star w * w = 1 ∧ w * star w = 1 - f ∧ + (∀ i j, star (g i) * g j = if i = j then f else 0) ∧ + (∑ i, g i * star (g i)) = f ∧ + (∀ i : Fin (n + 1), ‖s i * f - f * s i‖ < ε) ∧ + (∀ i : Fin (n + 1), ‖f * s i * f - g i‖ < ε) ∧ + ‖f * (1 - ∑ i : Fin (n + 1), s i * star (s i)) * f‖ < ε ∧ + f * s (n + 2) = 0 ∧ + ∃ A B : E, star A * A = f ∧ star B * B = f ∧ star A * B = 0 ∧ + A * star A + B * star B = f ∧ + ∀ i, g i = zeroCornerRow f A B n i := by + obtain ⟨f, w, g, hf, hfs, hff, hw, hwr, hg, hgs, hc, hfg, hfv, hfz, + A, B, hA, hB, hAB, hsum, he, _hz⟩ := + exists_canonical_vacuum_split_with_pair_and_isometry s hs n ε hε + exact ⟨f, w, g, hf, hfs, hff, hw, hwr, hg, hgs, hc, hfg, hfv, hfz, + A, B, hA, hB, hAB, hsum, he⟩ + +/-- Every finite canonical row admits the explicit vacuum-killing split. +The returned row is coisometric in `f`, and an actual isometry fills `1-f`. -/ +lemma exists_canonical_vacuum_split [Nontrivial E] (s : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (n : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ (f w : E) (g : Fin (n + 1) → E), + f ≠ 0 ∧ star f = f ∧ f * f = f ∧ + star w * w = 1 ∧ w * star w = 1 - f ∧ + (∀ i j, star (g i) * g j = if i = j then f else 0) ∧ + (∑ i, g i * star (g i)) = f ∧ + (∀ i : Fin (n + 1), ‖s i * f - f * s i‖ < ε) ∧ + (∀ i : Fin (n + 1), ‖f * s i * f - g i‖ < ε) ∧ + ‖f * (1 - ∑ i : Fin (n + 1), s i * star (s i)) * f‖ < ε ∧ + f * s (n + 2) = 0 := by + obtain ⟨f, w, g, hf, hfs, hff, hw, hwr, hg, hgs, hc, hfg, hfv, hfz, _hp⟩ := + exists_canonical_vacuum_split_with_pair s hs n ε hε + exact ⟨f, w, g, hf, hfs, hff, hw, hwr, hg, hgs, hc, hfg, hfv, hfz⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ZeroCorner.lean b/lean/OAI/Analysis/OInfinity/ZeroCorner.lean new file mode 100644 index 0000000000000000000000000000000000000000..e1ff5019dbe9836e538f9896b47ac91cb73ceb49 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ZeroCorner.lean @@ -0,0 +1,427 @@ +import OAI.Analysis.OInfinity.CentralIsometries + +namespace OAI + +/-! # An explicit coisometric pair in the complementary corner + +Three orthogonal isometries suffice to construct two relative isometries +whose ranges add up to `1 - r₀ * star r₀`. The construction uses the checked +two-swap completion, with its connected unitary retained explicitly. The +unit of this pair is the stated corner projection, not the ambient unit. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +lemma partialIsometrySwap_commutes (a y : E) + (ha : Commute a y) (hastar : Commute (star a) y) : + Commute (partialIsometrySwap a) y := by + exact (ha.add_left hastar).add_left + (((Commute.one_left y).sub_left (hastar.mul_left ha)).sub_left (ha.mul_left hastar)) + +lemma partialIsometryCompletion_commutes (r p v y : E) + (hr : Commute r y) (hrstar : Commute (star r) y) + (hp : Commute p y) (hpstar : Commute (star p) y) + (hv : Commute v y) (hvstar : Commute (star v) y) : + Commute (partialIsometryCompletion r p v) y := by + apply Commute.mul_left + · apply partialIsometrySwap_commutes + · exact hv.mul_left hrstar + · simpa only [star_mul, star_star] using hr.mul_left hvstar + · apply partialIsometrySwap_commutes + · exact hr.mul_left hp + · simpa only [star_mul] using hpstar.mul_left hrstar + +lemma exists_zero_corner_cuntz_pair [Nontrivial E] (r₀ r₁ r₂ : E) + (h₀ : star r₀ * r₀ = 1) (h₁ : star r₁ * r₁ = 1) (h₂ : star r₂ * r₂ = 1) + (h₀₁ : star r₀ * r₁ = 0) (h₀₂ : star r₀ * r₂ = 0) (h₁₂ : star r₁ * r₂ = 0) : + let q := 1 - r₀ * star r₀ + ∃ (a b : E) (u : unitary E), Joined (1 : unitary E) u ∧ + a = r₁ * q ∧ b = (u : E) * q ∧ + (u : E) = partialIsometryCompletion r₂ (r₀ * star r₀) + (((r₀ * star r₀) + r₁ * q) * star r₀) ∧ + star a * a = q ∧ star b * b = q ∧ star a * b = 0 ∧ + a * star a + b * star b = q := by + intro q + let p := r₀ * star r₀ + let a := r₁ * q + let z := p + a + let v := z * star r₀ + have hpstar : star p = p := by simp only [p, star_mul, star_star] + have hpp : p * p = p := by + dsimp only [p] + rw [mul_assoc, ← mul_assoc (star r₀), h₀, one_mul] + have hqstar : star q = q := by change star (1 - p) = 1 - p; rw [star_sub, star_one, hpstar] + have hqq : q * q = q := by change (1 - p) * (1 - p) = 1 - p; noncomm_ring [hpp] + have hpq : p * q = 0 := by change p * (1 - p) = 0; noncomm_ring [hpp] + have hqp : q * p = 0 := by change (1 - p) * p = 0; noncomm_ring [hpp] + have hpr₁ : p * r₁ = 0 := by + change (r₀ * star r₀) * r₁ = 0 + rw [mul_assoc, h₀₁, mul_zero] + have hr₁p : star r₁ * p = 0 := by + simpa only [star_mul, hpstar, star_zero] using congrArg star hpr₁ + have hpa : p * a = 0 := by dsimp only [a]; rw [← mul_assoc, hpr₁, zero_mul] + have hasp : star a * p = 0 := by + simpa only [star_mul, hpstar, star_zero] using congrArg star hpa + have hqa : q * a = a := by change (1 - p) * a = a; rw [sub_mul, one_mul, hpa, sub_zero] + have haq : a * q = a := by dsimp only [a]; rw [mul_assoc, hqq] + have haas : star a * a = q := by + dsimp only [a] + rw [star_mul, hqstar] + calc + _ = q * (star r₁ * r₁) * q := by noncomm_ring + _ = q := by rw [h₁, mul_one, hqq] + have hziso : star z * z = 1 := by + change star (p + a) * (p + a) = 1 + rw [star_add, hpstar, add_mul, mul_add, mul_add, hpp, hpa, hasp, haas] + change p + 0 + (0 + (1 - p)) = 1 + noncomm_ring + have hztarget : z * star z = p + a * star a := by + change (p + a) * star (p + a) = p + a * star a + rw [star_add, hpstar] + have hap : a * p = 0 := by dsimp only [a]; rw [mul_assoc, hqp, mul_zero] + have hpas' : p * star a = 0 := by + simpa only [star_mul, hpstar, star_zero] using congrArg star hap + noncomm_ring [hpp, hap, hpas'] + have hvsource : star v * v = p := by + change star (z * star r₀) * (z * star r₀) = p + rw [star_mul, star_star] + calc + _ = r₀ * (star z * z) * star r₀ := by noncomm_ring + _ = p := by rw [hziso, mul_one] + have hvtarget : v * star v = p + a * star a := by + change (z * star r₀) * star (z * star r₀) = _ + rw [star_mul, star_star] + calc + _ = z * (star r₀ * r₀) * star z := by noncomm_ring + _ = _ := by rw [h₀, mul_one, hztarget] + have hvpartial : v * star v * v = v := by + change (z * star r₀) * star (z * star r₀) * (z * star r₀) = z * star r₀ + rw [star_mul, star_star] + calc + _ = z * (star r₀ * r₀) * (star z * z) * star r₀ := by noncomm_ring + _ = _ := by rw [h₀, hziso, mul_one, mul_one] + have hpr₂ : p * r₂ = 0 := by + change (r₀ * star r₀) * r₂ = 0 + rw [mul_assoc, h₀₂, mul_zero] + have hasr₂ : star a * r₂ = 0 := by + dsimp only [a] + rw [star_mul, mul_assoc, h₁₂, mul_zero] + have hvr₂ : (v * star v) * r₂ = 0 := by + rw [hvtarget, add_mul, hpr₂, mul_assoc, hasr₂, mul_zero, add_zero] + obtain ⟨u, hu, hueq, huvp⟩ := exists_explicit_connected_unitary_extension v r₂ + hvpartial h₂ (by rw [hvsource]; exact hpr₂) hvr₂ + have hup : (u : E) * p = v := by simpa only [hvsource] using huvp + have hupu : (u : E) * p * star (u : E) = p + a * star a := by + calc + _ = ((u : E) * p) * star ((u : E) * p) := by + rw [star_mul, hpstar] + symm + calc + _ = (u : E) * (p * p) * star (u : E) := by noncomm_ring + _ = _ := by rw [hpp] + _ = _ := by rw [hup, hvtarget] + let b := (u : E) * q + have hbsource : star b * b = q := by + dsimp only [b] + rw [star_mul, hqstar] + calc + _ = q * (star (u : E) * (u : E)) * q := by noncomm_ring + _ = q := by rw [Unitary.coe_star_mul_self, mul_one, hqq] + have hbtarget : b * star b = q - a * star a := by + dsimp only [b] + rw [star_mul, hqstar] + calc + _ = (u : E) * q * star (u : E) := by + calc + _ = (u : E) * (q * q) * star (u : E) := by noncomm_ring + _ = _ := by rw [hqq] + _ = 1 - (p + a * star a) := by + change (u : E) * (1 - p) * star (u : E) = _ + rw [mul_sub, sub_mul, mul_one, Unitary.mul_star_self_of_mem u.property, hupu] + _ = _ := by change 1 - (p + a * star a) = (1 - p) - a * star a; abel + have hbq : b * q = b := by dsimp only [b]; rw [mul_assoc, hqq] + have hbpartial : b * star b * b = b := by rw [mul_assoc, hbsource, hbq] + have haapartial : (a * star a) * (a * star a) = a * star a := by + calc + _ = a * (star a * a) * star a := by noncomm_ring + _ = _ := by rw [haas, haq] + have haaq : (a * star a) * q = a * star a := by + have h := congrArg star hqa + simpa only [star_mul, hqstar, mul_assoc] using congrArg (fun y => a * y) h + have habproj : (a * star a) * (b * star b) = 0 := by + rw [hbtarget, mul_sub, haaq, haapartial, sub_self] + have haab : (a * star a) * b = 0 := by + rw [← hbpartial, ← mul_assoc, habproj, zero_mul] + have hab : star a * b = 0 := by + apply (CStarRing.star_mul_self_eq_zero_iff _).mp + rw [star_mul, star_star] + calc + _ = star b * ((a * star a) * b) := by noncomm_ring + _ = 0 := by rw [haab, mul_zero] + refine ⟨a, b, u, hu, rfl, rfl, ?_, haas, hbsource, hab, ?_⟩ + · simpa only [hvsource] using hueq + · rw [hbtarget] + abel + +/-- The zero-corner completion is a fixed finite polynomial, so it retains +exact commutation with every element commuting with the three input +isometries and their adjoints. -/ +lemma zeroCornerCompletion_commutes (r₀ r₁ r₂ y : E) + (h₀ : Commute r₀ y) (h₀s : Commute (star r₀) y) + (h₁ : Commute r₁ y) (h₁s : Commute (star r₁) y) + (h₂ : Commute r₂ y) (h₂s : Commute (star r₂) y) : + Commute (partialIsometryCompletion r₂ (r₀ * star r₀) + (((r₀ * star r₀) + r₁ * (1 - r₀ * star r₀)) * star r₀)) y := by + have hp := h₀.mul_left h₀s + have hps : Commute (star (r₀ * star r₀)) y := by + simpa only [star_mul, star_star] using hp + have hq := (Commute.one_left y).sub_left hp + have hqs : Commute (star (1 - r₀ * star r₀)) y := by + simpa only [star_sub, star_one, star_mul, star_star] using hq + apply partialIsometryCompletion_commutes _ _ _ _ h₂ h₂s hp hps + · exact (hp.add_left (h₁.mul_left hq)).mul_left h₀s + · simpa only [star_mul, star_add, star_star] using + h₀.mul_left (hps.add_left (hqs.mul_left h₁s)) + +private structure ZeroCornerControl (x a : E) (N C : ℝ) : Prop where + norm_bound : ‖a‖ ≤ N + bound : ‖a * x - x * a‖ ≤ C + star_bound : ‖star a * x - x * star a‖ ≤ C + +private lemma zeroCornerControl_one [Nontrivial E] (x : E) : ZeroCornerControl x 1 1 0 := by + constructor <;> simp + +private lemma zeroCornerControl_star {x a : E} {N C : ℝ} + (h : ZeroCornerControl x a N C) : ZeroCornerControl x (star a) N C := by + exact ⟨by simpa only [norm_star] using h.norm_bound, h.star_bound, + by simpa only [star_star] using h.bound⟩ + +private lemma zeroCornerControl_add {x a b : E} {N M C D : ℝ} + (ha : ZeroCornerControl x a N C) (hb : ZeroCornerControl x b M D) : + ZeroCornerControl x (a + b) (N + M) (C + D) := by + constructor + · exact (norm_add_le _ _).trans (add_le_add ha.norm_bound hb.norm_bound) + · have he : (a + b) * x - x * (a + b) = (a * x - x * a) + (b * x - x * b) := by + noncomm_ring + rw [he] + exact (norm_add_le _ _).trans (add_le_add ha.bound hb.bound) + · have he : star (a + b) * x - x * star (a + b) = + (star a * x - x * star a) + (star b * x - x * star b) := by + rw [star_add]; noncomm_ring + rw [he] + exact (norm_add_le _ _).trans (add_le_add ha.star_bound hb.star_bound) + +private lemma zeroCornerControl_sub {x a b : E} {N M C D : ℝ} + (ha : ZeroCornerControl x a N C) (hb : ZeroCornerControl x b M D) : + ZeroCornerControl x (a - b) (N + M) (C + D) := by + constructor + · exact (norm_sub_le _ _).trans (add_le_add ha.norm_bound hb.norm_bound) + · have he : (a - b) * x - x * (a - b) = (a * x - x * a) - (b * x - x * b) := by + noncomm_ring + rw [he] + exact (norm_sub_le _ _).trans (add_le_add ha.bound hb.bound) + · have he : star (a - b) * x - x * star (a - b) = + (star a * x - x * star a) - (star b * x - x * star b) := by + rw [star_sub]; noncomm_ring + rw [he] + exact (norm_sub_le _ _).trans (add_le_add ha.star_bound hb.star_bound) + +private lemma zeroCornerControl_mul_bound {x a b : E} {N M C D : ℝ} + (haN : ‖a‖ ≤ N) (hbM : ‖b‖ ≤ M) + (ha : ‖a * x - x * a‖ ≤ C) (hb : ‖b * x - x * b‖ ≤ D) : + ‖(a * b) * x - x * (a * b)‖ ≤ N * D + C * M := by + have hC : 0 ≤ C := (norm_nonneg _).trans ha + have hD : 0 ≤ D := (norm_nonneg _).trans hb + have he : (a * b) * x - x * (a * b) = + a * (b * x - x * b) + (a * x - x * a) * b := by noncomm_ring + rw [he] + calc + _ ≤ ‖a * (b * x - x * b)‖ + ‖(a * x - x * a) * b‖ := norm_add_le _ _ + _ ≤ ‖a‖ * ‖b * x - x * b‖ + ‖a * x - x * a‖ * ‖b‖ := + add_le_add (norm_mul_le _ _) (norm_mul_le _ _) + _ ≤ N * D + C * M := add_le_add + (mul_le_mul haN hb (norm_nonneg _) ((norm_nonneg _).trans haN)) + (mul_le_mul ha hbM (norm_nonneg _) hC) + +private lemma zeroCornerControl_mul {x a b : E} {N M C D : ℝ} + (ha : ZeroCornerControl x a N C) (hb : ZeroCornerControl x b M D) : + ZeroCornerControl x (a * b) (N * M) (N * D + C * M) := by + constructor + · exact (norm_mul_le _ _).trans + (mul_le_mul ha.norm_bound hb.norm_bound (norm_nonneg _) ((norm_nonneg _).trans ha.norm_bound)) + · exact zeroCornerControl_mul_bound ha.norm_bound hb.norm_bound ha.bound hb.bound + · rw [star_mul] + have h := zeroCornerControl_mul_bound + (zeroCornerControl_star hb).norm_bound (zeroCornerControl_star ha).norm_bound + hb.star_bound ha.star_bound + convert h using 1; ring + +private lemma zeroCornerControl_swap [Nontrivial E] {x a : E} {N C : ℝ} + (ha : ZeroCornerControl x a N C) : + ZeroCornerControl x (partialIsometrySwap a) + (N + N + (1 + N * N + N * N)) + (C + C + (0 + (N * C + C * N) + (N * C + C * N))) := by + exact zeroCornerControl_add (zeroCornerControl_add ha (zeroCornerControl_star ha)) + (zeroCornerControl_sub (zeroCornerControl_sub (zeroCornerControl_one x) + (zeroCornerControl_mul (zeroCornerControl_star ha) ha)) + (zeroCornerControl_mul ha (zeroCornerControl_star ha))) + +/-- A uniform polynomial estimate, valid before the Cuntz relations are used. +The deliberately coarse constant keeps the input tolerance independent of +the test element and of the ambient algebra. -/ +lemma zeroCornerCompletion_commutator_bound [Nontrivial E] (r₀ r₁ r₂ x : E) (δ : ℝ) + (hN : ∀ r ∈ ({r₀, r₁, r₂} : Set E), ‖r‖ ≤ 1) + (hC : ∀ r ∈ ({r₀, r₁, r₂} : Set E), + ‖r * x - x * r‖ ≤ δ ∧ ‖star r * x - x * star r‖ ≤ δ) : + let U := partialIsometryCompletion r₂ (r₀ * star r₀) + (((r₀ * star r₀) + r₁ * (1 - r₀ * star r₀)) * star r₀) + ‖U * x - x * U‖ ≤ 1290 * δ ∧ ‖star U * x - x * star U‖ ≤ 1290 * δ := by + have h₀ : ZeroCornerControl x r₀ 1 δ := + ⟨hN r₀ (by simp), (hC r₀ (by simp)).1, (hC r₀ (by simp)).2⟩ + have h₁ : ZeroCornerControl x r₁ 1 δ := + ⟨hN r₁ (by simp), (hC r₁ (by simp)).1, (hC r₁ (by simp)).2⟩ + have h₂ : ZeroCornerControl x r₂ 1 δ := + ⟨hN r₂ (by simp), (hC r₂ (by simp)).1, (hC r₂ (by simp)).2⟩ + have hp := zeroCornerControl_mul h₀ (zeroCornerControl_star h₀) + have hq := zeroCornerControl_sub (zeroCornerControl_one x) hp + have hz := zeroCornerControl_add hp (zeroCornerControl_mul h₁ hq) + have hv := zeroCornerControl_mul hz (zeroCornerControl_star h₀) + have hA := zeroCornerControl_swap (zeroCornerControl_mul hv (zeroCornerControl_star h₂)) + have hB := zeroCornerControl_swap (zeroCornerControl_mul h₂ hp) + have hU := zeroCornerControl_mul hA hB + dsimp only [partialIsometryCompletion] + constructor + · convert hU.bound using 1; ring + · convert hU.star_bound using 1; ring + +lemma zeroCornerPair_commutator_bound [Nontrivial E] (r₀ r₁ r₂ x : E) (δ : ℝ) (hδ : 0 ≤ δ) + (hN : ∀ r ∈ ({r₀, r₁, r₂} : Set E), ‖r‖ ≤ 1) + (hC : ∀ r ∈ ({r₀, r₁, r₂} : Set E), + ‖r * x - x * r‖ ≤ δ ∧ ‖star r * x - x * star r‖ ≤ δ) + (u : unitary E) + (hu : (u : E) = partialIsometryCompletion r₂ (r₀ * star r₀) + (((r₀ * star r₀) + r₁ * (1 - r₀ * star r₀)) * star r₀)) : + let q := 1 - r₀ * star r₀ + ‖(r₁ * q) * x - x * (r₁ * q)‖ ≤ 2582 * δ ∧ + ‖((u : E) * q) * x - x * ((u : E) * q)‖ ≤ 2582 * δ := by + have h₀ : ZeroCornerControl x r₀ 1 δ := + ⟨hN r₀ (by simp), (hC r₀ (by simp)).1, (hC r₀ (by simp)).2⟩ + have h₁ : ZeroCornerControl x r₁ 1 δ := + ⟨hN r₁ (by simp), (hC r₁ (by simp)).1, (hC r₁ (by simp)).2⟩ + have hq := zeroCornerControl_sub (zeroCornerControl_one x) + (zeroCornerControl_mul h₀ (zeroCornerControl_star h₀)) + have hubounds := zeroCornerCompletion_commutator_bound r₀ r₁ r₂ x δ hN hC + have hU : ZeroCornerControl x (u : E) 1 (1290 * δ) := by + refine ⟨(CStarRing.norm_coe_unitary u).le, ?_, ?_⟩ + · simpa only [hu] using hubounds.1 + · simpa only [hu] using hubounds.2 + constructor + · have hb := (zeroCornerControl_mul h₁ hq).bound + nlinarith + · have hb := (zeroCornerControl_mul hU hq).bound + nlinarith + +private lemma zeroCorner_star_commutator_norm (a x : E) : + ‖star a * x - x * star a‖ = ‖a * star x - star x * a‖ := by + rw [← norm_star (a * star x - star x * a)] + simp only [star_sub, star_mul, star_star] + exact norm_sub_rev _ _ + +/-- Global central rows produce a coisometric pair in their complementary +corner with arbitrarily small finite-set commutators. The corner unit is +kept explicit in the conclusion. -/ +lemma exists_approximately_central_zero_corner_pair [Nontrivial E] (s t : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hc : ∀ i j, Commute (s i) (t j) ∧ Commute (s i) (star (t j))) + (n : ℕ) (δ : ℝ) (hδ : 0 < δ) : + ∃ (q a b : E), q ≠ 0 ∧ star q = q ∧ q * q = q ∧ + star a * a = q ∧ star b * b = q ∧ star a * b = 0 ∧ + a * star a + b * star b = q ∧ + (∀ i < n, ‖a * s i - s i * a‖ < δ ∧ ‖b * s i - s i * b‖ < δ ∧ + ‖a * star (s i) - star (s i) * a‖ < δ ∧ + ‖b * star (s i) - star (s i) * b‖ < δ) ∧ + ∀ k, Commute a (t k) ∧ Commute b (t k) ∧ + Commute a (star (t k)) ∧ Commute b (star (t k)) := by + let η := δ / 3000 + have hη : 0 < η := by dsimp only [η]; positivity + obtain ⟨r, hr, hcomm, hother⟩ := exists_approximately_central_cuntz_row s t hs hc n η hη + have hiso (j : ℕ) : star (r j) * r j = 1 := by simpa using hr j j + have hnorm (j : ℕ) : ‖r j‖ = 1 := by + have h := congrArg norm (hiso j) + rw [CStarRing.norm_star_mul_self, norm_one] at h + nlinarith [norm_nonneg (r j)] + let q := 1 - r 0 * star (r 0) + obtain ⟨a, b, u, hujoin, ha, hb, hu, haa, hbb, hab, hsum⟩ := + exists_zero_corner_cuntz_pair (r 0) (r 1) (r 2) (hiso 0) (hiso 1) (hiso 2) + (by simpa using hr 0 1) (by simpa using hr 0 2) (by simpa using hr 1 2) + have hqstar : star q = q := by simp only [q, star_sub, star_one, star_mul, star_star] + have hp : (r 0 * star (r 0)) * (r 0 * star (r 0)) = r 0 * star (r 0) := by + rw [mul_assoc, ← mul_assoc (star (r 0)), hiso, one_mul] + have hqq : q * q = q := by dsimp only [q]; noncomm_ring [hp] + have hqne : q ≠ 0 := by + intro hzero + have hqr : q * r 1 = r 1 := by + dsimp only [q] + rw [sub_mul, one_mul, mul_assoc, show star (r 0) * r 1 = 0 by simpa using hr 0 1, + mul_zero, sub_zero] + rw [hzero, zero_mul] at hqr + have hz := hiso 1 + rw [← hqr, star_zero, zero_mul] at hz + exact zero_ne_one hz + have hN : ∀ z ∈ ({r 0, r 1, r 2} : Set E), ‖z‖ ≤ 1 := by + intro z hz + simp only [Set.mem_insert_iff, Set.mem_singleton_iff] at hz + rcases hz with rfl | rfl | rfl <;> exact (hnorm _).le + refine ⟨q, a, b, hqne, hqstar, hqq, haa, hbb, hab, hsum, ?_, ?_⟩ + · intro i hi + have hC : ∀ z ∈ ({r 0, r 1, r 2} : Set E), + ‖z * s i - s i * z‖ ≤ η ∧ ‖star z * s i - s i * star z‖ ≤ η := by + intro z hz + have hz' (j : ℕ) : ‖r j * s i - s i * r j‖ ≤ η ∧ + ‖star (r j) * s i - s i * star (r j)‖ ≤ η := by + exact ⟨(hcomm j i hi).1.le, + by rw [zeroCorner_star_commutator_norm]; exact (hcomm j i hi).2.le⟩ + simp only [Set.mem_insert_iff, Set.mem_singleton_iff] at hz + rcases hz with rfl | rfl | rfl <;> exact hz' _ + have hCs : ∀ z ∈ ({r 0, r 1, r 2} : Set E), + ‖z * star (s i) - star (s i) * z‖ ≤ η ∧ + ‖star z * star (s i) - star (s i) * star z‖ ≤ η := by + intro z hz + have hz' (j : ℕ) : ‖r j * star (s i) - star (s i) * r j‖ ≤ η ∧ + ‖star (r j) * star (s i) - star (s i) * star (r j)‖ ≤ η := by + exact ⟨(hcomm j i hi).2.le, by + rw [zeroCorner_star_commutator_norm, star_star] + exact (hcomm j i hi).1.le⟩ + simp only [Set.mem_insert_iff, Set.mem_singleton_iff] at hz + rcases hz with rfl | rfl | rfl <;> exact hz' _ + have hsmall : 2582 * η < δ := by dsimp only [η]; nlinarith + have h₁ := zeroCornerPair_commutator_bound (r 0) (r 1) (r 2) (s i) η hη.le hN hC u hu + have h₂ := zeroCornerPair_commutator_bound (r 0) (r 1) (r 2) (star (s i)) η hη.le hN hCs u hu + dsimp only at h₁ h₂ + rw [← ha, ← hb] at h₁ h₂ + exact ⟨h₁.1.trans_lt hsmall, h₁.2.trans_lt hsmall, + h₂.1.trans_lt hsmall, h₂.2.trans_lt hsmall⟩ + · intro k + have hpoly (y : E) (hry : ∀ j, Commute (r j) y ∧ Commute (star (r j)) y) : + Commute a y ∧ Commute b y := by + have hqc := (Commute.one_left y).sub_left ((hry 0).1.mul_left (hry 0).2) + have huc : Commute (u : E) y := by + rw [hu] + exact zeroCornerCompletion_commutes _ _ _ _ + (hry 0).1 (hry 0).2 (hry 1).1 (hry 1).2 (hry 2).1 (hry 2).2 + exact ⟨by rw [ha]; exact (hry 1).1.mul_left hqc, + by rw [hb]; exact huc.mul_left hqc⟩ + have h₁ := hpoly (t k) (fun j => ⟨(hother j k).1, (hother j k).2.star_left⟩) + have h₂ := hpoly (star (t k)) (fun j => ⟨(hother j k).2, (hother j k).1.star_star⟩) + exact ⟨h₁.1, h₁.2, h₂.1, h₂.2⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ZeroCornerRows.lean b/lean/OAI/Analysis/OInfinity/ZeroCornerRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..3710780f88a624381cf51fa73cefebae0ffab653 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ZeroCornerRows.lean @@ -0,0 +1,280 @@ +import OAI.Analysis.OInfinity.ZeroCorner + +namespace OAI + +/-! # Finite Cuntz rows in the explicit complementary corner + +Repeatedly splitting the first range of a relative Cuntz pair produces every +finite row size. All ranges still sum to the same projection `q`; the +complement `1 - q` is retained. The commutator estimate grows only linearly +with the number of splittings. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- Right support follows from the relative isometry equation. -/ +lemma relativeIsometry_mul_support (a q : E) (ha : star a * a = q) + (hqstar : star q = q) (hqq : q * q = q) : a * q = a := by + have hz : star (a * q - a) * (a * q - a) = 0 := by + rw [star_sub, star_mul, hqstar] + calc + _ = q * (star a * a) * q - q * (star a * a) - (star a * a) * q + star a * a := by + noncomm_ring + _ = 0 := by simp only [ha, hqq]; abel + exact sub_eq_zero.mp ((CStarRing.star_mul_self_eq_zero_iff _).mp hz) + +lemma relativeCuntzPair_support (q a b : E) (hqstar : star q = q) (hqq : q * q = q) + (ha : star a * a = q) (hb : star b * b = q) (hab : star a * b = 0) + (hsum : a * star a + b * star b = q) : + q * a = a ∧ a * q = a ∧ q * b = b ∧ b * q = b := by + have haq := relativeIsometry_mul_support a q ha hqstar hqq + have hbq := relativeIsometry_mul_support b q hb hqstar hqq + have hba : star b * a = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hab + refine ⟨?_, haq, ?_, hbq⟩ + · rw [← hsum, add_mul, mul_assoc, ha, haq, mul_assoc, hba, mul_zero, add_zero] + · rw [← hsum, add_mul, mul_assoc, hab, mul_zero, zero_add, mul_assoc, hb, hbq] + +/-- At stage zero the row is the corner unit. Every successor replaces it +by `b` followed by the old row multiplied on the left by `a`. -/ +def zeroCornerRow (q a b : E) : (n : ℕ) → Fin (n + 1) → E + | 0, _ => q + | n + 1, i => Fin.cases b (fun j => a * zeroCornerRow q a b n j) i + +lemma zeroCornerRow_support (q a b : E) (hqq : q * q = q) + (hqa : q * a = a) (hqb : q * b = b) (hbq : b * q = b) : + ∀ n i, q * zeroCornerRow q a b n i = zeroCornerRow q a b n i ∧ + zeroCornerRow q a b n i * q = zeroCornerRow q a b n i := by + intro n + induction n with + | zero => intro i; exact ⟨hqq, hqq⟩ + | succ n ih => + intro i + refine Fin.cases ?_ (fun j => ?_) i + · exact ⟨hqb, hbq⟩ + · change q * (a * zeroCornerRow q a b n j) = a * zeroCornerRow q a b n j ∧ + (a * zeroCornerRow q a b n j) * q = a * zeroCornerRow q a b n j + exact ⟨by rw [← mul_assoc, hqa], by rw [mul_assoc, (ih j).2]⟩ + +lemma zeroCornerRow_gram (q a b : E) (hqstar : star q = q) (hqq : q * q = q) + (ha : star a * a = q) (hb : star b * b = q) (hab : star a * b = 0) + (hqa : q * a = a) (hqb : q * b = b) (hbq : b * q = b) : + ∀ n i j, star (zeroCornerRow q a b n i) * zeroCornerRow q a b n j = + if i = j then q else 0 := by + have hba : star b * a = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hab + intro n + induction n with + | zero => + intro i j + have hij : i = j := by omega + simp only [zeroCornerRow, hqstar, hqq, hij, ite_true] + | succ n ih => + intro i j + refine Fin.cases ?_ (fun i => ?_) i + · refine Fin.cases ?_ (fun j => ?_) j + · simpa only [zeroCornerRow, Fin.cases_zero, ite_true] using hb + · simp only [zeroCornerRow, Fin.cases_zero, Fin.cases_succ, (Fin.succ_ne_zero j).symm, + ite_false, ← mul_assoc, hba, zero_mul] + · refine Fin.cases ?_ (fun j => ?_) j + · simp only [zeroCornerRow, Fin.cases_zero, Fin.cases_succ, Fin.succ_ne_zero, + ite_false, star_mul, mul_assoc, hab, mul_zero] + · simp only [zeroCornerRow, Fin.cases_succ, star_mul, Fin.succ_inj] + calc + _ = star (zeroCornerRow q a b n i) * (star a * a) * + zeroCornerRow q a b n j := by noncomm_ring + _ = star (zeroCornerRow q a b n i) * (q * zeroCornerRow q a b n j) := by + rw [ha, mul_assoc] + _ = _ := by + rw [(zeroCornerRow_support q a b hqq hqa hqb hbq n j).1, ih] + +lemma zeroCornerRow_range_sum (q a b : E) (hqstar : star q = q) (hqq : q * q = q) + (haq : a * q = a) (hsum : a * star a + b * star b = q) : + ∀ n, ∑ i, zeroCornerRow q a b n i * star (zeroCornerRow q a b n i) = q := by + intro n + induction n with + | zero => + change (∑ _i : Fin 1, q * star q) = q + rw [Fin.sum_univ_one, hqstar, hqq] + | succ n ih => + rw [Fin.sum_univ_succ] + simp only [zeroCornerRow, Fin.cases_zero, Fin.cases_succ, star_mul] + calc + _ = b * star b + a * (∑ i, zeroCornerRow q a b n i * + star (zeroCornerRow q a b n i)) * star a := by + rw [Finset.mul_sum, Finset.sum_mul] + congr 1 + apply Finset.sum_congr rfl + intro i _ + noncomm_ring + _ = q := by rw [ih, haq, add_comm, hsum] + +lemma zeroCornerRow_norm_le (q a b : E) (hq : ‖q‖ ≤ 1) (ha : ‖a‖ ≤ 1) (hb : ‖b‖ ≤ 1) : + ∀ n i, ‖zeroCornerRow q a b n i‖ ≤ 1 := by + intro n + induction n with + | zero => intro i; exact hq + | succ n ih => + intro i + refine Fin.cases hb (fun j => ?_) i + exact (norm_mul_le _ _).trans (by + simpa only [one_mul] using mul_le_mul ha (ih j) + (norm_nonneg (zeroCornerRow q a b n j)) zero_le_one) + +private lemma row_product_commutator_le (a b x : E) + (ha : ‖a‖ ≤ 1) (hb : ‖b‖ ≤ 1) : + ‖(a * b) * x - x * (a * b)‖ ≤ ‖a * x - x * a‖ + ‖b * x - x * b‖ := by + have he : (a * b) * x - x * (a * b) = + (a * x - x * a) * b + a * (b * x - x * b) := by noncomm_ring + rw [he] + calc + _ ≤ ‖(a * x - x * a) * b‖ + ‖a * (b * x - x * b)‖ := norm_add_le _ _ + _ ≤ ‖a * x - x * a‖ * ‖b‖ + ‖a‖ * ‖b * x - x * b‖ := + add_le_add (norm_mul_le _ _) (norm_mul_le _ _) + _ ≤ _ := add_le_add + (by simpa only [mul_one] using mul_le_mul_of_nonneg_left hb (norm_nonneg _)) + (by simpa only [one_mul] using mul_le_mul_of_nonneg_right ha (norm_nonneg _)) + +/-- Each splitting costs at most one extra input commutator. -/ +lemma zeroCornerRow_commutator_bound (q a b x : E) (δ γ : ℝ) (hδ : 0 ≤ δ) (hγ : 0 ≤ γ) + (hq : ‖q‖ ≤ 1) (ha : ‖a‖ ≤ 1) (hb : ‖b‖ ≤ 1) + (hqc : ‖q * x - x * q‖ ≤ γ) (hac : ‖a * x - x * a‖ ≤ δ) + (hbc : ‖b * x - x * b‖ ≤ δ) : + ∀ n i, ‖zeroCornerRow q a b n i * x - x * zeroCornerRow q a b n i‖ ≤ + (n : ℝ) * δ + γ := by + intro n + induction n with + | zero => intro i; simpa only [zeroCornerRow, Nat.cast_zero, zero_mul, zero_add] using hqc + | succ n ih => + intro i + refine Fin.cases ?_ (fun j => ?_) i + · change ‖b * x - x * b‖ ≤ _ + have hn : 0 ≤ (n : ℝ) * δ := mul_nonneg (Nat.cast_nonneg n) hδ + exact hbc.trans (by rw [Nat.cast_add, Nat.cast_one]; nlinarith) + · change ‖(a * zeroCornerRow q a b n j) * x - x * (a * zeroCornerRow q a b n j)‖ ≤ _ + have hp := row_product_commutator_le a (zeroCornerRow q a b n j) x ha + (zeroCornerRow_norm_le q a b hq ha hb n j) + have hi := ih j + rw [Nat.cast_add, Nat.cast_one] + linarith + +lemma zeroCornerRow_commutes (q a b x : E) (hq : Commute q x) + (ha : Commute a x) (hb : Commute b x) : + ∀ n i, Commute (zeroCornerRow q a b n i) x := by + intro n + induction n with + | zero => intro i; exact hq + | succ n ih => + intro i + exact Fin.cases hb (fun j => ha.mul_left (ih j)) i + + +private lemma projection_norm_le_one (q : E) (hqstar : star q = q) (hqq : q * q = q) : + ‖q‖ ≤ 1 := by + have h : ‖star q * q‖ = ‖q‖ * ‖q‖ := CStarRing.norm_star_mul_self + rw [hqstar, hqq] at h + nlinarith [norm_nonneg q] + +private lemma relativeIsometry_norm_le_one (a q : E) (ha : star a * a = q) + (hq : ‖q‖ ≤ 1) : ‖a‖ ≤ 1 := by + have h := congrArg norm ha + rw [CStarRing.norm_star_mul_self] at h + nlinarith [norm_nonneg a] + +private lemma row_star_commutator_norm (a x : E) : + ‖star a * x - x * star a‖ = ‖a * star x - star x * a‖ := by + rw [← norm_star (a * star x - star x * a)] + simp only [star_sub, star_mul, star_star] + exact norm_sub_rev _ _ + +private lemma pair_projection_commutator_le (q a b x : E) (δ : ℝ) + (hsum : a * star a + b * star b = q) (ha : ‖a‖ ≤ 1) (hb : ‖b‖ ≤ 1) + (hac : ‖a * x - x * a‖ ≤ δ) (hasc : ‖star a * x - x * star a‖ ≤ δ) + (hbc : ‖b * x - x * b‖ ≤ δ) (hbsc : ‖star b * x - x * star b‖ ≤ δ) : + ‖q * x - x * q‖ ≤ 4 * δ := by + have he : q * x - x * q = + ((a * star a) * x - x * (a * star a)) + + ((b * star b) * x - x * (b * star b)) := by rw [← hsum]; noncomm_ring + rw [he] + have h₁ := row_product_commutator_le a (star a) x ha (by simpa only [norm_star] using ha) + have h₂ := row_product_commutator_le b (star b) x hb (by simpa only [norm_star] using hb) + exact (norm_add_le _ _).trans (by linarith) + +/-- Every finite size occurs in a nonzero approximately central corner. +Choosing `m = 2*k+1` gives an even row of size `2*k+2`. -/ +lemma exists_approximately_central_finite_corner_row [Nontrivial E] + (s t : ℕ → E) + (hs : ∀ i j, star (s i) * s j = if i = j then 1 else 0) + (hc : ∀ i j, Commute (s i) (t j) ∧ Commute (s i) (star (t j))) + (n m : ℕ) (δ : ℝ) (hδ : 0 < δ) : + ∃ (q : E) (v : Fin (m + 1) → E), + q ≠ 0 ∧ star q = q ∧ q * q = q ∧ + (∀ i j, star (v i) * v j = if i = j then q else 0) ∧ + (∑ i, v i * star (v i)) = q ∧ + (∀ i, q * v i = v i ∧ v i * q = v i) ∧ + (∀ i k, k < n → ‖v i * s k - s k * v i‖ < δ ∧ + ‖v i * star (s k) - star (s k) * v i‖ < δ) ∧ + ∀ i k, Commute (v i) (t k) ∧ Commute (v i) (star (t k)) := by + let η := δ / ((m : ℝ) + 5) + have hη : 0 < η := by dsimp only [η]; positivity + obtain ⟨q, a, b, hqne, hqstar, hqq, haa, hbb, hab, hsum, hcomm, hother⟩ := + exists_approximately_central_zero_corner_pair s t hs hc n η hη + obtain ⟨hqa, haq, hqb, hbq⟩ := relativeCuntzPair_support q a b hqstar hqq haa hbb hab hsum + have hqn := projection_norm_le_one q hqstar hqq + have han := relativeIsometry_norm_le_one a q haa hqn + have hbn := relativeIsometry_norm_le_one b q hbb hqn + refine ⟨q, zeroCornerRow q a b m, hqne, hqstar, hqq, + zeroCornerRow_gram q a b hqstar hqq haa hbb hab hqa hqb hbq m, + zeroCornerRow_range_sum q a b hqstar hqq haq hsum m, + zeroCornerRow_support q a b hqq hqa hqb hbq m, ?_, ?_⟩ + · intro i k hk + have h := hcomm k hk + have hasc : ‖star a * s k - s k * star a‖ ≤ η := by + rw [row_star_commutator_norm] + exact h.2.2.1.le + have hbsc : ‖star b * s k - s k * star b‖ ≤ η := by + rw [row_star_commutator_norm] + exact h.2.2.2.le + have hascs : ‖star a * star (s k) - star (s k) * star a‖ ≤ η := by + rw [row_star_commutator_norm, star_star] + exact h.1.le + have hbscs : ‖star b * star (s k) - star (s k) * star b‖ ≤ η := by + rw [row_star_commutator_norm, star_star] + exact h.2.1.le + have hqc := pair_projection_commutator_le q a b (s k) η hsum han hbn + h.1.le hasc h.2.1.le hbsc + have hqcs := pair_projection_commutator_le q a b (star (s k)) η hsum han hbn + h.2.2.1.le hascs h.2.2.2.le hbscs + have h₁ := zeroCornerRow_commutator_bound q a b (s k) η (4 * η) hη.le + (by positivity) hqn han hbn hqc h.1.le h.2.1.le m i + have h₂ := zeroCornerRow_commutator_bound q a b (star (s k)) η (4 * η) hη.le + (by positivity) hqn han hbn hqcs h.2.2.1.le h.2.2.2.le m i + have hsmall : (m : ℝ) * η + 4 * η < δ := by + have hmul : η * ((m : ℝ) + 5) = δ := by + dsimp only [η] + exact div_mul_cancel₀ δ (by positivity) + nlinarith + exact ⟨h₁.trans_lt hsmall, h₂.trans_lt hsmall⟩ + · intro i k + have h := hother k + have has : Commute (star a) (t k) := h.2.2.1.star_left + have hbs : Commute (star b) (t k) := h.2.2.2.star_left + have hqc : Commute q (t k) := by + rw [← hsum] + exact (h.1.mul_left has).add_left (h.2.1.mul_left hbs) + have hqcs : Commute q (star (t k)) := by + rw [← hsum] + exact (h.2.2.1.mul_left h.1.star_star).add_left (h.2.2.2.mul_left h.2.1.star_star) + exact ⟨zeroCornerRow_commutes q a b (t k) hqc h.1 h.2.1 m i, + zeroCornerRow_commutes q a b (star (t k)) hqcs h.2.2.1 h.2.2.2 m i⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ZeroUnitBuffer.lean b/lean/OAI/Analysis/OInfinity/ZeroUnitBuffer.lean new file mode 100644 index 0000000000000000000000000000000000000000..981ea7fbef3580e9938ab4f23fc4621ada863113 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ZeroUnitBuffer.lean @@ -0,0 +1,194 @@ +import OAI.Analysis.OInfinity.NegativeGlobal +import OAI.Analysis.OInfinity.CentralBuffer + +namespace OAI + +/-! # Shrinking zero-unit rows against the actual third buffer + +The initial corner, its complementary isometry and the isometry inside it +remain explicit. These are the data supplied by the finite vacuum split; +no equivalence of arbitrary projections is assumed. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- A full binary row in any supported corner can be shrunk against an +orthogonal commuting buffer row, with no change in its finite-word error. -/ +lemma exists_commuting_binary_corner_shrink + (q : E) (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (a r : Fin 2 → E) + (ha : ∀ i j, star (a i) * a j = if i = j then q else 0) + (has : (∑ i, a i * star (a i)) = q) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (har : bergRowsCommute a r) + (hqr : ∀ j, Commute q (r j)) + (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ c : E, q * c = c ∧ c * q = c ∧ star c * c = q ∧ + c * star c = q * (1 - r 0 * star (r 0)) ∧ + ∀ i ≤ m, ‖c * (a 0 ^ i * a 1) * star c - + (a 0 ^ i * a 1) * (1 - r 0 * star (r 0))‖ < ε := by + let R : Fin 2 → E := fun i => r i * q + have hasp (i : Fin 2) : q * a i = a i ∧ a i * q = a i := + ⟨finiteRow_left_support q a hq hqq ha has i, + finiteRow_right_support q a hq hqq ha i⟩ + have hRsp (i : Fin 2) : q * R i = R i ∧ R i * q = R i := by + constructor + · change q * (r i * q) = r i * q + rw [← mul_assoc, (hqr i).eq, mul_assoc, hqq] + · change (r i * q) * q = r i * q + rw [mul_assoc, hqq] + have hR (i j : Fin 2) : star (R i) * R j = if i = j then q else 0 := by + change star (r i * q) * (r j * q) = _ + rw [star_mul, hq] + calc + _ = q * (star (r i) * r j) * q := by noncomm_ring + _ = _ := by rw [hr]; split_ifs <;> simp only [mul_one, mul_zero, zero_mul, hqq] + have haR : bergRowsCommute a R := by + intro i j + have haq : Commute (a i) q := (hasp i).2.trans (hasp i).1.symm + constructor + · exact (har i j).1.mul_right haq + · change Commute (a i) (star (r j * q)) + rw [star_mul, hq] + exact haq.mul_right (har i j).2 + have hfinal : q - R 0 * star (R 0) = q * (1 - r 0 * star (r 0)) := by + change q - (r 0 * q) * star (r 0 * q) = _ + rw [star_mul, hq] + have he : (r 0 * q) * (q * star (r 0)) = q * (r 0 * star (r 0)) := by + calc + _ = r 0 * (q * q) * star (r 0) := by noncomm_ring + _ = _ := by rw [hqq, ← (hqr 0).eq]; noncomm_ring + rw [he] + noncomm_ring + obtain ⟨c, hcl, hcr, hcg, hcc, he⟩ := exists_relative_binary_encoded_shrink + q hq hqq hq0 R a hRsp hasp hR ha has haR m ε hε + refine ⟨c, hcl, hcr, hcg, hcc.trans hfinal, fun i hi => ?_⟩ + have hxq : (a 0 ^ i * a 1) * q = a 0 ^ i * a 1 := by + rw [mul_assoc, (hasp 1).2] + have hh := he i hi + have hsimp : (a 0 ^ i * a 1) * (q * (1 - r 0 * star (r 0))) = + (a 0 ^ i * a 1) * (1 - r 0 * star (r 0)) := by + rw [← mul_assoc, hxq] + rw [hfinal, hsimp] at hh + exact hh + +/-- Every element of the buffer's closed row algebra inherits its exact +commutation with the supplied finite construction data. -/ +lemma closedCanonicalRowAlgebra_commutes_element + (r : ℕ → E) (x : E) + (hx : ∀ i, Commute (r i) x ∧ Commute (star (r i)) x) + (b : closedCanonicalRowAlgebra r) : Commute (b : E) x := by + have hxc : x ∈ StarSubalgebra.centralizer ℂ (Set.range r) := by + apply (StarSubalgebra.mem_centralizer_iff ℂ).mpr + rintro _ ⟨i, rfl⟩ + exact ⟨(hx i).1.eq, (hx i).2.eq⟩ + have hbc : (b : E) ∈ StarSubalgebra.centralizer ℂ + (StarSubalgebra.centralizer ℂ (Set.range r) : Set E) := + StarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer ℂ (Set.range r) b.property + exact (((StarSubalgebra.mem_centralizer_iff ℂ).mp hbc) x hxc).1.symm + +/-- The explicit complement isometry and an isometry inside `q` give the +reverse shrink. The initial corner is `p`; the final corner is exactly `pq`. +No equivalence of an unspecified complementary projection is required. -/ +lemma exists_complementary_binary_corner_shrink + (p q w z : E) + (hp : star p = p) (hpp : p * p = p) (hp0 : p ≠ 0) + (hw : star w * w = 1) (hww : w * star w = 1 - q) + (hz : star z * z = 1) (hqz : q * z = z) + (hpw : Commute p w) (hpz : Commute p z) + (b : Fin 2 → E) + (hb : ∀ i j, star (b i) * b j = if i = j then p else 0) + (hbs : (∑ i, b i * star (b i)) = p) + (hbw : ∀ i, Commute (b i) w ∧ Commute (b i) (star w)) + (hbz : ∀ i, Commute (b i) z ∧ Commute (b i) (star z)) + (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ d : E, p * d = d ∧ d * p = d ∧ star d * d = p ∧ + d * star d = p * q ∧ + ∀ i ≤ m, ‖d * (b 0 ^ i * b 1) * star d - (b 0 ^ i * b 1) * q‖ < ε := by + let v : Fin 2 → E := ![w, z] + have hwz : star w * z = 0 := by + have hwq : star w * q = 0 := by + calc + _ = star w * (1 - w * star w) := by rw [hww]; noncomm_ring + _ = 0 := by rw [mul_sub, mul_one, ← mul_assoc, hw, one_mul, sub_self] + calc + _ = star w * (q * z) := by rw [hqz] + _ = 0 := by rw [← mul_assoc, hwq, zero_mul] + have hzw : star z * w = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hwz + have hv : ∀ i j, star (v i) * v j = if i = j then 1 else 0 := by + intro i j + fin_cases i <;> fin_cases j <;> simp [v, hw, hz, hwz, hzw] + have hbv : bergRowsCommute b v := by + intro i j + fin_cases j + · exact hbw i + · exact hbz i + have hpv (i : Fin 2) : Commute p (v i) := by + fin_cases i + · exact hpw + · exact hpz + obtain ⟨d, hdl, hdr, hdg, hdf, he⟩ := + exists_commuting_binary_corner_shrink p hp hpp hp0 b v hb hbs hv hbv hpv m ε hε + have hfinal : 1 - v 0 * star (v 0) = q := by + change 1 - w * star w = q + rw [hww] + noncomm_ring + refine ⟨d, hdl, hdr, hdg, ?_, fun i hi => ?_⟩ + · exact hdf.trans (congrArg (fun x : E => p * x) hfinal) + · simpa only [hfinal] using he i hi + +/-- A third canonical row supplies its finite binary encoding inside the +closed buffer algebra. Consequently all supplied construction data commute +with the encoding, including their adjoints. -/ +lemma exists_buffer_binary_encoding [Nontrivial E] + (r : ℕ → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (m : ℕ) : + ∃ b : Fin 2 → closedCanonicalRowAlgebra r, + (∀ i j, star (b i : E) * (b j : E) = + if i = j then canonicalTailProjection r 1 else 0) ∧ + (∑ i, (b i : E) * star (b i : E)) = canonicalTailProjection r 1 ∧ + ∀ i ≤ m, (b 0 : E) ^ i * (b 1 : E) = canonicalNegativeRow r i := by + let C := closedCanonicalRowAlgebra r + let R : ℕ → C := fun i => ⟨r i, mem_closedCanonicalRowAlgebra r i⟩ + have hR (i j : ℕ) : star (R i) * R j = if i = j then 1 else 0 := by + by_cases hij : i = j + · rw [ite_eq_left hij] + apply Subtype.ext + change star (r i) * r j = 1 + simpa only [ite_eq_left hij] using hr i j + · rw [ite_eq_right hij] + apply Subtype.ext + change star (r i) * r j = 0 + simpa only [ite_eq_right hij] using hr i j + obtain ⟨b0, b1, h0, h1, h01, hsum, he⟩ := + exists_canonicalNegative_binary_encoding R hR m + let b : Fin 2 → C := ![b0, b1] + have h10 : star b1 * b0 = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star h01 + have hb (i j : Fin 2) : star (b i) * b j = + if i = j then canonicalTailProjection R 1 else 0 := by + fin_cases i <;> fin_cases j <;> simp [b, h0, h1, h01, h10] + refine ⟨b, fun i j => ?_, ?_, fun i hi => ?_⟩ + · have h := congrArg C.subtype (hb i j) + simpa only [map_mul, map_star, apply_ite, map_zero, + StarSubalgebra.subtype_apply, canonicalTailProjection_coe] using h + · have h := congrArg C.subtype hsum + simpa only [Fin.sum_univ_two, b, Matrix.cons_val_zero, Matrix.cons_val_one, + map_add, map_mul, map_star, StarSubalgebra.subtype_apply, + canonicalTailProjection_coe] using h + · have h := congrArg C.subtype (he i hi) + simpa only [map_mul, map_pow, StarSubalgebra.subtype_apply, + canonicalNegativeRow_coe, b, Matrix.cons_val_zero, Matrix.cons_val_one] using h + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ZeroUnitComparison.lean b/lean/OAI/Analysis/OInfinity/ZeroUnitComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..c15d12af38fa72e2867541d6a14a399144292ba4 --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ZeroUnitComparison.lean @@ -0,0 +1,331 @@ +import OAI.Analysis.OInfinity.ZeroUnitBuffer + +namespace OAI + +/-! # Zero-unit finite comparison with a concrete central buffer + +The two complementary isometries remain supplied as actual elements. The +common-corner restriction uses only the closed algebra of the buffer and +its commutant, so no arbitrary-map uniqueness theorem is invoked. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- Elements in the closed buffer algebra commute with its full star +commutant, not just with individual row generators. -/ +lemma bufferAlgebra_commutes_commutant (r : ℕ → E) + (x : StarSubalgebra.centralizer ℂ (Set.range r)) + (y : closedCanonicalRowAlgebra r) : Commute (x : E) (y : E) := by + have hy : (y : E) ∈ StarSubalgebra.centralizer ℂ + (StarSubalgebra.centralizer ℂ (Set.range r) : Set E) := + StarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer ℂ (Set.range r) y.property + exact (((StarSubalgebra.mem_centralizer_iff ℂ).mp hy) x x.property).1 + +/-- Restrict a full binary row in the buffer commutant and its finite +buffer encoding to their actual common unit, then compare them there. -/ +lemma exists_buffer_common_binary_comparison + (r : ℕ → E) + (q : StarSubalgebra.centralizer ℂ (Set.range r)) + (p : closedCanonicalRowAlgebra r) + (hq : star q = q) (hqq : q * q = q) + (hp : star p = p) (hpp : p * p = p) + (hqp0 : (q : E) * (p : E) ≠ 0) + (a : Fin 2 → StarSubalgebra.centralizer ℂ (Set.range r)) + (b : Fin 2 → closedCanonicalRowAlgebra r) + (ha : ∀ i j, star (a i) * a j = if i = j then q else 0) + (hb : ∀ i j, star (b i) * b j = if i = j then p else 0) + (has : (∑ i, a i * star (a i)) = q) + (hbs : (∑ i, b i * star (b i)) = p) + (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ u : unitary E, Joined (1 : unitary E) u ∧ + (u : E) * (1 - (q : E) * (p : E)) = 1 - (q : E) * (p : E) ∧ + (1 - (q : E) * (p : E)) * (u : E) = 1 - (q : E) * (p : E) ∧ + ∀ i ≤ m, ‖(u : E) * (((a 0 : E) ^ i * (a 1 : E)) * (p : E)) * + star (u : E) - ((b 0 : E) ^ i * (b 1 : E)) * (q : E)‖ < ε := by + let C := StarSubalgebra.centralizer ℂ (Set.range r) + let D := closedCanonicalRowAlgebra r + let : IsClosed (C : Set E) := Set.isClosed_centralizer _ + have hc (x : C) (y : D) : Commute (x : E) (y : E) := + bufferAlgebra_commutes_commutant r x y + let f := commutingProjectionRestriction C (p : E) + (congrArg D.subtype hp) (congrArg D.subtype hpp) (fun x => hc x p) + let g := commutingProjectionRestriction D (q : E) + (congrArg C.subtype hq) (congrArg C.subtype hqq) (fun y => (hc q y).symm) + have hrestr := restrict_commuting_binary_rows C D hc q p hq hqq hp hpp a b ha hb has hbs + change (∀ i j, star (f (a i)) * f (a j) = if i = j then (q : E) * (p : E) else 0) ∧ + (∀ i j, star (g (b i)) * g (b j) = if i = j then (q : E) * (p : E) else 0) ∧ + (∑ i, f (a i) * star (f (a i))) = (q : E) * (p : E) ∧ + (∑ i, g (b i) * star (g (b i))) = (q : E) * (p : E) ∧ + bergRowsCommute (fun i => f (a i)) (fun i => g (b i)) at hrestr + have hqp : Commute (q : E) (p : E) := hc q p + have hqs : star (q : E) = (q : E) := congrArg C.subtype hq + have hps : star (p : E) = (p : E) := congrArg D.subtype hp + have hq2 : (q : E) * (q : E) = (q : E) := congrArg C.subtype hqq + have hp2 : (p : E) * (p : E) = (p : E) := congrArg D.subtype hpp + have hstar : star ((q : E) * (p : E)) = (q : E) * (p : E) := by + rw [star_mul, hqs, hps, hqp.eq] + have hsq : ((q : E) * (p : E)) * ((q : E) * (p : E)) = (q : E) * (p : E) := by + calc + _ = (q : E) * ((p : E) * (q : E)) * (p : E) := by noncomm_ring + _ = _ := by rw [← hqp.eq, ← mul_assoc, hq2, mul_assoc, hp2] + obtain ⟨u, hu, hur, hul, he⟩ := exists_relative_binary_power_conjugacy + ((q : E) * (p : E)) hstar hsq hqp0 + (fun i => f (a i)) (fun i => g (b i)) + hrestr.1 hrestr.2.1 hrestr.2.2.1 hrestr.2.2.2.1 hrestr.2.2.2.2 m ε hε + refine ⟨u, hu, hur, hul, fun i hi => ?_⟩ + have haev : f (a 0) ^ i * f (a 1) = ((a 0 : E) ^ i * (a 1 : E)) * (p : E) := by + rw [← nonunital_map_pow_mul] + change ((a 0 ^ i * a 1 : C) : E) * (p : E) = _ + rfl + have hbev : g (b 0) ^ i * g (b 1) = ((b 0 : E) ^ i * (b 1 : E)) * (q : E) := by + rw [← nonunital_map_pow_mul] + change ((b 0 ^ i * b 1 : D) : E) * (q : E) = _ + rfl + simpa only [haev, hbev] using he i hi + +/-- Compare the finite encoding of a zero-unit row with the actual negative +buffer row. Both a complement isometry and an isometry inside the initial +corner are retained as concrete data. The resulting ambient unitary is +connected to one; this does not compare the original unsplit generators. -/ +lemma exists_zeroUnit_buffer_comparison_with_unit [Nontrivial E] + (r : ℕ → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (q w z : StarSubalgebra.centralizer ℂ (Set.range r)) + (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (hw : star w * w = 1) (hww : w * star w = 1 - q) + (hz : star z * z = 1) (hqz : q * z = z) + (a : Fin 2 → StarSubalgebra.centralizer ℂ (Set.range r)) + (ha : ∀ i j, star (a i) * a j = if i = j then q else 0) + (has : (∑ i, a i * star (a i)) = q) + (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ u : unitary E, Joined (1 : unitary E) u ∧ + (u : E) * (q : E) * star (u : E) = canonicalTailProjection r 1 ∧ + ∀ i ≤ m, ‖(u : E) * ((a 0 : E) ^ i * (a 1 : E)) * star (u : E) - + canonicalNegativeRow r i‖ < ε := by + let C := StarSubalgebra.centralizer ℂ (Set.range r) + let D := closedCanonicalRowAlgebra r + let : IsClosed (C : Set E) := Set.isClosed_centralizer _ + let R : ℕ → D := fun i => ⟨r i, mem_closedCanonicalRowAlgebra r i⟩ + have hR (i j : ℕ) : star (R i) * R j = if i = j then 1 else 0 := by + by_cases hij : i = j + · rw [ite_eq_left hij] + apply Subtype.ext + change star (r i) * r j = 1 + simpa only [ite_eq_left hij] using hr i j + · rw [ite_eq_right hij] + apply Subtype.ext + change star (r i) * r j = 0 + simpa only [ite_eq_right hij] using hr i j + let p := canonicalTailProjection R 1 + let P := canonicalTailProjection r 1 + have hpc : (p : E) = P := canonicalTailProjection_coe D R 1 + have hp : star p = p := canonicalTailProjection_star R 1 + have hpp : p * p = p := canonicalTailProjection_idempotent R hR 1 + have hP : star P = P := canonicalTailProjection_star r 1 + have hPP : P * P = P := canonicalTailProjection_idempotent r hr 1 + have hP0 : P ≠ 0 := canonicalTailProjection_ne_zero r hr 1 + have hPdef : P = 1 - r 0 * star (r 0) := by + dsimp only [P] + rw [show (1 : ℕ) = 0 + 1 by rfl, canonicalTailProjection_succ, canonicalTailProjection_zero] + have hqE : star (q : E) = (q : E) := congrArg C.subtype hq + have hqqE : (q : E) * (q : E) = (q : E) := congrArg C.subtype hqq + have hq0E : (q : E) ≠ 0 := fun h => hq0 (Subtype.ext h) + have hwE : star (w : E) * (w : E) = 1 := congrArg C.subtype hw + have hwwE : (w : E) * star (w : E) = 1 - (q : E) := congrArg C.subtype hww + have hzE : star (z : E) * (z : E) = 1 := congrArg C.subtype hz + have hqzE : (q : E) * (z : E) = (z : E) := congrArg C.subtype hqz + have hcomm (x : C) (y : D) : Commute (x : E) (y : E) := + bufferAlgebra_commutes_commutant r x y + have hxrow (x : C) (j : ℕ) : Commute (x : E) (r j) ∧ Commute (x : E) (star (r j)) := by + have h := (StarSubalgebra.mem_centralizer_iff ℂ).mp x.property (r j) ⟨j, rfl⟩ + exact ⟨h.1.symm, h.2.symm⟩ + have hqP : Commute (q : E) P := by simpa only [hpc] using hcomm q p + have hzP : Commute (z : E) P := by simpa only [hpc] using hcomm z p + have hPw : Commute P (w : E) := by simpa only [hpc] using (hcomm w p).symm + have hPz : Commute P (z : E) := hzP.symm + have hqP0 : (q : E) * P ≠ 0 := by + let v := (z : E) * r 1 + have hv : star v * v = 1 := by + dsimp only [v] + rw [star_mul] + calc + _ = star (r 1) * (star (z : E) * (z : E)) * r 1 := by noncomm_ring + _ = 1 := by rw [hzE, mul_one]; simpa only [ite_true] using hr 1 1 + have hPr : P * r 1 = r 1 := by + simpa only [Nat.lt_irrefl, ite_false] using canonicalTailProjection_mul_generator r hr 1 1 + have hs : ((q : E) * P) * v = v := by + dsimp only [v] + calc + _ = (q : E) * (P * (z : E)) * r 1 := by noncomm_ring + _ = ((q : E) * (z : E)) * (P * r 1) := by rw [← hzP.eq]; noncomm_ring + _ = _ := by rw [hqzE, hPr] + intro hzero + have hv0 : v = 0 := by simpa only [hzero, zero_mul] using hs.symm + have h10 : (1 : E) = 0 := by simpa only [hv0, star_zero, zero_mul] using hv.symm + exact one_ne_zero h10 + obtain ⟨b0, b1, hb0, hb1, hb01, hbs, hbe⟩ := + exists_canonicalNegative_binary_encoding R hR m + let b : Fin 2 → D := ![b0, b1] + have hb10 : star b1 * b0 = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hb01 + have hb (i j : Fin 2) : star (b i) * b j = if i = j then p else 0 := by + fin_cases i <;> fin_cases j <;> simp [b, p, hb0, hb1, hb01, hb10] + have hbs' : (∑ i, b i * star (b i)) = p := by + simpa only [Fin.sum_univ_two, b, Matrix.cons_val_zero, Matrix.cons_val_one] using hbs + let A : Fin 2 → E := fun i => a i + let B : Fin 2 → E := fun i => b i + have haE (i j : Fin 2) : star (A i) * A j = if i = j then (q : E) else 0 := by + have h := congrArg C.subtype (ha i j) + simpa only [map_mul, map_star, apply_ite, map_zero, StarSubalgebra.subtype_apply] using h + have hasE : (∑ i, A i * star (A i)) = (q : E) := by + have h := congrArg C.subtype has + simpa only [map_sum, map_mul, map_star, StarSubalgebra.subtype_apply] using h + have hbE (i j : Fin 2) : star (B i) * B j = if i = j then P else 0 := by + have h := congrArg D.subtype (hb i j) + simpa only [map_mul, map_star, apply_ite, map_zero, StarSubalgebra.subtype_apply, hpc] using h + have hbsE : (∑ i, B i * star (B i)) = P := by + have h := congrArg D.subtype hbs' + simpa only [map_sum, map_mul, map_star, StarSubalgebra.subtype_apply, hpc] using h + let δ := ε / 3 + have hδ : 0 < δ := by dsimp only [δ]; positivity + obtain ⟨c, _hcL, hcq, hcg, hcc, hec⟩ := exists_commuting_binary_corner_shrink + (q : E) hqE hqqE hq0E A (fun i : Fin 2 => r i) haE hasE + (fun i j => by simpa only [Fin.ext_iff] using hr i j) + (fun i j => hxrow (a i) j) (fun j => (hxrow q j).1) m δ hδ + simp only [Fin.val_zero] at hcc hec + rw [← hPdef] at hcc + have hbw (i : Fin 2) : Commute (B i) (w : E) ∧ Commute (B i) (star (w : E)) := + ⟨(hcomm w (b i)).symm, (hcomm (star w) (b i)).symm⟩ + have hbz (i : Fin 2) : Commute (B i) (z : E) ∧ Commute (B i) (star (z : E)) := + ⟨(hcomm z (b i)).symm, (hcomm (star z) (b i)).symm⟩ + obtain ⟨d, _hdL, hdp, hdg, hdd, hed⟩ := exists_complementary_binary_corner_shrink + P (q : E) (w : E) (z : E) hP hPP hP0 hwE hwwE hzE hqzE hPw hPz + B hbE hbsE hbw hbz m δ hδ + have hdd' : d * star d = (q : E) * P := hdd.trans hqP.eq.symm + have hqpc : (q : E) * (p : E) ≠ 0 := by simpa only [hpc] using hqP0 + obtain ⟨v, _hv, hvr, hvl, hev⟩ := exists_buffer_common_binary_comparison + r q p hq hqq hp hpp hqpc a b ha hb has hbs' m δ hδ + have hvR : Commute (v : E) ((q : E) * P) := by + have h := hvr.trans hvl.symm + rw [mul_sub, sub_mul, mul_one, one_mul] at h + change (v : E) * ((q : E) * P) = ((q : E) * P) * (v : E) + simpa only [hpc] using sub_right_inj.mp h + let W := star d * (v : E) * c + obtain ⟨hWq, hWP, hWright⟩ := commonCornerTransfer_products + (q : E) P ((q : E) * P) c d v hcg hcc hcq hdg hdd' hdp hvR + have hdn : ‖d‖ ≤ 1 := by + have hn := congrArg norm hdg + rw [CStarRing.norm_star_mul_self] at hn + have hPn : ‖P‖ ≤ 1 := IsStarProjection.norm_le P (isStarProjection_iff'.mpr ⟨hPP, hP⟩) + nlinarith [norm_nonneg d] + have hclose (i : ℕ) (hi : i ≤ m) : + ‖W * (A 0 ^ i * A 1) * star W - (B 0 ^ i * B 1)‖ < ε := by + have hbl : P * (B 0 ^ i * B 1) = B 0 ^ i * B 1 := by + have hs0 := finiteRow_left_support P B hP hPP hbE hbsE 0 + have hs1 := finiteRow_left_support P B hP hPP hbE hbsE 1 + cases i with + | zero => simpa only [pow_zero, one_mul] using hs1 + | succ i => + calc + _ = (P * B 0) * (B 0 ^ i * B 1) := by rw [pow_succ']; noncomm_ring + _ = _ := by rw [hs0, pow_succ']; noncomm_ring + have hbr : (B 0 ^ i * B 1) * P = B 0 ^ i * B 1 := by + rw [mul_assoc, finiteRow_right_support P B hP hPP hbE 1] + have hvclose := hev i hi + rw [hpc] at hvclose + have hcclose := hec i hi + rw [← hPdef] at hcclose + have he := commonCornerTransfer_error P c d (A 0 ^ i * A 1) (B 0 ^ i * B 1) + ((A 0 ^ i * A 1) * P) ((B 0 ^ i * B 1) * (q : E)) v hdg hbl hbr hdn δ + hcclose (hed i hi) hvclose + exact he.trans_eq (by dsimp only [δ]; ring) + let spare := (w : E) * r 0 + have hsGram : star spare * spare = 1 := by + dsimp only [spare] + rw [star_mul] + calc + _ = star (r 0) * (star (w : E) * (w : E)) * r 0 := by noncomm_ring + _ = 1 := by rw [hwE, mul_one]; simpa only [ite_true] using hr 0 0 + have hqw : (q : E) * (w : E) = 0 := by + calc + _ = (1 - (w : E) * star (w : E)) * (w : E) := by rw [hwwE]; noncomm_ring + _ = 0 := by rw [sub_mul, one_mul, mul_assoc, hwE, mul_one, sub_self] + have hqsp : (q : E) * spare = 0 := by dsimp only [spare]; rw [← mul_assoc, hqw, zero_mul] + have hPsp : P * spare = 0 := by + have hPr : P * r 0 = 0 := by + simpa only [show (0 : ℕ) < 1 by omega, ite_true] using canonicalTailProjection_mul_generator r hr 1 0 + dsimp only [spare] + rw [← mul_assoc, hPw.eq, mul_assoc, hPr, mul_zero] + have hWpartial : W * star W * W = W := by rw [mul_assoc, hWq, hWright] + obtain ⟨u, hu, _huEq, huq⟩ := exists_explicit_connected_unitary_extension W spare + hWpartial hsGram (by rw [hWq]; exact hqsp) (by rw [hWP]; exact hPsp) + have huq' : (u : E) * (q : E) = W := by + have hWq' : star W * W = (q : E) := hWq + rw [hWq'] at huq + exact huq + have huRange : (u : E) * (q : E) * star (u : E) = P := by + have hstar := congrArg star huq' + rw [star_mul, hqE] at hstar + calc + _ = (u : E) * ((q : E) * (q : E)) * star (u : E) := by rw [hqqE] + _ = ((u : E) * (q : E)) * ((q : E) * star (u : E)) := by noncomm_ring + _ = P := by rw [huq', hstar]; exact hWP + refine ⟨u, hu, huRange, fun i hi => ?_⟩ + have hxl : (q : E) * (A 0 ^ i * A 1) = A 0 ^ i * A 1 := by + have hs0 := finiteRow_left_support (q : E) A hqE hqqE haE hasE 0 + have hs1 := finiteRow_left_support (q : E) A hqE hqqE haE hasE 1 + cases i with + | zero => simpa only [pow_zero, one_mul] using hs1 + | succ i => + calc + _ = ((q : E) * A 0) * (A 0 ^ i * A 1) := by rw [pow_succ']; noncomm_ring + _ = _ := by rw [hs0, pow_succ']; noncomm_ring + have hxr : (A 0 ^ i * A 1) * (q : E) = A 0 ^ i * A 1 := by + rw [mul_assoc, finiteRow_right_support (q : E) A hqE hqqE haE 1] + have hue : (u : E) * (A 0 ^ i * A 1) * star (u : E) = + W * (A 0 ^ i * A 1) * star W := by + calc + _ = ((u : E) * (q : E)) * (A 0 ^ i * A 1) * star ((u : E) * (q : E)) := by + rw [star_mul, hqE] + symm + calc + _ = (u : E) * ((q : E) * (A 0 ^ i * A 1) * (q : E)) * star (u : E) := by noncomm_ring + _ = _ := by rw [hxl, hxr] + _ = _ := by rw [huq'] + have hbeE : B 0 ^ i * B 1 = canonicalNegativeRow r i := by + have h := congrArg D.subtype (hbe i hi) + simpa only [map_pow, map_mul, StarSubalgebra.subtype_apply, canonicalNegativeRow_coe, + B, b, Matrix.cons_val_zero, Matrix.cons_val_one] using h + change ‖(u : E) * (A 0 ^ i * A 1) * star (u : E) - canonicalNegativeRow r i‖ < ε + rw [hue, ← hbeE] + exact hclose i hi + +/-- The comparison-only form preserves the original finite interface. -/ +lemma exists_zeroUnit_buffer_comparison [Nontrivial E] + (r : ℕ → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (q w z : StarSubalgebra.centralizer ℂ (Set.range r)) + (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (hw : star w * w = 1) (hww : w * star w = 1 - q) + (hz : star z * z = 1) (hqz : q * z = z) + (a : Fin 2 → StarSubalgebra.centralizer ℂ (Set.range r)) + (ha : ∀ i j, star (a i) * a j = if i = j then q else 0) + (has : (∑ i, a i * star (a i)) = q) + (m : ℕ) (ε : ℝ) (hε : 0 < ε) : + ∃ u : unitary E, Joined (1 : unitary E) u ∧ + ∀ i ≤ m, ‖(u : E) * ((a 0 : E) ^ i * (a 1 : E)) * star (u : E) - + canonicalNegativeRow r i‖ < ε := by + obtain ⟨u, hu, _, he⟩ := exists_zeroUnit_buffer_comparison_with_unit + r hr q w z hq hqq hq0 hw hww hz hqz a ha has m ε hε + exact ⟨u, hu, he⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ZeroUnitCompletion.lean b/lean/OAI/Analysis/OInfinity/ZeroUnitCompletion.lean new file mode 100644 index 0000000000000000000000000000000000000000..34dc74d742db69e423f2fff8a6d99f17590048ce --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ZeroUnitCompletion.lean @@ -0,0 +1,368 @@ +import OAI.Analysis.OInfinity.NegativeBinary + +namespace OAI + +/-! # Finite range completion in a zero unit corner + +A proper finite row and an orthogonal spare are combined with a concrete +coisometric row. The resulting isometry fills exactly the missing range. +The construction is algebraic and does not use projection classification. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- Turn a coisometry into an isometry by moving its initial support into +one specified isometric range. -/ +lemma coisometry_range_filler (A y : E) + (hA : A * star A = 1) (hy : star y * y = 1) + (hpy : (star A * A) * y = y) : + let C := 1 - star A * A + y * A + star C * C = 1 ∧ C * star C = 1 - star A * A + y * star y := by + intro C + let p := star A * A + let e := 1 - p + have hp : star p = p := by simp only [p, star_mul, star_star] + have hpp : p * p = p := by + change (star A * A) * (star A * A) = star A * A + calc + _ = star A * (A * star A) * A := by noncomm_ring + _ = _ := by rw [hA, mul_one] + have he : star e = e := by simp only [e, star_sub, star_one, hp] + have hee : e * e = e := by dsimp only [e]; noncomm_ring [hpp] + have hey : e * y = 0 := by + change (1 - p) * y = 0 + rw [sub_mul, one_mul, hpy, sub_self] + have hAe : A * e = 0 := by + have hAp : A * p = A := by + change A * (star A * A) = A + rw [← mul_assoc, hA, one_mul] + dsimp only [e] + rw [mul_sub, mul_one, hAp, sub_self] + have h1 : e * (y * A) = 0 := by rw [← mul_assoc, hey, zero_mul] + have h2 : star (y * A) * e = 0 := by + have hh := congrArg star h1 + simpa only [star_mul, he, star_zero] using hh + have h3 : (y * A) * e = 0 := by rw [mul_assoc, hAe, mul_zero] + have h4 : e * star (y * A) = 0 := by + have hh := congrArg star h3 + simpa only [star_mul, he, star_zero] using hh + have hyy : star (y * A) * (y * A) = p := by + rw [star_mul] + calc + _ = star A * (star y * y) * A := by noncomm_ring + _ = p := by rw [hy, mul_one] + have haa : (y * A) * star (y * A) = y * star y := by + rw [star_mul] + calc + _ = y * (A * star A) * star y := by noncomm_ring + _ = _ := by rw [hA, mul_one] + constructor + · change star (e + y * A) * (e + y * A) = 1 + rw [star_add, he, add_mul, mul_add, mul_add, hee, h1, h2, hyy] + dsimp only [e] + noncomm_ring + · change (e + y * A) * star (e + y * A) = e + y * star y + rw [star_add, he, add_mul, mul_add, mul_add, hee, h4, h3, haa] + abel + +/-- A full finite target row fills the defect of an arbitrary finite +proper row with its given orthogonal spare. -/ +lemma finite_zero_unit_range_completion {n : ℕ} + (x : Fin n → E) (y : E) (a : Fin (n + 1) → E) + (hx : ∀ i j, star (x i) * x j = if i = j then 1 else 0) + (hy : star y * y = 1) (hyx : ∀ i, star y * x i = 0) + (ha : ∀ i j, star (a i) * a j = if i = j then 1 else 0) + (has : (∑ i, a i * star (a i)) = 1) : + ∃ C : E, star C * C = 1 ∧ + C * star C = 1 - ∑ i, x i * star (x i) := by + let r : Fin (n + 1) → E := Fin.cons y x + have hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0 := by + intro i j + refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j + · simpa only [r, Fin.cons_zero, ite_true] using hy + · simp only [r, Fin.cons_zero, Fin.cons_succ, hyx, (Fin.succ_ne_zero j).symm, ite_false] + · have hh := congrArg star (hyx i) + simpa only [r, Fin.cons_zero, Fin.cons_succ, star_mul, star_star, star_zero, + Fin.succ_ne_zero, ite_false] using hh + · simpa only [r, Fin.cons_succ, Fin.succ_inj] using hx i j + let A := finiteCuntzTransfer r a 1 + have hAst : star A = finiteCuntzTransfer a r 1 := by + simpa only [A, star_one] using finiteCuntzTransfer_star r a 1 + have hAA : A * star A = 1 := by + have hh := finiteCuntzTransfer_star_mul a r hr 1 + rw [← hAst, star_star] at hh + simpa only [star_one, one_mul, mul_one, has] using hh + have hAA' : star A * A = ∑ i, r i * star (r i) := by + simpa only [A, star_one, one_mul, mul_one] using + finiteCuntzTransfer_star_mul r a ha 1 + have hpy : (star A * A) * y = y := by + rw [hAA'] + have hh := finiteRowPermutation_mul_row 1 r (by simp) (by simp) hr 1 0 + simpa only [finiteRowPermutation, Equiv.Perm.one_apply, r, Fin.cons_zero] using hh + obtain ⟨hC, hC'⟩ := coisometry_range_filler A y hAA hy hpy + refine ⟨1 - star A * A + y * A, hC, ?_⟩ + rw [hC', hAA', Fin.sum_univ_succ] + simp only [r, Fin.cons_zero, Fin.cons_succ] + abel + +/-- A coisometric binary pair supplies every finite target size, so only +an actual orthogonal spare is needed to fill the prescribed proper row. -/ +lemma finite_zero_unit_completion_from_binary {n : ℕ} + (x : Fin n → E) (y a b : E) + (hx : ∀ i j, star (x i) * x j = if i = j then 1 else 0) + (hy : star y * y = 1) (hyx : ∀ i, star y * x i = 0) + (ha : star a * a = 1) (hb : star b * b = 1) (hab : star a * b = 0) + (hsum : a * star a + b * star b = 1) : + ∃ C : E, star C * C = 1 ∧ + C * star C = 1 - ∑ i, x i * star (x i) := by + exact finite_zero_unit_range_completion x y (zeroCornerRow 1 a b n) hx hy hyx + (zeroCornerRow_gram 1 a b (star_one _) (one_mul _) ha hb hab + (one_mul _) (one_mul _) (mul_one _) n) + (zeroCornerRow_range_sum 1 a b (star_one _) (one_mul _) (mul_one _) hsum n) + +/-- Appending the concrete missing-range isometry gives a full finite row. -/ +lemma finite_zero_unit_full_row {n : ℕ} + (x : Fin n → E) (y a b : E) + (hx : ∀ i j, star (x i) * x j = if i = j then 1 else 0) + (hy : star y * y = 1) (hyx : ∀ i, star y * x i = 0) + (ha : star a * a = 1) (hb : star b * b = 1) (hab : star a * b = 0) + (hsum : a * star a + b * star b = 1) : + ∃ r : Fin (n + 1) → E, + (∀ i : Fin n, r i.succ = x i) ∧ + (∀ i j, star (r i) * r j = if i = j then 1 else 0) ∧ + (∑ i, r i * star (r i)) = 1 := by + obtain ⟨C, hC, hCr⟩ := finite_zero_unit_completion_from_binary x y a b + hx hy hyx ha hb hab hsum + have hPx (i : Fin n) : (∑ j, x j * star (x j)) * x i = x i := by + simpa only [finiteRowPermutation, Equiv.Perm.one_apply] using + finiteRowPermutation_mul_row 1 x (by simp) (by simp) hx 1 i + have horth (i : Fin n) : star C * x i = 0 := by + have hr : (C * star C) * x i = 0 := by + rw [hCr, sub_mul, one_mul, hPx, sub_self] + have hh := congrArg (fun z => star C * z) hr + simpa only [← mul_assoc, hC, one_mul, mul_zero] using hh + let r : Fin (n + 1) → E := Fin.cons C x + refine ⟨r, fun i => rfl, ?_, ?_⟩ + · intro i j + refine Fin.cases ?_ (fun i => ?_) i <;> refine Fin.cases ?_ (fun j => ?_) j + · simpa only [r, Fin.cons_zero, ite_true] using hC + · simp only [r, Fin.cons_zero, Fin.cons_succ, horth, (Fin.succ_ne_zero j).symm, ite_false] + · have hh := congrArg star (horth i) + simpa only [r, Fin.cons_zero, Fin.cons_succ, star_mul, star_star, star_zero, + Fin.succ_ne_zero, ite_false] using hh + · simpa only [r, Fin.cons_succ, Fin.succ_inj] using hx i j + · rw [Fin.sum_univ_succ] + simp only [r, Fin.cons_zero, Fin.cons_succ, hCr] + abel + +/-- A countable orthogonal row in a zero-unit algebra has an exact binary +encoding of each prescribed finite prefix. The next row element is the spare. -/ +lemma exists_zero_unit_binary_encoding + (x : ℕ → E) + (hx : ∀ i j, star (x i) * x j = if i = j then 1 else 0) + (a b : E) (ha : star a * a = 1) (hb : star b * b = 1) + (hab : star a * b = 0) (hsum : a * star a + b * star b = 1) (m : ℕ) : + ∃ A B : E, star A * A = 1 ∧ star B * B = 1 ∧ star A * B = 0 ∧ + A * star A + B * star B = 1 ∧ ∀ i ≤ m, A ^ i * B = x i := by + have fill (n : ℕ) : ∃ r : Fin (n + 1) → E, + (∀ i : Fin n, r i.succ = x i) ∧ + (∀ i j, star (r i) * r j = if i = j then 1 else 0) ∧ + (∑ i, r i * star (r i)) = 1 := by + refine finite_zero_unit_full_row (fun i : Fin n => x i) (x n) a b + ?_ ?_ ?_ ha hb hab hsum + · intro i j + simpa only [Fin.ext_iff] using hx i j + · simpa only [ite_true] using hx n n + · intro i + have hne : n ≠ (i : ℕ) := Nat.ne_of_gt i.isLt + simpa only [hne, ite_false] using hx n i + obtain ⟨r, hrleaf, hr, hrs⟩ := fill m + obtain ⟨R, hRleaf, hR, hRs⟩ := fill (m + 1) + obtain ⟨A, B, hA, hB, hAB, hsum', hB0, hstep⟩ := + successive_full_rows_binary m r R hr hR hrs hRs + have hBx : B = x 0 := hB0.trans (hRleaf 0) + refine ⟨A, B, hA, hB, hAB, hsum', ?_⟩ + intro i + induction i with + | zero => intro _; simpa only [pow_zero, one_mul] using hBx + | succ i ih => + intro hi + rw [pow_succ', mul_assoc, ih (by omega)] + have h := hstep (⟨i, by omega⟩ : Fin m) + rw [hrleaf, hRleaf] at h + exact h + +/-- The same explicit filler in a supported corner with its actual unit +`q`. No relation between `q` and the ambient identity is needed. -/ +lemma relative_zero_unit_completion {n : ℕ} + (q : E) (hq : star q = q) (hqq : q * q = q) + (x : Fin n → E) (y a b : E) + (hxs : ∀ i, q * x i = x i ∧ x i * q = x i) + (hys : q * y = y ∧ y * q = y) + (hx : ∀ i j, star (x i) * x j = if i = j then q else 0) + (hy : star y * y = q) (hyx : ∀ i, star y * x i = 0) + (ha : star a * a = q) (hb : star b * b = q) (hab : star a * b = 0) + (hsum : a * star a + b * star b = q) : + ∃ C : E, q * C = C ∧ C * q = C ∧ star C * C = q ∧ + C * star C = q - ∑ i, x i * star (x i) := by + obtain ⟨hqa, haq, hqb, hbq⟩ := relativeCuntzPair_support q a b hq hqq ha hb hab hsum + let x' : Fin n → ProjectionCorner q hq hqq := fun i => + projectionCornerElement q hq hqq (x i) (hxs i) + let y' : ProjectionCorner q hq hqq := projectionCornerElement q hq hqq y hys + let a' : ProjectionCorner q hq hqq := projectionCornerElement q hq hqq a ⟨hqa, haq⟩ + let b' : ProjectionCorner q hq hqq := projectionCornerElement q hq hqq b ⟨hqb, hbq⟩ + have hx' : ∀ i j, star (x' i) * x' j = if i = j then 1 else 0 := + projectionCornerElement_gram q hq hqq x hxs hx + have hy' : star y' * y' = 1 := Subtype.ext hy + have hyx' (i : Fin n) : star y' * x' i = 0 := Subtype.ext (hyx i) + have ha' : star a' * a' = 1 := Subtype.ext ha + have hb' : star b' * b' = 1 := Subtype.ext hb + have hab' : star a' * b' = 0 := Subtype.ext hab + have hsum' : a' * star a' + b' * star b' = 1 := Subtype.ext hsum + obtain ⟨C, hC, hCC⟩ := finite_zero_unit_completion_from_binary x' y' a' b' + hx' hy' hyx' ha' hb' hab' hsum' + refine ⟨C, C.property.1, C.property.2, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hC, ?_⟩ + have h := congrArg (projectionCornerInclusion q hq hqq) hCC + simp only [map_sub, map_sum, map_mul, map_star, projectionCornerInclusion_one] at h + exact h + +/-- Exact finite binary encoding in the given corner. The countable +proper row supplies its own next unused isometry at every finite stage. -/ +lemma exists_relative_zero_unit_binary_encoding + (q : E) (hq : star q = q) (hqq : q * q = q) + (x : ℕ → E) (a b : E) + (hxs : ∀ i, q * x i = x i ∧ x i * q = x i) + (hx : ∀ i j, star (x i) * x j = if i = j then q else 0) + (ha : star a * a = q) (hb : star b * b = q) (hab : star a * b = 0) + (hsum : a * star a + b * star b = q) (m : ℕ) : + ∃ A B : E, q * A = A ∧ A * q = A ∧ q * B = B ∧ B * q = B ∧ + star A * A = q ∧ star B * B = q ∧ star A * B = 0 ∧ + A * star A + B * star B = q ∧ ∀ i ≤ m, A ^ i * B = x i := by + obtain ⟨hqa, haq, hqb, hbq⟩ := relativeCuntzPair_support q a b hq hqq ha hb hab hsum + let x' : ℕ → ProjectionCorner q hq hqq := fun i => + projectionCornerElement q hq hqq (x i) (hxs i) + let a' : ProjectionCorner q hq hqq := projectionCornerElement q hq hqq a ⟨hqa, haq⟩ + let b' : ProjectionCorner q hq hqq := projectionCornerElement q hq hqq b ⟨hqb, hbq⟩ + have hx' (i j : ℕ) : star (x' i) * x' j = if i = j then 1 else 0 := by + by_cases hij : i = j + · rw [ite_eq_left hij] + apply Subtype.ext + change star (x i) * x j = q + simpa only [ite_eq_left hij] using hx i j + · rw [ite_eq_right hij] + apply Subtype.ext + change star (x i) * x j = 0 + simpa only [ite_eq_right hij] using hx i j + obtain ⟨A, B, hA, hB, hAB, hsum', hencode⟩ := exists_zero_unit_binary_encoding x' hx' a' b' + (Subtype.ext ha) (Subtype.ext hb) (Subtype.ext hab) (Subtype.ext hsum) m + refine ⟨A, B, A.property.1, A.property.2, B.property.1, B.property.2, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hA, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hB, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hAB, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hsum', ?_⟩ + have hpow (i : ℕ) : ((A ^ i * B : ProjectionCorner q hq hqq) : E) = + (A : E) ^ i * (B : E) := by + induction i with + | zero => simp only [pow_zero, one_mul] + | succ i ih => + rw [pow_succ', mul_assoc, pow_succ', mul_assoc] + change (A : E) * ((A ^ i * B : ProjectionCorner q hq hqq) : E) = _ + rw [ih] + intro i hi + have h := congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) (hencode i hi) + rw [hpow] at h + exact h + +/-- On elements commuting with the initial projection, the filler has +an exact two-corner formula. This records the term that must be controlled +by the canonical-shift implementer. -/ +lemma coisometry_range_filler_conjugation (A y x : E) + (hA : A * star A = 1) (hx : Commute (star A * A) x) : + let C := 1 - star A * A + y * A + C * x * star C = (1 - star A * A) * x + y * (A * x * star A) * star y := by + intro C + let p := star A * A + let e := 1 - p + have hp : star p = p := by simp only [p, star_mul, star_star] + have hpp : p * p = p := by + change (star A * A) * (star A * A) = star A * A + calc + _ = star A * (A * star A) * A := by noncomm_ring + _ = _ := by rw [hA, mul_one] + have he : star e = e := by simp only [e, star_sub, star_one, hp] + have hee : e * e = e := by dsimp only [e]; noncomm_ring [hpp] + have hex : Commute e x := (Commute.one_left x).sub_left hx + have hAe : A * e = 0 := by + have hAp : A * p = A := by + change A * (star A * A) = A + rw [← mul_assoc, hA, one_mul] + dsimp only [e] + rw [mul_sub, mul_one, hAp, sub_self] + have hestar : e * star A = 0 := by + simpa only [star_mul, he, star_zero] using congrArg star hAe + have hexe : e * x * e = e * x := by + rw [hex.eq, mul_assoc, hee, ← hex.eq] + have hexA : e * x * star A = 0 := by + rw [hex.eq, mul_assoc, hestar, mul_zero] + have hAxe : A * x * e = 0 := by + rw [mul_assoc, ← hex.eq, ← mul_assoc, hAe, zero_mul] + change (e + y * A) * x * star (e + y * A) = e * x + y * (A * x * star A) * star y + rw [star_add, star_mul, he] + calc + _ = e * x * e + (e * x * star A) * star y + + y * (A * x * e) + y * (A * x * star A) * star y := by noncomm_ring + _ = _ := by rw [hexe, hexA, hAxe]; simp only [zero_mul, mul_zero, add_zero] + +/-- The concrete binary shift filler accepts any unitary inserted before +the coisometry. Its final projection is independent of that insertion. -/ +lemma binary_shift_shrink_products (r a : Fin 2 → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (ha : ∀ i j, star (a i) * a j = if i = j then 1 else 0) + (has : (∑ i, a i * star (a i)) = 1) (u : unitary E) : + let v := (u : E) * finiteCuntzTransfer r a 1 + let C := 1 - star v * v + r 1 * v + star C * C = 1 ∧ C * star C = 1 - r 0 * star (r 0) := by + intro v C + let A := finiteCuntzTransfer r a 1 + have hAs : star A = finiteCuntzTransfer a r 1 := by + simpa only [A, star_one] using finiteCuntzTransfer_star r a 1 + have hAA : A * star A = 1 := by + have hh := finiteCuntzTransfer_star_mul a r hr 1 + rw [← hAs, star_star] at hh + simpa only [star_one, one_mul, mul_one, has] using hh + have hAp : star A * A = ∑ i, r i * star (r i) := by + simpa only [A, star_one, one_mul, mul_one] using + finiteCuntzTransfer_star_mul r a ha 1 + have hvv : v * star v = 1 := by + change ((u : E) * A) * star ((u : E) * A) = 1 + rw [star_mul] + calc + _ = (u : E) * (A * star A) * star (u : E) := by noncomm_ring + _ = 1 := by rw [hAA, mul_one, u.property.2] + have hvp : star v * v = ∑ i, r i * star (r i) := by + change star ((u : E) * A) * ((u : E) * A) = _ + rw [star_mul] + calc + _ = star A * (star (u : E) * (u : E)) * A := by noncomm_ring + _ = _ := by rw [u.property.1, mul_one, hAp] + have hv1 : (star v * v) * r 1 = r 1 := by + rw [hvp] + simpa only [finiteRowPermutation, Equiv.Perm.one_apply] using + finiteRowPermutation_mul_row 1 r (by simp) (by simp) hr 1 1 + obtain ⟨hC, hCC⟩ := coisometry_range_filler v (r 1) hvv + (by simpa only [ite_true] using hr 1 1) hv1 + refine ⟨hC, ?_⟩ + rw [hCC, hvp, Fin.sum_univ_two] + abel + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OInfinity/ZeroUnitRows.lean b/lean/OAI/Analysis/OInfinity/ZeroUnitRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..c1e70e3d64a027b539c263bd9f950672b21631ca --- /dev/null +++ b/lean/OAI/Analysis/OInfinity/ZeroUnitRows.lean @@ -0,0 +1,138 @@ +import OAI.Analysis.OInfinity.ZeroUnitComparison + +namespace OAI + +/-! # Finite proper-row comparison through the zero-unit buffer + +Only one unused row element is needed for the finite binary encoding. +The unit and complementary isometries remain explicit throughout. +-/ + +noncomputable section +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +variable {E : Type*} [CStarAlgebra E] + +/-- The binary encoding construction needs only the tested finite prefix +and its next unused isometry, rather than a countable row extension. -/ +lemma exists_finite_zero_unit_binary_encoding (n : ℕ) + (x : Fin (n + 2) → E) + (hx : ∀ i j, star (x i) * x j = if i = j then 1 else 0) + (a b : E) (ha : star a * a = 1) (hb : star b * b = 1) + (hab : star a * b = 0) (hsum : a * star a + b * star b = 1) : + ∃ A B : E, star A * A = 1 ∧ star B * B = 1 ∧ star A * B = 0 ∧ + A * star A + B * star B = 1 ∧ + ∀ i : Fin (n + 1), A ^ (i : ℕ) * B = x i.castSucc := by + have fill (l : ℕ) (hl : l ≤ n + 1) : + ∃ r : Fin (l + 1) → E, + (∀ i : Fin l, r i.succ = x ⟨i, by omega⟩) ∧ + (∀ i j, star (r i) * r j = if i = j then 1 else 0) ∧ + (∑ i, r i * star (r i)) = 1 := by + refine finite_zero_unit_full_row (fun i : Fin l => x ⟨i, by omega⟩) + (x ⟨l, by omega⟩) a b ?_ ?_ ?_ ha hb hab hsum + · intro i j + simpa only [Fin.mk.injEq, Fin.ext_iff] using hx ⟨i, by omega⟩ ⟨j, by omega⟩ + · simpa only [ite_true] using hx ⟨l, by omega⟩ ⟨l, by omega⟩ + · intro i + have hne : (⟨l, by omega⟩ : Fin (n + 2)) ≠ ⟨i, by omega⟩ := by + intro h + have he := congrArg Fin.val h + change l = (i : ℕ) at he + have hi := i.isLt + omega + simpa only [ite_eq_right hne] using hx ⟨l, by omega⟩ ⟨i, by omega⟩ + obtain ⟨r, hrleaf, hr, hrs⟩ := fill n (by omega) + obtain ⟨R, hRleaf, hR, hRs⟩ := fill (n + 1) (by omega) + obtain ⟨A, B, hA, hB, hAB, hsum', hB0, hstep⟩ := + successive_full_rows_binary n r R hr hR hrs hRs + have hencode (i : ℕ) (hi : i ≤ n) : A ^ i * B = x ⟨i, by omega⟩ := by + induction i with + | zero => simpa only [pow_zero, one_mul, Fin.val_zero] using hB0.trans (hRleaf 0) + | succ i ih => + rw [pow_succ', mul_assoc, ih (by omega)] + have h := hstep (⟨i, by omega⟩ : Fin n) + rw [hrleaf, hRleaf] at h + exact h + refine ⟨A, B, hA, hB, hAB, hsum', fun i => ?_⟩ + exact hencode i (by omega) + +/-- Finite encoding in an actual projection corner. In particular this +applies to a proper prefix of the finite coisometric vacuum-split row. -/ +lemma exists_relative_finite_zero_unit_binary_encoding (n : ℕ) + (q : E) (hq : star q = q) (hqq : q * q = q) + (x : Fin (n + 2) → E) (a b : E) + (hxs : ∀ i, q * x i = x i ∧ x i * q = x i) + (hx : ∀ i j, star (x i) * x j = if i = j then q else 0) + (ha : star a * a = q) (hb : star b * b = q) (hab : star a * b = 0) + (hsum : a * star a + b * star b = q) : + ∃ A B : E, q * A = A ∧ A * q = A ∧ q * B = B ∧ B * q = B ∧ + star A * A = q ∧ star B * B = q ∧ star A * B = 0 ∧ + A * star A + B * star B = q ∧ + ∀ i : Fin (n + 1), A ^ (i : ℕ) * B = x i.castSucc := by + obtain ⟨hqa, haq, hqb, hbq⟩ := relativeCuntzPair_support q a b hq hqq ha hb hab hsum + let x' : Fin (n + 2) → ProjectionCorner q hq hqq := fun i => + projectionCornerElement q hq hqq (x i) (hxs i) + let a' : ProjectionCorner q hq hqq := projectionCornerElement q hq hqq a ⟨hqa, haq⟩ + let b' : ProjectionCorner q hq hqq := projectionCornerElement q hq hqq b ⟨hqb, hbq⟩ + have hx' : ∀ i j, star (x' i) * x' j = if i = j then 1 else 0 := + projectionCornerElement_gram q hq hqq x hxs hx + obtain ⟨A, B, hA, hB, hAB, hsum', he⟩ := exists_finite_zero_unit_binary_encoding n x' hx' + a' b' (Subtype.ext ha) (Subtype.ext hb) (Subtype.ext hab) (Subtype.ext hsum) + refine ⟨A, B, A.property.1, A.property.2, B.property.1, B.property.2, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hA, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hB, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hAB, + congrArg (fun z : ProjectionCorner q hq hqq => (z : E)) hsum', fun i => ?_⟩ + let f := projectionCornerInclusion q hq hqq + have hh := congrArg f (he i) + rw [nonunital_map_pow_mul] at hh + exact hh + +/-- A finite proper row in the buffer commutant has a connected ambient +comparison with the corresponding negative buffer prefix. Its initial unit +is carried to the buffer unit exactly. -/ +lemma exists_finite_zeroUnit_buffer_comparison [Nontrivial E] + (r : ℕ → E) + (hr : ∀ i j, star (r i) * r j = if i = j then 1 else 0) + (q w z : StarSubalgebra.centralizer ℂ (Set.range r)) + (hq : star q = q) (hqq : q * q = q) (hq0 : q ≠ 0) + (hw : star w * w = 1) (hww : w * star w = 1 - q) + (hz : star z * z = 1) (hqz : q * z = z) + (n : ℕ) (x : Fin (n + 2) → StarSubalgebra.centralizer ℂ (Set.range r)) + (hxs : ∀ i, q * x i = x i ∧ x i * q = x i) + (hx : ∀ i j, star (x i) * x j = if i = j then q else 0) + (a b : StarSubalgebra.centralizer ℂ (Set.range r)) + (ha : star a * a = q) (hb : star b * b = q) (hab : star a * b = 0) + (hsum : a * star a + b * star b = q) + (ε : ℝ) (hε : 0 < ε) : + ∃ u : unitary E, Joined (1 : unitary E) u ∧ + (u : E) * (q : E) * star (u : E) = canonicalTailProjection r 1 ∧ + ∀ i : Fin (n + 1), ‖(u : E) * (x i.castSucc : E) * star (u : E) - + canonicalNegativeRow r i‖ < ε := by + let C := StarSubalgebra.centralizer ℂ (Set.range r) + let : IsClosed (C : Set E) := Set.isClosed_centralizer _ + obtain ⟨A, B, _hAl, _hAr, _hBl, _hBr, hA, hB, hAB, hsum', he⟩ := + exists_relative_finite_zero_unit_binary_encoding n q hq hqq x a b hxs hx ha hb hab hsum + let c : Fin 2 → C := ![A, B] + have hBA : star B * A = 0 := by + simpa only [star_mul, star_star, star_zero] using congrArg star hAB + have hc (i j : Fin 2) : star (c i) * c j = if i = j then q else 0 := by + fin_cases i <;> fin_cases j <;> simp [c, hA, hB, hAB, hBA] + have hcs : (∑ i, c i * star (c i)) = q := by + simpa only [Fin.sum_univ_two, c, Matrix.cons_val_zero, Matrix.cons_val_one] using hsum' + obtain ⟨u, hu, huq, huclose⟩ := exists_zeroUnit_buffer_comparison_with_unit + r hr q w z hq hqq hq0 hw hww hz hqz c hc hcs n ε hε + refine ⟨u, hu, huq, fun i => ?_⟩ + have heE : (A : E) ^ (i : ℕ) * (B : E) = (x i.castSucc : E) := by + have hh := congrArg C.subtype (he i) + simpa only [map_pow, map_mul, StarSubalgebra.subtype_apply] using hh + have hh := huclose i (by omega) + simpa only [c, Matrix.cons_val_zero, Matrix.cons_val_one, heE] using hh + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/AntiunitaryCPConjugation.lean b/lean/OAI/Analysis/OperatorAlgebra/AntiunitaryCPConjugation.lean new file mode 100644 index 0000000000000000000000000000000000000000..99898d780890386d6012d44d1a95670495a9a11a --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/AntiunitaryCPConjugation.lean @@ -0,0 +1,116 @@ +import OAI.Analysis.ModularRecovery.TomitaResolvent +import OAI.Analysis.Nuclearity.CPWeakOperatorUltralimit + +namespace OAI + +/-! Conjugating an operator-valued completely positive map on both sides +by an involutive antiunitary preserves complete positivity. This is the +operator calculation needed to transfer a commutant expectation across +Tomita conjugation. -/ + +noncomputable section +open scoped InnerProductSpace CStarAlgebra ComplexOrder ComplexConjugate + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def antiunitaryConjugate (J : H ≃ₗᵢ⋆[ℂ] H) (T : H →L[ℂ] H) : H →L[ℂ] H where + toFun x := J (T (J x)) + map_add' _ _ := by simp only [map_add] + map_smul' c x := by + simp only [map_smulₛₗ, starRingEnd_self_apply, RingHom.id_apply] + cont := J.continuous.comp (T.continuous.comp J.continuous) + +omit [CompleteSpace H] in +@[simp] lemma antiunitaryConjugate_apply (J : H ≃ₗᵢ⋆[ℂ] H) (T : H →L[ℂ] H) (x : H) : + antiunitaryConjugate J T x = J (T (J x)) := rfl + +omit [CompleteSpace H] in +@[simp] lemma antiunitaryConjugate_add (J : H ≃ₗᵢ⋆[ℂ] H) (T U : H →L[ℂ] H) : + antiunitaryConjugate J (T + U) = antiunitaryConjugate J T + antiunitaryConjugate J U := by + ext x + simp only [antiunitaryConjugate_apply, add_apply, map_add] + +omit [CompleteSpace H] in +@[simp] lemma antiunitaryConjugate_smul (J : H ≃ₗᵢ⋆[ℂ] H) (c : ℂ) (T : H →L[ℂ] H) : + antiunitaryConjugate J (c • T) = star c • antiunitaryConjugate J T := by + ext x + simp only [antiunitaryConjugate_apply, smul_apply, + map_smulₛₗ, starRingEnd_apply] + +omit [CompleteSpace H] in +lemma antiunitaryConjugate_involutive (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + (T : H →L[ℂ] H) : antiunitaryConjugate J (antiunitaryConjugate J T) = T := by + ext x + simp only [antiunitaryConjugate_apply] + rw [hJ x, hJ (T x)] + +omit [CompleteSpace H] in +lemma antiunitaryConjugate_norm_le (J : H ≃ₗᵢ⋆[ℂ] H) (T : H →L[ℂ] H) : + ‖antiunitaryConjugate J T‖ ≤ ‖T‖ := by + apply ContinuousLinearMap.opNorm_le_bound _ (norm_nonneg T) + intro x + simpa only [antiunitaryConjugate_apply, J.norm_map] using T.le_opNorm (J x) + +def antiunitaryMatrix (J : H ≃ₗᵢ⋆[ℂ] H) {n : Type*} + (X : CStarMatrix n n (H →L[ℂ] H)) : CStarMatrix n n (H →L[ℂ] H) := + CStarMatrix.ofMatrix (fun i j => antiunitaryConjugate J (X i j)) + +lemma antiunitaryMatrix_nonneg (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + {n : Type*} [Fintype n] (X : CStarMatrix n n (H →L[ℂ] H)) (hX : 0 ≤ X) : + 0 ≤ antiunitaryMatrix J X := by + apply (NonUnitalStarAlgHom.map_le_map_iff + (matrixOperatorHom (n := n) (H := H)) matrixOperator_injective).mp + rw [map_zero] + apply ContinuousLinearMap.nonneg_iff_isPositive.mpr + rw [ContinuousLinearMap.isPositive_iff_complex] + intro x + let y : PiLp 2 (fun _ : n => H) := WithLp.toLp 2 (fun i => J (x i)) + have he : inner ℂ (matrixOperator (antiunitaryMatrix J X) x) x = + star (inner ℂ (matrixOperator X y) y) := by + simp only [PiLp.inner_apply, matrixOperator_apply, sum_inner, star_sum] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + change inner ℂ (J (X i j (J (x j)))) (x i) = + star (inner ℂ (X i j (J (x j))) (J (x i))) + conv_lhs => rw [← hJ (x i)] + exact BoundedRecovery.antiunitary_inner J _ _ + have hp := (ContinuousLinearMap.nonneg_iff_isPositive.mp + (map_nonneg (matrixOperatorHom (n := n) (H := H)) hX)).inner_nonneg_left y + have hn : 0 ≤ inner ℂ (matrixOperator (antiunitaryMatrix J X) x) x := by + rw [he] + exact star_nonneg_iff.mpr hp + exact ⟨Complex.ext rfl hn.2, hn.1⟩ + +def antiunitaryCPConjugate (J : H ≃ₗᵢ⋆[ℂ] H) + (P : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) : + (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H) := + LinearMap.mkContinuous + { toFun := fun T => antiunitaryConjugate J (P (antiunitaryConjugate J T)) + map_add' := by intros; simp only [antiunitaryConjugate_add, map_add] + map_smul' := by intros; simp only [antiunitaryConjugate_smul, map_smul, star_star, + RingHom.id_apply] } + ‖P‖ (fun T => (antiunitaryConjugate_norm_le J _).trans + ((P.le_opNorm _).trans (mul_le_mul_of_nonneg_left + (antiunitaryConjugate_norm_le J T) (norm_nonneg P)))) + +lemma antiunitaryCPConjugate_norm_le (J : H ≃ₗᵢ⋆[ℂ] H) + (P : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) : + ‖antiunitaryCPConjugate J P‖ ≤ ‖P‖ := + LinearMap.mkContinuous_norm_le _ (norm_nonneg P) _ + +lemma antiunitaryCPConjugate_cp (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + (P : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) (hP : CompletelyPositive P) : + CompletelyPositive (antiunitaryCPConjugate J P) := by + intro n X hX + exact antiunitaryMatrix_nonneg J hJ (matrixLinearMap P (antiunitaryMatrix J X)) + (hP n _ (antiunitaryMatrix_nonneg J hJ X hX)) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/AntiunitaryOperatorIdentities.lean b/lean/OAI/Analysis/OperatorAlgebra/AntiunitaryOperatorIdentities.lean new file mode 100644 index 0000000000000000000000000000000000000000..418256c6b97be6f5dcfe0241c7e35d7e1dbe7cd1 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/AntiunitaryOperatorIdentities.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.OperatorAlgebra.AntiunitaryCPConjugation + +namespace OAI + +/-! Multiplication and adjoints under an actual involutive antiunitary. -/ +noncomputable section +open scoped InnerProductSpace ComplexConjugate +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +omit [CompleteSpace H] in +lemma antiunitaryConjugate_mul (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + (a b : H →L[ℂ] H) : + antiunitaryConjugate J (a * b) = antiunitaryConjugate J a * antiunitaryConjugate J b := by + apply ContinuousLinearMap.ext + intro x + simp only [antiunitaryConjugate_apply, mul_apply_eq_comp] + rw [hJ (b (J x))] + +lemma antiunitaryConjugate_star (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + (a : H →L[ℂ] H) : + antiunitaryConjugate J (star a) = star (antiunitaryConjugate J a) := by + apply (ContinuousLinearMap.eq_adjoint_iff _ _).mpr + intro x y + change inner ℂ (J (star a (J x))) y = inner ℂ x (J (a (J y))) + calc + _ = star (inner ℂ (star a (J x)) (J y)) := by + conv_lhs => rw [← hJ y] + exact BoundedRecovery.antiunitary_inner J _ _ + _ = star (inner ℂ (J x) (a (J y))) := + congrArg star (ContinuousLinearMap.adjoint_inner_left a (J y) (J x)) + _ = _ := by + have h := BoundedRecovery.antiunitary_inner J (J x) (a (J y)) + simpa only [hJ x] using h.symm + +lemma antiunitaryConjugate_isStarProjection (J : H ≃ₗᵢ⋆[ℂ] H) + (hJ : Function.Involutive J) (p : H →L[ℂ] H) (hp : IsStarProjection p) : + IsStarProjection (antiunitaryConjugate J p) where + isSelfAdjoint := by + change star (antiunitaryConjugate J p) = antiunitaryConjugate J p + rw [← antiunitaryConjugate_star J hJ, hp.isSelfAdjoint.star_eq] + isIdempotentElem := by + change antiunitaryConjugate J p * antiunitaryConjugate J p = antiunitaryConjugate J p + rw [← antiunitaryConjugate_mul J hJ] + exact congrArg (antiunitaryConjugate J) hp.isIdempotentElem + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/BicommutantStrongStar.lean b/lean/OAI/Analysis/OperatorAlgebra/BicommutantStrongStar.lean new file mode 100644 index 0000000000000000000000000000000000000000..a6c85cc322e4d1423c3445ca16fc46f0babfddd7 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/BicommutantStrongStar.lean @@ -0,0 +1,93 @@ +import OAI.Analysis.IrrationalRotation.Operators.BicommutantDensity + +namespace OAI + +/-! Finite simultaneous strong approximation of an operator and its adjoint. +Only the algebraic star subalgebra is used; no norm bound is asserted. -/ + +noncomputable section +open scoped BigOperators InnerProductSpace + +namespace WeakPureInfiniteness +open Invariant233.BicommutantDensity + +variable {H I : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + [CompleteSpace H] [Fintype I] + +private def pairedOrbit (A : StarSubalgebra ℂ (H →L[ℂ] H)) (x y : I → H) : + A →ₗ[ℝ] PiLp 2 (fun _ : I ⊕ I => H) where + toFun a := WithLp.toLp 2 (Sum.elim (fun i => (a : H →L[ℂ] H) (x i)) + (fun i => (star (a : H →L[ℂ] H)) (y i))) + map_add' a b := by ext i; cases i <;> simp + map_smul' t a := by + ext i + cases i <;> simp [StarModule.star_smul] + +theorem pairedOrbit_mem_closure + (A : StarSubalgebra ℂ (H →L[ℂ] H)) {T : H →L[ℂ] H} + (hT : T ∈ Set.centralizer (Set.centralizer (A : Set (H →L[ℂ] H)))) + (x y : I → H) : + WithLp.toLp 2 (Sum.elim (fun i => T (x i)) (fun i => star T (y i))) ∈ + closure (Set.range (fun a : A => pairedOrbit A x y a)) := by + classical + let : InnerProductSpace ℝ (PiLp 2 (fun _ : I ⊕ I => H)) := + InnerProductSpace.rclikeToReal ℂ _ + let R := (pairedOrbit A x y).range + change _ ∈ R.topologicalClosure + rw [← R.orthogonal_orthogonal_eq_closure] + apply (Rᗮ.mem_orthogonal _).mpr + intro η hη + let ζ : PiLp 2 (fun _ : I ⊕ I => H) := + WithLp.toLp 2 (Sum.elim x (fun i => η (.inr i))) + let g : PiLp 2 (fun _ : I ⊕ I => H) → ℝ := fun z => + ∑ i, (inner ℂ (η (.inl i)) (z (.inl i))).re + + ∑ i, (inner ℂ (z (.inr i)) (y i)).re + have hg : Continuous g := by dsimp [g]; fun_prop + have hadj (a : H →L[ℂ] H) (i : I) : + inner ℂ (η (.inr i)) (star a (y i)) = inner ℂ (a (η (.inr i))) (y i) := by + rw [ContinuousLinearMap.star_eq_adjoint, ContinuousLinearMap.adjoint_inner_right] + have hzero (a : A) : g (amplify (I ⊕ I) (a : H →L[ℂ] H) ζ) = 0 := by + have hz := (R.mem_orthogonal' η).mp hη (pairedOrbit A x y a) ⟨a, rfl⟩ + rw [real_inner_eq_re_inner ℂ, PiLp.inner_apply] at hz + simpa [g, ζ, pairedOrbit, Fintype.sum_sum_type, Complex.re_sum, hadj] using hz + have hcl : amplify (I ⊕ I) T ζ ∈ + closure (Set.range (fun a : A => amplify (I ⊕ I) (a : H →L[ℂ] H) ζ)) := by + apply Metric.mem_closure_iff.mpr + intro ε hε + obtain ⟨a, ha, hclose⟩ := exists_amplified_approximation A hT ζ hε + exact ⟨_, ⟨⟨a, ha⟩, rfl⟩, by simpa [dist_eq_norm, norm_sub_rev] using hclose⟩ + have hclosed : IsClosed {z : PiLp 2 (fun _ : I ⊕ I => H) | g z = 0} := + isClosed_eq hg continuous_const + have ht : g (amplify (I ⊕ I) T ζ) = 0 := + hclosed.closure_subset_iff.mpr (by rintro _ ⟨a, rfl⟩; exact hzero a) hcl + rw [real_inner_eq_re_inner ℂ, PiLp.inner_apply] + simpa [g, ζ, Fintype.sum_sum_type, Complex.re_sum, hadj] using ht + +theorem exists_finite_strongStar_approximation + (A : StarSubalgebra ℂ (H →L[ℂ] H)) {T : H →L[ℂ] H} + (hT : T ∈ Set.centralizer (Set.centralizer (A : Set (H →L[ℂ] H)))) + (x y : I → H) {ε : ℝ} (hε : 0 < ε) : + ∃ a : H →L[ℂ] H, a ∈ A ∧ + (∀ i, ‖a (x i) - T (x i)‖ < ε) ∧ + (∀ i, ‖star a (y i) - star T (y i)‖ < ε) := by + obtain ⟨z, ⟨a, rfl⟩, hclose⟩ := Metric.mem_closure_iff.mp + (pairedOrbit_mem_closure A hT x y) ε hε + rw [dist_eq_norm] at hclose + rw [norm_sub_rev] at hclose + refine ⟨a, a.property, ?_, ?_⟩ + · intro i + have h := PiLp.norm_apply_le + (pairedOrbit A x y a - WithLp.toLp 2 + (Sum.elim (fun i => T (x i)) (fun i => star T (y i)))) (.inl i) + exact h.trans_lt hclose + · intro i + have h := PiLp.norm_apply_le + (pairedOrbit A x y a - WithLp.toLp 2 + (Sum.elim (fun i => T (x i)) (fun i => star T (y i)))) (.inr i) + exact h.trans_lt hclose + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/CanonicalLpOperations.lean b/lean/OAI/Analysis/OperatorAlgebra/CanonicalLpOperations.lean new file mode 100644 index 0000000000000000000000000000000000000000..414219ca7ac35d5d95fb0759a1f69799234d65bc --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/CanonicalLpOperations.lean @@ -0,0 +1,48 @@ +import OAI.Analysis.OperatorAlgebra.LpOperatorStructure +import OAI.Analysis.OperatorAlgebra.LpOperatorTensorBound + +namespace OAI + +/-! Algebraic and norm identities for the canonical L² operator conversion. -/ +noncomputable section +open MeasureTheory +namespace WeakPureInfiniteness +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + +lemma canonicalLpOperator_norm (T : HilbertOperatorSpace (Lp H 2 (volume : Measure ℝ))) : + ‖canonicalLpOperator T‖ = ‖T‖ := rfl + +lemma norm_le_canonicalLpOperator + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + {c : ℝ} (h : c ≤ ‖T‖) : c ≤ ‖canonicalLpOperator T‖ := + h.trans_eq (canonicalLpOperator_norm T).symm + +lemma canonicalLpOperator_sum {I : Type*} [Fintype I] + (T : I → HilbertOperatorSpace (Lp H 2 (volume : Measure ℝ))) : + canonicalLpOperator (∑ i, T i) = ∑ i, canonicalLpOperator (T i) := by + classical + apply ContinuousLinearMap.ext + intro x + simp only [canonicalLpOperator_apply, sum_apply] + +lemma canonicalLpOperator_tensor_bound [CompleteSpace H] {I : Type*} [Fintype I] + (l r a b : I → HilbertOperatorSpace (Lp H 2 (volume : Measure ℝ))) + (h : hilbertOperatorTensorBound l r a b) : + ‖∑ i, canonicalLpOperator (l i) * canonicalLpOperator (r i)‖ ≤ + ‖∑ i, minimalElementary (canonicalLpOperator (a i)) + (MulOpposite.op (canonicalLpOperator (b i)))‖ := by + simpa only [canonicalLpOperator_eq] using lp_operator_tensor_bound l r a b h + +lemma canonicalLpOperator_sum_bound [CompleteSpace H] {I : Type*} [Fintype I] + (l r a b : I → Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (h : ‖canonicalLpOperator (∑ i, l i * r i)‖ ≤ + ‖∑ i, minimalElementary (canonicalLpOperator (a i)) + (MulOpposite.op (canonicalLpOperator (b i)))‖) : + ‖∑ i, l i * r i‖ ≤ ‖∑ i, minimalElementary (a i) (MulOpposite.op (b i))‖ := by + simpa only [canonicalLpOperator_eq] using h + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ComplexSymmetricMean.lean b/lean/OAI/Analysis/OperatorAlgebra/ComplexSymmetricMean.lean new file mode 100644 index 0000000000000000000000000000000000000000..bb0f7e4fba1cfcb1c1921a4f4dcb574f29038a0c --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ComplexSymmetricMean.lean @@ -0,0 +1,118 @@ +import OAI.Analysis.ModularRecovery.Mean + +namespace OAI + +/-! The complex linear version of the proved symmetric-interval mean. +It is positive, normalized and translation invariant for a free ultrafilter. -/ + +noncomputable section +open Filter +open scoped ComplexOrder + +namespace WeakPureInfiniteness +open BoundedRecovery + +private def meanRealPart (f : BoundedContinuousFunction ℝ ℂ) : + BoundedContinuousFunction ℝ ℝ := Complex.reCLM.compLeftContinuousBounded ℝ f + +private def meanImagPart (f : BoundedContinuousFunction ℝ ℂ) : + BoundedContinuousFunction ℝ ℝ := Complex.imCLM.compLeftContinuousBounded ℝ f + +def complexSymmetricMean (ω : Ultrafilter ℕ) (f : BoundedContinuousFunction ℝ ℂ) : ℂ := + (fixedMean ω (meanRealPart f) : ℂ) + (fixedMean ω (meanImagPart f) : ℂ) * Complex.I + +lemma complexSymmetricMean_add (ω : Ultrafilter ℕ) + (f g : BoundedContinuousFunction ℝ ℂ) : + complexSymmetricMean ω (f + g) = complexSymmetricMean ω f + complexSymmetricMean ω g := by + have hr : meanRealPart (f + g) = meanRealPart f + meanRealPart g := by ext t; simp [meanRealPart] + have hi : meanImagPart (f + g) = meanImagPart f + meanImagPart g := by ext t; simp [meanImagPart] + unfold complexSymmetricMean + rw [hr, hi] + change ((meanCLM ω) (meanRealPart f + meanRealPart g) : ℂ) + + ((meanCLM ω) (meanImagPart f + meanImagPart g) : ℂ) * Complex.I = _ + rw [map_add, map_add] + simp only [Complex.ofReal_add, meanCLM_apply] + ring + +lemma complexSymmetricMean_smul (ω : Ultrafilter ℕ) + (c : ℂ) (f : BoundedContinuousFunction ℝ ℂ) : + complexSymmetricMean ω (c • f) = c * complexSymmetricMean ω f := by + have hr : meanRealPart (c • f) = c.re • meanRealPart f - c.im • meanImagPart f := by + ext t + simp [meanRealPart, meanImagPart, Complex.mul_re] + have hi : meanImagPart (c • f) = c.re • meanImagPart f + c.im • meanRealPart f := by + ext t + simp [meanRealPart, meanImagPart, Complex.mul_im] + unfold complexSymmetricMean + rw [hr, hi] + change ((meanCLM ω) (c.re • meanRealPart f - c.im • meanImagPart f) : ℂ) + + ((meanCLM ω) (c.re • meanImagPart f + c.im • meanRealPart f) : ℂ) * Complex.I = _ + rw [map_sub, map_add, map_smul, map_smul, map_smul, map_smul] + apply Complex.ext <;> simp [Complex.mul_re, Complex.mul_im] + +lemma complexSymmetricMean_norm_le (ω : Ultrafilter ℕ) + (f : BoundedContinuousFunction ℝ ℂ) : ‖complexSymmetricMean ω f‖ ≤ 2 * ‖f‖ := by + have hr : ‖meanRealPart f‖ ≤ ‖f‖ := by + apply (BoundedContinuousFunction.norm_le (norm_nonneg f)).mpr + intro t + exact (Complex.abs_re_le_norm (f t)).trans (f.norm_coe_le_norm t) + have hi : ‖meanImagPart f‖ ≤ ‖f‖ := by + apply (BoundedContinuousFunction.norm_le (norm_nonneg f)).mpr + intro t + exact (Complex.abs_im_le_norm (f t)).trans (f.norm_coe_le_norm t) + calc + _ ≤ ‖(fixedMean ω (meanRealPart f) : ℂ)‖ + + ‖(fixedMean ω (meanImagPart f) : ℂ) * Complex.I‖ := norm_add_le _ _ + _ = ‖fixedMean ω (meanRealPart f)‖ + ‖fixedMean ω (meanImagPart f)‖ := by simp + _ ≤ ‖f‖ + ‖f‖ := add_le_add ((norm_fixedMean_le ω _).trans hr) ((norm_fixedMean_le ω _).trans hi) + _ = _ := by ring + +def complexSymmetricMeanCLM (ω : Ultrafilter ℕ) : BoundedContinuousFunction ℝ ℂ →L[ℂ] ℂ := + LinearMap.mkContinuous + { toFun := complexSymmetricMean ω + map_add' := complexSymmetricMean_add ω + map_smul' := complexSymmetricMean_smul ω } + 2 (complexSymmetricMean_norm_le ω) + +lemma complexSymmetricMean_const (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) (c : ℂ) : + complexSymmetricMean ω (BoundedContinuousFunction.const ℝ c) = c := by + have hr : meanRealPart (BoundedContinuousFunction.const ℝ c) = + BoundedContinuousFunction.const ℝ c.re := rfl + have hi : meanImagPart (BoundedContinuousFunction.const ℝ c) = + BoundedContinuousFunction.const ℝ c.im := rfl + simp only [complexSymmetricMean, hr, hi, BoundedContinuousFunction.const_apply, + fixedMean_const ω hω, Complex.re_add_im] + +def complexTranslateBCF (f : BoundedContinuousFunction ℝ ℂ) (s : ℝ) : + BoundedContinuousFunction ℝ ℂ := + f.compContinuous ⟨fun t => t + s, continuous_id.add continuous_const⟩ + +lemma complexSymmetricMean_translate (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (f : BoundedContinuousFunction ℝ ℂ) (s : ℝ) : + complexSymmetricMean ω (complexTranslateBCF f s) = complexSymmetricMean ω f := by + have hr : meanRealPart (complexTranslateBCF f s) = translateBCF (meanRealPart f) s := rfl + have hi : meanImagPart (complexTranslateBCF f s) = translateBCF (meanImagPart f) s := rfl + simp only [complexSymmetricMean, hr, hi, fixedMean_translate ω hω] + +lemma complexSymmetricMean_nonneg (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (f : BoundedContinuousFunction ℝ ℂ) (hf : ∀ t, 0 ≤ f t) : + 0 ≤ complexSymmetricMean ω f := by + have hi : meanImagPart f = 0 := by + ext t + exact (Complex.le_def.mp (hf t)).2.symm + have hr : 0 ≤ fixedMean ω (meanRealPart f) := by + have h := fixedMean_mono ω (BoundedContinuousFunction.const ℝ 0) (meanRealPart f) + (fun t => (Complex.le_def.mp (hf t)).1) + change fixedMean ω (fun _ : ℝ => 0) ≤ _ at h + rw [fixedMean_const ω hω] at h + exact h + simp only [complexSymmetricMean, hi] + have hz : fixedMean ω (0 : BoundedContinuousFunction ℝ ℝ) = 0 := (meanCLM ω).map_zero + rw [hz, Complex.ofReal_zero, zero_mul, add_zero] + exact_mod_cast hr + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ContinuousLpFieldNorm.lean b/lean/OAI/Analysis/OperatorAlgebra/ContinuousLpFieldNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..d6b696807b663c588b277aa46d01ba3ba402b227 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ContinuousLpFieldNorm.lean @@ -0,0 +1,82 @@ +import OAI.Analysis.ModularTheory.LpFaithful + +namespace OAI + +/-! A continuous operator field is bounded pointwise by its represented L2 +operator. The proof tests a constant vector on a small positive-measure interval. -/ +noncomputable section +open MeasureTheory Set +open scoped Topology ENNReal +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [NormedSpace ℂ H] + +lemma continuousLpField_apply_norm_le + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (F : ℝ → H →L[ℂ] H) + (hF : ∀ f, T f =ᵐ[volume] fun t => F t (f t)) + (t₀ : ℝ) (x : H) (hc : ContinuousAt (fun t => F t x) t₀) : + ‖F t₀ x‖ ≤ ‖T‖ * ‖x‖ := by + by_contra hn + have hn' : ‖T‖ * ‖x‖ < ‖F t₀ x‖ := lt_of_not_ge hn + let c := (‖T‖ * ‖x‖ + ‖F t₀ x‖) / 2 + have hc₁ : ‖T‖ * ‖x‖ < c := by dsimp [c]; linarith + have hc₂ : c < ‖F t₀ x‖ := by dsimp [c]; linarith + have hc₀ : 0 ≤ c := (mul_nonneg (norm_nonneg _) (norm_nonneg _)).trans hc₁.le + obtain ⟨δ, hδ, hd⟩ := Metric.continuousAt_iff.mp hc.norm + (‖F t₀ x‖ - c) (sub_pos.mpr hc₂) + let l := t₀ - δ / 2 + let r := t₀ + δ / 2 + have hlr : l < r := by dsimp [l, r]; linarith + have hs : MeasurableSet (Ioo l r) := measurableSet_Ioo + have hm : volume (Ioo l r) ≠ ⊤ := by simp + let f : Lp H 2 (volume : Measure ℝ) := indicatorConstLp 2 hs hm x + let g : Lp ℝ 2 (volume : Measure ℝ) := indicatorConstLp 2 hs hm c + have he : ‖g‖ ≤ ‖T f‖ := by + apply Lp.norm_le_norm_of_ae_le + filter_upwards [hF f, + indicatorConstLp_coeFn (p := 2) (hs := hs) (hμs := hm) (c := x), + indicatorConstLp_coeFn (p := 2) (hs := hs) (hμs := hm) (c := c)] + with t hT hf hg + change ‖g t‖ ≤ ‖T f t‖ + rw [hg] + by_cases ht : t ∈ Ioo l r + · rw [indicator_of_mem ht, Real.norm_eq_abs, abs_of_nonneg hc₀, hT] + have hft : f t = x := hf.trans (indicator_of_mem ht _) + rw [hft] + have htδ : dist t t₀ < δ := by + rw [Real.dist_eq, abs_lt] + dsimp [l, r] at ht + constructor <;> linarith [ht.1, ht.2] + have hnorm := hd htδ + rw [Real.dist_eq] at hnorm + have hbelow := (abs_lt.mp hnorm).1 + linarith + · rw [indicator_of_notMem ht, norm_zero] + exact norm_nonneg _ + have he' := he.trans (T.le_opNorm f) + have hr : 0 < volume.real (Ioo l r) := by + rw [Real.volume_real_Ioo_of_le hlr.le] + exact sub_pos.mpr hlr + have hw : 0 < volume.real (Ioo l r) ^ (1 / (2 : ℝ≥0∞).toReal) := + Real.rpow_pos_of_pos hr _ + change ‖indicatorConstLp 2 hs hm c‖ ≤ ‖T‖ * ‖indicatorConstLp 2 hs hm x‖ at he' + rw [norm_indicatorConstLp (by norm_num) (by norm_num), + norm_indicatorConstLp (by norm_num) (by norm_num), Real.norm_eq_abs, + abs_of_nonneg hc₀, ← mul_assoc] at he' + exact (not_le_of_gt hc₁) ((mul_le_mul_iff_left₀ hw).mp he') + +lemma continuousLpField_norm_le + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (F : ℝ → H →L[ℂ] H) + (hF : ∀ f, T f =ᵐ[volume] fun t => F t (f t)) + (t₀ : ℝ) (hc : ∀ x, ContinuousAt (fun t => F t x) t₀) : + ‖F t₀‖ ≤ ‖T‖ := + (F t₀).opNorm_le_bound (norm_nonneg T) + (fun x => continuousLpField_apply_norm_le T F hF t₀ x (hc x)) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/CyclicCoefficientApproximation.lean b/lean/OAI/Analysis/OperatorAlgebra/CyclicCoefficientApproximation.lean new file mode 100644 index 0000000000000000000000000000000000000000..2419216828c557874341e69020beb9d19785e63a --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/CyclicCoefficientApproximation.lean @@ -0,0 +1,63 @@ +import OAI.Analysis.PureInfiniteness.NonunitalFunctionalRepresentation +import OAI.Analysis.Nuclearity.UnitizedCoefficients + +namespace OAI + +/-! The finite cyclic-vector approximation in KR02 Lemma 7.18. The cyclic +representation is on the unitization, so this applies to nonunital algebras +without assuming cyclicity of their restricted representations. -/ + +noncomputable section +open scoped BigOperators InnerProductSpace Topology ComplexOrder + +namespace WeakPureInfiniteness + +variable {D H I J : Type*} [NonUnitalCStarAlgebra D] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [Fintype I] [Fintype J] + +lemma finite_quadratic_coefficient_approximation + (π : Unitization ℂ D →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hcyc : DenseRange (fun a => π a ξ)) + (L : J → I → I → H →L[ℂ] H) (k : I → H) (ε : ℝ) (hε : 0 < ε) : + ∃ a : I → Unitization ℂ D, + ‖(fun j => ∑ i, ∑ r, ⟪k i, L j i r (k r)⟫_ℂ) - + (fun j => ∑ i, ∑ r, ⟪π (a i) ξ, L j i r (π (a r) ξ)⟫_ℂ)‖ < ε := by + let Q : (I → H) → J → ℂ := fun z j => ∑ i, ∑ r, ⟪z i, L j i r (z r)⟫_ℂ + have hQ : Continuous Q := by + apply continuous_pi + intro j + fun_prop + have hQat : ContinuousAt Q k := hQ.continuousAt + obtain ⟨δ, hδ, hclose⟩ := Metric.continuousAt_iff.mp hQat ε hε + have hd : DenseRange (fun a : I → Unitization ℂ D => fun i => π (a i) ξ) := + DenseRange.piMap (fun _ => hcyc) + obtain ⟨a, ha⟩ := Metric.denseRange_iff.mp hd k δ hδ + refine ⟨a, ?_⟩ + have h := hclose (by simpa only [dist_comm] using ha) + simpa only [dist_eq_norm, norm_sub_rev, Q] using h + +lemma unitized_coefficient_representation + {B : Type*} [NonUnitalCStarAlgebra B] + (π : Unitization ℂ D →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (T : B → D) (a : I → Unitization ℂ D) (c : I → B) (b : B) + (e : H →L[ℂ] H) (he : ∀ d, Commute (π d) e) : + ⟪ξ, π ((unitizedCoefficientEnlargement T a c b : D) : Unitization ℂ D) (e ξ)⟫_ℂ = + ∑ i, ∑ j, ⟪π (a i) ξ, + π ((T (star (c i) * b * c j) : D) : Unitization ℂ D) (e (π (a j) ξ))⟫_ℂ := by + rw [inr_unitizedCoefficientEnlargement] + simp only [map_sum, sum_apply, inner_sum, map_mul, map_star, + ContinuousLinearMap.star_eq_adjoint, mul_apply_eq_comp] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [ContinuousLinearMap.adjoint_inner_right] + congr 2 + exact congrArg (fun f : H →L[ℂ] H => f ξ) (he (a j)).eq + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/CyclicGNSUnitary.lean b/lean/OAI/Analysis/OperatorAlgebra/CyclicGNSUnitary.lean new file mode 100644 index 0000000000000000000000000000000000000000..a93f2b9f2059cda6418902a96949a81248f11b18 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/CyclicGNSUnitary.lean @@ -0,0 +1,86 @@ +import OAI.Analysis.OperatorAlgebra.CyclicStateNorm + +namespace OAI + +/-! The concrete cyclic vector realization of a positive functional is +unitarily equivalent to its GNS space. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder +open UniformSpace + +namespace WeakPureInfiniteness + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + (φ : A →ₚ[ℂ] ℂ) (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hφ : ∀ a, φ a = inner ℂ ξ (π a ξ)) + +def cyclicPreGNSIsometry : φ.PreGNS →ₗᵢ[ℂ] H where + toFun x := π (φ.ofPreGNS x) ξ + map_add' x y := by simp only [map_add, add_apply] + map_smul' c x := by simp only [map_smul, smul_apply, RingHom.id_apply] + norm_map' x := by + change ‖π (φ.ofPreGNS x) ξ‖ = ‖x‖ + have h := cyclic_vector_norm_eq_preGNS π (StarAlgHom.id ℂ A) φ ξ + (fun a => hφ a) (φ.ofPreGNS x) + change ‖π (φ.ofPreGNS x) ξ‖ = ‖φ.toPreGNS (φ.ofPreGNS x)‖ at h + simpa only [PositiveLinearMap.toPreGNS_ofPreGNS] using h + +def cyclicGNSIsometry : φ.GNS →ₗᵢ[ℂ] H := + (cyclicPreGNSIsometry φ π ξ hφ).fromCompletion + +@[simp] lemma cyclicGNSIsometry_coe (x : φ.PreGNS) : + cyclicGNSIsometry φ π ξ hφ (x : φ.GNS) = π (φ.ofPreGNS x) ξ := by + rw [cyclicGNSIsometry, LinearIsometry.fromCompletion_apply_coe] + rfl + +@[simp] lemma cyclicGNSIsometry_vector (a : A) : + cyclicGNSIsometry φ π ξ hφ (φ.toPreGNS a : φ.GNS) = π a ξ := by + rw [cyclicGNSIsometry_coe, PositiveLinearMap.ofPreGNS_toPreGNS] + +theorem cyclicGNSIsometry_surjective (hξ : DenseRange (fun a => π a ξ)) : + Function.Surjective (cyclicGNSIsometry φ π ξ hφ) := by + let V := cyclicGNSIsometry φ π ξ hφ + have hc : IsClosed (Set.range V) := V.isometry.isClosedEmbedding.isClosed_range + have hr : Set.range (fun a => π a ξ) ⊆ Set.range V := by + rintro _ ⟨a, rfl⟩ + exact ⟨(φ.toPreGNS a : φ.GNS), cyclicGNSIsometry_vector φ π ξ hφ a⟩ + have hall : Set.univ ⊆ Set.range V := by + rw [← hξ.closure_range] + exact closure_minimal hr hc + intro x + exact hall (Set.mem_univ x) + +def cyclicGNSUnitary (hξ : DenseRange (fun a => π a ξ)) : φ.GNS ≃ₗᵢ[ℂ] H := + LinearIsometryEquiv.ofSurjective (cyclicGNSIsometry φ π ξ hφ) + (cyclicGNSIsometry_surjective φ π ξ hφ hξ) + +theorem cyclicGNSIsometry_intertwines (a : A) (η : φ.GNS) : + cyclicGNSIsometry φ π ξ hφ (φ.gnsStarAlgHom a η) = + π a (cyclicGNSIsometry φ π ξ hφ η) := by + induction η using Completion.induction_on with + | hp => exact isClosed_eq (by fun_prop) (by fun_prop) + | ih x => + change cyclicGNSIsometry φ π ξ hφ (φ.gnsNonUnitalStarAlgHom a x) = _ + rw [PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, + cyclicGNSIsometry_coe, cyclicGNSIsometry_coe] + simp only [PositiveLinearMap.leftMulMapPreGNS_apply, + PositiveLinearMap.ofPreGNS_toPreGNS, map_mul, mul_apply_eq_comp] + +theorem cyclicGNSUnitary_conjugates (hξ : DenseRange (fun a => π a ξ)) (a : A) : + (cyclicGNSUnitary φ π ξ hφ hξ).conjStarAlgEquiv (φ.gnsStarAlgHom a) = π a := by + ext η + rw [LinearIsometryEquiv.conjStarAlgEquiv_apply_apply] + change cyclicGNSIsometry φ π ξ hφ + (φ.gnsStarAlgHom a ((cyclicGNSUnitary φ π ξ hφ hξ).symm η)) = π a η + rw [cyclicGNSIsometry_intertwines] + change π a ((cyclicGNSUnitary φ π ξ hφ hξ) + ((cyclicGNSUnitary φ π ξ hφ hξ).symm η)) = π a η + rw [LinearIsometryEquiv.apply_symm_apply] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/CyclicSeparatingCompression.lean b/lean/OAI/Analysis/OperatorAlgebra/CyclicSeparatingCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..ad416b14eeb2e171bce0b2cc7a45137fbaa3a550 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/CyclicSeparatingCompression.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.OperatorAlgebra.IntertwinerCompression +import OAI.Analysis.OperatorAlgebra.IsometricCornerOperators +import OAI.Analysis.ModularRecovery.TomitaFundamental + +namespace OAI + +/-! A separating vector remains separating on its cyclic subrepresentation. +The proof compresses the actual commuting operators and uses their dense +orbit, rather than assuming the compressed bicommutant is a normal image. -/ +noncomputable section +open scoped Topology +namespace WeakPureInfiniteness +open BoundedRecovery + +variable {A H K : Type*} [CStarAlgebra A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma separating_compression (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) + (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) (W : K →ₗᵢ[ℂ] H) + (hW : ∀ a, W.toContinuousLinearMap.comp (ρ a) = (π a).comp W.toContinuousLinearMap) + (M : VonNeumannAlgebra H) (hπ : ∀ a, π a ∈ M) (ξ : K) + (hsep : ∀ T : H →L[ℂ] H, T ∈ M → T (W ξ) = 0 → T = 0) + (U : K →L[ℂ] K) + (hU : ∀ R : K →L[ℂ] K, (∀ a, Commute (ρ a) R) → Commute R U) + (hzero : U ξ = 0) : U = 0 := by + have hd := commutant_cyclic M (W ξ) hsep + have hv (x : H) : U (W.toContinuousLinearMap.adjoint x) = 0 := by + apply closure_minimal (s := (operatorOrbit M.commutant (W ξ) : Set H)) ?_ + (isClosed_eq (U.continuous.comp W.toContinuousLinearMap.adjoint.continuous) + continuous_const) (hd x) + rintro _ ⟨T, hT, rfl⟩ + have hTπ (a : A) : Commute (π a) T := + VonNeumannAlgebra.mem_commutant_iff.mp hT (π a) (hπ a) + have hc := hU (isometricCornerCompress W T) + (fun a => intertwiner_compression_commutes ρ π W.toContinuousLinearMap hW T hTπ a) + have he := congrArg (fun V : K →L[ℂ] K => V ξ) hc.eq + change W.toContinuousLinearMap.adjoint (T (W (U ξ))) = + U (W.toContinuousLinearMap.adjoint (T (W ξ))) at he + rw [hzero, map_zero, map_zero, map_zero] at he + exact he.symm + apply ContinuousLinearMap.ext + intro x + have he := hv (W x) + rwa [isometricCorner_adjoint_apply] at he + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/CyclicStandardIntertwiner.lean b/lean/OAI/Analysis/OperatorAlgebra/CyclicStandardIntertwiner.lean new file mode 100644 index 0000000000000000000000000000000000000000..ca7e7e82f33af835d47ef08a8e2d821541dcdaff --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/CyclicStandardIntertwiner.lean @@ -0,0 +1,93 @@ +import OAI.Analysis.PureInfiniteness.NormalizedSeparatingSequence +import OAI.Analysis.OperatorAlgebra.GNSSeparableCyclic + +namespace OAI + +/-! The application-specific standard representation and bounded intertwiner +for a tested vector of a representation of a separable C*-algebra. -/ +noncomputable section +open TopologicalSpace +open scoped ComplexOrder +namespace WeakPureInfiniteness +open BoundedRecovery KirchbergRordam.GenericRW.GroupedFactors + +universe u v +variable {A : Type u} {H : Type v} [CStarAlgebra A] + [PartialOrder A] [StarOrderedRing A] [SeparableSpace A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +theorem exists_cyclic_standard_intertwiner + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) (hξ : ‖ξ‖ = 1) : + ∃ (K : ComplexHilbert.{u}) (S : StandardModularData K) + (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) (V : K →L[ℂ] H), + S.M = bicommutant ρ.range ∧ ‖V‖ ≤ 3 ∧ V S.xi = ξ ∧ + ∀ a, V.comp (ρ a) = (π a).comp V := by + let f₀ := vectorPositiveFunctional π ξ + let K₀ := gnsHilbert f₀ + let ρ₀ : A →⋆ₐ[ℂ] (K₀ →L[ℂ] K₀) := gnsBundledHom f₀ + let ξ₀ : K₀ := gnsVector f₀ 1 + let W₀ : K₀ →ₗᵢ[ℂ] H := cyclicBundledGNSIsometry f₀ π ξ + (vectorPositiveFunctional_apply π ξ) + have hW₀ : W₀ ξ₀ = ξ := cyclicBundledGNSIsometry_one f₀ π ξ _ + have hξ₀ : ‖ξ₀‖ = 1 := by + rw [← W₀.norm_map ξ₀, hW₀, hξ] + let : SeparableSpace K₀ := gns_separable_of_cyclic f₀ π ξ + (vectorPositiveFunctional_apply π ξ) + let d : ℕ → K₀ := TopologicalSpace.denseSeq K₀ + have hd : DenseRange d := TopologicalSpace.denseRange_denseSeq K₀ + let Ω := separatingSequence ξ₀ d + let ω := normalizedSeparatingSequence ξ₀ d + let f₁ := vectorPositiveFunctional (sequenceAmplification ρ₀) ω + let K₁ := gnsHilbert f₁ + let ρ₁ : A →⋆ₐ[ℂ] (K₁ →L[ℂ] K₁) := gnsBundledHom f₁ + let W₁ : K₁ →ₗᵢ[ℂ] SequenceHilbert K₀ := + cyclicBundledGNSIsometry f₁ (sequenceAmplification ρ₀) ω + (vectorPositiveFunctional_apply _ _) + let D := sequenceStandardGNSData ρ₀ ξ₀ hξ₀ d hd + let S : StandardModularData K₁ := D.toStandardModularData + let V : K₁ →L[ℂ] H := (‖Ω‖ : ℂ) • + (W₀.toContinuousLinearMap.comp + ((lp.evalCLM ℂ (fun _ : ℕ => K₀) 2 0).comp W₁.toContinuousLinearMap)) + have hV (x : K₁) : V x = (‖Ω‖ : ℂ) • W₀ (W₁ x 0) := rfl + have hΩn : ‖Ω‖ ≤ 3 := by + have h := separatingSequence_norm_le ξ₀ d + change ‖Ω‖ ≤ ‖ξ₀‖ + 2 at h + rw [hξ₀] at h + norm_num at h ⊢ + exact h + have hΩ : ‖Ω‖ ≠ 0 := norm_ne_zero_iff.mpr (separatingSequence_ne_zero ξ₀ hξ₀ d) + refine ⟨K₁, S, ρ₁, V, rfl, ?_, ?_, ?_⟩ + · apply ContinuousLinearMap.opNorm_le_bound V (by norm_num) + intro x + rw [hV, norm_smul, Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg (norm_nonneg Ω), W₀.norm_map] + calc + ‖Ω‖ * ‖W₁ x 0‖ ≤ ‖Ω‖ * ‖W₁ x‖ := + mul_le_mul_of_nonneg_left (lp.norm_apply_le_norm (by norm_num) _ _) (norm_nonneg _) + _ = ‖Ω‖ * ‖x‖ := by rw [W₁.norm_map] + _ ≤ 3 * ‖x‖ := mul_le_mul_of_nonneg_right hΩn (norm_nonneg _) + · change V (gnsVector f₁ 1) = ξ + rw [hV, cyclicBundledGNSIsometry_one] + change (‖Ω‖ : ℂ) • W₀ (((‖Ω‖⁻¹ : ℝ) : ℂ) • Ω 0) = ξ + rw [separatingSequence_zero, map_smul, smul_smul, ← Complex.ofReal_mul, + mul_inv_cancel₀ hΩ, Complex.ofReal_one, one_smul, hW₀] + · intro a + apply ContinuousLinearMap.ext + intro x + rw [ContinuousLinearMap.comp_apply, ContinuousLinearMap.comp_apply, hV, hV, map_smul] + congr 1 + have h₁ := congrArg (fun T : K₁ →L[ℂ] SequenceHilbert K₀ => T x) + (cyclicBundledGNSIsometry_intertwines f₁ (sequenceAmplification ρ₀) ω + (vectorPositiveFunctional_apply _ _) a) + have h₀ := congrArg (fun T : K₀ →L[ℂ] H => T (W₁ x 0)) + (cyclicBundledGNSIsometry_intertwines f₀ π ξ + (vectorPositiveFunctional_apply _ _) a) + change W₀ (W₁ (ρ₁ a x) 0) = π a (W₀ (W₁ x 0)) + rw [show W₁ (ρ₁ a x) = sequenceAmplification ρ₀ a (W₁ x) from h₁] + exact h₀ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/CyclicStateNorm.lean b/lean/OAI/Analysis/OperatorAlgebra/CyclicStateNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..443d335afc9c88cb025fa090f8c657ba8285158e --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/CyclicStateNorm.lean @@ -0,0 +1,60 @@ +import Mathlib.Analysis.CStarAlgebra.GelfandNaimarkSegal +import Mathlib.Analysis.InnerProductSpace.Adjoint +import Mathlib.Tactic + +namespace OAI + +/-! A cyclic representation is bounded by any C*-representation carrying +the same cyclic vector state. The source algebra need not carry a norm. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {A B H : Type*} [Ring A] [StarRing A] [Algebra ℂ A] + [CStarAlgebra B] [PartialOrder B] [StarOrderedRing B] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma cyclic_vector_norm_eq_preGNS (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) + (q : A →⋆ₐ[ℂ] B) (φ : B →ₚ[ℂ] ℂ) (ξ : H) + (hφ : ∀ a, φ (q a) = inner ℂ ξ (π a ξ)) (b : A) : + ‖π b ξ‖ = ‖φ.toPreGNS (q b)‖ := by + rw [PositiveLinearMap.preGNS_norm_def, + PositiveLinearMap.ofPreGNS_toPreGNS, ← map_star q, ← map_mul q, hφ] + simp only [map_mul, map_star, mul_apply_eq_comp, + ContinuousLinearMap.star_eq_adjoint, ContinuousLinearMap.adjoint_inner_right, + ] + have hnorm : (inner ℂ (π b ξ) (π b ξ)).re = ‖π b ξ‖ ^ 2 := + inner_self_eq_norm_sq (𝕜 := ℂ) (π b ξ) + rw [hnorm, Real.sqrt_sq (norm_nonneg _)] + +theorem cyclic_representation_norm_le (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) + (q : A →⋆ₐ[ℂ] B) (φ : B →ₚ[ℂ] ℂ) (ξ : H) + (hξ : DenseRange (fun a => π a ξ)) + (hφ : ∀ a, φ (q a) = inner ℂ ξ (π a ξ)) (a : A) : + ‖π a‖ ≤ ‖q a‖ := by + have hn := cyclic_vector_norm_eq_preGNS π q φ ξ hφ + have hmul : ‖φ.leftMulMapPreGNS (q a)‖ ≤ ‖q a‖ := by + unfold PositiveLinearMap.leftMulMapPreGNS + exact LinearMap.mkContinuous_norm_le _ (norm_nonneg _) _ + refine (π a).opNorm_le_bound (norm_nonneg _) ?_ + refine isClosed_property hξ (isClosed_le (by fun_prop) (by fun_prop)) ?_ + intro b + calc + ‖π a (π b ξ)‖ = ‖π (a * b) ξ‖ := by rw [map_mul]; rfl + _ = ‖φ.toPreGNS (q (a * b))‖ := hn (a * b) + _ = ‖φ.leftMulMapPreGNS (q a) (φ.toPreGNS (q b))‖ := by + simp only [map_mul, PositiveLinearMap.leftMulMapPreGNS_apply, + PositiveLinearMap.ofPreGNS_toPreGNS] + _ ≤ ‖φ.leftMulMapPreGNS (q a)‖ * ‖φ.toPreGNS (q b)‖ := + (φ.leftMulMapPreGNS (q a)).le_opNorm _ + _ ≤ ‖q a‖ * ‖φ.toPreGNS (q b)‖ := + mul_le_mul_of_nonneg_right hmul (norm_nonneg _) + _ = ‖q a‖ * ‖π b ξ‖ := by rw [hn b] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/DensityQuadraticCompression.lean b/lean/OAI/Analysis/OperatorAlgebra/DensityQuadraticCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..8814be9007b18fd1bef703827b0cd1d3a84d403a --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/DensityQuadraticCompression.lean @@ -0,0 +1,103 @@ +import OAI.Analysis.OperatorAlgebra.DensityRootTrace + +namespace OAI + +/-! Passing the density-root trace identity through a common finite +support, without finite-dimensionality of the represented Hilbert space. -/ + +noncomputable section +open scoped TensorProduct InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H E F K : Type*} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E] + [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma tensorIsometry_compression (f : F →ₗᵢ[ℂ] H) (g : K →ₗᵢ[ℂ] E) + (A : H →L[ℂ] H) (B : E →L[ℂ] E) (z w : F ⊗[ℂ] K) : + inner ℂ (TensorProduct.mapIsometry f g z) + (TensorProduct.mapL A B (TensorProduct.mapIsometry f g w)) = + inner ℂ z (TensorProduct.mapL + (f.toContinuousLinearMap.adjoint ∘L A ∘L f.toContinuousLinearMap) + (g.toContinuousLinearMap.adjoint ∘L B ∘L g.toContinuousLinearMap) w) := by + induction z using TensorProduct.inductionOn with + | tmul x y => + induction w using TensorProduct.inductionOn with + | tmul v t => + simp only [TensorProduct.mapIsometry_apply, TensorProduct.map_tmul, + TensorProduct.mapL_tmul, TensorProduct.inner_tmul] + change inner ℂ (f x) (A (f v)) * inner ℂ (g y) (B (g t)) = + inner ℂ x (f.toContinuousLinearMap.adjoint (A (f v))) * + inner ℂ y (g.toContinuousLinearMap.adjoint (B (g t))) + rw [ContinuousLinearMap.adjoint_inner_right, ContinuousLinearMap.adjoint_inner_right] + rfl + | add w₁ w₂ h₁ h₂ => + simpa only [map_add, inner_add_right (𝕜 := ℂ)] using congrArg₂ (· + ·) h₁ h₂ + | add z₁ z₂ h₁ h₂ => + simpa only [map_add, inner_add_left (𝕜 := ℂ)] using congrArg₂ (· + ·) h₁ h₂ + +lemma finiteTensorDensity_compression (f : F →ₗᵢ[ℂ] H) (z : E ⊗[ℂ] F) + (A : H →L[ℂ] H) : + (finiteTensorDensity (TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) f z)).val A = + (finiteTensorDensity z).val (f.toContinuousLinearMap.adjoint ∘L A ∘L f.toContinuousLinearMap) := by + rw [finiteTensorDensity_apply, finiteTensorDensity_apply] + have h := tensorIsometry_compression (LinearIsometry.id : E →ₗᵢ[ℂ] E) f + (ContinuousLinearMap.id ℂ E) A z z + have hi : (LinearIsometry.id : E →ₗᵢ[ℂ] E).toContinuousLinearMap.adjoint ∘L + (ContinuousLinearMap.id ℂ E) ∘L (LinearIsometry.id : E →ₗᵢ[ℂ] E).toContinuousLinearMap = + ContinuousLinearMap.id ℂ E := by + change (ContinuousLinearMap.id ℂ E).adjoint ∘L (ContinuousLinearMap.id ℂ E) ∘L + (ContinuousLinearMap.id ℂ E) = ContinuousLinearMap.id ℂ E + rw [ContinuousLinearMap.adjoint_id] + simp only [ContinuousLinearMap.comp_id] + rw [hi] at h + exact h + +theorem densityRoot_left_quadratic (z : E ⊗[ℂ] H) (A : H →L[ℂ] H) : + inner ℂ (NuclearUltrapower.densityRoot z) + (densityLeftRepresentation A (NuclearUltrapower.densityRoot z)) = + (finiteTensorDensity z).val A := by + obtain ⟨F, hF, hFz⟩ := TensorProduct.exists_finite_submodule_right_of_setFinite + ({z} : Set (E ⊗[ℂ] H)) (Set.finite_singleton z) + let : FiniteDimensional ℂ F := hF + let : CompleteSpace F := FiniteDimensional.complete ℂ F + let : InnerProductSpace ℂ (StrongDual ℂ F) := NuclearUltrapower.strongDualInner + let : NormedAddCommGroup (F ⊗[ℂ] StrongDual ℂ F) := + TensorProduct.instNormedAddCommGroup (𝕜 := ℂ) (E := F) (F := StrongDual ℂ F) + let : InnerProductSpace ℂ (F ⊗[ℂ] StrongDual ℂ F) := + TensorProduct.instInnerProductSpace (𝕜 := ℂ) (E := F) (F := StrongDual ℂ F) + obtain ⟨w, hw⟩ := hFz (Set.mem_singleton z) + have hm : TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) F.subtypeₗᵢ w = z := hw + rw [← hm] + simp only [NuclearUltrapower.densityRoot_mapIsometry, densityLeft_coe, + UniformSpace.Completion.inner_coe (𝕜 := ℂ) (E := H ⊗[ℂ] StrongDual ℂ H)] + let f := F.subtypeₗᵢ + let g := NuclearUltrapower.dualIsometry f + let t := NuclearUltrapower.finiteOperatorTensor (CFC.sqrt (NuclearUltrapower.reducedDensity w)) + change inner ℂ (TensorProduct.mapIsometry f g t) + (TensorProduct.mapL A (ContinuousLinearMap.id ℂ (StrongDual ℂ H)) + (TensorProduct.mapIsometry f g t)) = _ + rw [tensorIsometry_compression] + have hg : g.toContinuousLinearMap.adjoint ∘L (ContinuousLinearMap.id ℂ (StrongDual ℂ H)) ∘L + g.toContinuousLinearMap = ContinuousLinearMap.id ℂ (StrongDual ℂ F) := by + apply ContinuousLinearMap.ext + intro x + have hx := congrArg (fun T : StrongDual ℂ F →L[ℂ] StrongDual ℂ F => T x) + g.adjoint_comp_self + exact hx + rw [hg] + have ht := densityRoot_left_quadratic_finite w + (f.toContinuousLinearMap.adjoint ∘L A ∘L f.toContinuousLinearMap) + simp only [densityRoot_eq_finiteOperatorTensor, densityLeft_coe, + UniformSpace.Completion.inner_coe (𝕜 := ℂ) (E := F ⊗[ℂ] StrongDual ℂ F)] at ht + rw [ht] + exact (finiteTensorDensity_compression f w A).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/DensityRootTrace.lean b/lean/OAI/Analysis/OperatorAlgebra/DensityRootTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..1b6d1cff088bfba3024821ff68bb181d56cd217a --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/DensityRootTrace.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.OperatorAlgebra.DensitySpatialRepresentation + +namespace OAI + +/-! The left spatial vector functional of a density root is the original +finite positive functional. The finite-dimensional computation is the +trace identity used before passage to a common finite support. -/ + +noncomputable section +open scoped InnerProductSpace TensorProduct ComplexOrder + +namespace WeakPureInfiniteness + +variable {H E : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E] + +lemma finiteOperatorTensor_left [FiniteDimensional ℂ H] (A T : H →L[ℂ] H) : + TensorProduct.mapL A (ContinuousLinearMap.id ℂ (StrongDual ℂ H)) + (NuclearUltrapower.finiteOperatorTensor T) = + NuclearUltrapower.finiteOperatorTensor (A * T) := by + classical + simp only [NuclearUltrapower.finiteOperatorTensor, map_sum, TensorProduct.mapL_tmul, + ContinuousLinearMap.id_apply, mul_apply_eq_comp] + +lemma densityRoot_eq_finiteOperatorTensor [FiniteDimensional ℂ H] (z : E ⊗[ℂ] H) : + NuclearUltrapower.densityRoot z = + (NuclearUltrapower.finiteOperatorTensor (CFC.sqrt (NuclearUltrapower.reducedDensity z)) : + NuclearUltrapower.HilbertSchmidt H) := by + apply NuclearUltrapower.hsOperator_injective + rw [NuclearUltrapower.hsOperator_densityRoot, NuclearUltrapower.hsOperator_coe, + NuclearUltrapower.tensorOperator_finiteOperatorTensor] + +lemma densityRoot_left_quadratic_finite [FiniteDimensional ℂ H] + (z : E ⊗[ℂ] H) (A : H →L[ℂ] H) : + inner ℂ (NuclearUltrapower.densityRoot z) + (densityLeftRepresentation A (NuclearUltrapower.densityRoot z)) = + (finiteTensorDensity z).val A := by + rw [densityRoot_eq_finiteOperatorTensor, densityLeft_coe, + UniformSpace.Completion.inner_coe (𝕜 := ℂ) (E := H ⊗[ℂ] StrongDual ℂ H), finiteOperatorTensor_left, + NuclearUltrapower.finiteOperatorTensor_inner, + (CFC.sqrt_nonneg (NuclearUltrapower.reducedDensity z)).isSelfAdjoint.star_eq] + let r := CFC.sqrt (NuclearUltrapower.reducedDensity z) + change LinearMap.trace ℂ H ((r * (A * r)).toLinearMap) = _ + have hc : LinearMap.trace ℂ H ((r * (A * r)).toLinearMap) = + LinearMap.trace ℂ H (((A * r) * r).toLinearMap) := + LinearMap.trace_mul_comm ℂ r.toLinearMap (A * r).toLinearMap + rw [hc, mul_assoc] + have hr : r * r = NuclearUltrapower.reducedDensity z := + CFC.sqrt_mul_sqrt_self _ (NuclearUltrapower.reducedDensity_nonneg z) + rw [hr, NuclearUltrapower.trace_reducedDensity, finiteTensorDensity_apply] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/DensitySpatialRepresentation.lean b/lean/OAI/Analysis/OperatorAlgebra/DensitySpatialRepresentation.lean new file mode 100644 index 0000000000000000000000000000000000000000..f0a25f9639a91279bcd8d972ba14ef90c9d34f26 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/DensitySpatialRepresentation.lean @@ -0,0 +1,85 @@ +import OAI.Analysis.OperatorAlgebra.HilbertDualOperators +import OAI.Analysis.OperatorAlgebra.HilbertSchmidtUnitaryActions + +namespace OAI + +/-! The left/right actions used by the finite-density argument are genuine +spatial star representations on the Hilbert–Schmidt completion. -/ + +noncomputable section +open scoped TensorProduct InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +instance densityHSNormed : NormedAddCommGroup (NuclearUltrapower.HilbertSchmidt H) := inferInstance +instance densityHSInner : InnerProductSpace ℂ (NuclearUltrapower.HilbertSchmidt H) := inferInstance +instance densityHSComplete : CompleteSpace (NuclearUltrapower.HilbertSchmidt H) := inferInstance +instance densityHSScalar : NormedSpace ℂ (NuclearUltrapower.HilbertSchmidt H) := inferInstance +instance densityHSBounded : IsBoundedSMul ℂ (NuclearUltrapower.HilbertSchmidt H) := + NormedSpace.toIsBoundedSMul +instance densityHSContinuous : ContinuousSMul ℂ (NuclearUltrapower.HilbertSchmidt H) := + IsBoundedSMul.continuousSMul + +def densityLeftRepresentation : (H →L[ℂ] H) →⋆ₐ[ℂ] + (NuclearUltrapower.HilbertSchmidt H →L[ℂ] NuclearUltrapower.HilbertSchmidt H) := + Pureness.spatialLeftHom (K := StrongDual ℂ H) (StarAlgHom.id ℂ (H →L[ℂ] H)) + +def densityRightRepresentation : (H →L[ℂ] H)ᵐᵒᵖ →⋆ₐ[ℂ] + (NuclearUltrapower.HilbertSchmidt H →L[ℂ] NuclearUltrapower.HilbertSchmidt H) := + Pureness.spatialRightHom (H := H) hilbertDualRepresentation + +lemma densityLeftRight_commute (T S : H →L[ℂ] H) : + Commute (densityLeftRepresentation T) (densityRightRepresentation (MulOpposite.op S)) := by + unfold densityLeftRepresentation densityRightRepresentation + exact Pureness.spatialLeftRight_commute (StarAlgHom.id ℂ (H →L[ℂ] H)) + (hilbertDualRepresentation (H := H)) T (MulOpposite.op S) + +lemma densityLeft_coe (T : H →L[ℂ] H) (z : H ⊗[ℂ] StrongDual ℂ H) : + densityLeftRepresentation T (z : NuclearUltrapower.HilbertSchmidt H) = + (TensorProduct.mapL T (ContinuousLinearMap.id ℂ (StrongDual ℂ H)) z : + NuclearUltrapower.HilbertSchmidt H) := + UnitalTomsWinter.spatialTensorOp_coe T 1 z + +lemma densityLeft_unitary (U : H ≃ₗᵢ[ℂ] H) : + densityLeftRepresentation (U : H →L[ℂ] H) = + (hsLeftUnitary U : NuclearUltrapower.HilbertSchmidt H →L[ℂ] NuclearUltrapower.HilbertSchmidt H) := by + apply UnitalTomsWinter.spatialTensorOp_ext (H := H) (K := StrongDual ℂ H) + intro x f + change UnitalTomsWinter.spatialTensorOp (U : H →L[ℂ] H) 1 + ((x ⊗ₜ[ℂ] f : H ⊗[ℂ] StrongDual ℂ H) : NuclearUltrapower.HilbertSchmidt H) = _ + rw [UnitalTomsWinter.spatialTensorOp_coe] + change (TensorProduct.mapL (U : H →L[ℂ] H) (1 : StrongDual ℂ H →L[ℂ] StrongDual ℂ H) (x ⊗ₜ[ℂ] f) : + NuclearUltrapower.HilbertSchmidt H) = hsLeftUnitary U _ + simp only [TensorProduct.mapL_tmul, one_apply_eq_self, hsLeftUnitary, + NuclearUltrapower.completionUnitary_coe, TensorProduct.congrIsometry_apply, + TensorProduct.congr_tmul] + rfl + +lemma densityRight_unitary (U : H ≃ₗᵢ[ℂ] H) : + densityRightRepresentation (MulOpposite.op (U : H →L[ℂ] H)) = + (hsRightUnitary U : NuclearUltrapower.HilbertSchmidt H →L[ℂ] NuclearUltrapower.HilbertSchmidt H) := by + apply UnitalTomsWinter.spatialTensorOp_ext (H := H) (K := StrongDual ℂ H) + intro x f + change UnitalTomsWinter.spatialTensorOp 1 (hilbertDualOperator (U : H →L[ℂ] H)) + ((x ⊗ₜ[ℂ] f : H ⊗[ℂ] StrongDual ℂ H) : NuclearUltrapower.HilbertSchmidt H) = _ + rw [UnitalTomsWinter.spatialTensorOp_coe] + change (TensorProduct.mapL (1 : H →L[ℂ] H) (hilbertDualOperator (U : H →L[ℂ] H)) (x ⊗ₜ[ℂ] f) : + NuclearUltrapower.HilbertSchmidt H) = hsRightUnitary U _ + simp only [TensorProduct.mapL_tmul, one_apply_eq_self, hsRightUnitary, + NuclearUltrapower.completionUnitary_coe, TensorProduct.congrIsometry_apply, + TensorProduct.congr_tmul] + have hf : hilbertDualOperator (U : H →L[ℂ] H) f = NuclearUltrapower.dualUnitary U.symm f := by + ext y + rw [hilbertDualOperator_apply, NuclearUltrapower.dualUnitary_apply] + rfl + change ((x ⊗ₜ[ℂ] hilbertDualOperator (U : H →L[ℂ] H) f : H ⊗[ℂ] StrongDual ℂ H) : + NuclearUltrapower.HilbertSchmidt H) = (x ⊗ₜ[ℂ] NuclearUltrapower.dualUnitary U.symm f) + rw [hf] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/DensityUnitaryCoefficients.lean b/lean/OAI/Analysis/OperatorAlgebra/DensityUnitaryCoefficients.lean new file mode 100644 index 0000000000000000000000000000000000000000..bc726404d338e05101e9dfc60cfceefc8f81bdde --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/DensityUnitaryCoefficients.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.OperatorAlgebra.DensitySpatialRepresentation +import OAI.Analysis.Nuclearity.SpatialCoefficientEstimate + +namespace OAI + +/-! Pointwise unitary identities for the spatial Hilbert–Schmidt action. -/ + +noncomputable section +open scoped InnerProductSpace +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma densityLeft_unitary_apply (U : H ≃ₗᵢ[ℂ] H) + (z : NuclearUltrapower.HilbertSchmidt H) : + densityLeftRepresentation (U : H →L[ℂ] H) z = hsLeftUnitary U z := by + exact congrArg (fun V : NuclearUltrapower.HilbertSchmidt H →L[ℂ] + NuclearUltrapower.HilbertSchmidt H => V z) (densityLeft_unitary U) + +lemma densityRight_unitary_apply (U : H ≃ₗᵢ[ℂ] H) + (z : NuclearUltrapower.HilbertSchmidt H) : + densityRightRepresentation (MulOpposite.op (U : H →L[ℂ] H)) z = hsRightUnitary U z := by + exact congrArg (fun V : NuclearUltrapower.HilbertSchmidt H →L[ℂ] + NuclearUltrapower.HilbertSchmidt H => V z) (densityRight_unitary U) + +lemma densityLeft_unitary_product_apply (T : H →L[ℂ] H) (U : H ≃ₗᵢ[ℂ] H) + (z : NuclearUltrapower.HilbertSchmidt H) : + (densityLeftRepresentation T * densityLeftRepresentation (U : H →L[ℂ] H)) z = + densityLeftRepresentation (T * (U : H →L[ℂ] H)) z := + congrArg (fun V : NuclearUltrapower.HilbertSchmidt H →L[ℂ] + NuclearUltrapower.HilbertSchmidt H => V z) + (map_mul (densityLeftRepresentation (H := H)) T (U : H →L[ℂ] H)).symm + +lemma density_unitary_defect_norm (U : H ≃ₗᵢ[ℂ] H) + (z : NuclearUltrapower.HilbertSchmidt H) : + ‖densityRightRepresentation (MulOpposite.op (U : H →L[ℂ] H)) z - + densityLeftRepresentation (U : H →L[ℂ] H) z‖ = + ‖hsLeftUnitary U z - hsRightUnitary U z‖ := by + rw [densityRight_unitary_apply, densityLeft_unitary_apply, norm_sub_rev] + +lemma density_unitary_product_coefficient (T : H →L[ℂ] H) (U : H ≃ₗᵢ[ℂ] H) + (z : NuclearUltrapower.HilbertSchmidt H) : + inner ℂ z ((densityLeftRepresentation T * + densityLeftRepresentation (U : H →L[ℂ] H)) z) = + inner ℂ z (densityLeftRepresentation (T * (U : H →L[ℂ] H)) z) := + congrArg (inner ℂ z) (densityLeft_unitary_product_apply T U z) + +lemma density_unitary_product_error (T : H →L[ℂ] H) (U : H ≃ₗᵢ[ℂ] H) + (z : NuclearUltrapower.HilbertSchmidt H) (hzn : ‖z‖ = 1) (α : ℂ) : + ‖inner ℂ z ((densityLeftRepresentation T * + densityRightRepresentation (MulOpposite.op (U : H →L[ℂ] H))) z) - α‖ ≤ + ‖densityLeftRepresentation T‖ * ‖hsLeftUnitary U z - hsRightUnitary U z‖ + + ‖inner ℂ z (densityLeftRepresentation (T * (U : H →L[ℂ] H)) z) - α‖ := by + have hb := norm_product_coefficient_error_le + (H := NuclearUltrapower.HilbertSchmidt H) z hzn + (densityLeftRepresentation (H := H) T) + (densityRightRepresentation (H := H) (MulOpposite.op (U : H →L[ℂ] H))) + (densityLeftRepresentation (H := H) (U : H →L[ℂ] H)) α + exact hb.trans_eq (by rw [density_unitary_defect_norm, density_unitary_product_coefficient]) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ExpectationDensityRoots.lean b/lean/OAI/Analysis/OperatorAlgebra/ExpectationDensityRoots.lean new file mode 100644 index 0000000000000000000000000000000000000000..47db52d2d703e4d60ed7538ec041f3fe0367e062 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ExpectationDensityRoots.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.OperatorAlgebra.FiniteVectorDensityTensor +import OAI.Analysis.OperatorAlgebra.ExpectationFiniteDensity + +namespace OAI + +/-! Application of the hypertrace separation and Powers–Størmer estimates +to an actual completely positive expectation. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +open scoped TensorProduct + +theorem densityRoot_finite_support {E H : Type*} [NormedAddCommGroup E] + [InnerProductSpace ℂ E] [CompleteSpace E] [NormedAddCommGroup H] + [InnerProductSpace ℂ H] [CompleteSpace H] (z : E ⊗[ℂ] H) : + ∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ x, NuclearUltrapower.hsOperator (NuclearUltrapower.densityRoot z) x ∈ F := by + obtain ⟨F, hF, hFz⟩ := TensorProduct.exists_finite_submodule_right_of_setFinite + ({z} : Set (E ⊗[ℂ] H)) (Set.finite_singleton z) + let : FiniteDimensional ℂ F := hF + obtain ⟨w, hw⟩ := hFz (Set.mem_singleton z) + have hm : TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) F.subtypeₗᵢ w = z := hw + refine ⟨F, hF, ?_⟩ + intro x + rw [← hm, NuclearUltrapower.densityRoot_mapIsometry, NuclearUltrapower.hsOperator_coe, + NuclearUltrapower.tensorOperator_liftOperatorTensor] + exact Subtype.property _ + +variable {H I J : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + [CompleteSpace H] [Fintype I] [Fintype J] + +/-- A finite tracial expectation supplies positive finite-rank density roots +of norm at most one, approximately invariant under the prescribed unitaries. -/ +theorem expectation_finite_density_roots (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (a : I → selfAdjoint M.toStarSubalgebra) (u : J → unitary M.toStarSubalgebra) + {ε : ℝ} (hε : 0 < ε) : + ∃ (n : ℕ) (w : Fin n → ℝ) (x : Fin n → H), + (∀ k, 0 ≤ w k) ∧ (∑ k, w k = 1) ∧ (∀ k, ‖x k‖ ≤ 1) ∧ + (∀ i, |(τ.functional (a i)).re - + ∑ k, w k * (inner ℂ (x k) (((a i : M.toStarSubalgebra) : H →L[ℂ] H) (x k))).re| < ε) ∧ + let z := NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x) + ‖z‖ ≤ 1 ∧ 0 ≤ NuclearUltrapower.hsOperator z ∧ + (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator z y ∈ F) ∧ + ∀ j, ‖NuclearUltrapower.hsConjugation + (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z - z‖ ^ 2 < ε := by + obtain ⟨n, w, x, hw, hws, hx, ha, hu⟩ := + expectation_finite_density M τ E hE hEr hEf a u hε + refine ⟨n, w, x, hw, hws, hx, ha, ?_⟩ + dsimp only + refine ⟨?_, ?_, densityRoot_finite_support _, ?_⟩ + · rw [NuclearUltrapower.densityRoot_norm] + exact finiteVectorDensityTensor_norm_le_one w hw hws x hx + · rw [NuclearUltrapower.hsOperator_densityRoot] + exact CFC.sqrt_nonneg _ + · intro j + exact (finiteVectorDensity_root_central w hw x + (subalgebraUnitaryIsometry M.toStarSubalgebra (u j))).trans_lt (hu j) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ExpectationFiniteDensity.lean b/lean/OAI/Analysis/OperatorAlgebra/ExpectationFiniteDensity.lean new file mode 100644 index 0000000000000000000000000000000000000000..ce23f0749304405b1a6639c81ba327114f63e9bc --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ExpectationFiniteDensity.lean @@ -0,0 +1,73 @@ +import OAI.Analysis.OperatorAlgebra.HypertraceFiniteDensity +import OAI.Analysis.OperatorAlgebra.ExpectationHypertrace + +namespace OAI + +/-! The constructed conditional expectation supplies the finite hypertrace +witness. All conjugations below are the actual unitaries of the represented +algebra, and the errors are measured in the norm of vector functionals. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H I J : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def subalgebraUnitaryIsometry (M : StarSubalgebra ℂ (H →L[ℂ] H)) (u : unitary M) : H ≃ₗᵢ[ℂ] H := + Unitary.linearIsometryEquiv (Unitary.map (StarMonoidHom.ofClass M.subtype) u) + +lemma conjugatedOperator_subalgebraUnitary (M : StarSubalgebra ℂ (H →L[ℂ] H)) + (u : unitary M) (T : H →L[ℂ] H) : + conjugatedOperator (subalgebraUnitaryIsometry M u) T = + star ((u : M) : H →L[ℂ] H) * T * ((u : M) : H →L[ℂ] H) := by + ext x + rfl + +lemma hypertrace_subalgebraUnitary_invariant (M : StarSubalgebra ℂ (H →L[ℂ] H)) + (φ : (H →L[ℂ] H) →ₚ[ℂ] ℂ) + (hc : ∀ (a : M) (T : H →L[ℂ] H), φ ((a : H →L[ℂ] H) * T) = φ (T * (a : H →L[ℂ] H))) + (u : unitary M) (T : H →L[ℂ] H) : + φ (conjugatedOperator (subalgebraUnitaryIsometry M u) T) = φ T := by + let v := Unitary.map (StarMonoidHom.ofClass M.subtype) u + rw [conjugatedOperator_subalgebraUnitary] + change φ (star (v : H →L[ℂ] H) * T * (v : H →L[ℂ] H)) = φ T + rw [mul_assoc] + have hh := hc (star (u : M)) (T * (v : H →L[ℂ] H)) + change φ (star (v : H →L[ℂ] H) * (T * (v : H →L[ℂ] H))) = + φ ((T * (v : H →L[ℂ] H)) * star (v : H →L[ℂ] H)) at hh + rw [hh, mul_assoc, Unitary.mul_star_self_of_mem v.property, mul_one] + +variable [Fintype I] [Fintype J] + +/-- Finite normal positive approximations with norm-small unitary defects, +obtained from the actual expectation and a tracial state. -/ +theorem expectation_finite_density (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (a : I → selfAdjoint M.toStarSubalgebra) (u : J → unitary M.toStarSubalgebra) + {ε : ℝ} (hε : 0 < ε) : + ∃ (n : ℕ) (w : Fin n → ℝ) (x : Fin n → H), + (∀ k, 0 ≤ w k) ∧ (∑ k, w k = 1) ∧ (∀ k, ‖x k‖ ≤ 1) ∧ + (∀ i, |(τ.functional (a i)).re - + ∑ k, w k * (inner ℂ (x k) (((a i : M.toStarSubalgebra) : H →L[ℂ] H) (x k))).re| < ε) ∧ + ∀ j, ‖finitePredualUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) + (finiteVectorDensity w x) - finiteVectorDensity w x‖ < ε := by + obtain ⟨φ, hφ, hφa, hc⟩ := expectation_hypertrace M τ E hE hEr hEf + have ha (i : I) : IsSelfAdjoint ((a i : M.toStarSubalgebra) : H →L[ℂ] H) := + (a i).property.map M.toStarSubalgebra.subtype + have hu (j : J) (T : H →L[ℂ] H) : + φ (conjugatedOperator (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) T) = φ T := + hypertrace_subalgebraUnitary_invariant M.toStarSubalgebra φ hc (u j) T + simpa only [hφa] using hypertrace_finite_density + (fun i => ((a i : M.toStarSubalgebra) : H →L[ℂ] H)) ha + (fun j => subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) φ hφ hu hε + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ExpectationHypertrace.lean b/lean/OAI/Analysis/OperatorAlgebra/ExpectationHypertrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..1d552c4cdd5d8ef0f7c84d7398fd323504f5dbf0 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ExpectationHypertrace.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.ModularTheory.CommutantExpectation +import OAI.Analysis.Nuclearity.CPFaithfulRestriction +import OAI.Analysis.TracialSplitting.ChallengeDefinitions + +namespace OAI + +/-! The finite part of the injectivity argument starts with a hypertrace. +Composing a tracial state with the actual cpc expectation gives that +hypertrace, since the multiplicative-domain calculation is bimodular. -/ + +noncomputable section +open scoped CStarAlgebra ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +theorem expectation_hypertrace (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) : + ∃ φ : (H →L[ℂ] H) →ₚ[ℂ] ℂ, φ 1 = 1 ∧ + (∀ a : M.toStarSubalgebra, φ a = τ.functional a) ∧ + ∀ (a : M.toStarSubalgebra) (T : H →L[ℂ] H), + φ ((a : H →L[ℂ] H) * T) = φ (T * (a : H →L[ℂ] H)) := by + let ι := M.toStarSubalgebra.subtype + let F : (H →L[ℂ] H) →L[ℂ] M.toStarSubalgebra := + E.codRestrict M.toStarSubalgebra.toSubalgebra.toSubmodule hEr + have hF : CompletelyPositive F := by + apply completelyPositive_of_faithful_postcomp F ι.toNonUnitalStarAlgHom Subtype.val_injective + exact hE + have he (a : M.toStarSubalgebra) : F (ι a) = a := by + apply Subtype.ext + exact hEf _ a.property + let φ : (H →L[ℂ] H) →ₚ[ℂ] ℂ := + PositiveLinearMap.mk₀ (τ.functional.toLinearMap.comp F.toLinearMap) + (fun T hT => τ.functional.map_nonneg (completelyPositive_map_nonneg hF hT)) + refine ⟨φ, ?_, ?_, ?_⟩ + · change τ.functional (F 1) = 1 + have h1 : F 1 = 1 := by simpa only [map_one] using he 1 + rw [h1, τ.normalized] + · intro a + change τ.functional (F (ι a)) = τ.functional a + rw [he] + · intro a T + change τ.functional (F (ι a * T)) = τ.functional (F (T * ι a)) + rw [cp_extension_representation_mul_left ι (StarAlgHom.id ℂ M.toStarSubalgebra) + F hF he, cp_extension_representation_mul_right ι (StarAlgHom.id ℂ M.toStarSubalgebra) + F hF he] + exact τ.tracial a (F T) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/FiniteHilbertCompression.lean b/lean/OAI/Analysis/OperatorAlgebra/FiniteHilbertCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..c15f3ae1816ae634e18b0488b354e1d094389347 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/FiniteHilbertCompression.lean @@ -0,0 +1,120 @@ +import OAI.Analysis.WeakInfiniteness.MatrixRepresentation +import OAI.Analysis.WeakInfiniteness.CentralState + +namespace OAI + +/-! # Completely positive compression to a finite Hilbert space + +This is the compression used for the finite Fock-space approximations. +-/ + +noncomputable section +open scoped CStarAlgebra ComplexOrder InnerProductSpace + +namespace WeakPureInfiniteness + +section Amplification + +variable {E H n : Type*} [Fintype n] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def amplifyHilbertMap (V : E →L[ℂ] H) : + PiLp 2 (fun _ : n => E) →L[ℂ] PiLp 2 (fun _ : n => H) := + (PiLp.continuousLinearEquiv 2 ℂ (fun _ : n => H)).symm.toContinuousLinearMap.comp + ((ContinuousLinearMap.pi fun i => V.comp (ContinuousLinearMap.proj i)).comp + (PiLp.continuousLinearEquiv 2 ℂ (fun _ : n => E)).toContinuousLinearMap) + +omit [Fintype n] [CompleteSpace E] [CompleteSpace H] in +@[simp] lemma amplifyHilbertMap_apply (V : E →L[ℂ] H) + (x : PiLp 2 (fun _ : n => E)) (i : n) : + amplifyHilbertMap V x i = V (x i) := by simp [amplifyHilbertMap] + +lemma amplifyHilbertMap_adjoint (V : E →L[ℂ] H) : + amplifyHilbertMap (n := n) V.adjoint = (amplifyHilbertMap (n := n) V).adjoint := by + rw [ContinuousLinearMap.eq_adjoint_iff] + intro x y + simp only [PiLp.inner_apply, amplifyHilbertMap_apply, + ContinuousLinearMap.adjoint_inner_left] + +end Amplification + +section Compression + +variable {A E H : Type*} + [NonUnitalCStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def hilbertCompressionLinear (π : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) (V : E →L[ℂ] H) : + A →ₗ[ℂ] (E →L[ℂ] E) where + toFun a := V.adjoint.comp ((π a).comp V) + map_add' a b := by ext x; simp + map_smul' c a := by ext x; simp + +omit [PartialOrder A] [StarOrderedRing A] in +lemma hilbertCompressionLinear_bound (π : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) + (V : E →L[ℂ] H) (a : A) : + ‖hilbertCompressionLinear π V a‖ ≤ (‖V‖ * ‖V‖) * ‖a‖ := by + calc + _ ≤ ‖V.adjoint‖ * (‖π a‖ * ‖V‖) := + (ContinuousLinearMap.opNorm_comp_le _ _).trans + (mul_le_mul_of_nonneg_left (ContinuousLinearMap.opNorm_comp_le _ _) (norm_nonneg _)) + _ ≤ ‖V‖ * (‖a‖ * ‖V‖) := by + rw [ContinuousLinearMap.adjoint.norm_map] + gcongr + exact NonUnitalStarAlgHom.norm_apply_le π a + _ = _ := by ring + +def hilbertCompression (π : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) (V : E →L[ℂ] H) : + A →L[ℂ] (E →L[ℂ] E) := + (hilbertCompressionLinear π V).mkContinuous (‖V‖ * ‖V‖) + (hilbertCompressionLinear_bound π V) + +omit [PartialOrder A] [StarOrderedRing A] in +@[simp] lemma hilbertCompression_apply (π : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) + (V : E →L[ℂ] H) (a : A) : + hilbertCompression π V a = V.adjoint.comp ((π a).comp V) := rfl + +omit [PartialOrder A] [StarOrderedRing A] in +lemma hilbertCompression_norm_le (π : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) + (V : E →L[ℂ] H) : ‖hilbertCompression π V‖ ≤ ‖V‖ * ‖V‖ := + ContinuousLinearMap.opNorm_le_bound _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) + (hilbertCompressionLinear_bound π V) + +lemma hilbertCompression_cp (π : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) (V : E →L[ℂ] H) : + CompletelyPositive (hilbertCompression π V) := by + intro n X hX + let Y : CStarMatrix (Fin n) (Fin n) (E →L[ℂ] E) := + CStarMatrix.ofMatrix (fun i j => hilbertCompression π V (X i j)) + let Z := CStarMatrix.mapₙₐ π X + have hZ : 0 ≤ matrixOperator Z := by + change 0 ≤ matrixOperatorHom (n := Fin n) (H := H) Z + exact map_nonneg (matrixOperatorHom (n := Fin n) (H := H)) + (map_nonneg (CStarMatrix.mapₙₐ π) hX) + have he : matrixOperator Y = (amplifyHilbertMap (n := Fin n) V).adjoint.comp + ((matrixOperator Z).comp (amplifyHilbertMap V)) := by + rw [← amplifyHilbertMap_adjoint] + ext x i + simp only [matrixOperator_apply, ContinuousLinearMap.comp_apply, + amplifyHilbertMap_apply, map_sum] + rfl + have hY : 0 ≤ matrixOperator Y := by + rw [he, ContinuousLinearMap.nonneg_iff_isPositive] + exact (ContinuousLinearMap.nonneg_iff_isPositive.mp hZ).adjoint_conj + (amplifyHilbertMap (n := Fin n) V) + have hreflect := (NonUnitalStarAlgHom.map_le_map_iff + (matrixOperatorHom (n := Fin n) (H := E)) matrixOperator_injective + (x := 0) (y := Y)).mp + apply hreflect + rw [map_zero] + change 0 ≤ matrixOperator Y + exact hY + +end Compression + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/FiniteOperatorExtension.lean b/lean/OAI/Analysis/OperatorAlgebra/FiniteOperatorExtension.lean new file mode 100644 index 0000000000000000000000000000000000000000..2cf5bc4698338f161d67060037470b71b2d0499b --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/FiniteOperatorExtension.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.Nuclearity.MatrixCPMapExtension + +namespace OAI + +/-! Finite-dimensional Hilbert-operator form of the matrix cpc extension +theorem. An orthonormal basis transports the matrix extension without changing +its positivity or norm. -/ + +noncomputable section +open scoped InnerProductSpace CStarAlgebra ComplexOrder + +namespace WeakPureInfiniteness + +variable {A B E : Type*} [CStarAlgebra A] [CStarAlgebra B] + [PartialOrder A] [StarOrderedRing A] [PartialOrder B] [StarOrderedRing B] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E] + [FiniteDimensional ℂ E] [Nontrivial E] + +theorem finiteOperator_cpc_extension (ι : A →⋆ₐ[ℂ] B) (hι : Function.Injective ι) + (φ : A →L[ℂ] (E →L[ℂ] E)) (hφ : CompletelyPositive φ) (hφn : ‖φ‖ ≤ 1) : + ∃ Φ : B →L[ℂ] (E →L[ℂ] E), CompletelyPositive Φ ∧ ‖Φ‖ ≤ 1 ∧ + ∀ a, Φ (ι a) = φ a := by + let n := Module.finrank ℂ E + have hn : 0 < n := Module.finrank_pos + let b := stdOrthonormalBasis ℂ E + let e : (E →L[ℂ] E) ≃⋆ₐ[ℂ] CStarMatrix (Fin n) (Fin n) ℂ := + b.repr.conjStarAlgEquiv.trans (scalarMatrixOperatorEquiv (Fin n)).symm + let eL := starHomContinuousLinear e.toStarAlgHom.toNonUnitalStarAlgHom + let φ' := eL.comp φ + have hφ' : CompletelyPositive φ' := completelyPositive_comp _ _ hφ + (starHomContinuous_completelyPositive _) + have hφ'n : ‖φ'‖ ≤ 1 := by + apply ContinuousLinearMap.opNorm_le_bound _ zero_le_one + intro a + change ‖e (φ a)‖ ≤ _ + exact (NonUnitalStarAlgHom.norm_apply_le e.toStarAlgHom.toNonUnitalStarAlgHom + (φ a)).trans ((φ.le_opNorm a).trans + (mul_le_mul_of_nonneg_right hφn (norm_nonneg a))) + obtain ⟨Φ', hΦ', hΦ'n, hΦ'e⟩ := matrix_cpc_extension (⟨0, hn⟩ : Fin n) ι hι φ' hφ' hφ'n + let dL := starHomContinuousLinear e.symm.toStarAlgHom.toNonUnitalStarAlgHom + let Φ := dL.comp Φ' + refine ⟨Φ, completelyPositive_comp _ _ hΦ' (starHomContinuous_completelyPositive _), ?_, ?_⟩ + · apply ContinuousLinearMap.opNorm_le_bound _ zero_le_one + intro a + change ‖e.symm (Φ' a)‖ ≤ _ + exact (NonUnitalStarAlgHom.norm_apply_le e.symm.toStarAlgHom.toNonUnitalStarAlgHom + (Φ' a)).trans ((Φ'.le_opNorm a).trans + (mul_le_mul_of_nonneg_right hΦ'n (norm_nonneg a))) + · intro a + change e.symm (Φ' (ι a)) = φ a + rw [hΦ'e] + exact e.symm_apply_apply (φ a) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/FiniteOperatorPredual.lean b/lean/OAI/Analysis/OperatorAlgebra/FiniteOperatorPredual.lean new file mode 100644 index 0000000000000000000000000000000000000000..0f4c856206154cfb5412c8590d17ab0b08ca3526 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/FiniteOperatorPredual.lean @@ -0,0 +1,138 @@ +import OAI.Analysis.Nuclearity.TensorCoefficientFunctional +import Mathlib.Analysis.InnerProductSpace.Dual +import Mathlib.Analysis.InnerProductSpace.Adjoint +import Mathlib.Analysis.Normed.Operator.Bilinear +import Mathlib.Analysis.Normed.Module.RCLike.Extend + +namespace OAI + +/-! Finite sums of vector functionals, with their norm as functionals on +bounded operators, have bounded operators as their continuous dual. This +finite predual is sufficient for the convex separation step in the +hypertrace argument; no trace-class completion is required here. -/ + +noncomputable section +open scoped InnerProductSpace ComplexConjugate + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma operatorCoefficient_norm_le (x y : H) : + ‖operatorCoefficient x y‖ ≤ ‖x‖ * ‖y‖ := by + apply ContinuousLinearMap.opNorm_le_bound _ (mul_nonneg (norm_nonneg x) (norm_nonneg y)) + intro T + calc + ‖operatorCoefficient x y T‖ ≤ ‖x‖ * ‖T y‖ := norm_inner_le_norm x (T y) + _ ≤ ‖x‖ * (‖T‖ * ‖y‖) := mul_le_mul_of_nonneg_left (T.le_opNorm y) (norm_nonneg x) + _ = (‖x‖ * ‖y‖) * ‖T‖ := by ring + +abbrev finiteOperatorPredual : Submodule ℂ (StrongDual ℂ (H →L[ℂ] H)) := + Submodule.span ℂ (Set.range (fun p : H × H => operatorCoefficient p.1 p.2)) + +instance finitePredualNormed : NormedAddCommGroup (finiteOperatorPredual (H := H)) := + inferInstance + +instance finitePredualComplex : NormedSpace ℂ (finiteOperatorPredual (H := H)) := + inferInstance + +instance finitePredualReal : NormedSpace ℝ (finiteOperatorPredual (H := H)) := + inferInstance + +def finiteOperatorCoefficient (x y : H) : finiteOperatorPredual (H := H) := + ⟨operatorCoefficient x y, Submodule.subset_span ⟨(x, y), rfl⟩⟩ + +omit [CompleteSpace H] in +@[simp] lemma finiteOperatorCoefficient_add_left (x z y : H) : + finiteOperatorCoefficient (x + z) y = finiteOperatorCoefficient x y + finiteOperatorCoefficient z y := by + apply Subtype.ext + ext T + exact inner_add_left _ _ _ + +omit [CompleteSpace H] in +@[simp] lemma finiteOperatorCoefficient_add_right (x y z : H) : + finiteOperatorCoefficient x (y + z) = finiteOperatorCoefficient x y + finiteOperatorCoefficient x z := by + apply Subtype.ext + ext T + change inner ℂ x (T (y + z)) = inner ℂ x (T y) + inner ℂ x (T z) + simp only [map_add, inner_add_right] + +omit [CompleteSpace H] in +@[simp] lemma finiteOperatorCoefficient_smul_left (c : ℂ) (x y : H) : + finiteOperatorCoefficient (c • x) y = star c • finiteOperatorCoefficient x y := by + apply Subtype.ext + ext T + change inner ℂ (c • x) (T y) = star c * inner ℂ x (T y) + simp only [inner_smul_left, starRingEnd_apply] + +omit [CompleteSpace H] in +@[simp] lemma finiteOperatorCoefficient_smul_right (c : ℂ) (x y : H) : + finiteOperatorCoefficient x (c • y) = c • finiteOperatorCoefficient x y := by + apply Subtype.ext + ext T + change inner ℂ x (T (c • y)) = c * inner ℂ x (T y) + simp only [map_smul, inner_smul_right] + +private def predualFunctionalRight (f : StrongDual ℂ (finiteOperatorPredual (H := H))) + (x : H) : H →L[ℂ] ℂ := + ({ toFun := fun y => f (finiteOperatorCoefficient x y) + map_add' := by intros; simp only [finiteOperatorCoefficient_add_right, map_add] + map_smul' := by intros; simp only [finiteOperatorCoefficient_smul_right, map_smul, + RingHom.id_apply] } : H →ₗ[ℂ] ℂ).mkContinuous (‖f‖ * ‖x‖) (fun y => by + calc + ‖f (finiteOperatorCoefficient x y)‖ ≤ ‖f‖ * ‖finiteOperatorCoefficient x y‖ := f.le_opNorm _ + _ ≤ ‖f‖ * (‖x‖ * ‖y‖) := mul_le_mul_of_nonneg_left + (operatorCoefficient_norm_le x y) (norm_nonneg f) + _ = (‖f‖ * ‖x‖) * ‖y‖ := by ring) + +private def predualFunctionalForm (f : StrongDual ℂ (finiteOperatorPredual (H := H))) : + H →L⋆[ℂ] H →L[ℂ] ℂ := + ({ toFun := predualFunctionalRight f + map_add' := by intros; ext y; simp only [predualFunctionalRight, + LinearMap.mkContinuous_apply, LinearMap.coe_mk, AddHom.coe_mk, + finiteOperatorCoefficient_add_left, map_add, add_apply] + map_smul' := by intros; ext y; simp only [predualFunctionalRight, + LinearMap.mkContinuous_apply, LinearMap.coe_mk, AddHom.coe_mk, + finiteOperatorCoefficient_smul_left, map_smul, smul_apply, starRingEnd_apply] } : H →ₗ⋆[ℂ] H →L[ℂ] ℂ).mkContinuous ‖f‖ + (fun x => by + change ‖predualFunctionalRight f x‖ ≤ ‖f‖ * ‖x‖ + unfold predualFunctionalRight + exact LinearMap.mkContinuous_norm_le _ (mul_nonneg (norm_nonneg f) (norm_nonneg x)) _) + +def finitePredualOperator (f : StrongDual ℂ (finiteOperatorPredual (H := H))) : H →L[ℂ] H := + (InnerProductSpace.continuousLinearMapOfBilin (predualFunctionalForm f)).adjoint + +lemma finitePredualOperator_coefficient (f : StrongDual ℂ (finiteOperatorPredual (H := H))) + (x y : H) : operatorCoefficient x y (finitePredualOperator f) = f (finiteOperatorCoefficient x y) := by + change inner ℂ x ((InnerProductSpace.continuousLinearMapOfBilin + (predualFunctionalForm f)).adjoint y) = _ + rw [ContinuousLinearMap.adjoint_inner_right, InnerProductSpace.continuousLinearMapOfBilin_apply] + rfl + +theorem finitePredualOperator_represents (f : StrongDual ℂ (finiteOperatorPredual (H := H))) + (ψ : finiteOperatorPredual (H := H)) : ψ.val (finitePredualOperator f) = f ψ := by + obtain ⟨ψ, hψ⟩ := ψ + induction hψ using Submodule.span_induction with + | mem ψ hψ => + obtain ⟨⟨x, y⟩, rfl⟩ := hψ + exact finitePredualOperator_coefficient f x y + | zero => change (0 : ℂ) = f 0; rw [map_zero] + | add x y hx hy ihx ihy => + change (x + y) (finitePredualOperator f) = f (⟨x, hx⟩ + ⟨y, hy⟩) + simp only [add_apply, map_add, ihx, ihy] + | smul c x hx ih => + change (c • x) (finitePredualOperator f) = f (c • ⟨x, hx⟩) + simp only [smul_apply, map_smul, ih] + +theorem finitePredual_real_duality (f : StrongDual ℝ (finiteOperatorPredual (H := H))) : + ∃ T : H →L[ℂ] H, ∀ ψ : finiteOperatorPredual (H := H), f ψ = (ψ.val T).re := by + refine ⟨finitePredualOperator (f.extendRCLike (𝕜 := ℂ)), ?_⟩ + intro ψ + rw [finitePredualOperator_represents] + exact (StrongDual.re_extendRCLike_apply (𝕜 := ℂ) f ψ).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/FinitePredualConjugation.lean b/lean/OAI/Analysis/OperatorAlgebra/FinitePredualConjugation.lean new file mode 100644 index 0000000000000000000000000000000000000000..e370c3a0038854ee9fd0d4ff9405525579efa93f --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/FinitePredualConjugation.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.OperatorAlgebra.FiniteOperatorPredual +import OAI.Analysis.PureInfiniteness.TwoMatrixNuclear + +namespace OAI + +/-! Unitary conjugation preserves the finite operator predual, contractively, +and carries a vector functional to the functional of the transformed vectors. -/ + +noncomputable section +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def conjugatedOperator (U : H ≃ₗᵢ[ℂ] H) : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H) := + starHomContinuousLinear U.symm.conjStarAlgEquiv.toStarAlgHom.toNonUnitalStarAlgHom + +@[simp] lemma conjugatedOperator_apply (U : H ≃ₗᵢ[ℂ] H) (T : H →L[ℂ] H) (x : H) : + conjugatedOperator U T x = U.symm (T (U x)) := rfl + +def predualUnitaryAmbient (U : H ≃ₗᵢ[ℂ] H) : + StrongDual ℂ (H →L[ℂ] H) →L[ℂ] StrongDual ℂ (H →L[ℂ] H) := + ({ toFun := fun ψ => ψ.comp (conjugatedOperator U) + map_add' := by intros; ext T; rfl + map_smul' := by intros; ext T; rfl } : + StrongDual ℂ (H →L[ℂ] H) →ₗ[ℂ] StrongDual ℂ (H →L[ℂ] H)).mkContinuous 1 + (fun ψ => by + change ‖ψ.comp (conjugatedOperator U)‖ ≤ 1 * ‖ψ‖ + simpa only [one_mul, conjugatedOperator] using (ContinuousLinearMap.opNorm_comp_le _ _).trans + ((mul_le_mul_of_nonneg_left (starHomContinuousLinear_norm_le_one _) (norm_nonneg ψ)).trans_eq + (mul_one ‖ψ‖))) + +lemma predualUnitaryAmbient_coefficient (U : H ≃ₗᵢ[ℂ] H) (x y : H) : + predualUnitaryAmbient U (operatorCoefficient x y) = operatorCoefficient (U x) (U y) := by + ext T + change inner ℂ x (U.symm (T (U y))) = inner ℂ (U x) (T (U y)) + rw [← U.inner_map_map x (U.symm (T (U y))), U.apply_symm_apply] + +lemma predualUnitaryAmbient_mem (U : H ≃ₗᵢ[ℂ] H) + {ψ : StrongDual ℂ (H →L[ℂ] H)} (hψ : ψ ∈ finiteOperatorPredual (H := H)) : + predualUnitaryAmbient U ψ ∈ finiteOperatorPredual (H := H) := by + induction hψ using Submodule.span_induction with + | mem ψ hψ => + obtain ⟨⟨x, y⟩, rfl⟩ := hψ + rw [predualUnitaryAmbient_coefficient] + exact (finiteOperatorCoefficient (U x) (U y)).property + | zero => simpa only [map_zero] using (finiteOperatorPredual (H := H)).zero_mem + | add x y hx hy ihx ihy => + simpa only [map_add] using (finiteOperatorPredual (H := H)).add_mem ihx ihy + | smul c x hx ih => + simpa only [map_smul, RingHom.id_apply] using (finiteOperatorPredual (H := H)).smul_mem c ih + +def finitePredualUnitary (U : H ≃ₗᵢ[ℂ] H) : + finiteOperatorPredual (H := H) →L[ℂ] finiteOperatorPredual (H := H) := + ((predualUnitaryAmbient U).comp (finiteOperatorPredual (H := H)).subtypeL).codRestrict _ + (fun ψ => predualUnitaryAmbient_mem U ψ.property) + +@[simp] lemma finitePredualUnitary_apply (U : H ≃ₗᵢ[ℂ] H) + (ψ : finiteOperatorPredual (H := H)) (T : H →L[ℂ] H) : + (finitePredualUnitary U ψ).val T = ψ.val (conjugatedOperator U T) := rfl + +@[simp] lemma finitePredualUnitary_coefficient (U : H ≃ₗᵢ[ℂ] H) (x y : H) : + finitePredualUnitary U (finiteOperatorCoefficient x y) = finiteOperatorCoefficient (U x) (U y) := by + apply Subtype.ext + exact predualUnitaryAmbient_coefficient U x y + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/FiniteVectorDensityTensor.lean b/lean/OAI/Analysis/OperatorAlgebra/FiniteVectorDensityTensor.lean new file mode 100644 index 0000000000000000000000000000000000000000..9a821b5900339d122844778658e703072bf358ad --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/FiniteVectorDensityTensor.lean @@ -0,0 +1,88 @@ +import OAI.Analysis.OperatorAlgebra.ReducedDensityPredual +import OAI.Analysis.OperatorAlgebra.HypertraceFiniteDensity + +namespace OAI + +/-! The finite positive functionals obtained by separation have explicit +tensor-vector and positive Hilbert–Schmidt square-root realizations. -/ + +noncomputable section +open scoped InnerProductSpace TensorProduct ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] +variable {n : ℕ} + +def finiteVectorDensityTensor (w : Fin n → ℝ) (x : Fin n → H) : + EuclideanSpace ℂ (Fin n) ⊗[ℂ] H := + ∑ k, (EuclideanSpace.basisFun (Fin n) ℂ k) ⊗ₜ[ℂ] ((Real.sqrt (w k) : ℂ) • x k) + +omit [CompleteSpace H] in +lemma finiteVectorDensityTensor_functional (w : Fin n → ℝ) (hw : ∀ k, 0 ≤ w k) + (x : Fin n → H) : + finiteTensorDensity (finiteVectorDensityTensor w x) = finiteVectorDensity w x := by + apply Subtype.ext + ext T + rw [finiteTensorDensity_apply] + simp only [finiteVectorDensityTensor, map_sum, TensorProduct.mapL_tmul, + ContinuousLinearMap.id_apply, sum_inner (𝕜 := ℂ), inner_sum (𝕜 := ℂ), TensorProduct.inner_tmul, + (EuclideanSpace.basisFun (Fin n) ℂ).inner_eq_ite] + simp only [ite_mul, one_mul, zero_mul, Finset.sum_ite_eq, Finset.mem_univ, ite_true] + change (∑ k, inner ℂ ((Real.sqrt (w k) : ℂ) • x k) + (T ((Real.sqrt (w k) : ℂ) • x k))) = _ + simp only [map_smul, inner_smul_left (𝕜 := ℂ), inner_smul_right (𝕜 := ℂ), + finiteVectorDensity, Submodule.coe_sum, Submodule.coe_smul, sum_apply, smul_apply] + apply Finset.sum_congr rfl + intro k _ + change star (Real.sqrt (w k) : ℂ) * ((Real.sqrt (w k) : ℂ) * inner ℂ (x k) (T (x k))) = + (w k : ℂ) * inner ℂ (x k) (T (x k)) + rw [Complex.star_def, Complex.conj_ofReal, ← mul_assoc, ← Complex.ofReal_mul, + Real.mul_self_sqrt (hw k)] + +omit [CompleteSpace H] in +lemma finiteVectorDensityTensor_norm_sq (w : Fin n → ℝ) (hw : ∀ k, 0 ≤ w k) + (x : Fin n → H) : + ‖finiteVectorDensityTensor w x‖ ^ 2 = ∑ k, w k * ‖x k‖ ^ 2 := by + have he := congrArg (fun ψ : finiteOperatorPredual (H := H) => (ψ.val 1).re) + (finiteVectorDensityTensor_functional w hw x) + rw [finiteTensorDensity_apply] at he + change (inner ℂ (finiteVectorDensityTensor w x) + (TensorProduct.mapL (ContinuousLinearMap.id ℂ (EuclideanSpace ℂ (Fin n))) + (ContinuousLinearMap.id ℂ H) (finiteVectorDensityTensor w x))).re = _ at he + rw [TensorProduct.mapL_id_id, ContinuousLinearMap.id_apply] at he + have hn := inner_self_eq_norm_sq (𝕜 := ℂ) (finiteVectorDensityTensor w x) + change (inner ℂ (finiteVectorDensityTensor w x) (finiteVectorDensityTensor w x)).re = + ‖finiteVectorDensityTensor w x‖ ^ 2 at hn + rw [hn] at he + simpa [finiteVectorDensity, Submodule.coe_sum, Submodule.coe_smul, finiteOperatorCoefficient, + operatorCoefficient_apply, inner_self_eq_norm_sq_to_K, ← Complex.ofReal_pow, Complex.mul_re] using he + +omit [CompleteSpace H] in +lemma finiteVectorDensityTensor_norm_le_one (w : Fin n → ℝ) (hw : ∀ k, 0 ≤ w k) + (hws : ∑ k, w k = 1) (x : Fin n → H) (hx : ∀ k, ‖x k‖ ≤ 1) : + ‖finiteVectorDensityTensor w x‖ ≤ 1 := by + have he : ‖finiteVectorDensityTensor w x‖ ^ 2 ≤ 1 := by + rw [finiteVectorDensityTensor_norm_sq w hw x, ← hws] + apply Finset.sum_le_sum + intro k _ + exact (mul_le_mul_of_nonneg_left (pow_le_one₀ (norm_nonneg _) (hx k)) (hw k)).trans_eq + (mul_one _) + nlinarith [norm_nonneg (finiteVectorDensityTensor w x)] + +/-- The hypertrace construction's norm-central finite functional yields an +actual positive finite-rank density root with the same centrality bound. -/ +theorem finiteVectorDensity_root_central (w : Fin n → ℝ) (hw : ∀ k, 0 ≤ w k) + (x : Fin n → H) (U : H ≃ₗᵢ[ℂ] H) : + ‖NuclearUltrapower.hsConjugation U + (NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x)) - + NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x)‖ ^ 2 ≤ + ‖finitePredualUnitary U (finiteVectorDensity w x) - finiteVectorDensity w x‖ := by + simpa only [finiteVectorDensityTensor_functional w hw x] using + densityRoot_unitary_predual_bound U (finiteVectorDensityTensor w x) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/FunctionalCommutant.lean b/lean/OAI/Analysis/OperatorAlgebra/FunctionalCommutant.lean new file mode 100644 index 0000000000000000000000000000000000000000..ff1eef94a1a2428c64e0c8a07f1a85547bc8c44e --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/FunctionalCommutant.lean @@ -0,0 +1,74 @@ +import OAI.Analysis.PureInfiniteness.NonunitalFunctionalRepresentation + +namespace OAI + +/-! The simultaneous representing operators lie in a genuine closed +commutant C*-algebra. This is the second tensor factor in KR02 7.18. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {D H : Type*} [CStarAlgebra D] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def representationCommutant (π : D →⋆ₐ[ℂ] (H →L[ℂ] H)) : StarSubalgebra ℂ (H →L[ℂ] H) := + StarSubalgebra.centralizer ℂ (Set.range π) + +instance representationCommutant_closed (π : D →⋆ₐ[ℂ] (H →L[ℂ] H)) : + IsClosed (representationCommutant π : Set (H →L[ℂ] H)) := + Set.isClosed_centralizer _ + +instance representationCommutant_cstar (π : D →⋆ₐ[ℂ] (H →L[ℂ] H)) : + CStarAlgebra (representationCommutant π) := + StarSubalgebra.cstarAlgebra _ + +lemma mem_representationCommutant (π : D →⋆ₐ[ℂ] (H →L[ℂ] H)) (T : H →L[ℂ] H) + (hc : ∀ a, Commute T (π a)) : T ∈ representationCommutant π := by + apply (StarSubalgebra.mem_centralizer_iff ℂ).mpr + rintro _ ⟨a, rfl⟩ + refine ⟨(hc a).eq.symm, ?_⟩ + simpa only [map_star] using (hc (star a)).eq.symm + +lemma representationCommutant_commute (π : D →⋆ₐ[ℂ] (H →L[ℂ] H)) + (a : D) (c : representationCommutant π) : Commute (π a) (c : H →L[ℂ] H) := + (StarSubalgebra.mem_centralizer_iff ℂ |>.mp c.property (π a) (Set.mem_range_self a)).1 + +lemma gns_vector_cyclic [PartialOrder D] [StarOrderedRing D] (f : D →ₚ[ℂ] ℂ) : + DenseRange (fun a => f.gnsStarAlgHom a (Pureness.stateGNSVector f)) := by + simp only [Pureness.stateGNS_apply_vector] + exact UniformSpace.Completion.denseRange_coe.comp f.toPreGNS.surjective.denseRange + (UniformSpace.Completion.continuous_coe _) + +variable {A I : Type*} [NonUnitalCStarAlgebra A] [Fintype I] + +local instance commutantUnitizationOrder : PartialOrder (Unitization ℂ A) := + CStarAlgebra.spectralOrder _ +local instance commutantUnitizationOrdered : StarOrderedRing (Unitization ℂ A) := + CStarAlgebra.spectralOrderedRing _ + +theorem finite_functionals_in_commutant (l : I → selfAdjoint A →L[ℝ] ℝ) : + ∃ f : Unitization ℂ A →ₚ[ℂ] ℂ, f 1 = 1 ∧ + ∃ c : I → representationCommutant f.gnsStarAlgHom, + (∀ i, IsSelfAdjoint (c i)) ∧ + ∀ i (a : selfAdjoint A), l i a = + (⟪Pureness.stateGNSVector f, + f.gnsStarAlgHom (a : Unitization ℂ A) + ((c i : f.GNS →L[ℂ] f.GNS) (Pureness.stateGNSVector f))⟫_ℂ).re := by + obtain ⟨f, hf, T, hT, hc, hv⟩ := finite_nonunital_functional_representation l + let c (i : I) : representationCommutant f.gnsStarAlgHom := + ⟨T i, mem_representationCommutant f.gnsStarAlgHom (T i) (hc i)⟩ + refine ⟨f, hf, c, ?_, ?_⟩ + · intro i + exact Subtype.ext (hT i) + · intro i a + rw [hv] + have he := congrArg (fun S : f.GNS →L[ℂ] f.GNS => S (Pureness.stateGNSVector f)) (hc i (a : Unitization ℂ A)).eq + exact congrArg (fun v => (⟪Pureness.stateGNSVector f, v⟫_ℂ).re) he + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSBundledIntertwining.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSBundledIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..b9ef1a2993c11ef3874ba5a31f6e4a803270e0da --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSBundledIntertwining.lean @@ -0,0 +1,32 @@ +import OAI.Analysis.OperatorAlgebra.GNSBundledOperators + +namespace OAI + +/-! Intertwining from vector formulas, stated entirely in the bundled GNS space. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] + +lemma gnsBundledLeft_intertwines (f : A →ₚ[ℂ] ℂ) + (V : gnsHilbert f →ₗᵢ[ℂ] H) (c : ℂ) (v : A → H) + (hV : ∀ a, V (gnsVector f a) = c • v a) + (a : A) (T : H →L[ℂ] H) (hv : ∀ b, T (v b) = v (a * b)) + (x : gnsHilbert f) : T (V x) = V (gnsBundledLeft f a x) := + gns_left_intertwines_of_vector_formula f V c v hV a T hv x + +lemma gnsBundledRight_intertwines (f : A →ₚ[ℂ] ℂ) + (ht : ∀ a b, f (a * b) = f (b * a)) + (V : gnsHilbert f →ₗᵢ[ℂ] H) (c : ℂ) (v : A → H) + (hV : ∀ a, V (gnsVector f a) = c • v a) + (b : A) (T : H →L[ℂ] H) (hv : ∀ a, T (v a) = v (a * b)) + (x : gnsHilbert f) : T (V x) = V (gnsBundledRight f ht b x) := + gns_right_intertwines_of_vector_formula f ht V c v hV b T hv x + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSBundledOperators.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSBundledOperators.lean new file mode 100644 index 0000000000000000000000000000000000000000..3f3c162b38a1be4aab25d02352cd5d8c93f1bdcd --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSBundledOperators.lean @@ -0,0 +1,33 @@ +import OAI.Analysis.OperatorAlgebra.TracialGNSIntertwiner + +namespace OAI + +/-! GNS operators with the same bundled Hilbert-space structures as the inclusion. +The underlying operators are the canonical left and right GNS actions. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness + +variable {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + +def gnsBundledLeft (f : A →ₚ[ℂ] ℂ) (a : A) : gnsHilbert f →L[ℂ] gnsHilbert f := + f.gnsStarAlgHom a + +def gnsBundledRight (f : A →ₚ[ℂ] ℂ) (ht : ∀ a b, f (a * b) = f (b * a)) + (b : A) : gnsHilbert f →L[ℂ] gnsHilbert f := + NuclearTrace.rightGNS f ht (MulOpposite.op b) + +lemma gnsBundledLeft_vector (f : A →ₚ[ℂ] ℂ) (a b : A) : + gnsBundledLeft f a (gnsVector f b) = gnsVector f (a * b) := + gnsVector_left f a b + +lemma gnsBundledRight_vector (f : A →ₚ[ℂ] ℂ) + (ht : ∀ a b, f (a * b) = f (b * a)) (a b : A) : + gnsBundledRight f ht b (gnsVector f a) = gnsVector f (a * b) := + gnsVector_right f ht a b + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSCornerRange.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSCornerRange.lean new file mode 100644 index 0000000000000000000000000000000000000000..3f082b6a61cb44a55104c56151d158a55fd3dd64 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSCornerRange.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.OperatorAlgebra.GNSVectorDensity + +namespace OAI + +/-! Range criteria for a GNS inclusion with a normalized vector formula. -/ +noncomputable section +open scoped ComplexOrder Topology +namespace WeakPureInfiniteness + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma normalizedCornerGNSInclusion_gnsVector + {K : Type*} [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + (W : K →ₗᵢ[ℂ] H) (f : A →ₚ[ℂ] ℂ) (π : A →⋆ₐ[ℂ] (K →L[ℂ] K)) (z : H) + (hf : ∀ a, f a = inner ℂ + (((‖z‖⁻¹ : ℝ) : ℂ) • W.toContinuousLinearMap.adjoint z) + (π a (((‖z‖⁻¹ : ℝ) : ℂ) • W.toContinuousLinearMap.adjoint z))) (a : A) : + normalizedCornerGNSInclusion W f π z hf (gnsVector f a) = + (((‖z‖⁻¹ : ℝ) : ℂ)) • isometricCornerLift W (π a) z := + normalizedCornerGNSInclusion_vector W f π z hf a + +omit [CompleteSpace H] in +lemma gnsInclusion_fixed_of_vectors (f : A →ₚ[ℂ] ℂ) + (V : gnsHilbert f →ₗᵢ[ℂ] H) (P : H →L[ℂ] H) + (c : ℂ) (v : A → H) (hV : ∀ a, V (gnsVector f a) = c • v a) + (hv : ∀ a, P (v a) = v a) (x : gnsHilbert f) : P (V x) = V x := by + apply gnsVector_induction_on f x + · exact isClosed_eq (P.continuous.comp V.continuous) V.continuous + · intro a + rw [hV, map_smul, hv] + +omit [CompleteSpace H] in +lemma gnsInclusion_range_of_dense_vectors (f : A →ₚ[ℂ] ℂ) + (V : gnsHilbert f →ₗᵢ[ℂ] H) (P : H →L[ℂ] H) + (c : ℂ) (hc : c ≠ 0) (v : A → H) (hV : ∀ a, V (gnsVector f a) = c • v a) + {ι : Type*} (T : ι → H) (hT : DenseRange T) (a : ι → A) + (hP : ∀ i, P (T i) = v (a i)) (x : H) : P x ∈ Set.range V := by + have hclosed : IsClosed (Set.range V) := V.isometry.isClosedEmbedding.isClosed_range + refine hT.induction_on x (hclosed.preimage P.continuous) ?_ + intro i + refine ⟨c⁻¹ • gnsVector f (a i), ?_⟩ + rw [map_smul, hV, smul_smul, inv_mul_cancel₀ hc, one_smul, hP] + +lemma isometricCornerProjection_eq_of_range + {K : Type*} [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + (V : K →ₗᵢ[ℂ] H) (P : H →L[ℂ] H) (hP : IsStarProjection P) + (hV : ∀ x, P (V x) = V x) (hR : ∀ x, P x ∈ Set.range V) : + P = isometricCornerProjection V := by + let Q := isometricCornerProjection V + have hQ : IsStarProjection Q := isometricCornerProjection_isStarProjection V + have h₁ : P * Q = Q := by + apply ContinuousLinearMap.ext + intro x + exact hV _ + have h₂ : Q * P = P := by + apply ContinuousLinearMap.ext + intro x + obtain ⟨y, hy⟩ := hR x + change Q (P x) = P x + rw [← hy] + exact isometricCornerProjection_inclusion V y + have h₃ : P * Q = P := by + simpa only [star_mul, hP.isSelfAdjoint.star_eq, hQ.isSelfAdjoint.star_eq] + using congrArg star h₂ + exact h₃.symm.trans h₁ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSCyclicRepresentation.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSCyclicRepresentation.lean new file mode 100644 index 0000000000000000000000000000000000000000..9b7edb8fce5bb4f4fa16b968284645a445eeaaa8 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSCyclicRepresentation.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.OperatorAlgebra.GNSBundledOperators + +namespace OAI + +/-! The canonical GNS representation on the explicitly bundled Hilbert space. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness + +variable {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + +def gnsBundledHom (f : A →ₚ[ℂ] ℂ) : A →⋆ₐ[ℂ] (gnsHilbert f →L[ℂ] gnsHilbert f) := + f.gnsStarAlgHom + +lemma gnsBundledHom_apply (f : A →ₚ[ℂ] ℂ) (a : A) : + gnsBundledHom f a = gnsBundledLeft f a := rfl + +lemma gnsBundledHom_cyclic (f : A →ₚ[ℂ] ℂ) : + DenseRange (fun a => gnsBundledHom f a (gnsVector f 1)) := by + intro x + refine gnsVector_induction_on f x isClosed_closure ?_ + intro a + apply subset_closure + refine ⟨a, ?_⟩ + change gnsBundledLeft f a (gnsVector f 1) = gnsVector f a + rw [gnsBundledLeft_vector, mul_one] + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma cyclicBundledGNSIsometry_intertwines (f : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hf : ∀ a, f a = inner ℂ ξ (π a ξ)) (a : A) : + (cyclicBundledGNSIsometry f π ξ hf).toContinuousLinearMap.comp (gnsBundledHom f a) = + (π a).comp (cyclicBundledGNSIsometry f π ξ hf).toContinuousLinearMap := by + apply ContinuousLinearMap.ext + intro x + exact cyclicGNSIsometry_intertwines f π ξ hf a x + +lemma cyclicBundledGNSIsometry_one (f : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hf : ∀ a, f a = inner ℂ ξ (π a ξ)) : + cyclicBundledGNSIsometry f π ξ hf (gnsVector f 1) = ξ := by + exact (cyclicBundledGNSIsometry_vector f π ξ hf (1 : A)).trans (by + rw [map_one] + rfl) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSHilbertStructure.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSHilbertStructure.lean new file mode 100644 index 0000000000000000000000000000000000000000..81f03cdd991ea8d09b72c13459c0cc113cb5d0df --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSHilbertStructure.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.OperatorAlgebra.CyclicGNSUnitary +import OAI.Analysis.WeakInfiniteness.TensorFoundations +import OAI.Analysis.OperatorAlgebra.IsometricCornerOperators + +namespace OAI + +/-! Bundled GNS spaces keep the canonical Hilbert structures explicit when +specializing to concrete represented corners. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness + +variable {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + +/-- The usual GNS Hilbert space, with its existing canonical structures. -/ +def gnsHilbert (φ : A →ₚ[ℂ] ℂ) : ComplexHilbert where + Carrier := φ.GNS + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +/-- The cyclic isometry with a bundled source Hilbert space. -/ +def cyclicBundledGNSIsometry (φ : A →ₚ[ℂ] ℂ) (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) + (ξ : H) (hφ : ∀ a, φ a = inner ℂ ξ (π a ξ)) : + gnsHilbert φ →ₗᵢ[ℂ] H := cyclicGNSIsometry φ π ξ hφ + +lemma cyclicBundledGNSIsometry_vector (φ : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hφ : ∀ a, φ a = inner ℂ ξ (π a ξ)) (a : A) : + cyclicBundledGNSIsometry φ π ξ hφ (φ.toPreGNS a : φ.GNS) = π a ξ := + cyclicGNSIsometry_vector φ π ξ hφ a + +variable {K : Type*} [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +/-- A normalized corner vector realizes the state on its GNS space. -/ +def normalizedCornerGNSInclusion (V : K →ₗᵢ[ℂ] H) (φ : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (K →L[ℂ] K)) (z : H) + (hφ : ∀ a, φ a = inner ℂ + (((‖z‖⁻¹ : ℝ) : ℂ) • V.toContinuousLinearMap.adjoint z) + (π a (((‖z‖⁻¹ : ℝ) : ℂ) • V.toContinuousLinearMap.adjoint z))) : + gnsHilbert φ →ₗᵢ[ℂ] H := + V.comp (cyclicBundledGNSIsometry φ π + (((‖z‖⁻¹ : ℝ) : ℂ) • V.toContinuousLinearMap.adjoint z) hφ) + +lemma normalizedCornerGNSInclusion_vector (V : K →ₗᵢ[ℂ] H) (φ : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (K →L[ℂ] K)) (z : H) + (hφ : ∀ a, φ a = inner ℂ + (((‖z‖⁻¹ : ℝ) : ℂ) • V.toContinuousLinearMap.adjoint z) + (π a (((‖z‖⁻¹ : ℝ) : ℂ) • V.toContinuousLinearMap.adjoint z))) (a : A) : + normalizedCornerGNSInclusion V φ π z hφ (φ.toPreGNS a : φ.GNS) = + ((‖z‖⁻¹ : ℝ) : ℂ) • isometricCornerLift V (π a) z := by + change V (cyclicBundledGNSIsometry φ π _ hφ (φ.toPreGNS a : φ.GNS)) = _ + rw [cyclicBundledGNSIsometry_vector, map_smul, map_smul] + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSHomIntertwining.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSHomIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..3d5a8ff23b0abcf9127eeb8c4bb027151aebff98 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSHomIntertwining.lean @@ -0,0 +1,27 @@ +import OAI.Analysis.OperatorAlgebra.GNSBundledIntertwining + +namespace OAI + +/-! The vector-formula intertwiner for a multiplicative represented action. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma gnsBundledLeft_intertwines_hom (f : A →ₚ[ℂ] ℂ) + (V : gnsHilbert f →ₗᵢ[ℂ] H) (c : ℂ) + (π : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hV : ∀ a, V (gnsVector f a) = c • π a ξ) + (a : A) (x : gnsHilbert f) : + π a (V x) = V (gnsBundledLeft f a x) := by + refine gnsBundledLeft_intertwines f V c (fun b => π b ξ) hV a (π a) ?_ x + intro b + exact congrArg (fun T : H →L[ℂ] H => T ξ) (map_mul π a b).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSProductNorm.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSProductNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..fcb107ee7d329a1f24d3427e9c2a0c3c07b0641e --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSProductNorm.lean @@ -0,0 +1,36 @@ +import OAI.Analysis.OperatorAlgebra.GNSBundledOperators +import OAI.Analysis.OperatorAlgebra.IsometricCornerNorm + +namespace OAI + +/-! Finite product norms transfer through a supported GNS inclusion. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma gns_product_sum_norm (f : A →ₚ[ℂ] ℂ) + (ht : ∀ a b, f (a * b) = f (b * a)) (V : gnsHilbert f →ₗᵢ[ℂ] H) + (L R : A → H →L[ℂ] H) + (hL : ∀ a x, L a (V x) = V (gnsBundledLeft f a x)) + (hR : ∀ b x, R b (V x) = V (gnsBundledRight f ht b x)) + (hP : ∀ a b, (L a * R b) * isometricCornerProjection V = L a * R b) + {I : Type*} [Fintype I] (a b : I → A) : + ‖∑ i, L (a i) * R (b i)‖ = + ‖∑ i, gnsBundledLeft f (a i) * gnsBundledRight f ht (b i)‖ := by + apply norm_eq_of_corner_intertwines V + · rw [Finset.sum_mul] + exact Finset.sum_congr rfl (fun i _ => hP (a i) (b i)) + · intro x + simp only [sum_apply, mul_apply_eq_comp, map_sum] + apply Finset.sum_congr rfl + intro i _ + rw [hR, hL] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSSeparableCyclic.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSSeparableCyclic.lean new file mode 100644 index 0000000000000000000000000000000000000000..8668bdf11a63ca568852580f490bad152fc0d90e --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSSeparableCyclic.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.OperatorAlgebra.GNSCyclicRepresentation + +namespace OAI + +/-! The cyclic GNS subrepresentation of a separable algebra is separable, +even when the original Hilbert representation is not. -/ +noncomputable section +open TopologicalSpace +open scoped ComplexOrder +namespace WeakPureInfiniteness + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def gnsVectorLinear (f : A →ₚ[ℂ] ℂ) : A →ₗ[ℂ] gnsHilbert f where + toFun := gnsVector f + map_add' a b := by + change ((f.toPreGNS (a + b) : f.PreGNS) : f.GNS) = _ + rw [map_add, UniformSpace.Completion.coe_add] + rfl + map_smul' c a := by + change ((f.toPreGNS (c • a) : f.PreGNS) : f.GNS) = _ + rw [map_smul, UniformSpace.Completion.coe_smul] + rfl + +lemma gnsVector_norm_le (f : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hf : ∀ a, f a = inner ℂ ξ (π a ξ)) (a : A) : + ‖gnsVector f a‖ ≤ ‖ξ‖ * ‖a‖ := by + calc + _ = ‖cyclicBundledGNSIsometry f π ξ hf (gnsVector f a)‖ := + ((cyclicBundledGNSIsometry f π ξ hf).norm_map _).symm + _ = ‖π a ξ‖ := congrArg norm (cyclicBundledGNSIsometry_vector f π ξ hf a) + _ ≤ ‖π a‖ * ‖ξ‖ := (π a).le_opNorm ξ + _ ≤ ‖a‖ * ‖ξ‖ := mul_le_mul_of_nonneg_right + (NonUnitalStarAlgHom.norm_apply_le π.toNonUnitalStarAlgHom a) (norm_nonneg ξ) + _ = _ := mul_comm _ _ + +def gnsVectorContinuous (f : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hf : ∀ a, f a = inner ℂ ξ (π a ξ)) : A →L[ℂ] gnsHilbert f := + (gnsVectorLinear f).mkContinuous ‖ξ‖ (gnsVector_norm_le f π ξ hf) + +lemma gnsVector_dense (f : A →ₚ[ℂ] ℂ) : DenseRange (gnsVector f) := by + intro x + refine gnsVector_induction_on f x isClosed_closure ?_ + intro a + exact subset_closure ⟨a, rfl⟩ + +lemma gns_separable_of_cyclic [SeparableSpace A] (f : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hf : ∀ a, f a = inner ℂ ξ (π a ξ)) : SeparableSpace (gnsHilbert f) := + (gnsVector_dense f).separableSpace (gnsVectorContinuous f π ξ hf).continuous + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSSeparatingSequence.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSSeparatingSequence.lean new file mode 100644 index 0000000000000000000000000000000000000000..7b0a73410b2b5976283c6814198f166fe431ab64 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSSeparatingSequence.lean @@ -0,0 +1,128 @@ +import OAI.Analysis.OperatorAlgebra.GNSSequenceAmplification +import Mathlib.Analysis.SpecificLimits.Basic +import OAI.Analysis.ModularTheory.CommutantExpectation + +namespace OAI + +/-! A concrete square-summable separating vector for the countable diagonal +amplification. Its zeroth coordinate is the prescribed vector. -/ +noncomputable section +open scoped Topology +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def separatingSequenceWeight (d : ℕ → H) (n : ℕ) : ℝ := + (1 / 2 : ℝ) ^ n / (1 + ‖d n‖) + +omit [InnerProductSpace ℂ H] [CompleteSpace H] in +lemma separatingSequenceWeight_pos (d : ℕ → H) (n : ℕ) : + 0 < separatingSequenceWeight d n := by + unfold separatingSequenceWeight + positivity + +def separatingSequenceTerm (d : ℕ → H) (n : ℕ) : SequenceHilbert H := + lp.single 2 (n + 1) ((separatingSequenceWeight d n : ℂ) • d n) + +omit [CompleteSpace H] in +lemma separatingSequenceTerm_norm_le (d : ℕ → H) (n : ℕ) : + ‖separatingSequenceTerm d n‖ ≤ (1 / 2 : ℝ) ^ n := by + rw [separatingSequenceTerm, lp.norm_single (by norm_num), norm_smul, Complex.norm_real, + Real.norm_eq_abs, abs_of_pos (separatingSequenceWeight_pos d n)] + calc + separatingSequenceWeight d n * ‖d n‖ ≤ + separatingSequenceWeight d n * (1 + ‖d n‖) := by + exact mul_le_mul_of_nonneg_left (by linarith) + (separatingSequenceWeight_pos d n).le + _ = _ := div_mul_cancel₀ _ (by positivity) + +omit [CompleteSpace H] in +lemma separatingSequenceTerm_norm_summable (d : ℕ → H) : + Summable (fun n => ‖separatingSequenceTerm d n‖) := + Summable.of_nonneg_of_le (fun _ => norm_nonneg _) + (separatingSequenceTerm_norm_le d) summable_geometric_two + +omit [CompleteSpace H] in +lemma sequenceEval_apply (n : ℕ) (x : SequenceHilbert H) : + lp.evalCLM ℂ (fun _ : ℕ => H) 2 n x = x n := rfl + +lemma separatingSequenceTerm_summable (d : ℕ → H) : + Summable (separatingSequenceTerm d) := + Summable.of_norm_bounded summable_geometric_two (separatingSequenceTerm_norm_le d) + +def separatingSequence (ξ : H) (d : ℕ → H) : SequenceHilbert H := + lp.single 2 0 ξ + ∑' n, separatingSequenceTerm d n + +lemma separatingSequence_zero (ξ : H) (d : ℕ → H) : + separatingSequence ξ d 0 = ξ := by + have he := (lp.evalCLM ℂ (fun _ : ℕ => H) 2 0).map_tsum + (separatingSequenceTerm_summable d) + change ξ + (lp.evalCLM ℂ (fun _ : ℕ => H) 2 0) (∑' n, separatingSequenceTerm d n) = ξ + rw [he] + simp [separatingSequenceTerm, sequenceEval_apply, lp.single_apply] + +lemma separatingSequence_succ (ξ : H) (d : ℕ → H) (n : ℕ) : + separatingSequence ξ d (n + 1) = (separatingSequenceWeight d n : ℂ) • d n := by + have he := (lp.evalCLM ℂ (fun _ : ℕ => H) 2 (n + 1)).map_tsum + (separatingSequenceTerm_summable d) + change 0 + (lp.evalCLM ℂ (fun _ : ℕ => H) 2 (n + 1)) + (∑' k, separatingSequenceTerm d k) = _ + rw [zero_add, he] + rw [tsum_eq_single n] + · simp [separatingSequenceTerm, sequenceEval_apply, lp.single_apply] + · intro k hk + simp [separatingSequenceTerm, sequenceEval_apply, lp.single_apply, Ne.symm hk] + +omit [CompleteSpace H] in +lemma separatingSequence_norm_le (ξ : H) (d : ℕ → H) : + ‖separatingSequence ξ d‖ ≤ ‖ξ‖ + 2 := by + calc + _ ≤ ‖lp.single 2 0 ξ‖ + ‖∑' n, separatingSequenceTerm d n‖ := norm_add_le _ _ + _ ≤ ‖ξ‖ + ∑' n, ‖separatingSequenceTerm d n‖ := by + rw [lp.norm_single (by norm_num)] + exact add_le_add le_rfl (norm_tsum_le_tsum_norm + (separatingSequenceTerm_norm_summable d)) + _ ≤ ‖ξ‖ + ∑' n, (1 / 2 : ℝ) ^ n := by + exact add_le_add le_rfl (Summable.tsum_le_tsum + (separatingSequenceTerm_norm_le d) + (separatingSequenceTerm_norm_summable d) summable_geometric_two) + _ = _ := by rw [tsum_geometric_two] + +lemma separatingSequence_separates (ξ : H) (d : ℕ → H) (hd : DenseRange d) + (T : SequenceHilbert H →L[ℂ] SequenceHilbert H) + (hT : ∀ i j, Commute (sequenceMatrixUnit (H := H) i j) T) + (hzero : T (separatingSequence ξ d) = 0) : T = 0 := by + have hdiag := sequence_diagonal_of_matrixUnit_commutation T hT + have hentry : sequenceEntryZero T = 0 := by + apply ContinuousLinearMap.ext + intro x + refine hd.induction_on x (isClosed_eq (sequenceEntryZero T).continuous continuous_const) ?_ + intro n + have hv := congrArg (fun v : SequenceHilbert H => v (n + 1)) hzero + rw [hdiag, sequenceDiagonal_apply, separatingSequence_succ, map_smul] at hv + have hc : (separatingSequenceWeight d n : ℂ) ≠ 0 := by + exact_mod_cast ne_of_gt (separatingSequenceWeight_pos d n) + exact (smul_eq_zero.mp hv).resolve_left hc + rw [hdiag, hentry] + exact map_zero (sequenceDiagonalHom (H := H)) + +open KirchbergRordam.GenericRW.GroupedFactors + +lemma sequence_bicommutant_separating {A : Type*} [CStarAlgebra A] + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) (d : ℕ → H) (hd : DenseRange d) + (T : SequenceHilbert H →L[ℂ] SequenceHilbert H) + (hT : T ∈ bicommutant (sequenceAmplification π).range) + (hz : T (separatingSequence ξ d) = 0) : T = 0 := by + apply separatingSequence_separates ξ d hd T _ hz + intro i j + apply (commute_iff_eq _ _).mpr + apply VonNeumannAlgebra.mem_commutant_iff.mp hT + apply (mem_commutantOf_iff _ _).mpr + rintro _ ⟨a, rfl⟩ + exact sequenceDiagonal_matrixUnit_commute (π a) i j + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSSequenceAmplification.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSSequenceAmplification.lean new file mode 100644 index 0000000000000000000000000000000000000000..053691afe8dc2c1bb58b1dfb4d9a478027f1736c --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSSequenceAmplification.lean @@ -0,0 +1,106 @@ +import OAI.Analysis.Nuclearity.NuclearQuotientExpectation +import OAI.Analysis.ModularRecovery.TomitaFundamental + +namespace OAI + +/-! Countable diagonal amplification and its double commutant. This is the +concrete amplification used to produce a separating vector. -/ +noncomputable section +open scoped InnerProductSpace +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +abbrev SequenceHilbert (H : Type*) [NormedAddCommGroup H] := lp (fun _ : ℕ => H) 2 + +def sequenceDiagonal (T : H →L[ℂ] H) : SequenceHilbert H →L[ℂ] SequenceHilbert H := + lp.mapCLM 2 (fun _ => T) (norm_nonneg T) (fun _ => le_rfl) + +omit [CompleteSpace H] in +lemma sequenceDiagonal_apply (T : H →L[ℂ] H) (x : SequenceHilbert H) (n : ℕ) : + sequenceDiagonal T x n = T (x n) := rfl + +lemma sequenceDiagonal_star (T : H →L[ℂ] H) : + sequenceDiagonal (star T) = star (sequenceDiagonal T) := by + change sequenceDiagonal (star T) = (sequenceDiagonal T).adjoint + rw [ContinuousLinearMap.eq_adjoint_iff] + intro x y + simp only [lp.inner_eq_tsum, sequenceDiagonal_apply] + exact tsum_congr (fun n => ContinuousLinearMap.adjoint_inner_left T (y n) (x n)) + +def sequenceDiagonalHom : (H →L[ℂ] H) →⋆ₐ[ℂ] (SequenceHilbert H →L[ℂ] SequenceHilbert H) where + toFun := sequenceDiagonal + map_zero' := by ext x n; rfl + map_one' := by ext x n; rfl + map_add' T U := by ext x n; rfl + map_mul' T U := by ext x n; rfl + commutes' c := by ext x n; rfl + map_star' := sequenceDiagonal_star + +def sequenceMatrixUnit (i j : ℕ) : SequenceHilbert H →L[ℂ] SequenceHilbert H := + (lp.singleContinuousLinearMap (𝕜 := ℂ) (E := fun _ : ℕ => H) 2 i).comp + (lp.evalCLM ℂ (fun _ : ℕ => H) 2 j) + +omit [CompleteSpace H] in +lemma sequenceMatrixUnit_apply (i j : ℕ) (x : SequenceHilbert H) (k : ℕ) : + sequenceMatrixUnit i j x k = if k = i then x j else 0 := by + change (lp.single (E := fun _ : ℕ => H) 2 i (x j)) k = _ + simp [lp.single_apply, Pi.single_apply] + +omit [CompleteSpace H] in +lemma sequenceDiagonal_matrixUnit_commute (T : H →L[ℂ] H) (i j : ℕ) : + Commute (sequenceDiagonal T) (sequenceMatrixUnit i j) := by + apply (commute_iff_eq _ _).mpr + apply ContinuousLinearMap.ext + intro x + apply lp.ext + funext k + simp only [mul_apply_eq_comp, sequenceDiagonal_apply, + sequenceMatrixUnit_apply] + split_ifs <;> simp only [map_zero] + +def sequenceEntryZero (T : SequenceHilbert H →L[ℂ] SequenceHilbert H) : H →L[ℂ] H := + (lp.evalCLM ℂ (fun _ : ℕ => H) 2 0).comp + (T.comp (lp.singleContinuousLinearMap (𝕜 := ℂ) (E := fun _ : ℕ => H) 2 0)) + +omit [CompleteSpace H] in +lemma sequenceEntryZero_apply (T : SequenceHilbert H →L[ℂ] SequenceHilbert H) (x : H) : + sequenceEntryZero T x = T (lp.single 2 0 x) 0 := rfl + +omit [CompleteSpace H] in +lemma sequence_diagonal_of_matrixUnit_commutation + (T : SequenceHilbert H →L[ℂ] SequenceHilbert H) + (hT : ∀ i j, Commute (sequenceMatrixUnit (H := H) i j) T) : + T = sequenceDiagonal (sequenceEntryZero T) := by + apply ContinuousLinearMap.ext + intro x + apply lp.ext + funext n + have h := congrArg (fun U : SequenceHilbert H →L[ℂ] SequenceHilbert H => U x 0) + (hT 0 n).eq + change T x n = T (lp.single (E := fun _ : ℕ => H) 2 0 (x n)) 0 at h + exact h + + +variable {A : Type*} [CStarAlgebra A] + +def sequenceAmplification (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) : + A →⋆ₐ[ℂ] (SequenceHilbert H →L[ℂ] SequenceHilbert H) := sequenceDiagonalHom.comp π + +lemma sequence_double_commutant_diagonal + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) + (T : SequenceHilbert H →L[ℂ] SequenceHilbert H) + (hT : ∀ R : SequenceHilbert H →L[ℂ] SequenceHilbert H, + (∀ a, Commute (sequenceAmplification π a) R) → Commute R T) : + T = sequenceDiagonal (sequenceEntryZero T) := by + apply sequence_diagonal_of_matrixUnit_commutation + intro i j + apply hT + intro a + exact sequenceDiagonal_matrixUnit_commute (π a) i j + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSStandardForm.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSStandardForm.lean new file mode 100644 index 0000000000000000000000000000000000000000..ca91337a53bb60dc1d98d21e90d72c550a2a976f --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSStandardForm.lean @@ -0,0 +1,61 @@ +import OAI.Analysis.OperatorAlgebra.GNSCyclicRepresentation +import OAI.Analysis.OperatorAlgebra.CyclicSeparatingCompression +import OAI.Analysis.ModularTheory.CommutantExpectation + +namespace OAI + +/-! A separating vector gives the actual standard GNS representation. -/ +noncomputable section +open scoped ComplexOrder Topology +namespace WeakPureInfiniteness +open BoundedRecovery KirchbergRordam.GenericRW.GroupedFactors + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma gns_bicommutant_separating (f : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) + (hf : ∀ a, f a = inner ℂ ξ (π a ξ)) + (hsep : ∀ T : H →L[ℂ] H, T ∈ bicommutant π.range → T ξ = 0 → T = 0) + (T : gnsHilbert f →L[ℂ] gnsHilbert f) + (hT : T ∈ bicommutant (gnsBundledHom f).range) + (hz : T (gnsVector f 1) = 0) : T = 0 := by + let W := cyclicBundledGNSIsometry f π ξ hf + apply separating_compression π (gnsBundledHom f) W + (cyclicBundledGNSIsometry_intertwines f π ξ hf) + (bicommutant π.range) + (fun a => subset_bicommutant π.range (π a) ⟨a, rfl⟩) + (gnsVector f 1) _ T _ hz + · intro U hU hzero + apply hsep U hU + rw [← cyclicBundledGNSIsometry_one f π ξ hf] + exact hzero + · intro R hR + exact VonNeumannAlgebra.mem_commutant_iff.mp hT R + ((mem_commutantOf_iff _ _).mpr (by + rintro _ ⟨a, rfl⟩ + exact hR a)) + +def standardGNSData (f : A →ₚ[ℂ] ℂ) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (ξ : H) (hξ : ‖ξ‖ = 1) + (hf : ∀ a, f a = inner ℂ ξ (π a ξ)) + (hsep : ∀ T : H →L[ℂ] H, T ∈ bicommutant π.range → T ξ = 0 → T = 0) : + CyclicSeparatingData (gnsHilbert f) where + M := bicommutant (gnsBundledHom f).range + xi := gnsVector f 1 + norm_xi := by + calc + ‖gnsVector f 1‖ = ‖cyclicBundledGNSIsometry f π ξ hf (gnsVector f 1)‖ := + ((cyclicBundledGNSIsometry f π ξ hf).norm_map _).symm + _ = 1 := by rw [cyclicBundledGNSIsometry_one, hξ] + cyclic := by + apply (gnsBundledHom_cyclic f).mono + rintro _ ⟨a, rfl⟩ + exact ⟨gnsBundledHom f a, subset_bicommutant _ _ ⟨a, rfl⟩, rfl⟩ + separating := gns_bicommutant_separating f π ξ hf hsep + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GNSVectorDensity.lean b/lean/OAI/Analysis/OperatorAlgebra/GNSVectorDensity.lean new file mode 100644 index 0000000000000000000000000000000000000000..66af62e57652062ee2ca24e174dc5197a1b07ccb --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GNSVectorDensity.lean @@ -0,0 +1,28 @@ +import OAI.Analysis.OperatorAlgebra.GNSHilbertStructure + +namespace OAI + +/-! Algebra vectors are dense in the bundled GNS space. -/ +noncomputable section +open scoped ComplexOrder Topology +namespace WeakPureInfiniteness + +variable {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + +def gnsVector (φ : A →ₚ[ℂ] ℂ) (a : A) : gnsHilbert φ := + (φ.toPreGNS a : φ.GNS) + +lemma gnsVector_induction_on (φ : A →ₚ[ℂ] ℂ) (x : gnsHilbert φ) + {p : gnsHilbert φ → Prop} (hp : IsClosed {x | p x}) + (h : ∀ a : A, p (gnsVector φ a)) : p x := by + induction x using UniformSpace.Completion.induction_on with + | hp => exact hp + | ih y => + have hy := h (φ.ofPreGNS y) + simpa only [gnsVector, PositiveLinearMap.toPreGNS_ofPreGNS] using hy + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GaussianConvolutionApproximation.lean b/lean/OAI/Analysis/OperatorAlgebra/GaussianConvolutionApproximation.lean new file mode 100644 index 0000000000000000000000000000000000000000..2dd6046b6c0cecebcd7325ce4dfd69ea36cbad38 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GaussianConvolutionApproximation.lean @@ -0,0 +1,117 @@ +import OAI.Analysis.OperatorAlgebra.ScalarTranslationConvolution +import OAI.Analysis.OperatorAlgebra.SmallTimeOperatorAverage + +namespace OAI + +/-! Actual integrable L² Gaussian convolution kernels give a uniformly +contractive strong approximate identity on vector-valued L². -/ + +noncomputable section +open MeasureTheory Filter +open scoped Topology + +namespace WeakPureInfiniteness + +lemma realGaussianDensity_continuous : Continuous realGaussianDensity := by + unfold realGaussianDensity + fun_prop + +lemma realGaussianDensity_bound (t : ℝ) : realGaussianDensity t ≤ 1 / Real.sqrt Real.pi := by + exact div_le_div_of_nonneg_right + (Real.exp_le_one_iff.mpr (neg_nonpos.mpr (sq_nonneg t))) (Real.sqrt_nonneg _) + +def gaussianConvolutionKernel (n : ℕ) (t : ℝ) : ℂ := + ((n + 1 : ℝ) : ℂ) * (realGaussianDensity ((n + 1 : ℝ) * t) : ℂ) + +lemma gaussianConvolutionKernel_continuous (n : ℕ) : Continuous (gaussianConvolutionKernel n) := + continuous_const.mul (Complex.continuous_ofReal.comp + (realGaussianDensity_continuous.comp (continuous_const.mul continuous_id))) + +lemma gaussianConvolutionKernel_integrable (n : ℕ) : Integrable (gaussianConvolutionKernel n) := by + have hN : (n + 1 : ℝ) ≠ 0 := by positivity + have hi := (integrable_comp_mul_left_iff realGaussianDensity hN).mpr realGaussianDensity_integrable + exact hi.ofReal.const_mul ((n + 1 : ℝ) : ℂ) + +lemma gaussianConvolutionKernel_bound (n : ℕ) (t : ℝ) : + ‖gaussianConvolutionKernel n t‖ ≤ (n + 1 : ℝ) / Real.sqrt Real.pi := by + change ‖((n + 1 : ℝ) : ℂ) * (realGaussianDensity ((n + 1 : ℝ) * t) : ℂ)‖ ≤ _ + rw [norm_mul, Complex.norm_real, Complex.norm_real, Real.norm_eq_abs, Real.norm_eq_abs, + abs_of_nonneg (by positivity : 0 ≤ (n + 1 : ℝ)), + abs_of_nonneg (realGaussianDensity_nonneg _)] + exact (mul_le_mul_of_nonneg_left (realGaussianDensity_bound _) (by positivity)).trans_eq + (by ring) + +lemma gaussianConvolutionKernel_memLp (n : ℕ) : + MemLp (gaussianConvolutionKernel n) 2 (volume : Measure ℝ) := by + apply (memLp_two_iff_integrable_sq_norm + (gaussianConvolutionKernel_continuous n).aestronglyMeasurable).mpr + apply ((gaussianConvolutionKernel_integrable n).norm.const_mul + ((n + 1 : ℝ) / Real.sqrt Real.pi)).mono' + ((gaussianConvolutionKernel_continuous n).norm.pow 2).aestronglyMeasurable + filter_upwards [] with t + rw [Real.norm_eq_abs, abs_of_nonneg (sq_nonneg _), pow_two] + exact mul_le_mul_of_nonneg_right (gaussianConvolutionKernel_bound n t) (norm_nonneg _) + +def gaussianConvolutionVector (n : ℕ) : Lp ℂ 2 (volume : Measure ℝ) := + (gaussianConvolutionKernel_memLp n).toLp (gaussianConvolutionKernel n) + +lemma gaussianConvolutionVector_ae (n : ℕ) : + gaussianConvolutionVector n =ᵐ[volume] gaussianConvolutionKernel n := MemLp.coeFn_toLp _ + +lemma gaussianConvolutionVector_integrable (n : ℕ) : + Integrable (gaussianConvolutionVector n : ℝ → ℂ) := + (gaussianConvolutionKernel_integrable n).congr (gaussianConvolutionVector_ae n).symm + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +omit [CompleteSpace H] in +lemma gaussianConvolutionKernel_apply (n : ℕ) (f : Lp H 2 (volume : Measure ℝ)) : + integratedModularTranslation (gaussianConvolutionKernel n) (gaussianConvolutionKernel_integrable n) f = + smallTimeOperatorAverage (modularLpTranslateOperator (H := H)) + continuous_modularLpTranslate 1 modularLpTranslate_opNorm_le n f := by + let N : ℝ := n + 1 + have hN : 0 < N := by dsimp [N]; positivity + change (∫ t : ℝ, ((N : ℂ) * (realGaussianDensity (N * t) : ℂ)) • + modularLpTranslate volume t f) = + ∫ t : ℝ, (realGaussianDensity t : ℂ) • modularLpTranslate volume (t / N) f + calc + _ = (N : ℂ) • ∫ t : ℝ, (realGaussianDensity (N * t) : ℂ) • + modularLpTranslate volume ((N * t) / N) f := by + rw [← integral_smul] + apply integral_congr_ae + filter_upwards [] with t + rw [mul_div_cancel_left₀ t hN.ne', smul_smul] + _ = (N : ℂ) • (|N⁻¹| • + ∫ t : ℝ, (realGaussianDensity t : ℂ) • modularLpTranslate volume (t / N) f) := by + exact congrArg (fun v : Lp H 2 (volume : Measure ℝ) => (N : ℂ) • v) + (Measure.integral_comp_mul_left + (fun t : ℝ => (realGaussianDensity t : ℂ) • modularLpTranslate volume (t / N) f) N) + _ = _ := by + rw [abs_of_pos (inv_pos.mpr hN)] + change (N : ℂ) • ((N⁻¹ : ℝ) : ℂ) • + (∫ t : ℝ, (realGaussianDensity t : ℂ) • modularLpTranslate volume (t / N) f) = _ + rw [smul_smul, ← Complex.ofReal_mul, mul_inv_cancel₀ hN.ne', Complex.ofReal_one, one_smul] + +omit [CompleteSpace H] in +lemma gaussianConvolutionVector_apply (n : ℕ) (f : Lp H 2 (volume : Measure ℝ)) : + integratedModularTranslation (gaussianConvolutionVector n) (gaussianConvolutionVector_integrable n) f = + smallTimeOperatorAverage (modularLpTranslateOperator (H := H)) + continuous_modularLpTranslate 1 modularLpTranslate_opNorm_le n f := by + rw [← gaussianConvolutionKernel_apply] + apply integral_congr_ae + filter_upwards [gaussianConvolutionVector_ae n] with t ht + rw [ht] + +lemma gaussianConvolutionVector_strong (f : Lp H 2 (volume : Measure ℝ)) : + Tendsto (fun n => integratedModularTranslation (gaussianConvolutionVector n) + (gaussianConvolutionVector_integrable n) f) atTop (𝓝 f) := by + have h := smallTimeOperatorAverage_strong (modularLpTranslateOperator (H := H)) + continuous_modularLpTranslate 1 modularLpTranslate_opNorm_le f + simpa only [gaussianConvolutionVector_apply, modularLpTranslateOperator_apply, + modularLpTranslate_zero] using h + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GaussianKernelFubini.lean b/lean/OAI/Analysis/OperatorAlgebra/GaussianKernelFubini.lean new file mode 100644 index 0000000000000000000000000000000000000000..5aca1d28bf317e22e77851444a172a6c20aa9114 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GaussianKernelFubini.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.OperatorAlgebra.GaussianSchurFactor +import Mathlib.MeasureTheory.Integral.Prod + +namespace OAI + +/-! The Gaussian/character integral may be interchanged with an integrable +scalar kernel. This is the actual Fubini step of dual regularization. -/ + +noncomputable section +open MeasureTheory + +namespace WeakPureInfiniteness + +theorem gaussian_character_kernel_integral (A : ℝ × ℝ → ℂ) + (hA : Integrable A (volume.prod volume)) (n : ℕ) : + (∫ r : ℝ, (realGaussianDensity r : ℂ) * + ∫ p : ℝ × ℝ, BoundedRecovery.spectralCharacter (-(r / (n + 1 : ℝ))) + (p.2 - p.1) * A p ∂volume.prod volume) = + ∫ p : ℝ × ℝ, gaussianSchurFactor n (p.2 - p.1) * A p ∂volume.prod volume := by + have hρ : Integrable (fun r : ℝ => (realGaussianDensity r : ℂ)) := + realGaussianDensity_integrable.ofReal + have hc : Continuous (fun z : ℝ × (ℝ × ℝ) => + BoundedRecovery.spectralCharacter (-(z.1 / (n + 1 : ℝ))) (z.2.2 - z.2.1)) := by + simp only [BoundedRecovery.spectralCharacter_apply] + fun_prop + have hi : Integrable (fun z : ℝ × (ℝ × ℝ) => + (realGaussianDensity z.1 : ℂ) * + (BoundedRecovery.spectralCharacter (-(z.1 / (n + 1 : ℝ))) (z.2.2 - z.2.1) * A z.2)) + (volume.prod (volume.prod volume)) := by + apply (hρ.mul_prod hA).mono + (hρ.aestronglyMeasurable.comp_fst.mul + (hc.aestronglyMeasurable.mul hA.aestronglyMeasurable.comp_snd)) + filter_upwards [] with z + simp only [Pi.mul_apply, norm_mul, BoundedRecovery.spectralCharacter_norm, one_mul] + exact le_rfl + calc + _ = ∫ r : ℝ, ∫ p : ℝ × ℝ, (realGaussianDensity r : ℂ) * + (BoundedRecovery.spectralCharacter (-(r / (n + 1 : ℝ))) (p.2 - p.1) * A p) + ∂volume.prod volume := by simp only [integral_const_mul] + _ = ∫ p : ℝ × ℝ, (∫ r : ℝ, (realGaussianDensity r : ℂ) * + (BoundedRecovery.spectralCharacter (-(r / (n + 1 : ℝ))) (p.2 - p.1) * A p)) + ∂volume.prod volume := integral_integral_swap hi + _ = _ := by + apply integral_congr_ae + filter_upwards [] with p + change (∫ r : ℝ, (realGaussianDensity r : ℂ) * + (BoundedRecovery.spectralCharacter (-(r / (n + 1 : ℝ))) (p.2 - p.1) * A p)) = + (∫ r : ℝ, (realGaussianDensity r : ℂ) * + BoundedRecovery.spectralCharacter (-(r / (n + 1 : ℝ))) (p.2 - p.1)) * A p + rw [← integral_mul_const] + apply integral_congr_ae + filter_upwards [] with r + ring + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/GaussianSchurFactor.lean b/lean/OAI/Analysis/OperatorAlgebra/GaussianSchurFactor.lean new file mode 100644 index 0000000000000000000000000000000000000000..e739dd7ae99e9c7c9ebfc368d54adbe309804a5f --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/GaussianSchurFactor.lean @@ -0,0 +1,101 @@ +import OAI.Analysis.OperatorAlgebra.SmallTimeOperatorAverage +import OAI.Analysis.ModularRecovery.SpectralCalculus +import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform + +namespace OAI + +/-! The integrable Schur factors obtained by normalized Gaussian averaging +of the dual characters. No limit or integrability is postulated. -/ + +noncomputable section +open MeasureTheory Filter +open scoped Topology + +namespace WeakPureInfiniteness + +def gaussianSchurFactor (n : ℕ) (r : ℝ) : ℂ := + ∫ t : ℝ, (realGaussianDensity t : ℂ) * + BoundedRecovery.spectralCharacter (-(t / (n + 1 : ℝ))) r + +lemma gaussianSchurFactor_integrand (n : ℕ) (r : ℝ) : + Integrable (fun t : ℝ => (realGaussianDensity t : ℂ) * + BoundedRecovery.spectralCharacter (-(t / (n + 1 : ℝ))) r) := by + have hi : Integrable (fun t : ℝ => (realGaussianDensity t : ℂ)) := + realGaussianDensity_integrable.ofReal + have hc : Continuous (fun t : ℝ => + BoundedRecovery.spectralCharacter (-(t / (n + 1 : ℝ))) r) := by + simp only [BoundedRecovery.spectralCharacter_apply] + fun_prop + apply hi.norm.mono' (hi.aestronglyMeasurable.mul hc.aestronglyMeasurable) + filter_upwards [] with t + simp only [Pi.mul_apply] + rw [norm_mul, BoundedRecovery.spectralCharacter_norm, mul_one] + +lemma gaussianSchurFactor_norm_le (n : ℕ) (r : ℝ) : ‖gaussianSchurFactor n r‖ ≤ 1 := by + unfold gaussianSchurFactor + calc + _ ≤ ∫ t : ℝ, ‖(realGaussianDensity t : ℂ) * + BoundedRecovery.spectralCharacter (-(t / (n + 1 : ℝ))) r‖ := norm_integral_le_integral_norm _ + _ = ∫ t : ℝ, realGaussianDensity t := by + apply integral_congr_ae + filter_upwards [] with t + rw [norm_mul, BoundedRecovery.spectralCharacter_norm, mul_one, Complex.norm_real, + Real.norm_eq_abs, abs_of_nonneg (realGaussianDensity_nonneg t)] + _ = 1 := realGaussianDensity_integral + +lemma gaussianSchurFactor_formula (n : ℕ) (r : ℝ) : + gaussianSchurFactor n r = + ((Real.pi : ℂ) ^ (1 / 2 : ℂ) / (Real.sqrt Real.pi : ℂ)) * + (Real.exp (-(r / (n + 1 : ℝ)) ^ 2 / 4) : ℂ) := by + have he (t : ℝ) : (realGaussianDensity t : ℂ) * + BoundedRecovery.spectralCharacter (-(t / (n + 1 : ℝ))) r = + (Complex.exp (Complex.I * (-(r / (n + 1 : ℝ)) : ℂ) * t) * + Complex.exp (-(1 : ℂ) * (t : ℂ) ^ 2)) / (Real.sqrt Real.pi : ℂ) := by + have hc : BoundedRecovery.spectralCharacter (-(t / (n + 1 : ℝ))) r = + Complex.exp (Complex.I * (-(r / (n + 1 : ℝ)) : ℂ) * t) := by + change Complex.exp _ = Complex.exp _ + congr 1 + push_cast + ring + have hg : (realGaussianDensity t : ℂ) = + Complex.exp (-(1 : ℂ) * (t : ℂ) ^ 2) / (Real.sqrt Real.pi : ℂ) := by + simp only [realGaussianDensity, Complex.ofReal_div, Complex.ofReal_exp, + Complex.ofReal_neg, Complex.ofReal_pow, neg_mul, one_mul] + rw [hc, hg] + ring + unfold gaussianSchurFactor + simp_rw [he] + rw [integral_div, fourierIntegral_gaussian (by norm_num : (0 : ℝ) < (1 : ℂ).re)] + simp only [div_one, mul_one] + have hexp : Complex.exp (- (-(r / (n + 1 : ℝ)) : ℂ) ^ 2 / (4 : ℂ)) = + (Real.exp (-(r / (n + 1 : ℝ)) ^ 2 / 4) : ℂ) := by + rw [Complex.ofReal_exp] + congr 1 + push_cast + ring + rw [hexp] + ring + +lemma gaussianSchurFactor_integrable (n : ℕ) : Integrable (gaussianSchurFactor n) := by + have hi : Integrable (fun r : ℝ => Real.exp (-(1 / (4 * (n + 1 : ℝ) ^ 2)) * r ^ 2)) := + integrable_exp_neg_mul_sq (by positivity) + have he (r : ℝ) : -(r / (n + 1 : ℝ)) ^ 2 / 4 = + -(1 / (4 * (n + 1 : ℝ) ^ 2)) * r ^ 2 := by + field_simp + have hh := hi.ofReal.const_mul + ((Real.pi : ℂ) ^ (1 / 2 : ℂ) / (Real.sqrt Real.pi : ℂ)) + exact hh.congr (ae_of_all _ fun r => by rw [gaussianSchurFactor_formula, he]; rfl) + +lemma gaussianSchurFactor_continuous (n : ℕ) : Continuous (gaussianSchurFactor n) := by + have he : gaussianSchurFactor n = fun r : ℝ => + ((Real.pi : ℂ) ^ (1 / 2 : ℂ) / (Real.sqrt Real.pi : ℂ)) * + (Real.exp (-(r / (n + 1 : ℝ)) ^ 2 / 4) : ℂ) := + funext (gaussianSchurFactor_formula n) + rw [he] + fun_prop + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/HilbertDualOperators.lean b/lean/OAI/Analysis/OperatorAlgebra/HilbertDualOperators.lean new file mode 100644 index 0000000000000000000000000000000000000000..a9bdd2b8b5de44defa67780166e8ac73dbc87086 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/HilbertDualOperators.lean @@ -0,0 +1,53 @@ +import OAI.Analysis.NuclearUltrapower.HilbertSchmidt + +namespace OAI + +/-! The concrete opposite-algebra representation on the conjugate Hilbert +space, needed for the spatial vector functionals of finite density roots. -/ + +noncomputable section +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def hilbertDualOperator (T : H →L[ℂ] H) : StrongDual ℂ H →L[ℂ] StrongDual ℂ H := + (ContinuousLinearMap.compL ℂ H H ℂ).flip T + +@[simp] lemma hilbertDualOperator_apply (T : H →L[ℂ] H) (f : StrongDual ℂ H) (x : H) : + hilbertDualOperator T f x = f (T x) := rfl + +lemma hilbertDualOperator_toDual (T : H →L[ℂ] H) (x : H) : + hilbertDualOperator T (InnerProductSpace.toDual ℂ H x) = + InnerProductSpace.toDual ℂ H (star T x) := by + ext y + exact (ContinuousLinearMap.adjoint_inner_left T y x).symm + +lemma hilbertDualOperator_star (T : H →L[ℂ] H) : + hilbertDualOperator (star T) = star (hilbertDualOperator T) := by + apply (ContinuousLinearMap.eq_adjoint_iff _ _).mpr + intro f g + obtain ⟨x, rfl⟩ := (InnerProductSpace.toDual ℂ H).surjective f + obtain ⟨y, rfl⟩ := (InnerProductSpace.toDual ℂ H).surjective g + rw [hilbertDualOperator_toDual, hilbertDualOperator_toDual, star_star, + NuclearUltrapower.dual_inner_toDual, NuclearUltrapower.dual_inner_toDual] + exact (ContinuousLinearMap.adjoint_inner_left T x y).symm + +/-- Precomposition reverses multiplication, so the conjugate Hilbert space +carries an actual star representation of the opposite operator algebra. -/ +def hilbertDualRepresentation : + (H →L[ℂ] H)ᵐᵒᵖ →⋆ₐ[ℂ] (StrongDual ℂ H →L[ℂ] StrongDual ℂ H) where + toFun T := hilbertDualOperator (MulOpposite.unop T) + map_zero' := by ext f x; simp + map_one' := by ext f x; rfl + map_add' T S := by ext f x; simp + map_mul' T S := by ext f x; rfl + commutes' c := by ext f x; simp [Algebra.algebraMap_eq_smul_one] + map_star' T := hilbertDualOperator_star _ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/HilbertOperatorExtension.lean b/lean/OAI/Analysis/OperatorAlgebra/HilbertOperatorExtension.lean new file mode 100644 index 0000000000000000000000000000000000000000..b736ddcf179fee7460b92729a9a8108a0317c8c9 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/HilbertOperatorExtension.lean @@ -0,0 +1,112 @@ +import OAI.Analysis.Nuclearity.CPWeakOperatorUltralimit +import OAI.Analysis.OperatorAlgebra.FiniteOperatorExtension + +namespace OAI + +/-! Cpc maps into Hilbert-space operators extend along faithful unital +inclusions. Finite-dimensional compressions extend by the matrix theorem; +a weak operator ultralimit preserves complete positivity and all matrix +coefficients of the original map. -/ + +noncomputable section +open Filter Topology +open scoped InnerProductSpace CStarAlgebra ComplexOrder + +namespace WeakPureInfiniteness + +variable {A B H : Type*} [CStarAlgebra A] [CStarAlgebra B] + [PartialOrder A] [StarOrderedRing A] [PartialOrder B] [StarOrderedRing B] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +private lemma compression_contractive {E K : Type*} + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + (V : E →L[ℂ] K) (hV : ‖V‖ ≤ 1) : + ‖hilbertCompression (NonUnitalStarAlgHom.id ℂ (K →L[ℂ] K)) V‖ ≤ 1 := by + exact (hilbertCompression_norm_le _ V).trans + ((mul_le_mul hV hV (norm_nonneg V) zero_le_one).trans_eq (one_mul 1)) + +private lemma cpc_comp_norm {C D E : Type*} + [NormedAddCommGroup C] [NormedSpace ℂ C] + [NormedAddCommGroup D] [NormedSpace ℂ D] + [NormedAddCommGroup E] [NormedSpace ℂ E] + (f : C →L[ℂ] D) (g : D →L[ℂ] E) (hf : ‖f‖ ≤ 1) (hg : ‖g‖ ≤ 1) : + ‖g.comp f‖ ≤ 1 := + (ContinuousLinearMap.opNorm_comp_le _ _).trans + ((mul_le_mul hg hf (norm_nonneg f) zero_le_one).trans_eq (one_mul 1)) + +private theorem finiteCorner_cpc_extension (ι : A →⋆ₐ[ℂ] B) (hι : Function.Injective ι) + (φ : A →L[ℂ] (H →L[ℂ] H)) (hφ : CompletelyPositive φ) (hφn : ‖φ‖ ≤ 1) + (E : Submodule ℂ H) [FiniteDimensional ℂ E] [Nontrivial E] : + ∃ Φ : B →L[ℂ] (H →L[ℂ] H), CompletelyPositive Φ ∧ ‖Φ‖ ≤ 1 ∧ + ∀ a x y, x ∈ E → y ∈ E → inner ℂ (Φ (ι a) x) y = inner ℂ (φ a x) y := by + let : CompleteSpace E := FiniteDimensional.complete ℂ E + let V := E.subtypeL + let C := hilbertCompression (NonUnitalStarAlgHom.id ℂ (H →L[ℂ] H)) V + have hCn : ‖C‖ ≤ 1 := compression_contractive V (Submodule.norm_subtypeL_le E) + obtain ⟨ψ, hψ, hψn, hψe⟩ := finiteOperator_cpc_extension ι hι (C.comp φ) + (completelyPositive_comp _ _ hφ (hilbertCompression_cp _ _)) + (cpc_comp_norm _ _ hφn hCn) + let R := hilbertCompression (A := E →L[ℂ] E) (NonUnitalStarAlgHom.id ℂ (E →L[ℂ] E)) V.adjoint + have hRn : ‖R‖ ≤ 1 := compression_contractive V.adjoint (by + simpa only [ContinuousLinearMap.adjoint.norm_map] using Submodule.norm_subtypeL_le E) + refine ⟨R.comp ψ, completelyPositive_comp _ _ hψ (hilbertCompression_cp _ _), + cpc_comp_norm _ _ hψn hRn, ?_⟩ + intro a x y hx hy + change inner ℂ (V.adjoint.adjoint (ψ (ι a) (V.adjoint x))) y = _ + rw [ContinuousLinearMap.adjoint_adjoint, hψe] + change inner ℂ (V (V.adjoint (φ a (V (V.adjoint x))))) y = _ + have hPx : V (V.adjoint x) = x := by + change E.subtypeL (E.subtypeL.adjoint x) = x + rw [Submodule.adjoint_subtypeL] + exact E.starProjection_eq_self_iff.mpr hx + have hPy : V (V.adjoint y) = y := by + change E.subtypeL (E.subtypeL.adjoint y) = y + rw [Submodule.adjoint_subtypeL] + exact E.starProjection_eq_self_iff.mpr hy + rw [hPx, ← ContinuousLinearMap.adjoint_inner_right, + ContinuousLinearMap.adjoint_inner_left, hPy] + +/-- The Hilbert-operator cpc extension theorem, obtained from finite matrix +extensions and weak operator compactness. -/ +theorem hilbertOperator_cpc_extension [Nontrivial H] + (ι : A →⋆ₐ[ℂ] B) (hι : Function.Injective ι) + (φ : A →L[ℂ] (H →L[ℂ] H)) (hφ : CompletelyPositive φ) (hφn : ‖φ‖ ≤ 1) : + ∃ Φ : B →L[ℂ] (H →L[ℂ] H), CompletelyPositive Φ ∧ ‖Φ‖ ≤ 1 ∧ + ∀ a, Φ (ι a) = φ a := by + classical + obtain ⟨ξ, hξ⟩ := exists_ne (0 : H) + let E (s : Finset H) := Submodule.span ℂ ((insert ξ s : Finset H) : Set H) + have hE (s : Finset H) : Nontrivial (E s) := by + have hm : ξ ∈ E s := Submodule.subset_span (by simp) + exact ⟨⟨⟨ξ, hm⟩, 0, fun h => hξ (congrArg Subtype.val h)⟩⟩ + have hfin (s : Finset H) : FiniteDimensional ℂ (E s) := inferInstance + have hex (s : Finset H) := @finiteCorner_cpc_extension A B H _ _ _ _ _ _ _ _ _ + ι hι φ hφ hφn (E s) (hfin s) (hE s) + choose F hFcp hFn hFe using hex + let U := Ultrafilter.of (atTop : Filter (Finset H)) + let Φ := cpOperatorUltraLimit U F hFn + refine ⟨Φ, cpOperatorUltraLimit_completelyPositive U F hFn hFcp, + cpOperatorUltraLimit_norm_le U F hFn, ?_⟩ + intro a + apply ContinuousLinearMap.ext + intro x + apply ext_inner_right ℂ + intro y + have he : ∀ᶠ s in (U : Filter (Finset H)), + inner ℂ (F s (ι a) x) y = inner ℂ (φ a x) y := by + apply (Ultrafilter.of_le (atTop : Filter (Finset H))) + filter_upwards [eventually_ge_atTop ({x, y} : Finset H)] with s hs + apply hFe s a x y + · apply Submodule.subset_span + exact Finset.mem_insert_of_mem (hs (by simp)) + · apply Submodule.subset_span + exact Finset.mem_insert_of_mem (hs (by simp)) + exact tendsto_nhds_unique (cpOperatorUltraLimit_inner_tendsto U F hFn (ι a) x y) + (tendsto_const_nhds.congr' (Filter.EventuallyEq.symm he)) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/HilbertProjectionRange.lean b/lean/OAI/Analysis/OperatorAlgebra/HilbertProjectionRange.lean new file mode 100644 index 0000000000000000000000000000000000000000..97d7227d8d5e5ce12ecd077033be4605b1a674cd --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/HilbertProjectionRange.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.OperatorAlgebra.IsometricCornerOperators + +namespace OAI + +/-! The range of an actual orthogonal projection as a complete Hilbert +space, with its isometric inclusion recovering the original projection. -/ + +noncomputable section +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def HilbertProjectionRange (p : H →L[ℂ] H) (_hp : IsStarProjection p) := p.range + +instance hilbertProjectionRangeNorm (p : H →L[ℂ] H) (hp : IsStarProjection p) : + NormedAddCommGroup (HilbertProjectionRange p hp) := inferInstanceAs (NormedAddCommGroup p.range) + +instance hilbertProjectionRangeInner (p : H →L[ℂ] H) (hp : IsStarProjection p) : + InnerProductSpace ℂ (HilbertProjectionRange p hp) := inferInstanceAs (InnerProductSpace ℂ p.range) + +instance hilbertProjectionRangeComplete (p : H →L[ℂ] H) (hp : IsStarProjection p) : + CompleteSpace (HilbertProjectionRange p hp) := + (ContinuousLinearMap.IsIdempotentElem.isClosed_range hp.isIdempotentElem).completeSpace_coe + +def hilbertProjectionInclusion (p : H →L[ℂ] H) (hp : IsStarProjection p) : + HilbertProjectionRange p hp →ₗᵢ[ℂ] H := p.range.subtypeₗᵢ + +lemma hilbertProjectionInclusion_fixed (p : H →L[ℂ] H) (hp : IsStarProjection p) + (x : HilbertProjectionRange p hp) : p (hilbertProjectionInclusion p hp x) = + hilbertProjectionInclusion p hp x := by + obtain ⟨y, hy⟩ := x.property + change p x.val = x.val + rw [← hy] + exact congrArg (fun T : H →L[ℂ] H => T y) hp.isIdempotentElem.eq + +lemma hilbertProjectionInclusion_adjoint (p : H →L[ℂ] H) (hp : IsStarProjection p) (x : H) : + (hilbertProjectionInclusion p hp).toContinuousLinearMap.adjoint x = + (⟨p x, x, rfl⟩ : HilbertProjectionRange p hp) := by + apply ext_inner_right ℂ + intro y + rw [ContinuousLinearMap.adjoint_inner_left] + change inner ℂ x (hilbertProjectionInclusion p hp y) = + inner ℂ (p x) (hilbertProjectionInclusion p hp y) + have hs : p.adjoint = p := hp.isSelfAdjoint.star_eq + calc + _ = inner ℂ x (p (hilbertProjectionInclusion p hp y)) := by + rw [hilbertProjectionInclusion_fixed] + _ = inner ℂ (p.adjoint x) (hilbertProjectionInclusion p hp y) := + (ContinuousLinearMap.adjoint_inner_left p _ x).symm + _ = _ := congrArg (fun T : H →L[ℂ] H => + inner ℂ (T x) (hilbertProjectionInclusion p hp y)) hs + +@[simp] lemma hilbertProjectionInclusion_projection (p : H →L[ℂ] H) (hp : IsStarProjection p) : + isometricCornerProjection (hilbertProjectionInclusion p hp) = p := by + ext x + rw [isometricCornerProjection_apply, hilbertProjectionInclusion_adjoint] + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/HilbertSchmidtUnitaryActions.lean b/lean/OAI/Analysis/OperatorAlgebra/HilbertSchmidtUnitaryActions.lean new file mode 100644 index 0000000000000000000000000000000000000000..1eb8ace412901e30482f1672b64f6790cfa39fec --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/HilbertSchmidtUnitaryActions.lean @@ -0,0 +1,68 @@ +import OAI.Analysis.OperatorAlgebra.ReducedDensityPredual + +namespace OAI + +/-! Left and right unitary actions on Hilbert–Schmidt vectors. The +conjugation estimate gives the actual left/right intertwining estimate. -/ + +noncomputable section +open scoped InnerProductSpace TensorProduct + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def hsLeftUnitary (U : H ≃ₗᵢ[ℂ] H) : + NuclearUltrapower.HilbertSchmidt H ≃ₗᵢ[ℂ] NuclearUltrapower.HilbertSchmidt H := + NuclearUltrapower.completionUnitary (E := H ⊗[ℂ] StrongDual ℂ H) + (F := H ⊗[ℂ] StrongDual ℂ H) (TensorProduct.congrIsometry U + (LinearIsometryEquiv.refl ℂ (StrongDual ℂ H))) + +def hsRightUnitary (U : H ≃ₗᵢ[ℂ] H) : + NuclearUltrapower.HilbertSchmidt H ≃ₗᵢ[ℂ] NuclearUltrapower.HilbertSchmidt H := + NuclearUltrapower.completionUnitary (E := H ⊗[ℂ] StrongDual ℂ H) + (F := H ⊗[ℂ] StrongDual ℂ H) (TensorProduct.congrIsometry + (LinearIsometryEquiv.refl ℂ H) (NuclearUltrapower.dualUnitary U.symm)) + +lemma hsRight_conjugation (U : H ≃ₗᵢ[ℂ] H) (z : NuclearUltrapower.HilbertSchmidt H) : + hsRightUnitary U (NuclearUltrapower.hsConjugation U z) = hsLeftUnitary U z := by + induction z using UniformSpace.Completion.induction_on with + | hp => + exact isClosed_eq ((hsRightUnitary U).continuous.comp + (NuclearUltrapower.hsConjugation U).continuous) (hsLeftUnitary U).continuous + | ih z => + simp only [NuclearUltrapower.hsConjugation_coe, hsRightUnitary, hsLeftUnitary, + NuclearUltrapower.completionUnitary_coe] + apply congrArg (fun w : H ⊗[ℂ] StrongDual ℂ H => + (w : NuclearUltrapower.HilbertSchmidt H)) + induction z using TensorProduct.inductionOn with + | tmul x f => + obtain ⟨y, rfl⟩ := (InnerProductSpace.toDual ℂ H).surjective f + simp only [TensorProduct.congrIsometry_apply, TensorProduct.congr_tmul] + change U x ⊗ₜ[ℂ] NuclearUltrapower.dualUnitary U.symm + (NuclearUltrapower.dualUnitary U (InnerProductSpace.toDual ℂ H y)) = + U x ⊗ₜ[ℂ] InnerProductSpace.toDual ℂ H y + rw [NuclearUltrapower.dualUnitary_toDual, NuclearUltrapower.dualUnitary_toDual, + U.symm_apply_apply] + | add z w hz hw => simp only [map_add, hz, hw] + +lemma hsLeft_sub_right_norm (U : H ≃ₗᵢ[ℂ] H) (z : NuclearUltrapower.HilbertSchmidt H) : + ‖hsLeftUnitary U z - hsRightUnitary U z‖ = + ‖NuclearUltrapower.hsConjugation U z - z‖ := by + rw [← hsRight_conjugation U z, ← map_sub, (hsRightUnitary U).norm_map] + +/-- The square root of a nearly central finite density is an actual +approximate intertwiner for the left and right unitary actions. -/ +theorem densityRoot_left_right_bound {E : Type*} [NormedAddCommGroup E] + [InnerProductSpace ℂ E] [CompleteSpace E] (U : H ≃ₗᵢ[ℂ] H) (z : E ⊗[ℂ] H) : + ‖hsLeftUnitary U (NuclearUltrapower.densityRoot z) - + hsRightUnitary U (NuclearUltrapower.densityRoot z)‖ ^ 2 ≤ + ‖finitePredualUnitary U (finiteTensorDensity z) - finiteTensorDensity z‖ := by + rw [hsLeft_sub_right_norm] + exact densityRoot_unitary_predual_bound U z + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/HilbertTensorExtension.lean b/lean/OAI/Analysis/OperatorAlgebra/HilbertTensorExtension.lean new file mode 100644 index 0000000000000000000000000000000000000000..09c03d47122cdd9e9c3490d2faa0aa83f61b6e48 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/HilbertTensorExtension.lean @@ -0,0 +1,48 @@ +import OAI.Analysis.Nuclearity.MinimalTensorExtension +import OAI.Analysis.WeakInfiniteness.CrossUniverseTensorMap + +namespace OAI + +/-! Finite-sum bounds and minimal tensor completion, with the Hilbert +operator structure fixed before a concrete representation is substituted. -/ +noncomputable section +open scoped TensorProduct +namespace WeakPureInfiniteness + +lemma minimalSum_map_norm_le {A B C D : Type*} + [NonUnitalCStarAlgebra A] [NonUnitalCStarAlgebra B] + [NonUnitalCStarAlgebra C] [NonUnitalCStarAlgebra D] + (φ : A →⋆ₙₐ[ℂ] C) (ψ : B →⋆ₙₐ[ℂ] D) + {I : Type*} [Fintype I] (a : I → A) (b : I → B) : + ‖∑ i, minimalElementary (φ (a i)) (ψ (b i))‖ ≤ + ‖∑ i, minimalElementary (a i) (b i)‖ := by + have h := NonUnitalStarAlgHom.norm_apply_le (minimalMapAny φ ψ) + (∑ i, minimalElementary (a i) (b i)) + simpa only [map_sum, minimalMapAny_elementary] using h + +variable {A B H : Type*} [CStarAlgebra A] [CStarAlgebra B] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma hilbert_tensor_algebraic_bound (μ : A ⊗[ℂ] B →⋆ₐ[ℂ] (H →L[ℂ] H)) + (hn : ∀ (n : ℕ) (a : Fin n → A) (b : Fin n → B), + ‖∑ i, μ (a i ⊗ₜ[ℂ] b i)‖ ≤ ‖∑ i, minimalElementary (a i) (b i)‖) + (z : A ⊗[ℂ] B) : ‖μ z‖ ≤ ‖minimalAlgebraicLinear z‖ := by + apply algebraic_linear_norm_le μ.toLinearMap _ z + intro n a b + simpa only [map_sum, AlgHom.toLinearMap_apply, StarAlgHom.coe_toAlgHom] using hn n a b + +@[irreducible] def hilbertMinimalTensorExtend (μ : A ⊗[ℂ] B →⋆ₐ[ℂ] (H →L[ℂ] H)) + (hn : ∀ z, ‖μ z‖ ≤ ‖minimalAlgebraicLinear z‖) : + MinimalTensor A B →⋆ₙₐ[ℂ] (H →L[ℂ] H) := minimalTensorExtend μ hn + +lemma hilbertMinimalTensorExtend_elementary (μ : A ⊗[ℂ] B →⋆ₐ[ℂ] (H →L[ℂ] H)) + (hn : ∀ z, ‖μ z‖ ≤ ‖minimalAlgebraicLinear z‖) (a : A) (b : B) : + hilbertMinimalTensorExtend μ hn (minimalElementary a b) = μ (a ⊗ₜ[ℂ] b) := by + unfold hilbertMinimalTensorExtend + exact minimalTensorExtend_elementary μ hn a b + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/HypertraceFiniteDensity.lean b/lean/OAI/Analysis/OperatorAlgebra/HypertraceFiniteDensity.lean new file mode 100644 index 0000000000000000000000000000000000000000..a19ba5cf490653e3d474903a73ad7683b76bf766 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/HypertraceFiniteDensity.lean @@ -0,0 +1,193 @@ +import OAI.Analysis.OperatorAlgebra.FinitePredualConjugation +import OAI.Analysis.TracialSplitting.Hypertraces + +namespace OAI + +/-! The convex separation step in the finite hypertrace argument. +An invariant state can be approximated on a prescribed finite set by finite +vector functionals whose conjugation defects are small in the predual norm. +This is norm control of the defects, not merely weak convergence. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder ComplexStarModule +open Set + +namespace WeakPureInfiniteness + +variable {H I J : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [Fintype I] [Fintype J] + +abbrev HypertraceTestSpace (I J H : Type*) [NormedAddCommGroup H] + [InnerProductSpace ℂ H] [CompleteSpace H] := + (I → ℝ) × (J → finiteOperatorPredual (H := H)) + +instance hypertraceTestNormed : NormedAddCommGroup (HypertraceTestSpace I J H) := + inferInstance + +instance hypertraceTestReal : NormedSpace ℝ (HypertraceTestSpace I J H) := + inferInstance + +instance hypertraceTestBounded : IsBoundedSMul ℝ (HypertraceTestSpace I J H) := + NormedSpace.toIsBoundedSMul + +instance hypertraceTestContinuousSMul : ContinuousSMul ℝ (HypertraceTestSpace I J H) := + IsBoundedSMul.continuousSMul + +def hypertraceVectorTest (T : I → H →L[ℂ] H) (U : J → H ≃ₗᵢ[ℂ] H) (x : H) : + HypertraceTestSpace I J H := + (fun i => (inner ℂ x (T i x)).re, + fun j => finitePredualUnitary (U j) (finiteOperatorCoefficient x x) - finiteOperatorCoefficient x x) + +def hypertraceStateTest (T : I → H →L[ℂ] H) (φ : (H →L[ℂ] H) →ₚ[ℂ] ℂ) : + HypertraceTestSpace I J H := (fun i => (φ (T i)).re, 0) + +private def testScalarPart (f : HypertraceTestSpace I J H →L[ℝ] ℝ) : (I → ℝ) →L[ℝ] ℝ := + f.comp (ContinuousLinearMap.inl ℝ _ _) + +private def testPredualPart [DecidableEq J] (f : HypertraceTestSpace I J H →L[ℝ] ℝ) + (j : J) : finiteOperatorPredual (H := H) →L[ℝ] ℝ := + (f.comp (ContinuousLinearMap.inr ℝ (I → ℝ) (J → finiteOperatorPredual (H := H)))).comp + (ContinuousLinearMap.single ℝ (fun _ : J => finiteOperatorPredual (H := H)) j) + +private lemma testFunctional_expansion [DecidableEq I] [DecidableEq J] + (f : HypertraceTestSpace I J H →L[ℝ] ℝ) (s : I → ℝ) (z : J → finiteOperatorPredual (H := H)) : + f (s, z) = (∑ i, testScalarPart f (Pi.single i 1) * s i) + ∑ j, testPredualPart f j (z j) := by + have he : (s, z) = (s, 0) + (0, z) := by simp + rw [he, map_add] + congr 1 + · exact NuclearTrace.real_pi_linear_expansion (testScalarPart f) s + · have hz : (0, z) = ∑ j, ((0, Pi.single j (z j)) : HypertraceTestSpace I J H) := by + apply Prod.ext + · simp only [Prod.fst_sum, Finset.sum_const_zero] + · simpa only [Prod.snd_sum] using (Finset.univ_sum_single z).symm + rw [hz, map_sum] + rfl + +private lemma operator_realPart_quadratic (T : H →L[ℂ] H) (x : H) : + (inner ℂ x ((ℜ T : H →L[ℂ] H) x)).re = (inner ℂ x (T x)).re := by + have hs : (inner ℂ x ((star T) x)).re = (inner ℂ x (T x)).re := by + rw [ContinuousLinearMap.star_eq_adjoint, ContinuousLinearMap.adjoint_inner_right] + exact inner_re_symm (𝕜 := ℂ) (T x) x + rw [realPart_apply_coe] + simp only [smul_apply, add_apply, inner_smul_right_eq_smul, inner_add_right, + Complex.smul_re, Complex.add_re, smul_eq_mul, hs] + ring + +private lemma conjugatedOperator_inner (U : H ≃ₗᵢ[ℂ] H) (T : H →L[ℂ] H) (x : H) : + inner ℂ x (conjugatedOperator U T x) = inner ℂ (U x) (T (U x)) := by + change inner ℂ x (U.symm (T (U x))) = _ + rw [← U.inner_map_map x (U.symm (T (U x))), U.apply_symm_apply] + +theorem hypertraceStateTest_mem_closure (T : I → H →L[ℂ] H) + (hT : ∀ i, IsSelfAdjoint (T i)) (U : J → H ≃ₗᵢ[ℂ] H) + (φ : (H →L[ℂ] H) →ₚ[ℂ] ℂ) (hφ : φ 1 = 1) + (hU : ∀ j A, φ (conjugatedOperator (U j) A) = φ A) : + hypertraceStateTest (J := J) T φ ∈ + closure (convexHull ℝ (hypertraceVectorTest T U '' Metric.closedBall 0 1)) := by + classical + by_contra hn + obtain ⟨f, c, hf, hc⟩ := geometric_hahn_banach_closed_point + (convex_convexHull ℝ (hypertraceVectorTest T U '' Metric.closedBall 0 1)).closure + isClosed_closure hn + choose A hA using fun j => finitePredual_real_duality (testPredualPart f j) + let B (j : J) : H →L[ℂ] H := ℜ (A j) + let S : H →L[ℂ] H := + (∑ i, testScalarPart f (Pi.single i 1) • T i) + + ∑ j, (conjugatedOperator (U j) (B j) - B j) + have hB (j : J) : IsSelfAdjoint (B j) := (ℜ (A j)).property + have hS : IsSelfAdjoint S := by + apply IsSelfAdjoint.add + · exact isSelfAdjoint_sum _ fun i _ => (IsSelfAdjoint.all _).smul (hT i) + · apply isSelfAdjoint_sum + intro j _ + exact ((hB j).map (U j).symm.conjStarAlgEquiv).sub (hB j) + have hquad (x : H) : f (hypertraceVectorTest T U x) = (inner ℂ x (S x)).re := by + rw [testFunctional_expansion] + simp only [hypertraceVectorTest, S, add_apply, sum_apply, inner_add_right, + inner_sum, Complex.add_re, Complex.re_sum, smul_apply, + inner_smul_right_eq_smul, Complex.smul_re, smul_eq_mul] + congr 1 + apply Finset.sum_congr rfl + intro j _ + rw [hA j] + simp only [Submodule.coe_sub, sub_apply, finitePredualUnitary_apply, + finiteOperatorCoefficient, operatorCoefficient_apply, conjugatedOperator_inner, + inner_sub_right, Complex.sub_re, B, operator_realPart_quadratic] + have hle : S ≤ c • (1 : H →L[ℂ] H) := NuclearTrace.operator_le_of_unit_quadratic hS (by + intro x hx + rw [← hquad] + exact (hf _ (subset_closure (subset_convexHull ℝ _ + ⟨x, by simpa using hx, rfl⟩))).le) + have heval : f (hypertraceStateTest (J := J) T φ) = (φ S).re := by + rw [testFunctional_expansion] + simp only [hypertraceStateTest, Pi.zero_apply, map_zero, Finset.sum_const_zero, add_zero] + simp only [S, map_add, map_sum, φ.map_smul_of_tower, map_sub, hU, + sub_self, Finset.sum_const_zero, add_zero, Complex.re_sum, Complex.smul_re, smul_eq_mul] + have hb := (φ.monotone hle).1 + change (φ S).re ≤ (φ (c • 1)).re at hb + rw [φ.map_smul_of_tower, hφ, Complex.smul_re, Complex.one_re, smul_eq_mul, mul_one] at hb + exact (not_le_of_gt hc) (heval ▸ hb) + +def finiteVectorDensity {n : ℕ} (w : Fin n → ℝ) (x : Fin n → H) : + finiteOperatorPredual (H := H) := + ∑ k, (w k : ℂ) • finiteOperatorCoefficient (x k) (x k) + +/-- Simultaneous finite state tests and norm-small conjugation defects. +This is the finite-rank density step used before the Powers--Størmer estimate. -/ +theorem hypertrace_finite_density (T : I → H →L[ℂ] H) + (hT : ∀ i, IsSelfAdjoint (T i)) (U : J → H ≃ₗᵢ[ℂ] H) + (φ : (H →L[ℂ] H) →ₚ[ℂ] ℂ) (hφ : φ 1 = 1) + (hU : ∀ j A, φ (conjugatedOperator (U j) A) = φ A) + {ε : ℝ} (hε : 0 < ε) : + ∃ (n : ℕ) (w : Fin n → ℝ) (x : Fin n → H), + (∀ k, 0 ≤ w k) ∧ (∑ k, w k = 1) ∧ (∀ k, ‖x k‖ ≤ 1) ∧ + (∀ i, |(φ (T i)).re - ∑ k, w k * (inner ℂ (x k) (T i (x k))).re| < ε) ∧ + ∀ j, ‖finitePredualUnitary (U j) (finiteVectorDensity w x) - finiteVectorDensity w x‖ < ε := by + classical + obtain ⟨z, hz, hzε⟩ := Metric.mem_closure_iff.mp + (hypertraceStateTest_mem_closure T hT U φ hφ hU) ε hε + obtain ⟨K, _, w, v, hw, hw1, hv, hsum⟩ := mem_convexHull_iff_exists_fintype.mp hz + choose x hx hvx using hv + let e : Fin (Fintype.card K) ≃ K := (Fintype.equivFin K).symm + have hsum' : (∑ k : Fin (Fintype.card K), w (e k) • hypertraceVectorTest T U (x (e k))) = z := by + rw [e.sum_comp (fun k => w k • hypertraceVectorTest T U (x k))] + simpa only [← hvx] using hsum + refine ⟨Fintype.card K, w ∘ e, x ∘ e, fun k => hw (e k), + (e.sum_comp w).trans hw1, fun k => by simpa using hx (e k), ?_, ?_⟩ + · intro i + have hb := ((norm_le_pi_norm ((hypertraceStateTest (J := J) T φ - z).1) i).trans + (norm_fst_le (hypertraceStateTest (J := J) T φ - z))).trans_lt (by + simpa only [dist_eq_norm] using hzε) + have he : (∑ k : Fin (Fintype.card K), w (e k) * + (inner ℂ (x (e k)) (T i (x (e k)))).re) = z.1 i := by + simpa only [Prod.fst_sum, Finset.sum_apply, Prod.smul_fst, Pi.smul_apply, + smul_eq_mul, hypertraceVectorTest] using + congrArg (fun q : HypertraceTestSpace I J H => q.1 i) hsum' + change ‖(φ (T i)).re - z.1 i‖ < ε at hb + rw [← he] at hb + simpa only [Function.comp_apply, Real.norm_eq_abs] using hb + · intro j + have hb := ((norm_le_pi_norm ((hypertraceStateTest (J := J) T φ - z).2) j).trans + (norm_snd_le (hypertraceStateTest (J := J) T φ - z))).trans_lt (by + simpa only [dist_eq_norm] using hzε) + have he := congrArg (fun q : HypertraceTestSpace I J H => q.2 j) hsum' + have hd : finitePredualUnitary (U j) (finiteVectorDensity (w ∘ e) (x ∘ e)) - + finiteVectorDensity (w ∘ e) (x ∘ e) = z.2 j := by + calc + _ = ∑ k : Fin (Fintype.card K), (w (e k) : ℂ) • + (finitePredualUnitary (U j) (finiteOperatorCoefficient (x (e k)) (x (e k))) - + finiteOperatorCoefficient (x (e k)) (x (e k))) := by + simp only [finiteVectorDensity, Function.comp_apply, map_sum, map_smul, + smul_sub, Finset.sum_sub_distrib] + _ = z.2 j := by + simpa only [Prod.snd_sum, Finset.sum_apply, Prod.smul_snd, Pi.smul_apply, + hypertraceVectorTest, Complex.coe_smul] using he + change ‖0 - z.2 j‖ < ε at hb + rw [zero_sub, norm_neg] at hb + simpa only [hd] using hb + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/IntegratedModularField.lean b/lean/OAI/Analysis/OperatorAlgebra/IntegratedModularField.lean new file mode 100644 index 0000000000000000000000000000000000000000..77a2382d815500aa87a25ef1af714eaf41a9d44e --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/IntegratedModularField.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.ModularTheory.RightContinuity + +namespace OAI + +/-! Integrable bounded continuous coefficient fields give actual operators +in the modular crossed product. -/ + +noncomputable section +open MeasureTheory Filter +open scoped Topology + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + (S : BoundedRecovery.StandardModularData H) + +def modularFieldOperator (a : ℝ → H →L[ℂ] H) (r : ℝ) : + Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ) := + modularLpRepresentation volume S.D (a r) * modularLpTranslateOperator r + +lemma modularFieldOperator_continuous (a : ℝ → H →L[ℂ] H) (ha : Continuous a) + (f : Lp H 2 (volume : Measure ℝ)) : + Continuous (fun r => modularFieldOperator S a r f) := by + exact ((starHomContinuousLinear + (modularLpRepresentation volume S.D).toNonUnitalStarAlgHom).continuous.comp ha).clm_apply + (continuous_modularLpTranslate f) + +lemma modularFieldOperator_norm_le (a : ℝ → H →L[ℂ] H) (C : ℝ) + (hC : ∀ r, ‖a r‖ ≤ C) (r : ℝ) : ‖modularFieldOperator S a r‖ ≤ C := by + exact (norm_mul_le _ _).trans ((mul_le_mul + ((NonUnitalStarAlgHom.norm_apply_le + (modularLpRepresentation volume S.D).toNonUnitalStarAlgHom (a r)).trans (hC r)) + (modularLpTranslate_opNorm_le r) (norm_nonneg _) (le_trans (norm_nonneg _) (hC r))).trans_eq + (mul_one C)) + +def integratedModularField (a : ℝ → H →L[ℂ] H) (ha : Continuous a) + (C : ℝ) (hC : ∀ r, ‖a r‖ ≤ C) (k : ℝ → ℂ) (hk : Integrable k) : + Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ) := + BoundedRecovery.strongIntegral k hk (modularFieldOperator S a) + (modularFieldOperator_continuous S a ha) C (modularFieldOperator_norm_le S a C hC) + +lemma integratedModularField_mem (a : ℝ → H →L[ℂ] H) (ha : Continuous a) + (hM : ∀ r, a r ∈ S.M) (C : ℝ) (hC : ∀ r, ‖a r‖ ≤ C) + (k : ℝ → ℂ) (hk : Integrable k) : + integratedModularField S a ha C hC k hk ∈ modularCrossedProduct volume S := by + rw [← (modularCrossedProduct volume S).commutant_commutant, + VonNeumannAlgebra.mem_commutant_iff] + intro b hb + apply ContinuousLinearMap.ext + intro f + have hi := BoundedRecovery.integrable_smul_bounded_orbit hk + (modularFieldOperator_continuous S a ha f) + (fun r => (modularFieldOperator S a r).le_opNorm f |>.trans + (mul_le_mul_of_nonneg_right (modularFieldOperator_norm_le S a C hC r) (norm_nonneg f))) + change b (∫ r, k r • modularFieldOperator S a r f) = + ∫ r, k r • modularFieldOperator S a r (b f) + rw [← b.integral_comp_comm hi] + apply integral_congr_ae + filter_upwards [] with r + rw [map_smul] + congr 1 + have hm : modularFieldOperator S a r ∈ modularCrossedProduct volume S := + mul_mem (modularCrossedProduct_coeff volume S ⟨a r, hM r⟩) + (modularCrossedProduct_translate volume S r) + exact (congrArg (fun T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ) => T f) + (VonNeumannAlgebra.mem_commutant_iff.mp hb _ hm)).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/IntertwinerCommutantCP.lean b/lean/OAI/Analysis/OperatorAlgebra/IntertwinerCommutantCP.lean new file mode 100644 index 0000000000000000000000000000000000000000..90b76d2f834ce91779d939bd1837238b5a0b5c11 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/IntertwinerCommutantCP.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.OperatorAlgebra.IntertwinerCompression +import OAI.Analysis.OperatorAlgebra.StandardCommutantOpposite +import OAI.Analysis.Nuclearity.CPFaithfulRestriction +import OAI.Analysis.ModularTheory.CommutantExpectation + +namespace OAI + +/-! Compress a commuting representation through the constructed intertwiner. +The result is an actual CP map into the standard commutant. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness +open BoundedRecovery KirchbergRordam.GenericRW.GroupedFactors + +variable {A B H K : Type*} [CStarAlgebra A] [CStarAlgebra B] + [PartialOrder B] [StarOrderedRing B] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +omit [PartialOrder B] [StarOrderedRing B] in +lemma intertwiner_compression_mem (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) (b : B) : + hilbertCompression η.toNonUnitalStarAlgHom V b ∈ S.M.commutant := by + rw [hS, representation_bicommutant_commutant] + apply mem_representationCommutant ρ + intro a + exact (intertwiner_compression_commutes ρ π V hV (η b) (fun a => hc a b) a).symm + +def intertwinerCommutantCP (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + B →L[ℂ] S.M.commutant.toStarSubalgebra := + (hilbertCompression η.toNonUnitalStarAlgHom V).codRestrict + S.M.commutant.toStarSubalgebra.toSubalgebra.toSubmodule + (intertwiner_compression_mem ρ π V hV η hc S hS) + +lemma intertwinerCommutantCP_cp (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + CompletelyPositive (intertwinerCommutantCP ρ π V hV η hc S hS) := by + apply completelyPositive_of_faithful_postcomp _ + S.M.commutant.toStarSubalgebra.subtype.toNonUnitalStarAlgHom Subtype.val_injective + exact hilbertCompression_cp η.toNonUnitalStarAlgHom V + +omit [PartialOrder B] [StarOrderedRing B] in +lemma intertwinerCommutantCP_norm_le (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + ‖intertwinerCommutantCP ρ π V hV η hc S hS‖ ≤ ‖V‖ * ‖V‖ := by + apply ContinuousLinearMap.opNorm_le_bound _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) + intro b + exact hilbertCompressionLinear_bound η.toNonUnitalStarAlgHom V b + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/IntertwinerCompression.lean b/lean/OAI/Analysis/OperatorAlgebra/IntertwinerCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..4a3e9c3c33078928191ad8ff23befc5ba71b0e69 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/IntertwinerCompression.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.OperatorAlgebra.FiniteHilbertCompression + +namespace OAI + +/-! A compressed commuting action still commutes with the intertwined action. -/ +noncomputable section +namespace WeakPureInfiniteness + +variable {A H K : Type*} [CStarAlgebra A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma intertwiner_adjoint (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) (a : A) : + (ρ a).comp V.adjoint = V.adjoint.comp (π a) := by + have h := congrArg ContinuousLinearMap.adjoint (hV (star a)) + simpa only [ContinuousLinearMap.adjoint_comp, + ← ContinuousLinearMap.star_eq_adjoint, ← map_star, star_star] using h + +lemma intertwiner_compression_commutes (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (T : H →L[ℂ] H) (hT : ∀ a, Commute (π a) T) (a : A) : + Commute (ρ a) (V.adjoint.comp (T.comp V)) := by + apply (commute_iff_eq _ _).mpr + apply ContinuousLinearMap.ext + intro x + have hadj := congrArg (fun W : H →L[ℂ] K => W (T (V x))) + (intertwiner_adjoint ρ π V hV a) + have hvec := congrArg (fun W : K →L[ℂ] H => W x) (hV a) + have hcomm := congrArg (fun W : H →L[ℂ] H => W (V x)) (hT a).eq + change ρ a (V.adjoint (T (V x))) = V.adjoint (T (V (ρ a x))) + exact hadj.trans (congrArg V.adjoint (hcomm.trans (congrArg T hvec.symm))) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/IntertwinerTensorCompression.lean b/lean/OAI/Analysis/OperatorAlgebra/IntertwinerTensorCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..607274ba553fbf2e0d830d2d6bb810815adc402f --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/IntertwinerTensorCompression.lean @@ -0,0 +1,77 @@ +import OAI.Analysis.OperatorAlgebra.IntertwinerCommutantCP +import OAI.Analysis.Nuclearity.MinimalRightCPMap + +namespace OAI + +/-! Tensoring the actual commuting compression with the standard left action. +The bound is uniform in the finite tensor being tested. -/ +noncomputable section +open scoped ComplexOrder TensorProduct +namespace WeakPureInfiniteness +open BoundedRecovery KirchbergRordam.GenericRW.GroupedFactors + +variable {A B H K : Type*} [CStarAlgebra A] [CStarAlgebra B] + [PartialOrder B] [StarOrderedRing B] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +def standardLeftFactor (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + A →⋆ₐ[ℂ] S.M.toStarSubalgebra where + toFun a := ⟨ρ a, hS ▸ subset_bicommutant ρ.range (ρ a) ⟨a, rfl⟩⟩ + map_zero' := Subtype.ext (map_zero ρ) + map_one' := Subtype.ext (map_one ρ) + map_add' a b := Subtype.ext (map_add ρ a b) + map_mul' a b := Subtype.ext (map_mul ρ a b) + commutes' c := Subtype.ext (ρ.commutes c) + map_star' a := Subtype.ext (map_star ρ a) + +def intertwinerOppositeCP (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + B →L[ℂ] S.M.toStarSubalgebraᵐᵒᵖ := + (starHomContinuousLinear (standardCommutantEquiv S).symm.toNonUnitalStarAlgHom).comp + (intertwinerCommutantCP ρ π V hV η hc S hS) + +lemma intertwinerOppositeCP_cp (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + CompletelyPositive (intertwinerOppositeCP ρ π V hV η hc S hS) := + completelyPositive_comp _ _ (intertwinerCommutantCP_cp ρ π V hV η hc S hS) + (starHomContinuous_completelyPositive _) + +omit [PartialOrder B] [StarOrderedRing B] in +lemma intertwinerOppositeCP_norm_le (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + ‖intertwinerOppositeCP ρ π V hV η hc S hS‖ ≤ ‖V‖ * ‖V‖ := by + apply ContinuousLinearMap.opNorm_le_bound _ (mul_nonneg (norm_nonneg _) (norm_nonneg _)) + intro b + exact (NonUnitalStarAlgHom.norm_apply_le + (standardCommutantEquiv S).symm.toNonUnitalStarAlgHom _).trans + (hilbertCompressionLinear_bound η.toNonUnitalStarAlgHom V b) + +omit [PartialOrder B] [StarOrderedRing B] in +lemma intertwinerOppositeCP_evaluate (ρ : A →⋆ₐ[ℂ] (K →L[ℂ] K)) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) (V : K →L[ℂ] H) + (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) (b : B) : + ((standardCommutantEquiv S) (intertwinerOppositeCP ρ π V hV η hc S hS b)).val = + V.adjoint.comp ((η b).comp V) := by + change ((standardCommutantEquiv S) ((standardCommutantEquiv S).symm + (intertwinerCommutantCP ρ π V hV η hc S hS b))).val = _ + rw [StarAlgEquiv.apply_symm_apply] + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerExpectation.lean b/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerExpectation.lean new file mode 100644 index 0000000000000000000000000000000000000000..3350b321f0b50d03431aefbab6f64cccfab5c992 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerExpectation.lean @@ -0,0 +1,107 @@ +import OAI.Analysis.OperatorAlgebra.IsometricCornerOperators +import OAI.Analysis.CharacterCriterion.FactorIndependence +import OAI.Analysis.ModularRecovery.PositiveKernels +import OAI.Analysis.PureInfiniteness.TwoMatrixNuclear + +namespace OAI + +/-! A concrete cpc retraction onto a von Neumann algebra restricts to a +concrete cpc retraction onto each represented projection corner. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness +open KirchbergRordam.GenericRW.GroupedFactors + +variable {H K : Type*} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma isometricCorner_commutant_commutes (M : VonNeumannAlgebra H) (V : K →ₗᵢ[ℂ] H) + (hp : isometricCornerProjection V ∈ M) (b : M.commutant.toStarSubalgebra) : + Commute (b : H →L[ℂ] H) (isometricCornerProjection V) := + (show Commute (isometricCornerProjection V) (b : H →L[ℂ] H) from + VonNeumannAlgebra.mem_commutant_iff.mp b.property _ hp).symm + +def isometricCornerCommutantHom (M : VonNeumannAlgebra H) (V : K →ₗᵢ[ℂ] H) + (hp : isometricCornerProjection V ∈ M) : + M.commutant.toStarSubalgebra →⋆ₐ[ℂ] (K →L[ℂ] K) := + isometricCornerRestrictHom V M.commutant.toStarSubalgebra.subtype + (isometricCorner_commutant_commutes M V hp) + +def isometricCornerVonNeumann (M : VonNeumannAlgebra H) (V : K →ₗᵢ[ℂ] H) + (hp : isometricCornerProjection V ∈ M) : VonNeumannAlgebra K := + commutantOf (isometricCornerCommutantHom M V hp).range + +lemma isometricCornerVonNeumann_mem_iff (M : VonNeumannAlgebra H) (V : K →ₗᵢ[ℂ] H) + (hp : isometricCornerProjection V ∈ M) (T : K →L[ℂ] K) : + T ∈ isometricCornerVonNeumann M V hp ↔ isometricCornerLift V T ∈ M := by + rw [isometricCornerVonNeumann, mem_commutantOf_iff] + conv_rhs => rw [← M.commutant_commutant, VonNeumannAlgebra.mem_commutant_iff] + constructor + · intro h b hb + have hc := h _ (show isometricCornerCommutantHom M V hp + (⟨b, hb⟩ : M.commutant.toStarSubalgebra) ∈ + (isometricCornerCommutantHom M V hp).range from Set.mem_range_self _) + have ht : Commute T (isometricCornerCompress V b) := hc.symm + exact ((isometricCornerLift_commute_iff V T b + (isometricCorner_commutant_commutes M V hp ⟨b, hb⟩)).mpr ht).eq.symm + · intro h b hb + obtain ⟨c, rfl⟩ := hb + have hc : Commute (isometricCornerLift V T) (c : H →L[ℂ] H) := + (show Commute (c : H →L[ℂ] H) (isometricCornerLift V T) from h c c.property).symm + exact ((isometricCornerLift_commute_iff V T c + (isometricCorner_commutant_commutes M V hp c)).mp hc).symm + +lemma isometricCornerCompress_mem (M : VonNeumannAlgebra H) (V : K →ₗᵢ[ℂ] H) + (hp : isometricCornerProjection V ∈ M) (T : H →L[ℂ] H) (hT : T ∈ M) : + isometricCornerCompress V T ∈ isometricCornerVonNeumann M V hp := by + rw [isometricCornerVonNeumann_mem_iff, isometricCornerLift_compress] + exact M.mul_mem (M.mul_mem hp hT) hp + +def isometricCornerExpectation (V : K →ₗᵢ[ℂ] H) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) : + (K →L[ℂ] K) →L[ℂ] (K →L[ℂ] K) := + (isometricCornerCompress V).comp + (E.comp (starHomContinuousLinear (isometricCornerLiftHom V))) + +lemma isometricCornerExpectation_cp (V : K →ₗᵢ[ℂ] H) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) (hE : CompletelyPositive E) : + CompletelyPositive (isometricCornerExpectation V E) := + completelyPositive_comp _ _ + (completelyPositive_comp _ _ (starHomContinuous_completelyPositive _) hE) + (isometricCornerCompress_cp V) + +lemma isometricCornerExpectation_norm_le (V : K →ₗᵢ[ℂ] H) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) (hE : ‖E‖ ≤ 1) : + ‖isometricCornerExpectation V E‖ ≤ 1 := by + have hi : ‖E.comp (starHomContinuousLinear (isometricCornerLiftHom V))‖ ≤ 1 := + (ContinuousLinearMap.opNorm_comp_le _ _).trans + ((mul_le_mul hE (starHomContinuousLinear_norm_le_one _) (norm_nonneg _) zero_le_one).trans_eq + (one_mul 1)) + exact (ContinuousLinearMap.opNorm_comp_le _ _).trans + ((mul_le_mul (isometricCornerCompress_norm_le V) hi (norm_nonneg _) zero_le_one).trans_eq + (one_mul 1)) + +lemma isometricCornerExpectation_mem (M : VonNeumannAlgebra H) (V : K →ₗᵢ[ℂ] H) + (hp : isometricCornerProjection V ∈ M) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) (hE : ∀ T, E T ∈ M) + (T : K →L[ℂ] K) : + isometricCornerExpectation V E T ∈ isometricCornerVonNeumann M V hp := + isometricCornerCompress_mem M V hp _ (hE _) + +lemma isometricCornerExpectation_fixed (M : VonNeumannAlgebra H) (V : K →ₗᵢ[ℂ] H) + (hp : isometricCornerProjection V ∈ M) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) (hE : ∀ T, T ∈ M → E T = T) + (T : K →L[ℂ] K) (hT : T ∈ isometricCornerVonNeumann M V hp) : + isometricCornerExpectation V E T = T := by + change isometricCornerCompress V (E (isometricCornerLift V T)) = T + rw [hE _ ((isometricCornerVonNeumann_mem_iff M V hp T).mp hT), + isometricCornerCompress_lift] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerNorm.lean b/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..bacd248d0f9b328dc177fc54a2b6cd5f095b5b3b --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerNorm.lean @@ -0,0 +1,43 @@ +import OAI.Analysis.OperatorAlgebra.IsometricCornerOperators + +namespace OAI + +/-! Operator norm transfer through an isometric inclusion. -/ +noncomputable section +namespace WeakPureInfiniteness + +variable {H K : Type*} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma isometricCornerLift_norm (V : K →ₗᵢ[ℂ] H) (T : K →L[ℂ] K) : + ‖isometricCornerLift V T‖ = ‖T‖ := + NonUnitalStarAlgHom.norm_map (isometricCornerLiftHom V) + (isometricCornerLift_injective V) T + +lemma eq_isometricCornerLift_of_intertwines (V : K →ₗᵢ[ℂ] H) + (R : H →L[ℂ] H) (T : K →L[ℂ] K) + (hR : R * isometricCornerProjection V = R) + (hT : ∀ x : K, R (V x) = V (T x)) : + R = isometricCornerLift V T := by + apply ContinuousLinearMap.ext + intro x + calc + R x = R (isometricCornerProjection V x) := + (congrArg (fun A : H →L[ℂ] H => A x) hR).symm + _ = R (V (V.toContinuousLinearMap.adjoint x)) := rfl + _ = V (T (V.toContinuousLinearMap.adjoint x)) := hT _ + _ = isometricCornerLift V T x := rfl + +lemma norm_eq_of_corner_intertwines (V : K →ₗᵢ[ℂ] H) + (R : H →L[ℂ] H) (T : K →L[ℂ] K) + (hR : R * isometricCornerProjection V = R) + (hT : ∀ x : K, R (V x) = V (T x)) : ‖R‖ = ‖T‖ := by + rw [eq_isometricCornerLift_of_intertwines V R T hR hT, + isometricCornerLift_norm] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerOperators.lean b/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerOperators.lean new file mode 100644 index 0000000000000000000000000000000000000000..35e06c53f53e5478ec9e647659125441aa8a1fe0 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/IsometricCornerOperators.lean @@ -0,0 +1,176 @@ +import OAI.Analysis.OperatorAlgebra.FiniteHilbertCompression + +namespace OAI + +/-! Inclusion and compression of a closed Hilbert subspace transfer an +expectation to represented projection corners. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H K : Type*} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +abbrev isometricCornerCompress (V : K →ₗᵢ[ℂ] H) : + (H →L[ℂ] H) →L[ℂ] (K →L[ℂ] K) := + hilbertCompression (StarAlgHom.id ℂ (H →L[ℂ] H)).toNonUnitalStarAlgHom + V.toContinuousLinearMap + +def isometricCornerLift (V : K →ₗᵢ[ℂ] H) (T : K →L[ℂ] K) : H →L[ℂ] H := + V.toContinuousLinearMap.comp (T.comp V.toContinuousLinearMap.adjoint) + +abbrev isometricCornerProjection (V : K →ₗᵢ[ℂ] H) : H →L[ℂ] H := + V.toContinuousLinearMap.comp V.toContinuousLinearMap.adjoint + +lemma isometricCorner_adjoint_apply (V : K →ₗᵢ[ℂ] H) (x : K) : + V.toContinuousLinearMap.adjoint (V x) = x := by + exact congrArg (fun T : K →L[ℂ] K => T x) V.adjoint_comp_self + +@[simp] lemma isometricCornerCompress_apply (V : K →ₗᵢ[ℂ] H) + (T : H →L[ℂ] H) (x : K) : + isometricCornerCompress V T x = V.toContinuousLinearMap.adjoint (T (V x)) := rfl + +@[simp] lemma isometricCornerLift_apply (V : K →ₗᵢ[ℂ] H) + (T : K →L[ℂ] K) (x : H) : + isometricCornerLift V T x = V (T (V.toContinuousLinearMap.adjoint x)) := rfl + +@[simp] lemma isometricCornerCompress_lift (V : K →ₗᵢ[ℂ] H) (T : K →L[ℂ] K) : + isometricCornerCompress V (isometricCornerLift V T) = T := by + ext x + simp only [isometricCornerCompress_apply, isometricCornerLift_apply, + isometricCorner_adjoint_apply] + +lemma isometricCornerLift_injective (V : K →ₗᵢ[ℂ] H) : + Function.Injective (isometricCornerLift V) := by + intro T U h + have he := congrArg (isometricCornerCompress V) h + simpa only [isometricCornerCompress_lift] using he + +lemma isometricCornerLift_mul (V : K →ₗᵢ[ℂ] H) (T U : K →L[ℂ] K) : + isometricCornerLift V (T * U) = isometricCornerLift V T * isometricCornerLift V U := by + ext x + simp only [isometricCornerLift_apply, mul_apply_eq_comp, + isometricCorner_adjoint_apply] + +lemma isometricCornerLift_star (V : K →ₗᵢ[ℂ] H) (T : K →L[ℂ] K) : + isometricCornerLift V (star T) = star (isometricCornerLift V T) := by + change V.toContinuousLinearMap.comp (T.adjoint.comp V.toContinuousLinearMap.adjoint) = + (V.toContinuousLinearMap.comp (T.comp V.toContinuousLinearMap.adjoint)).adjoint + rw [ContinuousLinearMap.adjoint_comp, ContinuousLinearMap.adjoint_comp, + ContinuousLinearMap.adjoint_adjoint, ContinuousLinearMap.comp_assoc] + +def isometricCornerLiftHom (V : K →ₗᵢ[ℂ] H) : + (K →L[ℂ] K) →⋆ₙₐ[ℂ] (H →L[ℂ] H) where + toFun := isometricCornerLift V + map_zero' := by ext x; simp + map_add' T U := by ext x; simp + map_smul' c T := by ext x; simp + map_mul' := isometricCornerLift_mul V + map_star' := isometricCornerLift_star V + +lemma isometricCornerProjection_apply (V : K →ₗᵢ[ℂ] H) (x : H) : + isometricCornerProjection V x = V (V.toContinuousLinearMap.adjoint x) := rfl + +@[simp] lemma isometricCornerProjection_inclusion (V : K →ₗᵢ[ℂ] H) (x : K) : + isometricCornerProjection V (V x) = V x := by + rw [isometricCornerProjection_apply, isometricCorner_adjoint_apply] + +lemma isometricCornerProjection_isStarProjection (V : K →ₗᵢ[ℂ] H) : + IsStarProjection (isometricCornerProjection V) where + isSelfAdjoint := by + change (V.toContinuousLinearMap.comp V.toContinuousLinearMap.adjoint).adjoint = _ + rw [ContinuousLinearMap.adjoint_comp, ContinuousLinearMap.adjoint_adjoint] + isIdempotentElem := by + ext x + exact isometricCornerProjection_inclusion V _ + +lemma isometricCornerLift_compress (V : K →ₗᵢ[ℂ] H) (T : H →L[ℂ] H) : + isometricCornerLift V (isometricCornerCompress V T) = + isometricCornerProjection V * T * isometricCornerProjection V := by + ext x + rfl + +lemma isometricCornerCompress_cp (V : K →ₗᵢ[ℂ] H) : + CompletelyPositive (isometricCornerCompress V) := + hilbertCompression_cp _ _ + +lemma isometricCorner_inclusion_intertwines (V : K →ₗᵢ[ℂ] H) (T : H →L[ℂ] H) + (hT : Commute T (isometricCornerProjection V)) (x : K) : + T (V x) = V (isometricCornerCompress V T x) := by + have he := congrArg (fun R : H →L[ℂ] H => R (V x)) hT.eq + simpa only [mul_apply_eq_comp, isometricCornerProjection_inclusion, + isometricCornerProjection_apply, isometricCornerCompress_apply, + isometricCorner_adjoint_apply] using he + +lemma isometricCorner_adjoint_intertwines (V : K →ₗᵢ[ℂ] H) (T : H →L[ℂ] H) + (hT : Commute T (isometricCornerProjection V)) (x : H) : + isometricCornerCompress V T (V.toContinuousLinearMap.adjoint x) = + V.toContinuousLinearMap.adjoint (T x) := by + have he := congrArg (fun R : H →L[ℂ] H => R x) hT.eq + change T (isometricCornerProjection V x) = isometricCornerProjection V (T x) at he + change V.toContinuousLinearMap.adjoint (T (isometricCornerProjection V x)) = _ + rw [he, isometricCornerProjection_apply, isometricCorner_adjoint_apply] + +lemma isometricCornerLift_mul_right (V : K →ₗᵢ[ℂ] H) (T : K →L[ℂ] K) + (b : H →L[ℂ] H) (hb : Commute b (isometricCornerProjection V)) : + isometricCornerLift V T * b = isometricCornerLift V (T * isometricCornerCompress V b) := by + ext x + simp only [mul_apply_eq_comp, isometricCornerLift_apply] + rw [isometricCorner_adjoint_intertwines V b hb] + +lemma isometricCornerLift_mul_left (V : K →ₗᵢ[ℂ] H) (T : K →L[ℂ] K) + (b : H →L[ℂ] H) (hb : Commute b (isometricCornerProjection V)) : + b * isometricCornerLift V T = isometricCornerLift V (isometricCornerCompress V b * T) := by + ext x + simp only [mul_apply_eq_comp, isometricCornerLift_apply] + exact isometricCorner_inclusion_intertwines V b hb _ + +lemma isometricCornerLift_commute_iff (V : K →ₗᵢ[ℂ] H) (T : K →L[ℂ] K) + (b : H →L[ℂ] H) (hb : Commute b (isometricCornerProjection V)) : + Commute (isometricCornerLift V T) b ↔ Commute T (isometricCornerCompress V b) := by + simp only [Commute, SemiconjBy, isometricCornerLift_mul_right V T b hb, + isometricCornerLift_mul_left V T b hb, (isometricCornerLift_injective V).eq_iff] + +lemma isometricCornerCompress_norm_le (V : K →ₗᵢ[ℂ] H) : + ‖isometricCornerCompress V‖ ≤ 1 := by + have hv : ‖V.toContinuousLinearMap‖ ≤ 1 := + ContinuousLinearMap.opNorm_le_bound _ zero_le_one (fun x => by simp) + exact (hilbertCompression_norm_le _ _).trans + ((mul_le_mul hv hv (norm_nonneg _) zero_le_one).trans_eq (one_mul 1)) + +variable {A : Type*} [CStarAlgebra A] + +def isometricCornerRestrictHom (V : K →ₗᵢ[ℂ] H) + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) + (hπ : ∀ a, Commute (π a) (isometricCornerProjection V)) : + A →⋆ₐ[ℂ] (K →L[ℂ] K) where + toFun a := isometricCornerCompress V (π a) + map_zero' := by simp + map_one' := by ext x; simp [isometricCorner_adjoint_apply] + map_add' a b := by simp + map_mul' a b := by + ext x + simp only [map_mul, isometricCornerCompress_apply, mul_apply_eq_comp] + exact congrArg (fun y : H => V.toContinuousLinearMap.adjoint (π a y)) + (isometricCorner_inclusion_intertwines V (π b) (hπ b) x) + commutes' c := by + ext x + change V.toContinuousLinearMap.adjoint (π ((algebraMap ℂ A) c) (V x)) = _ + simp only [Algebra.algebraMap_eq_smul_one, map_smul, map_one, smul_apply, + one_apply_eq_self, isometricCorner_adjoint_apply] + map_star' a := by + change V.toContinuousLinearMap.adjoint.comp + ((π (star a)).comp V.toContinuousLinearMap) = + (V.toContinuousLinearMap.adjoint.comp ((π a).comp V.toContinuousLinearMap)).adjoint + rw [map_star, ContinuousLinearMap.star_eq_adjoint, + ContinuousLinearMap.adjoint_comp, ContinuousLinearMap.adjoint_comp, + ContinuousLinearMap.adjoint_adjoint, ContinuousLinearMap.comp_assoc] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/KernelIntegralBounds.lean b/lean/OAI/Analysis/OperatorAlgebra/KernelIntegralBounds.lean new file mode 100644 index 0000000000000000000000000000000000000000..cb3895eb1ea645f2a5c7fcbd87dceed096406e75 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/KernelIntegralBounds.lean @@ -0,0 +1,96 @@ +import OAI.Analysis.OperatorAlgebra.ScalarKernelPairing + +namespace OAI + +/-! Product-integrable bounds and a measure-preserving change of variables +for the scalar kernels used in crossed-product reconstruction. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +lemma integrable_weighted_scalar_kernel (u v : ℝ → ℂ) (hu : Integrable u) (hv : Integrable v) + (K : ℝ × ℝ → ℂ) (hK : Continuous K) (C : ℝ) (hC : ∀ p, ‖K p‖ ≤ C) : + Integrable (fun p : ℝ × ℝ => star (u p.1) * v p.2 * K p) (volume.prod volume) := by + apply ((hu.norm.mul_prod hv.norm).mul_const C).mono' + ((hu.aestronglyMeasurable.star.comp_fst.mul hv.aestronglyMeasurable.comp_snd).mul + hK.aestronglyMeasurable) + filter_upwards [] with p + simpa only [Pi.mul_apply, Pi.star_apply, norm_mul, norm_star] using + mul_le_mul_of_nonneg_left (hC p) (mul_nonneg (norm_nonneg (u p.1)) (norm_nonneg (v p.2))) + +lemma kernelDifference_measurePreserving : + MeasurePreserving (fun p : ℝ × ℝ => (p.2 - p.1, p.2)) + (volume.prod volume) (volume.prod volume) := by + have h := ((Measure.measurePreserving_neg (volume : Measure ℝ)).prod + (MeasurePreserving.id (volume : Measure ℝ))).comp + (measurePreserving_sub_prod (volume : Measure ℝ) (volume : Measure ℝ)) + simpa only [Function.comp_def, Prod.map_apply, id_eq, neg_sub] using h + +lemma kernel_integral_change_variables (A : ℝ × ℝ → ℂ) + (hA : Integrable A (volume.prod volume)) + (k : ℝ → ℂ) (hk : Continuous k) (C : ℝ) (hC : ∀ r, ‖k r‖ ≤ C) : + (∫ r : ℝ, ∫ s : ℝ, k r * A (s - r, s)) = + ∫ t : ℝ, ∫ s : ℝ, k (s - t) * A (t, s) := by + have hi : Integrable (fun p : ℝ × ℝ => A (p.2 - p.1, p.2)) (volume.prod volume) := + (kernelDifference_measurePreserving.integrable_comp hA.aestronglyMeasurable).mpr hA + have hi₁ : Integrable (fun p : ℝ × ℝ => k p.1 * A (p.2 - p.1, p.2)) + (volume.prod volume) := by + apply (hi.norm.const_mul C).mono' + ((hk.comp continuous_fst).aestronglyMeasurable.mul hi.aestronglyMeasurable) + filter_upwards [] with p + simpa only [Pi.mul_apply, Function.comp_def, norm_mul] using + mul_le_mul_of_nonneg_right (hC p.1) (norm_nonneg (A (p.2 - p.1, p.2))) + have hi₂ : Integrable (fun p : ℝ × ℝ => k (p.1 - p.2) * A (p.2, p.1)) + (volume.prod volume) := by + apply (hA.swap.norm.const_mul C).mono' + ((hk.comp (continuous_fst.sub continuous_snd)).aestronglyMeasurable.mul + hA.swap.aestronglyMeasurable) + filter_upwards [] with p + simpa only [Pi.mul_apply, Function.comp_def, Pi.sub_apply, Prod.swap, norm_mul] using + mul_le_mul_of_nonneg_right (hC (p.1 - p.2)) (norm_nonneg (A (p.2, p.1))) + calc + _ = ∫ s : ℝ, ∫ r : ℝ, k r * A (s - r, s) := integral_integral_swap hi₁ + _ = ∫ s : ℝ, ∫ t : ℝ, k (s - t) * A (t, s) := by + apply integral_congr_ae + filter_upwards [] with s + simpa only [sub_sub_cancel] using + (integral_sub_left_eq_self (fun r : ℝ => k r * A (s - r, s)) volume s).symm + _ = _ := integral_integral_swap hi₂ + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def scalarKernelMatrixCoefficient + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (f g : Lp ℂ 2 (volume : Measure ℝ)) (x y : H) (p : ℝ × ℝ) : ℂ := + inner ℂ (modularSliceKernel T f g p.2 p.1 x) y + +lemma scalarKernelMatrixCoefficient_continuous + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (f g : Lp ℂ 2 (volume : Measure ℝ)) (x y : H) : + Continuous (scalarKernelMatrixCoefficient T f g x y) := by + have hp : Continuous (fun p : ℝ × ℝ => (p.2, p.1)) := + continuous_snd.prodMk continuous_fst + have hc : Continuous (fun p : ℝ × ℝ => modularSliceKernel T f g p.2 p.1) := by + change Continuous ((fun p : ℝ × ℝ => modularSliceKernel T f g p.1 p.2) ∘ + (fun p : ℝ × ℝ => (p.2, p.1))) + exact (modularSliceKernel_continuous T f g).comp hp + exact (hc.clm_apply continuous_const).inner continuous_const + +lemma scalarKernelMatrixCoefficient_bound + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (f g : Lp ℂ 2 (volume : Measure ℝ)) (x y : H) (p : ℝ × ℝ) : + ‖scalarKernelMatrixCoefficient T f g x y p‖ ≤ + (‖f‖ * ‖T‖ * ‖g‖ * ‖x‖) * ‖y‖ := by + apply (norm_inner_le_norm _ _).trans + apply mul_le_mul_of_nonneg_right _ (norm_nonneg y) + exact ((modularSliceKernel T f g p.2 p.1).le_opNorm x).trans + (mul_le_mul_of_nonneg_right (modularSliceKernel_norm_le T f g p.2 p.1) (norm_nonneg x)) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/LpAlgebraicInstances.lean b/lean/OAI/Analysis/OperatorAlgebra/LpAlgebraicInstances.lean new file mode 100644 index 0000000000000000000000000000000000000000..234271db1366460da2df87d5d225928363805339 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/LpAlgebraicInstances.lean @@ -0,0 +1,27 @@ +import Mathlib + +namespace OAI + +/-! Compatibility of the algebraic structures used by the concrete L² +space and by the abstract normed-space estimates. -/ +noncomputable section +open MeasureTheory +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] + +lemma lp_addCommGroup_from_normed : + (inferInstance : NormedAddCommGroup (Lp H 2 (volume : Measure ℝ))).toAddCommGroup = + (Lp.instAddCommGroup (E := H) (p := 2) (μ := (volume : Measure ℝ))) := by + rfl + +lemma lp_addCommMonoid_from_normed : + (inferInstance : NormedAddCommGroup (Lp H 2 (volume : Measure ℝ))).toAddCommGroup.toAddCommMonoid = + (Lp.instAddCommGroup (E := H) (p := 2) (μ := (volume : Measure ℝ))).toAddCommMonoid := by + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/LpFourierCoefficients.lean b/lean/OAI/Analysis/OperatorAlgebra/LpFourierCoefficients.lean new file mode 100644 index 0000000000000000000000000000000000000000..8e6da843d16b418a4cce63f8deab0f0adf9c4245 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/LpFourierCoefficients.lean @@ -0,0 +1,61 @@ +import OAI.Analysis.ModularTheory.FourierTranslation + +namespace OAI + +/-! Fourier transform commutes with fixed vector coefficients, relating +the scalar inclusion to the vector regular representation. -/ + +noncomputable section +open MeasureTheory FourierTransform +open scoped SchwartzMap + +namespace WeakPureInfiniteness + +variable {H K : Type*} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma fourier_schwartz_postcomp (L : H →L[ℂ] K) (f : 𝓢(ℝ, H)) : + 𝓕 (f.postcompCLM L) = (𝓕 f).postcompCLM L := by + ext t + change 𝓕 (fun x => L (f x)) t = L (𝓕 (f : ℝ → H) t) + rw [Real.fourier_eq, Real.fourier_eq] + have hi := (Real.fourierIntegral_convergent_iff t).mpr + (f.integrable (μ := (volume : Measure ℝ))) + rw [← L.integral_comp_comm hi] + apply integral_congr_ae + filter_upwards [] with x + simp only [Circle.smul_def, map_smul] + +omit [CompleteSpace H] [CompleteSpace K] in +lemma compLp_schwartz (L : H →L[ℂ] K) (f : 𝓢(ℝ, H)) : + L.compLpL 2 volume (f.toLp 2) = (f.postcompCLM L).toLp 2 := by + apply Lp.ext + filter_upwards [L.coeFn_compLpL (p := 2) (μ := volume) (f.toLp 2), + f.coeFn_toLp 2 volume, (f.postcompCLM L).coeFn_toLp 2 volume] with t h₁ h₂ h₃ + rw [h₁, h₂, h₃, SchwartzMap.postcompCLM_apply] + +lemma fourier_compLp (L : H →L[ℂ] K) (f : Lp H 2 (volume : Measure ℝ)) : + 𝓕 (L.compLpL 2 volume f) = L.compLpL 2 volume (𝓕 f) := by + have hd : DenseRange (SchwartzMap.toLpCLM ℝ H 2 (volume : Measure ℝ)) := + SchwartzMap.denseRange_toLpCLM ENNReal.ofNat_ne_top + refine hd.induction_on f ?_ ?_ + · exact isClosed_eq + ((Lp.fourierTransformₗᵢ ℝ K).continuous.comp (L.compLpL 2 volume).continuous) + ((L.compLpL 2 volume).continuous.comp (Lp.fourierTransformₗᵢ ℝ H).continuous) + · intro g + change 𝓕 (L.compLpL 2 volume (g.toLp 2)) = L.compLpL 2 volume (𝓕 (g.toLp 2)) + rw [compLp_schwartz, SchwartzMap.toLp_fourier_eq, + SchwartzMap.toLp_fourier_eq, compLp_schwartz, fourier_schwartz_postcomp] + +lemma fourierInv_compLp (L : H →L[ℂ] K) (f : Lp H 2 (volume : Measure ℝ)) : + 𝓕⁻ (L.compLpL 2 volume f) = L.compLpL 2 volume (𝓕⁻ f) := by + apply (Lp.fourierTransformₗᵢ ℝ K).injective + change 𝓕 (𝓕⁻ (L.compLpL 2 volume f)) = 𝓕 (L.compLpL 2 volume (𝓕⁻ f)) + rw [fourier_fourierInv_eq, fourier_compLp, fourier_fourierInv_eq] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/LpFourierIntegral.lean b/lean/OAI/Analysis/OperatorAlgebra/LpFourierIntegral.lean new file mode 100644 index 0000000000000000000000000000000000000000..ab504c9454bf5ae5526898261a4c3791ecb4d0ee --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/LpFourierIntegral.lean @@ -0,0 +1,45 @@ +import Mathlib.Analysis.Fourier.LpSpace + +namespace OAI + +/-! Compatibility of the L² Fourier transform with the Bochner integral +when both the function and its classical transform are square integrable. +This is used for the regularized modular orbits. -/ + +noncomputable section +open MeasureTheory FourierTransform + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma fourier_toLp_of_integrable (f : ℝ → H) (hi : Integrable f) + (hf : MemLp f 2 (volume : Measure ℝ)) + (hF : MemLp (𝓕 f) 2 (volume : Measure ℝ)) : + 𝓕 (hf.toLp f) = hF.toLp (𝓕 f) := by + apply LinearMap.ker_eq_bot.mp + (Lp.ker_toTemperedDistributionCLM_eq_bot (F := H) (μ := volume) (p := 2)) + change Lp.toTemperedDistribution (𝓕 (hf.toLp f)) = + Lp.toTemperedDistribution (hF.toLp (𝓕 f)) + rw [← Lp.fourier_toTemperedDistribution_eq] + ext φ + rw [TemperedDistribution.fourier_apply, Lp.toTemperedDistribution_apply, + Lp.toTemperedDistribution_apply] + calc + (∫ t : ℝ, (𝓕 φ) t • (hf.toLp f) t) = ∫ t : ℝ, (𝓕 φ) t • f t := by + apply integral_congr_ae + filter_upwards [hf.coeFn_toLp] with t ht + rw [ht] + _ = ∫ ω : ℝ, φ ω • (𝓕 f) ω := by + simpa using! VectorFourier.integral_fourierIntegral_smul_eq_flip + (L := innerₗ ℝ) Real.continuous_fourierChar continuous_inner φ.integrable hi + _ = ∫ ω : ℝ, φ ω • (hF.toLp (𝓕 f)) ω := by + apply integral_congr_ae + filter_upwards [hF.coeFn_toLp] with ω hω + rw [hω] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/LpFourierIntegralAE.lean b/lean/OAI/Analysis/OperatorAlgebra/LpFourierIntegralAE.lean new file mode 100644 index 0000000000000000000000000000000000000000..8338f446b90f525d8ba1f6eac92c73162dd98386 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/LpFourierIntegralAE.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.OperatorAlgebra.LpFourierIntegral + +namespace OAI + +/-! The classical integral represents the L² Fourier transform on L¹∩L². +The proof tests the two locally integrable functions against compact smooth +functions, using the existing distributional Fourier compatibility. -/ + +noncomputable section +open MeasureTheory FourierTransform +open scoped ContDiff + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma fourier_toLp_ae_of_integrable (f : ℝ → H) (hi : Integrable f) + (hf : MemLp f 2 (volume : Measure ℝ)) : + (𝓕 (hf.toLp f) : Lp H 2 (volume : Measure ℝ)) =ᵐ[volume] 𝓕 f := by + have hc : Continuous (𝓕 f) := + VectorFourier.fourierIntegral_continuous Real.continuous_fourierChar + (innerSL ℝ).continuous₂ hi + apply ae_eq_of_integral_contDiff_smul_eq + ((Lp.memLp (𝓕 (hf.toLp f))).locallyIntegrable (by norm_num)) hc.locallyIntegrable + intro g hg hgc + have hgc' : HasCompactSupport (Complex.ofRealCLM ∘ g) := hgc.comp_left rfl + have hg' : ContDiff ℝ ∞ (Complex.ofRealCLM ∘ g) := by fun_prop + let φ : SchwartzMap ℝ ℂ := hgc'.toSchwartzMap hg' + have hd := congrArg (fun T : TemperedDistribution ℝ H => T φ) + (Lp.fourier_toTemperedDistribution_eq (hf.toLp f)) + simp only [TemperedDistribution.fourier_apply, Lp.toTemperedDistribution_apply] at hd + calc + (∫ t : ℝ, g t • (𝓕 (hf.toLp f) : Lp H 2 (volume : Measure ℝ)) t) = + ∫ t : ℝ, φ t • (𝓕 (hf.toLp f) : Lp H 2 (volume : Measure ℝ)) t := by + apply integral_congr_ae + exact ae_of_all _ (fun t => by change g t • _ = (g t : ℂ) • _; simp) + _ = ∫ t : ℝ, (𝓕 φ) t • (hf.toLp f) t := hd.symm + _ = ∫ t : ℝ, (𝓕 φ) t • f t := by + apply integral_congr_ae + filter_upwards [hf.coeFn_toLp] with t ht + rw [ht] + _ = ∫ t : ℝ, φ t • (𝓕 f) t := by + simpa using! VectorFourier.integral_fourierIntegral_smul_eq_flip + (L := innerₗ ℝ) Real.continuous_fourierChar continuous_inner φ.integrable hi + _ = ∫ t : ℝ, g t • (𝓕 f) t := by + apply integral_congr_ae + exact ae_of_all _ (fun t => by change (g t : ℂ) • _ = g t • _; simp) + + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/LpOperatorStructure.lean b/lean/OAI/Analysis/OperatorAlgebra/LpOperatorStructure.lean new file mode 100644 index 0000000000000000000000000000000000000000..c0719aa81c9e0d87e7d14513b29675b57cf7c2b7 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/LpOperatorStructure.lean @@ -0,0 +1,34 @@ +import Mathlib.MeasureTheory.Function.L2Space +import Mathlib.MeasureTheory.Measure.Lebesgue.Basic + +namespace OAI + +/-! Retype an operator from the abstract Hilbert-space structures to the +canonical L² structures before substituting concrete operator formulas. -/ +noncomputable section +open MeasureTheory +namespace WeakPureInfiniteness + +abbrev HilbertOperatorSpace (K : Type*) [NormedAddCommGroup K] + [InnerProductSpace ℂ K] := K →L[ℂ] K + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + +def canonicalLpOperator (T : HilbertOperatorSpace (Lp H 2 (volume : Measure ℝ))) : + Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ) := T + +lemma canonicalLpOperator_apply (T : HilbertOperatorSpace (Lp H 2 (volume : Measure ℝ))) + (x : Lp H 2 (volume : Measure ℝ)) : canonicalLpOperator T x = T x := rfl + +lemma canonicalLpOperator_eq (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] + Lp H 2 (volume : Measure ℝ)) : canonicalLpOperator T = T := rfl + +lemma canonicalLpOperator_mul + (T U : HilbertOperatorSpace (Lp H 2 (volume : Measure ℝ))) : + canonicalLpOperator (T * U) = canonicalLpOperator T * canonicalLpOperator U := rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/LpOperatorTensorBound.lean b/lean/OAI/Analysis/OperatorAlgebra/LpOperatorTensorBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..0478b5bcac1ff578fe56892de34482a114d2d927 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/LpOperatorTensorBound.lean @@ -0,0 +1,31 @@ +import OAI.Analysis.WeakInfiniteness.TensorFunctoriality +import Mathlib.MeasureTheory.Function.L2Space +import OAI.Analysis.OperatorAlgebra.LpAlgebraicInstances + +namespace OAI + +/-! An abstract Hilbert-space operator estimate transfers to the canonical +algebraic structures on the concrete L² space. -/ +noncomputable section +open MeasureTheory +open scoped TensorProduct +namespace WeakPureInfiniteness + +def hilbertOperatorTensorBound {K : Type*} [NormedAddCommGroup K] + [InnerProductSpace ℂ K] [CompleteSpace K] {I : Type*} [Fintype I] + (l r a b : I → K →L[ℂ] K) : Prop := + ‖∑ i, l i * r i‖ ≤ ‖∑ i, minimalElementary (a i) (MulOpposite.op (b i))‖ + +lemma lp_operator_tensor_bound {H : Type*} [NormedAddCommGroup H] + [InnerProductSpace ℂ H] [CompleteSpace H] {I : Type*} [Fintype I] + (l r a b : I → Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (h : hilbertOperatorTensorBound l r a b) : + ‖∑ i, l i * r i‖ ≤ ‖∑ i, minimalElementary (a i) (MulOpposite.op (b i))‖ := by + unfold hilbertOperatorTensorBound at h + convert h + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/LpTensorFunctoriality.lean b/lean/OAI/Analysis/OperatorAlgebra/LpTensorFunctoriality.lean new file mode 100644 index 0000000000000000000000000000000000000000..5389e52e7ec2a6603c16f37e5bf9f8cf5425883c --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/LpTensorFunctoriality.lean @@ -0,0 +1,31 @@ +import OAI.Analysis.Nuclearity.MinimalCornerNorm +import OAI.Analysis.OperatorAlgebra.CanonicalLpOperations + +namespace OAI + +/-! Contractive tensor maps into the canonical L² operator algebra. The +operator structures are fixed before substituting concrete representations. -/ +noncomputable section +open MeasureTheory +namespace WeakPureInfiniteness +universe u +variable {A B H : Type u} [NonUnitalCStarAlgebra A] [NonUnitalCStarAlgebra B] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma lp_norm_minimalSum_map_le {I : Type*} [Fintype I] + (φ : A →⋆ₙₐ[ℂ] (Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ))) + (ψ : B →⋆ₙₐ[ℂ] (Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ))ᵐᵒᵖ) + (a : I → A) (b : I → B) : + ‖∑ i, minimalElementary (canonicalLpOperator (φ (a i))) + (MulOpposite.op (canonicalLpOperator (ψ (b i)).unop))‖ ≤ + ‖∑ i, minimalElementary (a i) (b i)‖ := by + have h := NonUnitalStarAlgHom.norm_apply_le (minimalMapAny φ ψ) + (∑ i, minimalElementary (a i) (b i)) + simp only [map_sum, minimalMapAny_elementary] at h + simpa only [canonicalLpOperator_eq, MulOpposite.op_unop] using h + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/NormalizedExpectationRoots.lean b/lean/OAI/Analysis/OperatorAlgebra/NormalizedExpectationRoots.lean new file mode 100644 index 0000000000000000000000000000000000000000..53d2ef0b9805c3630fbb33b881efc815325aa71d --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/NormalizedExpectationRoots.lean @@ -0,0 +1,92 @@ +import OAI.Analysis.OperatorAlgebra.ExpectationDensityRoots +import OAI.Analysis.OperatorAlgebra.HilbertSchmidtUnitaryActions + +namespace OAI + +/-! A finite tracial expectation gives unit Hilbert–Schmidt vectors that +approximately intertwine any prescribed finite family of unitaries. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H J : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + [CompleteSpace H] [Fintype J] + +local instance hsNormedSpace : NormedSpace ℂ (NuclearUltrapower.HilbertSchmidt H) := inferInstance +local instance hsNormSMul : NormSMulClass ℂ (NuclearUltrapower.HilbertSchmidt H) := + NormedSpace.toNormSMulClass + +theorem expectation_unit_intertwiners (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (u : J → unitary M.toStarSubalgebra) {ε : ℝ} (hε : 0 < ε) : + ∃ z : NuclearUltrapower.HilbertSchmidt H, ‖z‖ = 1 ∧ + 0 ≤ NuclearUltrapower.hsOperator z ∧ + (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator z y ∈ F) ∧ + ∀ j, ‖hsLeftUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z - + hsRightUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z‖ ^ 2 < ε := by + let δ := min (ε / 4) (1 / 2) + have hδ : 0 < δ := lt_min (by positivity) (by norm_num) + obtain ⟨n, w, x, hw, _hws, _hx, ha, hrn, hrp, hrs, hru⟩ := + expectation_finite_density_roots M τ E hE hEr hEf + (fun _ : Unit => (1 : selfAdjoint M.toStarSubalgebra)) u hδ + let r := NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x) + change ‖r‖ ≤ 1 at hrn + change 0 ≤ NuclearUltrapower.hsOperator r at hrp + change (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator r y ∈ F) at hrs + have hm : |1 - ‖r‖ ^ 2| < δ := by + have ht := ha () + change |(τ.functional 1).re - ∑ k, w k * (inner ℂ (x k) (x k)).re| < δ at ht + rw [τ.normalized, Complex.one_re] at ht + have hq (k : Fin n) : (inner ℂ (x k) (x k)).re = ‖x k‖ ^ 2 := + inner_self_eq_norm_sq (𝕜 := ℂ) (x k) + simp_rw [hq] at ht + simpa only [r, NuclearUltrapower.densityRoot_norm, + finiteVectorDensityTensor_norm_sq w hw x] using ht + have hr2 : 1 / 2 < ‖r‖ ^ 2 := by + have hd : δ ≤ 1 / 2 := min_le_right _ _ + have hb := (abs_lt.mp hm).2 + linarith + have hr : 0 < ‖r‖ := by nlinarith [norm_nonneg r] + let c : ℂ := (‖r‖⁻¹ : ℝ) + let z := c • r + refine ⟨z, ?_, ?_, ?_, ?_⟩ + · change ‖c • r‖ = 1 + rw [norm_smul] + simp only [c, Complex.norm_real, Real.norm_of_nonneg (inv_nonneg.mpr hr.le), + inv_mul_cancel₀ hr.ne'] + · change 0 ≤ NuclearUltrapower.hsOperator (c • r) + rw [map_smul] + change 0 ≤ (‖r‖⁻¹ : ℝ) • NuclearUltrapower.hsOperator r + exact smul_nonneg (inv_nonneg.mpr hr.le) hrp + · obtain ⟨F, hF, hFs⟩ := hrs + refine ⟨F, hF, ?_⟩ + intro y + change NuclearUltrapower.hsOperator (c • r) y ∈ F + rw [map_smul, smul_apply] + exact F.smul_mem c (hFs y) + · intro j + rw [hsLeft_sub_right_norm] + have hj := hru j + change ‖NuclearUltrapower.hsConjugation _ r - r‖ ^ 2 < δ at hj + have hδe : δ ≤ ε / 4 := min_le_left _ _ + have hb : ‖NuclearUltrapower.hsConjugation + (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) r - r‖ ^ 2 < ε * ‖r‖ ^ 2 := by + nlinarith + change ‖NuclearUltrapower.hsConjugation _ (c • r) - c • r‖ ^ 2 < ε + rw [map_smul, ← smul_sub, norm_smul] + simp only [c, Complex.norm_real, Real.norm_of_nonneg (inv_nonneg.mpr hr.le), mul_pow, inv_pow] + exact (inv_mul_lt_iff₀ (sq_pos_of_pos hr)).mpr (by simpa only [mul_comm] using hb) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/PointwiseAntiunitary.lean b/lean/OAI/Analysis/OperatorAlgebra/PointwiseAntiunitary.lean new file mode 100644 index 0000000000000000000000000000000000000000..78a766a994afd38adfc6e0b67d75e764adcebc65 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/PointwiseAntiunitary.lean @@ -0,0 +1,82 @@ +import OAI.Analysis.ModularTheory.LpRepresentation +import OAI.Analysis.OperatorAlgebra.AntiunitaryCPConjugation + +namespace OAI + +/-! Pointwise antiunitary conjugation on the actual vector-valued L² space. -/ + +noncomputable section +open MeasureTheory Filter +open scoped InnerProductSpace ComplexConjugate + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + (μ : Measure ℝ) + +def pointwiseAntiunitaryMap (J : H ≃ₗᵢ⋆[ℂ] H) : Lp H 2 μ →L⋆[ℂ] Lp H 2 μ := + J.toContinuousLinearEquiv.toContinuousLinearMap.compLpL 2 μ + +lemma pointwiseAntiunitaryMap_ae (J : H ≃ₗᵢ⋆[ℂ] H) (f : Lp H 2 μ) : + pointwiseAntiunitaryMap μ J f =ᵐ[μ] fun t => J (f t) := + J.toContinuousLinearEquiv.toContinuousLinearMap.coeFn_compLpL f + +lemma pointwiseAntiunitaryMap_norm (J : H ≃ₗᵢ⋆[ℂ] H) (f : Lp H 2 μ) : + ‖pointwiseAntiunitaryMap μ J f‖ = ‖f‖ := by + rw [Lp.norm_def, Lp.norm_def] + congr 1 + apply eLpNorm_congr_norm_ae (Lp.aestronglyMeasurable _) (Lp.aestronglyMeasurable _) + filter_upwards [pointwiseAntiunitaryMap_ae μ J f] with t ht + rw [ht, J.norm_map] + +lemma pointwiseAntiunitaryMap_inverse (J : H ≃ₗᵢ⋆[ℂ] H) (f : Lp H 2 μ) : + pointwiseAntiunitaryMap μ J.symm (pointwiseAntiunitaryMap μ J f) = f := by + apply Lp.ext + filter_upwards [pointwiseAntiunitaryMap_ae μ J.symm (pointwiseAntiunitaryMap μ J f), + pointwiseAntiunitaryMap_ae μ J f] with t h₁ h₂ + rw [h₁, h₂, J.symm_apply_apply] + +def pointwiseAntiunitary (J : H ≃ₗᵢ⋆[ℂ] H) : Lp H 2 μ ≃ₗᵢ⋆[ℂ] Lp H 2 μ where + toFun := pointwiseAntiunitaryMap μ J + invFun := pointwiseAntiunitaryMap μ J.symm + left_inv := pointwiseAntiunitaryMap_inverse μ J + right_inv := pointwiseAntiunitaryMap_inverse μ J.symm + map_add' := map_add (pointwiseAntiunitaryMap μ J) + map_smul' c f := (pointwiseAntiunitaryMap μ J).map_smulₛₗ c f + norm_map' := pointwiseAntiunitaryMap_norm μ J + +lemma pointwiseAntiunitary_involutive (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) : + Function.Involutive (pointwiseAntiunitary μ J) := by + intro f + apply Lp.ext + filter_upwards [pointwiseAntiunitaryMap_ae μ J (pointwiseAntiunitaryMap μ J f), + pointwiseAntiunitaryMap_ae μ J f] with t h₁ h₂ + change (pointwiseAntiunitaryMap μ J (pointwiseAntiunitaryMap μ J f)) t = _ + rw [h₁, h₂, hJ] + +variable [CompleteSpace H] + +lemma pointwiseAntiunitary_conjugate (J : H ≃ₗᵢ⋆[ℂ] H) (T : H →L[ℂ] H) : + antiunitaryConjugate (pointwiseAntiunitary μ J) (pointwiseLpRepresentation μ T) = + pointwiseLpRepresentation μ (antiunitaryConjugate J T) := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [pointwiseAntiunitaryMap_ae μ J + (pointwiseLpRepresentation μ T (pointwiseAntiunitaryMap μ J f)), + T.coeFn_compLpL (p := 2) (μ := μ) (pointwiseAntiunitaryMap μ J f), + pointwiseAntiunitaryMap_ae μ J f, + (antiunitaryConjugate J T).coeFn_compLpL (p := 2) (μ := μ) f] with t h₁ h₂ h₃ h₄ + change (pointwiseAntiunitaryMap μ J + (pointwiseLpRepresentation μ T (pointwiseAntiunitaryMap μ J f))) t = + ((antiunitaryConjugate J T).compLpL 2 μ f) t + change (pointwiseLpRepresentation μ T (pointwiseAntiunitaryMap μ J f)) t = + T ((pointwiseAntiunitaryMap μ J f) t) at h₂ + rw [h₁, h₂, h₃, h₄] + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/PointwiseTomita.lean b/lean/OAI/Analysis/OperatorAlgebra/PointwiseTomita.lean new file mode 100644 index 0000000000000000000000000000000000000000..1a5fd412375a0fd992003c3dc80ac9be3e809f3d --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/PointwiseTomita.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.OperatorAlgebra.PointwiseAntiunitary +import OAI.Analysis.ModularTheory.CommutantExpectation + +namespace OAI + +/-! Commutation under the amplified Tomita conjugation. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace ComplexConjugate + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + +lemma antiunitaryConjugate_mul (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + (A B : H →L[ℂ] H) : + antiunitaryConjugate J (A * B) = antiunitaryConjugate J A * antiunitaryConjugate J B := by + apply ContinuousLinearMap.ext + intro x + simp only [antiunitaryConjugate_apply, mul_apply_eq_comp] + rw [hJ (B (J x))] + +lemma antiunitaryConjugate_commute (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + {A B : H →L[ℂ] H} (h : Commute A B) : + Commute (antiunitaryConjugate J A) (antiunitaryConjugate J B) := by + change _ * _ = _ * _ + rw [← antiunitaryConjugate_mul J hJ, ← antiunitaryConjugate_mul J hJ, h.eq] + +lemma antiunitaryConjugate_commute_iff (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) + (A B : H →L[ℂ] H) : + Commute A (antiunitaryConjugate J B) ↔ Commute (antiunitaryConjugate J A) B := by + constructor <;> intro h + · simpa only [antiunitaryConjugate_involutive J hJ] using antiunitaryConjugate_commute J hJ h + · simpa only [antiunitaryConjugate_involutive J hJ] using antiunitaryConjugate_commute J hJ h + +variable [CompleteSpace H] + +lemma pointwiseTomita_commute_iff (μ : Measure ℝ) (S : BoundedRecovery.StandardModularData H) + (A : H →L[ℂ] H) (R : Lp H 2 μ →L[ℂ] Lp H 2 μ) : + Commute (pointwiseLpRepresentation μ A) + (antiunitaryConjugate (pointwiseAntiunitary μ S.J) R) ↔ + Commute (pointwiseLpRepresentation μ (S.jConjugate A)) R := by + rw [antiunitaryConjugate_commute_iff _ + (pointwiseAntiunitary_involutive μ S.J S.conjugation), pointwiseAntiunitary_conjugate] + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ReducedDensityPredual.lean b/lean/OAI/Analysis/OperatorAlgebra/ReducedDensityPredual.lean new file mode 100644 index 0000000000000000000000000000000000000000..877eb122fad508bf55ab96177537b6832303af8c --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ReducedDensityPredual.lean @@ -0,0 +1,206 @@ +import OAI.Analysis.PureInfiniteness.FiniteDensityPowersStormer +import OAI.Analysis.OperatorAlgebra.FinitePredualConjugation + +namespace OAI + +/-! Finite tensor vectors give actual finite vector functionals. Their norm +controls the distance of their reduced-density square roots, without a +dimension bound on the ambient Hilbert spaces. -/ + +noncomputable section +open scoped InnerProductSpace TensorProduct ComplexOrder + +namespace WeakPureInfiniteness + +variable {E H : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +private def tensorActionOnVector (w : E ⊗[ℂ] H) : (H →L[ℂ] H) →L[ℂ] E ⊗[ℂ] H := + ({ toFun := fun T => T.lTensor E w + map_add' := by intros; simp only [ContinuousLinearMap.lTensor_add, add_apply] + map_smul' := by intros; simp only [ContinuousLinearMap.lTensor_smul, smul_apply, + RingHom.id_apply] } : (H →L[ℂ] H) →ₗ[ℂ] E ⊗[ℂ] H).mkContinuous ‖w‖ (fun T => by + calc + ‖T.lTensor E w‖ ≤ ‖T.lTensor E‖ * ‖w‖ := (T.lTensor E).le_opNorm w + _ ≤ ‖T‖ * ‖w‖ := mul_le_mul_of_nonneg_right (T.norm_lTensor_le E) (norm_nonneg w) + _ = ‖w‖ * ‖T‖ := mul_comm _ _) + +def tensorCoefficient (z w : E ⊗[ℂ] H) : StrongDual ℂ (H →L[ℂ] H) := + (innerSL ℂ z).comp (tensorActionOnVector w) + +omit [CompleteSpace E] [CompleteSpace H] in +lemma tensorCoefficient_apply (z w : E ⊗[ℂ] H) (T : H →L[ℂ] H) : + tensorCoefficient z w T = inner ℂ z (TensorProduct.mapL (ContinuousLinearMap.id ℂ E) T w) := by + change inner ℂ z (T.lTensor E w) = _ + rw [ContinuousLinearMap.lTensor_eq_mapL] + +omit [CompleteSpace E] [CompleteSpace H] in +lemma tensorCoefficient_mem (z w : E ⊗[ℂ] H) : + tensorCoefficient z w ∈ finiteOperatorPredual (H := H) := by + induction z using TensorProduct.inductionOn with + | tmul x y => + induction w using TensorProduct.inductionOn with + | tmul v t => + have he : tensorCoefficient (x ⊗ₜ[ℂ] y) (v ⊗ₜ[ℂ] t) = + inner ℂ x v • operatorCoefficient y t := by + ext T + simp only [tensorCoefficient_apply, TensorProduct.mapL_tmul, + ContinuousLinearMap.id_apply, TensorProduct.inner_tmul, smul_apply, + smul_eq_mul, operatorCoefficient_apply] + rw [he] + exact Submodule.smul_mem _ _ (finiteOperatorCoefficient y t).property + | add w₁ w₂ h₁ h₂ => + have he : tensorCoefficient (x ⊗ₜ[ℂ] y) (w₁ + w₂) = + tensorCoefficient (x ⊗ₜ[ℂ] y) w₁ + tensorCoefficient (x ⊗ₜ[ℂ] y) w₂ := by + ext T; simp only [tensorCoefficient_apply, map_add, add_apply, + inner_add_right (𝕜 := ℂ) (E := E ⊗[ℂ] H)] + rw [he]; exact Submodule.add_mem _ h₁ h₂ + | add z₁ z₂ h₁ h₂ => + have he : tensorCoefficient (z₁ + z₂) w = tensorCoefficient z₁ w + tensorCoefficient z₂ w := by + ext T; simp only [tensorCoefficient_apply, add_apply, + inner_add_left (𝕜 := ℂ) (E := E ⊗[ℂ] H)] + rw [he]; exact Submodule.add_mem _ h₁ h₂ + +def finiteTensorDensity (z : E ⊗[ℂ] H) : finiteOperatorPredual (H := H) := + ⟨tensorCoefficient z z, tensorCoefficient_mem z z⟩ + +omit [CompleteSpace E] [CompleteSpace H] in +@[simp] lemma finiteTensorDensity_apply (z : E ⊗[ℂ] H) (T : H →L[ℂ] H) : + (finiteTensorDensity z).val T = + inner ℂ z (TensorProduct.mapL (ContinuousLinearMap.id ℂ E) T z) := + tensorCoefficient_apply z z T + +lemma finiteTensorDensity_trace [FiniteDimensional ℂ H] (z : E ⊗[ℂ] H) : + finiteTensorDensity z = finiteOperatorTraceDensity (NuclearUltrapower.reducedDensity z) := by + apply Subtype.ext + ext T + rw [finiteTensorDensity_apply, finiteOperatorTraceDensity_apply, + NuclearUltrapower.trace_reducedDensity] + +variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] [CompleteSpace F] + +lemma operatorLift_norm_le (f : F →ₗᵢ[ℂ] H) (T : F →L[ℂ] F) : + ‖NuclearUltrapower.operatorLift f T‖ ≤ ‖T‖ := by + apply ContinuousLinearMap.opNorm_le_bound _ (norm_nonneg _) + intro x + change ‖f (T (f.toContinuousLinearMap.adjoint x))‖ ≤ ‖T‖ * ‖x‖ + calc + ‖f (T (f.toContinuousLinearMap.adjoint x))‖ = ‖T (f.toContinuousLinearMap.adjoint x)‖ := f.norm_map _ + _ ≤ ‖T‖ * ‖f.toContinuousLinearMap.adjoint x‖ := T.le_opNorm _ + _ ≤ ‖T‖ * (1 * ‖x‖) := mul_le_mul_of_nonneg_left + ((f.toContinuousLinearMap.adjoint.le_opNorm x).trans + (mul_le_mul_of_nonneg_right + ((ContinuousLinearMap.adjoint.norm_map _).trans_le f.norm_toContinuousLinearMap_le) + (norm_nonneg x))) (norm_nonneg T) + _ = ‖T‖ * ‖x‖ := by rw [one_mul] + +omit [CompleteSpace E] in +lemma finiteTensorDensity_operatorLift (f : F →ₗᵢ[ℂ] H) (z : E ⊗[ℂ] F) + (T : F →L[ℂ] F) : + (finiteTensorDensity (TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) f z)).val + (NuclearUltrapower.operatorLift f T) = (finiteTensorDensity z).val T := by + let g := TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) f + have hf (x : F) : f.toContinuousLinearMap.adjoint (f x) = x := + congrArg (fun S : F →L[ℂ] F => S x) f.adjoint_comp_self + have ht (w : E ⊗[ℂ] F) : + TensorProduct.mapL (ContinuousLinearMap.id ℂ E) (NuclearUltrapower.operatorLift f T) (g w) = + g (TensorProduct.mapL (ContinuousLinearMap.id ℂ E) T w) := by + induction w using TensorProduct.inductionOn with + | tmul x y => + simp only [g, TensorProduct.mapIsometry_apply, TensorProduct.map_tmul, + TensorProduct.mapL_tmul, ContinuousLinearMap.id_apply] + change x ⊗ₜ[ℂ] f (T (f.toContinuousLinearMap.adjoint (f y))) = x ⊗ₜ[ℂ] f (T y) + rw [hf] + | add w₁ w₂ h₁ h₂ => simp only [map_add, h₁, h₂] + rw [finiteTensorDensity_apply, finiteTensorDensity_apply] + change inner ℂ (g z) (TensorProduct.mapL _ _ (g z)) = _ + rw [ht, g.inner_map_map] + +omit [CompleteSpace E] in +lemma finiteTensorDensity_lift_norm_le (f : F →ₗᵢ[ℂ] H) (z w : E ⊗[ℂ] F) : + ‖finiteTensorDensity z - finiteTensorDensity w‖ ≤ + ‖finiteTensorDensity (TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) f z) - + finiteTensorDensity (TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) f w)‖ := by + let g := TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) f + let ψ := finiteTensorDensity (g z) - finiteTensorDensity (g w) + change ‖(finiteTensorDensity z - finiteTensorDensity w).val‖ ≤ ‖ψ.val‖ + apply ContinuousLinearMap.opNorm_le_bound _ (norm_nonneg _) + intro T + have he : (finiteTensorDensity z - finiteTensorDensity w).val T = + ψ.val (NuclearUltrapower.operatorLift f T) := by + change (finiteTensorDensity z).val T - (finiteTensorDensity w).val T = + (finiteTensorDensity (g z)).val _ - (finiteTensorDensity (g w)).val _ + rw [finiteTensorDensity_operatorLift, finiteTensorDensity_operatorLift] + rw [he] + exact (ψ.val.le_opNorm _).trans + (mul_le_mul_of_nonneg_left (operatorLift_norm_le f T) (norm_nonneg _)) + +/-- The predual norm estimate survives passage to the common finite support +of the two densities. No ambient finite-dimensionality is assumed. -/ +theorem densityRoot_predual_bound (z w : E ⊗[ℂ] H) : + ‖NuclearUltrapower.densityRoot z - NuclearUltrapower.densityRoot w‖ ^ 2 ≤ + ‖finiteTensorDensity z - finiteTensorDensity w‖ := by + obtain ⟨F, hF, hFzw⟩ := TensorProduct.exists_finite_submodule_right_of_setFinite + ({z, w} : Set (E ⊗[ℂ] H)) (Set.toFinite _) + let : FiniteDimensional ℂ F := hF + obtain ⟨z', hz⟩ := hFzw (by simp : z ∈ ({z, w} : Set (E ⊗[ℂ] H))) + obtain ⟨w', hw⟩ := hFzw (by simp : w ∈ ({z, w} : Set (E ⊗[ℂ] H))) + let f := TensorProduct.mapIsometry (LinearIsometry.id : E →ₗᵢ[ℂ] E) F.subtypeₗᵢ + have hz' : f z' = z := hz + have hw' : f w' = w := hw + rw [← hz', ← hw', NuclearUltrapower.densityRoot_mapIsometry, + NuclearUltrapower.densityRoot_mapIsometry, ← UniformSpace.Completion.coe_sub, + UniformSpace.Completion.norm_coe, ← NuclearUltrapower.liftOperatorTensor_sub, + NuclearUltrapower.liftOperatorTensor_norm, NuclearUltrapower.finiteOperatorTensor_sub] + refine (finite_density_root_predual_bound _ _ + (NuclearUltrapower.reducedDensity_nonneg z') (NuclearUltrapower.reducedDensity_nonneg w')).trans ?_ + have ht : finiteOperatorTraceDensity + (NuclearUltrapower.reducedDensity z' - NuclearUltrapower.reducedDensity w') = + finiteTensorDensity z' - finiteTensorDensity w' := by + apply Subtype.ext + ext T + rw [finiteOperatorTraceDensity_apply] + change LinearMap.trace ℂ F ((T * (NuclearUltrapower.reducedDensity z' - + NuclearUltrapower.reducedDensity w')).toLinearMap) = + (finiteTensorDensity z').val T - (finiteTensorDensity w').val T + rw [mul_sub, ContinuousLinearMap.toLinearMap_sub, map_sub, + ← finiteOperatorTraceDensity_apply, ← finiteOperatorTraceDensity_apply, + ← finiteTensorDensity_trace, ← finiteTensorDensity_trace] + rw [ht] + exact finiteTensorDensity_lift_norm_le F.subtypeₗᵢ z' w' + +omit [CompleteSpace E] in +lemma finiteTensorDensity_unitary (U : H ≃ₗᵢ[ℂ] H) (z : E ⊗[ℂ] H) : + finiteTensorDensity (TensorProduct.congrIsometry (LinearIsometryEquiv.refl ℂ E) U z) = + finitePredualUnitary U (finiteTensorDensity z) := by + apply Subtype.ext + ext T + have ht : NuclearUltrapower.operatorLift U.toLinearIsometry (conjugatedOperator U T) = T := by + unfold NuclearUltrapower.operatorLift + change (U : H →L[ℂ] H) ∘L conjugatedOperator U T ∘L + ContinuousLinearMap.adjoint (U : H →L[ℂ] H) = T + rw [U.adjoint_eq_symm] + ext x + change U (U.symm (T (U (U.symm x)))) = T x + simp only [U.apply_symm_apply] + change (finiteTensorDensity (TensorProduct.mapIsometry + (LinearIsometry.id : E →ₗᵢ[ℂ] E) U.toLinearIsometry z)).val T = + (finiteTensorDensity z).val (conjugatedOperator U T) + conv_lhs => rw [← ht] + exact finiteTensorDensity_operatorLift U.toLinearIsometry z (conjugatedOperator U T) + +/-- Norm-small conjugation defects of a finite positive functional yield +Hilbert–Schmidt-small conjugation defects of its positive square root. -/ +theorem densityRoot_unitary_predual_bound (U : H ≃ₗᵢ[ℂ] H) (z : E ⊗[ℂ] H) : + ‖NuclearUltrapower.hsConjugation U (NuclearUltrapower.densityRoot z) - + NuclearUltrapower.densityRoot z‖ ^ 2 ≤ + ‖finitePredualUnitary U (finiteTensorDensity z) - finiteTensorDensity z‖ := by + rw [← NuclearUltrapower.densityRoot_unitary (LinearIsometryEquiv.refl ℂ E) U z] + simpa only [finiteTensorDensity_unitary] using densityRoot_predual_bound + (TensorProduct.congrIsometry (LinearIsometryEquiv.refl ℂ E) U z) z + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarKernelPairing.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarKernelPairing.lean new file mode 100644 index 0000000000000000000000000000000000000000..7b71341c3eaa69948d070dedf096ff3a565c2a0a --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarKernelPairing.lean @@ -0,0 +1,95 @@ +import OAI.Analysis.OperatorAlgebra.ScalarTranslationConvolution +import OAI.Analysis.ModularTheory.CovariantKernel + +namespace OAI + +/-! Matrix coefficients of the actual convolution-smoothed operator are +the double integrals of its covariant scalar-slice kernel. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace ComplexConjugate + +namespace WeakPureInfiniteness + +variable {K : Type*} [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma inner_integral_left {F : ℝ → K} (hF : Integrable F) (y : K) : + inner ℂ (∫ t, F t) y = ∫ t, inner ℂ (F t) y := by + calc + _ = conj (inner ℂ y (∫ t, F t)) := (inner_conj_symm _ _).symm + _ = conj (∫ t, inner ℂ y (F t)) := congrArg conj (integral_inner hF y).symm + _ = ∫ t, conj (inner ℂ y (F t)) := integral_conj.symm + _ = _ := by simp only [inner_conj_symm] + +lemma inner_integral_pair (T : K →L[ℂ] K) {F G : ℝ → K} + (hF : Integrable F) (hG : Integrable G) : + inner ℂ (T (∫ t, F t)) (∫ s, G s) = + ∫ t, ∫ s, inner ℂ (T (F t)) (G s) := by + rw [← T.integral_comp_comm hF, inner_integral_left (T.integrable_comp hF)] + apply integral_congr_ae + filter_upwards [] with t + exact (integral_inner hG _).symm + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +omit [CompleteSpace H] in +lemma scalarTranslationSynthesis_integrable (g u : Lp ℂ 2 (volume : Measure ℝ)) + (hu : Integrable (u : ℝ → ℂ)) (x : H) : + Integrable (fun t : ℝ => u t • scalarVectorLp volume (modularLpTranslate volume t g) x) := by + have hc : Continuous (fun t => scalarVectorLp volume (modularLpTranslate volume t g) x) := + ((ContinuousLinearMap.toSpanSingleton ℂ x).compLpL 2 volume).continuous.comp + (continuous_modularLpTranslate g) + apply BoundedRecovery.integrable_smul_bounded_orbit hu hc + intro t + rw [scalarVectorLp_norm, (modularLpTranslate volume t).norm_map] + +theorem scalarKernel_convolution_pairing + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (f g u v : Lp ℂ 2 (volume : Measure ℝ)) + (hf : Integrable (f : ℝ → ℂ)) (hg : Integrable (g : ℝ → ℂ)) + (hu : Integrable (u : ℝ → ℂ)) (hv : Integrable (v : ℝ → ℂ)) (x y : H) : + inner ℂ (T (integratedModularTranslation g hg (scalarVectorLp volume u x))) + (integratedModularTranslation f hf (scalarVectorLp volume v y)) = + ∫ t : ℝ, ∫ s : ℝ, star (u t) * v s * inner ℂ (modularSliceKernel T f g s t x) y := by + rw [scalarVectorLp_convolution_synthesis g u hg hu, + scalarVectorLp_convolution_synthesis f v hf hv] + refine (inner_integral_pair T (scalarTranslationSynthesis_integrable g u hu x) + (scalarTranslationSynthesis_integrable f v hv y)).trans ?_ + apply integral_congr_ae + filter_upwards [] with t + apply integral_congr_ae + filter_upwards [] with s + rw [map_smul, inner_smul_left, inner_smul_right] + change _ = star (u t) * v s * inner ℂ + (scalarOperatorSlice volume T (modularLpTranslate volume s f) + (modularLpTranslate volume t g) x) y + rw [scalarOperatorSlice_inner] + simp only [starRingEnd_apply] + ring + +def convolutionSmoothedOperator + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (f g : Lp ℂ 2 (volume : Measure ℝ)) + (hf : Integrable (f : ℝ → ℂ)) (hg : Integrable (g : ℝ → ℂ)) : + Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ) := + (integratedModularTranslation f hf).adjoint * T * integratedModularTranslation g hg + +theorem convolutionSmoothedOperator_pairing + (T : Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ)) + (f g u v : Lp ℂ 2 (volume : Measure ℝ)) + (hf : Integrable (f : ℝ → ℂ)) (hg : Integrable (g : ℝ → ℂ)) + (hu : Integrable (u : ℝ → ℂ)) (hv : Integrable (v : ℝ → ℂ)) (x y : H) : + inner ℂ (convolutionSmoothedOperator T f g hf hg (scalarVectorLp volume u x)) + (scalarVectorLp volume v y) = + ∫ t : ℝ, ∫ s : ℝ, star (u t) * v s * inner ℂ (modularSliceKernel T f g s t x) y := by + change inner ℂ ((integratedModularTranslation f hf).adjoint + (T (integratedModularTranslation g hg (scalarVectorLp volume u x)))) _ = _ + rw [ContinuousLinearMap.adjoint_inner_left] + exact scalarKernel_convolution_pairing T f g u v hf hg hu hv x y + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpContinuousCutoffs.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpContinuousCutoffs.lean new file mode 100644 index 0000000000000000000000000000000000000000..685999b05392f113102948c1a4997f0cc86b68fe --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpContinuousCutoffs.lean @@ -0,0 +1,113 @@ +import OAI.Analysis.OperatorAlgebra.ScalarLpStrongConvergence +import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Commute +import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unique +import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Basic +import Mathlib.Analysis.CStarAlgebra.ContinuousLinearMap + +namespace OAI + +/-! Continuous functional calculus for scalar L² multiplication, in a form +that keeps pointwise cutoffs and their operator realizations connected. -/ + +noncomputable section +open MeasureTheory Filter +open scoped Topology CStarAlgebra + +namespace WeakPureInfiniteness + +instance scalarBoundedContinuousCStarAlgebra : + CommCStarAlgebra (BoundedContinuousFunction ℝ ℂ) where + +instance scalarBoundedContinuousComplexCFC : + ContinuousFunctionalCalculus ℂ (BoundedContinuousFunction ℝ ℂ) IsStarNormal := + IsStarNormal.instContinuousFunctionalCalculus + +instance scalarBoundedContinuousRealCFC : + ContinuousFunctionalCalculus ℝ (BoundedContinuousFunction ℝ ℂ) IsSelfAdjoint := + IsSelfAdjoint.instContinuousFunctionalCalculus + +def boundedFunctionEval (t : ℝ) : BoundedContinuousFunction ℝ ℂ →⋆ₐ[ℂ] ℂ where + toFun a := a t + map_one' := rfl + map_mul' _ _ := rfl + map_zero' := rfl + map_add' _ _ := rfl + commutes' _ := rfl + map_star' _ := rfl + +def scalarCosine (r : ℝ) : BoundedContinuousFunction ℝ ℂ := + BoundedContinuousFunction.ofNormedAddCommGroup + (fun t : ℝ => (Real.cos (r * t) : ℂ)) (by fun_prop) 1 (by + intro t + simpa only [Complex.norm_real, Real.norm_eq_abs] using Real.abs_cos_le_one (r * t)) + +@[simp] lemma scalarCosine_apply (r t : ℝ) : + scalarCosine r t = (Real.cos (r * t) : ℂ) := rfl + +lemma scalarCosine_selfAdjoint (r : ℝ) : IsSelfAdjoint (scalarCosine r) := by + change star (scalarCosine r) = scalarCosine r + ext t + simp only [BoundedContinuousFunction.coe_star, Pi.star_apply, scalarCosine_apply, + Complex.star_def, Complex.conj_ofReal] + +lemma scalarCosine_character (r : ℝ) : + scalarCosine r = (2 : ℂ)⁻¹ • + (BoundedRecovery.spectralCharacter r + star (BoundedRecovery.spectralCharacter r)) := by + ext t + simp only [scalarCosine_apply, BoundedContinuousFunction.coe_smul, + BoundedContinuousFunction.coe_add, BoundedContinuousFunction.coe_star, + Pi.add_apply, Pi.star_apply, smul_eq_mul, + BoundedRecovery.spectralCharacter_apply, Complex.exp_ofReal_mul_I, + star_add, star_mul, Complex.star_def, Complex.conj_ofReal, Complex.conj_I] + ring + +lemma scalarCosine_cfc_apply (r t : ℝ) (f : ℝ → ℝ) (hf : Continuous f) : + cfc f (scalarCosine r) t = (f (Real.cos (r * t)) : ℂ) := by + have h := (boundedFunctionEval t).map_cfc f (scalarCosine r) hf.continuousOn + (ha := scalarCosine_selfAdjoint r) + (hφa := (scalarCosine_selfAdjoint r).map (boundedFunctionEval t)) + change (cfc f (scalarCosine r)) t = cfc f (scalarCosine r t) at h + change (cfc f (scalarCosine r)) t = + cfc f (algebraMap ℝ ℂ (Real.cos (r * t))) at h + rw [cfc_algebraMap] at h + exact h + +lemma scalarLp_commute_cosine (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] + Lp ℂ 2 (volume : Measure ℝ)) (r : ℝ) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) : + Commute T (scalarLpRepresentation volume (scalarCosine r)) := by + rw [scalarCosine_character, map_smul, map_add, map_star] + have h₁ : Commute T (scalarLpRepresentation volume (BoundedRecovery.spectralCharacter r)) := by + simpa only [scalarLpRepresentation_character] using hc r + have h₂ : Commute T + (scalarLpRepresentation volume (star (BoundedRecovery.spectralCharacter r))) := by + rw [BoundedRecovery.spectralCharacter_star] + simpa only [scalarLpRepresentation_character] using hc (-r) + rw [map_star] at h₂ + exact (h₁.add_right h₂).smul_right _ + +lemma scalarLp_commute_cosine_cfc + (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) + (r : ℝ) (f : ℝ → ℝ) (hf : Continuous f) : + Commute T (scalarLpRepresentation volume (cfc f (scalarCosine r))) := by + have : ContinuousFunctionalCalculus ℂ + (Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) IsStarNormal := + IsStarNormal.instContinuousFunctionalCalculus + (A := Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + have : ContinuousFunctionalCalculus ℝ + (Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) IsSelfAdjoint := + IsSelfAdjoint.instContinuousFunctionalCalculus + (A := Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + rw [(scalarLpRepresentation volume).map_cfc f (scalarCosine r) hf.continuousOn + (ha := scalarCosine_selfAdjoint r) + (hφa := (scalarCosine_selfAdjoint r).map (scalarLpRepresentation volume))] + exact ((scalarLp_commute_cosine T r hc).symm.cfc_real f).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpCutoffConvergence.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpCutoffConvergence.lean new file mode 100644 index 0000000000000000000000000000000000000000..83885508f1577a8feec330c5b6f0778077695c09 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpCutoffConvergence.lean @@ -0,0 +1,83 @@ +import OAI.Analysis.OperatorAlgebra.ScalarLpProjection + +namespace OAI + +/-! The interval spectral cutoffs on scalar L² converge strongly to the +identity, giving a strongly exhausting family of projections. -/ + +noncomputable section +open MeasureTheory Filter Set +open scoped InnerProductSpace Topology + +namespace WeakPureInfiniteness + +lemma scalarLp_norm_sq_integral (f : Lp ℂ 2 (volume : Measure ℝ)) : + ‖f‖ ^ 2 = ∫ t : ℝ, ‖f t‖ ^ 2 := by + calc + ‖f‖ ^ 2 = (inner ℂ f f).re := (inner_self_eq_norm_sq (𝕜 := ℂ) f).symm + _ = ∫ t : ℝ, (inner ℂ (f t) (f t)).re := by + rw [L2.inner_def] + exact (integral_re (𝕜 := ℂ) (L2.integrable_inner (𝕜 := ℂ) f f)).symm + _ = ∫ t : ℝ, ‖f t‖ ^ 2 := by + congr 1 + funext t + exact inner_self_eq_norm_sq (𝕜 := ℂ) (f t) + +def scalarIntervalProjection (n : ℕ) : + Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ) := + scalarLpProjection volume (Icc (-(n : ℝ)) n) measurableSet_Icc + +lemma scalarIntervalProjection_ae (n : ℕ) (f : Lp ℂ 2 (volume : Measure ℝ)) : + scalarIntervalProjection n f =ᵐ[volume] (Icc (-(n : ℝ)) n).indicator f := + scalarLpProjection_ae volume _ _ f + +lemma scalarIntervalProjection_norm_le (n : ℕ) : ‖scalarIntervalProjection n‖ ≤ 1 := + scalarLpProjection_norm_le volume _ _ + +lemma scalarIntervalProjection_isStarProjection (n : ℕ) : + IsStarProjection (scalarIntervalProjection n) := + scalarLpProjection_isStarProjection volume _ _ + +lemma scalarIntervalProjection_strong (f : Lp ℂ 2 (volume : Measure ℝ)) : + Tendsto (fun n => scalarIntervalProjection n f) atTop (𝓝 f) := by + let F (n : ℕ) (t : ℝ) := ‖(Icc (-(n : ℝ)) n).indicator (f : ℝ → ℂ) t - f t‖ ^ 2 + have hbound (n : ℕ) (t : ℝ) : F n t ≤ ‖f t‖ ^ 2 := by + dsimp only [F] + by_cases ht : t ∈ Icc (-(n : ℝ)) n <;> simp [ht] + have hmeas (n : ℕ) : AEStronglyMeasurable (F n) volume := + (((Lp.aestronglyMeasurable f).indicator measurableSet_Icc).sub + (Lp.aestronglyMeasurable f)).norm.pow 2 + have hi : Integrable (fun t : ℝ => ‖f t‖ ^ 2) := + (memLp_two_iff_integrable_sq_norm (Lp.aestronglyMeasurable f)).mp (Lp.memLp f) + have hpoint (t : ℝ) : Tendsto (fun n => F n t) atTop (𝓝 0) := by + obtain ⟨N, hN⟩ := exists_nat_gt |t| + apply tendsto_const_nhds.congr' + filter_upwards [eventually_ge_atTop N] with n hn + have hnt : |t| ≤ (n : ℝ) := hN.le.trans (by exact_mod_cast hn) + have ht : t ∈ Icc (-(n : ℝ)) n := abs_le.mp hnt + simp [F, ht] + have hint : Tendsto (fun n => ∫ t : ℝ, F n t) atTop (𝓝 0) := by + have h := tendsto_integral_of_dominated_convergence (fun t : ℝ => ‖f t‖ ^ 2) + hmeas hi (fun n => ae_of_all _ (fun t => by + rw [Real.norm_eq_abs, abs_of_nonneg (sq_nonneg _)] + exact hbound n t)) (ae_of_all _ hpoint) + simpa only [integral_zero] using h + have heq (n : ℕ) : ‖scalarIntervalProjection n f - f‖ ^ 2 = ∫ t : ℝ, F n t := by + rw [scalarLp_norm_sq_integral] + apply integral_congr_ae + filter_upwards [Lp.coeFn_sub (scalarIntervalProjection n f) f, + scalarIntervalProjection_ae n f] with t hs hp + rw [hs, Pi.sub_apply, hp] + have hsq : Tendsto (fun n => ‖scalarIntervalProjection n f - f‖ ^ 2) atTop (𝓝 0) := + hint.congr' (Eventually.of_forall fun n => (heq n).symm) + have hn : Tendsto (fun n => Real.sqrt (‖scalarIntervalProjection n f - f‖ ^ 2)) + atTop (𝓝 (Real.sqrt 0)) := + Real.continuous_sqrt.continuousAt.tendsto.comp hsq + simp only [Real.sqrt_sq (norm_nonneg _), Real.sqrt_zero] at hn + exact tendsto_iff_norm_sub_tendsto_zero.mpr hn + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpIntervalCommutant.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpIntervalCommutant.lean new file mode 100644 index 0000000000000000000000000000000000000000..b3be0af368840ede90550159f2a04ff3827b1cf7 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpIntervalCommutant.lean @@ -0,0 +1,104 @@ +import OAI.Analysis.OperatorAlgebra.ScalarLpSuperlevel + +namespace OAI + +/-! Interval projections are strong limits of cosine superlevel projections. +Thus commuting with the real character group implies commuting with the +concrete exhausting spectral cutoffs used for modular weights. -/ + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology + +namespace WeakPureInfiniteness + +lemma cosineSuperlevel_eventually_interval (n : ℕ) (t : ℝ) : + ∀ᶠ k : ℕ in atTop, + (t ∈ scalarCosineSuperlevel ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ))) ↔ t ∈ Icc (-(n : ℝ)) n) := by + obtain ⟨N, hN⟩ := exists_nat_gt (max |t| (n : ℝ) / Real.pi) + filter_upwards [eventually_ge_atTop N] with k hk + have hd : 0 < ((k + 1 : ℕ) : ℝ) := by positivity + have hNk : (N : ℝ) ≤ ((k + 1 : ℕ) : ℝ) := by exact_mod_cast (hk.trans (Nat.le_succ k)) + have hmax : max |t| (n : ℝ) < ((k + 1 : ℕ) : ℝ) * Real.pi := + (div_lt_iff₀ Real.pi_pos).mp (hN.trans_le hNk) + have ht : |t| / ((k + 1 : ℕ) : ℝ) ∈ Icc 0 Real.pi := by + constructor + · positivity + · apply (div_le_iff₀ hd).mpr + simpa only [mul_comm] using (le_max_left |t| (n : ℝ)).trans hmax.le + have hn : (n : ℝ) / ((k + 1 : ℕ) : ℝ) ∈ Icc 0 Real.pi := by + constructor + · positivity + · apply (div_le_iff₀ hd).mpr + simpa only [mul_comm] using (le_max_right |t| (n : ℝ)).trans hmax.le + change (Real.cos ((n : ℝ) / ((k + 1 : ℕ) : ℝ)) ≤ + Real.cos (((k + 1 : ℕ) : ℝ)⁻¹ * t)) ↔ _ + have hct : Real.cos (t / ((k + 1 : ℕ) : ℝ)) = + Real.cos (|t| / ((k + 1 : ℕ) : ℝ)) := by + rw [← Real.cos_abs (t / ((k + 1 : ℕ) : ℝ)), abs_div, abs_of_pos hd] + rw [mul_comm _ t, ← div_eq_mul_inv, hct] + rw [Real.strictAntiOn_cos.le_iff_ge hn ht, div_le_div_iff_of_pos_right hd] + exact abs_le + +lemma scalarCosineSuperlevel_interval_strong (n : ℕ) + (f : Lp ℂ 2 (volume : Measure ℝ)) : + Tendsto (fun k => scalarCosineSuperlevelProjection ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ))) f) atTop (𝓝 (scalarIntervalProjection n f)) := by + let b (k : ℕ) : ℝ → ℂ := + (scalarCosineSuperlevel ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ)))).indicator (fun _ => 1) + let a : ℝ → ℂ := (Icc (-(n : ℝ)) n).indicator (fun _ => 1) + have hb (k : ℕ) : AEStronglyMeasurable (b k) volume := + (measurable_const.indicator (scalarCosineSuperlevel_measurable _ _)).aestronglyMeasurable + have ha : AEStronglyMeasurable a volume := + (measurable_const.indicator measurableSet_Icc).aestronglyMeasurable + have hbn (k : ℕ) (t : ℝ) : ‖b k t‖ ≤ 1 := by + change ‖(scalarCosineSuperlevel ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ)))).indicator (fun _ : ℝ => (1 : ℂ)) t‖ ≤ 1 + by_cases ht : t ∈ scalarCosineSuperlevel ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ))) + · rw [Set.indicator_of_mem ht] + norm_num + · rw [Set.indicator_of_notMem ht] + norm_num + have han (t : ℝ) : ‖a t‖ ≤ 1 := by + dsimp only [a] + simp only [Set.indicator_apply] + split_ifs <;> simp + have hlim (t : ℝ) : Tendsto (fun k => b k t) atTop (𝓝 (a t)) := by + apply tendsto_const_nhds.congr' + filter_upwards [cosineSuperlevel_eventually_interval n t] with k hk + change (Icc (-(n : ℝ)) n).indicator (fun _ : ℝ => (1 : ℂ)) t = + (scalarCosineSuperlevel ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ)))).indicator (fun _ : ℝ => (1 : ℂ)) t + by_cases ht : t ∈ Icc (-(n : ℝ)) n + · have hk' := hk.mpr ht + rw [Set.indicator_of_mem ht, Set.indicator_of_mem hk'] + · have hk' : t ∉ scalarCosineSuperlevel ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ))) := fun h => ht (hk.mp h) + rw [Set.indicator_of_notMem ht, Set.indicator_of_notMem hk'] + have heq (k : ℕ) : boundedScalarLp volume (b k) (hb k) 1 (hbn k) = + scalarCosineSuperlevelProjection ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ))) := by + rfl + have heqa : boundedScalarLp volume a ha 1 han = scalarIntervalProjection n := by rfl + simpa only [heq, heqa] using + boundedScalarLp_strong b a hb ha 1 zero_le_one hbn han hlim f + +theorem scalarLp_commute_intervalProjection + (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) + (n : ℕ) : Commute T (scalarIntervalProjection n) := + commute_of_strong_limit T (scalarIntervalProjection n) + (fun k => scalarCosineSuperlevelProjection ((k + 1 : ℕ) : ℝ)⁻¹ + (Real.cos ((n : ℝ) / (k + 1 : ℕ)))) + (fun _k => scalarLp_commute_cosine_superlevel T hc _ _) + (scalarCosineSuperlevel_interval_strong n) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpLocalizedFunctions.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpLocalizedFunctions.lean new file mode 100644 index 0000000000000000000000000000000000000000..ebf15875bac1eb15626058655066e971d88816d2 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpLocalizedFunctions.lean @@ -0,0 +1,175 @@ +import OAI.Analysis.OperatorAlgebra.ScalarLpIntervalCommutant +import Mathlib.Analysis.SpecialFunctions.Trigonometric.Inverse + +namespace OAI + +/-! A bounded spectral chart on each interval [-n,n]. This gives the +localized continuous multipliers needed to test the modular weight, using +only commutation with the actual character group. -/ + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +open scoped CStarAlgebra + +namespace WeakPureInfiniteness + +def scalarPhaseCosine (r c : ℝ) : BoundedContinuousFunction ℝ ℂ := + BoundedContinuousFunction.ofNormedAddCommGroup + (fun t : ℝ => (Real.cos (r * t + c) : ℂ)) (by fun_prop) 1 (by + intro t + simpa only [Complex.norm_real, Real.norm_eq_abs] using Real.abs_cos_le_one (r * t + c)) + +@[simp] lemma scalarPhaseCosine_apply (r c t : ℝ) : + scalarPhaseCosine r c t = (Real.cos (r * t + c) : ℂ) := rfl + +lemma scalarPhaseCosine_selfAdjoint (r c : ℝ) : IsSelfAdjoint (scalarPhaseCosine r c) := by + change star (scalarPhaseCosine r c) = scalarPhaseCosine r c + ext t + simp only [BoundedContinuousFunction.coe_star, Pi.star_apply, scalarPhaseCosine_apply, + Complex.star_def, Complex.conj_ofReal] + +lemma scalarPhaseCosine_character (r c : ℝ) : + scalarPhaseCosine r c = (2 : ℂ)⁻¹ • + ((BoundedRecovery.spectralCharacter c 1) • BoundedRecovery.spectralCharacter r + + star ((BoundedRecovery.spectralCharacter c 1) • BoundedRecovery.spectralCharacter r)) := by + ext t + simp only [scalarPhaseCosine_apply, BoundedContinuousFunction.coe_smul, + BoundedContinuousFunction.coe_add, BoundedContinuousFunction.coe_star, + Pi.add_apply, Pi.star_apply, smul_eq_mul, + BoundedRecovery.spectralCharacter_apply, mul_one, Complex.exp_ofReal_mul_I, + star_add, star_mul, Complex.star_def, Complex.conj_ofReal, Complex.conj_I, + Real.cos_add, Complex.ofReal_sub] + simp only [Complex.ofReal_mul] + ring_nf + simp [Complex.I_sq] + ring + +lemma scalarLp_commute_phaseCosine + (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) + (r c : ℝ) : Commute T (scalarLpRepresentation volume (scalarPhaseCosine r c)) := by + rw [scalarPhaseCosine_character, map_smul, map_add, map_star, map_smul] + have h₁ : Commute T (scalarLpRepresentation volume (BoundedRecovery.spectralCharacter r)) := by + simpa only [scalarLpRepresentation_character] using hc r + have h₂ : Commute T (star (scalarLpRepresentation volume (BoundedRecovery.spectralCharacter r))) := by + rw [← map_star, BoundedRecovery.spectralCharacter_star] + simpa only [scalarLpRepresentation_character] using hc (-r) + rw [star_smul] + exact ((h₁.smul_right _).add_right (h₂.smul_right _)).smul_right _ + +lemma scalarPhaseCosine_cfc_apply (r c t : ℝ) (f : ℂ → ℂ) (hf : Continuous f) : + cfc f (scalarPhaseCosine r c) t = f (Real.cos (r * t + c)) := by + have h := (boundedFunctionEval t).map_cfc f (scalarPhaseCosine r c) hf.continuousOn + (ha := (scalarPhaseCosine_selfAdjoint r c).isStarNormal) + (hφa := ((scalarPhaseCosine_selfAdjoint r c).map (boundedFunctionEval t)).isStarNormal) + change (cfc f (scalarPhaseCosine r c)) t = + cfc f (algebraMap ℂ ℂ (Real.cos (r * t + c) : ℂ)) at h + rw [cfc_algebraMap] at h + exact h + +lemma scalarLp_commute_phaseCosine_cfc + (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) + (r c : ℝ) (f : ℂ → ℂ) (hf : Continuous f) : + Commute T (scalarLpRepresentation volume (cfc f (scalarPhaseCosine r c))) := by + have : ContinuousFunctionalCalculus ℂ + (Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) IsStarNormal := + IsStarNormal.instContinuousFunctionalCalculus + (A := Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + rw [(scalarLpRepresentation volume).map_cfc f (scalarPhaseCosine r c) hf.continuousOn + (ha := (scalarPhaseCosine_selfAdjoint r c).isStarNormal) + (hφa := ((scalarPhaseCosine_selfAdjoint r c).map (scalarLpRepresentation volume)).isStarNormal)] + exact ((scalarPhaseCosine_selfAdjoint r c).map (scalarLpRepresentation volume)).commute_cfc + (scalarLp_commute_phaseCosine T hc r c).symm f |>.symm + +def intervalChartRate (n : ℕ) : ℝ := Real.pi / (2 * n + 1) + +lemma intervalChartRate_pos (n : ℕ) : 0 < intervalChartRate n := by + unfold intervalChartRate + positivity + +lemma intervalChart_inverse (n : ℕ) {t : ℝ} (ht : t ∈ Icc (-(n : ℝ)) n) : + Real.arccos (Real.cos (intervalChartRate n * t + intervalChartRate n * n)) / + intervalChartRate n - n = t := by + have hr := intervalChartRate_pos n + have he : intervalChartRate n * (2 * (n : ℝ) + 1) = Real.pi := by + unfold intervalChartRate + field_simp + have h₀ : 0 ≤ intervalChartRate n * t + intervalChartRate n * n := by nlinarith [ht.1] + have hπ : intervalChartRate n * t + intervalChartRate n * n ≤ Real.pi := by + nlinarith [ht.2] + rw [Real.arccos_cos h₀ hπ] + field_simp + ring + +def intervalChartFunction (n : ℕ) (f : BoundedContinuousFunction ℝ ℂ) : + BoundedContinuousFunction ℝ ℂ := + cfc (fun z : ℂ => f (Real.arccos z.re / intervalChartRate n - n)) + (scalarPhaseCosine (intervalChartRate n) (intervalChartRate n * n)) + +lemma intervalChartFunction_apply (n : ℕ) (f : BoundedContinuousFunction ℝ ℂ) + {t : ℝ} (ht : t ∈ Icc (-(n : ℝ)) n) : intervalChartFunction n f t = f t := by + rw [intervalChartFunction, scalarPhaseCosine_cfc_apply] + · simp only [Complex.ofReal_re, intervalChart_inverse n ht] + · exact f.continuous.comp ((Real.continuous_arccos.comp Complex.continuous_re).div_const + (intervalChartRate n) |>.sub continuous_const) + +lemma scalarLp_commute_intervalChart + (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) + (n : ℕ) (f : BoundedContinuousFunction ℝ ℂ) : + Commute T (scalarLpRepresentation volume (intervalChartFunction n f)) := by + apply scalarLp_commute_phaseCosine_cfc T hc + exact f.continuous.comp ((Real.continuous_arccos.comp Complex.continuous_re).div_const + (intervalChartRate n) |>.sub continuous_const) + +lemma intervalChartFunction_localized (n : ℕ) (f : BoundedContinuousFunction ℝ ℂ) : + scalarIntervalProjection n * scalarLpRepresentation volume (intervalChartFunction n f) = + scalarIntervalProjection n * scalarLpRepresentation volume f := by + apply ContinuousLinearMap.ext + intro g + apply Lp.ext + filter_upwards [scalarIntervalProjection_ae n + (scalarLpRepresentation volume (intervalChartFunction n f) g), + scalarIntervalProjection_ae n (scalarLpRepresentation volume f g), + scalarLpMultiplier_ae volume (intervalChartFunction n f) g, + scalarLpMultiplier_ae volume f g] with t h₁ h₂ h₃ h₄ + change (scalarIntervalProjection n (scalarLpRepresentation volume + (intervalChartFunction n f) g)) t = + (scalarIntervalProjection n (scalarLpRepresentation volume f g)) t + change (scalarLpRepresentation volume (intervalChartFunction n f) g) t = + intervalChartFunction n f t * g t at h₃ + change (scalarLpRepresentation volume f g) t = f t * g t at h₄ + rw [h₁, h₂] + by_cases ht : t ∈ Icc (-(n : ℝ)) n + · rw [indicator_of_mem ht, indicator_of_mem ht, h₃, h₄, + intervalChartFunction_apply n f ht] + · rw [indicator_of_notMem ht, indicator_of_notMem ht] + +/-- Every continuous scalar multiplier commutes with the Fourier compression +of a core element. The proof uses bounded spectral charts and interval +exhaustion, so it imposes no global uniform approximation premise. -/ +theorem scalarLp_commute_continuousMultiplier + (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) + (f : BoundedContinuousFunction ℝ ℂ) : + Commute T (scalarLpRepresentation volume f) := by + apply commute_of_strong_limit T (scalarLpRepresentation volume f) + (fun n => scalarIntervalProjection n * scalarLpRepresentation volume f) + · intro n + rw [← intervalChartFunction_localized n f] + exact (scalarLp_commute_intervalProjection T hc n).mul_right + (scalarLp_commute_intervalChart T hc n f) + · intro g + exact scalarIntervalProjection_strong (scalarLpRepresentation volume f g) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpMultiplier.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpMultiplier.lean new file mode 100644 index 0000000000000000000000000000000000000000..687ead6d5615c9e52f3910def43fcbf1677789c3 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpMultiplier.lean @@ -0,0 +1,168 @@ +import OAI.Analysis.ModularTheory.DualUnitary + +namespace OAI + +/-! Concrete bounded multipliers on scalar L². These are the actual spectral +cutoffs used in the modular-core weight construction. -/ + +noncomputable section +open MeasureTheory Filter +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable (μ : Measure ℝ) + +lemma boundedScalarLp_mem (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp ℂ 2 μ) : + MemLp (fun t => b t * f t) 2 μ := + (Lp.memLp f).of_le_mul (hb.mul (Lp.aestronglyMeasurable f)) + (Eventually.of_forall fun t => by + rw [norm_mul] + exact mul_le_mul_of_nonneg_right (hC t) (norm_nonneg _)) + +def boundedScalarLpApply (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp ℂ 2 μ) : Lp ℂ 2 μ := + (boundedScalarLp_mem μ b hb C hC f).toLp (fun t => b t * f t) + +lemma boundedScalarLpApply_ae (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp ℂ 2 μ) : + boundedScalarLpApply μ b hb C hC f =ᵐ[μ] fun t => b t * f t := + MemLp.coeFn_toLp _ + +def boundedScalarLpLinear (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) : Lp ℂ 2 μ →ₗ[ℂ] Lp ℂ 2 μ where + toFun := boundedScalarLpApply μ b hb C hC + map_add' := by + intro f g + apply Lp.ext + filter_upwards [boundedScalarLpApply_ae μ b hb C hC (f + g), + boundedScalarLpApply_ae μ b hb C hC f, + boundedScalarLpApply_ae μ b hb C hC g, Lp.coeFn_add f g, + Lp.coeFn_add (boundedScalarLpApply μ b hb C hC f) + (boundedScalarLpApply μ b hb C hC g)] with t hfg hf hg ha he + simp only [hfg, ha, he, Pi.add_apply, hf, hg, mul_add] + map_smul' := by + intro c f + apply Lp.ext + filter_upwards [boundedScalarLpApply_ae μ b hb C hC (c • f), + boundedScalarLpApply_ae μ b hb C hC f, Lp.coeFn_smul c f, + Lp.coeFn_smul c (boundedScalarLpApply μ b hb C hC f)] with t hcf hf ha he + simp only [hcf, ha, he, hf, Pi.smul_apply, smul_eq_mul, RingHom.id_apply] + ring + +def boundedScalarLp (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ := + LinearMap.mkContinuous (boundedScalarLpLinear μ b hb C hC) + C (fun f => Lp.norm_le_mul_norm_of_ae_le_mul (by + filter_upwards [boundedScalarLpApply_ae μ b hb C hC f] with t ht + change ‖(boundedScalarLpApply μ b hb C hC f) t‖ ≤ C * ‖f t‖ + rw [ht, norm_mul] + exact mul_le_mul_of_nonneg_right (hC t) (norm_nonneg _))) + +lemma boundedScalarLp_ae (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp ℂ 2 μ) : + boundedScalarLp μ b hb C hC f =ᵐ[μ] fun t => b t * f t := + boundedScalarLpApply_ae μ b hb C hC f + +lemma boundedScalarLp_norm_le (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC0 : 0 ≤ C) (hC : ∀ t, ‖b t‖ ≤ C) : + ‖boundedScalarLp μ b hb C hC‖ ≤ C := + LinearMap.mkContinuous_norm_le _ hC0 _ + +def scalarLpMultiplier (b : BoundedContinuousFunction ℝ ℂ) : + Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ := + boundedScalarLp μ b b.continuous.aestronglyMeasurable ‖b‖ b.norm_coe_le_norm + +lemma scalarLpMultiplier_ae (b : BoundedContinuousFunction ℝ ℂ) (f : Lp ℂ 2 μ) : + scalarLpMultiplier μ b f =ᵐ[μ] fun t => b t * f t := boundedScalarLp_ae μ _ _ _ _ _ + +lemma scalarLpMultiplier_mul (a b : BoundedContinuousFunction ℝ ℂ) : + scalarLpMultiplier μ (a * b) = scalarLpMultiplier μ a * scalarLpMultiplier μ b := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [scalarLpMultiplier_ae μ (a * b) f, + scalarLpMultiplier_ae μ a (scalarLpMultiplier μ b f), + scalarLpMultiplier_ae μ b f] with t hab ha hb + change (scalarLpMultiplier μ (a * b) f) t = + (scalarLpMultiplier μ a (scalarLpMultiplier μ b f)) t + rw [hab, ha, hb] + exact mul_assoc _ _ _ + +lemma scalarLpMultiplier_one : scalarLpMultiplier μ 1 = 1 := by + apply ContinuousLinearMap.ext + intro f + change scalarLpMultiplier μ 1 f = f + apply Lp.ext + filter_upwards [scalarLpMultiplier_ae μ 1 f] with t ht + simpa only [BoundedContinuousFunction.coe_one, Pi.one_apply, one_mul] using ht + +lemma scalarLpMultiplier_star (a : BoundedContinuousFunction ℝ ℂ) : + scalarLpMultiplier μ (star a) = star (scalarLpMultiplier μ a) := by + apply (ContinuousLinearMap.eq_adjoint_iff _ _).mpr + intro f g + simp only [MeasureTheory.L2.inner_def] + apply integral_congr_ae + filter_upwards [scalarLpMultiplier_ae μ (star a) f, + scalarLpMultiplier_ae μ a g] with t hf hg + rw [hf, hg] + simp only [RCLike.inner_apply, BoundedContinuousFunction.coe_star, Pi.star_apply, + map_mul, starRingEnd_apply, star_star] + ring + +/-- Multiplication by bounded continuous scalar functions on actual L². -/ +def scalarLpRepresentation : BoundedContinuousFunction ℝ ℂ →⋆ₐ[ℂ] + (Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) where + toFun := scalarLpMultiplier μ + map_one' := scalarLpMultiplier_one μ + map_mul' := scalarLpMultiplier_mul μ + map_zero' := by + apply ContinuousLinearMap.ext + intro f + change scalarLpMultiplier μ 0 f = 0 + apply Lp.ext + filter_upwards [scalarLpMultiplier_ae μ 0 f, (Lp.coeFn_zero (E := ℂ) (p := 2) (μ := μ))] + with t ht hz + simpa only [BoundedContinuousFunction.coe_zero, Pi.zero_apply, zero_mul, hz] using ht + map_add' a b := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [scalarLpMultiplier_ae μ (a + b) f, + scalarLpMultiplier_ae μ a f, scalarLpMultiplier_ae μ b f, + Lp.coeFn_add (scalarLpMultiplier μ a f) (scalarLpMultiplier μ b f)] with t hab ha hb he + change (scalarLpMultiplier μ (a + b) f) t = + (scalarLpMultiplier μ a f + scalarLpMultiplier μ b f) t + simp only [hab, he, Pi.add_apply, BoundedContinuousFunction.coe_add] + rw [ha, hb] + exact add_mul _ _ _ + commutes' c := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [scalarLpMultiplier_ae μ (algebraMap ℂ _ c) f, + Lp.coeFn_smul c f] with t ht hc + change (scalarLpMultiplier μ (algebraMap ℂ _ c) f) t = (c • f) t + rw [ht, hc] + rfl + map_star' := scalarLpMultiplier_star μ + +@[simp] lemma scalarLpRepresentation_character (r : ℝ) : + scalarLpRepresentation μ (BoundedRecovery.spectralCharacter r) = + (modularDualUnitary (H := ℂ) μ r : Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ) := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [scalarLpMultiplier_ae μ (BoundedRecovery.spectralCharacter r) f, + modularDual_ae μ r f] with t hm hd + change (scalarLpMultiplier μ (BoundedRecovery.spectralCharacter r) f) t = + (modularDual μ r f) t + rw [hm, hd] + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpProjection.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpProjection.lean new file mode 100644 index 0000000000000000000000000000000000000000..55faf7ef575790efe76eb0d001c8009e1ccc1077 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpProjection.lean @@ -0,0 +1,77 @@ +import OAI.Analysis.OperatorAlgebra.ScalarLpMultiplier + +namespace OAI + +/-! Measurable spectral projections on scalar L² as indicator +multiplication operators. -/ + +noncomputable section +open MeasureTheory Set +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable (μ : Measure ℝ) + +private lemma indicator_one_bound (s : Set ℝ) (t : ℝ) : + ‖s.indicator (fun _ => (1 : ℂ)) t‖ ≤ 1 := by + by_cases ht : t ∈ s <;> simp [ht] + +def scalarLpProjection (s : Set ℝ) (hs : MeasurableSet s) : + Lp ℂ 2 μ →L[ℂ] Lp ℂ 2 μ := + boundedScalarLp μ (s.indicator (fun _ => (1 : ℂ))) + ((measurable_const.indicator hs).aestronglyMeasurable) 1 (indicator_one_bound s) + +lemma scalarLpProjection_ae (s : Set ℝ) (hs : MeasurableSet s) (f : Lp ℂ 2 μ) : + scalarLpProjection μ s hs f =ᵐ[μ] s.indicator f := by + filter_upwards [boundedScalarLp_ae μ (s.indicator (fun _ => (1 : ℂ))) + ((measurable_const.indicator hs).aestronglyMeasurable) 1 (indicator_one_bound s) f] + with t ht + change (scalarLpProjection μ s hs f) t = + s.indicator (fun _ => (1 : ℂ)) t * f t at ht + rw [ht] + by_cases h : t ∈ s <;> simp [h] + +lemma scalarLpProjection_norm_le (s : Set ℝ) (hs : MeasurableSet s) : + ‖scalarLpProjection μ s hs‖ ≤ 1 := + boundedScalarLp_norm_le μ _ _ 1 zero_le_one _ + +lemma scalarLpProjection_mul (s t : Set ℝ) (hs : MeasurableSet s) (ht : MeasurableSet t) : + scalarLpProjection μ s hs * scalarLpProjection μ t ht = + scalarLpProjection μ (s ∩ t) (hs.inter ht) := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [scalarLpProjection_ae μ s hs (scalarLpProjection μ t ht f), + scalarLpProjection_ae μ t ht f, + scalarLpProjection_ae μ (s ∩ t) (hs.inter ht) f] with x hx hy hz + change (scalarLpProjection μ s hs (scalarLpProjection μ t ht f)) x = _ + rw [hx, hz] + by_cases hxs : x ∈ s <;> by_cases hxt : x ∈ t <;> simp [hxs, hxt, hy] + +lemma scalarLpProjection_idempotent (s : Set ℝ) (hs : MeasurableSet s) : + scalarLpProjection μ s hs * scalarLpProjection μ s hs = scalarLpProjection μ s hs := by + simpa only [inter_self] using scalarLpProjection_mul μ s s hs hs + +lemma scalarLpProjection_star (s : Set ℝ) (hs : MeasurableSet s) : + star (scalarLpProjection μ s hs) = scalarLpProjection μ s hs := by + symm + apply (ContinuousLinearMap.eq_adjoint_iff _ _).mpr + intro f g + simp only [MeasureTheory.L2.inner_def] + apply integral_congr_ae + filter_upwards [scalarLpProjection_ae μ s hs f, + scalarLpProjection_ae μ s hs g] with t hf hg + rw [hf, hg] + by_cases ht : t ∈ s <;> simp [ht] + +lemma scalarLpProjection_isStarProjection (s : Set ℝ) (hs : MeasurableSet s) : + IsStarProjection (scalarLpProjection μ s hs) := + isStarProjection_iff'.mpr + ⟨scalarLpProjection_idempotent μ s hs, scalarLpProjection_star μ s hs⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpStrongConvergence.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpStrongConvergence.lean new file mode 100644 index 0000000000000000000000000000000000000000..65e4591d25dc04abd30e248a7170f8aacb63f1d3 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpStrongConvergence.lean @@ -0,0 +1,104 @@ +import OAI.Analysis.OperatorAlgebra.ScalarLpCutoffConvergence + +namespace OAI + +/-! Bounded pointwise convergence of actual scalar multipliers gives strong +operator convergence. Commutation consequently passes to their strong limits. +These lemmas are used to obtain measurable cutoffs from continuous calculus. -/ + +noncomputable section +open MeasureTheory Filter +open scoped InnerProductSpace Topology + +namespace WeakPureInfiniteness + +lemma boundedScalarLp_strong + (b : ℕ → ℝ → ℂ) (a : ℝ → ℂ) + (hb : ∀ n, AEStronglyMeasurable (b n) volume) + (ha : AEStronglyMeasurable a volume) (C : ℝ) (hC : 0 ≤ C) + (hbn : ∀ n t, ‖b n t‖ ≤ C) (han : ∀ t, ‖a t‖ ≤ C) + (hlim : ∀ t, Tendsto (fun n => b n t) atTop (𝓝 (a t))) + (f : Lp ℂ 2 (volume : Measure ℝ)) : + Tendsto (fun n => boundedScalarLp volume (b n) (hb n) C (hbn n) f) + atTop (𝓝 (boundedScalarLp volume a ha C han f)) := by + let F (n : ℕ) (t : ℝ) := ‖(b n t - a t) * f t‖ ^ 2 + have hbound (n : ℕ) (t : ℝ) : F n t ≤ (2 * C) ^ 2 * ‖f t‖ ^ 2 := by + have hd : ‖b n t - a t‖ ≤ 2 * C := + (norm_sub_le _ _).trans (by linarith [hbn n t, han t]) + dsimp only [F] + rw [norm_mul, mul_pow] + exact mul_le_mul_of_nonneg_right + ((sq_le_sq₀ (norm_nonneg _) (mul_nonneg (by norm_num) hC)).mpr hd) + (sq_nonneg _) + have hm (n : ℕ) : AEStronglyMeasurable (F n) volume := + (((hb n).sub ha).mul (Lp.aestronglyMeasurable f)).norm.pow 2 + have hi : Integrable (fun t : ℝ => (2 * C) ^ 2 * ‖f t‖ ^ 2) := + ((memLp_two_iff_integrable_sq_norm (Lp.aestronglyMeasurable f)).mp + (Lp.memLp f)).const_mul _ + have hp (t : ℝ) : Tendsto (fun n => F n t) atTop (𝓝 0) := by + have h := (((hlim t).sub_const (a t)).mul_const (f t)).norm.pow 2 + simpa only [sub_self, zero_mul, norm_zero, ne_eq, OfNat.ofNat_ne_zero, + not_false_eq_true, zero_pow] using h + have hint : Tendsto (fun n => ∫ t : ℝ, F n t) atTop (𝓝 0) := by + have h := tendsto_integral_of_dominated_convergence + (fun t : ℝ => (2 * C) ^ 2 * ‖f t‖ ^ 2) hm hi + (fun n => ae_of_all _ (fun t => by + rw [Real.norm_eq_abs, abs_of_nonneg (sq_nonneg _)] + exact hbound n t)) (ae_of_all _ hp) + simpa only [integral_zero] using h + have heq (n : ℕ) : + ‖boundedScalarLp volume (b n) (hb n) C (hbn n) f - + boundedScalarLp volume a ha C han f‖ ^ 2 = ∫ t : ℝ, F n t := by + rw [scalarLp_norm_sq_integral] + apply integral_congr_ae + filter_upwards [Lp.coeFn_sub (boundedScalarLp volume (b n) (hb n) C (hbn n) f) + (boundedScalarLp volume a ha C han f), + boundedScalarLp_ae volume (b n) (hb n) C (hbn n) f, + boundedScalarLp_ae volume a ha C han f] with t hs hb' ha' + rw [hs, Pi.sub_apply, hb', ha', ← sub_mul] + have hsq : Tendsto (fun n => ‖boundedScalarLp volume (b n) (hb n) C (hbn n) f - + boundedScalarLp volume a ha C han f‖ ^ 2) atTop (𝓝 0) := + hint.congr' (Eventually.of_forall fun n => (heq n).symm) + have hn : Tendsto (fun n => Real.sqrt (‖boundedScalarLp volume (b n) (hb n) C (hbn n) f - + boundedScalarLp volume a ha C han f‖ ^ 2)) atTop (𝓝 (Real.sqrt 0)) := + Real.continuous_sqrt.continuousAt.tendsto.comp hsq + simp only [Real.sqrt_sq (norm_nonneg _), Real.sqrt_zero] at hn + exact tendsto_iff_norm_sub_tendsto_zero.mpr hn + +lemma scalarLpRepresentation_strong + (b : ℕ → BoundedContinuousFunction ℝ ℂ) (a : ℝ → ℂ) + (ha : AEStronglyMeasurable a volume) (C : ℝ) (hC : 0 ≤ C) + (hbn : ∀ n t, ‖b n t‖ ≤ C) (han : ∀ t, ‖a t‖ ≤ C) + (hlim : ∀ t, Tendsto (fun n => b n t) atTop (𝓝 (a t))) + (f : Lp ℂ 2 (volume : Measure ℝ)) : + Tendsto (fun n => scalarLpRepresentation volume (b n) f) + atTop (𝓝 (boundedScalarLp volume a ha C han f)) := by + have heq (n : ℕ) : boundedScalarLp volume (b n) + (b n).continuous.aestronglyMeasurable C (hbn n) = + scalarLpRepresentation volume (b n) := by + apply ContinuousLinearMap.ext + intro g + apply Lp.ext + filter_upwards [boundedScalarLp_ae volume (b n) + (b n).continuous.aestronglyMeasurable C (hbn n) g, + scalarLpMultiplier_ae volume (b n) g] with t hb hc + exact hb.trans hc.symm + simpa only [heq] using boundedScalarLp_strong (fun n => b n) a + (fun n => (b n).continuous.aestronglyMeasurable) ha C hC hbn han hlim f + +lemma commute_of_strong_limit {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + (T U : E →L[ℂ] E) (V : ℕ → E →L[ℂ] E) + (hc : ∀ n, Commute T (V n)) + (hv : ∀ x, Tendsto (fun n => V n x) atTop (𝓝 (U x))) : Commute T U := by + apply ContinuousLinearMap.ext + intro x + have hleft := T.continuous.continuousAt.tendsto.comp (hv x) + have hright := hv (T x) + exact tendsto_nhds_unique hleft (hright.congr' (Eventually.of_forall fun n => + congrArg (fun R : E →L[ℂ] E => R x) (hc n).eq.symm)) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarLpSuperlevel.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpSuperlevel.lean new file mode 100644 index 0000000000000000000000000000000000000000..a8f86fcf4d47c02aba5a3d62f0b8f97877dd6999 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarLpSuperlevel.lean @@ -0,0 +1,108 @@ +import OAI.Analysis.OperatorAlgebra.ScalarLpContinuousCutoffs + +namespace OAI + +/-! Superlevel spectral projections of cosine multipliers belong to the +strong commutant of every operator commuting with the character group. +The projections here are the actual indicator multipliers on scalar L². -/ + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology + +namespace WeakPureInfiniteness + +def realUpperCutoff (c : ℝ) (n : ℕ) (x : ℝ) : ℝ := + max 0 (min 1 (1 + (n : ℝ) * (x - c))) + +lemma realUpperCutoff_continuous (c : ℝ) (n : ℕ) : + Continuous (realUpperCutoff c n) := by unfold realUpperCutoff; fun_prop + +lemma realUpperCutoff_nonneg (c : ℝ) (n : ℕ) (x : ℝ) : + 0 ≤ realUpperCutoff c n x := le_max_left _ _ + +lemma realUpperCutoff_le_one (c : ℝ) (n : ℕ) (x : ℝ) : + realUpperCutoff c n x ≤ 1 := + max_le zero_le_one (min_le_left _ _) + +lemma realUpperCutoff_eventually (c x : ℝ) : + ∀ᶠ n : ℕ in atTop, realUpperCutoff c n x = if c ≤ x then 1 else 0 := by + by_cases hcx : c ≤ x + · filter_upwards [] with n + have hn : 0 ≤ (n : ℝ) * (x - c) := + mul_nonneg (Nat.cast_nonneg _) (sub_nonneg.mpr hcx) + have h : 1 ≤ 1 + (n : ℝ) * (x - c) := by linarith + simp only [realUpperCutoff, ite_eq_left hcx, min_eq_left h, max_eq_right zero_le_one] + · obtain ⟨N, hN⟩ := exists_nat_gt (1 / (c - x)) + filter_upwards [eventually_ge_atTop N] with n hn + have hp : 0 < c - x := sub_pos.mpr (lt_of_not_ge hcx) + have hn' : 1 / (c - x) < (n : ℝ) := hN.trans_le (by exact_mod_cast hn) + have hm : 1 < (n : ℝ) * (c - x) := (div_lt_iff₀ hp).mp hn' + have hz : 1 + (n : ℝ) * (x - c) ≤ 0 := by nlinarith + have hmz : min 1 (1 + (n : ℝ) * (x - c)) ≤ 0 := (min_le_right _ _).trans hz + simp only [realUpperCutoff, ite_eq_right hcx, max_eq_left hmz] + +def scalarCosineSuperlevel (r c : ℝ) : Set ℝ := {t | c ≤ Real.cos (r * t)} + +lemma scalarCosineSuperlevel_measurable (r c : ℝ) : + MeasurableSet (scalarCosineSuperlevel r c) := + measurableSet_le measurable_const (by fun_prop) + +def scalarCosineSuperlevelProjection (r c : ℝ) : + Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ) := + scalarLpProjection volume (scalarCosineSuperlevel r c) + (scalarCosineSuperlevel_measurable r c) + +lemma scalarCosineSuperlevel_strong (r c : ℝ) + (f : Lp ℂ 2 (volume : Measure ℝ)) : + Tendsto (fun n => scalarLpRepresentation volume + (cfc (realUpperCutoff c n) (scalarCosine r)) f) atTop + (𝓝 (scalarCosineSuperlevelProjection r c f)) := by + let s := scalarCosineSuperlevel r c + have hs : MeasurableSet s := scalarCosineSuperlevel_measurable r c + let a : ℝ → ℂ := s.indicator (fun _ => 1) + have ha : AEStronglyMeasurable a volume := + (measurable_const.indicator hs).aestronglyMeasurable + have han (t : ℝ) : ‖a t‖ ≤ 1 := by + dsimp only [a] + by_cases ht : t ∈ s <;> simp [ht] + have hbn (n : ℕ) (t : ℝ) : + ‖cfc (realUpperCutoff c n) (scalarCosine r) t‖ ≤ 1 := by + rw [scalarCosine_cfc_apply r t _ (realUpperCutoff_continuous c n)] + rw [Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg (realUpperCutoff_nonneg c n _)] + exact realUpperCutoff_le_one c n _ + have hlim (t : ℝ) : Tendsto + (fun n => cfc (realUpperCutoff c n) (scalarCosine r) t) atTop (𝓝 (a t)) := by + apply tendsto_const_nhds.congr' + filter_upwards [realUpperCutoff_eventually c (Real.cos (r * t))] with n hn + rw [scalarCosine_cfc_apply r t _ (realUpperCutoff_continuous c n), hn] + by_cases ht : c ≤ Real.cos (r * t) <;> simp [a, s, scalarCosineSuperlevel, ht] + have h := scalarLpRepresentation_strong + (fun n => cfc (realUpperCutoff c n) (scalarCosine r)) a ha 1 zero_le_one hbn han hlim f + have heq : boundedScalarLp volume a ha 1 han = scalarCosineSuperlevelProjection r c := by + apply ContinuousLinearMap.ext + intro g + apply Lp.ext + filter_upwards [boundedScalarLp_ae volume a ha 1 han g, + scalarLpProjection_ae volume s hs g] with t hb hp + change (scalarCosineSuperlevelProjection r c g) t = s.indicator (g : ℝ → ℂ) t at hp + rw [hb, hp] + by_cases ht : t ∈ s <;> simp [a, ht] + simpa only [heq] using h + +lemma scalarLp_commute_cosine_superlevel + (T : Lp ℂ 2 (volume : Measure ℝ) →L[ℂ] Lp ℂ 2 (volume : Measure ℝ)) + (hc : ∀ s, Commute T + (modularDualUnitary (H := ℂ) volume s : Lp ℂ 2 volume →L[ℂ] Lp ℂ 2 volume)) + (r c : ℝ) : Commute T (scalarCosineSuperlevelProjection r c) := + commute_of_strong_limit T (scalarCosineSuperlevelProjection r c) + (fun n => scalarLpRepresentation volume (cfc (realUpperCutoff c n) (scalarCosine r))) + (fun n => scalarLp_commute_cosine_cfc T hc r _ (realUpperCutoff_continuous c n)) + (scalarCosineSuperlevel_strong r c) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarOperatorSlices.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarOperatorSlices.lean new file mode 100644 index 0000000000000000000000000000000000000000..44802a18c961ba959f016dd341a24a25182399cf --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarOperatorSlices.lean @@ -0,0 +1,98 @@ +import OAI.Analysis.OperatorAlgebra.ScalarVectorDensity +import OAI.Analysis.ModularTheory.CommutantExpectation + +namespace OAI + +/-! Scalar L² slices characterize commutation in the amplification. In +particular, commutation with the represented C*-algebra automatically extends +to its concrete bicommutant, without assuming normality of any expectation. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace + +namespace WeakPureInfiniteness +open KirchbergRordam.GenericRW.GroupedFactors + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + (μ : Measure ℝ) + +def scalarOperatorSlice (R : Lp H 2 μ →L[ℂ] Lp H 2 μ) (f g : Lp ℂ 2 μ) : H →L[ℂ] H := + (scalarVectorLpCLM (H := H) μ f).adjoint.comp (R.comp (scalarVectorLpCLM (H := H) μ g)) + +lemma scalarOperatorSlice_inner (R : Lp H 2 μ →L[ℂ] Lp H 2 μ) + (f g : Lp ℂ 2 μ) (x y : H) : + inner ℂ (scalarOperatorSlice μ R f g x) y = + inner ℂ (R (scalarVectorLp μ g x)) (scalarVectorLp μ f y) := by + change inner ℂ ((scalarVectorLpCLM μ f).adjoint + (R (scalarVectorLpCLM μ g x))) y = _ + rw [ContinuousLinearMap.adjoint_inner_left] + rfl + +lemma scalarOperatorSlice_mul_pointwise (R : Lp H 2 μ →L[ℂ] Lp H 2 μ) + (T : H →L[ℂ] H) (f g : Lp ℂ 2 μ) : + scalarOperatorSlice μ (R * pointwiseLpRepresentation μ T) f g = + scalarOperatorSlice μ R f g * T := by + apply ContinuousLinearMap.ext + intro x + change (scalarVectorLpCLM μ f).adjoint + (R (pointwiseLpRepresentation μ T (scalarVectorLp μ g x))) = + (scalarVectorLpCLM μ f).adjoint (R (scalarVectorLp μ g (T x))) + rw [scalarVectorLp_pointwise] + +lemma scalarOperatorSlice_pointwise_mul (R : Lp H 2 μ →L[ℂ] Lp H 2 μ) + (T : H →L[ℂ] H) (f g : Lp ℂ 2 μ) : + scalarOperatorSlice μ (pointwiseLpRepresentation μ T * R) f g = + T * scalarOperatorSlice μ R f g := by + apply ContinuousLinearMap.ext + intro x + apply ext_inner_right ℂ + intro y + rw [scalarOperatorSlice_inner] + change inner ℂ (pointwiseLpRepresentation μ T (R (scalarVectorLp μ g x))) + (scalarVectorLp μ f y) = inner ℂ (T (scalarOperatorSlice μ R f g x)) y + rw [← ContinuousLinearMap.adjoint_inner_right] + have ht : (pointwiseLpRepresentation μ T).adjoint = pointwiseLpRepresentation μ (star T) := + (map_star (pointwiseLpRepresentation μ) T).symm + rw [ht, scalarVectorLp_pointwise, ← scalarOperatorSlice_inner] + exact ContinuousLinearMap.adjoint_inner_right T _ _ + +theorem pointwise_commute_iff_slices (R : Lp H 2 μ →L[ℂ] Lp H 2 μ) + (T : H →L[ℂ] H) : + Commute (pointwiseLpRepresentation μ T) R ↔ + ∀ f g, Commute T (scalarOperatorSlice μ R f g) := by + constructor + · intro h f g + have he := congrArg (fun X => scalarOperatorSlice μ X f g) h.eq + rw [scalarOperatorSlice_pointwise_mul, scalarOperatorSlice_mul_pointwise] at he + exact he + · intro h + apply scalarVectorLp_operator_ext μ + intro f x g y + have he := (h g f).eq + rw [← scalarOperatorSlice_pointwise_mul, ← scalarOperatorSlice_mul_pointwise] at he + exact (scalarOperatorSlice_inner μ _ g f x y).symm.trans + ((congrArg (fun A : H →L[ℂ] H => inner ℂ (A x) y) he).trans + (scalarOperatorSlice_inner μ _ g f x y)) + +theorem pointwise_commutation_extends_bicommutant {A : Type*} [CStarAlgebra A] + (π : A →⋆ₐ[ℂ] (H →L[ℂ] H)) + (R : Lp H 2 μ →L[ℂ] Lp H 2 μ) + (hR : ∀ a, Commute (pointwiseLpRepresentation μ (π a)) R) + (T : H →L[ℂ] H) (hT : T ∈ bicommutant π.range) : + Commute (pointwiseLpRepresentation μ T) R := by + apply (pointwise_commute_iff_slices μ R T).mpr + intro f g + have hs : scalarOperatorSlice μ R f g ∈ representationCommutant π := by + apply mem_representationCommutant π + intro a + exact ((pointwise_commute_iff_slices μ R (π a)).mp (hR a) f g).symm + have hc : scalarOperatorSlice μ R f g ∈ (bicommutant π.range).commutant := + (representation_bicommutant_commutant π _).mpr hs + exact VonNeumannAlgebra.mem_commutant_iff.mp hc T hT + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarSliceContinuity.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarSliceContinuity.lean new file mode 100644 index 0000000000000000000000000000000000000000..dc786405f33ddc3dcd5eb972c7f218960a2d4911 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarSliceContinuity.lean @@ -0,0 +1,69 @@ +import OAI.Analysis.OperatorAlgebra.ScalarOperatorSlices + +namespace OAI + +/-! Norm-continuous scalar slices, used to regularize operators in the +modular fixed-point algebra. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + (μ : Measure ℝ) + +omit [CompleteSpace H] in +lemma scalarVectorLpCLM_norm_le (f : Lp ℂ 2 μ) : ‖scalarVectorLpCLM (H := H) μ f‖ ≤ ‖f‖ := by + apply ContinuousLinearMap.opNorm_le_bound _ (norm_nonneg f) + intro x + exact (scalarVectorLp_norm μ f x).le + +def scalarVectorLpOperatorLinear : Lp ℂ 2 μ →ₗ[ℂ] (H →L[ℂ] Lp H 2 μ) where + toFun := scalarVectorLpCLM (H := H) μ + map_add' f g := by + apply ContinuousLinearMap.ext + intro x + exact map_add ((ContinuousLinearMap.toSpanSingleton ℂ x).compLpL 2 μ) f g + map_smul' c f := by + apply ContinuousLinearMap.ext + intro x + exact map_smul ((ContinuousLinearMap.toSpanSingleton ℂ x).compLpL 2 μ) c f + +def scalarVectorLpOperator : Lp ℂ 2 μ →L[ℂ] (H →L[ℂ] Lp H 2 μ) where + toLinearMap := scalarVectorLpOperatorLinear (H := H) μ + cont := AddMonoidHomClass.continuous_of_bound (scalarVectorLpOperatorLinear (H := H) μ) 1 + (fun f => by + change ‖scalarVectorLpCLM (H := H) μ f‖ ≤ 1 * ‖f‖ + simpa only [one_mul] using scalarVectorLpCLM_norm_le (H := H) μ f) + +lemma scalarOperatorSlice_continuous (T : Lp H 2 μ →L[ℂ] Lp H 2 μ) : + Continuous (fun p : Lp ℂ 2 μ × Lp ℂ 2 μ => scalarOperatorSlice μ T p.1 p.2) := by + have hf : Continuous (fun p : Lp ℂ 2 μ × Lp ℂ 2 μ => + scalarVectorLpCLM (H := H) μ p.1) := + (scalarVectorLpOperator (H := H) μ).continuous.comp continuous_fst + have hg : Continuous (fun p : Lp ℂ 2 μ × Lp ℂ 2 μ => + scalarVectorLpCLM (H := H) μ p.2) := + (scalarVectorLpOperator (H := H) μ).continuous.comp continuous_snd + exact (ContinuousLinearMap.adjoint.continuous.comp hf).clm_comp + (continuous_const.clm_comp hg) + +lemma scalarOperatorSlice_norm_le (T : Lp H 2 μ →L[ℂ] Lp H 2 μ) (f g : Lp ℂ 2 μ) : + ‖scalarOperatorSlice μ T f g‖ ≤ ‖f‖ * ‖T‖ * ‖g‖ := by + apply (ContinuousLinearMap.opNorm_comp_le _ _).trans + have ha : ‖(scalarVectorLpCLM (H := H) μ f).adjoint‖ ≤ ‖f‖ := by + rw [ContinuousLinearMap.adjoint.norm_map] + exact scalarVectorLpCLM_norm_le μ f + have hb : ‖T.comp (scalarVectorLpCLM (H := H) μ g)‖ ≤ ‖T‖ * ‖g‖ := + (ContinuousLinearMap.opNorm_comp_le _ _).trans + (mul_le_mul_of_nonneg_left (scalarVectorLpCLM_norm_le μ g) (norm_nonneg T)) + exact (mul_le_mul ha hb + (norm_nonneg (T.comp (scalarVectorLpCLM (H := H) μ g))) (norm_nonneg f)).trans_eq + (mul_assoc _ _ _).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarTranslationConvolution.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarTranslationConvolution.lean new file mode 100644 index 0000000000000000000000000000000000000000..d6d812ab885238e181e2bab6552f720d4af0f4e1 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarTranslationConvolution.lean @@ -0,0 +1,138 @@ +import OAI.Analysis.ModularTheory.CoreIntegrals +import OAI.Analysis.ModularTheory.FourierTranslation +import OAI.Analysis.OperatorAlgebra.ScalarSliceContinuity + +namespace OAI + +/-! Scalar translation integrals commute on integrable L² vectors. The +proof uses bounded Schwartz test vectors, so every Fubini interchange has +an explicit product-integrable majorant. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace SchwartzMap + +namespace WeakPureInfiniteness + +lemma scalar_convolution_test_center (g : ℝ → ℂ) + (h : BoundedContinuousFunction ℝ ℂ) (t : ℝ) : + (∫ s : ℝ, star (h s) * g (s - t)) = + ∫ r : ℝ, star (h (r + t)) * g r := by + simpa only [add_sub_cancel_right] using + (integral_add_right_eq_self (fun s : ℝ => star (h s) * g (s - t)) t).symm + +lemma scalar_convolution_test_swap (k g : ℝ → ℂ) + (hk : Integrable k) (hg : Integrable g) (h : BoundedContinuousFunction ℝ ℂ) : + (∫ t : ℝ, k t * ∫ s : ℝ, star (h s) * g (s - t)) = + ∫ t : ℝ, g t * ∫ s : ℝ, star (h s) * k (s - t) := by + have hi : Integrable (fun p : ℝ × ℝ => k p.1 * g p.2 * star (h (p.2 + p.1))) + (volume.prod volume) := by + apply ((hk.norm.mul_prod hg.norm).mul_const ‖h‖).mono' + ((hk.aestronglyMeasurable.comp_fst.mul hg.aestronglyMeasurable.comp_snd).mul + ((h.continuous.comp (continuous_snd.add continuous_fst)).star.aestronglyMeasurable)) + filter_upwards [] with p + simpa only [Pi.mul_apply, Function.comp_def, Pi.add_apply, norm_mul, norm_star] using + (mul_le_mul_of_nonneg_left (h.norm_coe_le_norm (p.2 + p.1)) + (mul_nonneg (norm_nonneg (k p.1)) (norm_nonneg (g p.2)))) + calc + _ = ∫ t : ℝ, ∫ r : ℝ, k t * g r * star (h (r + t)) := by + apply integral_congr_ae + filter_upwards [] with t + rw [scalar_convolution_test_center, ← integral_const_mul] + congr 1 + funext r + ring + _ = ∫ r : ℝ, ∫ t : ℝ, k t * g r * star (h (r + t)) := integral_integral_swap hi + _ = _ := by + apply integral_congr_ae + filter_upwards [] with r + rw [scalar_convolution_test_center, ← integral_const_mul] + congr 1 + funext t + rw [add_comm t r] + ring + +lemma scalar_translation_schwartz_inner (h : 𝓢(ℝ, ℂ)) + (g : Lp ℂ 2 (volume : Measure ℝ)) (t : ℝ) : + inner ℂ (h.toLp 2) (modularLpTranslate volume t g) = + ∫ s : ℝ, star (h s) * g (s - t) := by + rw [L2.inner_def] + apply integral_congr_ae + filter_upwards [h.coeFn_toLp 2 (volume : Measure ℝ), modularLpTranslate_ae volume t g] + with s hh hg + rw [hh, hg] + simp only [RCLike.inner_apply, starRingEnd_apply] + ring + +lemma integratedScalarTranslation_schwartz_inner (k : ℝ → ℂ) (hk : Integrable k) + (g : Lp ℂ 2 (volume : Measure ℝ)) (h : 𝓢(ℝ, ℂ)) : + inner ℂ (h.toLp 2) (integratedModularTranslation k hk g) = + ∫ t : ℝ, k t * ∫ s : ℝ, star (h s) * g (s - t) := by + have hi := BoundedRecovery.integrable_smul_bounded_orbit hk + (continuous_modularLpTranslate g) (fun t => (modularLpTranslate volume t).norm_map g |>.le) + rw [integratedModularTranslation_apply, ← integral_inner hi] + apply integral_congr_ae + filter_upwards [] with t + rw [inner_smul_right, scalar_translation_schwartz_inner] + +theorem integratedScalarTranslation_comm (k g : Lp ℂ 2 (volume : Measure ℝ)) + (hk : Integrable (k : ℝ → ℂ)) (hg : Integrable (g : ℝ → ℂ)) : + integratedModularTranslation k hk g = integratedModularTranslation g hg k := by + have hd : DenseRange (SchwartzMap.toLpCLM ℝ ℂ 2 (volume : Measure ℝ)) := + SchwartzMap.denseRange_toLpCLM ENNReal.ofNat_ne_top + apply ext_inner_left ℂ + intro h + apply hd.induction_on (p := fun h => + inner ℂ h (integratedModularTranslation k hk g) = + inner ℂ h (integratedModularTranslation g hg k)) h + · exact isClosed_eq (by fun_prop) (by fun_prop) + · intro h + change inner ℂ (h.toLp 2) (integratedModularTranslation k hk g) = + inner ℂ (h.toLp 2) (integratedModularTranslation g hg k) + rw [integratedScalarTranslation_schwartz_inner, integratedScalarTranslation_schwartz_inner] + exact scalar_convolution_test_swap k g hk hg h.toBoundedContinuousFunction + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +omit [CompleteSpace H] in +lemma scalarVectorLp_translate (g : Lp ℂ 2 (volume : Measure ℝ)) (x : H) (t : ℝ) : + modularLpTranslate volume t (scalarVectorLp volume g x) = + scalarVectorLp volume (modularLpTranslate volume t g) x := by + apply Lp.ext + filter_upwards [modularLpTranslate_ae volume t (scalarVectorLp volume g x), + (measurePreserving_sub_right volume t).quasiMeasurePreserving.ae + (scalarVectorLp_ae volume g x), + scalarVectorLp_ae volume (modularLpTranslate volume t g) x, + modularLpTranslate_ae volume t g] with s h₁ h₂ h₃ h₄ + rw [h₁, h₂, h₃, h₄] + +lemma scalarVectorLp_integratedTranslation (k : ℝ → ℂ) (hk : Integrable k) + (g : Lp ℂ 2 (volume : Measure ℝ)) (x : H) : + integratedModularTranslation k hk (scalarVectorLp volume g x) = + scalarVectorLp volume (integratedModularTranslation k hk g) x := by + have hi := BoundedRecovery.integrable_smul_bounded_orbit hk + (continuous_modularLpTranslate g) (fun t => (modularLpTranslate volume t).norm_map g |>.le) + change _ = (ContinuousLinearMap.toSpanSingleton ℂ x).compLpL 2 volume + (integratedModularTranslation k hk g) + rw [integratedModularTranslation_apply, integratedModularTranslation_apply, + ← ContinuousLinearMap.integral_comp_comm _ hi] + apply integral_congr_ae + filter_upwards [] with t + rw [map_smul, scalarVectorLp_translate] + rfl + +lemma scalarVectorLp_convolution_synthesis (g u : Lp ℂ 2 (volume : Measure ℝ)) + (hg : Integrable (g : ℝ → ℂ)) (hu : Integrable (u : ℝ → ℂ)) (x : H) : + integratedModularTranslation g hg (scalarVectorLp volume u x) = + ∫ t : ℝ, u t • scalarVectorLp volume (modularLpTranslate volume t g) x := by + rw [scalarVectorLp_integratedTranslation, integratedScalarTranslation_comm g u hg hu, + ← scalarVectorLp_integratedTranslation, integratedModularTranslation_apply] + apply integral_congr_ae + filter_upwards [] with t + rw [scalarVectorLp_translate] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarVectorDensity.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarVectorDensity.lean new file mode 100644 index 0000000000000000000000000000000000000000..a61aba5319495b94dbf4c49b1f8385f27272c035 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarVectorDensity.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.OperatorAlgebra.ScalarVectorLp + +namespace OAI + +/-! Elementary scalar/vector functions detect all vector-valued L² operators. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace ENNReal + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + (μ : Measure ℝ) + +omit [CompleteSpace H] in +lemma scalarVectorLp_indicator {s : Set ℝ} (hs : MeasurableSet s) (hμ : μ s ≠ ⊤) + (x : H) : + scalarVectorLp μ (indicatorConstLp 2 hs hμ (1 : ℂ)) x = indicatorConstLp 2 hs hμ x := by + apply Lp.ext + filter_upwards [scalarVectorLp_ae μ (indicatorConstLp 2 hs hμ (1 : ℂ)) x, + indicatorConstLp_coeFn (p := 2) (hs := hs) (hμs := hμ) (c := (1 : ℂ)), + indicatorConstLp_coeFn (p := 2) (hs := hs) (hμs := hμ) (c := x)] with t h₁ h₂ h₃ + rw [h₁, h₂, h₃] + by_cases ht : t ∈ s <;> simp [ht] + +omit [CompleteSpace H] in +theorem scalarVectorLp_induction (p : Lp H 2 μ → Prop) + (hc : IsClosed {f | p f}) + (ha : ∀ f g, p f → p g → p (f + g)) + (he : ∀ f x, p (scalarVectorLp μ f x)) (f : Lp H 2 μ) : p f := by + refine (Lp.simpleFunc.dense (E := H) (μ := μ) (by norm_num : (2 : ℝ≥0∞) ≠ ⊤)).induction + ?_ hc f + intro g hg + lift g to Lp.simpleFunc H 2 μ using hg + induction g using Lp.simpleFunc.induction (by norm_num : (2 : ℝ≥0∞) ≠ 0) + (by norm_num : (2 : ℝ≥0∞) ≠ ⊤) with + | indicatorConst x hs hμ => + change p (indicatorConstLp 2 hs hμ.ne x) + rw [← scalarVectorLp_indicator μ hs hμ.ne x] + exact he _ _ + | add hf hg hfg h₁ h₂ => exact ha _ _ h₁ h₂ + +omit [CompleteSpace H] in +lemma scalarVectorLp_inner_ext (f g : Lp H 2 μ) + (h : ∀ a x, inner ℂ f (scalarVectorLp μ a x) = inner ℂ g (scalarVectorLp μ a x)) : + f = g := by + apply ext_inner_right ℂ + intro y + apply scalarVectorLp_induction μ (fun z => inner ℂ f z = inner ℂ g z) + (isClosed_eq (by fun_prop) (by fun_prop)) + (fun a b ha hb => by rw [inner_add_right, inner_add_right, ha, hb]) h y + +omit [CompleteSpace H] in +lemma scalarVectorLp_operator_ext + (T R : Lp H 2 μ →L[ℂ] Lp H 2 μ) + (h : ∀ f x g y, inner ℂ (T (scalarVectorLp μ f x)) (scalarVectorLp μ g y) = + inner ℂ (R (scalarVectorLp μ f x)) (scalarVectorLp μ g y)) : T = R := by + apply ContinuousLinearMap.ext + intro z + apply scalarVectorLp_induction μ (fun z => T z = R z) + (isClosed_eq T.continuous R.continuous) + (fun a b ha hb => by simp only [map_add, ha, hb]) + (fun f x => scalarVectorLp_inner_ext μ _ _ (h f x)) z + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/ScalarVectorLp.lean b/lean/OAI/Analysis/OperatorAlgebra/ScalarVectorLp.lean new file mode 100644 index 0000000000000000000000000000000000000000..e1be645ebb4110c6e420aa759c0ee56f123effde --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/ScalarVectorLp.lean @@ -0,0 +1,83 @@ +import OAI.Analysis.ModularTheory.CoreSeparation + +namespace OAI + +/-! Elementary scalar/vector tensors in vector-valued L². These concrete +maps supply the finite scalar blocks for expectation amplification. -/ + +noncomputable section +open MeasureTheory +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + (μ : Measure ℝ) + +def scalarVectorLp (f : Lp ℂ 2 μ) (x : H) : Lp H 2 μ := + (ContinuousLinearMap.toSpanSingleton ℂ x).compLpL 2 μ f + +lemma scalarVectorLp_ae (f : Lp ℂ 2 μ) (x : H) : + scalarVectorLp μ f x =ᵐ[μ] fun t => f t • x := + (ContinuousLinearMap.toSpanSingleton ℂ x).coeFn_compLpL f + +lemma scalarVectorLp_norm (f : Lp ℂ 2 μ) (x : H) : + ‖scalarVectorLp μ f x‖ = ‖f‖ * ‖x‖ := by + have hn : ‖scalarVectorLp μ f x‖ = ‖(‖x‖ : ℂ) • f‖ := by + rw [Lp.norm_def, Lp.norm_def] + congr 1 + apply eLpNorm_congr_norm_ae (Lp.aestronglyMeasurable _) (Lp.aestronglyMeasurable _) + filter_upwards [scalarVectorLp_ae μ f x, Lp.coeFn_smul (‖x‖ : ℂ) f] with t hv hs + rw [hv, hs, Pi.smul_apply, norm_smul, norm_smul, Complex.norm_real, + Real.norm_eq_abs, abs_norm, mul_comm] + rw [hn, norm_smul, Complex.norm_real, Real.norm_eq_abs, abs_norm, mul_comm] + +lemma scalarVectorLp_add_right (f : Lp ℂ 2 μ) (x y : H) : + scalarVectorLp μ f (x + y) = scalarVectorLp μ f x + scalarVectorLp μ f y := by + apply Lp.ext + filter_upwards [scalarVectorLp_ae μ f (x + y), scalarVectorLp_ae μ f x, + scalarVectorLp_ae μ f y, Lp.coeFn_add (scalarVectorLp μ f x) (scalarVectorLp μ f y)] + with t h h₁ h₂ hs + rw [h, hs, Pi.add_apply, h₁, h₂, smul_add] + +lemma scalarVectorLp_smul_right (f : Lp ℂ 2 μ) (x : H) (c : ℂ) : + scalarVectorLp μ f (c • x) = c • scalarVectorLp μ f x := by + apply Lp.ext + filter_upwards [scalarVectorLp_ae μ f (c • x), scalarVectorLp_ae μ f x, + Lp.coeFn_smul c (scalarVectorLp μ f x)] with t h h₁ hs + rw [h, hs, Pi.smul_apply, h₁, smul_comm] + +def scalarVectorLpCLM (f : Lp ℂ 2 μ) : H →L[ℂ] Lp H 2 μ := + ({ toFun := scalarVectorLp μ f + map_add' := scalarVectorLp_add_right μ f + map_smul' := fun c x => scalarVectorLp_smul_right μ f x c } : H →ₗ[ℂ] Lp H 2 μ).mkContinuous + ‖f‖ (fun x => by + change ‖scalarVectorLp μ f x‖ ≤ ‖f‖ * ‖x‖ + exact (scalarVectorLp_norm μ f x).le) + +lemma scalarVectorLp_inner (f g : Lp ℂ 2 μ) (x y : H) : + inner ℂ (scalarVectorLp μ f x) (scalarVectorLp μ g y) = + inner ℂ f g * inner ℂ x y := by + simp only [L2.inner_def] + rw [← integral_mul_const] + apply integral_congr_ae + filter_upwards [scalarVectorLp_ae μ f x, scalarVectorLp_ae μ g y] with t hf hg + rw [hf, hg, inner_smul_left, inner_smul_right] + simp only [RCLike.inner_apply, starRingEnd_apply] + ring + +variable [CompleteSpace H] + +lemma scalarVectorLp_pointwise (T : H →L[ℂ] H) (f : Lp ℂ 2 μ) (x : H) : + pointwiseLpRepresentation μ T (scalarVectorLp μ f x) = scalarVectorLp μ f (T x) := by + apply Lp.ext + filter_upwards [T.coeFn_compLpL (p := 2) (μ := μ) (scalarVectorLp μ f x), + scalarVectorLp_ae μ f x, scalarVectorLp_ae μ f (T x)] with t hT hf hTx + change (T.compLpL 2 μ (scalarVectorLp μ f x)) t = _ + rw [hT, hf, hTx, map_smul] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/SmallTimeOperatorAverage.lean b/lean/OAI/Analysis/OperatorAlgebra/SmallTimeOperatorAverage.lean new file mode 100644 index 0000000000000000000000000000000000000000..5654a07ab61b6d94a2a1fd04e31700e349b24827 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/SmallTimeOperatorAverage.lean @@ -0,0 +1,98 @@ +import OAI.Analysis.ModularRecovery.StrongIntegrals +import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral + +namespace OAI + +/-! Strong convergence of normalized small-time operator averages. This +supplies the regularization limit in the modular commutation argument. -/ + +noncomputable section +open MeasureTheory Filter +open scoped Topology + +namespace WeakPureInfiniteness + +def realGaussianDensity (t : ℝ) : ℝ := Real.exp (-t ^ 2) / Real.sqrt Real.pi + +lemma realGaussianDensity_nonneg (t : ℝ) : 0 ≤ realGaussianDensity t := by + exact div_nonneg (Real.exp_pos _).le (Real.sqrt_nonneg _) + +lemma realGaussianDensity_integrable : Integrable realGaussianDensity := by + change Integrable (fun t : ℝ => Real.exp (-t ^ 2) / Real.sqrt Real.pi) + have h := (integrable_exp_neg_mul_sq (by norm_num : (0 : ℝ) < 1)).div_const + (Real.sqrt Real.pi) + simpa only [one_mul, neg_mul] using h + +lemma realGaussianDensity_integral : ∫ t, realGaussianDensity t = 1 := by + unfold realGaussianDensity + rw [integral_div] + have he : ∫ t : ℝ, Real.exp (-t ^ 2) = Real.sqrt Real.pi := by + simpa only [neg_mul, one_mul, div_one] using integral_gaussian (1 : ℝ) + rw [he, div_self (ne_of_gt (Real.sqrt_pos.2 Real.pi_pos))] + +variable {K : Type*} [NormedAddCommGroup K] [NormedSpace ℂ K] [CompleteSpace K] + +def smallTimeOperatorAverage (V : ℝ → K →L[ℂ] K) + (hc : ∀ x, Continuous (fun t => V t x)) (C : ℝ) (hC : ∀ t, ‖V t‖ ≤ C) (n : ℕ) : + K →L[ℂ] K := + BoundedRecovery.strongIntegral (fun t => (realGaussianDensity t : ℂ)) + realGaussianDensity_integrable.ofReal (fun t => V (t / (n + 1 : ℝ))) + (fun x => (hc x).comp (continuous_id.div_const _)) C (fun _ => hC _) + +omit [CompleteSpace K] in +lemma smallTimeOperatorAverage_norm_le (V : ℝ → K →L[ℂ] K) + (hc : ∀ x, Continuous (fun t => V t x)) (C : ℝ) (hC : ∀ t, ‖V t‖ ≤ C) (n : ℕ) : + ‖smallTimeOperatorAverage V hc C hC n‖ ≤ C := by + have hd : (∫ t : ℝ, ‖(realGaussianDensity t : ℂ)‖) = 1 := by + have he : (fun t : ℝ => ‖(realGaussianDensity t : ℂ)‖) = realGaussianDensity := by + funext t + simp only [Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg (realGaussianDensity_nonneg t)] + rw [he, realGaussianDensity_integral] + have hn := BoundedRecovery.norm_strongIntegral_le + (fun t => (realGaussianDensity t : ℂ)) realGaussianDensity_integrable.ofReal + (fun t => V (t / (n + 1 : ℝ))) + (fun x => (hc x).comp (continuous_id.div_const _)) + ((norm_nonneg (V 0)).trans (hC 0)) (fun _ => hC _) + rw [hd, one_mul] at hn + exact hn + +lemma smallTimeOperatorAverage_strong (V : ℝ → K →L[ℂ] K) + (hc : ∀ x, Continuous (fun t => V t x)) (C : ℝ) (hC : ∀ t, ‖V t‖ ≤ C) (x : K) : + Tendsto (fun n => smallTimeOperatorAverage V hc C hC n x) atTop (𝓝 (V 0 x)) := by + have hm (n : ℕ) : AEStronglyMeasurable + (fun t : ℝ => (realGaussianDensity t : ℂ) • V (t / (n + 1 : ℝ)) x) volume := by + exact realGaussianDensity_integrable.ofReal.aestronglyMeasurable.smul + ((hc x).comp (continuous_id.div_const _)).aestronglyMeasurable + have hb (n : ℕ) : ∀ᵐ t : ℝ, ‖(realGaussianDensity t : ℂ) • V (t / (n + 1 : ℝ)) x‖ ≤ + realGaussianDensity t * (C * ‖x‖) := by + filter_upwards [] with t + rw [norm_smul, Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg (realGaussianDensity_nonneg t)] + exact mul_le_mul_of_nonneg_left + (((V _).le_opNorm x).trans (mul_le_mul_of_nonneg_right (hC _) (norm_nonneg x))) + (realGaussianDensity_nonneg t) + have hp : ∀ᵐ t : ℝ, Tendsto + (fun n : ℕ => (realGaussianDensity t : ℂ) • V (t / (n + 1 : ℝ)) x) atTop + (𝓝 ((realGaussianDensity t : ℂ) • V 0 x)) := by + filter_upwards [] with t + have ht : Tendsto (fun n : ℕ => t / (n + 1 : ℝ)) atTop (𝓝 0) := by + simpa only [Function.comp_def, Nat.cast_add, Nat.cast_one] using + (tendsto_const_div_atTop_nhds_zero_nat t).comp (tendsto_add_atTop_nat 1) + exact ((hc x).continuousAt.tendsto.comp ht).const_smul _ + have hi := tendsto_integral_of_dominated_convergence + (fun t => realGaussianDensity t * (C * ‖x‖)) hm + (realGaussianDensity_integrable.mul_const _) hb hp + have he : (∫ t : ℝ, (realGaussianDensity t : ℂ) • V 0 x) = V 0 x := by + rw [integral_smul_const] + have hi : (∫ t : ℝ, (realGaussianDensity t : ℂ)) = 1 := + (integral_ofReal (𝕜 := ℂ) (μ := volume) (f := realGaussianDensity)).trans + (by rw [realGaussianDensity_integral]; rfl) + rw [hi, one_smul] + simpa only [smallTimeOperatorAverage, BoundedRecovery.strongIntegral_apply, he] using hi + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/StandardCommutantOpposite.lean b/lean/OAI/Analysis/OperatorAlgebra/StandardCommutantOpposite.lean new file mode 100644 index 0000000000000000000000000000000000000000..21560f7ad3d43ec7838e9ab5d5d5ab70dfc0aca1 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/StandardCommutantOpposite.lean @@ -0,0 +1,109 @@ +import OAI.Analysis.OperatorAlgebra.AntiunitaryOperatorIdentities +import OAI.Analysis.ModularRecovery.ModularCovariance +import OAI.Analysis.WeakInfiniteness.TensorSubalgebras + +namespace OAI + +/-! The actual opposite-algebra identification of a standard commutant. -/ +noncomputable section +open scoped ComplexOrder +namespace WeakPureInfiniteness +open BoundedRecovery + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +omit [CompleteSpace H] in +lemma antiunitaryConjugate_one (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) : + antiunitaryConjugate J 1 = 1 := by + apply ContinuousLinearMap.ext + intro x + exact hJ x + +def antiunitaryOppositeHom (J : H ≃ₗᵢ⋆[ℂ] H) (hJ : Function.Involutive J) : + (H →L[ℂ] H)ᵐᵒᵖ →⋆ₐ[ℂ] (H →L[ℂ] H) where + toFun a := antiunitaryConjugate J (star a.unop) + map_zero' := by + apply ContinuousLinearMap.ext + intro x + simp only [MulOpposite.unop_zero, star_zero, antiunitaryConjugate_apply, + zero_apply, map_zero] + map_one' := by + simpa only [MulOpposite.unop_one, star_one] using antiunitaryConjugate_one J hJ + map_add' a b := by + simp only [MulOpposite.unop_add, star_add, antiunitaryConjugate_add] + map_mul' a b := by + simp only [MulOpposite.unop_mul, star_mul, antiunitaryConjugate_mul J hJ] + commutes' c := by + change antiunitaryConjugate J (star (c • (1 : H →L[ℂ] H))) = c • 1 + rw [star_smul, star_one, antiunitaryConjugate_smul, star_star, + antiunitaryConjugate_one J hJ] + map_star' a := by + change antiunitaryConjugate J (star (star a.unop)) = + star (antiunitaryConjugate J (star a.unop)) + exact antiunitaryConjugate_star J hJ (star a.unop) + +lemma antiunitaryOppositeHom_involutive (J : H ≃ₗᵢ⋆[ℂ] H) + (hJ : Function.Involutive J) (a : H →L[ℂ] H) : + antiunitaryOppositeHom J hJ + (MulOpposite.op (antiunitaryOppositeHom J hJ (MulOpposite.op a))) = a := by + change antiunitaryConjugate J (star (antiunitaryConjugate J (star a))) = a + rw [← antiunitaryConjugate_star J hJ, star_star, + antiunitaryConjugate_involutive J hJ] + +def standardOppositeInclusion (S : StarSubalgebra ℂ (H →L[ℂ] H)) : + Sᵐᵒᵖ →⋆ₐ[ℂ] (H →L[ℂ] H)ᵐᵒᵖ where + __ := S.subtype.toAlgHom.op + map_star' a := congrArg MulOpposite.op (map_star S.subtype a.unop) + +lemma standardConjugate_mem (S : StandardModularData H) + (a : S.M.toStarSubalgebraᵐᵒᵖ) : + antiunitaryOppositeHom S.J S.conjugation (MulOpposite.op a.unop.val) ∈ S.M.commutant := by + change S.jConjugate (star a.unop.val) ∈ S.M.commutant + exact S.jConjugate_mem_commutant (star a.unop.val) + (show star a.unop.val ∈ S.M from star_mem a.unop.property) + +def standardCommutantHom (S : StandardModularData H) : + S.M.toStarSubalgebraᵐᵒᵖ →⋆ₐ[ℂ] S.M.commutant.toStarSubalgebra := + ((antiunitaryOppositeHom S.J S.conjugation).comp + (standardOppositeInclusion S.M.toStarSubalgebra)).codRestrict + S.M.commutant.toStarSubalgebra (standardConjugate_mem S) + +lemma standardCommutantHom_apply (S : StandardModularData H) + (a : S.M.toStarSubalgebraᵐᵒᵖ) : + (standardCommutantHom S a).val = + antiunitaryOppositeHom S.J S.conjugation (MulOpposite.op a.unop.val) := rfl + +lemma standardCommutantHom_bijective (S : StandardModularData H) : + Function.Bijective (standardCommutantHom S) := by + constructor + · intro a b h + apply MulOpposite.unop_injective + apply Subtype.ext + have he := congrArg + (fun c : S.M.commutant.toStarSubalgebra => + antiunitaryOppositeHom S.J S.conjugation (MulOpposite.op c.val)) h + change antiunitaryOppositeHom S.J S.conjugation + (MulOpposite.op (antiunitaryOppositeHom S.J S.conjugation (MulOpposite.op a.unop.val))) = + antiunitaryOppositeHom S.J S.conjugation + (MulOpposite.op (antiunitaryOppositeHom S.J S.conjugation (MulOpposite.op b.unop.val))) at he + simpa only [antiunitaryOppositeHom_involutive] using he + · intro b + have hb : antiunitaryOppositeHom S.J S.conjugation (MulOpposite.op b.val) ∈ S.M := by + change S.jConjugate (star b.val) ∈ S.M + exact S.jConjugate_mem (star b.val) + (show star b.val ∈ S.M.commutant from star_mem b.property) + let a : S.M.toStarSubalgebra := + ⟨antiunitaryOppositeHom S.J S.conjugation (MulOpposite.op b.val), hb⟩ + refine ⟨MulOpposite.op a, ?_⟩ + apply Subtype.ext + exact antiunitaryOppositeHom_involutive S.J S.conjugation b.val + +def standardCommutantEquiv (S : StandardModularData H) : + S.M.toStarSubalgebraᵐᵒᵖ ≃⋆ₐ[ℂ] S.M.commutant.toStarSubalgebra := + StarAlgEquiv.ofBijective (standardCommutantHom S) (standardCommutantHom_bijective S) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/StandardMinimalMultiplication.lean b/lean/OAI/Analysis/OperatorAlgebra/StandardMinimalMultiplication.lean new file mode 100644 index 0000000000000000000000000000000000000000..bdb5eec93c435cbb3d6791b2f16114ecd3a8703b --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/StandardMinimalMultiplication.lean @@ -0,0 +1,119 @@ +import OAI.Analysis.ModularTheory.StandardTensorBound +import OAI.Analysis.OperatorAlgebra.StandardCommutantOpposite +import OAI.Analysis.OperatorAlgebra.HilbertTensorExtension +import OAI.Analysis.Nuclearity.SubalgebraTensorNorm + +namespace OAI + +/-! The standard left/right multiplication representation extends to the +minimal tensor product for a represented quotient of a nuclear algebra. -/ +noncomputable section +open MeasureTheory Filter +open scoped TensorProduct ComplexOrder +namespace WeakPureInfiniteness +open BoundedRecovery KirchbergRordam.GenericRW.GroupedFactors + +universe u +variable {H : Type u} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def standardRightHom (S : StandardModularData H) : + S.M.toStarSubalgebraᵐᵒᵖ →⋆ₐ[ℂ] (H →L[ℂ] H) := + S.M.commutant.toStarSubalgebra.subtype.comp (standardCommutantHom S) + +lemma standardRightHom_apply (S : StandardModularData H) (b : S.M.toStarSubalgebraᵐᵒᵖ) : + standardRightHom S b = antiunitaryConjugate S.J (star b.unop.val) := rfl + +lemma standardLeftRight_commute (S : StandardModularData H) + (a : S.M.toStarSubalgebra) (b : S.M.toStarSubalgebraᵐᵒᵖ) : + Commute a.val (standardRightHom S b) := + VonNeumannAlgebra.mem_commutant_iff.mp (standardCommutantHom S b).property a.val a.property + +def standardAlgebraicMultiplication (S : StandardModularData H) : + S.M.toStarSubalgebra ⊗[ℂ] S.M.toStarSubalgebraᵐᵒᵖ →⋆ₐ[ℂ] (H →L[ℂ] H) := + Pureness.commutingStarTensorHom S.M.toStarSubalgebra.subtype + (standardRightHom S) (standardLeftRight_commute S) + +lemma standardAlgebraicMultiplication_tmul (S : StandardModularData H) + (a : S.M.toStarSubalgebra) (b : S.M.toStarSubalgebraᵐᵒᵖ) : + standardAlgebraicMultiplication S (a ⊗ₜ[ℂ] b) = + a.val * antiunitaryConjugate S.J (star b.unop.val) := rfl + +attribute [local irreducible] standardAlgebraicMultiplication + +def standardAlgebraicLinear (S : StandardModularData H) : + S.M.toStarSubalgebra ⊗[ℂ] S.M.toStarSubalgebraᵐᵒᵖ →ₗ[ℂ] (H →L[ℂ] H) where + toFun z := standardAlgebraicMultiplication S z + map_add' := map_add (standardAlgebraicMultiplication S) + map_smul' c z := map_smul (standardAlgebraicMultiplication S) c z + +lemma standardAlgebraicLinear_apply (S : StandardModularData H) + (z : S.M.toStarSubalgebra ⊗[ℂ] S.M.toStarSubalgebraᵐᵒᵖ) : + standardAlgebraicLinear S z = standardAlgebraicMultiplication S z := rfl + +variable {A B : Type*} [CStarAlgebra A] [CStarAlgebra B] + [PartialOrder A] [StarOrderedRing A] + +lemma nuclear_quotient_standard_finite_bound + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] B) (hq : Function.Surjective q) + (π : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (S : StandardModularData H) + (hS : S.M = bicommutant π.range) {I : Type*} [Fintype I] + (a : I → S.M.toStarSubalgebra) (b : I → S.M.toStarSubalgebraᵐᵒᵖ) : + ‖∑ i, standardAlgebraicMultiplication S (a i ⊗ₜ[ℂ] b i)‖ ≤ + ‖∑ i, minimalElementary (a i) (b i)‖ := by + simp only [standardAlgebraicMultiplication_tmul] + have h := nuclear_quotient_standard_tensor_sum_bound ω hω hA q hq π S hS + a (fun i => (b i).unop) + have he := subalgebra_minimalSum_norm_le S.M a b + exact h.trans he + +lemma nuclear_quotient_standard_algebraic_bound + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] B) (hq : Function.Surjective q) + (π : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (S : StandardModularData H) + (hS : S.M = bicommutant π.range) + (z : S.M.toStarSubalgebra ⊗[ℂ] S.M.toStarSubalgebraᵐᵒᵖ) : + ‖standardAlgebraicMultiplication S z‖ ≤ ‖minimalAlgebraicLinear z‖ := +by + apply algebraic_linear_norm_le (standardAlgebraicMultiplication S).toLinearMap _ z + intro n a b + simpa only [map_sum, AlgHom.toLinearMap_apply, StarAlgHom.coe_toAlgHom] using + nuclear_quotient_standard_finite_bound ω hω hA q hq π S hS a b + +lemma subalgebraAlgebraicLinear_mul (M : VonNeumannAlgebra H) + (z w : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + minimalAlgebraicLinear (z * w) = minimalAlgebraicLinear z * minimalAlgebraicLinear w := by + induction z using TensorProduct.inductionOn with + | tmul a b => + induction w using TensorProduct.inductionOn with + | tmul c d => + simp only [Algebra.TensorProduct.tmul_mul_tmul, minimalAlgebraicLinear_tmul, + minimalElementary_mul] + | add x y hx hy => simp only [mul_add, map_add, hx, hy] + | add x y hx hy => simp only [add_mul, map_add, hx, hy] + +lemma subalgebraAlgebraicLinear_star (M : VonNeumannAlgebra H) + (z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + minimalAlgebraicLinear (star z) = star (minimalAlgebraicLinear z) := by + induction z using TensorProduct.inductionOn with + | tmul a b => + simp only [TensorProduct.star_tmul, minimalAlgebraicLinear_tmul, minimalElementary_star] + | add x y hx hy => simp only [star_add, map_add, hx, hy] + +@[irreducible] def nuclearQuotientStandardMultiplication + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] B) (hq : Function.Surjective q) + (π : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (S : StandardModularData H) + (hS : S.M = bicommutant π.range) : + MinimalTensor S.M.toStarSubalgebra S.M.toStarSubalgebraᵐᵒᵖ →⋆ₙₐ[ℂ] (H →L[ℂ] H) := + denseLinearStarCompletion minimalAlgebraicLinear (standardAlgebraicLinear S) + minimalAlgebraicLinear_dense (subalgebraAlgebraicLinear_mul S.M) + (map_mul (standardAlgebraicMultiplication S)) (subalgebraAlgebraicLinear_star S.M) + (map_star (standardAlgebraicMultiplication S)) + (nuclear_quotient_standard_algebraic_bound ω hω hA q hq π S hS) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/StandardMultiplicationEvaluation.lean b/lean/OAI/Analysis/OperatorAlgebra/StandardMultiplicationEvaluation.lean new file mode 100644 index 0000000000000000000000000000000000000000..d372145b7be29b00e1f63b95cfcb505a05d41710 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/StandardMultiplicationEvaluation.lean @@ -0,0 +1,49 @@ +import OAI.Analysis.OperatorAlgebra.StandardMinimalMultiplication + +namespace OAI + +/-! Evaluation of the completed standard-form tensor representation. -/ +noncomputable section +open Filter +open scoped TensorProduct +namespace WeakPureInfiniteness +open BoundedRecovery KirchbergRordam.GenericRW.GroupedFactors + +variable {A B H : Type*} [CStarAlgebra A] [CStarAlgebra B] + [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +attribute [local irreducible] standardAlgebraicMultiplication + +lemma nuclearQuotientStandardMultiplication_apply + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] B) (hq : Function.Surjective q) + (π : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (S : StandardModularData H) + (hS : S.M = bicommutant π.range) + (z : S.M.toStarSubalgebra ⊗[ℂ] S.M.toStarSubalgebraᵐᵒᵖ) : + nuclearQuotientStandardMultiplication ω hω hA q hq π S hS (minimalAlgebraicLinear z) = + standardAlgebraicMultiplication S z := by + unfold nuclearQuotientStandardMultiplication + have h := denseLinearStarCompletion_apply minimalAlgebraicLinear + (standardAlgebraicLinear S) minimalAlgebraicLinear_dense + (subalgebraAlgebraicLinear_mul S.M) (map_mul (standardAlgebraicMultiplication S)) + (subalgebraAlgebraicLinear_star S.M) (map_star (standardAlgebraicMultiplication S)) + (nuclear_quotient_standard_algebraic_bound ω hω hA q hq π S hS) z + simpa only [standardAlgebraicLinear_apply] using h + +lemma nuclearQuotientStandardMultiplication_elementary + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] B) (hq : Function.Surjective q) + (π : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (S : StandardModularData H) + (hS : S.M = bicommutant π.range) + (a : S.M.toStarSubalgebra) (b : S.M.toStarSubalgebraᵐᵒᵖ) : + nuclearQuotientStandardMultiplication ω hω hA q hq π S hS (minimalElementary a b) = + a.val * antiunitaryConjugate S.J (star b.unop.val) := by + exact (nuclearQuotientStandardMultiplication_apply ω hω hA q hq π S hS + (a ⊗ₜ[ℂ] b)).trans (standardAlgebraicMultiplication_tmul S a b) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/StandardTensorCompression.lean b/lean/OAI/Analysis/OperatorAlgebra/StandardTensorCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..a016f11d55a87c6cd61a9201e1826cd919bbaeff --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/StandardTensorCompression.lean @@ -0,0 +1,143 @@ +import OAI.Analysis.OperatorAlgebra.IntertwinerTensorCompression +import OAI.Analysis.OperatorAlgebra.StandardMultiplicationEvaluation + +namespace OAI + +/-! The represented-quotient tensor map obtained from the actual standard +multiplication map and the completely positive commutant compression. -/ +noncomputable section +open Filter +open scoped ComplexOrder TensorProduct +namespace WeakPureInfiniteness +open BoundedRecovery KirchbergRordam.GenericRW.GroupedFactors + +attribute [local irreducible] minimalRightCPMap minimalMapAny + standardLeftFactor intertwinerOppositeCP standardCommutantEquiv + +lemma standard_starHomContinuousLinear_apply {X Y : Type*} + [NonUnitalCStarAlgebra X] [NonUnitalCStarAlgebra Y] + (f : X →⋆ₙₐ[ℂ] Y) (x : X) : starHomContinuousLinear f x = f x := rfl + +variable {A Q B H K : Type*} [CStarAlgebra A] [CStarAlgebra Q] [CStarAlgebra B] + [PartialOrder A] [StarOrderedRing A] [PartialOrder B] [StarOrderedRing B] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +def standardTensorCompression + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] Q) (hq : Function.Surjective q) + (ρ : Q →⋆ₐ[ℂ] (K →L[ℂ] K)) (π : Q →⋆ₐ[ℂ] (H →L[ℂ] H)) + (V : K →L[ℂ] H) (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) : + MinimalTensor Q B →L[ℂ] (K →L[ℂ] K) := + (starHomContinuousLinear (nuclearQuotientStandardMultiplication ω hω hA q hq ρ S hS)).comp + ((starHomContinuousLinear (minimalMapAny + (standardLeftFactor ρ S hS).toNonUnitalStarAlgHom + (NonUnitalStarAlgHom.id ℂ S.M.toStarSubalgebraᵐᵒᵖ))).comp + (minimalRightCPMap (intertwinerOppositeCP ρ π V hV η hc S hS))) + +lemma standardTensorCompression_norm_le + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] Q) (hq : Function.Surjective q) + (ρ : Q →⋆ₐ[ℂ] (K →L[ℂ] K)) (π : Q →⋆ₐ[ℂ] (H →L[ℂ] H)) + (V : K →L[ℂ] H) (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) + (z : MinimalTensor Q B) : + ‖standardTensorCompression ω hω hA q hq ρ π V hV η hc S hS z‖ ≤ + (4 * (‖V‖ * ‖V‖)) * ‖z‖ := by + let Φ := intertwinerOppositeCP ρ π V hV η hc S hS + let ψ := minimalMapAny (standardLeftFactor ρ S hS).toNonUnitalStarAlgHom + (NonUnitalStarAlgHom.id ℂ S.M.toStarSubalgebraᵐᵒᵖ) + let θ := nuclearQuotientStandardMultiplication ω hω hA q hq ρ S hS + unfold standardTensorCompression + simp only [ContinuousLinearMap.comp_apply, standard_starHomContinuousLinear_apply] + change ‖θ (ψ (minimalRightCPMap Φ z))‖ ≤ _ + calc + _ ≤ ‖minimalRightCPMap Φ z‖ := + (NonUnitalStarAlgHom.norm_apply_le θ _).trans + (NonUnitalStarAlgHom.norm_apply_le ψ _) + _ ≤ (4 * ‖Φ‖) * ‖z‖ := + minimalRightCPMap_norm_le Φ (intertwinerOppositeCP_cp ρ π V hV η hc S hS) z + _ ≤ (4 * (‖V‖ * ‖V‖)) * ‖z‖ := by + gcongr + exact intertwinerOppositeCP_norm_le ρ π V hV η hc S hS + +lemma standardTensorLegs_elementary + (ρ : Q →⋆ₐ[ℂ] (K →L[ℂ] K)) (π : Q →⋆ₐ[ℂ] (H →L[ℂ] H)) + (V : K →L[ℂ] H) (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) (a : Q) (b : B) : + minimalMapAny (standardLeftFactor ρ S hS).toNonUnitalStarAlgHom + (NonUnitalStarAlgHom.id ℂ S.M.toStarSubalgebraᵐᵒᵖ) + (minimalRightCPMap (intertwinerOppositeCP ρ π V hV η hc S hS) + (minimalElementary a b)) = + minimalElementary (standardLeftFactor ρ S hS a) + (intertwinerOppositeCP ρ π V hV η hc S hS b) := by + have h := congrArg (minimalMapAny (standardLeftFactor ρ S hS).toNonUnitalStarAlgHom + (NonUnitalStarAlgHom.id ℂ S.M.toStarSubalgebraᵐᵒᵖ)) + (minimalRightCPMap_elementary (A := Q) + (intertwinerOppositeCP ρ π V hV η hc S hS) + (intertwinerOppositeCP_cp ρ π V hV η hc S hS) a b) + exact h.trans (minimalMapAny_elementary + (standardLeftFactor ρ S hS).toNonUnitalStarAlgHom + (NonUnitalStarAlgHom.id ℂ S.M.toStarSubalgebraᵐᵒᵖ) + a (intertwinerOppositeCP ρ π V hV η hc S hS b)) + +lemma standardLeftFactor_val (ρ : Q →⋆ₐ[ℂ] (K →L[ℂ] K)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) (a : Q) : + (standardLeftFactor ρ S hS a).val = ρ a := by + unfold standardLeftFactor + rfl + +lemma standardCommutantEquiv_val (S : StandardModularData K) + (x : S.M.toStarSubalgebraᵐᵒᵖ) : + antiunitaryConjugate S.J (star x.unop.val) = (standardCommutantEquiv S x).val := by + unfold standardCommutantEquiv + rfl + +lemma standardTensorCompression_elementary + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] Q) (hq : Function.Surjective q) + (ρ : Q →⋆ₐ[ℂ] (K →L[ℂ] K)) (π : Q →⋆ₐ[ℂ] (H →L[ℂ] H)) + (V : K →L[ℂ] H) (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) (a : Q) (b : B) : + standardTensorCompression ω hω hA q hq ρ π V hV η hc S hS (minimalElementary a b) = + V.adjoint.comp (((π a) * (η b)).comp V) := by + have h₁ := congrArg (nuclearQuotientStandardMultiplication ω hω hA q hq ρ S hS) + (standardTensorLegs_elementary ρ π V hV η hc S hS a b) + have h₂ := nuclearQuotientStandardMultiplication_elementary ω hω hA q hq ρ S hS + (standardLeftFactor ρ S hS a) (intertwinerOppositeCP ρ π V hV η hc S hS b) + have h₃ : (standardLeftFactor ρ S hS a).val * + antiunitaryConjugate S.J + (star (intertwinerOppositeCP ρ π V hV η hc S hS b).unop.val) = + V.adjoint.comp (((π a) * (η b)).comp V) := by + rw [standardLeftFactor_val, standardCommutantEquiv_val, intertwinerOppositeCP_evaluate] + apply ContinuousLinearMap.ext + intro x + exact congrArg (fun T : H →L[ℂ] K => T (η b (V x))) + (intertwiner_adjoint ρ π V hV a) + exact h₁.trans (h₂.trans h₃) + +lemma standardTensorCompression_algebraic + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (hA : Nuclear A) (q : A →⋆ₐ[ℂ] Q) (hq : Function.Surjective q) + (ρ : Q →⋆ₐ[ℂ] (K →L[ℂ] K)) (π : Q →⋆ₐ[ℂ] (H →L[ℂ] H)) + (V : K →L[ℂ] H) (hV : ∀ a, V.comp (ρ a) = (π a).comp V) + (η : B →⋆ₐ[ℂ] (H →L[ℂ] H)) (hc : ∀ a b, Commute (π a) (η b)) + (S : StandardModularData K) (hS : S.M = bicommutant ρ.range) + (z : Q ⊗[ℂ] B) : + standardTensorCompression ω hω hA q hq ρ π V hV η hc S hS (minimalAlgebraicLinear z) = + V.adjoint.comp ((Pureness.commutingStarTensorHom π η hc z).comp V) := by + induction z using TensorProduct.inductionOn with + | tmul a b => exact standardTensorCompression_elementary ω hω hA q hq ρ π V hV η hc S hS a b + | add x y hx hy => + simp only [map_add, hx, hy, ContinuousLinearMap.add_comp, ContinuousLinearMap.comp_add] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/StrongCompressionBound.lean b/lean/OAI/Analysis/OperatorAlgebra/StrongCompressionBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..7f635e22bf6956340ffd652abe0f94467d3d3a29 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/StrongCompressionBound.lean @@ -0,0 +1,49 @@ +import Mathlib + +namespace OAI + +/-! Recovering an operator norm bound from finite-corner bounds in a +strongly exhausting family of compressions. -/ + +noncomputable section +open Filter Topology + +namespace WeakPureInfiniteness + +variable {ι H : Type*} [NormedAddCommGroup H] [NormedSpace ℂ H] + +/-- Uniformly contractive compressions converging strongly to the identity +recover every operator strongly, including on its moving input vector. -/ +lemma strong_compressions_tendsto (l : Filter ι) (P : ι → H →L[ℂ] H) + (hPn : ∀ i, ‖P i‖ ≤ 1) (hP : ∀ x, Tendsto (fun i => P i x) l (𝓝 x)) + (T : H →L[ℂ] H) (x : H) : + Tendsto (fun i => (P i * T * P i) x) l (𝓝 (T x)) := by + have ht : Tendsto (fun i => T (P i x) - T x) l (𝓝 0) := by + simpa only [Function.comp_apply, sub_self] using (T.continuous.continuousAt.tendsto.comp (hP x)).sub + (tendsto_const_nhds : Tendsto (fun _ : ι => T x) l (𝓝 (T x))) + have htn : Tendsto (fun i => ‖T (P i x) - T x‖) l (𝓝 0) := by + simpa only [norm_zero] using ht.norm + have he : Tendsto (fun i => P i (T (P i x) - T x)) l (𝓝 0) := by + apply squeeze_zero_norm (fun i => (P i).le_opNorm _ |>.trans ?_) htn + exact (mul_le_mul_of_nonneg_right (hPn i) (norm_nonneg _)).trans_eq (one_mul _) + have hh := he.add (hP (T x)) + simpa only [map_sub, sub_add_cancel, zero_add, mul_apply_eq_comp] using hh + +/-- A bound on every strongly exhausting compression is a bound on the +original operator. No norm convergence of the projections is needed. -/ +theorem norm_le_of_strong_compression_bound (l : Filter ι) [NeBot l] + (P : ι → H →L[ℂ] H) (hPn : ∀ i, ‖P i‖ ≤ 1) + (hP : ∀ x, Tendsto (fun i => P i x) l (𝓝 x)) + (T : H →L[ℂ] H) {C : ℝ} (hC : 0 ≤ C) + (hT : ∀ i, ‖P i * T * P i‖ ≤ C) : ‖T‖ ≤ C := by + apply ContinuousLinearMap.opNorm_le_bound T hC + intro x + apply le_of_tendsto (strong_compressions_tendsto l P hPn hP T x).norm + exact Eventually.of_forall fun i => ((P i * T * P i).le_opNorm x).trans + (mul_le_mul_of_nonneg_right (hT i) (norm_nonneg x)) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TotalTensorVectors.lean b/lean/OAI/Analysis/OperatorAlgebra/TotalTensorVectors.lean new file mode 100644 index 0000000000000000000000000000000000000000..7d3caba648ac5a8d460bd4b8e6270a4ca7986cbd --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TotalTensorVectors.lean @@ -0,0 +1,46 @@ +import OAI.Analysis.WeakInfiniteness.TensorFoundations + +namespace OAI + +/-! Testing operators on tensor products of two total families of vectors. -/ + +noncomputable section +open scoped TensorProduct +open UniformSpace + +namespace WeakPureInfiniteness + +variable {H K E I J : Type*} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] + [NormedAddCommGroup E] [NormedSpace ℂ E] + +theorem completed_tensor_operator_eq_zero (ξ : I → H) (η : J → K) + (hH : ∀ L : H →L[ℂ] E, (∀ i, L (ξ i) = 0) → L = 0) + (hK : ∀ L : K →L[ℂ] E, (∀ j, L (η j) = 0) → L = 0) + (T : Completion (H ⊗[ℂ] K) →L[ℂ] E) + (hT : ∀ i j, T ((ξ i ⊗ₜ[ℂ] η j : H ⊗[ℂ] K) : Completion _) = 0) : T = 0 := by + let C : H ⊗[ℂ] K →L[ℂ] Completion (H ⊗[ℂ] K) := Completion.toComplL + have hright (i : I) (y : K) : T (C (ξ i ⊗ₜ[ℂ] y)) = 0 := by + let L := T.comp (C.comp (TensorProduct.mkL ℂ H K (ξ i))) + have hz : L = 0 := hK L (hT i) + exact congrArg (fun F : K →L[ℂ] E => F y) hz + have hall (x : H) (y : K) : T (C (x ⊗ₜ[ℂ] y)) = 0 := by + let L := T.comp (C.comp ((TensorProduct.mkL ℂ H K).flip y)) + have hz : L = 0 := hH L (fun i => hright i y) + exact congrArg (fun F : H →L[ℂ] E => F x) hz + apply ContinuousLinearMap.ext + intro z + change T z = 0 + induction z using Completion.induction_on with + | hp => exact isClosed_eq T.continuous continuous_const + | ih z => + induction z using TensorProduct.inductionOn with + | add x y hx hy => simp only [Completion.coe_add, map_add, hx, hy, add_zero] + | tmul x y => exact hall x y + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialBundledFiniteBound.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialBundledFiniteBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..adb63d7f421be4b8684cb004b7234fd04da97eb4 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialBundledFiniteBound.lean @@ -0,0 +1,35 @@ +import OAI.Analysis.OperatorAlgebra.TracialExpectationBound +import OAI.Analysis.OperatorAlgebra.TracialTensorFiniteSum + +namespace OAI + +/-! The finite-tracial bound in the bundled GNS form needed by the actual +corner inclusions. All conversion of GNS structures is done abstractly. -/ +noncomputable section +open scoped TensorProduct ComplexOrder +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma tracialBundledFiniteProduct_norm_le (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (h : ∃ E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H), + CompletelyPositive E ∧ ‖E‖ ≤ 1 ∧ + (∀ T, E T ∈ M) ∧ (∀ T, T ∈ M → E T = T)) + {I : Type*} [Fintype I] (a b : I → M.toStarSubalgebra) : + ‖∑ i, gnsBundledLeft τ.functional (a i) * + gnsBundledRight τ.functional τ.tracial (b i)‖ ≤ + ‖∑ i, minimalElementary (a i) (MulOpposite.op (b i))‖ := by + have hb := tracialMinimalMultiplication_bound_of_expectation M τ h + (∑ i, a i ⊗ₜ[ℂ] MulOpposite.op (b i)) + change ‖traceTensor τ.functional τ.tracial + (∑ i, a i ⊗ₜ[ℂ] MulOpposite.op (b i))‖ ≤ _ at hb + rw [norm_traceTensor_sum] at hb + simpa only [map_sum, minimalAlgebraicLinear_tmul] using hb + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialCanonicalCornerBound.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialCanonicalCornerBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..9eba56eccb5f401a7c8687b7e60fe476d7448133 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialCanonicalCornerBound.lean @@ -0,0 +1,45 @@ +import OAI.Analysis.OperatorAlgebra.TracialCornerCompression +import OAI.Analysis.OperatorAlgebra.LpOperatorTensorBound +import OAI.Analysis.OperatorAlgebra.CanonicalLpOperations + +namespace OAI + +/-! Specialize the finite-tracial corner estimate to canonical L² operator +structures while all four operator families remain abstract. -/ +noncomputable section +open MeasureTheory +open scoped ComplexOrder TensorProduct +namespace WeakPureInfiniteness +universe u +variable {J K : Type u} + [NormedAddCommGroup J] [InnerProductSpace ℂ J] [CompleteSpace J] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma tracial_canonical_lp_corner_sum_bound (M : VonNeumannAlgebra K) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (hE : ∃ E : (K →L[ℂ] K) →L[ℂ] (K →L[ℂ] K), + CompletelyPositive E ∧ ‖E‖ ≤ 1 ∧ + (∀ T, E T ∈ M) ∧ (∀ T, T ∈ M → E T = T)) + (W : gnsHilbert τ.functional →ₗᵢ[ℂ] (Lp J 2 (volume : Measure ℝ))) + (L R : M.toStarSubalgebra → (Lp J 2 (volume : Measure ℝ)) →L[ℂ] (Lp J 2 (volume : Measure ℝ))) + (hL : ∀ a x, L a (W x) = W (gnsBundledLeft τ.functional a x)) + (hR : ∀ b x, R b (W x) = W (gnsBundledRight τ.functional τ.tracial b x)) + (hP : ∀ a b, (L a * R b) * isometricCornerProjection W = L a * R b) + (V : K →ₗᵢ[ℂ] (Lp J 2 (volume : Measure ℝ))) (p : (Lp J 2 (volume : Measure ℝ)) →L[ℂ] (Lp J 2 (volume : Measure ℝ))) (hp : ‖p‖ ≤ 1) + {I : Type*} [Fintype I] (a b : I → (Lp J 2 (volume : Measure ℝ)) →L[ℂ] (Lp J 2 (volume : Measure ℝ))) + (ac bc : I → M.toStarSubalgebra) + (ha : ∀ i, isometricCornerLift V (ac i).val = p * a i * p) + (hb : ∀ i, isometricCornerLift V (bc i).val = p * b i * p) : + ‖∑ i, canonicalLpOperator (L (ac i)) * canonicalLpOperator (R (bc i))‖ ≤ + ‖∑ i, minimalElementary (canonicalLpOperator (a i)) + (MulOpposite.op (canonicalLpOperator (b i)))‖ := by + have h : hilbertOperatorTensorBound (fun i => L (ac i)) (fun i => R (bc i)) a b := + tracial_represented_corner_sum_bound M τ hE W L R hL hR hP V p hp a b ac bc ha hb + exact canonicalLpOperator_tensor_bound (fun i => L (ac i)) (fun i => R (bc i)) a b h + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialCornerCompression.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialCornerCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..c76f46b7739fb7b940db6a2af2231dd922a09073 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialCornerCompression.lean @@ -0,0 +1,41 @@ +import OAI.Analysis.OperatorAlgebra.TracialRepresentedBound +import OAI.Analysis.Nuclearity.MinimalCornerCompression + +namespace OAI + +/-! Combine the finite-tracial estimate with corner compression before +specializing the concrete GNS structures. -/ +noncomputable section +open scoped ComplexOrder TensorProduct +namespace WeakPureInfiniteness +universe u +variable {H K : Type u} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma tracial_represented_corner_sum_bound (M : VonNeumannAlgebra K) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (hE : ∃ E : (K →L[ℂ] K) →L[ℂ] (K →L[ℂ] K), + CompletelyPositive E ∧ ‖E‖ ≤ 1 ∧ + (∀ T, E T ∈ M) ∧ (∀ T, T ∈ M → E T = T)) + (W : gnsHilbert τ.functional →ₗᵢ[ℂ] H) + (L R : M.toStarSubalgebra → H →L[ℂ] H) + (hL : ∀ a x, L a (W x) = W (gnsBundledLeft τ.functional a x)) + (hR : ∀ b x, R b (W x) = W (gnsBundledRight τ.functional τ.tracial b x)) + (hP : ∀ a b, (L a * R b) * isometricCornerProjection W = L a * R b) + (V : K →ₗᵢ[ℂ] H) (p : H →L[ℂ] H) (hp : ‖p‖ ≤ 1) + {I : Type*} [Fintype I] (a b : I → H →L[ℂ] H) + (ac bc : I → M.toStarSubalgebra) + (ha : ∀ i, isometricCornerLift V (ac i).val = p * a i * p) + (hb : ∀ i, isometricCornerLift V (bc i).val = p * b i * p) : + ‖∑ i, L (ac i) * R (bc i)‖ ≤ + ‖∑ i, minimalElementary (a i) (MulOpposite.op (b i))‖ := + (tracial_represented_sum_bound M τ hE W L R hL hR hP ac bc).trans + (norm_minimalSum_corner_compression M V p hp a b ac bc ha hb) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialExpectationBound.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialExpectationBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..29e99cdb10193f846d7a29ce592a5b4a0c72228e --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialExpectationBound.lean @@ -0,0 +1,28 @@ +import OAI.Analysis.OperatorAlgebra.TracialMinimalMultiplication + +namespace OAI + +/-! The minimal tensor norm bound for multiplication associated with a +finite-tracial representation carrying a completely positive expectation. -/ +noncomputable section +open scoped TensorProduct ComplexOrder +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma tracialMinimalMultiplication_bound_of_expectation (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (h : ∃ E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H), + CompletelyPositive E ∧ ‖E‖ ≤ 1 ∧ + (∀ T, E T ∈ M) ∧ (∀ T, T ∈ M → E T = T)) : + ∀ z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ, + ‖tracialMultiplicationTensor M τ z‖ ≤ ‖minimalAlgebraicLinear z‖ := by + obtain ⟨E, hE, _hn, hr, hf⟩ := h + exact tracialMinimalMultiplication_norm_le M τ E hE hr hf + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialGNSIntertwiner.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialGNSIntertwiner.lean new file mode 100644 index 0000000000000000000000000000000000000000..49409601b54d8a31663ad16a5d9ba4548c9254e6 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialGNSIntertwiner.lean @@ -0,0 +1,88 @@ +import OAI.Analysis.OperatorAlgebra.GNSVectorDensity +import OAI.Analysis.TracialSplitting.GNSRepresentations + +namespace OAI + +/-! Vector formulas determine the left and right actions on the full GNS space. -/ +noncomputable section +open scoped ComplexOrder Topology +namespace WeakPureInfiniteness + +variable {A H : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma gnsVector_left (f : A →ₚ[ℂ] ℂ) (a b : A) : + f.gnsStarAlgHom a (gnsVector f b) = gnsVector f (a * b) := by + change f.gnsNonUnitalStarAlgHom a (f.toPreGNS b : f.GNS) = _ + rw [PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe] + simp only [PositiveLinearMap.leftMulMapPreGNS_apply, + PositiveLinearMap.ofPreGNS_toPreGNS, gnsVector] + +lemma gnsVector_right (f : A →ₚ[ℂ] ℂ) (ht : ∀ a b, f (a * b) = f (b * a)) + (a b : A) : + NuclearTrace.rightGNS f ht (MulOpposite.op b) (gnsVector f a) = + gnsVector f (a * b) := by + change NuclearTrace.rightGNS f ht (MulOpposite.op b) (f.toPreGNS a : f.GNS) = _ + rw [NuclearTrace.rightGNS_coe] + simp only [PositiveLinearMap.ofPreGNS_toPreGNS, MulOpposite.unop_op, gnsVector] + +omit [CompleteSpace H] in +lemma gns_left_intertwines (f : A →ₚ[ℂ] ℂ) (V : gnsHilbert f →ₗᵢ[ℂ] H) + (a : A) (T : H →L[ℂ] H) + (hT : ∀ b : A, T (V (gnsVector f b)) = V (gnsVector f (a * b))) + (x : gnsHilbert f) : T (V x) = V (f.gnsStarAlgHom a x) := by + apply gnsVector_induction_on f x + · exact isClosed_eq (T.continuous.comp V.continuous) + (V.continuous.comp (f.gnsStarAlgHom a).continuous) + · intro b + rw [gnsVector_left] + exact hT b + +omit [CompleteSpace H] in +lemma gns_right_intertwines (f : A →ₚ[ℂ] ℂ) + (ht : ∀ a b, f (a * b) = f (b * a)) (V : gnsHilbert f →ₗᵢ[ℂ] H) + (b : A) (T : H →L[ℂ] H) + (hT : ∀ a : A, T (V (gnsVector f a)) = V (gnsVector f (a * b))) + (x : gnsHilbert f) : + T (V x) = V (NuclearTrace.rightGNS f ht (MulOpposite.op b) x) := by + apply gnsVector_induction_on f x + · exact isClosed_eq (T.continuous.comp V.continuous) + (V.continuous.comp (NuclearTrace.rightGNS f ht (MulOpposite.op b)).continuous) + · intro a + rw [gnsVector_right] + exact hT a + +omit [CompleteSpace H] in +lemma gns_left_intertwines_of_vector_formula (f : A →ₚ[ℂ] ℂ) + (V : gnsHilbert f →ₗᵢ[ℂ] H) (c : ℂ) (v : A → H) + (hV : ∀ a, V (gnsVector f a) = c • v a) + (a : A) (T : H →L[ℂ] H) (hv : ∀ b, T (v b) = v (a * b)) + (x : gnsHilbert f) : T (V x) = V (f.gnsStarAlgHom a x) := by + apply gns_left_intertwines f V a T + intro b + calc + T (V (gnsVector f b)) = T (c • v b) := congrArg T (hV b) + _ = c • T (v b) := T.map_smul c (v b) + _ = c • v (a * b) := congrArg (fun z => c • z) (hv b) + _ = V (gnsVector f (a * b)) := (hV (a * b)).symm + +omit [CompleteSpace H] in +lemma gns_right_intertwines_of_vector_formula (f : A →ₚ[ℂ] ℂ) + (ht : ∀ a b, f (a * b) = f (b * a)) + (V : gnsHilbert f →ₗᵢ[ℂ] H) (c : ℂ) (v : A → H) + (hV : ∀ a, V (gnsVector f a) = c • v a) + (b : A) (T : H →L[ℂ] H) (hv : ∀ a, T (v a) = v (a * b)) + (x : gnsHilbert f) : T (V x) = V (NuclearTrace.rightGNS f ht (MulOpposite.op b) x) := by + apply gns_right_intertwines f ht V b T + intro a + calc + T (V (gnsVector f a)) = T (c • v a) := congrArg T (hV a) + _ = c • T (v a) := T.map_smul c (v a) + _ = c • v (a * b) := congrArg (fun z => c • z) (hv a) + _ = V (gnsVector f (a * b)) := (hV (a * b)).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialMinimalBound.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialMinimalBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..13e8f75f4317dbb85d2a427474eb539a253c2cf0 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialMinimalBound.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.OperatorAlgebra.TracialSpatialMultiplication +import OAI.Analysis.Nuclearity.MinimalTensorExtension + +namespace OAI + +/-! The finite tracial multiplication representation satisfies the actual +minimal tensor norm bound. This uses its concrete spatial norm and the +preceding cyclic-state argument, without assuming nuclearity of the algebra. -/ + +noncomputable section +open scoped TensorProduct InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + (M : VonNeumannAlgebra H) + +lemma tracialSpatialTensor_completed_tmul (a : M.toStarSubalgebra) + (b : M.toStarSubalgebraᵐᵒᵖ) : + tracialSpatialTensor M (a ⊗ₜ[ℂ] b) = + (TensorProduct.mapL (a : H →L[ℂ] H) + ((hilbertDualRepresentation.comp (subalgebraOppositeHom M.toStarSubalgebra)) b)).completion := by + change UnitalTomsWinter.spatialTensorOp (a : H →L[ℂ] H) 1 * + UnitalTomsWinter.spatialTensorOp 1 + ((hilbertDualRepresentation.comp (subalgebraOppositeHom M.toStarSubalgebra)) b) = _ + rw [← UnitalTomsWinter.spatialTensorOp_mul, mul_one, one_mul] + rfl + +lemma tracialSpatialTensor_sum_norm_le_minimal {I : Type*} (s : Finset I) + (a : I → M.toStarSubalgebra) (b : I → M.toStarSubalgebraᵐᵒᵖ) : + ‖tracialSpatialTensor M (∑ i ∈ s, a i ⊗ₜ[ℂ] b i)‖ ≤ + ‖(∑ i ∈ s, minimalElementary (a i) (b i) : + MinimalTensor M.toStarSubalgebra M.toStarSubalgebraᵐᵒᵖ)‖ := by + rw [map_sum] + simp only [tracialSpatialTensor_completed_tmul] + exact norm_completed_tensor_sum_le_minimal s a b + M.toStarSubalgebra.subtype.toNonUnitalStarAlgHom + (hilbertDualRepresentation.comp (subalgebraOppositeHom M.toStarSubalgebra)).toNonUnitalStarAlgHom + +lemma tracialSpatialTensor_norm_le_minimal + (z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + ‖tracialSpatialTensor M z‖ ≤ + ‖minimalAlgebraicLinear z‖ := + algebraic_linear_norm_le (A := M.toStarSubalgebra) (B := M.toStarSubalgebraᵐᵒᵖ) + (tracialSpatialTensor M).toLinearMap + (fun _ a b => tracialSpatialTensor_sum_norm_le_minimal M Finset.univ a b) z + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialMinimalMultiplication.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialMinimalMultiplication.lean new file mode 100644 index 0000000000000000000000000000000000000000..c612c81ab8534c377b2268f236299cd66406ab92 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialMinimalMultiplication.lean @@ -0,0 +1,79 @@ +import OAI.Analysis.OperatorAlgebra.TracialMinimalBound +import OAI.Analysis.OperatorAlgebra.TracialTensorCompletion + +namespace OAI + +/-! Extension of the finite tracial multiplication representation to the actual +minimal tensor product. -/ + +noncomputable section +open scoped TensorProduct InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + (M : VonNeumannAlgebra H) + +lemma tracialMinimalAlgebraic_mul + (z w : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + minimalAlgebraicLinear (z * w) = + minimalAlgebraicLinear z * minimalAlgebraicLinear w := by + induction z using TensorProduct.inductionOn with + | tmul a b => + induction w using TensorProduct.inductionOn with + | tmul c d => + simp only [Algebra.TensorProduct.tmul_mul_tmul, minimalAlgebraicLinear_tmul, + minimalElementary_mul] + | add x y hx hy => simp only [mul_add, map_add, hx, hy] + | add x y hx hy => simp only [add_mul, map_add, hx, hy] + +lemma tracialMinimalAlgebraic_star + (z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + minimalAlgebraicLinear (star z) = star (minimalAlgebraicLinear z) := by + induction z using TensorProduct.inductionOn with + | tmul a b => + simp only [TensorProduct.star_tmul, minimalAlgebraicLinear_tmul, minimalElementary_star] + | add x y hx hy => simp only [star_add, map_add, hx, hy] + +variable [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + +include E hE hEr hEf in +lemma tracialMinimalMultiplication_norm_le + (z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + ‖tracialMultiplicationTensor M τ z‖ ≤ ‖minimalAlgebraicLinear z‖ := by + have h₁ := tracial_multiplication_norm_le M τ E hE hEr hEf z + have h₂ := tracialSpatialTensor_norm_le_minimal M z + exact h₁.trans h₂ + +/-- The finite tracial amenability representation, constructed from the +expectation by the existing minimal tensor extension theorem. -/ +def tracialMinimalMultiplication : + MinimalTensor M.toStarSubalgebra M.toStarSubalgebraᵐᵒᵖ →⋆ₙₐ[ℂ] + (τ.functional.GNS →L[ℂ] τ.functional.GNS) := + tracialTensorMinimal τ.functional τ.tracial + (tracialMinimalMultiplication_norm_le M τ E hE hEr hEf) + +lemma tracialMinimalMultiplication_algebraic + (z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + tracialMinimalMultiplication M τ E hE hEr hEf (minimalAlgebraicLinear z) = + tracialMultiplicationTensor M τ z := + tracialTensorMinimal_algebraic τ.functional τ.tracial + (tracialMinimalMultiplication_norm_le M τ E hE hEr hEf) z + +@[simp] lemma tracialMinimalMultiplication_elementary (a b : M.toStarSubalgebra) : + tracialMinimalMultiplication M τ E hE hEr hEf + (minimalElementary a (MulOpposite.op b)) = + τ.functional.gnsStarAlgHom a * + NuclearTrace.rightGNS τ.functional τ.tracial (MulOpposite.op b) := + tracialTensorMinimal_elementary τ.functional τ.tracial + (tracialMinimalMultiplication_norm_le M τ E hE hEr hEf) a b + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialProductApproximation.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialProductApproximation.lean new file mode 100644 index 0000000000000000000000000000000000000000..68a0b204742c5cd5cd9fb3934b5bdb6237b03b0f --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialProductApproximation.lean @@ -0,0 +1,89 @@ +import OAI.Analysis.OperatorAlgebra.TracialSpatialApproximation +import OAI.Analysis.OperatorAlgebra.DensityUnitaryCoefficients + +namespace OAI + +/-! Product-state approximation from the finite tracial vector construction. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder +namespace WeakPureInfiniteness + +variable {H I : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + [CompleteSpace H] [Fintype I] + +lemma tracial_product_error_lt (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (a : M.toStarSubalgebra) (u : unitary M.toStarSubalgebra) + (z : NuclearUltrapower.HilbertSchmidt H) (hzn : ‖z‖ = 1) + {D δ ε : ℝ} (hD : ‖a‖ + 1 ≤ D) (hδ : 0 ≤ δ) (hsmall : D * δ < ε) + (htrace : ‖τ.functional (a * (u : M.toStarSubalgebra)) - inner ℂ z + (densityLeftRepresentation ((a * (u : M.toStarSubalgebra)) : H →L[ℂ] H) z)‖ < δ) + (hcent : ‖hsLeftUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra u) z - + hsRightUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra u) z‖ < δ) : + ‖inner ℂ z ((densityLeftRepresentation (a : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op ((u : M.toStarSubalgebra) : H →L[ℂ] H))) z) - + τ.functional (a * (u : M.toStarSubalgebra))‖ < ε := by + let U := subalgebraUnitaryIsometry M.toStarSubalgebra u + have hb := density_unitary_product_error (H := H) (a : H →L[ℂ] H) U z hzn + (τ.functional (a * (u : M.toStarSubalgebra))) + have hn : ‖densityLeftRepresentation (a : H →L[ℂ] H)‖ ≤ ‖a‖ := + NonUnitalStarAlgHom.norm_apply_le (densityLeftRepresentation (H := H)).toNonUnitalStarAlgHom _ + rw [norm_sub_rev] at htrace + apply hb.trans_lt + apply lt_of_lt_of_le _ (le_of_lt hsmall) + have h₁ := add_lt_add_of_le_of_lt + (mul_le_mul_of_nonneg_left hcent.le (norm_nonneg (densityLeftRepresentation (a : H →L[ℂ] H)))) htrace + refine h₁.trans_le ?_ + calc + ‖densityLeftRepresentation (a : H →L[ℂ] H)‖ * δ + δ ≤ ‖a‖ * δ + δ := + add_le_add (mul_le_mul_of_nonneg_right hn hδ) (le_refl δ) + _ = (‖a‖ + 1) * δ := by ring + _ ≤ D * δ := mul_le_mul_of_nonneg_right hD hδ + +/-- A finite family of diagonal trace coefficients is approximated by +coefficients of the genuine spatial left/right representation. -/ +theorem expectation_spatial_product_approximation (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (a : I → M.toStarSubalgebra) (u : I → unitary M.toStarSubalgebra) + {ε : ℝ} (hε : 0 < ε) : + ∃ z : NuclearUltrapower.HilbertSchmidt H, ‖z‖ = 1 ∧ + 0 ≤ NuclearUltrapower.hsOperator z ∧ + (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator z y ∈ F) ∧ + ∀ i, ‖inner ℂ z ((densityLeftRepresentation (a i : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op ((u i : M.toStarSubalgebra) : H →L[ℂ] H))) z) - + τ.functional (a i * (u i : M.toStarSubalgebra))‖ < ε := by + classical + let D : ℝ := 1 + ∑ i, ‖a i‖ + have hD : 1 ≤ D := le_add_of_nonneg_right (Finset.sum_nonneg fun _ _ => norm_nonneg _) + have hD0 : 0 < D := lt_of_lt_of_le zero_lt_one hD + let δ : ℝ := ε / (2 * D) + have hδ : 0 < δ := div_pos hε (by positivity) + obtain ⟨z, hzn, hzp, hzf, hza, hzu⟩ := expectation_complex_spatial_approximation + M τ E hE hEr hEf (fun i => a i * (u i : M.toStarSubalgebra)) u hδ + have hsmall : D * δ < ε := by + have hd : D * δ = ε / 2 := by + dsimp only [δ] + field_simp [hD0.ne'] + rw [hd] + exact half_lt_self hε + refine ⟨z, hzn, hzp, hzf, ?_⟩ + intro i + have hi : ‖a i‖ + 1 ≤ D := by + have hh := Finset.single_le_sum (f := fun j : I => ‖a j‖) + (fun j _ => norm_nonneg (a j)) (Finset.mem_univ i) + dsimp only [D] + linarith + exact tracial_product_error_lt M τ (a i) (u i) z hzn hi hδ.le hsmall (hza i) (hzu i) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialRepresentedBound.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialRepresentedBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..daa6909b0fe4d4c75957b167de3f5a0db8560958 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialRepresentedBound.lean @@ -0,0 +1,36 @@ +import OAI.Analysis.OperatorAlgebra.TracialBundledFiniteBound +import OAI.Analysis.OperatorAlgebra.GNSProductNorm + +namespace OAI + +/-! Apply the finite-tracial estimate through a supported GNS inclusion before +specializing the represented Hilbert spaces. -/ +noncomputable section +open scoped ComplexOrder TensorProduct +namespace WeakPureInfiniteness +variable {H K : Type*} + [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + [NormedAddCommGroup K] [InnerProductSpace ℂ K] [CompleteSpace K] + +lemma tracial_represented_sum_bound (M : VonNeumannAlgebra K) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (hE : ∃ E : (K →L[ℂ] K) →L[ℂ] (K →L[ℂ] K), + CompletelyPositive E ∧ ‖E‖ ≤ 1 ∧ + (∀ T, E T ∈ M) ∧ (∀ T, T ∈ M → E T = T)) + (V : gnsHilbert τ.functional →ₗᵢ[ℂ] H) + (L R : M.toStarSubalgebra → H →L[ℂ] H) + (hL : ∀ a x, L a (V x) = V (gnsBundledLeft τ.functional a x)) + (hR : ∀ b x, R b (V x) = V (gnsBundledRight τ.functional τ.tracial b x)) + (hP : ∀ a b, (L a * R b) * isometricCornerProjection V = L a * R b) + {I : Type*} [Fintype I] (a b : I → M.toStarSubalgebra) : + ‖∑ i, L (a i) * R (b i)‖ ≤ + ‖∑ i, minimalElementary (a i) (MulOpposite.op (b i))‖ := + (gns_product_sum_norm τ.functional τ.tracial V L R hL hR hP a b).trans_le + (tracialBundledFiniteProduct_norm_le (H := K) M τ hE a b) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialApproximation.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialApproximation.lean new file mode 100644 index 0000000000000000000000000000000000000000..4c8431ab2eea2b2f0522c06afa40385f2ccde4f5 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialApproximation.lean @@ -0,0 +1,233 @@ +import OAI.Analysis.OperatorAlgebra.DensityQuadraticCompression +import OAI.Analysis.OperatorAlgebra.NormalizedExpectationRoots +import OAI.Analysis.PureInfiniteness.NormalizedQuadraticEstimate +import OAI.Analysis.Nuclearity.SpatialCoefficientEstimate + +namespace OAI + +/-! Normalized finite-rank spatial vectors preserving prescribed trace tests. +This is the finite tracial part of the injectivity argument. It does not +assert semidiscreteness for an arbitrary von Neumann algebra. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder TensorProduct ComplexStarModule + +namespace WeakPureInfiniteness + +variable {H I J : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + [CompleteSpace H] [Fintype I] [Fintype J] + +lemma finiteVectorDensity_root_left (n : ℕ) (w : Fin n → ℝ) + (hw : ∀ k, 0 ≤ w k) (x : Fin n → H) (T : H →L[ℂ] H) : + (inner ℂ (NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x)) + (densityLeftRepresentation T + (NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x)))).re = + ∑ k, w k * (inner ℂ (x k) (T (x k))).re := by + rw [densityRoot_left_quadratic, finiteVectorDensityTensor_functional w hw] + simp only [finiteVectorDensity, Submodule.coe_sum, Submodule.coe_smul, + sum_apply, smul_apply, finiteOperatorCoefficient, operatorCoefficient_apply, + Complex.re_sum, smul_eq_mul, Complex.re_ofReal_mul] + +/-- A trace-preserving finite family and a nearly central finite family are +realized by the same positive, finite-rank, unit Hilbert--Schmidt vector. -/ +theorem expectation_normalized_spatial_vectors (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (a : I → selfAdjoint M.toStarSubalgebra) (u : J → unitary M.toStarSubalgebra) + {δ : ℝ} (hδ : 0 < δ) (hδhalf : δ ≤ 1 / 2) : + ∃ z : NuclearUltrapower.HilbertSchmidt H, ‖z‖ = 1 ∧ + 0 ≤ NuclearUltrapower.hsOperator z ∧ + (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator z y ∈ F) ∧ + (∀ i, |(τ.functional (a i)).re - + (inner ℂ z (densityLeftRepresentation + (((a i : M.toStarSubalgebra) : H →L[ℂ] H)) z)).re| < + 2 * δ * (1 + |(τ.functional (a i)).re|)) ∧ + ∀ j, ‖hsLeftUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z - + hsRightUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z‖ ^ 2 < 2 * δ := by + classical + let tests : Option I → selfAdjoint M.toStarSubalgebra := + fun i => i.elim 1 a + obtain ⟨n, w, x, hw, _hws, _hx, ha, hrn, hrp, hrs, hru⟩ := + expectation_finite_density_roots M τ E hE hEr hEf tests u hδ + let r := NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x) + change ‖r‖ ≤ 1 at hrn + change 0 ≤ NuclearUltrapower.hsOperator r at hrp + change (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator r y ∈ F) at hrs + have hm : |1 - ‖r‖ ^ 2| < δ := by + have ht := ha none + change |(τ.functional 1).re - ∑ k, w k * (inner ℂ (x k) (x k)).re| < δ at ht + rw [τ.normalized, Complex.one_re] at ht + have hq (k : Fin n) : (inner ℂ (x k) (x k)).re = ‖x k‖ ^ 2 := + inner_self_eq_norm_sq (𝕜 := ℂ) (x k) + simp_rw [hq] at ht + simpa only [r, NuclearUltrapower.densityRoot_norm, + finiteVectorDensityTensor_norm_sq w hw x] using ht + have hr2 : 1 / 2 < ‖r‖ ^ 2 := by + have hb := (abs_lt.mp hm).2 + linarith + have hr : 0 < ‖r‖ := by nlinarith [norm_nonneg r] + let c : ℂ := (‖r‖⁻¹ : ℝ) + let z := c • r + refine ⟨z, ?_, ?_, ?_, ?_, ?_⟩ + · change ‖c • r‖ = 1 + rw [norm_smul] + simp only [c, Complex.norm_real, Real.norm_of_nonneg (inv_nonneg.mpr hr.le), + inv_mul_cancel₀ hr.ne'] + · change 0 ≤ NuclearUltrapower.hsOperator (c • r) + rw [map_smul] + change 0 ≤ (‖r‖⁻¹ : ℝ) • NuclearUltrapower.hsOperator r + exact smul_nonneg (inv_nonneg.mpr hr.le) hrp + · obtain ⟨F, hF, hFs⟩ := hrs + refine ⟨F, hF, ?_⟩ + intro y + change NuclearUltrapower.hsOperator (c • r) y ∈ F + rw [map_smul, smul_apply] + exact F.smul_mem c (hFs y) + · intro i + apply normalized_quadratic_error r _ hr2 hm + change |(τ.functional (a i)).re - + (inner ℂ r (densityLeftRepresentation (((a i : M.toStarSubalgebra) : H →L[ℂ] H)) r)).re| < δ + rw [show r = NuclearUltrapower.densityRoot (finiteVectorDensityTensor w x) from rfl, + finiteVectorDensity_root_left n w hw] + exact ha (some i) + · intro j + rw [hsLeft_sub_right_norm] + have hj := hru j + change ‖NuclearUltrapower.hsConjugation _ r - r‖ ^ 2 < δ at hj + have hb : ‖NuclearUltrapower.hsConjugation + (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) r - r‖ ^ 2 < + (2 * δ) * ‖r‖ ^ 2 := by + nlinarith [mul_pos hδ (sub_pos.mpr hr2)] + change ‖NuclearUltrapower.hsConjugation _ (c • r) - c • r‖ ^ 2 < 2 * δ + rw [map_smul, ← smul_sub, norm_smul] + simp only [c, Complex.norm_real, Real.norm_of_nonneg (inv_nonneg.mpr hr.le), mul_pow, inv_pow] + exact (inv_mul_lt_iff₀ (sq_pos_of_pos hr)).mpr (by simpa only [mul_comm] using hb) + +/-- The finite tracial approximation with a single prescribed error tolerance. -/ +theorem expectation_spatial_finite_approximation (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (a : I → selfAdjoint M.toStarSubalgebra) (u : J → unitary M.toStarSubalgebra) + {ε : ℝ} (hε : 0 < ε) : + ∃ z : NuclearUltrapower.HilbertSchmidt H, ‖z‖ = 1 ∧ + 0 ≤ NuclearUltrapower.hsOperator z ∧ + (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator z y ∈ F) ∧ + (∀ i, |(τ.functional (a i)).re - + (inner ℂ z (densityLeftRepresentation + (((a i : M.toStarSubalgebra) : H →L[ℂ] H)) z)).re| < ε) ∧ + ∀ j, ‖hsLeftUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z - + hsRightUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z‖ ^ 2 < ε := by + classical + let D := 1 + ∑ i, |(τ.functional (a i)).re| + have hD : 1 ≤ D := by + dsimp only [D] + exact le_add_of_nonneg_right (Finset.sum_nonneg (fun _ _ => abs_nonneg _)) + have hD0 : 0 < D := lt_of_lt_of_le zero_lt_one hD + let δ := min (1 / 2) (ε / (4 * D)) + have hδ : 0 < δ := lt_min (by norm_num) (div_pos hε (by positivity)) + have hδhalf : δ ≤ 1 / 2 := min_le_left _ _ + have hδε : δ * (4 * D) ≤ ε := + (le_div_iff₀ (by positivity : 0 < 4 * D)).mp (min_le_right _ _) + have hδD : 2 * δ * D < ε := by + nlinarith [mul_pos hδ hD0] + obtain ⟨z, hzn, hzp, hzf, hza, hzu⟩ := + expectation_normalized_spatial_vectors M τ E hE hEr hEf a u hδ hδhalf + refine ⟨z, hzn, hzp, hzf, ?_, ?_⟩ + · intro i + have hi : 1 + |(τ.functional (a i)).re| ≤ D := by + dsimp only [D] + exact add_le_add (le_refl (1 : ℝ)) + (Finset.single_le_sum (f := fun j : I => |(τ.functional (a j)).re|) + (fun j _ => abs_nonneg _) (Finset.mem_univ i)) + exact (hza i).trans_le ((mul_le_mul_of_nonneg_left hi (by positivity)).trans hδD.le) + · intro j + exact (hzu j).trans_le ((le_mul_of_one_le_right (by positivity : 0 ≤ 2 * δ) hD).trans hδD.le) + +/-- The same finite witness, with the intertwining error measured in norm +rather than squared norm. This is the form used for tensor coefficients. -/ +theorem expectation_spatial_norm_approximation (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (a : I → selfAdjoint M.toStarSubalgebra) (u : J → unitary M.toStarSubalgebra) + {ε : ℝ} (hε : 0 < ε) : + ∃ z : NuclearUltrapower.HilbertSchmidt H, ‖z‖ = 1 ∧ + 0 ≤ NuclearUltrapower.hsOperator z ∧ + (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator z y ∈ F) ∧ + (∀ i, |(τ.functional (a i)).re - + (inner ℂ z (densityLeftRepresentation + (((a i : M.toStarSubalgebra) : H →L[ℂ] H)) z)).re| < ε) ∧ + ∀ j, ‖hsLeftUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z - + hsRightUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z‖ < ε := by + obtain ⟨z, hzn, hzp, hzf, hza, hzu⟩ := expectation_spatial_finite_approximation + M τ E hE hEr hEf a u (lt_min hε (sq_pos_of_pos hε)) + refine ⟨z, hzn, hzp, hzf, fun i => (hza i).trans_le (min_le_left _ _), ?_⟩ + intro j + have hsq := (hzu j).trans_le (min_le_right _ _) + nlinarith [norm_nonneg (hsLeftUnitary + (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z - + hsRightUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z)] + +lemma tracial_complex_coefficient_error_le (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (a : M.toStarSubalgebra) (z : NuclearUltrapower.HilbertSchmidt H) : + ‖τ.functional a - inner ℂ z (densityLeftRepresentation (a : H →L[ℂ] H) z)‖ ≤ + |(τ.functional (ℜ a)).re - (inner ℂ z + (densityLeftRepresentation ((ℜ a : M.toStarSubalgebra) : H →L[ℂ] H) z)).re| + + |(τ.functional (ℑ a)).re - (inner ℂ z + (densityLeftRepresentation ((ℑ a : M.toStarSubalgebra) : H →L[ℂ] H) z)).re| := by + let π := densityLeftRepresentation.comp M.toStarSubalgebra.subtype + exact complex_coefficient_error_le τ.functional.toLinearMap + (fun b => map_star τ.functional b) π.toLinearMap (fun b => map_star π b) a z + +/-- Complex tests require two self-adjoint tests, with the same finite-rank +vector serving both and the prescribed unitary family. -/ +theorem expectation_complex_spatial_approximation (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (a : I → M.toStarSubalgebra) (u : J → unitary M.toStarSubalgebra) + {ε : ℝ} (hε : 0 < ε) : + ∃ z : NuclearUltrapower.HilbertSchmidt H, ‖z‖ = 1 ∧ + 0 ≤ NuclearUltrapower.hsOperator z ∧ + (∃ F : Submodule ℂ H, FiniteDimensional ℂ F ∧ + ∀ y, NuclearUltrapower.hsOperator z y ∈ F) ∧ + (∀ i, ‖τ.functional (a i) - + inner ℂ z (densityLeftRepresentation (a i : H →L[ℂ] H) z)‖ < ε) ∧ + ∀ j, ‖hsLeftUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z - + hsRightUnitary (subalgebraUnitaryIsometry M.toStarSubalgebra (u j)) z‖ < ε := by + let tests : I × Bool → selfAdjoint M.toStarSubalgebra := fun p => + if p.2 then ℑ (a p.1) else ℜ (a p.1) + obtain ⟨z, hzn, hzp, hzf, hza, hzu⟩ := expectation_spatial_norm_approximation + M τ E hE hEr hEf tests u (half_pos hε) + refine ⟨z, hzn, hzp, hzf, ?_, fun j => (hzu j).trans (half_lt_self hε)⟩ + intro i + have hb := tracial_complex_coefficient_error_le M τ (a i) z + have hr := hza (i, false) + have hi := hza (i, true) + change |(τ.functional (ℜ (a i))).re - + (inner ℂ z (densityLeftRepresentation ((ℜ (a i) : M.toStarSubalgebra) : H →L[ℂ] H) z)).re| < ε / 2 at hr + change |(τ.functional (ℑ (a i))).re - + (inner ℂ z (densityLeftRepresentation ((ℑ (a i) : M.toStarSubalgebra) : H →L[ℂ] H) z)).re| < ε / 2 at hi + exact hb.trans_lt ((add_lt_add hr hi).trans_eq (by ring)) + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialMultiplication.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialMultiplication.lean new file mode 100644 index 0000000000000000000000000000000000000000..08443fab9002d577a7b28c7a286ac4088fe89bbf --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialMultiplication.lean @@ -0,0 +1,88 @@ +import OAI.Analysis.OperatorAlgebra.TracialSpatialState +import OAI.Analysis.OperatorAlgebra.TracialTensorVector + +namespace OAI + +/-! The finite tracial multiplication representation is continuous for the +spatial tensor norm when the represented von Neumann algebra admits a c.p. +expectation. -/ + +noncomputable section +open scoped TensorProduct InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def subalgebraOppositeHom (S : StarSubalgebra ℂ (H →L[ℂ] H)) : + Sᵐᵒᵖ →⋆ₐ[ℂ] (H →L[ℂ] H)ᵐᵒᵖ where + __ := S.subtype.toAlgHom.op + map_star' a := congrArg MulOpposite.op (map_star S.subtype a.unop) + +def tracialSpatialTensor (M : VonNeumannAlgebra H) : + M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ →⋆ₐ[ℂ] + (NuclearUltrapower.HilbertSchmidt H →L[ℂ] NuclearUltrapower.HilbertSchmidt H) := + Pureness.commutingStarTensorHom + (densityLeftRepresentation.comp M.toStarSubalgebra.subtype) + (densityRightRepresentation.comp (subalgebraOppositeHom M.toStarSubalgebra)) + (fun a b => densityLeftRight_commute (a : H →L[ℂ] H) (b.unop : H →L[ℂ] H)) + +@[simp] lemma tracialSpatialTensor_tmul (M : VonNeumannAlgebra H) + (a b : M.toStarSubalgebra) : + tracialSpatialTensor M (a ⊗ₜ[ℂ] MulOpposite.op b) = + densityLeftRepresentation (a : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op (b : H →L[ℂ] H)) := rfl + +variable (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + +def tracialMultiplicationTensor : + M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ →⋆ₐ[ℂ] + (τ.functional.GNS →L[ℂ] τ.functional.GNS) := + traceTensor τ.functional τ.tracial + +lemma tracialMultiplicationTensor_vector (a b : M.toStarSubalgebra) : + tracialMultiplicationTensor M τ (a ⊗ₜ[ℂ] MulOpposite.op b) + (τ.functional.toPreGNS 1 : τ.functional.GNS) = + (τ.functional.toPreGNS (a * b) : τ.functional.GNS) := + traceTensor_vector τ.functional τ.tracial a b + +lemma tracialMultiplicationTensor_cyclic : + DenseRange (fun z => tracialMultiplicationTensor M τ z + (τ.functional.toPreGNS 1 : τ.functional.GNS)) := + traceTensor_cyclic τ.functional τ.tracial + +lemma tracial_multiplication_norm_le_of_state + (φ : (NuclearUltrapower.HilbertSchmidt H →L[ℂ] + NuclearUltrapower.HilbertSchmidt H) →ₚ[ℂ] ℂ) + (hφ : ∀ a b : M.toStarSubalgebra, + φ (densityLeftRepresentation (a : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op (b : H →L[ℂ] H))) = + τ.functional (a * b)) + (z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + ‖tracialMultiplicationTensor M τ z‖ ≤ ‖tracialSpatialTensor M z‖ := by + have hp : ∀ a b : M.toStarSubalgebra, + φ (tracialSpatialTensor M (a ⊗ₜ[ℂ] MulOpposite.op b)) = τ.functional (a * b) := by + intro a b + rw [tracialSpatialTensor_tmul] + exact hφ a b + change ‖traceTensor τ.functional τ.tracial z‖ ≤ ‖tracialSpatialTensor M z‖ + exact traceTensor_norm_le τ.functional τ.tracial (tracialSpatialTensor M) φ hp z + +/-- The finite tracial part of the injectivity/semidiscreteness argument: +the diagonal multiplication representation is bounded by the spatial norm. -/ +theorem tracial_multiplication_norm_le + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) + (z : M.toStarSubalgebra ⊗[ℂ] M.toStarSubalgebraᵐᵒᵖ) : + ‖tracialMultiplicationTensor M τ z‖ ≤ ‖tracialSpatialTensor M z‖ := by + let hex := expectation_tracial_spatial_state (H := H) M τ E hE hEr hEf + exact tracial_multiplication_norm_le_of_state M τ hex.choose hex.choose_spec.2 z + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialState.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialState.lean new file mode 100644 index 0000000000000000000000000000000000000000..d378c18450583a680fcb1b5a5b3ec97b38ae8186 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialState.lean @@ -0,0 +1,63 @@ +import OAI.Analysis.OperatorAlgebra.TracialSpatialUnitaryState +import OAI.Analysis.PureInfiniteness.UnitarySpanEquality + +namespace OAI + +/-! The spatial diagonal state in the finite tracial injectivity argument. +The finite-vector argument follows Anantharaman--Delaroche, +Pacific J. Math. 171 (1995), Lemma 3.7 and Proposition 3.6, pp. 328--330. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma tracial_spatial_state_extend (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (φ : (NuclearUltrapower.HilbertSchmidt H →L[ℂ] + NuclearUltrapower.HilbertSchmidt H) →ₚ[ℂ] ℂ) + (hprod : ∀ (a : M.toStarSubalgebra) (u : unitary M.toStarSubalgebra), + φ (densityLeftRepresentation (a : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op ((u : M.toStarSubalgebra) : H →L[ℂ] H))) = + τ.functional (a * (u : M.toStarSubalgebra))) (a b : M.toStarSubalgebra) : + φ (densityLeftRepresentation (a : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op (b : H →L[ℂ] H))) = + τ.functional (a * b) := by + let L := densityLeftRepresentation (H := H) (a : H →L[ℂ] H) + let ρ : M.toStarSubalgebra →ₗ[ℂ] + (NuclearUltrapower.HilbertSchmidt H →L[ℂ] NuclearUltrapower.HilbertSchmidt H) := + (densityRightRepresentation (H := H)).toLinearMap.comp + ((MulOpposite.opLinearEquiv ℂ (M := H →L[ℂ] H)).toLinearMap.comp + M.toStarSubalgebra.subtype.toLinearMap) + let f : M.toStarSubalgebra →ₗ[ℂ] ℂ := + φ.toLinearMap.comp ((LinearMap.mulLeft ℂ L).comp ρ) + let g : M.toStarSubalgebra →ₗ[ℂ] ℂ := + τ.functional.toLinearMap.comp (LinearMap.mulLeft ℂ a) + have hunit : ∀ u : unitary M.toStarSubalgebra, f u = g u := fun u => hprod a u + exact congrArg (fun k : M.toStarSubalgebra →ₗ[ℂ] ℂ => k b) + (linearMap_ext_unitaries f g hunit) + +/-- The trace diagonal is realized by an actual spatial state. -/ +theorem expectation_tracial_spatial_state (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) : + ∃ φ : (NuclearUltrapower.HilbertSchmidt H →L[ℂ] + NuclearUltrapower.HilbertSchmidt H) →ₚ[ℂ] ℂ, + φ 1 = 1 ∧ ∀ a b : M.toStarSubalgebra, + φ (densityLeftRepresentation (a : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op (b : H →L[ℂ] H))) = + τ.functional (a * b) := by + obtain ⟨φ, hφ, hprod⟩ := expectation_tracial_spatial_unitary_state M τ E hE hEr hEf + exact ⟨φ, hφ, tracial_spatial_state_extend M τ φ hprod⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialUnitaryState.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialUnitaryState.lean new file mode 100644 index 0000000000000000000000000000000000000000..ce82afa88f85f5ea040f667e233e9d4bd6566bbe --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialSpatialUnitaryState.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.OperatorAlgebra.TracialProductApproximation +import OAI.Analysis.Nuclearity.SpatialStateUltralimit + +namespace OAI + +/-! The spatial diagonal state in the finite tracial injectivity argument. +The finite-vector argument follows Anantharaman--Delaroche, +Pacific J. Math. 171 (1995), Lemma 3.7 and Proposition 3.6, pp. 328--330. -/ + +noncomputable section +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +theorem expectation_tracial_spatial_unitary_state (M : VonNeumannAlgebra H) + [PartialOrder M.toStarSubalgebra] [StarOrderedRing M.toStarSubalgebra] + (τ : Pureness.TracialState M.toStarSubalgebra) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEr : ∀ T, E T ∈ M) + (hEf : ∀ T, T ∈ M → E T = T) : + ∃ φ : (NuclearUltrapower.HilbertSchmidt H →L[ℂ] + NuclearUltrapower.HilbertSchmidt H) →ₚ[ℂ] ℂ, + φ 1 = 1 ∧ ∀ (a : M.toStarSubalgebra) (u : unitary M.toStarSubalgebra), + φ (densityLeftRepresentation (a : H →L[ℂ] H) * + densityRightRepresentation (MulOpposite.op ((u : M.toStarSubalgebra) : H →L[ℂ] H))) = + τ.functional (a * (u : M.toStarSubalgebra)) := by + classical + let T (p : M.toStarSubalgebra × unitary M.toStarSubalgebra) := + densityLeftRepresentation (p.1 : H →L[ℂ] H) * + densityRightRepresentation + (MulOpposite.op ((p.2 : M.toStarSubalgebra) : H →L[ℂ] H)) + let c (p : M.toStarSubalgebra × unitary M.toStarSubalgebra) := + τ.functional (p.1 * (p.2 : M.toStarSubalgebra)) + have happrox (s : Finset (M.toStarSubalgebra × unitary M.toStarSubalgebra)) + (ε : ℝ) (hε : 0 < ε) : + ∃ ξ : NuclearUltrapower.HilbertSchmidt H, ‖ξ‖ = 1 ∧ + ∀ p ∈ s, ‖inner ℂ ξ (T p ξ) - c p‖ < ε := by + obtain ⟨ξ, hξ, _, _, htest⟩ := expectation_spatial_product_approximation + M τ E hE hEr hEf (fun p : s => p.val.1) (fun p : s => p.val.2) hε + refine ⟨ξ, hξ, ?_⟩ + intro p hp + exact htest ⟨p, hp⟩ + obtain ⟨φ, hφ, hprod⟩ := exists_spatial_state_of_finite_approximation T c happrox + exact ⟨φ, hφ, fun a u => hprod (a, u)⟩ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialStatePullback.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialStatePullback.lean new file mode 100644 index 0000000000000000000000000000000000000000..ddb508c68b5052ca43effdc3bbc72635cf1ae6aa --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialStatePullback.lean @@ -0,0 +1,43 @@ +import OAI.Analysis.TracialSplitting.ChallengeDefinitions + +namespace OAI + +/-! Pullback of a tracial state by a unital star homomorphism. -/ +noncomputable section +open scoped ComplexOrder + +namespace WeakPureInfiniteness + +variable {C D : Type*} [CStarAlgebra C] [CStarAlgebra D] + [PartialOrder C] [StarOrderedRing C] [PartialOrder D] [StarOrderedRing D] + +def tracialStatePullback (τ : Pureness.TracialState D) (f : C →⋆ₐ[ℂ] D) : + Pureness.TracialState C where + functional := PositiveLinearMap.mk₀ (τ.functional.toLinearMap.comp f.toLinearMap) + (fun _ ha => τ.functional.map_nonneg (map_nonneg f ha)) + normalized := by + change τ.functional (f 1) = 1 + rw [map_one, τ.normalized] + tracial a b := by + change τ.functional (f (a * b)) = τ.functional (f (b * a)) + simp only [map_mul f] + exact τ.tracial (f a) (f b) + +lemma tracialStatePullback_apply (τ : Pureness.TracialState D) (f : C →⋆ₐ[ℂ] D) + (a : C) : (tracialStatePullback τ f).functional a = τ.functional (f a) := rfl + +lemma tracialStatePullback_faithful (τ : Pureness.TracialState D) (f : C →⋆ₐ[ℂ] D) + (hf : Function.Injective f) + (hτ : ∀ a, τ.functional (star a * a) = 0 → a = 0) + (a : C) (ha : (tracialStatePullback τ f).functional (star a * a) = 0) : a = 0 := by + apply hf + have he : f a = 0 := hτ (f a) (by + change τ.functional (f (star a * a)) = 0 at ha + simpa only [map_mul f, map_star f] using ha) + exact he.trans (map_zero f).symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialTensorCompletion.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialTensorCompletion.lean new file mode 100644 index 0000000000000000000000000000000000000000..b10f8f82c981d74031e5b1cdb93740ffe9e1734a --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialTensorCompletion.lean @@ -0,0 +1,66 @@ +import OAI.Analysis.OperatorAlgebra.TracialTensorVector +import OAI.Analysis.Nuclearity.MinimalTensorExtension + +namespace OAI + +/-! Completion of a tracial tensor representation that is continuous for +the minimal tensor norm. -/ + +noncomputable section +open scoped TensorProduct ComplexOrder + +namespace WeakPureInfiniteness + +variable {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + (f : A →ₚ[ℂ] ℂ) (ht : ∀ a b, f (a * b) = f (b * a)) + (hn : ∀ z : A ⊗[ℂ] Aᵐᵒᵖ, ‖traceTensor f ht z‖ ≤ ‖minimalAlgebraicLinear z‖) + +omit [PartialOrder A] [StarOrderedRing A] in +lemma tracialTensorAlgebraic_mul (z w : A ⊗[ℂ] Aᵐᵒᵖ) : + minimalAlgebraicLinear (z * w) = minimalAlgebraicLinear z * minimalAlgebraicLinear w := by + induction z using TensorProduct.inductionOn with + | tmul a b => + induction w using TensorProduct.inductionOn with + | tmul c d => + simp only [Algebra.TensorProduct.tmul_mul_tmul, minimalAlgebraicLinear_tmul, + minimalElementary_mul] + | add x y hx hy => simp only [mul_add, map_add, hx, hy] + | add x y hx hy => simp only [add_mul, map_add, hx, hy] + +omit [PartialOrder A] [StarOrderedRing A] in +lemma tracialTensorAlgebraic_star (z : A ⊗[ℂ] Aᵐᵒᵖ) : + minimalAlgebraicLinear (star z) = star (minimalAlgebraicLinear z) := by + induction z using TensorProduct.inductionOn with + | tmul a b => + simp only [TensorProduct.star_tmul, minimalAlgebraicLinear_tmul, minimalElementary_star] + | add x y hx hy => simp only [star_add, map_add, hx, hy] + +@[irreducible] def tracialTensorMinimal : + MinimalTensor A Aᵐᵒᵖ →⋆ₙₐ[ℂ] (f.GNS →L[ℂ] f.GNS) := + denseLinearStarCompletion (minimalAlgebraicLinear (A := A) (B := Aᵐᵒᵖ)) + (traceTensor f ht).toLinearMap minimalAlgebraicLinear_dense + tracialTensorAlgebraic_mul (fun x y => map_mul (traceTensor f ht) x y) + tracialTensorAlgebraic_star (fun x => map_star (traceTensor f ht) x) hn + +lemma tracialTensorMinimal_algebraic (z : A ⊗[ℂ] Aᵐᵒᵖ) : + tracialTensorMinimal f ht hn (minimalAlgebraicLinear z) = traceTensor f ht z := by + unfold tracialTensorMinimal + exact denseLinearStarCompletion_apply _ _ _ _ _ _ _ _ z + +lemma traceTensor_elementary (a b : A) : + traceTensor f ht (a ⊗ₜ[ℂ] MulOpposite.op b) = + f.gnsStarAlgHom a * NuclearTrace.rightGNS f ht (MulOpposite.op b) := by + unfold traceTensor + rfl + +@[simp] lemma tracialTensorMinimal_elementary (a b : A) : + tracialTensorMinimal f ht hn (minimalElementary a (MulOpposite.op b)) = + f.gnsStarAlgHom a * NuclearTrace.rightGNS f ht (MulOpposite.op b) := by + rw [← minimalAlgebraicLinear_tmul, tracialTensorMinimal_algebraic, + traceTensor_elementary] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialTensorFiniteSum.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialTensorFiniteSum.lean new file mode 100644 index 0000000000000000000000000000000000000000..07a3813e32f0c92a777f029b506ae6bc98074bfe --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialTensorFiniteSum.lean @@ -0,0 +1,31 @@ +import OAI.Analysis.OperatorAlgebra.TracialTensorVector +import OAI.Analysis.OperatorAlgebra.GNSBundledOperators + +namespace OAI + +/-! The algebraic tracial representation on finite tensor sums. -/ +noncomputable section +open scoped TensorProduct ComplexOrder +namespace WeakPureInfiniteness + +variable {A : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + +lemma traceTensor_sum (f : A →ₚ[ℂ] ℂ) (ht : ∀ a b, f (a * b) = f (b * a)) + {I : Type*} [Fintype I] (a b : I → A) : + traceTensor f ht (∑ i, a i ⊗ₜ[ℂ] MulOpposite.op (b i)) = + ∑ i, f.gnsStarAlgHom (a i) * NuclearTrace.rightGNS f ht (MulOpposite.op (b i)) := by + unfold traceTensor + simp only [map_sum, Pureness.commutingStarTensorHom_tmul] + +lemma norm_traceTensor_sum (f : A →ₚ[ℂ] ℂ) (ht : ∀ a b, f (a * b) = f (b * a)) + {I : Type*} [Fintype I] (a b : I → A) : + ‖traceTensor f ht (∑ i, a i ⊗ₜ[ℂ] MulOpposite.op (b i))‖ = + ‖∑ i, gnsBundledLeft f (a i) * gnsBundledRight f ht (b i)‖ := by + rw [traceTensor_sum] + rfl + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/TracialTensorVector.lean b/lean/OAI/Analysis/OperatorAlgebra/TracialTensorVector.lean new file mode 100644 index 0000000000000000000000000000000000000000..21070651f5cd074b716703e7cb9106c4c0767d6f --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/TracialTensorVector.lean @@ -0,0 +1,102 @@ +import OAI.Analysis.TracialSplitting.GNSRepresentations +import OAI.Analysis.OperatorAlgebra.CyclicStateNorm + +namespace OAI + +/-! The cyclic vector argument for the algebraic tracial multiplication +representation. -/ + +noncomputable section +open scoped TensorProduct InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {A B : Type*} [CStarAlgebra A] [PartialOrder A] [StarOrderedRing A] + [CStarAlgebra B] [PartialOrder B] [StarOrderedRing B] + (f : A →ₚ[ℂ] ℂ) (ht : ∀ a b, f (a * b) = f (b * a)) + +@[irreducible] def traceTensor : A ⊗[ℂ] Aᵐᵒᵖ →⋆ₐ[ℂ] (f.GNS →L[ℂ] f.GNS) := + Pureness.commutingStarTensorHom f.gnsStarAlgHom + (NuclearTrace.rightGNS f ht) (NuclearTrace.left_right_commute f ht) + +lemma traceTensor_vector (a b : A) : + traceTensor f ht (a ⊗ₜ[ℂ] MulOpposite.op b) (f.toPreGNS 1 : f.GNS) = + (f.toPreGNS (a * b) : f.GNS) := by + unfold traceTensor + change f.gnsStarAlgHom a + (NuclearTrace.rightGNS f ht (MulOpposite.op b) (f.toPreGNS 1 : f.GNS)) = _ + simp [PositiveLinearMap.gnsStarAlgHom, PositiveLinearMap.leftMulMapPreGNS] + +lemma traceTensor_cyclic : + DenseRange (fun z => traceTensor f ht z (f.toPreGNS 1 : f.GNS)) := by + have hd : DenseRange (fun x : f.PreGNS => (x : f.GNS)) := + UniformSpace.Completion.denseRange_coe + apply hd.mono + rintro _ ⟨x, rfl⟩ + refine ⟨f.ofPreGNS x ⊗ₜ[ℂ] MulOpposite.op (1 : A), ?_⟩ + change traceTensor f ht (f.ofPreGNS x ⊗ₜ[ℂ] MulOpposite.op 1) + (f.toPreGNS 1 : f.GNS) = (x : f.GNS) + rw [traceTensor_vector, mul_one, PositiveLinearMap.toPreGNS_ofPreGNS] + +omit [StarOrderedRing B] in +lemma traceTensor_vector_state (q : A ⊗[ℂ] Aᵐᵒᵖ →⋆ₐ[ℂ] B) (φ : B →ₚ[ℂ] ℂ) + (hφ : ∀ a b : A, φ (q (a ⊗ₜ[ℂ] MulOpposite.op b)) = f (a * b)) + (w : A ⊗[ℂ] Aᵐᵒᵖ) : + φ (q w) = inner ℂ (f.toPreGNS 1 : f.GNS) + (traceTensor f ht w (f.toPreGNS 1)) := by + induction w using TensorProduct.inductionOn with + | tmul a b => + have he : φ (q (a ⊗ₜ[ℂ] MulOpposite.op b.unop)) = + inner ℂ (f.toPreGNS 1 : f.GNS) + (traceTensor f ht (a ⊗ₜ[ℂ] MulOpposite.op b.unop) (f.toPreGNS 1)) := by + rw [hφ, traceTensor_vector, UniformSpace.Completion.inner_coe, + PositiveLinearMap.preGNS_inner_def] + simp only [PositiveLinearMap.ofPreGNS_toPreGNS, star_one, one_mul] + simpa only [MulOpposite.op_unop] using he + | add x y hx hy => + simp only [map_add, add_apply, inner_add_right, hx, hy] + +lemma traceTensor_vector_norm (q : A ⊗[ℂ] Aᵐᵒᵖ →⋆ₐ[ℂ] B) (φ : B →ₚ[ℂ] ℂ) + (hφ : ∀ a b : A, φ (q (a ⊗ₜ[ℂ] MulOpposite.op b)) = f (a * b)) + (z : A ⊗[ℂ] Aᵐᵒᵖ) : + ‖traceTensor f ht z (f.toPreGNS 1 : f.GNS)‖ = ‖φ.toPreGNS (q z)‖ := by + rw [PositiveLinearMap.preGNS_norm_def, + PositiveLinearMap.ofPreGNS_toPreGNS, ← map_star q, ← map_mul q, + traceTensor_vector_state f ht q φ hφ] + simp only [map_mul, map_star, mul_apply_eq_comp, + ContinuousLinearMap.star_eq_adjoint, ContinuousLinearMap.adjoint_inner_right] + have hn : (inner ℂ (traceTensor f ht z (f.toPreGNS 1 : f.GNS)) + (traceTensor f ht z (f.toPreGNS 1 : f.GNS))).re = + ‖traceTensor f ht z (f.toPreGNS 1 : f.GNS)‖ ^ 2 := + inner_self_eq_norm_sq (𝕜 := ℂ) _ + rw [hn, Real.sqrt_sq (norm_nonneg _)] + +lemma traceTensor_norm_le (q : A ⊗[ℂ] Aᵐᵒᵖ →⋆ₐ[ℂ] B) (φ : B →ₚ[ℂ] ℂ) + (hφ : ∀ a b : A, φ (q (a ⊗ₜ[ℂ] MulOpposite.op b)) = f (a * b)) + (z : A ⊗[ℂ] Aᵐᵒᵖ) : ‖traceTensor f ht z‖ ≤ ‖q z‖ := by + have hn := traceTensor_vector_norm f ht q φ hφ + have hm : ‖φ.leftMulMapPreGNS (q z)‖ ≤ ‖q z‖ := by + unfold PositiveLinearMap.leftMulMapPreGNS + exact LinearMap.mkContinuous_norm_le _ (norm_nonneg _) _ + apply (traceTensor f ht z).opNorm_le_bound (norm_nonneg _) + refine isClosed_property (traceTensor_cyclic f ht) + (isClosed_le (by fun_prop) (by fun_prop)) ?_ + intro b + calc + ‖traceTensor f ht z (traceTensor f ht b (f.toPreGNS 1 : f.GNS))‖ = + ‖traceTensor f ht (z * b) (f.toPreGNS 1 : f.GNS)‖ := by rw [map_mul]; rfl + _ = ‖φ.toPreGNS (q (z * b))‖ := hn (z * b) + _ = ‖φ.leftMulMapPreGNS (q z) (φ.toPreGNS (q b))‖ := by + simp only [map_mul, PositiveLinearMap.leftMulMapPreGNS_apply, + PositiveLinearMap.ofPreGNS_toPreGNS] + _ ≤ ‖φ.leftMulMapPreGNS (q z)‖ * ‖φ.toPreGNS (q b)‖ := + (φ.leftMulMapPreGNS (q z)).le_opNorm _ + _ ≤ ‖q z‖ * ‖φ.toPreGNS (q b)‖ := + mul_le_mul_of_nonneg_right hm (norm_nonneg _) + _ = ‖q z‖ * ‖traceTensor f ht b (f.toPreGNS 1 : f.GNS)‖ := by rw [hn b] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanCP.lean b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanCP.lean new file mode 100644 index 0000000000000000000000000000000000000000..7e3ec05ed4b81137892fc7701d496aab69b5f72b --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanCP.lean @@ -0,0 +1,74 @@ +import OAI.Analysis.OperatorAlgebra.UnitaryMeanProperties +import OAI.Analysis.OperatorAlgebra.FiniteHilbertCompression +import OAI.Analysis.Nuclearity.MatrixCPMapExtension + +namespace OAI + +/-! The concrete unitary-orbit average is unital and completely positive, +and hence contractive. -/ + +noncomputable section +open Filter +open scoped InnerProductSpace ComplexOrder CStarAlgebra + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +omit [CompleteSpace H] in +private lemma orbitMatrix_inner {n : ℕ} + (M : CStarMatrix (Fin n) (Fin n) (H →L[ℂ] H)) + (x : PiLp 2 (fun _ : Fin n => H)) : + inner ℂ (matrixOperator M x) x = ∑ j, ∑ k, inner ℂ (M j k (x k)) (x j) := by + simp only [PiLp.inner_apply, matrixOperator_apply, sum_inner] + +lemma unitaryOrbitMeanCLM_cp (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) : + CompletelyPositive (unitaryOrbitMeanCLM ω U hU) := by + intro n M hM + apply (NonUnitalStarAlgHom.map_le_map_iff + (matrixOperatorHom (n := Fin n) (H := H)) matrixOperator_injective).mp + rw [map_zero] + apply ContinuousLinearMap.nonneg_iff_isPositive.mpr + rw [ContinuousLinearMap.isPositive_iff_complex] + intro x + let f (j k : Fin n) := unitaryOrbitCoefficient U hU (M j k) (x k) (x j) + have hsum : complexSymmetricMean ω (∑ j, ∑ k, f j k) = + ∑ j, ∑ k, complexSymmetricMean ω (f j k) := by + change complexSymmetricMeanCLM ω (∑ j, ∑ k, f j k) = _ + simp only [map_sum] + rfl + have hn : 0 ≤ inner ℂ (matrixOperator (matrixLinearMap (unitaryOrbitMeanCLM ω U hU) M) x) x := by + rw [orbitMatrix_inner] + simp only [matrixLinearMap_apply] + change 0 ≤ ∑ j, ∑ k, inner ℂ (unitaryOrbitMean ω U hU (M j k) (x k)) (x j) + simp_rw [unitaryOrbitMean_inner] + change 0 ≤ ∑ j, ∑ k, complexSymmetricMean ω (f j k) + rw [← hsum] + apply complexSymmetricMean_nonneg ω hω + intro t + let y : PiLp 2 (fun _ : Fin n => H) := WithLp.toLp 2 (fun k => U t (x k)) + have hp : 0 ≤ matrixOperator M := map_nonneg (matrixOperatorHom (n := Fin n) (H := H)) hM + have hy := (ContinuousLinearMap.nonneg_iff_isPositive.mp hp).inner_nonneg_left y + rw [orbitMatrix_inner] at hy + simpa only [BoundedContinuousFunction.sum_apply, f, unitaryOrbitCoefficient_apply, + y] using hy + exact ⟨Complex.ext rfl hn.2, hn.1⟩ + +lemma unitaryOrbitMeanCLM_one (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) : + unitaryOrbitMeanCLM ω U hU 1 = 1 := + unitaryOrbitMean_fix ω hω U hU 1 (fun _ _ => rfl) + +lemma unitaryOrbitMeanCLM_norm_le (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) : + ‖unitaryOrbitMeanCLM ω U hU‖ ≤ 1 := by + apply cp_norm_le_one_of_one _ (unitaryOrbitMeanCLM_cp ω hω U hU) + rw [unitaryOrbitMeanCLM_one ω hω U hU] + exact ContinuousLinearMap.norm_id_le + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanExpectation.lean b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanExpectation.lean new file mode 100644 index 0000000000000000000000000000000000000000..258d2036ffa12e3574691ec96ff41156b9ebb622 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanExpectation.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.OperatorAlgebra.UnitaryMeanRange +import OAI.Analysis.Nuclearity.NuclearCommutantExpectation + +namespace OAI + +/-! Real-action averaging of a cpc projection onto an invariant von Neumann +algebra gives a cpc projection onto its fixed-point algebra. This follows +Anantharaman-Delaroche, Pacific J. Math. 171 (1995), Proposition 3.6, p. 329. -/ + +noncomputable section +open Filter +open scoped InnerProductSpace ComplexOrder CStarAlgebra + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +theorem realAction_fixedPoint_expectation + (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) + (hadd : ∀ t s x, U (t + s) x = U t (U s x)) + (M : VonNeumannAlgebra H) + (E : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H)) + (hE : CompletelyPositive E) (hEn : ‖E‖ ≤ 1) + (hEr : ∀ T, E T ∈ M) (hEf : ∀ T, T ∈ M → E T = T) + (hconj : ∀ t T, T ∈ M → orbitConjugate (U t) T ∈ M) : + ∃ Q : (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H), + CompletelyPositive Q ∧ ‖Q‖ ≤ 1 ∧ + (∀ T, Q T ∈ M) ∧ + (∀ T s x, Q T (U s x) = U s (Q T x)) ∧ + (∀ T, T ∈ M → (∀ s x, T (U s x) = U s (T x)) → Q T = T) := by + let Q := (unitaryOrbitMeanCLM ω U hU).comp E + refine ⟨Q, completelyPositive_comp _ _ hE (unitaryOrbitMeanCLM_cp ω hω U hU), + ?_, ?_, ?_, ?_⟩ + · exact (ContinuousLinearMap.opNorm_comp_le _ _).trans + ((mul_le_mul (unitaryOrbitMeanCLM_norm_le ω hω U hU) hEn + (norm_nonneg E) zero_le_one).trans_eq (one_mul 1)) + · intro T + exact unitaryOrbitMean_mem ω U hU M (E T) (fun t => hconj t _ (hEr T)) + · intro T s x + exact (unitaryOrbitMean_commutes ω hω U hU hadd (E T) s x).symm + · intro T hT hc + change unitaryOrbitMean ω U hU (E T) = T + rw [hEf T hT] + exact unitaryOrbitMean_fix ω hω U hU T hc + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanProperties.lean b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanProperties.lean new file mode 100644 index 0000000000000000000000000000000000000000..52e672f4eb795a21197d268135c7b3190a14c589 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanProperties.lean @@ -0,0 +1,106 @@ +import OAI.Analysis.OperatorAlgebra.UnitaryOrbitMean + +namespace OAI + +/-! Linearity, positivity and the fixed points of unitary orbit averaging. -/ + +noncomputable section +open Filter +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +lemma unitaryOrbitMean_add (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T R : H →L[ℂ] H) : + unitaryOrbitMean ω U hU (T + R) = + unitaryOrbitMean ω U hU T + unitaryOrbitMean ω U hU R := by + apply ContinuousLinearMap.ext + intro x + apply ext_inner_right ℂ + intro y + simp only [add_apply, inner_add_left, unitaryOrbitMean_inner] + have h : unitaryOrbitCoefficient U hU (T + R) x y = + unitaryOrbitCoefficient U hU T x y + unitaryOrbitCoefficient U hU R x y := by + ext t + simp only [unitaryOrbitCoefficient_apply, add_apply, inner_add_left, + BoundedContinuousFunction.add_apply] + rw [h, complexSymmetricMean_add] + +lemma unitaryOrbitMean_smul (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (c : ℂ) (T : H →L[ℂ] H) : + unitaryOrbitMean ω U hU (c • T) = c • unitaryOrbitMean ω U hU T := by + apply ContinuousLinearMap.ext + intro x + apply ext_inner_right ℂ + intro y + simp only [smul_apply, inner_smul_left, unitaryOrbitMean_inner] + have h : unitaryOrbitCoefficient U hU (c • T) x y = + star c • unitaryOrbitCoefficient U hU T x y := by + ext t + simp only [unitaryOrbitCoefficient_apply, smul_apply, inner_smul_left, + BoundedContinuousFunction.smul_apply, smul_eq_mul, starRingEnd_apply] + rw [h, complexSymmetricMean_smul] + rfl + +def unitaryOrbitMeanCLM (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) : + (H →L[ℂ] H) →L[ℂ] (H →L[ℂ] H) := + ({ toFun := unitaryOrbitMean ω U hU + map_add' := unitaryOrbitMean_add ω U hU + map_smul' := unitaryOrbitMean_smul ω U hU } : + (H →L[ℂ] H) →ₗ[ℂ] (H →L[ℂ] H)).mkContinuous 2 + (unitaryOrbitMean_norm_le ω U hU) + +lemma unitaryOrbitMean_fix (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) + (T : H →L[ℂ] H) (hT : ∀ t x, T (U t x) = U t (T x)) : + unitaryOrbitMean ω U hU T = T := by + apply ContinuousLinearMap.ext + intro x + apply ext_inner_right ℂ + intro y + rw [unitaryOrbitMean_inner] + have h : unitaryOrbitCoefficient U hU T x y = + BoundedContinuousFunction.const ℝ (inner ℂ (T x) y) := by + ext t + simp only [unitaryOrbitCoefficient_apply, hT, LinearIsometryEquiv.inner_map_map, + BoundedContinuousFunction.const_apply] + rw [h, complexSymmetricMean_const ω hω] + +lemma unitaryOrbitMean_positive (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) + (T : H →L[ℂ] H) (hT : 0 ≤ T) : 0 ≤ unitaryOrbitMean ω U hU T := by + apply ContinuousLinearMap.nonneg_iff_isPositive.mpr + rw [ContinuousLinearMap.isPositive_iff_complex] + intro x + have hn : 0 ≤ inner ℂ (unitaryOrbitMean ω U hU T x) x := by + rw [unitaryOrbitMean_inner] + apply complexSymmetricMean_nonneg ω hω + intro t + exact (ContinuousLinearMap.nonneg_iff_isPositive.mp hT).inner_nonneg_left _ + exact ⟨Complex.ext rfl hn.2, hn.1⟩ + +lemma unitaryOrbitMean_commutes (ω : Ultrafilter ℕ) (hω : (ω : Filter ℕ) ≤ atTop) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) + (hadd : ∀ t s x, U (t + s) x = U t (U s x)) + (T : H →L[ℂ] H) (s : ℝ) (x : H) : + U s (unitaryOrbitMean ω U hU T x) = unitaryOrbitMean ω U hU T (U s x) := by + apply ext_inner_right ℂ + intro z + obtain ⟨y, rfl⟩ := (U s).surjective z + rw [(U s).inner_map_map, unitaryOrbitMean_inner, unitaryOrbitMean_inner] + have h : unitaryOrbitCoefficient U hU T (U s x) (U s y) = + complexTranslateBCF (unitaryOrbitCoefficient U hU T x y) s := by + ext t + change inner ℂ (T (U t (U s x))) (U t (U s y)) = + inner ℂ (T (U (t + s) x)) (U (t + s) y) + rw [hadd, hadd] + rw [h, complexSymmetricMean_translate ω hω] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanRange.lean b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanRange.lean new file mode 100644 index 0000000000000000000000000000000000000000..54674458e7971d8f47654d18b552abb08582d7a6 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/UnitaryMeanRange.lean @@ -0,0 +1,57 @@ +import OAI.Analysis.OperatorAlgebra.UnitaryMeanCP +import Mathlib.Analysis.VonNeumannAlgebra.Basic + +namespace OAI + +/-! Averaging stays in a von Neumann algebra whenever each conjugate does. +This uses the actual double-commutant condition on matrix coefficients. -/ + +noncomputable section +open Filter +open scoped InnerProductSpace ComplexOrder CStarAlgebra + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +def orbitConjugate (U : H ≃ₗᵢ[ℂ] H) (T : H →L[ℂ] H) : H →L[ℂ] H := + U.symm.toContinuousLinearEquiv.toContinuousLinearMap * T * + U.toContinuousLinearEquiv.toContinuousLinearMap + +omit [CompleteSpace H] in +lemma orbitConjugate_inner (U : H ≃ₗᵢ[ℂ] H) (T : H →L[ℂ] H) (x y : H) : + inner ℂ (orbitConjugate U T x) y = inner ℂ (T (U x)) (U y) := by + change inner ℂ (U.symm (T (U x))) y = _ + rw [U.symm.inner_map_eq_flip] + rfl + +theorem unitaryOrbitMean_mem (ω : Ultrafilter ℕ) + (U : ℝ → H ≃ₗᵢ[ℂ] H) (hU : ∀ x, Continuous (fun t => U t x)) + (M : VonNeumannAlgebra H) (T : H →L[ℂ] H) + (hT : ∀ t, orbitConjugate (U t) T ∈ M) : + unitaryOrbitMean ω U hU T ∈ M := by + rw [← M.commutant_commutant] + apply VonNeumannAlgebra.mem_commutant_iff.mpr + intro R hR + apply ContinuousLinearMap.ext + intro x + apply ext_inner_right ℂ + intro y + change inner ℂ (R (unitaryOrbitMean ω U hU T x)) y = + inner ℂ (unitaryOrbitMean ω U hU T (R x)) y + rw [← ContinuousLinearMap.adjoint_inner_right, unitaryOrbitMean_inner, + unitaryOrbitMean_inner] + apply congrArg (complexSymmetricMean ω) + ext t + change inner ℂ (T (U t x)) (U t (R.adjoint y)) = + inner ℂ (T (U t (R x))) (U t y) + rw [← orbitConjugate_inner, ← orbitConjugate_inner, + ContinuousLinearMap.adjoint_inner_right] + have hc := VonNeumannAlgebra.mem_commutant_iff.mp hR _ (hT t) + exact congrArg (fun A : H →L[ℂ] H => inner ℂ (A x) y) hc.symm + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/UnitaryOrbitMean.lean b/lean/OAI/Analysis/OperatorAlgebra/UnitaryOrbitMean.lean new file mode 100644 index 0000000000000000000000000000000000000000..891e7440f4a502a87a281c98a6f9510309cffad4 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/UnitaryOrbitMean.lean @@ -0,0 +1,131 @@ +import OAI.Analysis.OperatorAlgebra.ComplexSymmetricMean +import Mathlib.Analysis.InnerProductSpace.Adjoint + +namespace OAI + +/-! Averaging a strongly continuous unitary orbit using the concrete +symmetric-interval mean. The operator is reconstructed from its bounded +matrix coefficients; no normality of the averaging map is asserted. -/ + +noncomputable section +open Filter +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + +def unitaryOrbitCoefficient (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y : H) : + BoundedContinuousFunction ℝ ℂ := + BoundedContinuousFunction.ofNormedAddCommGroup + (fun t => inner ℂ (T (U t x)) (U t y)) + ((T.continuous.comp (hU x)).inner (hU y)) (‖T‖ * ‖x‖ * ‖y‖) (by + intro t + calc + ‖inner ℂ (T (U t x)) (U t y)‖ ≤ ‖T (U t x)‖ * ‖U t y‖ := norm_inner_le_norm _ _ + _ ≤ (‖T‖ * ‖U t x‖) * ‖U t y‖ := + mul_le_mul_of_nonneg_right (T.le_opNorm _) (norm_nonneg _) + _ = _ := by rw [(U t).norm_map, (U t).norm_map]) + +@[simp] lemma unitaryOrbitCoefficient_apply (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y : H) (t : ℝ) : + unitaryOrbitCoefficient U hU T x y t = inner ℂ (T (U t x)) (U t y) := rfl + +lemma unitaryOrbitCoefficient_norm_le (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y : H) : + ‖unitaryOrbitCoefficient U hU T x y‖ ≤ ‖T‖ * ‖x‖ * ‖y‖ := by + apply (BoundedContinuousFunction.norm_le (by positivity)).mpr + intro t + exact (norm_inner_le_norm _ _).trans (by + simpa only [LinearIsometryEquiv.norm_map] using + mul_le_mul_of_nonneg_right (T.le_opNorm (U t x)) (norm_nonneg (U t y))) + +private def unitaryMeanForm (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y : H) : ℂ := + complexSymmetricMean ω (unitaryOrbitCoefficient U hU T x y) + +private lemma unitaryMeanForm_add_right (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y z : H) : + unitaryMeanForm ω U hU T x (y + z) = + unitaryMeanForm ω U hU T x y + unitaryMeanForm ω U hU T x z := by + have h : unitaryOrbitCoefficient U hU T x (y + z) = + unitaryOrbitCoefficient U hU T x y + unitaryOrbitCoefficient U hU T x z := by + ext t + simp only [unitaryOrbitCoefficient_apply, map_add, inner_add_right, + BoundedContinuousFunction.add_apply] + exact (congrArg (complexSymmetricMean ω) h).trans (complexSymmetricMean_add ω _ _) + +private lemma unitaryMeanForm_smul_right (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y : H) (c : ℂ) : + unitaryMeanForm ω U hU T x (c • y) = c * unitaryMeanForm ω U hU T x y := by + have h : unitaryOrbitCoefficient U hU T x (c • y) = + c • unitaryOrbitCoefficient U hU T x y := by + ext t + simp only [unitaryOrbitCoefficient_apply, map_smul, inner_smul_right, + BoundedContinuousFunction.smul_apply, smul_eq_mul] + exact (congrArg (complexSymmetricMean ω) h).trans (complexSymmetricMean_smul ω _ _) + +private lemma unitaryMeanForm_bound (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y : H) : + ‖unitaryMeanForm ω U hU T x y‖ ≤ (2 * ‖T‖ * ‖x‖) * ‖y‖ := by + exact (complexSymmetricMean_norm_le ω _).trans + ((mul_le_mul_of_nonneg_left (unitaryOrbitCoefficient_norm_le U hU T x y) + (by norm_num)).trans_eq (by ring)) + +private def unitaryMeanFunctional (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x : H) : H →L[ℂ] ℂ := + ({ toFun := unitaryMeanForm ω U hU T x + map_add' := unitaryMeanForm_add_right ω U hU T x + map_smul' := fun c y => unitaryMeanForm_smul_right ω U hU T x y c } : H →ₗ[ℂ] ℂ).mkContinuous + (2 * ‖T‖ * ‖x‖) (unitaryMeanForm_bound ω U hU T x) + +variable [CompleteSpace H] + +private def unitaryMeanLinear (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) : H →ₗ[ℂ] H where + toFun x := (InnerProductSpace.toDual ℂ H).symm (unitaryMeanFunctional ω U hU T x) + map_add' x z := by + apply ext_inner_right ℂ + intro y + simp only [InnerProductSpace.toDual_symm_apply, inner_add_left] + have h : unitaryOrbitCoefficient U hU T (x + z) y = + unitaryOrbitCoefficient U hU T x y + unitaryOrbitCoefficient U hU T z y := by + ext t + simp only [unitaryOrbitCoefficient_apply, map_add, inner_add_left, + BoundedContinuousFunction.add_apply] + exact (congrArg (complexSymmetricMean ω) h).trans (complexSymmetricMean_add ω _ _) + map_smul' c x := by + apply ext_inner_right ℂ + intro y + simp only [InnerProductSpace.toDual_symm_apply, inner_smul_left, RingHom.id_apply] + have h : unitaryOrbitCoefficient U hU T (c • x) y = + star c • unitaryOrbitCoefficient U hU T x y := by + ext t + simp only [unitaryOrbitCoefficient_apply, map_smul, inner_smul_left, + BoundedContinuousFunction.smul_apply, smul_eq_mul, starRingEnd_apply] + exact (congrArg (complexSymmetricMean ω) h).trans (complexSymmetricMean_smul ω _ _) + +def unitaryOrbitMean (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) : H →L[ℂ] H := + (unitaryMeanLinear ω U hU T).mkContinuous (2 * ‖T‖) (fun x => by + change ‖(InnerProductSpace.toDual ℂ H).symm (unitaryMeanFunctional ω U hU T x)‖ ≤ _ + rw [LinearIsometryEquiv.norm_map] + exact LinearMap.mkContinuous_norm_le _ (by positivity) _) + +lemma unitaryOrbitMean_inner (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) (x y : H) : + inner ℂ (unitaryOrbitMean ω U hU T x) y = + complexSymmetricMean ω (unitaryOrbitCoefficient U hU T x y) := + InnerProductSpace.toDual_symm_apply + +lemma unitaryOrbitMean_norm_le (ω : Ultrafilter ℕ) (U : ℝ → H ≃ₗᵢ[ℂ] H) + (hU : ∀ x, Continuous (fun t => U t x)) (T : H →L[ℂ] H) : + ‖unitaryOrbitMean ω U hU T‖ ≤ 2 * ‖T‖ := + LinearMap.mkContinuous_norm_le _ (by positivity) _ + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/VectorLpMultiplier.lean b/lean/OAI/Analysis/OperatorAlgebra/VectorLpMultiplier.lean new file mode 100644 index 0000000000000000000000000000000000000000..500b37e1c615e267d3fd8c839a105a3ac7e57a85 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/VectorLpMultiplier.lean @@ -0,0 +1,161 @@ +import OAI.Analysis.ModularTheory.DualUnitary + +namespace OAI + +/-! Scalar multiplication on vector-valued L², for the regular translation +functional calculus in the modular core. -/ + +noncomputable section +open MeasureTheory Filter +open scoped InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + (μ : Measure ℝ) + +lemma boundedVectorLp_mem (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp H 2 μ) : + MemLp (fun t => b t • f t) 2 μ := + (Lp.memLp f).of_le_mul (hb.smul (Lp.aestronglyMeasurable f)) + (Eventually.of_forall fun t => by + rw [norm_smul] + exact mul_le_mul_of_nonneg_right (hC t) (norm_nonneg _)) + +def boundedVectorLpApply (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp H 2 μ) : Lp H 2 μ := + (boundedVectorLp_mem μ b hb C hC f).toLp (fun t => b t • f t) + +lemma boundedVectorLpApply_ae (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp H 2 μ) : + boundedVectorLpApply μ b hb C hC f =ᵐ[μ] fun t => b t • f t := + MemLp.coeFn_toLp _ + +def boundedVectorLpLinear (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) : Lp H 2 μ →ₗ[ℂ] Lp H 2 μ where + toFun := boundedVectorLpApply μ b hb C hC + map_add' f g := by + apply Lp.ext + filter_upwards [boundedVectorLpApply_ae μ b hb C hC (f + g), + boundedVectorLpApply_ae μ b hb C hC f, + boundedVectorLpApply_ae μ b hb C hC g, Lp.coeFn_add f g, + Lp.coeFn_add (boundedVectorLpApply μ b hb C hC f) + (boundedVectorLpApply μ b hb C hC g)] with t hfg hf hg ha he + simp only [hfg, ha, he, Pi.add_apply, hf, hg, smul_add] + map_smul' c f := by + apply Lp.ext + filter_upwards [boundedVectorLpApply_ae μ b hb C hC (c • f), + boundedVectorLpApply_ae μ b hb C hC f, Lp.coeFn_smul c f, + Lp.coeFn_smul c (boundedVectorLpApply μ b hb C hC f)] with t hcf hf ha he + simp only [hcf, ha, he, hf, Pi.smul_apply, RingHom.id_apply] + exact smul_comm _ _ _ + +def boundedVectorLp (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) : Lp H 2 μ →L[ℂ] Lp H 2 μ := + (boundedVectorLpLinear μ b hb C hC).mkContinuous C (fun f => + Lp.norm_le_mul_norm_of_ae_le_mul (by + filter_upwards [boundedVectorLpApply_ae μ b hb C hC f] with t ht + change ‖boundedVectorLpApply μ b hb C hC f t‖ ≤ C * ‖f t‖ + rw [ht, norm_smul] + exact mul_le_mul_of_nonneg_right (hC t) (norm_nonneg _))) + +lemma boundedVectorLp_ae (b : ℝ → ℂ) (hb : AEStronglyMeasurable b μ) + (C : ℝ) (hC : ∀ t, ‖b t‖ ≤ C) (f : Lp H 2 μ) : + boundedVectorLp μ b hb C hC f =ᵐ[μ] fun t => b t • f t := + boundedVectorLpApply_ae μ b hb C hC f + +def vectorLpMultiplier (b : BoundedContinuousFunction ℝ ℂ) : Lp H 2 μ →L[ℂ] Lp H 2 μ := + boundedVectorLp μ b b.continuous.aestronglyMeasurable ‖b‖ b.norm_coe_le_norm + +lemma vectorLpMultiplier_ae (b : BoundedContinuousFunction ℝ ℂ) (f : Lp H 2 μ) : + vectorLpMultiplier μ b f =ᵐ[μ] fun t => b t • f t := boundedVectorLp_ae μ _ _ _ _ _ + +lemma vectorLpMultiplier_mul (a b : BoundedContinuousFunction ℝ ℂ) : + vectorLpMultiplier (H := H) μ (a * b) = vectorLpMultiplier μ a * vectorLpMultiplier μ b := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [vectorLpMultiplier_ae μ (a * b) f, + vectorLpMultiplier_ae μ a (vectorLpMultiplier μ b f), + vectorLpMultiplier_ae μ b f] with t hab ha hb + change (vectorLpMultiplier μ (a * b) f) t = + (vectorLpMultiplier μ a (vectorLpMultiplier μ b f)) t + rw [hab, ha, hb] + exact mul_smul _ _ _ + +lemma vectorLpMultiplier_one : vectorLpMultiplier (H := H) μ 1 = 1 := by + apply ContinuousLinearMap.ext + intro f + change vectorLpMultiplier μ 1 f = f + apply Lp.ext + filter_upwards [vectorLpMultiplier_ae μ 1 f] with t ht + simpa only [BoundedContinuousFunction.coe_one, Pi.one_apply, one_smul] using ht + +variable [CompleteSpace H] + +lemma vectorLpMultiplier_star (a : BoundedContinuousFunction ℝ ℂ) : + vectorLpMultiplier (H := H) μ (star a) = star (vectorLpMultiplier (H := H) μ a) := by + apply (ContinuousLinearMap.eq_adjoint_iff _ _).mpr + intro f g + simp only [L2.inner_def] + apply integral_congr_ae + filter_upwards [vectorLpMultiplier_ae μ (star a) f, + vectorLpMultiplier_ae μ a g] with t hf hg + rw [hf, hg] + simp only [BoundedContinuousFunction.coe_star, Pi.star_apply, + inner_smul_left, inner_smul_right, starRingEnd_apply, star_star] + +/-- Bounded continuous scalar multipliers on vector-valued L². -/ +def vectorLpRepresentation : BoundedContinuousFunction ℝ ℂ →⋆ₐ[ℂ] + (Lp H 2 μ →L[ℂ] Lp H 2 μ) where + toFun := vectorLpMultiplier μ + map_one' := vectorLpMultiplier_one μ + map_mul' := vectorLpMultiplier_mul μ + map_zero' := by + apply ContinuousLinearMap.ext + intro f + change vectorLpMultiplier μ 0 f = 0 + apply Lp.ext + filter_upwards [vectorLpMultiplier_ae μ 0 f, Lp.coeFn_zero (E := H) (p := 2) (μ := μ)] + with t ht hz + simpa only [BoundedContinuousFunction.coe_zero, Pi.zero_apply, zero_smul, hz] using ht + map_add' a b := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [vectorLpMultiplier_ae μ (a + b) f, + vectorLpMultiplier_ae μ a f, vectorLpMultiplier_ae μ b f, + Lp.coeFn_add (vectorLpMultiplier μ a f) (vectorLpMultiplier μ b f)] with t hab ha hb he + change (vectorLpMultiplier μ (a + b) f) t = + (vectorLpMultiplier μ a f + vectorLpMultiplier μ b f) t + simp only [hab, he, Pi.add_apply, BoundedContinuousFunction.coe_add] + rw [ha, hb] + exact add_smul _ _ _ + commutes' c := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [vectorLpMultiplier_ae μ (algebraMap ℂ _ c) f, + Lp.coeFn_smul c f] with t ht hc + change (vectorLpMultiplier μ (algebraMap ℂ _ c) f) t = (c • f) t + rw [ht, hc] + rfl + map_star' := vectorLpMultiplier_star μ + +@[simp] lemma vectorLpRepresentation_character (r : ℝ) : + vectorLpRepresentation (H := H) μ (BoundedRecovery.spectralCharacter r) = + (modularDualUnitary (H := H) μ r : Lp H 2 μ →L[ℂ] Lp H 2 μ) := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [vectorLpMultiplier_ae μ (BoundedRecovery.spectralCharacter r) f, + modularDual_ae μ r f] with t hm hd + change (vectorLpMultiplier μ (BoundedRecovery.spectralCharacter r) f) t = + (modularDual μ r f) t + rw [hm, hd] + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/VectorLpProjection.lean b/lean/OAI/Analysis/OperatorAlgebra/VectorLpProjection.lean new file mode 100644 index 0000000000000000000000000000000000000000..5ef288890fb3f74d7b1d8fdc3d7a136eb420ac15 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/VectorLpProjection.lean @@ -0,0 +1,114 @@ +import OAI.Analysis.OperatorAlgebra.VectorLpStrongConvergence +import OAI.Analysis.OperatorAlgebra.ScalarLpSuperlevel + +namespace OAI + +/-! Concrete spectral interval projections on vector-valued L². -/ + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] + +private lemma indicator_bound (s : Set ℝ) (t : ℝ) : + ‖s.indicator (fun _ => (1 : ℂ)) t‖ ≤ 1 := by + by_cases ht : t ∈ s <;> simp [ht] + +def vectorLpProjection (s : Set ℝ) (hs : MeasurableSet s) : + Lp H 2 (volume : Measure ℝ) →L[ℂ] Lp H 2 (volume : Measure ℝ) := + boundedVectorLp volume (s.indicator (fun _ => (1 : ℂ))) + ((measurable_const.indicator hs).aestronglyMeasurable) 1 (indicator_bound s) + +lemma vectorLpProjection_ae (s : Set ℝ) (hs : MeasurableSet s) + (f : Lp H 2 (volume : Measure ℝ)) : + vectorLpProjection s hs f =ᵐ[volume] s.indicator (f : ℝ → H) := by + filter_upwards [boundedVectorLp_ae volume (s.indicator (fun _ => (1 : ℂ))) + ((measurable_const.indicator hs).aestronglyMeasurable) 1 (indicator_bound s) f] with t ht + change (vectorLpProjection s hs f) t = _ at ht ⊢ + rw [ht] + by_cases h : t ∈ s <;> simp [h] + +lemma vectorLpProjection_norm_le (s : Set ℝ) (hs : MeasurableSet s) : + ‖vectorLpProjection (H := H) s hs‖ ≤ 1 := by + apply ContinuousLinearMap.opNorm_le_bound _ zero_le_one + intro f + apply Lp.norm_le_mul_norm_of_ae_le_mul + filter_upwards [vectorLpProjection_ae s hs f] with t ht + rw [ht] + by_cases h : t ∈ s <;> simp [h] + +lemma vectorLpProjection_mul (s t : Set ℝ) (hs : MeasurableSet s) (ht : MeasurableSet t) : + vectorLpProjection (H := H) s hs * vectorLpProjection t ht = + vectorLpProjection (s ∩ t) (hs.inter ht) := by + apply ContinuousLinearMap.ext + intro f + apply Lp.ext + filter_upwards [vectorLpProjection_ae s hs (vectorLpProjection t ht f), + vectorLpProjection_ae t ht f, vectorLpProjection_ae (s ∩ t) (hs.inter ht) f] + with x hx hy hz + change (vectorLpProjection s hs (vectorLpProjection t ht f)) x = _ + rw [hx, hz] + by_cases hxs : x ∈ s <;> by_cases hxt : x ∈ t <;> simp [hxs, hxt, hy] + +variable [CompleteSpace H] + +lemma vectorLpProjection_star (s : Set ℝ) (hs : MeasurableSet s) : + star (vectorLpProjection (H := H) s hs) = vectorLpProjection s hs := by + symm + apply (ContinuousLinearMap.eq_adjoint_iff _ _).mpr + intro f g + simp only [L2.inner_def] + apply integral_congr_ae + filter_upwards [vectorLpProjection_ae s hs f, vectorLpProjection_ae s hs g] with t hf hg + rw [hf, hg] + by_cases ht : t ∈ s <;> simp [ht] + +lemma vectorLpProjection_isStarProjection (s : Set ℝ) (hs : MeasurableSet s) : + IsStarProjection (vectorLpProjection (H := H) s hs) := by + apply isStarProjection_iff'.mpr + exact ⟨by simpa only [inter_self] using vectorLpProjection_mul (H := H) s s hs hs, + vectorLpProjection_star s hs⟩ + +def vectorIntervalCutoff (r : ℝ) (n : ℕ) : BoundedContinuousFunction ℝ ℂ := + BoundedContinuousFunction.ofNormedAddCommGroup + (fun t => (realUpperCutoff 0 n (r - |t|) : ℂ)) + (by apply Complex.continuous_ofReal.comp; apply (realUpperCutoff_continuous 0 n).comp; + fun_prop) 1 + (by intro t; rw [Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg (realUpperCutoff_nonneg _ _ _)]; exact realUpperCutoff_le_one _ _ _) + +lemma vectorIntervalCutoff_norm (r : ℝ) (n : ℕ) (t : ℝ) : + ‖vectorIntervalCutoff r n t‖ ≤ 1 := by + change ‖(realUpperCutoff 0 n (r - |t|) : ℂ)‖ ≤ 1 + rw [Complex.norm_real, Real.norm_eq_abs, abs_of_nonneg (realUpperCutoff_nonneg _ _ _)] + exact realUpperCutoff_le_one _ _ _ + +lemma vectorIntervalCutoff_tendsto (r t : ℝ) : + Tendsto (fun n => vectorIntervalCutoff r n t) atTop + (𝓝 ((Icc (-r) r).indicator (fun _ => (1 : ℂ)) t)) := by + apply tendsto_const_nhds.congr' + filter_upwards [realUpperCutoff_eventually 0 (r - |t|)] with n hn + change (Icc (-r) r).indicator (fun _ => (1 : ℂ)) t = + (realUpperCutoff 0 n (r - |t|) : ℂ) + rw [hn] + have he : 0 ≤ r - |t| ↔ t ∈ Icc (-r) r := by + rw [sub_nonneg, abs_le]; rfl + by_cases ht : t ∈ Icc (-r) r <;> simp [he, ht] + +lemma vectorIntervalCutoff_strong (r : ℝ) (f : Lp H 2 (volume : Measure ℝ)) : + Tendsto (fun n => vectorLpRepresentation volume (vectorIntervalCutoff r n) f) + atTop (𝓝 (vectorLpProjection (Icc (-r) r) measurableSet_Icc f)) := by + exact vectorLpRepresentation_strong (vectorIntervalCutoff r) + ((Icc (-r) r).indicator (fun _ => (1 : ℂ))) + ((measurable_const.indicator measurableSet_Icc).aestronglyMeasurable) + 1 zero_le_one (vectorIntervalCutoff_norm r) (indicator_bound _) + (vectorIntervalCutoff_tendsto r) f + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/VectorLpStrongConvergence.lean b/lean/OAI/Analysis/OperatorAlgebra/VectorLpStrongConvergence.lean new file mode 100644 index 0000000000000000000000000000000000000000..7d9505e03c9dd223ea9ac3de96e0a35890d8cb99 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/VectorLpStrongConvergence.lean @@ -0,0 +1,107 @@ +import OAI.Analysis.OperatorAlgebra.VectorLpMultiplier + +namespace OAI + +/-! Strong convergence of scalar multipliers on vector-valued L². This is +used to put frequency cutoffs and Gaussian regularizers into the actual +modular core. -/ + +noncomputable section +open MeasureTheory Filter +open scoped InnerProductSpace Topology + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +omit [CompleteSpace H] in +lemma vectorLp_norm_sq_integral (f : Lp H 2 (volume : Measure ℝ)) : + ‖f‖ ^ 2 = ∫ t : ℝ, ‖f t‖ ^ 2 := by + calc + ‖f‖ ^ 2 = (inner ℂ f f).re := (inner_self_eq_norm_sq (𝕜 := ℂ) f).symm + _ = ∫ t : ℝ, (inner ℂ (f t) (f t)).re := by + rw [L2.inner_def] + exact (integral_re (𝕜 := ℂ) (L2.integrable_inner (𝕜 := ℂ) f f)).symm + _ = ∫ t : ℝ, ‖f t‖ ^ 2 := by + congr 1 + funext t + exact inner_self_eq_norm_sq (𝕜 := ℂ) (f t) + +omit [CompleteSpace H] in +lemma boundedVectorLp_strong + (b : ℕ → ℝ → ℂ) (a : ℝ → ℂ) + (hb : ∀ n, AEStronglyMeasurable (b n) volume) + (ha : AEStronglyMeasurable a volume) (C : ℝ) (_hC : 0 ≤ C) + (hbn : ∀ n t, ‖b n t‖ ≤ C) (han : ∀ t, ‖a t‖ ≤ C) + (hlim : ∀ t, Tendsto (fun n => b n t) atTop (𝓝 (a t))) + (f : Lp H 2 (volume : Measure ℝ)) : + Tendsto (fun n => boundedVectorLp volume (b n) (hb n) C (hbn n) f) + atTop (𝓝 (boundedVectorLp volume a ha C han f)) := by + let F (n : ℕ) (t : ℝ) := ‖(b n t - a t) • f t‖ ^ 2 + have hbound (n : ℕ) (t : ℝ) : F n t ≤ (2 * C) ^ 2 * ‖f t‖ ^ 2 := by + have hd : ‖b n t - a t‖ ≤ 2 * C := + (norm_sub_le _ _).trans (by linarith [hbn n t, han t]) + dsimp only [F] + rw [norm_smul, mul_pow] + gcongr + have hm (n : ℕ) : AEStronglyMeasurable (F n) volume := + (((hb n).sub ha).smul (Lp.aestronglyMeasurable f)).norm.pow 2 + have hi : Integrable (fun t : ℝ => (2 * C) ^ 2 * ‖f t‖ ^ 2) := + ((memLp_two_iff_integrable_sq_norm (Lp.aestronglyMeasurable f)).mp + (Lp.memLp f)).const_mul _ + have hp (t : ℝ) : Tendsto (fun n => F n t) atTop (𝓝 0) := by + have h := (((hlim t).sub_const (a t)).smul_const (f t)).norm.pow 2 + simpa only [sub_self, zero_smul, norm_zero, ne_eq, OfNat.ofNat_ne_zero, + not_false_eq_true, zero_pow] using h + have hint : Tendsto (fun n => ∫ t : ℝ, F n t) atTop (𝓝 0) := by + have h := tendsto_integral_of_dominated_convergence + (fun t : ℝ => (2 * C) ^ 2 * ‖f t‖ ^ 2) hm hi + (fun n => ae_of_all _ (fun t => by + rw [Real.norm_eq_abs, abs_of_nonneg (sq_nonneg _)] + exact hbound n t)) (ae_of_all _ hp) + simpa only [integral_zero] using h + have heq (n : ℕ) : + ‖boundedVectorLp volume (b n) (hb n) C (hbn n) f - + boundedVectorLp volume a ha C han f‖ ^ 2 = ∫ t : ℝ, F n t := by + rw [vectorLp_norm_sq_integral] + apply integral_congr_ae + filter_upwards [Lp.coeFn_sub (boundedVectorLp volume (b n) (hb n) C (hbn n) f) + (boundedVectorLp volume a ha C han f), + boundedVectorLp_ae volume (b n) (hb n) C (hbn n) f, + boundedVectorLp_ae volume a ha C han f] with t hs hb' ha' + rw [hs, Pi.sub_apply, hb', ha', ← sub_smul] + have hsq : Tendsto (fun n => ‖boundedVectorLp volume (b n) (hb n) C (hbn n) f - + boundedVectorLp volume a ha C han f‖ ^ 2) atTop (𝓝 0) := + hint.congr' (Eventually.of_forall fun n => (heq n).symm) + have hn : Tendsto (fun n => Real.sqrt (‖boundedVectorLp volume (b n) (hb n) C (hbn n) f - + boundedVectorLp volume a ha C han f‖ ^ 2)) atTop (𝓝 (Real.sqrt 0)) := + Real.continuous_sqrt.continuousAt.tendsto.comp hsq + simp only [Real.sqrt_sq (norm_nonneg _), Real.sqrt_zero] at hn + exact tendsto_iff_norm_sub_tendsto_zero.mpr hn + +lemma vectorLpRepresentation_strong + (b : ℕ → BoundedContinuousFunction ℝ ℂ) (a : ℝ → ℂ) + (ha : AEStronglyMeasurable a volume) (C : ℝ) (hC : 0 ≤ C) + (hbn : ∀ n t, ‖b n t‖ ≤ C) (han : ∀ t, ‖a t‖ ≤ C) + (hlim : ∀ t, Tendsto (fun n => b n t) atTop (𝓝 (a t))) + (f : Lp H 2 (volume : Measure ℝ)) : + Tendsto (fun n => vectorLpRepresentation volume (b n) f) + atTop (𝓝 (boundedVectorLp volume a ha C han f)) := by + have heq (n : ℕ) : boundedVectorLp (H := H) volume (b n) + (b n).continuous.aestronglyMeasurable C (hbn n) = + vectorLpRepresentation (H := H) volume (b n) := by + apply ContinuousLinearMap.ext + intro g + apply Lp.ext + filter_upwards [boundedVectorLp_ae volume (b n) + (b n).continuous.aestronglyMeasurable C (hbn n) g, + vectorLpMultiplier_ae volume (b n) g] with t hb hc + exact hb.trans hc.symm + simpa only [heq] using boundedVectorLp_strong (fun n => b n) a + (fun n => (b n).continuous.aestronglyMeasurable) ha C hC hbn han hlim f + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/VonNeumannWeakConvergence.lean b/lean/OAI/Analysis/OperatorAlgebra/VonNeumannWeakConvergence.lean new file mode 100644 index 0000000000000000000000000000000000000000..fa84ddc2aa746dfb9e62b2a3307ddcffec930c3d --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/VonNeumannWeakConvergence.lean @@ -0,0 +1,57 @@ +import OAI.Analysis.OperatorAlgebra.ScalarKernelPairing + +namespace OAI + +/-! Weak operator limits suffice for removing the two convolution +regularizers from the modular fixed-point reconstruction. -/ + +noncomputable section +open Filter +open scoped Topology InnerProductSpace + +namespace WeakPureInfiniteness + +variable {H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +theorem vonNeumann_mem_of_matrixCoefficient_limit (M : VonNeumannAlgebra H) + (T : H →L[ℂ] H) (F : ℕ → H →L[ℂ] H) (hF : ∀ n, F n ∈ M) + (hlim : ∀ x y, Tendsto (fun n => inner ℂ (F n x) y) atTop (𝓝 (inner ℂ (T x) y))) : + T ∈ M := by + rw [← M.commutant_commutant, VonNeumannAlgebra.mem_commutant_iff] + intro b hb + apply ContinuousLinearMap.ext + intro x + apply ext_inner_right ℂ + intro y + have hl := hlim x (b.adjoint y) + have hr := hlim (b x) y + have he (n : ℕ) : inner ℂ (F n x) (b.adjoint y) = inner ℂ (F n (b x)) y := by + rw [ContinuousLinearMap.adjoint_inner_right] + have hc := VonNeumannAlgebra.mem_commutant_iff.mp hb (F n) (hF n) + have hc' := congrArg (fun R : H →L[ℂ] H => R x) hc.symm + change b (F n x) = F n (b x) at hc' + rw [hc'] + have hv := tendsto_nhds_unique (hl.congr he) hr + change inner ℂ (b (T x)) y = inner ℂ (T (b x)) y + rw [← ContinuousLinearMap.adjoint_inner_right] + exact hv + +lemma sandwich_matrixCoefficient_limit (C : ℕ → H →L[ℂ] H) + (hC : ∀ x, Tendsto (fun n => C n x) atTop (𝓝 x)) (T : H →L[ℂ] H) (x y : H) : + Tendsto (fun n => inner ℂ ((C n).adjoint (T (C n x))) y) atTop (𝓝 (inner ℂ (T x) y)) := by + have h := (T.continuous.continuousAt.tendsto.comp (hC x)).inner (𝕜 := ℂ) (hC y) + simpa only [ContinuousLinearMap.adjoint_inner_left, Function.comp_apply] using h + +theorem vonNeumann_mem_of_sandwiches (M : VonNeumannAlgebra H) + (C : ℕ → H →L[ℂ] H) (hC : ∀ x, Tendsto (fun n => C n x) atTop (𝓝 x)) + (T : H →L[ℂ] H) (hT : ∀ n, (C n).adjoint * T * C n ∈ M) : T ∈ M := by + apply vonNeumann_mem_of_matrixCoefficient_limit M T + (fun n => (C n).adjoint * T * C n) hT + intro x y + exact sandwich_matrixCoefficient_limit C hC T x y + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/OperatorAlgebra/WeakOperatorUltralimit.lean b/lean/OAI/Analysis/OperatorAlgebra/WeakOperatorUltralimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..2d88a956b42eb7bb88a0f21fe66f29014f1fbb18 --- /dev/null +++ b/lean/OAI/Analysis/OperatorAlgebra/WeakOperatorUltralimit.lean @@ -0,0 +1,115 @@ +import OAI.Analysis.TracialSplitting.Model +import Mathlib.Analysis.InnerProductSpace.WeakOperatorTopology + +namespace OAI + +/-! Bounded operator families have weak operator ultralimits. The construction +uses bounded scalar ultralimits and the Hilbert-space representation of each +limiting linear functional. This is the compactness step for extending finite +matrix cpc maps to Hilbert-space operator targets. -/ + +noncomputable section +open Filter Topology +open scoped InnerProductSpace ComplexOrder + +namespace WeakPureInfiniteness + +variable {ι H : Type*} [NormedAddCommGroup H] [InnerProductSpace ℂ H] [CompleteSpace H] + +private def ultraOperatorForm (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) (x y : H) : ℂ := + limUnder (U : Filter ι) (fun i => inner ℂ (T i x) y) + +omit [CompleteSpace H] in +private lemma ultraOperatorForm_tendsto (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hT : ∀ i, ‖T i‖ ≤ C) (x y : H) : + Tendsto (fun i => inner ℂ (T i x) y) (U : Filter ι) + (𝓝 (ultraOperatorForm U T x y)) := by + apply CurrentMain.bounded_ultrafilter_tendsto U _ (C * ‖x‖ * ‖y‖) + intro i + exact (norm_inner_le_norm _ _).trans (mul_le_mul_of_nonneg_right + ((T i).le_opNorm x |>.trans (mul_le_mul_of_nonneg_right (hT i) (norm_nonneg x))) + (norm_nonneg y)) + +omit [CompleteSpace H] in +private lemma ultraOperatorForm_bound (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hT : ∀ i, ‖T i‖ ≤ C) (x y : H) : + ‖ultraOperatorForm U T x y‖ ≤ (C * ‖x‖) * ‖y‖ := by + apply le_of_tendsto (ultraOperatorForm_tendsto U T hT x y).norm + exact Eventually.of_forall fun i => (norm_inner_le_norm _ _).trans + (mul_le_mul_of_nonneg_right ((T i).le_opNorm x |>.trans + (mul_le_mul_of_nonneg_right (hT i) (norm_nonneg x))) (norm_nonneg y)) + +private def ultraOperatorFunctional (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hT : ∀ i, ‖T i‖ ≤ C) (x : H) : H →L[ℂ] ℂ := + ({ toFun := ultraOperatorForm U T x + map_add' := by + intro y z + apply tendsto_nhds_unique (ultraOperatorForm_tendsto U T hT x (y + z)) + simpa only [inner_add_right] using + (ultraOperatorForm_tendsto U T hT x y).add (ultraOperatorForm_tendsto U T hT x z) + map_smul' := by + intro c y + apply tendsto_nhds_unique (ultraOperatorForm_tendsto U T hT x (c • y)) + simpa only [inner_smul_right, RingHom.id_apply, smul_eq_mul] using + (ultraOperatorForm_tendsto U T hT x y).const_mul c } : H →ₗ[ℂ] ℂ).mkContinuous + (C * ‖x‖) (ultraOperatorForm_bound U T hT x) + +omit [CompleteSpace H] in +private lemma ultraOperatorForm_add_left (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hT : ∀ i, ‖T i‖ ≤ C) (x z y : H) : + ultraOperatorForm U T (x + z) y = ultraOperatorForm U T x y + ultraOperatorForm U T z y := by + apply tendsto_nhds_unique (ultraOperatorForm_tendsto U T hT (x + z) y) + simpa only [map_add, inner_add_left] using + (ultraOperatorForm_tendsto U T hT x y).add (ultraOperatorForm_tendsto U T hT z y) + +omit [CompleteSpace H] in +private lemma ultraOperatorForm_smul_left (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hT : ∀ i, ‖T i‖ ≤ C) (c : ℂ) (x y : H) : + ultraOperatorForm U T (c • x) y = star c * ultraOperatorForm U T x y := by + apply tendsto_nhds_unique (ultraOperatorForm_tendsto U T hT (c • x) y) + simpa only [map_smul, inner_smul_left, RingHom.id_apply, starRingEnd_apply] using + (ultraOperatorForm_tendsto U T hT x y).const_mul (star c) + +private def operatorUltraLinear (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hT : ∀ i, ‖T i‖ ≤ C) : H →ₗ[ℂ] H where + toFun x := (InnerProductSpace.toDual ℂ H).symm (ultraOperatorFunctional U T hT x) + map_add' x z := by + apply ext_inner_right ℂ + intro y + simp only [InnerProductSpace.toDual_symm_apply, inner_add_left] + exact ultraOperatorForm_add_left U T hT x z y + map_smul' c x := by + apply ext_inner_right ℂ + intro y + simp only [InnerProductSpace.toDual_symm_apply, inner_smul_left, RingHom.id_apply] + exact ultraOperatorForm_smul_left U T hT c x y + +def operatorUltraLimit (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hC : 0 ≤ C) (hT : ∀ i, ‖T i‖ ≤ C) : H →L[ℂ] H := + (operatorUltraLinear U T hT).mkContinuous C (fun x => by + change ‖(InnerProductSpace.toDual ℂ H).symm (ultraOperatorFunctional U T hT x)‖ ≤ _ + rw [LinearIsometryEquiv.norm_map] + exact LinearMap.mkContinuous_norm_le _ (mul_nonneg hC (norm_nonneg x)) _) + +lemma operatorUltraLimit_inner (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hC : 0 ≤ C) (hT : ∀ i, ‖T i‖ ≤ C) (x y : H) : + inner ℂ (operatorUltraLimit U T hC hT x) y = ultraOperatorForm U T x y := by + exact InnerProductSpace.toDual_symm_apply + +lemma operatorUltraLimit_norm_le (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hC : 0 ≤ C) (hT : ∀ i, ‖T i‖ ≤ C) : + ‖operatorUltraLimit U T hC hT‖ ≤ C := + LinearMap.mkContinuous_norm_le _ hC _ + +lemma operatorUltraLimit_inner_tendsto (U : Ultrafilter ι) (T : ι → H →L[ℂ] H) + {C : ℝ} (hC : 0 ≤ C) (hT : ∀ i, ‖T i‖ ≤ C) (x y : H) : + Tendsto (fun i => inner ℂ (T i x) y) (U : Filter ι) + (𝓝 (inner ℂ (operatorUltraLimit U T hC hT x) y)) := by + rw [operatorUltraLimit_inner] + exact ultraOperatorForm_tendsto U T hT x y + +end WeakPureInfiniteness + +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/AdmissibleFunctions.lean b/lean/OAI/Analysis/PathSelection/AdmissibleFunctions.lean new file mode 100644 index 0000000000000000000000000000000000000000..da415d6f224d4ef2bd6a528bfb32448972f2c8d3 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/AdmissibleFunctions.lean @@ -0,0 +1,282 @@ +import Mathlib + +namespace OAI + +/-! Real-holomorphic representatives, recursively extracted coefficients and admissibility. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace PathSelection.Statement + +abbrev RealPoint (m n : ℕ) := (Fin m → ℝ) × (Fin n → ℝ) +abbrev ComplexPoint (m n : ℕ) := (Fin m → ℂ) × (Fin n → ℂ) + + +def complexify {m n : ℕ} (x : RealPoint m n) : ComplexPoint m n := + (fun i => (x.1 i : ℂ), fun a => (x.2 a : ℂ)) + +def conjugate {m n : ℕ} (x : ComplexPoint m n) : ComplexPoint m n := + (fun i => star (x.1 i), fun a => star (x.2 a)) + + + +def realValue {m n : ℕ} (P : ComplexPoint m n → ℂ) (x : RealPoint m n) : ℝ := + (P (complexify x)).re + + +def quadraticRegion (A c : ℝ) : Set ℂ := + {L | A < L.re ∧ |L.im| < c * L.re ^ 2} + +def tailBand (A c : ℝ) : Set ℂ := + {L | A < L.re ∧ |L.im| < c} + +def ordinaryPolydisc {n : ℕ} (z₀ : Fin n → ℝ) (r : ℝ) : Set (Fin n → ℂ) := + {z | ∀ a, ‖z a - (z₀ a : ℂ)‖ < r} + +def ordinaryClosedPolydisc {n : ℕ} (z₀ : Fin n → ℝ) (r : ℝ) : + Set (Fin n → ℂ) := + {z | ∀ a, ‖z a - (z₀ a : ℂ)‖ ≤ r} + + +def quadraticDomain {m n : ℕ} (S : Finset (Fin m)) (A c : ℝ) + (z₀ : Fin n → ℝ) (r : ℝ) : Set (ComplexPoint m n) := + {x | (∀ i, i ∉ S → x.1 i ∈ quadraticRegion A c) ∧ x.2 ∈ ordinaryPolydisc z₀ r} + + +def quadraticEstimateDomain {m n : ℕ} (S : Finset (Fin m)) (A c : ℝ) + (z₀ : Fin n → ℝ) (r : ℝ) : Set (ComplexPoint m n) := + {x | (∀ i, i ∉ S → x.1 i ∈ quadraticRegion A c) ∧ + x.2 ∈ ordinaryClosedPolydisc z₀ r} + +def commonBandDomain {m n : ℕ} (S : Finset (Fin m)) (A c : ℝ) + (z₀ : Fin n → ℝ) (r : ℝ) : Set (ComplexPoint m n) := + {x | (∀ i, i ∉ S → x.1 i ∈ tailBand A c) ∧ x.2 ∈ ordinaryPolydisc z₀ r} + +def RealHolomorphicOn {m n : ℕ} (f : ComplexPoint m n → ℂ) + (U : Set (ComplexPoint m n)) : Prop := + AnalyticOnNhd ℂ f U ∧ ∀ x ∈ U, f (conjugate x) = star (f x) + + + +structure Extraction (m : ℕ) where + coordinate : Fin m + exponent : ℝ + power : ℕ + +def expanded {m : ℕ} (h : List (Extraction m)) : Finset (Fin m) := + (h.map Extraction.coordinate).toFinset + + +structure CoefficientSystem (m n : ℕ) where + coefficient : List (Extraction m) → ComplexPoint m n → ℂ + exponents : List (Extraction m) → Fin m → Set ℝ + degree : List (Extraction m) → Fin m → ℝ → ℕ + +namespace CoefficientSystem + +def Valid {m n : ℕ} (T : CoefficientSystem m n) : List (Extraction m) → Prop + | [] => True + | e :: h => T.Valid h ∧ e.coordinate ∉ expanded h ∧ + e.exponent ∈ T.exponents h e.coordinate ∧ + e.power ≤ T.degree h e.coordinate e.exponent + + + +def IndependentOfExpanded {m n : ℕ} (T : CoefficientSystem m n) + (h : List (Extraction m)) : Prop := + ∀ x y : ComplexPoint m n, x.2 = y.2 → + (∀ i, i ∉ expanded h → x.1 i = y.1 i) → T.coefficient h x = T.coefficient h y + + +def QuadraticallyBounded {m n : ℕ} (T : CoefficientSystem m n) + (h : List (Extraction m)) (z₀ : Fin n → ℝ) (R : ℝ) : Prop := + ∃ A c : ℝ, 0 < A ∧ 0 < c ∧ + RealHolomorphicOn (T.coefficient h) (quadraticDomain (expanded h) A c z₀ R) ∧ + ∀ r : ℝ, 0 < r → r < R → ∃ C : ℝ, 0 < C ∧ + ∀ x ∈ quadraticEstimateDomain (expanded h) A c z₀ r, ‖T.coefficient h x‖ ≤ C + + + +def finiteSum {ι : Type*} (s : Set ι) (f : ι → ℂ) : ℂ := by + classical + exact if hs : s.Finite then ∑ i ∈ hs.toFinset, f i else 0 + + +def singlePartialSum {m n : ℕ} (T : CoefficientSystem m n) + (h : List (Extraction m)) (i : Fin m) (B : ℝ) (x : ComplexPoint m n) : ℂ := + finiteSum (T.exponents h i ∩ Iic B) (fun d => + Complex.exp (-(d : ℂ) * x.1 i) * + ∑ k ∈ Finset.range (T.degree h i d + 1), + (x.1 i) ^ k * T.coefficient (⟨i, d, k⟩ :: h) x) + + + +def SingleExpansion {m n : ℕ} (T : CoefficientSystem m n) + (h : List (Extraction m)) (i : Fin m) (z₀ : Fin n → ℝ) (R : ℝ) : Prop := + (∀ d ∈ T.exponents h i, 0 ≤ d) ∧ + (∀ B : ℝ, (T.exponents h i ∩ Iic B).Finite) ∧ + (0 ∈ T.exponents h i → T.degree h i 0 = 0) ∧ + ∀ B r : ℝ, 0 < r → r < R → + ∃ A c C ε : ℝ, 0 < A ∧ 0 < c ∧ 0 < C ∧ 0 < ε ∧ + ∀ x ∈ quadraticEstimateDomain (expanded h) A c z₀ r, + ‖T.coefficient h x - T.singlePartialSum h i B x‖ ≤ + C * Real.exp (-(B + ε) * (x.1 i).re) + + + +def iteratedHistories {m n : ℕ} (T : CoefficientSystem m n) + (h : List (Extraction m)) (I : List (Fin m)) : Set (List (Extraction m)) := + {q | q.map Extraction.coordinate = I ∧ T.Valid (q ++ h)} + +def weight {m : ℕ} (rates : Fin m → ℝ) (q : List (Extraction m)) : ℝ := + (q.map (fun e => rates e.coordinate * e.exponent)).sum + +def iteratedTerm {m n : ℕ} (T : CoefficientSystem m n) + (h q : List (Extraction m)) (x : ComplexPoint m n) : ℂ := + (q.map (fun e => Complex.exp (-(e.exponent : ℂ) * x.1 e.coordinate) * + (x.1 e.coordinate) ^ e.power)).prod * T.coefficient (q ++ h) x + +def groupedPartialSum {m n : ℕ} (T : CoefficientSystem m n) + (h : List (Extraction m)) (I : List (Fin m)) (rates : Fin m → ℝ) + (B : ℝ) (x : ComplexPoint m n) : ℂ := + finiteSum {q | q ∈ T.iteratedHistories h I ∧ weight rates q ≤ B} + (fun q => T.iteratedTerm h q x) + + + +def GroupedExpansion {m n : ℕ} (T : CoefficientSystem m n) + (h : List (Extraction m)) (z₀ : Fin n → ℝ) (R : ℝ) : Prop := + ∀ (I : List (Fin m)) (rates : Fin m → ℝ), + I.Nodup → (∀ i ∈ I, i ∉ expanded h) → (∀ i ∈ I, 0 < rates i) → + (∀ B : ℝ, + {q | q ∈ T.iteratedHistories h I ∧ weight rates q ≤ B}.Finite) ∧ + (∀ B : ℝ, + ((weight rates '' T.iteratedHistories h I) ∩ Iic B).Finite) ∧ + ∀ B r : ℝ, 0 < r → r < R → + ∃ A c C ε : ℝ, 0 < A ∧ 0 < c ∧ 0 < C ∧ 0 < ε ∧ + ∀ x : ℝ → ComplexPoint m n, + (∀ᶠ U in atTop, x U ∈ quadraticEstimateDomain (expanded h) A c z₀ r) → + (∀ i ∈ I, Tendsto (fun U => ((x U).1 i).re / U) atTop (𝓝 (rates i))) → + ∀ᶠ U in atTop, + ‖T.coefficient h (x U) - T.groupedPartialSum h I rates B (x U)‖ ≤ + C * Real.exp (-(B + ε) * U) + + + +def CommonCoefficientDomains {m n : ℕ} (T : CoefficientSystem m n) + (z₀ : Fin n → ℝ) (R : ℝ) : Prop := + ∀ S : Finset (Fin m), ∃ A c : ℝ, 0 < A ∧ 0 < c ∧ + ∀ h : List (Extraction m), T.Valid h → expanded h = S → + RealHolomorphicOn (T.coefficient h) (commonBandDomain S A c z₀ R) + +end CoefficientSystem + + + +def Admissible {m n : ℕ} (P : ComplexPoint m n → ℂ) (z₀ : Fin n → ℝ) : Prop := + ∃ T : CoefficientSystem m n, T.coefficient [] = P ∧ + ∃ R : ℝ, 0 < R ∧ T.CommonCoefficientDomains z₀ R ∧ + ∀ h : List (Extraction m), T.Valid h → + T.IndependentOfExpanded h ∧ T.QuadraticallyBounded h z₀ R ∧ + (∀ i : Fin m, i ∉ expanded h → T.SingleExpansion h i z₀ R) ∧ + T.GroupedExpansion h z₀ R + + + +inductive SignFormula (s : ℕ) where + | truth : SignFormula s + | falsity : SignFormula s + | positive : Fin s → SignFormula s + | zero : Fin s → SignFormula s + | negative : Fin s → SignFormula s + | not : SignFormula s → SignFormula s + | and : SignFormula s → SignFormula s → SignFormula s + | or : SignFormula s → SignFormula s → SignFormula s + +def SignFormula.Holds {s : ℕ} : SignFormula s → (Fin s → ℝ) → Prop + | .truth, _ => True + | .falsity, _ => False + | .positive j, v => 0 < v j + | .zero j, v => v j = 0 + | .negative j, v => v j < 0 + | .not p, v => ¬ p.Holds v + | .and p q, v => p.Holds v ∧ q.Holds v + | .or p q, v => p.Holds v ∨ q.Holds v + + + +def EventuallyMonotoneOrConstant (f : ℝ → ℝ) : Prop := + ∃ U : ℝ, MonotoneOn f (Ioi U) ∨ AntitoneOn f (Ioi U) ∨ + ∃ c : ℝ, EqOn f (fun _ => c) (Ioi U) + + + +def PathConclusion {m n s a t : ℕ} + (P : Fin s → ComplexPoint m n → ℂ) (φ : SignFormula s) + (Q : Fin a → ComplexPoint m n → ℂ) (R : Fin t → ComplexPoint m n → ℂ) + (z₀ : Fin n → ℝ) (ℓ : Fin t → ℝ) : Prop := + ∃ γ : ℝ → RealPoint m n, ∃ U : ℝ, + AnalyticOnNhd ℝ γ (Ioi U) ∧ + (∀ i : Fin m, Tendsto (fun u => (γ u).1 i) atTop atTop) ∧ + Tendsto (fun u => (γ u).2) atTop (𝓝 z₀) ∧ + (∀ᶠ u in atTop, φ.Holds (fun j => realValue (P j) (γ u))) ∧ + (∀ i : Fin m, EventuallyMonotoneOrConstant (fun u => (γ u).1 i)) ∧ + (∀ b : Fin n, EventuallyMonotoneOrConstant (fun u => (γ u).2 b)) ∧ + (∀ j : Fin a, EventuallyMonotoneOrConstant (fun u => realValue (Q j) (γ u))) ∧ + (∀ j : Fin t, Tendsto (fun u => realValue (R j) (γ u)) atTop (𝓝 (ℓ j))) + + + +lemma realValue_eq_of_realHolomorphicOn {m n : ℕ} + {P : ComplexPoint m n → ℂ} {V : Set (ComplexPoint m n)} + (hP : RealHolomorphicOn P V) {x : RealPoint m n} (hx : complexify x ∈ V) : + (realValue P x : ℂ) = P (complexify x) := by + have hc : conjugate (complexify x) = complexify x := by + simp [conjugate, complexify] + have hsym := hP.2 (complexify x) hx + rw [hc] at hsym + exact Complex.conj_eq_iff_re.mp hsym.symm + + + +lemma eventually_mem_quadraticDomain {ι : Type*} {l : Filter ι} {m n : ℕ} + {x : ι → RealPoint m n} {z₀ : Fin n → ℝ} + (hL : ∀ i : Fin m, Tendsto (fun v => (x v).1 i) l atTop) + (hz : Tendsto (fun v => (x v).2) l (𝓝 z₀)) + (S : Finset (Fin m)) {A c R : ℝ} (hA : 0 < A) (hc : 0 < c) (hR : 0 < R) : + ∀ᶠ v in l, complexify (x v) ∈ quadraticDomain S A c z₀ R := by + have hlen : ∀ᶠ v in l, ∀ i : Fin m, A < (x v).1 i := + Filter.eventually_all.mpr (fun i => (hL i).eventually (eventually_gt_atTop A)) + have hpar : ∀ᶠ v in l, ∀ a : Fin n, ‖((x v).2 a : ℂ) - (z₀ a : ℂ)‖ < R := by + apply Filter.eventually_all.mpr + intro a + have ht : Tendsto (fun v => ((x v).2 a : ℂ)) l (𝓝 (z₀ a : ℂ)) := + Complex.continuous_ofReal.continuousAt.tendsto.comp ((tendsto_pi_nhds.mp hz) a) + simpa only [dist_eq_norm] using Metric.tendsto_nhds.mp ht R hR + filter_upwards [hlen, hpar] with v hv hzv + refine ⟨?_, hzv⟩ + intro i _ + refine ⟨hv i, ?_⟩ + change |(0 : ℝ)| < c * ((x v).1 i) ^ 2 + simpa only [abs_zero] using mul_pos hc (pow_pos (hA.trans (hv i)) 2) + + + +lemma Admissible.eventually_realValue_eq {ι : Type*} {l : Filter ι} {m n : ℕ} + {P : ComplexPoint m n → ℂ} {z₀ : Fin n → ℝ} (hP : Admissible P z₀) + {x : ι → RealPoint m n} + (hL : ∀ i : Fin m, Tendsto (fun v => (x v).1 i) l atTop) + (hz : Tendsto (fun v => (x v).2) l (𝓝 z₀)) : + ∀ᶠ v in l, (realValue P (x v) : ℂ) = P (complexify (x v)) := by + obtain ⟨T, hT, R, hR, _, hrec⟩ := hP + obtain ⟨A, c, hA, hc, han, _⟩ := (hrec [] trivial).2.1 + rw [hT] at han + filter_upwards [eventually_mem_quadraticDomain hL hz (expanded []) hA hc hR] with v hv + exact realValue_eq_of_realHolomorphicOn han hv + +end PathSelection.Statement +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/AnalyticCharts.lean b/lean/OAI/Analysis/PathSelection/AnalyticCharts.lean new file mode 100644 index 0000000000000000000000000000000000000000..8479ce6fe35048a18f437830404e1ffc5fb559be --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/AnalyticCharts.lean @@ -0,0 +1,445 @@ +import Mathlib +import OAI.Analysis.PathSelection.PositiveCharts + +namespace OAI + +/-! Analytic Puiseux charts, zero leading data and clock perturbation estimates. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma PositiveSectorControl.tendsto {f : ℝ → ℝ} (hf : PositiveSectorControl f) : + ∃ G : ℂ → ℂ,(∀ᶠ z in sectorInfinity,AnalyticAt ℂ G z) ∧ + (fun t => (f t:ℂ)) =ᶠ[atTop] (fun t => G (t:ℂ)) ∧ + Tendsto G sectorInfinity sectorInfinity ∧ + (∀ᶠ z in sectorInfinity,|f ‖z‖|/4≤‖G z‖ ∧ ‖G z‖≤4*|f ‖z‖|) ∧ + ∀ ω S,AdmissibleAngularLoss ω → + ∃ η R,AdmissibleAngularLoss η ∧ + (∀ z∈lossSector η R,G z∈lossSector ω S) ∧ + (f =o[atTop] id → ∀ ε : ℝ,0<ε → ∃ A : ℝ, + ∀ z∈lossSector η A,|(G z).re|≤ε*z.re) := by + obtain ⟨G,R,hGa,he,hm,hmap⟩ := hf + refine ⟨G,sector_halfplane_analytic hGa,he,?_,?_,?_⟩ + · apply Filter.tendsto_def.mpr + intro U hU + obtain ⟨ω,S,hω,hU⟩ := hU + obtain ⟨η,T,hη,_,hT,_⟩ := hmap ω S hω + exact ⟨η,T,hη,fun z hz => hU _ (hT z hz)⟩ + · exact (tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop R)).mono hm + · intro ω S hω + obtain ⟨η,T,hη,_,hT,hsmall⟩ := hmap ω S hω + exact ⟨η,T,hη,hT,hsmall⟩ + + + +theorem PuiseuxSector.analytic_change_clock {H : ℂ → ℂ} + (hH : H∈PuiseuxSector) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re)) : + ∃ (I : ℝ → ℝ) (x : ℂ → ℂ),Puiseux (fun t => (I t:ℂ)) ∧ + Tendsto I atTop atTop ∧ I =o[atTop] id ∧ + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ x z ∧ H (x z)=z) ∧ + Tendsto x sectorInfinity sectorInfinity ∧ + (∀ᶠ t : ℝ in atTop,x (t:ℂ)=(I t:ℂ) ∧ H (I t:ℂ)=(t:ℂ)) ∧ + (∀ᶠ t : ℝ in atTop,x (H (t:ℂ))=(t:ℂ)) ∧ + (∀ᶠ z in sectorInfinity,I ‖z‖/4≤‖x z‖ ∧ ‖x z‖≤4*I ‖z‖) ∧ + ∀ F : ℂ → ℂ,F∈PuiseuxSector → + (∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) → + Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop → + (fun t : ℝ => (F (t:ℂ)).re) =O[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (x w)) z) ∧ + Tendsto (fun w => F (x w)) sectorInfinity sectorInfinity ∧ + (∀ᶠ z in sectorInfinity,‖F (x (‖z‖:ℂ))‖/4≤‖F (x z)‖ ∧ + ‖F (x z)‖≤4*‖F (x (‖z‖:ℂ))‖) ∧ + ∀ ω S,AdmissibleAngularLoss ω → + ∃ η R,AdmissibleAngularLoss η ∧ + (∀ z∈lossSector η R,F (x z)∈lossSector ω S) ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + ∀ ε : ℝ,0<ε → ∃ A : ℝ,∀ z∈lossSector η A,|(F (x z)).re|≤ε*z.re) := by + obtain ⟨I,hI,hIt,hl,hr,hIo,hIc,hfamily⟩ := (PuiseuxSector.real_puiseux hH hHr).change_clock hHt hfast + obtain ⟨x,hxa,he,hxt,hm,hmap⟩ := hIc.tendsto + have hxr : ∀ᶠ t : ℝ in atTop,x (t:ℂ)=(I t:ℂ) := he.symm + have hHreal : ∀ᶠ t : ℝ in atTop,H (t:ℂ)=((H (t:ℂ)).re:ℂ) := + hHr.mono fun _ ht => Complex.ext rfl (by simpa using ht) + have hleft : ∀ᶠ t : ℝ in atTop,H (I t:ℂ)=(t:ℂ) := by + filter_upwards [hl,hIt.eventually hHreal] with t ht hre + rw [hre,ht] + have hHa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => H (x z)) z := by + filter_upwards [hxa,hxt.eventually hH.1] with z hx hH + exact hH.comp hx + have hleftC : (fun z => H (x z)) =ᶠ[sectorInfinity] id := + sector_analytic_eq_of_ray hHa (Eventually.of_forall fun _ => analyticAt_id) + (by filter_upwards [hxr,hleft] with t hx hl; simpa [hx] using hl) + have hright : ∀ᶠ t : ℝ in atTop,x (H (t:ℂ))=(t:ℂ) := by + filter_upwards [hHreal,hr,hHt.eventually hxr] with t hre hr hx + rw [hre,hx,hr] + have hipos := hIt.eventually (eventually_gt_atTop (0:ℝ)) + refine ⟨I,x,hI,hIt,hIo,hxa.and hleftC,hxt,hxr.and hleft,hright,?_,?_⟩ + · filter_upwards [hm,tendsto_norm_sectorInfinity.eventually hipos] with z hm hp + simpa only [abs_of_pos hp] using hm + · intro F hF hFr hFt hFO + obtain ⟨hFc,hFo⟩ := hfamily _ (PuiseuxSector.real_puiseux hF hFr) hFt hFO + obtain ⟨G,hGa,hGe,hGt,hGm,hGmap⟩ := hFc.tendsto + have hFa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => F (x z)) z := by + filter_upwards [hxa,hxt.eventually hF.1] with z hx hf + exact hf.comp hx + have hray : ∀ᶠ t : ℝ in atTop,F (x (t:ℂ))=G (t:ℂ) := by + filter_upwards [hxr,hGe,hIt.eventually hFr] with t hx hg hr + rw [hx,←hg] + exact Complex.ext rfl (by simpa using hr) + have heq := sector_analytic_eq_of_ray hFa hGa hray + refine ⟨hFa,hGt.congr' heq.symm,?_,?_⟩ + · filter_upwards [hGm,heq,tendsto_norm_sectorInfinity.eventually hray, + tendsto_norm_sectorInfinity.eventually hGe] with z hm he hr hg + rw [he,hr,←hg,Complex.norm_real,Real.norm_eq_abs] + exact hm + · intro ω S hω + obtain ⟨η,R,hη,hmap,hsmall⟩ := hGmap ω S hω + obtain ⟨κ,K,hκ,hκe⟩ := heq + refine ⟨fun r => max (η r) (κ r),max R K,hη.max hκ,?_,?_⟩ + · intro z hz + have hηz : z∈lossSector η R := ⟨(le_max_left _ _).trans_lt hz.1, + hz.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩ + have hκz : z∈lossSector κ K := ⟨(le_max_right _ _).trans_lt hz.1, + hz.2.trans_le (sub_le_sub_left (le_max_right _ _) _)⟩ + have he : F (x z)=G z := hκe z hκz + rw [he] + exact hmap z hηz + · intro ho ε hε + obtain ⟨A,hA⟩ := hsmall (hFo ho) ε hε + refine ⟨max A K,fun z hz => ?_⟩ + have hηz : z∈lossSector η A := ⟨(le_max_left _ _).trans_lt hz.1, + hz.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩ + have hκz : z∈lossSector κ K := ⟨(le_max_right _ _).trans_lt hz.1, + hz.2.trans_le (sub_le_sub_left (le_max_right _ _) _)⟩ + have he : F (x z)=G z := hκe z hκz + rw [he] + exact hA z hηz + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma real_equivalent_of_relative {F g : ℂ → ℂ} + (hF : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) + (hg : ∀ᶠ t : ℝ in atTop,(g (t:ℂ)).im=0 ∧ 0<(g (t:ℂ)).re) + (he : ExpSmall 0 (fun z => F z/g z-1)) : + (fun t : ℝ => (F (t:ℂ)).re) ~[atTop] (fun t : ℝ => (g (t:ℂ)).re) := by + apply (Asymptotics.isEquivalent_iff_tendsto_one (hg.mono fun _ h => h.2.ne')).mpr + have ht : Tendsto (fun z => F z/g z) sectorInfinity (𝓝 1) := by + simpa only [sub_add_cancel,zero_add] using he.tendsto_zero.add_const 1 + have hr := (Complex.continuous_re.tendsto 1).comp (ht.comp tendsto_real_sectorInfinity) + apply hr.congr' + filter_upwards [hF,hg] with t hf hg + have ef : F (t:ℂ)=((F (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hf) + have eg : g (t:ℂ)=((g (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hg.1) + change (F (t:ℂ)/g (t:ℂ)).re=(F (t:ℂ)).re/(g (t:ℂ)).re + rw [ef,eg,←Complex.ofReal_div,Complex.ofReal_re] + rfl + +lemma Puiseux.log_littleO_unbounded {I : ℝ → ℝ} + (hI : Puiseux (fun t => (I t:ℂ))) (hIt : Tendsto I atTop atTop) : + Real.log =o[atTop] I := by + obtain ⟨q,a,C,K,R,G,hq,ha,hC,hK,hGa,he,herr⟩ := hI.positive_sector hIt + have hn := power_model_norm ha hC herr + have hb : (fun t : ℝ => t^(q:ℝ)) =O[atTop] I := by + apply Asymptotics.IsBigO.of_bound (2/C) + filter_upwards [hn,he] with t ht he + have hh := (ht.2 (t:ℂ) (Complex.norm_of_nonneg ht.1.le)).1 + simp only [←he,Complex.norm_real,Real.norm_eq_abs] at hh + rw [Real.norm_eq_abs,abs_of_pos (Real.rpow_pos_of_pos ht.1 _),Real.norm_eq_abs] + rw [div_mul_eq_mul_div] + apply (le_div_iff₀ hC).mpr + nlinarith + exact (isLittleO_log_rpow_atTop hq).trans_isBigO hb + +lemma ExpSmall.common_sector_bound {E F : ℂ → ℂ} (hE : ExpSmall 0 E) (hF : ExpSmall 0 F) : + ∃ ε C : ℝ,0<ε ∧ 0≤C ∧ ∀ᶠ z in sectorInfinity, + ‖E z‖≤C*Real.exp (-ε*z.re) ∧ ‖F z‖≤C*Real.exp (-ε*z.re) := by + obtain ⟨a,ha,hEa⟩ := hE + obtain ⟨b,hb,hFb⟩ := hF + obtain ⟨A,hA,hEA⟩ := hEa.exists_pos + obtain ⟨B,hB,hFB⟩ := hFb.exists_pos + refine ⟨-max a b,A+B,by have := max_lt ha hb; linarith,by positivity,?_⟩ + filter_upwards [hEA.bound,hFB.bound, + show ∀ᶠ z in sectorInfinity,0 (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : ∃ D : ℝ,0 (H (t:ℂ)).re)) + (htop : Tendsto (fun z => deriv H z/H z) sectorInfinity (𝓝 0)) : + ∃ g h : ℂ → ℂ,g∈PuiseuxSector ∧ h∈PuiseuxSector ∧ + (∀ᶠ z in sectorInfinity,g z≠0 ∧ h z≠0) ∧ + (∀ᶠ t : ℝ in atTop,(g (t:ℂ)).im=0 ∧ 0<(g (t:ℂ)).re) ∧ + (∀ᶠ t : ℝ in atTop,(h (t:ℂ)).im=0 ∧ 0<(h (t:ℂ)).re) ∧ + Tendsto (fun t : ℝ => (g (t:ℂ)).re) atTop atTop ∧ + Tendsto (fun t : ℝ => (h (t:ℂ)).re) atTop atTop ∧ + id =o[atTop] (fun t : ℝ => (h (t:ℂ)).re) ∧ + (fun t : ℝ => (g (t:ℂ)).re) =O[atTop] (fun t : ℝ => (h (t:ℂ)).re) ∧ + ExpSmall 0 (fun z => F z/g z-1) ∧ ExpSmall 0 (fun z => H z/h z-1) ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun t : ℝ => (g (t:ℂ)).re) =o[atTop] (fun t : ℝ => (h (t:ℂ)).re)) := by + obtain ⟨a,ha,g,hg,hg0,hgr,hFe,hFd⟩ := hF.puiseux_positive_leading hFr hFt + obtain ⟨b,hb,h,hh,hh0,hhr,hHe,hHd⟩ := hH.puiseux_positive_leading hHr hHt + have hb0 : b=0 := Complex.ofReal_eq_zero.mp (tendsto_nhds_unique hHd htop) + subst b + have hFa := hF.choose_spec.choose_spec.1.eventually_analytic + have hHa := hH.choose_spec.choose_spec.1.eventually_analytic + have hab : a≤0 := unbounded_log_exponent_order (le_refl 0) + (tendsto_real_sectorInfinity.eventually hFa) (tendsto_real_sectorInfinity.eventually hHa) + hFr hHr hFt (hFd.comp tendsto_real_sectorInfinity) (hHd.comp tendsto_real_sectorInfinity) hO + have ha0 := le_antisymm hab ha + subst a + have heF : ExpSmall 0 (fun z => F z/g z-1) := by simpa [div_eq_mul_inv,mul_comm] using hFe + have heH : ExpSmall 0 (fun z => H z/h z-1) := by simpa [div_eq_mul_inv,mul_comm] using hHe + have eqF := real_equivalent_of_relative (hFr.mono fun _ h => h.1) hgr heF + have eqH := real_equivalent_of_relative (hHr.mono fun _ h => h.1) hhr heH + have hbO : (fun t : ℝ => (F (t:ℂ)).re) =O[atTop] (fun t : ℝ => (H (t:ℂ)).re) := by + obtain ⟨D,hD,hO⟩ := hO + apply Asymptotics.IsBigO.of_bound D + filter_upwards [hO,hFr,hHr] with t ht hf hh + simpa only [Real.norm_eq_abs,abs_of_pos hf.2,abs_of_pos hh.2] using ht + refine ⟨g,h,hg,hh,hg0.and hh0,hgr,hhr,eqF.tendsto_atTop hFt,eqH.tendsto_atTop hHt, + hfast.trans_isBigO eqH.isBigO,eqF.symm.isBigO.trans (hbO.trans eqH.isBigO),heF,heH,?_⟩ + intro hl + exact (eqF.symm.isBigO.trans_isLittleO hl).trans_isBigO eqH.isBigO + +end DegeneratingTrees.Clock + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +theorem ExpansionOver.zero_leading_strip_data {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) {F H : ℂ → ℂ} + (hF : ExpansionOver K F) (hH : ExpansionOver K H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : ∃ D : ℝ,0 (H (t:ℂ)).re)) + (htop : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 0)) : + ∃ g h : ℂ → ℂ,g∈K ∧ h∈K ∧ + (∀ᶠ z in sectorInfinity,g z≠0 ∧ h z≠0) ∧ + (∀ᶠ t : ℝ in atTop,(g (t:ℂ)).im=0 ∧ 0<(g (t:ℂ)).re) ∧ + (∀ᶠ t : ℝ in atTop,(h (t:ℂ)).im=0 ∧ 0<(h (t:ℂ)).re) ∧ + Tendsto (fun t : ℝ => (g (t:ℂ)).re) atTop atTop ∧ + Tendsto (fun t : ℝ => (h (t:ℂ)).re) atTop atTop ∧ + id =o[atTop] (fun t : ℝ => (h (t:ℂ)).re) ∧ + (fun t : ℝ => (g (t:ℂ)).re) =O[atTop] (fun t : ℝ => (h (t:ℂ)).re) ∧ + ExpSmall 0 (fun z => F z/g z-1) ∧ ExpSmall 0 (fun z => H z/h z-1) ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun t : ℝ => (g (t:ℂ)).re) =o[atTop] (fun t : ℝ => (h (t:ℂ)).re)) := by + obtain ⟨a,ha,g,hg,hg0,hgr,hFe,hFd⟩ := hF.positive_leading_strip hK hconj hFr hFt + obtain ⟨b,hb,h,hh,hh0,hhr,hHe,hHd⟩ := hH.positive_leading_strip hK hconj hHr hHt + have hb0 : b=0 := Complex.ofReal_eq_zero.mp (tendsto_nhds_unique hHd htop) + subst b + have hFa := hF.choose_spec.choose_spec.1.eventually_analytic + have hHa := hH.choose_spec.choose_spec.1.eventually_analytic + have hab : a≤0 := unbounded_log_exponent_order (le_refl 0) + (tendsto_real_sectorInfinity.eventually hFa) (tendsto_real_sectorInfinity.eventually hHa) + hFr hHr hFt (hFd.comp tendsto_real_stripInfinity) (hHd.comp tendsto_real_stripInfinity) hO + have ha0 := le_antisymm hab ha + subst a + have heF : ExpSmall 0 (fun z => F z/g z-1) := by simpa [div_eq_mul_inv,mul_comm] using hFe + have heH : ExpSmall 0 (fun z => H z/h z-1) := by simpa [div_eq_mul_inv,mul_comm] using hHe + have eqF := real_equivalent_of_relative (hFr.mono fun _ h => h.1) hgr heF + have eqH := real_equivalent_of_relative (hHr.mono fun _ h => h.1) hhr heH + have hbO : (fun t : ℝ => (F (t:ℂ)).re) =O[atTop] (fun t : ℝ => (H (t:ℂ)).re) := by + obtain ⟨D,hD,hO⟩ := hO + apply Asymptotics.IsBigO.of_bound D + filter_upwards [hO,hFr,hHr] with t ht hf hh + simpa only [Real.norm_eq_abs,abs_of_pos hf.2,abs_of_pos hh.2] using ht + refine ⟨g,h,hg,hh,hg0.and hh0,hgr,hhr,eqF.tendsto_atTop hFt,eqH.tendsto_atTop hHt, + hfast.trans_isBigO eqH.isBigO,eqF.symm.isBigO.trans (hbO.trans eqH.isBigO),heF,heH,?_⟩ + intro hl + exact (eqF.symm.isBigO.trans_isLittleO hl).trans_isBigO eqH.isBigO + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +open scoped NNReal +namespace DegeneratingTrees.Clock + + + +theorem analytic_perturbative_inverse {f : ℂ → ℂ} {S V : Set ℂ} + (hV : IsOpen V) + (r : ℂ → ℝ) (hr : ContinuousOn r V) (hrpos : ∀ w ∈ V, 0 < r w) + (hdisc : ∀ w ∈ V, closedBall w (r w) ⊆ S) + (hf : AnalyticOnNhd ℂ f S) + (hder : ∀ w ∈ V, ∀ z ∈ ball w (r w), ‖deriv f z-1‖ ≤ (1/2:ℝ)) + (hsmall : ∀ w ∈ V, ‖f w-w‖ ≤ r w/4) : + ∃ g : ℂ → ℂ, AnalyticOnNhd ℂ g V ∧ + (∀ w ∈ V, g w ∈ S ∧ f (g w) = w ∧ ‖g w-w‖ ≤ 2*‖f w-w‖) ∧ + (∀ w ∈ V, ∀ z ∈ ball w (r w), f z = w → g w = z) := by + classical + have hlocal (w : ℂ) (hw : w ∈ V) := analytic_near_identity_inverse + (f := f) (s := ball w (r w)) (c := (1/2:ℝ≥0)) isOpen_ball + (convex_ball _ _) (by norm_num) (hf.mono (ball_subset_closedBall.trans (hdisc w hw))) + (by simpa using hder w hw) + have hex (w : ℂ) (hw : w ∈ V) : ∃ z : ℂ, + z ∈ ball w (r w) ∧ f z = w ∧ ‖z-w‖ ≤ 2*‖f w-w‖ := by + obtain ⟨g,hga,hgf,hfg,hmetric,hball⟩ := hlocal w hw + have hwball : w ∈ ball w (r w) := mem_ball_self (hrpos w hw) + have hhalf : closedBall w (r w/2) ⊆ ball w (r w) := + closedBall_subset_ball (by linarith [hrpos w hw]) + have himage : w ∈ f '' ball w (r w) := by + apply hball w (r w/2) (by linarith [hrpos w hw]) hhalf + rw [mem_closedBall_iff_norm, norm_sub_rev] + convert hsmall w hw using 1 + norm_num + ring + refine ⟨g w,(hfg w himage).1,(hfg w himage).2,?_⟩ + have hm := hmetric (g w) (hfg w himage).1 w hwball + rw [(hfg w himage).2,norm_sub_rev w (f w)] at hm + norm_num at hm + linarith + choose a ha using hex + let g : ℂ → ℂ := fun w => if hw : w ∈ V then a w hw else 0 + have hg (w : ℂ) (hw : w ∈ V) : + g w ∈ ball w (r w) ∧ f (g w) = w ∧ ‖g w-w‖ ≤ 2*‖f w-w‖ := by + simpa only [g,dite_eq_left hw] using ha w hw + have hgsmall (w : ℂ) (hw : w ∈ V) : ‖g w-w‖ ≤ r w/2 := by + have := (hg w hw).2.2 + linarith [hsmall w hw] + have huniq (w : ℂ) (hw : w ∈ V) (z : ℂ) (hz : z ∈ ball w (r w)) + (he : f z = w) : g w = z := by + obtain ⟨a,ha,haf,hfa,hm,hball⟩ := hlocal w hw + have h := hm (g w) (hg w hw).1 z hz + rw [(hg w hw).2.1,he,sub_self,norm_zero] at h + have hn : ‖g w-z‖ = 0 := by norm_num at h; nlinarith [norm_nonneg (g w-z)] + exact sub_eq_zero.mp (norm_eq_zero.mp hn) + refine ⟨g,?_,fun w hw => ⟨hdisc w hw (ball_subset_closedBall (hg w hw).1), + (hg w hw).2⟩,huniq⟩ + intro w hw + obtain ⟨a,ha,haf,hfa,hm,hball⟩ := hlocal w hw + have hwimage : w ∈ f '' ball w (r w) := ⟨g w,(hg w hw).1,(hg w hw).2.1⟩ + have hann := ha w hwimage + have hnear : ∀ᶠ v in 𝓝 w, v ∈ V ∧ g v ∈ ball w (r w) := by + have hrc : ContinuousAt r w := (hr w hw).continuousAt (hV.mem_nhds hw) + have hb : ∀ᶠ v in 𝓝 w, r v/2 + ‖v-w‖ < r w := + ((hrc.div_const 2).add (continuousAt_id.sub continuousAt_const).norm).eventually + (gt_mem_nhds (by simpa using (show r w/2 < r w by linarith [hrpos w hw]))) + filter_upwards [hV.mem_nhds hw,hb] with v hv hbound + refine ⟨hv,mem_ball_iff_norm.mpr ?_⟩ + calc ‖g v-w‖ ≤ ‖g v-v‖+‖v-w‖ := by simpa only [dist_eq_norm] using dist_triangle (g v) v w + _ ≤ r v/2 + ‖v-w‖ := add_le_add (hgsmall v hv) le_rfl + _ < r w := hbound + apply hann.congr + filter_upwards [hnear] with v hv + calc a v = a (f (g v)) := congrArg a (hg v hv.1).2.1.symm + _ = g v := haf (g v) hv.2 + +end DegeneratingTrees.Clock + + + + + + + +open Set Complex Metric +namespace DegeneratingTrees.Clock + +lemma closedBall_inside_double {w z : ℂ} {r : ℝ} (hz : z∈closedBall w r) : + closedBall z r ⊆ closedBall w (2*r) := by + intro u hu + rw [mem_closedBall] at * + exact (dist_triangle u z w).trans (by linarith) + +lemma cauchy_deriv_inner_disc {f : ℂ → ℂ} {w : ℂ} {r M : ℝ} + (hr : 0 < r) (hf : AnalyticOnNhd ℂ f (closedBall w (2*r))) + (hM : ∀ z∈closedBall w (2*r),‖f z‖ ≤ M) : + ∀ z∈closedBall w r,‖deriv f z‖ ≤ M/r := by + intro z hz + have hs := closedBall_inside_double hz + have hd := hf.differentiableOn.diffContOnCl_ball hs + exact Complex.norm_deriv_le_of_forall_mem_sphere_norm_le hr hd + (fun u hu => hM _ (hs (sphere_subset_closedBall hu))) + +lemma cauchy_increment_inner_disc {f : ℂ → ℂ} {w u v : ℂ} {r M : ℝ} + (hr : 0 < r) (hf : AnalyticOnNhd ℂ f (closedBall w (2*r))) + (hM : ∀ z∈closedBall w (2*r),‖f z‖ ≤ M) + (hu : u∈closedBall w r) (hv : v∈closedBall w r) : + ‖f v-f u‖ ≤ M/r*‖v-u‖ := by + have hs : closedBall w r ⊆ closedBall w (2*r) := closedBall_subset_closedBall (by linarith) + exact Convex.norm_image_sub_le_of_norm_deriv_le + (fun z hz => (hf z (hs hz)).differentiableAt) + (cauchy_deriv_inner_disc hr hf hM) (convex_closedBall w r) hu hv + + + +theorem analytic_inverse_of_disc_error {f : ℂ → ℂ} {S V : Set ℂ} + (hV : IsOpen V) (r : ℂ → ℝ) (hr : ContinuousOn r V) + (hrpos : ∀ w∈V,0 < r w) + (hdisc : ∀ w∈V,closedBall w (2*r w) ⊆ S) + (hf : AnalyticOnNhd ℂ f S) + (herr : ∀ w∈V,∀ z∈closedBall w (2*r w),‖f z-z‖ ≤ r w/4) : + ∃ g : ℂ → ℂ,AnalyticOnNhd ℂ g V ∧ + (∀ w∈V,g w∈S ∧ f (g w)=w ∧ ‖g w-w‖ ≤ 2*‖f w-w‖) ∧ + (∀ w∈V,∀ z∈ball w (r w),f z=w → g w=z) := by + apply analytic_perturbative_inverse hV r hr hrpos + (fun w hw => (closedBall_subset_closedBall (by linarith [hrpos w hw])).trans (hdisc w hw)) hf + · intro w hw z hz + let e : ℂ → ℂ := fun t => f t-t + have he : AnalyticOnNhd ℂ e (closedBall w (2*r w)) := + (hf.mono (hdisc w hw)).sub analyticOnNhd_id + have hd := cauchy_deriv_inner_disc (hrpos w hw) he (herr w hw) + z (ball_subset_closedBall hz) + have hzf : AnalyticAt ℂ f z := hf _ (hdisc w hw + ((closedBall_subset_closedBall (by linarith [hrpos w hw])) (ball_subset_closedBall hz))) + have hde : deriv e z=deriv f z-1 := by + exact (hzf.differentiableAt.hasDerivAt.sub (hasDerivAt_id z)).deriv + rw [hde] at hd + have heq : r w/4/r w=(1/4:ℝ) := by field_simp [(hrpos w hw).ne'] + rw [heq] at hd + linarith + · intro w hw + exact herr w hw w (mem_closedBall_self (by linarith [hrpos w hw])) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/AnalyticFactors.lean b/lean/OAI/Analysis/PathSelection/AnalyticFactors.lean new file mode 100644 index 0000000000000000000000000000000000000000..d380873a640073e7d888bf8bd64134db9f60a113 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/AnalyticFactors.lean @@ -0,0 +1,267 @@ +import Mathlib +import OAI.Analysis.PathSelection.MonicFamilies +import OAI.Analysis.PathSelection.RootClusters +import OAI.Analysis.PathSelection.ScalarFields + +namespace OAI + +/-! Normal root limits and algebraic factorization of analytic scalar families. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Metric Filter Topology Complex +open scoped BigOperators Polynomial +namespace DegeneratingTrees + +theorem analyticOrderAt_polynomial_eval (P : ℂ[X]) (hP : P ≠ 0) (a : ℂ) : + analyticOrderAt P.eval a = (P.rootMultiplicity a : ℕ∞) := by + obtain ⟨Q,hPQ,hQ⟩ := P.exists_eq_pow_rootMultiplicity_mul_and_not_dvd hP a + apply (AnalyticOnNhd.eval_polynomial P a (mem_univ a)).analyticOrderAt_eq_natCast.mpr + refine ⟨Q.eval,AnalyticOnNhd.eval_polynomial Q a (mem_univ a),?_,?_⟩ + · exact fun he => hQ (Polynomial.dvd_iff_isRoot.mpr he) + · filter_upwards [] with z + conv_lhs => rw [hPQ] + simp + + + +theorem analytic_polynomial_cluster {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + (P : A → ℂ[X]) (hP : P 0 ≠ 0) + (hF : AnalyticAt ℂ (fun x : A × ℂ => (P x.1).eval x.2) 0) : + ∃ (U : Set A) (W : A → ℂ[X]), IsOpen U ∧ (0 : A) ∈ U ∧ + (∀ k, AnalyticOnNhd ℂ (fun q => (W q).coeff k) U) ∧ + ∀ q ∈ U, (W q).Monic ∧ (W q).natDegree = (P 0).rootMultiplicity 0 ∧ W q ∣ P q := by + let d := (P 0).rootMultiplicity 0 + have hd : analyticOrderAt (fun y => (P (0 : A)).eval y) 0 = (d : ℕ∞) := + analyticOrderAt_polynomial_eval (P 0) hP 0 + obtain ⟨r,U,φ,hr,hU,h0,hFA,hφ,hφe,hφu,hm,hm0⟩ := fixed_circle_data hF hd + let W : A → ℂ[X] := fun q => contourPolynomial (P q).eval r d + refine ⟨U,W,hU,h0,?_,?_⟩ + · intro k q hq + exact (analytic_contourPolynomial_coeff (F := fun x : A × ℂ => (P x.1).eval x.2) + (r := r) (U := U) hm d k) q hq + · intro q hq + have hn (z : ℂ) (hz : z ∈ sphere (0 : ℂ) r) : (P q).eval z ≠ 0 := by + rw [← hφe q hq ⟨z,hz⟩] + exact (ContinuousMap.isUnit_iff_forall_ne_zero _).mp (hφu q hq) ⟨z,hz⟩ + have hf : AnalyticOnNhd ℂ (P q).eval (closedBall 0 r) := + fun z _ => AnalyticOnNhd.eval_polynomial (P q) z (mem_univ z) + obtain ⟨N,g,hN,hM,hD,hg,hgn,hEq⟩ := contour_fiber_factorization hr hf hn + have hNd : N = d := by exact_mod_cast hN.symm.trans (hm0 q hq) + subst N + exact ⟨hM,hD,contourPolynomial_dvd hr hn (hm0 q hq)⟩ + +end DegeneratingTrees + + + + + + + +open Set Metric Filter Topology Complex Polynomial +open scoped BigOperators +namespace DegeneratingTrees.ScalarEvaluation +variable {K α : Type*} [Field K] [Algebra ℂ K] {l : Filter α} +variable (e : ScalarEvaluation K α l) + +lemma lift_monic_polynomial (hhol : e.HolomorphicallyClosed) + {n m : ℕ} (a : Fin n → K) (c : Fin n → ℂ) + (ha : ∀ i, Tendsto (e.value (a i)) l (𝓝 (c i))) + (W : (Fin n → ℂ) → ℂ[X]) (hWa : ∀ k, AnalyticAt ℂ (fun q => (W q).coeff k) c) + (hW : ∀ᶠ q in 𝓝 c, (W q).Monic ∧ (W q).natDegree = m) : + ∃ V : K[X], V.Monic ∧ V.natDegree = m ∧ + e.polynomialValue V =ᶠ[l] fun x => W (fun i => e.value (a i) x) := by + classical + have hb : ∀ k : Fin m, ∃ b : K, + e.value b =ᶠ[l] fun x => (W (fun i => e.value (a i) x)).coeff k := by + intro k + exact hhol n a c ha _ (hWa k) + choose b hb using hb + let V : K[X] := monicFamily b + refine ⟨V,monicFamily_monic b,monicFamily_natDegree b,?_⟩ + have ht : Tendsto (fun x i => e.value (a i) x) l (𝓝 c) := tendsto_pi_nhds.mpr ha + have hec : ∀ᶠ x in l, ∀ k : Fin (m+1), + (e.polynomialValue V x).coeff k = e.value (V.coeff k) x := + Filter.eventually_all.mpr (fun k => e.polynomialValue_coeff_eventually V k) + filter_upwards [Filter.eventually_all.mpr hb,ht.eventually hW,hec,e.one] with x hx hWx hcx hone + ext k + by_cases hk : k < m + · rw [hcx ⟨k,by omega⟩] + rw [show V.coeff k = b ⟨k,hk⟩ by simp [V,monicFamily_coeff,hk]] + exact hx ⟨k,hk⟩ + · by_cases hkm : k = m + · subst k + rw [hcx ⟨m,by omega⟩,show V.coeff m = 1 by simp [V,monicFamily_coeff],hone] + exact (hWx.2 ▸ hWx.1.coeff_natDegree).symm + · have hmk : m < k := by omega + rw [coeff_eq_zero_of_natDegree_lt (lt_of_le_of_lt + (e.polynomialValue_natDegree_le V x) (by simpa [V,monicFamily_natDegree] using hmk)), + coeff_eq_zero_of_natDegree_lt (by simpa [hWx.2] using hmk)] + + + +lemma factor_of_finite_coeff_limits [NeBot l] (hhol : e.HolomorphicallyClosed) + {P : K[X]} (hP : P.Monic) (c : Fin P.natDegree → ℂ) + (hc : ∀ i : Fin P.natDegree, Tendsto (e.value (P.coeff i)) l (𝓝 (c i))) (a : ℂ) : + ∃ V : K[X], V.Monic ∧ V.natDegree = (monicFamily c).rootMultiplicity a ∧ V ∣ P := by + classical + let d := P.natDegree + let F : (Fin d → ℂ) → ℂ[X] := fun q => + (monicFamily (fun i => c i + q i)).comp (X + C a) + have hF0 : F 0 ≠ 0 := by + simpa [F,← taylor_apply] using (monicFamily_monic c).ne_zero + have hFa : AnalyticAt ℂ (fun x : (Fin d → ℂ) × ℂ => (F x.1).eval x.2) 0 := by + simpa [F,eval_comp] using monicFamily_eval_analytic c a + obtain ⟨U,W,hU,h0,hWa,hW⟩ := analytic_polynomial_cluster F hF0 hFa + let Z : (Fin d → ℂ) → ℂ[X] := fun q => + taylor (-a) (W (q-c)) + + have hZa : ∀ k, AnalyticAt ℂ (fun q => (Z q).coeff k) c := by + intro k + + have hma : ∀ j, AnalyticAt ℂ (fun q => (W (q-c)).coeff j) c := by + intro j + have h := (hWa j) 0 h0 + have ht : AnalyticAt ℂ (fun q : Fin d → ℂ => q-c) c := analyticAt_id.sub analyticAt_const + exact h.comp_of_eq ht (by simp) + have hUn : ∀ᶠ q in 𝓝 c, q-c ∈ U := by + have ht : ContinuousAt (fun q : Fin d → ℂ => q-c) c := continuousAt_id.sub continuousAt_const + exact ht.preimage_mem_nhds (by simpa using hU.mem_nhds h0) + have hdW : ∀ᶠ q in 𝓝 c, (W (q-c)).natDegree < (F 0).rootMultiplicity 0 + 1 := by + filter_upwards [hUn] with q hq + rw [(hW _ hq).2.1] + omega + have hformula : (fun q => (Z q).coeff k) =ᶠ[𝓝 c] + fun q => ∑ j ∈ Finset.range ((F 0).rootMultiplicity 0+1), + (W (q-c)).coeff j * ((-a)^(j-k) * (j.choose k : ℂ)) := by + filter_upwards [hdW] with q hq + change (taylor (-a) (W (q-c))).coeff k = _ + conv_lhs => rw [← Polynomial.sum_monomial_eq (W (q-c))] + simp only [Polynomial.sum_def,map_sum,taylor_monomial,finsetSum_coeff,coeff_C_mul,coeff_X_add_C_pow] + apply Finset.sum_subset + · intro j hj + exact Finset.mem_range.mpr (lt_of_le_of_lt (le_natDegree_of_mem_supp j hj) hq) + · intro j hj hjs + simp [Polynomial.notMem_support_iff.mp hjs] + exact (Finset.analyticAt_fun_sum _ (fun j hj => (hma j).mul analyticAt_const)).congr hformula.symm + have hZ : ∀ᶠ q in 𝓝 c, + (Z q).Monic ∧ (Z q).natDegree = (monicFamily c).rootMultiplicity a ∧ + Z q ∣ monicFamily q := by + have ht : ContinuousAt (fun q : Fin d → ℂ => q-c) c := continuousAt_id.sub continuousAt_const + have hu : ∀ᶠ q in 𝓝 c, q-c ∈ U := ht.preimage_mem_nhds (by simpa using hU.mem_nhds h0) + filter_upwards [hu] with q hq + obtain ⟨hm,hd,hdiv⟩ := hW (q-c) hq + have he : F (q-c) = taylor a (monicFamily q) := by + simp [F,taylor_apply,Pi.sub_apply] + have hr : (F 0).rootMultiplicity 0 = (monicFamily c).rootMultiplicity a := by + simpa [F] using (Polynomial.rootMultiplicity_eq_rootMultiplicity (p := monicFamily c) (t := a)).symm + refine ⟨by simpa [Z,Monic] using hm,by simpa [Z,hr] using hd,?_⟩ + have hv := (Polynomial.taylorEquiv (-a)).toRingHom.map_dvd hdiv + change taylor (-a) (W (q-c)) ∣ taylor (-a) (F (q-c)) at hv + simpa [Z,he,Polynomial.taylor_taylor] using hv + obtain ⟨V,hVm,hVd,hVe⟩ := e.lift_monic_polynomial hhol (fun i : Fin d => P.coeff i) c hc Z hZa + (hZ.mono (fun q hq => ⟨hq.1,hq.2.1⟩)) + refine ⟨V,hVm,hVd,e.polynomial_dvd_of_eventually hVm ?_⟩ + have ht : Tendsto (fun x i => e.value (P.coeff (i : Fin d)) x) l (𝓝 c) := tendsto_pi_nhds.mpr hc + have hPfun : e.polynomialValue P =ᶠ[l] + fun x => monicFamily (fun i : Fin d => e.value (P.coeff i) x) := by + + have hEc : ∀ᶠ x in l, ∀ k : Fin (d+1), + (e.polynomialValue P x).coeff k = e.value (P.coeff k) x := + Filter.eventually_all.mpr (fun k => e.polynomialValue_coeff_eventually P k) + filter_upwards [hEc,e.one] with x hx h1 + ext k + rw [monicFamily_coeff] + split_ifs with hk hkD + · exact hx ⟨k,by omega⟩ + · subst k + rw [hx ⟨d,by omega⟩,hP.coeff_natDegree,h1] + · exact coeff_eq_zero_of_natDegree_lt (lt_of_le_of_lt + (e.polynomialValue_natDegree_le P x) (by dsimp [d] at *; omega)) + filter_upwards [hVe,ht.eventually hZ,hPfun] with x hx hz hp + simpa [hx,hp] using hz.2.2 + +end DegeneratingTrees.ScalarEvaluation + + + + + +open Set Filter Topology Complex Polynomial +open scoped BigOperators +namespace DegeneratingTrees + +lemma proper_root_cluster {P : ℂ[X]} (hP : P.Monic) (hd : 0 < P.natDegree) + (hdep : P.coeff (P.natDegree-1) = 0) (hpow : P ≠ X^P.natDegree) : + ∃ a : ℂ, 0 < P.rootMultiplicity a ∧ P.rootMultiplicity a < P.natDegree := by + obtain ⟨a,ha⟩ := Complex.exists_root (natDegree_pos_iff_degree_pos.mp hd) + have hmpos : 0 < P.rootMultiplicity a := (rootMultiplicity_pos hP.ne_zero).mpr ha + have hmdvd := pow_rootMultiplicity_dvd P a + have hmle : P.rootMultiplicity a ≤ P.natDegree := by + simpa using natDegree_le_of_dvd hmdvd hP.ne_zero + refine ⟨a,hmpos,lt_of_le_of_ne hmle ?_⟩ + intro heq + have he : P = (X-C a)^P.natDegree := by + have hp := eq_of_monic_of_dvd_of_natDegree_le ((monic_X_sub_C a).pow (P.rootMultiplicity a)) + hP hmdvd (by simp [heq]) + simpa [heq] using hp + have hcoeff : P.coeff (P.natDegree-1) = (-a) * (P.natDegree : ℂ) := by + conv_lhs => arg 1; rw [he] + rw [sub_eq_add_neg,← C_neg,coeff_X_add_C_pow] + have hsub : P.natDegree - (P.natDegree-1) = 1 := by omega + have hchoose : P.natDegree.choose (P.natDegree-1) = P.natDegree := by + obtain ⟨n,hn⟩ := Nat.exists_eq_succ_of_ne_zero (Nat.ne_of_gt hd) + rw [hn] + simp + rw [hsub,hchoose,pow_one] + have ha0 : a = 0 := by + have hn : (P.natDegree : ℂ) ≠ 0 := Nat.cast_ne_zero.mpr (Nat.ne_of_gt hd) + rw [hdep] at hcoeff + exact neg_eq_zero.mp ((mul_eq_zero.mp hcoeff.symm).resolve_right hn) + apply hpow + simpa [ha0] using he + +lemma rescale_monic_eq {K : Type*} [Field K] {P : K[X]} (hP : P.Monic) + (ρ : K) (hρ : ρ ≠ 0) : + monicFamily (fun i : Fin P.natDegree => P.coeff i / ρ^(P.natDegree-i.val)) = + C (ρ^P.natDegree)⁻¹ * P.comp (C ρ * X) := by + ext k + rw [monicFamily_coeff,coeff_C_mul,comp_C_mul_X_coeff] + split_ifs with hk hkd + · dsimp only + rw [show ρ^P.natDegree = ρ^k * ρ^(P.natDegree-k) by + rw [← pow_add,Nat.add_sub_of_le hk.le]] + field_simp + · subst k + rw [hP.coeff_natDegree,one_mul] + exact (inv_mul_cancel₀ (pow_ne_zero _ hρ)).symm + · rw [coeff_eq_zero_of_natDegree_lt (by omega),zero_mul,mul_zero] + +lemma rescale_monic_irreducible {K : Type*} [Field K] {P : K[X]} (hP : P.Monic) + (hI : Irreducible P) (ρ : K) (hρ : ρ ≠ 0) : + Irreducible (monicFamily (fun i : Fin P.natDegree => P.coeff i / ρ^(P.natDegree-i.val))) := by + let : Invertible ρ := invertibleOfNonzero hρ + rw [rescale_monic_eq hP ρ hρ] + apply (irreducible_isUnit_mul (isUnit_C.mpr (isUnit_iff_ne_zero.mpr (inv_ne_zero (pow_ne_zero _ hρ))))).mpr + have h := hI.map (algEquivCMulXAddC ρ 0) + simpa [algEquivCMulXAddC_apply,← comp_eq_aeval] using h + +lemma irreducible_no_proper_monic_factor {K : Type*} [Field K] {P V : K[X]} + (hI : Irreducible P) (hV : V.Monic) (hdiv : V ∣ P) + (hpos : 0 < V.natDegree) (hsmall : V.natDegree < P.natDegree) : False := by + obtain ⟨Q,rfl⟩ := hdiv + rcases hI.isUnit_or_isUnit rfl with hv | hq + · have hdeg := natDegree_eq_zero_of_isUnit hv + omega + · have hq0 : Q ≠ 0 := hq.ne_zero + have hdeg := hV.natDegree_mul' hq0 + rw [natDegree_eq_zero_of_isUnit hq,Nat.add_zero] at hdeg + omega + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ClockAlgebra.lean b/lean/OAI/Analysis/PathSelection/ClockAlgebra.lean new file mode 100644 index 0000000000000000000000000000000000000000..6a75733bb9dc7405332be6523d111c22e0f4ace2 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ClockAlgebra.lean @@ -0,0 +1,428 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockExpansions + +namespace OAI + +/-! Multiplication, word polynomials, exponential decay and geometric inverses. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem SectorExpansion.mul {f g : ℂ → ℂ} {E F : Set ℝ} {b c : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) (hg : SectorExpansion g F c) + (hb : ∀ β ∈ E, SectorSlow (b β)) (hc : ∀ γ ∈ F, SectorSlow (c γ)) : + SectorExpansion (fun z => f z*g z) (exponentSum E F) + (exponentConvolution hf.bounded_above hg.bounded_above hf.finite_above hg.finite_above b c) := by + classical + obtain ⟨A,hA⟩ := hf.bounded_above + obtain ⟨C,hC⟩ := hg.bounded_above + apply SectorExpansion.of_expSmall + (exponentSum_bddAbove hf.bounded_above hg.bounded_above) + (exponentSum_finite hf.bounded_above hg.bounded_above hf.finite_above hg.finite_above) + · filter_upwards [hf.eventually_analytic,hg.eventually_analytic] with z hzf hzg + exact hzf.mul hzg + · intro B + let U := B-(C+1) + let V := B-(A+1) + let P : ℂ → ℂ := fun z => ∑ β ∈ (hf.finite_above U).toFinset,Complex.exp ((β:ℂ)*z)*b β z + let Q : ℂ → ℂ := fun z => ∑ γ ∈ (hg.finite_above V).toFinset,Complex.exp ((γ:ℂ)*z)*c γ z + have hP : ExpBound (A+1) P := truncation_expBound (fun β hβ => hA hβ) hb U (hf.finite_above U) + have hr1 : ExpSmall B (fun z => (f z-P z)*g z) := by + have h := (hf.expSmall_remainder U).mul (hg.expBound (fun γ hγ => hC hγ)) + simpa only [U,sub_add_cancel] using h + have hr2 : ExpSmall B (fun z => (g z-Q z)*P z) := by + have h := (hg.expSmall_remainder V).mul hP + simpa only [V,sub_add_cancel] using h + have hr : ExpSmall B (fun z => f z*g z-P z*Q z) := by + convert hr1.add hr2 using 1 + funext z + ring + let T := ((hf.finite_above U).toFinset ×ˢ (hg.finite_above V).toFinset).filter + (fun p => p.1+p.2 < B) + have hlow : ExpSmall B (fun z => ∑ p ∈ T, + Complex.exp (((p.1+p.2:ℝ):ℂ)*z)*(b p.1 z*c p.2 z)) := by + apply ExpSmall.sum + intro p hp + have hpr := Finset.mem_product.mp (Finset.mem_filter.mp hp).1 + have he := ((hf.finite_above U).mem_toFinset.mp hpr.1).1 + have hF := ((hg.finite_above V).mem_toFinset.mp hpr.2).1 + exact ((hb p.1 he).mul (hc p.2 hF)).expSmall (Finset.mem_filter.mp hp).2 + convert hr.add hlow using 1 + funext z + have hsplit := rectangle_split hf.bounded_above hg.bounded_above hf.finite_above hg.finite_above + (B := B) (U := U) (V := V) (fun β hβ => hA hβ) (fun γ hγ => hC hγ) + (by dsimp [U]; linarith) (by dsimp [V]; linarith) b c z + change P z*Q z = _ at hsplit + rw [hsplit] + dsimp [T] + ring + +lemma SectorSlow.sum {ι : Type*} (S : Finset ι) {f : ι → ℂ → ℂ} + (h : ∀ i ∈ S, SectorSlow (f i)) : SectorSlow (fun z => ∑ i ∈ S,f i z) := by + intro ε hε + exact ExpBound.sum S (fun i hi => h i hi ε hε) + +lemma convolution_slow {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (hFl : ∀ B : ℝ, (F ∩ Ici B).Finite) + {b c : ℝ → ℂ → ℂ} (hb : ∀ β ∈ E, SectorSlow (b β)) (hc : ∀ γ ∈ F, SectorSlow (c γ)) + (δ : ℝ) : SectorSlow (exponentConvolution hE hF hEl hFl b c δ) := by + apply SectorSlow.sum + intro p hp + have hh := (exponentFiber_finite hE hF hEl hFl δ).mem_toFinset.mp hp + exact (hb p.1 hh.1).mul (hc p.2 hh.2.1) + +lemma convolution_analytic {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (hFl : ∀ B : ℝ, (F ∩ Ici B).Finite) + {b c : ℝ → ℂ → ℂ} + (hb : ∀ β ∈ E, SectorEventually (fun z => AnalyticAt ℂ (b β) z)) + (hc : ∀ γ ∈ F, SectorEventually (fun z => AnalyticAt ℂ (c γ) z)) (δ : ℝ) : + SectorEventually (fun z => AnalyticAt ℂ (exponentConvolution hE hF hEl hFl b c δ) z) := by + have hp : ∀ p ∈ (exponentFiber_finite hE hF hEl hFl δ).toFinset, + SectorEventually (fun z => AnalyticAt ℂ (fun w => b p.1 w*c p.2 w) z) := by + intro p hp + have hh := (exponentFiber_finite hE hF hEl hFl δ).mem_toFinset.mp hp + exact ((hb p.1 hh.1).and (hc p.2 hh.2.1)).mono (fun _ hx => hx.1.mul hx.2) + exact (SectorEventually.finset_forall _ SectorEventually.truth hp).mono + (fun _ hz => Finset.analyticAt_fun_sum _ hz) + +end DegeneratingTrees.Clock + + + + + + + +open Set Complex +namespace DegeneratingTrees.Clock + +def wordCoefficient (b : ℝ → ℂ → ℂ) (w : List ℝ) (z : ℂ) : ℂ := + (w.map (fun β => b β z)).prod + +def wordTerm (b : ℝ → ℂ → ℂ) (w : List ℝ) (z : ℂ) : ℂ := + Complex.exp ((w.sum:ℂ)*z)*wordCoefficient b w z + +lemma wordTerm_nil (b : ℝ → ℂ → ℂ) (z : ℂ) : wordTerm b [] z=1 := by + simp [wordTerm,wordCoefficient] + +lemma wordTerm_cons (b : ℝ → ℂ → ℂ) (β : ℝ) (w : List ℝ) (z : ℂ) : + wordTerm b (β::w) z = (Complex.exp ((β:ℂ)*z)*b β z)*wordTerm b w z := by + simp only [wordTerm,wordCoefficient,List.sum_cons,List.map_cons,List.prod_cons, + ofReal_add,add_mul,Complex.exp_add] + ring + +lemma power_truncation_words (S : Finset ℝ) (b : ℝ → ℂ → ℂ) (n : ℕ) (z : ℂ) : + (∑ β ∈ S,Complex.exp ((β:ℂ)*z)*b β z)^n = + ∑ w ∈ wordsOfLength S n,wordTerm b w z := by + classical + induction n with + | zero => simp [wordsOfLength,wordTerm_nil] + | succ n ih => + rw [pow_succ',ih,Finset.sum_mul] + simp_rw [Finset.mul_sum] + rw [←Finset.sum_product (f := fun p : ℝ × List ℝ => + (Complex.exp ((p.1:ℂ)*z)*b p.1 z)*wordTerm b p.2 z)] + apply Finset.sum_bij (fun p _ => p.1::p.2) + · intro p hp + have hh := Finset.mem_product.mp hp + have hw := mem_wordsOfLength.mp hh.2 + exact mem_wordsOfLength.mpr ⟨by simp [hw.1],by simpa using And.intro hh.1 hw.2⟩ + · intro p hp q hq he + exact Prod.ext (List.cons.inj he).1 (List.cons.inj he).2 + · intro w hw + have hh := mem_wordsOfLength.mp hw + cases w with + | nil => simp at hh + | cons β w => + refine ⟨(β,w),Finset.mem_product.mpr ⟨hh.2 β (by simp),?_⟩,rfl⟩ + exact mem_wordsOfLength.mpr ⟨by simpa using hh.1, + fun γ hγ => hh.2 γ (List.mem_cons_of_mem _ hγ)⟩ + · intro p hp + exact (wordTerm_cons b p.1 p.2 z).symm + +lemma geometric_truncation_words (S : Finset ℝ) (b : ℝ → ℂ → ℂ) (N : ℕ) (z : ℂ) : + (∑ n ∈ Finset.range (N+1),(∑ β ∈ S,Complex.exp ((β:ℂ)*z)*b β z)^n) = + ∑ w ∈ wordsUpTo S N,wordTerm b w z := by + classical + simp_rw [power_truncation_words] + symm + apply Finset.sum_biUnion + intro n hn m hm hne + apply Finset.disjoint_left.mpr + intro w hwn hwm + exact hne ((mem_wordsOfLength.mp hwn).1.symm.trans (mem_wordsOfLength.mp hwm).1) + +variable {E : Set ℝ} {δ : ℝ} (hδ : 0 < δ) (hE : ∀ β ∈ E, β ≤ -δ) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) + +def geometricCoefficient (b : ℝ → ℂ → ℂ) (β : ℝ) (z : ℂ) : ℂ := + ∑ w ∈ (wordFiber_finite hδ hE hEl β).toFinset,wordCoefficient b w z + +lemma geometric_coefficient_truncation (b : ℝ → ℂ → ℂ) (B : ℝ) (z : ℂ) : + (∑ β ∈ (wordSupport_finite hδ hE hEl B).toFinset, + Complex.exp ((β:ℂ)*z)*geometricCoefficient hδ hE hEl b β z) = + ∑ w ∈ (wordCut_finite hδ hE hEl B).toFinset,wordTerm b w z := by + classical + let S := (wordSupport_finite hδ hE hEl B).toFinset + let T := (wordCut_finite hδ hE hEl B).toFinset + have hmaps : ∀ w ∈ T,w.sum ∈ S := by + intro w hw + have hh := (wordCut_finite hδ hE hEl B).mem_toFinset.mp hw + exact (wordSupport_finite hδ hE hEl B).mem_toFinset.mpr ⟨⟨w,hh.1,rfl⟩,hh.2⟩ + calc + _ = ∑ β ∈ S,∑ w ∈ T with w.sum=β,wordTerm b w z := by + apply Finset.sum_congr rfl + intro β hβ + have hB : B ≤ β := ((wordSupport_finite hδ hE hEl B).mem_toFinset.mp hβ).2 + have he : (wordFiber_finite hδ hE hEl β).toFinset = T.filter (fun w => w.sum=β) := by + ext w + simp only [Set.Finite.mem_toFinset,Finset.mem_filter,T,wordFiber,wordCut,mem_ofPred_eq] + constructor + · intro hw + exact ⟨⟨hw.1,by simpa only [hw.2] using hB⟩,hw.2⟩ + · intro hw + exact ⟨hw.1.1,hw.2⟩ + rw [geometricCoefficient,he,Finset.mul_sum] + apply Finset.sum_congr rfl + intro w hw + simp only [wordTerm,(Finset.mem_filter.mp hw).2] + _ = _ := Finset.sum_fiberwise_of_maps_to hmaps _ + +lemma words_high {B : ℝ} {N : ℕ} (hN : -δ*((N:ℝ)+1) < B) : + (wordsUpTo (hEl B).toFinset N).filter (fun w => B ≤ w.sum) = + (wordCut_finite hδ hE hEl B).toFinset := by + classical + ext w + simp only [Finset.mem_filter,Set.Finite.mem_toFinset] + constructor + · intro hw + exact ⟨fun β hβ => ((hEl B).mem_toFinset.mp ((mem_wordsUpTo.mp hw.1).2 β hβ)).1,hw.2⟩ + · intro hw + exact ⟨wordCut_subset_words hδ hE (hEl B) hN hw,hw.2⟩ + +lemma geometric_split (b : ℝ → ℂ → ℂ) {B : ℝ} {N : ℕ} + (hN : -δ*((N:ℝ)+1) < B) (z : ℂ) : + (∑ n ∈ Finset.range (N+1),(∑ β ∈ (hEl B).toFinset,Complex.exp ((β:ℂ)*z)*b β z)^n) = + (∑ β ∈ (wordSupport_finite hδ hE hEl B).toFinset, + Complex.exp ((β:ℂ)*z)*geometricCoefficient hδ hE hEl b β z) + + ∑ w ∈ (wordsUpTo (hEl B).toFinset N).filter (fun w => w.sum < B),wordTerm b w z := by + classical + rw [geometric_truncation_words,geometric_coefficient_truncation, + ←words_high hδ hE hEl hN] + symm + simpa only [not_le] using Finset.sum_filter_add_sum_filter_not + (wordsUpTo (hEl B).toFinset N) (fun w => B ≤ w.sum) (fun w => wordTerm b w z) + +lemma wordCoefficient_slow {b : ℝ → ℂ → ℂ} (hb : ∀ β ∈ E,SectorSlow (b β)) + {w : List ℝ} (hw : w ∈ exponentWords E) : SectorSlow (wordCoefficient b w) := by + induction w with + | nil => + intro ε hε + have h : ExpBound 0 (fun _ : ℂ => (1:ℂ)) := by + simpa only [ExpBound,zero_mul,Real.exp_zero] using Asymptotics.isBigO_const_one (1:ℂ) sectorInfinity (F := ℝ) + change ExpBound ε (fun _ => 1) + exact h.mono hε.le + | cons β w ih => + have hi := ih (fun γ hγ => hw γ (List.mem_cons_of_mem _ hγ)) + change SectorSlow (fun z => b β z*wordCoefficient b w z) + exact (hb β (hw β (by simp))).mul hi + +lemma geometricCoefficient_slow {b : ℝ → ℂ → ℂ} (hb : ∀ β ∈ E,SectorSlow (b β)) (β : ℝ) : + SectorSlow (geometricCoefficient hδ hE hEl b β) := by + apply SectorSlow.sum + intro w hw + exact wordCoefficient_slow hb ((wordFiber_finite hδ hE hEl β).mem_toFinset.mp hw).1 + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ExpBound.const (c : ℂ) : ExpBound 0 (fun _ : ℂ => c) := by + simpa only [ExpBound,zero_mul,Real.exp_zero] using + Asymptotics.isBigO_const_one c sectorInfinity (F := ℝ) + +lemma ExpBound.of_tendsto {f : ℂ → ℂ} {c : ℂ} (hf : Tendsto f sectorInfinity (𝓝 c)) : + ExpBound 0 f := by + simpa only [ExpBound,zero_mul,Real.exp_zero] using hf.isBigO_one ℝ + +lemma ExpBound.pow {a : ℝ} {f : ℂ → ℂ} (hf : ExpBound a f) (n : ℕ) : + ExpBound (a*(n:ℝ)) (fun z => f z^n) := by + induction n with + | zero => simpa using ExpBound.const 1 + | succ n ih => + convert ih.mul hf using 1 + · push_cast; ring + · funext z; rw [pow_succ] + +lemma ExpBound.congr {a : ℝ} {f g : ℂ → ℂ} (hf : ExpBound a f) + (he : f =ᶠ[sectorInfinity] g) : ExpBound a g := hf.congr' he (EventuallyEq.refl _ _) + +lemma ExpSmall.congr {B : ℝ} {f g : ℂ → ℂ} (hf : ExpSmall B f) + (he : f =ᶠ[sectorInfinity] g) : ExpSmall B g := by + obtain ⟨a,ha,hf⟩ := hf + exact ⟨a,ha,hf.congr he⟩ + +lemma ExpBound.tendsto_zero {a : ℝ} {f : ℂ → ℂ} (hf : ExpBound a f) (ha : a < 0) : + Tendsto f sectorInfinity (𝓝 0) := by + apply Asymptotics.IsBigO.trans_tendsto hf + apply Real.tendsto_exp_atBot.comp + exact tendsto_re_sectorInfinity.const_mul_atTop_of_neg ha + +lemma inverse_one_sub_tendsto {f : ℂ → ℂ} (hf : Tendsto f sectorInfinity (𝓝 0)) : + Tendsto (fun z => (1-f z)⁻¹) sectorInfinity (𝓝 1) := by + simpa using (tendsto_const_nhds.sub hf).inv₀ (by norm_num : (1:ℂ)-0≠0) + +lemma inverse_one_sub_bound {f : ℂ → ℂ} (hf : Tendsto f sectorInfinity (𝓝 0)) : + ExpBound 0 (fun z => (1-f z)⁻¹) := ExpBound.of_tendsto (inverse_one_sub_tendsto hf) + +lemma one_sub_eventually_ne {f : ℂ → ℂ} (hf : Tendsto f sectorInfinity (𝓝 0)) : + ∀ᶠ z in sectorInfinity, 1-f z≠0 := by + have ht : Tendsto (fun z => (1:ℂ)-f z) sectorInfinity (𝓝 1) := by + simpa using tendsto_const_nhds.sub hf + exact ht.eventually (eventually_ne_nhds (by norm_num : (1:ℂ)≠0)) + +lemma inverse_difference_small {B : ℝ} {f g : ℂ → ℂ} + (hf : Tendsto f sectorInfinity (𝓝 0)) (hg : Tendsto g sectorInfinity (𝓝 0)) + (he : ExpSmall B (fun z => f z-g z)) : + ExpSmall B (fun z => (1-f z)⁻¹-(1-g z)⁻¹) := by + have h := (he.mul (inverse_one_sub_bound hf)).mul (inverse_one_sub_bound hg) + simp only [add_zero] at h + apply h.congr + filter_upwards [one_sub_eventually_ne hf,one_sub_eventually_ne hg] with z hzf hzg + field_simp + ring + +lemma geom_inverse_error {f : ℂ → ℂ} {a B : ℝ} {N : ℕ} + (hf : ExpBound a f) (ha : a < 0) (hN : a*((N:ℝ)+1) < B) : + ExpSmall B (fun z => (1-f z)⁻¹-∑ n ∈ Finset.range (N+1),f z^n) := by + have ht := hf.tendsto_zero ha + have hpow := (hf.pow (N+1)).mul (inverse_one_sub_bound ht) + simp only [add_zero,Nat.cast_add,Nat.cast_one] at hpow + apply (show ExpSmall B (fun z => f z^(N+1)*(1-f z)⁻¹) from ⟨_,hN,hpow⟩).congr + filter_upwards [one_sub_eventually_ne ht] with z hz + have he := geom_sum_mul_neg (f z) (N+1) + apply (mul_right_cancel₀ hz) + rw [sub_mul,inv_mul_cancel₀ hz,mul_assoc,inv_mul_cancel₀ hz,mul_one,he] + ring + +lemma SectorExpansion.negative_bound {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) {δ : ℝ} (hδ : 0 < δ) (hE : ∀ β ∈ E,β ≤ -δ) : + ExpBound (-δ/2) f := by + have hem : (hf.finite_above (-δ/2)).toFinset=∅ := by + classical + apply Finset.eq_empty_iff_forall_notMem.mpr + intro β hβ + have hh := (hf.finite_above (-δ/2)).mem_toFinset.mp hβ + have hu := hE β hh.1 + have hl : -δ/2 ≤ β := hh.2 + linarith + obtain ⟨a,ha,he⟩ := hf.expSmall_remainder (-δ/2) + simp only [hem,Finset.sum_empty,sub_zero] at he + exact he.mono ha.le + +lemma truncation_negative_bound {E : Set ℝ} {b : ℝ → ℂ → ℂ} {δ : ℝ} + (hδ : 0 < δ) (hE : ∀ β ∈ E,β ≤ -δ) (hb : ∀ β ∈ E,SectorSlow (b β)) + (B : ℝ) (hEl : (E ∩ Ici B).Finite) : + ExpBound (-δ/2) (fun z => ∑ β ∈ hEl.toFinset,Complex.exp ((β:ℂ)*z)*b β z) := by + apply ExpBound.sum + intro β hβ + have he := (hEl.mem_toFinset.mp hβ).1 + exact ((hb β he (δ/2) (by positivity)).expTerm β).mono (by linarith [hE β he]) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem SectorExpansion.geometric_inverse {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) {δ : ℝ} (hδ : 0 < δ) + (hE : ∀ β ∈ E,β ≤ -δ) (hb : ∀ β ∈ E,SectorSlow (b β)) : + SectorExpansion (fun z => (1-f z)⁻¹) (wordSupport E) + (geometricCoefficient hδ hE hf.finite_above b) := by + classical + have hneg := hf.negative_bound hδ hE + have ht := hneg.tendsto_zero (by linarith : -δ/2<0) + apply SectorExpansion.of_expSmall (wordSupport_bddAbove hδ.le hE) + (wordSupport_finite hδ hE hf.finite_above) + · filter_upwards [hf.eventually_analytic,one_sub_eventually_ne ht] with z hzf hzne + exact (analyticAt_const.sub hzf).inv hzne + · intro B + let S := (hf.finite_above B).toFinset + let P : ℂ → ℂ := fun z => ∑ β ∈ S,Complex.exp ((β:ℂ)*z)*b β z + have hP : ExpBound (-δ/2) P := truncation_negative_bound hδ hE hb B (hf.finite_above B) + have hPt : Tendsto P sectorInfinity (𝓝 0) := hP.tendsto_zero (by linarith) + have hinv : ExpSmall B (fun z => (1-f z)⁻¹-(1-P z)⁻¹) := + inverse_difference_small ht hPt (hf.expSmall_remainder B) + obtain ⟨N,hN⟩ := exists_nat_gt (-2*B/δ) + have hN' : -δ/2*((N:ℝ)+1) < B := by + have hh := (div_lt_iff₀ hδ).mp hN + nlinarith + have hN'' : -δ*((N:ℝ)+1) < B := by + have hn : 0 ≤ (N:ℝ) := Nat.cast_nonneg N + nlinarith + have hgeom := geom_inverse_error hP (by linarith : -δ/2<0) hN' + let T := (wordsUpTo S N).filter (fun w => w.sum < B) + have hlow : ExpSmall B (fun z => ∑ w ∈ T,wordTerm b w z) := by + apply ExpSmall.sum + intro w hw + have hm := (mem_wordsUpTo.mp (Finset.mem_filter.mp hw).1).2 + have hwE : w ∈ exponentWords E := fun β hβ => + ((hf.finite_above B).mem_toFinset.mp (hm β hβ)).1 + exact (wordCoefficient_slow hb hwE).expSmall (Finset.mem_filter.mp hw).2 + convert (hinv.add hgeom).add hlow using 1 + funext z + have he := geometric_split hδ hE hf.finite_above b hN'' z + change (∑ n ∈ Finset.range (N+1),P z^n) = _ at he + rw [he] + dsimp [T,S] + ring + +lemma wordCoefficient_analytic {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hb : ∀ β ∈ E,SectorEventually (fun z => AnalyticAt ℂ (b β) z)) + {w : List ℝ} (hw : w ∈ exponentWords E) : + SectorEventually (fun z => AnalyticAt ℂ (wordCoefficient b w) z) := by + induction w with + | nil => + exact SectorEventually.truth.mono (fun z _ => by + change AnalyticAt ℂ (fun _ => (1:ℂ)) z + exact analyticAt_const) + | cons β w ih => + have hi := ih (fun γ hγ => hw γ (List.mem_cons_of_mem _ hγ)) + exact ((hb β (hw β (by simp))).and hi).mono (fun z hz => by + change AnalyticAt ℂ (fun z => b β z*wordCoefficient b w z) z + exact hz.1.mul hz.2) + +lemma geometricCoefficient_analytic {E : Set ℝ} {δ : ℝ} (hδ : 0 < δ) + (hE : ∀ β ∈ E, β ≤ -δ) (hEl : ∀ B : ℝ,(E ∩ Ici B).Finite) + {b : ℝ → ℂ → ℂ} + (hb : ∀ β ∈ E,SectorEventually (fun z => AnalyticAt ℂ (b β) z)) (β : ℝ) : + SectorEventually (fun z => AnalyticAt ℂ (geometricCoefficient hδ hE hEl b β) z) := by + have hw : ∀ w ∈ (wordFiber_finite hδ hE hEl β).toFinset, + SectorEventually (fun z => AnalyticAt ℂ (wordCoefficient b w) z) := by + intro w hw + exact wordCoefficient_analytic hb ((wordFiber_finite hδ hE hEl β).mem_toFinset.mp hw).1 + exact (SectorEventually.finset_forall _ SectorEventually.truth hw).mono + (fun z hz => Finset.analyticAt_fun_sum _ hz) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ClockComposition.lean b/lean/OAI/Analysis/PathSelection/ClockComposition.lean new file mode 100644 index 0000000000000000000000000000000000000000..d1780e868b2431e441592eed0c3ff39f74c215ba --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ClockComposition.lean @@ -0,0 +1,406 @@ +import Mathlib +import OAI.Analysis.PathSelection.TaylorCutoffs +import OAI.Analysis.PathSelection.UniformFamilies + +namespace OAI + +/-! Weighted words and holomorphic finite-clock and Puiseux tuple composition. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Complex +namespace DegeneratingTrees.Clock + +lemma weighted_truncation_words (S : Finset ℝ) (b : ℝ → ℂ → ℂ) + (h : ℕ → ℂ → ℂ) (N : ℕ) (z : ℂ) : + (∑ n ∈ Finset.range (N+1),h n z*(∑ β ∈ S,Complex.exp ((β:ℂ)*z)*b β z)^n) = + ∑ w ∈ wordsUpTo S N,h w.length z*wordTerm b w z := by + classical + simp_rw [power_truncation_words,Finset.mul_sum] + calc + _ = ∑ n ∈ Finset.range (N+1),∑ w ∈ wordsOfLength S n,h w.length z*wordTerm b w z := by + apply Finset.sum_congr rfl + intro n hn + apply Finset.sum_congr rfl + intro w hw + rw [(mem_wordsOfLength.mp hw).1] + _ = _ := by + symm + apply Finset.sum_biUnion + intro n hn m hm hne + apply Finset.disjoint_left.mpr + intro w hwn hwm + exact hne ((mem_wordsOfLength.mp hwn).1.symm.trans (mem_wordsOfLength.mp hwm).1) + +variable {E : Set ℝ} {δ : ℝ} (hδ : 0 < δ) (hE : ∀ β ∈ E, β ≤ -δ) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) + +def weightedCoefficient (b : ℝ → ℂ → ℂ) (h : ℕ → ℂ → ℂ) (β : ℝ) (z : ℂ) : ℂ := + ∑ w ∈ (wordFiber_finite hδ hE hEl β).toFinset,h w.length z*wordCoefficient b w z + +lemma weighted_coefficient_truncation (b : ℝ → ℂ → ℂ) (h : ℕ → ℂ → ℂ) + (B : ℝ) (z : ℂ) : + (∑ β ∈ (wordSupport_finite hδ hE hEl B).toFinset, + Complex.exp ((β:ℂ)*z)*weightedCoefficient hδ hE hEl b h β z) = + ∑ w ∈ (wordCut_finite hδ hE hEl B).toFinset,h w.length z*wordTerm b w z := by + classical + let S := (wordSupport_finite hδ hE hEl B).toFinset + let T := (wordCut_finite hδ hE hEl B).toFinset + have hmaps : ∀ w ∈ T,w.sum ∈ S := by + intro w hw + have hh := (wordCut_finite hδ hE hEl B).mem_toFinset.mp hw + exact (wordSupport_finite hδ hE hEl B).mem_toFinset.mpr ⟨⟨w,hh.1,rfl⟩,hh.2⟩ + calc + _ = ∑ β ∈ S,∑ w ∈ T with w.sum=β,h w.length z*wordTerm b w z := by + apply Finset.sum_congr rfl + intro β hβ + have hB : B ≤ β := ((wordSupport_finite hδ hE hEl B).mem_toFinset.mp hβ).2 + have he : (wordFiber_finite hδ hE hEl β).toFinset = T.filter (fun w => w.sum=β) := by + ext w + simp only [Set.Finite.mem_toFinset,Finset.mem_filter,T,wordFiber,wordCut,mem_ofPred_eq] + constructor + · intro hw + exact ⟨⟨hw.1,by simpa only [hw.2] using hB⟩,hw.2⟩ + · intro hw + exact ⟨hw.1.1,hw.2⟩ + rw [weightedCoefficient,he,Finset.mul_sum] + apply Finset.sum_congr rfl + intro w hw + simp only [wordTerm,(Finset.mem_filter.mp hw).2] + ring + _ = _ := Finset.sum_fiberwise_of_maps_to hmaps _ + +lemma weighted_split (b : ℝ → ℂ → ℂ) (h : ℕ → ℂ → ℂ) {B : ℝ} {N : ℕ} + (hN : -δ*((N:ℝ)+1) < B) (z : ℂ) : + (∑ n ∈ Finset.range (N+1),h n z*(∑ β ∈ (hEl B).toFinset,Complex.exp ((β:ℂ)*z)*b β z)^n) = + (∑ β ∈ (wordSupport_finite hδ hE hEl B).toFinset, + Complex.exp ((β:ℂ)*z)*weightedCoefficient hδ hE hEl b h β z) + + ∑ w ∈ (wordsUpTo (hEl B).toFinset N).filter (fun w => w.sum < B),h w.length z*wordTerm b w z := by + classical + rw [weighted_truncation_words,weighted_coefficient_truncation, + ←words_high hδ hE hEl hN] + symm + simpa only [not_le] using Finset.sum_filter_add_sum_filter_not + (wordsUpTo (hEl B).toFinset N) (fun w => B ≤ w.sum) + (fun w => h w.length z*wordTerm b w z) + +lemma weightedCoefficient_slow {b : ℝ → ℂ → ℂ} (hb : ∀ β ∈ E,SectorSlow (b β)) + {h : ℕ → ℂ → ℂ} (hh : ∀ n,SectorSlow (h n)) (β : ℝ) : + SectorSlow (weightedCoefficient hδ hE hEl b h β) := by + apply SectorSlow.sum + intro w hw + exact (hh _).mul (wordCoefficient_slow hb ((wordFiber_finite hδ hE hEl β).mem_toFinset.mp hw).1) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma ExpSmall.analytic_comp_difference {g : ℂ → ℂ} {d : ℂ} + (hg : AnalyticAt ℂ g d) {f h : ℂ → ℂ} + (hf : Tendsto f sectorInfinity (𝓝 d)) (hh : Tendsto h sectorInfinity (𝓝 d)) + {B : ℝ} (he : ExpSmall B (fun z => f z-h z)) : + ExpSmall B (fun z => g (f z)-g (h z)) := by + obtain ⟨a,ha,he⟩ := he + exact ⟨a,ha,(hg.hasStrictFDerivAt.isBigO_sub.comp_tendsto (hf.prodMk_nhds hh)).trans he⟩ + +lemma SectorSlow.of_tendsto {f : ℂ → ℂ} {d : ℂ} + (hf : Tendsto f sectorInfinity (𝓝 d)) : SectorSlow f := by + intro ε hε + exact (ExpBound.of_tendsto hf).mono hε.le + + + +theorem SectorExpansion.holomorphic_comp_negative {f : ℂ → ℂ} {E : Set ℝ} + {b : ℝ → ℂ → ℂ} (hf : SectorExpansion f E b) {δ : ℝ} (hδ : 0<δ) + (hE : ∀ β∈E,β≤-δ) (hb : ∀ β∈E,SectorSlow (b β)) + {a g : ℂ → ℂ} {d : ℂ} (ha : Tendsto a sectorInfinity (𝓝 d)) + (haa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ a z) (hg : AnalyticAt ℂ g d) : + ∃ c : ℕ → ℂ → ℂ,(∀ n,AnalyticAt ℂ (c n) d) ∧ + SectorExpansion (fun z => g (a z+f z)) (wordSupport E) + (weightedCoefficient hδ hE hf.finite_above b (fun n z => c n (a z))) := by + classical + obtain ⟨c,hc,hTaylor⟩ := TaylorCutoff.analytic_moving_taylor hg + refine ⟨c,hc,?_⟩ + have hneg := hf.negative_bound hδ hE + have hft := hneg.tendsto_zero (by linarith : -δ/2<0) + have hat : Tendsto (fun z => a z+f z) sectorInfinity (𝓝 d) := by + simpa only [add_zero] using ha.add hft + have hct : ∀ n,Tendsto (fun z => c n (a z)) sectorInfinity (𝓝 (c n d)) := + fun n => (hc n).continuousAt.tendsto.comp ha + apply SectorExpansion.of_expSmall (wordSupport_bddAbove hδ.le hE) + (wordSupport_finite hδ hE hf.finite_above) + · filter_upwards [hf.eventually_analytic,haa,hat.eventually hg.eventually_analyticAt] with z hf ha hg + exact hg.comp (f := fun z => a z+f z) (ha.add hf) + · intro B + let S := (hf.finite_above B).toFinset + let P : ℂ → ℂ := fun z => ∑ β ∈ S,Complex.exp ((β:ℂ)*z)*b β z + have hP : ExpBound (-δ/2) P := truncation_negative_bound hδ hE hb B (hf.finite_above B) + have hPt := hP.tendsto_zero (by linarith : -δ/2<0) + have haPt : Tendsto (fun z => a z+P z) sectorInfinity (𝓝 d) := by + simpa only [add_zero] using ha.add hPt + have hdiff : ExpSmall B (fun z => g (a z+f z)-g (a z+P z)) := by + apply ExpSmall.analytic_comp_difference hg hat haPt + simpa only [add_sub_add_left_eq_sub] using hf.expSmall_remainder B + obtain ⟨N,hN⟩ := exists_nat_gt (-2*B/δ) + have hN' : -δ/2*((N:ℝ)+1) < B := by + have hh := (div_lt_iff₀ hδ).mp hN + nlinarith + have hN'' : -δ*((N:ℝ)+1) < B := by + have hn : 0 ≤ (N:ℝ) := Nat.cast_nonneg N + nlinarith + have herr : ExpSmall B (fun z => g (a z+P z)- + ∑ n ∈ Finset.range (N+1),c n (a z)*P z^n) := by + refine ⟨-δ/2*((N:ℝ)+1),hN',?_⟩ + have h := hTaylor a P (δ/2) ha (by linarith) (by simpa only [neg_div] using hP) (N+1) + simpa only [neg_div,Nat.cast_add,Nat.cast_one] using h + let T := (wordsUpTo S N).filter (fun w => w.sum < B) + have hlow : ExpSmall B (fun z => ∑ w ∈ T,c w.length (a z)*wordTerm b w z) := by + apply ExpSmall.sum + intro w hw + have hm := (mem_wordsUpTo.mp (Finset.mem_filter.mp hw).1).2 + have hwE : w∈exponentWords E := fun β hβ => + ((hf.finite_above B).mem_toFinset.mp (hm β hβ)).1 + have h := ((SectorSlow.of_tendsto (hct w.length)).mul + (wordCoefficient_slow hb hwE)).expSmall (Finset.mem_filter.mp hw).2 + convert h using 1 + funext z + dsimp only [wordTerm] + ring + convert (hdiff.add herr).add hlow using 1 + funext z + have he := weighted_split hδ hE hf.finite_above b (fun n z => c n (a z)) hN'' z + change (∑ n ∈ Finset.range (N+1),c n (a z)*P z^n) = _ at he + rw [he] + dsimp [T,S] + ring + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma Puiseux.uniform {f : ℝ → ℂ} (hf : Puiseux f) : UniformPuiseux f := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + refine ⟨n,hn,m,F,hF,?_⟩ + simpa only [←Complex.ofReal_zpow,Complex.real_smul,smul_eq_mul] using he + +lemma SectorExpansion.uniform {F : ℂ → ℂ} {A : Set ℝ} {b : ℝ → ℂ → ℂ} + (hF : SectorExpansion F A b) : UniformSectorExpansion F A b := by + refine ⟨hF.bounded_above,hF.finite_above,?_⟩ + intro B + simpa only [smul_eq_mul] using hF.remainders B + +lemma ClockGerm.uniform {xs : List (ℝ → ℝ)} {f : ℝ → ℂ} + (hf : ClockGerm xs f) : UniformClockGerm xs f := by + induction xs generalizing f with + | nil => exact Puiseux.uniform hf + | cons X xs ih => + obtain ⟨F,A,b,hF,hb,he⟩ := hf + exact ⟨F,A,b,hF.uniform,fun β hβ => ⟨ih (hb β hβ).1,(hb β hβ).2⟩,he⟩ + +lemma Puiseux.analytic_comp_finite {f : ℝ → ℂ} (hf : Puiseux f) {d : ℂ} + (hlim : Tendsto f atTop (𝓝 d)) {g : ℂ → ℂ} (hg : AnalyticAt ℂ g d) : + Puiseux (fun t => g (f t)) := by + by_cases hz : f =ᶠ[atTop] fun _ => 0 + · apply (puiseux_const (g 0)).congr + filter_upwards [hz] with t ht + rw [ht] + obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.uniform.normalize hz + have hm := UniformPuiseux.finite_limit_nonnegative hlim hn hF hF0 he + let k := m.toNat + have hkm : (k:ℤ)=m := Int.toNat_of_nonneg hm + let H : ℂ → ℂ := fun v => v^k*F v + have hH : AnalyticAt ℂ H 0 := (analyticAt_id.pow k).mul hF + have heH : f =ᶠ[atTop] fun t => H (rootCoord n t) := by + simpa only [H,←zpow_natCast,hkm,smul_eq_mul] using he + have hd : H 0=d := tendsto_nhds_unique (hH.continuousAt.tendsto.comp + (rootCoord_complex_tendsto_zero hn)) (hlim.congr' heH) + refine ⟨n,hn,0,fun v => g (H v),?_,?_⟩ + · exact (hd ▸ hg).comp hH + · filter_upwards [heH] with t ht + simp only [zpow_zero,one_smul,ht] + + + +theorem ClockGerm.analytic_comp_finite {xs : List (ℝ → ℝ)} + (hvalid : ValidClocks xs) {f : ℝ → ℂ} (hf : ClockGerm xs f) {d : ℂ} + (hlim : Tendsto f atTop (𝓝 d)) {g : ℂ → ℂ} (hg : AnalyticAt ℂ g d) : + ClockGerm xs (fun t => g (f t)) := by + classical + induction xs generalizing f g d with + | nil => exact Puiseux.analytic_comp_finite hf hlim hg + | cons X xs ih => + obtain ⟨K,hK⟩ := hvalid.sectorData + obtain ⟨F,⟨E,b,hF,hb⟩,he⟩ := hK.expansion_iff.mp hf + have hXt := hvalid.2.2.1 + have hXc := (hvalid.2.1.real_eventually_analytic hvalid.1).mono + (fun _ h => h.continuousAt) + have hreal : Tendsto (fun t : ℝ => F (t:ℂ)) atTop (𝓝 d) := + tendsto_of_comp_clock hXt hXc (hlim.congr' he) + let D := nonzeroRaySupport E b + have htrim : SectorExpansion F D b := hF.trim_zero (fun β hβ => hK.lower.analytic (hb β hβ)) + have hDb : ∀ β∈D,b β∈K := fun β hβ => hb β hβ.1 + have hnonpos : ∀ β∈D,β≤0 := by + intro β hβ + by_contra h + exact hβ.2 (hF.positive_coeff_zero_of_limit hK.lower hb hreal hβ.1 (lt_of_not_ge h)) + have hgo : ∀ (a r : ℂ → ℂ) (A : Set ℝ) (c : ℝ → ℂ → ℂ), + a∈K → SectorExpansion r A c → (∀ β∈A,c β∈K) → + (∀ β∈A,β<0) → (∀ z,F z=a z+r z) → ExpansionOver K (fun z => g (F z)) := by + intro a r A c ham hr hc hneg heq + obtain ⟨δ,hδ,hgap⟩ := strict_negative_support_gap hr.finite_above hneg + have hr0 := (hr.negative_bound hδ hgap).tendsto_zero (by linarith : -δ/2<0) + have har : Tendsto (fun t : ℝ => a (t:ℂ)) atTop (𝓝 d) := by + have h := hreal.sub (hr0.comp tendsto_real_sectorInfinity) + simp only [sub_zero] at h + convert h using 1 + funext t + simp only [heq,Function.comp_apply,add_sub_cancel_right] + have halim : Tendsto (fun t => a (X t:ℂ)) atTop (𝓝 d) := har.comp hXt + have halower := (hK.membership a).mp ham + have ha : Tendsto a sectorInfinity (𝓝 d) := + halower.1.uniform.model_limit hvalid halower.2 EventuallyEq.rfl halim + obtain ⟨q,hq,hcomp⟩ := hr.holomorphic_comp_negative hδ hgap + (fun β hβ => hK.lower.slow (hc β hβ)) ha halower.2 hg + have hqm : ∀ n,(fun z => q n (a z))∈K := by + intro n + apply (hK.membership _).mpr + refine ⟨ih hvalid.1 halower.1 halim (hq n),?_⟩ + filter_upwards [halower.2,ha.eventually (hq n).eventually_analyticAt] with z haz hqz + exact hqz.comp (f := a) haz + have hmem : ∀ β,weightedCoefficient hδ hgap hr.finite_above c (fun n z => q n (a z)) β∈K := by + intro β + apply hK.lower.finset_sum_mem + intro w hw + exact hK.lower.mul_mem (hqm w.length) (hK.lower.word_mem hc + ((wordFiber_finite hδ hgap hr.finite_above β).mem_toFinset.mp hw).1) + exact (show ExpansionOver K (fun z => g (a z+r z)) from + ⟨wordSupport A,_,hcomp,fun β _ => hmem β⟩).congr + (Eventually.of_forall (fun z => by change g (a z+r z)=g (F z); rw [heq])) + have hcomp : ExpansionOver K (fun z => g (F z)) := by + by_cases h0 : (0:ℝ)∈D + · have hr := htrim.erase h0 (hK.lower.analytic (hDb 0 h0)) (hK.lower.slow (hDb 0 h0)) + simp only [Complex.ofReal_zero,zero_mul,Complex.exp_zero,one_mul] at hr + apply hgo (b 0) (fun z => F z-b 0 z) (D\{0}) b (hDb 0 h0) hr + (fun β hβ => hDb β hβ.1) + · intro β hβ + exact lt_of_le_of_ne (hnonpos β hβ.1) hβ.2 + · intro z; ring + · apply hgo (fun _ => 0) F D b (hK.lower.const_mem 0) htrim hDb + · intro β hβ + exact lt_of_le_of_ne (hnonpos β hβ) (fun h => h0 (h ▸ hβ)) + · intro z; simp + exact hK.expansion_iff.mpr ⟨fun z => g (F z),hcomp,he.mono (fun t ht => congrArg g ht)⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma Puiseux.finite_representation {f : ℝ → ℂ} (hf : Puiseux f) + {d : ℂ} (hlim : Tendsto f atTop (𝓝 d)) : + ∃ n : ℕ,0 F (rootCoord n t) := by + by_cases hz : f =ᶠ[atTop] fun _ => 0 + · have hd : d=0 := tendsto_nhds_unique hlim (tendsto_const_nhds.congr' hz.symm) + exact ⟨1,by omega,fun _ => 0,analyticAt_const,hd.symm,hz⟩ + obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.uniform.normalize hz + have hm := UniformPuiseux.finite_limit_nonnegative hlim hn hF hF0 he + let H : ℂ → ℂ := fun v => v^m.toNat*F v + have hkm : (m.toNat:ℤ)=m := Int.toNat_of_nonneg hm + have hH : AnalyticAt ℂ H 0 := (analyticAt_id.pow _).mul hF + have heH : f =ᶠ[atTop] fun t => H (rootCoord n t) := by + simpa only [H,←zpow_natCast,hkm,smul_eq_mul] using he + refine ⟨n,hn,H,hH,?_,heH⟩ + exact tendsto_nhds_unique (hH.continuousAt.tendsto.comp + (rootCoord_complex_tendsto_zero hn)) (hlim.congr' heH) + +lemma finite_representation_refine {n k : ℕ} (hn : 0 G (rootCoord n t)) : + AnalyticAt ℂ (fun z => G (z^k)) 0 ∧ + f =ᶠ[atTop] fun t => G ((rootCoord (n*k) t:ℂ)^k) := by + refine ⟨?_,?_⟩ + · have hG' : AnalyticAt ℂ G ((0:ℂ)^k) := by simpa [zero_pow hk.ne'] using hG + exact hG'.comp (f := fun z : ℂ => z^k) (analyticAt_id.pow k) + filter_upwards [he,eventually_gt_atTop (0:ℝ)] with t ht hpos + rw [ht,←rootCoord_pow hn hk hpos,Complex.ofReal_pow] + +lemma puiseux_tuple_finite_representation {k : ℕ} (f : Fin k → ℝ → ℂ) + (d : Fin k → ℂ) (hf : ∀ i,Puiseux (f i)) + (hlim : ∀ i,Tendsto (f i) atTop (𝓝 (d i))) : + ∃ n : ℕ,0 f i t) =ᶠ[atTop] fun t => F (rootCoord n t) := by + induction k with + | zero => + refine ⟨1,by omega,fun _ => d,analyticAt_const,rfl,Eventually.of_forall ?_⟩ + intro t + ext i + exact Fin.elim0 i + | succ k ih => + obtain ⟨n,hn,G,hG,hGd,heG⟩ := (hf 0).finite_representation (hlim 0) + obtain ⟨r,hr,H,hH,hHd,heH⟩ := ih (fun i => f i.succ) (fun i => d i.succ) + (fun i => hf i.succ) (fun i => hlim i.succ) + let J : ℂ → Fin (k+1) → ℂ := fun z => Fin.cons (G (z^r)) (H (z^n)) + have hGr : AnalyticAt ℂ (fun z => G (z^r)) 0 := + (finite_representation_refine hn hr hG heG).1 + have hHn : AnalyticAt ℂ (fun z => H (z^n)) 0 := by + have hH' : AnalyticAt ℂ H ((0:ℂ)^n) := by simpa [zero_pow hn.ne'] using hH + exact hH'.comp (f := fun z : ℂ => z^n) (analyticAt_id.pow n) + refine ⟨n*r,Nat.mul_pos hn hr,J,?_,?_,?_⟩ + · apply analyticAt_pi_iff.mpr + intro i + refine Fin.cases ?_ (fun j => ?_) i + · exact hGr + · exact (analyticAt_pi_iff.mp hHn j) + · ext i + refine Fin.cases ?_ (fun j => ?_) i + · simpa only [J,Fin.cons_zero,zero_pow hr.ne'] using hGd + · simpa only [J,Fin.cons_succ,zero_pow hn.ne'] using congrFun hHd j + · filter_upwards [heG,heH,eventually_gt_atTop (0:ℝ)] with t ht hht hpos + ext i + refine Fin.cases ?_ (fun j => ?_) i + · change f 0 t=G ((rootCoord (n*r) t:ℂ)^r) + rw [ht,←rootCoord_pow hn hr hpos,Complex.ofReal_pow] + · change f _ t=H ((rootCoord (n*r) t:ℂ)^n) j + have h := congrFun hht j + rw [h,←rootCoord_pow hr hn hpos,Complex.ofReal_pow,Nat.mul_comm r n] + + + +theorem Puiseux.analytic_comp_tuple_finite {k : ℕ} {f : Fin k → ℝ → ℂ} + (hf : ∀ i,Puiseux (f i)) {d : Fin k → ℂ} + (hlim : ∀ i,Tendsto (f i) atTop (𝓝 (d i))) + {g : (Fin k → ℂ) → ℂ} (hg : AnalyticAt ℂ g d) : + Puiseux (fun t => g (fun i => f i t)) := by + obtain ⟨n,hn,F,hF,hFd,he⟩ := puiseux_tuple_finite_representation f d hf hlim + refine ⟨n,hn,0,fun z => g (F z),?_,?_⟩ + · exact (hFd ▸ hg).comp hF + · filter_upwards [he] with t ht + simp only [zpow_zero,one_smul,ht] + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ClockDerivatives.lean b/lean/OAI/Analysis/PathSelection/ClockDerivatives.lean new file mode 100644 index 0000000000000000000000000000000000000000..0a7a3779b089ab0ecdd23bbe1faddb82e9d6edaa --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ClockDerivatives.lean @@ -0,0 +1,220 @@ +import Mathlib +import OAI.Analysis.PathSelection.RecursiveClocks + +namespace OAI + +/-! Differentiation and logarithmic derivatives of first clocks and Puiseux series. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma hasDerivAt_expTerm {b : ℂ → ℂ} {z : ℂ} (hb : AnalyticAt ℂ b z) (β : ℝ) : + HasDerivAt (fun w : ℂ => Complex.exp ((β:ℂ)*w)*b w) + (Complex.exp ((β:ℂ)*z)*((β:ℂ)*b z+deriv b z)) z := by + convert (((Complex.hasDerivAt_exp ((β:ℂ)*z)).comp z + ((hasDerivAt_id z).const_mul (β:ℂ))).mul hb.differentiableAt.hasDerivAt) using 1 <;> try rfl + simp only [Function.comp_apply, mul_one] + ring + +lemma analyticAt_expTerm {b : ℂ → ℂ} {z : ℂ} (hb : AnalyticAt ℂ b z) (β : ℝ) : + AnalyticAt ℂ (fun w : ℂ => Complex.exp ((β:ℂ)*w)*b w) z := + ((analyticAt_const.mul analyticAt_id).cexp).mul hb + + + +theorem SectorExpansion.deriv {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) + (ha : ∀ β ∈ E, SectorEventually (fun z => AnalyticAt ℂ (b β) z)) : + SectorExpansion (deriv f) E (fun β z => (β:ℂ)*b β z+deriv (b β) z) := by + classical + refine ⟨h.bounded_above,h.finite_above,?_⟩ + intro B + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hrem⟩ := h.remainders B + let S := (h.finite_above B).toFinset + have hcoeff : SectorEventually (fun z => ∀ β ∈ S, AnalyticAt ℂ (b β) z) := by + apply SectorEventually.finset_forall S SectorEventually.truth + intro β hβ + exact ha β ((h.finite_above B).mem_toFinset.mp hβ).1 + have horig : SectorEventually (fun z => z ∈ lossSector ω R) := ⟨ω,R,hω,fun _ hz => hz⟩ + obtain ⟨η,T,hη,hboth⟩ := hcoeff.and horig + let g : ℂ → ℂ := fun z => f z-∑ β ∈ S,Complex.exp ((β:ℂ)*z)*b β z + have hg : AnalyticOnNhd ℂ g (lossSector η T) := by + intro z hz + apply (hf z (hboth z hz).2).sub + exact (S.analyticAt_fun_sum (fun β hβ => analyticAt_expTerm ((hboth z hz).1 β hβ) β)) + have hgb : ∀ z ∈ lossSector η T, ‖g z‖ ≤ C*Real.exp ((B-ε)*z.re) := + fun z hz => hrem z (hboth z hz).2 + obtain ⟨ν,U,hν,hTU,hgd,hgdb⟩ := sector_deriv_bound hη hg hC hgb + have hnew : SectorEventually (fun z => z ∈ lossSector ν U) := ⟨ν,U,hν,fun _ hz => hz⟩ + have hold : SectorEventually (fun z => z ∈ lossSector η T) := ⟨η,T,hη,fun _ hz => hz⟩ + obtain ⟨ξ,V,hξ,hv⟩ := hnew.and hold + refine ⟨ξ,V,ε,C*Real.exp |B-ε|,hξ,hε,mul_nonneg hC (Real.exp_pos _).le,?_,?_⟩ + · intro z hz + exact (hf z (hboth z (hv z hz).2).2).deriv + · intro z hz + have hfa := hf z (hboth z (hv z hz).2).2 + have hba := (hboth z (hv z hz).2).1 + have hsum := HasDerivAt.fun_sum (u := S) (fun β hβ => hasDerivAt_expTerm (hba β hβ) β) + have hder := (hfa.differentiableAt.hasDerivAt.sub hsum).deriv + have hb := hgdb z (hv z hz).1 + change ‖_root_.deriv g z‖ ≤ _ at hb + rw [show _root_.deriv g z = _root_.deriv f z - ∑ β ∈ S, + Complex.exp ((β:ℂ)*z)*((β:ℂ)*b β z+_root_.deriv (b β) z) from hder] at hb + exact hb + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma PuiseuxSector.deriv_mem {f : ℂ → ℂ} (hf : f∈PuiseuxSector) : + deriv f∈PuiseuxSector := by + refine ⟨hf.1.mono (fun _ h => h.deriv),?_⟩ + apply hf.2.deriv.congr + filter_upwards [tendsto_real_sectorInfinity.eventually hf.1] with t ht + exact ht.differentiableAt.hasDerivAt.comp_ofReal.deriv + +lemma ExpansionOver.puiseux_deriv {F : ℂ → ℂ} (hF : ExpansionOver PuiseuxSector F) : + ExpansionOver PuiseuxSector (deriv F) := by + obtain ⟨E,b,hF,hb⟩ := hF + refine ⟨E,fun β z => (β:ℂ)*b β z+deriv (b β) z, + hF.deriv (fun β hβ => (hb β hβ).1),?_⟩ + intro β hβ + exact puiseux_lowerSectorData.add_mem + (puiseux_lowerSectorData.mul_mem (puiseux_lowerSectorData.const_mem (β:ℂ)) (hb β hβ)) + (PuiseuxSector.deriv_mem (hb β hβ)) + +lemma Puiseux.sector_representative {f : ℝ → ℂ} (hf : Puiseux f) : + ∃ F : ℂ → ℂ,F∈PuiseuxSector ∧ f =ᶠ[atTop] fun t => F (t:ℂ) := by + by_cases hz : f =ᶠ[atTop] fun _ => 0 + · exact ⟨fun _ => 0,puiseux_lowerSectorData.const_mem 0,hz⟩ + · obtain ⟨q,C,G,R,hC,ha,he,hl⟩ := hf.sector_leading hz + exact ⟨G,⟨sector_halfplane_analytic ha,hf.congr he⟩,he⟩ + +lemma ClockGerm.first_of_lower {X : ℝ → ℝ} (hX : Puiseux (fun t => (X t:ℂ))) + (hXt : Tendsto X atTop atTop) {f : ℝ → ℂ} (hf : Puiseux f) : ClockGerm (X :: []) f := by + obtain ⟨I,hI,hIt,hl,hr⟩ := hX.inverse_change hXt + obtain ⟨F,hF,he⟩ := (hf.comp_unbounded hI hIt).sector_representative + have hex : SectorExpansion F {0} (fun _ => F) := by + simpa only [Complex.ofReal_zero,zero_mul,Complex.exp_zero,one_mul] using + SectorExpansion.single 0 hF.1 (puiseux_lowerSectorData.slow hF) + apply (firstClock_expansion_iff hX hXt).mpr + refine ⟨F,⟨{0},fun _ => F,hex,fun _ _ => hF⟩,?_⟩ + filter_upwards [hXt.eventually he,hr] with t ht hr + simpa only [hr] using ht + +lemma ClockGerm.first_deriv {X : ℝ → ℝ} (hX : Puiseux (fun t => (X t:ℂ))) + (hXt : Tendsto X atTop atTop) {f : ℝ → ℂ} (hf : ClockGerm (X :: []) f) : + ClockGerm (X :: []) (deriv f) := by + obtain ⟨F,hF,he⟩ := (firstClock_expansion_iff hX hXt).mp hf + have hFx : ClockGerm (X :: []) (fun t => deriv F (X t:ℂ)) := + (firstClock_expansion_iff hX hXt).mpr ⟨deriv F,hF.puiseux_deriv,EventuallyEq.rfl⟩ + have hX' := ClockGerm.first_of_lower hX hXt hX.real_deriv + apply (hFx.first_mul hX hXt hX').congr + have hFa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z := by + obtain ⟨E,b,hF,hb⟩ := hF + exact hF.eventually_analytic + obtain ⟨T,hT⟩ := eventually_atTop.mp he + filter_upwards [hX.real_eventually_analytic, + hXt.eventually (tendsto_real_sectorInfinity.eventually hFa),eventually_gt_atTop T] with t hXa hFa ht + have hd := hFa.differentiableAt.hasDerivAt.comp_ofReal.scomp t hXa.differentiableAt.hasDerivAt + have hc : (fun s => F (X s:ℂ)) =ᶠ[𝓝 t] f := + (eventually_gt_nhds ht).mono (fun s hs => (hT s hs.le).symm) + simpa only [Complex.real_smul,mul_comm] using (hd.congr_of_eventuallyEq hc.symm).deriv.symm + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma Puiseux.log_deriv_tendsto {f : ℝ → ℂ} (hf : Puiseux f) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : + Tendsto (fun t => _root_.deriv f t / f t) atTop (𝓝 0) := by + obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.normalize hne + let q : ℝ := -(m:ℝ)/(n:ℝ) + let r : ℝ := -(n:ℝ)⁻¹ + have he' : f =ᶠ[atTop] fun x => ((x^q:ℝ):ℂ)*F (rootCoord n x) := by + filter_upwards [he,eventually_gt_atTop (0:ℝ)] with x hx hxpos + simp [hx,rootCoord_zpow hxpos,q,Complex.real_smul] + have hroot := rootCoord_complex_tendsto_zero hn + have hlim : Tendsto (fun x : ℝ => (x:ℂ)⁻¹ * + ((q:ℂ)+(r:ℂ)*(rootCoord n x:ℂ)*_root_.deriv F (rootCoord n x)/F (rootCoord n x))) + atTop (𝓝 0) := by + have hbr := (tendsto_const_nhds (x := (q:ℂ))).add + ((((tendsto_const_nhds (x := (r:ℂ))).mul hroot).mul (hF.deriv.continuousAt.tendsto.comp hroot)).div + (hF.continuousAt.tendsto.comp hroot) hF0) + convert! (tendsto_inv_atTop_zero.ofReal.mul hbr) using 1 <;> simp + apply hlim.congr' + filter_upwards [eventuallyEq_deriv_atTop he',he', + hroot.eventually hF.eventually_analyticAt, + hroot.eventually (hF.continuousAt.eventually_ne hF0), + eventually_gt_atTop (0:ℝ)] with x hdx hx hFx hFx0 hxpos + have hdroot : HasDerivAt (rootCoord n) (r*x^(r-1)) x := by + exact Real.hasDerivAt_rpow_const (Or.inl hxpos.ne') + have hdF := hFx.differentiableAt.hasDerivAt.comp_ofReal.scomp x hdroot + have hdp := (Real.hasDerivAt_rpow_const (p := q) (Or.inl hxpos.ne')).ofReal_comp + have hdprod := hdp.mul hdF + have hdpeq : _root_.deriv (fun y : ℝ => (y^q:ℝ)*F (rootCoord n y)) x = + (q*x^(q-1):ℝ)*F (rootCoord n x)+(x^q:ℝ)*(r*x^(r-1):ℝ)*_root_.deriv F (rootCoord n x) := by + convert! hdprod.deriv using 1; simp only [Function.comp_def,Complex.real_smul]; ring + rw [hdx,hdpeq,hx] + have hq : x^(q-1)=x^q/x := by rw [Real.rpow_sub hxpos,Real.rpow_one] + have hr : x^(r-1)=x^r/x := by rw [Real.rpow_sub hxpos,Real.rpow_one] + have hx0 : (x:ℂ)≠0 := Complex.ofReal_ne_zero.mpr hxpos.ne' + have hp0 : ((x^q:ℝ):ℂ)≠0 := Complex.ofReal_ne_zero.mpr (Real.rpow_pos_of_pos hxpos q).ne' + simp only [Complex.ofReal_mul,hq,hr, + Complex.ofReal_div] + change (x:ℂ)⁻¹*((q:ℂ)+(r:ℂ)*(x^r:ℝ)*_root_.deriv F (rootCoord n x)/F (rootCoord n x)) = _ + field_simp [hFx0,hx0,hp0] + +lemma PuiseuxSector.tendsto_of_ray {F : ℂ → ℂ} (hF : F∈PuiseuxSector) {c : ℂ} + (ht : Tendsto (fun t : ℝ => F (t:ℂ)) atTop (𝓝 c)) : + Tendsto F sectorInfinity (𝓝 c) := by + have hsub : (fun z => F z-c)∈PuiseuxSector := + puiseux_lowerSectorData.add_mem hF (puiseux_lowerSectorData.const_mem (-c)) + have ht0 : Tendsto (fun t : ℝ => F (t:ℂ)-c) atTop (𝓝 0) := by + simpa using ht.sub (tendsto_const_nhds (x := c)) + suffices hz : Tendsto (fun z => F z-c) sectorInfinity (𝓝 0) by + convert! hz.add_const c using 1 <;> simp + by_cases he : (fun t : ℝ => F (t:ℂ)-c) =ᶠ[atTop] fun _ => 0 + · exact tendsto_const_nhds.congr' + (sector_analytic_eq_of_ray hsub.1 (Eventually.of_forall (fun _ => analyticAt_const)) he).symm + obtain ⟨G,R,ha,hG,hbound⟩ := hsub.2.sector_modulus_comparable he + have hFG := sector_analytic_eq_of_ray hsub.1 (sector_halfplane_analytic ha) hG + apply squeeze_zero_norm' (a := fun z : ℂ => 4*‖F (‖z‖:ℂ)-c‖) + · filter_upwards [hFG,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop R)] with z hz hR + rw [hz] + exact (hbound z hR).2 + · convert! tendsto_const_nhds.mul (ht0.norm.comp tendsto_norm_sectorInfinity) using 1; simp + +lemma PuiseuxSector.log_deriv_tendsto {F : ℂ → ℂ} (hF : F∈PuiseuxSector) + (hne : ¬ (fun t : ℝ => F (t:ℂ)) =ᶠ[atTop] fun _ => 0) : + Tendsto (fun z => _root_.deriv F z / F z) sectorInfinity (𝓝 0) := by + have hq : (fun z => _root_.deriv F z / F z)∈PuiseuxSector := by + simpa only [div_eq_mul_inv] using puiseux_lowerSectorData.mul_mem + (PuiseuxSector.deriv_mem hF) (puiseux_lowerSectorData.inv_mem hF) + apply PuiseuxSector.tendsto_of_ray hq + apply (hF.2.log_deriv_tendsto hne).congr' + filter_upwards [tendsto_real_sectorInfinity.eventually hF.1] with t ht + rw [ht.differentiableAt.hasDerivAt.comp_ofReal.deriv] + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ClockExpansions.lean b/lean/OAI/Analysis/PathSelection/ClockExpansions.lean new file mode 100644 index 0000000000000000000000000000000000000000..6880e9f3a4a723c6e005c08c94a4060e273124ed --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ClockExpansions.lean @@ -0,0 +1,363 @@ +import Mathlib +import OAI.Analysis.PathSelection.ExponentSupports +import OAI.Analysis.PathSelection.SectorLimits + +namespace OAI + +/-! Clock expansions, uniform bounds and convolution. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +open scoped BigOperators +namespace DegeneratingTrees.Clock + + + +structure SectorExpansion (f : ℂ → ℂ) (E : Set ℝ) (b : ℝ → ℂ → ℂ) : Prop where + bounded_above : BddAbove E + finite_above : ∀ B : ℝ, (E ∩ Ici B).Finite + remainders : ∀ B : ℝ, ∃ (ω : ℝ → ℝ) (R ε C : ℝ), + AdmissibleAngularLoss ω ∧ 0 < ε ∧ 0 ≤ C ∧ + AnalyticOnNhd ℂ f (lossSector ω R) ∧ + ∀ z ∈ lossSector ω R, + ‖f z - ∑ β ∈ (finite_above B).toFinset, Complex.exp ((β:ℂ)*z)*b β z‖ ≤ + C*Real.exp ((B-ε)*z.re) + +lemma central_re_lower {z : ℂ} (hz : |z.arg| ≤ Real.pi/4) : ‖z‖/2 ≤ z.re := by + have hc : (1/2:ℝ) ≤ Real.cos z.arg := by + rw [←Real.cos_abs] + calc (1/2:ℝ) = Real.cos (Real.pi/3) := Real.cos_pi_div_three.symm + _ ≤ Real.cos |z.arg| := Real.cos_le_cos_of_nonneg_of_le_pi + (abs_nonneg _) (by linarith [Real.pi_pos]) (by linarith [Real.pi_pos]) + have hm := mul_le_mul_of_nonneg_left hc (norm_nonneg z) + rw [Complex.norm_mul_cos_arg] at hm + linarith + +lemma AdmissibleAngularLoss.central_tail {ω : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) (R : ℝ) : + ∃ T : ℝ, ∀ z : ℂ, T < ‖z‖ → |z.arg| ≤ Real.pi/4 → z ∈ lossSector ω R := by + obtain ⟨a,t,S,hS,ha,has,ht,hsmall,hbound⟩ := angularLoss_kernel_data hω + refine ⟨max S R,fun z hz hang => ⟨(le_max_right _ _).trans_lt hz,?_⟩⟩ + have hSn : S ≤ ‖z‖ := ((le_max_left _ _).trans_lt hz).le + have hbn := (hbound _ hSn).2.1 + have hp := Real.pi_gt_three + linarith + + + +lemma SectorExpansion.empty {f : ℂ → ℂ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f ∅ b) : (fun x : ℝ => f (x:ℂ)) =ᶠ[atTop] 0 := by + have hsum (B : ℝ) (z : ℂ) : + (∑ β ∈ (h.finite_above B).toFinset, Complex.exp ((β:ℂ)*z)*b β z) = 0 := by + apply Finset.sum_eq_zero + intro β hβ + exact ((h.finite_above B).mem_toFinset.mp hβ).1.elim + have hcentral : CentralSuperexponential f := by + intro B hB + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hbound⟩ := h.remainders (-2*B) + obtain ⟨T,hT⟩ := AdmissibleAngularLoss.central_tail hω R + refine ⟨C,max T 0,hC,?_⟩ + intro z hz hang + have hzT : T < ‖z‖ := (le_max_left _ _).trans_lt hz + have hn : 0 < ‖z‖ := (le_max_right _ _).trans_lt hz + have hb := hbound z (hT z hzT hang) + simp only [hsum,sub_zero] at hb + have hr := central_re_lower hang + refine hb.trans (mul_le_mul_of_nonneg_left (Real.exp_le_exp.mpr ?_) hC) + nlinarith + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hbound⟩ := h.remainders 0 + obtain ⟨a,t,S,hS,ha,has,ht,hsmall,hloss⟩ := angularLoss_kernel_data hω + have hsub : lossSector ω (max R S) ⊆ lossSector ω R := + fun z hz => ⟨(le_max_left _ _).trans_lt hz.1,hz.2⟩ + have hbounded : ∃ M : ℝ, ∀ z ∈ lossSector ω (max R S), ‖f z‖ ≤ M := by + refine ⟨C,?_⟩ + intro z hz + have hb := hbound z (hsub hz) + simp only [hsum,sub_zero,zero_sub] at hb + have hp := (hloss _ (((le_max_right _ _).trans_lt hz.1).le)).1 + have hre : 0 ≤ z.re := Complex.abs_arg_le_pi_div_two_iff.mp (by linarith [hz.2]) + calc ‖f z‖ ≤ C*Real.exp (-ε*z.re) := hb + _ ≤ C*1 := mul_le_mul_of_nonneg_left (Real.exp_le_one_iff.mpr (by nlinarith)) hC + _ = C := mul_one _ + obtain ⟨R',hRR',hf0⟩ := sector_uniqueness ω (max R S) f hω (hf.mono hsub) hbounded hcentral + filter_upwards [hω.real_discs R'] with x hx + exact hf0 (hx.2 (mem_closedBall_self (by linarith [hx.1]))) + +lemma exists_greatest_of_finite_above {E : Set ℝ} + (hE : ∀ B : ℝ, (E ∩ Ici B).Finite) (hne : E.Nonempty) : + ∃ β ∈ E, ∀ γ ∈ E, γ ≤ β := by + classical + obtain ⟨a,ha⟩ := hne + let S := (hE a).toFinset + have haS : a ∈ S := (hE a).mem_toFinset.mpr ⟨ha,show a ≤ a from le_rfl⟩ + let β := S.max' ⟨a,haS⟩ + have hβS : β ∈ S := Finset.max'_mem _ _ + have haβ : a ≤ β := Finset.le_max' _ _ haS + refine ⟨β,((hE a).mem_toFinset.mp hβS).1,?_⟩ + intro γ hγ + by_cases haγ : a ≤ γ + · exact Finset.le_max' _ _ ((hE a).mem_toFinset.mpr ⟨hγ,haγ⟩) + · exact (le_of_not_ge haγ).trans haβ + + + +theorem SectorExpansion.leading {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) (hne : E.Nonempty) + (hcoeff : ∀ β ∈ E, (∀ᶠ x : ℝ in atTop, b β (x:ℂ) ≠ 0) ∧ + Subexponential atTop id (fun x : ℝ => (b β (x:ℂ))⁻¹)) : + ∃ β ∈ E, (∀ γ ∈ E, γ ≤ β) ∧ + Tendsto (fun x : ℝ => (Real.exp (-β*x):ℂ)*(b β (x:ℂ))⁻¹*f (x:ℂ)) + atTop (𝓝 1) := by + classical + obtain ⟨β,hβ,hgreat⟩ := exists_greatest_of_finite_above h.finite_above hne + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hrem⟩ := h.remainders β + have hsingle : (h.finite_above β).toFinset = {β} := by + ext γ + simp only [Set.Finite.mem_toFinset,Set.mem_inter_iff,Set.mem_Ici,Finset.mem_singleton] + constructor + · intro hγ; exact le_antisymm (hgreat γ hγ.1) hγ.2 + · rintro rfl; exact ⟨hβ,le_rfl⟩ + have herr : ∀ᶠ x : ℝ in atTop, + ‖f (x:ℂ)-(Real.exp (-(-β)*x):ℂ) • b β (x:ℂ)‖ ≤ C*Real.exp (-(-β+ε)*x) := by + filter_upwards [hω.real_discs R] with x hx + have hp := hrem (x:ℂ) (hx.2 (mem_closedBall_self (by linarith [hx.1]))) + simp only [hsingle,Finset.sum_singleton,←Complex.ofReal_mul,←Complex.ofReal_exp, + Complex.ofReal_re] at hp + convert hp using 1 <;> try simp only [neg_neg,smul_eq_mul] + congr 2; ring + have hb : Tendsto (fun x : ℝ => (b β (x:ℂ))⁻¹ • b β (x:ℂ)) atTop (𝓝 (1:ℂ)) := by + apply tendsto_const_nhds.congr' + filter_upwards [(hcoeff β hβ).1] with x hx + simp [smul_eq_mul,hx] + have ht := grouped_leading_normalization (X := id) (d := -β) + tendsto_id (hcoeff β hβ).2 hε hC herr hb + exact ⟨β,hβ,hgreat,by simpa only [id_eq,smul_eq_mul] using ht⟩ + + + +theorem SectorExpansion.leading_or_zero {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) + (hcoeff : ∀ β ∈ E, (∀ᶠ x : ℝ in atTop, b β (x:ℂ) ≠ 0) ∧ + Subexponential atTop id (fun x : ℝ => (b β (x:ℂ))⁻¹)) : + (fun x : ℝ => f (x:ℂ)) =ᶠ[atTop] 0 ∨ + ∃ β ∈ E, (∀ γ ∈ E, γ ≤ β) ∧ + Tendsto (fun x : ℝ => (Real.exp (-β*x):ℂ)*(b β (x:ℂ))⁻¹*f (x:ℂ)) + atTop (𝓝 1) := by + rcases E.eq_empty_or_nonempty with he | he + · subst E; exact Or.inl h.empty + · exact Or.inr (h.leading he hcoeff) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ExpBound.zero (a : ℝ) : ExpBound a (fun _ => 0) := Asymptotics.isBigO_zero _ _ +lemma ExpBound.neg {a : ℝ} {f : ℂ → ℂ} (hf : ExpBound a f) : + ExpBound a (fun z => -f z) := Asymptotics.IsBigO.neg_left hf +lemma ExpBound.sub {a : ℝ} {f g : ℂ → ℂ} (hf : ExpBound a f) (hg : ExpBound a g) : + ExpBound a (fun z => f z-g z) := by simpa only [sub_eq_add_neg] using hf.add hg.neg + +lemma ExpBound.sum {ι : Type*} (S : Finset ι) {f : ι → ℂ → ℂ} {a : ℝ} + (h : ∀ i ∈ S, ExpBound a (f i)) : ExpBound a (fun z => ∑ i ∈ S,f i z) := by + classical + induction S using Finset.induction_on with + | empty => simpa only [Finset.sum_empty] using ExpBound.zero a + | @insert i S hi ih => + simpa only [Finset.sum_insert hi] using + (h _ (Finset.mem_insert_self _ _)).add (ih (fun j hj => h j (Finset.mem_insert_of_mem hj))) + +lemma ExpSmall.zero (B : ℝ) : ExpSmall B (fun _ => 0) := ⟨B-1,by linarith,ExpBound.zero _⟩ +lemma ExpSmall.neg {B : ℝ} {f : ℂ → ℂ} (hf : ExpSmall B f) : + ExpSmall B (fun z => -f z) := by + obtain ⟨a,ha,hf⟩ := hf + exact ⟨a,ha,hf.neg⟩ +lemma ExpSmall.sub {B : ℝ} {f g : ℂ → ℂ} (hf : ExpSmall B f) (hg : ExpSmall B g) : + ExpSmall B (fun z => f z-g z) := by simpa only [sub_eq_add_neg] using hf.add hg.neg + +lemma ExpSmall.sum {ι : Type*} (S : Finset ι) {f : ι → ℂ → ℂ} {B : ℝ} + (h : ∀ i ∈ S, ExpSmall B (f i)) : ExpSmall B (fun z => ∑ i ∈ S,f i z) := by + classical + induction S using Finset.induction_on with + | empty => simpa only [Finset.sum_empty] using ExpSmall.zero B + | @insert i S hi ih => + simpa only [Finset.sum_insert hi] using + (h _ (Finset.mem_insert_self _ _)).add (ih (fun j hj => h j (Finset.mem_insert_of_mem hj))) + +lemma ExpBound.cexp (β : ℝ) : ExpBound β (fun z => Complex.exp ((β:ℂ)*z)) := by + apply Asymptotics.IsBigO.of_bound 1 + exact Eventually.of_forall (fun z => by simp [Complex.norm_exp]) + +lemma ExpBound.expTerm {a : ℝ} {b : ℂ → ℂ} (hb : ExpBound a b) (β : ℝ) : + ExpBound (β+a) (fun z => Complex.exp ((β:ℂ)*z)*b z) := (ExpBound.cexp β).mul hb + +lemma SectorSlow.mul {f g : ℂ → ℂ} (hf : SectorSlow f) (hg : SectorSlow g) : + SectorSlow (fun z => f z*g z) := by + intro ε hε + have h := (hf (ε/2) (by linarith)).mul (hg (ε/2) (by linarith)) + simpa only [add_halves] using h + +lemma SectorSlow.expSmall {b : ℂ → ℂ} (hb : SectorSlow b) {β B : ℝ} (hβ : β < B) : + ExpSmall B (fun z => Complex.exp ((β:ℂ)*z)*b z) := by + refine ⟨β+(B-β)/2,by linarith,(hb ((B-β)/2) (by linarith)).expTerm β⟩ + +lemma SectorExpansion.eventually_analytic {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) : ∀ᶠ z in sectorInfinity, AnalyticAt ℂ f z := by + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hb⟩ := h.remainders 0 + exact ⟨ω,R,hω,hf⟩ + +lemma SectorExpansion.expSmall_remainder {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) (B : ℝ) : + ExpSmall B (fun z => f z-∑ β ∈ (h.finite_above B).toFinset,Complex.exp ((β:ℂ)*z)*b β z) := by + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hb⟩ := h.remainders B + refine ⟨B-ε,by linarith,Asymptotics.IsBigO.of_bound C ?_⟩ + exact ⟨ω,R,hω,fun z hz => by simpa only [Set.mem_ofPred_eq,Real.norm_eq_abs,abs_of_pos (Real.exp_pos _)] using hb z hz⟩ + +lemma SectorExpansion.of_expSmall {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hE : BddAbove E) (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) + (hf : ∀ᶠ z in sectorInfinity, AnalyticAt ℂ f z) + (hb : ∀ B : ℝ, ExpSmall B + (fun z => f z-∑ β ∈ (hEl B).toFinset,Complex.exp ((β:ℂ)*z)*b β z)) : + SectorExpansion f E b := by + refine ⟨hE,hEl,?_⟩ + intro B + obtain ⟨a,ha,hO⟩ := hb B + obtain ⟨C,hC,hbound⟩ := hO.exists_pos + obtain ⟨ω,R,hω,hboth⟩ := eventually_sectorInfinity.mp (hf.and hbound.bound) + refine ⟨ω,R,B-a,C,hω,by linarith,hC.le,fun z hz => (hboth z hz).1,?_⟩ + intro z hz + simpa only [sub_sub_cancel,Real.norm_eq_abs,abs_of_pos (Real.exp_pos _)] using (hboth z hz).2 + +lemma SectorExpansion.expBound {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) {A : ℝ} (hA : ∀ β ∈ E, β ≤ A) : ExpBound (A+1) f := by + have he : (h.finite_above (A+1)).toFinset = ∅ := by + classical + apply Finset.eq_empty_iff_forall_notMem.mpr + intro β hβ + have hh := (h.finite_above (A+1)).mem_toFinset.mp hβ + have := hA β hh.1 + have : A+1≤β := hh.2 + linarith + obtain ⟨a,ha,hO⟩ := h.expSmall_remainder (A+1) + simp only [he,Finset.sum_empty,sub_zero] at hO + exact hO.mono ha.le + +lemma truncation_expBound {E : Set ℝ} {b : ℝ → ℂ → ℂ} {A : ℝ} + (hA : ∀ β ∈ E, β ≤ A) (hb : ∀ β ∈ E, SectorSlow (b β)) + (B : ℝ) (hEl : (E ∩ Ici B).Finite) : + ExpBound (A+1) (fun z => ∑ β ∈ hEl.toFinset,Complex.exp ((β:ℂ)*z)*b β z) := by + apply ExpBound.sum + intro β hβ + have he := (hEl.mem_toFinset.mp hβ).1 + exact ((hb β he 1 zero_lt_one).expTerm β).mono (by linarith [hA β he]) + +end DegeneratingTrees.Clock + + + + + + + +open Set Complex +namespace DegeneratingTrees.Clock + +variable {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (hFl : ∀ B : ℝ, (F ∩ Ici B).Finite) + +def exponentConvolution (b c : ℝ → ℂ → ℂ) (δ : ℝ) (z : ℂ) : ℂ := + ∑ p ∈ (exponentFiber_finite hE hF hEl hFl δ).toFinset,b p.1 z*c p.2 z + +lemma convolution_truncation (b c : ℝ → ℂ → ℂ) (B : ℝ) (z : ℂ) : + (∑ δ ∈ (exponentSum_finite hE hF hEl hFl B).toFinset, + Complex.exp ((δ:ℂ)*z)*exponentConvolution hE hF hEl hFl b c δ z) = + ∑ p ∈ (exponentPairs_finite hE hF hEl hFl B).toFinset, + Complex.exp (((p.1+p.2:ℝ):ℂ)*z)*(b p.1 z*c p.2 z) := by + classical + let S := (exponentSum_finite hE hF hEl hFl B).toFinset + let T := (exponentPairs_finite hE hF hEl hFl B).toFinset + have hmaps : ∀ p ∈ T, p.1+p.2 ∈ S := by + intro p hp + have hh := (exponentPairs_finite hE hF hEl hFl B).mem_toFinset.mp hp + exact (exponentSum_finite hE hF hEl hFl B).mem_toFinset.mpr + ⟨⟨p,⟨hh.1,hh.2.1⟩,rfl⟩,hh.2.2⟩ + calc + _ = ∑ δ ∈ S,∑ p ∈ T with p.1+p.2=δ, + Complex.exp (((p.1+p.2:ℝ):ℂ)*z)*(b p.1 z*c p.2 z) := by + apply Finset.sum_congr rfl + intro δ hδ + have hB := ((exponentSum_finite hE hF hEl hFl B).mem_toFinset.mp hδ).2 + have he : (exponentFiber_finite hE hF hEl hFl δ).toFinset = + T.filter (fun p => p.1+p.2=δ) := by + ext p + simp only [Set.Finite.mem_toFinset,Finset.mem_filter,T,exponentFiber, + exponentPairs,mem_ofPred_eq] + constructor + · intro hp + exact ⟨⟨hp.1,hp.2.1,by simpa only [hp.2.2,Set.mem_Ici] using hB⟩,hp.2.2⟩ + · intro hp + exact ⟨hp.1.1,hp.1.2.1,hp.2⟩ + rw [exponentConvolution,he,Finset.mul_sum] + exact Finset.sum_congr rfl (fun p hp => by rw [(Finset.mem_filter.mp hp).2]) + _ = _ := Finset.sum_fiberwise_of_maps_to hmaps _ + +lemma product_truncation_rectangle (b c : ℝ → ℂ → ℂ) (U V : ℝ) (z : ℂ) : + (∑ β ∈ (hEl U).toFinset,Complex.exp ((β:ℂ)*z)*b β z) * + (∑ γ ∈ (hFl V).toFinset,Complex.exp ((γ:ℂ)*z)*c γ z) = + ∑ p ∈ (hEl U).toFinset ×ˢ (hFl V).toFinset, + Complex.exp (((p.1+p.2:ℝ):ℂ)*z)*(b p.1 z*c p.2 z) := by + classical + rw [Finset.sum_product,Finset.sum_mul] + apply Finset.sum_congr rfl + intro β hβ + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro γ hγ + simp only [Complex.ofReal_add,add_mul,Complex.exp_add] + ring + +lemma rectangle_high {A C B U V : ℝ} + (hA : ∀ β ∈ E, β ≤ A) (hC : ∀ γ ∈ F, γ ≤ C) + (hU : U ≤ B-C) (hV : V ≤ B-A) : + ((hEl U).toFinset ×ˢ (hFl V).toFinset).filter (fun p => B ≤ p.1+p.2) = + (exponentPairs_finite hE hF hEl hFl B).toFinset := by + classical + ext p + simp only [Finset.mem_filter,Finset.mem_product,Set.Finite.mem_toFinset] + constructor + · intro hp + exact ⟨hp.1.1.1,hp.1.2.1,hp.2⟩ + · intro hp + exact ⟨exponentPairs_subset_rectangle hA hC hU hV hp,hp.2.2⟩ + +lemma rectangle_split {A C B U V : ℝ} + (hA : ∀ β ∈ E, β ≤ A) (hC : ∀ γ ∈ F, γ ≤ C) + (hU : U ≤ B-C) (hV : V ≤ B-A) (b c : ℝ → ℂ → ℂ) (z : ℂ) : + (∑ β ∈ (hEl U).toFinset,Complex.exp ((β:ℂ)*z)*b β z) * + (∑ γ ∈ (hFl V).toFinset,Complex.exp ((γ:ℂ)*z)*c γ z) = + (∑ δ ∈ (exponentSum_finite hE hF hEl hFl B).toFinset, + Complex.exp ((δ:ℂ)*z)*exponentConvolution hE hF hEl hFl b c δ z) + + ∑ p ∈ ((hEl U).toFinset ×ˢ (hFl V).toFinset).filter (fun p => p.1+p.2 < B), + Complex.exp (((p.1+p.2:ℝ):ℂ)*z)*(b p.1 z*c p.2 z) := by + classical + rw [product_truncation_rectangle hEl hFl,convolution_truncation hE hF hEl hFl] + rw [←rectangle_high hE hF hEl hFl hA hC hU hV] + symm + simpa only [not_le] using Finset.sum_filter_add_sum_filter_not + ((hEl U).toFinset ×ˢ (hFl V).toFinset) (fun p => B ≤ p.1+p.2) + (fun p => Complex.exp (((p.1+p.2:ℝ):ℂ)*z)*(b p.1 z*c p.2 z)) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ClockInverses.lean b/lean/OAI/Analysis/PathSelection/ClockInverses.lean new file mode 100644 index 0000000000000000000000000000000000000000..9d8ae1c98938208d92ec6086ab7af388c5468ccc --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ClockInverses.lean @@ -0,0 +1,509 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockDerivatives + +namespace OAI + +/-! Clock inversion, logarithmic strips and exponential inverse charts. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +open scoped NNReal +namespace DegeneratingTrees.Clock + +lemma approximates_identity_of_deriv {f : ℂ → ℂ} {s : Set ℂ} {c : ℝ≥0} + (hs : Convex ℝ s) (hf : AnalyticOnNhd ℂ f s) + (hd : ∀ z ∈ s, ‖deriv f z-1‖ ≤ (c:ℝ)) : + ApproximatesLinearOn f (ContinuousLinearEquiv.refl ℂ ℂ : ℂ →L[ℂ] ℂ) s c := by + intro x hx y hy + have hdf : ∀ z ∈ s, DifferentiableAt ℂ (fun w => f w-w) z := + fun z hz => (hf z hz).differentiableAt.sub differentiableAt_id + have hb : ∀ z ∈ s, ‖deriv (fun w => f w-w) z‖ ≤ (c:ℝ) := by + intro z hz + have he : deriv (fun w => f w-w) z = deriv f z-1 := by + simpa only [Pi.sub_apply,id_eq] using! + ((hf z hz).differentiableAt.hasDerivAt.sub (hasDerivAt_id z)).deriv + rw [he] + exact hd z hz + have h := hs.norm_image_sub_le_of_norm_deriv_le hdf hb hy hx + change ‖f x-f y-(x-y)‖ ≤ (c:ℝ)*‖x-y‖ + convert h using 1; congr 1; ring + + + +theorem analytic_near_identity_inverse {f : ℂ → ℂ} {s : Set ℂ} {c : ℝ≥0} + (hs : IsOpen s) (hsc : Convex ℝ s) (hc : c < 1) + (hf : AnalyticOnNhd ℂ f s) (hd : ∀ z ∈ s, ‖deriv f z-1‖ ≤ (c:ℝ)) : + ∃ g : ℂ → ℂ, AnalyticOnNhd ℂ g (f '' s) ∧ + (∀ z ∈ s, g (f z) = z) ∧ + (∀ w ∈ f '' s, g w ∈ s ∧ f (g w) = w) ∧ + (∀ z ∈ s, ∀ w ∈ s, (1-(c:ℝ))*‖z-w‖ ≤ ‖f z-f w‖) ∧ + (∀ z : ℂ, ∀ r : ℝ, 0 ≤ r → closedBall z r ⊆ s → + closedBall (f z) ((1-(c:ℝ))*r) ⊆ f '' s) := by + have ha := approximates_identity_of_deriv hsc hf hd + have hcc : Subsingleton ℂ ∨ c < + ‖((ContinuousLinearEquiv.refl ℂ ℂ).symm : ℂ →L[ℂ] ℂ)‖₊⁻¹ := by + right + simpa using hc + let e := ha.toOpenPartialHomeomorph f s hcc hs + have heS : e.source = s := rfl + have heT : e.target = f '' s := rfl + have heF : (e : ℂ → ℂ) = f := rfl + have hdz : ∀ z ∈ s, deriv f z ≠ 0 := by + intro z hz he + have h1 := hd z hz + simp only [he,zero_sub,norm_neg,norm_one] at h1 + exact (not_le_of_gt (show (c:ℝ)<1 from hc)) h1 + refine ⟨e.symm,?_,?_,?_,?_,?_⟩ + · apply (Complex.analyticOnNhd_iff_differentiableOn (by simpa [heT] using e.open_target)).mpr + intro w hw + have hw' : w ∈ e.target := hw + have hg : e.symm w ∈ s := e.map_target hw' + exact (e.hasDerivAt_symm hw' (hdz _ hg) + (by simpa [heF] using (hf _ hg).differentiableAt.hasDerivAt)).differentiableAt.differentiableWithinAt + · intro z hz + exact e.left_inv hz + · intro w hw + exact ⟨e.map_target hw,e.right_inv hw⟩ + · intro z hz w hw + have h := ha z hz w hw + have ht : ‖z-w‖ ≤ ‖f z-f w‖+‖f z-f w-(z-w)‖ := by + calc + ‖z-w‖ = ‖(f z-f w)-(f z-f w-(z-w))‖ := by congr 1; ring + _ ≤ ‖f z-f w‖+‖f z-f w-(z-w)‖ := norm_sub_le _ _ + change ‖f z-f w-(z-w)‖ ≤ (c:ℝ)*‖z-w‖ at h + nlinarith + · intro z r hr hrs + simpa using ha.closedBall_subset_target hcc hs hr hrs + + + +def horizontalTail (A R : ℝ) : Set ℂ := {z | A < z.re ∧ |z.im| < R} + +lemma horizontalTail_open (A R : ℝ) : IsOpen (horizontalTail A R) := + (isOpen_lt continuous_const continuous_re).inter + (isOpen_lt continuous_im.abs continuous_const) + +lemma horizontalTail_convex (A R : ℝ) : Convex ℝ (horizontalTail A R) := by + have h := (convex_halfSpace_re_gt A).inter + ((convex_halfSpace_im_gt (-R)).inter (convex_halfSpace_im_lt R)) + simpa only [horizontalTail,abs_lt,Set.ofPred_and] using h + +lemma closedBall_real_subset_horizontalTail {A R r t : ℝ} + (hr : r < R) (ht : A+r < t) : closedBall (t:ℂ) r ⊆ horizontalTail A R := by + intro z hz + have hn : ‖z-(t:ℂ)‖ ≤ r := mem_closedBall_iff_norm.mp hz + have hre := (abs_re_le_norm (z-(t:ℂ))).trans hn + have him := (abs_im_le_norm (z-(t:ℂ))).trans hn + simp only [sub_re,sub_im,ofReal_re,ofReal_im,sub_zero] at hre him + exact ⟨by have := (abs_le.mp hre).1; linarith,him.trans_lt hr⟩ + + + +theorem analytic_inverse_on_tail_strip {A R d : ℝ} (hd : 0 < d) (hdR : 2*d < R) + {f : ℂ → ℂ} (hf : AnalyticOnNhd ℂ f (horizontalTail A R)) + (hderiv : ∀ z ∈ horizontalTail A R, ‖deriv f z-1‖ ≤ (1/2:ℝ)) + (hreal : ∀ t : ℝ, A < t → (f (t:ℂ)).im = 0) + (hlim : Tendsto (fun t : ℝ => (f (t:ℂ)).re) atTop atTop) : + ∃ (T : ℝ) (g : ℂ → ℂ), AnalyticOnNhd ℂ g (horizontalTail T d) ∧ + (∀ w ∈ horizontalTail T d, g w ∈ horizontalTail A R ∧ f (g w) = w) ∧ + (∀ t : ℝ, A < t → f (t:ℂ) ∈ horizontalTail T d → g (f (t:ℂ)) = (t:ℂ)) ∧ + (∀ w ∈ horizontalTail T d, ∃ t : ℝ, A+2*d < t ∧ + (f (t:ℂ)).re = w.re ∧ ‖g w-(t:ℂ)‖ ≤ 2*|w.im|) := by + have hR : 0 < R := lt_trans (by positivity) hdR + obtain ⟨g,hga,hgf,hfg,hmetric,hball⟩ := analytic_near_identity_inverse + (horizontalTail_open A R) (horizontalTail_convex A R) + (c := (1/2:ℝ≥0)) (by norm_num) hf (by simpa using hderiv) + let a := A+2*d+1 + have ha : A+2*d < a := by dsimp [a]; linarith + have hat : A < a := by linarith + have hcont : ContinuousOn (fun t:ℝ => (f (t:ℂ)).re) (Ici a) := by + intro t ht + have htf : (t:ℂ) ∈ horizontalTail A R := ⟨lt_of_lt_of_le hat ht,by simpa using hR⟩ + exact (continuous_re.continuousAt.comp ((hf _ htf).continuousAt.comp continuous_ofReal.continuousAt)).continuousWithinAt + let T := (f (a:ℂ)).re + have htarget : ∀ w ∈ horizontalTail T d, ∃ t : ℝ, A+2*d < t ∧ + (f (t:ℂ)).re = w.re ∧ w ∈ f '' horizontalTail A R := by + intro w hw + obtain ⟨t,ht,he⟩ := intermediate_value_Ici hcont hlim hw.1.le + have hat' : A+2*d < t := ha.trans_le ht + refine ⟨t,hat',he,?_⟩ + apply hball (t:ℂ) (2*d) (by positivity) + (closedBall_real_subset_horizontalTail hdR hat') + have hdiff : w-f (t:ℂ) = w.im*Complex.I := by + apply Complex.ext <;> simp [he,hreal t (by linarith)] + rw [mem_closedBall_iff_norm,hdiff] + simpa only [norm_mul, norm_real, Real.norm_eq_abs, norm_I, mul_one, + NNReal.coe_div, NNReal.coe_one, NNReal.coe_ofNat] using + (show |w.im| ≤ (1-(1/2:ℝ))*(2*d) by linarith [hw.2]) + have hsub : horizontalTail T d ⊆ f '' horizontalTail A R := + fun w hw => (htarget w hw).choose_spec.2.2 + refine ⟨T,g,hga.mono hsub,fun w hw => hfg w (hsub hw),?_,?_⟩ + · intro t ht htf + exact hgf (t:ℂ) ⟨ht,by simpa using hR⟩ + · intro w hw + obtain ⟨t,ht,he,hwt⟩ := htarget w hw + refine ⟨t,ht,he,?_⟩ + have htS : (t:ℂ) ∈ horizontalTail A R := ⟨by change A simp [he,hreal t (by linarith)] + rw [hdiff] at hm + simp only [norm_mul, norm_real,Real.norm_eq_abs,norm_I,mul_one] at hm + norm_num at hm + linarith + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees.Clock + +def stripInfinity : Filter ℂ where + sets := {s | ∀ R : ℝ,∃ A : ℝ,horizontalTail A R ⊆ s} + univ_sets := fun _ => ⟨0,subset_univ _⟩ + sets_of_superset := fun h hs R => by obtain ⟨A,hA⟩ := h R; exact ⟨A,hA.trans hs⟩ + inter_sets := fun h k R => by + obtain ⟨A,hA⟩ := h R + obtain ⟨B,hB⟩ := k R + exact ⟨max A B,fun z hz => ⟨hA ⟨(le_max_left _ _).trans_lt hz.1,hz.2⟩, + hB ⟨(le_max_right _ _).trans_lt hz.1,hz.2⟩⟩⟩ + +lemma eventually_stripInfinity {P : ℂ → Prop} : + (∀ᶠ z in stripInfinity,P z) ↔ ∀ R : ℝ,∃ A : ℝ,∀ z∈horizontalTail A R,P z := Iff.rfl + +instance stripInfinity_neBot : NeBot stripInfinity := by + refine ⟨?_⟩ + intro h + have hem : (∅ : Set ℂ)∈stripInfinity := by rw [h]; simp + obtain ⟨A,hA⟩ := hem 1 + exact hA (show ((A+1:ℝ):ℂ)∈horizontalTail A 1 from ⟨by simp,by simp⟩) + +lemma stripInfinity_le_sectorInfinity : stripInfinity ≤ sectorInfinity := by + intro s hs + obtain ⟨ω,S,hω,hS⟩ := hs + intro R + obtain ⟨T,hT⟩ := eventually_atTop.mp (hω.real_discs S) + refine ⟨max T (4*R),?_⟩ + intro z hz + apply hS z ((hT z.re ((le_max_left _ _).trans hz.1.le)).2 ?_) + rw [mem_closedBall_iff_norm] + have he : z-(z.re:ℂ)=(z.im:ℂ)*Complex.I := by apply Complex.ext <;> simp + rw [he,norm_mul,Complex.norm_real,Real.norm_eq_abs,Complex.norm_I,mul_one] + have hr := (le_max_right T (4*R)).trans_lt hz.1 + linarith [hz.2] + +lemma tendsto_real_stripInfinity : Tendsto (fun t : ℝ => (t:ℂ)) atTop stripInfinity := by + apply Filter.tendsto_def.mpr + intro s hs + obtain ⟨A,hA⟩ := hs 1 + filter_upwards [eventually_gt_atTop A] with t ht + exact hA ⟨ht,by simp⟩ + +lemma tendsto_re_stripInfinity : Tendsto Complex.re stripInfinity atTop := by + apply Filter.tendsto_atTop.mpr + intro A R + exact ⟨A,fun z hz => hz.1.le⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma SectorExpansion.log_deriv_tendsto {F : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hF : SectorExpansion F E b) (ha : ∀ β∈E,∀ᶠ z in sectorInfinity,AnalyticAt ℂ (b β) z) + {β : ℝ} (hβ : β∈E) (hmax : ∀ γ∈E,γ≤β) + (hb0 : ∀ᶠ z in sectorInfinity,b β z≠0) (hbi : SectorSlow (fun z => (b β z)⁻¹)) + (hq : Tendsto (fun z => _root_.deriv (b β) z/b β z) sectorInfinity (𝓝 0)) : + Tendsto (fun z => _root_.deriv F z/F z) sectorInfinity (𝓝 (β:ℂ)) := by + have hFd := hF.deriv ha + have herr := ((hFd.leading_error hβ hmax).mul (ExpBound.cexp (-β))).mul_slow hbi + simp only [add_neg_cancel] at herr + have hn : Tendsto (fun z => Complex.exp (((-β:ℝ):ℂ)*z)*(b β z)⁻¹*_root_.deriv F z) + sectorInfinity (𝓝 (β:ℂ)) := by + have ht := herr.tendsto_zero.add ((tendsto_const_nhds (x := (β:ℂ))).add hq) + simp only [add_zero,zero_add] at ht + apply ht.congr' + filter_upwards [hb0] with z hz + have he : Complex.exp (((-β:ℝ):ℂ)*z)=(Complex.exp ((β:ℂ)*z))⁻¹ := by + rw [←Complex.exp_neg]; congr 1; push_cast; ring + rw [he] + field_simp [hz,Complex.exp_ne_zero] + ring + have hu := hF.uniform_leading_tendsto hβ hmax hb0 hbi + have ht := hn.div hu (by norm_num : (1:ℂ)≠0) + simp only [div_one] at ht + apply ht.congr' + filter_upwards [hb0,hF.eventually_ne_of_leading hβ hmax hb0 hbi] with z hz hFz + change (Complex.exp (((-β:ℝ):ℂ)*z)*(b β z)⁻¹*_root_.deriv F z) / + (Complex.exp (((-β:ℝ):ℂ)*z)*(b β z)⁻¹*F z)=_root_.deriv F z/F z + field_simp [hz,hFz,Complex.exp_ne_zero] + + + +theorem ExpansionOver.puiseux_log_deriv {F : ℂ → ℂ} (hF : ExpansionOver PuiseuxSector F) + (hne : ¬ (fun t : ℝ => F (t:ℂ)) =ᶠ[atTop] fun _ => 0) : + ∃ β : ℝ,∃ b : ℂ → ℂ,b∈PuiseuxSector ∧ + (¬ (fun t : ℝ => b (t:ℂ)) =ᶠ[atTop] fun _ => 0) ∧ + ExpSmall 0 (fun z => Complex.exp (((-β:ℝ):ℂ)*z)*(b z)⁻¹*F z-1) ∧ + (∀ᶠ z in sectorInfinity,F z≠0) ∧ + Tendsto (fun z => deriv F z/F z) sectorInfinity (𝓝 (β:ℂ)) := by + obtain ⟨E,b,hF,hb⟩ := hF + have ht := hF.trim_zero (fun β hβ => (hb β hβ).1) + have hn : (nonzeroRaySupport E b).Nonempty := by + by_contra he + rw [Set.not_nonempty_iff_eq_empty.mp he] at ht + exact hne ht.empty + obtain ⟨β,hβ,hmax⟩ := exists_greatest_of_finite_above ht.finite_above hn + have hbi := puiseux_lowerSectorData.slow (puiseux_lowerSectorData.inv_mem (hb β hβ.1)) + have hb0 : ∀ᶠ z in sectorInfinity,b β z≠0 := by + rcases puiseux_lowerSectorData.zero_or_ne (hb β hβ.1) with hz | hz + · exact False.elim (hβ.2 (tendsto_real_sectorInfinity.eventually hz)) + · exact hz + exact ⟨β,b β,hb β hβ.1,hβ.2,ht.uniform_leading hβ hmax hb0 hbi, + ht.eventually_ne_of_leading hβ hmax hb0 hbi, + ht.log_deriv_tendsto (fun γ hγ => (hb γ hγ.1).1) hβ hmax hb0 hbi + (PuiseuxSector.log_deriv_tendsto (hb β hβ.1) hβ.2)⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma analytic_log_on_convex {S : Set ℂ} (hSo : IsOpen S) (hSc : Convex ℝ S) + (hSn : S.Nonempty) {H : ℂ → ℂ} (hH : AnalyticOnNhd ℂ H S) + (hH0 : ∀ z∈S,H z≠0) : + ∃ L : ℂ → ℂ,AnalyticOnNhd ℂ L S ∧ (∀ z∈S,Complex.exp (L z)=H z) ∧ + ∀ z∈S,deriv L z=deriv H z/H z := by + let := hSc.contractibleSpace hSn + have hsim : IsSimplyConnected S := by change SimplyConnectedSpace S; infer_instance + obtain ⟨L,hLc,hLe⟩ := Complex.exists_continuousOn_eqOn_exp_comp hsim hSo hH.continuousOn + (by rintro ⟨z,hz,he⟩; exact hH0 z hz he) + have hd (z : ℂ) (hz : z∈S) : HasDerivAt L (deriv H z/H z) z := by + have hh := HasDerivAt.of_comp_left ((hLc z hz).continuousAt (hSo.mem_nhds hz)) + (Complex.hasDerivAt_exp (L z)) (hH z hz).differentiableAt.hasDerivAt + (Complex.exp_ne_zero _) (Filter.Eventually.mono (hSo.mem_nhds hz) (fun w hw => hLe hw)) + simpa only [show Complex.exp (L z)=H z from hLe hz] using hh + refine ⟨L,?_,fun z hz => hLe hz,fun z hz => (hd z hz).deriv⟩ + exact (Complex.analyticOnNhd_iff_differentiableOn hSo).mpr + (fun z hz => (hd z hz).differentiableAt.differentiableWithinAt) + +lemma analytic_ray_deriv_im_zero {H : ℂ → ℂ} {A t : ℝ} (ht : A (H (s:ℂ)).im) =ᶠ[𝓝 t] fun _ => 0 := + (eventually_gt_nhds ht).mono (fun s hs => hr s hs) + have hz : HasDerivAt (fun s : ℝ => (H (s:ℂ)).im) 0 t := + (hasDerivAt_const t (0:ℝ)).congr_of_eventuallyEq he + exact hh.unique hz + + + +theorem analytic_real_log_on_strip {A R : ℝ} (hR : 0 (L (t:ℂ)).im) 0 t := by + have hd := Complex.imCLM.hasFDerivAt.comp_hasDerivAt t + (hLa _ (hray t ht)).differentiableAt.hasDerivAt.comp_ofReal + have hHz : (deriv H (t:ℂ)).im=0 := analytic_ray_deriv_im_zero ht + (hH _ (hray t ht)) (fun s hs => (hreal s hs).1) + have hi : (deriv L (t:ℂ)).im=0 := by + rw [hLd _ (hray t ht),Complex.div_im,hHz,(hreal t ht).1] + simp + change HasDerivAt (fun t : ℝ => (L (t:ℂ)).im) (deriv L (t:ℂ)).im t at hd + rwa [hi] at hd + have himconst (t : ℝ) (ht : A (himder t ht).differentiableAt.differentiableWithinAt) + (fun t ht => (himder t ht).deriv) ht (by change A L z-L (t0:ℂ)+(Real.log (H (t0:ℂ)).re:ℂ) + have hKexp (z : ℂ) (hz : z∈horizontalTail A R) : Complex.exp (K z)=H z := by + dsimp [K] + rw [Complex.exp_add,Complex.exp_sub,hLe _ hz,hLe _ (hray t0 ht0),←Complex.ofReal_exp, + Real.exp_log (hreal t0 ht0).2,←h0eq] + exact div_mul_cancel₀ _ (hH0 _ (hray t0 ht0)) + refine ⟨K,fun z hz => ((hLa z hz).sub analyticAt_const).add analyticAt_const, + hKexp,?_,?_⟩ + · intro z hz + have hd := ((hLa z hz).differentiableAt.hasDerivAt.sub_const (L (t0:ℂ))).add_const + (Real.log (H (t0:ℂ)).re:ℂ) + exact hd.deriv.trans (hLd z hz) + · intro t ht + have hi : (K (t:ℂ)).im=0 := by simp only [K,sub_im,add_im,ofReal_im,add_zero]; exact sub_eq_zero.mpr (himconst t ht) + have hn := congrArg norm (hKexp (t:ℂ) (hray t ht)) + rw [Complex.norm_exp] at hn + have hnorm : ‖H (t:ℂ)‖=(H (t:ℂ)).re := by + have heq : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext (by simp) (by simp [(hreal t ht).1]) + rw [heq,Complex.norm_of_nonneg (hreal t ht).2.le] + rfl + rw [hnorm] at hn + have hre := congrArg Real.log hn + rw [Real.log_exp] at hre + exact Complex.ext (by simpa using hre) (by simpa using hi) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + + + +theorem normalized_log_inverse {H : ℂ → ℂ} {b d R : ℝ} + (hb : 0 (H (t:ℂ)).re) atTop atTop) + (hq : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) : + ∃ (A T : ℝ) (f g : ℂ → ℂ), + AnalyticOnNhd ℂ f (horizontalTail A R) ∧ + (∀ z∈horizontalTail A R,Complex.exp ((b:ℂ)*f z)=H z) ∧ + (∀ z∈horizontalTail A R,‖deriv f z-1‖≤(1/2:ℝ)) ∧ + (∀ z∈horizontalTail A R,deriv f z=(deriv H z/H z)/(b:ℂ)) ∧ + (∀ t : ℝ,A ⟨(le_max_left _ _).trans_lt hz.1,hz.2⟩ + have hreal (t : ℝ) (ht : A (hA₀ z (hs hz)).1.1) (fun z hz => (hA₀ z (hs hz)).1.2) hreal + let f : ℂ → ℂ := fun z => L z/(b:ℂ) + have hfa : AnalyticOnNhd ℂ f (horizontalTail A R) := fun z hz => (hLa z hz).div_const + have hfd (z : ℂ) (hz : z∈horizontalTail A R) : deriv f z=(deriv H z/H z)/(b:ℂ) := by + rw [show deriv f z=deriv L z/(b:ℂ) from ((hLa z hz).differentiableAt.hasDerivAt.div_const (b:ℂ)).deriv] + rw [hLd z hz] + have hfn (z : ℂ) (hz : z∈horizontalTail A R) : ‖deriv f z-1‖≤(1/2:ℝ) := by + rw [hfd z hz,show (deriv H z/H z)/(b:ℂ)-1=(deriv H z/H z-(b:ℂ))/(b:ℂ) by field_simp] + rw [norm_div,Complex.norm_real,Real.norm_eq_abs,abs_of_pos hb] + exact (div_le_iff₀ hb).mpr (by linarith [(hA₀ z (hs hz)).2]) + have hfr (t : ℝ) (ht : A (f (t:ℂ)).re) atTop atTop := by + apply ((Real.tendsto_log_atTop.comp hlim).atTop_div_const hb).congr' + filter_upwards [eventually_gt_atTop A] with t ht + rw [hfr t ht,Complex.ofReal_re] + rfl + obtain ⟨T,g,hga,hgf,hfg,hgb⟩ := analytic_inverse_on_tail_strip hd hdR hfa hfn + (fun t ht => by rw [hfr t ht]; simp) hfl + refine ⟨A,T,f,g,hfa,?_,hfn,hfd,hfr,hga,hgf,hfg,hgb⟩ + intro z hz + simpa [f,mul_div_cancel₀ _ hb0] using hLe z hz + + + +theorem positive_exponential_inverse {H : ℂ → ℂ} {b : ℝ} (hb : 0 (H (t:ℂ)).re) atTop atTop) + (hq : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) : + ∃ A T : ℝ,0 g (Complex.log w/(b:ℂ)) + have hmap (w : ℂ) (hw : 0 Complex.log w/(b:ℂ)) + ((analyticAt_clog (Complex.mem_slitPlane_iff.mpr (Or.inl hw.1))).div_const) + · intro w hw hT + have hh := hgf _ (hmap w hw hT) + rw [←hfe _ hh.1,hh.2,mul_div_cancel₀ _ (show (b:ℂ)≠0 by exact_mod_cast hb.ne')] + exact Complex.exp_log (hzero w hw) + · intro w hw hT + obtain ⟨t,ht,htr,htb⟩ := hgb _ (hmap w hw hT) + have hat : A (f (t:ℂ)).re) atTop atTop := by + apply ((Real.tendsto_log_atTop.comp hlim).atTop_div_const hb).congr' + filter_upwards [eventually_gt_atTop A] with t ht + rw [hfr t ht,Complex.ofReal_re] + rfl + filter_upwards [eventually_gt_atTop A,hr,htlim.eventually (eventually_gt_atTop T₀)] with t ht hrt hft + have hfstrip : f (t:ℂ)∈horizontalTail T₀ d := ⟨hft,by rw [hfr t ht]; simpa using hd⟩ + have hHreal : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext (by simp) (by simp [hrt.1]) + have hh : Complex.log (H (t:ℂ))/(b:ℂ)=f (t:ℂ) := by + rw [hHreal,←Complex.ofReal_log hrt.2.le,hfr t ht,Complex.ofReal_div] + dsimp [x]; rw [hh]; exact hfg t ht hfstrip + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/CoefficientFields.lean b/lean/OAI/Analysis/PathSelection/CoefficientFields.lean new file mode 100644 index 0000000000000000000000000000000000000000..6c4a6a4aa1a24d974ec1ad0768b5db660d10a5c1 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/CoefficientFields.lean @@ -0,0 +1,217 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockAlgebra +import OAI.Analysis.PathSelection.ExpansionAlgebra + +namespace OAI + +/-! Local sectors, lower sector data and fields of expansion coefficients. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees + +lemma sector_eventually_nhds {P : ℂ → Prop} (h : ∀ᶠ z in sectorInfinity,P z) : + ∀ᶠ z in sectorInfinity,∀ᶠ w in 𝓝 z,P w := by + obtain ⟨ω,R,hω,hP⟩ := h + obtain ⟨η,S,hη,hRS,hdisc⟩ := hω.narrow_discs R + exact ⟨η,S,hη,fun z hz => Filter.mem_of_superset + (Metric.closedBall_mem_nhds z zero_lt_one) (fun w hw => hP w (hdisc z hz hw))⟩ + +lemma sector_eventually_analytic_congr {f g : ℂ → ℂ} + (hf : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ f z) (he : f =ᶠ[sectorInfinity] g) : + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ g z := by + filter_upwards [hf,sector_eventually_nhds he] with z hz hez + exact hz.congr hez + +lemma sector_eventually_deriv_congr {f g : ℂ → ℂ} (he : f =ᶠ[sectorInfinity] g) : + deriv f =ᶠ[sectorInfinity] deriv g := by + filter_upwards [sector_eventually_nhds he] with z hz + have hez : f =ᶠ[𝓝 z] g := hz + exact hez.deriv_eq + +namespace Clock +lemma SectorExpansion.congr {f g : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) (he : f =ᶠ[sectorInfinity] g) : SectorExpansion g E b := by + apply SectorExpansion.of_expSmall hf.bounded_above hf.finite_above + (sector_eventually_analytic_congr hf.eventually_analytic he) + intro B + obtain ⟨a,ha,hO⟩ := hf.expSmall_remainder B + exact ⟨a,ha,hO.congr' (he.sub (EventuallyEq.refl _ _)) (EventuallyEq.refl _ _)⟩ +end Clock +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +structure LowerSectorData (K : Set (ℂ → ℂ)) : Prop where + const_mem : ∀ c : ℂ,(fun _ => c) ∈ K + add_mem : ∀ {f g},f ∈ K → g ∈ K → (fun z => f z+g z) ∈ K + neg_mem : ∀ {f},f ∈ K → (fun z => -f z) ∈ K + mul_mem : ∀ {f g},f ∈ K → g ∈ K → (fun z => f z*g z) ∈ K + inv_mem : ∀ {f},f ∈ K → (fun z => (f z)⁻¹) ∈ K + analytic : ∀ {f},f ∈ K → ∀ᶠ z in sectorInfinity,AnalyticAt ℂ f z + slow : ∀ {f},f ∈ K → SectorSlow f + zero_or_ne : ∀ {f},f ∈ K → (∀ᶠ z in sectorInfinity,f z=0) ∨ + (∀ᶠ z in sectorInfinity,f z≠0) + +namespace LowerSectorData +variable {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) +include hK + +lemma finset_sum_mem {ι : Type*} (S : Finset ι) {f : ι → ℂ → ℂ} + (hf : ∀ i ∈ S,f i ∈ K) : (fun z => ∑ i ∈ S,f i z) ∈ K := by + classical + induction S using Finset.induction_on with + | empty => simpa only [Finset.sum_empty] using hK.const_mem 0 + | @insert i S hi ih => + simpa only [Finset.sum_insert hi] using hK.add_mem (hf i (Finset.mem_insert_self _ _)) + (ih (fun j hj => hf j (Finset.mem_insert_of_mem hj))) + +lemma word_mem {E : Set ℝ} {b : ℝ → ℂ → ℂ} (hb : ∀ β ∈ E,b β ∈ K) + {w : List ℝ} (hw : w ∈ exponentWords E) : wordCoefficient b w ∈ K := by + induction w with + | nil => exact hK.const_mem 1 + | cons β w ih => + exact hK.mul_mem (hb β (hw β (by simp))) + (ih (fun γ hγ => hw γ (List.mem_cons_of_mem _ hγ))) + +lemma geometric_mem {E : Set ℝ} {δ : ℝ} (hδ : 0 < δ) (hE : ∀ β ∈ E,β≤ -δ) + (hEl : ∀ B : ℝ,(E ∩ Ici B).Finite) {b : ℝ → ℂ → ℂ} (hb : ∀ β ∈ E,b β ∈ K) + (β : ℝ) : geometricCoefficient hδ hE hEl b β ∈ K := by + apply hK.finset_sum_mem + intro w hw + exact hK.word_mem hb ((wordFiber_finite hδ hE hEl β).mem_toFinset.mp hw).1 + +lemma convolution_mem {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) + (hEl : ∀ B : ℝ,(E ∩ Ici B).Finite) (hFl : ∀ B : ℝ,(F ∩ Ici B).Finite) + {b c : ℝ → ℂ → ℂ} (hb : ∀ β ∈ E,b β ∈ K) (hc : ∀ γ ∈ F,c γ ∈ K) + (δ : ℝ) : exponentConvolution hE hF hEl hFl b c δ ∈ K := by + apply hK.finset_sum_mem + intro p hp + have hh := (exponentFiber_finite hE hF hEl hFl δ).mem_toFinset.mp hp + exact hK.mul_mem (hb p.1 hh.1) (hc p.2 hh.2.1) +end LowerSectorData + +def ExpansionOver (K : Set (ℂ → ℂ)) (f : ℂ → ℂ) : Prop := + ∃ E : Set ℝ,∃ b : ℝ → ℂ → ℂ,SectorExpansion f E b ∧ ∀ β ∈ E,b β ∈ K + +namespace ExpansionOver +variable {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) +include hK + +lemma const (c : ℂ) : ExpansionOver K (fun _ => c) := + ⟨{0},fun _ _ => c,SectorExpansion.const c,fun _ _ => hK.const_mem c⟩ + +omit hK in +lemma congr {f g : ℂ → ℂ} (hf : ExpansionOver K f) (he : f =ᶠ[sectorInfinity] g) : + ExpansionOver K g := by + obtain ⟨E,b,hf,hb⟩ := hf + exact ⟨E,b,hf.congr he,hb⟩ + +lemma neg {f : ℂ → ℂ} (hf : ExpansionOver K f) : ExpansionOver K (fun z => -f z) := by + obtain ⟨E,b,hf,hb⟩ := hf + exact ⟨E,fun β z => -b β z,hf.neg,fun β hβ => hK.neg_mem (hb β hβ)⟩ + +lemma add {f g : ℂ → ℂ} (hf : ExpansionOver K f) (hg : ExpansionOver K g) : + ExpansionOver K (fun z => f z+g z) := by + classical + obtain ⟨E,b,hf,hb⟩ := hf + obtain ⟨F,c,hg,hc⟩ := hg + refine ⟨E ∪ F,fun β z => (if β∈E then b β z else 0)+(if β∈F then c β z else 0),hf.add hg,?_⟩ + intro β hβ + apply hK.add_mem + · by_cases he : β∈E + · simpa only [ite_eq_left he] using hb β he + · simpa only [ite_eq_right he] using hK.const_mem 0 + · by_cases he : β∈F + · simpa only [ite_eq_left he] using hc β he + · simpa only [ite_eq_right he] using hK.const_mem 0 + +lemma mul {f g : ℂ → ℂ} (hf : ExpansionOver K f) (hg : ExpansionOver K g) : + ExpansionOver K (fun z => f z*g z) := by + obtain ⟨E,b,hf,hb⟩ := hf + obtain ⟨F,c,hg,hc⟩ := hg + exact ⟨exponentSum E F,_,hf.mul hg (fun β hβ => hK.slow (hb β hβ)) + (fun γ hγ => hK.slow (hc γ hγ)), + fun δ _ => hK.convolution_mem hf.bounded_above hg.bounded_above hf.finite_above hg.finite_above hb hc δ⟩ + +lemma inverse_of_leading {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) (hb : ∀ β ∈ E,b β ∈ K) + {β : ℝ} (hβ : β∈E) (hmax : ∀ γ∈E,γ≤β) + (hbne : ∀ᶠ z in sectorInfinity,b β z≠0) : ExpansionOver K (fun z => (f z)⁻¹) := by + let q : ℂ → ℂ := fun z => (b β z)⁻¹ + have hq := hK.inv_mem (hb β hβ) + let r : ℂ → ℂ := fun z => -(Complex.exp (((-β:ℝ):ℂ)*z)* + (f z-Complex.exp ((β:ℂ)*z)*b β z))*q z + let D := translatedSupport (-β) (E \ {β}) + let c : ℝ → ℂ → ℂ := fun γ z => -b (γ-(-β)) z*q z + have hr : SectorExpansion r D c := + (((hf.erase hβ (hK.analytic (hb β hβ)) (hK.slow (hb β hβ))).exp_shift (-β)).neg).mul_lower + (hK.analytic hq) (hK.slow hq) + have hc : ∀ γ∈D,c γ ∈ K := by + rintro γ ⟨a,ha,rfl⟩ + dsimp [c] + simpa only [show -β+a-(-β)=a by ring] using hK.mul_mem (hK.neg_mem (hb a ha.1)) hq + have hn : ∀ γ∈D,γ<0 := by + rintro γ ⟨a,ha,rfl⟩ + change -β+a<0 + have hle := hmax a ha.1 + have hne : a≠β := ha.2 + have hlt : a<β := lt_of_le_of_ne hle hne + linarith + obtain ⟨δ,hδ,hd⟩ := strict_negative_support_gap hr.finite_above hn + have hri := hr.geometric_inverse hδ hd (fun γ hγ => hK.slow (hc γ hγ)) + have hfinal := (hri.mul_lower (hK.analytic hq) (hK.slow hq)).exp_shift (-β) + have hmem : ∀ γ ∈ translatedSupport (-β) (wordSupport D), + (fun z => geometricCoefficient hδ hd hr.finite_above c (γ-(-β)) z*q z) ∈ K := by + intro γ _ + exact hK.mul_mem (hK.geometric_mem hδ hd hr.finite_above hc (γ-(-β))) hq + apply (show ExpansionOver K (fun z => Complex.exp (((-β:ℝ):ℂ)*z)*((1-r z)⁻¹*q z)) from + ⟨_,_,hfinal,hmem⟩).congr + filter_upwards [hbne] with z hz + have hexp : Complex.exp (((-β:ℝ):ℂ)*z)=(Complex.exp ((β:ℂ)*z))⁻¹ := by + rw [Complex.ofReal_neg,neg_mul,Complex.exp_neg] + have he := Complex.exp_ne_zero ((β:ℂ)*z) + dsimp [r,q] + rw [hexp] + have hh : 1- -((Complex.exp ((β:ℂ)*z))⁻¹*(f z-Complex.exp ((β:ℂ)*z)*b β z))*(b β z)⁻¹ = + (Complex.exp ((β:ℂ)*z))⁻¹*f z*(b β z)⁻¹ := by + field_simp [he,hz] + ring + rw [hh,mul_inv_rev,mul_inv_rev,inv_inv,inv_inv] + field_simp [he,hz] + + + +theorem inv {f : ℂ → ℂ} (hf : ExpansionOver K f) : ExpansionOver K (fun z => (f z)⁻¹) := by + classical + obtain ⟨E,b,hf,hb⟩ := hf + have ht := hf.trim_zero (fun β hβ => hK.analytic (hb β hβ)) + rcases (nonzeroRaySupport E b).eq_empty_or_nonempty with he | he + · rw [he] at ht + have hz := ht.empty + obtain ⟨ω,R,hω,ha⟩ := hf.eventually_analytic + have hzero := sector_zero_of_ray_zero hω ha hz + apply (const hK 0).congr + exact hzero.mono (fun _ hz => by simp [hz]) + · obtain ⟨β,hβ,hmax⟩ := exists_greatest_of_finite_above ht.finite_above he + have hbne : ∀ᶠ z in sectorInfinity,b β z≠0 := by + rcases hK.zero_or_ne (hb β hβ.1) with hz | hn + · exact False.elim (hβ.2 (tendsto_real_sectorInfinity.eventually hz)) + · exact hn + exact inverse_of_leading hK ht (fun γ hγ => hb γ hγ.1) hβ hmax hbne + +end ExpansionOver +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/CompactProfiles.lean b/lean/OAI/Analysis/PathSelection/CompactProfiles.lean new file mode 100644 index 0000000000000000000000000000000000000000..21e3af7531fdf4c66b3446eee2b69eb0080fbdf3 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/CompactProfiles.lean @@ -0,0 +1,216 @@ +import Mathlib +import OAI.Analysis.PathSelection.ContourPolynomials +import OAI.Analysis.PathSelection.FunctionSeries + +namespace OAI + +/-! Compact analytic profiles and parameter-dependent contour integrals. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace DegeneratingTrees +open Set Metric Filter Topology + + + +def radialClip (a : ℝ) (z : ℂ) : ℂ := (a / max a ‖z‖) • z + +theorem continuous_radialClip {a : ℝ} (ha : 0 < a) : Continuous (radialClip a) := by + unfold radialClip + exact (continuous_const.div (continuous_const.max continuous_norm) + (fun z => ne_of_gt (ha.trans_le (le_max_left a ‖z‖)))).smul continuous_id + +theorem norm_radialClip_le {a : ℝ} (ha : 0 < a) (z : ℂ) : ‖radialClip a z‖ ≤ a := by + rw [radialClip, norm_smul, Real.norm_eq_abs, abs_of_nonneg (by positivity)] + have hm : 0 < max a ‖z‖ := ha.trans_le (le_max_left _ _) + rw [div_mul_eq_mul_div, div_le_iff₀ hm] + exact mul_le_mul_of_nonneg_left (le_max_right _ _) ha.le + +theorem radialClip_eq {a : ℝ} (ha : 0 < a) {z : ℂ} (hz : ‖z‖ ≤ a) : + radialClip a z = z := by + simp [radialClip, max_eq_left hz, ne_of_gt ha] + + + +theorem localized_profile {A K : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + [TopologicalSpace K] [CompactSpace K] (h : C(K, ℂ)) {q₀ : A} {z₀ : ℂ} + {F : A × ℂ → ℂ} (hF : AnalyticAt ℂ F (q₀,z₀)) : + ∃ (a : ℝ) (φ : A → C(K, ℂ)), 0 < a ∧ AnalyticAt ℂ φ q₀ ∧ + ∀ᶠ q in 𝓝 q₀, ∀ t : K, ‖h t - z₀‖ < a → φ q t = F (q, h t) := by + let H : A × ℂ → ℂ := fun v => F ((q₀,z₀) + v) + have hH : AnalyticAt ℂ H 0 := by + apply hF.comp_of_eq (analyticAt_const.add analyticAt_id) + simp + obtain ⟨p,R,hp⟩ := hH + obtain ⟨b,hb0,hbR⟩ := ENNReal.lt_iff_exists_nnreal_btwn.mp hp.r_pos + have hb : (0 : ℝ) < b := by exact_mod_cast hb0 + let a : ℝ := b / 2 + have ha : 0 < a := half_pos hb + let w : C(K, A × ℂ) := ⟨fun t => (0,radialClip a (h t-z₀)), + continuous_const.prodMk ((continuous_radialClip ha).comp (h.continuous.sub continuous_const))⟩ + let L : A →L[ℂ] C(K, A × ℂ) := + (ContinuousLinearMap.const ℂ K).comp (ContinuousLinearMap.inl ℂ A ℂ) + let v : A → C(K,A × ℂ) := fun q => L (q-q₀) + w + have hve (q : A) (t : K) : v q t = (q-q₀, radialClip a (h t-z₀)) := by + simp [v, L, w] + have hva : AnalyticAt ℂ v q₀ := + ((L.analyticAt _).comp (analyticAt_id.sub analyticAt_const)).add analyticAt_const + have hvb (q : A) (hq : q ∈ ball q₀ a) : v q ∈ ball 0 (b : ℝ) := by + have hnq : ‖q-q₀‖ < a := by simpa [dist_eq_norm] using hq + have hnv : ‖v q‖ ≤ a := by + apply (ContinuousMap.norm_le _ ha.le).2 + intro t + rw [hve] + rw [Prod.norm_def] + exact max_le hnq.le (norm_radialClip_le ha _) + have : ‖v q‖ < (b : ℝ) := hnv.trans_lt (half_lt_self hb) + simpa using this + obtain ⟨Φ,hΦ,hΦe⟩ := analytic_continuousMap_of_series (K := K) hp hbR + refine ⟨a, fun q => Φ (v q), ha, (hΦ _ (hvb q₀ (mem_ball_self ha))).comp hva, ?_⟩ + filter_upwards [ball_mem_nhds q₀ ha] with q hq + intro t ht + rw [hΦe _ (hvb q hq), hve] + change F ((q₀,z₀)+(q-q₀,radialClip a (h t-z₀))) = F (q,h t) + rw [radialClip_eq ha ht.le] + congr 1 + ext <;> simp + + + +theorem analytic_compact_profile {A K : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + [TopologicalSpace K] [CompactSpace K] [T2Space K] (h : C(K,ℂ)) {q₀ : A} + {F : A × ℂ → ℂ} (hF : ∀ t : K, AnalyticAt ℂ F (q₀,h t)) : + ∃ φ : A → C(K,ℂ), AnalyticAt ℂ φ q₀ ∧ + ∀ᶠ q in 𝓝 q₀, ∀ t : K, φ q t = F (q,h t) := by + classical + choose a φ ha hφ he using fun t => localized_profile h (hF t) + let V : K → Set K := fun t => {x | ‖h x-h t‖ < a t} + have hVo (t : K) : IsOpen (V t) := + isOpen_lt ((h.continuous.sub continuous_const).norm) continuous_const + have hVc : (univ : Set K) ⊆ ⋃ t, V t := by + intro t _ + exact mem_iUnion.2 ⟨t, by simpa [V] using ha t⟩ + obtain ⟨s,hs⟩ := isCompact_univ.elim_finite_subcover V hVo hVc + let I := {t // t ∈ s} + have hIc : (univ : Set K) ⊆ ⋃ t : I, V t := by + intro x hx + obtain ⟨t,ht,hxt⟩ := mem_iUnion₂.1 (hs hx) + exact mem_iUnion.2 ⟨⟨t,ht⟩,hxt⟩ + obtain ⟨ρ,hρ⟩ := PartitionOfUnity.exists_isSubordinate isClosed_univ + (fun t : I => V t) (fun t => hVo t) hIc + let χ : I → C(K,ℂ) := fun t => ⟨fun x => (ρ t x : ℂ), Complex.continuous_ofReal.comp (ρ t).continuous⟩ + let ψ : A → C(K,ℂ) := fun q => ∑ t : I, χ t * φ t q + refine ⟨ψ, ?_, ?_⟩ + · convert (Finset.analyticAt_sum (𝕜 := ℂ) + (f := fun t : I => fun q => χ t * φ (t : K) q) + Finset.univ (fun t _ => analyticAt_const.mul (hφ t))) using 1 + ext q t + simp [ψ] + · have hev : ∀ᶠ q in 𝓝 q₀, ∀ t : I, ∀ x : K, ‖h x-h t‖ < a t → φ t q x = F (q,h x) := + Filter.eventually_all.2 (fun t : I => he t) + filter_upwards [hev] with q hq + intro x + have heq (t : I) : χ t x * φ t q x = (ρ t x : ℂ) * F (q,h x) := by + by_cases ht : ρ t x = 0 + · simp [χ, ht] + · have hx : x ∈ V t := hρ t (subset_closure ht) + rw [hq t x hx] + rfl + change (∑ t : I, χ t * φ t q) x = _ + simp only [ContinuousMap.sum_apply, ContinuousMap.mul_apply, heq] + rw [← Finset.sum_mul] + have hsum : ∑ t : I, (ρ t x : ℂ) = 1 := by + exact_mod_cast (show ∑ t : I, ρ t x = 1 from by + simpa only [finsum_eq_sum_of_fintype] using ρ.sum_eq_one (mem_univ x)) + rw [hsum, one_mul] + +end DegeneratingTrees + +namespace DegeneratingTrees +open Set Metric Filter Topology + + + +def compactProfile {A K : Type*} [TopologicalSpace K] (h : C(K,ℂ)) + (F : A × ℂ → ℂ) (q : A) : C(K,ℂ) := by + classical + exact if hc : Continuous (fun t : K => F (q,h t)) then ⟨_,hc⟩ else 0 + +theorem compactProfile_apply {A K : Type*} [TopologicalSpace K] (h : C(K,ℂ)) + (F : A × ℂ → ℂ) (q : A) (hc : Continuous (fun t : K => F (q,h t))) (t : K) : + compactProfile h F q t = F (q,h t) := by + simp [compactProfile, hc] + +theorem analytic_compactProfile {A K : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + [TopologicalSpace K] [CompactSpace K] [T2Space K] (h : C(K,ℂ)) {U : Set A} + (hU : IsOpen U) {F : A × ℂ → ℂ} + (hF : ∀ q ∈ U, ∀ t : K, AnalyticAt ℂ F (q,h t)) : + AnalyticOnNhd ℂ (compactProfile h F) U := by + intro q hq + obtain ⟨φ,hφ,he⟩ := analytic_compact_profile h (hF q hq) + apply hφ.congr + filter_upwards [he,hU.mem_nhds hq] with x hx hxU + have hc : Continuous (fun t : K => F (x,h t)) := by + apply continuous_iff_continuousAt.mpr + intro t + exact (hF x hxU t).continuousAt.comp (f := fun point : K => (x,h point)) + (continuous_const.prodMk h.continuous).continuousAt + ext t + rw [compactProfile_apply h F x hc t] + exact hx t + +theorem analytic_circleIntegral {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {U : Set A} (hU : IsOpen U) {r : ℝ} (hr : 0 ≤ r) {F : A × ℂ → ℂ} + (hF : AnalyticOnNhd ℂ F (U ×ˢ sphere 0 r)) : + AnalyticOnNhd ℂ (fun q => ∮ z in C(0,r), F (q,z)) U := by + let h : C(sphere (0 : ℂ) r,ℂ) := ⟨Subtype.val,continuous_subtype_val⟩ + have ha : AnalyticOnNhd ℂ (compactProfile h F) U := + analytic_compactProfile h hU (fun q hq t => hF _ ⟨hq,t.property⟩) + have hc (q : A) (hq : q ∈ U) : Continuous (fun t : sphere (0 : ℂ) r => F (q,t)) := + hF.continuousOn.comp_continuous + (continuous_const.prodMk continuous_subtype_val) (fun t => ⟨hq,t.property⟩) + intro q hq + apply ((circleFunctional r hr).analyticAt _ |>.comp (ha q hq)).congr + filter_upwards [hU.mem_nhds hq] with x hx + exact circleFunctional_eq hr _ _ (compactProfile_apply h F x (hc x hx)) + +end DegeneratingTrees + +namespace DegeneratingTrees +open Set Metric Filter Topology Complex +open scoped BigOperators + + + +theorem analytic_contourMoment_general {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} {U : Set A} (hU : IsOpen U) {r : ℝ} (hr : 0 < r) + (hF : AnalyticOnNhd ℂ F (U ×ˢ sphere 0 r)) + (hn : ∀ q ∈ U, ∀ z ∈ sphere (0 : ℂ) r, F (q,z) ≠ 0) (k : ℕ) : + AnalyticOnNhd ℂ (fun q => contourMoment (fun y => F (q,y)) r k) U := by + let H : A × ℂ → ℂ := fun x => x.2 ^ k * fderiv ℂ F x (0,1) / F x + have hH : AnalyticOnNhd ℂ H (U ×ˢ sphere 0 r) := by + intro x hx + exact ((analyticAt_snd.pow k).mul + (((ContinuousLinearMap.apply ℂ ℂ ((0,1) : A × ℂ)).analyticAt _).comp + (hF x hx).fderiv)).div (hF x hx) (hn x.1 hx.1 x.2 hx.2) + have ha := analytic_circleIntegral hU hr.le hH + intro q hq + apply (analyticAt_const.mul (ha q hq)).congr + filter_upwards [hU.mem_nhds hq] with x hx + change (2 * Real.pi * I)⁻¹ * (∮ z in C(0,r), H (x,z)) = _ + unfold contourMoment + congr 1 + apply circleIntegral.integral_congr hr.le + intro z hz + have he := ((hF (x,z) ⟨hx,hz⟩).differentiableAt.hasFDerivAt.comp_hasDerivAt z + ((hasDerivAt_const z x).prodMk (hasDerivAt_id z))).deriv + dsimp [H] + rw [← he] + rfl + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ContourDivision.lean b/lean/OAI/Analysis/PathSelection/ContourDivision.lean new file mode 100644 index 0000000000000000000000000000000000000000..0c48aefff97e583a268cda82a0c98ea597b58dda --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ContourDivision.lean @@ -0,0 +1,516 @@ +import Mathlib +import OAI.Analysis.PathSelection.ContourPolynomials +import OAI.Analysis.PathSelection.FunctionSeries + +namespace OAI + +/-! Analytic contour moments and fixed-contour polynomial division. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace DegeneratingTrees +open Set Metric Filter Topology Complex +open scoped BigOperators NNReal ENNReal + + + +theorem analytic_contourMoment {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} {r : ℝ} (hr : 0 < r) {U : Set A} (hU : IsOpen U) + {φ ψ : A → C(sphere (0 : ℂ) r, ℂ)} + (hφ : AnalyticOnNhd ℂ φ U) (hψ : AnalyticOnNhd ℂ ψ U) + (hφe : ∀ q ∈ U, ∀ z : sphere (0 : ℂ) r, φ q z = F (q, z)) + (hψe : ∀ q ∈ U, ∀ z : sphere (0 : ℂ) r, ψ q z = deriv (fun y => F (q, y)) z) + (hφn : ∀ q ∈ U, IsUnit (φ q)) (k : ℕ) : + AnalyticOnNhd ℂ (fun q => contourMoment (fun y => F (q, y)) r k) U := by + let w : C(sphere (0 : ℂ) r, ℂ) := ⟨fun z => (z : ℂ) ^ k, continuous_subtype_val.pow k⟩ + let T : A → ℂ := fun q => (2 * Real.pi * I)⁻¹ * + circleFunctional r hr.le (w * ψ q * Ring.inverse (φ q)) + have hT : AnalyticOnNhd ℂ T U := by + intro q hq + apply AnalyticAt.mul analyticAt_const + apply (circleFunctional r hr.le).analyticAt _ |>.comp + apply AnalyticAt.mul (analyticAt_const.mul (hψ q hq)) + exact (analyticOnNhd_inverse _ (hφn q hq)).comp (hφ q hq) + have hTe : EqOn T (fun q => contourMoment (fun y => F (q, y)) r k) U := by + intro q hq + dsimp [T, contourMoment] + congr 1 + apply circleFunctional_eq + intro z + simp only [ContinuousMap.mul_apply, continuousMap_ringInverse_apply _ (hφn q hq), + hφe q hq, hψe q hq, w, ContinuousMap.coe_mk, div_eq_mul_inv] + intro q hq + apply (hT q hq).congr + filter_upwards [hU.mem_nhds hq] with x hx + exact hTe hx + + + +theorem contour_fiber_factorization {f : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hne : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) : + ∃ (d : ℕ) (g : ℂ → ℂ), contourMoment f r 0 = (d : ℂ) ∧ + (contourPolynomial f r d).Monic ∧ (contourPolynomial f r d).natDegree = d ∧ + AnalyticOnNhd ℂ g (closedBall 0 r) ∧ + (∀ z ∈ closedBall (0 : ℂ) r, g z ≠ 0) ∧ + EqOn f (fun z => (contourPolynomial f r d).eval z * g z) (closedBall 0 r) := by + classical + obtain ⟨s, m, g, hs, hg, hgn, hfg⟩ := factor_closedDisc hr hf hne + let ι := Σ a : s, Fin (m a) + let x : ι → ℂ := fun i => i.1 + have hm (k : ℕ) : contourMoment f r k = ∑ i : ι, x i ^ k := by + rw [contourMoment_eq_sum hr hf s m (fun a ha => (hs a ha).1) hg hgn hfg k] + simpa [ι, x, Fintype.sum_sigma] using + (Finset.sum_attach s (fun a => (m a : ℂ) * a ^ k)).symm + have hP := contourPolynomial_eq_prod (f := f) (r := r) x hm + refine ⟨Fintype.card ι, g, ?_, ?_, ?_, hg, hgn, ?_⟩ + · simpa using hm 0 + · rw [hP] + exact Polynomial.monic_prod_of_monic _ _ fun i _ => Polynomial.monic_X_sub_C (x i) + · rw [hP, Polynomial.natDegree_prod_of_monic _ _ + (fun i _ => Polynomial.monic_X_sub_C (x i))] + simp + · intro z hz + rw [hfg hz, hP] + dsimp only + rw [Polynomial.eval_prod] + congr 1 + simpa [ι, x, Fintype.prod_sigma] using + (Finset.prod_attach s (fun a => (z - a) ^ m a)).symm + +private theorem nat_eq_of_complex_dist_lt_one {m n : ℕ} + (h : dist (m : ℂ) (n : ℂ) < 1) : m = n := by + have h' : |((m : ℤ) - n : ℤ)| < 1 := by + have hc : ((m : ℂ) - n) = (((m : ℤ) - n : ℤ) : ℂ) := by push_cast; rfl + rw [dist_eq_norm, hc, Complex.norm_intCast] at h + exact_mod_cast h + have he := Int.abs_lt_one_iff.mp h' + omega + + + +theorem fixed_circle_data {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} (hF : AnalyticAt ℂ F 0) {d : ℕ} + (hd : analyticOrderAt (fun y => F (0, y)) 0 = (d : ℕ∞)) : + ∃ (r : ℝ) (U : Set A) (φ : A → C(sphere (0 : ℂ) r, ℂ)), + 0 < r ∧ IsOpen U ∧ (0 : A) ∈ U ∧ + AnalyticOnNhd ℂ F (U ×ˢ closedBall 0 r) ∧ + AnalyticOnNhd ℂ φ U ∧ + (∀ q ∈ U, ∀ z : sphere (0 : ℂ) r, φ q z = F (q, z)) ∧ + (∀ q ∈ U, IsUnit (φ q)) ∧ + (∀ k, AnalyticOnNhd ℂ (fun q => contourMoment (fun y => F (q, y)) r k) U) ∧ + (∀ q ∈ U, contourMoment (fun y => F (q, y)) r 0 = (d : ℂ)) := by + classical + obtain ⟨a, ha, hprof⟩ := analytic_circle_profiles hF + have hF₀ : AnalyticAt ℂ (fun y => F (0, y)) 0 := + hF.comp (f := fun y : ℂ => ((0 : A), y)) (x := 0) + (analyticAt_const.prod analyticAt_id) + obtain ⟨g, hg, hg0, hge⟩ := hF₀.analyticOrderAt_eq_natCast.mp hd + have hev : ∀ᶠ z in 𝓝 (0 : ℂ), AnalyticAt ℂ g z ∧ g z ≠ 0 ∧ + F (0, z) = z ^ d * g z := by + filter_upwards [hg.eventually_analyticAt, hg.continuousAt.eventually_ne hg0, hge] + with z hz hn he + exact ⟨hz, hn, by simpa using he⟩ + obtain ⟨ε, hε, hεe⟩ := Metric.mem_nhds_iff.mp hev + let r : ℝ := min a ε / 2 + have hr : 0 < r := half_pos (lt_min ha hε) + have hra : r < a := (half_lt_self (lt_min ha hε)).trans_le (min_le_left _ _) + have hrε : r < ε := (half_lt_self (lt_min ha hε)).trans_le (min_le_right _ _) + have hgeB (z : ℂ) (hz : z ∈ closedBall (0 : ℂ) r) : + AnalyticAt ℂ g z ∧ g z ≠ 0 ∧ F (0, z) = z ^ d * g z := + hεe (lt_of_le_of_lt (show dist z 0 ≤ r from hz) hrε) + obtain ⟨φ, ψ, hFA, hφ, hψ, hφe, hψe⟩ := hprof r hr hra + have h0a : (0 : A) ∈ ball 0 a := mem_ball_self ha + have hφ0 : IsUnit (φ 0) := by + rw [ContinuousMap.isUnit_iff_forall_ne_zero] + intro z + rw [hφe 0 h0a z, (hgeB z (sphere_subset_closedBall z.property)).2.2] + apply mul_ne_zero _ (hgeB z (sphere_subset_closedBall z.property)).2.1 + apply pow_ne_zero + have hnz : ‖(z : ℂ)‖ = r := by simp + intro he + exact hr.ne' (by simpa [he] using hnz.symm) + have hunitN : φ ⁻¹' {v | IsUnit v} ∈ 𝓝 (0 : A) := + (hφ 0 h0a).continuousAt.preimage_mem_nhds (Units.isOpen.mem_nhds hφ0) + obtain ⟨b, hb, hbU⟩ := Metric.mem_nhds_iff.mp hunitN + let V : Set A := ball 0 a ∩ ball 0 b + have hV : IsOpen V := isOpen_ball.inter isOpen_ball + have h0V : (0 : A) ∈ V := ⟨h0a, mem_ball_self hb⟩ + have hunit (q : A) (hq : q ∈ V) : IsUnit (φ q) := hbU hq.2 + have hm (k : ℕ) : AnalyticOnNhd ℂ + (fun q => contourMoment (fun y => F (q, y)) r k) V := + analytic_contourMoment hr hV (hφ.mono inter_subset_left) (hψ.mono inter_subset_left) + (fun q hq => hφe q hq.1) (fun q hq => hψe q hq.1) hunit k + have hm0 : contourMoment (fun y => F (0, y)) r 0 = (d : ℂ) := by + have heq : EqOn (fun z => F (0, z)) + (fun z => (∏ a ∈ ({0} : Finset ℂ), (z - a) ^ d) * g z) (closedBall 0 r) := by + intro z hz + simpa using (hgeB z hz).2.2 + have hfB : AnalyticOnNhd ℂ (fun z => F (0, z)) (closedBall 0 r) := by + intro z hz + exact (hFA (0, z) ⟨h0a, hz⟩).comp (analyticAt_const.prod analyticAt_id) + simpa using contourMoment_eq_sum hr hfB ({0} : Finset ℂ) (fun _ => d) + (by intro z hz; have he : z = 0 := Finset.mem_singleton.mp hz; + subst z; exact mem_ball_self hr) + (fun z hz => (hgeB z hz).1) (fun z hz => (hgeB z hz).2.1) heq 0 + have hcountN : {q : A | dist (contourMoment (fun y => F (q, y)) r 0) (d : ℂ) < 1} + ∈ 𝓝 (0 : A) := by + have hn := (hm 0 0 h0V).continuousAt.preimage_mem_nhds (ball_mem_nhds + (contourMoment (fun y => F (0, y)) r 0) (show (0 : ℝ) < 1 by norm_num)) + change {q : A | dist (contourMoment (fun y => F (q, y)) r 0) + (contourMoment (fun y => F (0, y)) r 0) < 1} ∈ 𝓝 (0 : A) at hn + simpa only [hm0] using hn + obtain ⟨c, hc, hcU⟩ := Metric.mem_nhds_iff.mp hcountN + let U : Set A := V ∩ ball 0 c + have hUV : U ⊆ V := inter_subset_left + refine ⟨r, U, φ, hr, hV.inter isOpen_ball, ⟨h0V, mem_ball_self hc⟩, + hFA.mono (fun x hx => ⟨hx.1.1.1, hx.2⟩), hφ.mono (fun q hq => hq.1.1), + (fun q hq => hφe q hq.1.1), (fun q hq => hunit q hq.1), + (fun k => (hm k).mono hUV), ?_⟩ + intro q hq + have hfB : AnalyticOnNhd ℂ (fun z => F (q, z)) (closedBall 0 r) := by + intro z hz + exact (hFA (q, z) ⟨hq.1.1, hz⟩).comp (analyticAt_const.prod analyticAt_id) + have hnB : ∀ z ∈ sphere (0 : ℂ) r, F (q, z) ≠ 0 := by + intro z hz + rw [← hφe q hq.1.1 ⟨z, hz⟩] + exact (ContinuousMap.isUnit_iff_forall_ne_zero _).1 (hunit q hq.1) ⟨z, hz⟩ + obtain ⟨N, _, hN, _⟩ := contour_fiber_factorization hr hfB hnB + have heNd : N = d := nat_eq_of_complex_dist_lt_one (by rw [← hN]; exact hcU hq.2) + simpa only [heNd] using hN + + +theorem analytic_contourNewtonCoeff {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {s : A → ℕ → ℂ} {U : Set A} + (hs : ∀ k, AnalyticOnNhd ℂ (fun q => s q k) U) (k : ℕ) : + AnalyticOnNhd ℂ (fun q => contourNewtonCoeff (s q) k) U := by + induction k using Nat.strong_induction_on with + | h k ih => + cases k with + | zero => simpa only [contourNewtonCoeff] using (analyticOnNhd_const : + AnalyticOnNhd ℂ (fun _ : A => (1 : ℂ)) U) + | succ k => + intro q hq + simp only [contourNewtonCoeff] + apply AnalyticAt.div_const + apply AnalyticAt.neg + apply Finset.analyticAt_fun_sum + intro j _ + exact (ih j (Fin.is_lt j) q hq).mul (hs (k + 1 - j) q hq) + + +theorem analytic_contourPolynomial_coeff {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} {r : ℝ} {U : Set A} + (hm : ∀ k, AnalyticOnNhd ℂ (fun q => contourMoment (fun y => F (q, y)) r k) U) + (d k : ℕ) : + AnalyticOnNhd ℂ (fun q => (contourPolynomial (fun y => F (q, y)) r d).coeff k) U := by + intro q hq + simp only [contourPolynomial, Polynomial.finsetSum_coeff, Polynomial.coeff_C_mul] + apply Finset.analyticAt_fun_sum + intro j _ + exact (analytic_contourNewtonCoeff hm j q hq).mul analyticAt_const + + +def contourPolynomialProfile {A : Type*} (F : A × ℂ → ℂ) (r : ℝ) (d : ℕ) (q : A) : + C(sphere (0 : ℂ) r, ℂ) := + ∑ k ∈ Finset.range (d + 1), + ContinuousMap.const _ (contourNewtonCoeff (contourMoment (fun y => F (q, y)) r) k) * + (⟨fun z => (z : ℂ), continuous_subtype_val⟩ : C(sphere (0 : ℂ) r, ℂ)) ^ (d - k) + +theorem contourPolynomialProfile_apply {A : Type*} (F : A × ℂ → ℂ) (r : ℝ) (d : ℕ) + (q : A) (z : sphere (0 : ℂ) r) : + contourPolynomialProfile F r d q z = (contourPolynomial (fun y => F (q, y)) r d).eval (z : ℂ) := by + simp [contourPolynomialProfile, contourPolynomial, Polynomial.eval_finsetSum] + +theorem analytic_contourPolynomialProfile {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} {r : ℝ} {U : Set A} + (hm : ∀ k, AnalyticOnNhd ℂ (fun q => contourMoment (fun y => F (q, y)) r k) U) (d : ℕ) : + AnalyticOnNhd ℂ (contourPolynomialProfile F r d) U := by + intro q hq + unfold contourPolynomialProfile + apply Finset.analyticAt_fun_sum + intro j _ + apply AnalyticAt.mul _ analyticAt_const + exact ((ContinuousLinearMap.const ℂ (sphere (0 : ℂ) r)).analyticAt _).comp + (analytic_contourNewtonCoeff hm j q hq) + + +def cauchyKernelProfile (r : ℝ) (y : ℂ) : C(sphere (0 : ℂ) r, ℂ) := + ⟨fun z => (z : ℂ), continuous_subtype_val⟩ - ContinuousMap.const _ y + +@[simp] theorem cauchyKernelProfile_apply (r : ℝ) (y : ℂ) (z : sphere (0 : ℂ) r) : + cauchyKernelProfile r y z = (z : ℂ) - y := rfl + +theorem cauchyKernelProfile_isUnit {r : ℝ} {y : ℂ} (hy : y ∈ ball (0 : ℂ) r) : + IsUnit (cauchyKernelProfile r y) := by + rw [ContinuousMap.isUnit_iff_forall_ne_zero] + intro z + apply sub_ne_zero.mpr + intro he + have hz : ‖(z : ℂ)‖ = r := by simp + have hy' : ‖y‖ < r := by simpa using hy + change (z : ℂ) = y at he + exact (not_lt_of_ge (by simpa only [he] using hz.ge)) hy' + +theorem analytic_cauchyKernelProfile (r : ℝ) : AnalyticOnNhd ℂ (cauchyKernelProfile r) univ := by + intro y _ + exact analyticAt_const.sub ((ContinuousLinearMap.const ℂ (sphere (0 : ℂ) r)).analyticAt y) + + + +def cauchyTransformProfile {A : Type*} (r : ℝ) (hr : 0 < r) + (κ : A → C(sphere (0 : ℂ) r, ℂ)) (x : A × ℂ) : ℂ := + (2 * Real.pi * I)⁻¹ * circleFunctional r hr.le + (κ x.1 * Ring.inverse (cauchyKernelProfile r x.2)) + +theorem analytic_cauchyTransformProfile {A : Type*} [NormedAddCommGroup A] + [NormedSpace ℂ A] {r : ℝ} (hr : 0 < r) {U : Set A} + {κ : A → C(sphere (0 : ℂ) r, ℂ)} (hκ : AnalyticOnNhd ℂ κ U) : + AnalyticOnNhd ℂ (cauchyTransformProfile r hr κ) (U ×ˢ ball 0 r) := by + intro x hx + apply analyticAt_const.mul + apply ((circleFunctional r hr.le).analyticAt _).comp + apply (hκ x.1 hx.1).comp analyticAt_fst |>.mul + have hi : AnalyticAt ℂ (fun y : ℂ => Ring.inverse (cauchyKernelProfile r y)) x.2 := + (analyticOnNhd_inverse _ (cauchyKernelProfile_isUnit hx.2)).comp + (analytic_cauchyKernelProfile r x.2 (mem_univ _)) + exact hi.comp analyticAt_snd + +theorem cauchyTransformProfile_eq {A : Type*} {r : ℝ} (hr : 0 < r) + {κ : A → C(sphere (0 : ℂ) r, ℂ)} {q : A} {g : ℂ → ℂ} + (hg : AnalyticOnNhd ℂ g (closedBall 0 r)) + (he : ∀ z : sphere (0 : ℂ) r, κ q z = g z) {y : ℂ} (hy : y ∈ ball 0 r) : + cauchyTransformProfile r hr κ (q, y) = g y := by + have hunit := cauchyKernelProfile_isUnit hy + have hEq : ∀ z : sphere (0 : ℂ) r, + (κ q * Ring.inverse (cauchyKernelProfile r y)) z = ((z : ℂ) - y)⁻¹ * g z := by + intro z + simp only [ContinuousMap.mul_apply, continuousMap_ringInverse_apply _ hunit, + cauchyKernelProfile_apply, he] + ring + rw [cauchyTransformProfile, circleFunctional_eq hr.le _ (fun z => (z - y)⁻¹ * g z) hEq] + have hdiff : DiffContOnCl ℂ g (ball 0 r) := + (hg.differentiableOn.mono closure_ball_subset_closedBall).diffContOnCl + simpa only [smul_eq_mul] using hdiff.two_pi_i_inv_smul_circleIntegral_sub_inv_smul hy + + + +theorem fixed_contour_preparation_on_ball {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} (hF : AnalyticAt ℂ F 0) {d : ℕ} + (hd : analyticOrderAt (fun y => F (0, y)) 0 = (d : ℕ∞)) : + ∃ (r : ℝ) (U : Set A) (g : A × ℂ → ℂ), + 0 < r ∧ IsOpen U ∧ (0 : A) ∈ U ∧ + AnalyticOnNhd ℂ F (U ×ˢ closedBall 0 r) ∧ + AnalyticOnNhd ℂ g (U ×ˢ ball 0 r) ∧ + (∀ q ∈ U, ∀ y ∈ ball (0 : ℂ) r, g (q, y) ≠ 0) ∧ + (∀ q ∈ U, ∀ y ∈ sphere (0 : ℂ) r, F (q, y) ≠ 0) ∧ + (∀ q ∈ U, (contourPolynomial (fun y => F (q, y)) r d).Monic ∧ + (contourPolynomial (fun y => F (q, y)) r d).natDegree = d) ∧ + (∀ k, AnalyticOnNhd ℂ + (fun q => (contourPolynomial (fun y => F (q, y)) r d).coeff k) U) ∧ + (∀ q ∈ U, ∀ y ∈ ball (0 : ℂ) r, + F (q, y) = (contourPolynomial (fun y => F (q, y)) r d).eval y * g (q, y)) := by + classical + obtain ⟨r, U, φ, hr, hU, h0U, hFA, hφ, hφe, hφu, hm, hm0⟩ := fixed_circle_data hF hd + have hfB (q : A) (hq : q ∈ U) : AnalyticOnNhd ℂ (fun y => F (q, y)) (closedBall 0 r) := by + intro y hy + exact (hFA (q, y) ⟨hq, hy⟩).comp (analyticAt_const.prod analyticAt_id) + have hnB (q : A) (hq : q ∈ U) (z : ℂ) (hz : z ∈ sphere (0 : ℂ) r) : F (q, z) ≠ 0 := by + rw [← hφe q hq ⟨z, hz⟩] + exact (ContinuousMap.isUnit_iff_forall_ne_zero _).1 (hφu q hq) ⟨z, hz⟩ + have hfac (q : A) (hq : q ∈ U) : + ∃ g : ℂ → ℂ, (contourPolynomial (fun y => F (q, y)) r d).Monic ∧ + (contourPolynomial (fun y => F (q, y)) r d).natDegree = d ∧ + AnalyticOnNhd ℂ g (closedBall 0 r) ∧ + (∀ z ∈ closedBall (0 : ℂ) r, g z ≠ 0) ∧ + EqOn (fun y => F (q, y)) + (fun y => (contourPolynomial (fun y => F (q, y)) r d).eval y * g y) (closedBall 0 r) := by + obtain ⟨N, g, hN, hM, hD, hg, hgn, hfg⟩ := contour_fiber_factorization hr (hfB q hq) (hnB q hq) + have hNd : N = d := by exact_mod_cast hN.symm.trans (hm0 q hq) + subst N + exact ⟨g, hM, hD, hg, hgn, hfg⟩ + have hpU (q : A) (hq : q ∈ U) : IsUnit (contourPolynomialProfile F r d q) := by + rw [ContinuousMap.isUnit_iff_forall_ne_zero] + intro z + rw [contourPolynomialProfile_apply] + obtain ⟨g, _, _, _, _, hfg⟩ := hfac q hq + have he := hfg (sphere_subset_closedBall z.property) + dsimp only at he + exact left_ne_zero_of_mul (by rw [← he]; exact hnB q hq z z.property) + let κ : A → C(sphere (0 : ℂ) r, ℂ) := fun q => φ q * Ring.inverse (contourPolynomialProfile F r d q) + have hκ : AnalyticOnNhd ℂ κ U := by + intro q hq + exact (hφ q hq).mul ((analyticOnNhd_inverse _ (hpU q hq)).comp + (analytic_contourPolynomialProfile hm d q hq)) + let g : A × ℂ → ℂ := cauchyTransformProfile r hr κ + have hgFiber (q : A) (hq : q ∈ U) (v : ℂ → ℂ) + (hv : AnalyticOnNhd ℂ v (closedBall 0 r)) + (hfv : EqOn (fun y => F (q, y)) + (fun y => (contourPolynomial (fun y => F (q, y)) r d).eval y * v y) (closedBall 0 r)) + (y : ℂ) (hy : y ∈ ball (0 : ℂ) r) : g (q, y) = v y := by + apply cauchyTransformProfile_eq hr hv _ hy + intro z + dsimp only [κ] + rw [ContinuousMap.mul_apply, continuousMap_ringInverse_apply _ (hpU q hq), + hφe q hq, contourPolynomialProfile_apply] + have he := hfv (sphere_subset_closedBall z.property) + dsimp only at he + rw [he] + have hn : (contourPolynomial (fun y => F (q, y)) r d).eval (z : ℂ) ≠ 0 := by + rw [← contourPolynomialProfile_apply] + exact (ContinuousMap.isUnit_iff_forall_ne_zero _).1 (hpU q hq) z + field_simp + refine ⟨r, U, g, hr, hU, h0U, hFA, analytic_cauchyTransformProfile hr hκ, ?_, hnB, ?_, + fun k => analytic_contourPolynomial_coeff hm d k, ?_⟩ + · intro q hq y hy + obtain ⟨v, _, _, hv, hvn, hfv⟩ := hfac q hq + rw [hgFiber q hq v hv hfv y hy] + exact hvn y (ball_subset_closedBall hy) + · intro q hq + obtain ⟨_, hM, hD, _⟩ := hfac q hq + exact ⟨hM, hD⟩ + · intro q hq y hy + obtain ⟨v, _, _, hv, _, hfv⟩ := hfac q hq + rw [hgFiber q hq v hv hfv y hy] + exact hfv (ball_subset_closedBall hy) + + +theorem fixed_contour_preparation : FixedContourPreparationStatement := by + intro n d F hF hd + obtain ⟨r, U, g, hr, hU, h0, hf, hg, hgn, hfn, hP, hc, he⟩ := + fixed_contour_preparation_on_ball hF hd + have hi : closedBall (0 : ℂ) (r / 2) ⊆ ball 0 r := + closedBall_subset_ball (half_lt_self hr) + exact ⟨r, U, g, hr, hU, h0, hf, hg.mono (fun x hx => ⟨hx.1, hi hx.2⟩), + (fun q hq y hy => hgn q hq y (hi hy)), hfn, hP, hc, + (fun q hq y hy => he q hq y (hi hy))⟩ + + +def normalizedCircleFunctional (r : ℝ) (hr : 0 < r) : C(sphere (0 : ℂ) r, ℂ) →L[ℂ] ℂ := + (2 * Real.pi * I)⁻¹ • circleFunctional r hr.le + + + +def dividedCoeffProfile (P : Polynomial ℂ) (d : ℕ) (r : ℝ) (k : ℕ) : + C(sphere (0 : ℂ) r, ℂ) := + ∑ i ∈ Finset.Icc (k + 1) d, + (⟨fun z => (z : ℂ), continuous_subtype_val⟩ : C(sphere (0 : ℂ) r, ℂ)) ^ (i - (k + 1)) * + ContinuousMap.const _ (P.coeff i) + +theorem dividedCoeffProfile_apply {P : Polynomial ℂ} {d : ℕ} (hd : P.natDegree = d) + (r : ℝ) (k : ℕ) (z : sphere (0 : ℂ) r) : + dividedCoeffProfile P d r k z = (P /ₘ (Polynomial.X - Polynomial.C (z : ℂ))).coeff k := by + rw [Polynomial.coeff_divByMonic_X_sub_C, hd] + simp [dividedCoeffProfile] + +theorem analytic_dividedCoeffProfile {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {P : A → Polynomial ℂ} {U : Set A} + (hP : ∀ k, AnalyticOnNhd ℂ (fun q => (P q).coeff k) U) (d : ℕ) (r : ℝ) (k : ℕ) : + AnalyticOnNhd ℂ (fun q => dividedCoeffProfile (P q) d r k) U := by + intro q hq + unfold dividedCoeffProfile + apply Finset.analyticAt_fun_sum + intro j _ + apply analyticAt_const.mul + exact ((ContinuousLinearMap.const ℂ (sphere (0 : ℂ) r)).analyticAt _).comp (hP j q hq) + +def divisionRemainder (P : Polynomial ℂ) (d : ℕ) (r : ℝ) (hr : 0 < r) + (κ : C(sphere (0 : ℂ) r, ℂ)) : Polynomial ℂ := + ∑ k : Fin d, Polynomial.C (normalizedCircleFunctional r hr (κ * dividedCoeffProfile P d r k)) * + Polynomial.X ^ (k : ℕ) + +theorem divisionRemainder_degree_lt (P : Polynomial ℂ) (d : ℕ) (r : ℝ) (hr : 0 < r) + (κ : C(sphere (0 : ℂ) r, ℂ)) : (divisionRemainder P d r hr κ).degree < d := + Polynomial.degree_sum_fin_lt _ + +theorem analytic_divisionRemainder_coeff {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {radius : ℝ} {P : A → Polynomial ℂ} {κ : A → C(sphere (0 : ℂ) radius, ℂ)} {U : Set A} + (hP : ∀ k, AnalyticOnNhd ℂ (fun q => (P q).coeff k) U) (hκ : AnalyticOnNhd ℂ κ U) + (d : ℕ) (hr : 0 < radius) (k : ℕ) : + AnalyticOnNhd ℂ (fun q => (divisionRemainder (P q) d radius hr (κ q)).coeff k) U := by + intro q hq + simp only [divisionRemainder, Polynomial.finsetSum_coeff, Polynomial.coeff_C_mul] + apply Finset.analyticAt_fun_sum + intro j _ + apply AnalyticAt.mul _ analyticAt_const + exact ((normalizedCircleFunctional radius hr).analyticAt _).comp + ((hκ q hq).mul (analytic_dividedCoeffProfile hP d radius j q hq)) + +private theorem eval_sum_of_degree_lt {P : Polynomial ℂ} {d : ℕ} + (hd : P.degree < d) (y : ℂ) : P.eval y = ∑ k : Fin d, P.coeff k * y ^ (k : ℕ) := by + by_cases hP : P = 0 + · simp [hP] + · rw [Polynomial.eval_eq_sum_range' ((Polynomial.natDegree_lt_iff_degree_lt hP).2 hd)] + exact (Fin.sum_univ_eq_sum_range _ _).symm + +def dividedEvaluationProfile (P : Polynomial ℂ) (d : ℕ) (r : ℝ) (y : ℂ) : + C(sphere (0 : ℂ) r, ℂ) := ∑ k : Fin d, (y ^ (k : ℕ)) • dividedCoeffProfile P d r k + +theorem dividedEvaluationProfile_apply {P : Polynomial ℂ} (hP : P.Monic) {d : ℕ} + (hd : P.natDegree = d) (r : ℝ) (y : ℂ) (z : sphere (0 : ℂ) r) : + dividedEvaluationProfile P d r y z = (P /ₘ (Polynomial.X - Polynomial.C (z : ℂ))).eval y := by + have hdeg : (P /ₘ (Polynomial.X - Polynomial.C (z : ℂ))).degree < d := by + have hi := Polynomial.degree_divByMonic_lt P (Polynomial.X - Polynomial.C (z : ℂ)) + hP.ne_zero (by simp) + simpa [Polynomial.degree_eq_natDegree hP.ne_zero, hd] using hi + rw [eval_sum_of_degree_lt hdeg] + simp only [dividedEvaluationProfile, ContinuousMap.coe_sum, Finset.sum_apply, + ContinuousMap.smul_apply, smul_eq_mul, dividedCoeffProfile_apply hd] + apply Finset.sum_congr rfl + intro k _ + ring + +theorem divisionRemainder_eval (P : Polynomial ℂ) (d : ℕ) (r : ℝ) (hr : 0 < r) + (κ : C(sphere (0 : ℂ) r, ℂ)) (y : ℂ) : + (divisionRemainder P d r hr κ).eval y = + normalizedCircleFunctional r hr (κ * dividedEvaluationProfile P d r y) := by + simp only [divisionRemainder, Polynomial.eval_finsetSum, Polynomial.eval_mul, + Polynomial.eval_C, Polynomial.eval_pow, Polynomial.eval_X, dividedEvaluationProfile, + Finset.mul_sum, mul_smul_comm, map_sum, map_smul, smul_eq_mul] + apply Finset.sum_congr rfl + intro k _ + ring + + + +theorem fixed_circle_division {P : Polynomial ℂ} (hP : P.Monic) {d : ℕ} + (hd : P.natDegree = d) {r : ℝ} (hr : 0 < r) {G : ℂ → ℂ} + (hG : AnalyticOnNhd ℂ G (closedBall 0 r)) + (hPn : ∀ z ∈ sphere (0 : ℂ) r, P.eval z ≠ 0) + (κ : C(sphere (0 : ℂ) r, ℂ)) + (hκ : ∀ z : sphere (0 : ℂ) r, κ z = G z / P.eval (z : ℂ)) + {y : ℂ} (hy : y ∈ ball (0 : ℂ) r) : + G y = P.eval y * cauchyTransformProfile r hr (fun _ : Unit => κ) ((), y) + + (divisionRemainder P d r hr κ).eval y := by + have hk := cauchyKernelProfile_isUnit hy + let T := κ * Ring.inverse (cauchyKernelProfile r y) + let R := κ * dividedEvaluationProfile P d r y + have hboundary : ∀ z : sphere (0 : ℂ) r, + ((P.eval y) • T + R) z = ((z : ℂ) - y)⁻¹ * G z := by + intro z + have hdiff := congrArg (Polynomial.eval y) (P.modByMonic_add_div (Polynomial.X - Polynomial.C (z : ℂ))) + rw [Polynomial.modByMonic_X_sub_C_eq_C_eval] at hdiff + simp only [Polynomial.eval_add, Polynomial.eval_C, Polynomial.eval_mul, + Polynomial.eval_sub, Polynomial.eval_X] at hdiff + have hn : (z : ℂ) - y ≠ 0 := + (ContinuousMap.isUnit_iff_forall_ne_zero _).1 hk z + simp only [T, R, ContinuousMap.add_apply, ContinuousMap.smul_apply, smul_eq_mul, + ContinuousMap.mul_apply, continuousMap_ringInverse_apply _ hk, + cauchyKernelProfile_apply, dividedEvaluationProfile_apply hP hd, hκ] + field_simp [hPn z z.property, hn] + linear_combination -(G (z : ℂ)) * hdiff + have hc : normalizedCircleFunctional r hr ((P.eval y) • T + R) = G y := by + change (2 * Real.pi * I)⁻¹ * circleFunctional r hr.le ((P.eval y) • T + R) = G y + rw [circleFunctional_eq hr.le _ (fun z => (z - y)⁻¹ * G z) hboundary] + have hdiff : DiffContOnCl ℂ G (ball 0 r) := + (hG.differentiableOn.mono closure_ball_subset_closedBall).diffContOnCl + simpa only [smul_eq_mul] using hdiff.two_pi_i_inv_smul_circleIntegral_sub_inv_smul hy + rw [divisionRemainder_eval, ← hc, map_add, map_smul] + rfl + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ContourPolynomials.lean b/lean/OAI/Analysis/PathSelection/ContourPolynomials.lean new file mode 100644 index 0000000000000000000000000000000000000000..0d410298f5c9cd68d44455ae3848bbc9287ebb26 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ContourPolynomials.lean @@ -0,0 +1,298 @@ +import Mathlib + +namespace OAI + +/-! Contour moments, Newton coefficients and monic root polynomials. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Metric Complex Topology +open scoped Polynomial BigOperators + +namespace DegeneratingTrees + + +def contourNewtonCoeff (s : ℕ → ℂ) : ℕ → ℂ + | 0 => 1 + | k + 1 => -(∑ j : Fin (k + 1), contourNewtonCoeff s j * s (k + 1 - j)) / (k + 1) +termination_by k => k + + +def contourMoment (f : ℂ → ℂ) (r : ℝ) (k : ℕ) : ℂ := + (2 * Real.pi * I)⁻¹ * ∮ z in C(0, r), z ^ k * deriv f z / f z + + +def contourPolynomial (f : ℂ → ℂ) (r : ℝ) (d : ℕ) : Polynomial ℂ := + ∑ k ∈ Finset.range (d + 1), + Polynomial.C (contourNewtonCoeff (contourMoment f r) k) * Polynomial.X ^ (d - k) + + + +def FixedContourPreparationStatement : Prop := + ∀ (n d : ℕ) (F : (Fin n → ℂ) × ℂ → ℂ), AnalyticAt ℂ F (0, 0) → + analyticOrderAt (fun y => F (0, y)) 0 = (d : ℕ∞) → + ∃ (r : ℝ) (U : Set (Fin n → ℂ)) (g : (Fin n → ℂ) × ℂ → ℂ), + 0 < r ∧ IsOpen U ∧ (0 : Fin n → ℂ) ∈ U ∧ + AnalyticOnNhd ℂ F (U ×ˢ closedBall 0 r) ∧ + AnalyticOnNhd ℂ g (U ×ˢ closedBall 0 (r / 2)) ∧ + (∀ q ∈ U, ∀ y ∈ closedBall (0 : ℂ) (r / 2), g (q, y) ≠ 0) ∧ + (∀ q ∈ U, ∀ y ∈ sphere (0 : ℂ) r, F (q, y) ≠ 0) ∧ + (∀ q ∈ U, (contourPolynomial (fun y => F (q, y)) r d).Monic ∧ + (contourPolynomial (fun y => F (q, y)) r d).natDegree = d) ∧ + (∀ k, AnalyticOnNhd ℂ + (fun q => (contourPolynomial (fun y => F (q, y)) r d).coeff k) U) ∧ + (∀ q ∈ U, ∀ y ∈ closedBall (0 : ℂ) (r / 2), + F (q, y) = (contourPolynomial (fun y => F (q, y)) r d).eval y * g (q, y)) + + + +theorem factor_closedDisc {f : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hne : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) : + ∃ (s : Finset ℂ) (m : ℂ → ℕ) (g : ℂ → ℂ), + (∀ a ∈ s, a ∈ ball (0 : ℂ) r ∧ 0 < m a) ∧ + AnalyticOnNhd ℂ g (closedBall 0 r) ∧ + (∀ z ∈ closedBall (0 : ℂ) r, g z ≠ 0) ∧ + EqOn f (fun z => (∏ a ∈ s, (z - a) ^ m a) * g z) (closedBall 0 r) := by + classical + let D := MeromorphicOn.divisor f (closedBall (0 : ℂ) r) + have hD : 0 ≤ D := + (hf.meromorphicNFOn.divisor_nonneg_iff_analyticOnNhd).2 hf + have hfin : D.support.Finite := D.finiteSupport (isCompact_closedBall _ _) + have hb : (r : ℂ) ∈ sphere (0 : ℂ) r := by + simp [abs_of_pos hr] + have hb' : (r : ℂ) ∈ closedBall (0 : ℂ) r := sphere_subset_closedBall hb + have hb0 : meromorphicOrderAt f (r : ℂ) = 0 := + ((hf _ hb').meromorphicNFAt.meromorphicOrderAt_eq_zero_iff).2 (hne _ hb) + have hfinite : ∀ z : closedBall (0 : ℂ) r, meromorphicOrderAt f z ≠ ⊤ := + (hf.meromorphicOn.exists_meromorphicOrderAt_ne_top_iff_forall + (isConnected_closedBall hr.le)).1 ⟨⟨r, hb'⟩, by simp [hb0]⟩ + obtain ⟨g, hg, hgn, hfg⟩ := hf.meromorphicOn.extract_zeros_poles hfinite hfin + let φ : ℂ → ℂ := ∏ᶠ a, (· - a) ^ D a + have hφ : AnalyticOnNhd ℂ φ (closedBall 0 r) := by + intro z hz + apply Function.FactorizedRational.analyticAt + exact hD z + have heq : EqOn f (fun z => φ z * g z) (closedBall 0 r) := by + apply hf.eqOn_of_preconnected_of_frequently_eq (hφ.mul hg) + isPreconnected_closedBall (mem_closedBall_self hr.le) (z₀ := 0) + have hloc : f =ᶠ[𝓝[≠] 0] fun z => φ z * g z := by + have hc := (mem_codiscreteWithin.mp hfg) 0 (mem_closedBall_self hr.le) + rw [disjoint_principal_right] at hc + have hnb : ∀ᶠ z : ℂ in 𝓝[≠] 0, z ∈ closedBall (0 : ℂ) r := + mem_nhdsWithin_of_mem_nhds (closedBall_mem_nhds (0 : ℂ) hr) + filter_upwards [hc, hnb] with z hz hz' + by_contra hn + exact hz ⟨hz', hn⟩ + exact hloc.frequently + refine ⟨hfin.toFinset, fun a => (D a).toNat, g, ?_, hg, + fun z hz => hgn ⟨z, hz⟩, ?_⟩ + · intro a ha + have haD : D a ≠ 0 := by simpa using ha + have haB := D.supportWithinDomain (by exact haD) + have ham : 0 < (D a).toNat := by + have ha0 : (0 : ℤ) ≤ D a := hD a + omega + refine ⟨?_, ham⟩ + rw [mem_ball_zero_iff] + have hle : ‖a‖ ≤ r := by simpa [mem_closedBall_zero_iff] using haB + apply lt_of_le_of_ne hle + intro he + have hs : a ∈ sphere (0 : ℂ) r := by simpa [mem_sphere_zero_iff_norm] using he + apply haD + dsimp [D] + rw [hf.meromorphicOn.divisor_apply haB] + rw [((hf _ haB).meromorphicNFAt.meromorphicOrderAt_eq_zero_iff).2 (hne a hs)] + simp + · intro z hz + calc + f z = φ z * g z := heq hz + _ = _ := ?_ + apply congrArg (fun w => w * g z) + dsimp [φ] + rw [finprod_eq_prod_of_mulSupport_subset (s := hfin.toFinset)] + · simp only [Finset.prod_apply, Pi.pow_apply] + apply Finset.prod_congr rfl + intro a ha + have hc : ((D a).toNat : ℤ) = D a := Int.toNat_of_nonneg (hD a) + simpa only [hc] using (zpow_natCast (z - a) (D a).toNat) + · intro a ha + apply hfin.mem_toFinset.mpr + simpa only [Function.FactorizedRational.mulSupport] using ha + +private theorem deriv_eqOn_closedDisc {f h : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hh : AnalyticOnNhd ℂ h (closedBall 0 r)) + (heq : EqOn f h (closedBall 0 r)) : + EqOn (deriv f) (deriv h) (closedBall 0 r) := by + have heq' := (heq.mono ball_subset_closedBall).deriv isOpen_ball + exact heq'.of_subset_closure hf.deriv.continuousOn hh.deriv.continuousOn + ball_subset_closedBall (by rw [closure_ball _ hr.ne']) + + + +theorem contourMoment_eq_sum {f g : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (s : Finset ℂ) (m : ℂ → ℕ) + (hs : ∀ a ∈ s, a ∈ ball (0 : ℂ) r) + (hg : AnalyticOnNhd ℂ g (closedBall 0 r)) + (hgn : ∀ z ∈ closedBall (0 : ℂ) r, g z ≠ 0) + (heq : EqOn f (fun z => (∏ a ∈ s, (z - a) ^ m a) * g z) + (closedBall 0 r)) (k : ℕ) : + contourMoment f r k = ∑ a ∈ s, (m a : ℂ) * a ^ k := by + classical + let P : ℂ → ℂ := fun z => ∏ a ∈ s, (z - a) ^ m a + have hp : AnalyticOnNhd ℂ P (closedBall 0 r) := by + intro z hz + exact s.analyticAt_fun_prod fun a ha => (analyticAt_id.sub analyticAt_const).pow _ + have hder := deriv_eqOn_closedDisc hr hf (hp.mul hg) heq + have hza : ∀ z ∈ sphere (0 : ℂ) r, ∀ a ∈ s, z - a ≠ 0 := by + intro z hz a ha he + have hza := sub_eq_zero.mp he + have hz' : ‖z‖ = r := by simpa using hz + have ha' : ‖a‖ < r := by simpa using hs a ha + rw [hza] at hz' + exact (ne_of_lt ha') hz' + have hld (z : ℂ) (hz : z ∈ sphere (0 : ℂ) r) : + logDeriv f z = (∑ a ∈ s, (m a : ℂ) / (z - a)) + logDeriv g z := by + have hzc := sphere_subset_closedBall hz + calc + logDeriv f z = logDeriv (fun z => P z * g z) z := by + simp only [logDeriv_apply, hder hzc, heq hzc, P] + _ = logDeriv P z + logDeriv g z := + logDeriv_mul z (Finset.prod_ne_zero_iff.mpr + fun a ha => pow_ne_zero _ (hza z hz a ha)) + (hgn z hzc) (hp z hzc).differentiableAt (hg z hzc).differentiableAt + _ = _ := by + congr 1 + rw [show P = ∏ a ∈ s, fun z => (z - a) ^ m a from by + ext point + simp only [P, Finset.prod_apply], + logDeriv_prod (f := fun (a z : ℂ) => (z - a) ^ m a) + (fun a ha => pow_ne_zero _ (hza z hz a ha)) + (fun a ha => by fun_prop)] + apply Finset.sum_congr rfl + intro a ha + rw [logDeriv_fun_pow (by fun_prop)] + simp [logDeriv_apply, div_eq_mul_inv] + let T : ℂ → ℂ → ℂ := fun a z => (m a : ℂ) * ((z - a)⁻¹ * z ^ k) + have hTc : ∀ a ∈ s, ContinuousOn (T a) (sphere (0 : ℂ) r) := by + intro a ha + exact continuousOn_const.mul + ((continuousOn_id.sub continuousOn_const).inv₀ (fun z hz => hza z hz a ha) + |>.mul (continuousOn_id.pow k)) + have hT : ∀ a ∈ s, CircleIntegrable (T a) 0 r := + fun a ha => (hTc a ha).circleIntegrable hr.le + have hunit : AnalyticOnNhd ℂ (fun z => z ^ k * logDeriv g z) (closedBall 0 r) := by + exact (analyticOnNhd_id.pow k).mul (hg.deriv.div hg hgn) + have hUi : CircleIntegrable (fun z => z ^ k * logDeriv g z) 0 r := + (hunit.continuousOn.mono sphere_subset_closedBall).circleIntegrable hr.le + have hSi : CircleIntegrable (fun z => ∑ a ∈ s, T a z) 0 r := by + exact (continuousOn_finsetSum s hTc).circleIntegrable hr.le + have hformula : (∮ z in C(0, r), z ^ k * deriv f z / f z) = + ∑ a ∈ s, (m a : ℂ) * ((2 * Real.pi * I) * a ^ k) := by + calc + (∮ z in C(0, r), z ^ k * deriv f z / f z) = + ∮ z in C(0, r), (∑ a ∈ s, T a z) + z ^ k * logDeriv g z := by + apply circleIntegral.integral_congr hr.le + intro z hz + dsimp only + rw [mul_div_assoc, ← logDeriv_apply, hld z hz, mul_add, Finset.mul_sum] + congr 1 + apply Finset.sum_congr rfl + intro a ha + dsimp [T] + ring + _ = (∑ a ∈ s, ∮ z in C(0, r), T a z) + 0 := by + rw [circleIntegral.integral_add hSi hUi, circleIntegral.integral_fun_sum hT] + rw [DiffContOnCl.circleIntegral_eq_zero hr.le + (hunit.differentiableOn.mono closure_ball_subset_closedBall).diffContOnCl] + _ = _ := by + rw [add_zero] + apply Finset.sum_congr rfl + intro a ha + dsimp [T] + rw [circleIntegral.integral_const_mul] + congr 1 + exact (by simpa only [smul_eq_mul] using + (show DifferentiableOn ℂ (fun z : ℂ => z ^ k) (closedBall 0 r) from + by fun_prop).circleIntegral_sub_inv_smul (hs a ha)) + rw [contourMoment, hformula] + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl + intro a ha + have hn : (2 * Real.pi * I : ℂ) ≠ 0 := by simp [Real.pi_ne_zero, I_ne_zero] + field_simp + + +theorem contourNewtonCoeff_powerSum {ι : Type*} [Fintype ι] (x : ι → ℂ) (k : ℕ) : + contourNewtonCoeff (fun j => ∑ i, x i ^ j) k = + (-1) ^ k * (Finset.univ.val.map x).esymm k := by + classical + induction k using Nat.strong_induction_on with + | h k ih => + cases k with + | zero => simp [contourNewtonCoeff, Multiset.esymm] + | succ k => + rw [contourNewtonCoeff] + have hn := congrArg (MvPolynomial.aeval x) + (MvPolynomial.mul_esymm_eq_sum ι ℂ (k + 1)) + simp only [map_mul, map_natCast, map_pow, map_neg, map_one, map_sum, + MvPolynomial.aeval_esymm_eq_multiset_esymm, MvPolynomial.psum, + MvPolynomial.aeval_X] at hn + rw [Finset.sum_filter, Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk, + Finset.sum_range_succ] at hn + simp only [lt_self_iff_false, ↓reduceIte, add_zero] at hn + have hs : (∑ j : Fin (k + 1), + contourNewtonCoeff (fun j => ∑ i, x i ^ j) j * ∑ i, x i ^ (k + 1 - j)) = + ∑ j ∈ Finset.range (k + 1), + (-1 : ℂ) ^ j * (Finset.univ.val.map x).esymm j * + ∑ i, x i ^ (k + 1 - j) := by + rw [Fin.sum_univ_eq_sum_range (fun j => + contourNewtonCoeff (fun j => ∑ i, x i ^ j) j * ∑ i, x i ^ (k + 1 - j))] + apply Finset.sum_congr rfl + intro j hj + rw [ih j (Finset.mem_range.mp hj)] + rw [hs] + have hn' : ((k + 1 : ℕ) : ℂ) * (Finset.univ.val.map x).esymm (k + 1) = + (-1 : ℂ) ^ (k + 1 + 1) * + ∑ j ∈ Finset.range (k + 1), + (-1 : ℂ) ^ j * (Finset.univ.val.map x).esymm j * + ∑ i, x i ^ (k + 1 - j) := by + convert hn using 2 + apply Finset.sum_congr rfl + intro j hj + simp [Finset.mem_range.mp hj] + have hz : ((k : ℂ) + 1) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero k + apply (div_eq_iff hz).2 + have hsign : (-1 : ℂ) ^ (k + 1) * (-1) ^ (k + 1 + 1) = -1 := by + rw [← pow_add] + convert (Odd.neg_one_pow (show Odd (k + 1 + (k + 1 + 1)) by exact ⟨k + 1, by omega⟩) : _) + have hmul := congrArg (fun z : ℂ => (-1) ^ (k + 1) * z) hn' + simp only [← mul_assoc, hsign, neg_one_mul, Nat.cast_add, Nat.cast_one] at hmul + linear_combination -hmul + + +theorem contourPolynomial_eq_prod {ι : Type*} [Fintype ι] (x : ι → ℂ) + {f : ℂ → ℂ} {r : ℝ} + (hs : ∀ k, contourMoment f r k = ∑ i, x i ^ k) : + contourPolynomial f r (Fintype.card ι) = ∏ i, (Polynomial.X - Polynomial.C (x i)) := by + classical + have hf : contourMoment f r = fun k => ∑ i, x i ^ k := funext hs + rw [contourPolynomial, hf] + simp_rw [contourNewtonCoeff_powerSum] + have hv := (Finset.univ.val.map x).prod_X_sub_X_eq_sum_esymm + simp only [Multiset.card_map, Finset.card_val, Finset.card_univ, + Multiset.map_map, Function.comp_def] at hv + change (∏ i, (Polynomial.X - Polynomial.C (x i))) = _ at hv + rw [hv] + apply Finset.sum_congr rfl + intro k hk + simp [map_mul, map_pow, mul_assoc] + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ContourPreparation.lean b/lean/OAI/Analysis/PathSelection/ContourPreparation.lean new file mode 100644 index 0000000000000000000000000000000000000000..73763f38d0922eef3ece7d72ae9e0ef3e26fab73 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ContourPreparation.lean @@ -0,0 +1,641 @@ +import Mathlib +import OAI.Analysis.PathSelection.ContourDivision + +namespace OAI + +/-! Fixed-contour preparation polynomials, division and stable root counts. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Metric Polynomial + +namespace PathSelection.Preparation + +lemma eqOn_closedBall_of_codiscrete {f g : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : ContinuousOn f (closedBall 0 r)) (hg : ContinuousOn g (closedBall 0 r)) + (heq : f =ᶠ[codiscreteWithin (closedBall 0 r)] g) : + EqOn f g (closedBall 0 r) := by + have hi : EqOn f g (ball 0 r) := by + intro z hz + have hznear : closedBall (0 : ℂ) r ∈ 𝓝 z := + mem_of_superset (isOpen_ball.mem_nhds hz) ball_subset_closedBall + have hle : 𝓝[≠] z ≤ codiscreteWithin (closedBall (0 : ℂ) r) := by + rw [codiscreteWithin] + exact le_iSup_of_le z (le_iSup_of_le (ball_subset_closedBall hz) (by + rw [sdiff_eq, nhdsWithin_inter_of_mem (mem_nhdsWithin_of_mem_nhds hznear)])) + have he := heq.filter_mono hle + have hfc := (hf z (ball_subset_closedBall hz)).continuousAt hznear + have hgc := (hg z (ball_subset_closedBall hz)).continuousAt hznear + exact tendsto_nhds_unique (hfc.tendsto.mono_left nhdsWithin_le_nhds) + ((hgc.tendsto.mono_left nhdsWithin_le_nhds).congr' he.symm) + exact hi.of_subset_closure hf hg ball_subset_closedBall (by rw [closure_ball _ hr.ne']) + + + +lemma nonnegative_factor_polynomial (d : ℂ → ℤ) (hd : d.HasFiniteSupport) + (hnonneg : ∀ z, 0 ≤ d z) : + ∃ P : ℂ[X], P.Monic ∧ + (∀ z, P.eval z = (∏ᶠ w : ℂ, (fun t : ℂ => t-w) ^ d w) z) ∧ + (∀ z, P.eval z = 0 → z ∈ Function.support d) := by + classical + let s := hd.toFinset + let P : ℂ[X] := ∏ w ∈ s, (X - C w) ^ (d w).toNat + have hP : P.Monic := monic_prod_of_monic s _ (fun w _ => (monic_X_sub_C w).pow _) + have heq (z : ℂ) : P.eval z = (∏ᶠ w : ℂ, (fun t : ℂ => t-w) ^ d w) z := by + rw [Function.FactorizedRational.finprod_eq_fun hd] + dsimp only + rw [finprod_eq_prod_of_mulSupport_subset _ (s := s) ?_] + · simp only [P, eval_prod, eval_pow, eval_sub, eval_X, eval_C] + apply Finset.prod_congr rfl + intro w _ + conv_rhs => rw [← Int.toNat_of_nonneg (hnonneg w), zpow_natCast] + · intro w hw + apply hd.mem_toFinset.mpr + by_contra hn + have : d w = 0 := by simpa using hn + simp [Function.mem_mulSupport, this] at hw + refine ⟨P, hP, heq, ?_⟩ + intro z hz + by_contra hn + have hprod : P.eval z ≠ 0 := by + simp only [P, eval_prod, eval_pow, eval_sub, eval_X, eval_C] + apply Finset.prod_ne_zero_iff.mpr + intro w hw + apply pow_ne_zero + apply sub_ne_zero.mpr + intro hzw + apply hn + rw [hzw] + exact hd.mem_toFinset.mp hw + exact hprod hz + + + +theorem exists_preparation_on_disc {f : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hnz : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) : + ∃ P : ℂ[X], P.Monic ∧ + (∀ z : ℂ, P.eval z = 0 → z ∈ ball 0 r) ∧ + ∃ u : ℂ → ℂ, AnalyticOnNhd ℂ u (closedBall 0 r) ∧ + (∀ z ∈ closedBall (0 : ℂ) r, u z ≠ 0) ∧ + EqOn f (fun z => P.eval z * u z) (closedBall 0 r) := by + have hz : (r : ℂ) ∈ sphere (0 : ℂ) r := by + simp [abs_of_pos hr] + have hzc := sphere_subset_closedBall hz + have horder : ∀ z ∈ closedBall (0 : ℂ) r, meromorphicOrderAt f z ≠ ⊤ := by + intro z hz' + apply hf.meromorphicOn.meromorphicOrderAt_ne_top_of_isPreconnected + (isConnected_closedBall hr.le).isPreconnected hzc hz' + rw [(hf _ hzc).meromorphicOrderAt_eq, (hf _ hzc).analyticOrderAt_eq_zero.mpr (hnz _ hz)] + simp + let d := MeromorphicOn.divisor f (closedBall (0 : ℂ) r) + have hd : (d : ℂ → ℤ).HasFiniteSupport := d.finiteSupport (isCompact_closedBall _ _) + have hdpos : ∀ z, 0 ≤ d z := MeromorphicOn.AnalyticOnNhd.divisor_nonneg hf + obtain ⟨P, hP, hPeq, hroot⟩ := nonnegative_factor_polynomial d hd hdpos + obtain ⟨u, hu, hunz, heq⟩ := hf.meromorphicOn.extract_zeros_poles + (fun z => horder z z.property) hd + refine ⟨P, hP, ?_, u, hu, fun z hz => hunz ⟨z, hz⟩, ?_⟩ + · intro z hz + have hs := hroot z hz + have hzc := d.supportWithinDomain hs + rcases lt_or_eq_of_le (mem_closedBall_zero_iff.mp hzc) with hlt | he + · exact mem_ball_zero_iff.mpr hlt + have hzsp : z ∈ sphere (0 : ℂ) r := mem_sphere_zero_iff_norm.mpr he + have hd0 : d z = 0 := by + dsimp [d] + rw [hf.meromorphicOn.divisor_apply hzc, (hf z hzc).meromorphicOrderAt_eq, + (hf z hzc).analyticOrderAt_eq_zero.mpr (hnz z hzsp)] + simp + exact False.elim (hs hd0) + · apply eqOn_closedBall_of_codiscrete hr hf.continuousOn + (P.continuous.continuousOn.mul hu.continuousOn) + filter_upwards [heq] with z hz + change f z = P.eval z * u z + rw [hPeq] + simpa only [d, Pi.smul_apply', smul_eq_mul] using hz + + +def divisionKernel (P : ℂ[X]) (w : ℂ) : ℂ[X] := + ∑ n ∈ Finset.range (P.natDegree + 1), + ∑ k ∈ Finset.range n, C (P.coeff n * w ^ (n - 1 - k)) * X ^ k + +lemma divisionKernel_eval (P : ℂ[X]) (w y : ℂ) : + (divisionKernel P w).eval y * (w-y) = P.eval w - P.eval y := by + simp only [divisionKernel, eval_finsetSum, eval_mul, eval_C, eval_pow, eval_X] + rw [Finset.sum_mul] + simp_rw [mul_assoc, ← Finset.mul_sum] + have hk (n : ℕ) : + (∑ k ∈ Finset.range n, w ^ (n - 1 - k) * y ^ k) * (w-y) = w^n-y^n := by + calc + _ = (∑ k ∈ Finset.range n, y ^ k * w ^ (n-1-k)) * (w-y) := by + congr 1 + apply Finset.sum_congr rfl + intro k _ + exact mul_comm _ _ + _ = (∑ k ∈ Finset.range n, w ^ k * y ^ (n-1-k)) * (w-y) := by + rw [geom_sum₂_comm y w n] + _ = _ := geom_sum₂_mul w y n + simp_rw [mul_assoc, hk, mul_sub] + rw [Finset.sum_sub_distrib, eval_eq_sum_range, eval_eq_sum_range] + +lemma divisionKernel_degree (P : ℂ[X]) (w : ℂ) : + (divisionKernel P w).degree < P.natDegree := by + rw [degree_lt_iff_coeff_zero] + intro m hm + simp only [divisionKernel, finsetSum_coeff, coeff_C_mul_X_pow] + apply Finset.sum_eq_zero + intro n hn + apply Finset.sum_eq_zero + intro k hk + have hkn : k < n := Finset.mem_range.mp hk + have hnd : n ≤ P.natDegree := Nat.lt_succ_iff.mp (Finset.mem_range.mp hn) + have hne : k ≠ m := by omega + simp [hne.symm] + +lemma divisionKernel_continuous (P : ℂ[X]) (y : ℂ) : + Continuous (fun w => (divisionKernel P w).eval y) := by + simp only [divisionKernel, eval_finsetSum, eval_mul, eval_C, eval_pow, eval_X] + fun_prop + +open scoped Real +open Complex + + + +theorem fixed_circle_division {G : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} + (hG : AnalyticOnNhd ℂ G (closedBall 0 r)) + (hP : ∀ w ∈ sphere (0 : ℂ) r, P.eval w ≠ 0) + {y : ℂ} (hy : y ∈ ball (0 : ℂ) r) : + G y = P.eval y * ((2 * π * I)⁻¹ * + ∮ w in C(0, r), G w / (P.eval w * (w-y))) + + (2 * π * I)⁻¹ * ∮ w in C(0, r), + G w / P.eval w * (divisionKernel P w).eval y := by + have hr : 0 < r := lt_of_le_of_lt (norm_nonneg y) (mem_ball_zero_iff.mp hy) + have hwy : ∀ w ∈ sphere (0 : ℂ) r, w-y ≠ 0 := by + intro w hw + apply sub_ne_zero.mpr + intro he + subst w + exact (ne_of_lt (mem_ball_zero_iff.mp hy)) (mem_sphere_zero_iff_norm.mp hw) + have hc₁ : ContinuousOn (fun w => G w / (P.eval w * (w-y))) (sphere 0 r) := + (hG.continuousOn.mono sphere_subset_closedBall).div + (P.continuous.continuousOn.mul (continuousOn_id.sub continuousOn_const)) + (fun w hw => mul_ne_zero (hP w hw) (hwy w hw)) + have hc₂ : ContinuousOn (fun w => G w / P.eval w * (divisionKernel P w).eval y) + (sphere 0 r) := + ((hG.continuousOn.mono sphere_subset_closedBall).div P.continuous.continuousOn hP).mul + (divisionKernel_continuous P y).continuousOn + have hi : (∮ w in C(0, r), G w / (w-y)) = + P.eval y * (∮ w in C(0, r), G w / (P.eval w * (w-y))) + + ∮ w in C(0, r), G w / P.eval w * (divisionKernel P w).eval y := by + have hci₁ : CircleIntegrable (fun w => P.eval y * (G w / (P.eval w * (w-y)))) 0 r := + (continuousOn_const.mul hc₁).circleIntegrable hr.le + rw [← circleIntegral.integral_const_mul, + ← circleIntegral.integral_add hci₁ (hc₂.circleIntegrable hr.le)] + apply circleIntegral.integral_congr hr.le + intro w hw + have hk := divisionKernel_eval P w y + field_simp [hP w hw, hwy w hw] + linear_combination -G w * hk + have hc := circleIntegral_div_sub_of_differentiable_on_off_countable + Set.countable_empty hy hG.continuousOn + (fun z hz => (hG z (ball_subset_closedBall hz.1)).differentiableAt) + rw [hc] at hi + have htwo : (2 * π * I : ℂ) ≠ 0 := by simp [Real.pi_ne_zero, I_ne_zero] + apply (mul_left_cancel₀ htwo) + rw [mul_add] + field_simp + simpa only [div_mul_eq_mul_div] using hi + + +def divisionRemainder (G : ℂ → ℂ) (P : ℂ[X]) (r : ℝ) : ℂ[X] := + ∑ n ∈ Finset.range (P.natDegree + 1), + ∑ k ∈ Finset.range n, + C ((2 * π * I)⁻¹ * ∮ w in C(0,r), + G w / P.eval w * (P.coeff n * w ^ (n-1-k))) * X ^ k + +lemma divisionRemainder_degree (G : ℂ → ℂ) (P : ℂ[X]) (r : ℝ) : + (divisionRemainder G P r).degree < P.natDegree := by + rw [degree_lt_iff_coeff_zero] + intro m hm + simp only [divisionRemainder, finsetSum_coeff, coeff_C_mul_X_pow] + apply Finset.sum_eq_zero + intro n hn + apply Finset.sum_eq_zero + intro k hk + have hkn : k < n := Finset.mem_range.mp hk + have hnd : n ≤ P.natDegree := Nat.lt_succ_iff.mp (Finset.mem_range.mp hn) + have hne : m ≠ k := by omega + simp [hne] + +lemma divisionRemainder_eval {G : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} (hr : 0 ≤ r) + (hG : ContinuousOn G (sphere 0 r)) + (hP : ∀ w ∈ sphere (0 : ℂ) r, P.eval w ≠ 0) (y : ℂ) : + (divisionRemainder G P r).eval y = + (2 * π * I)⁻¹ * ∮ w in C(0,r), G w / P.eval w * (divisionKernel P w).eval y := by + have hcont (n k : ℕ) : ContinuousOn + (fun w => G w / P.eval w * (P.coeff n * w ^ (n-1-k)) * y ^ k) (sphere 0 r) := + (((hG.div P.continuous.continuousOn hP).mul + (continuousOn_const.mul (continuousOn_id.pow _))).mul continuousOn_const) + simp only [divisionRemainder, divisionKernel, eval_finsetSum, eval_mul, eval_C, + eval_pow, eval_X] + simp_rw [Finset.mul_sum] + rw [circleIntegral.integral_fun_sum (fun n _ => + (continuousOn_finsetSum _ (fun k _ => by simpa only [mul_assoc] using hcont n k)).circleIntegrable hr)] + simp_rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro n _ + rw [circleIntegral.integral_fun_sum (fun k _ => + (by simpa only [mul_assoc] using (hcont n k).circleIntegrable hr))] + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro k _ + rw [show (fun w => G w / P.eval w * (P.coeff n * w ^ (n-1-k) * y^k)) = + (fun w => (G w / P.eval w * (P.coeff n * w ^ (n-1-k))) • y^k) by + funext w; simp only [smul_eq_mul, mul_assoc], circleIntegral.integral_smul_const] + simp only [smul_eq_mul, mul_assoc] + +def divisionQuotient (G : ℂ → ℂ) (P : ℂ[X]) (r : ℝ) (y : ℂ) : ℂ := + (2 * π * I)⁻¹ * ∮ w in C(0,r), G w / (P.eval w * (w-y)) + +lemma divisionQuotient_analyticOnNhd {G : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} (hr : 0 < r) + (hG : ContinuousOn G (sphere 0 r)) + (hP : ∀ w ∈ sphere (0 : ℂ) r, P.eval w ≠ 0) : + AnalyticOnNhd ℂ (divisionQuotient G P r) (ball 0 r) := by + have hi := (hG.div P.continuous.continuousOn hP).circleIntegrable hr.le + have ha := (hasFPowerSeriesOn_cauchy_integral (R := ⟨r, hr.le⟩) hi hr).analyticOnNhd + convert! ha using 1 + · funext y + simp only [divisionQuotient, smul_eq_mul, Pi.div_apply, div_eq_mul_inv, mul_inv_rev] + congr 1 + apply congrArg (fun f : ℂ → ℂ => ∮ w in C(0,r), f w) + funext w + ring + · exact (Metric.eball_coe (x := (0 : ℂ)) (ε := ⟨r, hr.le⟩)).symm + + + +theorem fixed_disc_division {G : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} (hr : 0 < r) + (hG : AnalyticOnNhd ℂ G (closedBall 0 r)) + (hP : ∀ w ∈ sphere (0 : ℂ) r, P.eval w ≠ 0) : + AnalyticOnNhd ℂ (divisionQuotient G P r) (ball 0 r) ∧ + (divisionRemainder G P r).degree < P.natDegree ∧ + EqOn G (fun y => P.eval y * divisionQuotient G P r y + + (divisionRemainder G P r).eval y) (ball 0 r) := by + refine ⟨divisionQuotient_analyticOnNhd hr (hG.continuousOn.mono sphere_subset_closedBall) hP, + divisionRemainder_degree G P r, ?_⟩ + intro y hy + dsimp only + rw [divisionRemainder_eval hr.le (hG.continuousOn.mono sphere_subset_closedBall) hP] + exact fixed_circle_division hG hP hy + + + +lemma eqOn_deriv_closedBall {f g : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hg : AnalyticOnNhd ℂ g (closedBall 0 r)) + (heq : EqOn f g (closedBall 0 r)) : EqOn (deriv f) (deriv g) (closedBall 0 r) := by + have hi := (heq.mono ball_subset_closedBall).deriv isOpen_ball + exact hi.of_subset_closure hf.deriv.continuousOn hg.deriv.continuousOn + ball_subset_closedBall (by rw [closure_ball _ hr.ne']) + +lemma circleIntegral_root_sum {r : ℝ} (hr : 0 < r) (l : ℕ) (a : Multiset ℂ) + (ha : ∀ w ∈ a, w ∈ ball (0 : ℂ) r) : + CircleIntegrable (fun z => (a.map (fun w => z^l / (z-w))).sum) 0 r ∧ + (∮ z in C(0,r), (a.map (fun w => z^l / (z-w))).sum) = + (2 * π * I) * (a.map (fun w => w^l)).sum := by + induction a using Multiset.induction_on with + | empty => simp [circleIntegral] + | cons a s ih => + have hai : a ∈ ball (0 : ℂ) r := ha a (by simp) + obtain ⟨hsi, hseq⟩ := ih (fun w hw => ha w (by simp [hw])) + have hane (z : ℂ) (hz : z ∈ sphere (0 : ℂ) r) : z-a ≠ 0 := by + apply sub_ne_zero.mpr + rintro rfl + exact (ne_of_lt (mem_ball_zero_iff.mp hai)) (mem_sphere_zero_iff_norm.mp hz) + have hai' : CircleIntegrable (fun z => z^l / (z-a)) 0 r := + ((continuousOn_id.pow l).div (continuousOn_id.sub continuousOn_const) hane).circleIntegrable hr.le + have haeq : (∮ z in C(0,r), z^l / (z-a)) = (2 * π * I) * a^l := + circleIntegral_div_sub_of_differentiable_on_off_countable Set.countable_empty hai + ((continuous_pow l).continuousOn) (fun z _ => by fun_prop) + simp only [Multiset.map_cons, Multiset.sum_cons] + exact ⟨hai'.add hsi, by rw [circleIntegral.integral_add hai' hsi, haeq, hseq, mul_add]⟩ + + +theorem polynomial_power_sum_contour {P : ℂ[X]} {r : ℝ} (hr : 0 < r) + (hP : P ≠ 0) (hroot : ∀ z : ℂ, P.eval z = 0 → z ∈ ball 0 r) (l : ℕ) : + (2 * π * I)⁻¹ * (∮ z in C(0,r), z^l * P.derivative.eval z / P.eval z) = + (P.roots.map (fun w => w^l)).sum := by + have ha : ∀ w ∈ P.roots, w ∈ ball (0 : ℂ) r := fun w hw => + hroot w ((mem_roots hP).mp hw) + have hi := (circleIntegral_root_sum hr l P.roots ha).2 + have he : (∮ z in C(0,r), z^l * P.derivative.eval z / P.eval z) = + ∮ z in C(0,r), (P.roots.map (fun w => z^l / (z-w))).sum := by + apply circleIntegral.integral_congr hr.le + intro z hz + have hnz : P.eval z ≠ 0 := by + intro he + exact (ne_of_lt (mem_ball_zero_iff.mp (hroot z he))) (mem_sphere_zero_iff_norm.mp hz) + dsimp only + rw [mul_div_assoc, (IsAlgClosed.splits P).eval_derivative_div_eval_of_ne_zero hnz, + ← Multiset.sum_map_mul_left] + simp only [mul_one_div] + rw [he, hi, ← mul_assoc, inv_mul_cancel₀, one_mul] + simp [Real.pi_ne_zero, I_ne_zero] + + + +theorem preparation_power_sum_contour {f u : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} + (hr : 0 < r) (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) (hP : P.Monic) + (hroot : ∀ z : ℂ, P.eval z = 0 → z ∈ ball 0 r) + (hu : AnalyticOnNhd ℂ u (closedBall 0 r)) + (hunz : ∀ z ∈ closedBall (0 : ℂ) r, u z ≠ 0) + (heq : EqOn f (fun z => P.eval z * u z) (closedBall 0 r)) (l : ℕ) : + (2 * π * I)⁻¹ * (∮ z in C(0,r), z^l * deriv f z / f z) = + (P.roots.map (fun w => w^l)).sum := by + have hPa : AnalyticOnNhd ℂ (fun z => P.eval z) (closedBall 0 r) := + fun z _ => AnalyticOnNhd.eval_polynomial P z (mem_univ z) + have hdeq := eqOn_deriv_closedBall hr hf (hPa.mul hu) heq + have hPn (z : ℂ) (hz : z ∈ sphere (0 : ℂ) r) : P.eval z ≠ 0 := by + intro he + exact (ne_of_lt (mem_ball_zero_iff.mp (hroot z he))) (mem_sphere_zero_iff_norm.mp hz) + have hunit : AnalyticOnNhd ℂ (fun z => z^l * deriv u z / u z) (closedBall 0 r) := + ((analyticOnNhd_id.pow l).mul hu.deriv).div hu hunz + have hzero : (∮ z in C(0,r), z^l * deriv u z / u z) = 0 := + circleIntegral_eq_zero_of_differentiable_on_off_countable hr.le Set.countable_empty + hunit.continuousOn (fun z hz => (hunit z (ball_subset_closedBall hz.1)).differentiableAt) + have hpoly : CircleIntegrable (fun z => z^l * P.derivative.eval z / P.eval z) 0 r := + (((continuousOn_id.pow l).mul P.derivative.continuous.continuousOn).div + P.continuous.continuousOn hPn).circleIntegrable hr.le + have hi : (∮ z in C(0,r), z^l * deriv f z / f z) = + (∮ z in C(0,r), z^l * P.derivative.eval z / P.eval z) + + ∮ z in C(0,r), z^l * deriv u z / u z := by + rw [← circleIntegral.integral_add hpoly + ((hunit.continuousOn.mono sphere_subset_closedBall).circleIntegrable hr.le)] + apply circleIntegral.integral_congr hr.le + intro z hz + have hzc := sphere_subset_closedBall hz + dsimp only + rw [heq hzc, hdeq hzc, deriv_fun_mul (P.differentiableAt) (hu z hzc).differentiableAt, + (P.hasDerivAt z).deriv] + field_simp [hPn z hz, hunz z hzc] + rw [hi, hzero, add_zero] + exact polynomial_power_sum_contour hr hP.ne_zero hroot l + + + +def newtonEsymm (powerSum : ℕ → ℂ) (n : ℕ) : ℂ := + if n = 0 then 1 else (n : ℂ)⁻¹ * (-1)^(n+1) * + ∑ a ∈ (Finset.HasAntidiagonal.antidiagonal n).filter (fun a => a.1 < n), + if h : a.1 < n then (-1)^a.1 * newtonEsymm powerSum a.1 * powerSum a.2 else 0 +termination_by n +decreasing_by assumption + +lemma multiset_newton_identity (a : Multiset ℂ) (n : ℕ) : + (n : ℂ) * a.esymm n = (-1)^(n+1) * + ∑ t ∈ (Finset.HasAntidiagonal.antidiagonal n).filter (fun t => t.1 < n), + (-1)^t.1 * a.esymm t.1 * (a.map (fun w => w^t.2)).sum := by + classical + have h := congrArg (MvPolynomial.aeval (R := ℂ) (fun w : a => (w : ℂ))) + (MvPolynomial.mul_esymm_eq_sum a ℂ n) + simp only [map_mul, map_natCast, map_pow, map_neg, map_one, map_sum, + MvPolynomial.aeval_esymm_eq_multiset_esymm, Multiset.map_univ_coe] at h + convert h using 2 + apply Finset.sum_congr rfl + intro t ht + congr 1 + simp only [MvPolynomial.psum, map_sum, map_pow, MvPolynomial.aeval_X] + rw [← Finset.sum_map_val (Finset.univ : Finset a)] + exact (congrArg Multiset.sum (Multiset.map_univ a (fun w => w^t.2))).symm + +lemma newtonEsymm_eq (a : Multiset ℂ) (n : ℕ) : + newtonEsymm (fun k => (a.map (fun w => w^k)).sum) n = a.esymm n := by + induction n using Nat.strong_induction_on with + | h n ih => + rw [newtonEsymm] + split_ifs with hn + · subst n + simp [Multiset.esymm] + · have hsum : (∑ t ∈ (Finset.HasAntidiagonal.antidiagonal n).filter (fun t => t.1 < n), + if h : t.1 < n then (-1 : ℂ)^t.1 * newtonEsymm (fun k => (a.map (fun w => w^k)).sum) t.1 * + (a.map (fun w => w^t.2)).sum else 0) = + ∑ t ∈ (Finset.HasAntidiagonal.antidiagonal n).filter (fun t => t.1 < n), + (-1 : ℂ)^t.1 * a.esymm t.1 * (a.map (fun w => w^t.2)).sum := by + apply Finset.sum_congr rfl + intro t ht + rw [dite_eq_left (Finset.mem_filter.mp ht).2, ih t.1 (Finset.mem_filter.mp ht).2] + rw [hsum, mul_assoc, ← multiset_newton_identity] + exact inv_mul_cancel_left₀ (by exact_mod_cast hn) _ + + + +def contourPowerSum (f : ℂ → ℂ) (r : ℝ) (l : ℕ) : ℂ := + (2 * π * I)⁻¹ * ∮ z in C(0,r), z^l * deriv f z / f z + + +def preparationPolynomial (f : ℂ → ℂ) (r : ℝ) (d : ℕ) : ℂ[X] := + ∑ k ∈ Finset.range (d+1), + C ((-1)^(d-k) * newtonEsymm (contourPowerSum f r) (d-k)) * X^k + +lemma polynomial_newton_formula (P : ℂ[X]) (hP : P.Monic) : + (∑ k ∈ Finset.range (P.natDegree+1), + C ((-1)^(P.natDegree-k) * + newtonEsymm (fun l => (P.roots.map (fun w => w^l)).sum) (P.natDegree-k)) * X^k) = P := by + conv_rhs => rw [P.as_sum_range_C_mul_X_pow] + apply Finset.sum_congr rfl + intro k hk + rw [newtonEsymm_eq, + coeff_eq_esymm_roots_of_splits (IsAlgClosed.splits P) (Nat.lt_succ_iff.mp (Finset.mem_range.mp hk)), + hP.leadingCoeff, one_mul] + +lemma preparationPolynomial_eq {f u : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} + (hr : 0 < r) (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) (hP : P.Monic) + (hroot : ∀ z : ℂ, P.eval z = 0 → z ∈ ball 0 r) + (hu : AnalyticOnNhd ℂ u (closedBall 0 r)) + (hunz : ∀ z ∈ closedBall (0 : ℂ) r, u z ≠ 0) + (heq : EqOn f (fun z => P.eval z * u z) (closedBall 0 r)) : + preparationPolynomial f r P.natDegree = P := by + have hs : contourPowerSum f r = fun l => (P.roots.map (fun w => w^l)).sum := + funext (preparation_power_sum_contour hr hf hP hroot hu hunz heq) + simpa only [preparationPolynomial, hs] using polynomial_newton_formula P hP + +lemma divisionQuotient_eq_unit {f u : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} + (hu : AnalyticOnNhd ℂ u (closedBall 0 r)) + (hPn : ∀ z ∈ sphere (0 : ℂ) r, P.eval z ≠ 0) + (heq : EqOn f (fun z => P.eval z * u z) (sphere 0 r)) : + EqOn (divisionQuotient f P r) u (ball 0 r) := by + intro y hy + have hr : 0 < r := (mem_ball_zero_iff.mp hy).trans_le' (norm_nonneg y) + have hi : (∮ z in C(0,r), f z / (P.eval z * (z-y))) = + ∮ z in C(0,r), u z / (z-y) := by + apply circleIntegral.integral_congr hr.le + intro z hz + dsimp only + rw [heq hz] + exact mul_div_mul_left (u z) (z-y) (hPn z hz) + have hc := circleIntegral_div_sub_of_differentiable_on_off_countable + Set.countable_empty hy hu.continuousOn + (fun z hz => (hu z (ball_subset_closedBall hz.1)).differentiableAt) + rw [divisionQuotient, hi, hc, ← mul_assoc, inv_mul_cancel₀, one_mul] + simp [Real.pi_ne_zero, I_ne_zero] + + + +theorem fixed_contour_preparation {f : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hnz : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) : + ∃ d : ℕ, let W := preparationPolynomial f r d + W.Monic ∧ W.natDegree = d ∧ + (∀ z : ℂ, W.eval z = 0 → z ∈ ball 0 r) ∧ + AnalyticOnNhd ℂ (divisionQuotient f W r) (ball 0 r) ∧ + (∀ z ∈ ball (0 : ℂ) r, divisionQuotient f W r z ≠ 0) ∧ + EqOn f (fun z => W.eval z * divisionQuotient f W r z) (ball 0 r) := by + obtain ⟨P, hP, hroot, u, hu, hunz, heq⟩ := exists_preparation_on_disc hr hf hnz + refine ⟨P.natDegree, ?_⟩ + dsimp only + rw [preparationPolynomial_eq hr hf hP hroot hu hunz heq] + have hPn (z : ℂ) (hz : z ∈ sphere (0 : ℂ) r) : P.eval z ≠ 0 := by + intro he + exact (ne_of_lt (mem_ball_zero_iff.mp (hroot z he))) (mem_sphere_zero_iff_norm.mp hz) + have hquot := divisionQuotient_eq_unit hu hPn (heq.mono sphere_subset_closedBall) + refine ⟨hP, rfl, hroot, + divisionQuotient_analyticOnNhd hr (hf.continuousOn.mono sphere_subset_closedBall) hPn, ?_, ?_⟩ + · intro z hz + rw [hquot hz] + exact hunz z (ball_subset_closedBall hz) + · intro z hz + simp only [heq (ball_subset_closedBall hz), hquot hz] + +lemma preparation_zero_count {f u : ℂ → ℂ} {P : ℂ[X]} {r : ℝ} + (hr : 0 < r) (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) (hP : P.Monic) + (hroot : ∀ z : ℂ, P.eval z = 0 → z ∈ ball 0 r) + (hu : AnalyticOnNhd ℂ u (closedBall 0 r)) + (hunz : ∀ z ∈ closedBall (0 : ℂ) r, u z ≠ 0) + (heq : EqOn f (fun z => P.eval z * u z) (closedBall 0 r)) : + contourPowerSum f r 0 = (P.natDegree : ℂ) := by + have h := preparation_power_sum_contour hr hf hP hroot hu hunz heq 0 + simpa [contourPowerSum, ← (IsAlgClosed.splits P).natDegree_eq_card_roots] using h + +lemma contour_zero_count_nat {f : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hnz : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) : + contourPowerSum f r 0 ∈ Set.range (fun n : ℕ => (n : ℂ)) := by + obtain ⟨P, hP, hroot, u, hu, hunz, heq⟩ := exists_preparation_on_disc hr hf hnz + exact ⟨P.natDegree, (preparation_zero_count hr hf hP hroot hu hunz heq).symm⟩ + +lemma continuousOn_circleIntegral {E : Type*} [NormedAddCommGroup E] + {A : Set E} {F : E → ℂ → ℂ} {r : ℝ} (hr : 0 ≤ r) + (hA : IsCompact A) (hF : ContinuousOn (Function.uncurry F) (A ×ˢ sphere 0 r)) : + ContinuousOn (fun a => ∮ z in C(0,r), F a z) A := by + have hu := (hA.prod (isCompact_sphere (0 : ℂ) r)).uniformContinuousOn_of_continuous hF + intro a ha + apply TendstoUniformlyOn.tendsto_circleIntegral_of_continuousOn hr + · filter_upwards [self_mem_nhdsWithin] with b hb + exact hF.comp (continuous_const.prodMk continuous_id).continuousOn + (fun z hz => ⟨hb, hz⟩) + · exact hu.tendstoUniformlyOn ha + + + +theorem contour_zero_count_constant {E : Type*} [NormedAddCommGroup E] + {A : Set E} {F : E → ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hA : IsCompact A) (hcA : IsPreconnected A) + (hf : ∀ a ∈ A, AnalyticOnNhd ℂ (F a) (closedBall 0 r)) + (hnz : ∀ a ∈ A, ∀ z ∈ sphere (0 : ℂ) r, F a z ≠ 0) + (hF : ContinuousOn (Function.uncurry F) (A ×ˢ sphere 0 r)) + (hdF : ContinuousOn (fun p : E × ℂ => deriv (F p.1) p.2) (A ×ˢ sphere 0 r)) + {a b : E} (ha : a ∈ A) (hb : b ∈ A) : + contourPowerSum (F a) r 0 = contourPowerSum (F b) r 0 := by + have hi : ContinuousOn (fun a => contourPowerSum (F a) r 0) A := by + have h := continuousOn_circleIntegral (F := fun a z => deriv (F a) z / F a z) hr.le hA + (hdF.div hF (fun p hp => hnz p.1 hp.1 p.2 hp.2)) + simpa only [contourPowerSum, pow_zero, one_mul] using h.const_mul ((2 * π * I)⁻¹) + have hc : (Set.range (fun n : ℕ => (n : ℂ))).Countable := countable_range _ + have hsub : (fun a => contourPowerSum (F a) r 0) '' A ⊆ + Set.range (fun n : ℕ => (n : ℂ)) := by + rintro _ ⟨a, ha, rfl⟩ + exact contour_zero_count_nat hr (hf a ha) (hnz a ha) + exact hc.isTotallyDisconnected _ hsub (hcA.image _ hi) + (mem_image_of_mem _ ha) (mem_image_of_mem _ hb) + + + +theorem contour_zero_count_eq_of_norm_sub_lt {f g : ℂ → ℂ} {r : ℝ} + (hr : 0 < r) (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hg : AnalyticOnNhd ℂ g (closedBall 0 r)) + (hsmall : ∀ z ∈ sphere (0 : ℂ) r, ‖g z - f z‖ < ‖f z‖) : + contourPowerSum f r 0 = contourPowerSum g r 0 := by + let F : ℝ → ℂ → ℂ := fun t z => f z + (t : ℂ) * (g z - f z) + have hfa (t : ℝ) : AnalyticOnNhd ℂ (F t) (closedBall 0 r) := + hf.add (analyticOnNhd_const.mul (hg.sub hf)) + have hnz (t : ℝ) (ht : t ∈ Icc 0 1) (z : ℂ) (hz : z ∈ sphere 0 r) : F t z ≠ 0 := by + have hn : ‖(t : ℂ) * (g z - f z)‖ < ‖f z‖ := by + rw [norm_mul, Complex.norm_of_nonneg ht.1] + exact (mul_le_of_le_one_left (norm_nonneg _) ht.2).trans_lt (hsmall z hz) + intro he + have he' : f z = -((t : ℂ) * (g z - f z)) := eq_neg_of_add_eq_zero_left he + have he'' := congrArg norm he' + rw [norm_neg] at he'' + exact (ne_of_lt hn) he''.symm + have hs : ∀ p ∈ (Icc (0 : ℝ) 1) ×ˢ sphere (0 : ℂ) r, p.2 ∈ closedBall (0 : ℂ) r := + fun _ hp => sphere_subset_closedBall hp.2 + have hfc : ContinuousOn (fun p : ℝ × ℂ => f p.2) (Icc (0 : ℝ) 1 ×ˢ sphere 0 r) := + hf.continuousOn.comp continuous_snd.continuousOn hs + have hgc : ContinuousOn (fun p : ℝ × ℂ => g p.2) (Icc (0 : ℝ) 1 ×ˢ sphere 0 r) := + hg.continuousOn.comp continuous_snd.continuousOn hs + have hdfc : ContinuousOn (fun p : ℝ × ℂ => deriv f p.2) (Icc (0 : ℝ) 1 ×ˢ sphere 0 r) := + hf.deriv.continuousOn.comp continuous_snd.continuousOn hs + have hdgc : ContinuousOn (fun p : ℝ × ℂ => deriv g p.2) (Icc (0 : ℝ) 1 ×ˢ sphere 0 r) := + hg.deriv.continuousOn.comp continuous_snd.continuousOn hs + have htc : ContinuousOn (fun p : ℝ × ℂ => (p.1 : ℂ)) (Icc (0 : ℝ) 1 ×ˢ sphere 0 r) := + (Complex.continuous_ofReal.comp continuous_fst).continuousOn + have hFc : ContinuousOn (Function.uncurry F) (Icc (0 : ℝ) 1 ×ˢ sphere 0 r) := + hfc.add (htc.mul (hgc.sub hfc)) + have hdFc : ContinuousOn (fun p : ℝ × ℂ => deriv (F p.1) p.2) + (Icc (0 : ℝ) 1 ×ˢ sphere 0 r) := by + apply (hdfc.add (htc.mul (hdgc.sub hdfc))).congr + intro p hp + have hfd := (hf p.2 (hs p hp)).differentiableAt + have hgd := (hg p.2 (hs p hp)).differentiableAt + dsimp only [F] + simpa only [Pi.sub_apply, Pi.add_apply, Pi.mul_apply, Pi.add_def] using + (hfd.hasDerivAt.add ((hgd.hasDerivAt.sub hfd.hasDerivAt).const_mul (p.1 : ℂ))).deriv + have h := contour_zero_count_constant hr isCompact_Icc isPreconnected_Icc + (fun t _ => hfa t) hnz hFc hdFc (left_mem_Icc.mpr zero_le_one) (right_mem_Icc.mpr zero_le_one) + simpa [F] using h + + + +theorem fixed_contour_preparation_of_count {f : ℂ → ℂ} {r : ℝ} {d : ℕ} + (hr : 0 < r) (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hnz : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) + (hcount : contourPowerSum f r 0 = (d : ℂ)) : + let W := preparationPolynomial f r d + W.Monic ∧ W.natDegree = d ∧ + (∀ z : ℂ, W.eval z = 0 → z ∈ ball 0 r) ∧ + AnalyticOnNhd ℂ (divisionQuotient f W r) (ball 0 r) ∧ + (∀ z ∈ ball (0 : ℂ) r, divisionQuotient f W r z ≠ 0) ∧ + EqOn f (fun z => W.eval z * divisionQuotient f W r z) (ball 0 r) := by + obtain ⟨P, hP, hroot, u, hu, hunz, heq⟩ := exists_preparation_on_disc hr hf hnz + have hd : P.natDegree = d := by + exact_mod_cast (preparation_zero_count hr hf hP hroot hu hunz heq).symm.trans hcount + dsimp only + rw [← hd, preparationPolynomial_eq hr hf hP hroot hu hunz heq] + have hPn (z : ℂ) (hz : z ∈ sphere (0 : ℂ) r) : P.eval z ≠ 0 := by + intro he + exact (ne_of_lt (mem_ball_zero_iff.mp (hroot z he))) (mem_sphere_zero_iff_norm.mp hz) + have hquot := divisionQuotient_eq_unit hu hPn (heq.mono sphere_subset_closedBall) + refine ⟨hP, rfl, hroot, + divisionQuotient_analyticOnNhd hr (hf.continuousOn.mono sphere_subset_closedBall) hPn, ?_, ?_⟩ + · intro z hz + rw [hquot hz] + exact hunz z (ball_subset_closedBall hz) + · intro z hz + simp only [heq (ball_subset_closedBall hz), hquot hz] + +end PathSelection.Preparation +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/DerivativeEstimates.lean b/lean/OAI/Analysis/PathSelection/DerivativeEstimates.lean new file mode 100644 index 0000000000000000000000000000000000000000..c13653b9476ff0529d27a198d7a0c9e4ffa520fa --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/DerivativeEstimates.lean @@ -0,0 +1,193 @@ +import Mathlib +import OAI.Analysis.PathSelection.ExponentialCharts + +namespace OAI + +/-! Strip derivative variation and equal-exponent error estimates. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees.Clock + +theorem affine_strip_estimate {F : ℂ → ℂ} + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ F z) + (hz : ∀ᶠ z in stripInfinity,deriv F z≠0) + (hd : Tendsto (fun z => deriv (deriv F) z/deriv F z) stripInfinity (𝓝 0)) + {R : ℝ} (hR : 0 hz.deriv)) hz hd hR hB + (show 0<ε/B by positivity) + obtain ⟨A₂,hA₂⟩ := eventually_stripInfinity.mp ha R + let A := max A₁ A₂ + have hsub₁ : horizontalTail A R ⊆ horizontalTail A₁ R := + fun z hz => ⟨(le_max_left _ _).trans_lt hz.1,hz.2⟩ + have hsub₂ : horizontalTail A R ⊆ horizontalTail A₂ R := + fun z hz => ⟨(le_max_right _ _).trans_lt hz.1,hz.2⟩ + refine ⟨A,?_⟩ + intro z hz w hw hdist + let S := horizontalTail A R ∩ closedBall w B + have hSw : w∈S := ⟨hw,mem_closedBall_self hB.le⟩ + have hSz : z∈S := ⟨hz,mem_closedBall_iff_norm.mpr hdist⟩ + have hDS (u : ℂ) (hu : u∈S) : + ‖deriv F u-deriv F w‖≤ε*‖deriv F w‖ := by + have hub : ‖u-w‖≤B := mem_closedBall_iff_norm.mp hu.2 + obtain ⟨hwn,hhh⟩ := hA₁ u (hsub₁ hu.1) w (hsub₁ hw) hub + have hrel : ‖deriv F u/deriv F w-1‖≤ε := by + have hm := mul_le_mul_of_nonneg_left hub (by positivity : 0≤ε/B) + have he : ε/B*B=ε := div_mul_cancel₀ _ hB.ne' + exact hhh.trans (hm.trans_eq he) + have he : deriv F u-deriv F w=(deriv F u/deriv F w-1)*deriv F w := by + field_simp [hwn] + rw [he,norm_mul] + exact mul_le_mul_of_nonneg_right hrel (norm_nonneg _) + let G : ℂ → ℂ := fun u => F u-deriv F w*u + have hGd (u : ℂ) (hu : u∈S) : HasDerivAt G (deriv F u-deriv F w) u := by + simpa only [G,Pi.sub_def,id_eq,mul_one] using (hA₂ u (hsub₂ hu.1)).differentiableAt.hasDerivAt.sub + (hasDerivAt_const_mul (deriv F w)) + have hcv : Convex ℝ S := (horizontalTail_convex A R).inter (convex_closedBall w B) + have hh := Convex.norm_image_sub_le_of_norm_deriv_le + (fun u hu => (hGd u hu).differentiableAt) + (fun u hu => by rw [(hGd u hu).deriv]; exact hDS u hu) hcv hSw hSz + convert hh using 1 + dsimp [G] + congr 1 + ring + +theorem strip_derivative_variation {F : ℂ → ℂ} + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ F z) + (hz : ∀ᶠ z in stripInfinity,deriv F z≠0) + (hd : Tendsto (fun z => deriv (deriv F) z/deriv F z) stripInfinity (𝓝 0)) + {R : ℝ} (hR : 0 (x (r:ℂ)).re) atTop atTop) + (hxi : ∃ U : ℝ,∀ w : ℂ,0 deriv J z/J z) stripInfinity (𝓝 0)) + (hJr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) + (hJl : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 c)) + (hJd0 : ∀ᶠ z in stripInfinity,deriv J z≠0) + (hJdd : Tendsto (fun z => deriv (deriv J) z/deriv J z) stripInfinity (𝓝 0)) + (he : ∀ᶠ z in stripInfinity,‖E z‖≤C*Real.exp (-ε*z.re)) + (hfactor : ∀ᶠ z in stripInfinity,F z/H z=J z*(1+E z)) : + ∃ K U : ℝ,0 max (baseLoss r) (neighboringLoss ω ((2:ℝ)^(ψ (Real.logb 2 r)))) + have hν : AdmissibleAngularLoss ν := hN.pullback_log_derivative hψa hψd + have hrad : ∀ᶠ r : ℝ in atTop,0<χ r ∧ |e r|≤χ r ∧ + (∀ s∈Icc (f r/2) (2*f r),ω s≤ν r) ∧ 2*R 4*max (κ r) (max (χ r) (ν r)) + have hη : AdmissibleAngularLoss η := (hκ.max (hχ.max hν)).const_mul (by norm_num) + have hpos : ∀ᶠ r : ℝ in atTop,0<κ r ∧ 0<χ r ∧ 0<ν r := by + filter_upwards [hκ.1,hχ.1,hν.1] with r hk hc hn + exact ⟨hk.1,hc.1,hn.1⟩ + obtain ⟨T,hT⟩ := eventually_atTop.mp hpos + refine ⟨η,max S T,hη,?_⟩ + intro z hz + have hp := hT ‖z‖ ((le_max_right _ _).trans hz.1.le) + have hk : κ ‖z‖ ≤ η ‖z‖ := by + dsimp [η] + have hh := le_max_left (κ ‖z‖) (max (χ ‖z‖) (ν ‖z‖)) + linarith [hp.1] + have hzκ : z∈lossSector κ S := ⟨(le_max_left _ _).trans_lt hz.1, + hz.2.trans_le (sub_le_sub_left hk _)⟩ + obtain ⟨⟨hm,ha⟩,hc,he,hu,hR⟩ := hdata z hzκ + have hωF := hu ‖F z‖ hm + have hην : χ ‖z‖+ν ‖z‖ ≤ η ‖z‖ := by + dsimp [η] + have hh₁ := (le_max_left (χ ‖z‖) (ν ‖z‖)).trans (le_max_right (κ ‖z‖) (max (χ ‖z‖) (ν ‖z‖))) + have hh₂ := (le_max_right (χ ‖z‖) (ν ‖z‖)).trans (le_max_right (κ ‖z‖) (max (χ ‖z‖) (ν ‖z‖))) + linarith [hp.2.1,hp.2.2] + refine ⟨by linarith [hm.1],?_⟩ + linarith [hz.2] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem vanishing_equal_exponent_chart {F H J E : ℂ → ℂ} {b ε C : ℝ} + (hb : 0 (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hFd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 (b:ℂ))) + (hHd : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) + (hJa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ J z) + (hJ0 : ∀ᶠ z in stripInfinity,J z≠0) + (hJr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re) + (hJd : Tendsto (fun z => deriv J z/J z) stripInfinity (𝓝 0)) + (hJdd : Tendsto (fun z => deriv (deriv J) z/deriv J z) stripInfinity (𝓝 0)) + (hJl : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 0)) + (hJm : ∃ A : ℝ,MonotoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A)) + (hqa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ (fun z => deriv J z/J z) z) + (hqne : ∀ᶠ z in stripInfinity,deriv J z/J z≠0) + (hqd : Tendsto (fun z => deriv (fun z => deriv J z/J z) z/(deriv J z/J z)) stripInfinity (𝓝 0)) + (hqr : ∀ᶠ t : ℝ in atTop,(deriv J (t:ℂ)/J (t:ℂ)).im=0 ∧ (deriv J (t:ℂ)/J (t:ℂ)).re<0) + (he : ∀ᶠ z in stripInfinity,‖E z‖≤C*Real.exp (-ε*z.re)) + (hfactor : ∀ᶠ z in stripInfinity,F z/H z=J z*(1+E z)) : + ∃ (T : ℝ) (x : ℂ → ℂ),0 (F (x (r:ℂ))).re) atTop atTop ∧ + (∀ᶠ w in sectorInfinity,AnalyticAt ℂ (fun z => F (x z)) w) ∧ + ∀ (ω : ℝ → ℝ) (S : ℝ),AdmissibleAngularLoss ω → + ∃ (η : ℝ → ℝ) (R : ℝ),AdmissibleAngularLoss η ∧ + (∀ w∈lossSector η R,F (x w)∈lossSector ω S) ∧ + (∀ w∈lossSector η R,(F (x (‖w‖:ℂ))).re/2≤‖F (x w)‖ ∧ + ‖F (x w)‖≤2*(F (x (‖w‖:ℂ))).re) ∧ + (∀ δ : ℝ,0<δ → ∃ U : ℝ,∀ w∈lossSector η U,|(F (x w)).re|≤δ*w.re) := by + obtain ⟨T,x,hT,hxa,hleft,hright,hxr,hxt,hxto,hinc,hxd,V,hphase⟩ := + equal_exponent_inward hb hHa hH0 hHr hHt hHd hJa hJ0 hJr hqa hqne hqd hqr + (hJd.comp tendsto_real_stripInfinity) + have hxr' : ∀ᶠ r : ℝ in atTop,(x (r:ℂ)).im=0 := (eventually_gt_atTop T).mono fun r hr => hxr r hr + have hdom : ∀ᶠ w in sectorInfinity,0 hxa w hw + have hi : ∀ δ : ℝ,0<δ → ∀ᶠ w in sectorInfinity, + ‖x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)‖≤δ*|w.arg| := by + intro δ hδ + obtain ⟨U,hU⟩ := hinc δ hδ + filter_upwards [SectorEventually.realpart_pos,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop U)] with w hw hUw + exact hU w hw hUw + have hi1 : ∃ U : ℝ,∀ w : ℂ,0 D*Real.exp (-ε*(x (r:ℂ)).re) + have hep (r : ℝ) : 0 by simp [he] at hw) hj + have hVarg : ∀ᶠ w in sectorInfinity,|(w*J (x w)).arg|≤|w.arg| := by + filter_upwards [SectorEventually.realpart_pos,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop V)] with w hw hwV + exact hphase w hw hwV + have hclose : ∀ᶠ w in sectorInfinity,‖F (x w)/(w*J (x w))-1‖≤|e ‖w‖| := by + filter_upwards [hdom,hxto.eventually hfactor,hxto.eventually hJ0,hEbound] with w hw hf hj he + rw [hleft w hw.1 hw.2] at hf + have hw0 : w≠0 := fun hz => by simpa [hz] using hw.1 + have hh : F (x w)/(w*J (x w))-1=E (x w) := by + have hf' := (div_eq_iff hw0).mp hf + rw [hf'] + field_simp + ring + rw [hh,abs_of_pos (hep ‖w‖)] + exact he + have harg := inward_phase_small_perturbation hV0 hVarg het hclose + have hri : ∀ᶠ r : ℝ in atTop,H ((x (r:ℂ)).re:ℂ)=(r:ℂ) := by + filter_upwards [hxr',eventually_gt_atTop T] with r hr hrt + have heq : x (r:ℂ)=((x (r:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hr) + rw [←heq] + exact hleft (r:ℂ) (by simpa using hT.trans hrt) + (by simpa only [Complex.norm_of_nonneg (hT.trans hrt).le] using hrt) + have hsmall := inverse_exponential_loss_absorption hb hε + (tendsto_real_stripInfinity.eventually hHa) hHr (hHd.comp tendsto_real_stripInfinity) + hxt hri admissible_baseLoss (2*D) 1 zero_lt_one + have hemajor : ∀ᶠ r : ℝ in atTop,|2*e r|≤baseLoss r := by + filter_upwards [hsmall] with r hr + rw [abs_of_pos (mul_pos (by norm_num) (hep r))] + simpa only [one_mul,mul_assoc,e] using hr + have harg' : ∀ᶠ w in sectorInfinity,|(F (x w)).arg|≤|w.arg|+|2*e ‖w‖| := by + filter_upwards [harg] with w hw + simpa only [abs_mul,abs_of_pos (show (0:ℝ)<2 by norm_num)] using hw + have hJd0 : ∀ᶠ z in stripInfinity,deriv J z≠0 := hqne.mono fun z hz => (div_ne_zero_iff.mp hz).1 + obtain ⟨θ,hθ,hsep⟩ := equal_exponent_realpart_separation hb hε hC hxr' hxt hi1 hleft + (tendsto_real_sectorInfinity.eventually hxa') (hxd.comp tendsto_real_sectorInfinity) + (tendsto_real_stripInfinity.eventually hHa) hHr (hHd.comp tendsto_real_stripInfinity) + hJa hJ0 hJd (hJr.mono fun _ h => h.1) hJl hJd0 hJdd hJm he hfactor + refine ⟨T,x,hT,hxa,hleft,hright,hxto,hxr'.and hGreal,hGft,hGa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hmap⟩ := comparable_sector_mapping hGft hψ hψa hψd hmod harg' + admissible_baseLoss hemajor ω S hω + obtain ⟨κ,U,hκ,hmod'⟩ := hmod + refine ⟨fun r => max (η r) (max (κ r) (θ r)),max R U,hη.max (hκ.max hθ),?_,?_,?_⟩ + · intro w hw + exact hmap w ⟨(le_max_left _ _).trans_lt hw.1,hw.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩ + · intro w hw + exact hmod' w ⟨(le_max_right _ _).trans_lt hw.1, + hw.2.trans_le (sub_le_sub_left ((le_max_left _ _).trans (le_max_right _ _)) _)⟩ + · intro δ hδ + obtain ⟨W,hW⟩ := hsep δ hδ + exact ⟨W,fun w hw => hW w ⟨hw.1,hw.2.trans_le + (sub_le_sub_left ((le_max_right _ _).trans (le_max_right _ _)) _)⟩⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem inverse_error_absorption {J H x : ℂ → ℂ} {b ε c M : ℝ} + (hb : 0 deriv (deriv J) z/deriv J z) stripInfinity (𝓝 0)) + (hJl : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 c)) + (hJm : ∃ A : ℝ,MonotoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A)) + (hxa : ∀ᶠ r : ℝ in atTop,AnalyticAt ℂ x (r:ℂ)) + (hxd : Tendsto (fun r : ℝ => (r:ℂ)*deriv x (r:ℂ)) atTop (𝓝 ((b:ℂ)⁻¹))) + (hHa : ∀ᶠ s : ℝ in atTop,AnalyticAt ℂ H (s:ℂ)) + (hHr : ∀ᶠ s : ℝ in atTop,(H (s:ℂ)).im=0 ∧ 0<(H (s:ℂ)).re) + (hHd : Tendsto (fun s : ℝ => deriv H (s:ℂ)/H (s:ℂ)) atTop (𝓝 (b:ℂ))) + (hxt : Tendsto (fun r : ℝ => (x (r:ℂ)).re) atTop atTop) + (hinv : ∀ᶠ r : ℝ in atTop,H ((x (r:ℂ)).re:ℂ)=(r:ℂ)) : + ∃ ω : ℝ → ℝ,AdmissibleAngularLoss ω ∧ + ∀ δ : ℝ,0<δ → ∀ᶠ r : ℝ in atTop, + |M*(‖deriv J ((x (r:ℂ)).re:ℂ)‖+Real.exp (-ε*(x (r:ℂ)).re))|≤δ*ω r := by + obtain ⟨ω,hω,hds⟩ := inverse_derivative_loss_absorption hb hJa hJr hJd0 hJdd hJl hJm hxa hxd + have hes := inverse_exponential_loss_absorption hb hε hHa hHr hHd hxt hinv hω M + refine ⟨ω,hω,?_⟩ + intro δ hδ + filter_upwards [hds (δ/(2*M)) (by positivity),hes (δ/2) (by positivity)] with r hd he + rw [abs_of_nonneg (show 0≤M*(‖deriv J ((x (r:ℂ)).re:ℂ)‖+Real.exp (-ε*(x (r:ℂ)).re)) by positivity)] + have hh := mul_le_mul_of_nonneg_left hd hM.le + have hkeq : M*(δ/(2*M)*ω r)=δ/2*ω r := by field_simp + rw [hkeq] at hh + nlinarith only [hh,he] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma strict_loss_tendsto_zero {e ω : ℝ → ℝ} (hω : AdmissibleAngularLoss ω) + (he : ∀ δ : ℝ,0<δ → ∀ᶠ r : ℝ in atTop,|e r|≤δ*ω r) : + Tendsto e atTop (𝓝 0) := by + apply tendsto_zero_iff_norm_tendsto_zero.mpr + apply squeeze_zero' (Eventually.of_forall (fun r => norm_nonneg (e r))) _ hω.tendsto_zero + simpa only [Real.norm_eq_abs,one_mul] using he 1 zero_lt_one + +theorem positive_limit_phase {F : ℂ → ℂ} {a e ω : ℝ → ℝ} {c : ℝ} + (hc : 0 by simp [he] at hr) + have hVarg : ∀ᶠ z in sectorInfinity,|((a ‖z‖:ℂ)*z).arg|≤|z.arg| := by + filter_upwards [tendsto_norm_sectorInfinity.eventually hap] with z hz + rw [Complex.arg_real_mul _ (show 0 (2/c)*e r + have hdt : Tendsto d atTop (𝓝 0) := by + simpa only [d,mul_zero] using (strict_loss_tendsto_zero hω he).const_mul (2/c) + have hclose : ∀ᶠ z in sectorInfinity,‖F z/((a ‖z‖:ℂ)*z)-1‖≤|d ‖z‖| := by + filter_upwards [heq,tendsto_norm_sectorInfinity.eventually hap,SectorEventually.realpart_pos] with z hz ha hr + change 0 by simp [he] at hr + have hap : 0 (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hFd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 (b:ℂ))) + (hHd : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) + (hJa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ J z) + (hJ0 : ∀ᶠ z in stripInfinity,J z≠0) + (hJr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) + (hJd : Tendsto (fun z => deriv J z/J z) stripInfinity (𝓝 0)) + (hJd0 : ∀ᶠ z in stripInfinity,deriv J z≠0) + (hJdd : Tendsto (fun z => deriv (deriv J) z/deriv J z) stripInfinity (𝓝 0)) + (hJl : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 c)) + (hJm : ∃ A : ℝ,MonotoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A)) + (he : ∀ᶠ z in stripInfinity,‖E z‖≤C*Real.exp (-ε*z.re)) + (hfactor : ∀ᶠ z in stripInfinity,F z/H z=J z*(1+E z)) : + ∃ (T : ℝ) (x : ℂ → ℂ),0 (F (x (r:ℂ))).re) atTop atTop ∧ + (∀ᶠ w in sectorInfinity,AnalyticAt ℂ (fun z => F (x z)) w) ∧ + ∀ (ω : ℝ → ℝ) (S : ℝ),AdmissibleAngularLoss ω → + ∃ (η : ℝ → ℝ) (R : ℝ),AdmissibleAngularLoss η ∧ + (∀ w∈lossSector η R,F (x w)∈lossSector ω S) ∧ + (∀ w∈lossSector η R,(F (x (‖w‖:ℂ))).re/2≤‖F (x w)‖ ∧ + ‖F (x w)‖≤2*(F (x (‖w‖:ℂ))).re) := by + obtain ⟨T,hT,x,hxa,hleft,hright,hxr,hxt,hxto,hinc,hxd⟩ := + positive_exponential_inverse_asymptotic hb hHa hH0 hHr hHt hHd + have hxr' : ∀ᶠ r : ℝ in atTop,(x (r:ℂ)).im=0 := (eventually_gt_atTop T).mono fun r hr => hxr r hr + have hdom : ∀ᶠ w in sectorInfinity,0 hxa w hw + have hi : ∀ δ : ℝ,0<δ → ∀ᶠ w in sectorInfinity, + ‖x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)‖≤δ*|w.arg| := by + intro δ hδ + obtain ⟨U,hU⟩ := hinc δ hδ + filter_upwards [SectorEventually.realpart_pos,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop U)] with w hw hUw + exact hU w hw hUw + have hi1 : ∃ U : ℝ,∀ w : ℂ,0 (abs_of_pos hr.1).le + refine ⟨T,x,hT,hxa,hleft,hright,hxto,hxr'.and hGreal,hGft,hGa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hmap⟩ := comparable_sector_mapping hGft hψ hψa hψd hmod harg' hχ hχbound ω S hω + obtain ⟨κ,V,hκ,hmod'⟩ := hmod + exact ⟨fun r => max (η r) (κ r),max R V,hη.max hκ, + fun w hw => hmap w ⟨(le_max_left _ _).trans_lt hw.1,hw.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩, + fun w hw => hmod' w ⟨(le_max_right _ _).trans_lt hw.1,hw.2.trans_le (sub_le_sub_left (le_max_right _ _) _)⟩⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem constant_equal_exponent_chart {F H E : ℂ → ℂ} {b ε C c : ℝ} + (hb : 0 (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hFd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 (b:ℂ))) + (hHd : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) + (he : ∀ᶠ z in stripInfinity,‖E z‖≤C*Real.exp (-ε*z.re)) + (hfactor : ∀ᶠ z in stripInfinity,F z/H z=(c:ℂ)*(1+E z)) : + ∃ (T : ℝ) (x : ℂ → ℂ),0 (F (x (r:ℂ))).re) atTop atTop ∧ + (∀ᶠ w in sectorInfinity,AnalyticAt ℂ (fun z => F (x z)) w) ∧ + ∀ (ω : ℝ → ℝ) (S : ℝ),AdmissibleAngularLoss ω → + ∃ (η : ℝ → ℝ) (R : ℝ),AdmissibleAngularLoss η ∧ + (∀ w∈lossSector η R,F (x w)∈lossSector ω S) ∧ + (∀ w∈lossSector η R,(F (x (‖w‖:ℂ))).re/2≤‖F (x w)‖ ∧ + ‖F (x w)‖≤2*(F (x (‖w‖:ℂ))).re) := by + obtain ⟨T,hT,x,hxa,hleft,hright,hxr,hxt,hxto,hinc,hxd⟩ := + positive_exponential_inverse_asymptotic hb hHa hH0 hHr hHt hHd + have hxr' : ∀ᶠ r : ℝ in atTop,(x (r:ℂ)).im=0 := (eventually_gt_atTop T).mono fun r hr => hxr r hr + have hdom : ∀ᶠ w in sectorInfinity,0 hxa w hw + have hi : ∀ δ : ℝ,0<δ → ∀ᶠ w in sectorInfinity, + ‖x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)‖≤δ*|w.arg| := by + intro δ hδ + obtain ⟨U,hU⟩ := hinc δ hδ + filter_upwards [SectorEventually.realpart_pos,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop U)] with w hw hUw + exact hU w hw hUw + have hi1 : ∃ U : ℝ,∀ w : ℂ,0 c*D*Real.exp (-ε*(x (r:ℂ)).re) + have hes : ∀ δ : ℝ,0<δ → ∀ᶠ r : ℝ in atTop,|e r|≤δ*baseLoss r := by + intro δ hδ + have hh := inverse_exponential_loss_absorption hb hε + (tendsto_real_stripInfinity.eventually hHa) hHr (hHd.comp tendsto_real_stripInfinity) + hxt hri admissible_baseLoss (c*D) δ hδ + filter_upwards [hh] with r hr + simpa only [e,abs_of_pos (show 0 (abs_of_pos hr.1).le + refine ⟨T,x,hT,hxa,hleft,hright,hxto,hxr'.and hGreal,hGft,hGa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hmap⟩ := comparable_sector_mapping hGft hψ hψa hψd hmod harg' hχ hχbound ω S hω + obtain ⟨κ,V,hκ,hmod'⟩ := hmod + exact ⟨fun r => max (η r) (κ r),max R V,hη.max hκ, + fun w hw => hmap w ⟨(le_max_left _ _).trans_lt hw.1,hw.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩, + fun w hw => hmod' w ⟨(le_max_right _ _).trans_lt hw.1,hw.2.trans_le (sub_le_sub_left (le_max_right _ _) _)⟩⟩ + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ExpansionAlgebra.lean b/lean/OAI/Analysis/PathSelection/ExpansionAlgebra.lean new file mode 100644 index 0000000000000000000000000000000000000000..ad507b0e942f496f79c1f54182f9c8b64d17ec28 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ExpansionAlgebra.lean @@ -0,0 +1,414 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockExpansions + +namespace OAI + +/-! Algebraic operations, shifts and leading terms of clock expansions. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +attribute [local instance] Classical.propDecidable +namespace DegeneratingTrees.Clock + +lemma SectorExpansion.const (c : ℂ) : SectorExpansion (fun _ => c) {0} (fun _ _ => c) := by + classical + have hfin (B : ℝ) : (({0}:Set ℝ) ∩ Ici B).Finite := (finite_singleton 0).inter_of_left _ + refine ⟨(finite_singleton 0).bddAbove,hfin,?_⟩ + intro B + obtain ⟨ω,R,hω,hre⟩ := SectorEventually.realpart_pos + by_cases hB : B ≤ 0 + · have he : (hfin B).toFinset = {0} := by ext x; simp [hB] + refine ⟨ω,R,1,0,hω,by norm_num,le_rfl,fun _ _ => analyticAt_const,?_⟩ + intro z hz + rw [he] + simp + · have hB : 0 < B := lt_of_not_ge hB + have he : (hfin B).toFinset = ∅ := by ext x; simp; intro h; subst x; linarith + refine ⟨ω,R,B/2,‖c‖,hω,by positivity,norm_nonneg _,fun _ _ => analyticAt_const,?_⟩ + intro z hz + simp only [he,Finset.sum_empty,sub_zero] + calc + ‖c‖ = ‖c‖*1 := (mul_one _).symm + _ ≤ ‖c‖*Real.exp ((B-B/2)*z.re) := mul_le_mul_of_nonneg_left + (Real.one_le_exp_iff.mpr (by nlinarith [hre z hz])) (norm_nonneg _) + +lemma SectorExpansion.neg {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) : SectorExpansion (fun z => -f z) E (fun β z => -b β z) := by + classical + refine ⟨h.bounded_above,h.finite_above,?_⟩ + intro B + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hb⟩ := h.remainders B + refine ⟨ω,R,ε,C,hω,hε,hC,fun z hz => (hf z hz).neg,?_⟩ + intro z hz + simpa only [mul_neg,Finset.sum_neg_distrib,neg_sub_neg,norm_sub_rev] using hb z hz + +private lemma sum_indicator {E U : Set ℝ} (B : ℝ) + (hE : (E ∩ Ici B).Finite) (hU : (U ∩ Ici B).Finite) (hsub : E ⊆ U) + (b : ℝ → ℂ → ℂ) (z : ℂ) : + (∑ β ∈ hU.toFinset,Complex.exp ((β:ℂ)*z)*(if β ∈ E then b β z else 0)) = + ∑ β ∈ hE.toFinset,Complex.exp ((β:ℂ)*z)*b β z := by + classical + have hs : hE.toFinset ⊆ hU.toFinset := by + intro β hβ + exact hU.mem_toFinset.mpr ⟨hsub (hE.mem_toFinset.mp hβ).1,(hE.mem_toFinset.mp hβ).2⟩ + calc + _ = ∑ β ∈ hE.toFinset,Complex.exp ((β:ℂ)*z)*(if β ∈ E then b β z else 0) := by + symm + apply Finset.sum_subset hs + intro β hβ hn + have hnot : β ∉ E := by + intro he + exact hn (hE.mem_toFinset.mpr ⟨he,(hU.mem_toFinset.mp hβ).2⟩) + simp only [ite_eq_right hnot,mul_zero] + _ = _ := Finset.sum_congr rfl (fun β hβ => by rw [ite_eq_left (hE.mem_toFinset.mp hβ).1]) + +lemma SectorExpansion.add {f g : ℂ → ℂ} {E F : Set ℝ} {b c : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) (hg : SectorExpansion g F c) : + SectorExpansion (fun z => f z+g z) (E ∪ F) + (fun β z => (if β ∈ E then b β z else 0)+(if β ∈ F then c β z else 0)) := by + classical + have hfin (B : ℝ) : ((E ∪ F) ∩ Ici B).Finite := by + have h := (hf.finite_above B).union (hg.finite_above B) + exact h.subset (by intro x hx; rcases hx.1 with h | h; exact Or.inl ⟨h,hx.2⟩; exact Or.inr ⟨h,hx.2⟩) + refine ⟨hf.bounded_above.union hg.bounded_above,hfin,?_⟩ + intro B + obtain ⟨ω,R,ε,C,hω,hε,hC,hfa,hfb⟩ := hf.remainders B + obtain ⟨η,S,δ,D,hη,hδ,hD,hga,hgb⟩ := hg.remainders B + have h1 : SectorEventually (fun z => z ∈ lossSector ω R) := ⟨ω,R,hω,fun _ h => h⟩ + have h2 : SectorEventually (fun z => z ∈ lossSector η S) := ⟨η,S,hη,fun _ h => h⟩ + obtain ⟨ν,T,hν,hboth⟩ := h1.and (h2.and SectorEventually.realpart_pos) + refine ⟨ν,T,min ε δ,C+D,hν,lt_min hε hδ,add_nonneg hC hD,?_,?_⟩ + · intro z hz + exact (hfa z (hboth z hz).1).add (hga z (hboth z hz).2.1) + · intro z hz + have hsum : (∑ β ∈ (hfin B).toFinset, Complex.exp ((β:ℂ)*z)* + ((if β ∈ E then b β z else 0)+(if β ∈ F then c β z else 0))) = + (∑ β ∈ (hf.finite_above B).toFinset,Complex.exp ((β:ℂ)*z)*b β z)+ + (∑ β ∈ (hg.finite_above B).toFinset,Complex.exp ((β:ℂ)*z)*c β z) := by + simp only [mul_add,Finset.sum_add_distrib] + rw [sum_indicator B (hf.finite_above B) (hfin B) subset_union_left, + sum_indicator B (hg.finite_above B) (hfin B) subset_union_right] + rw [hsum] + have he : B-ε ≤ B-min ε δ := by linarith [min_le_left ε δ] + have hd : B-δ ≤ B-min ε δ := by linarith [min_le_right ε δ] + have he' := Real.exp_le_exp.mpr (mul_le_mul_of_nonneg_right he (hboth z hz).2.2.le) + have hd' := Real.exp_le_exp.mpr (mul_le_mul_of_nonneg_right hd (hboth z hz).2.2.le) + have hb1 := (hfb z (hboth z hz).1).trans (mul_le_mul_of_nonneg_left he' hC) + have hb2 := (hgb z (hboth z hz).2.1).trans (mul_le_mul_of_nonneg_left hd' hD) + calc + ‖f z+g z-((∑ β ∈ (hf.finite_above B).toFinset,Complex.exp ((β:ℂ)*z)*b β z)+ + (∑ β ∈ (hg.finite_above B).toFinset,Complex.exp ((β:ℂ)*z)*c β z))‖ = + ‖(f z-(∑ β ∈ (hf.finite_above B).toFinset,Complex.exp ((β:ℂ)*z)*b β z))+ + (g z-(∑ β ∈ (hg.finite_above B).toFinset,Complex.exp ((β:ℂ)*z)*c β z))‖ := by congr 1; ring + _ ≤ _ := (norm_add_le _ _).trans (by nlinarith) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma ExpSmall.mul_slow {B : ℝ} {f g : ℂ → ℂ} (hf : ExpSmall B f) (hg : SectorSlow g) : + ExpSmall B (fun z => f z*g z) := by + obtain ⟨a,ha,hf⟩ := hf + exact ⟨a+(B-a)/2,by linarith,hf.mul (hg ((B-a)/2) (by linarith))⟩ + +lemma SectorExpansion.mul_lower {f g : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) (hg : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ g z) + (hgs : SectorSlow g) : SectorExpansion (fun z => f z*g z) E (fun β z => b β z*g z) := by + apply SectorExpansion.of_expSmall hf.bounded_above hf.finite_above + · filter_upwards [hf.eventually_analytic,hg] with z hzf hzg + exact hzf.mul hzg + · intro B + convert (hf.expSmall_remainder B).mul_slow hgs using 1 + funext z + rw [sub_mul,Finset.sum_mul] + congr 1 + apply Finset.sum_congr rfl + intro β hβ + ring + +def translatedSupport (a : ℝ) (E : Set ℝ) : Set ℝ := (fun β => a+β) '' E + +lemma translatedSupport_bddAbove (a : ℝ) {E : Set ℝ} (hE : BddAbove E) : + BddAbove (translatedSupport a E) := by + obtain ⟨A,hA⟩ := hE + refine ⟨a+A,?_⟩ + rintro _ ⟨β,hβ,rfl⟩ + change a+β ≤ a+A + linarith [hA hβ] + +lemma translatedSupport_finite (a : ℝ) {E : Set ℝ} + (hE : ∀ B : ℝ,(E ∩ Ici B).Finite) (B : ℝ) : + (translatedSupport a E ∩ Ici B).Finite := by + apply ((hE (B-a)).image (fun β => a+β)).subset + rintro _ ⟨⟨β,hβ,rfl⟩,hB⟩ + exact ⟨β,⟨hβ,by change B-a≤β; change B≤a+β at hB; linarith⟩,rfl⟩ + +lemma translated_truncation (a : ℝ) {E : Set ℝ} + (hE : ∀ B : ℝ,(E ∩ Ici B).Finite) (b : ℝ → ℂ → ℂ) (B : ℝ) (z : ℂ) : + (∑ β ∈ (translatedSupport_finite a hE B).toFinset,Complex.exp ((β:ℂ)*z)*b (β-a) z) = + Complex.exp ((a:ℂ)*z)*(∑ β ∈ (hE (B-a)).toFinset,Complex.exp ((β:ℂ)*z)*b β z) := by + classical + rw [Finset.mul_sum] + symm + apply Finset.sum_bij (fun β _ => a+β) + · intro β hβ + have hh := (hE (B-a)).mem_toFinset.mp hβ + refine (translatedSupport_finite a hE B).mem_toFinset.mpr ⟨⟨β,hh.1,rfl⟩,?_⟩ + change B≤a+β + have : B-a≤β := hh.2 + linarith + · intro β hβ γ hγ he + exact add_left_cancel he + · intro γ hγ + obtain ⟨⟨β,hβ,rfl⟩,hB⟩ := (translatedSupport_finite a hE B).mem_toFinset.mp hγ + refine ⟨β,(hE (B-a)).mem_toFinset.mpr ⟨hβ,?_⟩,rfl⟩ + change B-a≤β + change B≤a+β at hB + linarith + · intro β hβ + simp only [add_sub_cancel_left,Complex.ofReal_add,add_mul,Complex.exp_add] + ring + +lemma SectorExpansion.exp_shift {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) (a : ℝ) : + SectorExpansion (fun z => Complex.exp ((a:ℂ)*z)*f z) (translatedSupport a E) + (fun β => b (β-a)) := by + apply SectorExpansion.of_expSmall (translatedSupport_bddAbove a hf.bounded_above) + (translatedSupport_finite a hf.finite_above) + · filter_upwards [hf.eventually_analytic] with z hz + exact ((analyticAt_const.mul analyticAt_id).cexp).mul hz + · intro B + have hh := (hf.expSmall_remainder (B-a)).mul (ExpBound.cexp a) + simp only [sub_add_cancel] at hh + convert hh using 1 + funext z + rw [translated_truncation a hf.finite_above b B z] + ring + +lemma SectorExpansion.single (a : ℝ) {b : ℂ → ℂ} + (hb : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ b z) (hs : SectorSlow b) : + SectorExpansion (fun z => Complex.exp ((a:ℂ)*z)*b z) {a} (fun _ => b) := by + classical + apply SectorExpansion.of_expSmall bddAbove_singleton (fun _ => (finite_singleton a).inter_of_left _) + · filter_upwards [hb] with z hz + exact ((analyticAt_const.mul analyticAt_id).cexp).mul hz + · intro B + by_cases hB : B≤a + · have he : ((finite_singleton a).inter_of_left (Ici B)).toFinset={a} := by + ext β + simp only [Set.Finite.mem_toFinset,mem_inter_iff,mem_singleton_iff,mem_Ici,Finset.mem_singleton] + exact ⟨And.left,fun h => ⟨h,h ▸ hB⟩⟩ + simp only [he,Finset.sum_singleton,sub_self] + exact ExpSmall.zero B + · have he : ((finite_singleton a).inter_of_left (Ici B)).toFinset=∅ := by + ext β + simp only [Set.Finite.mem_toFinset,mem_inter_iff,mem_singleton_iff,mem_Ici,Finset.notMem_empty,iff_false] + rintro ⟨rfl,hh⟩ + exact hB hh + simpa only [he,Finset.sum_empty,sub_zero] using hs.expSmall (lt_of_not_ge hB) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma SectorExpansion.erase {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) {β : ℝ} (hβ : β ∈ E) + (hba : ∀ᶠ z in sectorInfinity, AnalyticAt ℂ (b β) z) (hbs : SectorSlow (b β)) : + SectorExpansion (fun z => f z-Complex.exp ((β:ℂ)*z)*b β z) (E \ {β}) b := by + classical + have hfin (B : ℝ) : ((E \ {β}) ∩ Ici B).Finite := + (hf.finite_above B).subset (fun _ hx => ⟨hx.1.1,hx.2⟩) + apply SectorExpansion.of_expSmall (hf.bounded_above.mono (sdiff_subset)) hfin + · filter_upwards [hf.eventually_analytic,hba] with z hzf hzb + exact hzf.sub (((analyticAt_const.mul analyticAt_id).cexp).mul hzb) + · intro B + have hs : (hfin B).toFinset = (hf.finite_above B).toFinset.erase β := by + ext γ + simp only [Set.Finite.mem_toFinset,Finset.mem_erase,mem_inter_iff,Set.mem_sdiff, + mem_singleton_iff] + tauto + rw [hs] + by_cases hB : B≤β + · have hm : β ∈ (hf.finite_above B).toFinset := + (hf.finite_above B).mem_toFinset.mpr ⟨hβ,hB⟩ + convert hf.expSmall_remainder B using 1 + funext z + have he := Finset.sum_erase_add (s := (hf.finite_above B).toFinset) + (fun γ => Complex.exp ((γ:ℂ)*z)*b γ z) hm + rw [←he] + ring + · have hm : β ∉ (hf.finite_above B).toFinset := by + intro hh + exact hB ((hf.finite_above B).mem_toFinset.mp hh).2 + rw [Finset.erase_eq_of_notMem hm] + convert (hf.expSmall_remainder B).sub (hbs.expSmall (lt_of_not_ge hB)) using 1 + funext z + ring + +lemma strict_negative_support_gap {E : Set ℝ} + (hEl : ∀ B : ℝ,(E ∩ Ici B).Finite) (hE : ∀ β ∈ E,β<0) : + ∃ δ : ℝ,0<δ ∧ ∀ β ∈ E,β≤ -δ := by + rcases E.eq_empty_or_nonempty with rfl | hne + · exact ⟨1,zero_lt_one,by simp⟩ + · obtain ⟨β,hβ,hmax⟩ := exists_greatest_of_finite_above hEl hne + exact ⟨-β,neg_pos.mpr (hE β hβ),by simpa only [neg_neg] using hmax⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +open scoped BigOperators +namespace DegeneratingTrees.Clock + +def nonzeroRaySupport (E : Set ℝ) (b : ℝ → ℂ → ℂ) : Set ℝ := + {β | β ∈ E ∧ ¬ (∀ᶠ x : ℝ in atTop, b β (x:ℂ)=0)} + +lemma SectorExpansion.trim_zero {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) + (ha : ∀ β ∈ E, SectorEventually (fun z => AnalyticAt ℂ (b β) z)) : + SectorExpansion f (nonzeroRaySupport E b) b := by + classical + have hsub : nonzeroRaySupport E b ⊆ E := fun _ hx => hx.1 + have hfin (B : ℝ) : (nonzeroRaySupport E b ∩ Ici B).Finite := + (h.finite_above B).subset (fun _ hx => ⟨hx.1.1,hx.2⟩) + refine ⟨h.bounded_above.mono hsub,hfin,?_⟩ + intro B + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hrem⟩ := h.remainders B + have hbase : SectorEventually (fun _ => True) := ⟨ω,R,hω,fun _ _ => True.intro⟩ + have hz : SectorEventually (fun z => ∀ β ∈ (h.finite_above B).toFinset, + β ∉ nonzeroRaySupport E b → b β z=0) := by + apply SectorEventually.finset_forall _ hbase + intro β hβ + have hβE := ((h.finite_above B).mem_toFinset.mp hβ).1 + by_cases hzero : ∀ᶠ x : ℝ in atTop, b β (x:ℂ)=0 + · obtain ⟨η,S,hη,hba⟩ := ha β hβE + exact (sector_zero_of_ray_zero hη hba hzero).mono (by tauto) + · exact hbase.mono (fun z _ hn => (hn ⟨hβE,hzero⟩).elim) + obtain ⟨η,S,hη,hboth⟩ := hz.and (show SectorEventually (fun z => z ∈ lossSector ω R) + from ⟨ω,R,hω,fun _ hz => hz⟩) + refine ⟨η,S,ε,C,hη,hε,hC,fun z hz => hf z (hboth z hz).2,?_⟩ + intro z hz + have hs : (hfin B).toFinset ⊆ (h.finite_above B).toFinset := by + intro β hβ + have hh := (hfin B).mem_toFinset.mp hβ + exact (h.finite_above B).mem_toFinset.mpr ⟨hh.1.1,hh.2⟩ + have he : (∑ β ∈ (hfin B).toFinset, Complex.exp ((β:ℂ)*z)*b β z) = + ∑ β ∈ (h.finite_above B).toFinset, Complex.exp ((β:ℂ)*z)*b β z := by + apply Finset.sum_subset hs + intro β hβ hn + have hn' : β ∉ nonzeroRaySupport E b := by + intro hh + apply hn + exact (hfin B).mem_toFinset.mpr ⟨hh,((h.finite_above B).mem_toFinset.mp hβ).2⟩ + rw [(hboth z hz).1 β hβ hn',mul_zero] + rw [he] + exact hrem z (hboth z hz).2 + + + +theorem SectorExpansion.leading_or_zero_general {f : ℂ → ℂ} {E : Set ℝ} + {b : ℝ → ℂ → ℂ} (h : SectorExpansion f E b) + (ha : ∀ β ∈ E, SectorEventually (fun z => AnalyticAt ℂ (b β) z)) + (hc : ∀ β ∈ E, (∀ᶠ x : ℝ in atTop, b β (x:ℂ)=0) ∨ + ((∀ᶠ x : ℝ in atTop, b β (x:ℂ) ≠ 0) ∧ + Subexponential atTop id (fun x : ℝ => (b β (x:ℂ))⁻¹))) : + (fun x : ℝ => f (x:ℂ)) =ᶠ[atTop] 0 ∨ + ∃ β ∈ E, (∀ᶠ x : ℝ in atTop, b β (x:ℂ) ≠ 0) ∧ + Tendsto (fun x : ℝ => (Real.exp (-β*x):ℂ)*(b β (x:ℂ))⁻¹*f (x:ℂ)) + atTop (𝓝 1) := by + have h' := h.trim_zero ha + have hb : ∀ β ∈ nonzeroRaySupport E b, (∀ᶠ x : ℝ in atTop, b β (x:ℂ) ≠ 0) ∧ + Subexponential atTop id (fun x : ℝ => (b β (x:ℂ))⁻¹) := by + intro β hβ + exact (hc β hβ.1).resolve_left hβ.2 + rcases h'.leading_or_zero hb with hz | ⟨β,hβ,hgreat,ht⟩ + · exact Or.inl hz + · exact Or.inr ⟨β,hβ.1,(hb β hβ).1,ht⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma SectorExpansion.leading_error {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) {β : ℝ} (hβ : β ∈ E) (hgreat : ∀ γ ∈ E,γ≤β) : + ExpSmall β (fun z => f z-Complex.exp ((β:ℂ)*z)*b β z) := by + classical + have hs : (hf.finite_above β).toFinset={β} := by + ext γ + simp only [Set.Finite.mem_toFinset,mem_inter_iff,mem_Ici,Finset.mem_singleton] + exact ⟨fun h => le_antisymm (hgreat γ h.1) h.2,fun h => by subst γ; exact ⟨hβ,le_rfl⟩⟩ + simpa only [hs,Finset.sum_singleton] using hf.expSmall_remainder β + +lemma ExpSmall.tendsto_zero {f : ℂ → ℂ} (hf : ExpSmall 0 f) : + Tendsto f sectorInfinity (𝓝 0) := by + obtain ⟨a,ha,hf⟩ := hf + exact hf.trans_tendsto (Real.tendsto_exp_atBot.comp + (tendsto_re_sectorInfinity.const_mul_atTop_of_neg ha)) + +lemma SectorExpansion.uniform_leading {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) {β : ℝ} (hβ : β ∈ E) (hgreat : ∀ γ ∈ E,γ≤β) + (hb : ∀ᶠ z in sectorInfinity,b β z≠0) (hs : SectorSlow (fun z => (b β z)⁻¹)) : + ExpSmall 0 (fun z => Complex.exp (((-β:ℝ):ℂ) * z)*(b β z)⁻¹*f z-1) := by + have he := ((hf.leading_error hβ hgreat).mul (ExpBound.cexp (-β))).mul_slow hs + simp only [add_neg_cancel] at he + obtain ⟨exponent,hexponent,hbound⟩ := he + refine ⟨exponent,hexponent,hbound.congr' ?_ (EventuallyEq.refl _ _)⟩ + filter_upwards [hb] with z hz + have hexp : Complex.exp (((-β:ℝ):ℂ) * z)*Complex.exp ((β:ℂ)*z)=1 := by + rw [←Complex.exp_add] + simp + have hn := Complex.exp_ne_zero ((β:ℂ)*z) + have hei : Complex.exp (((-β:ℝ):ℂ) * z)=(Complex.exp ((β:ℂ)*z))⁻¹ := by + apply (mul_right_cancel₀ hn) + rw [hexp,inv_mul_cancel₀ hn] + rw [hei] + field_simp + +lemma SectorExpansion.uniform_leading_tendsto {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) {β : ℝ} (hβ : β ∈ E) (hgreat : ∀ γ ∈ E,γ≤β) + (hb : ∀ᶠ z in sectorInfinity,b β z≠0) (hs : SectorSlow (fun z => (b β z)⁻¹)) : + Tendsto (fun z => Complex.exp (((-β:ℝ):ℂ) * z)*(b β z)⁻¹*f z) sectorInfinity (𝓝 1) := by + simpa only [sub_add_cancel,zero_add] using + (hf.uniform_leading hβ hgreat hb hs).tendsto_zero.add_const 1 + +lemma SectorExpansion.eventually_ne_of_leading {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hf : SectorExpansion f E b) {β : ℝ} (hβ : β ∈ E) (hgreat : ∀ γ ∈ E,γ≤β) + (hb : ∀ᶠ z in sectorInfinity,b β z≠0) (hs : SectorSlow (fun z => (b β z)⁻¹)) : + ∀ᶠ z in sectorInfinity,f z≠0 := by + have ht := hf.uniform_leading_tendsto hβ hgreat hb hs + filter_upwards [ht.eventually_ne (by norm_num : (1:ℂ)≠0)] with z hz + exact fun hfz => hz (by rw [hfz,mul_zero]) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ExponentSupports.lean b/lean/OAI/Analysis/PathSelection/ExponentSupports.lean new file mode 100644 index 0000000000000000000000000000000000000000..cafd80c59e2799fd9e35965127dfd9c876d76fee --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ExponentSupports.lean @@ -0,0 +1,193 @@ +import Mathlib + +namespace OAI + +/-! Locally finite real exponent supports, finite convolution and negative words. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set +namespace DegeneratingTrees.Clock + +def exponentSum (E F : Set ℝ) : Set ℝ := (fun p : ℝ×ℝ => p.1+p.2) '' (E ×ˢ F) +def exponentPairs (E F : Set ℝ) (B : ℝ) : Set (ℝ×ℝ) := + {p | p.1 ∈ E ∧ p.2 ∈ F ∧ B ≤ p.1+p.2} +def exponentFiber (E F : Set ℝ) (δ : ℝ) : Set (ℝ×ℝ) := + {p | p.1 ∈ E ∧ p.2 ∈ F ∧ p.1+p.2=δ} + +lemma exponentPairs_finite {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (hFl : ∀ B : ℝ, (F ∩ Ici B).Finite) (B : ℝ) : + (exponentPairs E F B).Finite := by + obtain ⟨A,hA⟩ := hE + obtain ⟨C,hC⟩ := hF + apply ((hEl (B-C)).prod (hFl (B-A))).subset + intro p hp + exact ⟨⟨hp.1,by change B-C ≤ p.1; have := hC hp.2.1; linarith [hp.2.2]⟩, + ⟨hp.2.1,by change B-A ≤ p.2; have := hA hp.1; linarith [hp.2.2]⟩⟩ + +lemma exponentFiber_finite {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (hFl : ∀ B : ℝ, (F ∩ Ici B).Finite) (δ : ℝ) : + (exponentFiber E F δ).Finite := + (exponentPairs_finite hE hF hEl hFl δ).subset (fun _ hp => ⟨hp.1,hp.2.1,hp.2.2.ge⟩) + +lemma exponentSum_bddAbove {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) : + BddAbove (exponentSum E F) := by + obtain ⟨A,hA⟩ := hE + obtain ⟨C,hC⟩ := hF + refine ⟨A+C,?_⟩ + rintro _ ⟨p,hp,rfl⟩ + exact add_le_add (hA hp.1) (hC hp.2) + +lemma exponentSum_finite {E F : Set ℝ} (hE : BddAbove E) (hF : BddAbove F) + (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (hFl : ∀ B : ℝ, (F ∩ Ici B).Finite) (B : ℝ) : + (exponentSum E F ∩ Ici B).Finite := by + apply ((exponentPairs_finite hE hF hEl hFl B).image (fun p => p.1+p.2)).subset + rintro δ ⟨⟨p,hp,rfl⟩,hB⟩ + exact ⟨p,⟨hp.1,hp.2,hB⟩,rfl⟩ + + + +lemma exponentPairs_subset_rectangle {E F : Set ℝ} {A C B U V : ℝ} + (hA : ∀ β ∈ E, β ≤ A) (hC : ∀ γ ∈ F, γ ≤ C) + (hU : U ≤ B-C) (hV : V ≤ B-A) : + exponentPairs E F B ⊆ (E ∩ Ici U) ×ˢ (F ∩ Ici V) := by + intro p hp + exact ⟨⟨hp.1,by change U ≤ p.1; have := hC _ hp.2.1; linarith [hp.2.2]⟩, + ⟨hp.2.1,by change V ≤ p.2; have := hA _ hp.1; linarith [hp.2.2]⟩⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set +namespace DegeneratingTrees.Clock + +private def prependPair (p : ℝ × List ℝ) : List ℝ := p.1::p.2 +private lemma prependPair_injective : Function.Injective prependPair := by + intro a b h + exact Prod.ext (List.cons.inj h).1 (List.cons.inj h).2 + +def wordsOfLength (S : Finset ℝ) : ℕ → Finset (List ℝ) + | 0 => {[]} + | n+1 => (S ×ˢ wordsOfLength S n).image prependPair + +lemma mem_wordsOfLength {S : Finset ℝ} {n : ℕ} {w : List ℝ} : + w ∈ wordsOfLength S n ↔ w.length=n ∧ ∀ β ∈ w, β ∈ S := by + induction n generalizing w with + | zero => + simp only [wordsOfLength, Finset.mem_singleton, List.length_eq_zero_iff] + constructor + · intro h; subst w; simp + · exact And.left + | succ n ih => + cases w with + | nil => simp [wordsOfLength,prependPair] + | cons β w => + simp only [wordsOfLength,Finset.mem_image,Finset.mem_product] + constructor + · rintro ⟨⟨γ,v⟩,⟨hγ,hv⟩,he⟩ + have hh := List.cons.inj he + dsimp [prependPair] at hh + rcases hh with ⟨rfl,rfl⟩ + exact ⟨by simpa using congrArg Nat.succ (ih.mp hv).1, + by simpa using And.intro hγ (ih.mp hv).2⟩ + · rintro ⟨hlen,hmem⟩ + refine ⟨(β,w),⟨hmem β (by simp),ih.mpr ⟨by simpa using hlen,?_⟩⟩,rfl⟩ + exact fun γ hγ => hmem γ (List.mem_cons_of_mem _ hγ) + +def wordsUpTo (S : Finset ℝ) (N : ℕ) : Finset (List ℝ) := + (Finset.range (N+1)).biUnion (wordsOfLength S) + +lemma mem_wordsUpTo {S : Finset ℝ} {N : ℕ} {w : List ℝ} : + w ∈ wordsUpTo S N ↔ w.length ≤ N ∧ ∀ β ∈ w, β ∈ S := by + simp only [wordsUpTo,Finset.mem_biUnion,Finset.mem_range,mem_wordsOfLength] + constructor + · rintro ⟨n,hn,he,hm⟩ + exact ⟨by omega,hm⟩ + · rintro ⟨hl,hm⟩ + exact ⟨w.length,by omega,rfl,hm⟩ + +def exponentWords (E : Set ℝ) : Set (List ℝ) := {w | ∀ β ∈ w, β ∈ E} +def wordCut (E : Set ℝ) (B : ℝ) : Set (List ℝ) := {w | w ∈ exponentWords E ∧ B ≤ w.sum} +def wordFiber (E : Set ℝ) (β : ℝ) : Set (List ℝ) := {w | w ∈ exponentWords E ∧ w.sum=β} +def wordSupport (E : Set ℝ) : Set ℝ := List.sum '' exponentWords E + +lemma list_sum_le_length {E : Set ℝ} {δ : ℝ} (hE : ∀ β ∈ E, β ≤ -δ) + {w : List ℝ} (hw : w ∈ exponentWords E) : w.sum ≤ -δ*(w.length:ℝ) := by + induction w with + | nil => simp + | cons a w ih => + have ha := hE a (hw a (by simp)) + have hi := ih (fun β hβ => hw β (List.mem_cons_of_mem _ hβ)) + simp only [List.sum_cons,List.length_cons,Nat.cast_add,Nat.cast_one] + nlinarith + +lemma list_sum_le_member {E : Set ℝ} (hE : ∀ β ∈ E, β ≤ 0) + {w : List ℝ} (hw : w ∈ exponentWords E) {β : ℝ} (hβ : β ∈ w) : w.sum ≤ β := by + induction w with + | nil => simp at hβ + | cons a w ih => + have hwa : ∀ γ ∈ w, γ ∈ E := fun γ hγ => hw γ (List.mem_cons_of_mem _ hγ) + have hw0 : w.sum ≤ 0 := by + simpa using list_sum_le_length (δ := 0) (by simpa using hE) hwa + rcases List.mem_cons.mp hβ with rfl | hβ + · simpa only [List.sum_cons] using add_le_of_nonpos_right hw0 + · have hi := ih hwa hβ + have ha := hE a (hw a (by simp)) + simp only [List.sum_cons] + linarith + +lemma wordCut_subset_words {E : Set ℝ} {δ B : ℝ} {N : ℕ} (hδ : 0 < δ) + (hE : ∀ β ∈ E, β ≤ -δ) (hEl : (E ∩ Ici B).Finite) + (hN : -δ*((N:ℝ)+1) < B) : + wordCut E B ⊆ (wordsUpTo hEl.toFinset N : Set (List ℝ)) := by + intro w hw + apply mem_wordsUpTo.mpr + constructor + · have hs := list_sum_le_length hE hw.1 + have hlen : (w.length:ℝ) < (N:ℝ)+1 := by + have hB : B ≤ w.sum := hw.2 + nlinarith + exact Nat.lt_succ_iff.mp (by exact_mod_cast hlen) + · intro β hβ + exact hEl.mem_toFinset.mpr ⟨hw.1 β hβ,hw.2.trans + (list_sum_le_member (fun γ hγ => (hE γ hγ).trans (by linarith)) hw.1 hβ)⟩ + +lemma wordCut_finite {E : Set ℝ} {δ : ℝ} (hδ : 0 < δ) + (hE : ∀ β ∈ E, β ≤ -δ) (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (B : ℝ) : + (wordCut E B).Finite := by + obtain ⟨N,hN⟩ := exists_nat_gt (-B/δ) + have hN' : -δ*((N:ℝ)+1) < B := by + have hn := (div_lt_iff₀ hδ).mp hN + nlinarith + exact (wordsUpTo (hEl B).toFinset N).finite_toSet.subset + (wordCut_subset_words hδ hE (hEl B) hN') + +lemma wordFiber_finite {E : Set ℝ} {δ : ℝ} (hδ : 0 < δ) + (hE : ∀ β ∈ E, β ≤ -δ) (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (β : ℝ) : + (wordFiber E β).Finite := + (wordCut_finite hδ hE hEl β).subset (fun _ hw => ⟨hw.1,hw.2.ge⟩) + +lemma wordSupport_bddAbove {E : Set ℝ} {δ : ℝ} (hδ : 0 ≤ δ) + (hE : ∀ β ∈ E, β ≤ -δ) : BddAbove (wordSupport E) := by + refine ⟨0,?_⟩ + rintro _ ⟨w,hw,rfl⟩ + exact (list_sum_le_length hE hw).trans (mul_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr hδ) (by positivity)) + +lemma wordSupport_finite {E : Set ℝ} {δ : ℝ} (hδ : 0 < δ) + (hE : ∀ β ∈ E, β ≤ -δ) (hEl : ∀ B : ℝ, (E ∩ Ici B).Finite) (B : ℝ) : + (wordSupport E ∩ Ici B).Finite := by + apply ((wordCut_finite hδ hE hEl B).image List.sum).subset + rintro β ⟨⟨w,hw,rfl⟩,hB⟩ + exact ⟨w,⟨hw,hB⟩,rfl⟩ + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ExponentialCharts.lean b/lean/OAI/Analysis/PathSelection/ExponentialCharts.lean new file mode 100644 index 0000000000000000000000000000000000000000..5467a99b028c97a2645f430c924dbf21c4a78da4 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ExponentialCharts.lean @@ -0,0 +1,503 @@ +import Mathlib +import OAI.Analysis.PathSelection.InverseAsymptotics +import OAI.Analysis.PathSelection.PhaseSectors +import OAI.Analysis.PathSelection.RelativeStrips + +namespace OAI + +/-! Exponential sector charts, phase contraction and inward equal-exponent maps. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem strict_exponential_chart {F H : ℂ → ℂ} {a b : ℝ} + (ha : 0≤a) (hab : a (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hFd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 (a:ℂ))) + (hHd : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) : + ∃ (T : ℝ) (x : ℂ → ℂ),0 (F (x (r:ℂ))).re) atTop atTop ∧ + (∀ᶠ w in sectorInfinity,AnalyticAt ℂ (fun z => F (x z)) w) ∧ + ∀ (ω : ℝ → ℝ) (S : ℝ),AdmissibleAngularLoss ω → + ∃ (η : ℝ → ℝ) (R : ℝ),AdmissibleAngularLoss η ∧ + (∀ w∈lossSector η R,F (x w)∈lossSector ω S) ∧ + (∀ w∈lossSector η R,(F (x (‖w‖:ℂ))).re/2≤‖F (x w)‖ ∧ + ‖F (x w)‖≤2*(F (x (‖w‖:ℂ))).re) ∧ + (∀ ε : ℝ,0<ε → ∃ U : ℝ,∀ w∈lossSector η U,|(F (x w)).re|≤ε*w.re) := by + have hb : 0 (F (x (r:ℂ))).re) atTop atTop := + (hFt.comp hxt).congr' (hreal.mono fun r hr => congrArg (fun z => (F z).re) hr.symm) + have hdom : ∀ᶠ w in sectorInfinity,0 F (x z)) w := by + filter_upwards [hdom,hxto.eventually hFa] with w hw hF + exact hF.comp (hxa w hw) + have hi : ∀ ε : ℝ,0<ε → ∀ᶠ w in sectorInfinity, + ‖x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)‖≤ε*|w.arg| := by + intro ε hε + obtain ⟨U,hU⟩ := hinc ε hε + filter_upwards [SectorEventually.realpart_pos,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop U)] with w hw hUw + exact hU w hw hUw + have hratio := inverse_clock_ratio_tendsto hb hFa hF0 hFd + (tendsto_re_stripInfinity.comp hxto) hxt + ((eventually_gt_atTop T).mono fun r hr => hxr r hr) hi + let f : ℝ → ℝ := fun r => (F (x (r:ℂ))).re + have hphase : Tendsto (fun w => Complex.exp (-Complex.I*((a/b)*w.arg:ℝ)) * (F (x w)/(f ‖w‖:ℂ))) + sectorInfinity (𝓝 1) := by + apply hratio.congr' + filter_upwards [tendsto_norm_sectorInfinity.eventually hFrx] with w hw + have he : F (x (‖w‖:ℂ))=(f ‖w‖:ℂ) := Complex.ext rfl (by simpa using hw.1) + rw [he] + congr 2 + push_cast + ring + have hq0 : 0≤a/b := div_nonneg ha hb.le + have hq1 : a/b<1 := (div_lt_one hb).mpr hab + let q := (a/b+1)/2 + have hq : q<1 := by dsimp [q]; linarith + have hqab : a (hmod z hz).2⟩ + filter_upwards [hh,tendsto_norm_sectorInfinity.eventually hpowx] with w hw hp + nlinarith + obtain ⟨θ,hθ,hsmall⟩ := sector_sublinear_realpart hq (show 0<2*C by positivity) hbound + refine ⟨T,x,hT,hxa,hleft,hright,hxto,?_,hFxt,hFaX,?_⟩ + · filter_upwards [hFrx,eventually_gt_atTop T] with r hr ht + exact ⟨hxr r ht,hr⟩ + · intro ω S hω + obtain ⟨η,R,hη,hmap,hmod⟩ := strict_phase_sector_mapping hq0 hq1 hFxt hphase ω S hω + refine ⟨fun r => max (η r) (θ r),R,hη.max hθ,?_,?_,?_⟩ + · intro w hw + exact hmap w ⟨hw.1,hw.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩ + · intro w hw + exact hmod w ⟨hw.1,hw.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩ + · intro ε hε + obtain ⟨U,hU⟩ := hsmall ε hε + exact ⟨U,fun w hw => hU w ⟨hw.1,hw.2.trans_le (sub_le_sub_left (le_max_right _ _) _)⟩⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem inverse_halfplane_strip {x : ℂ → ℂ} {b : ℝ} (hb : 0 (x (r:ℂ)).re) atTop atTop) + (hi : ∃ U : ℝ,∀ w : ℂ,0 (f (s:ℂ)).im) f'.im t := by + simpa only [Function.comp_def,Complex.imCLM_apply] using + Complex.imCLM.hasFDerivAt.comp_hasDerivAt t h.comp_ofReal + +lemma vertical_phase_derivative {G : ℂ → ℂ} {x t : ℝ} + (hG : AnalyticAt ℂ G ((x:ℂ)+Complex.I*(t:ℂ))) : + HasDerivAt (fun s : ℝ => s+(G ((x:ℂ)+Complex.I*(s:ℂ))).im) + (1+(deriv G ((x:ℂ)+Complex.I*(t:ℂ))).re) t := by + have hv : HasDerivAt (fun z : ℂ => (x:ℂ)+Complex.I*z) Complex.I (t:ℂ) := by + simpa only [mul_one,id_eq] using (hasDerivAt_id (t:ℂ)).const_mul Complex.I |>.const_add (x:ℂ) + have hcomp : HasDerivAt (fun z : ℂ => G ((x:ℂ)+Complex.I*z)) + (deriv G ((x:ℂ)+Complex.I*(t:ℂ))*Complex.I) (t:ℂ) := + hG.differentiableAt.hasDerivAt.comp (t:ℂ) hv + have hh := imaginary_derivative_of_complex hcomp + simpa only [Pi.add_def,id_eq,Complex.mul_im,Complex.I_re,Complex.I_im,mul_zero,mul_one,add_zero] using + (hasDerivAt_id t).add hh + +theorem vertical_phase_contraction {G : ℂ → ℂ} {x θ : ℝ} + (hG : ∀ t∈uIcc (0:ℝ) θ,AnalyticAt ℂ G ((x:ℂ)+Complex.I*(t:ℂ))) + (hr : (G (x:ℂ)).im=0) + (hder : ∀ t∈uIcc (0:ℝ) θ,-1 ≤ (deriv G ((x:ℂ)+Complex.I*(t:ℂ))).re ∧ + (deriv G ((x:ℂ)+Complex.I*(t:ℂ))).re ≤ 0) : + |θ+(G ((x:ℂ)+Complex.I*(θ:ℂ))).im| ≤ |θ| := by + let f : ℝ → ℝ := fun t => t+(G ((x:ℂ)+Complex.I*(t:ℂ))).im + have hd (t : ℝ) (ht : t∈uIcc (0:ℝ) θ) := vertical_phase_derivative (hG t ht) + have hf : ContinuousOn f (uIcc (0:ℝ) θ) := fun t ht => (hd t ht).continuousAt.continuousWithinAt + have hf' : DifferentiableOn ℝ f (interior (uIcc (0:ℝ) θ)) := + fun t ht => (hd t (interior_subset ht)).differentiableAt.differentiableWithinAt + have h0 : f 0=0 := by simp [f,hr] + have hlo := (convex_uIcc (0:ℝ) θ).mul_sub_le_image_sub_of_le_deriv hf hf' + (C := 0) (fun t ht => by rw [(hd t (interior_subset ht)).deriv]; linarith [(hder t (interior_subset ht)).1]) + have hup := (convex_uIcc (0:ℝ) θ).image_sub_le_mul_sub_of_deriv_le hf hf' + (C := 1) (fun t ht => by rw [(hd t (interior_subset ht)).deriv]; linarith [(hder t (interior_subset ht)).2]) + change |f θ| ≤ |θ| + by_cases hθ : 0 ≤ θ + · have hl := hlo 0 left_mem_uIcc θ right_mem_uIcc hθ + have hu := hup 0 left_mem_uIcc θ right_mem_uIcc hθ + rw [h0] at hl hu + rw [abs_of_nonneg hθ,abs_le] + constructor <;> linarith + · have hl := hlo θ right_mem_uIcc 0 left_mem_uIcc (le_of_not_ge hθ) + have hu := hup θ right_mem_uIcc 0 left_mem_uIcc (le_of_not_ge hθ) + rw [h0] at hl hu + rw [abs_of_neg (lt_of_not_ge hθ),abs_le] + constructor <;> linarith + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma positive_quotient_neighborhood {b : ℝ} (hb : 0 < b) : + ∃ δ : ℝ,0 < δ ∧ ∀ u v : ℂ,‖u-1‖ < δ → ‖v-(b:ℂ)‖ < δ → + 0 < (u/v).re ∧ ‖u/v‖ < 2/b := by + have hbn : (b:ℂ)≠0 := Complex.ofReal_ne_zero.mpr hb.ne' + have hc : ContinuousAt (fun p : ℂ × ℂ => p.1/p.2) (1,(b:ℂ)) := + continuousAt_fst.div continuousAt_snd hbn + have hr : (1/(b:ℂ)).re=1/b := by simp + have hn : ‖(1:ℂ)/(b:ℂ)‖=1/b := by simp [abs_of_pos hb] + have he : ∀ᶠ p : ℂ × ℂ in 𝓝 (1,(b:ℂ)),0 < (p.1/p.2).re ∧ ‖p.1/p.2‖ < 2/b := by + apply hc.eventually (p := fun z : ℂ => 0 < z.re ∧ ‖z‖ < 2/b) + filter_upwards [(show IsOpen {z : ℂ | (0:ℝ) < z.re} from isOpen_lt continuous_const Complex.continuous_re).mem_nhds (by change 0 < (1/(b:ℂ)).re; rw [hr]; positivity), + Metric.isOpen_ball.mem_nhds (show (1:ℂ)/(b:ℂ)∈Metric.ball 0 (2/b) by + simp only [Metric.mem_ball,dist_zero_right,hn] + exact (div_lt_div_iff_of_pos_right hb).mpr (by norm_num))] with z hz hzn + exact ⟨hz,by simpa only [Metric.mem_ball,dist_zero_right] using hzn⟩ + obtain ⟨δ,hδ,hδs⟩ := Metric.mem_nhds_iff.mp he + refine ⟨δ,hδ,?_⟩ + intro u v hu hv + apply hδs (a := (u,v)) + simpa only [Metric.mem_ball,Prod.dist_eq,dist_eq_norm,Prod.norm_def,Prod.fst_sub,Prod.snd_sub,max_lt_iff] using And.intro hu hv + +theorem negative_log_quotient_on_strip {q D : ℂ → ℂ} {b : ℝ} (hb : 0 < b) + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ q z) + (hz : ∀ᶠ z in stripInfinity,q z≠0) + (hd : Tendsto (fun z => deriv q z/q z) stripInfinity (𝓝 0)) + (hD : Tendsto D stripInfinity (𝓝 (b:ℂ))) + (hqr : ∀ᶠ t : ℝ in atTop,(q (t:ℂ)).im=0 ∧ (q (t:ℂ)).re < 0) + (hq0 : Tendsto (fun t : ℝ => q (t:ℂ)) atTop (𝓝 0)) + {R B : ℝ} (hR : 0 < R) (hB : 0 < B) : + ∃ A : ℝ,∀ t : ℝ,A < t → ∀ z∈horizontalTail A R,‖z-(t:ℂ)‖ ≤ B → + -1 ≤ (q z/D z).re ∧ (q z/D z).re < 0 := by + obtain ⟨δ,hδ,hnear⟩ := positive_quotient_neighborhood hb + obtain ⟨A₁,hA₁⟩ := relative_strip_pair_estimate ha hz hd hR hB + (show 0 < δ/(2*B) by positivity) + have heD : ∀ᶠ z in stripInfinity,‖D z-(b:ℂ)‖ < δ := by + simpa only [dist_eq_norm] using (Metric.tendsto_nhds.mp hD) δ hδ + obtain ⟨A₂,hA₂⟩ := eventually_stripInfinity.mp heD R + have heq : ∀ᶠ t : ℝ in atTop,‖q (t:ℂ)‖ < b/2 := by + simpa only [dist_zero_right] using (Metric.tendsto_nhds.mp hq0) (b/2) (by positivity) + obtain ⟨A₃,hA₃⟩ := eventually_atTop.mp (hqr.and heq) + let A := max (max A₁ A₂) A₃ + refine ⟨A,?_⟩ + intro t ht z hzA hdist + have ht₁ : A₁ < t := lt_of_le_of_lt ((le_max_left A₁ A₂).trans (le_max_left _ _)) ht + have ht₃ : A₃ ≤ t := (le_max_right _ _).trans ht.le + have hz₁ : z∈horizontalTail A₁ R := + ⟨lt_of_le_of_lt ((le_max_left A₁ A₂).trans (le_max_left _ _)) hzA.1,hzA.2⟩ + have hz₂ : z∈horizontalTail A₂ R := + ⟨lt_of_le_of_lt ((le_max_right A₁ A₂).trans (le_max_left _ _)) hzA.1,hzA.2⟩ + obtain ⟨hqtn,hratio⟩ := hA₁ z hz₁ (t:ℂ) ⟨ht₁,by simpa using hR⟩ hdist + have hratio' : ‖q z/q (t:ℂ)-1‖ < δ := by + have hh := mul_le_mul_of_nonneg_left hdist (by positivity : 0 ≤ δ/(2*B)) + have he : δ/(2*B)*B=δ/2 := by field_simp + rw [he] at hh + exact (hratio.trans hh).trans_lt (by linarith) + obtain ⟨hpos,hbn⟩ := hnear (q z/q (t:ℂ)) (D z) hratio' (hA₂ z hz₂) + have hqt := hA₃ t ht₃ + have heq : q z/D z=q (t:ℂ)*((q z/q (t:ℂ))/D z) := by field_simp + have hneg : (q z/D z).re < 0 := by + rw [heq,Complex.mul_re,hqt.1.1,zero_mul,sub_zero] + exact mul_neg_of_neg_of_pos hqt.1.2 hpos + have hn : ‖q z/D z‖ < 1 := by + rw [heq,norm_mul] + have hh' := mul_lt_mul_of_pos_right hqt.2 (by positivity : 0 < 2/b) + have hid : (b/2)*(2/b)=(1:ℝ) := by field_simp + rw [hid] at hh' + exact (mul_le_mul_of_nonneg_left hbn.le (norm_nonneg _)).trans_lt hh' + exact ⟨by have hh := (Complex.abs_re_le_norm (q z/D z)).trans hn.le + exact (abs_le.mp hh).1,hneg⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma arg_exp_eq_im_of_abs_lt_pi {w : ℂ} (hw : |w.im| < Real.pi) : + (Complex.exp w).arg=w.im := by + rw [Complex.arg_exp] + apply (toIocMod_eq_self Real.two_pi_pos).mpr + constructor + · exact (abs_lt.mp hw).1 + · linarith [(abs_lt.mp hw).2] + + + +theorem log_clock_phase_contraction {G : ℂ → ℂ} {A : ℝ} + (hG : AnalyticOnNhd ℂ G (horizontalTail A (Real.pi/2))) + (hr : ∀ t : ℝ,A hG _ (hθ t ht)) + (hr _ hw.1) (fun t ht => hder _ (hθ t ht)) + have hwform : (w.re:ℂ)+Complex.I*(w.im:ℂ)=w := by + simpa only [mul_comm] using Complex.re_add_im w + rw [hwform] at hphase + have hpi : |(w+G w).im| < Real.pi := by + simp only [Complex.add_im] + exact hphase.trans_lt (hw.2.trans (by linarith [Real.pi_pos])) + rw [arg_exp_eq_im_of_abs_lt_pi hpi,Complex.add_im] + exact hphase + + + +lemma log_inverse_ratio_derivative {H J Q X : ℂ → ℂ} {U : Set ℂ} + (hU : IsOpen U) {w : ℂ} (hw : w∈U) + (hX : AnalyticAt ℂ X w) (hH : AnalyticAt ℂ H (X w)) + (hQ : AnalyticAt ℂ Q (X w)) + (he : ∀ v∈U,H (X v)=Complex.exp v) + (hQd : deriv Q (X w)=deriv J (X w)/J (X w)) + (hHne : deriv H (X w)≠0) : + deriv (fun v => Q (X v)) w = + (deriv J (X w)/J (X w))/(deriv H (X w)/H (X w)) := by + have hd := hH.differentiableAt.hasDerivAt.comp w hX.differentiableAt.hasDerivAt + have heq : (fun v => H (X v)) =ᶠ[𝓝 w] Complex.exp := + Filter.Eventually.mono (hU.mem_nhds hw) (fun v hv => he v hv) + have hh := (hd.congr_of_eventuallyEq heq.symm).unique (Complex.hasDerivAt_exp w) + have hXd : deriv X w=Complex.exp w/deriv H (X w) := by + apply (eq_div_iff hHne).mpr + simpa only [mul_comm] using hh + change deriv (Q ∘ X) w = _ + rw [(hQ.differentiableAt.hasDerivAt.comp w hX.differentiableAt.hasDerivAt).deriv,hQd,hXd,←he w hw] + field_simp [hHne,show H (X w)≠0 by rw [he w hw]; exact Complex.exp_ne_zero w] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem equal_exponent_inward {H J : ℂ → ℂ} {b : ℝ} (hb : 0 (H (t:ℂ)).re) atTop atTop) + (hHd : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) + (hJa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ J z) + (hJ0 : ∀ᶠ z in stripInfinity,J z≠0) + (hJr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re) + (hqa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ (fun z => deriv J z/J z) z) + (hqne : ∀ᶠ z in stripInfinity,deriv J z/J z≠0) + (hqd : Tendsto (fun z => deriv (fun z => deriv J z/J z) z/(deriv J z/J z)) stripInfinity (𝓝 0)) + (hqr : ∀ᶠ t : ℝ in atTop,(deriv J (t:ℂ)/J (t:ℂ)).im=0 ∧ (deriv J (t:ℂ)/J (t:ℂ)).re<0) + (hq0 : Tendsto (fun t : ℝ => deriv J (t:ℂ)/J (t:ℂ)) atTop (𝓝 0)) : + ∃ (T : ℝ) (x : ℂ → ℂ),0 (x (r:ℂ)).re) atTop atTop ∧ + Tendsto x sectorInfinity stripInfinity ∧ + (∀ ε : ℝ,0<ε → ∃ U : ℝ,∀ w : ℂ,0 w*deriv x w) sectorInfinity (𝓝 ((b:ℂ)⁻¹)) ∧ + ∃ U : ℝ,∀ w : ℂ,0 hxr r hr) hxt (by simpa only [one_mul] using hinc 1 zero_lt_one) + obtain ⟨A₁,hA₁⟩ := negative_log_quotient_on_strip hb hqa hqne hqd hHd hqr hq0 hR hB + obtain ⟨A₂,hA₂⟩ := eventually_stripInfinity.mp ((hJa.and hJ0).and hHa) R + obtain ⟨A₃,hA₃⟩ := eventually_atTop.mp hJr + let A := max A₁ (max A₂ A₃) + have hAA₁ : A₁≤A := le_max_left _ _ + have hAA₂ : A₂≤A := (le_max_left _ _).trans (le_max_right _ _) + have hAA₃ : A₃≤A := (le_max_right _ _).trans (le_max_right _ _) + have hJ (z : ℂ) (hz : z∈horizontalTail A R) : AnalyticAt ℂ J z ∧ J z≠0 := + (hA₂ z ⟨lt_of_le_of_lt hAA₂ hz.1,hz.2⟩).1 + obtain ⟨Q,hQa,hQe,hQd,hQr⟩ := analytic_real_log_on_strip hR + (fun z hz => (hJ z hz).1) (fun z hz => (hJ z hz).2) + (fun t ht => hA₃ t (hAA₃.trans ht.le)) + obtain ⟨U,hU,hUf⟩ := hfull A + let V := max T U + have hV : 0 x (Complex.exp w) + have hexp (w : ℂ) (hw : w∈horizontalTail C (Real.pi/2)) : + 0<(Complex.exp w).re ∧ V<‖Complex.exp w‖ := by + refine ⟨exp_horizontalTail_right hw,?_⟩ + rw [Complex.norm_exp,←Real.exp_log hV] + exact Real.exp_strictMono hw.1 + have hXmap (w : ℂ) (hw : w∈horizontalTail C (Real.pi/2)) : + A<(x (‖Complex.exp w‖:ℂ)).re ∧ X w∈horizontalTail A R ∧ + ‖X w-((x (‖Complex.exp w‖:ℂ)).re:ℂ)‖≤B := by + exact hUf _ (hexp w hw).1 (lt_of_le_of_lt (le_max_right _ _) (hexp w hw).2) + have hXa : AnalyticOnNhd ℂ X (horizontalTail C (Real.pi/2)) := by + intro w hw + exact (hxa _ ⟨(hexp w hw).1,lt_of_le_of_lt (le_max_left _ _) (hexp w hw).2⟩).comp analyticAt_cexp + have hXe (w : ℂ) (hw : w∈horizontalTail C (Real.pi/2)) : H (X w)=Complex.exp w := + hleft _ (hexp w hw).1 (lt_of_le_of_lt (le_max_left _ _) (hexp w hw).2) + have hXr (t : ℝ) (ht : C Q (X w)) (horizontalTail C (Real.pi/2)) := + fun w hw => (hQa _ (hXmap w hw).2.1).comp (hXa w hw) + have hGr (t : ℝ) (ht : C Q (X w)) w).re ∧ (deriv (fun w => Q (X w)) w).re≤0 := by + have hmap := hXmap w hw + have hHaw : AnalyticAt ℂ H (X w) := (hA₂ _ ⟨hAA₂.trans_lt hmap.2.1.1,hmap.2.1.2⟩).2 + have hHne : deriv H (X w)≠0 := by + have heq : (fun v => H (X v)) =ᶠ[𝓝 w] Complex.exp := + Filter.Eventually.mono ((horizontalTail_open C (Real.pi/2)).mem_nhds hw) (fun v hv => hXe v hv) + have hd := hHaw.differentiableAt.hasDerivAt.comp w (hXa w hw).differentiableAt.hasDerivAt + have he := (hd.congr_of_eventuallyEq heq.symm).unique (Complex.hasDerivAt_exp w) + intro hh + have hh' := Complex.exp_ne_zero w + simp only [hh,zero_mul] at he + exact hh' he.symm + rw [log_inverse_ratio_derivative (horizontalTail_open C (Real.pi/2)) hw (hXa w hw) + hHaw (hQa _ hmap.2.1) hXe (hQd _ hmap.2.1) hHne] + have hh := hA₁ _ (hAA₁.trans_lt hmap.1) _ + ⟨hAA₁.trans_lt hmap.2.1.1,hmap.2.1.2⟩ hmap.2.2 + exact ⟨hh.1,hh.2.le⟩ + refine ⟨T,x,hT,hxa,hleft,hright,hxr,hxt,hxto,hinc,hxd,V,?_⟩ + intro w hw hwV + have hw0 : w≠0 := by intro he; simp [he] at hw + have hwlog : Complex.log w∈horizontalTail C (Real.pi/2) := by + constructor + · rw [Complex.log_re] + exact Real.log_lt_log hV hwV + · rw [Complex.log_im] + exact Complex.abs_arg_lt_pi_div_two_iff.mpr (Or.inl hw) + have hh := log_clock_phase_contraction hGa hGr hGd hwlog + rw [Complex.exp_add,hQe _ (hXmap _ hwlog).2.1,Complex.exp_log hw0] at hh + simpa only [X,Complex.exp_log hw0,Complex.log_im] using hh + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/FilteredExpansions.lean b/lean/OAI/Analysis/PathSelection/FilteredExpansions.lean new file mode 100644 index 0000000000000000000000000000000000000000..a08165d3b23733ddaa53489ca626e72eabf241d2 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/FilteredExpansions.lean @@ -0,0 +1,527 @@ +import Mathlib +import OAI.Analysis.PathSelection.SectorInduction + +namespace OAI + +/-! Filtered clock series, bounded expansions and finite decompositions. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +attribute [local instance] Classical.propDecidable +namespace DegeneratingTrees.Clock + +lemma negative_degree_cutoff {δ : ℝ} (hδ : 0<δ) + {E : ℕ → Set ℝ} (hE : ∀ n β,β∈E n → β≤-δ*(n:ℝ)) (B : ℝ) : + ∃ N : ℕ,∀ n≥N,∀ β∈E n,β hfin n B)).subset + rintro β ⟨hβ,hB⟩ + obtain ⟨n,hn⟩ := mem_iUnion.mp hβ + have hnN : n by + have hn' : β∉E n := by simpa only [S,Set.Finite.mem_toFinset,mem_ofPred_eq] using hns + simp only [ite_eq_right hn']) + +lemma degree_truncation (b : ℕ → ℝ → ℂ → ℂ) {B : ℝ} {N : ℕ} + (hN : ∀ n≥N,∀ β∈E n,β simp + _ = ∑ n ∈ Finset.range N,∑ β ∈ S, + if β∈E n then Complex.exp ((β:ℂ)*z)*b n β z else 0 := Finset.sum_comm + _ = _ := by + apply Finset.sum_congr rfl + intro n hn + symm + have hs : (hfin n B).toFinset ⊆ S := by + intro β hβ + have hh := (hfin n B).mem_toFinset.mp hβ + exact (negative_union_finite hδ hE hfin B).mem_toFinset.mpr + ⟨mem_iUnion.mpr ⟨n,hh.1⟩,hh.2⟩ + calc + _ = ∑ β ∈ (hfin n B).toFinset, + if β∈E n then Complex.exp ((β:ℂ)*z)*b n β z else 0 := by + apply Finset.sum_congr rfl + intro β hβ + simp only [ite_eq_left ((hfin n B).mem_toFinset.mp hβ).1] + _ = _ := Finset.sum_subset hs (fun β hβ hβn => by + have hB := ((negative_union_finite hδ hE hfin B).mem_toFinset.mp hβ).2 + have he : β∉E n := by + intro he + exact hβn ((hfin n B).mem_toFinset.mpr ⟨he,hB⟩) + simp only [ite_eq_right he]) + + + +theorem SectorExpansion.of_negative_degree_series {F : ℂ → ℂ} + {f : ℕ → ℂ → ℂ} {b : ℕ → ℝ → ℂ → ℂ} + (hf : ∀ n,SectorExpansion (f n) (E n) (b n)) + (ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (happrox : ∀ B : ℝ,∀ᶠ N : ℕ in atTop, + ExpSmall B (fun z => F z-∑ n ∈ Finset.range N,f n z)) : + SectorExpansion F (⋃ n,E n) (degreeCoefficient hδ hE b) := by + classical + have hfin : ∀ n B,(E n∩Ici B).Finite := fun n => (hf n).finite_above + have hbdd : BddAbove (⋃ n,E n) := by + refine ⟨0,?_⟩ + rintro β hβ + obtain ⟨n,hn⟩ := mem_iUnion.mp hβ + exact (hE n β hn).trans (mul_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr hδ.le) (Nat.cast_nonneg n)) + apply SectorExpansion.of_expSmall hbdd (negative_union_finite hδ hE hfin) ha + intro B + obtain ⟨N,hN⟩ := negative_degree_cutoff hδ hE B + obtain ⟨M,hM,he⟩ := ((eventually_ge_atTop N).and (happrox B)).exists + have hdeg : ∀ n≥M,∀ β∈E n,β hN n (hM.trans hn) + have hrem := ExpSmall.sum (Finset.range M) (fun n _ => (hf n).expSmall_remainder B) + convert he.add hrem using 1 + funext z + rw [Finset.sum_sub_distrib,degree_truncation hδ hE hfin b hdeg z] + ring + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +def BoundedExpansionOver (K : Set (ℂ → ℂ)) (α : ℝ) (f : ℂ → ℂ) : Prop := + ∃ E : Set ℝ,∃ b : ℝ → ℂ → ℂ,SectorExpansion f E b ∧ + (∀ β∈E,b β∈K) ∧ ∀ β∈E,β≤α + +namespace BoundedExpansionOver +variable {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) +include hK + +lemma lower {f : ℂ → ℂ} (hf : f∈K) : BoundedExpansionOver K 0 f := by + refine ⟨{0},fun _ => f,?_,fun _ _ => hf,fun β hβ => le_of_eq (mem_singleton_iff.mp hβ)⟩ + simpa only [Complex.ofReal_zero,zero_mul,Complex.exp_zero,one_mul] using + SectorExpansion.single 0 (hK.analytic hf) (hK.slow hf) + +omit hK in +lemma zero (α : ℝ) : BoundedExpansionOver K α (fun _ => 0) := by + refine ⟨∅,fun _ _ => 0,?_,by simp,by simp⟩ + apply SectorExpansion.of_expSmall (by simp) (by simp) + (Eventually.of_forall fun _ => analyticAt_const) + intro B + simpa using ExpSmall.zero B + +lemma add {α : ℝ} {f g : ℂ → ℂ} + (hf : BoundedExpansionOver K α f) (hg : BoundedExpansionOver K α g) : + BoundedExpansionOver K α (fun z => f z+g z) := by + classical + obtain ⟨E,b,hf,hb,hE⟩ := hf + obtain ⟨F,c,hg,hc,hF⟩ := hg + refine ⟨E∪F,fun β z => (if β∈E then b β z else 0)+(if β∈F then c β z else 0), + hf.add hg,?_,?_⟩ + · intro β hβ + apply hK.add_mem + · by_cases he : β∈E + · simpa only [ite_eq_left he] using hb β he + · simpa only [ite_eq_right he] using hK.const_mem 0 + · by_cases he : β∈F + · simpa only [ite_eq_left he] using hc β he + · simpa only [ite_eq_right he] using hK.const_mem 0 + · intro β hβ + exact hβ.elim (hE β) (hF β) + +lemma mul {α γ : ℝ} {f g : ℂ → ℂ} + (hf : BoundedExpansionOver K α f) (hg : BoundedExpansionOver K γ g) : + BoundedExpansionOver K (α+γ) (fun z => f z*g z) := by + obtain ⟨E,b,hf,hb,hE⟩ := hf + obtain ⟨F,c,hg,hc,hF⟩ := hg + refine ⟨exponentSum E F,_,hf.mul hg (fun β hβ => hK.slow (hb β hβ)) + (fun γ hγ => hK.slow (hc γ hγ)), + fun δ _ => hK.convolution_mem hf.bounded_above hg.bounded_above + hf.finite_above hg.finite_above hb hc δ,?_⟩ + rintro β ⟨⟨b,c⟩,⟨hb,hc⟩,rfl⟩ + exact add_le_add (hE b hb) (hF c hc) + +lemma sum {ι : Type*} (S : Finset ι) {α : ℝ} {f : ι → ℂ → ℂ} + (hf : ∀ i∈S,BoundedExpansionOver K α (f i)) : + BoundedExpansionOver K α (fun z => ∑ i∈S,f i z) := by + classical + induction S using Finset.induction_on with + | empty => simpa only [Finset.sum_empty] using zero α + | @insert i S hi ih => + simpa only [Finset.sum_insert hi] using add hK + (hf i (Finset.mem_insert_self _ _)) (ih (fun j hj => hf j (Finset.mem_insert_of_mem hj))) + +lemma prod {ι : Type*} (S : Finset ι) {α : ι → ℝ} {f : ι → ℂ → ℂ} + (hf : ∀ i∈S,BoundedExpansionOver K (α i) (f i)) : + BoundedExpansionOver K (∑ i∈S,α i) (fun z => ∏ i∈S,f i z) := by + classical + induction S using Finset.induction_on with + | empty => simpa only [Finset.sum_empty,Finset.prod_empty] using lower hK (hK.const_mem 1) + | @insert i S hi ih => + simpa only [Finset.sum_insert hi,Finset.prod_insert hi] using mul hK + (hf i (Finset.mem_insert_self _ _)) (ih (fun j hj => hf j (Finset.mem_insert_of_mem hj))) + +lemma negative_series {δ : ℝ} (hδ : 0<δ) {f : ℕ → ℂ → ℂ} + (hf : ∀ n : ℕ,BoundedExpansionOver K (-δ*(n:ℝ)) (f n)) {F : ℂ → ℂ} + (ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (happrox : ∀ B : ℝ,∀ᶠ N : ℕ in atTop, + ExpSmall B (fun z => F z-∑ n∈Finset.range N,f n z)) : ExpansionOver K F := by + classical + choose E b he hb hE using hf + refine ⟨⋃ n,E n,degreeCoefficient hδ hE b, + SectorExpansion.of_negative_degree_series hδ hE he ha happrox,?_⟩ + intro β hβ + apply hK.finset_sum_mem + intro n hn + exact hb n β ((negative_fiber_finite hδ hE β).mem_toFinset.mp hn) +end BoundedExpansionOver +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +private lemma filtered_positive_coeff_zero {field : Set (ℂ → ℂ)} + (hfield : LowerSectorData field) {func : ℂ → ℂ} {support : Set ℝ} + {coeff : ℝ → ℂ → ℂ} (hexp : SectorExpansion func support coeff) + (hcoeff : ∀ exponent∈support,coeff exponent∈field) {limit : ℂ} + (hlim : Tendsto (fun time : ℝ => func (time:ℂ)) atTop (𝓝 limit)) + {exponent : ℝ} (hmem : exponent∈support) (hpos : 0 hfield.analytic (hcoeff degree hdegree)) + have hsupport : exponent∈nonzeroRaySupport support coeff := ⟨hmem,hnonzero⟩ + obtain ⟨degree,hdegree,hmax⟩ := exists_greatest_of_finite_above htrim.finite_above ⟨exponent,hsupport⟩ + have hdegreepos : 0 Complex.exp (((-degree:ℝ):ℂ)*point)) := + ⟨-degree,by linarith,ExpBound.cexp (-degree)⟩ + have hzero := ((hexponential.mul_slow hslow).tendsto_zero.comp tendsto_real_sectorInfinity).mul hlim + exact zero_ne_one (by simpa only [zero_mul] using tendsto_nhds_unique hzero hone) + +private lemma filtered_first_clock_limit {func : ℝ → ℂ} (hfunc : Puiseux func) + {clock : ℝ → ℝ} {scale : ℝ} (hscale : 0 scale*time) + {model : ℂ → ℂ} (hanalytic : ∀ᶠ point in sectorInfinity,AnalyticAt ℂ model point) + (heq : func =ᶠ[atTop] fun time => model (clock time:ℂ)) {limit : ℂ} + (hlim : Tendsto func atTop (𝓝 limit)) : Tendsto model sectorInfinity (𝓝 limit) := by + have hrepresentative : ∃ (representative : ℂ → ℂ) (radius : ℝ), + (∀ point : ℂ,radius<‖point‖ → 0 representative (time:ℂ)) ∧ + Tendsto representative radialInfinity (𝓝 limit) := by + by_cases hzero : func =ᶠ[atTop] fun _ => 0 + · have hlimit : limit=0 := tendsto_nhds_unique hlim (tendsto_const_nhds.congr' hzero.symm) + subst limit + exact ⟨fun _ => 0,0,fun _ _ _ => analyticAt_const,hzero,tendsto_const_nhds⟩ + obtain ⟨order,horder,power,coefficient,hcoefficient,hconstant,hform⟩ := hfunc.normalize hzero + have hform' : func =ᶠ[atTop] fun time => + (rootCoord order time:ℂ)^power*coefficient (rootCoord order time) := by + simpa only [Complex.real_smul,Complex.ofReal_zpow] using hform + have hpower : 0≤power := by + by_contra hnegative + have hnegative : power<0 := lt_of_not_ge hnegative + let degree : ℕ := (-power).toNat + have hdegree : 0 (rootCoord order time:ℂ)^degree*func time) atTop (𝓝 0) := by + simpa only [zero_pow hdegree.ne',zero_mul] using + ((rootCoord_complex_tendsto_zero horder).pow degree).mul hlim + have hcancel : (fun time => (rootCoord order time:ℂ)^degree*func time) =ᶠ[atTop] + fun time => coefficient (rootCoord order time) := by + filter_upwards [hform',eventually_gt_atTop (0:ℝ)] with time hform htime + have hroot : (rootCoord order time:ℂ)≠0 := Complex.ofReal_ne_zero.mpr (rootCoord_pos htime).ne' + rw [hform,←mul_assoc,←zpow_natCast,←zpow_add₀ hroot,hcast,neg_add_cancel,zpow_zero,one_mul] + exact hconstant (tendsto_nhds_unique (hcoefficient.continuousAt.tendsto.comp + (rootCoord_complex_tendsto_zero horder)) (hzero.congr' hcancel)) + let degree := power.toNat + have hcast : (degree:ℤ)=power := Int.toNat_of_nonneg hpower + let representative : ℂ → ℂ := fun point => + (complexRoot order point)^degree*coefficient (complexRoot order point) + have heq' : func =ᶠ[atTop] fun time => representative (time:ℂ) := by + filter_upwards [hform',eventually_gt_atTop (0:ℝ)] with time hform htime + simpa only [representative,complexRoot_real htime.le,←zpow_natCast,hcast] using hform + have hlimit : limit=(0:ℂ)^degree*coefficient 0 := by + have htendsto := ((rootCoord_complex_tendsto_zero horder).pow degree).mul + (hcoefficient.continuousAt.tendsto.comp (rootCoord_complex_tendsto_zero horder)) + apply tendsto_nhds_unique hlim + apply htendsto.congr' + filter_upwards [hform'] with time hform + simpa only [Function.comp_apply,←zpow_natCast,hcast] using hform.symm + obtain ⟨radius,hradius⟩ := radial_eventually + ((complexRoot_tendsto_zero horder).eventually hcoefficient.eventually_analyticAt) + refine ⟨representative,radius,?_,heq',?_⟩ + · intro point hnorm hre + have hroot := complexRoot_analytic (n := order) hre + exact (hroot.pow degree).mul ((hradius point hnorm).comp hroot) + · rw [hlimit] + exact ((complexRoot_tendsto_zero horder).pow degree).mul + (hcoefficient.continuousAt.tendsto.comp (complexRoot_tendsto_zero horder)) + obtain ⟨representative,radius,hrep,heqrep,hreplimit⟩ := hrepresentative + let inverse : ℂ → ℂ := fun point => point/(scale:ℂ) + have hinverse : Tendsto inverse sectorInfinity radialInfinity := by + rw [radialInfinity,tendsto_comap_iff] + simpa only [inverse,Function.comp_def,norm_div,Complex.norm_of_nonneg hscale.le] using + tendsto_norm_sectorInfinity.atTop_div_const hscale + have hinverseanalytic : ∀ point : ℂ,AnalyticAt ℂ inverse point := fun _ => analyticAt_id.div_const + have hcomposition : ∀ᶠ point in sectorInfinity,AnalyticAt ℂ (fun point => representative (inverse point)) point := by + have hnorm : ∀ᶠ point in sectorInfinity,radius<‖inverse point‖ := + (tendsto_comap_iff.mp hinverse).eventually (eventually_gt_atTop radius) + filter_upwards [hnorm,tendsto_re_sectorInfinity.eventually (eventually_gt_atTop (0:ℝ))] + with point hnorm hre + have hre' : 0<(inverse point).re := by + simpa only [inverse,Complex.div_ofReal_re] using div_pos hre hscale + exact (hrep (inverse point) hnorm hre').comp (hinverseanalytic point) + have hline : (fun time : ℝ => model (time:ℂ)) =ᶠ[atTop] + fun time => representative (inverse (time:ℂ)) := by + have htendsto : Tendsto (fun time : ℝ => time/scale) atTop atTop := tendsto_id.atTop_div_const hscale + filter_upwards [htendsto.eventually heq,htendsto.eventually heqrep,htendsto.eventually hclock] + with time heq heqrep hclock + change func (time/scale)=model (clock (time/scale):ℂ) at heq + change func (time/scale)=representative (time/scale:ℝ) at heqrep + have hclock' : clock (time/scale)=time := by rw [hclock]; field_simp + rw [hclock'] at heq + simpa only [inverse,←Complex.ofReal_div] using heq.symm.trans heqrep + exact (hreplimit.comp hinverse).congr' (sector_analytic_eq_of_ray hanalytic hcomposition hline).symm + +private lemma filtered_previous_chart {clocks : List (ℝ → ℝ)} {clock lower : ℝ → ℝ} + (hvalid : ValidClocks (clock::lower::clocks)) : + ∃ inverse : ℂ → ℂ,(∀ᶠ point in sectorInfinity,AnalyticAt ℂ inverse point) ∧ + Tendsto inverse sectorInfinity sectorInfinity ∧ + (∀ᶠ time : ℝ in atTop,inverse (clock time:ℂ)=(lower time:ℂ)) := by + obtain ⟨field,hdata⟩ := hvalid.1.sectorData + have hlowert := hvalid.1.2.2.1 + have hclockt := hvalid.2.2.1 + have hlowerc := (hvalid.1.2.1.real_eventually_analytic hvalid.1.1).mono (fun _ hanalytic => hanalytic.continuousAt) + obtain ⟨model,hmodel,heq⟩ := hdata.expansion_iff.mp hvalid.2.1 + have hreal : ∀ᶠ time : ℝ in atTop,(model (time:ℂ)).im=0 ∧ 0<(model (time:ℂ)).re := by + apply eventually_of_comp_clock hlowert hlowerc + filter_upwards [heq,hclockt.eventually (eventually_gt_atTop 0)] with time heq htime + rw [←heq] + exact ⟨rfl,htime⟩ + have htendsto : Tendsto (fun time : ℝ => (model (time:ℂ)).re) atTop atTop := by + rw [Filter.tendsto_def] + intro bound hbound + apply eventually_of_comp_clock hlowert hlowerc + exact (hclockt.congr' (heq.mono fun _ heq => congrArg Complex.re heq)).eventually hbound + have hfast : Asymptotics.IsLittleO atTop id (fun time : ℝ => (model (time:ℂ)).re) := by + apply Asymptotics.IsLittleO.of_bound + intro epsilon hepsilon + apply eventually_of_comp_clock hlowert hlowerc + filter_upwards [heq,hvalid.2.2.2.def hepsilon] with time heq hbound + change ‖lower time‖≤epsilon*‖(model (lower time:ℂ)).re‖ + rwa [←heq] + obtain ⟨inverse,realInverse,hinverse,hfamily⟩ := hdata.charts model hmodel hreal htendsto hfast + refine ⟨inverse,hinverse.analytic_left.mono (fun _ hanalytic => hanalytic.1),hinverse.maps_sector,?_⟩ + filter_upwards [heq,hlowert.eventually hinverse.right] with time heq hinverse + rwa [heq] + +private lemma filtered_finite_decomposition {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} + {K : Set (ℂ → ℂ)} (hK : ClockSectorData xs X K) + (hlower : ∀ a∈K,∀ d : ℂ,Tendsto (fun t : ℝ => a (t:ℂ)) atTop (𝓝 d) → + Tendsto a sectorInfinity (𝓝 d)) + {F : ℂ → ℂ} (hF : ExpansionOver K F) {d : ℂ} + (hlim : Tendsto (fun t : ℝ => F (t:ℂ)) atTop (𝓝 d)) : + ∃ (a r : ℂ → ℂ) (δ : ℝ),0<δ ∧ a∈K ∧ Tendsto a sectorInfinity (𝓝 d) ∧ + BoundedExpansionOver K (-δ) r ∧ ExpBound (-δ/2) r ∧ + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ r z) ∧ ∀ z,F z=a z+r z := by + classical + obtain ⟨E,b,hF,hb⟩ := hF + let D := nonzeroRaySupport E b + have htrim : SectorExpansion F D b := hF.trim_zero (fun β hβ => hK.lower.analytic (hb β hβ)) + have hDb : ∀ β∈D,b β∈K := fun β hβ => hb β hβ.1 + have hnonpos : ∀ β∈D,β≤0 := by + intro β hβ + by_contra h + exact hβ.2 (filtered_positive_coeff_zero hK.lower hF hb hlim hβ.1 (lt_of_not_ge h)) + have hgo : ∀ (a r : ℂ → ℂ) (A : Set ℝ),a∈K → SectorExpansion r A b → + (∀ β∈A,b β∈K) → (∀ β∈A,β<0) → (∀ z,F z=a z+r z) → + ∃ δ : ℝ,0<δ ∧ Tendsto a sectorInfinity (𝓝 d) ∧ + BoundedExpansionOver K (-δ) r ∧ ExpBound (-δ/2) r := by + intro a r A ham hr hc hneg heq + obtain ⟨δ,hδ,hgap⟩ := strict_negative_support_gap hr.finite_above hneg + have hdec := hr.negative_bound hδ hgap + have hr0 := hdec.tendsto_zero (by linarith : -δ/2<0) + have har : Tendsto (fun t : ℝ => a (t:ℂ)) atTop (𝓝 d) := by + have h := hlim.sub (hr0.comp tendsto_real_sectorInfinity) + simp only [sub_zero] at h + convert h using 1 + funext t + simp only [heq,Function.comp_apply,add_sub_cancel_right] + exact ⟨δ,hδ,hlower a ham d har,⟨A,b,hr,hc,hgap⟩,hdec⟩ + by_cases h0 : (0:ℝ)∈D + · have hr := htrim.erase h0 (hK.lower.analytic (hDb 0 h0)) (hK.lower.slow (hDb 0 h0)) + simp only [Complex.ofReal_zero,zero_mul,Complex.exp_zero,one_mul] at hr + have he : ∀ z,F z=b 0 z+(F z-b 0 z) := fun z => by ring + obtain ⟨δ,hδ,ha,hbnd,hdec⟩ := hgo (b 0) (fun z => F z-b 0 z) (D\{0}) + (hDb 0 h0) hr (fun β hβ => hDb β hβ.1) + (fun β hβ => lt_of_le_of_ne (hnonpos β hβ.1) hβ.2) he + exact ⟨b 0,_,δ,hδ,hDb 0 h0,ha,hbnd,hdec,hr.eventually_analytic,he⟩ + · have he : ∀ z,F z=0+F z := fun z => (zero_add _).symm + obtain ⟨δ,hδ,ha,hbnd,hdec⟩ := hgo (fun _ => 0) F D (hK.lower.const_mem 0) + htrim hDb (fun β hβ => lt_of_le_of_ne (hnonpos β hβ) (fun h => h0 (h ▸ hβ))) he + exact ⟨_,F,δ,hδ,hK.lower.const_mem 0,ha,hbnd,hdec,htrim.eventually_analytic,he⟩ + +private lemma filtered_model_limit {clocks : List (ℝ → ℝ)} {clock : ℝ → ℝ} + (hvalid : ValidClocks (clock::clocks)) {func : ℝ → ℂ} (hfunc : ClockGerm clocks func) + {model : ℂ → ℂ} (hanalytic : ∀ᶠ point in sectorInfinity,AnalyticAt ℂ model point) + (heq : func =ᶠ[atTop] fun time => model (clock time:ℂ)) {limit : ℂ} + (hlim : Tendsto func atTop (𝓝 limit)) : Tendsto model sectorInfinity (𝓝 limit) := by + induction clocks generalizing clock func model limit with + | nil => + obtain ⟨scale,hscale,hclock⟩ := hvalid.2.2.2 + exact filtered_first_clock_limit hfunc hscale hclock hanalytic heq hlim + | cons lower clocks ih => + obtain ⟨representative,support,coeff,hexp,hcoeff,heqrep⟩ := hfunc + obtain ⟨field,hdata⟩ := hvalid.1.sectorData + have hlowerc := (hvalid.1.2.1.real_eventually_analytic hvalid.1.1).mono + (fun _ hanalytic => hanalytic.continuousAt) + have hreal : Tendsto (fun time : ℝ => representative (time:ℂ)) atTop (𝓝 limit) := by + rw [Filter.tendsto_def] + intro bound hbound + exact eventually_of_comp_clock hvalid.1.2.2.1 hlowerc + ((hlim.congr' heqrep).eventually hbound) + have hmembers : ∀ exponent∈support,coeff exponent∈field := + fun exponent hmem => (hdata.membership _).mpr (hcoeff exponent hmem) + obtain ⟨constant,remainder,gap,hgap,hconstant,hconstantlim,hbound,hdecay,hanalyticrep,hdecomp⟩ := + filtered_finite_decomposition hdata + (fun coefficient hmember value hlimit => ih hvalid.1 + ((hdata.membership _).mp hmember).1 ((hdata.membership _).mp hmember).2 + EventuallyEq.rfl (hlimit.comp hvalid.1.2.2.1)) + ⟨support,coeff,hexp,hmembers⟩ hreal + have hreplimit : Tendsto representative sectorInfinity (𝓝 limit) := by + have hzero := hdecay.tendsto_zero (by linarith : -gap/2<0) + have heq : representative = fun point => constant point + remainder point := + funext hdecomp + simpa only [heq,add_zero] using hconstantlim.add hzero + obtain ⟨inverse,hinverseanalytic,hinverse,heqinverse⟩ := filtered_previous_chart hvalid + have hcomposition : ∀ᶠ point in sectorInfinity, + AnalyticAt ℂ (fun point => representative (inverse point)) point := by + filter_upwards [hinverseanalytic,hinverse.eventually hexp.eventually_analytic] + with point hinverse hrep + exact hrep.comp hinverse + have hmodels : model =ᶠ[sectorInfinity] fun point => representative (inverse point) := by + apply sector_analytic_eq_of_ray hanalytic hcomposition + have hclockc := (hvalid.2.1.real_eventually_analytic hvalid.1).mono + (fun _ hanalytic => hanalytic.continuousAt) + apply eventually_of_comp_clock hvalid.2.2.1 hclockc + filter_upwards [heq,heqrep,heqinverse] with time heq heqrep heinverse + rw [heinverse,←heq,←heqrep] + exact (hreplimit.comp hinverse).congr' hmodels.symm + +lemma ClockSectorData.finite_decomposition {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} + (hvalid : ValidClocks (X::xs)) {K : Set (ℂ → ℂ)} (hK : ClockSectorData xs X K) + {F : ℂ → ℂ} (hF : ExpansionOver K F) {d : ℂ} + (hlim : Tendsto (fun t : ℝ => F (t:ℂ)) atTop (𝓝 d)) : + ∃ (a r : ℂ → ℂ) (δ : ℝ),0<δ ∧ a∈K ∧ Tendsto a sectorInfinity (𝓝 d) ∧ + BoundedExpansionOver K (-δ) r ∧ ExpBound (-δ/2) r ∧ + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ r z) ∧ ∀ z,F z=a z+r z := by + apply filtered_finite_decomposition hK _ hF hlim + intro coefficient hmember value hlimit + have hlower := (hK.membership _).mp hmember + exact filtered_model_limit hvalid hlower.1 hlower.2 EventuallyEq.rfl + (hlimit.comp hvalid.2.2.1) + +lemma finite_common_positive {ι : Type*} [Fintype ι] {δ : ι → ℝ} + (hδ : ∀ i,0<δ i) : ∃ ε : ℝ,0<ε ∧ ∀ i,ε≤δ i := by + classical + have h : ∀ S : Finset ι,∃ ε : ℝ,0<ε ∧ ∀ i∈S,ε≤δ i := by + intro S + induction S using Finset.induction_on with + | empty => exact ⟨1,zero_lt_one,by simp⟩ + | @insert i S hi ih => + obtain ⟨ε,hε,hh⟩ := ih + refine ⟨min ε (δ i),lt_min hε (hδ i),?_⟩ + intro j hj + rcases Finset.mem_insert.mp hj with rfl|hj + · exact min_le_right _ _ + · exact (min_le_left _ _).trans (hh j hj) + obtain ⟨ε,hε,hh⟩ := h Finset.univ + exact ⟨ε,hε,fun i => hh i (Finset.mem_univ i)⟩ + +lemma BoundedExpansionOver.mono {K : Set (ℂ → ℂ)} {α β : ℝ} {f : ℂ → ℂ} + (hf : BoundedExpansionOver K α f) (h : α≤β) : BoundedExpansionOver K β f := by + obtain ⟨E,b,hf,hb,hE⟩ := hf + exact ⟨E,b,hf,hb,fun γ hγ => (hE γ hγ).trans h⟩ + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/FirstLevelCharts.lean b/lean/OAI/Analysis/PathSelection/FirstLevelCharts.lean new file mode 100644 index 0000000000000000000000000000000000000000..36844b94c64b7918cdd3674ef200141fa34bdc88 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/FirstLevelCharts.lean @@ -0,0 +1,395 @@ +import Mathlib +import OAI.Analysis.PathSelection.RelativeErrors + +namespace OAI + +/-! First-level and lower-sector common clock charts. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +def SectorClockChart (F H : ℂ → ℂ) : Prop := + ∃ (y : ℂ → ℂ) (J : ℝ → ℝ), + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z ∧ H (y z)=z) ∧ + (∀ᶠ t : ℝ in atTop,y (H (t:ℂ))=(t:ℂ)) ∧ + Tendsto y sectorInfinity sectorInfinity ∧ Tendsto J atTop atTop ∧ + (∀ᶠ t : ℝ in atTop,y (t:ℂ)=(J t:ℂ)) ∧ + (∀ᶠ t : ℝ in atTop,(F (y (t:ℂ))).im=0 ∧ 0<(F (y (t:ℂ))).re) ∧ + Tendsto (fun t : ℝ => (F (y (t:ℂ))).re) atTop atTop ∧ + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (y w)) z) ∧ + Tendsto (fun w => F (y w)) sectorInfinity sectorInfinity ∧ + (∀ᶠ z in sectorInfinity,‖F (y (‖z‖:ℂ))‖/16≤‖F (y z)‖ ∧ + ‖F (y z)‖≤16*‖F (y (‖z‖:ℂ))‖) ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun z => (F (y z)).re) =o[sectorInfinity] Complex.re) + +theorem ExpansionOver.first_zero_chart {F H : ℂ → ℂ} + (hF : ExpansionOver PuiseuxSector F) (hH : ExpansionOver PuiseuxSector H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : ∃ D : ℝ,0 (H (t:ℂ)).re)) + (htop : Tendsto (fun z => deriv H z/H z) sectorInfinity (𝓝 0)) : + SectorClockChart F H := by + obtain ⟨g,h,hg,hh,hne,hgr,hhr,hgt,hht,hhfast,hgo,hFe,hHe,hgo'⟩ := + hF.zero_leading_data hH hFr hHr hFt hHt hO hfast htop + obtain ⟨I,x,hI,hIt,hIo,hxa,hxt,hxr,hxright,hxmod,hfamily⟩ := + PuiseuxSector.analytic_change_clock hh (hhr.mono fun _ h => h.1) hht hhfast + obtain ⟨hGa,hGt,hGmod,hGmap⟩ := hfamily g hg (hgr.mono fun _ h => h.1) hgt hgo + obtain ⟨ε,K,hε,hK,hErr⟩ := hFe.common_sector_bound hHe + have hFa := hF.choose_spec.choose_spec.1.eventually_analytic + have hHa := hH.choose_spec.choose_spec.1.eventually_analytic + let G : ℂ → ℂ := fun z => g (x z) + let E : ℂ → ℂ := fun z => F (x z)/g (x z)-1 + let P : ℂ → ℂ := fun z => H (x z) + have hPa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ P z := by + filter_upwards [hxa,hxt.eventually hHa] with z hx hh + exact hh.comp hx.1 + have hPr : ∀ᶠ t : ℝ in atTop,(P (t:ℂ)).im=0 := by + filter_upwards [hxr,hIt.eventually hHr] with t hx hh + simpa only [P,hx.1] using hh.1 + have hPt : Tendsto (fun t : ℝ => (P (t:ℂ)).re) atTop atTop := + (hHt.comp hIt).congr' (hxr.mono fun t ht => by simp only [P,ht.1,Function.comp_apply]) + have hEa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ E z := by + filter_upwards [hxa,hxt.eventually hFa,hxt.eventually hg.1,hxt.eventually hne] with z hx hf hg hn + exact ((hf.comp hx.1).div (hg.comp hx.1) hn.1).sub analyticAt_const + have hPe : ∀ᶠ z in sectorInfinity,‖P z-z‖≤K*‖z‖*Real.exp (-ε*(x z).re) := by + filter_upwards [hxa,hxt.eventually hErr,hxt.eventually hne] with z hx he hn + have heq : P z-z=z*(H (x z)/h (x z)-1) := by + calc + P z-z=H (x z)-h (x z) := by rw [hx.2] + _=h (x z)*(H (x z)/h (x z)-1) := by field_simp [hn.2] + _=z*(H (x z)/h (x z)-1) := by rw [hx.2] + rw [heq,norm_mul] + exact (mul_le_mul_of_nonneg_left he.2 (norm_nonneg z)).trans_eq (by ring) + have hEe : ∀ᶠ z in sectorInfinity,‖E z‖≤K*Real.exp (-ε*(x z).re) := + (hxt.eventually hErr).mono fun _ he => he.1 + obtain ⟨D,hD,hDb⟩ := hgo.exists_pos + have hGr : ∀ᶠ t : ℝ in atTop,‖G (t:ℂ)‖≤D*|t| := by + filter_upwards [hxr,hIt.eventually hDb.bound,hIt.eventually hgr] with t hx hd hg + have eh : (h (I t:ℂ)).re=t := congrArg Complex.re hx.2 + have eg : g (I t:ℂ)=((g (I t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hg.1) + change ‖g (x (t:ℂ))‖≤D*|t| + rw [hx.1,eg,Complex.norm_real,Real.norm_eq_abs] + simpa only [Real.norm_eq_abs,eh] using hd + have hGu : ∀ᶠ z in sectorInfinity,‖G z‖≤(4*D)*‖z‖ := by + filter_upwards [hGmod,tendsto_norm_sectorInfinity.eventually hGr] with z hm hr + have hr' : ‖g (x (‖z‖:ℂ))‖≤D*‖z‖ := by simpa only [abs_of_nonneg (norm_nonneg _)] using hr + exact hm.2.trans (by nlinarith) + obtain ⟨v,J,hva,hvt,hJt,hvr,hvright,hfva,hfvt,hfvm,hfsep⟩ := + zero_exponent_chart hPa hPr (by norm_num : (1:ℝ)≤4) hK hε hIt + (hI.log_littleO_unbounded hIt) hxmod hxt hPe hGa hEa hGt + (show (0:ℝ)≤4*D by positivity) hGu (by norm_num : (0:ℝ)<4) hGmod hEe + let y : ℂ → ℂ := fun z => x (v z) + let Q : ℂ → ℂ := fun z => G (v z)*(1+E (v z)) + have hyt : Tendsto y sectorInfinity sectorInfinity := hxt.comp hvt + have hyr : ∀ᶠ t : ℝ in atTop,y (t:ℂ)=(I (J t):ℂ) := by + filter_upwards [hvr,hJt.eventually hxr] with t hv hx + simp only [y,hv.1,hx.1] + have hQt : ∀ᶠ z in sectorInfinity,Q z=F (y z) := by + filter_upwards [hyt.eventually hne] with z hz + dsimp [Q,G,E,y] + have hn : g (x (v z))≠0 := hz.1 + field_simp [hn] + ring + have hvrightC : ∀ᶠ t : ℝ in atTop,v (P (t:ℂ))=(t:ℂ) := by + filter_upwards [hvright,hPr,hPt.eventually hvr] with t hi hp hv + have he : P (t:ℂ)=((P (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hp) + rw [he,hv.1,hi] + have hyrt : ∀ᶠ t : ℝ in atTop,y (H (t:ℂ))=(t:ℂ) := by + filter_upwards [hxright,hht.eventually hvrightC,hhr] with t hx hv hh + have eh : h (t:ℂ)=((h (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hh.1) + have hp : P (h (t:ℂ))=H (t:ℂ) := by simp only [P,hx] + rw [←eh,hp] at hv + dsimp [y] + rw [hv,hx] + have hIJt := hIt.comp hJt + refine ⟨y,fun t => I (J t),?_,hyrt,hyt,hIJt,hyr,?_,?_,?_,hfvt.congr' hQt,?_,?_⟩ + · filter_upwards [hva,hvt.eventually hxa] with z hv hx + exact ⟨hx.1.comp hv.1,hv.2⟩ + · filter_upwards [hyr,hIJt.eventually hFr] with t hy hf + simpa only [hy,Function.comp_apply] using hf + · exact (hFt.comp hIJt).congr' (hyr.mono fun t hy => by simp only [hy,Function.comp_apply]) + · filter_upwards [hva,hvt.eventually hxa,hyt.eventually hFa] with z hv hx hf + exact hf.comp (hx.1.comp hv.1) + · filter_upwards [hfvm,hQt,tendsto_norm_sectorInfinity.eventually (tendsto_real_sectorInfinity.eventually hQt)] with z hm he hr + change ‖Q (‖z‖:ℂ)‖/(4*4)≤‖Q z‖ ∧ ‖Q z‖≤(4*4)*‖Q (‖z‖:ℂ)‖ at hm + simpa only [he,hr,show (4:ℝ)*4=16 by norm_num] using hm + · intro hsmall + have hGs : (fun z => (G z).re) =o[sectorInfinity] Complex.re := by + obtain ⟨η,R,hη,hm,hs⟩ := hGmap baseLoss 1 admissible_baseLoss + apply Asymptotics.IsLittleO.of_bound + intro δ hδ + obtain ⟨A,hA⟩ := hs (hgo' hsmall) δ hδ + have hb : ∀ᶠ z in sectorInfinity,|(G z).re|≤δ*z.re := ⟨η,A,hη,hA⟩ + filter_upwards [hb] with z hz + simp only [Real.norm_eq_abs] + exact hz.trans (mul_le_mul_of_nonneg_left (le_abs_self _) hδ.le) + exact (hfsep hGs).congr' (hQt.mono fun _ he => congrArg Complex.re he) Filter.EventuallyEq.rfl + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma real_quotient_tendsto_zero {F H : ℂ → ℂ} + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0) + (ho : (fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re)) : + Tendsto (fun t : ℝ => F (t:ℂ)/H (t:ℂ)) atTop (𝓝 0) := by + have ht := Complex.continuous_ofReal.continuousAt.tendsto.comp ho.tendsto_div_nhds_zero + apply ht.congr' + filter_upwards [hFr,hHr] with t hf hh + have ef : F (t:ℂ)=((F (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hf) + have eh : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hh) + change (((F (t:ℂ)).re/(H (t:ℂ)).re:ℝ):ℂ)=F (t:ℂ)/H (t:ℂ) + rw [Complex.ofReal_div] + exact congrArg₂ (fun a b : ℂ => a/b) ef.symm eh.symm + +lemma PositiveExponentialChart.sector {F H : ℂ → ℂ} + (h : PositiveExponentialChart F H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0) : + SectorClockChart F H := by + obtain ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,hmap⟩ := h + have hJt : Tendsto (fun t : ℝ => (x (t:ℂ)).re) atTop atTop := + tendsto_re_stripInfinity.comp (hxt.comp tendsto_real_sectorInfinity) + have hyd : ∀ᶠ z in sectorInfinity,0 Complex.ext rfl (by simpa using ht.1) + have hmapping : Tendsto (fun z => F (x z)) sectorInfinity sectorInfinity := by + apply Filter.tendsto_def.mpr + intro U hU + obtain ⟨ω,S,hω,hU⟩ := hU + obtain ⟨η,R,hη,hm,hn,hs⟩ := hmap ω S hω + exact ⟨η,R,hη,fun z hz => hU _ (hm z hz)⟩ + obtain ⟨η,R,hη,hm,hn,hs⟩ := hmap baseLoss 1 admissible_baseLoss + refine ⟨x,fun t : ℝ => (x (t:ℂ)).re, + hyd.mono (fun z hz => ⟨hxa z hz,hl z hz.1 hz.2⟩),hr, + hxt.mono_right stripInfinity_le_sectorInfinity,hJt,hyr, + hxr.mono (fun _ ht => ht.2),hft,hfa,hmapping,?_,?_⟩ + · have hn' : ∀ᶠ z in sectorInfinity,(F (x (‖z‖:ℂ))).re/2≤‖F (x z)‖ ∧ + ‖F (x z)‖≤2*(F (x (‖z‖:ℂ))).re := ⟨η,R,hη,hn⟩ + filter_upwards [hn',tendsto_norm_sectorInfinity.eventually hxr] with z hn hr + have eq : F (x (‖z‖:ℂ))=((F (x (‖z‖:ℂ))).re:ℂ) := + Complex.ext rfl (by simpa using hr.2.1) + rw [eq,Complex.norm_of_nonneg hr.2.2.le] + constructor <;> nlinarith + · intro ho + have ht := real_quotient_tendsto_zero hFr hHr ho + apply Asymptotics.IsLittleO.of_bound + intro ε hε + obtain ⟨A,hA⟩ := hs ht ε hε + have hb : ∀ᶠ z in sectorInfinity,|(F (x z)).re|≤ε*z.re := ⟨η,A,hη,hA⟩ + filter_upwards [hb] with z hz + simp only [Real.norm_eq_abs] + exact hz.trans (mul_le_mul_of_nonneg_left (le_abs_self _) hε.le) + + + +theorem ExpansionOver.first_level_chart {F H : ℂ → ℂ} + (hF : ExpansionOver PuiseuxSector F) (hH : ExpansionOver PuiseuxSector H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : ∃ D : ℝ,0 (H (t:ℂ)).re)) : + SectorClockChart F H := by + obtain ⟨b,hb,g,hg,hg0,hgr,hHe,hHd⟩ := hH.puiseux_positive_leading hHr hHt + rcases hb.eq_or_lt with hb | hb + · have hzero : Tendsto (fun z => deriv H z/H z) sectorInfinity (𝓝 0) := by + simpa only [←hb,Complex.ofReal_zero] using hHd + exact hF.first_zero_chart hH hFr hHr hFt hHt hO hfast hzero + · exact (hF.first_positive_chart hH hFr hHr hFt hHt hO ⟨b,hb,hHd⟩).sector + (hFr.mono fun _ h => h.1) (hHr.mono fun _ h => h.1) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma sector_inverse_unique {H x y : ℂ → ℂ} + (hHa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ H z) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hxa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ x z) + (hya : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z) + (hx : ∀ᶠ t : ℝ in atTop,x (H (t:ℂ))=(t:ℂ)) + (hy : ∀ᶠ t : ℝ in atTop,y (H (t:ℂ))=(t:ℂ)) : + x =ᶠ[sectorInfinity] y := by + have hc : ∀ᶠ t : ℝ in atTop,ContinuousAt (fun t : ℝ => (H (t:ℂ)).re) t := by + filter_upwards [tendsto_real_sectorInfinity.eventually hHa] with t ht + exact Complex.continuous_re.continuousAt.comp + (ht.continuousAt.comp Complex.continuous_ofReal.continuousAt) + apply sector_analytic_eq_of_ray hxa hya + apply eventually_of_comp_clock hHt hc + filter_upwards [hx,hy,hHr] with t hx hy hr + have he : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hr) + change x ((H (t:ℂ)).re:ℂ)=y ((H (t:ℂ)).re:ℂ) + rw [←he,hx,hy] + + + +def ScalarChartAt (F y : ℂ → ℂ) : Prop := + (∀ᶠ t : ℝ in atTop,(F (y (t:ℂ))).im=0 ∧ 0<(F (y (t:ℂ))).re) ∧ + Tendsto (fun t : ℝ => (F (y (t:ℂ))).re) atTop atTop ∧ + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (y w)) z) ∧ + Tendsto (fun w => F (y w)) sectorInfinity sectorInfinity ∧ + (∀ᶠ z in sectorInfinity,‖F (y (‖z‖:ℂ))‖/16≤‖F (y z)‖ ∧ + ‖F (y z)‖≤16*‖F (y (‖z‖:ℂ))‖) + +theorem ExpansionOver.first_level_common_chart {H : ℂ → ℂ} + (hH : ExpansionOver PuiseuxSector H) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re)) : + ∃ (y : ℂ → ℂ) (J : ℝ → ℝ), + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z ∧ H (y z)=z) ∧ + (∀ᶠ t : ℝ in atTop,y (H (t:ℂ))=(t:ℂ)) ∧ + Tendsto y sectorInfinity sectorInfinity ∧ Tendsto J atTop atTop ∧ + (∀ᶠ t : ℝ in atTop,y (t:ℂ)=(J t:ℂ)) ∧ + ∀ F : ℂ → ℂ,ExpansionOver PuiseuxSector F → + (∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) → + Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop → + (∃ D : ℝ,0 (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun z => (F (y z)).re) =o[sectorInfinity] Complex.re) := by + have hself : ∃ D : ℝ,0 by simp⟩ + obtain ⟨y,J,hya,hyr,hyt,hJt,hyray,hyHr,hyHt,hyHa,hyHt',hyHm,hyHs⟩ := + hH.first_level_chart hH hHr hHr hHt hHt hself hfast + refine ⟨y,J,hya,hyr,hyt,hJt,hyray,?_⟩ + intro F hF hFr hFt hO + obtain ⟨v,I,hva,hvr,hvt,hIt,hvray,hFvr,hFvt,hFva,hFvt',hFvm,hFvs⟩ := + hF.first_level_chart hH hFr hHr hFt hHt hO hfast + have hvy := sector_inverse_unique hH.choose_spec.choose_spec.1.eventually_analytic + (hHr.mono fun _ h => h.1) hHt (hva.mono fun _ h => h.1) (hya.mono fun _ h => h.1) hvr hyr + have he : (fun z => F (v z)) =ᶠ[sectorInfinity] (fun z => F (y z)) := + hvy.mono fun _ ht => congrArg F ht + have her := tendsto_real_sectorInfinity.eventually he + refine ⟨⟨?_,hFvt.congr' (her.mono fun _ ht => congrArg Complex.re ht),?_,hFvt'.congr' he,?_⟩,?_⟩ + · filter_upwards [her,hFvr] with t he hr + rwa [←he] + · filter_upwards [hya,hyt.eventually hF.choose_spec.choose_spec.1.eventually_analytic] with z hy hf + exact hf.comp hy.1 + · filter_upwards [he,hFvm,tendsto_norm_sectorInfinity.eventually her] with z he hm hr + rwa [he,hr] at hm + · intro hs + exact (hFvs hs).congr' (he.mono fun _ ht => congrArg Complex.re ht) Filter.EventuallyEq.rfl + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +structure SectorInverse (H y : ℂ → ℂ) (I : ℝ → ℝ) : Prop where + analytic_left : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z ∧ H (y z)=z + right : ∀ᶠ t : ℝ in atTop,y (H (t:ℂ))=(t:ℂ) + maps_sector : Tendsto y sectorInfinity sectorInfinity + ray_unbounded : Tendsto I atTop atTop + real_ray : ∀ᶠ t : ℝ in atTop,y (t:ℂ)=(I t:ℂ) + +structure ScalarSectorChart (F y : ℂ → ℂ) : Prop where + positive : ∀ᶠ t : ℝ in atTop,(F (y (t:ℂ))).im=0 ∧ 0<(F (y (t:ℂ))).re + unbounded : Tendsto (fun t : ℝ => (F (y (t:ℂ))).re) atTop atTop + analytic : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (y w)) z + maps_sector : Tendsto (fun w => F (y w)) sectorInfinity sectorInfinity + radial : ∃ C : ℝ,0 (H (t:ℂ)).re) atTop atTop → + id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + ∃ (y : ℂ → ℂ) (I : ℝ → ℝ),SectorInverse H y I ∧ + ∀ F : ℂ → ℂ,ExpansionOver K F → + (∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) → + Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop → + (fun t : ℝ => (F (t:ℂ)).re) =O[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + ScalarSectorChart F y ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun z => (F (y z)).re) =o[sectorInfinity] Complex.re) + +lemma real_positive_bigO {F H : ℂ → ℂ} + (hFr : ∀ᶠ t : ℝ in atTop,0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,0<(H (t:ℂ)).re) + (hO : (fun t : ℝ => (F (t:ℂ)).re) =O[atTop] (fun t : ℝ => (H (t:ℂ)).re)) : + ∃ D : ℝ,0 h.2) (hr.mono fun _ h => h.2) hFO) + exact ⟨⟨hpos,hunb,hana,hmap,16,by norm_num,hnorm⟩,hsmall⟩ + +end DegeneratingTrees.Clock + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + + +def LowerSectorCharts (K : Set (ℂ → ℂ)) : Prop := + ∀ H : ℂ → ℂ,H∈K → + (∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) → + Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop → + id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + ∃ (y : ℂ → ℂ) (I : ℝ → ℝ),SectorInverse H y I ∧ + Real.log =o[atTop] I ∧ + (∃ C : ℝ,1≤C ∧ ∀ᶠ z in sectorInfinity,I ‖z‖/C≤‖y z‖ ∧ ‖y z‖≤C*I ‖z‖) ∧ + ∀ F : ℂ → ℂ,F∈K → + (∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) → + Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop → + (fun t : ℝ => (F (t:ℂ)).re) =O[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + ScalarSectorChart F y ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun z => (F (y z)).re) =o[sectorInfinity] Complex.re) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/FunctionSeries.lean b/lean/OAI/Analysis/PathSelection/FunctionSeries.lean new file mode 100644 index 0000000000000000000000000000000000000000..35a97c479b140402a9e2f7dd9fe0d74e81fac182 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/FunctionSeries.lean @@ -0,0 +1,253 @@ +import Mathlib + +namespace OAI + +/-! Analytic functions with values in continuous-function Banach spaces. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Metric Filter Topology +open scoped BigOperators NNReal ENNReal +namespace DegeneratingTrees + +variable {K E F : Type*} [TopologicalSpace K] [CompactSpace K] + [NormedAddCommGroup E] [NormedSpace ℂ E] + [NormedAddCommGroup F] [NormedSpace ℂ F] + + +def liftCML {n : ℕ} (p : E [×n]→L[ℂ] F) : C(K, E) [×n]→L[ℂ] C(K, F) := + let P : MultilinearMap ℂ (fun _ : Fin n => C(K, E)) C(K, F) := + { toFun := fun v => ⟨fun t => p (fun i => v i t), + p.cont.comp (continuous_pi fun i => (v i).continuous)⟩ + map_update_add' := by + intro _ v i a b + ext t + change p (fun j => Function.update v i (a + b) j t) = + p (fun j => Function.update v i a j t) + p (fun j => Function.update v i b j t) + have he (u : C(K, E)) : (fun j => Function.update v i u j t) = + Function.update (fun j => v j t) i (u t) := by + ext j + by_cases hj : j = i <;> simp [hj] + simp_rw [he] + exact p.map_update_add (fun j => v j t) i (a t) (b t) + map_update_smul' := by + intro _ v i c a + ext t + change p (fun j => Function.update v i (c • a) j t) = + c • p (fun j => Function.update v i a j t) + have he (u : C(K, E)) : (fun j => Function.update v i u j t) = + Function.update (fun j => v j t) i (u t) := by + ext j + by_cases hj : j = i <;> simp [hj] + simp_rw [he] + exact p.map_update_smul (fun j => v j t) i c (a t) } + P.mkContinuous ‖p‖ (by + intro v + apply (ContinuousMap.norm_le _ (by positivity)).2 + intro t + exact (p.le_opNorm _).trans (mul_le_mul_of_nonneg_left + (Finset.prod_le_prod₀ (fun _ _ => norm_nonneg _) + (fun i _ => (v i).norm_coe_le_norm t)) (norm_nonneg p))) + +@[simp] theorem liftCML_apply {n : ℕ} (p : E [×n]→L[ℂ] F) + (v : Fin n → C(K, E)) (t : K) : liftCML p v t = p (fun i => v i t) := rfl + +theorem liftCML_norm_le {n : ℕ} (p : E [×n]→L[ℂ] F) : + ‖liftCML (K := K) p‖ ≤ ‖p‖ := + by + unfold liftCML + apply MultilinearMap.mkContinuous_norm_le + exact norm_nonneg _ + + + +theorem liftSeries_radius {p : FormalMultilinearSeries ℂ E F} {r : ℝ≥0} + (hr : (r : ℝ≥0∞) < p.radius) : + (r : ℝ≥0∞) ≤ (show FormalMultilinearSeries ℂ C(K, E) C(K, F) from + fun n => liftCML (K := K) (p n)).radius := by + apply FormalMultilinearSeries.le_radius_of_summable + exact Summable.of_nonneg_of_le (fun _ => by positivity) + (fun n => mul_le_mul_of_nonneg_right (liftCML_norm_le (p n)) (by positivity)) + (p.summable_norm_mul_pow hr) + + + +theorem analytic_continuousMap_of_series [CompleteSpace F] {f : E → F} + {p : FormalMultilinearSeries ℂ E F} {R : ℝ≥0∞} + (hp : HasFPowerSeriesOnBall f p 0 R) {r : ℝ≥0} (hrR : (r : ℝ≥0∞) < R) : + ∃ Φ : C(K, E) → C(K, F), AnalyticOnNhd ℂ Φ (ball 0 (r : ℝ)) ∧ + ∀ v ∈ ball (0 : C(K, E)) (r : ℝ), ∀ t, Φ v t = f (v t) := by + let P : FormalMultilinearSeries ℂ C(K, E) C(K, F) := fun n => liftCML (p n) + have hrP : (r : ℝ≥0∞) ≤ P.radius := liftSeries_radius (hrR.trans_le hp.r_le) + refine ⟨P.sum, ?_, ?_⟩ + · apply P.analyticOnNhd.mono + intro v hv + rw [mem_eball_zero_iff] + apply lt_of_lt_of_le _ hrP + have hn : ‖v‖ < (r : ℝ) := by simpa using hv + exact_mod_cast hn + · intro v hv t + have hv' : (‖v‖₊ : ℝ≥0∞) < r := by + have hn : ‖v‖ < (r : ℝ) := by simpa using hv + exact_mod_cast hn + have hvP : v ∈ eball (0 : C(K, E)) P.radius := by + exact (mem_eball_zero_iff).2 (hv'.trans_le hrP) + have hvR : v t ∈ eball (0 : E) R := by + rw [mem_eball_zero_iff] + exact (show (‖v t‖₊ : ℝ≥0∞) ≤ ‖v‖₊ from by + exact_mod_cast v.norm_coe_le_norm t).trans_lt (hv'.trans hrR) + have h₁ := (ContinuousMap.evalCLM (R := ℂ) (M := F) t).hasSum (P.hasSum hvP) + have h₂ := hp.hasSum hvR + simp only [zero_add] at h₂ + exact h₁.unique h₂ + + + +theorem analytic_continuousMap_realization [CompleteSpace F] {f : E → F} + (hf : AnalyticAt ℂ f 0) : + ∃ (r : ℝ), 0 < r ∧ ∃ Φ : C(K, E) → C(K, F), + AnalyticOnNhd ℂ Φ (ball 0 r) ∧ + ∀ v ∈ ball (0 : C(K, E)) r, ∀ t, Φ v t = f (v t) := by + obtain ⟨p, R, hp⟩ := hf + obtain ⟨r, hr0, hrR⟩ := ENNReal.lt_iff_exists_nnreal_btwn.mp hp.r_pos + exact ⟨r, by exact_mod_cast hr0, analytic_continuousMap_of_series hp hrR⟩ + + + +def circleExtension {r : ℝ} (f : C(sphere (0 : ℂ) r, ℂ)) (z : ℂ) : ℂ := by + classical + exact if hz : z ∈ sphere (0 : ℂ) r then f ⟨z, hz⟩ else 0 + +@[simp] theorem circleExtension_on {r : ℝ} (f : C(sphere (0 : ℂ) r, ℂ)) + {z : ℂ} (hz : z ∈ sphere (0 : ℂ) r) : circleExtension f z = f ⟨z, hz⟩ := by + simp only [circleExtension, dite_eq_left hz] + +private theorem circleExtension_continuousOn {r : ℝ} (f : C(sphere (0 : ℂ) r, ℂ)) : + ContinuousOn (circleExtension f) (sphere (0 : ℂ) r) := by + rw [continuousOn_iff_continuous_domRestrict] + convert f.continuous using 1 + ext z + exact circleExtension_on f z.property + + +def circleFunctional (r : ℝ) (hr : 0 ≤ r) : C(sphere (0 : ℂ) r, ℂ) →L[ℂ] ℂ := + let L : C(sphere (0 : ℂ) r, ℂ) →ₗ[ℂ] ℂ := + { toFun := fun f => ∮ z in C(0, r), circleExtension f z + map_add' := by + intro f g + have he : circleExtension (f + g) = fun z => circleExtension f z + circleExtension g z := by + ext z + by_cases hz : z ∈ sphere (0 : ℂ) r <;> simp only [circleExtension, hz, dite_true, dite_false, ContinuousMap.add_apply, add_zero] + rw [he] + exact circleIntegral.integral_add + ((circleExtension_continuousOn f).circleIntegrable hr) + ((circleExtension_continuousOn g).circleIntegrable hr) + map_smul' := by + intro c f + have he : circleExtension (c • f) = fun z => c • circleExtension f z := by + ext z + by_cases hz : z ∈ sphere (0 : ℂ) r <;> simp only [circleExtension, hz, dite_true, dite_false, ContinuousMap.smul_apply, smul_zero] + rw [he, circleIntegral.integral_smul] + rfl } + L.mkContinuous (2 * Real.pi * r) (by + intro f + apply circleIntegral.norm_integral_le_of_norm_le_const hr + intro z hz + rw [circleExtension_on f hz] + exact f.norm_coe_le_norm ⟨z, hz⟩) + +theorem circleFunctional_eq {r : ℝ} (hr : 0 ≤ r) (f : C(sphere (0 : ℂ) r, ℂ)) + (h : ℂ → ℂ) (he : ∀ z : sphere (0 : ℂ) r, f z = h z) : + circleFunctional r hr f = ∮ z in C(0, r), h z := by + apply circleIntegral.integral_congr hr + intro z hz + rw [circleExtension_on f hz] + exact he ⟨z, hz⟩ + + + +theorem analytic_circle_profiles {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} (hF : AnalyticAt ℂ F 0) : + ∃ a : ℝ, 0 < a ∧ ∀ r : ℝ, 0 < r → r < a → + ∃ φ ψ : A → C(sphere (0 : ℂ) r, ℂ), + AnalyticOnNhd ℂ F (ball 0 a ×ˢ closedBall 0 r) ∧ + AnalyticOnNhd ℂ φ (ball 0 a) ∧ AnalyticOnNhd ℂ ψ (ball 0 a) ∧ + (∀ q ∈ ball (0 : A) a, ∀ z : sphere (0 : ℂ) r, φ q z = F (q, z)) ∧ + (∀ q ∈ ball (0 : A) a, ∀ z : sphere (0 : ℂ) r, + ψ q z = deriv (fun y => F (q, y)) z) := by + let H : A × ℂ → ℂ × ℂ := fun x => (F x, fderiv ℂ F x (0, 1)) + have hH : AnalyticAt ℂ H 0 := hF.prod + (((ContinuousLinearMap.apply ℂ ℂ ((0, 1) : A × ℂ)).analyticAt _).comp hF.fderiv) + obtain ⟨p, R, hp⟩ := hH + obtain ⟨b, hb0, hbR⟩ := ENNReal.lt_iff_exists_nnreal_btwn.mp hp.r_pos + have hb : (0 : ℝ) < b := by exact_mod_cast hb0 + refine ⟨b / 2, half_pos hb, ?_⟩ + intro r hr hra + let K := sphere (0 : ℂ) r + let w : C(K, A × ℂ) := ⟨fun z => (0, z), + continuous_const.prodMk continuous_subtype_val⟩ + let L : A →L[ℂ] C(K, A × ℂ) := + (ContinuousLinearMap.const ℂ K).comp (ContinuousLinearMap.inl ℂ A ℂ) + let v : A → C(K, A × ℂ) := fun q => L q + w + have hve (q : A) (z : K) : v q z = (q, (z : ℂ)) := by simp [v, L, w] + have hva : AnalyticOnNhd ℂ v (ball 0 ((b : ℝ) / 2)) := + fun q _ => (L.analyticAt q).add analyticAt_const + have hvb (q : A) (hq : q ∈ ball (0 : A) ((b : ℝ) / 2)) : + v q ∈ ball (0 : C(K, A × ℂ)) (b : ℝ) := by + have hnq : ‖q‖ < (b : ℝ) / 2 := by simpa using hq + have hnv : ‖v q‖ ≤ max ‖q‖ r := by + apply (ContinuousMap.norm_le _ (le_max_of_le_left (norm_nonneg q))).2 + intro z + rw [hve, Prod.norm_def] + have hnz : ‖(z : ℂ)‖ = r := by simp + rw [hnz] + have : ‖v q‖ < (b : ℝ) := hnv.trans_lt + ((max_lt hnq hra).trans (half_lt_self hb)) + simpa using this + obtain ⟨Φ, hΦ, hΦe⟩ := analytic_continuousMap_of_series (K := K) hp hbR + let π₁ := ContinuousLinearMap.compLeftContinuous ℂ K (ContinuousLinearMap.fst ℂ ℂ ℂ) + let π₂ := ContinuousLinearMap.compLeftContinuous ℂ K (ContinuousLinearMap.snd ℂ ℂ ℂ) + let φ : A → C(K, ℂ) := fun q => π₁ (Φ (v q)) + let ψ : A → C(K, ℂ) := fun q => π₂ (Φ (v q)) + have hFball : AnalyticOnNhd ℂ F (ball 0 ((b : ℝ) / 2) ×ˢ closedBall 0 r) := by + intro x hx + have hn : ‖x‖ < (b : ℝ) := by + rw [Prod.norm_def] + have hx₁ : ‖x.1‖ < (b : ℝ) / 2 := by simpa using hx.1 + have hx₂ : ‖x.2‖ ≤ r := by simpa using hx.2 + exact (max_lt hx₁ (hx₂.trans_lt hra)).trans (half_lt_self hb) + have hxR : x ∈ eball (0 : A × ℂ) R := by + rw [mem_eball_zero_iff] + exact (show (‖x‖₊ : ℝ≥0∞) < b from by exact_mod_cast hn).trans hbR + exact ((ContinuousLinearMap.fst ℂ ℂ ℂ).analyticAt _).comp (hp.analyticOnNhd x hxR) + refine ⟨φ, ψ, hFball, ?_, ?_, ?_, ?_⟩ + · intro q hq + exact (π₁.analyticAt _).comp ((hΦ _ (hvb q hq)).comp (hva q hq)) + · intro q hq + exact (π₂.analyticAt _).comp ((hΦ _ (hvb q hq)).comp (hva q hq)) + · intro q hq z + change (Φ (v q) z).1 = F (q, z) + rw [hΦe _ (hvb q hq), hve] + · intro q hq z + change (Φ (v q) z).2 = deriv (fun y => F (q, y)) z + rw [hΦe _ (hvb q hq), hve] + have hFd := (hFball (q, z) ⟨hq, sphere_subset_closedBall z.property⟩).differentiableAt + exact ((hFd.hasFDerivAt.comp_hasDerivAt (z : ℂ) + ((hasDerivAt_const (z : ℂ) q).prodMk (hasDerivAt_id (z : ℂ)))).deriv).symm + + + +omit [CompactSpace K] in +theorem continuousMap_ringInverse_apply (f : C(K, ℂ)) (hf : IsUnit f) (z : K) : + Ring.inverse f z = (f z)⁻¹ := by + have hn : f z ≠ 0 := (f.isUnit_iff_forall_ne_zero).1 hf z + apply mul_left_cancel₀ hn + rw [← ContinuousMap.mul_apply, Ring.mul_inverse_cancel f hf] + simp [hn] + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/IdentityDetection.lean b/lean/OAI/Analysis/PathSelection/IdentityDetection.lean new file mode 100644 index 0000000000000000000000000000000000000000..970eb14f6a186b136c9f0ed3c8ac29efb4e1a8c2 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/IdentityDetection.lean @@ -0,0 +1,173 @@ +import Mathlib + +namespace OAI + +/-! Analytic identity detection by strict submersions and pathwise eventual vanishing. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace PathSelection.Detection + +variable {E F G : Type*} + [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E] + [NormedAddCommGroup F] [NormedSpace ℝ F] [CompleteSpace F] + [NormedAddCommGroup G] [NormedSpace ℝ G] + + +def IsStrictSubmersionAt (e : E → F) (x : E) : Prop := + ∃ e' : E →L[ℝ] F, HasStrictFDerivAt e e' x ∧ e'.range = ⊤ + +omit [CompleteSpace E] [CompleteSpace F] in +lemma IsStrictSubmersionAt.continuousAt {e : E → F} {x : E} + (he : IsStrictSubmersionAt e x) : ContinuousAt e x := by + obtain ⟨e', hd, _⟩ := he + exact hd.continuousAt + +lemma IsStrictSubmersionAt.map_nhds_eq {e : E → F} {x : E} + (he : IsStrictSubmersionAt e x) : map e (𝓝 x) = 𝓝 (e x) := by + obtain ⟨e', hd, hr⟩ := he + exact hd.map_nhds_eq_of_surj hr + + + +theorem nowhereDense_zeros_of_submersion + {U : Set F} {V : Set E} {f : F → G} {e : E → F} + (hf : AnalyticOnNhd ℝ f U) (hU : IsPreconnected U) + (hnonzero : ¬ EqOn f 0 U) + (hV : IsOpen V) (heU : MapsTo e V U) + (he : ∀ x ∈ V, IsStrictSubmersionAt e x) : + IsNowhereDense {x | x ∈ V ∧ f (e x) = 0} := by + let Z : Set V := {x | f (e x) = 0} + have hcont : Continuous (fun x : V => f (e x)) := by + apply continuous_iff_continuousAt.mpr + intro x + exact ((hf (e x) (heU x.property)).continuousAt.comp + (he x x.property).continuousAt).comp continuous_subtype_val.continuousAt + have hclosed : IsClosed Z := isClosed_eq hcont continuous_const + have hinterior : interior Z = ∅ := by + apply Set.eq_empty_iff_forall_notMem.mpr + intro x hx + have hz : ∀ᶠ y : V in 𝓝 x, f (e y) = 0 := + mem_interior_iff_mem_nhds.mp hx + have hz' : ∀ᶠ y in 𝓝 (x : E), f (e y) = 0 := by + rw [← hV.isOpenEmbedding_subtypeVal.map_nhds_eq x] + exact hz + have hz'' : f =ᶠ[𝓝 (e x)] 0 := by + rw [← (he x x.property).map_nhds_eq] + exact hz' + exact hnonzero + (hf.eqOn_zero_of_preconnected_of_eventuallyEq_zero hU (heU x.property) hz'') + have hnd : IsNowhereDense Z := hclosed.isNowhereDense_iff.mpr hinterior + have himage : (Subtype.val '' Z : Set E) = {x | x ∈ V ∧ f (e x) = 0} := by + ext x + constructor + · rintro ⟨y, hy, rfl⟩ + exact ⟨y.property, hy⟩ + · rintro ⟨hx, hz⟩ + exact ⟨⟨x, hx⟩, hz, rfl⟩ + rw [← himage] + exact Topology.IsInducing.subtypeVal.isNowhereDense_image hnd + + + +theorem eqOn_zero_of_integer_evaluations + {U : Set F} {V : Set E} {f : F → G} + (hf : AnalyticOnNhd ℝ f U) (hU : IsPreconnected U) + (hV : IsOpen V) (hVne : V.Nonempty) + (D : ℕ → Set E) (hD : ∀ N, IsOpen (D N)) + (e : ℕ → E → F) (heU : ∀ N, MapsTo (e N) (D N) U) + (he : ∀ N x, x ∈ D N → IsStrictSubmersionAt (e N) x) + (hzero : ∀ x ∈ V, ∃ N, x ∈ D N ∧ f (e N x) = 0) : + EqOn f 0 U := by + by_contra hn + have hnd : ∀ N, IsNowhereDense {x | x ∈ D N ∧ f (e N x) = 0} := + fun N => nowhereDense_zeros_of_submersion hf hU hn (hD N) (heU N) (he N) + have hmeagre : IsMeagre (⋃ N, {x | x ∈ D N ∧ f (e N x) = 0}) := + isMeagre_iUnion (fun N => (hnd N).isMeagre) + exact not_isMeagre_of_isOpen hV hVne (hmeagre.mono (by + intro x hx + obtain ⟨N, hNx, hz⟩ := hzero x hx + exact mem_iUnion.mpr ⟨N, hNx, hz⟩)) + + + +theorem eqOn_zero_of_pathwise_eventually_zero + {U : Set F} {V : Set E} {f : F → G} + (hf : AnalyticOnNhd ℝ f U) (hU : IsPreconnected U) + (hV : IsOpen V) (hVne : V.Nonempty) + (D : ℕ → Set E) (hD : ∀ N, IsOpen (D N)) + (e : ℕ → E → F) (heU : ∀ N, MapsTo (e N) (D N) U) + (he : ∀ N x, x ∈ D N → IsStrictSubmersionAt (e N) x) + (hzero : ∀ x ∈ V, ∀ᶠ N in atTop, x ∈ D N ∧ f (e N x) = 0) : + EqOn f 0 U := by + apply eqOn_zero_of_integer_evaluations hf hU hV hVne D hD e heU he + intro x hx + exact (hzero x hx).exists + + +theorem eqOn_zero_of_analytic_evaluations + {U : Set F} {V : Set E} {f : F → G} + (hf : AnalyticOnNhd ℝ f U) (hU : IsPreconnected U) + (hV : IsOpen V) (hVne : V.Nonempty) + (D : ℕ → Set E) (hD : ∀ N, IsOpen (D N)) + (e : ℕ → E → F) (heU : ∀ N, MapsTo (e N) (D N) U) + (he : ∀ N, AnalyticOnNhd ℝ (e N) (D N)) + (hsub : ∀ N x, x ∈ D N → (fderiv ℝ (e N) x).range = ⊤) + (hzero : ∀ x ∈ V, ∀ᶠ N in atTop, x ∈ D N ∧ f (e N x) = 0) : + EqOn f 0 U := by + apply eqOn_zero_of_pathwise_eventually_zero hf hU hV hVne D hD e heU _ hzero + intro N x hx + exact ⟨fderiv ℝ (e N) x, (he N x hx).hasStrictFDerivAt, hsub N x hx⟩ + + + +theorem family_zero_of_pathwise_eventually_zero + {Y : Type*} {U : Set F} {V : Set E} {W : Set Y} {f : F → Y → G} + (hf : ∀ y ∈ W, AnalyticOnNhd ℝ (fun x => f x y) U) + (hU : IsPreconnected U) (hV : IsOpen V) (hVne : V.Nonempty) + (D : ℕ → Set E) (hD : ∀ N, IsOpen (D N)) + (e : ℕ → E → F) (heU : ∀ N, MapsTo (e N) (D N) U) + (he : ∀ N x, x ∈ D N → IsStrictSubmersionAt (e N) x) + (hzero : ∀ x ∈ V, ∀ y ∈ W, + ∀ᶠ N in atTop, x ∈ D N ∧ f (e N x) y = 0) : + ∀ x ∈ U, ∀ y ∈ W, f x y = 0 := by + intro x hx y hy + exact eqOn_zero_of_pathwise_eventually_zero (hf y hy) hU hV hVne D hD e heU he + (fun t ht => hzero t ht y hy) hx + +omit [CompleteSpace E] [CompleteSpace F] in + + +lemma IsStrictSubmersionAt.triangular + {e : E → F} {p : E × ℝ → ℝ} {x : E × ℝ} + (he : IsStrictSubmersionAt e x.1) + {p' : E × ℝ →L[ℝ] ℝ} (hp : HasStrictFDerivAt p p' x) + (hne : p' (0, 1) ≠ 0) : + IsStrictSubmersionAt (fun q : E × ℝ => (e q.1, p q)) x := by + obtain ⟨e', hd, hr⟩ := he + let D : E × ℝ →L[ℝ] F × ℝ := + (e'.comp (ContinuousLinearMap.fst ℝ E ℝ)).prod p' + refine ⟨D, (hd.comp x hasStrictFDerivAt_fst).prodMk hp, ?_⟩ + apply LinearMap.range_eq_top.mpr + intro y + obtain ⟨v, hv⟩ := LinearMap.range_eq_top.mp hr y.1 + let t := (y.2 - p' (v, 0)) / p' (0, 1) + refine ⟨(v, t), ?_⟩ + have hsplit : p' (v, t) = p' (v, 0) + t * p' (0, 1) := by + have ht : (v, t) = (v, (0 : ℝ)) + t • ((0 : E), (1 : ℝ)) := by simp + rw [ht, map_add, map_smul] + rfl + apply Prod.ext + · exact hv + · change p' (v, t) = y.2 + rw [hsplit] + dsimp only [t] + rw [div_mul_cancel₀ _ hne] + ring + +end PathSelection.Detection +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/InverseAsymptotics.lean b/lean/OAI/Analysis/PathSelection/InverseAsymptotics.lean new file mode 100644 index 0000000000000000000000000000000000000000..a5e3cf75f160a1108c8d95d17cc1f5e80918daf1 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/InverseAsymptotics.lean @@ -0,0 +1,380 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockInverses + +namespace OAI + +/-! Strip and exponential inverse asymptotics and logarithmic radii. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped NNReal +namespace DegeneratingTrees.Clock + +lemma inverse_strip_tail {A R T d : ℝ} {f g : ℂ → ℂ} + (hd : 0 ⟨(le_max_left _ _).trans_lt hz.1,hz.2⟩ + have hdb (z : ℂ) (hz : z∈horizontalTail C R) : ‖deriv f z-1‖≤ε/2 := + hB z ⟨(le_max_right _ _).trans_lt hz.1,hz.2⟩ + have happ := approximates_identity_of_deriv (horizontalTail_convex C R) (hf.mono hsub) + (c := ⟨ε/2,by positivity⟩) hdb + have hh := happ (g w) hgS (t:ℂ) htS + change ‖f (g w)-f (t:ℂ)-(g w-(t:ℂ))‖≤(ε/2)*‖g w-(t:ℂ)‖ at hh + have hft' : f (t:ℂ)=(w.re:ℂ) := Complex.ext hft (by simpa using hreal t htA) + have hwreal : (w.re:ℂ)∈horizontalTail T d := ⟨hwT.1,by simpa using hd⟩ + have hgr : g (w.re:ℂ)=(t:ℂ) := by rw [←hft']; exact hfg t htA (by rwa [hft']) + rw [(hgf w hwT).2,hft'] at hh + have he : w-(w.re:ℂ)=Complex.I*(w.im:ℂ) := by apply Complex.ext <;> simp + rw [he] at hh + rw [hgr,show g w-(t:ℂ)-Complex.I*(w.im:ℂ)=-(Complex.I*(w.im:ℂ)-(g w-(t:ℂ))) by ring,norm_neg] + calc + ‖Complex.I*(w.im:ℂ)-(g w-(t:ℂ))‖ ≤ (ε/2)*‖g w-(t:ℂ)‖ := hh + _ ≤ (ε/2)*(2*|w.im|) := mul_le_mul_of_nonneg_left hgt (by positivity) + _ = ε*|w.im| := by ring + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma tendsto_stripInfinity_of_re_and_bounded_im {ι : Type*} {l : Filter ι} + {x : ι → ℂ} (hre : Tendsto (fun t => (x t).re) l atTop) + {C : ℝ} (him : ∀ᶠ t in l,|(x t).im| (H (t:ℂ)).re) atTop atTop) + (hq : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) : + ∃ T : ℝ,0 (x (r:ℂ)).re) atTop atTop ∧ + Tendsto x sectorInfinity stripInfinity ∧ + (∀ ε : ℝ,0<ε → ∃ U : ℝ,∀ w : ℂ,0 w*deriv x w) sectorInfinity (𝓝 ((b:ℂ)⁻¹)) := by + let d := Real.pi/b+1 + let R := 2*d+1 + have hd : 0 g (Complex.log w/(b:ℂ)) + have hmap (U : ℝ) (w : ℂ) (hT : Real.exp (b*U)<‖w‖) : + Complex.log w/(b:ℂ)∈horizontalTail U d := by + constructor + · rw [Complex.div_ofReal_re,Complex.log_re] + apply (lt_div_iff₀ hb).mpr + have hh := Real.log_lt_log (Real.exp_pos (b*U)) hT + rw [Real.log_exp] at hh + simpa only [mul_comm] using hh + · rw [Complex.div_ofReal_im,Complex.log_im,abs_div,abs_of_pos hb] + have hh := div_le_div_of_nonneg_right (Complex.abs_arg_le_pi w) hb.le + dsimp [d] + linarith + have hxa : AnalyticOnNhd ℂ x {w | 0 Complex.log w/(b:ℂ)) + ((analyticAt_clog (Complex.mem_slitPlane_iff.mpr (Or.inl hw.1))).div_const) + have hxe (w : ℂ) (hw : 0 (f (t:ℂ)).re) atTop atTop := by + apply ((Real.tendsto_log_atTop.comp hlim).atTop_div_const hb).congr' + filter_upwards [eventually_gt_atTop A] with t ht + rw [hfr t ht,Complex.ofReal_re] + rfl + filter_upwards [eventually_gt_atTop A,hr,htlim.eventually (eventually_gt_atTop T₀)] with t ht hrt hft + have hfstrip : f (t:ℂ)∈horizontalTail T₀ d := ⟨hft,by rw [hfr t ht]; simpa using hd⟩ + have hHreal : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext (by simp) (by simp [hrt.1]) + have hh : Complex.log (H (t:ℂ))/(b:ℂ)=f (t:ℂ) := by + rw [hHreal,←Complex.ofReal_log hrt.2.le,hfr t ht,Complex.ofReal_div] + dsimp [x]; rw [hh]; exact hfg t ht hfstrip + have hdom : ∀ᶠ w in sectorInfinity,0 (x w).re) sectorInfinity atTop := by + apply Filter.tendsto_atTop.mpr + intro B + obtain ⟨U,hUT,hU⟩ := inverse_strip_tail hd hdR hfa hfn hgb B + filter_upwards [tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (Real.exp (b*U)))] with w hw + exact (hU _ (hmap U w hw)).1.le + have hxto : Tendsto x sectorInfinity stripInfinity := by + apply tendsto_stripInfinity_of_re_and_bounded_im hxre (C := R) + filter_upwards [hdom] with w hw + exact (hgf _ (hmap T₀ w hw.2)).1.2 + have hreal (r : ℝ) (hTr : T by rw [hfr t ht]; simp) hgf hfg hgb (ε*b) (mul_pos hε hb) + refine ⟨Real.exp (b*U),?_⟩ + intro w hw hwU + have hn : 0<‖w‖ := (Real.exp_pos _).trans hwU + have he : Complex.log (‖w‖:ℂ)/(b:ℂ)=((Complex.log w/(b:ℂ)).re:ℂ) := by + rw [←Complex.ofReal_log hn.le,Complex.div_ofReal_re,Complex.log_re,Complex.ofReal_div] + have hh := hU _ (hmap U w hwU) + change ‖g (Complex.log w/(b:ℂ))-g ((Complex.log w/(b:ℂ)).re:ℂ)- + Complex.I*((Complex.log w/(b:ℂ)).im:ℂ)‖≤_ at hh + simp only [Complex.div_ofReal_im,Complex.log_im,abs_div,abs_of_pos hb] at hh + have hc : ε*b*(|w.arg|/b)=ε*|w.arg| := by field_simp + rw [hc] at hh + simpa only [x,he] using hh + · have heq : (fun w => w*deriv x w) =ᶠ[sectorInfinity] (fun w => (deriv H (x w)/H (x w))⁻¹) := by + filter_upwards [hdom,hxto.eventually ha,hxto.eventually h0] with w hw hHa hH0 + have hopen : IsOpen {v : ℂ | 0 H (x v)) =ᶠ[𝓝 w] id := + Filter.Eventually.mono (hopen.mem_nhds hw) (fun v hv => hxe v hv.1 hv.2) + have hh := ((hHa.differentiableAt.hasDerivAt).comp w (hxa w hw).differentiableAt.hasDerivAt) + have hmul : deriv H (x w)*deriv x w=1 := (hh.congr_of_eventuallyEq hident.symm).unique (hasDerivAt_id w) + have hderne : deriv H (x w)≠0 := by intro hz; simp [hz] at hmul + rw [div_eq_mul_inv,mul_inv_rev,inv_inv,hxe w hw.1 hw.2] + congr 1 + apply (mul_left_cancel₀ hderne) + rw [hmul,mul_inv_cancel₀ hderne] + exact (((hq.comp hxto).inv₀ hb0)).congr' heq.symm + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma complex_real_limit {G : ℝ → ℂ} {c : ℝ} + (hr : ∀ᶠ r : ℝ in atTop,(G r).im=0) + (ht : Tendsto (fun r => (G r).re) atTop (𝓝 c)) : Tendsto G atTop (𝓝 (c:ℂ)) := by + apply (Complex.continuous_ofReal.tendsto c |>.comp ht).congr' + exact hr.mono (fun r hr => Complex.ext (by simp) (by simpa using hr.symm)) + +theorem logarithmic_radius_derivative {G : ℂ → ℂ} {a : ℝ} + (ha : ∀ᶠ r : ℝ in atTop,AnalyticAt ℂ G (r:ℂ)) + (hr : ∀ᶠ r : ℝ in atTop,(G (r:ℂ)).im=0 ∧ 0<(G (r:ℂ)).re) + (hd : Tendsto (fun r : ℝ => (r:ℂ)*deriv G (r:ℂ)/G (r:ℂ)) atTop (𝓝 (a:ℂ))) : + (∀ᶠ s : ℝ in atTop,DifferentiableAt ℝ (fun s => Real.logb 2 (G (((2:ℝ)^s:ℝ):ℂ)).re) s) ∧ + Tendsto (deriv (fun s : ℝ => Real.logb 2 (G (((2:ℝ)^s:ℝ):ℂ)).re)) atTop (𝓝 a) ∧ + (∀ᶠ r : ℝ in atTop,(G (r:ℂ)).re=(2:ℝ)^(Real.logb 2 (G (((2:ℝ)^(Real.logb 2 r):ℝ):ℂ)).re)) := by + have h2 : Tendsto (fun s : ℝ => (2:ℝ)^s) atTop atTop := + tendsto_rpow_atTop_of_base_gt_one 2 (by norm_num) + have hlog : Real.log 2≠0 := ne_of_gt (Real.log_pos (by norm_num)) + have hder : ∀ᶠ s : ℝ in atTop, + HasDerivAt (fun s : ℝ => Real.logb 2 (G (((2:ℝ)^s:ℝ):ℂ)).re) + ((((2:ℝ)^s:ℝ):ℂ)*deriv G (((2:ℝ)^s:ℝ):ℂ)/G (((2:ℝ)^s:ℝ):ℂ)).re s := by + filter_upwards [h2.eventually ha,h2.eventually hr] with s ha hr + have hg : HasDerivAt (fun r : ℝ => (G (r:ℂ)).re) (deriv G (((2:ℝ)^s:ℝ):ℂ)).re ((2:ℝ)^s) := + Complex.reCLM.hasFDerivAt.comp_hasDerivAt ((2:ℝ)^s) ha.differentiableAt.hasDerivAt.comp_ofReal + have hp : HasDerivAt (fun s : ℝ => (2:ℝ)^s) (Real.log 2*(2:ℝ)^s) s := by + simpa using (hasDerivAt_id s).const_rpow (by norm_num : (0:ℝ)<2) + have hh : HasDerivAt (fun s : ℝ => Real.logb 2 (G (((2:ℝ)^s:ℝ):ℂ)).re) + ((G (((2:ℝ)^s:ℝ):ℂ)).re⁻¹*((deriv G (((2:ℝ)^s:ℝ):ℂ)).re*(Real.log 2*(2:ℝ)^s))/Real.log 2) s := by + simpa only [Real.logb,Function.comp_def] using + ((Real.hasDerivAt_log hr.2.ne').comp s (hg.comp s hp)).div_const (Real.log 2) + have hreal : G (((2:ℝ)^s:ℝ):ℂ)=((G (((2:ℝ)^s:ℝ):ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hr.1) + convert hh using 1 + rw [hreal,Complex.div_ofReal_re,Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] + simp only [Complex.ofReal_re] + field_simp + refine ⟨hder.mono (fun _ h => h.differentiableAt),?_,?_⟩ + · have hh := (Complex.continuous_re.tendsto (a:ℂ)).comp (hd.comp h2) + apply hh.congr' + exact hder.mono (fun s h => h.deriv.symm) + · filter_upwards [hr,eventually_gt_atTop (0:ℝ)] with r hr hpos + rw [Real.rpow_logb (by norm_num : (0:ℝ)<2) (by norm_num) hpos, + Real.rpow_logb (by norm_num : (0:ℝ)<2) (by norm_num) hr.2] + +theorem inverse_radial_logarithmic_derivative {x : ℂ → ℂ} {a : ℝ} + (ha : ∀ᶠ r : ℝ in atTop,AnalyticAt ℂ x (r:ℂ)) + (hd : Tendsto (fun r : ℝ => (r:ℂ)*deriv x (r:ℂ)) atTop (𝓝 (a:ℂ))) : + (∀ᶠ s : ℝ in atTop,DifferentiableAt ℝ (fun s => (x (((2:ℝ)^s:ℝ):ℂ)).re) s) ∧ + Tendsto (deriv (fun s : ℝ => (x (((2:ℝ)^s:ℝ):ℂ)).re)) atTop (𝓝 (Real.log 2*a)) := by + have h2 : Tendsto (fun s : ℝ => (2:ℝ)^s) atTop atTop := + tendsto_rpow_atTop_of_base_gt_one 2 (by norm_num) + have hder : ∀ᶠ s : ℝ in atTop,HasDerivAt (fun s : ℝ => (x (((2:ℝ)^s:ℝ):ℂ)).re) + (Real.log 2*((((2:ℝ)^s:ℝ):ℂ)*deriv x (((2:ℝ)^s:ℝ):ℂ)).re) s := by + filter_upwards [h2.eventually ha] with s ha + have hg : HasDerivAt (fun r : ℝ => (x (r:ℂ)).re) (deriv x (((2:ℝ)^s:ℝ):ℂ)).re ((2:ℝ)^s) := + Complex.reCLM.hasFDerivAt.comp_hasDerivAt ((2:ℝ)^s) ha.differentiableAt.hasDerivAt.comp_ofReal + have hp : HasDerivAt (fun s : ℝ => (2:ℝ)^s) (Real.log 2*(2:ℝ)^s) s := by + simpa using (hasDerivAt_id s).const_rpow (by norm_num : (0:ℝ)<2) + have hh : HasDerivAt (fun s : ℝ => (x (((2:ℝ)^s:ℝ):ℂ)).re) + ((deriv x (((2:ℝ)^s:ℝ):ℂ)).re*(Real.log 2*(2:ℝ)^s)) s := hg.comp s hp + convert hh using 1 + simp only [Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] + ring + refine ⟨hder.mono (fun _ h => h.differentiableAt),?_⟩ + have hh := ((Complex.continuous_re.tendsto (a:ℂ)).comp (hd.comp h2)).const_mul (Real.log 2) + apply hh.congr' + exact hder.mono (fun s h => h.deriv.symm) + +theorem inverse_composition_logarithmic_slope {F x : ℂ → ℂ} {a b : ℂ} + (hxa : ∀ᶠ w in sectorInfinity,AnalyticAt ℂ x w) + (hFa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ F z) + (hxto : Tendsto x sectorInfinity stripInfinity) + (hFd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 a)) + (hxd : Tendsto (fun w => w*deriv x w) sectorInfinity (𝓝 b)) : + Tendsto (fun w => w*deriv (fun w => F (x w)) w/F (x w)) sectorInfinity (𝓝 (a*b)) := by + apply ((hFd.comp hxto).mul hxd).congr' + filter_upwards [hxa,hxto.eventually hFa] with w hxa hFa + have hh : HasDerivAt (fun w => F (x w)) (deriv F (x w)*deriv x w) w := + hFa.differentiableAt.hasDerivAt.comp w hxa.differentiableAt.hasDerivAt + rw [hh.deriv] + dsimp only [Function.comp_apply] + ring + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem strip_derivative_zero_constant {J : ℂ → ℂ} {c : ℝ} + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ J z) + (hd : ∀ᶠ z in stripInfinity,deriv J z=0) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) + (ht : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 c)) : + ∀ᶠ z in stripInfinity,J z=(c:ℂ) := by + have hlim := complex_real_limit hr ht + apply eventually_stripInfinity.mpr + intro R + obtain ⟨A,hA⟩ := eventually_stripInfinity.mp (ha.and hd) (max R 1) + refine ⟨A,fun z hz => ?_⟩ + have hz' : z∈horizontalTail A (max R 1) := ⟨hz.1,hz.2.trans_le (le_max_left _ _)⟩ + have heq : ∀ᶠ t : ℝ in atTop,J (t:ℂ)=J z := by + filter_upwards [eventually_gt_atTop A] with t ht + exact (horizontalTail_open A (max R 1)).is_const_of_deriv_eq_zero + (horizontalTail_convex A (max R 1)).isPreconnected + (fun w hw => (hA w hw).1.differentiableAt.differentiableWithinAt) + (fun w hw => (hA w hw).2) + (show (t:ℂ)∈horizontalTail A (max R 1) from + ⟨ht,by simp⟩) hz' + exact tendsto_nhds_unique (tendsto_const_nhds.congr' (heq.mono (fun _ h => h.symm))) hlim + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/InverseEstimates.lean b/lean/OAI/Analysis/PathSelection/InverseEstimates.lean new file mode 100644 index 0000000000000000000000000000000000000000..66c27a69cced13701aa21e300be6407b355446c3 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/InverseEstimates.lean @@ -0,0 +1,466 @@ +import Mathlib +import OAI.Analysis.PathSelection.DerivativeEstimates +import OAI.Analysis.PathSelection.LossPullbacks + +namespace OAI + +/-! Inverse derivative absorption, exponential decay and comparable inverse charts. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma summable_abs_variation {a : ℕ → ℝ} {M : ℝ} + (hb : ∀ n,|a n|≤M) (hm : Monotone a ∨ Antitone a) : + Summable (fun n => |a (n+1)-a n|) := by + apply summable_of_sum_range_le (fun n => abs_nonneg _) (c := 2*M) + intro n + rcases hm with hm | hm + · have he : ∀ i:ℕ,|a (i+1)-a i|=a (i+1)-a i := fun i => + abs_of_nonneg (sub_nonneg.mpr (hm (by omega))) + simp_rw [he] + rw [Finset.sum_range_sub] + linarith [(abs_le.mp (hb n)).2,(abs_le.mp (hb 0)).1] + · have he : ∀ i:ℕ,|a (i+1)-a i|=a i-a (i+1) := fun i => by + rw [abs_of_nonpos (sub_nonpos.mpr (hm (by omega)))]; ring + simp_rw [he] + rw [Finset.sum_range_sub'] + linarith [(abs_le.mp (hb 0)).2,(abs_le.mp (hb n)).1] + +theorem derivative_summable_unit_shells {F : ℂ → ℂ} + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ F z) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) + (hz : ∀ᶠ z in stripInfinity,deriv F z≠0) + (hd : Tendsto (fun z => deriv (deriv F) z/deriv F z) stripInfinity (𝓝 0)) + {c : ℝ} (hl : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop (𝓝 c)) + (hm : ∃ A : ℝ,MonotoneOn (fun t : ℝ => (F (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (F (t:ℂ)).re) (Ici A)) : + ∃ N : ℕ,∃ w : ℕ → ℝ,(∀ n,0≤w n) ∧ Summable w ∧ + ∀ n : ℕ,∀ t : ℝ,((n+N:ℕ):ℝ)≤t → t≤((n+N:ℕ):ℝ)+2 → + ‖deriv F (t:ℂ)‖≤w n := by + obtain ⟨A₁,hA₁⟩ := relative_strip_pair_estimate + (ha.mono (fun z h => h.deriv)) hz hd (show (0:ℝ)<1 by norm_num) + (show (0:ℝ)<2 by norm_num) (show (0:ℝ)<1/2 by norm_num) + obtain ⟨A₂,hA₂⟩ := eventually_stripInfinity.mp ha 1 + have hbound : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ |(F (t:ℂ)).re|≤|c|+1 := by + filter_upwards [hr,(Metric.tendsto_nhds.mp hl) 1 (by norm_num)] with t ht hb + refine ⟨ht,?_⟩ + have hh : |(F (t:ℂ)).re-c|<1 := by simpa only [Real.dist_eq] using hb + calc + |(F (t:ℂ)).re| = |((F (t:ℂ)).re-c)+c| := by congr 1; ring + _ ≤ |(F (t:ℂ)).re-c|+|c| := abs_add_le _ _ + _ ≤ |c|+1 := by linarith + obtain ⟨A₃,hA₃⟩ := eventually_atTop.mp hbound + obtain ⟨A₄,hA₄⟩ := hm + let A := max A₁ (max A₂ (max A₃ A₄)) + have hAA₁ : A₁≤A := le_max_left _ _ + have hAA₂ : A₂≤A := (le_max_left _ _).trans (le_max_right _ _) + have hAA₃ : A₃≤A := (le_max_left _ _).trans ((le_max_right _ _).trans (le_max_right _ _)) + have hAA₄ : A₄≤A := (le_max_right _ _).trans ((le_max_right _ _).trans (le_max_right _ _)) + have hFa (t : ℝ) (ht : A (F (t:ℂ)).re) (deriv F (t:ℂ)).re t := + Complex.reCLM.hasFDerivAt.comp_hasDerivAt t (hFa t ht).differentiableAt.hasDerivAt.comp_ofReal + obtain ⟨N,hN⟩ := exists_nat_gt A + let a : ℕ → ℝ := fun n => (F (↑(((n+N:ℕ):ℝ)+1) : ℂ)).re + have hab (n : ℕ) : |a n|≤|c|+1 := by + apply (hA₃ _ ?_).2 + have hh : (N:ℝ)≤((n+N:ℕ):ℝ) := by norm_num + exact hAA₃.trans (by linarith) + have ham : Monotone a ∨ Antitone a := by + rcases hA₄ with hh | hh + · left + intro i j hij + apply hh + · change A₄≤((i+N:ℕ):ℝ)+1 + apply hAA₄.trans + have hh : (N:ℝ)≤((i+N:ℕ):ℝ) := by norm_num + linarith + · change A₄≤((j+N:ℕ):ℝ)+1 + apply hAA₄.trans + have hh : (N:ℝ)≤((j+N:ℕ):ℝ) := by norm_num + linarith + · exact_mod_cast Nat.add_le_add_right (Nat.add_le_add_right hij N) 1 + · right + intro i j hij + apply hh + · change A₄≤((i+N:ℕ):ℝ)+1 + apply hAA₄.trans + have hh : (N:ℝ)≤((i+N:ℕ):ℝ) := by norm_num + linarith + · change A₄≤((j+N:ℕ):ℝ)+1 + apply hAA₄.trans + have hh : (N:ℝ)≤((j+N:ℕ):ℝ) := by norm_num + linarith + · exact_mod_cast Nat.add_le_add_right (Nat.add_le_add_right hij N) 1 + let w : ℕ → ℝ := fun n => 2*|a (n+1)-a n| + refine ⟨N,w,fun n => by dsimp [w]; positivity,(summable_abs_variation hab ham).mul_left 2,?_⟩ + intro n t htl htu + let u : ℝ := ((n+N:ℕ):ℝ)+1 + have huA : A (F (t:ℂ)).re) + (fun t : ℝ => (deriv F (t:ℂ)).re) (show u (hFd x (huA.trans_le hx.1)).continuousAt.continuousWithinAt) + (fun x hx => hFd x (huA.trans hx.1)) + rw [hun,div_one] at hds + have hsA : A linarith [hs.1,hs.2] + obtain ⟨hs0,hrat⟩ := hA₁ (t:ℂ) ⟨hAA₁.trans_lt htA,by simp⟩ + (s:ℂ) ⟨hAA₁.trans_lt hsA,by simp⟩ hts + have hrat1 : ‖deriv F (t:ℂ)/deriv F (s:ℂ)-1‖≤1 := by linarith + have hcomp : ‖deriv F (t:ℂ)‖≤2*‖deriv F (s:ℂ)‖ := by + have he : deriv F (t:ℂ)=(deriv F (t:ℂ)/deriv F (s:ℂ)-1)*deriv F (s:ℂ)+deriv F (s:ℂ) := by + field_simp [hs0] + ring + calc + ‖deriv F (t:ℂ)‖ = ‖(deriv F (t:ℂ)/deriv F (s:ℂ)-1)*deriv F (s:ℂ)+deriv F (s:ℂ)‖ := congrArg norm he + _ ≤ ‖(deriv F (t:ℂ)/deriv F (s:ℂ)-1)*deriv F (s:ℂ)‖+‖deriv F (s:ℂ)‖ := norm_add_le _ _ + _ ≤ 2*‖deriv F (s:ℂ)‖ := by rw [norm_mul]; nlinarith [norm_nonneg (deriv F (s:ℂ))] + have him : (deriv F (s:ℂ)).im=0 := analytic_ray_deriv_im_zero hsA (hFa s hsA) hFr + have heq : deriv F (s:ℂ)=((a (n+1)-a n:ℝ):ℂ) := by + apply Complex.ext + · change (deriv F (s:ℂ)).re=a (n+1)-a n + rw [hds] + dsimp [a,u] + congr 2 + push_cast + ring_nf + · simpa using him + rw [heq,Complex.norm_real,Real.norm_eq_abs] at hcomp + exact hcomp + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem inverse_derivative_loss_absorption {J x : ℂ → ℂ} {b c : ℝ} (hb : 0 deriv (deriv J) z/deriv J z) stripInfinity (𝓝 0)) + (hJl : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 c)) + (hJm : ∃ A : ℝ,MonotoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A)) + (hxa : ∀ᶠ r : ℝ in atTop,AnalyticAt ℂ x (r:ℂ)) + (hxd : Tendsto (fun r : ℝ => (r:ℂ)*deriv x (r:ℂ)) atTop (𝓝 ((b:ℂ)⁻¹))) : + ∃ ω : ℝ → ℝ,AdmissibleAngularLoss ω ∧ + ∀ ε : ℝ,0<ε → ∀ᶠ r : ℝ in atTop,‖deriv J ((x (r:ℂ)).re:ℂ)‖≤ε*ω r := by + obtain ⟨N,w,hw,hs,hbound⟩ := derivative_summable_unit_shells hJa hJr hJd0 hJdd hJl hJm + have hxda : Tendsto (fun r : ℝ => (r:ℂ)*deriv x (r:ℂ)) atTop (𝓝 ((b⁻¹:ℝ):ℂ)) := by + simpa only [Complex.ofReal_inv] using hxd + obtain ⟨hψa,hψd⟩ := inverse_radial_logarithmic_derivative hxa hxda + have hbp : 0 ‖deriv J (t:ℂ)‖) + hw hs (fun n t htl htu => by simpa only [abs_norm] using hbound n t htl htu) hbp hψa hψd + refine ⟨ω,hω,?_⟩ + intro ε hε + filter_upwards [hsmall ε hε,eventually_gt_atTop (0:ℝ)] with r hr hr0 + simpa only [Real.rpow_logb (by norm_num : (0:ℝ)<2) (by norm_num : (2:ℝ)≠1) hr0,abs_norm] using hr + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem inverse_exponential_decay {H : ℂ → ℂ} {t : ℝ → ℝ} {b ε : ℝ} + (hb : 0 deriv H (s:ℂ)/H (s:ℂ)) atTop (𝓝 (b:ℂ))) + (ht : Tendsto t atTop atTop) + (hinv : ∀ᶠ r : ℝ in atTop,H (t r:ℂ)=(r:ℂ)) : + ∃ C : ℝ,0 Complex.exp ((-ε:ℝ)*z) + have hFval (s : ℝ) : F (s:ℂ)=(Real.exp (-ε*s):ℂ) := by + dsimp [F] + rw [←Complex.ofReal_mul,←Complex.ofReal_exp] + have hFder (z : ℂ) : deriv F z/F z=(-ε:ℝ) := by + have hd := (Complex.hasDerivAt_exp ((-ε:ℝ)*z)).comp z ((hasDerivAt_id z).const_mul ((-ε:ℝ):ℂ)) + change HasDerivAt F _ z at hd + rw [hd.deriv] + simp only [mul_one,F] + exact mul_div_cancel_left₀ _ (Complex.exp_ne_zero _) + have hgap : -ε<(-(ε/(2*b)))*b := by + have he : (-(ε/(2*b)))*b= -ε/2 := by field_simp + rw [he]; linarith + obtain ⟨C,hC,hbound⟩ := complex_log_derivative_power_bound (F := F) (H := H) hgap + (Eventually.of_forall fun s => (analyticAt_const.mul analyticAt_id).cexp) hHa + (Eventually.of_forall fun s => by rw [hFval]; exact ⟨rfl,Real.exp_pos _⟩) + hHr ((tendsto_const_nhds (x := ((-ε:ℝ):ℂ))).congr' (Eventually.of_forall fun s => (hFder _).symm)) hHd + refine ⟨C,hC,?_⟩ + filter_upwards [ht.eventually hbound,hinv] with r hr hi + simpa only [hFval,hi,Complex.ofReal_re] using hr + +theorem inverse_exponential_loss_absorption {H : ℂ → ℂ} {t : ℝ → ℝ} {b ε : ℝ} + (hb : 0 deriv H (s:ℂ)/H (s:ℂ)) atTop (𝓝 (b:ℂ))) + (ht : Tendsto t atTop atTop) + (hinv : ∀ᶠ r : ℝ in atTop,H (t r:ℂ)=(r:ℂ)) + {ω : ℝ → ℝ} (hω : AdmissibleAngularLoss ω) (M : ℝ) : + ∀ δ : ℝ,0<δ → ∀ᶠ r : ℝ in atTop,M*Real.exp (-ε*t r)≤δ*ω r := by + obtain ⟨C,hC,hpow⟩ := inverse_exponential_decay hb hε hHa hHr hHd ht hinv + intro δ hδ + have ha : 0<ε/(2*b) := by positivity + filter_upwards [hpow,hω.power_absorption ha (max M 0*C/δ)] with r hr hbound + have h₁ := mul_le_mul_of_nonneg_left hr (show 0≤ max M 0 from le_max_right _ _) + have h₂ := mul_le_mul_of_nonneg_left hbound hδ.le + have he : δ*(max M 0*C/δ*r^(-(ε/(2*b))))=max M 0*C*r^(-(ε/(2*b))) := by field_simp + rw [he] at h₂ + have h₃ := mul_le_mul_of_nonneg_right (le_max_left M 0) (Real.exp_pos (-ε*t r)).le + exact h₃.trans (h₁.trans (by nlinarith [h₂])) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma realpart_of_ratio_error {F z : ℂ} {a e : ℝ} (hz : z≠0) (hr : 0 ≤ z.re) + (h : ‖F/z-(a:ℂ)‖ ≤ e) : |F.re| ≤ |a| *z.re+e*‖z‖ := by + have he : F=z*(a:ℂ)+z*(F/z-(a:ℂ)) := by field_simp; ring + rw [he,Complex.add_re] + calc + |(z*(a:ℂ)).re+(z*(F/z-(a:ℂ))).re| ≤ |(z*(a:ℂ)).re|+|(z*(F/z-(a:ℂ))).re| := abs_add_le _ _ + _ ≤ |a| *z.re+‖z*(F/z-(a:ℂ))‖ := by + have he : |(z*(a:ℂ)).re|=|a| *z.re := by + simp only [Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,mul_zero,sub_zero,abs_mul,abs_of_nonneg hr] + ring + rw [he] + exact add_le_add le_rfl (Complex.abs_re_le_norm _) + _ ≤ |a| *z.re+e*‖z‖ := by rw [norm_mul]; nlinarith [norm_nonneg z] + +theorem strict_loss_realpart_separation {F : ℂ → ℂ} {a e : ℝ → ℝ} + {η ω : ℝ → ℝ} (hη : AdmissibleAngularLoss η) (hω : AdmissibleAngularLoss ω) + (ha : Tendsto a atTop (𝓝 0)) + (he : ∀ ε : ℝ,0 < ε → ∀ᶠ r in atTop,|e r| ≤ ε*ω r) + (happrox : ∃ A : ℝ,∀ z∈lossSector η A,‖F z/z-(a ‖z‖:ℂ)‖ ≤ |e ‖z‖|) : + ∀ ε : ℝ,0 < ε → ∃ R : ℝ,∀ z∈lossSector (fun r => max (η r) (ω r)) R, + |(F z).re| ≤ ε*z.re := by + intro ε hε + obtain ⟨A,hA⟩ := happrox + let θ : ℝ → ℝ := fun r => max (η r) (ω r) + have hθ : AdmissibleAngularLoss θ := hη.max hω + have has : ∀ᶠ r in atTop,|a r| ≤ ε/2 := by + filter_upwards [(Metric.tendsto_nhds.mp ha) (ε/2) (by positivity)] with r hr + exact le_of_lt (by simpa only [dist_zero_right,Real.norm_eq_abs] using hr) + have hθs := hθ.tendsto_zero.eventually (eventually_lt_nhds (show (0:ℝ) < Real.pi/2 by linarith [Real.pi_pos])) + obtain ⟨R,hR⟩ := eventually_atTop.mp (has.and ((he (ε/4) (by positivity)).and + (hθ.1.and (hθs.and (eventually_gt_atTop (max A 1)))))) + refine ⟨R,?_⟩ + intro z hz + obtain ⟨haz,hez,hθz,hθsmall,hzlarge⟩ := hR ‖z‖ hz.1.le + have hrz : 0 < ‖z‖ := lt_of_lt_of_le (by norm_num : (0:ℝ) < 1) ((le_max_right A 1).trans hzlarge.le) + have hre := half_loss_norm_le_re hθz.1.le hθsmall.le hz.2 + have hre0 : 0 ≤ z.re := (mul_nonneg (by linarith [hθz.1] : 0 ≤ θ ‖z‖/2) hrz.le).trans hre + have hzη : z∈lossSector η A := ⟨(le_max_left _ _).trans_lt hzlarge, + hz.2.trans_le (sub_le_sub_left (le_max_left _ _) _)⟩ + have hmain := realpart_of_ratio_error (norm_ne_zero_iff.mp hrz.ne') hre0 (hA z hzη) + have heθ : |e ‖z‖| ≤ (ε/4)*θ ‖z‖ := + hez.trans (mul_le_mul_of_nonneg_left (le_max_right _ _) (by positivity)) + have hh := mul_le_mul_of_nonneg_right heθ hrz.le + have hh' := mul_le_mul_of_nonneg_left hre (show 0 ≤ ε/2 by positivity) + have hh'' := mul_le_mul_of_nonneg_right haz hre0 + nlinarith + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem equal_exponent_realpart_separation {F H J E x : ℂ → ℂ} {b ε C T : ℝ} + (hb : 0 (x (r:ℂ)).re) atTop atTop) + (hxi : ∃ U : ℝ,∀ w : ℂ,0 (r:ℂ)*deriv x (r:ℂ)) atTop (𝓝 ((b:ℂ)⁻¹))) + (hHa : ∀ᶠ s : ℝ in atTop,AnalyticAt ℂ H (s:ℂ)) + (hHr : ∀ᶠ s : ℝ in atTop,(H (s:ℂ)).im=0 ∧ 0<(H (s:ℂ)).re) + (hHd : Tendsto (fun s : ℝ => deriv H (s:ℂ)/H (s:ℂ)) atTop (𝓝 (b:ℂ))) + (hJa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ J z) + (hJ0 : ∀ᶠ z in stripInfinity,J z≠0) + (hJd : Tendsto (fun z => deriv J z/J z) stripInfinity (𝓝 0)) + (hJr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) + (hJl : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 0)) + (hJd0 : ∀ᶠ z in stripInfinity,deriv J z≠0) + (hJdd : Tendsto (fun z => deriv (deriv J) z/deriv J z) stripInfinity (𝓝 0)) + (hJm : ∃ A : ℝ,MonotoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A)) + (he : ∀ᶠ z in stripInfinity,‖E z‖≤C*Real.exp (-ε*z.re)) + (hfactor : ∀ᶠ z in stripInfinity,F z/H z=J z*(1+E z)) : + ∃ η : ℝ → ℝ,AdmissibleAngularLoss η ∧ + ∀ δ : ℝ,0<δ → ∃ R : ℝ,∀ w∈lossSector η R,|(F (x w)).re|≤δ*w.re := by + obtain ⟨K,U,hK,herr⟩ := equal_exponent_ratio_error hb hε hC hxr hxt hxi hinv + hJa hJ0 hJd hJr hJl hJd0 hJdd he hfactor + obtain ⟨ω,hω,hds⟩ := inverse_derivative_loss_absorption hb hJa hJr hJd0 hJdd hJl hJm hxa hxd + have hri : ∀ᶠ r : ℝ in atTop,H ((x (r:ℂ)).re:ℂ)=(r:ℂ) := by + filter_upwards [hxr,eventually_gt_atTop (max T 0)] with r hr hrt + have hreal : x (r:ℂ)=((x (r:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hr) + rw [←hreal] + exact hinv (r:ℂ) (by simpa using (le_max_right T 0).trans_lt hrt) + (by simpa only [Complex.norm_real,Real.norm_eq_abs,abs_of_pos ((le_max_right T 0).trans_lt hrt)] using (le_max_left T 0).trans_lt hrt) + have hes := inverse_exponential_loss_absorption hb hε hHa hHr hHd hxt hri hω K + let e : ℝ → ℝ := fun r => K*(‖deriv J ((x (r:ℂ)).re:ℂ)‖+Real.exp (-ε*(x (r:ℂ)).re)) + have hepos (r : ℝ) : 0≤e r := by dsimp [e]; positivity + have hsmall : ∀ δ : ℝ,0<δ → ∀ᶠ r : ℝ in atTop,|e r|≤δ*ω r := by + intro δ hδ + filter_upwards [hds (δ/(2*K)) (by positivity),hes (δ/2) (by positivity)] with r hd he + rw [abs_of_nonneg (hepos r)] + have hh := mul_le_mul_of_nonneg_left hd hK.le + have hkeq : K*(δ/(2*K)*ω r)=δ/2*ω r := by field_simp + rw [hkeq] at hh + dsimp [e] + nlinarith only [hh,he] + obtain ⟨κ,S,hκ,hdata⟩ := SectorEventually.realpart_pos.and + (tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop U)) + refine ⟨fun r => max (κ r) (ω r),hκ.max hω,?_⟩ + apply strict_loss_realpart_separation hκ hω (hJl.comp hxt) hsmall + refine ⟨S,?_⟩ + intro w hw + rw [abs_of_nonneg (hepos ‖w‖)] + exact herr w (hdata w hw).1 (hdata w hw).2 + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem inverse_chart_data {F x : ℂ → ℂ} {b : ℝ} (hb : 0 (F (t:ℂ)).re) atTop atTop) + (hFd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 (b:ℂ))) + (hxa : ∀ᶠ w in sectorInfinity,AnalyticAt ℂ x w) + (hxr : ∀ᶠ r : ℝ in atTop,(x (r:ℂ)).im=0) + (hxt : Tendsto (fun r : ℝ => (x (r:ℂ)).re) atTop atTop) + (hxto : Tendsto x sectorInfinity stripInfinity) + (hi : ∀ ε : ℝ,0<ε → ∀ᶠ w in sectorInfinity, + ‖x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)‖≤ε*|w.arg|) + (hxd : Tendsto (fun w => w*deriv x w) sectorInfinity (𝓝 ((b:ℂ)⁻¹))) : + (∀ᶠ r : ℝ in atTop,(F (x (r:ℂ))).im=0 ∧ 0<(F (x (r:ℂ))).re) ∧ + Tendsto (fun r : ℝ => (F (x (r:ℂ))).re) atTop atTop ∧ + (∀ᶠ w in sectorInfinity,AnalyticAt ℂ (fun w => F (x w)) w) ∧ + (∀ᶠ w in sectorInfinity,(F (x (‖w‖:ℂ))).re/2≤‖F (x w)‖ ∧ + ‖F (x w)‖≤2*(F (x (‖w‖:ℂ))).re) ∧ + ∃ ψ : ℝ → ℝ, + (∀ᶠ s : ℝ in atTop,DifferentiableAt ℝ ψ s) ∧ Tendsto (deriv ψ) atTop (𝓝 1) ∧ + (∀ᶠ r : ℝ in atTop,(F (x (r:ℂ))).re=(2:ℝ)^(ψ (Real.logb 2 r))) := by + have hreal : ∀ᶠ r : ℝ in atTop,x (r:ℂ)=((x (r:ℂ)).re:ℂ) := + hxr.mono (fun r hr => Complex.ext rfl (by simpa using hr)) + have hGreal : ∀ᶠ r : ℝ in atTop,(F (x (r:ℂ))).im=0 ∧ 0<(F (x (r:ℂ))).re := by + filter_upwards [hxt.eventually hFr,hreal] with r hr he + rwa [←he] at hr + have hGft : Tendsto (fun r : ℝ => (F (x (r:ℂ))).re) atTop atTop := + (hFt.comp hxt).congr' (hreal.mono fun r hr => congrArg (fun z => (F z).re) hr.symm) + have hGa : ∀ᶠ w in sectorInfinity,AnalyticAt ℂ (fun w => F (x w)) w := by + filter_upwards [hxa,hxto.eventually hFa] with w hx hF + exact hF.comp hx + have hGrd : Tendsto (fun w => w*deriv (fun w => F (x w)) w/F (x w)) sectorInfinity (𝓝 (1:ℂ)) := by + have hh := inverse_composition_logarithmic_slope hxa hFa hxto hFd hxd + simpa only [mul_inv_cancel₀ (show (b:ℂ)≠0 by exact_mod_cast hb.ne')] using hh + have hratio := inverse_clock_ratio_tendsto hb hFa hF0 hFd + (tendsto_re_stripInfinity.comp hxto) hxt hxr hi + have hmod := inverse_clock_modulus_tendsto hratio + refine ⟨hGreal,hGft,hGa,?_,?_⟩ + · have hs := (Metric.tendsto_nhds.mp hmod) (1/2) (by norm_num) + filter_upwards [hs,tendsto_norm_sectorInfinity.eventually hGreal] with w hs hr + have he : F (x (‖w‖:ℂ))=((F (x (‖w‖:ℂ))).re:ℂ) := Complex.ext rfl (by simpa using hr.1) + rw [he,Complex.norm_of_nonneg hr.2.le,Real.dist_eq] at hs + have hl : (1:ℝ)/2<‖F (x w)‖/(F (x (‖w‖:ℂ))).re := by linarith [(abs_lt.mp hs).1] + have hu : ‖F (x w)‖/(F (x (‖w‖:ℂ))).re<2 := by linarith [(abs_lt.mp hs).2] + exact ⟨by linarith [(lt_div_iff₀ hr.2).mp hl],by linarith [(div_lt_iff₀ hr.2).mp hu]⟩ + · obtain ⟨ha,hd,he⟩ := logarithmic_radius_derivative (tendsto_real_sectorInfinity.eventually hGa) + hGreal (hGrd.comp tendsto_real_sectorInfinity) + exact ⟨_,ha,hd,he⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem inverse_strip_exponential_error {E x : ℂ → ℂ} {b ε C : ℝ} + (hb : 0 (x (r:ℂ)).re) atTop atTop) + (hi : ∃ U : ℝ,∀ w : ℂ,0 F (a,w)) z = fderiv ℂ F (a,z) (0,1) := by + have hi : HasDerivAt (fun w : ℂ => (a,w)) (0,1) z := + (hasDerivAt_const z a).prodMk (hasDerivAt_id z) + exact (hF.differentiableAt.hasFDerivAt.comp_hasDerivAt z hi).deriv + +lemma analyticOnNhd_deriv_slice {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + {F : E × ℂ → ℂ} {S : Set (E × ℂ)} (hF : AnalyticOnNhd ℂ F S) : + AnalyticOnNhd ℂ (fun p => deriv (fun w => F (p.1,w)) p.2) S := by + intro p hp + have hh := ((ContinuousLinearMap.apply ℂ ℂ ((0,1) : E × ℂ)).analyticAt _).comp (hF p hp).fderiv + apply hh.congr + filter_upwards [(hF p hp).eventually_analyticAt] with q hq + exact (deriv_slice hq).symm + +lemma analyticOnNhd_contourPowerSum {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {U : Set E} {F : E × ℂ → ℂ} {r : ℝ} + (hU : IsOpen U) (hr : 0≤r) (hF : AnalyticOnNhd ℂ F (U ×ˢ sphere 0 r)) + (hnz : ∀ p∈U ×ˢ sphere (0:ℂ) r, F p≠0) (l : ℕ) : + AnalyticOnNhd ℂ (fun a => contourPowerSum (fun z => F (a,z)) r l) U := by + have hd := analyticOnNhd_deriv_slice hF + have hi := analyticOnNhd_circleIntegral hU hr + ((analyticOnNhd_snd.pow l).mul hd |>.div hF hnz) + exact analyticOnNhd_const.mul hi + +lemma analyticAt_newtonEsymm {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {s : E → ℕ → ℂ} {a : E} + (hs : ∀ l, AnalyticAt ℂ (fun x => s x l) a) (n : ℕ) : + AnalyticAt ℂ (fun x => newtonEsymm (s x) n) a := by + induction n using Nat.strong_induction_on with + | h n ih => + rw [show (fun x => newtonEsymm (s x) n) = + (fun x => if n=0 then 1 else (n:ℂ)⁻¹ * (-1)^(n+1) * + ∑ t ∈ (Finset.HasAntidiagonal.antidiagonal n).filter (fun t => t.1 + (preparationPolynomial (fun z => F (p.1,z)) r d).eval p.2) (U ×ˢ univ) := by + intro p hp + have hpoly : (fun q : E × ℂ => (preparationPolynomial (fun z => F (q.1,z)) r d).eval q.2) = + fun q => ∑ k ∈ Finset.range (d+1), + (-1)^(d-k) * newtonEsymm (contourPowerSum (fun z => F (q.1,z)) r) (d-k) * q.2^k := by + funext q + simp [preparationPolynomial,Polynomial.eval_finsetSum] + rw [hpoly] + apply Finset.analyticAt_fun_sum + intro k hk + apply AnalyticAt.mul _ (analyticAt_snd.pow k) + apply AnalyticAt.mul analyticAt_const + exact (analyticAt_newtonEsymm (fun l => + analyticOnNhd_contourPowerSum hU hr hF hnz l p.1 hp.1) (d-k)).comp analyticAt_fst + +lemma analyticOnNhd_divisionQuotient {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {U : Set E} {G : E × ℂ → ℂ} {P : E → ℂ[X]} {r : ℝ} + (hU : IsOpen U) (hr : 0 (P p.1).eval p.2) (U ×ˢ sphere 0 r)) + (hnz : ∀ a∈U, ∀ z∈sphere (0:ℂ) r, (P a).eval z≠0) : + AnalyticOnNhd ℂ (fun p : E × ℂ => divisionQuotient (fun z => G (p.1,z)) (P p.1) r p.2) + (U ×ˢ ball 0 r) := by + have hi : AnalyticOnNhd ℂ + (fun q : (E × ℂ) × ℂ => G (q.1.1,q.2) / + ((P q.1.1).eval q.2 * (q.2-q.1.2))) ((U ×ˢ ball 0 r) ×ˢ sphere 0 r) := by + intro q hq + have hc : AnalyticAt ℂ (fun x : (E × ℂ) × ℂ => (x.1.1,x.2)) q := + (analyticAt_fst.comp analyticAt_fst).prod analyticAt_snd + have hn : q.2-q.1.2≠0 := by + intro he + have hz := sub_eq_zero.mp he + have hball := hq.1.2 + rw [← hz] at hball + exact (ne_of_lt (mem_ball_zero_iff.mp hball)) (mem_sphere_zero_iff_norm.mp hq.2) + exact ((hG (q.1.1,q.2) ⟨hq.1.1,hq.2⟩).comp (f := fun x : (E × ℂ) × ℂ => (x.1.1,x.2)) hc).div + (((hP (q.1.1,q.2) ⟨hq.1.1,hq.2⟩).comp (f := fun x : (E × ℂ) × ℂ => (x.1.1,x.2)) hc).mul + (analyticAt_snd.sub (analyticAt_snd.comp analyticAt_fst))) + (mul_ne_zero (hnz q.1.1 hq.1.1 q.2 hq.2) hn) + exact analyticOnNhd_const.mul + (analyticOnNhd_circleIntegral (hU.prod isOpen_ball) hr.le hi) + +lemma analyticOnNhd_slice {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + {F : E × ℂ → ℂ} {U : Set E} {S : Set ℂ} + (hF : AnalyticOnNhd ℂ F (U ×ˢ S)) {a : E} (ha : a∈U) : + AnalyticOnNhd ℂ (fun z => F (a,z)) S := by + intro z hz + exact (hF (a,z) ⟨ha,hz⟩).comp (analyticAt_const.prod analyticAt_id) + +lemma zero_count_constant {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + {F : E × ℂ → ℂ} {U : Set E} {r : ℝ} (hU : IsOpen U) (hcU : IsPreconnected U) + (hr : 0 F (a,z)) r 0 = contourPowerSum (fun z => F (b,z)) r 0 := by + have hi := (analyticOnNhd_contourPowerSum hU hr.le + (hF.mono (prod_mono Subset.rfl sphere_subset_closedBall)) hnz 0).continuousOn + have hc : (range (fun n : ℕ => (n:ℂ))).Countable := countable_range _ + have hs : (fun a => contourPowerSum (fun z => F (a,z)) r 0) '' U ⊆ + range (fun n : ℕ => (n:ℂ)) := by + rintro _ ⟨a,ha,rfl⟩ + exact contour_zero_count_nat hr (analyticOnNhd_slice hF ha) (fun z hz => hnz (a,z) ⟨ha,hz⟩) + exact hc.isTotallyDisconnected _ hs (hcU.image _ hi) + (mem_image_of_mem _ ha) (mem_image_of_mem _ hb) + + + +theorem joint_fixed_contour_preparation {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {F : E × ℂ → ℂ} {U : Set E} {r : ℝ} {a₀ : E} {d : ℕ} + (hU : IsOpen U) (hcU : IsPreconnected U) (ha₀ : a₀∈U) (hr : 0 F (a₀,z)) r 0 = (d:ℂ)) : + let W := fun a => preparationPolynomial (fun z => F (a,z)) r d + let u := fun p : E × ℂ => divisionQuotient (fun z => F (p.1,z)) (W p.1) r p.2 + (∀ a∈U, (W a).Monic ∧ (W a).natDegree=d ∧ + ∀ z, (W a).eval z=0 → z∈ball 0 r) ∧ + AnalyticOnNhd ℂ (fun p : E × ℂ => (W p.1).eval p.2) (U ×ˢ univ) ∧ + AnalyticOnNhd ℂ u (U ×ˢ ball 0 r) ∧ + (∀ p∈U ×ˢ ball (0:ℂ) r, u p≠0) ∧ + EqOn F (fun p => (W p.1).eval p.2 * u p) (U ×ˢ ball 0 r) := by + dsimp only + let W := fun a => preparationPolynomial (fun z => F (a,z)) r d + have hcount' (a : E) (ha : a∈U) : contourPowerSum (fun z => F (a,z)) r 0 = (d:ℂ) := + (zero_count_constant hU hcU hr hF hnz ha ha₀).trans hcount + have hp (a : E) (ha : a∈U) := fixed_contour_preparation_of_count hr + (analyticOnNhd_slice hF ha) (fun z hz => hnz (a,z) ⟨ha,hz⟩) (hcount' a ha) + have hroot' : ∀ a∈U, ∀ z∈sphere (0:ℂ) r, (W a).eval z ≠0 := by + intro a ha z hz he + exact (ne_of_lt (mem_ball_zero_iff.mp ((hp a ha).2.2.1 z he))) + (mem_sphere_zero_iff_norm.mp hz) + have hW := analyticOnNhd_preparation_eval hU hr.le + (hF.mono (prod_mono Subset.rfl sphere_subset_closedBall)) hnz d + refine ⟨fun a ha => ⟨(hp a ha).1,(hp a ha).2.1,(hp a ha).2.2.1⟩,hW,?_,?_,?_⟩ + · exact analyticOnNhd_divisionQuotient (P := W) (G := F) hU hr + (hF.mono (prod_mono Subset.rfl sphere_subset_closedBall)) + (hW.mono (prod_mono Subset.rfl (subset_univ _))) hroot' + · intro p hp' + exact (hp p.1 hp'.1).2.2.2.2.1 p.2 hp'.2 + · intro p hp' + exact (hp p.1 hp'.1).2.2.2.2.2 hp'.2 + +lemma analyticOnNhd_preparation_coeff {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {U : Set E} {F : E × ℂ → ℂ} {r : ℝ} + (hU : IsOpen U) (hr : 0≤r) (hF : AnalyticOnNhd ℂ F (U ×ˢ sphere 0 r)) + (hnz : ∀ p∈U ×ˢ sphere (0:ℂ) r, F p≠0) (d n : ℕ) : + AnalyticOnNhd ℂ (fun a => (preparationPolynomial (fun z => F (a,z)) r d).coeff n) U := by + classical + simp only [preparationPolynomial,finsetSum_coeff,coeff_C_mul_X_pow] + intro a ha + apply Finset.analyticAt_fun_sum + intro k hk + split_ifs with hnk + · exact analyticAt_const.mul (analyticAt_newtonEsymm + (fun l => analyticOnNhd_contourPowerSum hU hr hF hnz l a ha) (d-k)) + · exact analyticAt_const + +lemma analyticOnNhd_divisionRemainder_coeff {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {U : Set E} {G : E × ℂ → ℂ} {P : E → ℂ[X]} {r : ℝ} {d : ℕ} + (hU : IsOpen U) (hr : 0≤r) (hG : AnalyticOnNhd ℂ G (U ×ˢ sphere 0 r)) + (hP : AnalyticOnNhd ℂ (fun p : E × ℂ => (P p.1).eval p.2) (U ×ˢ sphere 0 r)) + (hPc : ∀ n, AnalyticOnNhd ℂ (fun a => (P a).coeff n) U) + (hdeg : ∀ a∈U, (P a).natDegree=d) + (hnz : ∀ a∈U, ∀ z∈sphere (0:ℂ) r, (P a).eval z≠0) (m : ℕ) : + AnalyticOnNhd ℂ (fun a => (divisionRemainder (fun z => G (a,z)) (P a) r).coeff m) U := by + classical + let c := fun n k a => (2*Real.pi*Complex.I)⁻¹ * ∮ w in C(0,r), + G (a,w)/(P a).eval w*((P a).coeff n*w^(n-1-k)) + have hc (n k : ℕ) : AnalyticOnNhd ℂ (c n k) U := by + apply analyticOnNhd_const.mul + apply analyticOnNhd_circleIntegral (F := fun p : E × ℂ => + G p / (P p.1).eval p.2 * ((P p.1).coeff n * p.2^(n-1-k))) hU hr + intro p hp + exact ((hG p hp).div (hP p hp) (hnz p.1 hp.1 p.2 hp.2)).mul + (((hPc n p.1 hp.1).comp (f := fun p : E × ℂ => p.1) analyticAt_fst).mul + (analyticAt_snd.pow _)) + have hs : AnalyticOnNhd ℂ + (fun a => ∑ n ∈ Finset.range (d+1), ∑ k ∈ Finset.range n, + if m=k then c n k a else 0) U := by + intro a ha + apply Finset.analyticAt_fun_sum + intro n hn + apply Finset.analyticAt_fun_sum + intro k hk + split_ifs + · exact hc n k a ha + · exact analyticAt_const + intro a ha + apply (hs a ha).congr + filter_upwards [hU.mem_nhds ha] with x hx + simp only [divisionRemainder,finsetSum_coeff,coeff_C_mul_X_pow,hdeg x hx] + rfl + + + +theorem joint_fixed_contour_division {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {U : Set E} {G : E × ℂ → ℂ} {P : E → ℂ[X]} {r : ℝ} {d : ℕ} + (hU : IsOpen U) (hr : 0 (P p.1).eval p.2) (U ×ˢ sphere 0 r)) + (hPc : ∀ n, AnalyticOnNhd ℂ (fun a => (P a).coeff n) U) + (hdeg : ∀ a∈U, (P a).natDegree=d) + (hnz : ∀ a∈U, ∀ z∈sphere (0:ℂ) r, (P a).eval z≠0) : + let Q := fun p : E × ℂ => divisionQuotient (fun z => G (p.1,z)) (P p.1) r p.2 + let R := fun a => divisionRemainder (fun z => G (a,z)) (P a) r + AnalyticOnNhd ℂ Q (U ×ˢ ball 0 r) ∧ + (∀ n, AnalyticOnNhd ℂ (fun a => (R a).coeff n) U) ∧ + (∀ a∈U, (R a).degree < d) ∧ + EqOn G (fun p => (P p.1).eval p.2 * Q p + (R p.1).eval p.2) (U ×ˢ ball 0 r) := by + dsimp only + have hG' := hG.mono (prod_mono Subset.rfl sphere_subset_closedBall) + refine ⟨analyticOnNhd_divisionQuotient hU hr hG' hP hnz, + analyticOnNhd_divisionRemainder_coeff hU hr.le hG' hP hPc hdeg hnz,?_,?_⟩ + · intro a ha + rw [← hdeg a ha] + exact divisionRemainder_degree _ _ _ + · intro p hp + exact (fixed_disc_division hr (analyticOnNhd_slice hG hp.1) (hnz p.1 hp.1)).2.2 hp.2 + +end PathSelection.JointPreparation +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/LossPullbacks.lean b/lean/OAI/Analysis/PathSelection/LossPullbacks.lean new file mode 100644 index 0000000000000000000000000000000000000000..cfa115c7f3a51d4759b59d465f8accfcce8e88bd --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/LossPullbacks.lean @@ -0,0 +1,549 @@ +import Mathlib +import OAI.Analysis.PathSelection.SectorBounds + +namespace OAI + +/-! Discrete and logarithmic loss pullbacks, summable majorants and derivative transfer. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology +namespace DegeneratingTrees + +lemma summable_comp_four {w : ℕ → ℝ} (hw : Summable w) {k : ℕ → ℕ} + (hk : ∀ j : ℕ,j<4 → StrictMono (fun n => k (4*n+j))) : + Summable (fun n => w (k n)) := by + have hs (j : ℕ) (hj : j<4) : Summable (fun n => w (k (4*n+j))) := + hw.comp_injective (hk j hj).injective + apply Summable.even_add_odd + · apply Summable.even_add_odd + · simpa only [show ∀ n : ℕ,2*(2*n)=4*n+0 by omega] using hs 0 (by omega) + · convert hs 2 (by omega) using 1 + ext n + congr 2 + omega + · apply Summable.even_add_odd + · convert hs 1 (by omega) using 1 + ext n + congr 2 + omega + · convert hs 3 (by omega) using 1 + ext n + congr 2 + omega + +lemma dyadic_span_bound {ω : ℝ → ℝ} {n₀ : ℕ} {w : ℕ → ℝ} + (hw : ∀ n,0≤w n) + (hb : ∀ n r,(2:ℝ)^(n+n₀) hw (k+i)) (Finset.mem_range.mpr hjq)) + + + +lemma admissible_max_of_shell_bounds {v : ℝ → ℝ} {N : ℕ} {w : ℕ → ℝ} + (hw : ∀ n,0≤w n) (hs : Summable w) + (hb : ∀ n r,(2:ℝ)^(n+N) max (baseLoss r) (v r)) := by + obtain ⟨hp,M,a,ha,has,hab⟩ := admissible_baseLoss + refine ⟨?_,M+N,fun n => a (n+N)+w (n+M),?_,?_,?_⟩ + · filter_upwards [hp] with r hr + exact ⟨hr.1.trans_le (le_max_left _ _),hr.2.trans (le_max_left _ _)⟩ + · intro n + exact add_nonneg (ha _) (hw _) + · exact ((summable_nat_add_iff N).mpr has).add ((summable_nat_add_iff M).mpr hs) + · intro n r hl hu + have h1 := hab (n+N) r (by convert hl using 1; congr 1; omega) + (by convert hu using 1; congr 1; omega) + have h2 := hb (n+M) r (by convert hl using 1; congr 1; omega) + (by convert hu using 1; congr 1; omega) + exact max_le (h1.trans (le_add_of_nonneg_right (hw _))) + (h2.trans (le_add_of_nonneg_left (ha _))) + + + +lemma admissible_pullback_of_shell_control {ω f : ℝ → ℝ} {n₀ N q : ℕ} + {w : ℕ → ℝ} (hw : ∀ n,0≤w n) (hs : Summable w) + (hb : ∀ n r,(2:ℝ)^(n+n₀) k (4*n+j))) + (hmap : ∀ n r,(2:ℝ)^(n+N) max (baseLoss r) (ω (f r))) := by + have hsum (S : Finset ℕ) : Summable (fun n => ∑ j∈S,w (k n+j)) := by + classical + induction S using Finset.induction_on with + | empty => simp + | @insert j S hj ih => + have hh : Summable (fun n => w (k n+j)) := + summable_comp_four ((summable_nat_add_iff j).mpr hs) hk + simpa only [Finset.sum_insert hj] using hh.add ih + apply admissible_max_of_shell_bounds (N := N) + (w := fun n => ∑ j∈Finset.range q,w (k n+j)) + (fun n => Finset.sum_nonneg (fun j _ => hw _)) (hsum _) + intro n r hl hu + exact dyadic_span_bound hw hb (k n) q (hmap n r hl hu).1 (hmap n r hl hu).2 + +end DegeneratingTrees + + + + + +open Set Filter Topology +namespace DegeneratingTrees + +lemma summable_comp_mod {w : ℕ → ℝ} (hw₀ : ∀ n,0 ≤ w n) (hw : Summable w) + {k : ℕ → ℕ} {m : ℕ} (hm : 0 < m) + (hk : ∀ j : ℕ,j < m → StrictMono (fun n => k (m*n+j))) : + Summable (fun n => w (k n)) := by + let : NeZero m := ⟨hm.ne'⟩ + let e : ℕ ≃ Fin m × ℕ := (Nat.divModEquiv m).trans (Equiv.prodComm _ _) + have hs : Summable (fun p : Fin m × ℕ => w (k (p.2*m+p.1))) := by + apply (summable_prod_of_nonneg (fun p => hw₀ _)).mpr + refine ⟨?_,Summable.of_finite⟩ + intro j + simpa only [Function.comp_def,Nat.mul_comm] using hw.comp_injective (hk j j.isLt).injective + have hh := hs.comp_injective e.injective + have he (n : ℕ) : (e n).2*m+(e n).1=n := Nat.div_add_mod' n m + simpa only [Function.comp_def,he] using hh + +lemma summable_shell_window {w : ℕ → ℝ} (hw₀ : ∀ n,0 ≤ w n) (hw : Summable w) + {k : ℕ → ℕ} {m : ℕ} (hm : 0 < m) + (hk : ∀ j : ℕ,j < m → StrictMono (fun n => k (m*n+j))) (q : ℕ) : + Summable (fun n => ∑ j∈Finset.range q,w (k n+j)) := by + classical + have hh (S : Finset ℕ) : Summable (fun n => ∑ j∈S,w (k n+j)) := by + induction S using Finset.induction_on with + | empty => simp + | @insert j S hj ih => + have h := summable_comp_mod (fun n => hw₀ (n+j)) ((summable_nat_add_iff j).mpr hw) hm hk + simpa only [Finset.sum_insert hj] using h.add ih + exact hh _ + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +namespace DegeneratingTrees + +theorem log_scale_shell_control {ψ : ℝ → ℝ} {A c C : ℝ} + (hc : 0 < c) (hC : 0 < C) + (hψ : ∀ x y : ℝ,A ≤ x → x ≤ y → + c*(y-x) ≤ ψ y-ψ x ∧ ψ y-ψ x ≤ C*(y-x)) (n₀ : ℕ) : + ∃ N m q : ℕ,∃ k : ℕ → ℕ,0 < m ∧ + (∀ j : ℕ,j < m → StrictMono (fun n => k (m*n+j))) ∧ + ∀ n r,(2:ℝ)^(n+N) < r → r < 2^(n+N+2) → + (2:ℝ)^(k n+n₀+1) ≤ (2:ℝ)^(ψ (Real.logb 2 r)) ∧ + (2:ℝ)^(ψ (Real.logb 2 r)) < 2^(k n+n₀+q+1) := by + obtain ⟨N,hN⟩ := exists_nat_gt (Max.max A (A+((n₀:ℝ)+2-ψ A)/c)) + have hNA : A ≤ (N:ℝ) := le_of_lt ((le_max_left _ _).trans_lt hN) + have hNψ : (n₀:ℝ)+2 < ψ (N:ℝ) := by + have h := (hψ A (N:ℝ) le_rfl hNA).1 + have ht := (le_max_right _ _).trans_lt hN + have ht' : ((n₀:ℝ)+2-ψ A)/c < (N:ℝ)-A := by linarith + have ht'' := (div_lt_iff₀ hc).mp ht' + nlinarith + have hbase (n : ℕ) : (n₀:ℝ)+2 < ψ ((n+N:ℕ):ℝ) := by + have hn : (N:ℝ) ≤ ((n+N:ℕ):ℝ) := by norm_num + have h := (hψ (N:ℝ) ((n+N:ℕ):ℝ) hNA hn).1 + nlinarith + obtain ⟨m,hm⟩ := exists_nat_gt ((2:ℝ)/c) + have hm0 : 0 < m := by + have hh : (0:ℝ) < (m:ℝ) := (by positivity : (0:ℝ) < 2/c).trans hm + exact_mod_cast hh + have hcm : 2 < c*(m:ℝ) := by have hh := (div_lt_iff₀ hc).mp hm; nlinarith + obtain ⟨q,hq⟩ := exists_nat_gt (2*C+1) + let k : ℕ → ℕ := fun n => ⌊ψ ((n+N:ℕ):ℝ)⌋₊-n₀-1 + have hid (n : ℕ) : k n+n₀+1=⌊ψ ((n+N:ℕ):ℝ)⌋₊ := by + have hn : n₀+1 ≤ ⌊ψ ((n+N:ℕ):ℝ)⌋₊ := by + apply Nat.le_floor + have := hbase n + norm_num only [Nat.cast_add,Nat.cast_one] at this ⊢ + nlinarith + dsimp [k] + omega + have hk : ∀ j : ℕ,j < m → StrictMono (fun n => k (m*n+j)) := by + intro j hj + apply strictMono_nat_of_lt_succ + intro n + let x : ℝ := ((m*n+j+N:ℕ):ℝ) + let y : ℝ := ((m*(n+1)+j+N:ℕ):ℝ) + have hxA : A ≤ x := le_trans hNA (by dsimp [x]; exact_mod_cast (Nat.le_add_left N (m*n+j))) + have hxy : y-x=(m:ℝ) := by dsimp [y,x]; push_cast; ring + have hh := (hψ x y hxA (by linarith)).1 + have hxp : 0 ≤ ψ x := by + have hh := hbase (m*n+j) + exact (show (0:ℝ) ≤ (n₀:ℝ)+2 by positivity).trans hh.le + have hfloorx := Nat.floor_le hxp + have hfloory := Nat.lt_floor_add_one (ψ y) + have hfl : ⌊ψ x⌋₊ < ⌊ψ y⌋₊ := by + have hh' : (⌊ψ x⌋₊:ℝ) < (⌊ψ y⌋₊:ℝ) := by nlinarith + exact_mod_cast hh' + have hidx := hid (m*n+j) + have hidy := hid (m*(n+1)+j) + dsimp [x,y] at hfl + omega + refine ⟨N,m,q,k,hm0,hk,?_⟩ + intro n r hrl hru + have hrl0 : (0:ℝ) < 2^(n+N) := by positivity + have hr0 : 0 < r := hrl0.trans hrl + have hlogl : ((n+N:ℕ):ℝ) < Real.logb 2 r := by + have hh := Real.logb_lt_logb (by norm_num : (1:ℝ) < 2) hrl0 hrl + simpa only [Real.logb_pow,Real.logb_self_eq_one (by norm_num : (1:ℝ) < 2),mul_one] using hh + have hlogu : Real.logb 2 r < ((n+N:ℕ):ℝ)+2 := by + have hh := Real.logb_lt_logb (by norm_num : (1:ℝ) < 2) hr0 hru + simpa only [Real.logb_pow,Real.logb_self_eq_one (by norm_num : (1:ℝ) < 2),mul_one,Nat.cast_add,Nat.cast_ofNat] using hh + have hNA' : A ≤ ((n+N:ℕ):ℝ) := le_trans hNA (by norm_num) + have hh := hψ ((n+N:ℕ):ℝ) (Real.logb 2 r) hNA' hlogl.le + have hfloor := Nat.floor_le (show 0 ≤ ψ ((n+N:ℕ):ℝ) by + exact (show (0:ℝ) ≤ (n₀:ℝ)+2 by positivity).trans (hbase n).le) + have hfloor' := Nat.lt_floor_add_one (ψ ((n+N:ℕ):ℝ)) + constructor + · rw [←Real.rpow_natCast] + apply Real.rpow_le_rpow_of_exponent_le (by norm_num : (1:ℝ) ≤ 2) + rw [hid] + nlinarith + · rw [←Real.rpow_natCast] + apply Real.rpow_lt_rpow_of_exponent_lt (by norm_num : (1:ℝ) < 2) + have he : k n+n₀+q+1=⌊ψ ((n+N:ℕ):ℝ)⌋₊+q := by have := hid n; omega + rw [he] + norm_num only [Nat.cast_add,Nat.cast_ofNat] at hfloor' hh hlogu hlogl ⊢ + nlinarith + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +namespace DegeneratingTrees + +lemma summable_strict_majorant {w : ℕ → ℝ} (hw : ∀ n,0≤w n) (hs : Summable w) : + ∃ v : ℕ → ℝ,(∀ n,0≤v n) ∧ Summable v ∧ + ∀ ε : ℝ,0<ε → ∀ᶠ n in atTop,w n≤ε*v n := by + let T : ℕ → ℝ := fun n => ∑' k : ℕ,w (k+n) + have hTpos (n : ℕ) : 0≤T n := tsum_nonneg (fun k => hw _) + have hTrec (n : ℕ) : T n=w n+T (n+1) := by + have hh := ((summable_nat_add_iff n).mpr hs).tsum_eq_zero_add + simpa only [T,zero_add,Nat.add_assoc,show 1+n=n+1 by omega] using hh + have hTlim : Tendsto T atTop (𝓝 0) := by + have hh := (tendsto_const_nhds (x := ∑' k,w k)).sub hs.hasSum.tendsto_sum_nat + simp only [sub_self] at hh + apply hh.congr + intro n + have ht := hs.sum_add_tsum_nat_add n + dsimp [T] + linarith + let v : ℕ → ℝ := fun n => Real.sqrt (T n)-Real.sqrt (T (n+1)) + have hvpos (n : ℕ) : 0≤v n := by + apply sub_nonneg.mpr + apply Real.sqrt_le_sqrt + linarith [hTrec n,hw n] + have hvs : Summable v := by + apply summable_of_sum_range_le hvpos (c := Real.sqrt (T 0)) + intro n + dsimp [v] + rw [Finset.sum_range_sub'] + exact sub_le_self _ (Real.sqrt_nonneg _) + have hfac (n : ℕ) : w n=(Real.sqrt (T n)+Real.sqrt (T (n+1)))*v n := by + dsimp [v] + nlinarith [Real.sq_sqrt (hTpos n),Real.sq_sqrt (hTpos (n+1)),hTrec n] + have hlim : Tendsto (fun n => Real.sqrt (T n)+Real.sqrt (T (n+1))) atTop (𝓝 0) := by + have hh := (Real.continuous_sqrt.continuousAt.tendsto.comp hTlim).add + (Real.continuous_sqrt.continuousAt.tendsto.comp (hTlim.comp (tendsto_add_atTop_nat 1))) + simpa only [Real.sqrt_zero,add_zero,Function.comp_def] using hh + refine ⟨v,hvpos,hvs,?_⟩ + intro ε hε + filter_upwards [hlim.eventually (gt_mem_nhds hε)] with n hn + rw [hfac] + exact mul_le_mul_of_nonneg_right hn.le (hvpos n) + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +namespace DegeneratingTrees + + + +theorem AdmissibleAngularLoss.pullback_log_scale {ω ψ : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) {A : ℝ} + (hψ : ∀ x y : ℝ,A≤x → x≤y → + (y-x)/2≤ψ y-ψ x ∧ ψ y-ψ x≤2*(y-x)) : + AdmissibleAngularLoss (fun r => Max.max (baseLoss r) (ω ((2:ℝ)^(ψ (Real.logb 2 r))))) := by + obtain ⟨hp,n₀,w,hw,hs,hb⟩ := hω + obtain ⟨N,hN⟩ := exists_nat_gt (Max.max A (A+2*((n₀:ℝ)+2-ψ A))) + have hNA : A≤(N:ℝ) := le_of_lt ((le_max_left _ _).trans_lt hN) + have hNψ : (n₀:ℝ)+2<ψ (N:ℝ) := by + have h := (hψ A (N:ℝ) le_rfl hNA).1 + have ht := (le_max_right _ _).trans_lt hN + linarith + have hbase (n : ℕ) : (n₀:ℝ)+2<ψ ((n+N:ℕ):ℝ) := by + have hn : (N:ℝ)≤((n+N:ℕ):ℝ) := by norm_num + have h := (hψ (N:ℝ) ((n+N:ℕ):ℝ) hNA hn).1 + linarith + let k : ℕ → ℕ := fun n => ⌊ψ ((n+N:ℕ):ℝ)⌋₊-n₀-1 + have hid (n : ℕ) : k n+n₀+1=⌊ψ ((n+N:ℕ):ℝ)⌋₊ := by + have hn : n₀+1≤⌊ψ ((n+N:ℕ):ℝ)⌋₊ := by + apply Nat.le_floor + have := hbase n + norm_num only [Nat.cast_add,Nat.cast_one] at this ⊢ + linarith + dsimp [k] + omega + have hk : ∀ j : ℕ,j<4 → StrictMono (fun n => k (4*n+j)) := by + intro j hj + apply strictMono_nat_of_lt_succ + intro n + let x : ℝ := ((4*n+j+N:ℕ):ℝ) + let y : ℝ := ((4*(n+1)+j+N:ℕ):ℝ) + have hxA : A≤x := le_trans hNA (by dsimp [x]; exact_mod_cast (Nat.le_add_left N (4*n+j))) + have hxy : y-x=4 := by dsimp [y,x]; push_cast; ring + have hh := (hψ x y hxA (by linarith)).1 + have hxp : 0≤ψ x := by + have hh := hbase (4*n+j) + exact (show (0:ℝ)≤(n₀:ℝ)+2 by positivity).trans hh.le + have hfloorx := Nat.floor_le hxp + have hfloory := Nat.lt_floor_add_one (ψ y) + have hfl : ⌊ψ x⌋₊<⌊ψ y⌋₊ := by + have hh' : (⌊ψ x⌋₊:ℝ)<(⌊ψ y⌋₊:ℝ) := by linarith + exact_mod_cast hh' + have hidx := hid (4*n+j) + have hidy := hid (4*(n+1)+j) + dsimp [x,y] at hfl + omega + apply admissible_pullback_of_shell_control (N := N) (q := 5) hw hs hb k hk + intro n r hrl hru + have hrl0 : (0:ℝ)<2^(n+N) := by positivity + have hr0 : 0 rw [he] + rw [←Real.rpow_natCast] + apply Real.rpow_lt_rpow_of_exponent_lt (by norm_num : (1:ℝ)<2) + have hh : ((dyadicLossIndex N r+N:ℕ):ℝ)+1=(⌊Real.logb 2 r⌋₊:ℝ) := by exact_mod_cast hid + linarith + · conv_lhs => rw [he] + rw [←Real.rpow_natCast] + apply Real.rpow_lt_rpow_of_exponent_lt (by norm_num : (1:ℝ)<2) + have hh : dyadicLossIndex N r+N+2=⌊Real.logb 2 r⌋₊+1 := by omega + rw [hh] + simpa only [Nat.cast_add,Nat.cast_one] using hfloor' + +lemma admissible_dyadic_step {v : ℕ → ℝ} (hv : ∀ n,0≤v n) (hs : Summable v) (N : ℕ) : + AdmissibleAngularLoss (fun r => max (baseLoss r) (v (dyadicLossIndex N r))) := by + have hsum : Summable (fun n => v (n+1)+v (n+2)) := + ((summable_nat_add_iff 1).mpr hs).add ((summable_nat_add_iff 2).mpr hs) + apply admissible_max_of_shell_bounds (N := N+2) + (w := fun n => v (n+1)+v (n+2)) (fun n => add_nonneg (hv _) (hv _)) hsum + intro n r hl hu + have hp : (0:ℝ)<2^(n+(N+2)) := by positivity + have hr : 0 max (baseLoss r) (v (dyadicLossIndex N r)),admissible_dyadic_step hv hvs N,?_⟩ + intro ε hε + filter_upwards [dyadicLossIndex_shell N,(tendsto_dyadicLossIndex N).eventually (hlittle ε hε)] with r hr hvw + exact (hb _ r hr.1 hr.2).trans (hvw.trans + (mul_le_mul_of_nonneg_left (le_max_right _ _) hε.le)) + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +namespace DegeneratingTrees + +lemma logarithmic_clock_slopes {ψ : ℝ → ℝ} + (ha : ∀ᶠ x in atTop,DifferentiableAt ℝ ψ x) + (hd : Tendsto (deriv ψ) atTop (𝓝 1)) : + ∃ A : ℝ,∀ x y : ℝ,A≤x → x≤y → + (y-x)/2≤ψ y-ψ x ∧ ψ y-ψ x≤2*(y-x) := by + have hnear : ∀ᶠ x in atTop,‖deriv ψ x-1‖≤(1:ℝ)/2 := by + filter_upwards [(Metric.tendsto_nhds.mp hd) (1/2) (by norm_num)] with x hx + exact le_of_lt (by simpa only [dist_eq_norm] using hx) + obtain ⟨A,hA⟩ := eventually_atTop.mp (ha.and hnear) + refine ⟨A,?_⟩ + intro x y hx hxy + have hh := norm_image_sub_le_of_norm_deriv_le_segment' + (f := fun t => ψ t-t) (f' := fun t => deriv ψ t-1) (a := x) (b := y) + (fun t ht => ((hA t (hx.trans ht.1)).1.hasDerivAt.sub (hasDerivAt_id t)).hasDerivWithinAt) + (fun t ht => (hA t (hx.trans ht.1)).2) y ⟨hxy,le_rfl⟩ + rw [Real.norm_eq_abs,abs_le] at hh + constructor <;> linarith [hh.1,hh.2] + +theorem AdmissibleAngularLoss.pullback_log_derivative {ω ψ : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) + (ha : ∀ᶠ x in atTop,DifferentiableAt ℝ ψ x) + (hd : Tendsto (deriv ψ) atTop (𝓝 1)) : + AdmissibleAngularLoss (fun r => Max.max (baseLoss r) (ω ((2:ℝ)^(ψ (Real.logb 2 r))))) := by + obtain ⟨A,hA⟩ := logarithmic_clock_slopes ha hd + exact hω.pullback_log_scale hA + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +namespace DegeneratingTrees + +lemma logarithmic_clock_slopes_pos {ψ : ℝ → ℝ} {b : ℝ} (hb : 0 < b) + (ha : ∀ᶠ x in atTop,DifferentiableAt ℝ ψ x) + (hd : Tendsto (deriv ψ) atTop (𝓝 b)) : + ∃ A : ℝ,∀ x y : ℝ,A ≤ x → x ≤ y → + (b/2)*(y-x) ≤ ψ y-ψ x ∧ ψ y-ψ x ≤ (2*b)*(y-x) := by + have hnear : ∀ᶠ x in atTop,‖deriv ψ x-b‖ ≤ b/2 := by + filter_upwards [(Metric.tendsto_nhds.mp hd) (b/2) (by positivity)] with x hx + exact le_of_lt (by simpa only [dist_eq_norm] using hx) + obtain ⟨A,hA⟩ := eventually_atTop.mp (ha.and hnear) + refine ⟨A,?_⟩ + intro x y hx hxy + have hh := norm_image_sub_le_of_norm_deriv_le_segment' + (f := fun t => ψ t-b*t) (f' := fun t => deriv ψ t-b) (a := x) (b := y) + (fun t ht => ((hA t (hx.trans ht.1)).1.hasDerivAt.sub (hasDerivAt_const_mul b)).hasDerivWithinAt) + (fun t ht => (hA t (hx.trans ht.1)).2) y ⟨hxy,le_rfl⟩ + rw [Real.norm_eq_abs,abs_le] at hh + constructor <;> nlinarith [hh.1,hh.2] + +lemma unit_to_dyadic_shells {e : ℝ → ℝ} {w : ℕ → ℝ} {n₀ : ℕ} + (hb : ∀ n t,((n+n₀:ℕ):ℝ) ≤ t → t ≤ ((n+n₀:ℕ):ℝ)+2 → |e t| ≤ w n) : + ∀ n r,(2:ℝ)^(n+n₀) < r → r < 2^(n+n₀+2) → |e (Real.logb 2 r)| ≤ w n := by + intro n r hl hu + have hl₀ : (0:ℝ) < 2^(n+n₀) := by positivity + have hr : 0 < r := hl₀.trans hl + apply hb + · have hh := Real.logb_lt_logb (by norm_num : (1:ℝ) < 2) hl₀ hl + exact le_of_lt (by simpa only [Real.logb_pow,Real.logb_self_eq_one (by norm_num : (1:ℝ) < 2),mul_one] using hh) + · have hh := Real.logb_lt_logb (by norm_num : (1:ℝ) < 2) hr hu + exact le_of_lt (by simpa only [Real.logb_pow,Real.logb_self_eq_one (by norm_num : (1:ℝ) < 2),mul_one,Nat.cast_add,Nat.cast_ofNat] using hh) + +theorem strict_loss_from_unit_shells {e ψ : ℝ → ℝ} {w : ℕ → ℝ} {n₀ : ℕ} + (hw : ∀ n,0 ≤ w n) (hs : Summable w) + (hb : ∀ n t,((n+n₀:ℕ):ℝ) ≤ t → t ≤ ((n+n₀:ℕ):ℝ)+2 → |e t| ≤ w n) + {b : ℝ} (hb₀ : 0 < b) + (ha : ∀ᶠ x in atTop,DifferentiableAt ℝ ψ x) + (hd : Tendsto (deriv ψ) atTop (𝓝 b)) : + ∃ ω : ℝ → ℝ,AdmissibleAngularLoss ω ∧ + ∀ ε : ℝ,0 < ε → ∀ᶠ r in atTop,|e (ψ (Real.logb 2 r))| ≤ ε*ω r := by + obtain ⟨A,hA⟩ := logarithmic_clock_slopes_pos hb₀ ha hd + obtain ⟨N,m,q,k,hm,hk,hmap⟩ := log_scale_shell_control (by positivity : 0 < b/2) + (by positivity : 0 < 2*b) hA n₀ + apply admissible_strict_absorption (N := N) (w := fun n => ∑ j∈Finset.range q,w (k n+j)) + (fun n => Finset.sum_nonneg (fun j _ => hw _)) (summable_shell_window hw hs hm hk q) + intro n r hl hu + have hh := dyadic_span_bound hw (unit_to_dyadic_shells hb) (k n) q + (hmap n r hl hu).1 (hmap n r hl hu).2 + simpa only [Real.logb_rpow (by norm_num : (0:ℝ) < 2) (by norm_num : (2:ℝ)≠1)] using hh + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/LowerRatios.lean b/lean/OAI/Analysis/PathSelection/LowerRatios.lean new file mode 100644 index 0000000000000000000000000000000000000000..d586208c1991c15151456f8c63db3f0ea198c06c --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/LowerRatios.lean @@ -0,0 +1,371 @@ +import Mathlib +import OAI.Analysis.PathSelection.InverseAsymptotics +import OAI.Analysis.PathSelection.RealClocks + +namespace OAI + +/-! Lower Hardy fields, vanishing Puiseux ratios and leading-term comparison. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma PuiseuxSector.real_puiseux {J : ℂ → ℂ} (hJ : J∈PuiseuxSector) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) : + Puiseux (fun t : ℝ => ((J (t:ℂ)).re:ℂ)) := by + apply hJ.2.congr + filter_upwards [hr] with t ht + exact Complex.ext rfl (by simpa using ht) + +lemma sector_real_derivative {J : ℂ → ℂ} + (ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ J z) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) : + ∀ᶠ t : ℝ in atTop,deriv J (t:ℂ)=((deriv (fun s : ℝ => (J (s:ℂ)).re) t:ℝ):ℂ) := by + obtain ⟨A,hA⟩ := eventually_atTop.mp hr + filter_upwards [tendsto_real_sectorInfinity.eventually ha,eventually_gt_atTop A] with t ht hAt + have him := analytic_ray_deriv_im_zero hAt ht (fun s hs => hA s hs.le) + have hd := Complex.reCLM.hasFDerivAt.comp_hasDerivAt t ht.differentiableAt.hasDerivAt.comp_ofReal + apply Complex.ext + · exact hd.deriv.symm + · simpa using him + +lemma eventually_monotone_bounded_limit {f : ℝ → ℝ} + (hm : ∃ A : ℝ,MonotoneOn f (Ici A) ∨ AntitoneOn f (Ici A)) + (hb : ∃ M : ℝ,∀ᶠ t : ℝ in atTop,|f t|≤M) : + ∃ c : ℝ,Tendsto f atTop (𝓝 c) := by + obtain ⟨A,hA⟩ := hm + obtain ⟨M,hM⟩ := hb + obtain ⟨B,hB⟩ := eventually_atTop.mp hM + let C := max A B + let g : ℝ → ℝ := fun t => f (max C t) + have hg (t : ℝ) : |g t|≤M := hB _ ((le_max_right A B).trans (le_max_left C t)) + have he : g =ᶠ[atTop] f := (eventually_ge_atTop C).mono (fun t ht => by simp [g,max_eq_right ht]) + rcases hA with hA | hA + · have hm' : Monotone g := fun s t hst => hA + ((le_max_left A B).trans (le_max_left C s)) + ((le_max_left A B).trans (le_max_left C t)) (max_le_max_left C hst) + have hb' : BddAbove (range g) := ⟨M,by rintro _ ⟨t,rfl⟩; exact (abs_le.mp (hg t)).2⟩ + exact ⟨_,(tendsto_atTop_ciSup hm' hb').congr' he⟩ + · have hm' : Antitone g := fun s t hst => hA + ((le_max_left A B).trans (le_max_left C s)) + ((le_max_left A B).trans (le_max_left C t)) (max_le_max_left C hst) + have hb' : BddBelow (range g) := ⟨-M,by rintro _ ⟨t,rfl⟩; exact (abs_le.mp (hg t)).1⟩ + exact ⟨_,(tendsto_atTop_ciInf hm' hb').congr' he⟩ + +lemma PuiseuxSector.real_monotone {J : ℂ → ℂ} (hJ : J∈PuiseuxSector) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) : + ∃ A : ℝ,MonotoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) := by + obtain ⟨A,hA⟩ := (PuiseuxSector.real_puiseux hJ hr).eventually_monotone + have hsub : Ici (A+1)⊆Ioi A := fun t ht => by change A+1≤t at ht; change A h.mono hsub) (fun h => h.mono hsub)⟩ + +lemma PuiseuxSector.positive_bounded_limit {J : ℂ → ℂ} (hJ : J∈PuiseuxSector) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re) + (hb : ∃ M : ℝ,∀ᶠ t : ℝ in atTop,(J (t:ℂ)).re≤M) : + ∃ c : ℝ,0≤c ∧ Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 c) ∧ + Tendsto J sectorInfinity (𝓝 (c:ℂ)) := by + obtain ⟨M,hM⟩ := hb + obtain ⟨c,hc⟩ := eventually_monotone_bounded_limit (PuiseuxSector.real_monotone hJ (hr.mono fun _ h => h.1)) + ⟨M,by filter_upwards [hr,hM] with t ht hm; rwa [abs_of_pos ht.2]⟩ + have hc0 : 0≤c := ge_of_tendsto hc (hr.mono fun _ h => h.2.le) + exact ⟨c,hc0,hc,PuiseuxSector.tendsto_of_ray hJ (complex_real_limit (hr.mono fun _ h => h.1) hc)⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma positive_vanishing_not_deriv_nonneg {f : ℝ → ℝ} + (ha : ∀ᶠ t : ℝ in atTop,AnalyticAt ℝ f t) + (hp : ∀ᶠ t : ℝ in atTop,0 (hA x hx.le).1.continuousAt.continuousWithinAt + · exact fun x hx => (hA x (interior_subset hx).le).1.differentiableAt.differentiableWithinAt + · exact fun x hx => (hA x (interior_subset hx).le).2.2 + have hh : f (A+1)≤0 := ge_of_tendsto ht ((eventually_ge_atTop (A+1)).mono fun t ht => + hm (by change A (f t:ℂ))) + (hp : ∀ᶠ t : ℝ in atTop,0 0 := fun he => hn (he.mono (fun _ h => by rw [h])) + rcases hf.real_deriv.eventually_sign hne with hs | hs + · exact False.elim (hn (hs.mono fun _ h => h.le)) + · exact hs + +lemma PuiseuxSector.ray_nonzero_to_sector {J : ℂ → ℂ} (hJ : J∈PuiseuxSector) + (hn : ∀ᶠ t : ℝ in atTop,J (t:ℂ)≠0) : ∀ᶠ z in sectorInfinity,J z≠0 := by + rcases puiseux_lowerSectorData.zero_or_ne hJ with hz | hz + · obtain ⟨t,ht,h0⟩ := (hn.and (tendsto_real_sectorInfinity.eventually hz)).exists + exact False.elim (ht h0) + · exact hz + +lemma PuiseuxSector.vanishing_ratio_data {J : ℂ → ℂ} (hJ : J∈PuiseuxSector) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re) + (ht : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 0)) : + (∀ᶠ z in sectorInfinity,deriv J z≠0) ∧ + Tendsto (fun z => deriv (deriv J) z/deriv J z) sectorInfinity (𝓝 0) ∧ + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => deriv J z/J z) z) ∧ + (∀ᶠ z in sectorInfinity,deriv J z/J z≠0) ∧ + Tendsto (fun z => deriv (fun z => deriv J z/J z) z/(deriv J z/J z)) sectorInfinity (𝓝 0) ∧ + (∀ᶠ t : ℝ in atTop,(deriv J (t:ℂ)/J (t:ℂ)).im=0 ∧ (deriv J (t:ℂ)/J (t:ℂ)).re<0) := by + have hd := PuiseuxSector.deriv_mem hJ + have hD := sector_real_derivative hJ.1 (hr.mono fun _ h => h.1) + have hneg := (PuiseuxSector.real_puiseux hJ (hr.mono fun _ h => h.1)).positive_vanishing_derivative_negative + (hr.mono fun _ h => h.2) ht + have hdr : ∀ᶠ t : ℝ in atTop,deriv J (t:ℂ)≠0 := by + filter_upwards [hD,hneg] with t hd hn + rw [hd] + exact Complex.ofReal_ne_zero.mpr hn.ne + have hdn := PuiseuxSector.ray_nonzero_to_sector hd hdr + have hqr : ∀ᶠ t : ℝ in atTop,(deriv J (t:ℂ)/J (t:ℂ)).im=0 ∧ + (deriv J (t:ℂ)/J (t:ℂ)).re<0 := by + filter_upwards [hr,hD,hneg] with t hr hd hn + have he : J (t:ℂ)=((J (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hr.1) + rw [hd,he,←Complex.ofReal_div] + exact ⟨rfl,div_neg_of_neg_of_pos hn hr.2⟩ + have hq : (fun z => deriv J z/J z)∈PuiseuxSector := by + simpa only [div_eq_mul_inv] using puiseux_lowerSectorData.mul_mem hd (puiseux_lowerSectorData.inv_mem hJ) + have hqnray : ∀ᶠ t : ℝ in atTop,deriv J (t:ℂ)/J (t:ℂ)≠0 := hqr.mono fun t ht he => by + have hh := ht.2; rw [he,Complex.zero_re] at hh; exact lt_irrefl _ hh + have hqn := PuiseuxSector.ray_nonzero_to_sector hq hqnray + have hneq {f : ℂ → ℂ} (hn : ∀ᶠ t : ℝ in atTop,f (t:ℂ)≠0) : + ¬ (fun t : ℝ => f (t:ℂ)) =ᶠ[atTop] fun _ => 0 := by + intro he; obtain ⟨t,ht,h0⟩ := (hn.and he).exists; exact ht h0 + exact ⟨hdn,PuiseuxSector.log_deriv_tendsto hd (hneq hdr),hq.1,hqn, + PuiseuxSector.log_deriv_tendsto hq (hneq (f := fun z => deriv J z/J z) hqnray),hqr⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma real_nonzero_eventually_sign {f : ℝ → ℝ} + (hc : ∀ᶠ t : ℝ in atTop,ContinuousAt f t) + (hn : ∀ᶠ t : ℝ in atTop,f t≠0) : + (∀ᶠ t : ℝ in atTop,0 (hA t ht).1.continuousWithinAt + have hpos (u : ℝ) (hu : A≤u) (hp : 0 hpos A le_rfl hp t ht) + +lemma LowerSectorData.ray_nonzero_to_sector {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + {J : ℂ → ℂ} (hJ : J∈K) (hn : ∀ᶠ t : ℝ in atTop,J (t:ℂ)≠0) : + ∀ᶠ z in sectorInfinity,J z≠0 := by + rcases hK.zero_or_ne hJ with hz | hz + · obtain ⟨t,ht,h0⟩ := (hn.and (tendsto_real_sectorInfinity.eventually hz)).exists + exact False.elim (ht h0) + · exact hz + +lemma LowerSectorData.real_derivative_sign {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) + {J : ℂ → ℂ} (hJ : J∈K) (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) : + (∀ᶠ t : ℝ in atTop,0≤deriv (fun s : ℝ => (J (s:ℂ)).re) t) ∨ + (∀ᶠ t : ℝ in atTop,deriv (fun s : ℝ => (J (s:ℂ)).re) t<0) := by + have he := sector_real_derivative (hK.analytic hJ) hr + rcases hK.zero_or_ne (hKd _ hJ) with hz | hn + · left + filter_upwards [he,tendsto_real_sectorInfinity.eventually hz] with t ht hz + have hz' : deriv (fun s : ℝ => (J (s:ℂ)).re) t=0 := + Complex.ofReal_eq_zero.mp (ht.symm.trans hz) + rw [hz'] + · have hdn : ∀ᶠ t : ℝ in atTop,(deriv J (t:ℂ)).re≠0 := by + filter_upwards [he,tendsto_real_sectorInfinity.eventually hn] with t ht hn + rw [ht] at hn ⊢ + exact Complex.ofReal_ne_zero.mp hn + have hdc : ∀ᶠ t : ℝ in atTop,ContinuousAt (fun t : ℝ => (deriv J (t:ℂ)).re) t := by + filter_upwards [tendsto_real_sectorInfinity.eventually (hK.analytic (hKd _ hJ))] with t ht + exact Complex.continuous_re.continuousAt.comp + (ht.continuousAt.comp Complex.continuous_ofReal.continuousAt) + rcases real_nonzero_eventually_sign hdc hdn with hp | hm + · left + filter_upwards [he,hp] with t ht hp + simpa only [ht,Complex.ofReal_re] using hp.le + · right + filter_upwards [he,hm] with t ht hm + rwa [ht] at hm + +lemma LowerSectorData.real_monotone {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) + {J : ℂ → ℂ} (hJ : J∈K) (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0) : + ∃ A : ℝ,MonotoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) ∨ + AntitoneOn (fun t : ℝ => (J (t:ℂ)).re) (Ici A) := by + have ha : ∀ᶠ t : ℝ in atTop,AnalyticAt ℝ (fun t : ℝ => (J (t:ℂ)).re) t := by + filter_upwards [tendsto_real_sectorInfinity.eventually (hK.analytic hJ)] with t ht + exact (Complex.reCLM.analyticAt _).comp ((ht.restrictScalars (𝕜 := ℝ)).comp (Complex.ofRealCLM.analyticAt _)) + rcases hK.real_derivative_sign hKd hJ hr with hp | hm + · obtain ⟨A,hA⟩ := eventually_atTop.mp (ha.and hp) + refine ⟨A,Or.inl ?_⟩ + apply monotoneOn_of_deriv_nonneg (convex_Ici A) + · exact fun t ht => (hA t ht).1.continuousAt.continuousWithinAt + · exact fun t ht => (hA t (interior_subset ht)).1.differentiableAt.differentiableWithinAt + · exact fun t ht => (hA t (interior_subset ht)).2 + · obtain ⟨A,hA⟩ := eventually_atTop.mp (ha.and hm) + refine ⟨A,Or.inr ?_⟩ + apply antitoneOn_of_deriv_nonpos (convex_Ici A) + · exact fun t ht => (hA t ht).1.continuousAt.continuousWithinAt + · exact fun t ht => (hA t (interior_subset ht)).1.differentiableAt.differentiableWithinAt + · exact fun t ht => (hA t (interior_subset ht)).2.le + +lemma LowerSectorData.positive_bounded_limit {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) + {J : ℂ → ℂ} (hJ : J∈K) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re) + (hb : ∃ M : ℝ,∀ᶠ t : ℝ in atTop,(J (t:ℂ)).re≤M) : + ∃ c : ℝ,0≤c ∧ Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 c) ∧ + Tendsto (fun t : ℝ => J (t:ℂ)) atTop (𝓝 (c:ℂ)) := by + obtain ⟨M,hM⟩ := hb + obtain ⟨c,hc⟩ := eventually_monotone_bounded_limit (hK.real_monotone hKd hJ (hr.mono fun _ h => h.1)) + ⟨M,by filter_upwards [hr,hM] with t ht hm; rwa [abs_of_pos ht.2]⟩ + exact ⟨c,ge_of_tendsto hc (hr.mono fun _ h => h.2.le),hc,complex_real_limit (hr.mono fun _ h => h.1) hc⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma LowerSectorData.vanishing_ratio_data {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) {J : ℂ → ℂ} (hJ : J∈K) + (hr : ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re) + (ht : Tendsto (fun t : ℝ => (J (t:ℂ)).re) atTop (𝓝 0)) : + (∀ᶠ z in sectorInfinity,deriv J z≠0) ∧ + Tendsto (fun z => deriv (deriv J) z/deriv J z) stripInfinity (𝓝 0) ∧ + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => deriv J z/J z) z) ∧ + (∀ᶠ z in sectorInfinity,deriv J z/J z≠0) ∧ + Tendsto (fun z => deriv (fun z => deriv J z/J z) z/(deriv J z/J z)) stripInfinity (𝓝 0) ∧ + (∀ᶠ t : ℝ in atTop,(deriv J (t:ℂ)/J (t:ℂ)).im=0 ∧ (deriv J (t:ℂ)/J (t:ℂ)).re<0) := by + have hd := hKd _ hJ + have hD := sector_real_derivative (hK.analytic hJ) (hr.mono fun _ h => h.1) + have hneg : ∀ᶠ t : ℝ in atTop,deriv (fun s : ℝ => (J (s:ℂ)).re) t<0 := by + have ha : ∀ᶠ t : ℝ in atTop,AnalyticAt ℝ (fun s : ℝ => (J (s:ℂ)).re) t := by + filter_upwards [tendsto_real_sectorInfinity.eventually (hK.analytic hJ)] with t ht + exact (Complex.reCLM.analyticAt _).comp ((ht.restrictScalars (𝕜 := ℝ)).comp (Complex.ofRealCLM.analyticAt _)) + exact (hK.real_derivative_sign hKd hJ (hr.mono fun _ h => h.1)).resolve_left + (positive_vanishing_not_deriv_nonneg ha (hr.mono fun _ h => h.2) ht) + have hdr : ∀ᶠ t : ℝ in atTop,deriv J (t:ℂ)≠0 := by + filter_upwards [hD,hneg] with t hd hn + rw [hd] + exact Complex.ofReal_ne_zero.mpr hn.ne + have hdn := hK.ray_nonzero_to_sector hd hdr + have hqr : ∀ᶠ t : ℝ in atTop,(deriv J (t:ℂ)/J (t:ℂ)).im=0 ∧ + (deriv J (t:ℂ)/J (t:ℂ)).re<0 := by + filter_upwards [hr,hD,hneg] with t hr hd hn + have he : J (t:ℂ)=((J (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hr.1) + rw [hd,he,←Complex.ofReal_div] + exact ⟨rfl,div_neg_of_neg_of_pos hn hr.2⟩ + have hq : (fun z => deriv J z/J z)∈K := by + simpa only [div_eq_mul_inv] using hK.mul_mem hd (hK.inv_mem hJ) + have hqnray : ∀ᶠ t : ℝ in atTop,deriv J (t:ℂ)/J (t:ℂ)≠0 := hqr.mono fun t ht he => by + have hh := ht.2; rw [he,Complex.zero_re] at hh; exact lt_irrefl _ hh + have hqn := hK.ray_nonzero_to_sector hq hqnray + exact ⟨hdn,hK.log_deriv_strip hd hdn,hK.analytic hq,hqn, + hK.log_deriv_strip hq hqn,hqr⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma ExpSmall.relative_quotient {f g : ℂ → ℂ} (hf : ExpSmall 0 f) (hg : ExpSmall 0 g) : + ExpSmall 0 (fun z => (1+f z)/(1+g z)-1) := by + have hi : ExpBound 0 (fun z => (1+g z)⁻¹) := by + apply ExpBound.of_tendsto (c := 1) + simpa using (tendsto_const_nhds.add hg.tendsto_zero).inv₀ (by norm_num : (1:ℂ)+0≠0) + have hn : ∀ᶠ z in sectorInfinity,1+g z≠0 := by + have ht : Tendsto (fun z => 1+g z) sectorInfinity (𝓝 1) := by simpa using tendsto_const_nhds.add hg.tendsto_zero + exact ht.eventually_ne (by norm_num : (1:ℂ)≠0) + have hh := (hf.sub hg).mul hi + simp only [add_zero] at hh + apply hh.congr + filter_upwards [hn] with z hz + field_simp + ring + +lemma normalized_equal_exponent_ratio {F H g h : ℂ → ℂ} {b : ℝ} + (hg : ∀ᶠ z in sectorInfinity,g z≠0) (hh : ∀ᶠ z in sectorInfinity,h z≠0) + (hF : ExpSmall 0 (fun z => Complex.exp (((-b:ℝ):ℂ)*z)*(g z)⁻¹*F z-1)) + (hH : ExpSmall 0 (fun z => Complex.exp (((-b:ℝ):ℂ)*z)*(h z)⁻¹*H z-1)) : + ∃ E : ℂ → ℂ,ExpSmall 0 E ∧ + ∀ᶠ z in sectorInfinity,F z/H z=(g z/h z)*(1+E z) := by + let f := fun z => Complex.exp (((-b:ℝ):ℂ)*z)*(g z)⁻¹*F z-1 + let k := fun z => Complex.exp (((-b:ℝ):ℂ)*z)*(h z)⁻¹*H z-1 + refine ⟨fun z => (1+f z)/(1+k z)-1,hF.relative_quotient hH,?_⟩ + filter_upwards [hg,hh] with z hgz hhz + dsimp only [f,k] + have hc (a : ℂ) : 1+(a-1)=a := by ring + simp only [hc] + by_cases hz : H z=0 + · simp [hz] + · field_simp [hgz,hhz,hz,Complex.exp_ne_zero] + +lemma lower_ratio_bounded {F H J E : ℂ → ℂ} + (he : ExpSmall 0 E) + (hfactor : ∀ᶠ z in sectorInfinity,F z/H z=J z*(1+E z)) + (hbound : ∃ M : ℝ,∀ᶠ t : ℝ in atTop,‖F (t:ℂ)/H (t:ℂ)‖≤M) : + ∃ M : ℝ,∀ᶠ t : ℝ in atTop,‖J (t:ℂ)‖≤M := by + obtain ⟨M,hM⟩ := hbound + have hEt : Tendsto (fun t : ℝ => ‖E (t:ℂ)‖) atTop (𝓝 0) := by + simpa only [norm_zero,Function.comp_def] using ((he.tendsto_zero.norm).comp tendsto_real_sectorInfinity) + have hE := hEt.eventually (eventually_lt_nhds (show (0:ℝ)<1/2 by norm_num)) + refine ⟨2*M,?_⟩ + filter_upwards [hM,hE,tendsto_real_sectorInfinity.eventually hfactor] with t ht heq hf + have hl : 1/2≤‖1+E (t:ℂ)‖ := by + have hh : (1:ℝ)≤‖1+E (t:ℂ)‖+‖E (t:ℂ)‖ := by + calc + 1 = ‖(1+E (t:ℂ))-E (t:ℂ)‖ := by simp + _ ≤ _ := norm_sub_le _ _ + nlinarith + rw [hf,norm_mul] at ht + nlinarith [norm_nonneg (J (t:ℂ))] + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/Main.lean b/lean/OAI/Analysis/PathSelection/Main.lean new file mode 100644 index 0000000000000000000000000000000000000000..157b0eaf1a216abcb573b3aae407f42b7c12ad86 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/Main.lean @@ -0,0 +1,5 @@ +import OAI.Analysis.PathSelection.IdentityDetection +import OAI.Analysis.PathSelection.PathMonotonicity +import OAI.Analysis.PathSelection.PreparationStability +import OAI.Analysis.PathSelection.RootLimits +import OAI.Analysis.PathSelection.SectorFamilies diff --git a/lean/OAI/Analysis/PathSelection/MonicFamilies.lean b/lean/OAI/Analysis/PathSelection/MonicFamilies.lean new file mode 100644 index 0000000000000000000000000000000000000000..97415a7f211141b2abe75db281c7e7cf7069dfe9 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/MonicFamilies.lean @@ -0,0 +1,114 @@ +import Mathlib + +namespace OAI + +/-! Monic polynomial families and scalar specialization. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Metric Filter Topology Complex Polynomial +open scoped BigOperators +namespace DegeneratingTrees + +def monicFamily {R : Type*} [Semiring R] {d : ℕ} (c : Fin d → R) : R[X] := + X^d + ∑ i : Fin d, monomial (i : ℕ) (c i) + +lemma monicFamily_coeff {R : Type*} [Semiring R] {d : ℕ} (c : Fin d → R) (n : ℕ) : + (monicFamily c).coeff n = if hn : n < d then c ⟨n,hn⟩ else if n = d then 1 else 0 := by + classical + simp only [monicFamily,coeff_add,coeff_X_pow,finsetSum_coeff,coeff_monomial] + by_cases hn : n < d + · rw [dite_eq_left hn,ite_eq_right (ne_of_lt hn)] + rw [Finset.sum_eq_single (⟨n,hn⟩ : Fin d)] + · simp + · intro j hj hjn + have hjv : (j : ℕ) ≠ n := fun h => hjn (Fin.ext h) + simp [hjv] + · simp + · rw [dite_eq_right hn] + have hs : ∑ i : Fin d, (if (i : ℕ) = n then c i else 0) = 0 := by + apply Finset.sum_eq_zero + intro i hi + have hne : (i : ℕ) ≠ n := by + intro he + exact hn (he ▸ i.isLt) + simp [hne] + rw [hs,add_zero] + +lemma monicFamily_natDegree_le {R : Type*} [Semiring R] {d : ℕ} (c : Fin d → R) : + (monicFamily c).natDegree ≤ d := by + apply natDegree_le_iff_coeff_eq_zero.mpr + intro n hn + simp [monicFamily_coeff,not_lt.mpr hn.le,ne_of_gt hn] + +lemma monicFamily_monic {R : Type*} [Semiring R] {d : ℕ} (c : Fin d → R) : + (monicFamily c).Monic := + monic_of_natDegree_le_of_coeff_eq_one d (monicFamily_natDegree_le c) + (by simp [monicFamily_coeff]) + +lemma monicFamily_natDegree {R : Type*} [Semiring R] [Nontrivial R] {d : ℕ} + (c : Fin d → R) : (monicFamily c).natDegree = d := + natDegree_eq_of_le_of_coeff_ne_zero (monicFamily_natDegree_le c) + (by simp [monicFamily_coeff]) + +lemma eq_monicFamily {R : Type*} [Semiring R] {P : R[X]} (hP : P.Monic) : + P = monicFamily (fun i : Fin P.natDegree => P.coeff i) := by + ext n + rw [monicFamily_coeff] + split_ifs with hn hd + · rfl + · subst n; exact hP.coeff_natDegree + · exact coeff_eq_zero_of_natDegree_lt (lt_of_le_of_ne (Nat.le_of_not_gt hn) (Ne.symm hd)) + +lemma monicFamily_eval {R : Type*} [Semiring R] {d : ℕ} (c : Fin d → R) (z : R) : + (monicFamily c).eval z = z^d + ∑ i : Fin d, c i * z^(i : ℕ) := by + simp [monicFamily,eval_finsetSum,eval_X_pow] + +lemma monicFamily_eval_analytic {d : ℕ} (c : Fin d → ℂ) (a : ℂ) : + AnalyticAt ℂ (fun x : (Fin d → ℂ) × ℂ => + (monicFamily (fun i => c i + x.1 i)).eval (x.2 + a)) 0 := by + simp only [monicFamily_eval] + apply AnalyticAt.add + · exact (analyticAt_snd.add analyticAt_const).pow d + · apply Finset.analyticAt_fun_sum + intro i hi + have hcoord : AnalyticAt ℂ (fun x : (Fin d → ℂ) × ℂ => x.1 i) 0 := + ((ContinuousLinearMap.proj i : (Fin d → ℂ) →L[ℂ] ℂ).analyticAt _).comp analyticAt_fst + exact (analyticAt_const.add hcoord).mul ((analyticAt_snd.add analyticAt_const).pow i.val) + + +lemma taylor_coeff_penultimate {R : Type*} [CommRing R] {P : R[X]} + (hP : P.Monic) (hd : 0 < P.natDegree) (r : R) : + (taylor r P).coeff (P.natDegree-1) = P.coeff (P.natDegree-1) + (P.natDegree : R)*r := by + let d := P.natDegree + have hD : P = monicFamily (fun i : Fin d => P.coeff i) := eq_monicFamily hP + have htrans := congrArg (taylor r) hD + rw [htrans] + simp only [monicFamily,map_add,map_sum,taylor_X_pow,taylor_monomial,coeff_add, + finsetSum_coeff,coeff_C_mul,coeff_X_add_C_pow] + have hchoose : d.choose (d-1) = d := by + obtain ⟨n,hn⟩ := Nat.exists_eq_succ_of_ne_zero (show d ≠ 0 from Nat.ne_of_gt hd) + rw [hn] + simp + have hsub : d - (d-1) = 1 := by omega + have hs : ∑ i : Fin d, P.coeff i * (r ^ ((i : ℕ) - (d-1)) * + ((i : ℕ).choose (d-1) : R)) = P.coeff (d-1) := by + rw [Finset.sum_eq_single (⟨d-1,by omega⟩ : Fin d)] + · simp + · intro i hi hine + have hil : (i : ℕ) < d-1 := by + have := i.isLt + have hne : (i : ℕ) ≠ d-1 := fun he => hine (Fin.ext he) + omega + simp [Nat.choose_eq_zero_of_lt hil] + · simp + change r^(d-(d-1)) * (d.choose (d-1) : R) + _ = _ + rw [hchoose,hsub,pow_one,hs] + ring + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ParameterIntegrals.lean b/lean/OAI/Analysis/PathSelection/ParameterIntegrals.lean new file mode 100644 index 0000000000000000000000000000000000000000..37d5bcb96e3dbaa3b213704ae03961f8450f6848 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ParameterIntegrals.lean @@ -0,0 +1,354 @@ +import Mathlib + +namespace OAI + +/-! Analytic parameter integrals over compact sets and circles. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Metric MeasureTheory Complex +open scoped Real NNReal ENNReal + +namespace PathSelection.ParameterPreparation + +lemma differentiableAt_integral_compact {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] [FiniteDimensional ℂ E] + {U : Set E} {K : Set ℝ} {F : E → ℝ → ℂ} {D : E → ℝ → E →L[ℂ] ℂ} + (hU : IsOpen U) (hK : IsCompact K) + (hF : ContinuousOn (Function.uncurry F) (U ×ˢ K)) + (hD : ContinuousOn (Function.uncurry D) (U ×ˢ K)) + (hd : ∀ a∈U, ∀ t∈K, HasFDerivAt (fun x => F x t) (D a t) a) + {a : E} (ha : a∈U) : + DifferentiableAt ℂ (fun x => ∫ t in K, F x t) a := by + obtain ⟨r,hr,hrU⟩ := Metric.mem_nhds_iff.mp (hU.mem_nhds ha) + let A := closedBall a (r/2) + have hAU : A⊆U := (closedBall_subset_ball (by linarith : r/2 ⟨hx,ht⟩) + have hDc : ContinuousOn (D a) K := + hD.comp (continuous_const.prodMk continuous_id).continuousOn + (fun t ht => ⟨ha,ht⟩) + apply HasFDerivAt.differentiableAt + apply hasFDerivAt_integral_of_dominated_of_fderiv_le + (μ := volume.restrict K) (s := A) (bound := fun _ => C) + (closedBall_mem_nhds a (by linarith)) + · filter_upwards [hU.mem_nhds ha] with x hx + exact ((hFc x hx).integrableOn_compact hK).aestronglyMeasurable + · exact (hFc a ha).integrableOn_compact hK + · exact (hDc.integrableOn_compact hK).aestronglyMeasurable + · filter_upwards [ae_restrict_mem hK.measurableSet] with t ht + intro x hx + exact hC (x,t) ⟨hx,ht⟩ + · exact continuousOn_const.integrableOn_compact hK + · filter_upwards [ae_restrict_mem hK.measurableSet] with t ht + intro x hx + exact hd x (hAU hx) t ht + + + +theorem differentiableOn_circleIntegral {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] [FiniteDimensional ℂ E] + {U : Set E} {F : E × ℂ → ℂ} {r : ℝ} + (hU : IsOpen U) (hr : 0≤r) + (hf : AnalyticOnNhd ℂ F (U ×ˢ sphere 0 r)) : + DifferentiableOn ℂ (fun a => ∮ z in C(0,r), F (a,z)) U := by + let K : Set ℝ := Icc 0 (2*π) + let c : ℝ → ℂ := circleMap 0 r + let G : E → ℝ → ℂ := fun a t => deriv c t * F (a,c t) + let D : E → ℝ → E →L[ℂ] ℂ := fun a t => + deriv c t • (fderiv ℂ F (a,c t)).comp (ContinuousLinearMap.inl ℂ E ℂ) + have hc : Continuous c := continuous_circleMap 0 r + have hdc : Continuous (deriv c) := by + have he : deriv c = fun t => circleMap 0 r t * I := funext (deriv_circleMap 0 r) + rw [he] + exact (continuous_circleMap 0 r).mul continuous_const + have hcmem (t : ℝ) : c t∈sphere (0:ℂ) r := circleMap_mem_sphere 0 hr t + have hcomp : Continuous (fun p : E × ℝ => (p.1,c p.2)) := + continuous_fst.prodMk (hc.comp continuous_snd) + have hmaps : MapsTo (fun p : E × ℝ => (p.1,c p.2)) (U ×ˢ K) (U ×ˢ sphere 0 r) := + fun p hp => ⟨hp.1,hcmem p.2⟩ + have hG : ContinuousOn (Function.uncurry G) (U ×ˢ K) := + ((hdc.comp continuous_snd).continuousOn).mul + (hf.continuousOn.comp hcomp.continuousOn hmaps) + have hD : ContinuousOn (Function.uncurry D) (U ×ˢ K) := by + apply ((hdc.comp continuous_snd).continuousOn).smul + exact (hf.fderiv.continuousOn.comp hcomp.continuousOn hmaps).clm_comp continuousOn_const + have hd : ∀ a∈U, ∀ t∈K, HasFDerivAt (fun x => G x t) (D a t) a := by + intro a ha t ht + have hin : HasFDerivAt (fun x : E => (x,c t)) (ContinuousLinearMap.inl ℂ E ℂ) a := + hasFDerivAt_prodMk_left a (c t) + have h := (hf (a,c t) ⟨ha,hcmem t⟩).differentiableAt.hasFDerivAt.comp a hin + exact h.const_mul (deriv c t) + have hdiff : DifferentiableOn ℂ (fun a => ∮ z in C(0,r), F (a,z)) U := by + intro a ha + have hdif := differentiableAt_integral_compact hU isCompact_Icc hG hD hd ha + simp only [circleIntegral_def_Icc,smul_eq_mul] + exact hdif.differentiableWithinAt + exact hdiff + + + +theorem analyticOnNhd_circleIntegral_one_parameter + {U : Set ℂ} {F : ℂ × ℂ → ℂ} {r : ℝ} + (hU : IsOpen U) (hr : 0≤r) + (hf : AnalyticOnNhd ℂ F (U ×ˢ sphere 0 r)) : + AnalyticOnNhd ℂ (fun a => ∮ z in C(0,r), F (a,z)) U := + (differentiableOn_circleIntegral hU hr hf).analyticOnNhd hU + + + +theorem hasFPowerSeriesOnBall_integral + {α E : Type*} [MeasurableSpace α] {μ : Measure α} + [NormedAddCommGroup E] [NormedSpace ℂ E] + {F : α → E → ℂ} {p : α → FormalMultilinearSeries ℂ E ℂ} + {a : E} {R : ℝ≥0} (hR : 0 p t n) μ) + (hs : Summable (fun n => (∫ t, ‖p t n‖ ∂μ) * (R:ℝ)^n)) : + HasFPowerSeriesOnBall (fun x => ∫ t, F t x ∂μ) + (fun n => ∫ t, p t n ∂μ) a R := by + let q : FormalMultilinearSeries ℂ E ℂ := fun n => ∫ t, p t n ∂μ + have hb (n : ℕ) : ‖q n‖ * (R:ℝ)^n ≤ (∫ t, ‖p t n‖ ∂μ) * (R:ℝ)^n := + mul_le_mul_of_nonneg_right (norm_integral_le_integral_norm _) (by positivity) + refine ⟨?_,by exact_mod_cast hR,?_⟩ + · apply q.le_radius_of_bound (∑' n, (∫ t, ‖p t n‖ ∂μ) * (R:ℝ)^n) + intro n + exact (hb n).trans (hs.le_tsum n (fun _ _ => mul_nonneg (integral_nonneg fun _ => norm_nonneg _) (by positivity))) + · intro x hx + have hxR : ‖x‖≤(R:ℝ) := by + have hh : (‖x‖₊:ℝ≥0∞) p t n (fun _ => x)) μ := + (ContinuousMultilinearMap.apply ℂ (fun _ : Fin n => E) ℂ (fun _ => x)).integrable_comp (hi n) + have hpn (n : ℕ) : (∫ t, ‖p t n (fun _ => x)‖ ∂μ) ≤ + (∫ t, ‖p t n‖ ∂μ) * (R:ℝ)^n := by + rw [← integral_mul_const] + apply integral_mono (hpi n).norm ((hi n).norm.mul_const _) + intro t + apply ((p t n).le_opNorm (fun _ => x)).trans + simp only [Finset.prod_const,Finset.card_univ,Fintype.card_fin] + exact mul_le_mul_of_nonneg_left (pow_le_pow_left₀ (norm_nonneg x) hxR n) (norm_nonneg _) + have hsum : Summable (fun n => ∫ t, ‖p t n (fun _ => x)‖ ∂μ) := + Summable.of_nonneg_of_le (fun _ => integral_nonneg fun _ => norm_nonneg _) hpn hs + have hh := hasSum_integral_of_summable_integral_norm hpi hsum + have he : (∫ t, (∑' n, p t n (fun _ => x)) ∂μ) = ∫ t, F t (a+x) ∂μ := by + apply integral_congr_ae + filter_upwards [hp] with t ht + exact (ht.hasSum hx).tsum_eq + rw [he] at hh + simpa only [ContinuousMultilinearMap.integral_apply (hi _)] using hh + + + +lemma changeOrigin_uniform_majorant {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] (p : FormalMultilinearSeries ℂ E ℂ) + {r R : ℝ≥0} (hr : (r+R:ℝ≥0∞) (M n:ℝ)*(R:ℝ)^n) ∧ + ∀ x, ‖x‖₊≤r → ∀ n, ‖p.changeOrigin x n‖₊≤M n := by + let M : ℕ → ℝ≥0 := fun k => + ∑' s : Σ l : ℕ, {s : Finset (Fin (k+l)) // s.card=l}, ‖p (k+s.1)‖₊*r^s.1 + have hrp : (r:ℝ≥0∞) M n * R^n) := by + simpa only [M, NNReal.tsum_mul_right] using + (NNReal.summable_sigma.1 (p.changeOriginSeries_summable_aux₁ hr)).2 + refine ⟨M,by exact_mod_cast NNReal.summable_coe.mpr hsum,?_⟩ + intro x hx n + have hxp : (‖x‖₊:ℝ≥0∞) mul_le_mul_of_nonneg_left (pow_le_pow_left₀ (by positivity) hx s.1) (by positivity)) + (p.changeOriginSeries_summable_aux₂ hxp n) (p.changeOriginSeries_summable_aux₂ hrp n) + + + +theorem analyticAt_integral_shift_piece + {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + {K : Set ℝ} (hK : MeasurableSet K) + [IsFiniteMeasure (volume.restrict K)] + {F : E → ℂ} {p : FormalMultilinearSeries ℂ E ℂ} {a : E} {ρ : ℝ≥0∞} + (hp : HasFPowerSeriesOnBall F p a ρ) + {v : ℝ → E} {w : ℝ → ℂ} + (hv : ContinuousOn v K) (hw : ContinuousOn w K) + {r R : ℝ≥0} (hR : 0 ∫ t in K, w t * F (x+v t)) a := by + let μ := volume.restrict K + let q : ℝ → FormalMultilinearSeries ℂ E ℂ := fun t => w t • p.changeOrigin (v t) + have hrp : (r+R:ℝ≥0∞) q t n) K := by + apply hw.smul + exact (p.hasFPowerSeriesOnBall_changeOrigin n (hp.r_pos.trans_le hp.r_le)).continuousOn.comp hv + (fun t ht => mem_eball_zero_iff.mpr ((hvr t ht).trans_le hp.r_le)) + have hqn (n : ℕ) : ∀ t∈K, ‖q t n‖≤C*(M n:ℝ) := by + intro t ht + change ‖w t • p.changeOrigin (v t) n‖≤_ + rw [norm_smul] + exact mul_le_mul (hwb t ht) (by exact_mod_cast hbound (v t) (hb t ht) n) + (norm_nonneg _) hC + have hi (n : ℕ) : Integrable (fun t => q t n) μ := + Integrable.of_bound ((hq n).aestronglyMeasurable hK) (C*(M n:ℝ)) + (by filter_upwards [ae_restrict_mem hK] with t ht; exact hqn n t ht) + have hs : Summable (fun n => (∫ t, ‖q t n‖ ∂μ)*(R:ℝ)^n) := by + have hmajor := hM.mul_left (μ.real univ * C) + apply Summable.of_nonneg_of_le (fun _ => mul_nonneg (integral_nonneg fun _ => norm_nonneg _) (by positivity)) _ hmajor + intro n + have hn : (∫ t, ‖q t n‖ ∂μ) ≤ μ.real univ * (C*(M n:ℝ)) := by + calc + _ ≤ ∫ _t, C*(M n:ℝ) ∂μ := integral_mono_ae (hi n).norm (integrable_const _) + (by filter_upwards [ae_restrict_mem hK] with t ht; exact hqn n t ht) + _ = _ := by simp [integral_const] + calc + _ ≤ μ.real univ * (C*(M n:ℝ)) * (R:ℝ)^n := + mul_le_mul_of_nonneg_right hn (by positivity) + _ = _ := by ring + have hpq : ∀ᵐ t ∂μ, HasFPowerSeriesOnBall (fun x => w t * F (x+v t)) (q t) a R := by + filter_upwards [ae_restrict_mem hK] with t ht + have hrad : (R:ℝ≥0∞) ≤ ρ - (‖v t‖₊:ℝ≥0∞) := by + apply ENNReal.le_sub_of_add_le_right (by finiteness) + calc + (R:ℝ≥0∞) + (‖v t‖₊:ℝ≥0∞) ≤ R+r := add_le_add_right (by exact_mod_cast hb t ht : (‖v t‖₊:ℝ≥0∞)≤r) _ + _ ≤ ρ := by simpa [add_comm] using hr.le + have h := ((hp.changeOrigin (hvr t ht)).comp_sub (-(v t))).mono + (by exact_mod_cast hR) hrad + simpa [q,sub_neg_eq_add,Pi.smul_def,smul_eq_mul] using h.const_smul (c := w t) + exact (hasFPowerSeriesOnBall_integral hR hpq hi hs).analyticAt + + +lemma analyticAt_integral_finite_cover + {E ι : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + {a : E} {F : E → ℝ → ℂ} {K : Set ℝ} {B : ι → Set ℝ} + (T : Finset ι) (hB : ∀ i, MeasurableSet (B i)) + (hi : ∀ᶠ x in 𝓝 a, IntegrableOn (F x) K) + (hl : ∀ i∈T, ∀ S, MeasurableSet S → S⊆K → S⊆B i → + AnalyticAt ℂ (fun x => ∫ t in S, F x t) a) : + ∀ S, MeasurableSet S → S⊆K → S⊆⋃ i∈T, B i → + AnalyticAt ℂ (fun x => ∫ t in S, F x t) a := by + classical + induction T using Finset.induction_on with + | empty => + intro S hS hSK hc + have he : S=∅ := by simpa using hc + simpa only [he,setIntegral_empty] using + (analyticAt_const : AnalyticAt ℂ (fun _ : E => (0:ℂ)) a) + | @insert i T hiT ih => + intro S hS hSK hc + have h1 := hl i (Finset.mem_insert_self i T) (S∩B i) (hS.inter (hB i)) + (inter_subset_left.trans hSK) inter_subset_right + have h2 : AnalyticAt ℂ (fun x => ∫ t in S\B i, F x t) a := by + apply ih (fun j hj => hl j (Finset.mem_insert_of_mem hj)) (S\B i) + (hS.diff (hB i)) (sdiff_subset.trans hSK) + intro t ht + have hh := hc ht.1 + simp only [mem_iUnion,Finset.mem_insert,exists_prop] at hh ⊢ + obtain ⟨j,hj,htj⟩ := hh + rcases hj with rfl|hj + · exact False.elim (ht.2 htj) + · exact ⟨j,hj,htj⟩ + apply (h1.add h2).congr + filter_upwards [hi] with x hx + have he := setIntegral_union + (show Disjoint (S∩B i) (S\B i) from disjoint_left.mpr (fun t ht hu => hu.2 ht.2)) + (hS.diff (hB i)) (hx.mono_set (inter_subset_left.trans hSK)) + (hx.mono_set (sdiff_subset.trans hSK)) + simpa only [inter_union_sdiff,Pi.add_apply] using he.symm + + + +theorem analyticOnNhd_integral_compact + {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + {U : Set E} {K : Set ℝ} {c w : ℝ → ℂ} {F : E × ℂ → ℂ} + (hU : IsOpen U) (hK : IsCompact K) (hc : Continuous c) (hw : Continuous w) + (hf : AnalyticOnNhd ℂ F (U ×ˢ (c '' K))) : + AnalyticOnNhd ℂ (fun a => ∫ t in K, w t * F (a,c t)) U := by + classical + intro a ha + obtain ⟨C₀,hC₀⟩ := hK.exists_bound_of_continuousOn hw.continuousOn + let C := max C₀ 0 + have hC : 0≤C := le_max_right _ _ + have hwb : ∀ t∈K, ‖w t‖≤C := fun t ht => (hC₀ t ht).trans (le_max_left _ _) + have hchart : ∀ t : K, ∃ δ : ℝ, 0<δ ∧ ∀ S : Set ℝ, + MeasurableSet S → S⊆K → S⊆c ⁻¹' ball (c t) δ → + AnalyticAt ℂ (fun x => ∫ s in S, w s * F (x,c s)) a := by + intro t + obtain ⟨p,ρ,hp⟩ := hf (a,c t) ⟨ha,mem_image_of_mem c t.property⟩ + obtain ⟨b,hb0,hbρ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.mp hp.r_pos + have hb : (0:ℝ≥0) (0,c s-c t) + have hv : ContinuousOn v S := + (continuous_const.prodMk (hc.sub continuous_const)).continuousOn + have hvb : ∀ s∈S, ‖v s‖₊≤δ := by + intro s hs + have hh := hSB hs + have hn : ‖c s-c t‖≤(δ:ℝ) := (mem_ball_iff_norm.mp hh).le + change ‖((0,c s-c t) : E × ℂ)‖₊≤δ + rw [Prod.nnnorm_mk,nnnorm_zero,max_eq_right (by positivity)] + exact_mod_cast hn + have hh := analyticAt_integral_shift_piece hS hp hv hw.continuousOn hδ hrad hvb hC + (fun s hs => hwb s (hSK hs)) + have hi : AnalyticAt ℂ (fun x : E => (x,c t)) a := analyticAt_id.prod analyticAt_const + have hh' := hh.comp (f := fun x : E => (x,c t)) hi + apply hh'.congr + filter_upwards with x + apply integral_congr_ae + filter_upwards with s + congr 1 + apply congrArg F + change (x,c t)+(0,c s-c t)=(x,c s) + ext <;> simp + choose δ hδ hlocal using hchart + let B : K → Set ℝ := fun t => c ⁻¹' ball (c t) (δ t) + have hBo (t : K) : IsOpen (B t) := isOpen_ball.preimage hc + have hcover : K⊆⋃ t : K, B t := by + intro s hs + exact mem_iUnion.mpr ⟨⟨s,hs⟩,by simp [B,hδ]⟩ + obtain ⟨T,hT⟩ := hK.elim_finite_subcover B hBo hcover + have hi : ∀ᶠ x in 𝓝 a, IntegrableOn (fun t => w t * F (x,c t)) K := by + filter_upwards [hU.mem_nhds ha] with x hx + apply ContinuousOn.integrableOn_compact hK + apply hw.continuousOn.mul + exact hf.continuousOn.comp (continuous_const.prodMk hc).continuousOn + (fun t ht => ⟨hx,mem_image_of_mem c ht⟩) + exact analyticAt_integral_finite_cover T (fun t => (hBo t).measurableSet) hi + (fun t _ => hlocal t) K hK.measurableSet Subset.rfl hT + + + +theorem analyticOnNhd_circleIntegral + {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] + {U : Set E} {F : E × ℂ → ℂ} {r : ℝ} + (hU : IsOpen U) (hr : 0≤r) + (hf : AnalyticOnNhd ℂ F (U ×ˢ sphere 0 r)) : + AnalyticOnNhd ℂ (fun a => ∮ z in C(0,r), F (a,z)) U := by + have hdc : Continuous (deriv (circleMap 0 r)) := by + have he : deriv (circleMap 0 r) = fun t => circleMap 0 r t * I := + funext (deriv_circleMap 0 r) + rw [he] + exact (continuous_circleMap 0 r).mul continuous_const + have hh := analyticOnNhd_integral_compact (K := Icc 0 (2*π)) hU isCompact_Icc (continuous_circleMap 0 r) hdc + (hf.mono (prod_mono Subset.rfl (by rintro _ ⟨t,ht,rfl⟩; exact circleMap_mem_sphere 0 hr t))) + simpa only [circleIntegral_def_Icc,smul_eq_mul] using hh + +end PathSelection.ParameterPreparation +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PathMonotonicity.lean b/lean/OAI/Analysis/PathSelection/PathMonotonicity.lean new file mode 100644 index 0000000000000000000000000000000000000000..90fc3a7d7473d584e68722d25e3034c4e00f7d9c --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PathMonotonicity.lean @@ -0,0 +1,44 @@ +import Mathlib +import OAI.Analysis.PathSelection.RecursiveClocks +import OAI.Analysis.PathSelection.SectorInduction + +namespace OAI + +/-! Eventual monotonicity of clock representations of admissible functions. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace PathSelection.Statement + +open Set Filter Topology DegeneratingTrees.Clock + +lemma eventuallyMonotoneOrConstant_of_clock {xs : List (ℝ → ℝ)} + (hxs : ValidClocks xs) {f : ℝ → ℝ} + (hf : ClockGerm xs (fun u => (f u : ℂ))) : + EventuallyMonotoneOrConstant f := by + obtain ⟨U, hconst | hmono | hanti⟩ := hf.eventually_monotone hxs + · exact ⟨U, Or.inr (Or.inr hconst)⟩ + · exact ⟨U, Or.inl hmono.monotoneOn⟩ + · exact ⟨U, Or.inr (Or.inl hanti.antitoneOn)⟩ + + + +lemma Admissible.monotone_realValue_of_clock {m n : ℕ} + {P : ComplexPoint m n → ℂ} {z₀ : Fin n → ℝ} (hP : Admissible P z₀) + {γ : ℝ → RealPoint m n} + (hL : ∀ i : Fin m, Tendsto (fun u => (γ u).1 i) atTop atTop) + (hz : Tendsto (fun u => (γ u).2) atTop (𝓝 z₀)) + {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + (hclock : ClockGerm xs (fun u => P (complexify (γ u)))) : + EventuallyMonotoneOrConstant (fun u => realValue P (γ u)) := by + apply eventuallyMonotoneOrConstant_of_clock hxs + apply hclock.congr + filter_upwards [hP.eventually_realValue_eq hL hz] with u hu + exact hu.symm + +end PathSelection.Statement +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PerturbativeInverses.lean b/lean/OAI/Analysis/PathSelection/PerturbativeInverses.lean new file mode 100644 index 0000000000000000000000000000000000000000..632931957457010f3644654a7fe8e3fd7626f9eb --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PerturbativeInverses.lean @@ -0,0 +1,470 @@ +import Mathlib +import OAI.Analysis.PathSelection.AnalyticCharts + +namespace OAI + +/-! Logarithmic discs, perturbative inverse sectors and zero-exponent decay. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees + + theorem AdmissibleAngularLoss.logarithmic_discs {ω : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) (R : ℝ) {c : ℝ} (hc : 0 ≤ c) : + ∃ (η : ℝ → ℝ) (R' : ℝ), AdmissibleAngularLoss η ∧ R ≤ R' ∧ 1 < R' ∧ + ∀ z∈lossSector η R', closedBall z (c*‖z‖*(Real.log ‖z‖)⁻¹^2) ⊆ lossSector ω R := by + obtain ⟨hN,hup⟩ := hω.neighboring + let η : ℝ → ℝ := fun r => 16*(c+1)*neighboringLoss ω r + have hη : AdmissibleAngularLoss η := hN.const_mul (by linarith) + obtain ⟨a,t,S,hS,ha,has,ht,hsmall,hηsmall⟩ := angularLoss_kernel_data hη + obtain ⟨T,hT⟩ := eventually_atTop.mp (hup.and hN.1) + obtain ⟨W,hW⟩ := eventually_atTop.mp hω.1 + let Q := Max.max (Max.max R W) 1 + let R' := Max.max (Max.max S T) (4*Q) + have hQ : 1 ≤ Q := le_max_right _ _ + have hRQ : R ≤ Q := (le_max_left R W).trans (le_max_left _ _) + have hWQ : W ≤ Q := (le_max_right R W).trans (le_max_left _ _) + have hRR : R ≤ R' := by + have hh := le_max_right (Max.max S T) (4*Q) + dsimp [R']; linarith + have hR1 : 1 < R' := by + have hh := le_max_right (Max.max S T) (4*Q) + dsimp [R']; linarith + refine ⟨η,R',hη,hRR,hR1,?_⟩ + intro z hz w hw + have hrS : S < ‖z‖ := lt_of_le_of_lt ((le_max_left S T).trans (le_max_left _ _)) hz.1 + have hrT : T < ‖z‖ := lt_of_le_of_lt ((le_max_right S T).trans (le_max_left _ _)) hz.1 + have hrQ : 4*Q < ‖z‖ := lt_of_le_of_lt (le_max_right _ _) hz.1 + have hr0 : 0 < ‖z‖ := by linarith + let N := neighboringLoss ω ‖z‖ + let X := ‖z‖*N + have hNpos : 0 < N := (hT _ hrT.le).2.1 + have hX : 0 < X := mul_pos hr0 hNpos + have hbase : (Real.log ‖z‖)⁻¹^2 ≤ N := (hT _ hrT.le).2.2 + have hηb : 16*(c+1)*N ≤ 1/64 := (hηsmall _ hrS.le).2.1 + have hcn : c*N ≤ 1/4 := by nlinarith + have hd : ‖w-z‖ ≤ c*X := by + have hh := (mem_closedBall_iff_norm.mp hw).trans + (mul_le_mul_of_nonneg_left hbase (mul_nonneg hc hr0.le)) + change ‖w-z‖ ≤ c*(‖z‖*N) + nlinarith + have hd' : ‖w-z‖ ≤ ‖z‖/4 := by + have hh := mul_le_mul_of_nonneg_right hcn hr0.le + change ‖w-z‖ ≤ c*(‖z‖*N) at hd + nlinarith + have hwl : ‖z‖-‖z‖/4 ≤ ‖w‖ := by + have hh := norm_sub_le w (w-z) + rw [sub_sub_cancel] at hh + linarith + have hwu : ‖w‖ ≤ ‖z‖+‖z‖/4 := by + have hh := norm_add_le (w-z) z + rw [sub_add_cancel] at hh + linarith + have hwQ : Q < ‖w‖ := by linarith + have hωw : ω ‖w‖ ≤ N := (hT _ hrT.le).1 _ ⟨by linarith,by linarith⟩ + have hωpos : 0 < ω ‖w‖ := (hW _ (hWQ.trans hwQ.le)).1 + have hηπ : η ‖z‖ ≤ Real.pi/2 := by + have hh := (hηsmall _ hrS.le).2.1 + linarith [Real.pi_gt_three] + have hre := half_loss_norm_le_re (hηsmall _ hrS.le).1.le hηπ hz.2 + have hre' := (abs_le.mp ((abs_re_le_norm (w-z)).trans hd)).1 + simp only [Complex.sub_re] at hre' + have hh : ω ‖w‖*‖w‖ ≤ 2*X := by + have hh₁ := mul_le_mul_of_nonneg_right hωw (norm_nonneg w) + have hh₂ := mul_le_mul_of_nonneg_left (show ‖w‖ ≤ 2*‖z‖ by linarith) hNpos.le + change ω ‖w‖*‖w‖ ≤ 2*(‖z‖*N) + nlinarith + refine ⟨hRQ.trans_lt hwQ,arg_lt_of_re_lower hωpos (norm_pos_iff.mp (by linarith)) ?_⟩ + have hreX : 8*(c+1)*X ≤ z.re := by + dsimp [η,X,N] at * + nlinarith [hre] + have hcX := mul_nonneg hc hX.le + nlinarith + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +namespace DegeneratingTrees.Clock + +def logarithmicRadius (r : ℝ) : ℝ := r*(Real.log r)⁻¹^2 + +lemma logarithmicRadius_pos {r : ℝ} (hr : 1 < r) : 0 < logarithmicRadius r := + mul_pos (zero_lt_one.trans hr) (sq_pos_of_pos (inv_pos.mpr (Real.log_pos hr))) + +lemma continuousOn_logarithmicRadius : ContinuousOn logarithmicRadius (Ioi 1) := by + intro r hr + have hr' : 1 < r := hr + exact (continuousAt_id.mul (((Real.continuousAt_log (by linarith : r≠0)).inv₀ + (Real.log_pos hr).ne').pow 2)).continuousWithinAt + +lemma logarithmicRadius_neighbor {a b : ℝ} (ha : 4 ≤ a) + (hb : a/2 ≤ b) (hb' : b ≤ 2*a) : + logarithmicRadius b ≤ 8*logarithmicRadius a := by + have ha0 : 0 < a := by linarith + have hb1 : 1 < b := by linarith + have hb0 : 0 < b := zero_lt_one.trans hb1 + have hla : 0 < Real.log a := Real.log_pos (by linarith) + have hlb : 0 < Real.log b := Real.log_pos hb1 + have hab : a ≤ b^2 := by nlinarith + have hl : Real.log a ≤ 2*Real.log b := by + simpa only [Real.log_pow,Nat.cast_ofNat] using Real.log_le_log ha0 hab + have hsq : (Real.log a)^2 ≤ 4*(Real.log b)^2 := by nlinarith + have hh₁ := mul_le_mul_of_nonneg_left hsq hb0.le + have hh₂ := mul_le_mul_of_nonneg_right hb' (sq_nonneg (Real.log b)) + have he (r : ℝ) : logarithmicRadius r=r/(Real.log r)^2 := by + simp only [logarithmicRadius,div_eq_mul_inv,inv_pow] + rw [he b,he a] + rw [show 8*(a/(Real.log a)^2)=(8*a)/(Real.log a)^2 by ring] + apply (div_le_div_iff₀ (sq_pos_of_pos hlb) (sq_pos_of_pos hla)).mpr + nlinarith + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + theorem sector_perturbative_inverse_unique {f : ℂ → ℂ} + (hf : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ f z) + (he : (fun z => f z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) + (ω : ℝ → ℝ) (R : ℝ) (hω : AdmissibleAngularLoss ω) : + ∃ (η : ℝ → ℝ) (T : ℝ) (g : ℂ → ℂ),AdmissibleAngularLoss η ∧ + AnalyticOnNhd ℂ g (lossSector η T) ∧ + (∀ z∈lossSector η T,g z∈lossSector ω R ∧ f (g z)=z ∧ ‖g z-z‖ ≤ 2*‖f z-z‖ ∧ + ‖g z-z‖ ≤ logarithmicRadius ‖z‖/2) ∧ + (∀ z∈lossSector η T,∀ u∈ball z (logarithmicRadius ‖z‖),f u=z → g z=u) := by + have hbase : ∀ᶠ z in sectorInfinity,(Real.log ‖z‖)⁻¹^2 ≤ (1/4:ℝ) := by + have hh := admissible_baseLoss.tendsto_zero.eventually + (eventually_le_nhds (show (0:ℝ) < 1/4 by norm_num)) + exact tendsto_norm_sectorInfinity.eventually hh + have htarget : ∀ᶠ z in sectorInfinity,z∈lossSector ω R := ⟨ω,R,hω,fun _ h => h⟩ + obtain ⟨θ,S,hθ,hdata⟩ := hf.and ((he.bound (by norm_num : (0:ℝ) < 1/32)).and + (hbase.and ((tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (4:ℝ))).and htarget))) + obtain ⟨κ,U,hκ,hSU,hU1,hdisc⟩ := hθ.logarithmic_discs S (show (0:ℝ) ≤ 2 by norm_num) + let V := interior (lossSector κ U) + let r : ℂ → ℝ := fun z => logarithmicRadius ‖z‖ + have hV : IsOpen V := isOpen_interior + have hVU : V ⊆ lossSector κ U := interior_subset + have hrpos (w : ℂ) (hw : w∈V) : 0 < r w := + logarithmicRadius_pos (hU1.trans (hVU hw).1) + have hr : ContinuousOn r V := by + apply continuousOn_logarithmicRadius.comp continuous_norm.continuousOn + exact fun w hw => hU1.trans (hVU hw).1 + have hdouble (w : ℂ) (hw : w∈V) : closedBall w (2*r w) ⊆ lossSector θ S := by + convert hdisc w (hVU hw) using 1 + dsimp [r,logarithmicRadius]; ring_nf + have hfa : AnalyticOnNhd ℂ f (lossSector θ S) := fun z hz => (hdata z hz).1 + have herr (w : ℂ) (hw : w∈V) (z : ℂ) (hz : z∈closedBall w (2*r w)) : + ‖f z-z‖ ≤ r w/4 := by + have hwS := hdouble w hw (mem_closedBall_self (by linarith [hrpos w hw])) + have hwdata := hdata w hwS + have hzdata := hdata z (hdouble w hw hz) + have hdist : ‖z-w‖ ≤ 2*r w := mem_closedBall_iff_norm.mp hz + have hrbound : 2*r w ≤ ‖w‖/2 := by + have hh := mul_le_mul_of_nonneg_left hwdata.2.2.1 (norm_nonneg w) + dsimp [r,logarithmicRadius]; nlinarith + have hzl : ‖w‖/2 ≤ ‖z‖ := by + have hh := norm_sub_le z (z-w) + rw [sub_sub_cancel] at hh + linarith + have hzu : ‖z‖ ≤ 2*‖w‖ := by + have hh := norm_add_le (z-w) w + rw [sub_add_cancel] at hh + linarith [norm_nonneg w] + have hrz := logarithmicRadius_neighbor hwdata.2.2.2.1.le hzl hzu + have hzpos := logarithmicRadius_pos (show 1 < ‖z‖ by linarith [hzdata.2.2.2.1]) + have hez : ‖f z-z‖ ≤ (1/32:ℝ)*logarithmicRadius ‖z‖ := by + simpa only [Real.norm_eq_abs,abs_of_pos hzpos] using hzdata.2.1 + dsimp [r] + linarith + obtain ⟨g,hga,hg,hunique⟩ := analytic_inverse_of_disc_error hV r hr hrpos hdouble hfa herr + obtain ⟨η,T,hη,hUT,hunit⟩ := hκ.narrow_discs U + have hVη : lossSector η T ⊆ V := by + intro z hz + apply mem_interior_iff_mem_nhds.mpr + exact Filter.mem_of_superset (Metric.closedBall_mem_nhds z zero_lt_one) (hunit z hz) + refine ⟨η,T,g,hη,hga.mono hVη,?_,fun z hz => hunique z (hVη hz)⟩ + intro z hz + obtain ⟨hgS,hgz,hgb⟩ := hg z (hVη hz) + refine ⟨(hdata (g z) hgS).2.2.2.2,hgz,hgb,?_⟩ + have hh := herr z (hVη hz) z (mem_closedBall_self (by linarith [hrpos z (hVη hz)])) + change ‖g z-z‖ ≤ r z/2 + linarith + + theorem sector_perturbative_inverse {f : ℂ → ℂ} + (hf : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ f z) + (he : (fun z => f z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) + (ω : ℝ → ℝ) (R : ℝ) (hω : AdmissibleAngularLoss ω) : + ∃ (η : ℝ → ℝ) (T : ℝ) (g : ℂ → ℂ),AdmissibleAngularLoss η ∧ + AnalyticOnNhd ℂ g (lossSector η T) ∧ + (∀ z∈lossSector η T,g z∈lossSector ω R ∧ f (g z)=z ∧ ‖g z-z‖ ≤ 2*‖f z-z‖) := by + obtain ⟨η,T,g,hη,hga,hg,hu⟩ := sector_perturbative_inverse_unique hf he ω R hω + exact ⟨η,T,g,hη,hga,fun z hz => ⟨(hg z hz).1,(hg z hz).2.1,(hg z hz).2.2.1⟩⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma exp_logsquare_decay_bound {c : ℝ} (hc : 0 < c) (N : ℕ) : + ∀ᶠ x : ℝ in atTop,0 ≤ Real.exp (-c*x/(Real.log x)^2)*x^N ∧ + Real.exp (-c*x/(Real.log x)^2)*x^N ≤ 1/x := by + have hε : 0 < c/((N:ℝ)+1) := by positivity + have hh := (isLittleO_log_rpow_rpow_atTop (s := 1) 3 zero_lt_one).bound hε + filter_upwards [hh,eventually_gt_atTop (1:ℝ)] with x hx hx1 + have hx0 : 0 < x := lt_trans zero_lt_one hx1 + have hl : 0 < Real.log x := Real.log_pos hx1 + have hb : (Real.log x)^3 ≤ c/((N:ℝ)+1)*x := by + have hh : |(Real.log x)^3| ≤ c/((N:ℝ)+1)*x := by + norm_num [Real.rpow_natCast,Real.rpow_one,Real.norm_eq_abs,abs_of_pos hx0] at hx ⊢ + exact hx + exact (le_abs_self _).trans hh + have hb' : ((N:ℝ)+1)*Real.log x ≤ c*x/(Real.log x)^2 := by + apply (le_div_iff₀ (sq_pos_of_pos hl)).mpr + have hh := (le_div_iff₀ (show 0 < (N:ℝ)+1 by positivity)).mp + (show (Real.log x)^3 ≤ c*x/((N:ℝ)+1) by convert hb using 1; ring) + nlinarith + refine ⟨by positivity,?_⟩ + calc + Real.exp (-c*x/(Real.log x)^2)*x^N = + Real.exp (-c*x/(Real.log x)^2+(N:ℝ)*Real.log x) := by + rw [Real.exp_add,Real.exp_nat_mul,Real.exp_log hx0] + _ ≤ Real.exp (-Real.log x) := Real.exp_le_exp.mpr (by + have he : -c*x/(Real.log x)^2 = -(c*x/(Real.log x)^2) := by ring + rw [he] + nlinarith) + _ = 1/x := by rw [Real.exp_neg,Real.exp_log hx0,one_div] + +lemma tendsto_exp_logsquare_mul_pow {c : ℝ} (hc : 0 < c) (N : ℕ) : + Tendsto (fun x : ℝ => Real.exp (-c*x/(Real.log x)^2)*x^N) atTop (𝓝 0) := by + apply squeeze_zero' (exp_logsquare_decay_bound hc N |>.mono fun _ h => h.1) + (exp_logsquare_decay_bound hc N |>.mono fun _ h => h.2) + convert (tendsto_inv_atTop_zero : Tendsto (fun x:ℝ => x⁻¹) atTop (𝓝 0)) using 1 + ext x + simp only [one_div] + + + +theorem exp_logsquare_mul_smaller_pow {α : Type*} {l : Filter α} + {X w : α → ℝ} (hX : Tendsto X l atTop) (hw : w =o[l] X) + {c : ℝ} (hc : 0 < c) (N : ℕ) : + Tendsto (fun t => Real.exp (-c*X t/(Real.log (X t))^2)*(w t)^N) l (𝓝 0) := by + apply squeeze_zero_norm' (a := fun t => Real.exp (-c*X t/(Real.log (X t))^2)*(X t)^N) + · filter_upwards [hw.bound zero_lt_one,hX.eventually (eventually_gt_atTop (0:ℝ))] with t ht hXt + have ha : |w t| ≤ X t := by simpa only [Real.norm_eq_abs,abs_of_pos hXt,one_mul] using ht + simpa only [Real.norm_eq_abs,abs_mul,abs_pow,abs_of_pos (Real.exp_pos _)] using + mul_le_mul_of_nonneg_left (pow_le_pow_left₀ (abs_nonneg _) ha N) (Real.exp_nonneg _) + · exact (tendsto_exp_logsquare_mul_pow hc N).comp hX + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma logarithmicRadius_comparable {C a b : ℝ} (hC : 1 ≤ C) (ha : 1 < a) + (haC : C ≤ a) (hb : 1 < b) (hl : a/C ≤ b) (hu : b ≤ C*a) : + logarithmicRadius a ≤ 4*C*logarithmicRadius b := by + have hC0 : 0 < C := zero_lt_one.trans_le hC + have ha0 : 0 < a := zero_lt_one.trans ha + have hb0 : 0 < b := zero_lt_one.trans hb + have hla : 0 < Real.log a := Real.log_pos ha + have hlb : 0 < Real.log b := Real.log_pos hb + have hupper : b ≤ a^2 := hu.trans (by nlinarith) + have hlog : Real.log b ≤ 2*Real.log a := by + simpa only [Real.log_pow,Nat.cast_ofNat] using Real.log_le_log hb0 hupper + have hsq : (Real.log b)^2 ≤ 4*(Real.log a)^2 := by nlinarith + have hl' : a ≤ b*C := (div_le_iff₀ hC0).mp hl + have he (t : ℝ) : logarithmicRadius t=t/(Real.log t)^2 := by + simp only [logarithmicRadius,div_eq_mul_inv,inv_pow] + rw [he a,he b,show 4*C*(b/(Real.log b)^2)=(4*C*b)/(Real.log b)^2 by ring] + apply (div_le_div_iff₀ (sq_pos_of_pos hla) (sq_pos_of_pos hlb)).mpr + have h1 := mul_le_mul_of_nonneg_left hsq ha0.le + have h2 := mul_le_mul_of_nonneg_right hl' (sq_nonneg (Real.log a)) + nlinarith + +lemma re_lower_logarithmicRadius {x : ℂ} {ω : ℝ → ℝ} {R : ℝ} + (hx : x∈lossSector ω R) (hx1 : 1 < ‖x‖) + (hω : 0 ≤ ω ‖x‖ ∧ (Real.log ‖x‖)⁻¹^2 ≤ ω ‖x‖) + (hωπ : ω ‖x‖ ≤ Real.pi/2) : logarithmicRadius ‖x‖/2 ≤ x.re := by + have hh := half_loss_norm_le_re hω.1 hωπ hx.2 + have hb := mul_le_mul_of_nonneg_right hω.2 (zero_lt_one.trans hx1).le + dsimp [logarithmicRadius] + nlinarith + + + +lemma lower_chart_re_bound {x : ℂ → ℂ} {X : ℝ → ℝ} {C : ℝ} + (hC : 1 ≤ C) (hX : Tendsto X atTop atTop) + (hmod : ∀ᶠ z in sectorInfinity,X ‖z‖/C ≤ ‖x z‖ ∧ ‖x z‖ ≤ C*X ‖z‖) + (hx : Tendsto x sectorInfinity sectorInfinity) : + ∀ᶠ z in sectorInfinity,(1/(8*C))*logarithmicRadius (X ‖z‖) ≤ (x z).re := by + have hbase : ∀ᶠ w in sectorInfinity,logarithmicRadius ‖w‖/2 ≤ w.re := by + obtain ⟨R,hR⟩ := eventually_atTop.mp + (admissible_baseLoss.1.and ((admissible_baseLoss.tendsto_zero.eventually + (eventually_le_nhds (show (0:ℝ) < Real.pi/2 by linarith [Real.pi_pos]))).and + (eventually_gt_atTop (1:ℝ)))) + refine ⟨baseLoss,R,admissible_baseLoss,?_⟩ + intro w hw + obtain ⟨hω,hπ,hw1⟩ := hR ‖w‖ hw.1.le + exact re_lower_logarithmicRadius hw hw1 ⟨hω.1.le,hω.2⟩ hπ + filter_upwards [hmod,hx.eventually hbase, + (hX.comp tendsto_norm_sectorInfinity).eventually (eventually_gt_atTop (max C 1)), + (tendsto_norm_sectorInfinity.comp hx).eventually (eventually_gt_atTop (1:ℝ))] with z hz hb hXz hxz + have hcomp := logarithmicRadius_comparable hC ((le_max_right _ _).trans_lt hXz) + ((le_max_left _ _).trans hXz.le) hxz hz.1 hz.2 + have hC0 : 0 < C := zero_lt_one.trans_le hC + dsimp only [Function.comp_def] at hcomp + have hh : logarithmicRadius (X ‖z‖) ≤ (x z).re*(8*C) := by + have hm := mul_le_mul_of_nonneg_left hb (show 0 ≤ 8*C by positivity) + nlinarith + have he : (1/(8*C))*logarithmicRadius (X ‖z‖)=logarithmicRadius (X ‖z‖)/(8*C) := by ring + rw [he] + exact (div_le_iff₀ (by positivity)).mpr hh + + + +theorem zero_exponent_error_small {F x : ℂ → ℂ} {X : ℝ → ℝ} {C K ε : ℝ} + (hC : 1 ≤ C) (hK : 0 ≤ K) (hε : 0 < ε) + (hX : Tendsto X atTop atTop) (hlog : Real.log =o[atTop] X) + (hmod : ∀ᶠ z in sectorInfinity,X ‖z‖/C ≤ ‖x z‖ ∧ ‖x z‖ ≤ C*X ‖z‖) + (hx : Tendsto x sectorInfinity sectorInfinity) + (herr : ∀ᶠ z in sectorInfinity,‖F z-z‖ ≤ K*‖z‖*Real.exp (-ε*(x z).re)) : + (fun z => F z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖) := by + have hC0 : 0 < C := zero_lt_one.trans_le hC + have hc : 0 < ε/(8*C) := by positivity + have hrapid := exp_logsquare_mul_smaller_pow hX hlog hc 2 + have hrapid' := ((tendsto_const_nhds (x:=K)).mul hrapid).comp tendsto_norm_sectorInfinity + simp only [mul_zero] at hrapid' + apply Asymptotics.IsLittleO.of_bound + intro δ hδ + have hsmall := hrapid'.eventually (eventually_le_nhds hδ) + filter_upwards [hsmall,lower_chart_re_bound hC hX hmod hx,herr, + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hs hl he hz + have hL : 0 < Real.log ‖z‖ := Real.log_pos hz + have hrad : 0 < logarithmicRadius ‖z‖ := logarithmicRadius_pos hz + have heexp : Real.exp (-ε*(x z).re) ≤ + Real.exp (-(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2) := by + apply Real.exp_le_exp.mpr + have hh := mul_le_mul_of_nonneg_left hl hε.le + dsimp [logarithmicRadius] at hh + rw [inv_pow] at hh + have heq : ε*((1/(8*C))*(X ‖z‖*(Real.log (X ‖z‖)^2)⁻¹)) = + (ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2 := by ring + rw [heq] at hh + have heq' : -(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2 = + -((ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2) := by ring + rw [heq'] + nlinarith + have hb := mul_le_mul_of_nonneg_left heexp (mul_nonneg hK (norm_nonneg z)) + have hs' := mul_le_mul_of_nonneg_right hs hrad.le + have hcancel : K*(Real.exp (-(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2)* + (Real.log ‖z‖)^2)*logarithmicRadius ‖z‖ = + K*‖z‖*Real.exp (-(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2) := by + dsimp [logarithmicRadius] + field_simp [hL.ne'] + dsimp only [Function.comp_def] at hs' + rw [hcancel] at hs' + simpa only [Real.norm_eq_abs,abs_of_pos hrad] using he.trans (hb.trans hs') + + + +theorem zero_exponent_sector_inverse {F x : ℂ → ℂ} {X : ℝ → ℝ} {C K ε : ℝ} + (hF : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (hC : 1 ≤ C) (hK : 0 ≤ K) (hε : 0 < ε) + (hX : Tendsto X atTop atTop) (hlog : Real.log =o[atTop] X) + (hmod : ∀ᶠ z in sectorInfinity,X ‖z‖/C ≤ ‖x z‖ ∧ ‖x z‖ ≤ C*X ‖z‖) + (hx : Tendsto x sectorInfinity sectorInfinity) + (herr : ∀ᶠ z in sectorInfinity,‖F z-z‖ ≤ K*‖z‖*Real.exp (-ε*(x z).re)) + (ω : ℝ → ℝ) (R : ℝ) (hω : AdmissibleAngularLoss ω) : + ∃ (η : ℝ → ℝ) (T : ℝ) (g : ℂ → ℂ),AdmissibleAngularLoss η ∧ + AnalyticOnNhd ℂ g (lossSector η T) ∧ + (∀ z∈lossSector η T,g z∈lossSector ω R ∧ F (g z)=z ∧ ‖g z-z‖ ≤ 2*‖F z-z‖) := + sector_perturbative_inverse hF (zero_exponent_error_small hC hK hε hX hlog hmod hx herr) ω R hω + +end DegeneratingTrees.Clock + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + + +theorem zero_exponent_error_logpower {F x : ℂ → ℂ} {X : ℝ → ℝ} {C K ε : ℝ} + (N : ℕ) (hC : 1 ≤ C) (hK : 0 ≤ K) (hε : 0 < ε) + (hX : Tendsto X atTop atTop) (hlog : Real.log =o[atTop] X) + (hmod : ∀ᶠ z in sectorInfinity,X ‖z‖/C ≤ ‖x z‖ ∧ ‖x z‖ ≤ C*X ‖z‖) + (hx : Tendsto x sectorInfinity sectorInfinity) + (herr : ∀ᶠ z in sectorInfinity,‖F z-z‖ ≤ K*‖z‖*Real.exp (-ε*(x z).re)) : + (fun z => F z-z) =o[sectorInfinity] (fun z => ‖z‖/(Real.log ‖z‖)^N) := by + have hC0 : 0 < C := zero_lt_one.trans_le hC + have hc : 0 < ε/(8*C) := by positivity + have hrapid := exp_logsquare_mul_smaller_pow hX hlog hc N + have hrapid' := ((tendsto_const_nhds (x:=K)).mul hrapid).comp tendsto_norm_sectorInfinity + simp only [mul_zero] at hrapid' + apply Asymptotics.IsLittleO.of_bound + intro δ hδ + have hsmall := hrapid'.eventually (eventually_le_nhds hδ) + filter_upwards [hsmall,lower_chart_re_bound hC hX hmod hx,herr, + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hs hl he hz + have hL : 0 < Real.log ‖z‖ := Real.log_pos hz + have hrad : 0 < ‖z‖/(Real.log ‖z‖)^N := by positivity + have heexp : Real.exp (-ε*(x z).re) ≤ + Real.exp (-(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2) := by + apply Real.exp_le_exp.mpr + have hh := mul_le_mul_of_nonneg_left hl hε.le + dsimp [logarithmicRadius] at hh + rw [inv_pow] at hh + have heq : ε*((1/(8*C))*(X ‖z‖*(Real.log (X ‖z‖)^2)⁻¹)) = + (ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2 := by ring + rw [heq] at hh + have heq' : -(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2 = + -((ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2) := by ring + rw [heq'] + nlinarith + have hb := mul_le_mul_of_nonneg_left heexp (mul_nonneg hK (norm_nonneg z)) + have hs' := mul_le_mul_of_nonneg_right hs hrad.le + have hcancel : K*(Real.exp (-(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2)* + (Real.log ‖z‖)^N)*(‖z‖/(Real.log ‖z‖)^N) = + K*‖z‖*Real.exp (-(ε/(8*C))*X ‖z‖/(Real.log (X ‖z‖))^2) := by + field_simp [hL.ne'] + dsimp only [Function.comp_def] at hs' + rw [hcancel] at hs' + simpa only [Real.norm_eq_abs,abs_of_pos hrad] using he.trans (hb.trans hs') + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PhaseSectors.lean b/lean/OAI/Analysis/PathSelection/PhaseSectors.lean new file mode 100644 index 0000000000000000000000000000000000000000..a21740ebe85e0e43a7d9d93b36f3b1e3842b2a56 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PhaseSectors.lean @@ -0,0 +1,474 @@ +import Mathlib +import OAI.Analysis.PathSelection.PuiseuxInverses +import OAI.Analysis.PathSelection.SectorLimits + +namespace OAI + +/-! Positive Puiseux sectors, loss scales and strict phase estimates. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma analytic_root_error {n : ℕ} (hn : 0 < n) {F : ℂ → ℂ} + (hF : AnalyticAt ℂ F 0) : + ∃ K : ℝ, 0 < K ∧ ∀ᶠ z in radialInfinity, + ‖F (complexRoot n z)-F 0‖ ≤ K*‖z‖^(-(n:ℝ)⁻¹) := by + obtain ⟨K,hK,hbound⟩ := hF.differentiableAt.hasDerivAt.isBigO_sub.exists_pos + refine ⟨K,hK,?_⟩ + filter_upwards [(complexRoot_tendsto_zero hn).eventually hbound.bound] with z hz + simpa only [sub_zero,complexRoot_norm,rootCoord] using hz + + + +theorem Puiseux.positive_sector {f : ℝ → ℝ} + (hf : Puiseux (fun t => (f t:ℂ))) (hft : Tendsto f atTop atTop) : + ∃ (q : ℚ) (a C K R : ℝ) (G : ℂ → ℂ), 0 < (q:ℝ) ∧ 0 < a ∧ 0 < C ∧ 0 < K ∧ + (∀ z : ℂ, R < ‖z‖ → 0 < z.re → AnalyticAt ℂ G z) ∧ + (fun t => (f t:ℂ)) =ᶠ[atTop] (fun t => G (t:ℂ)) ∧ + ∀ z : ℂ, R < ‖z‖ → + ‖G z-(C:ℂ)*z^((q:ℝ):ℂ)‖ ≤ K * ‖z‖^((q:ℝ)-a) := by + obtain ⟨n,k,hn,hk,F,hF,hFre,hFim,he⟩ := hf.normalize_unbounded_real hft + let q : ℚ := (k:ℚ)/(n:ℚ) + let a : ℝ := (n:ℝ)⁻¹ + let G : ℂ → ℂ := fun z => (complexRoot n z)^(-(k:ℤ)) * F (complexRoot n z) + have hq : 0 < (q:ℝ) := by dsimp [q]; push_cast; positivity + have ha : 0 < a := inv_pos.mpr (Nat.cast_pos.mpr hn) + have hqeq : ((q:ℝ):ℂ) = ((-((-(k:ℤ)):ℝ)/(n:ℝ):ℝ):ℂ) := by + dsimp [q] + push_cast + ring + have hFreal : F 0 = ((F 0).re:ℂ) := Complex.ext rfl (by simpa using hFim) + obtain ⟨K,hK,hbound⟩ := analytic_root_error hn hF + obtain ⟨R,hR⟩ := radial_eventually + (((complexRoot_tendsto_zero hn).eventually hF.eventually_analyticAt).and hbound) + refine ⟨q,a,(F 0).re,K,max R 0,G,hq,ha,hFre,hK,?_,?_,?_⟩ + · intro z hz hzre + have hr := complexRoot_analytic (n := n) hzre + have hr0 : complexRoot n z ≠ 0 := Complex.cpow_ne_zero_iff.mpr (Or.inl (by + intro h; simp [h] at hzre)) + exact (hr.zpow hr0).mul (((hR z ((le_max_left _ _).trans_lt hz)).1).comp hr) + · filter_upwards [he,eventually_gt_atTop (0:ℝ)] with t ht htpos + simpa only [G,complexRoot_real htpos.le,←Complex.ofReal_zpow,Complex.real_smul] using ht + · intro z hz + have hzpos : 0 < ‖z‖ := (le_max_right _ _).trans_lt hz + have herr := (hR z ((le_max_left _ _).trans_lt hz)).2 + have heq : G z-(F 0).re*z^((q:ℝ):ℂ) = + z^((q:ℝ):ℂ) * (F (complexRoot n z)-F 0) := by + dsimp [G] + rw [complexRoot_zpow,hFreal] + have hexp : ((-((-(k:ℤ)):ℝ)/(n:ℝ):ℝ):ℂ) = ((q:ℝ):ℂ) := hqeq.symm + push_cast at hexp ⊢ + rw [hexp] + simp only [Complex.ofReal_re] + ring + rw [heq,norm_mul,Complex.norm_cpow_real] + calc + ‖z‖^(q:ℝ)*‖F (complexRoot n z)-F 0‖ ≤ + ‖z‖^(q:ℝ)*(K*‖z‖^(-a)) := mul_le_mul_of_nonneg_left herr (Real.rpow_nonneg (norm_nonneg _) _) + _ = K*‖z‖^((q:ℝ)-a) := by rw [sub_eq_add_neg,Real.rpow_add hzpos]; ring + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees + +def scaleEnvelope (ω : ℝ → ℝ) (k : ℕ) (r : ℝ) : ℝ := + sSup (ω '' Icc (r/(2:ℝ)^k) (2^k*r)) + +private lemma scale_window_bound {ω : ℝ → ℝ} {n₀ : ℕ} {w : ℕ → ℝ} + (hw : ∀ n, 0 ≤ w n) + (hb : ∀ n r, (2:ℝ)^(n+n₀) < r → r < (2:ℝ)^(n+n₀+2) → ω r ≤ w n) + (k n : ℕ) {r : ℝ} (hrl : (2:ℝ)^(n+(n₀+k+1)) < r) + (hru : r < (2:ℝ)^(n+(n₀+k+1)+2)) {s : ℝ} + (hsl : r/(2:ℝ)^k ≤ s) (hsu : s ≤ 2^k*r) : + ω s ≤ ∑ j ∈ Finset.range (2*k+2), w (n+j) := by + have hpow : (0:ℝ) < 2^k := by positivity + have hlo : (2:ℝ)^(n+n₀+1) < s := by + have hrl' : 2^(n+n₀+1)*2^k < r := by + simpa only [←pow_add,show n+n₀+1+k=n+(n₀+k+1) by omega] using hrl + exact (lt_div_iff₀ hpow).mpr hrl' |>.trans_le hsl + have hhi : s < (2:ℝ)^(n+n₀+1) * 2^(2*k+2) := by + have hu := mul_lt_mul_of_pos_left hru hpow + have he : (2:ℝ)^k*2^(n+(n₀+k+1)+2) = 2^(n+n₀+1)*2^(2*k+2) := by + simp only [←pow_add] + congr 1 + omega + exact hsu.trans_lt (he ▸ hu) + obtain ⟨j,hjl,hju⟩ := dyadic_shell (show (0:ℝ)<2^(n+n₀+1) by positivity) hlo.le + have hjlt : j < 2*k+2 := by + have hp : (2:ℝ)^j < 2^(2*k+2) := (mul_lt_mul_iff_of_pos_left (show (0:ℝ)<2^(n+n₀+1) by positivity)).mp (hjl.trans_lt hhi) + exact (pow_lt_pow_iff_right₀ (by norm_num : (1:ℝ)<2)).mp hp + have hl : (2:ℝ)^(n+j+n₀) < s := by + have hp : (2:ℝ)^(n+j+n₀) < 2^(n+n₀+1)*2^j := by + rw [←pow_add] + exact pow_lt_pow_right₀ (by norm_num) (by omega) + exact hp.trans_le hjl + have hu : s < (2:ℝ)^(n+j+n₀+2) := by + convert hju using 1 + simp only [←pow_add] + calc + (2:ℝ)^(n+j+n₀+2) = 2^((n+n₀+1+j)+1) := by congr 1; omega + _ = 2*2^(n+n₀+1+j) := by rw [pow_succ]; ring + exact (hb (n+j) s hl hu).trans + (Finset.single_le_sum (fun i _ => hw (n+i)) (Finset.mem_range.mpr hjlt)) + +private lemma scale_envelope_bdd {ω : ℝ → ℝ} {n₀ : ℕ} {w : ℕ → ℝ} + (hw : ∀ n, 0 ≤ w n) + (hb : ∀ n r, (2:ℝ)^(n+n₀) < r → r < (2:ℝ)^(n+n₀+2) → ω r ≤ w n) + (k : ℕ) {r : ℝ} (hr : (2:ℝ)^(n₀+k+2) ≤ r) : + BddAbove (ω '' Icc (r/(2:ℝ)^k) (2^k*r)) := by + obtain ⟨n,hnl,hnu⟩ := dyadic_shell (show (0:ℝ)<2^(n₀+k+2) by positivity) hr + have hrl : (2:ℝ)^(n+(n₀+k+1)) < r := by + have hp : (2:ℝ)^(n+(n₀+k+1)) < 2^(n₀+k+2)*2^n := by + rw [←pow_add] + exact pow_lt_pow_right₀ (by norm_num) (by omega) + exact hp.trans_le hnl + have hru : r < (2:ℝ)^(n+(n₀+k+1)+2) := by + convert hnu using 1 + rw [←pow_add] + calc + (2:ℝ)^(n+(n₀+k+1)+2) = 2^((n₀+k+2+n)+1) := by congr 1; omega + _ = 2*2^(n₀+k+2+n) := by rw [pow_succ]; ring + refine ⟨∑ j ∈ Finset.range (2*k+2),w (n+j),?_⟩ + rintro _ ⟨s,hs,rfl⟩ + exact scale_window_bound hw hb k n hrl hru hs.1 hs.2 + +lemma AdmissibleAngularLoss.scale_envelope {ω : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) (k : ℕ) : + AdmissibleAngularLoss (scaleEnvelope ω k) ∧ + ∀ᶠ r : ℝ in atTop, ∀ s ∈ Icc (r/(2:ℝ)^k) (2^k*r), + ω s ≤ scaleEnvelope ω k r := by + obtain ⟨hp,n₀,w,hw,hs,hb⟩ := hω + have hupper : ∀ᶠ r : ℝ in atTop, ∀ s ∈ Icc (r/(2:ℝ)^k) (2^k*r), + ω s ≤ scaleEnvelope ω k r := by + filter_upwards [eventually_ge_atTop ((2:ℝ)^(n₀+k+2))] with r hr s hs + exact le_csSup (scale_envelope_bdd hw hb k hr) (mem_image_of_mem _ hs) + have hpk : (1:ℝ) ≤ 2^k := one_le_pow₀ (by norm_num) + have hself {r : ℝ} (hr : 0 ≤ r) : r ∈ Icc (r/(2:ℝ)^k) (2^k*r) := + ⟨div_le_self hr hpk,le_mul_of_one_le_left hr hpk⟩ + refine ⟨⟨?_,n₀+k+1,fun n => ∑ j ∈ Finset.range (2*k+2),w (n+j),?_,?_,?_⟩,hupper⟩ + · filter_upwards [hp,hupper,eventually_ge_atTop (0:ℝ)] with r hp hu hr + have hh := hu r (hself hr) + exact ⟨hp.1.trans_le hh,hp.2.trans hh⟩ + · intro n + exact Finset.sum_nonneg (fun j _ => hw (n+j)) + · have hsum (s : Finset ℕ) : Summable (fun n => ∑ j ∈ s, w (n+j)) := by + induction s using Finset.induction_on with + | empty => simp + | @insert j s hj ih => + simpa only [Finset.sum_insert hj] using ((summable_nat_add_iff j).mpr hs).add ih + exact hsum _ + · intro n r hl hu + apply csSup_le + · have hr : 0 ≤ r := (show (0:ℝ)<2^(n+(n₀+k+1)) by positivity).trans hl |>.le + exact ⟨ω r,mem_image_of_mem _ (hself hr)⟩ + · rintro _ ⟨s,hs,rfl⟩ + exact scale_window_bound hw hb k n hl hu hs.1 hs.2 + +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma cpow_real_re {z : ℂ} (hz : z ≠ 0) (q : ℝ) : + (z ^ (q:ℂ)).re = ‖z‖^q * Real.cos (q*z.arg) := by + rw [Complex.cpow_def_of_ne_zero hz,Complex.exp_re] + simp only [Complex.mul_re,Complex.mul_im,Complex.ofReal_re,Complex.ofReal_im, + mul_zero,sub_zero,zero_add,Complex.log_re,Complex.log_im] + rw [←Real.rpow_def_of_pos (norm_pos_iff.mpr hz)] + congr 2 + ring + +lemma cpow_real_re_lower {z : ℂ} (hz : z ≠ 0) {q : ℝ} (hq : 0 ≤ q) + (hq1 : q ≤ 1) (hzarg : |z.arg| ≤ Real.pi/2) : + ‖z‖^q * Real.cos (q*Real.pi/2) ≤ (z^(q:ℂ)).re := by + rw [cpow_real_re hz] + apply mul_le_mul_of_nonneg_left _ (Real.rpow_nonneg (norm_nonneg _) _) + rw [←Real.cos_abs (q*z.arg),abs_mul,abs_of_nonneg hq] + apply Real.cos_le_cos_of_nonneg_of_le_pi + · positivity + · nlinarith [Real.pi_pos] + · nlinarith + + +lemma power_error_relative {a q K : ℝ} (ha : 0 < a) (ε : ℝ) (hε : 0 < ε) : + ∀ᶠ r : ℝ in atTop, 0 < r ∧ K*r^(q-a) ≤ ε*r^q := by + have ht : Tendsto (fun r : ℝ => K*r^(-a)) atTop (𝓝 0) := by + simpa using (tendsto_rpow_neg_atTop ha).const_mul K + filter_upwards [ht.eventually (eventually_lt_nhds hε),eventually_gt_atTop (0:ℝ)] with r hr hr0 + refine ⟨hr0,?_⟩ + rw [sub_eq_add_neg,Real.rpow_add hr0] + nlinarith [Real.rpow_pos_of_pos hr0 q] + +lemma power_model_norm {G : ℂ → ℂ} {q a C K R : ℝ} (ha : 0 < a) (hC : 0 < C) + (herr : ∀ z : ℂ, R < ‖z‖ → ‖G z-(C:ℂ)*z^(q:ℂ)‖ ≤ K*‖z‖^(q-a)) : + ∀ᶠ r : ℝ in atTop, 0 < r ∧ ∀ z : ℂ, ‖z‖=r → + C/2*r^q ≤ ‖G z‖ ∧ ‖G z‖ ≤ 2*C*r^q := by + filter_upwards [power_error_relative (q := q) (K := K) ha (C/2) (by positivity), + eventually_gt_atTop R] with r hr hR + refine ⟨hr.1,?_⟩ + intro z hz + have he := (herr z (hz ▸ hR)).trans (hz ▸ hr.2) + rw [hz] at he + have hm : ‖(C:ℂ)*z^(q:ℂ)‖ = C*r^q := by + rw [norm_mul,Complex.norm_of_nonneg hC.le,Complex.norm_cpow_real,hz] + have hu := norm_add_le (G z-(C:ℂ)*z^(q:ℂ)) ((C:ℂ)*z^(q:ℂ)) + have hl := norm_sub_le (G z) (G z-(C:ℂ)*z^(q:ℂ)) + rw [sub_add_cancel,hm] at hu + rw [sub_sub_cancel,hm] at hl + constructor <;> nlinarith [Real.rpow_pos_of_pos hr.1 q] + + + +theorem power_model_sublinear_sector {G : ℂ → ℂ} {q a C K R : ℝ} + (hq : 0 < q) (hq1 : q < 1) (ha : 0 < a) (hC : 0 < C) + (herr : ∀ z : ℂ, R < ‖z‖ → ‖G z-(C:ℂ)*z^(q:ℂ)‖ ≤ K*‖z‖^(q-a)) + {ω : ℝ → ℝ} (hω : AdmissibleAngularLoss ω) (S : ℝ) : + ∃ T : ℝ, ∀ z ∈ lossSector ω T, G z ∈ lossSector ω S := by + let d := Real.cos (q*Real.pi/2) + have hd : 0 < d := Real.cos_pos_of_mem_Ioo ⟨by nlinarith [Real.pi_pos],by nlinarith [Real.pi_pos]⟩ + have hωsmall : ∀ᶠ r : ℝ in atTop, 0 < ω r ∧ ω r < d/8 := + hω.1.mono (fun _ h => h.1) |>.and (hω.tendsto_zero.eventually (eventually_lt_nhds (by positivity))) + obtain ⟨W,hW⟩ := eventually_atTop.mp hωsmall + have hescape : Tendsto (fun r : ℝ => C/2*r^q) atTop atTop := + (tendsto_rpow_atTop hq).const_mul_atTop (by positivity) + obtain ⟨T,hT⟩ := eventually_atTop.mp ((power_model_norm ha hC herr).and + ((power_error_relative (q := q) (K := K) ha (C*d/2) (by positivity)).and + ((hescape.eventually (eventually_gt_atTop (max W S))).and + ((eventually_gt_atTop R).and hω.1)))) + refine ⟨T,?_⟩ + intro z hz + obtain ⟨hn,he,hes,hR,hωz⟩ := hT ‖z‖ hz.1.le + have hb := hn.2 z rfl + have hw := hW ‖G z‖ ((le_max_left _ _).trans (hes.le.trans hb.1)) + have harg : |z.arg| ≤ Real.pi/2 := by linarith [hωz.1,hz.2] + have hpow := cpow_real_re_lower (norm_pos_iff.mp hn.1) hq.le hq1.le harg + have herror := (abs_re_le_norm (G z-(C:ℂ)*z^(q:ℂ))).trans ((herr z hR).trans he.2) + simp only [Complex.sub_re,Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im, + zero_mul,sub_zero] at herror + have hlow : C*d/2*‖z‖^q ≤ (G z).re := by + dsimp [d] at * + nlinarith [(abs_le.mp herror).1] + have hnormpos : 0 < ‖G z‖ := (mul_pos (by positivity) (Real.rpow_pos_of_pos hn.1 q)).trans_le hb.1 + refine ⟨(le_max_right _ _).trans_lt (hes.trans_le hb.1), + arg_lt_of_re_lower hw.1 (norm_pos_iff.mp hnormpos) ?_⟩ + have hm := mul_le_mul_of_nonneg_left hb.2 hw.1.le + have hh := mul_lt_mul_of_pos_right hw.2 (mul_pos (by positivity : 0 < 2*C) (Real.rpow_pos_of_pos hn.1 q)) + nlinarith [Real.rpow_pos_of_pos hn.1 q] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma phase_ratio_error {G : ℂ → ℂ} {f : ℝ → ℝ} {q : ℝ} + (hf : ∀ᶠ r : ℝ in atTop,0 Complex.exp (-Complex.I*(q*z.arg:ℝ))*(G z/(f ‖z‖:ℂ))) + sectorInfinity (𝓝 1)) (ε : ℝ) (hε : 0<ε) : + ∀ᶠ z in sectorInfinity,‖G z-(f ‖z‖:ℂ)*Complex.exp (Complex.I*(q*z.arg:ℝ))‖≤ε*f ‖z‖ := by + have he := Metric.tendsto_nhds.mp h ε hε + filter_upwards [he,tendsto_norm_sectorInfinity.eventually hf] with z hz hfz + rw [dist_eq_norm] at hz + have hf0 : (f ‖z‖:ℂ)≠0 := by exact_mod_cast hfz.ne' + have hei : ‖Complex.exp (Complex.I*(q*z.arg:ℝ))‖=1 := by simp [Complex.norm_exp] + have heq : G z-(f ‖z‖:ℂ)*Complex.exp (Complex.I*(q*z.arg:ℝ)) = + ((f ‖z‖:ℂ)*Complex.exp (Complex.I*(q*z.arg:ℝ))) * + (Complex.exp (-Complex.I*(q*z.arg:ℝ))*(G z/(f ‖z‖:ℂ))-1) := by + have hx : Complex.exp (Complex.I*(q*z.arg:ℝ))*Complex.exp (-Complex.I*(q*z.arg:ℝ))=1 := by + rw [←Complex.exp_add,show Complex.I*(q*z.arg:ℝ)+ -Complex.I*(q*z.arg:ℝ)=0 by ring,Complex.exp_zero] + calc + G z-(f ‖z‖:ℂ)*Complex.exp (Complex.I*(q*z.arg:ℝ)) = + (Complex.exp (Complex.I*(q*z.arg:ℝ))*Complex.exp (-Complex.I*(q*z.arg:ℝ)))*G z- + (f ‖z‖:ℂ)*Complex.exp (Complex.I*(q*z.arg:ℝ)) := by rw [hx,one_mul] + _ = _ := by field_simp + rw [heq,norm_mul,norm_mul,Complex.norm_of_nonneg hfz.le,hei,mul_one] + nlinarith + +theorem strict_phase_sector_mapping {G : ℂ → ℂ} {f : ℝ → ℝ} {q : ℝ} + (hq : 0≤q) (hq1 : q<1) (hf : Tendsto f atTop atTop) + (h : Tendsto (fun z => Complex.exp (-Complex.I*(q*z.arg:ℝ))*(G z/(f ‖z‖:ℂ))) + sectorInfinity (𝓝 1)) (ω : ℝ → ℝ) (S : ℝ) (hω : AdmissibleAngularLoss ω) : + ∃ (η : ℝ → ℝ) (T : ℝ),AdmissibleAngularLoss η ∧ + (∀ z∈lossSector η T,G z∈lossSector ω S) ∧ + (∀ z∈lossSector η T,f ‖z‖/2≤‖G z‖ ∧ ‖G z‖≤2*f ‖z‖) := by + let d := Real.cos (q*Real.pi/2) + have hd : 0 nlinarith + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +theorem sublinear_sector_realpart {G : ℂ → ℂ} {q C : ℝ} (hq : q < 1) (hC : 0 < C) + (hb : ∀ᶠ r : ℝ in atTop, ∀ z : ℂ, ‖z‖=r → ‖G z‖ ≤ C*r^q) + {η : ℝ → ℝ} (hη : AdmissibleAngularLoss η) : + ∀ ε : ℝ, 0 < ε → ∃ R : ℝ, ∀ z ∈ lossSector η R, + |(G z).re| ≤ ε*z.re := by + intro ε hε + have hsmall := (isLittleO_log_rpow_rpow_atTop (s := 1-q) 2 (by linarith)).bound + (show 0 < ε/(2*C) by positivity) + have hηsmall := hη.tendsto_zero.eventually + (eventually_lt_nhds (by linarith [Real.pi_pos] : (0:ℝ) if z∈lossSector η T then G z else 0 + have hb' : ∀ᶠ r : ℝ in atTop,∀ z : ℂ,‖z‖=r → ‖G' z‖≤C*r^q := by + exact Eventually.of_forall fun r z hz => by + dsimp [G'] + split_ifs with h + · have hh := hT z h + change ‖G z‖≤C*‖z‖^q at hh + simpa only [hz] using hh + · simp only [norm_zero] + exact mul_nonneg hC.le (by rw [←hz]; exact Real.rpow_nonneg (norm_nonneg _) _) + refine ⟨η,hη,?_⟩ + intro ε hε + obtain ⟨R,hR⟩ := sublinear_sector_realpart hq hC hb' hη ε hε + refine ⟨max T R,?_⟩ + intro z hz + have hzT : z∈lossSector η T := ⟨(le_max_left _ _).trans_lt hz.1,hz.2⟩ + have hzR : z∈lossSector η R := ⟨(le_max_right _ _).trans_lt hz.1,hz.2⟩ + simpa only [G',ite_eq_left hzT] using hR z hzR + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PositiveCharts.lean b/lean/OAI/Analysis/PathSelection/PositiveCharts.lean new file mode 100644 index 0000000000000000000000000000000000000000..c1ed9f33e741a50b79c92ada40afcc4e03179b70 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PositiveCharts.lean @@ -0,0 +1,503 @@ +import Mathlib +import OAI.Analysis.PathSelection.EqualExponentCharts +import OAI.Analysis.PathSelection.LowerRatios + +namespace OAI + +/-! Positive clock charts, power sectors and changes of Puiseux clock. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +def PositiveExponentialChart (F H : ℂ → ℂ) : Prop := + ∃ (T : ℝ) (x : ℂ → ℂ),0 (F (x (r:ℂ))).re) atTop atTop ∧ + (∀ᶠ w in sectorInfinity,AnalyticAt ℂ (fun z => F (x z)) w) ∧ + ∀ (ω : ℝ → ℝ) (S : ℝ),AdmissibleAngularLoss ω → + ∃ (η : ℝ → ℝ) (R : ℝ),AdmissibleAngularLoss η ∧ + (∀ w∈lossSector η R,F (x w)∈lossSector ω S) ∧ + (∀ w∈lossSector η R,(F (x (‖w‖:ℂ))).re/2≤‖F (x w)‖ ∧ + ‖F (x w)‖≤2*(F (x (‖w‖:ℂ))).re) ∧ + (Tendsto (fun t : ℝ => F (t:ℂ)/H (t:ℂ)) atTop (𝓝 0) → + ∀ ε : ℝ,0<ε → ∃ U : ℝ,∀ w∈lossSector η U,|(F (x w)).re|≤ε*w.re) + +lemma normalized_leading_nonzero {F g : ℂ → ℂ} {a : ℝ} + (he : ExpSmall 0 (fun z => Complex.exp (((-a:ℝ):ℂ)*z)*(g z)⁻¹*F z-1)) : + ∀ᶠ z in sectorInfinity,F z≠0 := by + have ht : Tendsto (fun z => Complex.exp (((-a:ℝ):ℂ)*z)*(g z)⁻¹*F z) sectorInfinity (𝓝 1) := by + simpa only [sub_add_cancel,zero_add] using he.tendsto_zero.add_const 1 + filter_upwards [ht.eventually_ne (by norm_num : (1:ℂ)≠0)] with z hz + intro heq + simp [heq] at hz + +lemma ExpSmall.strip_bound {E : ℂ → ℂ} (he : ExpSmall 0 E) : + ∃ ε C : ℝ,0<ε ∧ 0≤C ∧ ∀ᶠ z in stripInfinity,‖E z‖≤C*Real.exp (-ε*z.re) := by + obtain ⟨a,ha,hO⟩ := he + obtain ⟨C,hC,hbound⟩ := hO.exists_pos + refine ⟨-a,C,by linarith,hC.le,?_⟩ + simpa only [neg_neg,Real.norm_eq_abs,abs_of_pos (Real.exp_pos _)] using + hbound.bound.filter_mono stripInfinity_le_sectorInfinity + +lemma real_positive_quotient {g h : ℂ → ℂ} + (hg : ∀ᶠ t : ℝ in atTop,(g (t:ℂ)).im=0 ∧ 0<(g (t:ℂ)).re) + (hh : ∀ᶠ t : ℝ in atTop,(h (t:ℂ)).im=0 ∧ 0<(h (t:ℂ)).re) : + ∀ᶠ t : ℝ in atTop,(g (t:ℂ)/h (t:ℂ)).im=0 ∧ 0<(g (t:ℂ)/h (t:ℂ)).re := by + filter_upwards [hg,hh] with t hg hh + have eg : g (t:ℂ)=((g (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hg.1) + have eh : h (t:ℂ)=((h (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hh.1) + rw [eg,eh,←Complex.ofReal_div] + exact ⟨rfl,div_pos hg.2 hh.2⟩ + + + +theorem ExpansionOver.first_positive_chart {F H : ℂ → ℂ} + (hF : ExpansionOver PuiseuxSector F) (hH : ExpansionOver PuiseuxSector H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : ∃ D : ℝ,0 deriv H z/H z) sectorInfinity (𝓝 (b:ℂ))) : + PositiveExponentialChart F H := by + obtain ⟨a,ha,g,hg,hg0,hgr,hFe,hFd⟩ := hF.puiseux_positive_leading hFr hFt + obtain ⟨b,hb,h,hh,hh0,hhr,hHe,hHd⟩ := hH.puiseux_positive_leading hHr hHt + obtain ⟨b',hb',hHd'⟩ := htop + have heq : b=b' := Complex.ofReal_injective (tendsto_nhds_unique hHd hHd') + have hbpos : 0 he⟩ + · subst a + let J : ℂ → ℂ := fun z => g z/h z + have hJ : J∈PuiseuxSector := by + simpa only [J,div_eq_mul_inv] using puiseux_lowerSectorData.mul_mem hg (puiseux_lowerSectorData.inv_mem hh) + have hJr := real_positive_quotient hgr hhr + change ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re at hJr + have hJray : ∀ᶠ t : ℝ in atTop,J (t:ℂ)≠0 := hJr.mono fun t ht he => by + have hn := ht.2; rw [he,Complex.zero_re] at hn; exact lt_irrefl _ hn + have hJnonzero : ¬ (fun t : ℝ => J (t:ℂ)) =ᶠ[atTop] fun _ => 0 := by + intro he; obtain ⟨t,ht,h0⟩ := (hJray.and he).exists; exact ht h0 + have hJ0 := PuiseuxSector.ray_nonzero_to_sector hJ hJray + have hJd := PuiseuxSector.log_deriv_tendsto hJ hJnonzero + have hJm := PuiseuxSector.real_monotone hJ (hJr.mono fun _ h => h.1) + obtain ⟨E,hE,hfactor⟩ := normalized_equal_exponent_ratio hg0 hh0 hFe hHe + change ∀ᶠ z in sectorInfinity,F z/H z=J z*(1+E z) at hfactor + have hbound : ∃ D : ℝ,∀ᶠ t : ℝ in atTop,‖F (t:ℂ)/H (t:ℂ)‖≤D := by + obtain ⟨D,hD,hO⟩ := hO + refine ⟨D,?_⟩ + filter_upwards [hFr,hHr,hO] with t hf hh ho + have ef : F (t:ℂ)=((F (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hf.1) + have eh : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hh.1) + rw [ef,eh,←Complex.ofReal_div,Complex.norm_of_nonneg (div_pos hf.2 hh.2).le] + exact (div_le_iff₀ hh.2).mpr ho + obtain ⟨M,hM⟩ := lower_ratio_bounded hE hfactor hbound + obtain ⟨c,hc,hJl,hJlim⟩ := PuiseuxSector.positive_bounded_limit hJ hJr + ⟨M,hM.mono fun t ht => (Complex.re_le_norm (J (t:ℂ))).trans ht⟩ + obtain ⟨ε,C,hε,hC,he⟩ := hE.strip_bound + rcases hc.eq_or_lt with hc | hc + · subst c + obtain ⟨hd0,hdd,hqa,hqn,hqd,hqr⟩ := PuiseuxSector.vanishing_ratio_data hJ hJr hJl + obtain ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,hmap⟩ := vanishing_equal_exponent_chart + hbpos hε hC (hs hFa) (hs hHa) (hs hF0) (hs hH0) hFr hHr hFt hHt hdfs hdhs + (hs hJ.1) (hs hJ0) hJr (hJd.mono_left stripInfinity_le_sectorInfinity) + (hdd.mono_left stripInfinity_le_sectorInfinity) hJl hJm (hs hqa) (hs hqn) + (hqd.mono_left stripInfinity_le_sectorInfinity) hqr he (hs hfactor) + refine ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hm,hn,hsep⟩ := hmap ω S hω + exact ⟨η,R,hη,hm,hn,fun _ => hsep⟩ + · have hlim : Tendsto (fun t : ℝ => F (t:ℂ)/H (t:ℂ)) atTop (𝓝 (c:ℂ)) := by + have ht : Tendsto (fun z => J z*(1+E z)) sectorInfinity (𝓝 (c:ℂ)) := by + simpa using hJlim.mul ((tendsto_const_nhds (x := (1:ℂ))).add hE.tendsto_zero) + exact (ht.congr' (hfactor.mono fun _ h => h.symm)).comp tendsto_real_sectorInfinity + have hnot : ¬ Tendsto (fun t : ℝ => F (t:ℂ)/H (t:ℂ)) atTop (𝓝 0) := by + intro hz + exact (Complex.ofReal_ne_zero.mpr hc.ne') (tendsto_nhds_unique hlim hz) + have hdJ := PuiseuxSector.deriv_mem hJ + rcases puiseux_lowerSectorData.zero_or_ne hdJ with hd0 | hdn + · have hconst := strip_derivative_zero_constant (hs hJ.1) (hs hd0) (hJr.mono fun _ h => h.1) hJl + have hf : ∀ᶠ z in stripInfinity,F z/H z=(c:ℂ)*(1+E z) := by + filter_upwards [hs hfactor,hconst] with z hf hc; rwa [hc] at hf + obtain ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,hmap⟩ := constant_equal_exponent_chart + hbpos hε hC hc (hs hFa) (hs hHa) (hs hF0) (hs hH0) hFr hHr hFt hHt hdfs hdhs he hf + refine ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hm,hn⟩ := hmap ω S hω + exact ⟨η,R,hη,hm,hn,fun h => False.elim (hnot h)⟩ + · have hdnray := tendsto_real_sectorInfinity.eventually hdn + have hdd := PuiseuxSector.log_deriv_tendsto hdJ (by + intro he; obtain ⟨t,ht,h0⟩ := (hdnray.and he).exists; exact ht h0) + obtain ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,hmap⟩ := positive_equal_exponent_chart + hbpos hε hC hc (hs hFa) (hs hHa) (hs hF0) (hs hH0) hFr hHr hFt hHt hdfs hdhs + (hs hJ.1) (hs hJ0) (hJr.mono fun _ h => h.1) (hJd.mono_left stripInfinity_le_sectorInfinity) + (hs hdn) (hdd.mono_left stripInfinity_le_sectorInfinity) hJl hJm he (hs hfactor) + refine ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hm,hn⟩ := hmap ω S hω + exact ⟨η,R,hη,hm,hn,fun h => False.elim (hnot h)⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem ExpansionOver.positive_chart {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) {F H : ℂ → ℂ} + (hF : ExpansionOver K F) (hH : ExpansionOver K H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : ∃ D : ℝ,0 deriv H z/H z) stripInfinity (𝓝 (b:ℂ))) : + PositiveExponentialChart F H := by + obtain ⟨a,ha,g,hg,hg0,hgr,hFe,hFd⟩ := hF.positive_leading_strip hK hconj hFr hFt + obtain ⟨b,hb,h,hh,hh0,hhr,hHe,hHd⟩ := hH.positive_leading_strip hK hconj hHr hHt + obtain ⟨b',hb',hHd'⟩ := htop + have heq : b=b' := Complex.ofReal_injective (tendsto_nhds_unique hHd hHd') + have hbpos : 0 he⟩ + · subst a + let J : ℂ → ℂ := fun z => g z/h z + have hJ : J∈K := by + simpa only [J,div_eq_mul_inv] using hK.mul_mem hg (hK.inv_mem hh) + have hJr := real_positive_quotient hgr hhr + change ∀ᶠ t : ℝ in atTop,(J (t:ℂ)).im=0 ∧ 0<(J (t:ℂ)).re at hJr + have hJray : ∀ᶠ t : ℝ in atTop,J (t:ℂ)≠0 := hJr.mono fun t ht he => by + have hn := ht.2; rw [he,Complex.zero_re] at hn; exact lt_irrefl _ hn + have hJ0 := hK.ray_nonzero_to_sector hJ hJray + have hJd := hK.log_deriv_strip hJ hJ0 + have hJm := hK.real_monotone hKd hJ (hJr.mono fun _ h => h.1) + obtain ⟨E,hE,hfactor⟩ := normalized_equal_exponent_ratio hg0 hh0 hFe hHe + change ∀ᶠ z in sectorInfinity,F z/H z=J z*(1+E z) at hfactor + have hbound : ∃ D : ℝ,∀ᶠ t : ℝ in atTop,‖F (t:ℂ)/H (t:ℂ)‖≤D := by + obtain ⟨D,hD,hO⟩ := hO + refine ⟨D,?_⟩ + filter_upwards [hFr,hHr,hO] with t hf hh ho + have ef : F (t:ℂ)=((F (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hf.1) + have eh : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hh.1) + rw [ef,eh,←Complex.ofReal_div,Complex.norm_of_nonneg (div_pos hf.2 hh.2).le] + exact (div_le_iff₀ hh.2).mpr ho + obtain ⟨M,hM⟩ := lower_ratio_bounded hE hfactor hbound + obtain ⟨c,hc,hJl,hJlim⟩ := hK.positive_bounded_limit hKd hJ hJr + ⟨M,hM.mono fun t ht => (Complex.re_le_norm (J (t:ℂ))).trans ht⟩ + obtain ⟨ε,C,hε,hC,he⟩ := hE.strip_bound + rcases hc.eq_or_lt with hc | hc + · subst c + obtain ⟨hd0,hdd,hqa,hqn,hqd,hqr⟩ := hK.vanishing_ratio_data hKd hJ hJr hJl + obtain ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,hmap⟩ := vanishing_equal_exponent_chart + hbpos hε hC (hs hFa) (hs hHa) (hs hF0) (hs hH0) hFr hHr hFt hHt hdfs hdhs + (hs (hK.analytic hJ)) (hs hJ0) hJr hJd + hdd hJl hJm (hs hqa) (hs hqn) + hqd hqr he (hs hfactor) + refine ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hm,hn,hsep⟩ := hmap ω S hω + exact ⟨η,R,hη,hm,hn,fun _ => hsep⟩ + · have hlim : Tendsto (fun t : ℝ => F (t:ℂ)/H (t:ℂ)) atTop (𝓝 (c:ℂ)) := by + have ht : Tendsto (fun t : ℝ => J (t:ℂ)*(1+E (t:ℂ))) atTop (𝓝 (c:ℂ)) := by + simpa using hJlim.mul ((tendsto_const_nhds (x := (1:ℂ))).add (hE.tendsto_zero.comp tendsto_real_sectorInfinity)) + exact ht.congr' ((tendsto_real_sectorInfinity.eventually hfactor).mono fun _ h => h.symm) + have hnot : ¬ Tendsto (fun t : ℝ => F (t:ℂ)/H (t:ℂ)) atTop (𝓝 0) := by + intro hz + exact (Complex.ofReal_ne_zero.mpr hc.ne') (tendsto_nhds_unique hlim hz) + have hdJ := hKd _ hJ + rcases hK.zero_or_ne hdJ with hd0 | hdn + · have hconst := strip_derivative_zero_constant (hs (hK.analytic hJ)) (hs hd0) (hJr.mono fun _ h => h.1) hJl + have hf : ∀ᶠ z in stripInfinity,F z/H z=(c:ℂ)*(1+E z) := by + filter_upwards [hs hfactor,hconst] with z hf hc; rwa [hc] at hf + obtain ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,hmap⟩ := constant_equal_exponent_chart + hbpos hε hC hc (hs hFa) (hs hHa) (hs hF0) (hs hH0) hFr hHr hFt hHt hdfs hdhs he hf + refine ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hm,hn⟩ := hmap ω S hω + exact ⟨η,R,hη,hm,hn,fun h => False.elim (hnot h)⟩ + · have hdnray := tendsto_real_sectorInfinity.eventually hdn + have hdd := hK.log_deriv_strip hdJ hdn + obtain ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,hmap⟩ := positive_equal_exponent_chart + hbpos hε hC hc (hs hFa) (hs hHa) (hs hF0) (hs hH0) hFr hHr hFt hHt hdfs hdhs + (hs (hK.analytic hJ)) (hs hJ0) (hJr.mono fun _ h => h.1) hJd + (hs hdn) hdd hJl hJm he (hs hfactor) + refine ⟨T,x,hT,hxa,hl,hr,hxt,hxr,hft,hfa,?_⟩ + intro ω S hω + obtain ⟨η,R,hη,hm,hn⟩ := hmap ω S hω + exact ⟨η,R,hη,hm,hn,fun h => False.elim (hnot h)⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem power_model_linear_sector {G : ℂ → ℂ} {a C K R : ℝ} + (ha : 0 < a) (hC : 0 < C) + (herr : ∀ z : ℂ, R < ‖z‖ → ‖G z-(C:ℂ)*z‖ ≤ K*‖z‖^(1-a)) + {ω : ℝ → ℝ} (hω : AdmissibleAngularLoss ω) (S : ℝ) : + ∃ (η : ℝ → ℝ) (T : ℝ), AdmissibleAngularLoss η ∧ + ∀ z ∈ lossSector η T, G z ∈ lossSector ω S := by + obtain ⟨k,hk⟩ := pow_unbounded_of_one_lt (max (2*C) (2/C)) (by norm_num : (1:ℝ)<2) + have hkC : 2*C ≤ (2:ℝ)^k := (le_max_left _ _).trans hk.le + have hkCi : 2/C ≤ (2:ℝ)^k := (le_max_right _ _).trans hk.le + have hkdiv : 1/(2:ℝ)^k ≤ C/2 := by + have hp : (0:ℝ)<2^k := by positivity + rw [div_le_iff₀ hp] + have hh := (div_le_iff₀ hC).mp hkCi + nlinarith + obtain ⟨hN,hup⟩ := hω.scale_envelope k + let N := scaleEnvelope ω k + let η : ℝ → ℝ := fun r => 16*N r + have hη : AdmissibleAngularLoss η := hN.const_mul (by norm_num) + have hηsmall := hη.tendsto_zero.eventually (eventually_lt_nhds (by linarith [Real.pi_pos] : (0:ℝ) C/2*r) atTop atTop := + tendsto_id.const_mul_atTop (by positivity) + obtain ⟨W,hW⟩ := eventually_atTop.mp hω.1 + obtain ⟨T,hT⟩ := eventually_atTop.mp (hnorm.and (hup.and + ((hN.power_absorption ha (K/C)).and ((hescape.eventually (eventually_gt_atTop (max W S))).and + (hηsmall.and (hη.1.and (eventually_gt_atTop R))))))) + refine ⟨η,T,hη,?_⟩ + intro z hz + obtain ⟨hn,hu,he,hes,hηπ,hηp,hR⟩ := hT ‖z‖ hz.1.le + have hb := hn.2 z rfl + simp only [Real.rpow_one] at hb + have hNk : ω ‖G z‖ ≤ N ‖z‖ := by + apply hu + constructor + · calc + ‖z‖/(2:ℝ)^k = (1/(2:ℝ)^k)*‖z‖ := by ring + _ ≤ C/2*‖z‖ := mul_le_mul_of_nonneg_right hkdiv hn.1.le + _ ≤ ‖G z‖ := hb.1 + · exact hb.2.trans (mul_le_mul_of_nonneg_right hkC hn.1.le) + have hw := (hW _ ((le_max_left _ _).trans (hes.le.trans hb.1))).1 + have hnpos : 0 < N ‖z‖ := by dsimp [η] at hηp; nlinarith [hηp.1] + have herror : ‖G z-(C:ℂ)*z‖ ≤ C*N ‖z‖*‖z‖ := by + apply (herr z hR).trans + have hmul := mul_le_mul_of_nonneg_left he (mul_pos hC hn.1).le + rw [sub_eq_add_neg,Real.rpow_add hn.1,Real.rpow_one] + field_simp at hmul + nlinarith + have hrelower := half_loss_norm_le_re hηp.1.le hηπ.le hz.2 + have hreerr := (abs_re_le_norm (G z-(C:ℂ)*z)).trans herror + simp only [Complex.sub_re,Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im, + zero_mul,sub_zero] at hreerr + have hnormpos : 0 < ‖G z‖ := (mul_pos (by positivity) hn.1).trans_le hb.1 + refine ⟨(le_max_right _ _).trans_lt (hes.trans_le hb.1), + arg_lt_of_re_lower hw (norm_pos_iff.mp hnormpos) ?_⟩ + have hm := mul_le_mul_of_nonneg_right hNk hnormpos.le + have hmu := mul_le_mul_of_nonneg_left hb.2 hnpos.le + have hrC := mul_le_mul_of_nonneg_left hrelower hC.le + dsimp [η] at hrC + nlinarith [(abs_le.mp hreerr).1,mul_pos (mul_pos hC hnpos) hn.1] + +end DegeneratingTrees.Clock + + + + + + + +open Filter Topology +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma power_exponent_le_one {f : ℝ → ℝ} {q C : ℝ} (hC : 0 < C) + (hl : ∀ᶠ t : ℝ in atTop, C*t^q ≤ |f t|) (hO : f =O[atTop] id) : q ≤ 1 := by + by_contra hq + have hq : 0 < q-1 := by linarith + obtain ⟨K,hK,hb⟩ := hO.exists_pos + have ht := (tendsto_rpow_atTop hq).eventually (eventually_gt_atTop (K/C)) + obtain ⟨t,hl,hb,ht,ht0⟩ := (hl.and (hb.bound.and (ht.and (eventually_gt_atTop (0:ℝ))))).exists + simp only [Real.norm_eq_abs,Function.id_def,abs_of_pos ht0] at hb + have hpow : t^q = t^(q-1)*t := by + calc + t^q = t^((q-1)+1) := by congr 1; ring + _ = t^(q-1)*t := by rw [Real.rpow_add ht0,Real.rpow_one] + rw [hpow] at hl + have hmul : K < C*t^(q-1) := by + have := (div_lt_iff₀ hC).mp ht + nlinarith + nlinarith + +lemma power_exponent_lt_one {f : ℝ → ℝ} {q C : ℝ} (hC : 0 < C) + (hl : ∀ᶠ t : ℝ in atTop, C*t^q ≤ |f t|) (ho : f =o[atTop] id) : q < 1 := by + by_contra hq + have hq : 1 ≤ q := le_of_not_gt hq + have hb := ho.bound (show 0 < C/2 by positivity) + obtain ⟨t,hl,hb,ht1⟩ := (hl.and (hb.and (eventually_gt_atTop (1:ℝ)))).exists + have ht0 : 0 < t := zero_lt_one.trans ht1 + simp only [Function.id_def,Real.norm_eq_abs,abs_of_pos ht0] at hb + have hp : t ≤ t^q := by + calc + t = t^(1:ℝ) := (Real.rpow_one t).symm + _ ≤ t^q := Real.rpow_le_rpow_of_exponent_le ht1.le hq + have hh := mul_le_mul_of_nonneg_left hp hC.le + nlinarith + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +theorem Puiseux.sector_control {f : ℝ → ℝ} + (hf : Puiseux (fun t => (f t:ℂ))) (ht : Tendsto f atTop atTop) + (hO : f =O[atTop] id) : + ∃ (G : ℂ → ℂ) (R : ℝ), + (∀ z : ℂ, R < ‖z‖ → 0 < z.re → AnalyticAt ℂ G z) ∧ + (fun t => (f t:ℂ)) =ᶠ[atTop] (fun t => G (t:ℂ)) ∧ + (∀ z : ℂ, R < ‖z‖ → |f ‖z‖|/4 ≤ ‖G z‖ ∧ ‖G z‖ ≤ 4*|f ‖z‖|) ∧ + ∀ (ω : ℝ → ℝ) (S : ℝ), AdmissibleAngularLoss ω → + ∃ (η : ℝ → ℝ) (T : ℝ), AdmissibleAngularLoss η ∧ R ≤ T ∧ + (∀ z ∈ lossSector η T, G z ∈ lossSector ω S) ∧ + (f =o[atTop] id → ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, + ∀ z ∈ lossSector η A, |(G z).re| ≤ ε*z.re) := by + obtain ⟨q,a,C,K,R,G,hq,ha,hC,hK,hGa,he,herr⟩ := hf.positive_sector ht + have hn := power_model_norm ha hC herr + have hlo : ∀ᶠ r : ℝ in atTop, C/2*r^(q:ℝ) ≤ |f r| := by + filter_upwards [hn,he] with r hr he + have hh := (hr.2 (r:ℂ) (Complex.norm_of_nonneg hr.1.le)).1 + simpa only [←he,Complex.norm_real,Real.norm_eq_abs] using hh + have hq1 : (q:ℝ) ≤ 1 := power_exponent_le_one (by positivity) hlo hO + obtain ⟨W,hW⟩ := eventually_atTop.mp (hn.and he) + let R' := max R W + refine ⟨G,R',fun z hz => hGa z ((le_max_left _ _).trans_lt hz),he,?_,?_⟩ + · intro z hz + obtain ⟨hn,he⟩ := hW ‖z‖ ((le_max_right _ _).trans hz.le) + have hb := hn.2 z rfl + have hb' := hn.2 (‖z‖:ℂ) (Complex.norm_of_nonneg hn.1.le) + simp only [←he,Complex.norm_real,Real.norm_eq_abs] at hb' + constructor <;> linarith + · intro ω S hω + have hmap : ∃ (η : ℝ → ℝ) (T : ℝ), AdmissibleAngularLoss η ∧ + ∀ z ∈ lossSector η T, G z ∈ lossSector ω S := by + rcases lt_or_eq_of_le hq1 with hlt | heq + · obtain ⟨T,hT⟩ := power_model_sublinear_sector hq hlt ha hC herr hω S + exact ⟨ω,T,hω,hT⟩ + · exact power_model_linear_sector (K := K) (R := R) ha hC + (by simpa only [heq,Complex.ofReal_one,Complex.cpow_one] using herr) hω S + obtain ⟨η,T,hη,hT⟩ := hmap + refine ⟨η,max R' T,hη,le_max_left _ _,?_,?_⟩ + · intro z hz + exact hT z ⟨(le_max_right _ _).trans_lt hz.1,hz.2⟩ + · intro ho + apply sublinear_sector_realpart (power_exponent_lt_one (by positivity) hlo ho) + (show (0:ℝ)<2*C by positivity) _ hη + exact hn.mono (fun r hr z hz => (hr.2 z hz).2) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + + +def PositiveSectorControl (f : ℝ → ℝ) : Prop := + ∃ (G : ℂ → ℂ) (R : ℝ), + (∀ z : ℂ, R < ‖z‖ → 0 < z.re → AnalyticAt ℂ G z) ∧ + (fun t => (f t:ℂ)) =ᶠ[atTop] (fun t => G (t:ℂ)) ∧ + (∀ z : ℂ, R < ‖z‖ → |f ‖z‖|/4 ≤ ‖G z‖ ∧ ‖G z‖ ≤ 4*|f ‖z‖|) ∧ + ∀ (ω : ℝ → ℝ) (S : ℝ), AdmissibleAngularLoss ω → + ∃ (η : ℝ → ℝ) (T : ℝ), AdmissibleAngularLoss η ∧ R ≤ T ∧ + (∀ z ∈ lossSector η T, G z ∈ lossSector ω S) ∧ + (f =o[atTop] id → ∀ ε : ℝ, 0 < ε → ∃ A : ℝ, + ∀ z ∈ lossSector η A, |(G z).re| ≤ ε*z.re) + +theorem Puiseux.change_clock {H : ℝ → ℝ} + (hH : Puiseux (fun t => (H t:ℂ))) (hHt : Tendsto H atTop atTop) + (hfast : id =o[atTop] H) : + ∃ I : ℝ → ℝ, Puiseux (fun t => (I t:ℂ)) ∧ Tendsto I atTop atTop ∧ + (∀ᶠ t in atTop, H (I t)=t) ∧ (∀ᶠ t in atTop, I (H t)=t) ∧ + I =o[atTop] id ∧ PositiveSectorControl I ∧ + ∀ f : ℝ → ℝ, Puiseux (fun t => (f t:ℂ)) → Tendsto f atTop atTop → + f =O[atTop] H → + PositiveSectorControl (fun t => f (I t)) ∧ + (f =o[atTop] H → (fun t => f (I t)) =o[atTop] id) := by + obtain ⟨I,hI,hIt,hl,hr,hcomp⟩ := hH.change_coordinate hHt + have hsmall : I =o[atTop] id := by + apply (hfast.comp_tendsto hIt).congr' Filter.EventuallyEq.rfl + exact hl + refine ⟨I,hI,hIt,hl,hr,hsmall,hI.sector_control hIt hsmall.isBigO,?_⟩ + intro f hf hft hO + have hO' : (fun t => f (I t)) =O[atTop] id := by + apply (hO.comp_tendsto hIt).congr' Filter.EventuallyEq.rfl + exact hl + refine ⟨(hcomp _ hf).sector_control (hft.comp hIt) hO',?_⟩ + intro ho + apply (ho.comp_tendsto hIt).congr' Filter.EventuallyEq.rfl + exact hl + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PreparationLimits.lean b/lean/OAI/Analysis/PathSelection/PreparationLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..7d41a3187c48d477ff3be27ec5fb84666f6cbcff --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PreparationLimits.lean @@ -0,0 +1,395 @@ +import Mathlib +import OAI.Analysis.PathSelection.ContourPreparation + +namespace OAI + +/-! Convergence of contour sums, preparation coefficients and division remainders. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace PathSelection.PreparationLimit + +open Complex PathSelection.Preparation +open scoped Real + + +lemma tendstoUniformlyOn_circleIntegral {ι A : Type*} {l : Filter ι} + {S : Set A} {F : ι → A → ℂ → ℂ} {f : A → ℂ → ℂ} {r : ℝ} + (hr : 0 F i p.1 p.2) + (fun p => f p.1 p.2) l (S ×ˢ sphere 0 r)) : + TendstoUniformlyOn (fun i a => ∮ z in C(0,r), F i a z) + (fun a => ∮ z in C(0,r), f a z) l S := by + rw [Metric.tendstoUniformlyOn_iff] at h ⊢ + intro ε hε + have hC : 0<2*π*r := by positivity + let δ := ε/(2*(2*π*r)) + have hδ : 0<δ := div_pos hε (mul_pos (by norm_num) hC) + filter_upwards [h δ hδ,hF] with i hi hiF + intro a ha + rw [dist_eq_norm,← circleIntegral.integral_sub ((hf a ha).circleIntegrable hr.le) + ((hiF a ha).circleIntegrable hr.le)] + have hb := circleIntegral.norm_integral_le_of_norm_le_const hr.le + (f := fun z => f a z-F i a z) (C := δ) + (fun z hz => (show ‖f a z-F i a z‖<δ from by + simpa only [dist_eq_norm] using hi (a,z) ⟨ha,hz⟩).le) + have he : (2*π*r)*δ=ε/2 := by dsimp [δ]; field_simp + exact hb.trans_lt (he ▸ by linarith) + +lemma circleIntegral_tendsto {ι : Type*} {l : Filter ι} + {F : ι → ℂ → ℂ} {f : ℂ → ℂ} {r : ℝ} (hr : 0 ∮ z in C(0,r), F i z) l (𝓝 (∮ z in C(0,r), f z)) := by + have hh := tendstoUniformlyOn_circleIntegral (A := Unit) (S := univ) + (F := fun i _ z => F i z) (f := fun _ z => f z) hr + (hF.mono (fun i hi _ _ => hi)) (fun _ _ => hf) (by + rw [Metric.tendstoUniformlyOn_iff] at h ⊢ + intro ε hε + filter_upwards [h ε hε] with i hi p hp + exact hi p.2 hp.2) + exact hh.tendsto_at (mem_univ ()) + +lemma eventual_uniform_nonzero {ι X : Type*} [TopologicalSpace X] + {l : Filter ι} {F : ι → X → ℂ} {f : X → ℂ} {K : Set X} + (hK : IsCompact K) (hf : ContinuousOn f K) (hnz : ∀ x∈K, f x≠0) + (h : TendstoUniformlyOn F f l K) : + ∀ᶠ i in l, ∀ x∈K, F i x≠0 := by + by_cases hne : K.Nonempty + · obtain ⟨x,hx,hm⟩ := hK.exists_isMinOn hne hf.norm + have hxpos : 0<‖f x‖ := norm_pos_iff.mpr (hnz x hx) + filter_upwards [(Metric.tendstoUniformlyOn_iff.mp h) ‖f x‖ hxpos] with i hi + intro y hy he + have hh := hi y hy + rw [he,dist_zero_right] at hh + exact (not_lt_of_ge (hm hy)) hh + · filter_upwards with i x hx + exact (hne ⟨x,hx⟩).elim + +lemma tendstoPowerSum {ι : Type*} {l : Filter ι} + {F : ι → ℂ → ℂ} {f : ℂ → ℂ} {U : Set ℂ} {r : ℝ} + (hU : IsOpen U) (hr : 0 contourPowerSum (F i) r n) l (𝓝 (contourPowerSum f r n)) := by + have hK := isCompact_sphere (0:ℂ) r + have hc {G : ι → ℂ → ℂ} {g : ℂ → ℂ} : + TendstoLocallyUniformlyOn G g l (sphere 0 r) ↔ + TendstoUniformlyOn G g l (sphere 0 r) := + tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact hK + have hd := h.deriv (hF.mono (fun i hi => hi.differentiableOn)) hU + have hf' := hf.mono hKU + have hd' := hf.deriv.continuousOn.mono hKU + have hdiv := (hd.mono hKU).div₀ (h.mono hKU) hd' hf'.continuousOn hnz + have hpow : TendstoLocallyUniformlyOn (fun _ : ι => fun z : ℂ => z^n) + (fun z => z^n) l (sphere 0 r) := by + apply TendstoUniformlyOn.tendstoLocallyUniformlyOn + rw [Metric.tendstoUniformlyOn_iff] + intro ε hε + filter_upwards with i z hz + simpa using hε + have hint := hpow.mul₀ hdiv (continuousOn_id.pow _) + (hd'.div hf'.continuousOn hnz) + have hev := eventual_uniform_nonzero hK hf'.continuousOn hnz (hc.mp (h.mono hKU)) + have hcF : ∀ᶠ i in l, ContinuousOn (fun z => z^n * (deriv (F i) z/F i z)) (sphere 0 r) := by + filter_upwards [hF,hev] with i hi hn + exact (continuousOn_id.pow _).mul + ((hi.deriv.continuousOn.mono hKU).div (hi.continuousOn.mono hKU) hn) + have hcf : ContinuousOn (fun z => z^n * (deriv f z/f z)) (sphere 0 r) := + (continuousOn_id.pow _).mul (hd'.div hf'.continuousOn hnz) + have ht := circleIntegral_tendsto hr hcF hcf (hc.mp hint) + simpa only [contourPowerSum,mul_div_assoc] using ht.const_mul ((2*π*I)⁻¹) + +lemma tendsto_newtonEsymm {ι : Type*} {l : Filter ι} {s : ι → ℕ → ℂ} {t : ℕ → ℂ} + (h : ∀ k, Tendsto (fun i => s i k) l (𝓝 (t k))) (n : ℕ) : + Tendsto (fun i => newtonEsymm (s i) n) l (𝓝 (newtonEsymm t n)) := by + induction n using Nat.strong_induction_on with + | h n ih => + rw [show (fun i => newtonEsymm (s i) n) = + (fun i => if n=0 then 1 else (n:ℂ)⁻¹ * (-1)^(n+1) * + ∑ a ∈ (Finset.HasAntidiagonal.antidiagonal n).filter (fun a => a.1 f) f l S := by + apply TendstoUniformlyOn.tendstoLocallyUniformlyOn + rw [Metric.tendstoUniformlyOn_iff] + intro ε hε + filter_upwards with i x hx + simpa using hε + +lemma tendsto_preparation_coeff {ι : Type*} {l : Filter ι} + {F : ι → ℂ → ℂ} {f : ℂ → ℂ} {r : ℝ} + (h : ∀ n, Tendsto (fun i => contourPowerSum (F i) r n) l (𝓝 (contourPowerSum f r n))) + (d k : ℕ) : + Tendsto (fun i => (preparationPolynomial (F i) r d).coeff k) l + (𝓝 ((preparationPolynomial f r d).coeff k)) := by + classical + simp only [preparationPolynomial,finsetSum_coeff,coeff_C_mul_X_pow] + apply tendsto_finsetSum + intro n hn + split_ifs + · exact (tendsto_newtonEsymm h (d-n)).const_mul _ + · exact tendsto_const_nhds + +lemma locallyUniform_finset_sum {ι X B : Type*} [TopologicalSpace X] + {l : Filter ι} {S : Set X} {F : B → ι → X → ℂ} {f : B → X → ℂ} + (s : Finset B) (h : ∀ b∈s, TendstoLocallyUniformlyOn (F b) (f b) l S) : + TendstoLocallyUniformlyOn (fun i x => ∑ b∈s, F b i x) + (fun x => ∑ b∈s, f b x) l S := by + classical + induction s using Finset.induction_on with + | empty => simpa using const_locallyUniform (l := l) (fun _ : X => (0:ℂ)) S + | @insert b s hb ih => + simp only [Finset.sum_insert hb] + exact (h b (Finset.mem_insert_self _ _)).add + (ih (fun c hc => h c (Finset.mem_insert_of_mem hc))) + +lemma tendsto_preparation_eval {ι : Type*} {l : Filter ι} + {F : ι → ℂ → ℂ} {f : ℂ → ℂ} {r : ℝ} + (h : ∀ n, Tendsto (fun i => contourPowerSum (F i) r n) l (𝓝 (contourPowerSum f r n))) + (d : ℕ) : + TendstoLocallyUniformlyOn (fun i z => (preparationPolynomial (F i) r d).eval z) + (fun z => (preparationPolynomial f r d).eval z) l univ := by + classical + simp only [preparationPolynomial,eval_finsetSum,eval_mul,eval_C,eval_pow,eval_X] + apply locallyUniform_finset_sum + intro k hk + have hc := ((tendsto_newtonEsymm h (d-k)).const_mul ((-1:ℂ)^(d-k))).tendstoUniformlyOn_const + (s := (univ : Set ℂ)) + exact hc.tendstoLocallyUniformlyOn.mul₀ (const_locallyUniform (fun z : ℂ => z^k) univ) + continuousOn_const (continuousOn_id.pow _) + + + +theorem tendsto_divisionQuotient {ι : Type*} {l : Filter ι} + {G : ι → ℂ → ℂ} {g : ℂ → ℂ} {P : ι → ℂ[X]} {p : ℂ[X]} {r : ℝ} + (hr : 0 (P i).eval w) p.eval l (sphere 0 r)) : + TendstoLocallyUniformlyOn (fun i y => divisionQuotient (G i) (P i) r y) + (divisionQuotient g p r) l (ball 0 r) := by + rw [tendstoLocallyUniformlyOn_iff_forall_isCompact isOpen_ball] + intro K hKb hK + let S : Set (ℂ × ℂ) := K ×ˢ sphere 0 r + have hS : IsCompact S := hK.prod (isCompact_sphere _ _) + have hn (z : ℂ × ℂ) (hz : z∈S) : z.2-z.1≠0 := by + apply sub_ne_zero.mpr + intro he + have hlt := mem_ball_zero_iff.mp (hKb hz.1) + have heq := mem_sphere_zero_iff_norm.mp hz.2 + rw [he] at heq + exact (ne_of_lt hlt) heq + have cg : ContinuousOn (fun z : ℂ × ℂ => g z.2) S := + hg.comp continuousOn_snd (fun z hz => hz.2) + have cp : ContinuousOn (fun z : ℂ × ℂ => p.eval z.2) S := + p.continuous.continuousOn.comp continuousOn_snd (fun _ _ => mem_univ _) + have cn : ContinuousOn (fun z : ℂ × ℂ => z.2-z.1) S := + continuousOn_snd.sub continuousOn_fst + have hg' := hlimG.tendstoLocallyUniformlyOn.comp Prod.snd + (t := S) (fun z hz => hz.2) continuousOn_snd + have hp' := hlimP.tendstoLocallyUniformlyOn.comp Prod.snd + (t := S) (fun z hz => hz.2) continuousOn_snd + have hden := hp'.mul₀ (const_locallyUniform (fun z : ℂ × ℂ => z.2-z.1) S) cp cn + have hd := hg'.div₀ hden cg (cp.mul cn) + (fun z hz => mul_ne_zero (hnz z.2 hz.2) (hn z hz)) + have hd' : TendstoUniformlyOn + (fun i (z : ℂ × ℂ) => G i z.2 / ((P i).eval z.2 * (z.2-z.1))) + (fun z : ℂ × ℂ => g z.2 / (p.eval z.2 * (z.2-z.1))) l S := + (tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact hS).mp hd + have hev := eventual_uniform_nonzero (isCompact_sphere (0:ℂ) r) + p.continuous.continuousOn hnz hlimP + have hci : ∀ᶠ i in l, ∀ y∈K, + ContinuousOn (fun w => G i w / ((P i).eval w*(w-y))) (sphere 0 r) := by + filter_upwards [hG,hev] with i hi hiP + intro y hy + exact hi.div ((P i).continuous.continuousOn.mul + (continuousOn_id.sub continuousOn_const)) + (fun w hw => mul_ne_zero (hiP w hw) (hn (y,w) ⟨hy,hw⟩)) + have hcg : ∀ y∈K, + ContinuousOn (fun w => g w / (p.eval w*(w-y))) (sphere 0 r) := by + intro y hy + exact hg.div (p.continuous.continuousOn.mul + (continuousOn_id.sub continuousOn_const)) + (fun w hw => mul_ne_zero (hnz w hw) (hn (y,w) ⟨hy,hw⟩)) + have ht := tendstoUniformlyOn_circleIntegral hr hci hcg hd' + have hqcont := (divisionQuotient_analyticOnNhd hr hg hnz).continuousOn.mono hKb + have hcint : ContinuousOn (fun y => ∮ w in C(0,r), g w / (p.eval w*(w-y))) K := by + have hc := hqcont.const_mul (2*π*I) + convert hc using 1 + funext y + simp only [divisionQuotient,← mul_assoc,mul_inv_cancel₀ (show (2*π*I:ℂ)≠0 by + simp [Real.pi_ne_zero,I_ne_zero]),one_mul] + have hscaled := (const_locallyUniform (l := l) (fun _ : ℂ => (2*π*I:ℂ)⁻¹) K).mul₀ + ht.tendstoLocallyUniformlyOn continuousOn_const hcint + exact (tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact hK).mp hscaled + +lemma tendsto_weighted_ratio_integral {ι : Type*} {l : Filter ι} + {G : ι → ℂ → ℂ} {g : ℂ → ℂ} {P : ι → ℂ[X]} {p : ℂ[X]} {r : ℝ} + (hr : 0 (P i).eval w) p.eval l (sphere 0 r)) + {c : ι → ℂ} {c₀ : ℂ} (hc : Tendsto c l (𝓝 c₀)) (m : ℕ) : + Tendsto (fun i => (2*π*I)⁻¹ * ∮ w in C(0,r), + G i w / (P i).eval w * (c i * w^m)) l + (𝓝 ((2*π*I)⁻¹ * ∮ w in C(0,r), g w / p.eval w * (c₀*w^m))) := by + have hdiv := hlimG.tendstoLocallyUniformlyOn.div₀ hlimP.tendstoLocallyUniformlyOn + hg p.continuous.continuousOn hnz + have hcw := (hc.tendstoUniformlyOn_const (s := sphere (0:ℂ) r)).tendstoLocallyUniformlyOn.mul₀ + (const_locallyUniform (fun w : ℂ => w^m) (sphere 0 r)) + continuousOn_const (continuousOn_id.pow _) + have hf := hdiv.mul₀ hcw (hg.div p.continuous.continuousOn hnz) + (continuousOn_const.mul (continuousOn_id.pow _)) + have hev := eventual_uniform_nonzero (isCompact_sphere (0:ℂ) r) + p.continuous.continuousOn hnz hlimP + have hFi : ∀ᶠ i in l, ContinuousOn (fun w => G i w/(P i).eval w*(c i*w^m)) (sphere 0 r) := by + filter_upwards [hG,hev] with i hi hiP + exact (hi.div (P i).continuous.continuousOn hiP).mul + (continuousOn_const.mul (continuousOn_id.pow _)) + exact (circleIntegral_tendsto hr hFi + ((hg.div p.continuous.continuousOn hnz).mul + (continuousOn_const.mul (continuousOn_id.pow _))) + ((tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact + (isCompact_sphere (0:ℂ) r)).mp hf)).const_mul _ + + + +theorem tendsto_divisionRemainder_coeff {ι : Type*} {l : Filter ι} + {G : ι → ℂ → ℂ} {g : ℂ → ℂ} {P : ι → ℂ[X]} {p : ℂ[X]} {r : ℝ} + (hr : 0 (P i).eval w) p.eval l (sphere 0 r)) + (hcoeff : ∀ n, Tendsto (fun i => (P i).coeff n) l (𝓝 (p.coeff n))) + (hdeg : ∀ᶠ i in l, (P i).natDegree=p.natDegree) (k : ℕ) : + Tendsto (fun i => (divisionRemainder (G i) (P i) r).coeff k) l + (𝓝 ((divisionRemainder g p r).coeff k)) := by + classical + have ht : Tendsto (fun i => ∑ n∈Finset.range (p.natDegree+1), + ∑ j∈Finset.range n, if k=j then (2*π*I)⁻¹ * ∮ w in C(0,r), + G i w / (P i).eval w * ((P i).coeff n * w^(n-1-j)) else 0) l + (𝓝 (∑ n∈Finset.range (p.natDegree+1), ∑ j∈Finset.range n, + if k=j then (2*π*I)⁻¹ * ∮ w in C(0,r), + g w / p.eval w * (p.coeff n * w^(n-1-j)) else 0)) := by + apply tendsto_finsetSum + intro n hn + apply tendsto_finsetSum + intro j hj + split_ifs + · exact tendsto_weighted_ratio_integral hr hG hg hnz hlimG hlimP (hcoeff n) _ + · exact tendsto_const_nhds + simp only [divisionRemainder,finsetSum_coeff,coeff_C_mul_X_pow] + apply ht.congr' + filter_upwards [hdeg] with i hi + rw [hi] + + + +theorem exists_preparation_circle {f : ℂ → ℂ} {U : Set ℂ} {d : ℕ} + (hU : U∈𝓝 (0:ℂ)) (hf : AnalyticAt ℂ f 0) + (hd : analyticOrderAt f 0=(d:ℕ∞)) : + ∃ r : ℝ, 0 (hh z hz).2.1 + have hga : AnalyticOnNhd ℂ g (closedBall 0 r) := fun z hz => (hh z hz).2.2.1 + have hgn : ∀ z∈closedBall (0:ℂ) r, g z≠0 := fun z hz => (hh z hz).2.2.2.1 + have hfe : EqOn f (fun z => (X^d : ℂ[X]).eval z*g z) (closedBall 0 r) := by + intro z hz + simpa only [eval_pow,eval_X] using (hh z hz).2.2.2.2 + have hroot : ∀ z : ℂ, (X^d : ℂ[X]).eval z=0 → z∈ball 0 r := by + intro z hz + simp only [eval_pow,eval_X] at hz + by_cases he : z=0 + · subst z + exact mem_ball_self hr + · exact (pow_ne_zero d he hz).elim + refine ⟨r,hr,(fun z hz => (hh z hz).1),hfa,?_,?_⟩ + · intro z hz + rw [(hh z (sphere_subset_closedBall hz)).2.2.2.2] + apply mul_ne_zero (pow_ne_zero _ ?_) (hgn z (sphere_subset_closedBall hz)) + intro he + have heq' := mem_sphere_zero_iff_norm.mp hz + simp only [he,norm_zero] at heq' + linarith + · simpa only [natDegree_X_pow] using preparation_zero_count + hr hfa (monic_X.pow d) hroot hga hgn hfe + +lemma analyticOnNhd_iteratedDeriv {f : ℂ → ℂ} {U : Set ℂ} + (hf : AnalyticOnNhd ℂ f U) (n : ℕ) : AnalyticOnNhd ℂ (iteratedDeriv n f) U := by + induction n with + | zero => simpa only [iteratedDeriv_zero] using hf + | succ n ih => simpa only [iteratedDeriv_succ] using ih.deriv + + + +lemma tendstoLocallyUniformlyOn_iteratedDeriv {ι : Type*} {l : Filter ι} + {F : ι → ℂ → ℂ} {f : ℂ → ℂ} {U : Set ℂ} + (hU : IsOpen U) (hF : ∀ᶠ i in l, AnalyticOnNhd ℂ (F i) U) + (h : TendstoLocallyUniformlyOn F f l U) (n : ℕ) : + TendstoLocallyUniformlyOn (fun i => iteratedDeriv n (F i)) (iteratedDeriv n f) l U := by + induction n with + | zero => simpa only [iteratedDeriv_zero] using h + | succ n ih => + simpa only [iteratedDeriv_succ,Function.comp_def] using ih.deriv + (hF.mono (fun i hi => (analyticOnNhd_iteratedDeriv hi n).differentiableOn)) hU +end PathSelection.PreparationLimit +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PreparationStability.lean b/lean/OAI/Analysis/PathSelection/PreparationStability.lean new file mode 100644 index 0000000000000000000000000000000000000000..6a86a131bd155fb155fd691636bf0aa819faadba --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PreparationStability.lean @@ -0,0 +1,264 @@ +import Mathlib +import OAI.Analysis.PathSelection.JointPreparation +import OAI.Analysis.PathSelection.PreparationLimits + +namespace OAI + +/-! Normalized preparation stability and common parameter domains. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace PathSelection.PreparationLimit + +open PathSelection.Preparation + +theorem normalized_preparation_stability {ι : Type*} {l : Filter ι} + {F : ι → ℂ → ℂ} {f : ℂ → ℂ} {U : Set ℂ} {r : ℝ} {d : ℕ} + (hU : IsOpen U) (hr : 0 preparationPolynomial (F i) r d + let W₀ := preparationPolynomial f r d + (∀ᶠ i in l, (W i).Monic ∧ (W i).natDegree=d ∧ + (∀ z : ℂ, (W i).eval z=0 → z∈ball 0 r) ∧ + AnalyticOnNhd ℂ (divisionQuotient (F i) (W i) r) (ball 0 r) ∧ + (∀ z∈ball (0:ℂ) r, divisionQuotient (F i) (W i) r z≠0) ∧ + EqOn (F i) (fun z => (W i).eval z * divisionQuotient (F i) (W i) r z) (ball 0 r)) ∧ + (∀ k, Tendsto (fun i => (W i).coeff k) l (𝓝 (W₀.coeff k))) ∧ + TendstoLocallyUniformlyOn (fun i z => (W i).eval z) W₀.eval l univ ∧ + TendstoLocallyUniformlyOn (fun i z => divisionQuotient (F i) (W i) r z) + (divisionQuotient f W₀ r) l (ball 0 r) := by + dsimp only + have hSU : sphere (0:ℂ) r⊆U := sphere_subset_closedBall.trans hKU + have hlim := (tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact + (isCompact_sphere (0:ℂ) r)).mp (h.mono hSU) + have hFn := eventual_uniform_nonzero (isCompact_sphere (0:ℂ) r) + (hf.continuousOn.mono hSU) hnz hlim + have hFc := eventually_count_eq hr (hF.mono (fun i hi => hi.mono hKU)) + (hf.mono hKU) hnz hlim + have hsp := tendstoPowerSum hU hr hSU hF hf hnz h + have hwlim := tendsto_preparation_eval hsp d + have hfprep := fixed_contour_preparation_of_count hr (hf.mono hKU) hnz hcount + have hWnz : ∀ z∈sphere (0:ℂ) r, (preparationPolynomial f r d).eval z≠0 := by + intro z hz he + exact (ne_of_lt (mem_ball_zero_iff.mp (hfprep.2.2.1 z he))) + (mem_sphere_zero_iff_norm.mp hz) + refine ⟨?_,tendsto_preparation_coeff hsp d,hwlim,?_⟩ + · filter_upwards [hF,hFn,hFc] with i hi hin hic + exact fixed_contour_preparation_of_count hr (hi.mono hKU) hin (hic.trans hcount) + · exact tendsto_divisionQuotient hr + (hF.mono (fun i hi => hi.continuousOn.mono hSU)) + (hf.continuousOn.mono hSU) hWnz hlim + ((tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact + (isCompact_sphere (0:ℂ) r)).mp (hwlim.mono (subset_univ _))) + + + +theorem normalized_division_stability {ι : Type*} {l : Filter ι} + {F G : ι → ℂ → ℂ} {f g : ℂ → ℂ} {U : Set ℂ} {r : ℝ} {d : ℕ} + (hU : IsOpen U) (hr : 0 preparationPolynomial (F i) r d + let W₀ := preparationPolynomial f r d + TendstoLocallyUniformlyOn (fun i z => divisionQuotient (G i) (W i) r z) + (divisionQuotient g W₀ r) l (ball 0 r) ∧ + (∀ k, Tendsto (fun i => (divisionRemainder (G i) (W i) r).coeff k) l + (𝓝 ((divisionRemainder g W₀ r).coeff k))) ∧ + (∀ᶠ i in l, + (divisionRemainder (G i) (W i) r).degree (W i).eval z * divisionQuotient (G i) (W i) r z + + (divisionRemainder (G i) (W i) r).eval z) (ball 0 r)) := by + dsimp only + obtain ⟨hprep,hcoeff,hwlim,hunit⟩ := normalized_preparation_stability + hU hr hKU hF hf hnz hcount h + have hfprep := fixed_contour_preparation_of_count hr (hf.mono hKU) hnz hcount + have hWnz : ∀ z∈sphere (0:ℂ) r, (preparationPolynomial f r d).eval z≠0 := by + intro z hz he + exact (ne_of_lt (mem_ball_zero_iff.mp (hfprep.2.2.1 z he))) + (mem_sphere_zero_iff_norm.mp hz) + have hSU : sphere (0:ℂ) r⊆U := sphere_subset_closedBall.trans hKU + have hlimG := (tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact + (isCompact_sphere (0:ℂ) r)).mp (h'.mono hSU) + have hlimW := (tendstoLocallyUniformlyOn_iff_tendstoUniformlyOn_of_compact + (isCompact_sphere (0:ℂ) r)).mp (hwlim.mono (subset_univ _)) + have hGcont := hG.mono (fun i hi => hi.continuousOn.mono hSU) + have hgcont := hg.continuousOn.mono hSU + refine ⟨tendsto_divisionQuotient hr hGcont hgcont hWnz hlimG hlimW,?_,?_⟩ + · exact tendsto_divisionRemainder_coeff hr hGcont hgcont hWnz hlimG hlimW hcoeff + (hprep.mono (fun i hi => hi.2.1.trans hfprep.2.1.symm)) + · filter_upwards [hprep,hG] with i hi hiG + have hiWnz : ∀ z∈sphere (0:ℂ) r, (preparationPolynomial (F i) r d).eval z≠0 := by + intro z hz he + exact (ne_of_lt (mem_ball_zero_iff.mp (hi.2.2.1 z he))) + (mem_sphere_zero_iff_norm.mp hz) + have hdiv := fixed_disc_division (G := G i) + (P := preparationPolynomial (F i) r d) hr (hiG.mono hKU) hiWnz + refine ⟨?_,hdiv.2.2⟩ + simpa only [hi.2.1] using hdiv.2.1 + + + +theorem normalized_unit_all_orders {ι : Type*} {l : Filter ι} + {F : ι → ℂ → ℂ} {f : ℂ → ℂ} {U : Set ℂ} {r : ℝ} {d : ℕ} + (hU : IsOpen U) (hr : 0 divisionQuotient (F i) (preparationPolynomial (F i) r d) r + let Q₀ := divisionQuotient f (preparationPolynomial f r d) r + (∀ᶠ i in l, ∀ n, AnalyticOnNhd ℂ (iteratedDeriv n (Q i)) (ball 0 r)) ∧ + (∀ n, TendstoLocallyUniformlyOn (fun i => iteratedDeriv n (Q i)) + (iteratedDeriv n Q₀) l (ball 0 r)) := by + dsimp only + have hp := normalized_preparation_stability hU hr hKU hF hf hnz hcount h + have hqa := hp.1.mono (fun i hi => hi.2.2.2.1) + exact ⟨hqa.mono (fun i hi n => analyticOnNhd_iteratedDeriv hi n), + tendstoLocallyUniformlyOn_iteratedDeriv isOpen_ball hqa hp.2.2.2⟩ + + + +theorem joint_preparation_from_regular_germ {E : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] {F : E × ℂ → ℂ} {a₀ : E} {d : ℕ} + (hF : AnalyticAt ℂ F (a₀,0)) + (horder : analyticOrderAt (fun z => F (a₀,z)) 0=(d:ℕ∞)) : + ∃ δ r : ℝ, 0<δ ∧ 0 preparationPolynomial (fun z => F (a,z)) r d + let u := fun p : E × ℂ => divisionQuotient (fun z => F (p.1,z)) (W p.1) r p.2 + (∀ a∈U, (W a).Monic ∧ (W a).natDegree=d ∧ + ∀ z, (W a).eval z=0 → z∈ball 0 r) ∧ + (∀ n, AnalyticOnNhd ℂ (fun a => (W a).coeff n) U) ∧ + AnalyticOnNhd ℂ (fun p : E × ℂ => (W p.1).eval p.2) (U ×ˢ univ) ∧ + AnalyticOnNhd ℂ u (U ×ˢ ball 0 r) ∧ + (∀ p∈U ×ˢ ball (0:ℂ) r, u p≠0) ∧ + EqOn F (fun p => (W p.1).eval p.2*u p) (U ×ˢ ball 0 r) := by + let : NormedSpace ℝ E := NormedSpace.restrictScalars ℝ ℂ E + obtain ⟨S,hS,T,hT,hST⟩ := mem_nhds_prod_iff.mp hF.eventually_analyticAt + obtain ⟨ε,hε,hεS⟩ := Metric.mem_nhds_iff.mp hS + obtain ⟨ρ,hρ,hρT⟩ := Metric.mem_nhds_iff.mp hT + have hFa : AnalyticOnNhd ℂ F (ball a₀ ε ×ˢ ball 0 ρ) := by + intro p hp + exact hST ⟨hεS hp.1,hρT hp.2⟩ + have hf : AnalyticAt ℂ (fun z => F (a₀,z)) 0 := + hF.comp (analyticAt_const.prod analyticAt_id) + obtain ⟨r,hr,hrρ,hfr,hnz,hcount⟩ := exists_preparation_circle + (isOpen_ball.mem_nhds (mem_ball_self hρ)) hf horder + have hev : ∀ᶠ a in 𝓝 a₀, ∀ z∈sphere (0:ℂ) r, F (a,z)≠0 := by + apply (isCompact_sphere (0:ℂ) r).eventually_forall_of_forall_eventually + intro z hz + exact (hFa (a₀,z) ⟨mem_ball_self hε,hrρ (sphere_subset_closedBall hz)⟩).continuousAt.eventually_ne + (hnz z hz) + have hb : ∀ᶠ a in 𝓝 a₀, a∈ball a₀ ε := isOpen_ball.mem_nhds (mem_ball_self hε) + have hev' : ∀ᶠ a in 𝓝 a₀, a∈ball a₀ ε ∧ ∀ z∈sphere (0:ℂ) r, F (a,z)≠0 := + hb.and hev + obtain ⟨δ,hδ,hδs⟩ := Metric.mem_nhds_iff.mp hev' + have hF' : AnalyticOnNhd ℂ F (ball a₀ δ ×ˢ closedBall 0 r) := by + intro p hp + exact hFa p ⟨(hδs hp.1).1,hrρ hp.2⟩ + have hnz' : ∀ p∈ball a₀ δ ×ˢ sphere (0:ℂ) r, F p≠0 := by + intro p hp + exact (hδs hp.1).2 p.2 hp.2 + have hp := JointPreparation.joint_fixed_contour_preparation isOpen_ball + (convex_ball a₀ δ).isPreconnected (mem_ball_self hδ) hr hF' hnz' hcount + refine ⟨δ,r,hδ,hr,hp.1,?_,hp.2.1,hp.2.2.1,hp.2.2.2.1,hp.2.2.2.2⟩ + exact JointPreparation.analyticOnNhd_preparation_coeff isOpen_ball hr.le + (hF'.mono (prod_mono Subset.rfl sphere_subset_closedBall)) hnz' d + + + +theorem common_preparation_domain {E J : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] [Finite J] {F : E × ℂ → ℂ} {G : J → E × ℂ → ℂ} + {a₀ : E} {d : ℕ} (hF : AnalyticAt ℂ F (a₀,0)) + (hG : ∀ j, AnalyticAt ℂ (G j) (a₀,0)) + (horder : analyticOrderAt (fun z => F (a₀,z)) 0=(d:ℕ∞)) : + ∃ δ r : ℝ, 0<δ ∧ 0 F (a₀,z)) r 0=(d:ℂ) := by + have hGa : ∀ᶠ p in 𝓝 (a₀,(0:ℂ)), ∀ j, AnalyticAt ℂ (G j) p := + Filter.eventually_all.mpr (fun j => (hG j).eventually_analyticAt) + obtain ⟨S,hS,T,hT,hST⟩ := mem_nhds_prod_iff.mp (hF.eventually_analyticAt.and hGa) + obtain ⟨ε,hε,hεS⟩ := Metric.mem_nhds_iff.mp hS + obtain ⟨ρ,hρ,hρT⟩ := Metric.mem_nhds_iff.mp hT + have hFa : AnalyticOnNhd ℂ F (ball a₀ ε ×ˢ ball 0 ρ) := by + intro p hp + exact (hST ⟨hεS hp.1,hρT hp.2⟩).1 + have hGa' : ∀ j, AnalyticOnNhd ℂ (G j) (ball a₀ ε ×ˢ ball 0 ρ) := by + intro j p hp + exact (hST ⟨hεS hp.1,hρT hp.2⟩).2 j + have hf : AnalyticAt ℂ (fun z => F (a₀,z)) 0 := + hF.comp (analyticAt_const.prod analyticAt_id) + obtain ⟨r,hr,hrρ,hfr,hnz,hcount⟩ := exists_preparation_circle + (isOpen_ball.mem_nhds (mem_ball_self hρ)) hf horder + have hev : ∀ᶠ a in 𝓝 a₀, ∀ z∈sphere (0:ℂ) r, F (a,z)≠0 := by + apply (isCompact_sphere (0:ℂ) r).eventually_forall_of_forall_eventually + intro z hz + exact (hFa (a₀,z) ⟨mem_ball_self hε,hrρ (sphere_subset_closedBall hz)⟩).continuousAt.eventually_ne + (hnz z hz) + have hb : ∀ᶠ a in 𝓝 a₀, a∈ball a₀ ε := isOpen_ball.mem_nhds (mem_ball_self hε) + obtain ⟨δ,hδ,hδs⟩ := Metric.mem_nhds_iff.mp (hb.and hev) + refine ⟨δ,r,hδ,hr,?_,?_,?_,hcount⟩ + · intro p hp + exact hFa p ⟨(hδs hp.1).1,hrρ hp.2⟩ + · intro j p hp + exact hGa' j p ⟨(hδs hp.1).1,hrρ hp.2⟩ + · intro p hp + exact (hδs hp.1).2 p.2 hp.2 + + + +theorem joint_preparation_and_divisions_from_germs {E J : Type*} [NormedAddCommGroup E] + [NormedSpace ℂ E] [Finite J] {F : E × ℂ → ℂ} {G : J → E × ℂ → ℂ} + {a₀ : E} {d : ℕ} (hF : AnalyticAt ℂ F (a₀,0)) + (hG : ∀ j, AnalyticAt ℂ (G j) (a₀,0)) + (horder : analyticOrderAt (fun z => F (a₀,z)) 0=(d:ℕ∞)) : + ∃ δ r : ℝ, 0<δ ∧ 0 preparationPolynomial (fun z => F (a,z)) r d + let u := fun p : E × ℂ => divisionQuotient (fun z => F (p.1,z)) (W p.1) r p.2 + (∀ a∈U, (W a).Monic ∧ (W a).natDegree=d ∧ + ∀ z, (W a).eval z=0 → z∈ball 0 r) ∧ + (∀ n, AnalyticOnNhd ℂ (fun a => (W a).coeff n) U) ∧ + AnalyticOnNhd ℂ u (U ×ˢ ball 0 r) ∧ + (∀ p∈U ×ˢ ball (0:ℂ) r, u p≠0) ∧ + EqOn F (fun p => (W p.1).eval p.2*u p) (U ×ˢ ball 0 r) ∧ + (∀ j, let Q := fun p : E × ℂ => divisionQuotient (fun z => G j (p.1,z)) (W p.1) r p.2 + let R := fun a => divisionRemainder (fun z => G j (a,z)) (W a) r + AnalyticOnNhd ℂ Q (U ×ˢ ball 0 r) ∧ + (∀ n, AnalyticOnNhd ℂ (fun a => (R a).coeff n) U) ∧ + (∀ a∈U, (R a).degree (W p.1).eval p.2*Q p+(R p.1).eval p.2) (U ×ˢ ball 0 r)) := by + let : NormedSpace ℝ E := NormedSpace.restrictScalars ℝ ℂ E + obtain ⟨δ,r,hδ,hr,hFa,hGa,hnz,hcount⟩ := common_preparation_domain hF hG horder + have hp := JointPreparation.joint_fixed_contour_preparation isOpen_ball + (convex_ball a₀ δ).isPreconnected (mem_ball_self hδ) hr hFa hnz hcount + have hc := JointPreparation.analyticOnNhd_preparation_coeff isOpen_ball hr.le + (hFa.mono (prod_mono Subset.rfl sphere_subset_closedBall)) hnz d + refine ⟨δ,r,hδ,hr,hp.1,hc,hp.2.2.1,hp.2.2.2.1,hp.2.2.2.2,?_⟩ + intro j + apply JointPreparation.joint_fixed_contour_division isOpen_ball hr (hGa j) + (hp.2.1.mono (prod_mono Subset.rfl (subset_univ _))) hc + (fun a ha => (hp.1 a ha).2.1) + intro a ha z hz he + exact (ne_of_lt (mem_ball_zero_iff.mp ((hp.1 a ha).2.2 z he))) + (mem_sphere_zero_iff_norm.mp hz) + +end PathSelection.PreparationLimit +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PuiseuxCalculus.lean b/lean/OAI/Analysis/PathSelection/PuiseuxCalculus.lean new file mode 100644 index 0000000000000000000000000000000000000000..2ec153ebe74fdbd2b4eb37e8f454a6303defaf89 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PuiseuxCalculus.lean @@ -0,0 +1,361 @@ +import Mathlib + +namespace OAI + +/-! Puiseux expansions, differentiation and analytic Hardy properties. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +def rootCoord (n : ℕ) (x : ℝ) : ℝ := x ^ (-(n:ℝ)⁻¹) + +def Puiseux (f : ℝ → ℂ) : Prop := + ∃ n : ℕ, 0 < n ∧ ∃ m : ℤ, ∃ F : ℂ → ℂ, + AnalyticAt ℂ F 0 ∧ f =ᶠ[atTop] fun x => ((rootCoord n x)^m : ℝ) • F (rootCoord n x) + +lemma rootCoord_pos {n : ℕ} {x : ℝ} (hx : 0 < x) : 0 < rootCoord n x := + Real.rpow_pos_of_pos hx _ + +lemma rootCoord_tendsto_zero {n : ℕ} (hn : 0 < n) : + Tendsto (rootCoord n) atTop (𝓝 0) := + tendsto_rpow_neg_atTop (inv_pos.mpr (Nat.cast_pos.mpr hn)) + +lemma rootCoord_complex_tendsto_zero {n : ℕ} (hn : 0 < n) : + Tendsto (fun x => (rootCoord n x : ℂ)) atTop (𝓝 0) := by + simpa only [Function.comp_def, Complex.ofReal_zero] using Complex.continuous_ofReal.continuousAt.tendsto.comp (rootCoord_tendsto_zero hn) + +lemma rootCoord_pow {n m : ℕ} (hn : 0 < n) (hm : 0 < m) {x : ℝ} (hx : 0 < x) : + (rootCoord (n*m) x)^m = rootCoord n x := by + rw [rootCoord,←Real.rpow_natCast,←Real.rpow_mul hx.le] + congr 1 + push_cast + field_simp + +lemma rootCoord_zpow {n : ℕ} {x : ℝ} (hx : 0 < x) (m : ℤ) : + (rootCoord n x)^m = x^(-(m:ℝ)/(n:ℝ)) := by + rw [rootCoord,←Real.rpow_intCast,←Real.rpow_mul hx.le] + congr 1 + ring + +lemma Puiseux.congr {f g : ℝ → ℂ} (hf : Puiseux f) (hfg : f =ᶠ[atTop] g) : Puiseux g := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + exact ⟨n,hn,m,F,hF,hfg.symm.trans he⟩ + +lemma puiseux_const (c : ℂ) : Puiseux (fun _ : ℝ => c) := by + refine ⟨1,by norm_num,0,fun _ => c,analyticAt_const,?_⟩ + exact Eventually.of_forall (fun x => by simp) + +lemma Puiseux.normalize {f : ℝ → ℂ} (hf : Puiseux f) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : + ∃ n : ℕ, 0 < n ∧ ∃ m : ℤ, ∃ F : ℂ → ℂ, + AnalyticAt ℂ F 0 ∧ F 0 ≠ 0 ∧ + f =ᶠ[atTop] fun x => ((rootCoord n x)^m : ℝ) • F (rootCoord n x) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + have hFne : ¬ F =ᶠ[𝓝 0] fun _ => 0 := by + intro h0 + apply hne + filter_upwards [he,(rootCoord_complex_tendsto_zero hn).eventually h0] with x hx hz + simp [hx,hz] + obtain ⟨k,G,hG,hG0,hfac⟩ := hF.exists_eventuallyEq_pow_smul_nonzero_iff.mpr hFne + refine ⟨n,hn,m+(k:ℤ),G,hG,hG0,?_⟩ + filter_upwards [he,(rootCoord_complex_tendsto_zero hn).eventually hfac, + eventually_gt_atTop (0:ℝ)] with x hx hfac hxpos + rw [hx,hfac,sub_zero] + rw [zpow_add₀ (rootCoord_pos hxpos).ne',zpow_natCast] + simp only [←Complex.ofReal_pow,Complex.real_smul,Complex.ofReal_mul,smul_eq_mul,mul_assoc] + + + +lemma Puiseux.leading {f : ℝ → ℂ} (hf : Puiseux f) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : + ∃ q : ℚ, ∃ C : ℂ, C ≠ 0 ∧ + Tendsto (fun x => ((x^(q:ℝ) : ℝ):ℂ)⁻¹ * f x) atTop (𝓝 C) := by + obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.normalize hne + refine ⟨-(m:ℚ)/(n:ℚ),F 0,hF0,?_⟩ + apply (hF.continuousAt.tendsto.comp (rootCoord_complex_tendsto_zero hn)).congr' + filter_upwards [he,eventually_gt_atTop (0:ℝ)] with x hx hxpos + rw [hx,rootCoord_zpow hxpos] + push_cast + rw [Complex.real_smul] + have hne : ((x^(-(m:ℝ)/(n:ℝ)) : ℝ):ℂ) ≠ 0 := by + exact_mod_cast (Real.rpow_pos_of_pos hxpos (-(m:ℝ)/(n:ℝ))).ne' + simp [hne] + +lemma Puiseux.eventually_nonzero {f : ℝ → ℂ} (hf : Puiseux f) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : ∀ᶠ x : ℝ in atTop, f x ≠ 0 := by + obtain ⟨q,C,hC,ht⟩ := hf.leading hne + filter_upwards [ht.eventually_ne hC] with x hx + exact (mul_ne_zero_iff.mp hx).2 + + +lemma Puiseux.eventually_sign {f : ℝ → ℝ} (hf : Puiseux (fun x => (f x : ℂ))) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : + (∀ᶠ x : ℝ in atTop, 0 < f x) ∨ (∀ᶠ x : ℝ in atTop, f x < 0) := by + have hcne : ¬ (fun x => (f x:ℂ)) =ᶠ[atTop] fun _ => 0 := by + intro h + apply hne + exact h.mono (fun x hx => Complex.ofReal_eq_zero.mp hx) + obtain ⟨q,C,hC,ht⟩ := hf.leading hcne + have ht' : Tendsto (fun x => (x^(q:ℝ))⁻¹*f x) atTop (𝓝 C.re) := by + simpa only [Function.comp_def, ← Complex.ofReal_inv, ← Complex.ofReal_mul, Complex.ofReal_re] using Complex.continuous_re.continuousAt.tendsto.comp ht + have hCim : C.im = 0 := by + have h : Tendsto (fun _ : ℝ => (0:ℝ)) atTop (𝓝 C.im) := by + simpa only [Function.comp_def, ← Complex.ofReal_inv, ← Complex.ofReal_mul, Complex.ofReal_im] using Complex.continuous_im.continuousAt.tendsto.comp ht + exact tendsto_nhds_unique h tendsto_const_nhds + have hCre : C.re ≠ 0 := by + intro h + apply hC + exact Complex.ext h hCim + rcases lt_or_gt_of_ne hCre with hneg | hpos + · right + filter_upwards [ht'.eventually_lt_const hneg,eventually_gt_atTop (0:ℝ)] with x hx hxpos + exact neg_of_mul_neg_right hx (inv_nonneg.mpr (Real.rpow_nonneg hxpos.le _)) + · left + filter_upwards [ht'.eventually_const_lt hpos,eventually_gt_atTop (0:ℝ)] with x hx hxpos + exact (mul_pos_iff_of_pos_left (inv_pos.mpr (Real.rpow_pos_of_pos hxpos _))).mp hx + +end DegeneratingTrees.Clock + + + + + +open Filter Topology Complex +namespace DegeneratingTrees.Clock + + +lemma puiseux_refine {f : ℝ → ℂ} {n : ℕ} (hn : 0 < n) {m : ℤ} {F : ℂ → ℂ} + (hF : AnalyticAt ℂ F 0) + (he : f =ᶠ[atTop] fun x => ((rootCoord n x)^m : ℝ) • F (rootCoord n x)) + {r : ℕ} (hr : 0 < r) : + ∃ G : ℂ → ℂ, AnalyticAt ℂ G 0 ∧ + f =ᶠ[atTop] fun x => ((rootCoord (n*r) x)^(m*(r:ℤ)) : ℝ) • G (rootCoord (n*r) x) := by + refine ⟨fun z => F (z^r), ?_, ?_⟩ + · have hF' : AnalyticAt ℂ F ((0:ℂ)^r) := by simpa [zero_pow hr.ne'] using hF + exact hF'.comp (f := fun z : ℂ => z^r) (analyticAt_id.pow r) + · filter_upwards [he,eventually_gt_atTop (0:ℝ)] with x hx hxpos + rw [hx,←rootCoord_pow hn hr hxpos,Complex.ofReal_pow] + congr 1 + rw [←zpow_natCast,←zpow_mul] + congr 1 + ring + +lemma Puiseux.mul {f g : ℝ → ℂ} (hf : Puiseux f) (hg : Puiseux g) : + Puiseux (fun x => f x * g x) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + obtain ⟨r,hr,k,G,hG,he'⟩ := hg + obtain ⟨F',hF',hf'⟩ := puiseux_refine hn hF he hr + obtain ⟨G',hG',hg'⟩ := puiseux_refine hr hG he' hn + rw [Nat.mul_comm r n] at hg' + refine ⟨n*r,Nat.mul_pos hn hr,m*(r:ℤ)+k*(n:ℤ),fun z => F' z * G' z, + hF'.mul hG',?_⟩ + filter_upwards [hf',hg',eventually_gt_atTop (0:ℝ)] with x hx hy hxpos + rw [hx,hy,zpow_add₀ (rootCoord_pos hxpos).ne'] + simp only [Complex.real_smul,Complex.ofReal_mul] + ring + +lemma Puiseux.neg {f : ℝ → ℂ} (hf : Puiseux f) : Puiseux (fun x => -f x) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + refine ⟨n,hn,m,fun z => -F z,hF.neg,?_⟩ + filter_upwards [he] with x hx + simp [hx] + +lemma Puiseux.add {f g : ℝ → ℂ} (hf : Puiseux f) (hg : Puiseux g) : + Puiseux (fun x => f x + g x) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + obtain ⟨r,hr,k,G,hG,he'⟩ := hg + obtain ⟨F',hF',hf'⟩ := puiseux_refine hn hF he hr + obtain ⟨G',hG',hg'⟩ := puiseux_refine hr hG he' hn + rw [Nat.mul_comm r n] at hg' + let a := m*(r:ℤ) + let b := k*(n:ℤ) + let c := min a b + have ha : 0 ≤ a-c := sub_nonneg.mpr (min_le_left _ _) + have hb : 0 ≤ b-c := sub_nonneg.mpr (min_le_right _ _) + refine ⟨n*r,Nat.mul_pos hn hr,c,fun z => z^(a-c).toNat*F' z+z^(b-c).toNat*G' z, + ((analyticAt_id.pow _).mul hF').add ((analyticAt_id.pow _).mul hG'),?_⟩ + filter_upwards [hf',hg',eventually_gt_atTop (0:ℝ)] with x hx hy hxpos + have ht : rootCoord (n*r) x ≠ 0 := (rootCoord_pos hxpos).ne' + have hpa : (rootCoord (n*r) x)^c * (rootCoord (n*r) x)^(a-c).toNat = + (rootCoord (n*r) x)^a := by + rw [←zpow_natCast,Int.toNat_of_nonneg ha,←zpow_add₀ ht] + congr 1 + ring + have hpb : (rootCoord (n*r) x)^c * (rootCoord (n*r) x)^(b-c).toNat = + (rootCoord (n*r) x)^b := by + rw [←zpow_natCast,Int.toNat_of_nonneg hb,←zpow_add₀ ht] + congr 1 + ring + rw [hx,hy] + simp only [Complex.real_smul,←Complex.ofReal_pow,mul_add,←mul_assoc,←Complex.ofReal_mul, + hpa,hpb] + rfl + +lemma Puiseux.sub {f g : ℝ → ℂ} (hf : Puiseux f) (hg : Puiseux g) : + Puiseux (fun x => f x - g x) := by + simpa only [sub_eq_add_neg] using hf.add hg.neg + +lemma Puiseux.inv {f : ℝ → ℂ} (hf : Puiseux f) : Puiseux (fun x => (f x)⁻¹) := by + by_cases hz : f =ᶠ[atTop] fun _ => 0 + · apply (puiseux_const 0).congr + exact hz.mono (fun x hx => by simp [hx]) + · obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.normalize hz + refine ⟨n,hn,-m,fun z => (F z)⁻¹,hF.inv hF0,?_⟩ + filter_upwards [he] with x hx + simp [hx,Complex.real_smul,zpow_neg,Complex.ofReal_inv,mul_inv_rev,mul_comm] + +lemma Puiseux.div {f g : ℝ → ℂ} (hf : Puiseux f) (hg : Puiseux g) : + Puiseux (fun x => f x / g x) := by + simpa only [div_eq_mul_inv] using hf.mul hg.inv + +end DegeneratingTrees.Clock + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma analyticAt_conj_conj {F : ℂ → ℂ} (hF : AnalyticAt ℂ F 0) : + AnalyticAt ℂ (fun z => star (F (star z))) 0 := by + rw [Complex.analyticAt_iff_eventually_differentiableAt] + have hc : Tendsto (star : ℂ → ℂ) (𝓝 0) (𝓝 0) := by + simpa using (continuous_star.continuousAt (x := (0:ℂ))).tendsto + filter_upwards [hc.eventually hF.eventually_analyticAt] with z hz + simpa only [Function.comp_def, Complex.star_def, Complex.conj_conj] using hz.differentiableAt.conj_conj + +lemma Puiseux.conj {f : ℝ → ℂ} (hf : Puiseux f) : Puiseux (fun x => star (f x)) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + refine ⟨n,hn,m,fun z => star (F (star z)),analyticAt_conj_conj hF,?_⟩ + filter_upwards [he] with x hx + simp [hx,Complex.real_smul] + +lemma puiseux_analytic_root {n : ℕ} (hn : 0 < n) {F : ℂ → ℂ} + (hF : AnalyticAt ℂ F 0) : Puiseux (fun x => F (rootCoord n x)) := by + refine ⟨n,hn,0,F,hF,?_⟩ + exact Eventually.of_forall (fun x => by simp) + +lemma puiseux_ratPower (q : ℚ) : Puiseux (fun x : ℝ => ((x^(q:ℝ):ℝ):ℂ)) := by + refine ⟨q.den,q.pos,-q.num,fun _ => 1,analyticAt_const,?_⟩ + filter_upwards [eventually_gt_atTop (0:ℝ)] with x hx + simp only [rootCoord_zpow hx,Int.cast_neg,neg_neg,Complex.real_smul,mul_one] + congr 2 + exact_mod_cast q.num_div_den.symm + +lemma eventuallyEq_deriv_atTop {f g : ℝ → ℂ} (he : f =ᶠ[atTop] g) : + deriv f =ᶠ[atTop] deriv g := by + obtain ⟨T,hT⟩ := eventually_atTop.mp he + filter_upwards [eventually_gt_atTop T] with x hx + apply Filter.EventuallyEq.deriv_eq + filter_upwards [eventually_gt_nhds hx] with y hy + exact hT y hy.le + +lemma Puiseux.deriv {f : ℝ → ℂ} (hf : Puiseux f) : Puiseux (deriv f) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + let q : ℚ := -(m:ℚ)/(n:ℚ) + let r : ℚ := -(n:ℚ)⁻¹ + have he' : f =ᶠ[atTop] fun x => ((x^(q:ℝ):ℝ):ℂ) * F (rootCoord n x) := by + filter_upwards [he,eventually_gt_atTop (0:ℝ)] with x hx hxpos + simp [hx,rootCoord_zpow hxpos,q,Complex.real_smul] + let g : ℝ → ℂ := fun x => + ((q:ℂ)*((x^((q-1:ℚ):ℝ):ℝ):ℂ))*F (rootCoord n x) + + ((x^(q:ℝ):ℝ):ℂ)*(_root_.deriv F (rootCoord n x)*((r:ℂ)*((x^((r-1:ℚ):ℝ):ℝ):ℂ))) + have hg : Puiseux g := + (((puiseux_const (q:ℂ)).mul (puiseux_ratPower (q-1))).mul (puiseux_analytic_root hn hF)).add + ((puiseux_ratPower q).mul ((puiseux_analytic_root hn hF.deriv).mul + ((puiseux_const (r:ℂ)).mul (puiseux_ratPower (r-1))))) + apply hg.congr + have hd := eventuallyEq_deriv_atTop he' + filter_upwards [hd,(rootCoord_complex_tendsto_zero hn).eventually hF.eventually_analyticAt, + eventually_gt_atTop (0:ℝ)] with x hx hFx hxpos + rw [hx] + have hdF := hFx.differentiableAt.hasDerivAt.comp_ofReal + have hdroot : HasDerivAt (rootCoord n) ((r:ℝ)*x^((r:ℝ)-1)) x := by + convert! (Real.hasDerivAt_rpow_const (p := -(n:ℝ)⁻¹) (Or.inl hxpos.ne')) using 1 + simp [r] + have hdFroot := hdF.scomp x hdroot + have hdpow := (Real.hasDerivAt_rpow_const (p := (q:ℝ)) (Or.inl hxpos.ne')).ofReal_comp + have hdprod := hdpow.mul hdFroot + convert! hdprod.deriv.symm using 1 + first | rfl | + (simp only [g,Rat.cast_sub,Rat.cast_one,Complex.ofReal_mul,Complex.ofReal_ratCast, + Complex.real_smul,Function.comp_def]; ring) + +end DegeneratingTrees.Clock + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma analyticAt_real_rpow {x : ℝ} (hx : 0 < x) (p : ℝ) : + AnalyticAt ℝ (fun y : ℝ => y^p) x := by + apply (((analyticAt_log hx).mul analyticAt_const).rexp).congr + filter_upwards [eventually_gt_nhds hx] with y hy + exact (Real.rpow_def_of_pos hy p).symm + +lemma Puiseux.eventually_analytic {f : ℝ → ℂ} (hf : Puiseux f) : + ∀ᶠ x : ℝ in atTop, AnalyticAt ℝ f x := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + obtain ⟨T,hT⟩ := eventually_atTop.mp he + filter_upwards [eventually_gt_atTop T,eventually_gt_atTop (0:ℝ), + (rootCoord_complex_tendsto_zero hn).eventually hF.eventually_analyticAt] with x hx hxpos hFx + have ht : AnalyticAt ℝ (rootCoord n) x := analyticAt_real_rpow hxpos _ + have htc : AnalyticAt ℝ (fun y => (rootCoord n y:ℂ)) x := + (Complex.ofRealCLM.analyticAt _).comp ht + have hP : AnalyticAt ℝ (fun y => ((y^(-(m:ℝ)/(n:ℝ)):ℝ):ℂ)) x := + (Complex.ofRealCLM.analyticAt _).comp (analyticAt_real_rpow hxpos _) + have hmodel := hP.mul ((hFx.restrictScalars (𝕜 := ℝ)).comp (f := fun y:ℝ => (rootCoord n y:ℂ)) htc) + apply hmodel.congr + filter_upwards [eventually_gt_nhds hx,eventually_gt_nhds hxpos] with y hy hypos + rw [hT y hy.le] + dsimp + rw [rootCoord_zpow hypos] + +lemma Puiseux.real_eventually_analytic {f : ℝ → ℝ} (hf : Puiseux (fun x => (f x:ℂ))) : + ∀ᶠ x : ℝ in atTop, AnalyticAt ℝ f x := by + filter_upwards [hf.eventually_analytic] with x hx + exact (Complex.reCLM.analyticAt _).comp hx + +lemma Puiseux.real_deriv {f : ℝ → ℝ} (hf : Puiseux (fun x => (f x:ℂ))) : + Puiseux (fun x => ((_root_.deriv f x : ℝ):ℂ)) := by + apply hf.deriv.congr + filter_upwards [hf.real_eventually_analytic] with x hx + exact hx.differentiableAt.hasDerivAt.ofReal_comp.deriv + + + +theorem Puiseux.eventually_monotone {f : ℝ → ℝ} (hf : Puiseux (fun x => (f x:ℂ))) : + ∃ T : ℝ, MonotoneOn f (Ioi T) ∨ AntitoneOn f (Ioi T) := by + have hder : (∀ᶠ x : ℝ in atTop, 0 ≤ _root_.deriv f x) ∨ + (∀ᶠ x : ℝ in atTop, _root_.deriv f x ≤ 0) := by + by_cases hz : _root_.deriv f =ᶠ[atTop] fun _ => 0 + · exact Or.inl (hz.mono fun x hx => hx.ge) + · rcases hf.real_deriv.eventually_sign hz with h | h + · exact Or.inl (h.mono fun _ hx => hx.le) + · exact Or.inr (h.mono fun _ hx => hx.le) + rcases hder with h | h + · obtain ⟨T,hT⟩ := eventually_atTop.mp (hf.real_eventually_analytic.and h) + refine ⟨T,Or.inl ?_⟩ + apply monotoneOn_of_deriv_nonneg (convex_Ioi T) + · exact fun x hx => (hT x hx.le).1.continuousAt.continuousWithinAt + · exact fun x hx => (hT x (interior_subset hx).le).1.differentiableAt.differentiableWithinAt + · exact fun x hx => (hT x (interior_subset hx).le).2 + · obtain ⟨T,hT⟩ := eventually_atTop.mp (hf.real_eventually_analytic.and h) + refine ⟨T,Or.inr ?_⟩ + apply antitoneOn_of_deriv_nonpos (convex_Ioi T) + · exact fun x hx => (hT x hx.le).1.continuousAt.continuousWithinAt + · exact fun x hx => (hT x (interior_subset hx).le).1.differentiableAt.differentiableWithinAt + · exact fun x hx => (hT x (interior_subset hx).le).2 + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/PuiseuxInverses.lean b/lean/OAI/Analysis/PathSelection/PuiseuxInverses.lean new file mode 100644 index 0000000000000000000000000000000000000000..101946cb2fa67651bee17a533b9395142eaf6f2e --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/PuiseuxInverses.lean @@ -0,0 +1,419 @@ +import Mathlib +import OAI.Analysis.PathSelection.PuiseuxCalculus + +namespace OAI + +/-! Puiseux inverses, composition and sector bounds. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma rootCoord_inverse_power {n : ℕ} (hn : 0 < n) {x : ℝ} (hx : 0 < x) : + (rootCoord n x)^(-(n:ℤ)) = x := by + rw [rootCoord_zpow hx] + have hd : -(-((n:ℤ):ℝ))/(n:ℝ) = 1 := by + push_cast + field_simp + push_cast at * + rw [hd,Real.rpow_one] + +lemma rootCoord_monomial {k : ℕ} (hk : 0 < k) {u a : ℝ} + (hu : 0 < u) (ha : 0 < a) : + rootCoord k (u^(-(k:ℤ))*a) = u * (a^(-(k:ℝ)⁻¹)) := by + rw [rootCoord,Real.mul_rpow (zpow_pos hu _).le ha.le] + congr 1 + rw [←Real.rpow_intCast,←Real.rpow_mul hu.le] + have hd : ((-(k:ℤ)):ℝ)*(-(k:ℝ)⁻¹) = 1 := by + push_cast + field_simp + push_cast at * + rw [hd,Real.rpow_one] + + + +lemma tail_right_inverse {f : ℝ → ℝ} + (hf : ∀ᶠ x in atTop, ContinuousAt f x) (hlim : Tendsto f atTop atTop) : + ∃ g : ℝ → ℝ, Tendsto g atTop atTop ∧ + (∀ᶠ y in atTop, f (g y) = y) := by + classical + obtain ⟨T,hT⟩ := eventually_atTop.mp hf + have hc : ContinuousOn f (Ici T) := fun x hx => (hT x hx).continuousWithinAt + have he (y : ℝ) (hy : f T ≤ y) : ∃ x ∈ Ici T, f x = y := + intermediate_value_Ici hc hlim hy + choose a ha using he + let g : ℝ → ℝ := fun y => if hy : f T ≤ y then a y hy else T + have hg (y : ℝ) (hy : f T ≤ y) : T ≤ g y ∧ f (g y) = y := by + simpa only [g,dite_eq_left hy,Set.mem_Ici] using ha y hy + refine ⟨g,?_,(eventually_ge_atTop (f T)).mono (fun y hy => (hg y hy).2)⟩ + rw [Filter.tendsto_atTop] + intro M + obtain ⟨B,hB⟩ := (isCompact_Icc (a := T) (b := max T M)).bddAbove_image + (hc.mono (Icc_subset_Ici_self)) + filter_upwards [eventually_ge_atTop (f T),eventually_gt_atTop B] with y hy hyB + by_contra h + have hM : g y ∈ Icc T (max T M) := ⟨(hg y hy).1,(not_le.mp h).le.trans (le_max_right _ _)⟩ + have := hB (mem_image_of_mem f hM) + rw [(hg y hy).2] at this + linarith + +lemma Puiseux.normalize_unbounded_real {f : ℝ → ℝ} + (hf : Puiseux (fun x => (f x:ℂ))) (hlim : Tendsto f atTop atTop) : + ∃ n k : ℕ, 0 < n ∧ 0 < k ∧ ∃ F : ℂ → ℂ, + AnalyticAt ℂ F 0 ∧ 0 < (F 0).re ∧ (F 0).im = 0 ∧ + (fun x => (f x:ℂ)) =ᶠ[atTop] + fun x => ((rootCoord n x)^(-(k:ℤ)) : ℝ) • F (rootCoord n x) := by + have hne : ¬ (fun x => (f x:ℂ)) =ᶠ[atTop] fun _ => 0 := by + intro he + have hz : f =ᶠ[atTop] fun _ => 0 := he.mono fun x hx => by simpa only [Pi.ofNat_apply,Complex.ofReal_eq_zero] using hx + exact not_tendsto_nhds_of_tendsto_atTop hlim 0 (tendsto_const_nhds.congr' hz.symm) + obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.normalize hne + have hm : m < 0 := by + by_contra h + have hm : 0 ≤ m := le_of_not_gt h + have ht := ((rootCoord_tendsto_zero hn).pow m.toNat).smul + (hF.continuousAt.tendsto.comp (rootCoord_complex_tendsto_zero hn)) + have ht' : Tendsto (fun x => (f x:ℂ)) atTop (𝓝 (((0:ℝ)^m.toNat) • F 0)) := by + apply ht.congr' + filter_upwards [he] with x hx + simpa only [←zpow_natCast,Int.toNat_of_nonneg hm,Function.comp_def] using hx.symm + have hr := Complex.continuous_re.continuousAt.tendsto.comp ht' + exact not_tendsto_nhds_of_tendsto_atTop hlim _ (by simpa only [Function.comp_def,Complex.ofReal_re] using hr) + let k := (-m).toNat + have hk : 0 < k := by dsimp [k]; omega + have hmk : m = -(k:ℤ) := by + dsimp [k] + rw [Int.toNat_of_nonneg (neg_nonneg.mpr hm.le),neg_neg] + have hreal : ∀ᶠ x : ℝ in atTop, (F (rootCoord n x)).im = 0 ∧ + 0 < (F (rootCoord n x)).re := by + filter_upwards [he,eventually_gt_atTop (0:ℝ),hlim.eventually (eventually_gt_atTop (0:ℝ))] + with x hx hxpos hfpos + have hp : 0 < (rootCoord n x)^m := zpow_pos (rootCoord_pos hxpos) _ + have hi := congrArg Complex.im hx + have hr := congrArg Complex.re hx + simp only [Complex.ofReal_im,Complex.smul_im,Complex.ofReal_re,Complex.smul_re,smul_eq_mul] at hi hr + exact ⟨(mul_eq_zero.mp hi.symm).resolve_left hp.ne',by nlinarith⟩ + have him : (F 0).im = 0 := by + have hi := Complex.continuous_im.continuousAt.tendsto.comp + (hF.continuousAt.tendsto.comp (rootCoord_complex_tendsto_zero hn)) + exact tendsto_nhds_unique hi ((tendsto_const_nhds (x := (0:ℝ))).congr' (hreal.mono fun x hx => hx.1.symm)) + have hre : 0 ≤ (F 0).re := ge_of_tendsto + (Complex.continuous_re.continuousAt.tendsto.comp + (hF.continuousAt.tendsto.comp (rootCoord_complex_tendsto_zero hn))) + (hreal.mono fun x hx => hx.2.le) + have hrne : (F 0).re ≠ 0 := by + intro hz + exact hF0 (Complex.ext hz him) + exact ⟨n,k,hn,hk,F,hF,lt_of_le_of_ne hre hrne.symm,him,by simpa only [hmk] using he⟩ + + +lemma analytic_inverse_factor {Q : ℂ → ℂ} (hQ : AnalyticAt ℂ Q 0) + (hQ0 : Q 0 ≠ 0) : + ∃ H : ℂ → ℂ, AnalyticAt ℂ H 0 ∧ H 0 ≠ 0 ∧ + ∀ᶠ u in 𝓝 (0:ℂ), (u*Q u)*H (u*Q u) = u := by + let P : ℂ → ℂ := fun u => u*Q u + have hP : AnalyticAt ℂ P 0 := analyticAt_id.mul hQ + have hP0 : P 0 = 0 := by simp [P] + have hd : deriv P 0 = Q 0 := by + simpa [P,Pi.mul_def,id_eq] using ((hasDerivAt_id (0:ℂ)).mul hQ.differentiableAt.hasDerivAt).deriv + have hd0 : deriv P 0 ≠ 0 := hd ▸ hQ0 + let G := hP.hasStrictDerivAt.localInverse _ _ _ hd0 + have hG : AnalyticAt ℂ G 0 := hP0 ▸ hP.analyticAt_localInverse hd0 + have he : ∀ᶠ u in 𝓝 (0:ℂ), G (P u) = u := + hP.hasStrictDerivAt.eventually_left_inverse hd0 + have hG0 : G 0 = 0 := by simpa only [hP0] using he.self_of_nhds + have hdG : deriv G 0 = (deriv P 0)⁻¹ := by + simpa only [hP0] using (hP.hasStrictDerivAt.to_localInverse hd0).hasDerivAt.deriv + refine ⟨dslope G 0,hG.hasFPowerSeriesAt.has_fpower_series_dslope_fslope.analyticAt,?_,?_⟩ + · simpa only [dslope_same,hdG,ne_eq,inv_eq_zero] using hd0 + · filter_upwards [he] with u hu + have h := sub_smul_dslope G 0 (P u) + simpa only [sub_zero,hG0,smul_eq_mul,hu] using h + + + +theorem Puiseux.inverse_change {f : ℝ → ℝ} + (hf : Puiseux (fun x => (f x:ℂ))) (hlim : Tendsto f atTop atTop) : + ∃ g : ℝ → ℝ, Puiseux (fun y => (g y:ℂ)) ∧ Tendsto g atTop atTop ∧ + (∀ᶠ y in atTop, f (g y) = y) ∧ (∀ᶠ x in atTop, g (f x) = x) := by + obtain ⟨n,k,hn,hk,F,hF,hFre,hFim,he⟩ := hf.normalize_unbounded_real hlim + let Q : ℂ → ℂ := fun u => (F u)^(-(k:ℂ)⁻¹) + have hslit : F 0 ∈ Complex.slitPlane := Complex.mem_slitPlane_iff.mpr (Or.inl hFre) + have hQ : AnalyticAt ℂ Q 0 := hF.cpow analyticAt_const hslit + have hF0 : F 0 ≠ 0 := by intro hz; simp [hz] at hFre + have hQ0 : Q 0 ≠ 0 := Complex.cpow_ne_zero_iff.mpr (Or.inl hF0) + obtain ⟨H,hH,hH0,hHinv⟩ := analytic_inverse_factor hQ hQ0 + have hcoord : ∀ᶠ x : ℝ in atTop, + (rootCoord k (f x):ℂ)*H (rootCoord k (f x)) = (rootCoord n x:ℂ) := by + filter_upwards [he,eventually_gt_atTop (0:ℝ),hlim.eventually (eventually_gt_atTop (0:ℝ)), + (rootCoord_complex_tendsto_zero hn).eventually hHinv] with x hx hxp hfpos hInv + have hpow : 0 < (rootCoord n x)^(-(k:ℤ)) := zpow_pos (rootCoord_pos hxp) _ + have hi := congrArg Complex.im hx + have hr := congrArg Complex.re hx + simp only [Complex.ofReal_im,Complex.smul_im,Complex.ofReal_re,Complex.smul_re,smul_eq_mul] at hi hr + have him : (F (rootCoord n x)).im = 0 := (mul_eq_zero.mp hi.symm).resolve_left hpow.ne' + have hre : 0 < (F (rootCoord n x)).re := by nlinarith + have hreal : F (rootCoord n x) = ((F (rootCoord n x)).re:ℂ) := by + apply Complex.ext <;> simp [him] + have hroot : (rootCoord k (f x):ℂ) = (rootCoord n x:ℂ)*Q (rootCoord n x) := by + rw [hr,rootCoord_monomial hk (rootCoord_pos hxp) hre,Complex.ofReal_mul, + Complex.ofReal_cpow hre.le] + simp only [Q,Complex.ofReal_neg,Complex.ofReal_inv,Complex.ofReal_natCast] + rw [hreal] + simp only [Complex.ofReal_re] + simpa only [hroot] using hInv + obtain ⟨g,hg,hfg⟩ := tail_right_inverse + (hf.real_eventually_analytic.mono fun _ h => h.continuousAt) hlim + have hgcoord : ∀ᶠ y : ℝ in atTop, + ((rootCoord k y:ℂ)*H (rootCoord k y))^(-(n:ℤ)) = (g y:ℂ) := by + filter_upwards [hg.eventually hcoord,hfg,hg.eventually (eventually_gt_atTop (0:ℝ))] + with y hy hfy hgy + rw [hfy] at hy + rw [hy,←Complex.ofReal_zpow,rootCoord_inverse_power hn hgy] + have hgP : Puiseux (fun y => (g y:ℂ)) := by + refine ⟨k,hk,-(n:ℤ),fun u => (H u)^(-(n:ℤ)),hH.zpow hH0,?_⟩ + filter_upwards [hgcoord] with y hy + rw [←hy,mul_zpow,←Complex.ofReal_zpow,Complex.real_smul] + refine ⟨g,hgP,hg,hfg,?_⟩ + filter_upwards [hcoord,hlim.eventually hgcoord,eventually_gt_atTop (0:ℝ)] with x hx hgf hxp + apply Complex.ofReal_injective + rw [←hgf,hx,←Complex.ofReal_zpow,rootCoord_inverse_power hn hxp] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + + + +def radialInfinity : Filter ℂ := comap norm atTop + +def complexRoot (n : ℕ) (z : ℂ) : ℂ := z ^ ((-(n:ℝ)⁻¹ : ℝ):ℂ) + +lemma complexRoot_norm (n : ℕ) (z : ℂ) : + ‖complexRoot n z‖ = rootCoord n ‖z‖ := Complex.norm_cpow_real _ _ + +lemma complexRoot_real {n : ℕ} {x : ℝ} (hx : 0 ≤ x) : + complexRoot n (x:ℂ) = (rootCoord n x:ℂ) := (Complex.ofReal_cpow hx _).symm + +lemma complexRoot_tendsto_zero {n : ℕ} (hn : 0 < n) : + Tendsto (complexRoot n) radialInfinity (𝓝 0) := by + rw [tendsto_zero_iff_norm_tendsto_zero] + simpa only [complexRoot_norm,Function.comp_def,radialInfinity] using + (rootCoord_tendsto_zero hn).comp (tendsto_comap : Tendsto (norm : ℂ → ℝ) radialInfinity atTop) + +lemma complexRoot_analytic {n : ℕ} {z : ℂ} (hz : 0 < z.re) : + AnalyticAt ℂ (complexRoot n) z := + analyticAt_id.cpow analyticAt_const (Complex.mem_slitPlane_iff.mpr (Or.inl hz)) + +lemma complexRoot_zpow (n : ℕ) (m : ℤ) (z : ℂ) : + (complexRoot n z)^m = z ^ ((-(m:ℝ)/(n:ℝ):ℝ):ℂ) := by + rw [complexRoot,←Complex.cpow_mul_int] + congr 1 + push_cast + ring + +lemma radial_eventually {P : ℂ → Prop} (hP : ∀ᶠ z in radialInfinity, P z) : + ∃ R : ℝ, ∀ z : ℂ, R < ‖z‖ → P z := by + obtain ⟨R,hR⟩ := eventually_atTop.mp (eventually_comap.mp hP) + exact ⟨R,fun z hz => hR ‖z‖ hz.le z rfl⟩ + + + +theorem Puiseux.sector_leading {f : ℝ → ℂ} (hf : Puiseux f) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : + ∃ (q : ℚ) (C : ℂ) (G : ℂ → ℂ) (R : ℝ), C ≠ 0 ∧ + (∀ z : ℂ, R < ‖z‖ → 0 < z.re → AnalyticAt ℂ G z) ∧ + f =ᶠ[atTop] (fun t => G (t:ℂ)) ∧ + Tendsto (fun z => (z ^ ((q:ℝ):ℂ))⁻¹ * G z) radialInfinity (𝓝 C) := by + obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.normalize hne + let q : ℚ := -(m:ℚ)/(n:ℚ) + let G : ℂ → ℂ := fun z => (complexRoot n z)^m * F (complexRoot n z) + have hqa : ((q:ℝ):ℂ) = ((-(m:ℝ)/(n:ℝ):ℝ):ℂ) := by dsimp [q]; push_cast; rfl + obtain ⟨R,hR⟩ := radial_eventually ((complexRoot_tendsto_zero hn).eventually hF.eventually_analyticAt) + refine ⟨q,F 0,G,R,hF0,?_,?_,?_⟩ + · intro z hz hzre + have hr := complexRoot_analytic (n := n) hzre + have hr0 : complexRoot n z ≠ 0 := Complex.cpow_ne_zero_iff.mpr (Or.inl (by intro h; simp [h] at hzre)) + exact (hr.zpow hr0).mul ((hR z hz).comp hr) + · filter_upwards [he,eventually_gt_atTop (0:ℝ)] with t ht htpos + simpa only [G,complexRoot_real htpos.le,←Complex.ofReal_zpow,Complex.real_smul] using ht + · apply (hF.continuousAt.tendsto.comp (complexRoot_tendsto_zero hn)).congr' + have hpos : ∀ᶠ z in radialInfinity, (0:ℝ) < ‖z‖ := + (tendsto_comap : Tendsto (norm : ℂ → ℝ) radialInfinity atTop).eventually (eventually_gt_atTop 0) + filter_upwards [hpos] with z hz + have hz0 : z ≠ 0 := norm_pos_iff.mp hz + have hpow : z^((q:ℝ):ℂ) ≠ 0 := Complex.cpow_ne_zero_iff.mpr (Or.inl hz0) + simp only [G,complexRoot_zpow,←hqa,inv_mul_cancel_left₀ hpow,Function.comp_def] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma rootCoord_scaled_power {n k : ℕ} (hn : 0 < n) {v a : ℝ} + (hv : 0 < v) (ha : 0 < a) : + rootCoord n (v^(-((n*k:ℕ):ℤ))*a) = v^k * (a^(-(n:ℝ)⁻¹)) := by + rw [rootCoord,Real.mul_rpow (zpow_pos hv _).le ha.le] + congr 1 + rw [←Real.rpow_intCast,←Real.rpow_mul hv.le,←Real.rpow_natCast] + congr 1 + push_cast + field_simp + + + +theorem Puiseux.comp_unbounded {f : ℝ → ℂ} {g : ℝ → ℝ} + (hf : Puiseux f) (hg : Puiseux (fun t => (g t:ℂ))) + (hgt : Tendsto g atTop atTop) : Puiseux (fun t => f (g t)) := by + obtain ⟨n,hn,a,F,hF,he⟩ := hf + obtain ⟨m,k,hm,hk,G,hG,hGre,hGim,hge⟩ := hg.normalize_unbounded_real hgt + let A : ℂ → ℂ := fun v => G (v^n) + let Q : ℂ → ℂ := fun v => (A v)^(-(n:ℂ)⁻¹) + have hA : AnalyticAt ℂ A 0 := by + have hG' : AnalyticAt ℂ G ((0:ℂ)^n) := by simpa only [zero_pow hn.ne'] using hG + exact hG'.comp (f := fun v : ℂ => v^n) (analyticAt_id.pow n) + have hA0 : A 0 = G 0 := by simp [A,zero_pow hn.ne'] + have hQ : AnalyticAt ℂ Q 0 := hA.cpow analyticAt_const + (Complex.mem_slitPlane_iff.mpr (Or.inl (by simpa only [hA0] using hGre))) + have hQ0 : Q 0 ≠ 0 := Complex.cpow_ne_zero_iff.mpr (Or.inl (by + intro h; have := hGre; rw [←hA0,h] at this; norm_num at this)) + let H : ℂ → ℂ := fun v => (Q v)^a * F (v^k*Q v) + have hH : AnalyticAt ℂ H 0 := (hQ.zpow hQ0).mul (by + have h := (analyticAt_id.pow k).mul hQ + have hf : AnalyticAt ℂ F ((0:ℂ)^k*Q 0) := by simpa only [zero_pow hk.ne',zero_mul] using hF + exact hf.comp (f := fun v : ℂ => v^k*Q v) h) + refine ⟨m*n,Nat.mul_pos hm hn,(k:ℤ)*a,H,hH,?_⟩ + filter_upwards [hge,hgt.eventually he,eventually_gt_atTop (0:ℝ), + hgt.eventually (eventually_gt_atTop (0:ℝ))] + with t hge he ht hgtpos + let v : ℝ := rootCoord (m*n) t + have hv : 0 < v := rootCoord_pos ht + have hvn : v^n = rootCoord m t := rootCoord_pow hm hn ht + have haim : (A (v:ℂ)).im = 0 := by + have hi := congrArg Complex.im hge + have hp : (rootCoord m t)^(-(k:ℤ)) ≠ 0 := (zpow_pos (rootCoord_pos ht) _).ne' + simp only [Complex.ofReal_im,Complex.smul_im,smul_eq_mul] at hi + have hzero := (mul_eq_zero.mp hi.symm).resolve_left hp + simpa only [A,←Complex.ofReal_pow,hvn] using hzero + have hare : 0 < (A (v:ℂ)).re := by + have hr := congrArg Complex.re hge + have hp : 0 < (rootCoord m t)^(-(k:ℤ)) := zpow_pos (rootCoord_pos ht) _ + simp only [Complex.ofReal_re,Complex.smul_re,smul_eq_mul] at hr + have hapos : 0 < (G (rootCoord m t)).re := by nlinarith + simpa only [A,←Complex.ofReal_pow,hvn] using hapos + have hrealA : A (v:ℂ) = ((A (v:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using haim) + have hgval : g t = v^(-((n*k:ℕ):ℤ)) * (A (v:ℂ)).re := by + have hr := congrArg Complex.re hge + simp only [Complex.ofReal_re,Complex.smul_re,smul_eq_mul] at hr + rw [←hvn] at hr + calc + g t = (v^n)^(-(k:ℤ)) * (A (v:ℂ)).re := by + simpa only [A,←Complex.ofReal_pow] using hr + _ = v^(-((n*k:ℕ):ℤ)) * (A (v:ℂ)).re := by + rw [←zpow_natCast,←zpow_mul] + congr 2 + push_cast + ring + have hroot : (rootCoord n (g t):ℂ) = (v:ℂ)^k * Q (v:ℂ) := by + rw [hgval,rootCoord_scaled_power hn hv hare] + simp only [Complex.ofReal_mul,Complex.ofReal_pow] + congr 1 + change _ = (A (v:ℂ))^(-(n:ℂ)⁻¹) + conv_rhs => rw [hrealA] + rw [Complex.ofReal_cpow hare.le] + push_cast + rfl + rw [he,Complex.real_smul,Complex.ofReal_zpow,hroot] + simp only [H,mul_zpow,←zpow_natCast,←zpow_mul,Complex.real_smul,Complex.ofReal_zpow,mul_assoc] + rfl + + + +theorem Puiseux.change_coordinate {H : ℝ → ℝ} + (hH : Puiseux (fun t => (H t:ℂ))) (hHt : Tendsto H atTop atTop) : + ∃ I : ℝ → ℝ, Puiseux (fun t => (I t:ℂ)) ∧ Tendsto I atTop atTop ∧ + (∀ᶠ t in atTop, H (I t)=t) ∧ (∀ᶠ t in atTop, I (H t)=t) ∧ + ∀ f : ℝ → ℂ, Puiseux f → Puiseux (fun t => f (I t)) := by + obtain ⟨I,hI,hIt,hl,hr⟩ := hH.inverse_change hHt + exact ⟨I,hI,hIt,hl,hr,fun f hf => hf.comp_unbounded hI hIt⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma radial_real_tendsto : Tendsto (fun t : ℝ => (t:ℂ)) atTop radialInfinity := by + rw [radialInfinity,tendsto_comap_iff] + simpa only [Function.comp_def,Complex.norm_real,Real.norm_eq_abs] using + (tendsto_abs_atTop_atTop : Tendsto (abs : ℝ → ℝ) atTop atTop) + +lemma radial_norm_equivalent {q : ℝ} {C : ℂ} {F : ℂ → ℂ} + (hC : C ≠ 0) + (hF : Tendsto (fun z => (z^(q:ℂ))⁻¹*F z) radialInfinity (𝓝 C)) : + ∀ᶠ z in radialInfinity, + ‖C‖/2 * ‖z‖^q ≤ ‖F z‖ ∧ ‖F z‖ ≤ 2*‖C‖*‖z‖^q := by + have hCpos : 0 < ‖C‖ := norm_pos_iff.mpr hC + have hn := hF.norm + have hbounds := ((eventually_gt_nhds (show ‖C‖/2 < ‖C‖ by linarith)).and + (eventually_lt_nhds (show ‖C‖ < 2*‖C‖ by linarith))) + filter_upwards [hn.eventually hbounds, + (tendsto_comap : Tendsto (norm : ℂ → ℝ) radialInfinity atTop).eventually (eventually_gt_atTop 0)] + with z hz hzpos + have hp : 0 < ‖z‖^q := Real.rpow_pos_of_pos hzpos _ + simp only [norm_mul,norm_inv,Complex.norm_cpow_real] at hz + have hz' : ‖C‖/2 < ‖F z‖ / ‖z‖^q ∧ ‖F z‖ / ‖z‖^q < 2*‖C‖ := by + simpa only [div_eq_mul_inv,mul_comm] using hz + exact ⟨((lt_div_iff₀ hp).mp hz'.1).le,((div_lt_iff₀ hp).mp hz'.2).le⟩ + + + +theorem Puiseux.sector_modulus_comparable {f : ℝ → ℂ} (hf : Puiseux f) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : + ∃ (G : ℂ → ℂ) (R : ℝ), + (∀ z : ℂ, R < ‖z‖ → 0 < z.re → AnalyticAt ℂ G z) ∧ + f =ᶠ[atTop] (fun t => G (t:ℂ)) ∧ + ∀ z : ℂ, R < ‖z‖ → ‖f ‖z‖‖/4 ≤ ‖G z‖ ∧ ‖G z‖ ≤ 4*‖f ‖z‖‖ := by + obtain ⟨q,C,G,R,hC,hGa,he,hlim⟩ := hf.sector_leading hne + have hb := radial_norm_equivalent hC hlim + obtain ⟨S,hS⟩ := radial_eventually hb + obtain ⟨T,hT⟩ := eventually_atTop.mp he + refine ⟨G,max R (max S (max T 0)),?_,he,?_⟩ + · intro z hz hzre + exact hGa z ((le_max_left _ _).trans_lt hz) hzre + · intro z hz + have hSlt : S < ‖z‖ := (le_max_of_le_right (le_max_left _ _)).trans_lt hz + have hTle : T ≤ ‖z‖ := (le_max_of_le_right (le_max_of_le_right (le_max_left _ _))).trans hz.le + have hnorm : 0 ≤ ‖z‖ := norm_nonneg _ + have hreal := hS (‖z‖:ℂ) (by simpa only [Complex.norm_of_nonneg hnorm] using hSlt) + have heq : f ‖z‖ = G (‖z‖:ℂ) := hT _ hTle + rw [←heq] at hreal + simp only [Complex.norm_of_nonneg hnorm] at hreal + have hc := hS z hSlt + constructor <;> linarith + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RealClocks.lean b/lean/OAI/Analysis/PathSelection/RealClocks.lean new file mode 100644 index 0000000000000000000000000000000000000000..3506339fedf1f3e2904ddaf0771a9579dbd055ee --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RealClocks.lean @@ -0,0 +1,498 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockInverses + +namespace OAI + +/-! Real leading terms, conjugation and logarithmic derivative bounds. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma SectorExpansion.top_nonnegative {F : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hF : SectorExpansion F E b) {β : ℝ} (hmax : ∀ γ∈E,γ≤β) + (hlim : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) : 0≤β := by + by_contra hn + have hβ : β<0 := lt_of_not_ge hn + have hh := hF.negative_bound (δ := -β) (by linarith) + (fun γ hγ => by simpa using hmax γ hγ) + have ht := hh.tendsto_zero (by linarith : -(-β)/2<0) + have hz := (Complex.continuous_re.tendsto 0).comp (ht.comp tendsto_real_sectorInfinity) + exact not_tendsto_nhds_of_tendsto_atTop hlim 0 hz + + + +theorem ExpansionOver.puiseux_unbounded_leading {F : ℂ → ℂ} + (hF : ExpansionOver PuiseuxSector F) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hlim : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) : + ∃ β : ℝ,0≤β ∧ ∃ b : ℂ → ℂ,b∈PuiseuxSector ∧ + (¬ (fun t : ℝ => b (t:ℂ)) =ᶠ[atTop] fun _ => 0) ∧ + ExpSmall 0 (fun z => Complex.exp (((-β:ℝ):ℂ)*z)*(b z)⁻¹*F z-1) ∧ + Tendsto (fun z => deriv F z/F z) sectorInfinity (𝓝 (β:ℂ)) ∧ + (0<β → ∃ A T : ℝ,0 (hb β hβ).1) + have hn : (nonzeroRaySupport E b).Nonempty := by + by_contra he + rw [Set.not_nonempty_iff_eq_empty.mp he] at ht + have hz := ht.empty + have hfalse : ∀ᶠ t : ℝ in atTop,False := by + filter_upwards [hr,hz] with t hr hz + simpa [hz] using hr.2 + obtain ⟨t,ht⟩ := hfalse.exists + exact ht + obtain ⟨β,hβ,hmax⟩ := exists_greatest_of_finite_above ht.finite_above hn + have hbi := puiseux_lowerSectorData.slow (puiseux_lowerSectorData.inv_mem (hb β hβ.1)) + have hb0 : ∀ᶠ z in sectorInfinity,b β z≠0 := by + rcases puiseux_lowerSectorData.zero_or_ne (hb β hβ.1) with hz | hz + · exact False.elim (hβ.2 (tendsto_real_sectorInfinity.eventually hz)) + · exact hz + have hq := ht.log_deriv_tendsto (fun γ hγ => (hb γ hγ.1).1) hβ hmax hb0 hbi + (PuiseuxSector.log_deriv_tendsto (hb β hβ.1) hβ.2) + refine ⟨β,ht.top_nonnegative hmax hlim,b β,hb β hβ.1,hβ.2, + ht.uniform_leading hβ hmax hb0 hbi,hq,?_⟩ + intro hpos + exact positive_exponential_inverse hpos + (Filter.Eventually.filter_mono stripInfinity_le_sectorInfinity ht.eventually_analytic) + (Filter.Eventually.filter_mono stripInfinity_le_sectorInfinity (ht.eventually_ne_of_leading hβ hmax hb0 hbi)) + hr hlim (hq.mono_left stripInfinity_le_sectorInfinity) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma analyticAt_reflection {F : ℂ → ℂ} {z : ℂ} (hF : AnalyticAt ℂ F (star z)) : + AnalyticAt ℂ (fun w => star (F (star w))) z := by + rw [Complex.analyticAt_iff_eventually_differentiableAt] + have hc : Tendsto (star : ℂ → ℂ) (𝓝 z) (𝓝 (star z)) := continuous_star.continuousAt.tendsto + filter_upwards [hc.eventually hF.eventually_analyticAt] with w hw + simpa only [Function.comp_def, Complex.star_def, Complex.conj_conj] using hw.differentiableAt.conj_conj + +lemma mem_lossSector_star {ω : ℝ → ℝ} {R : ℝ} {z : ℂ} + (hz : z ∈ lossSector ω R) : star z ∈ lossSector ω R := by + have harg : |(star z).arg|=|z.arg| := by + rw [Complex.star_def,Complex.arg_conj] + split_ifs with h + · rw [h] + · exact abs_neg _ + simpa only [lossSector,mem_ofPred_eq,norm_star,harg] using hz + +lemma SectorExpansion.conj {f : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (h : SectorExpansion f E b) : + SectorExpansion (fun z => star (f (star z))) E (fun β z => star (b β (star z))) := by + classical + refine ⟨h.bounded_above,h.finite_above,?_⟩ + intro B + obtain ⟨ω,R,ε,C,hω,hε,hC,hf,hb⟩ := h.remainders B + refine ⟨ω,R,ε,C,hω,hε,hC,fun z hz => analyticAt_reflection (hf _ (mem_lossSector_star hz)),?_⟩ + intro z hz + have hbound := hb (star z) (mem_lossSector_star hz) + rw [←norm_star] at hbound + simpa only [star_sub,star_sum,star_mul,Complex.star_def,←Complex.exp_conj, + map_mul,Complex.conj_ofReal,Complex.conj_conj,Complex.conj_re,mul_comm] using hbound + +lemma ClockGerm.conj {xs : List (ℝ → ℝ)} {f : ℝ → ℂ} (hf : ClockGerm xs f) : + ClockGerm xs (fun t => star (f t)) := by + induction xs generalizing f with + | nil => exact Puiseux.conj hf + | cons X xs ih => + obtain ⟨F,E,b,hF,hb,he⟩ := hf + refine ⟨fun z => star (F (star z)),E,fun β z => star (b β (star z)),hF.conj,?_,?_⟩ + · intro β hβ + constructor + · simpa only [Complex.star_def,Complex.conj_ofReal] using ih (hb β hβ).1 + · obtain ⟨ω,R,hω,ha⟩ := (hb β hβ).2 + exact ⟨ω,R,hω,fun z hz => analyticAt_reflection (ha _ (mem_lossSector_star hz))⟩ + · filter_upwards [he] with t ht + simp only [ht,Complex.star_def,Complex.conj_ofReal] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma SectorExpansion.congr_coeff {F : ℂ → ℂ} {E : Set ℝ} {b c : ℝ → ℂ → ℂ} + (h : SectorExpansion F E b) (he : ∀ β∈E,b β=c β) : SectorExpansion F E c := by + refine ⟨h.bounded_above,h.finite_above,?_⟩ + intro B + obtain ⟨ω,R,ε,C,hω,hε,hC,ha,hb⟩ := h.remainders B + refine ⟨ω,R,ε,C,hω,hε,hC,ha,?_⟩ + intro z hz + convert hb z hz using 1 + congr 2 + apply Finset.sum_congr rfl + intro β hβ + rw [he β ((h.finite_above B).mem_toFinset.mp hβ).1] + +lemma SectorExpansion.add_same {F G : ℂ → ℂ} {E : Set ℝ} {b c : ℝ → ℂ → ℂ} + (hF : SectorExpansion F E b) (hG : SectorExpansion G E c) : + SectorExpansion (fun z => F z+G z) E (fun β z => b β z+c β z) := by + classical + have hh := hF.add hG + rw [union_self] at hh + apply hh.congr_coeff + intro β hβ + simp only [ite_eq_left hβ] + +lemma PuiseuxSector.reflect {F : ℂ → ℂ} (hF : F∈PuiseuxSector) : + (fun z => star (F (star z)))∈PuiseuxSector := by + refine ⟨?_,?_⟩ + · obtain ⟨ω,R,hω,ha⟩ := hF.1 + exact ⟨ω,R,hω,fun z hz => analyticAt_reflection (ha _ (mem_lossSector_star hz))⟩ + · simpa only [Complex.star_def,Complex.conj_ofReal] using hF.2.conj + +lemma ExpansionOver.puiseux_real_expansion {F : ℂ → ℂ} (hF : ExpansionOver PuiseuxSector F) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) : + ∃ E : Set ℝ,∃ b : ℝ → ℂ → ℂ,SectorExpansion F E b ∧ + (∀ β∈E,b β∈PuiseuxSector) ∧ (∀ β t : ℝ,(b β (t:ℂ)).im=0) := by + obtain ⟨E,b,hF,hb⟩ := hF + let c : ℂ := 1/2 + have hc := puiseux_lowerSectorData.const_mem c + have hs := (hF.add_same hF.conj).mul_lower hc.1 (puiseux_lowerSectorData.slow hc) + have he : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)+star (F (star (t:ℂ))))*c=F (t:ℂ) := by + filter_upwards [hr] with t ht + have heq : F (t:ℂ)=((F (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using ht) + simp only [Complex.star_def,Complex.conj_ofReal] + rw [heq,Complex.conj_ofReal] + dsimp [c] + ring + have he' := sector_analytic_eq_of_ray hs.eventually_analytic hF.eventually_analytic he + refine ⟨E,fun β z => (b β z+star (b β (star z)))*c,hs.congr he',?_,?_⟩ + · intro β hβ + exact puiseux_lowerSectorData.mul_mem + (puiseux_lowerSectorData.add_mem (hb β hβ) (PuiseuxSector.reflect (hb β hβ))) hc + · intro β t + simp [c,Complex.mul_im] + +lemma positive_real_factor_of_normalized {F b : ℂ → ℂ} {β : ℝ} + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hbr : ∀ᶠ t : ℝ in atTop,(b (t:ℂ)).im=0) + (ht : Tendsto (fun t : ℝ => Complex.exp (((-β:ℝ):ℂ)*(t:ℂ))*(b (t:ℂ))⁻¹*F (t:ℂ)) atTop (𝓝 1)) : + ∀ᶠ t : ℝ in atTop,0<(b (t:ℂ)).re := by + have hr := (Complex.continuous_re.tendsto 1).comp ht + simp only [Complex.one_re] at hr + filter_upwards [hr.eventually (eventually_gt_nhds zero_lt_one),hFr,hbr] with t hp hf hb + have hF : F (t:ℂ)=((F (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hf.1) + have hB : b (t:ℂ)=((b (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hb) + dsimp only [Function.comp_apply] at hp + rw [hF,hB,←Complex.ofReal_mul,←Complex.ofReal_exp,←Complex.ofReal_inv,←Complex.ofReal_mul,←Complex.ofReal_mul,Complex.ofReal_re] at hp + have hinv : 0<((b (t:ℂ)).re)⁻¹ := by + have hm := (mul_pos_iff_of_pos_right hf.2).mp hp + exact (mul_pos_iff_of_pos_left (Real.exp_pos _)).mp hm + exact inv_pos.mp hinv + + + +theorem ExpansionOver.puiseux_positive_leading {F : ℂ → ℂ} + (hF : ExpansionOver PuiseuxSector F) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hlim : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) : + ∃ β : ℝ,0≤β ∧ ∃ b : ℂ → ℂ,b∈PuiseuxSector ∧ + (∀ᶠ z in sectorInfinity,b z≠0) ∧ + (∀ᶠ t : ℝ in atTop,(b (t:ℂ)).im=0 ∧ 0<(b (t:ℂ)).re) ∧ + ExpSmall 0 (fun z => Complex.exp (((-β:ℝ):ℂ)*z)*(b z)⁻¹*F z-1) ∧ + Tendsto (fun z => deriv F z/F z) sectorInfinity (𝓝 (β:ℂ)) := by + obtain ⟨E,b,hF,hb,hbr⟩ := hF.puiseux_real_expansion (hr.mono fun _ h => h.1) + have ht := hF.trim_zero (fun β hβ => (hb β hβ).1) + have hn : (nonzeroRaySupport E b).Nonempty := by + by_contra he + rw [Set.not_nonempty_iff_eq_empty.mp he] at ht + have hz := ht.empty + obtain ⟨t,hr,hz⟩ := (hr.and hz).exists + have hh : 0<(F (t:ℂ)).re := hr.2 + change F (t:ℂ)=0 at hz + rw [hz,Complex.zero_re] at hh + exact lt_irrefl _ hh + obtain ⟨β,hβ,hmax⟩ := exists_greatest_of_finite_above ht.finite_above hn + have hbi := puiseux_lowerSectorData.slow (puiseux_lowerSectorData.inv_mem (hb β hβ.1)) + have hb0 : ∀ᶠ z in sectorInfinity,b β z≠0 := by + rcases puiseux_lowerSectorData.zero_or_ne (hb β hβ.1) with hz | hz + · exact False.elim (hβ.2 (tendsto_real_sectorInfinity.eventually hz)) + · exact hz + have hu := ht.uniform_leading hβ hmax hb0 hbi + have hbt := positive_real_factor_of_normalized hr (Eventually.of_forall (hbr β)) + ((ht.uniform_leading_tendsto hβ hmax hb0 hbi).comp tendsto_real_sectorInfinity) + exact ⟨β,ht.top_nonnegative hmax hlim,b β,hb β hβ.1,hb0, + (Eventually.of_forall (hbr β)).and hbt,hu, + ht.log_deriv_tendsto (fun γ hγ => (hb γ hγ.1).1) hβ hmax hb0 hbi + (PuiseuxSector.log_deriv_tendsto (hb β hβ.1) hβ.2)⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Complex Metric +namespace DegeneratingTrees.Clock + +lemma log_deriv_bound_of_log_norm_bound {F : ℂ → ℂ} {z : ℂ} {R M : ℝ} + (hR : 0 L (z+v)-L z + have hmem {v : ℂ} (hv : v∈ball 0 R) : z+v∈ball z R := by + simpa only [mem_ball_iff_norm,add_sub_cancel_left,sub_zero] using hv + have hKa : AnalyticOnNhd ℂ K (ball 0 R) := by + intro v hv + exact ((hLa _ (hmem hv)).comp (analyticAt_const.add analyticAt_id)).sub analyticAt_const + have hKre : MapsTo K (ball 0 R) {v | v.re≤2*M} := by + intro v hv + change (L (z+v)).re-(L z).re≤2*M + have h1 := abs_le.mp (hLre _ (hmem hv)) + have h0 := abs_le.mp (hLre _ (mem_ball_self hR)) + linarith + have hKb (v : ℂ) (hv : v∈sphere 0 (R/2)) : ‖K v‖≤4*M := by + have hn : ‖v‖=R/2 := by simpa only [mem_sphere_iff_norm,sub_zero] using hv + have hvR : v∈ball 0 R := by rw [mem_ball_zero_iff,hn]; linarith + have hh := Complex.borelCaratheodory_zero (f := K) (by positivity : 0<2*M) + hKa.differentiableOn hKre hR hvR (by simp [K]) + rw [hn] at hh + convert hh using 1 + field_simp + ring + have hs : closure (ball (0:ℂ) (R/2)) ⊆ ball 0 R := by + rw [closure_ball _ (by positivity : R/2≠0)] + intro v hv + rw [mem_ball_zero_iff] + have hn : ‖v‖≤R/2 := by simpa only [mem_closedBall_iff_norm,sub_zero] using hv + linarith + have hc : DiffContOnCl ℂ K (ball 0 (R/2)) := + ((hKa.mono hs).differentiableOn).diffContOnCl + have hd := Complex.norm_deriv_le_of_forall_mem_sphere_norm_le (by positivity : 0 (F z)⁻¹)) : + Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 0) := by + apply Metric.tendsto_nhds.mpr + intro ε hε + let δ := ε/512 + have hδ : 0<δ := by dsimp [δ]; positivity + obtain ⟨C,hC,hCb⟩ := (hf δ hδ).exists_pos + obtain ⟨D,hD,hDb⟩ := (hi δ hδ).exists_pos + have hbound : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z ∧ F z≠0 ∧ + |Real.log ‖F z‖|≤|Real.log C|+|Real.log D|+δ*z.re := by + filter_upwards [hFa,hF0,hCb.bound,hDb.bound] with z ha hz hc hd + simp only [Real.norm_eq_abs,abs_of_pos (Real.exp_pos _),norm_inv] at hc hd + have hn : 0<‖F z‖ := norm_pos_iff.mpr hz + have hu := Real.log_le_log hn hc + have hl := Real.log_le_log (inv_pos.mpr hn) hd + rw [Real.log_mul hC.ne' (Real.exp_ne_zero _),Real.log_exp] at hu + rw [Real.log_mul hD.ne' (Real.exp_ne_zero _),Real.log_exp,Real.log_inv] at hl + refine ⟨ha,hz,abs_le.mpr ⟨?_,?_⟩⟩ + · linarith [le_abs_self (Real.log D),abs_nonneg (Real.log C)] + · linarith [le_abs_self (Real.log C),abs_nonneg (Real.log D)] + obtain ⟨ω,S,hω,hS⟩ := hbound + intro W + obtain ⟨T,hT⟩ := eventually_atTop.mp (hω.real_discs S) + let K := |Real.log C|+|Real.log D|+1 + have hK : 0 simp + rw [he,norm_mul,Complex.norm_I,Complex.norm_real,Real.norm_eq_abs,one_mul] + have hvn : ‖v-z‖ (hS v (hdisc hv)).1) (fun v hv => (hS v (hdisc hv)).2.1) hlog + change dist (deriv F z/F z) 0<ε + rw [dist_zero_right] + apply hd.trans_lt + rw [div_lt_iff₀ (by positivity : 0 deriv F z/F z) stripInfinity (𝓝 0) := + SectorSlow.log_deriv_tendsto (hK.analytic hF) hn (hK.slow hF) (hK.slow (hK.inv_mem hF)) + +lemma SectorExpansion.log_deriv_strip {F : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hF : SectorExpansion F E b) (ha : ∀ β∈E,∀ᶠ z in sectorInfinity,AnalyticAt ℂ (b β) z) + {β : ℝ} (hβ : β∈E) (hmax : ∀ γ∈E,γ≤β) + (hb0 : ∀ᶠ z in sectorInfinity,b β z≠0) (hbi : SectorSlow (fun z => (b β z)⁻¹)) + (hq : Tendsto (fun z => _root_.deriv (b β) z/b β z) stripInfinity (𝓝 0)) : + Tendsto (fun z => _root_.deriv F z/F z) stripInfinity (𝓝 (β:ℂ)) := by + have hFd := hF.deriv ha + have herr := ((hFd.leading_error hβ hmax).mul (ExpBound.cexp (-β))).mul_slow hbi + simp only [add_neg_cancel] at herr + have hn : Tendsto (fun z => Complex.exp (((-β:ℝ):ℂ)*z)*(b β z)⁻¹*_root_.deriv F z) + stripInfinity (𝓝 (β:ℂ)) := by + have ht := (herr.tendsto_zero.mono_left stripInfinity_le_sectorInfinity).add ((tendsto_const_nhds (x := (β:ℂ))).add hq) + simp only [add_zero,zero_add] at ht + apply ht.congr' + filter_upwards [hb0.filter_mono stripInfinity_le_sectorInfinity] with z hz + have he : Complex.exp (((-β:ℝ):ℂ)*z)=(Complex.exp ((β:ℂ)*z))⁻¹ := by + rw [←Complex.exp_neg]; congr 1; push_cast; ring + rw [he] + field_simp [hz,Complex.exp_ne_zero] + ring + have hu := (hF.uniform_leading_tendsto hβ hmax hb0 hbi).mono_left stripInfinity_le_sectorInfinity + have ht := hn.div hu (by norm_num : (1:ℂ)≠0) + simp only [div_one] at ht + apply ht.congr' + filter_upwards [hb0.filter_mono stripInfinity_le_sectorInfinity, + (hF.eventually_ne_of_leading hβ hmax hb0 hbi).filter_mono stripInfinity_le_sectorInfinity] with z hz hFz + change (Complex.exp (((-β:ℝ):ℂ)*z)*(b β z)⁻¹*_root_.deriv F z) / + (Complex.exp (((-β:ℝ):ℂ)*z)*(b β z)⁻¹*F z)=_root_.deriv F z/F z + field_simp [hz,hFz,Complex.exp_ne_zero] + +lemma ExpansionOver.real_expansion {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) {F : ℂ → ℂ} (hF : ExpansionOver K F) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) : + ∃ E : Set ℝ,∃ b : ℝ → ℂ → ℂ,SectorExpansion F E b ∧ + (∀ β∈E,b β∈K) ∧ (∀ β t : ℝ,(b β (t:ℂ)).im=0) := by + obtain ⟨E,b,hF,hb⟩ := hF + let c : ℂ := 1/2 + have hc := hK.const_mem c + have hs := (hF.add_same hF.conj).mul_lower (hK.analytic hc) (hK.slow hc) + have he : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)+star (F (star (t:ℂ))))*c=F (t:ℂ) := by + filter_upwards [hr] with t ht + have heq : F (t:ℂ)=((F (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using ht) + simp only [Complex.star_def,Complex.conj_ofReal] + rw [heq,Complex.conj_ofReal] + dsimp [c] + ring + have he' := sector_analytic_eq_of_ray hs.eventually_analytic hF.eventually_analytic he + refine ⟨E,fun β z => (b β z+star (b β (star z)))*c,hs.congr he',?_,?_⟩ + · intro β hβ + exact hK.mul_mem + (hK.add_mem (hb β hβ) (hconj _ (hb β hβ))) hc + · intro β t + simp [c,Complex.mul_im] + +theorem ExpansionOver.positive_leading_strip {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) {F : ℂ → ℂ} + (hF : ExpansionOver K F) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hlim : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) : + ∃ β : ℝ,0≤β ∧ ∃ b : ℂ → ℂ,b∈K ∧ + (∀ᶠ z in sectorInfinity,b z≠0) ∧ + (∀ᶠ t : ℝ in atTop,(b (t:ℂ)).im=0 ∧ 0<(b (t:ℂ)).re) ∧ + ExpSmall 0 (fun z => Complex.exp (((-β:ℝ):ℂ)*z)*(b z)⁻¹*F z-1) ∧ + Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 (β:ℂ)) := by + obtain ⟨E,b,hF,hb,hbr⟩ := hF.real_expansion hK hconj (hr.mono fun _ h => h.1) + have ht := hF.trim_zero (fun β hβ => hK.analytic (hb β hβ)) + have hn : (nonzeroRaySupport E b).Nonempty := by + by_contra he + rw [Set.not_nonempty_iff_eq_empty.mp he] at ht + have hz := ht.empty + obtain ⟨t,hr,hz⟩ := (hr.and hz).exists + have hh : 0<(F (t:ℂ)).re := hr.2 + change F (t:ℂ)=0 at hz + rw [hz,Complex.zero_re] at hh + exact lt_irrefl _ hh + obtain ⟨β,hβ,hmax⟩ := exists_greatest_of_finite_above ht.finite_above hn + have hbi := hK.slow (hK.inv_mem (hb β hβ.1)) + have hb0 : ∀ᶠ z in sectorInfinity,b β z≠0 := by + rcases hK.zero_or_ne (hb β hβ.1) with hz | hz + · exact False.elim (hβ.2 (tendsto_real_sectorInfinity.eventually hz)) + · exact hz + have hu := ht.uniform_leading hβ hmax hb0 hbi + have hbt := positive_real_factor_of_normalized hr (Eventually.of_forall (hbr β)) + ((ht.uniform_leading_tendsto hβ hmax hb0 hbi).comp tendsto_real_sectorInfinity) + exact ⟨β,ht.top_nonnegative hmax hlim,b β,hb β hβ.1,hb0, + (Eventually.of_forall (hbr β)).and hbt,hu, + ht.log_deriv_strip (fun γ hγ => hK.analytic (hb γ hγ.1)) hβ hmax hb0 hbi + (hK.log_deriv_strip (hb β hβ.1) hb0)⟩ + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RealInverses.lean b/lean/OAI/Analysis/PathSelection/RealInverses.lean new file mode 100644 index 0000000000000000000000000000000000000000..016fcc711770d5cfc63b7463d3c387e1bd7eef1d --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RealInverses.lean @@ -0,0 +1,347 @@ +import Mathlib +import OAI.Analysis.PathSelection.PerturbativeInverses +import OAI.Analysis.PathSelection.RealClocks + +namespace OAI + +/-! Real perturbative inverses and near-identity sector transfer. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma sector_reflection_of_real {F : ℂ → ℂ} + (hF : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) : + ∀ᶠ z in sectorInfinity,F (star z)=star (F z) := by + have ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => star (F (star z))) z := by + obtain ⟨ω,R,hω,hF⟩ := hF + exact ⟨ω,R,hω,fun z hz => analyticAt_reflection (hF _ (mem_lossSector_star hz))⟩ + obtain ⟨ω,R,hω,hA⟩ := (hF.and ha).mono (fun z hz => hz.1.sub hz.2) + have hz : ∀ᶠ t : ℝ in atTop,F (t:ℂ)-star (F (star (t:ℂ)))=0 := by + filter_upwards [hr] with t ht + apply sub_eq_zero.mpr + apply Complex.ext <;> simp [ht] + have hzero := sector_zero_of_ray_zero hω hA hz + filter_upwards [hzero] with z hz + have hh := congrArg star (sub_eq_zero.mp hz) + simpa only [star_star] using hh.symm + +lemma real_part_tendsto_of_perturbation {F : ℂ → ℂ} + (he : (fun z => F z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) : + Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop := by + have hbase := admissible_baseLoss.tendsto_zero.eventually + (eventually_le_nhds (show (0:ℝ) < 1/2 by norm_num)) + have hlower : ∀ᶠ t : ℝ in atTop,t/2 ≤ (F (t:ℂ)).re := by + filter_upwards [tendsto_real_sectorInfinity.eventually (he.bound zero_lt_one),hbase, + eventually_gt_atTop (1:ℝ)] with t ht hb ht1 + have ht0 : 0 < t := zero_lt_one.trans ht1 + have hn : ‖(t:ℂ)‖=t := Complex.norm_of_nonneg ht0.le + have hr : 0 < logarithmicRadius t := logarithmicRadius_pos ht1 + have hh : ‖F (t:ℂ)-(t:ℂ)‖ ≤ logarithmicRadius t := by + simpa only [hn,Real.norm_eq_abs,abs_of_pos hr,one_mul] using ht + have hrep := (Complex.abs_re_le_norm (F (t:ℂ)-(t:ℂ))).trans hh + rw [Complex.sub_re,Complex.ofReal_re,abs_le] at hrep + have hb' := mul_le_mul_of_nonneg_left hb ht0.le + dsimp [baseLoss] at hb' + dsimp [logarithmicRadius] at hrep + nlinarith [hrep.1] + exact tendsto_atTop_mono' atTop hlower ((tendsto_id.const_mul_atTop (by norm_num : (0:ℝ) < 1/2)).congr (fun t => by dsimp; ring)) + + + +theorem sector_perturbative_real_inverse {F : ℂ → ℂ} + (hF : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (he : (fun z => F z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) + (hr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0) + (ω : ℝ → ℝ) (R : ℝ) (hω : AdmissibleAngularLoss ω) : + ∃ (η : ℝ → ℝ) (T : ℝ) (g : ℂ → ℂ) (I : ℝ → ℝ),AdmissibleAngularLoss η ∧ + AnalyticOnNhd ℂ g (lossSector η T) ∧ + (∀ z∈lossSector η T,g z∈lossSector ω R ∧ F (g z)=z ∧ ‖g z-z‖ ≤ 2*‖F z-z‖) ∧ + Tendsto I atTop atTop ∧ + (∀ᶠ t : ℝ in atTop,g (t:ℂ)=(I t:ℂ) ∧ F (I t:ℂ)=(t:ℂ)) ∧ + (∀ᶠ t : ℝ in atTop,I ((F (t:ℂ)).re)=t) := by + have htarget : ∀ᶠ z in sectorInfinity,z∈lossSector ω R := ⟨ω,R,hω,fun _ h => h⟩ + obtain ⟨θ,S,hθ,hdata⟩ := htarget.and (sector_reflection_of_real hF hr) + obtain ⟨η,T,g,hη,hga,hg,hu⟩ := sector_perturbative_inverse_unique hF he θ S hθ + have hdom : ∀ᶠ z in sectorInfinity,z∈lossSector η T := ⟨η,T,hη,fun _ h => h⟩ + let I : ℝ → ℝ := fun t => (g (t:ℂ)).re + have hreal : ∀ᶠ t : ℝ in atTop,g (t:ℂ)=(I t:ℂ) ∧ F (I t:ℂ)=(t:ℂ) := by + filter_upwards [tendsto_real_sectorInfinity.eventually hdom,eventually_gt_atTop (1:ℝ)] with t ht ht1 + have hn : ‖(t:ℂ)‖=t := Complex.norm_of_nonneg (by linarith) + have hrad : 0 < logarithmicRadius ‖(t:ℂ)‖ := by rw [hn]; exact logarithmicRadius_pos ht1 + have hconj : ‖star (g (t:ℂ))-(t:ℂ)‖=‖g (t:ℂ)-(t:ℂ)‖ := by + rw [show star (g (t:ℂ))-(t:ℂ)=star (g (t:ℂ)-(t:ℂ)) by simp]; exact norm_star _ + have hmem : star (g (t:ℂ))∈ball (t:ℂ) (logarithmicRadius ‖(t:ℂ)‖) := by + rw [mem_ball_iff_norm,hconj] + exact (hg _ ht).2.2.2.trans_lt (by linarith) + have hroot : F (star (g (t:ℂ)))=(t:ℂ) := by + rw [(hdata _ (hg _ ht).1).2,(hg _ ht).2.1] + simp + have heq := hu _ ht _ hmem hroot + have him : (g (t:ℂ)).im=0 := by + have hh := congrArg Complex.im heq + simp only [Complex.star_def,Complex.conj_im] at hh + linarith + have heq' : g (t:ℂ)=(I t:ℂ) := Complex.ext rfl (by simpa using him) + exact ⟨heq',by rw [←heq']; exact (hg _ ht).2.1⟩ + have hIt : Tendsto I atTop atTop := by + have hlower : ∀ᶠ t : ℝ in atTop,t/2 ≤ I t := by + filter_upwards [tendsto_real_sectorInfinity.eventually hdom, + admissible_baseLoss.tendsto_zero.eventually (eventually_le_nhds zero_lt_one), + eventually_gt_atTop (1:ℝ)] with t ht hb ht1 + have ht0 : 0 < t := by linarith + have hn : ‖(t:ℂ)‖=t := Complex.norm_of_nonneg ht0.le + have hh := (Complex.abs_re_le_norm (g (t:ℂ)-(t:ℂ))).trans (hg _ ht).2.2.2 + rw [Complex.sub_re,Complex.ofReal_re,hn,abs_le] at hh + have hb' := mul_le_mul_of_nonneg_left hb ht0.le + dsimp [baseLoss] at hb' + dsimp [logarithmicRadius] at hh + dsimp [I] + nlinarith [hh.1] + exact tendsto_atTop_mono' atTop hlower ((tendsto_id.const_mul_atTop (by norm_num : (0:ℝ) < 1/2)).congr (fun t => by dsimp; ring)) + refine ⟨η,T,g,I,hη,hga,fun z hz => ⟨(hdata _ (hg z hz).1).1,(hg z hz).2.1,(hg z hz).2.2.1⟩,hIt,hreal,?_⟩ + have hFt := real_part_tendsto_of_perturbation he + have hFreal : ∀ᶠ t : ℝ in atTop,F (t:ℂ)=((F (t:ℂ)).re:ℂ) := hr.mono fun t ht => Complex.ext rfl (by simpa using ht) + filter_upwards [hFreal,hFt.eventually (tendsto_real_sectorInfinity.eventually hdom), + hFt.eventually (eventually_gt_atTop (4:ℝ)),eventually_gt_atTop (4:ℝ), + tendsto_real_sectorInfinity.eventually (he.bound (by norm_num : (0:ℝ) < 1/32)), + admissible_baseLoss.tendsto_zero.eventually (eventually_le_nhds zero_lt_one)] with t hrt htη hFt4 ht4 heb hb + have ht1 : 1 < t := by linarith + have ht0 : 0 < t := by linarith + have hF0 : 0 < (F (t:ℂ)).re := by linarith + have hn : ‖(t:ℂ)‖=t := Complex.norm_of_nonneg ht0.le + have hFn : ‖F (t:ℂ)‖=(F (t:ℂ)).re := by rw [hrt]; exact Complex.norm_of_nonneg hF0.le + have hηt : F (t:ℂ)∈lossSector η T := by rwa [hrt] + have hrad : 0 < logarithmicRadius t := logarithmicRadius_pos ht1 + have he' : ‖F (t:ℂ)-(t:ℂ)‖ ≤ (1/32:ℝ)*logarithmicRadius t := by + simpa only [hn,Real.norm_eq_abs,abs_of_pos hrad] using heb + have hrle : logarithmicRadius t ≤ t := by + have hh := mul_le_mul_of_nonneg_left hb ht0.le + simpa only [logarithmicRadius,baseLoss,mul_one] using hh + have hdist : |(F (t:ℂ)).re-t| ≤ t/2 := by + have hh := (Complex.abs_re_le_norm (F (t:ℂ)-(t:ℂ))).trans he' + simp only [Complex.sub_re,Complex.ofReal_re] at hh + exact hh.trans (by linarith) + have hneighbor := logarithmicRadius_neighbor hFt4.le + (show (F (t:ℂ)).re/2 ≤ t by linarith [(abs_le.mp hdist).2]) + (show t ≤ 2*(F (t:ℂ)).re by linarith [(abs_le.mp hdist).1]) + have hmem : (t:ℂ)∈ball (F (t:ℂ)) (logarithmicRadius ‖F (t:ℂ)‖) := by + rw [mem_ball_iff_norm,norm_sub_rev,hFn] + have hfrr := logarithmicRadius_pos (show 1 < (F (t:ℂ)).re by linarith) + linarith + have hleft := hu _ hηt _ hmem rfl + dsimp [I] + rw [←hrt,hleft] + simp + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +theorem sector_log_increment_small {Q g : ℂ → ℂ} {C : ℝ} + (hC : 0 ≤ C) (hQ : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ Q z) + (hQb : ∀ᶠ z in sectorInfinity,‖Q z‖ ≤ C*Real.log ‖z‖) + (hm : ∀ᶠ z in sectorInfinity,‖g z-z‖ ≤ logarithmicRadius ‖z‖) + (hg : (fun z => g z-z) =o[sectorInfinity] (fun z => ‖z‖/(Real.log ‖z‖)^5)) : + (fun z => Q (g z)-Q z) =o[sectorInfinity] (fun z => (Real.log ‖z‖)⁻¹^2) := by + obtain ⟨ω,R,hω,hdata⟩ := hQ.and hQb + obtain ⟨η,T,hη,hRT,hT1,hdiscs⟩ := hω.logarithmic_discs R (show (0:ℝ) ≤ 2 by norm_num) + have hdom : ∀ᶠ z in sectorInfinity,z∈lossSector η T := ⟨η,T,hη,fun _ h => h⟩ + have hbase : ∀ᶠ z in sectorInfinity,(Real.log ‖z‖)⁻¹^2 ≤ (1/4:ℝ) := + tendsto_norm_sectorInfinity.eventually (admissible_baseLoss.tendsto_zero.eventually + (eventually_le_nhds (by norm_num : (0:ℝ) < 1/4))) + apply Asymptotics.IsLittleO.of_bound + intro δ hδ + have hconst : 0 < δ/(2*(C+1)) := by positivity + filter_upwards [hdom,hbase,hm,hg.bound hconst, + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (4:ℝ))] with z hz hb hm he hz4 + let r := logarithmicRadius ‖z‖ + have hz1 : 1 < ‖z‖ := by linarith + have hL : 0 < Real.log ‖z‖ := Real.log_pos hz1 + have hr : 0 < r := logarithmicRadius_pos hz1 + have hrbound : 2*r ≤ ‖z‖/2 := by + have hh := mul_le_mul_of_nonneg_left hb (norm_nonneg z) + dsimp [r,logarithmicRadius] + nlinarith + have hdisc : closedBall z (2*r) ⊆ lossSector ω R := by + convert hdiscs z hz using 1 + dsimp [r,logarithmicRadius]; ring_nf + have hM (u : ℂ) (hu : u∈closedBall z (2*r)) : ‖Q u‖ ≤ 2*(C+1)*Real.log ‖z‖ := by + have hdist : ‖u-z‖ ≤ 2*r := mem_closedBall_iff_norm.mp hu + have hnu : ‖u‖ ≤ ‖z‖^2 := by + have hh := norm_add_le (u-z) z + rw [sub_add_cancel] at hh + nlinarith + have hlu : ‖z‖/2 ≤ ‖u‖ := by + have hh := norm_sub_le u (u-z) + rw [sub_sub_cancel] at hh + linarith + have hu0 : 0 < ‖u‖ := by linarith + have hl : Real.log ‖u‖ ≤ 2*Real.log ‖z‖ := by + simpa only [Real.log_pow,Nat.cast_ofNat] using Real.log_le_log hu0 hnu + have hh := mul_le_mul_of_nonneg_left hl hC + exact (hdata u (hdisc hu)).2.trans (by nlinarith) + have hinc := cauchy_increment_inner_disc hr (fun u hu => (hdata u (hdisc hu)).1) hM + (mem_closedBall_self hr.le) (mem_closedBall_iff_norm.mpr hm) + have hN : 0 < ‖z‖/(Real.log ‖z‖)^5 := by positivity + have he' : ‖g z-z‖ ≤ (δ/(2*(C+1)))*(‖z‖/(Real.log ‖z‖)^5) := by + simpa only [Real.norm_eq_abs,abs_of_pos hN] using he + have ht := mul_le_mul_of_nonneg_left he' (show 0 ≤ (2*(C+1)*Real.log ‖z‖)/r by positivity) + have heq : (2*(C+1)*Real.log ‖z‖)/r * ((δ/(2*(C+1)))*(‖z‖/(Real.log ‖z‖)^5)) = + δ*((Real.log ‖z‖)⁻¹^2) := by + dsimp [r,logarithmicRadius] + field_simp [hL.ne',show C+1≠0 by linarith,show ‖z‖≠0 by linarith] + rw [heq] at ht + simpa only [Real.norm_eq_abs,abs_of_nonneg (sq_nonneg ((Real.log ‖z‖)⁻¹))] using hinc.trans ht + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma tendsto_sectorInfinity_of_logarithmic_displacement {g : ℂ → ℂ} + (hg : ∀ᶠ z in sectorInfinity,‖g z-z‖ ≤ logarithmicRadius ‖z‖) : + Tendsto g sectorInfinity sectorInfinity := by + apply Filter.tendsto_def.mpr + intro s hs + obtain ⟨ω,R,hω,hs⟩ := hs + obtain ⟨η,T,hη,hRT,hT,hdisc⟩ := hω.logarithmic_discs R (show (0:ℝ) ≤ 1 by norm_num) + have hdom : ∀ᶠ z in sectorInfinity,z∈lossSector η T := ⟨η,T,hη,fun _ h => h⟩ + filter_upwards [hg,hdom] with z hg hz + apply hs + apply hdisc z hz + simpa only [mem_closedBall_iff_norm,one_mul,logarithmicRadius] using hg + +lemma logarithmicRadius_isBigO_re : + (fun z : ℂ => logarithmicRadius ‖z‖) =O[sectorInfinity] Complex.re := by + apply Asymptotics.IsBigO.of_bound 2 + have hb := tendsto_norm_sectorInfinity.eventually (admissible_baseLoss.tendsto_zero.eventually + (eventually_le_nhds (show (0:ℝ) < Real.pi/2 by positivity))) + have hdom : ∀ᶠ z in sectorInfinity,z∈lossSector baseLoss 1 := ⟨baseLoss,1,admissible_baseLoss,fun _ h => h⟩ + filter_upwards [hb,hdom,SectorEventually.realpart_pos] with z hb hz hzr + have hp := logarithmicRadius_pos hz.1 + have hh := half_loss_norm_le_re (by dsimp [baseLoss]; positivity : 0 ≤ baseLoss ‖z‖) hb hz.2 + rw [Real.norm_eq_abs,Real.norm_eq_abs,abs_of_pos hp,abs_of_pos hzr] + dsimp [logarithmicRadius,baseLoss] at * + linarith + +lemma logarithmicRadius_isBigO_norm : + (fun z : ℂ => logarithmicRadius ‖z‖) =O[sectorInfinity] (norm : ℂ → ℝ) := by + apply Asymptotics.IsBigO.of_bound 1 + filter_upwards [tendsto_norm_sectorInfinity.eventually + (admissible_baseLoss.tendsto_zero.eventually (eventually_le_nhds zero_lt_one)), + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hb hz + have hh := mul_le_mul_of_nonneg_left hb (norm_nonneg z) + rw [Real.norm_eq_abs,Real.norm_eq_abs,abs_of_pos (logarithmicRadius_pos hz),abs_of_nonneg (norm_nonneg z),one_mul] + simpa only [logarithmicRadius,baseLoss,mul_one] using hh + +lemma nearIdentity_re_tendsto {g : ℂ → ℂ} + (hg : (fun z => g z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) : + Tendsto (fun z => (g z).re/z.re) sectorInfinity (𝓝 1) := by + have hre : (fun z => (g z).re-z.re) =O[sectorInfinity] (fun z => g z-z) := by + apply Asymptotics.IsBigO.of_bound 1 + exact Eventually.of_forall fun z => by simpa only [Real.norm_eq_abs,one_mul,Complex.sub_re] using Complex.abs_re_le_norm (g z-z) + have ht := (hre.trans_isLittleO (hg.trans_isBigO logarithmicRadius_isBigO_re)).tendsto_div_nhds_zero + have hh := ht.add_const 1 + simp only [zero_add] at hh + apply hh.congr' + filter_upwards [SectorEventually.realpart_pos] with z hz + field_simp [ne_of_gt (show 0 g z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) : + (fun z => (g z).re) =O[sectorInfinity] Complex.re := by + have hre : (fun z => (g z).re-z.re) =O[sectorInfinity] (fun z => g z-z) := by + apply Asymptotics.IsBigO.of_bound 1 + exact Eventually.of_forall fun z => by simpa only [Real.norm_eq_abs,one_mul,Complex.sub_re] using Complex.abs_re_le_norm (g z-z) + have hh := (hre.trans (hg.isBigO.trans logarithmicRadius_isBigO_re)).add (Asymptotics.isBigO_refl Complex.re sectorInfinity) + simpa only [sub_add_cancel] using hh + + + +lemma nearIdentity_realpart_separation {F g e : ℂ → ℂ} + (hg : (fun z => g z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) + (hF : (fun z => (F z).re) =o[sectorInfinity] Complex.re) + (he : e =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) : + (fun z => (F (g z)+e z).re) =o[sectorInfinity] Complex.re := by + have hbound : ∀ᶠ z in sectorInfinity,‖g z-z‖ ≤ logarithmicRadius ‖z‖ := by + filter_upwards [hg.bound zero_lt_one,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hz hz1 + simpa only [Real.norm_eq_abs,abs_of_pos (logarithmicRadius_pos hz1),one_mul] using hz + have ht := tendsto_sectorInfinity_of_logarithmic_displacement hbound + have hcomp := (hF.comp_tendsto ht).trans_isBigO (nearIdentity_re_isBigO hg) + have hre : (fun z => (e z).re) =O[sectorInfinity] e := by + apply Asymptotics.IsBigO.of_bound 1 + exact Eventually.of_forall fun z => by simpa only [Real.norm_eq_abs,one_mul] using Complex.abs_re_le_norm (e z) + exact hcomp.add (hre.trans_isLittleO (he.trans_isBigO logarithmicRadius_isBigO_re)) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +theorem zero_exponent_real_inverse {F x : ℂ → ℂ} {X : ℝ → ℝ} {C K ε : ℝ} + (hF : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (hr : ∀ᶠ r : ℝ in atTop,(F (r:ℂ)).im=0) + (hC : 1≤C) (hK : 0≤K) (hε : 0<ε) + (hX : Tendsto X atTop atTop) (hlog : Real.log =o[atTop] X) + (hmod : ∀ᶠ z in sectorInfinity,X ‖z‖/C≤‖x z‖ ∧ ‖x z‖≤C*X ‖z‖) + (hx : Tendsto x sectorInfinity sectorInfinity) + (herr : ∀ᶠ z in sectorInfinity,‖F z-z‖≤K*‖z‖*Real.exp (-ε*(x z).re)) : + ∃ (g : ℂ → ℂ) (I : ℝ → ℝ), + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ g z ∧ F (g z)=z) ∧ + Tendsto g sectorInfinity sectorInfinity ∧ + Tendsto I atTop atTop ∧ + (∀ᶠ r : ℝ in atTop,g (r:ℂ)=(I r:ℂ) ∧ F (I r:ℂ)=(r:ℂ)) ∧ + (∀ᶠ r : ℝ in atTop,I ((F (r:ℂ)).re)=r) ∧ + (fun z => g z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖) ∧ + (∀ N : ℕ,(fun z => g z-z) =o[sectorInfinity] (fun z => ‖z‖/(Real.log ‖z‖)^N)) ∧ + Tendsto (fun z => (g z).re/z.re) sectorInfinity (𝓝 1) := by + have hsmall := zero_exponent_error_small hC hK hε hX hlog hmod hx herr + obtain ⟨η,T,g,I,hη,hga,hg,hIt,hreal,hri⟩ := + sector_perturbative_real_inverse hF hsmall hr baseLoss 1 admissible_baseLoss + have hdom : ∀ᶠ z in sectorInfinity,z∈lossSector η T := ⟨η,T,hη,fun _ h => h⟩ + have hbound : (fun z => g z-z) =O[sectorInfinity] (fun z => F z-z) := by + apply Asymptotics.IsBigO.of_bound 2 + exact hdom.mono fun z hz => (hg z hz).2.2 + have hgs := hbound.trans_isLittleO hsmall + have hdisp : ∀ᶠ z in sectorInfinity,‖g z-z‖≤logarithmicRadius ‖z‖ := by + filter_upwards [hgs.bound zero_lt_one,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hz hz1 + simpa only [one_mul,Real.norm_eq_abs,abs_of_pos (logarithmicRadius_pos hz1)] using hz + refine ⟨g,I,hdom.mono (fun z hz => ⟨hga z hz,(hg z hz).2.1⟩), + tendsto_sectorInfinity_of_logarithmic_displacement hdisp,hIt,hreal,hri,hgs,?_, + nearIdentity_re_tendsto hgs⟩ + intro N + exact hbound.trans_isLittleO (zero_exponent_error_logpower N hC hK hε hX hlog hmod hx herr) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RecursiveCharts.lean b/lean/OAI/Analysis/PathSelection/RecursiveCharts.lean new file mode 100644 index 0000000000000000000000000000000000000000..e197a5dc028527ff7287016d2ceda74f744cc9a9 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RecursiveCharts.lean @@ -0,0 +1,444 @@ +import Mathlib +import OAI.Analysis.PathSelection.FirstLevelCharts + +namespace OAI + +/-! General common charts, second-clock charts and slowly varying coefficients. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +theorem ExpansionOver.zero_chart {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) + (hcharts : LowerSectorCharts K) {F H : ℂ → ℂ} + (hF : ExpansionOver K F) (hH : ExpansionOver K H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : ∃ D : ℝ,0 (H (t:ℂ)).re)) + (htop : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 0)) : + ∃ (y : ℂ → ℂ) (I : ℝ → ℝ),SectorInverse H y I ∧ ScalarSectorChart F y ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun z => (F (y z)).re) =o[sectorInfinity] Complex.re) := by + obtain ⟨g,h,hg,hh,hne,hgr,hhr,hgt,hht,hhfast,hgo,hFe,hHe,hgo'⟩ := + hF.zero_leading_strip_data hK hconj hH hFr hHr hFt hHt hO hfast htop + obtain ⟨x,I,hxi,hlog,⟨C,hC,hxmod⟩,hfamily⟩ := hcharts h hh hhr hht hhfast + obtain ⟨hGi,hGs⟩ := hfamily g hg hgr hgt hgo + have hxa := hxi.analytic_left + have hxt := hxi.maps_sector + have hIt := hxi.ray_unbounded + have hxright := hxi.right + have hxr : ∀ᶠ t : ℝ in atTop,x (t:ℂ)=(I t:ℂ) ∧ h (I t:ℂ)=(t:ℂ) := by + filter_upwards [hxi.real_ray,tendsto_real_sectorInfinity.eventually hxa] with t hr hl + exact ⟨hr,by simpa only [hr] using hl.2⟩ + have hGa := hGi.analytic + have hGt := hGi.maps_sector + obtain ⟨M,hM,hGmod⟩ := hGi.radial + obtain ⟨ε,L,hε,hL,hErr⟩ := hFe.common_sector_bound hHe + have hFa := hF.choose_spec.choose_spec.1.eventually_analytic + have hHa := hH.choose_spec.choose_spec.1.eventually_analytic + let G : ℂ → ℂ := fun z => g (x z) + let E : ℂ → ℂ := fun z => F (x z)/g (x z)-1 + let P : ℂ → ℂ := fun z => H (x z) + have hPa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ P z := by + filter_upwards [hxa,hxt.eventually hHa] with z hx hh + exact hh.comp hx.1 + have hPr : ∀ᶠ t : ℝ in atTop,(P (t:ℂ)).im=0 := by + filter_upwards [hxr,hIt.eventually hHr] with t hx hh + simpa only [P,hx.1] using hh.1 + have hPt : Tendsto (fun t : ℝ => (P (t:ℂ)).re) atTop atTop := + (hHt.comp hIt).congr' (hxr.mono fun t ht => by simp only [P,ht.1,Function.comp_apply]) + have hEa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ E z := by + filter_upwards [hxa,hxt.eventually hFa,hxt.eventually (hK.analytic hg),hxt.eventually hne] with z hx hf hg hn + exact ((hf.comp hx.1).div (hg.comp hx.1) hn.1).sub analyticAt_const + have hPe : ∀ᶠ z in sectorInfinity,‖P z-z‖≤L*‖z‖*Real.exp (-ε*(x z).re) := by + filter_upwards [hxa,hxt.eventually hErr,hxt.eventually hne] with z hx he hn + have heq : P z-z=z*(H (x z)/h (x z)-1) := by + calc + P z-z=H (x z)-h (x z) := by rw [hx.2] + _=h (x z)*(H (x z)/h (x z)-1) := by field_simp [hn.2] + _=z*(H (x z)/h (x z)-1) := by rw [hx.2] + rw [heq,norm_mul] + exact (mul_le_mul_of_nonneg_left he.2 (norm_nonneg z)).trans_eq (by ring) + have hEe : ∀ᶠ z in sectorInfinity,‖E z‖≤L*Real.exp (-ε*(x z).re) := + (hxt.eventually hErr).mono fun _ he => he.1 + obtain ⟨D,hD,hDb⟩ := hgo.exists_pos + have hGr : ∀ᶠ t : ℝ in atTop,‖G (t:ℂ)‖≤D*|t| := by + filter_upwards [hxr,hIt.eventually hDb.bound,hIt.eventually hgr] with t hx hd hg + have eh : (h (I t:ℂ)).re=t := congrArg Complex.re hx.2 + have eg : g (I t:ℂ)=((g (I t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hg.1) + change ‖g (x (t:ℂ))‖≤D*|t| + rw [hx.1,eg,Complex.norm_real,Real.norm_eq_abs] + simpa only [Real.norm_eq_abs,eh] using hd + have hGu : ∀ᶠ z in sectorInfinity,‖G z‖≤(M*D)*‖z‖ := by + filter_upwards [hGmod,tendsto_norm_sectorInfinity.eventually hGr] with z hm hr + have hr' : ‖g (x (‖z‖:ℂ))‖≤D*‖z‖ := by simpa only [abs_of_nonneg (norm_nonneg _)] using hr + exact hm.2.trans (by nlinarith) + obtain ⟨v,J,hva,hvt,hJt,hvr,hvright,hfva,hfvt,hfvm,hfsep⟩ := + zero_exponent_chart hPa hPr hC hL hε hIt + hlog hxmod hxt hPe hGa hEa hGt + (show (0:ℝ)≤M*D by positivity) hGu hM hGmod hEe + let y : ℂ → ℂ := fun z => x (v z) + let Q : ℂ → ℂ := fun z => G (v z)*(1+E (v z)) + have hyt : Tendsto y sectorInfinity sectorInfinity := hxt.comp hvt + have hyr : ∀ᶠ t : ℝ in atTop,y (t:ℂ)=(I (J t):ℂ) := by + filter_upwards [hvr,hJt.eventually hxr] with t hv hx + simp only [y,hv.1,hx.1] + have hQt : ∀ᶠ z in sectorInfinity,Q z=F (y z) := by + filter_upwards [hyt.eventually hne] with z hz + dsimp [Q,G,E,y] + have hn : g (x (v z))≠0 := hz.1 + field_simp [hn] + ring + have hvrightC : ∀ᶠ t : ℝ in atTop,v (P (t:ℂ))=(t:ℂ) := by + filter_upwards [hvright,hPr,hPt.eventually hvr] with t hi hp hv + have he : P (t:ℂ)=((P (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hp) + rw [he,hv.1,hi] + have hyrt : ∀ᶠ t : ℝ in atTop,y (H (t:ℂ))=(t:ℂ) := by + filter_upwards [hxright,hht.eventually hvrightC,hhr] with t hx hv hh + have eh : h (t:ℂ)=((h (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hh.1) + have hp : P (h (t:ℂ))=H (t:ℂ) := by simp only [P,hx] + rw [←eh,hp] at hv + dsimp [y] + rw [hv,hx] + have hIJt := hIt.comp hJt + refine ⟨y,fun t => I (J t),⟨?_,hyrt,hyt,hIJt,hyr⟩,⟨?_,?_,?_,hfvt.congr' hQt,4*M,by positivity,?_⟩,?_⟩ + · filter_upwards [hva,hvt.eventually hxa] with z hv hx + exact ⟨hx.1.comp hv.1,hv.2⟩ + · filter_upwards [hyr,hIJt.eventually hFr] with t hy hf + simpa only [hy,Function.comp_apply] using hf + · exact (hFt.comp hIJt).congr' (hyr.mono fun t hy => by simp only [hy,Function.comp_apply]) + · filter_upwards [hva,hvt.eventually hxa,hyt.eventually hFa] with z hv hx hf + exact hf.comp (hx.1.comp hv.1) + · filter_upwards [hfvm,hQt,tendsto_norm_sectorInfinity.eventually (tendsto_real_sectorInfinity.eventually hQt)] with z hm he hr + change ‖Q (‖z‖:ℂ)‖/(4*M)≤‖Q z‖ ∧ ‖Q z‖≤(4*M)*‖Q (‖z‖:ℂ)‖ at hm + simpa only [he,hr] using hm + · intro hsmall + have hGsmall := hGs (hgo' hsmall) + exact (hfsep hGsmall).congr' (hQt.mono fun _ he => congrArg Complex.re he) Filter.EventuallyEq.rfl + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ExpansionOver.scalar_chart {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) + (hcharts : LowerSectorCharts K) {F H : ℂ → ℂ} + (hF : ExpansionOver K F) (hH : ExpansionOver K H) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hO : (fun t : ℝ => (F (t:ℂ)).re) =O[atTop] (fun t : ℝ => (H (t:ℂ)).re)) + (hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re)) : + ∃ (y : ℂ → ℂ) (I : ℝ → ℝ),SectorInverse H y I ∧ ScalarSectorChart F y ∧ + ((fun t : ℝ => (F (t:ℂ)).re) =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) → + (fun z => (F (y z)).re) =o[sectorInfinity] Complex.re) := by + obtain ⟨b,hb,g,hg,hg0,hgr,hHe,hHd⟩ := hH.positive_leading_strip hK hconj hHr hHt + have hO' := real_positive_bigO (hFr.mono fun _ h => h.2) (hHr.mono fun _ h => h.2) hO + rcases hb.eq_or_lt with hb | hb + · have hzero : Tendsto (fun z => deriv H z/H z) stripInfinity (𝓝 0) := by + simpa only [←hb,Complex.ofReal_zero] using hHd + exact hF.zero_chart hK hconj hcharts hH hFr hHr hFt hHt hO' hfast hzero + · obtain ⟨y,I,ha,hr,ht,hIt,hreal,hFr',hFt',hFa,hm,hn,hs⟩ := + (hF.positive_chart hK hKd hconj hH hFr hHr hFt hHt hO' ⟨b,hb,hHd⟩).sector + (hFr.mono fun _ h => h.1) (hHr.mono fun _ h => h.1) + exact ⟨y,I,⟨ha,hr,ht,hIt,hreal⟩,⟨hFr',hFt',hFa,hm,16,by norm_num,hn⟩,hs⟩ + +lemma ScalarSectorChart.congr_inverse {F x y : ℂ → ℂ} + (h : ScalarSectorChart F x) (he : x =ᶠ[sectorInfinity] y) : + ScalarSectorChart F y := by + have hf : (fun z => F (x z)) =ᶠ[sectorInfinity] (fun z => F (y z)) := + he.mono fun _ ht => congrArg F ht + have hr := tendsto_real_sectorInfinity.eventually hf + obtain ⟨C,hC,hm⟩ := h.radial + refine ⟨?_,h.unbounded.congr' (hr.mono fun _ e => congrArg Complex.re e), + sector_eventually_analytic_congr h.analytic hf,h.maps_sector.congr' hf,C,hC,?_⟩ + · filter_upwards [h.positive,hr] with t ht he + rwa [←he] + · filter_upwards [hm,hf,tendsto_norm_sectorInfinity.eventually hr] with z hm he hr + rwa [he,hr] at hm + +lemma lowerSectorData_hasSectorCharts {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) + (hcharts : LowerSectorCharts K) : HasSectorCharts K := by + intro H hH hHr hHt hfast + obtain ⟨y,I,hyi,_⟩ := hH.scalar_chart hK hKd hconj hcharts hH hHr hHr hHt hHt + (Asymptotics.isBigO_refl _ _) hfast + refine ⟨y,I,hyi,?_⟩ + intro F hF hFr hFt hO + obtain ⟨v,J,hvj,hFv,hs⟩ := hF.scalar_chart hK hKd hconj hcharts hH hFr hHr hFt hHt hO hfast + have he := sector_inverse_unique hH.choose_spec.choose_spec.1.eventually_analytic + (hHr.mono fun _ h => h.1) hHt (hvj.analytic_left.mono fun _ h => h.1) + (hyi.analytic_left.mono fun _ h => h.1) hvj.right hyi.right + refine ⟨hFv.congr_inverse he,fun hsmall => ?_⟩ + exact (hs hsmall).congr' (he.mono fun _ h => congrArg (fun w => (F w).re) h) Filter.EventuallyEq.rfl + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ExpBound.comp_slow {F y : ℂ → ℂ} {a : ℝ} (hF : ExpBound a F) + (hy : Tendsto y sectorInfinity sectorInfinity) + (hs : (fun z => (y z).re) =o[sectorInfinity] Complex.re) : + SectorSlow (fun z => F (y z)) := by + intro ε hε + obtain ⟨C,hC,hb⟩ := hF.exists_pos + apply Asymptotics.IsBigO.of_bound C + have hh := (hs.def (show 0 < ε/(|a|+1) by positivity)) + filter_upwards [hy.eventually hb.bound,hh,tendsto_re_sectorInfinity.eventually (eventually_gt_atTop 0)] with z h hz hpos + simp only [Real.norm_eq_abs,abs_of_pos (Real.exp_pos _)] at h ⊢ + apply h.trans + apply mul_le_mul_of_nonneg_left _ hC.le + apply Real.exp_le_exp.mpr + have ha : a*(y z).re ≤ |a| * |(y z).re| := le_trans (le_abs_self _) (by rw [abs_mul]) + have hz' : |(y z).re| ≤ ε/(|a|+1)*z.re := by simpa [Real.norm_eq_abs,abs_of_pos hpos] using hz + have hden : 0 < |a| + 1 := by positivity + have hh : |a| * (ε/(|a|+1)) ≤ ε := by + have hd : |a|/(|a|+1) ≤ 1 := (div_le_iff₀ hden).mpr (by linarith) + calc + |a| * (ε/(|a|+1)) = ε*(|a|/(|a|+1)) := by ring + _ ≤ ε*1 := mul_le_mul_of_nonneg_left hd hε.le + _ = ε := mul_one _ + calc + a*(y z).re ≤ |a| * |(y z).re| := ha + _ ≤ |a| * (ε/(|a|+1)*z.re) := mul_le_mul_of_nonneg_left hz' (abs_nonneg a) + _ ≤ ε*z.re := by nlinarith + +lemma ExpansionOver.expBound_some {K : Set (ℂ → ℂ)} {F : ℂ → ℂ} + (hF : ExpansionOver K F) : ∃ a : ℝ,ExpBound a F := by + obtain ⟨E,b,hF,hb⟩ := hF + obtain ⟨A,hA⟩ := hF.bounded_above + exact ⟨A+1,hF.expBound hA⟩ + +lemma ExpansionOver.zero_or_ne {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + {F : ℂ → ℂ} (hF : ExpansionOver K F) : + (∀ᶠ z in sectorInfinity,F z=0) ∨ (∀ᶠ z in sectorInfinity,F z≠0) := by + classical + obtain ⟨E,b,hF,hb⟩ := hF + have ht := hF.trim_zero (fun β hβ => hK.analytic (hb β hβ)) + rcases (nonzeroRaySupport E b).eq_empty_or_nonempty with he | he + · rw [he] at ht + obtain ⟨ω,R,hω,ha⟩ := hF.eventually_analytic + exact Or.inl (sector_zero_of_ray_zero hω ha ht.empty) + · obtain ⟨β,hβ,hmax⟩ := exists_greatest_of_finite_above ht.finite_above he + have hbne : ∀ᶠ z in sectorInfinity,b β z≠0 := by + rcases hK.zero_or_ne (hb β hβ.1) with hz | hn + · exact False.elim (hβ.2 (tendsto_real_sectorInfinity.eventually hz)) + · exact hn + exact Or.inr (ht.eventually_ne_of_leading hβ hmax hbne (hK.slow (hK.inv_mem (hb β hβ.1)))) + + +def TransportedFirstField (y : ℂ → ℂ) : Set (ℂ → ℂ) := + {b | ∃ F : ℂ → ℂ,ExpansionOver PuiseuxSector F ∧ b =ᶠ[sectorInfinity] fun z => F (y z)} + +lemma transported_first_lowerSectorData {y : ℂ → ℂ} + (hya : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z) + (hyt : Tendsto y sectorInfinity sectorInfinity) + (hys : (fun z => (y z).re) =o[sectorInfinity] Complex.re) : + LowerSectorData (TransportedFirstField y) := by + constructor + · intro c + exact ⟨fun _ => c,ExpansionOver.const puiseux_lowerSectorData c,EventuallyEq.rfl⟩ + · rintro f g ⟨F,hF,he⟩ ⟨G,hG,he'⟩ + exact ⟨fun z => F z+G z,hF.add puiseux_lowerSectorData hG,he.add he'⟩ + · rintro f ⟨F,hF,he⟩ + exact ⟨fun z => -F z,hF.neg puiseux_lowerSectorData,he.neg⟩ + · rintro f g ⟨F,hF,he⟩ ⟨G,hG,he'⟩ + exact ⟨fun z => F z*G z,hF.mul puiseux_lowerSectorData hG,he.mul he'⟩ + · rintro f ⟨F,hF,he⟩ + exact ⟨fun z => (F z)⁻¹,hF.inv puiseux_lowerSectorData,he.inv⟩ + · rintro f ⟨F,hF,he⟩ + have hg : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (y w)) z := by + filter_upwards [hya,hyt.eventually hF.choose_spec.choose_spec.1.eventually_analytic] with z hy hf + exact hf.comp hy + exact sector_eventually_analytic_congr hg he.symm + · rintro f ⟨F,hF,he⟩ + obtain ⟨a,ha⟩ := hF.expBound_some + intro ε hε + exact (ha.comp_slow hyt hys ε hε).congr' he.symm Filter.EventuallyEq.rfl + · rintro f ⟨F,hF,he⟩ + rcases hF.zero_or_ne puiseux_lowerSectorData with hz | hn + · exact Or.inl (he.trans (hyt.eventually hz)) + · exact Or.inr ((he.and (hyt.eventually hn)).mono fun z h => by rw [h.1]; exact h.2) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma puiseux_variable : Puiseux (fun t : ℝ => (t:ℂ)) := by + refine ⟨1,by norm_num,-1,fun _ => 1,analyticAt_const,?_⟩ + filter_upwards [eventually_gt_atTop (0:ℝ)] with t ht + simp [rootCoord,Real.rpow_neg_one] + +lemma ExpansionOver.puiseux_mem {F : ℂ → ℂ} (hF : F∈PuiseuxSector) : + ExpansionOver PuiseuxSector F := by + refine ⟨{0},fun _ => F,?_,fun _ _ => hF⟩ + simpa only [Complex.ofReal_zero,zero_mul,Complex.exp_zero,one_mul] using + SectorExpansion.single 0 hF.1 (puiseux_lowerSectorData.slow hF) + +lemma ExpansionOver.lower_field_chart {H : ℂ → ℂ} + (hH : ExpansionOver PuiseuxSector H) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re)) : + ∃ y : ℂ → ℂ, + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z ∧ H (y z)=z) ∧ + (∀ᶠ t : ℝ in atTop,y (H (t:ℂ))=(t:ℂ)) ∧ + Tendsto y sectorInfinity sectorInfinity ∧ + LowerSectorData (TransportedFirstField y) := by + have hid : ExpansionOver PuiseuxSector id := + ExpansionOver.puiseux_mem ⟨Eventually.of_forall fun _ => analyticAt_id,puiseux_variable⟩ + have hir : ∀ᶠ t : ℝ in atTop,(id (t:ℂ)).im=0 ∧ 0<(id (t:ℂ)).re := by + filter_upwards [eventually_gt_atTop (0:ℝ)] with t ht + exact ⟨rfl,ht⟩ + have hO : ∃ D : ℝ,0 h.1) hyt hs⟩ + + + +lemma transported_first_iff {X Y : ℝ → ℝ} {y : ℂ → ℂ} + (hX : Puiseux (fun t => (X t:ℂ))) (hXt : Tendsto X atTop atTop) + (hYt : Tendsto Y atTop atTop) + (hYc : ∀ᶠ t : ℝ in atTop,ContinuousAt Y t) + (hya : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z) + (hyt : Tendsto y sectorInfinity sectorInfinity) + (hyr : ∀ᶠ t : ℝ in atTop,y (Y t:ℂ)=(X t:ℂ)) + {b : ℂ → ℂ} (hba : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ b z) : + b ∈ TransportedFirstField y ↔ ClockGerm (X :: []) (fun t => b (Y t:ℂ)) := by + constructor + · rintro ⟨F,hF,he⟩ + apply (firstClock_expansion_iff hX hXt).mpr + refine ⟨F,hF,?_⟩ + filter_upwards [hYt.eventually (tendsto_real_sectorInfinity.eventually he),hyr] with t he hy + simpa only [hy] using he + · intro hb + obtain ⟨F,hF,he⟩ := (firstClock_expansion_iff hX hXt).mp hb + refine ⟨F,hF,?_⟩ + have hfa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (y w)) z := by + filter_upwards [hya,hyt.eventually hF.choose_spec.choose_spec.1.eventually_analytic] with z hy hf + exact hf.comp hy + apply sector_analytic_eq_of_ray hba hfa + apply eventually_of_comp_clock hYt hYc + filter_upwards [he,hyr] with t he hy + simpa only [hy] using he + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma finite_strict_gap (S : Finset ℝ) {β ε : ℝ} (hε : 0 < ε) + (hS : ∀ γ∈S,β < γ) : + ∃ δ : ℝ,0 < δ ∧ δ < ε ∧ ∀ γ∈S,β+δ < γ := by + classical + induction S using Finset.induction_on with + | empty => exact ⟨ε/2,by positivity,by linarith,by simp⟩ + | @insert γ S hγ ih => + obtain ⟨δ,hδ,hδε,hbound⟩ := ih (fun a ha => hS a (Finset.mem_insert_of_mem ha)) + have hg := hS γ (Finset.mem_insert_self _ _) + refine ⟨min δ ((γ-β)/2),lt_min hδ (by linarith), + (min_le_left _ _).trans_lt hδε,?_⟩ + intro a ha + rcases Finset.mem_insert.mp ha with rfl | ha + · have hh := min_le_right δ ((a-β)/2) + linarith + · have hmin := min_le_left δ ((γ-β)/2) + have hh := hbound a ha + linarith + +theorem SectorExpansion.coefficient_slow {F : ℂ → ℂ} {E : Set ℝ} {b : ℝ → ℂ → ℂ} + (hF : SectorExpansion F E b) {β : ℝ} (hβ : β∈E) : SectorSlow (b β) := by + classical + intro ε hε + let S := (hF.finite_above β).toFinset.erase β + obtain ⟨δ,hδ,hδε,hgap⟩ := finite_strict_gap S hε (fun γ hγ => by + have hh := Finset.mem_erase.mp hγ + have hge := ((hF.finite_above β).mem_toFinset.mp hh.2).2 + exact lt_of_le_of_ne hge (Ne.symm hh.1)) + have he : (hF.finite_above β).toFinset=insert β (hF.finite_above (β+δ)).toFinset := by + ext γ + simp only [Set.Finite.mem_toFinset,Set.mem_inter_iff,Set.mem_Ici,Finset.mem_insert] + constructor + · rintro ⟨hγ,hγβ⟩ + by_cases hh : γ=β + · exact Or.inl hh + · exact Or.inr ⟨hγ,(hgap γ (Finset.mem_erase.mpr ⟨hh,(hF.finite_above β).mem_toFinset.mpr ⟨hγ,hγβ⟩⟩)).le⟩ + · rintro (rfl | ⟨hγ,hγδ⟩) + · exact ⟨hβ,le_rfl⟩ + · exact ⟨hγ,by linarith⟩ + have hn : β∉(hF.finite_above (β+δ)).toFinset := by + intro hh + have hg := ((hF.finite_above (β+δ)).mem_toFinset.mp hh).2 + change β+δ ≤ β at hg + linarith + obtain ⟨a,ha,hA⟩ := hF.expSmall_remainder (β+δ) + obtain ⟨c,hc,hC⟩ := hF.expSmall_remainder β + have hh := ((hA.mono (le_of_lt (by linarith : a < β+ε))).sub + (hC.mono (le_of_lt (by linarith : c < β+ε)))).mul (ExpBound.cexp (-β)) + have hid : β+ε+-β=ε := by ring + rw [hid] at hh + apply hh.congr_left + intro z + rw [he,Finset.sum_insert hn] + have hexp : Complex.exp ((β:ℂ)*z)*Complex.exp (((-β:ℝ):ℂ)*z)=1 := by + rw [←Complex.exp_add] + convert Complex.exp_zero using 1 + push_cast + ring_nf + calc + ((F z-∑ a∈(hF.finite_above (β+δ)).toFinset,Complex.exp ((a:ℂ)*z)*b a z)- + (F z-(Complex.exp ((β:ℂ)*z)*b β z+∑ a∈(hF.finite_above (β+δ)).toFinset,Complex.exp ((a:ℂ)*z)*b a z)))* + Complex.exp (((-β:ℝ):ℂ)*z)= + (Complex.exp ((β:ℂ)*z)*Complex.exp (((-β:ℝ):ℂ)*z))*b β z := by ring + _ = b β z := by rw [hexp,one_mul] + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RecursiveClocks.lean b/lean/OAI/Analysis/PathSelection/RecursiveClocks.lean new file mode 100644 index 0000000000000000000000000000000000000000..88c34b9c6214666ae20fd64417f7ea3ea30ef929 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RecursiveClocks.lean @@ -0,0 +1,431 @@ +import Mathlib +import OAI.Analysis.PathSelection.SectorPolynomials + +namespace OAI + +/-! Recursive clock monomials, leading terms and coefficient-field algebra. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + + +def ClockGerm : List (ℝ → ℝ) → (ℝ → ℂ) → Prop + | [], f => Puiseux f + | X::xs, f => ∃ (F : ℂ → ℂ) (E : Set ℝ) (b : ℝ → ℂ → ℂ), + SectorExpansion F E b ∧ + (∀ β ∈ E, ClockGerm xs (fun t => b β (X t : ℂ)) ∧ + SectorEventually (fun z => AnalyticAt ℂ (b β) z)) ∧ + f =ᶠ[atTop] fun t => F (X t : ℂ) + + + +def ValidClocks : List (ℝ → ℝ) → Prop + | [] => True + | X::xs => ValidClocks xs ∧ ClockGerm xs (fun t => (X t : ℂ)) ∧ + Tendsto X atTop atTop ∧ + match xs with + | [] => ∃ c : ℝ, 0 < c ∧ X =ᶠ[atTop] fun t => c*t + | Y::_ => Y =o[atTop] X + +lemma ClockGerm.congr {xs : List (ℝ → ℝ)} {f g : ℝ → ℂ} + (hf : ClockGerm xs f) (hfg : f =ᶠ[atTop] g) : ClockGerm xs g := by + cases xs with + | nil => exact Puiseux.congr hf hfg + | cons X xs => + obtain ⟨F,E,b,hF,hb,he⟩ := hf + exact ⟨F,E,b,hF,hb,hfg.symm.trans he⟩ + +lemma eventually_analytic_congr {f g : ℝ → ℂ} + (hf : ∀ᶠ x : ℝ in atTop, AnalyticAt ℝ f x) (he : f =ᶠ[atTop] g) : + ∀ᶠ x : ℝ in atTop, AnalyticAt ℝ g x := by + obtain ⟨T,hT⟩ := eventually_atTop.mp he + filter_upwards [hf,eventually_gt_atTop T] with x hx hxT + exact hx.congr ((eventually_gt_nhds hxT).mono (fun y hy => hT y hy.le)) + + + +theorem ClockGerm.eventually_analytic {xs : List (ℝ → ℝ)} + (hxs : ValidClocks xs) {f : ℝ → ℂ} (hf : ClockGerm xs f) : + ∀ᶠ t : ℝ in atTop, AnalyticAt ℝ f t := by + induction xs generalizing f with + | nil => exact Puiseux.eventually_analytic hf + | cons X xs ih => + obtain ⟨hxs,hX,hXt,hrel⟩ := hxs + have hXa := ih hxs hX + obtain ⟨F,E,b,hF,hb,he⟩ := hf + obtain ⟨ω,R,ε,C,hω,hε,hC,hFa,hbound⟩ := hF.remainders 0 + apply eventually_analytic_congr (g := f) _ he.symm + filter_upwards [hXa,hXt.eventually (hω.real_discs R)] with t hXa ht + have hFpoint := hFa (X t:ℂ) (ht.2 (mem_closedBall_self (by linarith [ht.1]))) + exact (hFpoint.restrictScalars (𝕜 := ℝ)).comp (f := fun t : ℝ => (X t:ℂ)) hXa + +lemma ClockGerm.real_eventually_analytic {xs : List (ℝ → ℝ)} + (hxs : ValidClocks xs) {f : ℝ → ℝ} (hf : ClockGerm xs (fun t => (f t:ℂ))) : + ∀ᶠ t : ℝ in atTop, AnalyticAt ℝ f t := by + filter_upwards [hf.eventually_analytic hxs] with t ht + exact (Complex.reCLM.analyticAt _).comp ht + + + +inductive LogMonomial : List (ℝ → ℝ) → (ℝ → ℝ) → Prop + | base (p : ℚ) : LogMonomial [] (fun t => (p:ℝ)*Real.log t) + | step {xs : List (ℝ → ℝ)} {M X : ℝ → ℝ} (h : LogMonomial xs M) (β : ℝ) : + LogMonomial (X::xs) (fun t => β*X t+M t) + +def RayLeading (xs : List (ℝ → ℝ)) (f : ℝ → ℂ) : Prop := + ∃ M : ℝ → ℝ, LogMonomial xs M ∧ ∃ C : ℂ, C ≠ 0 ∧ + Tendsto (fun t => (Real.exp (-M t):ℂ)*f t) atTop (𝓝 C) + + + +lemma continuous_tail_surjective {X : ℝ → ℝ} (hX : Tendsto X atTop atTop) + (hc : ∀ᶠ t : ℝ in atTop, ContinuousAt X t) (T : ℝ) : + ∃ S : ℝ, ∀ y ≥ S, ∃ t ≥ T, X t=y := by + obtain ⟨A,hA⟩ := eventually_atTop.mp hc + let a := max A T + refine ⟨X a,?_⟩ + intro y hy + obtain ⟨b,hb,hby⟩ := ((eventually_ge_atTop a).and (hX.eventually_ge_atTop y)).exists + have hcont : ContinuousOn X (Icc a b) := fun t ht => + (hA t ((le_max_left _ _).trans ht.1)).continuousWithinAt + obtain ⟨t,ht,he⟩ := intermediate_value_Icc hb hcont ⟨hy,hby⟩ + exact ⟨t,(le_max_right _ _).trans ht.1,he⟩ + +lemma eventually_of_comp_clock {X : ℝ → ℝ} {P : ℝ → Prop} + (hX : Tendsto X atTop atTop) (hc : ∀ᶠ t : ℝ in atTop, ContinuousAt X t) + (hP : ∀ᶠ t : ℝ in atTop, P (X t)) : ∀ᶠ y : ℝ in atTop, P y := by + obtain ⟨T,hT⟩ := eventually_atTop.mp hP + obtain ⟨S,hS⟩ := continuous_tail_surjective hX hc T + filter_upwards [eventually_ge_atTop S] with y hy + obtain ⟨t,ht,rfl⟩ := hS y hy + exact hT t ht + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ValidClocks.lower_small {X : ℝ → ℝ} {xs : List (ℝ → ℝ)} + (h : ValidClocks (X::xs)) : Real.log =o[atTop] X ∧ ∀ Y ∈ xs, Y =o[atTop] X := by + induction xs generalizing X with + | nil => + obtain ⟨_,_,_,c,hc,he⟩ := h + refine ⟨?_,by simp⟩ + exact (Asymptotics.IsLittleO.const_mul_right hc.ne' Real.isLittleO_log_id_atTop).congr' + EventuallyEq.rfl he.symm + | cons Y ys ih => + obtain ⟨hys,hX,hXt,hYX⟩ := h + have hh := ih hys + refine ⟨hh.1.trans hYX,?_⟩ + intro Z hZ + rcases List.mem_cons.mp hZ with rfl | hZ + · exact hYX + · exact (hh.2 Z hZ).trans hYX + +lemma LogMonomial.isLittleO {xs : List (ℝ → ℝ)} {M H : ℝ → ℝ} + (hM : LogMonomial xs M) (hlog : Real.log =o[atTop] H) + (hxs : ∀ X ∈ xs, X =o[atTop] H) : M =o[atTop] H := by + induction hM with + | base p => exact hlog.const_mul_left _ + | @step xs M X hM β ih => + exact ((hxs X (List.mem_cons_self)).const_mul_left β).add + (ih (fun Y hY => hxs Y (List.mem_cons_of_mem _ hY))) + +lemma LogMonomial.neg {xs : List (ℝ → ℝ)} {M : ℝ → ℝ} + (hM : LogMonomial xs M) : LogMonomial xs (fun t => -M t) := by + induction hM with + | base p => + convert LogMonomial.base (-p) using 1 + funext t; push_cast; ring + | @step xs M X hM β ih => + convert LogMonomial.step (X := X) ih (-β) using 1 + funext t; ring + +lemma subexponential_exp_of_littleO {M X : ℝ → ℝ} + (hX : Tendsto X atTop atTop) (hM : M =o[atTop] X) : + Subexponential atTop X (fun t => (Real.exp (M t):ℂ)) := by + intro ε hε + filter_upwards [hM.bound hε,hX.eventually_gt_atTop 0] with t ht hXt + rw [Complex.norm_of_nonneg (Real.exp_pos _).le] + apply Real.exp_le_exp.mpr + simp only [Real.norm_eq_abs,abs_of_pos hXt] at ht + exact (le_abs_self _).trans ht + +lemma subexponential_of_eventually_bounded {X : ℝ → ℝ} {f : ℝ → ℂ} + (hX : Tendsto X atTop atTop) {C : ℝ} (hf : ∀ᶠ t in atTop, ‖f t‖ ≤ C) : + Subexponential atTop X f := by + intro ε hε + have ht : Tendsto (fun t => Real.exp (ε*X t)) atTop atTop := + Real.tendsto_exp_atTop.comp ((tendsto_const_mul_atTop_of_pos hε).mpr hX) + filter_upwards [hf,ht.eventually_ge_atTop C] with t ht hC + exact ht.trans hC + +lemma subexponential_congr {X : ℝ → ℝ} {f g : ℝ → ℂ} + (hf : Subexponential atTop X f) (he : f =ᶠ[atTop] g) : Subexponential atTop X g := by + intro ε hε + filter_upwards [hf ε hε,he] with t ht he + simpa only [←he] using ht + +lemma RayLeading.inv {xs : List (ℝ → ℝ)} {f : ℝ → ℂ} (h : RayLeading xs f) : + RayLeading xs (fun t => (f t)⁻¹) := by + obtain ⟨M,hM,C,hC,ht⟩ := h + refine ⟨fun t => -M t,hM.neg,C⁻¹,inv_ne_zero hC,?_⟩ + apply (ht.inv₀ hC).congr' + exact Eventually.of_forall (fun t => by + simp only [mul_inv_rev,←Complex.ofReal_inv,←Real.exp_neg,neg_neg,mul_comm]) + +lemma RayLeading.eventually_nonzero {xs : List (ℝ → ℝ)} {f : ℝ → ℂ} + (h : RayLeading xs f) : ∀ᶠ t : ℝ in atTop, f t ≠ 0 := by + obtain ⟨M,hM,C,hC,ht⟩ := h + filter_upwards [ht.eventually_ne hC] with t ht + exact (mul_ne_zero_iff.mp ht).2 + +lemma RayLeading.subexponential {xs : List (ℝ → ℝ)} {f : ℝ → ℂ} {X : ℝ → ℝ} + (h : RayLeading xs f) (hX : Tendsto X atTop atTop) + (hlog : Real.log =o[atTop] X) (hxs : ∀ Y ∈ xs, Y =o[atTop] X) : + Subexponential atTop X f := by + obtain ⟨M,hM,C,hC,ht⟩ := h + have hMb := subexponential_exp_of_littleO hX (hM.isLittleO hlog hxs) + have hb := subexponential_of_eventually_bounded hX + ((ht.norm.eventually_lt_const (show ‖C‖ < ‖C‖+1 by linarith)).mono (fun _ h => h.le)) + apply subexponential_congr (hMb.mul hb) + exact Eventually.of_forall (fun t => by + dsimp only + rw [←mul_assoc,←Complex.ofReal_mul,←Real.exp_add,add_neg_cancel] + simp) + + +lemma RayLeading.eventually_sign {xs : List (ℝ → ℝ)} {f : ℝ → ℝ} + (h : RayLeading xs (fun t => (f t:ℂ))) : + (∀ᶠ t : ℝ in atTop, 0 < f t) ∨ (∀ᶠ t : ℝ in atTop, f t < 0) := by + obtain ⟨M,hM,C,hC,ht⟩ := h + have ht' : Tendsto (fun t => Real.exp (-M t)*f t) atTop (𝓝 C.re) := by + simpa only [Function.comp_def,←Complex.ofReal_mul,Complex.ofReal_re] using + Complex.continuous_re.continuousAt.tendsto.comp ht + have hCi : C.im=0 := by + have hi : Tendsto (fun _ : ℝ => (0:ℝ)) atTop (𝓝 C.im) := by + simpa only [Function.comp_def,←Complex.ofReal_mul,Complex.ofReal_im] using + Complex.continuous_im.continuousAt.tendsto.comp ht + exact tendsto_nhds_unique hi tendsto_const_nhds + have hCr : C.re ≠ 0 := fun hz => hC (Complex.ext hz hCi) + rcases lt_or_gt_of_ne hCr with hn | hp + · right + filter_upwards [ht'.eventually_lt_const hn] with t ht + exact neg_of_mul_neg_right ht (Real.exp_pos _).le + · left + filter_upwards [ht'.eventually_const_lt hp] with t ht + exact (mul_pos_iff_of_pos_left (Real.exp_pos _)).mp ht + +lemma Puiseux.rayLeading {f : ℝ → ℂ} (hf : Puiseux f) + (hne : ¬ f =ᶠ[atTop] 0) : RayLeading [] f := by + obtain ⟨q,C,hC,ht⟩ := hf.leading hne + refine ⟨fun t => (q:ℝ)*Real.log t,LogMonomial.base q,C,hC,?_⟩ + apply ht.congr' + filter_upwards [eventually_gt_atTop (0:ℝ)] with t ht + rw [Real.rpow_def_of_pos ht,Real.exp_neg,Complex.ofReal_inv] + congr 2 + rw [mul_comm] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + + +theorem ClockGerm.leading_or_zero {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + {f : ℝ → ℂ} (hf : ClockGerm xs f) : f =ᶠ[atTop] 0 ∨ RayLeading xs f := by + induction xs generalizing f with + | nil => + by_cases hz : f =ᶠ[atTop] 0 + · exact Or.inl hz + · exact Or.inr (Puiseux.rayLeading hf hz) + | cons X xs ih => + have hsmall := hxs.lower_small + obtain ⟨hxs,hX,hXt,hrel⟩ := hxs + have hXcont := (hX.real_eventually_analytic hxs).mono (fun _ hx => hx.continuousAt) + obtain ⟨F,E,b,hF,hb,he⟩ := hf + have hcoeff : ∀ β ∈ E, (∀ᶠ x : ℝ in atTop, b β (x:ℂ)=0) ∨ + ((∀ᶠ x : ℝ in atTop, b β (x:ℂ) ≠ 0) ∧ + Subexponential atTop id (fun x : ℝ => (b β (x:ℂ))⁻¹)) := by + intro β hβ + rcases ih hxs (hb β hβ).1 with hz | hl + · exact Or.inl (eventually_of_comp_clock hXt hXcont hz) + · refine Or.inr ⟨eventually_of_comp_clock hXt hXcont hl.eventually_nonzero,?_⟩ + have hg := hl.inv.subexponential hXt hsmall.1 hsmall.2 + intro ε hε + exact eventually_of_comp_clock hXt hXcont (hg ε hε) + rcases hF.leading_or_zero_general (fun β hβ => (hb β hβ).2) hcoeff with + hz | ⟨β,hβ,hbne,ht⟩ + · left + filter_upwards [he,hXt.eventually hz] with t he hz + exact he.trans hz + · right + have hbcompne := hXt.eventually hbne + have hbnz : ¬ (fun t : ℝ => b β (X t:ℂ)) =ᶠ[atTop] 0 := by + intro hz + obtain ⟨t,ht,hz⟩ := (hbcompne.and hz).exists + exact ht hz + obtain ⟨M,hM,C,hC,htb⟩ := (ih hxs (hb β hβ).1).resolve_left hbnz + refine ⟨fun t => β*X t+M t,LogMonomial.step hM β,C,hC,?_⟩ + have hp := (ht.comp hXt).mul htb + simp only [one_mul] at hp + apply hp.congr' + filter_upwards [he,hbcompne] with t he hne + dsimp [Function.comp_def] + rw [he] + calc + ((Real.exp (-β*X t):ℂ)*(b β (X t:ℂ))⁻¹*F (X t:ℂ)) * + ((Real.exp (-M t):ℂ)*b β (X t:ℂ)) = + ((Real.exp (-β*X t):ℂ)*(Real.exp (-M t):ℂ)) * + ((b β (X t:ℂ))⁻¹*b β (X t:ℂ))*F (X t:ℂ) := by ring + _ = (Real.exp (-(β*X t+M t)):ℂ)*F (X t:ℂ) := by + rw [inv_mul_cancel₀ hne,mul_one,←Complex.ofReal_mul,←Real.exp_add] + congr 2; ring_nf + +lemma ClockGerm.leading {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + {f : ℝ → ℂ} (hf : ClockGerm xs f) (hne : ¬ f =ᶠ[atTop] 0) : RayLeading xs f := + (hf.leading_or_zero hxs).resolve_left hne + +lemma ClockGerm.eventually_nonzero {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + {f : ℝ → ℂ} (hf : ClockGerm xs f) (hne : ¬ f =ᶠ[atTop] 0) : + ∀ᶠ t : ℝ in atTop, f t ≠ 0 := (hf.leading hxs hne).eventually_nonzero + + + +theorem ClockGerm.eventually_sign {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + {f : ℝ → ℝ} (hf : ClockGerm xs (fun t => (f t:ℂ))) + (hne : ¬ f =ᶠ[atTop] 0) : + (∀ᶠ t : ℝ in atTop, 0 < f t) ∨ (∀ᶠ t : ℝ in atTop, f t < 0) := by + apply (hf.leading hxs ?_).eventually_sign + intro hz + exact hne (hz.mono (fun _ hx => Complex.ofReal_eq_zero.mp hx)) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +attribute [local instance] Classical.propDecidable +namespace DegeneratingTrees.Clock + +lemma ClockGerm.const (xs : List (ℝ → ℝ)) (c : ℂ) : ClockGerm xs (fun _ => c) := by + induction xs with + | nil => exact puiseux_const c + | cons X xs ih => + exact ⟨fun _ => c,{0},fun _ _ => c,SectorExpansion.const c, + fun _ _ => ⟨ih,SectorEventually.truth.mono (fun _ _ => analyticAt_const)⟩, + Filter.EventuallyEq.rfl⟩ + +lemma ClockGerm.neg {xs : List (ℝ → ℝ)} {f : ℝ → ℂ} (hf : ClockGerm xs f) : + ClockGerm xs (fun t => -f t) := by + induction xs generalizing f with + | nil => exact Puiseux.neg hf + | cons X xs ih => + obtain ⟨F,E,b,hF,hb,he⟩ := hf + refine ⟨fun z => -F z,E,fun β z => -b β z,hF.neg,?_,he.fun_comp Neg.neg⟩ + intro β hβ + exact ⟨ih (hb β hβ).1,((hb β hβ).2).mono (fun _ hx => hx.neg)⟩ + +lemma ClockGerm.add {xs : List (ℝ → ℝ)} {f g : ℝ → ℂ} + (hf : ClockGerm xs f) (hg : ClockGerm xs g) : ClockGerm xs (fun t => f t+g t) := by + induction xs generalizing f g with + | nil => exact Puiseux.add hf hg + | cons X xs ih => + obtain ⟨F,E,b,hF,hb,he⟩ := hf + obtain ⟨G,D,c,hG,hc,he'⟩ := hg + refine ⟨fun z => F z+G z,E ∪ D, + fun β z => (if β ∈ E then b β z else 0)+(if β ∈ D then c β z else 0), + hF.add hG,?_,he.add he'⟩ + intro β _ + have h1 : ClockGerm xs (fun t => if β ∈ E then b β (X t:ℂ) else 0) ∧ + SectorEventually (fun z => AnalyticAt ℂ (fun w => if β ∈ E then b β w else 0) z) := by + by_cases hβ : β ∈ E + · simpa only [ite_eq_left hβ] using hb β hβ + · simp only [ite_eq_right hβ] + exact ⟨ClockGerm.const _ 0,SectorEventually.truth.mono (fun _ _ => analyticAt_const)⟩ + have h2 : ClockGerm xs (fun t => if β ∈ D then c β (X t:ℂ) else 0) ∧ + SectorEventually (fun z => AnalyticAt ℂ (fun w => if β ∈ D then c β w else 0) z) := by + by_cases hβ : β ∈ D + · simpa only [ite_eq_left hβ] using hc β hβ + · simp only [ite_eq_right hβ] + exact ⟨ClockGerm.const _ 0,SectorEventually.truth.mono (fun _ _ => analyticAt_const)⟩ + exact ⟨ih h1.1 h2.1,(h1.2.and h2.2).mono (fun _ hx => hx.1.add hx.2)⟩ + +lemma ClockGerm.sub {xs : List (ℝ → ℝ)} {f g : ℝ → ℂ} + (hf : ClockGerm xs f) (hg : ClockGerm xs g) : ClockGerm xs (fun t => f t-g t) := by + simpa only [sub_eq_add_neg] using hf.add hg.neg + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma puiseux_of_comp_clock {X : ℝ → ℝ} {f : ℝ → ℂ} + (hX : Puiseux (fun t => (X t:ℂ))) (hXt : Tendsto X atTop atTop) + (hf : Puiseux (fun t => f (X t))) : Puiseux f := by + obtain ⟨I,hI,hIt,hl,hr⟩ := hX.inverse_change hXt + exact (hf.comp_unbounded hI hIt).congr (hl.mono (fun t ht => by simp [ht])) + +lemma firstClock_expansion_iff {X : ℝ → ℝ} (hX : Puiseux (fun t => (X t:ℂ))) + (hXt : Tendsto X atTop atTop) {f : ℝ → ℂ} : + ClockGerm (X :: []) f ↔ ∃ F : ℂ → ℂ,ExpansionOver PuiseuxSector F ∧ + f =ᶠ[atTop] fun t => F (X t:ℂ) := by + constructor + · rintro ⟨F,E,b,hF,hb,he⟩ + refine ⟨F,⟨E,b,hF,?_⟩,he⟩ + intro β hβ + exact ⟨(hb β hβ).2,puiseux_of_comp_clock hX hXt (hb β hβ).1⟩ + · rintro ⟨F,⟨E,b,hF,hb⟩,he⟩ + exact ⟨F,E,b,hF,fun β hβ => ⟨(hb β hβ).2.comp_unbounded hX hXt,(hb β hβ).1⟩,he⟩ + +lemma ClockGerm.first_mul {X : ℝ → ℝ} (hX : Puiseux (fun t => (X t:ℂ))) + (hXt : Tendsto X atTop atTop) {f g : ℝ → ℂ} + (hf : ClockGerm (X :: []) f) (hg : ClockGerm (X :: []) g) : + ClockGerm (X :: []) (fun t => f t*g t) := by + obtain ⟨F,hF,he⟩ := (firstClock_expansion_iff hX hXt).mp hf + obtain ⟨G,hG,he'⟩ := (firstClock_expansion_iff hX hXt).mp hg + exact (firstClock_expansion_iff hX hXt).mpr + ⟨fun z => F z*G z,hF.mul puiseux_lowerSectorData hG,he.mul he'⟩ + +lemma ClockGerm.first_inv {X : ℝ → ℝ} (hX : Puiseux (fun t => (X t:ℂ))) + (hXt : Tendsto X atTop atTop) {f : ℝ → ℂ} + (hf : ClockGerm (X :: []) f) : ClockGerm (X :: []) (fun t => (f t)⁻¹) := by + obtain ⟨F,hF,he⟩ := (firstClock_expansion_iff hX hXt).mp hf + exact (firstClock_expansion_iff hX hXt).mpr + ⟨fun z => (F z)⁻¹,hF.inv puiseux_lowerSectorData,he.inv⟩ + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RelativeErrors.lean b/lean/OAI/Analysis/PathSelection/RelativeErrors.lean new file mode 100644 index 0000000000000000000000000000000000000000..6f18e683821a9a97883565c44b528748ce316f17 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RelativeErrors.lean @@ -0,0 +1,315 @@ +import Mathlib +import OAI.Analysis.PathSelection.RealInverses + +namespace OAI + +/-! Relative perturbation errors, modulus estimates and zero-exponent charts. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma tendsto_sectorInfinity_of_close_map {G F : ℂ → ℂ} {C : ℝ} + (hC : 0≤C) (hG : Tendsto G sectorInfinity sectorInfinity) + (he : ∀ᶠ z in sectorInfinity,‖F z-G z‖≤C*logarithmicRadius ‖G z‖) : + Tendsto F sectorInfinity sectorInfinity := by + apply Filter.tendsto_def.mpr + intro S hS + obtain ⟨ω,R,hω,hS⟩ := hS + obtain ⟨η,T,hη,hRT,hT1,hdisc⟩ := hω.logarithmic_discs R hC + have hdom : ∀ᶠ w in sectorInfinity,w∈lossSector η T := ⟨η,T,hη,fun _ h => h⟩ + filter_upwards [hG.eventually hdom,he] with z hz hez + apply hS (F z) + apply hdisc (G z) hz + apply mem_closedBall_iff_norm.mpr + simpa only [logarithmicRadius,mul_assoc] using hez + +lemma baseLoss_le_of_upper {r s C : ℝ} (hr : 1 baseLoss ‖z‖)) : + Tendsto (fun z => G z*(1+E z)) sectorInfinity sectorInfinity := by + apply tendsto_sectorInfinity_of_close_map (C := 1) zero_le_one hG + filter_upwards [hupper,he.bound (by norm_num : (0:ℝ)<1/4), + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (max C 1)), + (tendsto_norm_sectorInfinity.comp hG).eventually (eventually_gt_atTop (1:ℝ))] with z hu hez hz hGz + have hz1 : 1<‖z‖ := (le_max_right _ _).trans_lt hz + have hlog : 0 baseLoss ‖z‖) := by + let F : ℂ → ℂ := fun z => z*(1+E z) + have hf : ∀ᶠ z in sectorInfinity,‖F z-z‖≤K*‖z‖*Real.exp (-ε*(x z).re) := by + filter_upwards [herr] with z hz + have he : F z-z=z*E z := by dsimp [F]; ring + rw [he,norm_mul] + nlinarith only [mul_le_mul_of_nonneg_left hz (norm_nonneg z)] + have hs := zero_exponent_error_small hC hK hε hX hlog hmod hx hf + apply Asymptotics.IsLittleO.of_bound + intro δ hδ + filter_upwards [hs.bound hδ,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hz hz1 + have hlog : 0 g z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) : + ∀ᶠ z in sectorInfinity,‖z‖/2≤‖g z‖ ∧ ‖g z‖≤2*‖z‖ := by + have hs := hg.trans_isBigO logarithmicRadius_isBigO_norm + filter_upwards [hs.bound (by norm_num : (0:ℝ)<1/2)] with z hz + simp only [Real.norm_eq_abs,abs_of_nonneg (norm_nonneg z)] at hz + have hl := norm_sub_le (g z) (g z-z) + rw [sub_sub_cancel] at hl + have hu := norm_add_le (g z-z) z + rw [sub_add_cancel] at hu + constructor <;> linarith [norm_nonneg z] + +theorem relative_error_comp_nearIdentity {E g : ℂ → ℂ} + (he : E =o[sectorInfinity] (fun z => baseLoss ‖z‖)) + (hg : (fun z => g z-z) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖)) : + (fun z => E (g z)) =o[sectorInfinity] (fun z => baseLoss ‖z‖) := by + have hdisp : ∀ᶠ z in sectorInfinity,‖g z-z‖≤logarithmicRadius ‖z‖ := by + filter_upwards [hg.bound zero_lt_one,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hz hz1 + simpa only [one_mul,Real.norm_eq_abs,abs_of_pos (logarithmicRadius_pos hz1)] using hz + have ht := tendsto_sectorInfinity_of_logarithmic_displacement hdisp + have hb : (fun z => baseLoss ‖g z‖) =O[sectorInfinity] (fun z => baseLoss ‖z‖) := by + apply Asymptotics.IsBigO.of_bound 4 + filter_upwards [nearIdentity_norm_bounds hg, + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ)), + (tendsto_norm_sectorInfinity.comp ht).eventually (eventually_gt_atTop (2:ℝ))] with z hz hz1 hg2 + have hg1 : 1<‖g z‖ := by dsimp only [Function.comp_apply] at hg2; linarith + simp only [Real.norm_eq_abs,abs_of_nonneg (show 0≤baseLoss ‖g z‖ by dsimp [baseLoss]; positivity), + abs_of_nonneg (show 0≤baseLoss ‖z‖ by dsimp [baseLoss]; positivity)] + exact baseLoss_le_of_upper hg1 hz1 hg2.le (by linarith [hz.1]) + exact (he.comp_tendsto ht).trans_isBigO hb + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma sector_principal_log_bound {G : ℂ → ℂ} {C : ℝ} + (hGa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ G z) + (hG : Tendsto G sectorInfinity sectorInfinity) + (hupper : ∀ᶠ z in sectorInfinity,‖G z‖≤C*‖z‖) : + (∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => Complex.log (G z)) z) ∧ + (∀ᶠ z in sectorInfinity,‖Complex.log (G z)‖≤(2+Real.pi)*Real.log ‖z‖) := by + constructor + · filter_upwards [hGa,hG.eventually SectorEventually.realpart_pos] with z ha hr + exact ha.clog (Complex.mem_slitPlane_iff.mpr (Or.inl hr)) + · filter_upwards [hupper, + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (max C (Real.exp 1))), + (tendsto_norm_sectorInfinity.comp hG).eventually (eventually_gt_atTop (1:ℝ))] with z hu hz hGz + have hr : Real.exp 1<‖z‖ := (le_max_right _ _).trans_lt hz + have hn : 0<‖z‖ := (Real.exp_pos 1).trans hr + have hlog : 1≤Real.log ‖z‖ := by + simpa only [Real.log_exp] using Real.log_le_log (Real.exp_pos 1) hr.le + have hG1 : 1<‖G z‖ := hGz + have hupper' : ‖G z‖≤‖z‖^2 := hu.trans (by have := (le_max_left _ _).trans hz.le; nlinarith) + have hlogG : Real.log ‖G z‖≤2*Real.log ‖z‖ := by + simpa only [Real.log_pow,Nat.cast_ofNat] using Real.log_le_log (zero_lt_one.trans hG1) hupper' + have hh := Complex.norm_le_abs_re_add_abs_im (Complex.log (G z)) + rw [Complex.log_re,Complex.log_im,abs_of_pos (Real.log_pos hG1)] at hh + nlinarith [Complex.abs_arg_le_pi (G z),mul_le_mul_of_nonneg_left hlog Real.pi_pos.le] + +lemma littleO_baseLoss_tendsto_zero {E : ℂ → ℂ} + (he : E =o[sectorInfinity] (fun z => baseLoss ‖z‖)) : Tendsto E sectorInfinity (𝓝 0) := by + apply tendsto_zero_iff_norm_tendsto_zero.mpr + apply squeeze_zero' (Eventually.of_forall fun z => norm_nonneg (E z)) _ + (admissible_baseLoss.tendsto_zero.comp tendsto_norm_sectorInfinity) + filter_upwards [he.bound zero_lt_one] with z hz + simpa only [Function.comp_apply,Real.norm_eq_abs,abs_of_nonneg (show 0≤baseLoss ‖z‖ by dsimp [baseLoss]; positivity),one_mul] using hz + +theorem nearIdentity_factor_ratio {G g : ℂ → ℂ} {C : ℝ} + (hGa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ G z) + (hG : Tendsto G sectorInfinity sectorInfinity) + (hupper : ∀ᶠ z in sectorInfinity,‖G z‖≤C*‖z‖) + (hgt : Tendsto g sectorInfinity sectorInfinity) + (hm : ∀ᶠ z in sectorInfinity,‖g z-z‖≤logarithmicRadius ‖z‖) + (hg : (fun z => g z-z) =o[sectorInfinity] (fun z => ‖z‖/(Real.log ‖z‖)^5)) : + Tendsto (fun z => G (g z)/G z) sectorInfinity (𝓝 1) := by + obtain ⟨ha,hb⟩ := sector_principal_log_bound hGa hG hupper + have hi := sector_log_increment_small (show 0≤2+Real.pi by positivity) ha hb hm hg + have hit : Tendsto (fun z => Complex.log (G (g z))-Complex.log (G z)) sectorInfinity (𝓝 0) := + littleO_baseLoss_tendsto_zero hi + have hlim := Complex.continuous_exp.tendsto 0 |>.comp hit + simp only [Complex.exp_zero] at hlim + apply hlim.congr' + filter_upwards [hG.eventually SectorEventually.realpart_pos, + (hG.comp hgt).eventually SectorEventually.realpart_pos] with z hz hgz + have h0 : G z≠0 := by + intro h + have hp : 0<(G z).re := hz + rw [h,Complex.zero_re] at hp + exact lt_irrefl _ hp + have hg0 : G (g z)≠0 := by + intro h + change 0<(G (g z)).re at hgz + simp [h] at hgz + dsimp only [Function.comp_apply] + rw [Complex.exp_sub,Complex.exp_log hg0,Complex.exp_log h0] + +lemma relative_modulus_bounds {F G : ℂ → ℂ} + (h : Tendsto (fun z => F z/G z) sectorInfinity (𝓝 1)) : + ∀ᶠ z in sectorInfinity,‖G z‖/2≤‖F z‖ ∧ ‖F z‖≤2*‖G z‖ := by + have hn := (continuous_norm.tendsto (1:ℂ)).comp h + simp only [norm_one] at hn + have hlo := hn.eventually (eventually_gt_nhds (by norm_num : (1/2:ℝ)<1)) + have hup := hn.eventually (eventually_lt_nhds (by norm_num : (1:ℝ)<2)) + filter_upwards [hlo,hup] with z hl hu + have hG0 : G z≠0 := by intro he; norm_num [Function.comp_apply,he] at hl + have hnG : 0<‖G z‖ := norm_pos_iff.mpr hG0 + simp only [Function.comp_apply,norm_div] at hl hu + have hl' := (lt_div_iff₀ hnG).mp hl + have hu' := (div_lt_iff₀ hnG).mp hu + constructor <;> linarith + +theorem relative_modulus_comparison {F G : ℂ → ℂ} {C : ℝ} + (hC : 0 F z/G z) sectorInfinity (𝓝 1)) + (hmod : ∀ᶠ z in sectorInfinity,‖G (‖z‖:ℂ)‖/C≤‖G z‖ ∧ ‖G z‖≤C*‖G (‖z‖:ℂ)‖) : + ∀ᶠ z in sectorInfinity,‖F (‖z‖:ℂ)‖/(4*C)≤‖F z‖ ∧ ‖F z‖≤4*C*‖F (‖z‖:ℂ)‖ := by + have hb := relative_modulus_bounds h + have hrad := tendsto_norm_sectorInfinity.eventually (tendsto_real_sectorInfinity.eventually hb) + filter_upwards [hb,hrad,hmod] with z hz hr hm + have hml := (div_le_iff₀ hC).mp hm.1 + have h1 := mul_le_mul_of_nonneg_left hz.1 hC.le + have h2 := mul_le_mul_of_nonneg_left hr.1 hC.le + constructor + · apply (div_le_iff₀ (show 0<4*C by positivity)).mpr + nlinarith [hr.2] + · nlinarith [hz.2,hm.2] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +theorem zero_exponent_chart {H G E x : ℂ → ℂ} {X : ℝ → ℝ} {C K ε D M : ℝ} + (hHa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ H z) + (hHr : ∀ᶠ r : ℝ in atTop,(H (r:ℂ)).im=0) + (hC : 1≤C) (hK : 0≤K) (hε : 0<ε) + (hX : Tendsto X atTop atTop) (hlog : Real.log =o[atTop] X) + (hxmod : ∀ᶠ z in sectorInfinity,X ‖z‖/C≤‖x z‖ ∧ ‖x z‖≤C*X ‖z‖) + (hx : Tendsto x sectorInfinity sectorInfinity) + (hHerr : ∀ᶠ z in sectorInfinity,‖H z-z‖≤K*‖z‖*Real.exp (-ε*(x z).re)) + (hGa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ G z) + (hEa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ E z) + (hG : Tendsto G sectorInfinity sectorInfinity) + (hD : 0≤D) (hupper : ∀ᶠ z in sectorInfinity,‖G z‖≤D*‖z‖) + (hM : 0 G (g z)*(1+E (g z))) z) ∧ + Tendsto (fun z => G (g z)*(1+E (g z))) sectorInfinity sectorInfinity ∧ + (∀ᶠ z in sectorInfinity, + ‖G (g (‖z‖:ℂ))*(1+E (g (‖z‖:ℂ)))‖/(4*M)≤‖G (g z)*(1+E (g z))‖ ∧ + ‖G (g z)*(1+E (g z))‖≤4*M*‖G (g (‖z‖:ℂ))*(1+E (g (‖z‖:ℂ)))‖) ∧ + ((fun z => (G z).re) =o[sectorInfinity] Complex.re → + (fun z => (G (g z)*(1+E (g z))).re) =o[sectorInfinity] Complex.re) := by + obtain ⟨g,I,hga,hgt,hIt,hreal,hri,hgs,hgN,hgre⟩ := + zero_exponent_real_inverse hHa hHr hC hK hε hX hlog hxmod hx hHerr + have he := relative_error_comp_nearIdentity + (zero_exponent_relative_error hC hK hε hX hlog hxmod hx hEerr) hgs + have hu : ∀ᶠ z in sectorInfinity,‖G (g z)‖≤(2*D)*‖z‖ := by + filter_upwards [hgt.eventually hupper,nearIdentity_norm_bounds hgs] with z hz hn + exact hz.trans (by nlinarith [mul_le_mul_of_nonneg_left hn.2 hD]) + have hdisp : ∀ᶠ z in sectorInfinity,‖g z-z‖≤logarithmicRadius ‖z‖ := by + filter_upwards [hgs.bound zero_lt_one,tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (1:ℝ))] with z hz hz1 + simpa only [one_mul,Real.norm_eq_abs,abs_of_pos (logarithmicRadius_pos hz1)] using hz + have hratio := nearIdentity_factor_ratio hGa hG hupper hgt hdisp (hgN 5) + have het := littleO_baseLoss_tendsto_zero he + have hrat : Tendsto (fun z => G (g z)*(1+E (g z))/G z) sectorInfinity (𝓝 1) := by + have hh := hratio.mul (het.const_add 1) + simp only [add_zero,mul_one] at hh + convert hh using 1 + ext z + ring + refine ⟨g,I,hga,hgt,hIt,hreal,hri,?_, + sector_relative_perturbation (hG.comp hgt) hu he, + relative_modulus_comparison hM hrat hGmod,?_⟩ + · filter_upwards [hga,hgt.eventually hGa,hgt.eventually hEa] with z hg hGz hEz + exact (hGz.comp hg.1).mul (analyticAt_const.add (hEz.comp hg.1)) + · intro hsmall + have hbig : (fun z => G (g z)) =O[sectorInfinity] (fun z => ‖z‖) := by + apply Asymptotics.IsBigO.of_bound (2*D) + simpa only [Real.norm_eq_abs,abs_of_nonneg (norm_nonneg _)] using hu + have hprod := hbig.mul_isLittleO he + have hep : (fun z => G (g z)*E (g z)) =o[sectorInfinity] (fun z => logarithmicRadius ‖z‖) := hprod + have hh := nearIdentity_realpart_separation hgs hsmall hep + convert hh using 1 + ext z + congr 1 + ring + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RelativeStrips.lean b/lean/OAI/Analysis/PathSelection/RelativeStrips.lean new file mode 100644 index 0000000000000000000000000000000000000000..4c3624c25ed7bb84a99d344f9dfb17e4fdd81e02 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RelativeStrips.lean @@ -0,0 +1,537 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockInverses + +namespace OAI + +/-! Derivative growth, relative strips and inverse clock ratios. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma real_log_derivative_bound {f g : ℝ → ℝ} {q : ℝ} + (hf : ∀ᶠ t : ℝ in atTop,DifferentiableAt ℝ f t ∧ 0 Real.log (f t)-q*Real.log (g t) + have hL (t : ℝ) (ht : t∈Ici T) : + HasDerivAt L (deriv f t/f t-q*(deriv g t/g t)) t := + ((hT t ht).1.1.hasDerivAt.log (hT t ht).1.2.ne').sub + (((hT t ht).2.1.1.hasDerivAt.log (hT t ht).2.1.2.ne').const_mul q) + have hanti : AntitoneOn L (Ici T) := antitoneOn_of_deriv_nonpos (convex_Ici T) + (fun t ht => (hL t ht).continuousAt.continuousWithinAt) + (fun t ht => (hL t (interior_subset ht)).differentiableAt.differentiableWithinAt) + (fun t ht => by rw [(hL t (interior_subset ht)).deriv]; exact (hT t (interior_subset ht)).2.2) + refine ⟨Real.exp (L T),Real.exp_pos _,?_⟩ + filter_upwards [eventually_ge_atTop T] with t ht + have hh := hanti (show T∈Ici T by simp) ht ht + have hft := (hT t ht).1.2 + have hgt := (hT t ht).2.1.2 + calc + f t = Real.exp (Real.log (f t)) := (Real.exp_log hft).symm + _ ≤ Real.exp (L T+q*Real.log (g t)) := Real.exp_le_exp.mpr (by dsimp [L] at hh; linarith) + _ = Real.exp (L T)*(g t)^q := by rw [Real.exp_add,Real.rpow_def_of_pos hgt]; congr 2; ring + +lemma complex_re_log_derivative {F : ℂ → ℂ} {t : ℝ} + (ha : AnalyticAt ℂ F (t:ℂ)) (hr : (F (t:ℂ)).im=0) : + DifferentiableAt ℝ (fun s : ℝ => (F (s:ℂ)).re) t ∧ + deriv (fun s : ℝ => (F (s:ℂ)).re) t/(F (t:ℂ)).re=(deriv F (t:ℂ)/F (t:ℂ)).re := by + have hd := Complex.reCLM.hasFDerivAt.comp_hasDerivAt t ha.differentiableAt.hasDerivAt.comp_ofReal + change HasDerivAt (fun s : ℝ => (F (s:ℂ)).re) (deriv F (t:ℂ)).re t at hd + refine ⟨hd.differentiableAt,?_⟩ + rw [hd.deriv,show F (t:ℂ)=((F (t:ℂ)).re:ℂ) from Complex.ext rfl (by simpa using hr)] + simp only [Complex.ofReal_re,Complex.div_ofReal_re] + +theorem complex_log_derivative_power_bound {F H : ℂ → ℂ} {a b q : ℝ} + (hgap : a deriv F (t:ℂ)/F (t:ℂ)) atTop (𝓝 (a:ℂ))) + (hHd : Tendsto (fun t : ℝ => deriv H (t:ℂ)/H (t:ℂ)) atTop (𝓝 (b:ℂ))) : + ∃ C : ℝ,0 (F (s:ℂ)).re) t ∧ + 0<(F (t:ℂ)).re ∧ deriv (fun s : ℝ => (F (s:ℂ)).re) t/(F (t:ℂ)).re=(deriv F (t:ℂ)/F (t:ℂ)).re := by + filter_upwards [hFa,hFr] with t ha hr + exact ⟨(complex_re_log_derivative ha hr.1).1,hr.2,(complex_re_log_derivative ha hr.1).2⟩ + have hHreal : ∀ᶠ t : ℝ in atTop,DifferentiableAt ℝ (fun s : ℝ => (H (s:ℂ)).re) t ∧ + 0<(H (t:ℂ)).re ∧ deriv (fun s : ℝ => (H (s:ℂ)).re) t/(H (t:ℂ)).re=(deriv H (t:ℂ)/H (t:ℂ)).re := by + filter_upwards [hHa,hHr] with t ha hr + exact ⟨(complex_re_log_derivative ha hr.1).1,hr.2,(complex_re_log_derivative ha hr.1).2⟩ + apply real_log_derivative_bound (hFreal.mono fun _ h => ⟨h.1,h.2.1⟩) + (hHreal.mono fun _ h => ⟨h.1,h.2.1⟩) + have ht := ((Complex.continuous_re.tendsto (a:ℂ)).comp hFd).sub + (((Complex.continuous_re.tendsto (b:ℂ)).comp hHd).const_mul q) + simp only [Complex.ofReal_re] at ht + have hn := ht.eventually (eventually_lt_nhds (show a-q*b<0 by linarith)) + filter_upwards [hFreal,hHreal,hn] with t hf hh hn + rw [hf.2.2,hh.2.2] + exact hn.le + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma unbounded_log_exponent_order {F H : ℂ → ℂ} {a b : ℝ} + (hb : 0≤b) + (hFa : ∀ᶠ t : ℝ in atTop,AnalyticAt ℂ F (t:ℂ)) + (hHa : ∀ᶠ t : ℝ in atTop,AnalyticAt ℂ H (t:ℂ)) + (hFr : ∀ᶠ t : ℝ in atTop,(F (t:ℂ)).im=0 ∧ 0<(F (t:ℂ)).re) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hFt : Tendsto (fun t : ℝ => (F (t:ℂ)).re) atTop atTop) + (hFd : Tendsto (fun t : ℝ => deriv F (t:ℂ)/F (t:ℂ)) atTop (𝓝 (a:ℂ))) + (hHd : Tendsto (fun t : ℝ => deriv H (t:ℂ)/H (t:ℂ)) atTop (𝓝 (b:ℂ))) + (hO : ∃ D : ℝ,0 simp + rw [he,norm_mul,Complex.norm_I,Complex.norm_real,Real.norm_eq_abs,one_mul] + +theorem relative_strip_estimate {F : ℂ → ℂ} + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ F z) + (hz : ∀ᶠ z in stripInfinity,F z≠0) + (hd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 0)) + {R : ℝ} (hR : 0 (hA z hz).1) (fun z hz => (hA z hz).2.1) + refine ⟨A,?_⟩ + intro z hz + have hzr : (z.re:ℂ)∈horizontalTail A R := ⟨hz.1,by simpa using hR⟩ + have hinc : ‖L z-L (z.re:ℂ)‖≤δ*|z.im| := by + have hh := Convex.norm_image_sub_le_of_norm_deriv_le + (fun z hz => (hLa z hz).differentiableAt) + (fun z hz => by rw [hLd z hz]; exact (hA z hz).2.2) + (horizontalTail_convex A R) hzr hz + simpa only [norm_sub_real_part] using hh + have hsmall : ‖L z-L (z.re:ℂ)‖≤1 := by + apply hinc.trans + have hδR : δ*(R+1)≤1 := by + have hh := mul_le_mul_of_nonneg_right (min_le_right (ε/2) (1/(R+1))) (by positivity : 0≤R+1) + simpa only [δ,one_div,inv_mul_cancel₀ (by positivity : R+1≠0)] using hh + nlinarith [hz.2] + have hratio : F z/F (z.re:ℂ)=Complex.exp (L z-L (z.re:ℂ)) := by + rw [Complex.exp_sub,hLe z hz,hLe _ hzr] + refine ⟨(hA _ hzr).2.1,?_⟩ + rw [hratio] + calc + ‖Complex.exp (L z-L (z.re:ℂ))-1‖ ≤ 2*‖L z-L (z.re:ℂ)‖ := Complex.norm_exp_sub_one_le hsmall + _ ≤ 2*(δ*|z.im|) := mul_le_mul_of_nonneg_left hinc (by norm_num) + _ ≤ ε*|z.im| := by + have hh := mul_le_mul_of_nonneg_right (min_le_left (ε/2) (1/(R+1))) (abs_nonneg z.im) + nlinarith + +private lemma relative_strip_log_deriv_bound {function : ℂ → ℂ} {center : ℂ} + {radius bound : ℝ} (hradius : 0 logarithm (center+point)-logarithm center + have hmem {point : ℂ} (hpoint : point∈ball 0 radius) : center+point∈ball center radius := by + simpa only [mem_ball_iff_norm,add_sub_cancel_left,sub_zero] using hpoint + have hnormalized : AnalyticOnNhd ℂ normalized (ball 0 radius) := by + intro point hpoint + exact ((hlogarithm _ (hmem hpoint)).comp + (analyticAt_const.add analyticAt_id)).sub analyticAt_const + have hreal_bound : MapsTo normalized (ball 0 radius) {point | point.re≤2*bound} := by + intro point hpoint + change (logarithm (center+point)).re-(logarithm center).re≤2*bound + have hpoint_bound := abs_le.mp (hreal _ (hmem hpoint)) + have hcenter_bound := abs_le.mp (hreal _ (mem_ball_self hradius)) + linarith + have hnorm_bound (point : ℂ) (hpoint : point∈sphere 0 (radius/2)) : + ‖normalized point‖≤4*bound := by + have hnorm : ‖point‖=radius/2 := by + simpa only [mem_sphere_iff_norm,sub_zero] using hpoint + have hinside : point∈ball 0 radius := by rw [mem_ball_zero_iff,hnorm]; linarith + have hestimate := Complex.borelCaratheodory_zero (f := normalized) + (by positivity : 0<2*bound) hnormalized.differentiableOn hreal_bound hradius hinside + (by simp [normalized]) + rw [hnorm] at hestimate + convert hestimate using 1 + field_simp + ring + have hclosure : closure (ball (0:ℂ) (radius/2)) ⊆ ball 0 radius := by + rw [closure_ball _ (by positivity : radius/2≠0)] + intro point hpoint + rw [mem_ball_zero_iff] + have hnorm : ‖point‖≤radius/2 := by + simpa only [mem_closedBall_iff_norm,sub_zero] using hpoint + linarith + have hcontinuous : DiffContOnCl ℂ normalized (ball 0 (radius/2)) := + ((hnormalized.mono hclosure).differentiableOn).diffContOnCl + have hestimate := Complex.norm_deriv_le_of_forall_mem_sphere_norm_le + (by positivity : 0 (function point)⁻¹)) : + Tendsto (fun point => deriv function point/function point) stripInfinity (𝓝 0) := by + apply Metric.tendsto_nhds.mpr + intro epsilon hepsilon + let delta := epsilon/512 + have hdelta : 0 simp + rw [heq,norm_mul,Complex.norm_I,Complex.norm_real,Real.norm_eq_abs,one_mul] + have hnearby_norm : ‖nearby-point‖ (hsector nearby (hdisc hnearby)).1) + (fun nearby hnearby => (hsector nearby (hdisc hnearby)).2.1) hlog + change dist (deriv function point/function point) 0 (F z)⁻¹)) + {R : ℝ} (hR : 0 deriv F z/F z) stripInfinity (𝓝 0)) + {R : ℝ} (hR : 0 (hA z hz).1) (fun z hz => (hA z hz).2.1) + refine ⟨A,?_⟩ + intro z hz w hzr hdist + have hinc : ‖L z-L w‖≤δ*‖z-w‖ := by + have hh := Convex.norm_image_sub_le_of_norm_deriv_le + (fun z hz => (hLa z hz).differentiableAt) + (fun z hz => by rw [hLd z hz]; exact (hA z hz).2.2) + (horizontalTail_convex A R) hzr hz + exact hh + have hsmall : ‖L z-L w‖≤1 := by + apply hinc.trans + have hδR : δ*(B+1)≤1 := by + have hh := mul_le_mul_of_nonneg_right (min_le_right (ε/2) (1/(B+1))) (by positivity : 0≤B+1) + simpa only [δ,one_div,inv_mul_cancel₀ (by positivity : B+1≠0)] using hh + nlinarith + have hratio : F z/F w=Complex.exp (L z-L w) := by + rw [Complex.exp_sub,hLe z hz,hLe _ hzr] + refine ⟨(hA _ hzr).2.1,?_⟩ + rw [hratio] + calc + ‖Complex.exp (L z-L w)-1‖ ≤ 2*‖L z-L w‖ := Complex.norm_exp_sub_one_le hsmall + _ ≤ 2*(δ*‖z-w‖) := mul_le_mul_of_nonneg_left hinc (by norm_num) + _ ≤ ε*‖z-w‖ := by + have hh := mul_le_mul_of_nonneg_right (min_le_left (ε/2) (1/(B+1))) (norm_nonneg (z-w)) + nlinarith + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma exponential_normalized_log_deriv {F : ℂ → ℂ} {a : ℂ} + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ F z) + (hz : ∀ᶠ z in stripInfinity,F z≠0) + (hd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 a)) : + Tendsto (fun z => deriv (fun w => Complex.exp (-a*w)*F w) z / + (Complex.exp (-a*z)*F z)) stripInfinity (𝓝 0) := by + have hh := hd.sub_const a + simp only [sub_self] at hh + apply hh.congr' + filter_upwards [ha,hz] with z ha hz + have hde := ((Complex.hasDerivAt_exp (-a*z)).comp z ((hasDerivAt_id z).const_mul (-a))).mul ha.differentiableAt.hasDerivAt + change HasDerivAt (fun w => Complex.exp (-a*w)*F w) _ z at hde + change deriv F z/F z-a=deriv (fun w => Complex.exp (-a*w)*F w) z/(Complex.exp (-a*z)*F z) + rw [hde.deriv] + simp only [Function.comp_apply,mul_one] + field_simp [hz,Complex.exp_ne_zero] + ring + +theorem affine_relative_strip_pair_estimate {F : ℂ → ℂ} {a : ℂ} + (ha : ∀ᶠ z in stripInfinity,AnalyticAt ℂ F z) + (hz : ∀ᶠ z in stripInfinity,F z≠0) + (hd : Tendsto (fun z => deriv F z/F z) stripInfinity (𝓝 a)) + {R : ℝ} (hR : 0 Complex.exp (-a*z)*F z + have hGa : ∀ᶠ z in stripInfinity,AnalyticAt ℂ G z := + ha.mono (fun z hz => ((analyticAt_const.mul analyticAt_id).cexp).mul hz) + have hG0 : ∀ᶠ z in stripInfinity,G z≠0 := hz.mono (fun z hz => mul_ne_zero (Complex.exp_ne_zero _) hz) + obtain ⟨A,hA⟩ := relative_strip_pair_estimate hGa hG0 + (exponential_normalized_log_deriv ha hz hd) hR hB hε + refine ⟨A,?_⟩ + intro z hz w hw hdzw + obtain ⟨hne,hbound⟩ := hA z hz w hw hdzw + have hFw : F w≠0 := fun he => hne (by simp [G,he]) + refine ⟨hFw,?_⟩ + have he : G z/G w=Complex.exp (-a*(z-w))*(F z/F w) := by + dsimp [G] + rw [show -a*(z-w)=(-a*z)-(-a*w) by ring,Complex.exp_sub] + ring + rwa [he] at hbound + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees.Clock + +lemma inverse_increment_error_tendsto {x : ℂ → ℂ} {b : ℝ} + (hi : ∀ ε : ℝ,0<ε → ∀ᶠ w in sectorInfinity, + ‖x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)‖≤ε*|w.arg|) : + Tendsto (fun w => x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)) sectorInfinity (𝓝 0) := by + apply Metric.tendsto_nhds.mpr + intro ε hε + filter_upwards [hi (ε/(Real.pi+1)) (by positivity)] with w hw + rw [dist_zero_right] + have hh := mul_le_mul_of_nonneg_left (Complex.abs_arg_le_pi w) (by positivity : 0≤ε/(Real.pi+1)) + apply (hw.trans hh).trans_lt + rw [div_mul_eq_mul_div] + exact (div_lt_iff₀ (by positivity : 0 deriv F z/F z) stripInfinity (𝓝 a)) + (hx : Tendsto (fun w => (x w).re) sectorInfinity atTop) + (ht : Tendsto (fun r : ℝ => (x (r:ℂ)).re) atTop atTop) + (hr : ∀ᶠ r : ℝ in atTop,(x (r:ℂ)).im=0) + (hi : ∀ ε : ℝ,0<ε → ∀ᶠ w in sectorInfinity, + ‖x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ)‖≤ε*|w.arg|) : + Tendsto (fun w => Complex.exp (-a*Complex.I*(w.arg/b:ℝ)) * + (F (x w)/F (x (‖w‖:ℂ)))) sectorInfinity (𝓝 1) := by + obtain ⟨B,hB,hbound⟩ := inverse_pair_bounded hb hr (by simpa only [one_mul] using hi 1 zero_lt_one) + have hpair : Tendsto (fun w => Complex.exp (-a*(x w-x (‖w‖:ℂ)))* + (F (x w)/F (x (‖w‖:ℂ)))) sectorInfinity (𝓝 1) := by + apply Metric.tendsto_nhds.mpr + intro ε hε + obtain ⟨A,hA⟩ := affine_relative_strip_pair_estimate ha hz hd + (show 0 by + change Complex.exp (a*(x w-x (‖w‖:ℂ)-Complex.I*(w.arg/b:ℝ))) * + (Complex.exp (-a*(x w-x (‖w‖:ℂ)))*(F (x w)/F (x (‖w‖:ℂ)))) = _ + rw [←mul_assoc,←Complex.exp_add] + congr 2 + ring + +lemma inverse_clock_modulus_tendsto {F x : ℂ → ℂ} {a b : ℝ} + (h : Tendsto (fun w => Complex.exp (-(a:ℂ)*Complex.I*(w.arg/b:ℝ)) * + (F (x w)/F (x (‖w‖:ℂ)))) sectorInfinity (𝓝 1)) : + Tendsto (fun w => ‖F (x w)‖/‖F (x (‖w‖:ℂ))‖) sectorInfinity (𝓝 1) := by + have hh := h.norm + simp only [norm_one] at hh + apply hh.congr' + exact Eventually.of_forall fun w => by + dsimp only + rw [norm_mul,norm_div,Complex.norm_exp] + have he : (-(a:ℂ)*Complex.I*(w.arg/b:ℝ)).re=0 := by simp + rw [he,Real.exp_zero,one_mul] + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RootClusters.lean b/lean/OAI/Analysis/PathSelection/RootClusters.lean new file mode 100644 index 0000000000000000000000000000000000000000..67544de246aa528c2f7cc3f96addd4f115b34f64 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RootClusters.lean @@ -0,0 +1,299 @@ +import Mathlib +import OAI.Analysis.PathSelection.CompactProfiles +import OAI.Analysis.PathSelection.ContourDivision + +namespace OAI + +/-! Constant root counts and joint preparation of fixed root clusters. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +namespace DegeneratingTrees +open Set Metric Filter Topology Complex + +theorem contour_rootCount_constant {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} {U : Set A} (hU : IsOpen U) (hUc : IsPreconnected U) + {r : ℝ} (hr : 0 < r) (hF : AnalyticOnNhd ℂ F (U ×ˢ closedBall 0 r)) + (hn : ∀ q ∈ U, ∀ z ∈ sphere (0 : ℂ) r, F (q,z) ≠ 0) + {q₀ : A} (hq₀ : q₀ ∈ U) : + ∀ q ∈ U, contourMoment (fun y => F (q,y)) r 0 = + contourMoment (fun y => F (q₀,y)) r 0 := by + let M : A → ℂ := fun q => contourMoment (fun y => F (q,y)) r 0 + have hM : AnalyticOnNhd ℂ M U := analytic_contourMoment_general hU hr + (hF.mono (fun x hx => ⟨hx.1,sphere_subset_closedBall hx.2⟩)) hn 0 + have hnat (q : A) (hq : q ∈ U) : ∃ n : ℕ, M q = (n : ℂ) := by + have hf : AnalyticOnNhd ℂ (fun y => F (q,y)) (closedBall 0 r) := by + intro y hy + exact (hF (q,y) ⟨hq,hy⟩).comp (analyticAt_const.prod analyticAt_id) + obtain ⟨n,_,he,_⟩ := contour_fiber_factorization hr hf (hn q hq) + exact ⟨n,he⟩ + obtain ⟨n,hn0⟩ := hnat q₀ hq₀ + have hev : M =ᶠ[𝓝 q₀] fun _ => M q₀ := by + have hd := (hM q₀ hq₀).continuousAt.preimage_mem_nhds + (ball_mem_nhds (M q₀) (show (0 : ℝ) < 1 by norm_num)) + filter_upwards [hU.mem_nhds hq₀,hd] with q hq hdq + obtain ⟨m,hm⟩ := hnat q hq + have he : m = n := by + have hdist : dist (m : ℂ) (n : ℂ) < 1 := by simpa [hm,hn0] using hdq + have hcast : ((m : ℂ) - n) = (((m : ℤ) - n : ℤ) : ℂ) := by push_cast; rfl + rw [dist_eq_norm,hcast,Complex.norm_intCast] at hdist + have hint : |((m : ℤ) - n : ℤ)| < 1 := by exact_mod_cast hdist + have hzero := Int.abs_lt_one_iff.mp hint + omega + rw [hm,hn0,he] + exact hM.eqOn_of_preconnected_of_eventuallyEq analyticOnNhd_const hUc hq₀ hev + + + +theorem contour_rootCount_eq_of_close {f g : ℂ → ℂ} {r : ℝ} (hr : 0 < r) + (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hg : AnalyticOnNhd ℂ g (closedBall 0 r)) + (hn : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) + (hc : ∀ z ∈ sphere (0 : ℂ) r, ‖g z-f z‖ < ‖f z‖ / 2) : + contourMoment g r 0 = contourMoment f r 0 := by + let H : ℂ × ℂ → ℂ := fun x => f x.2 + x.1 * (g x.2-f x.2) + have hH : AnalyticOnNhd ℂ H (ball 0 2 ×ˢ closedBall 0 r) := by + intro x hx + have hfa := (hf x.2 hx.2).comp analyticAt_snd + have hga := (hg x.2 hx.2).comp analyticAt_snd + exact hfa.add (analyticAt_fst.mul (hga.sub hfa)) + have hHn : ∀ t ∈ ball (0 : ℂ) 2, ∀ z ∈ sphere (0 : ℂ) r, H (t,z) ≠ 0 := by + intro t ht z hz + have ht' : ‖t‖ < 2 := by simpa using ht + have hd : ‖t * (g z-f z)‖ < ‖f z‖ := by + rw [norm_mul] + calc + ‖t‖ * ‖g z-f z‖ ≤ ‖t‖ * (‖f z‖ / 2) := + mul_le_mul_of_nonneg_left (hc z hz).le (norm_nonneg _) + _ < 2 * (‖f z‖ / 2) := + mul_lt_mul_of_pos_right ht' (half_pos (norm_pos_iff.mpr (hn z hz))) + _ = ‖f z‖ := by ring + intro he + have he' : f z = -(t * (g z-f z)) := eq_neg_of_add_eq_zero_left he + have heN : ‖f z‖ = ‖t * (g z-f z)‖ := by + calc + ‖f z‖ = ‖-(t * (g z-f z))‖ := congrArg norm he' + _ = _ := norm_neg _ + exact (lt_irrefl _ (hd.trans_eq heN)) + have he := contour_rootCount_constant isOpen_ball (convex_ball (0 : ℂ) 2).isPreconnected + hr hH hHn (show (0 : ℂ) ∈ ball 0 2 by simp) 1 (by simp) + simpa [H] using he + +end DegeneratingTrees + +namespace DegeneratingTrees +open Set Metric Filter Topology Complex + + + +theorem fixed_contour_preparation_general {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} {U : Set A} (hU : IsOpen U) {r : ℝ} (hr : 0 < r) {d : ℕ} + (hFA : AnalyticOnNhd ℂ F (U ×ˢ closedBall 0 r)) + (hnB : ∀ q ∈ U, ∀ z ∈ sphere (0 : ℂ) r, F (q,z) ≠ 0) + (hm0 : ∀ q ∈ U, contourMoment (fun y => F (q,y)) r 0 = (d : ℂ)) : + ∃ g : A × ℂ → ℂ, + AnalyticOnNhd ℂ g (U ×ˢ ball 0 r) ∧ + (∀ q ∈ U, ∀ y ∈ ball (0 : ℂ) r, g (q,y) ≠ 0) ∧ + (∀ q ∈ U, (contourPolynomial (fun y => F (q,y)) r d).Monic ∧ + (contourPolynomial (fun y => F (q,y)) r d).natDegree = d) ∧ + (∀ k, AnalyticOnNhd ℂ + (fun q => (contourPolynomial (fun y => F (q,y)) r d).coeff k) U) ∧ + (∀ q ∈ U, ∀ y ∈ ball (0 : ℂ) r, + F (q,y) = (contourPolynomial (fun y => F (q,y)) r d).eval y * g (q,y)) := by + classical + let h : C(sphere (0 : ℂ) r,ℂ) := ⟨Subtype.val,continuous_subtype_val⟩ + let φ := compactProfile h F + have hφ : AnalyticOnNhd ℂ φ U := analytic_compactProfile h hU + (fun q hq t => hFA _ ⟨hq,sphere_subset_closedBall t.property⟩) + have hφe (q : A) (hq : q ∈ U) (t : sphere (0 : ℂ) r) : φ q t = F (q,t) := by + apply compactProfile_apply + exact hFA.continuousOn.comp_continuous + (continuous_const.prodMk continuous_subtype_val) + (fun t => ⟨hq,sphere_subset_closedBall t.property⟩) + have hfB (q : A) (hq : q ∈ U) : AnalyticOnNhd ℂ (fun y => F (q,y)) (closedBall 0 r) := by + intro y hy + exact (hFA (q,y) ⟨hq,hy⟩).comp (analyticAt_const.prod analyticAt_id) + have hm (k : ℕ) : AnalyticOnNhd ℂ (fun q => contourMoment (fun y => F (q,y)) r k) U := + analytic_contourMoment_general hU hr + (hFA.mono (fun x hx => ⟨hx.1,sphere_subset_closedBall hx.2⟩)) hnB k + have hfac (q : A) (hq : q ∈ U) : + ∃ g : ℂ → ℂ, (contourPolynomial (fun y => F (q, y)) r d).Monic ∧ + (contourPolynomial (fun y => F (q, y)) r d).natDegree = d ∧ + AnalyticOnNhd ℂ g (closedBall 0 r) ∧ + (∀ z ∈ closedBall (0 : ℂ) r, g z ≠ 0) ∧ + EqOn (fun y => F (q, y)) + (fun y => (contourPolynomial (fun y => F (q, y)) r d).eval y * g y) (closedBall 0 r) := by + obtain ⟨N, g, hN, hM, hD, hg, hgn, hfg⟩ := contour_fiber_factorization hr (hfB q hq) (hnB q hq) + have hNd : N = d := by exact_mod_cast hN.symm.trans (hm0 q hq) + subst N + exact ⟨g, hM, hD, hg, hgn, hfg⟩ + have hpU (q : A) (hq : q ∈ U) : IsUnit (contourPolynomialProfile F r d q) := by + rw [ContinuousMap.isUnit_iff_forall_ne_zero] + intro z + rw [contourPolynomialProfile_apply] + obtain ⟨g, _, _, _, _, hfg⟩ := hfac q hq + have he := hfg (sphere_subset_closedBall z.property) + dsimp only at he + exact left_ne_zero_of_mul (by rw [← he]; exact hnB q hq z z.property) + let κ : A → C(sphere (0 : ℂ) r, ℂ) := fun q => φ q * Ring.inverse (contourPolynomialProfile F r d q) + have hκ : AnalyticOnNhd ℂ κ U := by + intro q hq + exact (hφ q hq).mul ((analyticOnNhd_inverse _ (hpU q hq)).comp + (analytic_contourPolynomialProfile hm d q hq)) + let g : A × ℂ → ℂ := cauchyTransformProfile r hr κ + have hgFiber (q : A) (hq : q ∈ U) (v : ℂ → ℂ) + (hv : AnalyticOnNhd ℂ v (closedBall 0 r)) + (hfv : EqOn (fun y => F (q, y)) + (fun y => (contourPolynomial (fun y => F (q, y)) r d).eval y * v y) (closedBall 0 r)) + (y : ℂ) (hy : y ∈ ball (0 : ℂ) r) : g (q, y) = v y := by + apply cauchyTransformProfile_eq hr hv _ hy + intro z + dsimp only [κ] + rw [ContinuousMap.mul_apply, continuousMap_ringInverse_apply _ (hpU q hq), + hφe q hq, contourPolynomialProfile_apply] + have he := hfv (sphere_subset_closedBall z.property) + dsimp only at he + rw [he] + have hn : (contourPolynomial (fun y => F (q, y)) r d).eval (z : ℂ) ≠ 0 := by + rw [← contourPolynomialProfile_apply] + exact (ContinuousMap.isUnit_iff_forall_ne_zero _).1 (hpU q hq) z + field_simp + refine ⟨g, analytic_cauchyTransformProfile hr hκ, ?_, ?_, + fun k => analytic_contourPolynomial_coeff hm d k, ?_⟩ + · intro q hq y hy + obtain ⟨v, _, _, hv, hvn, hfv⟩ := hfac q hq + rw [hgFiber q hq v hv hfv y hy] + exact hvn y (ball_subset_closedBall hy) + · intro q hq + obtain ⟨_, hM, hD, _⟩ := hfac q hq + exact ⟨hM, hD⟩ + · intro q hq y hy + obtain ⟨v, _, _, hv, _, hfv⟩ := hfac q hq + rw [hgFiber q hq v hv hfv y hy] + exact hfv (ball_subset_closedBall hy) + +end DegeneratingTrees + +namespace DegeneratingTrees +open Set Metric Filter Topology Complex + + + +theorem fixed_contour_preparation_of_close {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {F : A × ℂ → ℂ} {f : ℂ → ℂ} {U : Set A} (hU : IsOpen U) {r : ℝ} (hr : 0 < r) + {d : ℕ} (hf : AnalyticOnNhd ℂ f (closedBall 0 r)) + (hfn : ∀ z ∈ sphere (0 : ℂ) r, f z ≠ 0) + (hfm : contourMoment f r 0 = (d : ℂ)) + (hF : AnalyticOnNhd ℂ F (U ×ˢ closedBall 0 r)) + (hc : ∀ q ∈ U, ∀ z ∈ sphere (0 : ℂ) r, ‖F (q,z)-f z‖ < ‖f z‖ / 2) : + ∃ g : A × ℂ → ℂ, + AnalyticOnNhd ℂ g (U ×ˢ ball 0 r) ∧ + (∀ q ∈ U, ∀ y ∈ ball (0 : ℂ) r, g (q,y) ≠ 0) ∧ + (∀ q ∈ U, ∀ z ∈ sphere (0 : ℂ) r, F (q,z) ≠ 0) ∧ + (∀ q ∈ U, (contourPolynomial (fun y => F (q,y)) r d).Monic ∧ + (contourPolynomial (fun y => F (q,y)) r d).natDegree = d) ∧ + (∀ k, AnalyticOnNhd ℂ + (fun q => (contourPolynomial (fun y => F (q,y)) r d).coeff k) U) ∧ + (∀ q ∈ U, ∀ y ∈ ball (0 : ℂ) r, + F (q,y) = (contourPolynomial (fun y => F (q,y)) r d).eval y * g (q,y)) := by + have hn : ∀ q ∈ U, ∀ z ∈ sphere (0 : ℂ) r, F (q,z) ≠ 0 := by + intro q hq z hz he + have ht := hc q hq z hz + rw [he,zero_sub,norm_neg] at ht + linarith [norm_nonneg (f z)] + have hm : ∀ q ∈ U, contourMoment (fun y => F (q,y)) r 0 = (d : ℂ) := by + intro q hq + exact (contour_rootCount_eq_of_close (g := fun y => F (q,y)) hr hf (fun z hz => + (hF (q,z) ⟨hq,hz⟩).comp (analyticAt_const.prod analyticAt_id)) hfn (hc q hq)).trans hfm + obtain ⟨g,hg,hgn,hP,hcP,he⟩ := fixed_contour_preparation_general hU hr hF hn hm + exact ⟨g,hg,hgn,hn,hP,hcP,he⟩ + + + +theorem prepared_unit_all_orders {A : Type*} [NormedAddCommGroup A] [NormedSpace ℂ A] + {g : A × ℂ → ℂ} {U : Set A} {r : ℝ} + (hg : AnalyticOnNhd ℂ g (U ×ˢ ball 0 r)) : + ∀ n, AnalyticOnNhd ℂ (iteratedFDeriv ℂ n g) (U ×ˢ ball 0 r) := + fun n => hg.iteratedFDeriv n + +end DegeneratingTrees + +namespace DegeneratingTrees +open Set Metric Filter Topology Complex +open scoped BigOperators Polynomial + + + +theorem contourPolynomial_dvd {P : ℂ[X]} {r : ℝ} (hr : 0 < r) + (hn : ∀ z ∈ sphere (0 : ℂ) r, P.eval z ≠ 0) {d : ℕ} + (hd : contourMoment P.eval r 0 = (d : ℂ)) : + contourPolynomial P.eval r d ∣ P := by + classical + have hP0 : P ≠ 0 := by + intro he + apply hn (r : ℂ) (by simp [abs_of_pos hr]) + simp [he] + let s := P.roots.toFinset.filter (fun a => ‖a‖ < r) + let t := P.roots.toFinset.filter (fun a => ¬ ‖a‖ < r) + let m : ℂ → ℕ := fun a => P.roots.count a + let Q : ℂ[X] := ∏ a ∈ s, (Polynomial.X-Polynomial.C a) ^ m a + let R : ℂ[X] := Polynomial.C P.leadingCoeff * + ∏ a ∈ t, (Polynomial.X-Polynomial.C a) ^ m a + have hPQ : P = Q * R := by + rw [(IsAlgClosed.splits P).eq_prod_roots, Finset.prod_multiset_map_count] + dsimp only [Q,R,m,s,t] + rw [← Finset.prod_filter_mul_prod_filter_not (p := fun a : ℂ => ‖a‖ < r)] + ring + have hs (a : ℂ) (ha : a ∈ s) : a ∈ ball (0 : ℂ) r := by + simpa using (Finset.mem_filter.mp ha).2 + have ht (a : ℂ) (ha : a ∈ t) : r < ‖a‖ := by + have hae : P.eval a = 0 := Polynomial.mem_roots hP0 |>.mp + (Multiset.mem_toFinset.mp (Finset.mem_filter.mp ha).1) + have hal : r ≤ ‖a‖ := le_of_not_gt (Finset.mem_filter.mp ha).2 + apply lt_of_le_of_ne hal + intro he + exact hn a (by simpa [mem_sphere_zero_iff_norm] using he.symm) hae + have hR : ∀ z ∈ closedBall (0 : ℂ) r, R.eval z ≠ 0 := by + intro z hz + simp only [R,Polynomial.eval_mul,Polynomial.eval_C,Polynomial.eval_prod, + Polynomial.eval_pow,Polynomial.eval_sub,Polynomial.eval_X] + apply mul_ne_zero (Polynomial.leadingCoeff_ne_zero.mpr hP0) + apply Finset.prod_ne_zero_iff.mpr + intro a ha + apply pow_ne_zero + intro he + have hza := sub_eq_zero.mp he + have hzn : ‖z‖ ≤ r := by simpa using hz + rw [hza] at hzn + exact (not_lt_of_ge hzn (ht a ha)) + have hf : AnalyticOnNhd ℂ P.eval (closedBall 0 r) := fun z _ => AnalyticOnNhd.eval_polynomial P z (Set.mem_univ z) + have hg : AnalyticOnNhd ℂ R.eval (closedBall 0 r) := fun z _ => AnalyticOnNhd.eval_polynomial R z (Set.mem_univ z) + have heq : EqOn P.eval (fun z => (∏ a ∈ s, (z-a)^m a) * R.eval z) (closedBall 0 r) := by + intro z hz + change P.eval z = _ + rw [hPQ,Polynomial.eval_mul] + simp only [Q, Polynomial.eval_prod, Polynomial.eval_pow, + Polynomial.eval_sub, Polynomial.eval_X, Polynomial.eval_C] + let ι := Σ a : s, Fin (m a) + let x : ι → ℂ := fun i => i.1 + have hm (k : ℕ) : contourMoment P.eval r k = ∑ i : ι, x i ^ k := by + rw [contourMoment_eq_sum hr hf s m hs hg hR heq k] + simpa [ι,x,Fintype.sum_sigma] using + (Finset.sum_attach s (fun a => (m a : ℂ) * a ^ k)).symm + have hcard : Fintype.card ι = d := by + have hc : (Fintype.card ι : ℂ) = (d : ℂ) := by simpa using (hm 0).symm.trans hd + exact_mod_cast hc + have hcp : contourPolynomial P.eval r d = Q := by + rw [← hcard,contourPolynomial_eq_prod x hm] + dsimp only [Q] + simpa [ι,x,Fintype.prod_sigma] using + (Finset.prod_attach s (fun a => (Polynomial.X-Polynomial.C a)^m a)) + rw [hcp] + exact ⟨R,hPQ⟩ + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/RootLimits.lean b/lean/OAI/Analysis/PathSelection/RootLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..86ef3eb3e588043279c21b10f58232a741688ce4 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/RootLimits.lean @@ -0,0 +1,190 @@ +import Mathlib +import OAI.Analysis.PathSelection.ScalarRoots + +namespace OAI + +/-! Clock scalar limits and limits of monic roots. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma LogMonomial.trichotomy {xs : List (ℝ → ℝ)} {M : ℝ → ℝ} + (hM : LogMonomial xs M) (hxs : ValidClocks xs) : + M =ᶠ[atTop] 0 ∨ Tendsto M atTop atTop ∨ Tendsto M atTop atBot := by + induction hM with + | base p => + rcases lt_trichotomy (p:ℝ) 0 with hp | hp | hp + · exact Or.inr (Or.inr ((tendsto_const_mul_atBot_of_neg hp).mpr Real.tendsto_log_atTop)) + · exact Or.inl (Eventually.of_forall (fun t => by simp [hp])) + · exact Or.inr (Or.inl ((tendsto_const_mul_atTop_of_pos hp).mpr Real.tendsto_log_atTop)) + | @step xs M X hM β ih => + by_cases hβ : β=0 + · simpa [hβ] using ih hxs.1 + · have hsmall := hM.isLittleO hxs.lower_small.1 hxs.lower_small.2 + have he : (fun t => β*X t+M t) ~[atTop] (fun t => β*X t) := + Asymptotics.IsEquivalent.refl.add_isLittleO (hsmall.const_mul_right hβ) + rcases lt_or_gt_of_ne hβ with hb | hb + · exact Or.inr (Or.inr (he.symm.tendsto_atBot + ((tendsto_const_mul_atBot_of_neg hb).mpr hxs.2.2.1))) + · exact Or.inr (Or.inl (he.symm.tendsto_atTop + ((tendsto_const_mul_atTop_of_pos hb).mpr hxs.2.2.1))) + +lemma ClockGerm.scalar_limits {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + {f : ℝ → ℂ} (hf : ClockGerm xs f) : + (∃ c : ℂ,Tendsto f atTop (𝓝 c)) ∨ Tendsto (fun t => ‖f t‖) atTop atTop := by + rcases hf.leading_or_zero hxs with hz | hlead + · exact Or.inl ⟨0,tendsto_const_nhds.congr' hz.symm⟩ + obtain ⟨M,hM,c,hc,ht⟩ := hlead + have he : ∀ t,(Real.exp (M t):ℂ)*((Real.exp (-M t):ℂ)*f t)=f t := by + intro t + rw [←mul_assoc,←Complex.ofReal_mul,←Real.exp_add,add_neg_cancel] + simp + rcases hM.trichotomy hxs with hz | htop | hbot + · refine Or.inl ⟨c,ht.congr' ?_⟩ + filter_upwards [hz] with t ht + simp only [Pi.zero_apply] at ht + simp [ht] + · have hg := (Real.tendsto_exp_atTop.comp htop).atTop_mul_pos + (norm_pos_iff.mpr hc) ht.norm + refine Or.inr (hg.congr' (Eventually.of_forall (fun t => ?_))) + dsimp only [Function.comp_apply] + rw [←Complex.norm_of_nonneg (Real.exp_pos (M t)).le,←norm_mul,he] + · have hg := ((Real.tendsto_exp_atBot.comp hbot).ofReal).mul ht + simp only [Complex.ofReal_zero,zero_mul] at hg + exact Or.inl ⟨0,hg.congr' (Eventually.of_forall he)⟩ + +lemma clockEvaluation_limits (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] : + (clockEvaluation xs).HasScalarLimits := + fun a => a.value_mem.scalar_limits Fact.out + + + +theorem clockField_isAlgClosed (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] : + IsAlgClosed (ClockField xs) := + (clockEvaluation xs).isAlgClosed (clockEvaluation_limits xs) + (clockEvaluation_divisible xs) (clockEvaluation_holomorphic xs) + +lemma clockEvaluation_reflected (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] : + (clockEvaluation xs).Reflected := by + intro a + exact ⟨ClockField.ofFunction (fun t => star (a.value t)) a.value_mem.conj, + ClockField.ofFunction_value _ _⟩ + + + +theorem clockRealField_isRealClosed (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] : + IsRealClosed ((clockEvaluation xs).realPart (clockEvaluation_reflected xs)) := + (clockEvaluation xs).realPart_isRealClosed (clockEvaluation_limits xs) + (clockEvaluation_divisible xs) (clockEvaluation_holomorphic xs) + (clockEvaluation_reflected xs) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped BigOperators Polynomial +namespace DegeneratingTrees.ScalarEvaluation +variable {K α : Type*} [Field K] [Algebra ℂ K] {l : Filter α} +variable (e : ScalarEvaluation K α l) + +lemma tendsto_sum {ι : Type*} (s : Finset ι) {a : ι → K} {c : ι → ℂ} + (h : ∀ i ∈ s, Tendsto (e.value (a i)) l (𝓝 (c i))) : + Tendsto (e.value (∑ i ∈ s,a i)) l (𝓝 (∑ i ∈ s,c i)) := + (tendsto_finsetSum s h).congr' (e.sum s a).symm + +lemma tendsto_add {a b : K} {c d : ℂ} + (ha : Tendsto (e.value a) l (𝓝 c)) (hb : Tendsto (e.value b) l (𝓝 d)) : + Tendsto (e.value (a+b)) l (𝓝 (c+d)) := + (ha.add hb).congr' (e.add a b).symm + +lemma monic_root_limit [NeBot l] (hlim : e.HasScalarLimits) + {d : ℕ} (hd : 0 < d) (a : Fin d → K) + (ha : ∀ i,Tendsto (e.value (a i)) l (𝓝 0)) + {r : K} (hr : (monicFamily a).eval r = 0) : + Tendsto (e.value r) l (𝓝 0) := by + rw [monicFamily_eval] at hr + by_cases hz : r=0 + · subst r + exact tendsto_const_nhds.congr' e.zero.symm + rcases hlim r with ⟨c,hc⟩ | htop + · have hs : Tendsto (e.value (∑ i : Fin d,a i*r^(i:ℕ))) l (𝓝 0) := by + simpa using e.tendsto_sum Finset.univ (fun i _ => e.tendsto_mul (ha i) (e.tendsto_pow hc (i:ℕ))) + have ht := e.tendsto_add (e.tendsto_pow hc d) hs + rw [hr] at ht + have he : c^d=0 := by + simpa using tendsto_nhds_unique ht (tendsto_const_nhds.congr' e.zero.symm) + have : c=0 := (pow_eq_zero_iff (Nat.ne_of_gt hd)).mp he + simpa [this] using hc + · have hi := e.tendsto_inv_of_norm_atTop htop + have hident : (1:K)+∑ i : Fin d,a i*(r⁻¹)^(d-(i:ℕ))=0 := by + have ht := congrArg (fun x:K => x*(r⁻¹)^d) hr + rw [add_mul,Finset.sum_mul] at ht + have hpower : r^d*(r⁻¹)^d=(1:K) := by rw [←mul_pow]; simp [hz] + rw [hpower,zero_mul] at ht + convert ht using 2 + apply Finset.sum_congr rfl + intro i _ + have hsplit : (r⁻¹)^d = (r⁻¹)^(i:ℕ)*(r⁻¹)^(d-(i:ℕ)) := by + rw [←pow_add,Nat.add_sub_of_le i.isLt.le] + rw [hsplit] + have hcanc : r^(i:ℕ)*(r⁻¹)^(i:ℕ)=(1:K) := by rw [←mul_pow]; simp [hz] + calc + a i*(r⁻¹)^(d-(i:ℕ)) = a i*(r^(i:ℕ)*(r⁻¹)^(i:ℕ))*(r⁻¹)^(d-(i:ℕ)) := by rw [hcanc,mul_one] + _ = _ := by ring + have hs : Tendsto (e.value (∑ i : Fin d,a i*(r⁻¹)^(d-(i:ℕ)))) l (𝓝 0) := by + simpa using e.tendsto_sum Finset.univ + (fun i _ => e.tendsto_mul (ha i) (e.tendsto_pow hi (d-(i:ℕ)))) + have ht := e.tendsto_add (tendsto_const_nhds.congr' e.one.symm) hs + rw [hident] at ht + have he : (1:ℂ)=0 := by + simpa using tendsto_nhds_unique ht (tendsto_const_nhds.congr' e.zero.symm) + exact (one_ne_zero he).elim + +end DegeneratingTrees.ScalarEvaluation + + + + + + + +open Filter Topology Complex +namespace DegeneratingTrees.Clock + +theorem clock_monic_root_limit (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] + {d : ℕ} (hd : 0 < d) (a : Fin d → ClockField xs) + (ha : ∀ i,Tendsto (a i).value atTop (𝓝 0)) + {r : ClockField xs} (hr : (monicFamily a).eval r=0) : + Tendsto r.value atTop (𝓝 0) := + (clockEvaluation xs).monic_root_limit (clockEvaluation_limits xs) hd a ha hr + + + +theorem clock_exists_monic_root_limit (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] + {d : ℕ} (hd : 0 < d) (a : Fin d → ClockField xs) + (ha : ∀ i,Tendsto (a i).value atTop (𝓝 0)) : + ∃ r : ClockField xs,(monicFamily a).eval r=0 ∧ + Tendsto r.value atTop (𝓝 0) := by + let := clockField_isAlgClosed xs + have hdeg : (monicFamily a).degree ≠ 0 := by + intro he + have hn := Polynomial.natDegree_eq_of_degree_eq_some he + rw [monicFamily_natDegree] at hn + exact Nat.ne_of_gt hd hn + obtain ⟨r,hr⟩ := IsAlgClosed.exists_root (monicFamily a) hdeg + exact ⟨r,hr,clock_monic_root_limit xs hd a ha hr⟩ + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ScalarFields.lean b/lean/OAI/Analysis/PathSelection/ScalarFields.lean new file mode 100644 index 0000000000000000000000000000000000000000..e89efe53ab3bc06a85fe1db8a03fe43f1bf05f88 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ScalarFields.lean @@ -0,0 +1,497 @@ +import Mathlib +import OAI.Analysis.PathSelection.TupleTaylor + +namespace OAI + +/-! Regular scalar evaluation fields and germ polynomials. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped BigOperators Polynomial +namespace DegeneratingTrees + +structure ScalarEvaluation (K α : Type*) [Field K] [Algebra ℂ K] (l : Filter α) where + value : K → α → ℂ + const : ∀ c : ℂ, value (algebraMap ℂ K c) =ᶠ[l] fun _ => c + add : ∀ a b, value (a+b) =ᶠ[l] fun x => value a x + value b x + mul : ∀ a b, value (a*b) =ᶠ[l] fun x => value a x * value b x + +namespace ScalarEvaluation +variable {K α : Type*} [Field K] [Algebra ℂ K] {l : Filter α} +variable (e : ScalarEvaluation K α l) + +lemma zero : e.value 0 =ᶠ[l] fun _ => 0 := by simpa using e.const 0 +lemma one : e.value 1 =ᶠ[l] fun _ => 1 := by simpa using e.const 1 + + +def toGermHom : K →+* Germ l ℂ where + toFun a := (e.value a : Germ l ℂ) + map_zero' := Germ.coe_eq.mpr e.zero + map_one' := Germ.coe_eq.mpr e.one + map_add' a b := by exact Germ.coe_eq.mpr (e.add a b) + map_mul' a b := by exact Germ.coe_eq.mpr (e.mul a b) + +lemma faithful [NeBot l] {a : K} (h : e.value a =ᶠ[l] fun _ => 0) : a = 0 := by + apply e.toGermHom.injective + rw [map_zero] + exact Germ.coe_eq.mpr h + +lemma nonzero [NeBot l] {a : K} (ha : a ≠ 0) : ∀ᶠ x in l, e.value a x ≠ 0 := by + have hm := (e.mul a a⁻¹).symm.trans (by simpa [ha] using e.one) + filter_upwards [hm] with x hx + exact left_ne_zero_of_mul_eq_one hx + +lemma neg (a : K) : e.value (-a) =ᶠ[l] fun x => -e.value a x := by + have h := (e.add a (-a)).symm.trans (by simpa using e.zero) + filter_upwards [h] with x hx + exact eq_neg_of_add_eq_zero_right hx + +lemma sub (a b : K) : e.value (a-b) =ᶠ[l] fun x => e.value a x - e.value b x := by + filter_upwards [e.add a (-b), e.neg b] with x hx hy + simpa [sub_eq_add_neg,hy] using hx + +lemma inv (a : K) : e.value a⁻¹ =ᶠ[l] fun x => (e.value a x)⁻¹ := by + by_cases ha : a = 0 + · subst a + filter_upwards [e.zero] with x hx + simp [hx] + · have h := (e.mul a a⁻¹).symm.trans (by simpa [ha] using e.one) + filter_upwards [h] with x hx + exact eq_inv_of_mul_eq_one_left (by simpa [mul_comm] using hx) + +lemma div (a b : K) : e.value (a/b) =ᶠ[l] fun x => e.value a x / e.value b x := by + filter_upwards [e.mul a b⁻¹, e.inv b] with x hx hy + simpa [div_eq_mul_inv,hy] using hx + +lemma pow (a : K) (n : ℕ) : e.value (a^n) =ᶠ[l] fun x => e.value a x ^ n := by + induction n with + | zero => simpa using e.one + | succ n ih => + filter_upwards [e.mul (a^n) a, ih] with x hx hy + simpa [pow_succ,hy] using hx + +lemma sum {ι : Type*} (s : Finset ι) (a : ι → K) : + e.value (∑ i ∈ s, a i) =ᶠ[l] fun x => ∑ i ∈ s, e.value (a i) x := by + classical + induction s using Finset.induction_on with + | empty => simpa using e.zero + | @insert i s hi ih => + filter_upwards [e.add (a i) (∑ j ∈ s, a j), ih] with x hx hy + simpa [Finset.sum_insert hi,hy] using hx + + + +def HasScalarLimits : Prop := + ∀ a : K, (∃ c : ℂ, Tendsto (e.value a) l (𝓝 c)) ∨ + Tendsto (fun x => ‖e.value a x‖) l atTop + + + +def HasDivisibleSizes : Prop := + ∀ a : K, a ≠ 0 → ∀ n : ℕ, 0 < n → ∃ ρ : K, + (∀ᶠ x in l, 0 < (e.value ρ x).re ∧ (e.value ρ x).im = 0) ∧ + ∃ c : ℝ, 0 < c ∧ Tendsto (fun x => ‖e.value ρ x‖^n / ‖e.value a x‖) l (𝓝 c) + + + +def HolomorphicallyClosed : Prop := + ∀ (n : ℕ) (a : Fin n → K) (c : Fin n → ℂ), + (∀ j, Tendsto (e.value (a j)) l (𝓝 (c j))) → + ∀ f : (Fin n → ℂ) → ℂ, AnalyticAt ℂ f c → + ∃ b : K, e.value b =ᶠ[l] fun x => f (fun j => e.value (a j) x) + +lemma tendsto_mul {a b : K} {c d : ℂ} + (ha : Tendsto (e.value a) l (𝓝 c)) (hb : Tendsto (e.value b) l (𝓝 d)) : + Tendsto (e.value (a*b)) l (𝓝 (c*d)) := + (ha.mul hb).congr' (e.mul a b).symm + +lemma tendsto_pow {a : K} {c : ℂ} (ha : Tendsto (e.value a) l (𝓝 c)) (n : ℕ) : + Tendsto (e.value (a^n)) l (𝓝 (c^n)) := + (ha.pow n).congr' (e.pow a n).symm + +lemma tendsto_div {a b : K} {c d : ℂ} + (ha : Tendsto (e.value a) l (𝓝 c)) (hb : Tendsto (e.value b) l (𝓝 d)) (hd : d ≠ 0) : + Tendsto (e.value (a/b)) l (𝓝 (c/d)) := + (ha.div hb hd).congr' (e.div a b).symm + +lemma tendsto_inv_of_norm_atTop {a : K} + (ha : Tendsto (fun x => ‖e.value a x‖) l atTop) : + Tendsto (e.value a⁻¹) l (𝓝 0) := by + have hb : Tendsto (e.value a) l (Bornology.cobounded ℂ) := + tendsto_norm_atTop_iff_cobounded.mp ha + exact (tendsto_inv₀_cobounded.comp hb).congr' (e.inv a).symm + + +def BoundedRatio (a b : K) : Prop := ∃ c : ℂ, Tendsto (e.value (a/b)) l (𝓝 c) + +lemma boundedRatio_refl (a : K) : e.BoundedRatio a a := by + by_cases ha : a = 0 + · subst a + exact ⟨0, tendsto_const_nhds.congr' (by simpa using e.zero.symm)⟩ + · exact ⟨1, tendsto_const_nhds.congr' (by simpa [ha] using e.one.symm)⟩ + +lemma boundedRatio_trans {a b c : K} (hb : b ≠ 0) + (hab : e.BoundedRatio a b) (hbc : e.BoundedRatio b c) : e.BoundedRatio a c := by + obtain ⟨u,hu⟩ := hab + obtain ⟨v,hv⟩ := hbc + refine ⟨u*v,?_⟩ + convert e.tendsto_mul hu hv using 1 + congr 1 + field_simp + +lemma boundedRatio_total (hlim : e.HasScalarLimits) (a b : K) : + e.BoundedRatio a b ∨ e.BoundedRatio b a := by + rcases hlim (a/b) with h | h + · exact Or.inl h + · right + exact ⟨0, by simpa using e.tendsto_inv_of_norm_atTop h⟩ + + +lemma exists_max_scale {ι : Type*} [DecidableEq ι] (hlim : e.HasScalarLimits) + (s : Finset ι) (hs : s.Nonempty) (ρ : ι → K) (hρ : ∀ i ∈ s, ρ i ≠ 0) : + ∃ i ∈ s, ∀ j ∈ s, e.BoundedRatio (ρ j) (ρ i) := by + induction s using Finset.induction_on with + | empty => simp at hs + | @insert i s hi ih => + by_cases hse : s.Nonempty + · obtain ⟨j,hjs,hj⟩ := ih hse (fun j hj => hρ j (Finset.mem_insert_of_mem hj)) + rcases e.boundedRatio_total hlim (ρ i) (ρ j) with hij | hji + · refine ⟨j,Finset.mem_insert_of_mem hjs,?_⟩ + intro k hk + rcases Finset.mem_insert.mp hk with rfl | hks + · exact hij + · exact hj k hks + · refine ⟨i,Finset.mem_insert_self _ _,?_⟩ + intro k hk + rcases Finset.mem_insert.mp hk with rfl | hks + · exact e.boundedRatio_refl _ + · exact e.boundedRatio_trans (hρ j (Finset.mem_insert_of_mem hjs)) (hj k hks) hji + · have hsz : s = ∅ := Finset.not_nonempty_iff_eq_empty.mp hse + subst s + refine ⟨i,by simp,?_⟩ + intro j hj + simp at hj + subst j + exact e.boundedRatio_refl _ + + + +lemma exists_root_size [NeBot l] (hlim : e.HasScalarLimits) (hdiv : e.HasDivisibleSizes) + (a : K) (ha : a ≠ 0) (n : ℕ) (hn : 0 < n) : + ∃ ρ : K, ρ ≠ 0 ∧ ∃ c : ℂ, c ≠ 0 ∧ Tendsto (e.value (a/ρ^n)) l (𝓝 c) := by + obtain ⟨ρ,hρ,c,hc,ht⟩ := hdiv a ha n hn + have hρ0 : ρ ≠ 0 := by + intro he + subst ρ + obtain ⟨x,hx,hz⟩ := (hρ.and e.zero).exists + simpa [hz] using hx.1 + have hnorm : Tendsto (fun x => ‖e.value (a/ρ^n) x‖) l (𝓝 c⁻¹) := by + have he : (fun x => (‖e.value ρ x‖^n / ‖e.value a x‖)⁻¹) =ᶠ[l] + fun x => ‖e.value (a/ρ^n) x‖ := by + filter_upwards [e.div a (ρ^n), e.pow ρ n] with x hx hy + rw [hx,hy,norm_div,norm_pow,inv_div] + exact (ht.inv₀ hc.ne').congr' he + rcases hlim (a/ρ^n) with ⟨z,hz⟩ | hz + · refine ⟨ρ,hρ0,z,?_,hz⟩ + have he : ‖z‖ = c⁻¹ := tendsto_nhds_unique hz.norm hnorm + intro hzero + simp [hzero] at he + exact hc.ne' he.symm + · exact (not_tendsto_atTop_of_tendsto_nhds hnorm hz).elim + + + +lemma normalize_finite_coefficients [NeBot l] {ι : Type*} [Fintype ι] [DecidableEq ι] + (hlim : e.HasScalarLimits) (hdiv : e.HasDivisibleSizes) + (a : ι → K) (n : ι → ℕ) (hn : ∀ i, 0 < n i) (ha : ∃ i, a i ≠ 0) : + ∃ ρ : K, ρ ≠ 0 ∧ ∃ c : ι → ℂ, + (∀ i, Tendsto (e.value (a i / ρ ^ n i)) l (𝓝 (c i))) ∧ ∃ i, c i ≠ 0 := by + classical + have hsize : ∀ i : ι, ∃ ρ : K, ρ ≠ 0 ∧ ∃ c : ℂ, + (a i ≠ 0 → c ≠ 0) ∧ Tendsto (e.value (a i / ρ ^ n i)) l (𝓝 c) := by + intro i + by_cases hai : a i = 0 + · refine ⟨1,one_ne_zero,0,fun h => (h hai).elim,?_⟩ + simpa [hai] using tendsto_const_nhds.congr' e.zero.symm + · obtain ⟨ρ,hρ,c,hc,ht⟩ := e.exists_root_size hlim hdiv (a i) hai (n i) (hn i) + exact ⟨ρ,hρ,c,fun _ => hc,ht⟩ + choose ρ hρ b hb hbt using hsize + let s := Finset.univ.filter (fun i => a i ≠ 0) + have hs : s.Nonempty := by + obtain ⟨i,hi⟩ := ha + exact ⟨i,by simp [s,hi]⟩ + obtain ⟨j,hjs,hj⟩ := e.exists_max_scale hlim s hs ρ (fun i _ => hρ i) + have hcoeff : ∀ i, ∃ z : ℂ, Tendsto (e.value (a i / ρ j ^ n i)) l (𝓝 z) := by + intro i + by_cases hai : a i = 0 + · exact ⟨0,by simpa [hai] using tendsto_const_nhds.congr' e.zero.symm⟩ + · obtain ⟨v,hv⟩ := hj i (by simp [s,hai]) + refine ⟨b i * v ^ n i,?_⟩ + convert e.tendsto_mul (hbt i) (e.tendsto_pow hv (n i)) using 1 + congr 1 + simp only [div_pow] + field_simp [hρ i, hρ j] + choose c hc using hcoeff + refine ⟨ρ j,hρ j,c,hc,j,?_⟩ + have he : c j = b j := tendsto_nhds_unique (hc j) (hbt j) + rw [he] + exact hb j (Finset.mem_filter.mp hjs).2 + +end ScalarEvaluation +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + + + +def clockSubring (xs : List (ℝ → ℝ)) : Subring (Germ (atTop : Filter ℝ) ℂ) where + carrier := {a | ∃ f : ℝ → ℂ, ClockGerm xs f ∧ a = (f : Germ atTop ℂ)} + zero_mem' := ⟨fun _ => 0,ClockGerm.const xs 0,rfl⟩ + one_mem' := ⟨fun _ => 1,ClockGerm.const xs 1,rfl⟩ + add_mem' := by + rintro a b ⟨f,hf,rfl⟩ ⟨g,hg,rfl⟩ + exact ⟨fun t => f t+g t,hf.add hg,rfl⟩ + neg_mem' := by + rintro a ⟨f,hf,rfl⟩ + exact ⟨fun t => -f t,hf.neg,rfl⟩ + mul_mem' := by + rintro a b ⟨f,hf,rfl⟩ ⟨g,hg,rfl⟩ + exact ⟨fun t => f t*g t,hf.mul hg,rfl⟩ + +abbrev ClockField (xs : List (ℝ → ℝ)) : Type := ↥(clockSubring xs) + +def ClockField.ofFunction {xs : List (ℝ → ℝ)} (f : ℝ → ℂ) (hf : ClockGerm xs f) : + ClockField xs := ⟨(f : Germ atTop ℂ),f,hf,rfl⟩ + +def ClockField.value {xs : List (ℝ → ℝ)} (a : ClockField xs) : ℝ → ℂ := + a.property.choose + +lemma ClockField.value_mem {xs : List (ℝ → ℝ)} (a : ClockField xs) : + ClockGerm xs a.value := a.property.choose_spec.1 + +lemma ClockField.value_eq {xs : List (ℝ → ℝ)} (a : ClockField xs) : + (a.value : Germ atTop ℂ) = a.val := a.property.choose_spec.2.symm + +lemma ClockField.ofFunction_value {xs : List (ℝ → ℝ)} (f : ℝ → ℂ) (hf : ClockGerm xs f) : + (ClockField.ofFunction f hf).value =ᶠ[atTop] f := + Germ.coe_eq.mp (ClockField.value_eq _) + +lemma ClockField.value_zero_iff {xs : List (ℝ → ℝ)} (a : ClockField xs) : + a.value =ᶠ[atTop] 0 ↔ a=0 := by + rw [←Germ.coe_eq,a.value_eq] + change a.val = (0:ClockField xs).val ↔ a=0 + exact Subtype.val_inj + +lemma clockField_unit_or_zero {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + (a : ClockField xs) : IsUnit a ∨ a=0 := by + classical + by_cases ha : a=0 + · exact Or.inr ha + have hne : ¬ a.value =ᶠ[atTop] 0 := fun h => ha (a.value_zero_iff.mp h) + let b := ClockField.ofFunction (fun t => (a.value t)⁻¹) (a.value_mem.inv hxs) + have hab : a*b=1 := by + apply Subtype.ext + change a.val*b.val=1 + rw [←a.value_eq] + exact Germ.coe_eq.mpr ((a.value_mem.eventually_nonzero hxs hne).mono (fun t ht => mul_inv_cancel₀ ht)) + exact Or.inl ⟨⟨a,b,hab,by simpa [mul_comm] using hab⟩,rfl⟩ + +instance clockField {xs : List (ℝ → ℝ)} [Fact (ValidClocks xs)] : Field (ClockField xs) := + Field.ofIsUnitOrEqZero (clockField_unit_or_zero Fact.out) + +def clockConstHom (xs : List (ℝ → ℝ)) : ℂ →+* ClockField xs where + toFun c := ClockField.ofFunction (fun _ => c) (ClockGerm.const xs c) + map_zero' := rfl + map_one' := rfl + map_add' _ _ := rfl + map_mul' _ _ := rfl + +instance clockAlgebra (xs : List (ℝ → ℝ)) : Algebra ℂ (ClockField xs) := + (clockConstHom xs).toAlgebra + +def clockEvaluation (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] : + ScalarEvaluation (ClockField xs) ℝ atTop where + value := ClockField.value + const c := ClockField.ofFunction_value (fun _ => c) (ClockGerm.const xs c) + add a b := by + apply Germ.coe_eq.mp + rw [ClockField.value_eq] + change (a+b).val = (a.value:Germ atTop ℂ)+(b.value:Germ atTop ℂ) + rw [a.value_eq,b.value_eq] + rfl + mul a b := by + apply Germ.coe_eq.mp + rw [ClockField.value_eq] + change (a*b).val = (a.value:Germ atTop ℂ)*(b.value:Germ atTop ℂ) + rw [a.value_eq,b.value_eq] + rfl + +lemma clockEvaluation_divisible (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] : + (clockEvaluation xs).HasDivisibleSizes := by + intro a ha n hn + obtain ⟨ρ,hρ,hpos,c,hc,ht⟩ := a.value_mem.divisible_size Fact.out + (fun hz => ha (a.value_zero_iff.mp hz)) n hn + refine ⟨ClockField.ofFunction (fun t => (ρ t:ℂ)) hρ,?_,c,hc,?_⟩ + · filter_upwards [ClockField.ofFunction_value (fun t => (ρ t:ℂ)) hρ] with t he + change 0 < (ClockField.value (ClockField.ofFunction (fun t => (ρ t:ℂ)) hρ) t).re ∧ + (ClockField.value (ClockField.ofFunction (fun t => (ρ t:ℂ)) hρ) t).im = 0 + rw [he] + simpa using hpos t + · apply ht.congr' + filter_upwards [ClockField.ofFunction_value (fun t => (ρ t:ℂ)) hρ] with t he + change ρ t ^ n / ‖a.value t‖ = ‖ClockField.value (ClockField.ofFunction (fun t => (ρ t:ℂ)) hρ) t‖ ^ n / ‖a.value t‖ + rw [he,Complex.norm_of_nonneg (hpos t).le] + +lemma clockEvaluation_holomorphic (xs : List (ℝ → ℝ)) [Fact (ValidClocks xs)] : + (clockEvaluation xs).HolomorphicallyClosed := by + intro n a c hc f hf + exact ⟨ClockField.ofFunction _ (ClockGerm.analytic_comp_tuple_finite Fact.out + (fun i => (a i).value_mem) hc hf),ClockField.ofFunction_value _ _⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped BigOperators Polynomial +namespace DegeneratingTrees.ScalarEvaluation +variable {K α : Type*} [Field K] [Algebra ℂ K] {l : Filter α} +variable (e : ScalarEvaluation K α l) + +def coefficientGermHom : K →+* Germ l ℂ[X] where + toFun a := (fun x => Polynomial.C (e.value a x) : Germ l ℂ[X]) + map_zero' := by + apply Germ.coe_eq.mpr + filter_upwards [e.zero] with x hx + simp [hx] + map_one' := by + apply Germ.coe_eq.mpr + filter_upwards [e.one] with x hx + simp [hx] + map_add' a b := by + apply Germ.coe_eq.mpr + filter_upwards [e.add a b] with x hx + simp [hx] + map_mul' a b := by + apply Germ.coe_eq.mpr + filter_upwards [e.mul a b] with x hx + simp [hx] + +def toPolynomialGermHom : K[X] →+* Germ l ℂ[X] := + Polynomial.eval₂RingHom e.coefficientGermHom (Germ.const Polynomial.X) + +def polynomialValue (P : K[X]) (x : α) : ℂ[X] := + ∑ i ∈ P.support, Polynomial.monomial i (e.value (P.coeff i) x) + +lemma polynomialValue_coeff (P : K[X]) (x : α) (n : ℕ) : + (e.polynomialValue P x).coeff n = if n ∈ P.support then e.value (P.coeff n) x else 0 := by + classical + simp [polynomialValue,Polynomial.finsetSum_coeff,Polynomial.coeff_monomial, eq_comm] + +lemma polynomialValue_coeff_eventually (P : K[X]) (n : ℕ) : + (fun x => (e.polynomialValue P x).coeff n) =ᶠ[l] e.value (P.coeff n) := by + classical + by_cases hn : n ∈ P.support + · filter_upwards [] with x + simp [e.polynomialValue_coeff P x n,hn] + · have hc : P.coeff n = 0 := Polynomial.notMem_support_iff.mp hn + filter_upwards [e.zero] with x hx + simp [e.polynomialValue_coeff P x n,hn,hc,hx] + +lemma polynomialValue_germ (P : K[X]) : + (e.polynomialValue P : Germ l ℂ[X]) = e.toPolynomialGermHom P := by + classical + have hfun : e.polynomialValue P = + ∑ i ∈ P.support, fun x => Polynomial.C (e.value (P.coeff i) x) * Polynomial.X ^ i := by + funext x + simp [polynomialValue,Polynomial.C_mul_X_pow_eq_monomial] + rw [hfun] + change (Germ.coeRingHom l) _ = _ + rw [map_sum] + change _ = P.eval₂ e.coefficientGermHom (Germ.const Polynomial.X) + rw [Polynomial.eval₂_eq_sum,Polynomial.sum_def] + apply Finset.sum_congr rfl + intro i hi + rfl + +lemma polynomialValue_zero : e.polynomialValue 0 = fun _ => 0 := by + funext x + simp [polynomialValue] + +lemma polynomialValue_add (P Q : K[X]) : + e.polynomialValue (P+Q) =ᶠ[l] fun x => e.polynomialValue P x + e.polynomialValue Q x := by + apply Germ.coe_eq.mp + change (e.polynomialValue (P+Q) : Germ l ℂ[X]) = + (e.polynomialValue P : Germ l ℂ[X]) + e.polynomialValue Q + rw [e.polynomialValue_germ,e.polynomialValue_germ,e.polynomialValue_germ,map_add] + +lemma polynomialValue_mul (P Q : K[X]) : + e.polynomialValue (P*Q) =ᶠ[l] fun x => e.polynomialValue P x * e.polynomialValue Q x := by + apply Germ.coe_eq.mp + change (e.polynomialValue (P*Q) : Germ l ℂ[X]) = + (e.polynomialValue P : Germ l ℂ[X]) * e.polynomialValue Q + rw [e.polynomialValue_germ,e.polynomialValue_germ,e.polynomialValue_germ,map_mul] + +lemma polynomialValue_faithful [NeBot l] {P : K[X]} + (h : e.polynomialValue P =ᶠ[l] fun _ => 0) : P = 0 := by + ext n + apply e.faithful + filter_upwards [e.polynomialValue_coeff_eventually P n,h] with x hx hy + simpa [hy] using hx.symm + +lemma polynomialValue_natDegree_le (P : K[X]) (x : α) : + (e.polynomialValue P x).natDegree ≤ P.natDegree := by + classical + apply Polynomial.natDegree_le_iff_coeff_eq_zero.mpr + intro n hn + have hns : n ∉ P.support := by + intro he + exact (not_lt_of_ge (Polynomial.le_natDegree_of_mem_supp n he)) hn + simp [e.polynomialValue_coeff P x n,hns] + +lemma polynomialValue_monic {P : K[X]} (hP : P.Monic) : + ∀ᶠ x in l, (e.polynomialValue P x).Monic ∧ (e.polynomialValue P x).natDegree = P.natDegree := by + filter_upwards [e.polynomialValue_coeff_eventually P P.natDegree,e.one] with x hx hy + rw [hP.coeff_natDegree,hy] at hx + have hdeg := e.polynomialValue_natDegree_le P x + exact ⟨Polynomial.monic_of_natDegree_le_of_coeff_eq_one _ hdeg hx, + Polynomial.natDegree_eq_of_le_of_coeff_ne_zero hdeg (by simp [hx])⟩ + + + +lemma polynomial_dvd_of_eventually [NeBot l] {P W : K[X]} (hW : W.Monic) + (hdiv : ∀ᶠ x in l, e.polynomialValue W x ∣ e.polynomialValue P x) : W ∣ P := by + by_cases hW1 : W = 1 + · simp [hW1] + apply (Polynomial.modByMonic_eq_zero_iff_dvd hW).mp + apply e.polynomialValue_faithful + have he := e.polynomialValue_add (P %ₘ W) (W * (P /ₘ W)) + rw [Polynomial.modByMonic_add_div] at he + filter_upwards [hdiv,he,e.polynomialValue_mul W (P /ₘ W), + e.polynomialValue_monic hW] with x hx hxe hxm hxW + apply Polynomial.eq_zero_of_dvd_of_natDegree_lt + · apply (dvd_add_right (dvd_mul_right (e.polynomialValue W x) + (e.polynomialValue (P /ₘ W) x))).mp + simpa [hxe,hxm,add_comm] using hx + · rw [hxW.2] + exact lt_of_le_of_lt (e.polynomialValue_natDegree_le (P %ₘ W) x) + (Polynomial.natDegree_modByMonic_lt P hW hW1) + +end DegeneratingTrees.ScalarEvaluation +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/ScalarRoots.lean b/lean/OAI/Analysis/PathSelection/ScalarRoots.lean new file mode 100644 index 0000000000000000000000000000000000000000..530caf7c55d44d71c9c9f5d916d5960963feeabb --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/ScalarRoots.lean @@ -0,0 +1,318 @@ +import Mathlib +import OAI.Analysis.PathSelection.AnalyticFactors + +namespace OAI + +/-! Scalar roots, reflection and real algebraic roots. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Metric Filter Topology Complex Polynomial +open scoped BigOperators +namespace DegeneratingTrees.ScalarEvaluation +variable {K α : Type*} [Field K] [Algebra ℂ K] {l : Filter α} +variable (e : ScalarEvaluation K α l) + +lemma monic_irreducible_has_root [NeBot l] + (hlim : e.HasScalarLimits) (hdiv : e.HasDivisibleSizes) (hhol : e.HolomorphicallyClosed) + (P : K[X]) (hP : P.Monic) (hI : Irreducible P) : ∃ x : K, P.eval x = 0 := by + classical + have hd : 0 < P.natDegree := natDegree_pos_iff_degree_pos.mpr (degree_pos_of_irreducible hI) + have hdK : (P.natDegree : K) ≠ 0 := by + intro hz + have he : algebraMap ℂ K (P.natDegree : ℂ) = algebraMap ℂ K 0 := by simpa using hz + exact Nat.cast_ne_zero.mpr (Nat.ne_of_gt hd) ((algebraMap ℂ K).injective he) + let r : K := -P.coeff (P.natDegree-1) / (P.natDegree : K) + let Q : K[X] := taylor r P + have hQm : Q.Monic := by simpa [Q,Monic] using hP + have hQd : Q.natDegree = P.natDegree := natDegree_taylor P r + have hQpos : 0 < Q.natDegree := by omega + have hQI : Irreducible Q := by + have hi := hI.map (taylorEquiv r) + change Irreducible (taylor r P) at hi + exact hi + have hQdep : Q.coeff (Q.natDegree-1) = 0 := by + rw [hQd] + change (taylor r P).coeff (P.natDegree-1) = 0 + rw [taylor_coeff_penultimate hP hd] + dsimp [r] + field_simp + ring + by_cases hcoeff : ∀ i : Fin Q.natDegree, Q.coeff i = 0 + · have hQpure : Q = X^Q.natDegree := by + calc + Q = monicFamily (fun i : Fin Q.natDegree => Q.coeff i) := eq_monicFamily hQm + _ = X^Q.natDegree := by + simp only [monicFamily] + have hs : (∑ i : Fin Q.natDegree, monomial i (Q.coeff i)) = 0 := by + apply Finset.sum_eq_zero + intro i hi + simp [hcoeff i] + rw [hs,add_zero] + refine ⟨r,?_⟩ + have hv : Q.eval 0 = 0 := by rw [hQpure,eval_X_pow,zero_pow (Nat.ne_of_gt hQpos)] + simpa [Q,taylor_apply,eval_comp] using hv + · push Not at hcoeff + obtain ⟨ρ,hρ,c,hc,i,hci⟩ := e.normalize_finite_coefficients hlim hdiv + (fun i : Fin Q.natDegree => Q.coeff i) (fun i => Q.natDegree-i.val) + (fun i => by omega) hcoeff + let R : K[X] := monicFamily (fun i : Fin Q.natDegree => Q.coeff i / ρ^(Q.natDegree-i.val)) + have hRm : R.Monic := monicFamily_monic _ + have hRd : R.natDegree = Q.natDegree := monicFamily_natDegree _ + have hRI : Irreducible R := rescale_monic_irreducible hQm hQI ρ hρ + let L : ℂ[X] := monicFamily c + have hLm : L.Monic := monicFamily_monic c + have hLd : L.natDegree = Q.natDegree := monicFamily_natDegree c + have hLdep : L.coeff (L.natDegree-1) = 0 := by + rw [hLd] + let j : Fin Q.natDegree := ⟨Q.natDegree-1,by omega⟩ + have he : Q.coeff j = 0 := hQdep + have ht := hc j + rw [he,zero_div] at ht + have hz : c j = 0 := tendsto_nhds_unique ht (tendsto_const_nhds.congr' e.zero.symm) + simpa [L,monicFamily_coeff,j,show Q.natDegree-1 < Q.natDegree by omega] using hz + have hLnot : L ≠ X^L.natDegree := by + intro he + have hv := congrArg (fun p : ℂ[X] => p.coeff i.val) he + simp only [hLd,coeff_X_pow,ite_eq_right (ne_of_lt i.isLt)] at hv + have hco : L.coeff i = c i := by simp [L,monicFamily_coeff,i.isLt] + rw [hco] at hv + exact hci hv + obtain ⟨a,ha,hsmall⟩ := proper_root_cluster hLm (by omega) hLdep hLnot + have hf := e.factor_of_finite_coeff_limits hhol hRm + rw [hRd] at hf + have hcR : ∀ i : Fin Q.natDegree, Tendsto (e.value (R.coeff i)) l (𝓝 (c i)) := by + intro i + simpa [R,monicFamily_coeff,i.isLt] using hc i + obtain ⟨V,hVm,hVd,hVP⟩ := hf c hcR a + exact (irreducible_no_proper_monic_factor hRI hVm hVP + (by simpa [hVd,L] using ha) (by simpa [hVd,hRd,hLd,L] using hsmall)).elim + + + +theorem isAlgClosed [NeBot l] (hlim : e.HasScalarLimits) + (hdiv : e.HasDivisibleSizes) (hhol : e.HolomorphicallyClosed) : IsAlgClosed K := + IsAlgClosed.of_exists_root K (e.monic_irreducible_has_root hlim hdiv hhol) + +end DegeneratingTrees.ScalarEvaluation + + + + + + + +open Set Filter Topology Complex +open scoped ComplexConjugate +namespace DegeneratingTrees.ScalarEvaluation +variable {K α : Type*} [Field K] [Algebra ℂ K] {l : Filter α} +variable (e : ScalarEvaluation K α l) + +def Reflected : Prop := ∀ a : K, ∃ b : K, + e.value b =ᶠ[l] fun x => conj (e.value a x) + +lemma eq_of_eventuallyEq [NeBot l] {a b : K} (h : e.value a =ᶠ[l] e.value b) : a = b := + e.toGermHom.injective (Germ.coe_eq.mpr h) + +def reflectedValue (h : e.Reflected) (a : K) : K := (h a).choose +lemma reflectedValue_spec (h : e.Reflected) (a : K) : + e.value (e.reflectedValue h a) =ᶠ[l] fun x => conj (e.value a x) := + (h a).choose_spec + +lemma reflectedValue_involutive [NeBot l] (h : e.Reflected) : + Function.Involutive (e.reflectedValue h) := by + intro a + apply e.eq_of_eventuallyEq + filter_upwards [e.reflectedValue_spec h (e.reflectedValue h a), e.reflectedValue_spec h a] with x hx hy + simp [hx,hy] + +def conjugation [NeBot l] (h : e.Reflected) : K ≃+* K where + toFun := e.reflectedValue h + invFun := e.reflectedValue h + left_inv := e.reflectedValue_involutive h + right_inv := e.reflectedValue_involutive h + map_add' a b := by + apply e.eq_of_eventuallyEq + filter_upwards [e.reflectedValue_spec h (a+b), e.add a b, + e.add (e.reflectedValue h a) (e.reflectedValue h b), + e.reflectedValue_spec h a, e.reflectedValue_spec h b] with x h₁ h₂ h₃ h₄ h₅ + simp [h₁,h₂,h₃,h₄,h₅] + map_mul' a b := by + apply e.eq_of_eventuallyEq + filter_upwards [e.reflectedValue_spec h (a*b), e.mul a b, + e.mul (e.reflectedValue h a) (e.reflectedValue h b), + e.reflectedValue_spec h a, e.reflectedValue_spec h b] with x h₁ h₂ h₃ h₄ h₅ + simp [h₁,h₂,h₃,h₄,h₅] + +lemma conjugation_spec [NeBot l] (h : e.Reflected) (a : K) : + e.value (e.conjugation h a) =ᶠ[l] fun x => conj (e.value a x) := + e.reflectedValue_spec h a + +lemma conjugation_const [NeBot l] (h : e.Reflected) (z : ℂ) : + e.conjugation h (algebraMap ℂ K z) = algebraMap ℂ K (conj z) := by + apply e.eq_of_eventuallyEq + filter_upwards [e.conjugation_spec h (algebraMap ℂ K z), e.const z, e.const (conj z)] with x hx hy hz + simp [hx,hy,hz] + +lemma conjugation_involutive [NeBot l] (h : e.Reflected) : + Function.Involutive (e.conjugation h) := e.reflectedValue_involutive h + +def realPart [NeBot l] (h : e.Reflected) : Subfield K := + (e.conjugation h).toRingHom.eqLocusField (RingHom.id K) + +lemma mem_realPart [NeBot l] (h : e.Reflected) {a : K} : + a ∈ e.realPart h ↔ ∀ᶠ x in l, (e.value a x).im = 0 := by + change e.conjugation h a = a ↔ _ + constructor + · intro ha + filter_upwards [e.conjugation_spec h a] with x hx + rw [ha] at hx + exact conj_eq_iff_im.mp hx.symm + · intro ha + apply e.eq_of_eventuallyEq + filter_upwards [ha, e.conjugation_spec h a] with x hx hy + rw [hy,conj_eq_iff_im.mpr hx] + +lemma sumSq_eval_nonneg [NeBot l] (h : e.Reflected) {a : e.realPart h} (ha : IsSumSq a) : + ∀ᶠ x in l, 0 ≤ (e.value (a : K) x).re := by + induction ha with + | zero => + filter_upwards [e.zero] with x hx + simp [hx] + | @sq_add a s hs ih => + filter_upwards [ih, (e.mem_realPart h).mp a.property, e.mul (a:K) (a:K), + e.add ((a:K)*(a:K)) (s:K)] with x hi hr hm ha + change 0 ≤ (e.value ((a:K)*(a:K)+(s:K)) x).re + rw [ha,Complex.add_re,hm,Complex.mul_re,hr] + nlinarith [sq_nonneg (e.value (a:K) x).re] + +lemma realPart_semireal [NeBot l] (h : e.Reflected) : IsSemireal (e.realPart h) := by + apply IsSemireal.of_not_isSumSq_neg_one + intro hs + have ht := e.sumSq_eval_nonneg h hs + obtain ⟨x,hx,hneg,h1⟩ := (ht.and ((e.neg 1).and e.one)).exists + simp [hneg,h1] at hx + linarith + +end DegeneratingTrees.ScalarEvaluation + + + + + + + +open Polynomial +namespace DegeneratingTrees + +lemma odd_multiset_involution_fixed {A : Type*} (σ : A → A) (hinv : Function.Involutive σ) + (s : Multiset A) (hs : s.map σ = s) (ho : Odd s.card) : + ∃ a ∈ s, σ a = a := by + classical + induction s using Multiset.strongInductionOn with + | ih s ih => + obtain ⟨a,ha⟩ := Multiset.card_pos_iff_exists_mem.mp ho.pos + by_cases hf : σ a = a + · exact ⟨a,ha,hf⟩ + have hb : σ a ∈ s := hs ▸ Multiset.mem_map_of_mem σ ha + have hb' : σ a ∈ s.erase a := (Multiset.mem_erase_of_ne hf).mpr hb + let t := (s.erase a).erase (σ a) + have hlt : t < s := lt_trans (Multiset.erase_lt.mpr hb') (Multiset.erase_lt.mpr ha) + have ht : t.map σ = t := by + dsimp [t] + rw [Multiset.map_erase σ hinv.injective, Multiset.map_erase σ hinv.injective, + hs,hinv a,Multiset.erase_comm] + have hot : Odd t.card := by + dsimp [t] + rw [Multiset.card_erase_of_mem hb',Multiset.card_erase_of_mem ha] + obtain ⟨k,hk⟩ := ho + refine ⟨k-1,?_⟩ + have hc : 0 < (s.erase a).card := Multiset.card_pos_iff_exists_mem.mpr ⟨σ a,hb'⟩ + rw [Multiset.card_erase_of_mem ha] at hc + simp only [Nat.pred_eq_sub_one] at hc ⊢ + omega + obtain ⟨b,hbt,hbf⟩ := ih t hlt ht hot + exact ⟨b,Multiset.mem_of_mem_erase (Multiset.mem_of_mem_erase hbt),hbf⟩ + +lemma fixed_subfield_odd_root {K : Type*} [Field K] [IsAlgClosed K] + (σ : K ≃+* K) (hinv : Function.Involutive σ) + (P : (σ.toRingHom.eqLocusField (RingHom.id K))[X]) (ho : Odd P.natDegree) : + ∃ a : σ.toRingHom.eqLocusField (RingHom.id K), P.IsRoot a := by + let R := σ.toRingHom.eqLocusField (RingHom.id K) + let Q : K[X] := P.map R.subtype + have hσQ : Q.map σ.toRingHom = Q := by + ext i + simp only [Polynomial.coeff_map,Q] + exact (P.coeff i).property + have hd : Q.natDegree = P.natDegree := natDegree_map_eq_of_injective R.subtype.injective P + have hcard : Q.roots.card = Q.natDegree := (IsAlgClosed.splits Q).natDegree_eq_card_roots.symm + have hm : Q.roots.map σ = Q.roots := by + change Q.roots.map σ.toRingHom = Q.roots + rw [roots_map_of_injective_of_card_eq_natDegree (f := σ.toRingHom) σ.injective hcard,hσQ] + obtain ⟨a,ha,hfix⟩ := odd_multiset_involution_fixed σ hinv Q.roots hm (by simpa [hcard,hd] using ho) + refine ⟨⟨a,hfix⟩,?_⟩ + have hQne : Q ≠ 0 := by + intro hz + have : P.natDegree = 0 := by simpa [hz] using hd.symm + have hpos := ho.pos + omega + have hr := (mem_roots hQne).mp ha + change P.eval ⟨a,hfix⟩ = 0 + apply R.subtype.injective + rw [map_zero,←eval₂_at_apply] + simpa [Polynomial.IsRoot,Q,Polynomial.eval_map] using hr + +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex Polynomial +open scoped ComplexConjugate +namespace DegeneratingTrees.ScalarEvaluation +variable {K α : Type*} [Field K] [Algebra ℂ K] {l : Filter α} +variable (e : ScalarEvaluation K α l) + +lemma realPart_square_or_neg [NeBot l] [IsAlgClosed K] (h : e.Reflected) + (a : e.realPart h) : IsSquare a ∨ IsSquare (-a) := by + obtain ⟨r,hr⟩ := IsAlgClosed.exists_pow_nat_eq (a : K) zero_lt_two + have he : (e.conjugation h r)^2 = r^2 := by + rw [← map_pow,hr] + exact a.property + rcases eq_or_eq_neg_of_sq_eq_sq (e.conjugation h r) r he with hp | hn + · left + refine ⟨⟨r,hp⟩,?_⟩ + apply Subtype.ext + change (a:K) = r*r + simpa [pow_two] using hr.symm + · right + have hI : (algebraMap ℂ K I)^2 = -1 := by + rw [←map_pow,Complex.I_sq,map_neg,map_one] + have hfix : e.conjugation h (r * algebraMap ℂ K I) = r * algebraMap ℂ K I := by + rw [map_mul,hn,e.conjugation_const,Complex.conj_I,map_neg,neg_mul_neg] + refine ⟨⟨r*algebraMap ℂ K I,hfix⟩,?_⟩ + apply Subtype.ext + change -(a:K) = (r*algebraMap ℂ K I) * (r*algebraMap ℂ K I) + rw [←pow_two,mul_pow,hr,hI,mul_neg_one] + + + +theorem realPart_isRealClosed [NeBot l] (hlim : e.HasScalarLimits) + (hdiv : e.HasDivisibleSizes) (hhol : e.HolomorphicallyClosed) (href : e.Reflected) : + IsRealClosed (e.realPart href) := by + let : IsAlgClosed K := e.isAlgClosed hlim hdiv hhol + exact { + toIsSemireal := e.realPart_semireal href + isSquare_or_isSquare_neg := e.realPart_square_or_neg href + exists_isRoot_of_odd_natDegree := fun hp => + fixed_subfield_odd_root (e.conjugation href) (e.conjugation_involutive href) _ hp + } +end DegeneratingTrees.ScalarEvaluation +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/SecondClockFields.lean b/lean/OAI/Analysis/PathSelection/SecondClockFields.lean new file mode 100644 index 0000000000000000000000000000000000000000..ca765c53d1d54e8b65e85964d2cf8e5d730c979b --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/SecondClockFields.lean @@ -0,0 +1,394 @@ +import Mathlib +import OAI.Analysis.PathSelection.RecursiveCharts + +namespace OAI + +/-! Second-clock multiplication, differentiation and transported sector fields. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma ClockGerm.finset_sum {xs : List (ℝ → ℝ)} {ι : Type*} (S : Finset ι) + {f : ι → ℝ → ℂ} (h : ∀ i ∈ S,ClockGerm xs (f i)) : + ClockGerm xs (fun t => ∑ i ∈ S,f i t) := by + classical + induction S using Finset.induction_on with + | empty => simpa using ClockGerm.const xs 0 + | @insert i S hi ih => + simpa only [Finset.sum_insert hi] using + (h i (Finset.mem_insert_self _ _)).add (ih (fun j hj => h j (Finset.mem_insert_of_mem hj))) + +theorem ClockGerm.mul {xs : List (ℝ → ℝ)} {f g : ℝ → ℂ} + (hf : ClockGerm xs f) (hg : ClockGerm xs g) : ClockGerm xs (fun t => f t*g t) := by + classical + induction xs generalizing f g with + | nil => exact Puiseux.mul hf hg + | cons X xs ih => + obtain ⟨F,E,b,hF,hb,he⟩ := hf + obtain ⟨G,D,c,hG,hc,he'⟩ := hg + refine ⟨fun z => F z*G z,exponentSum E D, + exponentConvolution hF.bounded_above hG.bounded_above hF.finite_above hG.finite_above b c, + hF.mul hG (fun β hβ => hF.coefficient_slow hβ) (fun β hβ => hG.coefficient_slow hβ),?_,he.mul he'⟩ + intro δ _ + refine ⟨?_,convolution_analytic _ _ _ _ (fun β hβ => (hb β hβ).2) (fun β hβ => (hc β hβ).2) δ⟩ + apply ClockGerm.finset_sum + intro p hp + have hh := (exponentFiber_finite hF.bounded_above hG.bounded_above hF.finite_above hG.finite_above δ).mem_toFinset.mp hp + exact ih (hb p.1 hh.1).1 (hc p.2 hh.2.1).1 + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ValidClocks.second_lowerData {X Y : ℝ → ℝ} (hxs : ValidClocks [Y,X]) : + ∃ K : Set (ℂ → ℂ),LowerSectorData K ∧ + ∀ b : ℂ → ℂ,(b∈K ↔ + (ClockGerm (X :: []) (fun t => b (Y t:ℂ)) ∧ + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ b z)) := by + have hxv := hxs.1 + obtain ⟨hxv',hY,hYt,hrel⟩ := hxs + have hX : Puiseux (fun t => (X t:ℂ)) := hxv.2.1 + have hXt := hxv.2.2.1 + have hXc := hX.real_eventually_analytic.mono (fun _ h => h.continuousAt) + have hYc := (hY.real_eventually_analytic hxv).mono (fun _ h => h.continuousAt) + obtain ⟨H,hH,he⟩ := (firstClock_expansion_iff hX hXt).mp hY + have hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re := by + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hYt.eventually (eventually_gt_atTop 0)] with t he hy + rw [←he] + exact ⟨rfl,hy⟩ + have hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop := by + apply Filter.tendsto_atTop.2 + intro A + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hYt.eventually (eventually_ge_atTop A)] with t he hy + change A≤(H (X t:ℂ)).re + rwa [←he] + have hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) := by + apply Asymptotics.IsLittleO.of_bound + intro ε hε + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hrel.def hε] with t he ht + change ‖X t‖≤ε*‖(H (X t:ℂ)).re‖ + rwa [←he] + obtain ⟨y,hya,hyr,hyt,hK⟩ := hH.lower_field_chart hHr hHt hfast + have hyY : ∀ᶠ t : ℝ in atTop,y (Y t:ℂ)=(X t:ℂ) := by + filter_upwards [he,hXt.eventually hyr] with t he hy + rwa [he] + refine ⟨TransportedFirstField y,hK,?_⟩ + intro b + constructor + · intro hb + have hba := hK.analytic hb + exact ⟨(transported_first_iff hX hXt hYt hYc (hya.mono fun _ h => h.1) hyt hyY hba).mp hb,hba⟩ + · rintro ⟨hb,hba⟩ + exact (transported_first_iff hX hXt hYt hYc (hya.mono fun _ h => h.1) hyt hyY hba).mpr hb + +theorem ClockGerm.second_inv {X Y : ℝ → ℝ} (hxs : ValidClocks [Y,X]) + {f : ℝ → ℂ} (hf : ClockGerm [Y,X] f) : + ClockGerm [Y,X] (fun t => (f t)⁻¹) := by + obtain ⟨K,hK,hKm⟩ := hxs.second_lowerData + obtain ⟨F,E,b,hF,hb,he⟩ := hf + have hFK : ExpansionOver K F := ⟨E,b,hF,fun β hβ => (hKm _).mpr (hb β hβ)⟩ + obtain ⟨D,c,hF',hc⟩ := hFK.inv hK + exact ⟨fun z => (F z)⁻¹,D,c,hF',fun β hβ => (hKm _).mp (hc β hβ),he.inv⟩ + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma transported_first_deriv_mem {H y : ℂ → ℂ} + (hH : ExpansionOver PuiseuxSector H) + (hya : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z ∧ H (y z)=z) + (hyt : Tendsto y sectorInfinity sectorInfinity) + {b : ℂ → ℂ} (hb : b∈TransportedFirstField y) : + deriv b ∈ TransportedFirstField y := by + obtain ⟨F,hF,he⟩ := hb + let G : ℂ → ℂ := fun z => deriv F z*(deriv H z)⁻¹ + refine ⟨G,hF.puiseux_deriv.mul puiseux_lowerSectorData (hH.puiseux_deriv.inv puiseux_lowerSectorData),?_⟩ + have hid : (fun z => H (y z)) =ᶠ[sectorInfinity] id := hya.mono (fun _ h => h.2) + have hder := sector_eventually_deriv_congr hid + have heder := sector_eventually_deriv_congr he + filter_upwards [heder,hder,hya, + hyt.eventually hH.choose_spec.choose_spec.1.eventually_analytic, + hyt.eventually hF.choose_spec.choose_spec.1.eventually_analytic] with z he hd hy hh hf + have hchain := (hh.differentiableAt.hasDerivAt.comp z hy.1.differentiableAt.hasDerivAt).deriv + have hprod : deriv H (y z)*deriv y z=1 := by + change deriv (fun z => H (y z)) z=deriv H (y z)*deriv y z at hchain + rw [←hchain,hd] + simp + have hn : deriv H (y z)≠0 := left_ne_zero_of_mul_eq_one hprod + have hy' : deriv y z=(deriv H (y z))⁻¹ := by + apply (mul_left_cancel₀ hn) + rw [hprod,mul_inv_cancel₀ hn] + rw [he] + change deriv (F ∘ y) z=deriv F (y z)*(deriv H (y z))⁻¹ + rw [(hf.differentiableAt.hasDerivAt.comp z hy.1.differentiableAt.hasDerivAt).deriv,hy'] + +lemma ValidClocks.second_differentialData {X Y : ℝ → ℝ} (hxs : ValidClocks [Y,X]) : + ∃ K : Set (ℂ → ℂ),LowerSectorData K ∧ + (∀ b : ℂ → ℂ,b∈K → deriv b∈K) ∧ + (∀ f : ℝ → ℂ,ClockGerm (X :: []) f → ∃ b : ℂ → ℂ,b∈K ∧ f =ᶠ[atTop] fun t => b (Y t:ℂ)) ∧ + ∀ b : ℂ → ℂ,(b∈K ↔ + (ClockGerm (X :: []) (fun t => b (Y t:ℂ)) ∧ + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ b z)) := by + have hxv := hxs.1 + obtain ⟨hxv',hY,hYt,hrel⟩ := hxs + have hX : Puiseux (fun t => (X t:ℂ)) := hxv.2.1 + have hXt := hxv.2.2.1 + have hXc := hX.real_eventually_analytic.mono (fun _ h => h.continuousAt) + have hYc := (hY.real_eventually_analytic hxv).mono (fun _ h => h.continuousAt) + obtain ⟨H,hH,he⟩ := (firstClock_expansion_iff hX hXt).mp hY + have hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re := by + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hYt.eventually (eventually_gt_atTop 0)] with t he hy + rw [←he] + exact ⟨rfl,hy⟩ + have hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop := by + apply Filter.tendsto_atTop.2 + intro A + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hYt.eventually (eventually_ge_atTop A)] with t he hy + change A≤(H (X t:ℂ)).re + rwa [←he] + have hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) := by + apply Asymptotics.IsLittleO.of_bound + intro ε hε + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hrel.def hε] with t he ht + change ‖X t‖≤ε*‖(H (X t:ℂ)).re‖ + rwa [←he] + obtain ⟨y,hya,hyr,hyt,hK⟩ := hH.lower_field_chart hHr hHt hfast + have hyY : ∀ᶠ t : ℝ in atTop,y (Y t:ℂ)=(X t:ℂ) := by + filter_upwards [he,hXt.eventually hyr] with t he hy + rwa [he] + refine ⟨TransportedFirstField y,hK,fun _ hb => transported_first_deriv_mem hH hya hyt hb,?_,?_⟩ + · intro f hf + obtain ⟨F,hF,hef⟩ := (firstClock_expansion_iff hX hXt).mp hf + refine ⟨fun z => F (y z),⟨F,hF,EventuallyEq.rfl⟩,?_⟩ + filter_upwards [hef,hyY] with t hef hy + simpa only [hy] using hef + intro b + constructor + · intro hb + have hba := hK.analytic hb + exact ⟨(transported_first_iff hX hXt hYt hYc (hya.mono fun _ h => h.1) hyt hyY hba).mp hb,hba⟩ + · rintro ⟨hb,hba⟩ + exact (transported_first_iff hX hXt hYt hYc (hya.mono fun _ h => h.1) hyt hyY hba).mpr hb + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma ClockGerm.second_of_lower {X Y : ℝ → ℝ} (hxs : ValidClocks [Y,X]) + {f : ℝ → ℂ} (hf : ClockGerm (X :: []) f) : ClockGerm [Y,X] f := by + obtain ⟨K,hK,hKd,hKr,hKm⟩ := hxs.second_differentialData + obtain ⟨b,hb,he⟩ := hKr f hf + refine ⟨b,{0},fun _ => b,?_,fun _ _ => (hKm b).mp hb,he⟩ + simpa only [Complex.ofReal_zero,zero_mul,Complex.exp_zero,one_mul] using + SectorExpansion.single 0 (hK.analytic hb) (hK.slow hb) + +lemma ExpansionOver.deriv_mem {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) + {F : ℂ → ℂ} (hF : ExpansionOver K F) : ExpansionOver K (deriv F) := by + obtain ⟨E,b,hF,hb⟩ := hF + refine ⟨E,fun β z => (β:ℂ)*b β z+deriv (b β) z, + hF.deriv (fun β hβ => hK.analytic (hb β hβ)),?_⟩ + intro β hβ + exact hK.add_mem (hK.mul_mem (hK.const_mem (β:ℂ)) (hb β hβ)) (hKd _ (hb β hβ)) + +theorem ClockGerm.second_deriv {X Y : ℝ → ℝ} (hxs : ValidClocks [Y,X]) + {f : ℝ → ℂ} (hf : ClockGerm [Y,X] f) : ClockGerm [Y,X] (deriv f) := by + obtain ⟨K,hK,hKd,hKr,hKm⟩ := hxs.second_differentialData + obtain ⟨F,E,b,hF,hb,he⟩ := hf + have hF' : ExpansionOver K (deriv F) := + (show ExpansionOver K F from ⟨E,b,hF,fun β hβ => (hKm _).mpr (hb β hβ)⟩).deriv_mem hK hKd + have hFx : ClockGerm [Y,X] (fun t => deriv F (Y t:ℂ)) := by + obtain ⟨D,c,hF',hc⟩ := hF' + exact ⟨deriv F,D,c,hF',fun β hβ => (hKm _).mp (hc β hβ),EventuallyEq.rfl⟩ + have hYa := hxs.2.1.real_eventually_analytic hxs.1 + have hY' : ClockGerm (X :: []) (fun t => ((deriv Y t:ℝ):ℂ)) := by + apply (hxs.2.1.first_deriv hxs.1.2.1 hxs.1.2.2.1).congr + filter_upwards [hYa] with t ht + exact ht.differentiableAt.hasDerivAt.ofReal_comp.deriv + apply (hFx.mul (hY'.second_of_lower hxs)).congr + obtain ⟨T,hT⟩ := eventually_atTop.mp he + filter_upwards [hYa, + hxs.2.2.1.eventually (tendsto_real_sectorInfinity.eventually hF.eventually_analytic), + eventually_gt_atTop T] with t hYa hFa ht + have hd := hFa.differentiableAt.hasDerivAt.comp_ofReal.scomp t hYa.differentiableAt.hasDerivAt + have hc : (fun s => F (Y s:ℂ)) =ᶠ[𝓝 t] f := + (eventually_gt_nhds ht).mono (fun s hs => (hT s hs.le).symm) + simpa only [Complex.real_smul,mul_comm] using (hd.congr_of_eventuallyEq hc.symm).deriv.symm + +end DegeneratingTrees.Clock + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + +def TransportedField (K : Set (ℂ → ℂ)) (y : ℂ → ℂ) : Set (ℂ → ℂ) := + {b | ∃ F : ℂ → ℂ,ExpansionOver K F ∧ b =ᶠ[sectorInfinity] fun z => F (y z)} + +lemma transported_lowerSectorData {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) {y : ℂ → ℂ} + (hya : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z) + (hyt : Tendsto y sectorInfinity sectorInfinity) + (hys : (fun z => (y z).re) =o[sectorInfinity] Complex.re) : + LowerSectorData (TransportedField K y) := by + constructor + · intro c + exact ⟨fun _ => c,ExpansionOver.const hK c,EventuallyEq.rfl⟩ + · rintro f g ⟨F,hF,he⟩ ⟨G,hG,he'⟩ + exact ⟨fun z => F z+G z,hF.add hK hG,he.add he'⟩ + · rintro f ⟨F,hF,he⟩ + exact ⟨fun z => -F z,hF.neg hK,he.neg⟩ + · rintro f g ⟨F,hF,he⟩ ⟨G,hG,he'⟩ + exact ⟨fun z => F z*G z,hF.mul hK hG,he.mul he'⟩ + · rintro f ⟨F,hF,he⟩ + exact ⟨fun z => (F z)⁻¹,hF.inv hK,he.inv⟩ + · rintro f ⟨F,hF,he⟩ + have hg : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (y w)) z := by + filter_upwards [hya,hyt.eventually hF.choose_spec.choose_spec.1.eventually_analytic] with z hy hf + exact hf.comp hy + exact sector_eventually_analytic_congr hg he.symm + · rintro f ⟨F,hF,he⟩ + obtain ⟨a,ha⟩ := hF.expBound_some + intro ε hε + exact (ha.comp_slow hyt hys ε hε).congr' he.symm Filter.EventuallyEq.rfl + · rintro f ⟨F,hF,he⟩ + rcases hF.zero_or_ne hK with hz | hn + · exact Or.inl (he.trans (hyt.eventually hz)) + · exact Or.inr ((he.and (hyt.eventually hn)).mono fun z h => by rw [h.1]; exact h.2) + +lemma transported_deriv_mem {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hKd : ∀ b : ℂ → ℂ,b∈K → deriv b∈K) {H y : ℂ → ℂ} + (hH : ExpansionOver K H) + (hya : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z ∧ H (y z)=z) + (hyt : Tendsto y sectorInfinity sectorInfinity) + {b : ℂ → ℂ} (hb : b∈TransportedField K y) : + deriv b ∈ TransportedField K y := by + obtain ⟨F,hF,he⟩ := hb + let G : ℂ → ℂ := fun z => deriv F z*(deriv H z)⁻¹ + refine ⟨G,(hF.deriv_mem hK hKd).mul hK ((hH.deriv_mem hK hKd).inv hK),?_⟩ + have hid : (fun z => H (y z)) =ᶠ[sectorInfinity] id := hya.mono (fun _ h => h.2) + have hder := sector_eventually_deriv_congr hid + have heder := sector_eventually_deriv_congr he + filter_upwards [heder,hder,hya, + hyt.eventually hH.choose_spec.choose_spec.1.eventually_analytic, + hyt.eventually hF.choose_spec.choose_spec.1.eventually_analytic] with z he hd hy hh hf + have hchain := (hh.differentiableAt.hasDerivAt.comp z hy.1.differentiableAt.hasDerivAt).deriv + have hprod : deriv H (y z)*deriv y z=1 := by + change deriv (fun z => H (y z)) z=deriv H (y z)*deriv y z at hchain + rw [←hchain,hd] + simp + have hn : deriv H (y z)≠0 := left_ne_zero_of_mul_eq_one hprod + have hy' : deriv y z=(deriv H (y z))⁻¹ := by + apply (mul_left_cancel₀ hn) + rw [hprod,mul_inv_cancel₀ hn] + rw [he] + change deriv (F ∘ y) z=deriv F (y z)*(deriv H (y z))⁻¹ + rw [(hf.differentiableAt.hasDerivAt.comp z hy.1.differentiableAt.hasDerivAt).deriv,hy'] + +lemma tendsto_star_sectorInfinity : Tendsto (star : ℂ → ℂ) sectorInfinity sectorInfinity := by + apply Filter.tendsto_def.mpr + intro U hU + obtain ⟨ω,R,hω,hU⟩ := hU + exact ⟨ω,R,hω,fun z hz => hU _ (mem_lossSector_star hz)⟩ + +lemma SectorInverse.reflection_eq {H y : ℂ → ℂ} {I : ℝ → ℝ} (hi : SectorInverse H y I) : + (fun z => star (y (star z))) =ᶠ[sectorInfinity] y := by + have ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => star (y (star w))) z := by + filter_upwards [tendsto_star_sectorInfinity.eventually hi.analytic_left] with z hz + exact analyticAt_reflection hz.1 + apply sector_analytic_eq_of_ray ha (hi.analytic_left.mono fun _ h => h.1) + filter_upwards [hi.real_ray] with t ht + simp only [Complex.star_def,Complex.conj_ofReal,ht] + +lemma transported_conj_mem {K : Set (ℂ → ℂ)} + (hconj : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K) + {H y : ℂ → ℂ} {I : ℝ → ℝ} (hi : SectorInverse H y I) + {b : ℂ → ℂ} (hb : b∈TransportedField K y) : + (fun z => star (b (star z)))∈TransportedField K y := by + obtain ⟨F,⟨E,c,hF,hc⟩,he⟩ := hb + refine ⟨fun z => star (F (star z)),⟨E,fun β z => star (c β (star z)), + hF.conj,fun β hβ => hconj _ (hc β hβ)⟩,?_⟩ + filter_upwards [tendsto_star_sectorInfinity.eventually he,hi.reflection_eq] with z he hy + have hy' : y (star z)=star (y z) := by + simpa only [star_star] using congrArg star hy + simp only [he,hy'] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma SectorSlow.log_inverse {h : ℂ → ℂ} {I : ℝ → ℝ} + (hs : SectorSlow h) (hIt : Tendsto I atTop atTop) + (hi : ∀ᶠ t : ℝ in atTop,h (I t:ℂ)=(t:ℂ)) : + Real.log =o[atTop] I := by + apply Asymptotics.IsLittleO.of_bound + intro ε hε + obtain ⟨C,hC,hb⟩ := (hs (ε/2) (by positivity)).exists_pos + have hbound := hIt.eventually (tendsto_real_sectorInfinity.eventually hb.bound) + filter_upwards [hbound,hi,eventually_gt_atTop (1:ℝ), + hIt.eventually (eventually_gt_atTop (0:ℝ)), + hIt.eventually (eventually_ge_atTop (2*|Real.log C|/ε))] with t hb hi ht hI hIC + have htpos : 0.add + ((summable_nat_add_iff 3).mpr hs) + · intro n r hrl hru + have hr : 0 ≤ r := (show (0:ℝ)<2^(n+(n₀+2)) by positivity).trans hrl |>.le + apply csSup_le + · exact ⟨ω r,mem_image_of_mem _ ⟨by linarith,by linarith⟩⟩ + · rintro _ ⟨s,hs,rfl⟩ + exact window_bound hw hb n hrl hru hs.1 hs.2 + +lemma AdmissibleAngularLoss.const_mul {ω : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) {c : ℝ} (hc : 1 ≤ c) : + AdmissibleAngularLoss (fun r => c*ω r) := by + obtain ⟨hp,n₀,w,hw,hs,hb⟩ := hω + have hc0 : 0 < c := lt_of_lt_of_le zero_lt_one hc + refine ⟨?_,n₀,fun n => c*w n,fun n => mul_nonneg hc0.le (hw n),hs.mul_left c,?_⟩ + · filter_upwards [hp] with r hr + exact ⟨mul_pos hc0 hr.1,hr.2.trans (le_mul_of_one_le_left hr.1.le hc)⟩ + · intro n r hl hu + exact mul_le_mul_of_nonneg_left (hb n r hl hu) hc0.le + +lemma log_margin_grows : ∀ᶠ r : ℝ in atTop, 1 ≤ r*(Real.log r)⁻¹^2 := by + have h := (isLittleO_log_rpow_rpow_atTop (s := 1) 2 zero_lt_one).bound + (by norm_num : (0:ℝ)<1) + filter_upwards [h,eventually_gt_atTop (1:ℝ)] with r hr hr1 + have hr0 : 0 < r := lt_trans zero_lt_one hr1 + have hl : 0 < Real.log r := Real.log_pos hr1 + have hs : Real.log r ^ 2 ≤ r := by + simpa only [Real.rpow_two,Real.rpow_one,Real.norm_eq_abs,abs_of_nonneg (sq_nonneg (Real.log r)), + abs_of_pos hr0,one_mul] using hr + calc + 1 ≤ r/(Real.log r)^2 := (one_le_div (sq_pos_of_pos hl)).mpr hs + _ = r*(Real.log r)⁻¹^2 := by rw [div_eq_mul_inv,inv_pow] + +lemma half_loss_norm_le_re {η : ℝ} (hη0 : 0 ≤ η) (hηπ : η ≤ Real.pi/2) + {z : ℂ} (hz : |z.arg| < Real.pi/2-η) : η/2*‖z‖ ≤ z.re := by + have hc : η/2 ≤ Real.cos z.arg := by + have hp : (1/2:ℝ) ≤ 2/Real.pi := + (le_div_iff₀ Real.pi_pos).mpr (by linarith [Real.pi_lt_four]) + calc + η/2 ≤ 2/Real.pi*η := by nlinarith + _ ≤ Real.sin η := Real.mul_le_sin hη0 hηπ + _ = Real.cos (Real.pi/2-η) := (Real.cos_pi_div_two_sub η).symm + _ ≤ Real.cos |z.arg| := Real.cos_le_cos_of_nonneg_of_le_pi + (abs_nonneg _) (by linarith [Real.pi_pos]) hz.le + _ = Real.cos z.arg := Real.cos_abs _ + have hm := mul_le_mul_of_nonneg_left hc (norm_nonneg z) + rw [Complex.norm_mul_cos_arg] at hm + nlinarith + + + +theorem AdmissibleAngularLoss.narrow_discs {ω : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) (R : ℝ) : + ∃ (η : ℝ → ℝ) (R' : ℝ), AdmissibleAngularLoss η ∧ R ≤ R' ∧ + ∀ z ∈ lossSector η R', closedBall z 1 ⊆ lossSector ω R := by + obtain ⟨hN,hup⟩ := hω.neighboring + let η : ℝ → ℝ := fun r => 16*neighboringLoss ω r + have hη : AdmissibleAngularLoss η := hN.const_mul (by norm_num) + obtain ⟨a,t,S,hS,ha,has,ht,hsmall,hηsmall⟩ := angularLoss_kernel_data hη + obtain ⟨T,hT⟩ := eventually_atTop.mp + (hup.and (hN.1.and log_margin_grows)) + obtain ⟨W,hW⟩ := eventually_atTop.mp hω.1 + let R' := max (max (max S T) (W+2)) (max (R+2) 3) + have hR : R ≤ R' := by dsimp [R']; grind [le_max_left,le_max_right] + refine ⟨η,R',hη,hR,?_⟩ + intro z hz w hw + have hrS : S < ‖z‖ := lt_of_le_of_lt (by dsimp [R']; grind [le_max_left,le_max_right]) hz.1 + have hrT : T < ‖z‖ := lt_of_le_of_lt (by dsimp [R']; grind [le_max_left,le_max_right]) hz.1 + have hrW : W+2 < ‖z‖ := lt_of_le_of_lt (by dsimp [R']; grind [le_max_left,le_max_right]) hz.1 + have hrR : R+2 < ‖z‖ := lt_of_le_of_lt (by dsimp [R']; grind [le_max_left,le_max_right]) hz.1 + have hr3 : 3 < ‖z‖ := lt_of_le_of_lt (by dsimp [R']; grind [le_max_left,le_max_right]) hz.1 + have hd : ‖w-z‖ ≤ 1 := mem_closedBall_iff_norm.mp hw + have hwl : ‖z‖-1 ≤ ‖w‖ := by + have hh := norm_sub_le w (w-z) + rw [sub_sub_cancel] at hh + linarith + have hwu : ‖w‖ ≤ ‖z‖+1 := by + have hh := norm_add_le (w-z) z + rw [sub_add_cancel] at hh + linarith + have hNpos := (hT _ hrT.le).2.1.1 + have hNm : 1 ≤ ‖z‖*neighboringLoss ω ‖z‖ := + (hT _ hrT.le).2.2.trans (mul_le_mul_of_nonneg_left (hT _ hrT.le).2.1.2 (norm_nonneg z)) + have hωw : ω ‖w‖ ≤ neighboringLoss ω ‖z‖ := + (hT _ hrT.le).1 _ ⟨by linarith,by linarith⟩ + have hωpos : 0 < ω ‖w‖ := (hW _ (by linarith)).1 + have hηπ : η ‖z‖ ≤ Real.pi/2 := by + have hh := (hηsmall _ hrS.le).2.1 + linarith [Real.pi_gt_three] + have hre := half_loss_norm_le_re (hηsmall _ hrS.le).1.le hηπ hz.2 + have hre' := (abs_le.mp ((abs_re_le_norm (w-z)).trans hd)).1 + simp only [Complex.sub_re] at hre' + refine ⟨by linarith,arg_lt_of_re_lower hωpos (norm_pos_iff.mp (by linarith)) ?_⟩ + have hm := mul_le_mul_of_nonneg_right hωw (norm_nonneg w) + have hn := mul_le_mul_of_nonneg_left hwu hNpos.le + dsimp [η] at hre + nlinarith + + + +theorem sector_deriv_bound {ω : ℝ → ℝ} {R a C : ℝ} {f : ℂ → ℂ} + (hω : AdmissibleAngularLoss ω) (hf : AnalyticOnNhd ℂ f (lossSector ω R)) + (hC : 0 ≤ C) (hb : ∀ z ∈ lossSector ω R, ‖f z‖ ≤ C*Real.exp (a*z.re)) : + ∃ (η : ℝ → ℝ) (R' : ℝ), AdmissibleAngularLoss η ∧ R ≤ R' ∧ + AnalyticOnNhd ℂ (deriv f) (lossSector η R') ∧ + ∀ z ∈ lossSector η R', ‖deriv f z‖ ≤ (C*Real.exp |a|)*Real.exp (a*z.re) := by + obtain ⟨η,R',hη,hR,hdisc⟩ := hω.narrow_discs R + refine ⟨η,R',hη,hR,?_,?_⟩ + · intro z hz + exact (hf z (hdisc z hz (mem_closedBall_self (by norm_num)))).deriv + · intro z hz + have hd := hf.differentiableOn.diffContOnCl_ball (hdisc z hz) + have hc (w : ℂ) (hw : w ∈ sphere z 1) : + ‖f w‖ ≤ (C*Real.exp |a|)*Real.exp (a*z.re) := by + have hwr : |w.re-z.re| ≤ 1 := by + have hh := abs_re_le_norm (w-z) + simpa only [sub_re,mem_sphere_iff_norm.mp hw] using hh + have hm : a*(w.re-z.re) ≤ |a| := + (le_abs_self _).trans (by rw [abs_mul]; exact mul_le_of_le_one_right (abs_nonneg _) hwr) + calc + ‖f w‖ ≤ C*Real.exp (a*w.re) := hb _ (hdisc z hz (sphere_subset_closedBall hw)) + _ ≤ C*Real.exp (|a|+a*z.re) := mul_le_mul_of_nonneg_left + (Real.exp_le_exp.mpr (by linarith)) hC + _ = (C*Real.exp |a|)*Real.exp (a*z.re) := by rw [Real.exp_add,mul_assoc] + simpa using norm_deriv_le_of_forall_mem_sphere_norm_le (by norm_num : (0:ℝ)<1) hd hc + +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees + +lemma AdmissibleAngularLoss.max {ω η : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) (hη : AdmissibleAngularLoss η) : + AdmissibleAngularLoss (fun r => max (ω r) (η r)) := by + obtain ⟨hp,n,w,hw,hs,hb⟩ := hω + obtain ⟨hq,m,v,hv,ht,hc⟩ := hη + refine ⟨?_,n+m,fun k => w (k+m)+v (k+n),?_,?_,?_⟩ + · filter_upwards [hp] with r hr + exact ⟨hr.1.trans_le (le_max_left _ _),hr.2.trans (le_max_left _ _)⟩ + · intro k; exact add_nonneg (hw _) (hv _) + · exact ((summable_nat_add_iff m).mpr hs).add ((summable_nat_add_iff n).mpr ht) + · intro k r hl hu + have h1 := hb (k+m) r (by convert hl using 1; congr 1; omega) + (by convert hu using 1; congr 1; omega) + have h2 := hc (k+n) r (by convert hl using 1; congr 1; omega) + (by convert hu using 1; congr 1; omega) + exact max_le (h1.trans (le_add_of_nonneg_right (hv _))) + (h2.trans (le_add_of_nonneg_left (hw _))) + +def SectorEventually (P : ℂ → Prop) : Prop := + ∃ ω R, AdmissibleAngularLoss ω ∧ ∀ z ∈ lossSector ω R, P z + +lemma SectorEventually.mono {P Q : ℂ → Prop} (h : SectorEventually P) + (hpq : ∀ z, P z → Q z) : SectorEventually Q := by + obtain ⟨ω,R,hω,h⟩ := h + exact ⟨ω,R,hω,fun z hz => hpq z (h z hz)⟩ + +lemma SectorEventually.and {P Q : ℂ → Prop} + (h : SectorEventually P) (k : SectorEventually Q) : SectorEventually (fun z => P z ∧ Q z) := by + obtain ⟨ω,R,hω,h⟩ := h + obtain ⟨η,S,hη,k⟩ := k + refine ⟨fun r => max (ω r) (η r),max R S,hω.max hη,?_⟩ + intro z hz + exact ⟨h z ⟨(le_max_left _ _).trans_lt hz.1,by + have hh := le_max_left (ω ‖z‖) (η ‖z‖); linarith [hz.2]⟩, + k z ⟨(le_max_right _ _).trans_lt hz.1,by + have hh := le_max_right (ω ‖z‖) (η ‖z‖); linarith [hz.2]⟩⟩ + +lemma SectorEventually.finset_forall {ι : Type*} (s : Finset ι) {P : ι → ℂ → Prop} + (hbase : SectorEventually (fun _ => True)) + (h : ∀ i ∈ s, SectorEventually (P i)) : + SectorEventually (fun z => ∀ i ∈ s, P i z) := by + classical + induction s using Finset.induction_on with + | empty => exact hbase.mono (by simp) + | @insert i s hi ih => + have ht := (h i (Finset.mem_insert_self _ _)).and + (ih (fun j hj => h j (Finset.mem_insert_of_mem hj))) + exact ht.mono (by simp only [Finset.mem_insert,forall_eq_or_imp]; tauto) + + + +theorem sector_zero_of_ray_zero {ω : ℝ → ℝ} {R : ℝ} {f : ℂ → ℂ} + (hω : AdmissibleAngularLoss ω) (hf : AnalyticOnNhd ℂ f (lossSector ω R)) + (hz : ∀ᶠ x : ℝ in atTop, f (x:ℂ)=0) : SectorEventually (fun z => f z=0) := by + obtain ⟨a,t,S,hS,ha,has,ht,hsmall,hcontrol⟩ := angularLoss_kernel_data hω + obtain ⟨T,hT⟩ := eventually_atTop.mp hz + let W := max (max R S) (max T 1) + have hW0 : 0 < W := lt_of_lt_of_le zero_lt_one (by dsimp [W]; grind [le_max_left,le_max_right]) + have hWR : R ≤ W := by dsimp [W]; grind [le_max_left,le_max_right] + have hWS : S ≤ W := by dsimp [W]; grind [le_max_left,le_max_right] + have hWT : T ≤ W := by dsimp [W]; grind [le_max_left,le_max_right] + have hsub : lossSector ω W ⊆ lossSector ω R := fun z hz => ⟨hWR.trans_lt hz.1,hz.2⟩ + have hconn : IsPreconnected (lossSector ω W) := by + apply lossSector_isPreconnected hW0 + intro r hr + have hh := hcontrol r (hWS.trans hr.le) + exact ⟨hh.1,by linarith [hh.2.1,Real.pi_gt_three]⟩ + have hxmem : ((W+1:ℝ):ℂ) ∈ lossSector ω W := by + have hpos : 0 < W+1 := by linarith + have hh := hcontrol (W+1) (by linarith) + simp only [lossSector,mem_ofPred_eq,Complex.norm_of_nonneg hpos.le, + Complex.arg_ofReal_of_nonneg hpos.le,abs_zero] + constructor <;> linarith [hh.2.1,Real.pi_gt_three] + have hcl : ((W+1:ℝ):ℂ) ∈ closure ({z | f z=0} \ {((W+1:ℝ):ℂ)}) := by + rw [Metric.mem_closure_iff] + intro ε hε + refine ⟨((W+1+ε/2:ℝ):ℂ),⟨hT _ (by linarith),?_⟩,?_⟩ + · simp only [mem_singleton_iff,Complex.ofReal_inj] + linarith + · simp only [dist_eq_norm,←Complex.ofReal_sub,Complex.norm_real,Real.norm_eq_abs] + exact abs_lt.mpr ⟨by linarith,by linarith⟩ + exact ⟨ω,W,hω,(hf.mono hsub).eqOn_zero_of_preconnected_of_mem_closure hconn hxmem hcl⟩ + +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees + +lemma AdmissibleAngularLoss.tendsto_zero {ω : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) : Tendsto ω atTop (𝓝 0) := by + rw [Metric.tendsto_nhds] + intro ε hε + let c : ℝ := Max.max 1 ε⁻¹ + have hc : 1 ≤ c := le_max_left _ _ + have hcp : 0 < c := lt_of_lt_of_le zero_lt_one hc + have hcε : 1 ≤ c*ε := by + have h := mul_le_mul_of_nonneg_right (le_max_right (1:ℝ) ε⁻¹) hε.le + rw [inv_mul_cancel₀ hε.ne'] at h + exact h + obtain ⟨a,t,S,hS,ha,hs,ht,hsmall,hbound⟩ := angularLoss_kernel_data (hω.const_mul hc) + filter_upwards [eventually_ge_atTop S] with r hr + have hb := hbound r hr + have hw : 0 < ω r := (mul_pos_iff_of_pos_left hcp).mp hb.1 + simp only [Real.dist_eq,sub_zero,abs_of_pos hw] + have hmul : c*ω r < c*ε := by linarith [hb.2.1] + exact (mul_lt_mul_iff_of_pos_left hcp).mp hmul + + + +lemma AdmissibleAngularLoss.power_absorption {ω : ℝ → ℝ} + (hω : AdmissibleAngularLoss ω) {a : ℝ} (ha : 0 < a) (C : ℝ) : + ∀ᶠ r : ℝ in atTop, C*r^(-a) ≤ ω r := by + have h := (isLittleO_log_rpow_rpow_atTop (s := a) 2 ha).bound + (show (0:ℝ) < (Max.max C 0+1)⁻¹ by positivity) + filter_upwards [h,hω.1,eventually_gt_atTop (1:ℝ)] with r hr hωr hr1 + have hr0 : 0 < r := zero_lt_one.trans hr1 + have hl : 0 < Real.log r := Real.log_pos hr1 + have hp : 0 < r^a := Real.rpow_pos_of_pos hr0 _ + have hc : 0 < Max.max C 0+1 := by positivity + have hsq : (Real.log r)^2 ≤ (Max.max C 0+1)⁻¹ * r^a := by + simpa only [Real.rpow_two,Real.norm_eq_abs,abs_of_nonneg (sq_nonneg (Real.log r)),abs_of_pos hp] using hr + have hsmall : C*(Real.log r)^2 ≤ r^a := by + have hmul := mul_le_mul_of_nonneg_left hsq hc.le + have he : (Max.max C 0+1) * ((Max.max C 0+1)⁻¹ * r^a) = r^a := by field_simp + rw [he] at hmul + have hC := le_max_left C 0 + nlinarith [sq_nonneg (Real.log r)] + calc + C*r^(-a) = C/(r^a) := by rw [Real.rpow_neg hr0.le,div_eq_mul_inv] + _ ≤ (Real.log r)⁻¹^2 := by + rw [inv_pow,←one_div,div_le_div_iff₀ hp (sq_pos_of_pos hl)] + simpa only [one_mul] using hsmall + _ ≤ ω r := hωr.2 + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +namespace DegeneratingTrees + +def baseLoss (r : ℝ) : ℝ := (Real.log r)⁻¹^2 + +lemma admissible_baseLoss : AdmissibleAngularLoss baseLoss := by + have hlog : 0 < Real.log (2:ℝ) := Real.log_pos (by norm_num) + refine ⟨?_,1,fun n : ℕ => ((Real.log (2:ℝ))⁻¹)^2 * (((n+1:ℕ):ℝ)^2)⁻¹,?_,?_,?_⟩ + · filter_upwards [eventually_gt_atTop (1:ℝ)] with r hr + refine ⟨?_,le_rfl⟩ + exact sq_pos_of_pos (inv_pos.mpr (Real.log_pos hr)) + · intro n + positivity + · exact ((summable_nat_add_iff 1).mpr (Real.summable_nat_pow_inv.mpr (by norm_num : 1 < (2:ℕ)))).mul_left _ + · intro n r hl hu + have hr : 0 < r := (by positivity : (0:ℝ)<2^(n+1)).trans hl + have hnr : 0 < ((n+1:ℕ):ℝ) := by positivity + have hh : ((n+1:ℕ):ℝ)*Real.log (2:ℝ) < Real.log r := by + simpa only [Real.log_pow] using Real.strictMonoOn_log (by positivity : (0:ℝ)<2^(n+1)) hr hl + have hi := inv_le_inv₀ (mul_pos hnr hlog |>.trans hh) (mul_pos hnr hlog) + have hle : (Real.log r)⁻¹ ≤ (((n+1:ℕ):ℝ)*Real.log (2:ℝ))⁻¹ := hi.mpr hh.le + have hs := sq_le_sq₀ (inv_nonneg.mpr ((mul_pos hnr hlog).trans hh).le) + (inv_nonneg.mpr (mul_pos hnr hlog).le) |>.mpr hle + dsimp [baseLoss] + calc + (Real.log r)⁻¹^2 ≤ (((n+1:ℕ):ℝ)*Real.log (2:ℝ))⁻¹^2 := hs + _ = ((Real.log (2:ℝ))⁻¹)^2 * (((n+1:ℕ):ℝ)^2)⁻¹ := by + rw [mul_inv,mul_pow,inv_pow] + ring + +lemma SectorEventually.of_radial {P : ℂ → Prop} + (h : ∀ᶠ r : ℝ in atTop, ∀ z : ℂ, ‖z‖=r → P z) : SectorEventually P := by + obtain ⟨R,hR⟩ := eventually_atTop.mp h + exact ⟨baseLoss,R,admissible_baseLoss,fun z hz => hR ‖z‖ hz.1.le z rfl⟩ + +lemma SectorEventually.truth : SectorEventually (fun _ => True) := + ⟨baseLoss,0,admissible_baseLoss,fun _ _ => True.intro⟩ + +lemma SectorEventually.realpart_pos : SectorEventually (fun z => 0 < z.re) := by + obtain ⟨R,hR⟩ := eventually_atTop.mp admissible_baseLoss.1 + refine ⟨baseLoss,max R 0,admissible_baseLoss,?_⟩ + intro z hz + have hp := (hR ‖z‖ ((le_max_left _ _).trans hz.1.le)).1 + have hn : z ≠ 0 := norm_pos_iff.mp ((le_max_right _ _).trans_lt hz.1) + have harg : |z.arg| < Real.pi/2 := by linarith [hz.2] + exact (Complex.abs_arg_lt_pi_div_two_iff.mp harg).resolve_right hn + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/SectorFamilies.lean b/lean/OAI/Analysis/PathSelection/SectorFamilies.lean new file mode 100644 index 0000000000000000000000000000000000000000..54f70a81cdb9bb3de814f78fd120f71a07d9643c --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/SectorFamilies.lean @@ -0,0 +1,159 @@ +import Mathlib +import OAI.Analysis.PathSelection.LossPullbacks +import OAI.Analysis.PathSelection.SectorLimits + +namespace OAI + +/-! Countable sector narrowing and common fixed-sector asymptotics. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +/- No uniform angular losses and no uniform original tail thresholds are assumed. -/ + +open Set Filter Topology +namespace DegeneratingTrees + +lemma summable_common_eventual_majorant {a : ℕ → ℕ → ℝ} + (ha : ∀ i n,0≤a i n) (hs : ∀ i,Summable (a i)) : + ∃ v : ℕ → ℝ,(∀ n,0≤v n) ∧ Summable v ∧ + ∀ i,∀ᶠ n in atTop,a i n≤v n := by + let c : ℕ → ℝ := fun i => (1/2:ℝ)^i/(1+∑' n,a i n) + have hc (i : ℕ) : 0 c p.1*a p.1 p.2) := by + have hn : (0 : ℕ×ℕ → ℝ) ≤ (fun p => c p.1*a p.1 p.2) := + fun p => mul_nonneg (hc _).le (ha _ _) + have hrow (i : ℕ) : Summable (fun n => c i*a i n) := (hs i).mul_left (c i) + have hsum : Summable (fun i => c i*(∑' n,a i n)) := + Summable.of_nonneg_of_le (fun i => mul_nonneg (hc i).le (tsum_nonneg (ha i))) + hc_bound summable_geometric_two + have hsum' : Summable (fun i => ∑' n,c i*a i n) := by + simpa only [tsum_mul_left] using hsum + exact (summable_prod_of_nonneg hn).mpr ⟨hrow,hsum'⟩ + let w : ℕ → ℝ := fun n => ∑' i,c i*a i n + have hw (n : ℕ) : 0≤w n := tsum_nonneg (fun i => mul_nonneg (hc i).le (ha i n)) + have hws : Summable w := hprod.prod_symm.prod + obtain ⟨v,hv,hvs,hvw⟩ := summable_strict_majorant hw hws + refine ⟨v,hv,hvs,?_⟩ + intro i + filter_upwards [hvw (c i) (hc i)] with n hn + have hh : c i*a i n ≤ w n := + (hprod.prod_symm.prod_factor n).le_tsum i (fun j _ => mul_nonneg (hc j).le (ha j n)) + exact (mul_le_mul_iff_right₀ (hc i)).mp (hh.trans hn) + + + +theorem admissible_countable_majorant {ω : ℕ → ℝ → ℝ} + (hω : ∀ i,AdmissibleAngularLoss (ω i)) : + ∃ η : ℝ → ℝ,AdmissibleAngularLoss η ∧ + ∀ i,∀ᶠ r : ℝ in atTop,ω i r≤η r := by + choose N w hw hws hb using fun i => (hω i).2 + let a : ℕ → ℕ → ℝ := fun i n => w i (n-N i) + have ha (i n : ℕ) : 0≤a i n := hw i _ + have has (i : ℕ) : Summable (a i) := by + apply (summable_nat_add_iff (N i)).mp + simpa only [a,Nat.add_sub_cancel] using hws i + obtain ⟨v,hv,hvs,hdom⟩ := summable_common_eventual_majorant ha has + let η : ℝ → ℝ := fun r => max (baseLoss r) (v (dyadicLossIndex 0 r)) + refine ⟨η,admissible_dyadic_step hv hvs 0,?_⟩ + intro i + filter_upwards [dyadicLossIndex_shell 0, + (tendsto_dyadicLossIndex 0).eventually (eventually_ge_atTop (N i)), + (tendsto_dyadicLossIndex 0).eventually (hdom i)] with r hr hN hdom + have hidx : dyadicLossIndex 0 r-N i+N i=dyadicLossIndex 0 r := Nat.sub_add_cancel hN + have hbound : ω i r ≤ a i (dyadicLossIndex 0 r) := by + apply hb i _ r + · simpa only [hidx,Nat.add_zero] using hr.1 + · simpa only [hidx,Nat.add_zero] using hr.2 + exact hbound.trans (hdom.trans (le_max_right _ _)) + + + +theorem SectorEventually.countable {P : ℕ → ℂ → Prop} + (hP : ∀ n,SectorEventually (P n)) : + ∃ η : ℝ → ℝ,AdmissibleAngularLoss η ∧ + ∀ n,∃ R : ℝ,∀ z∈lossSector η R,P n z := by + choose ω R hω h using hP + obtain ⟨η,hη,he⟩ := admissible_countable_majorant hω + refine ⟨η,hη,?_⟩ + intro n + obtain ⟨T,hT⟩ := eventually_atTop.mp (he n) + refine ⟨max (R n) T,?_⟩ + intro z hz + apply h n z + refine ⟨(le_max_left _ _).trans_lt hz.1,?_⟩ + have hh := hT ‖z‖ ((le_max_right _ _).trans hz.1.le) + exact hz.2.trans_le (sub_le_sub_left hh _) + +end DegeneratingTrees + + + + + + + +open Set Filter Topology +open scoped Asymptotics +namespace DegeneratingTrees + +lemma fixed_sector_of_tendsto {E : Type*} [PseudoMetricSpace E] + {f : ℂ → E} {a : E} (hf : Tendsto f sectorInfinity (𝓝 a)) : + ∃ η : ℝ → ℝ,AdmissibleAngularLoss η ∧ + ∀ ε : ℝ,0<ε → ∃ R : ℝ,∀ z∈lossSector η R,dist (f z) a<ε := by + have hp (n : ℕ) : SectorEventually (fun z => dist (f z) a<1/((n:ℝ)+1)) := + Metric.tendsto_nhds.mp hf _ (by positivity) + obtain ⟨η,hη,h⟩ := SectorEventually.countable hp + refine ⟨η,hη,?_⟩ + intro ε hε + obtain ⟨n,hn⟩ := exists_nat_one_div_lt hε + obtain ⟨R,hR⟩ := h n + exact ⟨R,fun z hz => (hR z hz).trans hn⟩ + +lemma fixed_sector_of_littleO {E F : Type*} [Norm E] [SeminormedAddCommGroup F] + {f : ℂ → E} {g : ℂ → F} (hfg : f =o[sectorInfinity] g) : + ∃ η : ℝ → ℝ,AdmissibleAngularLoss η ∧ + ∀ ε : ℝ,0<ε → ∃ R : ℝ,∀ z∈lossSector η R,‖f z‖≤ε*‖g z‖ := by + have hp (n : ℕ) : SectorEventually (fun z => ‖f z‖≤(1/((n:ℝ)+1))*‖g z‖) := + hfg.bound (by positivity) + obtain ⟨η,hη,h⟩ := SectorEventually.countable hp + refine ⟨η,hη,?_⟩ + intro ε hε + obtain ⟨n,hn⟩ := exists_nat_one_div_lt hε + obtain ⟨R,hR⟩ := h n + exact ⟨R,fun z hz => (hR z hz).trans (mul_le_mul_of_nonneg_right hn.le (norm_nonneg _))⟩ + +lemma fixed_sector_realpart {F : ℂ → ℂ} + (hF : (fun z => (F z).re) =o[sectorInfinity] Complex.re) : + ∃ η : ℝ → ℝ,AdmissibleAngularLoss η ∧ + ∀ ε : ℝ,0<ε → ∃ R : ℝ,∀ z∈lossSector η R,|(F z).re|≤ε*z.re := by + have hp (n : ℕ) : SectorEventually (fun z => + ‖(F z).re‖≤(1/((n:ℝ)+1))*‖z.re‖ ∧ 0 (H (t:ℂ)).re) atTop atTop) + (he : b =ᶠ[sectorInfinity] fun z => F (y z)) : + ∀ᶠ t : ℝ in atTop,F (t:ℂ)=b (H (t:ℂ)) := by + filter_upwards [hi.right,hHr,hHt.eventually (tendsto_real_sectorInfinity.eventually he)] with t hr hH he + have eq : H (t:ℂ)=((H (t:ℂ)).re:ℂ) := Complex.ext rfl (by simpa using hH) + rw [←eq,hr] at he + exact he.symm + +lemma ScalarSectorChart.congr_composition {F x G y : ℂ → ℂ} + (h : ScalarSectorChart F x) + (he : (fun z => F (x z)) =ᶠ[sectorInfinity] (fun z => G (y z))) : + ScalarSectorChart G y := by + have hr := tendsto_real_sectorInfinity.eventually he + obtain ⟨C,hC,hm⟩ := h.radial + refine ⟨?_,h.unbounded.congr' (hr.mono fun _ e => congrArg Complex.re e), + sector_eventually_analytic_congr h.analytic he,h.maps_sector.congr' he,C,hC,?_⟩ + · filter_upwards [h.positive,hr] with t ht he + rwa [←he] + · filter_upwards [hm,he,tendsto_norm_sectorInfinity.eventually hr] with z hm he hr + rwa [he,hr] at hm + +lemma transported_lowerSectorCharts {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + (hcharts : HasSectorCharts K) {H y : ℂ → ℂ} {I : ℝ → ℝ} + (hH : ExpansionOver K H) (hi : SectorInverse H y I) + (hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re) + (hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop) + (hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re)) + (hys : (fun z => (y z).re) =o[sectorInfinity] Complex.re) : + LowerSectorCharts (TransportedField K y) := by + have hL := transported_lowerSectorData hK (hi.analytic_left.mono fun _ h => h.1) hi.maps_sector hys + intro h hh hhr hht hhfast + obtain ⟨A,hA,hea⟩ := hh + have hHr0 := hHr.mono fun _ h => h.1 + have hAH := hi.original_ray hHr0 hHt hea + have hAHr : ∀ᶠ t : ℝ in atTop,A (t:ℂ)=h ((H (t:ℂ)).re:ℂ) := by + filter_upwards [hAH,hHr] with t he hr + exact he.trans (congrArg h (Complex.ext rfl (by simpa using hr.1))) + have hAr : ∀ᶠ t : ℝ in atTop,(A (t:ℂ)).im=0 ∧ 0<(A (t:ℂ)).re := by + filter_upwards [hAHr,hHt.eventually hhr] with t he hr + rwa [he] + have hAt : Tendsto (fun t : ℝ => (A (t:ℂ)).re) atTop atTop := + (hht.comp hHt).congr' (hAHr.mono fun _ e => (congrArg Complex.re e).symm) + have hHA : (fun t : ℝ => (H (t:ℂ)).re) =o[atTop] (fun t : ℝ => (A (t:ℂ)).re) := + (hhfast.comp_tendsto hHt).congr' Filter.EventuallyEq.rfl + (hAHr.mono fun _ e => (congrArg Complex.re e).symm) + have hAfast : id =o[atTop] (fun t : ℝ => (A (t:ℂ)).re) := hfast.trans_isBigO hHA.isBigO + obtain ⟨v,J,hvj,hfamily⟩ := hcharts A hA hAr hAt hAfast + obtain ⟨hHv,hHvs⟩ := hfamily H hH hHr hHt hHA.isBigO + let x : ℂ → ℂ := fun z => H (v z) + let Q : ℝ → ℝ := fun t => (H (J t:ℂ)).re + have hQt : Tendsto Q atTop atTop := hHt.comp hvj.ray_unbounded + have hxreal : ∀ᶠ t : ℝ in atTop,x (t:ℂ)=(Q t:ℂ) := by + filter_upwards [hvj.real_ray,hvj.ray_unbounded.eventually hHr] with t hv hr + simp only [x,Q,hv] + exact Complex.ext rfl (by simpa using hr.1) + have hyx : (fun z => y (x z)) =ᶠ[sectorInfinity] v := by + have ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => y (x w)) z := by + filter_upwards [hHv.analytic,hHv.maps_sector.eventually hi.analytic_left] with z hx hy + exact (show AnalyticAt ℂ y (x z) from hy.1).comp (f := x) hx + apply sector_analytic_eq_of_ray ha (hvj.analytic_left.mono fun _ h => h.1) + filter_upwards [hvj.real_ray,hvj.ray_unbounded.eventually hi.right] with t hv hr + simpa only [x,hv] using hr + have hax : (fun z => h (x z)) =ᶠ[sectorInfinity] (fun z => A (v z)) := by + filter_upwards [hHv.maps_sector.eventually hea,hyx] with z he hy + change h (x z)=A (y (x z)) at he + simpa only [hy] using he + have hxi : SectorInverse h x Q := by + constructor + · filter_upwards [hHv.analytic,hax,hvj.analytic_left] with z hx he hv + exact ⟨hx,he.trans hv.2⟩ + · filter_upwards [tendsto_real_sectorInfinity.eventually hea,hi.real_ray, + hi.ray_unbounded.eventually hvj.right, + tendsto_real_sectorInfinity.eventually hi.analytic_left] with t he hir hvr hl + change H (v (h (t:ℂ)))=(t:ℂ) + rw [he,hir,hvr] + simpa only [hir] using hl.2 + · exact hHv.maps_sector + · exact hQt + · exact hxreal + refine ⟨x,Q,hxi,hxi.log_small hL ⟨A,hA,hea⟩,?_,?_⟩ + · obtain ⟨C,hC,hmod⟩ := hHv.radial + refine ⟨max C 1,le_max_right _ _,?_⟩ + filter_upwards [hmod,tendsto_norm_sectorInfinity.eventually hxreal, + tendsto_norm_sectorInfinity.eventually (hQt.eventually (eventually_gt_atTop (0:ℝ)))] with z hm he hq + change ‖x (‖z‖:ℂ)‖/C≤‖x z‖ ∧ ‖x z‖≤C*‖x (‖z‖:ℂ)‖ at hm + rw [he,Complex.norm_of_nonneg hq.le] at hm + constructor + · exact (div_le_div_of_nonneg_left hq.le hC (le_max_left C 1)).trans hm.1 + · exact hm.2.trans (mul_le_mul_of_nonneg_right (le_max_left C 1) hq.le) + · intro g hg hgr hgt hgo + obtain ⟨B,hB,heb⟩ := hg + have hBH := hi.original_ray hHr0 hHt heb + have hBHr : ∀ᶠ t : ℝ in atTop,B (t:ℂ)=g ((H (t:ℂ)).re:ℂ) := by + filter_upwards [hBH,hHr] with t he hr + exact he.trans (congrArg g (Complex.ext rfl (by simpa using hr.1))) + have hBr : ∀ᶠ t : ℝ in atTop,(B (t:ℂ)).im=0 ∧ 0<(B (t:ℂ)).re := by + filter_upwards [hBHr,hHt.eventually hgr] with t he hr + rwa [he] + have hBt : Tendsto (fun t : ℝ => (B (t:ℂ)).re) atTop atTop := + (hgt.comp hHt).congr' (hBHr.mono fun _ e => (congrArg Complex.re e).symm) + have hBA : (fun t : ℝ => (B (t:ℂ)).re) =O[atTop] (fun t : ℝ => (A (t:ℂ)).re) := + (hgo.comp_tendsto hHt).congr' + (hBHr.mono fun _ e => (congrArg Complex.re e).symm) + (hAHr.mono fun _ e => (congrArg Complex.re e).symm) + obtain ⟨hBv,hBvs⟩ := hfamily B hB hBr hBt hBA + have he : (fun z => B (v z)) =ᶠ[sectorInfinity] (fun z => g (x z)) := by + filter_upwards [hHv.maps_sector.eventually heb,hyx] with z he hy + change g (x z)=B (y (x z)) at he + simpa only [hy] using he.symm + refine ⟨hBv.congr_composition he,?_⟩ + intro hsmall + have hsmall' : (fun t : ℝ => (B (t:ℂ)).re) =o[atTop] (fun t : ℝ => (A (t:ℂ)).re) := + (hsmall.comp_tendsto hHt).congr' + (hBHr.mono fun _ e => (congrArg Complex.re e).symm) + (hAHr.mono fun _ e => (congrArg Complex.re e).symm) + exact (hBvs hsmall').congr' (he.mono fun _ e => congrArg Complex.re e) Filter.EventuallyEq.rfl + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ExpansionOver.of_lower {K : Set (ℂ → ℂ)} (hK : LowerSectorData K) + {F : ℂ → ℂ} (hF : F∈K) : ExpansionOver K F := by + refine ⟨{0},fun _ => F,?_,fun _ _ => hF⟩ + simpa only [Complex.ofReal_zero,zero_mul,Complex.exp_zero,one_mul] using + SectorExpansion.single 0 (hK.analytic hF) (hK.slow hF) + +structure ClockSectorData (xs : List (ℝ → ℝ)) (X : ℝ → ℝ) (K : Set (ℂ → ℂ)) : Prop where + lower : LowerSectorData K + differential : ∀ b : ℂ → ℂ,b∈K → deriv b∈K + reflection : ∀ b : ℂ → ℂ,b∈K → (fun z => star (b (star z)))∈K + charts : HasSectorCharts K + coordinate : ExpansionOver K id + represents : ∀ f : ℝ → ℂ,ClockGerm xs f → ∃ b : ℂ → ℂ,b∈K ∧ f =ᶠ[atTop] fun t => b (X t:ℂ) + membership : ∀ b : ℂ → ℂ,b∈K ↔ + (ClockGerm xs (fun t => b (X t:ℂ)) ∧ ∀ᶠ z in sectorInfinity,AnalyticAt ℂ b z) + +lemma ClockSectorData.expansion_iff {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} {K : Set (ℂ → ℂ)} + (hD : ClockSectorData xs X K) {f : ℝ → ℂ} : + ClockGerm (X::xs) f ↔ ∃ F : ℂ → ℂ,ExpansionOver K F ∧ f =ᶠ[atTop] fun t => F (X t:ℂ) := by + constructor + · rintro ⟨F,E,b,hF,hb,he⟩ + exact ⟨F,⟨E,b,hF,fun β hβ => (hD.membership _).mpr (hb β hβ)⟩,he⟩ + · rintro ⟨F,⟨E,b,hF,hb⟩,he⟩ + exact ⟨F,E,b,hF,fun β hβ => (hD.membership _).mp (hb β hβ),he⟩ + +lemma puiseux_clockSectorData {X : ℝ → ℝ} + (hX : Puiseux (fun t => (X t:ℂ))) (hXt : Tendsto X atTop atTop) : + ClockSectorData [] X PuiseuxSector := by + refine ⟨puiseux_lowerSectorData,fun _ hb => PuiseuxSector.deriv_mem hb,?_, + puiseux_hasSectorCharts,ExpansionOver.puiseux_mem ⟨Eventually.of_forall fun _ => analyticAt_id,puiseux_variable⟩,?_,?_⟩ + · intro b hb + refine ⟨?_,?_⟩ + · filter_upwards [tendsto_star_sectorInfinity.eventually hb.1] with z hz + exact analyticAt_reflection hz + · simpa only [Complex.star_def,Complex.conj_ofReal] using hb.2.conj + · intro f hf + obtain ⟨I,hI,hIt,hl,hr⟩ := hX.inverse_change hXt + obtain ⟨F,hF,he⟩ := (hf.comp_unbounded hI hIt).sector_representative + refine ⟨F,hF,?_⟩ + filter_upwards [hXt.eventually he,hr] with t he hr + simpa only [hr] using he + · intro b + constructor + · intro hb + exact ⟨hb.2.comp_unbounded hX hXt,hb.1⟩ + · rintro ⟨hb,hba⟩ + exact ⟨hba,puiseux_of_comp_clock hX hXt hb⟩ + +lemma ClockSectorData.step {xs : List (ℝ → ℝ)} {X Y : ℝ → ℝ} {K : Set (ℂ → ℂ)} + (hD : ClockSectorData xs X K) (hvalid : ValidClocks (Y::X::xs)) : + ∃ L : Set (ℂ → ℂ),ClockSectorData (X::xs) Y L := by + have hXt := hvalid.1.2.2.1 + have hYt := hvalid.2.2.1 + have hXc := (hvalid.1.2.1.real_eventually_analytic hvalid.1.1).mono (fun _ h => h.continuousAt) + have hYc := (hvalid.2.1.real_eventually_analytic hvalid.1).mono (fun _ h => h.continuousAt) + obtain ⟨H,hH,he⟩ := hD.expansion_iff.mp hvalid.2.1 + have hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re := by + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hYt.eventually (eventually_gt_atTop 0)] with t he hy + rw [←he] + exact ⟨rfl,hy⟩ + have hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop := by + apply Filter.tendsto_atTop.2 + intro A + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hYt.eventually (eventually_ge_atTop A)] with t he hy + change A≤(H (X t:ℂ)).re + rwa [←he] + have hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) := by + apply Asymptotics.IsLittleO.of_bound + intro ε hε + apply eventually_of_comp_clock hXt hXc + filter_upwards [he,hvalid.2.2.2.def hε] with t he ht + change ‖X t‖≤ε*‖(H (X t:ℂ)).re‖ + rwa [←he] + obtain ⟨y,I,hi,hfamily⟩ := hD.charts H hH hHr hHt hfast + have hir : ∀ᶠ t : ℝ in atTop,(id (t:ℂ)).im=0 ∧ 0<(id (t:ℂ)).re := by + filter_upwards [eventually_gt_atTop (0:ℝ)] with t ht + exact ⟨rfl,ht⟩ + have hys := (hfamily id hD.coordinate hir tendsto_id hfast.isBigO).2 hfast + have hL := transported_lowerSectorData hD.lower (hi.analytic_left.mono fun _ h => h.1) hi.maps_sector hys + have hLd := fun b hb => transported_deriv_mem hD.lower hD.differential hH hi.analytic_left hi.maps_sector (b := b) hb + have hLc := fun b hb => transported_conj_mem hD.reflection hi (b := b) hb + have hLcharts := lowerSectorData_hasSectorCharts hL hLd hLc + (transported_lowerSectorCharts hD.lower hD.charts hH hi hHr hHt hfast hys) + have hyY : ∀ᶠ t : ℝ in atTop,y (Y t:ℂ)=(X t:ℂ) := by + filter_upwards [he,hXt.eventually hi.right] with t he hy + rwa [he] + refine ⟨TransportedField K y,⟨hL,hLd,hLc,hLcharts,?_,?_,?_⟩⟩ + · apply ExpansionOver.of_lower hL + exact ⟨H,hH,hi.analytic_left.mono fun _ h => h.2.symm⟩ + · intro f hf + obtain ⟨F,hF,hef⟩ := hD.expansion_iff.mp hf + refine ⟨fun z => F (y z),⟨F,hF,EventuallyEq.rfl⟩,?_⟩ + filter_upwards [hef,hyY] with t hef hy + simpa only [hy] using hef + · intro b + constructor + · rintro ⟨F,hF,heb⟩ + refine ⟨hD.expansion_iff.mpr ⟨F,hF,?_⟩,hL.analytic ⟨F,hF,heb⟩⟩ + filter_upwards [hYt.eventually (tendsto_real_sectorInfinity.eventually heb),hyY] with t he hy + simpa only [hy] using he + · rintro ⟨hb,hba⟩ + obtain ⟨F,hF,heb⟩ := hD.expansion_iff.mp hb + refine ⟨F,hF,?_⟩ + have hfa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun w => F (y w)) z := by + filter_upwards [hi.analytic_left,hi.maps_sector.eventually hF.choose_spec.choose_spec.1.eventually_analytic] with z hy hf + exact hf.comp hy.1 + apply sector_analytic_eq_of_ray hba hfa + apply eventually_of_comp_clock hYt hYc + filter_upwards [heb,hyY] with t he hy + simpa only [hy] using he + + +theorem ValidClocks.sectorData {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} + (hvalid : ValidClocks (X::xs)) : ∃ K : Set (ℂ → ℂ),ClockSectorData xs X K := by + induction xs generalizing X with + | nil => exact ⟨PuiseuxSector,puiseux_clockSectorData hvalid.2.1 hvalid.2.2.1⟩ + | cons Y ys ih => + obtain ⟨K,hK⟩ := ih hvalid.1 + exact hK.step hvalid + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma ClockGerm.of_lower {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} + (hvalid : ValidClocks (X::xs)) {f : ℝ → ℂ} (hf : ClockGerm xs f) : + ClockGerm (X::xs) f := by + obtain ⟨K,hK⟩ := hvalid.sectorData + obtain ⟨b,hb,he⟩ := hK.represents f hf + exact hK.expansion_iff.mpr ⟨b,ExpansionOver.of_lower hK.lower hb,he⟩ + + + +theorem ClockGerm.inv {xs : List (ℝ → ℝ)} (hvalid : ValidClocks xs) + {f : ℝ → ℂ} (hf : ClockGerm xs f) : ClockGerm xs (fun t => (f t)⁻¹) := by + cases xs with + | nil => exact Puiseux.inv hf + | cons X xs => + obtain ⟨K,hK⟩ := hvalid.sectorData + obtain ⟨F,hF,he⟩ := hK.expansion_iff.mp hf + exact hK.expansion_iff.mpr ⟨fun z => (F z)⁻¹,hF.inv hK.lower,he.inv⟩ + + + +theorem ClockGerm.deriv {xs : List (ℝ → ℝ)} (hvalid : ValidClocks xs) + {f : ℝ → ℂ} (hf : ClockGerm xs f) : ClockGerm xs (_root_.deriv f) := by + induction xs generalizing f with + | nil => exact Puiseux.deriv hf + | cons X xs ih => + obtain ⟨K,hK⟩ := hvalid.sectorData + obtain ⟨F,hF,he⟩ := hK.expansion_iff.mp hf + have hFa := hF.choose_spec.choose_spec.1.eventually_analytic + have hFx : ClockGerm (X::xs) (fun t => _root_.deriv F (X t:ℂ)) := + hK.expansion_iff.mpr ⟨_root_.deriv F,hF.deriv_mem hK.lower hK.differential,EventuallyEq.rfl⟩ + have hXa := hvalid.2.1.real_eventually_analytic hvalid.1 + have hX' : ClockGerm xs (fun t => ((_root_.deriv X t:ℝ):ℂ)) := by + apply (ih hvalid.1 hvalid.2.1).congr + filter_upwards [hXa] with t ht + exact ht.differentiableAt.hasDerivAt.ofReal_comp.deriv + apply (hFx.mul (hX'.of_lower hvalid)).congr + obtain ⟨T,hT⟩ := eventually_atTop.mp he + filter_upwards [hXa,hvalid.2.2.1.eventually (tendsto_real_sectorInfinity.eventually hFa), + eventually_gt_atTop T] with t hXa hFa ht + have hd := hFa.differentiableAt.hasDerivAt.comp_ofReal.scomp t hXa.differentiableAt.hasDerivAt + have hc : (fun s => F (X s:ℂ)) =ᶠ[𝓝 t] f := + (eventually_gt_nhds ht).mono (fun s hs => (hT s hs.le).symm) + simpa only [Complex.real_smul,mul_comm] using (hd.congr_of_eventuallyEq hc.symm).deriv.symm + +lemma ClockGerm.real_deriv {xs : List (ℝ → ℝ)} (hvalid : ValidClocks xs) + {f : ℝ → ℝ} (hf : ClockGerm xs (fun t => (f t:ℂ))) : + ClockGerm xs (fun t => ((_root_.deriv f t:ℝ):ℂ)) := by + apply (hf.deriv hvalid).congr + filter_upwards [hf.real_eventually_analytic hvalid] with t ht + exact ht.differentiableAt.hasDerivAt.ofReal_comp.deriv + + +theorem ClockGerm.real_derivative_sign {xs : List (ℝ → ℝ)} (hvalid : ValidClocks xs) + {f : ℝ → ℝ} (hf : ClockGerm xs (fun t => (f t:ℂ))) : + (_root_.deriv f =ᶠ[atTop] 0) ∨ (∀ᶠ t : ℝ in atTop,0<_root_.deriv f t) ∨ + (∀ᶠ t : ℝ in atTop,_root_.deriv f t<0) := by + by_cases hz : _root_.deriv f =ᶠ[atTop] 0 + · exact Or.inl hz + · exact Or.inr ((hf.real_deriv hvalid).eventually_sign hvalid hz) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma LogMonomial.rat_mul {xs : List (ℝ → ℝ)} {M : ℝ → ℝ} + (hM : LogMonomial xs M) (q : ℚ) : + LogMonomial xs (fun t => (q:ℝ)*M t) := by + induction hM with + | base p => + convert LogMonomial.base (q*p) using 1 + funext t + push_cast + ring + | @step xs M X hM β ih => + convert LogMonomial.step (X := X) ih ((q:ℝ)*β) using 1 + funext t + ring + +lemma puiseux_exp_rat_log (q : ℚ) : + Puiseux (fun t => (Real.exp ((q:ℝ)*Real.log t):ℂ)) := by + refine ⟨q.den,q.den_pos,-q.num,fun _ => 1,analyticAt_const,?_⟩ + filter_upwards [eventually_gt_atTop (0:ℝ)] with t ht + simp only [Complex.real_smul,mul_one,rootCoord_zpow ht] + have hq : -((-q.num:ℤ):ℝ)/(q.den:ℝ)=(q:ℝ) := by + push_cast + simpa only [neg_neg] using (Rat.cast_def (K := ℝ) q).symm + rw [hq,Real.rpow_def_of_pos ht,mul_comm] + +lemma ClockGerm.exp_clock {X : ℝ → ℝ} (xs : List (ℝ → ℝ)) (β : ℝ) : + ClockGerm (X::xs) (fun t => (Real.exp (β*X t):ℂ)) := by + have hs : SectorSlow (fun _ : ℂ => (1:ℂ)) := fun _ hε => (ExpBound.const 1).mono hε.le + have ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun _ : ℂ => (1:ℂ)) z := + Eventually.of_forall (fun _ => analyticAt_const) + refine ⟨fun z => Complex.exp ((β:ℂ)*z)*1,{β},fun _ _ => 1, + SectorExpansion.single β ha hs,?_,?_⟩ + · exact fun _ _ => ⟨ClockGerm.const xs 1,SectorEventually.truth.mono (fun _ _ => analyticAt_const)⟩ + · exact Eventually.of_forall (fun t => by simp [←Complex.ofReal_mul,Complex.ofReal_exp]) + + + +lemma LogMonomial.exp_mem {xs : List (ℝ → ℝ)} {M : ℝ → ℝ} + (hM : LogMonomial xs M) (hxs : ValidClocks xs) : + ClockGerm xs (fun t => (Real.exp (M t):ℂ)) := by + induction hM with + | base p => exact puiseux_exp_rat_log p + | @step xs M X hM β ih => + apply ((ClockGerm.exp_clock xs β).mul ((ih hxs.1).of_lower hxs)).congr + exact Eventually.of_forall (fun t => by + simp only [Real.exp_add,Complex.ofReal_mul]) + + + +theorem ClockGerm.divisible_size {xs : List (ℝ → ℝ)} (hxs : ValidClocks xs) + {f : ℝ → ℂ} (hf : ClockGerm xs f) (hne : ¬ f =ᶠ[atTop] 0) + (n : ℕ) (hn : 0 (ρ t:ℂ)) ∧ + (∀ t,0<ρ t) ∧ ∃ c : ℝ,0 (ρ t)^n / ‖f t‖) atTop (𝓝 c) := by + obtain ⟨M,hM,d,hd,ht⟩ := hf.leading hxs hne + let q : ℚ := (n:ℚ)⁻¹ + have hq : (q:ℝ)=(n:ℝ)⁻¹ := by simp [q] + refine ⟨fun t => Real.exp ((q:ℝ)*M t),(hM.rat_mul q).exp_mem hxs, + fun t => Real.exp_pos _,‖d‖⁻¹,inv_pos.mpr (norm_pos_iff.mpr hd),?_⟩ + apply (ht.norm.inv₀ (norm_ne_zero_iff.mpr hd)).congr' + filter_upwards [] with t + rw [norm_mul,Complex.norm_of_nonneg (Real.exp_pos _).le] + rw [←Real.exp_nat_mul] + have hmul : (n:ℝ)*((q:ℝ)*M t)=M t := by + rw [hq,←mul_assoc,mul_inv_cancel₀ (Nat.cast_ne_zero.mpr hn.ne')] + simp + rw [hmul,Real.exp_neg,mul_inv_rev,inv_inv,div_eq_mul_inv,mul_comm] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + + + +theorem ClockGerm.eventually_monotone {xs : List (ℝ → ℝ)} + (hvalid : ValidClocks xs) {f : ℝ → ℝ} + (hf : ClockGerm xs (fun t => (f t:ℂ))) : + ∃ T : ℝ, (∃ c : ℝ, ∀ t ∈ Ioi T,f t=c) ∨ + StrictMonoOn f (Ioi T) ∨ StrictAntiOn f (Ioi T) := by + have ha := hf.real_eventually_analytic hvalid + rcases hf.real_derivative_sign hvalid with hz | hp | hn + · obtain ⟨T,hT⟩ := eventually_atTop.mp (ha.and hz) + have hd : DifferentiableOn ℝ f (interior (Ioi T)) := by + intro t ht + exact (hT t (interior_subset ht).le).1.differentiableAt.differentiableWithinAt + have hc : ContinuousOn f (Ioi T) := fun t ht => (hT t ht.le).1.continuousAt.continuousWithinAt + have hm := monotoneOn_of_deriv_nonneg (convex_Ioi T) hc hd + (fun t ht => (hT t (interior_subset ht).le).2.ge) + have hn := antitoneOn_of_deriv_nonpos (convex_Ioi T) hc hd + (fun t ht => (hT t (interior_subset ht).le).2.le) + refine ⟨T,Or.inl ⟨f (T+1),fun t ht => ?_⟩⟩ + have ht1 : T+1 ∈ Ioi T := by simp + rcases le_total t (T+1) with h | h + · exact le_antisymm (hm ht ht1 h) (hn ht ht1 h) + · exact le_antisymm (hn ht1 ht h) (hm ht1 ht h) + · obtain ⟨T,hT⟩ := eventually_atTop.mp (ha.and hp) + refine ⟨T,Or.inr (Or.inl ?_)⟩ + exact strictMonoOn_of_deriv_pos (convex_Ioi T) + (fun t ht => (hT t ht.le).1.continuousAt.continuousWithinAt) + (fun t ht => (hT t (interior_subset ht).le).2) + · obtain ⟨T,hT⟩ := eventually_atTop.mp (ha.and hn) + refine ⟨T,Or.inr (Or.inr ?_)⟩ + exact strictAntiOn_of_deriv_neg (convex_Ioi T) + (fun t ht => (hT t ht.le).1.continuousAt.continuousWithinAt) + (fun t ht => (hT t (interior_subset ht).le).2) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/SectorLimits.lean b/lean/OAI/Analysis/PathSelection/SectorLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..aaf191cb2517412f2fd3cb1638f2df7085e5f0ce --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/SectorLimits.lean @@ -0,0 +1,334 @@ +import Mathlib +import OAI.Analysis.PathSelection.SectorBounds + +namespace OAI + +/-! Sector filters, subexponential estimates and grouped leading coefficients. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees + +def sectorInfinity : Filter ℂ where + sets := {s | SectorEventually (fun z => z ∈ s)} + univ_sets := SectorEventually.truth + sets_of_superset := fun h hs => h.mono (fun _ hz => hs hz) + inter_sets := fun h k => h.and k + +lemma eventually_sectorInfinity {P : ℂ → Prop} : + (∀ᶠ z in sectorInfinity, P z) ↔ SectorEventually P := Iff.rfl + +instance sectorInfinity_neBot : NeBot sectorInfinity := by + refine ⟨?_⟩ + intro h + have hem : (∅ : Set ℂ) ∈ sectorInfinity := by rw [h]; simp + obtain ⟨ω,R,hω,hbad⟩ := hem + obtain ⟨t,ht⟩ := (hω.real_discs R).exists + exact hbad (t:ℂ) (ht.2 (Metric.mem_closedBall_self (by linarith [ht.1]))) + +lemma tendsto_norm_sectorInfinity : Tendsto (norm : ℂ → ℝ) sectorInfinity atTop := by + apply Filter.tendsto_atTop.mpr + intro R + apply SectorEventually.of_radial + filter_upwards [eventually_ge_atTop R] with r hr + intro z hz + simpa only [hz] using hr + +lemma tendsto_real_sectorInfinity : Tendsto (fun t : ℝ => (t:ℂ)) atTop sectorInfinity := by + apply Filter.tendsto_def.mpr + intro s hs + obtain ⟨ω,R,hω,h⟩ := hs + filter_upwards [hω.real_discs R] with t ht + exact h (t:ℂ) (ht.2 (Metric.mem_closedBall_self (by linarith [ht.1]))) + +lemma tendsto_re_sectorInfinity : Tendsto Complex.re sectorInfinity atTop := by + apply Filter.tendsto_atTop.mpr + intro A + have hg := (isLittleO_log_rpow_rpow_atTop (s := (1:ℝ)) 2 zero_lt_one).bound + (show (0:ℝ) < (2*(max A 0+1))⁻¹ by positivity) + have hdata : ∀ᶠ r : ℝ in atTop, + 0 ≤ baseLoss r ∧ baseLoss r ≤ Real.pi/2 ∧ 2*A ≤ r*baseLoss r := by + filter_upwards [hg,admissible_baseLoss.1, + admissible_baseLoss.tendsto_zero.eventually (gt_mem_nhds (show (0:ℝ) by + have ht := hT ‖z‖ hz.1.le + have hr := half_loss_norm_le_re ht.1 ht.2.1 hz.2 + change A ≤ z.re + calc + A = (2*A)/2 := by ring + _ ≤ (‖z‖*baseLoss ‖z‖)/2 := div_le_div_of_nonneg_right ht.2.2 (by norm_num) + _ = baseLoss ‖z‖/2*‖z‖ := by ring + _ ≤ z.re := hr⟩ + +namespace Clock + +def ExpBound (a : ℝ) (f : ℂ → ℂ) : Prop := + f =O[sectorInfinity] (fun z => Real.exp (a*z.re)) + +def ExpSmall (B : ℝ) (f : ℂ → ℂ) : Prop := ∃ a < B, ExpBound a f + +def SectorSlow (f : ℂ → ℂ) : Prop := ∀ ε : ℝ, 0 < ε → ExpBound ε f + +lemma ExpBound.mono {a b : ℝ} {f : ℂ → ℂ} (h : ExpBound a f) (hab : a ≤ b) : + ExpBound b f := by + apply h.trans + apply Asymptotics.IsBigO.of_bound 1 + filter_upwards [show ∀ᶠ z in sectorInfinity, 0 < z.re from SectorEventually.realpart_pos] with z hz + simpa only [Real.norm_eq_abs,abs_of_pos (Real.exp_pos _),one_mul] using + Real.exp_le_exp.mpr (mul_le_mul_of_nonneg_right hab hz.le) + +lemma ExpBound.mul {a b : ℝ} {f g : ℂ → ℂ} (hf : ExpBound a f) (hg : ExpBound b g) : + ExpBound (a+b) (fun z => f z*g z) := by + simpa only [ExpBound,←Real.exp_add,←add_mul] using Asymptotics.IsBigO.mul hf hg + +lemma ExpBound.add {a : ℝ} {f g : ℂ → ℂ} (hf : ExpBound a f) (hg : ExpBound a g) : + ExpBound a (fun z => f z+g z) := Asymptotics.IsBigO.add hf hg + +lemma ExpSmall.mono {a b : ℝ} {f : ℂ → ℂ} (hf : ExpSmall a f) (hab : a ≤ b) : + ExpSmall b f := by + obtain ⟨c,hc,h⟩ := hf + exact ⟨c,hc.trans_le hab,h⟩ + +lemma ExpSmall.add {a : ℝ} {f g : ℂ → ℂ} (hf : ExpSmall a f) (hg : ExpSmall a g) : + ExpSmall a (fun z => f z+g z) := by + obtain ⟨b,hb,hf⟩ := hf + obtain ⟨c,hc,hg⟩ := hg + exact ⟨max b c,max_lt hb hc,(hf.mono (le_max_left _ _)).add (hg.mono (le_max_right _ _))⟩ + +lemma ExpSmall.mul {a b : ℝ} {f g : ℂ → ℂ} (hf : ExpSmall a f) (hg : ExpBound b g) : + ExpSmall (a+b) (fun z => f z*g z) := by + obtain ⟨c,hc,hf⟩ := hf + exact ⟨c+b,by linarith,hf.mul hg⟩ + +end Clock +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees + + +def Subexponential {α : Type*} (l : Filter α) (X : α → ℝ) (a : α → ℂ) : Prop := + ∀ ε : ℝ, 0 < ε → ∀ᶠ x in l, ‖a x‖ ≤ Real.exp (ε*X x) + +lemma log_div_tendsto_zero {α : Type*} {l : Filter α} {X : α → ℝ} + (hX : Tendsto X l atTop) : + Tendsto (fun x => Real.log (X x)/X x) l (𝓝 0) := by + simpa only [Function.comp_apply, id_eq] using! Real.isLittleO_log_id_atTop.tendsto_div_nhds_zero.comp hX + +lemma exponent_ratio_zero {α : Type*} {l : Filter α} {X M : α → ℝ} + (hX : Tendsto X l atTop) (hM : Tendsto (fun x => M x/X x) l (𝓝 0)) + (C : ℝ) : + Tendsto (fun x => (C*(1+M x)+C*Real.log (X x))/X x) l (𝓝 0) := by + have hi : Tendsto (fun x => (X x)⁻¹) l (𝓝 0) := tendsto_inv_atTop_zero.comp hX + have ht := ((hi.add hM).const_mul C).add + ((log_div_tendsto_zero hX).const_mul C) + simp only [add_zero,mul_zero] at ht + convert ht using 1 + funext x + ring + + + +theorem subexponential_of_lower_size_bound {α : Type*} {l : Filter α} + {X M : α → ℝ} {a : α → ℂ} (hX : Tendsto X l atTop) + (hM : Tendsto (fun x => M x/X x) l (𝓝 0)) + (C : ℝ) (ha : ∀ᶠ x in l, + ‖a x‖ ≤ Real.exp (C*(1+M x))*(X x)^C) : Subexponential l X a := by + intro ε hε + have he := (exponent_ratio_zero hX hM C).eventually_lt_const hε + filter_upwards [ha,he,hX.eventually_gt_atTop 0] with x hx hex hp + apply hx.trans + rw [Real.rpow_def_of_pos hp,←Real.exp_add] + apply Real.exp_le_exp.mpr + have he' := (div_lt_iff₀ hp).mp hex + nlinarith + + + +theorem negative_exponential_times_subexponential {α : Type*} {l : Filter α} + {X : α → ℝ} {a : α → ℂ} (hX : Tendsto X l atTop) + (ha : Subexponential l X a) {ε : ℝ} (hε : 0 < ε) : + Tendsto (fun x => Real.exp (-ε*X x)*‖a x‖) l (𝓝 0) := by + have he : Tendsto (fun x => Real.exp (-(ε/2)*X x)) l (𝓝 0) := by + apply Real.tendsto_exp_atBot.comp + exact (tendsto_const_mul_atBot_of_neg (show -(ε/2) < 0 by linarith)).mpr hX + apply squeeze_zero' (Eventually.of_forall (fun x => by positivity)) _ he + filter_upwards [ha (ε/2) (by linarith)] with x hx + calc + Real.exp (-ε*X x)*‖a x‖ ≤ Real.exp (-ε*X x)*Real.exp ((ε/2)*X x) := + mul_le_mul_of_nonneg_left hx (Real.exp_pos _).le + _ = Real.exp (-(ε/2)*X x) := by rw [←Real.exp_add]; congr 1; ring + +lemma Subexponential.const {α : Type*} {l : Filter α} {X : α → ℝ} + (hX : Tendsto X l atTop) (c : ℂ) : Subexponential l X (fun _ => c) := by + intro ε hε + have he : Tendsto (fun x => Real.exp (ε*X x)) l atTop := + Real.tendsto_exp_atTop.comp ((tendsto_const_mul_atTop_of_pos hε).mpr hX) + exact he.eventually_ge_atTop ‖c‖ + +lemma Subexponential.mul {α : Type*} {l : Filter α} {X : α → ℝ} {a b : α → ℂ} + (ha : Subexponential l X a) (hb : Subexponential l X b) : + Subexponential l X (fun x => a x*b x) := by + intro ε hε + filter_upwards [ha (ε/2) (by linarith),hb (ε/2) (by linarith)] with x hx hy + rw [norm_mul] + calc + ‖a x‖*‖b x‖ ≤ Real.exp ((ε/2)*X x)*Real.exp ((ε/2)*X x) := + mul_le_mul hx hy (norm_nonneg _) (Real.exp_pos _).le + _ = Real.exp (ε*X x) := by rw [←Real.exp_add]; congr 1; ring + +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex +open scoped BigOperators +namespace DegeneratingTrees + + + +theorem exists_first_coefficient {α E : Type*} [Zero E] {l : Filter α} + (D : Set ℝ) (hD : ∀ B : ℝ, (D ∩ Iic B).Finite) + (b : ℝ → α → E) (hne : ∃ d ∈ D, ¬ b d =ᶠ[l] fun _ => 0) : + ∃ d ∈ D, (¬ b d =ᶠ[l] fun _ => 0) ∧ + ∀ e ∈ D, e < d → b e =ᶠ[l] fun _ => 0 := by + classical + obtain ⟨a,ha,hba⟩ := hne + let S : Finset ℝ := ((hD a).toFinset).filter fun d => ¬ b d =ᶠ[l] fun _ => 0 + have haS : a ∈ S := by simp [S,ha,hba] + let d := S.min' ⟨a,haS⟩ + have hd : d ∈ S := Finset.min'_mem _ _ + have hdD : d ∈ D := ((hD a).mem_toFinset.mp (Finset.mem_filter.mp hd).1).1 + have hda : d ≤ a := Finset.min'_le _ _ haS + refine ⟨d,hdD,(Finset.mem_filter.mp hd).2,?_⟩ + intro e he hed + by_contra hbe + have heS : e ∈ S := by + simp only [S,Finset.mem_filter,Set.Finite.mem_toFinset,Set.mem_inter_iff,Set.mem_Iic] + exact ⟨⟨he,hed.le.trans hda⟩,hbe⟩ + exact (not_le_of_gt hed) (Finset.min'_le _ _ heS) + +variable {α E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] +variable {l : Filter α} {X : α → ℝ} + + + +lemma normalized_grouped_error {F b : α → E} {k : α → ℂ} {d ε C : ℝ} + (hX : Tendsto X l atTop) (hk : Subexponential l X (fun x => (k x)⁻¹)) + (hε : 0 < ε) (hC : 0 ≤ C) + (herr : ∀ᶠ x in l, ‖F x-(Real.exp (-d*X x):ℂ) • b x‖ ≤ + C*Real.exp (-(d+ε)*X x)) : + Tendsto (fun x => ((Real.exp (d*X x):ℂ)*(k x)⁻¹) • + (F x-(Real.exp (-d*X x):ℂ) • b x)) l (𝓝 0) := by + apply tendsto_zero_iff_norm_tendsto_zero.mpr + have ht := (negative_exponential_times_subexponential hX hk hε).const_mul C + simp only [mul_zero] at ht + apply squeeze_zero' (Eventually.of_forall (fun x => norm_nonneg _)) _ ht + filter_upwards [herr] with x hx + rw [norm_smul,norm_mul,Complex.norm_of_nonneg (Real.exp_pos _).le] + calc + Real.exp (d*X x)*‖(k x)⁻¹‖*‖F x-(Real.exp (-d*X x):ℂ) • b x‖ ≤ + Real.exp (d*X x)*‖(k x)⁻¹‖*(C*Real.exp (-(d+ε)*X x)) := + mul_le_mul_of_nonneg le_rfl hx (by positivity) (mul_nonneg hC (Real.exp_pos _).le) + _ = C*(Real.exp (-ε*X x)*‖(k x)⁻¹‖) := by + have he : Real.exp (d*X x)*Real.exp (-(d+ε)*X x) = Real.exp (-ε*X x) := by + rw [←Real.exp_add]; congr 1; ring + calc + _ = C*(Real.exp (d*X x)*Real.exp (-(d+ε)*X x))*‖(k x)⁻¹‖ := by ring + _ = _ := by rw [he]; ring + + + +theorem grouped_leading_normalization {F b : α → E} {k : α → ℂ} {d ε C : ℝ} + (hX : Tendsto X l atTop) (hk : Subexponential l X (fun x => (k x)⁻¹)) + (hε : 0 < ε) (hC : 0 ≤ C) + (herr : ∀ᶠ x in l, ‖F x-(Real.exp (-d*X x):ℂ) • b x‖ ≤ + C*Real.exp (-(d+ε)*X x)) + {g : E} (hb : Tendsto (fun x => (k x)⁻¹ • b x) l (𝓝 g)) : + Tendsto (fun x => ((Real.exp (d*X x):ℂ)*(k x)⁻¹) • F x) l (𝓝 g) := by + have he := normalized_grouped_error hX hk hε hC herr + have heq : (fun x => ((Real.exp (d*X x):ℂ)*(k x)⁻¹) • + (F x-(Real.exp (-d*X x):ℂ) • b x) + (k x)⁻¹ • b x) = + (fun x => ((Real.exp (d*X x):ℂ)*(k x)⁻¹) • F x) := by + funext x + rw [smul_sub,smul_smul] + have hexp : (Real.exp (d*X x):ℂ)*(k x)⁻¹*(Real.exp (-d*X x):ℂ) = (k x)⁻¹ := by + rw [mul_right_comm,←Complex.ofReal_mul,←Real.exp_add] + simp + rw [hexp] + abel + simpa only [zero_add,heq] using he.add hb + + + +theorem grouped_normalization_or_zero_coefficients + (D : Set ℝ) (hD : ∀ B : ℝ, (D ∩ Iic B).Finite) + (b : ℝ → α → E) (F : α → E) (hX : Tendsto X l atTop) + (hnorm : ∀ d ∈ D, (¬ b d =ᶠ[l] fun _ => 0) → + ∃ k : α → ℂ, Subexponential l X (fun x => (k x)⁻¹) ∧ + ∃ g : E, g ≠ 0 ∧ Tendsto (fun x => (k x)⁻¹ • b d x) l (𝓝 g)) + (hrem : ∀ B ∈ D, ∃ ε C : ℝ, 0 < ε ∧ 0 ≤ C ∧ + ∀ᶠ x in l, ‖F x - ∑ d ∈ (hD B).toFinset, + (Real.exp (-d*X x):ℂ) • b d x‖ ≤ C*Real.exp (-(B+ε)*X x)) : + (∀ d ∈ D, b d =ᶠ[l] fun _ => 0) ∨ + (∃ d ∈ D, ∃ k : α → ℂ, ∃ g : E, g ≠ 0 ∧ + Tendsto (fun x => ((Real.exp (d*X x):ℂ)*(k x)⁻¹) • F x) l (𝓝 g)) := by + classical + by_cases hz : ∀ d ∈ D, b d =ᶠ[l] fun _ => 0 + · exact Or.inl hz + right + have hex : ∃ d ∈ D, ¬ b d =ᶠ[l] fun _ => 0 := by simpa using hz + obtain ⟨d,hd,hbd,hfirst⟩ := exists_first_coefficient D hD b hex + obtain ⟨k,hk,g,hg,hbg⟩ := hnorm d hd hbd + obtain ⟨ε,C,hε,hC,herr⟩ := hrem d hd + have hearly : ∀ᶠ x in l, ∀ e ∈ (hD d).toFinset, e ≠ d → b e x = 0 := by + rw [Filter.eventually_all_finset] + intro e he + by_cases heq : e = d + · exact Eventually.of_forall (fun _ hne => (hne heq).elim) + · have hed := (hD d).mem_toFinset.mp he + exact (hfirst e hed.1 (lt_of_le_of_ne hed.2 heq)).mono fun x hx _ => hx + refine ⟨d,hd,k,g,hg,grouped_leading_normalization hX hk hε hC ?_ hbg⟩ + filter_upwards [herr,hearly] with x hx he + have hsum : (∑ e ∈ (hD d).toFinset, (Real.exp (-e*X x):ℂ) • b e x) = + (Real.exp (-d*X x):ℂ) • b d x := by + apply Finset.sum_eq_single d + · intro e heS hed + rw [he e heS hed,smul_zero] + · intro hdS + exact (hdS ((hD d).mem_toFinset.mpr ⟨hd,by simpa only [Set.mem_Iic] using le_refl d⟩)).elim + simpa only [hsum] using hx + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/SectorPolynomials.lean b/lean/OAI/Analysis/PathSelection/SectorPolynomials.lean new file mode 100644 index 0000000000000000000000000000000000000000..6b810621642716841e5847b7b2a2085c9364061f --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/SectorPolynomials.lean @@ -0,0 +1,156 @@ +import Mathlib +import OAI.Analysis.PathSelection.CoefficientFields +import OAI.Analysis.PathSelection.PuiseuxInverses + +namespace OAI + +/-! Polynomial control and sector data for Puiseux expansions. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock + +lemma sector_sqrt_le_re : ∀ᶠ z in sectorInfinity, ‖z‖^(1/2:ℝ) ≤ z.re := by + have hdata : ∀ᶠ r : ℝ in atTop, 0 f (t:ℂ)) =ᶠ[atTop] fun t => g (t:ℂ)) : + f =ᶠ[sectorInfinity] g := by + obtain ⟨ω,R,hω,ha⟩ := hf.and hg + have hz := sector_zero_of_ray_zero hω (fun z hz => (ha z hz).1.sub (ha z hz).2) + (he.mono (fun _ h => sub_eq_zero.mpr h)) + exact hz.mono (fun _ h => sub_eq_zero.mp h) + + +def PuiseuxSector : Set (ℂ → ℂ) := {f | (∀ᶠ z in sectorInfinity,AnalyticAt ℂ f z) ∧ + Puiseux (fun t : ℝ => f (t:ℂ))} + +lemma PuiseuxSector.slow_and_dichotomy {f : ℂ → ℂ} (hf : f∈PuiseuxSector) : + SectorSlow f ∧ ((∀ᶠ z in sectorInfinity,f z=0) ∨ (∀ᶠ z in sectorInfinity,f z≠0)) := by + by_cases hz : (fun t : ℝ => f (t:ℂ)) =ᶠ[atTop] fun _ => 0 + · have he := sector_analytic_eq_of_ray hf.1 (Eventually.of_forall (fun _ => analyticAt_const)) hz + exact ⟨fun ε _ => (ExpBound.zero ε).congr he.symm,Or.inl he⟩ + · obtain ⟨q,C,G,R,hC,hGa,he,hlim⟩ := hf.2.sector_leading hz + have hGa' := sector_halfplane_analytic hGa + have hfg := sector_analytic_eq_of_ray hf.1 hGa' he + have hb := radial_norm_equivalent hC hlim + have hs := polynomial_sector_slow (show 0≤2*‖C‖ by positivity) (hb.mono (fun _ h => h.2)) + refine ⟨fun ε hε => (hs ε hε).congr hfg.symm,Or.inr ?_⟩ + filter_upwards [hfg,sector_radial_eventually hb, + tendsto_norm_sectorInfinity.eventually (eventually_gt_atTop (0:ℝ))] with z hz hb hn + rw [hz] + apply norm_pos_iff.mp + exact lt_of_lt_of_le (mul_pos (by exact div_pos (norm_pos_iff.mpr hC) (by norm_num)) + (Real.rpow_pos_of_pos hn _)) hb.1 + +lemma PuiseuxSector.inv_analytic {f : ℂ → ℂ} (hf : f∈PuiseuxSector) : + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => (f z)⁻¹) z := by + rcases (PuiseuxSector.slow_and_dichotomy hf).2 with hz | hn + · apply sector_eventually_analytic_congr (f := fun _ => 0) + (Eventually.of_forall (fun _ => analyticAt_const)) + exact hz.mono (fun _ hz => by simp [hz]) + · filter_upwards [hf.1,hn] with z ha hn + exact ha.inv hn + + +theorem puiseux_lowerSectorData : LowerSectorData PuiseuxSector where + const_mem c := ⟨Eventually.of_forall (fun _ => analyticAt_const),puiseux_const c⟩ + add_mem hf hg := ⟨by filter_upwards [hf.1,hg.1] with z hf hg; exact hf.add hg,hf.2.add hg.2⟩ + neg_mem hf := ⟨hf.1.mono (fun _ hf => hf.neg),hf.2.neg⟩ + mul_mem hf hg := ⟨by filter_upwards [hf.1,hg.1] with z hf hg; exact hf.mul hg,hf.2.mul hg.2⟩ + inv_mem hf := ⟨(PuiseuxSector.inv_analytic hf),hf.2.inv⟩ + analytic hf := hf.1 + slow hf := (PuiseuxSector.slow_and_dichotomy hf).1 + zero_or_ne hf := (PuiseuxSector.slow_and_dichotomy hf).2 + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/SectorUniqueness.lean b/lean/OAI/Analysis/PathSelection/SectorUniqueness.lean new file mode 100644 index 0000000000000000000000000000000000000000..7f506d81188f0956a324963197df84916ba34257 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/SectorUniqueness.lean @@ -0,0 +1,498 @@ +import Mathlib +import OAI.Analysis.PathSelection.AdmissibleFunctions + +namespace OAI + +/-! Uniqueness of holomorphic asymptotic expansions on sectors. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Complex +open scoped Topology + +namespace DegeneratingTrees + + +def quadraticRegion (A c : ℝ) : Set ℂ := + {z | A < z.re ∧ |z.im| < c * z.re ^ 2} + + +def lossSector (ω : ℝ → ℝ) (R : ℝ) : Set ℂ := + {z | R < ‖z‖ ∧ |z.arg| < Real.pi / 2 - ω ‖z‖} + + + +def AdmissibleAngularLoss (ω : ℝ → ℝ) : Prop := + (∀ᶠ r : ℝ in atTop, 0 < ω r ∧ (Real.log r)⁻¹ ^ 2 ≤ ω r) ∧ + ∃ (n₀ : ℕ) (w : ℕ → ℝ), + (∀ n, 0 ≤ w n) ∧ Summable w ∧ + ∀ n r, (2 : ℝ) ^ (n + n₀) < r → r < (2 : ℝ) ^ (n + n₀ + 2) → ω r ≤ w n + + + +def CentralSuperexponential (f : ℂ → ℂ) : Prop := + ∀ B : ℝ, 0 < B → ∃ C R : ℝ, 0 ≤ C ∧ + ∀ z : ℂ, R < ‖z‖ → |z.arg| ≤ Real.pi / 4 → + ‖f z‖ ≤ C * Real.exp (-B * ‖z‖) + + + +def SectorUniquenessStatement : Prop := + ∀ (ω : ℝ → ℝ) (R : ℝ) (f : ℂ → ℂ), + AdmissibleAngularLoss ω → + AnalyticOnNhd ℂ f (lossSector ω R) → + (∃ M : ℝ, ∀ z ∈ lossSector ω R, ‖f z‖ ≤ M) → + CentralSuperexponential f → + ∃ R' : ℝ, R ≤ R' ∧ EqOn f 0 (lossSector ω R') + + + +def sectorKernel (t : ℝ) (z : ℂ) : ℂ := (t : ℂ) / ((t : ℂ) + z) + +lemma kernel_den_ne {t : ℝ} (ht : 0 < t) {z : ℂ} (hz : 0 ≤ z.re) : + (t : ℂ) + z ≠ 0 := by + intro h + have := congrArg Complex.re h + simp only [add_re, ofReal_re, zero_re] at this + linarith + +lemma sectorKernel_norm_le {t : ℝ} (ht : 0 < t) {z : ℂ} (hz : 0 ≤ z.re) : + ‖sectorKernel t z‖ ≤ 1 := by + have hden : t ≤ ‖(t : ℂ) + z‖ := by + calc t ≤ ((t : ℂ) + z).re := by simp only [add_re, ofReal_re]; linarith + _ ≤ ‖(t : ℂ) + z‖ := re_le_norm _ + rw [sectorKernel, norm_div, Complex.norm_of_nonneg ht.le] + exact (div_le_one (ht.trans_le hden)).2 hden + +lemma sectorKernel_re_nonneg {t : ℝ} (ht : 0 < t) {z : ℂ} (hz : 0 ≤ z.re) : + 0 ≤ (sectorKernel t z).re := by + simp only [sectorKernel, Complex.div_re, ofReal_re, add_re, ofReal_im, + zero_mul, zero_div, add_zero] + exact div_nonneg (mul_nonneg ht.le (by linarith)) (normSq_nonneg _) + +lemma mul_sectorKernel_re {t : ℝ} (z : ℂ) : + (z * sectorKernel t z).re = + t * (t * z.re + ‖z‖ ^ 2) / ‖(t : ℂ) + z‖ ^ 2 := by + rw [sectorKernel, ← mul_div_assoc, Complex.div_re] + simp only [mul_re, ofReal_re, ofReal_im, mul_zero, sub_zero, mul_im, + zero_add, add_re, add_im, Complex.sq_norm, normSq_apply] + ring + +lemma mul_sectorKernel_re_nonneg {t : ℝ} (ht : 0 < t) {z : ℂ} (hz : 0 ≤ z.re) : + 0 ≤ (z * sectorKernel t z).re := by + rw [mul_sectorKernel_re] + positivity + +lemma mul_sectorKernel_re_lower {t : ℝ} (ht : 0 < t) {z : ℂ} + (hz : 0 ≤ z.re) (hlo : t ≤ ‖z‖) (hhi : ‖z‖ ≤ 2 * t) : + ‖z‖ / 8 ≤ (z * sectorKernel t z).re := by + have hr : 0 < ‖z‖ := ht.trans_le hlo + have hd : 0 < ‖(t : ℂ) + z‖ ^ 2 := sq_pos_of_pos (norm_pos_iff.mpr (kernel_den_ne ht hz)) + have hden : ‖(t : ℂ) + z‖ ^ 2 ≤ 4 * ‖z‖ ^ 2 := by + have ha := norm_add_le (t : ℂ) z + rw [Complex.norm_of_nonneg ht.le] at ha + nlinarith [norm_nonneg ((t : ℂ) + z)] + have hlower : t / 4 ≤ (z * sectorKernel t z).re := by + rw [mul_sectorKernel_re, le_div_iff₀ hd] + have hmul := mul_le_mul_of_nonneg_left hden ht.le + have hx : 0 ≤ t * (t * z.re) := by positivity + nlinarith + linarith + +lemma arg_lt_of_re_lower {z : ℂ} {η : ℝ} (hη : 0 < η) + (hz : z ≠ 0) (h : 2 * η * ‖z‖ ≤ z.re) : + |z.arg| < Real.pi / 2 - η := by + have hr : 0 ≤ z.re := (by positivity : 0 ≤ 2 * η * ‖z‖).trans h + have ha := Complex.abs_arg_le_pi_div_two_iff.mpr hr + have hs := Real.sin_le (sub_nonneg.mpr ha) + rw [Real.sin_pi_div_two_sub, Real.cos_abs, Complex.cos_arg hz] at hs + have hn := norm_pos_iff.mpr hz + have hdiv : 2 * η ≤ z.re / ‖z‖ := (le_div_iff₀ hn).mpr h + linarith + + +def sectorCorrection (a t : ℕ → ℝ) (z : ℂ) : ℂ := + ∑' n, (a n : ℂ) * sectorKernel (t n) z + +def sectorMap (a t : ℕ → ℝ) (z : ℂ) : ℂ := z * (1 + sectorCorrection a t z) + +section Series +variable {a t : ℕ → ℝ} (ha : ∀ n, 0 ≤ a n) (hs : Summable a) + (ht : ∀ n, 0 < t n) +include ha hs ht + +omit hs in +lemma sectorTerm_norm_le {z : ℂ} (hz : 0 ≤ z.re) (n : ℕ) : + ‖(a n : ℂ) * sectorKernel (t n) z‖ ≤ a n := by + rw [norm_mul, Complex.norm_of_nonneg (ha n)] + simpa using mul_le_mul_of_nonneg_left (sectorKernel_norm_le (ht n) hz) (ha n) + +lemma sectorTerms_summable {z : ℂ} (hz : 0 ≤ z.re) : + Summable (fun n => (a n : ℂ) * sectorKernel (t n) z) := + hs.of_norm_bounded (sectorTerm_norm_le ha ht hz) + +lemma sectorCorrection_norm_le {z : ℂ} (hz : 0 ≤ z.re) : + ‖sectorCorrection a t z‖ ≤ ∑' n, a n := by + have h := sectorTerms_summable ha hs ht hz + exact (norm_tsum_le_tsum_norm h.norm).trans + (h.norm.tsum_le_tsum (sectorTerm_norm_le ha ht hz) hs) + +lemma sectorCorrection_re_nonneg {z : ℂ} (hz : 0 ≤ z.re) : + 0 ≤ (sectorCorrection a t z).re := by + rw [sectorCorrection, Complex.re_tsum (sectorTerms_summable ha hs ht hz)] + apply tsum_nonneg + intro n + simpa only [re_ofReal_mul] using + mul_nonneg (ha n) (sectorKernel_re_nonneg (ht n) hz) + +lemma sectorMap_norm_lower {z : ℂ} (hz : 0 ≤ z.re) : + ‖z‖ ≤ ‖sectorMap a t z‖ := by + have hA := sectorCorrection_re_nonneg ha hs ht hz + have h : 1 ≤ ‖1 + sectorCorrection a t z‖ := by + calc 1 ≤ (1 + sectorCorrection a t z).re := by simpa only [add_re, one_re] using le_add_of_nonneg_right hA + _ ≤ _ := re_le_norm _ + simpa only [sectorMap, norm_mul, mul_one] using mul_le_mul_of_nonneg_left h (norm_nonneg z) + +lemma sectorMap_norm_upper (hsmall : (∑' n, a n) ≤ 1) {z : ℂ} (hz : 0 ≤ z.re) : + ‖sectorMap a t z‖ ≤ 2 * ‖z‖ := by + have hA : ‖sectorCorrection a t z‖ ≤ 1 := (sectorCorrection_norm_le ha hs ht hz).trans hsmall + have h : ‖1 + sectorCorrection a t z‖ ≤ 2 := by + calc _ ≤ ‖(1 : ℂ)‖ + ‖sectorCorrection a t z‖ := norm_add_le _ _ + _ ≤ 2 := by simp only [norm_one]; linarith + simpa only [sectorMap, norm_mul, mul_comm ‖z‖ 2] using mul_le_mul_of_nonneg_left h (norm_nonneg z) + +lemma sectorMap_re_lower {z : ℂ} (hz : 0 ≤ z.re) (n : ℕ) + (hlo : t n ≤ ‖z‖) (hhi : ‖z‖ ≤ 2 * t n) : + a n * (‖z‖ / 8) ≤ (sectorMap a t z).re := by + have hsum := (sectorTerms_summable ha hs ht hz).mul_left z + have hne : ∀ m, 0 ≤ (z * ((a m : ℂ) * sectorKernel (t m) z)).re := by + intro m + rw [mul_comm z, mul_assoc, re_ofReal_mul, mul_comm (sectorKernel (t m) z)] + exact mul_nonneg (ha m) (mul_sectorKernel_re_nonneg (ht m) hz) + have hsingle := (Complex.hasSum_re hsum.hasSum).summable.le_tsum n (fun i _ => hne i) + rw [sectorMap, mul_add, mul_one, add_re] + have heq : (z * sectorCorrection a t z).re = + ∑' m, (z * ((a m : ℂ) * sectorKernel (t m) z)).re := by + rw [sectorCorrection, ← tsum_mul_left, Complex.re_tsum hsum] + rw [heq] + calc a n * (‖z‖ / 8) ≤ a n * (z * sectorKernel (t n) z).re := + mul_le_mul_of_nonneg_left (mul_sectorKernel_re_lower (ht n) hz hlo hhi) (ha n) + _ = (z * ((a n : ℂ) * sectorKernel (t n) z)).re := by + rw [← re_ofReal_mul] + congr 1 + ring + _ ≤ ∑' m, (z * ((a m : ℂ) * sectorKernel (t m) z)).re := hsingle + _ ≤ z.re + ∑' m, (z * ((a m : ℂ) * sectorKernel (t m) z)).re := le_add_of_nonneg_left hz + +lemma sectorCorrection_differentiableOn : + DifferentiableOn ℂ (sectorCorrection a t) {z : ℂ | 0 < z.re} := by + apply Complex.differentiableOn_tsum_of_summable_norm hs + · intro n + apply (differentiableOn_const _).mul + exact (differentiableOn_const _).div ((differentiableOn_const _).add differentiableOn_id) + (fun z hz => kernel_den_ne (ht n) hz.le) + · exact isOpen_lt continuous_const continuous_re + · intro n z hz + exact sectorTerm_norm_le ha ht hz.le n + +lemma sectorMap_differentiableOn : + DifferentiableOn ℂ (sectorMap a t) {z : ℂ | 0 < z.re} := + differentiableOn_id.mul ((differentiableOn_const _).add (sectorCorrection_differentiableOn ha hs ht)) + +end Series + +lemma dyadic_shell {T r : ℝ} (hT : 0 < T) (hr : T ≤ r) : + ∃ n : ℕ, T * 2 ^ n ≤ r ∧ r < 2 * (T * 2 ^ n) := by + obtain ⟨n, hlo, hhi⟩ := exists_nat_pow_near + ((le_div_iff₀ hT).mpr (by simpa using hr)) (show (1 : ℝ) < 2 by norm_num) + refine ⟨n, ?_, ?_⟩ + · have := (le_div_iff₀ hT).mp hlo + nlinarith + · have := (div_lt_iff₀ hT).mp hhi + rw [pow_succ] at this + nlinarith + + + +lemma angularLoss_kernel_data {ω : ℝ → ℝ} (hω : AdmissibleAngularLoss ω) : + ∃ (a t : ℕ → ℝ) (S : ℝ), 0 < S ∧ + (∀ n, 0 ≤ a n) ∧ Summable a ∧ (∀ n, 0 < t n) ∧ (∑' n, a n) ≤ 1 ∧ + (∀ r, S ≤ r → 0 < ω r ∧ ω r ≤ 1 / 64 ∧ + ∃ n, t n ≤ r ∧ r < 2 * t n ∧ + ∀ s, r ≤ s → s ≤ 2 * r → ω s ≤ a n / 64) := by + rcases hω with ⟨hpos, n₀, w, hw, hws, hbound⟩ + obtain ⟨Rp, hRp⟩ := eventually_atTop.mp hpos + let b : ℕ → ℝ := fun n => w n + w (n + 1) + have hb : ∀ n, 0 ≤ b n := fun n => add_nonneg (hw n) (hw (n + 1)) + have hbs : Summable b := hws.add ((summable_nat_add_iff 1).mpr hws) + obtain ⟨N, hN⟩ := ((tendsto_sum_nat_add b).eventually + (gt_mem_nhds (show (0 : ℝ) < 1 / 64 by norm_num))).exists + let a : ℕ → ℝ := fun n => 64 * b (n + N) + let T : ℝ := 2 ^ (N + n₀ + 1) + let t : ℕ → ℝ := fun n => T * 2 ^ n + have hT : 0 < T := by dsimp [T]; positivity + have ha : ∀ n, 0 ≤ a n := fun n => mul_nonneg (by norm_num) (hb (n + N)) + have htail : Summable (fun n => b (n + N)) := (summable_nat_add_iff N).mpr hbs + have has : Summable a := htail.mul_left 64 + have hsmall : (∑' n, a n) ≤ 1 := by + dsimp [a] + rw [tsum_mul_left] + linarith + have ht : ∀ n, 0 < t n := by intro n; dsimp [t]; positivity + have t_eq (n : ℕ) : t n = 2 ^ (n + N + n₀ + 1) := by + dsimp [t, T] + rw [← pow_add] + congr 1 + omega + have hab (n : ℕ) : a n / 64 = b (n + N) := by dsimp [a]; ring + have hshell (n : ℕ) (s : ℝ) (hslo : t n ≤ s) (hshi : s < 4 * t n) : + ω s ≤ a n / 64 := by + rw [hab] + dsimp [b] + have hlo : 2 ^ (n + N + n₀) < t n := by + rw [t_eq, pow_succ] + have : (0 : ℝ) < 2 ^ (n + N + n₀) := by positivity + linarith + have hmid : 2 ^ (n + N + n₀ + 2) = 2 * t n := by + rw [t_eq] + rw [show n + N + n₀ + 2 = (n + N + n₀ + 1) + 1 by omega, pow_succ] + ring + by_cases hcase : s < 2 * t n + · have h := hbound (n + N) s (hlo.trans_le hslo) (by simpa only [hmid] using hcase) + exact h.trans (le_add_of_nonneg_right (hw (n + N + 1))) + · have hleft : 2 ^ (n + N + 1 + n₀) = t n := by rw [t_eq]; congr 1; omega + have hright : 2 ^ (n + N + 1 + n₀ + 2) = 4 * t n := by + rw [t_eq] + rw [show n + N + 1 + n₀ + 2 = (n + N + n₀ + 1) + 2 by omega, pow_add] + norm_num + ring + have h := hbound (n + N + 1) s (by rw [hleft]; linarith [ht n]) + (by simpa only [hright] using hshi) + exact h.trans (le_add_of_nonneg_left (hw (n + N))) + refine ⟨a, t, max T Rp, lt_of_lt_of_le hT (le_max_left _ _), ha, has, ht, hsmall, ?_⟩ + intro r hr + have hrT : T ≤ r := (le_max_left _ _).trans hr + have hrp : Rp ≤ r := (le_max_right _ _).trans hr + have hrpos : 0 < r := hT.trans_le hrT + obtain ⟨n, hnlo, hnhi⟩ := dyadic_shell hT hrT + change t n ≤ r at hnlo + change r < 2 * t n at hnhi + have hcontrol : ∀ s, r ≤ s → s ≤ 2 * r → ω s ≤ a n / 64 := by + intro s hslo hshi + exact hshell n s (hnlo.trans hslo) (by linarith) + refine ⟨(hRp r hrp).1, ?_, n, hnlo, hnhi, hcontrol⟩ + have hsingle : a n ≤ 1 := (has.le_tsum n (fun i _ => ha i)).trans hsmall + exact (hcontrol r le_rfl (by linarith)).trans ((div_le_div_iff_of_pos_right (by norm_num : (0 : ℝ) < 64)).mpr hsingle) + +lemma sectorMap_arg_real {a t : ℕ → ℝ} (ha : ∀ n, 0 ≤ a n) (hs : Summable a) + (ht : ∀ n, 0 < t n) {x : ℝ} (hx : 0 ≤ x) : + (sectorMap a t (x : ℂ)).arg = 0 := by + have hz : (0 : ℝ) ≤ (x : ℂ).re := hx + have hA := sectorCorrection_re_nonneg ha hs ht hz + have hI : (sectorCorrection a t (x : ℂ)).im = 0 := by + rw [sectorCorrection, Complex.im_tsum (sectorTerms_summable ha hs ht hz)] + simp [sectorKernel, Complex.div_im] + apply Complex.arg_eq_zero_iff.mpr + constructor + · simp only [sectorMap, mul_re, ofReal_re, ofReal_im, zero_mul, sub_zero, + add_re, one_re] + positivity + · simp [sectorMap, mul_im, hI] + +lemma sectorMap_mem_lossSector {ω : ℝ → ℝ} {a t : ℕ → ℝ} {S R : ℝ} + (hS : 0 < S) (ha : ∀ n, 0 ≤ a n) (hs : Summable a) + (ht : ∀ n, 0 < t n) (hsmall : (∑' n, a n) ≤ 1) + (hω : ∀ r, S ≤ r → 0 < ω r ∧ ω r ≤ 1 / 64 ∧ + ∃ n, t n ≤ r ∧ r < 2 * t n ∧ + ∀ s, r ≤ s → s ≤ 2 * r → ω s ≤ a n / 64) + {z : ℂ} (hz : 0 ≤ z.re) (hlo : S ≤ ‖z‖) (hR : R < ‖z‖) : + sectorMap a t z ∈ lossSector ω R := by + have hnormL := sectorMap_norm_lower ha hs ht hz + have hnormU := sectorMap_norm_upper ha hs ht hsmall hz + have hpos := (hω _ (hlo.trans hnormL)).1 + obtain ⟨n, hnlo, hnhi, hn⟩ := (hω _ hlo).2.2 + have hbound := hn _ hnormL hnormU + have hreal := sectorMap_re_lower ha hs ht hz n hnlo hnhi.le + constructor + · exact hR.trans_le hnormL + · apply arg_lt_of_re_lower hpos (norm_pos_iff.mp (hS.trans_le (hlo.trans hnormL))) + calc 2 * ω ‖sectorMap a t z‖ * ‖sectorMap a t z‖ ≤ + 2 * (a n / 64) * ‖sectorMap a t z‖ := by gcongr + _ ≤ 2 * (a n / 64) * (2 * ‖z‖) := + mul_le_mul_of_nonneg_left hnormU (by positivity [ha n]) + _ ≤ a n * (‖z‖ / 8) := by nlinarith [mul_nonneg (ha n) (norm_nonneg z)] + _ ≤ (sectorMap a t z).re := hreal + + + +lemma lossSector_isPreconnected {ω : ℝ → ℝ} {R : ℝ} (hR : 0 < R) + (hω : ∀ r, R < r → 0 < ω r ∧ ω r < Real.pi / 2) : + IsPreconnected (lossSector ω R) := by + let ray : Set ℂ := Complex.ofReal '' Ioi R + have hray : IsPreconnected ray := isPreconnected_Ioi.image _ continuous_ofReal.continuousOn + have hray_sub : ray ⊆ lossSector ω R := by + rintro _ ⟨r, hr, rfl⟩ + have hr0 : 0 ≤ r := (hR.trans hr).le + simp only [lossSector, mem_ofPred_eq, Complex.norm_of_nonneg hr0, + Complex.arg_ofReal_of_nonneg hr0, abs_zero] + exact ⟨hr, sub_pos.mpr (hω r hr).2⟩ + apply isPreconnected_of_forall ((R + 1 : ℝ) : ℂ) + intro z hz + let arc : ℝ → ℂ := fun θ => (‖z‖ : ℂ) * Complex.exp ((θ : ℂ) * I) + let J : Set ℝ := Icc (-|z.arg|) |z.arg| + have hc : Continuous arc := by dsimp [arc]; fun_prop + have hn : 0 < ‖z‖ := hR.trans hz.1 + have hnorm (θ : ℝ) : ‖arc θ‖ = ‖z‖ := by + dsimp [arc] + rw [norm_mul, norm_exp_ofReal_mul_I, mul_one, Complex.norm_of_nonneg (norm_nonneg z)] + have harg (θ : ℝ) (hθ : θ ∈ J) : (arc θ).arg = θ := by + dsimp [arc] + rw [arg_real_mul _ hn, arg_exp_mul_I] + apply (toIocMod_eq_self _).mpr + have hp := (hω ‖z‖ hz.1).1 + have hθabs : |θ| ≤ |z.arg| := abs_le.mpr hθ + have := abs_le.mp hθabs + constructor <;> linarith [hz.2, Real.pi_pos] + have harc_sub : arc '' J ⊆ lossSector ω R := by + rintro _ ⟨θ, hθ, rfl⟩ + change R < ‖arc θ‖ ∧ |(arc θ).arg| < Real.pi / 2 - ω ‖arc θ‖ + rw [hnorm, harg θ hθ] + exact ⟨hz.1, (abs_le.mpr hθ).trans_lt hz.2⟩ + have harc : IsPreconnected (arc '' J) := isPreconnected_Icc.image arc hc.continuousOn + have hzero : arc 0 = (‖z‖ : ℂ) := by simp [arc] + have hinray : (‖z‖ : ℂ) ∈ ray := ⟨‖z‖, hz.1, rfl⟩ + have hinarc : (‖z‖ : ℂ) ∈ arc '' J := by + refine ⟨0, ⟨?_, ?_⟩, hzero⟩ <;> linarith [abs_nonneg z.arg] + refine ⟨ray ∪ arc '' J, union_subset hray_sub harc_sub, ?_, ?_, + hray.union _ hinray hinarc harc⟩ + · exact Or.inl ⟨R + 1, by simp, rfl⟩ + · apply Or.inr + refine ⟨z.arg, ⟨neg_abs_le _, le_abs_self _⟩, ?_⟩ + exact Complex.norm_mul_exp_arg_mul_I z + +lemma superpolynomialDecay_of_ray_bounds {G : ℂ → ℂ} + (hG : ∀ B : ℝ, 0 < B → ∃ C R : ℝ, 0 ≤ C ∧ + ∀ x : ℝ, R ≤ x → ‖G x‖ ≤ C * Real.exp (-B * x)) : + Asymptotics.SuperpolynomialDecay atTop Real.exp (fun x : ℝ => ‖G x‖) := by + intro n + obtain ⟨C, R, hC, hbound⟩ := hG (n + 1) (by positivity) + have hlimit : Tendsto (fun x : ℝ => C * Real.exp (-x)) atTop (𝓝 0) := by + simpa using (Real.tendsto_exp_atBot.comp tendsto_neg_atTop_atBot).const_mul C + apply squeeze_zero' (Eventually.of_forall (fun x => by positivity)) _ hlimit + filter_upwards [eventually_ge_atTop R] with x hx + calc Real.exp x ^ n * ‖G x‖ ≤ Real.exp x ^ n * (C * Real.exp (-(n + 1) * x)) := by + gcongr + exact hbound x hx + _ = C * Real.exp (-x) := by + rw [← Real.exp_nat_mul] + calc Real.exp (n * x) * (C * Real.exp (-(n + 1) * x)) = + C * (Real.exp (n * x) * Real.exp (-(n + 1) * x)) := by ring + _ = C * Real.exp (-x) := by rw [← Real.exp_add]; congr 2; ring + + + +theorem sector_uniqueness : SectorUniquenessStatement := by + intro ω R f hω hf hbounded hdecay + obtain ⟨a, t, S, hS, ha, hs, ht, hsmall, hcontrol⟩ := angularLoss_kernel_data hω + let R' : ℝ := max S R + let q : ℝ := R' + 1 + have hR'S : S ≤ R' := le_max_left _ _ + have hR'R : R ≤ R' := le_max_right _ _ + have hR' : 0 < R' := hS.trans_le hR'S + have hq : 0 < q := by dsimp [q]; linarith + let H : ℂ → ℂ := fun z => sectorMap a t (z + (q : ℂ)) + have hshift (z : ℂ) (hz : 0 ≤ z.re) : 0 < (z + (q : ℂ)).re := by + simp only [add_re, ofReal_re] + linarith + have hnormshift (z : ℂ) : z.re + q ≤ ‖z + (q : ℂ)‖ := by + simpa only [add_re, ofReal_re] using re_le_norm (z + (q : ℂ)) + have hHmem (z : ℂ) (hz : 0 ≤ z.re) : H z ∈ lossSector ω R' := by + apply sectorMap_mem_lossSector hS ha hs ht hsmall hcontrol (hshift z hz).le + · have := hnormshift z + dsimp [q] at this + linarith + · have := hnormshift z + dsimp [q] at this + linarith + have hsubset : lossSector ω R' ⊆ lossSector ω R := by + intro z hz + exact ⟨lt_of_le_of_lt hR'R hz.1, hz.2⟩ + have hf' : AnalyticOnNhd ℂ f (lossSector ω R') := hf.mono hsubset + obtain ⟨M, hM⟩ := hbounded + have hHdiff (z : ℂ) (hz : 0 ≤ z.re) : DifferentiableAt ℂ H z := by + have hd := (sectorMap_differentiableOn ha hs ht).differentiableAt + ((isOpen_lt continuous_const continuous_re).mem_nhds (hshift z hz)) + exact hd.comp z (differentiableAt_id.add_const (q : ℂ)) + let G : ℂ → ℂ := fun z => f (H z) + have hGdiff : DiffContOnCl ℂ G {z : ℂ | 0 < z.re} := by + apply DifferentiableOn.diffContOnCl + rw [closure_setOfPred_lt_re] + intro z hz + exact ((hf' _ (hHmem z hz)).differentiableAt.comp z (hHdiff z hz)).differentiableWithinAt + have hGbound (z : ℂ) (hz : 0 ≤ z.re) : ‖G z‖ ≤ M := hM _ (hsubset (hHmem z hz)) + have hHnorm (x : ℝ) (hx : 0 ≤ x) : x ≤ ‖H (x : ℂ)‖ := by + have h1 := hnormshift (x : ℂ) + have h2 := sectorMap_norm_lower ha hs ht (hshift (x : ℂ) hx).le + change ‖(x : ℂ) + (q : ℂ)‖ ≤ ‖H (x : ℂ)‖ at h2 + simp only [ofReal_re] at h1 + linarith + have hGdecay : Asymptotics.SuperpolynomialDecay atTop Real.exp (fun x : ℝ => ‖G x‖) := by + apply superpolynomialDecay_of_ray_bounds + intro B hB + obtain ⟨C, T, hC, hCT⟩ := hdecay B hB + refine ⟨C, max 0 (T + 1), hC, ?_⟩ + intro x hx + have hx0 : 0 ≤ x := (le_max_left _ _).trans hx + have hxT : T < x := by have := (le_max_right 0 (T + 1)).trans hx; linarith + have harg : (H (x : ℂ)).arg = 0 := by + dsimp [H] + rw [← ofReal_add] + exact sectorMap_arg_real ha hs ht (by linarith) + have h := hCT (H (x : ℂ)) (hxT.trans_le (hHnorm x hx0)) + (by rw [harg, abs_zero]; positivity) + calc ‖G x‖ ≤ C * Real.exp (-B * ‖H (x : ℂ)‖) := h + _ ≤ C * Real.exp (-B * x) := by + apply mul_le_mul_of_nonneg_left _ hC + apply Real.exp_le_exp.mpr + exact mul_le_mul_of_nonpos_left (hHnorm x hx0) (neg_nonpos.mpr hB.le) + have hGzero : EqOn G 0 {z : ℂ | 0 ≤ z.re} := by + apply PhragmenLindelof.eq_zero_on_right_half_plane_of_superexponential_decay hGdiff + · refine ⟨0, by norm_num, 0, Asymptotics.IsBigO.of_bound M ?_⟩ + apply Eventually.filter_mono inf_le_right + rw [eventually_principal] + intro z hz + simpa using hGbound z hz.le + · exact hGdecay + · exact ⟨M, fun x => hGbound _ (by simp)⟩ + have hop : IsOpen {z : ℂ | 0 < z.re} := isOpen_lt continuous_const continuous_re + have hHd : DifferentiableOn ℂ H {z : ℂ | 0 < z.re} := by + intro z hz + exact (hHdiff z (le_of_lt hz)).differentiableWithinAt + have hanalytic : AnalyticOnNhd ℂ H {z : ℂ | 0 < z.re} := hHd.analyticOnNhd hop + have hopen : IsOpen (H '' {z : ℂ | 0 < z.re}) := by + rcases hanalytic.is_constant_or_isOpen (convex_halfSpace_re_gt 0).isPreconnected with + ⟨c, hc⟩ | ho + · have hx : (0 : ℝ) < ‖c‖ + 1 := by positivity + have h1 := hHnorm (‖c‖ + 1) hx.le + rw [hc _ (by simpa using hx)] at h1 + linarith + · exact ho _ Subset.rfl hop + have hzero : f =ᶠ[𝓝 (H 1)] 0 := by + filter_upwards [hopen.mem_nhds (show H 1 ∈ H '' {z : ℂ | 0 < z.re} from + ⟨1, by simp, rfl⟩)] with z hz + rcases hz with ⟨w, hw, rfl⟩ + exact hGzero (show 0 ≤ w.re from le_of_lt hw) + have hconn : IsPreconnected (lossSector ω R') := by + apply lossSector_isPreconnected hR' + intro r hr + have h := hcontrol r (hR'S.trans hr.le) + exact ⟨h.1, lt_of_le_of_lt h.2.1 (by linarith [Real.pi_gt_three])⟩ + exact ⟨R', hR'R, hf'.eqOn_zero_of_preconnected_of_eventuallyEq_zero hconn + (hHmem 1 (by simp)) hzero⟩ + +end DegeneratingTrees +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/TaylorCutoffs.lean b/lean/OAI/Analysis/PathSelection/TaylorCutoffs.lean new file mode 100644 index 0000000000000000000000000000000000000000..7e34ade22aef7fe21c60d03a9c8c32cfc0de5143 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/TaylorCutoffs.lean @@ -0,0 +1,399 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockAlgebra + +namespace OAI + +/-! Uniform Taylor cutoffs, compact family holomorphy and moving Taylor polynomials. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +open scoped BigOperators +namespace DegeneratingTrees.TaylorCutoff +variable {E : Type*} [NormedAddCommGroup E] + +private def extend {r : ℝ} (f : C(sphere (0 : ℂ) r,E)) (z : ℂ) : E := by + classical + exact if hz : z ∈ sphere (0 : ℂ) r then f ⟨z,hz⟩ else 0 + +private lemma extend_on {r : ℝ} (f : C(sphere (0 : ℂ) r,E)) + {z : ℂ} (hz : z ∈ sphere (0 : ℂ) r) : extend f z = f ⟨z,hz⟩ := by + simp only [extend,dite_eq_left hz] + +private lemma extend_continuousOn {r : ℝ} (f : C(sphere (0 : ℂ) r,E)) : + ContinuousOn (extend f) (sphere (0 : ℂ) r) := by + rw [continuousOn_iff_continuous_domRestrict] + convert f.continuous using 1 + ext z + exact extend_on f z.property + + +variable [NormedSpace ℂ E] + +def circleMap (r : ℝ) (hr : 0 ≤ r) : C(sphere (0 : ℂ) r,E) →L[ℂ] E := + let L : C(sphere (0 : ℂ) r,E) →ₗ[ℂ] E := + { toFun := fun f => ∮ z in C(0,r), extend f z + map_add' := by + intro f g + have he : extend (f+g) = fun z => extend f z + extend g z := by + ext z + by_cases hz : z ∈ sphere (0 : ℂ) r <;> + simp only [extend,hz,dite_true,dite_false,ContinuousMap.add_apply,add_zero] + rw [he] + exact circleIntegral.integral_add + ((extend_continuousOn f).circleIntegrable hr) + ((extend_continuousOn g).circleIntegrable hr) + map_smul' := by + intro c f + have he : extend (c • f) = fun z => c • extend f z := by + ext z + by_cases hz : z ∈ sphere (0 : ℂ) r <;> + simp only [extend,hz,dite_true,dite_false,ContinuousMap.smul_apply,smul_zero] + rw [he,circleIntegral.integral_smul] + rfl } + L.mkContinuous (2*Real.pi*r) (by + intro f + apply circleIntegral.norm_integral_le_of_norm_le_const hr + intro z hz + rw [extend_on f hz] + exact f.norm_coe_le_norm ⟨z,hz⟩) + +lemma circleMap_eq {r : ℝ} (hr : 0 ≤ r) (f : C(sphere (0 : ℂ) r,E)) + (F : ℂ → E) (hF : ∀ z : sphere (0 : ℂ) r, f z = F z) : + circleMap r hr f = ∮ z in C(0,r), F z := by + apply circleIntegral.integral_congr hr + intro z hz + rw [extend_on f hz] + exact hF ⟨z,hz⟩ + +lemma sphere_ne_zero {r : ℝ} (hr : 0 < r) (w : sphere (0:ℂ) r) : (w:ℂ) ≠ 0 := by + intro he + have hw : ‖(w:ℂ)‖ = r := by simpa only [mem_sphere,dist_zero_right] using w.property + rw [he,norm_zero] at hw + exact hr.ne' hw.symm + +lemma sphere_sub_ball_ne_zero {r : ℝ} (w : sphere (0:ℂ) r) (u : ball (0:ℂ) r) : + (w:ℂ)-(u:ℂ) ≠ 0 := by + apply sub_ne_zero.mpr + intro he + have hw : ‖(w:ℂ)‖ = r := by simpa only [mem_sphere,dist_zero_right] using w.property + have hu : ‖(u:ℂ)‖ < r := by simpa only [mem_ball,dist_zero_right] using u.property + rw [he] at hw + exact (ne_of_lt hu) hw + + +def tailProfile {r : ℝ} (hr : 0 < r) (n : ℕ) + (f : C(sphere (0:ℂ) r,E)) (u : ball (0:ℂ) r) : C(sphere (0:ℂ) r,E) := + ⟨fun w => ((w:ℂ)^n*((w:ℂ)-(u:ℂ)))⁻¹ • f w, + ((continuous_subtype_val.pow n).mul + (continuous_subtype_val.sub continuous_const)).inv₀ + (fun w => mul_ne_zero (pow_ne_zero _ (sphere_ne_zero hr w)) + (sphere_sub_ball_ne_zero w u)) |>.smul f.continuous⟩ + +def tail {r : ℝ} (hr : 0 < r) (n : ℕ) + (f : C(sphere (0:ℂ) r,E)) (u : ball (0:ℂ) r) : E := + (2*Real.pi*I : ℂ)⁻¹ • circleMap r hr.le (tailProfile hr n f u) + +lemma continuous_tailProfile {r : ℝ} (hr : 0 < r) (n : ℕ) : + Continuous (fun x : C(sphere (0:ℂ) r,E) × ball (0:ℂ) r => + tailProfile hr n x.1 x.2) := by + apply ContinuousMap.continuous_of_continuous_uncurry + change Continuous (fun x : (C(sphere (0:ℂ) r,E) × ball (0:ℂ) r) × sphere (0:ℂ) r => + ((x.2:ℂ)^n*((x.2:ℂ)-(x.1.2:ℂ)))⁻¹ • x.1.1 x.2) + apply Continuous.smul + · apply Continuous.inv₀ + · fun_prop + · intro x + exact mul_ne_zero (pow_ne_zero _ (sphere_ne_zero hr x.2)) + (sphere_sub_ball_ne_zero x.2 x.1.2) + · exact continuous_eval.comp (continuous_fst.fst.prodMk continuous_snd) + +lemma continuous_tail {r : ℝ} (hr : 0 < r) (n : ℕ) : + Continuous (fun x : C(sphere (0:ℂ) r,E) × ball (0:ℂ) r => tail hr n x.1 x.2) := + continuous_const.smul ((circleMap r hr.le).continuous.comp (continuous_tailProfile hr n)) + +attribute [local irreducible] tail tailProfile circleMap + + + +theorem tail_tendsto {α : Type*} {l : Filter α} {r : ℝ} (hr : 0 < r) + (n : ℕ) {f : α → C(sphere (0:ℂ) r,E)} {f₀ : C(sphere (0:ℂ) r,E)} + {u : α → ball (0:ℂ) r} {u₀ : ball (0:ℂ) r} + (hf : Tendsto f l (𝓝 f₀)) (hu : Tendsto u l (𝓝 u₀)) : + Tendsto (fun x => tail hr n (f x) (u x)) l + (𝓝 (tail hr n f₀ u₀)) := by + have ht : Tendsto (fun x : C(sphere (0:ℂ) r,E) × ball (0:ℂ) r => + tail hr n x.1 x.2) (𝓝 (f₀,u₀)) (𝓝 (tail hr n f₀ u₀)) := + (continuous_tail (E := E) hr n).tendsto (f₀,u₀) + have hp : Tendsto (fun x => (f x,u x)) l (𝓝 (f₀,u₀)) := hf.prodMk_nhds hu + exact ht.comp hp + +theorem tail_tendsto_zero {α : Type*} {l : Filter α} {r : ℝ} (hr : 0 < r) + (n : ℕ) {f : α → C(sphere (0:ℂ) r,E)} {f₀ : C(sphere (0:ℂ) r,E)} + {u : α → ball (0:ℂ) r} (hf : Tendsto f l (𝓝 f₀)) + (hu : Tendsto (fun x => (u x:ℂ)) l (𝓝 0)) : + Tendsto (fun x => tail hr n (f x) (u x)) l + (𝓝 (tail hr n f₀ ⟨0,by simpa only [mem_ball,dist_self] using hr⟩)) := by + apply tail_tendsto hr n hf + exact tendsto_subtype_rng.mpr hu + +lemma tail_kernel_step {w u : ℂ} (hw : w ≠ 0) (hwu : w-u ≠ 0) (n : ℕ) : + (w^n*(w-u))⁻¹ = (w^(n+1))⁻¹ + u*(w^(n+1)*(w-u))⁻¹ := by + field_simp + ring + +lemma tail_step {r : ℝ} (hr : 0 < r) (n : ℕ) + (f : C(sphere (0:ℂ) r,E)) (u : ball (0:ℂ) r) : + tail hr n f u = tail hr n f ⟨0,by simpa using hr⟩ + + (u:ℂ) • tail hr (n+1) f u := by + have he : tailProfile hr n f u = + tailProfile hr n f ⟨0,by simpa using hr⟩ + (u:ℂ) • tailProfile hr (n+1) f u := by + ext w + simpa only [tailProfile,ContinuousMap.coe_mk,ContinuousMap.add_apply, + ContinuousMap.smul_apply,sub_zero,pow_succ,add_smul,mul_smul] using + congrArg (fun z : ℂ => z • f w) + (tail_kernel_step (sphere_ne_zero hr w) (sphere_sub_ball_ne_zero w u) n) + simp only [tail,he,map_add,map_smul,smul_add,smul_comm (u:ℂ)] + + + +theorem finite_cutoff {r : ℝ} (hr : 0 < r) (n : ℕ) + (f : C(sphere (0:ℂ) r,E)) (u : ball (0:ℂ) r) : + tail hr 0 f u = (∑ k ∈ Finset.range n, (u:ℂ)^k • + tail hr k f ⟨0,by simpa using hr⟩) + (u:ℂ)^n • tail hr n f u := by + induction n with + | zero => simp + | succ n ih => + rw [ih,tail_step hr n f u,smul_add,Finset.sum_range_succ,pow_succ, + mul_smul] + module + +variable [CompleteSpace E] + +lemma tail_zero_eq {r : ℝ} (hr : 0 < r) {F : ℂ → E} + (hF : DifferentiableOn ℂ F (closedBall 0 r)) (u : ball (0:ℂ) r) : + tail hr 0 ⟨fun w => F w,hF.continuousOn.mono sphere_subset_closedBall + |>.domRestrict⟩ u = F u := by + unfold tail + rw [circleMap_eq hr.le _ (fun w => (w-(u:ℂ))⁻¹ • F w) (by intro w; simp only [tailProfile,ContinuousMap.coe_mk,pow_zero,one_mul]; rfl)] + rw [hF.circleIntegral_sub_inv_smul u.property] + rw [smul_smul,inv_mul_cancel₀] + · exact one_smul ℂ _ + · exact mul_ne_zero (mul_ne_zero (by norm_num) (by exact_mod_cast Real.pi_ne_zero)) I_ne_zero + +end DegeneratingTrees.TaylorCutoff + + + + + + + +open Set Filter Topology Complex MeasureTheory Metric +open scoped NNReal +namespace DegeneratingTrees.Clock + +lemma clm_circleIntegral {V W : Type*} [NormedAddCommGroup V] [NormedSpace ℂ V] + [CompleteSpace V] [NormedAddCommGroup W] [NormedSpace ℂ W] [CompleteSpace W] + (L : V →L[ℂ] W) {f : ℂ → V} {c : ℂ} {r : ℝ} + (hf : CircleIntegrable f c r) : + (∮ z in C(c,r),L (f z)) = L (∮ z in C(c,r),f z) := by + simpa only [circleIntegral,map_smul] using + L.intervalIntegral_comp_comm ((circleIntegrable_iff r).mp hf) + +lemma compact_family_analyticAt {S : Type*} [TopologicalSpace S] [CompactSpace S] + {F : ℂ → C(S,ℂ)} {c : ℂ} {r : ℝ≥0} (hr : 0 F z s) (ball c r)) : + AnalyticAt ℂ F c := by + let G : ℂ → C(S,ℂ) := fun w => (2*Real.pi*I:ℂ)⁻¹ • + ∮ z in C(c,r),(z-w)⁻¹ • F z + have hGa : AnalyticAt ℂ G c := + (hasFPowerSeriesOn_cauchy_integral + ((hc.mono sphere_subset_closedBall).circleIntegrable r.2) hr).analyticAt + apply hGa.congr + filter_upwards [ball_mem_nhds c hr] with w hw + apply ContinuousMap.ext + intro s + let L : C(S,ℂ) →L[ℂ] ℂ := ContinuousMap.evalCLM ℂ s + have hkernel : ContinuousOn (fun z : ℂ => (z-w)⁻¹ • F z) (sphere c r) := by + have hi : ContinuousOn (fun z : ℂ => (z-w)⁻¹) (sphere c r) := by + apply ContinuousOn.inv₀ (continuous_id.sub continuous_const).continuousOn + intro z hz he + have : z=w := sub_eq_zero.mp he + subst z + have : dist w c=(r:ℝ) := mem_sphere.mp hz + exact (ne_of_lt (mem_ball.mp hw)) this + exact hi.smul (hc.mono sphere_subset_closedBall) + have hcomm := clm_circleIntegral L (hkernel.circleIntegrable r.2) + change L (G w)=F w s + dsimp only [G] + rw [map_smul] + calc + _ = (2*Real.pi*I:ℂ)⁻¹ • (∮ z in C(c,r),L ((z-w)⁻¹ • F z)) := + congrArg (fun x : ℂ => (2*Real.pi*I:ℂ)⁻¹ • x) hcomm.symm + _ = F w s := by + simpa only [map_smul,ContinuousMap.evalCLM_apply,L] using + (ha s).two_pi_i_inv_smul_circleIntegral_sub_inv_smul hw + +lemma compact_family_analyticAt_of_joint {S : Type*} [TopologicalSpace S] [CompactSpace S] + {F : ℂ → C(S,ℂ)} {c : ℂ} {r : ℝ≥0} (hr : 0 F p.1 p.2) (closedBall c r ×ˢ univ)) + (ha : ∀ s : S,DiffContOnCl ℂ (fun z => F z s) (ball c r)) : + AnalyticAt ℂ F c := + compact_family_analyticAt hr (ContinuousMap.continuousOn_of_continuousOn_uncurry F hc) ha + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees.TaylorCutoff +attribute [local irreducible] tail tailProfile circleMap + + +def scalarTailCLM {r : ℝ} (hr : 0 tail hr n f u + map_add' := by + intro f g + have he : tailProfile hr n (f+g) u = tailProfile hr n f u+tailProfile hr n g u := by + ext w + simp only [tailProfile,ContinuousMap.coe_mk,ContinuousMap.add_apply,smul_add] + simp only [tail,he,map_add,smul_add] + map_smul' := by + intro c f + have he : tailProfile hr n (c • f) u = c • tailProfile hr n f u := by + ext w + simp only [tailProfile,ContinuousMap.coe_mk,ContinuousMap.smul_apply,smul_comm c] + simp only [tail,he,map_smul,smul_comm c,RingHom.id_apply] + cont := by + exact (continuous_tail (E := ℂ) hr n).comp (continuous_id.prodMk continuous_const) + +def shiftedBoundary (G : C(ℂ,ℂ)) (r : ℝ) (a : ℂ) : C(sphere (0:ℂ) r,ℂ) := + ⟨fun w => G (a+w),G.continuous.comp (continuous_const.add continuous_subtype_val)⟩ + +lemma continuous_shiftedBoundary (G : C(ℂ,ℂ)) (r : ℝ) : Continuous (shiftedBoundary G r) := by + apply ContinuousMap.continuous_of_continuous_uncurry + exact G.continuous.comp (continuous_fst.add (continuous_subtype_val.comp continuous_snd)) + +lemma shift_mem_disc {d a w : ℂ} {r : ℝ} (hr : 0 G (a+w)) (closedBall d r) := by + intro w a ha + exact (hG _ (shift_mem_disc hr ha (sphere_subset_closedBall w.property))).comp + (f := fun a : ℂ => a+(w:ℂ)) (analyticAt_id.add analyticAt_const) + apply Clock.compact_family_analyticAt (r := ⟨r,hr.le⟩) hr + (continuous_shiftedBoundary G r).continuousOn + intro w + change DiffContOnCl ℂ (fun a => G (a+(w:ℂ))) (ball d r) + refine ⟨((ha w).differentiableOn.mono ball_subset_closedBall),?_⟩ + simpa only [closure_ball _ hr.ne'] using (ha w).continuousOn + +lemma local_continuous_extension {g : ℂ → ℂ} {d : ℂ} (hg : AnalyticAt ℂ g d) : + ∃ (G : C(ℂ,ℂ)) (r : ℝ),0 g z,(hgR.continuousOn.mono hsub).domRestrict⟩ + obtain ⟨G,hG⟩ := gC.exists_restrict_eq isClosed_closedBall + have he : EqOn G g (closedBall d (3*r)) := by + intro z hz + exact DFunLike.congr_fun hG ⟨z,hz⟩ + refine ⟨G,r,hr,?_,he⟩ + intro z hz + apply (hgR z (hsub (ball_subset_closedBall hz))).congr + filter_upwards [isOpen_ball.mem_nhds hz] with w hw + exact (he (ball_subset_closedBall hw)).symm + + + +theorem analytic_moving_taylor {g : ℂ → ℂ} {d : ℂ} (hg : AnalyticAt ℂ g d) : + ∃ c : ℕ → ℂ → ℂ,(∀ n,AnalyticAt ℂ (c n) d) ∧ + ∀ (a f : ℂ → ℂ) (δ : ℝ),Tendsto a sectorInfinity (𝓝 d) → + 0<δ → Clock.ExpBound (-δ) f → ∀ N : ℕ, + Clock.ExpBound (-δ*(N:ℝ)) (fun z => g (a z+f z)- + ∑ n ∈ Finset.range N,c n (a z)*f z^n) := by + classical + obtain ⟨G,r,hr,hG,heG⟩ := local_continuous_extension hg + let u₀ : ball (0:ℂ) r := ⟨0,by simpa using hr⟩ + let c : ℕ → ℂ → ℂ := fun n a => scalarTailCLM hr n u₀ (shiftedBoundary G r a) + have hc : ∀ n,AnalyticAt ℂ (c n) d := by + intro n + exact ((scalarTailCLM hr n u₀).analyticAt _).comp (shiftedBoundary_analyticAt hr hG) + refine ⟨c,hc,?_⟩ + intro a f δ ha hδ hf N + have hft := hf.tendsto_zero (neg_neg_of_pos hδ) + let u : ℂ → ball (0:ℂ) r := fun z => + if hz : f z∈ball (0:ℂ) r then ⟨f z,hz⟩ else u₀ + have hue : (fun z => (u z:ℂ)) =ᶠ[sectorInfinity] f := by + filter_upwards [hft.eventually (ball_mem_nhds (0:ℂ) hr)] with z hz + dsimp only [u] + split_ifs with h + · rfl + · exact False.elim (h hz) + have hut : Tendsto (fun z => (u z:ℂ)) sectorInfinity (𝓝 0) := + hft.congr' hue.symm + have hboundary := (continuous_shiftedBoundary G r).continuousAt.tendsto.comp ha + have htail := tail_tendsto_zero hr N hboundary hut + have hbound := (hf.pow N).mul (Clock.ExpBound.of_tendsto htail) + simp only [add_zero] at hbound + apply hbound.congr + filter_upwards [hue,ha.eventually (ball_mem_nhds d hr)] with z hz hza + have hdiff : DifferentiableOn ℂ (fun w => G (a z+w)) (closedBall (0:ℂ) r) := by + intro w hw + exact ((hG _ (shift_mem_disc hr (ball_subset_closedBall hza) hw)).differentiableAt.comp w + ((differentiableAt_const (a z)).add differentiableAt_id)).differentiableWithinAt + have htail₀ : tail hr 0 (shiftedBoundary G r (a z)) (u z) = G (a z+f z) := by + have h := tail_zero_eq hr hdiff (u z) + rw [hz] at h + exact h + have hcut := finite_cutoff hr N (shiftedBoundary G r (a z)) (u z) + rw [htail₀] at hcut + have hazf : a z+f z∈closedBall d (3*r) := by + apply ball_subset_closedBall + apply shift_mem_disc hr (ball_subset_closedBall hza) + rw [←hz] + exact ball_subset_closedBall (u z).property + rw [heG hazf] at hcut + simp only [hz,smul_eq_mul] at hcut + change f z^N*tail hr N (shiftedBoundary G r (a z)) (u z) = _ + change _ = g (a z+f z)-∑ n ∈ Finset.range N, + tail hr n (shiftedBoundary G r (a z)) u₀*f z^n + simp_rw [mul_comm (tail hr _ _ _)] + exact (eq_sub_iff_add_eq.mpr (by simpa only [add_comm] using hcut.symm)) + +end DegeneratingTrees.TaylorCutoff +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/TupleTaylor.lean b/lean/OAI/Analysis/PathSelection/TupleTaylor.lean new file mode 100644 index 0000000000000000000000000000000000000000..be41760ecc7f8199673be35e869edcae24386cdf --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/TupleTaylor.lean @@ -0,0 +1,285 @@ +import Mathlib +import OAI.Analysis.PathSelection.ClockComposition +import OAI.Analysis.PathSelection.FilteredExpansions + +namespace OAI + +/-! Multivariate moving Taylor expansions and finite tuple-clock composition. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Metric +open scoped NNReal ENNReal +namespace DegeneratingTrees.MovingTaylor +variable {𝕜 E F : Type*} [NontriviallyNormedField 𝕜] + [NormedAddCommGroup E] [NormedSpace 𝕜 E] + [NormedAddCommGroup F] [NormedSpace 𝕜 F] + + + +lemma uniform_changeOrigin_coefficients [CompleteSpace F] (p : FormalMultilinearSeries 𝕜 E F) + {r : ℝ≥0} (hr : (r+r : ℝ≥0∞) < p.radius) : + ∃ C : ℝ≥0, ∀ x : E, ‖x‖₊ ≤ r → ∀ k : ℕ, + ‖p.changeOrigin x k‖₊ * r^k ≤ C := by + have hs := NNReal.summable_sigma.mp (p.changeOriginSeries_summable_aux₁ hr) + let C : ℝ≥0 := ∑' k : ℕ, ∑' s : Σ l : ℕ, + {s : Finset (Fin (k+l)) // s.card=l}, ‖p (k+s.1)‖₊ * r^s.1 * r^k + refine ⟨C,?_⟩ + intro x hx k + have hr' : (r : ℝ≥0∞) < p.radius := (le_add_of_nonneg_right bot_le).trans_lt hr + have hx' : (‖x‖₊ : ℝ≥0∞) < p.radius := + (ENNReal.coe_le_coe.mpr hx).trans_lt hr' + calc + ‖p.changeOrigin x k‖₊ * r^k ≤ + (∑' s : Σ l : ℕ, {s : Finset (Fin (k+l)) // s.card=l}, + ‖p (k+s.1)‖₊ * ‖x‖₊^s.1) * r^k := + mul_le_mul' (p.nnnorm_changeOrigin_le k hx') le_rfl + _ ≤ (∑' s : Σ l : ℕ, {s : Finset (Fin (k+l)) // s.card=l}, + ‖p (k+s.1)‖₊ * r^s.1) * r^k := by + apply mul_le_mul' ?_ le_rfl + exact Summable.tsum_le_tsum (fun s => by gcongr) + (p.changeOriginSeries_summable_aux₂ hx' k) + (p.changeOriginSeries_summable_aux₂ hr' k) + _ = ∑' s : Σ l : ℕ, {s : Finset (Fin (k+l)) // s.card=l}, + ‖p (k+s.1)‖₊ * r^s.1 * r^k := (NNReal.tsum_mul_right _ _).symm + _ ≤ C := hs.2.le_tsum k (fun _ _ => bot_le) + + + +theorem analytic_uniform_moving_taylor [CompleteSpace F] {g : E → F} {d : E} + (hg : AnalyticAt 𝕜 g d) : + ∃ c : (n : ℕ) → E → (E [×n]→L[𝕜] F), + (∀ n, AnalyticAt 𝕜 (c n) d) ∧ ∃ r C : ℝ, 0 v)‖ ≤ + C*(‖v‖/r)^N := by + classical + obtain ⟨p,R,hp⟩ := hg + obtain ⟨R₀,hR₀,hR⟩ := ENNReal.lt_iff_exists_nnreal_btwn.mp hp.r_pos + have hR₀' : 0 p.changeOrigin (a-d) n + refine ⟨c,?_,r,2*(C:ℝ),hr',by positivity,?_⟩ + · intro n + have h := (p.analyticAt_changeOrigin (hp.r_pos.trans_le hp.r_le) n) + have hs : AnalyticAt 𝕜 (fun a : E => a-d) d := analyticAt_id.sub analyticAt_const + have hs' : AnalyticAt 𝕜 (fun x : E => p.changeOrigin x n) (d-d) := by + simpa only [sub_self] using h + exact hs'.comp (f := fun a : E => a-d) hs + intro a v ha hv N + have hax : ‖a-d‖₊≤r := ha + have hav : (‖a-d‖₊ : ℝ≥0∞) v)‖ ≤ (C:ℝ)*q^n := by + intro n + have hn : ‖p.changeOrigin (a-d) n‖*(r:ℝ)^n≤(C:ℝ) := by + exact_mod_cast hC (a-d) hax n + calc + _ ≤ ‖p.changeOrigin (a-d) n‖*∏ _ : Fin n, ‖v‖ := + ContinuousMultilinearMap.le_opNorm _ _ + _ = (‖p.changeOrigin (a-d) n‖*(r:ℝ)^n)*q^n := by + simp only [Finset.prod_const,Finset.card_univ,Fintype.card_fin,q,div_pow] + field_simp + _ ≤ (C:ℝ)*q^n := mul_le_mul_of_nonneg_right hn (pow_nonneg hq0 n) + have herr := norm_sub_le_of_geometric_bound_of_hasSum (by linarith : q<1) hb hsum N + rw [norm_sub_rev] at herr + change ‖g (a+v)-∑ n ∈ Finset.range N,p.changeOrigin (a-d) n (fun _ => v)‖ ≤ + (2*(C:ℝ))*q^N + apply herr.trans + apply (div_le_iff₀ (by linarith : 0<1-q)).mpr + have hpos : 0≤(C:ℝ)*q^N := mul_nonneg C.coe_nonneg (pow_nonneg hq0 N) + nlinarith + +end DegeneratingTrees.MovingTaylor + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma multilinear_tuple_expansion {d n : ℕ} + (p : (Fin d → ℂ) [×n]→L[ℂ] ℂ) (v : Fin d → ℂ) : + p (fun _ => v) = ∑ j : Fin n → Fin d, + (∏ i, v (j i)) * p (fun i => Pi.single (j i) 1) := by + classical + have hv : v = ∑ j : Fin d,v j • Pi.single j (1:ℂ) := by + ext i + simp [Pi.single_apply] + conv_lhs => rw [hv] + rw [p.map_sum] + apply Finset.sum_congr rfl + intro j hj + simpa only [smul_eq_mul] using p.map_smul_univ (fun i => v (j i)) + (fun i => Pi.single (j i) 1) + +lemma BoundedExpansionOver.multilinear {K : Set (ℂ → ℂ)} + (hK : LowerSectorData K) {d n : ℕ} {δ : ℝ} + {v : ℂ → Fin d → ℂ} {p : ℂ → ((Fin d → ℂ) [×n]→L[ℂ] ℂ)} + (hv : ∀ i,BoundedExpansionOver K (-δ) (fun z => v z i)) + (hp : ∀ j : Fin n → Fin d,(fun z => p z (fun i => Pi.single (j i) 1))∈K) : + BoundedExpansionOver K (-δ*(n:ℝ)) (fun z => p z (fun _ => v z)) := by + have hterm : ∀ j : Fin n → Fin d,BoundedExpansionOver K (-δ*(n:ℝ)) + (fun z => (∏ i,v z (j i))*p z (fun i => Pi.single (j i) 1)) := by + intro j + have hprod := BoundedExpansionOver.prod hK (Finset.univ : Finset (Fin n)) + (fun i _ => hv (j i)) + have h := hprod.mul hK (BoundedExpansionOver.lower hK (hp j)) + simpa only [Finset.sum_const,Finset.card_univ,Fintype.card_fin,nsmul_eq_mul, + add_zero,mul_comm (n:ℝ)] using h + have h := BoundedExpansionOver.sum hK Finset.univ (fun j _ => hterm j) + simpa only [←multilinear_tuple_expansion] using h + + + +lemma tuple_taylor_expBound {d : ℕ} {g : (Fin d → ℂ) → ℂ} {center : Fin d → ℂ} + {c : (n : ℕ) → (Fin d → ℂ) → ((Fin d → ℂ) [×n]→L[ℂ] ℂ)} + {r C : ℝ} (hr : 0 v)‖≤C*(‖v‖/r)^N) + {a v : ℂ → Fin d → ℂ} (ha : Tendsto a sectorInfinity (𝓝 center)) + {δ : ℝ} (hδ : 0<δ) (hv : ∀ i,ExpBound (-δ) (fun z => v z i)) (N : ℕ) : + ExpBound (-δ*(N:ℝ)) (fun z => g (a z+v z)- + ∑ n∈Finset.range N,c n (a z) (fun _ => v z)) := by + have hvO : v =O[sectorInfinity] (fun z => Real.exp (-δ*z.re)) := + Asymptotics.isBigO_pi.mpr hv + obtain ⟨K,hK,hbound⟩ := hvO.exists_pos + have hv0 : Tendsto v sectorInfinity (𝓝 0) := tendsto_pi_nhds.mpr + (fun i => (hv i).tendsto_zero (neg_neg_of_pos hδ)) + apply Asymptotics.IsBigO.of_bound (C*(K/r)^N) + filter_upwards [hbound.bound,ha.eventually (Metric.ball_mem_nhds center hr), + hv0.eventually (Metric.ball_mem_nhds 0 (by linarith : 0 g (fun i => f i t)) := by + classical + induction xs generalizing d f center g with + | nil => exact Puiseux.analytic_comp_tuple_finite hf hlim hg + | cons X xs ih => + obtain ⟨K,hK⟩ := hvalid.sectorData + choose F hF he using fun i => hK.expansion_iff.mp (hf i) + have hXt := hvalid.2.2.1 + have hXc := (hvalid.2.1.real_eventually_analytic hvalid.1).mono + (fun _ h => h.continuousAt) + have hreal : ∀ i,Tendsto (fun t : ℝ => F i (t:ℂ)) atTop (𝓝 (center i)) := + fun i => tendsto_of_comp_clock hXt hXc ((hlim i).congr' (he i)) + choose a v δ hδ ham ha hv hdec hva heq using + fun i => hK.finite_decomposition hvalid (hF i) (hreal i) + obtain ⟨ε,hε,hεδ⟩ := finite_common_positive hδ + have hvs : ∀ i,BoundedExpansionOver K (-ε) (v i) := + fun i => (hv i).mono (neg_le_neg (hεδ i)) + have hvb : ∀ i,ExpBound (-(ε/2)) (v i) := fun i => + (hdec i).mono (by linarith [hεδ i]) + let A : ℂ → Fin d → ℂ := fun z i => a i z + let V : ℂ → Fin d → ℂ := fun z i => v i z + have hAt : Tendsto A sectorInfinity (𝓝 center) := tendsto_pi_nhds.mpr ha + have hVt : Tendsto V sectorInfinity (𝓝 0) := tendsto_pi_nhds.mpr + (fun i => (hvb i).tendsto_zero (by linarith : -(ε/2)<0)) + have hAa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ A z := by + filter_upwards [eventually_all.mpr (fun i => hK.lower.analytic (ham i))] with z hz + exact analyticAt_pi_iff.mpr hz + have hVa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ V z := by + filter_upwards [eventually_all.mpr hva] with z hz + exact analyticAt_pi_iff.mpr hz + have hAVt : Tendsto (fun z => A z+V z) sectorInfinity (𝓝 center) := by + simpa only [add_zero] using hAt.add hVt + obtain ⟨c,hc,r,C,hr,hC,hTaylor⟩ := MovingTaylor.analytic_uniform_moving_taylor hg + let q : (n : ℕ) → (Fin n → Fin d) → (Fin d → ℂ) → ℂ := + fun n j x => c n x (fun i => Pi.single (j i) 1) + have hq : ∀ n j,AnalyticAt ℂ (q n j) center := by + intro n j + exact ((ContinuousMultilinearMap.apply ℂ (fun _ : Fin n => Fin d → ℂ) ℂ + (fun i => Pi.single (j i) 1)).analyticAt _).comp (hc n) + have hqm : ∀ n j,(fun z => q n j (A z))∈K := by + intro n j + apply (hK.membership _).mpr + constructor + · exact ih hvalid.1 (fun i => ((hK.membership _).mp (ham i)).1) + (fun i => (ha i).comp (tendsto_real_sectorInfinity.comp hXt)) (hq n j) + · filter_upwards [hAa,hAt.eventually (hq n j).eventually_analyticAt] with z haz hqz + exact hqz.comp (f := A) haz + let term : ℕ → ℂ → ℂ := fun n z => c n (A z) (fun _ => V z) + have hterm : ∀ n : ℕ,BoundedExpansionOver K (-ε*(n:ℝ)) (term n) := by + intro n + exact BoundedExpansionOver.multilinear hK.lower hvs (hqm n) + have hcomp : ExpansionOver K (fun z => g (A z+V z)) := by + apply BoundedExpansionOver.negative_series hK.lower hε hterm + · filter_upwards [hAa,hVa,hAVt.eventually hg.eventually_analyticAt] with z haz hvz hgz + exact hgz.comp (f := fun z => A z+V z) (haz.add hvz) + · intro B + obtain ⟨N,hN⟩ := exists_nat_gt (-2*B/ε) + filter_upwards [eventually_ge_atTop N] with M hM + refine ⟨-(ε/2)*(M:ℝ),?_,?_⟩ + · have hh := (div_lt_iff₀ hε).mp hN + have hNM : (N:ℝ)≤M := Nat.cast_le.mpr hM + nlinarith + · exact tuple_taylor_expBound hr hC hTaylor hAt (by linarith : 0<ε/2) hvb M + apply hK.expansion_iff.mpr + refine ⟨fun z => g (A z+V z),hcomp,?_⟩ + filter_upwards [eventually_all.mpr he] with t ht + apply congrArg g + ext i + exact (ht i).trans (heq i (X t:ℂ)) + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PathSelection/UniformFamilies.lean b/lean/OAI/Analysis/PathSelection/UniformFamilies.lean new file mode 100644 index 0000000000000000000000000000000000000000..56651180b3ce87e1b4d20cb74f488ef63b0b3bd3 --- /dev/null +++ b/lean/OAI/Analysis/PathSelection/UniformFamilies.lean @@ -0,0 +1,515 @@ +import Mathlib +import OAI.Analysis.PathSelection.RecursiveClocks +import OAI.Analysis.PathSelection.SectorInduction + +namespace OAI + +/-! Coefficient vanishing, uniform clock expansions and holomorphic family limits. -/ + +noncomputable section +open Set Filter Topology Metric Polynomial +open scoped BigOperators NNReal ENNReal + +open Set Filter Topology Complex Metric +namespace DegeneratingTrees + + + +theorem sector_common_zero_of_ray_zero {ι : Type*} {ω : ℝ → ℝ} {R : ℝ} + (hω : AdmissibleAngularLoss ω) {f : ι → ℂ → ℂ} + (hf : ∀ i,AnalyticOnNhd ℂ (f i) (lossSector ω R)) + (hz : ∀ i,∀ᶠ t : ℝ in atTop,f i (t:ℂ)=0) : + ∃ W : ℝ,R≤W ∧ ∀ z∈lossSector ω W,∀ i,f i z=0 := by + obtain ⟨a,t,S,hS,ha,has,ht,hsmall,hcontrol⟩ := angularLoss_kernel_data hω + let W := max (max R S) 1 + have hW0 : 0 < W := lt_of_lt_of_le zero_lt_one (le_max_right _ _) + have hWR : R≤W := (le_max_left _ _).trans (le_max_left _ _) + have hWS : S≤W := (le_max_right _ _).trans (le_max_left _ _) + have hsub : lossSector ω W ⊆ lossSector ω R := fun z hz => ⟨hWR.trans_lt hz.1,hz.2⟩ + have hconn : IsPreconnected (lossSector ω W) := by + apply lossSector_isPreconnected hW0 + intro r hr + have hh := hcontrol r (hWS.trans hr.le) + exact ⟨hh.1,by linarith [hh.2.1,Real.pi_gt_three]⟩ + refine ⟨W,hWR,?_⟩ + intro z hzw i + obtain ⟨T,hT⟩ := eventually_atTop.mp (hz i) + let x := max W T+1 + have hxW : W F (t:ℂ)) atTop (𝓝 c)) + {β : ℝ} (hβ : β∈E) (hβpos : 0<β) : + ∀ᶠ t : ℝ in atTop,b β (t:ℂ)=0 := by + by_contra hn + have ht := hF.trim_zero (fun a ha => hK.analytic (hb a ha)) + have hβn : β∈nonzeroRaySupport E b := ⟨hβ,hn⟩ + obtain ⟨a,ha,hmax⟩ := exists_greatest_of_finite_above ht.finite_above ⟨β,hβn⟩ + have hapos : 0 Complex.exp (((-a:ℝ):ℂ)*z)) := + ⟨-a,by linarith,ExpBound.cexp (-a)⟩ + have h0 := ((he.mul_slow hs).tendsto_zero.comp tendsto_real_sectorInfinity).mul hlim + have heq := tendsto_nhds_unique h0 h1 + exact zero_ne_one (by simpa only [zero_mul] using heq) + +end Clock +end DegeneratingTrees + + + + + + + +open Set Filter Topology Complex +open scoped BigOperators +namespace DegeneratingTrees.Clock +variable {V : Type*} [NormedAddCommGroup V] [NormedSpace ℂ V] + +structure UniformSectorExpansion (F : ℂ → V) (A : Set ℝ) (b : ℝ → ℂ → V) : Prop where + bounded_above : BddAbove A + finite_above : ∀ B : ℝ,(A ∩ Ici B).Finite + remainders : ∀ B : ℝ,∃ (ω : ℝ → ℝ) (R ε C : ℝ), + AdmissibleAngularLoss ω ∧ 0<ε ∧ 0≤C ∧ + AnalyticOnNhd ℂ F (lossSector ω R) ∧ + ∀ z∈lossSector ω R, + ‖F z-∑ β∈(finite_above B).toFinset,Complex.exp ((β:ℂ)*z) • b β z‖ ≤ + C*Real.exp ((B-ε)*z.re) + +lemma UniformSectorExpansion.eventually_analytic [CompleteSpace V] {F : ℂ → V} {A : Set ℝ} {b : ℝ → ℂ → V} + (hF : UniformSectorExpansion F A b) : + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z := by + obtain ⟨ω,R,ε,C,hω,hε,hC,ha,hb⟩ := hF.remainders 0 + exact ⟨ω,R,hω,ha⟩ + +lemma UniformSectorExpansion.scalarize [CompleteSpace V] {F : ℂ → V} {A : Set ℝ} {b : ℝ → ℂ → V} + (hF : UniformSectorExpansion F A b) (L : V →L[ℂ] ℂ) : + SectorExpansion (fun z => L (F z)) A (fun β z => L (b β z)) := by + classical + refine ⟨hF.bounded_above,hF.finite_above,?_⟩ + intro B + obtain ⟨ω,R,ε,C,hω,hε,hC,ha,hb⟩ := hF.remainders B + refine ⟨ω,R,ε,‖L‖*C,hω,hε,mul_nonneg (norm_nonneg _) hC, + fun z hz => (L.analyticAt _).comp (ha z hz),?_⟩ + intro z hz + have hh := (L.le_opNorm (F z-∑ β∈(hF.finite_above B).toFinset, + Complex.exp ((β:ℂ)*z) • b β z)).trans + (mul_le_mul_of_nonneg_left (hb z hz) (norm_nonneg L)) + simpa only [map_sub,map_sum,map_smul,smul_eq_mul,mul_assoc] using hh + + + +lemma uniform_sector_eq_of_ray [CompleteSpace V] {F G : ℂ → V} + (ha : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (hb : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ G z) + (he : (fun t : ℝ => F (t:ℂ)) =ᶠ[atTop] fun t => G (t:ℂ)) : + F =ᶠ[sectorInfinity] G := by + obtain ⟨ω,R,hω,haa⟩ := ha.and hb + obtain ⟨W,hW,hz⟩ := sector_common_zero_of_ray_zero hω + (f := fun (L : V →L[ℂ] ℂ) z => L (F z-G z)) + (fun L z hz => (L.analyticAt _).comp ((haa z hz).1.sub (haa z hz).2)) + (fun L => he.mono (fun t ht => by + change F (t:ℂ)=G (t:ℂ) at ht + rw [ht,sub_self,map_zero])) + refine ⟨ω,W,hω,fun z hz' => sub_eq_zero.mp ?_⟩ + exact SeparatingDual.eq_zero_of_forall_dual_eq_zero (hz z hz') + + + +lemma UniformSectorExpansion.positive_coeff_zero [CompleteSpace V] {K : Set (ℂ → ℂ)} + (hK : LowerSectorData K) {F : ℂ → V} {A : Set ℝ} {b : ℝ → ℂ → V} + (hF : UniformSectorExpansion F A b) + (hba : ∀ β∈A,∀ᶠ z in sectorInfinity,AnalyticAt ℂ (b β) z) + (hb : ∀ (L : V →L[ℂ] ℂ) β,β∈A → (fun z => L (b β z))∈K) + {c : V} (hlim : Tendsto (fun t : ℝ => F (t:ℂ)) atTop (𝓝 c)) + {β : ℝ} (hβ : β∈A) (hβpos : 0<β) : + ∀ᶠ z in sectorInfinity,b β z=0 := by + obtain ⟨ω,R,hω,ha⟩ := hba β hβ + obtain ⟨W,hW,hz⟩ := sector_common_zero_of_ray_zero hω + (f := fun (L : V →L[ℂ] ℂ) z => L (b β z)) + (fun L z hz => (L.analyticAt _).comp (ha z hz)) + (fun L => (hF.scalarize L).positive_coeff_zero_of_limit hK (hb L) + (L.continuous.continuousAt.tendsto.comp hlim) hβ hβpos) + exact ⟨ω,W,hω,fun z hz' => SeparatingDual.eq_zero_of_forall_dual_eq_zero (hz z hz')⟩ + +noncomputable def zeroCoefficient (A : Set ℝ) (b : ℝ → ℂ → V) (z : ℂ) : V := by + classical + exact if 0∈A then b 0 z else 0 + + + +lemma UniformSectorExpansion.zero_cutoff_error [CompleteSpace V] {F : ℂ → V} {A : Set ℝ} {b : ℝ → ℂ → V} + (hF : UniformSectorExpansion F A b) + (hz : ∀ β∈A,0<β → ∀ᶠ z in sectorInfinity,b β z=0) : + Tendsto (fun z => F z-zeroCoefficient A b z) sectorInfinity (𝓝 0) := by + classical + unfold zeroCoefficient + obtain ⟨ω,R,ε,C,hω,hε,hC,hFa,hbound⟩ := hF.remainders 0 + have hh : ∀ᶠ z in sectorInfinity,∀ β∈(hF.finite_above 0).toFinset,β≠0 → b β z=0 := by + rw [Filter.eventually_all_finset] + intro β hβ + by_cases he : β=0 + · exact Eventually.of_forall (fun z hn => (hn he).elim) + · have hb := (hF.finite_above 0).mem_toFinset.mp hβ + exact (hz β hb.1 (lt_of_le_of_ne hb.2 (Ne.symm he))).mono (fun z hz _ => hz) + have hbd : ∀ᶠ z in sectorInfinity, + ‖F z-(if 0∈A then b 0 z else 0)‖≤C*Real.exp (-ε*z.re) := by + filter_upwards [hh,(show ∀ᶠ z in sectorInfinity,z∈lossSector ω R from ⟨ω,R,hω,fun _ h=>h⟩)] with z hz hzr + have hsum : (∑ β∈(hF.finite_above 0).toFinset,Complex.exp ((β:ℂ)*z) • b β z) = + if 0∈A then b 0 z else 0 := by + by_cases h0 : (0:ℝ)∈A + · rw [ite_eq_left h0,Finset.sum_eq_single 0] + · simp + · intro β hβ hβ0; rw [hz β hβ hβ0,smul_zero] + · intro hn + exact False.elim (hn ((hF.finite_above 0).mem_toFinset.mpr ⟨h0,by simp⟩)) + · rw [ite_eq_right h0] + apply Finset.sum_eq_zero + intro β hβ + have hn : β≠0 := by + intro he; subst β + exact h0 ((hF.finite_above 0).mem_toFinset.mp hβ).1 + rw [hz β hβ hn,smul_zero] + simpa only [hsum,zero_sub] using hbound z hzr + apply tendsto_zero_iff_norm_tendsto_zero.mpr + have ht : Tendsto (fun z : ℂ => C*Real.exp (-ε*z.re)) sectorInfinity (𝓝 0) := by + simpa only [Function.comp_apply,mul_zero] using (Real.tendsto_exp_atBot.comp + ((tendsto_const_mul_atBot_of_neg (show -ε<0 by linarith)).mpr + tendsto_re_sectorInfinity)).const_mul C + exact squeeze_zero' (Eventually.of_forall (fun _ => norm_nonneg _)) hbd ht + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock +variable {V : Type*} [NormedAddCommGroup V] [NormedSpace ℂ V] + +def UniformPuiseux (f : ℝ → V) : Prop := + ∃ n : ℕ,0 (rootCoord n t:ℂ)^m • F (rootCoord n t) + +lemma UniformPuiseux.scalarize [CompleteSpace V] {f : ℝ → V} (hf : UniformPuiseux f) + (L : V →L[ℂ] ℂ) : Puiseux (fun t => L (f t)) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + refine ⟨n,hn,m,fun z => L (F z),(L.analyticAt _).comp hF,?_⟩ + filter_upwards [he] with t ht + rw [ht,map_smul] + simp only [←Complex.ofReal_zpow,Complex.real_smul,smul_eq_mul] + +lemma UniformPuiseux.normalize [CompleteSpace V] {f : ℝ → V} (hf : UniformPuiseux f) + (hne : ¬ f =ᶠ[atTop] fun _ => 0) : + ∃ n : ℕ,0 (rootCoord n t:ℂ)^m • F (rootCoord n t) := by + obtain ⟨n,hn,m,F,hF,he⟩ := hf + have hFne : ¬ F =ᶠ[𝓝 0] fun _ => 0 := by + intro h0; apply hne + filter_upwards [he,(rootCoord_complex_tendsto_zero hn).eventually h0] with t ht hz + simp [ht,hz] + obtain ⟨k,G,hG,hG0,hfac⟩ := hF.exists_eventuallyEq_pow_smul_nonzero_iff.mpr hFne + refine ⟨n,hn,m+(k:ℤ),G,hG,hG0,?_⟩ + filter_upwards [he,(rootCoord_complex_tendsto_zero hn).eventually hfac, + eventually_gt_atTop (0:ℝ)] with t ht hfac htpos + have hr : (rootCoord n t:ℂ)≠0 := Complex.ofReal_ne_zero.mpr (rootCoord_pos htpos).ne' + rw [ht,hfac,sub_zero,zpow_add₀ hr,zpow_natCast,smul_smul] + +lemma UniformPuiseux.finite_limit_nonnegative [CompleteSpace V] {f : ℝ → V} {d : V} + (hlim : Tendsto f atTop (𝓝 d)) {n : ℕ} (hn : 0 (rootCoord n t:ℂ)^m • F (rootCoord n t)) : + 0 ≤ m := by + by_contra hmn + have hm : m<0 := lt_of_not_ge hmn + let k : ℕ := (-m).toNat + have hk : 0 (rootCoord n t:ℂ)^k • f t) atTop (𝓝 0) := by + simpa only [zero_pow hk.ne',zero_smul] using ((rootCoord_complex_tendsto_zero hn).pow k).smul hlim + have he' : (fun t => (rootCoord n t:ℂ)^k • f t) =ᶠ[atTop] + fun t => F (rootCoord n t) := by + filter_upwards [he,eventually_gt_atTop (0:ℝ)] with t ht htpos + have hr : (rootCoord n t:ℂ)≠0 := Complex.ofReal_ne_zero.mpr (rootCoord_pos htpos).ne' + rw [ht,smul_smul,←zpow_natCast,←zpow_add₀ hr,hkm,neg_add_cancel,zpow_zero,one_smul] + exact hF0 (tendsto_nhds_unique (hF.continuousAt.tendsto.comp + (rootCoord_complex_tendsto_zero hn)) (h0.congr' he')) + + + +lemma UniformPuiseux.finite_limit_representative [CompleteSpace V] {f : ℝ → V} (hf : UniformPuiseux f) + {d : V} (hlim : Tendsto f atTop (𝓝 d)) : + ∃ (G : ℂ → V) (R : ℝ), + (∀ z : ℂ,R<‖z‖ → 0 G (t:ℂ)) ∧ Tendsto G radialInfinity (𝓝 d) := by + by_cases hz : f =ᶠ[atTop] fun _ => 0 + · have hd : d=0 := tendsto_nhds_unique hlim (tendsto_const_nhds.congr' hz.symm) + subst d + exact ⟨fun _ => 0,0,fun _ _ _ => analyticAt_const,hz,tendsto_const_nhds⟩ + obtain ⟨n,hn,m,F,hF,hF0,he⟩ := hf.normalize hz + have hm := UniformPuiseux.finite_limit_nonnegative hlim hn hF hF0 he + let k := m.toNat + have hkm : (k:ℤ)=m := Int.toNat_of_nonneg hm + let G : ℂ → V := fun z => (complexRoot n z)^k • F (complexRoot n z) + have heG : f =ᶠ[atTop] fun t => G (t:ℂ) := by + filter_upwards [he,eventually_gt_atTop (0:ℝ)] with t ht htpos + simpa only [G,complexRoot_real htpos.le,←zpow_natCast,hkm] using ht + have hconst : d=(0:ℂ)^k • F 0 := by + have ht := ((rootCoord_complex_tendsto_zero hn).pow k).smul + (hF.continuousAt.tendsto.comp (rootCoord_complex_tendsto_zero hn)) + apply tendsto_nhds_unique hlim + apply ht.congr' + filter_upwards [he] with t ht + simpa only [Function.comp_apply,←zpow_natCast,hkm] using ht.symm + obtain ⟨R,hR⟩ := radial_eventually ((complexRoot_tendsto_zero hn).eventually hF.eventually_analyticAt) + refine ⟨G,R,?_,heG,?_⟩ + · intro z hz hzre + have hr := complexRoot_analytic (n := n) hzre + exact (hr.pow k).smul ((hR z hz).comp hr) + · rw [hconst] + exact ((complexRoot_tendsto_zero hn).pow k).smul + (hF.continuousAt.tendsto.comp (complexRoot_tendsto_zero hn)) + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock +variable {V : Type*} [NormedAddCommGroup V] [NormedSpace ℂ V] [CompleteSpace V] + +def UniformClockGerm : List (ℝ → ℝ) → (ℝ → V) → Prop + | [], f => UniformPuiseux f + | X::xs,f => ∃ (F : ℂ → V) (A : Set ℝ) (b : ℝ → ℂ → V), + UniformSectorExpansion F A b ∧ + (∀ β∈A,UniformClockGerm xs (fun t => b β (X t:ℂ)) ∧ + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (b β) z) ∧ + f =ᶠ[atTop] fun t => F (X t:ℂ) + +lemma UniformClockGerm.scalarize {xs : List (ℝ → ℝ)} {f : ℝ → V} + (hf : UniformClockGerm xs f) (L : V →L[ℂ] ℂ) : ClockGerm xs (fun t => L (f t)) := by + induction xs generalizing f with + | nil => exact UniformPuiseux.scalarize hf L + | cons X xs ih => + obtain ⟨F,A,b,hF,hb,he⟩ := hf + refine ⟨fun z => L (F z),A,fun β z => L (b β z),hF.scalarize L,?_,?_⟩ + · intro β hβ + exact ⟨ih (hb β hβ).1,((hb β hβ).2).mono (fun z ha => (L.analyticAt _).comp ha)⟩ + · exact he.mono (fun _ he => congrArg L he) + + + +lemma UniformPuiseux.first_clock_limit {f : ℝ → V} (hf : UniformPuiseux f) + {X : ℝ → ℝ} {a : ℝ} (ha : 0 a*t) + {F : ℂ → V} (hFa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (he : f =ᶠ[atTop] fun t => F (X t:ℂ)) {d : V} + (hlim : Tendsto f atTop (𝓝 d)) : Tendsto F sectorInfinity (𝓝 d) := by + obtain ⟨G,R,hGa,heG,hGt⟩ := hf.finite_limit_representative hlim + have ha0 : (a:ℂ)≠0 := Complex.ofReal_ne_zero.mpr ha.ne' + let I : ℂ → ℂ := fun z => z/(a:ℂ) + have hIt : Tendsto I sectorInfinity radialInfinity := by + rw [radialInfinity,tendsto_comap_iff] + simpa only [I,Function.comp_def,norm_div,Complex.norm_of_nonneg ha.le] using + tendsto_norm_sectorInfinity.atTop_div_const ha + have hIa : ∀ z : ℂ,AnalyticAt ℂ I z := fun z => analyticAt_id.div_const + have hGIa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => G (I z)) z := by + have hn : ∀ᶠ z in sectorInfinity,R<‖I z‖ := + (tendsto_comap_iff.mp hIt).eventually (eventually_gt_atTop R) + filter_upwards [hn,tendsto_re_sectorInfinity.eventually (eventually_gt_atTop (0:ℝ))] + with z hz hre + have hIre : 0<(I z).re := by + simpa only [I,Complex.div_ofReal_re] using div_pos hre ha + exact (hGa (I z) hz hIre).comp (hIa z) + have hline : (fun t : ℝ => F (t:ℂ)) =ᶠ[atTop] fun t => G (I (t:ℂ)) := by + have hscale : Tendsto (fun t : ℝ => t/a) atTop atTop := tendsto_id.atTop_div_const ha + filter_upwards [hscale.eventually he,hscale.eventually heG,hscale.eventually hX] with t he heG hX + change f (t/a)=F (X (t/a):ℂ) at he + change f (t/a)=G (t/a:ℝ) at heG + have hx : X (t/a)=t := by rw [hX]; field_simp + rw [hx] at he + simpa only [I,←Complex.ofReal_div] using he.symm.trans heG + exact (hGt.comp hIt).congr' (uniform_sector_eq_of_ray hFa hGIa hline).symm + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +open scoped Asymptotics +namespace DegeneratingTrees.Clock + +lemma tendsto_of_comp_clock {W : Type*} {l : Filter W} {F : ℝ → W} + {X : ℝ → ℝ} (hXt : Tendsto X atTop atTop) + (hXc : ∀ᶠ t in atTop,ContinuousAt X t) + (hF : Tendsto (fun t => F (X t)) atTop l) : Tendsto F atTop l := by + rw [Filter.tendsto_def] at hF ⊢ + intro s hs + exact eventually_of_comp_clock hXt hXc (hF s hs) + +lemma ValidClocks.previous_chart {xs : List (ℝ → ℝ)} {X Y : ℝ → ℝ} + (hvalid : ValidClocks (X::Y::xs)) : + ∃ y : ℂ → ℂ,(∀ᶠ z in sectorInfinity,AnalyticAt ℂ y z) ∧ + Tendsto y sectorInfinity sectorInfinity ∧ + (∀ᶠ t : ℝ in atTop,y (X t:ℂ)=(Y t:ℂ)) := by + obtain ⟨K,hD⟩ := hvalid.1.sectorData + have hYt := hvalid.1.2.2.1 + have hXt := hvalid.2.2.1 + have hYc := (hvalid.1.2.1.real_eventually_analytic hvalid.1.1).mono (fun _ h => h.continuousAt) + obtain ⟨H,hH,he⟩ := hD.expansion_iff.mp hvalid.2.1 + have hHr : ∀ᶠ t : ℝ in atTop,(H (t:ℂ)).im=0 ∧ 0<(H (t:ℂ)).re := by + apply eventually_of_comp_clock hYt hYc + filter_upwards [he,hXt.eventually (eventually_gt_atTop 0)] with t he hx + rw [←he] + exact ⟨rfl,hx⟩ + have hHt : Tendsto (fun t : ℝ => (H (t:ℂ)).re) atTop atTop := by + apply tendsto_of_comp_clock hYt hYc + apply hXt.congr' + exact he.mono (fun t ht => (congrArg Complex.re ht)) + have hfast : id =o[atTop] (fun t : ℝ => (H (t:ℂ)).re) := by + apply Asymptotics.IsLittleO.of_bound + intro ε hε + apply eventually_of_comp_clock hYt hYc + filter_upwards [he,hvalid.2.2.2.def hε] with t he ht + change ‖Y t‖≤ε*‖(H (Y t:ℂ)).re‖ + rwa [←he] + obtain ⟨y,I,hi,hfamily⟩ := hD.charts H hH hHr hHt hfast + refine ⟨y,hi.analytic_left.mono (fun _ h => h.1),hi.maps_sector,?_⟩ + filter_upwards [he,hYt.eventually hi.right] with t he hy + rwa [he] + +end DegeneratingTrees.Clock + + + + + + + +open Set Filter Topology Complex +namespace DegeneratingTrees.Clock +variable {V : Type*} [NormedAddCommGroup V] [NormedSpace ℂ V] [CompleteSpace V] + +lemma uniform_expansion_limit {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} + (hvalid : ValidClocks (X::xs)) {F : ℂ → V} {A : Set ℝ} {b : ℝ → ℂ → V} + (hF : UniformSectorExpansion F A b) + (hb : ∀ β∈A,UniformClockGerm xs (fun t => b β (X t:ℂ)) ∧ + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (b β) z) + (hlower : ∀ β∈A,∀ c : V,Tendsto (fun t => b β (X t:ℂ)) atTop (𝓝 c) → + Tendsto (b β) sectorInfinity (𝓝 c)) + {d : V} (hlim : Tendsto (fun t => F (X t:ℂ)) atTop (𝓝 d)) : + Tendsto F sectorInfinity (𝓝 d) := by + classical + obtain ⟨K,hD⟩ := hvalid.sectorData + have hXt := hvalid.2.2.1 + have hXc := (hvalid.2.1.real_eventually_analytic hvalid.1).mono (fun _ h => h.continuousAt) + have hreal : Tendsto (fun t : ℝ => F (t:ℂ)) atTop (𝓝 d) := + tendsto_of_comp_clock hXt hXc hlim + have hmembers : ∀ (L : V →L[ℂ] ℂ) β,β∈A → (fun z => L (b β z))∈K := by + intro L β hβ + exact (hD.membership _).mpr ⟨(hb β hβ).1.scalarize L, + ((hb β hβ).2).mono (fun z ha => (L.analyticAt _).comp ha)⟩ + have hz : ∀ β∈A,0<β → ∀ᶠ z in sectorInfinity,b β z=0 := + fun β hβ hpos => hF.positive_coeff_zero hD.lower + (fun β hβ => (hb β hβ).2) hmembers hreal hβ hpos + have herr := hF.zero_cutoff_error hz + have hBs : Tendsto (fun t => zeroCoefficient A b (X t:ℂ)) atTop (𝓝 d) := by + simpa only [sub_sub_cancel,sub_zero,Function.comp_apply] using + hlim.sub (herr.comp (tendsto_real_sectorInfinity.comp hXt)) + have hBb : Tendsto (zeroCoefficient A b) sectorInfinity (𝓝 d) := by + change Tendsto (fun z => if (0:ℝ)∈A then b 0 z else 0) sectorInfinity (𝓝 d) + by_cases h0 : (0:ℝ)∈A + · simpa only [zeroCoefficient,ite_eq_left h0] using + hlower 0 h0 d (by simpa only [zeroCoefficient,ite_eq_left h0] using hBs) + · have hd : d=0 := tendsto_nhds_unique + (show Tendsto (fun _ : ℝ => (0:V)) atTop (𝓝 d) by + simpa only [zeroCoefficient,ite_eq_right h0] using hBs) tendsto_const_nhds + subst d + simpa only [zeroCoefficient,ite_eq_right h0] using + (tendsto_const_nhds : Tendsto (fun _ : ℂ => (0:V)) sectorInfinity (𝓝 0)) + simpa only [sub_add_cancel,zero_add] using herr.add hBb + + + +theorem UniformClockGerm.model_limit {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} + (hvalid : ValidClocks (X::xs)) {f : ℝ → V} (hf : UniformClockGerm xs f) + {F : ℂ → V} (hFa : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ F z) + (he : f =ᶠ[atTop] fun t => F (X t:ℂ)) {d : V} + (hlim : Tendsto f atTop (𝓝 d)) : Tendsto F sectorInfinity (𝓝 d) := by + induction xs generalizing X f F d with + | nil => + obtain ⟨a,ha,hX⟩ := hvalid.2.2.2 + exact UniformPuiseux.first_clock_limit hf ha hX hFa he hlim + | cons Y ys ih => + obtain ⟨G,A,b,hG,hb,heG⟩ := hf + have hGt : Tendsto G sectorInfinity (𝓝 d) := + uniform_expansion_limit hvalid.1 hG hb + (fun β hβ c hc => ih hvalid.1 (hb β hβ).1 (hb β hβ).2 EventuallyEq.rfl hc) + (hlim.congr' heG) + obtain ⟨y,hya,hyt,hyr⟩ := hvalid.previous_chart + have hGya : ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (fun z => G (y z)) z := by + filter_upwards [hya,hyt.eventually hG.eventually_analytic] with z hy hg + exact hg.comp hy + have hfg : F =ᶠ[sectorInfinity] fun z => G (y z) := by + apply uniform_sector_eq_of_ray hFa hGya + have hXc := (hvalid.2.1.real_eventually_analytic hvalid.1).mono (fun _ h => h.continuousAt) + apply eventually_of_comp_clock hvalid.2.2.1 hXc + filter_upwards [he,heG,hyr] with t he heG hy + rw [hy,←he,←heG] + exact (hGt.comp hyt).congr' hfg.symm + + + +theorem UniformClockGerm.last_clock_limit {xs : List (ℝ → ℝ)} {X : ℝ → ℝ} + (hvalid : ValidClocks (X::xs)) {F : ℂ → V} {A : Set ℝ} {b : ℝ → ℂ → V} + (hF : UniformSectorExpansion F A b) + (hb : ∀ β∈A,UniformClockGerm xs (fun t => b β (X t:ℂ)) ∧ + ∀ᶠ z in sectorInfinity,AnalyticAt ℂ (b β) z) + {d : V} (hlim : Tendsto (fun t => F (X t:ℂ)) atTop (𝓝 d)) : + Tendsto F sectorInfinity (𝓝 d) := + uniform_expansion_limit hvalid hF hb + (fun β hβ c hc => (hb β hβ).1.model_limit hvalid (hb β hβ).2 EventuallyEq.rfl (d := c) hc) hlim + +end DegeneratingTrees.Clock +end + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Arithmetic.lean b/lean/OAI/Analysis/PeriodicLattice/Arithmetic.lean new file mode 100644 index 0000000000000000000000000000000000000000..c1e5348036cc9ab7337f3cf325d9c61513b0b68b --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Arithmetic.lean @@ -0,0 +1,260 @@ +import OAI.Analysis.PeriodicLattice.ProfileJets + +namespace OAI + +/-! Recursive arithmetic and effective profile syntax. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingArithmetic {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace RecursiveArithmetic +open Encodable Primrec + +theorem natPow : Primrec₂ (fun a b : ℕ => a ^ b) := + Primrec₂.unpaired'.mp Nat.Primrec.pow + +theorem factorial : Primrec Nat.factorial := by + have h := Primrec.nat_rec₁ (1 : ℕ) + ((Primrec.nat_mul.comp (Primrec.succ.comp Primrec.fst) Primrec.snd).to₂) + exact h.of_eq (fun n => by induction n <;> simp [Nat.factorial, *]) + +@[simp] theorem encode_int_ofNat (n : ℕ) : encode (n : ℤ) = 2 * n := rfl +@[simp] theorem encode_int_negSucc (n : ℕ) : encode (Int.negSucc n) = 2 * n + 1 := rfl + +theorem intOfNat : Primrec (fun n : ℕ => (n : ℤ)) := + Primrec.encode_iff.mp (Primrec.nat_double.of_eq (fun _ => rfl)) + +theorem intNegSucc : Primrec Int.negSucc := + Primrec.encode_iff.mp (Primrec.nat_double_succ.of_eq (fun _ => rfl)) + +theorem intNatAbs : Primrec Int.natAbs := by + have h := Primrec.cond (Primrec.nat_bodd.comp (Primrec.encode : Primrec (encode : ℤ → ℕ))) + (Primrec.succ.comp (Primrec.nat_div2.comp Primrec.encode)) + (Primrec.nat_div2.comp Primrec.encode) + exact h.of_eq (fun z => by cases z <;> simp [Nat.bodd, Nat.div2_val, show (2 : ℕ) ≠ 0 from by decide]) + +theorem intNegative : PrimrecPred (fun z : ℤ => z < 0) := by + refine ⟨inferInstance, ?_⟩ + exact (Primrec.nat_bodd.comp Primrec.encode).of_eq (fun z => by + cases z <;> simp [Nat.bodd]) + +theorem intAbsSign {α β : Type*} [Primcodable α] [Primcodable β] + {f : α → ℤ} {g h : α → ℕ → β} (hf : Primrec f) (hg : Primrec₂ g) (hh : Primrec₂ h) : + Primrec (fun a => if f a < 0 then h a (f a).natAbs else g a (f a).natAbs) := + Primrec.ite (intNegative.comp hf) (hh.comp Primrec.id (intNatAbs.comp hf)) + (hg.comp Primrec.id (intNatAbs.comp hf)) + +theorem intNeg : Primrec (fun z : ℤ => -z) := by + have hc : Primrec (fun z : ℤ => if z < 0 then (z.natAbs : ℤ) + else if z.natAbs = 0 then 0 else Int.negSucc (z.natAbs - 1)) := + Primrec.ite intNegative (intOfNat.comp intNatAbs) + (Primrec.ite (Primrec.eq.comp intNatAbs (Primrec.const 0)) (Primrec.const 0) + (intNegSucc.comp (Primrec.nat_sub.comp intNatAbs (Primrec.const 1)))) + exact hc.of_eq (fun z => by cases z <;> simp; split_ifs <;> omega) + +theorem intSubNat : Primrec₂ (fun a b : ℕ => (a : ℤ) - b) := by + have hc : Primrec (fun p : ℕ × ℕ => if p.2 ≤ p.1 then ((p.1 - p.2 : ℕ) : ℤ) + else Int.negSucc (p.2 - p.1 - 1)) := + Primrec.ite (Primrec.nat_le.comp Primrec.snd Primrec.fst) + (intOfNat.comp (Primrec.nat_sub.comp Primrec.fst Primrec.snd)) + (intNegSucc.comp (Primrec.nat_sub.comp (Primrec.nat_sub.comp Primrec.snd Primrec.fst) (Primrec.const 1))) + exact hc.of_eq (fun p => by dsimp only; split_ifs <;> omega) + +theorem intAdd : Primrec₂ (fun a b : ℤ => a + b) := by + have ap := Primrec.fst (α := ℤ) (β := ℤ) + have bp := Primrec.snd (α := ℤ) (β := ℤ) + have aa := intNatAbs.comp ap + have ab := intNatAbs.comp bp + have hp := intOfNat.comp (Primrec.nat_add.comp aa ab) + have hc := Primrec.ite (intNegative.comp ap) + (Primrec.ite (intNegative.comp bp) (intNeg.comp hp) (intSubNat.comp ab aa)) + (Primrec.ite (intNegative.comp bp) (intSubNat.comp aa ab) hp) + exact hc.of_eq (fun p => by + rcases p with ⟨a,b⟩ + cases a <;> cases b <;> + simp only [Int.natAbs_natCast, Int.natAbs_negSucc, Int.ofNat_eq_natCast, + Int.negSucc_lt_zero, not_lt_of_ge (Int.natCast_nonneg _), ↓reduceIte] + all_goals simp [Int.negSucc_eq] <;> omega) + +theorem intSub : Primrec₂ (fun a b : ℤ => a - b) := + (intAdd.comp Primrec.fst (intNeg.comp Primrec.snd)).of_eq (fun _ => by simp [sub_eq_add_neg]) + +theorem intMul : Primrec₂ (fun a b : ℤ => a * b) := by + have ap := Primrec.fst (α := ℤ) (β := ℤ) + have bp := Primrec.snd (α := ℤ) (β := ℤ) + have hp := intOfNat.comp (Primrec.nat_mul.comp (intNatAbs.comp ap) (intNatAbs.comp bp)) + have hc := Primrec.ite (intNegative.comp ap) + (Primrec.ite (intNegative.comp bp) hp (intNeg.comp hp)) + (Primrec.ite (intNegative.comp bp) (intNeg.comp hp) hp) + exact hc.of_eq (fun p => by + rcases p with ⟨a,b⟩ + cases a <;> cases b <;> + simp only [Int.natAbs_natCast, Int.natAbs_negSucc, Int.ofNat_eq_natCast, + Int.negSucc_lt_zero, not_lt_of_ge (Int.natCast_nonneg _), ↓reduceIte] + all_goals simp [Int.negSucc_eq] <;> ring) + +theorem intLE : PrimrecRel (fun a b : ℤ => a ≤ b) := by + exact (intNegative.comp (intSub.comp Primrec.snd Primrec.fst)).not.of_eq (fun p => by dsimp only; omega) + +end RecursiveArithmetic + +attribute [fun_prop] Primrec +attribute [fun_prop] Primrec.id Primrec.const Primrec.comp Primrec.pair Primrec.fst Primrec.snd +attribute [fun_prop] RecursiveArithmetic.intOfNat RecursiveArithmetic.intNatAbs +attribute [fun_prop] RecursiveArithmetic.intNeg RecursiveArithmetic.factorial +namespace RecursiveArithmetic +@[fun_prop] theorem int_add : Primrec (fun p : ℤ × ℤ => p.1 + p.2) := intAdd +@[fun_prop] theorem int_sub : Primrec (fun p : ℤ × ℤ => p.1 - p.2) := intSub +@[fun_prop] theorem int_mul : Primrec (fun p : ℤ × ℤ => p.1 * p.2) := intMul +@[fun_prop] theorem nat_add : Primrec (fun p : ℕ × ℕ => p.1 + p.2) := Primrec.nat_add +@[fun_prop] theorem nat_sub : Primrec (fun p : ℕ × ℕ => p.1 - p.2) := Primrec.nat_sub +@[fun_prop] theorem nat_mul : Primrec (fun p : ℕ × ℕ => p.1 * p.2) := Primrec.nat_mul +@[fun_prop] theorem nat_pow : Primrec (fun p : ℕ × ℕ => p.1 ^ p.2) := natPow +@[fun_prop] theorem nat_div : Primrec (fun p : ℕ × ℕ => p.1 / p.2) := Primrec.nat_div +@[fun_prop] theorem nat_mod : Primrec (fun p : ℕ × ℕ => p.1 % p.2) := Primrec.nat_mod +@[fun_prop] theorem nat_max : Primrec (fun p : ℕ × ℕ => max p.1 p.2) := Primrec.nat_max +@[fun_prop] theorem natSucc : Primrec Nat.succ := Primrec.succ + +@[fun_prop] theorem list_cons {α : Type*} [Primcodable α] : + Primrec (fun p : α × List α => p.1 :: p.2) := Primrec.list_cons + +@[fun_prop] theorem list_append {α : Type*} [Primcodable α] : + Primrec (fun p : List α × List α => p.1 ++ p.2) := Primrec.list_append + +@[fun_prop] theorem natListSum : Primrec (List.sum : List ℕ → ℕ) := + (Primrec.list_foldr Primrec.id (Primrec.const 0) (Primrec.nat_add.comp (Primrec.fst.comp Primrec.snd) (Primrec.snd.comp Primrec.snd)).to₂).of_eq + (fun l => by dsimp only; induction l <;> simp_all) + +@[fun_prop] theorem natListProd : Primrec (List.prod : List ℕ → ℕ) := + (Primrec.list_foldr Primrec.id (Primrec.const 1) (Primrec.nat_mul.comp (Primrec.fst.comp Primrec.snd) (Primrec.snd.comp Primrec.snd)).to₂).of_eq + (fun l => by dsimp only; induction l <;> simp_all) + +end RecursiveArithmetic + +namespace RecursiveArithmetic +@[fun_prop] theorem bool_cond {α β : Type*} [Primcodable α] [Primcodable β] + {p : α → Bool} {f g : α → β} (hp : Primrec p) (hf : Primrec f) (hg : Primrec g) : + Primrec (fun a => if p a then f a else g a) := + (Primrec.cond hp hf hg).of_eq (fun a => by cases p a <;> rfl) + +@[fun_prop] theorem listMap {α β γ : Type*} [Primcodable α] [Primcodable β] [Primcodable γ] + {f : α → List β} {g : α × β → γ} (hf : Primrec f) (hg : Primrec g) : + Primrec (fun a => (f a).map (fun b => g (a,b))) := Primrec.list_map hf hg + +@[fun_prop] theorem listFlatMap {α β γ : Type*} [Primcodable α] [Primcodable β] [Primcodable γ] + {f : α → List β} {g : α × β → List γ} (hf : Primrec f) (hg : Primrec g) : + Primrec (fun a => (f a).flatMap (fun b => g (a,b))) := Primrec.list_flatMap hf hg +end RecursiveArithmetic + +namespace ProfileJets +open RecursiveArithmetic + +@[fun_prop] theorem factorBound_primrec : Primrec factorBound := by + unfold factorBound; fun_prop +@[fun_prop] theorem productBound_primrec : Primrec productBound := by + exact natListProd.comp (Primrec.list_map Primrec.id (factorBound_primrec.comp Primrec.snd).to₂) +@[fun_prop] theorem termBound_primrec : Primrec termBound := by + unfold termBound; fun_prop +@[fun_prop] theorem bound_primrec : Primrec bound := by + exact natListSum.comp (Primrec.list_map Primrec.id (termBound_primrec.comp Primrec.snd).to₂) + +@[fun_prop] theorem multPrefix_primrec : + Primrec (fun p : ℤ × List Factor × Expr => multPrefix p.1 p.2.1 p.2.2) := by + have hh : Primrec (fun p : (ℤ × List Factor × Expr) × Term => + (p.1.1 * p.2.1, p.1.2.1 ++ p.2.2)) := by fun_prop + exact Primrec.list_map (Primrec.snd.comp Primrec.snd) hh.to₂ + +@[fun_prop] theorem diffFactor_primrec : Primrec diffFactor := by + unfold diffFactor; fun_prop + +@[fun_prop] theorem diffProduct_primrec : Primrec diffProduct := by + have hh : Primrec (fun p : List Factor × Factor × List Factor × Expr => + multPrefix 1 p.2.2.1 (diffFactor p.2.1) ++ multPrefix 1 [p.2.1] p.2.2.2) := by + fun_prop + exact (Primrec.list_rec Primrec.id (Primrec.const []) hh.to₂).of_eq + (fun l => by dsimp only; induction l <;> simp_all [diffProduct]) + +@[fun_prop] theorem diffTerm_primrec : Primrec diffTerm := by + unfold diffTerm; fun_prop +@[fun_prop] theorem diff_primrec : Primrec diff := by + exact Primrec.list_flatMap Primrec.id (diffTerm_primrec.comp Primrec.snd).to₂ +@[fun_prop] theorem jet_primrec : Primrec (fun p : Expr × ℕ => jet p.1 p.2) := by + exact Primrec.nat_iterate Primrec.snd Primrec.fst (diff_primrec.comp Primrec.snd) + +@[fun_prop] theorem pulseBound_primrec : Primrec pulseBound := by + unfold pulseBound; fun_prop +@[fun_prop] theorem bumpBound_primrec : Primrec bumpBound := by + unfold bumpBound; fun_prop +end ProfileJets + +namespace RecursiveArithmetic +@[fun_prop] theorem inputMachine : Primrec Input.machine := + Primrec.fst.comp (Primrec.of_equiv (e := Input.codeEquiv)) +@[fun_prop] theorem inputWord : Primrec Input.word := + Primrec.snd.comp (Primrec.of_equiv (e := Input.codeEquiv)) +@[fun_prop] theorem machineStates : Primrec Machine.states := + Primrec.fst.comp (Primrec.of_equiv (e := Machine.codeEquiv)) +@[fun_prop] theorem machineSymbols : Primrec Machine.symbols := + (Primrec.fst.comp Primrec.snd).comp (Primrec.of_equiv (e := Machine.codeEquiv)) +@[fun_prop] theorem machineStart : Primrec Machine.start := + (Primrec.fst.comp (Primrec.snd.comp Primrec.snd)).comp (Primrec.of_equiv (e := Machine.codeEquiv)) +@[fun_prop] theorem listLength {α : Type*} [Primcodable α] : Primrec (List.length : List α → ℕ) := + Primrec.list_length + +@[fun_prop] theorem ofDigits : Primrec (fun p : ℕ × List ℕ => Nat.ofDigits p.1 p.2) := by + have hg : Primrec (fun p : (ℕ × List ℕ) × ℕ × ℕ => p.2.1 + p.1.1 * p.2.2) := by fun_prop + exact (Primrec.list_foldr Primrec.snd (Primrec.const 0) hg.to₂).of_eq + (fun p => by dsimp only; induction p.2 <;> simp_all [Nat.ofDigits]) + +@[fun_prop] theorem sumRange {α : Type*} [Primcodable α] {f : α → ℕ} {g : α → ℕ → ℕ} + (hf : Primrec f) (hg : Primrec₂ g) : + Primrec (fun a => ∑ i ∈ Finset.range (f a), g a i) := by + have hh := natListSum.comp (Primrec.list_map (Primrec.list_range.comp hf) hg) + exact hh.of_eq (fun a => by simpa only [List.toFinset_range] using (List.sum_toFinset (g a) List.nodup_range).symm) +end RecursiveArithmetic + +namespace CompilerPlanar +@[fun_prop] theorem radix_primrec : Primrec radix := by unfold radix; fun_prop +@[fun_prop] theorem loadingCode_primrec : Primrec loadingCode := by + have he : loadingCode = fun d => Nat.ofDigits (radix d) d.word * radix d ^ (d.word.length+1) + + d.machine.start * radix d ^ (2*(d.word.length+1)) := by + funext d + simp [loadingCode, StackCode.configurationCode, StackCode.stackExecution, + StackCode.initialCode, StackCode.pack, Scales.width] + rw [pow_mul]; ring + rw [he]; fun_prop +end CompilerPlanar + +namespace Scales +open RecursiveArithmetic +@[fun_prop] theorem capacity_primrec : Primrec (fun p : ℕ × ℕ × ℕ => capacity p.1 p.2.1 p.2.2) := by + unfold capacity codeExponent width; fun_prop +@[fun_prop] theorem exponent_primrec : Primrec (fun p : ℕ × ℕ => exponent p.1 p.2) := by + unfold exponent codeExponent width; fun_prop +@[fun_prop] theorem crudeSlotBound_primrec : + Primrec (fun p : ℕ × ℕ × ℕ × ℕ => crudeSlotBound p.1 p.2.1 p.2.2.1 p.2.2.2) := by + unfold crudeSlotBound; fun_prop +@[fun_prop] theorem allSlotsBound_primrec : + Primrec (fun p : ℕ × ℕ × ℕ × ℕ => allSlotsBound p.1 p.2.1 p.2.2.1 p.2.2.2) := by + have h : Primrec (fun p : ℕ × ℕ × ℕ × ℕ => + ∑ n ∈ Finset.range (max 1 p.2.2.1), (n+3)^p.2.2.2 * crudeSlotBound p.1 p.2.1 p.2.2.1 n) := by + have hg : Primrec (fun p : (ℕ × ℕ × ℕ × ℕ) × ℕ => + (p.2+3)^p.1.2.2.2 * crudeSlotBound p.1.1 p.1.2.1 p.1.2.2.1 p.2) := by fun_prop + exact sumRange (by fun_prop) hg.to₂ + unfold allSlotsBound weightBound + exact Primrec.nat_add.comp (by fun_prop) h +end Scales +namespace Planar +@[fun_prop] theorem planarBound_primrec : Primrec (fun p : ℕ × ℕ × ℕ × ℕ × ℕ × ℕ × ℕ => + planarBound p.1 p.2.1 p.2.2.1 p.2.2.2.1 p.2.2.2.2.1 p.2.2.2.2.2.1 p.2.2.2.2.2.2) := by + unfold planarBound; fun_prop +end Planar + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Basic.lean b/lean/OAI/Analysis/PeriodicLattice/Basic.lean new file mode 100644 index 0000000000000000000000000000000000000000..3392b7e268f15f1df9c900d12f14d937f644ee51 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Basic.lean @@ -0,0 +1,257 @@ +import Mathlib + +namespace OAI + +/-! Finite machines, computable names, torus fields and the lattice conclusion. -/ + +namespace PeriodicLattice + +theorem neZeroThree : NeZero 3 := ⟨Nat.succ_ne_zero 2⟩ +theorem twoAtLeastTwo : Nat.AtLeastTwo 2 := ⟨Nat.le_refl 2⟩ +theorem threeAtLeastTwo : Nat.AtLeastTwo 3 := ⟨by decide⟩ +theorem fourAtLeastTwo : Nat.AtLeastTwo 4 := ⟨by decide⟩ +theorem eightAtLeastTwo : Nat.AtLeastTwo 8 := ⟨by decide⟩ + +local instance finiteFunctionEncodingBasic {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +structure Instruction where + nextState : ℕ + writeSymbol : ℕ + move : Fin 3 + deriving DecidableEq + +def Instruction.codeEquiv : Instruction ≃ ℕ × ℕ × Fin 3 where + toFun I := (I.nextState, I.writeSymbol, I.move) + invFun p := ⟨p.1, p.2.1, p.2.2⟩ + left_inv _ := rfl + right_inv _ := rfl + +instance : Primcodable Instruction := Primcodable.ofEquiv _ Instruction.codeEquiv + +structure Machine where + states : ℕ + symbols : ℕ + start : ℕ + table : List (List (Option Instruction)) + deriving DecidableEq + +def Machine.codeEquiv : Machine ≃ ℕ × ℕ × ℕ × List (List (Option Instruction)) where + toFun M := (M.states, M.symbols, M.start, M.table) + invFun p := ⟨p.1, p.2.1, p.2.2.1, p.2.2.2⟩ + left_inv _ := rfl + right_inv _ := rfl + +instance : Primcodable Machine := Primcodable.ofEquiv _ Machine.codeEquiv + +def Machine.lookup (M : Machine) (q a : ℕ) : Option Instruction := + (M.table.getD q []).getD a none + +def Machine.WellFormed (M : Machine) : Prop := + 0 < M.states ∧ 0 < M.symbols ∧ M.start < M.states ∧ + M.table.length ≤ M.states ∧ + (∀ row ∈ M.table, row.length ≤ M.symbols) ∧ + ∀ row ∈ M.table, ∀ entry ∈ row, ∀ I, entry = some I → + I.nextState < M.states ∧ I.writeSymbol < M.symbols + +structure Input where + machine : Machine + word : List ℕ + deriving DecidableEq + +def Input.codeEquiv : Input ≃ Machine × List ℕ where + toFun d := (d.machine, d.word) + invFun p := ⟨p.1, p.2⟩ + left_inv _ := rfl + right_inv _ := rfl + +instance : Primcodable Input := Primcodable.ofEquiv _ Input.codeEquiv + +def Input.WellFormed (d : Input) : Prop := + d.machine.WellFormed ∧ ∀ a ∈ d.word, a < d.machine.symbols + +structure Configuration where + state : ℕ + head : ℤ + tape : ℤ → ℕ + +def initialConfiguration (d : Input) : Configuration where + state := d.machine.start + head := 0 + tape i := if 0 ≤ i then d.word.getD i.toNat 0 else 0 + +def machineStep (M : Machine) (c : Configuration) : Configuration := + match M.lookup c.state (c.tape c.head) with + | none => c + | some I => + { state := I.nextState + head := c.head + ((I.move.val : ℤ) - 1) + tape := Function.update c.tape c.head I.writeSymbol } + +def execution (d : Input) (n : ℕ) : Configuration := + (machineStep d.machine)^[n] (initialConfiguration d) + +def Halts (d : Input) : Prop := + ∃ n : ℕ, d.machine.lookup (execution d n).state + ((execution d n).tape (execution d n).head) = none + +abbrev Space := EuclideanSpace ℝ (Fin 3) +abbrev Torus := UnitAddTorus (Fin 3) +abbrev Field (A : Type*) := ℝ → Torus → A +abbrev VectorField := Field Space +abbrev ScalarField := Field ℝ +abbrev MultiIndex := Fin 3 → ℕ + +noncomputable section + +def torusMk (x : Space) : Torus := fun i => (x i : UnitAddCircle) + +def torusVolume : MeasureTheory.Measure Torus := + MeasureTheory.Measure.pi (fun _ : Fin 3 => AddCircle.haarAddCircle) + +def initialParticle : Space := WithLp.toLp 2 ![(1 : ℝ) / 4, 1 / 2, 1 / 2] + +def detector : Set Torus := + {q | ∃ s : ℝ, 1 / 2 < s ∧ s < 1 ∧ (s : UnitAddCircle) = q 0} + +section Operators +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +def lifted (F : Field A) : ℝ × Space → A := + fun tx => F tx.1 (torusMk tx.2) + +def spaceLift (F : Field A) (t : ℝ) : Space → A := + fun x => F t (torusMk x) + +def Smooth (F : Field A) : Prop := + ContDiffOn ℝ (↑(⊤ : ℕ∞)) (lifted F) (Set.Ici (0 : ℝ) ×ˢ Set.univ) + +def timeD (F : Field A) : Field A := + fun t q => derivWithin (fun s => F s q) (Set.Ici (0 : ℝ)) t + +def spaceD (i : Fin 3) (F : Field A) : Field A := + fun t q => deriv (fun s : ℝ => + F t (q + torusMk (EuclideanSpace.single i s))) 0 + +def mixedD (r : ℕ) (α : MultiIndex) (F : Field A) : Field A := + timeD^[r] ((spaceD 2)^[α 2] ((spaceD 1)^[α 1] ((spaceD 0)^[α 0] F))) + +def laplacian (F : Field A) : Field A := + fun t q => ∑ i : Fin 3, spaceD i (spaceD i F) t q + +def MeanZero (F : Field A) : Prop := + ∀ t : ℝ, 0 ≤ t → ∫ q, F t q ∂torusVolume = 0 + +def spatialSup (F : Field A) (t : ℝ) : ℝ := + sSup (Set.range fun q => ‖F t q‖) + +def CylinderContinuous (F : Field A) : Prop := + ∀ T : ℝ, 0 ≤ T → ContinuousOn (Function.uncurry F) (Set.Icc 0 T ×ˢ Set.univ) + +end Operators + +def gradient (p : ScalarField) : VectorField := + fun t q => WithLp.toLp 2 (fun i => spaceD i p t q) + +def divergence (u : VectorField) : ScalarField := + fun t q => ∑ i : Fin 3, spaceD i (fun s x => u s x i) t q + +def advection (u : VectorField) : VectorField := + fun t q => ∑ i : Fin 3, u t q i • spaceD i u t q + +def Solenoidal (u : VectorField) : Prop := + ∀ t : ℝ, 0 ≤ t → ∀ q, divergence u t q = 0 + +def NavierStokes (ν : ℝ) (F u : VectorField) (p : ScalarField) : Prop := + (∀ t : ℝ, 0 ≤ t → ∀ q, + timeD u t q + advection u t q = + -gradient p t q + ν • laplacian u t q + F t q) ∧ + Solenoidal u ∧ ∀ q, u 0 q = 0 + +structure ClassicalSolution (ν : ℝ) (F u : VectorField) (p : ScalarField) : Prop where + velocityContinuous : CylinderContinuous u + timeDifferentiable : ∀ t : ℝ, 0 ≤ t → ∀ q, + DifferentiableWithinAt ℝ (fun s => u s q) (Set.Ici (0 : ℝ)) t + timeContinuous : CylinderContinuous (timeD u) + spaceTwiceDifferentiable : ∀ t : ℝ, 0 ≤ t → ContDiff ℝ 2 (spaceLift u t) + spaceFirstContinuous : ∀ i, CylinderContinuous (spaceD i u) + spaceSecondContinuous : ∀ i j, CylinderContinuous (spaceD i (spaceD j u)) + pressureContinuous : CylinderContinuous p + pressureDifferentiable : ∀ t : ℝ, 0 ≤ t → Differentiable ℝ (spaceLift p t) + pressureGradientContinuous : CylinderContinuous (gradient p) + pressureMeanZero : MeanZero p + equations : NavierStokes ν F u p + +def UniqueClassical (ν : ℝ) (F u : VectorField) (p : ScalarField) : Prop := + ∀ v q, ClassicalSolution ν F v q → + ∀ t : ℝ, 0 ≤ t → (∀ x, v t x = u t x) ∧ (∀ x, q t x = p t x) + +def IsParticle (u : VectorField) (X : ℝ → Space) : Prop := + X 0 = initialParticle ∧ + ∀ t : ℝ, 0 ≤ t → HasDerivWithinAt X (u t (torusMk (X t))) (Set.Ici 0) t + +def MaterialEvent (X : ℝ → Space) : Prop := + ∃ t : ℝ, 0 ≤ t ∧ torusMk (X t) ∈ detector + +abbrev Program := Nat.Partrec.Code +abbrev RationalPoint := ℚ × (Fin 3 → ℚ) + +def accuracy (n : ℕ) : ℝ := + letI := twoAtLeastTwo + (2 : ℝ) ^ (-(n : ℤ)) + +def ComputableReal (x : ℝ) : Prop := + ∃ P : Program, ∀ n : ℕ, ∃ q : ℚ, + Encodable.encode q ∈ P.eval n ∧ |x - (q : ℝ)| ≤ accuracy n + +def rationalVector (q : Fin 3 → ℚ) : Space := + WithLp.toLp 2 (fun i => (q i : ℝ)) + +def UniformlyEffective (F : Input → VectorField) : Prop := + ∃ modulus evaluate : Program, + ∀ d : Input, d.WellFormed → + ∀ (r : ℕ) (α : MultiIndex) (T n : ℕ), + ∃ m : ℕ, m ∈ modulus.eval (Encodable.encode (d, r, α, T, n)) ∧ + ∀ a : RationalPoint, ∃ b : Fin 3 → ℚ, + Encodable.encode b ∈ evaluate.eval (Encodable.encode (d, r, α, T, n, a)) ∧ + ∀ (t : ℝ) (x : Space), 0 ≤ t → t ≤ (T : ℝ) → + |t - (a.1 : ℝ)| ≤ accuracy m → + (∀ i, |x i - (a.2 i : ℝ)| ≤ accuracy m) → + ‖mixedD r α (F d) t (torusMk x) - rationalVector b‖ ≤ accuracy n + +def EffectiveConstants (C : Input → ℕ → MultiIndex → ℕ → ℕ) : Prop := + ∃ P : Program, ∀ d : Input, d.WellFormed → ∀ r α J, + C d r α J ∈ P.eval (Encodable.encode (d, r, α, J)) + +def RapidPair (u F : VectorField) (C : ℕ → MultiIndex → ℕ → ℕ) : Prop := + ∀ (r J : ℕ) (α : MultiIndex) (t : ℝ), 0 ≤ t → + spatialSup (mixedD r α u) t + spatialSup (mixedD r α F) t ≤ + (C r α J : ℝ) / (1 + t) ^ J + +def UniqueMeanZeroPoisson (g : VectorField) (φ : ScalarField) : Prop := + ∀ ψ : ScalarField, + (∀ t : ℝ, 0 ≤ t → ContDiff ℝ 2 (spaceLift ψ t)) → MeanZero ψ → + (∀ t : ℝ, 0 ≤ t → ∀ q, laplacian ψ t q = divergence g t q) → + ∀ t : ℝ, 0 ≤ t → ∀ q, ψ t q = φ t q + +def LatticeConclusion (ν : ℝ) (d : Input) + (U g f : VectorField) (φ : ScalarField) + (C : ℕ → MultiIndex → ℕ → ℕ) : Prop := + Smooth U ∧ Smooth g ∧ Smooth f ∧ Smooth φ ∧ + MeanZero U ∧ MeanZero g ∧ MeanZero f ∧ MeanZero φ ∧ + ClassicalSolution ν g U 0 ∧ + ClassicalSolution ν f U (-φ) ∧ + RapidPair U g C ∧ RapidPair U f C ∧ + Solenoidal f ∧ + (∀ t : ℝ, 0 ≤ t → ∀ q, laplacian φ t q = divergence g t q) ∧ + UniqueMeanZeroPoisson g φ ∧ + (∀ t : ℝ, 0 ≤ t → ∀ q, f t q = g t q - gradient φ t q) ∧ + UniqueClassical ν g U 0 ∧ UniqueClassical ν f U (-φ) ∧ + ∃ X : ℝ → Space, IsParticle U X ∧ + (∀ Y : ℝ → Space, IsParticle U Y → ∀ t : ℝ, 0 ≤ t → Y t = X t) ∧ + (MaterialEvent X ↔ Halts d) + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Certificates.lean b/lean/OAI/Analysis/PeriodicLattice/Certificates.lean new file mode 100644 index 0000000000000000000000000000000000000000..4c4b4264e0a3db58762ef16ac8a8f1e098f2f1b5 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Certificates.lean @@ -0,0 +1,315 @@ +import OAI.Analysis.PeriodicLattice.Arithmetic + +namespace OAI + +/-! Quantitative certificates for planar derivatives and products. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingCertificates {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Quantitative +open RapidCalculus Profiles TorusCalculus RecursiveArithmetic +open scoped ContDiff + +structure BiCertificate (F : Input → ℝ → ℝ → ℝ) where + budget : Input × ℕ × ℕ → ℕ + recursive : Primrec budget + smooth : ∀ d, ContDiff ℝ ∞ (Function.uncurry (F d)) + estimate : ∀ d, d.WellFormed → ∀ w n J, w.length ≤ n → ∀ t, 0 ≤ t → ∀ y, + (1+t)^J * ‖wordD w (F d) t y‖ ≤ (budget (d,n,J) : ℝ) + +theorem word_mul_estimate {F G : ℝ → ℝ → ℝ} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (hG : ContDiff ℝ ∞ (Function.uncurry G)) + (w : List Bool) (t y a C D : ℝ) (ha : 0 ≤ a) (hC : 0 ≤ C) (_hD : 0 ≤ D) + (hf : ∀ v : List Bool, v.length ≤ w.length → a * ‖wordD v F t y‖ ≤ C) + (hg : ∀ v : List Bool, v.length ≤ w.length → ‖wordD v G t y‖ ≤ D) : + a * ‖wordD w (F*G) t y‖ ≤ 2^w.length * C * D := by + induction w using List.reverseRecOn generalizing F G with + | nil => + simpa only [wordD_nil, Pi.mul_apply, norm_mul, List.length_nil, pow_zero, one_mul, + ← mul_assoc] using mul_le_mul (hf [] le_rfl) (hg [] le_rfl) (norm_nonneg _) hC + | append_singleton w i ih => + have hfi v (hv : v.length ≤ w.length) : a * ‖wordD v (biD i F) t y‖ ≤ C := by + simpa only [wordD_append, wordD_cons, wordD_nil] using + hf (v++[i]) (by simpa only [List.length_append, List.length_singleton] using Nat.add_le_add_right hv 1) + have hgi v (hv : v.length ≤ w.length) : ‖wordD v (biD i G) t y‖ ≤ D := by + simpa only [wordD_append, wordD_cons, wordD_nil] using + hg (v++[i]) (by simpa only [List.length_append, List.length_singleton] using Nat.add_le_add_right hv 1) + have hf' v (hv : v.length ≤ w.length) := hf v (hv.trans (by simp)) + have hg' v (hv : v.length ≤ w.length) := hg v (hv.trans (by simp)) + have H1 := ih (partial_contDiff hF i) hG hfi hg' + have H2 := ih hF (partial_contDiff hG i) hf' hgi + rw [wordD_append, wordD_cons, wordD_nil, biD_mul hF hG, + wordD_add (F := biD i F * G) (G := F * biD i G) ((partial_contDiff hF i).mul hG) (hF.mul (partial_contDiff hG i))] + calc + _ ≤ a * (‖wordD w (biD i F * G) t y‖ + ‖wordD w (F * biD i G) t y‖) := + mul_le_mul_of_nonneg_left (norm_add_le _ _) ha + _ ≤ 2^w.length*C*D + 2^w.length*C*D := by rw [mul_add]; exact add_le_add H1 H2 + _ = _ := by simp only [List.length_append, List.length_singleton, pow_succ]; ring + +namespace BiCertificate + +noncomputable def diff {F : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) (i : Bool) : + BiCertificate (fun d => biD i (F d)) where + budget p := h.budget (p.1, p.2.1+1, p.2.2) + recursive := h.recursive.comp (by fun_prop) + smooth d := partial_contDiff (h.smooth d) i + estimate d hd w n J hn t ht y := by + simpa only [wordD_append, wordD_cons, wordD_nil] using + h.estimate d hd (w++[i]) (n+1) J (by simpa using Nat.add_le_add_right hn 1) t ht y + +noncomputable def add {F G : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) (k : BiCertificate G) : + BiCertificate (fun d => F d + G d) where + budget p := h.budget p + k.budget p + recursive := Primrec.nat_add.comp h.recursive k.recursive + smooth d := (h.smooth d).add (k.smooth d) + estimate d hd w n J hn t ht y := by + rw [wordD_add (h.smooth d) (k.smooth d)] + calc + _ ≤ (1+t)^J * (‖wordD w (F d) t y‖ + ‖wordD w (G d) t y‖) := + mul_le_mul_of_nonneg_left (norm_add_le _ _) (by positivity) + _ ≤ _ := by rw [mul_add, Nat.cast_add]; exact add_le_add (h.estimate d hd w n J hn t ht y) (k.estimate d hd w n J hn t ht y) + +noncomputable def scale {F : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) (c : ℝ) (N : ℕ) + (hc : ‖c‖ ≤ N) : BiCertificate (fun d => c • F d) where + budget p := N * h.budget p + recursive := Primrec.nat_mul.comp (Primrec.const N) h.recursive + smooth d := (contDiff_const (c := c)).mul (h.smooth d) + estimate d hd w n J hn t ht y := by + rw [wordD_scale c (h.smooth d), Pi.smul_apply, Pi.smul_apply, norm_smul, mul_left_comm] + simpa only [Nat.cast_mul] using mul_le_mul hc (h.estimate d hd w n J hn t ht y) + (by positivity) (Nat.cast_nonneg N) + +noncomputable def mul {F G : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) (k : BiCertificate G) : + BiCertificate (fun d => F d * G d) where + budget p := 2^p.2.1 * h.budget p * k.budget (p.1,p.2.1,0) + recursive := by + have hp : Primrec (fun p : Input × ℕ × ℕ => k.budget (p.1,p.2.1,0)) := k.recursive.comp (by fun_prop) + exact Primrec.nat_mul.comp (Primrec.nat_mul.comp (by fun_prop) h.recursive) hp + smooth d := (h.smooth d).mul (k.smooth d) + estimate d hd w n J hn t ht y := by + have hh := word_mul_estimate (h.smooth d) (k.smooth d) w t y ((1+t)^J) + (h.budget (d,n,J)) (k.budget (d,n,0)) (by positivity) (by positivity) (by positivity) + (fun v hv => h.estimate d hd v n J (hv.trans hn) t ht y) + (fun v hv => by simpa using k.estimate d hd v n 0 (hv.trans hn) t ht y) + refine hh.trans ?_ + simp only [Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat] + gcongr + norm_num + +noncomputable def mean {F : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) : + BiCertificate (fun d => PeriodicInverse.mean (F d)) where + budget := h.budget + recursive := h.recursive + smooth d := PeriodicInverse.mean_contDiff (h.smooth d) + estimate d hd w n J hn t ht y := by + rw [PeriodicInverse.mean_wordD (h.smooth d)] + split_ifs + · simp + · have hi := intervalIntegral.norm_integral_le_of_norm_le_const (a := (0 : ℝ)) (b := 1) + (f := fun s => (1 + t) ^ J * wordD w (F d) t s) (C := (h.budget (d,n,J) : ℝ)) (fun s _ => by + rw [norm_mul, Real.norm_eq_abs ((1+t)^J), abs_of_nonneg (by positivity)] + exact h.estimate d hd w n J hn t ht s) + simpa only [intervalIntegral.integral_const_mul, norm_mul, Real.norm_eq_abs ((1+t)^J), + abs_of_nonneg (show 0 ≤ (1+t)^J by positivity), sub_zero, abs_one, mul_one, PeriodicInverse.mean] using hi + +noncomputable def first {F : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) (lam : ℝ) : + BiCertificate (fun d => PeriodicInverse.first lam (F d)) := by + let N : ℕ := ⌈‖(1 - Real.exp lam)⁻¹‖ * Real.exp |lam|⌉₊ + have hN : ‖(1 - Real.exp lam)⁻¹‖ * Real.exp |lam| ≤ N := Nat.le_ceil _ + refine ⟨(fun p => N * h.budget p), Primrec.nat_mul.comp (Primrec.const N) h.recursive, + (fun d => PeriodicInverse.first_contDiff lam (h.smooth d)), ?_⟩ + intro d hd w n J hn t ht y + rw [PeriodicInverse.first_wordD lam (h.smooth d)] + calc + _ ≤ ‖(1 - Real.exp lam)⁻¹‖ * Real.exp |lam| * h.budget (d,n,J) := + PeriodicInverse.first_weighted_bound lam t (by positivity) (h.estimate d hd w n J hn t ht) y + _ ≤ _ := by rw [Nat.cast_mul]; exact mul_le_mul_of_nonneg_right hN (by positivity) + +end BiCertificate +end Quantitative +namespace Quantitative +open RapidCalculus Profiles TorusCalculus RecursiveArithmetic +open scoped ContDiff + +def planarBudget (p : Input × ℕ × ℕ) : ℕ := + ∑ r ∈ Finset.range (p.2.1+1), ∑ k ∈ Finset.range (p.2.1+1), + Planar.planarBound (CompilerPlanar.radix p.1) p.1.word.length + (CompilerPlanar.loadingCode p.1) k p.2.2 (ProfileJets.pulseBound r) (ProfileJets.bumpBound k) + +@[fun_prop] theorem planarBudget_recursive : Primrec planarBudget := by + have hg : Primrec (fun p : ((Input × ℕ × ℕ) × ℕ) × ℕ => + Planar.planarBound (CompilerPlanar.radix p.1.1.1) p.1.1.1.word.length + (CompilerPlanar.loadingCode p.1.1.1) p.2 p.1.1.2.2 + (ProfileJets.pulseBound p.1.2) (ProfileJets.bumpBound p.2)) := by fun_prop + have hh := sumRange (f := fun p : (Input × ℕ × ℕ) × ℕ => p.1.2.1+1) (by fun_prop) hg.to₂ + exact sumRange (by fun_prop) hh.to₂ + +theorem planarBudget_bound (d : Input) (hd : d.WellFormed) (w : List Bool) + (n J : ℕ) (hn : w.length ≤ n) (t : ℝ) (ht : 0 ≤ t) (y : ℝ) : + (1+t)^J * ‖wordD w (FluidLift.v d) t y‖ ≤ (planarBudget (d,n,J) : ℝ) := by + let F : ℕ → ℤ → ℝ := fun n j => CompilerPlanar.nextTable d n j + let H : ℕ → ℤ → ℝ := fun n j => if CompilerPlanar.haltTable d n j then 1 else 0 + have hF (n : ℕ) (j : ℤ) : |F n j| ≤ (Scales.capacity (CompilerPlanar.radix d) d.word.length (n + 1) : ℝ) := by + simpa only [F, Nat.abs_cast] using + (Nat.cast_le.mpr (CompilerPlanar.nextTable_bound d hd n j).le : + (CompilerPlanar.nextTable d n j : ℝ) ≤ _) + have hH (n : ℕ) (j : ℤ) : |H n j| ≤ 1 := by dsimp [H]; split_ifs <;> norm_num + let V := Planar.coefficients (CompilerPlanar.radix d) d.word.length (CompilerPlanar.loadingCode d) F H + have hV (k : ℕ) : ContDiff ℝ ∞ (V k) := by + cases k with + | zero => exact contDiff_const + | succ k => exact Planar.slot_contDiff _ _ _ _ _ + change (1+t)^J * ‖wordD w (schedule V) t y‖ ≤ _ + rw [wordD_schedule V hV w ⌊t⌋₊ (Nat.floor_le ht) (Nat.lt_floor_add_one t).le] + apply (Planar.field_weighted_derivative_bound (CompilerPlanar.radix_ge_two d) d.word.length + (CompilerPlanar.loadingCode d) (w.count true) (w.count false) J + (ProfileJets.pulseBound (w.count true)) (ProfileJets.bumpBound (w.count false)) F H hF hH + (ProfileJets.pulseBound_spec _) (ProfileJets.bumpBound_spec _) ht y).trans + apply Nat.cast_le.mpr + let h (r k : ℕ) := Planar.planarBound (CompilerPlanar.radix d) d.word.length + (CompilerPlanar.loadingCode d) k J (ProfileJets.pulseBound r) (ProfileJets.bumpBound k) + have hk : w.count false ∈ Finset.range (n+1) := + Finset.mem_range.mpr (Nat.lt_succ_of_le ((List.count_le_length ..).trans hn)) + have hr : w.count true ∈ Finset.range (n+1) := + Finset.mem_range.mpr (Nat.lt_succ_of_le ((List.count_le_length ..).trans hn)) + exact (Finset.single_le_sum (f := h (w.count true)) (fun k _ => Nat.zero_le _) hk).trans + (Finset.single_le_sum (f := fun r => ∑ k ∈ Finset.range (n+1), h r k) + (fun r _ => Nat.zero_le _) hr) + +noncomputable def aCertificate : BiCertificate FluidLift.a where + budget := planarBudget + recursive := planarBudget_recursive + smooth := FluidLift.a_contDiff + estimate d hd w n J hn t ht y := by + have he : wordD w (FluidLift.v d) = fun t y => + (wordD w (FluidLift.a d) t y, wordD w (FluidLift.b d) t y) := + wordD_pair _ _ (FluidLift.a_contDiff d) (FluidLift.b_contDiff d) w + have hh := planarBudget_bound d hd w n J hn t ht y + rw [he] at hh + exact (mul_le_mul_of_nonneg_left (norm_fst_le _) (by positivity)).trans hh + +noncomputable def bCertificate : BiCertificate FluidLift.b where + budget := planarBudget + recursive := planarBudget_recursive + smooth := FluidLift.b_contDiff + estimate d hd w n J hn t ht y := by + have he : wordD w (FluidLift.v d) = fun t y => + (wordD w (FluidLift.a d) t y, wordD w (FluidLift.b d) t y) := + wordD_pair _ _ (FluidLift.a_contDiff d) (FluidLift.b_contDiff d) w + have hh := planarBudget_bound d hd w n J hn t ht y + rw [he] at hh + exact (mul_le_mul_of_nonneg_left (norm_snd_le _) (by positivity)).trans hh + +structure ProfileCertificate (f : ℝ → ℝ) where + budget : ℕ → ℕ + recursive : Primrec budget + smooth : ContDiff ℝ ∞ f + estimate : ∀ k n, k ≤ n → ∀ z, ‖iteratedDeriv k f z‖ ≤ (budget n : ℝ) + +namespace ProfileCertificate +noncomputable def one : ProfileCertificate (fun _ => 1) where + budget _ := 1 + recursive := Primrec.const _ + smooth := contDiff_const + estimate k n _ z := by rw [iteratedDeriv_const]; split_ifs <;> norm_num + +noncomputable def neg {f : ℝ → ℝ} (hf : ProfileCertificate f) : ProfileCertificate (-f) where + budget := hf.budget + recursive := hf.recursive + smooth := hf.smooth.neg + estimate k n hk z := by simpa only [iteratedDeriv_neg, Pi.neg_apply, norm_neg] using hf.estimate k n hk z +end ProfileCertificate + +theorem vertical_derivative_bound (k : ℕ) (z : ℝ) : + ‖iteratedDeriv k FluidLift.eta z‖ ≤ (64:ℝ)^k ∧ + ‖iteratedDeriv k FluidLift.slope z‖ ≤ (64:ℝ)^k := by + induction k with + | zero => + simp only [iteratedDeriv_zero, pow_zero] + constructor + · rw [FluidLift.eta, norm_div] + apply (div_le_one (norm_pos_iff.mpr (mul_ne_zero (by norm_num) Real.pi_ne_zero) : 0 < ‖2*Real.pi‖)).mpr + calc + ‖Real.sin (2 * Real.pi * (z - 1/2))‖ ≤ (1:ℝ) := by simpa only [Real.norm_eq_abs] using Real.abs_sin_le_one _ + _ ≤ ‖2*Real.pi‖ := by rw [Real.norm_eq_abs, abs_of_pos (by positivity)]; linarith [Real.two_le_pi] + · simpa only [FluidLift.slope, Real.norm_eq_abs] using Real.abs_cos_le_one _ + | succ k ih => + constructor + · rw [iteratedDeriv_succ', FluidLift.eta_deriv] + exact ih.2.trans (pow_le_pow_right₀ (by norm_num) (Nat.le_succ k)) + · rw [iteratedDeriv_succ', FluidLift.slope_deriv, iteratedDeriv_const_mul_field, norm_mul] + have hc : ‖-(2*Real.pi)^2‖ ≤ (64:ℝ) := by + rw [norm_neg, Real.norm_eq_abs, abs_of_nonneg (sq_nonneg _)] + nlinarith [Real.pi_lt_four, Real.pi_pos] + calc + _ ≤ 64 * 64^k := mul_le_mul hc ih.1 (norm_nonneg _) (by norm_num) + _ = _ := by ring + +noncomputable def etaCertificate : ProfileCertificate FluidLift.eta where + budget n := 64^n + recursive := by fun_prop + smooth := FluidLift.eta_contDiff + estimate k n hk z := (vertical_derivative_bound k z).1.trans (by + simp only [Nat.cast_pow, Nat.cast_ofNat]; exact pow_le_pow_right₀ (by norm_num) hk) + +noncomputable def slopeCertificate : ProfileCertificate FluidLift.slope where + budget n := 64^n + recursive := by fun_prop + smooth := FluidLift.slope_contDiff + estimate k n hk z := (vertical_derivative_bound k z).2.trans (by + simp only [Nat.cast_pow, Nat.cast_ofNat]; exact pow_le_pow_right₀ (by norm_num) hk) + +namespace BiCertificate +noncomputable def neg {F : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) : + BiCertificate (fun d => -F d) := by + simpa only [neg_one_smul] using h.scale (-1) 1 (by norm_num) +noncomputable def sub {F G : Input → ℝ → ℝ → ℝ} (h : BiCertificate F) (k : BiCertificate G) : + BiCertificate (fun d => F d - G d) := by simpa only [sub_eq_add_neg] using h.add k.neg +end BiCertificate + +noncomputable def pressureSourceCertificate : BiCertificate FluidLift.pressureSource := + ((bCertificate.diff false).mul (bCertificate.diff false)).sub + (bCertificate.mul ((bCertificate.diff false).diff false)) + +noncomputable def pressureBaseCertificate : BiCertificate FluidLift.pressureBase := + ((bCertificate.mul bCertificate).sub (bCertificate.mul bCertificate).mean).scale (1/2) 1 (by norm_num) + +noncomputable def pressureModeCertificate : BiCertificate FluidLift.pressureMode := + (pressureSourceCertificate.first (4*Real.pi)).first (-(4*Real.pi)) + +theorem trig_iterated_bound (k : ℕ) (z : ℝ) : + ‖iteratedDeriv k Real.sin z‖ ≤ 1 ∧ ‖iteratedDeriv k Real.cos z‖ ≤ 1 := by + induction k with + | zero => exact ⟨Real.abs_sin_le_one _, Real.abs_cos_le_one _⟩ + | succ k ih => simpa only [Real.iteratedDeriv_add_one_sin, Real.iteratedDeriv_add_one_cos, + Pi.neg_apply, norm_neg] using And.intro ih.2 ih.1 + +noncomputable def doubleSlopeCertificate : ProfileCertificate FluidLift.doubleSlope where + budget n := 16^n + recursive := by fun_prop + smooth := FluidLift.doubleSlope_contDiff + estimate k n hk z := by + have he : FluidLift.doubleSlope = fun x => Real.cos (4*Real.pi*(x-1/2)) := by + funext x + rw [show 4*Real.pi*(x-1/2) = 2*(2*Real.pi*(x-1/2)) by ring, Real.cos_two_mul] + rfl + rw [he, iteratedDeriv_comp_sub_const (f := fun u => Real.cos (4*Real.pi*u)), + iteratedDeriv_comp_const_mul (Real.contDiff_cos) (4*Real.pi), norm_mul, norm_pow] + have hc : ‖4*Real.pi‖ ≤ (16:ℝ) := by + rw [Real.norm_eq_abs, abs_of_pos (by positivity)]; linarith [Real.pi_lt_four] + calc + _ ≤ 16^k * 1 := mul_le_mul (pow_le_pow_left₀ (norm_nonneg _) hc _) (trig_iterated_bound k _).2 + (norm_nonneg _) (by positivity) + _ ≤ (16^n:ℕ) := by simp only [mul_one, Nat.cast_pow, Nat.cast_ofNat]; exact pow_le_pow_right₀ (by norm_num) hk + +end Quantitative + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Compiler.lean b/lean/OAI/Analysis/PeriodicLattice/Compiler.lean new file mode 100644 index 0000000000000000000000000000000000000000..5214dd005a11f3d2a42312b60774b06187b92a64 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Compiler.lean @@ -0,0 +1,96 @@ +import OAI.Analysis.PeriodicLattice.Tape + +namespace OAI + +/-! Compilation of finite machines into planar velocity data. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingCompiler {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace CompilerPlanar + +open Scales StackCode RuleTable Planar +open scoped ContDiff + +def radix (d : Input) : ℕ := max 2 (max d.machine.states d.machine.symbols) + +theorem radix_ge_two (d : Input) : 2 ≤ radix d := le_max_left _ _ +theorem states_le_radix (d : Input) : d.machine.states ≤ radix d := + (le_max_left _ _).trans (le_max_right _ _) +theorem symbols_le_radix (d : Input) : d.machine.symbols ≤ radix d := + (le_max_right _ _).trans (le_max_right _ _) + +def loadingCode (d : Input) : ℕ := configurationCode (radix d) d 0 + +def nextTable (d : Input) := RuleTable.next (radix d) d.word.length d.machine +def haltTable (d : Input) := RuleTable.halt (radix d) d.word.length d.machine + +def velocity (d : Input) : ℝ → Point → Point := + ruleField (radix d) d.word.length (loadingCode d) (nextTable d) (haltTable d) + +def path (d : Input) : ℝ → Point := + curve (radix d) d.word.length (codes (nextTable d) (loadingCode d)) (haltTable d) + +theorem loadingCode_bound (d : Input) (hd : d.WellFormed) : + loadingCode d < capacity (radix d) d.word.length 0 := + configurationCode_bound (radix_ge_two d) d hd (symbols_le_radix d) (states_le_radix d) 0 + +theorem nextTable_bound (d : Input) (hd : d.WellFormed) (n : ℕ) (j : ℤ) : + nextTable d n j < capacity (radix d) d.word.length (n + 1) := + next_bound (radix_ge_two d) _ _ hd.1 (symbols_le_radix d) (states_le_radix d) n j + +theorem nextTable_periodic (d : Input) (n : ℕ) : + Function.Periodic (nextTable d n) (capacity (radix d) d.word.length n : ℤ) := + next_periodic _ _ _ _ + +theorem haltTable_periodic (d : Input) (n : ℕ) : + Function.Periodic (haltTable d n) (capacity (radix d) d.word.length n : ℤ) := + halt_periodic _ _ _ _ + +theorem velocity_contDiff (d : Input) : ContDiff ℝ ∞ (fun tx : ℝ × Point => velocity d tx.1 tx.2) := + field_contDiff _ _ _ _ _ + +theorem velocity_start (d : Input) (x : Point) : velocity d 0 x = 0 := field_at_start _ _ _ _ _ x + +theorem velocity_periodic (d : Input) (t x : ℝ) : Function.Periodic (fun y => velocity d t (x, y)) 1 := by + apply field_periodic_y (radix_ge_two d) + · intro n j + simp only [nextTable_periodic d n j] + · intro n j + simp only [haltTable_periodic d n j] + +theorem path_contDiff (d : Input) : ContDiff ℝ ∞ (path d) := curve_contDiff _ _ _ _ + +theorem path_start (d : Input) : path d 0 = (1 / 4, 1 / 2) := curve_start _ _ _ _ + +theorem path_solves (d : Input) (hd : d.WellFormed) {t : ℝ} (ht : 0 ≤ t) : + HasDerivAt (path d) (velocity d t (path d t)) t := + curve_solves (radix_ge_two d) _ _ _ _ (loadingCode_bound d hd) + (nextTable_bound d hd) (nextTable_periodic d) (haltTable_periodic d) ht + +theorem path_unique (d : Input) (hd : d.WellFormed) {Y : ℝ → Point} + (hY₀ : Y 0 = (1 / 4, 1 / 2)) + (hY : ∀ t : ℝ, 0 ≤ t → HasDerivWithinAt Y (velocity d t (Y t)) (Set.Ici 0) t) + {t : ℝ} (ht : 0 ≤ t) : Y t = path d t := + curve_unique (radix_ge_two d) _ _ _ _ (loadingCode_bound d hd) + (nextTable_bound d hd) (nextTable_periodic d) (haltTable_periodic d) hY₀ hY ht + +theorem path_event_iff (d : Input) (hd : d.WellFormed) : + MaterialEvent (fun t => embed (path d t)) ↔ Halts d := by + rw [path, curve_event_iff (radix_ge_two d)] + unfold loadingCode + rw [codes_flag_iff (nextTable d) (haltTable d) (configurationCode (radix d) d) + (next_code (radix_ge_two d) d hd (symbols_le_radix d) (states_le_radix d))] + unfold Halts haltTable + simp only [halt_code (radix_ge_two d) d hd (symbols_le_radix d) (states_le_radix d), Option.isNone_iff_eq_none] + +end CompilerPlanar + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/DerivativeWords.lean b/lean/OAI/Analysis/PeriodicLattice/DerivativeWords.lean new file mode 100644 index 0000000000000000000000000000000000000000..48b0cabdc9bf9f7d4ab59464ac21551394e9a76e --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/DerivativeWords.lean @@ -0,0 +1,183 @@ +import OAI.Analysis.PeriodicLattice.Energy + +namespace OAI + +/-! Iterated derivatives of periodic fields and tensor profiles. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingDerivativeWords {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace FluidLift + +theorem force_classical_unique (ν : ℝ) (hν : 0 ≤ ν) (d : Input) : + UniqueClassical ν (force ν d) (velocity d) 0 := + TorusCalculus.classical_unique hν (classical_solution ν d) + +end FluidLift + +namespace RapidCalculus + +open Set Filter Topology +open scoped ContDiff + +section TwoVariables +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +def biD (i : Bool) (F : ℝ → ℝ → A) : ℝ → ℝ → A := + if i then fun t y => deriv (fun s => F s y) t else fun t y => deriv (F t) y + +def wordD (w : List Bool) (F : ℝ → ℝ → A) : ℝ → ℝ → A := + w.foldr biD F + +@[simp] theorem wordD_nil (F : ℝ → ℝ → A) : wordD [] F = F := rfl +@[simp] theorem wordD_cons (i : Bool) (w : List Bool) (F : ℝ → ℝ → A) : + wordD (i :: w) F = biD i (wordD w F) := rfl + +theorem wordD_append (w v : List Bool) (F : ℝ → ℝ → A) : + wordD (w ++ v) F = wordD w (wordD v F) := List.foldr_append + +theorem partial_contDiff {F : ℝ → ℝ → A} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (i : Bool) : + ContDiff ℝ ∞ (Function.uncurry (biD i F)) := by + cases i + · exact TorusCalculus.contDiff_partial hF + · have h := TorusCalculus.contDiff_partial (v := fun y t => F t y) + (hF.comp (contDiff_snd.prodMk contDiff_fst)) + exact h.comp (contDiff_snd.prodMk contDiff_fst) + +theorem wordD_contDiff {F : ℝ → ℝ → A} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (w : List Bool) : + ContDiff ℝ ∞ (Function.uncurry (wordD w F)) := by + induction w with + | nil => exact hF + | cons i w ih => exact partial_contDiff ih i + +theorem wordD_eventuallyEq {F G : ℝ → ℝ → A} {t : ℝ} + (h : F =ᶠ[𝓝 t] G) (w : List Bool) : wordD w F =ᶠ[𝓝 t] wordD w G := by + induction w with + | nil => exact h + | cons i w ih => + cases i + · filter_upwards [ih] with s hs + funext y + simp only [wordD_cons, biD, Bool.false_eq_true, ↓reduceIte, hs] + · filter_upwards [eventually_eventually_nhds.mpr ih] with s hs + funext y + have he : (fun u => wordD w F u y) =ᶠ[𝓝 s] (fun u => wordD w G u y) := + hs.mono fun u hu => congrFun hu y + exact he.deriv_eq + +theorem wordD_tensor (p : ℝ → ℝ) (V : ℝ → A) + (hp : ContDiff ℝ ∞ p) (hV : ContDiff ℝ ∞ V) (w : List Bool) : + wordD w (fun t y => p t • V y) = + fun t y => iteratedDeriv (w.count true) p t • iteratedDeriv (w.count false) V y := by + induction w with + | nil => rfl + | cons i w ih => + rw [wordD_cons, ih] + have hp' : ContDiff ℝ ∞ (iteratedDeriv (w.count true) p) := by + rw [iteratedDeriv_eq_iterate]; exact ContDiff.iterate_deriv _ hp + have hV' : ContDiff ℝ ∞ (iteratedDeriv (w.count false) V) := by + rw [iteratedDeriv_eq_iterate]; exact ContDiff.iterate_deriv _ hV + funext t y + cases i + · simpa [biD, List.count_cons, iteratedDeriv_succ, Pi.smul_def] using + (((hV'.differentiable (by simp) y).hasDerivAt).const_smul (iteratedDeriv (w.count true) p t)).deriv + · simpa [biD, List.count_cons, iteratedDeriv_succ, Pi.smul_def] using + (((hp'.differentiable (by simp) t).hasDerivAt).smul_const (iteratedDeriv (w.count false) V y)).deriv + +theorem wordD_schedule (V : ℕ → ℝ → A) (hV : ∀ n, ContDiff ℝ ∞ (V n)) + (w : List Bool) (n : ℕ) {t : ℝ} (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) + (y : ℝ) : + wordD w (Profiles.schedule V) t y = + Profiles.mixedPartial (w.count true) (w.count false) (Profiles.schedule V) t y := by + rw [Profiles.schedule_mixedPartial V _ _ n ht ht'] + have he := wordD_eventuallyEq (Profiles.schedule_eventually_on_slot V n ht ht') w + rw [congrFun he.eq_of_nhds y, wordD_tensor _ _ (Profiles.pulse_contDiff n) (hV n)] + +structure Rapid2 (F : ℝ → ℝ → A) : Prop where + smooth : ContDiff ℝ ∞ (Function.uncurry F) + bound : ∀ (w : List Bool) (J : ℕ), ∃ C : ℝ, ∀ t : ℝ, 0 ≤ t → ∀ y : ℝ, + (1 + t) ^ J * ‖wordD w F t y‖ ≤ C + +theorem Rapid2.biD {F : ℝ → ℝ → A} (hF : Rapid2 F) (i : Bool) : + Rapid2 (biD i F) := by + refine ⟨partial_contDiff hF.smooth i, fun w J => ?_⟩ + simpa only [wordD_append, wordD_cons, wordD_nil] using hF.bound (w ++ [i]) J + +end TwoVariables + +theorem wordD_pair (F G : ℝ → ℝ → ℝ) + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (hG : ContDiff ℝ ∞ (Function.uncurry G)) + (w : List Bool) : + wordD w (fun t y => (F t y, G t y)) = fun t y => (wordD w F t y, wordD w G t y) := by + induction w with + | nil => rfl + | cons i w ih => + rw [wordD_cons, ih] + have hhF := wordD_contDiff hF w + have hhG := wordD_contDiff hG w + funext t y + cases i + · exact (((hhF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y).hasDerivAt.prodMk + ((hhG.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y).hasDerivAt).deriv + · exact (((hhF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t).hasDerivAt.prodMk + ((hhG.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t).hasDerivAt).deriv + +end RapidCalculus + +namespace FluidLift +open scoped ContDiff +open RapidCalculus Profiles + +theorem v_rapid2 (d : Input) (hd : d.WellFormed) : Rapid2 (v d) := by + refine ⟨v_contDiff d, fun w J => ?_⟩ + let F : ℕ → ℤ → ℝ := fun n j => CompilerPlanar.nextTable d n j + let H : ℕ → ℤ → ℝ := fun n j => if CompilerPlanar.haltTable d n j then 1 else 0 + have hF (n : ℕ) (j : ℤ) : |F n j| ≤ (Scales.capacity (CompilerPlanar.radix d) d.word.length (n + 1) : ℝ) := by + simpa only [F, Nat.abs_cast] using + (Nat.cast_le.mpr (CompilerPlanar.nextTable_bound d hd n j).le : + (CompilerPlanar.nextTable d n j : ℝ) ≤ _) + have hH (n : ℕ) (j : ℤ) : |H n j| ≤ 1 := by dsimp [H]; split_ifs <;> norm_num + obtain ⟨C, hC⟩ := Planar.field_rapid (CompilerPlanar.radix_ge_two d) d.word.length + (CompilerPlanar.loadingCode d) (w.count true) (w.count false) J F H hF hH + refine ⟨C, fun t ht y => ?_⟩ + let V := Planar.coefficients (CompilerPlanar.radix d) d.word.length (CompilerPlanar.loadingCode d) F H + have hV (n : ℕ) : ContDiff ℝ ∞ (V n) := by + cases n with + | zero => exact contDiff_const + | succ n => exact Planar.slot_contDiff _ _ _ _ _ + change (1 + t) ^ J * ‖wordD w (schedule V) t y‖ ≤ (C : ℝ) + rw [wordD_schedule V hV w ⌊t⌋₊ (Nat.floor_le ht) (Nat.lt_floor_add_one t).le] + simpa only [mul_comm] using (le_div_iff₀ (by positivity : 0 < (1 + t) ^ J)).mp (hC t ht y) + +theorem a_rapid2 (d : Input) (hd : d.WellFormed) : Rapid2 (a d) := by + refine ⟨a_contDiff d, fun w J => ?_⟩ + obtain ⟨C, hC⟩ := (v_rapid2 d hd).bound w J + refine ⟨C, fun t ht y => ?_⟩ + have he : wordD w (v d) = fun t y => (wordD w (a d) t y, wordD w (b d) t y) := + wordD_pair _ _ (a_contDiff d) (b_contDiff d) w + have hn : ‖wordD w (a d) t y‖ ≤ ‖wordD w (v d) t y‖ := by + rw [he]; exact norm_fst_le (wordD w (a d) t y, wordD w (b d) t y) + exact (mul_le_mul_of_nonneg_left hn (by positivity)).trans (hC t ht y) + +theorem b_rapid2 (d : Input) (hd : d.WellFormed) : Rapid2 (b d) := by + refine ⟨b_contDiff d, fun w J => ?_⟩ + obtain ⟨C, hC⟩ := (v_rapid2 d hd).bound w J + refine ⟨C, fun t ht y => ?_⟩ + have he : wordD w (v d) = fun t y => (wordD w (a d) t y, wordD w (b d) t y) := + wordD_pair _ _ (a_contDiff d) (b_contDiff d) w + have hn : ‖wordD w (b d) t y‖ ≤ ‖wordD w (v d) t y‖ := by + rw [he]; exact norm_snd_le (wordD w (a d) t y, wordD w (b d) t y) + exact (mul_le_mul_of_nonneg_left hn (by positivity)).trans (hC t ht y) + +end FluidLift + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/EffectiveDerivatives.lean b/lean/OAI/Analysis/PeriodicLattice/EffectiveDerivatives.lean new file mode 100644 index 0000000000000000000000000000000000000000..b01b28c8587ac193ec4c7b1b60f3217127c0c667 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/EffectiveDerivatives.lean @@ -0,0 +1,293 @@ +import OAI.Analysis.PeriodicLattice.Trigonometry + +namespace OAI + +/-! Certified finite differences and uniform field evaluation. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingEffectiveDerivatives {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace CertifiedReal +open Encodable Filter Topology +local instance effectiveDerivativesLocal1 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable +section StencilBounds +variable {A B I : Type*} [Primcodable A] [Primcodable B] [Primcodable I] +variable (shift : I → B → ℕ → B) (q : (A × B) × ℕ → ℚ) + +omit [Primcodable A] [Primcodable B] [Primcodable I] in +theorem difference_bound (V : List I → A → B → ℝ) (a : A) (L : ℕ) (K : ℝ) + (hK : 1 ≤ K) + (hbase : ∀ b n, |V [] a b - (q ((a,b),n) : ℝ)| ≤ error n) + (htaylor : ∀ i w, (i::w).length ≤ L → ∀ b n, + |V (i::w) a b - (V w a (shift i b n) - V w a b) / error n| ≤ K * error n) + (w : List I) (hw : w.length ≤ L) (b : B) (n : ℕ) : + |V w a b - (difference shift q w a b n : ℝ)| ≤ K * 3^w.length * error n := by + induction w generalizing b n with + | nil => + simpa only [List.length_nil, pow_zero, mul_one, difference] using + (hbase b n).trans (le_mul_of_one_le_left (error_pos n).le hK) + | cons i w ih => + have ht := htaylor i w hw b n + have ha := ih (by simpa using Nat.le_of_succ_le hw) (shift i b n) (refinePrecision n) + have hb := ih (by simpa using Nat.le_of_succ_le hw) b (refinePrecision n) + rw [error_refine] at ha hb + have hp : (1 : ℝ) ≤ 3^w.length := one_le_pow₀ (by norm_num) + have hcoeff : 0 ≤ K * 3^w.length := mul_nonneg (by linarith) (by positivity) + have hdiff : |(V w a (shift i b n) - V w a b) / error n - + (difference shift q (i::w) a b n : ℝ)| ≤ 2*(K*3^w.length)*error n ^ 2 := by + simp only [difference, Rat.cast_div, Rat.cast_sub, cast_qerror] + have heq : (V w a (shift i b n) - V w a b) / error n - + ((difference shift q w a (shift i b n) (refinePrecision n) : ℝ) - + (difference shift q w a b (refinePrecision n) : ℝ)) / error n = + ((V w a (shift i b n) - (difference shift q w a (shift i b n) (refinePrecision n) : ℝ)) - + (V w a b - (difference shift q w a b (refinePrecision n) : ℝ))) / error n := by ring + rw [heq, abs_div, abs_of_pos (error_pos n)] + apply (div_le_div_of_nonneg_right ((abs_sub _ _).trans (add_le_add ha hb)) (error_pos n).le).trans_eq + field_simp [(error_pos n).ne'] + ring + calc + _ ≤ |V (i::w) a b - (V w a (shift i b n) - V w a b) / error n| + + |(V w a (shift i b n) - V w a b) / error n - (difference shift q (i::w) a b n : ℝ)| := abs_sub_le _ _ _ + _ ≤ K * error n + 2*(K*3^w.length)*error n ^ 2 := add_le_add ht hdiff + _ ≤ (K*3^w.length)*error n + 2*(K*3^w.length)*error n := by + apply add_le_add + · exact mul_le_mul_of_nonneg_right (le_mul_of_one_le_right (by linarith) hp) (error_pos n).le + · exact mul_le_mul_of_nonneg_left (by nlinarith [error_le_one n, error_pos n] : error n ^ 2 ≤ error n) (by positivity) + _ = K*3^(i::w).length*error n := by simp only [List.length_cons, pow_succ]; ring + +theorem effective_words (V : List I → A → B → ℝ) + (hs : Primrec (fun p : I × B × ℕ => shift p.1 p.2.1 p.2.2)) + (hbase : Effective (fun p : A × B => V [] p.1 p.2)) + (K : A × ℕ → ℕ) (hK : Computable K) + (htaylor : ∀ a i w L, (i::w).length ≤ L → ∀ b n, + |V (i::w) a b - (V w a (shift i b n) - V w a b) / error n| ≤ + ((K (a,L) : ℝ)+1) * error n) : + Effective (fun p : A × List I × B => V p.2.1 p.1 p.2.2) := by + obtain ⟨q,hq,bq⟩ := hbase + apply of_enclosures (q := fun p => difference shift q p.1.2.1 p.1.1 p.1.2.2 p.2) + (e := fun p => ((K (p.1.1,p.1.2.1.length) : ℚ)+1)*3^p.1.2.1.length*qerror p.2) + · exact difference_computable shift q hs hq + · have hb : Computable (fun p : (A × List I × B) × ℕ => K (p.1.1,p.1.2.1.length)) := + hK.comp ((Computable.fst.comp Computable.fst).pair + (Computable.list_length.comp (Computable.fst.comp (Computable.snd.comp Computable.fst)))) + fun_prop + · intro p n + simpa only [Rat.cast_mul, Rat.cast_add, Rat.cast_natCast, Rat.cast_one, Rat.cast_pow, + Rat.cast_ofNat, cast_qerror] using + difference_bound shift q V p.1 p.2.1.length ((K (p.1,p.2.1.length) : ℝ)+1) + (by exact le_add_of_nonneg_left (Nat.cast_nonneg _)) (fun b n => bq (p.1,b) n) + (fun i w hw => htaylor p.1 i w p.2.1.length hw) p.2.1 le_rfl p.2.2 n + · intro p + simpa only [Rat.cast_mul, Rat.cast_add, Rat.cast_natCast, Rat.cast_one, Rat.cast_pow, + Rat.cast_ofNat, cast_qerror, mul_zero] using + (tendsto_const_nhds.mul error_tendsto : + Tendsto (fun n => (((K (p.1,p.2.1.length) : ℝ)+1)*3^p.2.1.length)*error n) atTop (𝓝 _)) +end StencilBounds + +theorem quotient_error {f f' f'' : ℝ → ℝ} {h K : ℝ} (hh : 0 < h) + (hf : ∀ s, HasDerivAt f (f' s) s) (hf' : ∀ s, HasDerivAt f' (f'' s) s) + (hbound : ∀ s ∈ Set.Icc 0 h, |f'' s| ≤ K) : + |f' 0 - (f h - f 0)/h| ≤ K*h := by + have hp (s : ℝ) (hs : s ∈ Set.Icc 0 h) : |f' s - f' 0| ≤ K*h := by + have hv := norm_image_sub_le_of_norm_deriv_le_segment' (a := 0) (b := h) + (fun x _ => (hf' x).hasDerivWithinAt) + (fun x hx => by simpa only [Real.norm_eq_abs] using hbound x ⟨hx.1, hx.2.le⟩) s hs + have hK : 0 ≤ K := (abs_nonneg (f'' 0)).trans (hbound 0 ⟨le_rfl,hh.le⟩) + have hvs : |f' s - f' 0| ≤ K*s := by simpa only [Real.norm_eq_abs, sub_zero] using hv + exact hvs.trans (mul_le_mul_of_nonneg_left hs.2 hK) + have hd (s : ℝ) : HasDerivAt (fun x => f x - x * f' 0) (f' s - f' 0) s := by + convert! (hf s).fun_sub ((hasDerivAt_id s).mul_const (f' 0)) using 1 + simp + have hr := norm_image_sub_le_of_norm_deriv_le_segment' (a := 0) (b := h) + (fun x _ => (hd x).hasDerivWithinAt) + (fun x hx => by simpa only [Real.norm_eq_abs] using hp x ⟨hx.1, hx.2.le⟩) h ⟨hh.le,le_rfl⟩ + have heq : f' 0 - (f h - f 0)/h = -(f h - h * f' 0 - (f 0 - 0 * f' 0))/h := by field_simp [hh.ne']; ring + rw [heq, abs_div, abs_neg, abs_of_pos hh] + exact (div_le_iff₀ hh).mpr (by simpa only [Real.norm_eq_abs, sub_zero] using hr) +end CertifiedReal +namespace RecursiveArithmetic +local instance effectiveDerivativesLocal2 : Primcodable ℚ := ratPrimcodable +@[fun_prop] theorem ratMax : Primrec (fun p : ℚ × ℚ => max p.1 p.2) := by + exact (Primrec.ite ratLE Primrec.snd Primrec.fst).of_eq (fun p => by + split_ifs with h + · exact (max_eq_right h).symm + · exact (max_eq_left (le_of_not_ge h)).symm) +end RecursiveArithmetic + +namespace EffectiveFields +open CertifiedReal Quantitative RapidCalculus TorusCalculus +open scoped ContDiff +local instance effectiveDerivativesLocal3 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable +local instance effectiveDerivativesLocal4 : DecidablePred Input.WellFormed := Classical.decPred _ +local instance effectiveDerivativesLocal5 : Primcodable ValidInput := Primcodable.subtype RecursiveArithmetic.inputWellFormed + +@[fun_prop] theorem validData_recursive : Primrec (fun d : ValidInput => d.1) := Primrec.subtype_val + +def time (t : ℚ) : ℝ := (max t 0 : ℚ) +@[simp] theorem time_eq (t : ℚ) : time t = max (t : ℝ) 0 := by simp [time] +theorem time_nonneg (t : ℚ) : 0 ≤ time t := by simp + +abbrev BiPoint := ℚ × ℚ +def biValue (F : ℝ → ℝ → ℝ) (p : BiPoint) : ℝ := F (time p.1) p.2 + +def biShift (i : Bool) (p : BiPoint) (n : ℕ) : BiPoint := + bif i then (max p.1 0 + qerror n, p.2) else (p.1,p.2+qerror n) + +@[fun_prop] theorem biShift_recursive : Primrec (fun p : Bool × BiPoint × ℕ => biShift p.1 p.2.1 p.2.2) := by + unfold biShift + apply Primrec.cond Primrec.fst <;> fun_prop + +def biLine (i : Bool) (t y s : ℝ) : ℝ × ℝ := bif i then (t+s,y) else (t,y+s) + +@[simp] theorem biLine_zero (i : Bool) (t y : ℝ) : biLine i t y 0 = (t,y) := by cases i <;> simp [biLine] + +theorem biLine_nonneg (i : Bool) {t s : ℝ} (ht : 0 ≤ t) (hs : 0 ≤ s) (y : ℝ) : + 0 ≤ (biLine i t y s).1 := by cases i <;> simp [biLine] <;> positivity + +theorem biShift_value (i : Bool) (p : BiPoint) (n : ℕ) (F : ℝ → ℝ → ℝ) : + biValue F (biShift i p n) = + F (biLine i (time p.1) p.2 (error n)).1 (biLine i (time p.1) p.2 (error n)).2 := by + cases i + · simp [biShift, biValue, biLine] + · have h : 0 ≤ max (p.1 : ℝ) 0 + error n := add_nonneg (le_max_right _ _) (error_pos n).le + simp [biShift, biValue, biLine, max_eq_left h] + +theorem biLine_deriv {F : ℝ → ℝ → ℝ} (hF : ContDiff ℝ ∞ (Function.uncurry F)) + (i : Bool) (t y s : ℝ) : + HasDerivAt (fun z => F (biLine i t y z).1 (biLine i t y z).2) + (biD i F (biLine i t y s).1 (biLine i t y s).2) s := by + cases i + · have hh : Differentiable ℝ (F t) := (hF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) + convert! (hh (y+s)).hasDerivAt.comp s ((hasDerivAt_id s).const_add y) using 1 + simp [biLine,biD] + · have hh : Differentiable ℝ (fun t => F t y) := (hF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) + convert! (hh (t+s)).hasDerivAt.comp s ((hasDerivAt_id s).const_add t) using 1 + simp [biLine,biD] + +theorem bi_words {F : Input → ℝ → ℝ → ℝ} (hF : BiCertificate F) + (hbase : Effective (fun p : ValidInput × BiPoint => biValue (F p.1.1) p.2)) : + Effective (fun p : ValidInput × List Bool × BiPoint => biValue (wordD p.2.1 (F p.1.1)) p.2.2) := by + apply effective_words (A := ValidInput) (shift := biShift) (V := fun w (d : ValidInput) p => biValue (wordD w (F d.1)) p) biShift_recursive hbase + (fun dn : ValidInput × ℕ => hF.budget (dn.1.1,dn.2+1,0)) + · apply Primrec.to_comp + exact hF.recursive.comp (g := fun dn : ValidInput × ℕ => (dn.1.1,dn.2+1,0)) (by fun_prop) + intro d i w L hw p n + have hs := wordD_contDiff (hF.smooth d.1) w + have he := quotient_error (error_pos n) + (biLine_deriv hs i (time p.1) p.2) + (biLine_deriv (partial_contDiff hs i) i (time p.1) p.2) + (K := (hF.budget (d.1,L+1,0) : ℝ)) (fun s hs => by + have hb := hF.estimate d.1 d.2 (i::i::w) (L+1) 0 + (by simpa only [List.length_cons] using Nat.succ_le_succ hw) + (biLine i (time p.1) p.2 s).1 + (biLine_nonneg i (time_nonneg p.1) hs.1 _) (biLine i (time p.1) p.2 s).2 + simpa only [pow_zero,one_mul,wordD_cons,Real.norm_eq_abs] using hb) + rw [biShift_value] + dsimp only [biValue, wordD_cons] + simp only [biLine_zero] at he + exact he.trans (mul_le_mul_of_nonneg_right (by linarith) (error_pos n).le) +end EffectiveFields +namespace CertifiedReal +open Filter Topology RecursiveArithmetic +local instance effectiveDerivativesLocal6 : Primcodable ℚ := ratPrimcodable +variable {A : Type*} [Primcodable A] + +theorem quadrature_bound {f : ℝ → ℝ} (hf : Continuous f) (K : ℝ) + (hlip : ∀ x ∈ Set.Icc (0:ℝ) 1, ∀ y ∈ Set.Icc (0:ℝ) 1, + |f x-f y| ≤ K*|x-y|) (N : ℕ) (hN : 0 < N) : + |(∫ s in (0:ℝ)..1, f s) - (∑ i ∈ Finset.range N, f ((i:ℝ)/N))/N| ≤ K/N := by + have hN' : (0:ℝ) < N := Nat.cast_pos.mpr hN + let a : ℕ → ℝ := fun i => (i:ℝ)/N + have hadj (i : ℕ) : a (i+1)-a i = 1/(N:ℝ) := by dsimp [a]; push_cast; ring + have hal (i : ℕ) : a i ≤ a (i+1) := by dsimp [a]; gcongr; exact Nat.le_succ i + have hmem (i : ℕ) (hi : i ≤ N) : a i ∈ Set.Icc (0:ℝ) 1 := + ⟨by dsimp [a]; positivity, (div_le_one hN').mpr (Nat.cast_le.mpr hi)⟩ + have he (i : ℕ) (hi : i ∈ Finset.range N) : + |(∫ s in a i..a (i+1), f s)-f (a i)/N| ≤ K/N*(1/N) := by + have hinc : Set.uIcc (a i) (a (i+1)) ⊆ Set.Icc (0:ℝ) 1 := by + rw [Set.uIcc_of_le (hal i)] + exact Set.Icc_subset_Icc (hmem i (Nat.le_of_lt (Finset.mem_range.mp hi))).1 + (hmem (i+1) (Finset.mem_range.mp hi)).2 + have hh := intervalIntegral.norm_integral_le_of_norm_le_const + (a := a i) (b := a (i+1)) (f := fun s => f s-f (a i)) (C := K/N) + (fun s hs => by + have hs' : s ∈ Set.uIcc (a i) (a (i+1)) := Set.uIoc_subset_uIcc hs + have hd : |s-a i| ≤ 1/(N:ℝ) := by + rw [Set.uIcc_of_le (hal i)] at hs' + rw [abs_of_nonneg (sub_nonneg.mpr hs'.1)] + linarith [hs'.2, hadj i] + have hK : 0 ≤ K := by + have H := hlip 0 (by norm_num) 1 (by norm_num) + norm_num at H + exact le_trans (abs_nonneg _) H + exact (hlip s (hinc hs') (a i) (hmem i (Nat.le_of_lt (Finset.mem_range.mp hi)))).trans + (by simpa only [← mul_div_assoc, mul_one] using mul_le_mul_of_nonneg_left hd hK)) + rw [intervalIntegral.integral_sub (hf.intervalIntegrable ..) intervalIntegrable_const, + intervalIntegral.integral_const, smul_eq_mul, hadj i] at hh + simpa only [Real.norm_eq_abs, one_div, abs_of_pos (inv_pos.mpr hN'), inv_mul_eq_div] using hh + have hsum := intervalIntegral.sum_integral_adjacent_intervals + (a := a) (n := N) (f := f) (μ := MeasureTheory.volume) (fun k _ => hf.intervalIntegrable (a k) (a (k+1))) + have ha0 : a 0 = 0 := by simp [a] + have haN : a N = 1 := by simp [a,hN'.ne'] + rw [ha0,haN] at hsum + change |(∫ s in (0:ℝ)..1, f s) - (∑ i ∈ Finset.range N, f (a i))/N| ≤ K/N + rw [← hsum, Finset.sum_div, ← Finset.sum_sub_distrib] + calc + _ ≤ ∑ i ∈ Finset.range N, |(∫ s in a i..a (i+1), f s)-f (a i)/N| := Finset.abs_sum_le_sum_abs _ _ + _ ≤ ∑ i ∈ Finset.range N, K/N*(1/N) := Finset.sum_le_sum he + _ = _ := by simp only [Finset.sum_const,Finset.card_range,nsmul_eq_mul]; field_simp + +theorem integral {f : A → ℝ → ℝ} (hv : Effective (fun p : A × ℚ => f p.1 p.2)) + (hc : ∀ a, Continuous (f a)) (K : A → ℕ) (hK : Computable K) + (hlip : ∀ a x, x ∈ Set.Icc (0:ℝ) 1 → ∀ y, y ∈ Set.Icc (0:ℝ) 1 → + |f a x-f a y| ≤ (K a:ℝ)*|x-y|) : + Effective (fun a => ∫ s in (0:ℝ)..1, f a s) := by + obtain ⟨v,hv,herr⟩ := hv + let q : A × ℕ → ℚ := fun p => (∑ i ∈ Finset.range (p.2+1), + v ((p.1,(i:ℚ)/(p.2+1)),p.2))/(p.2+1) + let e : A × ℕ → ℚ := fun p => ((K p.1:ℚ)+1)*qerror p.2 + have hq : Computable q := by + have hden := rat_add.to_comp.comp ((ratNat.to_comp.comp (Computable.snd.comp + (Computable.fst : Computable (Prod.fst : (A×ℕ)×ℕ → A×ℕ)))).pair (Computable.const 1)) + have hrat := rat_div.to_comp.comp ((ratNat.to_comp.comp Computable.snd).pair hden) + have ha : Computable (fun p : (A×ℕ)×ℕ => ((p.1.1,(p.2:ℚ)/(p.1.2+1)),p.1.2)) := + (((Computable.fst.comp Computable.fst).pair hrat).pair (Computable.snd.comp Computable.fst)).of_eq (fun _ => rfl) + have hsum := computable_sum (Computable.succ.comp (Computable.snd : Computable (Prod.snd : A × ℕ → ℕ))) (hv.comp ha).to₂ + have hn : Computable (fun p : A × ℕ => (p.2:ℚ)+1) := + (rat_add.to_comp.comp ((ratNat.to_comp.comp (Computable.snd : Computable (Prod.snd : A × ℕ → ℕ))).pair (Computable.const (1 : ℚ)))).of_eq (fun p => rfl) + exact (rat_div.to_comp.comp (hsum.pair hn)).of_eq (fun p => by rfl) + have he : Computable e := by + unfold e + have hb := rat_add.to_comp.comp ((ratNat.to_comp.comp (hK.comp (Computable.fst : Computable (Prod.fst : A × ℕ → A)))).pair (Computable.const 1)) + exact (rat_mul.to_comp.comp (hb.pair (qerror_primrec.to_comp.comp Computable.snd))).of_eq (fun p => rfl) + apply of_enclosures hq he + · intro a n + let S : ℝ := (∑ i ∈ Finset.range (n+1), f a ((i:ℝ)/(n+1)))/(n+1) + have h1 := quadrature_bound (hc a) (K a) (hlip a) (n+1) (Nat.succ_pos _) + have h2 : |S-(q (a,n):ℝ)| ≤ error n := by + dsimp [S,q] + push_cast + rw [← sub_div,abs_div,abs_of_pos (by positivity : (0:ℝ) by simpa using herr (a,(i:ℚ)/(n+1)) n) + _ = _ := by simp; ring + calc + _ ≤ |(∫ s in (0:ℝ)..1, f a s)-S| + |S-(q (a,n):ℝ)| := abs_sub_le _ _ _ + _ ≤ (K a:ℝ)/(n+1) + error n := add_le_add (by simpa only [Nat.cast_add,Nat.cast_one] using h1) h2 + _ = (e (a,n):ℝ) := by simp [e,error]; ring + · intro a + simpa only [e,Rat.cast_mul,Rat.cast_add,Rat.cast_natCast,Rat.cast_one,cast_qerror,mul_zero] using + error_tendsto.const_mul ((K a:ℝ)+1) +end CertifiedReal + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/EffectiveForcing.lean b/lean/OAI/Analysis/PeriodicLattice/EffectiveForcing.lean new file mode 100644 index 0000000000000000000000000000000000000000..b4d26ca15d302a3b85a769d4a9030be47967af9c --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/EffectiveForcing.lean @@ -0,0 +1,235 @@ +import OAI.Analysis.PeriodicLattice.EffectivePotentials + +namespace OAI + +/-! Effective periodic velocity, pressure and solenoidal forces. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingEffectiveForcing {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace EffectiveFields +open CertifiedReal Quantitative RapidCalculus TorusCalculus RecursiveArithmetic +open scoped ContDiff +local instance effectiveForcingLocal1 : Primcodable ℚ := ratPrimcodable +local instance effectiveForcingLocal2 : DecidablePred Input.WellFormed := Classical.decPred _ +local instance effectiveForcingLocal3 : Primcodable ValidInput := Primcodable.subtype inputWellFormed + +theorem tensor_base {F : Input → ScalarField} {B : Input → ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hb : Effective (fun p : ValidInput × BiPoint => biValue (B p.1.1) p.2)) + (hh : Effective (fun z : ℚ => h z)) + (heq : ∀ d t x, F d t (torusMk x) = h (x 2) * B d t (x 1)) : + Effective (fun p : ValidInput × RationalPoint => fieldValue (F p.1.1) p.2) := by + have ha : Computable (fun p : ValidInput × RationalPoint => (p.1,p.2.1,p.2.2 1)) := + (Primrec.fst.pair ((Primrec.fst.comp Primrec.snd).pair + (Primrec.fin_app.comp (Primrec.snd.comp Primrec.snd) (Primrec.const 1)))).to_comp + have hz : Computable (fun p : ValidInput × RationalPoint => p.2.2 2) := + (Primrec.fin_app.comp (Primrec.snd.comp Primrec.snd) (Primrec.const 2)).to_comp + exact ((hh.comp hz).mul (hb.comp ha)).congr (fun p => by + dsimp only [fieldValue,biValue] + rw [heq] + rfl) + +theorem phase_effective : Effective (fun z : ℚ => 2*Real.pi*((z:ℝ)-1/2)) := by + have h := ((constant (A := ℚ) 2).mul pi).mul ((rational Computable.id).sub (constant (1/2))) + simpa only [Rat.cast_ofNat,Rat.cast_div,Rat.cast_one,id_eq] using h + +theorem eta_effective : Effective (fun z : ℚ => FluidLift.eta z) := by + have hd : Effective (fun _ : ℚ => 2*Real.pi) := by simpa only [Rat.cast_ofNat] using (constant (A := ℚ) 2).mul pi + exact phase_effective.sin.div hd (fun _ => mul_ne_zero (by norm_num) Real.pi_ne_zero) + +theorem slope_effective : Effective (fun z : ℚ => FluidLift.slope z) := phase_effective.cos + +theorem doubleSlope_effective : Effective (fun z : ℚ => FluidLift.doubleSlope z) := by + exact (((constant (A := ℚ) 2).mul (slope_effective.mul slope_effective)).sub (constant 1)).congr + (fun z => by simp only [FluidLift.doubleSlope,FluidLift.slope,Rat.cast_ofNat,Rat.cast_one]; ring) + +theorem velocity_effective : ComponentsEffective FluidLift.velocity := by + refine Fin.cases ?_ (Fin.cases ?_ (Fin.cases ?_ (fun i => i.elim0))) + · exact tensor_base (F := fun d t q => FluidLift.velocity d t q 0) a_base slope_effective (fun d t x => by simp) + · exact tensor_base (F := fun d t q => FluidLift.velocity d t q 1) b_base slope_effective (fun d t x => by simp) + · exact tensor_base (F := fun d t q => FluidLift.velocity d t q 2) (h := fun z => -FluidLift.eta z) bdy_base eta_effective.neg (fun d t x => by simp) + +theorem potential_effective : Effective (fun p : ValidInput × RationalPoint => fieldValue (FluidLift.potential p.1.1) p.2) := by + have hbase : Effective (fun p : ValidInput × RationalPoint => + fieldValue (PeriodicInverse.horizontal (FluidLift.pressureBase p.1.1) (FluidLift.pressureBase_periodic p.1.1)) p.2) := + tensor_base (F := fun d => PeriodicInverse.horizontal (FluidLift.pressureBase d) (FluidLift.pressureBase_periodic d)) (h := fun _ => 1) pressureBase_base (by simpa only [Rat.cast_one] using (constant (A := ℚ) 1)) (fun d t x => by simp) + exact hbase.add (tensor_base pressureMode_base doubleSlope_effective FluidLift.pressureOsc_cover) + +theorem ComponentsEffective.diffusion {F : Input → VectorField} (hf : ComponentsEffective F) + (hF : FieldCertificate F) : ComponentsEffective (fun d => laplacian (F d)) := by + have hd (i) := (hf.diff hF (some i)).diff (hF.diff (some i)) (some i) + intro j + exact (((hd 0 j).add (hd 1 j)).add (hd 2 j)).congr (fun p => by + simp only [laplacian,Fin.sum_univ_three,PiLp.add_apply,coordD]) + +theorem ComponentsEffective.transport {F : Input → VectorField} (hf : ComponentsEffective F) + (hF : FieldCertificate F) : ComponentsEffective (fun d => advection (F d)) := by + intro j + exact ((((hf 0).mul (hf.diff hF (some 0) j)).add ((hf 1).mul (hf.diff hF (some 1) j))).add + ((hf 2).mul (hf.diff hF (some 2) j))).congr (fun p => by + simp only [advection,Fin.sum_univ_three,PiLp.add_apply,PiLp.smul_apply,smul_eq_mul,coordD]) + +theorem ComponentsEffective.gradient {F : Input → ScalarField} + (hf : Effective (fun p : ValidInput × RationalPoint => fieldValue (F p.1.1) p.2)) + (hF : FieldCertificate F) : ComponentsEffective (fun d => gradient (F d)) := + fun i => field_diff hF hf (some i) + +theorem force_effective (ν : ℝ) (hc : Effective (fun _ : Unit => ν)) : ComponentsEffective (FluidLift.force ν) := + ((velocity_effective.diff velocityCertificate none).add (velocity_effective.transport velocityCertificate)).sub + ((velocity_effective.diffusion velocityCertificate).scale ν hc) + +theorem solenoidalForce_effective (ν : ℝ) (hc : Effective (fun _ : Unit => ν)) : ComponentsEffective (FluidLift.solenoidalForce ν) := + (force_effective ν hc).sub (ComponentsEffective.gradient potential_effective potentialCertificate) + +end EffectiveFields + +namespace CertifiedReal +open RecursiveArithmetic +local instance effectiveForcingLocal4 : Primcodable ℚ := ratPrimcodable + +theorem accuracy_as_inv (n : ℕ) : accuracy n = ((2:ℝ)^n)⁻¹ := by simp [accuracy,zpow_neg] + +theorem accuracy_le_error (n : ℕ) : accuracy n ≤ error n := by + rw [accuracy_as_inv,error,one_div] + apply inv_le_inv₀ (by positivity) (by positivity) |>.mpr + exact_mod_cast Nat.succ_le_of_lt (Nat.lt_two_pow_self (n := n)) + +theorem computableReal_effective {x : ℝ} (hx : ComputableReal x) : Effective (fun _ : Unit => x) := by + obtain ⟨P,hP⟩ := hx + choose q hq he using hP + have henc : Computable (fun n => Encodable.encode (q n)) := + (Nat.Partrec.Code.eval_part.comp (Computable.const P) Computable.id).of_eq_tot hq + have hc : Computable q := Computable.encode_iff.mp henc + exact ⟨fun p => q p.2,hc.comp Computable.snd,fun _ n => (he n).trans (accuracy_le_error n)⟩ + +end CertifiedReal +namespace EffectiveFields +open CertifiedReal Quantitative RapidCalculus TorusCalculus RecursiveArithmetic +open scoped ContDiff +local instance effectiveForcingLocal5 : Primcodable ℚ := ratPrimcodable +local instance effectiveForcingLocal6 : DecidablePred Input.WellFormed := Classical.decPred _ +local instance effectiveForcingLocal7 : Primcodable ValidInput := Primcodable.subtype inputWellFormed + +theorem time_error {t : ℝ} (ht : 0 ≤ t) (a : ℚ) : |t - time a| ≤ |t - (a:ℝ)| := by + rw [time_eq] + rcases le_total 0 (a:ℝ) with ha | ha + · rw [max_eq_left ha] + · rw [max_eq_right ha,sub_zero,abs_of_nonneg ht,abs_of_nonneg (by linarith : 0 ≤ t-(a:ℝ))] + linarith + +section Distance +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +theorem field_distance {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + {K δ t s : ℝ} (hK : 0 ≤ K) + (hb : ∀ i : Option (Fin 3), ∀ u : ℝ, 0 ≤ u → ∀ q, ‖coordD i F u q‖ ≤ K) + (ht : 0 ≤ t) (hs : 0 ≤ s) (x y : Space) + (hΔt : |t-s| ≤ δ) (hΔx : ∀ i, |x i-y i| ≤ δ) : + ‖F t (torusMk x) - F s (torusMk y)‖ ≤ 4*K*δ := by + have htime : ‖F t (torusMk x) - F s (torusMk x)‖ ≤ K*δ := by + have h := Convex.norm_image_sub_le_of_norm_hasDerivWithin_le + (fun u _ => (fullTime_hasDerivAt hF u (torusMk x)).hasDerivWithinAt) + (fun u hu => hb none u hu (torusMk x)) (convex_Ici (0:ℝ)) hs ht + exact h.trans (mul_le_mul_of_nonneg_left hΔt hK) + have hspace (z : Space) (i : Fin 3) : + ‖F s (torusMk (z+EuclideanSpace.single i (x i-y i))) - F s (torusMk z)‖ ≤ K*δ := by + have h := Convex.norm_image_sub_le_of_norm_hasDerivWithin_le (s := Set.univ) + (fun u _ => (translation_hasDerivAt (smooth_slice_differentiable hF s) (torusMk z) i u).hasDerivWithinAt) + (fun u _ => hb (some i) s hs (torusMk z+torusMk (EuclideanSpace.single i u))) + convex_univ (Set.mem_univ (0:ℝ)) (Set.mem_univ (x i-y i)) + simp only [sub_zero,Real.norm_eq_abs,single_zero,mk_zero,add_zero,← mk_add] at h + exact h.trans (mul_le_mul_of_nonneg_left (hΔx i) hK) + let z₁ := y+EuclideanSpace.single 0 (x 0-y 0) + let z₂ := z₁+EuclideanSpace.single 1 (x 1-y 1) + have hx : z₂+EuclideanSpace.single 2 (x 2-y 2) = x := by + ext i + fin_cases i <;> simp [z₂,z₁] + have h₀ := hspace y 0 + have h₁ := hspace z₁ 1 + have h₂ := hspace z₂ 2 + rw [hx] at h₂ + calc + _ ≤ ‖F t (torusMk x) - F s (torusMk x)‖ + ‖F s (torusMk x) - F s (torusMk y)‖ := norm_sub_le_norm_sub_add_norm_sub _ _ _ + _ ≤ K*δ + (‖F s (torusMk x) - F s (torusMk z₂)‖ + ‖F s (torusMk z₂) - F s (torusMk y)‖) := + add_le_add htime (norm_sub_le_norm_sub_add_norm_sub _ _ _) + _ ≤ K*δ + (K*δ + (‖F s (torusMk z₂) - F s (torusMk z₁)‖ + ‖F s (torusMk z₁) - F s (torusMk y)‖)) := + add_le_add le_rfl (add_le_add h₂ (norm_sub_le_norm_sub_add_norm_sub _ _ _)) + _ ≤ K*δ + (K*δ + (K*δ+K*δ)) := by gcongr + _ = _ := by ring + +theorem fieldWord_nearby {F : Input → Field A} (hF : FieldCertificate F) + (d : ValidInput) (w : List (Option (Fin 3))) (a : RationalPoint) + {δ t : ℝ} (ht : 0 ≤ t) (x : Space) + (hΔt : |t-(a.1:ℝ)| ≤ δ) (hΔx : ∀ i, |x i-(a.2 i:ℝ)| ≤ δ) : + ‖fieldWord w (F d.1) t (torusMk x) - fieldWord w (F d.1) (time a.1) (torusMk (rationalVector a.2))‖ ≤ + 4*(hF.budget (d.1,w.length+1,0):ℝ)*δ := by + apply field_distance (fieldWord_contDiff (hF.smooth d.1) w) (Nat.cast_nonneg _) _ ht (time_nonneg a.1) x (rationalVector a.2) + ((time_error ht a.1).trans hΔt) hΔx + intro i u hu q + simpa only [fieldWord_cons,pow_zero,one_mul] using + hF.estimate d.1 d.2 (i::w) (w.length+1) 0 (by simp) u hu q +end Distance + +theorem word_evaluator {F : Input → VectorField} (hF : FieldCertificate F) (hf : ComponentsEffective F) : + ∃ Q : (ValidInput × List (Option (Fin 3)) × RationalPoint) × ℕ → Fin 3 → ℚ, + Computable Q ∧ ∀ (d : ValidInput) w a n, + ‖fieldWord w (F d.1) (time a.1) (torusMk (rationalVector a.2)) - rationalVector (Q ((d,w,a),n))‖ ≤ 3*error n := by + have he (i : Fin 3) := field_words (hF.component i) (hf i) + choose q hq bq using he + let Q : (ValidInput × List (Option (Fin 3)) × RationalPoint) × ℕ → Fin 3 → ℚ := fun an i => q i an + have hQ : Computable Q := (Primrec.vector_get'.to_comp.comp (Computable.vector_ofFn hq)).of_eq (fun an => by + funext i + simp only [List.Vector.get_ofFn] + rfl) + refine ⟨Q,hQ,fun d w a n => ?_⟩ + have hcoord (i : Fin 3) : + ‖(fieldWord w (F d.1) (time a.1) (torusMk (rationalVector a.2)) - rationalVector (Q ((d,w,a),n))) i‖ ≤ error n := by + change |fieldWord w (F d.1) (time a.1) (torusMk (rationalVector a.2)) i - (q i ((d,w,a),n):ℝ)| ≤ error n + simpa only [fieldValue,fieldWord_component (hF.smooth d.1)] using bq i (d,w,a) n + calc + _ ≤ ∑ i : Fin 3, ‖(fieldWord w (F d.1) (time a.1) (torusMk (rationalVector a.2)) - rationalVector (Q ((d,w,a),n))) i‖ := norm_le_sum_components _ + _ ≤ ∑ _i : Fin 3, error n := Finset.sum_le_sum (fun i _ => hcoord i) + _ = _ := by simp + +end EffectiveFields +namespace CertifiedReal + +theorem accuracy_pos (n : ℕ) : 0 < accuracy n := by unfold accuracy; positivity + +theorem accuracy_add (n k : ℕ) : accuracy (n+k) = accuracy n * accuracy k := by + simp only [accuracy_as_inv,pow_add,mul_inv] + +theorem error_pow (n : ℕ) : error (2^n) ≤ accuracy n := by + rw [error,accuracy_as_inv,one_div] + apply (inv_le_inv₀ (by positivity) (by positivity)).mpr + simp only [Nat.cast_pow,Nat.cast_ofNat] + linarith + +theorem accuracy_budget (K : ℕ) : (K:ℝ)*accuracy K ≤ 1 := by + rw [accuracy_as_inv,← div_eq_mul_inv] + apply (div_le_iff₀ (by positivity)).mpr + rw [one_mul] + exact_mod_cast (Nat.lt_two_pow_self (n := K)).le + +theorem evaluation_tolerance (n K : ℕ) : + 4*(K:ℝ)*accuracy (n+K+6) + 3*error (2^(n+6)) ≤ accuracy n := by + have he : accuracy 6 = 1/64 := by norm_num [accuracy] + have hK := mul_le_mul_of_nonneg_left (accuracy_budget K) (accuracy_pos n).le + have hp : 0 < accuracy n := accuracy_pos n + calc + _ ≤ 4*(K:ℝ)*accuracy (n+K+6) + 3*accuracy (n+6) := by + gcongr + exact error_pow _ + _ ≤ _ := by + simp only [accuracy_add,he] + nlinarith +end CertifiedReal + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/EffectivePotentials.lean b/lean/OAI/Analysis/PeriodicLattice/EffectivePotentials.lean new file mode 100644 index 0000000000000000000000000000000000000000..024143aa3c10a72af7d92b2f298600df267f6af1 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/EffectivePotentials.lean @@ -0,0 +1,248 @@ +import OAI.Analysis.PeriodicLattice.EffectiveProfiles + +namespace OAI + +/-! Effective planar estimates and periodic pressure operators. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingEffectivePotentials {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace EffectiveFields +open CertifiedReal Quantitative RapidCalculus TorusCalculus RecursiveArithmetic +open scoped ContDiff +local instance effectivePotentialsLocal1 : Primcodable ℚ := ratPrimcodable +local instance effectivePotentialsLocal2 : DecidablePred Input.WellFormed := Classical.decPred _ +local instance effectivePotentialsLocal3 : Primcodable ValidInput := Primcodable.subtype inputWellFormed + +theorem bi_diff {F : Input → ℝ → ℝ → ℝ} (hF : BiCertificate F) + (hf : Effective (fun p : ValidInput × BiPoint => biValue (F p.1.1) p.2)) (i : Bool) : + Effective (fun p : ValidInput × BiPoint => biValue (biD i (F p.1.1)) p.2) := + (bi_words hF hf).comp (Primrec.fst.pair ((Primrec.const [i]).pair Primrec.snd)).to_comp + +theorem bi_estimate {F : Input → ℝ → ℝ → ℝ} (hF : BiCertificate F) (d : ValidInput) + (w : List Bool) (n : ℕ) (hn : w.length ≤ n) (t : ℝ) (ht : 0 ≤ t) (y : ℝ) : + |wordD w (F d.1) t y| ≤ (hF.budget (d.1,n,0) : ℝ) := by + simpa only [pow_zero,one_mul,Real.norm_eq_abs] using hF.estimate d.1 d.2 w n 0 hn t ht y + +theorem bi_mean {F : Input → ℝ → ℝ → ℝ} (hF : BiCertificate F) + (hf : Effective (fun p : ValidInput × BiPoint => biValue (F p.1.1) p.2)) : + Effective (fun p : ValidInput × BiPoint => biValue (PeriodicInverse.mean (F p.1.1)) p.2) := by + have hv := hf.comp (g := fun p : (ValidInput × BiPoint) × ℚ => (p.1.1,p.1.2.1,p.2)) (by fun_prop) + have harg : Primrec (fun p : ValidInput × BiPoint => (p.1.1,1,0)) := + (validData_recursive.comp Primrec.fst).pair (Primrec.const (1,0)) + refine integral (f := fun (p : ValidInput × BiPoint) s => F p.1.1 (time p.2.1) s) hv + (fun p => ((hF.smooth p.1.1).continuous.comp (continuous_const.prodMk continuous_id))) + (fun p : ValidInput × BiPoint => hF.budget (p.1.1,1,0)) + ((hF.recursive.comp harg).of_eq (fun _ => rfl)).to_comp ?_ + intro p x hx y hy + have hd (s : ℝ) : HasDerivAt (F p.1.1 (time p.2.1)) (biD false (F p.1.1) (time p.2.1) s) s := + (((hF.smooth p.1.1).comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) s).hasDerivAt + exact Convex.norm_image_sub_le_of_norm_hasDerivWithin_le (fun s _ => (hd s).hasDerivWithinAt) + (fun s _ => bi_estimate hF p.1 [false] 1 le_rfl _ (time_nonneg _) s) + (convex_Icc (0:ℝ) 1) hy hx + +theorem bi_first {F : Input → ℝ → ℝ → ℝ} (hF : BiCertificate F) + (hf : Effective (fun p : ValidInput × BiPoint => biValue (F p.1.1) p.2)) + (lam : ℝ) (hlam : lam ≠ 0) (he : Effective (fun _ : Unit => lam)) : + Effective (fun p : ValidInput × BiPoint => biValue (PeriodicInverse.first lam (F p.1.1)) p.2) := by + have hv : Effective (fun p : (ValidInput × BiPoint) × ℚ => + Real.exp (lam * (p.2:ℝ)) * F p.1.1.1 (time p.1.2.1) ((p.1.2.2:ℝ) - p.2)) := by + have hl := he.comp (Computable.const ()) (A := ((ValidInput × BiPoint) × ℚ)) + have harg : Computable (fun p : (ValidInput × BiPoint) × ℚ => (p.1.1,p.1.2.1,p.1.2.2-p.2)) := by fun_prop + exact ((hl.mul (rational Computable.snd)).exp.mul (hf.comp harg)).congr (fun p => by simp only [biValue,Rat.cast_sub]) + let M := ⌈Real.exp |lam| * (|lam|+1)⌉₊ + have hb : Real.exp |lam| * (|lam|+1) ≤ (M:ℝ) := Nat.le_ceil _ + have hbudget : Computable (fun p : ValidInput × BiPoint => M * hF.budget (p.1.1,1,0)) := by + have ha : Primrec (fun p : ValidInput × BiPoint => (p.1.1,1,0)) := + (validData_recursive.comp Primrec.fst).pair (Primrec.const (1,0)) + exact ((Primrec.nat_mul.comp (Primrec.const M) (hF.recursive.comp ha)).of_eq (fun _ => rfl)).to_comp + have hi := integral (f := fun (p : ValidInput × BiPoint) s => Real.exp (lam*s) * F p.1.1 (time p.2.1) ((p.2.2:ℝ)-s)) hv (fun p => by + exact (Real.continuous_exp.comp (continuous_const.mul continuous_id)).mul + ((hF.smooth p.1.1).continuous.comp (continuous_const.prodMk (continuous_const.sub continuous_id)))) + (fun p : ValidInput × BiPoint => M * hF.budget (p.1.1,1,0)) hbudget (by + intro p x hx y hy + have hd (s : ℝ) : HasDerivAt (fun s => Real.exp (lam*s) * F p.1.1 (time p.2.1) ((p.2.2:ℝ)-s)) + (Real.exp (lam*s)*lam*F p.1.1 (time p.2.1) ((p.2.2:ℝ)-s) + + Real.exp (lam*s)*(biD false (F p.1.1) (time p.2.1) ((p.2.2:ℝ)-s)*(-1))) s := by + have hh : HasDerivAt (F p.1.1 (time p.2.1)) + (biD false (F p.1.1) (time p.2.1) ((p.2.2:ℝ)-s)) ((p.2.2:ℝ)-s) := + (((hF.smooth p.1.1).comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) _).hasDerivAt + simpa only [mul_one, Function.comp_def, Pi.mul_def, id_eq] using + (((hasDerivAt_id s).const_mul lam).exp).mul (hh.comp s ((hasDerivAt_id s).const_sub (p.2.2:ℝ))) + apply Convex.norm_image_sub_le_of_norm_hasDerivWithin_le (fun s _ => (hd s).hasDerivWithinAt) _ (convex_Icc (0:ℝ) 1) hy hx + intro s hs + have he' : |Real.exp (lam*s)| ≤ Real.exp |lam| := by + rw [abs_of_pos (Real.exp_pos _)] + apply Real.exp_le_exp.mpr + calc + lam*s ≤ |lam| * s := mul_le_mul_of_nonneg_right (le_abs_self _) hs.1 + _ ≤ |lam| := mul_le_of_le_one_right (abs_nonneg _) hs.2 + have h0 := bi_estimate hF p.1 [] 1 (by simp) (time p.2.1) (time_nonneg p.2.1) ((p.2.2:ℝ)-s) + have h1 := bi_estimate hF p.1 [false] 1 le_rfl (time p.2.1) (time_nonneg p.2.1) ((p.2.2:ℝ)-s) + simp only [Real.norm_eq_abs] + calc + _ ≤ |Real.exp (lam*s)*lam*F p.1.1 (time p.2.1) ((p.2.2:ℝ)-s)| + + |Real.exp (lam*s)*(biD false (F p.1.1) (time p.2.1) ((p.2.2:ℝ)-s)*(-1))| := abs_add_le _ _ + _ ≤ Real.exp |lam| * |lam| * (hF.budget (p.1.1,1,0):ℝ) + + Real.exp |lam| * (hF.budget (p.1.1,1,0):ℝ) := by + simp only [abs_mul, abs_neg, abs_one, mul_one] + exact add_le_add (mul_le_mul (mul_le_mul_of_nonneg_right he' (abs_nonneg _)) h0 (abs_nonneg _) (by positivity)) + (mul_le_mul he' h1 (abs_nonneg _) (by positivity)) + _ = (Real.exp |lam| * (|lam|+1)) * (hF.budget (p.1.1,1,0):ℝ) := by ring + _ ≤ (M * hF.budget (p.1.1,1,0):ℕ) := by + rw [Nat.cast_mul]; exact mul_le_mul_of_nonneg_right hb (Nat.cast_nonneg _)) + have hh := (((constant (A := ValidInput × BiPoint) 1).sub ((he.comp (Computable.const ())).exp)).inv + (fun _ => sub_ne_zero.mpr ((fun h => hlam (Real.exp_injective (by simpa only [Real.exp_zero,Rat.cast_one] using h.symm)))))).mul hi + exact hh.congr (fun p => by dsimp only [biValue,PeriodicInverse.first]; norm_num) + +theorem bdy_base : Effective (fun p : ValidInput × BiPoint => biValue (FluidLift.bdy p.1.1) p.2) := + bi_diff bCertificate b_base false + +theorem pressureSource_base : Effective (fun p : ValidInput × BiPoint => biValue (FluidLift.pressureSource p.1.1) p.2) := + (bdy_base.mul bdy_base).sub (b_base.mul (bi_diff (bCertificate.diff false) bdy_base false)) + +theorem pressureBase_base : Effective (fun p : ValidInput × BiPoint => biValue (FluidLift.pressureBase p.1.1) p.2) := by + simpa only [Rat.cast_div,Rat.cast_one,Rat.cast_ofNat,biValue,FluidLift.pressureBase,Pi.mul_def] using + (constant (A := ValidInput × BiPoint) (1/2)).mul + ((b_base.mul b_base).sub (bi_mean (bCertificate.mul bCertificate) (b_base.mul b_base))) + +theorem pressureMode_base : Effective (fun p : ValidInput × BiPoint => biValue (FluidLift.pressureMode p.1.1) p.2) := by + have he : Effective (fun _ : Unit => 4*Real.pi) := by + simpa only [Rat.cast_ofNat] using (constant (A := Unit) 4).mul pi + exact bi_first (pressureSourceCertificate.first (4*Real.pi)) + (bi_first pressureSourceCertificate pressureSource_base (4*Real.pi) (mul_ne_zero (by norm_num) Real.pi_ne_zero) he) + (-(4*Real.pi)) (neg_ne_zero.mpr (mul_ne_zero (by norm_num) Real.pi_ne_zero)) he.neg +end EffectiveFields +namespace EffectiveFields +open CertifiedReal Quantitative RapidCalculus TorusCalculus RecursiveArithmetic +open scoped ContDiff +local instance effectivePotentialsLocal4 : Primcodable ℚ := ratPrimcodable +local instance effectivePotentialsLocal5 : DecidablePred Input.WellFormed := Classical.decPred _ +local instance effectivePotentialsLocal6 : Primcodable ValidInput := Primcodable.subtype inputWellFormed + +def fieldValue (F : ScalarField) (p : RationalPoint) : ℝ := F (time p.1) (torusMk (rationalVector p.2)) + +def fieldShift (i : Option (Fin 3)) (p : RationalPoint) (n : ℕ) : RationalPoint := + match i with + | none => (max p.1 0 + qerror n, p.2) + | some j => (p.1, fun k => if k = j then p.2 k + qerror n else p.2 k) + +@[fun_prop] theorem fieldShift_recursive : Primrec (fun p : Option (Fin 3) × RationalPoint × ℕ => fieldShift p.1 p.2.1 p.2.2) := by + have ht : Primrec (fun p : Option (Fin 3) × RationalPoint × ℕ => p.2.1.1) := + Primrec.fst.comp (Primrec.fst.comp Primrec.snd) + have hx : Primrec (fun p : Option (Fin 3) × RationalPoint × ℕ => p.2.1.2) := + Primrec.snd.comp (Primrec.fst.comp Primrec.snd) + have he : Primrec (fun p : Option (Fin 3) × RationalPoint × ℕ => qerror p.2.2) := + qerror_primrec.comp (Primrec.snd.comp Primrec.snd) + have hn : Primrec (fun p : Option (Fin 3) × RationalPoint × ℕ => (max p.2.1.1 0 + qerror p.2.2,p.2.1.2)) := + (rat_add.comp ((ratMax.comp (ht.pair (Primrec.const 0))).pair he)).pair hx + have hs : Primrec (fun p : (Option (Fin 3) × RationalPoint × ℕ) × Fin 3 => + (p.1.2.1.1,fun k => if k = p.2 then p.1.2.1.2 k + qerror p.1.2.2 else p.1.2.1.2 k)) := by + refine (ht.comp Primrec.fst).pair (Primrec.fin_curry.mpr ?_) + have hv : Primrec (fun p : ((Option (Fin 3) × RationalPoint × ℕ) × Fin 3) × Fin 3 => p.1.1.2.1.2 p.2) := + Primrec.fin_app.comp (hx.comp (Primrec.fst.comp Primrec.fst)) Primrec.snd + exact Primrec.ite (Primrec.eq.comp Primrec.snd (Primrec.snd.comp Primrec.fst)) + (rat_add.comp (hv.pair (he.comp (Primrec.fst.comp Primrec.fst)))) hv + exact (Primrec.option_casesOn Primrec.fst hn hs.to₂).of_eq (fun p => by cases p.1 <;> rfl) + +def fieldLine (i : Option (Fin 3)) (t : ℝ) (q : Torus) (s : ℝ) : ℝ × Torus := + match i with + | none => (t+s,q) + | some j => (t,q+torusMk (EuclideanSpace.single j s)) + +@[simp] theorem fieldLine_zero (i : Option (Fin 3)) (t : ℝ) (q : Torus) : fieldLine i t q 0 = (t,q) := by + cases i <;> simp [fieldLine,single_zero,mk_zero] + +theorem fieldLine_nonneg (i : Option (Fin 3)) {t s : ℝ} (ht : 0 ≤ t) (hs : 0 ≤ s) (q : Torus) : + 0 ≤ (fieldLine i t q s).1 := by cases i <;> simp [fieldLine] <;> positivity + +theorem fieldShift_value (i : Option (Fin 3)) (p : RationalPoint) (n : ℕ) (F : ScalarField) : + fieldValue F (fieldShift i p n) = + F (fieldLine i (time p.1) (torusMk (rationalVector p.2)) (error n)).1 + (fieldLine i (time p.1) (torusMk (rationalVector p.2)) (error n)).2 := by + cases i with + | none => + have h : 0 ≤ max (p.1:ℝ) 0 + error n := add_nonneg (le_max_right _ _) (error_pos n).le + simp [fieldValue,fieldShift,fieldLine,max_eq_left h] + | some j => + dsimp only [fieldValue,fieldShift,fieldLine] + congr 2 + rw [← mk_add] + congr 1 + ext k + by_cases hk : k = j + · subst k; simp [rationalVector] + · simp [rationalVector,hk] + +theorem fieldLine_deriv {F : ScalarField} (hF : ContDiff ℝ ∞ (lifted F)) + (i : Option (Fin 3)) (t : ℝ) (q : Torus) (s : ℝ) : + HasDerivAt (fun z => F (fieldLine i t q z).1 (fieldLine i t q z).2) + (coordD i F (fieldLine i t q s).1 (fieldLine i t q s).2) s := by + cases i with + | none => + simpa only [fieldLine,coordD,one_mul,mul_one,Function.comp_def] using + (fullTime_hasDerivAt hF (t+s) q).comp s ((hasDerivAt_id s).const_add t) + | some j => exact translation_hasDerivAt (smooth_slice_differentiable hF t) q j s + +theorem field_words {F : Input → ScalarField} (hF : FieldCertificate F) + (hbase : Effective (fun p : ValidInput × RationalPoint => fieldValue (F p.1.1) p.2)) : + Effective (fun p : ValidInput × List (Option (Fin 3)) × RationalPoint => fieldValue (fieldWord p.2.1 (F p.1.1)) p.2.2) := by + apply effective_words (A := ValidInput) (shift := fieldShift) + (V := fun w (d : ValidInput) p => fieldValue (fieldWord w (F d.1)) p) + fieldShift_recursive hbase (fun dn : ValidInput × ℕ => hF.budget (dn.1.1,dn.2+1,0)) + · apply Primrec.to_comp + have ha : Primrec (fun dn : ValidInput × ℕ => (dn.1.1,dn.2+1,0)) := + (validData_recursive.comp Primrec.fst).pair ((Primrec.nat_add.comp Primrec.snd (Primrec.const 1)).pair (Primrec.const 0)) + exact (hF.recursive.comp ha).of_eq (fun _ => rfl) + intro d i w L hw p n + have hs := fieldWord_contDiff (hF.smooth d.1) w + have he := quotient_error (error_pos n) + (fieldLine_deriv hs i (time p.1) (torusMk (rationalVector p.2))) + (fieldLine_deriv (coordD_contDiff hs i) i (time p.1) (torusMk (rationalVector p.2))) + (K := (hF.budget (d.1,L+1,0):ℝ)) (fun s hs => by + have hb := hF.estimate d.1 d.2 (i::i::w) (L+1) 0 + (by simpa only [List.length_cons] using Nat.succ_le_succ hw) + (fieldLine i (time p.1) (torusMk (rationalVector p.2)) s).1 + (fieldLine_nonneg i (time_nonneg p.1) hs.1 _) + (fieldLine i (time p.1) (torusMk (rationalVector p.2)) s).2 + simpa only [pow_zero,one_mul,fieldWord_cons,Real.norm_eq_abs] using hb) + rw [fieldShift_value] + dsimp only [fieldValue,fieldWord_cons] + simp only [fieldLine_zero] at he + exact he.trans (mul_le_mul_of_nonneg_right (by linarith) (error_pos n).le) + +theorem field_diff {F : Input → ScalarField} (hF : FieldCertificate F) + (hf : Effective (fun p : ValidInput × RationalPoint => fieldValue (F p.1.1) p.2)) (i : Option (Fin 3)) : + Effective (fun p : ValidInput × RationalPoint => fieldValue (coordD i (F p.1.1)) p.2) := + (field_words hF hf).comp (Primrec.fst.pair ((Primrec.const [i]).pair Primrec.snd)).to_comp + +def ComponentsEffective (F : Input → VectorField) : Prop := + ∀ i : Fin 3, Effective (fun p : ValidInput × RationalPoint => F p.1.1 (time p.2.1) (torusMk (rationalVector p.2.2)) i) + +theorem ComponentsEffective.diff {F : Input → VectorField} (hf : ComponentsEffective F) + (hF : FieldCertificate F) (j : Option (Fin 3)) : ComponentsEffective (fun d => coordD j (F d)) := by + intro i + exact (field_diff (hF.component i) (hf i) j).congr (fun p => by + dsimp only [fieldValue] + rw [coordD_component (hF.smooth p.1.1)]) + +theorem ComponentsEffective.add {F G : Input → VectorField} (hf : ComponentsEffective F) + (hg : ComponentsEffective G) : ComponentsEffective (fun d => F d + G d) := fun i => (hf i).add (hg i) + +theorem ComponentsEffective.sub {F G : Input → VectorField} (hf : ComponentsEffective F) + (hg : ComponentsEffective G) : ComponentsEffective (fun d => F d - G d) := fun i => (hf i).sub (hg i) + +theorem ComponentsEffective.scale {F : Input → VectorField} (hf : ComponentsEffective F) + (c : ℝ) (hc : Effective (fun _ : Unit => c)) : ComponentsEffective (fun d => c • F d) := + fun i => (hc.comp (Computable.const ())).mul (hf i) + +end EffectiveFields + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/EffectiveProfiles.lean b/lean/OAI/Analysis/PeriodicLattice/EffectiveProfiles.lean new file mode 100644 index 0000000000000000000000000000000000000000..51674b86c9b621319085548ae3d1cfef52c4b2bd --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/EffectiveProfiles.lean @@ -0,0 +1,299 @@ +import OAI.Analysis.PeriodicLattice.EffectiveDerivatives + +namespace OAI + +/-! Effective smooth profiles, stack codes and planar compilation. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingEffectiveProfiles {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace EffectiveProfiles +open CertifiedReal RecursiveArithmetic ProfileJets +local instance effectiveProfilesLocal1 : Primcodable ℚ := ratPrimcodable + +theorem rho : Effective (fun q : ℚ => expNegInvGlue (q : ℝ)) := by + have h := (rational (q := fun q : ℚ => -q⁻¹) (by fun_prop)).exp + exact ((constant 0).ite h (ratLE.comp Primrec.id (Primrec.const 0))).congr + (fun q => by simp [expNegInvGlue]) + +theorem rhoTerm (k : ℕ) : Effective (fun q : ℚ => ProfileJets.rhoTerm k (q : ℝ)) := by + have h := (rational (q := fun q : ℚ => q⁻¹^k) (by fun_prop)).mul rho + exact h.congr (fun q => by simp [ProfileJets.rhoTerm]) + +theorem denomInv (k : ℕ) : Effective (fun q : ℚ => ProfileJets.denomInv k (q : ℝ)) := by + have h := rho.add (rho.comp (g := fun q : ℚ => 1-q) (by fun_prop)) + have h' := h.inv (fun q => by + simpa only [Rat.cast_sub,Rat.cast_one] using (Real.smoothTransition.pos_denom (q : ℝ)).ne') + exact (h'.pow (Computable.const k)).congr (fun q => by simp [ProfileJets.denomInv]) + +theorem factor (f : Factor) : Effective (fun q : ℚ => evalFactor f (q : ℝ)) := by + have ha : Computable (fun q : ℚ => (f.2.1 : ℚ)*q+f.2.2.1) := by fun_prop + cases hf : f.1 + · exact ((rhoTerm f.2.2.2).comp ha).congr (fun q => by simp [evalFactor,hf]) + · exact ((denomInv f.2.2.2).comp ha).congr (fun q => by simp [evalFactor,hf]) + +theorem product (l : List Factor) : Effective (fun q : ℚ => evalProduct l (q : ℝ)) := by + induction l with + | nil => simpa [evalProduct] using constant (A := ℚ) 1 + | cons f l ih => exact ((factor f).mul ih).congr (fun q => (evalProduct_cons _ _ _).symm) + +theorem expression (e : Expr) : Effective (fun q : ℚ => eval e (q : ℝ)) := by + induction e with + | nil => simpa [eval] using constant (A := ℚ) 0 + | cons f l ih => + have h := ((constant (A := ℚ) (f.1 : ℚ)).mul (product f.2)).add ih + exact h.congr (fun q => by simp [eval_cons,evalTerm]) + +theorem pulse : Effective (fun q : ℚ => deriv Profiles.clock (q : ℝ)) := by + simpa only [jet_correct, eval_clockExpr, iteratedDeriv_one] using expression (jet clockExpr 1) + +theorem bump : Effective (fun q : ℚ => Profiles.bump (q : ℝ)) := by + simpa only [eval_bumpExpr] using expression bumpExpr +end EffectiveProfiles + +namespace RecursiveArithmetic +@[fun_prop] theorem intToNat : Primrec Int.toNat := by + exact (Primrec.ite intNegative (Primrec.const 0) intNatAbs).of_eq (fun z => by + cases z <;> simp) +@[fun_prop] theorem int_mod : Primrec (fun p : ℤ × ℤ => p.1 % p.2) := by + exact (intSub.comp Primrec.fst (intMul.comp Primrec.snd int_div)).of_eq + (fun p => (Int.emod_def p.1 p.2).symm) +@[fun_prop] theorem finVal {n : ℕ} : Primrec (fun i : Fin n => i.val) := Primrec.fin_val +@[fun_prop] theorem machineLookup : Primrec (fun p : Machine × ℕ × ℕ => p.1.lookup p.2.1 p.2.2) := by + exact (Primrec.list_getD none).comp + ((Primrec.list_getD []).comp (machineTable.comp Primrec.fst) (Primrec.fst.comp Primrec.snd)) + (Primrec.snd.comp Primrec.snd) +@[fun_prop] theorem optionNone {A : Type*} [Primcodable A] : Primrec (Option.isNone : Option A → Bool) := by + exact (Primrec.option_casesOn Primrec.id (Primrec.const true) (Primrec.const false).to₂).of_eq (fun o => by cases o <;> rfl) +end RecursiveArithmetic + +namespace StackCode +open RecursiveArithmetic + +def Code.equiv : Code ≃ ℕ × ℕ × ℕ where + toFun c := (c.left,c.right,c.state) + invFun p := ⟨p.1,p.2.1,p.2.2⟩ + left_inv _ := rfl + right_inv _ := rfl +instance : Primcodable Code := Primcodable.ofEquiv _ Code.equiv +@[fun_prop] theorem codeLeft : Primrec Code.left := Primrec.fst.comp (Primrec.of_equiv (e := Code.equiv)) +@[fun_prop] theorem codeRight : Primrec Code.right := (Primrec.fst.comp Primrec.snd).comp (Primrec.of_equiv (e := Code.equiv)) +@[fun_prop] theorem codeState : Primrec Code.state := (Primrec.snd.comp Primrec.snd).comp (Primrec.of_equiv (e := Code.equiv)) +@[fun_prop] theorem codeMk : Primrec (fun p : ℕ × ℕ × ℕ => Code.mk p.1 p.2.1 p.2.2) := Primrec.of_equiv_symm (e := Code.equiv) +@[fun_prop] theorem pack_recursive : Primrec (fun p : ℕ × ℕ × Code => pack p.1 p.2.1 p.2.2) := by + unfold pack; fun_prop +@[fun_prop] theorem unpack_recursive : Primrec (fun p : ℕ × ℕ × ℤ => unpack p.1 p.2.1 p.2.2) := by + have hr : Primrec (fun p : ℕ × ℕ × ℤ => residue p.1 p.2.1 p.2.2) := by + unfold residue; fun_prop + have hu : Primrec (fun p : ℕ × ℕ × ℕ => unpackNat p.1 p.2.1 p.2.2) := by + exact codeMk.comp (g := fun p : ℕ × ℕ × ℕ => (p.2.2 % p.1^p.2.1, p.2.2 / p.1^p.2.1 % p.1^p.2.1, p.2.2 / p.1^p.2.1 / p.1^p.2.1)) (by fun_prop) + exact hu.comp (Primrec.fst.pair ((Primrec.fst.comp Primrec.snd).pair hr)) +@[fun_prop] theorem stepRight_recursive : Primrec (fun p : ℕ × Code × Instruction => + (p.2.2.writeSymbol + p.1*p.2.1.left, p.2.1.right / p.1, p.2.2.nextState)) := by + have hl := codeLeft.comp (Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hr := codeRight.comp (Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hw := instructionSymbol.comp (Primrec.snd.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hs := instructionState.comp (Primrec.snd.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + exact ((Primrec.nat_add.comp hw (Primrec.nat_mul.comp Primrec.fst hl)).pair + ((Primrec.nat_div.comp hr Primrec.fst).pair hs)).of_eq (fun _ => rfl) +@[fun_prop] theorem stepLeft_recursive : Primrec (fun p : ℕ × Code × Instruction => + (p.2.1.left / p.1, p.2.1.left % p.1 + p.1*p.2.2.writeSymbol + p.1*(p.2.1.right-p.2.1.right % p.1), p.2.2.nextState)) := by + have hl := codeLeft.comp (Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hr := codeRight.comp (Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hw := instructionSymbol.comp (Primrec.snd.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hs := instructionState.comp (Primrec.snd.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + exact ((Primrec.nat_div.comp hl Primrec.fst).pair + ((Primrec.nat_add.comp (Primrec.nat_add.comp (Primrec.nat_mod.comp hl Primrec.fst) + (Primrec.nat_mul.comp Primrec.fst hw)) + (Primrec.nat_mul.comp Primrec.fst (Primrec.nat_sub.comp hr (Primrec.nat_mod.comp hr Primrec.fst)))).pair hs)).of_eq (fun _ => rfl) +@[fun_prop] theorem stepStay_recursive : Primrec (fun p : ℕ × Code × Instruction => + (p.2.1.left, p.2.1.right-p.2.1.right % p.1+p.2.2.writeSymbol, p.2.2.nextState)) := by + have hl := codeLeft.comp (Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hr := codeRight.comp (Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hw := instructionSymbol.comp (Primrec.snd.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + have hs := instructionState.comp (Primrec.snd.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction))) + exact (hl.pair ((Primrec.nat_add.comp + (Primrec.nat_sub.comp hr (Primrec.nat_mod.comp hr Primrec.fst)) hw).pair hs)).of_eq (fun _ => rfl) +@[fun_prop] theorem step_recursive : Primrec (fun p : ℕ × Code × Instruction => step p.1 p.2.1 p.2.2) := by + have hm := Primrec.fin_val.comp (instructionMove.comp (Primrec.snd.comp (Primrec.snd : Primrec (Prod.snd : ℕ × Code × Instruction → Code × Instruction)))) + exact (Primrec.ite (Primrec.eq.comp hm (Primrec.const 2)) (codeMk.comp stepRight_recursive) + (Primrec.ite (Primrec.eq.comp hm (Primrec.const 0)) (codeMk.comp stepLeft_recursive) (codeMk.comp stepStay_recursive))).of_eq (fun p => rfl) +end StackCode + +namespace CompilerPlanar +open RecursiveArithmetic +@[fun_prop] theorem width_recursive : Primrec (fun p : Input × ℕ => Scales.width p.1.word.length p.2) := by + have hL := Primrec.list_length.comp (inputWord.comp (Primrec.fst : Primrec (Prod.fst : Input × ℕ → Input))) + exact (Primrec.nat_add.comp (Primrec.nat_add.comp hL (Primrec.const 1)) + (Primrec.nat_mul.comp (Primrec.const 2) Primrec.snd)).of_eq (fun _ => rfl) +@[fun_prop] theorem decode_recursive : Primrec (fun p : Input × ℕ × ℤ => + StackCode.unpack (radix p.1) (Scales.width p.1.word.length p.2.1) p.2.2) := by + have hw := width_recursive.comp ((Primrec.fst : Primrec (Prod.fst : Input × ℕ × ℤ → Input)).pair (Primrec.fst.comp Primrec.snd)) + exact (StackCode.unpack_recursive.comp ((radix_primrec.comp Primrec.fst).pair (hw.pair (Primrec.snd.comp Primrec.snd)))).of_eq (fun _ => rfl) +@[fun_prop] theorem lookupAddress_recursive : Primrec (fun p : Input × ℕ × ℤ => + p.1.machine.lookup (StackCode.Code.state (StackCode.unpack (radix p.1) (Scales.width p.1.word.length p.2.1) p.2.2)) + ((StackCode.Code.right (StackCode.unpack (radix p.1) (Scales.width p.1.word.length p.2.1) p.2.2)) % radix p.1)) := by + have hM := inputMachine.comp (Primrec.fst : Primrec (Prod.fst : Input × ℕ × ℤ → Input)) + have hs := StackCode.codeState.comp decode_recursive + have hr := Primrec.nat_mod.comp (StackCode.codeRight.comp decode_recursive) (radix_primrec.comp Primrec.fst) + exact (machineLookup.comp (hM.pair (hs.pair hr))).of_eq (fun _ => rfl) +@[fun_prop] theorem haltTable_recursive : Primrec (fun p : Input × ℕ × ℤ => haltTable p.1 p.2.1 p.2.2) := by + exact (optionNone.comp lookupAddress_recursive).of_eq (fun p => rfl) +@[fun_prop] theorem nextArgs_recursive : Primrec (fun p : (Input × ℕ × ℤ) × Instruction => + (radix p.1.1, Scales.width p.1.1.word.length (p.1.2.1+1), + StackCode.step (radix p.1.1) (StackCode.unpack (radix p.1.1) (Scales.width p.1.1.word.length p.1.2.1) p.1.2.2) p.2)) := by + have hr := radix_primrec.comp (Primrec.fst.comp (Primrec.fst : Primrec (Prod.fst : (Input × ℕ × ℤ) × Instruction → Input × ℕ × ℤ))) + have hw := width_recursive.comp ((Primrec.fst.comp (Primrec.fst : Primrec (Prod.fst : (Input × ℕ × ℤ) × Instruction → Input × ℕ × ℤ))).pair + (Primrec.nat_add.comp (Primrec.fst.comp (Primrec.snd.comp Primrec.fst)) (Primrec.const 1))) + have hs := StackCode.step_recursive.comp (hr.pair ((decode_recursive.comp Primrec.fst).pair Primrec.snd)) + exact (hr.pair (hw.pair hs)).of_eq (fun _ => rfl) +@[fun_prop] theorem nextTable_recursive : Primrec (fun p : Input × ℕ × ℤ => nextTable p.1 p.2.1 p.2.2) := by + exact (Primrec.option_casesOn lookupAddress_recursive (Primrec.const 0) + (StackCode.pack_recursive.comp nextArgs_recursive).to₂).of_eq (fun p => by + dsimp only + unfold nextTable RuleTable.next + dsimp only + cases p.1.machine.lookup (StackCode.unpack (radix p.1) (Scales.width p.1.word.length p.2.1) p.2.2).state + ((StackCode.unpack (radix p.1) (Scales.width p.1.word.length p.2.1) p.2.2).right % radix p.1) <;> rfl) +end CompilerPlanar +namespace EffectiveFields +open CertifiedReal Quantitative RapidCalculus TorusCalculus RecursiveArithmetic CompilerPlanar +open scoped ContDiff +local instance effectiveProfilesLocal2 : Primcodable ℚ := ratPrimcodable +local instance effectiveProfilesLocal3 : DecidablePred Input.WellFormed := Classical.decPred _ +local instance effectiveProfilesLocal4 : Primcodable ValidInput := Primcodable.subtype RecursiveArithmetic.inputWellFormed + +@[fun_prop] theorem rat_natFloor : Primrec (fun q : ℚ => ⌊q⌋₊) := + (intToNat.comp rat_floor).of_eq (fun q => Int.floor_toNat q) + +def qepsilon (d : Input) (n : ℕ) : ℚ := ((radix d : ℚ)^Scales.exponent d.word.length n)⁻¹ +def qbeta (d : Input) (n : ℕ) : ℚ := if n=0 then 1/4 else qepsilon d n +@[simp] theorem cast_qepsilon (d : Input) (n : ℕ) : + (qepsilon d n : ℝ) = Scales.epsilon (radix d) d.word.length n := by simp [qepsilon,Scales.epsilon] +@[simp] theorem cast_qbeta (d : Input) (n : ℕ) : + (qbeta d n : ℝ) = Scales.beta (radix d) d.word.length n := by simp [qbeta,Scales.beta]; split_ifs <;> simp +@[fun_prop] theorem qepsilon_recursive : Primrec (fun p : Input × ℕ => qepsilon p.1 p.2) := by + have hb := ratNat.comp (radix_primrec.comp (Primrec.fst : Primrec (Prod.fst : Input × ℕ → Input))) + have he := Scales.exponent_primrec.comp ((listLength.comp (inputWord.comp (Primrec.fst : Primrec (Prod.fst : Input × ℕ → Input)))).pair Primrec.snd) + exact (ratInv.comp (rat_pow.comp (hb.pair he))).of_eq (fun _ => rfl) +@[fun_prop] theorem qbeta_recursive : Primrec (fun p : Input × ℕ => qbeta p.1 p.2) := by + exact Primrec.ite (Primrec.eq.comp Primrec.snd (Primrec.const 0)) (Primrec.const (1/4)) qepsilon_recursive + +theorem selector_effective {A : Type*} [Primcodable A] {e : A → ℚ} {c : A × ℤ → ℚ} + (he : Computable e) (hc : Computable c) : + Effective (fun p : A × ℚ => Profiles.selector (e p.1) (fun j => (c (p.1,j):ℝ)) p.2) := by + let z : A × ℚ → ℚ := fun p => (p.2-1/2)/(e p.1) + have hz : Computable z := by + have hs := rat_sub.to_comp.comp ((Computable.snd : Computable (Prod.snd : A × ℚ → ℚ)).pair (Computable.const (1/2 : ℚ))) + exact (rat_div.to_comp.comp (hs.pair (he.comp Computable.fst))).of_eq (fun _ => rfl) + let j : A × ℚ → ℤ := fun p => ⌊z p+1/2⌋ + have hj : Computable j := by + exact (rat_floor.to_comp.comp (rat_add.to_comp.comp (hz.pair (Computable.const (1/2 : ℚ))))).of_eq (fun _ => rfl) + have hcoeff := rational (hc.comp (Computable.fst.pair hj)) + have hb : Computable (fun p : A × ℚ => z p - j p) := by + exact (rat_sub.to_comp.comp (hz.pair (ratInt.to_comp.comp hj))).of_eq (fun _ => rfl) + exact (hcoeff.mul (EffectiveProfiles.bump.comp hb)).congr (fun p => by + have hl : (j p : ℝ) ≤ (z p : ℝ)+1/2 := by + dsimp only [j] + simpa using (Rat.cast_le (K:=ℝ)).mpr (Int.floor_le (z p+1/2)) + have hu : (z p : ℝ)+1/2 < (j p : ℝ)+1 := by + dsimp only [j] + simpa using (Rat.cast_lt (K:=ℝ)).mpr (Int.lt_floor_add_one (z p+1/2)) + have hnear : |((p.2:ℝ)-1/2)/(e p.1) - (j p:ℝ)| < 5/8 := by + have hzcast : (z p : ℝ) = ((p.2:ℝ)-1/2)/(e p.1) := by simp [z] + rw [← hzcast]; apply abs_lt.mpr; constructor <;> linarith + rw [Profiles.selector_single _ hnear] + simp [Profiles.latticeBump,z]) + +abbrev SlotPoint := Input × ℕ × ℚ +private theorem slotIndex_recursive : Primrec (fun p : SlotPoint => (p.1,p.2.1)) := + Primrec.fst.pair (Primrec.fst.comp Primrec.snd) +private theorem slotNext_recursive : Primrec (fun p : SlotPoint => (p.1,p.2.1+1)) := + (Primrec.fst.pair (Primrec.succ.comp (Primrec.fst.comp Primrec.snd))).of_eq (fun _ => rfl) +private theorem slotPrev_recursive : Primrec (fun p : SlotPoint => (p.1,p.2.1-1,p.2.2)) := + Primrec.fst.pair ((Primrec.nat_sub.comp (Primrec.fst.comp Primrec.snd) (Primrec.const 1)).pair + (Primrec.snd.comp Primrec.snd)) + +theorem halt_selector : Effective (fun p : SlotPoint => Profiles.selector + (Scales.epsilon (radix p.1) p.1.word.length p.2.1) + (fun j => if haltTable p.1 p.2.1 j then 1 else 0) p.2.2) := by + have hc : Computable (fun p : (Input × ℕ) × ℤ => (if haltTable p.1.1 p.1.2 p.2 then 1 else 0 : ℚ)) := by + have ha : Primrec (fun p : (Input × ℕ) × ℤ => (p.1.1,p.1.2,p.2)) := + (Primrec.fst.comp Primrec.fst).pair ((Primrec.snd.comp Primrec.fst).pair Primrec.snd) + exact ((Primrec.cond (haltTable_recursive.comp ha) (Primrec.const (1 : ℚ)) (Primrec.const (0 : ℚ))).of_eq (fun _ => Bool.cond_eq_ite _ _ _)).to_comp + have h := selector_effective qepsilon_recursive.to_comp hc + exact (h.comp (g := fun p : SlotPoint => ((p.1,p.2.1),p.2.2)) (by fun_prop)).congr (fun p => by + simp only [cast_qepsilon] + congr 1 + funext j + split_ifs <;> norm_num) + +theorem next_selector : Effective (fun p : SlotPoint => Profiles.selector + (Scales.epsilon (radix p.1) p.1.word.length p.2.1) + (fun j => (nextTable p.1 p.2.1 j : ℝ)) p.2.2) := by + have hc : Computable (fun p : (Input × ℕ) × ℤ => (nextTable p.1.1 p.1.2 p.2 : ℚ)) := by + have ha : Primrec (fun p : (Input × ℕ) × ℤ => (p.1.1,p.1.2,p.2)) := + (Primrec.fst.comp Primrec.fst).pair ((Primrec.snd.comp Primrec.fst).pair Primrec.snd) + exact ((ratNat.comp (nextTable_recursive.comp ha)).of_eq (fun _ => rfl)).to_comp + have h := selector_effective qepsilon_recursive.to_comp hc + exact (h.comp (g := fun p : SlotPoint => ((p.1,p.2.1),p.2.2)) (by fun_prop)).congr (fun p => by simp) + +theorem coeff_a : Effective (fun p : SlotPoint => (Planar.coefficients (radix p.1) p.1.word.length (loadingCode p.1) + (fun n j => nextTable p.1 n j) (fun n j => if haltTable p.1 n j then 1 else 0) p.2.1 p.2.2).1) := by + have hb0 := rational (q := fun p : SlotPoint => qbeta p.1 p.2.1) ((qbeta_recursive.comp slotIndex_recursive).to_comp) + have hb1 := rational (q := fun p : SlotPoint => qbeta p.1 (p.2.1+1)) ((qbeta_recursive.comp slotNext_recursive).to_comp) + have hslot := (hb0.sub hb1).add (((constant 2).mul hb1).mul halt_selector) + have h := (constant 0).ite (hslot.comp (g := fun p : SlotPoint => (p.1,p.2.1-1,p.2.2)) slotPrev_recursive.to_comp) + (Primrec.eq.comp (Primrec.fst.comp Primrec.snd) (Primrec.const 0)) + exact h.congr (fun p => by cases hn : p.2.1 <;> simp [Planar.coefficients,Planar.slot]) + +theorem coeff_b : Effective (fun p : SlotPoint => (Planar.coefficients (radix p.1) p.1.word.length (loadingCode p.1) + (fun n j => nextTable p.1 n j) (fun n j => if haltTable p.1 n j then 1 else 0) p.2.1 p.2.2).2) := by + have hload := (rational ((qepsilon_recursive.comp (Primrec.fst.pair (Primrec.const 0) : Primrec (fun p : SlotPoint => (p.1,0)))).to_comp)).mul + (rational ((ratNat.comp (loadingCode_primrec.comp (Primrec.fst : Primrec (Prod.fst : SlotPoint → Input)))).to_comp)) + have he := rational (q := fun p : SlotPoint => qepsilon p.1 (p.2.1+1)) (qepsilon_recursive.comp slotNext_recursive).to_comp + have hslot := he.mul next_selector + have h := hload.ite (hslot.comp (g := fun p : SlotPoint => (p.1,p.2.1-1,p.2.2)) slotPrev_recursive.to_comp) + (Primrec.eq.comp (Primrec.fst.comp Primrec.snd) (Primrec.const 0)) + exact h.congr (fun p => by cases hn : p.2.1 <;> simp [Planar.coefficients,Planar.slot]) + +private theorem slot_value (d : Input) (p : BiPoint) : + FluidLift.v d (time p.1) p.2 = Profiles.pulse ⌊max p.1 0⌋₊ (time p.1) • + Planar.coefficients (radix d) d.word.length (loadingCode d) + (fun n j => nextTable d n j) (fun n j => if haltTable d n j then 1 else 0) ⌊max p.1 0⌋₊ p.2 := by + apply Profiles.schedule_on_slot + · dsimp only [time]; exact_mod_cast Nat.floor_le (le_max_right p.1 0) + · dsimp only [time]; exact_mod_cast (Nat.lt_floor_add_one (max p.1 0)).le + +private theorem pointSlot_recursive : Computable (fun p : ValidInput × BiPoint => (p.1.1,⌊max p.2.1 0⌋₊,p.2.2)) := by + have ht := ratMax.comp ((Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ValidInput × BiPoint → BiPoint))).pair (Primrec.const 0)) + exact ((validData_recursive.comp Primrec.fst).pair ((rat_natFloor.comp ht).pair (Primrec.snd.comp Primrec.snd))).to_comp +private theorem pointPulse_recursive : Computable (fun p : ValidInput × BiPoint => max p.2.1 0 - (⌊max p.2.1 0⌋₊:ℚ)) := by + have ht := ratMax.comp ((Primrec.fst.comp (Primrec.snd : Primrec (Prod.snd : ValidInput × BiPoint → BiPoint))).pair (Primrec.const 0)) + exact ((rat_sub.comp (ht.pair (ratNat.comp (rat_natFloor.comp ht)))).of_eq (fun _ => rfl)).to_comp + +theorem a_base : Effective (fun p : ValidInput × BiPoint => biValue (FluidLift.a p.1.1) p.2) := by + have ha := pointSlot_recursive + have ht := pointPulse_recursive + exact ((EffectiveProfiles.pulse.comp ht).mul (coeff_a.comp ha)).congr (fun p => by + dsimp only [biValue,FluidLift.a] + rw [slot_value p.1.1 p.2] + simp only [Prod.smul_fst,smul_eq_mul,Profiles.pulse,time]; push_cast; rfl) + +theorem b_base : Effective (fun p : ValidInput × BiPoint => biValue (FluidLift.b p.1.1) p.2) := by + have ha := pointSlot_recursive + have ht := pointPulse_recursive + exact ((EffectiveProfiles.pulse.comp ht).mul (coeff_b.comp ha)).congr (fun p => by + dsimp only [biValue,FluidLift.b] + rw [slot_value p.1.1 p.2] + simp only [Prod.smul_snd,smul_eq_mul,Profiles.pulse,time]; push_cast; rfl) +end EffectiveFields + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/EffectiveReals.lean b/lean/OAI/Analysis/PeriodicLattice/EffectiveReals.lean new file mode 100644 index 0000000000000000000000000000000000000000..cc6974a4b639836308154f0a97d5403d16974953 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/EffectiveReals.lean @@ -0,0 +1,241 @@ +import OAI.Analysis.PeriodicLattice.RationalArithmetic + +namespace OAI + +/-! Well-formed input encodings and effective real enclosures. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingEffectiveReals {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace RecursiveArithmetic +open Encodable Primrec +local instance effectiveRealsLocal1 : Primcodable ℚ := ratPrimcodable + +@[fun_prop] theorem rat_abs : Primrec (abs : ℚ → ℚ) := by + have hn : PrimrecPred (fun q : ℚ => q < 0) := + (intNegative.comp ratNum).of_eq (fun q => Rat.num_neg) + exact (Primrec.ite hn ratNeg Primrec.id).of_eq (fun q => by split_ifs with h; exact (abs_of_neg h).symm; exact (abs_of_nonneg (not_lt.mp h)).symm) + +theorem ratLE : PrimrecRel (fun a b : ℚ => a ≤ b) := by + exact (intLE.comp (by fun_prop : Primrec (fun p : ℚ × ℚ => p.1.num * p.2.den)) + (by fun_prop : Primrec (fun p : ℚ × ℚ => p.2.num * p.1.den))).of_eq (fun p => (Rat.le_iff p.1 p.2).symm) + +theorem ratLT : PrimrecRel (fun a b : ℚ => a < b) := + (ratLE.comp Primrec.snd Primrec.fst).not.of_eq (fun _ => not_le) + +@[fun_prop] theorem rat_floor : Primrec (fun q : ℚ => ⌊q⌋) := + (int_div.comp (ratNum.pair (intOfNat.comp ratDen))).of_eq (fun q => (Rat.floor_def q).symm) + +@[fun_prop] theorem listSumRat : Primrec (List.sum : List ℚ → ℚ) := by + exact (Primrec.list_foldr Primrec.id (Primrec.const 0) + (rat_add.comp ((Primrec.fst.comp Primrec.snd).pair (Primrec.snd.comp Primrec.snd))).to₂).of_eq + (fun l => by dsimp only; induction l <;> simp_all) + +@[fun_prop] theorem sumRangeRat {α : Type*} [Primcodable α] {f : α → ℕ} {g : α → ℕ → ℚ} + (hf : Primrec f) (hg : Primrec₂ g) : Primrec (fun a => ∑ i ∈ Finset.range (f a), g a i) := + (listSumRat.comp (Primrec.list_map (Primrec.list_range.comp hf) hg)).of_eq + (fun a => by simpa only [List.toFinset_range] using (List.sum_toFinset (g a) List.nodup_range).symm) + +theorem allList {α β : Type*} [Primcodable α] [Primcodable β] + {p : α × β → Prop} {l : α → List β} (hp : PrimrecPred p) (hl : Primrec l) : + PrimrecPred (fun a => ∀ b ∈ l a, p (a,b)) := + (hp.forall_mem_list.comp (Primrec.list_map hl (Primrec.fst.pair Primrec.snd).to₂)).of_eq + (fun a => by simp) + +@[fun_prop] theorem machineTable : Primrec Machine.table := + (Primrec.snd.comp (Primrec.snd.comp Primrec.snd)).comp (Primrec.of_equiv (e := Machine.codeEquiv)) +@[fun_prop] theorem instructionState : Primrec Instruction.nextState := + Primrec.fst.comp (Primrec.of_equiv (e := Instruction.codeEquiv)) +@[fun_prop] theorem instructionSymbol : Primrec Instruction.writeSymbol := + (Primrec.fst.comp Primrec.snd).comp (Primrec.of_equiv (e := Instruction.codeEquiv)) +@[fun_prop] theorem instructionMove : Primrec Instruction.move := + (Primrec.snd.comp Primrec.snd).comp (Primrec.of_equiv (e := Instruction.codeEquiv)) + +theorem entryValid : PrimrecPred (fun p : Machine × Option Instruction => + ∀ I, p.2 = some I → I.nextState < p.1.states ∧ I.writeSymbol < p.1.symbols) := by + have hp : PrimrecPred (fun p : Machine × Instruction => + p.2.nextState < p.1.states ∧ p.2.writeSymbol < p.1.symbols) := + (Primrec.nat_lt.comp (by fun_prop) (by fun_prop)).and + (Primrec.nat_lt.comp (by fun_prop) (by fun_prop)) + have hg : Primrec (fun p : (Machine × Option Instruction) × Instruction => + decide (p.2.nextState < p.1.1.states ∧ p.2.writeSymbol < p.1.1.symbols)) := + hp.decide.comp (g := fun p : (Machine × Option Instruction) × Instruction => (p.1.1,p.2)) + ((Primrec.fst.comp Primrec.fst).pair Primrec.snd) + have hc := Primrec.option_casesOn (o := fun p : Machine × Option Instruction => p.2) + (f := fun _ => true) (g := fun p I => decide (I.nextState < p.1.states ∧ I.writeSymbol < p.1.symbols)) + Primrec.snd (Primrec.const true) hg.to₂ + exact (Primrec.eq.comp hc (Primrec.const true)).of_eq (fun p => by cases p.2 <;> simp) + +theorem machineWellFormed : PrimrecPred Machine.WellFormed := by + have hi : PrimrecPred (fun p : Machine × List (Option Instruction) => + ∀ e ∈ p.2, ∀ I, e = some I → I.nextState < p.1.states ∧ I.writeSymbol < p.1.symbols) := + allList (entryValid.comp ((Primrec.fst.comp Primrec.fst).pair Primrec.snd)) Primrec.snd + exact ((Primrec.nat_lt.comp (Primrec.const 0) machineStates).and + ((Primrec.nat_lt.comp (Primrec.const 0) machineSymbols).and + ((Primrec.nat_lt.comp machineStart machineStates).and + ((Primrec.nat_le.comp (Primrec.list_length.comp machineTable) machineStates).and + ((allList (Primrec.nat_le.comp (Primrec.list_length.comp Primrec.snd) + (machineSymbols.comp Primrec.fst)) machineTable).and (allList hi machineTable)))))).of_eq + (fun _ => Iff.rfl) + +theorem inputWellFormed : PrimrecPred Input.WellFormed := + ((machineWellFormed.comp inputMachine).and + (allList (Primrec.nat_lt.comp Primrec.snd (machineSymbols.comp (inputMachine.comp Primrec.fst))) inputWord)).of_eq + (fun _ => Iff.rfl) +end RecursiveArithmetic + +abbrev ValidInput := {d : Input // d.WellFormed} +local instance validInputDec : DecidablePred Input.WellFormed := Classical.decPred _ +local instance validInputCode : Primcodable ValidInput := Primcodable.subtype RecursiveArithmetic.inputWellFormed + +namespace CertifiedReal +open Encodable Filter Topology +local instance effectiveRealsLocal2 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable + +def error (n : ℕ) : ℝ := 1 / ((n : ℝ) + 1) +def qerror (n : ℕ) : ℚ := 1 / ((n : ℚ) + 1) + +@[simp] theorem cast_qerror (n : ℕ) : (qerror n : ℝ) = error n := by simp [qerror, error] +theorem error_pos (n : ℕ) : 0 < error n := by unfold error; positivity +theorem error_le_one (n : ℕ) : error n ≤ 1 := by unfold error; exact (div_le_one (by positivity)).mpr (by linarith [Nat.cast_nonneg (α := ℝ) n]) +theorem error_tendsto : Tendsto error atTop (𝓝 0) := by + exact tendsto_one_div_add_atTop_nhds_zero_nat (𝕜 := ℝ) + +@[fun_prop] theorem qerror_primrec : Primrec qerror := by unfold qerror; fun_prop + +def Effective {A : Type*} [Primcodable A] (f : A → ℝ) : Prop := + ∃ q : A × ℕ → ℚ, Computable q ∧ ∀ a n, |f a - (q (a,n) : ℝ)| ≤ error n + +section +variable {A B : Type*} [Primcodable A] [Primcodable B] + +theorem computable_find {p : A → ℕ → Prop} [DecidableRel p] + (hp : Computable (fun an : A × ℕ => decide (p an.1 an.2))) (he : ∀ a, ∃ n, p a n) : + Computable (fun a => Nat.find (he a)) := by + have hr : Partrec (fun a => Nat.rfind (fun n => Part.some (decide (p a n)))) := + Partrec.rfind hp.partrec.to₂ + apply hr.of_eq_tot + intro a + apply (Nat.mem_rfind (p := (fun n => Part.some (decide (p a n))) )).mpr + constructor + · simpa using Nat.find_spec (he a) + · intro m hm + simpa only [Part.mem_some_iff, eq_comm (a := false), decide_eq_false_iff_not] using Nat.find_min (he a) hm + +theorem of_enclosures {f : A → ℝ} {q e : A × ℕ → ℚ} + (hq : Computable q) (he : Computable e) + (bound : ∀ a n, |f a - (q (a,n) : ℝ)| ≤ (e (a,n) : ℝ)) + (small : ∀ a, Tendsto (fun n => (e (a,n) : ℝ)) atTop (𝓝 0)) : Effective f := by + have existsSmall : ∀ an : A × ℕ, ∃ k, e (an.1,k) ≤ qerror an.2 := by + intro an + have hh := (small an.1).eventually (gt_mem_nhds (error_pos an.2)) + obtain ⟨k,hk⟩ := hh.exists + exact ⟨k, by exact_mod_cast (show (e (an.1,k) : ℝ) ≤ (qerror an.2 : ℝ) by simpa using hk.le)⟩ + have hc : Computable (fun p : (A × ℕ) × ℕ => decide (e (p.1.1,p.2) ≤ qerror p.1.2)) := + RecursiveArithmetic.ratLE.decide.to_comp.comp + (he.comp ((Computable.fst.comp Computable.fst).pair Computable.snd)) + (qerror_primrec.to_comp.comp (Computable.snd.comp Computable.fst)) + let pick (an : A × ℕ) := Nat.find (existsSmall an) + have hpick := computable_find (A := A × ℕ) (p := fun (an : A × ℕ) (k : ℕ) => e (an.1,k) ≤ qerror an.2) hc existsSmall + have hfinal : Computable (fun an => q (an.1,pick an)) := hq.comp (Computable.fst.pair hpick) + refine ⟨fun an => q (an.1,pick an), hfinal, ?_⟩ + intro a n + apply (bound a (pick (a,n))).trans + rw [← cast_qerror] + exact_mod_cast Nat.find_spec (existsSmall (a,n)) + +theorem Effective.comp {f : B → ℝ} (hf : Effective f) {g : A → B} (hg : Computable g) : + Effective (fun a => f (g a)) := by + obtain ⟨q,hq,he⟩ := hf + exact ⟨fun an => q (g an.1,an.2), hq.comp ((hg.comp Computable.fst).pair Computable.snd), + fun a n => he (g a) n⟩ + +theorem Effective.congr {f g : A → ℝ} (hf : Effective f) (h : ∀ a, f a = g a) : Effective g := by + simpa only [funext h] using hf + +theorem rational {q : A → ℚ} (hq : Computable q) : Effective (fun a => (q a : ℝ)) := + ⟨fun an => q an.1, hq.comp Computable.fst, fun a n => by simpa using (error_pos n).le⟩ + +omit [Primcodable A] in +theorem Effective.approximants_tendsto {f : A → ℝ} {q : A × ℕ → ℚ} + (he : ∀ a n, |f a - (q (a,n) : ℝ)| ≤ error n) (a : A) : + Tendsto (fun n => (q (a,n) : ℝ)) atTop (𝓝 (f a)) := by + apply tendsto_iff_dist_tendsto_zero.mpr + apply squeeze_zero (fun _ => dist_nonneg) _ error_tendsto + intro n + simpa [Real.dist_eq, abs_sub_comm] using he a n +end +end CertifiedReal + +attribute [fun_prop] Computable +attribute [fun_prop] Computable.id Computable.const Computable.comp Computable.pair Computable.fst Computable.snd +attribute [fun_prop] Primrec.to_comp + +namespace CertifiedReal +open Encodable Filter Topology +local instance effectiveRealsLocal3 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable +section +variable {A B : Type*} [Primcodable A] [Primcodable B] + +theorem constant (q : ℚ) : Effective (fun _ : A => (q : ℝ)) := rational (Computable.const _) + +theorem Effective.add {f g : A → ℝ} (hf : Effective f) (hg : Effective g) : + Effective (fun a => f a + g a) := by + obtain ⟨q,hq,bq⟩ := hf + obtain ⟨v,hv,bv⟩ := hg + refine of_enclosures (q := fun an => q an + v an) (e := fun an => 2 * qerror an.2) + (by fun_prop) (by fun_prop) ?_ ?_ + · intro a n + simpa only [Rat.cast_add, Rat.cast_mul, Rat.cast_ofNat, cast_qerror, two_mul, sub_add_sub_comm] using + abs_add_le (f a - (q (a,n) : ℝ)) (g a - (v (a,n) : ℝ)) |>.trans (add_le_add (bq a n) (bv a n)) + · intro a + simpa using error_tendsto.const_mul 2 + +theorem Effective.neg {f : A → ℝ} (hf : Effective f) : Effective (fun a => -f a) := by + obtain ⟨q,hq,bq⟩ := hf + refine ⟨fun an => -q an, by fun_prop, fun a n => ?_⟩ + rw [Rat.cast_neg, show -f a - -(q (a,n) : ℝ) = -(f a - (q (a,n) : ℝ)) by ring, abs_neg] + exact bq a n + +theorem Effective.sub {f g : A → ℝ} (hf : Effective f) (hg : Effective g) : + Effective (fun a => f a - g a) := by simpa only [sub_eq_add_neg] using hf.add hg.neg + +theorem Effective.mul {f g : A → ℝ} (hf : Effective f) (hg : Effective g) : + Effective (fun a => f a * g a) := by + obtain ⟨q,hq,bq⟩ := hf + obtain ⟨v,hv,bv⟩ := hg + refine of_enclosures (q := fun an => q an * v an) + (e := fun an => qerror an.2 * (|q an| + |v an| + qerror an.2)) + (by fun_prop) (by fun_prop) ?_ ?_ + · intro a n + simp only [Rat.cast_mul, Rat.cast_add, Rat.cast_abs, cast_qerror] + have bg : |g a| ≤ |(v (a,n) : ℝ)| + error n := by + have := abs_add_le (g a - (v (a,n) : ℝ)) (v (a,n) : ℝ) + have := this.trans (add_le_add (bv a n) le_rfl) + rw [sub_add_cancel] at this + exact this.trans_eq (add_comm _ _) + calc + |f a * g a - (q (a,n) : ℝ) * (v (a,n) : ℝ)| = + |(f a - q (a,n)) * g a + (q (a,n) : ℝ) * (g a - v (a,n))| := by congr 1; ring + _ ≤ |f a - (q (a,n) : ℝ)| * |g a| + |(q (a,n) : ℝ)| * |g a - (v (a,n) : ℝ)| := by + simpa only [abs_mul] using abs_add_le ((f a - q (a,n)) * g a) ((q (a,n) : ℝ) * (g a - v (a,n))) + _ ≤ error n * (|(v (a,n) : ℝ)| + error n) + |(q (a,n) : ℝ)| * error n := by + exact add_le_add (mul_le_mul (bq a n) bg (abs_nonneg _) (error_pos n).le) + (mul_le_mul_of_nonneg_left (bv a n) (abs_nonneg _)) + _ = _ := by ring + · intro a + have hqa := Effective.approximants_tendsto bq a + have hva := Effective.approximants_tendsto bv a + simpa using error_tendsto.mul ((hqa.abs.add hva.abs).add error_tendsto) + +end +end CertifiedReal + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/ElementaryFunctions.lean b/lean/OAI/Analysis/PeriodicLattice/ElementaryFunctions.lean new file mode 100644 index 0000000000000000000000000000000000000000..ba6088601df71753382fb06d884dd923f3afac0e --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/ElementaryFunctions.lean @@ -0,0 +1,254 @@ +import OAI.Analysis.PeriodicLattice.EffectiveReals + +namespace OAI + +/-! Certified effective inversion, powers and exponential evaluation. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingElementaryFunctions {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace CertifiedReal +open Encodable Filter Topology +local instance elementaryFunctionsLocal1 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable +section +variable {A : Type*} [Primcodable A] + +theorem Effective.abs {f : A → ℝ} (hf : Effective f) : Effective (fun a => |f a|) := by + obtain ⟨q,hq,bq⟩ := hf + refine ⟨fun an => |q an|, by fun_prop, ?_⟩ + intro a n + simpa only [Rat.cast_abs] using (abs_abs_sub_abs_le (f a) (q (a,n))).trans (bq a n) + +theorem Effective.inv {f : A → ℝ} (hf : Effective f) (hzero : ∀ a, f a ≠ 0) : + Effective (fun a => (f a)⁻¹) := by + obtain ⟨q,hq,bq⟩ := hf + let test (an : A × ℕ) (k : ℕ) : Prop := + qerror k < |q (an.1,k)| ∧ + qerror k / ((|q (an.1,k)| - qerror k) * |q (an.1,k)|) ≤ qerror an.2 + have existsGood : ∀ an : A × ℕ, ∃ k, test an k := by + intro an + have hq' := Effective.approximants_tendsto bq an.1 + have hpos : 0 < |f an.1| := abs_pos.mpr (hzero _) + have hlt : ∀ᶠ k in atTop, error k < |(q (an.1,k) : ℝ)| := + Filter.Tendsto.eventually_lt error_tendsto hq'.abs hpos + have hlim : Tendsto (fun k => error k / + ((|(q (an.1,k) : ℝ)| - error k) * |(q (an.1,k) : ℝ)|)) atTop (𝓝 0) := by + convert error_tendsto.div ((hq'.abs.sub error_tendsto).mul hq'.abs) + (mul_ne_zero (by simpa using hpos.ne') hpos.ne') using 1 + simp + obtain ⟨k,hk,hk'⟩ := (hlt.and (hlim.eventually (gt_mem_nhds (error_pos an.2)))).exists + refine ⟨k, ?_, ?_⟩ + · exact_mod_cast (show (qerror k : ℝ) < |(q (an.1,k) : ℝ)| by simpa using hk) + · exact_mod_cast (show (qerror k : ℝ) / + ((|(q (an.1,k) : ℝ)| - (qerror k : ℝ)) * |(q (an.1,k) : ℝ)|) ≤ (qerror an.2 : ℝ) by + simpa using hk'.le) + have htest : Computable (fun p : (A × ℕ) × ℕ => decide (test p.1 p.2)) := by + simp only [test, Bool.decide_and] + apply (Primrec.and.to_comp.comp _ _) + · exact RecursiveArithmetic.ratLT.decide.to_comp.comp (by fun_prop) (by fun_prop) + · exact RecursiveArithmetic.ratLE.decide.to_comp.comp (by fun_prop) (by fun_prop) + let pick (an : A × ℕ) := Nat.find (existsGood an) + have hpick := computable_find (A := A × ℕ) (p := test) htest existsGood + refine ⟨fun an => (q (an.1,pick an))⁻¹, by fun_prop, ?_⟩ + intro a n + have htest' := Nat.find_spec (existsGood (a,n)) + let k := pick (a,n) + have hk : error k < |(q (a,k) : ℝ)| := by + rw [← cast_qerror] + exact_mod_cast htest'.1 + have hk' : error k / ((|(q (a,k) : ℝ)| - error k) * |(q (a,k) : ℝ)|) ≤ error n := by + rw [← cast_qerror k, ← cast_qerror n] + exact_mod_cast htest'.2 + have hqne : (q (a,k) : ℝ) ≠ 0 := abs_pos.mp ((error_pos k).trans hk) + have hlower : |(q (a,k) : ℝ)| - error k ≤ |f a| := by + have hb := (abs_sub_abs_le_abs_sub (q (a,k) : ℝ) (f a)).trans + (by simpa only [abs_sub_comm] using bq a k) + linarith + rw [Rat.cast_inv, inv_sub_inv (hzero a) hqne, abs_div, abs_mul, abs_sub_comm] + calc + |f a - (q (a,k) : ℝ)| / (|f a| * |(q (a,k) : ℝ)|) ≤ + error k / ((|(q (a,k) : ℝ)| - error k) * |(q (a,k) : ℝ)|) := by + apply div_le_div₀ (error_pos k).le (bq a k) (mul_pos (sub_pos.mpr hk) ((error_pos k).trans hk)) + exact mul_le_mul_of_nonneg_right hlower (abs_nonneg _) + _ ≤ _ := hk' + +theorem Effective.div {f g : A → ℝ} (hf : Effective f) (hg : Effective g) (hz : ∀ a, g a ≠ 0) : + Effective (fun a => f a / g a) := by simpa only [div_eq_mul_inv] using hf.mul (hg.inv hz) + +theorem Effective.pow {f : A → ℝ} (hf : Effective f) {m : A → ℕ} (hm : Computable m) : + Effective (fun a => f a ^ m a) := by + obtain ⟨q,hq,bq⟩ := hf + refine of_enclosures (q := fun an => q an ^ m an.1) + (e := fun an => qerror an.2 * (m an.1 : ℚ) * (|q an| + qerror an.2) ^ (m an.1 - 1)) + (by fun_prop) (by fun_prop) ?_ ?_ + · intro a n + simp only [Rat.cast_pow, Rat.cast_mul, Rat.cast_natCast, Rat.cast_add, Rat.cast_abs, cast_qerror] + have hfbound : |f a| ≤ |(q (a,n) : ℝ)| + error n := by + have ht := (abs_add_le (f a - (q (a,n) : ℝ)) (q (a,n) : ℝ)).trans + (add_le_add (bq a n) le_rfl) + rw [sub_add_cancel] at ht + exact ht.trans_eq (add_comm _ _) + apply (abs_pow_sub_pow_le (f a) (q (a,n)) (m a)).trans + apply mul_le_mul (mul_le_mul_of_nonneg_right (bq a n) (Nat.cast_nonneg _)) + (pow_le_pow_left₀ (le_max_of_le_left (abs_nonneg _)) + (max_le hfbound (le_add_of_nonneg_right (error_pos n).le)) _) (by positivity) + (mul_nonneg (error_pos n).le (Nat.cast_nonneg _)) + · intro a + have ha := Effective.approximants_tendsto bq a + simpa using (error_tendsto.mul_const (m a : ℝ)).mul + ((ha.abs.add error_tendsto).pow (m a - 1)) + +end +end CertifiedReal +namespace CertifiedReal +open Encodable Filter Topology +local instance elementaryFunctionsLocal2 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable +section +variable {A B : Type*} [Primcodable A] [Primcodable B] + +@[fun_prop] theorem computable_sum {m : A → ℕ} {f : A → ℕ → ℚ} + (hm : Computable m) (hf : Computable₂ f) : + Computable (fun a => ∑ i ∈ Finset.range (m a), f a i) := by + have hv := hf.comp (g := fun p : A × (ℕ × ℚ) => p.1) + (h := fun p => p.2.1) Computable.fst (Computable.fst.comp Computable.snd) + have hstep := RecursiveArithmetic.rat_add.to_comp.comp + (g := fun p : A × (ℕ × ℚ) => (p.2.2, f p.1 p.2.1)) + ((Computable.snd.comp Computable.snd).pair hv) + exact (Computable.nat_rec hm (Computable.const 0) hstep.to₂).of_eq (fun a => by + induction m a with + | zero => simp + | succ n ih => simp [Finset.sum_range_succ, ih]) + +theorem rat_abs_bound (q : ℚ) : |(q : ℝ)| ≤ (q.num.natAbs : ℝ) := by + have heq : (q : ℝ) = (q.num : ℝ) / (q.den : ℝ) := by + exact_mod_cast (Rat.num_div_den q).symm + rw [heq, abs_div, abs_of_pos (show (0 : ℝ) < (q.den : ℝ) from Nat.cast_pos.mpr q.den_pos), ← Int.cast_abs, + Int.abs_eq_natAbs, Int.cast_natCast] + exact (div_le_self (Nat.cast_nonneg _) (by exact_mod_cast q.den_pos)).trans le_rfl + +theorem Effective.exp {f : A → ℝ} (hf : Effective f) : Effective (fun a => Real.exp (f a)) := by + obtain ⟨q,hq,bq⟩ := hf + let M (a : A) : ℕ := (q (a,0)).num.natAbs + 3 + have hM : Computable M := by unfold M; fun_prop + have b (a : A) (n : ℕ) : |(q (a,n) : ℝ)| ≤ (M a : ℝ) := by + have hf0 : |f a| ≤ (q (a,0)).num.natAbs + 1 := by + have ht := (abs_add_le (f a - q (a,0)) (q (a,0))).trans + (add_le_add ((bq a 0).trans (error_le_one 0)) (rat_abs_bound _)) + rw [sub_add_cancel] at ht + linarith + have ht := (abs_add_le ((q (a,n) : ℝ) - f a) (f a)).trans + (add_le_add (by simpa only [abs_sub_comm] using (bq a n).trans (error_le_one n)) hf0) + rw [sub_add_cancel] at ht + dsimp [M]; push_cast; linarith + have diff (a : A) (n : ℕ) : + |Real.exp (f a) - Real.exp (q (a,n))| ≤ 2 * 3 ^ M a * error n := by + have he := Real.abs_exp_sub_one_le ((bq a n).trans (error_le_one n)) + have hqM : Real.exp (q (a,n)) ≤ 3 ^ M a := by + apply (Real.exp_le_exp.mpr ((le_abs_self _).trans (b a n))).trans + simpa only [← Real.exp_nat_mul, mul_one] using + (pow_le_pow_left₀ (Real.exp_pos 1).le Real.exp_one_lt_three.le (M a)) + calc + |Real.exp (f a) - Real.exp (q (a,n))| = + |Real.exp (f a - q (a,n)) - 1| * Real.exp (q (a,n)) := by + have heq : Real.exp (f a) - Real.exp (q (a,n)) = + (Real.exp (f a - q (a,n)) - 1) * Real.exp (q (a,n)) := by + rw [sub_mul, one_mul, ← Real.exp_add, sub_add_cancel] + rw [heq, abs_mul, abs_of_pos (Real.exp_pos _)] + _ ≤ (2 * error n) * 3 ^ M a := + mul_le_mul (he.trans (mul_le_mul_of_nonneg_left (bq a n) (by norm_num))) hqM + (Real.exp_pos _).le (mul_nonneg (by norm_num) (error_pos n).le) + _ = _ := by ring + let N (a : A) (n : ℕ) := 2 * M a + 1 + n + refine of_enclosures + (q := fun an => ∑ i ∈ Finset.range (N an.1 an.2), q an ^ i / (i.factorial : ℚ)) + (e := fun an => 2 * 3 ^ M an.1 * qerror an.2 + + 2 * (M an.1 : ℚ) ^ N an.1 an.2 / (N an.1 an.2).factorial) + (by + apply computable_sum + · unfold N; fun_prop + · change Computable (fun p : (A × ℕ) × ℕ => q p.1 ^ p.2 / (p.2.factorial : ℚ)) + fun_prop) + (by unfold N; fun_prop) ?_ ?_ + · intro a n + have htail := Complex.exp_bound' (x := (q (a,n) : ℝ)) (n := N a n) (by + rw [Complex.norm_real, Real.norm_eq_abs] + apply (div_le_div_of_nonneg_right (b a n) (by positivity)).trans + apply (div_le_iff₀ (by positivity)).mpr + dsimp [N]; push_cast; linarith [Nat.cast_nonneg (α := ℝ) n]) + have htail' : |Real.exp (q (a,n)) - ∑ i ∈ Finset.range (N a n), (q (a,n) : ℝ)^i / i.factorial| ≤ + 2 * (M a : ℝ) ^ N a n / (N a n).factorial := by + have htailR : |Real.exp (q (a,n)) - ∑ i ∈ Finset.range (N a n), (q (a,n) : ℝ)^i / i.factorial| ≤ + |(q (a,n) : ℝ)| ^ N a n / (N a n).factorial * 2 := by + simpa only [← Complex.ofReal_exp, ← Complex.ofReal_pow, ← Complex.ofReal_natCast, + ← Complex.ofReal_div, ← Complex.ofReal_sum, ← Complex.ofReal_sub, + Complex.norm_real, Real.norm_eq_abs] using htail + apply htailR.trans + rw [div_mul_eq_mul_div, mul_comm _ (2 : ℝ)] + gcongr + exact b a n + simp only [Rat.cast_add, Rat.cast_mul, Rat.cast_pow, Rat.cast_ofNat, Rat.cast_div, + Rat.cast_natCast, Rat.cast_sum, cast_qerror] + exact (abs_sub_le _ _ _).trans (add_le_add (diff a n) htail') + · intro a + have hn : Tendsto (fun n => N a n) atTop atTop := + tendsto_atTop_mono (fun n : ℕ => show n ≤ N a n by dsimp [N]; omega) tendsto_id + have ht := (Real.summable_pow_div_factorial (M a : ℝ)).tendsto_atTop_zero.comp hn + simpa only [Rat.cast_add, Rat.cast_mul, Rat.cast_ofNat, Rat.cast_pow, Rat.cast_natCast, + cast_qerror, Rat.cast_div, Function.comp_apply, mul_div_assoc, mul_zero, add_zero] using + (error_tendsto.const_mul (2 * 3 ^ M a)).add (ht.const_mul 2) + +end +end CertifiedReal + +namespace CertifiedReal +open Encodable Filter Topology Finset +local instance elementaryFunctionsLocal3 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable +section +variable {A : Type*} [Primcodable A] + +@[fun_prop] theorem piTerm_recursive : Primrec (fun i : ℕ => (-1 : ℚ)^i / (2 * (i : ℚ) + 1)) := by + have ht := RecursiveArithmetic.rat_pow.comp ((Primrec.const (-1)).pair Primrec.id) + have hd := RecursiveArithmetic.rat_add.comp + ((RecursiveArithmetic.rat_mul.comp ((Primrec.const 2).pair RecursiveArithmetic.ratNat)).pair (Primrec.const 1)) + exact RecursiveArithmetic.rat_div.comp (ht.pair hd) + +@[fun_prop] theorem piApprox_recursive : Primrec (fun n : ℕ => + 4 * ∑ i ∈ range (2*n), (-1 : ℚ)^i / (2*i+1)) := by + have hm : Primrec (fun n : ℕ => 2*n) := Primrec.nat_mul.comp (Primrec.const 2) Primrec.id + have hs := RecursiveArithmetic.sumRangeRat hm (piTerm_recursive.comp Primrec.snd).to₂ + exact RecursiveArithmetic.rat_mul.comp ((Primrec.const 4).pair hs) + +theorem pi : Effective (fun _ : A => Real.pi) := by + refine of_enclosures + (q := fun an => 4 * ∑ i ∈ range (2 * an.2), (-1 : ℚ) ^ i / (2 * i + 1)) + (e := fun an => 4 * qerror an.2) + (piApprox_recursive.to_comp.comp Computable.snd) (by fun_prop) ?_ ?_ + · intro a n + have hl : Tendsto (fun k => ∑ i ∈ range k, (-1 : ℝ) ^ i * (1 / (2 * i + 1))) atTop (𝓝 (Real.pi / 4)) := by + simpa only [mul_one_div] using Real.tendsto_sum_pi_div_four + have hanti : Antitone (fun i : ℕ => (1 : ℝ) / (2 * i + 1)) := by + intro k m hkm + exact one_div_le_one_div_of_le (by positivity) (by exact_mod_cast (show 2*k+1 ≤ 2*m+1 from by omega)) + have hlo := hanti.alternating_series_le_tendsto hl n + have hhi := hanti.tendsto_le_alternating_series hl n + simp only [sum_range_succ, even_two, Even.mul_right, Even.neg_pow, one_pow, one_mul] at hhi + have hfrac : (1 : ℝ) / (2 * ↑(2*n) + 1) ≤ error n := by unfold error; push_cast; gcongr; nlinarith [Nat.cast_nonneg (α := ℝ) n] + simp only [Rat.cast_mul, Rat.cast_ofNat, Rat.cast_sum, Rat.cast_div, Rat.cast_pow, + Rat.cast_neg, Rat.cast_one, Rat.cast_add, Rat.cast_natCast, cast_qerror] + simp only [mul_one_div] at hlo hhi + rw [abs_of_nonneg (by linarith)] + linarith + · intro a + simpa using error_tendsto.const_mul 4 + +end +end CertifiedReal + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Energy.lean b/lean/OAI/Analysis/PeriodicLattice/Energy.lean new file mode 100644 index 0000000000000000000000000000000000000000..1ec7b2a3445c6614abc51f6f13abde334c60be23 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Energy.lean @@ -0,0 +1,400 @@ +import OAI.Analysis.PeriodicLattice.TorusIntegration + +namespace OAI + +/-! Energy inequalities and uniqueness of classical periodic solutions. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingEnergy {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace TorusCalculus + +open scoped ContDiff Topology +open Filter Set MeasureTheory + +section EnergyTime +variable {A : Type*} [NormedAddCommGroup A] [InnerProductSpace ℝ A] + +theorem time_hasDerivAt {F : Field A} {t : ℝ} (ht : 0 < t) (q : Torus) + (hd : DifferentiableWithinAt ℝ (fun s => F s q) (Ici 0) t) : + HasDerivAt (fun s => F s q) (timeD F t q) t := + hd.hasDerivWithinAt.hasDerivAt (Ici_mem_nhds ht) + +def energy (F : Field A) (t : ℝ) : ℝ := ∫ q, ‖F t q‖ ^ 2 ∂torusVolume + +omit [InnerProductSpace ℝ A] in +theorem energy_nonneg (F : Field A) (t : ℝ) : 0 ≤ energy F t := + integral_nonneg (fun q => sq_nonneg ‖F t q‖) + +omit [InnerProductSpace ℝ A] in +theorem energy_continuousOn {F : Field A} (hF : CylinderContinuous F) + (T : ℝ) (hT : 0 ≤ T) : ContinuousOn (energy F) (Icc 0 T) := + continuousOn_integral_of_compact_support isCompact_univ + ((hF T hT).norm.pow 2) (by simp) + +theorem energy_hasDerivAt {F : Field A} + (hF : CylinderContinuous F) (hDt : CylinderContinuous (timeD F)) + (hd : ∀ t : ℝ, 0 ≤ t → ∀ q, + DifferentiableWithinAt ℝ (fun s => F s q) (Ici 0) t) + {t : ℝ} (ht : 0 < t) : + HasDerivAt (energy F) (∫ q, 2 * inner ℝ (F t q) (timeD F t q) ∂torusVolume) t := by + let G : ℝ → Torus → ℝ := fun s q => ‖F s q‖ ^ 2 + let G' : ℝ → Torus → ℝ := fun s q => 2 * inner ℝ (F s q) (timeD F s q) + have hbody : ContinuousOn (Function.uncurry G') (Icc 0 (t + 1) ×ˢ univ) := + continuousOn_const.mul ((hF (t + 1) (by linarith)).inner (hDt (t + 1) (by linarith))) + obtain ⟨C, hC⟩ := (isCompact_Icc.prod isCompact_univ).exists_bound_of_continuousOn hbody + have hloc : Ioo 0 (t + 1) ∈ 𝓝 t := Ioo_mem_nhds ht (by linarith) + have hi : Integrable (G t) torusVolume := + ((cylinder_slice_continuous hF ht.le).norm.pow 2).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _) + apply (hasDerivAt_integral_of_dominated_loc_of_deriv_le (μ := torusVolume) + (F := G) (F' := G') (s := Ioo 0 (t + 1)) (x₀ := t) (bound := fun _ => C) + hloc ?_ hi ?_ ?_ (integrable_const C) ?_).2 + · exact Filter.mem_of_superset hloc (fun s hs => + ((cylinder_slice_continuous hF hs.1.le).norm.pow 2).aestronglyMeasurable) + · exact (continuous_const.mul ((cylinder_slice_continuous hF ht.le).inner + (cylinder_slice_continuous hDt ht.le))).aestronglyMeasurable + · exact Eventually.of_forall (fun q s hs => hC (s,q) ⟨⟨hs.1.le, hs.2.le⟩, mem_univ q⟩) + · exact Eventually.of_forall (fun q s hs => (time_hasDerivAt hs.1 q (hd s hs.1.le q)).norm_sq) + +end EnergyTime + +theorem eq_zero_of_linear_deriv_bound {E E' : ℝ → ℝ} {T K : ℝ} + (hE : ContinuousOn E (Icc 0 T)) + (hd : ∀ s ∈ Ioo 0 T, HasDerivAt E (E' s) s) + (hbound : ∀ s ∈ Ioo 0 T, E' s ≤ K * E s) + (hzero : E 0 = 0) (hpos : ∀ s ∈ Icc 0 T, 0 ≤ E s) + {t : ℝ} (ht : t ∈ Icc 0 T) : E t = 0 := by + let B : ℝ → ℝ := fun s => Real.exp (-K * s) * E s + have hBd (s : ℝ) (hs : s ∈ Ioo 0 T) : + HasDerivAt B (Real.exp (-K * s) * (E' s - K * E s)) s := by + have hlinear : HasDerivAt (fun r : ℝ => -K * r) (-K) s := by + simpa only [id_eq, mul_one] using (hasDerivAt_id s).const_mul (-K) + exact (hlinear.exp.mul (hd s hs)).congr_deriv (by ring) + have hBmono : AntitoneOn B (Icc 0 T) := by + apply antitoneOn_of_deriv_nonpos (convex_Icc 0 T) + ((Real.continuous_exp.comp (continuous_const.mul continuous_id)).continuousOn.mul hE) + · intro s hs + rw [interior_Icc] at hs + exact (hBd s hs).differentiableAt.differentiableWithinAt + · intro s hs + rw [interior_Icc] at hs + change deriv B s ≤ 0 + rw [(hBd s hs).deriv] + exact mul_nonpos_of_nonneg_of_nonpos (Real.exp_pos _).le (sub_nonpos.mpr (hbound s hs)) + have he : B t ≤ B 0 := hBmono ⟨le_rfl, ht.1.trans ht.2⟩ ht ht.1 + have hn : E t ≤ 0 := by + have : Real.exp (-K * t) * E t ≤ 0 := by simpa [B, hzero] using he + exact nonpos_of_mul_nonpos_right this (Real.exp_pos _) + exact le_antisymm hn (hpos t ht) + +end TorusCalculus + +namespace TorusCalculus + +open scoped ContDiff +open MeasureTheory + +section Differences +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +omit [NormedSpace ℝ A] in +theorem cylinder_sub {F G : Field A} (hF : CylinderContinuous F) (hG : CylinderContinuous G) : + CylinderContinuous (F - G) := fun T hT => (hF T hT).sub (hG T hT) + +theorem timeD_sub {F G : Field A} {t : ℝ} {q : Torus} + (hF : DifferentiableWithinAt ℝ (fun s => F s q) (Set.Ici 0) t) + (hG : DifferentiableWithinAt ℝ (fun s => G s q) (Set.Ici 0) t) : + timeD (F - G) t q = timeD F t q - timeD G t q := derivWithin_sub hF hG + +theorem timeD_congr_nonneg {F G : Field A} + (h : ∀ t : ℝ, 0 ≤ t → ∀ q, F t q = G t q) {t : ℝ} (ht : 0 ≤ t) (q : Torus) : + timeD F t q = timeD G t q := by + apply derivWithin_congr + · intro s hs + exact h s hs q + · exact h t ht q + +end Differences + +theorem divergence_sub {F G : VectorField} {t : ℝ} + (hF : Differentiable ℝ (spaceLift F t)) (hG : Differentiable ℝ (spaceLift G t)) (q : Torus) : + divergence (F - G) t q = divergence F t q - divergence G t q := by + simp only [divergence, spaceD_component (U := F - G) (hF.sub hG), spaceD_component hF, + spaceD_component hG, spaceD_sub hF hG] + simp only [PiLp.sub_apply, Finset.sum_sub_distrib] + +theorem gradient_sub {p q : ScalarField} {t : ℝ} + (hp : Differentiable ℝ (spaceLift p t)) (hq : Differentiable ℝ (spaceLift q t)) (x : Torus) : + gradient (p - q) t x = gradient p t x - gradient q t x := by + ext i + exact spaceD_sub hp hq i x + +theorem advection_sub {V U : VectorField} {t : ℝ} + (hV : Differentiable ℝ (spaceLift V t)) (hU : Differentiable ℝ (spaceLift U t)) (q : Torus) : + advection V t q - advection U t q = transport V (V - U) t q + transport (V - U) U t q := by + simp only [advection, transport, spaceD_sub hV hU, Pi.sub_apply, PiLp.sub_apply, + sub_smul, smul_sub, ← Finset.sum_sub_distrib, ← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro i _ + abel + +def gradientSize (U : VectorField) : ScalarField := fun t q => ∑ i : Fin 3, ‖spaceD i U t q‖ + +theorem gradientSize_nonneg (U : VectorField) (t : ℝ) (q : Torus) : 0 ≤ gradientSize U t q := + Finset.sum_nonneg (fun _ _ => norm_nonneg _) + +theorem gradientSize_cylinderContinuous {U : VectorField} + (hU : ∀ i, CylinderContinuous (spaceD i U)) : CylinderContinuous (gradientSize U) := by + intro T hT + exact continuousOn_finsetSum Finset.univ (fun i _ => (hU i T hT).norm) + +theorem transport_norm_le (W U : VectorField) (t : ℝ) (q : Torus) : + ‖transport W U t q‖ ≤ ‖W t q‖ * gradientSize U t q := by + unfold transport gradientSize + rw [Finset.mul_sum] + apply (norm_sum_le _ _).trans + apply Finset.sum_le_sum + intro i _ + rw [norm_smul] + exact mul_le_mul_of_nonneg_right (PiLp.norm_apply_le (W t q) i) (norm_nonneg _) + +theorem inner_transport_bound (W U : VectorField) (t : ℝ) (q : Torus) : + |inner ℝ (W t q) (transport W U t q)| ≤ gradientSize U t q * ‖W t q‖ ^ 2 := by + calc + _ ≤ ‖W t q‖ * ‖transport W U t q‖ := by + simpa only [Real.norm_eq_abs] using norm_inner_le_norm (𝕜 := ℝ) (W t q) (transport W U t q) + _ ≤ ‖W t q‖ * (‖W t q‖ * gradientSize U t q) := + mul_le_mul_of_nonneg_left (transport_norm_le W U t q) (norm_nonneg _) + _ = _ := by ring + +theorem gradientSize_bounded {U : VectorField} + (hU : ∀ i, CylinderContinuous (spaceD i U)) (T : ℝ) (hT : 0 ≤ T) : + ∃ K : ℝ, 0 ≤ K ∧ ∀ t : ℝ, t ∈ Set.Icc 0 T → ∀ q, gradientSize U t q ≤ K := by + obtain ⟨C, hC⟩ := (isCompact_Icc.prod isCompact_univ).exists_bound_of_continuousOn + (gradientSize_cylinderContinuous hU T hT) + refine ⟨max C 0, le_max_right _ _, fun t ht q => ?_⟩ + exact (le_abs_self _).trans ((hC (t,q) ⟨ht, Set.mem_univ q⟩).trans (le_max_left _ _)) + +end TorusCalculus + +namespace TorusCalculus + +open scoped ContDiff +open MeasureTheory + +theorem timeD_sub_cylinderContinuous {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {F G : Field A} (hFc : CylinderContinuous (timeD F)) (hGc : CylinderContinuous (timeD G)) + (hF : ∀ t : ℝ, 0 ≤ t → ∀ q, DifferentiableWithinAt ℝ (fun s => F s q) (Set.Ici 0) t) + (hG : ∀ t : ℝ, 0 ≤ t → ∀ q, DifferentiableWithinAt ℝ (fun s => G s q) (Set.Ici 0) t) : + CylinderContinuous (timeD (F - G)) := by + intro T hT + apply ((hFc T hT).sub (hGc T hT)).congr + intro tq htq + exact timeD_sub (hF tq.1 htq.1.1 tq.2) (hG tq.1 htq.1.1 tq.2) + +theorem classical_difference_equation {ν : ℝ} {F U V : VectorField} {p q : ScalarField} + (hU : ClassicalSolution ν F U p) (hV : ClassicalSolution ν F V q) + {t : ℝ} (ht : 0 ≤ t) (x : Torus) : + timeD (V - U) t x = -transport V (V - U) t x - transport (V - U) U t x - + gradient (q - p) t x + ν • laplacian (V - U) t x := by + have hUs := hU.spaceTwiceDifferentiable t ht + have hVs := hV.spaceTwiceDifferentiable t ht + calc + _ = timeD V t x - timeD U t x := + timeD_sub (hV.timeDifferentiable t ht x) (hU.timeDifferentiable t ht x) + _ = (-gradient q t x + ν • laplacian V t x + F t x - advection V t x) - + (-gradient p t x + ν • laplacian U t x + F t x - advection U t x) := by + rw [eq_sub_of_add_eq (hV.equations.1 t ht x), eq_sub_of_add_eq (hU.equations.1 t ht x)] + _ = -(advection V t x - advection U t x) - gradient (q - p) t x + + ν • laplacian (V - U) t x := by + rw [gradient_sub (hV.pressureDifferentiable t ht) (hU.pressureDifferentiable t ht), + laplacian_sub hVs hUs, smul_sub] + abel + _ = _ := by + rw [advection_sub (hVs.differentiable (by norm_num)) (hUs.differentiable (by norm_num))] + abel + +theorem classical_energy_identity {ν : ℝ} {F U V : VectorField} {p q : ScalarField} + (hU : ClassicalSolution ν F U p) (hV : ClassicalSolution ν F V q) + {t : ℝ} (ht : 0 ≤ t) : + (∫ x, inner ℝ ((V - U) t x) (timeD (V - U) t x) ∂torusVolume) = + -(∫ x, inner ℝ ((V - U) t x) (transport (V - U) U t x) ∂torusVolume) - + ν * ∑ i : Fin 3, ∫ x, ‖spaceD i (V - U) t x‖ ^ 2 ∂torusVolume := by + let W := V - U + have hUs₂ := hU.spaceTwiceDifferentiable t ht + have hVs₂ := hV.spaceTwiceDifferentiable t ht + have hUs : ContDiff ℝ 1 (spaceLift U t) := hUs₂.of_le (by norm_num) + have hVs : ContDiff ℝ 1 (spaceLift V t) := hVs₂.of_le (by norm_num) + have hWs₂ : ContDiff ℝ 2 (spaceLift W t) := hVs₂.sub hUs₂ + have hWs : ContDiff ℝ 1 (spaceLift W t) := hVs.sub hUs + have hWc := (slice_continuous_iff W t).mpr hWs.continuous + have hA : Integrable (fun x => inner ℝ (W t x) (transport V W t x)) torusVolume := + (hWc.inner (transport_continuous hVs hWs)).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _) + have hB : Integrable (fun x => inner ℝ (W t x) (transport W U t x)) torusVolume := + (hWc.inner (transport_continuous hWs hUs)).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _) + have hP : Continuous (gradient (q - p) t) := by + have heq : gradient (q - p) t = gradient q t - gradient p t := + funext (gradient_sub (hV.pressureDifferentiable t ht) (hU.pressureDifferentiable t ht)) + rw [heq] + exact (cylinder_slice_continuous hV.pressureGradientContinuous ht).sub + (cylinder_slice_continuous hU.pressureGradientContinuous ht) + have hC : Integrable (fun x => inner ℝ (W t x) (gradient (q - p) t x)) torusVolume := + (hWc.inner hP).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _) + have hLap : Continuous (laplacian W t) := by + apply continuous_finsetSum _ (fun i _ => ?_) + exact (slice_continuous_iff _ t).mpr + (slice_contDiff_spaceD (n := 0) (by + simpa using slice_contDiff_spaceD (n := 1) (by convert hWs₂ using 1; norm_num) i) i).continuous + have hD : Integrable (fun x => inner ℝ (W t x) (laplacian W t x)) torusVolume := + (hWc.inner hLap).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _) + have hWdiv : ∀ x, divergence W t x = 0 := by + intro x + rw [divergence_sub (hVs.differentiable one_ne_zero) (hUs.differentiable one_ne_zero), + hV.equations.2.1 t ht, hU.equations.2.1 t ht, sub_self] + have hzeroA := integral_inner_transport_self hVs hWs (hV.equations.2.1 t ht) + have hzeroC := integral_inner_gradient (p := q - p) hWs hWdiv + ((cylinder_slice_continuous hV.pressureContinuous ht).sub + (cylinder_slice_continuous hU.pressureContinuous ht)) + ((hV.pressureDifferentiable t ht).sub (hU.pressureDifferentiable t ht)) hP + have hdiffusion := integral_inner_laplacian hWs₂ + calc + _ = ∫ x, -inner ℝ (W t x) (transport V W t x) - inner ℝ (W t x) (transport W U t x) - + inner ℝ (W t x) (gradient (q - p) t x) + ν * inner ℝ (W t x) (laplacian W t x) ∂torusVolume := by + apply integral_congr_ae + exact Filter.Eventually.of_forall (fun x => by + dsimp only + rw [classical_difference_equation hU hV ht] + simp only [inner_add_right, inner_sub_right, inner_neg_right, inner_smul_right, W]) + _ = -(∫ x, inner ℝ (W t x) (transport V W t x) ∂torusVolume) - + (∫ x, inner ℝ (W t x) (transport W U t x) ∂torusVolume) - + (∫ x, inner ℝ (W t x) (gradient (q - p) t x) ∂torusVolume) + + ν * ∫ x, inner ℝ (W t x) (laplacian W t x) ∂torusVolume := by + rw [integral_add + (f := fun x => -inner ℝ (W t x) (transport V W t x) - inner ℝ (W t x) (transport W U t x) - + inner ℝ (W t x) (gradient (q - p) t x)) + (g := fun x => ν * inner ℝ (W t x) (laplacian W t x)) + ((hA.neg.sub hB).sub hC) (hD.const_mul ν), + integral_sub (f := fun x => -inner ℝ (W t x) (transport V W t x) - inner ℝ (W t x) (transport W U t x)) + (g := fun x => inner ℝ (W t x) (gradient (q - p) t x)) (hA.neg.sub hB) hC, + integral_sub (f := fun x => -inner ℝ (W t x) (transport V W t x)) + (g := fun x => inner ℝ (W t x) (transport W U t x)) hA.neg hB, integral_neg, integral_const_mul] + _ = _ := by rw [hzeroA, hzeroC, hdiffusion]; dsimp [W]; ring + +end TorusCalculus + +namespace TorusCalculus + +open scoped ContDiff +open MeasureTheory + +theorem classical_energy_derivative_le {ν K : ℝ} {F U V : VectorField} {p q : ScalarField} + (hν : 0 ≤ ν) (hU : ClassicalSolution ν F U p) (hV : ClassicalSolution ν F V q) + {t : ℝ} (ht : 0 ≤ t) (hK : ∀ x, gradientSize U t x ≤ K) : + (∫ x, 2 * inner ℝ ((V - U) t x) (timeD (V - U) t x) ∂torusVolume) ≤ + (2 * K) * energy (V - U) t := by + let W := V - U + have hUs : ContDiff ℝ 1 (spaceLift U t) := (hU.spaceTwiceDifferentiable t ht).of_le (by norm_num) + have hWs : ContDiff ℝ 1 (spaceLift W t) := + ((hV.spaceTwiceDifferentiable t ht).of_le (by norm_num)).sub hUs + have hWc := (slice_continuous_iff W t).mpr hWs.continuous + have hi : Integrable (fun x => inner ℝ (W t x) (transport W U t x)) torusVolume := + (hWc.inner (transport_continuous hWs hUs)).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _) + have hsq : Integrable (fun x => ‖W t x‖ ^ 2) torusVolume := + (hWc.norm.pow 2).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _) + have hestimate : -(∫ x, inner ℝ (W t x) (transport W U t x) ∂torusVolume) ≤ K * energy W t := by + calc + _ = ∫ x, -inner ℝ (W t x) (transport W U t x) ∂torusVolume := (integral_neg _).symm + _ ≤ ∫ x, K * ‖W t x‖ ^ 2 ∂torusVolume := by + apply integral_mono hi.neg (hsq.const_mul K) + intro x + exact (neg_le_abs _).trans ((inner_transport_bound W U t x).trans + (mul_le_mul_of_nonneg_right (hK x) (sq_nonneg _))) + _ = _ := integral_const_mul _ _ + have hdiff : 0 ≤ ν * ∑ i : Fin 3, ∫ x, ‖spaceD i W t x‖ ^ 2 ∂torusVolume := + mul_nonneg hν (Finset.sum_nonneg (fun _ _ => integral_nonneg (fun _ => sq_nonneg _))) + rw [integral_const_mul, classical_energy_identity hU hV ht] + dsimp only [W] at hestimate hdiff + nlinarith + +theorem classical_velocity_unique {ν : ℝ} {F U V : VectorField} {p q : ScalarField} + (hν : 0 ≤ ν) (hU : ClassicalSolution ν F U p) (hV : ClassicalSolution ν F V q) + (t : ℝ) (ht : 0 ≤ t) (x : Torus) : V t x = U t x := by + let W := V - U + have hWc : CylinderContinuous W := cylinder_sub hV.velocityContinuous hU.velocityContinuous + have hDtc : CylinderContinuous (timeD W) := timeD_sub_cylinderContinuous + hV.timeContinuous hU.timeContinuous hV.timeDifferentiable hU.timeDifferentiable + have hWd (s : ℝ) (hs : 0 ≤ s) (y : Torus) : + DifferentiableWithinAt ℝ (fun r => W r y) (Set.Ici 0) s := + (hV.timeDifferentiable s hs y).sub (hU.timeDifferentiable s hs y) + obtain ⟨K, _, hK⟩ := gradientSize_bounded hU.spaceFirstContinuous t ht + have hEzero : energy W t = 0 := by + apply eq_zero_of_linear_deriv_bound (E' := fun s => + ∫ y, 2 * inner ℝ (W s y) (timeD W s y) ∂torusVolume) (K := 2 * K) + (energy_continuousOn hWc t ht) + · intro s hs + exact energy_hasDerivAt hWc hDtc hWd hs.1 + · intro s hs + exact classical_energy_derivative_le hν hU hV hs.1.le (hK s ⟨hs.1.le, hs.2.le⟩) + · simp only [energy, W, Pi.sub_apply, hV.equations.2.2, hU.equations.2.2, sub_self, + norm_zero, zero_pow (by decide : (2 : ℕ) ≠ 0), integral_zero] + · exact fun s _ => energy_nonneg W s + · exact ⟨ht, le_rfl⟩ + have hzero : W t x = 0 := eq_zero_of_integral_norm_sq_eq_zero + (cylinder_slice_continuous hWc ht) hEzero x + exact sub_eq_zero.mp hzero + +theorem classical_pressure_unique {ν : ℝ} {F U V : VectorField} {p q : ScalarField} + (hU : ClassicalSolution ν F U p) (hV : ClassicalSolution ν F V q) + (hvel : ∀ t : ℝ, 0 ≤ t → ∀ x, V t x = U t x) + (t : ℝ) (ht : 0 ≤ t) (x : Torus) : q t x = p t x := by + have hs (i : Fin 3) (y : Torus) : spaceD i V t y = spaceD i U t y := + spaceD_congr_slice (hvel t ht) i y + have hss (i : Fin 3) (y : Torus) : spaceD i (spaceD i V) t y = spaceD i (spaceD i U) t y := + spaceD_congr_slice (hs i) i y + have ha (y : Torus) : advection V t y = advection U t y := by + simp only [advection, hvel t ht, hs] + have hl (y : Torus) : laplacian V t y = laplacian U t y := by + simp only [laplacian, hss] + have hg (y : Torus) : gradient q t y = gradient p t y := by + have h := hV.equations.1 t ht y + rw [timeD_congr_nonneg hvel ht y, ha y, hl y] at h + have he := h.symm.trans (hU.equations.1 t ht y) + exact neg_injective (add_right_cancel (add_right_cancel he)) + have hpartial (i : Fin 3) (y : Torus) : spaceD i (q - p) t y = 0 := by + have he := congrArg (fun v : Space => v i) (hg y) + rw [spaceD_sub (hV.pressureDifferentiable t ht) (hU.pressureDifferentiable t ht)] + exact sub_eq_zero.mpr he + have hconstant (y : Torus) : (q - p) t y = (q - p) t x := + spatially_constant_of_partials_zero (F := q - p) + ((hV.pressureDifferentiable t ht).sub (hU.pressureDifferentiable t ht)) hpartial y x + have hmean : (∫ y, (q - p) t y ∂torusVolume) = 0 := by + change (∫ y, q t y - p t y ∂torusVolume) = 0 + rw [integral_sub + ((cylinder_slice_continuous hV.pressureContinuous ht).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _)) + ((cylinder_slice_continuous hU.pressureContinuous ht).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _)), hV.pressureMeanZero t ht, hU.pressureMeanZero t ht, sub_self] + simp_rw [hconstant, integral_const] at hmean + have hz : (q - p) t x = 0 := by simpa using hmean + exact sub_eq_zero.mp hz + +theorem classical_unique {ν : ℝ} {F U : VectorField} {p : ScalarField} + (hν : 0 ≤ ν) (hU : ClassicalSolution ν F U p) : UniqueClassical ν F U p := by + intro V q hV t ht + have hv := classical_velocity_unique hν hU hV + exact ⟨hv t ht, classical_pressure_unique hU hV hv t ht⟩ + +end TorusCalculus + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/FieldCertificates.lean b/lean/OAI/Analysis/PeriodicLattice/FieldCertificates.lean new file mode 100644 index 0000000000000000000000000000000000000000..331dc8af0980df26778457e865103e9373436ff2 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/FieldCertificates.lean @@ -0,0 +1,398 @@ +import OAI.Analysis.PeriodicLattice.Certificates + +namespace OAI + +/-! Uniform certificates for all field derivative words. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingFieldCertificates {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Quantitative +open RapidCalculus Profiles TorusCalculus RecursiveArithmetic +open scoped ContDiff + +section FieldWords +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +def coordD (i : Option (Fin 3)) (F : Field A) : Field A := + match i with + | none => fullTimeD F + | some j => spaceD j F + +def fieldWord (w : List (Option (Fin 3))) (F : Field A) : Field A := w.foldr coordD F + +@[simp] theorem fieldWord_nil (F : Field A) : fieldWord [] F = F := rfl +@[simp] theorem fieldWord_cons (i : Option (Fin 3)) (w : List (Option (Fin 3))) (F : Field A) : + fieldWord (i::w) F = coordD i (fieldWord w F) := rfl + +theorem fieldWord_append (w v : List (Option (Fin 3))) (F : Field A) : + fieldWord (w++v) F = fieldWord w (fieldWord v F) := List.foldr_append + +theorem coordD_contDiff {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (i : Option (Fin 3)) : + ContDiff ℝ ∞ (lifted (coordD i F)) := by + cases i with + | none => exact contDiff_fullTimeD hF + | some j => exact contDiff_spaceD hF j + +theorem fieldWord_contDiff {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (w : List (Option (Fin 3))) : + ContDiff ℝ ∞ (lifted (fieldWord w F)) := by + induction w with + | nil => exact hF + | cons i w ih => exact coordD_contDiff ih i + +theorem coordD_add {F G : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + (hG : ContDiff ℝ ∞ (lifted G)) (i : Option (Fin 3)) : + coordD i (F+G) = coordD i F + coordD i G := by + funext t q + cases i with + | none => + exact deriv_add (fullTime_hasDerivAt hF t q).differentiableAt + (fullTime_hasDerivAt hG t q).differentiableAt + | some j => exact spaceD_add (smooth_slice_differentiable hF t) (smooth_slice_differentiable hG t) j q + +theorem fieldWord_add {F G : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + (hG : ContDiff ℝ ∞ (lifted G)) (w : List (Option (Fin 3))) : + fieldWord w (F+G) = fieldWord w F + fieldWord w G := by + induction w with + | nil => rfl + | cons i w ih => rw [fieldWord_cons, ih, coordD_add (fieldWord_contDiff hF w) (fieldWord_contDiff hG w)]; rfl + +theorem coordD_scale {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (c : ℝ) (i : Option (Fin 3)) : + coordD i (c • F) = c • coordD i F := by + cases i with + | none => exact funext (fun t => funext (fun q => ((fullTime_hasDerivAt hF t q).const_smul c).deriv)) + | some j => exact spaceD_scale hF c j + +theorem fieldWord_scale {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (c : ℝ) + (w : List (Option (Fin 3))) : fieldWord w (c • F) = c • fieldWord w F := by + induction w with + | nil => rfl + | cons i w ih => rw [fieldWord_cons, ih, coordD_scale (fieldWord_contDiff hF w) c]; rfl + +theorem coordD_zero (i : Option (Fin 3)) : coordD i (0 : Field A) = 0 := by + funext t q; cases i <;> exact deriv_const _ _ + +@[simp] theorem fieldWord_zero (w : List (Option (Fin 3))) : fieldWord w (0 : Field A) = 0 := by + induction w with + | nil => rfl + | cons i w ih => rw [fieldWord_cons, ih, coordD_zero] + +structure FieldCertificate (F : Input → Field A) where + budget : Input × ℕ × ℕ → ℕ + recursive : Primrec budget + smooth : ∀ d, ContDiff ℝ ∞ (lifted (F d)) + estimate : ∀ d, d.WellFormed → ∀ w n J, w.length ≤ n → ∀ t, 0 ≤ t → ∀ q, + (1+t)^J * ‖fieldWord w (F d) t q‖ ≤ (budget (d,n,J) : ℝ) + +namespace FieldCertificate +noncomputable def diff {F : Input → Field A} (h : FieldCertificate F) (i : Option (Fin 3)) : + FieldCertificate (fun d => coordD i (F d)) where + budget p := h.budget (p.1,p.2.1+1,p.2.2) + recursive := h.recursive.comp (by fun_prop) + smooth d := coordD_contDiff (h.smooth d) i + estimate d hd w n J hn t ht q := by + simpa only [fieldWord_append, fieldWord_cons, fieldWord_nil] using + h.estimate d hd (w++[i]) (n+1) J (by simpa using Nat.add_le_add_right hn 1) t ht q + +noncomputable def add {F G : Input → Field A} (h : FieldCertificate F) (k : FieldCertificate G) : + FieldCertificate (fun d => F d + G d) where + budget p := h.budget p + k.budget p + recursive := Primrec.nat_add.comp h.recursive k.recursive + smooth d := (h.smooth d).add (k.smooth d) + estimate d hd w n J hn t ht q := by + rw [fieldWord_add (h.smooth d) (k.smooth d)] + calc + _ ≤ (1+t)^J * (‖fieldWord w (F d) t q‖ + ‖fieldWord w (G d) t q‖) := + mul_le_mul_of_nonneg_left (norm_add_le _ _) (by positivity) + _ ≤ _ := by rw [mul_add, Nat.cast_add]; exact add_le_add (h.estimate d hd w n J hn t ht q) (k.estimate d hd w n J hn t ht q) + +noncomputable def scale {F : Input → Field A} (h : FieldCertificate F) (c : ℝ) (N : ℕ) + (hc : ‖c‖ ≤ N) : FieldCertificate (fun d => c • F d) where + budget p := N * h.budget p + recursive := Primrec.nat_mul.comp (Primrec.const N) h.recursive + smooth d := (h.smooth d).const_smul c + estimate d hd w n J hn t ht q := by + rw [fieldWord_scale (h.smooth d) c, Pi.smul_apply, Pi.smul_apply, norm_smul, mul_left_comm] + simpa only [Nat.cast_mul] using mul_le_mul hc (h.estimate d hd w n J hn t ht q) + (by positivity) (Nat.cast_nonneg N) + +noncomputable def neg {F : Input → Field A} (h : FieldCertificate F) : + FieldCertificate (fun d => -F d) := by + simpa only [neg_one_smul] using h.scale (-1) 1 (by norm_num) +noncomputable def sub {F G : Input → Field A} (h : FieldCertificate F) (k : FieldCertificate G) : + FieldCertificate (fun d => F d - G d) := by simpa only [sub_eq_add_neg] using h.add k.neg + +noncomputable def zero : FieldCertificate (fun _ => (0 : Field A)) where + budget _ := 0 + recursive := Primrec.const _ + smooth _ := contDiff_const + estimate d hd w n J hn t ht q := by simp +end FieldCertificate +end FieldWords + +theorem coordD_mul {F G : ScalarField} (hF : ContDiff ℝ ∞ (lifted F)) + (hG : ContDiff ℝ ∞ (lifted G)) (i : Option (Fin 3)) : + coordD i (F*G) = coordD i F * G + F * coordD i G := by + funext t q + cases i with + | none => + exact deriv_mul (fullTime_hasDerivAt hF t q).differentiableAt + (fullTime_hasDerivAt hG t q).differentiableAt + | some j => exact spaceD_smul hF hG j t q + +theorem fieldWord_mul_estimate {F G : ScalarField} + (hF : ContDiff ℝ ∞ (lifted F)) (hG : ContDiff ℝ ∞ (lifted G)) + (w : List (Option (Fin 3))) (t : ℝ) (q : Torus) (a C D : ℝ) (ha : 0 ≤ a) (hC : 0 ≤ C) + (hf : ∀ v : List (Option (Fin 3)), v.length ≤ w.length → a * ‖fieldWord v F t q‖ ≤ C) + (hg : ∀ v : List (Option (Fin 3)), v.length ≤ w.length → ‖fieldWord v G t q‖ ≤ D) : + a * ‖fieldWord w (F*G) t q‖ ≤ 2^w.length * C * D := by + induction w using List.reverseRecOn generalizing F G with + | nil => + simpa only [fieldWord_nil, Pi.mul_apply, norm_mul, List.length_nil, pow_zero, one_mul, + ← mul_assoc] using mul_le_mul (hf [] le_rfl) (hg [] le_rfl) (norm_nonneg _) hC + | append_singleton w i ih => + have hfi v (hv : v.length ≤ w.length) : a * ‖fieldWord v (coordD i F) t q‖ ≤ C := by + simpa only [fieldWord_append, fieldWord_cons, fieldWord_nil] using + hf (v++[i]) (by simpa only [List.length_append, List.length_singleton] using Nat.add_le_add_right hv 1) + have hgi v (hv : v.length ≤ w.length) : ‖fieldWord v (coordD i G) t q‖ ≤ D := by + simpa only [fieldWord_append, fieldWord_cons, fieldWord_nil] using + hg (v++[i]) (by simpa only [List.length_append, List.length_singleton] using Nat.add_le_add_right hv 1) + have hf' v (hv : v.length ≤ w.length) := hf v (hv.trans (by simp)) + have hg' v (hv : v.length ≤ w.length) := hg v (hv.trans (by simp)) + have H1 := ih (coordD_contDiff hF i) hG hfi hg' + have H2 := ih hF (coordD_contDiff hG i) hf' hgi + rw [fieldWord_append, fieldWord_cons, fieldWord_nil, coordD_mul hF hG, + fieldWord_add (F := coordD i F * G) (G := F * coordD i G) + ((coordD_contDiff hF i).mul hG) (hF.mul (coordD_contDiff hG i))] + calc + _ ≤ a * (‖fieldWord w (coordD i F * G) t q‖ + ‖fieldWord w (F * coordD i G) t q‖) := + mul_le_mul_of_nonneg_left (norm_add_le _ _) ha + _ ≤ 2^w.length*C*D + 2^w.length*C*D := by rw [mul_add]; exact add_le_add H1 H2 + _ = _ := by simp only [List.length_append, List.length_singleton, pow_succ]; ring + +namespace FieldCertificate +noncomputable def mul {F G : Input → ScalarField} (h : FieldCertificate F) (k : FieldCertificate G) : + FieldCertificate (fun d => F d * G d) where + budget p := 2^p.2.1 * h.budget p * k.budget (p.1,p.2.1,0) + recursive := by + have hp : Primrec (fun p : Input × ℕ × ℕ => k.budget (p.1,p.2.1,0)) := k.recursive.comp (by fun_prop) + exact Primrec.nat_mul.comp (Primrec.nat_mul.comp (by fun_prop) h.recursive) hp + smooth d := (h.smooth d).mul (k.smooth d) + estimate d hd w n J hn t ht q := by + have hh := fieldWord_mul_estimate (h.smooth d) (k.smooth d) w t q ((1+t)^J) + (h.budget (d,n,J)) (k.budget (d,n,0)) (by positivity) (by positivity) + (fun v hv => h.estimate d hd v n J (hv.trans hn) t ht q) + (fun v hv => by simpa using k.estimate d hd v n 0 (hv.trans hn) t ht q) + refine hh.trans ?_ + simp only [Nat.cast_mul, Nat.cast_pow, Nat.cast_ofNat] + gcongr + norm_num +end FieldCertificate + +theorem fieldWord_tensor_estimate {F : ScalarField} {f : ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hf : ContDiff ℝ ∞ (Function.uncurry f)) (hh : ContDiff ℝ ∞ h) + (he : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) + (w : List (Option (Fin 3))) (t : ℝ) (x : Space) (a C D : ℝ) + (ha : 0 ≤ a) (hC : 0 ≤ C) (hD : 0 ≤ D) + (hfB : ∀ v : List Bool, v.length ≤ w.length → a * ‖wordD v f t (x 1)‖ ≤ C) + (hhB : ∀ k : ℕ, k ≤ w.length → ‖iteratedDeriv k h (x 2)‖ ≤ D) : + a * ‖fieldWord w F t (torusMk x)‖ ≤ D * C := by + induction w using List.reverseRecOn generalizing F f h with + | nil => + rw [fieldWord_nil, he, norm_mul, mul_left_comm] + exact mul_le_mul (hhB 0 le_rfl) (hfB [] le_rfl) (by positivity) hD + | append_singleton w i ih => + rw [fieldWord_append, fieldWord_cons, fieldWord_nil] + have hf' v (hv : v.length ≤ w.length) := hfB v (hv.trans (by simp)) + have hh' k (hk : k ≤ w.length) := hhB k (hk.trans (by simp)) + have hfi (j : Bool) v (hv : v.length ≤ w.length) : a * ‖wordD v (biD j f) t (x 1)‖ ≤ C := by + simpa only [wordD_append, wordD_cons, wordD_nil] using + hfB (v++[j]) (by simpa only [List.length_append, List.length_singleton] using Nat.add_le_add_right hv 1) + cases i with + | none => exact ih (partial_contDiff hf true) hh (tensor_fullTimeD hf he) (hfi true) hh' + | some i => + fin_cases i + · change a * ‖fieldWord w (spaceD 0 F) t (torusMk x)‖ ≤ D*C + rw [tensor_spaceD_zero he] + simp only [fieldWord_zero, Pi.zero_apply, norm_zero, mul_zero] + exact mul_nonneg hD hC + · exact ih (partial_contDiff hf false) hh (tensor_spaceD_one hf he) (hfi false) hh' + · have hhder : ContDiff ℝ ∞ (deriv h) := by simpa using ContDiff.iterate_deriv 1 hh + exact ih hf hhder (tensor_spaceD_two hh he) hf' + (fun k hk => by + simpa only [← iteratedDeriv_succ'] using + hhB (k+1) (by simpa only [List.length_append, List.length_singleton] using Nat.add_le_add_right hk 1)) + +namespace FieldCertificate +noncomputable def tensor {F : Input → ScalarField} {f : Input → ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hf : BiCertificate f) (hh : ProfileCertificate h) + (he : ∀ d t x, F d t (torusMk x) = h (x 2) * f d t (x 1)) : FieldCertificate F where + budget p := hh.budget p.2.1 * hf.budget p + recursive := Primrec.nat_mul.comp (hh.recursive.comp (by fun_prop)) hf.recursive + smooth d := tensor_contDiff (hf.smooth d) hh.smooth (he d) + estimate d hd w n J hn t ht q := by + obtain ⟨x,rfl⟩ := mk_surjective q + simpa only [Nat.cast_mul] using fieldWord_tensor_estimate (hf.smooth d) hh.smooth (he d) + w t x ((1+t)^J) (hf.budget (d,n,J)) (hh.budget n) (by positivity) (by positivity) (by positivity) + (fun v hv => hf.estimate d hd v n J (hv.trans hn) t ht (x 1)) + (fun k hk => hh.estimate k n (hk.trans hn) (x 2)) +end FieldCertificate + +theorem coordD_component {F : VectorField} (hF : ContDiff ℝ ∞ (lifted F)) + (i : Option (Fin 3)) (j : Fin 3) : + coordD i (fun t q => F t q j) = fun t q => coordD i F t q j := by + funext t q + cases i with + | none => + exact ((PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) j).hasFDerivAt.comp_hasDerivAt t + (fullTime_hasDerivAt hF t q)).deriv + | some i => exact spaceD_component (smooth_slice_differentiable hF t) i j q + +theorem fieldWord_component {F : VectorField} (hF : ContDiff ℝ ∞ (lifted F)) + (w : List (Option (Fin 3))) (j : Fin 3) : + fieldWord w (fun t q => F t q j) = fun t q => fieldWord w F t q j := by + induction w with + | nil => rfl + | cons i w ih => rw [fieldWord_cons, ih, coordD_component (fieldWord_contDiff hF w) i]; rfl + +namespace FieldCertificate +noncomputable def components {F : Input → VectorField} + (h : ∀ i : Fin 3, FieldCertificate (fun d t q => F d t q i)) : FieldCertificate F where + budget p := (h 0).budget p + (h 1).budget p + (h 2).budget p + recursive := Primrec.nat_add.comp (Primrec.nat_add.comp (h 0).recursive (h 1).recursive) (h 2).recursive + smooth d := contDiff_euclidean.mpr (fun i => (h i).smooth d) + estimate d hd w n J hn t ht q := by + have hs : ContDiff ℝ ∞ (lifted (F d)) := contDiff_euclidean.mpr (fun i => (h i).smooth d) + have H (i : Fin 3) := (h i).estimate d hd w n J hn t ht q + simp_rw [fieldWord_component hs] at H + calc + _ ≤ (1+t)^J * ∑ i : Fin 3, ‖fieldWord w (F d) t q i‖ := + mul_le_mul_of_nonneg_left (norm_le_sum_components _) (by positivity) + _ ≤ _ := by + rw [Fin.sum_univ_three, mul_add, mul_add, Nat.cast_add, Nat.cast_add] + exact add_le_add (add_le_add (H 0) (H 1)) (H 2) +noncomputable def component {F : Input → VectorField} (h : FieldCertificate F) (i : Fin 3) : + FieldCertificate (fun d t q => F d t q i) where + budget := h.budget + recursive := h.recursive + smooth d := (contDiff_euclidean.mp (h.smooth d)) i + estimate d hd w n J hn t ht q := by + rw [fieldWord_component (h.smooth d)] + exact (mul_le_mul_of_nonneg_left (PiLp.norm_apply_le (fieldWord w (F d) t q) i) (by positivity)).trans + (h.estimate d hd w n J hn t ht q) + +noncomputable def diffusion {F : Input → VectorField} (h : FieldCertificate F) : + FieldCertificate (fun d => laplacian (F d)) := by + have he : (fun d => laplacian (F d)) = fun d => + spaceD 0 (spaceD 0 (F d)) + spaceD 1 (spaceD 1 (F d)) + spaceD 2 (spaceD 2 (F d)) := by + funext d t q; exact Fin.sum_univ_three _ + rw [he] + exact ((h.diff (some 0)).diff (some 0)).add ((h.diff (some 1)).diff (some 1)) |>.add + ((h.diff (some 2)).diff (some 2)) + +noncomputable def transport {F : Input → VectorField} (h : FieldCertificate F) : + FieldCertificate (fun d => advection (F d)) := by + apply components + intro j + have he : (fun d t q => advection (F d) t q j) = fun d => + (fun t q => F d t q 0 * spaceD 0 (F d) t q j) + + (fun t q => F d t q 1 * spaceD 1 (F d) t q j) + + (fun t q => F d t q 2 * spaceD 2 (F d) t q j) := by + funext d t q + simp only [advection, Fin.sum_univ_three, PiLp.add_apply, PiLp.smul_apply, Pi.add_apply, smul_eq_mul] + rw [he] + exact ((h.component 0).mul ((h.diff (some 0)).component j)).add + ((h.component 1).mul ((h.diff (some 1)).component j)) |>.add + ((h.component 2).mul ((h.diff (some 2)).component j)) + +noncomputable def gradient {F : Input → ScalarField} (h : FieldCertificate F) : + FieldCertificate (fun d => PeriodicLattice.gradient (F d)) := + components (fun i => h.diff (some i)) + +noncomputable def residual {F : Input → VectorField} (h : FieldCertificate F) (ν : ℝ) (N : ℕ) + (hν : ‖ν‖ ≤ N) : FieldCertificate (fun d => Residual.fullForce ν (F d)) := + ((h.diff none).add h.transport).sub (h.diffusion.scale ν N hν) +end FieldCertificate + +noncomputable def velocityCertificate : FieldCertificate FluidLift.velocity := by + apply FieldCertificate.components + refine Fin.cases ?_ (Fin.cases ?_ (Fin.cases ?_ (fun i => i.elim0))) + · exact FieldCertificate.tensor aCertificate slopeCertificate (fun d t x => by simp) + · exact FieldCertificate.tensor bCertificate slopeCertificate (fun d t x => by simp) + · exact FieldCertificate.tensor (bCertificate.diff false) etaCertificate.neg (fun d t x => by simp [FluidLift.bdy, biD]) + +noncomputable def potentialCertificate : FieldCertificate FluidLift.potential := + (FieldCertificate.tensor pressureBaseCertificate ProfileCertificate.one + (fun d t x => by simp [PeriodicInverse.horizontal, torusMk, Function.Periodic.lift_coe])).add + (FieldCertificate.tensor pressureModeCertificate doubleSlopeCertificate FluidLift.pressureOsc_cover) + +noncomputable def forceCertificate (ν : ℝ) (N : ℕ) (hν : ‖ν‖ ≤ N) : FieldCertificate (FluidLift.force ν) := + velocityCertificate.residual ν N hν + +noncomputable def solenoidalForceCertificate (ν : ℝ) (N : ℕ) (hν : ‖ν‖ ≤ N) : + FieldCertificate (FluidLift.solenoidalForce ν) := + (forceCertificate ν N hν).sub potentialCertificate.gradient + +section MixedWords +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +theorem fieldWord_replicate (i : Option (Fin 3)) (n : ℕ) (F : Field A) : + fieldWord (List.replicate n i) F = (coordD i)^[n] F := by + induction n with + | zero => rfl + | succ n ih => simp only [List.replicate_succ, fieldWord_cons, Function.iterate_succ_apply', ih] + +def spatialWord (α : MultiIndex) : List (Option (Fin 3)) := + List.replicate (α 2) (some 2) ++ List.replicate (α 1) (some 1) ++ List.replicate (α 0) (some 0) +def mixedWord (r : ℕ) (α : MultiIndex) : List (Option (Fin 3)) := + List.replicate r none ++ spatialWord α + +theorem mixedD_eq_fieldWord {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + (r : ℕ) (α : MultiIndex) {t : ℝ} (ht : 0 ≤ t) (q : Torus) : + mixedD r α F t q = fieldWord (mixedWord r α) F t q := by + have hh := fieldWord_contDiff hF (spatialWord α) + simp only [spatialWord, fieldWord_append, fieldWord_replicate] at hh + simp only [mixedD, mixedWord, spatialWord, fieldWord_append, fieldWord_replicate] + exact iterate_timeD_eq_fullTimeD hh r t ht q +end MixedWords + +def mixedOrder (r : ℕ) (α : MultiIndex) : ℕ := r + (α 2 + α 1 + α 0) + +@[fun_prop] theorem mixedOrder_recursive : Primrec (fun p : ℕ × MultiIndex => mixedOrder p.1 p.2) := by + have hi (i : Fin 3) : Primrec (fun p : ℕ × MultiIndex => p.2 i) := + Primrec.fin_app.comp Primrec.snd (Primrec.const i) + exact Primrec.nat_add.comp Primrec.fst (Primrec.nat_add.comp (Primrec.nat_add.comp (hi 2) (hi 1)) (hi 0)) + +namespace FieldCertificate +noncomputable def mixedBudget {F : Input → VectorField} (h : FieldCertificate F) + (d : Input) (r : ℕ) (α : MultiIndex) (J : ℕ) : ℕ := h.budget (d,mixedOrder r α,J) + +theorem mixedBudget_recursive {F : Input → VectorField} (h : FieldCertificate F) : + Primrec (fun p : Input × ℕ × MultiIndex × ℕ => h.mixedBudget p.1 p.2.1 p.2.2.1 p.2.2.2) := by + unfold mixedBudget + exact h.recursive.comp (by fun_prop) + +theorem mixed_estimate {F : Input → VectorField} (h : FieldCertificate F) (d : Input) (hd : d.WellFormed) + (r : ℕ) (α : MultiIndex) (J : ℕ) {t : ℝ} (ht : 0 ≤ t) (q : Torus) : + (1+t)^J * ‖mixedD r α (F d) t q‖ ≤ (h.mixedBudget d r α J : ℝ) := by + rw [mixedD_eq_fieldWord (h.smooth d) r α ht] + exact h.estimate d hd (mixedWord r α) (mixedOrder r α) J + (by simp [mixedWord, spatialWord, mixedOrder, Nat.add_assoc]) t ht q + +theorem sup_estimate {F : Input → VectorField} (h : FieldCertificate F) (d : Input) (hd : d.WellFormed) + (r : ℕ) (α : MultiIndex) (J : ℕ) {t : ℝ} (ht : 0 ≤ t) : + spatialSup (mixedD r α (F d)) t ≤ (h.mixedBudget d r α J : ℝ) / (1+t)^J := by + apply csSup_le (Set.range_nonempty _) + rintro _ ⟨q,rfl⟩ + exact (le_div_iff₀ (by positivity)).mpr (by simpa only [mul_comm] using h.mixed_estimate d hd r α J ht q) +end FieldCertificate +end Quantitative + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/FluidLift.lean b/lean/OAI/Analysis/PeriodicLattice/FluidLift.lean new file mode 100644 index 0000000000000000000000000000000000000000..597e94466f6cd3d64104aec1356a6b803b37ab97 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/FluidLift.lean @@ -0,0 +1,275 @@ +import OAI.Analysis.PeriodicLattice.Compiler + +namespace OAI + +/-! Periodic fluid lift of the planar dynamics. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingFluidLift {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace TorusCalculus + +open scoped ContDiff + +theorem mk_surjective : Function.Surjective torusMk := by + intro q + choose x hx using (fun i : Fin 3 => + (QuotientAddGroup.mk_surjective : Function.Surjective ((↑) : ℝ → UnitAddCircle)) (q i)) + exact ⟨WithLp.toLp 2 x, funext hx⟩ + +@[simp] theorem mk_add (x y : Space) : torusMk (x + y) = torusMk x + torusMk y := by + ext i + exact AddCircle.coe_add 1 (x i) (y i) + +theorem spaceD_cover {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + (i : Fin 3) (F : Field A) (t : ℝ) (x : Space) : + spaceD i F t (torusMk x) = + deriv (fun s : ℝ => spaceLift F t (x + EuclideanSpace.single i s)) 0 := by + simp only [spaceD, spaceLift, mk_add] + +theorem periodic_deriv {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {f : ℝ → A} {c : ℝ} (hf : Function.Periodic f c) : + Function.Periodic (deriv f) c := by + intro x + rw [← deriv_comp_add_const] + congr 1 + exact funext hf + +theorem contDiff_partial {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {v : ℝ → ℝ → A} (hv : ContDiff ℝ ∞ (Function.uncurry v)) : + ContDiff ℝ ∞ (fun ty : ℝ × ℝ => deriv (v ty.1) ty.2) := by + let f : (ℝ × ℝ) → ℝ → A := fun ty y => v ty.1 y + have hf : ContDiff ℝ ∞ (Function.uncurry f) := + hv.comp (contDiff_fst.fst.prodMk contDiff_snd) + exact hf.fderiv_apply contDiff_snd contDiff_const (by simp) + +end TorusCalculus + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus + +def eta (z : ℝ) : ℝ := + letI := twoAtLeastTwo + Real.sin (2 * Real.pi * (z - 1 / 2)) / (2 * Real.pi) +def slope (z : ℝ) : ℝ := + letI := twoAtLeastTwo + Real.cos (2 * Real.pi * (z - 1 / 2)) + +theorem eta_contDiff : ContDiff ℝ ∞ eta := + (Real.contDiff_sin.comp (contDiff_const.mul (contDiff_id.sub contDiff_const))).div_const _ + +theorem slope_contDiff : ContDiff ℝ ∞ slope := + Real.contDiff_cos.comp (contDiff_const.mul (contDiff_id.sub contDiff_const)) + +theorem eta_periodic : Function.Periodic eta 1 := by + intro z + dsimp [eta] + rw [show 2 * Real.pi * (z + 1 - 1 / 2) = 2 * Real.pi * (z - 1 / 2) + 2 * Real.pi by ring, + Real.sin_add_two_pi] + +theorem slope_periodic : Function.Periodic slope 1 := by + intro z + dsimp [slope] + rw [show 2 * Real.pi * (z + 1 - 1 / 2) = 2 * Real.pi * (z - 1 / 2) + 2 * Real.pi by ring, + Real.cos_add_two_pi] + +theorem eta_hasDerivAt (z : ℝ) : HasDerivAt eta (slope z) z := by + have h := (((hasDerivAt_id z).sub_const (1 / 2)).const_mul (2 * Real.pi)).sin.div_const + (2 * Real.pi) + change HasDerivAt (fun z => Real.sin (2 * Real.pi * (z - 1 / 2)) / (2 * Real.pi)) _ z + simpa [slope, Real.pi_ne_zero] using h + +@[simp] theorem eta_center : eta (1 / 2) = 0 := by simp [eta] +@[simp] theorem slope_center : slope (1 / 2) = 1 := by simp [slope] + +def v (d : Input) (t y : ℝ) : Planar.Point := CompilerPlanar.velocity d t (0, y) +def a (d : Input) (t y : ℝ) : ℝ := (v d t y).1 +def b (d : Input) (t y : ℝ) : ℝ := (v d t y).2 +def bdy (d : Input) (t y : ℝ) : ℝ := deriv (b d t) y + +theorem velocity_eq (d : Input) (t : ℝ) (p : Planar.Point) : + CompilerPlanar.velocity d t p = v d t p.2 := rfl + +theorem v_contDiff (d : Input) : ContDiff ℝ ∞ (Function.uncurry (v d)) := + (CompilerPlanar.velocity_contDiff d).comp + (contDiff_fst.prodMk (contDiff_const.prodMk contDiff_snd)) + +theorem a_contDiff (d : Input) : ContDiff ℝ ∞ (Function.uncurry (a d)) := (v_contDiff d).fst + +theorem b_contDiff (d : Input) : ContDiff ℝ ∞ (Function.uncurry (b d)) := (v_contDiff d).snd + +theorem bdy_contDiff (d : Input) : ContDiff ℝ ∞ (Function.uncurry (bdy d)) := + contDiff_partial (b_contDiff d) + +theorem a_periodic (d : Input) (t : ℝ) : Function.Periodic (a d t) 1 := + fun y => congrArg Prod.fst (CompilerPlanar.velocity_periodic d t 0 y) + +theorem b_periodic (d : Input) (t : ℝ) : Function.Periodic (b d t) 1 := + fun y => congrArg Prod.snd (CompilerPlanar.velocity_periodic d t 0 y) + +theorem bdy_periodic (d : Input) (t : ℝ) : Function.Periodic (bdy d t) 1 := + periodic_deriv (b_periodic d t) + +def velocity (d : Input) : VectorField := + letI := twoAtLeastTwo + letI := neZeroThree + fun t q => WithLp.toLp 2 + ![slope_periodic.lift (q 2) * (a_periodic d t).lift (q 1), + slope_periodic.lift (q 2) * (b_periodic d t).lift (q 1), + -eta_periodic.lift (q 2) * (bdy_periodic d t).lift (q 1)] + +@[simp] theorem velocity_cover (d : Input) (t : ℝ) (x : Space) : + velocity d t (torusMk x) = WithLp.toLp 2 + ![slope (x 2) * a d t (x 1), slope (x 2) * b d t (x 1), + -eta (x 2) * bdy d t (x 1)] := by + simp only [velocity, torusMk, Function.Periodic.lift_coe] + +theorem velocity_contDiff (d : Input) : ContDiff ℝ ∞ (lifted (velocity d)) := by + have hcoord (i : Fin 3) : ContDiff ℝ ∞ (fun tx : ℝ × Space => tx.2 i) := by + have hi : ContDiff ℝ ∞ (fun x : Space => x i) := (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) i).contDiff + exact hi.comp contDiff_snd + have ha := (a_contDiff d).comp (contDiff_fst.prodMk (hcoord 1)) + have hb := (b_contDiff d).comp (contDiff_fst.prodMk (hcoord 1)) + have hc := (bdy_contDiff d).comp (contDiff_fst.prodMk (hcoord 1)) + apply contDiff_euclidean.mpr + intro i + fin_cases i + · exact (slope_contDiff.comp (hcoord 2)).mul ha + · exact (slope_contDiff.comp (hcoord 2)).mul hb + · exact (eta_contDiff.comp (hcoord 2)).neg.mul hc + +theorem velocity_smooth (d : Input) : Smooth (velocity d) := (velocity_contDiff d).contDiffOn + +theorem velocity_on_plane (d : Input) (t : ℝ) (p : Planar.Point) : + velocity d t (torusMk (Planar.embed p)) = + WithLp.toLp 2 ![(CompilerPlanar.velocity d t p).1, (CompilerPlanar.velocity d t p).2, 0] := by + rw [velocity_cover] + simp [Planar.embed, eta, slope, a, b, ← velocity_eq] + +theorem b_hasDerivAt (d : Input) (t y : ℝ) : HasDerivAt (b d t) (bdy d t y) y := + (((b_contDiff d).comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y).hasDerivAt + +theorem divergence_zero (d : Input) (t : ℝ) (q : Torus) : divergence (velocity d) t q = 0 := by + obtain ⟨x, rfl⟩ := mk_surjective q + have h₀ : spaceD 0 (fun s q => velocity d s q 0) t (torusMk x) = 0 := by + rw [spaceD_cover] + change deriv (fun s : ℝ => slope (x 2 + 0) * a d t (x 1 + 0)) 0 = 0 + exact deriv_const _ _ + have h₁ : spaceD 1 (fun s q => velocity d s q 1) t (torusMk x) = + slope (x 2) * bdy d t (x 1) := by + rw [spaceD_cover] + change deriv (fun s : ℝ => slope (x 2 + 0) * b d t (x 1 + s)) 0 = _ + have h := ((b_hasDerivAt d t (x 1 + 0)).comp 0 + ((hasDerivAt_id (0 : ℝ)).const_add (x 1))).const_mul (slope (x 2)) + simpa [Function.comp_def] using h.deriv + have h₂ : spaceD 2 (fun s q => velocity d s q 2) t (torusMk x) = + -slope (x 2) * bdy d t (x 1) := by + rw [spaceD_cover] + change deriv (fun s : ℝ => -eta (x 2 + s) * bdy d t (x 1 + 0)) 0 = _ + have h := ((eta_hasDerivAt (x 2 + 0)).comp 0 + ((hasDerivAt_id (0 : ℝ)).const_add (x 2))).neg.mul_const (bdy d t (x 1)) + simpa [Function.comp_def] using h.deriv + simp only [divergence, Fin.sum_univ_three, h₀, h₁, h₂] + ring + +theorem velocity_solenoidal (d : Input) : Solenoidal (velocity d) := + fun t _ q => divergence_zero d t q + +theorem velocity_start (d : Input) (q : Torus) : velocity d 0 q = 0 := by + obtain ⟨x, rfl⟩ := mk_surjective q + have ha : a d 0 = fun _ => 0 := funext (fun y => + congrArg Prod.fst (CompilerPlanar.velocity_start d (0, y))) + have hb : b d 0 = fun _ => 0 := funext (fun y => + congrArg Prod.snd (CompilerPlanar.velocity_start d (0, y))) + rw [velocity_cover] + ext i + fin_cases i <;> simp [ha, hb, bdy] + +def path (d : Input) : ℝ → Space := fun t => Planar.embed (CompilerPlanar.path d t) + +theorem path_contDiff (d : Input) : ContDiff ℝ ∞ (path d) := by + apply contDiff_euclidean.mpr + intro i + fin_cases i + · exact (CompilerPlanar.path_contDiff d).fst + · exact (CompilerPlanar.path_contDiff d).snd + · exact contDiff_const + +theorem path_start (d : Input) : path d 0 = initialParticle := by + simp only [path, CompilerPlanar.path_start] + rfl + +theorem path_hasDerivAt (d : Input) (hd : d.WellFormed) {t : ℝ} (ht : 0 ≤ t) : + HasDerivAt (path d) (velocity d t (torusMk (path d t))) t := by + have h := CompilerPlanar.path_solves d hd ht + have hx : HasDerivAt (fun s => (CompilerPlanar.path d s).1) + (CompilerPlanar.velocity d t (CompilerPlanar.path d t)).1 t := by + simpa using h.hasFDerivAt.fst.hasDerivAt + have hy : HasDerivAt (fun s => (CompilerPlanar.path d s).2) + (CompilerPlanar.velocity d t (CompilerPlanar.path d t)).2 t := by + simpa using h.hasFDerivAt.snd.hasDerivAt + have hp : HasDerivAt (fun s => ![(CompilerPlanar.path d s).1, + (CompilerPlanar.path d s).2, (1 : ℝ) / 2]) + ![(CompilerPlanar.velocity d t (CompilerPlanar.path d t)).1, + (CompilerPlanar.velocity d t (CompilerPlanar.path d t)).2, (0 : ℝ)] t := by + apply hasDerivAt_pi.mpr + intro i + fin_cases i + · exact hx + · exact hy + · exact hasDerivAt_const _ _ + rw [path, velocity_on_plane] + exact (PiLp.hasFDerivAt_toLp 2 _).comp_hasDerivAt t hp + +theorem path_isParticle (d : Input) (hd : d.WellFormed) : IsParticle (velocity d) (path d) := + ⟨path_start d, fun _t ht => (path_hasDerivAt d hd ht).hasDerivWithinAt⟩ + +theorem path_unique (d : Input) (hd : d.WellFormed) {Y : ℝ → Space} + (hY : IsParticle (velocity d) Y) {t : ℝ} (ht : 0 ≤ t) : Y t = path d t := by + apply Trajectories.unique (v := fun t x => velocity d t (torusMk x)) + ((velocity_contDiff d).of_le (by exact WithTop.coe_le_coe.mpr le_top)) hY.2 + (path_isParticle d hd).2 _ ht + rw [hY.1, path_start] + +theorem path_event_iff (d : Input) (hd : d.WellFormed) : MaterialEvent (path d) ↔ Halts d := + CompilerPlanar.path_event_iff d hd + +theorem eta_half_shift (z : ℝ) : eta (z + 1 / 2) = -eta z := by + dsimp [eta] + rw [show 2 * Real.pi * (z + 1 / 2 - 1 / 2) = + 2 * Real.pi * (z - 1 / 2) + Real.pi by ring, Real.sin_add_pi, neg_div] + +theorem slope_half_shift (z : ℝ) : slope (z + 1 / 2) = -slope z := by + dsimp [slope] + rw [show 2 * Real.pi * (z + 1 / 2 - 1 / 2) = + 2 * Real.pi * (z - 1 / 2) + Real.pi by ring, Real.cos_add_pi] + +theorem velocity_half_shift (d : Input) (t : ℝ) (q : Torus) : + velocity d t (q + torusMk (EuclideanSpace.single 2 (1 / 2))) = -velocity d t q := by + obtain ⟨x, rfl⟩ := mk_surjective q + rw [← mk_add, velocity_cover, velocity_cover] + have he := eta_half_shift (x 2) + have hs := slope_half_shift (x 2) + simp only [one_div] at he hs + ext i + fin_cases i <;> simp [he, hs] + +theorem velocity_meanZero (d : Input) : MeanZero (velocity d) := by + intro t _ht + have : torusVolume.IsAddRightInvariant := by + dsimp [torusVolume] + infer_instance + exact MeasureTheory.integral_eq_zero_of_add_right_eq_neg (velocity_half_shift d t) + +end FluidLift + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Machines.lean b/lean/OAI/Analysis/PeriodicLattice/Machines.lean new file mode 100644 index 0000000000000000000000000000000000000000..cc529cc1ad288a690049c3b2eba0b406bcb57e00 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Machines.lean @@ -0,0 +1,257 @@ +import OAI.Analysis.PeriodicLattice.Scales + +namespace OAI + +/-! Machine histories, encoded stacks and the open particle detector. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingMachines {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace History + +open Scales + +def address (b L : ℕ) (c : ℕ → ℕ) (n : ℕ) : ℕ := + (∑ k ∈ Finset.range n, b ^ (exponent L n - exponent L k) * c k) + c n + +def coordinate (b L : ℕ) (c : ℕ → ℕ) (n : ℕ) : ℝ := + 1 / 2 + ∑ k ∈ Finset.range (n + 1), epsilon b L k * (c k : ℝ) + +theorem epsilon_ratio {b : ℕ} (hb : 2 ≤ b) (L : ℕ) {k n : ℕ} (hkn : k ≤ n) : + epsilon b L k / epsilon b L n = (b : ℝ) ^ (exponent L n - exponent L k) := by + unfold epsilon + rw [inv_div_inv, div_eq_mul_inv] + exact (pow_sub₀ _ (by exact_mod_cast (by omega : b ≠ 0)) + ((exponent_strictMono L).monotone hkn)).symm + +theorem read_coordinate {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (c : ℕ → ℕ) (n : ℕ) : + (coordinate b L c n - 1 / 2) / epsilon b L n = (address b L c n : ℝ) := by + unfold coordinate address + rw [add_sub_cancel_left, Finset.sum_range_succ, add_div] + simp only [Nat.cast_add, Nat.cast_sum, Nat.cast_mul, Nat.cast_pow] + rw [Finset.sum_div] + congr 1 + · apply Finset.sum_congr rfl + intro k hk + rw [mul_div_right_comm, epsilon_ratio hb L (Nat.le_of_lt (Finset.mem_range.mp hk))] + · have he : epsilon b L n ≠ 0 := (epsilon_pos hb L n).ne' + field_simp + +theorem read_residue (b L : ℕ) (c : ℕ → ℕ) (n : ℕ) + (hc : c n < capacity b L n) : + address b L c n % capacity b L n = c n := by + have hd : capacity b L n ∣ + ∑ k ∈ Finset.range n, b ^ (exponent L n - exponent L k) * c k := by + apply Finset.dvd_sum + intro k hk + exact dvd_mul_of_dvd_left (capacity_dvd_scaleRatio b L (Finset.mem_range.mp hk)) _ + rw [address, Nat.add_mod, Nat.dvd_iff_mod_eq_zero.mp hd, + zero_add, Nat.mod_mod, Nat.mod_eq_of_lt hc] + +theorem lift_invariant_residue (b L : ℕ) (c : ℕ → ℕ) (n : ℕ) + (hc : c n < capacity b L n) (z : ℤ) : + ((address b L c n : ℤ) + z * (b ^ exponent L n : ℕ)) % (capacity b L n : ℤ) = + (c n : ℤ) := by + have hd : (capacity b L n : ℤ) ∣ z * (b ^ exponent L n : ℕ) := by + apply dvd_mul_of_dvd_right + exact_mod_cast capacity_dvd_inverseScale b L n + have hr : (address b L c n : ℤ) % (capacity b L n : ℤ) = (c n : ℤ) := by + exact_mod_cast read_residue b L c n hc + rw [Int.add_emod, Int.emod_eq_zero_of_dvd hd, add_zero, Int.emod_emod, hr] + +theorem read_any_lift {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (c : ℕ → ℕ) (n : ℕ) + (hc : c n < capacity b L n) (z : ℤ) : + ∃ j : ℤ, + (coordinate b L c n + (z : ℝ) - 1 / 2) / epsilon b L n = (j : ℝ) ∧ + j % (capacity b L n : ℤ) = c n := by + refine ⟨(address b L c n : ℤ) + z * (b ^ exponent L n : ℕ), ?_, + lift_invariant_residue b L c n hc z⟩ + rw [show coordinate b L c n + (z : ℝ) - 1 / 2 = + (coordinate b L c n - 1 / 2) + z by ring, add_div, read_coordinate hb] + push_cast + simp [epsilon, div_eq_mul_inv] + +end History + +namespace StackCode + +structure Code where + left : ℕ + right : ℕ + state : ℕ + deriving DecidableEq + +def pack (b d : ℕ) (c : Code) : ℕ := + c.left + b ^ d * (c.right + b ^ d * c.state) + +def unpackNat (b d c : ℕ) : Code where + left := c % b ^ d + right := c / b ^ d % b ^ d + state := c / b ^ d / b ^ d + +def residue (b d : ℕ) (j : ℤ) : ℕ := (j % (b ^ (2 * d + 1) : ℕ)).toNat + +def unpack (b d : ℕ) (j : ℤ) : Code := unpackNat b d (residue b d j) + +theorem pack_eq (b d : ℕ) (c : Code) : + pack b d c = c.left + b ^ d * c.right + b ^ (2 * d) * c.state := by + rw [pack, mul_add, pow_mul, sq] + ring + +theorem pack_lt {b d : ℕ} (hb : 2 ≤ b) (c : Code) + (hl : c.left < b ^ d) (hr : c.right < b ^ d) (hs : c.state < b) : + pack b d c < b ^ (2 * d + 1) := by + have hp : 0 < b ^ d := pow_pos (by omega : 0 < b) _ + have h1 : c.right + b ^ d * c.state < b ^ d * b := by + have hm := Nat.mul_le_mul_left (b ^ d) (Nat.succ_le_of_lt hs) + nlinarith + have h2 := Nat.mul_le_mul_left (b ^ d) (Nat.succ_le_of_lt h1) + rw [pack, show 2 * d + 1 = d * 2 + 1 by omega, pow_succ, pow_mul, sq] + nlinarith + +theorem unpackNat_pack {b d : ℕ} (hb : 2 ≤ b) (c : Code) + (hl : c.left < b ^ d) (hr : c.right < b ^ d) : + unpackNat b d (pack b d c) = c := by + have hp : 0 < b ^ d := pow_pos (by omega : 0 < b) _ + simp [unpackNat, pack, Nat.add_mul_div_left, Nat.div_eq_of_lt hl, + Nat.div_eq_of_lt hr, Nat.mod_eq_of_lt hl, Nat.mod_eq_of_lt hr, hp] + +theorem unpackNat_state (b d c : ℕ) : + (unpackNat b d c).state = c / b ^ (2 * d) := by + simp [unpackNat, Nat.div_div_eq_div_mul, show 2 * d = d * 2 by omega, pow_mul, sq] + +theorem residue_periodic (b d : ℕ) : + Function.Periodic (residue b d) (b ^ (2 * d + 1) : ℕ) := by + intro j + simp [residue] + +theorem unpack_periodic (b d : ℕ) : + Function.Periodic (unpack b d) (b ^ (2 * d + 1) : ℕ) := by + intro j + simp only [unpack, residue_periodic b d j] + +theorem residue_lt {b d : ℕ} (hb : 2 ≤ b) (j : ℤ) : + residue b d j < b ^ (2 * d + 1) := by + have hp : (0 : ℤ) < (b ^ (2 * d + 1) : ℕ) := by + exact_mod_cast pow_pos (by omega : 0 < b) (2 * d + 1) + have hlo := Int.emod_nonneg j (ne_of_gt hp) + have hhi := Int.emod_lt_of_pos j hp + unfold residue + omega + +theorem unpack_pack {b d : ℕ} (hb : 2 ≤ b) (c : Code) + (hl : c.left < b ^ d) (hr : c.right < b ^ d) (hs : c.state < b) : + unpack b d (pack b d c : ℕ) = c := by + have hp := pack_lt hb c hl hr hs + have he : residue b d (pack b d c : ℕ) = pack b d c := by + simp only [residue, ← Int.natCast_mod, Nat.mod_eq_of_lt hp, Int.toNat_natCast] + rw [unpack, he, unpackNat_pack hb c hl hr] + +theorem tail_bound {b d R : ℕ} (hb : 2 ≤ b) (hd : 0 < d) (hR : R < b ^ d) : + R - R % b + b ≤ b ^ d := by + obtain ⟨e, rfl⟩ := Nat.exists_eq_succ_of_ne_zero (by omega : d ≠ 0) + have hbpos : 0 < b := by omega + have hdiv : R / b < b ^ e := by + apply (Nat.div_lt_iff_lt_mul hbpos).2 + simpa only [pow_succ] using hR + have hmod := Nat.div_add_mod R b + have hle := Nat.mod_le R b + have hsub : R - R % b = b * (R / b) := by omega + rw [hsub, pow_succ] + have hm := Nat.mul_le_mul_left b (Nat.succ_le_of_lt hdiv) + nlinarith + +def step (b : ℕ) (c : Code) (I : Instruction) : Code := + if I.move.val = 2 then + ⟨I.writeSymbol + b * c.left, c.right / b, I.nextState⟩ + else if I.move.val = 0 then + ⟨c.left / b, c.left % b + b * I.writeSymbol + b * (c.right - c.right % b), + I.nextState⟩ + else + ⟨c.left, c.right - c.right % b + I.writeSymbol, I.nextState⟩ + +theorem step_stacks_lt {b d : ℕ} (hb : 2 ≤ b) (hd : 0 < d) + (c : Code) (I : Instruction) (hl : c.left < b ^ d) (hr : c.right < b ^ d) + (hw : I.writeSymbol < b) : + (step b c I).left < b ^ (d + 1) ∧ (step b c I).right < b ^ (d + 1) := by + have hp : b ^ d ≤ b ^ (d + 1) := Nat.pow_le_pow_right (by omega) (by omega) + have ht := tail_bound hb hd hr + have htop : c.left % b < b := Nat.mod_lt _ (by omega) + have hsq : b ^ (d + 1) = b ^ d * b := pow_succ _ _ + unfold step + split_ifs + · dsimp + constructor + · rw [hsq] + have hm := Nat.mul_le_mul_left b (Nat.succ_le_of_lt hl) + nlinarith + · exact (Nat.div_le_self _ _).trans_lt (hr.trans_le hp) + · dsimp + constructor + · exact (Nat.div_le_self _ _).trans_lt (hl.trans_le hp) + · rw [hsq] + have hm := Nat.mul_le_mul_left b ht + have hw' := Nat.mul_le_mul_left b (Nat.succ_le_of_lt hw) + nlinarith + · dsimp + constructor + · exact hl.trans_le hp + · have hstay : c.right - c.right % b + I.writeSymbol < b ^ d := by omega + exact hstay.trans_le hp + +@[simp] theorem step_state (b : ℕ) (c : Code) (I : Instruction) : + (step b c I).state = I.nextState := by + unfold step + split_ifs <;> rfl + +theorem step_pack_lt {b d : ℕ} (hb : 2 ≤ b) (hd : 0 < d) + (c : Code) (I : Instruction) (hl : c.left < b ^ d) (hr : c.right < b ^ d) + (hw : I.writeSymbol < b) (hs : I.nextState < b) : + pack b (d + 2) (step b c I) < b ^ (2 * (d + 2) + 1) := by + obtain ⟨hl', hr'⟩ := step_stacks_lt hb hd c I hl hr hw + have hp : b ^ (d + 1) ≤ b ^ (d + 2) := Nat.pow_le_pow_right (by omega) (by omega) + exact pack_lt hb _ (hl'.trans_le hp) (hr'.trans_le hp) (by simpa using hs) + +end StackCode + +namespace Detector + +theorem isOpen : IsOpen detector := by + have heq : detector = (fun q : Torus => q 0) ⁻¹' + ((fun s : ℝ => (s : UnitAddCircle)) '' Set.Ioo (1 / 2 : ℝ) 1) := by + ext q + simp [detector, and_assoc] + rw [heq] + have hopen : IsOpen ((fun s : ℝ => (s : UnitAddCircle)) '' Set.Ioo (1 / 2 : ℝ) 1) := + QuotientAddGroup.isOpenMap_coe _ isOpen_Ioo + exact hopen.preimage (continuous_apply 0) + +theorem mem_iff {x : Space} (hlo : 0 ≤ x 0) (hhi : x 0 < 1) : + torusMk x ∈ detector ↔ 1 / 2 < x 0 := by + constructor + · rintro ⟨s, hslo, hshi, hs⟩ + have hx : x 0 ∈ Set.Ico (0 : ℝ) (0 + 1) := by + simp only [zero_add, Set.mem_Ico] + exact ⟨hlo, hhi⟩ + have hs' : s ∈ Set.Ico (0 : ℝ) (0 + 1) := by + simp only [zero_add, Set.mem_Ico] + exact ⟨by linarith, hshi⟩ + have h : s = x 0 := (AddCircle.coe_eq_coe_iff_of_mem_Ico hs' hx).1 hs + simpa [h] using hslo + · intro h + exact ⟨x 0, h, hhi, rfl⟩ + +theorem initial_not_mem : torusMk initialParticle ∉ detector := by + rw [mem_iff (by norm_num [initialParticle]) (by norm_num [initialParticle])] + norm_num [initialParticle] + +end Detector + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Main.lean b/lean/OAI/Analysis/PeriodicLattice/Main.lean new file mode 100644 index 0000000000000000000000000000000000000000..af2fe12b3e727bef41047af0f63339d0ffa90bbe --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Main.lean @@ -0,0 +1,107 @@ +import OAI.Analysis.PeriodicLattice.EffectiveForcing + +namespace OAI + +/-! Uniform force compilers and the complete periodic lattice memory theorem. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingMain {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace EffectiveFields +open CertifiedReal Quantitative RapidCalculus TorusCalculus RecursiveArithmetic +open scoped ContDiff +local instance mainLocal1 : Primcodable ℚ := ratPrimcodable +local instance mainLocal2 : DecidablePred Input.WellFormed := Classical.decPred _ +local instance mainLocal3 : Primcodable ValidInput := Primcodable.subtype inputWellFormed + +@[fun_prop] theorem mixedWord_recursive : Primrec (fun p : ℕ × MultiIndex => mixedWord p.1 p.2) := by + have hr (i : Option (Fin 3)) : Primrec (fun n : ℕ => List.replicate n i) := + (Primrec.list_map Primrec.list_range (Primrec.const i).to₂).of_eq (fun n => by simp) + have hα (i : Fin 3) : Primrec (fun p : ℕ × MultiIndex => p.2 i) := + Primrec.fin_app.comp Primrec.snd (Primrec.const i) + exact (Primrec.list_append.comp (hr none |>.comp Primrec.fst) + (Primrec.list_append.comp ((hr (some 2)).comp (hα 2)) + (Primrec.list_append.comp ((hr (some 1)).comp (hα 1)) ((hr (some 0)).comp (hα 0))))).of_eq + (fun p => by simp only [mixedWord,spatialWord,List.append_assoc]) + +theorem uniformlyEffective_of_certificate {F : Input → VectorField} + (hF : FieldCertificate F) (hf : ComponentsEffective F) : UniformlyEffective F := by + obtain ⟨Q,hQ,bQ⟩ := word_evaluator hF hf + let M : ValidInput × ℕ × MultiIndex × ℕ × ℕ → ℕ := fun p => + p.2.2.2.2 + hF.budget (p.1.1,mixedOrder p.2.1 p.2.2.1+1,0) + 6 + have hM : Primrec M := by + have ha : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ => (p.2.1, p.2.2.1)) := + (Primrec.fst.comp Primrec.snd).pair (Primrec.fst.comp (Primrec.snd.comp Primrec.snd)) + have ho : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ => mixedOrder p.2.1 p.2.2.1) := + (mixedOrder_recursive.comp ha).of_eq (fun _ => rfl) + have hK : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ => hF.budget (p.1.1,mixedOrder p.2.1 p.2.2.1+1,0)) := + (hF.recursive.comp ((validData_recursive.comp Primrec.fst).pair + ((Primrec.nat_add.comp ho (Primrec.const 1)).pair (Primrec.const 0)))).of_eq (fun _ => rfl) + exact (Primrec.nat_add.comp (Primrec.nat_add.comp + (Primrec.snd.comp (Primrec.snd.comp (Primrec.snd.comp Primrec.snd))) hK) (Primrec.const 6)).of_eq (fun _ => rfl) + let E : ValidInput × ℕ × MultiIndex × ℕ × ℕ × RationalPoint → Fin 3 → ℚ := fun p => + Q ((p.1,mixedWord p.2.1 p.2.2.1,p.2.2.2.2.2), 2^(p.2.2.2.2.1+6)) + have hE : Computable E := by + have harg : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ × RationalPoint => (p.2.1, p.2.2.1)) := + (Primrec.fst.comp Primrec.snd).pair (Primrec.fst.comp (Primrec.snd.comp Primrec.snd)) + have hw : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ × RationalPoint => mixedWord p.2.1 p.2.2.1) := + (mixedWord_recursive.comp harg).of_eq (fun _ => rfl) + have hn : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ × RationalPoint => p.2.2.2.2.1) := + Primrec.fst.comp (Primrec.snd.comp (Primrec.snd.comp (Primrec.snd.comp Primrec.snd))) + have ha : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ × RationalPoint => p.2.2.2.2.2) := + Primrec.snd.comp (Primrec.snd.comp (Primrec.snd.comp (Primrec.snd.comp Primrec.snd))) + have hp : Primrec (fun p : ValidInput × ℕ × MultiIndex × ℕ × ℕ × RationalPoint => + ((p.1,mixedWord p.2.1 p.2.2.1,p.2.2.2.2.2),2^(p.2.2.2.2.1+6))) := + (Primrec.fst.pair (hw.pair ha)).pair (natPow.comp (Primrec.const 2) (Primrec.nat_add.comp hn (Primrec.const 6))) + exact (hQ.comp hp.to_comp).of_eq (fun _ => rfl) + obtain ⟨P,hP⟩ := program_of_computable hM.to_comp + obtain ⟨R,hR⟩ := program_of_computable hE + refine ⟨P,R,fun d hd r α T n => ?_⟩ + let v : ValidInput := ⟨d,hd⟩ + refine ⟨M (v,r,α,T,n), hP (v,r,α,T,n), fun a => ?_⟩ + refine ⟨E (v,r,α,T,n,a),hR (v,r,α,T,n,a),fun t x ht _hT hta hxa => ?_⟩ + rw [mixedD_eq_fieldWord (hF.smooth d) r α ht] + have hlen : (mixedWord r α).length = mixedOrder r α := by + simp [mixedWord,spatialWord,mixedOrder,Nat.add_assoc] + have hb := fieldWord_nearby hF v (mixedWord r α) a ht x hta hxa + rw [hlen] at hb + calc + _ ≤ ‖fieldWord (mixedWord r α) (F d) t (torusMk x) - + fieldWord (mixedWord r α) (F d) (time a.1) (torusMk (rationalVector a.2))‖ + + ‖fieldWord (mixedWord r α) (F d) (time a.1) (torusMk (rationalVector a.2)) - rationalVector (E (v,r,α,T,n,a))‖ := + norm_sub_le_norm_sub_add_norm_sub _ _ _ + _ ≤ 4*(hF.budget (d,mixedOrder r α+1,0):ℝ)*accuracy (M (v,r,α,T,n)) + 3*error (2^(n+6)) := + add_le_add hb (bQ v (mixedWord r α) a (2^(n+6))) + _ ≤ _ := evaluation_tolerance n _ + +end EffectiveFields + +theorem periodic_lattice_memory (ν : ℝ) (hν : 0 < ν) (hνcomp : ComputableReal ν) : + IsOpen detector ∧ + ∃ (U g f : Input → VectorField) (φ : Input → ScalarField) + (C : Input → ℕ → MultiIndex → ℕ → ℕ), + UniformlyEffective g ∧ UniformlyEffective f ∧ EffectiveConstants C ∧ + ∀ d : Input, d.WellFormed → + LatticeConclusion ν d (U d) (g d) (f d) (φ d) (C d) := by + obtain ⟨N, hN⟩ := exists_nat_ge ‖ν‖ + have hc := CertifiedReal.computableReal_effective hνcomp + refine ⟨Detector.isOpen, FluidLift.velocity, FluidLift.force ν, + FluidLift.solenoidalForce ν, FluidLift.potential, Quantitative.latticeConstants ν N hN, + EffectiveFields.uniformlyEffective_of_certificate (Quantitative.forceCertificate ν N hN) + (EffectiveFields.force_effective ν hc), + EffectiveFields.uniformlyEffective_of_certificate (Quantitative.solenoidalForceCertificate ν N hN) + (EffectiveFields.solenoidalForce_effective ν hc), + Quantitative.latticeConstants_effective ν N hN, fun d hd => ?_⟩ + obtain ⟨C₀, hU, hg, hf, hφ, mU, mg, mf, mφ, eg, ef, _Rg, _Rf, + sf, eφ, uφ, efφ, ug, uf, particle⟩ := FluidLift.analytic_lattice_conclusion ν hν.le d hd + obtain ⟨Rg, Rf⟩ := Quantitative.latticeConstants_bounds ν N hN d hd + exact ⟨hU, hg, hf, hφ, mU, mg, mf, mφ, eg, ef, Rg, Rf, sf, eφ, uφ, efφ, ug, uf, particle⟩ + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/MeanBounds.lean b/lean/OAI/Analysis/PeriodicLattice/MeanBounds.lean new file mode 100644 index 0000000000000000000000000000000000000000..5c85279af3b264b429c0090c81cbdb083ea45d5a --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/MeanBounds.lean @@ -0,0 +1,348 @@ +import OAI.Analysis.PeriodicLattice.PeriodicInverse + +namespace OAI + +/-! Mean-zero corrections and rapid derivative bounds. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingMeanBounds {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace PeriodicInverse +open scoped ContDiff +open RapidCalculus Set MeasureTheory + +def mean (H : ℝ → ℝ → ℝ) (t _y : ℝ) : ℝ := ∫ s in (0 : ℝ)..1, H t s + +theorem mean_contDiff {H : ℝ → ℝ → ℝ} (hH : ContDiff ℝ ∞ (Function.uncurry H)) : + ContDiff ℝ ∞ (Function.uncurry (mean H)) := + (contDiff_intervalIntegral hH 0 1).comp contDiff_fst + +theorem mean_periodic (H : ℝ → ℝ → ℝ) (t : ℝ) : Function.Periodic (mean H t) 1 := fun _ => rfl + +theorem mean_timeD {H : ℝ → ℝ → ℝ} (hH : ContDiff ℝ ∞ (Function.uncurry H)) : + biD true (mean H) = mean (biD true H) := by + funext t y + exact (hasDerivAt_intervalIntegral hH 0 1 t).deriv + +theorem mean_spaceD (H : ℝ → ℝ → ℝ) : biD false (mean H) = 0 := by + funext t y + exact deriv_const _ _ + +theorem biD_zero (i : Bool) : biD i (0 : ℝ → ℝ → ℝ) = 0 := by + funext t y + cases i <;> exact deriv_const _ _ + +theorem mean_wordD {H : ℝ → ℝ → ℝ} (hH : ContDiff ℝ ∞ (Function.uncurry H)) (w : List Bool) : + wordD w (mean H) = if false ∈ w then 0 else mean (wordD w H) := by + induction w with + | nil => simp + | cons i w ih => + rw [wordD_cons, ih] + by_cases hw : false ∈ w + · simp only [hw, ↓reduceIte, biD_zero, List.mem_cons, or_true] + · simp only [hw, ↓reduceIte, List.mem_cons, or_false] + cases i + · simp only [↓reduceIte, mean_spaceD] + · simp only [Bool.false_eq_true, ↓reduceIte, mean_timeD (wordD_contDiff hH w)] + rfl + +theorem mean_rapid {H : ℝ → ℝ → ℝ} (hH : Rapid2 H) : Rapid2 (mean H) := by + refine ⟨mean_contDiff hH.smooth, fun w J => ?_⟩ + rw [mean_wordD hH.smooth] + split_ifs + · exact ⟨0, fun t _ y => by simp⟩ + · obtain ⟨C, hC⟩ := hH.bound w J + refine ⟨C, fun t ht y => ?_⟩ + have hi := intervalIntegral.norm_integral_le_of_norm_le_const (a := (0 : ℝ)) (b := 1) + (f := fun s => (1 + t) ^ J * wordD w H t s) (C := C) (fun s _ => by + rw [norm_mul, Real.norm_eq_abs ((1 + t)^J), abs_of_nonneg (by positivity)] + exact hC t ht s) + simpa only [intervalIntegral.integral_const_mul, norm_mul, Real.norm_eq_abs ((1 + t)^J), + abs_of_nonneg (show 0 ≤ (1 + t)^J by positivity), sub_zero, abs_one, mul_one, mean] using hi + +end PeriodicInverse +namespace TorusCalculus + +open scoped ContDiff + +section Schwarz +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] +variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + +theorem directional_commute {F : E → A} (hF : ContDiff ℝ ∞ F) (u v x : E) : + fderiv ℝ (fun y => fderiv ℝ F y v) x u = + fderiv ℝ (fun y => fderiv ℝ F y u) x v := by + have hd : Differentiable ℝ (fderiv ℝ F) := + (hF.fderiv_right (m := ∞) (by simp)).differentiable (by simp) + have heq (w z : E) : fderiv ℝ (fun y => fderiv ℝ F y w) x z = + fderiv ℝ (fderiv ℝ F) x z w := by + rw [((hd x).hasFDerivAt.clm_apply (hasFDerivAt_const w x)).fderiv] + simp + rw [heq, heq] + exact hF.contDiffAt.isSymmSndFDerivAt (by simp) u v + +theorem lifted_spaceD_eq {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (i : Fin 3) : + lifted (spaceD i F) = fun tx => fderiv ℝ (lifted F) tx (0, EuclideanSpace.single i 1) := by + funext tx + rw [lifted, spaceD_cover] + have heq : (fun s : ℝ => spaceLift F tx.1 (tx.2 + EuclideanSpace.single i s)) = + fun s : ℝ => lifted F (tx + s • (0, EuclideanSpace.single i 1)) := by + funext s + rw [single_eq_smul] + simp only [spaceLift, lifted, Prod.fst_add, Prod.snd_add, Prod.smul_fst, Prod.smul_snd, + smul_zero, add_zero] + rw [heq] + have hc : HasDerivAt (fun s : ℝ => tx + s • (0, EuclideanSpace.single i 1)) + (0, EuclideanSpace.single i 1) 0 := by + simpa only [one_smul, id_eq] using (((hasDerivAt_id (0 : ℝ)).smul_const + ((0 : ℝ), EuclideanSpace.single i 1)).const_add tx) + have hf : HasFDerivAt (lifted F) (fderiv ℝ (lifted F) tx) + (tx + (0 : ℝ) • (0, EuclideanSpace.single i 1)) := by + simpa using (hF.differentiable (by simp) tx).hasFDerivAt + exact (hf.comp_hasDerivAt 0 hc).deriv + +theorem lifted_fullTimeD_eq {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) : + lifted (fullTimeD F) = fun tx => fderiv ℝ (lifted F) tx (1, 0) := by + funext tx + have hc : HasDerivAt (fun s : ℝ => (s, tx.2)) (1, 0) tx.1 := + (hasDerivAt_id tx.1).prodMk (hasDerivAt_const _ _) + exact ((hF.differentiable (by simp) tx).hasFDerivAt.comp_hasDerivAt tx.1 hc).deriv + +theorem spaceD_commute {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (i j : Fin 3) : + spaceD i (spaceD j F) = spaceD j (spaceD i F) := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + change lifted (spaceD i (spaceD j F)) (t, x) = lifted (spaceD j (spaceD i F)) (t, x) + rw [lifted_spaceD_eq (contDiff_spaceD hF j), lifted_spaceD_eq (contDiff_spaceD hF i), + lifted_spaceD_eq hF j, lifted_spaceD_eq hF i] + exact directional_commute hF _ _ _ + +theorem spaceD_fullTimeD {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (i : Fin 3) : + spaceD i (fullTimeD F) = fullTimeD (spaceD i F) := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + change lifted (spaceD i (fullTimeD F)) (t, x) = lifted (fullTimeD (spaceD i F)) (t, x) + rw [lifted_spaceD_eq (contDiff_fullTimeD hF), lifted_fullTimeD_eq (contDiff_spaceD hF i), + lifted_fullTimeD_eq hF, lifted_spaceD_eq hF i] + exact directional_commute hF _ _ _ + +end Schwarz +end TorusCalculus + +namespace TorusCalculus + +open scoped ContDiff + +section LinearOperators +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] +variable {ι : Type*} [Fintype ι] + +theorem smooth_slice_differentiable {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (t : ℝ) : + Differentiable ℝ (spaceLift F t) := + (hF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) + +theorem fullTime_hasDerivAt {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (t : ℝ) (q : Torus) : + HasDerivAt (fun s => F s q) (fullTimeD F t q) t := by + obtain ⟨x, rfl⟩ := mk_surjective q + exact ((hF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t).hasDerivAt + +theorem spaceD_finite_sum {F : ι → Field A} (hF : ∀ j, ContDiff ℝ ∞ (lifted (F j))) (i : Fin 3) : + spaceD i (∑ j, F j) = ∑ j, spaceD i (F j) := by + funext t q + have hh := HasDerivAt.sum (u := Finset.univ) + (fun j _ => translation_hasDerivAt (smooth_slice_differentiable (hF j) t) q i 0) + simpa only [spaceD, single_zero, mk_zero, add_zero, Finset.sum_apply, Finset.sum_fn] using hh.deriv + +theorem fullTimeD_finite_sum {F : ι → Field A} (hF : ∀ j, ContDiff ℝ ∞ (lifted (F j))) : + fullTimeD (∑ j, F j) = ∑ j, fullTimeD (F j) := by + funext t q + have hh := HasDerivAt.sum (u := Finset.univ) (fun j _ => fullTime_hasDerivAt (hF j) t q) + simpa only [fullTimeD, Finset.sum_apply, Finset.sum_fn] using hh.deriv + +theorem spaceD_scale {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (c : ℝ) (i : Fin 3) : + spaceD i (c • F) = c • spaceD i F := by + funext t q + have hh := (translation_hasDerivAt (smooth_slice_differentiable hF t) q i 0).const_smul c + simpa only [spaceD, single_zero, mk_zero, add_zero, Pi.smul_apply, Pi.smul_def] using hh.deriv + +theorem laplacian_as_sum (F : Field A) : + laplacian F = ∑ i : Fin 3, spaceD i (spaceD i F) := by + funext t q + simp only [laplacian, Finset.sum_apply] + +end LinearOperators + +theorem spaceD_component_eq {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) (i j : Fin 3) : + (fun t q => spaceD i U t q j) = spaceD i (fun t q => U t q j) := + funext fun t => funext fun q => (spaceD_component (smooth_slice_differentiable hU t) i j q).symm + +theorem fullTimeD_component_eq {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) (j : Fin 3) : + (fun t q => fullTimeD U t q j) = fullTimeD (fun t q => U t q j) := by + funext t q + exact ((PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) j).hasFDerivAt.comp_hasDerivAt t + (fullTime_hasDerivAt hU t q)).deriv.symm + +theorem divergence_as_sum (U : VectorField) : + divergence U = ∑ j : Fin 3, spaceD j (fun t q => U t q j) := by + funext t q + simp only [divergence, Finset.sum_apply] + +theorem contDiff_divergence {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) : + ContDiff ℝ ∞ (lifted (divergence U)) := + ContDiff.sum (s := Finset.univ) (fun j _ => contDiff_spaceD (contDiff_component hU j) j) + +theorem divergence_fullTimeD {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) : + divergence (fullTimeD U) = fullTimeD (divergence U) := by + rw [divergence_as_sum, divergence_as_sum, + fullTimeD_finite_sum (fun j => contDiff_spaceD (contDiff_component hU j) j)] + simp_rw [fullTimeD_component_eq hU, spaceD_fullTimeD (contDiff_component hU _)] + +theorem divergence_spaceD {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) (i : Fin 3) : + divergence (spaceD i U) = spaceD i (divergence U) := by + rw [divergence_as_sum, divergence_as_sum, + spaceD_finite_sum (fun j => contDiff_spaceD (contDiff_component hU j) j)] + apply Finset.sum_congr rfl + intro j _hj + rw [spaceD_component_eq hU, spaceD_commute (contDiff_component hU _)] + +theorem divergence_finite_sum {ι : Type*} [Fintype ι] {U : ι → VectorField} + (hU : ∀ j, ContDiff ℝ ∞ (lifted (U j))) : + divergence (∑ j, U j) = ∑ j, divergence (U j) := by + simp only [divergence_as_sum] + have he (k : Fin 3) : (fun t q => (∑ j, U j) t q k) = ∑ j, (fun t q => U j t q k) := by + funext t q + simp only [Finset.sum_apply, WithLp.ofLp_sum] + simp_rw [he, spaceD_finite_sum (fun j => contDiff_component (hU j) _)] + exact Finset.sum_comm + +theorem divergence_laplacian {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) : + divergence (laplacian U) = laplacian (divergence U) := by + rw [laplacian_as_sum, divergence_finite_sum (fun i => contDiff_spaceD (contDiff_spaceD hU i) i), laplacian_as_sum] + simp_rw [divergence_spaceD (contDiff_spaceD hU _), divergence_spaceD hU] + +theorem divergence_add {U V : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) + (hV : ContDiff ℝ ∞ (lifted V)) : divergence (U + V) = divergence U + divergence V := by + funext t q + simp only [divergence, Pi.add_apply, ← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro i _hi + exact spaceD_add (smooth_slice_differentiable (contDiff_component hU i) t) + (smooth_slice_differentiable (contDiff_component hV i) t) i q + +theorem divergence_scale {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) (c : ℝ) : + divergence (c • U) = c • divergence U := by + rw [divergence_as_sum, divergence_as_sum, Finset.smul_sum] + apply Finset.sum_congr rfl + intro i _hi + exact spaceD_scale (contDiff_component hU i) c i + +theorem divergence_fullForce {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) + (hdiv : divergence U = 0) (ν : ℝ) : + divergence (Residual.fullForce ν U) = divergence (advection U) := by + have he : Residual.fullForce ν U = fullTimeD U + advection U - ν • laplacian U := rfl + rw [he] + have hs : divergence (fullTimeD U + advection U - ν • laplacian U) = + divergence (fullTimeD U + advection U) - divergence (ν • laplacian U) := by + funext t q + exact divergence_sub (smooth_slice_differentiable (F := fullTimeD U + advection U) + ((contDiff_fullTimeD hU).add (contDiff_advection hU)) t) + (smooth_slice_differentiable (F := ν • laplacian U) ((contDiff_laplacian hU).const_smul ν) t) q + rw [hs, divergence_add (contDiff_fullTimeD hU) (contDiff_advection hU), + divergence_scale (contDiff_laplacian hU), divergence_fullTimeD hU, divergence_laplacian hU, hdiv] + have hz : fullTimeD (0 : ScalarField) = 0 := by + funext t q + exact deriv_const _ _ + have hl : laplacian (0 : ScalarField) = 0 := by + simp [laplacian_as_sum, Residual.spaceD_zero] + simp [hz, hl] + +end TorusCalculus + +namespace TorusCalculus +open scoped ContDiff + +theorem divergence_advection {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) + (hdiv : divergence U = 0) (t : ℝ) (q : Torus) : + divergence (advection U) t q = + ∑ i : Fin 3, ∑ j : Fin 3, spaceD i (fun t q => U t q j) t q * + spaceD j (fun t q => U t q i) t q := by + let C (i : Fin 3) : ScalarField := fun t q => U t q i + have hC (i : Fin 3) : ContDiff ℝ ∞ (lifted (C i)) := contDiff_component hU i + have hd (i : Fin 3) : (fun t q => advection U t q i) = + ∑ j : Fin 3, C j * spaceD j (C i) := by + funext t q + simp only [advection, WithLp.ofLp_sum, Finset.sum_apply, PiLp.smul_apply, Pi.mul_apply, + smul_eq_mul, C, spaceD_component (smooth_slice_differentiable hU t)] + have hp (i j k : Fin 3) : spaceD i (C k * spaceD k (C j)) = + (spaceD i (C k)) * spaceD k (C j) + C k * spaceD i (spaceD k (C j)) := by + funext t q + exact spaceD_smul (hC k) (contDiff_spaceD (hC j) k) i t q + have hh (k : Fin 3) : (∑ i : Fin 3, spaceD i (spaceD k (C i))) = 0 := by + simp_rw [spaceD_commute (hC _) _ k] + rw [← spaceD_finite_sum (fun i => contDiff_spaceD (hC i) i)] + change spaceD k (divergence U) = 0 + rw [hdiv, Residual.spaceD_zero] + have hprod (i k : Fin 3) : ContDiff ℝ ∞ (lifted (C k * spaceD k (C i))) := + (hC k).mul (contDiff_spaceD (hC i) k) + simp only [divergence, hd, + spaceD_finite_sum (hprod _), hp, + Finset.sum_apply, Pi.add_apply, Pi.mul_apply, Finset.sum_add_distrib] + change _ + (∑ i : Fin 3, ∑ k : Fin 3, C k t q * spaceD i (spaceD k (C i)) t q) = _ + rw [Finset.sum_comm (f := fun i k : Fin 3 => C k t q * spaceD i (spaceD k (C i)) t q)] + simp_rw [← Finset.mul_sum] + have he (k : Fin 3) : (∑ i : Fin 3, spaceD i (spaceD k (C i)) t q) = 0 := by + simpa only [Finset.sum_apply, Pi.zero_apply] using congrFun (congrFun (hh k) t) q + simp only [he, mul_zero, Finset.sum_const_zero, add_zero] + rfl + +end TorusCalculus + +namespace PeriodicInverse + +open scoped ContDiff +open MeasureTheory TorusCalculus RapidCalculus + +def horizontal (H : ℝ → ℝ → ℝ) (hp : ∀ t, Function.Periodic (H t) 1) : ScalarField := + fun t q => (hp t).lift (q 1) + +@[simp] theorem horizontal_cover (H : ℝ → ℝ → ℝ) (hp : ∀ t, Function.Periodic (H t) 1) + (t : ℝ) (x : Space) : horizontal H hp t (torusMk x) = H t (x 1) := + (hp t).lift_coe _ + +theorem horizontal_contDiff {H : ℝ → ℝ → ℝ} (hp : ∀ t, Function.Periodic (H t) 1) + (hH : ContDiff ℝ ∞ (Function.uncurry H)) : ContDiff ℝ ∞ (lifted (horizontal H hp)) := + hH.comp (contDiff_fst.prodMk + ((PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) 1).contDiff.comp contDiff_snd)) + +theorem horizontal_algebra {H : ℝ → ℝ → ℝ} (hp : ∀ t, Function.Periodic (H t) 1) + (hH : Rapid2 H) : Algebra (horizontal H hp) := by + apply Algebra.tensor _ H (fun _ => 1) hH + (boundedProfile_of_periodic contDiff_const (fun _ => rfl)) + intro t x + simp + +theorem horizontal_integral {H : ℝ → ℝ → ℝ} (hp : ∀ t, Function.Periodic (H t) 1) + (hH : ContDiff ℝ ∞ (Function.uncurry H)) (t : ℝ) : + (∫ q, horizontal H hp t q ∂torusVolume) = ∫ y in (0 : ℝ)..1, H t y := by + have hc : Continuous (hp t).lift := by + apply QuotientAddGroup.isOpenQuotientMap_mk.isQuotientMap.continuous_iff.mpr + simpa only [Function.comp_def, Function.Periodic.lift_coe, Function.uncurry_def, id_eq] using + hH.continuous.comp (continuous_const.prodMk continuous_id) + change (∫ q, (hp t).lift (q 1) ∂Measure.pi (fun _ : Fin 3 => AddCircle.haarAddCircle)) = _ + rw [integral_comp_eval (μ := fun _ : Fin 3 => (AddCircle.haarAddCircle : Measure UnitAddCircle)) + (i := (1 : Fin 3)) hc.aestronglyMeasurable] + have hm : (volume : Measure UnitAddCircle) = AddCircle.haarAddCircle := by + simpa using (AddCircle.volume_eq_smul_haarAddCircle (T := 1)) + have he := UnitAddCircle.intervalIntegral_preimage 0 (hp t).lift + simpa only [zero_add, Function.Periodic.lift_coe, hm] using he.symm + +end PeriodicInverse + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/PeriodicInverse.lean b/lean/OAI/Analysis/PeriodicLattice/PeriodicInverse.lean new file mode 100644 index 0000000000000000000000000000000000000000..8d402aed90636fce827896c0c7933326d4da8135 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/PeriodicInverse.lean @@ -0,0 +1,371 @@ +import OAI.Analysis.PeriodicLattice.RapidBounds + +namespace OAI + +/-! Periodic primitives and regularity of the inverse operator. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingPeriodicInverse {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace PeriodicInverse + +open Set Filter MeasureTheory TorusCalculus RapidCalculus +open scoped ContDiff Topology + +section ParameterIntegral +variable {E A : Type} [NormedAddCommGroup E] [NormedSpace ℝ E] [ProperSpace E] + [NormedAddCommGroup A] [NormedSpace ℝ A] [CompleteSpace A] + +omit [CompleteSpace A] in +theorem hasFDerivAt_intervalIntegral {F : E × ℝ → A} (hF : ContDiff ℝ ∞ F) + (a b : ℝ) (x : E) : + HasFDerivAt (fun u => ∫ s in a..b, F (u, s)) + (∫ s in a..b, fderiv ℝ (fun u => F (u, s)) x) x := by + let D : E × ℝ → E →L[ℝ] A := fun us => fderiv ℝ (fun v => F (v, us.2)) us.1 + have hD : ContDiff ℝ ∞ D := by + let G : (E × ℝ) → E → A := fun us v => F (v, us.2) + have hG : ContDiff ℝ ∞ (Function.uncurry G) := hF.comp (contDiff_snd.prodMk contDiff_fst.snd) + exact hG.fderiv contDiff_fst (by simp) + obtain ⟨C, hC⟩ := ((isCompact_closedBall x 1).prod (isCompact_uIcc (a := a) (b := b))).exists_bound_of_continuousOn hD.continuous.continuousOn + apply hasFDerivAt_integral_of_dominated_of_fderiv_le'' (F := fun u s => F (u, s)) + (F' := fun u s => D (u, s)) (s := Metric.ball x 1) (bound := fun _ => C) + (Metric.ball_mem_nhds x (by norm_num)) + · exact Eventually.of_forall fun u => (hF.continuous.comp (continuous_const.prodMk continuous_id)).aestronglyMeasurable + · exact (hF.continuous.comp (continuous_const.prodMk continuous_id)).intervalIntegrable _ _ + · exact (hD.continuous.comp (continuous_const.prodMk continuous_id)).aestronglyMeasurable + · filter_upwards [ae_restrict_mem measurableSet_uIoc] with s hs + intro u hu + exact hC (u, s) ⟨Metric.ball_subset_closedBall hu, uIoc_subset_uIcc hs⟩ + · exact intervalIntegrable_const + · exact Eventually.of_forall fun s u _ => + ((hF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) u).hasFDerivAt + +theorem contDiff_intervalIntegral {F : E × ℝ → A} (hF : ContDiff ℝ ∞ F) (a b : ℝ) : + ContDiff ℝ ∞ (fun u => ∫ s in a..b, F (u, s)) := by + have hn (n : ℕ) : ∀ {B : Type} [NormedAddCommGroup B] [NormedSpace ℝ B] [CompleteSpace B] + (G : E × ℝ → B), ContDiff ℝ ∞ G → + ContDiff ℝ n (fun u => ∫ s in a..b, G (u, s)) := by + intro B _ _ _ G hG + induction n generalizing B with + | zero => + exact contDiff_zero.mpr (intervalIntegral.continuous_parametric_intervalIntegral_of_continuous' (f := fun u s => G (u, s)) hG.continuous a b) + | succ n ih => + let D : E × ℝ → E →L[ℝ] B := fun us => fderiv ℝ (fun u => G (u, us.2)) us.1 + have hD : ContDiff ℝ ∞ D := by + have hh : ContDiff ℝ ∞ (fun p : (E × ℝ) × E => G (p.2, p.1.2)) := + hG.comp (contDiff_snd.prodMk contDiff_fst.snd) + exact hh.fderiv contDiff_fst (by simp) + have hd : ∀ u, HasFDerivAt (fun u => ∫ s in a..b, G (u, s)) + (∫ s in a..b, D (u, s)) u := fun u => hasFDerivAt_intervalIntegral hG a b u + rw [Nat.cast_add, Nat.cast_one] + exact contDiff_succ_iff_hasFDerivAt.mpr ⟨_, ih D hD, hd⟩ + exact contDiff_infty.mpr fun n => hn n F hF + +end ParameterIntegral + +theorem hasDerivAt_intervalIntegral {A : Type} [NormedAddCommGroup A] + [NormedSpace ℝ A] [CompleteSpace A] {F : ℝ × ℝ → A} + (hF : ContDiff ℝ ∞ F) (a b x : ℝ) : + HasDerivAt (fun u => ∫ s in a..b, F (u, s)) + (∫ s in a..b, deriv (fun u => F (u, s)) x) x := by + have hD : ContDiff ℝ ∞ (fun us : ℝ × ℝ => fderiv ℝ (fun v => F (v, us.2)) us.1) := by + have hh : ContDiff ℝ ∞ (fun p : (ℝ × ℝ) × ℝ => F (p.2, p.1.2)) := + hF.comp (contDiff_snd.prodMk contDiff_fst.snd) + exact hh.fderiv contDiff_fst (by simp) + have hi : IntervalIntegrable (fun s => fderiv ℝ (fun u => F (u, s)) x) volume a b := + (hD.continuous.comp (continuous_const.prodMk continuous_id)).intervalIntegrable _ _ + simpa only [ContinuousLinearMap.intervalIntegral_apply hi, fderiv_apply_one_eq_deriv] using + (hasFDerivAt_intervalIntegral hF a b x).hasDerivAt + +def first (lam : ℝ) (H : ℝ → ℝ → ℝ) (t y : ℝ) : ℝ := + (1 - Real.exp lam)⁻¹ * ∫ s in (0 : ℝ)..1, Real.exp (lam * s) * H t (y - s) + +theorem first_contDiff (lam : ℝ) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) : + ContDiff ℝ ∞ (Function.uncurry (first lam H)) := by + have hh : ContDiff ℝ ∞ (fun p : (ℝ × ℝ) × ℝ => + Real.exp (lam * p.2) * H p.1.1 (p.1.2 - p.2)) := + (Real.contDiff_exp.comp (contDiff_const.mul contDiff_snd)).mul + (hH.comp (contDiff_fst.fst.prodMk (contDiff_fst.snd.sub contDiff_snd))) + exact contDiff_const.mul (contDiff_intervalIntegral hh 0 1) + +theorem first_periodic (lam : ℝ) {H : ℝ → ℝ → ℝ} (hH : ∀ t, Function.Periodic (H t) 1) + (t : ℝ) : Function.Periodic (first lam H t) 1 := by + intro y + unfold first + congr 1 + apply intervalIntegral.integral_congr + intro s _ + dsimp only + rw [show y + 1 - s = y - s + 1 by ring, hH t] + +theorem first_space_deriv (lam : ℝ) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) (t y : ℝ) : + HasDerivAt (first lam H t) (first lam (biD false H) t y) y := by + have hh : ContDiff ℝ ∞ (fun p : ℝ × ℝ => Real.exp (lam * p.2) * H t (p.1 - p.2)) := + (Real.contDiff_exp.comp (contDiff_const.mul contDiff_snd)).mul + (hH.comp (contDiff_const.prodMk (contDiff_fst.sub contDiff_snd))) + have he (s : ℝ) : deriv (fun u => Real.exp (lam * s) * H t (u - s)) y = + Real.exp (lam * s) * biD false H t (y - s) := by + have hs := (((hH.comp ((contDiff_const (c := t)).prodMk contDiff_id)).differentiable + (by simp) (y - s)).hasDerivAt.comp y ((hasDerivAt_id y).sub_const s)).const_mul (Real.exp (lam * s)) + simpa only [Function.comp_def, Function.uncurry_apply_pair, id_eq, mul_one, biD, Bool.false_eq_true, ↓reduceIte] using hs.deriv + have h := (hasDerivAt_intervalIntegral hh 0 1 y).const_mul ((1 - Real.exp lam)⁻¹) + change HasDerivAt (fun z => first lam H t z) (first lam (biD false H) t y) y + simp only [first] + simpa only [he] using h + +theorem first_time_deriv (lam : ℝ) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) (t y : ℝ) : + HasDerivAt (fun u => first lam H u y) (first lam (biD true H) t y) t := by + have hh : ContDiff ℝ ∞ (fun p : ℝ × ℝ => Real.exp (lam * p.2) * H p.1 (y - p.2)) := + (Real.contDiff_exp.comp (contDiff_const.mul contDiff_snd)).mul + (hH.comp (contDiff_fst.prodMk (contDiff_const.sub contDiff_snd))) + have he (s : ℝ) : deriv (fun u => Real.exp (lam * s) * H u (y - s)) t = + Real.exp (lam * s) * biD true H t (y - s) := by + have hs := ((hH.comp (contDiff_id.prodMk (contDiff_const (c := y - s)))).differentiable + (by simp) t).hasDerivAt.const_mul (Real.exp (lam * s)) + exact hs.deriv + have h := (hasDerivAt_intervalIntegral hh 0 1 t).const_mul ((1 - Real.exp lam)⁻¹) + dsimp only [first] + simpa only [he] using h + +theorem first_biD (lam : ℝ) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) (i : Bool) : + biD i (first lam H) = first lam (biD i H) := by + funext t y + cases i + · exact (first_space_deriv lam hH t y).deriv + · exact (first_time_deriv lam hH t y).deriv + +theorem first_wordD (lam : ℝ) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) (w : List Bool) : + wordD w (first lam H) = first lam (wordD w H) := by + induction w with + | nil => rfl + | cons i w ih => rw [wordD_cons, ih, first_biD lam (wordD_contDiff hH w)]; rfl + +theorem first_equation (lam : ℝ) (hlam : lam ≠ 0) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) (hp : ∀ t, Function.Periodic (H t) 1) + (t y : ℝ) : biD false (first lam H) t y = lam * first lam H t y + H t y := by + have hs : ContDiff ℝ ∞ (H t) := hH.comp (contDiff_const.prodMk contDiff_id) + have hu (s : ℝ) : HasDerivAt (fun s => Real.exp (lam * s)) (lam * Real.exp (lam * s)) s := by + simpa only [id_eq, mul_one, mul_comm] using ((hasDerivAt_id s).const_mul lam).exp + have hv (s : ℝ) : HasDerivAt (fun s => H t (y - s)) (-deriv (H t) (y - s)) s := by + simpa only [Function.comp_def, id_eq, mul_neg_one] using + ((hs.differentiable (by simp) (y - s)).hasDerivAt.comp s ((hasDerivAt_id s).const_sub y)) + have hu' : IntervalIntegrable (fun s => lam * Real.exp (lam * s)) volume 0 1 := + (continuous_const.mul (Real.continuous_exp.comp (continuous_const.mul continuous_id))).intervalIntegrable _ _ + have hv' : IntervalIntegrable (fun s => -deriv (H t) (y - s)) volume 0 1 := + (hs.continuous_deriv (by simp)).comp (continuous_const.sub continuous_id) |>.neg |>.intervalIntegrable _ _ + have hi := intervalIntegral.integral_mul_deriv_eq_deriv_mul (a := 0) (b := 1) + (fun s _ => hu s) (fun s _ => hv s) hu' hv' + have hp' : H t (y - 1) = H t y := by + have hh := hp t (y - 1) + simpa only [sub_add_cancel] using hh.symm + have hden : 1 - Real.exp lam ≠ 0 := by + intro hh + apply hlam + apply (Real.exp_eq_one_iff lam).mp + linarith + simp only [mul_one, mul_zero, Real.exp_zero, one_mul, sub_zero, hp', mul_neg, + intervalIntegral.integral_neg] at hi + simp_rw [mul_assoc, intervalIntegral.integral_const_mul] at hi + rw [first_biD lam hH] + simp only [first, biD, Bool.false_eq_true, ↓reduceIte] + field_simp [hden] + nlinarith [hi] + +theorem first_weighted_bound (lam t : ℝ) {H : ℝ → ℝ → ℝ} {w C : ℝ} (hw : 0 ≤ w) + (hC : ∀ y : ℝ, w * ‖H t y‖ ≤ C) (y : ℝ) : + w * ‖first lam H t y‖ ≤ ‖(1 - Real.exp lam)⁻¹‖ * Real.exp |lam| * C := by + have hC₀ : 0 ≤ C := (mul_nonneg hw (norm_nonneg _)).trans (hC 0) + have hi : ‖∫ s in (0 : ℝ)..1, w * (Real.exp (lam * s) * H t (y - s))‖ ≤ Real.exp |lam| * C := by + have hz := intervalIntegral.norm_integral_le_of_norm_le_const (a := 0) (b := 1) + (C := Real.exp |lam| * C) (f := fun s => w * (Real.exp (lam * s) * H t (y - s))) + apply (by simpa only [sub_zero, abs_one, mul_one] using hz : (∀ s ∈ uIoc (0 : ℝ) 1, + ‖w * (Real.exp (lam * s) * H t (y - s))‖ ≤ Real.exp |lam| * C) → _) + intro s hs + have hs' : 0 ≤ s ∧ s ≤ 1 := by + rw [uIoc_of_le (by norm_num : (0 : ℝ) ≤ 1)] at hs + exact ⟨hs.1.le, hs.2⟩ + have he : Real.exp (lam * s) ≤ Real.exp |lam| := by + apply Real.exp_le_exp.mpr + calc lam * s ≤ |lam| * s := mul_le_mul_of_nonneg_right (le_abs_self lam) hs'.1 + _ ≤ |lam| := by nlinarith [abs_nonneg lam] + rw [norm_mul, norm_mul, Real.norm_eq_abs, abs_of_nonneg hw, + Real.norm_eq_abs (Real.exp _), abs_of_pos (Real.exp_pos _)] + calc + _ = Real.exp (lam * s) * (w * ‖H t (y - s)‖) := by ring + _ ≤ Real.exp (lam * s) * C := mul_le_mul_of_nonneg_left (hC (y - s)) (Real.exp_pos _).le + _ ≤ Real.exp |lam| * C := mul_le_mul_of_nonneg_right he hC₀ + rw [intervalIntegral.integral_const_mul, norm_mul, Real.norm_eq_abs w, abs_of_nonneg hw] at hi + dsimp only [first] + rw [norm_mul, mul_left_comm, mul_assoc] + exact mul_le_mul_of_nonneg_left hi (norm_nonneg _) + +theorem first_rapid (lam : ℝ) {H : ℝ → ℝ → ℝ} (hH : Rapid2 H) : Rapid2 (first lam H) := by + refine ⟨first_contDiff lam hH.smooth, fun w J => ?_⟩ + obtain ⟨C, hC⟩ := hH.bound w J + refine ⟨‖(1 - Real.exp lam)⁻¹‖ * Real.exp |lam| * C, fun t ht y => ?_⟩ + rw [first_wordD lam hH.smooth] + exact first_weighted_bound lam t (by positivity) (hC t ht) y + +end PeriodicInverse + +namespace RapidCalculus +open scoped ContDiff + +section LinearWords +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +theorem biD_add {F G : ℝ → ℝ → A} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (hG : ContDiff ℝ ∞ (Function.uncurry G)) + (i : Bool) : biD i (F + G) = biD i F + biD i G := by + funext t y + cases i + · exact deriv_add ((hF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y) + ((hG.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y) + · exact deriv_add ((hF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + ((hG.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + +theorem wordD_add {F G : ℝ → ℝ → A} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (hG : ContDiff ℝ ∞ (Function.uncurry G)) + (w : List Bool) : wordD w (F + G) = wordD w F + wordD w G := by + induction w with + | nil => rfl + | cons i w ih => rw [wordD_cons, ih, biD_add (wordD_contDiff hF w) (wordD_contDiff hG w)]; rfl + +theorem biD_scale (c : ℝ) {F : ℝ → ℝ → A} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (i : Bool) : + biD i (c • F) = c • biD i F := by + funext t y + cases i + · exact (((hF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y).hasDerivAt.const_smul c).deriv + · exact (((hF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t).hasDerivAt.const_smul c).deriv + +theorem wordD_scale (c : ℝ) {F : ℝ → ℝ → A} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (w : List Bool) : + wordD w (c • F) = c • wordD w F := by + induction w with + | nil => rfl + | cons i w ih => rw [wordD_cons, ih, biD_scale c (wordD_contDiff hF w)]; rfl + +theorem Rapid2.add {F G : ℝ → ℝ → A} (hF : Rapid2 F) (hG : Rapid2 G) : Rapid2 (F + G) := by + refine ⟨hF.smooth.add hG.smooth, fun w J => ?_⟩ + obtain ⟨C, hC⟩ := hF.bound w J + obtain ⟨D, hD⟩ := hG.bound w J + refine ⟨C + D, fun t ht y => ?_⟩ + rw [wordD_add hF.smooth hG.smooth] + change (1 + t) ^ J * ‖wordD w F t y + wordD w G t y‖ ≤ C + D + calc + _ ≤ (1 + t) ^ J * (‖wordD w F t y‖ + ‖wordD w G t y‖) := mul_le_mul_of_nonneg_left (norm_add_le _ _) (by positivity) + _ ≤ C + D := by rw [mul_add]; exact add_le_add (hC t ht y) (hD t ht y) + +theorem Rapid2.scale {F : ℝ → ℝ → A} (hF : Rapid2 F) (c : ℝ) : Rapid2 (c • F) := by + refine ⟨contDiff_const.smul hF.smooth, fun w J => ?_⟩ + obtain ⟨C, hC⟩ := hF.bound w J + refine ⟨‖c‖ * C, fun t ht y => ?_⟩ + rw [wordD_scale c hF.smooth] + change (1 + t) ^ J * ‖c • wordD w F t y‖ ≤ ‖c‖ * C + rw [norm_smul, mul_left_comm] + exact mul_le_mul_of_nonneg_left (hC t ht y) (norm_nonneg _) + +theorem Rapid2.neg {F : ℝ → ℝ → A} (hF : Rapid2 F) : Rapid2 (-F) := by + simpa only [neg_one_smul] using hF.scale (-1) + +theorem Rapid2.sub {F G : ℝ → ℝ → A} (hF : Rapid2 F) (hG : Rapid2 G) : Rapid2 (F - G) := by + simpa only [sub_eq_add_neg] using hF.add hG.neg +end LinearWords + +theorem biD_mul {F G : ℝ → ℝ → ℝ} + (hF : ContDiff ℝ ∞ (Function.uncurry F)) (hG : ContDiff ℝ ∞ (Function.uncurry G)) + (i : Bool) : biD i (F * G) = biD i F * G + F * biD i G := by + funext t y + cases i + · exact deriv_mul ((hF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y) + ((hG.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y) + · exact deriv_mul ((hF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + ((hG.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + +theorem Rapid2.mul {F G : ℝ → ℝ → ℝ} (hF : Rapid2 F) (hG : Rapid2 G) : Rapid2 (F * G) := by + refine ⟨hF.smooth.mul hG.smooth, fun w J => ?_⟩ + induction w using List.reverseRecOn generalizing F G with + | nil => + obtain ⟨C, hC⟩ := hF.bound [] J + obtain ⟨D, hD⟩ := hG.bound [] 0 + have hD₀ : 0 ≤ D := by + have hz : ‖G 0 0‖ ≤ D := by simpa using hD 0 le_rfl 0 + exact (norm_nonneg _).trans hz + refine ⟨C * D, fun t ht y => ?_⟩ + change (1 + t) ^ J * ‖F t y * G t y‖ ≤ C * D + rw [norm_mul, ← mul_assoc] + calc + _ ≤ ((1 + t) ^ J * ‖F t y‖) * D := mul_le_mul_of_nonneg_left (by simpa using hD t ht y) (by positivity) + _ ≤ C * D := mul_le_mul_of_nonneg_right (hC t ht y) hD₀ + | append_singleton w i ih => + obtain ⟨C, hC⟩ := ih (hF.biD i) hG + obtain ⟨D, hD⟩ := ih hF (hG.biD i) + refine ⟨C + D, fun t ht y => ?_⟩ + rw [wordD_append, wordD_cons, wordD_nil, biD_mul hF.smooth hG.smooth, + wordD_add (F := RapidCalculus.biD i F * G) (G := F * RapidCalculus.biD i G) ((partial_contDiff hF.smooth i).mul hG.smooth) (hF.smooth.mul (partial_contDiff hG.smooth i))] + change (1 + t) ^ J * ‖wordD w (RapidCalculus.biD i F * G) t y + wordD w (F * RapidCalculus.biD i G) t y‖ ≤ C + D + calc + _ ≤ (1 + t) ^ J * (‖wordD w (RapidCalculus.biD i F * G) t y‖ + ‖wordD w (F * RapidCalculus.biD i G) t y‖) := + mul_le_mul_of_nonneg_left (norm_add_le _ _) (by positivity) + _ ≤ C + D := by rw [mul_add]; exact add_le_add (hC t ht y) (hD t ht y) + +end RapidCalculus + +namespace PeriodicInverse +open scoped ContDiff +open RapidCalculus + +def screened (lam : ℝ) (H : ℝ → ℝ → ℝ) : ℝ → ℝ → ℝ := first (-lam) (first lam H) + +theorem screened_contDiff (lam : ℝ) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) : + ContDiff ℝ ∞ (Function.uncurry (screened lam H)) := + first_contDiff (-lam) (first_contDiff lam hH) + +theorem screened_periodic (lam : ℝ) {H : ℝ → ℝ → ℝ} + (hp : ∀ t, Function.Periodic (H t) 1) (t : ℝ) : + Function.Periodic (screened lam H t) 1 := + first_periodic (-lam) (first_periodic lam hp) t + +theorem screened_rapid (lam : ℝ) {H : ℝ → ℝ → ℝ} (hH : Rapid2 H) : Rapid2 (screened lam H) := + first_rapid (-lam) (first_rapid lam hH) + +theorem screened_equation (lam : ℝ) (hlam : lam ≠ 0) {H : ℝ → ℝ → ℝ} + (hH : ContDiff ℝ ∞ (Function.uncurry H)) (hp : ∀ t, Function.Periodic (H t) 1) + (t y : ℝ) : biD false (biD false (screened lam H)) t y = + lam ^ 2 * screened lam H t y + H t y := by + have hs : ContDiff ℝ ∞ (first lam H t) := + (first_contDiff lam hH).comp (contDiff_const.prodMk contDiff_id) + have hw : ContDiff ℝ ∞ (screened lam H t) := + (screened_contDiff lam hH).comp (contDiff_const.prodMk contDiff_id) + have hid : deriv (screened lam H t) = fun z => -lam * screened lam H t z + first lam H t z := by + funext z + exact first_equation (-lam) (neg_ne_zero.mpr hlam) (first_contDiff lam hH) (first_periodic lam hp) t z + change deriv (deriv (screened lam H t)) y = _ + rw [hid] + have hd := (((hw.differentiable (by simp) y).hasDerivAt).const_mul (-lam)).add + ((hs.differentiable (by simp) y).hasDerivAt) + have hd' : deriv (fun z => -lam * screened lam H t z + first lam H t z) y = + -lam * deriv (screened lam H t) y + deriv (first lam H t) y := hd.deriv + rw [hd', congrFun hid y] + have hh := first_equation lam hlam hH hp t y + change deriv (first lam H t) y = _ at hh + rw [hh] + ring + +end PeriodicInverse + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Planar.lean b/lean/OAI/Analysis/PeriodicLattice/Planar.lean new file mode 100644 index 0000000000000000000000000000000000000000..dfe3884ffc701244db04acfeb9f2e31c06a6f574 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Planar.lean @@ -0,0 +1,123 @@ +import OAI.Analysis.PeriodicLattice.Profiles + +namespace OAI + +/-! Planar velocity fields implementing the encoded dynamics. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingPlanar {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Planar + +open Profiles Scales +open scoped ContDiff + +abbrev Point := ℝ × ℝ + +def slot (b L n : ℕ) (F H : ℤ → ℝ) (y : ℝ) : Point := + letI := twoAtLeastTwo + (beta b L n - beta b L (n + 1) + + 2 * beta b L (n + 1) * selector (epsilon b L n) H y, + epsilon b L (n + 1) * selector (epsilon b L n) F y) + +def coefficients (b L c₀ : ℕ) (F H : ℕ → ℤ → ℝ) : ℕ → ℝ → Point := + fun n => Nat.casesOn n (fun _ => (0, epsilon b L 0 * c₀)) + (fun k => slot b L k (F k) (H k)) + +def field (b L c₀ : ℕ) (F H : ℕ → ℤ → ℝ) (t : ℝ) (x : Point) : Point := + schedule (coefficients b L c₀ F H) t x.2 + +theorem slot_contDiff (b L n : ℕ) (F H : ℤ → ℝ) : + ContDiff ℝ ∞ (slot b L n F H) := + (contDiff_const.add (contDiff_const.mul (selector_contDiff _ _))).prodMk + (contDiff_const.mul (selector_contDiff _ _)) + +theorem field_contDiff (b L c₀ : ℕ) (F H : ℕ → ℤ → ℝ) : + ContDiff ℝ ∞ (fun tx : ℝ × Point => field b L c₀ F H tx.1 tx.2) := by + have hV : ∀ n, ContDiff ℝ ∞ (coefficients b L c₀ F H n) := by + intro n + cases n with + | zero => exact contDiff_const + | succ n => exact slot_contDiff b L n (F n) (H n) + exact (schedule_contDiff _ hV).comp (contDiff_fst.prodMk (contDiff_snd.snd)) + +theorem field_at_start (b L c₀ : ℕ) (F H : ℕ → ℤ → ℝ) (x : Point) : + field b L c₀ F H 0 x = 0 := schedule_zero_at_start _ _ + +theorem field_on_loader (b L c₀ : ℕ) (F H : ℕ → ℤ → ℝ) {t : ℝ} + (ht : 0 ≤ t) (ht' : t ≤ 1) (x : Point) : + field b L c₀ F H t x = deriv clock t • (0, epsilon b L 0 * c₀) := by + simpa [field, coefficients, pulse] using + schedule_on_slot (coefficients b L c₀ F H) 0 (by simpa using ht) (by simpa using ht') x.2 + +theorem field_on_slot (b L c₀ n : ℕ) (F H : ℕ → ℤ → ℝ) {t : ℝ} + (ht : n + 1 ≤ t) (ht' : t ≤ n + 2) (x : Point) : + field b L c₀ F H t x = deriv clock (t - 1 - n) • slot b L n (F n) (H n) x.2 := by + have hl : ((n + 1 : ℕ) : ℝ) ≤ t := by exact_mod_cast ht + have hu : t ≤ ((n + 1 : ℕ) : ℝ) + 1 := by push_cast; linarith + simpa only [field, coefficients, pulse, Nat.cast_add, Nat.cast_one, + sub_add_eq_sub_sub, sub_right_comm] using + schedule_on_slot (coefficients b L c₀ F H) (n + 1) hl hu x.2 + +theorem field_periodic_y {b : ℕ} (hb : 2 ≤ b) (L c₀ : ℕ) (F H : ℕ → ℤ → ℝ) + (hF : ∀ n, Function.Periodic (F n) (capacity b L n : ℤ)) + (hH : ∀ n, Function.Periodic (H n) (capacity b L n : ℤ)) (t x : ℝ) : + Function.Periodic (fun y => field b L c₀ F H t (x, y)) 1 := by + intro y + apply finsum_congr + intro n + congr 1 + cases n with + | zero => rfl + | succ n => + dsimp [coefficients, slot] + rw [selector_unit_periodic hb L n (H n) (hH n) y, + selector_unit_periodic hb L n (F n) (hF n) y] + +def slotCurve (b L n : ℕ) (F H : ℤ → ℝ) (j : ℤ) (a : Point) (τ : ℝ) : Point := + a + clock τ • (beta b L n - beta b L (n + 1) + 2 * beta b L (n + 1) * H j, + epsilon b L (n + 1) * F j) + +theorem slotCurve_hasDerivAt {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) (F H : ℤ → ℝ) + (j : ℤ) (a : Point) (ha : (a.2 - 1 / 2) / epsilon b L n = (j : ℝ)) + (hF : 0 ≤ F j) (hF' : F j ≤ capacity b L (n + 1)) (τ : ℝ) : + HasDerivAt (slotCurve b L n F H j a) + (deriv clock τ • slot b L n F H (slotCurve b L n F H j a τ).2) τ := by + have he := epsilon_pos hb L n + have he' := epsilon_pos hb L (n + 1) + have hplo := mul_nonneg (clock_nonneg τ) (mul_nonneg he'.le hF) + have hphi : clock τ * (epsilon b L (n + 1) * F j) < epsilon b L n / 4 := by + have hbound : clock τ * (epsilon b L (n + 1) * F j) ≤ + (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) := calc + _ ≤ 1 * (epsilon b L (n + 1) * F j) := + mul_le_mul_of_nonneg_right (clock_le_one τ) (mul_nonneg he'.le hF) + _ ≤ (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) := by + simpa [mul_comm] using mul_le_mul_of_nonneg_left hF' he'.le + obtain ⟨h₁, h₂, h₃⟩ := plateau_bound hb L n + exact hbound.trans_lt (h₁.trans h₂ |>.trans_lt h₃) + have hplateau : |((slotCurve b L n F H j a τ).2 - 1 / 2) / epsilon b L n - j| ≤ + 1 / 4 := by + change |(a.2 + clock τ * (epsilon b L (n + 1) * F j) - 1 / 2) / + epsilon b L n - j| ≤ 1 / 4 + rw [show a.2 + clock τ * (epsilon b L (n + 1) * F j) - 1 / 2 = + (a.2 - 1 / 2) + clock τ * (epsilon b L (n + 1) * F j) by ring, + add_div, ha, add_sub_cancel_left, abs_of_nonneg (div_nonneg hplo he.le)] + exact (div_le_iff₀ he).mpr (by linarith) + have hslot : slot b L n F H (slotCurve b L n F H j a τ).2 = + (beta b L n - beta b L (n + 1) + 2 * beta b L (n + 1) * H j, + epsilon b L (n + 1) * F j) := by + dsimp [slot] + rw [selector_plateau _ _ hplateau, selector_plateau _ _ hplateau] + rw [hslot] + exact (((contDiff_infty_iff_deriv.mp clock_contDiff).1 τ).hasDerivAt.smul_const _).const_add a + +end Planar + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/PlanarFlow.lean b/lean/OAI/Analysis/PeriodicLattice/PlanarFlow.lean new file mode 100644 index 0000000000000000000000000000000000000000..8cecf07ccea49eda5f5e52b20fa4044eaa0aabf0 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/PlanarFlow.lean @@ -0,0 +1,464 @@ +import OAI.Analysis.PeriodicLattice.Planar +import OAI.Analysis.PeriodicLattice.Trajectories + +namespace OAI + +/-! Planar trajectories, support control and dynamical identities. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingPlanarFlow {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Planar + +open Profiles Scales +open scoped ContDiff + +def codes (F : ℕ → ℤ → ℕ) (c₀ : ℕ) : ℕ → ℕ + | 0 => c₀ + | n + 1 => F n (codes F c₀ n) + +theorem codes_bound {b : ℕ} (L c₀ : ℕ) (F : ℕ → ℤ → ℕ) + (hc₀ : c₀ < capacity b L 0) + (hF : ∀ n j, F n j < capacity b L (n + 1)) : + ∀ n, codes F c₀ n < capacity b L n := by + intro n + cases n with + | zero => exact hc₀ + | succ n => exact hF n _ + +theorem table_residue {A : Type*} (V : ℤ → A) (P : ℤ) + (hV : Function.Periodic V P) (j : ℤ) : V j = V (j % P) := by + have h := hV.int_mul (j / P) (j % P) + rw [Int.cast_id, mul_comm, Int.emod_add_mul_ediv] at h + exact h + +theorem table_history {A : Type*} (V : ℤ → A) (b L : ℕ) (c : ℕ → ℕ) (n : ℕ) + (hV : Function.Periodic V (capacity b L n : ℤ)) (hc : c n < capacity b L n) : + V (History.address b L c n) = V (c n) := by + rw [table_residue V _ hV] + congr 1 + exact_mod_cast History.read_residue b L c n hc + +def increments (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) : ℕ → Point + | 0 => (0, epsilon b L 0 * c 0) + | n + 1 => + (beta b L n - beta b L (n + 1) + + 2 * beta b L (n + 1) * (if H n (c n) then 1 else 0), + epsilon b L (n + 1) * c (n + 1)) + +def curve (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) (t : ℝ) : Point := + (1 / 4, 1 / 2) + accumulated (increments b L c H) t + +theorem curve_contDiff (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) : + ContDiff ℝ ∞ (curve b L c H) := contDiff_const.add (accumulated_contDiff _) + +theorem curve_start (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) : + curve b L c H 0 = (1 / 4, 1 / 2) := by + have ha := accumulated_at_integer (increments b L c H) 0 + simpa only [Nat.cast_zero, Finset.sum_range_zero, curve, add_eq_left] using ha + +theorem curve_succ (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) (n : ℕ) : + curve b L c H (n + 1) = curve b L c H n + increments b L c H n := by + have hn : (n : ℝ) + 1 = ((n + 1 : ℕ) : ℝ) := by push_cast; rfl + rw [hn, curve, accumulated_at_integer, Finset.sum_range_succ] + rw [curve, accumulated_at_integer, add_assoc] + +theorem curve_on_slot (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) (n : ℕ) + {t : ℝ} (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) : + curve b L c H t = curve b L c H n + shiftedClock n t • increments b L c H n := by + rw [curve, accumulated_on_slot _ n ht ht', curve, accumulated_at_integer, add_assoc] + +theorem curve_y_integer (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) (n : ℕ) : + (curve b L c H (n + 1)).2 = History.coordinate b L c n := by + induction n with + | zero => + have he := congrArg Prod.snd (curve_succ b L c H 0) + simpa [curve_start, increments, History.coordinate] using he + | succ n ih => + have he := congrArg Prod.snd (curve_succ b L c H (n + 1)) + simp only [Prod.snd_add, Nat.cast_add, Nat.cast_one, increments] at he + rw [Nat.cast_add, Nat.cast_one, he, ih] + change (1 / 2 + ∑ k ∈ Finset.range (n + 1), epsilon b L k * (c k : ℝ)) + + epsilon b L (n + 1) * c (n + 1) = + 1 / 2 + ∑ k ∈ Finset.range ((n + 1) + 1), epsilon b L k * (c k : ℝ) + rw [Finset.sum_range_succ _ (n + 1), add_assoc] + +theorem curve_y_slot (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) (n : ℕ) + {t : ℝ} (ht : (n : ℝ) + 1 ≤ t) (ht' : t ≤ n + 2) : + (curve b L c H t).2 = History.coordinate b L c n + + clock (t - 1 - n) * (epsilon b L (n + 1) * c (n + 1)) := by + rw [curve_on_slot _ _ _ _ (n + 1) (by push_cast; exact ht) (by push_cast; linarith)] + simp only [Prod.snd_add, Prod.smul_snd, smul_eq_mul, Nat.cast_add, Nat.cast_one, + curve_y_integer, shiftedClock, increments, sub_add_eq_sub_sub, sub_right_comm] + +theorem curve_plateau {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (c : ℕ → ℕ) + (H : ℕ → ℤ → Bool) (n : ℕ) (hc : c (n + 1) < capacity b L (n + 1)) + {t : ℝ} (ht : (n : ℝ) + 1 ≤ t) (ht' : t ≤ n + 2) : + |((curve b L c H t).2 - 1 / 2) / epsilon b L n - + (History.address b L c n : ℝ)| ≤ 1 / 4 := by + rw [curve_y_slot b L c H n ht ht'] + simpa only [mul_assoc] using + (Signal.history_in_plateau hb L n c hc (clock_nonneg (t - 1 - n)) (clock_le_one _)).le + +end Planar + +namespace Planar + +open Profiles Scales +open scoped ContDiff + +def ruleField (b L c₀ : ℕ) (F : ℕ → ℤ → ℕ) (H : ℕ → ℤ → Bool) : ℝ → Point → Point := + field b L c₀ (fun n j => F n j) (fun n j => if H n j then 1 else 0) + +theorem coefficients_on_curve {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (F : ℕ → ℤ → ℕ) + (H : ℕ → ℤ → Bool) (c : ℕ → ℕ) + (hc : ∀ n, c n < capacity b L n) + (hstep : ∀ n, c (n + 1) = F n (c n)) + (hF : ∀ n, Function.Periodic (F n) (capacity b L n : ℤ)) + (hH : ∀ n, Function.Periodic (H n) (capacity b L n : ℤ)) + (n : ℕ) {t : ℝ} (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) : + coefficients b L (c 0) (fun m j => F m j) (fun m j => if H m j then 1 else 0) + n (curve b L c H t).2 = increments b L c H n := by + cases n with + | zero => rfl + | succ n => + have hl : (n : ℝ) + 1 ≤ t := by simpa using ht + have hu : t ≤ (n : ℝ) + 2 := by push_cast at ht'; linarith + have hp : |((curve b L c H t).2 - 1 / 2) / epsilon b L n - + ((History.address b L c n : ℤ) : ℝ)| ≤ 1 / 4 := by + simpa using curve_plateau hb L c H n (hc (n + 1)) hl hu + dsimp only [coefficients, slot, increments] + rw [selector_plateau _ _ hp, selector_plateau _ _ hp, + table_history (H n) b L c n (hH n) (hc n), + table_history (F n) b L c n (hF n) (hc n), ← hstep n] + +theorem curve_solves {b : ℕ} (hb : 2 ≤ b) (L c₀ : ℕ) (F : ℕ → ℤ → ℕ) + (H : ℕ → ℤ → Bool) (hc₀ : c₀ < capacity b L 0) + (hbound : ∀ n j, F n j < capacity b L (n + 1)) + (hF : ∀ n, Function.Periodic (F n) (capacity b L n : ℤ)) + (hH : ∀ n, Function.Periodic (H n) (capacity b L n : ℤ)) + {t : ℝ} (ht : 0 ≤ t) : + HasDerivAt (curve b L (codes F c₀) H) + (ruleField b L c₀ F H t (curve b L (codes F c₀) H t)) t := by + let n : ℕ := ⌊t⌋₊ + have hl : (n : ℝ) ≤ t := Nat.floor_le ht + have hu : t ≤ n + 1 := (Nat.lt_floor_add_one t).le + have hc := codes_bound L c₀ F hc₀ hbound + have heq : ruleField b L c₀ F H t (curve b L (codes F c₀) H t) = + pulse n t • increments b L (codes F c₀) H n := by + rw [ruleField, field, schedule_on_slot _ n hl hu] + congr 1 + exact coefficients_on_curve hb L F H (codes F c₀) hc (fun _ => rfl) hF hH n hl hu + rw [heq] + exact (accumulated_hasDerivAt (increments b L (codes F c₀) H) n hl hu).const_add (1 / 4, 1 / 2) + +theorem curve_unique {b : ℕ} (hb : 2 ≤ b) (L c₀ : ℕ) (F : ℕ → ℤ → ℕ) + (H : ℕ → ℤ → Bool) (hc₀ : c₀ < capacity b L 0) + (hbound : ∀ n j, F n j < capacity b L (n + 1)) + (hF : ∀ n, Function.Periodic (F n) (capacity b L n : ℤ)) + (hH : ∀ n, Function.Periodic (H n) (capacity b L n : ℤ)) + {Y : ℝ → Point} (hY₀ : Y 0 = (1 / 4, 1 / 2)) + (hY : ∀ t : ℝ, 0 ≤ t → + HasDerivWithinAt Y (ruleField b L c₀ F H t (Y t)) (Set.Ici 0) t) + {t : ℝ} (ht : 0 ≤ t) : Y t = curve b L (codes F c₀) H t := by + apply Trajectories.unique + ((field_contDiff b L c₀ (fun n j => F n j) (fun n j => if H n j then 1 else 0)).of_le + (by exact WithTop.coe_le_coe.mpr le_top)) hY + (fun s hs => (curve_solves hb L c₀ F H hc₀ hbound hF hH hs).hasDerivWithinAt) _ ht + rw [hY₀, curve_start] + +end Planar + +namespace Planar + +open Profiles Scales + +theorem curve_x_before (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) (n : ℕ) + (hH : ∀ m < n, H m (c m) = false) : + (curve b L c H (n + 1)).1 = 1 / 2 - beta b L n := by + induction n with + | zero => + have he := congrArg Prod.fst (curve_succ b L c H 0) + norm_num [curve_start, increments, beta] at he ⊢ + exact he + | succ n ih => + have hn : H n (c n) = false := hH n (Nat.lt_succ_self n) + have hi := ih (fun m hm => hH m (Nat.lt_succ_of_lt hm)) + have he := congrArg Prod.fst (curve_succ b L c H (n + 1)) + simp only [Prod.fst_add, Nat.cast_add, Nat.cast_one, increments, hn, + Bool.false_eq_true, ↓reduceIte, mul_zero, add_zero] at he + rw [Nat.cast_add, Nat.cast_one, he, hi] + ring + +theorem curve_x_loader (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) {t : ℝ} + (ht : 0 ≤ t) (ht' : t ≤ 1) : (curve b L c H t).1 = 1 / 4 := by + rw [curve_on_slot b L c H 0 (by simpa using ht) (by simpa using ht')] + simp [curve_start, increments] + +theorem curve_x_slot (b L : ℕ) (c : ℕ → ℕ) (H : ℕ → ℤ → Bool) (n : ℕ) + (hH : ∀ m < n, H m (c m) = false) + {t : ℝ} (ht : (n : ℝ) + 1 ≤ t) (ht' : t ≤ n + 2) : + (curve b L c H t).1 = Signal.inSlot b L n (H n (c n)) (clock (t - 1 - n)) := by + rw [curve_on_slot b L c H (n + 1) (by push_cast; exact ht) (by push_cast; linarith)] + simp only [Prod.fst_add, Prod.smul_fst, smul_eq_mul, Nat.cast_add, Nat.cast_one, + curve_x_before b L c H n hH, increments, shiftedClock, Signal.inSlot, + sub_add_eq_sub_sub, sub_right_comm] + cases H n (c n) <;> simp + +theorem curve_no_signal {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (c : ℕ → ℕ) + (H : ℕ → ℤ → Bool) (hH : ∀ n, H n (c n) = false) {t : ℝ} (ht : 0 ≤ t) : + 1 / 4 ≤ (curve b L c H t).1 ∧ (curve b L c H t).1 < 1 / 2 := by + by_cases ht' : t ≤ 1 + · rw [curve_x_loader b L c H ht ht'] + norm_num + · let n : ℕ := ⌊t - 1⌋₊ + have hl : (n : ℝ) + 1 ≤ t := by + have := Nat.floor_le (show 0 ≤ t - 1 by linarith) + dsimp [n]; linarith + have hu : t ≤ (n : ℝ) + 2 := by + have := Nat.lt_floor_add_one (t - 1) + dsimp [n]; linarith + rw [curve_x_slot b L c H n (fun m _ => hH m) hl hu, hH] + exact (Signal.nonhalting_interval hb L n (clock_nonneg _) (clock_le_one _)).2.2 + +theorem curve_first_signal {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (c : ℕ → ℕ) + (H : ℕ → ℤ → Bool) (n : ℕ) (hbefore : ∀ m < n, H m (c m) = false) + (hn : H n (c n) = true) : + 1 / 2 < (curve b L c H (n + 2)).1 ∧ (curve b L c H (n + 2)).1 < 1 := by + rw [curve_x_slot b L c H n hbefore (by linarith) le_rfl, hn, + clock_one (by linarith)] + exact Signal.halting_interval hb L n + +def embed (x : Point) : Space := WithLp.toLp 2 ![x.1, x.2, 1 / 2] + +@[simp] theorem embed_first (x : Point) : embed x 0 = x.1 := rfl + +theorem curve_event_iff {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (c : ℕ → ℕ) + (H : ℕ → ℤ → Bool) : + MaterialEvent (fun t => embed (curve b L c H t)) ↔ ∃ n : ℕ, H n (c n) = true := by + constructor + · rintro ⟨t, ht, hevent⟩ + by_contra hn + have hh : ∀ n, H n (c n) = false := by + intro n + exact Bool.eq_false_iff.mpr (fun h => hn ⟨n, h⟩) + obtain ⟨hlo, hhi⟩ := curve_no_signal hb L c H hh ht + have hlo' : 0 ≤ embed (curve b L c H t) 0 := by simp only [embed_first]; linarith + have hhi' : embed (curve b L c H t) 0 < 1 := by simp only [embed_first]; linarith + have := (Detector.mem_iff hlo' hhi').mp hevent + exact (not_lt_of_ge hhi.le) this + · intro hn + let n := Nat.find hn + have hsig : H n (c n) = true := Nat.find_spec hn + have hbefore : ∀ m < n, H m (c m) = false := by + intro m hm + exact Bool.eq_false_iff.mpr (Nat.find_min hn hm) + obtain ⟨hlo, hhi⟩ := curve_first_signal hb L c H n hbefore hsig + refine ⟨(n : ℝ) + 2, by positivity, ?_⟩ + apply (Detector.mem_iff (x := embed (curve b L c H (n + 2))) ?_ ?_).mpr + · exact hlo + · simp only [embed_first]; linarith + · exact hhi + +end Planar + +namespace Profiles + +open scoped ContDiff + +theorem iteratedDeriv_pair {a d : ℝ → ℝ} (ha : ContDiff ℝ ∞ a) (hd : ContDiff ℝ ∞ d) + (k : ℕ) : iteratedDeriv k (fun y => (a y, d y)) = + fun y => (iteratedDeriv k a y, iteratedDeriv k d y) := by + induction k with + | zero => rfl + | succ k ih => + rw [iteratedDeriv_succ, ih] + funext y + have ha' : DifferentiableAt ℝ (iteratedDeriv k a) y := by + rw [iteratedDeriv_eq_iterate] + exact (ContDiff.iterate_deriv k ha).differentiable (by norm_num) y + have hd' : DifferentiableAt ℝ (iteratedDeriv k d) y := by + rw [iteratedDeriv_eq_iterate] + exact (ContDiff.iterate_deriv k hd).differentiable (by norm_num) y + simpa only [iteratedDeriv_succ] using (ha'.hasDerivAt.prodMk hd'.hasDerivAt).deriv + +end Profiles + +namespace Planar + +open Profiles Scales +open scoped ContDiff + +theorem slot_iteratedDeriv (b L n k : ℕ) (F H : ℤ → ℝ) (y : ℝ) : + iteratedDeriv k (slot b L n F H) y = + ((if k = 0 then beta b L n - beta b L (n + 1) else 0) + + 2 * beta b L (n + 1) * iteratedDeriv k (selector (epsilon b L n) H) y, + epsilon b L (n + 1) * iteratedDeriv k (selector (epsilon b L n) F) y) := by + have hh : ContDiff ℝ ∞ (fun y => beta b L n - beta b L (n + 1) + + 2 * beta b L (n + 1) * selector (epsilon b L n) H y) := + contDiff_const.add (contDiff_const.mul (selector_contDiff _ _)) + have hf : ContDiff ℝ ∞ (fun y => epsilon b L (n + 1) * selector (epsilon b L n) F y) := + contDiff_const.mul (selector_contDiff _ _) + unfold slot + rw [iteratedDeriv_pair hh hf] + dsimp only + apply Prod.ext + · rw [iteratedDeriv_fun_add contDiffAt_const + ((contDiff_const.mul (selector_contDiff _ _)).of_le + (WithTop.coe_le_coe.mpr le_top)).contDiffAt, iteratedDeriv_const, + iteratedDeriv_const_mul_field] + · rw [iteratedDeriv_const_mul_field] + +theorem slot_derivative_bound {b : ℕ} (hb : 2 ≤ b) (L n k : ℕ) (F H : ℤ → ℝ) + {D : ℝ} (hF : ∀ j, |F j| ≤ (capacity b L (n + 1) : ℝ)) + (hH : ∀ j, |H j| ≤ 1) (hD : ∀ z, |iteratedDeriv k bump z| ≤ D) (y : ℝ) : + ‖iteratedDeriv k (slot b L n F H) y‖ ≤ (1 + 2 * D) * slotSize b L k n := by + have he := epsilon_pos hb L n + have he' := epsilon_pos hb L (n + 1) + have hD₀ : 0 ≤ D := (abs_nonneg _).trans (hD 0) + have hP : (1 : ℝ) ≤ capacity b L (n + 1) := by + exact_mod_cast Nat.one_le_pow (codeExponent L (n + 1)) b (by omega) + have hdH := selector_derivative_bound he H k hH hD y + have hdF := selector_derivative_bound he F k hF hD y + simp only [one_mul] at hdH + let E : ℝ := (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) / epsilon b L n ^ k + have hE : E = (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) * + (epsilon b L n)⁻¹ ^ k := by simp only [E, div_eq_mul_inv, inv_pow] + have hE₀ : 0 ≤ E := by dsimp [E]; positivity + have hE' : epsilon b L (n + 1) * (epsilon b L n)⁻¹ ^ k ≤ E := by + rw [hE] + have hh := mul_le_mul_of_nonneg_right hP + (show 0 ≤ epsilon b L (n + 1) * (epsilon b L n)⁻¹ ^ k by positivity) + simpa only [one_mul, mul_assoc] using hh + let A : ℝ := if k = 0 then beta b L n else 0 + have hA₀ : 0 ≤ A := by + dsimp [A] + split_ifs + · exact (beta_pos hb L n).le + · exact le_rfl + have hconst : |if k = 0 then beta b L n - beta b L (n + 1) else 0| ≤ A := by + dsimp [A] + split_ifs + · rw [abs_of_nonneg (sub_nonneg.mpr ((beta_strictAnti hb L).antitone (Nat.le_succ n)))] + linarith [beta_pos hb L (n + 1)] + · simp + have hbeta : beta b L (n + 1) = epsilon b L (n + 1) := by simp [beta] + rw [slot_iteratedDeriv, norm_prod_le_iff] + change _ ≤ (1 + 2 * D) * (A + E) ∧ _ ≤ (1 + 2 * D) * (A + E) + constructor + · rw [Real.norm_eq_abs] + calc + _ ≤ |if k = 0 then beta b L n - beta b L (n + 1) else 0| + + |2 * beta b L (n + 1) * iteratedDeriv k (selector (epsilon b L n) H) y| := + abs_add_le _ _ + _ ≤ A + 2 * epsilon b L (n + 1) * ((epsilon b L n)⁻¹ ^ k * D) := by + rw [abs_mul, hbeta, abs_of_nonneg (by positivity : 0 ≤ 2 * epsilon b L (n + 1))] + exact add_le_add hconst (mul_le_mul_of_nonneg_left hdH (by positivity)) + _ ≤ A + 2 * D * E := by nlinarith [mul_le_mul_of_nonneg_left hE' hD₀] + _ ≤ (1 + 2 * D) * (A + E) := by nlinarith + · rw [Real.norm_eq_abs, abs_mul, abs_of_pos he'] + calc + _ ≤ epsilon b L (n + 1) * + ((capacity b L (n + 1) : ℝ) * (epsilon b L n)⁻¹ ^ k * D) := + mul_le_mul_of_nonneg_left hdF he'.le + _ = D * E := by rw [hE]; ring + _ ≤ (1 + 2 * D) * (A + E) := by nlinarith + +end Planar + +namespace Planar + +open Profiles Scales +open scoped ContDiff + +theorem field_slot_derivative_bound {b : ℕ} (hb : 2 ≤ b) (L c₀ r k n : ℕ) + (F H : ℕ → ℤ → ℝ) {T D : ℝ} + (hF : ∀ m j, |F m j| ≤ (capacity b L (m + 1) : ℝ)) + (hH : ∀ m j, |H m j| ≤ 1) + (hT : ∀ s, |iteratedDeriv r (deriv clock) s| ≤ T) + (hD : ∀ z, |iteratedDeriv k bump z| ≤ D) + {t : ℝ} (ht : (n : ℝ) + 1 ≤ t) (ht' : t ≤ n + 2) (y : ℝ) : + ‖mixedPartial r k (schedule (coefficients b L c₀ F H)) t y‖ ≤ + T * (1 + 2 * D) * slotSize b L k n := by + rw [schedule_mixedPartial _ r k (n + 1) (by push_cast; exact ht) (by push_cast; linarith), + norm_smul, Real.norm_eq_abs, pulse_iteratedDeriv] + have h := slot_derivative_bound hb L n k (F n) (H n) (hF n) (hH n) hD y + have hT₀ : 0 ≤ T := (abs_nonneg _).trans (hT 0) + have hbound := mul_le_mul (hT (t - (n + 1 : ℕ))) h (norm_nonneg _) hT₀ + simpa only [coefficients, mul_assoc] using hbound + +def planarBound (b L c₀ k J T D : ℕ) : ℕ := + T * ((1 + 2 * D) * allSlotsBound b L k J + c₀ * 2 ^ J) + +theorem field_weighted_derivative_bound {b : ℕ} (hb : 2 ≤ b) (L c₀ r k J T D : ℕ) + (F H : ℕ → ℤ → ℝ) + (hF : ∀ m j, |F m j| ≤ (capacity b L (m + 1) : ℝ)) + (hH : ∀ m j, |H m j| ≤ 1) + (hT : ∀ s, |iteratedDeriv r (deriv clock) s| ≤ T) + (hD : ∀ z, |iteratedDeriv k bump z| ≤ D) + {t : ℝ} (ht : 0 ≤ t) (y : ℝ) : + (1 + t) ^ J * ‖mixedPartial r k (schedule (coefficients b L c₀ F H)) t y‖ ≤ + (planarBound b L c₀ k J T D : ℝ) := by + have hweight : 0 ≤ (1 + t) ^ J := by positivity + have hbudget : ((T : ℝ) * (1 + 2 * D) * allSlotsBound b L k J) ≤ + (planarBound b L c₀ k J T D : ℝ) := by + simp only [planarBound, Nat.cast_mul, Nat.cast_add, Nat.cast_one, Nat.cast_ofNat, Nat.cast_pow] + nlinarith [show 0 ≤ (T : ℝ) * (c₀ * 2 ^ J) by positivity] + by_cases ht' : t ≤ 1 + · rw [schedule_mixedPartial _ r k 0 (by simpa using ht) (by simpa using ht')] + dsimp only [coefficients] + rw [Nat.rec_zero, iteratedDeriv_const, norm_smul, Real.norm_eq_abs, pulse_iteratedDeriv] + have hloader : ‖if k = 0 then ((0 : ℝ), epsilon b L 0 * c₀) else 0‖ ≤ (c₀ : ℝ) := by + split_ifs + · rw [norm_prod_le_iff] + constructor + · simp + · rw [Real.norm_eq_abs, abs_of_nonneg (mul_nonneg (epsilon_pos hb L 0).le (Nat.cast_nonneg c₀))] + simpa using mul_le_mul_of_nonneg_right (epsilon_le_one hb L 0) (Nat.cast_nonneg c₀) + · simp + have hpulse : |iteratedDeriv r (deriv clock) (t - (0 : ℕ))| ≤ (T : ℝ) := hT _ + have hw : (1 + t) ^ J ≤ (2 : ℝ) ^ J := + pow_le_pow_left₀ (by linarith) (by linarith) J + calc + _ ≤ (2 : ℝ) ^ J * ((T : ℝ) * c₀) := + mul_le_mul hw (mul_le_mul hpulse hloader (norm_nonneg _) (Nat.cast_nonneg T)) + (by positivity) (by positivity) + _ ≤ (planarBound b L c₀ k J T D : ℝ) := by + simp only [planarBound, Nat.cast_mul, Nat.cast_add, Nat.cast_one, Nat.cast_ofNat, Nat.cast_pow] + nlinarith [show 0 ≤ (T : ℝ) * ((1 + 2 * D) * allSlotsBound b L k J) by positivity] + · let n : ℕ := ⌊t - 1⌋₊ + have hl : (n : ℝ) + 1 ≤ t := by + have := Nat.floor_le (show 0 ≤ t - 1 by linarith) + dsimp [n]; linarith + have hu : t ≤ (n : ℝ) + 2 := by + have := Nat.lt_floor_add_one (t - 1) + dsimp [n]; linarith + calc + _ ≤ (1 + t) ^ J * ((T : ℝ) * (1 + 2 * D) * slotSize b L k n) := + mul_le_mul_of_nonneg_left + (field_slot_derivative_bound hb L c₀ r k n F H hF hH hT hD hl hu y) hweight + _ = (T : ℝ) * (1 + 2 * D) * ((1 + t) ^ J * slotSize b L k n) := by ring + _ ≤ (T : ℝ) * (1 + 2 * D) * allSlotsBound b L k J := + mul_le_mul_of_nonneg_left (weighted_slotSize_bound_all hb L k J n ht hu) (by positivity) + _ ≤ (planarBound b L c₀ k J T D : ℝ) := hbudget + +theorem field_rapid {b : ℕ} (hb : 2 ≤ b) (L c₀ r k J : ℕ) (F H : ℕ → ℤ → ℝ) + (hF : ∀ m j, |F m j| ≤ (capacity b L (m + 1) : ℝ)) + (hH : ∀ m j, |H m j| ≤ 1) : + ∃ C : ℕ, ∀ t : ℝ, 0 ≤ t → ∀ y : ℝ, + ‖mixedPartial r k (schedule (coefficients b L c₀ F H)) t y‖ ≤ (C : ℝ) / (1 + t) ^ J := by + obtain ⟨T, D, hT, hD⟩ := profile_derivative_bounds r k + refine ⟨planarBound b L c₀ k J T D, fun t ht y => ?_⟩ + apply (le_div_iff₀ (by positivity : 0 < (1 + t) ^ J)).mpr + simpa only [mul_comm] using field_weighted_derivative_bound hb L c₀ r k J T D F H hF hH hT hD ht y + +end Planar + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/ProfileJets.lean b/lean/OAI/Analysis/PeriodicLattice/ProfileJets.lean new file mode 100644 index 0000000000000000000000000000000000000000..c6c1fa17be674986e44a920aaca7585398b92788 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/ProfileJets.lean @@ -0,0 +1,274 @@ +import OAI.Analysis.PeriodicLattice.Solenoidal + +namespace OAI + +/-! Explicit jets and uniform profile derivative estimates. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingProfileJets {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace ProfileJets + +open scoped ContDiff +open Polynomial + +def rhoTerm (k : ℕ) (x : ℝ) : ℝ := x⁻¹ ^ k * expNegInvGlue x + +theorem rhoTerm_contDiff (k : ℕ) : ContDiff ℝ ∞ (rhoTerm k) := by + change ContDiff ℝ ∞ (fun x : ℝ => x⁻¹ ^ k * expNegInvGlue x) + simpa only [Polynomial.eval_pow, Polynomial.eval_X] using + (expNegInvGlue.contDiff_polynomial_eval_inv_mul (n := ⊤) (X ^ k)) + +theorem rhoTerm_hasDerivAt (k : ℕ) (x : ℝ) : + HasDerivAt (rhoTerm k) (rhoTerm (k + 2) x - (k : ℝ) * rhoTerm (k + 1) x) x := by + have hh := expNegInvGlue.hasDerivAt_polynomial_eval_inv_mul ((X : ℝ[X]) ^ k) x + convert hh using 1 + · funext y + simp only [rhoTerm, Polynomial.eval_pow, Polynomial.eval_X] + · simp only [rhoTerm, Polynomial.eval_mul, Polynomial.eval_pow, Polynomial.eval_sub, + Polynomial.eval_X, Polynomial.derivative_X_pow, Polynomial.eval_C] + rcases k with _ | k + · simp + · simp only [Nat.cast_add, Nat.cast_one, Nat.add_sub_cancel, pow_succ] + ring + +theorem rhoTerm_bound (k : ℕ) (x : ℝ) : |rhoTerm k x| ≤ (Nat.factorial k : ℝ) := by + by_cases hx : x ≤ 0 + · simp only [rhoTerm, expNegInvGlue.zero_of_nonpos hx, mul_zero, abs_zero] + positivity + · have hx' : 0 < x := lt_of_not_ge hx + have h := Real.pow_div_factorial_le_exp (x⁻¹) (inv_nonneg.mpr hx'.le) k + have hf : (0 : ℝ) < Nat.factorial k := by exact_mod_cast Nat.factorial_pos k + rw [rhoTerm, expNegInvGlue, ite_eq_right hx, abs_of_nonneg (by positivity), Real.exp_neg] + rw [← div_eq_mul_inv, div_le_iff₀ (Real.exp_pos _)] + exact (div_le_iff₀ hf).mp h |>.trans_eq (mul_comm _ _) + +theorem denominator_lower (x : ℝ) : + (1 : ℝ) / 9 ≤ expNegInvGlue x + expNegInvGlue (1 - x) := by + have hh : (1 : ℝ) / 9 ≤ expNegInvGlue (1 / 2) := by + norm_num only [expNegInvGlue, show ¬((1 : ℝ) / 2 ≤ 0) by norm_num, ↓reduceIte, inv_div, inv_one] + rw [Real.exp_neg, ← one_div] + apply one_div_le_one_div_of_le (Real.exp_pos _) + have he := Real.exp_one_lt_three + have hz := Real.exp_pos 1 + rw [show (2 : ℝ) = 1 + 1 by norm_num, Real.exp_add] + nlinarith + rcases le_total (1 / 2 : ℝ) x with hx | hx + · exact hh.trans ((expNegInvGlue.monotone hx).trans (le_add_of_nonneg_right (expNegInvGlue.nonneg _))) + · exact hh.trans ((expNegInvGlue.monotone (show (1 / 2 : ℝ) ≤ 1 - x by linarith)).trans + (le_add_of_nonneg_left (expNegInvGlue.nonneg _))) + +def denomInv (k : ℕ) (x : ℝ) : ℝ := + (expNegInvGlue x + expNegInvGlue (1 - x))⁻¹ ^ k + +theorem denomInv_contDiff (k : ℕ) : ContDiff ℝ ∞ (denomInv k) := + (expNegInvGlue.contDiff.add (expNegInvGlue.contDiff.comp + (contDiff_const.sub contDiff_id))).inv (fun x => (Real.smoothTransition.pos_denom x).ne') |>.pow k + +theorem denomInv_bound (k : ℕ) (x : ℝ) : |denomInv k x| ≤ (9 : ℝ)^k := by + have hp := Real.smoothTransition.pos_denom x + rw [denomInv, abs_of_nonneg (by positivity)] + exact pow_le_pow_left₀ (inv_nonneg.mpr hp.le) ((inv_le_comm₀ hp (by norm_num)).mpr (by simpa using denominator_lower x)) k + +theorem denomInv_hasDerivAt (k : ℕ) (x : ℝ) : + HasDerivAt (denomInv k) + (-(k : ℝ) * denomInv (k + 1) x * (rhoTerm 2 x - rhoTerm 2 (1-x))) x := by + have hr (y : ℝ) : HasDerivAt expNegInvGlue (rhoTerm 2 y) y := by + have he : rhoTerm 0 = expNegInvGlue := by funext z; simp [rhoTerm] + simpa only [he, Nat.reduceAdd, Nat.cast_zero, zero_mul, sub_zero] using rhoTerm_hasDerivAt 0 y + have hd := ((hr x).add ((hr (1-x)).comp x ((hasDerivAt_id x).const_sub 1))).inv + (Real.smoothTransition.pos_denom x).ne' + have hh := hd.pow k + change HasDerivAt (denomInv k) _ x at hh + convert hh using 1 + rcases k with _ | k + · simp + · dsimp only [denomInv] + simp only [Nat.add_sub_cancel, Nat.cast_add, Nat.cast_one, Pi.inv_apply, Pi.add_apply, Function.comp_apply, div_eq_mul_inv] + rw [← inv_pow] + simp only [pow_succ] + ring + +abbrev Factor := Bool × ℤ × ℤ × ℕ +abbrev Term := ℤ × List Factor +abbrev Expr := List Term + +def evalFactor (f : Factor) (x : ℝ) : ℝ := + if f.1 then denomInv f.2.2.2 ((f.2.1 : ℝ) * x + f.2.2.1) + else rhoTerm f.2.2.2 ((f.2.1 : ℝ) * x + f.2.2.1) + +def evalProduct (l : List Factor) (x : ℝ) : ℝ := (l.map (fun f => evalFactor f x)).prod + +def evalTerm (t : Term) (x : ℝ) : ℝ := t.1 * evalProduct t.2 x + +def eval (e : Expr) (x : ℝ) : ℝ := (e.map (fun t => evalTerm t x)).sum + +def factorBound (f : Factor) : ℕ := if f.1 then 9 ^ f.2.2.2 else Nat.factorial f.2.2.2 + +def productBound (l : List Factor) : ℕ := (l.map factorBound).prod + +def termBound (t : Term) : ℕ := t.1.natAbs * productBound t.2 + +def bound (e : Expr) : ℕ := (e.map termBound).sum + +theorem evalFactor_bound (f : Factor) (x : ℝ) : |evalFactor f x| ≤ factorBound f := by + rcases f with ⟨i, a, c, k⟩ + cases i + · exact rhoTerm_bound k _ + · simpa [factorBound, evalFactor] using denomInv_bound k ((a : ℝ) * x + c) + +theorem evalProduct_bound (l : List Factor) (x : ℝ) : |evalProduct l x| ≤ productBound l := by + induction l with + | nil => norm_num [evalProduct, productBound] + | cons f l ih => + simp only [evalProduct, List.map_cons, List.prod_cons, abs_mul, productBound, Nat.cast_mul] at * + exact mul_le_mul (evalFactor_bound f x) ih (abs_nonneg _) (by positivity) + +theorem evalTerm_bound (t : Term) (x : ℝ) : |evalTerm t x| ≤ termBound t := by + simp only [evalTerm, abs_mul, termBound, Nat.cast_mul, Nat.cast_natAbs, Int.cast_abs] + exact mul_le_mul_of_nonneg_left (evalProduct_bound t.2 x) (abs_nonneg _) +theorem eval_bound (e : Expr) (x : ℝ) : |eval e x| ≤ bound e := by + induction e with + | nil => norm_num [eval, bound] + | cons t e ih => + simp only [eval, List.map_cons, List.sum_cons, bound, Nat.cast_add] at * + exact (abs_add_le _ _).trans (add_le_add (evalTerm_bound t x) ih) + +def multPrefix (c : ℤ) (l : List Factor) (e : Expr) : Expr := + e.map (fun t => (c * t.1, l ++ t.2)) + +def diffFactor (f : Factor) : Expr := + if f.1 then + [(-f.2.1 * f.2.2.2, [(true, f.2.1, f.2.2.1, f.2.2.2 + 1), (false, f.2.1, f.2.2.1, 2)]), + (f.2.1 * f.2.2.2, [(true, f.2.1, f.2.2.1, f.2.2.2 + 1), (false, -f.2.1, 1-f.2.2.1, 2)])] + else + [(f.2.1, [(false, f.2.1, f.2.2.1, f.2.2.2 + 2)]), + (-f.2.1 * f.2.2.2, [(false, f.2.1, f.2.2.1, f.2.2.2 + 1)])] + +def diffProduct : List Factor → Expr + | [] => [] + | f :: l => multPrefix 1 l (diffFactor f) ++ multPrefix 1 [f] (diffProduct l) + +def diffTerm (t : Term) : Expr := multPrefix t.1 [] (diffProduct t.2) + +def diff (e : Expr) : Expr := e.flatMap diffTerm + +@[simp] theorem eval_nil (x : ℝ) : eval [] x = 0 := rfl + +@[simp] theorem eval_cons (t : Term) (e : Expr) (x : ℝ) : + eval (t :: e) x = evalTerm t x + eval e x := rfl + +@[simp] theorem eval_append (e d : Expr) (x : ℝ) : eval (e ++ d) x = eval e x + eval d x := by + simp [eval] + +@[simp] theorem evalProduct_nil (x : ℝ) : evalProduct [] x = 1 := rfl + +@[simp] theorem evalProduct_cons (f : Factor) (l : List Factor) (x : ℝ) : + evalProduct (f :: l) x = evalFactor f x * evalProduct l x := rfl + +@[simp] theorem evalProduct_append (l m : List Factor) (x : ℝ) : + evalProduct (l ++ m) x = evalProduct l x * evalProduct m x := by + simp [evalProduct] + +theorem eval_multPrefix (c : ℤ) (l : List Factor) (e : Expr) (x : ℝ) : + eval (multPrefix c l e) x = ((c : ℝ) * evalProduct l x) * eval e x := by + induction e with + | nil => simp [multPrefix] + | cons t e ih => + simp only [multPrefix, List.map_cons, eval_cons] at * + rw [ih] + simp only [evalTerm, evalProduct_append, Int.cast_mul] + ring + +theorem diffFactor_correct (f : Factor) (x : ℝ) : + HasDerivAt (evalFactor f) (eval (diffFactor f) x) x := by + rcases f with ⟨i, a, c, k⟩ + have ha : HasDerivAt (fun x : ℝ => (a : ℝ)*x+c) (a : ℝ) x := + by + convert HasDerivAt.add_const (c : ℝ) (HasDerivAt.const_mul (a : ℝ) (hasDerivAt_id x)) using 1 <;> first | rfl | simp + cases i + · have hh := (rhoTerm_hasDerivAt k ((a : ℝ)*x+c)).comp x ha + convert hh using 1 <;> try rfl + simp only [diffFactor, Bool.false_eq_true, ↓reduceIte, eval_cons, eval_nil, evalTerm, + evalProduct_cons, evalProduct_nil, evalFactor, Int.cast_neg, Int.cast_mul, Int.cast_natCast] + ring + · have hh := (denomInv_hasDerivAt k ((a : ℝ)*x+c)).comp x ha + convert hh using 1 <;> try rfl + simp only [diffFactor, ↓reduceIte, eval_cons, eval_nil, evalTerm, + evalProduct_cons, evalProduct_nil, evalFactor, Bool.false_eq_true, + Int.cast_neg, Int.cast_mul, Int.cast_natCast, Int.cast_sub, Int.cast_one] + rw [show -(a : ℝ)*x+(1-c) = 1-((a : ℝ)*x+c) by ring] + ring + +theorem diffProduct_correct (l : List Factor) (x : ℝ) : + HasDerivAt (evalProduct l) (eval (diffProduct l) x) x := by + induction l with + | nil => exact hasDerivAt_const x 1 + | cons f l ih => + have hh := (diffFactor_correct f x).mul ih + convert hh using 1 <;> try rfl + simp [diffProduct, eval_multPrefix, mul_comm] + +theorem diffTerm_correct (t : Term) (x : ℝ) : + HasDerivAt (evalTerm t) (eval (diffTerm t) x) x := by + convert (diffProduct_correct t.2 x).const_mul (t.1 : ℝ) using 1 <;> try rfl + simp [diffTerm, eval_multPrefix] + +theorem diff_correct (e : Expr) (x : ℝ) : HasDerivAt (eval e) (eval (diff e) x) x := by + induction e with + | nil => exact hasDerivAt_const x 0 + | cons t e ih => + convert (diffTerm_correct t x).add ih using 1 <;> try rfl + simp [diff, List.flatMap_cons] + +def jet (e : Expr) (n : ℕ) : Expr := diff^[n] e + +theorem jet_correct (e : Expr) (n : ℕ) : eval (jet e n) = iteratedDeriv n (eval e) := by + induction n with + | zero => rfl + | succ n ih => + rw [jet, Function.iterate_succ_apply'] + change eval (diff (jet e n)) = _ + rw [iteratedDeriv_succ, ← ih] + exact funext (fun x => (diff_correct (jet e n) x).deriv.symm) + +def clockExpr : Expr := [(1, [(false, 3, -1, 0), (true, 3, -1, 1)])] + +def bumpExpr : Expr := [(1, [(false, 8, 3, 0), (true, 8, 3, 1), + (false, -8, 3, 0), (true, -8, 3, 1)])] + +theorem eval_clockExpr : eval clockExpr = Profiles.clock := by + funext x + simp [clockExpr, eval, evalTerm, evalProduct, evalFactor, rhoTerm, denomInv, + Profiles.clock, Real.smoothTransition, div_eq_mul_inv, sub_eq_add_neg] + +theorem eval_bumpExpr : eval bumpExpr = Profiles.bump := by + funext x + norm_num [bumpExpr, eval, evalTerm, evalProduct, evalFactor, rhoTerm, denomInv, + Profiles.bump, Real.smoothTransition, div_eq_mul_inv, sub_eq_add_neg] + ring_nf + +def pulseBound (r : ℕ) : ℕ := bound (jet clockExpr (r+1)) + +def bumpBound (k : ℕ) : ℕ := bound (jet bumpExpr k) + +theorem pulseBound_spec (r : ℕ) (t : ℝ) : + |iteratedDeriv r (deriv Profiles.clock) t| ≤ (pulseBound r : ℝ) := by + have hc := eval_bound (jet clockExpr (r+1)) t + rwa [jet_correct, eval_clockExpr, iteratedDeriv_succ'] at hc + +theorem bumpBound_spec (k : ℕ) (y : ℝ) : + |iteratedDeriv k Profiles.bump y| ≤ (bumpBound k : ℝ) := by + have hc := eval_bound (jet bumpExpr k) y + rwa [jet_correct, eval_bumpExpr] at hc + +end ProfileJets + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Profiles.lean b/lean/OAI/Analysis/PeriodicLattice/Profiles.lean new file mode 100644 index 0000000000000000000000000000000000000000..5c5e577fbb2392de8fcbaeca3654ec73f8c2f867 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Profiles.lean @@ -0,0 +1,400 @@ +import OAI.Analysis.PeriodicLattice.Signals + +namespace OAI + +/-! Locally finite smooth profiles and their parameter estimates. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingProfiles {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Profiles + +open scoped ContDiff Topology +open Filter Set + +def clock (t : ℝ) : ℝ := + letI := threeAtLeastTwo + Real.smoothTransition (3 * t - 1) + +def bump (x : ℝ) : ℝ := + letI := threeAtLeastTwo + letI := eightAtLeastTwo + Real.smoothTransition (8 * x + 3) * Real.smoothTransition (3 - 8 * x) + +theorem clock_contDiff : ContDiff ℝ ∞ clock := by + unfold clock + fun_prop + +theorem clock_nonneg (t : ℝ) : 0 ≤ clock t := Real.smoothTransition.nonneg _ + +theorem clock_le_one (t : ℝ) : clock t ≤ 1 := Real.smoothTransition.le_one _ + +theorem clock_zero {t : ℝ} (ht : t ≤ 1 / 3) : clock t = 0 := by + apply Real.smoothTransition.zero_of_nonpos + linarith + +theorem clock_one {t : ℝ} (ht : 2 / 3 ≤ t) : clock t = 1 := by + apply Real.smoothTransition.one_of_one_le + linarith + +theorem clock_monotone : Monotone clock := by + intro t s h + exact Real.smoothTransition.monotone (by linarith) + +theorem bump_contDiff : ContDiff ℝ ∞ bump := by + unfold bump + fun_prop + +theorem bump_nonneg (x : ℝ) : 0 ≤ bump x := + mul_nonneg (Real.smoothTransition.nonneg _) (Real.smoothTransition.nonneg _) + +theorem bump_le_one (x : ℝ) : bump x ≤ 1 := by + unfold bump + exact (mul_le_of_le_one_left (Real.smoothTransition.nonneg _) + (Real.smoothTransition.le_one _)).trans (Real.smoothTransition.le_one _) + +theorem bump_one {x : ℝ} (hx : |x| ≤ 1 / 4) : bump x = 1 := by + obtain ⟨hlo, hhi⟩ := abs_le.mp hx + rw [bump, Real.smoothTransition.one_of_one_le (by linarith), + Real.smoothTransition.one_of_one_le (by linarith), one_mul] + +theorem bump_zero {x : ℝ} (hx : 3 / 8 ≤ |x|) : bump x = 0 := by + rcases le_abs.mp hx with h | h + · rw [bump, Real.smoothTransition.zero_of_nonpos (x := 3 - 8 * x) (by linarith), mul_zero] + · rw [bump, Real.smoothTransition.zero_of_nonpos (x := 8 * x + 3) (by linarith), zero_mul] + +theorem bump_support : Function.support bump ⊆ Set.Icc (-(3 / 8 : ℝ)) (3 / 8) := by + intro x hx + have h : |x| < 3 / 8 := lt_of_not_ge (fun h => hx (bump_zero h)) + exact ⟨by have := (abs_lt.mp h).1; linarith, (abs_lt.mp h).2.le⟩ + +theorem clock_deriv_eq_zero {t : ℝ} (ht : t < 1 / 3 ∨ 2 / 3 < t) : + deriv clock t = 0 := by + rcases ht with ht | ht + · have hev : clock =ᶠ[𝓝 t] (fun _ => (0 : ℝ)) := by + filter_upwards [Iio_mem_nhds ht] with s hs + exact clock_zero hs.le + simpa using hev.deriv_eq + · have hev : clock =ᶠ[𝓝 t] (fun _ => (1 : ℝ)) := by + filter_upwards [Ioi_mem_nhds ht] with s hs + exact clock_one hs.le + simpa using hev.deriv_eq + +theorem clock_deriv_contDiff : ContDiff ℝ ∞ (deriv clock) := + (contDiff_infty_iff_deriv.mp clock_contDiff).2 + +theorem lattice_intervals_locallyFinite : + LocallyFinite (fun j : ℤ => Set.Icc ((j : ℝ) - 3 / 8) ((j : ℝ) + 3 / 8)) := by + apply locallyFinite_Icc_of_tendsto + · simpa only [sub_eq_add_neg] using + tendsto_atTop_add_const_right atTop (-(3 / 8 : ℝ)) + (tendsto_intCast_atTop_atTop : Tendsto (fun j : ℤ => (j : ℝ)) atTop atTop) + · exact tendsto_atBot_add_const_right atBot (3 / 8 : ℝ) + (tendsto_intCast_atBot_iff.mpr tendsto_id) + +def latticeBump (e : ℝ) (j : ℤ) (y : ℝ) : ℝ := + letI := twoAtLeastTwo + bump ((y - 1 / 2) / e - j) + +theorem latticeBump_contDiff (e : ℝ) (j : ℤ) : ContDiff ℝ ∞ (latticeBump e j) := by + unfold latticeBump + exact bump_contDiff.comp ((contDiff_id.sub contDiff_const).div_const e |>.sub contDiff_const) + +theorem latticeBump_locallyFinite (e : ℝ) : + LocallyFinite (fun j : ℤ => Function.support (latticeBump e j)) := by + have hc : Continuous (fun y : ℝ => (y - 1 / 2) / e) := by fun_prop + apply (lattice_intervals_locallyFinite.preimage_continuous hc).subset + intro j y hy + have h := bump_support hy + simp only [Set.mem_preimage, Set.mem_Icc] at * + change -(3 / 8) ≤ (y - 1 / 2) / e - (j : ℝ) ∧ + (y - 1 / 2) / e - (j : ℝ) ≤ 3 / 8 at h + constructor <;> linarith + +def selector (e : ℝ) (A : ℤ → ℝ) (y : ℝ) : ℝ := ∑ᶠ j : ℤ, A j * latticeBump e j y + +theorem selector_contDiff (e : ℝ) (A : ℤ → ℝ) : ContDiff ℝ ∞ (selector e A) := by + apply contMDiff_iff_contDiff.mp + apply contMDiff_finsum + · intro j + exact contMDiff_iff_contDiff.mpr (contDiff_const.mul (latticeBump_contDiff e j)) + · apply (latticeBump_locallyFinite e).subset + intro j y hy + exact fun hz => hy (by simp [hz]) + +theorem other_bump_zero (e : ℝ) {y : ℝ} {j k : ℤ} + (hj : |(y - 1 / 2) / e - j| ≤ 1 / 4) (hkj : k ≠ j) : latticeBump e k y = 0 := by + obtain ⟨hlo, hhi⟩ := abs_le.mp hj + apply bump_zero + rcases lt_or_gt_of_ne hkj with hk | hk + · have hk' : (k : ℝ) + 1 ≤ (j : ℝ) := by exact_mod_cast (by omega : k + 1 ≤ j) + apply (le_abs).mpr (Or.inl ?_) + linarith + · have hk' : (j : ℝ) + 1 ≤ (k : ℝ) := by exact_mod_cast (by omega : j + 1 ≤ k) + apply (le_abs).mpr (Or.inr ?_) + linarith + +theorem selector_plateau (e : ℝ) (A : ℤ → ℝ) {y : ℝ} {j : ℤ} + (hj : |(y - 1 / 2) / e - j| ≤ 1 / 4) : selector e A y = A j := by + unfold selector + rw [finsum_eq_single _ j (fun k hk => by rw [other_bump_zero e hj hk, mul_zero])] + rw [latticeBump, bump_one hj, mul_one] + +theorem selector_shift (e : ℝ) (he : e ≠ 0) (A : ℤ → ℝ) (N : ℤ) + (hA : Function.Periodic A N) (y : ℝ) : + selector e A (y + e * N) = selector e A y := by + unfold selector + rw [← finsum_comp_equiv (Equiv.addRight N)] + apply finsum_congr + intro j + simp only [Equiv.coe_addRight, latticeBump, Int.cast_add] + rw [hA j] + congr 2 + field_simp + ring + +theorem selector_single {e y : ℝ} (A : ℤ → ℝ) {j : ℤ} + (hj : |(y - 1 / 2) / e - j| < 5 / 8) : + selector e A y = A j * latticeBump e j y := by + unfold selector + apply finsum_eq_single + intro k hk + have hz : latticeBump e k y = 0 := by + obtain ⟨hlo, hhi⟩ := abs_lt.mp hj + apply bump_zero + rcases lt_or_gt_of_ne hk with h | h + · have h' : (k : ℝ) + 1 ≤ (j : ℝ) := by exact_mod_cast (by omega : k + 1 ≤ j) + apply (le_abs).mpr (Or.inl ?_) + linarith + · have h' : (j : ℝ) + 1 ≤ (k : ℝ) := by exact_mod_cast (by omega : j + 1 ≤ k) + apply (le_abs).mpr (Or.inr ?_) + linarith + rw [hz, mul_zero] + +theorem selector_eventually_single {e y : ℝ} (A : ℤ → ℝ) {j : ℤ} + (hj : |(y - 1 / 2) / e - j| ≤ 1 / 2) : + selector e A =ᶠ[𝓝 y] (fun z => A j * latticeBump e j z) := by + have hc : Continuous (fun z : ℝ => |(z - 1 / 2) / e - (j : ℝ)|) := by fun_prop + have hy : |(y - 1 / 2) / e - j| < 5 / 8 := by linarith + filter_upwards [hc.continuousAt.eventually (gt_mem_nhds hy)] with z hz + exact selector_single A hz + +theorem latticeBump_iteratedDeriv (e : ℝ) (j : ℤ) (k : ℕ) : + iteratedDeriv k (latticeBump e j) = + fun y => (e⁻¹) ^ k * iteratedDeriv k bump ((y - 1 / 2) / e - j) := by + have ih : ContDiff ℝ k (fun z : ℝ => bump (z - j)) := + (bump_contDiff.comp (contDiff_id.sub contDiff_const)).of_le (WithTop.coe_le_coe.mpr le_top) + have heq : latticeBump e j = (fun z : ℝ => + (fun w : ℝ => bump (w - j)) (e⁻¹ * (z - 1 / 2))) := by + ext z + simp only [latticeBump, div_eq_mul_inv, mul_comm] + rw [heq, iteratedDeriv_comp_sub_const k (fun w => bump (e⁻¹ * w - j)) (1 / 2), + iteratedDeriv_comp_const_mul ih e⁻¹, iteratedDeriv_comp_sub_const] + simp only [div_eq_mul_inv, mul_comm] + +theorem selector_iteratedDeriv {e y : ℝ} (A : ℤ → ℝ) {j : ℤ} + (hj : |(y - 1 / 2) / e - j| ≤ 1 / 2) (k : ℕ) : + iteratedDeriv k (selector e A) y = + A j * (e⁻¹) ^ k * iteratedDeriv k bump ((y - 1 / 2) / e - j) := by + rw [(selector_eventually_single A hj).iteratedDeriv_eq, + iteratedDeriv_const_mul_field, latticeBump_iteratedDeriv] + exact (mul_assoc _ _ _).symm + +theorem selector_derivative_bound {e B D : ℝ} (he : 0 < e) (A : ℤ → ℝ) (k : ℕ) + (hA : ∀ j, |A j| ≤ B) (hD : ∀ z, |iteratedDeriv k bump z| ≤ D) (y : ℝ) : + |iteratedDeriv k (selector e A) y| ≤ B * (e⁻¹) ^ k * D := by + let z : ℝ := (y - 1 / 2) / e + let j : ℤ := ⌊z + 1 / 2⌋ + have hj₁ := Int.floor_le (z + 1 / 2) + have hj₂ := Int.lt_floor_add_one (z + 1 / 2) + have hj : |(y - 1 / 2) / e - (j : ℝ)| ≤ 1 / 2 := by + apply abs_le.mpr + dsimp [z, j] at * + constructor <;> linarith + rw [selector_iteratedDeriv A hj, abs_mul, abs_mul, + abs_of_nonneg (pow_nonneg (inv_nonneg.mpr he.le) k)] + have hB : 0 ≤ B := (abs_nonneg _).trans (hA j) + exact mul_le_mul (mul_le_mul_of_nonneg_right (hA j) (by positivity)) + (hD _) (abs_nonneg _) (by positivity) + +def shiftedClock (n : ℕ) (t : ℝ) : ℝ := clock (t - n) + +def pulse (n : ℕ) (t : ℝ) : ℝ := deriv clock (t - n) + +theorem shiftedClock_contDiff (n : ℕ) : ContDiff ℝ ∞ (shiftedClock n) := + clock_contDiff.comp (contDiff_id.sub contDiff_const) + +theorem pulse_contDiff (n : ℕ) : ContDiff ℝ ∞ (pulse n) := + clock_deriv_contDiff.comp (contDiff_id.sub contDiff_const) + +theorem shiftedClock_hasDerivAt (n : ℕ) (t : ℝ) : + HasDerivAt (shiftedClock n) (pulse n t) t := by + have hd := ((contDiff_infty_iff_deriv.mp clock_contDiff).1 (t - n)).hasDerivAt + exact hd.comp_sub_const t (n : ℝ) + +theorem pulse_eq_zero {n : ℕ} {t : ℝ} (ht : t < n + 1 / 3 ∨ n + 2 / 3 < t) : + pulse n t = 0 := by + apply clock_deriv_eq_zero + rcases ht with ht | ht + · exact Or.inl (by linarith) + · exact Or.inr (by linarith) + +theorem pulse_support (n : ℕ) : + Function.support (pulse n) ⊆ Icc ((n : ℝ) + 1 / 3) (n + 2 / 3) := by + intro t ht + constructor + · by_contra h + exact ht (pulse_eq_zero (Or.inl (lt_of_not_ge h))) + · by_contra h + exact ht (pulse_eq_zero (Or.inr (lt_of_not_ge h))) + +theorem time_tails_locallyFinite : LocallyFinite (fun n : ℕ => Ici (n : ℝ)) := by + intro t + refine ⟨Iio (t + 1), Iio_mem_nhds (by linarith), ?_⟩ + apply (finite_Iic ⌈t + 1⌉₊).subset + rintro n ⟨s, hs, hs'⟩ + have hn : (n : ℝ) ≤ (⌈t + 1⌉₊ : ℝ) := + hs.trans ((le_of_lt hs').trans (Nat.le_ceil _)) + exact_mod_cast hn + +theorem shiftedClock_locallyFinite : + LocallyFinite (fun n : ℕ => Function.support (shiftedClock n)) := by + apply time_tails_locallyFinite.subset + intro n t ht + by_contra h + have hn : t < (n : ℝ) := lt_of_not_ge h + exact ht (clock_zero (by linarith)) + +theorem pulse_locallyFinite : LocallyFinite (fun n : ℕ => Function.support (pulse n)) := by + apply time_tails_locallyFinite.subset + intro n t ht + have := (pulse_support n ht).1 + change (n : ℝ) ≤ t + linarith + +theorem other_pulse_zero {n m : ℕ} (hne : m ≠ n) {t : ℝ} + (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) : pulse m t = 0 := by + apply pulse_eq_zero + rcases lt_or_gt_of_ne hne with h | h + · have h' : (m : ℝ) + 1 ≤ (n : ℝ) := by exact_mod_cast h + exact Or.inr (by linarith) + · have h' : (n : ℝ) + 1 ≤ (m : ℝ) := by exact_mod_cast h + exact Or.inl (by linarith) + +def schedule {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + (V : ℕ → ℝ → E) (t y : ℝ) : E := ∑ᶠ n : ℕ, pulse n t • V n y + +theorem schedule_contDiff {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + (V : ℕ → ℝ → E) (hV : ∀ n, ContDiff ℝ ∞ (V n)) : + ContDiff ℝ ∞ (fun ty : ℝ × ℝ => schedule V ty.1 ty.2) := by + apply contMDiff_iff_contDiff.mp + apply contMDiff_finsum + · intro n + exact contMDiff_iff_contDiff.mpr + (((pulse_contDiff n).comp contDiff_fst).smul ((hV n).comp contDiff_snd)) + · apply (pulse_locallyFinite.preimage_continuous continuous_fst).subset + intro n ty hty + exact fun hz => hty (by simp [hz]) + +theorem schedule_on_slot {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + (V : ℕ → ℝ → E) (n : ℕ) {t : ℝ} (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) + (y : ℝ) : schedule V t y = pulse n t • V n y := by + apply finsum_eq_single + intro m hm + rw [other_pulse_zero hm ht ht', zero_smul] + +theorem schedule_zero_at_start {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + (V : ℕ → ℝ → E) (y : ℝ) : schedule V 0 y = 0 := by + rw [schedule_on_slot V 0 (by norm_num) (by norm_num), + pulse_eq_zero (Or.inl (by norm_num)), zero_smul] + +theorem selector_unit_periodic {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) + (A : ℤ → ℝ) (hA : Function.Periodic A (Scales.capacity b L n : ℤ)) : + Function.Periodic (selector (Scales.epsilon b L n) A) 1 := by + obtain ⟨m, hm⟩ := Scales.capacity_dvd_inverseScale b L n + have hp : Function.Periodic A (b ^ Scales.exponent L n : ℕ) := by + rw [hm, Nat.cast_mul, mul_comm] + exact hA.nat_mul m + have he := Scales.epsilon_pos hb L n + have hscale : Scales.epsilon b L n * ((b ^ Scales.exponent L n : ℕ) : ℤ) = (1 : ℝ) := by + have hb0 : (b : ℝ) ≠ 0 := by exact_mod_cast (show b ≠ 0 by omega) + simpa [Scales.epsilon] using inv_mul_cancel₀ (pow_ne_zero (Scales.exponent L n) hb0) + intro y + simpa only [hscale] using selector_shift _ (ne_of_gt he) A _ hp y + +theorem schedule_eventually_on_slot {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + (V : ℕ → ℝ → E) (n : ℕ) {t : ℝ} (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) : + (fun s => schedule V s) =ᶠ[𝓝 t] (fun s y => pulse n s • V n y) := by + filter_upwards [Ioo_mem_nhds (show (n : ℝ) - 1 / 3 < t by linarith) + (show t < n + 4 / 3 by linarith)] with s hs + funext y + apply finsum_eq_single + intro m hm + have hz : pulse m s = 0 := by + apply pulse_eq_zero + rcases lt_or_gt_of_ne hm with h | h + · have h' : (m : ℝ) + 1 ≤ (n : ℝ) := by exact_mod_cast h + exact Or.inr (by linarith [hs.1]) + · have h' : (n : ℝ) + 1 ≤ (m : ℝ) := by exact_mod_cast h + exact Or.inl (by linarith [hs.2]) + rw [hz, zero_smul] + +def mixedPartial {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + (r k : ℕ) (v : ℝ → ℝ → E) (t y : ℝ) : E := + iteratedDeriv r (fun s => iteratedDeriv k (v s) y) t + +theorem schedule_mixedPartial {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + (V : ℕ → ℝ → E) (r k n : ℕ) {t : ℝ} (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) + (y : ℝ) : + mixedPartial r k (schedule V) t y = + iteratedDeriv r (pulse n) t • iteratedDeriv k (V n) y := by + have heq : (fun s => iteratedDeriv k (schedule V s) y) =ᶠ[𝓝 t] + (fun s => pulse n s • iteratedDeriv k (V n) y) := by + filter_upwards [schedule_eventually_on_slot V n ht ht'] with s hs + rw [hs, iteratedDeriv_fun_const_smul_field] + rw [mixedPartial, heq.iteratedDeriv_eq r] + exact iteratedDeriv_smul_const + ((pulse_contDiff n).of_le (WithTop.coe_le_coe.mpr le_top)).contDiffAt _ + +theorem pulse_iteratedDeriv (n r : ℕ) (t : ℝ) : + iteratedDeriv r (pulse n) t = iteratedDeriv r (deriv clock) (t - n) := by + exact congrFun (iteratedDeriv_comp_sub_const r (deriv clock) (n : ℝ)) t + +theorem compact_iteratedDeriv {f : ℝ → ℝ} (h : HasCompactSupport f) (k : ℕ) : + HasCompactSupport (iteratedDeriv k f) := by + induction k with + | zero => simpa using h + | succ k ih => rw [iteratedDeriv_succ]; exact ih.deriv + +theorem bump_hasCompactSupport : HasCompactSupport bump := + HasCompactSupport.of_support_subset_isCompact isCompact_Icc bump_support + +theorem clock_deriv_hasCompactSupport : HasCompactSupport (deriv clock) := by + apply HasCompactSupport.intro (K := Icc (1 / 3 : ℝ) (2 / 3)) isCompact_Icc + intro t ht + apply clock_deriv_eq_zero + simpa only [mem_Icc, not_and_or, not_le] using ht + +theorem profile_derivative_bounds (r k : ℕ) : + ∃ T D : ℕ, (∀ t, |iteratedDeriv r (deriv clock) t| ≤ T) ∧ + (∀ y, |iteratedDeriv k bump y| ≤ D) := by + obtain ⟨T, hT⟩ := (clock_deriv_contDiff.continuous_iteratedDeriv r + (WithTop.coe_le_coe.mpr le_top)).bounded_above_of_compact_support + (compact_iteratedDeriv clock_deriv_hasCompactSupport r) + obtain ⟨D, hD⟩ := (bump_contDiff.continuous_iteratedDeriv k + (WithTop.coe_le_coe.mpr le_top)).bounded_above_of_compact_support + (compact_iteratedDeriv bump_hasCompactSupport k) + obtain ⟨T', hT'⟩ := exists_nat_gt T + obtain ⟨D', hD'⟩ := exists_nat_gt D + exact ⟨T', D', fun t => (hT t).trans hT'.le, fun y => (hD y).trans hD'.le⟩ + +end Profiles + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/RapidBounds.lean b/lean/OAI/Analysis/PeriodicLattice/RapidBounds.lean new file mode 100644 index 0000000000000000000000000000000000000000..be501c4ff1f36fde91e979fe3b2b98232c7e5a33 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/RapidBounds.lean @@ -0,0 +1,367 @@ +import OAI.Analysis.PeriodicLattice.DerivativeWords + +namespace OAI + +/-! Rapid decay estimates for all profile derivatives. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingRapidBounds {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace RapidCalculus + +open Set Filter Topology TorusCalculus +open scoped ContDiff + +structure BoundedProfile (h : ℝ → ℝ) : Prop where + smooth : ContDiff ℝ ∞ h + bound : ∀ k : ℕ, ∃ C : ℝ, ∀ z : ℝ, ‖iteratedDeriv k h z‖ ≤ C + +theorem BoundedProfile.deriv {h : ℝ → ℝ} (hh : BoundedProfile h) : + BoundedProfile (deriv h) := by + refine ⟨ContDiff.iterate_deriv 1 hh.smooth, fun k => ?_⟩ + simpa only [iteratedDeriv_succ'] using hh.bound (k + 1) + +theorem BoundedProfile.neg {h : ℝ → ℝ} (hh : BoundedProfile h) : + BoundedProfile (-h) := by + refine ⟨hh.smooth.neg, fun k => ?_⟩ + obtain ⟨C, hC⟩ := hh.bound k + exact ⟨C, fun z => by simpa only [iteratedDeriv_neg, Pi.neg_apply, norm_neg] using hC z⟩ + +inductive Algebra : ScalarField → Prop + | zero : Algebra 0 + | tensor (F : ScalarField) (f : ℝ → ℝ → ℝ) (h : ℝ → ℝ) + (hf : Rapid2 f) (hh : BoundedProfile h) + (cover : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) : Algebra F + | add {F G : ScalarField} : Algebra F → Algebra G → Algebra (F + G) + | mul {F G : ScalarField} : Algebra F → Algebra G → Algebra (F * G) + | scale (c : ℝ) {F : ScalarField} : Algebra F → Algebra (c • F) + +theorem Algebra.smooth {F : ScalarField} (hF : Algebra F) : ContDiff ℝ ∞ (lifted F) := by + induction hF with + | zero => exact contDiff_const + | tensor F f h hf hh he => + have hc (i : Fin 3) : ContDiff ℝ ∞ (fun tx : ℝ × Space => tx.2 i) := + (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) i).contDiff.comp contDiff_snd + change ContDiff ℝ ∞ (fun tx : ℝ × Space => F tx.1 (torusMk tx.2)) + simp_rw [he] + exact (hh.smooth.comp (hc 2)).mul (hf.smooth.comp (contDiff_fst.prodMk (hc 1))) + | add hF hG ihF ihG => exact ihF.add ihG + | mul hF hG ihF ihG => exact ihF.mul ihG + | scale c hF ihF => exact (contDiff_const : ContDiff ℝ ∞ (fun _ : ℝ × Space => c)).smul ihF + +theorem Algebra.bound {F : ScalarField} (hF : Algebra F) (J : ℕ) : + ∃ C : ℝ, ∀ t : ℝ, 0 ≤ t → ∀ q : Torus, (1 + t) ^ J * ‖F t q‖ ≤ C := by + induction hF generalizing J with + | zero => exact ⟨0, fun t _ q => by simp⟩ + | tensor F f h hf hh he => + obtain ⟨C, hC⟩ := hf.bound [] J + obtain ⟨D, hD⟩ := hh.bound 0 + have hD₀ : 0 ≤ D := (norm_nonneg _).trans (hD 0) + refine ⟨D * C, fun t ht q => ?_⟩ + obtain ⟨x, rfl⟩ := mk_surjective q + rw [he, norm_mul] + calc + _ = ‖h (x 2)‖ * ((1 + t) ^ J * ‖f t (x 1)‖) := by ring + _ ≤ D * ((1 + t) ^ J * ‖f t (x 1)‖) := + mul_le_mul_of_nonneg_right (hD (x 2)) (by positivity) + _ ≤ D * C := mul_le_mul_of_nonneg_left (hC t ht (x 1)) hD₀ + | @add F G hF hG ihF ihG => + obtain ⟨C, hC⟩ := ihF J + obtain ⟨D, hD⟩ := ihG J + refine ⟨C + D, fun t ht q => ?_⟩ + change (1 + t) ^ J * ‖F t q + G t q‖ ≤ C + D + calc + _ ≤ (1 + t) ^ J * (‖F t q‖ + ‖G t q‖) := mul_le_mul_of_nonneg_left (norm_add_le _ _) (by positivity) + _ ≤ C + D := by rw [mul_add]; exact add_le_add (hC t ht q) (hD t ht q) + | @mul F G hF hG ihF ihG => + obtain ⟨C, hC⟩ := ihF J + obtain ⟨D, hD⟩ := ihG 0 + have hD₀ : 0 ≤ D := by + have hz : ‖G 0 0‖ ≤ D := by simpa only [pow_zero, one_mul] using hD 0 le_rfl 0 + exact (norm_nonneg _).trans hz + refine ⟨C * D, fun t ht q => ?_⟩ + change (1 + t) ^ J * ‖F t q * G t q‖ ≤ C * D + rw [norm_mul, ← mul_assoc] + calc + _ ≤ ((1 + t) ^ J * ‖F t q‖) * D := mul_le_mul_of_nonneg_left (by simpa using hD t ht q) (by positivity) + _ ≤ C * D := mul_le_mul_of_nonneg_right (hC t ht q) hD₀ + | @scale c F hF ihF => + obtain ⟨C, hC⟩ := ihF J + refine ⟨‖c‖ * C, fun t ht q => ?_⟩ + change (1 + t) ^ J * ‖c • F t q‖ ≤ ‖c‖ * C + rw [norm_smul, mul_left_comm] + exact mul_le_mul_of_nonneg_left (hC t ht q) (norm_nonneg _) + +theorem tensor_spaceD_zero {F : ScalarField} {f : ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (he : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) : spaceD 0 F = 0 := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + rw [spaceD_cover] + simp only [spaceLift, he] + change deriv (fun s : ℝ => h (x 2 + 0) * f t (x 1 + 0)) 0 = 0 + exact deriv_const _ _ + +theorem tensor_spaceD_one {F : ScalarField} {f : ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hf : ContDiff ℝ ∞ (Function.uncurry f)) + (he : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) (t : ℝ) (x : Space) : + spaceD 1 F t (torusMk x) = h (x 2) * biD false f t (x 1) := by + rw [spaceD_cover] + simp only [spaceLift, he] + change deriv (fun s : ℝ => h (x 2 + 0) * f t (x 1 + s)) 0 = _ + have hd := (((hf.comp ((contDiff_const (c := t)).prodMk contDiff_id)).differentiable (by simp) (x 1 + 0)).hasDerivAt.comp 0 + ((hasDerivAt_id (0 : ℝ)).const_add (x 1))).const_mul (h (x 2)) + simpa [biD, Function.comp_def] using hd.deriv + +theorem tensor_spaceD_two {F : ScalarField} {f : ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hh : ContDiff ℝ ∞ h) + (he : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) (t : ℝ) (x : Space) : + spaceD 2 F t (torusMk x) = deriv h (x 2) * f t (x 1) := by + rw [spaceD_cover] + simp only [spaceLift, he] + change deriv (fun s : ℝ => h (x 2 + s) * f t (x 1 + 0)) 0 = _ + have hd := (((hh.differentiable (by simp) (x 2 + 0)).hasDerivAt.comp 0 + ((hasDerivAt_id (0 : ℝ)).const_add (x 2))).mul_const (f t (x 1))) + simpa [Function.comp_def] using hd.deriv + +theorem tensor_fullTimeD {F : ScalarField} {f : ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hf : ContDiff ℝ ∞ (Function.uncurry f)) + (he : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) (t : ℝ) (x : Space) : + fullTimeD F t (torusMk x) = h (x 2) * biD true f t (x 1) := by + simp only [fullTimeD, he] + exact deriv_const_mul _ ((hf.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + +theorem Algebra.spaceDeriv {F : ScalarField} (hF : Algebra F) (i : Fin 3) : Algebra (spaceD i F) := by + induction hF with + | zero => + have hz : spaceD i (0 : ScalarField) = 0 := by funext t q; exact deriv_const _ _ + rw [hz]; exact Algebra.zero + | tensor F f h hf hh he => + fin_cases i + · change Algebra (spaceD 0 F) + rw [tensor_spaceD_zero he]; exact Algebra.zero + · exact Algebra.tensor _ _ _ (hf.biD false) hh (tensor_spaceD_one hf.smooth he) + · exact Algebra.tensor _ _ _ hf hh.deriv (tensor_spaceD_two hh.smooth he) + | @add F G hF hG ihF ihG => + have he : spaceD i (F + G) = spaceD i F + spaceD i G := by + funext t q + exact TorusCalculus.spaceD_add + ((hF.smooth.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp)) + ((hG.smooth.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp)) i q + rw [he]; exact ihF.add ihG + | @mul F G hF hG ihF ihG => + have he : spaceD i (F * G) = spaceD i F * G + F * spaceD i G := by + funext t q + exact spaceD_smul hF.smooth hG.smooth i t q + rw [he]; exact (ihF.mul hG).add (hF.mul ihG) + | @scale c F hF ihF => + have he : spaceD i (c • F) = c • spaceD i F := by + funext t q + exact deriv_const_mul _ (hasDerivAt_translation hF.smooth t q i 0).differentiableAt + rw [he]; exact ihF.scale c + +theorem Algebra.timeDeriv {F : ScalarField} (hF : Algebra F) : Algebra (fullTimeD F) := by + induction hF with + | zero => + have hz : fullTimeD (0 : ScalarField) = 0 := by funext t q; exact deriv_const _ _ + rw [hz]; exact Algebra.zero + | tensor F f h hf hh he => + exact Algebra.tensor _ _ _ (hf.biD true) hh (tensor_fullTimeD hf.smooth he) + | @add F G hF hG ihF ihG => + have he : fullTimeD (F + G) = fullTimeD F + fullTimeD G := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + exact deriv_add + ((hF.smooth.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + ((hG.smooth.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + rw [he]; exact ihF.add ihG + | @mul F G hF hG ihF ihG => + have he : fullTimeD (F * G) = fullTimeD F * G + F * fullTimeD G := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + exact deriv_mul + ((hF.smooth.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + ((hG.smooth.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + rw [he]; exact (ihF.mul hG).add (hF.mul ihG) + | @scale c F hF ihF => + have he : fullTimeD (c • F) = c • fullTimeD F := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + exact deriv_const_mul _ + ((hF.smooth.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) t) + rw [he]; exact ihF.scale c + +theorem boundedProfile_of_periodic {h : ℝ → ℝ} (hs : ContDiff ℝ ∞ h) + (hp : Function.Periodic h 1) : BoundedProfile h := by + refine ⟨hs, fun k => ?_⟩ + have hpk : Function.Periodic (iteratedDeriv k h) 1 := by + induction k with + | zero => exact hp + | succ k ih => simpa only [iteratedDeriv_succ] using periodic_deriv ih + have hsk : ContDiff ℝ ∞ (iteratedDeriv k h) := by + rw [iteratedDeriv_eq_iterate]; exact ContDiff.iterate_deriv _ hs + obtain ⟨C, hC⟩ := (hpk.isBounded_of_continuous (by norm_num) hsk.continuous).exists_norm_le + exact ⟨C, fun z => hC _ (mem_range_self z)⟩ + +def VectorAlgebra (U : VectorField) : Prop := ∀ j : Fin 3, Algebra (fun t q => U t q j) + +theorem VectorAlgebra.smooth {U : VectorField} (hU : VectorAlgebra U) : + ContDiff ℝ ∞ (lifted U) := contDiff_euclidean.mpr fun j => (hU j).smooth + +theorem VectorAlgebra.spaceDeriv {U : VectorField} (hU : VectorAlgebra U) (i : Fin 3) : + VectorAlgebra (spaceD i U) := by + intro j + have he : (fun t q => spaceD i U t q j) = spaceD i (fun t q => U t q j) := by + funext t q + exact (spaceD_component ((hU.smooth.comp (contDiff_const.prodMk contDiff_id)).differentiable + (by simp)) i j q).symm + rw [he]; exact (hU j).spaceDeriv i + +theorem VectorAlgebra.timeDeriv {U : VectorField} (hU : VectorAlgebra U) : + VectorAlgebra (fullTimeD U) := by + intro j + have he : (fun t q => fullTimeD U t q j) = fullTimeD (fun t q => U t q j) := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + have ht := ((hU.smooth.comp (contDiff_id.prodMk (contDiff_const (c := x)))).differentiable (by simp) t).hasDerivAt + exact ((PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) j).hasFDerivAt.comp_hasDerivAt t ht).deriv.symm + rw [he]; exact (hU j).timeDeriv + +theorem VectorAlgebra.add {U V : VectorField} (hU : VectorAlgebra U) (hV : VectorAlgebra V) : + VectorAlgebra (U + V) := fun j => (hU j).add (hV j) + +theorem VectorAlgebra.scale {U : VectorField} (hU : VectorAlgebra U) (c : ℝ) : + VectorAlgebra (c • U) := fun j => (hU j).scale c + +theorem VectorAlgebra.sub {U V : VectorField} (hU : VectorAlgebra U) (hV : VectorAlgebra V) : + VectorAlgebra (U - V) := by + have he : U - V = U + (-1 : ℝ) • V := by simp [sub_eq_add_neg] + rw [he]; exact hU.add (hV.scale (-1)) + +theorem VectorAlgebra.diffusion {U : VectorField} (hU : VectorAlgebra U) : + VectorAlgebra (laplacian U) := by + have he : laplacian U = spaceD 0 (spaceD 0 U) + spaceD 1 (spaceD 1 U) + + spaceD 2 (spaceD 2 U) := by funext t q; exact Fin.sum_univ_three _ + rw [he] + exact ((hU.spaceDeriv 0).spaceDeriv 0).add + ((hU.spaceDeriv 1).spaceDeriv 1) |>.add ((hU.spaceDeriv 2).spaceDeriv 2) + +theorem VectorAlgebra.selfTransport {U : VectorField} (hU : VectorAlgebra U) : + VectorAlgebra (advection U) := by + intro j + have he : (fun t q => advection U t q j) = + (fun t q => U t q 0 * spaceD 0 U t q j) + + (fun t q => U t q 1 * spaceD 1 U t q j) + + (fun t q => U t q 2 * spaceD 2 U t q j) := by + funext t q + simp only [advection, Fin.sum_univ_three, PiLp.add_apply, PiLp.smul_apply, Pi.add_apply, smul_eq_mul] + rw [he] + exact ((hU 0).mul (hU.spaceDeriv 0 j)).add + ((hU 1).mul (hU.spaceDeriv 1 j)) |>.add ((hU 2).mul (hU.spaceDeriv 2 j)) + +theorem VectorAlgebra.fullForce {U : VectorField} (hU : VectorAlgebra U) (ν : ℝ) : + VectorAlgebra (Residual.fullForce ν U) := (hU.timeDeriv.add hU.selfTransport).sub (hU.diffusion.scale ν) + +theorem norm_le_sum_components (x : Space) : ‖x‖ ≤ ∑ i : Fin 3, ‖x i‖ := by + have hx : x = ∑ i : Fin 3, EuclideanSpace.single i (x i) := by + ext j + fin_cases j <;> simp [Fin.sum_univ_three] + calc + ‖x‖ = ‖∑ i : Fin 3, EuclideanSpace.single i (x i)‖ := congrArg norm hx + _ ≤ ∑ i : Fin 3, ‖EuclideanSpace.single i (x i)‖ := norm_sum_le _ _ + _ = _ := by simp + +theorem VectorAlgebra.bound {U : VectorField} (hU : VectorAlgebra U) (J : ℕ) : + ∃ C : ℝ, ∀ t : ℝ, 0 ≤ t → ∀ q : Torus, (1 + t) ^ J * ‖U t q‖ ≤ C := by + choose C hC using fun i => (hU i).bound J + refine ⟨∑ i : Fin 3, C i, fun t ht q => ?_⟩ + calc + _ ≤ (1 + t) ^ J * ∑ i : Fin 3, ‖U t q i‖ := + mul_le_mul_of_nonneg_left (norm_le_sum_components (U t q)) (by positivity) + _ = ∑ i : Fin 3, (1 + t) ^ J * ‖U t q i‖ := Finset.mul_sum _ _ _ + _ ≤ _ := Finset.sum_le_sum (fun i _ => hC i t ht q) + +theorem iterate_timeD_eq_fullTimeD {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (r : ℕ) : + ∀ t : ℝ, 0 ≤ t → ∀ q, timeD^[r] F t q = fullTimeD^[r] F t q := by + have hsm (k : ℕ) : ContDiff ℝ ∞ (lifted (fullTimeD^[k] F)) := by + induction k with + | zero => exact hF + | succ k ih => rw [Function.iterate_succ_apply']; exact contDiff_fullTimeD ih + induction r with + | zero => exact fun _ _ _ => rfl + | succ r ih => + intro t ht q + rw [Function.iterate_succ_apply', Function.iterate_succ_apply'] + rw [timeD_congr_nonneg ih ht] + exact timeD_eq_fullTimeD (hsm r) ht q + +theorem VectorAlgebra.mixed_bound {U : VectorField} (hU : VectorAlgebra U) + (r J : ℕ) (α : MultiIndex) : + ∃ C : ℝ, ∀ t : ℝ, 0 ≤ t → ∀ q : Torus, (1 + t) ^ J * ‖mixedD r α U t q‖ ≤ C := by + have hsp (V : VectorField) (hV : VectorAlgebra V) (i : Fin 3) (k : ℕ) : + VectorAlgebra ((spaceD i)^[k] V) := by + induction k with + | zero => exact hV + | succ k ih => rw [Function.iterate_succ_apply']; exact ih.spaceDeriv i + let V := (spaceD 2)^[α 2] ((spaceD 1)^[α 1] ((spaceD 0)^[α 0] U)) + have hV : VectorAlgebra V := hsp _ (hsp _ (hsp _ hU 0 _) 1 _) 2 _ + have htime : VectorAlgebra (fullTimeD^[r] V) := by + induction r with + | zero => exact hV + | succ r ih => rw [Function.iterate_succ_apply']; exact ih.timeDeriv + obtain ⟨C, hC⟩ := htime.bound J + refine ⟨C, fun t ht q => ?_⟩ + change (1 + t) ^ J * ‖timeD^[r] V t q‖ ≤ C + rw [iterate_timeD_eq_fullTimeD hV.smooth r t ht] + exact hC t ht q + +theorem rapidPair_of_algebra {U G : VectorField} (hU : VectorAlgebra U) (hG : VectorAlgebra G) : + ∃ C : ℕ → MultiIndex → ℕ → ℕ, RapidPair U G C := by + have hc (r : ℕ) (α : MultiIndex) (J : ℕ) : ∃ N : ℕ, ∀ t : ℝ, 0 ≤ t → + spatialSup (mixedD r α U) t + spatialSup (mixedD r α G) t ≤ (N : ℝ) / (1 + t) ^ J := by + obtain ⟨C, hC⟩ := hU.mixed_bound r J α + obtain ⟨D, hD⟩ := hG.mixed_bound r J α + obtain ⟨N, hN⟩ := exists_nat_ge (C + D) + refine ⟨N, fun t ht => ?_⟩ + have hpos : 0 < (1 + t) ^ J := by positivity + have hsup {F : VectorField} {B : ℝ} (hF : ∀ q, (1 + t) ^ J * ‖F t q‖ ≤ B) : + spatialSup F t ≤ B / (1 + t) ^ J := by + apply csSup_le (Set.range_nonempty _) + rintro _ ⟨q, rfl⟩ + exact (le_div_iff₀ hpos).mpr (by simpa only [mul_comm] using hF q) + calc + _ ≤ C / (1 + t) ^ J + D / (1 + t) ^ J := add_le_add (hsup (hC t ht)) (hsup (hD t ht)) + _ = (C + D) / (1 + t) ^ J := (add_div _ _ _).symm + _ ≤ _ := div_le_div_of_nonneg_right hN hpos.le + choose C hC using hc + exact ⟨C, fun r J α t ht => hC r α J t ht⟩ + +end RapidCalculus + +namespace FluidLift +open scoped ContDiff +open RapidCalculus + +theorem velocity_algebra (d : Input) (hd : d.WellFormed) : VectorAlgebra (velocity d) := by + intro i + have hs := boundedProfile_of_periodic slope_contDiff slope_periodic + have he := boundedProfile_of_periodic eta_contDiff eta_periodic + fin_cases i + · exact Algebra.tensor _ _ _ (a_rapid2 d hd) hs (fun t x => by simp) + · exact Algebra.tensor _ _ _ (b_rapid2 d hd) hs (fun t x => by simp) + · exact Algebra.tensor _ _ _ ((b_rapid2 d hd).biD false) he.neg (fun t x => by simp [bdy, biD]) + +theorem force_rapid (ν : ℝ) (d : Input) (hd : d.WellFormed) : + ∃ C : ℕ → MultiIndex → ℕ → ℕ, RapidPair (velocity d) (force ν d) C := + rapidPair_of_algebra (velocity_algebra d hd) ((velocity_algebra d hd).fullForce ν) + +end FluidLift + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/RationalArithmetic.lean b/lean/OAI/Analysis/PeriodicLattice/RationalArithmetic.lean new file mode 100644 index 0000000000000000000000000000000000000000..3b6281f4034f2afdc1b792eea4853b037311433f --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/RationalArithmetic.lean @@ -0,0 +1,256 @@ +import OAI.Analysis.PeriodicLattice.FieldCertificates + +namespace OAI + +/-! Uniform lattice constants and computable reduced rational arithmetic. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingRationalArithmetic {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace RecursiveArithmetic + +theorem program_of_computable {α β : Type*} [Primcodable α] [Primcodable β] + {f : α → β} (hf : Computable f) : + ∃ P : Program, ∀ a, Encodable.encode (f a) ∈ P.eval (Encodable.encode a) := by + obtain ⟨P,hP⟩ := Nat.Partrec.Code.exists_code.mp hf + refine ⟨P,fun a => ?_⟩ + rw [hP] + simp +end RecursiveArithmetic + +namespace Quantitative + +noncomputable def latticeConstants (ν : ℝ) (N : ℕ) (hν : ‖ν‖ ≤ N) + (d : Input) (r : ℕ) (α : MultiIndex) (J : ℕ) : ℕ := + velocityCertificate.mixedBudget d r α J + (forceCertificate ν N hν).mixedBudget d r α J + + (solenoidalForceCertificate ν N hν).mixedBudget d r α J + +theorem latticeConstants_effective (ν : ℝ) (N : ℕ) (hν : ‖ν‖ ≤ N) : + EffectiveConstants (latticeConstants ν N hν) := by + have hc : Primrec (fun p : Input × ℕ × MultiIndex × ℕ => + latticeConstants ν N hν p.1 p.2.1 p.2.2.1 p.2.2.2) := + Primrec.nat_add.comp (Primrec.nat_add.comp velocityCertificate.mixedBudget_recursive + (forceCertificate ν N hν).mixedBudget_recursive) (solenoidalForceCertificate ν N hν).mixedBudget_recursive + obtain ⟨P,hP⟩ := RecursiveArithmetic.program_of_computable hc.to_comp + exact ⟨P,fun d _ r α J => hP (d,r,α,J)⟩ + +theorem latticeConstants_bounds (ν : ℝ) (N : ℕ) (hν : ‖ν‖ ≤ N) (d : Input) (hd : d.WellFormed) : + RapidPair (FluidLift.velocity d) (FluidLift.force ν d) (latticeConstants ν N hν d) ∧ + RapidPair (FluidLift.velocity d) (FluidLift.solenoidalForce ν d) (latticeConstants ν N hν d) := by + have hpair {F G : Input → VectorField} (hf : FieldCertificate F) (hg : FieldCertificate G) + {C : ℕ → MultiIndex → ℕ → ℕ} + (hc : ∀ r α J, hf.mixedBudget d r α J + hg.mixedBudget d r α J ≤ C r α J) : RapidPair (F d) (G d) C := by + intro r J α t ht + calc + _ ≤ (hf.mixedBudget d r α J : ℝ) / (1+t)^J + (hg.mixedBudget d r α J : ℝ) / (1+t)^J := + add_le_add (hf.sup_estimate d hd r α J ht) (hg.sup_estimate d hd r α J ht) + _ = ((hf.mixedBudget d r α J + hg.mixedBudget d r α J : ℕ) : ℝ) / (1+t)^J := by rw [Nat.cast_add, add_div] + _ ≤ _ := div_le_div_of_nonneg_right (Nat.cast_le.mpr (hc r α J)) (by positivity) + constructor + · exact hpair velocityCertificate (forceCertificate ν N hν) (fun r α J => Nat.le_add_right _ _) + · apply hpair velocityCertificate (solenoidalForceCertificate ν N hν) + intro r α J + exact Nat.add_le_add_right (Nat.le_add_right _ _) _ +end Quantitative + +namespace RecursiveArithmetic +open Encodable Primrec + +theorem natDvd : PrimrecRel (fun a b : ℕ => a ∣ b) := + (Primrec.eq.comp (Primrec.nat_mod.comp Primrec.snd Primrec.fst) (Primrec.const 0)).of_eq + (fun _ => Nat.dvd_iff_mod_eq_zero.symm) + +def gcdSearch (a b : ℕ) : ℕ := + Nat.findGreatest (fun k => k ∣ a ∧ k ∣ b) (a+b) + +theorem gcdSearch_eq (a b : ℕ) : gcdSearch a b = Nat.gcd a b := by + unfold gcdSearch + by_cases hab : a + b = 0 + · have ha : a = 0 := by omega + have hb : b = 0 := by omega + simp [ha, hb] + have hpos : 0 < Nat.gcd a b := Nat.gcd_pos_iff.mpr (by omega) + have hle : Nat.gcd a b ≤ a + b := Nat.le_of_dvd (by omega) + (dvd_add (Nat.gcd_dvd_left a b) (Nat.gcd_dvd_right a b)) + have hs : (Nat.findGreatest (fun k => k ∣ a ∧ k ∣ b) (a+b)) ∣ a ∧ + (Nat.findGreatest (fun k => k ∣ a ∧ k ∣ b) (a+b)) ∣ b := + Nat.findGreatest_spec (P := fun k => k ∣ a ∧ k ∣ b) hle ⟨Nat.gcd_dvd_left _ _, Nat.gcd_dvd_right _ _⟩ + apply le_antisymm + · exact Nat.le_of_dvd hpos (Nat.dvd_gcd + hs.1 + hs.2) + · exact Nat.le_findGreatest hle ⟨Nat.gcd_dvd_left _ _, Nat.gcd_dvd_right _ _⟩ + +@[fun_prop] theorem nat_gcd : Primrec (fun p : ℕ × ℕ => Nat.gcd p.1 p.2) := by + have h := Primrec.nat_findGreatest (Primrec.nat_add.comp Primrec.fst Primrec.snd) + ((natDvd.comp (Primrec.snd) (Primrec.fst.comp Primrec.fst)).and + (natDvd.comp (Primrec.snd) (Primrec.snd.comp Primrec.fst))).primrecRel + exact h.of_eq (fun p => gcdSearch_eq p.1 p.2) + +theorem natCoprime : PrimrecRel Nat.Coprime := + (Primrec.eq.comp nat_gcd (Primrec.const 1)).of_eq (fun _ => Iff.rfl) + +theorem reducedPred : PrimrecPred (fun p : ℤ × ℕ => 0 < p.2 ∧ p.1.natAbs.Coprime p.2) := + (Primrec.nat_lt.comp (Primrec.const 0) Primrec.snd).and + (natCoprime.comp (intNatAbs.comp Primrec.fst) Primrec.snd) + +abbrev ReducedPair := {p : ℤ × ℕ // 0 < p.2 ∧ p.1.natAbs.Coprime p.2} +local instance rationalArithmeticLocal1 : Primcodable ReducedPair := Primcodable.subtype reducedPred + +def ratEquiv : ℚ ≃ ReducedPair where + toFun q := ⟨(q.num, q.den), Nat.pos_of_ne_zero q.den_nz, q.reduced⟩ + invFun p := ⟨p.1.1, p.1.2, Nat.ne_of_gt p.2.1, p.2.2⟩ + left_inv _ := rfl + right_inv _ := rfl + +@[instance_reducible] def rationalPrimcodable : Primcodable ℚ := Primcodable.ofEquiv _ ratEquiv + +private theorem encodable_ext {α : Type*} {e f : Encodable α} + (he : e.encode = f.encode) (hd : e.decode = f.decode) : e = f := by + cases e + cases f + cases he + cases hd + rfl + +theorem rational_encoding : rationalPrimcodable.toEncodable = Rat.instEncodable := by + refine encodable_ext (e := rationalPrimcodable.toEncodable) (f := Rat.instEncodable) rfl ?_ + funext n + dsimp +instances only [rationalPrimcodable, rationalArithmeticLocal1, Primcodable.ofEquiv, Primcodable.subtype, Primcodable.prod, Primcodable.ofDenumerable, Denumerable.int, Denumerable.nat, ratEquiv, + Rat.instEncodable, Encodable.ofEquiv, Encodable.ofLeftInverse, Encodable.ofLeftInjection, + Encodable.decodeSubtype, Encodable.decodeSigma, Encodable.Prod.encodable, + Subtype.encodable, Sigma.encodable, Int.encodable, Nat.encodable, + Option.bind_some, Option.map_some, Equiv.symm_symm, Equiv.sigmaEquivProd, Equiv.coe_fn_mk, Equiv.coe_fn_symm_mk] + simp only [Function.comp_apply, Option.bind_some] + split_ifs with h + · cases h with + | intro hp hc => rfl + · rfl + +local instance ratPrimcodable : Primcodable ℚ := + { toEncodable := Rat.instEncodable + prim := by + rw [← rational_encoding] + exact @Primcodable.prim ℚ rationalPrimcodable } + +@[simp] theorem ratEncoding (q : ℚ) : encode q = Nat.pair (encode q.num) q.den := rfl + +@[fun_prop] theorem ratNum : Primrec Rat.num := by + exact Primrec.encode_iff.mp (((Primrec.fst.comp Primrec.unpair).comp + (Primrec.encode : Primrec (encode : ℚ → ℕ))).of_eq (fun q => by simp)) + +@[fun_prop] theorem ratDen : Primrec Rat.den := by + exact ((Primrec.snd.comp Primrec.unpair).comp + (Primrec.encode : Primrec (encode : ℚ → ℕ))).of_eq (fun q => by simp) + +@[fun_prop] theorem int_div : Primrec (fun p : ℤ × ℤ => p.1 / p.2) := by + have hc : Primrec (fun p : ℤ × ℤ => + if p.2 = 0 then 0 else if p.1 < 0 then + if p.2 < 0 then (((p.1.natAbs-1) / p.2.natAbs + 1 : ℕ) : ℤ) + else Int.negSucc ((p.1.natAbs-1) / p.2.natAbs) + else if p.2 < 0 then -((p.1.natAbs / p.2.natAbs : ℕ) : ℤ) + else ((p.1.natAbs / p.2.natAbs : ℕ) : ℤ)) := by + apply Primrec.ite (Primrec.eq.comp Primrec.snd (Primrec.const 0)) (Primrec.const 0) + apply Primrec.ite (intNegative.comp Primrec.fst) + · apply Primrec.ite (intNegative.comp Primrec.snd) + · fun_prop + · exact intNegSucc.comp (by fun_prop) + · apply Primrec.ite (intNegative.comp Primrec.snd) <;> fun_prop + exact hc.of_eq (fun p => by + rcases p with ⟨a,b⟩ + cases a with + | ofNat a => + cases b with + | ofNat b => + simp only [Int.ofNat_eq_natCast, Int.natAbs_natCast, + not_lt_of_ge (Int.natCast_nonneg _), ↓reduceIte, Int.natCast_ediv] + split_ifs with hb <;> simp_all + | negSucc b => + rw [Int.ofNat_ediv_negSucc] + simp only [Int.ofNat_eq_natCast, Int.negSucc_ne_zero, Int.negSucc_lt_zero, + not_lt_of_ge (Int.natCast_nonneg _), ↓reduceIte, + Int.natAbs_natCast, Int.natAbs_negSucc] + | negSucc a => + cases b with + | ofNat b => + cases b with + | zero => simp + | succ b => simp only [Int.ofNat_eq_natCast, + Int.natCast_eq_zero, Nat.succ_ne_zero, Int.negSucc_lt_zero, + not_lt_of_ge (Int.natCast_nonneg _), ↓reduceIte, Int.natAbs_natCast, + Int.natAbs_negSucc, + Int.negSucc_ediv_ofNat_succ, Nat.succ_sub_one] + | negSucc b => simp [Int.negSucc_ediv_negSucc]) + +@[fun_prop] theorem ratMk : Primrec (fun p : ℤ × ℕ => mkRat p.1 p.2) := by + apply Primrec.encode_iff.mp + have hc : Primrec (fun p : ℤ × ℕ => + if p.2 = 0 then encode (0 : ℚ) else + Nat.pair (encode (p.1 / (Nat.gcd p.2 p.1.natAbs : ℤ))) + (p.2 / Nat.gcd p.2 p.1.natAbs)) := by + apply Primrec.ite (Primrec.eq.comp Primrec.snd (Primrec.const 0)) (Primrec.const _) + apply Primrec₂.natPair.comp + · exact Primrec.encode.comp (by fun_prop) + · fun_prop + exact hc.of_eq (fun p => by + simp only [ratEncoding, Rat.num_mkRat, Rat.den_mkRat] + split_ifs <;> simp [*]) + +@[fun_prop] theorem ratInt : Primrec (fun z : ℤ => (z : ℚ)) := by + apply Primrec.encode_iff.mp + exact (Primrec₂.natPair.comp Primrec.encode (Primrec.const 1)).of_eq + (fun z => by simp) + +@[fun_prop] theorem ratNat : Primrec (fun n : ℕ => (n : ℚ)) := + (ratInt.comp intOfNat).of_eq (fun _ => by simp) + +@[fun_prop] theorem rat_add : Primrec (fun p : ℚ × ℚ => p.1 + p.2) := by + have hc : Primrec (fun p : ℚ × ℚ => + mkRat (p.1.num * p.2.den + p.2.num * p.1.den) (p.1.den * p.2.den)) := by + exact ratMk.comp (show Primrec (fun p : ℚ × ℚ => + (p.1.num * p.2.den + p.2.num * p.1.den, p.1.den * p.2.den)) from by fun_prop) + exact hc.of_eq (fun p => by simp [Rat.add_def, Rat.normalize_eq_mkRat]) + +@[fun_prop] theorem rat_mul : Primrec (fun p : ℚ × ℚ => p.1 * p.2) := by + have hc : Primrec (fun p : ℚ × ℚ => mkRat (p.1.num * p.2.num) (p.1.den * p.2.den)) := by + exact ratMk.comp (show Primrec (fun p : ℚ × ℚ => + (p.1.num * p.2.num, p.1.den * p.2.den)) from by fun_prop) + exact hc.of_eq (fun p => by simp [Rat.mul_def, Rat.normalize_eq_mkRat]) + +@[fun_prop] theorem ratNeg : Primrec (fun q : ℚ => -q) := by + have hc : Primrec (fun q : ℚ => mkRat (-q.num) q.den) := by + exact ratMk.comp (show Primrec (fun q : ℚ => (-q.num, q.den)) from by fun_prop) + exact hc.of_eq (fun q => by simp [Rat.neg_def, Rat.divInt_ofNat]) + +@[fun_prop] theorem ratDivInt : Primrec (fun p : ℤ × ℤ => Rat.divInt p.1 p.2) := by + have hc : Primrec (fun p : ℤ × ℤ => + if p.2 < 0 then mkRat (-p.1) p.2.natAbs else mkRat p.1 p.2.natAbs) := + Primrec.ite (intNegative.comp Primrec.snd) (by fun_prop) (by fun_prop) + exact hc.of_eq (fun p => by + rcases p with ⟨a,b⟩ + cases b <;> simp [Rat.divInt, Rat.normalize_eq_mkRat]) + +@[fun_prop] theorem ratInv : Primrec (fun q : ℚ => q⁻¹) := by + exact (ratDivInt.comp (show Primrec (fun q : ℚ => ((q.den : ℤ), q.num)) from by fun_prop)).of_eq (fun q => (Rat.inv_def q).symm) + +@[fun_prop] theorem rat_sub : Primrec (fun p : ℚ × ℚ => p.1 - p.2) := by + simpa only [sub_eq_add_neg] using rat_add.comp (Primrec.fst.pair (ratNeg.comp Primrec.snd)) + +@[fun_prop] theorem rat_div : Primrec (fun p : ℚ × ℚ => p.1 / p.2) := by + simpa only [div_eq_mul_inv] using rat_mul.comp (Primrec.fst.pair (ratInv.comp Primrec.snd)) + +@[fun_prop] theorem rat_pow : Primrec (fun p : ℚ × ℕ => p.1 ^ p.2) := by + exact (Primrec.nat_iterate Primrec.snd (Primrec.const (1 : ℚ)) + (rat_mul.comp (Primrec.snd.pair (Primrec.fst.comp Primrec.fst))).to₂).of_eq + (fun p => by dsimp only; induction p.2 <;> simp_all [pow_succ']) + +end RecursiveArithmetic + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Scales.lean b/lean/OAI/Analysis/PeriodicLattice/Scales.lean new file mode 100644 index 0000000000000000000000000000000000000000..2e3313ceaa1c1f4a19e3d09200dc722934858641 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Scales.lean @@ -0,0 +1,335 @@ +import OAI.Analysis.PeriodicLattice.Basic + +namespace OAI + +/-! Temporal scales, smooth profile parameters and derivative budgets. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingScales {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Scales + +def width (wordLength n : ℕ) : ℕ := wordLength + 1 + 2 * n + +def codeExponent (wordLength n : ℕ) : ℕ := 2 * width wordLength n + 1 + +def capacity (b wordLength n : ℕ) : ℕ := b ^ codeExponent wordLength n + +def exponent (wordLength n : ℕ) : ℕ := + (codeExponent wordLength 0 + 10) * 2 ^ (n * (n + 1)) + +def epsilon (b wordLength n : ℕ) : ℝ := ((b : ℝ) ^ exponent wordLength n)⁻¹ + +def beta (b wordLength : ℕ) (n : ℕ) : ℝ := + letI := fourAtLeastTwo + if n = 0 then 1 / 4 else epsilon b wordLength n + +@[simp] theorem width_succ (L n : ℕ) : width L (n + 1) = width L n + 2 := by + simp only [width] + omega + +@[simp] theorem codeExponent_zero (L : ℕ) : codeExponent L 0 = 2 * L + 3 := by + simp [codeExponent, width] + omega + +theorem codeExponent_eq (L n : ℕ) : + codeExponent L n = codeExponent L 0 + 4 * n := by + simp only [codeExponent, width] + omega + +@[simp] theorem codeExponent_succ (L n : ℕ) : + codeExponent L (n + 1) = codeExponent L n + 4 := by + simp only [codeExponent, width_succ] + omega + +@[simp] theorem exponent_zero (L : ℕ) : exponent L 0 = 2 * L + 13 := by + simp [exponent] + +theorem exponent_pos (L n : ℕ) : 0 < exponent L n := by + unfold exponent + positivity + +theorem exponent_succ (L n : ℕ) : + exponent L (n + 1) = 2 ^ (2 * n + 2) * exponent L n := by + unfold exponent + have h : (n + 1) * (n + 1 + 1) = (2 * n + 2) + n * (n + 1) := by ring + rw [h, pow_add] + ac_rfl + +theorem growthFactor_ge_four (n : ℕ) : 4 ≤ 2 ^ (2 * n + 2) := by + calc + 4 = (2 : ℕ) ^ 2 := by norm_num + _ ≤ 2 ^ (2 * n + 2) := Nat.pow_le_pow_right (by decide) (by omega) + +theorem four_mul_exponent_le (L n : ℕ) : + 4 * exponent L n ≤ exponent L (n + 1) := by + rw [exponent_succ] + exact Nat.mul_le_mul_right _ (growthFactor_ge_four n) + +theorem exponent_strictMono (L : ℕ) : StrictMono (exponent L) := by + apply strictMono_nat_of_lt_succ + intro n + have hp := exponent_pos L n + have hg := four_mul_exponent_le L n + omega + +theorem exponent_ge_nextCode (L n : ℕ) : codeExponent L (n + 1) ≤ exponent L n := by + induction n with + | zero => simp + | succ n ih => + have h := four_mul_exponent_le L n + have hp : 3 ≤ codeExponent L (n + 1) := by + rw [codeExponent_eq, codeExponent_zero] + omega + rw [codeExponent_succ] + omega + +theorem codeExponent_le_exponent (L n : ℕ) : codeExponent L n ≤ exponent L n := by + have := exponent_ge_nextCode L n + rw [codeExponent_succ] at this + omega + +theorem exponent_gap (L : ℕ) {k n : ℕ} (hkn : k < n) : + codeExponent L n ≤ exponent L n - exponent L k := by + obtain ⟨m, rfl⟩ := Nat.exists_eq_succ_of_ne_zero (by omega : n ≠ 0) + have hk : k ≤ m := by omega + have hm := (exponent_strictMono L).monotone hk + have hg := four_mul_exponent_le L m + have hc := exponent_ge_nextCode L m + simp only [Nat.succ_eq_add_one] at * + omega + +theorem capacity_dvd_inverseScale (b L n : ℕ) : + capacity b L n ∣ b ^ exponent L n := by + exact pow_dvd_pow b (codeExponent_le_exponent L n) + +theorem capacity_dvd_scaleRatio (b L : ℕ) {k n : ℕ} (hkn : k < n) : + capacity b L n ∣ b ^ (exponent L n - exponent L k) := by + exact pow_dvd_pow b (exponent_gap L hkn) + +theorem index_le_exponent (L n : ℕ) : n ≤ exponent L n := by + induction n with + | zero => omega + | succ n ih => + have := exponent_strictMono L (Nat.lt_succ_self n) + simp only [Nat.succ_eq_add_one] at * + omega + +theorem exponent_ge_thirteen (L n : ℕ) : 13 ≤ exponent L n := by + have h := (exponent_strictMono L).monotone (Nat.zero_le n) + simp only [exponent_zero] at h + omega + +theorem epsilon_pos {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : 0 < epsilon b L n := by + unfold epsilon + have : (0 : ℝ) < b := by exact_mod_cast (by omega : 0 < b) + positivity + +theorem epsilon_le_one {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : epsilon b L n ≤ 1 := by + unfold epsilon + have hb' : (1 : ℝ) ≤ b := by exact_mod_cast (by omega : 1 ≤ b) + exact inv_le_one_of_one_le₀ (one_le_pow₀ hb') + +theorem epsilon_antitone {b : ℕ} (hb : 2 ≤ b) (L : ℕ) : + StrictAnti (epsilon b L) := by + intro m n hmn + unfold epsilon + have hb' : (1 : ℝ) < b := by exact_mod_cast (by omega : 1 < b) + have hm : (0 : ℝ) < (b : ℝ) ^ exponent L m := by positivity + have hpow : (b : ℝ) ^ exponent L m < (b : ℝ) ^ exponent L n := + pow_lt_pow_right₀ hb' (exponent_strictMono L hmn) + simpa only [one_div] using one_div_lt_one_div_of_lt hm hpow + +theorem plateau_power_bound {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : + (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) ≤ + epsilon b L n ^ (2 ^ (2 * n + 2) - 1) := by + have hb' : (1 : ℝ) ≤ b := by exact_mod_cast (by omega : 1 ≤ b) + have hbpos : (0 : ℝ) < b := by exact_mod_cast (by omega : 0 < b) + have hA : 1 ≤ 2 ^ (2 * n + 2) := by have := growthFactor_ge_four n; omega + have hpow : (b : ℝ) ^ codeExponent L (n + 1) ≤ (b : ℝ) ^ exponent L n := + pow_le_pow_right₀ hb' (exponent_ge_nextCode L n) + have hid : (b : ℝ) ^ exponent L (n + 1) = + (b : ℝ) ^ exponent L n * + ((b : ℝ) ^ exponent L n) ^ (2 ^ (2 * n + 2) - 1) := by + rw [← pow_mul, ← pow_add, exponent_succ] + congr 1 + have ha : 2 ^ (2 * n + 2) - 1 + 1 = 2 ^ (2 * n + 2) := by omega + nlinarith + unfold epsilon capacity + push_cast + calc + (b : ℝ) ^ codeExponent L (n + 1) * ((b : ℝ) ^ exponent L (n + 1))⁻¹ ≤ + (b : ℝ) ^ exponent L n * ((b : ℝ) ^ exponent L (n + 1))⁻¹ := + mul_le_mul_of_nonneg_right hpow (by positivity) + _ = (((b : ℝ) ^ exponent L n)⁻¹) ^ (2 ^ (2 * n + 2) - 1) := by + rw [hid, mul_inv, inv_pow] + have hne : (b : ℝ) ^ exponent L n ≠ 0 := by positivity + field_simp + +theorem epsilon_le_small {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : + epsilon b L n ≤ 1 / 8192 := by + have hb' : (2 : ℝ) ≤ b := by exact_mod_cast hb + have hpow : (8192 : ℝ) ≤ (b : ℝ) ^ exponent L n := by + calc + (8192 : ℝ) = (2 : ℝ) ^ 13 := by norm_num + _ ≤ (2 : ℝ) ^ exponent L n := + pow_le_pow_right₀ (by norm_num) (exponent_ge_thirteen L n) + _ ≤ (b : ℝ) ^ exponent L n := pow_le_pow_left₀ (by norm_num) hb' _ + simpa only [epsilon, one_div] using + one_div_le_one_div_of_le (by norm_num : (0 : ℝ) < 8192) hpow + +theorem epsilon_cube_lt_quarter {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : + epsilon b L n ^ 3 < epsilon b L n / 4 := by + have he := epsilon_pos hb L n + have hs := epsilon_le_small hb L n + have hsq : epsilon b L n ^ 2 < 1 / 4 := by nlinarith + have h := mul_lt_mul_of_pos_right hsq he + nlinarith + +theorem plateau_bound {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : + (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) ≤ + epsilon b L n ^ (2 ^ (2 * n + 2) - 1) ∧ + epsilon b L n ^ (2 ^ (2 * n + 2) - 1) ≤ epsilon b L n ^ 3 ∧ + epsilon b L n ^ 3 < epsilon b L n / 4 := by + refine ⟨plateau_power_bound hb L n, ?_, epsilon_cube_lt_quarter hb L n⟩ + apply pow_le_pow_of_le_one (epsilon_pos hb L n).le (epsilon_le_one hb L n) + have := growthFactor_ge_four n + omega + +theorem epsilon_le_geometric {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : + epsilon b L n ≤ accuracy n := by + have hb' : (2 : ℝ) ≤ b := by exact_mod_cast hb + have hpow : (2 : ℝ) ^ n ≤ (b : ℝ) ^ exponent L n := by + calc + (2 : ℝ) ^ n ≤ (2 : ℝ) ^ exponent L n := + pow_le_pow_right₀ (by norm_num) (index_le_exponent L n) + _ ≤ (b : ℝ) ^ exponent L n := pow_le_pow_left₀ (by norm_num) hb' _ + simpa only [epsilon, accuracy, zpow_neg, zpow_natCast, one_div] using + one_div_le_one_div_of_le (by positivity : (0 : ℝ) < (2 : ℝ) ^ n) hpow + +@[simp] theorem beta_zero (b L : ℕ) : beta b L 0 = 1 / 4 := by simp [beta] + +@[simp] theorem beta_succ (b L n : ℕ) : beta b L (n + 1) = epsilon b L (n + 1) := by + simp [beta] + +theorem beta_pos {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : 0 < beta b L n := by + unfold beta + split_ifs + · norm_num + · exact epsilon_pos hb L n + +theorem beta_strictAnti {b : ℕ} (hb : 2 ≤ b) (L : ℕ) : StrictAnti (beta b L) := by + apply strictAnti_nat_of_succ_lt + intro n + rw [beta_succ] + by_cases hn : n = 0 + · rw [hn, beta_zero] + have := epsilon_le_small hb L (0 + 1) + linarith + · rw [beta, ite_eq_right hn] + exact epsilon_antitone hb L (Nat.lt_succ_self n) + +theorem beta_le_quarter {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : beta b L n ≤ 1 / 4 := by + simpa only [beta_zero] using (beta_strictAnti hb L).antitone (Nat.zero_le n) + +theorem growthFactor_ge_index (n : ℕ) : n + 4 ≤ 2 ^ (2 * n + 2) := by + induction n with + | zero => norm_num + | succ n ih => + have h : 2 * (n + 1) + 2 = (2 * n + 2) + 2 := by omega + rw [h, pow_add] + norm_num at * + omega + +theorem differentiated_record_bound {b : ℕ} (hb : 2 ≤ b) (L : ℕ) + {k n : ℕ} (hkn : k ≤ n) : + (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) / + epsilon b L n ^ k ≤ epsilon b L n := by + apply (div_le_iff₀ (pow_pos (epsilon_pos hb L n) k)).2 + calc + (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) ≤ + epsilon b L n ^ (2 ^ (2 * n + 2) - 1) := plateau_power_bound hb L n + _ ≤ epsilon b L n ^ (k + 1) := by + apply pow_le_pow_of_le_one (epsilon_pos hb L n).le (epsilon_le_one hb L n) + have := growthFactor_ge_index n + omega + _ = epsilon b L n * epsilon b L n ^ k := by ring + +def slotSize (b L k n : ℕ) : ℝ := + (if k = 0 then beta b L n else 0) + + (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) / epsilon b L n ^ k + +theorem slotSize_le {b : ℕ} (hb : 2 ≤ b) (L : ℕ) + {k n : ℕ} (hn : 1 ≤ n) (hkn : k ≤ n) : + slotSize b L k n ≤ 2 * epsilon b L n := by + have hrec := differentiated_record_bound hb L hkn + have hbeta : beta b L n = epsilon b L n := by simp [beta, show n ≠ 0 by omega] + unfold slotSize + split_ifs + · rw [hbeta] + linarith + · have := (epsilon_pos hb L n).le + linarith + +def weightBound (J : ℕ) : ℕ := 2 ^ (J + 3) * J.factorial + +theorem polynomial_geometric_bound (J n : ℕ) : + ((n : ℝ) + 3) ^ J * accuracy n ≤ (weightBound J : ℝ) := by + have hexp_half : Real.exp (1 / 2) ≤ 2 := by + have h := Real.exp_bound_div_one_sub_of_interval + (by norm_num : (0 : ℝ) ≤ 1 / 2) (by norm_num : (1 / 2 : ℝ) < 1) + norm_num at h + exact h + have hexp : Real.exp (((n : ℝ) + 3) / 2) ≤ (2 : ℝ) ^ (n + 3) := by + calc + Real.exp (((n : ℝ) + 3) / 2) = (Real.exp (1 / 2)) ^ (n + 3) := by + rw [← Real.exp_nat_mul] + congr 1 + push_cast + ring + _ ≤ (2 : ℝ) ^ (n + 3) := + pow_le_pow_left₀ (Real.exp_pos _).le hexp_half _ + have hfac : (0 : ℝ) < (J.factorial : ℝ) := by positivity + have h := Real.pow_div_factorial_le_exp (((n : ℝ) + 3) / 2) (by positivity) J + have hpoly : ((n : ℝ) + 3) ^ J ≤ + (2 : ℝ) ^ J * (J.factorial : ℝ) * (2 : ℝ) ^ (n + 3) := by + rw [div_pow, div_div] at h + have h' := (div_le_iff₀ (mul_pos (by positivity) hfac)).1 (h.trans hexp) + nlinarith + unfold accuracy weightBound + rw [zpow_neg, zpow_natCast] + push_cast + calc + ((n : ℝ) + 3) ^ J * ((2 : ℝ) ^ n)⁻¹ ≤ + ((2 : ℝ) ^ J * (J.factorial : ℝ) * (2 : ℝ) ^ (n + 3)) * + ((2 : ℝ) ^ n)⁻¹ := mul_le_mul_of_nonneg_right hpoly (by positivity) + _ = (2 : ℝ) ^ (J + 3) * (J.factorial : ℝ) := by + rw [pow_add, pow_add] + have hne : (2 : ℝ) ^ n ≠ 0 := by positivity + field_simp + +theorem weighted_slotSize_bound {b : ℕ} (hb : 2 ≤ b) (L J : ℕ) + {k n : ℕ} (hn : 1 ≤ n) (hkn : k ≤ n) {t : ℝ} + (ht : 0 ≤ t) (htop : t ≤ (n : ℝ) + 2) : + (1 + t) ^ J * slotSize b L k n ≤ 2 * (weightBound J : ℝ) := by + have hslot := slotSize_le hb L hn hkn + have heps : (1 + t) ^ J * epsilon b L n ≤ (weightBound J : ℝ) := by + calc + (1 + t) ^ J * epsilon b L n ≤ + ((n : ℝ) + 3) ^ J * accuracy n := + mul_le_mul (pow_le_pow_left₀ (by linarith) (by linarith) J) + (epsilon_le_geometric hb L n) (epsilon_pos hb L n).le (by positivity) + _ ≤ (weightBound J : ℝ) := polynomial_geometric_bound J n + have h := mul_le_mul_of_nonneg_left hslot (by positivity : (0 : ℝ) ≤ (1 + t) ^ J) + nlinarith + +end Scales + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Signals.lean b/lean/OAI/Analysis/PeriodicLattice/Signals.lean new file mode 100644 index 0000000000000000000000000000000000000000..a44b22ec6da9db9838270a67acd09ade6a4761c3 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Signals.lean @@ -0,0 +1,205 @@ +import OAI.Analysis.PeriodicLattice.Machines + +namespace OAI + +/-! Smooth machine signals and planar residual fields. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingSignals {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Signal + +open Scales + +def inSlot (b L n : ℕ) (halt : Bool) (s : ℝ) : ℝ := + 1 / 2 - beta b L n + + s * (beta b L n - beta b L (n + 1) + if halt then 2 * beta b L (n + 1) else 0) + +theorem start (b L n : ℕ) (h : Bool) : + inSlot b L n h 0 = 1 / 2 - beta b L n := by simp [inSlot] + +theorem nonhalting_end (b L n : ℕ) : + inSlot b L n false 1 = 1 / 2 - beta b L (n + 1) := by + simp only [inSlot, Bool.false_eq_true, ↓reduceIte, add_zero, one_mul] + ring + +theorem halting_end (b L n : ℕ) : + inSlot b L n true 1 = 1 / 2 + beta b L (n + 1) := by + simp only [inSlot, ↓reduceIte, one_mul] + ring + +theorem nonhalting_interval {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) {s : ℝ} + (hs : 0 ≤ s) (hs' : s ≤ 1) : + 1 / 2 - beta b L n ≤ inSlot b L n false s ∧ + inSlot b L n false s ≤ 1 / 2 - beta b L (n + 1) ∧ + 1 / 4 ≤ inSlot b L n false s ∧ inSlot b L n false s < 1 / 2 := by + have hdec := beta_strictAnti hb L (Nat.lt_succ_self n) + have hδ : 0 ≤ beta b L n - beta b L (n + 1) := by linarith + have hmlo := mul_nonneg hs hδ + have hmhi := mul_le_mul_of_nonneg_right hs' hδ + have hβ := beta_pos hb L (n + 1) + have hβ' := beta_le_quarter hb L n + simp only [inSlot, Bool.false_eq_true, ↓reduceIte, add_zero, one_mul] at * + constructor + · linarith + constructor + · linarith + constructor <;> linarith + +theorem halting_interval {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) : + 1 / 2 < inSlot b L n true 1 ∧ inSlot b L n true 1 < 1 := by + rw [halting_end] + have hp := beta_pos hb L (n + 1) + have hq := beta_le_quarter hb L (n + 1) + constructor <;> linarith + +theorem displacement_in_plateau {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) + {c : ℕ} (hc : c < capacity b L (n + 1)) {s : ℝ} (hs : 0 ≤ s) (hs' : s ≤ 1) : + 0 ≤ s * epsilon b L (n + 1) * c ∧ + s * epsilon b L (n + 1) * c < epsilon b L n / 4 := by + have he := epsilon_pos hb L (n + 1) + have hc' : (c : ℝ) ≤ (capacity b L (n + 1) : ℝ) := by exact_mod_cast hc.le + have hle : s * epsilon b L (n + 1) * c ≤ + (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) := by + calc + s * epsilon b L (n + 1) * c ≤ 1 * epsilon b L (n + 1) * c := + mul_le_mul_of_nonneg_right (mul_le_mul_of_nonneg_right hs' he.le) (by positivity) + _ ≤ (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) := by + simpa only [one_mul, mul_comm] using mul_le_mul_of_nonneg_right hc' he.le + obtain ⟨ha, hb', hc'⟩ := plateau_bound hb L n + exact ⟨mul_nonneg (mul_nonneg hs he.le) (by positivity), hle.trans_lt (ha.trans hb' |>.trans_lt hc')⟩ + +theorem history_in_plateau {b : ℕ} (hb : 2 ≤ b) (L n : ℕ) (c : ℕ → ℕ) + (hc : c (n + 1) < capacity b L (n + 1)) {s : ℝ} (hs : 0 ≤ s) (hs' : s ≤ 1) : + |(History.coordinate b L c n + s * epsilon b L (n + 1) * c (n + 1) - 1 / 2) / + epsilon b L n - (History.address b L c n : ℝ)| < 1 / 4 := by + have he := epsilon_pos hb L n + obtain ⟨hlo, hhi⟩ := displacement_in_plateau hb L n hc hs hs' + rw [show History.coordinate b L c n + + s * epsilon b L (n + 1) * (c (n + 1) : ℝ) - 1 / 2 = + (History.coordinate b L c n - 1 / 2) + + s * epsilon b L (n + 1) * (c (n + 1) : ℝ) by ring, + add_div, History.read_coordinate hb, add_sub_cancel_left, + abs_of_nonneg (div_nonneg hlo he.le)] + apply (div_lt_iff₀ he).2 + linarith + +end Signal + +namespace Residual + +def force (ν : ℝ) (u : VectorField) : VectorField := + fun t q => timeD u t q + advection u t q - ν • laplacian u t q + +@[simp] theorem spaceD_zero (i : Fin 3) : spaceD i (0 : ScalarField) = 0 := by + funext t q + simp [spaceD] + +@[simp] theorem gradient_zero : gradient (0 : ScalarField) = 0 := by + funext t q + ext i + simp [gradient, spaceD_zero] + +theorem spaceD_neg (i : Fin 3) (p : ScalarField) : spaceD i (-p) = -spaceD i p := by + funext t q + exact deriv.neg + +@[simp] theorem gradient_neg (p : ScalarField) : gradient (-p) = -gradient p := by + funext t q + ext i + change spaceD i (-p) t q = -spaceD i p t q + exact congrFun (congrFun (spaceD_neg i p) t) q + +theorem divergence_gradient (p : ScalarField) : divergence (gradient p) = laplacian p := by + rfl + +theorem equations (ν : ℝ) (u : VectorField) (hdiv : Solenoidal u) + (hinit : ∀ q, u 0 q = 0) : NavierStokes ν (force ν u) u 0 := by + refine ⟨?_, hdiv, hinit⟩ + intro t ht q + rw [gradient_zero] + simp only [Pi.zero_apply, neg_zero, zero_add, force] + abel + +theorem projection_equations (ν : ℝ) (g u : VectorField) (φ : ScalarField) + (h : NavierStokes ν g u 0) : + NavierStokes ν (fun t q => g t q - gradient φ t q) u (-φ) := by + refine ⟨?_, h.2⟩ + intro t ht q + have heq := h.1 t ht q + rw [gradient_zero] at heq + rw [gradient_neg] + simp only [Pi.zero_apply, neg_zero, zero_add] at heq + simp only [Pi.neg_apply, neg_neg] + rw [heq] + abel + +end Residual + +namespace Scales + +def crudeSlotBound (b L k n : ℕ) : ℕ := + 1 + capacity b L (n + 1) * b ^ (exponent L n * k) + +theorem slotSize_le_crude {b : ℕ} (hb : 2 ≤ b) (L k n : ℕ) : + slotSize b L k n ≤ (crudeSlotBound b L k n : ℝ) := by + have hβ : (if k = 0 then beta b L n else (0 : ℝ)) ≤ 1 := by + split_ifs + · have := beta_le_quarter hb L n + linarith + · norm_num + have he := epsilon_le_one hb L (n + 1) + have hmul : 0 ≤ (capacity b L (n + 1) : ℝ) * (b : ℝ) ^ (exponent L n * k) := by + positivity + have hrec : (capacity b L (n + 1) : ℝ) * epsilon b L (n + 1) / + epsilon b L n ^ k ≤ + (capacity b L (n + 1) : ℝ) * (b : ℝ) ^ (exponent L n * k) := by + rw [show epsilon b L n = ((b : ℝ) ^ exponent L n)⁻¹ from rfl, + inv_pow, div_inv_eq_mul, ← pow_mul] + have h := mul_le_mul_of_nonneg_right he hmul + nlinarith + unfold slotSize crudeSlotBound + push_cast + linarith + +def allSlotsBound (b L k J : ℕ) : ℕ := + 2 * weightBound J + ∑ n ∈ Finset.range (max 1 k), (n + 3) ^ J * crudeSlotBound b L k n + +theorem weighted_slotSize_bound_all {b : ℕ} (hb : 2 ≤ b) (L k J n : ℕ) {t : ℝ} + (ht : 0 ≤ t) (hT : t ≤ (n : ℝ) + 2) : + (1 + t) ^ J * slotSize b L k n ≤ (allSlotsBound b L k J : ℝ) := by + by_cases hn : max 1 k ≤ n + · have hsharp := weighted_slotSize_bound hb L J + ((le_max_left 1 k).trans hn) ((le_max_right 1 k).trans hn) ht hT + apply hsharp.trans + have hnat : 2 * weightBound J ≤ allSlotsBound b L k J := by + unfold allSlotsBound + omega + exact_mod_cast hnat + · have hmem : n ∈ Finset.range (max 1 k) := Finset.mem_range.mpr (by omega) + have hsingle : (n + 3) ^ J * crudeSlotBound b L k n ≤ + ∑ m ∈ Finset.range (max 1 k), (m + 3) ^ J * crudeSlotBound b L k m := + Finset.single_le_sum (f := fun m : ℕ => (m + 3) ^ J * crudeSlotBound b L k m) + (by intro i hi; exact Nat.zero_le _) hmem + have hnat : (n + 3) ^ J * crudeSlotBound b L k n ≤ allSlotsBound b L k J := by + unfold allSlotsBound + omega + calc + (1 + t) ^ J * slotSize b L k n ≤ + (1 + t) ^ J * (crudeSlotBound b L k n : ℝ) := + mul_le_mul_of_nonneg_left (slotSize_le_crude hb L k n) (by positivity) + _ ≤ ((n : ℝ) + 3) ^ J * (crudeSlotBound b L k n : ℝ) := + mul_le_mul_of_nonneg_right + (pow_le_pow_left₀ (by linarith) (by linarith) J) (by positivity) + _ ≤ (allSlotsBound b L k J : ℝ) := by exact_mod_cast hnat + +end Scales + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Solenoidal.lean b/lean/OAI/Analysis/PeriodicLattice/Solenoidal.lean new file mode 100644 index 0000000000000000000000000000000000000000..d53a4afb79311a47eface5fad275cbdf92d87127 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Solenoidal.lean @@ -0,0 +1,421 @@ +import OAI.Analysis.PeriodicLattice.MeanBounds + +namespace OAI + +/-! Pressure potentials, solenoidal forcing and the analytic lattice conclusion. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingSolenoidal {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus RapidCalculus + +def doubleSlope (z : ℝ) : ℝ := 2 * slope z ^ 2 - 1 + +theorem doubleSlope_contDiff : ContDiff ℝ ∞ doubleSlope := + ((contDiff_const.mul (slope_contDiff.pow 2)).sub contDiff_const) + +theorem doubleSlope_periodic : Function.Periodic doubleSlope 1 := by + intro z + simp only [doubleSlope, slope_periodic z] + +theorem slope_hasDerivAt (z : ℝ) : + HasDerivAt slope (-(2 * Real.pi)^2 * eta z) z := by + have h := (((hasDerivAt_id z).sub_const (1 / 2)).const_mul (2 * Real.pi)).cos + simp only [id_eq, mul_one] at h + change HasDerivAt slope (-Real.sin (2 * Real.pi * (z - 1 / 2)) * (2 * Real.pi)) z at h + convert h using 1 + dsimp only [eta] + field_simp + +@[simp] theorem eta_deriv : deriv eta = slope := funext (fun z => (eta_hasDerivAt z).deriv) +@[simp] theorem slope_deriv : deriv slope = fun z => -(2 * Real.pi)^2 * eta z := + funext (fun z => (slope_hasDerivAt z).deriv) + +theorem vertical_energy (z : ℝ) : slope z ^ 2 + (2 * Real.pi)^2 * eta z ^ 2 = 1 := by + dsimp only [slope, eta] + rw [div_pow, mul_div_cancel₀ _ (pow_ne_zero 2 (mul_ne_zero (by norm_num) Real.pi_ne_zero))] + exact Real.cos_sq_add_sin_sq _ + +theorem doubleSlope_second (z : ℝ) : + deriv (deriv doubleSlope) z = -(4 * Real.pi)^2 * doubleSlope z := by + have h₁ (z : ℝ) : HasDerivAt doubleSlope (4 * slope z * (-(2 * Real.pi)^2 * eta z)) z := by + convert (((slope_hasDerivAt z).pow 2).const_mul 2).sub_const 1 using 1 <;> first | rfl | ring + have he : deriv doubleSlope = fun z => 4 * slope z * (-(2 * Real.pi)^2 * eta z) := + funext fun z => (h₁ z).deriv + rw [he, (((slope_hasDerivAt z).const_mul 4).fun_mul + ((eta_hasDerivAt z).const_mul (-(2 * Real.pi)^2))).deriv] + have hv := vertical_energy z + dsimp [doubleSlope] + nlinarith [hv] + +def pressureSource (d : Input) (t y : ℝ) : ℝ := + bdy d t y * bdy d t y - b d t y * biD false (bdy d) t y + +theorem pressureSource_contDiff (d : Input) : + ContDiff ℝ ∞ (Function.uncurry (pressureSource d)) := + ((bdy_contDiff d).mul (bdy_contDiff d)).sub + ((b_contDiff d).mul (partial_contDiff (bdy_contDiff d) false)) + +theorem pressureSource_periodic (d : Input) (t : ℝ) : + Function.Periodic (pressureSource d t) 1 := + ((bdy_periodic d t).mul (bdy_periodic d t)).sub + ((b_periodic d t).mul (periodic_deriv (bdy_periodic d t))) + +theorem pressureSource_rapid (d : Input) (hd : d.WellFormed) : Rapid2 (pressureSource d) := + (((b_rapid2 d hd).biD false).mul ((b_rapid2 d hd).biD false)).sub + ((b_rapid2 d hd).mul (((b_rapid2 d hd).biD false).biD false)) + +end FluidLift + +namespace RapidCalculus + +open scoped ContDiff +open TorusCalculus + +theorem tensor_contDiff {F : ScalarField} {f : ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hf : ContDiff ℝ ∞ (Function.uncurry f)) (hh : ContDiff ℝ ∞ h) + (he : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) : ContDiff ℝ ∞ (lifted F) := by + have hc (i : Fin 3) : ContDiff ℝ ∞ (fun tx : ℝ × Space => tx.2 i) := + (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) i).contDiff.comp contDiff_snd + change ContDiff ℝ ∞ (fun tx : ℝ × Space => F tx.1 (torusMk tx.2)) + simp_rw [he] + exact (hh.comp (hc 2)).mul (hf.comp (contDiff_fst.prodMk (hc 1))) + +theorem tensor_laplacian {F : ScalarField} {f : ℝ → ℝ → ℝ} {h : ℝ → ℝ} + (hf : ContDiff ℝ ∞ (Function.uncurry f)) (hh : ContDiff ℝ ∞ h) + (he : ∀ t x, F t (torusMk x) = h (x 2) * f t (x 1)) (t : ℝ) (x : Space) : + laplacian F t (torusMk x) = h (x 2) * biD false (biD false f) t (x 1) + + deriv (deriv h) (x 2) * f t (x 1) := by + have h₁ := tensor_spaceD_one hf he + have h₂ := tensor_spaceD_two hh he + have hh' : ContDiff ℝ ∞ (deriv h) := by simpa using ContDiff.iterate_deriv 1 hh + simp only [laplacian, Fin.sum_univ_three, tensor_spaceD_zero he, Residual.spaceD_zero, Pi.zero_apply, + zero_add, tensor_spaceD_one (partial_contDiff hf false) h₁, tensor_spaceD_two hh' h₂] + +end RapidCalculus + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus RapidCalculus PeriodicInverse MeasureTheory + +def pressureBase (d : Input) (t y : ℝ) : ℝ := + (1 / 2 : ℝ) * (b d t y * b d t y - mean (fun t y => b d t y * b d t y) t y) + +theorem pressureBase_contDiff (d : Input) : ContDiff ℝ ∞ (Function.uncurry (pressureBase d)) := + contDiff_const.mul (((b_contDiff d).mul (b_contDiff d)).sub + (mean_contDiff ((b_contDiff d).mul (b_contDiff d)))) + +theorem pressureBase_periodic (d : Input) (t : ℝ) : Function.Periodic (pressureBase d t) 1 := by + intro y + simp only [pressureBase, b_periodic d t y, mean] + +theorem pressureBase_rapid (d : Input) (hd : d.WellFormed) : Rapid2 (pressureBase d) := + (((b_rapid2 d hd).mul (b_rapid2 d hd)).sub + (mean_rapid ((b_rapid2 d hd).mul (b_rapid2 d hd)))).scale (1 / 2) + +theorem pressureBase_deriv (d : Input) : + biD false (pressureBase d) = fun t y => b d t y * bdy d t y := by + funext t y + have hh := (((b_hasDerivAt d t y).fun_mul (b_hasDerivAt d t y)).sub_const + (mean (fun t y => b d t y * b d t y) t y)).const_mul (1 / 2) + have he : (1 / 2 : ℝ) * (bdy d t y * b d t y + b d t y * bdy d t y) = b d t y * bdy d t y := by ring + change deriv (fun z => (1 / 2 : ℝ) * (b d t z * b d t z - ∫ s in (0 : ℝ)..1, b d t s * b d t s)) y = _ + simpa only [he, mean] using hh.deriv + +theorem pressureBase_second (d : Input) (t y : ℝ) : + biD false (biD false (pressureBase d)) t y = + bdy d t y * bdy d t y + b d t y * biD false (bdy d) t y := by + rw [pressureBase_deriv] + exact ((b_hasDerivAt d t y).fun_mul + (((bdy_contDiff d).comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) y).hasDerivAt).deriv + +def pressureMode (d : Input) := screened (4 * Real.pi) (pressureSource d) + +theorem pressureMode_contDiff (d : Input) : ContDiff ℝ ∞ (Function.uncurry (pressureMode d)) := + screened_contDiff (4 * Real.pi) (pressureSource_contDiff d) + +theorem pressureMode_periodic (d : Input) : ∀ t, Function.Periodic (pressureMode d t) 1 := + screened_periodic (4 * Real.pi) (pressureSource_periodic d) + +theorem pressureMode_rapid (d : Input) (hd : d.WellFormed) : Rapid2 (pressureMode d) := + screened_rapid (4 * Real.pi) (pressureSource_rapid d hd) + +def pressureOsc (d : Input) : ScalarField := fun t q => + doubleSlope_periodic.lift (q 2) * (pressureMode_periodic d t).lift (q 1) + +@[simp] theorem pressureOsc_cover (d : Input) (t : ℝ) (x : Space) : + pressureOsc d t (torusMk x) = doubleSlope (x 2) * pressureMode d t (x 1) := by + simp only [pressureOsc, torusMk, Function.Periodic.lift_coe] + +theorem pressureOsc_contDiff (d : Input) : ContDiff ℝ ∞ (lifted (pressureOsc d)) := + tensor_contDiff (pressureMode_contDiff d) doubleSlope_contDiff (pressureOsc_cover d) + +theorem pressureOsc_algebra (d : Input) (hd : d.WellFormed) : Algebra (pressureOsc d) := + Algebra.tensor _ _ _ (pressureMode_rapid d hd) + (boundedProfile_of_periodic doubleSlope_contDiff doubleSlope_periodic) (pressureOsc_cover d) + +def potential (d : Input) : ScalarField := + horizontal (pressureBase d) (pressureBase_periodic d) + pressureOsc d + +theorem potential_contDiff (d : Input) : ContDiff ℝ ∞ (lifted (potential d)) := + (horizontal_contDiff (pressureBase_periodic d) (pressureBase_contDiff d)).add (pressureOsc_contDiff d) + +theorem potential_algebra (d : Input) (hd : d.WellFormed) : Algebra (potential d) := + (horizontal_algebra (pressureBase_periodic d) (pressureBase_rapid d hd)).add (pressureOsc_algebra d hd) + +theorem potential_meanZero (d : Input) : MeanZero (potential d) := by + have ho (t : ℝ) : (∫ q, pressureOsc d t q ∂torusVolume) = 0 := by + have he : spaceD 2 (spaceD 2 (pressureOsc d)) = -(4 * Real.pi)^2 • pressureOsc d := by + funext t q + obtain ⟨x, rfl⟩ := mk_surjective q + rw [tensor_spaceD_two (show ContDiff ℝ ∞ (deriv doubleSlope) from + ContDiff.iterate_deriv 1 doubleSlope_contDiff) + (tensor_spaceD_two doubleSlope_contDiff (pressureOsc_cover d)), doubleSlope_second] + change -(4 * Real.pi)^2 * doubleSlope (x 2) * pressureMode d t (x 1) = + -(4 * Real.pi)^2 * (doubleSlope (x 2) * pressureMode d t (x 1)) + ring + have hi := integral_spaceD (contDiff_spaceD (pressureOsc_contDiff d) 2) t 2 + rw [he] at hi + change (∫ q, -(4 * Real.pi)^2 * pressureOsc d t q ∂torusVolume) = 0 at hi + rw [integral_const_mul] at hi + exact (mul_eq_zero.mp hi).resolve_left (neg_ne_zero.mpr (pow_ne_zero 2 (mul_ne_zero (by norm_num) Real.pi_ne_zero))) + intro t ht + change (∫ q, horizontal (pressureBase d) (pressureBase_periodic d) t q + pressureOsc d t q ∂torusVolume) = 0 + rw [integral_add (smooth_slice_integrable + (horizontal_contDiff (pressureBase_periodic d) (pressureBase_contDiff d)) t) + (smooth_slice_integrable (pressureOsc_contDiff d) t), ho, add_zero, + horizontal_integral (pressureBase_periodic d) (pressureBase_contDiff d)] + have hi : IntervalIntegrable (fun y => b d t y * b d t y) volume 0 1 := + (((b_contDiff d).mul (b_contDiff d)).continuous.comp + (continuous_const.prodMk continuous_id)).intervalIntegrable _ _ + simp only [pressureBase, mean, intervalIntegral.integral_const_mul, + intervalIntegral.integral_sub hi (intervalIntegrable_const), intervalIntegral.integral_const, + sub_zero, one_smul, sub_self, mul_zero] + +end FluidLift + +namespace TorusCalculus +open scoped ContDiff + +section Addition +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +theorem spaceD_add_eq {F G : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + (hG : ContDiff ℝ ∞ (lifted G)) (i : Fin 3) : + spaceD i (F + G) = spaceD i F + spaceD i G := by + funext t q + exact spaceD_add (smooth_slice_differentiable hF t) (smooth_slice_differentiable hG t) i q + +theorem laplacian_add {F G : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + (hG : ContDiff ℝ ∞ (lifted G)) : laplacian (F + G) = laplacian F + laplacian G := by + simp only [laplacian_as_sum, spaceD_add_eq hF hG, + spaceD_add_eq (contDiff_spaceD hF _) (contDiff_spaceD hG _), Finset.sum_add_distrib] + +end Addition + +end TorusCalculus + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus RapidCalculus PeriodicInverse + +theorem force_divergence (ν : ℝ) (d : Input) (t : ℝ) (x : Space) : + divergence (force ν d) t (torusMk x) = + bdy d t (x 1) * bdy d t (x 1) + b d t (x 1) * biD false (bdy d) t (x 1) + + doubleSlope (x 2) * pressureSource d t (x 1) := by + have hdiv : divergence (velocity d) = 0 := funext fun t => funext fun q => divergence_zero d t q + change divergence (Residual.fullForce ν (velocity d)) t (torusMk x) = _ + rw [divergence_fullForce (velocity_contDiff d) hdiv, + divergence_advection (velocity_contDiff d) hdiv] + have hzero (j : Fin 3) : spaceD 0 (fun t q => velocity d t q j) = 0 := by + fin_cases j + · exact tensor_spaceD_zero (f := a d) (h := slope) (fun t x => by simp only [velocity_cover]; rfl) + · exact tensor_spaceD_zero (f := b d) (h := slope) (fun t x => by simp only [velocity_cover]; rfl) + · exact tensor_spaceD_zero (f := bdy d) (h := fun z => -eta z) (fun t x => by simp only [velocity_cover]; rfl) + have hc₁ : ∀ t x, (velocity d t (torusMk x)) 1 = slope (x 2) * b d t (x 1) := by + intro t x + simp only [velocity_cover]; rfl + have hc₂ : ∀ t x, (velocity d t (torusMk x)) 2 = (-eta (x 2)) * bdy d t (x 1) := by + intro t x + simp only [velocity_cover]; rfl + simp only [Fin.sum_univ_three, hzero, Pi.zero_apply, zero_mul, mul_zero, zero_add, add_zero, + tensor_spaceD_one (F := fun t q => velocity d t q 1) (h := slope) (b_contDiff d) hc₁, tensor_spaceD_one (F := fun t q => velocity d t q 2) (h := fun z => -eta z) (bdy_contDiff d) hc₂, + tensor_spaceD_two (F := fun t q => velocity d t q 1) (f := b d) slope_contDiff hc₁, tensor_spaceD_two (F := fun t q => velocity d t q 2) (f := bdy d) eta_contDiff.neg hc₂, + slope_deriv, deriv.fun_neg, eta_deriv] + change slope (x 2) * bdy d t (x 1) * (slope (x 2) * bdy d t (x 1)) + + -eta (x 2) * biD false (bdy d) t (x 1) * (-(2 * Real.pi)^2 * eta (x 2) * b d t (x 1)) + + (-(2 * Real.pi)^2 * eta (x 2) * b d t (x 1) * (-eta (x 2) * biD false (bdy d) t (x 1)) + + -slope (x 2) * bdy d t (x 1) * (-slope (x 2) * bdy d t (x 1))) = _ + dsimp only [doubleSlope, pressureSource] + linear_combination 2 * b d t (x 1) * biD false (bdy d) t (x 1) * vertical_energy (x 2) + +theorem potential_poisson (ν : ℝ) (d : Input) (t : ℝ) (q : Torus) : + laplacian (potential d) t q = divergence (force ν d) t q := by + obtain ⟨x, rfl⟩ := mk_surjective q + have hb : ∀ t x, horizontal (pressureBase d) (pressureBase_periodic d) t (torusMk x) = + 1 * pressureBase d t (x 1) := fun t x => by simp + rw [potential, laplacian_add (horizontal_contDiff (pressureBase_periodic d) (pressureBase_contDiff d)) + (pressureOsc_contDiff d)] + change laplacian (horizontal (pressureBase d) (pressureBase_periodic d)) t (torusMk x) + + laplacian (pressureOsc d) t (torusMk x) = _ + rw [tensor_laplacian (pressureBase_contDiff d) contDiff_const hb, + tensor_laplacian (pressureMode_contDiff d) doubleSlope_contDiff (pressureOsc_cover d), + pressureBase_second, doubleSlope_second] + have hs := screened_equation (4 * Real.pi) (mul_ne_zero (by norm_num) Real.pi_ne_zero) + (pressureSource_contDiff d) (pressureSource_periodic d) t (x 1) + change biD false (biD false (pressureMode d)) t (x 1) = + (4 * Real.pi)^2 * pressureMode d t (x 1) + pressureSource d t (x 1) at hs + rw [hs, force_divergence] + have hd (c : ℝ) : deriv (fun _ : ℝ => c) = fun _ => 0 := by funext z; exact deriv_const z c + simp only [hd, one_mul, zero_mul, add_zero] + ring + +end FluidLift + +namespace TorusCalculus + +open scoped ContDiff +open MeasureTheory + +theorem contDiff_gradient {p : ScalarField} (hp : ContDiff ℝ ∞ (lifted p)) : + ContDiff ℝ ∞ (lifted (gradient p)) := + (contDiff_piLp _).mpr (fun i => contDiff_spaceD hp i) + +theorem divergence_gradient (p : ScalarField) : divergence (gradient p) = laplacian p := rfl + +theorem gradient_neg {p : ScalarField} : gradient (-p) = -gradient p := by + funext t q + ext i + exact deriv.neg + +theorem integral_gradient {p : ScalarField} (hp : ContDiff ℝ ∞ (lifted p)) (t : ℝ) : + (∫ q, gradient p t q ∂torusVolume) = 0 := by + ext i + have hi := (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) i).integral_comp_comm + (smooth_slice_integrable (contDiff_gradient hp) t) + simpa only [PiLp.proj_apply, gradient, WithLp.toLp_ofLp, PiLp.zero_apply] using + hi.symm.trans (integral_spaceD hp t i) + +theorem classical_of_smooth_pressure {ν : ℝ} {F U : VectorField} {p : ScalarField} + (hU : ContDiff ℝ ∞ (lifted U)) (hp : ContDiff ℝ ∞ (lifted p)) + (hm : MeanZero p) (hNS : NavierStokes ν F U p) : ClassicalSolution ν F U p where + velocityContinuous := cylinderContinuous hU + timeDifferentiable := by + intro t _ht q + obtain ⟨x, rfl⟩ := mk_surjective q + exact (((hU.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp)) t).differentiableWithinAt + timeContinuous := timeD_cylinderContinuous hU + spaceTwiceDifferentiable := fun _t _ht => + (hU.comp (contDiff_const.prodMk contDiff_id)).of_le (by exact WithTop.coe_le_coe.mpr le_top) + spaceFirstContinuous := fun i => cylinderContinuous (contDiff_spaceD hU i) + spaceSecondContinuous := fun i j => cylinderContinuous (contDiff_spaceD (contDiff_spaceD hU j) i) + pressureContinuous := cylinderContinuous hp + pressureDifferentiable := fun t _ => smooth_slice_differentiable hp t + pressureGradientContinuous := cylinderContinuous (contDiff_gradient hp) + pressureMeanZero := hm + equations := hNS + +end TorusCalculus + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus RapidCalculus MeasureTheory + +def solenoidalForce (ν : ℝ) (d : Input) : VectorField := force ν d - gradient (potential d) + +theorem solenoidalForce_contDiff (ν : ℝ) (d : Input) : + ContDiff ℝ ∞ (lifted (solenoidalForce ν d)) := + (force_contDiff ν d).sub (contDiff_gradient (potential_contDiff d)) + +theorem solenoidalForce_solenoidal (ν : ℝ) (d : Input) : Solenoidal (solenoidalForce ν d) := by + intro t ht q + rw [solenoidalForce, divergence_sub (smooth_slice_differentiable (force_contDiff ν d) t) + (smooth_slice_differentiable (contDiff_gradient (potential_contDiff d)) t), + ← Pi.sub_apply, ← Pi.sub_apply, divergence_gradient] + change divergence (force ν d) t q - laplacian (potential d) t q = 0 + rw [potential_poisson, sub_self] + +theorem solenoidalForce_meanZero (ν : ℝ) (d : Input) : MeanZero (solenoidalForce ν d) := by + intro t ht + change (∫ q, force ν d t q - gradient (potential d) t q ∂torusVolume) = 0 + rw [integral_sub (smooth_slice_integrable (force_contDiff ν d) t) + (smooth_slice_integrable (contDiff_gradient (potential_contDiff d)) t), + force_meanZero ν d t ht, integral_gradient (potential_contDiff d) t, sub_self] + +theorem solenoidalForce_equations (ν : ℝ) (d : Input) : + NavierStokes ν (solenoidalForce ν d) (velocity d) (-potential d) := by + refine ⟨?_, (equations ν d).2⟩ + intro t ht q + rw [(equations ν d).1 t ht q, Residual.gradient_zero, Pi.zero_apply, Pi.zero_apply, + neg_zero, zero_add, gradient_neg] + change ν • laplacian (velocity d) t q + force ν d t q = + -(-gradient (potential d) t q) + ν • laplacian (velocity d) t q + + (force ν d t q - gradient (potential d) t q) + abel + +theorem solenoidalForce_classical_solution (ν : ℝ) (d : Input) : + ClassicalSolution ν (solenoidalForce ν d) (velocity d) (-potential d) := by + refine classical_of_smooth_pressure (velocity_contDiff d) (potential_contDiff d).neg ?_ + (solenoidalForce_equations ν d) + intro t ht + change (∫ q, -potential d t q ∂torusVolume) = 0 + rw [integral_neg, potential_meanZero d t ht, neg_zero] + +theorem gradient_algebra {p : ScalarField} (hp : Algebra p) : VectorAlgebra (gradient p) := + fun i => hp.spaceDeriv i + +theorem solenoidalForce_algebra (ν : ℝ) (d : Input) (hd : d.WellFormed) : + VectorAlgebra (solenoidalForce ν d) := + ((velocity_algebra d hd).fullForce ν).sub (gradient_algebra (potential_algebra d hd)) + +end FluidLift + +namespace RapidCalculus + +theorem RapidPair.mono {U F : VectorField} {C D : ℕ → MultiIndex → ℕ → ℕ} + (hC : RapidPair U F C) (hCD : ∀ r α J, C r α J ≤ D r α J) : RapidPair U F D := by + intro r J α t ht + exact (hC r J α t ht).trans (div_le_div_of_nonneg_right + (Nat.cast_le.mpr (hCD r α J)) (by positivity)) + +end RapidCalculus + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus RapidCalculus + +theorem analytic_lattice_conclusion (ν : ℝ) (hν : 0 ≤ ν) (d : Input) (hd : d.WellFormed) : + ∃ C : ℕ → MultiIndex → ℕ → ℕ, + LatticeConclusion ν d (velocity d) (force ν d) (solenoidalForce ν d) (potential d) C := by + obtain ⟨Cg, hg⟩ := force_rapid ν d hd + obtain ⟨Cf, hf⟩ := rapidPair_of_algebra (velocity_algebra d hd) (solenoidalForce_algebra ν d hd) + refine ⟨fun r α J => max (Cg r α J) (Cf r α J), + velocity_smooth d, force_smooth ν d, (solenoidalForce_contDiff ν d).contDiffOn, + (potential_contDiff d).contDiffOn, velocity_meanZero d, force_meanZero ν d, + solenoidalForce_meanZero ν d, potential_meanZero d, classical_solution ν d, + solenoidalForce_classical_solution ν d, RapidPair.mono hg (fun _ _ _ => le_max_left _ _), + RapidPair.mono hf (fun _ _ _ => le_max_right _ _), solenoidalForce_solenoidal ν d, + fun t _ q => potential_poisson ν d t q, ?_, fun _ _ _ => rfl, + force_classical_unique ν hν d, classical_unique hν (solenoidalForce_classical_solution ν d), + path d, path_isParticle d hd, fun _Y hY _t ht => path_unique d hd hY ht, path_event_iff d hd⟩ + exact poisson_unique (fun t _ => ((potential_contDiff d).comp + (contDiff_const.prodMk contDiff_id)).of_le (by exact WithTop.coe_le_coe.mpr le_top)) + (potential_meanZero d) (fun t _ q => potential_poisson ν d t q) + +end FluidLift + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Tape.lean b/lean/OAI/Analysis/PeriodicLattice/Tape.lean new file mode 100644 index 0000000000000000000000000000000000000000..95e761c227d2601025b056b1b68ed835b4b93a4b --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Tape.lean @@ -0,0 +1,348 @@ +import OAI.Analysis.PeriodicLattice.PlanarFlow + +namespace OAI + +/-! Tape digits, stack evolution and effective local transition tables. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingTape {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace MachineFacts + +theorem lookup_bounds {M : Machine} (hM : M.WellFormed) {q a : ℕ} {I : Instruction} + (hI : M.lookup q a = some I) : I.nextState < M.states ∧ I.writeSymbol < M.symbols := by + have hq : q < M.table.length := by + by_contra h + simp only [Machine.lookup, List.getD_eq_default _ _ (Nat.le_of_not_gt h), + List.getD_nil] at hI + contradiction + have ha : a < (M.table[q]).length := by + by_contra h + simp only [Machine.lookup, List.getD_eq_getElem _ _ hq, + List.getD_eq_default _ _ (Nat.le_of_not_gt h)] at hI + contradiction + apply hM.2.2.2.2.2 (M.table[q]) (List.getElem_mem hq) + ((M.table[q])[a]) (List.getElem_mem ha) I + simpa only [Machine.lookup, List.getD_eq_getElem _ _ hq, + List.getD_eq_getElem _ _ ha] using hI + +end MachineFacts + +namespace TapeDigits + +def digit (b N i : ℕ) : ℕ := N / b ^ i % b + +@[simp] theorem digit_zero (b N : ℕ) : digit b N 0 = N % b := by simp [digit] + +@[simp] theorem digit_blank (b i : ℕ) : digit b 0 i = 0 := by simp [digit] + +theorem digit_succ (b N i : ℕ) : digit b N (i + 1) = digit b (N / b) i := by + simp only [digit, pow_succ, Nat.div_div_eq_div_mul, mul_comm] + +@[simp] theorem digit_cons_zero {b a : ℕ} (ha : a < b) (N : ℕ) : + digit b (a + b * N) 0 = a := by simp [Nat.mod_eq_of_lt ha] + +@[simp] theorem digit_cons_succ {b a : ℕ} (ha : a < b) (N i : ℕ) : + digit b (a + b * N) (i + 1) = digit b N i := by + rw [digit_succ] + simp only [Nat.add_mul_div_left _ _ (by omega : 0 < b), Nat.div_eq_of_lt ha, zero_add] + +theorem sub_top (b N : ℕ) : N - N % b = b * (N / b) := by + have := Nat.mod_add_div N b + omega + +theorem digit_ofDigits {b : ℕ} (_hb : 2 ≤ b) (w : List ℕ) + (hw : ∀ a ∈ w, a < b) (i : ℕ) : digit b (Nat.ofDigits b w) i = w.getD i 0 := by + induction i generalizing w with + | zero => + cases w with + | nil => simp + | cons a w => simpa only [Nat.ofDigits_cons, List.getD_cons_zero] using + digit_cons_zero (hw a List.mem_cons_self) (Nat.ofDigits b w) + | succ i ih => + cases w with + | nil => simp + | cons a w => + rw [Nat.ofDigits_cons, digit_cons_succ (hw a List.mem_cons_self)] + exact ih w (fun a ha => hw a (List.mem_cons_of_mem _ ha)) + +end TapeDigits + +namespace StackCode + +open TapeDigits + +def Represents (b : ℕ) (s : Code) (c : Configuration) : Prop := + s.state = c.state ∧ + (∀ i : ℕ, c.tape (c.head - 1 - (i : ℤ)) = digit b s.left i) ∧ + ∀ i : ℕ, c.tape (c.head + (i : ℤ)) = digit b s.right i + +def initialCode (b : ℕ) (d : Input) : Code := + ⟨0, Nat.ofDigits b d.word, d.machine.start⟩ + +theorem initial_represents {b : ℕ} (hb : 2 ≤ b) (d : Input) + (hw : ∀ a ∈ d.word, a < b) : Represents b (initialCode b d) (initialConfiguration d) := by + constructor + · rfl + constructor + · intro i + simp only [initialConfiguration, initialCode, zero_sub, TapeDigits.digit_blank] + rw [ite_eq_right (by omega)] + · intro i + simp only [initialConfiguration, initialCode, zero_add, Int.natCast_nonneg, + ↓reduceIte, Int.toNat_natCast] + exact (digit_ofDigits hb d.word hw i).symm + +theorem scan_eq {b : ℕ} {s : Code} {c : Configuration} (h : Represents b s c) : + c.tape c.head = s.right % b := by simpa only [Nat.cast_zero, add_zero, digit_zero] using h.2.2 0 + +theorem step_represents {b : ℕ} (hb : 2 ≤ b) {s : Code} {c : Configuration} + {M : Machine} {I : Instruction} (h : Represents b s c) + (hI : M.lookup c.state (c.tape c.head) = some I) (hw : I.writeSymbol < b) : + Represents b (step b s I) (machineStep M c) := by + have hl : s.left % b < b := Nat.mod_lt _ (by omega) + have hm := I.move.isLt + rw [machineStep, hI] + dsimp only + constructor + · exact step_state b s I + by_cases hR : I.move.val = 2 + · have hmove : ((I.move.val : ℤ) - 1) = 1 := by omega + simp only [hmove, step, ite_eq_left hR] + constructor + · intro i + cases i with + | zero => simp [digit_cons_zero hw] + | succ i => + have he : c.head + 1 - 1 - ((i + 1 : ℕ) : ℤ) = c.head - 1 - i := by omega + rw [he, Function.update_of_ne (by omega), digit_cons_succ hw] + exact h.2.1 i + · intro i + rw [Function.update_of_ne (by omega)] + have he : c.head + 1 + (i : ℤ) = c.head + ((i + 1 : ℕ) : ℤ) := by omega + rw [he, h.2.2, digit_succ] + · by_cases hL : I.move.val = 0 + · have hmove : ((I.move.val : ℤ) - 1) = -1 := by omega + simp only [hmove, step, ite_eq_right hR, ite_eq_left hL] + constructor + · intro i + rw [Function.update_of_ne (by omega)] + have he : c.head + -1 - 1 - (i : ℤ) = c.head - 1 - ((i + 1 : ℕ) : ℤ) := by omega + rw [he, h.2.1, digit_succ] + · intro i + have hform : s.left % b + b * I.writeSymbol + b * (s.right - s.right % b) = + s.left % b + b * (I.writeSymbol + b * (s.right / b)) := by + rw [sub_top]; ring + rw [hform] + cases i with + | zero => + rw [digit_cons_zero hl] + simp only [Nat.cast_zero, add_zero] + rw [Function.update_of_ne (by omega)] + simpa only [Nat.cast_zero, sub_zero, sub_eq_add_neg, neg_zero, add_zero, TapeDigits.digit_zero] using h.2.1 0 + | succ i => + rw [digit_cons_succ hl] + cases i with + | zero => simp [digit_cons_zero hw] + | succ i => + rw [digit_cons_succ hw, ← digit_succ] + rw [Function.update_of_ne (by omega)] + have he : c.head + -1 + (((i + 1) + 1 : ℕ) : ℤ) = c.head + ((i + 1 : ℕ) : ℤ) := by omega + rw [he, h.2.2] + · have hmove : ((I.move.val : ℤ) - 1) = 0 := by omega + simp only [hmove, step, ite_eq_right hR, ite_eq_right hL, add_zero] + constructor + · intro i + rw [Function.update_of_ne (by omega)] + exact h.2.1 i + · intro i + rw [sub_top, Nat.add_comm (b * _) I.writeSymbol] + cases i with + | zero => simp [digit_cons_zero hw] + | succ i => + rw [digit_cons_succ hw, ← digit_succ, Function.update_of_ne (by omega)] + exact h.2.2 (i + 1) + +end StackCode + +namespace StackCode + +open Scales + +def machineStackStep (b : ℕ) (M : Machine) (s : Code) : Code := + (M.lookup s.state (s.right % b)).elim s (fun I => step b s I) + +def stackExecution (b : ℕ) (d : Input) (n : ℕ) : Code := + (machineStackStep b d.machine)^[n] (initialCode b d) + +@[simp] theorem stackExecution_zero (b : ℕ) (d : Input) : + stackExecution b d 0 = initialCode b d := rfl + +theorem stackExecution_succ (b : ℕ) (d : Input) (n : ℕ) : + stackExecution b d (n + 1) = machineStackStep b d.machine (stackExecution b d n) := + Function.iterate_succ_apply' _ _ _ + +theorem stackExecution_represents {b : ℕ} (hb : 2 ≤ b) (d : Input) (hd : d.WellFormed) + (hsymbol : d.machine.symbols ≤ b) (n : ℕ) : + Represents b (stackExecution b d n) (execution d n) := by + induction n with + | zero => exact initial_represents hb d (fun a ha => (hd.2 a ha).trans_le hsymbol) + | succ n ih => + have hex : execution d (n + 1) = machineStep d.machine (execution d n) := + Function.iterate_succ_apply' _ _ _ + rw [stackExecution_succ, hex] + have hread : d.machine.lookup (execution d n).state ((execution d n).tape (execution d n).head) = + d.machine.lookup (stackExecution b d n).state ((stackExecution b d n).right % b) := by + rw [← ih.1, scan_eq ih] + cases hI : d.machine.lookup (stackExecution b d n).state ((stackExecution b d n).right % b) with + | none => simpa only [machineStackStep, Option.elim, hI, machineStep, hread] using ih + | some I => + rw [machineStackStep, hI] + exact step_represents hb ih (hread.trans hI) + ((MachineFacts.lookup_bounds hd.1 hI).2.trans_le hsymbol) + +theorem stackExecution_bounds {b : ℕ} (hb : 2 ≤ b) (d : Input) (hd : d.WellFormed) + (hsymbol : d.machine.symbols ≤ b) (hstate : d.machine.states ≤ b) (n : ℕ) : + (stackExecution b d n).left < b ^ width d.word.length n ∧ + (stackExecution b d n).right < b ^ width d.word.length n ∧ + (stackExecution b d n).state < b := by + induction n with + | zero => + dsimp only [stackExecution_zero, initialCode] + refine ⟨pow_pos (by omega) _, ?_, hd.1.2.2.1.trans_le hstate⟩ + exact (Nat.ofDigits_lt_base_pow_length (by omega) (fun a ha => (hd.2 a ha).trans_le hsymbol)).trans_le + (Nat.pow_le_pow_right (by omega) (by simp [width])) + | succ n ih => + rw [stackExecution_succ] + have hw : 0 < width d.word.length n := by simp [width] + have hp : b ^ width d.word.length n ≤ b ^ width d.word.length (n + 1) := by + apply Nat.pow_le_pow_right (by omega) + rw [width_succ]; omega + cases hI : d.machine.lookup (stackExecution b d n).state ((stackExecution b d n).right % b) with + | none => simpa only [machineStackStep, Option.elim, hI] using + And.intro (ih.1.trans_le hp) (And.intro (ih.2.1.trans_le hp) ih.2.2) + | some I => + obtain ⟨hs, ha⟩ := MachineFacts.lookup_bounds hd.1 hI + obtain ⟨hl', hr'⟩ := step_stacks_lt hb hw (stackExecution b d n) I ih.1 ih.2.1 + (ha.trans_le hsymbol) + have hp' : b ^ (width d.word.length n + 1) ≤ b ^ width d.word.length (n + 1) := by + apply Nat.pow_le_pow_right (by omega) + rw [width_succ]; omega + simpa only [machineStackStep, Option.elim, hI, step_state] using + And.intro (hl'.trans_le hp') (And.intro (hr'.trans_le hp') (hs.trans_le hstate)) + +def configurationCode (b : ℕ) (d : Input) (n : ℕ) : ℕ := + pack b (width d.word.length n) (stackExecution b d n) + +theorem configurationCode_bound {b : ℕ} (hb : 2 ≤ b) (d : Input) (hd : d.WellFormed) + (hsymbol : d.machine.symbols ≤ b) (hstate : d.machine.states ≤ b) (n : ℕ) : + configurationCode b d n < capacity b d.word.length n := by + obtain ⟨hl, hr, hs⟩ := stackExecution_bounds hb d hd hsymbol hstate n + exact pack_lt hb _ hl hr hs + +theorem decode_configurationCode {b : ℕ} (hb : 2 ≤ b) (d : Input) (hd : d.WellFormed) + (hsymbol : d.machine.symbols ≤ b) (hstate : d.machine.states ≤ b) (n : ℕ) : + unpack b (width d.word.length n) (configurationCode b d n) = stackExecution b d n := by + obtain ⟨hl, hr, hs⟩ := stackExecution_bounds hb d hd hsymbol hstate n + exact unpack_pack hb _ hl hr hs + +end StackCode + +namespace RuleTable + +open Scales StackCode + +def halt (b L : ℕ) (M : Machine) (n : ℕ) (j : ℤ) : Bool := + let c := unpack b (width L n) j + (M.lookup c.state (c.right % b)).isNone + +def next (b L : ℕ) (M : Machine) (n : ℕ) (j : ℤ) : ℕ := + let c := unpack b (width L n) j + (M.lookup c.state (c.right % b)).elim 0 (fun I => pack b (width L (n + 1)) (step b c I)) + +theorem halt_periodic (b L : ℕ) (M : Machine) (n : ℕ) : + Function.Periodic (halt b L M n) (capacity b L n : ℤ) := by + intro j + simp only [halt, capacity, codeExponent, unpack_periodic b (width L n) j] + +theorem next_periodic (b L : ℕ) (M : Machine) (n : ℕ) : + Function.Periodic (next b L M n) (capacity b L n : ℤ) := by + intro j + simp only [next, capacity, codeExponent, unpack_periodic b (width L n) j] + +theorem next_bound {b : ℕ} (hb : 2 ≤ b) (L : ℕ) (M : Machine) (hM : M.WellFormed) + (hsymbol : M.symbols ≤ b) (hstate : M.states ≤ b) (n : ℕ) (j : ℤ) : + next b L M n j < capacity b L (n + 1) := by + have hp : 0 < b ^ width L n := pow_pos (by omega) _ + have hl : (unpack b (width L n) j).left < b ^ width L n := Nat.mod_lt _ hp + have hr : (unpack b (width L n) j).right < b ^ width L n := Nat.mod_lt _ hp + unfold next + dsimp only + unfold Option.elim + split + · rename_i I hI + obtain ⟨hs, ha⟩ := MachineFacts.lookup_bounds hM hI + simpa only [capacity, codeExponent, width_succ] using + step_pack_lt hb (show 0 < width L n by simp [width]) _ I hl hr + (ha.trans_le hsymbol) (hs.trans_le hstate) + · exact pow_pos (by omega) _ + +theorem halt_code {b : ℕ} (hb : 2 ≤ b) (d : Input) (hd : d.WellFormed) + (hsymbol : d.machine.symbols ≤ b) (hstate : d.machine.states ≤ b) (n : ℕ) : + halt b d.word.length d.machine n (configurationCode b d n) = + (d.machine.lookup (execution d n).state ((execution d n).tape (execution d n).head)).isNone := by + have hrep := stackExecution_represents hb d hd hsymbol n + simp only [halt, decode_configurationCode hb d hd hsymbol hstate, hrep.1, scan_eq hrep] + +theorem next_code {b : ℕ} (hb : 2 ≤ b) (d : Input) (hd : d.WellFormed) + (hsymbol : d.machine.symbols ≤ b) (hstate : d.machine.states ≤ b) (n : ℕ) + (hn : halt b d.word.length d.machine n (configurationCode b d n) = false) : + next b d.word.length d.machine n (configurationCode b d n) = configurationCode b d (n + 1) := by + simp only [halt, decode_configurationCode hb d hd hsymbol hstate] at hn + simp only [next, decode_configurationCode hb d hd hsymbol hstate] + rw [configurationCode, stackExecution_succ] + unfold machineStackStep + cases hI : d.machine.lookup (stackExecution b d n).state ((stackExecution b d n).right % b) with + | none => simp only [hI, Option.isNone_none, Bool.true_eq_false] at hn + | some I => rfl + +end RuleTable + +namespace Planar + +theorem codes_prefix (F : ℕ → ℤ → ℕ) (H : ℕ → ℤ → Bool) (s : ℕ → ℕ) + (hstep : ∀ n, H n (s n) = false → F n (s n) = s (n + 1)) (n : ℕ) + (hprevious : ∀ k < n, H k (s k) = false) : codes F (s 0) n = s n := by + induction n with + | zero => rfl + | succ n ih => + have hi := ih (fun k hk => hprevious k (Nat.lt_succ_of_lt hk)) + rw [codes, hi, hstep n (hprevious n (Nat.lt_succ_self n))] + +theorem codes_flag_iff (F : ℕ → ℤ → ℕ) (H : ℕ → ℤ → Bool) (s : ℕ → ℕ) + (hstep : ∀ n, H n (s n) = false → F n (s n) = s (n + 1)) : + (∃ n, H n (codes F (s 0) n) = true) ↔ ∃ n, H n (s n) = true := by + constructor + · rintro ⟨n, hn⟩ + by_contra hfalse + have ha : ∀ k, H k (s k) = false := fun k => + Bool.eq_false_iff.mpr (fun hk => hfalse ⟨k, hk⟩) + rw [codes_prefix F H s hstep n (fun k _ => ha k), ha] at hn + contradiction + · intro htrue + let n := Nat.find htrue + have hn := Nat.find_spec htrue + refine ⟨n, ?_⟩ + rw [codes_prefix F H s hstep n (fun k hk => Bool.eq_false_iff.mpr (Nat.find_min htrue hk))] + exact hn + +end Planar + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/TorusDerivatives.lean b/lean/OAI/Analysis/PeriodicLattice/TorusDerivatives.lean new file mode 100644 index 0000000000000000000000000000000000000000..f1113398fea04da764f9e6a8c9bca2095d461e0b --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/TorusDerivatives.lean @@ -0,0 +1,354 @@ +import OAI.Analysis.PeriodicLattice.FluidLift + +namespace OAI + +/-! Translation derivatives and smooth periodic lifts. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingTorusDerivatives {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace TorusCalculus + +open scoped ContDiff + +theorem mk_isOpenQuotientMap : IsOpenQuotientMap torusMk := by + have h : IsOpenQuotientMap (fun x : Fin 3 → ℝ => fun i => (x i : UnitAddCircle)) := + IsOpenQuotientMap.piMap (fun _ : Fin 3 => QuotientAddGroup.isOpenQuotientMap_mk) + exact h.comp (PiLp.continuousLinearEquiv 2 ℝ (fun _ : Fin 3 => ℝ)).toHomeomorph.isOpenQuotientMap + +theorem continuous_iff_lifted {A : Type*} [TopologicalSpace A] (F : ℝ → Torus → A) : + Continuous (Function.uncurry F) ↔ + Continuous (fun tx : ℝ × Space => F tx.1 (torusMk tx.2)) := + (IsOpenQuotientMap.id.prodMap mk_isOpenQuotientMap).isQuotientMap.continuous_iff + +theorem single_eq_smul (i : Fin 3) (s : ℝ) : + EuclideanSpace.single i s = s • EuclideanSpace.single i 1 := by + ext j + simp only [PiLp.single_apply, PiLp.smul_apply, smul_eq_mul] + split <;> simp + +section Derivatives +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +theorem spaceD_eq_fderiv (i : Fin 3) {F : Field A} {t : ℝ} (x : Space) + (hF : Differentiable ℝ (spaceLift F t)) : + spaceD i F t (torusMk x) = + (fderiv ℝ (spaceLift F t) x) (EuclideanSpace.single i 1) := by + rw [spaceD_cover] + have heq : (fun s : ℝ => spaceLift F t (x + EuclideanSpace.single i s)) = + (fun s : ℝ => spaceLift F t (x + s • EuclideanSpace.single i 1)) := by + funext s + rw [single_eq_smul i s] + rw [heq] + have h := (hF (x + (0 : ℝ) • EuclideanSpace.single i 1)).hasFDerivAt.comp_hasDerivAt 0 + (((hasDerivAt_id (0 : ℝ)).smul_const (EuclideanSpace.single i 1)).const_add x) + simpa only [Function.comp_def, id_eq, zero_smul, add_zero, one_smul] using h.deriv + +theorem contDiff_spaceD {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (i : Fin 3) : + ContDiff ℝ ∞ (lifted (spaceD i F)) := by + let f : (ℝ × Space) → Space → A := fun tx x => F tx.1 (torusMk x) + have hf : ContDiff ℝ ∞ (Function.uncurry f) := + hF.comp (contDiff_fst.fst.prodMk contDiff_snd) + have hd := hf.fderiv_apply contDiff_snd + (show ContDiff ℝ ∞ (fun _ : ℝ × Space => EuclideanSpace.single i 1) from contDiff_const) + (by simp) + have heq : lifted (spaceD i F) = fun tx : ℝ × Space => + (fderiv ℝ (f tx) tx.2) (EuclideanSpace.single i 1) := by + funext tx + exact spaceD_eq_fderiv i tx.2 + ((hF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp)) + rw [heq] + exact hd + +def fullTimeD (F : Field A) : Field A := fun t q => deriv (fun s => F s q) t + +theorem contDiff_fullTimeD {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) : + ContDiff ℝ ∞ (lifted (fullTimeD F)) := by + let f : (ℝ × Space) → ℝ → A := fun tx s => F s (torusMk tx.2) + have hf : ContDiff ℝ ∞ (Function.uncurry f) := + hF.comp (contDiff_snd.prodMk contDiff_fst.snd) + exact hf.fderiv_apply contDiff_fst contDiff_const (by simp) + +theorem timeD_eq_fullTimeD {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + {t : ℝ} (ht : 0 ≤ t) (q : Torus) : timeD F t q = fullTimeD F t q := by + obtain ⟨x, rfl⟩ := mk_surjective q + have hd : Differentiable ℝ (fun s => F s (torusMk x)) := + (hF.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp) + exact (hd t).hasDerivAt.hasDerivWithinAt.derivWithin (uniqueDiffOn_Ici 0 t ht) + +theorem contDiff_laplacian {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) : + ContDiff ℝ ∞ (lifted (laplacian F)) := by + unfold lifted laplacian + exact ContDiff.sum (s := Finset.univ) (fun i _ => (contDiff_spaceD (contDiff_spaceD hF i) i)) + +theorem cylinderContinuous {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) : CylinderContinuous F := + fun _ _ => ((continuous_iff_lifted F).mpr hF.continuous).continuousOn + +theorem timeD_cylinderContinuous {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) : + CylinderContinuous (timeD F) := by + intro T _hT + apply (cylinderContinuous (contDiff_fullTimeD hF) T _hT).congr + intro tq htq + exact timeD_eq_fullTimeD hF htq.1.1 tq.2 + +end Derivatives + +theorem contDiff_advection {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) : + ContDiff ℝ ∞ (lifted (advection U)) := by + unfold lifted advection + apply ContDiff.sum (s := Finset.univ) + intro i _ + have hi : ContDiff ℝ ∞ (fun tx : ℝ × Space => lifted U tx i) := + (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) i).contDiff.comp hU + exact hi.smul (contDiff_spaceD hU i) + +theorem classical_of_smooth {ν : ℝ} {F U : VectorField} + (hU : ContDiff ℝ ∞ (lifted U)) (hNS : NavierStokes ν F U 0) : + ClassicalSolution ν F U 0 where + velocityContinuous := cylinderContinuous hU + timeDifferentiable := by + intro t _ht q + obtain ⟨x, rfl⟩ := mk_surjective q + exact (((hU.comp (contDiff_id.prodMk contDiff_const)).differentiable (by simp)) t).differentiableWithinAt + timeContinuous := timeD_cylinderContinuous hU + spaceTwiceDifferentiable := fun _t _ht => + (hU.comp (contDiff_const.prodMk contDiff_id)).of_le (by exact WithTop.coe_le_coe.mpr le_top) + spaceFirstContinuous := fun i => cylinderContinuous (contDiff_spaceD hU i) + spaceSecondContinuous := fun i j => cylinderContinuous (contDiff_spaceD (contDiff_spaceD hU j) i) + pressureContinuous := fun _ _ => continuousOn_const + pressureDifferentiable := fun _t _ht => differentiable_const _ + pressureGradientContinuous := by + simp only [Residual.gradient_zero] + exact fun _ _ => continuousOn_const + pressureMeanZero := fun _t _ht => MeasureTheory.integral_zero _ _ + equations := hNS + +end TorusCalculus +namespace TorusCalculus + +open scoped ContDiff Topology +open Filter Set MeasureTheory + +@[simp] theorem mk_zero : torusMk 0 = 0 := by + ext i + simp [torusMk] + +@[simp] theorem single_zero (i : Fin 3) : EuclideanSpace.single i (0 : ℝ) = 0 := by + ext j + simp only [PiLp.single_apply, PiLp.zero_apply] + split <;> rfl + +instance volume_probability : IsProbabilityMeasure torusVolume := by + dsimp [torusVolume] + infer_instance + +instance volume_rightInvariant : torusVolume.IsAddRightInvariant := by + dsimp [torusVolume] + infer_instance + +section Integrals +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +omit [NormedSpace ℝ A] in +theorem slice_integrable {F : Field A} (hF : Continuous (Function.uncurry F)) (t : ℝ) : + Integrable (F t) torusVolume := + (hF.comp (continuous_const.prodMk continuous_id)).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _) + +theorem smooth_slice_integrable {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (t : ℝ) : + Integrable (F t) torusVolume := + slice_integrable ((continuous_iff_lifted F).mpr hF.continuous) t + +theorem hasDerivAt_translation {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) + (t : ℝ) (q : Torus) (i : Fin 3) (s : ℝ) : + HasDerivAt (fun s => F t (q + torusMk (EuclideanSpace.single i s))) + (spaceD i F t (q + torusMk (EuclideanSpace.single i s))) s := by + obtain ⟨x, rfl⟩ := mk_surjective q + have hsp : Differentiable ℝ (spaceLift F t) := + (hF.comp (contDiff_const.prodMk contDiff_id)).differentiable (by simp) + simp only [← mk_add, spaceD_eq_fderiv i _ hsp] + have hcv : HasDerivAt (fun r : ℝ => x + EuclideanSpace.single i r) + (EuclideanSpace.single i 1) s := by + have heq : (fun r : ℝ => x + EuclideanSpace.single i r) = + (fun r : ℝ => x + r • EuclideanSpace.single i 1) := by + funext r + rw [single_eq_smul i r] + rw [heq] + simpa only [id_eq, one_smul] using + (((hasDerivAt_id s).smul_const (EuclideanSpace.single i 1)).const_add x) + exact (hsp _).hasFDerivAt.comp_hasDerivAt s hcv + +theorem integral_spaceD {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (t : ℝ) (i : Fin 3) : + (∫ q, spaceD i F t q ∂torusVolume) = 0 := by + have hFc := (continuous_iff_lifted F).mpr hF.continuous + have hDc := (continuous_iff_lifted (spaceD i F)).mpr (contDiff_spaceD hF i).continuous + have hFct : Continuous (F t) := hFc.comp (continuous_const.prodMk continuous_id) + have hDct : Continuous (spaceD i F t) := hDc.comp (continuous_const.prodMk continuous_id) + obtain ⟨C, hC⟩ := isCompact_univ.exists_bound_of_continuousOn hDct.continuousOn + let G : ℝ → Torus → A := fun s q => F t (q + torusMk (EuclideanSpace.single i s)) + let G' : ℝ → Torus → A := fun s q => spaceD i F t (q + torusMk (EuclideanSpace.single i s)) + have h := hasDerivAt_integral_of_dominated_loc_of_deriv_le (μ := torusVolume) + (F := G) (F' := G') (s := univ) (x₀ := 0) (bound := fun _ => C) + (Filter.univ_mem) + (Filter.Eventually.of_forall (fun s => + (hFct.comp (continuous_id.add continuous_const)).aestronglyMeasurable)) + (by simpa [G] using (smooth_slice_integrable hF t)) + ((hDct.comp (continuous_id.add continuous_const)).aestronglyMeasurable) + (Filter.Eventually.of_forall (fun q s _ => hC _ (mem_univ _))) + (integrable_const C) + (Filter.Eventually.of_forall (fun q s _ => hasDerivAt_translation hF t q i s)) + have heq : (fun s => ∫ q, G s q ∂torusVolume) = + fun _ : ℝ => ∫ q, F t q ∂torusVolume := by + funext s + exact integral_add_right_eq_self _ _ + rw [heq] at h + have hz := h.2.unique (hasDerivAt_const (0 : ℝ) (∫ q, F t q ∂torusVolume)) + simpa [G'] using hz + +theorem integral_laplacian {F : Field A} (hF : ContDiff ℝ ∞ (lifted F)) (t : ℝ) : + (∫ q, laplacian F t q ∂torusVolume) = 0 := by + rw [show (laplacian F t) = fun q => ∑ i : Fin 3, spaceD i (spaceD i F) t q from rfl, + integral_finsetSum Finset.univ (fun i _ => smooth_slice_integrable + (contDiff_spaceD (contDiff_spaceD hF i) i) t)] + simp only [integral_spaceD (contDiff_spaceD hF _) t, Finset.sum_const_zero] + +end Integrals +end TorusCalculus + +namespace Residual + +open scoped ContDiff +open TorusCalculus + +def fullForce (ν : ℝ) (U : VectorField) : VectorField := fun t q => + fullTimeD U t q + advection U t q - ν • laplacian U t q + +theorem fullForce_contDiff (ν : ℝ) {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) : + ContDiff ℝ ∞ (lifted (fullForce ν U)) := + ((contDiff_fullTimeD hU).add (contDiff_advection hU)).sub + ((contDiff_laplacian hU).const_smul ν) + +theorem fullForce_eq (ν : ℝ) {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) + {t : ℝ} (ht : 0 ≤ t) (q : Torus) : fullForce ν U t q = force ν U t q := by + rw [fullForce, force, timeD_eq_fullTimeD hU ht] + +theorem fullForce_equations (ν : ℝ) {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) + (hdiv : Solenoidal U) (hinit : ∀ q, U 0 q = 0) : + NavierStokes ν (fullForce ν U) U 0 := by + refine ⟨?_, hdiv, hinit⟩ + intro t ht q + rw [fullForce_eq ν hU ht] + exact (equations ν U hdiv hinit).1 t ht q + +end Residual + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus + +def force (ν : ℝ) (d : Input) : VectorField := Residual.fullForce ν (velocity d) + +theorem force_contDiff (ν : ℝ) (d : Input) : ContDiff ℝ ∞ (lifted (force ν d)) := + Residual.fullForce_contDiff ν (velocity_contDiff d) + +theorem force_smooth (ν : ℝ) (d : Input) : Smooth (force ν d) := + (force_contDiff ν d).contDiffOn + +theorem equations (ν : ℝ) (d : Input) : NavierStokes ν (force ν d) (velocity d) 0 := + Residual.fullForce_equations ν (velocity_contDiff d) (velocity_solenoidal d) (velocity_start d) + +theorem classical_solution (ν : ℝ) (d : Input) : + ClassicalSolution ν (force ν d) (velocity d) 0 := + classical_of_smooth (velocity_contDiff d) (equations ν d) + +end FluidLift + +namespace TorusCalculus + +open scoped ContDiff +open MeasureTheory + +theorem contDiff_component {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) (j : Fin 3) : + ContDiff ℝ ∞ (lifted (fun t q => U t q j)) := + (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) j).contDiff.comp hU + +theorem spaceD_smul {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {c : ScalarField} {F : Field A} (hc : ContDiff ℝ ∞ (lifted c)) + (hF : ContDiff ℝ ∞ (lifted F)) (i : Fin 3) (t : ℝ) (q : Torus) : + spaceD i (fun t q => c t q • F t q) t q = + spaceD i c t q • F t q + c t q • spaceD i F t q := by + have h := ((hasDerivAt_translation hc t q i 0).fun_smul + (hasDerivAt_translation hF t q i 0)).deriv + simpa only [single_zero, mk_zero, add_zero, spaceD, Pi.smul_apply, add_comm] using h + +theorem advection_eq_tensor_divergence {U : VectorField} + (hU : ContDiff ℝ ∞ (lifted U)) (t : ℝ) (hdiv : ∀ q, divergence U t q = 0) (q : Torus) : + advection U t q = ∑ i : Fin 3, spaceD i (fun t q => U t q i • U t q) t q := by + simp_rw [spaceD_smul (contDiff_component hU _) hU] + rw [Finset.sum_add_distrib, ← Finset.sum_smul] + change advection U t q = divergence U t q • U t q + advection U t q + rw [hdiv q, zero_smul, zero_add] + +theorem integral_advection {U : VectorField} (hU : ContDiff ℝ ∞ (lifted U)) + (t : ℝ) (hdiv : ∀ q, divergence U t q = 0) : + (∫ q, advection U t q ∂torusVolume) = 0 := by + have hprod (i : Fin 3) : ContDiff ℝ ∞ (lifted (fun t q => U t q i • U t q)) := + (contDiff_component hU i).smul hU + simp_rw [advection_eq_tensor_divergence hU t hdiv] + rw [integral_finsetSum Finset.univ (fun i _ => + smooth_slice_integrable (contDiff_spaceD (hprod i) i) t)] + simp only [integral_spaceD (hprod _) t, Finset.sum_const_zero] + +end TorusCalculus + +namespace FluidLift + +open scoped ContDiff +open TorusCalculus MeasureTheory + +theorem timeDerivative_half_shift (d : Input) (t : ℝ) (q : Torus) : + fullTimeD (velocity d) t (q + torusMk (EuclideanSpace.single 2 (1 / 2))) = + -fullTimeD (velocity d) t q := by + unfold fullTimeD + simp_rw [velocity_half_shift] + exact deriv.neg + +theorem integral_timeDerivative (d : Input) (t : ℝ) : + (∫ q, fullTimeD (velocity d) t q ∂torusVolume) = 0 := + integral_eq_zero_of_add_right_eq_neg (timeDerivative_half_shift d t) + +theorem force_meanZero (ν : ℝ) (d : Input) : MeanZero (force ν d) := by + intro t _ht + have hU := velocity_contDiff d + have h₁ := smooth_slice_integrable (contDiff_fullTimeD hU) t + have h₂ := smooth_slice_integrable (contDiff_advection hU) t + have h₃ : Integrable (fun q => ν • laplacian (velocity d) t q) torusVolume := + (smooth_slice_integrable (contDiff_laplacian hU) t).fun_smul ν + change (∫ q, fullTimeD (velocity d) t q + advection (velocity d) t q - + ν • laplacian (velocity d) t q ∂torusVolume) = 0 + rw [integral_sub (h₁.fun_add h₂) h₃, integral_add h₁ h₂, integral_smul, + integral_timeDerivative, integral_advection hU t (divergence_zero d t), integral_laplacian hU t] + simp + +theorem residual_computation (ν : ℝ) (d : Input) (hd : d.WellFormed) : + Smooth (velocity d) ∧ Smooth (force ν d) ∧ + MeanZero (velocity d) ∧ MeanZero (force ν d) ∧ + ClassicalSolution ν (force ν d) (velocity d) 0 ∧ + IsParticle (velocity d) (path d) ∧ + (∀ Y : ℝ → Space, IsParticle (velocity d) Y → ∀ t : ℝ, 0 ≤ t → Y t = path d t) ∧ + (MaterialEvent (path d) ↔ Halts d) := + ⟨velocity_smooth d, force_smooth ν d, velocity_meanZero d, force_meanZero ν d, + classical_solution ν d, path_isParticle d hd, + fun _Y hY _t ht => path_unique d hd hY ht, path_event_iff d hd⟩ + +end FluidLift + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/TorusIntegration.lean b/lean/OAI/Analysis/PeriodicLattice/TorusIntegration.lean new file mode 100644 index 0000000000000000000000000000000000000000..7bece8afe16bc02a9e7c13c7c36e0ba2876c8c8d --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/TorusIntegration.lean @@ -0,0 +1,413 @@ +import OAI.Analysis.PeriodicLattice.TorusDerivatives + +namespace OAI + +/-! Periodic integration and differentiation identities. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingTorusIntegration {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace TorusCalculus + +open scoped ContDiff Topology +open Filter Set MeasureTheory + +instance volume_haar : torusVolume.IsAddHaarMeasure := by + dsimp [torusVolume] + infer_instance + +section SpatialSlices +variable {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + +omit [NormedSpace ℝ A] in +theorem slice_continuous_iff (F : Field A) (t : ℝ) : + Continuous (F t) ↔ Continuous (spaceLift F t) := + mk_isOpenQuotientMap.isQuotientMap.continuous_iff + +theorem slice_contDiff_spaceD {F : Field A} {t : ℝ} {n : WithTop ℕ∞} + (hF : ContDiff ℝ (n + 1) (spaceLift F t)) (i : Fin 3) : + ContDiff ℝ n (spaceLift (spaceD i F) t) := by + have hd : Differentiable ℝ (spaceLift F t) := hF.differentiable (by simp) + have heq : spaceLift (spaceD i F) t = fun x => + (fderiv ℝ (spaceLift F t) x) (EuclideanSpace.single i 1) := by + funext x + exact spaceD_eq_fderiv i x hd + rw [heq] + exact (hF.fderiv_right le_rfl).clm_apply contDiff_const + +theorem translation_hasDerivAt {F : Field A} {t : ℝ} + (hF : Differentiable ℝ (spaceLift F t)) (q : Torus) (i : Fin 3) (s : ℝ) : + HasDerivAt (fun s => F t (q + torusMk (EuclideanSpace.single i s))) + (spaceD i F t (q + torusMk (EuclideanSpace.single i s))) s := by + obtain ⟨x, rfl⟩ := mk_surjective q + simp only [← mk_add, spaceD_eq_fderiv i _ hF] + have hcv : HasDerivAt (fun r : ℝ => x + EuclideanSpace.single i r) + (EuclideanSpace.single i 1) s := by + have heq : (fun r : ℝ => x + EuclideanSpace.single i r) = + (fun r : ℝ => x + r • EuclideanSpace.single i 1) := by + funext r + rw [single_eq_smul i r] + rw [heq] + simpa only [id_eq, one_smul] using + (((hasDerivAt_id s).smul_const (EuclideanSpace.single i 1)).const_add x) + exact (hF _).hasFDerivAt.comp_hasDerivAt s hcv + +theorem integral_spaceD_of_continuous {F : Field A} {t : ℝ} (i : Fin 3) + (hF : Differentiable ℝ (spaceLift F t)) + (hFc : Continuous (F t)) (hDc : Continuous (spaceD i F t)) : + (∫ q, spaceD i F t q ∂torusVolume) = 0 := by + have hFi : Integrable (F t) torusVolume := hFc.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _) + obtain ⟨C, hC⟩ := isCompact_univ.exists_bound_of_continuousOn hDc.continuousOn + let G : ℝ → Torus → A := fun s q => F t (q + torusMk (EuclideanSpace.single i s)) + let G' : ℝ → Torus → A := fun s q => spaceD i F t (q + torusMk (EuclideanSpace.single i s)) + have h := hasDerivAt_integral_of_dominated_loc_of_deriv_le (μ := torusVolume) + (F := G) (F' := G') (s := univ) (x₀ := 0) (bound := fun _ => C) + (Filter.univ_mem) + (Filter.Eventually.of_forall (fun s => + (hFc.comp (continuous_id.add continuous_const)).aestronglyMeasurable)) + (by simpa [G] using hFi) + ((hDc.comp (continuous_id.add continuous_const)).aestronglyMeasurable) + (Filter.Eventually.of_forall (fun q s _ => hC _ (mem_univ _))) + (integrable_const C) + (Filter.Eventually.of_forall (fun q s _ => + translation_hasDerivAt hF q i s)) + have heq : (fun s => ∫ q, G s q ∂torusVolume) = + fun _ : ℝ => ∫ q, F t q ∂torusVolume := by + funext s + exact integral_add_right_eq_self _ _ + rw [heq] at h + have hz := h.2.unique (hasDerivAt_const (0 : ℝ) (∫ q, F t q ∂torusVolume)) + simpa [G'] using hz + +theorem integral_spaceD_C1 {F : Field A} {t : ℝ} + (hF : ContDiff ℝ 1 (spaceLift F t)) (i : Fin 3) : + (∫ q, spaceD i F t q ∂torusVolume) = 0 := + integral_spaceD_of_continuous i (hF.differentiable one_ne_zero) + ((slice_continuous_iff F t).mpr hF.continuous) + ((slice_continuous_iff (spaceD i F) t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using hF) i).continuous) + +theorem spaceD_add {F G : Field A} {t : ℝ} + (hF : Differentiable ℝ (spaceLift F t)) (hG : Differentiable ℝ (spaceLift G t)) + (i : Fin 3) (q : Torus) : + spaceD i (F + G) t q = spaceD i F t q + spaceD i G t q := by + have h := ((translation_hasDerivAt hF q i 0).fun_add + (translation_hasDerivAt hG q i 0)).deriv + simpa only [single_zero, mk_zero, add_zero, spaceD, Pi.add_apply] using h + +theorem spaceD_sub {F G : Field A} {t : ℝ} + (hF : Differentiable ℝ (spaceLift F t)) (hG : Differentiable ℝ (spaceLift G t)) + (i : Fin 3) (q : Torus) : + spaceD i (F - G) t q = spaceD i F t q - spaceD i G t q := by + have h := ((translation_hasDerivAt hF q i 0).fun_sub + (translation_hasDerivAt hG q i 0)).deriv + simpa only [single_zero, mk_zero, add_zero, spaceD, Pi.sub_apply] using h + +end SpatialSlices + +section InnerProducts +variable {A : Type*} [NormedAddCommGroup A] [InnerProductSpace ℝ A] + +theorem spaceD_inner {F G : Field A} {t : ℝ} + (hF : Differentiable ℝ (spaceLift F t)) (hG : Differentiable ℝ (spaceLift G t)) + (i : Fin 3) (q : Torus) : + spaceD i (fun t q => inner ℝ (F t q) (G t q)) t q = + inner ℝ (F t q) (spaceD i G t q) + inner ℝ (spaceD i F t q) (G t q) := by + have h := (HasDerivAt.inner ℝ (translation_hasDerivAt hF q i 0) + (translation_hasDerivAt hG q i 0)).deriv + simpa only [single_zero, mk_zero, add_zero, spaceD] using h + +theorem integration_by_parts {F G : Field A} {t : ℝ} + (hF : ContDiff ℝ 1 (spaceLift F t)) (hG : ContDiff ℝ 1 (spaceLift G t)) + (i : Fin 3) : + (∫ q, inner ℝ (F t q) (spaceD i G t q) ∂torusVolume) = + -(∫ q, inner ℝ (spaceD i F t q) (G t q) ∂torusVolume) := by + have hP : ContDiff ℝ 1 (spaceLift (fun t q => inner ℝ (F t q) (G t q)) t) := hF.inner ℝ hG + have hFc := (slice_continuous_iff F t).mpr hF.continuous + have hGc := (slice_continuous_iff G t).mpr hG.continuous + have hDF := (slice_continuous_iff (spaceD i F) t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using hF) i).continuous + have hDG := (slice_continuous_iff (spaceD i G) t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using hG) i).continuous + have h := integral_spaceD_C1 hP i + simp_rw [spaceD_inner (hF.differentiable one_ne_zero) (hG.differentiable one_ne_zero)] at h + rw [integral_add + ((hFc.inner hDG).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)) + ((hDF.inner hGc).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _))] at h + linarith + +theorem integral_inner_laplacian {F : Field A} {t : ℝ} + (hF : ContDiff ℝ 2 (spaceLift F t)) : + (∫ q, inner ℝ (F t q) (laplacian F t q) ∂torusVolume) = + -∑ i : Fin 3, ∫ q, ‖spaceD i F t q‖ ^ 2 ∂torusVolume := by + have hF₁ : ContDiff ℝ 1 (spaceLift F t) := hF.of_le (by norm_num) + have hD₁ (i : Fin 3) : ContDiff ℝ 1 (spaceLift (spaceD i F) t) := + slice_contDiff_spaceD (n := 1) (by convert hF using 1; norm_num) i + have hFi := (slice_continuous_iff F t).mpr hF.continuous + have hDDi (i : Fin 3) := (slice_continuous_iff (spaceD i (spaceD i F)) t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using hD₁ i) i).continuous + simp_rw [laplacian, inner_sum] + rw [integral_finsetSum Finset.univ (fun i _ => + (hFi.inner (hDDi i)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _))] + simp_rw [integration_by_parts hF₁ (hD₁ _), real_inner_self_eq_norm_sq] + exact Finset.sum_neg_distrib _ + +end InnerProducts + +end TorusCalculus + +namespace TorusCalculus + +open scoped ContDiff +open MeasureTheory + +theorem spaceD_congr_slice {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {F G : Field A} {t : ℝ} (h : ∀ q, F t q = G t q) (i : Fin 3) (q : Torus) : + spaceD i F t q = spaceD i G t q := by + unfold spaceD + simp_rw [h] + +theorem laplacian_sub {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {F G : Field A} {t : ℝ} + (hF : ContDiff ℝ 2 (spaceLift F t)) (hG : ContDiff ℝ 2 (spaceLift G t)) (q : Torus) : + laplacian (F - G) t q = laplacian F t q - laplacian G t q := by + unfold laplacian + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro i _ + rw [spaceD_congr_slice (G := spaceD i F - spaceD i G) + (fun x => spaceD_sub (hF.differentiable (by norm_num)) (hG.differentiable (by norm_num)) i x)] + exact spaceD_sub + ((slice_contDiff_spaceD (n := 1) (by convert hF using 1; norm_num) i).differentiable one_ne_zero) + ((slice_contDiff_spaceD (n := 1) (by convert hG using 1; norm_num) i).differentiable one_ne_zero) i q + +theorem eq_zero_of_integral_norm_sq_eq_zero {A : Type*} [NormedAddCommGroup A] + {F : Torus → A} (hF : Continuous F) + (hzero : (∫ q, ‖F q‖ ^ 2 ∂torusVolume) = 0) : ∀ q, F q = 0 := by + have hc : Continuous (fun q => ‖F q‖ ^ 2) := hF.norm.pow 2 + have ha := (integral_eq_zero_iff_of_nonneg (fun q => sq_nonneg ‖F q‖) + (hc.integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _))).mp hzero + have heq := (hc.ae_eq_iff_eq torusVolume continuous_const).mp ha + intro q + have hq : ‖F q‖ ^ 2 = 0 := congrFun heq q + exact norm_eq_zero.mp ((pow_eq_zero_iff (by norm_num : (2 : ℕ) ≠ 0)).mp hq) + +theorem spatially_constant_of_partials_zero {A : Type*} + [NormedAddCommGroup A] [NormedSpace ℝ A] {F : Field A} {t : ℝ} + (hF : Differentiable ℝ (spaceLift F t)) (hzero : ∀ i q, spaceD i F t q = 0) + (q r : Torus) : F t q = F t r := by + obtain ⟨x, rfl⟩ := mk_surjective q + obtain ⟨y, rfl⟩ := mk_surjective r + apply is_const_of_fderiv_eq_zero hF _ x y + intro z + have hz : (fderiv ℝ (spaceLift F t) z).toLinearMap = 0 := by + apply (EuclideanSpace.basisFun (Fin 3) ℝ).toBasis.ext + intro i + change (fderiv ℝ (spaceLift F t) z) ((EuclideanSpace.basisFun (Fin 3) ℝ) i) = 0 + rw [EuclideanSpace.basisFun_apply, ← spaceD_eq_fderiv i z hF, hzero] + ext w + exact DFunLike.congr_fun hz w + +theorem harmonic_constant {F : ScalarField} {t : ℝ} + (hF : ContDiff ℝ 2 (spaceLift F t)) (hΔ : ∀ q, laplacian F t q = 0) + (q r : Torus) : F t q = F t r := by + have hE := integral_inner_laplacian hF + simp only [hΔ, inner_zero_right, integral_zero] at hE + have hI : ∀ i : Fin 3, (∫ q, ‖spaceD i F t q‖ ^ 2 ∂torusVolume) = 0 := by + have hsum : (∑ i : Fin 3, ∫ q, ‖spaceD i F t q‖ ^ 2 ∂torusVolume) = 0 := by + linarith + exact fun i => (Finset.sum_eq_zero_iff_of_nonneg (fun i _ => + integral_nonneg (fun q => sq_nonneg ‖spaceD i F t q‖))).mp hsum i (Finset.mem_univ i) + apply spatially_constant_of_partials_zero (hF.differentiable (by norm_num)) _ q r + intro i + exact eq_zero_of_integral_norm_sq_eq_zero + ((slice_continuous_iff (spaceD i F) t).mpr + (slice_contDiff_spaceD (n := 1) (by convert hF using 1; norm_num) i).continuous) (hI i) + +theorem harmonic_meanZero_eq_zero {F : ScalarField} {t : ℝ} + (hF : ContDiff ℝ 2 (spaceLift F t)) (hΔ : ∀ q, laplacian F t q = 0) + (hmean : (∫ q, F t q ∂torusVolume) = 0) (q : Torus) : F t q = 0 := by + have heq : F t = fun _ => F t q := funext (fun r => harmonic_constant hF hΔ r q) + rw [heq, integral_const] at hmean + simpa using hmean + +theorem poisson_unique {g : VectorField} {φ : ScalarField} + (hφ : ∀ t : ℝ, 0 ≤ t → ContDiff ℝ 2 (spaceLift φ t)) (hmean : MeanZero φ) + (hΔ : ∀ t : ℝ, 0 ≤ t → ∀ q, laplacian φ t q = divergence g t q) : + UniqueMeanZeroPoisson g φ := by + intro ψ hψ hψmean hψΔ t ht q + have hF : ContDiff ℝ 2 (spaceLift (ψ - φ) t) := (hψ t ht).sub (hφ t ht) + have hzero : (ψ - φ) t q = 0 := harmonic_meanZero_eq_zero hF + (fun r => by rw [laplacian_sub (hψ t ht) (hφ t ht), hψΔ t ht, hΔ t ht, sub_self]) + (by + change (∫ r, ψ t r - φ t r ∂torusVolume) = 0 + rw [integral_sub + (((slice_continuous_iff ψ t).mpr (hψ t ht).continuous).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _)) + (((slice_continuous_iff φ t).mpr (hφ t ht).continuous).integrable_of_hasCompactSupport + (HasCompactSupport.of_compactSpace _)), hψmean t ht, hmean t ht, sub_self]) q + exact sub_eq_zero.mp hzero + +end TorusCalculus + +namespace TorusCalculus + +open scoped ContDiff +open MeasureTheory + +section ClassicalOperations + +theorem cylinder_slice_continuous {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {F : Field A} (hF : CylinderContinuous F) {t : ℝ} (ht : 0 ≤ t) : Continuous (F t) := by + apply continuousOn_univ.mp + exact (hF t ht).comp (continuous_const.prodMk continuous_id).continuousOn + (fun q _ => ⟨⟨ht, le_rfl⟩, Set.mem_univ q⟩) + +theorem spaceD_component {U : VectorField} {t : ℝ} + (hU : Differentiable ℝ (spaceLift U t)) (i j : Fin 3) (q : Torus) : + spaceD i (fun t q => U t q j) t q = spaceD i U t q j := by + have h := ((PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) j).hasFDerivAt.comp_hasDerivAt 0 + (translation_hasDerivAt hU q i 0)).deriv + simpa only [single_zero, mk_zero, add_zero, spaceD, Function.comp_def, PiLp.proj_apply] using h + +theorem contDiff_component_slice {U : VectorField} {t : ℝ} {n : WithTop ℕ∞} + (hU : ContDiff ℝ n (spaceLift U t)) (i : Fin 3) : + ContDiff ℝ n (spaceLift (fun t q => U t q i) t) := + (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) i).contDiff.comp hU + +theorem spaceD_smul_slice {A : Type*} [NormedAddCommGroup A] [NormedSpace ℝ A] + {c : ScalarField} {F : Field A} {t : ℝ} + (hc : Differentiable ℝ (spaceLift c t)) (hF : Differentiable ℝ (spaceLift F t)) + (i : Fin 3) (q : Torus) : + spaceD i (fun t q => c t q • F t q) t q = + spaceD i c t q • F t q + c t q • spaceD i F t q := by + have h := ((translation_hasDerivAt hc q i 0).fun_smul + (translation_hasDerivAt hF q i 0)).deriv + simpa only [single_zero, mk_zero, add_zero, spaceD, add_comm] using h + +def transport (V W : VectorField) : VectorField := fun t q => + ∑ i : Fin 3, V t q i • spaceD i W t q + +theorem transport_continuous {V W : VectorField} {t : ℝ} + (hV : ContDiff ℝ 1 (spaceLift V t)) (hW : ContDiff ℝ 1 (spaceLift W t)) : + Continuous (transport V W t) := by + apply continuous_finsetSum _ (fun i _ => ?_) + exact + ((PiLp.continuous_apply 2 (fun _ : Fin 3 => ℝ) i).comp ((slice_continuous_iff V t).mpr hV.continuous)).smul + ((slice_continuous_iff (spaceD i W) t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using hW) i).continuous) + +theorem transport_eq_divergence_tensor {V W : VectorField} {t : ℝ} + (hV : Differentiable ℝ (spaceLift V t)) (hW : Differentiable ℝ (spaceLift W t)) + (hdiv : ∀ q, divergence V t q = 0) (q : Torus) : + (∑ i : Fin 3, spaceD i (fun t q => V t q i • W t q) t q) = transport V W t q := by + have hc (i : Fin 3) : Differentiable ℝ (spaceLift (fun t q => V t q i) t) := + (PiLp.proj (𝕜 := ℝ) 2 (fun _ : Fin 3 => ℝ) i).differentiable.comp hV + simp_rw [spaceD_smul_slice (hc _) hW] + rw [Finset.sum_add_distrib, ← Finset.sum_smul] + change divergence V t q • W t q + transport V W t q = _ + rw [hdiv q, zero_smul, zero_add] + +theorem integral_inner_transport {V W Z : VectorField} {t : ℝ} + (hV : ContDiff ℝ 1 (spaceLift V t)) (hW : ContDiff ℝ 1 (spaceLift W t)) + (hZ : ContDiff ℝ 1 (spaceLift Z t)) (hdiv : ∀ q, divergence V t q = 0) : + (∫ q, inner ℝ (W t q) (transport V Z t q) ∂torusVolume) = + -(∫ q, inner ℝ (transport V W t q) (Z t q) ∂torusVolume) := by + have hP (i : Fin 3) : ContDiff ℝ 1 (spaceLift (fun t q => V t q i • W t q) t) := + (contDiff_component_slice hV i).smul hW + have hWc := (slice_continuous_iff W t).mpr hW.continuous + have hZc := (slice_continuous_iff Z t).mpr hZ.continuous + have hDc (i : Fin 3) := (slice_continuous_iff (spaceD i Z) t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using hZ) i).continuous + have hPc (i : Fin 3) := (slice_continuous_iff (fun t q => V t q i • W t q) t).mpr + (hP i).continuous + have hDPc (i : Fin 3) := (slice_continuous_iff (spaceD i (fun t q => V t q i • W t q)) t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using hP i) i).continuous + calc + _ = ∑ i : Fin 3, ∫ q, inner ℝ (V t q i • W t q) (spaceD i Z t q) ∂torusVolume := by + simp_rw [transport, inner_sum, inner_smul_right, real_inner_smul_left] + rw [integral_finsetSum Finset.univ (fun i _ => by + simpa only [real_inner_smul_left] using + ((((hPc i).inner (hDc i)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)) : Integrable (fun q => inner ℝ (V t q i • W t q) (spaceD i Z t q)) torusVolume))] + _ = ∑ i : Fin 3, -(∫ q, inner ℝ (spaceD i (fun t q => V t q i • W t q) t q) (Z t q) + ∂torusVolume) := by + apply Finset.sum_congr rfl + intro i _ + exact integration_by_parts (hP i) hZ i + _ = -(∫ q, inner ℝ (∑ i : Fin 3, spaceD i (fun t q => V t q i • W t q) t q) (Z t q) + ∂torusVolume) := by + simp_rw [sum_inner] + rw [integral_finsetSum Finset.univ (fun i _ => + ((hDPc i).inner hZc).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _))] + exact Finset.sum_neg_distrib _ + _ = _ := by + simp_rw [transport_eq_divergence_tensor (hV.differentiable one_ne_zero) + (hW.differentiable one_ne_zero) hdiv] + +theorem integral_inner_transport_self {V W : VectorField} {t : ℝ} + (hV : ContDiff ℝ 1 (spaceLift V t)) (hW : ContDiff ℝ 1 (spaceLift W t)) + (hdiv : ∀ q, divergence V t q = 0) : + (∫ q, inner ℝ (W t q) (transport V W t q) ∂torusVolume) = 0 := by + have h := integral_inner_transport hV hW hW hdiv + have he : (∫ q, inner ℝ (transport V W t q) (W t q) ∂torusVolume) = + (∫ q, inner ℝ (W t q) (transport V W t q) ∂torusVolume) := by + apply integral_congr_ae + exact Filter.Eventually.of_forall (fun q => real_inner_comm _ _) + rw [he] at h + linarith + +theorem integral_inner_gradient {W : VectorField} {p : ScalarField} {t : ℝ} + (hW : ContDiff ℝ 1 (spaceLift W t)) (hdiv : ∀ q, divergence W t q = 0) + (hpc : Continuous (p t)) (hp : Differentiable ℝ (spaceLift p t)) + (hdp : Continuous (gradient p t)) : + (∫ q, inner ℝ (W t q) (gradient p t q) ∂torusVolume) = 0 := by + have hWc := (slice_continuous_iff W t).mpr hW.continuous + have hD (i : Fin 3) : Continuous (spaceD i (fun t q => W t q i) t) := + (slice_continuous_iff _ t).mpr + (slice_contDiff_spaceD (n := 0) (by simpa using contDiff_component_slice hW i) i).continuous + have hDP (i : Fin 3) : Continuous (spaceD i p t) := (PiLp.continuous_apply 2 (fun _ : Fin 3 => ℝ) i).comp hdp + have hrule (i : Fin 3) (q : Torus) : + spaceD i (fun t q => W t q i * p t q) t q = + spaceD i (fun t q => W t q i) t q * p t q + W t q i * spaceD i p t q := + spaceD_smul_slice ((contDiff_component_slice hW i).differentiable one_ne_zero) hp i q + have hI (i : Fin 3) : (∫ q, W t q i * spaceD i p t q ∂torusVolume) = + -(∫ q, spaceD i (fun t q => W t q i) t q * p t q ∂torusVolume) := by + have hPdiff : Differentiable ℝ (spaceLift (fun t q => W t q i * p t q) t) := + ((contDiff_component_slice hW i).differentiable one_ne_zero).mul hp + have hPcont : Continuous (fun q => W t q i * p t q) := ((PiLp.continuous_apply 2 (fun _ : Fin 3 => ℝ) i).comp hWc).mul hpc + have hPderiv : Continuous (spaceD i (fun t q => W t q i * p t q) t) := by + change Continuous (fun q => spaceD i (fun t q => W t q i * p t q) t q) + simp_rw [hrule] + exact ((hD i).mul hpc).add (((PiLp.continuous_apply 2 (fun _ : Fin 3 => ℝ) i).comp hWc).mul (hDP i)) + have h := integral_spaceD_of_continuous i hPdiff hPcont hPderiv + simp_rw [hrule] at h + rw [integral_add (f := fun q => spaceD i (fun t q => W t q i) t q * p t q) + (g := fun q => W t q i * spaceD i p t q) + ((((hD i).mul hpc).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)) : Integrable (fun q => spaceD i (fun t q => W t q i) t q * p t q) torusVolume) + (((((PiLp.continuous_apply 2 (fun _ : Fin 3 => ℝ) i).comp hWc).mul (hDP i)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)) : Integrable (fun q => W t q i * spaceD i p t q) torusVolume)] at h + linarith + have hinner (q : Torus) : inner ℝ (W t q) (gradient p t q) = + ∑ i : Fin 3, W t q i * spaceD i p t q := by + simp [PiLp.inner_apply, gradient, mul_comm] + simp_rw [hinner] + rw [integral_finsetSum (f := fun i q => W t q i * spaceD i p t q) Finset.univ (fun i _ => + (((((PiLp.continuous_apply 2 (fun _ : Fin 3 => ℝ) i).comp hWc).mul (hDP i)).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)) : Integrable (fun q => W t q i * spaceD i p t q) torusVolume))] + simp_rw [hI] + rw [Finset.sum_neg_distrib, ← integral_finsetSum + (f := fun i q => spaceD i (fun t q => W t q i) t q * p t q) Finset.univ (fun i _ => + ((((hD i).mul hpc).integrable_of_hasCompactSupport (HasCompactSupport.of_compactSpace _)) : Integrable (fun q => spaceD i (fun t q => W t q i) t q * p t q) torusVolume))] + simp_rw [← Finset.sum_mul] + change -(∫ q, divergence W t q * p t q ∂torusVolume) = 0 + simp only [hdiv, zero_mul, integral_zero, neg_zero] + +end ClassicalOperations +end TorusCalculus + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Trajectories.lean b/lean/OAI/Analysis/PeriodicLattice/Trajectories.lean new file mode 100644 index 0000000000000000000000000000000000000000..1a4fe3de965fcd14678088c701e4ee72c4d0bbde --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Trajectories.lean @@ -0,0 +1,133 @@ +import OAI.Analysis.PeriodicLattice.Profiles + +namespace OAI + +/-! Uniqueness of trajectories and smooth flow estimates. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingTrajectories {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace Trajectories + +open Set +open scoped ContDiff + +variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + [FiniteDimensional ℝ E] + +theorem unique {v : ℝ → E → E} (hv : ContDiff ℝ 1 (fun tx : ℝ × E => v tx.1 tx.2)) + {X Y : ℝ → E} (hX : ∀ t : ℝ, 0 ≤ t → HasDerivWithinAt X (v t (X t)) (Ici 0) t) + (hY : ∀ t : ℝ, 0 ≤ t → HasDerivWithinAt Y (v t (Y t)) (Ici 0) t) + (h₀ : X 0 = Y 0) {T : ℝ} (hT : 0 ≤ T) : X T = Y T := by + have hcX : ContinuousOn X (Icc 0 T) := fun t ht => + ((hX t ht.1).mono Icc_subset_Ici_self).continuousWithinAt + have hcY : ContinuousOn Y (Icc 0 T) := fun t ht => + ((hY t ht.1).mono Icc_subset_Ici_self).continuousWithinAt + obtain ⟨R₁, hR₁⟩ := isCompact_Icc.exists_bound_of_continuousOn hcX + obtain ⟨R₂, hR₂⟩ := isCompact_Icc.exists_bound_of_continuousOn hcY + let R := max R₁ R₂ + have hBX : ∀ t ∈ Icc 0 T, X t ∈ Metric.closedBall (0 : E) R := by + intro t ht + rw [Metric.mem_closedBall, dist_zero_right] + exact (hR₁ t ht).trans (le_max_left _ _) + have hBY : ∀ t ∈ Icc 0 T, Y t ∈ Metric.closedBall (0 : E) R := by + intro t ht + rw [Metric.mem_closedBall, dist_zero_right] + exact (hR₂ t ht).trans (le_max_right _ _) + let S : Set (ℝ × E) := Icc 0 T ×ˢ Metric.closedBall 0 R + have hcS : IsCompact S := isCompact_Icc.prod (isCompact_closedBall _ _) + obtain ⟨B, hB⟩ := hcS.exists_bound_of_continuousOn + (hv.continuous_fderiv (by norm_num)).continuousOn + have hlip : LipschitzOnWith B.toNNReal (fun tx : ℝ × E => v tx.1 tx.2) S := by + apply Convex.lipschitzOnWith_of_nnnorm_fderiv_le (𝕜 := ℝ) + · intro tx htx + exact (hv.differentiable (by norm_num)).differentiableAt + · intro tx htx + simpa only [norm_toNNReal] using Real.toNNReal_le_toNNReal (hB tx htx) + · exact (convex_Icc (0 : ℝ) T).prod (convex_closedBall (0 : E) R) + have hlip' : ∀ t ∈ Ico 0 T, LipschitzOnWith B.toNNReal (v t) (Metric.closedBall 0 R) := by + intro t ht + apply LipschitzOnWith.of_dist_le_mul + intro x hx y hy + simpa using hlip.dist_le_mul (t, x) ⟨⟨ht.1, ht.2.le⟩, hx⟩ + (t, y) ⟨⟨ht.1, ht.2.le⟩, hy⟩ + have heq := ODE_solution_unique_of_mem_Icc_right hlip' hcX + (fun t ht => (hX t ht.1).mono (Ici_subset_Ici.mpr ht.1)) + (fun t ht => hBX t ⟨ht.1, ht.2.le⟩) hcY + (fun t ht => (hY t ht.1).mono (Ici_subset_Ici.mpr ht.1)) + (fun t ht => hBY t ⟨ht.1, ht.2.le⟩) h₀ + exact heq ⟨hT, le_rfl⟩ + +end Trajectories + +namespace Profiles + +open Filter Set +open scoped ContDiff Topology + +variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] + +def accumulated (W : ℕ → E) (t : ℝ) : E := ∑ᶠ n : ℕ, shiftedClock n t • W n + +theorem accumulated_contDiff (W : ℕ → E) : ContDiff ℝ ∞ (accumulated W) := by + apply contMDiff_iff_contDiff.mp + apply contMDiff_finsum + · intro n + exact contMDiff_iff_contDiff.mpr ((shiftedClock_contDiff n).smul contDiff_const) + · apply shiftedClock_locallyFinite.subset + intro n t ht hz + exact ht (by simp [hz]) + +theorem accumulated_in_collar (W : ℕ → E) (n : ℕ) {t : ℝ} + (ht : (n : ℝ) - 1 / 3 < t) (ht' : t < n + 4 / 3) : + accumulated W t = (∑ m ∈ Finset.range n, W m) + shiftedClock n t • W n := by + have hs : Function.support (fun m : ℕ => shiftedClock m t • W m) ⊆ + (Finset.range (n + 1) : Set ℕ) := by + intro m hm + by_contra h + have hm' : n + 1 ≤ m := by simpa only [Finset.mem_coe, Finset.mem_range, not_lt] using h + have hm'' : (n : ℝ) + 1 ≤ (m : ℝ) := by exact_mod_cast hm' + have hz : shiftedClock m t = 0 := clock_zero (by linarith) + exact hm (by simp only [hz, zero_smul]) + rw [accumulated, finsum_eq_sum_of_support_subset _ hs, Finset.sum_range_succ] + congr 1 + apply Finset.sum_congr rfl + intro m hm + have hm' : (m : ℝ) + 1 ≤ (n : ℝ) := by exact_mod_cast Finset.mem_range.mp hm + rw [show shiftedClock m t = 1 from clock_one (by linarith), one_smul] + +theorem accumulated_eventually (W : ℕ → E) (n : ℕ) {t : ℝ} + (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) : + accumulated W =ᶠ[𝓝 t] + (fun s => (∑ m ∈ Finset.range n, W m) + shiftedClock n s • W n) := by + filter_upwards [Ioo_mem_nhds (show (n : ℝ) - 1 / 3 < t by linarith) + (show t < n + 4 / 3 by linarith)] with s hs + exact accumulated_in_collar W n hs.1 hs.2 + +theorem accumulated_on_slot (W : ℕ → E) (n : ℕ) {t : ℝ} + (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) : + accumulated W t = (∑ m ∈ Finset.range n, W m) + shiftedClock n t • W n := + (accumulated_eventually W n ht ht').eq_of_nhds + +theorem accumulated_at_integer (W : ℕ → E) (n : ℕ) : + accumulated W n = ∑ m ∈ Finset.range n, W m := by + rw [accumulated_on_slot W n le_rfl (by linarith)] + have hz : shiftedClock n n = 0 := clock_zero (by norm_num) + rw [hz, zero_smul, add_zero] + +theorem accumulated_hasDerivAt (W : ℕ → E) (n : ℕ) {t : ℝ} + (ht : (n : ℝ) ≤ t) (ht' : t ≤ n + 1) : + HasDerivAt (accumulated W) (pulse n t • W n) t := by + apply (accumulated_eventually W n ht ht').hasDerivAt_iff.mpr + exact ((shiftedClock_hasDerivAt n t).smul_const (W n)).const_add _ + +end Profiles + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PeriodicLattice/Trigonometry.lean b/lean/OAI/Analysis/PeriodicLattice/Trigonometry.lean new file mode 100644 index 0000000000000000000000000000000000000000..8d3ddfc5356ae401a48a207dc4bbeb90e30174a6 --- /dev/null +++ b/lean/OAI/Analysis/PeriodicLattice/Trigonometry.lean @@ -0,0 +1,279 @@ +import OAI.Analysis.PeriodicLattice.ElementaryFunctions + +namespace OAI + +/-! Effective trigonometric values and derivative stencils. -/ + +namespace PeriodicLattice + +local instance finiteFunctionEncodingTrigonometry {n : ℕ} {A : Type*} [Encodable A] : + Encodable (Fin n → A) := Encodable.finArrow + +noncomputable section + +namespace CertifiedReal +open Encodable Filter Topology Finset +local instance trigonometryLocal1 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable + +def phaseCoeff (sinFlag : Bool) (i : ℕ) : ℤ := + if sinFlag then (if i % 4 = 1 then 1 else if i % 4 = 3 then -1 else 0) + else (if i % 4 = 0 then 1 else if i % 4 = 2 then -1 else 0) + +@[fun_prop] theorem phaseCoeff_recursive : Primrec (fun p : Bool × ℕ => phaseCoeff p.1 p.2) := by + unfold phaseCoeff + apply RecursiveArithmetic.bool_cond Primrec.fst + · apply Primrec.ite (Primrec.eq.comp (by fun_prop) (Primrec.const 1)) (Primrec.const 1) + exact Primrec.ite (Primrec.eq.comp (by fun_prop) (Primrec.const 3)) (Primrec.const (-1)) (Primrec.const 0) + · apply Primrec.ite (Primrec.eq.comp (by fun_prop) (Primrec.const 0)) (Primrec.const 1) + exact Primrec.ite (Primrec.eq.comp (by fun_prop) (Primrec.const 2)) (Primrec.const (-1)) (Primrec.const 0) + +def complexPart (b : Bool) (z : ℂ) : ℝ := if b then z.im else z.re + +def trig (b : Bool) (x : ℝ) : ℝ := if b then Real.sin x else Real.cos x + +theorem phaseCoeff_spec (b : Bool) (n : ℕ) : + (phaseCoeff b n : ℝ) = complexPart b (Complex.I ^ n) := by + have hm := Nat.mod_lt n (by decide : 0 < 4) + dsimp [complexPart] + rw [Complex.I_pow_eq_pow_mod] + cases b <;> interval_cases h : n % 4 <;> norm_num [phaseCoeff, h] + +theorem complexPart_linear (b : Bool) (x : ℝ) (n : ℕ) (k : ℕ) : + complexPart b (((x : ℂ) * Complex.I) ^ n / k) = (phaseCoeff b n : ℝ) * x ^ n / k := by + rw [phaseCoeff_spec, mul_pow, ← Complex.ofReal_pow] + cases b <;> simp [complexPart, mul_comm] <;> + simp only [← Complex.ofReal_pow, Complex.ofReal_re, Complex.ofReal_im] <;> ring + +theorem trig_taylor (b : Bool) (x : ℝ) (M N : ℕ) (hx : |x| ≤ M) + (hN : 2 * M + 1 ≤ N) : + |trig b x - ∑ i ∈ range N, (phaseCoeff b i : ℝ) * x ^ i / i.factorial| ≤ + 2 * (M : ℝ) ^ N / N.factorial := by + have htail := Complex.exp_bound' (x := (x : ℂ) * Complex.I) (n := N) (by + rw [norm_mul, Complex.norm_I, mul_one, Complex.norm_real, Real.norm_eq_abs] + apply (div_le_div_of_nonneg_right hx (by positivity)).trans + apply (div_le_iff₀ (by positivity)).mpr + have hnR : 2 * (M : ℝ) + 1 ≤ N := by exact_mod_cast hN + push_cast; linarith) + have partBound (z : ℂ) : |complexPart b z| ≤ ‖z‖ := by + cases b + · exact Complex.abs_re_le_norm z + · exact Complex.abs_im_le_norm z + have h := (partBound (Complex.exp ((x : ℂ) * Complex.I) - + ∑ i ∈ range N, ((x : ℂ) * Complex.I)^i / i.factorial)).trans htail + have heq : complexPart b (Complex.exp ((x : ℂ) * Complex.I) - + ∑ i ∈ range N, ((x : ℂ) * Complex.I)^i / i.factorial) = + trig b x - ∑ i ∈ range N, (phaseCoeff b i : ℝ) * x ^ i / i.factorial := by + have hsum : complexPart b (∑ i ∈ range N, ((x : ℂ) * Complex.I)^i / i.factorial) = + ∑ i ∈ range N, (phaseCoeff b i : ℝ) * x ^ i / i.factorial := by + simp_rw [← complexPart_linear b x] + cases b <;> simp [complexPart] + cases b <;> simp only [complexPart, Bool.false_eq_true, ↓reduceIte, Complex.sub_re, Complex.sub_im, + Complex.exp_ofReal_mul_I_re, Complex.exp_ofReal_mul_I_im, trig] at hsum ⊢ <;> rw [hsum] + rw [heq, norm_mul, Complex.norm_I, mul_one, Complex.norm_real, Real.norm_eq_abs] at h + apply h.trans + rw [div_mul_eq_mul_div, mul_comm _ (2 : ℝ)] + gcongr + +section +variable {A : Type*} [Primcodable A] + +theorem Effective.trig {f : A → ℝ} (hf : Effective f) (flag : Bool) : + Effective (fun a => trig flag (f a)) := by + obtain ⟨q,hq,bq⟩ := hf + let M (a : A) : ℕ := (q (a,0)).num.natAbs + 3 + have hM : Computable M := by unfold M; fun_prop + have b (a : A) (n : ℕ) : |(q (a,n) : ℝ)| ≤ (M a : ℝ) := by + have hf0 : |f a| ≤ (q (a,0)).num.natAbs + 1 := by + have ht := (abs_add_le (f a - q (a,0)) (q (a,0))).trans + (add_le_add ((bq a 0).trans (error_le_one 0)) (rat_abs_bound _)) + rw [sub_add_cancel] at ht + linarith + have ht := (abs_add_le ((q (a,n) : ℝ) - f a) (f a)).trans + (add_le_add (by simpa only [abs_sub_comm] using (bq a n).trans (error_le_one n)) hf0) + rw [sub_add_cancel] at ht + dsimp [M]; push_cast; linarith + let N (a : A) (n : ℕ) := 2 * M a + 1 + n + refine of_enclosures + (q := fun an => ∑ i ∈ range (N an.1 an.2), (phaseCoeff flag i : ℚ) * q an ^ i / (i.factorial : ℚ)) + (e := fun an => qerror an.2 + + 2 * (M an.1 : ℚ) ^ N an.1 an.2 / (N an.1 an.2).factorial) + (by + apply computable_sum + · unfold N; fun_prop + · change Computable (fun p : (A × ℕ) × ℕ => (phaseCoeff flag p.2 : ℚ) * q p.1 ^ p.2 / (p.2.factorial : ℚ)) + fun_prop) + (by unfold N; fun_prop) ?_ ?_ + · intro a n + have hd : |CertifiedReal.trig flag (f a) - CertifiedReal.trig flag (q (a,n))| ≤ error n := by + cases flag + · exact (Real.abs_cos_sub_cos_le _ _).trans (bq a n) + · exact (Real.abs_sin_sub_sin_le _ _).trans (bq a n) + simp only [Rat.cast_add, Rat.cast_mul, Rat.cast_pow, Rat.cast_ofNat, Rat.cast_div, + Rat.cast_natCast, Rat.cast_intCast, Rat.cast_sum, cast_qerror] + exact (abs_sub_le _ _ _).trans (add_le_add hd (trig_taylor flag (q (a,n)) (M a) (N a n) + (b a n) (by dsimp [N]; omega))) + · intro a + have hn : Tendsto (fun n => N a n) atTop atTop := + tendsto_atTop_mono (fun n : ℕ => show n ≤ N a n by dsimp [N]; omega) tendsto_id + have ht := (Real.summable_pow_div_factorial (M a : ℝ)).tendsto_atTop_zero.comp hn + simpa only [Rat.cast_add, Rat.cast_mul, Rat.cast_ofNat, Rat.cast_pow, Rat.cast_natCast, + cast_qerror, Rat.cast_div, Function.comp_apply, mul_div_assoc, mul_zero, add_zero] using + error_tendsto.add (ht.const_mul 2) + +theorem Effective.sin {f : A → ℝ} (hf : Effective f) : Effective (fun a => Real.sin (f a)) := hf.trig true + +theorem Effective.cos {f : A → ℝ} (hf : Effective f) : Effective (fun a => Real.cos (f a)) := hf.trig false + +end +end CertifiedReal +namespace CertifiedReal +open Encodable Filter Topology +local instance trigonometryLocal2 : Primcodable ℚ := RecursiveArithmetic.ratPrimcodable +section +variable {A : Type*} [Primcodable A] + +theorem Effective.cond {f g : A → ℝ} (hf : Effective f) (hg : Effective g) + {b : A → Bool} (hb : Computable b) : Effective (fun a => if b a then f a else g a) := by + obtain ⟨q,hq,bq⟩ := hf + obtain ⟨v,hv,bv⟩ := hg + refine ⟨fun an => if b an.1 then q an else v an, + (by simpa only [Bool.cond_eq_ite] using Computable.cond (hb.comp Computable.fst) hq hv), ?_⟩ + intro a n + cases h : b a + · simpa [h] using bv a n + · simpa [h] using bq a n + +theorem Effective.ite {f g : A → ℝ} (hf : Effective f) (hg : Effective g) + {p : A → Prop} [DecidablePred p] (hp : PrimrecPred p) : + Effective (fun a => if p a then f a else g a) := by + simpa only [decide_eq_true_eq] using hf.cond hg hp.decide.to_comp + +end + +def refinePrecision (n : ℕ) : ℕ := (n+1)^3-1 + +@[fun_prop] theorem refinePrecision_recursive : Primrec refinePrecision := by + unfold refinePrecision; fun_prop + +theorem error_refine (n : ℕ) : error (refinePrecision n) = error n ^ 3 := by + have h : 1 ≤ (n+1)^3 := by exact Nat.one_le_pow _ _ (by omega) + simp only [error, refinePrecision, Nat.cast_sub h, Nat.cast_pow, Nat.cast_add, Nat.cast_one] + rw [sub_add_cancel, one_div_pow] + +section Stencils +variable {A B I : Type*} [Primcodable A] [Primcodable B] [Primcodable I] +variable (shift : I → B → ℕ → B) +abbrev Task (B : Type*) := B × ℕ × ℚ + +def spawn (i : I) (v : Task B) : List (Task B) := + [(shift i v.1 v.2.1, refinePrecision v.2.1, v.2.2 / qerror v.2.1), + (v.1, refinePrecision v.2.1, -v.2.2 / qerror v.2.1)] + +def stencil (w : List I) (vs : List (Task B)) : List (Task B) := + w.foldl (fun vs i => vs.flatMap (spawn shift i)) vs + +omit [Primcodable B] [Primcodable I] in +@[simp] theorem stencil_nil (vs : List (Task B)) : stencil shift [] vs = vs := rfl +omit [Primcodable B] [Primcodable I] in +@[simp] theorem stencil_cons (i : I) (w : List I) (vs : List (Task B)) : + stencil shift (i::w) vs = stencil shift w (vs.flatMap (spawn shift i)) := rfl + +theorem spawn_recursive (hs : Primrec (fun p : I × B × ℕ => shift p.1 p.2.1 p.2.2)) : + Primrec (fun p : I × Task B => spawn shift p.1 p.2) := by + unfold spawn + have h₁ : Primrec (fun p : I × Task B => + (shift p.1 p.2.1 p.2.2.1, refinePrecision p.2.2.1, p.2.2.2 / qerror p.2.2.1)) := by + apply (hs.comp (g := fun p : I × Task B => (p.1,p.2.1,p.2.2.1)) (by fun_prop)).pair + fun_prop + have h₂ : Primrec (fun p : I × Task B => + (p.2.1, refinePrecision p.2.2.1, -p.2.2.2 / qerror p.2.2.1)) := by fun_prop + exact Primrec.list_cons.comp h₁ (Primrec.list_cons.comp h₂ (Primrec.const [])) + +theorem stencil_recursive (hs : Primrec (fun p : I × B × ℕ => shift p.1 p.2.1 p.2.2)) : + Primrec (fun p : List I × List (Task B) => stencil shift p.1 p.2) := by + have hstep : Primrec (fun p : List (Task B) × I => p.1.flatMap (spawn shift p.2)) := + Primrec.list_flatMap Primrec.fst + ((spawn_recursive shift hs).comp (g := fun p : (List (Task B) × I) × Task B => (p.1.2,p.2)) (by fun_prop)).to₂ + exact Primrec.list_foldl Primrec.fst Primrec.snd (hstep.comp Primrec.snd).to₂ + +variable (q : (A × B) × ℕ → ℚ) +def difference : List I → A → B → ℕ → ℚ + | [], a, b, n => q ((a,b),n) + | i::w, a, b, n => (difference w a (shift i b n) (refinePrecision n) - + difference w a b (refinePrecision n)) / qerror n + +omit [Primcodable A] [Primcodable B] [Primcodable I] in +theorem stencil_correct (w : List I) (vs : List (Task B)) (a : A) : + ((stencil shift w vs).map (fun v => v.2.2 * q ((a,v.1),v.2.1))).sum = + (vs.map (fun v => v.2.2 * difference shift q w a v.1 v.2.1)).sum := by + induction w generalizing vs with + | nil => rfl + | cons i w ih => + rw [stencil_cons, ih] + induction vs with + | nil => simp + | cons v vs hiv => + simp only [List.flatMap_cons, List.map_append, List.sum_append, List.map_cons, + List.sum_cons] at * + rw [hiv] + congr 1 + simp only [spawn, List.map_cons, List.map_nil, List.sum_cons, List.sum_nil, add_zero, difference] + ring + +theorem computable_list_sum {f : A → List ℚ} (hf : Computable f) : + Computable (fun a => (f a).sum) := RecursiveArithmetic.listSumRat.to_comp.comp hf + +theorem computable_list_map {l : A → List B} {f : A → B → ℚ} + (hl : Computable l) (hf : Computable₂ f) : + Computable (fun a => ((l a).map (f a)).sum) := by + have hi : Computable (fun p : A × ℕ => (l p.1)[p.2]?) := + Computable.list_getElem?.comp (hl.comp Computable.fst) Computable.snd + have ht : Computable (fun p : A × ℕ => ((l p.1)[p.2]?.map (f p.1)).getD 0) := by + apply Computable.option_getD + · exact Computable.option_map hi (hf.comp + (g := fun p : (A × ℕ) × B => p.1.1) (h := fun p => p.2) + (Computable.fst.comp Computable.fst) Computable.snd).to₂ + · exact Computable.const 0 + apply (computable_sum (Computable.list_length.comp hl) ht.to₂).of_eq + intro a + dsimp only + generalize l a = v + induction v with + | nil => simp + | cons b v ih => + simp only [List.length_cons, Finset.sum_range_succ', List.getElem?_cons_succ, + List.getElem?_cons_zero, Option.map_some, Option.getD_some, List.map_cons, List.sum_cons] + rw [ih, add_comm] + +theorem difference_computable + (hs : Primrec (fun p : I × B × ℕ => shift p.1 p.2.1 p.2.2)) (hq : Computable q) : + Computable (fun p : (A × List I × B) × ℕ => difference shift q p.1.2.1 p.1.1 p.1.2.2 p.2) := by + have ha : Primrec (fun p : (A × List I × B) × ℕ => + (p.1.2.1, [(p.1.2.2,p.2,(1 : ℚ))])) := + (Primrec.fst.comp (Primrec.snd.comp Primrec.fst)).pair + (Primrec.list_cons.comp ((Primrec.snd.comp (Primrec.snd.comp Primrec.fst)).pair + (Primrec.snd.pair (Primrec.const 1))) (Primrec.const [])) + have hl : Computable (fun p : (A × List I × B) × ℕ => + stencil shift p.1.2.1 [(p.1.2.2,p.2,(1 : ℚ))]) := + (stencil_recursive shift hs).to_comp.comp ha.to_comp + have harg : Computable (fun p : ((A × List I × B) × ℕ) × Task B => + ((p.1.1.1,p.2.1),p.2.2.1)) := + ((Computable.fst.comp (Computable.fst.comp Computable.fst)).pair + (Computable.fst.comp Computable.snd)).pair + (Computable.fst.comp (Computable.snd.comp Computable.snd)) + have hf : Computable (fun p : ((A × List I × B) × ℕ) × Task B => + p.2.2.2 * q ((p.1.1.1,p.2.1),p.2.2.1)) := + RecursiveArithmetic.rat_mul.to_comp.comp (g := fun p : ((A × List I × B) × ℕ) × Task B => + (p.2.2.2, q ((p.1.1.1,p.2.1),p.2.2.1))) + ((Computable.snd.comp (Computable.snd.comp Computable.snd)).pair (hq.comp harg)) + apply (computable_list_map hl hf.to₂).of_eq + intro p + simpa using stencil_correct shift q p.1.2.1 [(p.1.2.2,p.2,1)] p.1.1 + +end Stencils +end CertifiedReal + +end +end PeriodicLattice + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/AlmostOrthogonal.lean b/lean/OAI/Analysis/PlanarEndpoint/AlmostOrthogonal.lean new file mode 100644 index 0000000000000000000000000000000000000000..91dd4a73150aee0252d20f1f61db41ad1aa805fc --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/AlmostOrthogonal.lean @@ -0,0 +1,113 @@ +import Mathlib + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open scoped BigOperators +namespace PlanarEndpoint + +lemma near_sum_first {ι : Type*} [Fintype ι] (R : ι → ι → Prop) + [DecidableRel R] (a : ι → ℝ) : + (∑ i, ∑ j, if R i j then a i else 0) = + ∑ i, ((Finset.univ.filter (R i)).card : ℝ) * a i := by + apply Finset.sum_congr rfl + intro i _ + rw [← Finset.sum_filter] + simp + +lemma symmetric_near_sum {ι : Type*} [Fintype ι] (R : ι → ι → Prop) + [DecidableRel R] (hR : ∀ ⦃first second⦄, R first second → R second first) (a : ι → ℝ) : + (∑ i, ∑ j, if R i j then (a i+a j)/2 else 0) = + ∑ i, ((Finset.univ.filter (R i)).card : ℝ) * a i := by + have he (i j : ι) : (if R i j then (a i+a j)/2 else 0) = + ((if R i j then a i else 0)+(if R i j then a j else 0))/2 := by + split_ifs <;> ring + simp_rw [he, ← Finset.sum_div, Finset.sum_add_distrib] + have hs : (∑ i, ∑ j, if R i j then a j else 0) = ∑ i, ∑ j, if R i j then a i else 0 := by + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + simp only [show R j i ↔ R i j from ⟨fun h => hR h, fun h => hR h⟩] + rw [hs, near_sum_first] + ring + +lemma norm_sum_sq_le_near_far {ι E : Type*} [Fintype ι] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] + (G : ι → E) (R : ι → ι → Prop) [DecidableRel R] + (hR : ∀ ⦃first second⦄, R first second → R second first) + (m : ι → ℝ) (hm : ∀ i, 0 ≤ m i) {D B : ℝ} (hB : 0 ≤ B) + (hdegree : ∀ i, ((Finset.univ.filter (R i)).card : ℝ) ≤ D) + (hfar : ∀ i j, ¬R i j → ‖inner ℂ (G i) (G j)‖ ≤ B * m i * m j) : + ‖∑ i, G i‖^2 ≤ D * (∑ i, ‖G i‖^2) + B * (∑ i, m i)^2 := by + have hp (i j : ι) : (inner ℂ (G i) (G j)).re ≤ + (if R i j then (‖G i‖^2+‖G j‖^2)/2 else 0) + B*m i*m j := by + have hnn : 0 ≤ B*m i*m j := mul_nonneg (mul_nonneg hB (hm i)) (hm j) + by_cases hij : R i j + · rw [ite_eq_left hij] + have hc := norm_inner_le_norm (𝕜 := ℂ) (G i) (G j) + have hr := Complex.re_le_norm (inner ℂ (G i) (G j)) + nlinarith [sq_nonneg (‖G i‖-‖G j‖)] + · rw [ite_eq_right hij, zero_add] + exact (Complex.re_le_norm _).trans (hfar i j hij) + calc + _ = ∑ i, ∑ j, (inner ℂ (G i) (G j)).re := by + rw [← @inner_self_eq_norm_sq ℂ E _ _] + simp only [sum_inner, inner_sum, map_sum] + exact Finset.sum_comm + _ ≤ ∑ i, ∑ j, ((if R i j then (‖G i‖^2+‖G j‖^2)/2 else 0) + B*m i*m j) := + Finset.sum_le_sum (fun i _ => Finset.sum_le_sum (fun j _ => hp i j)) + _ = (∑ i, ((Finset.univ.filter (R i)).card : ℝ) * ‖G i‖^2) + + B * (∑ i, m i)^2 := by + simp_rw [Finset.sum_add_distrib] + rw [symmetric_near_sum R hR] + congr 1 + simp only [Finset.mul_sum, Finset.sum_mul, pow_two] + rw [Finset.sum_comm] + simp only [mul_assoc] + _ ≤ _ := by + apply add_le_add_left + rw [Finset.mul_sum] + exact Finset.sum_le_sum fun i _ => mul_le_mul_of_nonneg_right (hdegree i) (sq_nonneg _) + +lemma norm_sum_sq_le_near_error {ι E : Type*} [Fintype ι] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] + (G : ι → E) (R : ι → ι → Prop) [DecidableRel R] + (hR : ∀ ⦃first second⦄, R first second → R second first) + (A : ι → ι → ℝ) (hA : ∀ i j, 0 ≤ A i j) {D : ℝ} + (hdegree : ∀ i, ((Finset.univ.filter (R i)).card : ℝ) ≤ D) + (hfar : ∀ i j, ¬R i j → ‖inner ℂ (G i) (G j)‖ ≤ A i j) : + ‖∑ i, G i‖^2 ≤ D * (∑ i, ‖G i‖^2) + ∑ i, ∑ j, A i j := by + have hp (i j : ι) : (inner ℂ (G i) (G j)).re ≤ + (if R i j then (‖G i‖^2+‖G j‖^2)/2 else 0) + A i j := by + by_cases hij : R i j + · rw [ite_eq_left hij] + have hc := norm_inner_le_norm (𝕜 := ℂ) (G i) (G j) + have hr := Complex.re_le_norm (inner ℂ (G i) (G j)) + nlinarith [sq_nonneg (‖G i‖-‖G j‖), hA i j] + · rw [ite_eq_right hij, zero_add] + exact (Complex.re_le_norm _).trans (hfar i j hij) + calc + _ = ∑ i, ∑ j, (inner ℂ (G i) (G j)).re := by + rw [← @inner_self_eq_norm_sq ℂ E _ _] + simp only [sum_inner, inner_sum, map_sum] + exact Finset.sum_comm + _ ≤ ∑ i, ∑ j, ((if R i j then (‖G i‖^2+‖G j‖^2)/2 else 0) + A i j) := + Finset.sum_le_sum (fun i _ => Finset.sum_le_sum (fun j _ => hp i j)) + _ = (∑ i, ((Finset.univ.filter (R i)).card : ℝ) * ‖G i‖^2) + + ∑ i, ∑ j, A i j := by + simp_rw [Finset.sum_add_distrib] + rw [symmetric_near_sum R hR] + _ ≤ _ := by + apply add_le_add_left + rw [Finset.mul_sum] + exact Finset.sum_le_sum fun i _ => mul_le_mul_of_nonneg_right (hdegree i) (sq_nonneg _) + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/AnnularCutoff.lean b/lean/OAI/Analysis/PlanarEndpoint/AnnularCutoff.lean new file mode 100644 index 0000000000000000000000000000000000000000..d417aa2ac1309b5a10e1e9aa290d1f3c2019a76d --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/AnnularCutoff.lean @@ -0,0 +1,88 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set +open scoped Topology ContDiff +namespace PlanarEndpoint + +def outerBump : ContDiffBump (0 : Plane) := ⟨2,4,by norm_num,by norm_num⟩ +def innerBump : ContDiffBump (0 : Plane) := ⟨1/4,1,by norm_num,by norm_num⟩ +def annularCutoff (ξ : Plane) : ℂ := ((outerBump ξ-innerBump ξ : ℝ) : ℂ) + +lemma annularCutoff_smooth : ContDiff ℝ ∞ annularCutoff := + Complex.ofRealCLM.contDiff.comp (outerBump.contDiff.sub innerBump.contDiff) + +lemma annularCutoff_zero_small {ξ : Plane} (hξ : ‖ξ‖ ≤ 1/4) : annularCutoff ξ=0 := by + have hi := innerBump.one_of_mem_closedBall (x := ξ) (by simpa [innerBump] using hξ) + have ho := outerBump.one_of_mem_closedBall (x := ξ) (by + simpa [outerBump] using (show ‖ξ‖ ≤ 2 by linarith)) + simp [annularCutoff, hi, ho] + +lemma annularCutoff_zero_large {ξ : Plane} (hξ : 4 ≤ ‖ξ‖) : annularCutoff ξ=0 := by + have ho := outerBump.zero_of_le_dist (x := ξ) (by simpa [outerBump] using hξ) + have hi := innerBump.zero_of_le_dist (x := ξ) (by + simpa [innerBump] using (show 1 ≤ ‖ξ‖ by linarith)) + simp [annularCutoff, hi, ho] + +lemma annularCutoff_support : ∀ ξ ∈ tsupport annularCutoff, 1/4 ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ 4 := by + apply closure_minimal + · intro ξ hξ + have hn : annularCutoff ξ ≠ 0 := hξ + exact ⟨le_of_not_gt (fun h => hn (annularCutoff_zero_small h.le)), + le_of_not_gt (fun h => hn (annularCutoff_zero_large h.le))⟩ + · exact (isClosed_le continuous_const continuous_norm).inter + (isClosed_le continuous_norm continuous_const) + +lemma annularCutoff_compact : HasCompactSupport annularCutoff := by + apply HasCompactSupport.intro (isCompact_closedBall (0 : Plane) 4) + intro ξ hξ + exact annularCutoff_zero_large (le_of_lt (by simpa using hξ)) + +lemma annularCutoff_bound (ξ : Plane) : ‖annularCutoff ξ‖ ≤ 2 := by + rw [annularCutoff, Complex.norm_real, Real.norm_eq_abs] + exact abs_le.mpr ⟨by linarith [outerBump.nonneg (x := ξ), innerBump.le_one (x := ξ)], + by linarith [outerBump.le_one (x := ξ), innerBump.nonneg (x := ξ)]⟩ + +lemma annularCutoff_one {ξ : Plane} (hξ : 1 ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ 2) : annularCutoff ξ=1 := by + have hi := innerBump.zero_of_le_dist (x := ξ) (by simpa [innerBump] using hξ.1) + have ho := outerBump.one_of_mem_closedBall (x := ξ) (by simpa [outerBump] using hξ.2) + simp [annularCutoff, hi, ho] + +lemma dyadic_annular_cover {r : ℝ} (hr : 1 ≤ r) (n : ℕ) (hn : r < (2:ℝ)^n) : + ∃ j < n, (2:ℝ)^j ≤ r ∧ r < (2:ℝ)^(j+1) := by + obtain ⟨j,hj,hj'⟩ := exists_nat_pow_near hr (by norm_num : (1:ℝ)<2) + refine ⟨j,?_,hj,hj'⟩ + by_contra hh + have hnj : n ≤ j := by omega + have hpow := pow_le_pow_right₀ (by norm_num : (1:ℝ) ≤ 2) hnj + linarith + +lemma scaled_annularCutoff_one (j : ℕ) {ξ : Plane} + (hξ : (2:ℝ)^j ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ (2:ℝ)^(j+1)) : + annularCutoff (((2:ℝ)^j)⁻¹ • ξ) = 1 := by + apply annularCutoff_one + rw [norm_smul, Real.norm_eq_abs, abs_of_pos (by positivity)] + rw [← div_eq_inv_mul, le_div_iff₀ (by positivity), div_le_iff₀ (by positivity)] + simpa only [one_mul, pow_succ, mul_comm] using hξ + +lemma graph_square_sum_of_shortTime {p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate (1/4) 4 p) : + ∃ C : ℝ, 0 < C ∧ ∀ (x₀ : Plane) (T : Plane → ℝ) (w : Plane → ℂ) + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1), + (∀ x ∈ Metric.ball x₀ 1, T x ∈ Ico 0 1) → ∀ n : ℕ, + (∑ j ∈ Finset.range n, ‖normalizedDyadicVector annularCutoff annularCutoff_smooth + annularCutoff_compact j (volume.restrict (Metric.ball x₀ 1)) T w hT hw hb []‖^2) ≤ C := + graph_root_sum_of_shortTime (by norm_num) hp (by norm_num) hshort annularCutoff + annularCutoff_smooth annularCutoff_compact annularCutoff_support 2 (by norm_num) + annularCutoff_bound + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/BanachHeat.lean b/lean/OAI/Analysis/PlanarEndpoint/BanachHeat.lean new file mode 100644 index 0000000000000000000000000000000000000000..f1c35c1e2228d3940ae4a5d5ad8fb427a193b1a8 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/BanachHeat.lean @@ -0,0 +1,122 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.Heat + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set Metric +open scoped Topology ENNReal NNReal +namespace PlanarEndpoint + +variable {B : Type*} [NormedAddCommGroup B] [NormedSpace ℝ B] [CompleteSpace B] + +omit [NormedSpace ℝ B] [CompleteSpace B] in +lemma locallyIntegrable_reflect_banach {U : Plane → B} + (hU : LocallyIntegrable U volume) (x : Plane) : + LocallyIntegrable (fun z => U (x-z)) volume := by + intro y + refine ⟨ball y 1, ball_mem_nhds y zero_lt_one, ?_⟩ + have hi := (hU.integrableOn_isCompact (isCompact_closedBall (x-y) 1)).mono_set + ball_subset_closedBall + have hm := (volume.measurePreserving_sub_left x).restrict_preimage + (measurableSet_ball (x := x-y) (ε := (1 : ℝ))) + have hh := (hm.integrable_comp hi.aestronglyMeasurable).mpr hi + simpa only [IntegrableOn, Function.comp_def, reflect_preimage_ball, sub_sub_cancel] using hh + +omit [NormedSpace ℝ B] [CompleteSpace B] in +lemma locallyIntegrable_norm {U : Plane → B} (hU : LocallyIntegrable U volume) : + LocallyIntegrable (fun y => ‖U y‖) volume := by + rw [← locallyIntegrableOn_univ] + exact (hU.locallyIntegrableOn univ).norm + +omit [NormedSpace ℝ B] [CompleteSpace B] in +lemma diskNormAverage_eq_average_banach (U : Plane → B) (x : Plane) (z : B) + {r : ℝ} (hr : 0 ≤ r) : + (Real.pi * r ^ 2)⁻¹ * (∫ y in ball x r, ‖U y - z‖) = + ⨍ y in closedBall x r, ‖U y - z‖ := by + rw [setAverage_congr (closedBall_ae_eq_ball x r), setAverage_eq] + simp only [Measure.real, EuclideanSpace.volume_ball_fin_two, ENNReal.toReal_mul, + ENNReal.toReal_pow, ENNReal.toReal_ofReal hr, ENNReal.toReal_ofReal Real.pi_nonneg, + smul_eq_mul] + rw [mul_comm (r ^ 2) Real.pi] + +omit [NormedSpace ℝ B] [CompleteSpace B] in +lemma ae_banachLebesguePoint {U : Plane → B} (hU : LocallyIntegrable U volume) : + ∀ᵐ x : Plane ∂volume, Tendsto (fun r : ℝ => (Real.pi*r^2)⁻¹ * + ∫ y in ball x r, ‖U y-U x‖) (𝓝[>] 0) (𝓝 0) := by + filter_upwards [IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub volume hU 1] with x hx + have hc : ∀ᶠ r : ℝ in 𝓝[>] 0, x ∈ closedBall x (1*r) := by + filter_upwards [self_mem_nhdsWithin] with r hr + simpa only [one_mul, mem_closedBall, dist_self] using (le_of_lt hr) + have ht := hx (fun _ : ℝ => x) (fun r : ℝ => r) tendsto_id hc + apply ht.congr' + filter_upwards [self_mem_nhdsWithin] with r hr + exact (diskNormAverage_eq_average_banach U x (U x) (le_of_lt hr)).symm + +omit [NormedSpace ℝ B] [CompleteSpace B] in +lemma integral_norm_sub_unit_ball_le {U : Plane → B} (hU : LocallyIntegrable U volume) + {A : ℝ} (hball : ∀ x : Plane, ∫ y in ball x 1, ‖U y‖ ≤ A) (x c : Plane) : + ∫ y in ball c 1, ‖U y-U x‖ ≤ A + Real.pi * ‖U x‖ := by + have hi := (hU.integrableOn_isCompact (isCompact_closedBall c 1)).mono_set ball_subset_closedBall + have hc : IntegrableOn (fun _ : Plane => U x) (ball c 1) volume := integrableOn_const + calc + _ ≤ ∫ y in ball c 1, ‖U y‖ + ‖U x‖ := integral_mono (hi.sub hc).norm + (hi.norm.add hc.norm) (fun y => norm_sub_le _ _) + _ = (∫ y in ball c 1, ‖U y‖) + Real.pi * ‖U x‖ := by + rw [integral_add hi.norm hc.norm, setIntegral_const] + simp [measureReal_def, EuclideanSpace.volume_ball_fin_two, Real.pi_nonneg, smul_eq_mul] + _ ≤ _ := add_le_add (hball c) le_rfl + +omit [CompleteSpace B] in +lemma integrable_heat_smul {U : Plane → B} (hU : LocallyIntegrable U volume) + (A : ℝ≥0) (hball : ∀ x : Plane, ∫ y in ball x 1, ‖U y‖ ≤ A) + {a : ℝ} (ha : 0 < a) (x : Plane) : + Integrable (fun z => heatKernel a z • U (x-z)) volume := by + have hh := (heat_envelope (locallyIntegrable_norm hU) (fun y => norm_nonneg _) A hball x).1 a ha + apply hh.mono' + · exact (by unfold heatKernel gaussianWeight; fun_prop : Continuous (heatKernel a)).aestronglyMeasurable.smul + (locallyIntegrable_reflect_banach hU x).aestronglyMeasurable + · filter_upwards [] with z + simp only [norm_smul, Real.norm_eq_abs, abs_of_nonneg (heatKernel_nonneg ha.le z), le_refl] + +lemma tendsto_heat_smul_of_lebesgue {U : Plane → B} (hU : LocallyIntegrable U volume) + (A : ℝ≥0) (hball : ∀ x : Plane, ∫ y in ball x 1, ‖U y‖ ≤ A) (x : Plane) + (hLeb : Tendsto (fun r : ℝ => (Real.pi*r^2)⁻¹ * ∫ y in ball x r, ‖U y-U x‖) + (𝓝[>] 0) (𝓝 0)) : + Tendsto (fun a : ℝ => ∫ z, heatKernel a z • U (x-z)) (𝓝[>] 0) (𝓝 (U x)) := by + let h : Plane → ℝ := fun y => ‖U y-U x‖ + have hl : LocallyIntegrable h volume := + locallyIntegrable_norm (hU.sub (locallyIntegrable_const (U x))) + let A' : ℝ≥0 := A + ⟨Real.pi * ‖U x‖, mul_nonneg Real.pi_nonneg (norm_nonneg _)⟩ + have hb : ∀ c : Plane, ∫ y in ball c 1, h y ≤ A' := + integral_norm_sub_unit_ball_le hU hball x + have hh := (heat_envelope hl (fun y => norm_nonneg _) A' hb x).2 + have hlim : Tendsto (fun a : ℝ => ∫ z, heatKernel a z * h (x-z)) (𝓝[>] 0) (𝓝 0) := by + simpa only [h, sub_self, norm_zero, sub_zero, abs_norm] using + hh (by simpa only [h, sub_self, norm_zero, sub_zero, abs_norm] using hLeb) + apply Metric.tendsto_nhds.2 + intro ε hε + filter_upwards [self_mem_nhdsWithin, hlim.eventually (eventually_lt_nhds hε)] with a ha he + have hi := integrable_heat_smul hU A hball ha x + have hc := (integrable_heatKernel ha).smul_const (U x) + have heq : (∫ z, heatKernel a z • U (x-z)) - U x = + ∫ z, heatKernel a z • (U (x-z)-U x) := by + simp_rw [smul_sub] + rw [integral_sub hi hc, integral_smul_const, integral_heatKernel ha, one_smul] + rw [dist_eq_norm, heq] + calc + _ ≤ ∫ z, ‖heatKernel a z • (U (x-z)-U x)‖ := norm_integral_le_integral_norm _ + _ = ∫ z, heatKernel a z * h (x-z) := by + congr 1 + ext z + rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg (heatKernel_nonneg ha.le z)] + _ < ε := he + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Convolution.lean b/lean/OAI/Analysis/PlanarEndpoint/Convolution.lean new file mode 100644 index 0000000000000000000000000000000000000000..486f6231490df6b01fe84839c8301500398a8b79 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Convolution.lean @@ -0,0 +1,152 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.Heat + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set FourierTransform +open scoped Topology +namespace PlanarEndpoint + +def heatFrequency (a : ℝ) (x η : Plane) : ℂ := + Complex.exp (-((4*a*Real.pi^2 : ℝ) : ℂ) * (‖η‖ : ℂ)^2 + + 2 * (Real.pi : ℂ) * Complex.I * ((inner ℝ (-x) η : ℝ) : ℂ)) + +lemma norm_heatFrequency (a : ℝ) (x η : Plane) : + ‖heatFrequency a x η‖ = gaussianWeight (4*a*Real.pi^2) η := by + simp only [heatFrequency, Complex.norm_exp, ← Complex.ofReal_pow, Complex.add_re, Complex.mul_re, + Complex.neg_re, Complex.ofReal_re, Complex.ofReal_im, Complex.I_re, Complex.I_im, + mul_zero, sub_zero, Complex.mul_im, zero_add, add_zero] + simp [gaussianWeight] + +lemma integrable_heatFrequency {a : ℝ} (ha : 0 < a) (x : Plane) : + Integrable (heatFrequency a x) volume := by + exact (integrable_gaussianWeight (by positivity : 0 < 4*a*Real.pi^2)).mono' + (by unfold heatFrequency; fun_prop) (Eventually.of_forall fun η => (norm_heatFrequency _ _ _).le) + +lemma memLp_heatFrequency {a : ℝ} (ha : 0 < a) (x : Plane) : + MemLp (heatFrequency a x) 2 volume := by + apply (memLp_gaussian (show 0 < 4*a*Real.pi^2 by positivity)).mono + (by unfold heatFrequency; fun_prop) + filter_upwards [] with η + rw [norm_heatFrequency] + simp only [Complex.norm_exp, ← Complex.ofReal_neg, Complex.ofReal_re] + simp [gaussianWeight] + +lemma inverse_heatFrequency {a : ℝ} (ha : 0 < a) (x y : Plane) : + (𝓕⁻ (heatFrequency a x)) y = (heatKernel a (x-y) : ℂ) := by + rw [Real.fourierInv_eq_fourier_neg] + unfold heatFrequency + rw [fourier_gaussian_innerProductSpace' (by simpa only [← Complex.ofReal_pow, ← Complex.ofReal_mul, Complex.ofReal_re, + Complex.ofReal_ofNat] using (show 0 < 4*a*Real.pi^2 by positivity))] + have hd : (Module.finrank ℝ Plane : ℂ) / 2 = 1 := by + simp [Plane, finrank_euclideanSpace] + rw [hd, Complex.cpow_one] + have hn : ‖-x - -y‖ = ‖x-y‖ := by rw [neg_sub_neg, norm_sub_rev] + rw [hn] + simp only [heatKernel, gaussianWeight, Complex.ofReal_mul, Complex.ofReal_inv, + Complex.ofReal_exp, Complex.ofReal_neg, Complex.ofReal_pow, Complex.ofReal_ofNat] + congr 1 + · field_simp [ha.ne', Real.pi_ne_zero] + + · congr 1 + field_simp [ha.ne', Real.pi_ne_zero] + +lemma inverse_heatFrequency_l2_ae {a : ℝ} (ha : 0 < a) (x : Plane) : + ((Lp.fourierTransformₗᵢ Plane ℂ).symm + ((memLp_heatFrequency ha x).toLp (heatFrequency a x)) : Plane → ℂ) =ᵐ[volume] + fun y => (heatKernel a (x-y) : ℂ) := by + have hto := (memLp_heatFrequency ha x).coeFn_toLp + have hi : Integrable ((memLp_heatFrequency ha x).toLp (heatFrequency a x) : Plane → ℂ) + volume := (integrable_heatFrequency ha x).congr hto.symm + have hh := l2_inverse_fourier_ae ((memLp_heatFrequency ha x).toLp (heatFrequency a x)) hi + filter_upwards [hh] with y hy + rw [hy] + have he : (𝓕⁻ ((memLp_heatFrequency ha x).toLp (heatFrequency a x) : Plane → ℂ)) y = + (𝓕⁻ (heatFrequency a x)) y := by + rw [Real.fourierInv_eq', Real.fourierInv_eq'] + exact integral_congr_ae (hto.mono fun η hη => by dsimp only; rw [hη]) + rw [he, inverse_heatFrequency ha] + +lemma conjugate_heatFrequency (a : ℝ) (x η : Plane) : + starRingEnd ℂ (heatFrequency a x η) = + phase x 0 ((2 * Real.pi) • η) * + (gaussianWeight a ((2 * Real.pi) • η) : ℂ) := by + unfold heatFrequency phase gaussianWeight + rw [← Complex.exp_conj, Complex.ofReal_exp, ← Complex.exp_add] + congr 1 + simp only [map_add, map_mul, map_neg, map_pow, map_ofNat, Complex.conj_ofReal, + Complex.conj_I, inner_neg_left, inner_smul_right, zero_mul, sub_zero, + norm_smul, Real.norm_eq_abs, abs_of_pos (by positivity : 0 < 2 * Real.pi)] + push_cast + ring + +lemma abel_eq_frequency_pairing (f : L2) (a : ℝ) (x : Plane) (t : ℝ) : + abel f a x t = ∫ η : Plane, + (evolutionMultiplier t η * (Lp.fourierTransformₗᵢ Plane ℂ f) η) * + starRingEnd ℂ (heatFrequency a x η) := by + let q : Plane → ℂ := fun η => + (evolutionMultiplier t η * (Lp.fourierTransformₗᵢ Plane ℂ f) η) * + starRingEnd ℂ (heatFrequency a x η) + have he : ∫ ξ : Plane, phase x t ξ * (gaussianWeight a ξ : ℂ) * fourier f ξ = + ∫ ξ : Plane, q ((2 * Real.pi)⁻¹ • ξ) := by + apply integral_congr_ae + filter_upwards [] with ξ + dsimp only [q] + rw [conjugate_heatFrequency] + simp only [evolutionMultiplier, smul_smul, mul_inv_cancel₀ + (mul_ne_zero (by norm_num : (2 : ℝ) ≠ 0) Real.pi_ne_zero), one_smul] + change phase x t ξ * (gaussianWeight a ξ : ℂ) * fourier f ξ = + (phase 0 t ξ * fourier f ξ) * (phase x 0 ξ * (gaussianWeight a ξ : ℂ)) + have hp : phase x t ξ = phase x 0 ξ * phase 0 t ξ := by + simp only [phase, inner_zero_left, zero_mul, sub_zero, zero_sub, ← Complex.exp_add] + congr 1 + push_cast + ring + rw [hp] + ring + rw [abel_eq_weighted, he, Measure.integral_comp_inv_smul_of_nonneg volume q + (by positivity : 0 ≤ 2 * Real.pi)] + simp only [finrank_euclideanSpace, Fintype.card_fin, smul_smul, + inv_mul_cancel₀ (by positivity : (2 * Real.pi)^2 ≠ 0), one_smul] + rfl + +lemma abel_eq_heat_convolution (f : L2) {a : ℝ} (ha : 0 < a) (x : Plane) (t : ℝ) : + abel f a x t = ∫ y : Plane, (heatKernel a (x-y) : ℂ) * l2Evolution f t y := by + let k : L2 := (memLp_heatFrequency ha x).toLp (heatFrequency a x) + let F := Lp.fourierTransformₗᵢ Plane ℂ + have hk : (k : Plane → ℂ) =ᵐ[volume] heatFrequency a x := + (memLp_heatFrequency ha x).coeFn_toLp + have hki := inverse_heatFrequency_l2_ae ha x + calc + abel f a x t = inner ℂ k (F (l2Evolution f t)) := by + rw [abel_eq_frequency_pairing, L2.inner_def] + apply integral_congr_ae + filter_upwards [hk, l2Evolution_fourier_ae f t] with η hη hFη + rw [RCLike.inner_apply, hη, hFη] + _ = inner ℂ (F.symm k) (l2Evolution f t) := by + simpa using (F.symm.inner_map_map k (F (l2Evolution f t))).symm + _ = ∫ y : Plane, (heatKernel a (x-y) : ℂ) * l2Evolution f t y := by + rw [L2.inner_def] + apply integral_congr_ae + filter_upwards [hki] with y hy + rw [RCLike.inner_apply, hy, Complex.conj_ofReal, mul_comm] + +lemma integrable_heat_convolution (f : L2) {a : ℝ} (ha : 0 < a) + (x : Plane) (t : ℝ) : + Integrable (fun y : Plane => (heatKernel a (x-y) : ℂ) * l2Evolution f t y) volume := by + let k : L2 := (memLp_heatFrequency ha x).toLp (heatFrequency a x) + have hi := MeasureTheory.L2.integrable_inner (𝕜 := ℂ) + ((Lp.fourierTransformₗᵢ Plane ℂ).symm k) (l2Evolution f t) + apply hi.congr + filter_upwards [inverse_heatFrequency_l2_ae ha x] with y hy + rw [RCLike.inner_apply, hy, Complex.conj_ofReal, mul_comm] + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/DualMass.lean b/lean/OAI/Analysis/PlanarEndpoint/DualMass.lean new file mode 100644 index 0000000000000000000000000000000000000000..d1f35945734d05b0e4d4cbfb868a3279434f1473 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/DualMass.lean @@ -0,0 +1,205 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.FrequencyWeak +import OAI.Analysis.PlanarEndpoint.GraphDual +import OAI.Analysis.PlanarEndpoint.WeakIntegration + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology ComplexConjugate +namespace PlanarEndpoint + +lemma integrable_of_memLp_annular {v : Plane → ℂ} (hv : MemLp v 2 volume) + {c₀ C₀ N : ℝ} + (hs : ∀ᵐ ξ : Plane ∂volume, ξ ∉ {ξ | c₀*N ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*N} → v ξ = 0) : + Integrable v volume := by + have hi := ((hv.locallyIntegrable (by norm_num)).integrableOn_isCompact + (isCompact_closedBall (0 : Plane) (C₀*N))).integrable_indicator measurableSet_closedBall + apply hi.congr + filter_upwards [hs] with ξ hξ + by_cases h : ξ ∈ Metric.closedBall (0 : Plane) (C₀*N) + · rw [indicator_of_mem h] + · rw [indicator_of_notMem h] + symm + apply hξ + intro hh + exact h (by simpa using hh.2) + +lemma frequency_graph_integral_bound {c₀ C₀ p : ℝ} (hp : 1 < p) + {C : ℝ} (hC : 0 ≤ C) {j : ℕ} {v : Plane → ℂ} (hv : MemLp v 2 volume) + (hs : ∀ᵐ ξ : Plane ∂volume, ξ ∉ {ξ | c₀*(2:ℝ)^j ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*(2:ℝ)^j} → v ξ = 0) + {x₀ : Plane} {t₀ s : ℝ} + (hweak : ∀ lam : ℝ, 0 < lam → + volume (Metric.ball x₀ 1 ∩ {x | ∃ t ∈ Icc t₀ (t₀+s), lam < ‖frequencyExtension v x t‖}) ≤ + ENNReal.ofReal ((C*((2:ℝ)^j)^(1/3:ℝ)*‖hv.toLp v‖/lam)^p)) + {E : Set Plane} (hE : MeasurableSet E) (hEB : E ⊆ Metric.ball x₀ 1) + {T : Plane → ℝ} (hT : Measurable T) (hTs : ∀ x ∈ E, T x ∈ Icc t₀ (t₀+s)) : + IntegrableOn (fun x => frequencyExtension v x (T x)) E volume ∧ + (∫ x in E, ‖frequencyExtension v x (T x)‖) ≤ + p/(p-1)*C*((2:ℝ)^j)^(1/3:ℝ)*‖hv.toLp v‖*(volume.real E)^(1-1/p) := by + have hfin : volume E ≠ ⊤ := (measure_mono hEB |>.trans_lt measure_ball_lt_top).ne + let : IsFiniteMeasure (volume.restrict E) := isFiniteMeasure_restrict.2 hfin + have hi := integrable_of_memLp_annular hv hs + have hm : Measurable (fun x => frequencyExtension v x (T x)) := + by simpa only [Function.comp_def, id_eq] using + (continuous_frequencyExtension hi).measurable.comp (measurable_id.prodMk hT) + have hw : ∀ lam : ℝ, 0 < lam → + (volume.restrict E) {x | lam < ‖frequencyExtension v x (T x)‖} ≤ + ENNReal.ofReal ((C*((2:ℝ)^j)^(1/3:ℝ)*‖hv.toLp v‖/lam)^p) := by + intro lam hlam + rw [Measure.restrict_apply' hE] + apply le_trans (measure_mono ?_) (hweak lam hlam) + rintro x ⟨hx,hxE⟩ + exact ⟨hEB hxE, T x, hTs x hxE, hx⟩ + have hh := weak_integral_norm_bound (volume.restrict E) hm.aestronglyMeasurable hp + (show 0 ≤ C*((2:ℝ)^j)^(1/3:ℝ)*‖hv.toLp v‖ by positivity) hw + simpa only [IntegrableOn, Measure.restrict_apply_univ, measureReal_def, mul_assoc] using hh + +lemma graphFourier_frequency_pairing {v : Plane → ℂ} (hv : Integrable v volume) + (μ : Measure Plane) [IsFiniteMeasure μ] {T : Plane → ℝ} {w : Plane → ℂ} + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1) : + (∫ ξ, v ξ * graphFourier μ T w ξ) = ∫ x, w x * frequencyExtension v x (T x) ∂μ := by + have hi : Integrable (fun z : Plane × Plane => v z.1 * (w z.2 * phase z.2 (T z.2) z.1)) + (volume.prod μ) := by + apply (hv.norm.comp_fst μ).mono' + · exact ((hv.aestronglyMeasurable.comp_fst).mul + ((hw.comp measurable_snd).aestronglyMeasurable.mul + ((measurable_graph_phase hT).comp measurable_swap).aestronglyMeasurable)) + · filter_upwards [] with z + simp only [norm_mul, norm_phase, mul_one] + simpa only [mul_one] using mul_le_mul_of_nonneg_left (hb z.2) (norm_nonneg (v z.1)) + calc + _ = ∫ ξ, ∫ x, v ξ * (w x * phase x (T x) ξ) ∂μ := by + apply integral_congr_ae + filter_upwards [] with ξ + rw [integral_const_mul] + rfl + _ = ∫ x, (∫ ξ, v ξ * (w x * phase x (T x) ξ)) ∂μ := integral_integral_swap hi + _ = _ := by + apply integral_congr_ae + filter_upwards [] with x + unfold frequencyExtension + rw [← integral_const_mul] + congr 1 + funext ξ + ring + +lemma norm_toLp_le_const_mul {v g : Plane → ℂ} (hv : MemLp v 2 volume) + (hg : MemLp g 2 volume) {B : ℝ} (hB : 0 ≤ B) + (hb : ∀ᵐ ξ ∂volume, ‖v ξ‖ ≤ B * ‖g ξ‖) : + ‖hv.toLp v‖ ≤ B * ‖hg.toLp g‖ := by + have hi : ∫ ξ, ‖v ξ‖^2 ≤ B^2 * ∫ ξ, ‖g ξ‖^2 := by + rw [← integral_const_mul] + apply integral_mono_ae ((memLp_two_iff_integrable_sq_norm hv.aestronglyMeasurable).1 hv) + (((memLp_two_iff_integrable_sq_norm hg.aestronglyMeasurable).1 hg).const_mul _) + filter_upwards [hb] with ξ hξ + nlinarith [norm_nonneg (v ξ), norm_nonneg (g ξ)] + have he {a : Plane → ℂ} (ha : MemLp a 2 volume) : (∫ ξ, ‖a ξ‖^2) = ‖ha.toLp a‖^2 := by + rw [← real_inner_self_eq_norm_sq, L2.inner_def] + apply integral_congr_ae + filter_upwards [ha.coeFn_toLp] with ξ hξ + simp only [hξ, real_inner_self_eq_norm_sq] + rw [he hv, he hg] at hi + have hn : 0 ≤ B * ‖hg.toLp g‖ := by positivity + nlinarith [norm_nonneg (hv.toLp v)] + +lemma memLp_mul_conj_bounded {χ g : Plane → ℂ} (hχ : Measurable χ) + (hg : MemLp g 2 volume) {B : ℝ} (hB : 0 ≤ B) (hb : ∀ ξ, ‖χ ξ‖ ≤ B) : + MemLp (fun ξ => χ ξ * conj (g ξ)) 2 volume := by + apply (hg.const_mul (B : ℂ)).mono + · exact hχ.aestronglyMeasurable.mul hg.aestronglyMeasurable.star + · filter_upwards [] with ξ + simp only [norm_mul, Complex.norm_conj, Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg hB] + exact mul_le_mul_of_nonneg_right (hb ξ) (norm_nonneg (g ξ)) + +lemma graphLp_dual_test_identity (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] (T : Plane → ℝ) (w : Plane → ℂ) + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1) + (hv : Integrable (fun ξ => χ ξ * conj (graphDual χ μ T w ξ)) volume) : + ‖graphLp χ hχ μ T w hT hw hb‖^2 = + ‖∫ x, w x * frequencyExtension (fun ξ => χ ξ * conj (graphDual χ μ T w ξ)) x (T x) ∂μ‖ := by + rw [← graphFourier_frequency_pairing hv μ hT hw hb] + calc + _ = ‖inner ℂ (graphLp χ hχ μ T w hT hw hb) (graphLp χ hχ μ T w hT hw hb)‖ := by + rw [← inner_self_re_eq_norm, norm_sq_eq_re_inner (𝕜 := ℂ)] + _ = ‖∫ ξ, graphDual χ μ T w ξ * conj (graphDual χ μ T w ξ)‖ := + congrArg norm (inner_graphLp χ hχ μ μ T w hT hw hb) + _ = _ := by + congr 1 + apply integral_congr_ae + filter_upwards [] with ξ + unfold graphDual + ring + +lemma graph_mass_bound_of_shortTime {c₀ C₀ p : ℝ} (hp : 1 < p) + (hshort : ShortTimeWeakEstimate c₀ C₀ p) : + ∃ C : ℝ, 0 < C ∧ ∀ j : ℕ, ∀ (χ : Plane → ℂ) (_ : Measurable χ) + (hχ : MemLp χ 2 volume) (B : ℝ), 0 ≤ B → (∀ ξ, ‖χ ξ‖ ≤ B) → + (∀ᵐ ξ : Plane ∂volume, + ξ ∉ {ξ | c₀*(2:ℝ)^j ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*(2:ℝ)^j} → χ ξ = 0) → + ∀ (x₀ : Plane) (t₀ s : ℝ), 0 ≤ s → s ≤ ((2:ℝ)^j)⁻¹ → + ∀ (E : Set Plane), MeasurableSet E → E ⊆ Metric.ball x₀ 1 → + ∀ (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1), (∀ x ∈ E, T x ∈ Icc t₀ (t₀+s)) → + ∀ [IsFiniteMeasure (volume.restrict E)], + ‖graphLp χ hχ (volume.restrict E) T w hT hw hb‖ ≤ + C * B * ((2:ℝ)^j)^(1/3:ℝ) * (volume.real E)^(1-1/p) := by + obtain ⟨C,hC,hwk⟩ := frequency_weak_of_shortTime hshort + refine ⟨p/(p-1)*C, mul_pos (div_pos (by linarith) (by linarith)) hC, ?_⟩ + intro j χ hχm hχ B hB hχB hχs x₀ t₀ s hs hs' E hE hEB T w hT hw hb hTs inst + let μ := volume.restrict E + let g := graphDual χ μ T w + have hg : MemLp g 2 volume := graphDual_memLp χ hχ μ hT hw hb + let v : Plane → ℂ := fun ξ => χ ξ * conj (g ξ) + have hv : MemLp v 2 volume := memLp_mul_conj_bounded hχm hg hB hχB + have hvs : ∀ᵐ ξ : Plane ∂volume, + ξ ∉ {ξ | c₀*(2:ℝ)^j ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*(2:ℝ)^j} → v ξ = 0 := by + filter_upwards [hχs] with ξ hξ hh + simp only [v, hξ hh, zero_mul] + have hn : ‖hv.toLp v‖ ≤ B * ‖hg.toLp g‖ := by + apply norm_toLp_le_const_mul hv hg hB + filter_upwards [] with ξ + simp only [v, norm_mul, Complex.norm_conj] + exact mul_le_mul_of_nonneg_right (hχB ξ) (norm_nonneg (g ξ)) + have hh := frequency_graph_integral_bound hp hC.le hv hvs + (fun lam hlam => hwk j v hv hvs x₀ t₀ s lam hs hs' hlam) hE hEB hT hTs + have hpair := graphLp_dual_test_identity χ hχ μ T w hT hw hb + (integrable_of_memLp_annular hv hvs) + have hhi : Integrable (fun x => frequencyExtension v x (T x)) μ := hh.1 + have hi : Integrable (fun x => w x * frequencyExtension v x (T x)) μ := by + apply hhi.norm.mono' + · exact hw.aestronglyMeasurable.mul hhi.aestronglyMeasurable + · filter_upwards [] with x + simpa only [norm_mul, one_mul] using + mul_le_mul_of_nonneg_right (hb x) (norm_nonneg (frequencyExtension v x (T x))) + have hh' : ‖graphLp χ hχ μ T w hT hw hb‖^2 ≤ + p/(p-1)*C*((2:ℝ)^j)^(1/3:ℝ)*‖hv.toLp v‖*(volume.real E)^(1-1/p) := by + rw [hpair] + apply (norm_integral_le_integral_norm _).trans + apply le_trans (integral_mono hi.norm hhi.norm ?_) hh.2 + intro x + simpa only [norm_mul, one_mul] using + mul_le_mul_of_nonneg_right (hb x) (norm_nonneg (frequencyExtension v x (T x))) + change ‖hg.toLp g‖ ≤ _ + change ‖hg.toLp g‖^2 ≤ _ at hh' + have hfac : 0 ≤ p/(p-1)*C*((2:ℝ)^j)^(1/3:ℝ) * (volume.real E)^(1-1/p) := by + have : 0 ≤ p/(p-1) := div_nonneg (by linarith) (by linarith) + positivity + have hmul := mul_le_mul_of_nonneg_left hn hfac + have hzero := norm_nonneg (hg.toLp g) + by_cases hz : ‖hg.toLp g‖ = 0 + · rw [hz] + have := mul_nonneg hfac hB + nlinarith + · have hpos : 0 < ‖hg.toLp g‖ := lt_of_le_of_ne hzero (Ne.symm hz) + nlinarith + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/DyadicArithmetic.lean b/lean/OAI/Analysis/PlanarEndpoint/DyadicArithmetic.lean new file mode 100644 index 0000000000000000000000000000000000000000..eb0501d98cc13a8cff11f79ef0accd09ba5bcda0 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/DyadicArithmetic.lean @@ -0,0 +1,69 @@ +import Mathlib + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open scoped Real +namespace PlanarEndpoint + +lemma interpolate_energy {e m r A B p : ℝ} (he : 0 ≤ e) (hm : 0 ≤ m) + (hr : 0 < r) (hA : 0 ≤ A) (hB : 0 ≤ B) (hp : 2 < p) + (h1 : e ≤ A*m^(2-2/p)) (h2 : e ≤ B*r^(2/3:ℝ)*m) : + e ≤ (A+B)*r^(1/3:ℝ)*m^(3/2-1/p) := by + have hα : 0 < 3/2-1/p := by + have : 1/p < (1:ℝ)/2 := (div_lt_div_iff₀ (by linarith) (by norm_num)).2 (by linarith) + linarith + have heq : (r^(1/3:ℝ)*m^(3/2-1/p))^2 = r^(2/3:ℝ)*m^(2-2/p)*m := by + have hrid : (r^(1/3:ℝ))^2 = r^(2/3:ℝ) := by + rw [← Real.rpow_mul_natCast hr.le] + norm_num + have hmid : (m^(3/2-1/p))^2 = m^(2-2/p)*m := by + rw [← Real.rpow_mul_natCast hm, + ← Real.rpow_add_one' hm (by + have he : (2-2/p)+1 = 2*(3/2-1/p) := by ring + rw [he] + positivity)] + congr 1 + norm_num + ring + rw [mul_pow, hrid, hmid, mul_assoc] + have hR : 0 ≤ r^(1/3:ℝ)*m^(3/2-1/p) := mul_nonneg + (Real.rpow_nonneg hr.le _) (Real.rpow_nonneg hm _) + have hAB : 0 ≤ A*B := mul_nonneg hA hB + have hh := mul_le_mul h1 h2 he (mul_nonneg hA (Real.rpow_nonneg hm _)) + have hh' : e^2 ≤ A*B*(r^(1/3:ℝ)*m^(3/2-1/p))^2 := by + rw [heq] + nlinarith only [hh] + have hp' : A*B ≤ (A+B)^2 := by nlinarith [sq_nonneg (A-B)] + have hq := mul_le_mul_of_nonneg_right hp' (sq_nonneg (r^(1/3:ℝ)*m^(3/2-1/p))) + have hn : 0 ≤ (A+B)*(r^(1/3:ℝ)*m^(3/2-1/p)) := mul_nonneg (add_nonneg hA hB) hR + have := (sq_le_sq₀ he hn).1 (hh'.trans (by nlinarith only [hq])) + simpa only [mul_assoc] using this + +lemma dyadic_rpow_mul (n : ℕ) (a : ℝ) : ((2:ℝ)^n)^a = (2:ℝ)^((n:ℝ)*a) := by + rw [← Real.rpow_natCast, ← Real.rpow_mul (by norm_num : (0:ℝ) ≤ 2)] + +lemma dyadic_scale (j k : ℕ) (hk : k ≤ j) : + (2:ℝ)^j * ((2:ℝ)^k)⁻¹ = (2:ℝ)^(j-k) := by + exact (pow_sub₀ (2:ℝ) (by norm_num) hk).symm + +lemma dyadic_width (j k : ℕ) : + (1/2:ℝ)^(j+k) = ((2:ℝ)^k)⁻¹ / (2:ℝ)^j := by + rw [one_div, inv_pow, pow_add] + field_simp + +lemma dyadic_decay (k : ℕ) : + (((2:ℝ)^k)⁻¹)^(1/3:ℝ) = (((2:ℝ)^(-(1/6:ℝ)))^k)^2 := by + rw [Real.inv_rpow (by positivity), dyadic_rpow_mul, ← Real.rpow_mul_natCast (by positivity), + ← Real.rpow_mul_natCast (by positivity), + ← Real.rpow_neg (by norm_num : (0:ℝ) ≤ 2)] + congr 1 + ring + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/DyadicGraph.lean b/lean/OAI/Analysis/PlanarEndpoint/DyadicGraph.lean new file mode 100644 index 0000000000000000000000000000000000000000..d19cf7590fc29ffe39a651e56b7915fdd3529096 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/DyadicGraph.lean @@ -0,0 +1,208 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphDual +import OAI.Analysis.PlanarEndpoint.TimeTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set +namespace PlanarEndpoint.DyadicGraph + +def width (s : List Bool) : ℝ := (1 / 2 : ℝ) ^ s.length + +def left : List Bool → ℝ + | [] => 0 + | false :: s => left s + | true :: s => left s + width s / 2 + +def interval (s : List Bool) : Set ℝ := Ico (left s) (left s + width s) + +lemma width_pos (s : List Bool) : 0 < width s := pow_pos (by norm_num) _ + +lemma width_cons (b : Bool) (s : List Bool) : width (b :: s) = width s / 2 := by + simp only [width, List.length_cons, pow_succ] + ring + +@[simp] lemma interval_nil : interval [] = Ico 0 1 := by norm_num [interval, left, width] + +lemma interval_false (s : List Bool) : + interval (false :: s) = Ico (left s) (left s + width s / 2) := by + simp only [interval, left, width_cons] + +lemma interval_true (s : List Bool) : + interval (true :: s) = Ico (left s + width s / 2) (left s + width s) := by + simp only [interval, left, width_cons] + congr 1 + ring + +lemma interval_split (s : List Bool) : + interval s = interval (false :: s) ∪ interval (true :: s) := by + rw [interval_false, interval_true] + exact (Ico_union_Ico_eq_Ico (by linarith [width_pos s]) (by linarith [width_pos s])).symm + +lemma interval_disjoint (s : List Bool) : + Disjoint (interval (false :: s)) (interval (true :: s)) := by + rw [interval_false, interval_true] + apply Set.disjoint_left.mpr + intro t ht hf + exact (not_lt_of_ge hf.1) ht.2 + +lemma interval_child_subset (b : Bool) (s : List Bool) : + interval (b :: s) ⊆ interval s := by + rw [interval_split s] + cases b + · exact subset_union_left + · exact subset_union_right + +lemma interval_subset_root (s : List Bool) : interval s ⊆ Ico 0 1 := by + induction s with + | nil => rw [interval_nil] + | cons b s ih => exact (interval_child_subset b s).trans ih + +lemma interval_measurable (s : List Bool) : MeasurableSet (interval s) := measurableSet_Ico + +lemma interval_level_partition (n : ℕ) : + ⋃ s ∈ TimeTree.level n, interval s = Ico 0 1 := by + induction n with + | zero => simp [TimeTree.level] + | succ n ih => + calc + _ = ⋃ s ∈ TimeTree.level n, (interval (false :: s) ∪ interval (true :: s)) := by + ext t + simp only [TimeTree.level, Finset.mem_union, Finset.mem_image, Set.mem_iUnion, + Set.mem_union] + constructor + · rintro ⟨s, (⟨a, ha, rfl⟩ | ⟨a, ha, rfl⟩), ht⟩ + · exact ⟨a, ha, Or.inl ht⟩ + · exact ⟨a, ha, Or.inr ht⟩ + · rintro ⟨s, hs, ht | ht⟩ + · exact ⟨false :: s, Or.inl ⟨s, hs, rfl⟩, ht⟩ + · exact ⟨true :: s, Or.inr ⟨s, hs, rfl⟩, ht⟩ + _ = _ := by simp_rw [← interval_split]; exact ih + +def index : List Bool → ℕ + | [] => 0 + | false :: s => 2 * index s + | true :: s => 2 * index s + 1 + +lemma index_lt (s : List Bool) : index s < 2 ^ s.length := by + induction s with + | nil => simp [index] + | cons b s ih => cases b <;> simp only [index, List.length_cons, pow_succ] <;> omega + +lemma index_injective {s t : List Bool} (hlen : s.length = t.length) + (hi : index s = index t) : s = t := by + induction s generalizing t with + | nil => simpa using hlen.symm + | cons b s ih => + cases t with + | nil => simp at hlen + | cons c t => + have hl : s.length = t.length := by simpa using hlen + cases b <;> cases c <;> simp only [index] at hi + · exact congrArg (List.cons false) (ih hl (by omega)) + · omega + · omega + · exact congrArg (List.cons true) (ih hl (by omega)) + +lemma left_eq (s : List Bool) : left s = (index s : ℝ) * width s := by + induction s with + | nil => simp [left, index] + | cons b s ih => + cases b <;> simp only [left, index, width_cons, Nat.cast_add, Nat.cast_mul, + Nat.cast_ofNat, Nat.cast_one, ih] <;> ring + +lemma interval_eq (s : List Bool) : + interval s = Ico ((index s : ℝ) * width s) (((index s : ℝ)+1) * width s) := by + rw [interval, left_eq] + congr 1 + ring + +lemma sum_level {E : Type*} [AddCommMonoid E] (G : List Bool → E) + (hsplit : ∀ s, G s = G (false :: s) + G (true :: s)) (n : ℕ) : + ∑ s ∈ TimeTree.level n, G s = G [] := by + classical + induction n with + | zero => simp [TimeTree.level] + | succ n ih => + rw [TimeTree.level, Finset.sum_union (TimeTree.level_children_disjoint n)] + rw [Finset.sum_image (fun a _ b _ h => List.cons.inj h |>.2), + Finset.sum_image (fun a _ b _ h => List.cons.inj h |>.2)] + rw [← Finset.sum_add_distrib] + simp_rw [← hsplit] + exact ih + +def fiber {X : Type*} (T : X → ℝ) (s : List Bool) : Set X := T ⁻¹' interval s + +lemma fiber_split {X : Type*} (T : X → ℝ) (s : List Bool) : + fiber T s = fiber T (false :: s) ∪ fiber T (true :: s) := by + simp only [fiber, interval_split s, preimage_union] + +lemma fiber_disjoint {X : Type*} (T : X → ℝ) (s : List Bool) : + Disjoint (fiber T (false :: s)) (fiber T (true :: s)) := + (interval_disjoint s).preimage T + +lemma fiber_measurable {X : Type*} [MeasurableSpace X] {T : X → ℝ} + (hT : Measurable T) (s : List Bool) : MeasurableSet (fiber T s) := + hT (interval_measurable s) + +def massTree {X : Type*} [MeasurableSpace X] (μ : Measure X) [IsFiniteMeasure μ] + (T : X → ℝ) (hT : Measurable T) : TimeTree.MassTree where + mass s := μ.real (fiber T s) + nonneg _ := ENNReal.toReal_nonneg + split s := by + rw [fiber_split T s, measureReal_union (fiber_disjoint T s) (fiber_measurable hT _)] + +lemma massTree_root {X : Type*} [MeasurableSpace X] (μ : Measure X) [IsFiniteMeasure μ] + (T : X → ℝ) (hT : Measurable T) (ht : ∀ᵐ x ∂μ, T x ∈ Ico 0 1) : + (massTree μ T hT).mass [] = μ.real univ := by + dsimp [massTree] + apply measureReal_congr + filter_upwards [ht] with x hx + apply propext + change (T x ∈ interval []) ↔ True + simpa only [interval_nil, iff_true] using hx + +lemma restrict_fiber_split {X : Type*} [MeasurableSpace X] (μ : Measure X) + (T : X → ℝ) (hT : Measurable T) (s : List Bool) : + μ.restrict (fiber T s) = μ.restrict (fiber T (false :: s)) + + μ.restrict (fiber T (true :: s)) := by + rw [fiber_split T s, Measure.restrict_union (fiber_disjoint T s) (fiber_measurable hT _)] + +def vector (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (s : List Bool) : L2 := + graphLp χ hχ (μ.restrict (fiber T s)) T w hT hw hb + +lemma vector_split (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (s : List Bool) : + vector χ hχ μ T w hT hw hb s = vector χ hχ μ T w hT hw hb (false :: s) + + vector χ hχ μ T w hT hw hb (true :: s) := by + unfold vector + simpa only [restrict_fiber_split μ T hT s] using + graphLp_add_measure χ hχ (μ.restrict (fiber T (false :: s))) + (μ.restrict (fiber T (true :: s))) T w hT hw hb + +lemma vector_level_sum (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (n : ℕ) : + ∑ s ∈ TimeTree.level n, vector χ hχ μ T w hT hw hb s = + vector χ hχ μ T w hT hw hb [] := + sum_level _ (vector_split χ hχ μ T w hT hw hb) n + +lemma mass_level_sum {X : Type*} [MeasurableSpace X] (μ : Measure X) [IsFiniteMeasure μ] + (T : X → ℝ) (hT : Measurable T) (n : ℕ) : + ∑ s ∈ TimeTree.level n, (massTree μ T hT).mass s = (massTree μ T hT).mass [] := + sum_level _ (massTree μ T hT).split n + +end PlanarEndpoint.DyadicGraph +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Extension.lean b/lean/OAI/Analysis/PlanarEndpoint/Extension.lean new file mode 100644 index 0000000000000000000000000000000000000000..5b12b8d1b618fb35ddc3cb55bd959f9f44b4aae7 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Extension.lean @@ -0,0 +1,226 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology ContDiff +namespace PlanarEndpoint + +def BoundedFourierSupport (f : L2) : Prop := + ∃ R : ℝ, ∀ᵐ ξ : Plane ∂volume, R < ‖ξ‖ → fourier f ξ = 0 + +lemma BoundedFourierSupport.integrable {f : L2} (hf : BoundedFourierSupport f) : + Integrable (fourier f) volume := by + obtain ⟨R, hR⟩ := hf + exact fourier_integrable_of_bounded_support hR + +lemma BoundedFourierSupport.sub {f g : L2} + (hf : BoundedFourierSupport f) (hg : BoundedFourierSupport g) : + BoundedFourierSupport (f - g) := by + obtain ⟨R, hR⟩ := hf + obtain ⟨S, hS⟩ := hg + refine ⟨max R S, ?_⟩ + filter_upwards [hR, hS, fourier_sub_ae f g] with ξ hr hs hsub hξ + rw [hsub, hr ((le_max_left _ _).trans_lt hξ), + hs ((le_max_right _ _).trans_lt hξ), sub_self] + +lemma inverseCompactFourier_boundedSupport (g : Plane → ℂ) (hc : HasCompactSupport g) + (hd : ContDiff ℝ ∞ g) : + BoundedFourierSupport ((inverseCompactFourier g hc hd).toLp 2 volume) := by + obtain ⟨R, hR⟩ := hc.isCompact.isBounded.subset_closedBall (0 : Plane) + refine ⟨R, ?_⟩ + filter_upwards [fourier_inverseCompactFourier_ae g hc hd] with ξ hξ hnorm + rw [hξ] + by_contra hn + have ht : ξ ∈ tsupport g := subset_closure hn + have := hR ht + simp only [Metric.mem_closedBall, dist_zero_right, not_le.mpr hnorm] at this + +lemma inHThird_sub {f g : L2} (hf : InHThird f) (hg : InHThird g) : + InHThird (f - g) := by + apply inHThird_of_fourier_memLp_sobolev + have he : fourier (f - g) =ᵐ[sobolevMeasure] (fun ξ => fourier f ξ - fourier g ξ) := + (withDensity_absolutelyContinuous _ _).ae_le (fourier_sub_ae f g) + exact (memLp_congr_ae he).2 ((fourier_memLp_sobolev hf).sub (fourier_memLp_sobolev hg)) + +lemma hThirdNorm_nonneg (f : L2) : 0 ≤ hThirdNorm f := Real.sqrt_nonneg _ + +lemma hThirdNorm_sub_le {f g : L2} (hf : InHThird f) (hg : InHThird g) : + hThirdNorm (f - g) ≤ hThirdNorm f + hThirdNorm g := by + have he : fourier (f - g) =ᵐ[sobolevMeasure] (fun ξ => fourier f ξ - fourier g ξ) := + (withDensity_absolutelyContinuous _ _).ae_le (fourier_sub_ae f g) + have hfm := fourier_memLp_sobolev hf + have hgm := fourier_memLp_sobolev hg + have hle := eLpNorm_sub_le (f := fourier f) (g := fourier g) (μ := sobolevMeasure) + (show (1 : ENNReal) ≤ 2 by norm_num) + have hle' := ENNReal.toReal_mono (ENNReal.add_ne_top.mpr ⟨hfm.eLpNorm_ne_top, + hgm.eLpNorm_ne_top⟩) hle + rw [ENNReal.toReal_add hfm.eLpNorm_ne_top hgm.eLpNorm_ne_top] at hle' + rw [hThirdNorm_eq_weighted_eLpNorm (inHThird_sub hf hg), + hThirdNorm_eq_weighted_eLpNorm hf, hThirdNorm_eq_weighted_eLpNorm hg, + eLpNorm_congr_ae he, ← mul_add] + exact mul_le_mul_of_nonneg_left hle' (by positivity) + +lemma hThirdNorm_sub_comm (f g : L2) : hThirdNorm (f - g) = hThirdNorm (g - f) := by + unfold hThirdNorm + congr 2 + apply integral_congr_ae + filter_upwards [fourier_sub_ae f g, fourier_sub_ae g f] with ξ hfg hgf + rw [hfg, hgf, norm_sub_rev] + +lemma evolution_sub {f g : L2} (hf : Integrable (fourier f) volume) + (hg : Integrable (fourier g) volume) (x : Plane) (t : ℝ) : + evolution (f - g) x t = evolution f x t - evolution g x t := by + have he : (fun ξ => phase x t ξ * fourier (f - g) ξ) =ᵐ[volume] + (fun ξ => phase x t ξ * fourier f ξ - phase x t ξ * fourier g ξ) := by + filter_upwards [fourier_sub_ae f g] with ξ hξ + rw [hξ, mul_sub] + simp only [evolution] + rw [integral_congr_ae he, integral_sub (evolution_integrable hf x t) + (evolution_integrable hg x t), smul_sub] + +lemma evolutionPath_sub {f g : L2} (hf : BoundedFourierSupport f) + (hg : BoundedFourierSupport g) (x : Plane) : + evolutionPath (f - g) (hf.sub hg).integrable x = + evolutionPath f hf.integrable x - evolutionPath g hg.integrable x := by + ext t + exact evolution_sub hf.integrable hg.integrable x t + +lemma exists_schwartz_bounded_hThird_approx {f : L2} (hf : InHThird f) + {ε : ℝ} (hε : 0 < ε) : + ∃ φ : SchwartzMap Plane ℂ, BoundedFourierSupport (φ.toLp 2 volume) ∧ InHThird (φ.toLp 2 volume) ∧ + InHThird (f - φ.toLp 2 volume) ∧ hThirdNorm (f - φ.toLp 2 volume) ≤ ε := by + have hc : 0 < 2 * Real.pi := by positivity + obtain ⟨g, hgcompact, hgsmooth, hgap⟩ := + exists_smooth_compact_fourier_approx hf (mul_pos hc hε) + let φ := inverseCompactFourier g hgcompact hgsmooth + have hφ : fourier (φ.toLp 2 volume) =ᵐ[volume] g := + fourier_inverseCompactFourier_ae g hgcompact hgsmooth + have hφw : fourier (φ.toLp 2 volume) =ᵐ[sobolevMeasure] g := + (withDensity_absolutelyContinuous _ _).ae_le hφ + have hgw : MemLp g 2 sobolevMeasure := + hgsmooth.continuous.memLp_of_hasCompactSupport hgcompact + have hφmem : MemLp (fourier (φ.toLp 2 volume)) 2 sobolevMeasure := + (memLp_congr_ae hφw).2 hgw + have hsub : fourier (f - φ.toLp 2 volume) =ᵐ[volume] fun ξ => fourier f ξ - g ξ := by + filter_upwards [fourier_sub_ae f (φ.toLp 2 volume), hφ] with ξ hξ hφξ + rw [hξ, hφξ] + have hsubw : fourier (f - φ.toLp 2 volume) =ᵐ[sobolevMeasure] fun ξ => fourier f ξ - g ξ := + (withDensity_absolutelyContinuous _ _).ae_le hsub + have hsubmem : MemLp (fourier (f - φ.toLp 2 volume)) 2 sobolevMeasure := + (memLp_congr_ae hsubw).2 ((fourier_memLp_sobolev hf).sub hgw) + have hH := inHThird_of_fourier_memLp_sobolev hsubmem + refine ⟨φ, inverseCompactFourier_boundedSupport g hgcompact hgsmooth, inHThird_of_fourier_memLp_sobolev hφmem, hH, ?_⟩ + rw [hThirdNorm_eq_weighted_eLpNorm hH, eLpNorm_congr_ae hsubw] + have hgap' := ENNReal.toReal_mono ENNReal.ofReal_ne_top hgap + rw [ENNReal.toReal_ofReal (mul_pos hc hε).le] at hgap' + calc + _ ≤ (2 * Real.pi)⁻¹ * (2 * Real.pi * ε) := + mul_le_mul_of_nonneg_left hgap' (inv_nonneg.mpr hc.le) + _ = ε := by rw [← mul_assoc, inv_mul_cancel₀ hc.ne', one_mul] + +lemma exists_fast_bounded_approximation {f : L2} (hf : InHThird f) : + ∃ F : ℕ → L2, (∀ n, BoundedFourierSupport (F n)) ∧ + (∀ n, InHThird (F n)) ∧ + (∀ n, hThirdNorm (f - F n) ≤ (1 / 2 : ℝ)^n) ∧ + Tendsto F atTop (𝓝 f) ∧ + Summable (fun n => hThirdNorm (F (n + 1) - F n)) := by + have hx (n : ℕ) := exists_schwartz_bounded_hThird_approx hf + (pow_pos (by norm_num : (0 : ℝ) < 1 / 2) n) + choose φ hφb hφh hφsub hφerr using hx + let F : ℕ → L2 := fun n => (φ n).toLp 2 volume + have he (n : ℕ) : hThirdNorm (f - F n) ≤ (1 / 2 : ℝ)^n := hφerr n + have hgeom : Summable (fun n : ℕ => (1 / 2 : ℝ)^n) := + summable_geometric_of_lt_one (by norm_num) (by norm_num) + have hinc (n : ℕ) : hThirdNorm (F (n + 1) - F n) ≤ + (1 / 2 : ℝ)^(n + 1) + (1 / 2 : ℝ)^n := by + have hineq := hThirdNorm_sub_le (hφsub n) (hφsub (n + 1)) + have hsub : (f - F n) - (f - F (n + 1)) = F (n + 1) - F n := by abel + change hThirdNorm ((f - F n) - (f - F (n + 1))) ≤ _ at hineq + rw [hsub] at hineq + exact hineq.trans (by linarith [he n, he (n + 1)]) + refine ⟨F, hφb, hφh, he, ?_, ?_⟩ + · apply tendsto_iff_norm_sub_tendsto_zero.2 + apply squeeze_zero (fun _ => norm_nonneg _) ?_ + (tendsto_pow_atTop_nhds_zero_of_lt_one (by norm_num : (0 : ℝ) ≤ 1 / 2) + (by norm_num)) + intro n + rw [norm_sub_rev] + exact (norm_le_hThirdNorm (hφsub n)).trans (he n) + · exact Summable.of_nonneg_of_le (fun _ => hThirdNorm_nonneg _) hinc + (((summable_nat_add_iff 1).2 hgeom).add hgeom) + +lemma exists_timePath_limit_of_summable (F : ℕ → TimePath) + (hF : Summable (fun n => ‖F (n + 1) - F n‖)) : + ∃ g : TimePath, Tendsto F atTop (𝓝 g) := by + apply cauchySeq_tendsto_of_complete + apply cauchySeq_of_summable_dist + simpa only [dist_eq_norm, norm_sub_rev] using hF + +lemma ae_summable_path_increments (F : ℕ → Plane → TimePath) + (_hF : ∀ n, StronglyMeasurable (F n)) + (hlocal : ∀ k : ℕ, (∑' n, eLpNorm (fun x => F (n + 1) x - F n x) 1 + (volume.restrict (Metric.ball (0 : Plane) (k : ℝ)))) ≠ ⊤) : + ∀ᵐ x : Plane ∂volume, Summable (fun n => ‖F (n + 1) x - F n x‖) := by + have hball (k : ℕ) : ∀ᵐ x : Plane ∂volume, + x ∈ Metric.ball (0 : Plane) (k : ℝ) → + Summable (fun n => ‖F (n + 1) x - F n x‖) := by + apply (ae_restrict_iff' measurableSet_ball).1 + exact summable_norm_of_tsum_eLpNorm_ne_top le_rfl (hlocal k) + filter_upwards [ae_all_iff.2 hball] with x hx + obtain ⟨k, hk⟩ := exists_nat_gt ‖x‖ + exact hx k (by simpa only [Metric.mem_ball, dist_zero_right] using hk) + +def pathLimit (F : ℕ → Plane → TimePath) (x : Plane) : TimePath := + limUnder atTop (fun n => F n x) + +lemma stronglyMeasurable_pathLimit (F : ℕ → Plane → TimePath) + (hF : ∀ n, StronglyMeasurable (F n)) : StronglyMeasurable (pathLimit F) := + StronglyMeasurable.limUnder hF + +lemma ae_tendsto_pathLimit_of_local_summable (F : ℕ → Plane → TimePath) + (hF : ∀ n, StronglyMeasurable (F n)) + (hlocal : ∀ k : ℕ, (∑' n, eLpNorm (fun x => F (n + 1) x - F n x) 1 + (volume.restrict (Metric.ball (0 : Plane) (k : ℝ)))) ≠ ⊤) : + ∀ᵐ x : Plane ∂volume, Tendsto (fun n => F n x) atTop (𝓝 (pathLimit F x)) := by + filter_upwards [ae_summable_path_increments F hF hlocal] with x hx + obtain ⟨g, hg⟩ := exists_timePath_limit_of_summable (fun n => F n x) hx + simpa only [pathLimit, hg.limUnder_eq] using hg + +lemma isometry_l2Evolution (t : ℝ) : Isometry (fun f : L2 => l2Evolution f t) := + isometry_iff_dist_eq.2 (fun f g => dist_l2Evolution f g t) + +lemma pathLimit_ae_l2Evolution (F : ℕ → L2) (hF : ∀ n, BoundedFourierSupport (F n)) + {f : L2} (hlim : Tendsto F atTop (𝓝 f)) + (hpath : ∀ᵐ x : Plane ∂volume, + Tendsto (fun n => evolutionPath (F n) (hF n).integrable x) atTop + (𝓝 (pathLimit (fun n => evolutionPath (F n) (hF n).integrable) x))) + (t : Time) : + (fun x => pathLimit (fun n => evolutionPath (F n) (hF n).integrable) x t) + =ᵐ[volume] (l2Evolution f (t : ℝ) : Plane → ℂ) := by + have hL2 : Tendsto (fun n => l2Evolution (F n) (t : ℝ)) atTop + (𝓝 (l2Evolution f (t : ℝ))) := + ((isometry_l2Evolution (t : ℝ)).continuous.tendsto f).comp hlim + obtain ⟨ns, hns, hae⟩ := (tendstoInMeasure_of_tendsto_Lp hL2).exists_seq_tendsto_ae + have hid : ∀ᵐ x : Plane ∂volume, ∀ n : ℕ, + l2Evolution (F n) (t : ℝ) x = evolution (F n) x (t : ℝ) := + ae_all_iff.2 (fun n => l2Evolution_ae_evolution (hF n).integrable _) + filter_upwards [hpath, hae, hid] with x hp hl hi + have he : Tendsto (fun n => evolution (F n) x (t : ℝ)) atTop + (𝓝 (pathLimit (fun n => evolutionPath (F n) (hF n).integrable) x t)) := + (continuous_eval_const t).continuousAt.tendsto.comp hp + have he' := he.comp hns.tendsto_atTop + have hl' : Tendsto (fun n => evolution (F (ns n)) x (t : ℝ)) + atTop (𝓝 (l2Evolution f (t : ℝ) x)) := by + simpa only [hi] using hl + exact tendsto_nhds_unique he' hl' + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Fourier.lean b/lean/OAI/Analysis/PlanarEndpoint/Fourier.lean new file mode 100644 index 0000000000000000000000000000000000000000..72abefd1f0eb8b0720b44ce9806c19066bd0d2d8 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Fourier.lean @@ -0,0 +1,957 @@ +import Mathlib + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology ContDiff +namespace PlanarEndpoint + +abbrev Plane := EuclideanSpace ℝ (Fin 2) +abbrev L2 := MeasureTheory.Lp ℂ 2 (volume : Measure Plane) + +def fourier (f : L2) (ξ : Plane) : ℂ := + (MeasureTheory.Lp.fourierTransformₗᵢ Plane ℂ f) ((2 * Real.pi)⁻¹ • ξ) + +def InHThird (f : L2) : Prop := + Integrable (fun ξ : Plane => + (1 + ‖ξ‖ ^ 2) ^ (1 / 3 : ℝ) * ‖fourier f ξ‖ ^ 2) volume + +def hThirdNorm (f : L2) : ℝ := + Real.sqrt (((2 * Real.pi) ^ 2)⁻¹ * ∫ ξ : Plane, + (1 + ‖ξ‖ ^ 2) ^ (1 / 3 : ℝ) * ‖fourier f ξ‖ ^ 2) + +def abel (f : L2) (a : ℝ) (x : Plane) (t : ℝ) : ℂ := + (((2 * Real.pi) ^ 2)⁻¹ : ℝ) • ∫ ξ : Plane, + Complex.exp (Complex.I * ((inner ℝ x ξ - t * ‖ξ‖ ^ 2 : ℝ) : ℂ) - + ((a * ‖ξ‖ ^ 2 : ℝ) : ℂ)) * fourier f ξ + +def diskAverage (f : L2) (x : Plane) (r : ℝ) : ℂ := + (Real.pi * r ^ 2)⁻¹ • ∫ y in Metric.ball x r, f y + +def lebesgueRepresentative (f : L2) (x : Plane) : ℂ := + limUnder (𝓝[>] (0 : ℝ)) (diskAverage f x) + +def IsLebesguePoint (f : L2) (x : Plane) : Prop := + ∃ z : ℂ, Tendsto (fun r : ℝ => + (Real.pi * r ^ 2)⁻¹ * ∫ y in Metric.ball x r, ‖f y - z‖) + (𝓝[>] (0 : ℝ)) (𝓝 0) + +def MainConclusion (f : L2) : Prop := + ∃ E : Set Plane, volume Eᶜ = 0 ∧ + ∀ x ∈ E, IsLebesguePoint f x ∧ + ∃ u : ℝ → ℂ, + ContinuousOn u (Ico 0 1) ∧ + u 0 = lebesgueRepresentative f x ∧ + Tendsto (diskAverage f x) (𝓝[>] (0 : ℝ)) (𝓝 (u 0)) ∧ + (∀ t ∈ Ioo (0 : ℝ) 1, + Tendsto (fun a => abel f a x t) (𝓝[>] (0 : ℝ)) (𝓝 (u t))) ∧ + Tendsto u (𝓝[>] (0 : ℝ)) (𝓝 (lebesgueRepresentative f x)) ∧ + TendstoUniformlyOn (fun a t => abel f a x t) u + (𝓝[>] (0 : ℝ)) (Ioo (0 : ℝ) 1) + +end PlanarEndpoint + +namespace PlanarEndpoint + +lemma fourier_memLp (f : L2) : MemLp (fourier f) 2 volume := by + let g := MeasureTheory.Lp.fourierTransformₗᵢ Plane ℂ f + have hg := (Lp.memLp g).smul_measure + (c := ENNReal.ofReal |(((2 * Real.pi)⁻¹) ^ Module.finrank ℝ Plane)⁻¹|) + ENNReal.ofReal_ne_top + have hc : (2 * Real.pi)⁻¹ ≠ 0 := inv_ne_zero (mul_ne_zero (by norm_num) Real.pi_ne_zero) + rw [← Measure.map_addHaar_smul (volume : Measure Plane) hc] at hg + exact hg.comp_of_map (measurable_const_smul _).aemeasurable + +def phase (x : Plane) (t : ℝ) (ξ : Plane) : ℂ := + Complex.exp (Complex.I * ((inner ℝ x ξ - t * ‖ξ‖ ^ 2 : ℝ) : ℂ)) + +@[simp] lemma norm_phase (x ξ : Plane) (t : ℝ) : ‖phase x t ξ‖ = 1 := by + simp only [phase, Complex.norm_exp, Complex.mul_re, Complex.I_re, Complex.I_im, + Complex.ofReal_re, Complex.ofReal_im, zero_mul, mul_zero, sub_zero, Real.exp_zero] + +lemma continuous_phase (x : Plane) (t : ℝ) : Continuous (phase x t) := by + unfold phase + fun_prop + +lemma continuous_phase_parameters (ξ : Plane) : + Continuous (fun z : Plane × ℝ => phase z.1 z.2 ξ) := by + unfold phase + fun_prop + +lemma memLp_gaussian {a : ℝ} (ha : 0 < a) : + MemLp (fun ξ : Plane => Complex.exp (-((a * ‖ξ‖ ^ 2 : ℝ) : ℂ))) 2 volume := by + apply (memLp_two_iff_integrable_sq_norm (by fun_prop)).2 + have hi := GaussianFourier.integrable_cexp_neg_mul_sq_norm_add + (show 0 < ((2 * a : ℝ) : ℂ).re by simpa using (mul_pos (by norm_num : (0:ℝ) < 2) ha)) + (0 : ℂ) (0 : Plane) + have hn := hi.norm + convert hn using 1 + ext ξ + simp only [Complex.norm_exp, Complex.neg_re, Complex.ofReal_re, Complex.add_re, + Complex.mul_re, Complex.ofReal_im, zero_mul, mul_zero, sub_zero, + Complex.zero_re, ← Complex.ofReal_pow, Complex.ofReal_re] + rw [← Real.exp_nat_mul] + congr 1 + simp + ring + +lemma abel_integrable (f : L2) {a : ℝ} (ha : 0 < a) (x : Plane) (t : ℝ) : + Integrable (fun ξ : Plane => + Complex.exp (Complex.I * ((inner ℝ x ξ - t * ‖ξ‖ ^ 2 : ℝ) : ℂ) - + ((a * ‖ξ‖ ^ 2 : ℝ) : ℂ)) * fourier f ξ) volume := by + have hg := (memLp_gaussian ha).integrable_mul (fourier_memLp f) + have hc : Continuous (fun ξ : Plane => + Complex.exp (Complex.I * ((inner ℝ x ξ - t * ‖ξ‖ ^ 2 : ℝ) : ℂ) - + ((a * ‖ξ‖ ^ 2 : ℝ) : ℂ))) := by fun_prop + apply hg.mono (hc.aestronglyMeasurable.mul (fourier_memLp f).aestronglyMeasurable) + filter_upwards with ξ + change ‖Complex.exp (Complex.I * ((inner ℝ x ξ - t * ‖ξ‖ ^ 2 : ℝ) : ℂ) - + ((a * ‖ξ‖ ^ 2 : ℝ) : ℂ)) * fourier f ξ‖ ≤ + ‖Complex.exp (-((a * ‖ξ‖ ^ 2 : ℝ) : ℂ)) * fourier f ξ‖ + simp only [norm_mul, Complex.norm_exp, Complex.sub_re, Complex.mul_re, + Complex.I_re, Complex.I_im, Complex.ofReal_re, Complex.ofReal_im, + Complex.neg_re, zero_mul, mul_zero, sub_zero, zero_sub, le_refl] + +def evolution (f : L2) (x : Plane) (t : ℝ) : ℂ := + (((2 * Real.pi) ^ 2)⁻¹ : ℝ) • ∫ ξ : Plane, phase x t ξ * fourier f ξ + +lemma evolution_integrable {f : L2} (hf : Integrable (fourier f) volume) + (x : Plane) (t : ℝ) : + Integrable (fun ξ => phase x t ξ * fourier f ξ) volume := by + apply hf.mono ((continuous_phase x t).aestronglyMeasurable.mul hf.1) + filter_upwards with ξ + simp + +lemma continuous_evolution {f : L2} (hf : Integrable (fourier f) volume) : + Continuous (fun z : Plane × ℝ => evolution f z.1 z.2) := by + have hc : Continuous (fun z : Plane × ℝ => + ∫ ξ : Plane, phase z.1 z.2 ξ * fourier f ξ) := by + apply continuous_of_dominated (bound := fun ξ => ‖fourier f ξ‖) + · intro z + exact ((continuous_phase z.1 z.2).aestronglyMeasurable.mul hf.1) + · intro z + filter_upwards with ξ + simp + · exact hf.norm + · filter_upwards with ξ + exact (continuous_phase_parameters ξ).mul continuous_const + have hm : Continuous (fun z : Plane × ℝ => + (((((2 * Real.pi) ^ 2)⁻¹ : ℝ) : ℂ)) * + ∫ ξ : Plane, phase z.1 z.2 ξ * fourier f ξ) := + continuous_const.mul hc + simpa only [evolution, Complex.real_smul] using hm + +def gaussianWeight (a : ℝ) (ξ : Plane) : ℝ := Real.exp (-a * ‖ξ‖ ^ 2) + +lemma gaussianWeight_pos (a : ℝ) (ξ : Plane) : 0 < gaussianWeight a ξ := Real.exp_pos _ + +lemma gaussianWeight_le_one {a : ℝ} (ha : 0 ≤ a) (ξ : Plane) : + gaussianWeight a ξ ≤ 1 := by + apply Real.exp_le_one_iff.mpr + exact mul_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr ha) (sq_nonneg _) + +lemma abel_eq_weighted (f : L2) (a : ℝ) (x : Plane) (t : ℝ) : + abel f a x t = (((2 * Real.pi) ^ 2)⁻¹ : ℝ) • + ∫ ξ : Plane, phase x t ξ * (gaussianWeight a ξ : ℂ) * fourier f ξ := by + unfold abel + congr 1 + apply integral_congr_ae + filter_upwards with ξ + simp only [phase, gaussianWeight, sub_eq_add_neg, Complex.exp_add, + Complex.ofReal_exp, Complex.ofReal_mul, Complex.ofReal_neg, neg_mul] + +lemma gaussian_error_integrable {f : L2} (hf : Integrable (fourier f) volume) + {a : ℝ} (ha : 0 ≤ a) : + Integrable (fun ξ => (1 - gaussianWeight a ξ) * ‖fourier f ξ‖) volume := by + apply hf.norm.mono + · exact (by unfold gaussianWeight; fun_prop : Continuous (fun ξ => 1 - gaussianWeight a ξ)).aestronglyMeasurable.mul + hf.norm.aestronglyMeasurable + · filter_upwards with ξ + simpa only [norm_mul, Real.norm_eq_abs, abs_norm, + abs_of_nonneg (sub_nonneg.mpr (gaussianWeight_le_one ha ξ))] using + (mul_le_of_le_one_left (norm_nonneg (fourier f ξ)) + (show 1 - gaussianWeight a ξ ≤ 1 by linarith [gaussianWeight_pos a ξ])) + +lemma gaussian_error_tendsto_zero {f : L2} (hf : Integrable (fourier f) volume) : + Tendsto (fun a : ℝ => ∫ ξ : Plane, (1 - gaussianWeight a ξ) * ‖fourier f ξ‖) + (𝓝[>] (0 : ℝ)) (𝓝 0) := by + have he : ∀ᶠ a : ℝ in 𝓝[>] (0 : ℝ), 0 ≤ a := by + filter_upwards [self_mem_nhdsWithin] with a ha using le_of_lt ha + have h := tendsto_integral_filter_of_dominated_convergence + (f := fun _ : Plane => (0 : ℝ)) (fun ξ => ‖fourier f ξ‖) + (he.mono (fun a ha => (gaussian_error_integrable hf ha).1)) + (he.mono (fun a ha => by + filter_upwards with ξ + rw [Real.norm_eq_abs, abs_mul, abs_of_nonneg (norm_nonneg _), + abs_of_nonneg (sub_nonneg.mpr (gaussianWeight_le_one ha ξ))] + exact mul_le_of_le_one_left (norm_nonneg (fourier f ξ)) (show 1 - gaussianWeight a ξ ≤ 1 by linarith [gaussianWeight_pos a ξ]))) + hf.norm (by + filter_upwards with ξ + have hc : Continuous (fun a : ℝ => (1 - gaussianWeight a ξ) * ‖fourier f ξ‖) := by + unfold gaussianWeight + fun_prop + simpa [gaussianWeight] using (hc.continuousAt (x := 0)).tendsto.mono_left nhdsWithin_le_nhds) + simpa only [integral_zero] using h + +lemma weighted_evolution_integrable {f : L2} (hf : Integrable (fourier f) volume) + {a : ℝ} (ha : 0 ≤ a) (x : Plane) (t : ℝ) : + Integrable (fun ξ => phase x t ξ * (gaussianWeight a ξ : ℂ) * fourier f ξ) volume := by + apply hf.mono + · have hg : Continuous (fun ξ : Plane => (gaussianWeight a ξ : ℂ)) := by + unfold gaussianWeight + fun_prop + exact ((continuous_phase x t).mul hg).aestronglyMeasurable.mul hf.1 + · filter_upwards with ξ + simp only [norm_mul, norm_phase, one_mul, Complex.norm_real, Real.norm_eq_abs, + abs_of_pos (gaussianWeight_pos a ξ)] + exact mul_le_of_le_one_left (norm_nonneg _) (gaussianWeight_le_one ha ξ) + +lemma norm_abel_sub_evolution_le {f : L2} (hf : Integrable (fourier f) volume) + {a : ℝ} (ha : 0 ≤ a) (x : Plane) (t : ℝ) : + ‖abel f a x t - evolution f x t‖ ≤ + ((2 * Real.pi) ^ 2)⁻¹ * ∫ ξ : Plane, (1 - gaussianWeight a ξ) * ‖fourier f ξ‖ := by + have hc : 0 ≤ ((2 * Real.pi) ^ 2)⁻¹ := by positivity + rw [abel_eq_weighted, evolution, ← smul_sub, + ← integral_sub (weighted_evolution_integrable hf ha x t) (evolution_integrable hf x t), + norm_smul, Real.norm_eq_abs, abs_of_nonneg hc] + apply mul_le_mul_of_nonneg_left _ hc + calc + _ ≤ ∫ ξ : Plane, ‖phase x t ξ * (gaussianWeight a ξ : ℂ) * fourier f ξ - + phase x t ξ * fourier f ξ‖ := norm_integral_le_integral_norm _ + _ = _ := by + apply integral_congr_ae + filter_upwards with ξ + have he : phase x t ξ * (gaussianWeight a ξ : ℂ) * fourier f ξ - + phase x t ξ * fourier f ξ = + phase x t ξ * (((gaussianWeight a ξ - 1 : ℝ) : ℂ)) * fourier f ξ := by + push_cast + ring + rw [he] + simp only [norm_mul, norm_phase, one_mul, Complex.norm_real, Real.norm_eq_abs, + abs_of_nonpos (sub_nonpos.mpr (gaussianWeight_le_one ha ξ))] + ring + +lemma abel_tendstoUniformly {f : L2} (hf : Integrable (fourier f) volume) : + TendstoUniformly (fun a (z : Plane × ℝ) => abel f a z.1 z.2) + (fun z => evolution f z.1 z.2) (𝓝[>] (0 : ℝ)) := by + apply Metric.tendstoUniformly_iff.2 + intro ε hε + have hlim := (gaussian_error_tendsto_zero hf).const_mul (((2 * Real.pi) ^ 2)⁻¹) + simp only [mul_zero] at hlim + have he := (tendsto_order.1 hlim).2 ε hε + filter_upwards [he, self_mem_nhdsWithin] with a ha ha' + intro z + rw [dist_comm, dist_eq_norm] + exact (norm_abel_sub_evolution_le hf (le_of_lt ha') z.1 z.2).trans_lt ha + +def AnnularFourierSupport (f : L2) (c₀ C₀ N : ℝ) : Prop := + ∀ᵐ ξ : Plane ∂volume, ξ ∉ {ξ | c₀ * N ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀ * N} → fourier f ξ = 0 + +lemma fourier_integrable_of_bounded_support {f : L2} {R : ℝ} + (hs : ∀ᵐ ξ : Plane ∂volume, R < ‖ξ‖ → fourier f ξ = 0) : + Integrable (fourier f) volume := by + have hi := ((fourier_memLp f).locallyIntegrable (by norm_num)).integrableOn_isCompact + (isCompact_closedBall (0 : Plane) R) + apply hi.integrable_of_ae_notMem_eq_zero + filter_upwards [hs] with ξ hξ hξ' + apply hξ + simpa only [Metric.mem_closedBall, dist_zero_right, not_le] using hξ' + +lemma AnnularFourierSupport.integrable {f : L2} {c₀ C₀ N : ℝ} + (hs : AnnularFourierSupport f c₀ C₀ N) : Integrable (fourier f) volume := by + apply fourier_integrable_of_bounded_support (R := C₀ * N) + filter_upwards [hs] with ξ hξ hξ' + apply hξ + intro h + exact (not_le.mpr hξ') h.2 + +def shortTimeLevel (f : L2) (x₀ : Plane) (t₀ s lam : ℝ) : Set Plane := + Metric.ball x₀ 1 ∩ {x | ∃ t ∈ Icc t₀ (t₀ + s), lam < ‖evolution f x t‖} + +lemma isOpen_timeLevel {f : L2} (hf : Integrable (fourier f) volume) + (t₀ s lam : ℝ) : IsOpen {x : Plane | ∃ t ∈ Icc t₀ (t₀ + s), lam < ‖evolution f x t‖} := by + have he : {x : Plane | ∃ t ∈ Icc t₀ (t₀ + s), lam < ‖evolution f x t‖} = + ⋃ t ∈ Icc t₀ (t₀ + s), {x | lam < ‖evolution f x t‖} := by + ext x + simp + rw [he] + apply isOpen_iUnion + intro t + apply isOpen_iUnion + intro _ + apply isOpen_lt continuous_const + exact ((continuous_evolution hf).comp (continuous_id.prodMk continuous_const)).norm + +lemma measurableSet_shortTimeLevel {f : L2} (hf : Integrable (fourier f) volume) + (x₀ : Plane) (t₀ s lam : ℝ) : MeasurableSet (shortTimeLevel f x₀ t₀ s lam) := + Metric.isOpen_ball.measurableSet.inter (isOpen_timeLevel hf t₀ s lam).measurableSet + +def ShortTimeWeakEstimate (c₀ C₀ p : ℝ) : Prop := + ∃ C : ℝ, 0 < C ∧ ∀ (j : ℕ) (f : L2), + AnnularFourierSupport f c₀ C₀ ((2 : ℝ) ^ j) → + ∀ (x₀ : Plane) (t₀ s : ℝ), 0 ≤ s → s ≤ ((2 : ℝ) ^ j)⁻¹ → + ∀ lam : ℝ, 0 < lam → + volume (shortTimeLevel f x₀ t₀ s lam) ≤ + ENNReal.ofReal ((C * (((2 : ℝ) ^ j) ^ (1 / 3 : ℝ)) * ‖f‖ / lam) ^ p) + +lemma fourier_energy (f : L2) : + ∫ ξ : Plane, ‖fourier f ξ‖ ^ 2 = (2 * Real.pi) ^ 2 * ‖f‖ ^ 2 := by + let g := MeasureTheory.Lp.fourierTransformₗᵢ Plane ℂ f + have hg : ∫ ξ : Plane, ‖g ξ‖ ^ 2 = ‖f‖ ^ 2 := by + calc + _ = inner ℝ g g := by simp only [L2.inner_def, real_inner_self_eq_norm_sq] + _ = ‖g‖ ^ 2 := real_inner_self_eq_norm_sq g + _ = ‖f‖ ^ 2 := by rw [show ‖g‖ = ‖f‖ from LinearIsometryEquiv.norm_map _ _] + change (∫ ξ : Plane, (fun η : Plane => ‖g η‖ ^ 2) ((2 * Real.pi)⁻¹ • ξ)) = _ + rw [Measure.integral_comp_inv_smul_of_nonneg volume (fun η : Plane => ‖g η‖ ^ 2) + (show 0 ≤ 2 * Real.pi by positivity)] + simp only [finrank_euclideanSpace, Fintype.card_fin, + smul_eq_mul] + rw [hg] + +lemma norm_evolution_le_fourierL1 (f : L2) (x : Plane) (t : ℝ) : + ‖evolution f x t‖ ≤ ((2 * Real.pi) ^ 2)⁻¹ * ∫ ξ : Plane, ‖fourier f ξ‖ := by + unfold evolution + rw [norm_smul, Real.norm_eq_abs, abs_of_pos (by positivity : 0 < ((2 * Real.pi)^2)⁻¹)] + apply mul_le_mul_of_nonneg_left _ (by positivity) + simpa only [norm_mul, norm_phase, one_mul] using + norm_integral_le_integral_norm (fun ξ => phase x t ξ * fourier f ξ) + +lemma fourierL1_le_support_energy {f : L2} {R : ℝ} + (hs : ∀ᵐ ξ : Plane ∂volume, R < ‖ξ‖ → fourier f ξ = 0) : + (∫ ξ : Plane, ‖fourier f ξ‖) ≤ + (2 * Real.pi) * ‖f‖ * Real.sqrt (volume (Metric.closedBall (0 : Plane) R)).toReal := by + let b : Plane → ℂ := (Metric.closedBall (0 : Plane) R).indicator (fun _ => 1) + have hb : MemLp b 2 volume := memLp_indicator_const _ measurableSet_closedBall _ + (Or.inr (isCompact_closedBall (0 : Plane) R).measure_ne_top) + have hpq : (2 : ℝ).HolderConjugate 2 := Real.HolderConjugate.two_two + have hh := integral_mul_norm_le_Lp_mul_Lq hpq + (show MemLp (fourier f) (ENNReal.ofReal (2 : ℝ)) volume by simpa using fourier_memLp f) + (show MemLp b (ENNReal.ofReal (2 : ℝ)) volume by simpa using hb) + have he : ∫ ξ : Plane, ‖fourier f ξ‖ * ‖b ξ‖ = ∫ ξ : Plane, ‖fourier f ξ‖ := by + apply integral_congr_ae + filter_upwards [hs] with ξ hξ + by_cases hm : ξ ∈ Metric.closedBall (0 : Plane) R + · simp [b, hm] + · have hz : fourier f ξ = 0 := hξ (by simpa only [Metric.mem_closedBall, + dist_zero_right, not_le] using hm) + simp [hz] + have hb2 : ∫ ξ : Plane, ‖b ξ‖ ^ (2 : ℝ) = + (volume (Metric.closedBall (0 : Plane) R)).toReal := by + calc + _ = ∫ ξ : Plane, (Metric.closedBall (0 : Plane) R).indicator (fun _ => (1 : ℝ)) ξ := by + apply integral_congr_ae + filter_upwards with ξ + by_cases hm : ξ ∈ Metric.closedBall (0 : Plane) R <;> simp [b, hm] + _ = _ := by simp [integral_indicator measurableSet_closedBall, measureReal_def] + rw [he, hb2] at hh + simp only [Real.rpow_two] at hh + rw [fourier_energy, ← Real.sqrt_eq_rpow, ← Real.sqrt_eq_rpow] at hh + have he2 : Real.sqrt ((2 * Real.pi)^2 * ‖f‖^2) = (2 * Real.pi) * ‖f‖ := by + rw [Real.sqrt_mul (sq_nonneg _), Real.sqrt_sq (by positivity), Real.sqrt_sq (norm_nonneg _)] + rwa [he2] at hh + +lemma sobolevWeight_one_le (ξ : Plane) : 1 ≤ (1 + ‖ξ‖^2) ^ (1 / 3 : ℝ) := by + exact Real.one_le_rpow (by nlinarith [sq_nonneg ‖ξ‖]) (by norm_num) + +lemma sobolev_energy_nonneg (f : L2) : + 0 ≤ ∫ ξ : Plane, (1 + ‖ξ‖^2) ^ (1 / 3 : ℝ) * ‖fourier f ξ‖^2 := by + apply integral_nonneg + intro ξ + positivity + +lemma norm_le_hThirdNorm {f : L2} (hf : InHThird f) : ‖f‖ ≤ hThirdNorm f := by + have hm : ∫ ξ : Plane, ‖fourier f ξ‖^2 ≤ + ∫ ξ : Plane, (1 + ‖ξ‖^2) ^ (1 / 3 : ℝ) * ‖fourier f ξ‖^2 := by + apply integral_mono ((fourier_memLp f).integrable_norm_pow (by norm_num)) hf + intro ξ + exact le_mul_of_one_le_left (sq_nonneg _) (sobolevWeight_one_le ξ) + rw [fourier_energy] at hm + have hc : 0 < (2 * Real.pi)^2 := by positivity + have hm' := mul_le_mul_of_nonneg_left hm (inv_nonneg.mpr hc.le) + rw [← mul_assoc, inv_mul_cancel₀ hc.ne', one_mul] at hm' + unfold hThirdNorm + exact (Real.le_sqrt (norm_nonneg _) (mul_nonneg (inv_nonneg.mpr hc.le) + (sobolev_energy_nonneg f))).mpr hm' + +lemma norm_evolution_le_bounded_frequency {f : L2} {R : ℝ} + (hR : 0 ≤ R) (hs : ∀ᵐ ξ : Plane ∂volume, R < ‖ξ‖ → fourier f ξ = 0) + (x : Plane) (t : ℝ) : + ‖evolution f x t‖ ≤ (Real.sqrt Real.pi / (2 * Real.pi)) * R * ‖f‖ := by + have hh := (norm_evolution_le_fourierL1 f x t).trans + (mul_le_mul_of_nonneg_left (fourierL1_le_support_energy hs) (by positivity)) + have hv : Real.sqrt (volume (Metric.closedBall (0 : Plane) R)).toReal = + R * Real.sqrt Real.pi := by + rw [EuclideanSpace.volume_closedBall_fin_two, ENNReal.toReal_mul, + ENNReal.toReal_pow, ENNReal.toReal_ofReal hR, + ENNReal.toReal_ofReal Real.pi_pos.le, Real.sqrt_mul (sq_nonneg _), Real.sqrt_sq hR] + rw [hv] at hh + have hid : ((2 * Real.pi)^2)⁻¹ * ((2 * Real.pi) * ‖f‖ * (R * Real.sqrt Real.pi)) = + (Real.sqrt Real.pi / (2 * Real.pi)) * R * ‖f‖ := by + field_simp + rwa [hid] at hh + +lemma norm_evolution_le_low_frequency {f : L2} (hf : InHThird f) + (hs : ∀ᵐ ξ : Plane ∂volume, 1 < ‖ξ‖ → fourier f ξ = 0) + (x : Plane) (t : ℝ) : + ‖evolution f x t‖ ≤ (Real.sqrt Real.pi / (2 * Real.pi)) * hThirdNorm f := by + have he := norm_evolution_le_bounded_frequency (by norm_num : (0 : ℝ) ≤ 1) hs x t + rw [mul_one] at he + exact he.trans (mul_le_mul_of_nonneg_left (norm_le_hThirdNorm hf) (by positivity)) + +open FourierTransform + +lemma fourier_schwartz_ae (φ : SchwartzMap Plane ℂ) : + fourier (φ.toLp 2 volume) =ᵐ[volume] + (fun ξ => (𝓕 φ) ((2 * Real.pi)⁻¹ • ξ)) := by + have he : (MeasureTheory.Lp.fourierTransformₗᵢ Plane ℂ (φ.toLp 2 volume) : Plane → ℂ) =ᵐ[volume] + (fun ξ => (𝓕 φ) ξ) := by + change ((𝓕 (φ.toLp 2 volume) : L2) : Plane → ℂ) =ᵐ[volume] _ + rw [SchwartzMap.toLp_fourier_eq] + exact (𝓕 φ).coeFn_toLp 2 volume + exact (Measure.quasiMeasurePreserving_smul volume + (inv_ne_zero (mul_ne_zero (by norm_num) Real.pi_ne_zero))).ae_eq_comp he + +lemma fourier_schwartz_integrable (φ : SchwartzMap Plane ℂ) : + Integrable (fourier (φ.toLp 2 volume)) volume := by + apply Integrable.congr _ (fourier_schwartz_ae φ).symm + exact (𝓕 φ).integrable.comp_smul (inv_ne_zero (mul_ne_zero (by norm_num) Real.pi_ne_zero)) + +lemma phase_zero_eq_scaled_inverse_character (x ξ : Plane) : + phase x 0 ξ = Complex.exp (((2 * Real.pi * inner ℝ ((2 * Real.pi)⁻¹ • ξ) x : ℝ) : ℂ) + * Complex.I) := by + simp only [phase, zero_mul, sub_zero, real_inner_smul_left, real_inner_comm ξ x] + congr 1 + have hc : 2 * Real.pi * ((2 * Real.pi)⁻¹ * inner ℝ ξ x) = inner ℝ ξ x := by + field_simp + rw [hc, mul_comm] + +lemma evolution_schwartz_zero (φ : SchwartzMap Plane ℂ) (x : Plane) : + evolution (φ.toLp 2 volume) x 0 = φ x := by + let q : Plane → ℂ := fun η => + Complex.exp (((2 * Real.pi * inner ℝ η x : ℝ) : ℂ) * Complex.I) * (𝓕 φ) η + have he : ∫ ξ : Plane, phase x 0 ξ * fourier (φ.toLp 2 volume) ξ = + ∫ ξ : Plane, q ((2 * Real.pi)⁻¹ • ξ) := by + apply integral_congr_ae + filter_upwards [fourier_schwartz_ae φ] with ξ hξ + rw [hξ, phase_zero_eq_scaled_inverse_character] + unfold evolution + rw [he, Measure.integral_comp_inv_smul_of_nonneg volume q (by positivity : 0 ≤ 2 * Real.pi)] + have hconst : (2 * Real.pi)^2 ≠ 0 := by positivity + simp only [finrank_euclideanSpace, Fintype.card_fin, smul_smul, + inv_mul_cancel₀ hconst, one_smul] + have hfi : ∫ η : Plane, q η = (𝓕⁻ ((𝓕 φ : SchwartzMap Plane ℂ) : Plane → ℂ)) x := by + rw [Real.fourierInv_eq'] + simp only [q, smul_eq_mul] + change (∫ η : Plane, q η) = _ + rw [hfi, ← SchwartzMap.fourierInv_coe, FourierTransform.fourierInv_fourier_eq] + +lemma closedBall_ae_eq_ball (x : Plane) (r : ℝ) : + Metric.closedBall x r =ᵐ[volume] Metric.ball x r := by + exact (ae_eq_of_subset_of_measure_ge Metric.ball_subset_closedBall + (le_of_eq (Measure.addHaar_closedBall_eq_addHaar_ball volume x r)) + measurableSet_ball.nullMeasurableSet measure_closedBall_lt_top.ne).symm + +lemma diskAverage_eq_average (f : L2) (x : Plane) {r : ℝ} (hr : 0 ≤ r) : + diskAverage f x r = ⨍ y in Metric.closedBall x r, f y := by + rw [setAverage_congr (closedBall_ae_eq_ball x r), setAverage_eq] + simp only [Measure.real, EuclideanSpace.volume_ball_fin_two, ENNReal.toReal_mul, + ENNReal.toReal_pow, ENNReal.toReal_ofReal hr, ENNReal.toReal_ofReal Real.pi_nonneg] + rw [mul_comm (r ^ 2) Real.pi] + rfl + +lemma diskNormAverage_eq_average (f : Plane → ℂ) (x : Plane) (z : ℂ) + {r : ℝ} (hr : 0 ≤ r) : + (Real.pi * r ^ 2)⁻¹ * (∫ y in Metric.ball x r, ‖f y - z‖) = + ⨍ y in Metric.closedBall x r, ‖f y - z‖ := by + rw [setAverage_congr (closedBall_ae_eq_ball x r), setAverage_eq] + simp only [Measure.real, EuclideanSpace.volume_ball_fin_two, ENNReal.toReal_mul, + ENNReal.toReal_pow, ENNReal.toReal_ofReal hr, ENNReal.toReal_ofReal Real.pi_nonneg, + smul_eq_mul] + rw [mul_comm (r ^ 2) Real.pi] + +lemma ae_isLebesguePoint (f : L2) : ∀ᵐ x : Plane ∂volume, IsLebesguePoint f x := by + have hf := (Lp.memLp f).locallyIntegrable (by norm_num) + filter_upwards [IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub volume hf 1] with x hx + refine ⟨f x, ?_⟩ + have hc : ∀ᶠ r : ℝ in 𝓝[>] 0, x ∈ Metric.closedBall x (1 * r) := by + filter_upwards [self_mem_nhdsWithin] with r hr + simpa only [one_mul, Metric.mem_closedBall, dist_self] using (le_of_lt hr) + have ht := hx (fun _ : ℝ => x) (fun r : ℝ => r) tendsto_id hc + apply ht.congr' + filter_upwards [self_mem_nhdsWithin] with r hr + exact (diskNormAverage_eq_average f x (f x) (le_of_lt hr)).symm + +lemma ae_diskAverage_tendsto (f : L2) : ∀ᵐ x : Plane ∂volume, + Tendsto (diskAverage f x) (𝓝[>] (0 : ℝ)) (𝓝 (f x)) := by + have hf := (Lp.memLp f).locallyIntegrable (by norm_num) + filter_upwards [IsUnifLocDoublingMeasure.ae_tendsto_average volume hf 1] with x hx + have hc : ∀ᶠ r : ℝ in 𝓝[>] 0, x ∈ Metric.closedBall x (1 * r) := by + filter_upwards [self_mem_nhdsWithin] with r hr + simpa only [one_mul, Metric.mem_closedBall, dist_self] using (le_of_lt hr) + have ht := hx (fun _ : ℝ => x) (fun r : ℝ => r) tendsto_id hc + apply ht.congr' + filter_upwards [self_mem_nhdsWithin] with r hr + exact (diskAverage_eq_average f x (le_of_lt hr)).symm + +lemma lebesgueRepresentative_ae (f : L2) : lebesgueRepresentative f =ᵐ[volume] f := by + filter_upwards [ae_diskAverage_tendsto f] with x hx + exact hx.limUnder_eq + +end PlanarEndpoint + +namespace PlanarEndpoint + +def sobolevWeight (ξ : Plane) : ℝ := (1 + ‖ξ‖ ^ 2) ^ (1 / 3 : ℝ) +def sobolevMeasure : Measure Plane := volume.withDensity (fun ξ => ENNReal.ofReal (sobolevWeight ξ)) + +lemma continuous_sobolevWeight : Continuous sobolevWeight := by + unfold sobolevWeight + fun_prop (disch := norm_num) + +lemma sobolevWeight_pos (ξ : Plane) : 0 < sobolevWeight ξ := by + exact lt_of_lt_of_le zero_lt_one (sobolevWeight_one_le ξ) + +instance sobolevMeasure_locallyFinite : IsLocallyFiniteMeasure sobolevMeasure := + IsLocallyFiniteMeasure.withDensity_ofReal continuous_sobolevWeight + +lemma integrable_sq_sobolevMeasure_iff (g : Plane → ℂ) : + Integrable (fun ξ => ‖g ξ‖ ^ 2) sobolevMeasure ↔ + Integrable (fun ξ => sobolevWeight ξ * ‖g ξ‖ ^ 2) volume := by + rw [sobolevMeasure, integrable_withDensity_iff_integrable_smul' + (continuous_sobolevWeight.measurable.ennreal_ofReal) + (Filter.Eventually.of_forall (fun _ => ENNReal.ofReal_lt_top))] + simp only [ENNReal.toReal_ofReal (sobolevWeight_pos _).le, smul_eq_mul] + +lemma integral_sq_sobolevMeasure (g : Plane → ℂ) : + (∫ ξ, ‖g ξ‖ ^ 2 ∂sobolevMeasure) = + ∫ ξ, sobolevWeight ξ * ‖g ξ‖ ^ 2 := by + rw [sobolevMeasure, integral_withDensity_eq_integral_toReal_smul + (continuous_sobolevWeight.measurable.ennreal_ofReal) + (Filter.Eventually.of_forall (fun _ => ENNReal.ofReal_lt_top))] + simp only [ENNReal.toReal_ofReal (sobolevWeight_pos _).le, smul_eq_mul] + +lemma fourier_memLp_sobolev {f : L2} (hf : InHThird f) : + MemLp (fourier f) 2 sobolevMeasure := by + apply (memLp_two_iff_integrable_sq_norm + ((fourier_memLp f).aestronglyMeasurable.mono_ac + (withDensity_absolutelyContinuous _ _))).2 + exact (integrable_sq_sobolevMeasure_iff _).2 hf + +lemma fourier_sub_ae (f g : L2) : + fourier (f - g) =ᵐ[volume] fun ξ => fourier f ξ - fourier g ξ := by + have he := Lp.coeFn_sub (Lp.fourierTransformₗᵢ Plane ℂ f) (Lp.fourierTransformₗᵢ Plane ℂ g) + rw [← (Lp.fourierTransformₗᵢ Plane ℂ).map_sub] at he + exact (Measure.quasiMeasurePreserving_smul volume + (inv_ne_zero (mul_ne_zero (by norm_num) Real.pi_ne_zero))).ae_eq_comp he + +lemma hThirdNorm_eq_weighted_eLpNorm {f : L2} (hf : InHThird f) : + hThirdNorm f = (2 * Real.pi)⁻¹ * (eLpNorm (fourier f) 2 sobolevMeasure).toReal := by + rw [MemLp.eLpNorm_eq_integral_rpow_norm (by norm_num) (by norm_num) + (fourier_memLp_sobolev hf)] + have he (y : ℝ) : y ^ ((2 : ℝ)⁻¹) = Real.sqrt y := by + rw [Real.sqrt_eq_rpow] + congr 1 + norm_num + simp only [ENNReal.toReal_ofNat, Real.rpow_two, he, + ENNReal.toReal_ofReal (Real.sqrt_nonneg _), integral_sq_sobolevMeasure] + unfold hThirdNorm sobolevWeight + rw [Real.sqrt_mul (by positivity), Real.sqrt_inv, Real.sqrt_sq (by positivity)] + +lemma exists_smooth_compact_fourier_approx {f : L2} (hf : InHThird f) + {ε : ℝ} (hε : 0 < ε) : + ∃ g : Plane → ℂ, HasCompactSupport g ∧ ContDiff ℝ ∞ g ∧ + eLpNorm (fun ξ => fourier f ξ - g ξ) 2 sobolevMeasure ≤ ENNReal.ofReal ε := by + exact MemLp.exist_eLpNorm_sub_le (by norm_num) (by norm_num) + (fourier_memLp_sobolev hf) hε + +end PlanarEndpoint + +namespace PlanarEndpoint +open FourierTransform + +lemma inHThird_of_fourier_memLp_sobolev {f : L2} + (hf : MemLp (fourier f) 2 sobolevMeasure) : InHThird f := + (integrable_sq_sobolevMeasure_iff _).1 + ((memLp_two_iff_integrable_sq_norm hf.aestronglyMeasurable).1 hf) + +def frequencyDilation : Plane ≃L[ℝ] Plane := + ContinuousLinearEquiv.smulLeft (Units.mk0 (2 * Real.pi) + (mul_ne_zero (by norm_num) Real.pi_ne_zero)) + +@[simp] lemma frequencyDilation_apply (ξ : Plane) : + frequencyDilation ξ = (2 * Real.pi) • ξ := rfl + +def inverseCompactFourier (g : Plane → ℂ) (hc : HasCompactSupport g) + (hd : ContDiff ℝ ∞ g) : SchwartzMap Plane ℂ := + 𝓕⁻ ((SchwartzMap.compCLMOfContinuousLinearEquiv ℂ frequencyDilation) + (hc.toSchwartzMap hd)) + +lemma fourier_inverseCompactFourier_ae (g : Plane → ℂ) (hc : HasCompactSupport g) + (hd : ContDiff ℝ ∞ g) : + fourier ((inverseCompactFourier g hc hd).toLp 2) =ᵐ[volume] g := by + refine (fourier_schwartz_ae _).trans (Filter.Eventually.of_forall (fun ξ => ?_)) + simp only [inverseCompactFourier, FourierTransform.fourier_fourierInv_eq, + SchwartzMap.compCLMOfContinuousLinearEquiv_apply, Function.comp_apply, + frequencyDilation_apply, smul_smul] + rw [mul_inv_cancel₀ (mul_ne_zero (by norm_num : (2 : ℝ) ≠ 0) Real.pi_ne_zero), one_smul] + rfl + +lemma exists_schwartz_hThird_approx {f : L2} (hf : InHThird f) + {ε : ℝ} (hε : 0 < ε) : + ∃ φ : SchwartzMap Plane ℂ, InHThird (φ.toLp 2 volume) ∧ + InHThird (f - φ.toLp 2 volume) ∧ hThirdNorm (f - φ.toLp 2 volume) ≤ ε := by + have hc : 0 < 2 * Real.pi := by positivity + obtain ⟨g, hgcompact, hgsmooth, hgap⟩ := + exists_smooth_compact_fourier_approx hf (mul_pos hc hε) + let φ := inverseCompactFourier g hgcompact hgsmooth + have hφ : fourier (φ.toLp 2 volume) =ᵐ[volume] g := + fourier_inverseCompactFourier_ae g hgcompact hgsmooth + have hφw : fourier (φ.toLp 2 volume) =ᵐ[sobolevMeasure] g := + (withDensity_absolutelyContinuous _ _).ae_le hφ + have hgw : MemLp g 2 sobolevMeasure := + hgsmooth.continuous.memLp_of_hasCompactSupport hgcompact + have hφmem : MemLp (fourier (φ.toLp 2 volume)) 2 sobolevMeasure := + (memLp_congr_ae hφw).2 hgw + have hsub : fourier (f - φ.toLp 2 volume) =ᵐ[volume] fun ξ => fourier f ξ - g ξ := by + filter_upwards [fourier_sub_ae f (φ.toLp 2 volume), hφ] with ξ hξ hφξ + rw [hξ, hφξ] + have hsubw : fourier (f - φ.toLp 2 volume) =ᵐ[sobolevMeasure] fun ξ => fourier f ξ - g ξ := + (withDensity_absolutelyContinuous _ _).ae_le hsub + have hsubmem : MemLp (fourier (f - φ.toLp 2 volume)) 2 sobolevMeasure := + (memLp_congr_ae hsubw).2 ((fourier_memLp_sobolev hf).sub hgw) + have hH := inHThird_of_fourier_memLp_sobolev hsubmem + refine ⟨φ, inHThird_of_fourier_memLp_sobolev hφmem, hH, ?_⟩ + rw [hThirdNorm_eq_weighted_eLpNorm hH, eLpNorm_congr_ae hsubw] + have hgap' := ENNReal.toReal_mono ENNReal.ofReal_ne_top hgap + rw [ENNReal.toReal_ofReal (mul_pos hc hε).le] at hgap' + calc + _ ≤ (2 * Real.pi)⁻¹ * (2 * Real.pi * ε) := + mul_le_mul_of_nonneg_left hgap' (inv_nonneg.mpr hc.le) + _ = ε := by rw [← mul_assoc, inv_mul_cancel₀ hc.ne', one_mul] + +end PlanarEndpoint + +namespace PlanarEndpoint + +lemma gaussian_fourier_norm_integrable (f : L2) {a : ℝ} (ha : 0 < a) : + Integrable (fun ξ => gaussianWeight a ξ * ‖fourier f ξ‖) volume := by + have hh := ((memLp_gaussian ha).integrable_mul (fourier_memLp f)).norm + convert hh using 1 + ext ξ + simp only [Pi.mul_apply, gaussianWeight, norm_mul, Complex.norm_exp, Complex.neg_re, + Complex.ofReal_re, neg_mul] + +lemma continuousAt_abel_parameters (f : L2) (z : ℝ × Plane × ℝ) (hz : 0 < z.1) : + ContinuousAt (fun w : ℝ × Plane × ℝ => abel f w.1 w.2.1 w.2.2) z := by + let F : (ℝ × Plane × ℝ) → Plane → ℂ := fun w ξ => + phase w.2.1 w.2.2 ξ * (gaussianWeight w.1 ξ : ℂ) * fourier f ξ + have hm (w : ℝ × Plane × ℝ) : AEStronglyMeasurable (F w) volume := by + exact (((continuous_phase w.2.1 w.2.2).mul (by + unfold gaussianWeight + fun_prop)).aestronglyMeasurable).mul (fourier_memLp f).aestronglyMeasurable + have hnear : ∀ᶠ w : ℝ × Plane × ℝ in 𝓝 z, z.1 / 2 < w.1 := + (continuous_fst.tendsto z).eventually (Ioi_mem_nhds (half_lt_self hz)) + have hc : ContinuousAt (fun w => ∫ ξ, F w ξ) z := by + apply continuousAt_of_dominated (bound := fun ξ => gaussianWeight (z.1 / 2) ξ * ‖fourier f ξ‖) + · exact Filter.Eventually.of_forall hm + · filter_upwards [hnear] with w hw + filter_upwards with ξ + simp only [F, norm_mul, norm_phase, one_mul, Complex.norm_real, + Real.norm_eq_abs, abs_of_pos (gaussianWeight_pos _ _)] + apply mul_le_mul_of_nonneg_right _ (norm_nonneg _) + apply Real.exp_le_exp.mpr + exact mul_le_mul_of_nonneg_right (neg_le_neg hw.le) (sq_nonneg _) + · exact gaussian_fourier_norm_integrable f (half_pos hz) + · filter_upwards with ξ + apply Continuous.continuousAt + dsimp [F, phase, gaussianWeight] + fun_prop + have ha : (fun w : ℝ × Plane × ℝ => abel f w.1 w.2.1 w.2.2) = + fun w => (((2 * Real.pi)^2)⁻¹ : ℝ) • ∫ ξ, F w ξ := by + funext w + exact abel_eq_weighted f w.1 w.2.1 w.2.2 + rw [ha] + have hconst : ContinuousAt (fun _ : ℝ × Plane × ℝ => (((2 * Real.pi)^2)⁻¹ : ℝ)) z := + continuousAt_const + exact hconst.smul hc + +lemma continuousOn_abel_parameters (f : L2) : + ContinuousOn (fun w : ℝ × Plane × ℝ => abel f w.1 w.2.1 w.2.2) {w | 0 < w.1} := by + intro z hz + exact (continuousAt_abel_parameters f z hz).continuousWithinAt + +end PlanarEndpoint + +namespace PlanarEndpoint + +def evolutionMultiplier (t : ℝ) (η : Plane) : ℂ := + phase 0 t ((2 * Real.pi) • η) + +@[simp] lemma norm_evolutionMultiplier (t : ℝ) (η : Plane) : + ‖evolutionMultiplier t η‖ = 1 := norm_phase _ _ _ + +lemma continuous_evolutionMultiplier (t : ℝ) : Continuous (evolutionMultiplier t) := by + unfold evolutionMultiplier phase + fun_prop + +lemma memLp_evolutionFourier (f : L2) (t : ℝ) : + MemLp (fun η => evolutionMultiplier t η * (Lp.fourierTransformₗᵢ Plane ℂ f) η) + 2 volume := by + apply (Lp.memLp (Lp.fourierTransformₗᵢ Plane ℂ f)).mono + ((continuous_evolutionMultiplier t).aestronglyMeasurable.mul (Lp.aestronglyMeasurable _)) + filter_upwards with η + simp + +def l2Evolution (f : L2) (t : ℝ) : L2 := + (Lp.fourierTransformₗᵢ Plane ℂ).symm + ((memLp_evolutionFourier f t).toLp + (fun η => evolutionMultiplier t η * (Lp.fourierTransformₗᵢ Plane ℂ f) η)) + +lemma l2Evolution_fourier_ae (f : L2) (t : ℝ) : + (Lp.fourierTransformₗᵢ Plane ℂ (l2Evolution f t) : Plane → ℂ) =ᵐ[volume] + fun η => evolutionMultiplier t η * (Lp.fourierTransformₗᵢ Plane ℂ f) η := by + simp only [l2Evolution, LinearIsometryEquiv.apply_symm_apply] + exact (memLp_evolutionFourier f t).coeFn_toLp + +lemma fourier_l2Evolution_ae (f : L2) (t : ℝ) : + fourier (l2Evolution f t) =ᵐ[volume] fun ξ => phase 0 t ξ * fourier f ξ := by + have h := (Measure.quasiMeasurePreserving_smul volume (r := (2 * Real.pi)⁻¹) + (inv_ne_zero (mul_ne_zero (by norm_num) Real.pi_ne_zero))).ae_eq_comp + (l2Evolution_fourier_ae f t) + filter_upwards [h] with ξ hξ + simpa only [fourier, evolutionMultiplier, Function.comp_apply, smul_smul, + mul_inv_cancel₀ (mul_ne_zero (by norm_num : (2 : ℝ) ≠ 0) Real.pi_ne_zero), one_smul] using hξ + +lemma norm_l2Evolution (f : L2) (t : ℝ) : ‖l2Evolution f t‖ = ‖f‖ := by + rw [l2Evolution, LinearIsometryEquiv.norm_map, Lp.norm_toLp] + calc + _ = (eLpNorm (Lp.fourierTransformₗᵢ Plane ℂ f) 2 volume).toReal := by + congr 1 + apply eLpNorm_congr_norm_ae (memLp_evolutionFourier f t).aestronglyMeasurable + (Lp.aestronglyMeasurable _) + filter_upwards with η + simp + _ = ‖Lp.fourierTransformₗᵢ Plane ℂ f‖ := (Lp.norm_def _).symm + _ = ‖f‖ := (Lp.fourierTransformₗᵢ Plane ℂ).norm_map f + +lemma l2Evolution_zero (f : L2) : l2Evolution f 0 = f := by + apply (Lp.fourierTransformₗᵢ Plane ℂ).injective + apply Lp.ext + filter_upwards [l2Evolution_fourier_ae f 0] with η hη + simpa [evolutionMultiplier, phase] using hη + +lemma l2Evolution_sub (f g : L2) (t : ℝ) : + l2Evolution (f - g) t = l2Evolution f t - l2Evolution g t := by + apply (Lp.fourierTransformₗᵢ Plane ℂ).injective + rw [map_sub] + apply Lp.ext + have hs : (Lp.fourierTransformₗᵢ Plane ℂ (f - g) : Plane → ℂ) =ᵐ[volume] + fun η => (Lp.fourierTransformₗᵢ Plane ℂ f) η - + (Lp.fourierTransformₗᵢ Plane ℂ g) η := by + rw [map_sub] + exact Lp.coeFn_sub _ _ + filter_upwards [l2Evolution_fourier_ae (f - g) t, + l2Evolution_fourier_ae f t, l2Evolution_fourier_ae g t, + hs, Lp.coeFn_sub (Lp.fourierTransformₗᵢ Plane ℂ (l2Evolution f t)) + (Lp.fourierTransformₗᵢ Plane ℂ (l2Evolution g t))] with η hfg hf hg hs hsub + rw [hfg, hs, hsub] + simp only [Pi.sub_apply, hf, hg, mul_sub] + +lemma dist_l2Evolution (f g : L2) (t : ℝ) : + dist (l2Evolution f t) (l2Evolution g t) = dist f g := by + rw [dist_eq_norm, ← l2Evolution_sub, norm_l2Evolution, dist_eq_norm] + +lemma inHThird_l2Evolution {f : L2} (hf : InHThird f) (t : ℝ) : + InHThird (l2Evolution f t) := by + apply (show InHThird f from hf).congr + filter_upwards [fourier_l2Evolution_ae f t] with ξ hξ + simp [hξ] + +lemma hThirdNorm_l2Evolution (f : L2) (t : ℝ) : + hThirdNorm (l2Evolution f t) = hThirdNorm f := by + unfold hThirdNorm + congr 2 + apply integral_congr_ae + filter_upwards [fourier_l2Evolution_ae f t] with ξ hξ + simp [hξ] + +end PlanarEndpoint + +namespace PlanarEndpoint +open FourierTransform +open scoped SchwartzMap + +lemma inverse_fourier_continuous {g : Plane → ℂ} (hg : Integrable g volume) : + Continuous (𝓕⁻ g) := by + exact VectorFourier.fourierIntegral_continuous Real.continuous_fourierChar + continuous_inner.neg hg + +lemma inverse_fourier_pairing {g h : Plane → ℂ} + (hg : Integrable g volume) (hh : Integrable h volume) : + (∫ x, (𝓕⁻ g) x * h x) = ∫ ξ, g ξ * (𝓕⁻ h) ξ := by + have hsym : (-innerₗ Plane).flip = -innerₗ Plane := by + ext x y + change -(inner ℝ y x) = -(inner ℝ x y) + rw [real_inner_comm y x] + have hp := VectorFourier.integral_fourierIntegral_smul_eq_flip + (L := -innerₗ Plane) Real.continuous_fourierChar continuous_inner.neg hg hh + rw [hsym] at hp + exact hp + +lemma l2_inverse_fourier_ae (g : L2) (hg : Integrable (g : Plane → ℂ) volume) : + ((Lp.fourierTransformₗᵢ Plane ℂ).symm g : Plane → ℂ) =ᵐ[volume] + 𝓕⁻ (g : Plane → ℂ) := by + apply ae_eq_of_integral_contDiff_smul_eq + ((Lp.memLp _).locallyIntegrable (by norm_num : (1 : ENNReal) ≤ 2)) + ((inverse_fourier_continuous hg).locallyIntegrable) + intro q hqd hqc + have hcc : HasCompactSupport (fun x => (q x : ℂ)) := + hqc.comp_left (show (fun r : ℝ => (r : ℂ)) 0 = 0 by simp) + have hcd : ContDiff ℝ ∞ (fun x => (q x : ℂ)) := + Complex.ofRealCLM.contDiff.comp hqd + let φ : SchwartzMap Plane ℂ := hcc.toSchwartzMap hcd + have hdist := congrArg (fun T : 𝓢'(Plane, ℂ) => T φ) + (Lp.fourierInv_toTemperedDistribution_eq g) + simp only [TemperedDistribution.fourierInv_apply, Lp.toTemperedDistribution_apply] at hdist + have hp := inverse_fourier_pairing hg φ.integrable + have hφ : (fun x => φ x) = fun x => (q x : ℂ) := rfl + calc + (∫ x, q x • ((Lp.fourierTransformₗᵢ Plane ℂ).symm g) x) = + ∫ x, φ x * ((Lp.fourierTransformₗᵢ Plane ℂ).symm g) x := by + apply integral_congr_ae + filter_upwards [] with x + simp only [hφ, Complex.real_smul] + _ = ∫ ξ, (𝓕⁻ φ) ξ * g ξ := hdist.symm + _ = ∫ ξ, g ξ * (𝓕⁻ (φ : Plane → ℂ)) ξ := by + simp only [← SchwartzMap.fourierInv_coe, mul_comm] + _ = ∫ x, (𝓕⁻ (g : Plane → ℂ)) x * φ x := hp.symm + _ = ∫ x, q x • (𝓕⁻ (g : Plane → ℂ)) x := by + apply integral_congr_ae + filter_upwards [] with x + simp only [hφ, Complex.real_smul, mul_comm] + + all_goals rfl + +end PlanarEndpoint + +namespace PlanarEndpoint +open FourierTransform + +lemma integrable_mathlib_fourier {f : L2} (hf : Integrable (fourier f) volume) : + Integrable (fun η => (Lp.fourierTransformₗᵢ Plane ℂ f) η) volume := by + have hi := hf.comp_smul (mul_ne_zero (by norm_num : (2 : ℝ) ≠ 0) Real.pi_ne_zero) + simpa only [fourier, smul_smul, inv_mul_cancel₀ (mul_ne_zero + (by norm_num : (2 : ℝ) ≠ 0) Real.pi_ne_zero), one_smul] using hi + +lemma integrable_evolutionFourier {f : L2} (hf : Integrable (fourier f) volume) + (t : ℝ) : Integrable (fun η => evolutionMultiplier t η * + (Lp.fourierTransformₗᵢ Plane ℂ f) η) volume := by + have hi := integrable_mathlib_fourier hf + apply hi.mono ((continuous_evolutionMultiplier t).aestronglyMeasurable.mul hi.1) + filter_upwards [] with η + simp + +lemma evolution_eq_mathlib_inverse (f : L2) (x : Plane) (t : ℝ) : + evolution f x t = (𝓕⁻ (fun η => evolutionMultiplier t η * + (Lp.fourierTransformₗᵢ Plane ℂ f) η)) x := by + let q : Plane → ℂ := fun η => + Complex.exp (((2 * Real.pi * inner ℝ η x : ℝ) : ℂ) * Complex.I) * + (evolutionMultiplier t η * (Lp.fourierTransformₗᵢ Plane ℂ f) η) + have he : ∫ ξ : Plane, phase x t ξ * fourier f ξ = + ∫ ξ : Plane, q ((2 * Real.pi)⁻¹ • ξ) := by + apply integral_congr_ae + filter_upwards [] with ξ + dsimp only [q] + rw [← phase_zero_eq_scaled_inverse_character] + simp only [evolutionMultiplier, smul_smul, mul_inv_cancel₀ + (mul_ne_zero (by norm_num : (2 : ℝ) ≠ 0) Real.pi_ne_zero), one_smul, + ← mul_assoc] + change phase x t ξ * fourier f ξ = (phase x 0 ξ * phase 0 t ξ) * fourier f ξ + congr 1 + simp only [phase, inner_zero_left, zero_mul, sub_zero, zero_sub, ← Complex.exp_add] + congr 1 + push_cast + ring + unfold evolution + rw [he, Measure.integral_comp_inv_smul_of_nonneg volume q + (by positivity : 0 ≤ 2 * Real.pi)] + simp only [finrank_euclideanSpace, Fintype.card_fin, smul_smul, + inv_mul_cancel₀ (by positivity : (2 * Real.pi)^2 ≠ 0), one_smul] + rw [Real.fourierInv_eq'] + rfl + +lemma l2Evolution_ae_evolution {f : L2} (hf : Integrable (fourier f) volume) (t : ℝ) : + (l2Evolution f t : Plane → ℂ) =ᵐ[volume] (fun x => evolution f x t) := by + let g : L2 := (memLp_evolutionFourier f t).toLp _ + have hg := (memLp_evolutionFourier f t).coeFn_toLp + have hi : Integrable (g : Plane → ℂ) volume := + (integrable_evolutionFourier hf t).congr hg.symm + have ha := l2_inverse_fourier_ae g hi + filter_upwards [ha] with x hx + change ((Lp.fourierTransformₗᵢ Plane ℂ).symm g) x = _ + rw [hx, Real.fourierInv_congr_ae hg, evolution_eq_mathlib_inverse] + +abbrev Time := ↥(Set.Icc (0 : ℝ) 1) +abbrev TimePath := C(Time, ℂ) + +lemma continuous_evolution_time (f : L2) (hf : Integrable (fourier f) volume) + (x : Plane) : Continuous (fun t : Time => evolution f x (t : ℝ)) := by + have ht : Continuous (fun t : Time => (x, (t : ℝ))) := + continuous_const.prodMk continuous_subtype_val + have hh := (continuous_evolution (f := f) hf).comp ht + simpa only [Function.comp_def] using hh + +def evolutionPath (f : L2) (hf : Integrable (fourier f) volume) (x : Plane) : TimePath := + ⟨fun t : Time => evolution f x (t : ℝ), continuous_evolution_time f hf x⟩ + +lemma continuous_evolutionPath (f : L2) (hf : Integrable (fourier f) volume) : + Continuous (evolutionPath f hf) := by + apply ContinuousMap.continuous_of_continuous_uncurry + have ht : Continuous (fun z : Plane × Time => (z.1, (z.2 : ℝ))) := + continuous_fst.prodMk (continuous_subtype_val.comp continuous_snd) + have hh := (continuous_evolution (f := f) hf).comp ht + simpa only [Function.comp_def, Function.uncurry_def, evolutionPath, ContinuousMap.coe_mk] using hh + +end PlanarEndpoint + +namespace PlanarEndpoint + +lemma mainConclusion_of_fourier_integrable (f : L2) + (hf : Integrable (fourier f) volume) : MainConclusion f := by + have hzero : ∀ᵐ x : Plane ∂volume, evolution f x 0 = f x := by + have h := l2Evolution_ae_evolution (f := f) hf 0 + rw [l2Evolution_zero] at h + exact h.symm + let E : Set Plane := {x | IsLebesguePoint f x ∧ + Tendsto (diskAverage f x) (𝓝[>] (0 : ℝ)) (𝓝 (f x)) ∧ + lebesgueRepresentative f x = f x ∧ evolution f x 0 = f x} + have hE : volume Eᶜ = 0 := by + apply ae_iff.mp + filter_upwards [ae_isLebesguePoint f, ae_diskAverage_tendsto f, + lebesgueRepresentative_ae f, hzero] with x h₁ h₂ h₃ h₄ + exact ⟨h₁, h₂, h₃, h₄⟩ + refine ⟨E, hE, ?_⟩ + intro x hx + obtain ⟨hl, hd, hr, hz⟩ := hx + have ht : Continuous (fun t : ℝ => (x, t)) := continuous_const.prodMk continuous_id + have hhh := (continuous_evolution (f := f) hf).comp ht + have hc : Continuous (evolution f x) := by + simpa only [Function.comp_def] using hhh + have hu := (abel_tendstoUniformly (f := f) hf).comp (fun t : ℝ => (x, t)) + refine ⟨hl, evolution f x, hc.continuousOn, hz.trans hr.symm, ?_, ?_, ?_, ?_⟩ + · simpa only [hz] using hd + · intro t _ + exact hu.tendsto_at t + · rw [hr, ← hz] + exact hc.continuousAt.tendsto.mono_left nhdsWithin_le_nhds + · exact hu.tendstoUniformlyOn + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/FrequencyWeak.lean b/lean/OAI/Analysis/PlanarEndpoint/FrequencyWeak.lean new file mode 100644 index 0000000000000000000000000000000000000000..4e0fa570d8e8864f5cf8556e352b5b6d24d037c3 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/FrequencyWeak.lean @@ -0,0 +1,115 @@ +import OAI.Analysis.PlanarEndpoint.Fourier + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology ComplexConjugate +namespace PlanarEndpoint + +lemma memLp_comp_real_smul {v : Plane → ℂ} (hv : MemLp v 2 volume) + {r : ℝ} (hr : r ≠ 0) : MemLp (fun ξ : Plane => v (r • ξ)) 2 volume := by + have h := hv.smul_measure + (c := ENNReal.ofReal |(r ^ Module.finrank ℝ Plane)⁻¹|) ENNReal.ofReal_ne_top + rw [← Measure.map_addHaar_smul (volume : Measure Plane) hr] at h + exact h.comp_of_map (measurable_const_smul _).aemeasurable + +def inverseFrequency (v : Plane → ℂ) (hv : MemLp v 2 volume) : L2 := + (Lp.fourierTransformₗᵢ Plane ℂ).symm + ((memLp_comp_real_smul hv (by positivity : (2 * Real.pi : ℝ) ≠ 0)).toLp + (fun ξ => v ((2 * Real.pi) • ξ))) + +lemma fourier_inverseFrequency_ae (v : Plane → ℂ) (hv : MemLp v 2 volume) : + fourier (inverseFrequency v hv) =ᵐ[volume] v := by + have h := (memLp_comp_real_smul hv (by positivity : (2 * Real.pi : ℝ) ≠ 0)).coeFn_toLp + have hh := (Measure.quasiMeasurePreserving_smul volume + (r := (2 * Real.pi)⁻¹) (by positivity)).ae_eq_comp h + filter_upwards [hh] with ξ hξ + simpa only [fourier, inverseFrequency, LinearIsometryEquiv.apply_symm_apply, + Function.comp_apply, smul_smul, mul_inv_cancel₀ (by positivity : (2 * Real.pi : ℝ) ≠ 0), + one_smul] using hξ + +lemma inverseFrequency_norm (v : Plane → ℂ) (hv : MemLp v 2 volume) : + (2 * Real.pi) * ‖inverseFrequency v hv‖ = ‖hv.toLp v‖ := by + have h := fourier_energy (inverseFrequency v hv) + have he : (∫ ξ, ‖fourier (inverseFrequency v hv) ξ‖^2) = ∫ ξ, ‖v ξ‖^2 := + integral_congr_ae ((fourier_inverseFrequency_ae v hv).fun_comp (fun z : ℂ => ‖z‖^2)) + rw [he] at h + have ht : (∫ ξ, ‖v ξ‖^2) = ‖hv.toLp v‖^2 := by + calc + _ = ∫ ξ, ‖(hv.toLp v) ξ‖^2 := integral_congr_ae + ((hv.coeFn_toLp).symm.fun_comp (fun z : ℂ => ‖z‖^2)) + _ = ‖hv.toLp v‖^2 := by rw [← real_inner_self_eq_norm_sq]; simp only [L2.inner_def, real_inner_self_eq_norm_sq] + rw [ht] at h + have hn : 0 ≤ (2 * Real.pi) * ‖inverseFrequency v hv‖ := by positivity + nlinarith [norm_nonneg (hv.toLp v)] + +def frequencyExtension (v : Plane → ℂ) (x : Plane) (t : ℝ) : ℂ := + ∫ ξ, phase x t ξ * v ξ + +lemma evolution_inverseFrequency (v : Plane → ℂ) (hv : MemLp v 2 volume) + (x : Plane) (t : ℝ) : + evolution (inverseFrequency v hv) x t = + (((2 * Real.pi)^2)⁻¹ : ℝ) • frequencyExtension v x t := by + unfold evolution frequencyExtension + congr 1 + apply integral_congr_ae + filter_upwards [fourier_inverseFrequency_ae v hv] with ξ hξ + rw [hξ] + +lemma continuous_frequencyExtension {v : Plane → ℂ} (hv : Integrable v volume) : + Continuous (fun z : Plane × ℝ => frequencyExtension v z.1 z.2) := by + apply continuous_iff_continuousAt.2 + intro z + apply continuousAt_of_dominated (bound := fun ξ => ‖v ξ‖) + · exact Eventually.of_forall (fun w => ((continuous_phase w.1 w.2).aestronglyMeasurable.mul hv.aestronglyMeasurable)) + · exact Eventually.of_forall (fun w => Eventually.of_forall (fun ξ => by simp)) + · exact hv.norm + · filter_upwards [] with ξ + exact (continuous_phase_parameters ξ).mul_const (v ξ) |>.continuousAt + +lemma norm_frequencyExtension (v : Plane → ℂ) (hv : MemLp v 2 volume) + (x : Plane) (t : ℝ) : ‖frequencyExtension v x t‖ = + (2 * Real.pi)^2 * ‖evolution (inverseFrequency v hv) x t‖ := by + rw [evolution_inverseFrequency, norm_smul, Real.norm_eq_abs, + abs_of_pos (by positivity : 0 < ((2 * Real.pi)^2)⁻¹)] + field_simp + +lemma frequency_weak_of_shortTime {c₀ C₀ p : ℝ} + (h : ShortTimeWeakEstimate c₀ C₀ p) : + ∃ C : ℝ, 0 < C ∧ ∀ j : ℕ, ∀ (v : Plane → ℂ) (hv : MemLp v 2 volume), + (∀ᵐ ξ : Plane ∂volume, ξ ∉ {ξ | c₀ * (2:ℝ)^j ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*(2:ℝ)^j} → v ξ = 0) → + ∀ (x₀ : Plane) (t₀ s lam : ℝ), 0 ≤ s → s ≤ ((2:ℝ)^j)⁻¹ → 0 < lam → + volume (Metric.ball x₀ 1 ∩ {x | ∃ t ∈ Icc t₀ (t₀+s), lam < ‖frequencyExtension v x t‖}) ≤ + ENNReal.ofReal ((C * ((2:ℝ)^j)^(1/3:ℝ) * ‖hv.toLp v‖ / lam)^p) := by + obtain ⟨C,hC,h⟩ := h + refine ⟨(2*Real.pi)*C, mul_pos (by positivity) hC, ?_⟩ + intro j v hv hs x₀ t₀ s lam hs0 hs1 hlam + let f := inverseFrequency v hv + have hf : AnnularFourierSupport f c₀ C₀ ((2:ℝ)^j) := by + filter_upwards [fourier_inverseFrequency_ae v hv, hs] with ξ hξ hsξ + rw [hξ] + exact hsξ + have he : (Metric.ball x₀ 1 ∩ {x | ∃ t ∈ Icc t₀ (t₀+s), lam < ‖frequencyExtension v x t‖}) = + shortTimeLevel f x₀ t₀ s (lam / (2*Real.pi)^2) := by + ext x + simp only [shortTimeLevel, mem_inter_iff, mem_ofPred_eq] + apply and_congr_right' + congr! 2 with t + rw [norm_frequencyExtension, div_lt_iff₀ (by positivity : 0 < (2 * Real.pi)^2)] + dsimp [f] + rw [mul_comm] + rw [he] + convert h j f hf x₀ t₀ s hs0 hs1 (lam/(2*Real.pi)^2) (by positivity) using 2 + congr 1 + rw [← inverseFrequency_norm v hv] + dsimp [f] + field_simp + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphDistribution.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphDistribution.lean new file mode 100644 index 0000000000000000000000000000000000000000..78b4d5c0601c0a0ba380a24ed0be998a8f9fc695 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphDistribution.lean @@ -0,0 +1,74 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.FrequencyWeak +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.UnitReduction + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set +namespace PlanarEndpoint + +def SourceGraphDistribution (c₀ C₀ p : ℝ) : Prop := + ∃ C : ℝ, 0 < C ∧ ∀ L : ℝ, 1 ≤ L → + ∀ v : Plane → ℂ, ∀ hv : MemLp v 2 volume, + (∀ᵐ η : Plane ∂volume, η ∉ {η | c₀ ≤ ‖η‖ ∧ ‖η‖ ≤ C₀} → v η = 0) → + ∀ (x₀ : Plane) (T : Plane → ℝ), Measurable T → + (∀ X, T X ∈ Icc (0:ℝ) (L^2)) → ∀ lam : ℝ, 0 < lam → + volume (Metric.ball x₀ (L^2) ∩ {X | lam < ‖frequencyExtension v X (T X)‖}) ≤ + ENNReal.ofReal (C * L^4 * (lam * L^(4/3:ℝ))^(-p) * ‖hv.toLp v‖^p) + +lemma graphDistribution_scale_identity {L C lam : ℝ} (hL : 0 < L) + (hC : 0 < C) (hlam : 0 < lam) {p : ℝ} (hp : p ≠ 0) {b : ℝ} (hb : 0 ≤ b) : + C * L^4 * (lam * L^(4/3:ℝ))^(-p) * b^p = + (L^2)^2 * (C^(p⁻¹) * (L^2)^(-2/3:ℝ) * b / lam)^p := by + have hscale : (L^2)^(-2/3:ℝ) = (L^(4/3:ℝ))⁻¹ := by + rw [← Real.rpow_natCast L 2, ← Real.rpow_mul hL.le] + norm_num [Real.rpow_neg hL.le] + rw [hscale, Real.div_rpow (by positivity) hlam.le, + Real.mul_rpow (mul_nonneg (Real.rpow_nonneg hC.le _) (by positivity)) hb, + Real.mul_rpow (Real.rpow_nonneg hC.le _) (show 0 ≤ (L^(4/3:ℝ))⁻¹ by positivity), + Real.rpow_inv_rpow hC.le hp, Real.inv_rpow (Real.rpow_nonneg hL.le _), + Real.mul_rpow hlam.le (Real.rpow_nonneg hL.le _), + Real.rpow_neg hlam.le, Real.rpow_neg (Real.rpow_nonneg hL.le _)] + ring + +lemma unitFrequencyGraphEstimate_of_source {c₀ C₀ p : ℝ} (hp : p ≠ 0) + (hs : SourceGraphDistribution c₀ C₀ p) : UnitFrequencyGraphEstimate c₀ C₀ p := by + obtain ⟨C,hC,hs⟩ := hs + refine ⟨C^(p⁻¹),Real.rpow_pos_of_pos hC _,?_⟩ + intro R hR v hv hsup x₀ T hT hr lam hlam + have hR0 : 0 ≤ R := le_trans (by norm_num) hR + have hL : 1 ≤ Real.sqrt R := by + simpa using (Real.sqrt_le_sqrt hR) + have hL0 : 0 < Real.sqrt R := lt_of_lt_of_le (by norm_num) hL + have hsq : (Real.sqrt R)^2 = R := Real.sq_sqrt hR0 + have he := hs (Real.sqrt R) hL v hv hsup x₀ T hT (by simpa [hsq] using hr) lam hlam + rw [graphDistribution_scale_identity hL0 hC hlam hp (norm_nonneg _),hsq] at he + exact he + +lemma sourceGraphDistribution_of_unitFrequency {c₀ C₀ p : ℝ} (hp : p ≠ 0) + (hg : UnitFrequencyGraphEstimate c₀ C₀ p) : SourceGraphDistribution c₀ C₀ p := by + obtain ⟨K,hK,hg⟩ := hg + refine ⟨K^p,Real.rpow_pos_of_pos hK _,?_⟩ + intro L hL v hv hsup x₀ T hT hr lam hlam + have hL0 : 0 < L := lt_of_lt_of_le (by norm_num) hL + have hL2 : 1 ≤ L^2 := one_le_pow₀ hL + have he := hg (L^2) hL2 v hv hsup x₀ T hT hr lam hlam + rw [graphDistribution_scale_identity hL0 (Real.rpow_pos_of_pos hK _) hlam hp + (norm_nonneg _),Real.rpow_rpow_inv hK.le hp] + exact he + +lemma mainConclusion_of_sourceGraphDistribution {p : ℝ} (hp : 2 < p) + (hs : SourceGraphDistribution (1/4) 4 p) {f : L2} (hf : InHThird f) : + MainConclusion f := + mainConclusion_of_unitFrequencyGraph hp + (unitFrequencyGraphEstimate_of_source (by linarith) hs) hf + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphDual.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphDual.lean new file mode 100644 index 0000000000000000000000000000000000000000..fc368e293680ec362768293830afc64fc0cb5f34 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphDual.lean @@ -0,0 +1,248 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.Oscillation + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set +open scoped Topology ComplexConjugate ContDiff +namespace PlanarEndpoint + +def graphFourier (μ : Measure Plane) (T : Plane → ℝ) (w : Plane → ℂ) (ξ : Plane) : ℂ := + ∫ x, w x * phase x (T x) ξ ∂μ + +def graphDual (χ : Plane → ℂ) (μ : Measure Plane) (T : Plane → ℝ) (w : Plane → ℂ) : Plane → ℂ := + fun ξ => χ ξ * graphFourier μ T w ξ + +lemma measurable_graph_phase {T : Plane → ℝ} (hT : Measurable T) : + Measurable (fun z : Plane × Plane => phase z.1 (T z.1) z.2) := by + unfold phase + fun_prop + +lemma integrable_graph_phase (μ : Measure Plane) [IsFiniteMeasure μ] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (ξ : Plane) : + Integrable (fun x => w x * phase x (T x) ξ) μ := by + apply (integrable_const (1 : ℝ)).mono' + · exact (hw.mul ((measurable_graph_phase hT).comp + (measurable_id.prodMk measurable_const))).aestronglyMeasurable + · filter_upwards [] with x + simpa only [norm_mul, norm_phase, mul_one] using hb x + +lemma norm_graphFourier_le (μ : Measure Plane) [IsFiniteMeasure μ] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (ξ : Plane) : + ‖graphFourier μ T w ξ‖ ≤ μ.real univ := by + calc + _ ≤ ∫ x, ‖w x * phase x (T x) ξ‖ ∂μ := norm_integral_le_integral_norm _ + _ ≤ ∫ x, (1 : ℝ) ∂μ := integral_mono (integrable_graph_phase μ hT hw hb ξ).norm + (integrable_const _) (fun x => by simpa using hb x) + _ = μ.real univ := by simp + +lemma continuous_graphFourier (μ : Measure Plane) [IsFiniteMeasure μ] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : Continuous (graphFourier μ T w) := by + apply continuous_iff_continuousAt.2 + intro ξ + apply continuousAt_of_dominated (bound := fun _ => (1 : ℝ)) + · exact Filter.Eventually.of_forall (fun η => (integrable_graph_phase μ hT hw hb η).aestronglyMeasurable) + · exact Filter.Eventually.of_forall (fun η => Filter.Eventually.of_forall + (fun x => by simpa using hb x)) + · exact integrable_const _ + · filter_upwards [] with x + apply Continuous.continuousAt + unfold phase + have hi : Continuous (fun η : Plane => inner ℝ x η) := (innerSL ℝ x).continuous + fun_prop + +lemma graphDual_memLp (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : MemLp (graphDual χ μ T w) 2 volume := by + apply (hχ.const_mul (μ.real univ : ℂ)).mono + · exact ((continuous_graphFourier μ hT hw hb).aestronglyMeasurable.mul + hχ.aestronglyMeasurable).congr (Filter.Eventually.of_forall (fun ξ => mul_comm _ _)) + · filter_upwards [] with ξ + have hμ : 0 ≤ μ.real univ := ENNReal.toReal_nonneg + simp only [graphDual, norm_mul, Complex.norm_real, Real.norm_eq_abs, + abs_of_nonneg hμ] + nlinarith [norm_graphFourier_le μ hT hw hb ξ, norm_nonneg (χ ξ)] + +lemma phase_mul_conj (x y ξ : Plane) (t s : ℝ) : + phase x t ξ * conj (phase y s ξ) = phase (x-y) (t-s) ξ := by + unfold phase + rw [← Complex.exp_conj, map_mul, Complex.conj_I, Complex.conj_ofReal, ← Complex.exp_add] + congr 1 + simp only [inner_sub_left, Complex.ofReal_sub, Complex.ofReal_mul] + ring + +lemma phase_eq_kernel_oscillation (z ξ : Plane) (t : ℝ) : + phase z t ξ = EndpointKernel.oscillation (EndpointKernel.quadraticPhase (z,t)) 1 ξ := by + simp only [phase, EndpointKernel.oscillation, EndpointKernel.quadraticPhase, one_mul, mul_comm] + +def frequencyKernel (χ : Plane → ℂ) (z : Plane) (t : ℝ) : ℂ := + ∫ ξ, χ ξ * conj (χ ξ) * phase z t ξ + +lemma integrable_graph_pairing (χ : Plane → ℂ) (hχm : Measurable χ) + (hχ : MemLp χ 2 volume) (μ ν : Measure Plane) [IsFiniteMeasure μ] [IsFiniteMeasure ν] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + Integrable (fun q : Plane × (Plane × Plane) => + χ q.1 * conj (χ q.1) * (w q.2.1 * conj (w q.2.2)) * + phase (q.2.1-q.2.2) (T q.2.1-T q.2.2) q.1) (volume.prod (μ.prod ν)) := by + apply ((hχ.integrable_norm_pow (by norm_num : (2 : ℕ) ≠ 0)).comp_fst (μ.prod ν)).mono' + · apply Measurable.aestronglyMeasurable + unfold phase + fun_prop + · filter_upwards [] with q + simp only [norm_mul, Complex.norm_conj, norm_phase, mul_one, pow_two] + have hww : ‖w q.2.1‖ * ‖w q.2.2‖ ≤ 1 := by + nlinarith [hb q.2.1, hb q.2.2, norm_nonneg (w q.2.1), norm_nonneg (w q.2.2)] + nlinarith [mul_self_nonneg ‖χ q.1‖] + +lemma graphDual_pairing (χ : Plane → ℂ) (hχm : Measurable χ) + (hχ : MemLp χ 2 volume) (μ ν : Measure Plane) [IsFiniteMeasure μ] [IsFiniteMeasure ν] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + (∫ ξ, graphDual χ μ T w ξ * conj (graphDual χ ν T w ξ)) = + ∫ z : Plane × Plane, w z.1 * conj (w z.2) * + frequencyKernel χ (z.1-z.2) (T z.1-T z.2) ∂μ.prod ν := by + have hp (ξ : Plane) : graphDual χ μ T w ξ * conj (graphDual χ ν T w ξ) = + ∫ z : Plane × Plane, χ ξ * conj (χ ξ) * (w z.1 * conj (w z.2)) * + phase (z.1-z.2) (T z.1-T z.2) ξ ∂μ.prod ν := by + simp only [graphDual, graphFourier, map_mul] + rw [← integral_conj] + rw [show (χ ξ * (∫ x, w x * phase x (T x) ξ ∂μ)) * + (conj (χ ξ) * (∫ x, conj (w x * phase x (T x) ξ) ∂ν)) = + (χ ξ * conj (χ ξ)) * ((∫ x, w x * phase x (T x) ξ ∂μ) * + (∫ x, conj (w x * phase x (T x) ξ) ∂ν)) by ring] + rw [← integral_prod_mul, ← integral_const_mul] + apply integral_congr_ae + filter_upwards [] with z + rw [map_mul, ← phase_mul_conj] + ring + simp_rw [hp] + rw [integral_integral_swap (integrable_graph_pairing χ hχm hχ μ ν hT hw hb)] + apply integral_congr_ae + filter_upwards [] with z + rw [frequencyKernel, ← integral_const_mul] + apply integral_congr_ae + filter_upwards [] with ξ + ring + +lemma norm_graphDual_pairing_le (χ : Plane → ℂ) (hχm : Measurable χ) + (hχ : MemLp χ 2 volume) (μ ν : Measure Plane) [IsFiniteMeasure μ] [IsFiniteMeasure ν] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) {B : ℝ} + (hK : ∀ᵐ z : Plane × Plane ∂μ.prod ν, + ‖frequencyKernel χ (z.1-z.2) (T z.1-T z.2)‖ ≤ B) : + ‖∫ ξ, graphDual χ μ T w ξ * conj (graphDual χ ν T w ξ)‖ ≤ + B * μ.real univ * ν.real univ := by + rw [graphDual_pairing χ hχm hχ μ ν hT hw hb] + have hbound : ∀ᵐ z : Plane × Plane ∂μ.prod ν, + ‖w z.1 * conj (w z.2) * frequencyKernel χ (z.1-z.2) (T z.1-T z.2)‖ ≤ B := by + filter_upwards [hK] with z hz + simp only [norm_mul, Complex.norm_conj] + have hwprod : ‖w z.1‖ * ‖w z.2‖ ≤ 1 := by + nlinarith [hb z.1, hb z.2, norm_nonneg (w z.1), norm_nonneg (w z.2)] + exact (mul_le_mul_of_nonneg_right hwprod (norm_nonneg _)).trans (by simpa using hz) + have hh := norm_integral_le_of_norm_le_const hbound + have hm : (μ.prod ν).real univ = μ.real univ * ν.real univ := by + simpa only [univ_prod_univ] using (measureReal_prod_prod (μ := μ) (ν := ν) univ univ) + simpa only [hm, mul_assoc] using hh + +lemma frequencyKernel_scaled (χ : Plane → ℂ) (N : ℝ) (z : Plane) (t : ℝ) : + frequencyKernel (fun ξ => χ (N⁻¹ • ξ)) z t = + EndpointKernel.scaledKernel (fun ξ => χ ξ * conj (χ ξ)) N z t := by + unfold frequencyKernel EndpointKernel.scaledKernel + congr 1 + funext ξ + rw [phase_eq_kernel_oscillation] + +lemma frequencyKernel_time_decay {χ : Plane → ℂ} {c : ℝ} + (hc : 0 < c) (hχ : ContDiff ℝ ∞ χ) (hcomp : HasCompactSupport χ) + (hann : ∀ ξ ∈ tsupport χ, c ≤ ‖ξ‖) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ N : ℝ, 0 < N → ∀ (z : Plane) (t : ℝ), + ‖z‖ ≤ c * N * |t| → + (N^2 * |t|)^k * ‖frequencyKernel (fun ξ => χ (N⁻¹ • ξ)) z t‖ ≤ C * N^2 := by + have hs : ContDiff ℝ ∞ (fun ξ => χ ξ * conj (χ ξ)) := by exact hχ.mul (Complex.conjCLE.contDiff.comp hχ) + obtain ⟨C,hC,hK⟩ := EndpointKernel.scaledKernel_time_decay hc hs hcomp.mul_right + (fun ξ hξ => hann ξ (tsupport_mul_subset_left hξ)) k + exact ⟨C,hC,fun N hN z t hz => by rw [frequencyKernel_scaled]; exact hK N hN z t hz⟩ + +lemma frequencyKernel_spatial_decay {χ : Plane → ℂ} {R : ℝ} + (hR : 0 < R) (hχ : ContDiff ℝ ∞ χ) (hcomp : HasCompactSupport χ) + (hsupp : ∀ ξ ∈ tsupport χ, ‖ξ‖ ≤ R) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ N : ℝ, 0 < N → ∀ (z : Plane) (t : ℝ), + 4 * R * N * |t| ≤ ‖z‖ → + ‖frequencyKernel (fun ξ => χ (N⁻¹ • ξ)) z t‖ ≤ C * N^2 / (1+N*‖z‖)^k := by + have hs : ContDiff ℝ ∞ (fun ξ => χ ξ * conj (χ ξ)) := by exact hχ.mul (Complex.conjCLE.contDiff.comp hχ) + obtain ⟨C,hC,hK⟩ := EndpointKernel.scaledKernel_spatial_decay hR hs hcomp.mul_right + (fun ξ hξ => hsupp ξ (tsupport_mul_subset_left hξ)) k + exact ⟨C,hC,fun N hN z t hz => by rw [frequencyKernel_scaled]; exact hK N hN z t hz⟩ + +def graphLp (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : L2 := + (graphDual_memLp χ hχ μ hT hw hb).toLp (graphDual χ μ T w) + +lemma graphLp_ae (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + ⇑(graphLp χ hχ μ T w hT hw hb) =ᵐ[volume] graphDual χ μ T w := + MemLp.coeFn_toLp _ + +lemma inner_graphLp (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ ν : Measure Plane) [IsFiniteMeasure μ] [IsFiniteMeasure ν] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + inner ℂ (graphLp χ hχ ν T w hT hw hb) (graphLp χ hχ μ T w hT hw hb) = + ∫ ξ, graphDual χ μ T w ξ * conj (graphDual χ ν T w ξ) := by + rw [L2.inner_def] + apply integral_congr_ae + filter_upwards [graphLp_ae χ hχ μ T w hT hw hb, graphLp_ae χ hχ ν T w hT hw hb] with ξ hμ hν + simp only [hμ, hν, RCLike.inner_apply] + +lemma graphLp_add_measure (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ ν : Measure Plane) [IsFiniteMeasure μ] [IsFiniteMeasure ν] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + graphLp χ hχ (μ+ν) T w hT hw hb = + graphLp χ hχ μ T w hT hw hb + graphLp χ hχ ν T w hT hw hb := by + apply Lp.ext + filter_upwards [graphLp_ae χ hχ (μ+ν) T w hT hw hb, + graphLp_ae χ hχ μ T w hT hw hb, graphLp_ae χ hχ ν T w hT hw hb, + Lp.coeFn_add (graphLp χ hχ μ T w hT hw hb) (graphLp χ hχ ν T w hT hw hb)] with ξ hh hμ hν hadd + rw [hadd, Pi.add_apply, hh, hμ, hν] + unfold graphDual graphFourier + rw [integral_add_measure (integrable_graph_phase μ hT hw hb ξ) + (integrable_graph_phase ν hT hw hb ξ), mul_add] + +lemma graphLp_zero_measure (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : graphLp χ hχ 0 T w hT hw hb = 0 := by + apply Lp.ext + filter_upwards [graphLp_ae χ hχ 0 T w hT hw hb, Lp.coeFn_zero ℂ 2 volume] with ξ hh hz + simp only [hh, hz, graphDual, graphFourier, integral_zero_measure, mul_zero, Pi.zero_apply] + +lemma graphLp_finsetSum_measure {ι : Type*} (s : Finset ι) (χ : Plane → ℂ) + (hχ : MemLp χ 2 volume) (μ : ι → Measure Plane) [∀ i, IsFiniteMeasure (μ i)] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + graphLp χ hχ (∑ i ∈ s, μ i) T w hT hw hb = ∑ i ∈ s, graphLp χ hχ (μ i) T w hT hw hb := by + classical + induction s using Finset.induction_on with + | empty => simpa using graphLp_zero_measure χ hχ T w hT hw hb + | @insert i s hi ih => + simp only [Finset.sum_insert hi] + rw [graphLp_add_measure, ih] + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphEnergy.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphEnergy.lean new file mode 100644 index 0000000000000000000000000000000000000000..a60ad1850a13372238ddc63951f5128965c1073b --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphEnergy.lean @@ -0,0 +1,105 @@ +import OAI.Analysis.PlanarEndpoint.DualMass +import OAI.Analysis.PlanarEndpoint.DyadicArithmetic +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphDual +import OAI.Analysis.PlanarEndpoint.GraphLocalization +import OAI.Analysis.PlanarEndpoint.TimeSeparation + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology ContDiff +namespace PlanarEndpoint + +lemma normalize_mass_energy {V : Type*} [SeminormedAddCommGroup V] [NormedSpace ℝ V] + (v : V) {N C m p : ℝ} (hN : 0 < N) (hC : 0 ≤ C) (hm : 0 ≤ m) + (hb : ‖v‖ ≤ C*N^(1/3:ℝ)*m^(1-1/p)) : + ‖(N^(-(1/3:ℝ))) • v‖^2 ≤ C^2*m^(2-2/p) := by + have hcan : N^(-(1/3:ℝ))*N^(1/3:ℝ)=1 := by + rw [← Real.rpow_add hN] + norm_num + have h : ‖(N^(-(1/3:ℝ))) • v‖ ≤ C*m^(1-1/p) := by + rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg hN.le _)] + have hh := mul_le_mul_of_nonneg_left hb (Real.rpow_nonneg hN.le (-(1/3:ℝ))) + calc + _ ≤ N^(-(1/3:ℝ))*(C*N^(1/3:ℝ)*m^(1-1/p)) := hh + _ = (N^(-(1/3:ℝ))*N^(1/3:ℝ))*(C*m^(1-1/p)) := by ring + _ = _ := by rw [hcan, one_mul] + have hh := (sq_le_sq₀ (norm_nonneg _) (by positivity : 0 ≤ C*m^(1-1/p))).2 h + have he : (m^(1-1/p))^2 = m^(2-2/p) := by + rw [← Real.rpow_mul_natCast hm] + congr 1 + norm_num + ring + simpa only [mul_pow, he] using hh + +lemma normalize_spatial_energy {V : Type*} [SeminormedAddCommGroup V] [NormedSpace ℝ V] + (v : V) {N r C m : ℝ} (hN : 0 < N) (hr : 0 < r) + (hb : ‖v‖^2 ≤ C*(N*r)^(2/3:ℝ)*m) : + ‖(N^(-(1/3:ℝ))) • v‖^2 ≤ C*r^(2/3:ℝ)*m := by + rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg hN.le _), mul_pow] + have hcan : (N^(-(1/3:ℝ)))^2*N^(2/3:ℝ)=1 := by + rw [← Real.rpow_mul_natCast hN.le, ← Real.rpow_add hN] + norm_num + have hh := mul_le_mul_of_nonneg_left hb (sq_nonneg (N^(-(1/3:ℝ)))) + apply hh.trans_eq + rw [Real.mul_rpow hN.le hr.le] + calc + _ = ((N^(-(1/3:ℝ)))^2*N^(2/3:ℝ))*(C*r^(2/3:ℝ)*m) := by ring + _ = _ := by rw [hcan, one_mul] + +lemma graph_interpolated_bound_of_shortTime {c₀ C₀ p : ℝ} (hp : 2 < p) (hC₀ : 0 < C₀) + (hshort : ShortTimeWeakEstimate c₀ C₀ p) + (χ : Plane → ℂ) (hχ : ContDiff ℝ ∞ χ) (hc : HasCompactSupport χ) + (hann : ∀ ξ ∈ tsupport χ, c₀ ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀) + (B : ℝ) (hB : 0 ≤ B) (hχB : ∀ ξ, ‖χ ξ‖ ≤ B) : + ∃ C : ℝ, 0 < C ∧ ∀ j k : ℕ, k ≤ j → + ∀ (x₀ : Plane) (t₀ s : ℝ), 0 ≤ s → s ≤ (1/2:ℝ)^(j+k) → + ∀ (E : Set Plane), MeasurableSet E → E ⊆ Metric.ball x₀ 1 → + ∀ (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1), (∀ x ∈ E, T x ∈ Icc t₀ (t₀+s)) → + ∀ [IsFiniteMeasure (volume.restrict E)], + ‖(((2:ℝ)^j)^(-(1/3:ℝ))) • + graphLp (fun ξ => χ (((2:ℝ)^j)⁻¹ • ξ)) + (scaled_cutoff_memLp χ hχ.continuous hc (by positivity)) + (volume.restrict E) T w hT hw hb‖^2 ≤ + C*((((2:ℝ)^(-(1/6:ℝ)))^k)^2)*(volume.real E)^(3/2-1/p) := by + obtain ⟨Cm,hCm,hmass⟩ := graph_mass_bound_of_shortTime (by linarith : 1 < p) hshort + obtain ⟨Cs,hCs,hsp⟩ := graph_spatial_bound_of_shortTime hp hC₀ hshort χ hχ hc hann B hB hχB + refine ⟨(Cm*B)^2+Cs, by positivity, ?_⟩ + intro j k hk x₀ t₀ s hs hs' E hE hEB T w hT hw hb hTs inst + let N : ℝ := (2:ℝ)^j + let r : ℝ := ((2:ℝ)^k)⁻¹ + have hN : 0 < N := by positivity + have hr : 0 < r := by positivity + have hr1 : r ≤ 1 := inv_le_one_of_one_le₀ (one_le_pow₀ (by norm_num)) + have hs1 : s ≤ N⁻¹ := by + have hw := hs'.trans_eq (dyadic_width j k) + exact hw.trans (by dsimp only [N,r] at *; exact div_le_iff₀ hN |>.2 (by simpa using hr1)) + have hs2 : s ≤ r/N := hs'.trans_eq (dyadic_width j k) + let χN : Plane → ℂ := fun ξ => χ (N⁻¹ • ξ) + have hχN := scaled_cutoff_memLp χ hχ.continuous hc hN + have χNm : Measurable χN := (hχ.continuous.comp (continuous_const_smul _)).measurable + let v := graphLp χN hχN (volume.restrict E) T w hT hw hb + have hm : 0 ≤ volume.real E := measureReal_nonneg + have hm1 := hmass j χN χNm hχN B hB (fun ξ => hχB _) (ae_of_all _ (scaled_cutoff_annular hN hann)) + x₀ t₀ s hs hs1 E hE hEB T w hT hw hb hTs + have h1 : ‖(N^(-(1/3:ℝ))) • v‖^2 ≤ (Cm*B)^2*(volume.real E)^(2-2/p) := + normalize_mass_energy v hN (mul_nonneg hCm.le hB) hm hm1 + have hsp1 := hsp (j-k) N r hN hr (dyadic_scale j k hk) x₀ t₀ s hs hs2 + E hE hEB T w hT hw hb hTs + have hsp2 : ‖v‖^2 ≤ Cs*(N*r)^(2/3:ℝ)*volume.real E := by + simpa only [v, ← dyadic_scale j k hk] using hsp1 + have h2 := normalize_spatial_energy v hN hr hsp2 + have hh := interpolate_energy (sq_nonneg _) hm hr (sq_nonneg (Cm*B)) hCs.le hp h1 h2 + change _ ≤ ((Cm*B)^2+Cs)*r^(1/3:ℝ)*(volume.real E)^(3/2-1/p) at hh + simpa only [r, dyadic_decay] using hh + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphLocalization.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphLocalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..7b10fbc803c536f5371869b66e756c3f5f119b94 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphLocalization.lean @@ -0,0 +1,142 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphDual +import OAI.Analysis.PlanarEndpoint.GraphScaling +import OAI.Analysis.PlanarEndpoint.SpatialGrid +import OAI.Analysis.PlanarEndpoint.SpatialOrthogonal +import OAI.Analysis.PlanarEndpoint.TimeSeparation + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology BigOperators ContDiff +namespace PlanarEndpoint +attribute [local instance] Classical.propDecidable + +lemma scaled_cutoff_annular {χ : Plane → ℂ} {c₀ C₀ N : ℝ} (hN : 0 < N) + (hs : ∀ ξ ∈ tsupport χ, c₀ ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀) : + ∀ ξ : Plane, ξ ∉ {ξ | c₀*N ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*N} → χ (N⁻¹ • ξ) = 0 := by + intro ξ hξ + by_contra hne + have hh := hs (N⁻¹ • ξ) (subset_tsupport χ (by exact hne)) + simp only [norm_smul, Real.norm_eq_abs, abs_of_pos (inv_pos.mpr hN)] at hh + have he : N⁻¹*‖ξ‖*N=‖ξ‖ := by field_simp + apply hξ + constructor + · have := mul_le_mul_of_nonneg_right hh.1 hN.le + simpa only [he] using this + · have := mul_le_mul_of_nonneg_right hh.2 hN.le + simpa only [he] using this + +lemma real_univ_finsetSum {ι : Type*} [Fintype ι] (μ : ι → Measure Plane) + [∀ i, IsFiniteMeasure (μ i)] : (∑ i, μ i).real univ = ∑ i, (μ i).real univ := by + simp only [measureReal_def, ← Measure.sum_fintype, Measure.sum_apply _ MeasurableSet.univ, + tsum_fintype] + exact ENNReal.toReal_sum (fun i _ => measure_ne_top _ _) + +lemma graphLp_congr_measure (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + {μ ν : Measure Plane} [IsFiniteMeasure μ] [IsFiniteMeasure ν] (h : μ = ν) + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + graphLp χ hχ μ T w hT hw hb = graphLp χ hχ ν T w hT hw hb := by + subst ν + rfl + +lemma graph_spatial_bound_of_shortTime {c₀ C₀ p : ℝ} (hp : 2 < p) (hC₀ : 0 < C₀) + (hshort : ShortTimeWeakEstimate c₀ C₀ p) + (χ : Plane → ℂ) (hχ : ContDiff ℝ ∞ χ) (hc : HasCompactSupport χ) + (hann : ∀ ξ ∈ tsupport χ, c₀ ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀) + (B : ℝ) (hB : 0 ≤ B) (hχB : ∀ ξ, ‖χ ξ‖ ≤ B) : + ∃ C : ℝ, 0 < C ∧ ∀ l : ℕ, ∀ (N r : ℝ) (hN : 0 < N), 0 < r → N*r=(2:ℝ)^l → + ∀ (x₀ : Plane) (t₀ s : ℝ), 0 ≤ s → s ≤ r/N → + ∀ (E : Set Plane), MeasurableSet E → E ⊆ Metric.ball x₀ 1 → + ∀ (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1), (∀ x ∈ E, T x ∈ Icc t₀ (t₀+s)) → + ∀ [IsFiniteMeasure (volume.restrict E)], + ‖graphLp (fun ξ => χ (N⁻¹ • ξ)) (scaled_cutoff_memLp χ hχ.continuous hc hN) + (volume.restrict E) T w hT hw hb‖^2 ≤ + C*((2:ℝ)^l)^(2/3:ℝ)*volume.real E := by + obtain ⟨Cb,hCb,hball⟩ := graph_ball_bound_of_shortTime hp hshort + obtain ⟨Cf,hCf,hker⟩ := frequencyKernel_spatial_decay hC₀ hχ hc (fun ξ hξ => (hann ξ hξ).2) 4 + obtain ⟨K,hK⟩ := exists_nat_ge (4*C₀) + let D : ℝ := Fintype.card (GridBox K) + let A : ℝ := ∫ z, spatialDecay 1 z + have hA : 0 ≤ A := integral_nonneg (spatialDecay_nonneg (N:=1)) + have hD : 0 ≤ D := Nat.cast_nonneg _ + refine ⟨D*Cb*B^2+Cf*A+1, by positivity, ?_⟩ + intro l N r hN hr hNr x₀ t₀ s hs hs' E hE hEB T w hT hw hb hTs inst + let χN : Plane → ℂ := fun ξ => χ (N⁻¹ • ξ) + have hχN := scaled_cutoff_memLp χ hχ.continuous hc hN + have hχNm : Measurable χN := (hχ.continuous.comp (continuous_const_smul _)).measurable + obtain ⟨M,hM⟩ := exists_nat_ge (1/r+1) + let F : GridBox M → Set Plane := fun a => E ∩ gridCell x₀ r (fun i => (a i:ℤ)) + let μ : GridBox M → Measure Plane := fun a => volume.restrict (F a) + have hFm (a : GridBox M) : MeasurableSet (F a) := hE.inter (measurableSet_gridCell _ _ _) + have hfin : volume E ≠ ⊤ := isFiniteMeasure_restrict.mp inst + let (a : GridBox M) : IsFiniteMeasure (μ a) := isFiniteMeasure_restrict.mpr + (ne_top_of_le_ne_top hfin (measure_mono Set.inter_subset_left)) + have hsum : ∑ a, μ a = volume.restrict E := (grid_restrict_eq_sum hr hM hE hEB).symm + have hμ : (∑ a, μ a) ≤ volume := by rw [hsum]; exact Measure.restrict_le_self + have hwindow : s ≤ r^2/((2:ℝ)^l) := by + have he : r^2/((2:ℝ)^l) = r/N := by rw [← hNr]; field_simp + rwa [he] + have hbnd (a : GridBox M) : ‖graphLp χN hχN (μ a) T w hT hw hb‖^2 ≤ + Cb*B^2*((2:ℝ)^l)^(2/3:ℝ)*volume.real (F a) := + hball l N r hr hNr χN hχNm hχN B hB (fun ξ => hχB (N⁻¹ • ξ)) + (ae_of_all _ (scaled_cutoff_annular hN hann)) (gridCenter x₀ r (fun i => (a i:ℤ))) + t₀ s hs hwindow (F a) (hFm a) + (Set.inter_subset_right.trans (gridCell_in_ball hr _)) + T w hT hw hb (fun x hx => hTs x hx.1) + have hgood (a : GridBox M) : ∀ᵐ x ∂μ a, x ∈ E ∧ x ∈ gridCell x₀ r (fun i => (a i:ℤ)) := + ae_restrict_mem (hFm a) + have hfar (a b : GridBox M) (hab : ¬gridNear K a b) : + ∀ᵐ z : Plane × Plane ∂(μ b).prod (μ a), + ‖frequencyKernel χN (z.1-z.2) (T z.1-T z.2)‖ ≤ Cf*spatialDecay N (z.1-z.2) := by + filter_upwards [Measure.quasiMeasurePreserving_fst.ae (hgood b), + Measure.quasiMeasurePreserving_snd.ae (hgood a)] with z hz hy + have hab' : ¬gridNear K b a := by + intro h + exact hab (fun i => by simpa only [abs_sub_comm] using h i) + have hdist := grid_far_distance hr hab' hz.2 hy.2 + have ht1 := hTs z.1 hz.1 + have ht2 := hTs z.2 hy.1 + have htd : |T z.1-T z.2| ≤ r/N := (abs_le.mpr ⟨by linarith [ht1.1, ht2.2],by linarith [ht1.2, ht2.1]⟩).trans hs' + have hg : 4*C₀*N*|T z.1-T z.2| ≤ ‖z.1-z.2‖ := by + have hmul := mul_le_mul_of_nonneg_left htd (show 0 ≤ 4*C₀*N by positivity) + have he : 4*C₀*N*(r/N)=4*C₀*r := by field_simp + rw [he] at hmul + exact hmul.trans ((mul_le_mul_of_nonneg_right hK hr.le).trans hdist) + simpa only [spatialDecay, ← mul_div_assoc] using hker N hN (z.1-z.2) (T z.1-T z.2) hg + have hh := graphPartition_near_far χN hχNm hχN μ hμ T w hT hw hb + (D:=D) (gridNear K) (fun a b h i => by simpa only [abs_sub_comm] using h i) + hCf hN (fun a => by dsimp only [D]; exact_mod_cast gridNear_degree K a) hfar + rw [graphLp_congr_measure χN hχN hsum T w hT hw hb] at hh + have hreal : (∑ a, μ a).real univ = volume.real E := by + rw [hsum, measureReal_restrict_apply_univ] + rw [hreal] at hh + have hmass : ∑ a, volume.real (F a) = volume.real E := by + calc + _ = ∑ a, (μ a).real univ := by simp only [μ, measureReal_restrict_apply_univ] + _ = (∑ a, μ a).real univ := (real_univ_finsetSum μ).symm + _ = volume.real E := by rw [hsum, measureReal_restrict_apply_univ] + have hsumB : (∑ a, ‖graphLp χN hχN (μ a) T w hT hw hb‖^2) ≤ + Cb*B^2*((2:ℝ)^l)^(2/3:ℝ)*volume.real E := by + calc + _ ≤ ∑ a, Cb*B^2*((2:ℝ)^l)^(2/3:ℝ)*volume.real (F a) := + Finset.sum_le_sum (fun a _ => hbnd a) + _ = _ := by rw [← Finset.mul_sum, hmass] + have hf : 1 ≤ ((2:ℝ)^l)^(2/3:ℝ) := Real.one_le_rpow (one_le_pow₀ (by norm_num)) (by norm_num) + have hm : 0 ≤ volume.real E := measureReal_nonneg + have hbound := hh.trans (add_le_add (mul_le_mul_of_nonneg_left hsumB hD) le_rfl) + change _ ≤ D*(Cb*B^2*((2:ℝ)^l)^(2/3:ℝ)*volume.real E)+Cf*A*volume.real E at hbound + apply hbound.trans + nlinarith [mul_le_mul_of_nonneg_right hf (mul_nonneg (mul_nonneg hCf hA) hm), + mul_nonneg (Real.rpow_nonneg (by positivity) (2/3:ℝ)) hm] + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphReduction.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphReduction.lean new file mode 100644 index 0000000000000000000000000000000000000000..bea2dbb532c59da88dee7e5f1350a47c44fa7d50 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphReduction.lean @@ -0,0 +1,123 @@ +import OAI.Analysis.PlanarEndpoint.Extension +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphSelection +import OAI.Analysis.PlanarEndpoint.GraphTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology +namespace PlanarEndpoint + +def ShortTimeGraphEstimate (c₀ C₀ p : ℝ) : Prop := + ∃ C : ℝ, 0 < C ∧ ∀ (j : ℕ) (f : L2), + AnnularFourierSupport f c₀ C₀ ((2 : ℝ) ^ j) → + ∀ (x₀ : Plane) (t₀ s : ℝ), 0 ≤ s → s ≤ ((2 : ℝ) ^ j)⁻¹ → + ∀ T : Plane → ℝ, Measurable T → (∀ x, T x ∈ Icc t₀ (t₀+s)) → + ∀ lam : ℝ, 0 < lam → + volume (Metric.ball x₀ 1 ∩ {x | lam < ‖evolution f x (T x)‖}) ≤ + ENNReal.ofReal ((C * (((2 : ℝ) ^ j) ^ (1 / 3 : ℝ)) * ‖f‖ / lam) ^ p) + +lemma affine_dense_time_bound {g : ℝ → ℂ} (hg : Continuous g) + {t₀ s B : ℝ} (hs : 0 ≤ s) + (h : ∀ n, ‖g (t₀+s*(denseTime n).val)‖ ≤ B) : + ∀ t ∈ Icc t₀ (t₀+s), ‖g t‖ ≤ B := by + have hh := denseTime_bound (show Continuous (fun u => g (t₀+s*u)) by fun_prop) h + intro t ht + by_cases hz : s = 0 + · have he : t = t₀ := le_antisymm (by simpa [hz] using ht.2) ht.1 + simpa [he,hz] using h 0 + · have hs' : 0 < s := lt_of_le_of_ne hs (Ne.symm hz) + have hu : (t-t₀)/s ∈ Icc (0:ℝ) 1 := by + constructor + · exact div_nonneg (sub_nonneg.mpr ht.1) hs + · exact (div_le_one hs').mpr (by linarith [ht.2]) + have he : t₀+s*((t-t₀)/s) = t := by field_simp; ring + simpa only [he] using hh ((t-t₀)/s) hu + +lemma exists_measurable_superlevel_time (f : L2) + (hf : Integrable (fourier f) volume) (t₀ s lam : ℝ) (hs : 0 ≤ s) : + ∃ T : Plane → ℝ, Measurable T ∧ (∀ x, T x ∈ Icc t₀ (t₀+s)) ∧ + ∀ x, (∃ t ∈ Icc t₀ (t₀+s), lam < ‖evolution f x t‖) ↔ + lam < ‖evolution f x (T x)‖ := by + classical + let P (n : ℕ) (x : Plane) : Prop := + lam < ‖evolution f x (t₀+s*(denseTime n).val)‖ + let M (x : Plane) : Prop := ∃ n, P n x + have hp : ∀ n, MeasurableSet {x | P n x} := by + intro n + exact measurableSet_lt measurable_const + (((continuous_evolution hf).comp (continuous_id.prodMk continuous_const)).norm.measurable) + have hm : MeasurableSet {x | M x} := by + have he : {x | M x} = ⋃ n, {x | P n x} := by ext x; simp [M] + rw [he] + exact MeasurableSet.iUnion hp + have hex : ∀ x, ∃ n, ¬M x ∨ P n x := by + intro x + by_cases h : M x + · obtain ⟨n,hn⟩ := h + exact ⟨n,Or.inr hn⟩ + · exact ⟨0,Or.inl h⟩ + let T (x : Plane) : ℝ := t₀+s*(denseTime (Nat.find (hex x))).val + have hr : ∀ x, T x ∈ Icc t₀ (t₀+s) := by + intro x + have hv := (denseTime (Nat.find (hex x))).property + dsimp [T] + constructor + · nlinarith [hv.1] + · nlinarith [hv.2] + refine ⟨T,?_,hr,?_⟩ + · exact Measurable.find (p := fun n x => ¬M x ∨ P n x) + (f := fun n (_ : Plane) => t₀+s*(denseTime n).val) + (fun n => measurable_const) (fun n => hm.compl.union (hp n)) hex + · intro x + constructor + · rintro ⟨t,ht,hlt⟩ + have hx : M x := by + by_contra! hn + have hb : ∀ n, ‖evolution f x (t₀+s*(denseTime n).val)‖ ≤ lam := by + intro n + exact le_of_not_gt (fun h => hn ⟨n,h⟩) + exact (not_lt_of_ge (affine_dense_time_bound + ((continuous_evolution hf).comp (continuous_const.prodMk continuous_id)) hs hb t ht)) hlt + have hh := Nat.find_spec (hex x) + exact hh.resolve_left (not_not.mpr hx) + · intro hx + exact ⟨T x,hr x,hx⟩ + +lemma shortTimeWeakEstimate_of_graph {c₀ C₀ p : ℝ} + (hg : ShortTimeGraphEstimate c₀ C₀ p) : ShortTimeWeakEstimate c₀ C₀ p := by + obtain ⟨C,hC,hg⟩ := hg + refine ⟨C,hC,?_⟩ + intro j f hf x₀ t₀ s hs hsN lam hlam + obtain ⟨T,hT,hr,he⟩ := exists_measurable_superlevel_time f hf.integrable t₀ s lam hs + have heq : shortTimeLevel f x₀ t₀ s lam = + Metric.ball x₀ 1 ∩ {x | lam < ‖evolution f x (T x)‖} := by + ext x + exact and_congr_right (fun _ => he x) + rw [heq] + exact hg j f hf x₀ t₀ s hs hsN T hT hr lam hlam + +lemma shortTimeGraphEstimate_of_weak {c₀ C₀ p : ℝ} + (hw : ShortTimeWeakEstimate c₀ C₀ p) : ShortTimeGraphEstimate c₀ C₀ p := by + obtain ⟨C,hC,hw⟩ := hw + refine ⟨C,hC,?_⟩ + intro j f hf x₀ t₀ s hs hsN T _ hr lam hlam + apply le_trans (measure_mono (show + (Metric.ball x₀ 1 ∩ {x | lam < ‖evolution f x (T x)‖}) ⊆ + shortTimeLevel f x₀ t₀ s lam from fun x hx => ⟨hx.1,T x,hr x,hx.2⟩)) + exact hw j f hf x₀ t₀ s hs hsN lam hlam + +lemma mainConclusion_of_shortTimeGraph {p : ℝ} (hp : 2 < p) + (hg : ShortTimeGraphEstimate (1/4) 4 p) {f : L2} (hf : InHThird f) : + MainConclusion f := + mainConclusion_of_shortTime hp (shortTimeWeakEstimate_of_graph hg) hf + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphScaling.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphScaling.lean new file mode 100644 index 0000000000000000000000000000000000000000..7bbbf3747ec7dea20d12400990fdee9c8c16739c --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphScaling.lean @@ -0,0 +1,241 @@ +import OAI.Analysis.PlanarEndpoint.DualMass +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.FrequencyWeak +import OAI.Analysis.PlanarEndpoint.GraphDual + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology ComplexConjugate +namespace PlanarEndpoint + +def affineScale (x₀ : Plane) (r : ℝ) (X : Plane) : Plane := x₀ + r • X + +def scaledTime (x₀ : Plane) (t₀ r : ℝ) (T : Plane → ℝ) (X : Plane) : ℝ := + (T (affineScale x₀ r X) - t₀) / r^2 + +lemma measurable_affineScale (x₀ : Plane) (r : ℝ) : Measurable (affineScale x₀ r) := by + unfold affineScale + fun_prop + +lemma measurable_scaledTime (x₀ : Plane) (t₀ r : ℝ) {T : Plane → ℝ} + (hT : Measurable T) : Measurable (scaledTime x₀ t₀ r T) := by + exact ((hT.comp (measurable_affineScale x₀ r)).sub measurable_const).div_const _ + +lemma integral_affineScale {V : Type*} [NormedAddCommGroup V] [NormedSpace ℝ V] + (f : Plane → V) (x₀ : Plane) {r : ℝ} (hr : 0 < r) : + (∫ x, f x) = r^2 • ∫ X, f (affineScale x₀ r X) := by + change _ = r^2 • ∫ X, (fun x => f (x₀+x)) (r • X) + rw [Measure.integral_comp_smul_of_nonneg (volume : Measure Plane) (fun x => f (x₀+x)) r (hR := hr.le)] + simp only [finrank_euclideanSpace, Fintype.card_fin, integral_add_left_eq_self, + smul_smul, mul_inv_cancel₀ (pow_ne_zero _ hr.ne'), one_smul] + +lemma setIntegral_affineScale {V : Type*} [NormedAddCommGroup V] [NormedSpace ℝ V] + (f : Plane → V) {E : Set Plane} (hE : MeasurableSet E) + (x₀ : Plane) {r : ℝ} (hr : 0 < r) : + (∫ x in E, f x) = r^2 • ∫ X in affineScale x₀ r ⁻¹' E, f (affineScale x₀ r X) := by + rw [← integral_indicator hE, integral_affineScale _ x₀ hr] + congr 1 + rw [← integral_indicator (hE.preimage (measurable_affineScale x₀ r))] + apply integral_congr_ae + filter_upwards [] with X + by_cases hx : affineScale x₀ r X ∈ E <;> simp [hx] + +lemma volumeReal_affineScale {E : Set Plane} (hE : MeasurableSet E) + (x₀ : Plane) {r : ℝ} (hr : 0 < r) : + volume.real E = r^2 * volume.real (affineScale x₀ r ⁻¹' E) := by + simpa using setIntegral_affineScale (fun _ => (1 : ℝ)) hE x₀ hr + +lemma phase_affineScale (x₀ X η : Plane) (t₀ s : ℝ) {r : ℝ} (hr : 0 < r) : + phase (affineScale x₀ r X) (t₀+r^2*s) (r⁻¹ • η) = + phase x₀ t₀ (r⁻¹ • η) * phase X s η := by + have he : inner ℝ (x₀+r • X) (r⁻¹ • η) - (t₀+r^2*s)*‖r⁻¹ • η‖^2 = + (inner ℝ x₀ (r⁻¹ • η) - t₀*‖r⁻¹ • η‖^2) + + (inner ℝ X η - s*‖η‖^2) := by + simp only [inner_add_left, inner_smul_left, inner_smul_right, norm_smul, + Real.norm_eq_abs, abs_inv, abs_of_pos hr, starRingEnd_apply, star_trivial] + field_simp + ring + unfold phase affineScale + rw [he, ← Complex.exp_add] + congr 1 + push_cast + ring + +lemma graphDual_affineScale (χ : Plane → ℂ) {E : Set Plane} (hE : MeasurableSet E) + (x₀ : Plane) (t₀ : ℝ) {r : ℝ} (hr : 0 < r) + (T : Plane → ℝ) (w : Plane → ℂ) (η : Plane) : + graphDual χ (volume.restrict E) T w (r⁻¹ • η) = + (r^2 : ℝ) • (phase x₀ t₀ (r⁻¹ • η) * + graphDual (fun ξ => χ (r⁻¹ • ξ)) (volume.restrict (affineScale x₀ r ⁻¹' E)) + (scaledTime x₀ t₀ r T) (w ∘ affineScale x₀ r) η) := by + unfold graphDual graphFourier + rw [setIntegral_affineScale _ hE x₀ hr] + have he (X : Plane) : T (affineScale x₀ r X) = + t₀ + r^2 * scaledTime x₀ t₀ r T X := by + unfold scaledTime + field_simp + ring + simp_rw [he, phase_affineScale x₀ _ η t₀ _ hr] + have hprod : (fun X => w (affineScale x₀ r X) * + (phase x₀ t₀ (r⁻¹ • η) * phase X (scaledTime x₀ t₀ r T X) η)) = + (fun X => phase x₀ t₀ (r⁻¹ • η) * + (w (affineScale x₀ r X) * phase X (scaledTime x₀ t₀ r T X) η)) := by + funext X + ring + rw [hprod, integral_const_mul] + simp only [Complex.real_smul, Function.comp_apply] + ring + +lemma graphLp_norm_sq_integral (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + ‖graphLp χ hχ μ T w hT hw hb‖^2 = ∫ ξ, ‖graphDual χ μ T w ξ‖^2 := by + rw [← real_inner_self_eq_norm_sq] + simp only [L2.inner_def, real_inner_self_eq_norm_sq] + exact integral_congr_ae ((graphLp_ae χ hχ μ T w hT hw hb).fun_comp (fun z : ℂ => ‖z‖^2)) + +lemma norm_graphDual_affineScale (χ : Plane → ℂ) {E : Set Plane} (hE : MeasurableSet E) + (x₀ : Plane) (t₀ : ℝ) {r : ℝ} (hr : 0 < r) + (T : Plane → ℝ) (w : Plane → ℂ) (η : Plane) : + ‖graphDual χ (volume.restrict E) T w (r⁻¹ • η)‖ = r^2 * + ‖graphDual (fun ξ => χ (r⁻¹ • ξ)) (volume.restrict (affineScale x₀ r ⁻¹' E)) + (scaledTime x₀ t₀ r T) (w ∘ affineScale x₀ r) η‖ := by + rw [graphDual_affineScale χ hE x₀ t₀ hr, norm_smul, norm_mul, norm_phase, one_mul] + simp [Real.norm_eq_abs, abs_of_pos hr] + +lemma graphLp_norm_sq_affineScale (χ : Plane → ℂ) (hχ : MemLp χ 2 volume) + {E : Set Plane} (hE : MeasurableSet E) [IsFiniteMeasure (volume.restrict E)] + (x₀ : Plane) (t₀ : ℝ) {r : ℝ} (hr : 0 < r) + [IsFiniteMeasure (volume.restrict (affineScale x₀ r ⁻¹' E))] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : + ‖graphLp χ hχ (volume.restrict E) T w hT hw hb‖^2 = r^2 * + ‖graphLp (fun ξ => χ (r⁻¹ • ξ)) (memLp_comp_real_smul hχ (inv_ne_zero hr.ne')) + (volume.restrict (affineScale x₀ r ⁻¹' E)) + (scaledTime x₀ t₀ r T) (w ∘ affineScale x₀ r) + (measurable_scaledTime x₀ t₀ r hT) (hw.comp (measurable_affineScale x₀ r)) + (fun point => hb (affineScale x₀ r point))‖^2 := by + rw [graphLp_norm_sq_integral, graphLp_norm_sq_integral] + have he := Measure.integral_comp_inv_smul_of_nonneg volume + (fun ξ => ‖graphDual χ (volume.restrict E) T w ξ‖^2) hr.le + simp only [finrank_euclideanSpace, Fintype.card_fin, smul_eq_mul, + norm_graphDual_affineScale χ hE x₀ t₀ hr T w] at he + simp_rw [mul_pow] at he + rw [integral_const_mul] at he + nlinarith [sq_pos_of_pos hr] + +lemma affineScale_preimage_ball {E : Set Plane} {x₀ : Plane} {r : ℝ} + (hr : 0 < r) (hE : E ⊆ Metric.ball x₀ r) : + affineScale x₀ r ⁻¹' E ⊆ Metric.ball (0 : Plane) 1 := by + intro X hX + have hx := hE hX + have he : affineScale x₀ r X - x₀ = r • X := by unfold affineScale; abel + rw [Metric.mem_ball, dist_eq_norm, he, norm_smul, Real.norm_eq_abs, abs_of_pos hr] at hx + simpa using (mul_lt_mul_iff_right₀ hr).mp (show r*‖X‖ < r*1 by simpa using hx) + +lemma annular_support_rescale {χ : Plane → ℂ} {c₀ C₀ N r : ℝ} (hr : 0 < r) + (hs : ∀ᵐ ξ : Plane ∂volume, + ξ ∉ {ξ | c₀*N ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*N} → χ ξ = 0) : + ∀ᵐ η : Plane ∂volume, + η ∉ {η | c₀*(N*r) ≤ ‖η‖ ∧ ‖η‖ ≤ C₀*(N*r)} → χ (r⁻¹ • η) = 0 := by + have h := (Measure.quasiMeasurePreserving_smul volume (r := r⁻¹) + (inv_ne_zero hr.ne')).ae hs + filter_upwards [h] with η hη hn + apply hη + intro hh + apply hn + rcases hh with ⟨h1,h2⟩ + simp only [norm_smul, Real.norm_eq_abs, abs_inv, abs_of_pos hr] at h1 h2 + have h1' := mul_le_mul_of_nonneg_left h1 hr.le + have h2' := mul_le_mul_of_nonneg_left h2 hr.le + simp only [← mul_assoc, mul_inv_cancel₀ hr.ne', one_mul] at h1' h2' + constructor <;> nlinarith + +lemma rpow_mass_sq_le {p m M : ℝ} (hp : 2 < p) (hm : 0 ≤ m) (hM : m ≤ M) : + (m^(1-1/p))^2 ≤ M^(1-2/p)*m := by + have hp0 : 0 < p := by linarith + have hql : 0 < 1-1/p := by have := (div_lt_iff₀ hp0).2 (show 1 < 1*p by linarith); linarith + have hq : 0 ≤ 1-2/p := by have := (div_lt_iff₀ hp0).2 (show 2 < 1*p by linarith); linarith + rcases hm.eq_or_lt with hm0 | hmpos + · rw [← hm0] + rw [Real.zero_rpow hql.ne'] + simp + · rw [← Real.rpow_two, ← Real.rpow_mul hm, + show (1-1/p)*2 = (1-2/p)+1 by ring, Real.rpow_add hmpos, Real.rpow_one] + exact mul_le_mul_of_nonneg_right (Real.rpow_le_rpow hm hM hq) hm + +lemma graph_ball_bound_of_shortTime {c₀ C₀ p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate c₀ C₀ p) : + ∃ C : ℝ, 0 < C ∧ ∀ l : ℕ, ∀ (N r : ℝ), 0 < r → N*r=(2:ℝ)^l → + ∀ (χ : Plane → ℂ) (_ : Measurable χ) (hχ : MemLp χ 2 volume) + (B : ℝ), 0 ≤ B → (∀ ξ, ‖χ ξ‖ ≤ B) → + (∀ᵐ ξ : Plane ∂volume, ξ ∉ {ξ | c₀*N ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀*N} → χ ξ = 0) → + ∀ (x₀ : Plane) (t₀ s : ℝ), 0 ≤ s → s ≤ r^2/((2:ℝ)^l) → + ∀ (E : Set Plane), MeasurableSet E → E ⊆ Metric.ball x₀ r → + ∀ (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1), (∀ x ∈ E, T x ∈ Icc t₀ (t₀+s)) → + ∀ [IsFiniteMeasure (volume.restrict E)], + ‖graphLp χ hχ (volume.restrict E) T w hT hw hb‖^2 ≤ + C*B^2*((2:ℝ)^l)^(2/3:ℝ)*volume.real E := by + obtain ⟨K,hK,hbnd⟩ := graph_mass_bound_of_shortTime (show 1 < p by linarith) hshort + refine ⟨K^2*Real.pi^(1-2/p), mul_pos (sq_pos_of_pos hK) (Real.rpow_pos_of_pos Real.pi_pos _), ?_⟩ + intro l N r hr hNr χ hχm hχ B hB hχB hχs x₀ t₀ s hs hs' E hE hEB T w hT hw hb hTs inst + let F := affineScale x₀ r ⁻¹' E + have hF : MeasurableSet F := hE.preimage (measurable_affineScale x₀ r) + have hFB : F ⊆ Metric.ball (0 : Plane) 1 := affineScale_preimage_ball hr hEB + let : IsFiniteMeasure (volume.restrict F) := isFiniteMeasure_restrict.2 + ((measure_mono hFB).trans_lt measure_ball_lt_top).ne + have hFs : ∀ X ∈ F, scaledTime x₀ t₀ r T X ∈ Icc 0 (0+s/r^2) := by + intro X hX + rcases hTs _ hX with ⟨h1,h2⟩ + dsimp [scaledTime] + constructor + · exact div_nonneg (sub_nonneg.mpr h1) (sq_nonneg r) + · simp only [zero_add] + exact div_le_div_of_nonneg_right (by linarith) (sq_nonneg r) + have htime : s/r^2 ≤ ((2:ℝ)^l)⁻¹ := by + rw [div_le_iff₀ (sq_pos_of_pos hr)] + simpa [div_eq_mul_inv, mul_comm] using hs' + have hscl := annular_support_rescale hr hχs + rw [hNr] at hscl + have hsc := memLp_comp_real_smul hχ (inv_ne_zero hr.ne') + have hm : ‖graphLp (fun ξ => χ (r⁻¹ • ξ)) hsc (volume.restrict F) + (scaledTime x₀ t₀ r T) (w ∘ affineScale x₀ r) + (measurable_scaledTime x₀ t₀ r hT) (hw.comp (measurable_affineScale x₀ r)) + (fun X => hb _)‖ ≤ K*B*((2:ℝ)^l)^(1/3:ℝ)*(volume.real F)^(1-1/p) := + hbnd l _ (hχm.comp (measurable_const_smul _)) hsc B hB (fun ξ => hχB _) hscl + 0 0 (s/r^2) (div_nonneg hs (sq_nonneg r)) htime F hF hFB _ _ + (measurable_scaledTime x₀ t₀ r hT) (hw.comp (measurable_affineScale x₀ r)) + (fun X => hb _) hFs + have hm0 : 0 ≤ volume.real F := ENNReal.toReal_nonneg + have hmπ : volume.real F ≤ Real.pi := by + apply le_trans (measureReal_mono hFB) + simp [measureReal_def, EuclideanSpace.volume_ball_fin_two, ENNReal.toReal_ofReal Real.pi_nonneg] + have hpow := rpow_mass_sq_le hp hm0 hmπ + have hmsq := (sq_le_sq₀ (norm_nonneg _) (show 0 ≤ K*B*((2:ℝ)^l)^(1/3:ℝ)* + (volume.real F)^(1-1/p) by positivity)).2 hm + simp only [mul_pow] at hmsq + have hfreq : (((2:ℝ)^l)^(1/3:ℝ))^2 = ((2:ℝ)^l)^(2/3:ℝ) := by + rw [← Real.rpow_two, ← Real.rpow_mul (by positivity)] + norm_num + rw [hfreq] at hmsq + have hmsq' := hmsq.trans (mul_le_mul_of_nonneg_left hpow + (show 0 ≤ K^2*B^2*((2:ℝ)^l)^(2/3:ℝ) by positivity)) + rw [graphLp_norm_sq_affineScale χ hχ hE x₀ t₀ hr T w hT hw hb] + have hmE := volumeReal_affineScale hE x₀ hr + change volume.real E = r^2 * volume.real F at hmE + calc + _ ≤ r^2*(K^2*B^2*((2:ℝ)^l)^(2/3:ℝ)*(Real.pi^(1-2/p)*volume.real F)) := + mul_le_mul_of_nonneg_left hmsq' (sq_nonneg r) + _ = _ := by rw [hmE]; ring + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphSelection.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphSelection.lean new file mode 100644 index 0000000000000000000000000000000000000000..2f786030a2fd3af0724ef1cde42f9ef1bc70e113 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphSelection.lean @@ -0,0 +1,169 @@ +import OAI.Analysis.PlanarEndpoint.DualMass +import OAI.Analysis.PlanarEndpoint.Extension +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.FrequencyWeak +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.MaximalBridge +import OAI.Analysis.PlanarEndpoint.SobolevGraph +import OAI.Analysis.PlanarEndpoint.WeightedGraph + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +namespace PlanarEndpoint + +lemma graph_evolution_pairing_bound {p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate (1/4) 4 p) : + ∃ C : ℝ, 0 < C ∧ ∀ (f : L2), BoundedFourierSupport f → InHThird f → + ∀ (x₀ : Plane) (T : Plane → ℝ) (w : Plane → ℂ), Measurable T → Measurable w → + (∀ x, ‖w x‖ ≤ 1) → (∀ x ∈ Metric.ball x₀ 1, T x ∈ Ico 0 1) → + ‖∫ x in Metric.ball x₀ 1, w x * evolution f x (T x)‖ ≤ C*hThirdNorm f := by + obtain ⟨C,hC,hbound⟩ := graph_sobolev_pairing_bound hp hshort + refine ⟨((2*Real.pi)^2)⁻¹*C,by positivity,?_⟩ + intro f hf hH x₀ T w hT hw hb ht + have hh := hbound f hf hH x₀ T w hT hw hb ht + rw [graphFourier_frequency_pairing hf.integrable _ hT hw hb] at hh + have he : (∫ x in Metric.ball x₀ 1, w x*evolution f x (T x)) = + (((2*Real.pi)^2)⁻¹:ℝ) • ∫ x in Metric.ball x₀ 1, + w x*frequencyExtension (fourier f) x (T x) := by + rw [← integral_smul] + apply integral_congr_ae + filter_upwards [] with x + simp only [evolution,frequencyExtension,Complex.real_smul] + ring + rw [he,norm_smul,Real.norm_eq_abs,abs_of_pos (by positivity : 0 < ((2*Real.pi)^2)⁻¹)] + exact (mul_le_mul_of_nonneg_left hh (by positivity)).trans_eq (by ring) + +def normingPhase (z : ℂ) : ℂ := (starRingEnd ℂ) z / (‖z‖ : ℂ) + +lemma normingPhase_measurable : Measurable normingPhase := + Complex.continuous_conj.measurable.div (Complex.measurable_ofReal.comp measurable_norm) + +lemma normingPhase_norm (z : ℂ) : ‖normingPhase z‖ ≤ 1 := by + rw [normingPhase,norm_div,Complex.norm_conj,Complex.norm_real,Real.norm_eq_abs, + abs_of_nonneg (norm_nonneg z)] + exact div_self_le_one _ + +lemma normingPhase_mul (z : ℂ) : normingPhase z*z = (‖z‖ : ℂ) := by + by_cases hz : z=0 + · simp [hz,normingPhase] + · have hn : (‖z‖:ℂ) ≠ 0 := by exact_mod_cast (norm_ne_zero_iff.mpr hz) + rw [normingPhase,div_mul_eq_mul_div,Complex.conj_mul'] + field_simp + +lemma measurable_graph_evolution (f : L2) (hf : Integrable (fourier f) volume) + {T : Plane → ℝ} (hT : Measurable T) : Measurable (fun x => evolution f x (T x)) := by + have hgraph : Measurable (fun x : Plane => (x,T x)) := measurable_id.prodMk hT + change Measurable ((fun z : Plane × ℝ => evolution f z.1 z.2) ∘ (fun x => (x,T x))) + exact (continuous_evolution hf).measurable.comp hgraph + +lemma graph_evolution_norm_integrable (f : L2) (hf : Integrable (fourier f) volume) + (x₀ : Plane) {T : Plane → ℝ} (hT : Measurable T) : + Integrable (fun x => ‖evolution f x (T x)‖) (volume.restrict (Metric.ball x₀ 1)) := by + have hm : Measurable (fun x => evolution f x (T x)) := + measurable_graph_evolution f hf hT + apply (integrable_const ((((2*Real.pi)^2)⁻¹:ℝ) * ∫ ξ, ‖fourier f ξ‖)).mono' + hm.norm.aestronglyMeasurable + filter_upwards [] with x + simpa only [Real.norm_eq_abs,abs_of_nonneg (norm_nonneg _)] using + norm_evolution_le_fourierL1 f x (T x) + +lemma graph_evolution_norm_bound {p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate (1/4) 4 p) : + ∃ C : ℝ, 0 < C ∧ ∀ (f : L2), BoundedFourierSupport f → InHThird f → + ∀ (x₀ : Plane) (T : Plane → ℝ), Measurable T → + (∀ x ∈ Metric.ball x₀ 1, T x ∈ Ico 0 1) → + (∫ x in Metric.ball x₀ 1, ‖evolution f x (T x)‖) ≤ C*hThirdNorm f := by + obtain ⟨C,hC,hbound⟩ := graph_evolution_pairing_bound hp hshort + refine ⟨C,hC,?_⟩ + intro f hf hH x₀ T hT ht + let w := fun x => normingPhase (evolution f x (T x)) + have hw : Measurable w := normingPhase_measurable.comp + (measurable_graph_evolution f hf.integrable hT) + have hh := hbound f hf hH x₀ T w hT hw (fun x => normingPhase_norm _) ht + have he : (fun x => w x*evolution f x (T x)) = fun x => (‖evolution f x (T x)‖ : ℂ) := + funext (fun x => normingPhase_mul _) + rw [he,integral_complex_ofReal,Complex.norm_real,Real.norm_eq_abs, + abs_of_nonneg (integral_nonneg (fun _ => norm_nonneg _))] at hh + exact hh + +abbrev HalfTime := ↥(Ico (0:ℝ) 1) +instance halfTime_nonempty : Nonempty HalfTime := ⟨⟨0,by constructor <;> norm_num⟩⟩ + +def denseTime : ℕ → HalfTime := TopologicalSpace.denseSeq HalfTime +lemma denseTime_dense : DenseRange denseTime := TopologicalSpace.denseRange_denseSeq HalfTime + +lemma denseTime_bound {g : ℝ → ℂ} (hg : Continuous g) {B : ℝ} + (hB : ∀ n, ‖g (denseTime n)‖ ≤ B) : ∀ t ∈ Icc (0:ℝ) 1, ‖g t‖ ≤ B := by + have hh : Ico (0:ℝ) 1 ⊆ {t | ‖g t‖ ≤ B} := by + intro t ht + exact denseTime_dense.induction_on (p := fun s : HalfTime => ‖g s.val‖ ≤ B) (⟨t,ht⟩ : HalfTime) + (isClosed_le (hg.comp continuous_subtype_val).norm continuous_const) hB + have hc := closure_minimal hh (isClosed_le hg.norm continuous_const) + rw [closure_Ico (by norm_num : (0:ℝ)≠1)] at hc + exact hc + +lemma exists_denseTime_near_path (f : L2) (hf : Integrable (fourier f) volume) + (x : Plane) {ε : ℝ} (hε : 0 < ε) : + ∃ n : ℕ, ‖evolutionPath f hf x‖-ε < ‖evolution f x (denseTime n)‖ := by + by_contra! hh + have hpos : 0 ≤ ‖evolutionPath f hf x‖-ε := (norm_nonneg _).trans (hh 0) + have hbound := denseTime_bound ((continuous_evolution hf).comp + (continuous_const.prodMk continuous_id)) hh + have hn : ‖evolutionPath f hf x‖ ≤ ‖evolutionPath f hf x‖-ε := + (ContinuousMap.norm_le _ hpos).2 (fun t => hbound t.val t.property) + linarith + +lemma exists_measurable_near_time (f : L2) (hf : Integrable (fourier f) volume) + {ε : ℝ} (hε : 0 < ε) : + ∃ T : Plane → ℝ, Measurable T ∧ (∀ x, T x ∈ Ico 0 1) ∧ + ∀ x, ‖evolutionPath f hf x‖ ≤ ‖evolution f x (T x)‖+ε := by + classical + let h := fun x => exists_denseTime_near_path f hf x hε + let T := fun x => (denseTime (Nat.find (h x))).val + refine ⟨T,?_,fun x => (denseTime (Nat.find (h x))).property,?_⟩ + · exact Measurable.find (f := fun n (_ : Plane) => (denseTime n).val) + (fun n => measurable_const) (fun n => + measurableSet_lt ((continuous_evolutionPath f hf).norm.measurable.sub measurable_const) + (((continuous_evolution hf).comp (continuous_id.prodMk continuous_const)).norm.measurable)) h + · intro x + have hh := Nat.find_spec (h x) + dsimp [T] + linarith + +lemma localMaximalBound_of_shortTime {p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate (1/4) 4 p) : LocalMaximalBound := by + obtain ⟨C,hC,hbound⟩ := graph_evolution_norm_bound hp hshort + refine ⟨C,hC,?_⟩ + intro f hf hH x₀ + apply le_of_forall_pos_le_add + intro ε hε + obtain ⟨T,hT,ht,ha⟩ := exists_measurable_near_time f hf.integrable + (div_pos hε Real.pi_pos) + have hmono := integral_mono (integrableOn_evolutionPath_ball f hf.integrable x₀).norm + ((graph_evolution_norm_integrable f hf.integrable x₀ hT).add (integrable_const (ε/Real.pi))) ha + simp only [Pi.add_apply] at hmono + rw [integral_add (graph_evolution_norm_integrable f hf.integrable x₀ hT) + (integrable_const (ε/Real.pi)), integral_const] at hmono + have hm : (volume.restrict (Metric.ball x₀ 1)).real univ = Real.pi := by + simpa only [measureReal_def,Measure.restrict_apply_univ] using unit_ball_real x₀ + rw [hm,smul_eq_mul] at hmono + have hh := hbound f hf hH x₀ T hT (fun x _ => ht x) + have he : Real.pi*(ε/Real.pi)=ε := by field_simp + rw [he] at hmono + linarith + +lemma mainConclusion_of_shortTime {p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate (1/4) 4 p) {f : L2} (hf : InHThird f) : + MainConclusion f := mainConclusion_of_localMaximalBound + (localMaximalBound_of_shortTime hp hshort) hf + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/GraphTree.lean b/lean/OAI/Analysis/PlanarEndpoint/GraphTree.lean new file mode 100644 index 0000000000000000000000000000000000000000..5d8da9e8f3776732f20b41ca40627e0a3e6d8517 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/GraphTree.lean @@ -0,0 +1,181 @@ +import OAI.Analysis.PlanarEndpoint.DyadicGraph +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphEnergy +import OAI.Analysis.PlanarEndpoint.GraphLocalization +import OAI.Analysis.PlanarEndpoint.TimeSeparation +import OAI.Analysis.PlanarEndpoint.TimeTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology ContDiff BigOperators +namespace PlanarEndpoint + +instance volume_ball_isFiniteMeasure (x₀ : Plane) (r : ℝ) : + IsFiniteMeasure (volume.restrict (Metric.ball x₀ r)) := + isFiniteMeasure_restrict.mpr measure_ball_lt_top.ne + +lemma graph_node_energy_of_shortTime {c₀ C₀ p : ℝ} (hp : 2 < p) (hC₀ : 0 < C₀) + (hshort : ShortTimeWeakEstimate c₀ C₀ p) + (χ : Plane → ℂ) (hχ : ContDiff ℝ ∞ χ) (hc : HasCompactSupport χ) + (hann : ∀ ξ ∈ tsupport χ, c₀ ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀) + (B : ℝ) (hB : 0 ≤ B) (hχB : ∀ ξ, ‖χ ξ‖ ≤ B) : + ∃ C : ℝ, 0 < C ∧ ∀ j k : ℕ, k ≤ j → ∀ s : List Bool, s.length=j+k → + ∀ (x₀ : Plane) (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) + (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1), + let μ := volume.restrict (Metric.ball x₀ 1) + let χN := fun ξ : Plane => χ (((2:ℝ)^j)⁻¹ • ξ) + let hχN := scaled_cutoff_memLp χ hχ.continuous hc (by positivity : 0 < (2:ℝ)^j) + ‖(((2:ℝ)^j)^(-(1/3:ℝ))) • DyadicGraph.vector χN hχN μ T w hT hw hb s‖^2 ≤ + C*((((2:ℝ)^(-(1/6:ℝ)))^k)^2)*(DyadicGraph.massTree μ T hT).mass s ^(3/2-1/p) := by + obtain ⟨C,hC,hh⟩ := graph_interpolated_bound_of_shortTime hp hC₀ hshort χ hχ hc hann B hB hχB + refine ⟨C,hC,?_⟩ + intro j k hk s hs x₀ T w hT hw hb + dsimp only + let E := DyadicGraph.fiber T s ∩ Metric.ball x₀ 1 + have hE : MeasurableSet E := (DyadicGraph.fiber_measurable hT s).inter measurableSet_ball + have hν : (volume.restrict (Metric.ball x₀ 1)).restrict (DyadicGraph.fiber T s) = + volume.restrict E := Measure.restrict_restrict (DyadicGraph.fiber_measurable hT s) + let : IsFiniteMeasure (volume.restrict E) := isFiniteMeasure_restrict.mpr + ((measure_mono Set.inter_subset_right).trans_lt measure_ball_lt_top).ne + have hwidth : DyadicGraph.width s = (1/2:ℝ)^(j+k) := by rw [DyadicGraph.width, hs] + have htime : ∀ x ∈ E, T x ∈ Icc (DyadicGraph.left s) + (DyadicGraph.left s+DyadicGraph.width s) := fun x hx => ⟨hx.1.1,hx.1.2.le⟩ + have hbnd := hh j k hk x₀ (DyadicGraph.left s) (DyadicGraph.width s) + (DyadicGraph.width_pos s).le hwidth.le E hE Set.inter_subset_right T w hT hw hb htime + have hmass : (DyadicGraph.massTree (volume.restrict (Metric.ball x₀ 1)) T hT).mass s = + volume.real E := measureReal_restrict_apply (DyadicGraph.fiber_measurable hT s) + dsimp only [DyadicGraph.vector] + rw [graphLp_congr_measure _ _ hν T w hT hw hb, hmass] + exact hbnd + +def normalizedDyadicVector (χ : Plane → ℂ) (hχ : ContDiff ℝ ∞ χ) + (hc : HasCompactSupport χ) (j : ℕ) (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (s : List Bool) : L2 := + (((2:ℝ)^j)^(-(1/3:ℝ))) • DyadicGraph.vector (fun ξ => χ (((2:ℝ)^j)⁻¹ • ξ)) + (scaled_cutoff_memLp χ hχ.continuous hc (pow_pos (by norm_num) j)) μ T w hT hw hb s + +lemma graph_tree_levels_of_shortTime {c₀ C₀ p : ℝ} (hp : 2 < p) (hC₀ : 0 < C₀) + (hshort : ShortTimeWeakEstimate c₀ C₀ p) + (χ : Plane → ℂ) (hχ : ContDiff ℝ ∞ χ) (hc : HasCompactSupport χ) + (hann : ∀ ξ ∈ tsupport χ, c₀ ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀) + (B : ℝ) (hB : 0 ≤ B) (hχB : ∀ ξ, ‖χ ξ‖ ≤ B) : + ∃ C : ℝ, 0 < C ∧ ∀ (x₀ : Plane) (T : Plane → ℝ) (w : Plane → ℂ) + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1), + (∀ x ∈ Metric.ball x₀ 1, T x ∈ Ico 0 1) → + ∀ n : ℕ, + let μ := volume.restrict (Metric.ball x₀ 1) + (∑ j ∈ Finset.range n, ∑ s ∈ TimeTree.level j, + ‖normalizedDyadicVector χ hχ hc j μ T w hT hw hb s‖^2) ≤ C := by + obtain ⟨C,hC,hh⟩ := graph_node_energy_of_shortTime hp hC₀ hshort χ hχ hc hann B hB hχB + let α : ℝ := 3/2-1/p + let q : ℝ := (2:ℝ)^(-(1/6:ℝ)) + have hα : 1 < α := by + have hdiv : 1/p < (1:ℝ)/2 := (div_lt_div_iff₀ (by linarith) (by norm_num)).2 (by linarith) + dsimp only [α] + linarith + have hq : 0 ≤ q := Real.rpow_nonneg (by norm_num) _ + have hq1 : q < 1 := Real.rpow_lt_one_of_one_lt_of_neg (by norm_num) (by norm_num) + let A := C*(1-q)⁻¹*(Real.pi^α*(1-q)⁻¹*(1+q/((2:ℝ)^α-2))) + have hA : 0 ≤ A := by + have hd := TimeTree.MassTree.convexity_constant_pos hα + exact mul_nonneg (mul_nonneg hC.le (inv_nonneg.mpr (by linarith))) + (mul_nonneg (mul_nonneg (Real.rpow_nonneg Real.pi_nonneg _) (inv_nonneg.mpr (by linarith))) + (by positivity)) + refine ⟨A+1,by positivity,?_⟩ + intro x₀ T w hT hw hb ht n + dsimp only + let μ := volume.restrict (Metric.ball x₀ 1) + let m := DyadicGraph.massTree μ T hT + let G (j : ℕ) (s : List Bool) : L2 := + normalizedDyadicVector χ hχ hc j μ T w hT hw hb s + have hsplit (j : ℕ) (s : List Bool) : G j s = G j (false::s)+G j (true::s) := by + dsimp only [G, normalizedDyadicVector] + rw [DyadicGraph.vector_split, smul_add] + have hlight (s : List Bool) (k : ℕ) (hk : k < s.length) : + ‖G s.length (m.light (m.heavyPath s k))‖^2 ≤ + C*(q^(k+1))^2*m.mass (m.light (m.heavyPath s k))^α := by + apply hh s.length (k+1) (by omega) _ _ x₀ T w hT hw hb + rw [m.light_length, m.heavyPath_length] + omega + have hterminal (s : List Bool) : ‖G s.length (m.heavyPath s s.length)‖^2 ≤ + C*(q^s.length)^2*m.mass (m.heavyPath s s.length)^α := by + exact hh s.length s.length le_rfl _ (m.heavyPath_length s s.length) x₀ T w hT hw hb + have hroot : m.mass [] = Real.pi := by + rw [DyadicGraph.massTree_root μ T hT] + · simp [μ, measureReal_def, EuclideanSpace.volume_ball_fin_two, + ENNReal.toReal_ofReal Real.pi_nonneg] + · filter_upwards [ae_restrict_mem measurableSet_ball] with x hx + exact ht x hx + have hbound := m.common_tree_energy_sum_le G hsplit hα hq hq1 hC.le hlight hterminal n + rw [hroot] at hbound + exact hbound.trans (by dsimp only [A]; linarith) + +lemma norm_smul_sq_bound {V : Type*} [SeminormedAddCommGroup V] [NormedSpace ℝ V] + {ι : Type*} (s : Finset ι) (v : V) (f : ι → V) {a D E : ℝ} + (ha : 0 ≤ a) (ha1 : a ≤ 1) (hE : 0 ≤ E) + (h : ‖v‖^2 ≤ D*(∑ i ∈ s, ‖f i‖^2)+E) : + ‖a • v‖^2 ≤ D*(∑ i ∈ s, ‖a • f i‖^2)+E := by + have ha2 : a^2 ≤ 1 := by nlinarith + simp only [norm_smul, Real.norm_eq_abs, abs_of_nonneg ha, mul_pow] + simp_rw [← Finset.mul_sum] + have hh := mul_le_mul_of_nonneg_left h (sq_nonneg a) + have he := mul_le_mul_of_nonneg_right ha2 hE + nlinarith + +lemma graph_root_sum_of_shortTime {c₀ C₀ p : ℝ} (hc₀ : 0 < c₀) (hp : 2 < p) + (hC₀ : 0 < C₀) (hshort : ShortTimeWeakEstimate c₀ C₀ p) + (χ : Plane → ℂ) (hχ : ContDiff ℝ ∞ χ) (hc : HasCompactSupport χ) + (hann : ∀ ξ ∈ tsupport χ, c₀ ≤ ‖ξ‖ ∧ ‖ξ‖ ≤ C₀) + (B : ℝ) (hB : 0 ≤ B) (hχB : ∀ ξ, ‖χ ξ‖ ≤ B) : + ∃ C : ℝ, 0 < C ∧ ∀ (x₀ : Plane) (T : Plane → ℝ) (w : Plane → ℂ) + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1), + (∀ x ∈ Metric.ball x₀ 1, T x ∈ Ico 0 1) → ∀ n : ℕ, + (∑ j ∈ Finset.range n, ‖normalizedDyadicVector χ hχ hc j + (volume.restrict (Metric.ball x₀ 1)) T w hT hw hb []‖^2) ≤ C := by + obtain ⟨A,hA,hlevels⟩ := graph_tree_levels_of_shortTime hp hC₀ hshort χ hχ hc hann B hB hχB + obtain ⟨C,D,hC,hD,hsep⟩ := time_separation_uniform hc₀ hχ hc (fun ξ hξ => (hann ξ hξ).1) + refine ⟨D*A+2*C*Real.pi^2+1, by positivity, ?_⟩ + intro x₀ T w hT hw hb ht n + let μ := volume.restrict (Metric.ball x₀ 1) + let G (j : ℕ) (s : List Bool) : L2 := normalizedDyadicVector χ hχ hc j μ T w hT hw hb s + have hmass : (DyadicGraph.massTree μ T hT).mass [] = Real.pi := by + rw [DyadicGraph.massTree_root μ T hT] + · simp [μ, measureReal_def, EuclideanSpace.volume_ball_fin_two, + ENNReal.toReal_ofReal Real.pi_nonneg] + · filter_upwards [ae_restrict_mem measurableSet_ball] with x hx + exact ht x hx + have hs (j : ℕ) : ‖G j []‖^2 ≤ D*(∑ s ∈ TimeTree.level j, ‖G j s‖^2) + + C/((2:ℝ)^j)^2*Real.pi^2 := by + have hh := hsep j μ T w hT hw hb x₀ (by + filter_upwards [ae_restrict_mem measurableSet_ball] with x hx + exact (by simpa only [Metric.mem_ball, dist_eq_norm] using hx : ‖x-x₀‖ < 1).le) + rw [hmass] at hh + exact norm_smul_sq_bound _ _ _ (Real.rpow_nonneg (by positivity) _) + (Real.rpow_le_one_of_one_le_of_nonpos (one_le_pow₀ (by norm_num)) (by norm_num)) + (by positivity) hh + have heq (j : ℕ) : C/((2:ℝ)^j)^2*Real.pi^2 = C*Real.pi^2*(1/4:ℝ)^j := by + rw [← pow_mul, mul_comm j 2, pow_mul, div_pow] + norm_num + ring + have hgeom : ∑ j ∈ Finset.range n, (1/4:ℝ)^j ≤ 2 := by + exact (Finset.sum_le_sum (fun j _ => pow_le_pow_left₀ (by norm_num) (by norm_num) j)).trans + (sum_geometric_two_le n) + have he : (∑ j ∈ Finset.range n, C/((2:ℝ)^j)^2*Real.pi^2) ≤ 2*C*Real.pi^2 := by + simp_rw [heq] + rw [← Finset.mul_sum] + nlinarith [mul_le_mul_of_nonneg_left hgeom (mul_nonneg hC (sq_nonneg Real.pi))] + have hh := Finset.sum_le_sum (fun j (_ : j ∈ Finset.range n) => hs j) + rw [Finset.sum_add_distrib, ← Finset.mul_sum] at hh + have hl := mul_le_mul_of_nonneg_left (hlevels x₀ T w hT hw hb ht n) hD + exact hh.trans ((add_le_add hl he).trans (by linarith)) + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Heat.lean b/lean/OAI/Analysis/PlanarEndpoint/Heat.lean new file mode 100644 index 0000000000000000000000000000000000000000..63b88ca0fefc0215e74673799868006c27419759 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Heat.lean @@ -0,0 +1,559 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set Metric +open scoped Topology ENNReal NNReal +namespace PlanarEndpoint + +lemma gaussianWeight_superlevel {a t : ℝ} (ha : 0 < a) (ht : 0 < t) (_ht1 : t < 1) : + {z : Plane | t < gaussianWeight a z} = ball 0 (Real.sqrt (-Real.log t / a)) := by + ext z + simp only [mem_ofPred_eq, mem_ball, dist_zero_right] + rw [Real.lt_sqrt (norm_nonneg z), lt_div_iff₀ ha] + unfold gaussianWeight + rw [← Real.log_lt_iff_lt_exp ht] + constructor <;> intro h <;> nlinarith + +lemma gaussianWeight_superlevel_empty {a t : ℝ} (ha : 0 ≤ a) (ht : 1 ≤ t) : + {z : Plane | t < gaussianWeight a z} = ∅ := by + apply eq_empty_iff_forall_notMem.mpr + intro z hz + exact (not_lt_of_ge (le_trans (gaussianWeight_le_one ha z) ht)) hz + +lemma lintegral_gaussianWeight_le_of_ball (μ ν : Measure Plane) (C : ℝ≥0) + (hball : ∀ r : ℝ, 0 < r → μ (ball 0 r) ≤ (C : ℝ≥0∞) * ν (ball 0 r)) + {a : ℝ} (ha : 0 < a) : + ∫⁻ z, ENNReal.ofReal (gaussianWeight a z) ∂μ ≤ + (C : ℝ≥0∞) * ∫⁻ z, ENNReal.ofReal (gaussianWeight a z) ∂ν := by + have hc : Continuous (gaussianWeight a) := by unfold gaussianWeight; fun_prop + rw [lintegral_eq_lintegral_meas_lt μ + (Eventually.of_forall fun z => (gaussianWeight_pos a z).le) hc.aemeasurable, + lintegral_eq_lintegral_meas_lt ν + (Eventually.of_forall fun z => (gaussianWeight_pos a z).le) hc.aemeasurable, + ← lintegral_const_mul' _ _ ENNReal.coe_ne_top] + apply lintegral_mono_ae + filter_upwards [ae_restrict_mem measurableSet_Ioi] with t ht + by_cases ht1 : t < 1 + · rw [gaussianWeight_superlevel ha ht ht1] + apply hball + apply Real.sqrt_pos.2 + exact div_pos (neg_pos.mpr (Real.log_neg ht ht1)) ha + · rw [gaussianWeight_superlevel_empty ha.le (le_of_not_gt ht1)] + simp + +def heatKernel (a : ℝ) (z : Plane) : ℝ := + (4 * Real.pi * a)⁻¹ * gaussianWeight (4*a)⁻¹ z + +lemma heatKernel_nonneg {a : ℝ} (ha : 0 ≤ a) (z : Plane) : 0 ≤ heatKernel a z := by + unfold heatKernel + exact mul_nonneg (inv_nonneg.mpr (by positivity)) (gaussianWeight_pos _ _).le + +lemma integral_gaussianWeight {a : ℝ} (ha : 0 < a) : + ∫ z : Plane, gaussianWeight a z = Real.pi / a := by + simpa [gaussianWeight, Plane, finrank_euclideanSpace, Real.rpow_one] using + (GaussianFourier.integral_rexp_neg_mul_sq_norm (V := Plane) ha) + +lemma integral_heatKernel {a : ℝ} (ha : 0 < a) : ∫ z : Plane, heatKernel a z = 1 := by + simp only [heatKernel, integral_const_mul] + rw [integral_gaussianWeight (inv_pos.mpr (by positivity))] + field_simp [ha.ne', Real.pi_ne_zero] + +lemma integrable_gaussianWeight {a : ℝ} (ha : 0 < a) : + Integrable (gaussianWeight a) volume := by + apply Integrable.of_integral_ne_zero + rw [integral_gaussianWeight ha] + exact div_ne_zero Real.pi_ne_zero ha.ne' + +lemma continuous_heatKernel (a : ℝ) : Continuous (heatKernel a) := by + unfold heatKernel gaussianWeight + fun_prop + +lemma integrable_heatKernel {a : ℝ} (ha : 0 < a) : Integrable (heatKernel a) volume := by + apply Integrable.of_integral_ne_zero + rw [integral_heatKernel ha] + norm_num + +lemma lintegral_heatKernel {a : ℝ} (ha : 0 < a) : + ∫⁻ z : Plane, ENNReal.ofReal (heatKernel a z) = 1 := by + rw [← ofReal_integral_eq_lintegral_ofReal (integrable_heatKernel ha) + (Eventually.of_forall (heatKernel_nonneg ha.le)), integral_heatKernel ha] + simp + +lemma lintegral_heatKernel_le_of_ball (μ : Measure Plane) (C : ℝ≥0) + (hball : ∀ r : ℝ, 0 < r → μ (ball 0 r) ≤ (C : ℝ≥0∞) * volume (ball (0 : Plane) r)) + {a : ℝ} (ha : 0 < a) : + ∫⁻ z, ENNReal.ofReal (heatKernel a z) ∂μ ≤ C := by + have hp : 0 ≤ (4 * Real.pi * a)⁻¹ := inv_nonneg.mpr (by positivity) + have hg (ν : Measure Plane) : + ∫⁻ z, ENNReal.ofReal (heatKernel a z) ∂ν = + ENNReal.ofReal ((4 * Real.pi * a)⁻¹) * + ∫⁻ z, ENNReal.ofReal (gaussianWeight (4*a)⁻¹ z) ∂ν := by + simp only [heatKernel, ENNReal.ofReal_mul hp] + exact lintegral_const_mul' _ _ ENNReal.ofReal_ne_top + calc + _ ≤ ENNReal.ofReal ((4 * Real.pi * a)⁻¹) * + ((C : ℝ≥0∞) * ∫⁻ z, ENNReal.ofReal (gaussianWeight (4*a)⁻¹ z)) := by + rw [hg] + exact mul_le_mul_right (lintegral_gaussianWeight_le_of_ball μ volume C hball + (inv_pos.mpr (by positivity))) _ + _ = (C : ℝ≥0∞) * ∫⁻ z, ENNReal.ofReal (heatKernel a z) := by rw [hg]; ring + _ = C := by rw [lintegral_heatKernel ha, mul_one] + +lemma heat_mul_le_of_ball {h : Plane → ℝ} (hm : AEStronglyMeasurable h volume) + (hn : ∀ z, 0 ≤ h z) (C : ℝ≥0) + (hball : ∀ r : ℝ, 0 < r → + ∫⁻ z in ball (0 : Plane) r, ENNReal.ofReal (h z) ≤ + (C : ℝ≥0∞) * volume (ball (0 : Plane) r)) + {a : ℝ} (ha : 0 < a) : + Integrable (fun z => heatKernel a z * h z) volume ∧ + ∫ z, heatKernel a z * h z ≤ C := by + let μ := volume.withDensity (fun z => ENNReal.ofReal (h z)) + have hb : ∀ r : ℝ, 0 < r → μ (ball 0 r) ≤ + (C : ℝ≥0∞) * volume (ball (0 : Plane) r) := by + intro r hr + simpa only [μ, withDensity_apply _ measurableSet_ball] using hball r hr + have hlin : ∫⁻ z, ENNReal.ofReal (heatKernel a z * h z) ≤ C := by + have hh := lintegral_heatKernel_le_of_ball μ C hb ha + dsimp only [μ] at hh + have he := lintegral_withDensity_eq_lintegral_mul₀ + (ENNReal.continuous_ofReal.measurable.comp_aemeasurable hm.aemeasurable) + (ENNReal.continuous_ofReal.comp (continuous_heatKernel a)).aemeasurable + simp only [Function.comp_def, Pi.mul_apply] at he + rw [he] at hh + have heq (z : Plane) : ENNReal.ofReal (heatKernel a z * h z) = + ENNReal.ofReal (h z) * ENNReal.ofReal (heatKernel a z) := by + rw [ENNReal.ofReal_mul (heatKernel_nonneg ha.le z), mul_comm] + simpa only [heq] using hh + have hnon : 0 ≤ᵐ[volume] (fun z => heatKernel a z * h z) := + Eventually.of_forall fun z => mul_nonneg (heatKernel_nonneg ha.le z) (hn z) + have hi : Integrable (fun z => heatKernel a z * h z) volume := + ⟨(continuous_heatKernel a).aestronglyMeasurable.mul hm, + (hasFiniteIntegral_iff_ofReal hnon).2 (hlin.trans_lt ENNReal.coe_lt_top)⟩ + refine ⟨hi, ?_⟩ + rw [integral_eq_lintegral_of_nonneg_ae hnon hi.aestronglyMeasurable] + exact ENNReal.toReal_mono ENNReal.coe_ne_top hlin + +lemma cutoff_ball_mass {h : Plane → ℝ} (hn : ∀ z, 0 ≤ h z) + (C : ℝ≥0) {ρ : ℝ} (hρ : 0 < ρ) + (hball : ∀ r : ℝ, 0 < r → r ≤ ρ → + ∫⁻ z in ball (0 : Plane) r, ENNReal.ofReal (h z) ≤ + (C : ℝ≥0∞) * volume (ball (0 : Plane) r)) + (r : ℝ) (hr : 0 < r) : + ∫⁻ z in ball (0 : Plane) r, + ENNReal.ofReal ((ball (0 : Plane) ρ).indicator h z) ≤ + (C : ℝ≥0∞) * volume (ball (0 : Plane) r) := by + by_cases hrs : r ≤ ρ + · apply le_trans _ (hball r hr hrs) + apply lintegral_mono + intro z + apply ENNReal.ofReal_le_ofReal + by_cases hz : z ∈ ball (0 : Plane) ρ <;> simp [hz, hn z] + · have hle : ρ ≤ r := le_of_not_ge hrs + calc + _ ≤ ∫⁻ z, ENNReal.ofReal ((ball (0 : Plane) ρ).indicator h z) := + setLIntegral_le_lintegral _ _ + _ = ∫⁻ z in ball (0 : Plane) ρ, ENNReal.ofReal (h z) := by + have he : (fun z => ENNReal.ofReal ((ball (0 : Plane) ρ).indicator h z)) = + (ball (0 : Plane) ρ).indicator (fun z => ENNReal.ofReal (h z)) := by + ext z + by_cases hz : z ∈ ball (0 : Plane) ρ <;> simp [hz] + rw [he, lintegral_indicator measurableSet_ball] + _ ≤ (C : ℝ≥0∞) * volume (ball (0 : Plane) ρ) := hball ρ hρ le_rfl + _ ≤ (C : ℝ≥0∞) * volume (ball (0 : Plane) r) := by + exact mul_le_mul_right (measure_mono (ball_subset_ball hle)) _ + +lemma heat_mul_cutoff_le {h : Plane → ℝ} (hm : AEStronglyMeasurable h volume) + (hn : ∀ z, 0 ≤ h z) (C : ℝ≥0) {ρ : ℝ} (hρ : 0 < ρ) + (hball : ∀ r : ℝ, 0 < r → r ≤ ρ → + ∫⁻ z in ball (0 : Plane) r, ENNReal.ofReal (h z) ≤ + (C : ℝ≥0∞) * volume (ball (0 : Plane) r)) + {a : ℝ} (ha : 0 < a) : + Integrable (fun z => heatKernel a z * (ball (0 : Plane) ρ).indicator h z) volume ∧ + ∫ z, heatKernel a z * (ball (0 : Plane) ρ).indicator h z ≤ C := by + exact heat_mul_le_of_ball (hm.indicator measurableSet_ball) + (fun z => indicator_nonneg (fun y _ => hn y) z) C + (cutoff_ball_mass hn C hρ hball) ha + +def heatTailCoefficient (a ρ : ℝ) : ℝ := + (4 * Real.pi * a)⁻¹ * Real.exp (-(ρ ^ 2) / (8*a)) + +lemma heatTailCoefficient_nonneg {a : ℝ} (ha : 0 ≤ a) (ρ : ℝ) : + 0 ≤ heatTailCoefficient a ρ := by + unfold heatTailCoefficient + positivity + +lemma heatKernel_le_tail {a b ρ : ℝ} (ha : 0 < a) (hρ : 0 ≤ ρ) + (hab : 8 * a * b ≤ 1) (z : Plane) (hz : ρ ≤ ‖z‖) : + heatKernel a z ≤ heatTailCoefficient a ρ * gaussianWeight b z := by + have hc : b ≤ (8*a)⁻¹ := by + rw [inv_eq_one_div, le_div_iff₀ (by positivity : 0 < 8*a)] + nlinarith [hab] + have hn : ρ^2 ≤ ‖z‖^2 := by nlinarith [norm_nonneg z] + have hh : -(4*a)⁻¹ * ‖z‖^2 ≤ -(ρ^2) / (8*a) + -b * ‖z‖^2 := by + have h1 := mul_le_mul_of_nonpos_left hn (neg_nonpos.mpr + (inv_nonneg.mpr (by positivity : 0 ≤ 8*a))) + have h2 := mul_le_mul_of_nonneg_right hc (sq_nonneg ‖z‖) + have he : (4*a)⁻¹ = 2*(8*a)⁻¹ := by field_simp; ring + rw [he] + rw [div_eq_mul_inv] + nlinarith [h1, h2] + unfold heatKernel heatTailCoefficient gaussianWeight + rw [mul_assoc _ (Real.exp _) (Real.exp _), ← Real.exp_add] + exact mul_le_mul_of_nonneg_left (Real.exp_le_exp.mpr hh) (by positivity) + +lemma heatTailCoefficient_tendsto {ρ : ℝ} (hρ : 0 < ρ) : + Tendsto (fun a : ℝ => heatTailCoefficient a ρ) (𝓝[>] 0) (𝓝 0) := by + have hu : Tendsto (fun a : ℝ => (ρ^2/8) * a⁻¹) (𝓝[>] 0) atTop := + tendsto_inv_nhdsGT_zero.const_mul_atTop (by positivity) + have hh := ((Real.tendsto_pow_mul_exp_neg_atTop_nhds_zero 1).comp hu).const_mul + (2 / (Real.pi * ρ^2)) + simp only [pow_one, mul_zero] at hh + apply hh.congr' + filter_upwards [self_mem_nhdsWithin] with a ha + have han : a ≠ 0 := ne_of_gt ha + dsimp only [Function.comp_def] + unfold heatTailCoefficient + have he : -(ρ^2) / (8*a) = -((ρ^2/8) * a⁻¹) := by field_simp + rw [he] + field_simp + ring + +lemma heat_mul_tail_bound {h : Plane → ℝ} (hm : AEStronglyMeasurable h volume) + (hn : ∀ z, 0 ≤ h z) {b ρ a : ℝ} (hρ : 0 ≤ ρ) (ha : 0 < a) + (hab : 8 * a * b ≤ 1) (hi : Integrable (fun z => gaussianWeight b z * h z) volume) : + IntegrableOn (fun z => heatKernel a z * h z) (ball (0 : Plane) ρ)ᶜ volume ∧ + ∫ z in (ball (0 : Plane) ρ)ᶜ, heatKernel a z * h z ≤ + heatTailCoefficient a ρ * ∫ z, gaussianWeight b z * h z := by + have maj : IntegrableOn (fun z => heatTailCoefficient a ρ * (gaussianWeight b z * h z)) + (ball (0 : Plane) ρ)ᶜ volume := + (hi.const_mul (heatTailCoefficient a ρ)).integrableOn + have hbound : ∀ᵐ z ∂volume.restrict (ball (0 : Plane) ρ)ᶜ, + ‖heatKernel a z * h z‖ ≤ heatTailCoefficient a ρ * (gaussianWeight b z * h z) := by + filter_upwards [ae_restrict_mem measurableSet_ball.compl] with z hz + have hz' : ρ ≤ ‖z‖ := by simpa [mem_ball, dist_zero_right, not_lt] using hz + rw [Real.norm_eq_abs, abs_of_nonneg (mul_nonneg (heatKernel_nonneg ha.le z) (hn z))] + simpa only [mul_assoc] using mul_le_mul_of_nonneg_right + (heatKernel_le_tail ha hρ hab z hz') (hn z) + have hInt : IntegrableOn (fun z => heatKernel a z * h z) (ball (0 : Plane) ρ)ᶜ volume := + maj.mono' ((continuous_heatKernel a).aestronglyMeasurable.mul hm).restrict hbound + refine ⟨hInt, ?_⟩ + calc + _ ≤ ∫ z in (ball (0 : Plane) ρ)ᶜ, + heatTailCoefficient a ρ * (gaussianWeight b z * h z) := by + apply integral_mono_ae hInt maj + filter_upwards [hbound] with z hz using (le_abs_self _).trans hz + _ = heatTailCoefficient a ρ * ∫ z in (ball (0 : Plane) ρ)ᶜ, + gaussianWeight b z * h z := by rw [integral_const_mul] + _ ≤ heatTailCoefficient a ρ * ∫ z, gaussianWeight b z * h z := by + apply mul_le_mul_of_nonneg_left _ (heatTailCoefficient_nonneg ha.le ρ) + exact setIntegral_le_integral hi (Eventually.of_forall fun z => + mul_nonneg (gaussianWeight_pos b z).le (hn z)) + +lemma tendsto_heat_mul_tail {h : Plane → ℝ} (hm : AEStronglyMeasurable h volume) + (hn : ∀ z, 0 ≤ h z) {b ρ : ℝ} (hb : 0 < b) (hρ : 0 < ρ) + (hi : Integrable (fun z => gaussianWeight b z * h z) volume) : + Tendsto (fun a : ℝ => ∫ z in (ball (0 : Plane) ρ)ᶜ, heatKernel a z * h z) + (𝓝[>] 0) (𝓝 0) := by + have hc := (heatTailCoefficient_tendsto hρ).mul_const + (∫ z, gaussianWeight b z * h z) + rw [zero_mul] at hc + refine squeeze_zero' ?_ ?_ hc + · filter_upwards [self_mem_nhdsWithin] with a ha + exact integral_nonneg fun z => mul_nonneg (heatKernel_nonneg (le_of_lt ha) z) (hn z) + · have he : ∀ᶠ a : ℝ in 𝓝[>] 0, a < (8*b)⁻¹ := + (eventually_lt_nhds (inv_pos.mpr (by positivity : 0 < 8*b))).filter_mono nhdsWithin_le_nhds + filter_upwards [self_mem_nhdsWithin, he] with a ha hab + apply (heat_mul_tail_bound hm hn hρ.le ha _ hi).2 + rw [inv_eq_one_div, lt_div_iff₀ (by positivity : 0 < 8*b)] at hab + nlinarith + +lemma heat_mul_cutoff_eq (h : Plane → ℝ) (a ρ : ℝ) : + (fun z => heatKernel a z * (ball (0 : Plane) ρ).indicator h z) = + (ball (0 : Plane) ρ).indicator (fun z => heatKernel a z * h z) := by + ext z + by_cases hz : z ∈ ball (0 : Plane) ρ <;> simp [hz] + +lemma tendsto_heat_mul_zero_of_small_balls {h : Plane → ℝ} + (hm : AEStronglyMeasurable h volume) (hn : ∀ z, 0 ≤ h z) + {b : ℝ} (hb : 0 < b) (hi : Integrable (fun z => gaussianWeight b z * h z) volume) + (hsmall : ∀ C : ℝ≥0, 0 < C → ∃ ρ : ℝ, 0 < ρ ∧ + ∀ r : ℝ, 0 < r → r ≤ ρ → + ∫⁻ z in ball (0 : Plane) r, ENNReal.ofReal (h z) ≤ + (C : ℝ≥0∞) * volume (ball (0 : Plane) r)) : + Tendsto (fun a : ℝ => ∫ z, heatKernel a z * h z) (𝓝[>] 0) (𝓝 0) := by + apply Metric.tendsto_nhds.2 + intro ε hε + let C : ℝ≥0 := ⟨ε/2, (half_pos hε).le⟩ + obtain ⟨ρ, hρ, hball⟩ := hsmall C (half_pos hε) + have htail := tendsto_heat_mul_tail hm hn hb hρ hi + have htail' : ∀ᶠ a : ℝ in 𝓝[>] 0, + ∫ z in (ball (0 : Plane) ρ)ᶜ, heatKernel a z * h z < ε/2 := + htail.eventually (eventually_lt_nhds (half_pos hε)) + have he : ∀ᶠ a : ℝ in 𝓝[>] 0, a < (8*b)⁻¹ := + (eventually_lt_nhds (inv_pos.mpr (by positivity : 0 < 8*b))).filter_mono nhdsWithin_le_nhds + filter_upwards [self_mem_nhdsWithin, he, htail'] with a ha hab htaila + have hab' : 8*a*b ≤ 1 := by + rw [inv_eq_one_div, lt_div_iff₀ (by positivity : 0 < 8*b)] at hab + nlinarith + obtain ⟨hloc, hlocBound⟩ := heat_mul_cutoff_le hm hn C hρ hball ha + rw [heat_mul_cutoff_eq h a ρ] at hloc hlocBound + rw [integral_indicator measurableSet_ball] at hlocBound + have hloc' := (integrable_indicator_iff measurableSet_ball).mp hloc + have hfar := (heat_mul_tail_bound hm hn hρ.le ha hab' hi).1 + have hiAll : Integrable (fun z => heatKernel a z * h z) volume := by + have hh := hloc'.union hfar + simpa only [union_compl_self, integrableOn_univ] using hh + rw [Real.dist_eq, sub_zero, abs_of_nonneg (integral_nonneg + (fun z => mul_nonneg (heatKernel_nonneg (le_of_lt ha) z) (hn z))), + ← integral_add_compl (s := ball (0 : Plane) ρ) measurableSet_ball hiAll] + change ∫ z in ball (0 : Plane) ρ, heatKernel a z * h z ≤ ε/2 at hlocBound + linarith + +lemma small_ball_mass_of_tendsto_average {h : Plane → ℝ} + (hloc : LocallyIntegrable h volume) (hn : ∀ z, 0 ≤ h z) + (hlim : Tendsto (fun r : ℝ => (Real.pi*r^2)⁻¹ * ∫ z in ball (0 : Plane) r, h z) + (𝓝[>] 0) (𝓝 0)) (C : ℝ≥0) (hC : 0 < C) : + ∃ ρ : ℝ, 0 < ρ ∧ ∀ r : ℝ, 0 < r → r ≤ ρ → + ∫⁻ z in ball (0 : Plane) r, ENNReal.ofReal (h z) ≤ + (C : ℝ≥0∞) * volume (ball (0 : Plane) r) := by + have he : ∀ᶠ r : ℝ in 𝓝[>] 0, + (Real.pi*r^2)⁻¹ * (∫ z in ball (0 : Plane) r, h z) < (C : ℝ) := + hlim.eventually (eventually_lt_nhds hC) + obtain ⟨ρ, hρ, hr⟩ := mem_nhdsGT_iff_exists_Ioc_subset.mp he + refine ⟨ρ, hρ, fun r hr0 hrr => ?_⟩ + have hr' : (Real.pi*r^2)⁻¹ * (∫ z in ball (0 : Plane) r, h z) < (C : ℝ) := + hr ⟨hr0, hrr⟩ + have hbound := hr'.le + have hrpos : 0 < Real.pi * r^2 := by positivity + have hreal : (∫ z in ball (0 : Plane) r, h z) ≤ (C : ℝ) * (Real.pi*r^2) := by + exact (inv_mul_le_iff₀' hrpos).mp hbound + have hi := (hloc.integrableOn_isCompact (isCompact_closedBall (0 : Plane) r)).mono_set + ball_subset_closedBall + rw [← ofReal_integral_eq_lintegral_ofReal hi (Eventually.of_forall hn)] + have hv : (C : ℝ≥0∞) * volume (ball (0 : Plane) r) = + ENNReal.ofReal ((C : ℝ) * (Real.pi*r^2)) := by + rw [EuclideanSpace.volume_ball_fin_two] + rw [ENNReal.ofReal_mul C.coe_nonneg, ENNReal.ofReal_mul Real.pi_nonneg, + ENNReal.ofReal_pow hr0.le] + simp only [ENNReal.ofReal_coe_nnreal] + ring + rw [hv] + exact ENNReal.ofReal_le_ofReal hreal + +lemma tendsto_heat_mul_zero_of_lebesgue {h : Plane → ℝ} + (hm : AEStronglyMeasurable h volume) (hloc : LocallyIntegrable h volume) + (hn : ∀ z, 0 ≤ h z) {b : ℝ} (hb : 0 < b) + (hi : Integrable (fun z => gaussianWeight b z * h z) volume) + (hlim : Tendsto (fun r : ℝ => (Real.pi*r^2)⁻¹ * ∫ z in ball (0 : Plane) r, h z) + (𝓝[>] 0) (𝓝 0)) : + Tendsto (fun a : ℝ => ∫ z, heatKernel a z * h z) (𝓝[>] 0) (𝓝 0) := + tendsto_heat_mul_zero_of_small_balls hm hn hb hi + (small_ball_mass_of_tendsto_average hloc hn hlim) + +lemma gaussianWeight_lower_on_unit_ball {b : ℝ} (hb : 0 ≤ b) (x y : Plane) + (hx : x ∈ ball y 1) : + Real.exp (-b) * gaussianWeight b y ≤ gaussianWeight (b/2) x := by + have hx' : dist x y < 1 := hx + have hn : ‖x‖ ≤ ‖y‖ + 1 := by + calc + ‖x‖ = ‖(x-y)+y‖ := by congr 1; abel + _ ≤ ‖x-y‖ + ‖y‖ := norm_add_le _ _ + _ ≤ ‖y‖ + 1 := by rw [← dist_eq_norm]; linarith + have hs : ‖x‖^2 ≤ 2*‖y‖^2 + 2 := by + have hxy : ‖x‖^2 ≤ (‖y‖+1)^2 := by + nlinarith [norm_nonneg x, norm_nonneg y] + nlinarith [sq_nonneg (‖y‖-1)] + unfold gaussianWeight + rw [← Real.exp_add, Real.exp_le_exp] + nlinarith [mul_le_mul_of_nonneg_left hs hb] + +lemma gaussianWeight_lintegral_unit_ball_lower {b : ℝ} (hb : 0 ≤ b) (y : Plane) : + ENNReal.ofReal (Real.pi * Real.exp (-b)) * ENNReal.ofReal (gaussianWeight b y) ≤ + ∫⁻ x in ball y 1, ENNReal.ofReal (gaussianWeight (b/2) x) := by + calc + _ = ∫⁻ x in ball y 1, ENNReal.ofReal (Real.exp (-b) * gaussianWeight b y) := by + rw [lintegral_const, Measure.restrict_apply_univ, + EuclideanSpace.volume_ball_fin_two] + simp only [ENNReal.ofReal_one, one_pow, one_mul, + ENNReal.ofReal_mul Real.pi_nonneg, ENNReal.ofReal_mul (Real.exp_pos _).le] + ring + _ ≤ _ := by + apply lintegral_mono_ae + filter_upwards [ae_restrict_mem measurableSet_ball] with x hx + exact ENNReal.ofReal_le_ofReal (gaussianWeight_lower_on_unit_ball hb x y hx) + +lemma lintegral_gaussian_mul_lt_top_of_unit_ball_mass + {H : Plane → ℝ≥0∞} (hH : AEMeasurable H volume) (A : ℝ≥0) + (hball : ∀ x : Plane, ∫⁻ y in ball x 1, H y ≤ A) {b : ℝ} (hb : 0 < b) : + ∫⁻ y, ENNReal.ofReal (gaussianWeight b y) * H y < ⊤ := by + let G : Plane → ℝ≥0∞ := fun x => ENNReal.ofReal (gaussianWeight (b/2) x) + have hG : Measurable G := by dsimp [G, gaussianWeight]; fun_prop + let F : Plane → Plane → ℝ≥0∞ := fun x y => G x * (ball x 1).indicator H y + have hF : AEMeasurable (Function.uncurry F) (volume.prod volume) := by + have hs : MeasurableSet {p : Plane × Plane | dist p.2 p.1 < 1} := + measurableSet_lt (continuous_snd.dist continuous_fst).measurable measurable_const + have hh : AEMeasurable (fun p : Plane × Plane => G p.1 * + {p : Plane × Plane | dist p.2 p.1 < 1}.indicator (fun p => H p.2) p) + (volume.prod volume) := + (hG.comp measurable_fst).aemeasurable.mul (hH.comp_snd.indicator hs) + convert hh using 1 + ext p + by_cases hp : dist p.2 p.1 < 1 <;> simp [F, Function.uncurry_def, mem_ball, hp] + have hleft (x : Plane) : ∫⁻ y, F x y = G x * ∫⁻ y in ball x 1, H y := by + dsimp only [F] + rw [lintegral_const_mul' _ _ (by exact ENNReal.ofReal_ne_top), + lintegral_indicator measurableSet_ball] + have hright (y : Plane) : ∫⁻ x, F x y = (∫⁻ x in ball y 1, G x) * H y := by + have he : (fun x => F x y) = (ball y 1).indicator (fun x => G x * H y) := by + ext x + by_cases hx : dist x y < 1 <;> simp [F, mem_ball, dist_comm y x, hx] + rw [he, lintegral_indicator measurableSet_ball, lintegral_mul_const _ hG] + have hswap := lintegral_lintegral_swap hF + simp only [hleft, hright] at hswap + have hupper : ∫⁻ y, (∫⁻ x in ball y 1, G x) * H y ≤ + (∫⁻ x, G x) * (A : ℝ≥0∞) := by + rw [← hswap, ← lintegral_mul_const' _ _ ENNReal.coe_ne_top] + exact lintegral_mono fun x => mul_le_mul_right (hball x) _ + let C : ℝ≥0∞ := ENNReal.ofReal (Real.pi * Real.exp (-b)) + have hC : C ≠ 0 := by dsimp [C]; positivity + have hClt : C ≠ ⊤ := ENNReal.ofReal_ne_top + have hlower : C * ∫⁻ y, ENNReal.ofReal (gaussianWeight b y) * H y ≤ + ∫⁻ y, (∫⁻ x in ball y 1, G x) * H y := by + rw [← lintegral_const_mul' _ _ hClt] + apply lintegral_mono + intro y + dsimp only + rw [← mul_assoc] + exact mul_le_mul_left (gaussianWeight_lintegral_unit_ball_lower hb.le y) _ + have hgfin : ∫⁻ x, G x < ⊤ := by + dsimp only [G] + rw [← ofReal_integral_eq_lintegral_ofReal (integrable_gaussianWeight (half_pos hb)) + (Eventually.of_forall fun x => (gaussianWeight_pos _ x).le)] + exact ENNReal.ofReal_lt_top + have hfin := hlower.trans_lt (hupper.trans_lt (ENNReal.mul_lt_top hgfin ENNReal.coe_lt_top)) + exact ENNReal.lt_top_of_mul_ne_top_right hfin.ne hC + +lemma integrable_gaussian_mul_of_unit_ball_mass {h : Plane → ℝ} + (hloc : LocallyIntegrable h volume) (hn : ∀ z, 0 ≤ h z) (A : ℝ≥0) + (hball : ∀ x : Plane, ∫ y in ball x 1, h y ≤ A) {b : ℝ} (hb : 0 < b) : + Integrable (fun z => gaussianWeight b z * h z) volume := by + have hm := hloc.aestronglyMeasurable + have hb' (x : Plane) : ∫⁻ y in ball x 1, ENNReal.ofReal (h y) ≤ A := by + have hi := (hloc.integrableOn_isCompact (isCompact_closedBall x 1)).mono_set ball_subset_closedBall + rw [← ofReal_integral_eq_lintegral_ofReal hi (Eventually.of_forall hn)] + simpa only [ENNReal.ofReal_coe_nnreal] using ENNReal.ofReal_le_ofReal (hball x) + have hh := lintegral_gaussian_mul_lt_top_of_unit_ball_mass + (ENNReal.continuous_ofReal.measurable.comp_aemeasurable hm.aemeasurable) A hb' hb + refine ⟨(by unfold gaussianWeight; fun_prop : Continuous (gaussianWeight b)).aestronglyMeasurable.mul hm, ?_⟩ + rw [hasFiniteIntegral_iff_ofReal (Eventually.of_forall fun z => + mul_nonneg (gaussianWeight_pos b z).le (hn z))] + simpa only [Function.comp_def, ENNReal.ofReal_mul (gaussianWeight_pos b _).le] using hh + +lemma reflect_preimage_ball (x y : Plane) (r : ℝ) : + (fun z : Plane => x-z) ⁻¹' ball y r = ball (x-y) r := by + ext z + simp only [mem_preimage, mem_ball, dist_eq_norm] + have he : x-z-y = -(z-(x-y)) := by abel + rw [he, norm_neg] + +lemma locallyIntegrable_reflect {h : Plane → ℝ} + (hloc : LocallyIntegrable h volume) (x : Plane) : + LocallyIntegrable (fun z => h (x-z)) volume := by + intro y + refine ⟨ball y 1, ball_mem_nhds y zero_lt_one, ?_⟩ + have hi := (hloc.integrableOn_isCompact (isCompact_closedBall (x-y) 1)).mono_set + ball_subset_closedBall + have hm := (volume.measurePreserving_sub_left x).restrict_preimage + (measurableSet_ball (x := x-y) (ε := (1 : ℝ))) + have hh := (hm.integrable_comp hi.aestronglyMeasurable).mpr hi + simpa only [IntegrableOn, Function.comp_def, reflect_preimage_ball, sub_sub_cancel] using hh + +lemma integral_reflect_ball (h : Plane → ℝ) (x y : Plane) (r : ℝ) : + ∫ z in ball y r, h (x-z) = ∫ z in ball (x-y) r, h z := by + have hm := (volume.measurePreserving_sub_left x).restrict_preimage + (measurableSet_ball (x := x-y) (ε := r)) + have hh := hm.integral_comp (MeasurableEquiv.subLeft x).measurableEmbedding h + simpa only [reflect_preimage_ball, sub_sub_cancel] using hh + +lemma integrable_heat_mul_of_unit_ball_mass {h : Plane → ℝ} + (hloc : LocallyIntegrable h volume) (hn : ∀ z, 0 ≤ h z) (A : ℝ≥0) + (hball : ∀ x : Plane, ∫ y in ball x 1, h y ≤ A) {a : ℝ} (ha : 0 < a) : + Integrable (fun z => heatKernel a z * h z) volume := by + have hh := integrable_gaussian_mul_of_unit_ball_mass hloc hn A hball + (show 0 < (4*a)⁻¹ by positivity) + simpa only [heatKernel, mul_assoc] using hh.const_mul (4*Real.pi*a)⁻¹ + +lemma heat_envelope {h : Plane → ℝ} + (hloc : LocallyIntegrable h volume) (hn : ∀ z, 0 ≤ h z) (A : ℝ≥0) + (hball : ∀ x : Plane, ∫ y in ball x 1, h y ≤ A) (x : Plane) : + (∀ a : ℝ, 0 < a → Integrable (fun z => heatKernel a z * h (x-z)) volume) ∧ + (Tendsto (fun r : ℝ => (Real.pi*r^2)⁻¹ * + ∫ y in ball x r, |h y-h x|) (𝓝[>] 0) (𝓝 0) → + Tendsto (fun a : ℝ => ∫ z, heatKernel a z * h (x-z)) (𝓝[>] 0) (𝓝 (h x))) := by + have hloc' := locallyIntegrable_reflect hloc x + have hn' : ∀ z, 0 ≤ h (x-z) := fun z => hn _ + have hball' (y : Plane) : ∫ z in ball y 1, h (x-z) ≤ A := by + rw [integral_reflect_ball] + exact hball _ + have hfinite : ∀ a : ℝ, 0 < a → + Integrable (fun z => heatKernel a z * h (x-z)) volume := + fun a ha => integrable_heat_mul_of_unit_ball_mass hloc' hn' A hball' ha + refine ⟨hfinite, ?_⟩ + intro hlim + let e : Plane → ℝ := fun z => |h (x-z)-h x| + have eloc : LocallyIntegrable e volume := by + rw [← locallyIntegrableOn_univ] + simpa only [Pi.sub_apply, Real.norm_eq_abs] using + ((hloc'.sub (locallyIntegrable_const (h x))).locallyIntegrableOn univ).norm + have en : ∀ z, 0 ≤ e z := fun z => abs_nonneg _ + have emean : Tendsto (fun r : ℝ => (Real.pi*r^2)⁻¹ * ∫ z in ball (0 : Plane) r, e z) + (𝓝[>] 0) (𝓝 0) := by + have heq (r : ℝ) : (∫ z in ball (0 : Plane) r, e z) = + ∫ y in ball x r, |h y-h x| := by + simpa only [e, sub_zero] using integral_reflect_ball (fun y => |h y-h x|) x 0 r + simpa only [heq] using hlim + have eg : Integrable (fun z => gaussianWeight 1 z * e z) volume := by + have hgi := integrable_gaussian_mul_of_unit_ball_mass hloc' hn' A hball' zero_lt_one + have hconst := (integrable_gaussianWeight zero_lt_one).mul_const |h x| + refine (hgi.add hconst).mono' ((by unfold gaussianWeight; fun_prop : + Continuous (gaussianWeight 1)).aestronglyMeasurable.mul eloc.aestronglyMeasurable) ?_ + filter_upwards [] with z + simp only [Pi.add_apply] + rw [Real.norm_eq_abs, abs_of_nonneg (mul_nonneg (gaussianWeight_pos _ _).le (en z)), + ← mul_add] + apply mul_le_mul_of_nonneg_left _ (gaussianWeight_pos _ _).le + dsimp only [e] + have hh := abs_sub_le (h (x-z)) 0 (h x) + simpa only [sub_zero, zero_sub, abs_neg, abs_of_nonneg (hn (x-z))] using hh + have he := tendsto_heat_mul_zero_of_lebesgue eloc.aestronglyMeasurable eloc en + zero_lt_one eg emean + apply Metric.tendsto_nhds.2 + intro ε hε + have hε' := he.eventually (eventually_lt_nhds hε) + filter_upwards [self_mem_nhdsWithin, hε'] with a ha hae + have hc := (integrable_heatKernel ha).mul_const (h x) + have hi := (hfinite a ha).sub hc + have heq : (∫ z, heatKernel a z * h (x-z)) - h x = + ∫ z, heatKernel a z * (h (x-z)-h x) := by + simp_rw [mul_sub] + rw [integral_sub (hfinite a ha) hc, integral_mul_const, integral_heatKernel ha, one_mul] + rw [Real.dist_eq, heq, ← Real.norm_eq_abs] + calc + _ ≤ ∫ z, ‖heatKernel a z * (h (x-z)-h x)‖ := norm_integral_le_integral_norm _ + _ = ∫ z, heatKernel a z * e z := by + congr 1 + ext z + rw [norm_mul, Real.norm_eq_abs, abs_of_nonneg (heatKernel_nonneg ha.le z)] + rfl + _ < ε := hae + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/ChainRule.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/ChainRule.lean new file mode 100644 index 0000000000000000000000000000000000000000..b50fd3bbe0fd69864c2efbf20196feea93925211 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/ChainRule.lean @@ -0,0 +1,94 @@ +import OAI.Analysis.PlanarEndpoint.Information.FiniteLaws +import OAI.Analysis.PlanarEndpoint.Information.FiniteTables +import OAI.Analysis.PlanarEndpoint.Information.Logarithms +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S V W Y : Type*} [Fintype S] [Fintype V] [Fintype W] [Fintype Y] + +omit [Fintype V] [Fintype Y] in +lemma le_sampledTable_self (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (v : S → V) (y : S → Y) (s : S) : a s ≤ sampledTable a v y (v s) (y s) := by + unfold sampledTable + have h := Finset.single_le_sum (s := Finset.univ) + (f := fun t => if v t = v s ∧ y t = y s then a t else 0) + (fun t _ => by split_ifs; exact ha t; exact le_rfl) (Finset.mem_univ s) + simpa only [and_self, ite_true] using h + +omit [Fintype V] in +lemma sampledTable_row (a : S → ℝ) (v : S → V) (y : S → Y) (b : V) : + rowMass (sampledTable a v y) b = ∑ s, if v s = b then a s else 0 := by + unfold rowMass sampledTable + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro s _ + by_cases h : v s = b <;> simp [h, eq_comm] + +omit [Fintype V] [Fintype W] [Fintype Y] in +lemma sampledTable_pair_target (a : S → ℝ) (v : S → V) (u : S → W) + (y : S → Y) (b : V) (c : W) (z : Y) : + sampledTable a v (fun s => (u s, y s)) b (c,z) = + sampledTable a (fun s => (v s, u s)) y (b,c) z := by + unfold sampledTable + simp only [Prod.mk.injEq, and_assoc] + +omit [Fintype V] [Fintype W] in +lemma sampledTable_pair_row (a : S → ℝ) (v : S → V) (u : S → W) + (y : S → Y) (b : V) (c : W) : + rowMass (sampledTable a (fun s => (v s, u s)) y) (b,c) = + sampledTable a v u b c := by + rw [sampledTable_row] + simp only [sampledTable, Prod.mk.injEq] + +omit [Fintype V] + +lemma sampledInformation_chain (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (v : S → V) (u : S → W) (y : S → Y) {s : S} (hs : 0 < a s) (L : ℝ) : + sampledInformation L a v (fun s => (u s, y s)) s = + sampledInformation L a v u s + + sampledInformation L a (fun s => (v s, u s)) y s := by + let A := sampledTable a (fun s => (v s, u s)) y (v s,u s) (y s) + let B := sampledTable a v u (v s) (u s) + let D := rowMass (sampledTable a v u) (v s) + have hA : 0 < A := hs.trans_le (le_sampledTable_self a ha _ y s) + have hB : 0 < B := hs.trans_le (le_sampledTable_self a ha v u s) + have hD : 0 < D := hB.trans_le (le_rowMass _ (sampledTable_nonneg a ha v u) _ _) + have hrow : rowMass (sampledTable a v (fun s => (u s,y s))) (v s) = D := by + rw [sampledTable_row] + exact (sampledTable_row a v u (v s)).symm + change information L (_ / _) = information L (B / D) + information L (_ / _) + rw [sampledTable_pair_target, hrow, sampledTable_pair_row] + change information L (A / D) = information L (B / D) + information L (A / B) + have h := conditional_information_chain (L := L) (div_pos hA hD) (div_pos hB hD) + have heq : (A / D) / (B / D) = A / B := by field_simp + rwa [heq] at h + +variable {Ω : Type*} [TopologicalSpace Ω] [MeasurableSpace Ω] [OpensMeasurableSpace Ω] + +lemma finiteInformationLaw_chain (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (v : S → V) (u : S → W) (y : S → Y) + (L : ℝ) (X : S → Ω) {f g h : Ω → ℝ} + (hf : Continuous f) (hg : Continuous g) (hh : Continuous h) + (hrep : ∀ s, f (X s) = sampledInformation L a v (fun s => (u s,y s)) s ∧ + g (X s) = sampledInformation L a v u s ∧ + h (X s) = sampledInformation L a (fun s => (v s,u s)) y s) : + f =ᵐ[(finiteInformationLaw a ha ha1 X : Measure Ω)] (fun x => g x + h x) := by + apply finiteInformationLaw_ae a ha ha1 X (fun x => f x = g x + h x) + (isClosed_eq hf (hg.add hh)).measurableSet + intro s hs + rw [(hrep s).1, (hrep s).2.1, (hrep s).2.2] + exact sampledInformation_chain a ha v u y hs L + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/Conditioning.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/Conditioning.lean new file mode 100644 index 0000000000000000000000000000000000000000..c5b19dd6573828de228b20ef0f088b07e0e4a738 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/Conditioning.lean @@ -0,0 +1,145 @@ +import OAI.Analysis.PlanarEndpoint.Information.FiniteTables +import OAI.Analysis.PlanarEndpoint.Information.Logarithms +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {V W Y : Type*} [Fintype V] [Fintype W] [Fintype Y] + +def totalMass (q : V → Y → ℝ) : ℝ := ∑ v, rowMass q v + +lemma rowMass_le_totalMass (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) (v : V) : + rowMass q v ≤ totalMass q := + Finset.single_le_sum (fun b _ => rowMass_nonneg q hq b) (Finset.mem_univ v) + +lemma totalMass_nonneg (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) : + 0 ≤ totalMass q := Finset.sum_nonneg (fun v _ => rowMass_nonneg q hq v) + +lemma colMass_sum (q : V → Y → ℝ) : (∑ y, colMass q y) = totalMass q := by + unfold colMass totalMass rowMass + rw [Finset.sum_comm] + +lemma joint_conditioning_exception_le_mass (q : V → Y → ℝ) + (hq : ∀ v y, 0 ≤ q v y) {L η : ℝ} (hL : 1 < L) : + (∑ v, ∑ y, if information L (colMass q y / totalMass q) - + information L (conditionalMass q v y) < -η then q v y else 0) ≤ + L ^ (-η) * totalMass q := by + have hL0 : 0 < L := lt_trans zero_lt_one hL + have hε : 0 ≤ L ^ (-η) := Real.rpow_nonneg hL0.le _ + have hp : ∀ y, 0 ≤ colMass q y / totalMass q := + fun y => div_nonneg (colMass_nonneg q hq y) (totalMass_nonneg q hq) + calc + _ ≤ ∑ v, ∑ y, L ^ (-η) * rowMass q v * (colMass q y / totalMass q) := by + apply Finset.sum_le_sum + intro v _ + apply Finset.sum_le_sum + intro y _ + by_cases hzero : q v y = 0 + · simp only [hzero, ite_self] + exact mul_nonneg (mul_nonneg hε (rowMass_nonneg q hq v)) (hp y) + · have hqpos : 0 < q v y := lt_of_le_of_ne (hq v y) (Ne.symm hzero) + have hvpos : 0 < rowMass q v := hqpos.trans_le (le_rowMass q hq v y) + have hmpos : 0 < totalMass q := hvpos.trans_le (rowMass_le_totalMass q hq v) + have hypos : 0 < colMass q y := hqpos.trans_le (le_colMass q hq v y) + split_ifs with hbad + · have h := (information_bad_iff hL (div_pos hypos hmpos) + (div_pos hqpos hvpos)).mp hbad + have h' := (div_lt_iff₀ hvpos).mp h + nlinarith + · exact mul_nonneg (mul_nonneg hε hvpos.le) (hp y) + _ = _ := by + simp_rw [← Finset.mul_sum] + rw [← Finset.sum_div, colMass_sum] + by_cases hm : totalMass q = 0 + · simp [hm] + · rw [div_self hm] + simp_rw [mul_one] + rw [← Finset.mul_sum] + rfl + +variable {S : Type*} [Fintype S] + +lemma sampledTable_event_mass (a : S → ℝ) (v : S → V) (y : S → Y) + (P : V → Y → Prop) : + (∑ b, ∑ z, if P b z then sampledTable a v y b z else 0) = + ∑ s, if P (v s) (y s) then a s else 0 := by + calc + _ = ∑ b, ∑ z, sampledTable a v y b z * (if P b z then (1 : ℝ) else 0) := by + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro z _ + split_ifs <;> simp + _ = ∑ s, a s * (if P (v s) (y s) then (1 : ℝ) else 0) := + sampledTable_sum a v y (fun b z => if P b z then (1 : ℝ) else 0) + _ = _ := by + apply Finset.sum_congr rfl + intro s _ + split_ifs <;> simp + +omit [Fintype V] [Fintype Y] in +lemma sampledTable_pair_first (a : S → ℝ) (v : S → V) (u : S → W) + (y : S → Y) (b : V) (z : Y) : + (∑ c, sampledTable a (fun s => (v s, u s)) y (b,c) z) = sampledTable a v y b z := by + unfold sampledTable + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro s _ + by_cases hv : v s = b <;> by_cases hy : y s = z <;> simp [Prod.mk.injEq, hv, hy] + +omit [Fintype V] in +lemma sampledTable_pair_total (a : S → ℝ) (v : S → V) (u : S → W) + (y : S → Y) (b : V) : + totalMass (fun c z => sampledTable a (fun s => (v s, u s)) y (b,c) z) = + rowMass (sampledTable a v y) b := by + unfold totalMass rowMass + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro z _ + exact sampledTable_pair_first a v u y b z + +lemma sampled_conditioning_exception_le (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (v : S → V) (u : S → W) (y : S → Y) + {L η : ℝ} (hL : 1 < L) : + (∑ s, if sampledInformation L a v y s - + sampledInformation L a (fun s => (v s, u s)) y s < -η then a s else 0) + ≤ L ^ (-η) := by + let q : V → W → Y → ℝ := fun b c z => + sampledTable a (fun s => (v s, u s)) y (b,c) z + let P : (V × W) → Y → Prop := fun b z => + information L (conditionalMass (sampledTable a v y) b.1 z) - + information L (conditionalMass (sampledTable a (fun s => (v s, u s)) y) b z) < -η + change (∑ s, if P (v s, u s) (y s) then a s else 0) ≤ _ + rw [← sampledTable_event_mass a (fun s => (v s, u s)) y P, Fintype.sum_prod_type] + calc + _ ≤ ∑ b, L ^ (-η) * totalMass (q b) := by + apply Finset.sum_le_sum + intro b _ + have h := joint_conditioning_exception_le_mass (q b) + (fun c z => sampledTable_nonneg a ha _ y (b,c) z) hL (η := η) + have hcol : ∀ z, colMass (q b) z = sampledTable a v y b z := + sampledTable_pair_first a v u y b + have ht : totalMass (q b) = rowMass (sampledTable a v y) b := + sampledTable_pair_total a v u y b + simp_rw [hcol, ht] at h + rw [ht] + exact h + _ = _ := by + rw [← Finset.mul_sum] + have ht : (∑ b, totalMass (q b)) = 1 := by + simp only [q, sampledTable_pair_total, rowMass] + rw [sampledTable_total, ha1] + rw [ht, mul_one] + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/ConditioningLimits.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/ConditioningLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..d55fd33620eb90a14a6c796310993d0c443e9de3 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/ConditioningLimits.lean @@ -0,0 +1,63 @@ +import OAI.Analysis.PlanarEndpoint.Information.Conditioning +import OAI.Analysis.PlanarEndpoint.Information.FiniteLaws +import OAI.Analysis.PlanarEndpoint.Information.Sampling +import OAI.Analysis.PlanarEndpoint.Information.WeakLimits + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S Ω V W Y : Type*} [Fintype S] [Fintype V] [Fintype W] [Fintype Y] + [TopologicalSpace Ω] [MeasurableSpace Ω] [OpensMeasurableSpace Ω] + +lemma finiteInformationLaw_conditioning_tail (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (v : S → V) (u : S → W) (y : S → Y) + {L η : ℝ} (hL : 1 < L) (X : S → Ω) {d : Ω → ℝ} (hd : Continuous d) + (hrep : ∀ s, d (X s) = sampledInformation L a v y s - + sampledInformation L a (fun s => (v s, u s)) y s) : + (finiteInformationLaw a ha ha1 X : Measure Ω) {x | d x < -η} ≤ + ENNReal.ofReal (L ^ (-η)) := by + rw [finiteInformationLaw_apply a ha ha1 X _ + (isOpen_lt hd continuous_const).measurableSet] + apply ENNReal.ofReal_le_ofReal + change (∑ s, if d (X s) < -η then a s else 0) ≤ _ + simp_rw [hrep] + exact sampled_conditioning_exception_le a ha ha1 v u y hL + +section Varying +variable [HasOuterApproxClosed Ω] +variable {S' V' W' Y' : ℕ → Type*} [∀ n, Fintype (S' n)] + [∀ n, Fintype (V' n)] [∀ n, Fintype (W' n)] [∀ n, Fintype (Y' n)] + (L : ℕ → ℝ) (a : (n : ℕ) → S' n → ℝ) + (ha : ∀ n s, 0 ≤ a n s) (ha1 : ∀ n, ∑ s, a n s = 1) + (v : (n : ℕ) → S' n → V' n) (u : (n : ℕ) → S' n → W' n) + (y : (n : ℕ) → S' n → Y' n) (X : (n : ℕ) → S' n → Ω) + +lemma ae_conditioning_in_limit {μ : ProbabilityMeasure Ω} + (hμ : Tendsto (fun n => finiteInformationLaw (a n) (ha n) (ha1 n) (X n)) + atTop (𝓝 μ)) (hL : ∀ n, 1 < L n) (hLlim : Tendsto L atTop atTop) + {d : Ω → ℝ} (hd : Continuous d) + (hrep : ∀ n s, d (X n s) = sampledInformation (L n) (a n) (v n) (y n) s - + sampledInformation (L n) (a n) (fun s => (v n s, u n s)) (y n) s) : + ∀ᵐ x ∂(μ : Measure Ω), 0 ≤ d x := by + apply ae_nonneg_of_weak_limit_tails hμ hd + intro η hη + have henv : Tendsto (fun n => ENNReal.ofReal ((L n) ^ (-η))) atTop (𝓝 0) := by + simpa only [ENNReal.ofReal_zero, Function.comp_def] using + ENNReal.tendsto_ofReal ((tendsto_rpow_neg_atTop hη).comp hLlim) + exact tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds henv + (Eventually.of_forall (fun _ => bot_le)) + (Eventually.of_forall (fun n => finiteInformationLaw_conditioning_tail + (a n) (ha n) (ha1 n) (v n) (u n) (y n) (hL n) (X n) hd (hrep n))) + +end Varying +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/CountableCompactness.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/CountableCompactness.lean new file mode 100644 index 0000000000000000000000000000000000000000..36934175fbf74c3f18d5dc8cf7c3d6e0a09a53be --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/CountableCompactness.lean @@ -0,0 +1,72 @@ +import Mathlib + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +section CountableIndex +variable {ι : Type*} [Countable ι] + +lemma joint_laws_tight_countable {μs : ℕ → ProbabilityMeasure (ι → ℝ)} + (htail : ∀ i : ι, ∀ ε : ℝ≥0∞, 0 < ε → ∃ R : ℝ, + ∀ n, (μs n : Measure (ι → ℝ)) {x | R < |x i|} ≤ ε) : + IsTightMeasureSet (Set.range (fun n => (μs n : Measure (ι → ℝ)))) := by + rw [isTightMeasureSet_iff_exists_isCompact_measure_compl_le] + intro ε hε + obtain ⟨δ, hδpos, hδsum⟩ := ENNReal.exists_pos_sum_of_countable' hε.ne' ι + choose R hR using fun i => htail i (δ i) (hδpos i) + let K : Set (ι → ℝ) := {x | ∀ i, x i ∈ Set.Icc (-(R i)) (R i)} + have hK : IsCompact K := isCompact_pi_infinite (fun _ => isCompact_Icc) + refine ⟨K, hK, ?_⟩ + rintro μ ⟨n, rfl⟩ + have hsubset : Kᶜ ⊆ ⋃ i, {x : ι → ℝ | R i < |x i|} := by + intro x hx + change ¬ (∀ i, -(R i) ≤ x i ∧ x i ≤ R i) at hx + push Not at hx + obtain ⟨i, hi⟩ := hx + refine Set.mem_iUnion.mpr ⟨i, ?_⟩ + change R i < |x i| + rw [lt_abs] + by_cases hlo : -(R i) ≤ x i + · exact Or.inl (hi hlo) + · exact Or.inr (by linarith) + calc + (μs n : Measure (ι → ℝ)) Kᶜ ≤ + (μs n : Measure (ι → ℝ)) (⋃ i, {x | R i < |x i|}) := measure_mono hsubset + _ ≤ ∑' i, (μs n : Measure (ι → ℝ)) {x | R i < |x i|} := measure_iUnion_le _ + _ ≤ ∑' i, δ i := ENNReal.tsum_le_tsum (fun i => hR i n) + _ ≤ ε := hδsum.le + +lemma exists_joint_weak_limit_countable {μs : ℕ → ProbabilityMeasure (ι → ℝ)} + (htail : ∀ i : ι, ∀ ε : ℝ≥0∞, 0 < ε → ∃ R : ℝ, + ∀ n, (μs n : Measure (ι → ℝ)) {x | R < |x i|} ≤ ε) : + ∃ μ : ProbabilityMeasure (ι → ℝ), ∃ φ : ℕ → ℕ, + StrictMono φ ∧ Tendsto (μs ∘ φ) atTop (𝓝 μ) := by + have ht : IsTightMeasureSet + {((μ : ProbabilityMeasure (ι → ℝ)) : Measure (ι → ℝ)) | μ ∈ Set.range μs} := by + convert joint_laws_tight_countable htail using 1 + ext m + simp only [mem_ofPred_eq, mem_range] + constructor + · rintro ⟨μ, ⟨n, rfl⟩, rfl⟩ + exact ⟨n, rfl⟩ + · rintro ⟨n, rfl⟩ + exact ⟨μs n, ⟨n, rfl⟩, rfl⟩ + have hc := isCompact_closure_of_isTightMeasureSet ht + obtain ⟨μ, _, φ, hφ, hlim⟩ := hc.isSeqCompact.subseq_of_frequently_in + (Filter.Eventually.frequently (Filter.Eventually.of_forall + (fun n => subset_closure (Set.mem_range_self n)))) + exact ⟨μ, φ, hφ, hlim⟩ + +end CountableIndex + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/Determination.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/Determination.lean new file mode 100644 index 0000000000000000000000000000000000000000..217a7b44a8cd1630e24374f3fb49a979acb17f49 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/Determination.lean @@ -0,0 +1,106 @@ +import OAI.Analysis.PlanarEndpoint.Information.Conditioning +import OAI.Analysis.PlanarEndpoint.Information.FiniteLaws +import OAI.Analysis.PlanarEndpoint.Information.FiniteTables +import OAI.Analysis.PlanarEndpoint.Information.Logarithms +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S V Y : Type*} [Fintype S] [Fintype V] [Fintype Y] + +omit [Fintype V] [Fintype Y] in +lemma sampledTable_mono {a b : S → ℝ} (hab : ∀ s, a s ≤ b s) + (v : S → V) (y : S → Y) (c : V) (z : Y) : + sampledTable a v y c z ≤ sampledTable b v y c z := by + unfold sampledTable + apply Finset.sum_le_sum + intro s _ + split_ifs + · exact hab s + · exact le_rfl + +omit [Fintype V] [Fintype Y] in +lemma sampledTable_restricted_zero (a : S → ℝ) (v : S → V) (y : S → Y) + (E : S → Prop) (A : V → Finset Y) (hA : ∀ s, E s → y s ∈ A (v s)) + (b : V) (z : Y) (hz : z ∉ A b) : + sampledTable (fun s => if E s then a s else 0) v y b z = 0 := by + unfold sampledTable + apply Finset.sum_eq_zero + intro s _ + by_cases hs : E s + · by_cases h : v s = b ∧ y s = z + · exact (hz (by simpa only [h.1, h.2] using hA s hs)).elim + · simp [h] + · simp [hs] + +lemma sampled_determination_exception_le (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (v : S → V) (y : S → Y) + (E : S → Prop) (A : V → Finset Y) (hA : ∀ s, E s → y s ∈ A (v s)) + {M : ℝ} (hcard : ∀ b, ((A b).card : ℝ) ≤ M) {L t : ℝ} (hL : 1 < L) : + (∑ s, if E s ∧ t < sampledInformation L a v y s then a s else 0) ≤ + M * L ^ (-t) := by + let e : S → ℝ := fun s => if E s then a s else 0 + have he : ∀ s, 0 ≤ e s := fun s => by dsimp [e]; split_ifs; exact ha s; exact le_rfl + have hea : ∀ s, e s ≤ a s := fun s => by dsimp [e]; split_ifs; exact le_rfl; exact ha s + let q := sampledTable a v y + let r := sampledTable e v y + have heq : (∑ s, if E s ∧ t < sampledInformation L a v y s then a s else 0) = + ∑ s, if t < information L (conditionalMass q (v s) (y s)) then e s else 0 := by + apply Finset.sum_congr rfl + intro s _ + by_cases hE : E s <;> + by_cases ht : t < sampledInformation L a v y s <;> + simp [e, q, sampledInformation] at ht ⊢ <;> simp_all + rw [heq, ← sampledTable_event_mass e v y (fun b z => t < information L (conditionalMass q b z))] + calc + _ ≤ ∑ b, M * L ^ (-t) * rowMass q b := by + apply Finset.sum_le_sum + intro b _ + have h := conditional_determination_exception_le (q b) (r b) (A b) + (sampledTable_nonneg a ha v y b) + (fun z => ⟨sampledTable_nonneg e he v y b z, sampledTable_mono hea v y b z⟩) + (fun z hz => sampledTable_restricted_zero a v y E A hA b z hz) hL (γ := t) + exact h.trans (mul_le_mul_of_nonneg_right + (mul_le_mul_of_nonneg_right (hcard b) (Real.rpow_nonneg (by linarith) _)) + (rowMass_nonneg q (sampledTable_nonneg a ha v y) b)) + _ = _ := by + rw [← Finset.mul_sum] + have ht : (∑ b, rowMass q b) = 1 := by + change (∑ b, ∑ z, sampledTable a v y b z) = 1 + rw [sampledTable_total, ha1] + rw [ht, mul_one] + +variable {Ω : Type*} [TopologicalSpace Ω] [MeasurableSpace Ω] [OpensMeasurableSpace Ω] + +lemma finiteInformationLaw_determination_tail (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (v : S → V) (y : S → Y) + (E : S → Prop) (A : V → Finset Y) (hA : ∀ s, E s → y s ∈ A (v s)) + {M : ℝ} (hcard : ∀ b, ((A b).card : ℝ) ≤ M) {L t : ℝ} (hL : 1 < L) + (X : S → Ω) {d b : Ω → ℝ} (hd : Continuous d) (hb : Continuous b) + (hrep : ∀ s, d (X s) = sampledInformation L a v y s ∧ + b (X s) = if E s then 1 else 0) : + (finiteInformationLaw a ha ha1 X : Measure Ω) ({x | 1/2 < b x} ∩ {x | t < d x}) ≤ + ENNReal.ofReal (M * L ^ (-t)) := by + rw [finiteInformationLaw_apply a ha ha1 X _ + ((isOpen_lt continuous_const hb).inter (isOpen_lt continuous_const hd)).measurableSet] + apply ENNReal.ofReal_le_ofReal + calc + _ = ∑ s, if E s ∧ t < sampledInformation L a v y s then a s else 0 := by + apply Finset.sum_congr rfl + intro s _ + simp only [Set.mem_inter_iff, Set.mem_ofPred_eq, (hrep s).1, (hrep s).2] + by_cases hs : E s <;> norm_num [hs] + _ ≤ _ := sampled_determination_exception_le a ha ha1 v y E A hA hcard hL + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/DeterminationLimits.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/DeterminationLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..6ae819d4702c45bdbc89a7da23229ce2c0ad5f2e --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/DeterminationLimits.lean @@ -0,0 +1,100 @@ +import OAI.Analysis.PlanarEndpoint.Extension +import OAI.Analysis.PlanarEndpoint.Information.ChainRule +import OAI.Analysis.PlanarEndpoint.Information.Determination +import OAI.Analysis.PlanarEndpoint.Information.FiniteLaws +import OAI.Analysis.PlanarEndpoint.Information.Sampling +import OAI.Analysis.PlanarEndpoint.Information.WeakLimits + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {Ω : Type*} [TopologicalSpace Ω] [MeasurableSpace Ω] + [OpensMeasurableSpace Ω] [HasOuterApproxClosed Ω] + {S V Y : ℕ → Type*} [∀ n, Fintype (S n)] + [∀ n, Fintype (V n)] [∀ n, Fintype (Y n)] + (L : ℕ → ℝ) (a : (n : ℕ) → S n → ℝ) + (ha : ∀ n s, 0 ≤ a n s) (ha1 : ∀ n, ∑ s, a n s = 1) + (v : (n : ℕ) → S n → V n) (y : (n : ℕ) → S n → Y n) + (X : (n : ℕ) → S n → Ω) + +lemma ae_determination_in_limit {μ : ProbabilityMeasure Ω} + (hμ : Tendsto (fun n => finiteInformationLaw (a n) (ha n) (ha1 n) (X n)) + atTop (𝓝 μ)) (hL : ∀ n, 1 < L n) (hLlim : Tendsto L atTop atTop) + (E : (n : ℕ) → S n → Prop) (A : (n : ℕ) → V n → Finset (Y n)) + (hA : ∀ n s, E n s → y n s ∈ A n (v n s)) + {c : ℕ → ℝ} {γ : ℝ} (hc : Tendsto c atTop (𝓝 γ)) + (hcard : ∀ n z, ((A n z).card : ℝ) ≤ (L n) ^ (c n)) + {d b : Ω → ℝ} (hd : Continuous d) (hb : Continuous b) + (hrep : ∀ n s, d (X n s) = sampledInformation (L n) (a n) (v n) (y n) s ∧ + b (X n s) = if E n s then 1 else 0) : + ∀ᵐ x ∂(μ : Measure Ω), b x = 1 → d x ≤ γ := by + have hbound : ∀ᵐ x ∂(μ : Measure Ω), x ∈ {x | 1/2 < b x} → d x ≤ γ := by + apply ae_le_on_open_of_weak_limit_tails hμ (isOpen_lt continuous_const hb) hd γ + intro η hη + have henv : Tendsto (fun n => ENNReal.ofReal ((L n) ^ (-(η/2)))) atTop (𝓝 0) := by + simpa only [ENNReal.ofReal_zero, Function.comp_def] using + ENNReal.tendsto_ofReal ((tendsto_rpow_neg_atTop (half_pos hη)).comp hLlim) + apply tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds henv + (Eventually.of_forall (fun _ => bot_le)) + filter_upwards [hc.eventually (gt_mem_nhds (by linarith : γ < γ+η/2))] with n hn + apply (finiteInformationLaw_determination_tail (a n) (ha n) (ha1 n) (v n) (y n) + (E n) (A n) (hA n) (hcard n) (hL n) (X n) hd hb (hrep n)).trans + apply ENNReal.ofReal_le_ofReal + calc + (L n) ^ (c n) * (L n) ^ (-(γ+η)) = (L n) ^ (c n - (γ+η)) := by + rw [sub_eq_add_neg, Real.rpow_add (lt_trans zero_lt_one (hL n))] + _ ≤ _ := Real.rpow_le_rpow_of_exponent_le (hL n).le (by linarith) + filter_upwards [hbound] with x hx hbx + apply hx + rw [hbx] + norm_num + +lemma ae_indicator_in_limit {μ : ProbabilityMeasure Ω} + (hμ : Tendsto (fun n => finiteInformationLaw (a n) (ha n) (ha1 n) (X n)) + atTop (𝓝 μ)) {b : Ω → ℝ} (hb : Continuous b) + (hrep : ∀ n s, 0 < a n s → b (X n s) = 0 ∨ b (X n s) = 1) : + ∀ᵐ x ∂(μ : Measure Ω), b x = 0 ∨ b x = 1 := by + have heq : (fun x => b x * (b x-1)) =ᵐ[(μ : Measure Ω)] (fun _ => 0) := by + apply ae_eq_of_weak_limit hμ (hb.mul (hb.sub continuous_const)) continuous_const + intro n + apply finiteInformationLaw_ae (a n) (ha n) (ha1 n) (X n) + (fun x => b x * (b x-1) = 0) + (isClosed_eq (hb.mul (hb.sub continuous_const)) continuous_const).measurableSet + intro s hs + rcases hrep n s hs with h | h <;> simp [h] + filter_upwards [heq] with x hx + rcases mul_eq_zero.mp hx with h | h + · exact Or.inl h + · exact Or.inr (sub_eq_zero.mp h) + +section Chain +variable {W : ℕ → Type*} [∀ n, Fintype (W n)] + (u : (n : ℕ) → S n → W n) + +omit [∀ n, Fintype (V n)] in +lemma ae_chain_in_limit {μ : ProbabilityMeasure Ω} + (hμ : Tendsto (fun n => finiteInformationLaw (a n) (ha n) (ha1 n) (X n)) + atTop (𝓝 μ)) {f g h : Ω → ℝ} + (hf : Continuous f) (hg : Continuous g) (hh : Continuous h) + (hrep : ∀ n s, + f (X n s) = sampledInformation (L n) (a n) (v n) (fun s => (u n s,y n s)) s ∧ + g (X n s) = sampledInformation (L n) (a n) (v n) (u n) s ∧ + h (X n s) = sampledInformation (L n) (a n) (fun s => (v n s,u n s)) (y n) s) : + f =ᵐ[(μ : Measure Ω)] (fun x => g x + h x) := by + apply ae_eq_of_weak_limit hμ hf (hg.add hh) + intro n + exact finiteInformationLaw_chain (a n) (ha n) (ha1 n) (v n) (u n) (y n) + (L n) (X n) hf hg hh (hrep n) + +end Chain +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/Entropy.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/Entropy.lean new file mode 100644 index 0000000000000000000000000000000000000000..686a088c281b8a0e5ec21060b4c02216845ab77d --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/Entropy.lean @@ -0,0 +1,119 @@ +import OAI.Analysis.PlanarEndpoint.Information.ChainRule +import OAI.Analysis.PlanarEndpoint.Information.Conditioning +import OAI.Analysis.PlanarEndpoint.Information.FiniteTables +import OAI.Analysis.PlanarEndpoint.Information.Logarithms +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {V W Y S : Type*} [Fintype V] [Fintype W] [Fintype Y] [Fintype S] + +lemma expected_conditioning_decrement_nonneg_mass (q : V → Y → ℝ) + (hq : ∀ v y, 0 ≤ q v y) {L : ℝ} (hL : 1 < L) : + 0 ≤ ∑ v, ∑ y, q v y * (information L (colMass q y / totalMass q) - + information L (conditionalMass q v y)) := by + by_cases ht : totalMass q = 0 + · have hzero : ∀ v y, q v y = 0 := by + intro v y + apply le_antisymm _ (hq v y) + exact (le_rowMass q hq v y).trans ((rowMass_le_totalMass q hq v).trans_eq ht) + simp only [hzero, zero_mul, Finset.sum_const_zero, le_refl] + have htpos : 0 < totalMass q := lt_of_le_of_ne (totalMass_nonneg q hq) (Ne.symm ht) + have hcol : ∑ y, colMass q y / totalMass q = 1 := by + rw [← Finset.sum_div, colMass_sum, div_self ht] + have hsum : ∑ v, ∑ y, (q v y - rowMass q v * (colMass q y / totalMass q)) = 0 := by + simp_rw [Finset.sum_sub_distrib, ← Finset.mul_sum, hcol, mul_one] + exact sub_self _ + calc + _ = ∑ v, ∑ y, (q v y - rowMass q v * (colMass q y / totalMass q)) / + Real.log L := by + simp_rw [← Finset.sum_div] + rw [hsum, zero_div] + _ ≤ _ := by + apply Finset.sum_le_sum + intro v _ + apply Finset.sum_le_sum + intro y _ + by_cases hq0 : q v y = 0 + · simp only [hq0, zero_sub, zero_mul] + exact div_nonpos_of_nonpos_of_nonneg + (neg_nonpos.mpr (mul_nonneg (rowMass_nonneg q hq v) + (div_nonneg (colMass_nonneg q hq y) htpos.le))) (Real.log_pos hL).le + · have hqy : 0 < q v y := lt_of_le_of_ne (hq v y) (Ne.symm hq0) + have hr : 0 < rowMass q v := hqy.trans_le (le_rowMass q hq v y) + have hc : 0 < colMass q y := hqy.trans_le (le_colMass q hq v y) + have hp : 0 < colMass q y / totalMass q := div_pos hc htpos + have h := sub_le_mul_log_div (hq v y) (mul_nonneg hr.le hp.le) + (fun _ => mul_pos hr hp) + have h' := div_le_div_of_nonneg_right h (Real.log_pos hL).le + unfold information conditionalMass + rw [Real.log_div hq0 (mul_pos hr hp).ne', Real.log_mul hr.ne' hp.ne', + Real.log_div hc.ne' ht] at h' + rw [Real.log_div hc.ne' ht, Real.log_div hq0 hr.ne'] + convert h' using 1 + ring + +def sampledEntropy (L : ℝ) (a : S → ℝ) (v : S → V) (y : S → Y) : ℝ := + ∑ s, a s * sampledInformation L a v y s + +lemma sampledEntropy_eq (L : ℝ) (a : S → ℝ) (v : S → V) (y : S → Y) : + sampledEntropy L a v y = conditionalEntropy L (sampledTable a v y) := by + exact (sampledTable_sum a v y (fun b z => + information L (conditionalMass (sampledTable a v y) b z))).symm + +lemma sampledEntropy_nonneg (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (v : S → V) (y : S → Y) {L : ℝ} (hL : 1 < L) : + 0 ≤ sampledEntropy L a v y := by + rw [sampledEntropy_eq] + exact conditionalEntropy_nonneg _ (sampledTable_nonneg a ha v y) hL + +lemma sampledEntropy_conditioning_le (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (v : S → V) (u : S → W) (y : S → Y) {L : ℝ} (hL : 1 < L) : + sampledEntropy L a (fun s => (v s,u s)) y ≤ sampledEntropy L a v y := by + apply sub_nonneg.mp + let q : V → W → Y → ℝ := fun b c z => + sampledTable a (fun s => (v s,u s)) y (b,c) z + let F : (V × W) → Y → ℝ := fun b z => + information L (conditionalMass (sampledTable a v y) b.1 z) - + information L (conditionalMass (sampledTable a (fun s => (v s,u s)) y) b z) + have heq : sampledEntropy L a v y - sampledEntropy L a (fun s => (v s,u s)) y = + ∑ s, a s * F (v s,u s) (y s) := by + simp only [sampledEntropy, sampledInformation, F, Finset.sum_sub_distrib, mul_sub] + rw [heq, ← sampledTable_sum a (fun s => (v s,u s)) y F, Fintype.sum_prod_type] + apply Finset.sum_nonneg + intro b _ + have h := expected_conditioning_decrement_nonneg_mass (q b) + (fun c z => sampledTable_nonneg a ha _ y (b,c) z) hL + have hcol : ∀ z, colMass (q b) z = sampledTable a v y b z := + sampledTable_pair_first a v u y b + have ht : totalMass (q b) = rowMass (sampledTable a v y) b := + sampledTable_pair_total a v u y b + simp_rw [hcol, ht] at h + exact h + +omit [Fintype V] in +lemma sampledEntropy_chain (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (v : S → V) (u : S → W) (y : S → Y) (L : ℝ) : + sampledEntropy L a v (fun s => (u s,y s)) = + sampledEntropy L a v u + sampledEntropy L a (fun s => (v s,u s)) y := by + unfold sampledEntropy + rw [← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro s _ + by_cases hs : a s = 0 + · simp only [hs, zero_mul, zero_add] + · rw [sampledInformation_chain a ha v u y (lt_of_le_of_ne (ha s) (Ne.symm hs)) L] + ring + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/EntropyLaws.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/EntropyLaws.lean new file mode 100644 index 0000000000000000000000000000000000000000..6c72105fda8f251ae940030d404a6e6e0f3ef69d --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/EntropyLaws.lean @@ -0,0 +1,81 @@ +import OAI.Analysis.PlanarEndpoint.Information.ChainRule +import OAI.Analysis.PlanarEndpoint.Information.Entropy +import OAI.Analysis.PlanarEndpoint.Information.FiniteTables +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S V V' Y Y' W : Type*} [Fintype S] [Fintype V] [Fintype V'] + [Fintype Y] [Fintype Y'] [Fintype W] + +omit [Fintype V] [Fintype V'] in +lemma sampledInformation_congr_fibers (L : ℝ) (a : S → ℝ) + (v : S → V) (v' : S → V') (y : S → Y) (y' : S → Y') + (hv : ∀ r s, v r = v s ↔ v' r = v' s) + (hy : ∀ r s, y r = y s ↔ y' r = y' s) (s : S) : + sampledInformation L a v y s = sampledInformation L a v' y' s := by + unfold sampledInformation conditionalMass + rw [sampledTable_row, sampledTable_row] + have hnum : sampledTable a v y (v s) (y s) = sampledTable a v' y' (v' s) (y' s) := by + unfold sampledTable + apply Finset.sum_congr rfl + intro r _ + rw [hv r s, hy r s] + have hden : (∑ r, if v r = v s then a r else 0) = + ∑ r, if v' r = v' s then a r else 0 := by + apply Finset.sum_congr rfl + intro r _ + rw [hv r s] + rw [hnum, hden] + +omit [Fintype V] [Fintype V'] in +lemma sampledEntropy_congr_fibers (L : ℝ) (a : S → ℝ) + (v : S → V) (v' : S → V') (y : S → Y) (y' : S → Y') + (hv : ∀ r s, v r = v s ↔ v' r = v' s) + (hy : ∀ r s, y r = y s ↔ y' r = y' s) : + sampledEntropy L a v y = sampledEntropy L a v' y' := by + apply Finset.sum_congr rfl + intro s _ + rw [sampledInformation_congr_fibers L a v v' y y' hv hy s] + +omit [Fintype V] in +lemma sampledEntropy_mutual_information (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (v : S → V) (u : S → W) (y : S → Y) (L : ℝ) : + sampledEntropy L a v y - sampledEntropy L a (fun s => (v s,u s)) y = + sampledEntropy L a v u - sampledEntropy L a (fun s => (v s,y s)) u := by + have h1 := sampledEntropy_chain a ha v u y L + have h2 := sampledEntropy_chain a ha v y u L + have hswap : sampledEntropy L a v (fun s => (u s,y s)) = + sampledEntropy L a v (fun s => (y s,u s)) := by + apply sampledEntropy_congr_fibers + · intro r s + rfl + · intro r s + simp only [Prod.mk.injEq, and_comm] + rw [hswap] at h1 + linarith + +lemma sampledEntropy_le_log_card (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (v : S → V) (y : S → Y) {L : ℝ} (hL : 1 < L) : + sampledEntropy L a v y ≤ Real.log (Fintype.card Y) / Real.log L := by + rw [sampledEntropy_eq] + apply (entropy_conditioning_le (sampledTable a v y) (sampledTable_nonneg a ha v y) + (by rw [sampledTable_total, ha1]) hL).trans + apply entropy_le_log_card + · exact colMass_nonneg _ (sampledTable_nonneg a ha v y) + · change (∑ z, ∑ b, sampledTable a v y b z) = 1 + rw [Finset.sum_comm, sampledTable_total, ha1] + · exact hL + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/EventLimits.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/EventLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..63f6079c636b980a5b373acd23c458c7c2717461 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/EventLimits.lean @@ -0,0 +1,66 @@ +import OAI.Analysis.PlanarEndpoint.Information.DeterminationLimits +import OAI.Analysis.PlanarEndpoint.Information.MixedLaws +import OAI.Analysis.PlanarEndpoint.Information.MixedLimits +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S : ℕ → Type} [∀ n, Fintype (S n)] + {V Y : ℕ → ℕ → Type} [∀ n i, Fintype (V n i)] [∀ n i, Fintype (Y n i)] + (L : ℕ → ℝ) (w : (n : ℕ) → S n → ℝ) + (hw : ∀ n s, 0 ≤ w n s) (hw1 : ∀ n, ∑ s, w n s = 1) + (v : (n i : ℕ) → S n → V n i) (y : (n i : ℕ) → S n → Y n i) + (P : (n : ℕ) → ℕ → S n → Prop) + +def originalEventObservables (n i : ℕ) (s : S n) : ℝ := if P n i s then 1 else 0 + +omit [∀ index, Fintype (S index)] in +lemma originalEventObservables_bound (n i : ℕ) (s : S n) : + |originalEventObservables P n i s| ≤ 1 := by + unfold originalEventObservables + split_ifs <;> norm_num + +theorem exists_original_information_event_limit (hL : ∀ n, 2 ≤ L n) + (hLlim : Tendsto L atTop atTop) (c : ℕ → ℕ → ℝ) (C : ℕ → ℝ) + (hc : ∀ i, Tendsto (fun n => c n i) atTop (𝓝 (C i))) + (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (c n i)) : + ∃ μ : ProbabilityMeasure ((ℕ ⊕ ℕ) → ℝ), ∃ φ : ℕ → ℕ, + StrictMono φ ∧ Tendsto + ((mixedInformationLaws L w hw hw1 v y (originalEventObservables P)) ∘ φ) + atTop (𝓝 μ) ∧ + (∀ᵐ x ∂(μ : Measure ((ℕ ⊕ ℕ) → ℝ)), + (∀ i, 0 ≤ x (.inl i) ∧ x (.inl i) ≤ C i) ∧ + (∀ i, x (.inr i) = 0 ∨ x (.inr i) = 1)) ∧ + ∀ i, Integrable (fun x => x (.inl i)) (μ : Measure ((ℕ ⊕ ℕ) → ℝ)) ∧ + Tendsto (fun n => ∑ s, w (φ n) s * + sampledInformation (L (φ n)) (w (φ n)) (v (φ n) i) (y (φ n) i) s) + atTop (𝓝 (∫ x, x (.inl i) ∂(μ : Measure ((ℕ ⊕ ℕ) → ℝ)))) := by + obtain ⟨μ, φ, hφ, hμ, hsupp, hmeans⟩ := + exists_mixed_information_sharp_limit L w hw hw1 v y (originalEventObservables P) + hL hLlim c C hc hcard (fun _ => 1) (originalEventObservables_bound P) + have hbool : ∀ i, ∀ᵐ x ∂(μ : Measure ((ℕ ⊕ ℕ) → ℝ)), + x (.inr i) = 0 ∨ x (.inr i) = 1 := by + intro i + apply ae_indicator_in_limit (fun n => w (φ n)) (fun n => hw (φ n)) + (fun n => hw1 (φ n)) + (fun n => mixedInformationVector (L (φ n)) (w (φ n)) + (v (φ n)) (y (φ n)) (originalEventObservables P (φ n))) + hμ (continuous_apply (Sum.inr i : ℕ ⊕ ℕ)) + intro n s _ + change (if P (φ n) i s then (1 : ℝ) else 0) = 0 ∨ + (if P (φ n) i s then (1 : ℝ) else 0) = 1 + split_ifs <;> simp + exact ⟨μ, φ, hφ, hμ, hsupp.and (ae_all_iff.mpr hbool), hmeans⟩ + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/Expectations.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/Expectations.lean new file mode 100644 index 0000000000000000000000000000000000000000..1015e4917fecc8f52c8b6b117e4548912fe52fbf --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/Expectations.lean @@ -0,0 +1,124 @@ +import OAI.Analysis.PlanarEndpoint.Extension +import OAI.Analysis.PlanarEndpoint.Fourier + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BoundedContinuousFunction +namespace PlanarEndpoint.TransverseInformation + +variable {Ω : Type*} [MeasurableSpace Ω] [TopologicalSpace Ω] + [OpensMeasurableSpace Ω] + +def informationClip (A : ℝ) (x : ℝ) : ℝ := min (max x 0) (max A 0) + +lemma informationClip_nonneg (A x : ℝ) : 0 ≤ informationClip A x := + le_min (le_max_right _ _) (le_max_right _ _) + +lemma informationClip_le_bound (A x : ℝ) : informationClip A x ≤ max A 0 := + min_le_right _ _ + +lemma informationClip_eq {A x : ℝ} (hx : 0 ≤ x) (hA : x ≤ A) : + informationClip A x = x := by + simp [informationClip, max_eq_left hx, max_eq_left (hx.trans hA), min_eq_left hA] + +lemma continuous_informationClip (A : ℝ) : Continuous (informationClip A) := + (continuous_id.max continuous_const).min continuous_const + +def clippedInformation (A : ℝ) (f : Ω → ℝ) (hf : Continuous f) : Ω →ᵇ ℝ := + BoundedContinuousFunction.mkOfBound + ⟨fun x => informationClip A (f x), (continuous_informationClip A).comp hf⟩ + (2 * max A 0) (by + intro x y + rw [Real.dist_eq, abs_le] + have hx0 := informationClip_nonneg A (f x) + have hy0 := informationClip_nonneg A (f y) + have hxb := informationClip_le_bound A (f x) + have hyb := informationClip_le_bound A (f y) + change -(2 * max A 0) ≤ informationClip A (f x) - informationClip A (f y) ∧ + informationClip A (f x) - informationClip A (f y) ≤ 2 * max A 0 + constructor <;> linarith [le_max_right A 0]) + +lemma informationClip_error_le {A x : ℝ} (hA : 0 ≤ A) (hx : 0 ≤ x) : + |x - informationClip A x| ≤ if A < x then x else 0 := by + classical + by_cases h : A < x + · simp only [h, ↓reduceIte, informationClip, max_eq_left hx, max_eq_left hA, + min_eq_right h.le] + rw [abs_of_nonneg (by linarith)] + linarith + · rw [informationClip_eq hx (le_of_not_gt h)] + simp only [sub_self, abs_zero, h, ↓reduceIte, le_refl] + +lemma integral_informationClip_error_le {μ : Measure Ω} [IsFiniteMeasure μ] + {f : Ω → ℝ} (hf : Continuous f) (hfi : Integrable f μ) + (hfn : 0 ≤ᵐ[μ] f) {A : ℝ} (hA : 0 ≤ A) : + |(∫ x, f x ∂μ) - ∫ x, clippedInformation A f hf x ∂μ| ≤ + ∫ x, if A < f x then f x else 0 ∂μ := by + have hc := (clippedInformation A f hf).integrable (μ := μ) + have ht : Integrable (fun x => if A < f x then f x else 0) μ := by + exact hfi.indicator (isOpen_lt continuous_const hf).measurableSet + rw [← integral_sub hfi hc, ← Real.norm_eq_abs] + refine (norm_integral_le_integral_norm _).trans ?_ + apply integral_mono_ae (hfi.sub hc).norm ht + filter_upwards [hfn] with x hx + exact informationClip_error_le hA hx + +theorem expected_information_tendsto {μ : ProbabilityMeasure Ω} + {μs : ℕ → ProbabilityMeasure Ω} (hμ : Tendsto μs atTop (𝓝 μ)) + {f : Ω → ℝ} (hf : Continuous f) + (hfi : ∀ n, Integrable f (μs n : Measure Ω)) + (hfn : ∀ n, 0 ≤ᵐ[(μs n : Measure Ω)] f) + (hfμ : 0 ≤ᵐ[(μ : Measure Ω)] f) + {C : ℝ} (hC : ∀ᵐ x ∂(μ : Measure Ω), f x ≤ C) + (htail : ∀ ε : ℝ, 0 < ε → ∃ A₀ : ℝ, ∀ A : ℝ, A₀ ≤ A → ∀ n, + (∫ x, if A < f x then f x else 0 ∂(μs n : Measure Ω)) < ε) : + Integrable f (μ : Measure Ω) ∧ + Tendsto (fun n => ∫ x, f x ∂(μs n : Measure Ω)) atTop + (𝓝 (∫ x, f x ∂(μ : Measure Ω))) := by + have heq : ∀ A : ℝ, C ≤ A → + (fun x => clippedInformation A f hf x) =ᵐ[(μ : Measure Ω)] f := by + intro A hA + filter_upwards [hfμ, hC] with x hx0 hxC + exact informationClip_eq hx0 (hxC.trans hA) + refine ⟨((clippedInformation C f hf).integrable (μ := (μ : Measure Ω))).congr + (heq C le_rfl), ?_⟩ + rw [Metric.tendsto_nhds] + intro ε hε + obtain ⟨A₀, hA₀⟩ := htail (ε/2) (half_pos hε) + let A := max (max A₀ C) 0 + have hA0 : 0 ≤ A := le_max_right _ _ + have hAA : A₀ ≤ A := (le_max_left _ _).trans (le_max_left _ _) + have hAC : C ≤ A := (le_max_right _ _).trans (le_max_left _ _) + have hc := ProbabilityMeasure.tendsto_iff_forall_integral_tendsto.mp hμ + (clippedInformation A f hf) + have hlim : (∫ x, clippedInformation A f hf x ∂(μ : Measure Ω)) = + (∫ x, f x ∂(μ : Measure Ω)) := integral_congr_ae (heq A hAC) + rw [hlim] at hc + filter_upwards [hc.eventually (Metric.ball_mem_nhds _ (half_pos hε))] with n hn + have hn' : dist (∫ x, clippedInformation A f hf x ∂(μs n : Measure Ω)) + (∫ x, f x ∂(μ : Measure Ω)) < ε/2 := hn + have herr := integral_informationClip_error_le hf (hfi n) (hfn n) hA0 + have htailn := hA₀ A hAA n + calc + dist (∫ x, f x ∂(μs n : Measure Ω)) (∫ x, f x ∂(μ : Measure Ω)) ≤ + dist (∫ x, f x ∂(μs n : Measure Ω)) + (∫ x, clippedInformation A f hf x ∂(μs n : Measure Ω)) + + dist (∫ x, clippedInformation A f hf x ∂(μs n : Measure Ω)) + (∫ x, f x ∂(μ : Measure Ω)) := dist_triangle _ _ _ + _ ≤ (∫ x, if A < f x then f x else 0 ∂(μs n : Measure Ω)) + + dist (∫ x, clippedInformation A f hf x ∂(μs n : Measure Ω)) + (∫ x, f x ∂(μ : Measure Ω)) := by + apply add_le_add + · simpa only [Real.dist_eq] using herr + · exact le_rfl + _ < ε := by linarith + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/FiltrationCosts.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/FiltrationCosts.lean new file mode 100644 index 0000000000000000000000000000000000000000..3bfbcd49ed2e9fe989756628a58a680e8bfd6ba7 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/FiltrationCosts.lean @@ -0,0 +1,85 @@ +import OAI.Analysis.PlanarEndpoint.Information.Entropy +import OAI.Analysis.PlanarEndpoint.Information.EntropyLaws + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S C D : Type*} [Fintype S] [Fintype C] [Fintype D] + {X : ℕ → Type*} [∀ j, Fintype (X j)] + +def directionFiltrationCost (L : ℝ) (a : S → ℝ) (c : S → C) (d : S → D) + (x : (j : ℕ) → S → X j) (j : ℕ) : ℝ := + sampledEntropy L a (fun s => (c s,x j s)) (x (j+1)) - + sampledEntropy L a (fun s => ((c s,x j s),d s)) (x (j+1)) + +lemma directionFiltrationCost_nonneg (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (c : S → C) (d : S → D) (x : (j : ℕ) → S → X j) + {L : ℝ} (hL : 1 < L) (j : ℕ) : 0 ≤ directionFiltrationCost L a c d x j := + sub_nonneg.mpr (sampledEntropy_conditioning_le a ha _ d _ hL) + +omit [Fintype C] in +lemma directionFiltrationCost_eq (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (c : S → C) (d : S → D) (x : (j : ℕ) → S → X j) + (parent : (j : ℕ) → X (j+1) → X j) + (hnest : ∀ j s, x j s = parent j (x (j+1) s)) (L : ℝ) (j : ℕ) : + directionFiltrationCost L a c d x j = + sampledEntropy L a (fun s => (c s,x j s)) d - + sampledEntropy L a (fun s => (c s,x (j+1) s)) d := by + unfold directionFiltrationCost + rw [sampledEntropy_mutual_information a ha _ d _ L] + congr 1 + apply sampledEntropy_congr_fibers + · intro r s + simp only [Prod.mk.injEq] + constructor + · intro h + exact ⟨h.1.1,h.2⟩ + · rintro ⟨hc,hx⟩ + exact ⟨⟨hc,by rw [hnest j r, hnest j s, hx]⟩,hx⟩ + · intro r s + rfl + +omit [Fintype C] in +lemma directionFiltrationCost_sum_eq (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (c : S → C) (d : S → D) (x : (j : ℕ) → S → X j) + (parent : (j : ℕ) → X (j+1) → X j) + (hnest : ∀ j s, x j s = parent j (x (j+1) s)) (L : ℝ) (n : ℕ) : + (∑ j ∈ Finset.range n, directionFiltrationCost L a c d x j) = + sampledEntropy L a (fun s => (c s,x 0 s)) d - + sampledEntropy L a (fun s => (c s,x n s)) d := by + induction n with + | zero => simp + | succ n ih => + rw [Finset.sum_range_succ, ih, directionFiltrationCost_eq a ha c d x parent hnest] + ring + +theorem directionFiltrationCost_sum_le (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (c : S → C) (d : S → D) (x : (j : ℕ) → S → X j) + (parent : (j : ℕ) → X (j+1) → X j) + (hnest : ∀ j s, x j s = parent j (x (j+1) s)) {L : ℝ} (hL : 1 < L) + (n : ℕ) (J : Finset ℕ) (hJ : J ⊆ Finset.range n) : + 0 ≤ ∑ j ∈ J, directionFiltrationCost L a c d x j ∧ + (∑ j ∈ J, directionFiltrationCost L a c d x j) ≤ + Real.log (Fintype.card D) / Real.log L := by + constructor + · exact Finset.sum_nonneg (fun j _ => directionFiltrationCost_nonneg a ha c d x hL j) + · calc + _ ≤ ∑ j ∈ Finset.range n, directionFiltrationCost L a c d x j := + Finset.sum_le_sum_of_subset_of_nonneg hJ + (fun j _ _ => directionFiltrationCost_nonneg a ha c d x hL j) + _ = _ := directionFiltrationCost_sum_eq a ha c d x parent hnest L n + _ ≤ sampledEntropy L a (fun s => (c s,x 0 s)) d := + sub_le_self _ (sampledEntropy_nonneg a ha _ d hL) + _ ≤ _ := sampledEntropy_le_log_card a ha ha1 _ d hL + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/FiniteLaws.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/FiniteLaws.lean new file mode 100644 index 0000000000000000000000000000000000000000..d8157e74af9522bbf4d15432680166c6a08cbabb --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/FiniteLaws.lean @@ -0,0 +1,82 @@ +import Mathlib + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S Ω : Type*} [Fintype S] [MeasurableSpace Ω] + +def finiteInformationPMF (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) : + PMF S := + PMF.ofFintype (fun s => ENNReal.ofReal (w s)) (by + rw [← ENNReal.ofReal_sum_of_nonneg (fun s _ => hw s), hw1] + simp) + +def finiteInformationLaw (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (X : S → Ω) : ProbabilityMeasure Ω := + ⟨((finiteInformationPMF w hw hw1).map X).toMeasure, inferInstance⟩ + +lemma finiteInformationLaw_integral (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (hw1 : ∑ s, w s = 1) (X : S → Ω) (f : Ω → ℝ) (hf : Measurable f) : + (∫ x, f x ∂(finiteInformationLaw w hw hw1 X : Measure Ω)) = + ∑ s, w s * f (X s) := by + let : MeasurableSpace S := ⊤ + have hX : Measurable X := measurable_of_countable X + change (∫ x, f x ∂(((finiteInformationPMF w hw hw1).map X).toMeasure)) = _ + rw [← PMF.toMeasure_map X _ hX, integral_map hX.aemeasurable hf.aestronglyMeasurable, + PMF.integral_eq_sum] + simp only [finiteInformationPMF, PMF.ofFintype_apply, ENNReal.toReal_ofReal (hw _), + smul_eq_mul] + +lemma finiteInformationLaw_apply (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (hw1 : ∑ s, w s = 1) (X : S → Ω) (G : Set Ω) (hG : MeasurableSet G) : + (finiteInformationLaw w hw hw1 X : Measure Ω) G = + ENNReal.ofReal (∑ s, if X s ∈ G then w s else 0) := by + classical + let : MeasurableSpace S := ⊤ + have hX : Measurable X := measurable_of_countable X + change (((finiteInformationPMF w hw hw1).map X).toMeasure) G = _ + rw [← PMF.toMeasure_map X _ hX, Measure.map_apply hX hG, + PMF.toMeasure_apply _ (hX hG), tsum_fintype, + ENNReal.ofReal_sum_of_nonneg (fun s _ => by split_ifs; exact hw s; exact le_rfl)] + apply Finset.sum_congr rfl + intro s _ + simp only [Set.indicator_apply, Set.mem_preimage, finiteInformationPMF, PMF.ofFintype_apply] + split_ifs <;> simp + +lemma finiteInformationLaw_integrable (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (hw1 : ∑ s, w s = 1) (X : S → Ω) (f : Ω → ℝ) (hf : Measurable f) : + Integrable f (finiteInformationLaw w hw hw1 X : Measure Ω) := by + let : MeasurableSpace S := ⊤ + have hX : Measurable X := measurable_of_countable X + change Integrable f (((finiteInformationPMF w hw hw1).map X).toMeasure) + rw [← PMF.toMeasure_map X _ hX] + exact (integrable_map_measure hf.aestronglyMeasurable hX.aemeasurable).mpr + (Integrable.of_finite) + +lemma finiteInformationLaw_ae (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (hw1 : ∑ s, w s = 1) (X : S → Ω) (P : Ω → Prop) + (hP : MeasurableSet {x | P x}) (hs : ∀ s, 0 < w s → P (X s)) : + ∀ᵐ x ∂(finiteInformationLaw w hw hw1 X : Measure Ω), P x := by + classical + apply ae_iff.mpr + rw [finiteInformationLaw_apply w hw hw1 X {x | ¬P x} (by exact hP.compl)] + apply ENNReal.ofReal_eq_zero.mpr + apply le_of_eq + apply Finset.sum_eq_zero + intro s _ + by_cases hp : P (X s) + · simp [hp] + · have hz : w s = 0 := le_antisymm (le_of_not_gt (fun h => hp (hs s h))) (hw s) + simp [hz] + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/FiniteTables.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/FiniteTables.lean new file mode 100644 index 0000000000000000000000000000000000000000..87502fe47f78b954000964bfa76e4e68681699e5 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/FiniteTables.lean @@ -0,0 +1,325 @@ +import OAI.Analysis.PlanarEndpoint.Information.Logarithms + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open scoped BigOperators +open Finset +namespace PlanarEndpoint.TransverseInformation + +variable {V Y : Type*} [Fintype V] [Fintype Y] + +def rowMass (q : V → Y → ℝ) (v : V) : ℝ := ∑ y, q v y +def colMass (q : V → Y → ℝ) (y : Y) : ℝ := ∑ v, q v y +def conditionalMass (q : V → Y → ℝ) (v : V) (y : Y) : ℝ := + q v y / rowMass q v + +omit [Fintype V] in +lemma rowMass_nonneg (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) (v : V) : + 0 ≤ rowMass q v := Finset.sum_nonneg (fun y _ => hq v y) + +omit [Fintype Y] in +lemma colMass_nonneg (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) (y : Y) : + 0 ≤ colMass q y := Finset.sum_nonneg (fun v _ => hq v y) + +omit [Fintype V] in +lemma le_rowMass (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) (v : V) (y : Y) : + q v y ≤ rowMass q v := Finset.single_le_sum (fun z _ => hq v z) (Finset.mem_univ y) + +omit [Fintype Y] in +lemma le_colMass (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) (v : V) (y : Y) : + q v y ≤ colMass q y := Finset.single_le_sum (fun z _ => hq z y) (Finset.mem_univ v) + +lemma conditional_information_chain {L a b : ℝ} (ha : 0 < a) (hb : 0 < b) : + information L a = information L b + information L (a/b) := by + unfold information + rw [Real.log_div ha.ne' hb.ne'] + ring + +omit [Fintype V] in +lemma joint_information_chain (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) + {v : V} {y : Y} (h : 0 < q v y) (L : ℝ) : + information L (q v y) = information L (rowMass q v) + + information L (conditionalMass q v y) := + conditional_information_chain h (h.trans_le (le_rowMass q hq v y)) + +lemma joint_conditioning_exception_le (q : V → Y → ℝ) + (hq : ∀ v y, 0 ≤ q v y) (hq1 : ∑ v, ∑ y, q v y = 1) + {L η : ℝ} (hL : 1 < L) : + (∑ v, ∑ y, if information L (colMass q y) - + information L (conditionalMass q v y) < -η then q v y else 0) + ≤ L ^ (-η) := by + classical + have hL0 : 0 < L := lt_trans zero_lt_one hL + have hε : 0 ≤ L ^ (-η) := Real.rpow_nonneg hL0.le _ + have hcol : ∑ y, colMass q y = 1 := by + change (∑ y, ∑ v, q v y) = 1 + rw [Finset.sum_comm] + exact hq1 + calc + _ ≤ ∑ v, ∑ y, L ^ (-η) * rowMass q v * colMass q y := by + apply Finset.sum_le_sum + intro v _ + apply Finset.sum_le_sum + intro y _ + by_cases hqvy : q v y = 0 + · simp only [hqvy, ite_self] + exact mul_nonneg (mul_nonneg hε (rowMass_nonneg q hq v)) + (colMass_nonneg q hq y) + · have hvy : 0 < q v y := lt_of_le_of_ne (hq v y) (Ne.symm hqvy) + have hv : 0 < rowMass q v := hvy.trans_le (le_rowMass q hq v y) + have hy : 0 < colMass q y := hvy.trans_le (le_colMass q hq v y) + split_ifs with h + · have h' := (information_bad_iff hL hy (div_pos hvy hv)).mp h + have h'' := (div_lt_iff₀ hv).mp h' + nlinarith + · exact mul_nonneg (mul_nonneg hε hv.le) hy.le + _ = L ^ (-η) := by + simp_rw [← Finset.mul_sum, hcol, mul_one] + rw [← Finset.mul_sum] + simp only [rowMass, hq1, mul_one] + +lemma information_gt_iff {L p γ : ℝ} (hL : 1 < L) (hp : 0 < p) : + γ < information L p ↔ p < L ^ (-γ) := by + unfold information + rw [lt_div_iff₀ (Real.log_pos hL)] + have hL0 : 0 < L := lt_trans zero_lt_one hL + constructor + · intro h + have : Real.log p < Real.log (L ^ (-γ)) := by + rw [Real.log_rpow hL0] + linarith + exact (Real.log_lt_log_iff hp (Real.rpow_pos_of_pos hL0 _)).mp this + · intro h + have := Real.log_lt_log hp h + rw [Real.log_rpow hL0] at this + linarith + +lemma conditional_determination_exception_le (q e : Y → ℝ) (S : Finset Y) + (hq : ∀ y, 0 ≤ q y) (he : ∀ y, 0 ≤ e y ∧ e y ≤ q y) + (hs : ∀ y, y ∉ S → e y = 0) {L γ : ℝ} (hL : 1 < L) : + (∑ y, if γ < information L (q y / ∑ z, q z) then e y else 0) + ≤ S.card * L ^ (-γ) * ∑ z, q z := by + classical + have hm : 0 ≤ ∑ z, q z := Finset.sum_nonneg (fun z _ => hq z) + have hε : 0 ≤ L ^ (-γ) := Real.rpow_nonneg (by linarith) _ + calc + _ = ∑ y ∈ S, if γ < information L (q y / ∑ z, q z) then e y else 0 := by + symm + apply Finset.sum_subset (Finset.subset_univ S) + intro y _ hy + simp only [hs y hy, ite_self] + _ ≤ ∑ y ∈ S, L ^ (-γ) * ∑ z, q z := by + apply Finset.sum_le_sum + intro y hy + by_cases he0 : e y = 0 + · simp only [he0, ite_self] + exact mul_nonneg hε hm + · have hey : 0 < e y := lt_of_le_of_ne (he y).1 (Ne.symm he0) + have hqy : 0 < q y := hey.trans_le (he y).2 + have hmq : 0 < ∑ z, q z := hqy.trans_le + (Finset.single_le_sum (fun z _ => hq z) (Finset.mem_univ y)) + split_ifs with h + · have h' := (information_gt_iff hL (div_pos hqy hmq)).mp h + exact (he y).2.trans ((div_lt_iff₀ hmq).mp h').le + · exact mul_nonneg hε hm + _ = _ := by simp [mul_assoc] + +lemma sub_le_mul_log_div {a b : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) + (hab : 0 < a → 0 < b) : a - b ≤ a * Real.log (a / b) := by + by_cases ha0 : a = 0 + · simp only [ha0, zero_sub, zero_mul] + exact neg_nonpos.mpr hb + · have ha' : 0 < a := lt_of_le_of_ne ha (Ne.symm ha0) + have hb' := hab ha' + have hlog := Real.log_le_sub_one_of_pos (div_pos hb' ha') + have hh := mul_le_mul_of_nonneg_left hlog ha + rw [Real.log_div hb'.ne' ha0] at hh + rw [Real.log_div ha0 hb'.ne'] + have hc : a * (b / a) = b := mul_div_cancel₀ b ha0 + nlinarith + +lemma information_nonneg {L p : ℝ} (hL : 1 < L) (hp : 0 ≤ p) (hp1 : p ≤ 1) : + 0 ≤ information L p := by + unfold information + apply div_nonneg _ (Real.log_pos hL).le + exact neg_nonneg.mpr (Real.log_nonpos hp hp1) + +lemma expected_conditioning_decrement_nonneg (q : V → Y → ℝ) + (hq : ∀ v y, 0 ≤ q v y) (hq1 : ∑ v, ∑ y, q v y = 1) + {L : ℝ} (hL : 1 < L) : + 0 ≤ ∑ v, ∑ y, q v y * (information L (colMass q y) - + information L (conditionalMass q v y)) := by + classical + have hcol : ∑ y, colMass q y = 1 := by + change (∑ y, ∑ v, q v y) = 1 + rw [Finset.sum_comm] + exact hq1 + have hrow : ∑ v, rowMass q v = 1 := hq1 + have hsum : ∑ v, ∑ y, (q v y - rowMass q v * colMass q y) = 0 := by + simp_rw [Finset.sum_sub_distrib, ← Finset.mul_sum, hcol, mul_one] + rw [hq1, hrow, sub_self] + calc + _ = ∑ v, ∑ y, (q v y - rowMass q v * colMass q y) / Real.log L := by + simp_rw [← Finset.sum_div] + rw [hsum, zero_div] + _ ≤ _ := by + apply Finset.sum_le_sum + intro v _ + apply Finset.sum_le_sum + intro y _ + by_cases hq0 : q v y = 0 + · simp only [hq0, zero_sub, zero_mul] + exact div_nonpos_of_nonpos_of_nonneg + (neg_nonpos.mpr (mul_nonneg (rowMass_nonneg q hq v) (colMass_nonneg q hq y))) + (Real.log_pos hL).le + · have hqy : 0 < q v y := lt_of_le_of_ne (hq v y) (Ne.symm hq0) + have hr : 0 < rowMass q v := hqy.trans_le (le_rowMass q hq v y) + have hc : 0 < colMass q y := hqy.trans_le (le_colMass q hq v y) + have h := sub_le_mul_log_div (hq v y) (mul_nonneg hr.le hc.le) + (fun _ => mul_pos hr hc) + have h' := div_le_div_of_nonneg_right h (Real.log_pos hL).le + unfold information conditionalMass + rw [Real.log_div hq0 (mul_pos hr hc).ne', Real.log_mul hr.ne' hc.ne'] at h' + rw [Real.log_div hq0 hr.ne'] + convert h' using 1 + ring + +def entropy (L : ℝ) (p : Y → ℝ) : ℝ := ∑ y, p y * information L (p y) + +def conditionalEntropy (L : ℝ) (q : V → Y → ℝ) : ℝ := + ∑ v, ∑ y, q v y * information L (conditionalMass q v y) + +lemma expected_conditioning_decrement_eq (L : ℝ) (q : V → Y → ℝ) : + (∑ v, ∑ y, q v y * (information L (colMass q y) - + information L (conditionalMass q v y))) = + entropy L (colMass q) - conditionalEntropy L q := by + unfold entropy conditionalEntropy + simp_rw [mul_sub, Finset.sum_sub_distrib] + congr 1 + rw [Finset.sum_comm] + simp only [colMass, Finset.sum_mul] + +lemma entropy_conditioning_le (q : V → Y → ℝ) + (hq : ∀ v y, 0 ≤ q v y) (hq1 : ∑ v, ∑ y, q v y = 1) + {L : ℝ} (hL : 1 < L) : + conditionalEntropy L q ≤ entropy L (colMass q) := by + have h := expected_conditioning_decrement_nonneg q hq hq1 hL + rw [expected_conditioning_decrement_eq] at h + linarith + +lemma conditionalEntropy_nonneg (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) + {L : ℝ} (hL : 1 < L) : 0 ≤ conditionalEntropy L q := by + apply Finset.sum_nonneg + intro v _ + apply Finset.sum_nonneg + intro y _ + apply mul_nonneg (hq v y) + apply information_nonneg hL + · exact div_nonneg (hq v y) (rowMass_nonneg q hq v) + · unfold conditionalMass + by_cases hr : rowMass q v = 0 + · simp only [hr, div_zero, zero_le_one] + · apply (div_le_one (lt_of_le_of_ne (rowMass_nonneg q hq v) (Ne.symm hr))).mpr + exact le_rowMass q hq v y + +lemma entropy_nonneg (p : Y → ℝ) (hp : ∀ y, 0 ≤ p y) (hp1 : ∑ y, p y = 1) + {L : ℝ} (hL : 1 < L) : 0 ≤ entropy L p := by + apply Finset.sum_nonneg + intro y _ + apply mul_nonneg (hp y) (information_nonneg hL (hp y) _) + rw [← hp1] + exact Finset.single_le_sum (fun z _ => hp z) (Finset.mem_univ y) + +lemma entropy_joint_eq (L : ℝ) (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) : + entropy L (fun vy : V × Y => q vy.1 vy.2) = + entropy L (rowMass q) + conditionalEntropy L q := by + classical + unfold entropy conditionalEntropy + rw [Fintype.sum_prod_type] + calc + _ = ∑ v, ∑ y, q v y * (information L (rowMass q v) + + information L (conditionalMass q v y)) := by + apply Finset.sum_congr rfl + intro v _ + apply Finset.sum_congr rfl + intro y _ + by_cases hq0 : q v y = 0 + · simp only [hq0, zero_mul] + · rw [joint_information_chain q hq (lt_of_le_of_ne (hq v y) (Ne.symm hq0)) L] + _ = _ := by + simp_rw [mul_add, Finset.sum_add_distrib, ← Finset.sum_mul] + rfl + +lemma entropy_joint_swap (L : ℝ) (q : V → Y → ℝ) : + entropy L (fun vy : V × Y => q vy.1 vy.2) = + entropy L (fun yv : Y × V => q yv.2 yv.1) := by + unfold entropy + rw [Fintype.sum_prod_type, Fintype.sum_prod_type, Finset.sum_comm] + +lemma conditioning_decrement_le_label_entropy (q : V → Y → ℝ) + (hq : ∀ v y, 0 ≤ q v y) {L : ℝ} (hL : 1 < L) : + entropy L (colMass q) - conditionalEntropy L q ≤ entropy L (rowMass q) := by + have h1 := entropy_joint_eq L q hq + have h2 := entropy_joint_eq L (fun y v => q v y) (fun y v => hq v y) + rw [← entropy_joint_swap L q] at h2 + have h3 := conditionalEntropy_nonneg (fun y v => q v y) (fun y v => hq v y) hL + change entropy L (fun vy : V × Y => q vy.1 vy.2) = + entropy L (colMass q) + conditionalEntropy L (fun y v => q v y) at h2 + linarith + +lemma entropy_le_log_card (p : Y → ℝ) (hp : ∀ y, 0 ≤ p y) (hp1 : ∑ y, p y = 1) + {L : ℝ} (hL : 1 < L) : + entropy L p ≤ Real.log (Fintype.card Y) / Real.log L := by + classical + have hnonempty : Nonempty Y := by + by_contra h + let : IsEmpty Y := not_nonempty_iff.mp h + simp only [Finset.univ_eq_empty, Finset.sum_empty] at hp1 + norm_num at hp1 + let : Nonempty Y := hnonempty + have hn : 0 < (Fintype.card Y : ℝ) := Nat.cast_pos.mpr Fintype.card_pos + have hu : 0 < (Fintype.card Y : ℝ)⁻¹ := inv_pos.mpr hn + have hsum : ∑ y, (p y - (Fintype.card Y : ℝ)⁻¹) = 0 := by + rw [Finset.sum_sub_distrib, hp1] + simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_inv_cancel₀ hn.ne', sub_self] + have hbound : 0 ≤ ∑ y, p y * Real.log (p y / (Fintype.card Y : ℝ)⁻¹) := by + rw [← hsum] + exact Finset.sum_le_sum (fun y _ => sub_le_mul_log_div (hp y) hu.le (fun _ => hu)) + have hid : (∑ y, p y * Real.log (p y / (Fintype.card Y : ℝ)⁻¹)) = + (∑ y, p y * Real.log (p y)) + Real.log (Fintype.card Y) := by + calc + _ = ∑ y, (p y * Real.log (p y) + p y * Real.log (Fintype.card Y)) := by + apply Finset.sum_congr rfl + intro y _ + by_cases hp0 : p y = 0 + · simp only [hp0, zero_mul, add_zero] + · rw [Real.log_div hp0 hu.ne', Real.log_inv] + ring + _ = _ := by rw [Finset.sum_add_distrib, ← Finset.sum_mul, hp1, one_mul] + rw [hid] at hbound + unfold entropy information + have heq : (∑ y, p y * (-Real.log (p y) / Real.log L)) = + -(∑ y, p y * Real.log (p y)) / Real.log L := by + simp_rw [← mul_div_assoc, mul_neg, ← Finset.sum_div, Finset.sum_neg_distrib] + rw [heq] + exact div_le_div_of_nonneg_right (by linarith) (Real.log_pos hL).le + +lemma direction_bin_cost_bound (q : V → Y → ℝ) + (hq : ∀ v y, 0 ≤ q v y) (hq1 : ∑ v, ∑ y, q v y = 1) + {L : ℝ} (hL : 1 < L) : + 0 ≤ entropy L (colMass q) - conditionalEntropy L q ∧ + entropy L (colMass q) - conditionalEntropy L q ≤ + Real.log (Fintype.card V) / Real.log L := by + constructor + · exact sub_nonneg.mpr (entropy_conditioning_le q hq hq1 hL) + · exact (conditioning_decrement_le_label_entropy q hq hL).trans + (entropy_le_log_card (rowMass q) (rowMass_nonneg q hq) hq1 hL) + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/JointCompactness.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/JointCompactness.lean new file mode 100644 index 0000000000000000000000000000000000000000..2bc67fba8f48b02d16da401aaf3323b0495a04e0 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/JointCompactness.lean @@ -0,0 +1,67 @@ +import Mathlib + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology ENNReal +namespace PlanarEndpoint.TransverseInformation + +lemma joint_laws_tight {μs : ℕ → ProbabilityMeasure (ℕ → ℝ)} + (htail : ∀ i : ℕ, ∀ ε : ℝ≥0∞, 0 < ε → ∃ R : ℝ, + ∀ n, (μs n : Measure (ℕ → ℝ)) {x | R < |x i|} ≤ ε) : + IsTightMeasureSet (Set.range (fun n => (μs n : Measure (ℕ → ℝ)))) := by + rw [isTightMeasureSet_iff_exists_isCompact_measure_compl_le] + intro ε hε + obtain ⟨δ, hδpos, hδsum⟩ := ENNReal.exists_pos_sum_of_countable' hε.ne' ℕ + choose R hR using fun i => htail i (δ i) (hδpos i) + let K : Set (ℕ → ℝ) := {x | ∀ i, x i ∈ Set.Icc (-(R i)) (R i)} + have hK : IsCompact K := isCompact_pi_infinite (fun _ => isCompact_Icc) + refine ⟨K, hK, ?_⟩ + rintro μ ⟨n, rfl⟩ + have hsubset : Kᶜ ⊆ ⋃ i, {x : ℕ → ℝ | R i < |x i|} := by + intro x hx + change ¬ (∀ i, -(R i) ≤ x i ∧ x i ≤ R i) at hx + push Not at hx + obtain ⟨i, hi⟩ := hx + refine Set.mem_iUnion.mpr ⟨i, ?_⟩ + change R i < |x i| + rw [lt_abs] + by_cases hlo : -(R i) ≤ x i + · exact Or.inl (hi hlo) + · exact Or.inr (by linarith) + calc + (μs n : Measure (ℕ → ℝ)) Kᶜ ≤ + (μs n : Measure (ℕ → ℝ)) (⋃ i, {x | R i < |x i|}) := measure_mono hsubset + _ ≤ ∑' i, (μs n : Measure (ℕ → ℝ)) {x | R i < |x i|} := measure_iUnion_le _ + _ ≤ ∑' i, δ i := ENNReal.tsum_le_tsum (fun i => hR i n) + _ ≤ ε := hδsum.le + +lemma exists_joint_weak_limit {μs : ℕ → ProbabilityMeasure (ℕ → ℝ)} + (htail : ∀ i : ℕ, ∀ ε : ℝ≥0∞, 0 < ε → ∃ R : ℝ, + ∀ n, (μs n : Measure (ℕ → ℝ)) {x | R < |x i|} ≤ ε) : + ∃ μ : ProbabilityMeasure (ℕ → ℝ), ∃ φ : ℕ → ℕ, + StrictMono φ ∧ Tendsto (μs ∘ φ) atTop (𝓝 μ) := by + have ht : IsTightMeasureSet + {((μ : ProbabilityMeasure (ℕ → ℝ)) : Measure (ℕ → ℝ)) | μ ∈ Set.range μs} := by + convert joint_laws_tight htail using 1 + ext m + simp only [mem_ofPred_eq, mem_range] + constructor + · rintro ⟨μ, ⟨n, rfl⟩, rfl⟩ + exact ⟨n, rfl⟩ + · rintro ⟨n, rfl⟩ + exact ⟨μs n, ⟨n, rfl⟩, rfl⟩ + have hc := isCompact_closure_of_isTightMeasureSet ht + obtain ⟨μ, _, φ, hφ, hlim⟩ := hc.isSeqCompact.subseq_of_frequently_in + (Filter.Eventually.frequently (Filter.Eventually.of_forall + (fun n => subset_closure (Set.mem_range_self n)))) + exact ⟨μ, φ, hφ, hlim⟩ + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/JointLaws.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/JointLaws.lean new file mode 100644 index 0000000000000000000000000000000000000000..612fe9ddb99a2900eda6c672fbf5dd09a9622a52 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/JointLaws.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.PlanarEndpoint.Information.FiniteLaws +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S : Type} [Fintype S] {V Y : ℕ → Type} + [∀ i, Fintype (V i)] [∀ i, Fintype (Y i)] + +def informationVector (L : ℝ) (w : S → ℝ) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) (s : S) : ℕ → ℝ := + fun i => sampledInformation L w (v i) (y i) s + +def sampledJointLaw (L : ℝ) (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (hw1 : ∑ s, w s = 1) (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) : + ProbabilityMeasure (ℕ → ℝ) := + finiteInformationLaw w hw hw1 (informationVector L w v y) + +lemma sampledJointLaw_nonneg (L : ℝ) (hL : 1 < L) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) (i : ℕ) : + ∀ᵐ x ∂(sampledJointLaw L w hw hw1 v y : Measure (ℕ → ℝ)), 0 ≤ x i := by + apply finiteInformationLaw_ae w hw hw1 (informationVector L w v y) (fun x => 0 ≤ x i) + · exact measurableSet_le measurable_const (measurable_pi_apply i) + · intro s _ + exact sampledInformation_nonneg w hw (v i) (y i) hL s + +omit [∀ index, Fintype (V index)] in +lemma sampledJointLaw_integrable (L : ℝ) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) (i : ℕ) : + Integrable (fun x => x i) (sampledJointLaw L w hw hw1 v y : Measure (ℕ → ℝ)) := + finiteInformationLaw_integrable w hw hw1 _ _ (measurable_pi_apply i) + +omit [∀ index, Fintype (V index)] in +lemma sampledJointLaw_integral (L : ℝ) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) (i : ℕ) : + (∫ x, x i ∂(sampledJointLaw L w hw hw1 v y : Measure (ℕ → ℝ))) = + ∑ s, w s * sampledInformation L w (v i) (y i) s := + finiteInformationLaw_integral w hw hw1 _ _ (measurable_pi_apply i) + +lemma sampledJointLaw_mass_tail_le (L : ℝ) (hL : 1 < L) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) (i : ℕ) (A : ℝ) : + (sampledJointLaw L w hw hw1 v y : Measure (ℕ → ℝ)) {x | A < |x i|} ≤ + ENNReal.ofReal ((Fintype.card (Y i) : ℝ) * L ^ (-A)) := by + change (finiteInformationLaw w hw hw1 (informationVector L w v y) : Measure (ℕ → ℝ)) _ ≤ _ + rw [finiteInformationLaw_apply _ _ _ _ _ + (isOpen_lt continuous_const (continuous_apply i).abs).measurableSet] + apply ENNReal.ofReal_le_ofReal + have heq : (∑ s, if |informationVector L w v y s i| > A then w s else 0) = + ∑ s, if A < sampledInformation L w (v i) (y i) s then w s else 0 := by + apply Finset.sum_congr rfl + intro s _ + rw [informationVector, abs_of_nonneg (sampledInformation_nonneg w hw (v i) (y i) hL s)] + change (∑ s, if A < |informationVector L w v y s i| then w s else 0) ≤ _ + rw [heq] + exact sampledInformation_mass_tail_le w hw hw1 (v i) (y i) hL + +lemma sampledJointLaw_expected_tail_le (L : ℝ) (hL : 1 < L) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) (i : ℕ) (A : ℝ) : + (∫ x, if A < x i then x i else 0 + ∂(sampledJointLaw L w hw hw1 v y : Measure (ℕ → ℝ))) ≤ + (Fintype.card (Y i) : ℝ) * (2 / Real.log L) * Real.sqrt (L ^ (-A)) := by + have hm : Measurable (fun x : ℕ → ℝ => if A < x i then x i else 0) := + (measurable_pi_apply i).piecewise + (isOpen_lt continuous_const (continuous_apply i)).measurableSet measurable_const + change (∫ x, _ ∂(finiteInformationLaw w hw hw1 (informationVector L w v y) : Measure (ℕ → ℝ))) ≤ _ + rw [finiteInformationLaw_integral w hw hw1 _ _ hm] + calc + _ = ∑ s, if A < sampledInformation L w (v i) (y i) s then + w s * sampledInformation L w (v i) (y i) s else 0 := by + apply Finset.sum_congr rfl + intro s _ + unfold informationVector + split_ifs <;> simp + _ ≤ _ := sampledInformation_expected_tail_le w hw hw1 (v i) (y i) hL + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/Logarithms.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/Logarithms.lean new file mode 100644 index 0000000000000000000000000000000000000000..1a96564212477e53f65adc62e3352684d31dc969 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/Logarithms.lean @@ -0,0 +1,93 @@ +import Mathlib + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open scoped BigOperators +open Filter Set +namespace PlanarEndpoint.TransverseInformation + +lemma bad_conditioning_mass_le {Y : Type*} [Fintype Y] + (p q : Y → ℝ) (hp : ∀ y, 0 ≤ p y) (_hq : ∀ y, 0 ≤ q y) + {ε : ℝ} (hε : 0 ≤ ε) : + (∑ y, if q y < ε * p y then q y else 0) ≤ ε * ∑ y, p y := by + classical + calc + _ ≤ ∑ y, ε * p y := Finset.sum_le_sum (fun y _ => by + split_ifs with h + · exact h.le + · exact mul_nonneg hε (hp y)) + _ = _ := (Finset.mul_sum _ _ _).symm + +lemma bad_conditioning_probability_le {Y : Type*} [Fintype Y] + (p q : Y → ℝ) (hp : ∀ y, 0 ≤ p y) (hq : ∀ y, 0 ≤ q y) + (hp1 : ∑ y, p y = 1) {ε : ℝ} (hε : 0 ≤ ε) : + (∑ y, if q y < ε * p y then q y else 0) ≤ ε := by + simpa only [hp1,mul_one] using bad_conditioning_mass_le p q hp hq hε + +lemma mixture_bad_conditioning_probability_le {Y V : Type*} [Fintype Y] [Fintype V] + (w : V → ℝ) (p q : V → Y → ℝ) + (hw : ∀ v, 0 ≤ w v) (hw1 : ∑ v, w v = 1) + (hp : ∀ v y, 0 ≤ p v y) (hq : ∀ v y, 0 ≤ q v y) + (hp1 : ∀ v, ∑ y, p v y = 1) {ε : ℝ} (hε : 0 ≤ ε) : + (∑ v, w v * ∑ y, if q v y < ε * p v y then q v y else 0) ≤ ε := by + classical + calc + _ ≤ ∑ v, w v * ε := Finset.sum_le_sum (fun v _ => + mul_le_mul_of_nonneg_left + (bad_conditioning_probability_le (p v) (q v) (hp v) (hq v) (hp1 v) hε) (hw v)) + _ = ε := by rw [← Finset.sum_mul,hw1,one_mul] + +lemma low_probability_mass_le {Y : Type*} (S : Finset Y) (p : Y → ℝ) + {δ : ℝ} (hδ : 0 ≤ δ) : + (∑ y ∈ S, if p y < δ then p y else 0) ≤ S.card * δ := by + classical + calc + _ ≤ ∑ _y ∈ S, δ := Finset.sum_le_sum (fun y _ => by + split_ifs with h + · exact h.le + · exact hδ) + _ = _ := by simp + +lemma restricted_low_probability_mass_le {Y : Type*} (S : Finset Y) + (p e : Y → ℝ) (_hp : ∀ y, 0 ≤ p y) + (he : ∀ y, 0 ≤ e y ∧ e y ≤ p y) {δ : ℝ} (hδ : 0 ≤ δ) : + (∑ y ∈ S, if p y < δ then e y else 0) ≤ S.card * δ := by + classical + apply le_trans _ (low_probability_mass_le S p hδ) + exact Finset.sum_le_sum (fun y _ => by + split_ifs <;> simp_all only [le_refl]) + +def information (L p : ℝ) : ℝ := -Real.log p / Real.log L + +lemma information_difference_eq (L p q : ℝ) (hp : 0 < p) (hq : 0 < q) : + information L p - information L q = Real.log (q/p) / Real.log L := by + rw [Real.log_div hq.ne' hp.ne'] + unfold information + ring + +lemma information_bad_iff {L p q η : ℝ} (hL : 1 < L) (hp : 0 < p) (hq : 0 < q) : + information L p - information L q < -η ↔ q < L ^ (-η) * p := by + rw [information_difference_eq L p q hp hq] + rw [div_lt_iff₀ (Real.log_pos hL)] + rw [← Real.log_rpow (by linarith : 0 < L) (-η)] + rw [Real.log_lt_log_iff (div_pos hq hp) (Real.rpow_pos_of_pos (by linarith) _)] + exact div_lt_iff₀ hp + +lemma conditioning_information_exception_le {Y : Type*} [Fintype Y] + (p q : Y → ℝ) (hp : ∀ y, 0 < p y) (hq : ∀ y, 0 < q y) + (hp1 : ∑ y, p y = 1) {L η : ℝ} (hL : 1 < L) : + (∑ y, if information L (p y) - information L (q y) < -η then q y else 0) + ≤ L ^ (-η) := by + classical + simp_rw [information_bad_iff hL (hp _) (hq _)] + exact bad_conditioning_probability_le p q (fun y => (hp y).le) + (fun y => (hq y).le) hp1 (Real.rpow_nonneg (by linarith) _) + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/MixedLaws.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/MixedLaws.lean new file mode 100644 index 0000000000000000000000000000000000000000..c907d6ff1c75054a291ef98f40668470f0137f8c --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/MixedLaws.lean @@ -0,0 +1,110 @@ +import OAI.Analysis.PlanarEndpoint.Information.CountableCompactness +import OAI.Analysis.PlanarEndpoint.Information.FiniteLaws +import OAI.Analysis.PlanarEndpoint.Information.JointLaws +import OAI.Analysis.PlanarEndpoint.Information.Sampling +import OAI.Analysis.PlanarEndpoint.Information.TailBounds + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S : Type} [Fintype S] {V Y : ℕ → Type} + [∀ i, Fintype (V i)] [∀ i, Fintype (Y i)] + +def mixedInformationVector (L : ℝ) (a : S → ℝ) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) (s : S) : (ℕ ⊕ ℕ) → ℝ := + Sum.elim (informationVector L a v y s) (fun i => z i s) + +def mixedInformationLaw (L : ℝ) (a : S → ℝ) (ha : ∀ s, 0 ≤ a s) + (ha1 : ∑ s, a s = 1) (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) : ProbabilityMeasure ((ℕ ⊕ ℕ) → ℝ) := + finiteInformationLaw a ha ha1 (mixedInformationVector L a v y z) + +lemma mixedInformationLaw_mass_tail_le (L : ℝ) (hL : 1 < L) (a : S → ℝ) + (ha : ∀ s, 0 ≤ a s) (ha1 : ∑ s, a s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) (i : ℕ) (A : ℝ) : + (mixedInformationLaw L a ha ha1 v y z : Measure ((ℕ ⊕ ℕ) → ℝ)) + {x | A < |x (.inl i)|} ≤ ENNReal.ofReal ((Fintype.card (Y i) : ℝ) * L ^ (-A)) := by + change (finiteInformationLaw a ha ha1 (mixedInformationVector L a v y z) : + Measure ((ℕ ⊕ ℕ) → ℝ)) _ ≤ _ + rw [finiteInformationLaw_apply a ha ha1 (mixedInformationVector L a v y z) + {x | A < |x (.inl i)|} + (isOpen_lt continuous_const (continuous_apply (Sum.inl i : ℕ ⊕ ℕ)).abs).measurableSet] + apply ENNReal.ofReal_le_ofReal + calc + _ = ∑ s, if A < sampledInformation L a (v i) (y i) s then a s else 0 := by + apply Finset.sum_congr rfl + intro s _ + change (if A < |sampledInformation L a (v i) (y i) s| then a s else 0) = _ + rw [abs_of_nonneg (sampledInformation_nonneg a ha (v i) (y i) hL s)] + _ ≤ _ := sampledInformation_mass_tail_le a ha ha1 (v i) (y i) hL + +omit [∀ index, Fintype (V index)] in +lemma mixedInformationLaw_aux_tail_zero (L : ℝ) (a : S → ℝ) + (ha : ∀ s, 0 ≤ a s) (ha1 : ∑ s, a s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) (i : ℕ) {D : ℝ} (hz : ∀ s, |z i s| ≤ D) : + (mixedInformationLaw L a ha ha1 v y z : Measure ((ℕ ⊕ ℕ) → ℝ)) + {x | D < |x (.inr i)|} = 0 := by + change (finiteInformationLaw a ha ha1 (mixedInformationVector L a v y z) : + Measure ((ℕ ⊕ ℕ) → ℝ)) _ = _ + rw [finiteInformationLaw_apply a ha ha1 (mixedInformationVector L a v y z) + {x | D < |x (.inr i)|} + (isOpen_lt continuous_const (continuous_apply (Sum.inr i : ℕ ⊕ ℕ)).abs).measurableSet] + have hzero : (∑ s, if D < |z i s| then a s else 0) = 0 := by + apply Finset.sum_eq_zero + intro s _ + rw [ite_eq_right (not_lt_of_ge (hz s))] + change ENNReal.ofReal (∑ sample, if D < |z i sample| then a sample else 0) = 0 + rw [hzero, ENNReal.ofReal_zero] + +section Varying +variable {S' : ℕ → Type} [∀ n, Fintype (S' n)] {V' Y' : ℕ → ℕ → Type} + [∀ n i, Fintype (V' n i)] [∀ n i, Fintype (Y' n i)] + (L : ℕ → ℝ) (a : (n : ℕ) → S' n → ℝ) + (ha : ∀ n s, 0 ≤ a n s) (ha1 : ∀ n, ∑ s, a n s = 1) + (v : (n i : ℕ) → S' n → V' n i) (y : (n i : ℕ) → S' n → Y' n i) + (z : (n : ℕ) → ℕ → S' n → ℝ) + +def mixedInformationLaws (n : ℕ) : ProbabilityMeasure ((ℕ ⊕ ℕ) → ℝ) := + mixedInformationLaw (L n) (a n) (ha n) (ha1 n) (v n) (y n) (z n) + +theorem exists_mixed_information_limit (hL : ∀ n, 2 ≤ L n) + (C D : ℕ → ℝ) (hcard : ∀ n i, (Fintype.card (Y' n i) : ℝ) ≤ (L n) ^ (C i)) + (hz : ∀ n i s, |z n i s| ≤ D i) : + ∃ μ : ProbabilityMeasure ((ℕ ⊕ ℕ) → ℝ), ∃ φ : ℕ → ℕ, + StrictMono φ ∧ Tendsto ((mixedInformationLaws L a ha ha1 v y z) ∘ φ) + atTop (𝓝 μ) := by + apply exists_joint_weak_limit_countable + intro j ε hε + cases j with + | inl i => + have ht : Tendsto (fun A : ℝ => ENNReal.ofReal ((2 : ℝ) ^ (C i-A))) atTop (𝓝 0) := by + simpa only [ENNReal.ofReal_zero] using + ENNReal.tendsto_ofReal (polynomial_alphabet_mass_envelope_tendsto_zero (C i)) + obtain ⟨R, hRC, hRε⟩ := ((eventually_ge_atTop (C i)).and + (ht.eventually (gt_mem_nhds hε))).exists + refine ⟨R, fun n => ?_⟩ + exact ((mixedInformationLaw_mass_tail_le (L n) (by linarith [hL n]) (a n) + (ha n) (ha1 n) (v n) (y n) (z n) i R).trans + (ENNReal.ofReal_le_ofReal (polynomial_alphabet_mass_bound (hL n) (hcard n i) hRC))).trans hRε.le + | inr i => + refine ⟨D i, fun n => ?_⟩ + change (mixedInformationLaw (L n) (a n) (ha n) (ha1 n) (v n) (y n) (z n) : + Measure ((ℕ ⊕ ℕ) → ℝ)) _ ≤ ε + rw [mixedInformationLaw_aux_tail_zero (L n) (a n) (ha n) (ha1 n) (v n) (y n) (z n) i (hz n i)] + exact bot_le + +end Varying +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/MixedLimits.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/MixedLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..3dc42c0de4829da5e0402ce5ee0a444e778f2b73 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/MixedLimits.lean @@ -0,0 +1,134 @@ +import OAI.Analysis.PlanarEndpoint.Information.Expectations +import OAI.Analysis.PlanarEndpoint.Information.MixedLaws +import OAI.Analysis.PlanarEndpoint.Information.MixedMoments +import OAI.Analysis.PlanarEndpoint.Information.Sampling +import OAI.Analysis.PlanarEndpoint.Information.TailBounds +import OAI.Analysis.PlanarEndpoint.Information.WeakLimits + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S : ℕ → Type} [∀ n, Fintype (S n)] + {V Y : ℕ → ℕ → Type} [∀ n i, Fintype (V n i)] [∀ n i, Fintype (Y n i)] + (L : ℕ → ℝ) (w : (n : ℕ) → S n → ℝ) + (hw : ∀ n s, 0 ≤ w n s) (hw1 : ∀ n, ∑ s, w n s = 1) + (v : (n i : ℕ) → S n → V n i) (y : (n i : ℕ) → S n → Y n i) + (z : (n : ℕ) → ℕ → S n → ℝ) + +lemma mixedInformationLaws_uniform_expected_tail (hL : ∀ n, 2 ≤ L n) + (C : ℕ → ℝ) (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (C i)) + (i : ℕ) : + ∀ ε : ℝ, 0 < ε → ∃ A₀ : ℝ, ∀ A : ℝ, A₀ ≤ A → ∀ n, + (∫ x, if A < x (.inl i) then x (.inl i) else 0 + ∂(mixedInformationLaws L w hw hw1 v y z n : Measure ((ℕ ⊕ ℕ) → ℝ))) < ε := by + intro ε hε + obtain ⟨a, ha⟩ := eventually_atTop.mp + ((polynomial_alphabet_envelope_tendsto_zero (C i)).eventually (gt_mem_nhds hε)) + refine ⟨max a (2*C i), fun A hA n => ?_⟩ + exact ((mixedInformationLaw_expected_tail_le (L n) (by linarith [hL n]) (w n) + (hw n) (hw1 n) (v n) (y n) (z n) i A).trans + (polynomial_alphabet_tail_bound (hL n) (hcard n i) + ((le_max_right _ _).trans hA))).trans_lt (ha A ((le_max_left _ _).trans hA)) + +lemma mixedInformationLaws_sharp_upper_tails (hL : ∀ n, 2 ≤ L n) + (hLlim : Tendsto L atTop atTop) (c : ℕ → ℕ → ℝ) (C : ℕ → ℝ) + (hc : ∀ i, Tendsto (fun n => c n i) atTop (𝓝 (C i))) + (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (c n i)) + (i : ℕ) {η : ℝ} (hη : 0 < η) : + Tendsto (fun n => (mixedInformationLaws L w hw hw1 v y z n : Measure ((ℕ ⊕ ℕ) → ℝ)) + {x | C i + η < x (.inl i)}) atTop (𝓝 0) := by + have henv : Tendsto (fun n => ENNReal.ofReal ((L n) ^ (-(η/2)))) atTop (𝓝 0) := by + simpa only [ENNReal.ofReal_zero, Function.comp_def] using ENNReal.tendsto_ofReal + ((tendsto_rpow_neg_atTop (half_pos hη)).comp hLlim) + apply tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds henv + (Eventually.of_forall (fun _ => bot_le)) + filter_upwards [(hc i).eventually (gt_mem_nhds (by linarith : C i < C i + η/2))] with n hn + have hLn : 0 < L n := by linarith [hL n] + have hsub : {x : (ℕ ⊕ ℕ) → ℝ | C i + η < x (.inl i)} ⊆ {x | C i + η < |x (.inl i)|} := by + intro x hx + change C i + η < x (.inl i) at hx + change C i + η < |x (.inl i)| + exact lt_of_lt_of_le hx (le_abs_self _) + refine (measure_mono hsub).trans ?_ + apply (mixedInformationLaw_mass_tail_le (L n) (by linarith [hL n]) (w n) + (hw n) (hw1 n) (v n) (y n) (z n) i (C i+η)).trans + apply ENNReal.ofReal_le_ofReal + calc + (Fintype.card (Y n i) : ℝ) * (L n) ^ (-(C i+η)) ≤ + (L n) ^ (c n i) * (L n) ^ (-(C i+η)) := + mul_le_mul_of_nonneg_right (hcard n i) (Real.rpow_nonneg hLn.le _) + _ = (L n) ^ (c n i - (C i+η)) := by + rw [sub_eq_add_neg, Real.rpow_add hLn] + _ ≤ _ := Real.rpow_le_rpow_of_exponent_le (by linarith [hL n]) (by linarith) + +theorem exists_mixed_information_sharp_limit (hL : ∀ n, 2 ≤ L n) + (hLlim : Tendsto L atTop atTop) (c : ℕ → ℕ → ℝ) (C : ℕ → ℝ) + (hc : ∀ i, Tendsto (fun n => c n i) atTop (𝓝 (C i))) + (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (c n i)) + (E : ℕ → ℝ) (hz : ∀ n i s, |z n i s| ≤ E i) : + ∃ μ : ProbabilityMeasure ((ℕ ⊕ ℕ) → ℝ), ∃ φ : ℕ → ℕ, + StrictMono φ ∧ Tendsto ((mixedInformationLaws L w hw hw1 v y z) ∘ φ) atTop (𝓝 μ) ∧ + (∀ᵐ x ∂(μ : Measure ((ℕ ⊕ ℕ) → ℝ)), ∀ i, 0 ≤ x (.inl i) ∧ x (.inl i) ≤ C i) ∧ + ∀ i, Integrable (fun x => x (.inl i)) (μ : Measure ((ℕ ⊕ ℕ) → ℝ)) ∧ + Tendsto (fun n => ∑ s, w (φ n) s * + sampledInformation (L (φ n)) (w (φ n)) (v (φ n) i) (y (φ n) i) s) + atTop (𝓝 (∫ x, x (.inl i) ∂(μ : Measure ((ℕ ⊕ ℕ) → ℝ)))) := by + have hb : ∀ i, ∃ D : ℝ, ∀ n, c n i ≤ D := by + intro i + obtain ⟨D, hD⟩ := (Metric.isBounded_range_of_tendsto _ (hc i)).bddAbove + exact ⟨D, fun n => hD (Set.mem_range_self n)⟩ + choose D hD using hb + have hcardD : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (D i) := by + intro n i + exact (hcard n i).trans + (Real.rpow_le_rpow_of_exponent_le (by linarith [hL n]) (hD i n)) + obtain ⟨μ, φ, hφ, hμ⟩ := exists_mixed_information_limit + L w hw hw1 v y z hL D E hcardD hz + have hnonneg : ∀ i, ∀ᵐ x ∂(μ : Measure ((ℕ ⊕ ℕ) → ℝ)), 0 ≤ x (.inl i) := by + intro i + apply ae_nonneg_of_weak_limit_tails hμ (continuous_apply (Sum.inl i : ℕ ⊕ ℕ)) + intro η hη + have hz : ∀ n, (mixedInformationLaws L w hw hw1 v y z (φ n) : Measure ((ℕ ⊕ ℕ) → ℝ)) + {x | x (.inl i) < -η} = 0 := by + intro n + apply le_antisymm _ bot_le + have hn := mixedInformationLaw_nonneg (L (φ n)) (by linarith [hL (φ n)]) + (w (φ n)) (hw (φ n)) (hw1 (φ n)) (v (φ n)) (y (φ n)) (z (φ n)) i + have hn' := ae_iff.mp hn + exact (measure_mono (fun x hx => by + change x (.inl i) < -η at hx + change ¬0 ≤ x (.inl i) + linarith)).trans_eq hn' + simpa only [Function.comp_apply, hz] using (tendsto_const_nhds : + Tendsto (fun _ : ℕ => (0 : ℝ≥0∞)) atTop (𝓝 0)) + have hupper : ∀ i, ∀ᵐ x ∂(μ : Measure ((ℕ ⊕ ℕ) → ℝ)), x (.inl i) ≤ C i := by + intro i + have h := ae_le_on_open_of_weak_limit_tails hμ isOpen_univ (continuous_apply (Sum.inl i : ℕ ⊕ ℕ)) (C i) + (fun η hη => by + simpa only [Set.univ_inter, Function.comp_def] using + (mixedInformationLaws_sharp_upper_tails L w hw hw1 v y z hL hLlim c C hc hcard i hη).comp hφ.tendsto_atTop) + exact h.mono (fun x hx => hx (Set.mem_univ x)) + refine ⟨μ, φ, hφ, hμ, ae_all_iff.mpr (fun i => (hnonneg i).and (hupper i)), ?_⟩ + intro i + have he := expected_information_tendsto hμ (continuous_apply (Sum.inl i : ℕ ⊕ ℕ)) + (fun n => mixedInformationLaw_integrable (L (φ n)) (w (φ n)) (hw (φ n)) (hw1 (φ n)) + (v (φ n)) (y (φ n)) (z (φ n)) i) + (fun n => mixedInformationLaw_nonneg (L (φ n)) (by linarith [hL (φ n)]) + (w (φ n)) (hw (φ n)) (hw1 (φ n)) (v (φ n)) (y (φ n)) (z (φ n)) i) + (hnonneg i) (hupper i) (fun ε hε => by + obtain ⟨A₀, hA₀⟩ := mixedInformationLaws_uniform_expected_tail L w hw hw1 v y z hL D hcardD i ε hε + exact ⟨A₀, fun A hA n => hA₀ A hA (φ n)⟩) + refine ⟨he.1, ?_⟩ + simpa only [Function.comp_apply, mixedInformationLaws, mixedInformationLaw_integral] using he.2 + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/MixedMoments.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/MixedMoments.lean new file mode 100644 index 0000000000000000000000000000000000000000..d1a684d30141f7ad41c1c746b3b780cc68d83c21 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/MixedMoments.lean @@ -0,0 +1,77 @@ +import OAI.Analysis.PlanarEndpoint.Information.FiniteLaws +import OAI.Analysis.PlanarEndpoint.Information.MixedLaws +import OAI.Analysis.PlanarEndpoint.Information.Sampling + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S : Type} [Fintype S] {V Y : ℕ → Type} + [∀ i, Fintype (V i)] [∀ i, Fintype (Y i)] + +lemma mixedInformationLaw_nonneg (L : ℝ) (hL : 1 < L) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) (i : ℕ) : + ∀ᵐ x ∂(mixedInformationLaw L w hw hw1 v y z : Measure ((ℕ ⊕ ℕ) → ℝ)), + 0 ≤ x (.inl i) := by + apply finiteInformationLaw_ae w hw hw1 (mixedInformationVector L w v y z) + (fun x => 0 ≤ x (.inl i)) + · exact measurableSet_le measurable_const (measurable_pi_apply _) + · intro s _ + exact sampledInformation_nonneg w hw (v i) (y i) hL s + +omit [∀ index, Fintype (V index)] in +lemma mixedInformationLaw_integrable (L : ℝ) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) (i : ℕ) : + Integrable (fun x => x (.inl i)) + (mixedInformationLaw L w hw hw1 v y z : Measure ((ℕ ⊕ ℕ) → ℝ)) := + finiteInformationLaw_integrable w hw hw1 _ _ (measurable_pi_apply _) + +omit [∀ index, Fintype (V index)] in +lemma mixedInformationLaw_integral (L : ℝ) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) (i : ℕ) : + (∫ x, x (.inl i) + ∂(mixedInformationLaw L w hw hw1 v y z : Measure ((ℕ ⊕ ℕ) → ℝ))) = + ∑ s, w s * sampledInformation L w (v i) (y i) s := + finiteInformationLaw_integral w hw hw1 _ _ (measurable_pi_apply _) + +lemma mixedInformationLaw_expected_tail_le (L : ℝ) (hL : 1 < L) (w : S → ℝ) + (hw : ∀ s, 0 ≤ w s) (hw1 : ∑ s, w s = 1) + (v : (i : ℕ) → S → V i) (y : (i : ℕ) → S → Y i) + (z : ℕ → S → ℝ) (i : ℕ) (A : ℝ) : + (∫ x, if A < x (.inl i) then x (.inl i) else 0 + ∂(mixedInformationLaw L w hw hw1 v y z : Measure ((ℕ ⊕ ℕ) → ℝ))) ≤ + (Fintype.card (Y i) : ℝ) * (2 / Real.log L) * Real.sqrt (L ^ (-A)) := by + have hm : Measurable (fun x : (ℕ ⊕ ℕ) → ℝ => + if A < x (.inl i) then x (.inl i) else 0) := + (measurable_pi_apply (Sum.inl i : ℕ ⊕ ℕ)).piecewise + (isOpen_lt continuous_const (continuous_apply (Sum.inl i : ℕ ⊕ ℕ))).measurableSet + measurable_const + change (∫ x, _ ∂(finiteInformationLaw w hw hw1 + (mixedInformationVector L w v y z) : Measure ((ℕ ⊕ ℕ) → ℝ))) ≤ _ + rw [finiteInformationLaw_integral w hw hw1 _ _ hm] + calc + _ = ∑ s, if A < sampledInformation L w (v i) (y i) s then + w s * sampledInformation L w (v i) (y i) s else 0 := by + apply Finset.sum_congr rfl + intro s _ + change w s * (if A < sampledInformation L w (v i) (y i) s then + sampledInformation L w (v i) (y i) s else 0) = _ + by_cases h : A < sampledInformation L w (v i) (y i) s <;> simp [h] + _ ≤ _ := sampledInformation_expected_tail_le w hw hw1 (v i) (y i) hL + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/Sampling.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/Sampling.lean new file mode 100644 index 0000000000000000000000000000000000000000..c5a8e44c142c8b74ee2c8a500cb20a223fffe93e --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/Sampling.lean @@ -0,0 +1,117 @@ +import OAI.Analysis.PlanarEndpoint.Information.FiniteTables +import OAI.Analysis.PlanarEndpoint.Information.Logarithms +import OAI.Analysis.PlanarEndpoint.Information.TailBounds + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal +namespace PlanarEndpoint.TransverseInformation + +variable {S V Y : Type*} [Fintype S] [Fintype V] [Fintype Y] + +open scoped Classical in +def sampledTable (w : S → ℝ) (v : S → V) (y : S → Y) (b : V) (a : Y) : ℝ := + ∑ s, if v s = b ∧ y s = a then w s else 0 + +omit [Fintype V] [Fintype Y] in +lemma sampledTable_nonneg (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (v : S → V) (y : S → Y) (b : V) (a : Y) : 0 ≤ sampledTable w v y b a := by + classical + unfold sampledTable + exact Finset.sum_nonneg (fun s _ => by split_ifs; exact hw s; exact le_rfl) + +lemma sampledTable_sum (w : S → ℝ) (v : S → V) (y : S → Y) (f : V → Y → ℝ) : + (∑ b, ∑ a, sampledTable w v y b a * f b a) = ∑ s, w s * f (v s) (y s) := by + classical + unfold sampledTable + simp_rw [Finset.sum_mul] + calc + _ = ∑ b, ∑ s, ∑ a, (if v s = b ∧ y s = a then w s else 0) * f b a := by + apply Finset.sum_congr rfl + intro b _ + rw [Finset.sum_comm] + _ = ∑ s, ∑ b, ∑ a, (if v s = b ∧ y s = a then w s else 0) * f b a := by + rw [Finset.sum_comm] + _ = _ := by + apply Finset.sum_congr rfl + intro s _ + simp [ite_and, ite_mul, eq_comm] + +lemma sampledTable_total (w : S → ℝ) (v : S → V) (y : S → Y) : + (∑ b, ∑ a, sampledTable w v y b a) = ∑ s, w s := by + simpa only [mul_one] using sampledTable_sum w v y (fun _ _ => 1) + +def sampledInformation (L : ℝ) (w : S → ℝ) (v : S → V) (y : S → Y) (s : S) : ℝ := + information L (conditionalMass (sampledTable w v y) (v s) (y s)) + +lemma sampledInformation_nonneg (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (v : S → V) (y : S → Y) {L : ℝ} (hL : 1 < L) (s : S) : + 0 ≤ sampledInformation L w v y s := + conditional_information_nonneg _ (sampledTable_nonneg w hw v y) hL _ _ + +lemma sampledInformation_mass_tail_le (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (hw1 : ∑ s, w s = 1) (v : S → V) (y : S → Y) {L A : ℝ} (hL : 1 < L) : + (∑ s, if A < sampledInformation L w v y s then w s else 0) ≤ + (Fintype.card Y : ℝ) * L ^ (-A) := by + classical + unfold sampledInformation + calc + _ = ∑ s, w s * (if A < information L + (conditionalMass (sampledTable w v y) (v s) (y s)) then 1 else 0) := by + apply Finset.sum_congr rfl + intro s _ + split_ifs <;> simp + _ = ∑ b, ∑ a, sampledTable w v y b a * (if A < information L + (conditionalMass (sampledTable w v y) b a) then 1 else 0) := + (sampledTable_sum w v y (fun b a => if A < information L + (conditionalMass (sampledTable w v y) b a) then (1 : ℝ) else 0)).symm + _ = ∑ b, ∑ a, if A < information L (conditionalMass (sampledTable w v y) b a) + then sampledTable w v y b a else 0 := by + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro a _ + split_ifs <;> simp + _ ≤ _ := conditional_information_mass_tail_le _ (sampledTable_nonneg w hw v y) + (by rw [sampledTable_total, hw1]) hL + +lemma sampledInformation_expected_tail_le (w : S → ℝ) (hw : ∀ s, 0 ≤ w s) + (hw1 : ∑ s, w s = 1) (v : S → V) (y : S → Y) {L A : ℝ} (hL : 1 < L) : + (∑ s, if A < sampledInformation L w v y s then + w s * sampledInformation L w v y s else 0) ≤ + (Fintype.card Y : ℝ) * (2 / Real.log L) * Real.sqrt (L ^ (-A)) := by + classical + unfold sampledInformation + calc + _ = ∑ s, w s * (if A < information L + (conditionalMass (sampledTable w v y) (v s) (y s)) then + information L (conditionalMass (sampledTable w v y) (v s) (y s)) else 0) := by + apply Finset.sum_congr rfl + intro s _ + split_ifs <;> simp + _ = ∑ b, ∑ a, sampledTable w v y b a * (if A < information L + (conditionalMass (sampledTable w v y) b a) then + information L (conditionalMass (sampledTable w v y) b a) else 0) := + (sampledTable_sum w v y (fun b a => if A < information L + (conditionalMass (sampledTable w v y) b a) then + information L (conditionalMass (sampledTable w v y) b a) else 0)).symm + _ = ∑ b, ∑ a, if A < information L (conditionalMass (sampledTable w v y) b a) + then sampledTable w v y b a * information L (conditionalMass (sampledTable w v y) b a) + else 0 := by + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro a _ + split_ifs <;> simp + _ ≤ _ := conditional_information_expected_tail_le _ (sampledTable_nonneg w hw v y) + (by rw [sampledTable_total, hw1]) hL + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/SamplingLimits.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/SamplingLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..4fb76f666478134229a55e371fce44a75e5e8989 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/SamplingLimits.lean @@ -0,0 +1,151 @@ +import OAI.Analysis.PlanarEndpoint.Information.Expectations +import OAI.Analysis.PlanarEndpoint.Information.JointCompactness +import OAI.Analysis.PlanarEndpoint.Information.JointLaws +import OAI.Analysis.PlanarEndpoint.Information.Sampling +import OAI.Analysis.PlanarEndpoint.Information.TailBounds +import OAI.Analysis.PlanarEndpoint.Information.WeakLimits + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology BigOperators ENNReal Classical +namespace PlanarEndpoint.TransverseInformation + +variable {S : ℕ → Type} [∀ n, Fintype (S n)] + {V Y : ℕ → ℕ → Type} [∀ n i, Fintype (V n i)] [∀ n i, Fintype (Y n i)] + (L : ℕ → ℝ) (w : (n : ℕ) → S n → ℝ) + (hw : ∀ n s, 0 ≤ w n s) (hw1 : ∀ n, ∑ s, w n s = 1) + (v : (n i : ℕ) → S n → V n i) (y : (n i : ℕ) → S n → Y n i) + +def sampledJointLaws (n : ℕ) : ProbabilityMeasure (ℕ → ℝ) := + sampledJointLaw (L n) (w n) (hw n) (hw1 n) (v n) (y n) + +lemma sampledJointLaws_coordinate_tight (hL : ∀ n, 2 ≤ L n) + (C : ℕ → ℝ) (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (C i)) : + ∀ i : ℕ, ∀ ε : ℝ≥0∞, 0 < ε → ∃ R : ℝ, ∀ n, + (sampledJointLaws L w hw hw1 v y n : Measure (ℕ → ℝ)) + {x | R < |x i|} ≤ ε := by + intro i ε hε + have ht : Tendsto (fun A : ℝ => ENNReal.ofReal ((2 : ℝ) ^ (C i-A))) atTop (𝓝 0) := by + simpa only [ENNReal.ofReal_zero] using + ENNReal.tendsto_ofReal (polynomial_alphabet_mass_envelope_tendsto_zero (C i)) + obtain ⟨R, hRC, hRε⟩ := ((eventually_ge_atTop (C i)).and + (ht.eventually (gt_mem_nhds hε))).exists + refine ⟨R, fun n => ?_⟩ + exact ((sampledJointLaw_mass_tail_le (L n) (by linarith [hL n]) (w n) + (hw n) (hw1 n) (v n) (y n) i R).trans + (ENNReal.ofReal_le_ofReal (polynomial_alphabet_mass_bound (hL n) (hcard n i) hRC))).trans hRε.le + +lemma sampledJointLaws_uniform_expected_tail (hL : ∀ n, 2 ≤ L n) + (C : ℕ → ℝ) (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (C i)) + (i : ℕ) : + ∀ ε : ℝ, 0 < ε → ∃ A₀ : ℝ, ∀ A : ℝ, A₀ ≤ A → ∀ n, + (∫ x, if A < x i then x i else 0 + ∂(sampledJointLaws L w hw hw1 v y n : Measure (ℕ → ℝ))) < ε := by + intro ε hε + obtain ⟨a, ha⟩ := eventually_atTop.mp + ((polynomial_alphabet_envelope_tendsto_zero (C i)).eventually (gt_mem_nhds hε)) + refine ⟨max a (2*C i), fun A hA n => ?_⟩ + exact ((sampledJointLaw_expected_tail_le (L n) (by linarith [hL n]) (w n) + (hw n) (hw1 n) (v n) (y n) i A).trans + (polynomial_alphabet_tail_bound (hL n) (hcard n i) + ((le_max_right _ _).trans hA))).trans_lt (ha A ((le_max_left _ _).trans hA)) + +lemma sampledJointLaws_sharp_upper_tails (hL : ∀ n, 2 ≤ L n) + (hLlim : Tendsto L atTop atTop) (c : ℕ → ℕ → ℝ) (C : ℕ → ℝ) + (hc : ∀ i, Tendsto (fun n => c n i) atTop (𝓝 (C i))) + (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (c n i)) + (i : ℕ) {η : ℝ} (hη : 0 < η) : + Tendsto (fun n => (sampledJointLaws L w hw hw1 v y n : Measure (ℕ → ℝ)) + {x | C i + η < x i}) atTop (𝓝 0) := by + have henv : Tendsto (fun n => ENNReal.ofReal ((L n) ^ (-(η/2)))) atTop (𝓝 0) := by + simpa only [ENNReal.ofReal_zero, Function.comp_def] using ENNReal.tendsto_ofReal + ((tendsto_rpow_neg_atTop (half_pos hη)).comp hLlim) + apply tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds henv + (Eventually.of_forall (fun _ => bot_le)) + filter_upwards [(hc i).eventually (gt_mem_nhds (by linarith : C i < C i + η/2))] with n hn + have hLn : 0 < L n := by linarith [hL n] + have hsub : {x : ℕ → ℝ | C i + η < x i} ⊆ {x | C i + η < |x i|} := by + intro x hx + change C i + η < x i at hx + change C i + η < |x i| + exact lt_of_lt_of_le hx (le_abs_self _) + refine (measure_mono hsub).trans ?_ + apply (sampledJointLaw_mass_tail_le (L n) (by linarith [hL n]) (w n) + (hw n) (hw1 n) (v n) (y n) i (C i+η)).trans + apply ENNReal.ofReal_le_ofReal + calc + (Fintype.card (Y n i) : ℝ) * (L n) ^ (-(C i+η)) ≤ + (L n) ^ (c n i) * (L n) ^ (-(C i+η)) := + mul_le_mul_of_nonneg_right (hcard n i) (Real.rpow_nonneg hLn.le _) + _ = (L n) ^ (c n i - (C i+η)) := by + rw [sub_eq_add_neg, Real.rpow_add hLn] + _ ≤ _ := Real.rpow_le_rpow_of_exponent_le (by linarith [hL n]) (by linarith) + +theorem exists_sampled_information_limit (hL : ∀ n, 2 ≤ L n) + (hLlim : Tendsto L atTop atTop) (c : ℕ → ℕ → ℝ) (C : ℕ → ℝ) + (hc : ∀ i, Tendsto (fun n => c n i) atTop (𝓝 (C i))) + (hcard : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (c n i)) : + ∃ μ : ProbabilityMeasure (ℕ → ℝ), ∃ φ : ℕ → ℕ, + StrictMono φ ∧ Tendsto ((sampledJointLaws L w hw hw1 v y) ∘ φ) atTop (𝓝 μ) ∧ + (∀ᵐ x ∂(μ : Measure (ℕ → ℝ)), ∀ i, 0 ≤ x i ∧ x i ≤ C i) ∧ + ∀ i, Integrable (fun x => x i) (μ : Measure (ℕ → ℝ)) ∧ + Tendsto (fun n => ∑ s, w (φ n) s * + sampledInformation (L (φ n)) (w (φ n)) (v (φ n) i) (y (φ n) i) s) + atTop (𝓝 (∫ x, x i ∂(μ : Measure (ℕ → ℝ)))) := by + have hb : ∀ i, ∃ D : ℝ, ∀ n, c n i ≤ D := by + intro i + obtain ⟨D, hD⟩ := (Metric.isBounded_range_of_tendsto _ (hc i)).bddAbove + exact ⟨D, fun n => hD (Set.mem_range_self n)⟩ + choose D hD using hb + have hcardD : ∀ n i, (Fintype.card (Y n i) : ℝ) ≤ (L n) ^ (D i) := by + intro n i + exact (hcard n i).trans + (Real.rpow_le_rpow_of_exponent_le (by linarith [hL n]) (hD i n)) + obtain ⟨μ, φ, hφ, hμ⟩ := exists_joint_weak_limit + (sampledJointLaws_coordinate_tight L w hw hw1 v y hL D hcardD) + have hnonneg : ∀ i, ∀ᵐ x ∂(μ : Measure (ℕ → ℝ)), 0 ≤ x i := by + intro i + apply ae_nonneg_of_weak_limit_tails hμ (continuous_apply i) + intro η hη + have hz : ∀ n, (sampledJointLaws L w hw hw1 v y (φ n) : Measure (ℕ → ℝ)) + {x | x i < -η} = 0 := by + intro n + apply le_antisymm _ bot_le + have hn := sampledJointLaw_nonneg (L (φ n)) (by linarith [hL (φ n)]) + (w (φ n)) (hw (φ n)) (hw1 (φ n)) (v (φ n)) (y (φ n)) i + have hn' := ae_iff.mp hn + exact (measure_mono (fun x hx => by + change x i < -η at hx + change ¬0 ≤ x i + linarith)).trans_eq hn' + simpa only [Function.comp_apply, hz] using (tendsto_const_nhds : + Tendsto (fun _ : ℕ => (0 : ℝ≥0∞)) atTop (𝓝 0)) + have hupper : ∀ i, ∀ᵐ x ∂(μ : Measure (ℕ → ℝ)), x i ≤ C i := by + intro i + have h := ae_le_on_open_of_weak_limit_tails hμ isOpen_univ (continuous_apply i) (C i) + (fun η hη => by + simpa only [Set.univ_inter, Function.comp_def] using + (sampledJointLaws_sharp_upper_tails L w hw hw1 v y hL hLlim c C hc hcard i hη).comp hφ.tendsto_atTop) + exact h.mono (fun x hx => hx (Set.mem_univ x)) + refine ⟨μ, φ, hφ, hμ, ae_all_iff.mpr (fun i => (hnonneg i).and (hupper i)), ?_⟩ + intro i + have he := expected_information_tendsto hμ (continuous_apply i) + (fun n => sampledJointLaw_integrable (L (φ n)) (w (φ n)) (hw (φ n)) (hw1 (φ n)) + (v (φ n)) (y (φ n)) i) + (fun n => sampledJointLaw_nonneg (L (φ n)) (by linarith [hL (φ n)]) + (w (φ n)) (hw (φ n)) (hw1 (φ n)) (v (φ n)) (y (φ n)) i) + (hnonneg i) (hupper i) (fun ε hε => by + obtain ⟨A₀, hA₀⟩ := sampledJointLaws_uniform_expected_tail L w hw hw1 v y hL D hcardD i ε hε + exact ⟨A₀, fun A hA n => hA₀ A hA (φ n)⟩) + refine ⟨he.1, ?_⟩ + simpa only [Function.comp_apply, sampledJointLaws, sampledJointLaw_integral] using he.2 + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/TailBounds.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/TailBounds.lean new file mode 100644 index 0000000000000000000000000000000000000000..9afa2c5ca4908aea2410d07e81d27c0bbb159de1 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/TailBounds.lean @@ -0,0 +1,245 @@ +import OAI.Analysis.PlanarEndpoint.Information.FiniteTables +import OAI.Analysis.PlanarEndpoint.Information.Logarithms + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open scoped BigOperators +namespace PlanarEndpoint.TransverseInformation + +lemma neg_mul_log_le_two_sqrt {p : ℝ} (hp : 0 ≤ p) : + -p * Real.log p ≤ 2 * Real.sqrt p := by + by_cases hp0 : p = 0 + · simp only [hp0, neg_zero, zero_mul, Real.sqrt_zero, mul_zero, le_refl] + have hp' : 0 < p := lt_of_le_of_ne hp (Ne.symm hp0) + have hs : 0 < Real.sqrt p := Real.sqrt_pos.mpr hp' + have hlog := Real.log_le_sub_one_of_pos (inv_pos.mpr hs) + rw [Real.log_inv, Real.log_sqrt hp] at hlog + have hmul := mul_le_mul_of_nonneg_left hlog (mul_nonneg (by norm_num : (0:ℝ) ≤ 2) hp) + have hid : p * (Real.sqrt p)⁻¹ = Real.sqrt p := by + calc + p * (Real.sqrt p)⁻¹ = ((Real.sqrt p) * (Real.sqrt p)) * (Real.sqrt p)⁻¹ := by + rw [← pow_two, Real.sq_sqrt hp] + _ = Real.sqrt p := by rw [mul_assoc, mul_inv_cancel₀ hs.ne', mul_one] + calc + -p * Real.log p = (2 * p) * (-(Real.log p / 2)) := by ring + _ ≤ (2 * p) * ((Real.sqrt p)⁻¹ - 1) := hmul + _ = 2 * Real.sqrt p - 2 * p := by rw [mul_sub, mul_one, mul_assoc, hid] + _ ≤ 2 * Real.sqrt p := by linarith + +lemma information_tail_pointwise {L p A : ℝ} (hL : 1 < L) (hp : 0 ≤ p) : + (if A < information L p then p * information L p else 0) ≤ + (2 / Real.log L) * Real.sqrt (L ^ (-A)) := by + classical + have hL0 : 0 < L := lt_trans zero_lt_one hL + have hl : 0 < Real.log L := Real.log_pos hL + have hr : 0 ≤ (2 / Real.log L) * Real.sqrt (L ^ (-A)) := + mul_nonneg (div_nonneg (by norm_num) hl.le) (Real.sqrt_nonneg _) + by_cases hp0 : p = 0 + · simp only [hp0, zero_mul, ite_self] + exact hr + have hp' : 0 < p := lt_of_le_of_ne hp (Ne.symm hp0) + split_ifs with h + · have hsmall := (information_gt_iff hL hp').mp h + calc + p * information L p = (-p * Real.log p) / Real.log L := by + unfold information + ring + _ ≤ (2 * Real.sqrt p) / Real.log L := + div_le_div_of_nonneg_right (neg_mul_log_le_two_sqrt hp) hl.le + _ = (2 / Real.log L) * Real.sqrt p := by ring + _ ≤ _ := mul_le_mul_of_nonneg_left (Real.sqrt_le_sqrt hsmall.le) + (div_nonneg (by norm_num) hl.le) + · exact hr + +lemma information_mass_tail_le {Y : Type*} [Fintype Y] + (p : Y → ℝ) (hp : ∀ y, 0 ≤ p y) {L A : ℝ} (hL : 1 < L) : + (∑ y, if A < information L (p y) then p y else 0) ≤ + (Fintype.card Y : ℝ) * L ^ (-A) := by + classical + calc + _ ≤ ∑ _y : Y, L ^ (-A) := by + apply Finset.sum_le_sum + intro y _ + by_cases hp0 : p y = 0 + · simp only [hp0, ite_self] + exact Real.rpow_nonneg (by linarith) _ + have hp' : 0 < p y := lt_of_le_of_ne (hp y) (Ne.symm hp0) + split_ifs with h + · exact ((information_gt_iff hL hp').mp h).le + · exact Real.rpow_nonneg (by linarith) _ + _ = _ := by simp + +lemma information_expected_tail_le {Y : Type*} [Fintype Y] + (p : Y → ℝ) (hp : ∀ y, 0 ≤ p y) {L A : ℝ} (hL : 1 < L) : + (∑ y, if A < information L (p y) then p y * information L (p y) else 0) ≤ + (Fintype.card Y : ℝ) * (2 / Real.log L) * Real.sqrt (L ^ (-A)) := by + classical + calc + _ ≤ ∑ _y : Y, (2 / Real.log L) * Real.sqrt (L ^ (-A)) := + Finset.sum_le_sum (fun y _ => information_tail_pointwise hL (hp y)) + _ = _ := by simp [mul_assoc] + +lemma jointMass_eq_row_mul_conditional {V Y : Type*} [Fintype V] [Fintype Y] + (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) (v : V) (y : Y) : + q v y = rowMass q v * conditionalMass q v y := by + by_cases hv : rowMass q v = 0 + · have hq0 : q v y = 0 := le_antisymm (by simpa [hv] using le_rowMass q hq v y) (hq v y) + simp [hv, hq0] + · unfold conditionalMass + field_simp + +lemma conditional_information_nonneg {V Y : Type*} [Fintype V] [Fintype Y] + (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) {L : ℝ} (hL : 1 < L) + (v : V) (y : Y) : 0 ≤ information L (conditionalMass q v y) := by + have hp0 : 0 ≤ conditionalMass q v y := + div_nonneg (hq v y) (rowMass_nonneg q hq v) + have hp1 : conditionalMass q v y ≤ 1 := by + by_cases hr : rowMass q v = 0 + · simp [conditionalMass, hr] + · exact (div_le_one (lt_of_le_of_ne (rowMass_nonneg q hq v) (Ne.symm hr))).mpr + (le_rowMass q hq v y) + exact div_nonneg (neg_nonneg.mpr (Real.log_nonpos hp0 hp1)) (Real.log_pos hL).le + +lemma conditional_information_mass_tail_le {V Y : Type*} [Fintype V] [Fintype Y] + (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) + (hq1 : ∑ v, ∑ y, q v y = 1) {L A : ℝ} (hL : 1 < L) : + (∑ v, ∑ y, if A < information L (conditionalMass q v y) then q v y else 0) ≤ + (Fintype.card Y : ℝ) * L ^ (-A) := by + classical + have hc : ∀ v y, 0 ≤ conditionalMass q v y := fun v y => + div_nonneg (hq v y) (rowMass_nonneg q hq v) + calc + _ = ∑ v, rowMass q v * (∑ y, if A < information L (conditionalMass q v y) + then conditionalMass q v y else 0) := by + apply Finset.sum_congr rfl + intro v _ + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro y _ + split_ifs + · exact jointMass_eq_row_mul_conditional q hq v y + · simp + _ ≤ ∑ v, rowMass q v * ((Fintype.card Y : ℝ) * L ^ (-A)) := by + apply Finset.sum_le_sum + intro v _ + exact mul_le_mul_of_nonneg_left + (information_mass_tail_le (conditionalMass q v) (hc v) hL) + (rowMass_nonneg q hq v) + _ = _ := by + rw [← Finset.sum_mul] + simp only [rowMass, hq1, one_mul] + +lemma conditional_information_expected_tail_le {V Y : Type*} [Fintype V] [Fintype Y] + (q : V → Y → ℝ) (hq : ∀ v y, 0 ≤ q v y) + (hq1 : ∑ v, ∑ y, q v y = 1) {L A : ℝ} (hL : 1 < L) : + (∑ v, ∑ y, if A < information L (conditionalMass q v y) then + q v y * information L (conditionalMass q v y) else 0) ≤ + (Fintype.card Y : ℝ) * (2 / Real.log L) * Real.sqrt (L ^ (-A)) := by + classical + have hc : ∀ v y, 0 ≤ conditionalMass q v y := fun v y => + div_nonneg (hq v y) (rowMass_nonneg q hq v) + calc + _ = ∑ v, rowMass q v * (∑ y, if A < information L (conditionalMass q v y) + then conditionalMass q v y * information L (conditionalMass q v y) else 0) := by + apply Finset.sum_congr rfl + intro v _ + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro y _ + split_ifs + · rw [← mul_assoc, ← jointMass_eq_row_mul_conditional q hq] + · simp + _ ≤ ∑ v, rowMass q v * ((Fintype.card Y : ℝ) * (2 / Real.log L) * + Real.sqrt (L ^ (-A))) := by + apply Finset.sum_le_sum + intro v _ + exact mul_le_mul_of_nonneg_left + (information_expected_tail_le (conditionalMass q v) (hc v) hL) + (rowMass_nonneg q hq v) + _ = _ := by + rw [← Finset.sum_mul] + simp only [rowMass, hq1, one_mul] + +lemma polynomial_alphabet_tail_bound {n : ℕ} {L C A : ℝ} + (hL : 2 ≤ L) (hn : (n : ℝ) ≤ L ^ C) (hA : 2 * C ≤ A) : + (n : ℝ) * (2 / Real.log L) * Real.sqrt (L ^ (-A)) ≤ + (2 / Real.log 2) * (2 : ℝ) ^ (C - A / 2) := by + have hL0 : 0 < L := by linarith + have hl : 0 < Real.log L := Real.log_pos (by linarith) + have hl2 : 0 < Real.log 2 := Real.log_pos (by norm_num) + have hs : Real.sqrt (L ^ (-A)) = L ^ (-A / 2) := by + rw [Real.sqrt_eq_rpow, ← Real.rpow_mul hL0.le] + congr 1 + ring + rw [hs] + calc + _ ≤ (L ^ C) * (2 / Real.log L) * (L ^ (-A / 2)) := + mul_le_mul_of_nonneg_right + (mul_le_mul_of_nonneg_right hn (div_nonneg (by norm_num) hl.le)) + (Real.rpow_nonneg hL0.le _) + _ = (2 / Real.log L) * (L ^ (C - A / 2)) := by + rw [sub_eq_add_neg, Real.rpow_add hL0, neg_div] + ring + _ ≤ (2 / Real.log 2) * (2 : ℝ) ^ (C - A / 2) := by + apply mul_le_mul + · exact div_le_div_of_nonneg_left (by norm_num) hl2 (Real.log_le_log (by norm_num) hL) + · exact Real.rpow_le_rpow_of_nonpos (by norm_num) hL (by linarith) + · exact Real.rpow_nonneg hL0.le _ + · exact div_nonneg (by norm_num) hl2.le + +lemma polynomial_alphabet_mass_bound {n : ℕ} {L C A : ℝ} + (hL : 2 ≤ L) (hn : (n : ℝ) ≤ L ^ C) (hA : C ≤ A) : + (n : ℝ) * L ^ (-A) ≤ (2 : ℝ) ^ (C - A) := by + have hL0 : 0 < L := by linarith + calc + _ ≤ L ^ C * L ^ (-A) := + mul_le_mul_of_nonneg_right hn (Real.rpow_nonneg hL0.le _) + _ = L ^ (C-A) := by rw [sub_eq_add_neg, Real.rpow_add hL0] + _ ≤ _ := Real.rpow_le_rpow_of_nonpos (by norm_num) hL (sub_nonpos.mpr hA) + +open Filter in +lemma polynomial_alphabet_mass_envelope_tendsto_zero (C : ℝ) : + Tendsto (fun A : ℝ => (2 : ℝ) ^ (C-A)) atTop (nhds 0) := by + have ht : Tendsto (fun A : ℝ => C-A) atTop atBot := by + apply tendsto_atBot.mpr + intro b + filter_upwards [eventually_ge_atTop (C-b)] with A hA + linarith + exact (tendsto_rpow_atBot_of_base_gt_one 2 (by norm_num)).comp ht + +open Filter in +lemma polynomial_alphabet_envelope_tendsto_zero (C : ℝ) : + Tendsto (fun A : ℝ => (2 / Real.log 2) * (2 : ℝ) ^ (C - A / 2)) + atTop (nhds 0) := by + have ht : Tendsto (fun A : ℝ => C - A / 2) atTop atBot := by + apply tendsto_atBot.mpr + intro b + filter_upwards [eventually_ge_atTop (2 * (C-b))] with A hA + linarith + simpa only [Function.comp_def, mul_zero] using + ((tendsto_rpow_atBot_of_base_gt_one 2 (by norm_num)).comp ht).const_mul (2 / Real.log 2) + +lemma conditional_information_uniform_tail (C : ℝ) {ε : ℝ} (hε : 0 < ε) : + ∃ A₀ : ℝ, ∀ A : ℝ, A₀ ≤ A → + ∀ (V Y : Type) [Fintype V] [Fintype Y] (q : V → Y → ℝ), + (∀ v y, 0 ≤ q v y) → (∑ v, ∑ y, q v y = 1) → + ∀ L : ℝ, 2 ≤ L → (Fintype.card Y : ℝ) ≤ L ^ C → + (∑ v, ∑ y, if A < information L (conditionalMass q v y) then + q v y * information L (conditionalMass q v y) else 0) < ε := by + classical + have he := (polynomial_alphabet_envelope_tendsto_zero C).eventually + (gt_mem_nhds hε) + obtain ⟨a, ha⟩ := Filter.eventually_atTop.mp he + refine ⟨max a (2*C), fun A hA V Y _ _ q hq hq1 L hL hn => ?_⟩ + exact ((conditional_information_expected_tail_le q hq hq1 (by linarith)).trans + (polynomial_alphabet_tail_bound hL hn ((le_max_right _ _).trans hA))).trans_lt + (ha A ((le_max_left _ _).trans hA)) + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Information/WeakLimits.lean b/lean/OAI/Analysis/PlanarEndpoint/Information/WeakLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..5c7a1eba36d4622edce41ec11a8e800c7345fa85 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Information/WeakLimits.lean @@ -0,0 +1,108 @@ +import Mathlib + +namespace OAI + +/-! Finite information laws, entropy and convergence of probability measures. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology ENNReal +namespace PlanarEndpoint.TransverseInformation + +variable {Ω : Type*} [MeasurableSpace Ω] [TopologicalSpace Ω] + [OpensMeasurableSpace Ω] [HasOuterApproxClosed Ω] + +lemma open_null_of_weak_limit {μ : ProbabilityMeasure Ω} + {μs : ℕ → ProbabilityMeasure Ω} (hμ : Tendsto μs atTop (𝓝 μ)) + {G : Set Ω} (hG : IsOpen G) + (h0 : Tendsto (fun n => (μs n : Measure Ω) G) atTop (𝓝 0)) : + (μ : Measure Ω) G = 0 := by + apply le_antisymm _ bot_le + have h := ProbabilityMeasure.le_liminf_measure_open_of_tendsto hμ hG + rw [h0.liminf_eq] at h + exact h + +lemma open_null_of_weak_limit_bound {μ : ProbabilityMeasure Ω} + {μs : ℕ → ProbabilityMeasure Ω} (hμ : Tendsto μs atTop (𝓝 μ)) + {G : Set Ω} (hG : IsOpen G) {ε : ℕ → ℝ≥0∞} + (hε : Tendsto ε atTop (𝓝 0)) + (hb : ∀ᶠ n in atTop, (μs n : Measure Ω) G ≤ ε n) : + (μ : Measure Ω) G = 0 := by + apply open_null_of_weak_limit hμ hG + exact tendsto_of_tendsto_of_tendsto_of_le_of_le' tendsto_const_nhds hε + (Eventually.of_forall (fun _ => bot_le)) hb + +lemma ae_nonneg_of_weak_limit_tails {μ : ProbabilityMeasure Ω} + {μs : ℕ → ProbabilityMeasure Ω} (hμ : Tendsto μs atTop (𝓝 μ)) + {d : Ω → ℝ} (hd : Continuous d) + (htail : ∀ η : ℝ, 0 < η → + Tendsto (fun n => (μs n : Measure Ω) {x | d x < -η}) atTop (𝓝 0)) : + ∀ᵐ x ∂(μ : Measure Ω), 0 ≤ d x := by + have ha : ∀ q : ℚ, ∀ᵐ x ∂(μ : Measure Ω), + 0 < (q : ℝ) → -(q : ℝ) ≤ d x := by + intro q + by_cases hq : 0 < (q : ℝ) + · have hnull := open_null_of_weak_limit hμ + (isOpen_lt hd continuous_const) (htail q hq) + have hb : ∀ᵐ x ∂(μ : Measure Ω), -(q : ℝ) ≤ d x := by + apply ae_iff.mpr + simpa only [not_le] using hnull + exact hb.mono (fun _ h _ => h) + · exact Eventually.of_forall (fun _ h => (hq h).elim) + filter_upwards [ae_all_iff.mpr ha] with x hx + by_contra hn + have hneg : d x < 0 := lt_of_not_ge hn + obtain ⟨q, hq0, hq1⟩ := exists_rat_btwn (neg_pos.mpr hneg) + have h := hx q hq0 + linarith + +lemma ae_le_on_open_of_weak_limit_tails {μ : ProbabilityMeasure Ω} + {μs : ℕ → ProbabilityMeasure Ω} (hμ : Tendsto μs atTop (𝓝 μ)) + {G : Set Ω} (hG : IsOpen G) {d : Ω → ℝ} (hd : Continuous d) (γ : ℝ) + (htail : ∀ η : ℝ, 0 < η → Tendsto + (fun n => (μs n : Measure Ω) (G ∩ {x | γ + η < d x})) atTop (𝓝 0)) : + ∀ᵐ x ∂(μ : Measure Ω), x ∈ G → d x ≤ γ := by + have ha : ∀ q : ℚ, ∀ᵐ x ∂(μ : Measure Ω), + 0 < (q : ℝ) → x ∈ G → d x ≤ γ + q := by + intro q + by_cases hq : 0 < (q : ℝ) + · have hnull := open_null_of_weak_limit hμ + (hG.inter (isOpen_lt continuous_const hd)) (htail q hq) + have hb : ∀ᵐ x ∂(μ : Measure Ω), x ∈ G → d x ≤ γ + q := by + apply ae_iff.mpr + change (μ : Measure Ω) {x | x ∈ G ∧ γ + (q : ℝ) < d x} = 0 at hnull + simpa only [not_forall, not_le, exists_prop] using hnull + exact hb.mono (fun _ h _ => h) + · exact Eventually.of_forall (fun _ h => (hq h).elim) + filter_upwards [ae_all_iff.mpr ha] with x hx + intro hxG + by_contra hn + have hpos : 0 < d x - γ := sub_pos.mpr (lt_of_not_ge hn) + obtain ⟨q, hq0, hq1⟩ := exists_rat_btwn hpos + have h := hx q hq0 hxG + linarith + +lemma open_positive_persists {μ : ProbabilityMeasure Ω} + {μs : ℕ → ProbabilityMeasure Ω} (hμ : Tendsto μs atTop (𝓝 μ)) + {G : Set Ω} (hG : IsOpen G) {a : ℝ≥0∞} (ha : a < (μ : Measure Ω) G) : + ∀ᶠ n in atTop, a < (μs n : Measure Ω) G := by + exact Filter.eventually_lt_of_lt_liminf + (ha.trans_le (ProbabilityMeasure.le_liminf_measure_open_of_tendsto hμ hG)) + +lemma ae_eq_of_weak_limit {μ : ProbabilityMeasure Ω} + {μs : ℕ → ProbabilityMeasure Ω} (hμ : Tendsto μs atTop (𝓝 μ)) + {a b : Ω → ℝ} (ha : Continuous a) (hb : Continuous b) + (heq : ∀ n, a =ᵐ[(μs n : Measure Ω)] b) : + a =ᵐ[(μ : Measure Ω)] b := by + apply ae_iff.mpr + apply open_null_of_weak_limit hμ (isOpen_ne_fun ha hb) + have hz : ∀ n, (μs n : Measure Ω) {x | ¬a x = b x} = 0 := + fun n => ae_iff.mp (heq n) + simp only [hz] + exact tendsto_const_nhds + +end PlanarEndpoint.TransverseInformation +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Main.lean b/lean/OAI/Analysis/PlanarEndpoint/Main.lean new file mode 100644 index 0000000000000000000000000000000000000000..933a63ffc1a2c222f7b06cb975b5926e3b5e337d --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Main.lean @@ -0,0 +1,5 @@ +import OAI.Analysis.PlanarEndpoint.GraphDistribution +import OAI.Analysis.PlanarEndpoint.Information.ConditioningLimits +import OAI.Analysis.PlanarEndpoint.Information.EventLimits +import OAI.Analysis.PlanarEndpoint.Information.FiltrationCosts +import OAI.Analysis.PlanarEndpoint.Information.SamplingLimits diff --git a/lean/OAI/Analysis/PlanarEndpoint/MaximalBridge.lean b/lean/OAI/Analysis/PlanarEndpoint/MaximalBridge.lean new file mode 100644 index 0000000000000000000000000000000000000000..0824149dd25ccadbbb646546f386b54081fbc2f4 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/MaximalBridge.lean @@ -0,0 +1,117 @@ +import OAI.Analysis.PlanarEndpoint.Extension +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.Representative + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set Metric +open scoped Topology ENNReal NNReal +namespace PlanarEndpoint + +def LocalMaximalBound : Prop := + ∃ C : ℝ, 0 < C ∧ ∀ (f : L2) (hb : BoundedFourierSupport f), InHThird f → + ∀ x : Plane, ∫ y in ball x 1, ‖evolutionPath f hb.integrable y‖ ≤ C * hThirdNorm f + +lemma integrableOn_evolutionPath_ball (f : L2) (hf : Integrable (fourier f) volume) + (x : Plane) : IntegrableOn (evolutionPath f hf) (ball x 1) volume := + ((continuous_evolutionPath f hf).locallyIntegrable.integrableOn_isCompact + (isCompact_closedBall x 1)).mono_set ball_subset_closedBall + +lemma hThirdNorm_approx_le {f g : L2} (hf : InHThird f) (hg : InHThird g) : + hThirdNorm g ≤ hThirdNorm f + hThirdNorm (f-g) := by + have h := hThirdNorm_sub_le hf (inHThird_sub hf hg) + simpa only [sub_sub_cancel] using h + +lemma ae_summable_paths_of_unit_ball (F : ℕ → Plane → TimePath) + (_hF : ∀ n, StronglyMeasurable (F n)) + (hb : ∀ x : Plane, (∑' n, eLpNorm (fun y => F (n+1) y - F n y) 1 + (volume.restrict (ball x 1))) ≠ ⊤) : + ∀ᵐ x : Plane ∂volume, Summable (fun n => ‖F (n+1) x-F n x‖) := by + obtain ⟨D, hc, hd⟩ := TopologicalSpace.exists_countable_dense Plane + have hu := (dense_iff_iUnion_ball D).1 hd 1 (by norm_num) + have hh : ∀ᵐ x ∂volume.restrict (⋃ c ∈ D, ball c 1), + Summable (fun n => ‖F (n+1) x-F n x‖) := by + apply (ae_restrict_biUnion_iff _ hc _).2 + intro c _ + exact summable_norm_of_tsum_eLpNorm_ne_top le_rfl (hb c) + simpa only [hu, Measure.restrict_univ] using hh + +lemma paths_tsum_finite_of_maximal {C : ℝ} (_hC : 0 < C) + (hmax : ∀ (f : L2) (hb : BoundedFourierSupport f), InHThird f → + ∀ x : Plane, ∫ y in ball x 1, ‖evolutionPath f hb.integrable y‖ ≤ C * hThirdNorm f) + (F : ℕ → L2) (hb : ∀ n, BoundedFourierSupport (F n)) (hH : ∀ n, InHThird (F n)) + (hs : Summable (fun n => hThirdNorm (F (n+1)-F n))) (x : Plane) : + (∑' n, eLpNorm (fun y => evolutionPath (F (n+1)) (hb (n+1)).integrable y - + evolutionPath (F n) (hb n).integrable y) 1 (volume.restrict (ball x 1))) ≠ ⊤ := by + have hle (n : ℕ) : eLpNorm (fun y => evolutionPath (F (n+1)) (hb (n+1)).integrable y - + evolutionPath (F n) (hb n).integrable y) 1 (volume.restrict (ball x 1)) ≤ + ENNReal.ofReal (C * hThirdNorm (F (n+1)-F n)) := by + have hbn := (hb (n+1)).sub (hb n) + have he : (fun y => evolutionPath (F (n+1)) (hb (n+1)).integrable y - + evolutionPath (F n) (hb n).integrable y) = evolutionPath (F (n+1)-F n) hbn.integrable := by + funext y + exact (evolutionPath_sub (hb (n+1)) (hb n) y).symm + rw [he, eLpNorm_one_eq_lintegral_enorm + (integrableOn_evolutionPath_ball _ _ x).aestronglyMeasurable, + ← ofReal_integral_norm_eq_lintegral_enorm (integrableOn_evolutionPath_ball _ _ x)] + exact ENNReal.ofReal_le_ofReal (hmax _ hbn (inHThird_sub (hH _) (hH _)) x) + exact ne_of_lt ((ENNReal.tsum_le_tsum hle).trans_lt (hs.mul_left C).tsum_ofReal_lt_top) + +lemma pathLimit_integrable_of_uniform_bounds (F : ℕ → Plane → TimePath) + (hF : ∀ n, Continuous (F n)) (A : ℝ) (hA : 0 ≤ A) + (hb : ∀ (n : ℕ) (x : Plane), ∫ y in ball x 1, ‖F n y‖ ≤ A) + (hl : ∀ᵐ x ∂volume, Tendsto (fun n => F n x) atTop (𝓝 (pathLimit F x))) : + LocallyIntegrable (pathLimit F) volume ∧ + ∀ x : Plane, ∫ y in ball x 1, ‖pathLimit F y‖ ≤ A := by + have hm := stronglyMeasurable_pathLimit F (fun n => (hF n).stronglyMeasurable) + have hbound (x : Plane) : eLpNorm (pathLimit F) 1 (volume.restrict (ball x 1)) ≤ + ENNReal.ofReal A := by + apply Lp.eLpNorm_le_of_ae_tendsto (Filter.Eventually.of_forall ?_) + (fun n => (hF n).aestronglyMeasurable) hm.aestronglyMeasurable (ae_restrict_of_ae hl) + intro n + have hi : IntegrableOn (F n) (ball x 1) volume := + ((hF n).locallyIntegrable.integrableOn_isCompact + (isCompact_closedBall x 1)).mono_set ball_subset_closedBall + rw [eLpNorm_one_eq_lintegral_enorm hi.aestronglyMeasurable, + ← ofReal_integral_norm_eq_lintegral_enorm hi] + exact ENNReal.ofReal_le_ofReal (hb n x) + have hi (x : Plane) : IntegrableOn (pathLimit F) (ball x 1) volume := + memLp_one_iff_integrable.1 ((hbound x).trans_lt ENNReal.ofReal_lt_top) + refine ⟨fun x => ⟨ball x 1, ball_mem_nhds x (by norm_num), hi x⟩, ?_⟩ + intro x + have hb' := ENNReal.toReal_mono ENNReal.ofReal_ne_top (hbound x) + rw [ENNReal.toReal_ofReal hA, eLpNorm_one_eq_lintegral_enorm hm.aestronglyMeasurable, + ← integral_norm_eq_lintegral_enorm hm.aestronglyMeasurable] at hb' + exact hb' + +lemma mainConclusion_of_localMaximalBound (hmax : LocalMaximalBound) + {f : L2} (hf : InHThird f) : MainConclusion f := by + obtain ⟨C, hC, hmax⟩ := hmax + obtain ⟨F, hb, hH, herr, hlim, hs⟩ := exists_fast_bounded_approximation hf + let P : ℕ → Plane → TimePath := fun n => evolutionPath (F n) (hb n).integrable + have hP (n : ℕ) : Continuous (P n) := continuous_evolutionPath _ _ + have hsum := ae_summable_paths_of_unit_ball P (fun n => (hP n).stronglyMeasurable) + (paths_tsum_finite_of_maximal hC hmax F hb hH hs) + have hp : ∀ᵐ x ∂volume, Tendsto (fun n => P n x) atTop (𝓝 (pathLimit P x)) := by + filter_upwards [hsum] with x hx + obtain ⟨g, hg⟩ := exists_timePath_limit_of_summable (fun n => P n x) hx + simpa only [pathLimit, hg.limUnder_eq] using hg + let A : ℝ≥0 := ⟨C * (hThirdNorm f+1), mul_nonneg hC.le (add_nonneg (hThirdNorm_nonneg f) (by norm_num))⟩ + have hbound (n : ℕ) (x : Plane) : ∫ y in ball x 1, ‖P n y‖ ≤ A := by + apply (hmax (F n) (hb n) (hH n) x).trans + apply mul_le_mul_of_nonneg_left _ hC.le + have hn : (1/2 : ℝ)^n ≤ 1 := pow_le_one₀ (by norm_num) (by norm_num) + exact (hThirdNorm_approx_le hf (hH n)).trans (add_le_add_right ((herr n).trans hn) _) + have hpath := pathLimit_integrable_of_uniform_bounds P hP A A.coe_nonneg hbound hp + exact mainConclusion_of_integrable_paths f (pathLimit P) hpath.1 A hpath.2 + (pathLimit_ae_l2Evolution F hb hlim hp) + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Oscillation.lean b/lean/OAI/Analysis/PlanarEndpoint/Oscillation.lean new file mode 100644 index 0000000000000000000000000000000000000000..1f3ca73e9d29efdaf57d8192df812b5aa6d2c804 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Oscillation.lean @@ -0,0 +1,550 @@ +import Mathlib + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set +open scoped ContDiff Topology +namespace EndpointKernel + +abbrev Space (n : ℕ) := EuclideanSpace ℝ (Fin n) + +def oscillation {n : ℕ} (φ : Space n → ℝ) (lam : ℝ) (x : Space n) : ℂ := + Complex.exp (((lam * φ x : ℝ) : ℂ) * Complex.I) + +@[simp] lemma norm_oscillation {n : ℕ} (φ : Space n → ℝ) (lam : ℝ) (x : Space n) : + ‖oscillation φ lam x‖ = 1 := Complex.norm_exp_ofReal_mul_I _ + +lemma contDiff_oscillation {n : ℕ} {φ : Space n → ℝ} + (hφ : ContDiff ℝ ∞ φ) (lam : ℝ) : ContDiff ℝ ∞ (oscillation φ lam) := by + exact ((Complex.ofRealCLM.contDiff.comp (contDiff_const.mul hφ)).mul contDiff_const).cexp + +lemma fderiv_oscillation {n : ℕ} {φ : Space n → ℝ} + (hφ : Differentiable ℝ φ) (lam : ℝ) (x v : Space n) : + fderiv ℝ (oscillation φ lam) x v = + (lam : ℂ) * Complex.I * (fderiv ℝ φ x v : ℂ) * oscillation φ lam x := by + have h := ((Complex.ofRealCLM.hasFDerivAt.comp x + ((hφ x).hasFDerivAt.const_mul lam)).mul_const Complex.I).cexp + change HasFDerivAt (oscillation φ lam) _ x at h + rw [h.fderiv] + simp only [smul_apply, ContinuousLinearMap.comp_apply, + Complex.ofRealCLM_apply, Function.comp_apply, + Complex.ofReal_mul, smul_eq_mul, oscillation] + ring + +lemma contDiff_mul_of_tsupport {n : ℕ} {u a : Space n → ℂ} + (hu : ContDiff ℝ ∞ u) (ha : ∀ x ∈ tsupport u, ContDiffAt ℝ ∞ a x) : + ContDiff ℝ ∞ (fun x => u x * a x) := by + apply contDiff_iff_contDiffAt.2 + intro x + by_cases hx : x ∈ tsupport u + · exact hu.contDiffAt.mul (ha x hx) + · have hz := (notMem_tsupport_iff_eventuallyEq.1 hx) + have hm : (fun y => u y * a y) =ᶠ[𝓝 x] (fun _ => (0 : ℂ)) := by + filter_upwards [hz] with y hy + simp only [hy, Pi.zero_apply, zero_mul] + exact contDiffAt_const.congr_of_eventuallyEq hm + +def weightedDiv {n : ℕ} (A : Fin n → Space n → ℂ) (u : Space n → ℂ) + (x : Space n) : ℂ := + ∑ i, fderiv ℝ (fun y => u y * A i y) x (EuclideanSpace.single i 1) + +lemma contDiff_weightedDiv {n : ℕ} {A : Fin n → Space n → ℂ} {u : Space n → ℂ} + (hA : ∀ i x, x ∈ tsupport u → ContDiffAt ℝ ∞ (A i) x) (hu : ContDiff ℝ ∞ u) : + ContDiff ℝ ∞ (weightedDiv A u) := by + apply ContDiff.sum + intro i _ + exact ((contDiff_mul_of_tsupport hu (hA i)).fderiv_right (by simp)).clm_apply contDiff_const + +lemma tsupport_weightedDiv_subset {n : ℕ} (A : Fin n → Space n → ℂ) + (u : Space n → ℂ) : tsupport (weightedDiv A u) ⊆ tsupport u := by + apply closure_minimal _ (isClosed_tsupport u) + intro x hx + by_contra hxu + have hz : weightedDiv A u x = 0 := by + apply Finset.sum_eq_zero + intro i _ + have hn : x ∉ tsupport (fun y => u y * A i y) := + fun h => hxu (tsupport_mul_subset_left h) + rw [fderiv_of_notMem_tsupport ℝ hn] + rfl + exact hx hz + +lemma compactSupport_weightedDiv {n : ℕ} (A : Fin n → Space n → ℂ) + {u : Space n → ℂ} (hu : HasCompactSupport u) : HasCompactSupport (weightedDiv A u) := + hu.of_isClosed_subset (isClosed_tsupport _) (tsupport_weightedDiv_subset A u) + +lemma integration_by_parts {n : ℕ} {A : Fin n → Space n → ℂ} + {u : Space n → ℂ} {φ : Space n → ℝ} + (hA : ∀ i x, x ∈ tsupport u → ContDiffAt ℝ ∞ (A i) x) (hu : ContDiff ℝ ∞ u) + (hcu : HasCompactSupport u) (hφ : ContDiff ℝ ∞ φ) (lam : ℝ) + (hcancel : ∀ x ∈ tsupport u, + ∑ i, A i x * (fderiv ℝ φ x (EuclideanSpace.single i 1) : ℂ) = 1) : + (lam : ℂ) * Complex.I * (∫ x, u x * oscillation φ lam x) = + -(∫ x, weightedDiv A u x * oscillation φ lam x) := by + let e := oscillation φ lam + have he : ContDiff ℝ ∞ e := contDiff_oscillation hφ lam + have hed : Differentiable ℝ e := he.differentiable (by simp) + have hprod (i : Fin n) : ContDiff ℝ ∞ (fun x => u x * A i x) := contDiff_mul_of_tsupport hu (hA i) + have hcp (i : Fin n) : HasCompactSupport (fun x => u x * A i x) := hcu.mul_right + have hd (i : Fin n) : ContDiff ℝ ∞ (fun x => + fderiv ℝ (fun y => u y * A i y) x (EuclideanSpace.single i 1)) := + ((hprod i).fderiv_right (by simp)).clm_apply contDiff_const + have hid (i : Fin n) : Integrable (fun x => + fderiv ℝ (fun y => u y * A i y) x (EuclideanSpace.single i 1) * e x) := + ((hd i).continuous.mul he.continuous).integrable_of_hasCompactSupport + ((hcp i).fderiv_apply ℝ _).mul_right + have hi (i : Fin n) : Integrable (fun x => + (u x * A i x) * fderiv ℝ e x (EuclideanSpace.single i 1)) := + ((hprod i).continuous.mul + ((he.fderiv_right (m := ∞) (by simp)).clm_apply contDiff_const).continuous).integrable_of_hasCompactSupport + (hcp i).mul_right + have hip (i : Fin n) : Integrable (fun x => u x * A i x * e x) := + ((hprod i).continuous.mul he.continuous).integrable_of_hasCompactSupport (hcp i).mul_right + have ih (i : Fin n) := integral_mul_fderiv_eq_neg_fderiv_mul_of_integrable + (hid i) (hi i) (hip i) + (fun x _ => (hprod i).differentiable (by simp) x) (fun x _ => hed x) + have hc (x : Space n) : (∑ i, u x * A i x * fderiv ℝ e x (EuclideanSpace.single i 1)) = + (lam : ℂ) * Complex.I * (u x * e x) := by + by_cases hx : x ∈ tsupport u + · simp only [e, fderiv_oscillation (hφ.differentiable (by simp))] + calc + _ = ((lam : ℂ) * Complex.I * (u x * oscillation φ lam x)) * + (∑ i, A i x * (fderiv ℝ φ x (EuclideanSpace.single i 1) : ℂ)) := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro i _ + ring + _ = _ := by rw [hcancel x hx, mul_one] + · have hz : u x = 0 := image_eq_zero_of_notMem_tsupport hx + simp [hz] + calc + _ = ∫ x, ∑ i, u x * A i x * fderiv ℝ e x (EuclideanSpace.single i 1) := by + simp only [hc, integral_const_mul, e] + _ = ∑ i, ∫ x, u x * A i x * fderiv ℝ e x (EuclideanSpace.single i 1) := + integral_finsetSum _ (fun i _ => hi i) + _ = -(∑ i, ∫ x, + fderiv ℝ (fun y => u y * A i y) x (EuclideanSpace.single i 1) * e x) := by + simp only [ih, Finset.sum_neg_distrib] + _ = -(∫ x, weightedDiv A u x * e x) := by + simp only [weightedDiv, Finset.sum_mul] + rw [integral_finsetSum _ (fun i _ => hid i)] + +def iteratedAmplitude {n : ℕ} (A : Fin n → Space n → ℂ) (u : Space n → ℂ) + (k : ℕ) : Space n → ℂ := (weightedDiv A)^[k] u + +@[simp] lemma iteratedAmplitude_zero {n : ℕ} (A : Fin n → Space n → ℂ) (u : Space n → ℂ) : + iteratedAmplitude A u 0 = u := rfl + +lemma iteratedAmplitude_succ {n : ℕ} (A : Fin n → Space n → ℂ) (u : Space n → ℂ) (k : ℕ) : + iteratedAmplitude A u (k+1) = weightedDiv A (iteratedAmplitude A u k) := + Function.iterate_succ_apply' _ _ _ + +lemma tsupport_iteratedAmplitude_subset {n : ℕ} (A : Fin n → Space n → ℂ) + (u : Space n → ℂ) (k : ℕ) : tsupport (iteratedAmplitude A u k) ⊆ tsupport u := by + induction k with + | zero => exact Subset.rfl + | succ k ih => + rw [iteratedAmplitude_succ] + exact (tsupport_weightedDiv_subset A _).trans ih + +lemma contDiff_iteratedAmplitude {n : ℕ} {A : Fin n → Space n → ℂ} {u : Space n → ℂ} + (hA : ∀ i x, x ∈ tsupport u → ContDiffAt ℝ ∞ (A i) x) (hu : ContDiff ℝ ∞ u) + (k : ℕ) : ContDiff ℝ ∞ (iteratedAmplitude A u k) := by + induction k with + | zero => exact hu + | succ k ih => + rw [iteratedAmplitude_succ] + exact contDiff_weightedDiv (fun i x hx => hA i x (tsupport_iteratedAmplitude_subset A u k hx)) ih + +lemma compactSupport_iteratedAmplitude {n : ℕ} (A : Fin n → Space n → ℂ) + {u : Space n → ℂ} (hu : HasCompactSupport u) (k : ℕ) : + HasCompactSupport (iteratedAmplitude A u k) := + hu.of_isClosed_subset (isClosed_tsupport _) (tsupport_iteratedAmplitude_subset A u k) + +lemma iterated_integration_by_parts {n : ℕ} {A : Fin n → Space n → ℂ} + {u : Space n → ℂ} {φ : Space n → ℝ} + (hA : ∀ i x, x ∈ tsupport u → ContDiffAt ℝ ∞ (A i) x) (hu : ContDiff ℝ ∞ u) + (hcu : HasCompactSupport u) (hφ : ContDiff ℝ ∞ φ) (lam : ℝ) + (hcancel : ∀ x ∈ tsupport u, + ∑ i, A i x * (fderiv ℝ φ x (EuclideanSpace.single i 1) : ℂ) = 1) (k : ℕ) : + ((lam : ℂ) * Complex.I) ^ k * (∫ x, u x * oscillation φ lam x) = + (-1 : ℂ) ^ k * (∫ x, iteratedAmplitude A u k x * oscillation φ lam x) := by + induction k with + | zero => simp + | succ k ih => + have hk := integration_by_parts + (fun i x hx => hA i x (tsupport_iteratedAmplitude_subset A u k hx)) + (contDiff_iteratedAmplitude hA hu k) (compactSupport_iteratedAmplitude A hcu k) hφ lam + (fun x hx => hcancel x (tsupport_iteratedAmplitude_subset A u k hx)) + rw [← iteratedAmplitude_succ] at hk + calc + _ = (lam : ℂ) * Complex.I * + (((lam : ℂ) * Complex.I) ^ k * ∫ x, u x * oscillation φ lam x) := by ring + _ = (lam : ℂ) * Complex.I * + ((-1 : ℂ) ^ k * ∫ x, iteratedAmplitude A u k x * oscillation φ lam x) := by rw [ih] + _ = (-1 : ℂ) ^ k * + ((lam : ℂ) * Complex.I * ∫ x, iteratedAmplitude A u k x * oscillation φ lam x) := by ring + _ = _ := by rw [hk]; ring + +lemma nonstationary_phase_bound {n : ℕ} {A : Fin n → Space n → ℂ} + {u : Space n → ℂ} {φ : Space n → ℝ} + (hA : ∀ i x, x ∈ tsupport u → ContDiffAt ℝ ∞ (A i) x) (hu : ContDiff ℝ ∞ u) + (hcu : HasCompactSupport u) (hφ : ContDiff ℝ ∞ φ) (lam : ℝ) + (hcancel : ∀ x ∈ tsupport u, + ∑ i, A i x * (fderiv ℝ φ x (EuclideanSpace.single i 1) : ℂ) = 1) (k : ℕ) : + |lam| ^ k * ‖∫ x, u x * oscillation φ lam x‖ ≤ ∫ x, ‖iteratedAmplitude A u k x‖ := by + have hi := congrArg norm (iterated_integration_by_parts hA hu hcu hφ lam hcancel k) + simp only [norm_mul, norm_pow, Complex.norm_real, Real.norm_eq_abs, Complex.norm_I, + mul_one, norm_neg, norm_one, one_pow, one_mul] at hi + rw [hi] + convert norm_integral_le_integral_norm (fun x => iteratedAmplitude A u k x * oscillation φ lam x) + using 1 + simp only [norm_mul, norm_oscillation, mul_one] + +section Parameters +variable {P : Type*} [NormedAddCommGroup P] [NormedSpace ℝ P] + +lemma contDiffAt_partial_fderiv {n : ℕ} {F : P × Space n → ℂ} {p : P} {x : Space n} + (hF : ContDiffAt ℝ ∞ F (p,x)) (v : Space n) : + ContDiffAt ℝ ∞ (fun z : P × Space n => fderiv ℝ (fun y => F (z.1,y)) z.2 v) (p,x) := by + have hh : ContDiffAt ℝ ∞ + (Function.uncurry (fun (z : P × Space n) (y : Space n) => F (z.1,y))) ((p,x),x) := + hF.comp ((p,x),x) (contDiffAt_fst.fst.prodMk contDiffAt_snd) + exact (hh.fderiv contDiffAt_snd (by simp)).clm_apply contDiffAt_const + +lemma contDiffAt_iteratedAmplitude_family {n : ℕ} {A : Fin n → P → Space n → ℂ} + {u : Space n → ℂ} {p : P} + (hA : ∀ i x, x ∈ tsupport u → + ContDiffAt ℝ ∞ (fun z : P × Space n => A i z.1 z.2) (p,x)) + (hu : ContDiff ℝ ∞ u) (k : ℕ) (x : Space n) : + ContDiffAt ℝ ∞ (fun z : P × Space n => iteratedAmplitude (A · z.1) u k z.2) (p,x) := by + induction k generalizing x with + | zero => exact hu.contDiffAt.comp (p,x) contDiffAt_snd + | succ k ih => + simp only [iteratedAmplitude_succ, weightedDiv] + apply ContDiffAt.sum + intro i _ + have hh : ContDiffAt ℝ ∞ + (fun z : P × Space n => iteratedAmplitude (A · z.1) u k z.2 * A i z.1 z.2) (p,x) := by + by_cases hx : x ∈ tsupport u + · exact (ih x).mul (hA i x hx) + · have hev : ∀ᶠ z : P × Space n in 𝓝 (p,x), z.2 ∉ tsupport u := + (continuous_snd.continuousAt : ContinuousAt (Prod.snd : P × Space n → Space n) (p,x)).preimage_mem_nhds + ((isClosed_tsupport u).isOpen_compl.mem_nhds hx) + apply (contDiffAt_const (c := (0 : ℂ))).congr_of_eventuallyEq + filter_upwards [hev] with z hz + have hn : z.2 ∉ tsupport (iteratedAmplitude (A · z.1) u k) := + fun h => hz (tsupport_iteratedAmplitude_subset _ u k h) + simp only [image_eq_zero_of_notMem_tsupport hn, zero_mul] + exact contDiffAt_partial_fderiv hh _ + +lemma iteratedAmplitude_uniform_integral_bound {n : ℕ} + {A : Fin n → P → Space n → ℂ} {u : Space n → ℂ} {K : Set P} + (hK : IsCompact K) + (hA : ∀ p ∈ K, ∀ i x, x ∈ tsupport u → + ContDiffAt ℝ ∞ (fun z : P × Space n => A i z.1 z.2) (p,x)) + (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ p ∈ K, ∫ x, ‖iteratedAmplitude (A · p) u k x‖ ≤ C := by + let F : P × Space n → ℂ := fun z => iteratedAmplitude (A · z.1) u k z.2 + have hF : ContinuousOn F (K ×ˢ tsupport u) := by + intro z hz + exact (contDiffAt_iteratedAmplitude_family (hA z.1 hz.1) hu k z.2).continuousAt.continuousWithinAt + obtain ⟨M, hM⟩ := ((hK.prod hcu).image_of_continuousOn hF).isBounded.exists_norm_le + let B := max M 0 + refine ⟨volume.real (tsupport u) * B, mul_nonneg ENNReal.toReal_nonneg (le_max_right _ _), ?_⟩ + intro p hp + have hac (i : Fin n) (x : Space n) (hx : x ∈ tsupport u) : ContDiffAt ℝ ∞ (A i p) x := + (hA p hp i x hx).comp x (contDiffAt_const.prodMk contDiffAt_id) + have hi : Integrable (fun x => ‖iteratedAmplitude (A · p) u k x‖) := + ((contDiff_iteratedAmplitude hac hu k).continuous.integrable_of_hasCompactSupport + (compactSupport_iteratedAmplitude _ hcu k)).norm + have hib : Integrable ((tsupport u).indicator (fun _ : Space n => B)) := + (integrable_indicator_iff hcu.measurableSet).2 + ((continuous_const : Continuous (fun _ : Space n => B)).locallyIntegrable.integrableOn_isCompact hcu) + calc + _ ≤ ∫ x, (tsupport u).indicator (fun _ : Space n => B) x := by + apply integral_mono hi hib + intro x + by_cases hx : x ∈ tsupport u + · rw [indicator_of_mem hx] + exact (hM (F (p,x)) ⟨(p,x), ⟨hp,hx⟩, rfl⟩).trans (le_max_left _ _) + · rw [indicator_of_notMem hx] + have hz : x ∉ tsupport (iteratedAmplitude (A · p) u k) := + fun h => hx (tsupport_iteratedAmplitude_subset _ u k h) + simp [image_eq_zero_of_notMem_tsupport hz] + _ = _ := by rw [integral_indicator hcu.measurableSet, setIntegral_const, smul_eq_mul] + +lemma uniform_nonstationary_phase {n : ℕ} {A : Fin n → P → Space n → ℂ} + {u : Space n → ℂ} {φ : P → Space n → ℝ} {K : Set P} + (hK : IsCompact K) + (hA : ∀ p ∈ K, ∀ i x, x ∈ tsupport u → + ContDiffAt ℝ ∞ (fun z : P × Space n => A i z.1 z.2) (p,x)) + (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) + (hφ : ∀ p ∈ K, ContDiff ℝ ∞ (φ p)) + (hcancel : ∀ p ∈ K, ∀ x ∈ tsupport u, + ∑ i, A i p x * (fderiv ℝ (φ p) x (EuclideanSpace.single i 1) : ℂ) = 1) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ p ∈ K, ∀ lam : ℝ, + |lam| ^ k * ‖∫ x, u x * oscillation (φ p) lam x‖ ≤ C := by + obtain ⟨C, hC, hb⟩ := iteratedAmplitude_uniform_integral_bound hK hA hu hcu k + refine ⟨C, hC, fun p hp lam => ?_⟩ + have hac (i : Fin n) (x : Space n) (hx : x ∈ tsupport u) : ContDiffAt ℝ ∞ (A i p) x := + (hA p hp i x hx).comp x (contDiffAt_const.prodMk contDiffAt_id) + exact (nonstationary_phase_bound hac hu hcu (hφ p hp) lam (hcancel p hp) k).trans (hb p hp) + +end Parameters + +def quadraticPhase {n : ℕ} (p : Space n × ℝ) (x : Space n) : ℝ := + inner ℝ p.1 x - p.2 * ‖x‖ ^ 2 + +def quadraticGradient {n : ℕ} (p : Space n × ℝ) (x : Space n) : Space n := + p.1 - (2*p.2) • x + +lemma contDiff_quadraticPhase {n : ℕ} (p : Space n × ℝ) : ContDiff ℝ ∞ (quadraticPhase p) := by + exact (innerSL ℝ p.1).contDiff.sub (contDiff_const.mul (contDiff_id.norm_sq ℝ)) + +lemma fderiv_quadraticPhase {n : ℕ} (p : Space n × ℝ) (x v : Space n) : + fderiv ℝ (quadraticPhase p) x v = inner ℝ (quadraticGradient p x) v := by + have h := (innerSL ℝ p.1).hasFDerivAt.sub (((hasFDerivAt_id x).norm_sq).const_mul p.2) + change HasFDerivAt (quadraticPhase p) _ x at h + rw [h.fderiv] + simp only [sub_apply, smul_apply, ContinuousLinearMap.comp_apply, + ContinuousLinearMap.id_apply, innerSL_apply_apply, id_eq, smul_eq_mul, quadraticGradient, + inner_sub_left, real_inner_smul_left] + ring + +lemma fderiv_quadraticPhase_single {n : ℕ} (p : Space n × ℝ) (x : Space n) (i : Fin n) : + fderiv ℝ (quadraticPhase p) x (EuclideanSpace.single i 1) = quadraticGradient p x i := by + rw [fderiv_quadraticPhase, EuclideanSpace.inner_single_right] + simp + +def quadraticNormalizer {n : ℕ} (i : Fin n) (p : Space n × ℝ) (x : Space n) : ℂ := + ((quadraticGradient p x i / ‖quadraticGradient p x‖ ^ 2 : ℝ) : ℂ) + +lemma contDiffAt_quadraticNormalizer {n : ℕ} (i : Fin n) {p : Space n × ℝ} {x : Space n} + (h : quadraticGradient p x ≠ 0) : + ContDiffAt ℝ ∞ (fun z : (Space n × ℝ) × Space n => quadraticNormalizer i z.1 z.2) (p,x) := by + have hg : ContDiffAt ℝ ∞ + (fun z : (Space n × ℝ) × Space n => quadraticGradient z.1 z.2) (p,x) := by + unfold quadraticGradient + fun_prop + have hn : ‖quadraticGradient p x‖ ^ 2 ≠ 0 := pow_ne_zero _ (norm_ne_zero_iff.2 h) + exact Complex.ofRealCLM.contDiff.contDiffAt.comp (p,x) + (((EuclideanSpace.proj (𝕜 := ℝ) i).contDiff.contDiffAt.comp (p,x) hg).div (hg.norm_sq ℝ) hn) + +lemma quadraticNormalizer_cancels {n : ℕ} {p : Space n × ℝ} {x : Space n} + (h : quadraticGradient p x ≠ 0) : + ∑ i, quadraticNormalizer i p x * + (fderiv ℝ (quadraticPhase p) x (EuclideanSpace.single i 1) : ℂ) = 1 := by + have hn : ‖quadraticGradient p x‖ ^ 2 ≠ 0 := pow_ne_zero _ (norm_ne_zero_iff.2 h) + simp only [quadraticNormalizer, fderiv_quadraticPhase_single, ← Complex.ofReal_mul, ← Complex.ofReal_sum] + have hl : (∑ i, quadraticGradient p x i / ‖quadraticGradient p x‖ ^ 2 * quadraticGradient p x i) = 1 := by + simp_rw [div_mul_eq_mul_div, ← sq] + rw [← Finset.sum_div, ← EuclideanSpace.real_norm_sq_eq, div_self hn] + rw [hl, Complex.ofReal_one] + +lemma uniform_quadratic_nonstationary {n : ℕ} {u : Space n → ℂ} {K : Set (Space n × ℝ)} + (hK : IsCompact K) (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) + (hgrad : ∀ p ∈ K, ∀ x ∈ tsupport u, quadraticGradient p x ≠ 0) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ p ∈ K, ∀ lam : ℝ, + |lam| ^ k * ‖∫ x, u x * oscillation (quadraticPhase p) lam x‖ ≤ C := by + apply uniform_nonstationary_phase hK + (fun p hp i x hx => contDiffAt_quadraticNormalizer i (hgrad p hp x hx)) hu hcu + (fun p _ => contDiff_quadraticPhase p) + (fun p hp x hx => quadraticNormalizer_cancels (hgrad p hp x hx)) k + +lemma time_dominated_decay {n : ℕ} {u : Space n → ℂ} {c : ℝ} + (hc : 0 < c) (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) + (hann : ∀ x ∈ tsupport u, c ≤ ‖x‖) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ (z : Space n) (t : ℝ), + ‖z‖ ≤ c * |t| → + |t| ^ k * ‖∫ x, u x * oscillation (quadraticPhase (z,t)) 1 x‖ ≤ C := by + let K : Set (Space n × ℝ) := Metric.closedBall 0 c ×ˢ {1} + have hK : IsCompact K := (isCompact_closedBall 0 c).prod isCompact_singleton + have hg : ∀ p ∈ K, ∀ x ∈ tsupport u, quadraticGradient p x ≠ 0 := by + intro p hp x hx hz + have hv : ‖p.1‖ ≤ c := by simpa using hp.1 + have ht : p.2 = 1 := hp.2 + have he : p.1 = (2 : ℝ) • x := by + simpa [quadraticGradient, ht] using sub_eq_zero.mp hz + have hnorm : ‖p.1‖ = 2 * ‖x‖ := by rw [he, norm_smul]; norm_num + have hr := hann x hx + nlinarith + obtain ⟨C, hC, hb⟩ := uniform_quadratic_nonstationary hK hu hcu hg k + let C₀ := ∫ x, ‖u x‖ + have hC₀ : 0 ≤ C₀ := integral_nonneg (fun _ => norm_nonneg _) + refine ⟨max C C₀, le_max_of_le_left hC, fun z t hzt => ?_⟩ + by_cases ht : t = 0 + · have hz : z = 0 := norm_eq_zero.mp (le_antisymm (by simpa [ht] using hzt) (norm_nonneg _)) + have hi : ‖∫ x, u x * oscillation (quadraticPhase (z,t)) 1 x‖ ≤ C₀ := by + calc + _ ≤ ∫ x, ‖u x * oscillation (quadraticPhase (z,t)) 1 x‖ := norm_integral_le_integral_norm _ + _ = C₀ := by simp [C₀] + calc + _ ≤ 1 * C₀ := mul_le_mul (by rw [ht, abs_zero]; exact pow_le_one₀ (by norm_num) (by norm_num)) hi + (norm_nonneg _) (by positivity) + _ ≤ max C C₀ := by simp + · have hab : 0 < |t| := abs_pos.mpr ht + have hp : (t⁻¹ • z, (1 : ℝ)) ∈ K := by + constructor + · change dist (t⁻¹ • z) 0 ≤ c + rw [dist_zero_right, norm_smul, Real.norm_eq_abs, abs_inv] + exact (inv_mul_le_iff₀ hab).mpr (by simpa [mul_comm] using hzt) + · rfl + have he : oscillation (quadraticPhase (z,t)) 1 = + oscillation (quadraticPhase (t⁻¹ • z,1)) t := by + funext x + unfold oscillation quadraticPhase + congr 3 + simp only [one_mul, real_inner_smul_left] + field_simp + rw [he] + exact (hb _ hp t).trans (le_max_left _ _) + +lemma spatial_dominated_decay_power {n : ℕ} {u : Space n → ℂ} {R : ℝ} + (hR : 0 < R) (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) + (hsupp : ∀ x ∈ tsupport u, ‖x‖ ≤ R) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ (z : Space n) (t : ℝ), + 4 * R * |t| ≤ ‖z‖ → + ‖z‖ ^ k * ‖∫ x, u x * oscillation (quadraticPhase (z,t)) 1 x‖ ≤ C := by + let K : Set (Space n × ℝ) := Metric.sphere 0 1 ×ˢ Set.Icc (-(4*R)⁻¹) ((4*R)⁻¹) + have hr4 : 0 < 4*R := by positivity + have hK : IsCompact K := (isCompact_sphere 0 1).prod isCompact_Icc + have hg : ∀ p ∈ K, ∀ x ∈ tsupport u, quadraticGradient p x ≠ 0 := by + intro p hp x hx hz + have hv : ‖p.1‖ = 1 := by simpa using hp.1 + have ht : |p.2| ≤ (4*R)⁻¹ := abs_le.mpr hp.2 + have he : p.1 = (2*p.2) • x := sub_eq_zero.mp hz + have hnorm : 1 = 2 * |p.2| * ‖x‖ := by + rw [← hv, he, norm_smul, Real.norm_eq_abs, abs_mul]; norm_num + have hb : |p.2| * (4*R) ≤ 1 := by + simpa only [inv_mul_cancel₀ hr4.ne'] using mul_le_mul_of_nonneg_right ht hr4.le + have hh := mul_le_mul_of_nonneg_left (hsupp x hx) (abs_nonneg p.2) + nlinarith + obtain ⟨C, hC, hb⟩ := uniform_quadratic_nonstationary hK hu hcu hg k + let C₀ := ∫ x, ‖u x‖ + have hC₀ : 0 ≤ C₀ := integral_nonneg (fun _ => norm_nonneg _) + have hi (z : Space n) (t : ℝ) : + ‖∫ x, u x * oscillation (quadraticPhase (z,t)) 1 x‖ ≤ C₀ := by + calc + _ ≤ ∫ x, ‖u x * oscillation (quadraticPhase (z,t)) 1 x‖ := norm_integral_le_integral_norm _ + _ = C₀ := by simp [C₀] + refine ⟨max C C₀, le_max_of_le_left hC, fun z t hzt => ?_⟩ + by_cases hz : z = 0 + · calc + _ ≤ 1 * C₀ := mul_le_mul (by rw [hz, norm_zero]; exact pow_le_one₀ (by norm_num) (by norm_num)) + (hi z t) (norm_nonneg _) (by positivity) + _ ≤ max C C₀ := by simp + · have hn : 0 < ‖z‖ := norm_pos_iff.mpr hz + have hp : (‖z‖⁻¹ • z, t / ‖z‖) ∈ K := by + constructor + · change dist (‖z‖⁻¹ • z) 0 = 1 + rw [dist_zero_right, norm_smul, Real.norm_eq_abs, abs_inv, abs_of_pos hn, inv_mul_cancel₀ hn.ne'] + · apply abs_le.mp + rw [abs_div, abs_of_pos hn] + apply (div_le_iff₀ hn).mpr + apply (le_inv_mul_iff₀ hr4).mpr + nlinarith + have he : oscillation (quadraticPhase (z,t)) 1 = + oscillation (quadraticPhase (‖z‖⁻¹ • z,t/‖z‖)) ‖z‖ := by + funext x + unfold oscillation quadraticPhase + congr 3 + simp only [one_mul, real_inner_smul_left] + field_simp + rw [he] + simpa only [abs_of_pos hn] using (hb _ hp ‖z‖).trans (le_max_left _ _) + +lemma one_add_weight_bound {a b C D : ℝ} (ha : 0 ≤ a) (hb : 0 ≤ b) + (hC : 0 ≤ C) (hD : 0 ≤ D) (k : ℕ) (h : a ^ k * b ≤ C) (h' : b ≤ D) : + (1+a) ^ k * b ≤ 2 ^ k * max C D := by + by_cases ha1 : a ≤ 1 + · calc + (1+a)^k*b ≤ 2^k*D := mul_le_mul (pow_le_pow_left₀ (by positivity) (by linarith) k) h' hb (by positivity) + _ ≤ 2^k*max C D := mul_le_mul le_rfl (le_max_right _ _) hD (by positivity) + · have ha1 : 1 ≤ a := le_of_lt (lt_of_not_ge ha1) + calc + (1+a)^k*b ≤ (2*a)^k*b := mul_le_mul_of_nonneg_right + (pow_le_pow_left₀ (by positivity) (by linarith) k) hb + _ = 2^k*(a^k*b) := by rw [mul_pow, mul_assoc] + _ ≤ 2^k*C := mul_le_mul_of_nonneg_left h (by positivity) + _ ≤ 2^k*max C D := mul_le_mul le_rfl (le_max_left _ _) hC (by positivity) + +lemma spatial_dominated_decay {n : ℕ} {u : Space n → ℂ} {R : ℝ} + (hR : 0 < R) (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) + (hsupp : ∀ x ∈ tsupport u, ‖x‖ ≤ R) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ (z : Space n) (t : ℝ), + 4 * R * |t| ≤ ‖z‖ → + (1+‖z‖) ^ k * ‖∫ x, u x * oscillation (quadraticPhase (z,t)) 1 x‖ ≤ C := by + obtain ⟨C,hC,hb⟩ := spatial_dominated_decay_power hR hu hcu hsupp k + let C₀ := ∫ x, ‖u x‖ + have hC₀ : 0 ≤ C₀ := integral_nonneg (fun _ => norm_nonneg _) + refine ⟨2^k * max C C₀, by positivity, fun z t hzt => ?_⟩ + apply one_add_weight_bound (norm_nonneg _) (norm_nonneg _) hC hC₀ k (hb z t hzt) + calc + _ ≤ ∫ x, ‖u x * oscillation (quadraticPhase (z,t)) 1 x‖ := norm_integral_le_integral_norm _ + _ = C₀ := by simp [C₀] + +def scaledKernel (u : Space 2 → ℂ) (N : ℝ) (z : Space 2) (t : ℝ) : ℂ := + ∫ ξ, u (N⁻¹ • ξ) * oscillation (quadraticPhase (z,t)) 1 ξ + +lemma scaledKernel_eq (u : Space 2 → ℂ) {N : ℝ} (hN : 0 < N) (z : Space 2) (t : ℝ) : + scaledKernel u N z t = (N^2 : ℝ) • + ∫ η, u η * oscillation (quadraticPhase (N • z, N^2*t)) 1 η := by + let q : Space 2 → ℂ := fun η => u η * oscillation (quadraticPhase (N • z, N^2*t)) 1 η + have he : (fun ξ => u (N⁻¹ • ξ) * oscillation (quadraticPhase (z,t)) 1 ξ) = + fun ξ => q (N⁻¹ • ξ) := by + funext ξ + dsimp only [q] + congr 1 + unfold oscillation quadraticPhase + congr 3 + simp only [real_inner_smul_left, real_inner_smul_right, norm_smul, Real.norm_eq_abs, + abs_inv, abs_of_pos hN] + field_simp + unfold scaledKernel + rw [he, Measure.integral_comp_inv_smul_of_nonneg volume q hN.le] + simp only [Space, finrank_euclideanSpace, Fintype.card_fin] + rfl + +lemma scaledKernel_time_decay {u : Space 2 → ℂ} {c : ℝ} + (hc : 0 < c) (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) + (hann : ∀ x ∈ tsupport u, c ≤ ‖x‖) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ (N : ℝ), 0 < N → ∀ (z : Space 2) (t : ℝ), + ‖z‖ ≤ c * N * |t| → + (N^2 * |t|) ^ k * ‖scaledKernel u N z t‖ ≤ C * N^2 := by + obtain ⟨C,hC,hb⟩ := time_dominated_decay hc hu hcu hann k + refine ⟨C,hC,fun N hN z t hzt => ?_⟩ + have hz : ‖N • z‖ ≤ c * |N^2*t| := by + rw [norm_smul, Real.norm_eq_abs, abs_of_pos hN, abs_mul, abs_of_nonneg (sq_nonneg N)] + nlinarith [mul_le_mul_of_nonneg_left hzt hN.le] + have hh := hb (N • z) (N^2*t) hz + rw [scaledKernel_eq u hN, norm_smul, Real.norm_eq_abs, abs_of_nonneg (sq_nonneg N)] + have hht : |N^2*t| = N^2*|t| := by rw [abs_mul, abs_of_nonneg (sq_nonneg N)] + rw [hht] at hh + nlinarith [mul_le_mul_of_nonneg_left hh (sq_nonneg N)] + +lemma scaledKernel_spatial_decay {u : Space 2 → ℂ} {R : ℝ} + (hR : 0 < R) (hu : ContDiff ℝ ∞ u) (hcu : HasCompactSupport u) + (hsupp : ∀ x ∈ tsupport u, ‖x‖ ≤ R) (k : ℕ) : + ∃ C : ℝ, 0 ≤ C ∧ ∀ (N : ℝ), 0 < N → ∀ (z : Space 2) (t : ℝ), + 4 * R * N * |t| ≤ ‖z‖ → + ‖scaledKernel u N z t‖ ≤ C * N^2 / (1+N*‖z‖)^k := by + obtain ⟨C,hC,hb⟩ := spatial_dominated_decay hR hu hcu hsupp k + refine ⟨C,hC,fun N hN z t hzt => ?_⟩ + have hz : 4*R*|N^2*t| ≤ ‖N • z‖ := by + rw [norm_smul, Real.norm_eq_abs, abs_of_pos hN, abs_mul, abs_of_nonneg (sq_nonneg N)] + nlinarith [mul_le_mul_of_nonneg_left hzt hN.le] + have hh := hb (N • z) (N^2*t) hz + rw [norm_smul, Real.norm_eq_abs, abs_of_pos hN] at hh + rw [le_div_iff₀ (pow_pos (by positivity) k), scaledKernel_eq u hN, + norm_smul, Real.norm_eq_abs, abs_of_nonneg (sq_nonneg N)] + nlinarith [mul_le_mul_of_nonneg_left hh (sq_nonneg N)] + +end EndpointKernel +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/Representative.lean b/lean/OAI/Analysis/PlanarEndpoint/Representative.lean new file mode 100644 index 0000000000000000000000000000000000000000..adb30497e61d433925548f2fe660338a7f7ef64d --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/Representative.lean @@ -0,0 +1,81 @@ +import OAI.Analysis.PlanarEndpoint.BanachHeat +import OAI.Analysis.PlanarEndpoint.Convolution +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.Heat + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set Metric +open scoped Topology ENNReal NNReal +namespace PlanarEndpoint + +lemma heatPath_eq_abel {f : L2} {U : Plane → TimePath} + (hU : LocallyIntegrable U volume) (A : ℝ≥0) + (hball : ∀ x : Plane, ∫ y in ball x 1, ‖U y‖ ≤ A) + (hid : ∀ t : Time, (fun y => U y t) =ᵐ[volume] (l2Evolution f (t : ℝ) : Plane → ℂ)) + {a : ℝ} (ha : 0 < a) (x : Plane) (t : Time) : + (∫ z, heatKernel a z • U (x-z)) t = abel f a x (t : ℝ) := by + rw [ContinuousMap.integral_apply (integrable_heat_smul hU A hball ha x), abel_eq_heat_convolution f ha] + calc + _ = ∫ y : Plane, (heatKernel a (x-y) : ℂ) * U y t := by + simpa only [ContinuousMap.smul_apply, Complex.real_smul, smul_eq_mul, sub_sub_cancel] + using integral_sub_left_eq_self + (fun y : Plane => (heatKernel a (x-y) : ℂ) * U y t) volume x + _ = _ := integral_congr_ae ((hid t).mono fun y hy => by exact congrArg (fun z : ℂ => (heatKernel a (x-y) : ℂ) * z) hy) + +lemma mainConclusion_of_integrable_paths (f : L2) (U : Plane → TimePath) + (hU : LocallyIntegrable U volume) (A : ℝ≥0) + (hball : ∀ x : Plane, ∫ y in ball x 1, ‖U y‖ ≤ A) + (hid : ∀ t : Time, (fun y => U y t) =ᵐ[volume] (l2Evolution f (t : ℝ) : Plane → ℂ)) : + MainConclusion f := by + let tzero : Time := ⟨0, by constructor <;> norm_num⟩ + have hzero : (fun y => U y tzero) =ᵐ[volume] (f : Plane → ℂ) := by + simpa only [tzero, l2Evolution_zero] using hid tzero + let E : Set Plane := {x | + Tendsto (fun r : ℝ => (Real.pi*r^2)⁻¹ * ∫ y in ball x r, ‖U y-U x‖) (𝓝[>] 0) (𝓝 0) ∧ + IsLebesguePoint f x ∧ + Tendsto (diskAverage f x) (𝓝[>] (0 : ℝ)) (𝓝 (f x)) ∧ + lebesgueRepresentative f x = f x ∧ U x tzero = f x} + have hE : volume Eᶜ = 0 := by + apply ae_iff.1 + filter_upwards [ae_banachLebesguePoint hU, ae_isLebesguePoint f, + ae_diskAverage_tendsto f, lebesgueRepresentative_ae f, hzero] with x h₁ h₂ h₃ h₄ h₅ + exact ⟨h₁, h₂, h₃, h₄, h₅⟩ + refine ⟨E, hE, ?_⟩ + intro x hx + obtain ⟨hLeb, hpoint, hdisk, hrep, hzero⟩ := hx + let u : ℝ → ℂ := fun t => U x (projIcc 0 1 (by norm_num) t) + have hc : Continuous u := (U x).continuous.comp continuous_projIcc + have hu0 : u 0 = lebesgueRepresentative f x := by + dsimp only [u] + rw [projIcc_of_mem (show (0 : ℝ) ≤ 1 by norm_num) (show (0 : ℝ) ∈ Icc 0 1 by simp)] + exact hzero.trans hrep.symm + have ht := tendsto_heat_smul_of_lebesgue hU A hball x hLeb + have htu := ContinuousMap.tendsto_iff_tendstoUniformly.1 ht + have huni : TendstoUniformlyOn (fun a t => abel f a x t) u + (𝓝[>] (0 : ℝ)) (Ioo (0 : ℝ) 1) := by + apply Metric.tendstoUniformlyOn_iff.2 + intro ε hε + have hh := (Metric.tendstoUniformly_iff.1 htu) ε hε + filter_upwards [self_mem_nhdsWithin, hh] with a ha hae + intro t ht + let tt : Time := ⟨t, ht.1.le, ht.2.le⟩ + have he := hae tt + rw [heatPath_eq_abel hU A hball hid ha x tt] at he + simpa only [u, projIcc_of_mem (show (0 : ℝ) ≤ 1 by norm_num) (show t ∈ Icc 0 1 from ⟨ht.1.le, ht.2.le⟩)] using he + refine ⟨hpoint, u, hc.continuousOn, hu0, ?_, ?_, ?_, huni⟩ + · simpa only [hu0, hrep] using hdisk + · intro t ht + exact huni.tendsto_at ht + · rw [← hu0] + exact hc.continuousAt.tendsto.mono_left nhdsWithin_le_nhds + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/SobolevGraph.lean b/lean/OAI/Analysis/PlanarEndpoint/SobolevGraph.lean new file mode 100644 index 0000000000000000000000000000000000000000..702f43a0b1252e91fd16c7f08be707bb8aacc941 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/SobolevGraph.lean @@ -0,0 +1,115 @@ +import OAI.Analysis.PlanarEndpoint.Extension +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphDual +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.WeightedGraph + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +namespace PlanarEndpoint + +lemma weighted_cauchy_schwarz {X : Type*} [MeasurableSpace X] (μ : Measure X) + {W a b : X → ℝ} (hW : Measurable W) (hpos : ∀ x, 0 < W x) + (ha : AEStronglyMeasurable a μ) (hb : AEStronglyMeasurable b μ) + (ha0 : ∀ x, 0 ≤ a x) (hb0 : ∀ x, 0 ≤ b x) + (hia : Integrable (fun x => W x * a x^2) μ) + (hib : Integrable (fun x => (W x)⁻¹ * b x^2) μ) : + (∫ x, a x*b x ∂μ) ≤ Real.sqrt (∫ x, W x*a x^2 ∂μ) * + Real.sqrt (∫ x, (W x)⁻¹*b x^2 ∂μ) := by + let A := fun x => Real.sqrt (W x) * a x + let B := fun x => (Real.sqrt (W x))⁻¹ * b x + have hA0 x : 0 ≤ A x := mul_nonneg (Real.sqrt_nonneg _) (ha0 x) + have hB0 x : 0 ≤ B x := mul_nonneg (inv_nonneg.mpr (Real.sqrt_nonneg _)) (hb0 x) + have hA x : ‖A x‖^2 = W x * a x^2 := by + simp only [A, Real.norm_eq_abs, sq_abs, mul_pow, Real.sq_sqrt (hpos x).le] + have hB x : ‖B x‖^2 = (W x)⁻¹ * b x^2 := by + simp only [B, Real.norm_eq_abs, sq_abs, mul_pow, inv_pow, Real.sq_sqrt (hpos x).le] + have hma : MemLp A 2 μ := (memLp_two_iff_integrable_sq_norm + (show AEStronglyMeasurable A μ from hW.sqrt.aestronglyMeasurable.mul ha)).2 + (by simpa only [hA] using hia) + have hmb : MemLp B 2 μ := (memLp_two_iff_integrable_sq_norm + (show AEStronglyMeasurable B μ from hW.sqrt.inv.aestronglyMeasurable.mul hb)).2 + (by simpa only [hB] using hib) + have hh := integral_mul_norm_le_Lp_mul_Lq Real.HolderConjugate.two_two + (by simpa using hma) (by simpa using hmb) + simp only [Real.rpow_two, hA, hB] at hh + norm_num only [show (1/(2:ℝ))=(1/2:ℝ) from rfl] at hh + rw [← Real.sqrt_eq_rpow, ← Real.sqrt_eq_rpow] at hh + convert hh using 1 + apply integral_congr_ae + filter_upwards [] with x + rw [Real.norm_eq_abs, Real.norm_eq_abs, abs_of_nonneg (hA0 x), abs_of_nonneg (hB0 x)] + dsimp [A,B] + have hs : Real.sqrt (W x) ≠ 0 := (Real.sqrt_pos.2 (hpos x)).ne' + field_simp + +lemma hThirdNorm_energy_sqrt (f : L2) : + Real.sqrt (∫ ξ, sobolevWeight ξ * ‖fourier f ξ‖^2) = (2*Real.pi)*hThirdNorm f := by + rw [hThirdNorm, Real.sqrt_mul (by positivity), Real.sqrt_inv, Real.sqrt_sq (by positivity)] + dsimp [sobolevWeight] + field_simp + +lemma BoundedFourierSupport.dyadic {f : L2} (hf : BoundedFourierSupport f) : + ∃ n : ℕ, ∀ᵐ ξ ∂volume, ξ ∉ Metric.ball (0:Plane) ((2:ℝ)^n) → fourier f ξ=0 := by + obtain ⟨R,hs⟩ := hf + obtain ⟨n,hn⟩ := pow_unbounded_of_one_lt R (by norm_num : (1:ℝ)<2) + refine ⟨n,hs.mono ?_⟩ + intro ξ hξ hout + apply hξ + have ho : (2:ℝ)^n ≤ ‖ξ‖ := by simpa only [Metric.mem_ball, dist_zero_right, not_lt] using hout + exact lt_of_lt_of_le hn ho + +lemma graph_sobolev_pairing_bound {p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate (1/4) 4 p) : + ∃ C : ℝ, 0 < C ∧ ∀ (f : L2), BoundedFourierSupport f → InHThird f → + ∀ (x₀ : Plane) (T : Plane → ℝ) (w : Plane → ℂ), Measurable T → Measurable w → + (∀ x, ‖w x‖ ≤ 1) → (∀ x ∈ Metric.ball x₀ 1, T x ∈ Ico 0 1) → + ‖∫ ξ, fourier f ξ * graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖ ≤ + C*hThirdNorm f := by + obtain ⟨C,hC,hbound⟩ := graph_weighted_sum_bound hp hshort + refine ⟨(2*Real.pi)*Real.sqrt C,by positivity,?_⟩ + intro f hf hH x₀ T w hT hw hb ht + obtain ⟨n,hn⟩ := hf.dyadic + let S := Metric.ball (0:Plane) ((2:ℝ)^n) + let G := graphFourier (volume.restrict (Metric.ball x₀ 1)) T w + have hg : Continuous G := continuous_graphFourier _ hT hw hb + have he : (∫ ξ, fourier f ξ*G ξ) = ∫ ξ in S, fourier f ξ*G ξ := by + rw [← integral_indicator measurableSet_ball] + apply integral_congr_ae + filter_upwards [hn] with ξ hξ + by_cases hs : ξ ∈ S + · rw [indicator_of_mem hs] + · rw [indicator_of_notMem hs,hξ hs,zero_mul] + rw [he] + have hnorm := norm_integral_le_integral_norm (fun ξ => fourier f ξ*G ξ) + (μ := volume.restrict S) + simp only [norm_mul] at hnorm + have hia : Integrable (fun ξ => sobolevWeight ξ*‖fourier f ξ‖^2) (volume.restrict S) := + hH.mono_measure Measure.restrict_le_self + have hib : Integrable (fun ξ => (sobolevWeight ξ)⁻¹*‖G ξ‖^2) (volume.restrict S) := + graph_weighted_integrableOn x₀ hT hw hb _ + have hcs := weighted_cauchy_schwarz (volume.restrict S) continuous_sobolevWeight.measurable + sobolevWeight_pos ((fourier_memLp f).aestronglyMeasurable.restrict.norm) + (hg.aestronglyMeasurable.norm) (fun _ => norm_nonneg _) (fun _ => norm_nonneg _) hia hib + apply hnorm.trans (hcs.trans ?_) + have hleft : (∫ ξ in S, sobolevWeight ξ*‖fourier f ξ‖^2) ≤ + ∫ ξ, sobolevWeight ξ*‖fourier f ξ‖^2 := + integral_mono_measure Measure.restrict_le_self + (Eventually.of_forall (fun ξ => mul_nonneg (sobolevWeight_pos ξ).le (sq_nonneg _))) hH + have hright := hbound x₀ T w hT hw hb ht n + calc + _ ≤ Real.sqrt (∫ ξ, sobolevWeight ξ*‖fourier f ξ‖^2) * Real.sqrt C := + mul_le_mul (Real.sqrt_le_sqrt hleft) (Real.sqrt_le_sqrt hright) + (Real.sqrt_nonneg _) (Real.sqrt_nonneg _) + _ = _ := by rw [hThirdNorm_energy_sqrt]; ring + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/SpatialGrid.lean b/lean/OAI/Analysis/PlanarEndpoint/SpatialGrid.lean new file mode 100644 index 0000000000000000000000000000000000000000..286450af9c16652cf96b033113f0fee8361674a3 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/SpatialGrid.lean @@ -0,0 +1,169 @@ +import OAI.Analysis.PlanarEndpoint.Fourier + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set +open scoped Topology BigOperators +namespace PlanarEndpoint +attribute [local instance] Classical.propDecidable + +abbrev GridBox (M : ℕ) := Fin 2 → Set.Icc (-(M : ℤ)) (M : ℤ) + +def gridLabel (x₀ : Plane) (r : ℝ) (x : Plane) (i : Fin 2) : ℤ := + ⌊(x i-x₀ i)/r⌋ + +def gridCell (x₀ : Plane) (r : ℝ) (a : Fin 2 → ℤ) : Set Plane := + {x | gridLabel x₀ r x = a} + +def gridCenter (x₀ : Plane) (r : ℝ) (a : Fin 2 → ℤ) : Plane := + WithLp.toLp 2 (fun i => x₀ i+r*((a i:ℝ)+1/2)) + +lemma measurable_gridLabel (x₀ : Plane) (r : ℝ) : Measurable (gridLabel x₀ r) := by + apply measurable_pi_iff.mpr + intro i + unfold gridLabel + exact Int.measurable_floor.comp (((EuclideanSpace.proj i).continuous.measurable.sub + measurable_const).div_const r) + +lemma measurableSet_gridCell (x₀ : Plane) (r : ℝ) (a : Fin 2 → ℤ) : + MeasurableSet (gridCell x₀ r a) := + (measurable_gridLabel x₀ r) (measurableSet_singleton a) + +lemma gridCell_coord {x₀ : Plane} {r : ℝ} (hr : 0 < r) {a : Fin 2 → ℤ} + {x : Plane} (hx : x ∈ gridCell x₀ r a) (i : Fin 2) : + x₀ i+r*(a i:ℝ) ≤ x i ∧ x i < x₀ i+r*((a i:ℝ)+1) := by + have he : ⌊(x i-x₀ i)/r⌋ = a i := congrFun hx i + constructor + · have h := Int.floor_le ((x i-x₀ i)/r) + rw [he] at h + have := (le_div_iff₀ hr).mp h + nlinarith + · have h := Int.lt_floor_add_one ((x i-x₀ i)/r) + rw [he] at h + have := (div_lt_iff₀ hr).mp h + nlinarith + +lemma gridCell_in_ball {x₀ : Plane} {r : ℝ} (hr : 0 < r) (a : Fin 2 → ℤ) : + gridCell x₀ r a ⊆ Metric.ball (gridCenter x₀ r a) r := by + intro x hx + have hc (i : Fin 2) : |(x-gridCenter x₀ r a) i| ≤ r/2 := by + have hh := gridCell_coord hr hx i + change |x i-(x₀ i+r*((a i:ℝ)+1/2))| ≤ r/2 + apply abs_le.mpr + constructor <;> linarith [hh.1,hh.2] + have hsq (i : Fin 2) : ‖(x-gridCenter x₀ r a) i‖^2 ≤ (r/2)^2 := by + simpa only [Real.norm_eq_abs] using (sq_le_sq₀ (abs_nonneg _) (by positivity)).2 (hc i) + rw [Metric.mem_ball, dist_eq_norm] + have hn := EuclideanSpace.norm_sq_eq (x-gridCenter x₀ r a) + simp only [Fin.sum_univ_two] at hn + nlinarith [hsq 0, hsq 1, norm_nonneg (x-gridCenter x₀ r a)] + +lemma gridLabel_mem_box {x₀ : Plane} {r : ℝ} (hr : 0 < r) {M : ℕ} + (hM : 1/r+1 ≤ (M:ℝ)) {x : Plane} (hx : x ∈ Metric.ball x₀ 1) : + ∀ i, gridLabel x₀ r x i ∈ Set.Icc (-(M:ℤ)) (M:ℤ) := by + intro i + have hc : |x i-x₀ i| < 1 := by + have := PiLp.norm_apply_le (x-x₀) i + simp only [PiLp.sub_apply, Real.norm_eq_abs] at this + exact this.trans_lt (by simpa only [Metric.mem_ball, dist_eq_norm] using hx) + have hq : |(x i-x₀ i)/r| < 1/r := by + rw [abs_div, abs_of_pos hr] + exact div_lt_div_of_pos_right hc hr + simp only [Set.mem_Icc, gridLabel] + constructor + · apply Int.le_floor.mpr + have h := (abs_lt.mp hq).1 + push_cast + linarith + · have hlt : ⌊(x i-x₀ i)/r⌋ < (M:ℤ)+1 := by + apply Int.floor_lt.mpr + push_cast + linarith [(abs_lt.mp hq).2] + omega + +lemma gridCell_disjoint {x₀ : Plane} {r : ℝ} {a b : Fin 2 → ℤ} (hab : a ≠ b) : + Disjoint (gridCell x₀ r a) (gridCell x₀ r b) := by + apply Set.disjoint_left.mpr + intro x hx hy + exact hab (hx.symm.trans hy) + +lemma gridBox_injective (M : ℕ) : + Function.Injective (fun a : GridBox M => fun i => (a i : ℤ)) := by + intro a b hab + funext i + exact Subtype.ext (congrFun hab i) + +lemma grid_partition {x₀ : Plane} {r : ℝ} (hr : 0 < r) {M : ℕ} + (hM : 1/r+1 ≤ (M:ℝ)) {E : Set Plane} (hE : E ⊆ Metric.ball x₀ 1) : + ⋃ a : GridBox M, E ∩ gridCell x₀ r (fun i => (a i:ℤ)) = E := by + apply Set.Subset.antisymm + · exact Set.iUnion_subset (fun a => Set.inter_subset_left) + · intro x hx + let a : GridBox M := fun i => ⟨gridLabel x₀ r x i, gridLabel_mem_box hr hM (hE hx) i⟩ + exact Set.mem_iUnion.mpr ⟨a,hx,rfl⟩ + +lemma grid_restrict_eq_sum {x₀ : Plane} {r : ℝ} (hr : 0 < r) {M : ℕ} + (hM : 1/r+1 ≤ (M:ℝ)) {E : Set Plane} (hEm : MeasurableSet E) + (hE : E ⊆ Metric.ball x₀ 1) : + volume.restrict E = ∑ a : GridBox M, + volume.restrict (E ∩ gridCell x₀ r (fun i => (a i:ℤ))) := by + rw [← Measure.sum_fintype, ← Measure.restrict_iUnion] + · rw [grid_partition hr hM hE] + · intro a b hab + exact (gridCell_disjoint (fun h => hab (gridBox_injective M h))).mono + Set.inter_subset_right Set.inter_subset_right + · exact fun a => hEm.inter (measurableSet_gridCell _ _ _) + +def gridNear {M : ℕ} (K : ℕ) (a b : GridBox M) : Prop := + ∀ i, |(a i:ℤ)-(b i:ℤ)| ≤ (K:ℤ) + +lemma gridNear_symm {M K : ℕ} : Std.Symm (gridNear (M:=M) K) := by + constructor + intro a b hab i + simpa only [abs_sub_comm] using hab i + +lemma gridNear_degree {M : ℕ} (K : ℕ) (a : GridBox M) : + (Finset.univ.filter (gridNear K a)).card ≤ Fintype.card (GridBox K) := by + classical + let f : {b : GridBox M // b ∈ Finset.univ.filter (gridNear K a)} → GridBox K := + fun b i => ⟨(a i:ℤ)-(b.1 i:ℤ), abs_le.mp ((Finset.mem_filter.mp b.2).2 i)⟩ + have hf : Function.Injective f := by + intro b c he + apply Subtype.ext + funext i + apply Subtype.ext + have h := congrArg (fun x : GridBox K => (x i:ℤ)) he + change (a i:ℤ)-(b.1 i:ℤ) = (a i:ℤ)-(c.1 i:ℤ) at h + omega + simpa only [Fintype.card_coe] using Fintype.card_le_of_injective f hf + +lemma grid_far_distance {x₀ : Plane} {r : ℝ} (hr : 0 < r) {M K : ℕ} + {a b : GridBox M} (hab : ¬gridNear K a b) {x y : Plane} + (hx : x ∈ gridCell x₀ r (fun i => (a i:ℤ))) + (hy : y ∈ gridCell x₀ r (fun i => (b i:ℤ))) : + (K:ℝ)*r ≤ ‖x-y‖ := by + classical + obtain ⟨i,hi⟩ := not_forall.mp hab + have hc := gridCell_coord hr hx i + have hd := gridCell_coord hr hy i + have hnorm : |x i-y i| ≤ ‖x-y‖ := by + simpa only [PiLp.sub_apply, Real.norm_eq_abs] using PiLp.norm_apply_le (x-y) i + apply le_trans _ hnorm + have hi' : (K:ℤ)+1 ≤ |(a i:ℤ)-(b i:ℤ)| := by omega + have hiR : (K:ℝ)+1 ≤ |((a i:ℤ):ℝ)-((b i:ℤ):ℝ)| := by exact_mod_cast hi' + rcases le_total ((a i:ℤ):ℝ) ((b i:ℤ):ℝ) with hle | hle + · rw [abs_of_nonpos (sub_nonpos.mpr hle)] at hiR + rw [abs_of_nonpos (by nlinarith : x i-y i ≤ 0)] + nlinarith + · rw [abs_of_nonneg (sub_nonneg.mpr hle)] at hiR + rw [abs_of_nonneg (by nlinarith : 0 ≤ x i-y i)] + nlinarith + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/SpatialOrthogonal.lean b/lean/OAI/Analysis/PlanarEndpoint/SpatialOrthogonal.lean new file mode 100644 index 0000000000000000000000000000000000000000..88a25bcaba407122e7b6573af9afc9b14cf9a039 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/SpatialOrthogonal.lean @@ -0,0 +1,144 @@ +import OAI.Analysis.PlanarEndpoint.AlmostOrthogonal +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphDual + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology ComplexConjugate BigOperators +namespace PlanarEndpoint + +def spatialDecay (N : ℝ) (z : Plane) : ℝ := N^2/(1+N*‖z‖)^4 + +lemma spatialDecay_nonneg {N : ℝ} (z : Plane) : 0 ≤ spatialDecay N z := by + unfold spatialDecay + positivity + +lemma spatialDecay_le {N : ℝ} (hN : 0 ≤ N) (z : Plane) : spatialDecay N z ≤ N^2 := by + have h : 1 ≤ 1+N*‖z‖ := by linarith [mul_nonneg hN (norm_nonneg z)] + have h4 : 1 ≤ (1+N*‖z‖)^4 := one_le_pow₀ h + unfold spatialDecay + exact div_le_self (sq_nonneg _) h4 + +lemma spatialDecay_one_integrable : Integrable (spatialDecay 1) volume := by + have h := (integrable_one_add_norm (μ := (volume : Measure Plane)) + (show (Module.finrank ℝ Plane : ℝ) < (4 : ℝ) by norm_num)) + convert h using 1 + funext z + simp [spatialDecay] + +lemma spatialDecay_scale {N : ℝ} (hN : 0 ≤ N) (z : Plane) : + spatialDecay N z = N^2 * spatialDecay 1 (N • z) := by + simp [spatialDecay, norm_smul, Real.norm_eq_abs, abs_of_nonneg hN, div_eq_mul_inv] + +lemma spatialDecay_integrable {N : ℝ} (hN : 0 < N) : Integrable (spatialDecay N) volume := by + convert (spatialDecay_one_integrable.comp_smul hN.ne').const_mul (N^2) using 1 + funext z + exact spatialDecay_scale hN.le z + +lemma integral_spatialDecay {N : ℝ} (hN : 0 < N) : + (∫ z, spatialDecay N z) = ∫ z, spatialDecay 1 z := by + simp_rw [spatialDecay_scale hN.le] + rw [integral_const_mul, Measure.integral_comp_smul_of_nonneg volume _ N (hR := hN.le)] + simp only [finrank_euclideanSpace, Fintype.card_fin, smul_eq_mul, + ← mul_assoc, mul_inv_cancel₀ (pow_ne_zero _ hN.ne'), one_mul] + +lemma integrable_spatialDecay_prod (μ : Measure Plane) [IsFiniteMeasure μ] + {N : ℝ} (hN : 0 < N) : + Integrable (fun z : Plane × Plane => spatialDecay N (z.1-z.2)) (μ.prod volume) := by + have hm : AEStronglyMeasurable (fun z : Plane × Plane => spatialDecay N (z.1-z.2)) + (μ.prod volume) := by + apply Measurable.aestronglyMeasurable + unfold spatialDecay + fun_prop + apply (integrable_prod_iff hm).2 + constructor + · filter_upwards [] with x + exact (spatialDecay_integrable hN).comp_sub_left x + · simp_rw [Real.norm_eq_abs, abs_of_nonneg (spatialDecay_nonneg _), + integral_sub_left_eq_self] + exact integrable_const _ + +lemma spatialDecay_schur (μ : Measure Plane) [IsFiniteMeasure μ] + (hμ : μ ≤ volume) {N : ℝ} (hN : 0 < N) : + (∫ z : Plane × Plane, spatialDecay N (z.1-z.2) ∂μ.prod μ) ≤ + (∫ z, spatialDecay 1 z) * μ.real univ := by + apply le_trans (integral_mono_measure (Measure.prod_mono le_rfl hμ) + (ae_of_all _ (fun z => spatialDecay_nonneg _)) (integrable_spatialDecay_prod μ hN)) + rw [integral_prod (f := fun z : Plane × Plane => spatialDecay N (z.1-z.2)) + (integrable_spatialDecay_prod μ hN)] + simp_rw [integral_sub_left_eq_self, integral_spatialDecay hN] + simp [mul_comm] + +lemma norm_graphDual_pairing_le_integral (χ : Plane → ℂ) (hχm : Measurable χ) + (hχ : MemLp χ 2 volume) (μ ν : Measure Plane) [IsFiniteMeasure μ] [IsFiniteMeasure ν] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) {H : Plane × Plane → ℝ} (hH : Integrable H (μ.prod ν)) + (hK : ∀ᵐ z : Plane × Plane ∂μ.prod ν, + ‖frequencyKernel χ (z.1-z.2) (T z.1-T z.2)‖ ≤ H z) : + ‖∫ ξ, graphDual χ μ T w ξ * conj (graphDual χ ν T w ξ)‖ ≤ + ∫ z, H z ∂μ.prod ν := by + rw [graphDual_pairing χ hχm hχ μ ν hT hw hb] + apply norm_integral_le_of_norm_le hH + filter_upwards [hK] with z hz + simp only [norm_mul, Complex.norm_conj] + have hww : ‖w z.1‖ * ‖w z.2‖ ≤ 1 := by + nlinarith [hb z.1, hb z.2, norm_nonneg (w z.1), norm_nonneg (w z.2)] + exact (mul_le_mul_of_nonneg_right hww (norm_nonneg _)).trans (by simpa using hz) + +lemma finite_sum_prod_integral {ι : Type*} [Fintype ι] + (μ : ι → Measure Plane) [∀ i, IsFiniteMeasure (μ i)] + {H : Plane × Plane → ℝ} (hH : Integrable H ((∑ i, μ i).prod (∑ i, μ i))) : + (∑ i, ∑ j, ∫ z, H z ∂(μ j).prod (μ i)) = + ∫ z, H z ∂(∑ i, μ i).prod (∑ i, μ i) := by + have he : (∑ i, μ i).prod (∑ i, μ i) = ∑ p : ι × ι, (μ p.1).prod (μ p.2) := by + rw [← Measure.sum_fintype, ← Measure.sum_fintype, Measure.prod_sum, Measure.sum_fintype] + have hi (p : ι × ι) : Integrable H ((μ p.1).prod (μ p.2)) := hH.mono_measure + (Measure.prod_mono (Finset.single_le_sum (fun i _ => bot_le) (Finset.mem_univ _)) + (Finset.single_le_sum (fun i _ => bot_le) (Finset.mem_univ _))) + rw [he, integral_finsetSum_measure (fun p _ => hi p), Fintype.sum_prod_type] + exact Finset.sum_comm + +lemma graphPartition_near_far {ι : Type*} [Fintype ι] + (χ : Plane → ℂ) (hχm : Measurable χ) (hχ : MemLp χ 2 volume) + (μ : ι → Measure Plane) [∀ i, IsFiniteMeasure (μ i)] + (hμ : (∑ i, μ i) ≤ volume) (T : Plane → ℝ) (w : Plane → ℂ) + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1) + (R : ι → ι → Prop) [DecidableRel R] + (hR : ∀ ⦃first second⦄, R first second → R second first) + {D C N : ℝ} (hC : 0 ≤ C) (hN : 0 < N) + (hdegree : ∀ i, ((Finset.univ.filter (R i)).card : ℝ) ≤ D) + (hfar : ∀ i j, ¬R i j → ∀ᵐ z : Plane × Plane ∂(μ j).prod (μ i), + ‖frequencyKernel χ (z.1-z.2) (T z.1-T z.2)‖ ≤ C*spatialDecay N (z.1-z.2)) : + ‖graphLp χ hχ (∑ i, μ i) T w hT hw hb‖^2 ≤ + D * (∑ i, ‖graphLp χ hχ (μ i) T w hT hw hb‖^2) + + C * (∫ z, spatialDecay 1 z) * (∑ i, μ i).real univ := by + let M := ∑ i, μ i + have hh : Integrable (fun z : Plane × Plane => C*spatialDecay N (z.1-z.2)) (M.prod M) := + ((integrable_spatialDecay_prod M hN).mono_measure (Measure.prod_mono le_rfl hμ)).const_mul C + have hi (i j : ι) : Integrable (fun z : Plane × Plane => C*spatialDecay N (z.1-z.2)) + ((μ j).prod (μ i)) := hh.mono_measure + (Measure.prod_mono (Finset.single_le_sum (fun i _ => bot_le) (Finset.mem_univ _)) + (Finset.single_le_sum (fun i _ => bot_le) (Finset.mem_univ _))) + have hA (i j : ι) : 0 ≤ ∫ z : Plane × Plane, C*spatialDecay N (z.1-z.2) ∂(μ j).prod (μ i) := + integral_nonneg (fun z => mul_nonneg hC (spatialDecay_nonneg _)) + have hk (i j : ι) (hij : ¬R i j) := norm_graphDual_pairing_le_integral χ hχm hχ + (μ j) (μ i) hT hw hb (hi i j) (hfar i j hij) + simp_rw [← inner_graphLp χ hχ _ _ T w hT hw hb] at hk + have hh' := norm_sum_sq_le_near_error (fun i => graphLp χ hχ (μ i) T w hT hw hb) + R hR _ hA hdegree hk + rw [← graphLp_finsetSum_measure Finset.univ χ hχ μ T w hT hw hb] at hh' + rw [finite_sum_prod_integral μ hh, integral_const_mul] at hh' + apply hh'.trans + apply add_le_add le_rfl + simpa only [M, mul_assoc] using + mul_le_mul_of_nonneg_left (spatialDecay_schur M hμ hN) hC + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/TimeSeparation.lean b/lean/OAI/Analysis/PlanarEndpoint/TimeSeparation.lean new file mode 100644 index 0000000000000000000000000000000000000000..9b3240b029aa90996d45ba59347e734118b975f0 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/TimeSeparation.lean @@ -0,0 +1,196 @@ +import OAI.Analysis.PlanarEndpoint.AlmostOrthogonal +import OAI.Analysis.PlanarEndpoint.DyadicGraph +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphDual +import OAI.Analysis.PlanarEndpoint.TimeTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set +open scoped BigOperators ContDiff +namespace PlanarEndpoint + +lemma card_integer_neighbors {ι : Type*} [Fintype ι] (f : ι → ℤ) + (hf : Function.Injective f) (K : ℕ) (i : ι) : + ((Finset.univ.filter fun j => |f j-f i| ≤ (K : ℤ)).card : ℝ) ≤ 2*K+1 := by + classical + have hh : (Finset.univ.filter fun j => |f j-f i| ≤ (K : ℤ)).card ≤ + (Finset.Icc (f i-K) (f i+K)).card := by + apply Finset.card_le_card_of_injOn f + · intro j hj + have hj' := Finset.mem_filter.mp hj |>.2 + simpa only [Finset.mem_coe, Finset.mem_Icc] using (show f i-K ≤ f j ∧ f j ≤ f i+K by + have h := abs_le.mp hj' + omega) + · exact hf.injOn + have hc : (Finset.Icc (f i-K) (f i+K)).card = 2*K+1 := by + rw [Int.card_Icc] + omega + rw [hc] at hh + exact_mod_cast hh + +lemma separated_interval_points {i j K w x y : ℝ} (hw : 0 ≤ w) + (hx : x ∈ Ico (i*w) ((i+1)*w)) (hy : y ∈ Ico (j*w) ((j+1)*w)) + (hij : K ≤ |i-j|) : (K-1)*w ≤ |x-y| := by + rcases hx with ⟨hx0,hx1⟩ + rcases hy with ⟨hy0,hy1⟩ + rcases le_total i j with h | h + · rw [abs_of_nonpos (sub_nonpos.mpr h)] at hij + have hxy := neg_le_abs (x-y) + nlinarith [mul_le_mul_of_nonneg_right hij hw] + · rw [abs_of_nonneg (sub_nonneg.mpr h)] at hij + have hxy := le_abs_self (x-y) + nlinarith [mul_le_mul_of_nonneg_right hij hw] + +lemma scaled_cutoff_memLp (χ : Plane → ℂ) (hχ : Continuous χ) + (hc : HasCompactSupport χ) {N : ℝ} (hN : 0 < N) : + MemLp (fun ξ => χ (N⁻¹ • ξ)) 2 volume := by + apply (hχ.comp (continuous_const_smul _)).memLp_of_hasCompactSupport + exact hc.comp_homeomorph (Homeomorph.smulOfNeZero N⁻¹ (inv_ne_zero hN.ne')) + +namespace DyadicGraph + +abbrev Node (n : ℕ) := ↥(TimeTree.level n) + +def nodeIndex {n : ℕ} (s : Node n) : ℤ := index s.val + +lemma nodeIndex_injective (n : ℕ) : Function.Injective (@nodeIndex n) := by + intro s t h + apply Subtype.ext + apply index_injective + · exact (TimeTree.mem_level _ _ |>.mp s.property).trans + (TimeTree.mem_level _ _ |>.mp t.property).symm + · dsimp only [nodeIndex] at h + exact_mod_cast h + +lemma width_node {n : ℕ} (s : Node n) : width s.val = ((2 : ℝ)^n)⁻¹ := by + simp only [width, (TimeTree.mem_level _ _).mp s.property, one_div, inv_pow] + +lemma interval_node {n : ℕ} (s : Node n) : interval s.val = + Ico ((nodeIndex s : ℝ) * ((2 : ℝ)^n)⁻¹) + (((nodeIndex s : ℝ)+1) * ((2 : ℝ)^n)⁻¹) := by + rw [interval_eq, width_node] + simp only [nodeIndex, Int.cast_natCast] + +lemma node_interval_separation {n : ℕ} (s t : Node n) {K : ℕ} + (hfar : ¬ |nodeIndex t-nodeIndex s| ≤ (K : ℤ)) + {x y : ℝ} (hx : x ∈ interval s.val) (hy : y ∈ interval t.val) : + (K-1 : ℝ) * ((2 : ℝ)^n)⁻¹ ≤ |x-y| := by + have hij : (K : ℝ) ≤ |(nodeIndex s : ℝ)-(nodeIndex t : ℝ)| := by + rw [abs_sub_comm] + exact_mod_cast (le_of_lt (lt_of_not_ge hfar)) + rw [interval_node] at hx hy + exact separated_interval_points (by positivity) hx hy hij + +end DyadicGraph + +lemma time_kernel_bound {χ : Plane → ℂ} {c C : ℝ} (_hc : 0 < c) + (hK : ∀ N : ℝ, 0 < N → ∀ (z : Plane) (t : ℝ), ‖z‖ ≤ c*N*|t| → + (N^2*|t|)^4 * ‖frequencyKernel (fun ξ => χ (N⁻¹ • ξ)) z t‖ ≤ C*N^2) + {N : ℝ} (hN : 0 < N) (z : Plane) (t : ℝ) (hz : ‖z‖ ≤ 2) + (ht : 1 ≤ N*|t|) (htc : 2 ≤ c*N*|t|) : + ‖frequencyKernel (fun ξ => χ (N⁻¹ • ξ)) z t‖ ≤ C/N^2 := by + have hh := hK N hN z t (hz.trans htc) + have hp : N ≤ N^2*|t| := by nlinarith [mul_le_mul_of_nonneg_left ht hN.le] + have hpow := pow_le_pow_left₀ hN.le hp 4 + have hmul := mul_le_mul_of_nonneg_right hpow + (norm_nonneg (frequencyKernel (fun ξ => χ (N⁻¹ • ξ)) z t)) + have hb := hmul.trans hh + apply (le_div_iff₀ (sq_pos_of_pos hN)).mpr + apply (mul_le_mul_iff_right₀ (sq_pos_of_pos hN)).mp + convert hb using 1 <;> ring + +lemma time_separation_uniform {χ : Plane → ℂ} {c : ℝ} + (hc : 0 < c) (hχ : ContDiff ℝ ∞ χ) (hcomp : HasCompactSupport χ) + (hann : ∀ ξ ∈ tsupport χ, c ≤ ‖ξ‖) : + ∃ C D : ℝ, 0 ≤ C ∧ 0 ≤ D ∧ + ∀ (n : ℕ) (μ : Measure Plane) [IsFiniteMeasure μ] + (T : Plane → ℝ) (w : Plane → ℂ) (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (x₀ : Plane), + (∀ᵐ x ∂μ, ‖x-x₀‖ ≤ 1) → + let N := (2 : ℝ)^n + let χN := fun ξ => χ (N⁻¹ • ξ) + let hχN := scaled_cutoff_memLp χ hχ.continuous hcomp (pow_pos (by norm_num) n) + ‖DyadicGraph.vector χN hχN μ T w hT hw hb []‖^2 ≤ + D * (∑ s ∈ TimeTree.level n, ‖DyadicGraph.vector χN hχN μ T w hT hw hb s‖^2) + + C / N^2 * (DyadicGraph.massTree μ T hT).mass [] ^ 2 := by + classical + obtain ⟨C,hC,hker⟩ := frequencyKernel_time_decay hc hχ hcomp hann 4 + obtain ⟨K,hK⟩ := exists_nat_gt (2+2/c) + have hK1 : 1 ≤ (K : ℝ)-1 := by + have hc' : 0 < 2/c := by positivity + linarith + have hKc : 2 ≤ c*((K : ℝ)-1) := by + have hd : 2/c ≤ (K : ℝ)-1 := by linarith + have hh := (div_le_iff₀ hc).mp hd + nlinarith + refine ⟨C,2*K+1,hC,by positivity,?_⟩ + intro n μ inst T w hT hw hb x₀ hμ + dsimp only + let N : ℝ := 2^n + have hN : 0 < N := pow_pos (by norm_num) n + let χN : Plane → ℂ := fun ξ => χ (N⁻¹ • ξ) + have hχN := scaled_cutoff_memLp χ hχ.continuous hcomp hN + let G : DyadicGraph.Node n → L2 := fun s => DyadicGraph.vector χN hχN μ T w hT hw hb s.val + let m : DyadicGraph.Node n → ℝ := fun s => (DyadicGraph.massTree μ T hT).mass s.val + let R : DyadicGraph.Node n → DyadicGraph.Node n → Prop := fun s t => + |DyadicGraph.nodeIndex t-DyadicGraph.nodeIndex s| ≤ (K : ℤ) + have hsym : ∀ ⦃first second⦄, R first second → R second first := by + intro first second hrelated + dsimp [R] at * + rwa [abs_sub_comm] + have hm : ∀ s, 0 ≤ m s := fun s => (DyadicGraph.massTree μ T hT).nonneg s.val + have hdegree : ∀ s, ((Finset.univ.filter (R s)).card : ℝ) ≤ 2*K+1 := + card_integer_neighbors DyadicGraph.nodeIndex (DyadicGraph.nodeIndex_injective n) K + have hgood (s : DyadicGraph.Node n) : + ∀ᵐ x ∂μ.restrict (DyadicGraph.fiber T s.val), + T x ∈ DyadicGraph.interval s.val ∧ ‖x-x₀‖ ≤ 1 := + (ae_restrict_mem (DyadicGraph.fiber_measurable hT s.val)).and (ae_restrict_of_ae hμ) + have hmass (s : DyadicGraph.Node n) : + (μ.restrict (DyadicGraph.fiber T s.val)).real univ = m s := by + simp only [m, DyadicGraph.massTree, measureReal_def, Measure.restrict_apply_univ] + have hfar : ∀ s t, ¬ R s t → ‖inner ℂ (G s) (G t)‖ ≤ C/N^2*m s*m t := by + intro s t hst + dsimp only [G, DyadicGraph.vector] + rw [inner_graphLp] + have hpair := norm_graphDual_pairing_le χN (hχ.continuous.comp (continuous_const_smul _)).measurable + hχN (μ.restrict (DyadicGraph.fiber T t.val)) (μ.restrict (DyadicGraph.fiber T s.val)) + hT hw hb (B := C/N^2) + have hh := hpair (by + filter_upwards [Measure.quasiMeasurePreserving_fst.ae (hgood t), + Measure.quasiMeasurePreserving_snd.ae (hgood s)] with z hz hy + have ht := DyadicGraph.node_interval_separation t s (by + rw [abs_sub_comm]; exact hst) hz.1 hy.1 + have htn : (K : ℝ)-1 ≤ N*|T z.1-T z.2| := by + have ht' := mul_le_mul_of_nonneg_left ht hN.le + have hni : N * ((K : ℝ)-1) * N⁻¹ = (K : ℝ)-1 := by field_simp + dsimp only [N] at hni + nlinarith [ht'] + have hzc : ‖z.1-z.2‖ ≤ 2 := by + calc + _ = ‖(z.1-x₀)-(z.2-x₀)‖ := by congr 1; abel + _ ≤ ‖z.1-x₀‖+‖z.2-x₀‖ := norm_sub_le _ _ + _ ≤ 2 := by linarith [hz.2,hy.2] + exact time_kernel_bound hc hker hN (z.1-z.2) (T z.1-T z.2) hzc + (hK1.trans htn) (by nlinarith [mul_le_mul_of_nonneg_left htn hc.le])) + rw [hmass,hmass] at hh + simpa only [mul_assoc, mul_left_comm, mul_comm] using hh + have hh := norm_sum_sq_le_near_far G R hsym m hm (by positivity : 0 ≤ C/N^2) hdegree hfar + dsimp only [G,m] at hh + have hsumsq : (∑ s : DyadicGraph.Node n, + ‖DyadicGraph.vector χN hχN μ T w hT hw hb s.val‖^2) = + ∑ s ∈ TimeTree.level n, ‖DyadicGraph.vector χN hχN μ T w hT hw hb s‖^2 := + Finset.sum_coe_sort _ (fun s => ‖DyadicGraph.vector χN hχN μ T w hT hw hb s‖^2) + rw [hsumsq] at hh + simp only [DyadicGraph.Node, Finset.sum_coe_sort, DyadicGraph.vector_level_sum, + DyadicGraph.mass_level_sum] at hh + exact hh + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/TimeTree.lean b/lean/OAI/Analysis/PlanarEndpoint/TimeTree.lean new file mode 100644 index 0000000000000000000000000000000000000000..c7f6d123d8fd2e4cb1c0fe974bd210fcb964fdef --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/TimeTree.lean @@ -0,0 +1,558 @@ +import Mathlib + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open Finset Set +namespace PlanarEndpoint.TimeTree + +theorem convexity_deficit {a b α : ℝ} (hb : 0 ≤ b) (hba : b ≤ a) (hα : 1 < α) : + ((2 : ℝ) ^ α - 2) * b ^ α ≤ (a + b) ^ α - a ^ α - b ^ α := by + let f : ℝ → ℝ := fun u => (u + b) ^ α - u ^ α + have hd (u : ℝ) : HasDerivAt f + (α * (u + b) ^ (α - 1) - α * u ^ (α - 1)) u := by + dsimp [f] + convert! (((hasDerivAt_id u).add_const b).rpow_const (Or.inr hα.le)).sub + (Real.hasDerivAt_rpow_const (Or.inr hα.le)) using 1 + simp + have hm : MonotoneOn f (Ici 0) := by + apply monotoneOn_of_deriv_nonneg (convex_Ici 0) + · exact (continuous_iff_continuousAt.mpr (fun u => (hd u).continuousAt)).continuousOn + · exact (show Differentiable ℝ f from fun u => (hd u).differentiableAt).differentiableOn + · intro u hu + rw [(hd u).deriv] + have hu' : 0 ≤ u := (interior_subset hu : u ∈ Ici (0 : ℝ)) + apply sub_nonneg.mpr + exact mul_le_mul_of_nonneg_left + (Real.rpow_le_rpow hu' (le_add_of_nonneg_right hb) (by linarith)) + (by linarith) + have h := hm hb (hb.trans hba) hba + dsimp [f] at h + have heq : (b + b) ^ α = (2 : ℝ) ^ α * b ^ α := by + rw [← two_mul, Real.mul_rpow (by norm_num : (0 : ℝ) ≤ 2) hb] + rw [heq] at h + nlinarith + +structure MassTree where + mass : List Bool → ℝ + nonneg : ∀ s, 0 ≤ mass s + split : ∀ s, mass s = mass (false :: s) + mass (true :: s) + +namespace MassTree +variable (m : MassTree) + +def lighterMass (s : List Bool) : ℝ := min (m.mass (false :: s)) (m.mass (true :: s)) + +def deficit (α : ℝ) (s : List Bool) : ℝ := + m.mass s ^ α - m.mass (false :: s) ^ α - m.mass (true :: s) ^ α + +lemma lighterMass_nonneg (s : List Bool) : 0 ≤ m.lighterMass s := + le_min (m.nonneg _) (m.nonneg _) + +lemma deficit_nonneg {α : ℝ} (hα : 1 ≤ α) (s : List Bool) : 0 ≤ m.deficit α s := by + dsimp [deficit] + rw [m.split s] + have := Real.add_rpow_le_rpow_add (m.nonneg (false :: s)) (m.nonneg (true :: s)) hα + linarith + +lemma lighterMass_bound {α : ℝ} (hα : 1 < α) (s : List Bool) : + ((2 : ℝ) ^ α - 2) * m.lighterMass s ^ α ≤ m.deficit α s := by + dsimp [lighterMass, deficit] + rw [m.split s] + rcases le_total (m.mass (false :: s)) (m.mass (true :: s)) with h | h + · rw [min_eq_left h] + have he := convexity_deficit (m.nonneg (false :: s)) h hα + rw [add_comm (m.mass (true :: s)) (m.mass (false :: s))] at he + linarith + · rw [min_eq_right h] + exact convexity_deficit (m.nonneg (true :: s)) h hα + +end MassTree + +def level : ℕ → Finset (List Bool) + | 0 => {[]} + | n + 1 => (level n).image (List.cons false) ∪ (level n).image (List.cons true) + +@[simp] lemma mem_level (s : List Bool) (n : ℕ) : s ∈ level n ↔ s.length = n := by + induction n generalizing s with + | zero => simp [level] + | succ n ih => + cases s with + | nil => simp [level] + | cons b s => + cases b <;> simp [level, ih] + +lemma level_children_disjoint (n : ℕ) : + Disjoint ((level n).image (List.cons false)) ((level n).image (List.cons true)) := by + apply Finset.disjoint_left.mpr + intro s h₀ h₁ + obtain ⟨s₀, _, rfl⟩ := Finset.mem_image.mp h₀ + obtain ⟨s₁, _, h⟩ := Finset.mem_image.mp h₁ + cases h + +lemma sum_level_succ (F : List Bool → ℝ) (n : ℕ) : + ∑ s ∈ level (n + 1), F s = + ∑ s ∈ level n, (F (false :: s) + F (true :: s)) := by + rw [level, Finset.sum_union (level_children_disjoint n), Finset.sum_add_distrib] + congr 1 <;> exact Finset.sum_image (fun a _ b _ h => List.cons.inj h |>.2) + +def internal (n : ℕ) : Finset (List Bool) := + (Finset.range n).biUnion level + +@[simp] lemma mem_internal (s : List Bool) (n : ℕ) : + s ∈ internal n ↔ s.length < n := by + simp [internal] + +lemma internal_succ (n : ℕ) : internal (n + 1) = internal n ∪ level n := by + ext s + simp only [mem_internal, Finset.mem_union, mem_level] + omega + +lemma internal_level_disjoint (n : ℕ) : Disjoint (internal n) (level n) := by + apply Finset.disjoint_left.mpr + intro s hi hl + simp only [mem_internal, mem_level] at hi hl + omega + +lemma sum_internal (F : List Bool → ℝ) (n : ℕ) : + ∑ s ∈ internal n, F s = ∑ j ∈ Finset.range n, ∑ s ∈ level j, F s := by + induction n with + | zero => simp [internal] + | succ n ih => + rw [internal_succ, Finset.sum_union (internal_level_disjoint n), ih, + Finset.sum_range_succ] + +namespace MassTree +variable (m : MassTree) + +def potential (α : ℝ) (n : ℕ) : ℝ := ∑ s ∈ level n, m.mass s ^ α + +lemma potential_nonneg (α : ℝ) (n : ℕ) : 0 ≤ m.potential α n := + Finset.sum_nonneg (fun s _ => Real.rpow_nonneg (m.nonneg s) α) + +lemma sum_deficit_level (α : ℝ) (n : ℕ) : + ∑ s ∈ level n, m.deficit α s = m.potential α n - m.potential α (n + 1) := by + dsimp [deficit, potential] + rw [sum_level_succ] + simp only [Finset.sum_sub_distrib, Finset.sum_add_distrib] + ring + +lemma deficits_telescope (α : ℝ) (n : ℕ) : + ∑ k ∈ Finset.range n, ∑ s ∈ level k, m.deficit α s = + m.mass [] ^ α - m.potential α n := by + induction n with + | zero => simp [potential, level] + | succ n ih => + rw [Finset.sum_range_succ, ih, m.sum_deficit_level] + ring + +lemma sum_deficit_internal (α : ℝ) (n : ℕ) : + ∑ s ∈ internal n, m.deficit α s = m.mass [] ^ α - m.potential α n := by + induction n with + | zero => simp [internal, potential, level] + | succ n ih => + rw [internal_succ, Finset.sum_union (internal_level_disjoint n), ih, + m.sum_deficit_level] + ring + +lemma potential_le_root {α : ℝ} (hα : 1 ≤ α) (n : ℕ) : + m.potential α n ≤ m.mass [] ^ α := by + have h : 0 ≤ ∑ s ∈ internal n, m.deficit α s := + Finset.sum_nonneg (fun s _ => m.deficit_nonneg hα s) + rw [m.sum_deficit_internal] at h + linarith + +lemma deficit_sum_le_root {α : ℝ} (hα : 1 ≤ α) (S : Finset (List Bool)) : + ∑ s ∈ S, m.deficit α s ≤ m.mass [] ^ α := by + let n := S.sup List.length + 1 + have hs : S ⊆ internal n := by + intro s hs + apply (mem_internal s n).mpr + exact Nat.lt_succ_of_le (Finset.le_sup hs) + calc + _ ≤ ∑ s ∈ internal n, m.deficit α s := + Finset.sum_le_sum_of_subset_of_nonneg hs (fun s _ _ => m.deficit_nonneg hα s) + _ = m.mass [] ^ α - m.potential α n := m.sum_deficit_internal α n + _ ≤ m.mass [] ^ α := sub_le_self _ (m.potential_nonneg α n) + +lemma convexity_constant_pos {α : ℝ} (hα : 1 < α) : 0 < (2 : ℝ) ^ α - 2 := by + have h := Real.rpow_lt_rpow_of_exponent_lt (by norm_num : (1 : ℝ) < 2) hα + simpa using sub_pos.mpr h + +lemma lighterMass_sum_le {α : ℝ} (hα : 1 < α) (S : Finset (List Bool)) : + ∑ s ∈ S, m.lighterMass s ^ α ≤ m.mass [] ^ α / ((2 : ℝ) ^ α - 2) := by + apply (le_div_iff₀ (convexity_constant_pos hα)).mpr + rw [mul_comm, Finset.mul_sum] + exact (Finset.sum_le_sum (fun s _ => m.lighterMass_bound hα s)).trans + (m.deficit_sum_le_root hα.le S) + +lemma lighterMass_summable {α : ℝ} (hα : 1 < α) : + Summable (fun s : List Bool => m.lighterMass s ^ α) := + summable_of_sum_le (fun s => Real.rpow_nonneg (m.lighterMass_nonneg s) α) + (m.lighterMass_sum_le hα) + +lemma lighterMass_tsum_le {α : ℝ} (hα : 1 < α) : + ∑' s : List Bool, m.lighterMass s ^ α ≤ m.mass [] ^ α / ((2 : ℝ) ^ α - 2) := + Real.tsum_le_of_sum_le (fun s => Real.rpow_nonneg (m.lighterMass_nonneg s) α) + (m.lighterMass_sum_le hα) + +def heavy (s : List Bool) : List Bool := + if m.mass (false :: s) < m.mass (true :: s) then true :: s else false :: s + +def light (s : List Bool) : List Bool := + if m.mass (false :: s) < m.mass (true :: s) then false :: s else true :: s + +lemma light_mass (s : List Bool) : m.mass (m.light s) = m.lighterMass s := by + dsimp [light, lighterMass] + split_ifs with h + · exact (min_eq_left h.le).symm + · exact (min_eq_right (le_of_not_gt h)).symm + +lemma heavy_injective : Function.Injective m.heavy := by + intro s t h + have ht := congrArg List.tail h + simpa only [heavy, List.tail_cons, apply_ite, ite_self] using ht + +def heavyPath (s : List Bool) (k : ℕ) : List Bool := (m.heavy)^[k] s + +lemma heavyPath_injective (k : ℕ) : Function.Injective (fun s => m.heavyPath s k) := + m.heavy_injective.iterate k + +lemma heavyPath_length (s : List Bool) (k : ℕ) : (m.heavyPath s k).length = s.length + k := by + change ((m.heavy)^[k] s).length = _ + induction k with + | zero => simp + | succ k ih => + rw [Function.iterate_succ_apply'] + simp only [heavy] + split_ifs <;> simp only [List.length_cons, ih] <;> omega + +lemma offspring_sum_le {α : ℝ} (hα : 1 < α) (S : Finset (List Bool)) (k : ℕ) : + ∑ s ∈ S, m.mass (m.light (m.heavyPath s k)) ^ α ≤ + m.mass [] ^ α / ((2 : ℝ) ^ α - 2) := by + simpa only [m.light_mass, Finset.sum_image, + m.heavyPath_injective k |>.injOn] using + m.lighterMass_sum_le hα (S.image (fun s => m.heavyPath s k)) + +def offspringPenalty (α q : ℝ) (s : List Bool) : ℝ := + ∑ k ∈ Finset.range s.length, q ^ (k + 1) * m.mass (m.light (m.heavyPath s k)) ^ α + +lemma offspringPenalty_nonneg (α : ℝ) {q : ℝ} (hq : 0 ≤ q) (s : List Bool) : + 0 ≤ m.offspringPenalty α q s := + Finset.sum_nonneg (fun _ _ => mul_nonneg (pow_nonneg hq _) (Real.rpow_nonneg (m.nonneg _) _)) + +lemma offspringPenalty_sum_le {α q : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (n : ℕ) : + ∑ s ∈ internal n, m.offspringPenalty α q s ≤ + (m.mass [] ^ α / ((2 : ℝ) ^ α - 2)) * ∑ k ∈ Finset.range n, q ^ (k + 1) := by + calc + _ ≤ ∑ s ∈ internal n, ∑ k ∈ Finset.range n, + q ^ (k + 1) * m.mass (m.light (m.heavyPath s k)) ^ α := by + apply Finset.sum_le_sum + intro s hs + apply Finset.sum_le_sum_of_subset_of_nonneg + · exact Finset.range_mono ((mem_internal s n).mp hs).le + · intro k _ _ + exact mul_nonneg (pow_nonneg hq _) (Real.rpow_nonneg (m.nonneg _) _) + _ = ∑ k ∈ Finset.range n, q ^ (k + 1) * + ∑ s ∈ internal n, m.mass (m.light (m.heavyPath s k)) ^ α := by + rw [Finset.sum_comm] + simp only [Finset.mul_sum] + _ ≤ ∑ k ∈ Finset.range n, q ^ (k + 1) * + (m.mass [] ^ α / ((2 : ℝ) ^ α - 2)) := by + exact Finset.sum_le_sum (fun k _ => mul_le_mul_of_nonneg_left + (m.offspring_sum_le hα (internal n) k) (pow_nonneg hq _)) + _ = _ := by rw [← Finset.sum_mul, mul_comm] + +lemma terminal_sum_le {α q : ℝ} (hα : 1 ≤ α) (hq : 0 ≤ q) (n : ℕ) : + ∑ s ∈ internal n, q ^ s.length * m.mass s ^ α ≤ + m.mass [] ^ α * ∑ j ∈ Finset.range n, q ^ j := by + rw [sum_internal] + calc + _ = ∑ j ∈ Finset.range n, q ^ j * m.potential α j := by + apply Finset.sum_congr rfl + intro j hj + dsimp [potential] + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro s hs + rw [(mem_level s j).mp hs] + _ ≤ ∑ j ∈ Finset.range n, q ^ j * m.mass [] ^ α := by + exact Finset.sum_le_sum (fun j _ => mul_le_mul_of_nonneg_left + (m.potential_le_root hα j) (pow_nonneg hq j)) + _ = _ := by rw [← Finset.sum_mul, mul_comm] + +def pathBudget (α q : ℝ) (s : List Bool) : ℝ := + m.offspringPenalty α q s + q ^ s.length * m.mass s ^ α + +lemma pathBudget_nonneg (α : ℝ) {q : ℝ} (hq : 0 ≤ q) (s : List Bool) : + 0 ≤ m.pathBudget α q s := + add_nonneg (m.offspringPenalty_nonneg α hq s) + (mul_nonneg (pow_nonneg hq _) (Real.rpow_nonneg (m.nonneg _) _)) + +lemma geom_sum_le {q : ℝ} (hq : 0 ≤ q) (hq1 : q < 1) (n : ℕ) : + ∑ j ∈ Finset.range n, q ^ j ≤ (1 - q)⁻¹ := by + have hs := summable_geometric_of_lt_one hq hq1 + simpa only [tsum_geometric_of_lt_one hq hq1, one_div] using + hs.sum_le_tsum (Finset.range n) (fun _ _ => pow_nonneg hq _) + +lemma next_geom_sum_le {q : ℝ} (hq : 0 ≤ q) (hq1 : q < 1) (n : ℕ) : + ∑ j ∈ Finset.range n, q ^ (j + 1) ≤ q * (1 - q)⁻¹ := by + simp only [pow_succ, ← Finset.sum_mul] + rw [mul_comm q] + exact mul_le_mul_of_nonneg_right (geom_sum_le hq hq1 n) hq + +lemma pathBudget_internal_le {α q : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (hq1 : q < 1) + (n : ℕ) : + ∑ s ∈ internal n, m.pathBudget α q s ≤ + m.mass [] ^ α * (1 - q)⁻¹ * (1 + q / ((2 : ℝ) ^ α - 2)) := by + have hroot := Real.rpow_nonneg (m.nonneg []) α + have hc := convexity_constant_pos hα + calc + _ = (∑ s ∈ internal n, m.offspringPenalty α q s) + + ∑ s ∈ internal n, q ^ s.length * m.mass s ^ α := by + simp only [pathBudget, Finset.sum_add_distrib] + _ ≤ (m.mass [] ^ α / ((2 : ℝ) ^ α - 2)) * + (∑ k ∈ Finset.range n, q ^ (k + 1)) + + m.mass [] ^ α * ∑ j ∈ Finset.range n, q ^ j := + add_le_add (m.offspringPenalty_sum_le hα hq n) (m.terminal_sum_le hα.le hq n) + _ ≤ (m.mass [] ^ α / ((2 : ℝ) ^ α - 2)) * (q * (1 - q)⁻¹) + + m.mass [] ^ α * (1 - q)⁻¹ := + add_le_add (mul_le_mul_of_nonneg_left (next_geom_sum_le hq hq1 n) + (div_nonneg hroot hc.le)) + (mul_le_mul_of_nonneg_left (geom_sum_le hq hq1 n) hroot) + _ = _ := by ring + +lemma pathBudget_sum_le {α q : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (hq1 : q < 1) + (S : Finset (List Bool)) : + ∑ s ∈ S, m.pathBudget α q s ≤ + m.mass [] ^ α * (1 - q)⁻¹ * (1 + q / ((2 : ℝ) ^ α - 2)) := by + let n := S.sup List.length + 1 + have hs : S ⊆ internal n := fun s hs => (mem_internal s n).mpr + (Nat.lt_succ_of_le (Finset.le_sup hs)) + exact (Finset.sum_le_sum_of_subset_of_nonneg hs + (fun s _ _ => m.pathBudget_nonneg α hq s)).trans + (m.pathBudget_internal_le hα hq hq1 n) + +lemma pathBudget_summable {α q : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (hq1 : q < 1) : + Summable (m.pathBudget α q) := + summable_of_sum_le (m.pathBudget_nonneg α hq) (m.pathBudget_sum_le hα hq hq1) + +lemma pathBudget_tsum_le {α q : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (hq1 : q < 1) : + ∑' s : List Bool, m.pathBudget α q s ≤ + m.mass [] ^ α * (1 - q)⁻¹ * (1 + q / ((2 : ℝ) ^ α - 2)) := + Real.tsum_le_of_sum_le (m.pathBudget_nonneg α hq) (m.pathBudget_sum_le hα hq hq1) + +lemma heavy_light_mass (s : List Bool) : + m.mass s = m.mass (m.heavy s) + m.mass (m.light s) := by + dsimp [heavy, light] + split_ifs <;> simpa [add_comm] using m.split s + +lemma heavy_mass_le (s : List Bool) : m.mass (m.heavy s) ≤ m.mass s := by + rw [m.heavy_light_mass s] + exact le_add_of_nonneg_right (m.nonneg _) + +lemma heavyPath_mass_le (s : List Bool) (n : ℕ) : + m.mass (m.heavyPath s n) ≤ m.mass s := by + induction n with + | zero => exact le_rfl + | succ n ih => + simpa only [heavyPath, Function.iterate_succ_apply'] using + (m.heavy_mass_le (m.heavyPath s n)).trans ih + +lemma light_length (s : List Bool) : (m.light s).length = s.length + 1 := by + dsimp [light] + split_ifs <;> rfl + +lemma heavy_light_add {E : Type*} [AddCommMonoid E] (G : List Bool → E) + (hsplit : ∀ s, G s = G (false :: s) + G (true :: s)) (s : List Bool) : + G s = G (m.light s) + G (m.heavy s) := by + dsimp [heavy, light] + split_ifs <;> simpa [add_comm] using hsplit s + +lemma heavyPath_partition {E : Type*} [AddCommMonoid E] (G : List Bool → E) + (hsplit : ∀ s, G s = G (false :: s) + G (true :: s)) (s : List Bool) (n : ℕ) : + G s = (∑ k ∈ Finset.range n, G (m.light (m.heavyPath s k))) + + G (m.heavyPath s n) := by + induction n with + | zero => simp [heavyPath] + | succ n ih => + rw [Finset.sum_range_succ, add_assoc] + have hp : m.heavyPath s (n + 1) = m.heavy (m.heavyPath s n) := by + simp only [heavyPath, Function.iterate_succ_apply'] + rw [hp, ← m.heavy_light_add G hsplit (m.heavyPath s n)] + exact ih + +lemma norm_heavyPath_le {E : Type*} [SeminormedAddCommGroup E] (G : List Bool → E) + (hsplit : ∀ s, G s = G (false :: s) + G (true :: s)) (s : List Bool) (n : ℕ) : + ‖G s‖ ≤ (∑ k ∈ Finset.range n, ‖G (m.light (m.heavyPath s k))‖) + + ‖G (m.heavyPath s n)‖ := by + calc + ‖G s‖ = ‖(∑ k ∈ Finset.range n, G (m.light (m.heavyPath s k))) + + G (m.heavyPath s n)‖ := congrArg norm (m.heavyPath_partition G hsplit s n) + _ ≤ _ := (norm_add_le _ _).trans (add_le_add (norm_sum_le _ _) le_rfl) + +end MassTree + +lemma weighted_norm_sum_sq {E ι : Type*} [SeminormedAddCommGroup E] + (S : Finset ι) (G : ι → E) (w B : ι → ℝ) + (hw : ∀ i ∈ S, 0 ≤ w i) (hB : ∀ i ∈ S, 0 ≤ B i) + (hG : ∀ i ∈ S, ‖G i‖ ^ 2 ≤ w i * B i) : + ‖∑ i ∈ S, G i‖ ^ 2 ≤ (∑ i ∈ S, w i) * ∑ i ∈ S, B i := by + calc + _ ≤ (∑ i ∈ S, ‖G i‖) ^ 2 := by + have hn := norm_sum_le S G + have hp : 0 ≤ ∑ i ∈ S, ‖G i‖ := Finset.sum_nonneg (fun i _ => norm_nonneg _) + nlinarith [norm_nonneg (∑ i ∈ S, G i)] + _ ≤ _ := Finset.sum_sq_le_sum_mul_sum_of_sq_le_mul S hw hB hG + +namespace MassTree +variable (m : MassTree) + +def pathPiece {E : Type*} (G : List Bool → E) (s : List Bool) (k : ℕ) : E := + if k < s.length then G (m.light (m.heavyPath s k)) else G (m.heavyPath s s.length) + +lemma sum_pathPiece {E : Type*} [AddCommMonoid E] (G : List Bool → E) + (hsplit : ∀ s, G s = G (false :: s) + G (true :: s)) (s : List Bool) : + ∑ k ∈ Finset.range (s.length + 1), m.pathPiece G s k = G s := by + rw [Finset.sum_range_succ, m.heavyPath_partition G hsplit s s.length] + simp only [pathPiece, lt_self_iff_false, ↓reduceIte] + congr 1 + apply Finset.sum_congr rfl + intro k hk + simp only [Finset.mem_range.mp hk, ↓reduceIte] + +def pathWeight (q : ℝ) (s : List Bool) (k : ℕ) : ℝ := + if k < s.length then q ^ (k + 1) else q ^ s.length + +lemma pathWeight_nonneg {q : ℝ} (hq : 0 ≤ q) (s : List Bool) (k : ℕ) : + 0 ≤ pathWeight q s k := by + unfold pathWeight + split_ifs <;> exact pow_nonneg hq _ + +lemma sum_pathWeight_le {q : ℝ} (hq : 0 ≤ q) (hq1 : q < 1) (s : List Bool) : + ∑ k ∈ Finset.range (s.length + 1), pathWeight q s k ≤ (1 - q)⁻¹ := by + have he : ∑ k ∈ Finset.range (s.length + 1), pathWeight q s k = + (∑ k ∈ Finset.range s.length, q ^ (k + 1)) + q ^ s.length := by + rw [Finset.sum_range_succ] + simp only [pathWeight, lt_self_iff_false, ↓reduceIte] + congr 1 + apply Finset.sum_congr rfl + intro k hk + simp only [Finset.mem_range.mp hk, ↓reduceIte] + rw [he] + calc + _ ≤ q * (1 - q)⁻¹ + 1 := add_le_add (next_geom_sum_le hq hq1 _) + (pow_le_one₀ hq hq1.le) + _ = (1 - q)⁻¹ := by + field_simp [sub_ne_zero.mpr (ne_of_gt hq1)] + ring + +lemma energy_le_pathBudget {E : Type*} [SeminormedAddCommGroup E] + (G : List Bool → E) (hsplit : ∀ s, G s = G (false :: s) + G (true :: s)) + {α q C : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (hq1 : q < 1) (hC : 0 ≤ C) + (s : List Bool) + (hlight : ∀ k < s.length, ‖G (m.light (m.heavyPath s k))‖ ^ 2 ≤ + C * (q ^ (k + 1)) ^ 2 * m.mass (m.light (m.heavyPath s k)) ^ α) + (hterminal : ‖G (m.heavyPath s s.length)‖ ^ 2 ≤ + C * (q ^ s.length) ^ 2 * m.mass (m.heavyPath s s.length) ^ α) : + ‖G s‖ ^ 2 ≤ C * (1 - q)⁻¹ * m.pathBudget α q s := by + let w := pathWeight q s + let B : ℕ → ℝ := fun k => C * w k * m.mass + (if k < s.length then m.light (m.heavyPath s k) else m.heavyPath s s.length) ^ α + have hw : ∀ k ∈ Finset.range (s.length + 1), 0 ≤ w k := + fun k _ => pathWeight_nonneg hq s k + have hB : ∀ k ∈ Finset.range (s.length + 1), 0 ≤ B k := by + intro k hk + exact mul_nonneg (mul_nonneg hC (hw k hk)) (Real.rpow_nonneg (m.nonneg _) _) + have hPiece : ∀ k ∈ Finset.range (s.length + 1), + ‖m.pathPiece G s k‖ ^ 2 ≤ w k * B k := by + intro k hk + dsimp [pathPiece, B, w, pathWeight] + split_ifs with hk' + · nlinarith [hlight k hk'] + · nlinarith [hterminal] + have hsumB : ∑ k ∈ Finset.range (s.length + 1), B k ≤ C * m.pathBudget α q s := by + rw [Finset.sum_range_succ] + have hterminal_mass : m.mass (m.heavyPath s s.length) ^ α ≤ m.mass s ^ α := + Real.rpow_le_rpow (m.nonneg _) (m.heavyPath_mass_le s _) (le_trans (by norm_num) hα.le) + calc + _ = C * m.offspringPenalty α q s + C * q ^ s.length * + m.mass (m.heavyPath s s.length) ^ α := by + simp only [B, w, pathWeight, lt_self_iff_false, ↓reduceIte, offspringPenalty, + Finset.mul_sum] + congr 1 + apply Finset.sum_congr rfl + intro k hk + simp only [Finset.mem_range.mp hk, ↓reduceIte] + ring + _ ≤ C * m.offspringPenalty α q s + C * q ^ s.length * m.mass s ^ α := + add_le_add le_rfl (mul_le_mul_of_nonneg_left hterminal_mass + (mul_nonneg hC (pow_nonneg hq _))) + _ = C * m.pathBudget α q s := by dsimp [pathBudget]; ring + calc + ‖G s‖ ^ 2 = ‖∑ k ∈ Finset.range (s.length + 1), m.pathPiece G s k‖ ^ 2 := by + rw [m.sum_pathPiece G hsplit] + _ ≤ (∑ k ∈ Finset.range (s.length + 1), w k) * + ∑ k ∈ Finset.range (s.length + 1), B k := + weighted_norm_sum_sq _ _ _ _ hw hB hPiece + _ ≤ (1 - q)⁻¹ * (C * m.pathBudget α q s) := mul_le_mul + (sum_pathWeight_le hq hq1 s) hsumB (Finset.sum_nonneg hB) (by positivity) + _ = _ := by ring + +lemma common_tree_energy_sum_le {E : Type*} [SeminormedAddCommGroup E] + (G : ℕ → List Bool → E) + (hsplit : ∀ j s, G j s = G j (false :: s) + G j (true :: s)) + {α q C : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (hq1 : q < 1) (hC : 0 ≤ C) + (hlight : ∀ s k, k < s.length → + ‖G s.length (m.light (m.heavyPath s k))‖ ^ 2 ≤ + C * (q ^ (k + 1)) ^ 2 * m.mass (m.light (m.heavyPath s k)) ^ α) + (hterminal : ∀ s, ‖G s.length (m.heavyPath s s.length)‖ ^ 2 ≤ + C * (q ^ s.length) ^ 2 * m.mass (m.heavyPath s s.length) ^ α) + (n : ℕ) : + (∑ j ∈ Finset.range n, ∑ s ∈ level j, ‖G j s‖ ^ 2) ≤ + C * (1 - q)⁻¹ * + (m.mass [] ^ α * (1 - q)⁻¹ * (1 + q / ((2 : ℝ) ^ α - 2))) := by + have he (s : List Bool) : ‖G s.length s‖ ^ 2 ≤ + C * (1 - q)⁻¹ * m.pathBudget α q s := + m.energy_le_pathBudget (G s.length) (hsplit s.length) + hα hq hq1 hC s (hlight s) (hterminal s) + have hv : 0 ≤ C * (1 - q)⁻¹ := by positivity + calc + _ = ∑ s ∈ internal n, ‖G s.length s‖ ^ 2 := by + rw [sum_internal] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro s hs + rw [(mem_level s j).mp hs] + _ ≤ ∑ s ∈ internal n, C * (1 - q)⁻¹ * m.pathBudget α q s := + Finset.sum_le_sum (fun s _ => he s) + _ = C * (1 - q)⁻¹ * (∑ s ∈ internal n, m.pathBudget α q s) := by + rw [Finset.mul_sum] + _ ≤ _ := mul_le_mul_of_nonneg_left (m.pathBudget_internal_le hα hq hq1 n) hv + +lemma common_tree_energy_tsum_le {E : Type*} [SeminormedAddCommGroup E] + (G : ℕ → List Bool → E) + (hsplit : ∀ j s, G j s = G j (false :: s) + G j (true :: s)) + {α q C : ℝ} (hα : 1 < α) (hq : 0 ≤ q) (hq1 : q < 1) (hC : 0 ≤ C) + (hlight : ∀ s k, k < s.length → + ‖G s.length (m.light (m.heavyPath s k))‖ ^ 2 ≤ + C * (q ^ (k + 1)) ^ 2 * m.mass (m.light (m.heavyPath s k)) ^ α) + (hterminal : ∀ s, ‖G s.length (m.heavyPath s s.length)‖ ^ 2 ≤ + C * (q ^ s.length) ^ 2 * m.mass (m.heavyPath s s.length) ^ α) : + (∑' j, ∑ s ∈ level j, ‖G j s‖ ^ 2) ≤ + C * (1 - q)⁻¹ * + (m.mass [] ^ α * (1 - q)⁻¹ * (1 + q / ((2 : ℝ) ^ α - 2))) := by + apply Real.tsum_le_of_sum_range_le + (fun j => Finset.sum_nonneg (fun _ _ => sq_nonneg _)) + exact m.common_tree_energy_sum_le G hsplit hα hq hq1 hC hlight hterminal + +end MassTree + +end PlanarEndpoint.TimeTree +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/UnitReduction.lean b/lean/OAI/Analysis/PlanarEndpoint/UnitReduction.lean new file mode 100644 index 0000000000000000000000000000000000000000..c41621ff590002e904e076d69ca6eead1f504d18 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/UnitReduction.lean @@ -0,0 +1,131 @@ +import OAI.Analysis.PlanarEndpoint.Extension +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.FrequencyWeak +import OAI.Analysis.PlanarEndpoint.GraphReduction +import OAI.Analysis.PlanarEndpoint.GraphScaling +import OAI.Analysis.PlanarEndpoint.GraphSelection +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.UnitScaling + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology +namespace PlanarEndpoint + +def UnitFrequencyGraphEstimate (c₀ C₀ p : ℝ) : Prop := + ∃ K : ℝ, 0 < K ∧ ∀ R : ℝ, 1 ≤ R → + ∀ v : Plane → ℂ, ∀ hv : MemLp v 2 volume, + (∀ᵐ η : Plane ∂volume, η ∉ {η | c₀ ≤ ‖η‖ ∧ ‖η‖ ≤ C₀} → v η = 0) → + ∀ (x₀ : Plane) (T : Plane → ℝ), Measurable T → + (∀ X, T X ∈ Icc (0:ℝ) R) → ∀ lam : ℝ, 0 < lam → + volume (Metric.ball x₀ R ∩ {X | lam < ‖frequencyExtension v X (T X)‖}) ≤ + ENNReal.ofReal (R^2 * (K * R^(-2/3:ℝ) * ‖hv.toLp v‖ / lam)^p) + +lemma inverse_smul_ball (x x₀ : Plane) {N : ℝ} (hN : 0 < N) : + N⁻¹ • x ∈ Metric.ball x₀ 1 ↔ x ∈ Metric.ball (N • x₀) N := by + have he : dist x (N • x₀) = N * dist (N⁻¹ • x) x₀ := by + calc + _ = dist (N • (N⁻¹ • x)) (N • x₀) := by simp [smul_smul,hN.ne'] + _ = _ := by simp [dist_smul₀,Real.norm_eq_abs,abs_of_pos hN] + simp only [Metric.mem_ball,he] + exact ⟨fun h => by nlinarith,fun h => (mul_lt_mul_iff_right₀ hN).mp (by simpa using h)⟩ + +lemma unitGraph_time_range {N t₀ s : ℝ} (hN : 0 < N) (hsN : s ≤ N⁻¹) + {T : Plane → ℝ} (hT : ∀ x, T x ∈ Icc t₀ (t₀+s)) (X : Plane) : + N^2*(T (N⁻¹ • X)-t₀) ∈ Icc (0:ℝ) N := by + have ht := hT (N⁻¹ • X) + constructor + · exact mul_nonneg (sq_nonneg _) (sub_nonneg.mpr ht.1) + · have hh : N^2*(T (N⁻¹ • X)-t₀) ≤ N^2*N⁻¹ := + mul_le_mul_of_nonneg_left ((by linarith [ht.2] : T (N⁻¹ • X)-t₀ ≤ s).trans hsN) + (sq_nonneg _) + have he : N^2*N⁻¹ = N := by field_simp + simpa only [he] using hh + +lemma unitGraph_threshold_identity (f : L2) {N : ℝ} (hN : 0 < N) (t₀ K lam : ℝ) : + K * N^(-2/3:ℝ) * + ‖(unitFrequencyInput_memLp f hN t₀).toLp (unitFrequencyInput f N t₀)‖ / + (lam / (((2*Real.pi)^2)⁻¹*N)) = + (K/(2*Real.pi)) * N^(1/3:ℝ) * ‖f‖ / lam := by + rw [unitFrequencyInput_norm f hN t₀] + have hp : N^(-2/3:ℝ)*N = N^(1/3:ℝ) := by + calc + _ = N^(-2/3:ℝ)*N^(1:ℝ) := by rw [Real.rpow_one] + _ = N^((-2/3:ℝ)+1) := (Real.rpow_add hN _ _).symm + _ = _ := by norm_num + rw [← hp] + field_simp + +lemma shortTimeGraphEstimate_of_unitFrequency {c₀ C₀ p : ℝ} + (hg : UnitFrequencyGraphEstimate c₀ C₀ p) : ShortTimeGraphEstimate c₀ C₀ p := by + obtain ⟨K,hK,hg⟩ := hg + refine ⟨K/(2*Real.pi),div_pos hK (by positivity),?_⟩ + intro j f hf x₀ t₀ s hs hsN T hT hr lam hlam + let N : ℝ := 2^j + have hN : 0 < N := by positivity + have hN1 : 1 ≤ N := one_le_pow₀ (by norm_num : (1:ℝ) ≤ 2) + let v := unitFrequencyInput f N t₀ + let hv := unitFrequencyInput_memLp f hN t₀ + let Q (X : Plane) : ℝ := N^2*(T (N⁻¹ • X)-t₀) + have hQ : Measurable Q := by + exact measurable_const.mul ((hT.comp (measurable_const_smul _)).sub measurable_const) + have hQr : ∀ X, Q X ∈ Icc (0:ℝ) N := unitGraph_time_range hN hsN hr + let a : ℝ := ((2*Real.pi)^2)⁻¹*N + have ha : 0 < a := by dsimp [a]; positivity + let E : Set Plane := Metric.ball x₀ 1 ∩ {x | lam < ‖evolution f x (T x)‖} + let F : Set Plane := Metric.ball (N • x₀) N ∩ + {X | lam/a < ‖frequencyExtension v X (Q X)‖} + have hE : MeasurableSet E := Metric.isOpen_ball.measurableSet.inter + (measurableSet_lt measurable_const (measurable_graph_evolution f hf.integrable hT).norm) + have hEF : affineScale 0 N⁻¹ ⁻¹' E = F := by + ext X + simp only [affineScale,zero_add,mem_preimage,mem_inter_iff,mem_ofPred_eq,E,F] + rw [inverse_smul_ball X x₀ hN] + apply and_congr_right' + rw [norm_evolution_unitFrequency_scaling f (N⁻¹ • X) hN (T (N⁻¹ • X)) t₀] + simp only [smul_smul,mul_inv_cancel₀ hN.ne',one_smul] + change lam < a * ‖frequencyExtension v X (Q X)‖ ↔ + lam/a < ‖frequencyExtension v X (Q X)‖ + rw [mul_comm a] + exact (div_lt_iff₀ ha).symm + have hb := hg N hN1 v hv (unitFrequencyInput_support hN hf t₀) + (N • x₀) Q hQ hQr (lam/a) (div_pos hlam ha) + have hnn : 0 ≤ N^2 * (K*N^(-2/3:ℝ)*‖hv.toLp v‖/(lam/a))^p := by positivity + have hbR : volume.real F ≤ N^2 * (K*N^(-2/3:ℝ)*‖hv.toLp v‖/(lam/a))^p := by + exact (ENNReal.toReal_mono ENNReal.ofReal_ne_top hb).trans_eq + (ENNReal.toReal_ofReal hnn) + have he := volumeReal_affineScale hE 0 (inv_pos.mpr hN) + rw [hEF] at he + have hbfinal : volume.real E ≤ ((K/(2*Real.pi))*N^(1/3:ℝ)*‖f‖/lam)^p := by + calc + _ = (N⁻¹)^2 * volume.real F := he + _ ≤ (N⁻¹)^2 * (N^2*(K*N^(-2/3:ℝ)*‖hv.toLp v‖/(lam/a))^p) := + mul_le_mul_of_nonneg_left hbR (sq_nonneg _) + _ = ((K/(2*Real.pi))*N^(1/3:ℝ)*‖f‖/lam)^p := by + dsimp [a,hv,v] + rw [unitGraph_threshold_identity f hN t₀ K lam] + field_simp + have hfin : volume E ≠ ⊤ := + ne_top_of_le_ne_top (measure_ball_lt_top (μ := volume) (x := x₀) (r := 1)).ne (measure_mono inter_subset_left) + change volume E ≤ _ + rw [← ENNReal.ofReal_toReal hfin] + exact ENNReal.ofReal_le_ofReal hbfinal + +lemma shortTimeWeakEstimate_of_unitFrequency {c₀ C₀ p : ℝ} + (hg : UnitFrequencyGraphEstimate c₀ C₀ p) : ShortTimeWeakEstimate c₀ C₀ p := + shortTimeWeakEstimate_of_graph (shortTimeGraphEstimate_of_unitFrequency hg) + +lemma mainConclusion_of_unitFrequencyGraph {p : ℝ} (hp : 2 < p) + (hg : UnitFrequencyGraphEstimate (1/4) 4 p) {f : L2} (hf : InHThird f) : + MainConclusion f := + mainConclusion_of_shortTime hp (shortTimeWeakEstimate_of_unitFrequency hg) hf + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/UnitScaling.lean b/lean/OAI/Analysis/PlanarEndpoint/UnitScaling.lean new file mode 100644 index 0000000000000000000000000000000000000000..c34a44e571266688737edde9dc1b1ac5ddac5233 --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/UnitScaling.lean @@ -0,0 +1,105 @@ +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.FrequencyWeak +import OAI.Analysis.PlanarEndpoint.GraphScaling +import OAI.Analysis.PlanarEndpoint.GraphTree + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Filter Set +open scoped Topology +namespace PlanarEndpoint + +def unitFrequencyInput (f : L2) (N t₀ : ℝ) (η : Plane) : ℂ := + (N : ℂ) * (phase 0 t₀ (N • η) * fourier f (N • η)) + +lemma unitFrequencyInput_memLp (f : L2) {N : ℝ} (hN : 0 < N) (t₀ : ℝ) : + MemLp (unitFrequencyInput f N t₀) 2 volume := by + have hv := memLp_comp_real_smul (fourier_memLp f) hN.ne' + apply (hv.const_mul (N : ℂ)).of_le + · exact aestronglyMeasurable_const.mul + (((continuous_phase 0 t₀).comp (continuous_const_smul N)).aestronglyMeasurable.mul + hv.aestronglyMeasurable) + · exact Eventually.of_forall (fun η => by simp [unitFrequencyInput]) + +lemma norm_unitFrequencyInput (f : L2) {N : ℝ} (hN : 0 < N) (t₀ : ℝ) (η : Plane) : + ‖unitFrequencyInput f N t₀ η‖ = N * ‖fourier f (N • η)‖ := by + simp [unitFrequencyInput,Complex.norm_real,Real.norm_eq_abs,abs_of_pos hN] + +lemma unitFrequencyInput_support {f : L2} {c₀ C₀ N : ℝ} (hN : 0 < N) + (hf : AnnularFourierSupport f c₀ C₀ N) (t₀ : ℝ) : + ∀ᵐ η : Plane ∂volume, + η ∉ {η | c₀ ≤ ‖η‖ ∧ ‖η‖ ≤ C₀} → unitFrequencyInput f N t₀ η = 0 := by + have hh := (Measure.quasiMeasurePreserving_smul volume hN.ne').ae hf + filter_upwards [hh] with η hη hn + have hz : fourier f (N • η) = 0 := by + apply hη + intro hp + simp only [norm_smul,Real.norm_eq_abs,abs_of_pos hN] at hp + apply hn + exact ⟨(mul_le_mul_iff_right₀ hN).mp (by simpa [mul_comm] using hp.1), + (mul_le_mul_iff_left₀ hN).mp (by simpa [mul_comm] using hp.2)⟩ + simp [unitFrequencyInput,hz] + +lemma unitFrequencyInput_norm (f : L2) {N : ℝ} (hN : 0 < N) (t₀ : ℝ) : + ‖(unitFrequencyInput_memLp f hN t₀).toLp (unitFrequencyInput f N t₀)‖ = + (2 * Real.pi) * ‖f‖ := by + let hv := unitFrequencyInput_memLp f hN t₀ + have he : ‖hv.toLp (unitFrequencyInput f N t₀)‖^2 = + ∫ η, ‖unitFrequencyInput f N t₀ η‖^2 := by + rw [← real_inner_self_eq_norm_sq] + simp only [L2.inner_def,real_inner_self_eq_norm_sq] + exact integral_congr_ae (hv.coeFn_toLp.fun_comp (fun z : ℂ => ‖z‖^2)) + simp_rw [norm_unitFrequencyInput f hN t₀,mul_pow] at he + rw [integral_const_mul, + Measure.integral_comp_smul_of_nonneg volume (fun ξ => ‖fourier f ξ‖^2) N (hR := hN.le)] at he + simp only [finrank_euclideanSpace,Fintype.card_fin,smul_eq_mul] at he + rw [← mul_assoc,mul_inv_cancel₀ (pow_ne_zero 2 hN.ne'),one_mul,fourier_energy] at he + have hp : 0 ≤ (2 * Real.pi) * ‖f‖ := by positivity + nlinarith [norm_nonneg (hv.toLp (unitFrequencyInput f N t₀))] + +lemma phase_unitFrequency_scaling (x η : Plane) {N : ℝ} (hN : 0 < N) (t t₀ : ℝ) : + phase (N • x) (N^2*(t-t₀)) η * phase 0 t₀ (N • η) = phase x t (N • η) := by + have he : (inner ℝ (N • x) η - N^2*(t-t₀)*‖η‖^2) + + (inner ℝ (0:Plane) (N • η) - t₀*‖N • η‖^2) = + inner ℝ x (N • η) - t*‖N • η‖^2 := by + simp only [inner_smul_left,inner_smul_right,inner_zero_left,Real.norm_eq_abs, + starRingEnd_apply,star_trivial,norm_smul,abs_of_pos hN] + ring + unfold phase + rw [← Complex.exp_add,← mul_add,← Complex.ofReal_add,he] + +lemma evolution_unitFrequency_scaling (f : L2) (x : Plane) {N : ℝ} + (hN : 0 < N) (t t₀ : ℝ) : + evolution f x t = ((((2*Real.pi)^2)⁻¹ * N : ℝ) : ℂ) * + frequencyExtension (unitFrequencyInput f N t₀) (N • x) (N^2*(t-t₀)) := by + have he : frequencyExtension (unitFrequencyInput f N t₀) (N • x) (N^2*(t-t₀)) = + (N : ℂ) * ∫ η, phase x t (N • η) * fourier f (N • η) := by + unfold frequencyExtension unitFrequencyInput + have hh (η : Plane) : phase (N • x) (N^2*(t-t₀)) η * + ((N:ℂ)*(phase 0 t₀ (N • η)*fourier f (N • η))) = + (N:ℂ)*(phase x t (N • η)*fourier f (N • η)) := by + rw [← phase_unitFrequency_scaling x η hN t t₀] + ring + simp_rw [hh] + exact integral_const_mul _ _ + rw [he] + unfold evolution + rw [integral_affineScale (fun ξ => phase x t ξ * fourier f ξ) 0 hN] + simp only [affineScale,zero_add,Complex.real_smul,Complex.ofReal_mul,Complex.ofReal_pow] + ring + +lemma norm_evolution_unitFrequency_scaling (f : L2) (x : Plane) {N : ℝ} + (hN : 0 < N) (t t₀ : ℝ) : + ‖evolution f x t‖ = ((2*Real.pi)^2)⁻¹ * N * + ‖frequencyExtension (unitFrequencyInput f N t₀) (N • x) (N^2*(t-t₀))‖ := by + rw [evolution_unitFrequency_scaling f x hN t t₀,norm_mul,Complex.norm_real, + Real.norm_eq_abs,abs_of_pos (by positivity : 0 < ((2*Real.pi)^2)⁻¹*N)] + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/WeakIntegration.lean b/lean/OAI/Analysis/PlanarEndpoint/WeakIntegration.lean new file mode 100644 index 0000000000000000000000000000000000000000..947574c7c0d0777c4ab6e46c0918e0017898ad5b --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/WeakIntegration.lean @@ -0,0 +1,133 @@ +import Mathlib + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped ENNReal NNReal Topology +namespace PlanarEndpoint + +lemma weak_lintegral_split {α : Type*} [MeasurableSpace α] + (μ : Measure α) [IsFiniteMeasure μ] {f : α → ℝ} + (hf : AEMeasurable f μ) (hn : 0 ≤ᵐ[μ] f) + {p A T : ℝ} (hp : 1 < p) (hA : 0 ≤ A) (hT : 0 < T) + (hw : ∀ t : ℝ, 0 < t → μ {x | t < f x} ≤ ENNReal.ofReal (A ^ p * t ^ (-p))) : + ∫⁻ x, ENNReal.ofReal (f x) ∂μ ≤ + ENNReal.ofReal ((μ univ).toReal * T + A ^ p * (T ^ (1-p) / (p-1))) := by + rw [lintegral_eq_lintegral_meas_lt μ hn hf] + have hs : Ioi (0 : ℝ) = Ioc 0 T ∪ Ioi T := by + ext t + simp only [mem_Ioi, mem_union, mem_Ioc] + constructor + · intro ht + by_cases h : t ≤ T + · exact Or.inl ⟨ht, h⟩ + · exact Or.inr (lt_of_not_ge h) + · rintro (⟨ht, _⟩ | ht) + · exact ht + · exact hT.trans ht + rw [hs, lintegral_union measurableSet_Ioi (Set.disjoint_left.mpr + (by intro x hx hy; exact (not_lt_of_ge hx.2) hy))] + have hlo : (∫⁻ t in Ioc (0 : ℝ) T, μ {x | t < f x}) ≤ + ENNReal.ofReal ((μ univ).toReal * T) := by + calc + _ ≤ ∫⁻ _ in Ioc (0 : ℝ) T, μ univ := lintegral_mono (fun _ => measure_mono (subset_univ _)) + _ = ENNReal.ofReal ((μ univ).toReal * T) := by + simp [Real.volume_Ioc, hT.le, ENNReal.ofReal_mul, mul_comm] + have hi : IntegrableOn (fun t : ℝ => A ^ p * t ^ (-p)) (Ioi T) volume := + (integrableOn_Ioi_rpow_of_lt (by linarith : -p < -1) hT).const_mul _ + have htail : (∫⁻ t in Ioi T, μ {x | t < f x}) ≤ + ENNReal.ofReal (A ^ p * (T ^ (1-p) / (p-1))) := by + calc + _ ≤ ∫⁻ t in Ioi T, ENNReal.ofReal (A ^ p * t ^ (-p)) := by + apply lintegral_mono_ae + filter_upwards [self_mem_ae_restrict measurableSet_Ioi] with t ht + exact hw t (hT.trans ht) + _ = ENNReal.ofReal (∫ t in Ioi T, A ^ p * t ^ (-p)) := + (ofReal_integral_eq_lintegral_ofReal hi (by + filter_upwards [self_mem_ae_restrict measurableSet_Ioi] with t ht + exact mul_nonneg (Real.rpow_nonneg hA _) (Real.rpow_nonneg (hT.trans ht).le _))).symm + _ = ENNReal.ofReal (A ^ p * (T ^ (1-p) / (p-1))) := by + rw [integral_const_mul, integral_Ioi_rpow_of_lt (by linarith : -p < -1) hT] + congr 2 + rw [show -p + 1 = 1-p by ring] + have h1 : 1-p ≠ 0 := by linarith + have h2 : p-1 ≠ 0 := by linarith + field_simp [h1, h2] + ring + exact (add_le_add hlo htail).trans_eq (by + rw [← ENNReal.ofReal_add (mul_nonneg ENNReal.toReal_nonneg hT.le) + (mul_nonneg (Real.rpow_nonneg hA _) + (div_nonneg (Real.rpow_nonneg hT.le _) (by linarith)))]) + +lemma weak_split_threshold {p A m : ℝ} (hp : 1 < p) (hA : 0 < A) + (hm : 0 < m) : + m * (A * m ^ (-p⁻¹)) + A ^ p * ((A * m ^ (-p⁻¹)) ^ (1-p) / (p-1)) = + p / (p-1) * A * m ^ (1-1/p) := by + have hp0 : p ≠ 0 := ne_of_gt (lt_trans zero_lt_one hp) + have hp1 : p-1 ≠ 0 := sub_ne_zero.mpr (ne_of_gt hp) + have he : (-p⁻¹) * (1-p) = 1 - 1/p := by field_simp; ring + have hpow : A ^ p * (A * m ^ (-p⁻¹)) ^ (1-p) = A * m ^ (1-1/p) := by + rw [Real.mul_rpow hA.le (Real.rpow_nonneg hm.le _), ← Real.rpow_mul hm.le, + he, ← mul_assoc, ← Real.rpow_add hA, show p+(1-p) = 1 by ring, Real.rpow_one] + have hlin : m * (A * m ^ (-p⁻¹)) = A * m ^ (1-1/p) := by + calc + _ = A * (m ^ (1 : ℝ) * m ^ (-p⁻¹)) := by rw [Real.rpow_one]; ring + _ = _ := by rw [← Real.rpow_add hm]; congr 2; simp [sub_eq_add_neg] + rw [hlin, ← mul_div_assoc, hpow] + field_simp + ring + +lemma weak_lintegral_bound {α : Type*} [MeasurableSpace α] + (μ : Measure α) [IsFiniteMeasure μ] {f : α → ℝ} + (hf : AEMeasurable f μ) (hn : 0 ≤ᵐ[μ] f) + {p A : ℝ} (hp : 1 < p) (hA : 0 ≤ A) + (hw : ∀ t : ℝ, 0 < t → μ {x | t < f x} ≤ ENNReal.ofReal ((A / t) ^ p)) : + ∫⁻ x, ENNReal.ofReal (f x) ∂μ ≤ + ENNReal.ofReal (p/(p-1) * A * (μ univ).toReal ^ (1-1/p)) := by + by_cases hm : μ univ = 0 + · have hμ : μ = 0 := Measure.measure_univ_eq_zero.mp hm + simp [hμ] + have hmpos : 0 < (μ univ).toReal := ENNReal.toReal_pos hm (measure_ne_top _ _) + by_cases hAz : A = 0 + · subst A + rw [lintegral_eq_lintegral_meas_lt μ hn hf] + have hh : (fun t : ℝ => μ {x | t < f x}) =ᵐ[volume.restrict (Ioi 0)] 0 := by + filter_upwards [self_mem_ae_restrict measurableSet_Ioi] with t ht + have h := hw t ht + simpa [Real.zero_rpow (ne_of_gt (lt_trans zero_lt_one hp))] using h + simp [lintegral_congr_ae hh] + have hApos := lt_of_le_of_ne hA (Ne.symm hAz) + have hwp (t : ℝ) (ht : 0 < t) : + μ {x | t < f x} ≤ ENNReal.ofReal (A ^ p * t ^ (-p)) := by + convert hw t ht using 2 + rw [Real.div_rpow hA ht.le, Real.rpow_neg ht.le, div_eq_mul_inv] + have hbound := weak_lintegral_split μ hf hn hp hA + (T := A * (μ univ).toReal ^ (-p⁻¹)) + (mul_pos hApos (Real.rpow_pos_of_pos hmpos _)) hwp + simpa only [weak_split_threshold hp hApos hmpos] using hbound + +lemma weak_integral_norm_bound {α E : Type*} [MeasurableSpace α] + [NormedAddCommGroup E] (μ : Measure α) [IsFiniteMeasure μ] + {f : α → E} (hf : AEStronglyMeasurable f μ) + {p A : ℝ} (hp : 1 < p) (hA : 0 ≤ A) + (hw : ∀ t : ℝ, 0 < t → μ {x | t < ‖f x‖} ≤ ENNReal.ofReal ((A / t) ^ p)) : + Integrable f μ ∧ ∫ x, ‖f x‖ ∂μ ≤ p/(p-1) * A * (μ univ).toReal ^ (1-1/p) := by + have hl := weak_lintegral_bound μ hf.norm.aemeasurable + (Filter.Eventually.of_forall (fun x => norm_nonneg (f x))) hp hA hw + have hi : Integrable f μ := ⟨hf, (hasFiniteIntegral_iff_norm f).2 + (hl.trans_lt ENNReal.ofReal_lt_top)⟩ + refine ⟨hi, ?_⟩ + rw [← ofReal_integral_eq_lintegral_ofReal hi.norm + (Filter.Eventually.of_forall (fun x => norm_nonneg (f x)))] at hl + apply (ENNReal.ofReal_le_ofReal_iff _).1 hl + exact mul_nonneg (mul_nonneg (div_nonneg (by linarith) (by linarith)) hA) + (Real.rpow_nonneg ENNReal.toReal_nonneg _) + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarEndpoint/WeightedGraph.lean b/lean/OAI/Analysis/PlanarEndpoint/WeightedGraph.lean new file mode 100644 index 0000000000000000000000000000000000000000..776ce9f57db9bc29d1580c011169c132d3a769ed --- /dev/null +++ b/lean/OAI/Analysis/PlanarEndpoint/WeightedGraph.lean @@ -0,0 +1,179 @@ +import OAI.Analysis.PlanarEndpoint.AnnularCutoff +import OAI.Analysis.PlanarEndpoint.DyadicGraph +import OAI.Analysis.PlanarEndpoint.Fourier +import OAI.Analysis.PlanarEndpoint.GraphDual +import OAI.Analysis.PlanarEndpoint.GraphLocalization +import OAI.Analysis.PlanarEndpoint.GraphTree +import OAI.Analysis.PlanarEndpoint.TimeSeparation + +namespace OAI + +/-! Gaussian regularization, Fourier evolution and endpoint maximal estimates. -/ + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology ContDiff BigOperators +namespace PlanarEndpoint + +lemma annularCutoff_scaled_memLp (j : ℕ) : + MemLp (fun ξ => annularCutoff (((2:ℝ)^j)⁻¹ • ξ)) 2 volume := + scaled_cutoff_memLp annularCutoff annularCutoff_smooth.continuous + annularCutoff_compact (pow_pos (by norm_num : (0:ℝ)<2) j) + +def normalizedGraphDensity (j : ℕ) (μ : Measure Plane) + (T : Plane → ℝ) (w : Plane → ℂ) (ξ : Plane) : ℂ := + (((2:ℝ)^j)^(-(1/3:ℝ))) • + graphDual (fun η => annularCutoff (((2:ℝ)^j)⁻¹ • η)) μ T w ξ + +lemma normalizedGraphDensity_memLp (j : ℕ) (μ : Measure Plane) [IsFiniteMeasure μ] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) : MemLp (normalizedGraphDensity j μ T w) 2 volume := + by + exact (graphDual_memLp _ (annularCutoff_scaled_memLp j) μ hT hw hb).const_smul + (((2:ℝ)^j)^(-(1/3:ℝ))) + +lemma integral_sq_norm_toLp {X : Type*} [MeasurableSpace X] {μ : Measure X} + {v : X → ℂ} (hv : MemLp v 2 μ) : (∫ x, ‖v x‖^2 ∂μ) = ‖hv.toLp v‖^2 := by + rw [← real_inner_self_eq_norm_sq, L2.inner_def] + apply integral_congr_ae + filter_upwards [hv.coeFn_toLp] with x hx + simp only [hx, real_inner_self_eq_norm_sq] + +lemma normalizedGraphDensity_energy (j : ℕ) (μ : Measure Plane) [IsFiniteMeasure μ] + {T : Plane → ℝ} {w : Plane → ℂ} (hT : Measurable T) (hw : Measurable w) + (hb : ∀ x, ‖w x‖ ≤ 1) (ht : ∀ᵐ x ∂μ, T x ∈ Ico 0 1) : + (∫ ξ, ‖normalizedGraphDensity j μ T w ξ‖^2) = + ‖normalizedDyadicVector annularCutoff annularCutoff_smooth annularCutoff_compact + j μ T w hT hw hb []‖^2 := by + have hμ : μ.restrict (DyadicGraph.fiber T []) = μ := + Measure.restrict_eq_self_of_ae_mem (by simpa [DyadicGraph.fiber] using ht) + dsimp only [normalizedDyadicVector, DyadicGraph.vector] + rw [graphLp_congr_measure _ _ hμ T w hT hw hb] + simp only [normalizedGraphDensity, norm_smul, mul_pow, integral_const_mul] + congr 1 + exact integral_sq_norm_toLp (graphDual_memLp _ (annularCutoff_scaled_memLp j) μ hT hw hb) + +lemma sobolevWeight_inv_le_dyadic (j : ℕ) {ξ : Plane} (hξ : (2:ℝ)^j ≤ ‖ξ‖) : + (sobolevWeight ξ)⁻¹ ≤ (((2:ℝ)^j)^(-(1/3:ℝ)))^2 := by + have hN : 0 < (2:ℝ)^j := by positivity + rw [sobolevWeight, ← Real.rpow_neg (by positivity), ← Real.rpow_mul_natCast hN.le] + have hh := Real.rpow_le_rpow_of_nonpos (sq_pos_of_pos hN) + (show ((2:ℝ)^j)^2 ≤ 1+‖ξ‖^2 by nlinarith [norm_nonneg ξ]) + (by norm_num : -(1/3:ℝ) ≤ 0) + rw [← Real.rpow_natCast_mul hN.le] at hh + convert hh using 1 + congr 1 + norm_num + +lemma unit_ball_real (x : Plane) : volume.real (Metric.ball x 1) = Real.pi := by + simp [measureReal_def, EuclideanSpace.volume_ball_fin_two, ENNReal.toReal_ofReal Real.pi_nonneg] + +lemma graphFourier_unit_bound (x₀ : Plane) {T : Plane → ℝ} {w : Plane → ℂ} + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1) (ξ : Plane) : + ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖ ≤ Real.pi := by + exact (norm_graphFourier_le _ hT hw hb ξ).trans_eq (by + simp only [measureReal_def, Measure.restrict_apply_univ] + exact unit_ball_real x₀) + +def graphLowMajorant : Plane → ℝ := + (Metric.ball (0 : Plane) 1).indicator (fun _ => Real.pi^2) + +lemma graphLowMajorant_nonneg (ξ : Plane) : 0 ≤ graphLowMajorant ξ := by + exact Set.indicator_nonneg (fun _ _ => sq_nonneg _) ξ + +lemma graphLowMajorant_integrable : Integrable graphLowMajorant volume := by + exact IntegrableOn.integrable_indicator + (integrable_const (Real.pi^2) (μ := volume.restrict (Metric.ball (0:Plane) 1))) measurableSet_ball + +lemma graphLowMajorant_integral : (∫ ξ, graphLowMajorant ξ) = Real.pi^3 := by + rw [graphLowMajorant, integral_indicator measurableSet_ball, integral_const] + simp only [smul_eq_mul, measureReal_def, Measure.restrict_apply_univ] + change volume.real (Metric.ball (0:Plane) 1)*Real.pi^2=Real.pi^3 + rw [unit_ball_real] + ring + +lemma graph_weighted_pointwise (x₀ : Plane) {T : Plane → ℝ} {w : Plane → ℂ} + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1) + (n : ℕ) (ξ : Plane) (hξ : ‖ξ‖ < (2:ℝ)^n) : + (sobolevWeight ξ)⁻¹*‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2 ≤ + graphLowMajorant ξ + ∑ j ∈ Finset.range n, + ‖normalizedGraphDensity j (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2 := by + have hnonneg : 0 ≤ ∑ j ∈ Finset.range n, + ‖normalizedGraphDensity j (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2 := + Finset.sum_nonneg (fun _ _ => sq_nonneg _) + by_cases hsmall : ‖ξ‖ < 1 + · have hlow : graphLowMajorant ξ = Real.pi^2 := by + rw [graphLowMajorant, indicator_of_mem (by simpa using hsmall)] + rw [hlow] + have hi : (sobolevWeight ξ)⁻¹ ≤ 1 := inv_le_one_of_one_le₀ (sobolevWeight_one_le ξ) + have hg := graphFourier_unit_bound x₀ hT hw hb ξ + have hsq : ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2 ≤ Real.pi^2 := + (sq_le_sq₀ (norm_nonneg _) Real.pi_nonneg).2 hg + nlinarith [mul_le_mul_of_nonneg_right hi (sq_nonneg + ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖)] + · obtain ⟨j,hj,hj0,hj1⟩ := dyadic_annular_cover (le_of_not_gt hsmall) n hξ + have hc := scaled_annularCutoff_one j ⟨hj0,hj1.le⟩ + have he : ‖normalizedGraphDensity j (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2 = + (((2:ℝ)^j)^(-(1/3:ℝ)))^2 * + ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2 := by + simp only [normalizedGraphDensity, graphDual, hc, one_mul, norm_smul, Real.norm_eq_abs, + sq_abs, mul_pow] + have hh := mul_le_mul_of_nonneg_right (sobolevWeight_inv_le_dyadic j hj0) + (sq_nonneg ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖) + rw [← he] at hh + have hs := Finset.single_le_sum (fun j (_ : j ∈ Finset.range n) => + sq_nonneg ‖normalizedGraphDensity j (volume.restrict (Metric.ball x₀ 1)) T w ξ‖) + (Finset.mem_range.mpr hj) + exact hh.trans (hs.trans (le_add_of_nonneg_left (graphLowMajorant_nonneg ξ))) + +lemma graph_weighted_integrableOn (x₀ : Plane) {T : Plane → ℝ} {w : Plane → ℂ} + (hT : Measurable T) (hw : Measurable w) (hb : ∀ x, ‖w x‖ ≤ 1) (R : ℝ) : + IntegrableOn (fun ξ => (sobolevWeight ξ)⁻¹ * + ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2) + (Metric.ball (0:Plane) R) volume := by + have hc : Continuous (fun ξ => (sobolevWeight ξ)⁻¹ * + ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2) := + (continuous_sobolevWeight.inv₀ (fun ξ => (sobolevWeight_pos ξ).ne')).mul + ((continuous_graphFourier _ hT hw hb).norm.pow 2) + exact (hc.locallyIntegrable.integrableOn_isCompact (isCompact_closedBall (0:Plane) R)).mono_set + Metric.ball_subset_closedBall + +lemma graph_weighted_sum_bound {p : ℝ} (hp : 2 < p) + (hshort : ShortTimeWeakEstimate (1/4) 4 p) : + ∃ C : ℝ, 0 < C ∧ ∀ (x₀ : Plane) (T : Plane → ℝ) (w : Plane → ℂ) + (_ : Measurable T) (_ : Measurable w) (_ : ∀ x, ‖w x‖ ≤ 1), + (∀ x ∈ Metric.ball x₀ 1, T x ∈ Ico 0 1) → ∀ n : ℕ, + (∫ ξ in Metric.ball (0:Plane) ((2:ℝ)^n), (sobolevWeight ξ)⁻¹ * + ‖graphFourier (volume.restrict (Metric.ball x₀ 1)) T w ξ‖^2) ≤ C := by + obtain ⟨C,hC,hbnd⟩ := graph_square_sum_of_shortTime hp hshort + refine ⟨Real.pi^3+C,by positivity,?_⟩ + intro x₀ T w hT hw hb ht n + let μ := volume.restrict (Metric.ball x₀ 1) + have hti : ∀ᵐ x ∂μ, T x ∈ Ico 0 1 := by + filter_upwards [ae_restrict_mem measurableSet_ball] with x hx + exact ht x hx + have hsq (j : ℕ) : Integrable (fun ξ => ‖normalizedGraphDensity j μ T w ξ‖^2) volume := + (memLp_two_iff_integrable_sq_norm (normalizedGraphDensity_memLp j μ hT hw hb).aestronglyMeasurable).1 + (normalizedGraphDensity_memLp j μ hT hw hb) + have hmajor := graphLowMajorant_integrable.add (integrable_finsetSum (Finset.range n) (fun j _ => hsq j)) + rw [← integral_indicator measurableSet_ball] + have hle := integral_mono ((graph_weighted_integrableOn x₀ hT hw hb _).integrable_indicator + measurableSet_ball) hmajor (show ∀ ξ, _ ≤ _ from fun ξ => by + by_cases hξ : ξ ∈ Metric.ball (0:Plane) ((2:ℝ)^n) + · rw [indicator_of_mem hξ] + exact graph_weighted_pointwise x₀ hT hw hb n ξ (by simpa using hξ) + · rw [indicator_of_notMem hξ] + exact add_nonneg (graphLowMajorant_nonneg ξ) (Finset.sum_nonneg (fun _ _ => sq_nonneg _))) + apply hle.trans + change (∫ ξ, graphLowMajorant ξ + ∑ j ∈ Finset.range n, + ‖normalizedGraphDensity j μ T w ξ‖^2) ≤ Real.pi^3+C + rw [integral_add graphLowMajorant_integrable (integrable_finsetSum (Finset.range n) (fun j _ => hsq j)), + graphLowMajorant_integral, integral_finsetSum _ (fun j _ => hsq j)] + simp_rw [normalizedGraphDensity_energy _ μ hT hw hb hti] + exact add_le_add_right (hbnd x₀ T w hT hw hb ht n) _ + +end PlanarEndpoint +end + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/AtomTail.lean b/lean/OAI/Analysis/PlanarPacking/AtomTail.lean new file mode 100644 index 0000000000000000000000000000000000000000..8aa4c2e916fbb440792c0f4b34e1e327bf713711 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/AtomTail.lean @@ -0,0 +1,106 @@ +import OAI.Analysis.PlanarPacking.CanonicalRows + +namespace OAI + +namespace SharpPlanar +open IntegerBasis +noncomputable def atomBase : Fin 7 → ℝ := ![1/10000,469/1000000,7279/1000000,59165/1000000,219974/1000000,494744/1000000,828986/1000000] +lemma atomBase_pos (j : Fin 7) : 0 norm_num [atomBase] +lemma atomBase_lt_one (j : Fin 7) : atomBase j<1 := by fin_cases j <;> norm_num [atomBase] +lemma atomBase_contains (j : Fin 7) : Real.exp (-(314159/100000:ℝ)*dampingCap j) ≤ atomBase j := by + have hp := Real.sum_le_exp_of_nonneg (mul_nonneg (by norm_num : (0:ℝ)≤314159/100000) (dampingCap_pos j).le) 30 + rw [neg_mul,Real.exp_neg] + apply (inv_le_iff_one_le_mul₀ (Real.exp_pos _)).mpr + have ht : 1 ≤ atomBase j*(∑ i ∈ Finset.range 30,((314159/100000:ℝ)*dampingCap j)^i/(i.factorial:ℝ)) := by + fin_cases j <;> norm_num [atomBase,dampingCap,Finset.sum_range_succ] + exact ht.trans (mul_le_mul_of_nonneg_left hp (atomBase_pos j).le) +lemma decay_atomBase (j : Fin 7) (n : ℕ) : + Real.exp (-Real.pi*dampingCap j*n) ≤ atomBase j^n := by + have he : Real.exp (-Real.pi*dampingCap j)≤atomBase j := + (Real.exp_le_exp.mpr (by nlinarith [pi_fine,dampingCap_pos j])).trans (atomBase_contains j) + rw [mul_comm _ (n:ℝ),Real.exp_nat_mul] + exact pow_le_pow_left₀ (Real.exp_pos _).le he n +noncomputable def atomRowFactor (j : Fin 7) (n : ℕ) : ℝ := (1+|D n|+Real.pi*zCap j)/Q n +noncomputable def atomRow (j : Fin 7) (n : ℕ) : ℝ := + if n%12∈residues then atomRowFactor j n*atomL j n else 0 +noncomputable def atomRowTable (N : ℕ) : ℝ := + ∑ j : Fin 7, (∑ a : Fin 12, atomRow j (N+1+a.val))/(1-Real.exp (-12*Real.pi*dampingCap j)) +lemma atomRowFactor_nonneg (j : Fin 7) (n : ℕ) : 0≤atomRowFactor j n := by + unfold atomRowFactor + have hz := zCap_nonneg j + exact div_nonneg (by positivity) (Q_pos n).le +lemma atomRow_nonneg (j : Fin 7) (n : ℕ) : 0≤atomRow j n := by + unfold atomRow; split_ifs + · exact mul_nonneg (atomRowFactor_nonneg _ _) (atomL_nonneg _ _) + · rfl +lemma atomRow_period (j : Fin 7) (n k : ℕ) : + atomRow j (n+12*k)=(Real.exp (-12*Real.pi*dampingCap j))^k*atomRow j n := by + have hmod : (n+12*k)%12=n%12 := by omega + have hfac : atomRowFactor j (n+12*k)=atomRowFactor j n := by simp [atomRowFactor,Q,D,hmod] + unfold atomRow + rw [hmod] + split_ifs + · rw [hfac] + simp only [Nat.cast_add,Nat.cast_mul,Nat.cast_ofNat] + rw [atomL_shift] + have he : Real.exp (-Real.pi*dampingCap j*(12*(k:ℝ)))=(Real.exp (-12*Real.pi*dampingCap j))^k := by + rw [← Real.exp_nat_mul]; congr 1; ring + rw [he]; ring + · simp +lemma atomRow_tail_sum (j : Fin 7) (N : ℕ) : + Summable (fun n : ℕ => atomRow j (N+1+n)) ∧ + (∑' n : ℕ, atomRow j (N+1+n)) ≤ + (∑ a : Fin 12,atomRow j (N+1+a.val))/(1-Real.exp (-12*Real.pi*dampingCap j)) := by + apply periodic_geometric_sum (fun _ => atomRow_nonneg j _) (Real.exp_pos _).le + · apply Real.exp_lt_one_iff.mpr + nlinarith [Real.pi_pos,dampingCap_pos j,mul_pos Real.pi_pos (dampingCap_pos j)] + · intro a k + convert (atomRow_period j (N+1+a.val) k).le using 1; congr 1; omega +noncomputable def atomFactorRat (j : Fin 7) (n : ℕ) : ℝ := (1+rowDUpper n+(31416/10000:ℝ)*zCap j)/rowQLower n +noncomputable def atomRowRat (j : Fin 7) (n : ℕ) : ℝ := + if n%12∈residues then atomFactorRat j n*(atomMass j*lambdaCap j*atomBase j^n) else 0 +noncomputable def atomTableRat (N : ℕ) : ℝ := ∑ j : Fin 7,(∑ a : Fin 12,atomRowRat j (N+1+a.val))/(1-atomBase j^12) +lemma atomFactorRat_nonneg (j : Fin 7) (n : ℕ) : 0≤atomFactorRat j n := by + have hq : 0≤rowQLower n := by unfold rowQLower; split_ifs <;> norm_num + have hd : 0≤rowDUpper n := by unfold rowDUpper; split_ifs <;> norm_num + have hz := zCap_nonneg j + unfold atomFactorRat + positivity +lemma atomRowFactor_le (j : Fin 7) (n : ℕ) (hn : n%12∈residues) : atomRowFactor j n≤atomFactorRat j n := by + unfold atomRowFactor atomFactorRat + have hq := rowQLower_bound n hn + have hd := rowDUpper_bound n hn + have hz := zCap_nonneg j + have hd0 := (abs_nonneg (D n)).trans hd.le + apply div_le_div₀ (by positivity) + · exact add_le_add (add_le_add le_rfl hd.le) (mul_le_mul_of_nonneg_right pi_fine.2.le hz) + · exact hq.1 + · exact hq.2.le +lemma atomRow_le (j : Fin 7) (n : ℕ) : atomRow j n≤atomRowRat j n := by + unfold atomRow atomRowRat + split_ifs with hn + · apply mul_le_mul (atomRowFactor_le j n hn) + · exact mul_le_mul_of_nonneg_left (decay_atomBase j n) (by fin_cases j <;> norm_num [atomMass,lambdaCap]) + · exact atomL_nonneg j n + · exact atomFactorRat_nonneg j n + · rfl +lemma atomRowTable_le (N : ℕ) : atomRowTable N≤atomTableRat N := by + unfold atomRowTable atomTableRat + apply Finset.sum_le_sum + intro j _ + have hd : 0<1-atomBase j^12 := sub_pos.mpr (pow_lt_one₀ (atomBase_pos j).le (atomBase_lt_one j) (by norm_num)) + apply div_le_div₀ + · exact Finset.sum_nonneg (fun a _ => (atomRow_nonneg j _).trans (atomRow_le j _)) + · exact Finset.sum_le_sum (fun a _ => atomRow_le j _) + · exact hd + · have he := decay_atomBase j 12 + have heq : Real.exp (-Real.pi*dampingCap j*(12:ℕ))=Real.exp (-12*Real.pi*dampingCap j) := by congr 1; push_cast; ring + rw [heq] at he + exact sub_le_sub_left he 1 +lemma atomTableRat_hundred : atomTableRat 100<(32:ℝ)/10^9 := by + norm_num [atomTableRat,atomRowRat,atomFactorRat,atomBase,atomMass,rowDUpper,rowQLower,lambdaCap,zCap,residues,Fin.sum_univ_succ] +lemma atomRowTable_hundred : atomRowTable 100<(32:ℝ)/10^9 := + (atomRowTable_le 100).trans_lt atomTableRat_hundred +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Barrier.lean b/lean/OAI/Analysis/PlanarPacking/Barrier.lean new file mode 100644 index 0000000000000000000000000000000000000000..76b4a0838d5562c325d025090474623f346bda99 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Barrier.lean @@ -0,0 +1,90 @@ +import OAI.Analysis.PlanarPacking.BarrierEndpoints + +namespace OAI + +namespace SharpPlanar +open Set +lemma dividedP_lower (a : ℕ) (ha : a ∈ residues) {u : ℝ} + (hu : u ∈ Icc (-leftHalf a) (rightHalf a)) : (17/25:ℝ) ≤ dividedP a u := by + have hpos := half_pos a ha + have hend := barrier_endpoints a ha + have hcenter : (17/25:ℝ) ≤ dividedP a 0 := by + rw [dividedP_zero a (residue_lt ha)] + have hh := Q_lower a (by simpa only [Nat.mod_eq_of_lt (residue_lt ha)] using ha) + linarith + by_cases hu0 : u ≤ 0 + · have hab : -leftHalf a ≤ (0:ℝ) := by linarith + have hsub : Icc (-leftHalf a) 0 ⊆ Icc (-leftHalf a) (rightHalf a) := by + intro v hv + exact ⟨hv.1, le_trans hv.2 hpos.2.le⟩ + have hc := dividedP_log_concave a ha (convex_Icc _ _) hsub (by simp [interior_Icc]) + apply lower_of_log_concave (v := -leftHalf a) (w := 0) (by norm_num) + · simpa only [uIcc_of_le hab] using fun v hv => dividedP_pos a ha (hsub hv) + · simpa only [uIcc_of_le hab] using hc + · exact hend.1 + · exact hcenter + · simpa only [uIcc_of_le hab] using show u ∈ Icc (-leftHalf a) 0 from ⟨hu.1,hu0⟩ + · have hab : (0:ℝ) ≤ rightHalf a := hpos.2.le + have hsub : Icc 0 (rightHalf a) ⊆ Icc (-leftHalf a) (rightHalf a) := by + intro v hv + exact ⟨le_trans (by linarith) hv.1,hv.2⟩ + have hc := dividedP_log_concave a ha (convex_Icc _ _) hsub (by simp [interior_Icc]) + apply lower_of_log_concave (v := 0) (w := rightHalf a) (by norm_num) + · simpa only [uIcc_of_le hab] using fun v hv => dividedP_pos a ha (hsub hv) + · simpa only [uIcc_of_le hab] using hc + · exact hcenter + · exact hend.2 + · simpa only [uIcc_of_le hab] using show u ∈ Icc 0 (rightHalf a) from ⟨by linarith,hu.2⟩ + + +def zeroGrid (m : ℝ) : Prop := ∃ k : ℤ, ∃ a ∈ residues, m=12*(k:ℝ)+(a:ℝ) +lemma zeroGrid_shift {m : ℝ} (hm : zeroGrid m) (j : ℤ) : zeroGrid (12*(j:ℝ)+m) := by + rcases hm with ⟨k,a,ha,rfl⟩ + refine ⟨j+k,a,ha,?_⟩ + push_cast + ring +lemma neighboring_zeros (a : ℕ) (ha : a ∈ residues) : + zeroGrid ((a:ℝ)-2*leftHalf a) ∧ zeroGrid ((a:ℝ)+2*rightHalf a) := by + simp only [residues,Finset.mem_insert,Finset.mem_singleton] at ha + rcases ha with rfl|rfl|rfl|rfl|rfl|rfl + · constructor + · exact ⟨-1,9,by decide,by norm_num [leftHalf]⟩ + · exact ⟨0,1,by decide,by norm_num [rightHalf]⟩ + · constructor + · exact ⟨0,0,by decide,by norm_num [leftHalf]⟩ + · exact ⟨0,3,by decide,by norm_num [rightHalf]⟩ + · constructor + · exact ⟨0,1,by decide,by norm_num [leftHalf]⟩ + · exact ⟨0,4,by decide,by norm_num [rightHalf]⟩ + · constructor + · exact ⟨0,3,by decide,by norm_num [leftHalf]⟩ + · exact ⟨0,7,by decide,by norm_num [rightHalf]⟩ + · constructor + · exact ⟨0,4,by decide,by norm_num [leftHalf]⟩ + · exact ⟨0,9,by decide,by norm_num [rightHalf]⟩ + · constructor + · exact ⟨0,7,by decide,by norm_num [leftHalf]⟩ + · exact ⟨1,0,by decide,by norm_num [rightHalf]⟩ + + +theorem P_nearest_lower (s m : ℝ) (hm : zeroGrid m) + (hnear : ∀ n : ℝ, zeroGrid n → |s-m| ≤ |s-n|) : (17/25:ℝ)*(s-m)^2 ≤ P s := by + rcases hm with ⟨k,a,ha,rfl⟩ + have hl := hnear _ (zeroGrid_shift (neighboring_zeros a ha).1 k) + have hr := hnear _ (zeroGrid_shift (neighboring_zeros a ha).2 k) + have hls := sq_le_sq.mpr hl + have hrs := sq_le_sq.mpr hr + have hp := half_pos a ha + have hu : s-(12*(k:ℝ)+a) ∈ Icc (-leftHalf a) (rightHalf a) := by + constructor <;> nlinarith + have hv := dividedP_lower a ha hu + have hf := dividedP_factor a ha (s-(12*(k:ℝ)+a)) + have hperiod : P (a+(s-(12*(k:ℝ)+a)))=P s := by + convert (show Function.Periodic P (12:ℝ) from P_period).sub_int_mul_eq k (x := s) using 1 + congr 1 + ring + rw [hperiod] at hf + nlinarith [mul_nonneg (sq_nonneg (s-(12*(k:ℝ)+a))) (sub_nonneg.mpr hv)] +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/BarrierEndpoints.lean b/lean/OAI/Analysis/PlanarPacking/BarrierEndpoints.lean new file mode 100644 index 0000000000000000000000000000000000000000..a0f63f9d3cd6c810e8ff9ad1df56ddc2c949befa --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/BarrierEndpoints.lean @@ -0,0 +1,76 @@ +import OAI.Analysis.PlanarPacking.Entire +import OAI.Analysis.PlanarPacking.BarrierProduct + +namespace OAI + +namespace SharpPlanar +open Set +lemma P_period (s : ℝ) : P (s+12) = P s := by + simp only [P_cos_factor, show Real.pi*(s+12-2)/6 = Real.pi*(s-2)/6 + 2*Real.pi by ring, + Real.cos_add_two_pi] +lemma P_reflect (s : ℝ) : P (4-s) = P s := by + simp only [P_cos_factor, show Real.pi*(4-s-2)/6 = -(Real.pi*(s-2)/6) by ring, + Real.cos_neg] +lemma P_half : P (1/2) = 3-2*Real.sqrt 2 := by + rw [P_cos_factor,show Real.pi*((1/2:ℝ)-2)/6 = -(Real.pi/4) by ring, + Real.cos_neg,Real.cos_pi_div_four] + have hh := Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2) + have he : 4*(Real.sqrt 2/2)^2-3 = (-1:ℝ) := by nlinarith + rw [he] + nlinarith +lemma P_two : P 2 = 1 := by norm_num [P_cos_factor] +lemma P_eight : P 8 = 9 := by + rw [P_cos_factor,show Real.pi*((8:ℝ)-2)/6 = Real.pi by ring,Real.cos_pi] + norm_num +lemma P_short_lower : (17/100:ℝ) < P (1/2) := by + rw [P_half] + have hh := Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2) + have hp := Real.sqrt_nonneg (2:ℝ) + have hb : Real.sqrt 2 < 283/200 := by nlinarith + linarith +lemma P_long_lower : (4:ℝ) ≤ P (11/2) := by + rw [P_cos_factor] + have ha : Real.pi*((11/2:ℝ)-2)/6 = 7*Real.pi/12 := by ring + rw [ha] + have hc1 : Real.cos (7*Real.pi/12) ≤ 0 := by + have hh := Real.cos_le_cos_of_nonneg_of_le_pi (by positivity : 0 ≤ Real.pi/2) + (by linarith [Real.pi_pos] : 7*Real.pi/12 ≤ Real.pi) + (by linarith [Real.pi_pos] : Real.pi/2 ≤ 7*Real.pi/12) + simpa using hh + have hc2 : -(1/2:ℝ) ≤ Real.cos (7*Real.pi/12) := by + have hh := Real.cos_le_cos_of_nonneg_of_le_pi (by positivity : 0 ≤ 7*Real.pi/12) + (by linarith [Real.pi_pos] : 2*Real.pi/3 ≤ Real.pi) + (by linarith [Real.pi_pos] : 7*Real.pi/12 ≤ 2*Real.pi/3) + have he : Real.cos (2*Real.pi/3) = -(1/2:ℝ) := by + rw [show 2*Real.pi/3 = Real.pi-Real.pi/3 by ring,Real.cos_pi_sub,Real.cos_pi_div_three] + rwa [he] at hh + have hsq : Real.cos (7*Real.pi/12)^2 ≤ 1/4 := by nlinarith + have h1 : (4*Real.cos (7*Real.pi/12)^2-3)^2 ≥ 4 := by nlinarith [sq_nonneg (Real.cos (7*Real.pi/12))] + have h2 : (1-2*Real.cos (7*Real.pi/12))^2 ≥ 1 := by nlinarith + nlinarith [mul_nonneg (sub_nonneg.mpr h1) (sub_nonneg.mpr h2)] +lemma P_other_midpoints : P (7/2) = P (1/2) ∧ P (21/2) = P (11/2) ∧ P (-3/2) = P (11/2) := by + constructor + · convert P_reflect (1/2) using 1; congr 1; norm_num + constructor + · have hp := P_period (-(3/2)) + have hr := P_reflect (11/2) + norm_num at hp hr + exact hp.trans hr + · convert P_reflect (11/2) using 1; congr 1; norm_num + +lemma barrier_endpoints (a : ℕ) (ha : a ∈ residues) : + (17/25:ℝ) ≤ dividedP a (-leftHalf a) ∧ (17/25:ℝ) ≤ dividedP a (rightHalf a) := by + have hl := dividedP_factor a ha (-leftHalf a) + have hr := dividedP_factor a ha (rightHalf a) + have hs := P_short_lower + have ht := P_two + have he := P_eight + have hg := P_long_lower + have hm := P_other_midpoints + simp only [residues,Finset.mem_insert,Finset.mem_singleton] at ha + rcases ha with rfl|rfl|rfl|rfl|rfl|rfl <;> + norm_num [leftHalf,rightHalf] at hl hr ⊢ <;> + norm_num at hm <;> constructor <;> nlinarith [hm.1,hm.2.1,hm.2.2] +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/BarrierProduct.lean b/lean/OAI/Analysis/PlanarPacking/BarrierProduct.lean new file mode 100644 index 0000000000000000000000000000000000000000..ae4643ed17a3d383385c30c2743cb05a21b83abc --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/BarrierProduct.lean @@ -0,0 +1,252 @@ +import OAI.Analysis.PlanarPacking.Cardinal +import Mathlib.Analysis.Convex.Deriv +import Mathlib.Analysis.SpecialFunctions.Log.Deriv +import Mathlib.Analysis.SpecialFunctions.Trigonometric.Deriv +import Mathlib.Analysis.SpecialFunctions.Trigonometric.Sinc + +namespace OAI + +namespace SharpPlanar +open Set Filter +open scoped Topology +open scoped BigOperators +lemma logSin_hasDeriv (a r x : ℝ) (hx : Real.sin (a*(x-r)) ≠ 0) : + HasDerivAt (fun u : ℝ => Real.log (Real.sin (a*(u-r)))) + (a*Real.cos (a*(x-r))/Real.sin (a*(x-r))) x := by + have hd := (((hasDerivAt_id x).sub_const r).const_mul a).sin.log hx + simpa only [id_eq, mul_one, mul_comm] using hd + +lemma cot_scaled_hasDeriv (a r x : ℝ) (hx : Real.sin (a*(x-r)) ≠ 0) : + HasDerivAt (fun u : ℝ => a*Real.cos (a*(u-r))/Real.sin (a*(u-r))) + (-a^2/(Real.sin (a*(x-r)))^2) x := by + have hp := ((hasDerivAt_id x).sub_const r).const_mul a + have hd := (hp.cos.const_mul a).div hp.sin hx + simp only [id_eq, mul_one] at hd + apply hd.congr_deriv + congr 1 + nlinarith [sq_nonneg a, Real.sin_sq_add_cos_sq (a*(x-r)), + congrArg (fun t : ℝ => a^2*t) (Real.sin_sq_add_cos_sq (a*(x-r)))] + +lemma logSin_concaveOn {D : Set ℝ} (hD : Convex ℝ D) (a r : ℝ) + (hs : ∀ x ∈ D, Real.sin (a*(x-r)) ≠ 0) : + ConcaveOn ℝ D (fun x : ℝ => Real.log (Real.sin (a*(x-r)))) := by + apply concaveOn_of_hasDerivWithinAt2_nonpos hD + (f' := fun x => a*Real.cos (a*(x-r))/Real.sin (a*(x-r))) + (f'' := fun x => -a^2/Real.sin (a*(x-r))^2) + · exact (by fun_prop : Continuous fun x : ℝ => Real.sin (a*(x-r))).continuousOn.log hs + · intro x hx + exact (logSin_hasDeriv a r x (hs _ (interior_subset hx))).hasDerivWithinAt + · intro x hx + exact (cot_scaled_hasDeriv a r x (hs _ (interior_subset hx))).hasDerivWithinAt + · intro x hx + exact div_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr (sq_nonneg _)) (sq_nonneg _) + +lemma sinc_ne_zero {a x : ℝ} (ha : a ≠ 0) + (hs : x ≠ 0 → Real.sin (a*x) ≠ 0) : Real.sinc (a*x) ≠ 0 := by + by_cases hx : x = 0 + · simp [hx] + · rw [Real.sinc_of_ne_zero (mul_ne_zero ha hx)] + exact div_ne_zero (hs hx) (mul_ne_zero ha hx) + +lemma logSinc_hasDeriv (a x : ℝ) (ha : a ≠ 0) (hx : x ≠ 0) + (hs : Real.sin (a*x) ≠ 0) : + HasDerivAt (fun u : ℝ => Real.log (Real.sinc (a*u))) + (a*Real.cos (a*x)/Real.sin (a*x) - 1/x) x := by + have hp := (hasDerivAt_id x).const_mul a + have hd := (hp.sin.div hp (mul_ne_zero ha hx)).log (div_ne_zero hs (mul_ne_zero ha hx)) + have he : (fun u : ℝ => Real.log (Real.sinc (a*u))) =ᶠ[𝓝 x] + (fun u : ℝ => Real.log (Real.sin (a*u)/(a*u))) := by + filter_upwards [eventually_ne_nhds hx] with u hu + rw [Real.sinc_of_ne_zero (mul_ne_zero ha hu)] + apply HasDerivAt.congr_of_eventuallyEq (f := fun u : ℝ => Real.log (Real.sin (a*u)/(a*u))) _ he + simp only [Pi.div_apply, id_eq, mul_one] at hd + apply hd.congr_deriv + field_simp + +lemma logSinc_deriv_hasDeriv (a x : ℝ) (hx : x ≠ 0) + (hs : Real.sin (a*x) ≠ 0) : + HasDerivAt (fun u : ℝ => a*Real.cos (a*u)/Real.sin (a*u) - 1/u) + (1/x^2 - a^2/Real.sin (a*x)^2) x := by + have hd := (cot_scaled_hasDeriv a 0 x (by simpa using hs)).sub + ((hasDerivAt_const x (1 : ℝ)).div (hasDerivAt_id x) hx) + simp only [id_eq, sub_zero, zero_mul, one_mul, zero_sub] at hd + apply hd.congr_deriv + ring + + +lemma logSinc_concaveOn {D : Set ℝ} (hD : Convex ℝ D) (a : ℝ) (ha : a ≠ 0) + (h0 : (0 : ℝ) ∉ interior D) + (hs : ∀ x ∈ D, x ≠ 0 → Real.sin (a*x) ≠ 0) : + ConcaveOn ℝ D (fun x : ℝ => Real.log (Real.sinc (a*x))) := by + apply concaveOn_of_hasDerivWithinAt2_nonpos hD + (f' := fun x => a*Real.cos (a*x)/Real.sin (a*x) - 1/x) + (f'' := fun x => 1/x^2 - a^2/Real.sin (a*x)^2) + · apply (Real.continuous_sinc.comp (by fun_prop)).continuousOn.log + exact fun x hx => sinc_ne_zero ha (hs x hx) + · intro x hx + have hx0 : x ≠ 0 := fun he => h0 (he ▸ hx) + exact (logSinc_hasDeriv a x ha hx0 (hs x (interior_subset hx) hx0)).hasDerivWithinAt + · intro x hx + have hx0 : x ≠ 0 := fun he => h0 (he ▸ hx) + exact (logSinc_deriv_hasDeriv a x hx0 (hs x (interior_subset hx) hx0)).hasDerivWithinAt + · intro x hx + have hx0 : x ≠ 0 := fun he => h0 (he ▸ hx) + have hsin : Real.sin (a*x) ≠ 0 := hs x (interior_subset hx) hx0 + apply sub_nonpos.mpr + apply (div_le_div_iff₀ (sq_pos_of_ne_zero hx0) (sq_pos_of_ne_zero hsin)).mpr + have hh : Real.sin (a*x)^2 ≤ (a*x)^2 := by + exact sq_le_sq.mpr Real.abs_sin_le_abs + nlinarith + +end SharpPlanar + + +namespace SharpPlanar +open Set Filter +open scoped Topology + +noncomputable def dividedP (a : ℕ) (u : ℝ) : ℝ := + (Real.pi/6)^2 * (Real.sinc (Real.pi*u/12))^2 * + ∏ r ∈ residues.erase a, (2*Real.sin (Real.pi*(a+u-r)/12))^2 + +lemma dividedP_zero (a : ℕ) (ha : a < 12) : dividedP a 0 = Q a := by + simp [dividedP,Q,Nat.mod_eq_of_lt ha] + +lemma dividedP_factor (a : ℕ) (ha : a ∈ residues) (u : ℝ) : + u^2 * dividedP a u = P (a+u) := by + rw [P,← Finset.mul_prod_erase residues (fun r : ℕ => (2*Real.sin (Real.pi*(a+u-r)/12))^2) ha] + unfold dividedP + rw [show ((a:ℝ)+u-a)=u by ring] + have hs : (Real.pi*u/12)*Real.sinc (Real.pi*u/12) = Real.sin (Real.pi*u/12) := by + by_cases hz : Real.pi*u/12 = 0 + · simp [hz] + · rw [Real.sinc_of_ne_zero hz,mul_div_cancel₀ _ hz] + rw [← hs] + ring + +lemma sine_twelfth_ne {v : ℝ} (hl : -12 < v) (hr : v < 12) (hv : v ≠ 0) : + Real.sin (Real.pi*v/12) ≠ 0 := by + rw [ne_eq,Real.sin_eq_zero_iff_of_lt_of_lt + (by nlinarith [Real.pi_pos,mul_pos Real.pi_pos (show 0 < v+12 by linarith)]) + (by nlinarith [Real.pi_pos,mul_pos Real.pi_pos (show 0 < 12-v by linarith)])] + exact div_ne_zero (mul_ne_zero Real.pi_ne_zero hv) (by norm_num) + +noncomputable def leftHalf : ℕ → ℝ + | 0 => 3/2 | 1 => 1/2 | 3 => 1 | 4 => 1/2 | 7 => 3/2 | 9 => 1 | _ => 0 +noncomputable def rightHalf : ℕ → ℝ + | 0 => 1/2 | 1 => 1 | 3 => 1/2 | 4 => 3/2 | 7 => 1 | 9 => 3/2 | _ => 0 + +lemma half_pos (a : ℕ) (ha : a ∈ residues) : 0 < leftHalf a ∧ 0 < rightHalf a := by + simp only [residues,Finset.mem_insert,Finset.mem_singleton] at ha + rcases ha with rfl|rfl|rfl|rfl|rfl|rfl <;> norm_num [leftHalf,rightHalf] +lemma half_bounds (a : ℕ) (ha : a ∈ residues) {u : ℝ} + (hu : u ∈ Icc (-leftHalf a) (rightHalf a)) : -12 < u ∧ u < 12 := by + simp only [residues,Finset.mem_insert,Finset.mem_singleton] at ha + rcases ha with rfl|rfl|rfl|rfl|rfl|rfl <;> norm_num [leftHalf,rightHalf,mem_Icc] at hu <;> + constructor <;> linarith +lemma other_sine_ne (a : ℕ) (ha : a ∈ residues) {u : ℝ} + (hu : u ∈ Icc (-leftHalf a) (rightHalf a)) (r : ℕ) (hr : r ∈ residues.erase a) : + Real.sin (Real.pi*(a+u-r)/12) ≠ 0 := by + apply sine_twelfth_ne + all_goals + have hra := (Finset.mem_erase.mp hr).1 + have hrr := (Finset.mem_erase.mp hr).2 + simp only [residues,Finset.mem_insert,Finset.mem_singleton] at ha hrr + rcases ha with rfl|rfl|rfl|rfl|rfl|rfl <;> + rcases hrr with rfl|rfl|rfl|rfl|rfl|rfl <;> + first | contradiction | (norm_num [leftHalf,rightHalf,mem_Icc] at hu ⊢; grind) + +lemma dividedP_pos (a : ℕ) (ha : a ∈ residues) {u : ℝ} + (hu : u ∈ Icc (-leftHalf a) (rightHalf a)) : 0 < dividedP a u := by + apply mul_pos + · apply mul_pos (sq_pos_of_pos (by positivity)) + apply sq_pos_of_ne_zero + rw [show Real.pi*u/12=(Real.pi/12)*u by ring] + apply sinc_ne_zero (a := Real.pi/12) (by positivity) + intro hu0 + have hb := half_bounds a ha hu + convert sine_twelfth_ne hb.1 hb.2 hu0 using 1; congr 1; ring + · exact Finset.prod_pos (fun r hr => sq_pos_of_ne_zero (mul_ne_zero (by norm_num) (other_sine_ne a ha hu r hr))) + +lemma dividedP_log (a : ℕ) (ha : a ∈ residues) {u : ℝ} + (hu : u ∈ Icc (-leftHalf a) (rightHalf a)) : + Real.log (dividedP a u) = 2*Real.log (Real.pi/6) + + 2*Real.log (Real.sinc (Real.pi*u/12)) + + ∑ r ∈ residues.erase a, (2*Real.log 2 + 2*Real.log (Real.sin (Real.pi*(a+u-r)/12))) := by + have hn (r : ℕ) (hr : r ∈ residues.erase a) : 2*Real.sin (Real.pi*(a+u-r)/12) ≠ 0 := + mul_ne_zero (by norm_num) (other_sine_ne a ha hu r hr) + have hb := half_bounds a ha hu + have hsi : Real.sinc (Real.pi*u/12) ≠ 0 := by + convert sinc_ne_zero (a := Real.pi/12) (by positivity) + (fun hu0 => by convert sine_twelfth_ne hb.1 hb.2 hu0 using 1; congr 1; ring) using 1; congr 1; ring + unfold dividedP + rw [Real.log_mul (mul_ne_zero (pow_ne_zero 2 (by positivity)) (pow_ne_zero 2 hsi)) (Finset.prod_ne_zero_iff.mpr (fun r hr => pow_ne_zero 2 (hn r hr))), + Real.log_mul (pow_ne_zero 2 (by positivity)) (pow_ne_zero 2 hsi),Real.log_pow,Real.log_pow,Real.log_prod (fun r hr => pow_ne_zero 2 (hn r hr))] + simp only [Nat.cast_ofNat] + congr 1 + apply Finset.sum_congr rfl + intro r hr + rw [Real.log_pow,Real.log_mul (by norm_num) (other_sine_ne a ha hu r hr)] + push_cast + ring + +end SharpPlanar + + +namespace SharpPlanar +open Set Filter +open scoped Topology + +lemma concaveOn_finset_sum {ι : Type*} (s : Finset ι) {D : Set ℝ} + (hD : Convex ℝ D) (g : ι → ℝ → ℝ) (hg : ∀ r ∈ s, ConcaveOn ℝ D (g r)) : + ConcaveOn ℝ D (fun u => ∑ r ∈ s, g r u) := by + classical + induction s using Finset.induction_on with + | empty => simpa using concaveOn_const (0:ℝ) hD + | @insert r s hrs ih => + have hh : ConcaveOn ℝ D (fun u => g r u + ∑ r ∈ s, g r u) := (hg r (Finset.mem_insert_self ..)).add (ih (fun v hv => hg v (Finset.mem_insert_of_mem hv))) + simpa only [Finset.sum_insert hrs, Pi.add_apply] using hh + +lemma dividedP_log_concave (a : ℕ) (ha : a ∈ residues) {D : Set ℝ} + (hD : Convex ℝ D) (hsub : D ⊆ Icc (-leftHalf a) (rightHalf a)) + (h0 : (0:ℝ) ∉ interior D) : ConcaveOn ℝ D (fun u => Real.log (dividedP a u)) := by + have hsinc0 := logSinc_concaveOn hD (Real.pi/12) (by positivity) h0 (fun u hu hu0 => by + have hb := half_bounds a ha (hsub hu) + rw [show (Real.pi/12)*u = Real.pi*u/12 by ring] + exact sine_twelfth_ne hb.1 hb.2 hu0) + have hsinc : ConcaveOn ℝ D (fun u => Real.log (Real.sinc (Real.pi*u/12))) := by + apply hsinc0.congr + intro u hu + dsimp only + rw [show (Real.pi/12)*u = Real.pi*u/12 by ring] + have hother (r : ℕ) (hr : r ∈ residues.erase a) : + ConcaveOn ℝ D (fun u => 2*Real.log 2 + 2*Real.log (Real.sin (Real.pi*(a+u-r)/12))) := by + have hh0 := logSin_concaveOn hD (Real.pi/12) ((r:ℝ)-a) (fun u hu => by + rw [show (Real.pi/12)*(u-((r:ℝ)-a)) = Real.pi*(a+u-r)/12 by ring] + exact other_sine_ne a ha (hsub hu) r hr) + have hh : ConcaveOn ℝ D (fun u => Real.log (Real.sin (Real.pi*(a+u-r)/12))) := by + apply hh0.congr + intro u hu + dsimp only + rw [show (Real.pi/12)*(u-((r:ℝ)-a)) = Real.pi*(a+u-r)/12 by ring] + exact (concaveOn_const (2*Real.log 2) hD).add (ConcaveOn.smul (by norm_num : 0 ≤ (2:ℝ)) hh) + have hh : ConcaveOn ℝ D (fun u => 2*Real.log (Real.pi/6) + 2*Real.log (Real.sinc (Real.pi*u/12)) + ∑ r ∈ residues.erase a, (2*Real.log 2 + 2*Real.log (Real.sin (Real.pi*(a+u-r)/12)))) := ((concaveOn_const (2*Real.log (Real.pi/6)) hD).add + (ConcaveOn.smul (by norm_num : 0 ≤ (2:ℝ)) hsinc)).add + (concaveOn_finset_sum (residues.erase a) hD _ hother) + apply hh.congr + intro u hu + exact (dividedP_log a ha (hsub hu)).symm + +lemma lower_of_log_concave {f : ℝ → ℝ} {v w l : ℝ} (hl : 0 < l) + (hp : ∀ u ∈ uIcc v w, 0 < f u) + (hc : ConcaveOn ℝ (uIcc v w) (fun u => Real.log (f u))) + (hv : l ≤ f v) (hw : l ≤ f w) {u : ℝ} (hu : u ∈ uIcc v w) : l ≤ f u := by + have hs := hc.ge_on_segment (left_mem_uIcc) (right_mem_uIcc) + (show u ∈ segment ℝ v w by simpa only [segment_eq_uIcc] using hu) + have hj : Real.log l ≤ Real.log (f u) := le_trans (le_min + (Real.log_le_log hl hv) (Real.log_le_log hl hw)) hs + exact (Real.log_le_log_iff hl (hp u hu)).mp hj + +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Basic.lean b/lean/OAI/Analysis/PlanarPacking/Basic.lean new file mode 100644 index 0000000000000000000000000000000000000000..180b8d8f5c6734e59b1dd793245855afa927acd3 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Basic.lean @@ -0,0 +1,37 @@ +import Mathlib.Analysis.Distribution.SchwartzSpace.Basic +import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace +import OAI.Analysis.PlanarPacking.Cardinal + +namespace OAI + +/-! +# Sharp Fourier certificates in the plane + +The radial Schwartz certificate uses the Fourier kernel `exp (-2πi⟪x, ξ⟫)` +and the sharp triangular packing normalization. +-/ + +open MeasureTheory + +namespace SharpPlanar + + + + +def Radial (f : Plane → ℝ) : Prop := + ∀ x y, ‖x‖ = ‖y‖ → f x = f y + + +noncomputable def fourier (f : Plane → ℝ) (ξ : Plane) : ℂ := + ∫ x : Plane, (f x : ℂ) * + Complex.exp (((-2 * Real.pi * inner ℝ x ξ : ℝ) : ℂ) * Complex.I) + + +def SharpCertificate (f : SchwartzMap Plane ℝ) : Prop := + Radial f ∧ fourier f 0 = 1 ∧ f 0 = 2 / Real.sqrt 3 ∧ + (∀ ξ, (fourier f ξ).im = 0 ∧ 0 ≤ (fourier f ξ).re) ∧ + (∀ x, 1 ≤ ‖x‖ → f x ≤ 0) + +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/BasisIntervals.lean b/lean/OAI/Analysis/PlanarPacking/BasisIntervals.lean new file mode 100644 index 0000000000000000000000000000000000000000..8052635426403da277c3bbcfc67f0eba2df3de40 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/BasisIntervals.lean @@ -0,0 +1,1469 @@ +import OAI.Analysis.PlanarPacking.Quadrature + +namespace OAI + +namespace SharpPlanar.IntegerBasis +open IntegerIntervals + +noncomputable def phase12 (n : ℕ) : ℂ := Complex.exp (Complex.I*Real.pi*((n:ℂ)/6)) +lemma phase12_eq_pow (n : ℕ) : phase12 n = phase12 1^n := by + rw [phase12,phase12,← Complex.exp_nat_mul] + congr 1 + push_cast + ring +lemma phase12_periodic (n : ℕ) : phase12 (n+12) = phase12 n := by + unfold phase12 + have he : Complex.I*Real.pi*(((n+12:ℕ):ℂ)/6) = + Complex.I*Real.pi*((n:ℂ)/6)+2*Real.pi*Complex.I := by push_cast; ring + rw [he,Complex.exp_add,Complex.exp_two_pi_mul_I,mul_one] +lemma phase12_mod (n : ℕ) : phase12 (n%12) = phase12 n := + (show Function.Periodic phase12 12 from phase12_periodic).map_mod_nat n + +def phaseBase : CBox := (piI.scale 1 6).exp 1 +lemma phaseBase_contains : phaseBase.Contains (phase12 1) := by + have hi := CBox.contains_scale piI_contains 1 6 (by norm_num) + have he := CBox.contains_exp hi 1 (by decide +kernel) + unfold phaseBase + convert he using 1 + unfold phase12 + congr 1 + norm_num + ring + +def phaseBox (n : ℕ) : CBox := phaseBase.powBin 4 (n%12) +lemma phaseBox_contains (n : ℕ) : (phaseBox n).Contains (phase12 n) := by + have hh := CBox.contains_powBin phaseBase_contains 4 (n%12) (by omega) + rw [← phase12_eq_pow,phase12_mod] at hh + exact hh + +def coefficientBox : ℕ → CBox + | 0 => CBox.rat 5 1 0 1 + | 1 => ⟨RBox.rat (-1) 1,bBounds.scale 2 1⟩ + | 2 => ⟨RBox.rat 1 1,bBounds.scale 2 1⟩ + | 3 => CBox.rat (-2) 1 0 1 + | 4 => ⟨RBox.rat (-1) 2,bBounds⟩ + | 5 => ⟨RBox.rat (-1) 1,bBounds.scale (-2) 1⟩ + | 6 => CBox.rat 1 1 0 1 + | _ => CBox.rat 0 1 0 1 +lemma coefficientBox_contains (n : ℕ) : (coefficientBox n).Contains (Pcoeff n) := by + have hb : bBounds.Contains b := bBounds_contains + have hp := RBox.contains_scale hb 2 1 (by norm_num) + have hm := RBox.contains_scale hb (-2) 1 (by norm_num) + have h0 (m k : ℤ) (hk : 0 < k) := CBox.contains_rat m k 0 1 hk (by norm_num) + have hr (m k : ℤ) (hk : 0 < k) := RBox.contains_rat m k hk + rcases n with _|_|_|_|_|_|_|n + · simpa [coefficientBox,Pcoeff] using h0 5 1 (by norm_num) + · constructor + · simpa [coefficientBox,Pcoeff] using hr (-1) 1 (by norm_num) + · simpa [coefficientBox,Pcoeff] using hp + · constructor + · simpa [coefficientBox,Pcoeff] using hr 1 1 (by norm_num) + · simpa [coefficientBox,Pcoeff] using hp + · simpa [coefficientBox,Pcoeff] using h0 (-2) 1 (by norm_num) + · constructor + · convert hr (-1) 2 (by norm_num) using 1 <;> norm_num [coefficientBox,Pcoeff] + · simpa [coefficientBox,Pcoeff] using hb + · constructor + · simpa [coefficientBox,Pcoeff] using hr (-1) 1 (by norm_num) + · simpa [coefficientBox,Pcoeff] using hm + · simpa [coefficientBox,Pcoeff] using h0 1 1 (by norm_num) + · simpa [coefficientBox,Pcoeff] using h0 0 1 (by norm_num) + +noncomputable def spectralCoefficient (n l : ℕ) : ℂ := + Pcoeff l*Complex.exp (Complex.I*Real.pi*(l:ℂ)/6*n) +def spectralCoefficientBox (n l : ℕ) : CBox := (coefficientBox l).mul (phaseBox (l*n)) +lemma spectralCoefficientBox_contains (n l : ℕ) : + (spectralCoefficientBox n l).Contains (spectralCoefficient n l) := by + have hh := CBox.contains_mul (coefficientBox_contains l) (phaseBox_contains (l*n)) + unfold spectralCoefficientBox + convert hh using 1 + unfold spectralCoefficient phase12 + congr 2 + push_cast + ring + +end SharpPlanar.IntegerBasis + +namespace SharpPlanar.IntegerIntervals + +def zeroBox : CBox := ⟨⟨0,0⟩,⟨0,0⟩⟩ +lemma zeroBox_contains : zeroBox.Contains 0 := by simp [zeroBox,CBox.Contains,RBox.Contains] +def boxSum (f : ℕ → CBox) : ℕ → CBox + | 0 => zeroBox + | N+1 => (boxSum f N).add (f N) +lemma boxSum_contains {f : ℕ → CBox} {g : ℕ → ℂ} (N : ℕ) + (h : ∀ n < N, (f n).Contains (g n)) : + (boxSum f N).Contains (∑ n ∈ Finset.range N, g n) := by + induction N with + | zero => simpa [boxSum] using zeroBox_contains + | succ N ih => + rw [Finset.sum_range_succ] + exact CBox.contains_add (ih (fun n hn => h n (by omega))) (h N (by omega)) +end SharpPlanar.IntegerIntervals + +namespace SharpPlanar.IntegerBasis +open IntegerIntervals + +noncomputable def basisAlpha (n j : ℕ) : ℂ := ∑ l ∈ Finset.Icc (j+1) 6, spectralCoefficient n l +noncomputable def basisBeta (n j : ℕ) : ℂ := + ∑ l ∈ Finset.Icc (j+1) 6, ((l:ℂ)/6)*spectralCoefficient n l + +def alphaBox (n j : ℕ) : CBox := boxSum + (fun l => if j if j first | exact spectralCoefficientBox_contains n l | exact zeroBox_contains + have hs := boxSum_contains 7 (fun l _ => hh l) + rwa [sum_seven_Icc] at hs +lemma betaBox_contains (n j : ℕ) : (betaBox n j).Contains (basisBeta n j) := by + have hh (l : ℕ) : (if j hh l) + rwa [sum_seven_Icc] at hs + +lemma u_factored (n j : ℕ) (t : ℝ) : u n j t = + -2*(Real.pi:ℂ)^2*Complex.exp (-Complex.I*Real.pi*t*n)* + (basisBeta n j-(t:ℂ)*basisAlpha n j) := by + unfold u basisBeta basisAlpha spectralCoefficient + congr 1 + rw [Finset.mul_sum,← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro l _ + ring +lemma v_factored (n j : ℕ) (t : ℝ) : v n j t = + 2*Complex.I*Real.pi*Complex.exp (-Complex.I*Real.pi*t*n)*basisAlpha n j := by + unfold v basisAlpha spectralCoefficient + rfl + +end SharpPlanar.IntegerBasis + +namespace SharpPlanar.IntegerIntervals + +def CBox.powFast (a : CBox) : ℕ → ℕ → CBox + | 0, _ => CBox.rat 1 1 0 1 + | k+1,n => if n=0 then CBox.rat 1 1 0 1 else if n=1 then a else + let b := a.powFast k (n/2) + let b2 := b.mul b + if n%2=0 then b2 else b2.mul a + +lemma CBox.contains_powFast {a : CBox} {z : ℂ} (hz : a.Contains z) (k n : ℕ) + (hn : n < 2^k) : (a.powFast k n).Contains (z^n) := by + induction k generalizing n with + | zero => + have : n=0 := by simpa using hn + subst n + simpa [CBox.powFast] using CBox.contains_rat 1 1 0 1 (by norm_num) (by norm_num) + | succ k ih => + have hd : n/2 < 2^k := by rw [pow_succ] at hn; omega + have he : n%2+2*(n/2)=n := Nat.mod_add_div n 2 + simp only [CBox.powFast] + split_ifs with h0 h1 h2 + · subst n + simpa using CBox.contains_rat 1 1 0 1 (by norm_num) (by norm_num) + · subst n + simpa using hz + · have hh := CBox.contains_mul (ih (n/2) hd) (ih (n/2) hd) + have ht : n/2+n/2=n := by omega + simpa only [← pow_add,ht] using hh + · have hh := CBox.contains_mul (CBox.contains_mul (ih (n/2) hd) (ih (n/2) hd)) hz + have ht : n/2+n/2+1=n := by omega + simpa only [← pow_add,pow_one,← pow_succ,ht] using hh + +end SharpPlanar.IntegerIntervals + +namespace SharpPlanar.IntegerBasis +open IntegerIntervals + +lemma spectralCoefficient_eq_phase (n l : ℕ) : + spectralCoefficient n l = Pcoeff l*phase12 (l*n) := by + unfold spectralCoefficient phase12 + congr 2 + push_cast + ring +lemma spectralCoefficient_mod (n l : ℕ) : + spectralCoefficient (n%12) l = spectralCoefficient n l := by + simp only [spectralCoefficient_eq_phase] + rw [← phase12_mod (l*(n%12)),← phase12_mod (l*n)] + congr 2 + simp only [Nat.mul_mod, Nat.mod_mod] +lemma basisAlpha_mod (n j : ℕ) : basisAlpha (n%12) j = basisAlpha n j := by + unfold basisAlpha + simp only [spectralCoefficient_mod] +lemma basisBeta_mod (n j : ℕ) : basisBeta (n%12) j = basisBeta n j := by + unfold basisBeta + simp only [spectralCoefficient_mod] + +def uBox (p : PointBox) (a b : CBox) (n : ℕ) : CBox := + (((rcast (piBounds.mul piBounds)).scale (-2) 1).mul (p.direct.powFast 7 n)).mul + (b.add (((rcast p.t).mul a).neg)) +def vBox (p : PointBox) (a : CBox) (n : ℕ) : CBox := + ((piI.scale 2 1).mul (p.direct.powFast 7 n)).mul a +lemma direct_power_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) {n : ℕ} + (hn : n < 128) : (p.direct.powFast 7 n).Contains + (Complex.exp (-Complex.I*Real.pi*t*n)) := by + have he := CBox.contains_powFast hp.2.2.2.1 7 n hn + rw [← Complex.exp_nat_mul] at he + convert he using 1 + congr 1 + ring +lemma uBox_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) {a b : CBox} + {n j : ℕ} (ha : a.Contains (basisAlpha n j)) (hb : b.Contains (basisBeta n j)) + (hn : n < 128) : (uBox p a b n).Contains (u n j t) := by + have hpi := CBox.contains_scale (rcast_contains + (RBox.contains_mul piBounds_contains piBounds_contains)) (-2) 1 (by norm_num) + have he := CBox.contains_mul (CBox.contains_mul hpi (direct_power_contains hp hn)) + (CBox.contains_add hb (CBox.neg_contains (CBox.contains_mul (rcast_contains hp.1) ha))) + unfold uBox + convert he using 1 + rw [u_factored] + push_cast + ring +lemma vBox_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) {a : CBox} + {n j : ℕ} (ha : a.Contains (basisAlpha n j)) (hn : n < 128) : + (vBox p a n).Contains (v n j t) := by + have he := CBox.contains_mul + (CBox.contains_mul (CBox.contains_scale piI_contains 2 1 (by norm_num)) + (direct_power_contains hp hn)) ha + unfold vBox + convert he using 1 + rw [v_factored] + push_cast + ring + +lemma pointLambda_eq (t : ℝ) : pointLambda t = lambda t := by + unfold pointLambda lambda b h + push_cast + rfl +lemma pointZ_eq (t : ℝ) : pointZ t = z t := by + unfold pointZ z B h + push_cast + rfl + +def kernel0Box (p : PointBox) (m : ℕ) : CBox := p.lam.mul (p.quarter.powFast 9 (4*m)) +lemma kernel0Box_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) {m : ℕ} + (hm : m < 128) : (kernel0Box p m).Contains + (lambda t*Complex.exp (Complex.I*Real.pi*z t*m)) := by + have he := CBox.contains_powFast hp.2.2.2.2 9 (4*m) (by omega) + rw [← Complex.exp_nat_mul] at he + have hz := CBox.contains_mul hp.2.1 he + unfold kernel0Box + convert hz using 1 + rw [pointLambda_eq,pointZ_eq] + congr 2 + push_cast + ring + +noncomputable def basisFunction (d : Bool) (n j : ℕ) (t : ℝ) : ℂ := + if d then v n j t else u n j t +noncomputable def basisMoment (d e : Bool) (n j m : ℕ) (t : ℝ) : ℂ := + basisFunction d n j t * (lambda t*Complex.exp (Complex.I*Real.pi*z t*m)) * + (if e then Complex.I*Real.pi*z t else 1) +def basisFunctionBox (p : PointBox) (a b : CBox) (n : ℕ) (d : Bool) : CBox := + if d then vBox p a n else uBox p a b n +def basisMomentBox (p : PointBox) (a b : CBox) (n m : ℕ) (d e : Bool) : CBox := + let k := (basisFunctionBox p a b n d).mul (kernel0Box p m) + if e then k.mul (piI.mul p.z) else k +lemma basisFunctionBox_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) {a b : CBox} + {n j : ℕ} (ha : a.Contains (basisAlpha n j)) (hb : b.Contains (basisBeta n j)) + (hn : n < 128) (d : Bool) : + (basisFunctionBox p a b n d).Contains (basisFunction d n j t) := by + cases d + · exact uBox_contains hp ha hb hn + · exact vBox_contains hp ha hn +lemma basisMomentBox_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) {a b : CBox} + {n j m : ℕ} (ha : a.Contains (basisAlpha n j)) (hb : b.Contains (basisBeta n j)) + (hn : n < 128) (hm : m < 128) (d e : Bool) : + (basisMomentBox p a b n m d e).Contains (basisMoment d e n j m t) := by + have hk := CBox.contains_mul (basisFunctionBox_contains hp ha hb hn d) + (kernel0Box_contains hp hm) + cases e + · simpa [basisMomentBox,basisMoment] using hk + · have hh := CBox.contains_mul hk (CBox.contains_mul piI_contains hp.2.2.1) + simpa only [basisMomentBox,basisMoment,pointZ_eq,ite_true] using hh + +end SharpPlanar.IntegerBasis + +namespace SharpPlanar.IntegerIntervals + +def finSum : {N : ℕ} → (Fin N → CBox) → CBox + | 0, _ => zeroBox + | N+1, f => (f 0).add (finSum (fun i : Fin N => f i.succ)) +lemma finSum_contains {N : ℕ} {f : Fin N → CBox} {g : Fin N → ℂ} + (h : ∀ i, (f i).Contains (g i)) : (finSum f).Contains (∑ i, g i) := by + induction N with + | zero => simpa [finSum] using zeroBox_contains + | succ N ih => + rw [Fin.sum_univ_succ] + exact CBox.contains_add (h 0) (ih (fun i => h i.succ)) + +end SharpPlanar.IntegerIntervals + +namespace SharpPlanar.IntegerBasis +open IntegerIntervals + +lemma sum_fin_square (N : ℕ) (f : ℕ → ℂ) : + (∑ i : Fin N, ∑ k : Fin N, f (N*i.val+k.val)) = + ∑ v : Fin (N*N), f v.val := by + calc + _ = ∑ x : Fin N × Fin N, f (N*x.1.val+x.2.val) := + (Fintype.sum_prod_type _).symm + _ = _ := by + convert (finProdFinEquiv.sum_comp (fun v : Fin (N*N) => f v.val)) using 1 + apply Finset.sum_congr rfl + intro x _ + congr 1 + exact Nat.add_comm _ _ + +noncomputable def momentRuleValue (t : ℕ → ℕ → ℝ) (w : ℕ → ℝ) + (n m : ℕ) (d e : Bool) : ℂ := + ∑ j : Fin 6, (1/6:ℂ)*∑ v : Fin 256, (w v.val:ℂ)* + basisMoment d e n j.val m (t j.val v.val) + +def momentRuleBox (p : Fin 6 → Fin 16 → Fin 16 → PointBox) + (w : Fin 16 → Fin 16 → RBox) (a b : Fin 6 → CBox) + (n m : ℕ) (d e : Bool) : CBox := + finSum (fun j => (finSum (fun i => finSum (fun k => + (rcast (w i k)).mul (basisMomentBox (p j i k) (a j) (b j) n m d e)))).scale 1 6) + +lemma momentRuleBox_contains + {p : Fin 6 → Fin 16 → Fin 16 → PointBox} {t : ℕ → ℕ → ℝ} + {w : Fin 16 → Fin 16 → RBox} {wr : ℕ → ℝ} {a b : Fin 6 → CBox} + {n m : ℕ} (d e : Bool) + (hp : ∀ j i k, (p j i k).Contains (t j.val (16*i.val+k.val))) + (hw : ∀ i k, (w i k).Contains (wr (16*i.val+k.val))) + (ha : ∀ j, (a j).Contains (basisAlpha n j.val)) + (hb : ∀ j, (b j).Contains (basisBeta n j.val)) + (hn : n < 128) (hm : m < 128) : + (momentRuleBox p w a b n m d e).Contains (momentRuleValue t wr n m d e) := by + unfold momentRuleBox momentRuleValue + apply finSum_contains + intro j + rw [← sum_fin_square 16 (fun v => (wr v:ℂ)*basisMoment d e n j.val m (t j.val v))] + have hh := finSum_contains (fun i => finSum_contains (fun k => + CBox.contains_mul (rcast_contains (hw i k)) + (basisMomentBox_contains (hp j i k) (ha j) (hb j) hn hm d e))) + simpa only [Int.cast_one,Int.cast_ofNat] using CBox.contains_scale hh 1 6 (by norm_num) + +end SharpPlanar.IntegerBasis + +namespace SharpPlanar.IntegerAlpha +open IntegerIntervals IntegerBasis +def a0_0 : CBox := ⟨⟨(-2500000000000000000000000000000),(-2500000000000000000000000000000)⟩,⟨2598076211353315940260000000000,2598076211353315940330000000000⟩⟩ +lemma a0_0_contains : a0_0.Contains (basisAlpha 0 0) := by + have he : alphaBox 0 0 = a0_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 0 0 +def b0_0 : CBox := ⟨⟨(-1000000000000000000000000000002),(-999999999999999999999999999998)⟩,⟨(-16666666669),16666666669⟩⟩ +lemma b0_0_contains : b0_0.Contains (basisBeta 0 0) := by + have he : betaBox 0 0 = b0_0 := by decide +kernel + rw [← he] + exact betaBox_contains 0 0 +def a0_1 : CBox := ⟨⟨(-1500000000000000000000000000000),(-1500000000000000000000000000000)⟩,⟨866025403784438646740000000000,866025403784438646790000000000⟩⟩ +lemma a0_1_contains : a0_1.Contains (basisAlpha 0 1) := by + have he : alphaBox 0 1 = a0_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 0 1 +def b0_1 : CBox := ⟨⟨(-833333333333333333333333333335),(-833333333333333333333333333332)⟩,⟨(-288675134594812882270000000002),(-288675134594812882239999999998)⟩⟩ +lemma b0_1_contains : b0_1.Contains (basisBeta 0 1) := by + have he : betaBox 0 1 = b0_1 := by decide +kernel + rw [← he] + exact betaBox_contains 0 1 +def a0_2 : CBox := ⟨⟨(-2500000000000000000000000000000),(-2500000000000000000000000000000)⟩,⟨(-866025403784438646780000000000),(-866025403784438646750000000000)⟩⟩ +lemma a0_2_contains : a0_2.Contains (basisAlpha 0 2) := by + have he : alphaBox 0 2 = a0_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 0 2 +def b0_2 : CBox := ⟨⟨(-1166666666666666666666666666668),(-1166666666666666666666666666666)⟩,⟨(-866025403784438646776666666668),(-866025403784438646753333333332)⟩⟩ +lemma b0_2_contains : b0_2.Contains (basisBeta 0 2) := by + have he : betaBox 0 2 = b0_2 := by decide +kernel + rw [← he] + exact betaBox_contains 0 2 +def a0_3 : CBox := ⟨⟨(-500000000000000000000000000000),(-500000000000000000000000000000)⟩,⟨(-866025403784438646780000000000),(-866025403784438646750000000000)⟩⟩ +lemma a0_3_contains : a0_3.Contains (basisAlpha 0 3) := by + have he : alphaBox 0 3 = a0_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 0 3 +def b0_3 : CBox := ⟨⟨(-166666666666666666666666666668),(-166666666666666666666666666666)⟩,⟨(-866025403784438646776666666668),(-866025403784438646753333333332)⟩⟩ +lemma b0_3_contains : b0_3.Contains (basisBeta 0 3) := by + have he : betaBox 0 3 = b0_3 := by decide +kernel + rw [← he] + exact betaBox_contains 0 3 +def a0_4 : CBox := ⟨⟨0,0⟩,⟨(-1732050807568877293540000000000),(-1732050807568877293520000000000)⟩⟩ +lemma a0_4_contains : a0_4.Contains (basisAlpha 0 4) := by + have he : alphaBox 0 4 = a0_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 0 4 +def b0_4 : CBox := ⟨⟨166666666666666666666666666666,166666666666666666666666666667⟩,⟨(-1443375672974064411283333333334),(-1443375672974064411266666666666)⟩⟩ +lemma b0_4_contains : b0_4.Contains (basisBeta 0 4) := by + have he : betaBox 0 4 = b0_4 := by decide +kernel + rw [← he] + exact betaBox_contains 0 4 +def a0_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma a0_5_contains : a0_5.Contains (basisAlpha 0 5) := by + have he : alphaBox 0 5 = a0_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 0 5 +def b0_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma b0_5_contains : b0_5.Contains (basisBeta 0 5) := by + have he : betaBox 0 5 = b0_5 := by decide +kernel + rw [← he] + exact betaBox_contains 0 5 +def aRow0 : Fin 6 → CBox := ![a0_0,a0_1,a0_2,a0_3,a0_4,a0_5] +lemma aRow0_contains (j : Fin 6) : (aRow0 j).Contains (basisAlpha 0 j.val) := by + fin_cases j + · exact a0_0_contains + · exact a0_1_contains + · exact a0_2_contains + · exact a0_3_contains + · exact a0_4_contains + · exact a0_5_contains +def bRow0 : Fin 6 → CBox := ![b0_0,b0_1,b0_2,b0_3,b0_4,b0_5] +lemma bRow0_contains (j : Fin 6) : (bRow0 j).Contains (basisBeta 0 j.val) := by + fin_cases j + · exact b0_0_contains + · exact b0_1_contains + · exact b0_2_contains + · exact b0_3_contains + · exact b0_4_contains + · exact b0_5_contains +def a1_0 : CBox := ⟨⟨(-2500000000000000000073478665491),(-2499999999999999999933155933893)⟩,⟨866025403784438646695878312244,866025403784438646839277975147⟩⟩ +lemma a1_0_contains : a1_0.Contains (basisAlpha 1 0) := by + have he : alphaBox 1 0 = a1_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 1 0 +def b1_0 : CBox := ⟨⟨(-511966128287415137693146900620),(-511966128287415137604977905556)⟩,⟨(-43633798654),47214926849⟩⟩ +lemma b1_0_contains : b1_0.Contains (basisBeta 1 0) := by + have he : betaBox 1 0 = b1_0 := by decide +kernel + rw [← he] + exact betaBox_contains 1 0 +def a1_1 : CBox := ⟨⟨(-767949192431122706537425858341),(-767949192431122706410976860631)⟩,⟨(-133974596215561353295379180206),(-133974596215561353172527005361)⟩⟩ +lemma a1_1_contains : a1_1.Contains (basisAlpha 1 1) := by + have he : alphaBox 1 1 = a1_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 1 1 +def b1_1 : CBox := ⟨⟨(-223290993692602255437138099428),(-223290993692602255351281393346)⟩,⟨(-166666666666666666708843380729),(-166666666666666666621419236569)⟩⟩ +lemma b1_1_contains : b1_1.Contains (basisBeta 1 1) := by + have he : betaBox 1 1 = b1_1 := by decide +kernel + rw [← he] + exact betaBox_contains 1 1 +def a1_2 : CBox := ⟨⟨232050807568877293479774764070,232050807568877293578966769811⟩,⟨(-1866025403784438646813585298464),(-1866025403784438646710196150793)⟩⟩ +lemma a1_2_contains : a1_2.Contains (basisAlpha 1 2) := by + have he : alphaBox 1 2 = a1_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 1 2 +def b1_2 : CBox := ⟨⟨110042339640731077901928774709,110042339640731077978699816801⟩,⟨(-744016935856292431214912086815),(-744016935856292431133975618380)⟩⟩ +lemma b1_2_contains : b1_2.Contains (basisBeta 1 2) := by + have he : betaBox 1 2 = b1_2 := by decide +kernel + rw [← he] + exact betaBox_contains 1 2 +def a1_3 : CBox := ⟨⟨232050807568877293484086527880,232050807568877293569941772559⟩,⟨133974596215561353192996433472,133974596215561353283222117267⟩⟩ +lemma a1_3_contains : a1_3.Contains (basisAlpha 1 3) := by + have he : alphaBox 1 3 = a1_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 1 3 +def b1_3 : CBox := ⟨⟨110042339640731077904084656614,110042339640731077974187318175⟩,⟨255983064143707568788378779153,255983064143707568862733515650⟩⟩ +lemma b1_3_contains : b1_3.Contains (basisBeta 1 3) := by + have he : betaBox 1 3 = b1_3 := by decide +kernel + rw [← he] + exact betaBox_contains 1 3 +def a1_4 : CBox := ⟨⟨732050807568877293494743560103,732050807568877293558775086867⟩,⟨999999999999999999967311938286,1000000000000000000039200861018⟩⟩ +lemma a1_4_contains : a1_4.Contains (basisAlpha 1 4) := by + have he : alphaBox 1 4 = a1_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 1 4 +def b1_4 : CBox := ⟨⟨443375672974064411244522678096,443375672974064411300076194380⟩,⟨833333333333333333304589115696,833333333333333333366719344817⟩⟩ +lemma b1_4_contains : b1_4.Contains (basisBeta 1 4) := by + have he : betaBox 1 4 = b1_4 := by decide +kernel + rw [← he] + exact betaBox_contains 1 4 +def a1_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma a1_5_contains : a1_5.Contains (basisAlpha 1 5) := by + have he : alphaBox 1 5 = a1_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 1 5 +def b1_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma b1_5_contains : b1_5.Contains (basisBeta 1 5) := by + have he : betaBox 1 5 = b1_5 := by decide +kernel + rw [← he] + exact betaBox_contains 1 5 +def aRow1 : Fin 6 → CBox := ![a1_0,a1_1,a1_2,a1_3,a1_4,a1_5] +lemma aRow1_contains (j : Fin 6) : (aRow1 j).Contains (basisAlpha 1 j.val) := by + fin_cases j + · exact a1_0_contains + · exact a1_1_contains + · exact a1_2_contains + · exact a1_3_contains + · exact a1_4_contains + · exact a1_5_contains +def bRow1 : Fin 6 → CBox := ![b1_0,b1_1,b1_2,b1_3,b1_4,b1_5] +lemma bRow1_contains (j : Fin 6) : (bRow1 j).Contains (basisBeta 1 j.val) := by + fin_cases j + · exact b1_0_contains + · exact b1_1_contains + · exact b1_2_contains + · exact b1_3_contains + · exact b1_4_contains + · exact b1_5_contains +def a2_0 : CBox := ⟨⟨(-2000000000000000000141275204934),(-1999999999999999999869782460702)⟩,⟨(-129743478571),116486523947⟩⟩ +lemma a2_0_contains : a2_0.Contains (basisAlpha 2 0) := by + have he : alphaBox 2 0 = a2_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 2 0 +def b2_0 : CBox := ⟨⟨(-87204526845),82781460593⟩,⟨(-84172586257),73959704406⟩⟩ +lemma b2_0_contains : b2_0.Contains (basisBeta 2 0) := by + have he : betaBox 2 0 = b2_0 := by decide +kernel + rw [← he] + exact betaBox_contains 2 0 +def a2_1 : CBox := ⟨⟨(-125435175822),118800576441⟩,⟨(-119717716417),107049258927⟩⟩ +lemma a2_1_contains : a2_1.Contains (basisAlpha 2 1) := by + have he : alphaBox 2 1 = a2_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 2 1 +def b2_1 : CBox := ⟨⟨333333333333333333248768811341,333333333333333333414211966783⟩,⟨(-82501625898),72386826902⟩⟩ +lemma b2_1_contains : b2_1.Contains (basisBeta 2 1) := by + have he : betaBox 2 1 = b2_1 := by decide +kernel + rw [← he] + exact betaBox_contains 2 1 +def a2_2 : CBox := ⟨⟨1999999999999999999898600075218,2000000000000000000099188391653⟩,⟨(-96961970479),93131482739⟩⟩ +lemma a2_2_contains : a2_2.Contains (basisAlpha 2 2) := by + have he : alphaBox 2 2 = a2_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 2 2 +def b2_2 : CBox := ⟨⟨999999999999999999923447228355,1000000000000000000074341238520⟩,⟨(-74916377252),67747568172⟩⟩ +lemma b2_2_contains : b2_2.Contains (basisBeta 2 2) := by + have he : betaBox 2 2 = b2_2 := by decide +kernel + rw [← he] + exact betaBox_contains 2 2 +def a2_3 : CBox := ⟨⟨(-88236460900),86024927779⟩,⟨(-88338442857),75081488233⟩⟩ +lemma a2_3_contains : a2_3.Contains (basisAlpha 2 3) := by + have he : alphaBox 2 3 = a2_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 2 3 +def b2_3 : CBox := ⟨⟨(-69971039704),67759506583⟩,⟨(-70604613441),58722570919⟩⟩ +lemma b2_3_contains : b2_3.Contains (basisBeta 2 3) := by + have he : betaBox 2 3 = b2_3 := by decide +kernel + rw [← he] + exact betaBox_contains 2 3 +def a2_4 : CBox := ⟨⟨(-1000000000000000000066880394620),(-999999999999999999937542671626)⟩,⟨(-70273909211),52009472578⟩⟩ +lemma a2_4_contains : a2_4.Contains (basisAlpha 2 4) := by + have he : alphaBox 2 4 = a2_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 2 4 +def b2_4 : CBox := ⟨⟨(-666666666666666666722400328850),(-666666666666666666614618893021)⟩,⟨(-58561591010),43341227149⟩⟩ +lemma b2_4_contains : b2_4.Contains (basisBeta 2 4) := by + have he : betaBox 2 4 = b2_4 := by decide +kernel + rw [← he] + exact betaBox_contains 2 4 +def a2_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma a2_5_contains : a2_5.Contains (basisAlpha 2 5) := by + have he : alphaBox 2 5 = a2_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 2 5 +def b2_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma b2_5_contains : b2_5.Contains (basisBeta 2 5) := by + have he : betaBox 2 5 = b2_5 := by decide +kernel + rw [← he] + exact betaBox_contains 2 5 +def aRow2 : Fin 6 → CBox := ![a2_0,a2_1,a2_2,a2_3,a2_4,a2_5] +lemma aRow2_contains (j : Fin 6) : (aRow2 j).Contains (basisAlpha 2 j.val) := by + fin_cases j + · exact a2_0_contains + · exact a2_1_contains + · exact a2_2_contains + · exact a2_3_contains + · exact a2_4_contains + · exact a2_5_contains +def bRow2 : Fin 6 → CBox := ![b2_0,b2_1,b2_2,b2_3,b2_4,b2_5] +lemma bRow2_contains (j : Fin 6) : (bRow2 j).Contains (basisBeta 2 j.val) := by + fin_cases j + · exact b2_0_contains + · exact b2_1_contains + · exact b2_2_contains + · exact b2_3_contains + · exact b2_4_contains + · exact b2_5_contains +def a3_0 : CBox := ⟨⟨(-2500000000000000000101486582202),(-2499999999999999999899776324884)⟩,⟨(-866025403784438646865458496086),(-866025403784438646673967970795)⟩⟩ +lemma a3_0_contains : a3_0.Contains (basisAlpha 3 0) := by + have he : alphaBox 3 0 = a3_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 3 0 +def b3_0 : CBox := ⟨⟨(-511966128287415137698359169417),(-511966128287415137596966210758)⟩,⟨(-49143671478),45580546819⟩⟩ +lemma b3_0_contains : b3_0.Contains (basisBeta 3 0) := by + have he : betaBox 3 0 = b3_0 := by decide +kernel + rw [← he] + exact betaBox_contains 3 0 +def a3_1 : CBox := ⟨⟨(-767949192431122706553630753239),(-767949192431122706389988770571)⟩,⟨133974596215561353145648246772,133974596215561353319007066240⟩⟩ +lemma a3_1_contains : a3_1.Contains (basisAlpha 3 1) := by + have he : alphaBox 3 1 = a3_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 3 1 +def b3_1 : CBox := ⟨⟨(-223290993692602255440383197923),(-223290993692602255345334951706)⟩,⟨166666666666666666619374118999,166666666666666666711076386324⟩⟩ +lemma b3_1_contains : b3_1.Contains (basisBeta 3 1) := by + have he : betaBox 3 1 = b3_1 := by decide +kernel + rw [← he] + exact betaBox_contains 3 1 +def a3_2 : CBox := ⟨⟨232050807568877293460419172689,232050807568877293587797743707⟩,⟨1866025403784438646706073138142,1866025403784438646823295408305⟩⟩ +lemma a3_2_contains : a3_2.Contains (basisAlpha 3 2) := by + have he : alphaBox 3 2 = a3_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 3 2 +def b3_2 : CBox := ⟨⟨110042339640731077897633444053,110042339640731077980593886386⟩,⟨744016935856292431139515749456,744016935856292431212505833679⟩⟩ +lemma b3_2_contains : b3_2.Contains (basisBeta 3 2) := by + have he : betaBox 3 2 = b3_2 := by decide +kernel + rw [← he] + exact betaBox_contains 3 2 +def a3_3 : CBox := ⟨⟨232050807568877293505562439097,232050807568877293556794177625⟩,⟨(-133974596215561353256049960216),(-133974596215561353214581493329)⟩⟩ +lemma a3_3_contains : a3_3.Contains (basisAlpha 3 3) := by + have he : alphaBox 3 3 = a3_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 3 3 +def b3_3 : CBox := ⟨⟨110042339640731077920205077257,110042339640731077965092103345⟩,⟨(-255983064143707568841545799723),(-255983064143707568806432617138)⟩⟩ +lemma b3_3_contains : b3_3.Contains (basisBeta 3 3) := by + have he : betaBox 3 3 = b3_3 := by decide +kernel + rw [← he] + exact betaBox_contains 3 3 +def a3_4 : CBox := ⟨⟨732050807568877293505562439097,732050807568877293556794177625⟩,⟨(-1000000000000000000016049960216),(-999999999999999999984581493329)⟩⟩ +lemma a3_4_contains : a3_4.Contains (basisAlpha 3 4) := by + have he : alphaBox 3 4 = a3_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 3 4 +def b3_4 : CBox := ⟨⟨443375672974064411253538410591,443375672974064411298425436678⟩,⟨(-833333333333333333348212466389),(-833333333333333333319765950472)⟩⟩ +lemma b3_4_contains : b3_4.Contains (basisBeta 3 4) := by + have he : betaBox 3 4 = b3_4 := by decide +kernel + rw [← he] + exact betaBox_contains 3 4 +def a3_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma a3_5_contains : a3_5.Contains (basisAlpha 3 5) := by + have he : alphaBox 3 5 = a3_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 3 5 +def b3_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma b3_5_contains : b3_5.Contains (basisBeta 3 5) := by + have he : betaBox 3 5 = b3_5 := by decide +kernel + rw [← he] + exact betaBox_contains 3 5 +def aRow3 : Fin 6 → CBox := ![a3_0,a3_1,a3_2,a3_3,a3_4,a3_5] +lemma aRow3_contains (j : Fin 6) : (aRow3 j).Contains (basisAlpha 3 j.val) := by + fin_cases j + · exact a3_0_contains + · exact a3_1_contains + · exact a3_2_contains + · exact a3_3_contains + · exact a3_4_contains + · exact a3_5_contains +def bRow3 : Fin 6 → CBox := ![b3_0,b3_1,b3_2,b3_3,b3_4,b3_5] +lemma bRow3_contains (j : Fin 6) : (bRow3 j).Contains (basisBeta 3 j.val) := by + fin_cases j + · exact b3_0_contains + · exact b3_1_contains + · exact b3_2_contains + · exact b3_3_contains + · exact b3_4_contains + · exact b3_5_contains +def a4_0 : CBox := ⟨⟨(-2500000000000000000121818428037),(-2499999999999999999876652611556)⟩,⟨(-2598076211353315940405219613044),(-2598076211353315940185663132651)⟩⟩ +lemma a4_0_contains : a4_0.Contains (basisAlpha 4 0) := by + have he : alphaBox 4 0 = a4_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 4 0 +def b4_0 : CBox := ⟨⟨(-1000000000000000000066894928682),(-999999999999999999940249324168)⟩,⟨(-59517638106),54804404662⟩⟩ +lemma b4_0_contains : b4_0.Contains (basisBeta 4 0) := by + have he : betaBox 4 0 = b4_0 := by decide +kernel + rw [← he] + exact betaBox_contains 4 0 +def a4_1 : CBox := ⟨⟨(-1500000000000000000100504363592),(-1499999999999999999898985982939)⟩,⟨(-866025403784438646856588603416),(-866025403784438646673705645149)⟩⟩ +lemma a4_1_contains : a4_1.Contains (basisAlpha 4 1) := by + have he : alphaBox 4 1 = a4_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 4 1 +def b4_1 : CBox := ⟨⟨(-833333333333333333396675917941),(-833333333333333333277304886066)⟩,⟨288675134594812882198587530166,288675134594812882306797319245⟩⟩ +lemma b4_1_contains : b4_1.Contains (basisBeta 4 1) := by + have he : betaBox 4 1 = b4_1 := by decide +kernel + rw [← he] + exact betaBox_contains 4 1 +def a4_2 : CBox := ⟨⟨(-2500000000000000000063234604227),(-2499999999999999999951563554943)⟩,⟨866025403784438646710128961006,866025403784438646810738820671⟩⟩ +lemma a4_2_contains : a4_2.Contains (basisAlpha 4 2) := by + have he : alphaBox 4 2 = a4_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 4 2 +def b4_2 : CBox := ⟨⟨(-1166666666666666666717585998152),(-1166666666666666666628164076734)⟩,⟨866025403784438646720826718307,866025403784438646801612141185⟩⟩ +lemma b4_2_contains : b4_2.Contains (basisBeta 4 2) := by + have he : betaBox 4 2 = b4_2 := by decide +kernel + rw [← he] + exact betaBox_contains 4 2 +def a4_3 : CBox := ⟨⟨(-500000000000000000063234604227),(-499999999999999999951563554943)⟩,⟨866025403784438646710128961006,866025403784438646810738820671⟩⟩ +lemma a4_3_contains : a4_3.Contains (basisAlpha 4 3) := by + have he : alphaBox 4 3 = a4_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 4 3 +def b4_3 : CBox := ⟨⟨(-166666666666666666717585998152),(-166666666666666666628164076734)⟩,⟨866025403784438646720826718307,866025403784438646801612141185⟩⟩ +lemma b4_3_contains : b4_3.Contains (basisBeta 4 3) := by + have he : betaBox 4 3 = b4_3 := by decide +kernel + rw [← he] + exact betaBox_contains 4 3 +def a4_4 : CBox := ⟨⟨(-52577572004),37269759365⟩,⟨1732050807568877293484444465820,1732050807568877293566717564422⟩⟩ +lemma a4_4_contains : a4_4.Contains (basisAlpha 4 4) := by + have he : alphaBox 4 4 = a4_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 4 4 +def b4_4 : CBox := ⟨⟨166666666666666666622852023330,166666666666666666697724799471⟩,⟨1443375672974064411237037054850,1443375672974064411305597970352⟩⟩ +lemma b4_4_contains : b4_4.Contains (basisBeta 4 4) := by + have he : betaBox 4 4 = b4_4 := by decide +kernel + rw [← he] + exact betaBox_contains 4 4 +def a4_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma a4_5_contains : a4_5.Contains (basisAlpha 4 5) := by + have he : alphaBox 4 5 = a4_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 4 5 +def b4_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma b4_5_contains : b4_5.Contains (basisBeta 4 5) := by + have he : betaBox 4 5 = b4_5 := by decide +kernel + rw [← he] + exact betaBox_contains 4 5 +def aRow4 : Fin 6 → CBox := ![a4_0,a4_1,a4_2,a4_3,a4_4,a4_5] +lemma aRow4_contains (j : Fin 6) : (aRow4 j).Contains (basisAlpha 4 j.val) := by + fin_cases j + · exact a4_0_contains + · exact a4_1_contains + · exact a4_2_contains + · exact a4_3_contains + · exact a4_4_contains + · exact a4_5_contains +def bRow4 : Fin 6 → CBox := ![b4_0,b4_1,b4_2,b4_3,b4_4,b4_5] +lemma bRow4_contains (j : Fin 6) : (bRow4 j).Contains (basisBeta 4 j.val) := by + fin_cases j + · exact b4_0_contains + · exact b4_1_contains + · exact b4_2_contains + · exact b4_3_contains + · exact b4_4_contains + · exact b4_5_contains +def a5_0 : CBox := ⟨⟨1999999999999999999877635444654,2000000000000000000143138855047⟩,⟨(-6000000000000000000129653626530),(-5999999999999999999860633820774)⟩⟩ +lemma a5_0_contains : a5_0.Contains (basisAlpha 5 0) := by + have he : alphaBox 5 0 = a5_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 5 0 +def b5_0 : CBox := ⟨⟨333333333333333333281679955827,333333333333333333394612940415⟩,⟨(-3000000000000000000057347709804),(-2999999999999999999942362123009)⟩⟩ +lemma b5_0_contains : b5_0.Contains (basisBeta 5 0) := by + have he : betaBox 5 0 = b5_0 := by decide +kernel + rw [← he] + exact betaBox_contains 5 0 +def a5_1 : CBox := ⟨⟨1999999999999999999900418610809,2000000000000000000115053958316⟩,⟨(-4000000000000000000098166012570),(-3999999999999999999887698368482)⟩⟩ +lemma a5_1_contains : a5_1.Contains (basisAlpha 5 1) := by + have he : alphaBox 5 1 = a5_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 5 1 +def b5_1 : CBox := ⟨⟨333333333333333333285477150187,333333333333333333389932124293⟩,⟨(-2666666666666666666718766440810),(-2666666666666666666613539547627)⟩⟩ +lemma b5_1_contains : b5_1.Contains (basisBeta 5 1) := by + have he : betaBox 5 1 = b5_1 := by decide +kernel + rw [← he] + exact betaBox_contains 5 1 +def a5_2 : CBox := ⟨⟨(-37124060817),48173563696⟩,⟨(-4000000000000000000046156539992),(-3999999999999999999957972277693)⟩⟩ +lemma a5_2_contains : a5_2.Contains (basisAlpha 5 2) := by + have he : alphaBox 5 2 = a5_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 5 2 +def b5_2 : CBox := ⟨⟨(-333333333333333333360370407021),(-333333333333333333299028007247)⟩,⟨(-2666666666666666666701429949950),(-2666666666666666666636964184031)⟩⟩ +lemma b5_2_contains : b5_2.Contains (basisBeta 5 2) := by + have he : betaBox 5 2 = b5_2 := by decide +kernel + rw [← he] + exact betaBox_contains 5 2 +def a5_3 : CBox := ⟨⟨(-32812297007),39148566444⟩,⟨(-2000000000000000000039574808056),(-1999999999999999999964554009633)⟩⟩ +lemma a5_3_contains : a5_3.Contains (basisAlpha 5 3) := by + have he : alphaBox 5 3 = a5_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 5 3 +def b5_3 : CBox := ⟨⟨(-333333333333333333358214525116),(-333333333333333333303540505873)⟩,⟨(-1666666666666666666698139083982),(-1666666666666666666640255050001)⟩⟩ +lemma b5_3_contains : b5_3.Contains (basisBeta 5 3) := by + have he : betaBox 5 3 = b5_3 := by decide +kernel + rw [← he] + exact betaBox_contains 5 3 +def a5_4 : CBox := ⟨⟨(-1000000000000000000011456230727),(-999999999999999999984419032961)⟩,⟨(-2000000000000000000021510274410),(-1999999999999999999987626025288)⟩⟩ +lemma a5_4_contains : a5_4.Contains (basisAlpha 5 4) := by + have he : alphaBox 5 4 = a5_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 5 4 +def b5_4 : CBox := ⟨⟨(-1000000000000000000010643814262),(-999999999999999999985918905477)⟩,⟨(-1666666666666666666686096061551),(-1666666666666666666655636393771)⟩⟩ +lemma b5_4_contains : b5_4.Contains (basisBeta 5 4) := by + have he : betaBox 5 4 = b5_4 := by decide +kernel + rw [← he] + exact betaBox_contains 5 4 +def a5_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma a5_5_contains : a5_5.Contains (basisAlpha 5 5) := by + have he : alphaBox 5 5 = a5_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 5 5 +def b5_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma b5_5_contains : b5_5.Contains (basisBeta 5 5) := by + have he : betaBox 5 5 = b5_5 := by decide +kernel + rw [← he] + exact betaBox_contains 5 5 +def aRow5 : Fin 6 → CBox := ![a5_0,a5_1,a5_2,a5_3,a5_4,a5_5] +lemma aRow5_contains (j : Fin 6) : (aRow5 j).Contains (basisAlpha 5 j.val) := by + fin_cases j + · exact a5_0_contains + · exact a5_1_contains + · exact a5_2_contains + · exact a5_3_contains + · exact a5_4_contains + · exact a5_5_contains +def bRow5 : Fin 6 → CBox := ![b5_0,b5_1,b5_2,b5_3,b5_4,b5_5] +lemma bRow5_contains (j : Fin 6) : (bRow5 j).Contains (basisBeta 5 j.val) := by + fin_cases j + · exact b5_0_contains + · exact b5_1_contains + · exact b5_2_contains + · exact b5_3_contains + · exact b5_4_contains + · exact b5_5_contains +def a6_0 : CBox := ⟨⟨5499999999999999999950573124464,5500000000000000000049426875520⟩,⟨2598076211353315940219953156515,2598076211353315940388899777253⟩⟩ +lemma a6_0_contains : a6_0.Contains (basisAlpha 6 0) := by + have he : alphaBox 6 0 = a6_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 6 0 +def b6_0 : CBox := ⟨⟨2999999999999999999972565375633,3000000000000000000021992251165⟩,⟨2309401076758503058003309911586,2309401076758503058086116555293⟩⟩ +lemma b6_0_contains : b6_0.Contains (basisBeta 6 0) := by + have he : betaBox 6 0 = b6_0 := by decide +kernel + rw [← he] + exact betaBox_contains 6 0 +def a6_1 : CBox := ⟨⟨4499999999999999999964623050396,4500000000000000000027213389802⟩,⟨4330127018922193233775664814443,4330127018922193233888474885876⟩⟩ +lemma a6_1_contains : a6_1.Contains (basisAlpha 6 1) := by + have he : alphaBox 6 1 = a6_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 6 1 +def b6_1 : CBox := ⟨⟨2833333333333333333308240363289,2833333333333333333351623336878⟩,⟨2598076211353315940262595187908,2598076211353315940336045740063⟩⟩ +lemma b6_1_contains : b6_1.Contains (basisBeta 6 1) := by + have he : betaBox 6 1 = b6_1 := by decide +kernel + rw [← he] + exact betaBox_contains 6 1 +def a6_2 : CBox := ⟨⟨3499999999999999999964623050396,3500000000000000000027213389802⟩,⟨2598076211353315940255664814443,2598076211353315940348474885876⟩⟩ +lemma a6_2_contains : a6_2.Contains (basisAlpha 6 2) := by + have he : alphaBox 6 2 = a6_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 6 2 +def b6_2 : CBox := ⟨⟨2499999999999999999974907029956,2500000000000000000018290003544⟩,⟨2020725942163690175755928521242,2020725942163690175822712406729⟩⟩ +lemma b6_2_contains : b6_2.Contains (basisBeta 6 2) := by + have he : betaBox 6 2 = b6_2 := by decide +kernel + rw [← he] + exact betaBox_contains 6 2 +def a6_3 : CBox := ⟨⟨1499999999999999999977786514278,1500000000000000000014049925928⟩,⟨2598076211353315940264288342065,2598076211353315940330424891370⟩⟩ +lemma a6_3_contains : a6_3.Contains (basisAlpha 6 3) := by + have he : alphaBox 6 3 = a6_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 6 3 +def b6_3 : CBox := ⟨⟨1499999999999999999981488761897,1500000000000000000011708271607⟩,⟨2020725942163690175760240285053,2020725942163690175813687409476⟩⟩ +lemma b6_3_contains : b6_3.Contains (basisBeta 6 3) := by + have he : betaBox 6 3 = b6_3 := by decide +kernel + rw [← he] + exact betaBox_contains 6 3 +def a6_4 : CBox := ⟨⟨1999999999999999999977786514278,2000000000000000000014049925928⟩,⟨1732050807568877293504288342065,1732050807568877293560424891370⟩⟩ +lemma a6_4_contains : a6_4.Contains (basisAlpha 6 4) := by + have he : alphaBox 6 4 = a6_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 6 4 +def b6_4 : CBox := ⟨⟨1833333333333333333314822095231,1833333333333333333345041604940⟩,⟨1443375672974064411253573618387,1443375672974064411300354076142⟩⟩ +lemma b6_4_contains : b6_4.Contains (basisBeta 6 4) := by + have he : betaBox 6 4 = b6_4 := by decide +kernel + rw [← he] + exact betaBox_contains 6 4 +def a6_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma a6_5_contains : a6_5.Contains (basisAlpha 6 5) := by + have he : alphaBox 6 5 = a6_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 6 5 +def b6_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma b6_5_contains : b6_5.Contains (basisBeta 6 5) := by + have he : betaBox 6 5 = b6_5 := by decide +kernel + rw [← he] + exact betaBox_contains 6 5 +def aRow6 : Fin 6 → CBox := ![a6_0,a6_1,a6_2,a6_3,a6_4,a6_5] +lemma aRow6_contains (j : Fin 6) : (aRow6 j).Contains (basisAlpha 6 j.val) := by + fin_cases j + · exact a6_0_contains + · exact a6_1_contains + · exact a6_2_contains + · exact a6_3_contains + · exact a6_4_contains + · exact a6_5_contains +def bRow6 : Fin 6 → CBox := ![b6_0,b6_1,b6_2,b6_3,b6_4,b6_5] +lemma bRow6_contains (j : Fin 6) : (bRow6 j).Contains (basisBeta 6 j.val) := by + fin_cases j + · exact b6_0_contains + · exact b6_1_contains + · exact b6_2_contains + · exact b6_3_contains + · exact b6_4_contains + · exact b6_5_contains +def a7_0 : CBox := ⟨⟨(-2500000000000000000188127804075),(-2499999999999999999818506795302)⟩,⟨866025403784438646567088470640,866025403784438646939490805340⟩⟩ +lemma a7_0_contains : a7_0.Contains (basisAlpha 7 0) := by + have he : alphaBox 7 0 = a7_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 7 0 +def b7_0 : CBox := ⟨⟨(-2821367205045918195798978576537),(-2821367205045918195573646581217)⟩,⟨(-124730856205),103138732310⟩⟩ +lemma b7_0_contains : b7_0.Contains (basisBeta 7 0) := by + have he : betaBox 7 0 = b7_0 := by decide +kernel + rw [← he] + exact betaBox_contains 7 0 +def a7_1 : CBox := ⟨⟨(-4232050807568877293687926838870),(-4232050807568877293381652874355)⟩,⟨1866025403784438646599525109016,1866025403784438646901953080128⟩⟩ +lemma a7_1_contains : a7_1.Contains (basisAlpha 7 1) := by + have he : alphaBox 7 1 = a7_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 7 1 +def b7_1 : CBox := ⟨⟨(-3110042339640731078048945082336),(-3110042339640731077834170927726)⟩,⟨166666666666666666547341916858,166666666666666666763549111441⟩⟩ +lemma b7_1_contains : b7_1.Contains (basisBeta 7 1) := by + have he : betaBox 7 1 = b7_1 := by decide +kernel + rw [← he] + exact betaBox_contains 7 1 +def a7_2 : CBox := ⟨⟨(-3232050807568877293670726216459),(-3232050807568877293391709243913)⟩,⟨133974596215561353081318990758,133974596215561353364283934696⟩⟩ +lemma a7_2_contains : a7_2.Contains (basisAlpha 7 2) := by + have he : alphaBox 7 2 = a7_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 7 2 +def b7_2 : CBox := ⟨⟨(-2776709006307397744709878208199),(-2776709006307397744504189717579)⟩,⟨(-410683602522959097958726789228),(-410683602522959097749007270370)⟩⟩ +lemma b7_2_contains : b7_2.Contains (basisBeta 7 2) := by + have he : betaBox 7 2 = b7_2 := by decide +kernel + rw [← he] + exact betaBox_contains 7 2 +def a7_3 : CBox := ⟨⟨(-3232050807568877293625582950051),(-3232050807568877293422712809995)⟩,⟨(-1866025403784438646880804107600),(-1866025403784438646673592966938)⟩⟩ +lemma a7_3_contains : a7_3.Contains (basisAlpha 7 3) := by + have he : alphaBox 7 3 = a7_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 7 3 +def b7_3 : CBox := ⟨⟨(-2776709006307397744687306574995),(-2776709006307397744519691500620)⟩,⟨(-1410683602522959097939788338407),(-1410683602522959097767945721187)⟩⟩ +lemma b7_3_contains : b7_3.Contains (basisBeta 7 3) := by + have he : betaBox 7 3 = b7_3 := by decide +kernel + rw [← he] + exact betaBox_contains 7 3 +def a7_4 : CBox := ⟨⟨(-2732050807568877293614925917828),(-2732050807568877293433879495687)⟩,⟨(-1000000000000000000106488602786),(-999999999999999999917614223187)⟩⟩ +lemma a7_4_contains : a7_4.Contains (basisAlpha 7 4) := by + have he : alphaBox 7 4 = a7_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 7 4 +def b7_4 : CBox := ⟨⟨(-2443375672974064411346868553513),(-2443375672974064411193802624415)⟩,⟨(-833333333333333333423578001864),(-833333333333333333263959892020)⟩⟩ +lemma b7_4_contains : b7_4.Contains (basisBeta 7 4) := by + have he : betaBox 7 4 = b7_4 := by decide +kernel + rw [← he] + exact betaBox_contains 7 4 +def a7_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma a7_5_contains : a7_5.Contains (basisAlpha 7 5) := by + have he : alphaBox 7 5 = a7_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 7 5 +def b7_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma b7_5_contains : b7_5.Contains (basisBeta 7 5) := by + have he : betaBox 7 5 = b7_5 := by decide +kernel + rw [← he] + exact betaBox_contains 7 5 +def aRow7 : Fin 6 → CBox := ![a7_0,a7_1,a7_2,a7_3,a7_4,a7_5] +lemma aRow7_contains (j : Fin 6) : (aRow7 j).Contains (basisAlpha 7 j.val) := by + fin_cases j + · exact a7_0_contains + · exact a7_1_contains + · exact a7_2_contains + · exact a7_3_contains + · exact a7_4_contains + · exact a7_5_contains +def bRow7 : Fin 6 → CBox := ![b7_0,b7_1,b7_2,b7_3,b7_4,b7_5] +lemma bRow7_contains (j : Fin 6) : (bRow7 j).Contains (basisBeta 7 j.val) := by + fin_cases j + · exact b7_0_contains + · exact b7_1_contains + · exact b7_2_contains + · exact b7_3_contains + · exact b7_4_contains + · exact b7_5_contains +def a8_0 : CBox := ⟨⟨1999999999999999999892284365332,2000000000000000000114350234042⟩,⟨(-90867123064),105889569091⟩⟩ +lemma a8_0_contains : a8_0.Contains (basisAlpha 8 0) := by + have he : alphaBox 8 0 = a8_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 8 0 +def b8_0 : CBox := ⟨⟨1999999999999999999954288696048,2000000000000000000050134370203⟩,⟨(-37247929117),46674396000⟩⟩ +lemma b8_0_contains : b8_0.Contains (basisBeta 8 0) := by + have he : betaBox 8 0 = b8_0 := by decide +kernel + rw [← he] + exact betaBox_contains 8 0 +def a8_1 : CBox := ⟨⟨(-65003502108),67215035233⟩,⟨(-54738055772),59745537781⟩⟩ +lemma a8_1_contains : a8_1.Contains (basisAlpha 8 1) := by + have he : alphaBox 8 1 = a8_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 8 1 +def b8_1 : CBox := ⟨⟨1666666666666666666628074051475,1666666666666666666708945170401⟩,⟨(-31226417901),38983724115⟩⟩ +lemma b8_1_contains : b8_1.Contains (basisBeta 8 1) := by + have he : betaBox 8 1 = b8_1 := by decide +kernel + rw [← he] + exact betaBox_contains 8 1 +def a8_2 : CBox := ⟨⟨1999999999999999999959031748932,2000000000000000000047602850445⟩,⟨(-31982309834),45827761593⟩⟩ +lemma a8_2_contains : a8_2.Contains (basisAlpha 8 2) := by + have he : alphaBox 8 2 = a8_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 8 2 +def b8_2 : CBox := ⟨⟨2333333333333333333302752468489,2333333333333333333369074442138⟩,⟨(-23641169255),34344465385⟩⟩ +lemma b8_2_contains : b8_2.Contains (basisBeta 8 2) := by + have he : betaBox 8 2 = b8_2 := by decide +kernel + rw [← he] + exact betaBox_contains 8 2 +def a8_3 : CBox := ⟨⟨3999999999999999999959031748932,4000000000000000000047602850445⟩,⟨(-31982309834),45827761593⟩⟩ +lemma a8_3_contains : a8_3.Contains (basisAlpha 8 3) := by + have he : alphaBox 8 3 = a8_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 8 3 +def b8_3 : CBox := ⟨⟨3333333333333333333302752468489,3333333333333333333369074442138⟩,⟨(-23641169255),34344465385⟩⟩ +lemma b8_3_contains : b8_3.Contains (basisBeta 8 3) := by + have he : betaBox 8 3 = b8_3 := by decide +kernel + rw [← he] + exact betaBox_contains 8 3 +def a8_4 : CBox := ⟨⟨2999999999999999999980387815212,3000000000000000000024035251040⟩,⟨(-13917776188),22755745938⟩⟩ +lemma a8_4_contains : a8_4.Contains (basisAlpha 8 4) := by + have he : alphaBox 8 4 = a8_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 8 4 +def b8_4 : CBox := ⟨⟨2666666666666666666650323179343,2666666666666666666686696042534⟩,⟨(-11598146824),18963121615⟩⟩ +lemma b8_4_contains : b8_4.Contains (basisBeta 8 4) := by + have he : betaBox 8 4 = b8_4 := by decide +kernel + rw [← he] + exact betaBox_contains 8 4 +def a8_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma a8_5_contains : a8_5.Contains (basisAlpha 8 5) := by + have he : alphaBox 8 5 = a8_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 8 5 +def b8_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma b8_5_contains : b8_5.Contains (basisBeta 8 5) := by + have he : betaBox 8 5 = b8_5 := by decide +kernel + rw [← he] + exact betaBox_contains 8 5 +def aRow8 : Fin 6 → CBox := ![a8_0,a8_1,a8_2,a8_3,a8_4,a8_5] +lemma aRow8_contains (j : Fin 6) : (aRow8 j).Contains (basisAlpha 8 j.val) := by + fin_cases j + · exact a8_0_contains + · exact a8_1_contains + · exact a8_2_contains + · exact a8_3_contains + · exact a8_4_contains + · exact a8_5_contains +def bRow8 : Fin 6 → CBox := ![b8_0,b8_1,b8_2,b8_3,b8_4,b8_5] +lemma bRow8_contains (j : Fin 6) : (bRow8 j).Contains (basisBeta 8 j.val) := by + fin_cases j + · exact b8_0_contains + · exact b8_1_contains + · exact b8_2_contains + · exact b8_3_contains + · exact b8_4_contains + · exact b8_5_contains +def a9_0 : CBox := ⟨⟨(-2500000000000000000155691406154),(-2499999999999999999845571500932)⟩,⟨(-866025403784438646919853613556),(-866025403784438646619572853325)⟩⟩ +lemma a9_0_contains : a9_0.Contains (basisAlpha 9 0) := by + have he : alphaBox 9 0 = a9_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 9 0 +def b9_0 : CBox := ⟨⟨(-2821367205045918195765461581390),(-2821367205045918195609863798778)⟩,⟨(-81783603407),67335732360⟩⟩ +lemma b9_0_contains : b9_0.Contains (basisBeta 9 0) := by + have he : betaBox 9 0 = b9_0 := by decide +kernel + rw [← he] + exact betaBox_contains 9 0 +def a9_1 : CBox := ⟨⟨(-4232050807568877293620317413911),(-4232050807568877293433875643005)⟩,⟨(-1866025403784438646874065286900),(-1866025403784438646677606519662)⟩⟩ +lemma a9_1_contains : a9_1.Contains (basisAlpha 9 1) := by + have he : alphaBox 9 1 = a9_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 9 1 +def b9_1 : CBox := ⟨⟨(-3110042339640731078009565916016),(-3110042339640731077874581155791)⟩,⟨(-166666666666666666740818882297),(-166666666666666666609003212030)⟩⟩ +lemma b9_1_contains : b9_1.Contains (basisBeta 9 1) := by + have he : betaBox 9 1 = b9_1 := by decide +kernel + rw [← he] + exact betaBox_contains 9 1 +def a9_2 : CBox := ⟨⟨(-3232050807568877293606267487983),(-3232050807568877293456089128727)⟩,⟨(-133974596215561353313640395530),(-133974596215561353173318177597)⟩⟩ +lemma a9_2_contains : a9_2.Contains (basisAlpha 9 2) := by + have he : alphaBox 9 2 = a9_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 9 2 +def b9_2 : CBox := ⟨⟨(-2776709006307397744671549274040),(-2776709006307397744548652317699)⟩,⟨410683602522959097779322748160,410683602522959097892426235325⟩⟩ +lemma b9_2_contains : b9_2.Contains (basisBeta 9 2) := by + have he : betaBox 9 2 = b9_2 := by decide +kernel + rw [← he] + exact betaBox_contains 9 2 +def a9_3 : CBox := ⟨⟨(-3232050807568877293601955724173),(-3232050807568877293465114125979)⟩,⟨1866025403784438646692941336406,1866025403784438646820100090463⟩⟩ +lemma a9_3_contains : a9_3.Contains (basisAlpha 9 3) := by + have he : alphaBox 9 3 = a9_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 9 3 +def b9_3 : CBox := ⟨⟨(-2776709006307397744669393392135),(-2776709006307397744553164816325)⟩,⟨1410683602522959097782613614128,1410683602522959097889135369355⟩⟩ +lemma b9_3_contains : b9_3.Contains (basisBeta 9 3) := by + have he : betaBox 9 3 = b9_3 := by decide +kernel + rw [← he] + exact betaBox_contains 9 3 +def a9_4 : CBox := ⟨⟨(-2732050807568877293601955724173),(-2732050807568877293465114125979)⟩,⟨999999999999999999932941336406,1000000000000000000050100090463⟩⟩ +lemma a9_4_contains : a9_4.Contains (basisAlpha 9 4) := by + have he : alphaBox 9 4 = a9_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 9 4 +def b9_4 : CBox := ⟨⟨(-2443375672974064411336060058801),(-2443375672974064411219831482992)⟩,⟨833333333333333333275946947462,833333333333333333375802036021⟩⟩ +lemma b9_4_contains : b9_4.Contains (basisBeta 9 4) := by + have he : betaBox 9 4 = b9_4 := by decide +kernel + rw [← he] + exact betaBox_contains 9 4 +def a9_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma a9_5_contains : a9_5.Contains (basisAlpha 9 5) := by + have he : alphaBox 9 5 = a9_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 9 5 +def b9_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma b9_5_contains : b9_5.Contains (basisBeta 9 5) := by + have he : betaBox 9 5 = b9_5 := by decide +kernel + rw [← he] + exact betaBox_contains 9 5 +def aRow9 : Fin 6 → CBox := ![a9_0,a9_1,a9_2,a9_3,a9_4,a9_5] +lemma aRow9_contains (j : Fin 6) : (aRow9 j).Contains (basisAlpha 9 j.val) := by + fin_cases j + · exact a9_0_contains + · exact a9_1_contains + · exact a9_2_contains + · exact a9_3_contains + · exact a9_4_contains + · exact a9_5_contains +def bRow9 : Fin 6 → CBox := ![b9_0,b9_1,b9_2,b9_3,b9_4,b9_5] +lemma bRow9_contains (j : Fin 6) : (bRow9 j).Contains (basisBeta 9 j.val) := by + fin_cases j + · exact b9_0_contains + · exact b9_1_contains + · exact b9_2_contains + · exact b9_3_contains + · exact b9_4_contains + · exact b9_5_contains +def a10_0 : CBox := ⟨⟨5499999999999999999859593080110,5500000000000000000154185772113⟩,⟨(-2598076211353315940415816567902),(-2598076211353315940146786777146)⟩⟩ +lemma a10_0_contains : a10_0.Contains (basisAlpha 10 0) := by + have he : alphaBox 10 0 = a10_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 10 0 +def b10_0 : CBox := ⟨⟨2999999999999999999953966636345,3000000000000000000055898803099⟩,⟨(-2309401076758503058078900713958),(-2309401076758503057989315326372)⟩⟩ +lemma b10_0_contains : b10_0.Contains (basisBeta 10 0) := by + have he : betaBox 10 0 = b10_0 := by decide +kernel + rw [← he] + exact betaBox_contains 10 0 +def a10_1 : CBox := ⟨⟨4499999999999999999928853374972,4500000000000000000094108343981⟩,⟨(-4330127018922193233887325742290),(-4330127018922193233740579333323)⟩⟩ +lemma a10_1_contains : a10_1.Contains (basisAlpha 10 1) := by + have he : alphaBox 10 1 = a10_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 10 1 +def b10_1 : CBox := ⟨⟨2833333333333333333298843352156,2833333333333333333379219231743⟩,⟨(-2598076211353315940324152243022),(-2598076211353315940254947419069)⟩⟩ +lemma b10_1_contains : b10_1.Contains (basisBeta 10 1) := by + have he : betaBox 10 1 = b10_1 := by decide +kernel + rw [← he] + exact betaBox_contains 10 1 +def a10_2 : CBox := ⟨⟨3499999999999999999966123134337,3500000000000000000041530771977⟩,⟨(-2598076211353315940320608177868),(-2598076211353315940256134867503)⟩⟩ +lemma a10_2_contains : a10_2.Contains (basisAlpha 10 2) := by + have he : alphaBox 10 2 = a10_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 10 2 +def b10_2 : CBox := ⟨⟨2499999999999999999977933271945,2500000000000000000028360041075⟩,⟨(-2020725942163690175801913054881),(-2020725942163690175760132597129)⟩⟩ +lemma b10_2_contains : b10_2.Contains (basisBeta 10 2) := by + have he : betaBox 10 2 = b10_2 := by decide +kernel + rw [← he] + exact betaBox_contains 10 2 +def a10_3 : CBox := ⟨⟨1499999999999999999979286598219,1500000000000000000028367308103⟩,⟨(-2598076211353315940311984650246),(-2598076211353315940274184862009)⟩⟩ +lemma a10_3_contains : a10_3.Contains (basisAlpha 10 3) := by + have he : alphaBox 10 3 = a10_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 10 3 +def b10_3 : CBox := ⟨⟨1499999999999999999984515003886,1500000000000000000021778309138⟩,⟨(-2020725942163690175797601291070),(-2020725942163690175769157594382)⟩⟩ +lemma b10_3_contains : b10_3.Contains (basisBeta 10 3) := by + have he : betaBox 10 3 = b10_3 := by decide +kernel + rw [← he] + exact betaBox_contains 10 3 +def a10_4 : CBox := ⟨⟨1999999999999999999989943630442,2000000000000000000017200622411⟩,⟨(-1732050807568877293537669145432),(-1732050807568877293518206118258)⟩⟩ +lemma a10_4_contains : a10_4.Contains (basisAlpha 10 4) := by + have he : alphaBox 10 4 = a10_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 10 4 +def b10_4 : CBox := ⟨⟨1833333333333333333324953025368,1833333333333333333347667185343⟩,⟨(-1443375672974064411281390954527),(-1443375672974064411265171765215)⟩⟩ +lemma b10_4_contains : b10_4.Contains (basisBeta 10 4) := by + have he : betaBox 10 4 = b10_4 := by decide +kernel + rw [← he] + exact betaBox_contains 10 4 +def a10_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma a10_5_contains : a10_5.Contains (basisAlpha 10 5) := by + have he : alphaBox 10 5 = a10_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 10 5 +def b10_5 : CBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩ +lemma b10_5_contains : b10_5.Contains (basisBeta 10 5) := by + have he : betaBox 10 5 = b10_5 := by decide +kernel + rw [← he] + exact betaBox_contains 10 5 +def aRow10 : Fin 6 → CBox := ![a10_0,a10_1,a10_2,a10_3,a10_4,a10_5] +lemma aRow10_contains (j : Fin 6) : (aRow10 j).Contains (basisAlpha 10 j.val) := by + fin_cases j + · exact a10_0_contains + · exact a10_1_contains + · exact a10_2_contains + · exact a10_3_contains + · exact a10_4_contains + · exact a10_5_contains +def bRow10 : Fin 6 → CBox := ![b10_0,b10_1,b10_2,b10_3,b10_4,b10_5] +lemma bRow10_contains (j : Fin 6) : (bRow10 j).Contains (basisBeta 10 j.val) := by + fin_cases j + · exact b10_0_contains + · exact b10_1_contains + · exact b10_2_contains + · exact b10_3_contains + · exact b10_4_contains + · exact b10_5_contains +def a11_0 : CBox := ⟨⟨1999999999999999999734706905414,2000000000000000000229508592982⟩,⟨5999999999999999999764691170066,6000000000000000000262713647619⟩⟩ +lemma a11_0_contains : a11_0.Contains (basisAlpha 11 0) := by + have he : alphaBox 11 0 = a11_0 := by decide +kernel + rw [← he] + exact alphaBox_contains 11 0 +def b11_0 : CBox := ⟨⟨333333333333333333221864948463,333333333333333333426933209970⟩,⟨2999999999999999999901084452052,3000000000000000000108051847632⟩⟩ +lemma b11_0_contains : b11_0.Contains (basisBeta 11 0) := by + have he : betaBox 11 0 = b11_0 := by decide +kernel + rw [← he] + exact betaBox_contains 11 0 +def a11_1 : CBox := ⟨⟨1999999999999999999826012483275,2000000000000000000152931212580⟩,⟨3999999999999999999850248446211,4000000000000000000172733305229⟩⟩ +lemma a11_1_contains : a11_1.Contains (basisAlpha 11 1) := by + have he : alphaBox 11 1 = a11_1 := by decide +kernel + rw [← he] + exact alphaBox_contains 11 1 +def b11_1 : CBox := ⟨⟨333333333333333333237082544774,333333333333333333414170313236⟩,⟨2666666666666666666582010664743,2666666666666666666759721790567⟩⟩ +lemma b11_1_contains : b11_1.Contains (basisBeta 11 1) := by + have he : betaBox 11 1 = b11_1 := by decide +kernel + rw [← he] + exact betaBox_contains 11 1 +def a11_2 : CBox := ⟨⟨(-111530188351),86050817960⟩,⟨3999999999999999999902257918789,4000000000000000000102459396018⟩⟩ +lemma a11_2_contains : a11_2.Contains (basisAlpha 11 2) := by + have he : alphaBox 11 2 = a11_2 := by decide +kernel + rw [← he] + exact alphaBox_contains 11 2 +def b11_2 : CBox := ⟨⟨(-333333333333333333408765012434),(-333333333333333333274789818304)⟩,⟨2666666666666666666599347155603,2666666666666666666736297154163⟩⟩ +lemma b11_2_contains : b11_2.Contains (basisBeta 11 2) := by + have he : betaBox 11 2 = b11_2 := by decide +kernel + rw [← he] + exact betaBox_contains 11 2 +def a11_3 : CBox := ⟨⟨(-66386921943),55047251878⟩,⟨1999999999999999999940134820431,2000000000000000000064582494384⟩⟩ +lemma a11_3_contains : a11_3.Contains (basisAlpha 11 3) := by + have he : alphaBox 11 3 = a11_3 := by decide +kernel + rw [← he] + exact alphaBox_contains 11 3 +def b11_3 : CBox := ⟨⟨(-333333333333333333386193379230),(-333333333333333333290291601345)⟩,⟨1666666666666666666618285606424,1666666666666666666717358703346⟩⟩ +lemma b11_3_contains : b11_3.Contains (basisBeta 11 3) := by + have he : betaBox 11 3 = b11_3 := by decide +kernel + rw [← he] + exact betaBox_contains 11 3 +def a11_4 : CBox := ⟨⟨(-1000000000000000000045030855663),(-999999999999999999968520347527)⟩,⟨1999999999999999999958199354077,2000000000000000000041510478729⟩⟩ +lemma a11_4_contains : a11_4.Contains (basisAlpha 11 4) := by + have he : alphaBox 11 4 = a11_4 := by decide +kernel + rw [← he] + exact alphaBox_contains 11 4 +def b11_4 : CBox := ⟨⟨(-1000000000000000000038622668376),(-999999999999999999972670000949)⟩,⟨1666666666666666666630328628855,1666666666666666666701977359576⟩⟩ +lemma b11_4_contains : b11_4.Contains (basisBeta 11 4) := by + have he : betaBox 11 4 = b11_4 := by decide +kernel + rw [← he] + exact betaBox_contains 11 4 +def a11_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma a11_5_contains : a11_5.Contains (basisAlpha 11 5) := by + have he : alphaBox 11 5 = a11_5 := by decide +kernel + rw [← he] + exact alphaBox_contains 11 5 +def b11_5 : CBox := ⟨⟨(-1000000000000000000006581731937),(-999999999999999999993418268059)⟩,⟨(-9024997253),4311763811⟩⟩ +lemma b11_5_contains : b11_5.Contains (basisBeta 11 5) := by + have he : betaBox 11 5 = b11_5 := by decide +kernel + rw [← he] + exact betaBox_contains 11 5 +def aRow11 : Fin 6 → CBox := ![a11_0,a11_1,a11_2,a11_3,a11_4,a11_5] +lemma aRow11_contains (j : Fin 6) : (aRow11 j).Contains (basisAlpha 11 j.val) := by + fin_cases j + · exact a11_0_contains + · exact a11_1_contains + · exact a11_2_contains + · exact a11_3_contains + · exact a11_4_contains + · exact a11_5_contains +def bRow11 : Fin 6 → CBox := ![b11_0,b11_1,b11_2,b11_3,b11_4,b11_5] +lemma bRow11_contains (j : Fin 6) : (bRow11 j).Contains (basisBeta 11 j.val) := by + fin_cases j + · exact b11_0_contains + · exact b11_1_contains + · exact b11_2_contains + · exact b11_3_contains + · exact b11_4_contains + · exact b11_5_contains +def aTable : Fin 12 → Fin 6 → CBox := ![aRow0,aRow1,aRow2,aRow3,aRow4,aRow5,aRow6,aRow7,aRow8,aRow9,aRow10,aRow11] +lemma aTable_contains (n : Fin 12) (j : Fin 6) : (aTable n j).Contains (basisAlpha n.val j.val) := by + fin_cases n + · exact aRow0_contains j + · exact aRow1_contains j + · exact aRow2_contains j + · exact aRow3_contains j + · exact aRow4_contains j + · exact aRow5_contains j + · exact aRow6_contains j + · exact aRow7_contains j + · exact aRow8_contains j + · exact aRow9_contains j + · exact aRow10_contains j + · exact aRow11_contains j +def aLookup (n : ℕ) (j : Fin 6) : CBox := aTable ⟨n%12,by omega⟩ j +lemma aLookup_contains (n : ℕ) (j : Fin 6) : (aLookup n j).Contains (basisAlpha n j.val) := by + simpa only [aLookup,basisAlpha_mod] using aTable_contains ⟨n%12,by omega⟩ j +def bTable : Fin 12 → Fin 6 → CBox := ![bRow0,bRow1,bRow2,bRow3,bRow4,bRow5,bRow6,bRow7,bRow8,bRow9,bRow10,bRow11] +lemma bTable_contains (n : Fin 12) (j : Fin 6) : (bTable n j).Contains (basisBeta n.val j.val) := by + fin_cases n + · exact bRow0_contains j + · exact bRow1_contains j + · exact bRow2_contains j + · exact bRow3_contains j + · exact bRow4_contains j + · exact bRow5_contains j + · exact bRow6_contains j + · exact bRow7_contains j + · exact bRow8_contains j + · exact bRow9_contains j + · exact bRow10_contains j + · exact bRow11_contains j +def bLookup (n : ℕ) (j : Fin 6) : CBox := bTable ⟨n%12,by omega⟩ j +lemma bLookup_contains (n : ℕ) (j : Fin 6) : (bLookup n j).Contains (basisBeta n j.val) := by + simpa only [bLookup,basisBeta_mod] using bTable_contains ⟨n%12,by omega⟩ j +end SharpPlanar.IntegerAlpha + +namespace SharpPlanar.IntegerBasis +open IntegerIntervals + +def weightedColumnBox (p : PointBox) (w : RBox) (a b : CBox) (n : ℕ) (d : Bool) : CBox := + (rcast w).mul (basisFunctionBox p a b n d) +def momentKernelBox (p : PointBox) (m : ℕ) (e : Bool) : CBox := + if e then (kernel0Box p m).mul (piI.mul p.z) else kernel0Box p m + +def cachedMomentRuleBox (c k : Fin 6 → Fin 16 → Fin 16 → CBox) : CBox := + finSum fun j => (finSum (fun i => finSum (fun v => (c j i v).mul (k j i v)))).scale 1 6 + +lemma weightedColumnBox_contains {p : PointBox} {t w : ℝ} {wb : RBox} (hp : p.Contains t) + (hw : wb.Contains w) {a b : CBox} {n j : ℕ} (ha : a.Contains (basisAlpha n j)) + (hb : b.Contains (basisBeta n j)) (hn : n < 128) (d : Bool) : + (weightedColumnBox p wb a b n d).Contains ((w:ℂ)*basisFunction d n j t) := + CBox.contains_mul (rcast_contains hw) (basisFunctionBox_contains hp ha hb hn d) +lemma momentKernelBox_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) {m : ℕ} + (hm : m < 128) (e : Bool) : + (momentKernelBox p m e).Contains (lambda t*Complex.exp (Complex.I*Real.pi*z t*m)* + (if e then Complex.I*Real.pi*z t else 1)) := by + cases e + · simpa only [momentKernelBox,Bool.false_eq_true,ite_false,mul_one] using kernel0Box_contains hp hm + · simpa only [momentKernelBox,ite_true,pointZ_eq] using + CBox.contains_mul (kernel0Box_contains hp hm) (CBox.contains_mul piI_contains hp.2.2.1) + +lemma cachedMomentRuleBox_contains + {c k : Fin 6 → Fin 16 → Fin 16 → CBox} {t : ℕ → ℕ → ℝ} {w : ℕ → ℝ} + {n m : ℕ} {d e : Bool} + (hc : ∀ j i v, (c j i v).Contains ((w (16*i.val+v.val):ℂ)* + basisFunction d n j.val (t j.val (16*i.val+v.val)))) + (hk : ∀ j i v, (k j i v).Contains + (lambda (t j.val (16*i.val+v.val))*Complex.exp (Complex.I*Real.pi*z (t j.val (16*i.val+v.val))*m)* + (if e then Complex.I*Real.pi*z (t j.val (16*i.val+v.val)) else 1))) : + (cachedMomentRuleBox c k).Contains (momentRuleValue t w n m d e) := by + unfold cachedMomentRuleBox momentRuleValue + apply finSum_contains + intro j + rw [← sum_fin_square 16 (fun v => (w v:ℂ)*basisMoment d e n j.val m (t j.val v))] + have hh := finSum_contains (fun i => finSum_contains (fun v => CBox.contains_mul (hc j i v) (hk j i v))) + have hs := CBox.contains_scale hh 1 6 (by norm_num) + simpa only [Int.cast_one,Int.cast_ofNat,basisMoment,mul_assoc] using hs + +end SharpPlanar.IntegerBasis + +namespace SharpPlanar +open IntegerIntervals IntegerBasis IntegerAlpha IntegerCompact + +lemma complexU_ofReal (n j : ℕ) (t : ℝ) : complexU n j t = u n j t := rfl +lemma complexV_ofReal (n j : ℕ) (t : ℝ) : complexV n j t = v n j t := rfl +lemma complexLambda_ofReal (t : ℝ) : complexLambda t = lambda t := rfl +lemma complexZ_ofReal (t : ℝ) : complexZ t = z t := rfl +lemma complexBasisMoment_ofReal (d e : Bool) (n j m : ℕ) (t : ℝ) : + complexBasisMoment d e n j m t = basisMoment d e n j m t := by + unfold complexBasisMoment complexBasis basisMoment basisFunction complexTransformedFactor + rw [complexU_ofReal,complexV_ofReal,complexLambda_ofReal,complexZ_ofReal] + cases d <;> cases e <;> simp <;> ring + + +end SharpPlanar + +namespace SharpPlanar.IntegerBasis +open IntegerIntervals + +lemma exp_direct_step {p q : CBox} {t : ℝ} {n : ℕ} + (hp : p.Contains (Complex.exp (-Complex.I*Real.pi*t*n))) + (hq : q.Contains (Complex.exp (-Complex.I*Real.pi*t))) : + (p.mul q).Contains (Complex.exp (-Complex.I*Real.pi*t*(n+1))) := by + have hh := CBox.contains_mul hp hq + rw [← Complex.exp_add] at hh + convert hh using 1 + congr 1 + ring +lemma exp_transformed_step {p q : CBox} {t : ℝ} {n : ℕ} + (hp : p.Contains (Complex.exp (Complex.I*Real.pi*z t*n))) + (hq : q.Contains (Complex.exp (Complex.I*Real.pi*z t))) : + (p.mul q).Contains (Complex.exp (Complex.I*Real.pi*z t*(n+1))) := by + have hh := CBox.contains_mul hp hq + rw [← Complex.exp_add] at hh + convert hh using 1 + congr 1 + ring + +def transformedStepBox (p : PointBox) : CBox := p.quarter.powFast 3 4 +lemma transformedStepBox_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) : + (transformedStepBox p).Contains (Complex.exp (Complex.I*Real.pi*z t)) := by + have hh := CBox.contains_powFast hp.2.2.2.2 3 4 (by norm_num) + rw [← Complex.exp_nat_mul] at hh + change (p.quarter.powFast 3 4).Contains _ + convert hh using 1 + rw [pointZ_eq] + congr 1 + push_cast + ring + +noncomputable def waveAmplitude (d : Bool) (n j : ℕ) (t : ℝ) : ℂ := + if d then 2*Complex.I*Real.pi*basisAlpha n j + else -2*(Real.pi:ℂ)^2*(basisBeta n j-(t:ℂ)*basisAlpha n j) +def waveAmplitudeBox (p : PointBox) (a b : CBox) (d : Bool) : CBox := + if d then (piI.scale 2 1).mul a + else (((rcast piBounds).mul (rcast piBounds)).scale (-2) 1).mul + (b.add ((rcast p.t).mul a).neg) +lemma waveAmplitude_mod (d : Bool) (n j : ℕ) (t : ℝ) : + waveAmplitude d (n%12) j t = waveAmplitude d n j t := by + simp only [waveAmplitude,basisAlpha_mod,basisBeta_mod] +lemma basisFunction_wave (d : Bool) (n j : ℕ) (t : ℝ) : + basisFunction d n j t = waveAmplitude d n j t*Complex.exp (-Complex.I*Real.pi*t*n) := by + cases d <;> simp only [basisFunction,waveAmplitude,Bool.false_eq_true,ite_false,ite_true] + · rw [u_factored]; ring + · rw [v_factored]; ring +lemma waveAmplitudeBox_contains {p : PointBox} {t : ℝ} (hp : p.Contains t) + {a b : CBox} {n j : ℕ} (ha : a.Contains (basisAlpha n j)) + (hb : b.Contains (basisBeta n j)) (d : Bool) : + (waveAmplitudeBox p a b d).Contains (waveAmplitude d n j t) := by + cases d + · have hh := CBox.contains_mul + (CBox.contains_scale (CBox.contains_mul (rcast_contains piBounds_contains) + (rcast_contains piBounds_contains)) (-2) 1 (by norm_num)) + (CBox.contains_add hb (CBox.neg_contains (CBox.contains_mul (rcast_contains hp.1) ha))) + convert hh using 1 <;> simp only [waveAmplitudeBox,waveAmplitude,Bool.false_eq_true,ite_false,Int.cast_neg,Int.cast_ofNat,Int.cast_one]; ring + · have hh := CBox.contains_mul (CBox.contains_scale piI_contains 2 1 (by norm_num)) ha + convert hh using 1 <;> simp only [waveAmplitudeBox,waveAmplitude,ite_true,Int.cast_ofNat,Int.cast_one]; ring + +lemma cached_weighted_wave {p q : CBox} {t w : ℝ} {n j : ℕ} {d : Bool} + (hp : p.Contains ((w:ℂ)*waveAmplitude d n j t)) + (hq : q.Contains (Complex.exp (-Complex.I*Real.pi*t*n))) : + (p.mul q).Contains ((w:ℂ)*basisFunction d n j t) := by + rw [basisFunction_wave,← mul_assoc] + exact CBox.contains_mul hp hq + +end SharpPlanar.IntegerBasis + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/BasisQuadrature.lean b/lean/OAI/Analysis/PlanarPacking/BasisQuadrature.lean new file mode 100644 index 0000000000000000000000000000000000000000..7abe74d2f642dd3b6343b76211d9150b6adf1e32 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/BasisQuadrature.lean @@ -0,0 +1,46 @@ +import OAI.Analysis.PlanarPacking.BasisIntervals +import OAI.Analysis.PlanarPacking.Grid + +namespace OAI + +/-! +# Quadrature enclosures for cardinal moments + +The certified quadrature grid and cardinal basis enclosures bound the finite moment rule. +-/ + +namespace SharpPlanar +open IntegerIntervals IntegerBasis IntegerAlpha IntegerGrid IntegerCompact + +lemma basis_rule_value (n m : ℕ) (d e : Bool) : + (∑ j : Fin 6, pieceRule (complexBasisMoment d e n j.val m) j.val) = + momentRuleValue quadraturePoint fejerWeight n m d e := by + unfold pieceRule momentRuleValue + apply Finset.sum_congr rfl + intro j _ + congr 1 + apply Finset.sum_congr rfl + intro v _ + have ht : diskAffine j.val (fejerNode v.val) = (quadraturePoint j.val v.val:ℂ) := by + unfold diskAffine diskCenter quadraturePoint + push_cast + ring + rw [ht,complexBasisMoment_ofReal] + +lemma actual_grid_contains (j : Fin 6) (i k : Fin 16) : + (gridRows j i k).Contains (quadraturePoint j.val (16*i.val+k.val)) := gridRows_contains j i k + +lemma actual_rule_contains {n m : ℕ} (hn : n < 128) (hm : m < 128) (d e : Bool) : + (momentRuleBox gridRows weightRows (aLookup n) (bLookup n) n m d e).Contains + (momentRuleValue quadraturePoint fejerWeight n m d e) := by + apply momentRuleBox_contains d e + · exact actual_grid_contains + · exact weightRows_contains + · exact aLookup_contains n + · exact bLookup_contains n + · exact hn + · exact hm + +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/BernsteinBoxes.lean b/lean/OAI/Analysis/PlanarPacking/BernsteinBoxes.lean new file mode 100644 index 0000000000000000000000000000000000000000..8679864543dbaf369993dcd71f6bbfebd65dd9eb --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/BernsteinBoxes.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.PlanarPacking.MatrixIntervals +import OAI.Analysis.PlanarPacking.HighMomentsBase +import OAI.Analysis.PlanarPacking.BernsteinSign + +namespace OAI + +namespace SharpPlanar +open IntegerIntervals IntegerBasis Numerical +open scoped BigOperators +noncomputable def normalizedH (a : Bool) (m : ℝ) (ell : ℕ) : ℝ := + fullMoment a false m ell+fullMoment (!a) true m ell +noncomputable def sourcePower (a : Bool) (m y : ℝ) (nu r : ℕ) : ℝ := + (if a then 1 else -1)*y^r*normalizedH a m (r+nu) +def bernsteinBox (T : Fin 29 → RBox) (k : Fin 29) : RBox := + sumBox (fun r : Fin (k.val+1) => (T ⟨r.val,by omega⟩).scale (k.val.choose r.val) ((28).choose r.val)) +lemma bernsteinBox_contains {T : Fin 29 → RBox} {t : ℕ → ℝ} + (hT : ∀ r : Fin 29,(T r).Contains (t r.val)) (k : Fin 29) : + (bernsteinBox T k).Contains (powerToBernstein 28 t k.val) := by + have hh := sumBox_contains (fun r : Fin (k.val+1) => + RBox.contains_scale (hT ⟨r.val,by omega⟩) (k.val.choose r.val) ((28).choose r.val) + (by exact_mod_cast Nat.choose_pos (by omega : r.val≤28))) + change (bernsteinBox T k).Contains _ at hh + convert hh using 1 + unfold powerToBernstein + simp only [Int.cast_natCast] + change (∑ r ∈ Finset.range (k.val+1),_)=(∑ i : Fin (k.val+1), (k.val.choose i.val:ℝ)/(Nat.choose 28 i.val:ℝ)*t i.val) + exact (Fin.sum_univ_eq_sum_range (fun r : ℕ => (k.val.choose r:ℝ)/(Nat.choose 28 r:ℝ)*t r) (k.val+1)).symm +lemma RBox.lower_lt {box : RBox} {x : ℝ} {u v : ℤ} (hh : box.Contains x) + (hv : 0 (k.choose r : ℝ) / (d.choose r : ℝ) * T r * bernsteinWeight d k v) + simp only [Nat.Ico_zero_eq_range] at hswap + rw [← hswap] + apply sum_congr rfl + intro r hr + have hrd : r ≤ d := by simpa only [mem_range,Nat.lt_succ_iff] using hr + rw [← monomial_bernstein hrd v,mul_sum] + apply sum_congr rfl + intro k hk + ring + +lemma bernsteinWeight_nonneg {v : ℝ} (hv : v ∈ Set.Icc 0 1) (d k : ℕ) : + 0 ≤ bernsteinWeight d k v := by + unfold bernsteinWeight + have : 0 ≤ 1-v := sub_nonneg.mpr hv.2 + have hv0 : 0 ≤ v := hv.1 + positivity +lemma sum_bernsteinWeight (d : ℕ) (v : ℝ) : + (∑ k ∈ range (d+1), bernsteinWeight d k v) = 1 := by + have h := add_pow v (1-v) d + simp only [add_sub_cancel,one_pow] at h + rw [h] + apply sum_congr rfl + intro k hk + unfold bernsteinWeight + ring + + +lemma bernstein_lower {d : ℕ} {T : ℕ → ℝ} {a v : ℝ} + (hv : v ∈ Set.Icc 0 1) + (hB : ∀ k ∈ range (d+1), a ≤ powerToBernstein d T k) : + a ≤ ∑ r ∈ range (d+1), T r * v^r := by + rw [bernstein_identity] + calc + a = ∑ k ∈ range (d+1), a * bernsteinWeight d k v := by rw [← mul_sum,sum_bernsteinWeight,mul_one] + _ ≤ _ := sum_le_sum fun k hk => mul_le_mul_of_nonneg_right (hB k hk) (bernsteinWeight_nonneg hv d k) + +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/CanonicalRows.lean b/lean/OAI/Analysis/PlanarPacking/CanonicalRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..48b396c7495fe40a8446602dd9499b8d30f1b171 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/CanonicalRows.lean @@ -0,0 +1,868 @@ +import OAI.Analysis.PlanarPacking.BasisIntervals +import OAI.Analysis.PlanarPacking.Nodes + +namespace OAI + +open scoped BigOperators ComplexConjugate ENNReal +open MeasureTheory + +namespace SharpPlanar.IntegerIntervals + +def CBox.SqNormCheck (a : CBox) (m n : ℤ) : Prop := + 0 < n ∧ 0 ≤ m ∧ (a.re.bound^2+a.im.bound^2)*n^2 ≤ (precision*m)^2 +instance (a : CBox) (m n : ℤ) : Decidable (a.SqNormCheck m n) := + inferInstanceAs (Decidable (_ ∧ _ ∧ _)) + +lemma CBox.norm_le_rat {a : CBox} {z : ℂ} {m n : ℤ} (hz : a.Contains z) + (hc : a.SqNormCheck m n) : ‖z‖ ≤ (m:ℝ)/n := by + have hn : (0:ℝ) < n := by exact_mod_cast hc.1 + have hm : (0:ℝ) ≤ m := by exact_mod_cast hc.2.1 + have hr := RBox.abs_bound hz.1 + have hi := RBox.abs_bound hz.2 + have hb1 : (0:ℝ) ≤ a.re.bound := (mul_nonneg precision_pos.le (abs_nonneg _)).trans hr + have hb2 : (0:ℝ) ≤ a.im.bound := (mul_nonneg precision_pos.le (abs_nonneg _)).trans hi + have hs1 : (precision:ℝ)^2*z.re^2 ≤ (a.re.bound:ℝ)^2 := by + simpa only [mul_pow, sq_abs] using + (sq_le_sq₀ (mul_nonneg precision_pos.le (abs_nonneg _)) hb1).mpr hr + have hs2 : (precision:ℝ)^2*z.im^2 ≤ (a.im.bound:ℝ)^2 := by + simpa only [mul_pow, sq_abs] using + (sq_le_sq₀ (mul_nonneg precision_pos.le (abs_nonneg _)) hb2).mpr hi + have hh : (((a.re.bound:ℝ)^2+(a.im.bound:ℝ)^2)*(n:ℝ)^2) ≤ ((precision:ℝ)*m)^2 := by + exact_mod_cast hc.2.2 + have he : ‖z‖^2 = z.re^2+z.im^2 := by + rw [← Complex.normSq_eq_norm_sq,Complex.normSq_apply] + ring + have hk : ((precision:ℝ)*‖z‖)^2 ≤ (a.re.bound:ℝ)^2+(a.im.bound:ℝ)^2 := by + rw [mul_pow,he]; nlinarith only [hs1,hs2] + have hkn := mul_le_mul_of_nonneg_right hk (sq_nonneg (n:ℝ)) + have hbound : (‖z‖*(n:ℝ))^2 ≤ (m:ℝ)^2 := by + apply (mul_le_mul_iff_right₀ (sq_pos_of_pos precision_pos)).mp + nlinarith only [hkn,hh] + apply (le_div_iff₀ hn).mpr + nlinarith only [hbound,mul_nonneg (norm_nonneg z) hn.le,hm] + +end SharpPlanar.IntegerIntervals + +namespace SharpPlanar + + +noncomputable def lambdaCap : Fin 7 → ℝ := ![2887/1000,2665/1000,2218/1000,1804/1000,1486/1000,1250/1000,1073/1000] +noncomputable def zCap : Fin 7 → ℝ := ![2934/1000,2713/1000,2269/1000,1859/1000,1548/1000,1320/1000,1151/1000] +noncomputable def dampingCap : Fin 7 → ℝ := ![2933/1000,2440/1000,1567/1000,900/1000,482/1000,224/1000,597/10000] +noncomputable def slopeCap : Fin 6 → ℝ := ![0,48/10,317/100,1946/1000,1217/1000,792/1000] + +lemma kernel_den_sq (t : ℝ) : ‖(t:ℂ)+Complex.I*h‖^2 = t^2+h^2 := by + rw [← Complex.normSq_eq_norm_sq] + simp [Complex.normSq_apply,pow_two] +lemma z_re (t : ℝ) : (z t).re = -B*t/(t^2+h^2) := by + simp [z,Complex.div_re,Complex.normSq_apply,pow_two] +lemma lambda_sq (t : ℝ) : ‖lambda t‖^2 = (4/3:ℝ)/(t^2+h^2) := by + rw [lambda,norm_div,norm_mul,Complex.norm_I,Complex.norm_real,Real.norm_eq_abs, + abs_of_pos b_pos,div_pow,mul_pow,kernel_den_sq,b_sq] + field_simp +lemma z_sq (t : ℝ) : ‖z t‖^2 = (4/25:ℝ)+(304/225:ℝ)/(t^2+h^2) := by + have hd : t^2+h^2 ≠ 0 := ne_of_gt (by unfold h; positivity : 0 < t^2+h^2) + rw [← Complex.normSq_eq_norm_sq,Complex.normSq_apply,z_re,z_im] + dsimp [B,h] at hd ⊢ + field_simp + ring + +lemma lambda_sq_antitone {s t : ℝ} (hs : 0 ≤ s) (hst : s ≤ t) : + ‖lambda t‖^2 ≤ ‖lambda s‖^2 := by + rw [lambda_sq,lambda_sq] + apply div_le_div_of_nonneg_left (by norm_num) (by unfold h; positivity) + nlinarith +lemma z_sq_antitone {s t : ℝ} (hs : 0 ≤ s) (hst : s ≤ t) : + ‖z t‖^2 ≤ ‖z s‖^2 := by + rw [z_sq,z_sq] + apply add_le_add le_rfl + apply div_le_div_of_nonneg_left (by norm_num) (by unfold h; positivity) + nlinarith + +lemma endpoint_kernel_bounds (j : Fin 7) : + ‖lambda ((j.val:ℝ)/6)‖ ≤ lambdaCap j ∧ + ‖z ((j.val:ℝ)/6)‖ ≤ zCap j ∧ + dampingCap j ≤ (z ((j.val:ℝ)/6)).im := by + have hb : 0 ≤ lambdaCap j := by fin_cases j <;> norm_num [lambdaCap] + have ha : 0 ≤ zCap j := by fin_cases j <;> norm_num [zCap] + refine ⟨(sq_le_sq₀ (norm_nonneg _) hb).mp ?_,(sq_le_sq₀ (norm_nonneg _) ha).mp ?_,?_⟩ + · rw [lambda_sq]; fin_cases j <;> norm_num [lambdaCap,h] + · rw [z_sq]; fin_cases j <;> norm_num [zCap,h] + · rw [z_im]; fin_cases j <;> norm_num [dampingCap,h,B] + +lemma piece_secant_bound (j : Fin 6) {t : ℝ} + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : + slopeCap j*(t^2+h^2)*((((j.val:ℝ)+1)/6)^2+h^2) ≤ + h*B*(t+((j.val:ℝ)+1)/6) := by + have hp := mul_nonneg (sub_nonneg.mpr ht.1) (sub_nonneg.mpr ht.2) + fin_cases j <;> norm_num [slopeCap,h,B] at * <;> nlinarith + +lemma piece_damping_bound (j : Fin 6) {t : ℝ} + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : + dampingCap ⟨j.val+1,by omega⟩+slopeCap j*(((j.val:ℝ)+1)/6-t) ≤ (z t).im := by + let u : ℝ := ((j.val:ℝ)+1)/6 + have hd : 0 < t^2+h^2 := by unfold h; positivity + have hu : 0 < u^2+h^2 := by unfold h; positivity + have hid : ((z t).im-(z u).im)*(t^2+h^2)*(u^2+h^2) = h*B*(u-t)*(u+t) := by + rw [z_im,z_im] + field_simp + ring + have hs := mul_le_mul_of_nonneg_right (piece_secant_bound j ht) (sub_nonneg.mpr ht.2) + have hm : slopeCap j*(u-t) ≤ (z t).im-(z u).im := by + apply (mul_le_mul_iff_right₀ (mul_pos hd hu)).mp + dsimp [u] at hid ⊢ + nlinarith only [hs,hid] + have he := (endpoint_kernel_bounds ⟨j.val+1,by omega⟩).2.2 + simp only [Nat.cast_add,Nat.cast_one] at he + change dampingCap ⟨j.val+1,by omega⟩ ≤ (z u).im at he + dsimp [u] at hm he + linarith only [hm,he] + + +lemma piece_kernel_bounds (j : Fin 6) {t : ℝ} + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : + ‖lambda t‖ ≤ lambdaCap ⟨j.val,by omega⟩ ∧ + ‖z t‖ ≤ zCap ⟨j.val,by omega⟩ ∧ + dampingCap ⟨j.val+1,by omega⟩+slopeCap j*(((j.val:ℝ)+1)/6-t) ≤ (z t).im := by + have hs : 0 ≤ (j.val:ℝ)/6 := by positivity + have hb := (endpoint_kernel_bounds ⟨j.val,by omega⟩).1 + have ha := (endpoint_kernel_bounds ⟨j.val,by omega⟩).2.1 + refine ⟨?_,?_,piece_damping_bound j ht⟩ + · exact ((sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mp (lambda_sq_antitone hs ht.1)).trans hb + · exact ((sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mp (z_sq_antitone hs ht.1)).trans ha + +end SharpPlanar + +namespace SharpPlanar.IntegerBasis +open IntegerIntervals IntegerAlpha + +noncomputable def uAmplitude (n j : ℕ) (t : ℝ) : ℂ := + -2*(Real.pi:ℂ)^2*(basisBeta n j-(t:ℂ)*basisAlpha n j) +noncomputable def vAmplitude (n j : ℕ) : ℂ := + 2*Complex.I*Real.pi*basisAlpha n j + +def uAmplitudeBox (t : RBox) (a b : CBox) : CBox := + ((rcast (piBounds.mul piBounds)).scale (-2) 1).mul + (b.add (((rcast t).mul a).neg)) +def vAmplitudeBox (a : CBox) : CBox := (piI.scale 2 1).mul a + +lemma uAmplitudeBox_contains {t : RBox} {a b : CBox} {s : ℝ} {n j : ℕ} + (ht : t.Contains s) (ha : a.Contains (basisAlpha n j)) (hb : b.Contains (basisBeta n j)) : + (uAmplitudeBox t a b).Contains (uAmplitude n j s) := by + have hp := CBox.contains_scale (rcast_contains + (RBox.contains_mul piBounds_contains piBounds_contains)) (-2) 1 (by norm_num) + have he := CBox.contains_mul hp + (CBox.contains_add hb (CBox.neg_contains (CBox.contains_mul (rcast_contains ht) ha))) + unfold uAmplitudeBox + convert he using 1 + unfold uAmplitude + push_cast + ring +lemma vAmplitudeBox_contains {a : CBox} {n j : ℕ} (ha : a.Contains (basisAlpha n j)) : + (vAmplitudeBox a).Contains (vAmplitude n j) := by + have he := CBox.contains_mul (CBox.contains_scale piI_contains 2 1 (by norm_num)) ha + unfold vAmplitudeBox + convert he using 1 + unfold vAmplitude + push_cast + ring + +-- Zero-based piece indexing: this is exactly the source M_1,...,M_6. +def densityNum : Fin 6 → ℤ := ![56,48,35,25,19,1571] +def densityDen : Fin 6 → ℤ := ![1,1,1,1,1,250] +noncomputable def densityCap (j : Fin 6) : ℝ := (densityNum j:ℝ)/(densityDen j:ℝ) +lemma densityDen_pos (j : Fin 6) : 0 < densityDen j := by fin_cases j <;> norm_num [densityDen] + +def DensityCheck (n : ℕ) (j : Fin 6) : Prop := + (uAmplitudeBox (RBox.rat j.val 6) (aLookup n j) (bLookup n j)).SqNormCheck (densityNum j) (densityDen j) ∧ + (uAmplitudeBox (RBox.rat (j.val+1) 6) (aLookup n j) (bLookup n j)).SqNormCheck (densityNum j) (densityDen j) ∧ + (vAmplitudeBox (aLookup n j)).SqNormCheck (densityNum j) (densityDen j) +instance (n : ℕ) (j : Fin 6) : Decidable (DensityCheck n j) := inferInstanceAs (Decidable (_ ∧ _ ∧ _)) + +lemma density_finite_check (n : Fin 12) (hn : n.val ∈ residues) (j : Fin 6) : DensityCheck n.val j := by + fin_cases n <;> simp only [residues,Finset.mem_insert,Finset.mem_singleton] at hn + all_goals first | omega | (fin_cases j <;> decide +kernel) + +lemma density_check (n : ℕ) (hn : n%12 ∈ residues) (j : Fin 6) : DensityCheck n j := by + have hc := density_finite_check ⟨n%12,by omega⟩ hn j + simpa only [DensityCheck,aLookup,bLookup,Nat.mod_mod] using hc + +lemma amplitude_endpoints (n : ℕ) (hn : n%12 ∈ residues) (j : Fin 6) : + ‖uAmplitude n j.val ((j.val:ℝ)/6)‖ ≤ densityCap j ∧ + ‖uAmplitude n j.val (((j.val:ℝ)+1)/6)‖ ≤ densityCap j ∧ + ‖vAmplitude n j.val‖ ≤ densityCap j := by + obtain ⟨hc0,hc1,hcv⟩ := density_check n hn j + have ha := aLookup_contains n j + have hb := bLookup_contains n j + refine ⟨?_,?_,CBox.norm_le_rat (vAmplitudeBox_contains ha) hcv⟩ + · exact CBox.norm_le_rat + (uAmplitudeBox_contains (by simpa using RBox.contains_rat j.val 6 (by norm_num)) ha hb) hc0 + · exact CBox.norm_le_rat + (uAmplitudeBox_contains (by simpa using RBox.contains_rat (j.val+1) 6 (by norm_num)) ha hb) hc1 + +lemma uAmplitude_bound (n : ℕ) (hn : n%12 ∈ residues) (j : Fin 6) {t : ℝ} + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : ‖uAmplitude n j.val t‖ ≤ densityCap j := by + obtain ⟨h0,h1,_⟩ := amplitude_endpoints n hn j + let θ : ℝ := 6*t-j.val + have hθ0 : 0 ≤ θ := by dsimp [θ]; linarith [ht.1] + have hθ1 : θ ≤ 1 := by dsimp [θ]; linarith [ht.2] + have hid : uAmplitude n j.val t = ((1-θ:ℝ):ℂ)*uAmplitude n j.val ((j.val:ℝ)/6)+ + (θ:ℂ)*uAmplitude n j.val (((j.val:ℝ)+1)/6) := by + unfold uAmplitude θ + push_cast + ring + rw [hid] + calc + _ ≤ ‖((1-θ:ℝ):ℂ)*uAmplitude n j.val ((j.val:ℝ)/6)‖+ + ‖(θ:ℂ)*uAmplitude n j.val (((j.val:ℝ)+1)/6)‖ := norm_add_le _ _ + _ = (1-θ)*‖uAmplitude n j.val ((j.val:ℝ)/6)‖+ + θ*‖uAmplitude n j.val (((j.val:ℝ)+1)/6)‖ := by + simp only [norm_mul,Complex.norm_real,Real.norm_eq_abs,abs_of_nonneg hθ0, + abs_of_nonneg (sub_nonneg.mpr hθ1)] + _ ≤ (1-θ)*densityCap j+θ*densityCap j := by gcongr + _ = densityCap j := by ring + +lemma unit_phase_norm (n : ℕ) (t : ℝ) : ‖Complex.exp (-Complex.I*Real.pi*t*n)‖ = 1 := by + rw [Complex.norm_exp] + simp +lemma u_norm_amplitude (n j : ℕ) (t : ℝ) : ‖u n j t‖ = ‖uAmplitude n j t‖ := by + rw [u_factored] + have he : -2*(Real.pi:ℂ)^2*Complex.exp (-Complex.I*Real.pi*t*n)* + (basisBeta n j-(t:ℂ)*basisAlpha n j) = Complex.exp (-Complex.I*Real.pi*t*n)*uAmplitude n j t := by + unfold uAmplitude; ring + rw [he,norm_mul,unit_phase_norm,one_mul] +lemma v_norm_amplitude (n j : ℕ) (t : ℝ) : ‖v n j t‖ = ‖vAmplitude n j‖ := by + rw [v_factored] + have he : 2*Complex.I*Real.pi*Complex.exp (-Complex.I*Real.pi*t*n)*basisAlpha n j = + Complex.exp (-Complex.I*Real.pi*t*n)*vAmplitude n j := by + unfold vAmplitude; ring + rw [he,norm_mul,unit_phase_norm,one_mul] + + +lemma basis_density_bounds (n : ℕ) (hn : n%12 ∈ residues) (j : Fin 6) {t : ℝ} + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : + ‖u n j.val t‖ ≤ densityCap j ∧ ‖v n j.val t‖ ≤ densityCap j := by + rw [u_norm_amplitude,v_norm_amplitude] + exact ⟨uAmplitude_bound n hn j ht,(amplitude_endpoints n hn j).2.2⟩ + +end SharpPlanar.IntegerBasis + +namespace SharpPlanar +open IntegerBasis + +lemma densityCap_nonneg (j : Fin 6) : 0 ≤ densityCap j := by + fin_cases j <;> norm_num [densityCap,densityNum,densityDen] +lemma piece_summand_bound (x : X) (n : Node) (j : Fin 6) {t : ℝ} + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : + ‖(x (n,false):ℂ)*u n.val j.val t+(x (n,true):ℂ)*v n.val j.val t‖ ≤ + densityCap j*(|x (n,false)|+|x (n,true)|) := by + obtain ⟨hu,hv⟩ := basis_density_bounds n.val n.prop.2 j ht + calc + _ ≤ ‖(x (n,false):ℂ)*u n.val j.val t‖+‖(x (n,true):ℂ)*v n.val j.val t‖ := norm_add_le _ _ + _ = |x (n,false)| *‖u n.val j.val t‖+|x (n,true)| *‖v n.val j.val t‖ := by simp + _ ≤ |x (n,false)| *densityCap j+|x (n,true)| *densityCap j := by gcongr + _ = _ := by ring + +lemma piece_density_bound (p : CardinalData) (j : Fin 6) {t : ℝ} + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : + ‖density p j.val t‖ ≤ densityCap j*(|p.c₀|+|p.d₀|+‖p.x‖) := by + have hnorm : Summable (fun n : Node => ‖(p.x (n,false):ℂ)*u n.val j.val t+ + (p.x (n,true):ℂ)*v n.val j.val t‖) := + Summable.of_nonneg_of_le (fun _ => norm_nonneg _) (fun n => piece_summand_bound p.x n j ht) + ((X_summable_pairs p.x).mul_left (densityCap j)) + have hsum : ‖∑' n : Node, ((p.x (n,false):ℂ)*u n.val j.val t+ + (p.x (n,true):ℂ)*v n.val j.val t)‖ ≤ densityCap j*‖p.x‖ := by + calc + _ ≤ ∑' n : Node, ‖(p.x (n,false):ℂ)*u n.val j.val t+ + (p.x (n,true):ℂ)*v n.val j.val t‖ := norm_tsum_le_tsum_norm hnorm + _ ≤ ∑' n : Node, densityCap j*(|p.x (n,false)|+|p.x (n,true)|) := + hnorm.tsum_le_tsum (fun n => piece_summand_bound p.x n j ht) + ((X_summable_pairs p.x).mul_left (densityCap j)) + _ = _ := by rw [tsum_mul_left,← X_norm] + obtain ⟨hu,hv⟩ := basis_density_bounds 0 (by simp [residues]) j ht + unfold density + calc + _ ≤ ‖(p.c₀:ℂ)*u 0 j.val t‖+‖(p.d₀:ℂ)*v 0 j.val t‖+ + ‖∑' n : Node, ((p.x (n,false):ℂ)*u n.val j.val t+ + (p.x (n,true):ℂ)*v n.val j.val t)‖ := + (norm_add_le _ _).trans (add_le_add (norm_add_le _ _) le_rfl) + _ ≤ |p.c₀| *densityCap j+|p.d₀| *densityCap j+densityCap j*‖p.x‖ := by + simp only [norm_mul,Complex.norm_real,Real.norm_eq_abs] + gcongr + _ = _ := by ring + +lemma lambdaCap_nonneg (j : Fin 7) : 0 ≤ lambdaCap j := by fin_cases j <;> norm_num [lambdaCap] +lemma zCap_nonneg (j : Fin 7) : 0 ≤ zCap j := by fin_cases j <;> norm_num [zCap] +lemma dampingCap_pos (j : Fin 7) : 0 < dampingCap j := by fin_cases j <;> norm_num [dampingCap] +lemma slopeCap_nonneg (j : Fin 6) : 0 ≤ slopeCap j := by fin_cases j <;> norm_num [slopeCap] + +noncomputable def pieceMass (j : Fin 6) (s : ℝ) : ℝ := + if slopeCap j*s=0 then 1/6 else min (1/6) (1/(Real.pi*slopeCap j*s)) +noncomputable def pieceL (j : Fin 6) (s : ℝ) : ℝ := + lambdaCap ⟨j.val,by omega⟩*Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*s)*pieceMass j s +noncomputable def atomMass : Fin 7 → ℝ := ![5,4,4,4,2,4,2] +noncomputable def atomL (j : Fin 7) (s : ℝ) : ℝ := + atomMass j*lambdaCap j*Real.exp (-Real.pi*dampingCap j*s) +noncomputable def segmentEnvelope (j : Fin 6) (ell : ℕ) (s t : ℝ) : ℝ := + lambdaCap ⟨j.val,by omega⟩*(Real.pi*zCap ⟨j.val,by omega⟩)^ell * + Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*s)* + Real.exp (-(Real.pi*slopeCap j*s)*(((j.val:ℝ)+1)/6-t)) + +lemma segmentEnvelope_nonneg (j : Fin 6) (ell : ℕ) (s t : ℝ) : + 0 ≤ segmentEnvelope j ell s t := by + unfold segmentEnvelope + exact mul_nonneg (mul_nonneg (mul_nonneg (lambdaCap_nonneg _) + (pow_nonneg (mul_nonneg Real.pi_pos.le (zCap_nonneg _)) _)) (Real.exp_pos _).le) (Real.exp_pos _).le +lemma kernelMoment_segment_bound (j : Fin 6) (ell : ℕ) {s t : ℝ} (hs : 0 ≤ s) + (ht : (j.val:ℝ)/6 ≤ t ∧ t ≤ ((j.val:ℝ)+1)/6) : + ‖kernelMoment ell s t‖ ≤ segmentEnvelope j ell s t := by + obtain ⟨hl,hz,hi⟩ := piece_kernel_bounds j ht + have hex : ‖Complex.exp (Complex.I*Real.pi*z t*s)‖ ≤ + Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*s)* + Real.exp (-(Real.pi*slopeCap j*s)*(((j.val:ℝ)+1)/6-t)) := by + rw [← Real.exp_add,Complex.norm_exp] + apply Real.exp_le_exp.mpr + simp only [Complex.mul_re,Complex.mul_im,Complex.I_re,Complex.I_im, + Complex.ofReal_re,Complex.ofReal_im,zero_mul,mul_zero,one_mul,zero_sub, + sub_zero,zero_add] + nlinarith [mul_le_mul_of_nonneg_right hi (mul_nonneg Real.pi_pos.le hs)] + unfold kernelMoment segmentEnvelope + rw [norm_mul,norm_mul,norm_pow,norm_mul,norm_mul,Complex.norm_I, + Complex.norm_real,Real.norm_eq_abs,abs_of_pos Real.pi_pos,one_mul] + have hp : (Real.pi*‖z t‖)^ell ≤ (Real.pi*zCap ⟨j.val,by omega⟩)^ell := by + gcongr + calc + _ ≤ lambdaCap ⟨j.val,by omega⟩*(Real.pi*zCap ⟨j.val,by omega⟩)^ell * + (Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*s)* + Real.exp (-(Real.pi*slopeCap j*s)*(((j.val:ℝ)+1)/6-t))) := + mul_le_mul (mul_le_mul hl hp (by positivity) (lambdaCap_nonneg _)) hex + (norm_nonneg _) (mul_nonneg (lambdaCap_nonneg _) (pow_nonneg (mul_nonneg Real.pi_pos.le (zCap_nonneg _)) _)) + _ = _ := by ring + +lemma exp_segment_bound {a l u : ℝ} (ha : 0 ≤ a) (hlu : l ≤ u) : + (∫ t in l..u, Real.exp (-a*(u-t))) ≤ if a=0 then u-l else min (u-l) (1/a) := by + have hc : Continuous (fun t : ℝ => Real.exp (-a*(u-t))) := by fun_prop + have hcl : (∫ t in l..u, Real.exp (-a*(u-t))) ≤ u-l := by + calc + _ ≤ ∫ t in l..u, (1:ℝ) := by + apply intervalIntegral.integral_mono_on hlu (hc.intervalIntegrable l u) (continuous_const.intervalIntegrable l u) + intro t ht + apply Real.exp_le_one_iff.mpr + exact mul_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr ha) (sub_nonneg.mpr ht.2) + _ = u-l := by simp + split_ifs with h0 + · exact hcl + · apply le_min hcl + have hapos : 0 < a := lt_of_le_of_ne ha (Ne.symm h0) + have hp : ∀ t ∈ Set.uIcc l u, HasDerivAt (fun t : ℝ => Real.exp (-a*(u-t))/a) + (Real.exp (-a*(u-t))) t := by + intro t _ + exact ((((hasDerivAt_id t).const_sub u).const_mul (-a)).exp.div_const a).congr_deriv (by simp [h0]) + rw [intervalIntegral.integral_eq_sub_of_hasDerivAt hp (hc.intervalIntegrable l u)] + simp only [sub_self,mul_zero,Real.exp_zero] + exact sub_le_self _ (div_nonneg (Real.exp_pos _).le ha) + +lemma pieceMass_nonneg (j : Fin 6) {s : ℝ} (hs : 0 ≤ s) : 0 ≤ pieceMass j s := by + unfold pieceMass + split_ifs + · norm_num + · exact le_min (by norm_num) (div_nonneg (by norm_num) (mul_nonneg (mul_nonneg Real.pi_pos.le (slopeCap_nonneg _)) hs)) + +lemma segment_exp_integral_bound (j : Fin 6) {s : ℝ} (hs : 0 ≤ s) : + (∫ t in (j.val:ℝ)/6..((j.val:ℝ)+1)/6, + Real.exp (-(Real.pi*slopeCap j*s)*(((j.val:ℝ)+1)/6-t))) ≤ pieceMass j s := by + have he := exp_segment_bound (mul_nonneg (mul_nonneg Real.pi_pos.le (slopeCap_nonneg j)) hs) + (by linarith : (j.val:ℝ)/6 ≤ ((j.val:ℝ)+1)/6) + have hlen : ((j.val:ℝ)+1)/6-(j.val:ℝ)/6=1/6 := by ring + simpa only [pieceMass,hlen,mul_assoc,mul_eq_zero,Real.pi_ne_zero,false_or] using he + +end SharpPlanar + +namespace SharpPlanar +open IntegerBasis + +lemma segmentEnvelope_integral_bound (j : Fin 6) (ell : ℕ) {s : ℝ} (hs : 0 ≤ s) : + (∫ t in (j.val:ℝ)/6..((j.val:ℝ)+1)/6, segmentEnvelope j ell s t) ≤ + pieceL j s*(Real.pi*zCap ⟨j.val,by omega⟩)^ell := by + unfold segmentEnvelope + rw [intervalIntegral.integral_const_mul] + have hb := mul_le_mul_of_nonneg_left (segment_exp_integral_bound j hs) + (mul_nonneg (mul_nonneg (lambdaCap_nonneg ⟨j.val,by omega⟩) + (pow_nonneg (mul_nonneg Real.pi_pos.le (zCap_nonneg ⟨j.val,by omega⟩)) ell)) + (Real.exp_pos (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*s)).le) + convert hb using 1; first | rfl | (unfold pieceL; ring) + +lemma sharp_integral_piece_bound (p : CardinalData) (j : Fin 6) (ell : ℕ) {s : ℝ} + (hs : 0 ≤ s) : + ‖∫ t in (j.val:ℝ)/6..((j.val:ℝ)+1)/6, density p j.val t*kernelMoment ell s t‖ ≤ + (|p.c₀|+|p.d₀|+‖p.x‖)*densityCap j*pieceL j s*(Real.pi*zCap ⟨j.val,by omega⟩)^ell := by + let w : ℝ := |p.c₀|+|p.d₀|+‖p.x‖ + have hw : 0 ≤ w := by dsimp [w]; positivity + have hlu : (j.val:ℝ)/6 ≤ ((j.val:ℝ)+1)/6 := by linarith + calc + _ ≤ ∫ t in (j.val:ℝ)/6..((j.val:ℝ)+1)/6, ‖density p j.val t*kernelMoment ell s t‖ := + intervalIntegral.norm_integral_le_integral_norm hlu + _ ≤ ∫ t in (j.val:ℝ)/6..((j.val:ℝ)+1)/6, (w*densityCap j)*segmentEnvelope j ell s t := by + apply intervalIntegral.integral_mono_on hlu (piece_integrable p ell j.val j.isLt s).norm + ((by unfold segmentEnvelope; fun_prop : Continuous (fun t : ℝ => (w*densityCap j)*segmentEnvelope j ell s t)).intervalIntegrable _ _) + intro t ht + rw [norm_mul] + have hd := piece_density_bound p j ht + have hk := kernelMoment_segment_bound j ell hs ht + rw [mul_comm w] + exact mul_le_mul hd hk (norm_nonneg _) (mul_nonneg (densityCap_nonneg _) hw) + _ = (w*densityCap j)*(∫ t in (j.val:ℝ)/6..((j.val:ℝ)+1)/6, segmentEnvelope j ell s t) := + intervalIntegral.integral_const_mul _ _ + _ ≤ (w*densityCap j)*(pieceL j s*(Real.pi*zCap ⟨j.val,by omega⟩)^ell) := + mul_le_mul_of_nonneg_left (segmentEnvelope_integral_bound j ell hs) (mul_nonneg hw (densityCap_nonneg _)) + _ = _ := by dsimp [w]; ring + +lemma kernelMoment_endpoint_bound (j : Fin 7) (ell : ℕ) {s : ℝ} (hs : 0 ≤ s) : + ‖kernelMoment ell s ((j.val:ℝ)/6)‖ ≤ + lambdaCap j*Real.exp (-Real.pi*dampingCap j*s)*(Real.pi*zCap j)^ell := by + obtain ⟨hl,hz,hi⟩ := endpoint_kernel_bounds j + have hex : ‖Complex.exp (Complex.I*Real.pi*z ((j.val:ℝ)/6)*s)‖ ≤ + Real.exp (-Real.pi*dampingCap j*s) := by + rw [Complex.norm_exp] + apply Real.exp_le_exp.mpr + simp only [Complex.mul_re,Complex.mul_im,Complex.I_re,Complex.I_im, + Complex.ofReal_re,Complex.ofReal_im,zero_mul,mul_zero,one_mul,zero_sub, + sub_zero,zero_add] + nlinarith [mul_le_mul_of_nonneg_right hi (mul_nonneg Real.pi_pos.le hs)] + unfold kernelMoment + rw [norm_mul,norm_mul,norm_pow,norm_mul,norm_mul,Complex.norm_I, + Complex.norm_real,Real.norm_eq_abs,abs_of_pos Real.pi_pos,one_mul] + have hp : (Real.pi*‖z ((j.val:ℝ)/6)‖)^ell ≤ (Real.pi*zCap j)^ell := by gcongr + calc + _ ≤ lambdaCap j*(Real.pi*zCap j)^ell*Real.exp (-Real.pi*dampingCap j*s) := + mul_le_mul (mul_le_mul hl hp (by positivity) (lambdaCap_nonneg _)) hex + (norm_nonneg _) (mul_nonneg (lambdaCap_nonneg _) (pow_nonneg (mul_nonneg Real.pi_pos.le (zCap_nonneg _)) _)) + _ = _ := by ring + +noncomputable def atomicCoefficient (j : Fin 7) : ℂ := if j.val=0 then Pcoeff 0 else 2*Pcoeff j.val +lemma atomicCoefficient_norm (j : Fin 7) : ‖atomicCoefficient j‖ = atomMass j := by + fin_cases j <;> norm_num [atomicCoefficient,atomMass,norm_mul,Pcoeff_norm,coeffMass] + +lemma sharp_atomic_bound (ell : ℕ) {s : ℝ} (hs : 0 ≤ s) : + ‖Pcoeff 0*kernelMoment ell s 0+ + ∑ j ∈ Finset.Icc 1 6, 2*Pcoeff j*kernelMoment ell s ((j:ℝ)/6)‖ ≤ + ∑ j : Fin 7, atomL j s*(Real.pi*zCap j)^ell := by + have he : Pcoeff 0*kernelMoment ell s 0+ + ∑ j ∈ Finset.Icc 1 6, 2*Pcoeff j*kernelMoment ell s ((j:ℝ)/6) = + ∑ j : Fin 7, atomicCoefficient j*kernelMoment ell s ((j.val:ℝ)/6) := by + norm_num [Fin.sum_univ_succ,Finset.sum_Icc_succ_top,atomicCoefficient] + ring + rw [he] + apply (norm_sum_le _ _).trans + apply Finset.sum_le_sum + intro j _ + rw [norm_mul,atomicCoefficient_norm] + have hh := mul_le_mul_of_nonneg_left (kernelMoment_endpoint_bound j ell hs) + (by fin_cases j <;> norm_num [atomMass] : 0 ≤ atomMass j) + convert hh using 1 + unfold atomL + ring + + +theorem sharp_moment_bound (p : CardinalData) (ell : ℕ) {s : ℝ} (hs : 0 ≤ s) : + |K p ell s| ≤ + (|p.c₀|+|p.d₀|+‖p.x‖)*(∑ j : Fin 6, densityCap j*pieceL j s*(Real.pi*zCap ⟨j.val,by omega⟩)^ell) + +|p.C| *(∑ j : Fin 7, atomL j s*(Real.pi*zCap j)^ell) := by + have hatom : ‖(p.C:ℂ)*(Pcoeff 0*kernelMoment ell s 0+ + ∑ j ∈ Finset.Icc 1 6, 2*Pcoeff j*kernelMoment ell s ((j:ℝ)/6))‖ ≤ + |p.C| *(∑ j : Fin 7, atomL j s*(Real.pi*zCap j)^ell) := by + rw [norm_mul,Complex.norm_real,Real.norm_eq_abs] + exact mul_le_mul_of_nonneg_left (sharp_atomic_bound ell hs) (abs_nonneg _) + have hsum : ‖∑ j ∈ Finset.range 6, ∫ t in (j:ℝ)/6..((j:ℝ)+1)/6, + density p j t*kernelMoment ell s t‖ ≤ + (|p.c₀|+|p.d₀|+‖p.x‖)*(∑ j : Fin 6, densityCap j*pieceL j s*(Real.pi*zCap ⟨j.val,by omega⟩)^ell) := by + rw [← Fin.sum_univ_eq_sum_range,Finset.mul_sum] + apply (norm_sum_le _ _).trans + apply Finset.sum_le_sum + intro j _ + simpa only [mul_assoc] using sharp_integral_piece_bound p j ell hs + unfold K + exact (Complex.abs_re_le_norm _).trans ((norm_add_le _ _).trans (by linarith)) + +end SharpPlanar + +namespace SharpPlanar + +lemma pieceMass_antitone (j : Fin 6) {s t : ℝ} (hs : 0 ≤ s) (hst : s ≤ t) : + pieceMass j t ≤ pieceMass j s := by + have ht : 0 ≤ t := hs.trans hst + unfold pieceMass + split_ifs with htz hsz hsz + · rfl + · exfalso + have hz : slopeCap j*s=0 := by + apply le_antisymm + · calc + _ ≤ slopeCap j*t := mul_le_mul_of_nonneg_left hst (slopeCap_nonneg _) + _ = 0 := htz + · exact mul_nonneg (slopeCap_nonneg _) hs + exact hsz hz + · exact min_le_left _ _ + · apply min_le_min_left + apply one_div_le_one_div_of_le + · have hh : 0 < slopeCap j*s := lt_of_le_of_ne (mul_nonneg (slopeCap_nonneg _) hs) (Ne.symm hsz) + simpa only [mul_assoc] using mul_pos Real.pi_pos hh + · exact mul_le_mul_of_nonneg_left hst (mul_nonneg Real.pi_pos.le (slopeCap_nonneg _)) + +lemma pieceL_nonneg (j : Fin 6) {s : ℝ} (hs : 0 ≤ s) : 0 ≤ pieceL j s := by + exact mul_nonneg (mul_nonneg (lambdaCap_nonneg _) (Real.exp_pos _).le) (pieceMass_nonneg j hs) +lemma atomL_nonneg (j : Fin 7) (s : ℝ) : 0 ≤ atomL j s := by + unfold atomL + apply mul_nonneg _ (Real.exp_pos _).le + apply mul_nonneg _ (lambdaCap_nonneg _) + fin_cases j <;> norm_num [atomMass] + +lemma pieceL_shift_bound (j : Fin 6) {s t : ℝ} (hs : 0 ≤ s) (ht : 0 ≤ t) : + pieceL j (s+t) ≤ Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*t)*pieceL j s := by + have hm := pieceMass_antitone j hs (show s ≤ s+t by linarith) + unfold pieceL + rw [mul_add,Real.exp_add] + calc + _ ≤ lambdaCap ⟨j.val,by omega⟩*(Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*s)* + Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*t))*pieceMass j s := by + exact mul_le_mul_of_nonneg_left hm (mul_nonneg (lambdaCap_nonneg _) (mul_nonneg (Real.exp_pos _).le (Real.exp_pos _).le)) + _ = _ := by ring + +lemma atomL_shift (j : Fin 7) (s t : ℝ) : + atomL j (s+t) = Real.exp (-Real.pi*dampingCap j*t)*atomL j s := by + unfold atomL + rw [mul_add,Real.exp_add] + ring + +lemma pieceL_period_bound (j : Fin 6) {s : ℝ} (hs : 0 ≤ s) (k : ℕ) : + pieceL j (s+12*k) ≤ (Real.exp (-12*Real.pi*dampingCap ⟨j.val+1,by omega⟩))^k*pieceL j s := by + have hh := pieceL_shift_bound j hs (by positivity : (0:ℝ) ≤ 12*k) + convert hh using 1 + rw [← Real.exp_nat_mul] + congr 2 + ring + +end SharpPlanar + +namespace SharpPlanar +open IntegerBasis + + +lemma periodic_geometric_sum {f : ℕ → ℝ} {q : ℝ} (hf : ∀ n, 0 ≤ f n) + (hq0 : 0 ≤ q) (hq1 : q < 1) + (hb : ∀ (a : Fin 12) (k : ℕ), f (k*12+a.val) ≤ q^k*f a.val) : + Summable f ∧ (∑' n, f n) ≤ (∑ a : Fin 12, f a.val)/(1-q) := by + let g : ℕ × Fin 12 → ℝ := fun p => q^p.1*f p.2.val + have hgeom := (hasSum_geometric_of_lt_one hq0 hq1).summable + have hg : Summable g := by + apply (summable_prod_of_nonneg (fun p => mul_nonneg (pow_nonneg hq0 _) (hf _))).mpr + constructor + · intro k; exact summable_of_hasFiniteSupport (Set.toFinite _) + · simpa only [g,← Finset.mul_sum,tsum_fintype] using hgeom.mul_right (∑ a : Fin 12, f a.val) + have hh : Summable (fun p : ℕ × Fin 12 => f (p.1*12+p.2.val)) := + Summable.of_nonneg_of_le (fun _ => hf _) (fun p => hb p.2 p.1) hg + have heq : (fun p : ℕ × Fin 12 => f (p.1*12+p.2.val)) = f ∘ (Nat.divModEquiv 12).symm := rfl + have hs : Summable f := ((Nat.divModEquiv 12).symm.summable_iff).mp (heq ▸ hh) + refine ⟨hs,?_⟩ + calc + (∑' n, f n) = ∑' p : ℕ × Fin 12, f (p.1*12+p.2.val) := by + exact ((Nat.divModEquiv 12).symm.tsum_eq f).symm + _ ≤ ∑' p : ℕ × Fin 12, g p := hh.tsum_le_tsum (fun p => hb p.2 p.1) hg + _ = (∑ a : Fin 12, f a.val)/(1-q) := by + rw [hg.tsum_prod] + simp only [g,tsum_fintype,← Finset.mul_sum,tsum_mul_right] + rw [tsum_geometric_of_lt_one hq0 hq1] + rw [div_eq_mul_inv] + ring + +noncomputable def rowFactor (j : Fin 6) (n : ℕ) : ℝ := + (1+|D n|+Real.pi*zCap ⟨j.val,by omega⟩)/Q n*densityCap j +noncomputable def rowPiece (j : Fin 6) (n : ℕ) : ℝ := + if n%12 ∈ residues then rowFactor j n * pieceL j n else 0 +noncomputable def rowTable (N : ℕ) : ℝ := + ∑ j : Fin 6, (∑ a : Fin 12, rowPiece j (N+1+a.val)) / + (1-Real.exp (-12*Real.pi*dampingCap ⟨j.val+1,by omega⟩)) + +lemma rowFactor_nonneg (j : Fin 6) (n : ℕ) : 0 ≤ rowFactor j n := by + unfold rowFactor + exact mul_nonneg (div_nonneg (by have hz := zCap_nonneg (⟨j.val,by omega⟩ : Fin 7); positivity) (Q_pos _).le) (densityCap_nonneg _) +lemma rowFactor_periodic (j : Fin 6) (n k : ℕ) : rowFactor j (n+12*k) = rowFactor j n := by + have hmod : (n+12*k)%12 = n%12 := by omega + unfold rowFactor Q D + rw [hmod] +lemma rowPiece_nonneg (j : Fin 6) (n : ℕ) : 0 ≤ rowPiece j n := by + unfold rowPiece + split_ifs + · exact mul_nonneg (rowFactor_nonneg _ _) (pieceL_nonneg _ (Nat.cast_nonneg _)) + · rfl +lemma rowPiece_period_bound (j : Fin 6) (n k : ℕ) : + rowPiece j (n+12*k) ≤ (Real.exp (-12*Real.pi*dampingCap ⟨j.val+1,by omega⟩))^k*rowPiece j n := by + have hmod : (n+12*k)%12 = n%12 := by omega + unfold rowPiece + rw [hmod] + split_ifs with hn + · rw [rowFactor_periodic] + simp only [Nat.cast_add,Nat.cast_mul,Nat.cast_ofNat] + calc + _ ≤ rowFactor j n*((Real.exp (-12*Real.pi*dampingCap ⟨j.val+1,by omega⟩))^k*pieceL j n) := + mul_le_mul_of_nonneg_left (pieceL_period_bound j (Nat.cast_nonneg _) k) (rowFactor_nonneg _ _) + _ = _ := by ring + · simp + +lemma rowPiece_tail_sum (j : Fin 6) (N : ℕ) : + Summable (fun n : ℕ => rowPiece j (N+1+n)) ∧ + (∑' n : ℕ, rowPiece j (N+1+n)) ≤ + (∑ a : Fin 12, rowPiece j (N+1+a.val)) / + (1-Real.exp (-12*Real.pi*dampingCap ⟨j.val+1,by omega⟩)) := by + apply periodic_geometric_sum (fun _ => rowPiece_nonneg j _) (Real.exp_pos _).le + · apply Real.exp_lt_one_iff.mpr + have hg := dampingCap_pos (⟨j.val+1,by omega⟩ : Fin 7) + nlinarith [Real.pi_pos,mul_pos Real.pi_pos hg] + · intro a k + convert rowPiece_period_bound j (N+1+a.val) k using 1 + congr 1 + omega + +end SharpPlanar + +namespace SharpPlanar +open IntegerBasis + +lemma paired_jet_bound {q : ℝ} (hq : 0 < q) (d a b : ℝ) : + |-a/q|+|(d*a-b)/q| ≤ ((1+|d|)*|a|+|b|)/q := by + rw [abs_div,abs_div,abs_neg,abs_of_pos hq,← add_div] + apply div_le_div_of_nonneg_right _ hq.le + have hh := abs_sub (d*a) b + rw [abs_mul] at hh + nlinarith + +lemma sharp_S_row (x : X) (n : Node) : + |S x (n,false)|+|S x (n,true)| ≤ ‖x‖*(∑ j : Fin 6, rowPiece j n.val) := by + have hs : (0:ℝ) ≤ n.val := Nat.cast_nonneg _ + have h0 := sharp_moment_bound (positiveData x) 0 hs + have h1 := sharp_moment_bound (positiveData x) 1 hs + simp only [positiveData,abs_zero,zero_add,zero_mul,add_zero,pow_zero,mul_one] at h0 + simp only [positiveData,abs_zero,zero_add,zero_mul,add_zero,pow_one] at h1 + have hq := Q_pos n.val + rw [S_apply,S_apply] + simp only [Scoords,Bool.false_eq_true,ite_false,ite_true] + calc + _ ≤ ((1+|D n.val|)*|K (positiveData x) 0 n.val|+|K (positiveData x) 1 n.val|)/Q n.val := + paired_jet_bound hq _ _ _ + _ ≤ ((1+|D n.val|)*(‖x‖*(∑ j : Fin 6, densityCap j*pieceL j n.val))+ + ‖x‖*(∑ j : Fin 6, densityCap j*pieceL j n.val*(Real.pi*zCap ⟨j.val,by omega⟩)))/Q n.val := by + exact div_le_div_of_nonneg_right (add_le_add (mul_le_mul_of_nonneg_left h0 (by positivity)) h1) hq.le + _ = _ := by + simp only [rowPiece,n.prop.2,ite_true,rowFactor,div_eq_mul_inv] + rw [Finset.mul_sum,Finset.mul_sum,Finset.mul_sum,← Finset.sum_add_distrib,Finset.sum_mul, Finset.mul_sum] + apply Finset.sum_congr rfl + intro j _ + ring + +noncomputable def rowTailNorm (x : X) (N : ℕ) : ℝ := + ∑' n : {n : Node // N |x (n.val,false)|+|x (n.val,true)|) := by + exact (X_summable_pairs x).subtype _ + +lemma natural_row_tail_summable (N : ℕ) : + Summable (fun k : ℕ => ∑ j : Fin 6, rowPiece j (N+1+k)) := by + exact (hasSum_sum (fun j _ => (rowPiece_tail_sum j N).1.hasSum)).summable + +lemma natural_row_tail_bound (N : ℕ) : + (∑' k : ℕ, ∑ j : Fin 6, rowPiece j (N+1+k)) ≤ rowTable N := by + rw [Summable.tsum_finsetSum (fun j _ => (rowPiece_tail_sum j N).1)] + exact Finset.sum_le_sum (fun j _ => (rowPiece_tail_sum j N).2) + + +theorem sharp_S_tail (x : X) (N : ℕ) : rowTailNorm (S x) N ≤ rowTable N*‖x‖ := by + let f : ℕ → ℝ := fun k => ∑ j : Fin 6, rowPiece j (N+1+k) + let index : {n : Node // N n.val.val-(N+1) + have hi : Function.Injective index := by + intro a b hab + apply Subtype.ext + apply Subtype.ext + have ha := a.prop; have hb := b.prop + dsimp only [index] at hab + omega + have he (n : {n : Node // N Finset.sum_nonneg (fun _ _ => rowPiece_nonneg _ _) + have hfi : Summable (f ∘ index) := hf.comp_injective hi + have hsum : (∑' n, f (index n)) ≤ rowTable N := + (tsum_comp_le_tsum_of_inj hf hfn hi).trans (natural_row_tail_bound N) + calc + rowTailNorm (S x) N ≤ ∑' n : {n : Node // N linarith [Real.pi_gt_d6,Real.pi_lt_d6] +lemma b_fine : (86602/100000:ℝ) < b ∧ b < 86603/100000 := by + constructor <;> nlinarith [b_pos,b_sq] + +lemma rowQLower_bound (n : ℕ) (hn : n%12 ∈ residues) : 0 < rowQLower n ∧ rowQLower n < Q n := by + have hp := pi_fine + have hb := b_fine + have hp2 : (314159/100000:ℝ)^2 < Real.pi^2 := by nlinarith [Real.pi_pos] + have hsmall : (2*(314159/100000:ℝ)^2/3)*(2-2*(86603/100000)) < (2*Real.pi^2/3)*(2-2*b) := by + gcongr; linarith + have hlarge : (2*(314159/100000:ℝ)^2/3)*(2+2*(86602/100000)) < (2*Real.pi^2/3)*(2+2*b) := by + gcongr; linarith + rw [← Q_mod] + simp only [residues,Finset.mem_insert,Finset.mem_singleton] at hn + rcases hn with hn | hn | hn | hn | hn | hn <;> + simp [rowQLower,hn,Q_0,Q_1,Q_3,Q_4,Q_7,Q_9] <;> nlinarith + +lemma rowDUpper_bound (n : ℕ) (hn : n%12 ∈ residues) : |D n| < rowDUpper n := by + have hp := pi_fine + have hb := b_fine + have hpb : Real.pi*b < (31416/10000:ℝ)*(86603/100000) := by gcongr <;> linarith + have hpb0 : (314159/100000:ℝ)*(86602/100000) < Real.pi*b := by gcongr <;> linarith + have hpbpos : 0 < Real.pi*b := mul_pos Real.pi_pos b_pos + rw [← D_mod] + simp only [residues,Finset.mem_insert,Finset.mem_singleton] at hn + rcases hn with hn | hn | hn | hn | hn | hn <;> + norm_num [rowDUpper,hn] + all_goals first | rw [D_0] | rw [D_1] | rw [D_3] | rw [D_4] | rw [D_7] | rw [D_9] + all_goals apply abs_lt.mpr; constructor <;> nlinarith + +end SharpPlanar + +namespace SharpPlanar +open IntegerBasis +noncomputable def pieceBase : Fin 6 → ℝ := ![469/1000000,7279/1000000,59165/1000000,219974/1000000,494744/1000000,828986/1000000] +lemma pieceBase_pos (j : Fin 6) : 0 < pieceBase j := by fin_cases j <;> norm_num [pieceBase] +lemma pieceBase_lt_one (j : Fin 6) : pieceBase j < 1 := by fin_cases j <;> norm_num [pieceBase] +lemma pieceBase_contains (j : Fin 6) : + Real.exp (-(314159/100000:ℝ)*dampingCap ⟨j.val+1,by omega⟩) ≤ pieceBase j := by + have hg : 0 ≤ (314159/100000:ℝ)*dampingCap ⟨j.val+1,by omega⟩ := by + exact mul_nonneg (by norm_num) (dampingCap_pos _).le + have hp := Real.sum_le_exp_of_nonneg hg 20 + rw [neg_mul,Real.exp_neg] + apply (inv_le_iff_one_le_mul₀ (Real.exp_pos _)).mpr + have ht : 1 ≤ pieceBase j * (∑ i ∈ Finset.range 20, + ((314159/100000:ℝ)*dampingCap ⟨j.val+1,by omega⟩)^i/(i.factorial:ℝ)) := by + fin_cases j <;> norm_num [pieceBase,dampingCap,Finset.sum_range_succ] + exact ht.trans (mul_le_mul_of_nonneg_left hp (pieceBase_pos j).le) + +lemma decay_pieceBase (j : Fin 6) (n : ℕ) : + Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*n) ≤ pieceBase j^n := by + have he : Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩) ≤ pieceBase j := + (Real.exp_le_exp.mpr (by nlinarith [pi_fine,(dampingCap_pos ⟨j.val+1,by omega⟩)])).trans + (pieceBase_contains j) + rw [mul_comm _ (n:ℝ),Real.exp_nat_mul] + exact pow_le_pow_left₀ (Real.exp_pos _).le he n + +noncomputable def massRational (j : Fin 6) (n : ℕ) : ℝ := + if slopeCap j*(n:ℝ)=0 then 1/6 else min (1/6) (1/((314159/100000:ℝ)*slopeCap j*n)) +lemma massRational_nonneg (j : Fin 6) (n : ℕ) : 0 ≤ massRational j n := by + have hs := slopeCap_nonneg j + unfold massRational + split_ifs <;> positivity +lemma pieceMass_le (j : Fin 6) (n : ℕ) : pieceMass j n ≤ massRational j n := by + unfold pieceMass massRational + split_ifs with hz + · rfl + · apply min_le_min_left + have hpos : 0 < slopeCap j*(n:ℝ) := lt_of_le_of_ne (mul_nonneg (slopeCap_nonneg j) (Nat.cast_nonneg n)) (Ne.symm hz) + apply one_div_le_one_div_of_le + · nlinarith + · nlinarith [pi_fine] + +noncomputable def factorRational (j : Fin 6) (n : ℕ) : ℝ := + (1+rowDUpper n+(31416/10000:ℝ)*zCap ⟨j.val,by omega⟩)/rowQLower n*densityCap j +noncomputable def pieceRational (j : Fin 6) (n : ℕ) : ℝ := + if n%12 ∈ residues then factorRational j n * + (lambdaCap ⟨j.val,by omega⟩*pieceBase j^n*massRational j n) else 0 +noncomputable def tableRational (N : ℕ) : ℝ := + ∑ j : Fin 6, (∑ a : Fin 12, pieceRational j (N+1+a.val))/(1-pieceBase j^12) +lemma factorRational_nonneg (j : Fin 6) (n : ℕ) : 0 ≤ factorRational j n := by + have hq : 0 ≤ rowQLower n := by unfold rowQLower; split_ifs <;> norm_num + have hd : 0 ≤ rowDUpper n := by unfold rowDUpper; split_ifs <;> norm_num + have hz := zCap_nonneg ⟨j.val,by omega⟩ + unfold factorRational + exact mul_nonneg (div_nonneg (by positivity) hq) (densityCap_nonneg j) +lemma rowFactor_le (j : Fin 6) (n : ℕ) (hn : n%12 ∈ residues) : + rowFactor j n ≤ factorRational j n := by + unfold rowFactor factorRational + have hq := rowQLower_bound n hn + have hd := rowDUpper_bound n hn + have hz := zCap_nonneg ⟨j.val,by omega⟩ + apply mul_le_mul_of_nonneg_right _ (densityCap_nonneg j) + have hd0 : 0 ≤ rowDUpper n := (abs_nonneg (D n)).trans hd.le + apply div_le_div₀ (by positivity) + · exact add_le_add (add_le_add le_rfl hd.le) (mul_le_mul_of_nonneg_right pi_fine.2.le hz) + · exact hq.1 + · exact hq.2.le +lemma rowPiece_le (j : Fin 6) (n : ℕ) : rowPiece j n ≤ pieceRational j n := by + unfold rowPiece pieceRational + split_ifs with hn + · unfold pieceL + apply mul_le_mul (rowFactor_le j n hn) + · apply mul_le_mul + · exact mul_le_mul_of_nonneg_left (decay_pieceBase j n) (lambdaCap_nonneg _) + · exact pieceMass_le j n + · exact pieceMass_nonneg j (Nat.cast_nonneg n) + · exact mul_nonneg (lambdaCap_nonneg _) (pow_nonneg (pieceBase_pos j).le _) + · exact pieceL_nonneg j (Nat.cast_nonneg n) + · exact factorRational_nonneg j n + · rfl +lemma rowTable_le (N : ℕ) : rowTable N ≤ tableRational N := by + unfold rowTable tableRational + apply Finset.sum_le_sum + intro j _ + have hd : 0 < 1-pieceBase j^12 := sub_pos.mpr (pow_lt_one₀ (pieceBase_pos j).le (pieceBase_lt_one j) (by norm_num)) + apply div_le_div₀ + · exact Finset.sum_nonneg (fun a _ => (rowPiece_nonneg j _).trans (rowPiece_le j _)) + · exact Finset.sum_le_sum (fun a _ => rowPiece_le j _) + · exact hd + · have he := decay_pieceBase j 12 + have heq : Real.exp (-Real.pi*dampingCap ⟨j.val+1,by omega⟩*(12:ℕ)) = Real.exp (-12*Real.pi*dampingCap ⟨j.val+1,by omega⟩) := by congr 1; push_cast; ring + rw [heq] at he + exact sub_le_sub_left he 1 + +lemma tableRational_zero : tableRational 0 < 28 := by + norm_num [tableRational,pieceRational,factorRational,massRational,pieceBase, + rowDUpper,rowQLower,lambdaCap,zCap,densityCap,densityNum,densityDen,slopeCap, + residues,Fin.sum_univ_succ] +lemma tableRational_four : tableRational 4 < 28/100 := by + norm_num [tableRational,pieceRational,factorRational,massRational,pieceBase, + rowDUpper,rowQLower,lambdaCap,zCap,densityCap,densityNum,densityDen,slopeCap, + residues,Fin.sum_univ_succ] +lemma tableRational_sixteen : tableRational 16 < 15/1000 := by + norm_num [tableRational,pieceRational,factorRational,massRational,pieceBase, + rowDUpper,rowQLower,lambdaCap,zCap,densityCap,densityNum,densityDen,slopeCap, + residues,Fin.sum_univ_succ] +lemma tableRational_hundred : tableRational 100 < 5/10^10 := by + norm_num [tableRational,pieceRational,factorRational,massRational,pieceBase, + rowDUpper,rowQLower,lambdaCap,zCap,densityCap,densityNum,densityDen,slopeCap, + residues,Fin.sum_univ_succ] + +theorem rowTable_bounds : rowTable 0 < 28 ∧ rowTable 4 < 28/100 ∧ + rowTable 16 < 15/1000 ∧ rowTable 100 < 5/10^10 := + ⟨(rowTable_le 0).trans_lt tableRational_zero,(rowTable_le 4).trans_lt tableRational_four, + (rowTable_le 16).trans_lt tableRational_sixteen,(rowTable_le 100).trans_lt tableRational_hundred⟩ +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Cardinal.lean b/lean/OAI/Analysis/PlanarPacking/Cardinal.lean new file mode 100644 index 0000000000000000000000000000000000000000..86790308e5d8148937e4a0d8d52b2b896591ce4a --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Cardinal.lean @@ -0,0 +1,1128 @@ +import Mathlib.Analysis.Complex.ExponentialBounds +import Mathlib.Analysis.InnerProductSpace.EuclideanDist +import Mathlib.Analysis.Normed.Group.FunctionSeries +import Mathlib.Analysis.Normed.Lp.lpSpace +import Mathlib.Analysis.Real.Pi.Bounds +import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic +import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic +import Mathlib.Tactic + +namespace OAI + +/-! +# Gaussian cardinal functions for planar packing + +The cardinal family and Fourier kernel follow the construction in +*A sharp Fourier certificate for planar circle packing* (OpenAI, 2026). +-/ + +open scoped BigOperators ComplexConjugate ENNReal +open MeasureTheory + +namespace SharpPlanar + +abbrev Plane := EuclideanSpace ℝ (Fin 2) + +noncomputable def b : ℝ := Real.sqrt 3 / 2 +noncomputable def h : ℝ := 2 / 5 +noncomputable def B : ℝ := 4 / 3 + +def residues : Finset ℕ := {0, 1, 3, 4, 7, 9} + + +abbrev Node := {n : ℕ // 0 < n ∧ n % 12 ∈ residues} + + +abbrev X := lp (fun _ : Node × Bool => ℝ) 1 + +noncomputable def P (s : ℝ) : ℝ := + ∏ a ∈ residues, (2 * Real.sin (Real.pi * (s - a) / 12)) ^ 2 + +noncomputable def Pcoeff : ℕ → ℂ + | 0 => 5 + | 1 => -1 + 2 * Complex.I * b + | 2 => 1 + 2 * Complex.I * b + | 3 => -2 + | 4 => -(1 / 2) + Complex.I * b + | 5 => -1 - 2 * Complex.I * b + | 6 => 1 + | _ => 0 + +noncomputable def Q (n : ℕ) : ℝ := + (Real.pi / 6) ^ 2 * ∏ a ∈ residues.erase (n % 12), + (2 * Real.sin (Real.pi * (((n % 12 : ℕ) : ℝ) - (a : ℝ)) / 12)) ^ 2 + +noncomputable def D (n : ℕ) : ℝ := + (Real.pi / 6) * ∑ a ∈ residues.erase (n % 12), + (Real.cos (Real.pi * (((n % 12 : ℕ) : ℝ) - (a : ℝ)) / 12) / + Real.sin (Real.pi * (((n % 12 : ℕ) : ℝ) - (a : ℝ)) / 12)) + +noncomputable def lambda (t : ℝ) : ℂ := + Complex.I / ((b : ℂ) * ((t : ℂ) + Complex.I * (h : ℂ))) +noncomputable def z (t : ℝ) : ℂ := + -(B : ℂ) / ((t : ℂ) + Complex.I * (h : ℂ)) - Complex.I * (h : ℂ) + + +noncomputable def u (n j : ℕ) (t : ℝ) : ℂ := + -2 * (Real.pi : ℂ) ^ 2 * Complex.exp (-Complex.I * Real.pi * t * n) * + ∑ l ∈ Finset.Icc (j+1) 6, + ((l : ℂ) / 6 - t) * Pcoeff l * Complex.exp (Complex.I * Real.pi * (l : ℂ) / 6 * n) + +noncomputable def v (n j : ℕ) (t : ℝ) : ℂ := + 2 * Complex.I * Real.pi * Complex.exp (-Complex.I * Real.pi * t * n) * + ∑ l ∈ Finset.Icc (j+1) 6, + Pcoeff l * Complex.exp (Complex.I * Real.pi * (l : ℂ) / 6 * n) + +structure CardinalData where + C : ℝ + c₀ : ℝ + d₀ : ℝ + x : X + +noncomputable def density (p : CardinalData) (j : ℕ) (t : ℝ) : ℂ := + (p.c₀ : ℂ) * u 0 j t + (p.d₀ : ℂ) * v 0 j t + + ∑' n : Node, ((p.x (n, false) : ℂ) * u n.val j t + + (p.x (n, true) : ℂ) * v n.val j t) + + +noncomputable def kernelMoment (ell : ℕ) (s t : ℝ) : ℂ := + lambda t * (Complex.I * Real.pi * z t) ^ ell * + Complex.exp (Complex.I * Real.pi * z t * s) + + +noncomputable def K (p : CardinalData) (ell : ℕ) (s : ℝ) : ℝ := + ((p.C : ℂ) * (Pcoeff 0 * kernelMoment ell s 0 + + ∑ j ∈ Finset.Icc 1 6, 2 * Pcoeff j * kernelMoment ell s ((j : ℝ) / 6)) + + ∑ j ∈ Finset.range 6, + ∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, + density p j t * kernelMoment ell s t).re + +noncomputable def positiveData (x : X) : CardinalData := ⟨0, 0, 0, x⟩ + + +noncomputable def Scoords (x : X) (ni : Node × Bool) : ℝ := + if ni.2 then + (D ni.1.val * K (positiveData x) 0 ni.1.val - K (positiveData x) 1 ni.1.val) / + Q ni.1.val + else -K (positiveData x) 0 ni.1.val / Q ni.1.val + +noncomputable def fixed₁ (x : X) : CardinalData := ⟨-13/1000, 1, 11/25, x⟩ +noncomputable def fixed₂ (x : X) : CardinalData := ⟨17/1000, 0, -46/125, x⟩ + +theorem b_pos : 0 < b := by unfold b; positivity + +theorem b_sq : b ^ 2 = 3 / 4 := by + unfold b + rw [div_pow, Real.sq_sqrt (by norm_num : (0 : ℝ) ≤ 3)] + norm_num + +theorem B_eq_inv_b_sq : B = (b ^ 2)⁻¹ := by rw [b_sq]; norm_num [B] + +theorem z_im (t : ℝ) : (z t).im = h * (B / (t ^ 2 + h ^ 2) - 1) := by + simp [z, Complex.div_im, Complex.normSq, pow_two] + ring + +theorem strict_damping {t : ℝ} (ht : |t| ≤ 1) : (26 : ℝ) / 435 ≤ (z t).im := by + rw [z_im] + have ht2 : t ^ 2 ≤ 1 := by + have := sq_le_sq₀ (abs_nonneg t) (show (0 : ℝ) ≤ 1 by norm_num) + simpa using this.mpr ht + have hd : 0 < t ^ 2 + h ^ 2 := by unfold h; positivity + have hb : (4 : ℝ) / 3 / ((29 : ℝ) / 25) ≤ B / (t ^ 2 + h ^ 2) := by + apply div_le_div_of_nonneg_left (by norm_num : (0 : ℝ) ≤ 4/3) hd + change t ^ 2 + (2/5 : ℝ) ^ 2 ≤ 29/25 + linarith + unfold h at * + norm_num at hb ⊢ + linarith + + + +theorem X_summable (x : X) : Summable (fun ni : Node × Bool => |x ni|) := by + simpa using (lp.memℓp x).summable (by norm_num : 0 < (1 : ℝ≥0∞).toReal) + +theorem X_summable_coord (x : X) (i : Bool) : Summable (fun n : Node => |x (n, i)|) := by + exact (X_summable x).comp_injective (fun _ _ hh => congrArg Prod.fst hh) + + +theorem X_norm (x : X) : ‖x‖ = ∑' n : Node, (|x (n, false)| + |x (n, true)|) := by + rw [lp.norm_eq_tsum_rpow (by norm_num : 0 < (1 : ℝ≥0∞).toReal)] + simp only [ENNReal.toReal_one, Real.rpow_one, one_div_one, Real.norm_eq_abs] + rw [(X_summable x).tsum_prod] + simp only [tsum_bool] + +theorem X_summable_pairs (x : X) : + Summable (fun n : Node => |x (n, false)| + |x (n, true)|) := by + exact (X_summable_coord x false).add (X_summable_coord x true) + + +theorem h_pos : 0 < h := by norm_num [h] +theorem B_pos : 0 < B := by norm_num [B] + +theorem imaginary_gaussian_denominator (t : ℝ) : + h ≤ ‖(t : ℂ) + Complex.I * (h : ℂ)‖ := by + have hh := Complex.abs_im_le_norm ((t : ℂ) + Complex.I * (h : ℂ)) + simpa [abs_of_pos h_pos] using hh + +theorem lambda_bound (t : ℝ) : ‖lambda t‖ ≤ 1 / (b * h) := by + rw [lambda, norm_div, norm_mul, Complex.norm_I, Complex.norm_real, + Real.norm_eq_abs, abs_of_pos b_pos] + apply div_le_div_of_nonneg_left (by norm_num) (mul_pos b_pos h_pos) + exact mul_le_mul_of_nonneg_left (imaginary_gaussian_denominator t) b_pos.le + +theorem z_bound (t : ℝ) : ‖z t‖ ≤ B / h + h := by + have hden : 0 < ‖(t : ℂ) + Complex.I * (h : ℂ)‖ := + h_pos.trans_le (imaginary_gaussian_denominator t) + calc + ‖z t‖ ≤ ‖-(B : ℂ) / ((t : ℂ) + Complex.I * (h : ℂ))‖ + + ‖Complex.I * (h : ℂ)‖ := norm_sub_le _ _ + _ = B / ‖(t : ℂ) + Complex.I * (h : ℂ)‖ + h := by + simp [Complex.norm_real, abs_of_pos B_pos, abs_of_pos h_pos] + _ ≤ B / h + h := add_le_add + (div_le_div_of_nonneg_left B_pos.le h_pos (imaginary_gaussian_denominator t)) le_rfl + +noncomputable def kappa : ℝ := 26 * Real.pi / 435 + +theorem kappa_pos : 0 < kappa := by unfold kappa; positivity + + +theorem kernelMoment_bound (ell : ℕ) {s t : ℝ} (hs : 0 ≤ s) (ht : |t| ≤ 1) : + ‖kernelMoment ell s t‖ ≤ (1 / (b*h)) * (Real.pi * (B/h+h))^ell * + Real.exp (-kappa*s) := by + have hex : ‖Complex.exp (Complex.I * Real.pi * z t * s)‖ ≤ + Real.exp (-kappa*s) := by + rw [Complex.norm_exp] + apply Real.exp_le_exp.mpr + simp only [Complex.mul_re, Complex.mul_im, Complex.I_re, Complex.I_im, + Complex.ofReal_re, Complex.ofReal_im, zero_mul, mul_zero, one_mul, zero_sub, + sub_zero, zero_add] + have hd := strict_damping ht + dsimp [kappa] + nlinarith [mul_nonneg Real.pi_pos.le hs] + unfold kernelMoment + rw [norm_mul, norm_mul, norm_pow, norm_mul, norm_mul, Complex.norm_I, + Complex.norm_real, Real.norm_eq_abs, abs_of_pos Real.pi_pos, one_mul] + have hb' := b_pos + have hh' := h_pos + have hB' := B_pos + have hl := lambda_bound t + have hz := z_bound t + gcongr + + +def coeffMass : ℕ → ℝ + | 0 => 5 + | 1 => 2 + | 2 => 2 + | 3 => 2 + | 4 => 1 + | 5 => 2 + | 6 => 1 + | _ => 0 + +theorem Pcoeff_norm (j : ℕ) : ‖Pcoeff j‖ = coeffMass j := by + have hb := b_sq + rcases lt_or_ge j 7 with hj | hj + · interval_cases j <;> + apply (sq_eq_sq₀ (norm_nonneg _) (by norm_num [coeffMass])).mp + all_goals + rw [← Complex.normSq_eq_norm_sq] + norm_num [Pcoeff, coeffMass, Complex.normSq] + all_goals nlinarith [hb] + · have hj0 : j ≠ 0 := by omega + have hj1 : j ≠ 1 := by omega + have hj2 : j ≠ 2 := by omega + have hj3 : j ≠ 3 := by omega + have hj4 : j ≠ 4 := by omega + have hj5 : j ≠ 5 := by omega + have hj6 : j ≠ 6 := by omega + simp [Pcoeff, coeffMass] + + +lemma positive_coeff_mass : ∑ l ∈ Finset.Icc 1 6, ‖Pcoeff l‖ = 10 := by + simp only [Pcoeff_norm] + norm_num [Finset.sum_Icc_succ_top, coeffMass] + +lemma positive_coeff_mass_le (j : ℕ) : ∑ l ∈ Finset.Icc (j+1) 6, ‖Pcoeff l‖ ≤ 10 := by + rw [← positive_coeff_mass] + apply Finset.sum_le_sum_of_subset_of_nonneg + · intro l hl + simp only [Finset.mem_Icc] at hl ⊢ + omega + · intro l _ _; exact norm_nonneg _ + +lemma phase_norm (n : ℕ) (t : ℝ) : + ‖Complex.exp (-Complex.I * Real.pi * t * n)‖ = 1 := by + simp [Complex.norm_exp] + +lemma atom_phase_norm (n l : ℕ) : + ‖Complex.exp (Complex.I * Real.pi * (l : ℂ) / 6 * n)‖ = 1 := by + simp [Complex.norm_exp] + +lemma frequency_distance_le {l : ℕ} (hl : l ≤ 6) {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : + ‖(l : ℂ)/6 - (t : ℂ)‖ ≤ 1 := by + have he : (l : ℂ)/6 - (t : ℂ) = (((l : ℝ)/6 - t : ℝ) : ℂ) := by push_cast; rfl + rw [he, Complex.norm_real, Real.norm_eq_abs, abs_le] + have hln : (0 : ℝ) ≤ l := Nat.cast_nonneg l + have hlu : (l : ℝ) ≤ 6 := by exact_mod_cast hl + constructor <;> linarith [ht.1, ht.2] + + +lemma u_bound (n j : ℕ) {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : + ‖u n j t‖ ≤ 20 * Real.pi^2 := by + have hs : ‖∑ l ∈ Finset.Icc (j+1) 6, + ((l : ℂ)/6-t) * Pcoeff l * Complex.exp (Complex.I * Real.pi * (l : ℂ)/6*n)‖ ≤ 10 := by + calc + _ ≤ ∑ l ∈ Finset.Icc (j+1) 6, + ‖((l : ℂ)/6-t) * Pcoeff l * Complex.exp (Complex.I * Real.pi * (l : ℂ)/6*n)‖ := + norm_sum_le _ _ + _ ≤ ∑ l ∈ Finset.Icc (j+1) 6, ‖Pcoeff l‖ := by + apply Finset.sum_le_sum + intro l hl + rw [norm_mul, norm_mul, atom_phase_norm, mul_one] + exact (mul_le_mul_of_nonneg_right (frequency_distance_le (Finset.mem_Icc.mp hl).2 ht) + (norm_nonneg _)).trans_eq (one_mul _) + _ ≤ 10 := positive_coeff_mass_le j + unfold u + rw [norm_mul, norm_mul, norm_mul, norm_pow, phase_norm] + simp only [norm_neg, Complex.norm_ofNat, Complex.norm_real, Real.norm_eq_abs, + abs_of_pos Real.pi_pos, mul_one] + nlinarith [sq_nonneg Real.pi] + +lemma v_bound (n j : ℕ) {t : ℝ} (_ : t ∈ Set.Icc (0 : ℝ) 1) : + ‖v n j t‖ ≤ 20 * Real.pi := by + have hs : ‖∑ l ∈ Finset.Icc (j+1) 6, + Pcoeff l * Complex.exp (Complex.I * Real.pi * (l : ℂ)/6*n)‖ ≤ 10 := by + calc + _ ≤ ∑ l ∈ Finset.Icc (j+1) 6, + ‖Pcoeff l * Complex.exp (Complex.I * Real.pi * (l : ℂ)/6*n)‖ := norm_sum_le _ _ + _ = ∑ l ∈ Finset.Icc (j+1) 6, ‖Pcoeff l‖ := by simp only [norm_mul, atom_phase_norm, mul_one] + _ ≤ 10 := positive_coeff_mass_le j + unfold v + rw [norm_mul, norm_mul, norm_mul, norm_mul, phase_norm] + simp only [Complex.norm_ofNat, Complex.norm_I, Complex.norm_real, Real.norm_eq_abs, + abs_of_pos Real.pi_pos, mul_one] + nlinarith [Real.pi_pos] + +noncomputable def densityBound : ℝ := 20 * Real.pi^2 + +lemma densityBound_nonneg : 0 ≤ densityBound := by unfold densityBound; positivity + +lemma v_bound' (n j : ℕ) {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : + ‖v n j t‖ ≤ densityBound := by + apply (v_bound n j ht).trans + unfold densityBound + nlinarith [Real.pi_gt_three] + +lemma summand_bound (x : X) (n : Node) (j : ℕ) {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : + ‖(x (n, false) : ℂ) * u n.val j t + (x (n, true) : ℂ) * v n.val j t‖ ≤ + densityBound * (|x (n, false)| + |x (n, true)|) := by + calc + _ ≤ ‖(x (n, false) : ℂ) * u n.val j t‖ + ‖(x (n, true) : ℂ) * v n.val j t‖ := norm_add_le _ _ + _ = |x (n, false)| * ‖u n.val j t‖ + |x (n, true)| * ‖v n.val j t‖ := by + simp [Complex.norm_real] + _ ≤ |x (n, false)| * densityBound + |x (n, true)| * densityBound := by + gcongr + exacts [u_bound _ _ ht, v_bound' _ _ ht] + _ = _ := by ring + +lemma density_summable (x : X) (j : ℕ) {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : + Summable (fun n : Node => (x (n, false) : ℂ) * u n.val j t + + (x (n, true) : ℂ) * v n.val j t) := by + exact ((X_summable_pairs x).mul_left densityBound).of_norm_bounded + (fun n => summand_bound x n j ht) + +lemma density_bound (p : CardinalData) (j : ℕ) {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : + ‖density p j t‖ ≤ densityBound * (|p.c₀| + |p.d₀| + ‖p.x‖) := by + have hnorm : Summable (fun n : Node => ‖(p.x (n, false) : ℂ) * u n.val j t + + (p.x (n, true) : ℂ) * v n.val j t‖) := by + apply Summable.of_nonneg_of_le (fun _ => norm_nonneg _) + (fun n => summand_bound p.x n j ht) + exact (X_summable_pairs p.x).mul_left densityBound + have hsum : ‖∑' n : Node, ((p.x (n, false) : ℂ) * u n.val j t + + (p.x (n, true) : ℂ) * v n.val j t)‖ ≤ densityBound * ‖p.x‖ := by + calc + _ ≤ ∑' n : Node, ‖(p.x (n, false) : ℂ) * u n.val j t + + (p.x (n, true) : ℂ) * v n.val j t‖ := norm_tsum_le_tsum_norm hnorm + _ ≤ ∑' n : Node, densityBound * (|p.x (n, false)| + |p.x (n, true)|) := + hnorm.tsum_le_tsum (fun n => summand_bound p.x n j ht) + ((X_summable_pairs p.x).mul_left densityBound) + _ = densityBound * ‖p.x‖ := by rw [tsum_mul_left, ← X_norm] + unfold density + calc + _ ≤ ‖(p.c₀ : ℂ) * u 0 j t‖ + ‖(p.d₀ : ℂ) * v 0 j t‖ + + ‖∑' n : Node, ((p.x (n, false) : ℂ) * u n.val j t + + (p.x (n, true) : ℂ) * v n.val j t)‖ := + (norm_add_le _ _).trans (add_le_add (norm_add_le _ _) le_rfl) + _ ≤ |p.c₀| * densityBound + |p.d₀| * densityBound + densityBound * ‖p.x‖ := by + simp only [norm_mul, Complex.norm_real, Real.norm_eq_abs] + gcongr + exacts [u_bound _ _ ht, v_bound' _ _ ht] + _ = _ := by ring + + +noncomputable def kernelEnvelope (ell : ℕ) (s : ℝ) : ℝ := + (1/(b*h)) * (Real.pi*(B/h+h))^ell * Real.exp (-kappa*s) + +lemma kernelEnvelope_nonneg (ell : ℕ) (s : ℝ) : 0 ≤ kernelEnvelope ell s := by + have := b_pos + have := h_pos + have := B_pos + unfold kernelEnvelope + positivity + +lemma kernelMoment_bound' (ell : ℕ) {s t : ℝ} (hs : 0 ≤ s) (ht : t ∈ Set.Icc (0 : ℝ) 1) : + ‖kernelMoment ell s t‖ ≤ kernelEnvelope ell s := by + apply kernelMoment_bound ell hs + rw [abs_of_nonneg ht.1] + exact ht.2 + +lemma atomic_bound (ell : ℕ) {s : ℝ} (hs : 0 ≤ s) : + ‖Pcoeff 0 * kernelMoment ell s 0 + + ∑ j ∈ Finset.Icc 1 6, 2 * Pcoeff j * kernelMoment ell s ((j : ℝ)/6)‖ ≤ + 25 * kernelEnvelope ell s := by + have hzero : ‖Pcoeff 0 * kernelMoment ell s 0‖ ≤ 5 * kernelEnvelope ell s := by + rw [norm_mul, Pcoeff_norm] + apply mul_le_mul_of_nonneg_left (kernelMoment_bound' ell hs (by simp)) (by norm_num [coeffMass]) + have hsum : ‖∑ j ∈ Finset.Icc 1 6, 2 * Pcoeff j * kernelMoment ell s ((j : ℝ)/6)‖ ≤ + 20 * kernelEnvelope ell s := by + calc + _ ≤ ∑ j ∈ Finset.Icc 1 6, ‖2 * Pcoeff j * kernelMoment ell s ((j : ℝ)/6)‖ := norm_sum_le _ _ + _ ≤ ∑ j ∈ Finset.Icc 1 6, 2 * ‖Pcoeff j‖ * kernelEnvelope ell s := by + apply Finset.sum_le_sum + intro j hj + rw [norm_mul, norm_mul, Complex.norm_ofNat] + gcongr + apply kernelMoment_bound' ell hs + have hju : (j : ℝ) ≤ 6 := by exact_mod_cast (Finset.mem_Icc.mp hj).2 + constructor + · positivity + · linarith + _ = 20 * kernelEnvelope ell s := by + rw [← Finset.sum_mul, ← Finset.mul_sum, positive_coeff_mass] + ring + exact (norm_add_le _ _).trans (by linarith) + +lemma piece_interval {j : ℕ} (hj : j < 6) {t : ℝ} + (ht : t ∈ Set.uIcc ((j : ℝ)/6) (((j : ℝ)+1)/6)) : t ∈ Set.Icc (0 : ℝ) 1 := by + rw [Set.uIcc_of_le (by linarith : (j : ℝ)/6 ≤ ((j : ℝ)+1)/6)] at ht + have hj0 : (0 : ℝ) ≤ j := Nat.cast_nonneg j + have hj5 : (j : ℝ) ≤ 5 := by exact_mod_cast (show j ≤ 5 by omega) + constructor <;> linarith [ht.1, ht.2] + +lemma integral_piece_bound (p : CardinalData) (ell j : ℕ) (hj : j < 6) + {s : ℝ} (hs : 0 ≤ s) : + ‖∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, density p j t * kernelMoment ell s t‖ ≤ + densityBound * (|p.c₀| + |p.d₀| + ‖p.x‖) * kernelEnvelope ell s / 6 := by + have hb := intervalIntegral.norm_integral_le_of_norm_le_const + (f := fun t => density p j t * kernelMoment ell s t) + (a := (j : ℝ)/6) (b := ((j : ℝ)+1)/6) + (C := densityBound * (|p.c₀| + |p.d₀| + ‖p.x‖) * kernelEnvelope ell s) ?_ + · convert hb using 1 + rw [show ((j : ℝ)+1)/6 - (j : ℝ)/6 = 1/6 by ring, abs_of_pos (by norm_num : (0 : ℝ) < 1/6)] + ring + · intro t ht + have htr := piece_interval hj (Set.uIoc_subset_uIcc ht) + rw [norm_mul] + exact mul_le_mul (density_bound p j htr) (kernelMoment_bound' ell hs htr) + (norm_nonneg _) (by have := densityBound_nonneg; positivity) + + +lemma K_bound (p : CardinalData) (ell : ℕ) {s : ℝ} (hs : 0 ≤ s) : + |K p ell s| ≤ + (25 * |p.C| + densityBound * (|p.c₀| + |p.d₀| + ‖p.x‖)) * kernelEnvelope ell s := by + have hatom : ‖(p.C : ℂ) * (Pcoeff 0 * kernelMoment ell s 0 + + ∑ j ∈ Finset.Icc 1 6, 2 * Pcoeff j * kernelMoment ell s ((j : ℝ)/6))‖ ≤ + 25 * |p.C| * kernelEnvelope ell s := by + rw [norm_mul, Complex.norm_real, Real.norm_eq_abs] + calc + _ ≤ |p.C| * (25 * kernelEnvelope ell s) := by + gcongr; exact atomic_bound ell hs + _ = _ := by ring + have hsum : ‖∑ j ∈ Finset.range 6, + ∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, density p j t * kernelMoment ell s t‖ ≤ + densityBound * (|p.c₀| + |p.d₀| + ‖p.x‖) * kernelEnvelope ell s := by + calc + _ ≤ ∑ j ∈ Finset.range 6, + ‖∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, density p j t * kernelMoment ell s t‖ := norm_sum_le _ _ + _ ≤ ∑ j ∈ Finset.range 6, + (densityBound * (|p.c₀| + |p.d₀| + ‖p.x‖) * kernelEnvelope ell s / 6) := by + exact Finset.sum_le_sum fun j hj => integral_piece_bound p ell j (Finset.mem_range.mp hj) hs + _ = _ := by simp; ring + unfold K + exact (Complex.abs_re_le_norm _).trans ((norm_add_le _ _).trans (by nlinarith)) + + +lemma continuous_u (n j : ℕ) : Continuous (u n j) := by + unfold u + fun_prop + +lemma continuous_v (n j : ℕ) : Continuous (v n j) := by + unfold v + fun_prop + +lemma continuousOn_density (p : CardinalData) (j : ℕ) : + ContinuousOn (density p j) (Set.Icc (0 : ℝ) 1) := by + unfold density + refine ((continuous_const.mul (continuous_u 0 j)).add + (continuous_const.mul (continuous_v 0 j))).continuousOn.add ?_ + apply continuousOn_tsum (u := fun n : Node => + densityBound * (|p.x (n, false)| + |p.x (n, true)|)) + · intro n + exact ((continuous_const.mul (continuous_u n.val j)).add + (continuous_const.mul (continuous_v n.val j))).continuousOn + · exact (X_summable_pairs p.x).mul_left densityBound + · intro n t ht + exact summand_bound p.x n j ht + +lemma denominator_ne (t : ℝ) : (t : ℂ) + Complex.I * h ≠ 0 := by + intro he + have hh := congrArg Complex.im he + simp only [Complex.add_im, Complex.ofReal_im, Complex.mul_im, Complex.I_re, + Complex.ofReal_re, Complex.I_im, zero_mul, one_mul, zero_add, Complex.zero_im] at hh + exact (ne_of_gt h_pos) hh + +lemma continuous_lambda : Continuous lambda := by + unfold lambda + fun_prop (disch := intro t; exact mul_ne_zero (by exact_mod_cast b_pos.ne') (denominator_ne t)) + +lemma continuous_z : Continuous z := by + unfold z + fun_prop (disch := intro t; exact denominator_ne t) + +lemma continuous_kernelMoment (ell : ℕ) (s : ℝ) : Continuous (kernelMoment ell s) := by + unfold kernelMoment + exact (continuous_lambda.mul ((continuous_const.mul continuous_z).pow ell)).mul + (Complex.continuous_exp.comp ((continuous_const.mul continuous_z).mul continuous_const)) + +lemma piece_integrable (p : CardinalData) (ell j : ℕ) (hj : j < 6) (s : ℝ) : + IntervalIntegrable (fun t => density p j t * kernelMoment ell s t) volume + ((j : ℝ)/6) (((j : ℝ)+1)/6) := by + exact ((continuousOn_density p j).mul (continuous_kernelMoment ell s).continuousOn).mono + (fun _ ht => piece_interval hj ht) |>.intervalIntegrable + +lemma density_positive_add (x y : X) (j : ℕ) {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : + density (positiveData (x+y)) j t = density (positiveData x) j t + + density (positiveData y) j t := by + simp only [density, positiveData, Complex.ofReal_zero, zero_mul, zero_add, + lp.coeFn_add, Pi.add_apply, Complex.ofReal_add] + simp_rw [add_mul] + simp_rw [show ∀ n : Node, + (x (n, false) : ℂ) * u n.val j t + (y (n, false) : ℂ) * u n.val j t + + ((x (n, true) : ℂ) * v n.val j t + (y (n, true) : ℂ) * v n.val j t) = + ((x (n, false) : ℂ) * u n.val j t + (x (n, true) : ℂ) * v n.val j t) + + ((y (n, false) : ℂ) * u n.val j t + (y (n, true) : ℂ) * v n.val j t) from fun n => by ring] + exact (density_summable x j ht).tsum_add (density_summable y j ht) + +lemma density_positive_smul (r : ℝ) (x : X) (j : ℕ) (t : ℝ) : + density (positiveData (r • x)) j t = (r : ℂ) * density (positiveData x) j t := by + simp only [density, positiveData, Complex.ofReal_zero, zero_mul, zero_add, + lp.coeFn_smul, Pi.smul_apply, smul_eq_mul, Complex.ofReal_mul] + simp_rw [mul_assoc, ← mul_add, tsum_mul_left] + +lemma K_positive_add (x y : X) (ell : ℕ) (s : ℝ) : + K (positiveData (x+y)) ell s = K (positiveData x) ell s + K (positiveData y) ell s := by + have hp (j : ℕ) (hj : j < 6) : + (∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, + density (positiveData (x+y)) j t * kernelMoment ell s t) = + (∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, + density (positiveData x) j t * kernelMoment ell s t) + + (∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, + density (positiveData y) j t * kernelMoment ell s t) := by + rw [← intervalIntegral.integral_add (piece_integrable _ ell j hj s) (piece_integrable _ ell j hj s)] + apply intervalIntegral.integral_congr + intro t ht + dsimp only + rw [density_positive_add x y j (piece_interval hj ht), add_mul] + unfold K + simp only [positiveData, Complex.ofReal_zero, zero_mul, zero_add] + rw [← Complex.add_re, ← Finset.sum_add_distrib] + congr 1 + apply Finset.sum_congr rfl + intro j hj + exact hp j (Finset.mem_range.mp hj) + +lemma K_positive_smul (r : ℝ) (x : X) (ell : ℕ) (s : ℝ) : + K (positiveData (r • x)) ell s = r * K (positiveData x) ell s := by + unfold K + simp only [positiveData, Complex.ofReal_zero, zero_mul, zero_add] + change (∑ j ∈ Finset.range 6, ∫ t in (j : ℝ)/6..((j : ℝ)+1)/6, + density (positiveData (r • x)) j t * kernelMoment ell s t).re = _ + simp_rw [density_positive_smul, mul_assoc, intervalIntegral.integral_const_mul, + ← Finset.mul_sum] + simp [Complex.mul_re, positiveData] + + +lemma residue_lt {a : ℕ} (ha : a ∈ residues) : a < 12 := by + simp only [residues, Finset.mem_insert, Finset.mem_singleton] at ha + omega + +lemma Q_pos (n : ℕ) : 0 < Q n := by + unfold Q + apply mul_pos (sq_pos_of_pos (by positivity)) + apply Finset.prod_pos + intro a ha + have hane : a ≠ n % 12 := (Finset.mem_erase.mp ha).1 + have hal : a < 12 := residue_lt (Finset.mem_erase.mp ha).2 + have hnl : n % 12 < 12 := Nat.mod_lt _ (by norm_num) + have hh1 : (-12 : ℝ) < ((n % 12 : ℕ) : ℝ) - a := by + have ha' : (a : ℝ) < 12 := by exact_mod_cast hal + have hn' : (0 : ℝ) ≤ ((n % 12 : ℕ) : ℝ) := Nat.cast_nonneg _ + linarith + have hh2 : (((n % 12 : ℕ) : ℝ) - a) < 12 := by + have hn' : ((n % 12 : ℕ) : ℝ) < 12 := by exact_mod_cast hnl + have ha' : (0 : ℝ) ≤ a := Nat.cast_nonneg _ + linarith + have hs : Real.sin (Real.pi * (((n % 12 : ℕ) : ℝ) - a) / 12) ≠ 0 := by + rw [ne_eq, Real.sin_eq_zero_iff_of_lt_of_lt + (by nlinarith [Real.pi_pos, mul_pos Real.pi_pos (by linarith : (0 : ℝ) < ((n%12 : ℕ):ℝ)-a+12)]) + (by nlinarith [Real.pi_pos, mul_pos Real.pi_pos (by linarith : (0 : ℝ) < 12-(((n%12 : ℕ):ℝ)-a))])] + apply div_ne_zero + · apply mul_ne_zero Real.pi_ne_zero + exact sub_ne_zero.mpr (by exact_mod_cast Ne.symm hane) + · norm_num + exact sq_pos_of_ne_zero (mul_ne_zero (by norm_num) hs) + +lemma Q_mod (n : ℕ) : Q (n % 12) = Q n := by simp [Q] +lemma D_mod (n : ℕ) : D (n % 12) = D n := by simp [D] + +noncomputable def nodeWeight (n : ℕ) : ℝ := (1 + |D n|) / Q n +noncomputable def allNodeWeight : ℝ := ∑ a ∈ residues, nodeWeight a + +lemma nodeWeight_pos (n : ℕ) : 0 < nodeWeight n := by + unfold nodeWeight + exact div_pos (by positivity) (Q_pos n) + +lemma allNodeWeight_nonneg : 0 ≤ allNodeWeight := by + exact Finset.sum_nonneg fun a _ => (nodeWeight_pos a).le + +lemma nodeWeight_le (n : Node) : nodeWeight n.val ≤ allNodeWeight := by + have he : nodeWeight n.val = nodeWeight (n.val % 12) := by rw [nodeWeight, nodeWeight, Q_mod, D_mod] + rw [he] + exact Finset.single_le_sum (fun a _ => (nodeWeight_pos a).le) n.property.2 + +lemma K_positive_bound (x : X) (ell : ℕ) {s : ℝ} (hs : 0 ≤ s) : + |K (positiveData x) ell s| ≤ densityBound * ‖x‖ * kernelEnvelope ell s := by + simpa [positiveData] using K_bound (positiveData x) ell hs + +lemma Scoords_bound (x : X) (ni : Node × Bool) : + |Scoords x ni| ≤ allNodeWeight * densityBound * ‖x‖ * + (kernelEnvelope 0 ni.1.val + kernelEnvelope 1 ni.1.val) := by + have he0 := kernelEnvelope_nonneg 0 (ni.1.val : ℝ) + have he1 := kernelEnvelope_nonneg 1 (ni.1.val : ℝ) + have hd := densityBound_nonneg + have hx := norm_nonneg x + have hq := Q_pos ni.1.val + have hc0 := K_positive_bound x 0 (Nat.cast_nonneg ni.1.val) + have hc1 := K_positive_bound x 1 (Nat.cast_nonneg ni.1.val) + have hlocal : |Scoords x ni| ≤ nodeWeight ni.1.val * densityBound * ‖x‖ * + (kernelEnvelope 0 ni.1.val + kernelEnvelope 1 ni.1.val) := by + unfold Scoords nodeWeight + split + · rw [abs_div, abs_of_pos hq] + calc + _ ≤ (|D ni.1.val| * |K (positiveData x) 0 ni.1.val| + + |K (positiveData x) 1 ni.1.val|) / Q ni.1.val := by + apply div_le_div_of_nonneg_right _ hq.le + exact (abs_sub _ _).trans (by rw [abs_mul]) + _ ≤ (|D ni.1.val| * (densityBound * ‖x‖ * kernelEnvelope 0 ni.1.val) + + densityBound * ‖x‖ * kernelEnvelope 1 ni.1.val) / Q ni.1.val := by gcongr + _ ≤ _ := by + apply (div_le_iff₀ hq).mpr + field_simp + nlinarith [mul_nonneg (abs_nonneg (D ni.1.val)) + (mul_nonneg (mul_nonneg hd hx) he1), mul_nonneg (mul_nonneg hd hx) he0] + · rw [abs_div, abs_neg, abs_of_pos hq] + calc + _ ≤ (densityBound * ‖x‖ * kernelEnvelope 0 ni.1.val) / Q ni.1.val := by gcongr + _ ≤ _ := by + apply (div_le_iff₀ hq).mpr + field_simp + nlinarith [mul_nonneg (abs_nonneg (D ni.1.val)) + (mul_nonneg (mul_nonneg hd hx) (add_nonneg he0 he1)), + mul_nonneg (mul_nonneg hd hx) he1] + exact hlocal.trans (by gcongr; exact nodeWeight_le ni.1) + + +lemma exp_nat_summable : Summable (fun n : ℕ => Real.exp (-kappa * n)) := by + have he : Real.exp (-kappa) < 1 := by rw [Real.exp_lt_one_iff]; linarith [kappa_pos] + have hh := summable_geometric_of_lt_one (Real.exp_pos (-kappa)).le he + simpa only [← Real.exp_nat_mul, mul_comm] using hh + +lemma kernelEnvelope_summable (ell : ℕ) : Summable (fun n : Node => kernelEnvelope ell n.val) := by + have hh := exp_nat_summable.comp_injective (i := fun n : Node => n.val) Subtype.val_injective + exact hh.mul_left ((1/(b*h)) * (Real.pi*(B/h+h))^ell) + +lemma pairEnvelope_summable : Summable (fun ni : Node × Bool => + kernelEnvelope 0 ni.1.val + kernelEnvelope 1 ni.1.val) := by + apply (summable_prod_of_nonneg (fun ni => + add_nonneg (kernelEnvelope_nonneg _ _) (kernelEnvelope_nonneg _ _))).mpr + constructor + · intro n; exact Summable.of_finite + · simpa only [tsum_bool] using + ((kernelEnvelope_summable 0).add (kernelEnvelope_summable 1)).add + ((kernelEnvelope_summable 0).add (kernelEnvelope_summable 1)) + +lemma Scoords_summable (x : X) : Summable (fun ni : Node × Bool => |Scoords x ni|) := by + apply Summable.of_nonneg_of_le (fun _ => abs_nonneg _) (fun ni => Scoords_bound x ni) + exact pairEnvelope_summable.mul_left (allNodeWeight * densityBound * ‖x‖) + +lemma Scoords_mem (x : X) : Memℓp (Scoords x) 1 := by + apply memℓp_gen + simpa using Scoords_summable x + +lemma Scoords_add (x y : X) (ni : Node × Bool) : + Scoords (x+y) ni = Scoords x ni + Scoords y ni := by + unfold Scoords + split <;> simp only [K_positive_add] <;> ring + +lemma Scoords_smul (r : ℝ) (x : X) (ni : Node × Bool) : + Scoords (r • x) ni = r * Scoords x ni := by + unfold Scoords + split <;> simp only [K_positive_smul] <;> ring + +noncomputable def Slinear : X →ₗ[ℝ] X where + toFun x := ⟨Scoords x, Scoords_mem x⟩ + map_add' x y := lp.ext (funext fun ni => Scoords_add x y ni) + map_smul' r x := lp.ext (funext fun ni => Scoords_smul r x ni) + +noncomputable def Sbound : ℝ := allNodeWeight * densityBound * + ∑' ni : Node × Bool, (kernelEnvelope 0 ni.1.val + kernelEnvelope 1 ni.1.val) + +lemma Sbound_nonneg : 0 ≤ Sbound := by + unfold Sbound + exact mul_nonneg (mul_nonneg allNodeWeight_nonneg densityBound_nonneg) + (tsum_nonneg (fun ni => add_nonneg (kernelEnvelope_nonneg _ _) (kernelEnvelope_nonneg _ _))) + +lemma Slinear_bound (x : X) : ‖Slinear x‖ ≤ Sbound * ‖x‖ := by + rw [lp.norm_eq_tsum_rpow (by norm_num : 0 < (1 : ℝ≥0∞).toReal)] + simp only [ENNReal.toReal_one, Real.rpow_one, one_div_one, Real.norm_eq_abs] + change (∑' ni : Node × Bool, |Scoords x ni|) ≤ _ + calc + _ ≤ ∑' ni : Node × Bool, allNodeWeight * densityBound * ‖x‖ * + (kernelEnvelope 0 ni.1.val + kernelEnvelope 1 ni.1.val) := + (Scoords_summable x).tsum_le_tsum (fun ni => Scoords_bound x ni) + (pairEnvelope_summable.mul_left _) + _ = Sbound * ‖x‖ := by rw [tsum_mul_left]; unfold Sbound; ring + + +noncomputable def S : X →L[ℝ] X := Slinear.mkContinuous Sbound Slinear_bound + +lemma S_apply (x : X) (ni : Node × Bool) : S x ni = Scoords x ni := rfl + +end SharpPlanar + +namespace SharpPlanar +open Complex + +noncomputable def complexLambda (t : ℂ) : ℂ := + Complex.I / ((b:ℂ) * (t+Complex.I*(h:ℂ))) +noncomputable def complexZ (t : ℂ) : ℂ := + -(B:ℂ)/(t+Complex.I*(h:ℂ))-Complex.I*(h:ℂ) + +lemma complexLambda_real (t : ℝ) : complexLambda t = lambda t := rfl +lemma complexZ_real (t : ℝ) : complexZ t = z t := rfl + + +lemma reciprocal_disk_identity (a ζ : ℂ) (r : ℝ) + (hΔ : Complex.normSq a-r^2 ≠ 0) : + Complex.normSq (1-a*ζ)-r^2*Complex.normSq ζ = + (Complex.normSq a-r^2)*Complex.normSq + (ζ-(((Complex.normSq a-r^2)⁻¹:ℝ):ℂ)*conj a) - + r^2/(Complex.normSq a-r^2) := by + simp only [Complex.normSq_apply,Complex.sub_re,Complex.sub_im,Complex.mul_re, + Complex.mul_im,Complex.one_re,Complex.one_im,Complex.ofReal_re,Complex.ofReal_im, + Complex.conj_re,Complex.conj_im,zero_mul] at * + simp only [← sq] at hΔ + field_simp [hΔ] + ring + +lemma reciprocal_disk_bound {a u : ℂ} {r : ℝ} (hr : 0 ≤ r) + (hΔ : 0 < Complex.normSq a-r^2) (hu : ‖u-a‖ ≤ r) (hu0 : u ≠ 0) : + ‖u⁻¹-(((Complex.normSq a-r^2)⁻¹:ℝ):ℂ)*conj a‖ ≤ r/(Complex.normSq a-r^2) := by + let Δ := Complex.normSq a-r^2 + have hid := reciprocal_disk_identity a u⁻¹ r (ne_of_gt hΔ) + have he : (1:ℂ)-a*u⁻¹ = (u-a)*u⁻¹ := by field_simp + rw [he,Complex.normSq_mul,Complex.normSq_eq_norm_sq (u-a)] at hid + have hnon : 0 ≤ Complex.normSq u⁻¹ := Complex.normSq_nonneg _ + have hsmall : Complex.normSq a-r^2 > 0 := hΔ + have hprod : (‖u-a‖^2-r^2)*Complex.normSq u⁻¹ ≤ 0 := + mul_nonpos_of_nonpos_of_nonneg (by nlinarith [norm_nonneg (u-a)]) hnon + rw [Complex.normSq_eq_norm_sq (u⁻¹-(((Complex.normSq a-r^2)⁻¹:ℝ):ℂ)*conj a)] at hid + have hdpos : 0 < Δ := hΔ + have hdne : Δ ≠ 0 := ne_of_gt hdpos + have hratio : 0 ≤ r/Δ := div_nonneg hr hdpos.le + have hn := norm_nonneg (u⁻¹-((Δ⁻¹:ℝ):ℂ)*conj a) + have hsq : ‖u⁻¹-((Δ⁻¹:ℝ):ℂ)*conj a‖^2 ≤ (r/Δ)^2 := by + apply (mul_le_mul_iff_right₀ (sq_pos_of_pos hdpos)).mp + have heq : Δ^2*(r/Δ)^2 = r^2 := by field_simp + rw [heq] + have hprod' : Δ*‖u⁻¹-((Δ⁻¹:ℝ):ℂ)*conj a‖^2 ≤ r^2/Δ := by + dsimp [Δ] + nlinarith only [hid,hprod] + have hh := mul_le_mul_of_nonneg_left hprod' hdpos.le + have heq' : Δ*(r^2/Δ) = r^2 := by field_simp + rw [heq'] at hh + nlinarith only [hh] + dsimp [Δ] at * + nlinarith only [hsq, hn, hratio] + + +noncomputable def diskCenter (j : ℕ) : ℝ := (2*(j:ℝ)+1)/12 + +lemma disk_coordinate_bounds {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + ‖t‖ ≤ 13/12 ∧ -(1/6:ℝ) ≤ t.im ∧ t.im ≤ 1/6 := by + have hc0 : 0 ≤ diskCenter j := by unfold diskCenter; positivity + have hc1 : diskCenter j ≤ 11/12 := by + unfold diskCenter + have : (j:ℝ) ≤ 5 := by exact_mod_cast (by omega : j ≤ 5) + linarith + have hi := (Complex.abs_im_le_norm (t-(diskCenter j:ℂ))).trans ht + simp only [Complex.sub_im,Complex.ofReal_im,sub_zero,abs_le] at hi + refine ⟨?_, hi⟩ + have hn := norm_add_le (t-(diskCenter j:ℂ)) (diskCenter j:ℂ) + rw [sub_add_cancel,Complex.norm_real,Real.norm_eq_abs,abs_of_nonneg hc0] at hn + linarith + +lemma disk_denominator_lower {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + 7/30 ≤ ‖t+Complex.I*(h:ℂ)‖ := by + have hi := (disk_coordinate_bounds hj ht).2.1 + have hn := (le_abs_self (t+Complex.I*(h:ℂ)).im).trans (Complex.abs_im_le_norm _) + simp only [Complex.add_im,Complex.I_mul_im,Complex.ofReal_re] at hn + norm_num [h] at hn ⊢ + linarith + +lemma disk_denominator_ne {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : t+Complex.I*(h:ℂ) ≠ 0 := by + have hb := disk_denominator_lower hj ht + intro he + rw [he,norm_zero] at hb + norm_num at hb + +lemma b_lower_simple : 43/50 < b := by + have hh := b_sq + have hp := b_pos + nlinarith + +lemma disk_lambda_bound {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : ‖complexLambda t‖ < 5 := by + have hd := disk_denominator_lower hj ht + have hb := b_lower_simple + rw [complexLambda,norm_div,norm_mul,Complex.norm_I,Complex.norm_real, + Real.norm_eq_abs,abs_of_pos b_pos] + apply (div_lt_iff₀ (mul_pos b_pos (by linarith))).mpr + nlinarith + +lemma disk_z_bound {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : ‖complexZ t‖ < 31/5 := by + have hd := disk_denominator_lower hj ht + have hm := norm_sub_le (-(B:ℂ)/(t+Complex.I*(h:ℂ))) (Complex.I*(h:ℂ)) + simp only [norm_div,norm_neg,Complex.norm_real,Real.norm_eq_abs,norm_mul, + Complex.norm_I,one_mul,abs_of_pos B_pos,abs_of_pos h_pos] at hm + have hb : B/‖t+Complex.I*(h:ℂ)‖ ≤ (40:ℝ)/7 := by + apply (div_le_iff₀ (by linarith : 0 < ‖t+Complex.I*(h:ℂ)‖)).mpr + norm_num [B] + linarith + change ‖-(B:ℂ)/(t+Complex.I*(h:ℂ))-Complex.I*(h:ℂ)‖ < _ + norm_num [h] at hm hb ⊢ + linarith + +lemma disk_delta_bounds {j : ℕ} (hj : j < 6) : + 167/1200 ≤ Complex.normSq ((diskCenter j:ℂ)+Complex.I*(h:ℂ))-(1/6:ℝ)^2 ∧ + Complex.normSq ((diskCenter j:ℂ)+Complex.I*(h:ℂ))-(1/6:ℝ)^2 ≤ 389/400 := by + have hj0 : (0:ℝ) ≤ j := Nat.cast_nonneg _ + have hj5 : (j:ℝ) ≤ 5 := by exact_mod_cast (by omega : j ≤ 5) + simp only [Complex.normSq_apply,Complex.add_re,Complex.add_im, + Complex.ofReal_re,Complex.ofReal_im,Complex.I_mul_re,Complex.I_mul_im, + neg_zero,add_zero,zero_add] + unfold diskCenter h + constructor <;> nlinarith [sq_nonneg (j:ℝ)] + +lemma disk_z_imaginary {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + -(1402/17505:ℝ) ≤ (complexZ t).im := by + let a : ℂ := (diskCenter j:ℂ)+Complex.I*(h:ℂ) + let Δ : ℝ := Complex.normSq a-(1/6:ℝ)^2 + have hΔ : 0 < Δ := by + have hh := (disk_delta_bounds hj).1 + change 167/1200 ≤ Δ at hh + linarith + have hΔ1 : Δ ≤ 389/400 := (disk_delta_bounds hj).2 + have hrec := reciprocal_disk_bound (a:=a) (u:=t+Complex.I*(h:ℂ)) + (by norm_num : (0:ℝ) ≤ 1/6) hΔ + (by simpa [a] using ht) (disk_denominator_ne hj ht) + have hi := (le_abs_self _).trans ((Complex.abs_im_le_norm + ((t+Complex.I*(h:ℂ))⁻¹-((Δ⁻¹:ℝ):ℂ)*conj a)).trans hrec) + have haim : a.im = h := by simp [a] + simp only [Complex.sub_im,Complex.mul_im,Complex.ofReal_re,Complex.ofReal_im, + Complex.conj_im,zero_mul,add_zero,haim] at hi + change (t+Complex.I*(h:ℂ))⁻¹.im-Δ⁻¹*(-h) ≤ (1/6)/Δ at hi + have htop : (t+Complex.I*(h:ℂ))⁻¹.im ≤ ((1/6:ℝ)-h)/Δ := by + rw [div_eq_mul_inv] at hi ⊢ + nlinarith only [hi] + have heq : (complexZ t).im = -B*(t+Complex.I*(h:ℂ))⁻¹.im-h := by + simp [complexZ,div_eq_mul_inv,Complex.mul_im] + rw [heq] + have hb := mul_le_mul_of_nonpos_left htop (neg_nonpos.mpr B_pos.le) + have hq : -(1402/17505:ℝ) ≤ -B*((1/6-h)/Δ)-h := by + have hh : (-(1402/17505:ℝ)+h)*Δ ≤ -B*(1/6-h) := by + norm_num [B,h] at * + nlinarith + have hh' := (le_div_iff₀ hΔ).mpr hh + linear_combination hh' + linarith + +lemma disk_z_imaginary_simple {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + -(81/1000:ℝ) < (complexZ t).im := by + have hh := disk_z_imaginary hj ht + linarith + +end SharpPlanar + +namespace SharpPlanar +open MeasureTheory Set + + +noncomputable def complexU (n j : ℕ) (t : ℂ) : ℂ := + -2 * (Real.pi:ℂ)^2 * Complex.exp (-Complex.I*Real.pi*t*n) * + ∑ l ∈ Finset.Icc (j+1) 6, + ((l:ℂ)/6-t)*Pcoeff l*Complex.exp (Complex.I*Real.pi*(l:ℂ)/6*n) +noncomputable def complexV (n j : ℕ) (t : ℂ) : ℂ := + 2*Complex.I*Real.pi*Complex.exp (-Complex.I*Real.pi*t*n) * + ∑ l ∈ Finset.Icc (j+1) 6, + Pcoeff l*Complex.exp (Complex.I*Real.pi*(l:ℂ)/6*n) + +lemma complexU_real (n j : ℕ) (t : ℝ) : complexU n j t = u n j t := rfl +lemma complexV_real (n j : ℕ) (t : ℝ) : complexV n j t = v n j t := rfl + +lemma disk_frequency_distance {j : ℕ} (hj : j < 6) {l : ℕ} + (hl : l ∈ Finset.Icc (j+1) 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : ‖(l:ℂ)/6-t‖ ≤ 13/12 := by + have hjr : (j:ℝ) ≤ 5 := by exact_mod_cast (by omega : j ≤ 5) + have hl0 : (0:ℝ) ≤ l := Nat.cast_nonneg l + have hl1 : (l:ℝ) ≤ 6 := by exact_mod_cast (Finset.mem_Icc.mp hl).2 + have hj0 : (0:ℝ) ≤ j := Nat.cast_nonneg j + have hh : ‖(l:ℂ)/6-(diskCenter j:ℂ)‖ ≤ 11/12 := by + rw [show (l:ℂ)/6-(diskCenter j:ℂ) = (((l:ℝ)/6-diskCenter j:ℝ):ℂ) by push_cast; rfl] + rw [Complex.norm_real,Real.norm_eq_abs,abs_le] + unfold diskCenter + constructor <;> linarith + have hn := norm_sub_le ((l:ℂ)/6-(diskCenter j:ℂ)) (t-(diskCenter j:ℂ)) + rw [sub_sub_sub_cancel_right] at hn + linarith + +lemma disk_phase_bound {j n : ℕ} (hj : j < 6) (hn : n ≤ 100) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + ‖Complex.exp (-Complex.I*Real.pi*t*n)‖ ≤ Real.exp (100*Real.pi/6) := by + rw [Complex.norm_exp] + apply Real.exp_le_exp.mpr + have ht' := (disk_coordinate_bounds hj ht).2.2 + have hn' : (n:ℝ) ≤ 100 := by exact_mod_cast hn + have hn0 : (0:ℝ) ≤ n := Nat.cast_nonneg n + simp only [Complex.mul_re,Complex.neg_re,Complex.neg_im,Complex.I_re,Complex.I_im, + Complex.ofReal_re,Complex.ofReal_im,Complex.natCast_re,Complex.natCast_im,zero_mul, + mul_zero,sub_zero,neg_zero,Complex.mul_im,zero_add] + nlinarith [Real.pi_pos,mul_nonneg Real.pi_pos.le hn0, + mul_nonneg Real.pi_pos.le (show 0 ≤ 100-(n:ℝ) by linarith)] + +lemma complexU_disk_bound {j n : ℕ} (hj : j < 6) (hn : n ≤ 100) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + ‖complexU n j t‖ ≤ 250*Real.exp (100*Real.pi/6) := by + have hs : ‖∑ l ∈ Finset.Icc (j+1) 6, + ((l:ℂ)/6-t)*Pcoeff l*Complex.exp (Complex.I*Real.pi*(l:ℂ)/6*n)‖ ≤ (13/12)*10 := by + calc + _ ≤ ∑ l ∈ Finset.Icc (j+1) 6, + ‖((l:ℂ)/6-t)*Pcoeff l*Complex.exp (Complex.I*Real.pi*(l:ℂ)/6*n)‖ := norm_sum_le _ _ + _ ≤ ∑ l ∈ Finset.Icc (j+1) 6, (13/12)*‖Pcoeff l‖ := by + apply Finset.sum_le_sum + intro l hl + rw [norm_mul,norm_mul,atom_phase_norm,mul_one] + exact mul_le_mul_of_nonneg_right (disk_frequency_distance hj hl ht) (norm_nonneg _) + _ ≤ (13/12)*10 := by + rw [← Finset.mul_sum] + exact mul_le_mul_of_nonneg_left (positive_coeff_mass_le j) (by norm_num) + unfold complexU + simp only [norm_mul,norm_pow,norm_neg,Complex.norm_ofNat,Complex.norm_real, + Real.norm_eq_abs,abs_of_pos Real.pi_pos] + calc + _ ≤ 2*Real.pi^2 * Real.exp (100*Real.pi/6) * ((13/12)*10) := by + gcongr + exact disk_phase_bound hj hn ht + _ ≤ _ := by + have hp := Real.pi_lt_d2 + have hp0 := Real.pi_pos + have hp2 : Real.pi^2 < 10 := by nlinarith + have he := Real.exp_pos (100*Real.pi/6) + nlinarith + +lemma complexV_disk_bound {j n : ℕ} (hj : j < 6) (hn : n ≤ 100) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + ‖complexV n j t‖ ≤ 250*Real.exp (100*Real.pi/6) := by + have hs : ‖∑ l ∈ Finset.Icc (j+1) 6, + Pcoeff l*Complex.exp (Complex.I*Real.pi*(l:ℂ)/6*n)‖ ≤ 10 := by + calc + _ ≤ ∑ l ∈ Finset.Icc (j+1) 6, ‖Pcoeff l*Complex.exp (Complex.I*Real.pi*(l:ℂ)/6*n)‖ := norm_sum_le _ _ + _ = ∑ l ∈ Finset.Icc (j+1) 6, ‖Pcoeff l‖ := by simp only [norm_mul,atom_phase_norm,mul_one] + _ ≤ 10 := positive_coeff_mass_le j + unfold complexV + simp only [norm_mul,Complex.norm_I,Complex.norm_ofNat,mul_one,Complex.norm_real, + Real.norm_eq_abs,abs_of_pos Real.pi_pos] + calc + _ ≤ 2*Real.pi*Real.exp (100*Real.pi/6)*10 := by + gcongr + exact disk_phase_bound hj hn ht + _ ≤ _ := by + have := Real.pi_lt_d2 + have := Real.exp_pos (100*Real.pi/6) + nlinarith + +noncomputable def finiteDensity (c d : ℕ → ℝ) (j : ℕ) (t : ℂ) : ℂ := + ∑ n ∈ Finset.range 101, ((c n:ℂ)*complexU n j t + (d n:ℂ)*complexV n j t) + +lemma finiteDensity_disk_bound (c d : ℕ → ℝ) + (hw : ∑ n ∈ Finset.range 101, (|c n|+|d n|) ≤ 3) + {j : ℕ} (hj : j < 6) {t : ℂ} (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) : + ‖finiteDensity c d j t‖ ≤ 1000*Real.exp (100*Real.pi/6) := by + unfold finiteDensity + calc + _ ≤ ∑ n ∈ Finset.range 101, ‖(c n:ℂ)*complexU n j t + (d n:ℂ)*complexV n j t‖ := norm_sum_le _ _ + _ ≤ ∑ n ∈ Finset.range 101, (|c n|+|d n|)*(250*Real.exp (100*Real.pi/6)) := by + apply Finset.sum_le_sum + intro n hn + calc + _ ≤ ‖(c n:ℂ)*complexU n j t‖ + ‖(d n:ℂ)*complexV n j t‖ := norm_add_le _ _ + _ ≤ |c n| *(250*Real.exp (100*Real.pi/6)) + |d n| *(250*Real.exp (100*Real.pi/6)) := by + simp only [norm_mul,Complex.norm_real,Real.norm_eq_abs] + gcongr + · exact complexU_disk_bound hj (by have := Finset.mem_range.mp hn; omega) ht + · exact complexV_disk_bound hj (by have := Finset.mem_range.mp hn; omega) ht + _ = _ := by ring + _ ≤ 3*(250*Real.exp (100*Real.pi/6)) := by + rw [← Finset.sum_mul] + exact mul_le_mul_of_nonneg_right hw (by positivity) + _ ≤ _ := by have := Real.exp_pos (100*Real.pi/6); linarith + +end SharpPlanar + +namespace SharpPlanar +open Complex + +noncomputable def complexDirectFactor (m y : ℝ) (ell : ℕ) (t : ℂ) : ℂ := + Complex.exp (Complex.I*Real.pi*t*m) * (Complex.I*Real.pi*t*y)^ell / (ell.factorial:ℂ) +noncomputable def complexTransformedFactor (m y : ℝ) (ell : ℕ) (t : ℂ) : ℂ := + complexLambda t * Complex.exp (Complex.I*Real.pi*complexZ t*m) * + (Complex.I*Real.pi*complexZ t*y)^ell / (ell.factorial:ℂ) + +lemma divided_power_norm (w : ℂ) (ell : ℕ) : + ‖w^ell / (ell.factorial:ℂ)‖ ≤ Real.exp ‖w‖ := by + simpa only [norm_div,norm_pow,Complex.norm_natCast] using + Real.pow_div_factorial_le_exp ‖w‖ (norm_nonneg w) ell + +lemma phase_exp_norm_bound {w : ℂ} {m L : ℝ} (hm : 0 ≤ m) (hw : -L ≤ w.im) : + ‖Complex.exp (Complex.I*Real.pi*w*m)‖ ≤ Real.exp (Real.pi*m*L) := by + rw [Complex.norm_exp] + apply Real.exp_le_exp.mpr + simp only [Complex.mul_re,Complex.mul_im,Complex.I_re,Complex.I_im, + Complex.ofReal_re,Complex.ofReal_im,zero_mul,mul_zero,one_mul, + zero_sub,sub_zero,zero_add] + nlinarith [mul_nonneg (mul_nonneg Real.pi_pos.le hm) (show 0 ≤ w.im+L by linarith)] + +lemma complexDirectFactor_disk_bound {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) {m y : ℝ} + (hm0 : 0 ≤ m) (hm1 : m ≤ 100) (hy : |y| ≤ 3/2) (ell : ℕ) : + ‖complexDirectFactor m y ell t‖ ≤ Real.exp (Real.pi*(100/6+13/8)) := by + have htn := (disk_coordinate_bounds hj ht).1 + have hti := (disk_coordinate_bounds hj ht).2.1 + have he : ‖Complex.exp (Complex.I*Real.pi*t*m)‖ ≤ Real.exp (Real.pi*100/6) := by + refine (phase_exp_norm_bound hm0 hti).trans ?_ + apply Real.exp_le_exp.mpr + nlinarith [Real.pi_pos] + have hp : ‖(Complex.I*Real.pi*t*y)^ell/(ell.factorial:ℂ)‖ ≤ + Real.exp (Real.pi*(13/8)) := by + refine (divided_power_norm _ ell).trans (Real.exp_le_exp.mpr ?_) + simp only [norm_mul,Complex.norm_I,one_mul,Complex.norm_real,Real.norm_eq_abs, + abs_of_pos Real.pi_pos] + have hh := mul_le_mul htn hy (abs_nonneg y) (by norm_num : (0:ℝ) ≤ 13/12) + nlinarith [Real.pi_pos] + rw [complexDirectFactor,mul_div_assoc,norm_mul] + calc + _ ≤ Real.exp (Real.pi*100/6)*Real.exp (Real.pi*(13/8)) := + mul_le_mul he hp (norm_nonneg _) (Real.exp_pos _).le + _ = _ := by rw [← Real.exp_add]; congr 1; ring + +lemma complexTransformedFactor_disk_bound {j : ℕ} (hj : j < 6) {t : ℂ} + (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) {m y : ℝ} + (hm0 : 0 ≤ m) (hm1 : m ≤ 100) (hy : |y| ≤ 3/2) (ell : ℕ) : + ‖complexTransformedFactor m y ell t‖ ≤ 5*Real.exp (Real.pi*(87/5)) := by + have htn := (disk_z_bound hj ht).le + have hti := (disk_z_imaginary_simple hj ht).le + have he : ‖Complex.exp (Complex.I*Real.pi*complexZ t*m)‖ ≤ Real.exp (Real.pi*(81/10)) := by + refine (phase_exp_norm_bound hm0 hti).trans ?_ + apply Real.exp_le_exp.mpr + nlinarith [Real.pi_pos] + have hp : ‖(Complex.I*Real.pi*complexZ t*y)^ell/(ell.factorial:ℂ)‖ ≤ + Real.exp (Real.pi*(93/10)) := by + refine (divided_power_norm _ ell).trans (Real.exp_le_exp.mpr ?_) + simp only [norm_mul,Complex.norm_I,one_mul,Complex.norm_real,Real.norm_eq_abs, + abs_of_pos Real.pi_pos] + have hh := mul_le_mul htn hy (abs_nonneg y) (by norm_num : (0:ℝ) ≤ 31/5) + nlinarith [Real.pi_pos] + rw [complexTransformedFactor,mul_div_assoc,norm_mul,norm_mul] + calc + _ ≤ (5*Real.exp (Real.pi*(81/10)))*Real.exp (Real.pi*(93/10)) := + mul_le_mul (mul_le_mul (disk_lambda_bound hj ht).le he (norm_nonneg _) + (by norm_num)) hp (norm_nonneg _) (by positivity) + _ = _ := by rw [mul_assoc,← Real.exp_add]; congr 2; ring + +lemma numerical_moment_bound : (5000:ℝ)*Real.exp 111 < (10:ℝ)^53 := by + have he : Real.exp 1 < 11/4 := by linarith [Real.exp_one_lt_d9] + have hex : Real.exp 111 = (Real.exp 1)^111 := by + rw [← Real.exp_nat_mul]; norm_num + rw [hex] + have hp : (Real.exp 1)^111 ≤ (11/4:ℝ)^111 := + pow_le_pow_left₀ (Real.exp_pos 1).le he.le 111 + calc + _ ≤ 5000*(11/4:ℝ)^111 := mul_le_mul_of_nonneg_left hp (by norm_num) + _ < _ := by norm_num + +lemma directIntegrand_disk_bound (c d : ℕ → ℝ) + (hw : ∑ n ∈ Finset.range 101, (|c n|+|d n|) ≤ 3) + {j : ℕ} (hj : j < 6) {t : ℂ} (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) + {m y : ℝ} (hm0 : 0 ≤ m) (hm1 : m ≤ 100) (hy : |y| ≤ 3/2) (ell : ℕ) : + ‖finiteDensity c d j t * complexDirectFactor m y ell t‖ ≤ (10:ℝ)^53 := by + rw [norm_mul] + calc + _ ≤ (1000*Real.exp (100*Real.pi/6))*Real.exp (Real.pi*(100/6+13/8)) := + mul_le_mul (finiteDensity_disk_bound c d hw hj ht) + (complexDirectFactor_disk_bound hj ht hm0 hm1 hy ell) (norm_nonneg _) (by positivity) + _ ≤ 5000*Real.exp 111 := by + rw [mul_assoc,← Real.exp_add] + apply mul_le_mul (by norm_num) _ (Real.exp_pos _).le (by norm_num) + apply Real.exp_le_exp.mpr + have hp := Real.pi_lt_d4 + linarith + _ ≤ _ := numerical_moment_bound.le + +lemma transformedIntegrand_disk_bound (c d : ℕ → ℝ) + (hw : ∑ n ∈ Finset.range 101, (|c n|+|d n|) ≤ 3) + {j : ℕ} (hj : j < 6) {t : ℂ} (ht : ‖t-(diskCenter j:ℂ)‖ ≤ 1/6) + {m y : ℝ} (hm0 : 0 ≤ m) (hm1 : m ≤ 100) (hy : |y| ≤ 3/2) (ell : ℕ) : + ‖finiteDensity c d j t * complexTransformedFactor m y ell t‖ ≤ (10:ℝ)^53 := by + rw [norm_mul] + calc + _ ≤ (1000*Real.exp (100*Real.pi/6))*(5*Real.exp (Real.pi*(87/5))) := + mul_le_mul (finiteDensity_disk_bound c d hw hj ht) + (complexTransformedFactor_disk_bound hj ht hm0 hm1 hy ell) (norm_nonneg _) (by positivity) + _ = 5000*Real.exp ((100*Real.pi/6)+Real.pi*(87/5)) := by rw [Real.exp_add]; ring + _ ≤ 5000*Real.exp 111 := by + apply mul_le_mul_of_nonneg_left (Real.exp_le_exp.mpr ?_) (by norm_num) + have hp := Real.pi_lt_d4 + linarith + _ ≤ _ := numerical_moment_bound.le + +end SharpPlanar + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/Amplitudes.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/Amplitudes.lean new file mode 100644 index 0000000000000000000000000000000000000000..a0aa1b9b7e96b2d6fa7a9e36eaad460da32d07bf --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/Amplitudes.lean @@ -0,0 +1,3869 @@ +import OAI.Analysis.PlanarPacking.Grid +import OAI.Analysis.PlanarPacking.BasisIntervals + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid IntegerAlpha IntegerCompact +noncomputable def amp0_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 0 j) (bLookup 0 j) false) +noncomputable def amp0_00_0 : Fin 16 → CBox := ![⟨⟨378311542062827993430688825,378311542062827993434397457⟩,⟨280818959643395448657707351,280818959643395448689644023⟩⟩,⟨⟨1331666599228979130210897591,1331666599228979130227801655⟩,⟨988362551579579482715436309,988362551579579482830702752⟩⟩,⟨⟨2146962531497788175833216495,2146962531497788175863401629⟩,⟨1593063641956354776640142239,1593063641956354776828125440⟩⟩,⟨⟨3049969189616626462228450039,3049969189616626462272103102⟩,⟨2262225812854807899257953502,2262225812854807899525511561⟩⟩,⟨⟨3889714875854835024013253273,3889714875854835024070022203⟩,⟨2883593774158631961166344740,2883593774158631961508274943⟩⟩,⟨⟨4778913502483939793046275845,4778913502483939793116559310⟩,⟨3540505553352508841079744403,3540505553352508841500072815⟩⟩,⟨⟨5627665378449837346635413898,5627665378449837346718987218⟩,⟨4166085584841394394714453145,4166085584841394395209796595⟩⟩,⟨⟨6510766371253528028654317922,6510766371253528028751471596⟩,⟨4815483346992079747556848999,4815483346992079748129950394⟩⟩,⟨⟨7364201298529060707722156516,7364201298529060707832690202⟩,⟨5441083017277562734612862063,5441083017277562735261153326⟩⟩,⟨⟨8243940560523596549966810136,8243940560523596550089991109⟩,⟨6084019434821486145636492800,6084019434821486146361303512⟩⟩,⟨⟨9100286616793075457456003657,9100286616793075457593089109⟩,⟨6707350587306729155093710509,6707350587306729155893998532⟩⟩,⟨⟨9977942994475396346020494176,9977942994475396346171209194⟩,⟨7343808658336446105046576812,7343808658336446105923587380⟩⟩,⟨⟨10836308992460680810680839485,10836308992460680810844505861⟩,⟨7963250310596706817095728122,7963250310596706818047274910⟩⟩,⟨⟨11712581613479463386098539267,11712581613479463386274754432⟩,⟨8592797556414290800326265139,8592797556414290801353204030⟩⟩,⟨⟨12572455852226421910154495626,12572455852226421910344883232⟩,⟨9207026715255997825398427476,9207026715255997826500452347⟩⟩,⟨⟨13447764927121316313707797874,13447764927121316313912313945⟩,⟨9829041362201440437024276438,9829041362201440438202277393⟩⟩] +lemma amp0_00_0_eq : ∀ k : Fin 16, amp0_0Expr 0 0 k = amp0_00_0 k := by decide +kernel +noncomputable def amp0_00_1 : Fin 16 → CBox := ![⟨⟨14308822311873111078686857634,14308822311873111078904925050⟩,⟨10436892708345744392246456417,10436892708345744393498646171⟩⟩,⟨⟨15183434235972487698913149171,15183434235972487699144166908⟩,⟨11050659397441600063159255445,11050659397441600064485941038⟩⟩,⟨⟨16045448831436297202682759275,16045448831436297202926237549⟩,⟨11651063188190215523986643800,11651063188190215525386203018⟩⟩,⟨⟨16919535355801448301074391929,16919535355801448301334319766⟩,⟨12255819690029389626741591744,12255819690029389628217514672⟩⟩,⟨⟨17782335736979317989927100379,17782335736979317990198496056⟩,⟨12847771376303458639048444236,12847771376303458640595922897⟩⟩,⟨⟨18656004585714032501125315467,18656004585714032501408367766⟩,⟨13442734050447643211342716015,13442734050447643212962365938⟩⟩,⟨⟨19519448836556444547035768529,19519448836556444547335547500⟩,⟨14025278416402922418350761055,14025278416402922420045087277⟩⟩,⟨⟨20392760588543402486738556135,20392760588543402487049144778⟩,⟨14609657408285129582514561527,14609657408285129584279674927⟩⟩,⟨⟨21256721204025116439833208668,21256721204025116440159654945⟩,⟨15181879993059881249450777811,15181879993059881251289188999⟩⟩,⟨⟨22129699016728950112682772901,22129699016728950113026128145⟩,⟨15754889044419873612481774019,15754889044419873614394488742⟩⟩,⟨⟨22994053180899398037616537760,22994053180899398037969404769⟩,⟨16315911478453393615071932916,16315911478453393617052608712⟩⟩,⟨⟨23866688543885904278088930043,23866688543885904278458038123⟩,⟨16876774711011986281539721682,16876774711011986283593318720⟩⟩,⟨⟨24731311510389197931172609394,24731311510389197931548898887⟩,⟨17425752272733752565617488840,17425752272733752567736553660⟩⟩,⟨⟨25603567686077201656160832709,25603567686077201656556058896⟩,⟨17973709169137016177459783530,17973709169137016179652706487⟩⟩,⟨⟨26468328045561050646134816628,26468328045561050646544837308⟩,⟨18509829653360925939424497841,18509829653360925941687312662⟩⟩,⟨⟨27340142110550102090222557350,27340142110550102090649117184⟩,⟨19044138907209704660497971245,19044138907209704662831921059⟩⟩] +lemma amp0_00_1_eq : ∀ k : Fin 16, amp0_0Expr 0 1 k = amp0_00_1 k := by decide +kernel +noncomputable def amp0_00_2 : Fin 16 → CBox := ![⟨⟨28204898260586856221040224542,28204898260586856221472436376⟩,⟨19566622291115746823395139553,19566622291115746825791624206⟩⟩,⟨⟨29076182276017907754051154799,29076182276017907754501407854⟩,⟨20086564912406391954881087014,20086564912406391957348681137⟩⟩,⟨⟨29940779691262844416908054211,29940779691262844417374463124⟩,⟨20594663514638012992199997309,20594663514638012994736354523⟩⟩,⟨⟨30811421321048063678279175682,30811421321048063678763027497⟩,⟨21099545421570495252051229556,21099545421570495254657125800⟩⟩,⟨⟨31675690378430352253614927193,31675690378430352254118177316⟩,⟨21592544366820899012975086290,21592544366820899015650811183⟩⟩,⟨⟨32545553154869964859143803385,32545553154869964859647902246⟩,⟨22081698606609540010238897349,22081698606609540012971682807⟩⟩,⟨⟨33409307359673668454705931423,33409307359673668455226772126⟩,⟨22558916475928545985105558832,22558916475928545987905201731⟩⟩,⟨⟨34278230725412291629380855406,34278230725412291629916010275⟩,⟨23031705165133992404320309024,23031705165133992407184960653⟩⟩,⟨⟨35141265238770782233887808782,35141265238770782234439826335⟩,⟨23492494753040581282218623758,23492494753040581285148966175⟩⟩,⟨⟨36009064450886533007781582273,36009064450886533008351144693⟩,⟨23948310796182392936841348272,23948310796182392939837567903⟩⟩,⟨⟨36871154853038013024675934706,36871154853038013025262904945⟩,⟨24392059921062462114720685405,24392059921062462117781646217⟩⟩,⟨⟨37737620807858560762393564022,37737620807858560762976454036⟩,⟨24830328546372219500602684874,24830328546372219503713930651⟩⟩,⟨⟨38598522052996473288517933757,38598522052996473289121886964⟩,⟨25256460876888086316807525274,25256460876888086319984616559⟩⟩,⟨⟨39463421072625266671623914143,39463421072625266672245569840⟩,⟨25676641015292465000447350579,25676641015292465003687714230⟩⟩,⟨⟨40322866605140757566123963765,40322866605140757566766225691⟩,⟨26084616886204301238602945601,26084616886204301241907407400⟩⟩,⟨⟨41185940214987332205277881576,41185940214987332205933160420⟩,⟨26486202411263563020390396553,26486202411263563023753650678⟩⟩] +lemma amp0_00_2_eq : ∀ k : Fin 16, amp0_0Expr 0 2 k = amp0_00_2 k := by decide +kernel +noncomputable def amp0_00_3 : Fin 16 → CBox := ![⟨⟨42043641226155268002392648332,42043641226155268003065794520⟩,⟨26875519609251160951742022670,26875519609251160955166147981⟩⟩,⟨⟨42904605944822856761823993661,42904605944822856762515987405⟩,⟨27258040450207141513625997314,27258040450207141517111174555⟩⟩,⟨⟨43760250755218848583754502396,43760250755218848584466058581⟩,⟨27628234955237454796424907591,27628234955237454799970517487⟩⟩,⟨⟨44618797912588186054663784207,44618797912588186055357460075⟩,⟨27991258091564023351005517757,27991258091564023354587578616⟩⟩,⟨⟨45472051469783390772308783444,45472051469783390773024767927⟩,⟨28341904762848345332271418520,28341904762848345335914201166⟩⟩,⟨⟨46327847065219614779673637224,46327847065219614780408643976⟩,⟨28685035106133977553842457415,28685035106133977557543380554⟩⟩,⟨⟨47178350549239536336495346944,47178350549239536337249026231⟩,⟨29015748304245134030180141551,29015748304245134033937909526⟩⟩,⟨⟨48031035159014761746081528642,48031035159014761746852248315⟩,⟨29338629471481362460335520807,29338629471481362464148587298⟩⟩,⟨⟨48878405690090595141535607400,48878405690090595142325647516⟩,⟨29649063610068885735413664321,29649063610068885739282342407⟩⟩,⟨⟨49727594431017382780815346187,49727594431017382781615397326⟩,⟨29951378591216227304150521747,29951378591216227308068621045⟩⟩,⟨⟨50571424875580975783382489078,50571424875580975784201619648⟩,⟨30241228613171176483341832023,30241228613171176487313763197⟩⟩,⟨⟨51416707430266351707627924701,51416707430266351708462292397⟩,⟨30522700335057660488297952507,30522700335057660492320824723⟩⟩,⟨⟨52256566302127791384157556113,52256566302127791385008890708⟩,⟨30791702109075164743222931648,30791702109075164747296701956⟩⟩,⟨⟨53097507010032401755134589885,53097507010032401756002509515⟩,⟨31052093897138619170812420917,31052093897138619174936250574⟩⟩,⟨⟨53932938464358250329050156493,53932938464358250329935526537⟩,⟨31300024531497769248276607812,31300024531497769252449923167⟩⟩,⟨⟨54769076481877509093063068010,54769076481877509093965378207⟩,⟨31539140470534109143746569204,31539140470534109147968431628⟩⟩] +lemma amp0_00_3_eq : ∀ k : Fin 16, amp0_0Expr 0 3 k = amp0_00_3 k := by decide +kernel +noncomputable def amp0_00_4 : Fin 16 → CBox := ![⟨⟨55599600400044430279596489633,55599600400044430280456632785⟩,⟨31765818541624915217593638770,31765818541624915221829193764⟩⟩,⟨⟨56430449932046836989392908483,56430449932046836990279579119⟩,⟨31983503736496996977353924506,31983503736496996981641985495⟩⟩,⟨⟨57255562095740320694089553746,57255562095740320695000482168⟩,⟨32188789430216819427944000471,32188789430216819432282120505⟩⟩,⟨⟨58080612700352613174711325380,58080612700352613175644185321⟩,⟨32384930167374050207444275863,32384930167374050211830409703⟩⟩,⟨⟨58899785053456634287209128171,58899785053456634288163208010⟩,⟨32568725332022144157566479144,32568725332022144161999098508⟩⟩,⟨⟨59718502021340807282109275788,59718502021340807283086640234⟩,⟨32743249142652864305519028991,32743249142652864309998529253⟩⟩,⟨⟨60531183018252352425183986271,60531183018252352426178685880⟩,⟨32905497252393420829650359909,32905497252393420834172359693⟩⟩,⟨⟨61343007827150606228860883385,61343007827150606229877004345⟩,⟨33058372878060483774607458770,33058372878060483779173439925⟩⟩,⟨⟨62148622866175471732993758074,62148622866175471734032478056⟩,⟨33199058906417518824755352795,33199058906417518829364808638⟩⟩,⟨⟨62952973711087682697120138470,62952973711087682698163325364⟩,⟨33330296168098077477786605860,33330296168098077482429155116⟩⟩,⟨⟨63750925651547277112551372332,63750925651547277113618222993⟩,⟨33449446371301043488697933130,33449446371301043493382676848⟩⟩,⟨⟨64547198050538409955757745431,64547198050538409956844854451⟩,⟨33559095942853610773244644570,33559095942853610777969002653⟩⟩,⟨⟨65336867812153771335287373530,65336867812153771336396725978⟩,⟨33656777553178897444358582383,33656777553178897449122450996⟩⟩,⟨⟨66124435287456141003171750407,66124435287456141004296306269⟩,⟨33744930640386218782541189321,33744930640386218787340171569⟩⟩,⟨⟨66905182530484269066554498451,66905182530484269067701630570⟩,⟨33821251469942742889923228753,33821251469942742894759978541⟩⟩,⟨⟨67683397364254630713157974755,67683397364254630714323274317⟩,⟨33888039396421746758640197394,33888039396421746763511684498⟩⟩] +lemma amp0_00_4_eq : ∀ k : Fin 16, amp0_0Expr 0 4 k = amp0_00_4 k := by decide +kernel +noncomputable def amp0_00_5 : Fin 16 → CBox := ![⟨⟨68454561248740610753682223460,68454561248740610754867729884⟩,⟨33943147352112959452511102406,33943147352112959457417229970⟩⟩,⟨⟨69222755312549499249678731997,69222755312549499250884213562⟩,⟨33988741053538277635043324134,33988741053538277639983176081⟩⟩,⟨⟨69983655334931225535412067878,69983655334931225536639444594⟩,⟨34022823564201310977360324779,34022823564201310982333717437⟩⟩,⟨⟨70741140991797938939394144737,70741140991797938940642733996⟩,⟨34047432992452848340755956017,34047432992452848345761727092⟩⟩,⟨⟨71491077896962809045276583913,71491077896962809046547086011⟩,⟨34060716349430478757259584231,34060716349430478762296932961⟩⟩,⟨⟨72237148974501104277606170243,72237148974501104278772623100⟩,⟨34064589788445292320981030046,34064589788445292325989723380⟩⟩,⟨⟨72975405741249243426677587221,72975405741249243427872519602⟩,⟨34057338401089569234851897418,34057338401089569239893881070⟩⟩,⟨⟨73709338574254111153858595339,73709338574254111155078681792⟩,⟨34040761696371490594698940881,34040761696371490599771769546⟩⟩,⟨⟨74435181471973219696829608534,74435181471973219698072632230⟩,⟨34013277264210434426079473895,34013277264210434431180963425⟩⟩,⟨⟨75156236012556517648894909829,75156236012556517650160454226⟩,⟨33976572968125476016651537086,33976572968125476021780650052⟩⟩,⟨⟨75868915726761529186672883607,75868915726761529187957737027⟩,⟨33929193571647001170631834161,33929193571647001175786002704⟩⟩,⟨⟨76576336719932691822346499543,76576336719932691823649948635⟩,⟨33872720006806996585805953076,33872720006806996590984034533⟩⟩,⟨⟨77275089544170907711176407328,77275089544170907712502705049⟩,⟨33805819119027701456513582375,33805819119027701461716337042⟩⟩,⟨⟨77968107766557648954671650666,77968107766557648956014205854⟩,⟨33729969362237472569331976994,33729969362237472574555700770⟩⟩,⟨⟨78652156858028397931898229276,78652156858028397933260945208⟩,⟨33643954783428495738555404099,33643954783428495743800703836⟩⟩,⟨⟨79329990417240758869727769888,79329990417240758871111803575⟩,⟨33549155572841946465039061201,33549155572841946470305588904⟩⟩] +lemma amp0_00_5_eq : ∀ k : Fin 16, amp0_0Expr 0 5 k = amp0_00_5 k := by decide +kernel +noncomputable def amp0_00_6 : Fin 16 → CBox := ![⟨⟨79998547113329202162620917337,79998547113329202164012247017⟩,⟨33444468290979898864827480874,33444468290979898870108250763⟩⟩,⟨⟨80660402805288127033634284472,80660402805288127035049521322⟩,⟨33331178859276799385126875153,33331178859276799390428055621⟩⟩,⟨⟨81312667998066685698607006669,81312667998066685700037353347⟩,⟨33208291838974914275371920264,33208291838974914280688791191⟩⟩,⟨⟨81957742719445335929154776602,81957742719445335930608640189⟩,⟨33077002675531881644904503464,33077002675531881650239671945⟩⟩,⟨⟨82592908285054304001344565134,82592908285054304002816974566⟩,⟨32936419578384960680792644590,32936419578384960686142995161⟩⟩,⟨⟨83220390497816444449627148836,83220390497816444451120614705⟩,⟨32787651123570488537913784401,32787651123570488543279505200⟩⟩,⟨⟨83837640777498492328767881131,83837640777498492330236789461⟩,⟨32629904963016883350875974823,32629904963016883356238224457⟩⟩,⟨⟨84446712022363487013130798019,84446712022363487014624468843⟩,⟨32464206237890538533488414364,32464206237890538538865752372⟩⟩,⟨⟨85045225351795677437490159990,85045225351795677439003888455⟩,⟨32289857971855168716594406353,32289857971855168721983906253⟩⟩,⟨⟨85635061807313951479219174215,85635061807313951480750403638⟩,⟨32107805146694643151844844671,32107805146694643157244748167⟩⟩,⟨⟨86214012090756224588174849418,86214012090756224589726126899⟩,⟨31917442211428757987634565651,31917442211428757993044773521⟩⟩,⟨⟨86783786174542563212201494211,86783786174542563213767466703⟩,⟨31719637116644790279297073013,31719637116644790284714813114⟩⟩,⟨⟨87342344500203965546376282936,87342344500203965547959393023⟩,⟨31513871905320657643131487400,31513871905320657648556610884⟩⟩,⟨⟨87891226508748835868769632856,87891226508748835870373022195⟩,⟨31300940488448425337160912281,31300940488448425342593777345⟩⟩,⟨⟨88428562801662577380483245677,88428562801662577382084107826⟩,⟨31080408778200190330966056523,31080408778200190336397592926⟩⟩,⟨⟨88955722585023898047184466234,88955722585023898048802950078⟩,⟨30852999510776174648816819497,30852999510776174654253424329⟩⟩] +lemma amp0_00_6_eq : ∀ k : Fin 16, amp0_0Expr 0 6 k = amp0_00_6 k := by decide +kernel +noncomputable def amp0_00_7 : Fin 16 → CBox := ![⟨⟨89471007293620074307810677720,89471007293620074309443933417⟩,⟨30618358842001581721573877913,30618358842001581727013521497⟩⟩,⟨⟨89975615961189654862530761412,89975615961189654864181566675⟩,⟨30377141080246719419684262068,30377141080246719425127169766⟩⟩,⟨⟨90468021773660573981235773166,90468021773660573982891446607⟩,⟨30129069092098045360784377827,30129069092098045366225311931⟩⟩,⟨⟨90949253427100935871843847663,90949253427100935873514325468⟩,⟨29874731395430845528018937522,29874731395430845533460517286⟩⟩,⟨⟨91417957013568803474833549159,91417957013568803476510882515⟩,⟨29613924121527062974308344712,29613924121527062979746985194⟩⟩,⟨⟨91874990502927410905285324762,91874990502927410906977927820⟩,⟨29347172533023955868096515070,29347172533023955873534277918⟩⟩,⟨⟨92319174279347974813818738906,92319174279347974815520235899⟩,⟨29074342661509663607442172222,29074342661509663612876071063⟩⟩,⟨⟨92751194978277172134517374702,92751194978277172136227833982⟩,⟨28795898954513875379776267720,28795898954513875385205661197⟩⟩,⟨⟨93170048887946097646631548034,93170048887946097648351022607⟩,⟨28511774056673731132603971601,28511774056673731138027921077⟩⟩,⟨⟨93576250483888385773688812475,93576250483888385775418524332⟩,⟨28222373951828187648550883000,28222373951828187653969143556⟩⟩,⟨⟨93968973792359875157989034458,93968973792359875159725569197⟩,⟨27927694683538314643623659589,27927694683538314649034298201⟩⟩,⟨⟨94348560087499663882190541655,94348560087499663883934663776⟩,⟨27628086040582247213596903024,27628086040582247218999520129⟩⟩,⟨⟨94714363186679370151508024400,94714363186679370153256465559⟩,⟨27323604320942228393626537092,27323604320942228399019265710⟩⟩,⟨⟨95066549905414100952799530219,95066549905414100954551388242⟩,⟨27014545309665093313693105191,27014545309665093319075134389⟩⟩,⟨⟨95404656122550905998424816123,95404656122550906000177246728⟩,⟨26701022481205605924545629791,26701022481205605929915319235⟩⟩,⟨⟨95728672721196517279186313519,95728672721196517280935896815⟩,⟨26383279735995478162471650861,26383279735995478167827510336⟩⟩] +lemma amp0_00_7_eq : ∀ k : Fin 16, amp0_0Expr 0 7 k = amp0_00_7 k := by decide +kernel +noncomputable def amp0_00_8 : Fin 16 → CBox := ![⟨⟨96038320128470408682068971885,96038320128470408683825627402⟩,⟨26061484710897266570438870431,26061484710897266575782752868⟩⟩,⟨⟨96333411602888557765900804993,96333411602888557767675046831⟩,⟨25735831473353895756343611802,25735831473353895761677788714⟩⟩,⟨⟨96613854823274779851720659088,96613854823274779853508781229⟩,⟨25406538870143562773074529561,25406538870143562778397077653⟩⟩,⟨⟨96879283510092067015075575088,96879283510092067016875105056⟩,⟨25073753124248686427113741522,25073753124248686432423385410⟩⟩,⟨⟨97129795515175046070067854734,97129795515175046071877434394⟩,⟨24737741399455656692429239499,24737741399455656697724699126⟩⟩,⟨⟨97364842882257704880083396055,97364842882257704881900130165⟩,⟨24398604003804880042800071543,24398604003804880048080076970⟩⟩,⟨⟨97584716777672036418018038405,97584716777672036419842338956⟩,⟨24056653583071829665580732130,24056653583071829670844540426⟩⟩,⟨⟨97788685199523136198329241955,97788685199523136200157868995⟩,⟨23711946404673360898115636842,23711946404673360903361905898⟩⟩,⟨⟨97977235993713229902425052518,97977235993713229904258727175⟩,⟨23364837817809415750288238356,23364837817809415755516261913⟩⟩,⟨⟨98149450507473328229586139009,98149450507473328231425363846⟩,⟨23015341871945175862205809638,23015341871945175867415246925⟩⟩,⟨⟨98306016859488166684744778620,98306016859488166686589203357⟩,⟨22663853896397280871731705560,22663853896397280876921661008⟩⟩,⟨⟨98445826897244472657423417441,98445826897244472659266478389⟩,⟨22310347497021402254751579345,22310347497021402259920054611⟩⟩,⟨⟨98569772839319364473440794305,98569772839319364475290978304⟩,⟨21955255314214504301162199798,21955255314214504306310276060⟩⟩,⟨⟨98676553932462718222644921692,98676553932462718224493993438⟩,⟨21598512239333033173831772514,21598512239333033178957191224⟩⟩,⟨⟨98767270563185905651422500775,98767270563185905653280842644⟩,⟨21240585608294173820440640889,21240585608294173825544888237⟩⟩,⟨⟨98840426014599106789809813349,98840426014599106791663759429⟩,⟨20881373284727967358959779292,20881373284727967364039453461⟩⟩] +lemma amp0_00_8_eq : ∀ k : Fin 16, amp0_0Expr 0 8 k = amp0_00_8 k := by decide +kernel +noncomputable def amp0_00_9 : Fin 16 → CBox := ![⟨⟨98897333158517595057090896926,98897333158517595058942811558⟩,⟨20521374737363146309806282733,20521374737363146314861077759⟩⟩,⟨⟨98936295678432651043101658185,98936295678432651044948698708⟩,⟨20160452449243601362522908740,20160452449243601367551911480⟩⟩,⟨⟨98958843508018617606173104419,98958843508018617608037371252⟩,⟨19799135511579469413225469068,19799135511579469418232398602⟩⟩,⟨⟨98963076809444127018199745586,98963076809444127020055831092⟩,⟨19437252636863958055812962623,19437252636863958060792283708⟩⟩,⟨⟨98950747425420686208614516907,98950747425420686210465253859⟩,⟨19075360080499176050502396461,19075360080499176055453916943⟩⟩,⟨⟨98919747775113580444137262947,98919747775113580445985712956⟩,⟨18713254359720041978644876886,18713254359720041983568876650⟩⟩,⟨⟨98872056741226453902939850054,98872056741226453904779268266⟩,⟨18351516487653670746215804907,18351516487653670751110326999⟩⟩,⟨⟨98805354462264414166599777431,98805354462264414168433214921⟩,⟨17989912329031533152543390293,17989912329031533157408661403⟩⟩,⟨⟨98721852290684114163515870886,98721852290684114165339575443⟩,⟨17629045299948293362883940737,17629045299948293367718526253⟩⟩,⟨⟨98619013212785837645955933017,98619013212785837647764600143⟩,⟨17268652124907410023478112121,17268652124907410028280863886⟩⟩,⟨⟨98499286796433229677422563007,98499286796433229679273837166⟩,⟨16909356319902288730801788940,16909356319902288735582002487⟩⟩,⟨⟨98359913650272973194591800585,98359913650272973196432082752⟩,⟨16550866952923070452781569245,16550866952923070457529567337⟩⟩,⟨⟨98203587638479469102478860879,98203587638479469104310354613⟩,⟨16193825388540794257788327040,16193825388540794262503774762⟩⟩,⟨⟨98027321390349533912971444605,98027321390349533914788359595⟩,⟨15837914495172485311863216161,15837914495172485316544961161⟩⟩,⟨⟨97834059504391608457756838561,97834059504391608459568640817⟩,⟨15483791286521092673150734586,15483791286521092677799687930⟩⟩,⟨⟨97620580627681174498107489003,97620580627681174499903566843⟩,⟨15131113863256406166234031472,15131113863256406170848238788⟩⟩] +lemma amp0_00_9_eq : ∀ k : Fin 16, amp0_0Expr 0 9 k = amp0_00_9 k := by decide +kernel +noncomputable def amp0_00_10 : Fin 16 → CBox := ![⟨⟨97390086912867344350276195086,97390086912867344352076033281⟩,⟨14780552740828819564628757785,14780552740828819569210489084⟩⟩,⟨⟨97139116592947780557212736810,97139116592947780558999409213⟩,⟨14431742660412235113254431996,14431742660412235117800932220⟩⟩,⟨⟨96871136604084608377349144251,96871136604084608379123372866⟩,⟨14085365544115665067314126000,14085365544115665071824920811⟩⟩,⟨⟨96582437873319470368819799000,96582437873319470370586490577⟩,⟨13741034159718472474575369687,13741034159718472479050915172⟩⟩,⟨⟨96276759790541569261825832662,96276759790541569263575929424⟩,⟨13399439793469008081012805458,13399439793469008085451144826⟩⟩,⟨⟨95950138590273254141891629098,95950138590273254143630610788⟩,⟨13060174605017349705162481040,13060174605017349709564243475⟩⟩,⟨⟨95606594262390733484756258978,95606594262390733486482528441⟩,⟨12723937255106552652234238777,12723937255106552656598638096⟩⟩,⟨⟨95241900428894401739103182556,95241900428894401740812650644⟩,⟨12390300640894033490724794980,12390300640894033495051076666⟩⟩,⟨⟨94860366341589850359573188914,94860366341589850361264406725⟩,⟨12059968861176121737131284003,12059968861176121741418610749⟩⟩,⟨⟨94457494513127834908259498846,94457494513127834909929712416⟩,⟨11732496877730393754033078244,11732496877730393758281049109⟩⟩,⟨⟨94037892679524014081614329130,94037892679524014083258410785⟩,⟨11408592344513062947908348434,11408592344513062952115845349⟩⟩,⟨⟨93596783121779459642338349168,93596783121779459644129670995⟩,⟨11087793597516540845287794195,11087793597516540849475224794⟩⟩,⟨⟨93139081893098735486275151796,93139081893098735488048855202⟩,⟨10770810016866029135305634606,10770810016866029139452396747⟩⟩,⟨⟨92659721240414412433476265140,92659721240414412435233354915⟩,⟨10457164605754967822352841454,10457164605754967826458982298⟩⟩,⟨⟨92163936034662120541360157310,92163936034662120543098975003⟩,⟨10147566695747042483571559275,10147566695747042487636400828⟩⟩,⟨⟨91646357944657780216571631681,91646357944657780218294689364⟩,⟨9841525234431027346778192389,9841525234431027350801846139⟩⟩] +lemma amp0_00_10_eq : ∀ k : Fin 16, amp0_0Expr 0 10 k = amp0_00_10 k := by decide +kernel +noncomputable def amp0_00_11 : Fin 16 → CBox := ![⟨⟨91112551891484927867706724524,91112551891484927869412804422⟩,⟨9539747784694594551684359779,9539747784694594555666066034⟩⟩,⟨⟨90556837610772477109466595138,90556837610772477111158586629⟩,⟨9241730500650504852354936742,9241730500650504856294974073⟩⟩,⟨⟨89985122110909477398115349059,89985122110909477399786542087⟩,⟨8948177511359966319749472818,8948177511359966323646688825⟩⟩,⟨⟨89391400949767563554521896610,89391400949767563556182291287⟩,⟨8658573425161124298861227095,8658573425161124302716454661⟩⟩,⟨⟨88781936147671460061573034442,88781936147671460063212150503⟩,⟨8373617327437889149261623485,8373617327437889153073274967⟩⟩,⟨⟨88150385861677238790378049944,88150385861677238791998670254⟩,⟨8092783514580870336734144823,8092783514580870340502456471⟩⟩,⟨⟨87503381030302004590924749110,87503381030302004592521397367⟩,⟨7816764474064052210196796286,7816764474064052213920842333⟩⟩,⟨⟨86834228107044795690566264991,86834228107044795692165643205⟩,⟨7545025410752985480427589493,7545025410752985484109575863⟩⟩,⟨⟨86149941943930302384149631883,86149941943930302385725594913⟩,⟨7278250715894759869913026740,7278250715894759873550072616⟩⟩,⟨⟨85443461793045652414065212446,85443461793045652415619476618⟩,⟨7015897710236379092422004661,7015897710236379096014283542⟩⟩,⟨⟨84722202627229175139732967734,84722202627229175141270572986⟩,⟨6758641246669239888520605279,6758641246669239892068126490⟩⟩,⟨⟨83978719672087676251858128560,83978719672087676253370546706⟩,⟨6505931956521962205391399288,6505931956521962208893356421⟩⟩,⟨⟨83220845581676824493155966098,83220845581676824494645245891⟩,⟨6258433768633704357824861519,6258433768633704361280929626⟩⟩,⟨⟨82440733251133709762982431376,82440733251133709764447570653⟩,⟨6015591807141111062193489425,6015591807141111065603596898⟩⟩,⟨⟨81646652091747448070933348693,81646652091747448072370224976⟩,⟨5778057747779290293595655983,5778057747779290296959159454⟩⟩,⟨⟨80830332710398563826900101242,80830332710398563828305258324⟩,⟨5545272377403089911637629214,5545272377403089914954196249⟩⟩] +lemma amp0_00_11_eq : ∀ k : Fin 16, amp0_0Expr 0 11 k = amp0_00_11 k := by decide +kernel +noncomputable def amp0_00_12 : Fin 16 → CBox := ![⟨⟨80000502055091529490123526957,80000502055091529491596314820⟩,⟨5317873846414489121261198724,5317873846414489124536965365⟩⟩,⟨⟨79148446630478481508131449333,79148446630478481509586052894⟩,⟨5095299762064869340484686412,5095299762064869343713793100⟩⟩,⟨⟨78283373622223876847967369462,78283373622223876849402358015⟩,⟨4878173534157658307021174060,4878173534157658310203191437⟩⟩,⟨⟨77396101527372456284348535043,77396101527372456285765112056⟩,⟨4665930735800409119982889215,4665930735800409123117755145⟩⟩,⟨⟨76496342645704898941408768483,76496342645704898942805570826⟩,⟨4459178877997746728919889536,4459178877997746732007083636⟩⟩,⟨⟨75574421195248408632044040037,75574421195248408633423703960⟩,⟨4257352632898190135347403560,4257352632898190138387058571⟩⟩,⟨⟨74640581939279942146709028286,74640581939279942148065145285⟩,⟨4061042511632516489307701700,4061042511632516492299164131⟩⟩,⟨⟨73684625857188758862289807357,73684625857188758863635936218⟩,⟨3869683406176638908315998746,3869683406176638911259852707⟩⟩,⟨⟨72717360347935638420236403166,72717360347935638421557721364⟩,⟨3683847783854369402533120466,3683847783854369405428147995⟩⟩,⟨⟨71728031124513723025901056977,71728031124513723027201076159⟩,⟨3502971864668152943746851418,3502971864668152946593253176⟩⟩,⟨⟨70728041630345612353238674551,70728041630345612354514257732⟩,⟨3327609085315448674140741267,3327609085315448676938124086⟩⟩,⟨⟨69706046765619109355573657502,69706046765619109356824151894⟩,⟨3157198089184767472311414447,3157198089184767475059609758⟩⟩,⟨⟨68674083155717387051473281206,68674083155717387052692846697⟩,⟨2992272352567045737578527473,2992272352567045740276950460⟩⟩,⟨⟨67620175285568061753780518015,67620175285568061755031217350⟩,⟨2832274024443162824423719330,2832274024443162827074965393⟩⟩,⟨⟨66557034417628224688557757480,66557034417628224689781308803⟩,⟨2677715747834554773920167371,2677715747834554776521519967⟩⟩,⟨⟨65472010317928385324973030721,65472010317928385326170410419⟩,⟨2528044245994749679767516052,2528044245994749682318864181⟩⟩] +lemma amp0_00_12_eq : ∀ k : Fin 16, amp0_0Expr 0 12 k = amp0_00_12 k := by decide +kernel +noncomputable def amp0_00_13 : Fin 16 → CBox := ![⟨⟨64378535368065489524248171022,64378535368065489525420116960⟩,⟨2383750512559332013143702897,2383750512559332015644754825⟩⟩,⟨⟨63263234830527651836873102096,63263234830527651838027273052⟩,⟨2244286899779031620255011252,2244286899779031622706037891⟩⟩,⟨⟨62140314575590477618887176169,62140314575590477620011076854⟩,⟨2110121992313872811145872227,2110121992313872813546295078⟩⟩,⟨⟨60995619146876161668795981245,60995619146876161669894046707⟩,⟨1980714811696364918366012008,1980714811696364920715808720⟩⟩,⟨⟨59844187212359458890024580831,59844187212359458891090783581⟩,⟨1856510830277743880984716839,1856510830277743883283482398⟩⟩,⟨⟨58671018784936478611624800568,58671018784936478612699109809⟩,⟨1736976764180635341971203044,1736976764180635344220060883⟩⟩,⟨⟨57492052875717392047115812747,57492052875717392048163592447⟩,⟨1622534326049713407210348197,1622534326049713409408155314⟩⟩,⟨⟨56291372114626450545302811306,56291372114626450546323718946⟩,⟨1512658936344256479336264933,1512658936344256481482801657⟩⟩,⟨⟨55085893251315210129462843121,55085893251315210130457287955⟩,⟨1407747956167503323980338131,1407747956167503326075432793⟩⟩,⟨⟨53858697834819218658392192670,53858697834819218659364313023⟩,⟨1307286503868251436893393964,1307286503868251438937065631⟩⟩,⟨⟨52627769626328846110318238101,52627769626328846111263620753⟩,⟨1211647052311521194711346766,1211647052311521196703480775⟩⟩,⟨⟨51375092269471411817834776926,51375092269471411818779080078⟩,⟨1120325394419977580946962420,1120325394419977582887866131⟩⟩,⟨⟨50119820263601198825673833870,50119820263601198826586439452⟩,⟨1033668632783766789029662649,1033668632783766790918570963⟩⟩,⟨⟨48842726480580325910958142916,48842726480580325911842203465⟩,⟨951184194001238312573533747,951184194001238314410353179⟩⟩,⟨⟨47564257650757907183994369916,47564257650757907184851517976⟩,⟨873193382478778129266985523,873193382478778131051824403⟩⟩,⟨⟨46263843192459105094237101481,46263843192459105095064128514⟩,⟨799216199261019384376208436,799216199261019386108707476⟩⟩] +lemma amp0_00_13_eq : ∀ k : Fin 16, amp0_0Expr 0 13 k = amp0_00_13 k := by decide +kernel +noncomputable def amp0_00_14 : Fin 16 → CBox := ![⟨⟨44963365643193229008547209192,44963365643193229009363900444⟩,⟨729547776200882343574877828,729547776200882345255341261⟩⟩,⟨⟨43640753516496572730994291626,43640753516496572731782810261⟩,⟨663721610450788541166099018,663721610450788542794030911⟩⟩,⟨⟨42319496527379578949875403835,42319496527379578950638220084⟩,⟨602006339832014249171260384,602006339832014250746861768⟩⟩,⟨⟨40975833456671023115907269591,40975833456671023116637414032⟩,⟨543949859357081181646498795,543949859357081183169304816⟩⟩,⟨⟨39635068043190852236975408004,39635068043190852237691907815⟩,⟨489794043517787819130304230,489794043517787820600681353⟩⟩,⟨⟨38271520160944685274903817786,38271520160944685275591637752⟩,⟨439102066216815581084101517,439102066216815582501539531⟩⟩,⟨⟨36912560424497651083511352883,36912560424497651084181362749⟩,⟨392088820717132348098431522,392088820717132349463318108⟩⟩,⟨⟨35530307857230846713844512723,35530307857230846714484277120⟩,⟨348333619306281088130976886,348333619306281089442719959⟩⟩,⟨⟨34154513553232396885049512305,34154513553232396885660357091⟩,⟨308024206653351163175461003,308024206653351164434300276⟩⟩,⟨⟨32754743364966791659453834760,32754743364966791660044225003⟩,⟨270756870595871614279114917,270756870595871615484728568⟩⟩,⟨⟨31363524387602547695831624896,31363524387602547696391354191⟩,⟨236692089412541807792396842,236692089412541808945099126⟩⟩,⟨⟨29947420983976246643248026662,29947420983976246643785512498⟩,⟨205443940580299416306709924,205443940580299417405994689⟩⟩,⟨⟨28542244950103857905565917281,28542244950103857906081174196⟩,⟨177145566659373585826136067,177145566659373586872404914⟩⟩,⟨⟨27110976386795096436684723387,27110976386795096437169315218⟩,⟨151429625129291871077879168,151429625129291872070513408⟩⟩,⟨⟨25693381412495025249036712935,25693381412495025249497163567⟩,⟨128401900680338309851939701,128401900680338310791549660⟩⟩,⟨⟨24248078776185217400427539396,24248078776185217400862917835⟩,⟨107714396958163729381202407,107714396958163730267050860⟩⟩] +lemma amp0_00_14_eq : ∀ k : Fin 16, amp0_0Expr 0 14 k = amp0_00_14 k := by decide +kernel +noncomputable def amp0_00_15 : Fin 16 → CBox := ![⟨⟨22819695353392487777180970236,22819695353392487777590002934⟩,⟨89445564220051466975057184,89445564220051467807737801⟩⟩,⟨⟨21361419760645051439078504827,21361419760645051439460186668⟩,⟨73267494093875803124120946,73267494093875803902879203⟩⟩,⟨⟨19924009505566803118013104315,19924009505566803118367220001⟩,⟨59231369344202456936556168,59231369344202457662211626⟩⟩,⟨⟨18453695453727093463806778261,18453695453727093464135974941⟩,⟨47030087516273334130242158,47030087516273334801823534⟩⟩,⟨⟨17009223442553061767317147552,17009223442553061767620600429⟩,⟨36687671334739435305077397,36687671334739435923527200⟩⟩,⟨⟨15527573120279843514137754873,15527573120279843514414233558⟩,⟨27918520002247788793583632,27918520002247789357785564⟩⟩,⟨⟨14078353508990555872071829531,14078353508990555872320812923⟩,⟨20719639371979333188875078,20719639371979333700051968⟩⟩,⟨⟨12585618000455526853329608154,12585618000455526853553106121⟩,⟨14827608142347008284844809,14827608142347008741575161⟩⟩,⟨⟨11134640317483545321410296670,11134640317483545321607020696⟩,⟨10212585393443974171467746,10212585393443974575261628⟩⟩,⟨⟨9630099532377512377933085041,9630099532377512378102576425⟩,⟨6633999710382994776162343,6633999710382995125247423⟩⟩,⟨⟨8181883550284142958286774049,8181883550284142958429600246⟩,⟨4035341697483126378993632,4035341697483126675442683⟩⟩,⟨⟨6662337732184249128497174259,6662337732184249128612745255⟩,⟨2199579725058594788103673,2199579725058595029423765⟩⟩,⟨⟨5225792715938785250197728549,5225792715938785250286884195⟩,⟨1043675318613417551057325,1043675318613417740262698⟩⟩,⟨⟨3679527966689603314330843893,3679527966689603314392694236⟩,⟨374922150676004235574085,374922150676004368771687⟩⟩,⟨⟨2282638338302584531647945235,2282638338302584531683192216⟩,⟨83730397008744458447737,83730397008744541060019⟩⟩,⟨⟨648527168554654566893053535,648527168554654566901193333⟩,⟨2643193656450817007879,2643193656450840477794⟩⟩] +lemma amp0_00_15_eq : ∀ k : Fin 16, amp0_0Expr 0 15 k = amp0_00_15 k := by decide +kernel +noncomputable def amp0_00 : Fin 16 → Fin 16 → CBox := ![amp0_00_0,amp0_00_1,amp0_00_2,amp0_00_3,amp0_00_4,amp0_00_5,amp0_00_6,amp0_00_7,amp0_00_8,amp0_00_9,amp0_00_10,amp0_00_11,amp0_00_12,amp0_00_13,amp0_00_14,amp0_00_15] +lemma amp0_00_eq (i k : Fin 16) : amp0_0Expr 0 i k = amp0_00 i k := by + fin_cases i + · exact amp0_00_0_eq k + · exact amp0_00_1_eq k + · exact amp0_00_2_eq k + · exact amp0_00_3_eq k + · exact amp0_00_4_eq k + · exact amp0_00_5_eq k + · exact amp0_00_6_eq k + · exact amp0_00_7_eq k + · exact amp0_00_8_eq k + · exact amp0_00_9_eq k + · exact amp0_00_10_eq k + · exact amp0_00_11_eq k + · exact amp0_00_12_eq k + · exact amp0_00_13_eq k + · exact amp0_00_14_eq k + · exact amp0_00_15_eq k +noncomputable def amp0_01_0 : Fin 16 → CBox := ![⟨⟨216178096704881190160259279,216178096704881190162378499⟩,⟨374427922718183715710011504,374427922718183715743946722⟩⟩,⟨⟨760954644405476281685886359,760954644405476281695545868⟩,⟨1317900465836448054802240882,1317900465836448054925495131⟩⟩,⟨⟨1226846039970384574024466031,1226846039970384574041714891⟩,⟨2124459778092482373180281474,2124459778092482373381869653⟩⟩,⟨⟨1742868230553603122469351522,1742868230553603122494296725⟩,⟨3017344759125023950024544968,3017344759125023950311624035⟩⟩,⟨⟨2222754687533542233855115818,2222754687533542233887556478⟩,⟨3846991278603234543175146674,3846991278603234543542248858⟩⟩,⟨⟨2730918658829647215287301713,2730918658829647215327466037⟩,⟨4724709412834161581355013662,4724709412834161581806408718⟩⟩,⟨⟨3215991175376982937196180784,3215991175376982937243940844⟩,⟨5561414779498908854634527279,5561414779498908855166665352⟩⟩,⟨⟨3720718699712779202981227767,3720718699712779203036750138⟩,⟨6430857048049550304523853589,6430857048049550305139653081⟩⟩,⟨⟨4208522681233388134516782951,4208522681233388134579953781⟩,⟨7269604964512430654748173697,7269604964512430655444938310⟩⟩,⟨⟨4711392819792956325537377450,4711392819792956325607778727⟩,⟨8132745552467294194387684444,8132745552467294195166643758⟩⟩,⟨⟨5200931341264551390561872753,5200931341264551390640223755⟩,⟨8971052636411219995971660708,8971052636411219996832025972⟩⟩,⟨⟨5702690360505990880103243491,5702690360505990880189388023⟩,⟨9828432549116667575790792349,9828432549116667576733810008⟩⟩,⟨⟨6193469559200747704571536721,6193469559200747704665088127⟩,⟨10664697168311882424051175264,10664697168311882425074444392⟩⟩,⟨⟨6694532219466138384247147786,6694532219466138384347877027⟩,⟨11516294777896590191201875463,11516294777896590192306212427⟩⟩,⟨⟨7186274820674048163468898982,7186274820674048163577735208⟩,⟨12349303114435206237521954054,12349303114435206238707422147⟩⟩,⟨⟨7686896216477907639899222115,7686896216477907640016141459⟩,⟨13194834047155305383577541606,13194834047155305384845076118⟩⟩] +lemma amp0_01_0_eq : ∀ k : Fin 16, amp0_0Expr 1 0 k = amp0_01_0 k := by decide +kernel +noncomputable def amp0_01_1 : Fin 16 → CBox := ![⟨⟨8179431270407463189536895589,8179431270407463189661569463⟩,⟨14023571341419156252982872081,14023571341419156254330513462⟩⟩,⟨⟨8679778271599624062000700173,8679778271599624062132786398⟩,⟨14862614430602471728040703663,14862614430602471729468659920⟩⟩,⟨⟨9172991138669868914879104775,9172991138669868915018324756⟩,⟨15686180542716245903739304850,15686180542716245905245808300⟩⟩,⟨⟨9673176157629234178469089686,9673176157629234178617725509⟩,⟨16518238486698559755530682335,16518238486698559757120276033⟩⟩,⟨⟨10166982950388058534659277571,10166982950388058534814482712⟩,⟨17335805775651577602456455296,17335805775651577604123060049⟩⟩,⟨⟨10667081393814560761759433635,10667081393814560761921317617⟩,⟨18160337490009399423704176075,18160337490009399425448500018⟩⟩,⟨⟨11161414647180990557626397040,11161414647180990557797860567⟩,⟨18971128092466434839570835250,18971128092466434841396654020⟩⟩,⟨⟨11661474520054717288129121857,11661474520054717288306783397⟩,⟨19787567417700190607388383682,19787567417700190609290354327⟩⟩,⟨⟨12156274521770270251755478603,12156274521770270251942226642⟩,⟨20590840276719456088294623813,20590840276719456090276530279⟩⟩,⟨⟨12656321942234984791859765281,12656321942234984792056203256⟩,⟨21398607546610297165672657087,21398607546610297167735819701⟩⟩,⟨⟨13151531136520227419279731728,13151531136520227419481631021⟩,⟨22193650704154673735480728172,22193650704154673737616912761⟩⟩,⟨⟨13651573583309681971957425473,13651573583309681972168637013⟩,⟨22992160324867102862186328292,22992160324867102864402257274⟩⟩,⟨⟨14147132748685516431891663626,14147132748685516432107007303⟩,⟨23778286223002084603508235699,23778286223002084605794130283⟩⟩,⟨⟨14647160988346775934685042036,14647160988346775934911244482⟩,⟨24566951898681369153524814619,24566951898681369155892125831⟩⟩,⟨⟨15143006495104444878447386706,15143006495104444878682080761⟩,⟨25343494481598689794841012298,25343494481598689797284712538⟩⟩,⟨⟨15642995711027499874145904510,15642995711027499874390090892⟩,⟨26121732985813821892049571975,26121732985813821894571398782⟩⟩] +lemma amp0_01_1_eq : ∀ k : Fin 16, amp0_0Expr 1 1 k = amp0_01_1 k := by decide +kernel +noncomputable def amp0_01_2 : Fin 16 → CBox := ![⟨⟨16139057467372682560883777949,16139057467372682561131229523⟩,⟨26888045920748681816748682127,26888045920748681819337217274⟩⟩,⟨⟨16638967892697315021503288514,16638967892697315021761096832⟩,⟨27655279932353967403655580624,27655279932353967406322652270⟩⟩,⟨⟨17135167749790936436166669713,17135167749790936436433758608⟩,⟨28410735546851922303421880364,28410735546851922306164662324⟩⟩,⟨⟨17634944986474635443767362767,17634944986474635444044471735⟩,⟨29166395861544427126380864581,29166395861544427129200513068⟩⟩,⟨⟨18131195462343455940889886481,18131195462343455941178137668⟩,⟨29910384550181176266230933070,29910384550181176269128265526⟩⟩,⟨⟨18630770600488307221070227362,18630770600488307221359005347⟩,⟨30653911861124241209714614289,30653911861124241212672024302⟩⟩,⟨⟨19126973834809539103211321307,19126973834809539103509726206⟩,⟨31385841805106312751752793708,31385841805106312754784266476⟩⟩,⟨⟨19626263446018664432797888898,19626263446018664433104533866⟩,⟨32116688176346159864493269659,32116688176346159867596355741⟩⟩,⟨⟨20122310329016182679498395235,20122310329016182679814742268⟩,⟨32835985273731698190413933649,32835985273731698193590006298⟩⟩,⟨⟨20621216382883457435669313037,20621216382883457435995756079⟩,⟨33553615387626237324485146304,33553615387626237327734615270⟩⟩,⟨⟨21116985820896760534422718791,21116985820896760534759182478⟩,⟨34259723325597251496451664039,34259723325597251499773376930⟩⟩,⟨⟨21615395558186525724252049193,21615395558186525724586229005⟩,⟨34963615558774036550007618346,34963615558774036553381391086⟩⟩,⟨⟨22110753850746593078822492240,22110753850746593079168791960⟩,⟨35655995980880480009028258218,35655995980880480012476409541⟩⟩,⟨⟨22608539636751836378862941518,22608539636751836379219439764⟩,⟨36345643346037159480027253260,36345643346037159483546348044⟩⟩,⟨⟨23103339947972155493326265094,23103339947972155493694628832⟩,⟨37023776081384766606709613389,37023776081384766610301289259⟩⟩,⟨⟨23600359122855001199697247741,23600359122855001200073132134⟩,⟨37698687060910749375347180491,37698687060910749379004111160⟩⟩] +lemma amp0_01_2_eq : ∀ k : Fin 16, amp0_0Expr 1 2 k = amp0_01_2 k := by decide +kernel +noncomputable def amp0_01_3 : Fin 16 → CBox := ![⟨⟨24094441035229122345357257506,24094441035229122345743444904⟩,⟨38362070391662964283805251441,38362070391662964287530859388⟩⟩,⟨⟨24590535773604755304984306778,24590535773604755305381362768⟩,⟨39021769681444076793835031967,39021769681444076797629804157⟩⟩,⟨⟨25083724915859867988804145750,25083724915859867989212483561⟩,⟨39669920631426435888102026523,39669920631426435891965570187⟩⟩,⟨⟨25578722104728642442206526110,25578722104728642442604684883⟩,⟨40313949807985743540729013224,40313949807985743544627046692⟩⟩,⟨⟨26070829847813166040985668608,26070829847813166041396688803⟩,⟨40946404439649227917180929975,40946404439649227921148822932⟩⟩,⟨⟨26564540989704766476930573403,26564540989704766477352575118⟩,⟨41574322560160752081135857773,41574322560160752085170157164⟩⟩,⟨⟨27055364206662108545450072569,27055364206662108545882858722⟩,⟨42190636270328331652556164076,42190636270328331656655509765⟩⟩,⟨⟨27547585353230431782739441353,27547585353230431783182079892⟩,⟨42802020412496186018246652572,42802020412496186022409075722⟩⟩,⟨⟨28036906239872469148038115335,28036906239872469148491917236⟩,⟨43401768219601819890830586206,43401768219601819895057075105⟩⟩,⟨⟨28527417959975720985040698488,28527417959975720985500327458⟩,⟨43996213966587486230167959998,43996213966587486234449726142⟩⟩,⟨⟨29015003914076697213024110396,29015003914076697213494771580⟩,⟨44578990783793092115159004076,44578990783793092119503046224⟩⟩,⟨⟨29503571299465376807217573106,29503571299465376807697065956⟩,⟨45156112658074627382035639521,45156112658074627386438004413⟩⟩,⟨⟨29989174856755619591877770093,29989174856755619592367090096⟩,⟨45721533547900628779694396024,45721533547900628784155568034⟩⟩,⟨⟨30475547567785164436205079446,30475547567785164436704011487⟩,⟨46280965397009150536880765782,46280965397009150541399817096⟩⟩,⟨⟨30958906393406142493879888613,30958906393406142494388932467⟩,⟨46828665804061895006991690856,46828665804061895011568331310⟩⟩,⟨⟨31442818746632094523382313237,31442818746632094523901180044⟩,⟨47370061140459967981756342716,47370061140459967986389507941⟩⟩] +lemma amp0_01_3_eq : ∀ k : Fin 16, amp0_0Expr 1 3 k = amp0_01_3 k := by decide +kernel +noncomputable def amp0_01_4 : Fin 16 → CBox := ![⟨⟨31923655680969363492951726009,31923655680969363493446481028⟩,⟨47899697099569643537290204762,47899697099569643541927930694⟩⟩,⟨⟨32404826780030267614052416727,32404826780030267614562502903⟩,⟨48422729396441952932289545013,48422729396441952936990534445⟩⟩,⟨⟨32882849938003413148483599343,32882849938003413149007717474⟩,⟨48933977714096870301701471088,48933977714096870306462673258⟩⟩,⟨⟨33360983848821784350427232232,33360983848821784350964051266⟩,⟨49438340658465771303360199378,49438340658465771308178916288⟩⟩,⟨⟨33835886771805093092965906640,33835886771805093093515021215⟩,⟨49930899065884821084449779833,49930899065884821089324330450⟩⟩,⟨⟨34310672742819537185876779385,34310672742819537186439380629⟩,⟨50416306770206392298208747612,50416306770206392303140152560⟩⟩,⟨⟨34782134602411432456801525818,34782134602411432457374198792⟩,⟨50889894046760940200978001489,50889894046760940205960168469⟩⟩,⟨⟨35253247330278985751915434630,35253247330278985752500531807⟩,⟨51356081219975404905104206163,51356081219975404910139842481⟩⟩,⟨⟨35720933183145069698494631259,35720933183145069699092832635⟩,⟨51810437285976343915841467973,51810437285976343920930482517⟩⟩,⟨⟨36188033124111665541554824621,36188033124111665542155712306⟩,⟨52257159364861488849677402075,52257159364861488854803968582⟩⟩,⟨⟨36651594217104950310656879696,36651594217104950311271490953⟩,⟨52692045342982261657454618863,52692045342982261662633649076⟩⟩,⟨⟨37114327944026099973271211195,37114327944026099973897593117⟩,⟨53119078584576036849402091410,53119078584576036854629986064⟩⟩,⟨⟨37573402068745722433910260947,37573402068745722434549557795⟩,⟨53534276829399654227177750631,53534276829399654232455074492⟩⟩,⟨⟨38031402673543520197677958487,38031402673543520198326126411⟩,⟨53941418365208258032333156993,53941418365208258037653359099⟩⟩,⟨⟨38485614569435227269657770541,38485614569435227270319052599⟩,⟨54336732460574162041471389308,54336732460574162046839430669⟩⟩,⟨⟨38938502110597625179674130398,38938502110597625180345995249⟩,⟨54723800313256923565779745080,54723800313256923571191238640⟩⟩] +lemma amp0_01_4_eq : ∀ k : Fin 16, amp0_0Expr 1 4 k = amp0_01_4 k := by decide +kernel +noncomputable def amp0_01_5 : Fin 16 → CBox := ![⟨⟨39387463915629646547258261778,39387463915629646547941884856⟩,⟨55099055037248306619390857367,55099055037248306624846405820⟩⟩,⟨⟨39834845910190629867795268332,39834845910190629868490521332⟩,⟨55465888100464745999582768872,55465888100464746005081360431⟩⟩,⟨⟨40278157658060360184731586879,40278157658060360185439577279⟩,⟨55820929358023382461475319799,55820929358023382467017431820⟩⟩,⟨⟨40719629617343008895996819658,40719629617343008896717159533⟩,⟨56167387340136493592310462376,56167387340136493597894706922⟩⟩,⟨⟨41156879780085661546242640043,41156879780085661546975734717⟩,⟨56502082063423845857652030335,56502082063423845863277907967⟩⟩,⟨⟨41592025788342503425939277683,41592025788342503426612607207⟩,⟨56828045395773452711921930687,56828045395773452717489484476⟩⟩,⟨⟨42022791863124524178795633441,42022791863124524179485497067⟩,⟨57142281412516486069894907503,57142281412516486075507773940⟩⟩,⟨⟨42451185198069898676383238803,42451185198069898677087727354⟩,⟨57447651123004775866142485349,57447651123004775871797154859⟩⟩,⟨⟨42875034336859009487192147528,42875034336859009487909986395⟩,⟨57741336993174612728263080423,57741336993174612733956765402⟩⟩,⟨⟨43296238130955518472139553454,43296238130955518472870508300⟩,⟨58026034545940520677221137513,58026034545940520682952620682⟩⟩,⟨⟨43712727811667077687491456914,43712727811667077688233679438⟩,⟨58299099367213351268808629408,58299099367213351274574392797⟩⟩,⟨⟨44126295752901991292520805088,44126295752901991293273888857⟩,⟨58563066469211670198242842287,58563066469211670204041469680⟩⟩,⟨⟨44534974490528961699546915818,44534974490528961700313312806⟩,⟨58815459651755407752767002524,58815459651755407758600724097⟩⟩,⟨⟨44940451561296249821938537806,44940451561296249822714454504⟩,⟨59058658027098961829281202255,59058658027098961835144113186⟩⟩,⟨⟨45340859657438342143463006481,45340859657438342144250693799⟩,⟨59290349038316896100869971006,59290349038316896106764024516⟩⟩,⟨⟨45737782910027527919519750076,45737782910027527920319879868⟩,⟨59512760171284748187572597719,59512760171284748193497769057⟩⟩] +lemma amp0_01_5_eq : ∀ k : Fin 16, amp0_0Expr 1 5 k = amp0_01_5 k := by decide +kernel +noncomputable def amp0_01_6 : Fin 16 → CBox := ![⟨⟨46129453239144780490616430583,46129453239144780491420918237⟩,⟨59723738251229604655578877906,59723738251229604661523692157⟩⟩,⟨⟨46517352606228879004480631136,46517352606228879005299059830⟩,⟨59925363098890158522910692943,59925363098890158528886674590⟩⟩,⟨⟨46899811436856682791672816346,46899811436856682792500113468⟩,⟨60115636947139037681965447952,60115636947139037687965065974⟩⟩,⟨⟨47278210575267993083474580120,47278210575267993084315599399⟩,⟨60296495622583303120615738496,60296495622583303126644309684⟩⟩,⟨⟨47650978424344926851374737623,47650978424344926852226611788⟩,⟨60466093057436351363474558257,60466093057436351369527438210⟩⟩,⟨⟨48019395590329343784227303920,48019395590329343785091486718⟩,⟨60626224484662940117670503696,60626224484662940123748614337⟩⟩,⟨⟨48381988108706628765946750620,48381988108706628766796919284⟩,⟨60775192075596587827643564464,60775192075596587833712853495⟩⟩,⟨⟨48739937062754433248123206357,48739937062754433248987824797⟩,⟨60914653617135678077212644416,60914653617135678083308094890⟩⟩,⟨⟨49091865949876773919292049966,49091865949876773920168402582⟩,⟨61043056291505091444359723913,61043056291505091450476969579⟩⟩,⟨⟨49438856889140577146665572324,49438856889140577147552188668⟩,⟨61161923349913194951711836455,61161923349913194957848122715⟩⟩,⟨⟨49779630834812999963089995831,49779630834812999963988346275⟩,⟨61269843974958385965205911480,61269843974958385971362109935⟩⟩,⟨⟨50115171351041714249205940739,50115171351041714250112938864⟩,⟨61368209569358896425958325648,61368209569358896432129732847⟩⟩,⟨⟨50444297002126083616618601448,50444297002126083617535656300⟩,⟨61455748510624834916392608135,61455748510624834922580046972⟩⟩,⟨⟨50767893062967538853103382075,50767893062967538854032313428⟩,⟨61533722829510703199188327059,61533722829510703205393086761⟩⟩,⟨⟨51084876012786017708040578211,51084876012786017708968210506⟩,⟨61600997486843855140236183817,61600997486843855146441443378⟩⟩,⟨⟨51396032964240217848264568164,51396032964240217849202544315⟩,⟨61658707418398045844663639661,61658707418398045850882601896⟩⟩] +lemma amp0_01_6_eq : ∀ k : Fin 16, amp0_0Expr 1 6 k = amp0_01_6 k := by decide +kernel +noncomputable def amp0_01_7 : Fin 16 → CBox := ![⟨⟨51700378762401316362605081687,51700378762401316363551752937⟩,⟨61705851740730076324169210794,61705851740730076330399023554⟩⟩,⟨⟨51998602350141418596317838972,51998602350141418597274815695⟩,⟨61743440381956466383139391929,61743440381956466389381061465⟩⟩,⟨⟨52289817530447678155015293053,52289817530447678155975244286⟩,⟨61770604362130426991339048275,61770604362130426997583027342⟩⟩,⟨⟨52574614937666663624733779904,52574614937666663625702452052⟩,⟨61788230508122298341656763799,61788230508122298347908986653⟩⟩,⟨⟨52852208061711668651927891073,52852208061711668652900685917⟩,⟨61795579659057486223639465763,61795579659057486229893716024⟩⟩,⟨⟨53123088961099440463275028259,53123088961099440464256814775⟩,⟨61793417273762555365677421076,61793417273762555371938515476⟩⟩,⟨⟨53386571675115929066780604700,53386571675115929067767693890⟩,⟨61781132087291394008618884381,61781132087291394014881710673⟩⟩,⟨⟨53643049292524299048741495847,53643049292524299049733930535⟩,⟨61759369757161249593152761959,61759369757161249599416523440⟩⟩,⟨⟨53891937395004824547504542677,53891937395004824548502349209⟩,⟨61727645146905002411422640852,61727645146905002417686600924⟩⟩,⟨⟨54133529582316605967457363601,54133529582316605968461253427⟩,⟨61686485518842746533488652156,61686485518842746539752757358⟩⟩,⟨⟨54367344099893634778602069202,54367344099893634779610063705⟩,⟨61635530248522632904142927708,61635530248522632910404155035⟩⟩,⟨⟨54593574414576906645605226328,54593574414576906646617770950⟩,⟨61575189453565319647073827844,61575189453565319653331851240⟩⟩,⟨⟨54811842683620554331255450338,54811842683620554332270648893⟩,⟨61505225552171657621801447624,61505225552171657628053407793⟩⟩,⟨⟨55022241472420156563209968565,55022241472420156564227302700⟩,⟨61425932616363687194520768454,61425932616363687200765261240⟩⟩,⟨⟨55224498223789075559429293314,55224498223789075560447112119⟩,⟨61337194781628036992262511722,61337194781628036998496998208⟩⟩,⟨⟨55418603707984574304760616301,55418603707984574305776942263⟩,⟨61239191025557904123594603469,61239191025557904129816116042⟩⟩] +lemma amp0_01_7_eq : ∀ k : Fin 16, amp0_0Expr 1 7 k = amp0_01_7 k := by decide +kernel +noncomputable def amp0_01_8 : Fin 16 → CBox := ![⟨⟨55604392152348909146490211321,55604392152348909147510780614⟩,⟨61131926017191833592918661446,61131926017191833599132878766⟩⟩,⟨⟨55781751511991666619914886635,55781751511991666620945792181⟩,⟨61015464445677466936200125755,61015464445677466942412868005⟩⟩,⟨⟨55950624423136563902562645887,55950624423136563903601738492⟩,⟨60889930469856510347656162204,60889930469856510353864323369⟩⟩,⟨⟨56110794877668172449395980750,56110794877668172450441832591⟩,⟨60755275153273810299642062009,60755275153273810305843234784⟩⟩,⟨⟨56262315671182135958331614176,56262315671182135959383433321⟩,⟨60611741239856456140032773258,60611741239856456146225410983⟩⟩,⟨⟨56404865553832332611858686160,56404865553832332612914800286⟩,⟨60459166688611488037219842995,60459166688611488043401303323⟩⟩,⟨⟨56538609358586796354054899159,56538609358586796355115542201⟩,⟨60297912062590627205853313686,60297912062590627212023177828⟩⟩,⟨⟨56663119181951047678523159029,56663119181951047679586457041⟩,⟨60127702596238212333284495326,60127702596238212339439963137⟩⟩,⟨⟨56778673901785933709486102537,56778673901785933710552466452⟩,⟨59949016044926429716684624389,59949016044926429722825518127⟩⟩,⟨⟨56884737411991141116241044762,56884737411991141117310770658⟩,⟨59761465157436564760237858326,59761465157436564766363674487⟩⟩,⟨⟨56981704775035893930950700574,56981704775035893932023580097⟩,⟨59565644394886997033590116714,59565644394886997039700011033⟩⟩,⟨⟨57068929991917070161481812043,57068929991917070162554043441⟩,⟨59361054117555599317158025946,59361054117555599323247257191⟩⟩,⟨⟨57146926584997720785691947889,57146926584997720786768443753⟩,⟨59148405147716851266078493995,59148405147716851272151596807⟩⟩,⟨⟨57214936825728964699860782169,57214936825728964700936772384⟩,⟨58927085411208756262398625342,58927085411208756268449874935⟩⟩,⟨⟨57273595111339169069652882590,57273595111339169070734381276⟩,⟨58697921891305617850105073693,58697921891305617856140078798⟩⟩,⟨⟨57322029994988735851804563064,57322029994988735852883648545⟩,⟨58460189888305538203347814820,58460189888305538209357697309⟩⟩] +lemma amp0_01_8_eq : ∀ k : Fin 16, amp0_0Expr 1 8 k = amp0_01_8 k := by decide +kernel +noncomputable def amp0_01_9 : Fin 16 → CBox := ![⟨⟨57360999308336436054208426579,57360999308336436055286461203⟩,⟨58214832493927036398379815996,58214832493927036404365464449⟩⟩,⟨⟨57389515738848061905611625716,57389515738848061906686965035⟩,⟨57961012043858325484144509131,57961012043858325490103508321⟩⟩,⟨⟨57408463262529407895545465012,57408463262529407896630922862⟩,⟨57699787837221051224602206611,57699787837221051230546933223⟩⟩,⟨⟨57416736387670180499712679037,57416736387670180500793519142⟩,⟨57430208754472601720681743782,57430208754472601726596627342⟩⟩,⟨⟨57415348101568588047053754356,57415348101568588048131611158⟩,⟨57153450557310358349758323924,57153450557310358355644543664⟩⟩,⟨⟨57403072245427413476667443949,57403072245427413477744097909⟩,⟨56868448024388813962277112482,56868448024388813968135713721⟩⟩,⟨⟨57381053849488078600897977827,57381053849488078601969507445⟩,⟨56576493796899537483239420507,56576493796899537489066051686⟩⟩,⟨⟨57347943416158015956757820431,57347943416158015957825998462⟩,⟨56276407743897212923082772582,56276407743897212928878500607⟩⟩,⟨⟨57305021223746809538354250076,57305021223746809539416888757⟩,⟨55969599971154929687087287289,55969599971154929692849552102⟩⟩,⟨⟨57250811569879035956259581752,57250811569879035957313605693⟩,⟨55654774462893430051923110883,55654774462893430057648232651⟩⟩,⟨⟨57186733369499414920904552423,57186733369499414921983420195⟩,⟨55333459550106873515381325990,55333459550106873521101292653⟩⟩,⟨⟨57111181643476128367323078894,57111181643476128368395676700⟩,⟨55004242182282387954221623837,55004242182282387959905538240⟩⟩,⟨⟨57025717526688472987469030685,57025717526688472988536628053⟩,⟨54668769860252940658330324195,54668769860252940663979032783⟩⟩,⟨⟨56928603472226391720291479108,56928603472226391721350717217⟩,⟨54325511165871561360885024736,54325511165871561366494644479⟩⟩,⟨⟨56821546625690967858954163589,56821546625690967860010531527⟩,⟨53976233907971589619010238924,53976233907971589624585625857⟩⟩,⟨⟨56702673347755963891908373582,56702673347755963892955710133⟩,⟨53619286775321773756141712284,53619286775321773761676370653⟩⟩] +lemma amp0_01_9_eq : ∀ k : Fin 16, amp0_0Expr 1 9 k = amp0_01_9 k := by decide +kernel +noncomputable def amp0_01_10 : Fin 16 → CBox := ![⟨⟨56573840807403479207848805195,56573840807403479208898417691⟩,⟨53256559227280372554198817094,53256559227280372559703081936⟩⟩,⟨⟨56433035498389971718651711002,56433035498389971719693772202⟩,⟨52886278330644809225868244090,52886278330644809231332170192⟩⟩,⟨⟨56282268863812425475545033957,56282268863812425476579954711⟩,⟨52510456754391692662042734745,52510456754391692667466370379⟩⟩,⟨⟨56119383488018099294132950821,56119383488018099295163584123⟩,⟨52127197998652331425557237486,52127197998652331430942610950⟩⟩,⟨⟨55946549595267317756208404960,55946549595267317757229477331⟩,⟨51738639731432340696750195338,51738639731432340702092104188⟩⟩,⟨⟨55761461529774112660622704209,55761461529774112661637403694⟩,⟨51342759711670134113759278224,51342759711670134119060039865⟩⟩,⟨⟨55566453080856047973656362943,55566453080856047974663752829⟩,⟨50941822641600879555857773320,50941822641600879561116214786⟩⟩,⟨⟨55359065711011718712556291941,55359065711011718713553997444⟩,⟨50533678118735812416589156619,50533678118735812421802500648⟩⟩,⟨⟨55141801858471342199811994948,55141801858471342200799162313⟩,⟨50120720177939652913732738538,50120720177939652918899963112⟩⟩,⟨⟨54912045126251679067744780416,54912045126251679068719812755⟩,⟨49700667571396760909736538918,49700667571396760914855592147⟩⟩,⟨⟨54672472011356249308344173015,54672472011356249309304079817⟩,⟨49276046247796042921013974116,49276046247796042926081921166⟩⟩,⟨⟨54420302914975651904479699196,54420302914975651905525285707⟩,⟨48844441146119199887112664084,48844441146119199892219441483⟩⟩,⟨⟨54158394158123486824125423893,54158394158123486825160832257⟩,⟨48408513014940887190613144257,48408513014940887195672141123⟩⟩,⟨⟨53883797201350272323570105236,53883797201350272324595923472⟩,⟨47965709705207934743260431041,47965709705207934748271581089⟩⟩,⟨⟨53599554343458202642804123520,53599554343458202643819378196⟩,⟨47518829981201000949214533549,47518829981201000954176749049⟩⟩,⟨⟨53302541933179948224991906711,53302541933179948225998060544⟩,⟨47065180998020995917603576944,47065180998020995922517588294⟩⟩] +lemma amp0_01_10_eq : ∀ k : Fin 16, amp0_0Expr 1 10 k = amp0_01_10 k := by decide +kernel +noncomputable def amp0_01_11 : Fin 16 → CBox := ![⟨⟨52995994826935803472403380259,52995994826935803473399713312⟩,⟨46607703109347872830252754699,46607703109347872835117743661⟩⟩,⟨⟨52676607617608152095405028554,52676607617608152096393226234⟩,⟨46143558804143416029074767465,46143558804143416033891620353⟩⟩,⟨⟨52347814767615522034644117677,52347814767615522035620267902⟩,⟨45675833988866173878196508489,45675833988866173882961607854⟩⟩,⟨⟨52006121951313997765450974795,52006121951313997766420896980⟩,⟨45201542120060396512140256378,45201542120060396516858118204⟩⟩,⟨⟨51655170802305930036760384601,51655170802305930037717970749⟩,⟨44723919046104129641537002985,44723919046104129646202158232⟩⟩,⟨⟨51291270343182927317352886264,51291270343182927318299759309⟩,⟨44239824390742203940263486549,44239824390742203944876778496⟩⟩,⟨⟨50918277515640258677837591004,50918277515640258678770555508⟩,⟨43752648800183480427278401056,43752648800183480431836928815⟩⟩,⟨⟨50532296327666664073038135410,50532296327666664073972731725⟩,⟨43259092787421499467863870100,43259092787421499472380415031⟩⟩,⟨⟨50137407800346803445088683729,50137407800346803446009686148⟩,⟨42762707165920163603671699135,42762707165920163608133083063⟩⟩,⟨⟨49729501867287412450130261522,49729501867287412451038673235⟩,⟨42260027532708592955368081893,42260027532708592959774610932⟩⟩,⟨⟨49312893106352557900450994553,49312893106352557901349740281⟩,⟨41754770804878517492675959444,41754770804878517497029998569⟩⟩,⟨⟨48883247542983718271755306873,48883247542983718272639424433⟩,⟨41243301274051427100525174199,41243301274051427104821995436⟩⟩,⟨⟨48445123577616311141494016663,48445123577616311142364687607⟩,⟨40729508525552322686954475839,40729508525552322691195008354⟩⟩,⟨⟨47993952631239446589819325921,47993952631239446590675970564⟩,⟨40209578506404967513252288319,40209578506404967517435511143⟩⟩,⟨⟨47534548075850634262976680853,47534548075850634263816890417⟩,⟨39687580733536050704504608583,39687580733536050708628439353⟩⟩,⟨⟨47062095067181843621333892974,47062095067181843622155656352⟩,⟨39159515044829035102106098816,39159515044829035106168367617⟩⟩] +lemma amp0_01_11_eq : ∀ k : Fin 16, amp0_0Expr 1 11 k = amp0_01_11 k := by decide +kernel +noncomputable def amp0_01_12 : Fin 16 → CBox := ![⟨⟨46581674090560506761618588605,46581674090560506762479742012⟩,⟨38629638932420094641062453493,38629638932420094645111118250⟩⟩,⟨⟨46088211293078281201328664317,46088211293078281202179248282⟩,⟨38093757547584261704528866433,38093757547584261708521805244⟩⟩,⟨⟨45587067535100049491904747192,45587067535100049492743920587⟩,⟨37556325276015496915751341452,37556325276015496919687806095⟩⟩,⟨⟨45072895991902418531992357451,45072895991902418532820822905⟩,⟨37012943090142376905415126067,37012943090142376909295174910⟩⟩,⟨⟨44551352428728505147486079376,44551352428728505148303033014⟩,⟨36468272172387989462376709918,36468272172387989466199665996⟩⟩,⟨⟨44016801705877156922221040972,44016801705877156923028022167⟩,⟨35917698790368763332627543902,35917698790368763336394128701⟩⟩,⟨⟨43475210464933256604576907747,43475210464933256605370176233⟩,⟨35366101940059582625353222583,35366101940059582629060371238⟩⟩,⟨⟨42920638340131367380490635309,42920638340131367381278090457⟩,⟨34808641484971070948596997522,34808641484971070952250612031⟩⟩,⟨⟨42359380466582957787232366068,42359380466582957788005363722⟩,⟨34250426516620521665777512860,34250426516620521669370602220⟩⟩,⟨⟨41785172551826620559093498588,41785172551826620559854088679⟩,⟨33686377457136004623875998995,33686377457136004627409692685⟩⟩,⟨⟨41204657728780365021069595799,41204657728780365021815943372⟩,⟨33121847219887909121365420094,33121847219887909124838270637⟩⟩,⟨⟨40611227025314597190944593043,40611227025314597191676319183⟩,⟨32551502215094701963990176592,32551502215094701967401377822⟩⟩,⟨⟨40011893250606163040292224309,40011893250606163041005916856⟩,⟨31980954561653417669714977984,31980954561653417673061875786⟩⟩,⟨⟨39399679634069395890819755121,39399679634069395891551578823⟩,⟨31404600321161671897562216700,31404600321161671900873133224⟩⟩,⟨⟨38781992857287976061024565070,38781992857287976061740555606⟩,⟨30828328113986547880725901605,30828328113986547883973773009⟩⟩,⟨⟨38151462490292992738905486939,38151462490292992739606214444⟩,⟨30246245270577493859938700537,30246245270577493863123480153⟩⟩] +lemma amp0_01_12_eq : ∀ k : Fin 16, amp0_0Expr 1 12 k = amp0_01_12 k := by decide +kernel +noncomputable def amp0_01_13 : Fin 16 → CBox := ![⟨⟨37515916214701895591079421409,37515916214701895591765306058⟩,⟨29664536428009339039721976446,29664536428009339042844118702⟩⟩,⟨⟨36867560883204292055775748093,36867560883204292056451257249⟩,⟨29076999419243010067382650570,29076999419243010070445150792⟩⟩,⟨⟨36214675738530962947220898734,36214675738530962947878743972⟩,⟨28490137005044295417047703908,28490137005044295420044931561⟩⟩,⟨⟨35549012107074406106989320733,35549012107074406107632087806⟩,⟨27897413959149906209667204981,27897413959149906212600689077⟩⟩,⟨⟨34879335400887064600830659278,34879335400887064601454826731⟩,⟨27305676320075878010252864022,27305676320075878013120006648⟩⟩,⟨⟨34196904180035839886592038309,34196904180035839887220905397⟩,⟨26708028939969975905651435860,26708028939969975908469915878⟩⟩,⟨⟨33511009437781972859269851322,33511009437781972859883224731⟩,⟨26111689897582010814722722217,26111689897582010817476901802⟩⟩,⟨⟨32812374454529583666347396750,32812374454529583666945077835⟩,⟨25509373334832923256232614611,25509373334832923258921817556⟩⟩,⟨⟨32110860961560415532847081527,32110860961560415533429300474⟩,⟨24908702440023996837824253562,24908702440023996840448872254⟩⟩,⟨⟨31396608119896869225423078055,31396608119896869225992250744⟩,⟨24301965147752881235791135501,24301965147752881238352491027⟩⟩,⟨⟨30680100483363635971774888192,30680100483363635972328436451⟩,⟨23697228009691568271312535916,23697228009691568273808851804⟩⟩,⟨⟨29950836596968091679421796321,29950836596968091679974679325⟩,⟨23086311559380869122326621924,23086311559380869124768887032⟩⟩,⟨⟨29219984352006516532204157679,29219984352006516532738518908⟩,⟨22477770265282184305476653740,22477770265282184307851349995⟩⟩,⟨⟨28476335823381425332596722937,28476335823381425333114402812⟩,⟨21862909106639664076980536226,21862909106639664079288518160⟩⟩,⟨⟨27731813117541314679469217585,27731813117541314679971162905⟩,⟨21250822755711429461882816529,21250822755711429464125096957⟩⟩,⟨⟨26974424426496031884801904113,26974424426496031885286244806⟩,⟨20632243890130439337172019460,20632243890130439339346597324⟩⟩] +lemma amp0_01_13_eq : ∀ k : Fin 16, amp0_0Expr 1 13 k = amp0_01_13 k := by decide +kernel +noncomputable def amp0_01_14 : Fin 16 → CBox := ![⟨⟨26216929830613376025140695615,26216929830613376025618960848⟩,⟨20016869275477547786502531361,20016869275477547788618548324⟩⟩,⟨⟨25446461777665758129363071705,25446461777665758129824864533⟩,⟨19394791800628643995513132293,19394791800628643997562032352⟩⟩,⟨⟨24676718293128202310913784712,24676718293128202311360541194⟩,⟨18776384288913035177517791858,18776384288913035179501025971⟩⟩,⟨⟨23893845916454611542732459744,23893845916454611543160116390⟩,⟨18151018751876527475604543135,18151018751876527477518409884⟩⟩,⟨⟨23112601282892650747289312250,23112601282892650747708958829⟩,⟨17529833435702370041467287165,17529833435702370043320613461⟩⟩,⟨⟨22318011324547399761652099744,22318011324547399762054970810⟩,⟨16901380900075814390899597529,16901380900075814392685076544⟩⟩,⟨⟨21526038786896205374356913270,21526038786896205374749344019⟩,⟨16277674138709383410957051516,16277674138709383412679920896⟩⟩,⟨⟨20720426513693708416162261036,20720426513693708416536999948⟩,⟨15646324818801589367930815967,15646324818801589369584914804⟩⟩,⟨⟨19918526298868113927115695560,19918526298868113927473510785⟩,⟨15020356350489597801015412857,15020356350489597802601833427⟩⟩,⟨⟨19102591364227198825077236778,19102591364227198825423067069⟩,⟨14386287577197417904950874775,14386287577197417906472612879⟩⟩,⟨⟨18291593274947669878583219292,18291593274947669878911109472⟩,⟨13758323502997698955921843123,13758323502997698957374970975⟩⟩,⟨⟨17466034098586215726651833340,17466034098586215726966692577⟩,⟨13121696630410524528274090979,13121696630410524529661536858⟩⟩,⟨⟨16646801914210679941164004897,16646801914210679941465838167⟩,⟨12492013778908554408620851561,12492013778908554409943251662⟩⟩,⟨⟨15812307671885148455280283242,15812307671885148455564171357⟩,⟨11852969355029271352828732787,11852969355029271354081562283⟩⟩,⟨⟨14985746577513146592074838432,14985746577513146592344584394⟩,⟨11221861931682051143660984800,11221861931682051144847809743⟩⟩,⟨⟨14142985148994726982581304647,14142985148994726982836365134⟩,⟨10580511904289962698747463445,10580511904289962699866972323⟩⟩] +lemma amp0_01_14_eq : ∀ k : Fin 16, amp0_0Expr 1 14 k = amp0_01_14 k := by decide +kernel +noncomputable def amp0_01_15 : Fin 16 → CBox := ![⟨⟨13310054472240610517983125532,13310054472240610518222754853⟩,⟨9948302114494842393611118817,9948302114494842394663579291⟩⟩,⟨⟨12459653165725225880823304503,12459653165725225881046917270⟩,⟨9304716707381165563477393019,9304716707381165564461356624⟩⟩,⟨⟨11621388954718542223395886814,11621388954718542223603356368⟩,⟨8671772715539894076782433422,8671772715539894077698754010⟩⟩,⟨⟨10763901435960595296447099986,10763901435960595296639969575⟩,⟨8025957093951737929769972671,8025957093951737930618667872⟩⟩,⟨⟨9921458629352590132881235517,9921458629352590133059022764⟩,⟨7392725553449432019247792706,7392725553449432020029623119⟩⟩,⟨⟨9057303243356612224570923482,9057303243356612224732910425⟩,⟨6744575280643059540572563944,6744575280643059541285676121⟩⟩,⟨⟨8212040588873131918800389088,8212040588873131918946271815⟩,⟨6111645620650791923602928739,6111645620650791924248443041⟩⟩,⟨⟨7341372702389267821881253934,7341372702389267822012203333⟩,⟨5460853161467358746000015501,5460853161467358746577231366⟩⟩,⟨⟨6495043067450789578634815016,6495043067450789578750079598⟩,⟨4829100127516671713420053832,4829100127516671713930096164⟩⟩,⟨⟨5617451667733587955974783470,5617451667733587956074094368⟩,⟨4174930917788571721343109994,4174930917788571721783802645⟩⟩,⟨⟨4772700687509769114431600636,4772700687509769114515290598⟩,⟨3545886008949153009806245912,3545886008949153010180049500⟩⟩,⟨⟨3886328401331190696545468409,3886328401331190696613190309⟩,⟨2886526547125376754397186973,2886526547125376754701177811⟩⟩,⟨⟨3048362346346898395250918627,3048362346346898395303165381⟩,⟨2263617379946292456133850634,2263617379946292456371603355⟩⟩,⟨⟨2146385301085473657123042470,2146385301085473657159290455⟩,⟨1593563538157256115720265771,1593563538157256115887244720⟩⟩,⟨⟨1331537687849639522548114945,1331537687849639522568780205⟩,⟨988474192108924475388316540,988474192108924475490542371⟩⟩,⟨⟨378307472599977134237678104,378307472599977134242456024⟩,⟨280822483901604049764552830,280822483901604049792783496⟩⟩] +lemma amp0_01_15_eq : ∀ k : Fin 16, amp0_0Expr 1 15 k = amp0_01_15 k := by decide +kernel +noncomputable def amp0_01 : Fin 16 → Fin 16 → CBox := ![amp0_01_0,amp0_01_1,amp0_01_2,amp0_01_3,amp0_01_4,amp0_01_5,amp0_01_6,amp0_01_7,amp0_01_8,amp0_01_9,amp0_01_10,amp0_01_11,amp0_01_12,amp0_01_13,amp0_01_14,amp0_01_15] +lemma amp0_01_eq (i k : Fin 16) : amp0_0Expr 1 i k = amp0_01 i k := by + fin_cases i + · exact amp0_01_0_eq k + · exact amp0_01_1_eq k + · exact amp0_01_2_eq k + · exact amp0_01_3_eq k + · exact amp0_01_4_eq k + · exact amp0_01_5_eq k + · exact amp0_01_6_eq k + · exact amp0_01_7_eq k + · exact amp0_01_8_eq k + · exact amp0_01_9_eq k + · exact amp0_01_10_eq k + · exact amp0_01_11_eq k + · exact amp0_01_12_eq k + · exact amp0_01_13_eq k + · exact amp0_01_14_eq k + · exact amp0_01_15_eq k +noncomputable def amp0_02_0 : Fin 16 → CBox := ![⟨⟨(-54041599249796242496001597),(-54041599249796242495471805)⟩,⟨280822483901604049764862236,280822483901604049792475440⟩⟩,⟨⟨(-190146006047468727417603867),(-190146006047468727415189717)⟩,⟨988474192108924475389411267,988474192108924475489461925⟩⟩,⟨⟨(-306296625633745083189644171),(-306296625633745083185335802)⟩,⟨1593563538157256115722043537,1593563538157256115885505327⟩⟩,⟨⟨(-434562139038283732486508832),(-434562139038283732480283555)⟩,⟨2263617379946292456136393022,2263617379946292456369137265⟩⟩,⟨⟨(-553254643319516198108265154),(-553254643319516198100178936)⟩,⟨2886526547125376754400461054,2886526547125376754698028791⟩⟩,⟨⟨(-678264203944726628582247595),(-678264203944726628572250976)⟩,⟨3545886008949153009810301260,3545886008949153010176181855⟩⟩,⟨⟨(-796656689266941484779113192),(-796656689266941484767247349)⟩,⟨4174930917788571721347934204,4174930917788571721779239505⟩⟩,⟨⟨(-918878550319976539813904150),(-918878550319976539800138565)⟩,⟨4829100127516671713425688319,4829100127516671713924809934⟩⟩,⟨⟨(-1035722616832870896953814748),(-1035722616832870896938190460)⟩,⟨5460853161467358746006469708,5460853161467358746571223220⟩⟩,⟨⟨(-1154920100324467627758774041),(-1154920100324467627741407495)⟩,⟨6111645620650791923610232149,6111645620650791924241697211⟩⟩,⟨⟨(-1269338535658679899032271168),(-1269338535658679899013002128)⟩,⟨6744575280643059540580728541,6744575280643059541278191112⟩⟩,⟨⟨(-1385074452694480754362516333),(-1385074452694480754341400577)⟩,⟨7392725553449432019256852211,7392725553449432020021378782⟩⟩,⟨⟨(-1496324458565750462820399105),(-1496324458565750462797549921)⟩,⟨8025957093951737929779956084,8025957093951737930609645543⟩⟩,⟨⟨(-1608088331382122510404635286),(-1608088331382122510380127308)⟩,⟨8671772715539894076793365232,8671772715539894077688942601⟩⟩,⟨⟨(-1715491774245777394823356694),(-1715491774245777394796989420)⟩,⟨9304716707381165563489301247,9304716707381165564450738270⟩⟩,⟨⟨(-1822744664673969619338112545),(-1822744664673969619309916319)⟩,⟨9948302114494842393624034996,9948302114494842394652135656⟩⟩] +lemma amp0_02_0_eq : ∀ k : Fin 16, amp0_0Expr 2 0 k = amp0_02_0 k := by decide +kernel +noncomputable def amp0_02_1 : Fin 16 → CBox := ![⟨⟨(-1925662356783027228351160071),(-1925662356783027228321239562)⟩,⟨10580511904289962698761437242,10580511904289962699854663690⟩⟩,⟨⟨(-2027856563382254595005172612),(-2027856563382254594973634339)⟩,⟨11221861931682051143676033430,11221861931682051144834631862⟩⟩,⟨⟨(-2125677576240079066571404593),(-2125677576240079066538341118)⟩,⟨11852969355029271352844897419,11852969355029271354067483700⟩⟩,⟨⟨(-2222266878263943785981423621),(-2222266878263943785946337556)⟩,⟨12492013778908554408638163218,12492013778908554409928254059⟩⟩,⟨⟨(-2314403935001972381987364119),(-2314403935001972381950942602)⟩,⟨13121696630410524528292609546,13121696630410524529645569810⟩⟩,⟨⟨(-2404849718840317055541209523),(-2404849718840317055503454775)⟩,⟨13758323502997698955941587441,13758323502997698957358028053⟩⟩,⟨⟨(-2490737353558602276804834781),(-2490737353558602276765129628)⟩,⟨14386287577197417904971897554,14386287577197417906454650547⟩⟩,⟨⟨(-2574512734309565669860888345),(-2574512734309565669820022455)⟩,⟨15020356350489597801037745189,15020356350489597802582832692⟩⟩,⟨⟨(-2653606821766868045985140124),(-2653606821766868045942513160)⟩,⟨15646324818801589367954534890,15646324818801589369564807492⟩⟩,⟨⟨(-2730199695366460917355228610),(-2730199695366460917310753960)⟩,⟨16277674138709383410982169927,16277674138709383412658705865⟩⟩,⟨⟨(-2801977699877058094033769464),(-2801977699877058093988398777)⟩,⟨16901380900075814390926178507,16901380900075814392662699249⟩⟩,⟨⟨(-2870893176988519517792409178),(-2870893176988519517745359175)⟩,⟨17529833435702370041495361956,17529833435702370043297054041⟩⟩,⟨⟨(-2934854791530895141347728096),(-2934854791530895141300125216)⟩,⟨18151018751876527475634195797,18151018751876527477493592457⟩⟩,⟨⟨(-2995617245904600704343278995),(-2995617245904600704293767211)⟩,⟨18776384288913035177549038000,18776384288913035179474945920⟩⟩,⟨⟨(-3051285243726369723252110917),(-3051285243726369723201230933)⟩,⟨19394791800628643995546044295,19394791800628643997534625095⟩⟩,⟨⟨(-3103440101552353109330548793),(-3103440101552353109278149387)⟩,⟨20016869275477547786537140500,20016869275477547788589793161⟩⟩] +lemma amp0_02_1_eq : ∀ k : Fin 16, amp0_0Expr 2 1 k = amp0_02_1 k := by decide +kernel +noncomputable def amp0_02_2 : Fin 16 → CBox := ![⟨⟨(-3150361298590390648621773334),(-3150361298590390648569128883)⟩,⟨20632243890130439337208426903,20632243890130439339316400484⟩⟩,⟨⟨(-3193476640519277483093881466),(-3193476640519277483039645701)⟩,⟨21250822755711429461921029618,21250822755711429464093461235⟩⟩,⟨⟨(-3231222907407964142268161609),(-3231222907407964142212604256)⟩,⟨21862909106639664077020635638,21862909106639664079255369854⟩⟩,⟨⟨(-3264890925120046849777126444),(-3264890925120046849720166614)⟩,⟨22477770265282184305518670472,22477770265282184307816667783⟩⟩,⟨⟨(-3293060210159864197599467995),(-3293060210159864197540969763)⟩,⟨23086311559380869122370659183,23086311559380869124732574244⟩⟩,⟨⟨(-3316898542476902917548998533),(-3316898542476902917490922628)⟩,⟨23697228009691568271358606098,23697228009691568273770905236⟩⟩,⟨⟨(-3335115880112810329834760309),(-3335115880112810329775520822)⟩,⟨24301965147752881235839326517,24301965147752881238312828847⟩⟩,⟨⟨(-3348768843736130163895552605),(-3348768843736130163835447512)⟩,⟨24908702440023996837874595776,24908702440023996840407472786⟩⟩,⟨⟨(-3356687331080684199535631298),(-3356687331080684199474476260)⟩,⟨25509373334832923256285224829,25509373334832923258878569597⟩⟩,⟨⟨(-3359827055051961752256081118),(-3359827055051961752193874453)⟩,⟨26111689897582010814777605167,26111689897582010817431808796⟩⟩,⟨⟨(-3357128784003878190690216022),(-3357128784003878190627045180)⟩,⟨26708028939969975905708685633,26708028939969975908422888843⟩⟩,⟨⟨(-3349456253285868565020724487),(-3349456253285868564958562956)⟩,⟨27305676320075878010312509873,27305676320075878013071023962⟩⟩,⟨⟨(-3335853189055162483063928141),(-3335853189055162483000580431)⟩,⟨27897413959149906209729364233,27897413959149906212549638020⟩⟩,⟨⟨(-3317099200307678292883524417),(-3317099200307678292819355926)⟩,⟨28490137005044295417112384891,28490137005044295419991810884⟩⟩,⟨⟨(-3292333999351204287851873374),(-3292333999351204287786727045)⟩,⟨29076999419243010067449952429,29076999419243010070389865433⟩⟩,⟨⟨(-3262260030508592733552105525),(-3262260030508592733486665367)⟩,⟨29664536428009339039791926845,29664536428009339042786647511⟩⟩] +lemma amp0_02_2_eq : ∀ k : Fin 16, amp0_0Expr 2 2 k = amp0_02_2 k := by decide +kernel +noncomputable def amp0_02_3 : Fin 16 → CBox := ![⟨⟨(-3226106792406270240791067267),(-3226106792406270240725021946)⟩,⟨30246245270577493860011429773,30246245270577493863063696382⟩⟩,⟨⟨(-3184505786735493322629718769),(-3184505786735493322563063920)⟩,⟨30828328113986547880801407745,30828328113986547883911684522⟩⟩,⟨⟨(-3136770735638797874237477587),(-3136770735638797874170252442)⟩,⟨31404600321161671897640602841,31404600321161671900808639934⟩⟩,⟨⟨(-3083467800382581569052653946),(-3083467800382581568987524845)⟩,⟨31980954561653417669796269610,31980954561653417672994957544⟩⟩,⟨⟨(-3023989892491346123721593718),(-3023989892491346123655791379)⟩,⟨32551502215094701964074499984,32551502215094701967331910804⟩⟩,⟨⟨(-2958842911860480855316350958),(-2958842911860480855250175796)⟩,⟨33121847219887909121452778089,33121847219887909124766256740⟩⟩,⟨⟨(-2887494366024993921434881351),(-2887494366024993921368450027)⟩,⟨33686377457136004623966497458,33686377457136004627335027936⟩⟩,⟨⟨(-2810394528122248850341269629),(-2810394528122248850274750546)⟩,⟨34250426516620521665871174543,34250426516620521669293267990⟩⟩,⟨⟨(-2727081277184922333837102271),(-2727081277184922333770457998)⟩,⟨34808641484971070948693957656,34808641484971070952170474416⟩⟩,⟨⟨(-2637953514370964557166132842),(-2637953514370964557099930137)⟩,⟨35366101940059582625453474246,35366101940059582628977440659⟩⟩,⟨⟨(-2542615575294554496872694357),(-2542615575294554496806527297)⟩,⟨35917698790368763332731194592,35917698790368763336308298414⟩⟩,⟨⟨(-2441418917511016986777653199),(-2441418917511016986711777547)⟩,⟨36468272172387989462483779008,36468272172387989466110919502⟩⟩,⟨⟨(-2334030678714418160549723440),(-2334030678714418160484145919)⟩,⟨37012943090142376905525743566,37012943090142376909203382375⟩⟩,⟨⟨(-2220758519338662919927427751),(-2220758519338662919862221143)⟩,⟨37556325276015496915865502909,37556325276015496919592974214⟩⟩,⟨⟨(-2101328943994057812991322767),(-2101328943994057812926543702)⟩,⟨38093757547584261704646679794,38093757547584261708423825665⟩⟩,⟨⟨(-1976009217898928205189401949),(-1976009217898928205125129785)⟩,⟨38629638932420094641183934141,38629638932420094645009977199⟩⟩] +lemma amp0_02_3_eq : ∀ k : Fin 16, amp0_0Expr 2 3 k = amp0_02_3 k := by decide +kernel +noncomputable def amp0_02_4 : Fin 16 → CBox := ![⟨⟨(-1844581962247356712677619309),(-1844581962247356712615914823)⟩,⟨39159515044829035102231385053,39159515044829035106063925808⟩⟩,⟨⟨(-1707277235866546193965969742),(-1707277235866546193904459907)⟩,⟨39687580733536050704633683268,39687580733536050708520714897⟩⟩,⟨⟨(-1563930681890850024739627262),(-1563930681890850024678526105)⟩,⟨40209578506404967513385258732,40209578506404967517324395193⟩⟩,⟨⟨(-1414738155238729001292973080),(-1414738155238729001232433154)⟩,⟨40729508525552322687091352685,40729508525552322691080490541⟩⟩,⟨⟨(-1259585357298864887193223978),(-1259585357298864887133393990)⟩,⟨41243301274051427100666086147,41243301274051427104703944946⟩⟩,⟨⟨(-1098636778057080053459377791),(-1098636778057080053400290141)⟩,⟨41754770804878517492820892648,41754770804878517496908428947⟩⟩,⟨⟨(-931825323346807507185294874),(-931825323346807507127180223)⟩,⟨42260027532708592955517141818,42260027532708592959649413991⟩⟩,⟨⟨(-759286813304513187194951378),(-759286813304513187137808920)⟩,⟨42762707165920163603824891181,42762707165920163608004252471⟩⟩,⟨⟨(-580998596233061919080458610),(-580998596233061919024416593)⟩,⟨43259092787421499468021326731,43259092787421499472247815031⟩⟩,⟨⟨(-397070390550080371576473989),(-397070390550080371521717106)⟩,⟨43752648800183480427440096650,43752648800183480431700583466⟩⟩,⟨⟨(-207521301389361162409685178),(-207521301389361162356181333)⟩,⟨44239824390742203940429523696,44239824390742203944736581351⟩⟩,⟨⟨(-12437401339430051579896582),(-12437401339430051527728237)⟩,⟨44723919046104129641707381095,44723919046104129646058107696⟩⟩,⟨⟨188123070292156644800846698,188123070292156644857614288⟩,⟨45201542120060396512315098017,45201542120060396516710087298⟩⟩,⟨⟨394095330249564834168080106,394095330249564834230012260⟩,⟨45675833988866173878375788154,45675833988866173882809619276⟩⟩,⟨⟨605384576270902255557357285,605384576270902255624600844⟩,⟨46143558804143416029258583817,46143558804143416033735570481⟩⟩,⟨⟨821945046048500784331796560,821945046048500784404500681⟩,⟨46607703109347872830441100529,46607703109347872834957636292⟩⟩] +lemma amp0_02_4_eq : ∀ k : Fin 16, amp0_0Expr 2 4 k = amp0_02_4 k := by decide +kernel +noncomputable def amp0_02_5 : Fin 16 → CBox := ![⟨⟨1043647904151814555639331550,1043647904151814555717606905⟩,⟨47065180998020995917796577621,47065180998020995922353292560⟩⟩,⟨⟨1270464218986711969199897367,1270464218986711969283941331⟩,⟨47518829981201000949412149419,47518829981201000954008300595⟩⟩,⟨⟨1502233618996220074785913980,1502233618996220074875865519⟩,⟨47965709705207934743462755885,47965709705207934748098880104⟩⟩,⟨⟨1738941882367760233807457369,1738941882367760233903499414⟩,⟨48408513014940887190820163584,48408513014940887195495197506⟩⟩,⟨⟨1980399573281853808344171717,1980399573281853808446410420⟩,⟨48844441146119199887324490122,48844441146119199892038136463⟩⟩,⟨⟨2226605120174738652629191734,2226605120174738652733956941⟩,⟨49276046247796042921230567367,49276046247796042925896289075⟩⟩,⟨⟨2477342476248368338240831566,2477342476248368338351931818⟩,⟨49700667571396760909957987353,49700667571396760914665537970⟩⟩,⟨⟨2732620714951390516581859319,2732620714951390516699412911⟩,⟨50120720177939652913959019797,50120720177939652918705503482⟩⟩,⟨⟨2992199618976326460604904847,2992199618976326460728914508⟩,⟨50533678118735812416820382140,50533678118735812421603516601⟩⟩,⟨⟨3256096949420832960999212107,3256096949420832961129884800⟩,⟨50941822641600879556093889999,50941822641600879560912753153⟩⟩,⟨⟨3524050751167936206181953605,3524050751167936206319225884⟩,⟨51342759711670134114000367417,51342759711670134118852011296⟩⟩,⟨⟨3796085557627739786862714052,3796085557627739787006735688⟩,⟨51738639731432340696996226213,51738639731432340701879532714⟩⟩,⟨⟨4071920105227590624819264174,4071920105227590624970296126⟩,⟨52127197998652331425808308355,52127197998652331430725389816⟩⟩,⟨⟨4351583821024066920093546937,4351583821024066920251445510⟩,⟨52510456754391692662298789849,52510456754391692667244548034⟩⟩,⟨⟨4634778562880533304860985915,4634778562880533305026012162⟩,⟨52886278330644809226129357413,52886278330644809231105663779⟩⟩,⟨⟨4921536804563662777051295625,4921536804563662777223712475⟩,⟨53256559227280372554464948803,53256559227280372559471923483⟩⟩] +lemma amp0_02_5_eq : ∀ k : Fin 16, amp0_0Expr 2 5 k = amp0_02_5 k := by decide +kernel +noncomputable def amp0_02_6 : Fin 16 → CBox := ![⟨⟨5211545959219569884376124545,5211545959219569884555048081⟩,⟨53619286775321773756412959597,53619286775321773761440453658⟩⟩,⟨⟨5504839727528238405636702587,5504839727528238405823402802⟩,⟨53976233907971589619286530215,53976233907971589624345013671⟩⟩,⟨⟨5801093518733540598951500463,5801093518733540599145411735⟩,⟨54325511165871561361166425987,54325511165871561366249261449⟩⟩,⟨⟨6100340463476996968423342940,6100340463476996968625251586⟩,⟨54668769860252940658616786057,54668769860252940663728919532⟩⟩,⟨⟨6402246417548082024064506852,6402246417548082024274056484⟩,⟨55004242182282387954513227937,55004242182282387959650603102⟩⟩,⟨⟨6706842163395529027667733598,6706842163395529027885330492⟩,⟨55333459550106873515677998233,55333459550106873520841600566⟩⟩,⟨⟨7013786465799827076208758800,7013786465799827076430613745⟩,⟨55654774462893430052224908682,55654774462893430057383715823⟩⟩,⟨⟨7323105995817128622919899828,7323105995817128623150208498⟩,⟨55969599971154929687394151355,55969599971154929692580260260⟩⟩,⟨⟨7634454903770375709408318881,7634454903770375709646668826⟩,⟨56276407743897212923394780637,56276407743897212928604345326⟩⟩,⟨⟨7947853997402201844581886001,7947853997402201844828263032⟩,⟨56576493796899537483556483415,56576493796899537488787112161⟩⟩,⟨⟨8262955305126832995578296631,8262955305126832995832932293⟩,⟨56868448024388813962599278648,56868448024388813967851930550⟩⟩,⟨⟨8579772027189616087603262703,8579772027189616087865820394⟩,⟨57153450557310358350085523725,57153450557310358355355976170⟩⟩,⟨⟨8897956580352137098089550382,8897956580352137098360212488⟩,⟨57430208754472601721014040248,57430208754472601726303201231⟩⟩,⟨⟨9217512817478329142433727307,9217512817478329142713026617⟩,⟨57699787837221051224939505596,57699787837221051230248732010⟩⟩,⟨⟨9538096073201428570508477881,9538096073201428570793940223⟩,⟨57961012043858325484486849687,57961012043858325489800481447⟩⟩,⟨⟨9859699114059058845340003183,9859699114059058845633920807⟩,⟨58214832493927036398727117863,58214832493927036404057681237⟩⟩] +lemma amp0_02_6_eq : ∀ k : Fin 16, amp0_0Expr 2 6 k = amp0_02_6 k := by decide +kernel +noncomputable def amp0_02_7 : Fin 16 → CBox := ![⟨⟨10181982742790945424557679911,10181982742790945424859648902⟩,⟨58460189888305538203700137419,58460189888305538209045086615⟩⟩,⟨⟨10504926898294682014506046399,10504926898294682014816594270⟩,⟨58697921891305617850462306235,58697921891305617855822740198⟩⟩,⟨⟨10828200423713924632188939311,10828200423713924632506499451⟩,⟨58927085411208756262760797302,58927085411208756268127767042⟩⟩,⟨⟨11151768683345019936942699906,11151768683345019937268596288⟩,⟨59148405147716851266445514227,59148405147716851271824799303⟩⟩,⟨⟨11475311156384266155944012288,11475311156384266156277138832⟩,⟨59361054117555599317529937902,59361054117555599322915714555⟩⟩,⟨⟨11798776876647167709438660848,11798776876647167709780251127⟩,⟨59565644394886997033966804937,59565644394886997039363827032⟩⟩,⟨⟨12121858579633741953393193182,12121858579633741953742329906⟩,⟨59761465157436564760619342587,59761465157436564766022817151⟩⟩,⟨⟨12444487200597002855760215740,12444487200597002856117039836⟩,⟨59949016044926429717070802508,59949016044926429722480077756⟩⟩,⟨⟨12766371377432736027656102282,12766371377432736028020448382⟩,⟨60127702596238212333675405754,60127702596238212339089888976⟩⟩,⟨⟨13087422163231365903451857103,13087422163231365903824077431⟩,⟨60297912062590627206248825154,60297912062590627211668589098⟩⟩,⟨⟨13407366771468262510334975537,13407366771468262510714456665⟩,⟨60459166688611488037619965560,60459166688611488043042177593⟩⟩,⟨⟨13726094570583996533826595064,13726094570583996534213571145⟩,⟨60611741239856456140437393627,60611741239856456145861849366⟩⟩,⟨⟨14043354051196659765533452312,14043354051196659765927247834⟩,⟨60755275153273810300051203991,60755275153273810305475201052⟩⟩,⟨⟨14359011072281940614009547581,14359011072281940614410178429⟩,⟨60889930469856510348069688372,60889930469856510353491942659⟩⟩,⟨⟨14672838132892184413400961712,14672838132892184413807810008⟩,⟨61015464445677466936618036547,61015464445677466942036127451⟩⟩,⟨⟨14984675731863074769139441106,14984675731863074769552063734⟩,⟨61131926017191833593340832473,61131926017191833598751890389⟩⟩] +lemma amp0_02_7_eq : ∀ k : Fin 16, amp0_0Expr 2 7 k = amp0_02_7 k := by decide +kernel +noncomputable def amp0_02_8 : Fin 16 → CBox := ![⟨⟨15294323139136966172022099472,15294323139136966172441794320⟩,⟨61239191025557904124021055063,61239191025557904129430847099⟩⟩,⟨⟨15601593613229836180876950582,15601593613229836181305610111⟩,⟨61337194781628036992693089348,61337194781628036998107590820⟩⟩,⟨⟨15906315990142619512930676450,15906315990142619513367571417⟩,⟨61425932616363687194955463133,61425932616363687200371712020⟩⟩,⟨⟨16208274374609356629101002999,16208274374609356629545887331⟩,⟨61505225552171657622240123983,61505225552171657627655839683⟩⟩,⟨⟨16507329998259378721703908144,16507329998259378722156341763⟩,⟨61575189453565319647516490883,61575189453565319652930246953⟩⟩,⟨⟨16803235861366092232429337135,16803235861366092232889017633⟩,⟨61635530248522632904589418049,61635530248522632909998661530⟩⟩,⟨⟨17095888457015016547781083033,17095888457015016548247892056⟩,⟨61686485518842746533938951710,61686485518842746539343380543⟩⟩,⟨⟨17385007689009774579353796203,17385007689009774579827294770⟩,⟨61727645146905002411876603466,61727645146905002417273474577⟩⟩,⟨⟨17670528216033060623667893556,17670528216033060624147933030⟩,⟨61759369757161249593610388665,61759369757161249598999634480⟩⟩,⟨⟨17952134807759095369160593285,17952134807759095369647457853⟩,⟨61781132087291394009080000202,61781132087291394014461221777⟩⟩,⟨⟨18229803233207923488898114707,18229803233207923489391526664⟩,⟨61793417273762555366141999212,61793417273762555371514441563⟩⟩,⟨⟨18503181040059935338533880570,18503181040059935339032734705⟩,⟨61795579659057486224107349585,61795579659057486229466201521⟩⟩,⟨⟨18772288095563448538539646547,18772288095563448539045249124⟩,⟨61788230508122298342127941142,61788230508122298347478032037⟩⟩,⟨⟨19036732582516068873598087836,19036732582516068874109046282⟩,⟨61770604362130426991813338596,61770604362130426997148801088⟩⟩,⟨⟨19296581500290932803397785762,19296581500290932803915870239⟩,⟨61743440381956466383616760219,61743440381956466388943587116⟩⟩,⟨⟨19551401463769977906556815540,19551401463769977907079474914⟩,⟨61705851740730076324649490346,61705851740730076329958455908⟩⟩] +lemma amp0_02_8_eq : ∀ k : Fin 16, amp0_0Expr 2 8 k = amp0_02_8 k := by decide +kernel +noncomputable def amp0_02_9 : Fin 16 → CBox := ![⟨⟨19801309687552755855246433874,19801309687552755855773782287⟩,⟨61658707418398045845146816684,61658707418398045850438943528⟩⟩,⟨⟨20045828949971502233126890389,20045828949971502233658531105⟩,⟨61600997486843855140722061610,61600997486843855145994879266⟩⟩,⟨⟨20285129816748110879837198871,20285129816748110880377375674⟩,⟨61533722829510703199676862983,61533722829510703204943648608⟩⟩,⟨⟨20518688889592298569913013032,20518688889592298570456650557⟩,⟨61455748510624834916883625904,61455748510624834922127899559⟩⟩,⟨⟨20746733278067739084016285400,20746733278067739084563607550⟩,⟨61368209569358896426451798295,61368209569358896431674892507⟩⟩,⟨⟨20968690989484188851540710160,20968690989484188852092518350⟩,⟨61269843974958385965701638877,61269843974958385970904765534⟩⟩,⟨⟨21184848931314704268302561840,21184848931314704268857127660⟩,⟨61161923349913194952209769009,61161923349913194957388313544⟩⟩,⟨⟨21394584014239112438517936323,21394584014239112439075995292⟩,⟨61043056291505091444859676336,61043056291505091450014869930⟩⟩,⟨⟨21598246264137755773304972694,21598246264137755773865315098⟩,⟨60914653617135678077714588634,60914653617135678082843722895⟩⟩,⟨⟨21795158901087172393396810686,21795158901087172393958424428⟩,⟨60775192075596587828147286179,60775192075596587833246412750⟩⟩,⟨⟨21985738462012314255463147770,21985738462012314256038552953⟩,⟨60626224484662940118175947093,60626224484662940123280151098⟩⟩,⟨⟨22169251782766751217311742303,22169251782766751217889164671⟩,⟨60466093057436351363981529737,60466093057436351369057135692⟩⟩,⟨⟨22346185382511130141747427216,22346185382511130142326966010⟩,⟨60296495622583303121124199268,60296495622583303126172197524⟩⟩,⟨⟨22515746911016388813315938400,22515746911016388813896417983⟩,⟨60115636947139037682475180667,60115636947139037687491351480⟩⟩,⟨⟨22678496426631719829759256675,22678496426631719830342522297⟩,⟨59925363098890158523421636389,59925363098890158528411410251⟩⟩,⟨⟨22833579473571542219862696210,22833579473571542220446367907⟩,⟨59723738251229604656090830923,59723738251229604661047069458⟩⟩] +lemma amp0_02_9_eq : ∀ k : Fin 16, amp0_0Expr 2 9 k = amp0_02_9 k := by decide +kernel +noncomputable def amp0_02_10 : Fin 16 → CBox := ![⟨⟨22981633300190248257599720823,22981633300190248258187942181⟩,⟨59512760171284748188085523802,59512760171284748193019816229⟩⟩,⟨⟨23121738297799915930175493449,23121738297799915930764476168⟩,⟨59290349038316896101383638376,59290349038316896106284964055⟩⟩,⟨⟨23254612658551026342771040522,23254612658551026343360612522⟩,⟨59058658027098961829795545150,59058658027098961834664003051⟩⟩,⟨⟨23379268434376153282462655845,23379268434376153283054081654⟩,⟨58815459651755407753281813084,58815459651755407758119763272⟩⟩,⟨⟨23496508628236617226342047171,23496508628236617226932716477⟩,⟨58563066469211670198758073326,58563066469211670203559698043⟩⟩,⟨⟨23605273614679661161400699096,23605273614679661161992099645⟩,⟨58299099367213351269324049489,58299099367213351274092033341⟩⟩,⟨⟨23706455199255048796860561255,23706455199255048797451959016⟩,⟨58026034545940520677736677270,58026034545940520682469735970⟩⟩,⟨⟨23798918575897508502878478868,23798918575897508503468932923⟩,⟨57741336993174612728778526194,57741336993174612733473561105⟩⟩,⟨⟨23883648482287129722296452894,23883648482287129722885137844⟩,⟨57447651123004775866657792898,57447651123004775871313668939⟩⟩,⟨⟨23959431248126959819822743192,23959431248126959820409124631⟩,⟨57142281412516486070409833958,57142281412516486075024241743⟩⟩,⟨⟨24027348825197648456637350620,24027348825197648457219744626⟩,⟨56828045395773452712436404035,56828045395773452717005972288⟩⟩,⟨⟨24086104798098504405405936972,24086104798098504406028995403⟩,⟨56502082063423845858165832098,56502082063423845862794627222⟩⟩,⟨⟨24136882783668556780688464429,24136882783668556781309620619⟩,⟨56167387340136493592823540751,56167387340136493597411704258⟩⟩,⟨⟨24178299524479406972850111243,24178299524479406973469775840⟩,⟨55820929358023382461987433032,55820929358023382466534942446⟩⟩,⟨⟨24211644941099333260881322680,24211644941099333261498702771⟩,⟨55465888100464746000093843329,55465888100464746004599453390⟩⟩,⟨⟨24235444600068984018528739771,24235444600068984019144566385⟩,⟨55099055037248306619900670766,55099055037248306624365297363⟩⟩] +lemma amp0_02_10_eq : ∀ k : Fin 16, amp0_0Expr 2 10 k = amp0_02_10 k := by decide +kernel +noncomputable def amp0_02_11 : Fin 16 → CBox := ![⟨⟨24251099573278797938880546329,24251099573278797939494030786⟩,⟨54723800313256923566288252235,54723800313256923570710969947⟩⟩,⟨⟨24257039656559110298469453973,24257039656559110299081556903⟩,⟨54336732460574162041978337415,54336732460574162046360249041⟩⟩,⟨⟨24254782153702901229111678757,24254782153702901229720248078⟩,⟨53941418365208258032838471815,53941418365208258037175335365⟩⟩,⟨⟨24242656207905948864035369778,24242656207905948864643179598⟩,⟨53534276829399654227681207172,53534276829399654231978428683⟩⟩,⟨⟨24222300695793620054235591887,24222300695793620054839368357⟩,⟨53119078584576036849903637228,53119078584576036854154767820⟩⟩,⟨⟨24191938908740600515420301842,24191938908740600516020956520⟩,⟨52692045342982261657954006188,52692045342982261662160101754⟩⟩,⟨⟨24153336928664241522234410659,24153336928664241522830080889⟩,⟨52257159364861488850174557167,52257159364861488854332163735⟩⟩,⟨⟨24104606644636262038501321599,24104606644636262039099475265⟩,⟨51810437285976343916336164187,51810437285976343920460642933⟩⟩,⟨⟨24047647303475182968105815855,24047647303475182968698762913⟩,⟨51356081219975404905596398518,51356081219975404909672011580⟩⟩,⟨⟨23980453451446492481710574639,23980453451446492482298967177⟩,⟨50889894046760940201467434632,50889894046760940205494598311⟩⟩,⟨⟨23905063827831287804181524237,23905063827831287804766432529⟩,⟨50416306770206392298695349377,50416306770206392302676914376⟩⟩,⟨⟨23819349261332177077475318051,23819349261332177078054403066⟩,⟨49930899065884821084933323047,49930899065884821088863648694⟩⟩,⟨⟨23725494726085482317173446256,23725494726085482317746848798⟩,⟨49438340658465771303840635074,49438340658465771307720839626⟩⟩,⟨⟨23621240473502539044177115191,23621240473502539044744697557⟩,⟨48933977714096870302178550065,48933977714096870306007448744⟩⟩,⟨⟨23508924923834064887600214192,23508924923834064888160442226⟩,⟨48422729396441952932763197828,48422729396441952936538231858⟩⟩,⟨⟨23386150348106776834653390404,23386150348106776835205312613⟩,⟨47899697099569643537760204777,47899697099569643541478775107⟩⟩] +lemma amp0_02_11_eq : ∀ k : Fin 16, amp0_0Expr 2 11 k = amp0_02_11 k := by decide +kernel +noncomputable def amp0_02_12 : Fin 16 → CBox := ![⟨⟨23255416355315092191902424202,23255416355315092192474439625⟩,⟨47370061140459967982222652522,47370061140459967985943537733⟩⟩,⟨⟨23114179222126173366123238027,23114179222126173366690714702⟩,⟨46828665804061895007454053951,46828665804061895011125801998⟩⟩,⟨⟨22965108092852812172940390067,22965108092852812173502589116⟩,⟨46280965397009150537339116555,46280965397009150540960795898⟩⟩,⟨⟨22805504546530246739677992027,22805504546530246740235338891⟩,⟨45721533547900628780148509460,45721533547900628783720279563⟩⟩,⟨⟨22638216297927530247041499924,22638216297927530247593191541⟩,⟨45156112658074627382485474290,45156112658074627386006492239⟩⟩,⟨⟨22460380744372878351828718027,22460380744372878352375695591⟩,⟨44578990783793092115604314194,44578990783793092119075556509⟩⟩,⟨⟨22275033993891594808768659318,22275033993891594809308707760⟩,⟨43996213966587486230608684899,43996213966587486234026322326⟩⟩,⟨⟨22079138889913241386959843139,22079138889913241387497085251⟩,⟨43401768219601819891266503460,43401768219601819894637980370⟩⟩,⟨⟨21875930660798627823857369898,21875930660798627824386957500⟩,⟨42802020412496186018677732639,42802020412496186021994323108⟩⟩,⟨⟨21662186209249192768015633067,21662186209249192768538795515⟩,⟨42190636270328331652982157776,42190636270328331656245349779⟩⟩,⟨⟨21441351653265516718294317291,21441351653265516718809807039⟩,⟨41574322560160752081556710775,41574322560160752084764648259⟩⟩,⟨⟨21210005403344372459589599163,21210005403344372460097273765⟩,⟨40946404439649227917596423371,40946404439649227920748185910⟩⟩,⟨⟨20971817442746619427803504622,20971817442746619428301200207⟩,⟨40313949807985743541139117640,40313949807985743544231315661⟩⟩,⟨⟨20723153794710415295838290510,20723153794710415296345153850⟩,⟨39669920631426435888506503448,39669920631426435891574986112⟩⟩,⟨⟨20467922686069874604154180757,20467922686069874604652121770⟩,⟨39021769681444076794233834598,39021769681444076797244419180⟩⟩,⟨⟨20202262299366847081839770986,20202262299366847082329138090⟩,⟨38362070391662964284198165150,38362070391662964287150891144⟩⟩] +lemma amp0_02_12_eq : ∀ k : Fin 16, amp0_0Expr 2 12 k = amp0_02_12 k := by decide +kernel +noncomputable def amp0_02_13 : Fin 16 → CBox := ![⟨⟨19930335122569564585468922857,19930335122569564585949552237⟩,⟨37698687060910749375734191302,37698687060910749378629579557⟩⟩,⟨⟨19648034226035689982948575515,19648034226035689983423009758⟩,⟨37023776081384766607090480037,37023776081384766609932439112⟩⟩,⟨⟨19359794302657532654430897458,19359794302657532654894991239⟩,⟨36345643346037159480401937786,36345643346037159483183223824⟩⟩,⟨⟨19061243904824525897265260699,19061243904824525897720437959⟩,⟨35655995980880480009396550914,35655995980880480012119225041⟩⟩,⟨⟨18757110151215029562661012019,18757110151215029563105046893⟩,⟨34963615558774036550369506431,34963615558774036553030166167⟩⟩,⟨⟨18442735147894587396311119276,18442735147894587396756690249⟩,⟨34259723325597251496806919841,34259723325597251499428343866⟩⟩,⟨⟨18123161369778897287130359689,18123161369778897287566362967⟩,⟨33553615387626237324833742213,33553615387626237327395809305⟩⟩,⟨⟨17793419544774984111931209951,17793419544774984112357577627⟩,⟨32835985273731698190755665216,32835985273731698193257636991⟩⟩,⟨⟨17458893682166788336237869302,17458893682166788336654395975⟩,⟨32116688176346159864828140187,32116688176346159867270427959⟩⟩,⟨⟨17114274595032739873902690794,17114274595032739874310830218⟩,⟨31385841805106312752080575760,31385841805106312754465013260⟩⟩,⟨⟨16765317928981978333676051338,16765317928981978334074180725⟩,⟨30653911861124241210035292238,30653911861124241212359469968⟩⟩,⟨⟨16406341680881195366671983536,16406341680881195367068331200⟩,⟨29910384550181176266544307789,29910384550181176268822615279⟩⟩,⟨⟨16043508017433088297668128162,16043508017433088298052648922⟩,⟨29166395861544427126686945492,29166395861544427128901766677⟩⟩,⟨⟨15670723881909517351831630391,15670723881909517352205432790⟩,⟨28410735546851922303720452085,28410735546851922305873041710⟩⟩,⟨⟨15294598734220721946898195311,15294598734220721947261602761⟩,⟨27655279932353967403946641492,27655279932353967406038168769⟩⟩,⟨⟨14908583633281858224622830466,14908583633281858224974836394⟩,⟨26888045920748681817032037882,26888045920748681819060072121⟩⟩] +lemma amp0_02_13_eq : ∀ k : Fin 16, amp0_0Expr 2 13 k = amp0_02_13 k := by decide +kernel +noncomputable def amp0_02_14 : Fin 16 → CBox := ![⟨⟨14519783431090773809042013217,14519783431090773809388723704⟩,⟨26121732985813821892325252634,26121732985813821894301572099⟩⟩,⟨⟨14121140227209152361654160798,14121140227209152361989945304⟩,⟨25343494481598689795108801174,25343494481598689797022428407⟩⟩,⟨⟨13720311595397776589417100265,13720311595397776589742585842⟩,⟨24566951898681369153784726418,24566951898681369155637380124⟩⟩,⟨⟨13309667154750930043431189178,13309667154750930043744132852⟩,⟨23778286223002084603760079935,23778286223002084605547121282⟩⟩,⟨⟨12897486322316428441138105901,12897486322316428441444473399⟩,⟨22992160324867102862430144689,22992160324867102864162956247⟩⟩,⟨⟨12475489280168229143296180660,12475489280168229143591164108⟩,⟨22193650704154673735716311185,22193650704154673737385533431⟩⟩,⟨⟨12052661712402240053515414504,12052661712402240053802417512⟩,⟨21398607546610297165900041044,21398607546610297167512339126⟩⟩,⟨⟨11619979831438862228066648811,11619979831438862228341624135⟩,⟨20590840276719456088513619781,20590840276719456090061145923⟩⟩,⟨⟨11187240230379428728489039371,11187240230379428728752218313⟩,⟨19787567417700190607599055680,19787567417700190609083013926⟩⟩,⟨⟨10744557174851744835651271648,10744557174851744835905507676⟩,⟨18971128092466434839772974781,18971128092466434841197574937⟩⟩,⟨⟨10302670083048198139201399096,10302670083048198139443232460⟩,⟨18160337490009399423897841696,18160337490009399425257635793⟩⟩,⟨⟨9850681311994956271368720395,9850681311994956271600915608⟩,⟨17335805775651577602641455644,17335805775651577603940611219⟩⟩,⟨⟨9400442716038465818544098417,9400442716038465818766520189⟩,⟨16518238486698559755707102755,16518238486698559756946169668⟩⟩,⟨⟨8939849979118720167462691801,8939849979118720167672604269⟩,⟨15686180542716245903906937532,15686180542716245905080261668⟩⟩,⟨⟨8482090613140282955149139764,8482090613140282955348613709⟩,⟨14862614430602471728199638690,14862614430602471729311595642⟩⟩,⟨⟨8013594107529079093418779767,8013594107529079093607495148⟩,⟨14023571341419156253132908295,14023571341419156254182142412⟩⟩] +lemma amp0_02_14_eq : ∀ k : Fin 16, amp0_0Expr 2 14 k = amp0_02_14 k := by decide +kernel +noncomputable def amp0_02_15 : Fin 16 → CBox := ![⟨⟨7549185761597201844162705881,7549185761597201844340126606⟩,⟨13194834047155305383718803067,13194834047155305384705287200⟩⟩,⟨⟨7073472134172852134126569101,7073472134172852134292397423⟩,⟨12349303114435206237654215176,12349303114435206238576450899⟩⟩,⟨⟨6603339560705217221534073333,6603339560705217221688194689⟩,⟨11516294777896590191325270754,11516294777896590192183937537⟩⟩,⟨⟨6121062002700662190328099473,6121062002700662190471359356⟩,⟨10664697168311882424165479270,10664697168311882424961101471⟩⟩,⟨⟨5646205995383184666955026997,5646205995383184667087100704⟩,⟨9828432549116667575896178186,9828432549116667576629239338⟩⟩,⟨⟨5157947967828088157668577214,5157947967828088157789045156⟩,⟨8971052636411219996067871951,8971052636411219996736494317⟩⟩,⟨⟨4679492848142491694363484296,4679492848142491694472175377⟩,⟨8132745552467294194474927220,8132745552467294195079958562⟩⟩,⟨⟨4185694085093595248669169819,4185694085093595248766692530⟩,⟨7269604964512430654826164791,7269604964512430655367393278⟩⟩,⟨⟨3704995395910040752955777220,3704995395910040753041707913⟩,⟨6430857048049550304592863809,6430857048049550305070991118⟩⟩,⟨⟨3205777464660733546530382861,3205777464660733546604516948⟩,⟨5561414779498908854694207360,5561414779498908855107246341⟩⟩,⟨⟨2724705843855476536668222301,2724705843855476536730818269⟩,⟨4724709412834161581405717794,4724709412834161581755892289⟩⟩,⟨⟨2219368213009897906383728439,2219368213009897906434471508⟩,⟨3846991278603234543216427349,3846991278603234543501093244⟩⟩,⟨⟨1741261387283875055488988479,1741261387283875055528278736⟩,⟨3017344759125023950056924192,3017344759125023950279321110⟩⟩,⟨⟨1226268809558070055312289258,1226268809558070055339650773⟩,⟨2124459778092482373203074672,2124459778092482373359114827⟩⟩,⟨⟨760825733026136674021857398,760825733026136674037787223⟩,⟨1317900465836448054816378562,1317900465836448054911371731⟩⟩,⟨⟨216174027242030330966892886,216174027242030330970794298⟩,⟨374427922718183715714026980,374427922718183715739932597⟩⟩] +lemma amp0_02_15_eq : ∀ k : Fin 16, amp0_0Expr 2 15 k = amp0_02_15 k := by decide +kernel +noncomputable def amp0_02 : Fin 16 → Fin 16 → CBox := ![amp0_02_0,amp0_02_1,amp0_02_2,amp0_02_3,amp0_02_4,amp0_02_5,amp0_02_6,amp0_02_7,amp0_02_8,amp0_02_9,amp0_02_10,amp0_02_11,amp0_02_12,amp0_02_13,amp0_02_14,amp0_02_15] +lemma amp0_02_eq (i k : Fin 16) : amp0_0Expr 2 i k = amp0_02 i k := by + fin_cases i + · exact amp0_02_0_eq k + · exact amp0_02_1_eq k + · exact amp0_02_2_eq k + · exact amp0_02_3_eq k + · exact amp0_02_4_eq k + · exact amp0_02_5_eq k + · exact amp0_02_6_eq k + · exact amp0_02_7_eq k + · exact amp0_02_8_eq k + · exact amp0_02_9_eq k + · exact amp0_02_10_eq k + · exact amp0_02_11_eq k + · exact amp0_02_12_eq k + · exact amp0_02_13_eq k + · exact amp0_02_14_eq k + · exact amp0_02_15_eq k +noncomputable def amp0_03_0 : Fin 16 → CBox := ![⟨⟨(-108087776645299701583540103),(-108087776645299701582480506)⟩,⟨187215282955920083262892881,187215282955920083292831096⟩⟩,⟨⟨(-380437037396694513453736897),(-380437037396694513448907706)⟩,⟨658992098116728399628180670,658992098116728399735462635⟩⟩,⟨⟨(-613242635481343999924863614),(-613242635481343999916241953)⟩,⟨1062417350121579188704455912,1062417350121579188878850096⟩⟩,⟨⟨(-870931976755011540317987995),(-870931976755011540305523226)⟩,⟨1509194217221818683782888453,1509194217221818684030970508⟩⟩,⟨⟨(-1110319070478132264611764624),(-1110319070478132264595561096)⟩,⟨1924595429164146568975397363,1924595429164146569292251713⟩⟩,⟨⟨(-1363517824735395270598675464),(-1363517824735395270578624338)⟩,⟨2364372377265822353859385913,2364372377265822354248824988⟩⟩,⟨⟨(-1604803803089663534042886021),(-1604803803089663534019057460)⟩,⟨2784024389604645924696425274,2784024389604645925155267530⟩⟩,⟨⟨(-1855445817418033835889976207),(-1855445817418033835862294589)⟩,⟨3220534816721497139337391958,3220534816721497139868248450⟩⟩,⟨⟨(-2097127404323008790467706008),(-2097127404323008790436236717)⟩,⟨3642216286327388831504978291,3642216286327388832105456790⟩⟩,⟨⟨(-2345727668755707965567698256),(-2345727668755707965532659176)⟩,⟨4076732595919636763775440827,4076732595919636764447023167⟩⟩,⟨⟨(-2587033366433380935047121625),(-2587033366433380935008165399)⟩,⟨4499485578206733892368544938,4499485578206733893110002382⟩⟩,⟨⟨(-2833693816152118498492540705),(-2833693816152118498449757240)⟩,⟨4932560110225703505532590853,4932560110225703506345235376⟩⟩,⟨⟨(-3074107418194097129138618328),(-3074107418194097129092212711)⟩,⟨5355863627914077879074178294,5355863627914077879956106007⟩⟩,⟨⟨(-3318768403870281328833707753),(-3318768403870281328783807432)⟩,⟨5787763073620396324051463046,5787763073620396325003645398⟩⟩,⟨⟨(-3557886570805400322627423920),(-3557886570805400322573583422)⟩,⟨6211285304264541020304130007,6211285304264541021325992979⟩⟩,⟨⟨(-3800413591088733258848844683),(-3800413591088733258791092743)⟩,⟨6642139805687678425256215575,6642139805687678426348699594⟩⟩] +lemma amp0_03_0_eq : ∀ k : Fin 16, amp0_0Expr 3 0 k = amp0_03_0 k := by decide +kernel +noncomputable def amp0_03_1 : Fin 16 → CBox := ![⟨⟨(-4037891521804236564802702119),(-4037891521804236564741218829)⟩,⟨7065642869188659991160868092,7065642869188659992322449058⟩⟩,⟨⟨(-4278111742531267935184458241),(-4278111742531267935119430831)⟩,⟨7495508165641405018924026296,7495508165641405020155206299⟩⟩,⟨⟨(-4513638956975200473951040883),(-4513638956975200473882625330)⟩,⟨7918805083922768887385241018,7918805083922768888684640920⟩⟩,⟨⟨(-4751358878317501976842081876),(-4751358878317501976769176755)⟩,⟨8347692026678966670653983534,8347692026678966672024237223⟩⟩,⟨⟨(-4984647213196184810139007124),(-4984647213196184810063032430)⟩,⟨8770624858115938509356174402,8770624858115938510793762854⟩⟩,⟨⟨(-5219662162292792061421569294),(-5219662162292792061342491760)⟩,⟨9198514789710970615721858796,9198514789710970617227429328⟩⟩,⟨⟨(-5450439363487605990792178355),(-5450439363487605990708602625)⟩,⟨9620942481531153226897603591,9620942481531153228472653458⟩⟩,⟨⟨(-5682539044503830969276508894),(-5682539044503830969190110901)⟩,⟨10047795812176770885253588425,10047795812176770886895658615⟩⟩,⟨⟨(-5910545170156570118579124947),(-5910545170156570118488522012)⟩,⟨10469586948012868588183610988,10469586948012868589894231898⟩⟩,⟨⟨(-6139517149294759665306308401),(-6139517149294759665211236927)⟩,⟨10895348183663714756855453260,10895348183663714758635515021⟩⟩,⟨⟨(-6364502488150114248506860463),(-6364502488150114248409398108)⟩,⟨11316376385185744658251503571,11316376385185744660096442943⟩⟩,⟨⟨(-6590134522594449257714154580),(-6590134522594449257612464808)⟩,⟨11740977184192445340626565466,11740977184192445342539993164⟩⟩,⟨⟨(-6811858376238199969670533885),(-6811858376238199969567143136)⟩,⟨12161118041179582892544885678,12161118041179582894521451970⟩⟩,⟨⟨(-7033940058876825672070173504),(-7033940058876825671961871745)⟩,⟨12584479119256691701314781750,12584479119256691703360498689⟩⟩,⟨⟨(-7252170038834943527853816799),(-7252170038834943527741775623)⟩,⟨13003608046024739167969613207,13003608046024739170081571293⟩⟩,⟨⟨(-7470494018033523041860524526),(-7470494018033523041744298971)⟩,⟨13425640381007352117777575091,13425640381007352119956800797⟩⟩] +lemma amp0_03_1_eq : ∀ k : Fin 16, amp0_0Expr 3 1 k = amp0_03_1 k := by decide +kernel +noncomputable def amp0_03_2 : Fin 16 → CBox := ![⟨⟨(-7685005660532958675494445394),(-7685005660532958675377036755)⟩,⟨13843631060004850600527215310,13843631060004850602767508251⟩⟩,⟨⟨(-7899368584324722175076507217),(-7899368584324722174954568426)⟩,⟨14264236657416372766425415689,14264236657416372768732971771⟩⟩,⟨⟨(-8109945166182524754371905724),(-8109945166182524754245986169)⟩,⟨14680959870426580307961295681,14680959870426580310334345786⟩⟩,⟨⟨(-8320148440411834238875528158),(-8320148440411834238745317107)⟩,⟨15100032247164096957668285738,15100032247164096960107521674⟩⟩,⟨⟨(-8526580924464771541154812097),(-8526580924464771541019822465)⟩,⟨15515354972300576923551527717,15515354972300576926057072564⟩⟩,⟨⟨(-8732431340398425833377423714),(-8732431340398425833242676547)⟩,⟨15932779456717881202175067385,15932779456717881204737851103⟩⟩,⟨⟨(-8934518404974519792603985693),(-8934518404974519792465242086)⟩,⟨16346564154487282094284786546,16346564154487282096911766597⟩⟩,⟨⟨(-9135828671805620936384761217),(-9135828671805620936242708611)⟩,⟨16762218066256831594198077863,16762218066256831596888034418⟩⟩,⟨⟨(-9333376794432716787549508057),(-9333376794432716787403505557)⟩,⟨17174322105037977334836094462,17174322105037977337589452196⟩⟩,⟨⟨(-9529965999846553671585592857),(-9529965999846553671435501828)⟩,⟨17588074856837975365808400312,17588074856837975368625417146⟩⟩,⟨⟨(-9722789575135201161725087606),(-9722789575135201161570987326)⟩,⟨17998350044888943419171848523,17998350044888943422051638032⟩⟩,⟨⟨(-9914483589414670311800935653),(-9914483589414670311648515573)⟩,⟨18410063194525890215456317606,18410063194525890218388281477⟩⟩,⟨⟨(-10102405067272650545351847597),(-10102405067272650545194528209)⟩,⟨18818355396288422463657157157,18818355396288422466652749380⟩⟩,⟨⟨(-10289036901471448275727824147),(-10289036901471448275566533895)⟩,⟨19227882669175516145546398627,19227882669175516148603826137⟩⟩,⟨⟨(-10471886935880932274856333916),(-10471886935880932274690363889)⟩,⟨19634031490581899113442070477,19634031490581899116561930170⟩⟩,⟨⟨(-10653297061338301658091298168),(-10653297061338301657922663910)⟩,⟨20041218786735040694205092878,20041218786735040697383500620⟩⟩] +lemma amp0_03_2_eq : ∀ k : Fin 16, amp0_0Expr 3 2 k = amp0_03_2 k := by decide +kernel +noncomputable def amp0_03_3 : Fin 16 → CBox := ![⟨⟨(-10830914662657600153022499728),(-10830914662657600152849987829)⟩,⟨20445057318828856981746081617,20445057318828856984984582112⟩⟩,⟨⟨(-11006951296947727433680010837),(-11006951296947727433503417546)⟩,⟨20849742714639315783837271169,20849742714639315787136117043⟩⟩,⟨⟨(-11179183982570730028051859805),(-11179183982570730027871051677)⟩,⟨21251097327934799356222630227,21251097327934799359581349764⟩⟩,⟨⟨(-11349703345494939029298651250),(-11349703345494939029123204700)⟩,⟨21653111080276394639113581746,21653111080276394642513747254⟩⟩,⟨⟨(-11516407285010085026507866323),(-11516407285010085026327571402)⟩,⟨22051801264416997694706183595,22051801264416997698166489522⟩⟩,⟨⟨(-11681273827215117689096771598),(-11681273827215117688912515542)⟩,⟨22450965822738100377598446260,22450965822738100381117010031⟩⟩,⟨⟨(-11842313979139518092485989415),(-11842313979139518092297910385)⟩,⟨22846804067498242298111904945,22846804067498242301687734844⟩⟩,⟨⟨(-12001400585230277154431675796),(-12001400585230277154240232594)⟩,⟨23242934098175277710350500045,23242934098175277713982489513⟩⟩,⟨⟨(-12156650823073975898898661922),(-12156650823073975898703333548)⟩,⟨23635725812889229399534280683,23635725812889229403222709477⟩⟩,⟨⟨(-12309838990586571062653425012),(-12309838990586571062456569045)⟩,⟨24028628239110001359699116808,24028628239110001363439140805⟩⟩,⟨⟨(-12459182216505905212610340755),(-12459182216505905212409752911)⟩,⟨24418171708345641125214904790,24418171708345641129010082030⟩⟩,⟨⟨(-12606362211752111353778315979),(-12606362211752111353574990935)⟩,⟨24807645768036187055439843922,24807645768036187059287948525⟩⟩,⟨⟨(-12749690456432380779854143651),(-12749690456432380779647701362)⟩,⟨25193732141850518949801251077,25193732141850518953702290579⟩⟩,⟨⟨(-12890761447976222136062933553),(-12890761447976222135853514592)⟩,⟨25579569465583404421914037363,25579569465583404425867431188⟩⟩,⟨⟨(-13027975955678080894749715647),(-13027975955678080894537156284)⟩,⟨25961982783063382173701833621,25961982783063382177707167892⟩⟩,⟨⟨(-13162846126029484033340302309),(-13162846126029484033124774077)⟩,⟨26343967493437228551472954261,26343967493437228555529562508⟩⟩] +lemma amp0_03_3_eq : ∀ k : Fin 16, amp0_0Expr 3 3 k = amp0_03_3 k := by decide +kernel +noncomputable def amp0_03_4 : Fin 16 → CBox := ![⟨⟨(-13293857423965123415983011647),(-13293857423965123415778692903)⟩,⟨26722484738486366724428802873,26722484738486366728507444227⟩⟩,⟨⟨(-13422444059953820455240395067),(-13422444059953820455030847244)⟩,⟨27100393572110621612908104060,27100393572110621617041368729⟩⟩,⟨⟨(-13547172011345183416881071900),(-13547172011345183416666901362)⟩,⟨27474784760618990681913720572,27474784760618990686099676457⟩⟩,⟨⟨(-13669401573555797790060733962),(-13669401573555797789842553595)⟩,⟨27848387213549737830559466105,27848387213549737834796525851⟩⟩,⟨⟨(-13787775413879760291884777115),(-13787775413879760291662811162)⟩,⟨28218415511203391644888371827,28218415511203391649175353355⟩⟩,⟨⟨(-13903583585475940661405307162),(-13903583585475940661179132815)⟩,⟨28587474008437816093333230723,28587474008437816097670630620⟩⟩,⟨⟨(-14015541941529172486434173600),(-14015541941529172486205229551)⟩,⟨28952895878498659646669448082,28952895878498659651053575474⟩⟩,⟨⟨(-14124873656763304506270027476),(-14124873656763304506037420390)⟩,⟨29317165967935082387478908441,29317165967935082391911207740⟩⟩,⟨⟨(-14230364548288532455755979509),(-14230364548288532455519495581)⟩,⟨29677731348364664698105826940,29677731348364664702586015928⟩⟩,⟨⟨(-14333174000978512764995841006),(-14333174000978512764759669572)⟩,⟨30036961919462770529909317980,30036961919462770534428212026⟩⟩,⟨⟨(-14432154824688615844576922626),(-14432154824688615844336729589)⟩,⟨30392414428781565997067638825,30392414428781566001633555795⟩⟩,⟨⟨(-14528405456940400012199855300),(-14528405456940400011956470222)⟩,⟨30746347956006962999306106528,30746347956006963003916872798⟩⟩,⟨⟨(-14620842952860431976635522904),(-14620842952860431976388553567)⟩,⟨31096425127280389262994877989,31096425127280389267650591548⟩⟩,⟨⟨(-14710507424321566671430025910),(-14710507424321566671181097587)⟩,⟨31444797938284112176017765804,31444797938284112180714509695⟩⟩,⟨⟨(-14796377624443827081603888135),(-14796377624443827081351408689)⟩,⟨31789231480612333446890791349,31789231480612333451631223766⟩⟩,⟨⟨(-14879437762386679077362678445),(-14879437762386679077107676269)⟩,⟨32131774048975759058710809828,32131774048975759063492252631⟩⟩] +lemma amp0_03_4_eq : ∀ k : Fin 16, amp0_0Expr 3 4 k = amp0_03_4 k := by decide +kernel +noncomputable def amp0_03_5 : Fin 16 → CBox := ![⟨⟨(-14958725921702116233677482956),(-14958725921702116233419557703)⟩,⟨32470290135839666983064567020,32470290135839666987887141250⟩⟩,⟨⟨(-15035172652254284744515888407),(-15035172652254284744255142898)⟩,⟨32806727398105894241558400415,32806727398105894246421395411⟩⟩,⟨⟨(-15107873162286132213934632301),(-15107873162286132213670701718)⟩,⟨33139046981889175141896624183,33139046981889175146800099291⟩⟩,⟨⟨(-15177706423148238162249027181),(-15177706423148238161982113901)⟩,⟨33469098678501261363791848634,33469098678501261368734865258⟩⟩,⟨⟨(-15243822708171844166897160765),(-15243822708171844166627167560)⟩,⟨33794937830470193351455110095,33794937830470193356437150078⟩⟩,⟨⟨(-15307051343188484535326108388),(-15307051343188484535079781928)⟩,⟨34118318870143257829901653772,34118318870143257834862592441⟩⟩,⟨⟨(-15366595739375523227486348642),(-15366595739375523227235500955)⟩,⟨34437389145123439911951933117,34437389145123439916953562668⟩⟩,⟨⟨(-15423237375352834040310474079),(-15423237375352834040055872578)⟩,⟨34753809992090448801626198111,34753809992090448806666301813⟩⟩,⟨⟨(-15476230993129035686271982132),(-15476230993129035686014148814)⟩,⟨35065818817034323109484768883,35065818817034323114561452062⟩⟩,⟨⟨(-15526311899321362462821756854),(-15526311899321362462560833873)⟩,⟨35374985900523536664719946418,35374985900523536669832353684⟩⟩,⟨⟨(-15572784469274971179621094131),(-15572784469274971179357794229)⟩,⟨35679636986115350486979346267,35679636986115350492125118029⟩⟩,⟨⟨(-15616339399993066250860085378),(-15616339399993066250594599323)⟩,⟨35981253131340339139623092625,35981253131340339144801227603⟩⟩,⟨⟨(-15656329102716728219717864362),(-15656329102716728219449372796)⟩,⟨36278246905736940113668063808,36278246905736940118879716536⟩⟩,⟨⟨(-15693401123540242574013906322),(-15693401123540242573743789605)⟩,⟨36572011785607313448296066916,36572011785607313453537463349⟩⟩,⟨⟨(-15726954403832162880365663501),(-15726954403832162880093176575)⟩,⟨36861045849364565607062230476,36861045849364565612334359756⟩⟩,⟨⟨(-15757594701939614065698533579),(-15757594701939614065423492008)⟩,⟨37146656456056783876102275682,37146656456056783881404991023⟩⟩] +lemma amp0_03_5_eq : ∀ k : Fin 16, amp0_0Expr 3 5 k = amp0_03_5 k := by decide +kernel +noncomputable def amp0_03_6 : Fin 16 → CBox := ![⟨⟨(-15784766067830753285985747503),(-15784766067830753285710966111)⟩,⟨37427426057243005410909756349,37427426057243005416235659289⟩⟩,⟨⟨(-15809033746990327260430539086),(-15809033746990327260152772427)⟩,⟨37704577192705625598035624744,37704577192705625603391788940⟩⟩,⟨⟨(-15829885554103249527891389213),(-15829885554103249527612404106)⟩,⟨37976775721155761496920948401,37976775721155761502302424554⟩⟩,⟨⟨(-15847847414897476872741457774),(-15847847414897476872459658330)⟩,⟨38245160505562048689210295056,38245160505562048694620302852⟩⟩,⟨⟨(-15862449636679283540338031759),(-15862449636679283540054425256)⟩,⟨38508480005179710908138091002,38508480005179710913573478964⟩⟩,⟨⟨(-15874179942565600164672024813),(-15874179942565600164386169746)⟩,⟨38767790402282614424247852379,38767790402282614429709072588⟩⟩,⟨⟨(-15882609926972234266841867333),(-15882609926972234266562450218)⟩,⟨39021922100251998925574313684,39021922100251998931039304755⟩⟩,⟨⟨(-15888190156809504913473736646),(-15888190156809504913191402360)⟩,⟨39271849458541985720063475731,39271849458541985725554485752⟩⟩,⟨⟨(-15890532370051617747198554400),(-15890532370051617746914236724)⟩,⟨39516484310268312298468566919,39516484310268312303982584836⟩⟩,⟨⟨(-15890050957749703299139814859),(-15890050957749703298854026818)⟩,⟨39756719918783432848982563255,39756719918783432854517667357⟩⟩,⟨⟨(-15886396715741246509482820178),(-15886396715741246509195127201)⟩,⟨39991549167339213971945954164,39991549167339213977502507803⟩⟩,⟨⟨(-15879948777716489885778618320),(-15879948777716489885490037570)⟩,⟨40221784824929036238252674721,40221784824929036243827459689⟩⟩,⟨⟨(-15870395965896233981512131317),(-15870395965896233981222246554)⟩,⟨40446500573744396486126957841,40446500573744396491720298411⟩⟩,⟨⟨(-15858083017040198185205727128),(-15858083017040198184913999841)⟩,⟨40666429170545086306232841018,40666429170545086311845446384⟩⟩,⟨⟨(-15842735799263472768406784972),(-15842735799263472768117341872)⟩,⟨40880724968043728251407338191,40880724968043728257027856039⟩⟩,⟨⟨(-15824665458155277051612008242),(-15824665458155277051321242733)⟩,⟨41090041077880596077264536228,41090041077880596082901542778⟩⟩] +lemma amp0_03_6_eq : ∀ k : Fin 16, amp0_0Expr 3 6 k = amp0_03_6 k := by decide +kernel +noncomputable def amp0_03_7 : Fin 16 → CBox := ![⟨⟨(-15803633975378364914085736320),(-15803633975378364913794186440)⟩,⟨41293612512729021841595958278,41293612512729021847247343130⟩⟩,⟨⟨(-15779919659492432488170476811),(-15779919659492432487877674725)⟩,⟨41492012995125320101823271139,41492012995125320107489561033⟩⟩,⟨⟨(-15753319718995211177362438027),(-15753319718995211177070624948)⟩,⟨41684558300731730082620528703,41684558300731730088295087075⟩⟩,⟨⟨(-15724080330676077098229167798),(-15724080330676077097936620275)⟩,⟨41871742911168401321446395726,41871742911168401327133051520⟩⟩,⟨⟨(-15692033086589667665825199227),(-15692033086589667665533308674)⟩,⟨42052963578039444239234322333,42052963578039444244928639517⟩⟩,⟨⟨(-15657392690583621177441932269),(-15657392690583621177149261972)⟩,⟨42228635585079918118745158522,42228635585079918124450249372⟩⟩,⟨⟨(-15620024316508954003180508246),(-15620024316508954002888163773)⟩,⟨42398236979618284935454803176,42398236979618284941166963021⟩⟩,⟨⟨(-15580111809858637516830933135),(-15580111809858637516538905199)⟩,⟨42562103787485332671764747256,42562103787485332677483252198⟩⟩,⟨⟨(-15537553164378959159000125705),(-15537553164378959158708418657)⟩,⟨42719795775789181654815264887,42719795775789181660539381770⟩⟩,⟨⟨(-15492501939501556290374233715),(-15492501939501556290082644890)⟩,⟨42871569550957288099582600262,42871569550957288105312124881⟩⟩,⟨⟨(-15444888225406960343915336016),(-15444888225406960343624441121)⟩,⟨43017067126163756473521248761,43017067126163756479253862122⟩⟩,⟨⟨(-15394835827189225846875715604),(-15394835827189225846585384980)⟩,⟨43156465426510488169803051744,43156465426510488175538345238⟩⟩,⟨⟨(-15342306245244277883995219698),(-15342306245244277883705992981)⟩,⟨43289489338210172024510956651,43289489338210172030246696898⟩⟩,⟨⟨(-15287394022998347953681782212),(-15287394022998347953393790887)⟩,⟨43416235743253624983852762539,43416235743253624989587774103⟩⟩,⟨⟨(-15230091421094775474204019569),(-15230091421094775473917716591)⟩,⟨43536513127490966374359979078,43536513127490966380092231502⟩⟩,⟨⟨(-15170464176227409611183850912),(-15170464176227409610899756856)⟩,⟨43650337868227585347075383981,43650337868227585352802561399⟩⟩] +lemma amp0_03_7_eq : ∀ k : Fin 16, amp0_0Expr 3 7 k = amp0_03_7 k := by decide +kernel +noncomputable def amp0_03_8 : Fin 16 → CBox := ![⟨⟨(-15108534694772631330606293810),(-15108534694772631330322836168)⟩,⟨43757602876593655877755606571,43757602876593655883481518109⟩⟩,⟨⟨(-15044340325027245120705725824),(-15044340325027245120421252542)⟩,⟨43858243463441536430435031879,43858243463441536436163694870⟩⟩,⟨⟨(-14977933039426212173892375360),(-14977933039426212173607493368)⟩,⟨43952237889760801830738537300,43952237889760801836467543464⟩⟩,⟨⟨(-14909322180561738511274438795),(-14909322180561738510989535847)⟩,⟨44039439737108019346699876643,44039439737108019352427335529⟩⟩,⟨⟨(-14838588741654149409290889487),(-14838588741654149409006194357)⟩,⟨44119913640219351676882149000,44119913640219351682606742825⟩⟩,⟨⟨(-14765714407427394399485023070),(-14765714407427394399200969554)⟩,⟨44193430686074901340490701250,44193430686074901346210346058⟩⟩,⟨⟨(-14690808680744826161494867500),(-14690808680744826161211402994)⟩,⟨44260143007209407427272726817,44260143007209407432986916326⟩⟩,⟨⟨(-14613825902063551448645018365),(-14613825902063551448362617935)⟩,⟨44319738326455971733016462600,44319738326455971738722967371⟩⟩,⟨⟨(-14534903606771425963231779734),(-14534903606771425962950344399)⟩,⟨44372457499720152548304333414,44372457499720152554002808923⟩⟩,⟨⟨(-14453969070883883320007365138),(-14453969070883883319726801270)⟩,⟨44417903909473114183915460791,44417903909473114189605367646⟩⟩,⟨⟨(-14371187419271470021528341174),(-14371187419271470021248707188)⟩,⟨44456408463955476450920352797,44456408463955476456600863904⟩⟩,⟨⟨(-14286459109854533829283591350),(-14286459109854533829005823720)⟩,⟨44487489119541331145811734016,44487489119541331151479126484⟩⟩,⟨⟨(-14199976448232391377884097437),(-14199976448232391377606970740)⟩,⟨44511568271573848397128822642,44511568271573848402786284255⟩⟩,⟨⟨(-14111613287234782329053024267),(-14111613287234782328777699637)⟩,⟨44528077251653400811673069997,44528077251653400817316121121⟩⟩,⟨⟨(-14021588739093182330362475036),(-14021588739093182330087473433)⟩,⟨44537531485776168634977725123,44537531485776168640610407951⟩⟩,⟨⟨(-13929750231182558417654446120),(-13929750231182558417381684313)⟩,⟨44539274365153559962545311204,44539274365153559968160712423⟩⟩] +lemma amp0_03_8_eq : ∀ k : Fin 16, amp0_0Expr 3 8 k = amp0_03_8 k := by decide +kernel +noncomputable def amp0_03_9 : Fin 16 → CBox := ![⟨⟨(-13836343343456537649597425053),(-13836343343456537649326567487)⟩,⟨44533916002351605523684235048,44533916002351605529282805069⟩⟩,⟨⟨(-13741189223909458035848061811),(-13741189223909458035579464355)⟩,⟨44520710411029257907642550114,44520710411029257913222253858⟩⟩,⟨⟨(-13644559617186241837687778895),(-13644559617186241837418383949)⟩,⟨44500364162834738280970198405,44500364162834738286540362983⟩⟩,⟨⟨(-13546249504048201687108553643),(-13546249504048201686841844084)⟩,⟨44472040329896629681996543498,44472040329896629687544996739⟩⟩,⟨⟨(-13446556527540865286455456790),(-13446556527540865286191037129)⟩,⟨44436543836977574314618949291,44436543836977574320146376027⟩⟩,⟨⟨(-13345249578869775338248067902),(-13345249578869775337985479560)⟩,⟨44392945117908785975048314393,44392945117908785980555342787⟩⟩,⟨⟨(-13242651970967202814351894916),(-13242651970967202814092038668)⟩,⟨44342149471797090317635848849,44342149471797090323118868740⟩⟩,⟨⟨(-13138506547957870401331290004),(-13138506547957870401073712339)⟩,⟨44283132857876190819933462618,44283132857876190825393109441⟩⟩,⟨⟨(-13033162103145379483349953845),(-13033162103145379483095149268)⟩,⟨44216903104522734110383913011,44216903104522734115817948387⟩⟩,⟨⟨(-12926335439914765203356268839),(-12926335439914765203104876199)⟩,⟨44142339712955156701496691181,44142339712955156706902001682⟩⟩,⟨⟨(-12818400682842243119061986637),(-12818400682842243118806480594)⟩,⟨44060555336838681026745801238,44060555336838681032147623119⟩⟩,⟨⟨(-12709048563635549701636317063),(-12709048563635549701383671224)⟩,⟨43970330880333674317606392802,43970330880333674322980011554⟩⟩,⟨⟨(-12598678431090650238023016447),(-12598678431090650237772939918)⟩,⟨43872886267892411151717708266,43872886267892411157063580844⟩⟩,⟨⟨(-12486954875646679884963764085),(-12486954875646679884716940397)⟩,⟨43766901502423237818229703082,43766901502423237823544514585⟩⟩,⟨⟨(-12374302407169630975549882149),(-12374302407169630975305094648)⟩,⟨43653706383624194502170730918,43653706383624194507458185519⟩⟩,⟨⟨(-12260359364960358818831297408),(-12260359364960358818589837908)⟩,⟨43531877533150836310587627675,43531877533150836315842275089⟩⟩] +lemma amp0_03_9_eq : ∀ k : Fin 16, amp0_0Expr 3 9 k = amp0_03_9 k := by decide +kernel +noncomputable def amp0_03_10 : Fin 16 → CBox := ![⟨⟨(-12145575402814296969530032865),(-12145575402814296969289461741)⟩,⟨43402857400061159509722850681,43402857400061159514952883770⟩⟩,⟨⟨(-12029562456848286355242933771),(-12029562456848286355005311997)⟩,⟨43265116557036652482316511439,43265116557036652487513660032⟩⟩,⟨⟨(-11912795356034850689417569095),(-11912795356034850689182794712)⟩,⟨43120213058314582615792822217,43120213058314582620956918366⟩⟩,⟨⟨(-11794859436887015688127190718),(-11794859436887015687894610999)⟩,⟨42966508558840016441141568537,42966508558840016446274089992⟩⟩,⟨⟨(-11676254785871290762901451146),(-11676254785871290762672170773)⟩,⟨42805679869119668641384939738,42805679869119668646481392931⟩⟩,⟨⟨(-11556539896572626188513636758),(-11556539896572626188286927751)⟩,⟨42635976641658567642303028339,42635976641658567647365140073⟩⟩,⟨⟨(-11436240249354519295584929338),(-11436240249354519295360976716)⟩,⟨42459197804863177786362733689,42459197804863177791389336501⟩⟩,⟨⟨(-11314887201744799277752088048),(-11314887201744799277531324411)⟩,⟨42273477691473123421442912937,42273477691473123426431496566⟩⟩,⟨⟨(-11193031821885686199101844511),(-11193031821885686198884438444)⟩,⟨42080740937155571754324971212,42080740937155571759274467270⟩⟩,⟨⟨(-11070177984999804931103913501),(-11070177984999804930890115209)⟩,⟨41879002986243165072403779722,41879002986243165077312266441⟩⟩,⟨⟨(-10946902602183902574458356340),(-10946902602183902574248744661)⟩,⟨41670318018120667621107490440,41670318018120667625972275653⟩⟩,⟨⟨(-10822681663208514047410501760),(-10822681663208514047184956517)⟩,⟨41452578747774839322296452070,41452578747774839327193640837⟩⟩,⟨⟨(-10698118242888078852798002982),(-10698118242888078852575712448)⟩,⟨41227973003696867765795225801,41227973003696867770651372010⟩⟩,⟨⟨(-10572659981189494834246466351),(-10572659981189494834027246151)⟩,⟨40994266634704622860421301330,40994266634704622865236161633⟩⟩,⟨⟨(-10446936507831760486103882269),(-10446936507831760485887911685)⟩,⟨40753785517369639292240094324,40753785517369639297012548206⟩⟩,⟨⟨(-10320366582518682341023415791),(-10320366582518682340810351328)⟩,⟨40504164175066977685168660165,40504164175066977689899146054⟩⟩] +lemma amp0_03_10_eq : ∀ k : Fin 16, amp0_0Expr 3 10 k = amp0_03_10 k := by decide +kernel +noncomputable def amp0_03_11 : Fin 16 → CBox := ![⟨⟨(-10193606856940619646376356456),(-10193606856940619646166342283)⟩,⟨40247871252884809794557961533,40247871252884809799245586285⟩⟩,⟨⟨(-10066046608386185472944421348),(-10066046608386185472737064927)⟩,⟨39982405137043079459610544948,39982405137043079464255902327⟩⟩,⟨⟨(-9938370059630899392364157844),(-9938370059630899392160198758)⟩,⟨39710382314626196330480449465,39710382314626196335080225783⟩⟩,⟨⟨(-9809936325337673532710890198),(-9809936325337673532509168594)⟩,⟨39429159836619646978360987144,39429159836619646982918932934⟩⟩,⟨⟨(-9681457837513789990959067245),(-9681457837513789990760741264)⟩,⟨39141507494478870207502362660,39141507494478870212013532922⟩⟩,⟨⟨(-9552262782662623508933765918),(-9552262782662623508738461323)⟩,⟨38844635381021623714592121317,38844635381021623719057076198⟩⟩,⟨⟨(-9423092537135648386157335922),(-9423092537135648385965638127)⟩,⟨38541472484140778952643778496,38541472484140778957059792295⟩⟩,⟨⟨(-9293243500114667664162676968),(-9293243500114667663971663709)⟩,⟨38229075846919509146420664397,38229075846919509150798843830⟩⟩,⟨⟨(-9163486833407365275133744084),(-9163486833407365274946235968)⟩,⟨37910540021990323689250415778,37910540021990323693578966849⟩⟩,⟨⟨(-9033086186570512488579630657),(-9033086186570512488395369111)⟩,⟨37582762392551006892619740896,37582762392551006896898759794⟩⟩,⟨⟨(-8902843464298267089802232468),(-8902843464298267089620682569)⟩,⟨37249009973765690899207687452,37249009973765690903439116049⟩⟩,⟨⟨(-8771988490153551898877160397),(-8771988490153551898699160064)⟩,⟨36906013303036785629155608727,36906013303036785633335057102⟩⟩,⟨⟨(-8641354997290955526294403578),(-8641354997290955526119743722)⟩,⟨36557219346463186447308748494,36557219346463186451436874936⟩⟩,⟨⟨(-8510137780266505603025633676),(-8510137780266505602854346363)⟩,⟨36199183968310893470707011905,36199183968310893474782730008⟩⟩,⟨⟨(-8379203628013698238856260917),(-8379203628013698238688764180)⟩,⟨35835542235016523841037618621,35835542235016523845058885691⟩⟩,⟨⟨(-8247710961894296706447337469),(-8247710961894296706283919652)⟩,⟨35462666793226975159957622597,35462666793226975163922293527⟩⟩] +lemma amp0_03_11_eq : ∀ k : Fin 16, amp0_0Expr 3 11 k = amp0_03_11 k := by decide +kernel +noncomputable def amp0_03_12 : Fin 16 → CBox := ![⟨⟨(-8116561011386679953848105705),(-8116561011386679953678691568)⟩,⟨35084389701477101892511672642,35084389701477101896463123042⟩⟩,⟨⟨(-7984874322454034658853615381),(-7984874322454034658686892710)⟩,⟨34696891039541015476509207777,34696891039541015480409144225⟩⟩,⟨⟨(-7853588125537927117416903128),(-7853588125537927117253019401)⟩,⟨34304209586577058043387651009,34304209586577058047235252873⟩⟩,⟨⟨(-7721783411383447799736810988),(-7721783411383447799575593969)⟩,⟨33902322599608770824424016970,33902322599608770828219187767⟩⟩,⟨⟨(-7590435168664401906943440182),(-7590435168664401906785042290)⟩,⟨33495486253722824975441539204,33495486253722824979183521261⟩⟩,⟨⟨(-7458582952572418642799634516),(-7458582952572418642643732095)⟩,⟨33079463701769969908088024391,33079463701769969911777340125⟩⟩,⟨⟨(-7327241488934059189397039426),(-7327241488934059189244268619)⟩,⟨32658740265637904964854327461,32658740265637904968488022472⟩⟩,⟨⟨(-7195406789654343154670057243),(-7195406789654343154519040495)⟩,⟨32228852547519978342106826487,32228852547519978345690215431⟩⟩,⟨⟨(-7064135547446101819523815095),(-7064135547446101819376023780)⟩,⟨31794527994050942063157058141,31794527994050942066683544631⟩⟩,⟨⟨(-6932377864084680754528661399),(-6932377864084680754383686408)⟩,⟨31351062880690569327127565264,31351062880690569330598056687⟩⟩,⟨⟨(-6801234914189918174308504757),(-6801234914189918174166652167)⟩,⟨30903441163010943337702378946,30903441163010943341115401550⟩⟩,⟨⟨(-6669608225842941309780652498),(-6669608225842941309641933621)⟩,⟨30446703488971523648228106981,30446703488971523651582764629⟩⟩,⟨⟨(-6538646296869098829863946979),(-6538646296869098829728932246)⟩,⟨29986106326608720510456429777,29986106326608720513750105371⟩⟩,⟨⟨(-6407199076500887393970967991),(-6407199076500887393833708613)⟩,⟨29516417638199563347088530834,29516417638199563350347695942⟩⟩,⟨⟨(-6276465602386653848258783017),(-6276465602386653848124828323)⟩,⟨29043184282096844697269698021,29043184282096844700468851700⟩⟩,⟨⟨(-6145240844302976688433139960),(-6145240844302976688302347939)⟩,⟨28560882439914327405932816994,28560882439914327409071776874⟩⟩] +lemma amp0_03_12_eq : ∀ k : Fin 16, amp0_0Expr 3 12 k = amp0_03_12 k := by decide +kernel +noncomputable def amp0_03_13 : Fin 16 → CBox := ![⟨⟨(-6014778030722670194225095963),(-6014778030722670194097416918)⟩,⟨28075369419636451030147357334,28075369419636451033226432666⟩⟩,⟨⟨(-5883813290803553420635001773),(-5883813290803553420509658894)⟩,⟨27580808152723655653082598084,27580808152723655656104503849⟩⟩,⟨⟨(-5753658200878406086205222285),(-5753658200878406086083381949)⟩,⟨27083389010168380208835951522,27083389010168380211795239077⟩⟩,⟨⟨(-5622985648496712869227564943),(-5622985648496712869108769416)⟩,⟨26576937418018996263324343838,26576937418018996266222336401⟩⟩,⟨⟨(-5493170308514490686207781822),(-5493170308514490686092600134)⟩,⟨26068002433224048755513314164,26068002433224048758347423681⟩⟩,⟨⟨(-5362816788755508044267171289),(-5362816788755508044151889498)⟩,⟨25550044430516219010270082731,25550044430516219013057093055⟩⟩,⟨⟨(-5233368314880381863651979397),(-5233368314880381863539779643)⟩,⟨25030000346882201875864537357,25030000346882201878589417655⟩⟩,⟨⟨(-5103355419261583125201181565),(-5103355419261583125092053022)⟩,⟨24500934043936752269306534849,24500934043936752271968519591⟩⟩,⟨⟨(-4974296166625037236304446135),(-4974296166625037236198370614)⟩,⟨23970203802578994621151622275,23970203802578994623750989591⟩⟩,⟨⟨(-4844640309945409751803958932),(-4844640309945409751700508419)⟩,⟨23430440811840713610526035788,23430440811840713613063951010⟩⟩,⟨⟨(-4715988046106649583081246713),(-4715988046106649582980822902)⟩,⟨22889463308150554140851753525,22889463308150554143326415834⟩⟩,⟨⟨(-4586700546256559628249104769),(-4586700546256559628149379293)⟩,⟨22339427963100884067725176323,22339427963100884070147113599⟩⟩,⟨⟨(-4458468651901207209336751592),(-4458468651901207209240479645)⟩,⟨21788657843426339778836560758,21788657843426339781192620568⟩⟩,⟨⟨(-4329555808319028455503737304),(-4329555808319028455410588780)⟩,⟨21228786310638838534661112127,21228786310638838536952017642⟩⟩,⟨⟨(-4201753509376722289031288984),(-4201753509376722288941121611)⟩,⟨20668693834058910708451027564,20668693834058910710677679305⟩⟩,⟨⟨(-4073216674158508900800352679),(-4073216674158508900713415654)⟩,⟨20099433090623093080350826289,20099433090623093082511179888⟩⟩] +lemma amp0_03_13_eq : ∀ k : Fin 16, amp0_0Expr 3 13 k = amp0_03_13 k := by decide +kernel +noncomputable def amp0_03_14 : Fin 16 → CBox := ![⟨⟨(-3945849311504897658141181532),(-3945849311504897658055754944)⟩,⟨19530504091343626223565687224,19530504091343626225668579735⟩⟩,⟨⟨(-3817684944647839110829248053),(-3817684944647839110746854778)⟩,⟨18952310726994784967532370087,18952310726994784969569374605⟩⟩,⟨⟨(-3690754290616350213276136224),(-3690754290616350213196562562)⟩,⟨18375046729025025677550470167,18375046729025025679522932893⟩⟩,⟨⟨(-3562953986981834932674608957),(-3562953986981834932598432995)⟩,⟨17788385512305140020670769816,17788385512305140022574980795⟩⟩,⟨⟨(-3436458622733459665888484217),(-3436458622733459665814065640)⟩,⟨17203304073357178161561348200,17203304073357178163405895370⟩⟩,⟨⟨(-3309009092141056801002873680),(-3309009092141056800931482290)⟩,⟨16608646189264604003041636249,16608646189264604004819277125⟩⟩,⟨⟨(-3182944867741019471095041637),(-3182944867741019471025740773)⟩,⟨16016281591564628511773324377,16016281591564628513489148282⟩⟩,⟨⟨(-3055827839515424063733311003),(-3055827839515424063667150709)⟩,⟨15414102405930735308742695878,15414102405930735310390570329⟩⟩,⟨⟨(-2930188451566032089572654104),(-2930188451566032089509531995)⟩,⟨14815006879387363691814898916,14815006879387363693395839849⟩⟩,⟨⟨(-2803380457805536568268137463),(-2803380457805536568207294770)⟩,⟨14205782996800170161698680817,14205782996800170163215577847⟩⟩,⟨⟨(-2678158201915089022441945538),(-2678158201915089022384256345)⟩,⟨13600528776722671083678113051,13600528776722671085127037068⟩⟩,⟨⟨(-2551630163796799079437861779),(-2551630163796799079382589231)⟩,⟨12984734003356991583705020499,12984734003356991585088804264⟩⟩,⟨⟨(-2426816959457020055908215496),(-2426816959457020055855367179)⟩,⟨12373916734468972017722923070,12373916734468972019042152832⟩⟩,⟨⟨(-2300533445903440627117194195),(-2300533445903440627067463661)⟩,⟨11752016271609743438447281130,11752016271609743439697418888⟩⟩,⟨⟨(-2176122307226760425127872792),(-2176122307226760425080704195)⟩,⟨11136260664561825603447631556,11136260664561825604632170079⟩⟩,⟨⟨(-2050040228941815300424362807),(-2050040228941815300379823231)⟩,⟨10508702306317853545532339145,10508702306317853546649927779⟩⟩] +lemma amp0_03_14_eq : ∀ k : Fin 16, amp0_0Expr 3 14 k = amp0_03_14 k := by decide +kernel +noncomputable def amp0_03_15 : Fin 16 → CBox := ![⟨⟨(-1926027505834498966125780887),(-1926027505834498966083984269)⟩,⟨9888671738348141415350983647,9888671738348141416401851139⟩⟩,⟨⟨(-1800093789121674416816066428),(-1800093789121674416777078386)⟩,⟨9255871711318581694469043936,9255871711318581695451705608⟩⟩,⟨⟨(-1676482825452813382426137740),(-1676482825452813382389971322)⟩,⟨8632285135977092438583368568,8632285135977092439498640334⟩⟩,⟨⟨(-1550630125940814598490461392),(-1550630125940814598456888076)⟩,⟨7994603702274222373459701480,7994603702274222374307561935⟩⟩,⟨⟨(-1427437726536585414212000610),(-1427437726536585414181088412)⟩,⟨7368267105892939062171916828,7368267105892939062953095932⟩⟩,⟨⟨(-1301576065736027323691431709),(-1301576065736027323663276181)⟩,⟨6725962933974894347855688348,6725962933974894348568305586⟩⟩,⟨⟨(-1178845079062316101129276877),(-1178845079062316101103912314)⟩,⟨6097832527736139034640135897,6097832527736139035285284518⟩⟩,⟨⟨(-1052844063937715561330554364),(-1052844063937715561307814849)⟩,⟨5450968089372460740324673374,5450968089372460740901626847⟩⟩,⟨⟨(-930671028172030377324989908),(-930671028172030377304975318)⟩,⟨4822291737254375730504567447,4822291737254375731014429633⟩⟩,⟨⟨(-804316972304128527771470031),(-804316972304128527754221380)⟩,⟨4170508251314983058042698429,4170508251314983058483274366⟩⟩,⟨⟨(-682923815175354637540569880),(-682923815175354637526022095)⟩,⟨3543195781150830925454802448,3543195781150830925828535421⟩⟩,⟨⟨(-555794499212249443706889289),(-555794499212249443695107623)⟩,⟨2885060160642004357791363658,2885060160642004358095316167⟩⟩,⟨⟨(-435767271490579782717904868),(-435767271490579782708794433)⟩,⟨2262921596400550177703419622,2262921596400550177941154352⟩⟩,⟨⟨(-306729548442980972221029060),(-306729548442980972214692506)⟩,⟨1593313590056805446185487047,1593313590056805446352459596⟩⟩,⟨⟨(-190242689581973433163913133),(-190242689581973433160243829)⟩,⟨988418371844251979055147965,988418371844251979157372442⟩⟩,⟨⟨(-54044651346934386890537372),(-54044651346934386889651120)⟩,⟨280820721772499749212057624,280820721772499749240288253⟩⟩] +lemma amp0_03_15_eq : ∀ k : Fin 16, amp0_0Expr 3 15 k = amp0_03_15 k := by decide +kernel +noncomputable def amp0_03 : Fin 16 → Fin 16 → CBox := ![amp0_03_0,amp0_03_1,amp0_03_2,amp0_03_3,amp0_03_4,amp0_03_5,amp0_03_6,amp0_03_7,amp0_03_8,amp0_03_9,amp0_03_10,amp0_03_11,amp0_03_12,amp0_03_13,amp0_03_14,amp0_03_15] +lemma amp0_03_eq (i k : Fin 16) : amp0_0Expr 3 i k = amp0_03 i k := by + fin_cases i + · exact amp0_03_0_eq k + · exact amp0_03_1_eq k + · exact amp0_03_2_eq k + · exact amp0_03_3_eq k + · exact amp0_03_4_eq k + · exact amp0_03_5_eq k + · exact amp0_03_6_eq k + · exact amp0_03_7_eq k + · exact amp0_03_8_eq k + · exact amp0_03_9_eq k + · exact amp0_03_10_eq k + · exact amp0_03_11_eq k + · exact amp0_03_12_eq k + · exact amp0_03_13_eq k + · exact amp0_03_14_eq k + · exact amp0_03_15_eq k +noncomputable def amp0_04_0 : Fin 16 → CBox := ![⟨⟨(-108088285328156058982599759),(-108088285328156058981540162)⟩,⟨1762129104300541687742,1762129104300563305409⟩⟩,⟨⟨(-380453151319111964411351249),(-380453151319111964406521959)⟩,⟨55820264672496295138002,55820264672496371229063⟩⟩,⟨⟨(-613314789282883314763260866),(-613314789282883314754638658)⟩,⟨249948100450669473487693,249948100450669596152899⟩⟩,⟨⟨(-871132832163727548689651365),(-871132832163727548677185017)⟩,⟨695783545742278343399818,695783545742278517632794⟩⟩,⟨⟨(-1110742379793587805544568437),(-1110742379793587805528361454)⟩,⟨1466386483372396494886356,1466386483372396717048725⟩⟩,⟨⟨(-1364294426607166605424695495),(-1364294426607166605404637937)⟩,⟨2690227798322084215224153,2690227798322084488108796⟩⟩,⟨⟨(-1606080516929194707874514870),(-1606080516929194707850675545)⟩,⟨4422666473588663140101472,4422666473588663461360513⟩⟩,⟨⟨(-1857411230393376142141328196),(-1857411230393376142113629862)⟩,⟨6808390262295982730150325,6808390262295983101699106⟩⟩,⟨⟨(-2099980978840482901196603398),(-2099980978840482901165109583)⟩,⟨9885072094898005465872587,9885072094898005885966183⟩⟩,⟨⟨(-2349715165212016044462159387),(-2349715165212016044427086308)⟩,⟨13813092914652888728494201,13813092914652889198572323⟩⟩,⟨⟨(-2592406288112938839156297101),(-2592406288112938839117294414)⟩,⟨18612346668165192458469932,18612346668165192977135374⟩⟩,⟨⟨(-2840754361792469275133374932),(-2840754361792469275090530138)⟩,⟨24458447556492956792819811,24458447556492957361213589⟩⟩,⟨⟨(-3083158362756607818416153897),(-3083158362756607818369669696)⟩,⟨31353391677515556003178232,31353391677515556620121065⟩⟩,⟨⟨(-3330167486215396474169756328),(-3330167486215396474119757745)⟩,⟨39487579562801637867498235,39487579562801638533921097⟩⟩,⟨⟨(-3571986906618049826291947312),(-3571986906618049826237983931)⟩,⟨48844996062583868652848159,48844996062583869367731688⟩⟩,⟨⟨(-3817627397948821483312469083),(-3817627397948821483254566088)⟩,⟨59630376146700977880342945,59630376146700978644465466⟩⟩] +lemma amp0_04_0_eq : ∀ k : Fin 16, amp0_0Expr 4 0 k = amp0_04_0 k := by decide +kernel +noncomputable def amp0_04_1 : Fin 16 → CBox := ![⟨⟨(-4058621167164034576813855672),(-4058621167164034576752189907)⟩,⟨71809597972109152811527059,71809597972109153623972113⟩⟩,⟨⟨(-4302822699838685573537137465),(-4302822699838685573471893292)⟩,⟨85601267120225539785656614,85601267120225540647077791⟩⟩,⟨⟨(-4542781601919094067374177738),(-4542781601919094067305507896)⟩,⟨100953083419527913930102677,100953083419527914839664474⟩⟩,⟨⟨(-4785450558516348021828663502),(-4785450558516348021755454716)⟩,⟨118097044439582390422683784,118097044439582391380971646⟩⟩,⟨⟨(-5024184917995322593046149223),(-5024184917995322592969826566)⟩,⟨136962627053532944070347400,136962627053532945076558712⟩⟩,⟨⟨(-5265213576138587389237030433),(-5265213576138587389157556449)⟩,⟨157794726275027871721327946,157794726275027872775938824⟩⟩,⟨⟨(-5502546547528761706034679332),(-5502546547528761705950640777)⟩,⟨180504580397247742706507281,180504580397247743808842604⟩⟩,⟨⟨(-5741818330713242039227034695),(-5741818330713242039140118233)⟩,⟨205349471102234108631378656,205349471102234109781792058⟩⟩,⟨⟨(-5977582006447996121535663247),(-5977582006447996121444465977)⟩,⟨232222412870854058595912933,232222412870854059793774853⟩⟩,⟨⟨(-6214974678023852757594736310),(-6214974678023852757498984594)⟩,⟨261392547144754898568315980,261392547144754899813990536⟩⟩,⟨⟨(-6449007720194114033000118412),(-6449007720194114032901909281)⟩,⟨292734710811210387219708888,292734710811210388512459176⟩⟩,⟨⟨(-6684395430218605949061858605),(-6684395430218605948959325525)⟩,⟨326529362345191879244741535,326529362345191880584946262⟩⟩,⟨⟨(-6916541575480023268223320296),(-6916541575480023268119020103)⟩,⟨362633239571387454249982703,362633239571387455636890174⟩⟩,⟨⟨(-7149796232995450590223908561),(-7149796232995450590114575892)⟩,⟨401337559888009499260859424,401337559888009500694887528⟩⟩,⟨⟨(-7379903322321855092448216240),(-7379903322321855092335032707)⟩,⟨442481073633859027251971465,442481073633859028732457979⟩⟩,⟨⟨(-7610895553025613799993794186),(-7610895553025613799876298993)⟩,⟨486365184133921562185669502,486365184133921563712851176⟩⟩] +lemma amp0_04_1_eq : ∀ k : Fin 16, amp0_0Expr 4 1 k = amp0_04_1 k := by decide +kernel +noncomputable def amp0_04_2 : Fin 16 → CBox := ![⟨⟨(-7838814889794311717522323031),(-7838814889794311717403567753)⟩,⟨532810799507346256047971152,532810799507346257621060662⟩⟩,⟨⟨(-8067414729134296309397478804),(-8067414729134296309274043651)⟩,⟨582128921652518752636485061,582128921652518754255876290⟩⟩,⟨⟨(-8293000649667702139909192669),(-8293000649667702139781628131)⟩,⟨634122796000825541502369455,634122796000825543167457375⟩⟩,⟨⟨(-8519078061542027632133447633),(-8519078061542027632001426426)⟩,⟨689112421855844525801272530,689112421855844527512218919⟩⟩,⟨⟨(-8742187647147554112927687220),(-8742187647147554112790698347)⟩,⟨746883596279985053741186582,746883596279985055497481395⟩⟩,⟨⟨(-8965612924336716944297360008),(-8965612924336716944160546690)⟩,⟨807764701541014129579087497,807764701541014131380378093⟩⟩,⟨⟨(-9186105809946619696263370702),(-9186105809946619696122375468)⟩,⟨871524335912167624362292989,871524335912167626208404411⟩⟩,⟨⟨(-9406749892287105448450722995),(-9406749892287105448306243454)⟩,⟨938498637445002215748732205,938498637445002217639667238⟩⟩,⟨⟨(-9624488142462866608491535330),(-9624488142462866608342900338)⟩,⟨1008439290896170985981410396,1008439290896170987916691851⟩⟩,⟨⟨(-9842222876484623690149307370),(-9842222876484623689996363264)⟩,⟨1081689550699808937892779960,1081689550699808939872468934⟩⟩,⟨⟨(-10057070909260472803985604891),(-10057070909260472803828420323)⟩,⟨1157984509453756894395532953,1157984509453756896419088474⟩⟩,⟨⟨(-10271769265286107331996434173),(-10271769265286107331840892203)⟩,⟨1237673886851829253733363955,1237673886851829255800095199⟩⟩,⟨⟨(-10483593810512908943043402188),(-10483593810512908942882680136)⟩,⟨1320476541130909945316629101,1320476541130909947426801109⟩⟩,⟨⟨(-10695130068233236241279021404),(-10695130068233236241114069677)⟩,⟨1406747994875915207165537087,1406747994875915209319028397⟩⟩,⟨⟨(-10903800151122990463651065824),(-10903800151122990463481131645)⟩,⟨1496191266519354413234172648,1496191266519354415430559783⟩⟩,⟨⟨(-11112050061373981234867641181),(-11112050061373981234694812041)⟩,⟨1589167008372888008489150780,1589167008372888010728112783⟩⟩] +lemma amp0_04_2_eq : ∀ k : Fin 16, amp0_0Expr 4 2 k = amp0_04_2 k := by decide +kernel +noncomputable def amp0_04_3 : Fin 16 → CBox := ![⟨⟨(-11317437004640384560960318083),(-11317437004640384560783314933)⟩,⟨1685362830663166452901145855,1685362830663166455182331897⟩⟩,⟨⟨(-11522277932889587521282296759),(-11522277932889587521100894180)⟩,⟨1785143831889703182332284111,1785143831889703184655676088⟩⟩,⟨⟨(-11724255372714411614671515876),(-11724255372714411614485556876)⟩,⟨1888182682962108549330903325,1888182682962108551696005523⟩⟩,⟨⟨(-11925566428242691906097911623),(-11925566428242691905917444145)⟩,⟨1994848235044697158097002132,1994848235044697160502063259⟩⟩,⟨⟨(-12124010340568684224181719533),(-12124010340568684223996014584)⟩,⟨2104798726123178314582079785,2104798726123178317028315766⟩⟩,⟨⟨(-12321672494270023908926112674),(-12321672494270023908736089315)⟩,⟨2218406056876965782464717209,2218406056876965784951881221⟩⟩,⟨⟨(-12516461228816132564665570161),(-12516461228816132564471355977)⟩,⟨2335314576445435295532095421,2335314576445435298059641737⟩⟩,⟨⟨(-12710357421784252649292690966),(-12710357421784252649094758317)⟩,⟨2455898522569579601386222458,2455898522569579603953944756⟩⟩,⟨⟨(-12901371741818879369034712742),(-12901371741818879368832491054)⟩,⟨2579788937451092605238366422,2579788937451092607845846250⟩⟩,⟨⟨(-13091386986347086834689109382),(-13091386986347086834485092241)⟩,⟨2707361674421677659229647081,2707361674421677661876238976⟩⟩,⟨⟨(-13278510112718882570262002093),(-13278510112718882570053830502)⟩,⟨2838235088598793423253149479,2838235088598793425938799414⟩⟩,⟨⟨(-13464531586944342173803094822),(-13464531586944342173591817139)⟩,⟨2972785918665164485631817675,2972785918665164488356142964⟩⟩,⟨⟨(-13647649245210552386382443292),(-13647649245210552386167635754)⟩,⟨3110620490533606079671096679,3110620490533606082433649490⟩⟩,⟨⟨(-13829566382342766168974942225),(-13829566382342766168756744848)⟩,⟨3252115689438438871027164948,3252115689438438873827737868⟩⟩,⟨⟨(-14008566852088077035723834549),(-14008566852088077035502052826)⟩,⟨3396866508043246226666943620,3396866508043246229505043620⟩⟩,⟨⟨(-14186271424944109324780468799),(-14186271424944109324555275688)⟩,⟨3545249230942992747182031705,3545249230942992750057423549⟩⟩] +lemma amp0_04_3_eq : ∀ k : Fin 16, amp0_0Expr 4 3 k = amp0_04_3 k := by decide +kernel +noncomputable def amp0_04_4 : Fin 16 → CBox := ![⟨⟨(-14361045590572946748274986428),(-14361045590572946748061677709)⟩,⟨3696848251602059940764019534,3696848251602059943672219629⟩⟩,⟨⟨(-14534431791978345796052445688),(-14534431791978345795833283625)⟩,⟨3852038498519526862066986777,3852038498519526865012257305⟩⟩,⟨⟨(-14704873194407792679925718275),(-14704873194407792679701329046)⟩,⟨4010394538094074041130052560,4010394538094074044111713915⟩⟩,⟨⟨(-14873837713897835544224599274),(-14873837713897835543995629960)⟩,⟨4172289179089136238215452741,4172289179089136241233126088⟩⟩,⟨⟨(-15039842602688874793829035910),(-15039842602688874793595702627)⟩,⟨4337287971014641469924569063,4337287971014641472977657657⟩⟩,⟨⟨(-15204284699849471834126035115),(-15204284699849471833887860874)⟩,⟨4505760831112826592008728334,4505760831112826595097153342⟩⟩,⟨⟨(-15365752085399789983330127361),(-15365752085399789983088659451)⟩,⟨4677265140157586061274578274,4677265140157586064397339829⟩⟩,⟨⟨(-15525573660113779854256708001),(-15525573660113779854010954006)⟩,⟨4852167143929839912933484129,4852167143929839916090638349⟩⟩,⟨⟨(-15682405365602133413266541986),(-15682405365602133413016235848)⟩,⟨5030016940501990319941702268,5030016940501990323132787897⟩⟩,⟨⟨(-15837511025409440767422829120),(-15837511025409440767172584612)⟩,⟨5211176316042701473119600223,5211176316042701476342859347⟩⟩,⟨⟨(-15989611738234159568994428434),(-15989611738234159568739437025)⟩,⟨5395189009720580224143154474,5395189009720580227399593061⟩⟩,⟨⟨(-16139908862969460002093195537),(-16139908862969460001834360638)⟩,⟨5582411551625259432493434598,5582411551625259435782486186⟩⟩,⟨⟨(-16287186185465403672884777923),(-16287186185465403672621631707)⟩,⟨5772382283440749532225403099,5772382283440749535546672869⟩⟩,⟨⟨(-16432584989301644042516573503),(-16432584989301644042250917575)⟩,⟨5965451674239977546149727803,5965451674239977549502295467⟩⟩,⟨⟨(-16574949488553341703019257432),(-16574949488553341702749285291)⟩,⟨6161153667100336567885758841,6161153667100336571269714661⟩⟩,⟨⟨(-16715363079551532482479693410),(-16715363079551532482206544548)⟩,⟨6359831856463063034104399714,6359831856463063037519027751⟩⟩] +lemma amp0_04_4_eq : ∀ k : Fin 16, amp0_0Expr 4 4 k = amp0_04_4 k := by decide +kernel +noncomputable def amp0_04_5 : Fin 16 → CBox := ![⟨⟨(-16852728336147199049787530745),(-16852728336147199049510722977)⟩,⟨6561016822954018230832931776,6561016822954018234277837127⟩⟩,⟨⟨(-16988072773390696820400068058),(-16988072773390696820119708657)⟩,⟨6765044463831361655361064819,6765044463831361658835910080⟩⟩,⟨⟨(-17120355428983751365440894769),(-17120355428983751365156538474)⟩,⟨6971443070503311881214700464,6971443070503311884719096423⟩⟩,⟨⟨(-17250549777357544676684808646),(-17250549777357544676396671841)⟩,⟨7180540011244019423182644686,7180540011244019426716194304⟩⟩,⟨⟨(-17377669580920238809525168898),(-17377669580920238809233103048)⟩,⟨7391862398344360563170433513,7391862398344360566732621183⟩⟩,⟨⟨(-17502635963581591406509666540),(-17502635963581591406244244627)⟩,⟨7605728229675375298250409694,7605728229675375301827641814⟩⟩,⟨⟨(-17624515816250218772380146947),(-17624515816250218772109188913)⟩,⟨7821664585153595835666725965,7821664585153595839272147453⟩⟩,⟨⟨(-17744179464825680159594817221),(-17744179464825680159319184004)⟩,⟨8039979240784081157731991276,8039979240784081161364915150⟩⟩,⟨⟨(-17860745463249223309335929431),(-17860745463249223309056175921)⟩,⟨8260200427262688993461068162,8260200427262688997120662548⟩⟩,⟨⟨(-17975034765783921172257642357),(-17975034765783921171973924430)⟩,⟨8482624836737701767800677249,8482624836737701771486550758⟩⟩,⟨⟨(-18086216243898398245409627786),(-18086216243898398245122732500)⟩,⟨8706783070011566469753038239,8706783070011566473464232684⟩⟩,⟨⟨(-18195062790576238009160803237),(-18195062790576238008870946372)⟩,⟨8932959862312672053653415779,8932959862312672057389469880⟩⟩,⟨⟨(-18300792359735829271883102231),(-18300792359735829271589285788)⟩,⟨9160689439812314982695545215,9160689439812314986456344163⟩⟩,⟨⟨(-18404130986383395508940690087),(-18404130986383395508644525932)⟩,⟨9390243696077110044521721722,9390243696077110048306108337⟩⟩,⟨⟨(-18504344573786966157058733262),(-18504344573786966156759310840)⟩,⟨9621161773608156741815813407,9621161773608156745623643222⟩⟩,⟨⟨(-18602113403169274023472022776),(-18602113403169274023169118565)⟩,⟨9853701827219213042732543082,9853701827219213046563568009⟩⟩] +lemma amp0_04_5_eq : ∀ k : Fin 16, amp0_0Expr 4 5 k = amp0_04_5 k := by decide +kernel +noncomputable def amp0_04_6 : Fin 16 → CBox := ![⟨⟨(-18696750288527408069864299735),(-18696750288527408069561198198)⟩,⟨10087409242170937443803505403,10087409242170937447655335406⟩⟩,⟨⟨(-18788890769439972157306529631),(-18788890769439972156999395471)⟩,⟨10322527524347395115081989293,10322527524347395118956317263⟩⟩,⟨⟨(-18877893619833286275222985404),(-18877893619833286274913876551)⟩,⟨10558609663448323540891202736,10558609663448323544786285255⟩⟩,⟨⟨(-18964350563992084740495847151),(-18964350563992084740182858415)⟩,⟨10795883592360529504842123106,10795883592360529508758641985⟩⟩,⟨⟨(-19047665466876555494635729521),(-19047665466876555494320014570)⟩,⟨11033911301948713634838712036,11033911301948713638775383607⟩⟩,⟨⟨(-19128387083605228855808821054),(-19128387083605228855489853809)⟩,⟨11272904213268192486853198212,11272904213268192490809956388⟩⟩,⟨⟨(-19205963577924666313451543929),(-19205963577924666313139780582)⟩,⟨11512434749938273348638625218,11512434749938273352608587394⟩⟩,⟨⟨(-19280901506636589597868565087),(-19280901506636589597552724547)⟩,⟨11752696866632195574910338846,11752696866632195578899783593⟩⟩,⟨⟨(-19352692612006325432339304908),(-19352692612006325432020460277)⟩,⟨11993274886021022101351384930,11993274886021022105359021749⟩⟩,⟨⟨(-19421801952477937408980535152),(-19421801952477937408659322053)⟩,⟨12234344325102447163800972262,12234344325102447167826029108⟩⟩,⟨⟨(-19487764196407347898473298652),(-19487764196407347898149138196)⟩,⟨12475502906480027985421863818,12475502906480027989464071195⟩⟩,⟨⟨(-19551003536838236781475411578),(-19551003536838236781149557876)⟩,⟨12716906720332784033328332015,12716906720332784037386474869⟩⟩,⟨⟨(-19611096979962957112399795134),(-19611096979962957112071683138)⟩,⟨12958168424575972036870399353,12958168424575972040944172245⟩⟩,⟨⟨(-19668428422817626681914998895),(-19668428422817626681583976387)⟩,⟨13199423674386312941813664162,13199423674386312945903109828⟩⟩,⟨⟨(-19722616682115287202822541901),(-19722616682115287202493691948)⟩,⟨13440301632829067574680410832,13440301632829067578781430011⟩⟩,⟨⟨(-19774005867741209800792257318),(-19774005867741209800461115762)⟩,⟨13680916491575430872871053588,13680916491575430876986224048⟩⟩] +lemma amp0_04_6_eq : ∀ k : Fin 16, amp0_0Expr 4 6 k = amp0_04_6 k := by decide +kernel +noncomputable def amp0_04_7 : Fin 16 → CBox := ![⟨⟨(-19822256137707282221146071129),(-19822256137707282220813249452)⟩,⟨13920915523151978238975351453,13920915523151978243103560859⟩⟩,⟨⟨(-19867672265723743212341243102),(-19867672265723743212006178753)⟩,⟨14160390405529449213297779689,14160390405529449217439027610⟩⟩,⟨⟨(-19909955337486662337596236790),(-19909955337486662337261708463)⟩,⟨14399008159555355448893907760,14399008159555355453045529533⟩⟩,⟨⟨(-19949371185938978984061432296),(-19949371185938978983725286939)⟩,⟨14636836876143002867116167477,14636836876143002871279261884⟩⟩,⟨⟨(-19985661464296134330058435921),(-19985661464296134329722384217)⟩,⟨14873564998014268169511282776,14873564998014268173683878499⟩⟩,⟨⟨(-20019053406570060799299419174),(-20019053406570060798961665978)⟩,⟨15109235930931520580833456706,15109235930931520585016462785⟩⟩,⟨⟨(-20049328924928558215444476499),(-20049328924928558215106386430)⟩,⟨15343561247963450574485128887,15343561247963450578676829340⟩⟩,⟨⟨(-20076676944420042320027698537),(-20076676944420042319689289740)⟩,⟨15576558545206277166542279829,15576558545206277170742195844⟩⟩,⟨⟨(-20100919377628340405082643557),(-20100919377628340404743861437)⟩,⟨15807964269782240598429633924,15807964269782240602637067102⟩⟩,⟨⟨(-20122207080164254967898611726),(-20122207080164254967559238843)⟩,⟨16037769055381219776741998307,16037769055381219780956695541⟩⟩,⟨⟨(-20140401755222903162252778134),(-20140401755222903161913514730)⟩,⟨16265736002536586694890698172,16265736002536586699111394510⟩⟩,⟨⟨(-20155616379228916837430273158),(-20155616379228916837090986647)⟩,⟨16491827599637104461312540339,16491827599637104465538869581⟩⟩,⟨⟨(-20167752283870677596832304432),(-20167752283870677596493643022)⟩,⟨16715835416165790951104811605,16715835416165790955335489515⟩⟩,⟨⟨(-20176884708283040085035302454),(-20176884708283040084697495659)⟩,⟨16937692580095708515081156756,16937692580095708519315538970⟩⟩,⟨⟨(-20182954497414680396592359180),(-20182954497414680396255963602)⟩,⟨17157220982235930503929863747,17157220982235930508166743738⟩⟩,⟨⟨(-20185999247333360627845958271),(-20185999247333360627511718103)⟩,⟨17374323140598177713329272427,17374323140598177717567508406⟩⟩] +lemma amp0_04_7_eq : ∀ k : Fin 16, amp0_0Expr 4 7 k = amp0_04_7 k := by decide +kernel +noncomputable def amp0_04_8 : Fin 16 → CBox := ![⟨⟨(-20185999247333360627845958271),(-20185999247333360627511718103)⟩,⟨17588853157330318774687240427,17588853157330318778927899005⟩⟩,⟨⟨(-20182954497414680396592359180),(-20182954497414680396255963602)⟩,⟨17800681654137070616072539307,17800681654137070620317100519⟩⟩,⟨⟨(-20176884708283040085035302454),(-20176884708283040084697495659)⟩,⟨18009696873110062208840327838,18009696873110062213087456131⟩⟩,⟨⟨(-20167752283870677596832304432),(-20167752283870677596493643022)⟩,⟨18215736213961485595465332227,18215736213961485599714086140⟩⟩,⟨⟨(-20155616379228916837430273158),(-20155616379228916837090986647)⟩,⟨18418724027054831475448484967,18418724027054831479697914638⟩⟩,⟨⟨(-20140401755222903162252778134),(-20140401755222903161913514730)⟩,⟨18618463122358876428802436197,18618463122358876433051529336⟩⟩,⟨⟨(-20122207080164254967898611726),(-20122207080164254967559238843)⟩,⟨18814915967885458432090183687,18814915967885458436338346160⟩⟩,⟨⟨(-20100919377628340405082643557),(-20100919377628340404743861437)⟩,⟨19007849371115820754795080258,19007849371115820759041187393⟩⟩,⟨⟨(-20076676944420042320027698537),(-20076676944420042319689289740)⟩,⟨19197265969675916919579643817,19197265969675916923823117621⟩⟩,⟨⟨(-20049328924928558215444476499),(-20049328924928558215106386430)⟩,⟨19382895107673109071359801907,19382895107673109075600280800⟩⟩,⟨⟨(-20019053406570060799299419174),(-20019053406570060798961665978)⟩,⟨19564781688682637245132397046,19564781688682637249369140058⟩⟩,⟨⟨(-19985661464296134330058435921),(-19985661464296134329722384217)⟩,⟨19742616081018041982609883185,19742616081018041986841075391⟩⟩,⟨⟨(-19949371185938978984061432296),(-19949371185938978983725286939)⟩,⟨19916487596953897018420057153,19916487596953897022646691508⟩⟩,⟨⟨(-19909955337486662337596236790),(-19909955337486662337261708463)⟩,⟨20086046061398696906933322090,20086046061398696911153265882⟩⟩,⟨⟨(-19867672265723743212341243102),(-19867672265723743212006178753)⟩,⟨20251427386831146279536354422,20251427386831146283751054683⟩⟩,⟨⟨(-19822256137707282221146071129),(-19822256137707282220813249452)⟩,⟨20412239228001054480799101956,20412239228001054485005254795⟩⟩] +lemma amp0_04_8_eq : ∀ k : Fin 16, amp0_0Expr 4 8 k = amp0_04_8 k := by decide +kernel +noncomputable def amp0_04_9 : Fin 16 → CBox := ![⟨⟨(-19774005867741209800792257318),(-19774005867741209800461115762)⟩,⟨20568666340517449765630918345,20568666340517449769828281515⟩⟩,⟨⟨(-19722616682115287202822541901),(-19722616682115287202493691948)⟩,⟨20720272518800126887066772816,20720272518800126891254287512⟩⟩,⟨⟨(-19668428422817626681914998895),(-19668428422817626681583976387)⟩,⟨20867293658965616891199838000,20867293658965616895381483961⟩⟩,⟨⟨(-19611096979962957112399795134),(-19611096979962957112071683138)⟩,⟨21009247936880438428516604807,21009247936880438432686534759⟩⟩,⟨⟨(-19551003536838236781475411578),(-19551003536838236781149557876)⟩,⟨21146424744429860185963545465,21146424744429860190121643234⟩⟩,⟨⟨(-19487764196407347898473298652),(-19487764196407347898149138196)⟩,⟨21278294807619171991524938389,21278294807619171995671387048⟩⟩,⟨⟨(-19421801952477937408980535152),(-19421801952477937408659322053)⟩,⟨21405203431129762101001647490,21405203431129762105134327833⟩⟩,⟨⟨(-19352692612006325432339304908),(-19352692612006325432020460277)⟩,⟨21526571981236779144171095295,21526571981236779148290151990⟩⟩,⟨⟨(-19280901506636589597868565087),(-19280901506636589597552724547)⟩,⟨21642804158593692355437012284,21642804158593692359540909986⟩⟩,⟨⟨(-19205963577924666313451543929),(-19205963577924666313139780582)⟩,⟨21753269975344588900365129233,21753269975344588904452232228⟩⟩,⟨⟨(-19128387083605228855808821054),(-19128387083605228855489853809)⟩,⟨21858434082380325691726864761,21858434082380325695809288621⟩⟩,⟨⟨(-19047665466876555494635729521),(-19047665466876555494320014570)⟩,⟨21957613052256640453649179594,21957613052256640457714584829⟩⟩,⟨⟨(-18964350563992084740495847151),(-18964350563992084740182858415)⟩,⟨22051335117021254429726982767,22051335117021254433775164728⟩⟩,⟨⟨(-18877893619833286275222985404),(-18877893619833286274913876551)⟩,⟨22138861225983276183374994869,22138861225983276187404182544⟩⟩,⟨⟨(-18788890769439972157306529631),(-18788890769439972156999395471)⟩,⟨22220785906184532923214812386,22220785906184532927226499676⟩⟩,⟨⟨(-18696750288527408069864299735),(-18696750288527408069561198198)⟩,⟨22296312193986599243018271787,22296312193986599247009543274⟩⟩] +lemma amp0_04_9_eq : ∀ k : Fin 16, amp0_0Expr 4 9 k = amp0_04_9 k := by decide +kernel +noncomputable def amp0_04_10 : Fin 16 → CBox := ![⟨⟨(-18602113403169274023472022776),(-18602113403169274023169118565)⟩,⟨22366103715227964309829212306,22366103715227964313803834275⟩⟩,⟨⟨(-18504344573786966157058733262),(-18504344573786966156759310840)⟩,⟨22429303188952330492176479655,22429303188952330496130139452⟩⟩,⟨⟨(-18404130986383395508940690087),(-18404130986383395508644525932)⟩,⟨22486646241491648379364008093,22486646241491648383296242601⟩⟩,⟨⟨(-18300792359735829271883102231),(-18300792359735829271589285788)⟩,⟨22537212746018467637488095886,22537212746018467641399549863⟩⟩,⟨⟨(-18195062790576238009160803237),(-18195062790576238008870946372)⟩,⟨22581813337871331057019506621,22581813337871331060907403922⟩⟩,⟨⟨(-18086216243898398245409627786),(-18086216243898398245122732500)⟩,⟨22619462381098000780239752600,22619462381098000784104926557⟩⟩,⟨⟨(-17975034765783921172257642357),(-17975034765783921171973924430)⟩,⟨22651048645416984010922648925,22651048645416984014764119258⟩⟩,⟨⟨(-17860745463249223309335929431),(-17860745463249223309056175921)⟩,⟨22675518176140289617210902519,22675518176140289621027205308⟩⟩,⟨⟨(-17744179464825680159594817221),(-17744179464825680159319184004)⟩,⟨22693841130914327062960329256,22693841130914327066750454287⟩⟩,⟨⟨(-17624515816250218772380146947),(-17624515816250218772109188913)⟩,⟨22704892267393046156398562465,22704892267393046160161411709⟩⟩,⟨⟨(-17502635963581591406509666540),(-17502635963581591406244244627)⟩,⟨22709726525630194880487677081,22709726525630194884221414190⟩⟩,⟨⟨(-17377669580920238809525168898),(-17377669580920238809233103048)⟩,⟨22707144232953652504676271822,22707144232953652508422448343⟩⟩,⟨⟨(-17250549777357544676684808646),(-17250549777357544676396671841)⟩,⟨22698288661635232227010215492,22698288661635232230728391336⟩⟩,⟨⟨(-17120355428983751365440894769),(-17120355428983751365156538474)⟩,⟨22681882376134207318082646229,22681882376134207321772629634⟩⟩,⟨⟨(-16988072773390696820400068058),(-16988072773390696820119708657)⟩,⟨22659160702358851756540923192,22659160702358851760201745116⟩⟩,⟨⟨(-16852728336147199049787530745),(-16852728336147199049510722977)⟩,⟨22628764901408639634855583693,22628764901408639638487381107⟩⟩] +lemma amp0_04_10_eq : ∀ k : Fin 16, amp0_0Expr 4 10 k = amp0_04_10 k := by decide +kernel +noncomputable def amp0_04_11 : Fin 16 → CBox := ![⟨⟨(-16715363079551532482479693410),(-16715363079551532482206544548)⟩,⟨22592026264281164505611269889,22592026264281164509213128296⟩⟩,⟨⟨(-16574949488553341703019257432),(-16574949488553341702749285291)⟩,⟨22547500979961828593136052798,22547500979961828596708285023⟩⟩,⟨⟨(-16432584989301644042516573503),(-16432584989301644042250917575)⟩,⟨22496620426924145854884209631,22496620426924145858424613138⟩⟩,⟨⟨(-16287186185465403672884777923),(-16287186185465403672621631707)⟩,⟨22437851702119264962765185144,22437851702119264966275791905⟩⟩,⟨⟨(-16139908862969460002093195537),(-16139908862969460001834360638)⟩,⟨22372730628569073848692068959,22372730628569073852169684339⟩⟩,⟨⟨(-15989611738234159568994428434),(-15989611738234159568739437025)⟩,⟨22299630914200695658996923776,22299630914200695662441829548⟩⟩,⟨⟨(-15837511025409440767422829120),(-15837511025409440767172584612)⟩,⟨22220197445398718318392117998,22220197445398718321802423144⟩⟩,⟨⟨(-15682405365602133413266541986),(-15682405365602133413016235848)⟩,⟨22132705937611679216373892339,22132705937611679219755928543⟩⟩,⟨⟨(-15525573660113779854256708001),(-15525573660113779854010954006)⟩,⟨22038915252040322516278043330,22038915252040322519624612041⟩⟩,⟨⟨(-15365752085399789983330127361),(-15365752085399789983088659451)⟩,⟨21936998168262280552975865671,21936998168262280556287006698⟩⟩,⟨⟨(-15204284699849471834126035115),(-15204284699849471833887860874)⟩,⟨21828832761768576203557612186,21828832761768576206834153806⟩⟩,⟨⟨(-15039842602688874793829035910),(-15039842602688874793595702627)⟩,⟨21712483554681429438258411386,21712483554681429441497696630⟩⟩,⟨⟨(-14873837713897835544224599274),(-14873837713897835543995629960)⟩,⟨21589953444916033471512895656,21589953444916033474714946121⟩⟩,⟨⟨(-14704873194407792679925718275),(-14704873194407792679701329046)⟩,⟨21459192953477879618515153857,21459192953477879621679302386⟩⟩,⟨⟨(-14534431791978345796052445688),(-14534431791978345795833283625)⟩,⟨21322335824331331318124286280,21322335824331331321249020845⟩⟩,⟨⟨(-14361045590572946748274986428),(-14361045590572946748061677709)⟩,⟨21177212361083276811619813123,21177212361083276814703764087⟩⟩] +lemma amp0_04_11_eq : ∀ k : Fin 16, amp0_0Expr 4 11 k = amp0_04_11 k := by decide +kernel +noncomputable def amp0_04_12 : Fin 16 → CBox := ![⟨⟨(-14186271424944109324780468799),(-14186271424944109324555275688)⟩,⟨21026093647022739429057617061,21026093647022739432126396022⟩⟩,⟨⟨(-14008566852088077035723834549),(-14008566852088077035502052826)⟩,⟨20866683020998512832079967866,20866683020998512835110720351⟩⟩,⟨⟨(-13829566382342766168974942225),(-13829566382342766168756744848)⟩,⟨20701395931425746113772905308,20701395931425746116764868170⟩⟩,⟨⟨(-13647649245210552386382443292),(-13647649245210552386167635754)⟩,⟨20527801406050109828715512184,20527801406050109831668560148⟩⟩,⟨⟨(-13464531586944342173803094822),(-13464531586944342173591817139)⟩,⟨20348466890038440325434571159,20348466890038440328347925520⟩⟩,⟨⟨(-13278510112718882570262002093),(-13278510112718882570053830502)⟩,⟨20160819075447450988799364711,20160819075447450991673339575⟩⟩,⟨⟨(-13091386986347086834689109382),(-13091386986347086834485092241)⟩,⟨19967585727477484869340764487,19967585727477484872173306210⟩⟩,⟨⟨(-12901371741818879369034712742),(-12901371741818879368832491054)⟩,⟨19766042406712590490185008269,19766042406712590492979307920⟩⟩,⟨⟨(-12710357421784252649292690966),(-12710357421784252649094758317)⟩,⟨19559086314320908306801848050,19559086314320908309553545594⟩⟩,⟨⟨(-12516461228816132564665570161),(-12516461228816132564471355977)⟩,⟨19343832202830089353367018613,19343832202830089356076682867⟩⟩,⟨⟨(-12321672494270023908926112674),(-12321672494270023908736089315)⟩,⟨19123356737422651702477381024,19123356737422651705143865816⟩⟩,⟨⟨(-12124010340568684224181719533),(-12124010340568684223996014584)⟩,⟨18894603175232230221432054596,18894603175232230224054737942⟩⟩,⟨⟨(-11925566428242691906097911623),(-11925566428242691905917444145)⟩,⟨18660838727709348900590255910,18660838727709348903167221774⟩⟩,⟨⟨(-11724255372714411614671515876),(-11724255372714411614485556876)⟩,⟨18418823303491636530871825143,18418823303491636533419577276⟩⟩,⟨⟨(-11522277932889587521282296759),(-11522277932889587521100894180)⟩,⟨18172026966804761009007918388,18172026966804761011510364831⟩⟩,⟨⟨(-11317437004640384560960318083),(-11317437004640384560783314933)⟩,⟨17917013072834107301087189656,17917013072834107303544148375⟩⟩] +lemma amp0_04_12_eq : ∀ k : Fin 16, amp0_0Expr 4 12 k = amp0_04_12 k := by decide +kernel +noncomputable def amp0_04_13 : Fin 16 → CBox := ![⟨⟨(-11112050061373981234867641181),(-11112050061373981234694812041)⟩,⟨17657468274175708680188138932,17657468274175708682599517636⟩⟩,⟨⟨(-10903800151122990463651065824),(-10903800151122990463481131645)⟩,⟨17389744590802867492331704918,17389744590802867494699230085⟩⟩,⟨⟨(-10695130068233236241279021404),(-10695130068233236241114069677)⟩,⟨17117760676861643333563227728,17117760676861643335883269424⟩⟩,⟨⟨(-10483593810512908943043402188),(-10483593810512908942882680136)⟩,⟨16837640584592057544471825685,16837640584592057546745151928⟩⟩,⟨⟨(-10271769265286107331996434173),(-10271769265286107331840892203)⟩,⟨16553552364248146333670504541,16553552364248146335895232139⟩⟩,⟨⟨(-10057070909260472803985604891),(-10057070909260472803828420323)⟩,⟨16261373280708308076417602458,16261373280708308078604397432⟩⟩,⟨⟨(-9842222876484623690149307370),(-9842222876484623689996363264)⟩,⟨15965540530788261957833190143,15965540530788261959972333860⟩⟩,⟨⟨(-9624488142462866608491535330),(-9624488142462866608342900338)⟩,⟨15661663168693720854753090313,15661663168693720856844027495⟩⟩,⟨⟨(-9406749892287105448450722995),(-9406749892287105448306243454)⟩,⟨15354470110089328269489359728,15354470110089328271532038883⟩⟩,⟨⟨(-9186105809946619696263370702),(-9186105809946619696122375468)⟩,⟨15039277650619030656681196351,15039277650619030658676368362⟩⟩,⟨⟨(-8965612924336716944297360008),(-8965612924336716944160546690)⟩,⟨14721132404406360006771802045,14721132404406360008718165288⟩⟩,⟨⟨(-8742187647147554112927687220),(-8742187647147554112790698347)⟩,⟨14395029577880599341930888579,14395029577880599343835158679⟩⟩,⟨⟨(-8519078061542027632133447633),(-8519078061542027632001426426)⟩,⟨14066363614380330167983355379,14066363614380330169836883900⟩⟩,⟨⟨(-8293000649667702139909192669),(-8293000649667702139781628131)⟩,⟨13729775676425341994750786774,13729775676425341996554016661⟩⟩,⟨⟨(-8067414729134296309397478804),(-8067414729134296309274043651)⟩,⟨13391043274937594636539804206,13391043274937594638293195961⟩⟩,⟨⟨(-7838814889794311717522323031),(-7838814889794311717403567753)⟩,⟨13044414860743831215550721551,13044414860743831217252875495⟩⟩] +lemma amp0_04_13_eq : ∀ k : Fin 16, amp0_0Expr 4 13 k = amp0_04_13 k := by decide +kernel +noncomputable def amp0_04_14 : Fin 16 → CBox := ![⟨⟨(-7610895553025613799993794186),(-7610895553025613799876298993)⟩,⟨12696092604806469773620907980,12696092604806469775277394841⟩⟩,⟨⟨(-7379903322321855092448216240),(-7379903322321855092335032707)⟩,⟨12339886435573950626240105820,12339886435573950627845444006⟩⟩,⟨⟨(-7149796232995450590223908561),(-7149796232995450590114575892)⟩,⟨11982472779424677451598508828,11982472779424677453153483367⟩⟩,⟨⟨(-6916541575480023268223320296),(-6916541575480023268119020103)⟩,⟨11617168181822501710371794804,11617168181822501711873903999⟩⟩,⟨⟨(-6684395430218605949061858605),(-6684395430218605948959325525)⟩,⟨11251183140674657520988159967,11251183140674657522442897710⟩⟩,⟨⟨(-6449007720194114033000118412),(-6449007720194114032901909281)⟩,⟨10877274318968929076677754508,10877274318968929078080347276⟩⟩,⟨⟨(-6214974678023852757594736310),(-6214974678023852757498984594)⟩,⟨10503259362946582408285795321,10503259362946582409639519948⟩⟩,⟨⟨(-5977582006447996121535663247),(-5977582006447996121444465977)⟩,⟨10121253328706587499599894021,10121253328706587500900640409⟩⟩,⟨⟨(-5741818330713242039227034695),(-5741818330713242039140118233)⟩,⟨9739771605523419721643905614,9739771605523419722892248549⟩⟩,⟨⟨(-5502546547528761706034679332),(-5502546547528761705950640777)⟩,⟨9350185610935281612202779377,9350185610935281613400573739⟩⟩,⟨⟨(-5265213576138587389237030433),(-5265213576138587389157556449)⟩,⟨8961822700298428807532176298,8961822700298428808676814463⟩⟩,⟨⟨(-5024184917995322593046149223),(-5024184917995322592969826566)⟩,⟨8565180917535639092670718913,8565180917535639093763962213⟩⟩,⟨⟨(-4785450558516348021828663502),(-4785450558516348021755454716)⟩,⟨8170546460019593084467581181,8170546460019593085509784540⟩⟩,⟨⟨(-4542781601919094067374177738),(-4542781601919094067305507896)⟩,⟨7767375458793477015965658681,7767375458793477016953744630⟩⟩,⟨⟨(-4302822699838685573537137465),(-4302822699838685573471893292)⟩,⟨7367106264961066708748787557,7367106264961066709685084928⟩⟩,⟨⟨(-4058621167164034576813855672),(-4058621167164034576752189907)⟩,⟨6957928472230496261474955112,6957928472230496262358443607⟩⟩] +lemma amp0_04_14_eq : ∀ k : Fin 16, amp0_0Expr 4 14 k = amp0_04_14 k := by decide +kernel +noncomputable def amp0_04_15 : Fin 16 → CBox := ![⟨⟨(-3817627397948821483312469083),(-3817627397948821483254566088)⟩,⟨6552694241467626957994903644,6552694241467626958825743998⟩⟩,⟨⟨(-3571986906618049826291947312),(-3571986906618049826237983931)⟩,⟨6138017810170665216912364306,6138017810170665217689468657⟩⟩,⟨⟨(-3330167486215396474169756328),(-3330167486215396474119757745)⟩,⟨5728531704276193866865617856,5728531704276193867589602392⟩⟩,⟨⟨(-3083158362756607818416153897),(-3083158362756607818369669696)⟩,⟨5308833540397804544713285512,5308833540397804545383972013⟩⟩,⟨⟨(-2840754361792469275133374932),(-2840754361792469275090530138)⟩,⟨4895872438890964070015221518,4895872438890964070633184945⟩⟩,⟨⟨(-2592406288112938839156297101),(-2592406288112938839117294414)⟩,⟨4471567058204486103381338461,4471567058204486103945160075⟩⟩,⟨⟨(-2349715165212016044462159387),(-2349715165212016044427086308)⟩,⟨4056012956547657430411209038,4056012956547657430921770329⟩⟩,⟨⟨(-2099980978840482901196603398),(-2099980978840482901165109583)⟩,⟨3627388678185041823063491419,3627388678185041823520077631⟩⟩,⟨⟨(-1857411230393376142141328196),(-1857411230393376142113629862)⟩,⟨3210322231328053165027510312,3210322231328053165431052465⟩⟩,⟨⟨(-1606080516929194707874514870),(-1606080516929194707850675545)⟩,⟨2777390389894262929800628310,2777390389894262930149393658⟩⟩,⟨⟨(-1364294426607166605424695495),(-1364294426607166605404637937)⟩,⟨2360337035568339227378833461,2360337035568339227674753423⟩⟩,⟨⟨(-1110742379793587805544568437),(-1110742379793587805528361454)⟩,⟨1922395849439087974104637962,1922395849439087974345358615⟩⟩,⟨⟨(-871132832163727548689651365),(-871132832163727548677185017)⟩,⟨1508150541903205266167055568,1508150541903205266355407071⟩⟩,⟨⟨(-613314789282883314763260866),(-613314789282883314754638658)⟩,⟨1062042427970903184423289440,1062042427970903184555632423⟩⟩,⟨⟨(-380453151319111964411351249),(-380453151319111964406521959)⟩,⟨658908367719719655141464818,658908367719719655222656451⟩⟩,⟨⟨(-108088285328156058982599759),(-108088285328156058981540162)⟩,⟨187212639762263632437855504,187212639762263632460381448⟩⟩] +lemma amp0_04_15_eq : ∀ k : Fin 16, amp0_0Expr 4 15 k = amp0_04_15 k := by decide +kernel +noncomputable def amp0_04 : Fin 16 → Fin 16 → CBox := ![amp0_04_0,amp0_04_1,amp0_04_2,amp0_04_3,amp0_04_4,amp0_04_5,amp0_04_6,amp0_04_7,amp0_04_8,amp0_04_9,amp0_04_10,amp0_04_11,amp0_04_12,amp0_04_13,amp0_04_14,amp0_04_15] +lemma amp0_04_eq (i k : Fin 16) : amp0_0Expr 4 i k = amp0_04 i k := by + fin_cases i + · exact amp0_04_0_eq k + · exact amp0_04_1_eq k + · exact amp0_04_2_eq k + · exact amp0_04_3_eq k + · exact amp0_04_4_eq k + · exact amp0_04_5_eq k + · exact amp0_04_6_eq k + · exact amp0_04_7_eq k + · exact amp0_04_8_eq k + · exact amp0_04_9_eq k + · exact amp0_04_10_eq k + · exact amp0_04_11_eq k + · exact amp0_04_12_eq k + · exact amp0_04_13_eq k + · exact amp0_04_14_eq k + · exact amp0_04_15_eq k +noncomputable def amp0_05_0 : Fin 16 → CBox := ![⟨⟨(-1017365712714798119321),(-1017365712714798119303)⟩,⟨0,0⟩⟩,⟨⟨(-32227844834901915228914),(-32227844834901915228293)⟩,⟨0,0⟩⟩,⟨⟨(-144307603078629676795440),(-144307603078629676792476)⟩,⟨0,0⟩⟩,⟨⟨(-401710817432016743329331),(-401710817432016743320991)⟩,⟨0,0⟩⟩,⟨⟨(-846618630911081865613070),(-846618630911081865595272)⟩,⟨0,0⟩⟩,⟨⟨(-1553203743542669652050032),(-1553203743542669652017226)⟩,⟨0,0⟩⟩,⟨⟨(-2553427679062347663274071),(-2553427679062347663219796)⟩,⟨0,0⟩⟩,⟨⟨(-3930825950684612502729165),(-3930825950684612502645361)⟩,⟨0,0⟩⟩,⟨⟨(-5707149034948221457831324),(-5707149034948221457709189)⟩,⟨0,0⟩⟩,⟨⟨(-7974992912616157788973303),(-7974992912616157788803222)⟩,⟨0,0⟩⟩,⟨⟨(-10745843359115808218419703),(-10745843359115808218189282)⟩,⟨0,0⟩⟩,⟨⟨(-14121091280701553281758774),(-14121091280701553281455476)⟩,⟨0,0⟩⟩,⟨⟨(-18101889125021378555186890),(-18101889125021378554798218)⟩,⟨0,0⟩⟩,⟨⟨(-22798164690230290672242914),(-22798164690230290671754863)⟩,⟨0,0⟩⟩,⟨⟨(-28200671625299007329227057),(-28200671625299007328620746)⟩,⟨0,0⟩⟩,⟨⟨(-34427613720176448927468864),(-34427613720176448926726625)⟩,⟨0,0⟩⟩] +lemma amp0_05_0_eq : ∀ k : Fin 16, amp0_0Expr 5 0 k = amp0_05_0 k := by decide +kernel +noncomputable def amp0_05_1 : Fin 16 → CBox := ![⟨⟨(-41459290719596024022572080),(-41459290719596024021677183)⟩,⟨0,0⟩⟩,⟨⟨(-49421914614835276705674313),(-49421914614835276704609058)⟩,⟨0,0⟩⟩,⟨⟨(-58285289887787186846646188),(-58285289887787186845392655)⟩,⟨0,0⟩⟩,⟨⟨(-68183360397692089973599004),(-68183360397692089972120169)⟩,⟨0,0⟩⟩,⟨⟨(-79075409598275565814789512),(-79075409598275565813082958)⟩,⟨0,0⟩⟩,⟨⟨(-91102827691590655631504501),(-91102827691590655629547156)⟩,⟨0,0⟩⟩,⟨⟨(-104214368082311430485667936),(-104214368082311430483410322)⟩,⟨0,0⟩⟩,⟨⟨(-118558572418822139901809339),(-118558572418822139899256927)⟩,⟨0,0⟩⟩,⟨⟨(-134073672582852005913933433),(-134073672582852005911031098)⟩,⟨0,0⟩⟩,⟨⟨(-150915057458186184577820425),(-150915057458186184574530728)⟩,⟨0,0⟩⟩,⟨⟨(-169010464087999568987596133),(-169010464087999568983942109)⟩,⟨0,0⟩⟩,⟨⟨(-188521815248313382696613204),(-188521815248313382692516281)⟩,⟨0,0⟩⟩,⟨⟨(-209366398483646597106911142),(-209366398483646597102415613)⟩,⟨0,0⟩⟩,⟨⟨(-231712348237249836308951574),(-231712348237249836303926834)⟩,⟨0,0⟩⟩,⟨⟨(-255466566973823129190432188),(-255466566973823129184880861)⟩,⟨0,0⟩⟩,⟨⟨(-280803069984181516268335015),(-280803069984181516262204349)⟩,⟨0,0⟩⟩] +lemma amp0_05_1_eq : ∀ k : Fin 16, amp0_0Expr 5 1 k = amp0_05_1 k := by decide +kernel +noncomputable def amp0_05_2 : Fin 16 → CBox := ![⟨⟨(-307618458522706084057722309),(-307618458522706084051094961)⟩,⟨0,0⟩⟩,⟨⟨(-336092289619148268644092817),(-336092289619148268636800808)⟩,⟨0,0⟩⟩,⟨⟨(-366110966970354771076915514),(-366110966970354771068942300)⟩,⟨0,0⟩⟩,⟨⟨(-397859242260386786518384314),(-397859242260386786509673275)⟩,⟨0,0⟩⟩,⟨⟨(-431213445365565143548508820),(-431213445365565143538993191)⟩,⟨0,0⟩⟩,⟨⟨(-466363167876582221842856889),(-466363167876582221832755987)⟩,⟨0,0⟩⟩,⟨⟨(-503174809944199807321989869),(-503174809944199807311046913)⟩,⟨0,0⟩⟩,⟨⟨(-541842440962969024135391917),(-541842440962969024123601326)⟩,⟨0,0⟩⟩,⟨⟨(-582222696060299641887781073),(-582222696060299641875063038)⟩,⟨0,0⟩⟩,⟨⟨(-624513753276140037131427559),(-624513753276140037117724339)⟩,⟨0,0⟩⟩,⟨⟨(-668562668250543284525315132),(-668562668250543284510585430)⟩,⟨0,0⟩⟩,⟨⟨(-714571351742874040395573774),(-714571351742874040380176524)⟩,⟨0,0⟩⟩,⟨⟨(-762377486480516795387991724),(-762377486480516795371421312)⟩,⟨0,0⟩⟩,⟨⟨(-812186333523575931107597971),(-812186333523575931089868108)⟩,⟨0,0⟩⟩,⟨⟨(-863826430484116377594998124),(-863826430484116377576001202)⟩,⟨0,0⟩⟩,⟨⟨(-917506000071359153558566515),(-917506000071359153538415772)⟩,⟨0,0⟩⟩] +lemma amp0_05_2_eq : ∀ k : Fin 16, amp0_0Expr 5 2 k = amp0_05_2 k := by decide +kernel +noncomputable def amp0_05_3 : Fin 16 → CBox := ![⟨⟨(-973044683965568815881872493),(-973044683965568815860418425)⟩,⟨0,0⟩⟩,⟨⟨(-1030653271883720175211179501),(-1030653271883720175188345611)⟩,⟨0,0⟩⟩,⟨⟨(-1090142780287363173246301208),(-1090142780287363173222021331)⟩,⟨0,0⟩⟩,⟨⟨(-1151726165495505753605907759),(-1151726165495505753581091878)⟩,⟨0,0⟩⟩,⟨⟨(-1215206111117198395355499826),(-1215206111117198395329092959)⟩,⟨0,0⟩⟩,⟨⟨(-1280797334109812439666899848),(-1280797334109812439638929848)⟩,⟨0,0⟩⟩,⟨⟨(-1348294499353228944367812267),(-1348294499353228944338240409)⟩,⟨0,0⟩⟩,⟨⟨(-1417913673107950989731131974),(-1417913673107950989699949813)⟩,⟨0,0⟩⟩,⟨⟨(-1489441837489806940281661168),(-1489441837489806940248755484)⟩,⟨0,0⟩⟩,⟨⟨(-1563095991521031544081405797),(-1563095991521031544047009336)⟩,⟨0,0⟩⟩,⟨⟨(-1638655792425954715313844930),(-1638655792425954715277632927)⟩,⟨0,0⟩⟩,⟨⟨(-1716338750384461640060584209),(-1716338750384461640022625884)⟩,⟨0,0⟩⟩,⟨⟨(-1795917577556343213068135676),(-1795917577556343213028332389)⟩,⟨0,0⟩⟩,⟨⟨(-1877609868733088065836084692),(-1877609868733088065794393165)⟩,⟨0,0⟩⟩,⟨⟨(-1961181792819992281960842248),(-1961181792819992281917188640)⟩,⟨0,0⟩⟩,⟨⟨(-2046850597829250582893494965),(-2046850597829250582847841239)⟩,⟨0,0⟩⟩] +lemma amp0_05_3_eq : ∀ k : Fin 16, amp0_0Expr 5 3 k = amp0_05_3 k := by decide +kernel +noncomputable def amp0_05_4 : Fin 16 → CBox := ![⟨⟨(-2134376333215646664597672115),(-2134376333215646664552247059)⟩,⟨0,0⟩⟩,⟨⟨(-2223975464049050681638407685),(-2223975464049050681590566318)⟩,⟨0,0⟩⟩,⟨⟨(-2315402366125218526104187284),(-2315402366125218526053960833)⟩,⟨0,0⟩⟩,⟨⟨(-2408872280684075508343235146),(-2408872280684075508290648207)⟩,⟨0,0⟩⟩,⟨⟨(-2504134377618229003904632930),(-2504134377618229003849667590)⟩,⟨0,0⟩⟩,⟨⟨(-2601402228747062345458206934),(-2601402228747062345400705091)⟩,⟨0,0⟩⟩,⟨⟨(-2700420287741234993809296048),(-2700420287741234993749471276)⟩,⟨0,0⟩⟩,⟨⟨(-2801400006700950695991410538),(-2801400006700950695929017744)⟩,⟨0,0⟩⟩,⟨⟨(-2904081634627201915039832444),(-2904081634627201914974773042)⟩,⟨0,0⟩⟩,⟨⟨(-3008674048861856004873369378),(-3008674048861856004806436930)⟩,⟨0,0⟩⟩,⟨⟨(-3114913827091087448855089391),(-3114913827091087448785337097)⟩,⟨0,0⟩⟩,⟨⟨(-3223006812058119979807468030),(-3223006812058119979734993278)⟩,⟨0,0⟩⟩,⟨⟨(-3332686465209943392520001300),(-3332686465209943392444665021)⟩,⟨0,0⟩⟩,⟨⟨(-3444155129960154742195319605),(-3444155129960154742117415557)⟩,⟨0,0⟩⟩,⟨⟨(-3557143728219029242853691824),(-3557143728219029242772799972)⟩,⟨0,0⟩⟩,⟨⟨(-3671850634329706810257738954),(-3671850634329706810174027533)⟩,⟨0,0⟩⟩] +lemma amp0_05_4_eq : ∀ k : Fin 16, amp0_0Expr 5 4 k = amp0_05_4 k := by decide +kernel +noncomputable def amp0_05_5 : Fin 16 → CBox := ![⟨⟨(-3788004828890165632244548911),(-3788004828890165632157877215)⟩,⟨0,0⟩⟩,⟨⟨(-3905800242272824151793590144),(-3905800242272824151703900678)⟩,⟨0,0⟩⟩,⟨⟨(-4024964533395238303038525162),(-4024964533395238302945673287)⟩,⟨0,0⟩⟩,⟨⟨(-4145686708418613028898361495),(-4145686708418613028802317316)⟩,⟨0,0⟩⟩,⟨⟨(-4267693745496789285283597948),(-4267693745496789285184289296)⟩,⟨0,0⟩⟩,⟨⟨(-4391169240786213742395516085),(-4391169240786213742300525619)⟩,⟨0,0⟩⟩,⟨⟨(-4515840153749391089816802117),(-4515840153749391089718170409)⟩,⟨0,0⟩⟩,⟨⟨(-4641884178945692238598728609),(-4641884178945692238496580528)⟩,⟨0,0⟩⟩,⟨⟨(-4769028940240375246158751690),(-4769028940240375246053197123)⟩,⟨0,0⟩⟩,⟨⟨(-4897445732925117418903482392),(-4897445732925117418794469729)⟩,⟨0,0⟩⟩,⟨⟨(-5026863549246854131609615911),(-5026863549246854131497327942)⟩,⟨0,0⟩⟩,⟨⟨(-5157446781166343516634854923),(-5157446781166343516519274895)⟩,⟨0,0⟩⟩,⟨⟨(-5288926514038202104364738897),(-5288926514038202104245562827)⟩,⟨0,0⟩⟩,⟨⟨(-5421459725686305869888716221),(-5421459725686305869766323961)⟩,⟨0,0⟩⟩,⟨⟨(-5554780339909606553422151517),(-5554780339909606553296256534)⟩,⟨0,0⟩⟩,⟨⟨(-5689037402459319915583889545),(-5689037402459319915454341963)⟩,⟨0,0⟩⟩] +lemma amp0_05_5_eq : ∀ k : Fin 16, amp0_0Expr 5 5 k = amp0_05_5 k := by decide +kernel +noncomputable def amp0_05_6 : Fin 16 → CBox := ![⟨⟨(-5823968441393309567794879179),(-5823968441393309567662689457)⟩,⟨0,0⟩⟩,⟨⟨(-5959714044899289793790667047),(-5959714044899289793654560129)⟩,⟨0,0⟩⟩,⟨⟨(-6096016131460073494702761775),(-6096016131460073494563375495)⟩,⟨0,0⟩⟩,⟨⟨(-6233006298189215735549270065),(-6233006298189215735405908859)⟩,⟨0,0⟩⟩,⟨⟨(-6370431660394543908636768498),(-6370431660394543908489805655)⟩,⟨0,0⟩⟩,⟨⟨(-6508414282079257382315896408),(-6508414282079257382165064201)⟩,⟨0,0⟩⟩,⟨⟨(-6646707301904864093262554284),(-6646707301904864093111459636)⟩,⟨0,0⟩⟩,⟨⟨(-6785422699654169368833796417),(-6785422699654169368678504840)⟩,⟨0,0⟩⟩,⟨⟨(-6924320483909415370326528512),(-6924320483909415370167419608)⟩,⟨0,0⟩⟩,⟨⟨(-7063501989456468219727412243),(-7063501989456468219564618811)⟩,⟨0,0⟩⟩,⟨⟨(-7202734961332202778027832648),(-7202734961332202777861146291)⟩,⟨0,0⟩⟩,⟨⟨(-7342109518243493791441410473),(-7342109518243493791271216656)⟩,⟨0,0⟩⟩,⟨⟨(-7481402028133446261824044022),(-7481402028133446261650156780)⟩,⟨0,0⟩⟩,⟨⟨(-7620690811554856993468210426),(-7620690811554856993290286200)⟩,⟨0,0⟩⟩,⟨⟨(-7759761765703628868882084470),(-7759761765703628868702129542)⟩,⟨0,0⟩⟩,⟨⟨(-7898680819171865498412019786),(-7898680819171865498228224425)⟩,⟨0,0⟩⟩] +lemma amp0_05_6_eq : ∀ k : Fin 16, amp0_0Expr 5 6 k = amp0_05_6 k := by decide +kernel +noncomputable def amp0_05_7 : Fin 16 → CBox := ![⟨⟨(-8037244324657834614173073787),(-8037244324657834613985721855)⟩,⟨0,0⟩⟩,⟨⟨(-8175505212462621448394886328),(-8175505212462621448203654310)⟩,⟨0,0⟩⟩,⟨⟨(-8313271236982902320521847138),(-8313271236982902320327917417)⟩,⟨0,0⟩⟩,⟨⟨(-8450581710525803771719724974),(-8450581710525803771522137350)⟩,⟨0,0⟩⟩,⟨⟨(-8587256755412933328522542717),(-8587256755412933328322081758)⟩,⟨0,0⟩⟩,⟨⟨(-8723321431972879243771984286),(-8723321431972879243567797535)⟩,⟨0,0⟩⟩,⟨⟨(-8858609216839208424585827262),(-8858609216839208424378554559)⟩,⟨0,0⟩⟩,⟨⟨(-8993130269122809606452355642),(-8993130269122809606241944244)⟩,⟨0,0⟩⟩,⟨⟨(-9126732426498762492224708064),(-9126732426498762492011213200)⟩,⟨0,0⟩⟩,⟨⟨(-9259410281325397355109353318),(-9259410281325397354892590610)⟩,⟨0,0⟩⟩,⟨⟨(-9391027059631885636736338293),(-9391027059631885636516693161)⟩,⟨0,0⟩⟩,⟨⟨(-9521561104079381981171483090),(-9521561104079381980948835355)⟩,⟨0,0⟩⟩,⟨⟨(-9650892077252799425737360020),(-9650892077252799425512109529)⟩,⟨0,0⟩⟩,⟨⟨(-9778981370569384262771131863),(-9778981370569384262543318164)⟩,⟨0,0⟩⟩,⟨⟨(-9905726152639809844841595839),(-9905726152639809844611577405)⟩,⟨0,0⟩⟩,⟨⟨(-10031070142211902033390017148),(-10031070142211902033158120063)⟩,⟨0,0⟩⟩] +lemma amp0_05_7_eq : ∀ k : Fin 16, amp0_0Expr 5 7 k = amp0_05_7 k := by decide +kernel +noncomputable def amp0_05_8 : Fin 16 → CBox := ![⟨⟨(-10154929105121458594545909382),(-10154929105121458594311183409)⟩,⟨0,0⟩⟩,⟨⟨(-10277228344774870551840715881),(-10277228344774870551601972953)⟩,⟨0,0⟩⟩,⟨⟨(-10397903337713655822354089057),(-10397903337713655822111769712)⟩,⟨0,0⟩⟩,⟨⟨(-10516860206617878171184815819),(-10516860206617878170939129804)⟩,⟨0,0⟩⟩,⟨⟨(-10634055275149534856348591337),(-10634055275149534856099760587)⟩,⟨0,0⟩⟩,⟨⟨(-10749374695591017525606162680),(-10749374695591017525354437800)⟩,⟨0,0⟩⟩,⟨⟨(-10862796798838857612878879168),(-10862796798838857612624280982)⟩,⟨0,0⟩⟩,⟨⟨(-10974186951129577912947446620),(-10974186951129577912690290769)⟩,⟨0,0⟩⟩,⟨⟨(-11083546675297232713664712919),(-11083546675297232713405015370)⟩,⟨0,0⟩⟩,⟨⟨(-11190719708089349790947878441),(-11190719708089349790685514600)⟩,⟨0,0⟩⟩,⟨⟨(-11295731974597181555616494500),(-11295731974597181555351579078)⟩,⟨0,0⟩⟩,⟨⟨(-11398404708883201001624781067),(-11398404708883201001358029071)⟩,⟨0,0⟩⟩,⟨⟨(-11498789475413175212430386109),(-11498789475413175212160916007)⟩,⟨0,0⟩⟩,⟨⟨(-11596684100503760017162865871),(-11596684100503760016891576827)⟩,⟨0,0⟩⟩,⟨⟨(-11692167053261121764034596716),(-11692167053261121763760350055)⟩,⟨0,0⟩⟩,⟨⟨(-11785011813049447607061004192),(-11785011813049447606785376106)⟩,⟨0,0⟩⟩] +lemma amp0_05_8_eq : ∀ k : Fin 16, amp0_0Expr 5 8 k = amp0_05_8 k := by decide +kernel +noncomputable def amp0_05_9 : Fin 16 → CBox := ![⟨⟨(-11875325048569344302467964378),(-11875325048569344302190796702)⟩,⟨0,0⟩⟩,⟨⟨(-11962854916411658334027920822),(-11962854916411658333749494545)⟩,⟨0,0⟩⟩,⟨⟨(-12047737611262769688533950049),(-12047737611262769688251674825)⟩,⟨0,0⟩⟩,⟨⟨(-12129694951829510850662619250),(-12129694951829510850379541840)⟩,⟨0,0⟩⟩,⟨⟨(-12208894018594742990120525336),(-12208894018594742989836425735)⟩,⟨0,0⟩⟩,⟨⟨(-12285029235075145120531667071),(-12285029235075145120246111703)⟩,⟨0,0⟩⟩,⟨⟨(-12358299963021469189338958095),(-12358299963021469189052889147)⟩,⟨0,0⟩⟩,⟨⟨(-12428372128096910062098259099),(-12428372128096910061811266584)⟩,⟨0,0⟩⟩,⟨⟨(-12495478806982420229119839057),(-12495478806982420228832533987)⟩,⟨0,0⟩⟩,⟨⟨(-12559256276019802220273678557),(-12559256276019802219986680391)⟩,⟨0,0⟩⟩,⟨⟨(-12619972801525971473577185392),(-12619972801525971473283229869)⟩,⟨0,0⟩⟩,⟨⟨(-12677233806482011586082811773),(-12677233806482011585788699835)⟩,⟨0,0⟩⟩,⟨⟨(-12731344265802869005029955834),(-12731344265802869004735542569)⟩,⟨0,0⟩⟩,⟨⟨(-12781877488373212780603164274),(-12781877488373212780309150670)⟩,⟨0,0⟩⟩,⟨⟨(-12829176724540682363598314845),(-12829176724540682363303581764)⟩,⟨0,0⟩⟩,⟨⟨(-12872781847134098502151407110),(-12872781847134098501857318123)⟩,⟨0,0⟩⟩] +lemma amp0_05_9_eq : ∀ k : Fin 16, amp0_0Expr 5 9 k = amp0_05_9 k := by decide +kernel +noncomputable def amp0_05_10 : Fin 16 → CBox := ![⟨⟨(-12913076000709954107969581428),(-12913076000709954107673712042)⟩,⟨0,0⟩⟩,⟨⟨(-12949564233877359603717537120),(-12949564233877359603422059547)⟩,⟨0,0⟩⟩,⟨⟨(-12982671260697089639132383026),(-12982671260697089638837321395)⟩,⟨0,0⟩⟩,⟨⟨(-13011865845697627167598253108),(-13011865845697627167302919496)⟩,⟨0,0⟩⟩,⟨⟨(-13037616009409894492605247238),(-13037616009409894492311008143)⟩,⟨0,0⟩⟩,⟨⟨(-13059352694651544113878765415),(-13059352694651544113584826138)⟩,⟨0,0⟩⟩,⟨⟨(-13077589032858803753432312078),(-13077589032858803753139009388)⟩,⟨0,0⟩⟩,⟨⟨(-13091716523008848063254759055),(-13091716523008848062962626732)⟩,⟨0,0⟩⟩,⟨⟨(-13102295285879987921073018582),(-13102295285879987920782417958)⟩,⟨0,0⟩⟩,⟨⟨(-13108675662500827682639679242),(-13108675662500827682350935059)⟩,⟨0,0⟩⟩,⟨⟨(-13111466722795377664189831159),(-13111466722795377663903789173)⟩,⟨0,0⟩⟩,⟨⟨(-13109975835423449524316631941),(-13109975835423449524008995398)⟩,⟨0,0⟩⟩,⟨⟨(-13104863068938931647860809977),(-13104863068938931647554720140)⟩,⟨0,0⟩⟩,⟨⟨(-13095390895588513062476089290),(-13095390895588513062171352192)⟩,⟨0,0⟩⟩,⟨⟨(-13082272531117872668679494720),(-13082272531117872668376470803)⟩,⟨0,0⟩⟩,⟨⟨(-13064723507257033417615332703),(-13064723507257033417313640504)⟩,⟨0,0⟩⟩] +lemma amp0_05_10_eq : ∀ k : Fin 16, amp0_0Expr 5 10 k = amp0_05_10 k := by decide +kernel +noncomputable def amp0_05_11 : Fin 16 → CBox := ![⟨⟨(-13043512445221825672293550996),(-13043512445221825671993527441)⟩,⟨0,0⟩⟩,⟨⟨(-13017805760334312460236474248),(-13017805760334312459937638647)⟩,⟨0,0⟩⟩,⟨⟨(-12988429859341489300391413932),(-12988429859341489300094855018)⟩,⟨0,0⟩⟩,⟨⟨(-12954499720255460280434227424),(-12954499720255460280138474253)⟩,⟨0,0⟩⟩,⟨⟨(-12916902050911340022354386450),(-12916902050911340022061108882)⟩,⟨0,0⟩⟩,⟨⟨(-12874697911143072120207268295),(-12874697911143072119916008142)⟩,⟨0,0⟩⟩,⟨⟨(-12828836976547584762616598180),(-12828836976547584762328281186)⟩,⟨0,0⟩⟩,⟨⟨(-12778323730974931498293098503),(-12778323730974931498003775809)⟩,⟨0,0⟩⟩,⟨⟨(-12724173653412829158330846765),(-12724173653412829158044517143)⟩,⟨0,0⟩⟩,⟨⟨(-12665331797658554989585612343),(-12665331797658554989301961746)⟩,⟨0,0⟩⟩,⟨⟨(-12602882471102409488731780035),(-12602882471102409488450181869)⟩,⟨0,0⟩⟩,⟨⟨(-12535708225070645789987568409),(-12535708225070645789709267745)⟩,⟨0,0⟩⟩,⟨⟨(-12464965433213760035943659374),(-12464965433213760035668504494)⟩,⟨0,0⟩⟩,⟨⟨(-12389470828282574153883022678),(-12389470828282574153611111885)⟩,⟨0,0⟩⟩,⟨⟨(-12310456327929295114474666028),(-12310456327929295114206742402)⟩,⟨0,0⟩⟩,⟨⟨(-12226669257357300083737122331),(-12226669257357300083473691703)⟩,⟨0,0⟩⟩] +lemma amp0_05_11_eq : ∀ k : Fin 16, amp0_0Expr 5 11 k = amp0_05_11 k := by decide +kernel +noncomputable def amp0_05_12 : Fin 16 → CBox := ![⟨⟨(-12139420827114858741945869610),(-12139420827114858741672024818)⟩,⟨0,0⟩⟩,⟨⟨(-12047385059268084753821052791),(-12047385059268084753549705776)⟩,⟨0,0⟩⟩,⟨⟨(-11951956513609678103196024092),(-11951956513609678102927504996)⟩,⟨0,0⟩⟩,⟨⟨(-11851731667654209173370624215),(-11851731667654209173104723961)⟩,⟨0,0⟩⟩,⟨⟨(-11748192836559880533797895581),(-11748192836559880533534963397)⟩,⟨0,0⟩⟩,⟨⟨(-11639854320292927855002678655),(-11639854320292927854742253311)⟩,⟨0,0⟩⟩,⟨⟨(-11528290994826055290661304981),(-11528290994826055290404482175)⟩,⟨0,0⟩⟩,⟨⟨(-11411929904329072428805776649),(-11411929904329072428550435466)⟩,⟨0,0⟩⟩,⟨⟨(-11292443748676301659613321193),(-11292443748676301659361899622)⟩,⟨0,0⟩⟩,⟨⟨(-11168166729462903620348632239),(-11168166729462903620100524422)⟩,⟨0,0⟩⟩,⟨⟨(-11040875160160211469309145351),(-11040875160160211469064944779)⟩,⟨0,0⟩⟩,⟨⟨(-10908804229451485828875253413),(-10908804229451485828635042582)⟩,⟨0,0⟩⟩,⟨⟨(-10773840262747186152540062408),(-10773840262747186152304890678)⟩,⟨0,0⟩⟩,⟨⟨(-10634112592427048441472364715),(-10634112592427048441232427579)⟩,⟨0,0⟩⟩,⟨⟨(-10491624661005867346117308060),(-10491624661005867345881851139)⟩,⟨0,0⟩⟩,⟨⟨(-10344392320674815745123718853),(-10344392320674815744892571381)⟩,⟨0,0⟩⟩] +lemma amp0_05_12_eq : ∀ k : Fin 16, amp0_0Expr 5 12 k = amp0_05_12 k := by decide +kernel +noncomputable def amp0_05_13 : Fin 16 → CBox := ![⟨⟨(-10194544061302622081353349131),(-10194544061302622081126531551)⟩,⟨0,0⟩⟩,⟨⟨(-10039973720638874086099417068),(-10039973720638874085875656535)⟩,⟨0,0⟩⟩,⟨⟨(-9882943734709660310213800777),(-9882943734709660309995172919)⟩,⟨0,0⟩⟩,⟨⟨(-9721216324032392147696855621),(-9721216324032392147482640307)⟩,⟨0,0⟩⟩,⟨⟨(-9557197913543233291641305592),(-9557197913543233291432583248)⟩,⟨0,0⟩⟩,⟨⟨(-9388508241009929519499797078),(-9388508241009929519290131775)⟩,⟨0,0⟩⟩,⟨⟨(-9217709123208483653056406661),(-9217709123208483652851416528)⟩,⟨0,0⟩⟩,⟨⟨(-9042265446402566966641338117),(-9042265446402566966441064048)⟩,⟨0,0⟩⟩,⟨⟨(-8864907451324136424351902989),(-8864907451324136424156396412)⟩,⟨0,0⟩⟩,⟨⟨(-8682931000002419888977006228),(-8682931000002419888785551411)⟩,⟨0,0⟩⟩,⟨⟨(-8499249756460134722489144291),(-8499249756460134722302529873)⟩,⟨0,0⟩⟩,⟨⟨(-8310974201781988969412869924),(-8310974201781988969226933084)⟩,⟨0,0⟩⟩,⟨⟨(-8121218819281640845647749096),(-8121218819281640845467536550)⟩,⟨0,0⟩⟩,⟨⟨(-7926889682697347368864011650),(-7926889682697347368688977782)⟩,⟨0,0⟩⟩,⟨⟨(-7731322439515148040784136865),(-7731322439515148040614086854)⟩,⟨0,0⟩⟩,⟨⟨(-7531196431271605633494399164),(-7531196431271605633329845737)⟩,⟨0,0⟩⟩] +lemma amp0_05_13_eq : ∀ k : Fin 16, amp0_0Expr 5 13 k = amp0_05_13 k := by decide +kernel +noncomputable def amp0_05_14 : Fin 16 → CBox := ![⟨⟨(-7330092483041432283754248319),(-7330092483041432283592065085)⟩,⟨0,0⟩⟩,⟨⟨(-7124436755348031963285621370),(-7124436755348031963128670860)⟩,⟨0,0⟩⟩,⟨⟨(-6918083884758200753941816049),(-6918083884758200753789755284)⟩,⟨0,0⟩⟩,⟨⟨(-6707175176996376671142317200),(-6707175176996376670996279692)⟩,⟨0,0⟩⟩,⟨⟨(-6495873614970292566390161081),(-6495873614970292566247107465)⟩,⟨0,0⟩⟩,⟨⟨(-6279997256106114464036489326),(-6279997256106114463898854120)⟩,⟨0,0⟩⟩,⟨⟨(-6064059620565666573039914267),(-6064059620565666572905962720)⟩,⟨0,0⟩⟩,⟨⟨(-5843508333865144115643782304),(-5843508333865144115515552720)⟩,⟨0,0⟩⟩,⟨⟨(-5623259758294419899346294264),(-5623259758294419899223639395)⟩,⟨0,0⟩⟩,⟨⟨(-5398332179446450275569138937),(-5398332179446450275450636815)⟩,⟨0,0⟩⟩,⟨⟨(-5174110748446996733624699071),(-5174110748446996733512070928)⟩,⟨0,0⟩⟩,⟨⟨(-4945109508397047027249596088),(-4945109508397047027141453471)⟩,⟨0,0⟩⟩,⟨⟨(-4717267198118655931872340776),(-4717267198118655931768730310)⟩,⟨0,0⟩⟩,⟨⟨(-4484496312031306880543877255),(-4484496312031306880446178299)⟩,⟨0,0⟩⟩,⟨⟨(-4253400785223850296846872977),(-4253400785223850296754034564)⟩,⟨0,0⟩⟩,⟨⟨(-4017161876444438552805769194),(-4017161876444438552717949888)⟩,⟨0,0⟩⟩] +lemma amp0_05_14_eq : ∀ k : Fin 16, amp0_0Expr 5 14 k = amp0_05_14 k := by decide +kernel +noncomputable def amp0_05_15 : Fin 16 → CBox := ![⟨⟨(-3783199784228645034398544459),(-3783199784228645034315995570)⟩,⟨0,0⟩⟩,⟨⟨(-3543786234992750818975348432),(-3543786234992750818898224426)⟩,⟨0,0⟩⟩,⟨⟨(-3307369321525166183509229142),(-3307369321525166183437580882)⟩,⟨0,0⟩⟩,⟨⟨(-3065056473631586439871774522),(-3065056473631586439805173728)⟩,⟨0,0⟩⟩,⟨⟨(-2826633270511767721861515268),(-2826633270511767721800116826)⟩,⟨0,0⟩⟩,⟨⟨(-2581660444753823030946877483),(-2581660444753823030890889768)⟩,⟨0,0⟩⟩,⟨⟨(-2341740172299399886681302029),(-2341740172299399886630810980)⟩,⟨0,0⟩⟩,⟨⟨(-2094273829805534679745997692),(-2094273829805534679700689844)⟩,⟨0,0⟩⟩,⟨⟨(-1853480404442691529644948805),(-1853480404442691529605036860)⟩,⟨0,0⟩⟩,⟨⟨(-1603527089250132360216709753),(-1603527089250132360182288253)⟩,⟨0,0⟩⟩,⟨⟨(-1362741222863623935777266407),(-1362741222863623935748216507)⟩,⟨0,0⟩⟩,⟨⟨(-1109895761162676723682702291),(-1109895761162676723659163666)⟩,⟨0,0⟩⟩,⟨⟨(-870731121346295531949241768),(-870731121346295531931032395)⟩,⟨0,0⟩⟩,⟨⟨(-613170481679804685088512483),(-613170481679804685075843434)⟩,⟨0,0⟩⟩,⟨⟨(-380420923474277062497385139),(-380420923474277062490047351)⟩,⟨0,0⟩⟩,⟨⟨(-108087267962443344184837671),(-108087267962443344183065187)⟩,⟨0,0⟩⟩] +lemma amp0_05_15_eq : ∀ k : Fin 16, amp0_0Expr 5 15 k = amp0_05_15 k := by decide +kernel +noncomputable def amp0_05 : Fin 16 → Fin 16 → CBox := ![amp0_05_0,amp0_05_1,amp0_05_2,amp0_05_3,amp0_05_4,amp0_05_5,amp0_05_6,amp0_05_7,amp0_05_8,amp0_05_9,amp0_05_10,amp0_05_11,amp0_05_12,amp0_05_13,amp0_05_14,amp0_05_15] +lemma amp0_05_eq (i k : Fin 16) : amp0_0Expr 5 i k = amp0_05 i k := by + fin_cases i + · exact amp0_05_0_eq k + · exact amp0_05_1_eq k + · exact amp0_05_2_eq k + · exact amp0_05_3_eq k + · exact amp0_05_4_eq k + · exact amp0_05_5_eq k + · exact amp0_05_6_eq k + · exact amp0_05_7_eq k + · exact amp0_05_8_eq k + · exact amp0_05_9_eq k + · exact amp0_05_10_eq k + · exact amp0_05_11_eq k + · exact amp0_05_12_eq k + · exact amp0_05_13_eq k + · exact amp0_05_14_eq k + · exact amp0_05_15_eq k +noncomputable def amp0_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp0_00,amp0_01,amp0_02,amp0_03,amp0_04,amp0_05] +lemma amp0_0_eq (j : Fin 6) (i k : Fin 16) : amp0_0Expr j i k = amp0_0 j i k := by + fin_cases j + · exact amp0_00_eq i k + · exact amp0_01_eq i k + · exact amp0_02_eq i k + · exact amp0_03_eq i k + · exact amp0_04_eq i k + · exact amp0_05_eq i k +lemma amp0_0_contains (j : Fin 6) (i k : Fin 16) : + (amp0_0 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude false 0 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp0_0_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 0 j) (bLookup_contains 0 j) false) +noncomputable def amp0_1Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 0 j) (bLookup 0 j) true) +noncomputable def amp0_10_0 : Fin 16 → CBox := ![⟨⟨(-536329754622069946055195813),(-536329754622069946037194987)⟩,⟨(-516083547009096694060614982),(-516083547009096694057198524)⟩⟩,⟨⟨(-1887793341088553155446880160),(-1887793341088553155378063613)⟩,⟨(-1816529989419765287734937456),(-1816529989419765287717661492)⟩⟩,⟨⟨(-3043243487890630820824762057),(-3043243487890630820709671808)⟩,⟨(-2928362411572052199892260607),(-2928362411572052199860413868)⟩⟩,⟨⟨(-4322526319102367440630104977),(-4322526319102367440465544606)⟩,⟨(-4159352889854990063696727991),(-4159352889854990063650445197)⟩⟩,⟨⟨(-5511459324147942579986754002),(-5511459324147942579775383806)⟩,⟨(-5303404207374145887011630210),(-5303404207374145886951128831)⟩⟩,⟨⟨(-6769574453262926753952261586),(-6769574453262926753691892283)⟩,⟨(-6514026054817607366941342927),(-6514026054817607366866309934)⟩⟩,⟨⟨(-7969307376213303340133165057),(-7969307376213303339825525225)⟩,⟨(-7668469598186034814264267358),(-7668469598186034814174852464)⟩⟩,⟨⟨(-9216400337971305960888228836),(-9216400337971305960531809935)⟩,⟨(-8868485360145152284717966999),(-8868485360145152284613946464)⟩⟩,⟨⟨(-10420021741238073901778753196),(-10420021741238073901374903331)⟩,⟨(-10026670595442591581713583048),(-10026670595442591581595127046)⟩⟩,⟨⟨(-11659192799329569796510885923),(-11659192799329569796059833298)⟩,⟨(-11219063502044455816169433770),(-11219063502044455816037683548)⟩⟩,⟨⟨(-12863416457788331101576610517),(-12863416457788331101077447083)⟩,⟨(-12377828257670592144088338098),(-12377828257670592143941513841)⟩⟩,⟨⟨(-14095709680065119182972449216),(-14095709680065119182424942221)⟩,⟨(-13563602963674017036776548538),(-13563602963674017036615154012)⟩⟩,⟨⟨(-15298508650941552845630333349),(-15298508650941552845036189363)⟩,⟨(-14720996813034873395591659908),(-14720996813034873395416572593)⟩⟩,⟨⟨(-16524158055702303954067411539),(-16524158055702303953426708000)⟩,⟨(-15900378502652747126400926080),(-15900378502652747126212812910)⟩⟩,⟨⟨(-17724056361181499483814182569),(-17724056361181499483125296384)⟩,⟨(-17054981185433729370571370137),(-17054981185433729370368001668)⟩⟩,⟨⟨(-18942914667987845094823913273),(-18942914667987845094086518914)⟩,⟨(-18227828137998154550020369747),(-18227828137998154549801924296)⟩⟩] +lemma amp0_10_0_eq : ∀ k : Fin 16, amp0_1Expr 0 0 k = amp0_10_0 k := by decide +kernel +noncomputable def amp0_10_1 : Fin 16 → CBox := ![⟨⟨(-20138716125252464465636544887),(-20138716125252464464852067671)⟩,⟨(-19378488626746612489096907573),(-19378488626746612488864158882)⟩⟩,⟨⟨(-21350434376680880407104511624),(-21350434376680880406273488171)⟩,⟨(-20544465057820243452158183025),(-20544465057820243451912060114)⟩⟩,⟨⟨(-22541100864556438565584475368),(-22541100864556438564708163749)⟩,⟨(-21690184419970276426078355164),(-21690184419970276425819522827)⟩⟩,⟨⟨(-23745214534701743939296977839),(-23745214534701743938369534520)⟩,⟨(-22848843339292443595823170274),(-22848843339292443595546354198)⟩⟩,⟨⟨(-24929804891098692667014519638),(-24929804891098692666043479656)⟩,⟨(-23988715941201132046954245460),(-23988715941201132046666190077)⟩⟩,⟨⟨(-26125779465830798798399375439),(-26125779465830798797384282444)⟩,⟨(-25139543012310348165201504618),(-25139543012310348164902065951)⟩⟩,⟨⟨(-27303416190504248021624539702),(-27303416190504248020558816942)⟩,⟨(-26272724478973356682546472239),(-26272724478973356682228846381)⟩⟩,⟨⟨(-28490673221862566553249567413),(-28490673221862566552141355467)⟩,⟨(-27415163090060025285632028068),(-27415163090060025285304297709)⟩⟩,⟨⟨(-29660523164173378280824280942),(-29660523164173378279667032268)⟩,⟨(-28540851721901050822607348422),(-28540851721901050822262761892)⟩⟩,⟨⟨(-30838456118783685884717469114),(-30838456118783685883509633873)⟩,⟨(-29674318235953704693155370567),(-29674318235953704692792646094)⟩⟩,⟨⟨(-31999718726471072330800252651),(-31999718726471072329552632317)⟩,⟨(-30791743701200636930357765413),(-30791743701200636929986864525)⟩⟩,⟨⟨(-33167703141944086271752816216),(-33167703141944086270455989412)⟩,⟨(-31915637229005024094955224892),(-31915637229005024094567256132)⟩⟩,⟨⟨(-34319603042534723127695399920),(-34319603042534723126362435725)⟩,⟨(-33024053425147536339850786898),(-33024053425147536339457908990)⟩⟩,⟨⟨(-35477003336654443686195981296),(-35477003336654443684810546426)⟩,⟨(-34137762377431157503618652492),(-34137762377431157503205291328)⟩⟩,⟨⟨(-36618785523137895750346176208),(-36618785523137895748914504857)⟩,⟨(-35236442798634725059103185713),(-35236442798634725058674935234)⟩⟩,⟨⟨(-37764959745782167173247791561),(-37764959745782167171767492929)⟩,⟨(-36339349458604525326671467925),(-36339349458604525326226141451)⟩⟩] +lemma amp0_10_1_eq : ∀ k : Fin 16, amp0_1Expr 0 1 k = amp0_10_1 k := by decide +kernel +noncomputable def amp0_10_2 : Fin 16 → CBox := ![⟨⟨(-38895886391455750092010672385),(-38895886391455750090497250542)⟩,⟨(-37427584130793464683540494601),(-37427584130793464683092615623)⟩⟩,⟨⟨(-40030189663707965554003518417),(-40030189663707965552439924268)⟩,⟨(-38519067963422614613546822131),(-38519067963422614613080072692)⟩⟩,⟨⟨(-41149537991221482707985011583),(-41149537991221482706374331971)⟩,⟨(-39596161393767425467437586120),(-39596161393767425466954548815)⟩⟩,⟨⟨(-42271325079137887374608309479),(-42271325079137887372948862495)⟩,⟨(-40675601522404063164005546779),(-40675601522404063163504666417)⟩⟩,⟨⟨(-43378385931647065403971604445),(-43378385931647065402261204427)⟩,⟨(-41740871324413180698551277289),(-41740871324413180698030068925)⟩⟩,⟨⟨(-44487013233185145102336874035),(-44487013233185145100601004227)⟩,⟨(-42807648442703145243876167110),(-42807648442703145243359192619)⟩⟩,⟨⟨(-45581090124830186185157187920),(-45581090124830186183374572440)⟩,⟨(-43860424422545501058347671712),(-43860424422545501057814081133)⟩⟩,⟨⟨(-46675917248613400674147712577),(-46675917248613400672321795103)⟩,⟨(-44913922313599405413758795382),(-44913922313599405413211921845)⟩⟩,⟨⟨(-47756325749257686644692101436),(-47756325749257686642819894368)⟩,⟨(-45953545878068969524282565434),(-45953545878068969523719160307)⟩⟩,⟨⟨(-48836716802886243802220521142),(-48836716802886243800301262422)⟩,⟨(-46993152654139820991757141621),(-46993152654139820991176471158)⟩⟩,⟨⟨(-49902784160230928602498832578),(-49902784160230928600533203189)⟩,⟨(-48018976447035198879767856707),(-48018976447035198879170204831)⟩⟩,⟨⟨(-50968108827519318223063657208),(-50968108827519318221080866302)⟩,⟨(-49044085586090699300577410363),(-49044085586090699299990864339)⟩⟩,⟨⟨(-52019173760407361914113762955),(-52019173760407361912080295479)⟩,⟨(-50055473289321845906160934112),(-50055473289321845905552874366)⟩⟩,⟨⟨(-53068808222202830134706524392),(-53068808222202830132627130212)⟩,⟨(-51065484521102381801834666514),(-51065484521102381801209626522)⟩⟩,⟨⟨(-54104220838967467992301157031),(-54104220838967467990172438808)⟩,⟨(-52061810776121379278163538194),(-52061810776121379277517880150)⟩⟩,⟨⟨(-55137548575880762631362308747),(-55137548575880762629194674063)⟩,⟨(-53056130854568041697546853732),(-53056130854568041696890538285)⟩⟩] +lemma amp0_10_2_eq : ∀ k : Fin 16, amp0_1Expr 0 2 k = amp0_10_2 k := by decide +kernel +noncomputable def amp0_10_3 : Fin 16 → CBox := ![⟨⟨(-56156670384966882376654981138),(-56156670384966882374442420941)⟩,⟨(-54036781272589524416343593922),(-54036781272589524415670470557)⟩⟩,⟨⟨(-57173082889346151025923505354),(-57173082889346151023664965493)⟩,⟨(-55014824660941311801125686987),(-55014824660941311800434671105)⟩⟩,⟨⟨(-58175286878534826679423900689),(-58175286878534826677118939768)⟩,⟨(-55979195899176309597688315858),(-55979195899176309596978614357)⟩⟩,⟨⟨(-59174184295460243032643081828),(-59174184295460243030341635905)⟩,⟨(-56940385386767494549038598812),(-56940385386767494548358176959)⟩⟩,⟨⟨(-60158855062333057633661438364),(-60158855062333057631310608627)⟩,⟨(-57887885273962785791763009442),(-57887885273962785791060596493)⟩⟩,⟨⟨(-61139646774134726473646370158),(-61139646774134726471250809112)⟩,⟨(-58831652538675531387730314863),(-58831652538675531387010287126)⟩⟩,⟨⟨(-62106180694855959235220775132),(-62106180694855959232781454616)⟩,⟨(-59761700237524378291962055058),(-59761700237524378291224978038)⟩⟩,⟨⟨(-63068285859916397837216097893),(-63068285859916397834735466964)⟩,⟨(-60687486364251667551252835021),(-60687486364251667550500950505)⟩⟩,⟨⟨(-64016091286586316731224394903),(-64016091286586316728699962163)⟩,⟨(-61599512561297110511742664154),(-61599512561297110510973204058)⟩⟩,⟨⟨(-64958939340497661771417715742),(-64958939340497661768861972052)⟩,⟨(-62506768524181493585306323643),(-62506768524181493584531178781)⟩⟩,⟨⟨(-65887436819631572712811394911),(-65887436819631572710212975984)⟩,⟨(-63400215640047914274228418944),(-63400215640047914273436281973)⟩⟩,⟨⟨(-66810467944816676739410142660),(-66810467944816676736774380290)⟩,⟨(-64288402754374619219763036442),(-64288402754374619218958896163)⟩⟩,⟨⟨(-67719090451193890521909756262),(-67719090451193890519234890096)⟩,⟨(-65162725168789013936781064745),(-65162725168789013935962853700)⟩⟩,⟨⟨(-68621756019654473383875633062),(-68621756019654473381162499396)⟩,⟨(-66031315517020554069715103316),(-66031315517020554068883471792)⟩⟩,⟨⟨(-69509949201036450703228543189),(-69509949201036450700476520750)⟩,⟨(-66885979804292678583255116402),(-66885979804292678582409091370)⟩⟩,⟨⟨(-70391712193813509571261216155),(-70391712193813509568471315931)⟩,⟨(-67734456639694820210090308617),(-67734456639694820209230696191)⟩⟩] +lemma amp0_10_3_eq : ∀ k : Fin 16, amp0_1Expr 0 3 k = amp0_10_3 k := by decide +kernel +noncomputable def amp0_10_4 : Fin 16 → CBox := ![⟨⟨(-71258934622973220004441036119),(-71258934622973220001689500642)⟩,⟨(-68568941811232553507890114505),(-68568941811232553507089902119)⟩⟩,⟨⟨(-72119270029093191232088571444),(-72119270029093191229287550412)⟩,⟨(-69396799941760439164001663619),(-69396799941760439163176138727)⟩⟩,⟨⟨(-72964993460313304081693344011),(-72964993460313304078846291677)⟩,⟨(-70210597692885282670886311360),(-70210597692885282670038418990)⟩⟩,⟨⟨(-73803388657376576763326359251),(-73803388657376576760436660520)⟩,⟨(-71017343847404899042482744242),(-71017343847404899041615551529)⟩⟩,⟨⟨(-74627098285122606642259781063),(-74627098285122606639328857219)⟩,⟨(-71809958806260327012769457566),(-71809958806260327011883951404)⟩⟩,⟨⟨(-75443053403218161398860781080),(-75443053403218161395886449575)⟩,⟨(-72595111984725529378594121498),(-72595111984725529377688000688)⟩⟩,⟨⟨(-76244248121117075183087653386),(-76244248121117075180077942512)⟩,⟨(-73366061961479269626971708983),(-73366061961479269626052316073)⟩⟩,⟨⟨(-77037276391381794198302620273),(-77037276391381794195252799735)⟩,⟨(-74129153770333134321410456297),(-74129153770333134320473027837)⟩⟩,⟨⟨(-77815469049967882124212914938),(-77815469049967882121122017054)⟩,⟨(-74877970005193248323902188961),(-74877970005193248322945409172)⟩⟩,⟨⟨(-78585097138824961219922227188),(-78585097138824961216813348812)⟩,⟨(-75618544978989134712556598574),(-75618544978989134711602470369)⟩⟩,⟨⟨(-79339814800775635972487733416),(-79339814800775635969337369081)⟩,⟨(-76344772387804779790481006927),(-76344772387804779789506525593)⟩⟩,⟨⟨(-80085583130664096360457272141),(-80085583130664096357270117172)⟩,⟨(-77062388297828446848290061402),(-77062388297828446847299513000)⟩⟩,⟨⟨(-80816367322455405387783327158),(-80816367322455405384557416238)⟩,⟨(-77765585714245505798026974174),(-77765585714245505797018079097)⟩⟩,⟨⟨(-81537830379687563398483073656),(-81537830379687563395227567744)⟩,⟨(-78459813864751100475884530408),(-78459813864751100474865862133)⟩⟩,⟨⟨(-82244237338764998506096491586),(-82244237338764998502802784629)⟩,⟨(-79139554278052403994008191766),(-79139554278052403992971078774)⟩⟩,⟨⟨(-82940963969010156757994619333),(-82940963969010156754668595451)⟩,⟨(-79809979790591775614989963296),(-79809979790591775613939816612)⟩⟩] +lemma amp0_10_4_eq : ∀ k : Fin 16, amp0_1Expr 0 4 k = amp0_10_4 k := by decide +kernel +noncomputable def amp0_10_5 : Fin 16 → CBox := ![⟨⟨(-83622564885704135709083887254),(-83622564885704135705723513243)⟩,⟨(-80465850578480383003330092519),(-80465850578480383002264563541)⟩⟩,⟨⟨(-84294138577486610823527343222),(-84294138577486610820133389617)⟩,⟨(-81112072664699187622550798139),(-81112072664699187621470368352)⟩⟩,⟨⟨(-84950519831010831763220955576),(-84950519831010831759791573980)⟩,⟨(-81743675820387909213468931074),(-81743675820387909212371427979)⟩⟩,⟨⟨(-85596538987522582851765946406),(-85596538987522582848302456714)⟩,⟨(-82365308043577433328582289436),(-82365308043577433327468714456)⟩⟩,⟨⟨(-86227302375482680929414301763),(-86227302375482680925916329422)⟩,⟨(-82972260396633638288678176781),(-82972260396633638287547773981)⟩⟩,⟨⟨(-86847380574940545547894445563),(-86847380574940545544513946367)⟩,⟨(-83568930922259665945790504721),(-83568930922259665944789216608)⟩⟩,⟨⟨(-87452143535854231264692411860),(-87452143535854231261270073541)⟩,⟨(-84150864352725385234423203519),(-84150864352725385233397334731)⟩⟩,⟨⟨(-88045909780575486901515800262),(-88045909780575486898056156037)⟩,⟨(-84722216188101268817802570883),(-84722216188101268816756198410)⟩⟩,⟨⟨(-88624305608966800484512975713),(-88624305608966800481019144123)⟩,⟨(-85278777833467737960384883144),(-85278777833467737959320609312)⟩⟩,⟨⟨(-89191404563291638404211500946),(-89191404563291638400684523854)⟩,⟨(-85824469056695405392185944281),(-85824469056695405391104478741)⟩⟩,⟨⟨(-89743082616973589530106354832),(-89743082616973589526550503988)⟩,⟨(-86355321511360877551632353502),(-86355321511360877550537406944)⟩⟩,⟨⟨(-90283174834126918863586418502),(-90283174834126918860003039877)⟩,⟨(-86875025489628705059146997311),(-86875025489628705058039564524)⟩⟩,⟨⟨(-90807800733330533654376050980),(-90807800733330533650760560019)⟩,⟨(-87379846996510465846560382513),(-87379846996510465845435651029)⟩⟩,⟨⟨(-91320562871286602585775190276),(-91320562871286602582135866880)⟩,⟨(-87873252593809106546798176151),(-87873252593809106545663805728)⟩⟩,⟨⟨(-91817818689331794955892159586),(-91817818689331794952224854042)⟩,⟨(-88351737227816605519619727411),(-88351737227816605518471322972)⟩⟩,⟨⟨(-92302943715722059947064674368),(-92302943715722059943368565801)⟩,⟨(-88818549002111678512356932192),(-88818549002111678511193389348)⟩⟩] +lemma amp0_10_5_eq : ∀ k : Fin 16, amp0_1Expr 0 5 k = amp0_10_5 k := by decide +kernel +noncomputable def amp0_10_6 : Fin 16 → CBox := ![⟨⟨(-92772528160957989227115770474),(-92772528160957989223407525495)⟩,⟨(-89270406845218719925236752568),(-89270406845218719924073705867)⟩⟩,⟨⟨(-93229725547044399277221031926),(-93229725547044399273481914264)⟩,⟨(-89710345235101690097798170885),(-89710345235101690096617270196)⟩⟩,⟨⟨(-93671354135815031221513325066),(-93671354135815031217753915999)⟩,⟨(-90135302542782621582978279564),(-90135302542782621581789303092)⟩⟩,⟨⟨(-94100350039536556448039010088),(-94100350039536556444250156288)⟩,⟨(-90548104043607403861037739204),(-90548104043607403859831551640)⟩⟩,⟨⟨(-94513755259951778682684345347),(-94513755259951778678872141705)⟩,⟨(-90945903402425945744099418931),(-90945903402425945742881480884)⟩⟩,⟨⟨(-94914292698040905299411556159),(-94914292698040905295573698031)⟩,⟨(-91331320731928079604184827779),(-91331320731928079602952587994)⟩⟩,⟨⟨(-95299224164355378711106447001),(-95299224164355378707295188387)⟩,⟨(-91701721208088443914877462899),(-91701721208088443913680798214)⟩⟩,⟨⟨(-95671063173512853653450618885),(-95671063173512853649610294543)⟩,⟨(-92059523461475563711053744716),(-92059523461475563709838751793)⟩⟩,⟨⟨(-96027287770934307127236272133),(-96027287770934307123372577743)⟩,⟨(-92402300740164300762855518641),(-92402300740164300761627273330)⟩⟩,⟨⟨(-96370205558044188550015047379),(-96370205558044188546131453049)⟩,⟨(-92732273534660635462090462589),(-92732273534660635460851959013)⟩⟩,⟨⟨(-96697507577810490789096431396),(-96697507577810490785190435731)⟩,⟨(-93047220050024606813073277046),(-93047220050024606811821703384)⟩⟩,⟨⟨(-97011298659173172573791241330),(-97011298659173172569869388199)⟩,⟨(-93349165658848020294159596942),(-93349165658848020292900899750)⟩⟩,⟨⟨(-97309479923753571667728085180),(-97309479923753571663787941719)⟩,⟨(-93636090714469347692938901950),(-93636090714469347691670335505)⟩⟩,⟨⟨(-97593956253311594762938170702),(-97593956253311594758976826263)⟩,⟨(-93909828190216683237276397667),(-93909828190216683235994805884)⟩⟩,⟨⟨(-97862836231602274215172783283),(-97862836231602274211215830412)⟩,⟨(-94168558069959724092914196798),(-94168558069959724091643801766)⟩⟩,⟨⟨(-98117827318132162268174432267),(-98117827318132162264200049987)⟩,⟨(-94413923357374700799021590985),(-94413923357374700797741035377)⟩⟩] +lemma amp0_10_6_eq : ∀ k : Fin 16, amp0_1Expr 0 6 k = amp0_10_6 k := by decide +kernel +noncomputable def amp0_10_7 : Fin 16 → CBox := ![⟨⟨(-98357243230529944045536423398),(-98357243230529944041548015921)⟩,⟨(-94644301426493266081663695205),(-94644301426493266080375850924)⟩⟩,⟨⟨(-98582596243772795321767800536),(-98582596243772795317762910645)⟩,⟨(-94861147464590688555126779087),(-94861147464590688553828917080)⟩⟩,⟨⟨(-98792403157023610422967910744),(-98792403157023610418960695582)⟩,⟨(-95063034260996026154243155586),(-95063034260996026152948495524)⟩⟩,⟨⟨(-98987983022727566818459607280),(-98987983022727566814439721516)⟩,⟨(-95251231074516442955670527425),(-95251231074516442954368745661)⟩⟩,⟨⟨(-99168053934458365226699122860),(-99168053934458365222675423328)⟩,⟨(-95424504390118105957142384760),(-95424504390118105955841601700)⟩⟩,⟨⟨(-99333743418307214337002106454),(-99333743418307214332966027419)⟩,⟨(-95583939170288144597506339404),(-95583939170288144596197939817)⟩⟩,⟨⟨(-99483969331161427442182522209),(-99483969331161427438141202272)⟩,⟨(-95728494122330873260226350991),(-95728494122330873258916803089)⟩⟩,⟨⟨(-99619669111565349576516121840),(-99619669111565349572469996169)⟩,⟨(-95859071296906169172750024775),(-95859071296906169171439370696)⟩⟩,⟨⟨(-99739959096872957559385893088),(-99739959096872957555335056928)⟩,⟨(-95974820389236441834553560239),(-95974820389236441833241492118)⟩⟩,⟨⟨(-99845587826599698676110944615),(-99845587826599698672054667379)⟩,⟨(-96076461681806262182657261844),(-96076461681806262181342696567)⟩⟩,⟨⟨(-99935869077523485122343951305),(-99935869077523485118286072225)⟩,⟨(-96163334856012302606753373030),(-96163334856012302605439607004)⟩⟩,⟨⟨(-100011363434150925725337744828),(-100011363434150925721277957352)⟩,⟨(-96235979334547553340104943367),(-96235979334547553338791298247)⟩⟩,⟨⟨(-100071581308260701151181549311),(-100071581308260701147123432790)⟩,⟨(-96293924010926396403530230522),(-96293924010926396402219754483)⟩⟩,⟨⟨(-100116896033434818521914884191),(-100116896033434818517859931563)⟩,⟨(-96337528125555614028921458148),(-96337528125555614027615201393)⟩⟩,⟨⟨(-100147014084671332583670559412),(-100147014084671332579621893581)⟩,⟨(-96366509233870394586701310657),(-96366509233870394585401884214)⟩⟩,⟨⟨(-100162122012156846651245317311),(-100162122012156846647206987577)⟩,⟨(-96381046843871492741396360109),(-96381046843871492740107271266)⟩⟩] +lemma amp0_10_7_eq : ∀ k : Fin 16, amp0_1Expr 0 7 k = amp0_10_7 k := by decide +kernel +noncomputable def amp0_10_8 : Fin 16 → CBox := ![⟨⟨(-100162122012156846651245317311),(-100162122012156846647206987577)⟩,⟨(-96381046843871492741396360109),(-96381046843871492740107271266)⟩⟩,⟨⟨(-100147014084671332583670559412),(-100147014084671332579621893581)⟩,⟨(-96366509233870394586701310657),(-96366509233870394585401884214)⟩⟩,⟨⟨(-100116896033434818521914884191),(-100116896033434818517859931563)⟩,⟨(-96337528125555614028921458148),(-96337528125555614027615201393)⟩⟩,⟨⟨(-100071581308260701151181549311),(-100071581308260701147123432790)⟩,⟨(-96293924010926396403530230522),(-96293924010926396402219754483)⟩⟩,⟨⟨(-100011363434150925725337744828),(-100011363434150925721277957352)⟩,⟨(-96235979334547553340104943367),(-96235979334547553338791298247)⟩⟩,⟨⟨(-99935869077523485122343951305),(-99935869077523485118286072225)⟩,⟨(-96163334856012302606753373030),(-96163334856012302605439607004)⟩⟩,⟨⟨(-99845587826599698676110944615),(-99845587826599698672054667379)⟩,⟨(-96076461681806262182657261844),(-96076461681806262181342696567)⟩⟩,⟨⟨(-99739959096872957559385893088),(-99739959096872957555335056928)⟩,⟨(-95974820389236441834553560239),(-95974820389236441833241492118)⟩⟩,⟨⟨(-99619669111565349576516121840),(-99619669111565349572469996169)⟩,⟨(-95859071296906169172750024775),(-95859071296906169171439370696)⟩⟩,⟨⟨(-99483969331161427442182522209),(-99483969331161427438141202272)⟩,⟨(-95728494122330873260226350991),(-95728494122330873258916803089)⟩⟩,⟨⟨(-99333743418307214337002106454),(-99333743418307214332966027419)⟩,⟨(-95583939170288144597506339404),(-95583939170288144596197939817)⟩⟩,⟨⟨(-99168053934458365226699122860),(-99168053934458365222675423328)⟩,⟨(-95424504390118105957142384760),(-95424504390118105955841601700)⟩⟩,⟨⟨(-98987983022727566818459607280),(-98987983022727566814439721516)⟩,⟨(-95251231074516442955670527425),(-95251231074516442954368745661)⟩⟩,⟨⟨(-98792403157023610422967910744),(-98792403157023610418960695582)⟩,⟨(-95063034260996026154243155586),(-95063034260996026152948495524)⟩⟩,⟨⟨(-98582596243772795321767800536),(-98582596243772795317762910645)⟩,⟨(-94861147464590688555126779087),(-94861147464590688553828917080)⟩⟩,⟨⟨(-98357243230529944045536423398),(-98357243230529944041548015921)⟩,⟨(-94644301426493266081663695205),(-94644301426493266080375850924)⟩⟩] +lemma amp0_10_8_eq : ∀ k : Fin 16, amp0_1Expr 0 8 k = amp0_10_8 k := by decide +kernel +noncomputable def amp0_10_9 : Fin 16 → CBox := ![⟨⟨(-98117827318132162268174432267),(-98117827318132162264200049987)⟩,⟨(-94413923357374700799021590985),(-94413923357374700797741035377)⟩⟩,⟨⟨(-97862836231602274215172783283),(-97862836231602274211215830412)⟩,⟨(-94168558069959724092914196798),(-94168558069959724091643801766)⟩⟩,⟨⟨(-97593956253311594762938170702),(-97593956253311594758976826263)⟩,⟨(-93909828190216683237276397667),(-93909828190216683235994805884)⟩⟩,⟨⟨(-97309479923753571667728085180),(-97309479923753571663787941719)⟩,⟨(-93636090714469347692938901950),(-93636090714469347691670335505)⟩⟩,⟨⟨(-97011298659173172573791241330),(-97011298659173172569869388199)⟩,⟨(-93349165658848020294159596942),(-93349165658848020292900899750)⟩⟩,⟨⟨(-96697507577810490789096431396),(-96697507577810490785190435731)⟩,⟨(-93047220050024606813073277046),(-93047220050024606811821703384)⟩⟩,⟨⟨(-96370205558044188550015047379),(-96370205558044188546131453049)⟩,⟨(-92732273534660635462090462589),(-92732273534660635460851959013)⟩⟩,⟨⟨(-96027287770934307127236272133),(-96027287770934307123372577743)⟩,⟨(-92402300740164300762855518641),(-92402300740164300761627273330)⟩⟩,⟨⟨(-95671063173512853653450618885),(-95671063173512853649610294543)⟩,⟨(-92059523461475563711053744716),(-92059523461475563709838751793)⟩⟩,⟨⟨(-95299224164355378711106447001),(-95299224164355378707295188387)⟩,⟨(-91701721208088443914877462899),(-91701721208088443913680798214)⟩⟩,⟨⟨(-94914292698040905299411556159),(-94914292698040905295573698031)⟩,⟨(-91331320731928079604184827779),(-91331320731928079602952587994)⟩⟩,⟨⟨(-94513755259951778682684345347),(-94513755259951778678872141705)⟩,⟨(-90945903402425945744099418931),(-90945903402425945742881480884)⟩⟩,⟨⟨(-94100350039536556448039010088),(-94100350039536556444250156288)⟩,⟨(-90548104043607403861037739204),(-90548104043607403859831551640)⟩⟩,⟨⟨(-93671354135815031221513325066),(-93671354135815031217753915999)⟩,⟨(-90135302542782621582978279564),(-90135302542782621581789303092)⟩⟩,⟨⟨(-93229725547044399277221031926),(-93229725547044399273481914264)⟩,⟨(-89710345235101690097798170885),(-89710345235101690096617270196)⟩⟩,⟨⟨(-92772528160957989227115770474),(-92772528160957989223407525495)⟩,⟨(-89270406845218719925236752568),(-89270406845218719924073705867)⟩⟩] +lemma amp0_10_9_eq : ∀ k : Fin 16, amp0_1Expr 0 9 k = amp0_10_9 k := by decide +kernel +noncomputable def amp0_10_10 : Fin 16 → CBox := ![⟨⟨(-92302943715722059947064674368),(-92302943715722059943368565801)⟩,⟨(-88818549002111678512356932192),(-88818549002111678511193389348)⟩⟩,⟨⟨(-91817818689331794955892159586),(-91817818689331794952224854042)⟩,⟨(-88351737227816605519619727411),(-88351737227816605518471322972)⟩⟩,⟨⟨(-91320562871286602585775190276),(-91320562871286602582135866880)⟩,⟨(-87873252593809106546798176151),(-87873252593809106545663805728)⟩⟩,⟨⟨(-90807800733330533654376050980),(-90807800733330533650760560019)⟩,⟨(-87379846996510465846560382513),(-87379846996510465845435651029)⟩⟩,⟨⟨(-90283174834126918863586418502),(-90283174834126918860003039877)⟩,⟨(-86875025489628705059146997311),(-86875025489628705058039564524)⟩⟩,⟨⟨(-89743082616973589530106354832),(-89743082616973589526550503988)⟩,⟨(-86355321511360877551632353502),(-86355321511360877550537406944)⟩⟩,⟨⟨(-89191404563291638404211500946),(-89191404563291638400684523854)⟩,⟨(-85824469056695405392185944281),(-85824469056695405391104478741)⟩⟩,⟨⟨(-88624305608966800484512975713),(-88624305608966800481019144123)⟩,⟨(-85278777833467737960384883144),(-85278777833467737959320609312)⟩⟩,⟨⟨(-88045909780575486901515800262),(-88045909780575486898056156037)⟩,⟨(-84722216188101268817802570883),(-84722216188101268816756198410)⟩⟩,⟨⟨(-87452143535854231264692411860),(-87452143535854231261270073541)⟩,⟨(-84150864352725385234423203519),(-84150864352725385233397334731)⟩⟩,⟨⟨(-86847380574940545547894445563),(-86847380574940545544513946367)⟩,⟨(-83568930922259665945790504721),(-83568930922259665944789216608)⟩⟩,⟨⟨(-86227302375482680929414301763),(-86227302375482680925916329422)⟩,⟨(-82972260396633638288678176781),(-82972260396633638287547773981)⟩⟩,⟨⟨(-85596538987522582851765946406),(-85596538987522582848302456714)⟩,⟨(-82365308043577433328582289436),(-82365308043577433327468714456)⟩⟩,⟨⟨(-84950519831010831763220955576),(-84950519831010831759791573980)⟩,⟨(-81743675820387909213468931074),(-81743675820387909212371427979)⟩⟩,⟨⟨(-84294138577486610823527343222),(-84294138577486610820133389617)⟩,⟨(-81112072664699187622550798139),(-81112072664699187621470368352)⟩⟩,⟨⟨(-83622564885704135709083887254),(-83622564885704135705723513243)⟩,⟨(-80465850578480383003330092519),(-80465850578480383002264563541)⟩⟩] +lemma amp0_10_10_eq : ∀ k : Fin 16, amp0_1Expr 0 10 k = amp0_10_10 k := by decide +kernel +noncomputable def amp0_10_11 : Fin 16 → CBox := ![⟨⟨(-82940963969010156757994619333),(-82940963969010156754668595451)⟩,⟨(-79809979790591775614989963296),(-79809979790591775613939816612)⟩⟩,⟨⟨(-82244237338764998506096491586),(-82244237338764998502802784629)⟩,⟨(-79139554278052403994008191766),(-79139554278052403992971078774)⟩⟩,⟨⟨(-81537830379687563398483073656),(-81537830379687563395227567744)⟩,⟨(-78459813864751100475884530408),(-78459813864751100474865862133)⟩⟩,⟨⟨(-80816367322455405387783327158),(-80816367322455405384557416238)⟩,⟨(-77765585714245505798026974174),(-77765585714245505797018079097)⟩⟩,⟨⟨(-80085583130664096360457272141),(-80085583130664096357270117172)⟩,⟨(-77062388297828446848290061402),(-77062388297828446847299513000)⟩⟩,⟨⟨(-79339814800775635972487733416),(-79339814800775635969337369081)⟩,⟨(-76344772387804779790481006927),(-76344772387804779789506525593)⟩⟩,⟨⟨(-78585097138824961219922227188),(-78585097138824961216813348812)⟩,⟨(-75618544978989134712556598574),(-75618544978989134711602470369)⟩⟩,⟨⟨(-77815469049967882124212914938),(-77815469049967882121122017054)⟩,⟨(-74877970005193248323902188961),(-74877970005193248322945409172)⟩⟩,⟨⟨(-77037276391381794198302620273),(-77037276391381794195252799735)⟩,⟨(-74129153770333134321410456297),(-74129153770333134320473027837)⟩⟩,⟨⟨(-76244248121117075183087653386),(-76244248121117075180077942512)⟩,⟨(-73366061961479269626971708983),(-73366061961479269626052316073)⟩⟩,⟨⟨(-75443053403218161398860781080),(-75443053403218161395886449575)⟩,⟨(-72595111984725529378594121498),(-72595111984725529377688000688)⟩⟩,⟨⟨(-74627098285122606642259781063),(-74627098285122606639328857219)⟩,⟨(-71809958806260327012769457566),(-71809958806260327011883951404)⟩⟩,⟨⟨(-73803388657376576763326359251),(-73803388657376576760436660520)⟩,⟨(-71017343847404899042482744242),(-71017343847404899041615551529)⟩⟩,⟨⟨(-72964993460313304081693344011),(-72964993460313304078846291677)⟩,⟨(-70210597692885282670886311360),(-70210597692885282670038418990)⟩⟩,⟨⟨(-72119270029093191232088571444),(-72119270029093191229287550412)⟩,⟨(-69396799941760439164001663619),(-69396799941760439163176138727)⟩⟩,⟨⟨(-71258934622973220004441036119),(-71258934622973220001689500642)⟩,⟨(-68568941811232553507890114505),(-68568941811232553507089902119)⟩⟩] +lemma amp0_10_11_eq : ∀ k : Fin 16, amp0_1Expr 0 11 k = amp0_10_11 k := by decide +kernel +noncomputable def amp0_10_12 : Fin 16 → CBox := ![⟨⟨(-70391712193813509571261216155),(-70391712193813509568471315931)⟩,⟨(-67734456639694820210090308617),(-67734456639694820209230696191)⟩⟩,⟨⟨(-69509949201036450703228543189),(-69509949201036450700476520750)⟩,⟨(-66885979804292678583255116402),(-66885979804292678582409091370)⟩⟩,⟨⟨(-68621756019654473383875633062),(-68621756019654473381162499396)⟩,⟨(-66031315517020554069715103316),(-66031315517020554068883471792)⟩⟩,⟨⟨(-67719090451193890521909756262),(-67719090451193890519234890096)⟩,⟨(-65162725168789013936781064745),(-65162725168789013935962853700)⟩⟩,⟨⟨(-66810467944816676739410142660),(-66810467944816676736774380290)⟩,⟨(-64288402754374619219763036442),(-64288402754374619218958896163)⟩⟩,⟨⟨(-65887436819631572712811394911),(-65887436819631572710212975984)⟩,⟨(-63400215640047914274228418944),(-63400215640047914273436281973)⟩⟩,⟨⟨(-64958939340497661771417715742),(-64958939340497661768861972052)⟩,⟨(-62506768524181493585306323643),(-62506768524181493584531178781)⟩⟩,⟨⟨(-64016091286586316731224394903),(-64016091286586316728699962163)⟩,⟨(-61599512561297110511742664154),(-61599512561297110510973204058)⟩⟩,⟨⟨(-63068285859916397837216097893),(-63068285859916397834735466964)⟩,⟨(-60687486364251667551252835021),(-60687486364251667550500950505)⟩⟩,⟨⟨(-62106180694855959235220775132),(-62106180694855959232781454616)⟩,⟨(-59761700237524378291962055058),(-59761700237524378291224978038)⟩⟩,⟨⟨(-61139646774134726473646370158),(-61139646774134726471250809112)⟩,⟨(-58831652538675531387730314863),(-58831652538675531387010287126)⟩⟩,⟨⟨(-60158855062333057633661438364),(-60158855062333057631310608627)⟩,⟨(-57887885273962785791763009442),(-57887885273962785791060596493)⟩⟩,⟨⟨(-59174184295460243032643081828),(-59174184295460243030341635905)⟩,⟨(-56940385386767494549038598812),(-56940385386767494548358176959)⟩⟩,⟨⟨(-58175286878534826679423900689),(-58175286878534826677118939768)⟩,⟨(-55979195899176309597688315858),(-55979195899176309596978614357)⟩⟩,⟨⟨(-57173082889346151025923505354),(-57173082889346151023664965493)⟩,⟨(-55014824660941311801125686987),(-55014824660941311800434671105)⟩⟩,⟨⟨(-56156670384966882376654981138),(-56156670384966882374442420941)⟩,⟨(-54036781272589524416343593922),(-54036781272589524415670470557)⟩⟩] +lemma amp0_10_12_eq : ∀ k : Fin 16, amp0_1Expr 0 12 k = amp0_10_12 k := by decide +kernel +noncomputable def amp0_10_13 : Fin 16 → CBox := ![⟨⟨(-55137548575880762631362308747),(-55137548575880762629194674063)⟩,⟨(-53056130854568041697546853732),(-53056130854568041696890538285)⟩⟩,⟨⟨(-54104220838967467992301157031),(-54104220838967467990172438808)⟩,⟨(-52061810776121379278163538194),(-52061810776121379277517880150)⟩⟩,⟨⟨(-53068808222202830134706524392),(-53068808222202830132627130212)⟩,⟨(-51065484521102381801834666514),(-51065484521102381801209626522)⟩⟩,⟨⟨(-52019173760407361914113762955),(-52019173760407361912080295479)⟩,⟨(-50055473289321845906160934112),(-50055473289321845905552874366)⟩⟩,⟨⟨(-50968108827519318223063657208),(-50968108827519318221080866302)⟩,⟨(-49044085586090699300577410363),(-49044085586090699299990864339)⟩⟩,⟨⟨(-49902784160230928602498832578),(-49902784160230928600533203189)⟩,⟨(-48018976447035198879767856707),(-48018976447035198879170204831)⟩⟩,⟨⟨(-48836716802886243802220521142),(-48836716802886243800301262422)⟩,⟨(-46993152654139820991757141621),(-46993152654139820991176471158)⟩⟩,⟨⟨(-47756325749257686644692101436),(-47756325749257686642819894368)⟩,⟨(-45953545878068969524282565434),(-45953545878068969523719160307)⟩⟩,⟨⟨(-46675917248613400674147712577),(-46675917248613400672321795103)⟩,⟨(-44913922313599405413758795382),(-44913922313599405413211921845)⟩⟩,⟨⟨(-45581090124830186185157187920),(-45581090124830186183374572440)⟩,⟨(-43860424422545501058347671712),(-43860424422545501057814081133)⟩⟩,⟨⟨(-44487013233185145102336874035),(-44487013233185145100601004227)⟩,⟨(-42807648442703145243876167110),(-42807648442703145243359192619)⟩⟩,⟨⟨(-43378385931647065403971604445),(-43378385931647065402261204427)⟩,⟨(-41740871324413180698551277289),(-41740871324413180698030068925)⟩⟩,⟨⟨(-42271325079137887374608309479),(-42271325079137887372948862495)⟩,⟨(-40675601522404063164005546779),(-40675601522404063163504666417)⟩⟩,⟨⟨(-41149537991221482707985011583),(-41149537991221482706374331971)⟩,⟨(-39596161393767425467437586120),(-39596161393767425466954548815)⟩⟩,⟨⟨(-40030189663707965554003518417),(-40030189663707965552439924268)⟩,⟨(-38519067963422614613546822131),(-38519067963422614613080072692)⟩⟩,⟨⟨(-38895886391455750092010672385),(-38895886391455750090497250542)⟩,⟨(-37427584130793464683540494601),(-37427584130793464683092615623)⟩⟩] +lemma amp0_10_13_eq : ∀ k : Fin 16, amp0_1Expr 0 13 k = amp0_10_13 k := by decide +kernel +noncomputable def amp0_10_14 : Fin 16 → CBox := ![⟨⟨(-37764959745782167173247791561),(-37764959745782167171767492929)⟩,⟨(-36339349458604525326671467925),(-36339349458604525326226141451)⟩⟩,⟨⟨(-36618785523137895750346176208),(-36618785523137895748914504857)⟩,⟨(-35236442798634725059103185713),(-35236442798634725058674935234)⟩⟩,⟨⟨(-35477003336654443686195981296),(-35477003336654443684810546426)⟩,⟨(-34137762377431157503618652492),(-34137762377431157503205291328)⟩⟩,⟨⟨(-34319603042534723127695399920),(-34319603042534723126362435725)⟩,⟨(-33024053425147536339850786898),(-33024053425147536339457908990)⟩⟩,⟨⟨(-33167703141944086271752816216),(-33167703141944086270455989412)⟩,⟨(-31915637229005024094955224892),(-31915637229005024094567256132)⟩⟩,⟨⟨(-31999718726471072330800252651),(-31999718726471072329552632317)⟩,⟨(-30791743701200636930357765413),(-30791743701200636929986864525)⟩⟩,⟨⟨(-30838456118783685884717469114),(-30838456118783685883509633873)⟩,⟨(-29674318235953704693155370567),(-29674318235953704692792646094)⟩⟩,⟨⟨(-29660523164173378280824280942),(-29660523164173378279667032268)⟩,⟨(-28540851721901050822607348422),(-28540851721901050822262761892)⟩⟩,⟨⟨(-28490673221862566553249567413),(-28490673221862566552141355467)⟩,⟨(-27415163090060025285632028068),(-27415163090060025285304297709)⟩⟩,⟨⟨(-27303416190504248021624539702),(-27303416190504248020558816942)⟩,⟨(-26272724478973356682546472239),(-26272724478973356682228846381)⟩⟩,⟨⟨(-26125779465830798798399375439),(-26125779465830798797384282444)⟩,⟨(-25139543012310348165201504618),(-25139543012310348164902065951)⟩⟩,⟨⟨(-24929804891098692667014519638),(-24929804891098692666043479656)⟩,⟨(-23988715941201132046954245460),(-23988715941201132046666190077)⟩⟩,⟨⟨(-23745214534701743939296977839),(-23745214534701743938369534520)⟩,⟨(-22848843339292443595823170274),(-22848843339292443595546354198)⟩⟩,⟨⟨(-22541100864556438565584475368),(-22541100864556438564708163749)⟩,⟨(-21690184419970276426078355164),(-21690184419970276425819522827)⟩⟩,⟨⟨(-21350434376680880407104511624),(-21350434376680880406273488171)⟩,⟨(-20544465057820243452158183025),(-20544465057820243451912060114)⟩⟩,⟨⟨(-20138716125252464465636544887),(-20138716125252464464852067671)⟩,⟨(-19378488626746612489096907573),(-19378488626746612488864158882)⟩⟩] +lemma amp0_10_14_eq : ∀ k : Fin 16, amp0_1Expr 0 14 k = amp0_10_14 k := by decide +kernel +noncomputable def amp0_10_15 : Fin 16 → CBox := ![⟨⟨(-18942914667987845094823913273),(-18942914667987845094086518914)⟩,⟨(-18227828137998154550020369747),(-18227828137998154549801924296)⟩⟩,⟨⟨(-17724056361181499483814182569),(-17724056361181499483125296384)⟩,⟨(-17054981185433729370571370137),(-17054981185433729370368001668)⟩⟩,⟨⟨(-16524158055702303954067411539),(-16524158055702303953426708000)⟩,⟨(-15900378502652747126400926080),(-15900378502652747126212812910)⟩⟩,⟨⟨(-15298508650941552845630333349),(-15298508650941552845036189363)⟩,⟨(-14720996813034873395591659908),(-14720996813034873395416572593)⟩⟩,⟨⟨(-14095709680065119182972449216),(-14095709680065119182424942221)⟩,⟨(-13563602963674017036776548538),(-13563602963674017036615154012)⟩⟩,⟨⟨(-12863416457788331101576610517),(-12863416457788331101077447083)⟩,⟨(-12377828257670592144088338098),(-12377828257670592143941513841)⟩⟩,⟨⟨(-11659192799329569796510885923),(-11659192799329569796059833298)⟩,⟨(-11219063502044455816169433770),(-11219063502044455816037683548)⟩⟩,⟨⟨(-10420021741238073901778753196),(-10420021741238073901374903331)⟩,⟨(-10026670595442591581713583048),(-10026670595442591581595127046)⟩⟩,⟨⟨(-9216400337971305960888228836),(-9216400337971305960531809935)⟩,⟨(-8868485360145152284717966999),(-8868485360145152284613946464)⟩⟩,⟨⟨(-7969307376213303340133165057),(-7969307376213303339825525225)⟩,⟨(-7668469598186034814264267358),(-7668469598186034814174852464)⟩⟩,⟨⟨(-6769574453262926753952261586),(-6769574453262926753691892283)⟩,⟨(-6514026054817607366941342927),(-6514026054817607366866309934)⟩⟩,⟨⟨(-5511459324147942579986754002),(-5511459324147942579775383806)⟩,⟨(-5303404207374145887011630210),(-5303404207374145886951128831)⟩⟩,⟨⟨(-4322526319102367440630104977),(-4322526319102367440465544606)⟩,⟨(-4159352889854990063696727991),(-4159352889854990063650445197)⟩⟩,⟨⟨(-3043243487890630820824762057),(-3043243487890630820709671808)⟩,⟨(-2928362411572052199892260607),(-2928362411572052199860413868)⟩⟩,⟨⟨(-1887793341088553155446880160),(-1887793341088553155378063613)⟩,⟨(-1816529989419765287734937456),(-1816529989419765287717661492)⟩⟩,⟨⟨(-536329754622069946055195813),(-536329754622069946037194987)⟩,⟨(-516083547009096694060614982),(-516083547009096694057198524)⟩⟩] +lemma amp0_10_15_eq : ∀ k : Fin 16, amp0_1Expr 0 15 k = amp0_10_15 k := by decide +kernel +noncomputable def amp0_10 : Fin 16 → Fin 16 → CBox := ![amp0_10_0,amp0_10_1,amp0_10_2,amp0_10_3,amp0_10_4,amp0_10_5,amp0_10_6,amp0_10_7,amp0_10_8,amp0_10_9,amp0_10_10,amp0_10_11,amp0_10_12,amp0_10_13,amp0_10_14,amp0_10_15] +lemma amp0_10_eq (i k : Fin 16) : amp0_1Expr 0 i k = amp0_10 i k := by + fin_cases i + · exact amp0_10_0_eq k + · exact amp0_10_1_eq k + · exact amp0_10_2_eq k + · exact amp0_10_3_eq k + · exact amp0_10_4_eq k + · exact amp0_10_5_eq k + · exact amp0_10_6_eq k + · exact amp0_10_7_eq k + · exact amp0_10_8_eq k + · exact amp0_10_9_eq k + · exact amp0_10_10_eq k + · exact amp0_10_11_eq k + · exact amp0_10_12_eq k + · exact amp0_10_13_eq k + · exact amp0_10_14_eq k + · exact amp0_10_15_eq k +noncomputable def amp0_11_0 : Fin 16 → CBox := ![⟨⟨(-178776584874023315354484384),(-178776584874023315342979216)⟩,⟨(-309650128205458016436368989),(-309650128205458016434319114)⟩⟩,⟨⟨(-629264447029517718491981547),(-629264447029517718449666377)⟩,⟨(-1089917993651859172640962474),(-1089917993651859172630596895)⟩⟩,⟨⟨(-1014414495963543606957205285),(-1014414495963543606887606003)⟩,⟨(-1757017446943231319935356364),(-1757017446943231319916248321)⟩⟩,⟨⟨(-1440842106367455813565551541),(-1440842106367455813466331653)⟩,⟨(-2495611733912994038218036795),(-2495611733912994038190267118)⟩⟩,⟨⟨(-1837153108049314193357202823),(-1837153108049314193230176446)⟩,⟨(-3182042524424487532206978126),(-3182042524424487532170677298)⟩⟩,⟨⟨(-2256524817754308918018828668),(-2256524817754308917862555955)⟩,⟨(-3908415632890564420164805757),(-3908415632890564420119785960)⟩⟩,⟨⟨(-2656435792071101113418620190),(-2656435792071101113234276570)⟩,⟨(-4601081758911620888558560415),(-4601081758911620888504911478)⟩⟩,⟨⟨(-3072133445990435320343374868),(-3072133445990435320129971389)⟩,⟨(-5321091216087091370830780200),(-5321091216087091370768367878)⟩⟩,⟨⟨(-3473340580412691300646393309),(-3473340580412691300404825533)⟩,⟨(-6016002357265554949028149829),(-6016002357265554948957076227)⟩⟩,⟨⟨(-3886397599776523265563463647),(-3886397599776523265293442760)⟩,⟨(-6731438101226673489701660262),(-6731438101226673489622610128)⟩⟩,⟨⟨(-4287805485929443700591551923),(-4287805485929443700293133943)⟩,⟨(-7426696954602355286453002859),(-7426696954602355286364908304)⟩⟩,⟨⟨(-4698569893355039727729822288),(-4698569893355039727402641524)⟩,⟨(-8138161778204410222065929123),(-8138161778204410221969092407)⟩⟩,⟨⟨(-5099502883647184281955289766),(-5099502883647184281600217804)⟩,⟨(-8832598087820924037354995945),(-8832598087820924037249943555)⟩⟩,⟨⟨(-5508052685234101318107272532),(-5508052685234101317724100648)⟩,⟨(-9540227101591648275840555648),(-9540227101591648275727687746)⟩⟩,⟨⟨(-5908018787060499828029020756),(-5908018787060499827617472228)⟩,⟨(-10232988711260237622342822082),(-10232988711260237622220801001)⟩⟩,⟨⟨(-6314304889329281698371852841),(-6314304889329281697931624554)⟩,⟨(-10936696882798892730012221848),(-10936696882798892729881154577)⟩⟩] +lemma amp0_11_0_eq : ∀ k : Fin 16, amp0_1Expr 1 0 k = amp0_11_0 k := by decide +kernel +noncomputable def amp0_11_1 : Fin 16 → CBox := ![⟨⟨(-6712905375084154821982200235),(-6712905375084154821514003951)⟩,⟨(-11627093176047967493458144544),(-11627093176047967493318495329)⟩⟩,⟨⟨(-7116811458893626802477741022),(-7116811458893626801981592243)⟩,⟨(-12326679034692146071294909815),(-12326679034692146071147236068)⟩⟩,⟨⟨(-7513700288185479521977172773),(-7513700288185479521453706932)⟩,⟨(-13014110651982165855647013099),(-13014110651982165855491713696)⟩⟩,⟨⟨(-7915071511567247979887519778),(-7915071511567247979334651009)⟩,⟨(-13709306003575466157493902165),(-13709306003575466157327812518)⟩⟩,⟨⟨(-8309934963699564222466113031),(-8309934963699564221886553400)⟩,⟨(-14393229564720679228172547276),(-14393229564720679227999714046)⟩⟩,⟨⟨(-8708593155276932932933869376),(-8708593155276932932327349918)⟩,⟨(-15083725807386208899120902771),(-15083725807386208898941239571)⟩⟩,⟨⟨(-9101138730168082674014967765),(-9101138730168082673379484450)⟩,⟨(-15763634687384014009527883344),(-15763634687384014009337307828)⟩⟩,⟨⟨(-9496891073954188851229403341),(-9496891073954188850567570952)⟩,⟨(-16449097854036015171379216841),(-16449097854036015171182578625)⟩⟩,⟨⟨(-9886841054724459427093644857),(-9886841054724459426403459546)⟩,⟨(-17124511033140630493564409054),(-17124511033140630493357657135)⟩⟩,⟨⟨(-10279485372927895295064086069),(-10279485372927895294344948260)⟩,⟨(-17804590941572222815893222340),(-17804590941572222815675587656)⟩⟩,⟨⟨(-10666572908823690777097640184),(-10666572908823690776353321472)⟩,⟨(-18475046220720382158214659248),(-18475046220720382157992118715)⟩⟩,⟨⟨(-11055901047314695424087822138),(-11055901047314695423315113072)⟩,⟨(-19149382337403014456973134935),(-19149382337403014456740353679)⟩⟩,⟨⟨(-11439867680844907709407928259),(-11439867680844907708611350290)⟩,⟨(-19814432055088521803910472139),(-19814432055088521803674745394)⟩⟩,⟨⟨(-11825667778884814562247395165),(-11825667778884814561421447409)⟩,⟨(-20482657426458694502171191496),(-20482657426458694501923174796)⟩⟩,⟨⟨(-12206261841045965250303319765),(-12206261841045965249450240590)⟩,⟨(-21141865679180835035461911428),(-21141865679180835035204961140)⟩⟩,⟨⟨(-12588319915260722391276407051),(-12588319915260722390395354446)⟩,⟨(-21803609675162715196002880755),(-21803609675162715195735684870)⟩⟩] +lemma amp0_11_1_eq : ∀ k : Fin 16, amp0_1Expr 1 1 k = amp0_11_1 k := by decide +kernel +noncomputable def amp0_11_2 : Fin 16 → CBox := ![⟨⟨(-12965295463818583364203171244),(-12965295463818583363299469731)⟩,⟨(-22456550478476078810124296761),(-22456550478476078809855569374)⟩⟩,⟨⟨(-13343396554569321851539941168),(-13343396554569321850607873060)⟩,⟨(-23111440778053568768128093279),(-23111440778053568767848043615)⟩⟩,⟨⟨(-13716512663740494236206183389),(-13716512663740494235246931129)⟩,⟨(-23757696836260455280462551672),(-23757696836260455280172729289)⟩⟩,⟨⟨(-14090441693045962458419706368),(-14090441693045962457432684290)⟩,⟨(-24405360913442437898403328068),(-24405360913442437898102799850)⟩⟩,⟨⟨(-14459461977215688468213152796),(-14459461977215688467197783495)⟩,⟨(-25044522794647908419130766374),(-25044522794647908418818041355)⟩⟩,⟨⟨(-14829004411061715034340598804),(-14829004411061715033305360617)⟩,⟨(-25684589065621887146325700266),(-25684589065621887146015515571)⟩⟩,⟨⟨(-15193696708276728728619651571),(-15193696708276728727557601883)⟩,⟨(-26316254653527300635008603027),(-26316254653527300634688448679)⟩⟩,⟨⟨(-15558639082871133558288778445),(-15558639082871133557201057448)⟩,⟨(-26948353388159643248255277229),(-26948353388159643247927153107)⟩⟩,⟨⟨(-15918775249752562215142452724),(-15918775249752562214028212544)⟩,⟨(-27572127526841381714569539261),(-27572127526841381714231496184)⟩⟩,⟨⟨(-16278905600962081267657470528),(-16278905600962081266516457326)⟩,⟨(-28195891592483892595054284973),(-28195891592483892594705882695)⟩⟩,⟨⟨(-16634261386743642867755712067),(-16634261386743642866588299855)⟩,⟨(-28811385868221119327860714024),(-28811385868221119327502122898)⟩⟩,⟨⟨(-16989369609173106074616120860),(-16989369609173106073432053644)⟩,⟨(-29426451351654419580346446218),(-29426451351654419579994518603)⟩⟩,⟨⟨(-17339724586802453971638216843),(-17339724586802453970426469302)⟩,⟨(-30033283973593107543696560467),(-30033283973593107543331724619)⟩⟩,⟨⟨(-17689602740734276711841190715),(-17689602740734276710603360819)⟩,⟨(-30639290712661429081100799909),(-30639290712661429080725775913)⟩⟩,⟨⟨(-18034740279655822664378048668),(-18034740279655822663113149945)⟩,⟨(-31237086465672827566898122916),(-31237086465672827566510728090)⟩⟩,⟨⟨(-18379182858626920877403735614),(-18379182858626920876115258656)⟩,⟨(-31833678512740825018528112239),(-31833678512740825018134322971)⟩⟩] +lemma amp0_11_2_eq : ∀ k : Fin 16, amp0_1Expr 1 2 k = amp0_11_2 k := by decide +kernel +noncomputable def amp0_11_3 : Fin 16 → CBox := ![⟨⟨(-18718890128322294125839856546),(-18718890128322294124525944147)⟩,⟨(-32422068763553714649806156353),(-32422068763553714649402282334)⟩⟩,⟨⟨(-19057694296448717008934580850),(-19057694296448717007594909433)⟩,⟨(-33008894796564787080675412193),(-33008894796564787080260802663)⟩⟩,⟨⟨(-19391762292844942226773189275),(-19391762292844942225407757544)⟩,⟨(-33587517539505785758612989515),(-33587517539505785758187168614)⟩⟩,⟨⟨(-19724728098486747677851375998),(-19724728098486747676476863246)⟩,⟨(-34164231232060496729423159288),(-34164231232060496729014906175)⟩⟩,⟨⟨(-20052951687444352544862548176),(-20052951687444352543461467487)⟩,⟨(-34732731164377671475057805666),(-34732731164377671474636357896)⟩⟩,⟨⟨(-20379882258044908824862558866),(-20379882258044908823436500890)⟩,⟨(-35298991523205318832638188918),(-35298991523205318832206172275)⟩⟩,⟨⟨(-20702060231618653078725654112),(-20702060231618653077275089137)⟩,⟨(-35857020142514626975177233035),(-35857020142514626974734986823)⟩⟩,⟨⟨(-21022761953305465946062365892),(-21022761953305465944588155727)⟩,⟨(-36412491818551000530751701013),(-36412491818551000530300570303)⟩⟩,⟨⟨(-21338697095528772244069995702),(-21338697095528772242571456654)⟩,⟨(-36959707536778266307045598493),(-36959707536778266306583922435)⟩⟩,⟨⟨(-21652979780165887257472608013),(-21652979780165887255953954585)⟩,⟨(-37504061114508896151183794186),(-37504061114508896150718707268)⟩⟩,⟨⟨(-21962478939877190904608599454),(-21962478939877190903066190844)⟩,⟨(-38040129384028748564537051367),(-38040129384028748564061769183)⟩⟩,⟨⟨(-22270155981605558913479585702),(-22270155981605558911915255282)⟩,⟨(-38573041652624771531857821866),(-38573041652624771531375337697)⟩⟩,⟨⟨(-22573030150397963507650786622),(-22573030150397963506064095498)⟩,⟨(-39097635101273408362068638847),(-39097635101273408361577712220)⟩⟩,⟨⟨(-22873918673218157794977378037),(-22873918673218157793368666115)⟩,⟨(-39618789310212332441829061990),(-39618789310212332441330083075)⟩⟩,⟨⟨(-23169983067012150234766239622),(-23169983067012150233135448357)⟩,⟨(-40131587882575607149953069841),(-40131587882575607149445454822)⟩⟩,⟨⟨(-23463904064604503190781655821),(-23463904064604503189129188208)⟩,⟨(-40640673983816892126054185171),(-40640673983816892125538417715)⟩⟩] +lemma amp0_11_3_eq : ∀ k : Fin 16, amp0_1Expr 1 3 k = amp0_11_3 k := by decide +kernel +noncomputable def amp0_11_4 : Fin 16 → CBox := ![⟨⟨(-23752978207657740001846046396),(-23752978207657740000197465857)⟩,⟨(-41141365086739532104734068703),(-41141365086739532104253941271)⟩⟩,⟨⟨(-24039756676364397077732973415),(-24039756676364397076059067204)⟩,⟨(-41638079965056263498400998171),(-41638079965056263497905683236)⟩⟩,⟨⟨(-24321664486771101360938904525),(-24321664486771101359240974038)⟩,⟨(-42126358615731169602531786816),(-42126358615731169602023051394)⟩⟩,⟨⟨(-24601129552458858921487545584),(-24601129552458858919766794339)⟩,⟨(-42610406308442939425489646545),(-42610406308442939424969330917)⟩⟩,⟨⟨(-24875699428374202214469580135),(-24875699428374202212726632626)⟩,⟨(-43085975283756196207661674540),(-43085975283756196207130370842)⟩⟩,⟨⟨(-25147684467739387133340767624),(-25147684467739387131574975927)⟩,⟨(-43557067190835317627156472899),(-43557067190835317626612800413)⟩⟩,⟨⟨(-25414749373705691728087170126),(-25414749373705691726301361840)⟩,⟨(-44019637176887561776183025390),(-44019637176887561775631389644)⟩⟩,⟨⟨(-25679092130460598066496228911),(-25679092130460598064688911091)⟩,⟨(-44477492262199880592846273778),(-44477492262199880592283816702)⟩⟩,⟨⟨(-25938489683322627375136987486),(-25938489683322627373307989844)⟩,⟨(-44926782003115948994341313377),(-44926782003115948993767245503)⟩⟩,⟨⟨(-26195032379608320407044041303),(-26195032379608320405201150697)⟩,⟨(-45371126987393480827533959144),(-45371126987393480826961482221)⟩⟩,⟨⟨(-26446604933591878657903083258),(-26446604933591878656038617574)⟩,⟨(-45806863432682867874288604156),(-45806863432682867873703915356)⟩⟩,⟨⟨(-26695194376888032120563423452),(-26695194376888032118679039653)⟩,⟨(-46237432978697068108974036841),(-46237432978697068108379707800)⟩⟩,⟨⟨(-26938789107485135129675858844),(-26938789107485135127771055622)⟩,⟨(-46659351428547303478816184505),(-46659351428547303478210847458)⟩⟩,⟨⟨(-27179276793229187799912810226),(-27179276793229187797990736907)⟩,⟨(-47075888318850660285530718245),(-47075888318850660284919517280)⟩⟩,⟨⟨(-27414745779588332835787574819),(-27414745779588332833845517253)⟩,⟨(-47483732566831442396404915060),(-47483732566831442395782647264)⟩⟩,⟨⟨(-27646987989670052253090526337),(-27646987989670052251130545258)⟩,⟨(-47885987874355065368993977978),(-47885987874355065368363889967)⟩⟩] +lemma amp0_11_4_eq : ∀ k : Fin 16, amp0_1Expr 1 4 k = amp0_11_4 k := by decide +kernel +noncomputable def amp0_11_5 : Fin 16 → CBox := ![⟨⟨(-27874188295234711903457113622),(-27874188295234711901478686544)⟩,⟨(-48279510347088229801998055511),(-48279510347088229801358738124)⟩⟩,⟨⟨(-28098046192495536941608378795),(-28098046192495536939611865484)⟩,⟨(-48667243598819512573530478884),(-48667243598819512572882221011)⟩⟩,⟨⟨(-28316839943670277254842951463),(-28316839943670277252827891722)⟩,⟨(-49046205492232745528081358645),(-49046205492232745527422856787)⟩⟩,⟨⟨(-28532179662507527617694597112),(-28532179662507527615661537261)⟩,⟨(-49419184826146459997149373662),(-49419184826146459996481228673)⟩⟩,⟨⟨(-28742434125160893643580619310),(-28742434125160893641529591085)⟩,⟨(-49783356237980182973206906069),(-49783356237980182972528664388)⟩⟩,⟨⟨(-28949126858313515183077182820),(-28949126858313515181058947824)⟩,⟨(-50141358553355799567474302833),(-50141358553355799566873529965)⟩⟩,⟨⟨(-29150714511951410422012941897),(-29150714511951410419974553237)⟩,⟨(-50490518611635231140653922111),(-50490518611635231140038400838)⟩⟩,⟨⟨(-29348636593525162300957118574),(-29348636593525162298900200192)⟩,⟨(-50833329712860761290681542530),(-50833329712860761290053719046)⟩⟩,⟨⟨(-29541435202988933495292478720),(-29541435202988933493218227892)⟩,⟨(-51167266700080642776230929886),(-51167266700080642775592365587)⟩⟩,⟨⟨(-29730468187763879468528230817),(-29730468187763879466437110783)⟩,⟨(-51494681434017243235311566569),(-51494681434017243234662687244)⟩⟩,⟨⟨(-29914360872324529843829346659),(-29914360872324529841722939614)⟩,⟨(-51813192906816526530979412101),(-51813192906816526530322444166)⟩⟩,⟨⟨(-30094391611375639621658806304),(-30094391611375639619537679823)⟩,⟨(-52125015293777223035488198387),(-52125015293777223034823738714)⟩⟩,⟨⟨(-30269266911110177885258042844),(-30269266911110177883120827489)⟩,⟨(-52427908197906279507936229508),(-52427908197906279507261390617)⟩⟩,⟨⟨(-30440187623762200862393720773),(-30440187623762200860243298279)⟩,⟨(-52723951556285463928078905691),(-52723951556285463927398283437)⟩⟩,⟨⟨(-30605939563110598319101929127),(-30605939563110598316937075415)⟩,⟨(-53011042336689963311771836447),(-53011042336689963311082793783)⟩⟩,⟨⟨(-30767647905240686649495257051),(-30767647905240686647315823005)⟩,⟨(-53291129401267007107414159316),(-53291129401267007106716033608)⟩⟩] +lemma amp0_11_5_eq : ∀ k : Fin 16, amp0_1Expr 1 5 k = amp0_11_5 k := by decide +kernel +noncomputable def amp0_11_6 : Fin 16 → CBox := ![⟨⟨(-30924176053652663076181365661),(-30924176053652663073993066328)⟩,⟨(-53562244107131231955142051541),(-53562244107131231954444223520)⟩⟩,⟨⟨(-31076575182348133092885465817),(-31076575182348133090682182913)⟩,⟨(-53826207141061014058678902531),(-53826207141061014057970362117)⟩⟩,⟨⟨(-31223784711938343740985163303),(-31223784711938343738770583719)⟩,⟨(-54081181525669572949786967739),(-54081181525669572949073581855)⟩⟩,⟨⟨(-31366783346512185483162593251),(-31366783346512185480933795541)⟩,⟨(-54328862426164442316622643522),(-54328862426164442315898930984)⟩⟩,⟨⟨(-31504585086650592894713159934),(-31504585086650592892472335750)⟩,⟨(-54567542041455567446459651359),(-54567542041455567445728888530)⟩⟩,⟨⟨(-31638097566013635100290952431),(-31638097566013635098037465633)⟩,⟨(-54798792439156847762510896667),(-54798792439156847761771552796)⟩⟩,⟨⟨(-31766408054785126237524558180),(-31766408054785126235275986949)⟩,⟨(-55021032724853066348926477740),(-55021032724853066348208478928)⟩⟩,⟨⟨(-31890354391170951218307857087),(-31890354391170951216045780722)⟩,⟨(-55235714076885338226632246830),(-55235714076885338225903251076)⟩⟩,⟨⟨(-32009095923644769042904902982),(-32009095923644769040631380310)⟩,⟨(-55441380444098580457713311185),(-55441380444098580456976363998)⟩⟩,⟨⟨(-32123401852681396183832921252),(-32123401852681396181549245557)⟩,⟨(-55639364120796381277254277554),(-55639364120796381276511175407)⟩⟩,⟨⟨(-32232502525936830263528395639),(-32232502525936830261233893403)⟩,⟨(-55828332030014764087843966228),(-55828332030014764087093022030)⟩⟩,⟨⟨(-32337099553057724191761609327),(-32337099553057724189458600516)⟩,⟨(-56009499395308812176495758165),(-56009499395308812175740539850)⟩⟩,⟨⟨(-32436493307917857223075420878),(-32436493307917857220763254755)⟩,⟨(-56181654428681608615763341170),(-56181654428681608615002201303)⟩⟩,⟨⟨(-32531318751103864921480242651),(-32531318751103864919158089670)⟩,⟨(-56345896914130009942365838601),(-56345896914130009941596883530)⟩⟩,⟨⟨(-32620945410534091405559826738),(-32620945410534091403236377827)⟩,⟨(-56501134841975834455748518079),(-56501134841975834454986281059)⟩⟩,⟨⟨(-32705942439377387423228351680),(-32705942439377387420896475738)⟩,⟨(-56648354014424820479412954591),(-56648354014424820478644621226)⟩⟩] +lemma amp0_11_6_eq : ∀ k : Fin 16, amp0_1Expr 1 6 k = amp0_11_6 k := by decide +kernel +noncomputable def amp0_11_7 : Fin 16 → CBox := ![⟨⟨(-32785747743509981349016910741),(-32785747743509981346677902366)⟩,⟨(-56786580855895959648998217123),(-56786580855895959648225510554)⟩⟩,⟨⟨(-32860865414590931774428526299),(-32860865414590931772081710761)⟩,⟨(-56916688478754413133076067452),(-56916688478754413132297350248)⟩⟩,⟨⟨(-32930801052341203474829639764),(-32930801052341203472479895678)⟩,⟨(-57037820556597615692545893352),(-57037820556597615691769097314)⟩⟩,⟨⟨(-32995994340909188939994542326),(-32995994340909188937638567273)⟩,⟨(-57150738644709865773402316455),(-57150738644709865772621247396)⟩⟩,⟨⟨(-33056017978152788409408638310),(-33056017978152788407049543752)⟩,⟨(-57254702634070863574285430856),(-57254702634070863573504961020)⟩⟩,⟨⟨(-33111247806102404779510483160),(-33111247806102404777145561464)⟩,⟨(-57350363502172886758503803643),(-57350363502172886757718763890)⟩⟩,⟨⟨(-33161323110387142481238059372),(-33161323110387142478869848788)⟩,⟨(-57437096473398523956135810595),(-57437096473398523955350081853)⟩⟩,⟨⟨(-33206556370521783192683288994),(-33206556370521783190312083676)⟩,⟨(-57515442778143701503650014865),(-57515442778143701502863622417)⟩⟩,⟨⟨(-33246653032290985853640496739),(-33246653032290985851266486600)⟩,⟨(-57584892233541865100732136144),(-57584892233541865099944895271)⟩⟩,⟨⟨(-33281862608866566225882722668),(-33281862608866566223505814664)⟩,⟨(-57645877009083757309594357106),(-57645877009083757308805617940)⟩⟩,⟨⟨(-33311956359174495041294188221),(-33311956359174495038915819622)⟩,⟨(-57698000913607381564052023818),(-57698000913607381563263764202)⟩⟩,⟨⟨(-33337121144716975242292506833),(-33337121144716975239912727227)⟩,⟨(-57741587600728532004062966020),(-57741587600728532003274778948)⟩⟩,⟨⟨(-33357193769420233717574084032),(-33357193769420233715194243335)⟩,⟨(-57776354406555837842118138313),(-57776354406555837841331852689)⟩⟩,⟨⟨(-33372298677811606174485428214),(-33372298677811606172106177037)⟩,⟨(-57802516875333368417352874889),(-57802516875333368416569120836)⟩⟩,⟨⟨(-33382338028223777528404141187),(-33382338028223777526026676478)⟩,⟨(-57819905540322236752020786394),(-57819905540322236751241130528)⟩⟩,⟨⟨(-33387374004052282217595804687),(-33387374004052282215221630275)⟩,⟨(-57828628106322895644837816066),(-57828628106322895644064362760)⟩⟩] +lemma amp0_11_7_eq : ∀ k : Fin 16, amp0_1Expr 1 7 k = amp0_11_7 k := by decide +kernel +noncomputable def amp0_11_8 : Fin 16 → CBox := ![⟨⟨(-33387374004052282217595804687),(-33387374004052282215221630275)⟩,⟨(-57828628106322895644837816066),(-57828628106322895644064362760)⟩⟩,⟨⟨(-33382338028223777528404141187),(-33382338028223777526026676478)⟩,⟨(-57819905540322236752020786394),(-57819905540322236751241130528)⟩⟩,⟨⟨(-33372298677811606174485428214),(-33372298677811606172106177037)⟩,⟨(-57802516875333368417352874889),(-57802516875333368416569120836)⟩⟩,⟨⟨(-33357193769420233717574084032),(-33357193769420233715194243335)⟩,⟨(-57776354406555837842118138313),(-57776354406555837841331852689)⟩⟩,⟨⟨(-33337121144716975242292506833),(-33337121144716975239912727227)⟩,⟨(-57741587600728532004062966020),(-57741587600728532003274778948)⟩⟩,⟨⟨(-33311956359174495041294188221),(-33311956359174495038915819622)⟩,⟨(-57698000913607381564052023818),(-57698000913607381563263764202)⟩⟩,⟨⟨(-33281862608866566225882722668),(-33281862608866566223505814664)⟩,⟨(-57645877009083757309594357106),(-57645877009083757308805617940)⟩⟩,⟨⟨(-33246653032290985853640496739),(-33246653032290985851266486600)⟩,⟨(-57584892233541865100732136144),(-57584892233541865099944895271)⟩⟩,⟨⟨(-33206556370521783192683288994),(-33206556370521783190312083676)⟩,⟨(-57515442778143701503650014865),(-57515442778143701502863622417)⟩⟩,⟨⟨(-33161323110387142481238059372),(-33161323110387142478869848788)⟩,⟨(-57437096473398523956135810595),(-57437096473398523955350081853)⟩⟩,⟨⟨(-33111247806102404779510483160),(-33111247806102404777145561464)⟩,⟨(-57350363502172886758503803643),(-57350363502172886757718763890)⟩⟩,⟨⟨(-33056017978152788409408638310),(-33056017978152788407049543752)⟩,⟨(-57254702634070863574285430856),(-57254702634070863573504961020)⟩⟩,⟨⟨(-32995994340909188939994542326),(-32995994340909188937638567273)⟩,⟨(-57150738644709865773402316455),(-57150738644709865772621247396)⟩⟩,⟨⟨(-32930801052341203474829639764),(-32930801052341203472479895678)⟩,⟨(-57037820556597615692545893352),(-57037820556597615691769097314)⟩⟩,⟨⟨(-32860865414590931774428526299),(-32860865414590931772081710761)⟩,⟨(-56916688478754413133076067452),(-56916688478754413132297350248)⟩⟩,⟨⟨(-32785747743509981349016910741),(-32785747743509981346677902366)⟩,⟨(-56786580855895959648998217123),(-56786580855895959648225510554)⟩⟩] +lemma amp0_11_8_eq : ∀ k : Fin 16, amp0_1Expr 1 8 k = amp0_11_8 k := by decide +kernel +noncomputable def amp0_11_9 : Fin 16 → CBox := ![⟨⟨(-32705942439377387423228351680),(-32705942439377387420896475738)⟩,⟨(-56648354014424820479412954591),(-56648354014424820478644621226)⟩⟩,⟨⟨(-32620945410534091405559826738),(-32620945410534091403236377827)⟩,⟨(-56501134841975834455748518079),(-56501134841975834454986281059)⟩⟩,⟨⟨(-32531318751103864921480242651),(-32531318751103864919158089670)⟩,⟨(-56345896914130009942365838601),(-56345896914130009941596883530)⟩⟩,⟨⟨(-32436493307917857223075420878),(-32436493307917857220763254755)⟩,⟨(-56181654428681608615763341170),(-56181654428681608615002201303)⟩⟩,⟨⟨(-32337099553057724191761609327),(-32337099553057724189458600516)⟩,⟨(-56009499395308812176495758165),(-56009499395308812175740539850)⟩⟩,⟨⟨(-32232502525936830263528395639),(-32232502525936830261233893403)⟩,⟨(-55828332030014764087843966228),(-55828332030014764087093022030)⟩⟩,⟨⟨(-32123401852681396183832921252),(-32123401852681396181549245557)⟩,⟨(-55639364120796381277254277554),(-55639364120796381276511175407)⟩⟩,⟨⟨(-32009095923644769042904902982),(-32009095923644769040631380310)⟩,⟨(-55441380444098580457713311185),(-55441380444098580456976363998)⟩⟩,⟨⟨(-31890354391170951218307857087),(-31890354391170951216045780722)⟩,⟨(-55235714076885338226632246830),(-55235714076885338225903251076)⟩⟩,⟨⟨(-31766408054785126237524558180),(-31766408054785126235275986949)⟩,⟨(-55021032724853066348926477740),(-55021032724853066348208478928)⟩⟩,⟨⟨(-31638097566013635100290952431),(-31638097566013635098037465633)⟩,⟨(-54798792439156847762510896667),(-54798792439156847761771552796)⟩⟩,⟨⟨(-31504585086650592894713159934),(-31504585086650592892472335750)⟩,⟨(-54567542041455567446459651359),(-54567542041455567445728888530)⟩⟩,⟨⟨(-31366783346512185483162593251),(-31366783346512185480933795541)⟩,⟨(-54328862426164442316622643522),(-54328862426164442315898930984)⟩⟩,⟨⟨(-31223784711938343740985163303),(-31223784711938343738770583719)⟩,⟨(-54081181525669572949786967739),(-54081181525669572949073581855)⟩⟩,⟨⟨(-31076575182348133092885465817),(-31076575182348133090682182913)⟩,⟨(-53826207141061014058678902531),(-53826207141061014057970362117)⟩⟩,⟨⟨(-30924176053652663076181365661),(-30924176053652663073993066328)⟩,⟨(-53562244107131231955142051541),(-53562244107131231954444223520)⟩⟩] +lemma amp0_11_9_eq : ∀ k : Fin 16, amp0_1Expr 1 9 k = amp0_11_9 k := by decide +kernel +noncomputable def amp0_11_10 : Fin 16 → CBox := ![⟨⟨(-30767647905240686649495257051),(-30767647905240686647315823005)⟩,⟨(-53291129401267007107414159316),(-53291129401267007106716033608)⟩⟩,⟨⟨(-30605939563110598319101929127),(-30605939563110598316937075415)⟩,⟨(-53011042336689963311771836447),(-53011042336689963311082793783)⟩⟩,⟨⟨(-30440187623762200862393720773),(-30440187623762200860243298279)⟩,⟨(-52723951556285463928078905691),(-52723951556285463927398283437)⟩⟩,⟨⟨(-30269266911110177885258042844),(-30269266911110177883120827489)⟩,⟨(-52427908197906279507936229508),(-52427908197906279507261390617)⟩⟩,⟨⟨(-30094391611375639621658806304),(-30094391611375639619537679823)⟩,⟨(-52125015293777223035488198387),(-52125015293777223034823738714)⟩⟩,⟨⟨(-29914360872324529843829346659),(-29914360872324529841722939614)⟩,⟨(-51813192906816526530979412101),(-51813192906816526530322444166)⟩⟩,⟨⟨(-29730468187763879468528230817),(-29730468187763879466437110783)⟩,⟨(-51494681434017243235311566569),(-51494681434017243234662687244)⟩⟩,⟨⟨(-29541435202988933495292478720),(-29541435202988933493218227892)⟩,⟨(-51167266700080642776230929886),(-51167266700080642775592365587)⟩⟩,⟨⟨(-29348636593525162300957118574),(-29348636593525162298900200192)⟩,⟨(-50833329712860761290681542530),(-50833329712860761290053719046)⟩⟩,⟨⟨(-29150714511951410422012941897),(-29150714511951410419974553237)⟩,⟨(-50490518611635231140653922111),(-50490518611635231140038400838)⟩⟩,⟨⟨(-28949126858313515183077182820),(-28949126858313515181058947824)⟩,⟨(-50141358553355799567474302833),(-50141358553355799566873529965)⟩⟩,⟨⟨(-28742434125160893643580619310),(-28742434125160893641529591085)⟩,⟨(-49783356237980182973206906069),(-49783356237980182972528664388)⟩⟩,⟨⟨(-28532179662507527617694597112),(-28532179662507527615661537261)⟩,⟨(-49419184826146459997149373662),(-49419184826146459996481228673)⟩⟩,⟨⟨(-28316839943670277254842951463),(-28316839943670277252827891722)⟩,⟨(-49046205492232745528081358645),(-49046205492232745527422856787)⟩⟩,⟨⟨(-28098046192495536941608378795),(-28098046192495536939611865484)⟩,⟨(-48667243598819512573530478884),(-48667243598819512572882221011)⟩⟩,⟨⟨(-27874188295234711903457113622),(-27874188295234711901478686544)⟩,⟨(-48279510347088229801998055511),(-48279510347088229801358738124)⟩⟩] +lemma amp0_11_10_eq : ∀ k : Fin 16, amp0_1Expr 1 10 k = amp0_11_10 k := by decide +kernel +noncomputable def amp0_11_11 : Fin 16 → CBox := ![⟨⟨(-27646987989670052253090526337),(-27646987989670052251130545258)⟩,⟨(-47885987874355065368993977978),(-47885987874355065368363889967)⟩⟩,⟨⟨(-27414745779588332835787574819),(-27414745779588332833845517253)⟩,⟨(-47483732566831442396404915060),(-47483732566831442395782647264)⟩⟩,⟨⟨(-27179276793229187799912810226),(-27179276793229187797990736907)⟩,⟨(-47075888318850660285530718245),(-47075888318850660284919517280)⟩⟩,⟨⟨(-26938789107485135129675858844),(-26938789107485135127771055622)⟩,⟨(-46659351428547303478816184505),(-46659351428547303478210847458)⟩⟩,⟨⟨(-26695194376888032120563423452),(-26695194376888032118679039653)⟩,⟨(-46237432978697068108974036841),(-46237432978697068108379707800)⟩⟩,⟨⟨(-26446604933591878657903083258),(-26446604933591878656038617574)⟩,⟨(-45806863432682867874288604156),(-45806863432682867873703915356)⟩⟩,⟨⟨(-26195032379608320407044041303),(-26195032379608320405201150697)⟩,⟨(-45371126987393480827533959144),(-45371126987393480826961482221)⟩⟩,⟨⟨(-25938489683322627375136987486),(-25938489683322627373307989844)⟩,⟨(-44926782003115948994341313377),(-44926782003115948993767245503)⟩⟩,⟨⟨(-25679092130460598066496228911),(-25679092130460598064688911091)⟩,⟨(-44477492262199880592846273778),(-44477492262199880592283816702)⟩⟩,⟨⟨(-25414749373705691728087170126),(-25414749373705691726301361840)⟩,⟨(-44019637176887561776183025390),(-44019637176887561775631389644)⟩⟩,⟨⟨(-25147684467739387133340767624),(-25147684467739387131574975927)⟩,⟨(-43557067190835317627156472899),(-43557067190835317626612800413)⟩⟩,⟨⟨(-24875699428374202214469580135),(-24875699428374202212726632626)⟩,⟨(-43085975283756196207661674540),(-43085975283756196207130370842)⟩⟩,⟨⟨(-24601129552458858921487545584),(-24601129552458858919766794339)⟩,⟨(-42610406308442939425489646545),(-42610406308442939424969330917)⟩⟩,⟨⟨(-24321664486771101360938904525),(-24321664486771101359240974038)⟩,⟨(-42126358615731169602531786816),(-42126358615731169602023051394)⟩⟩,⟨⟨(-24039756676364397077732973415),(-24039756676364397076059067204)⟩,⟨(-41638079965056263498400998171),(-41638079965056263497905683236)⟩⟩,⟨⟨(-23752978207657740001846046396),(-23752978207657740000197465857)⟩,⟨(-41141365086739532104734068703),(-41141365086739532104253941271)⟩⟩] +lemma amp0_11_11_eq : ∀ k : Fin 16, amp0_1Expr 1 11 k = amp0_11_11 k := by decide +kernel +noncomputable def amp0_11_12 : Fin 16 → CBox := ![⟨⟨(-23463904064604503190781655821),(-23463904064604503189129188208)⟩,⟨(-40640673983816892126054185171),(-40640673983816892125538417715)⟩⟩,⟨⟨(-23169983067012150234766239622),(-23169983067012150233135448357)⟩,⟨(-40131587882575607149953069841),(-40131587882575607149445454822)⟩⟩,⟨⟨(-22873918673218157794977378037),(-22873918673218157793368666115)⟩,⟨(-39618789310212332441829061990),(-39618789310212332441330083075)⟩⟩,⟨⟨(-22573030150397963507650786622),(-22573030150397963506064095498)⟩,⟨(-39097635101273408362068638847),(-39097635101273408361577712220)⟩⟩,⟨⟨(-22270155981605558913479585702),(-22270155981605558911915255282)⟩,⟨(-38573041652624771531857821866),(-38573041652624771531375337697)⟩⟩,⟨⟨(-21962478939877190904608599454),(-21962478939877190903066190844)⟩,⟨(-38040129384028748564537051367),(-38040129384028748564061769183)⟩⟩,⟨⟨(-21652979780165887257472608013),(-21652979780165887255953954585)⟩,⟨(-37504061114508896151183794186),(-37504061114508896150718707268)⟩⟩,⟨⟨(-21338697095528772244069995702),(-21338697095528772242571456654)⟩,⟨(-36959707536778266307045598493),(-36959707536778266306583922435)⟩⟩,⟨⟨(-21022761953305465946062365892),(-21022761953305465944588155727)⟩,⟨(-36412491818551000530751701013),(-36412491818551000530300570303)⟩⟩,⟨⟨(-20702060231618653078725654112),(-20702060231618653077275089137)⟩,⟨(-35857020142514626975177233035),(-35857020142514626974734986823)⟩⟩,⟨⟨(-20379882258044908824862558866),(-20379882258044908823436500890)⟩,⟨(-35298991523205318832638188918),(-35298991523205318832206172275)⟩⟩,⟨⟨(-20052951687444352544862548176),(-20052951687444352543461467487)⟩,⟨(-34732731164377671475057805666),(-34732731164377671474636357896)⟩⟩,⟨⟨(-19724728098486747677851375998),(-19724728098486747676476863246)⟩,⟨(-34164231232060496729423159288),(-34164231232060496729014906175)⟩⟩,⟨⟨(-19391762292844942226773189275),(-19391762292844942225407757544)⟩,⟨(-33587517539505785758612989515),(-33587517539505785758187168614)⟩⟩,⟨⟨(-19057694296448717008934580850),(-19057694296448717007594909433)⟩,⟨(-33008894796564787080675412193),(-33008894796564787080260802663)⟩⟩,⟨⟨(-18718890128322294125839856546),(-18718890128322294124525944147)⟩,⟨(-32422068763553714649806156353),(-32422068763553714649402282334)⟩⟩] +lemma amp0_11_12_eq : ∀ k : Fin 16, amp0_1Expr 1 12 k = amp0_11_12 k := by decide +kernel +noncomputable def amp0_11_13 : Fin 16 → CBox := ![⟨⟨(-18379182858626920877403735614),(-18379182858626920876115258656)⟩,⟨(-31833678512740825018528112239),(-31833678512740825018134322971)⟩⟩,⟨⟨(-18034740279655822664378048668),(-18034740279655822663113149945)⟩,⟨(-31237086465672827566898122916),(-31237086465672827566510728090)⟩⟩,⟨⟨(-17689602740734276711841190715),(-17689602740734276710603360819)⟩,⟨(-30639290712661429081100799909),(-30639290712661429080725775913)⟩⟩,⟨⟨(-17339724586802453971638216843),(-17339724586802453970426469302)⟩,⟨(-30033283973593107543696560467),(-30033283973593107543331724619)⟩⟩,⟨⟨(-16989369609173106074616120860),(-16989369609173106073432053644)⟩,⟨(-29426451351654419580346446218),(-29426451351654419579994518603)⟩⟩,⟨⟨(-16634261386743642867755712067),(-16634261386743642866588299855)⟩,⟨(-28811385868221119327860714024),(-28811385868221119327502122898)⟩⟩,⟨⟨(-16278905600962081267657470528),(-16278905600962081266516457326)⟩,⟨(-28195891592483892595054284973),(-28195891592483892594705882695)⟩⟩,⟨⟨(-15918775249752562215142452724),(-15918775249752562214028212544)⟩,⟨(-27572127526841381714569539261),(-27572127526841381714231496184)⟩⟩,⟨⟨(-15558639082871133558288778445),(-15558639082871133557201057448)⟩,⟨(-26948353388159643248255277229),(-26948353388159643247927153107)⟩⟩,⟨⟨(-15193696708276728728619651571),(-15193696708276728727557601883)⟩,⟨(-26316254653527300635008603027),(-26316254653527300634688448679)⟩⟩,⟨⟨(-14829004411061715034340598804),(-14829004411061715033305360617)⟩,⟨(-25684589065621887146325700266),(-25684589065621887146015515571)⟩⟩,⟨⟨(-14459461977215688468213152796),(-14459461977215688467197783495)⟩,⟨(-25044522794647908419130766374),(-25044522794647908418818041355)⟩⟩,⟨⟨(-14090441693045962458419706368),(-14090441693045962457432684290)⟩,⟨(-24405360913442437898403328068),(-24405360913442437898102799850)⟩⟩,⟨⟨(-13716512663740494236206183389),(-13716512663740494235246931129)⟩,⟨(-23757696836260455280462551672),(-23757696836260455280172729289)⟩⟩,⟨⟨(-13343396554569321851539941168),(-13343396554569321850607873060)⟩,⟨(-23111440778053568768128093279),(-23111440778053568767848043615)⟩⟩,⟨⟨(-12965295463818583364203171244),(-12965295463818583363299469731)⟩,⟨(-22456550478476078810124296761),(-22456550478476078809855569374)⟩⟩] +lemma amp0_11_13_eq : ∀ k : Fin 16, amp0_1Expr 1 13 k = amp0_11_13 k := by decide +kernel +noncomputable def amp0_11_14 : Fin 16 → CBox := ![⟨⟨(-12588319915260722391276407051),(-12588319915260722390395354446)⟩,⟨(-21803609675162715196002880755),(-21803609675162715195735684870)⟩⟩,⟨⟨(-12206261841045965250303319765),(-12206261841045965249450240590)⟩,⟨(-21141865679180835035461911428),(-21141865679180835035204961140)⟩⟩,⟨⟨(-11825667778884814562247395165),(-11825667778884814561421447409)⟩,⟨(-20482657426458694502171191496),(-20482657426458694501923174796)⟩⟩,⟨⟨(-11439867680844907709407928259),(-11439867680844907708611350290)⟩,⟨(-19814432055088521803910472139),(-19814432055088521803674745394)⟩⟩,⟨⟨(-11055901047314695424087822138),(-11055901047314695423315113072)⟩,⟨(-19149382337403014456973134935),(-19149382337403014456740353679)⟩⟩,⟨⟨(-10666572908823690777097640184),(-10666572908823690776353321472)⟩,⟨(-18475046220720382158214659248),(-18475046220720382157992118715)⟩⟩,⟨⟨(-10279485372927895295064086069),(-10279485372927895294344948260)⟩,⟨(-17804590941572222815893222340),(-17804590941572222815675587656)⟩⟩,⟨⟨(-9886841054724459427093644857),(-9886841054724459426403459546)⟩,⟨(-17124511033140630493564409054),(-17124511033140630493357657135)⟩⟩,⟨⟨(-9496891073954188851229403341),(-9496891073954188850567570952)⟩,⟨(-16449097854036015171379216841),(-16449097854036015171182578625)⟩⟩,⟨⟨(-9101138730168082674014967765),(-9101138730168082673379484450)⟩,⟨(-15763634687384014009527883344),(-15763634687384014009337307828)⟩⟩,⟨⟨(-8708593155276932932933869376),(-8708593155276932932327349918)⟩,⟨(-15083725807386208899120902771),(-15083725807386208898941239571)⟩⟩,⟨⟨(-8309934963699564222466113031),(-8309934963699564221886553400)⟩,⟨(-14393229564720679228172547276),(-14393229564720679227999714046)⟩⟩,⟨⟨(-7915071511567247979887519778),(-7915071511567247979334651009)⟩,⟨(-13709306003575466157493902165),(-13709306003575466157327812518)⟩⟩,⟨⟨(-7513700288185479521977172773),(-7513700288185479521453706932)⟩,⟨(-13014110651982165855647013099),(-13014110651982165855491713696)⟩⟩,⟨⟨(-7116811458893626802477741022),(-7116811458893626801981592243)⟩,⟨(-12326679034692146071294909815),(-12326679034692146071147236068)⟩⟩,⟨⟨(-6712905375084154821982200235),(-6712905375084154821514003951)⟩,⟨(-11627093176047967493458144544),(-11627093176047967493318495329)⟩⟩] +lemma amp0_11_14_eq : ∀ k : Fin 16, amp0_1Expr 1 14 k = amp0_11_14 k := by decide +kernel +noncomputable def amp0_11_15 : Fin 16 → CBox := ![⟨⟨(-6314304889329281698371852841),(-6314304889329281697931624554)⟩,⟨(-10936696882798892730012221848),(-10936696882798892729881154577)⟩⟩,⟨⟨(-5908018787060499828029020756),(-5908018787060499827617472228)⟩,⟨(-10232988711260237622342822082),(-10232988711260237622220801001)⟩⟩,⟨⟨(-5508052685234101318107272532),(-5508052685234101317724100648)⟩,⟨(-9540227101591648275840555648),(-9540227101591648275727687746)⟩⟩,⟨⟨(-5099502883647184281955289766),(-5099502883647184281600217804)⟩,⟨(-8832598087820924037354995945),(-8832598087820924037249943555)⟩⟩,⟨⟨(-4698569893355039727729822288),(-4698569893355039727402641524)⟩,⟨(-8138161778204410222065929123),(-8138161778204410221969092407)⟩⟩,⟨⟨(-4287805485929443700591551923),(-4287805485929443700293133943)⟩,⟨(-7426696954602355286453002859),(-7426696954602355286364908304)⟩⟩,⟨⟨(-3886397599776523265563463647),(-3886397599776523265293442760)⟩,⟨(-6731438101226673489701660262),(-6731438101226673489622610128)⟩⟩,⟨⟨(-3473340580412691300646393309),(-3473340580412691300404825533)⟩,⟨(-6016002357265554949028149829),(-6016002357265554948957076227)⟩⟩,⟨⟨(-3072133445990435320343374868),(-3072133445990435320129971389)⟩,⟨(-5321091216087091370830780200),(-5321091216087091370768367878)⟩⟩,⟨⟨(-2656435792071101113418620190),(-2656435792071101113234276570)⟩,⟨(-4601081758911620888558560415),(-4601081758911620888504911478)⟩⟩,⟨⟨(-2256524817754308918018828668),(-2256524817754308917862555955)⟩,⟨(-3908415632890564420164805757),(-3908415632890564420119785960)⟩⟩,⟨⟨(-1837153108049314193357202823),(-1837153108049314193230176446)⟩,⟨(-3182042524424487532206978126),(-3182042524424487532170677298)⟩⟩,⟨⟨(-1440842106367455813565551541),(-1440842106367455813466331653)⟩,⟨(-2495611733912994038218036795),(-2495611733912994038190267118)⟩⟩,⟨⟨(-1014414495963543606957205285),(-1014414495963543606887606003)⟩,⟨(-1757017446943231319935356364),(-1757017446943231319916248321)⟩⟩,⟨⟨(-629264447029517718491981547),(-629264447029517718449666377)⟩,⟨(-1089917993651859172640962474),(-1089917993651859172630596895)⟩⟩,⟨⟨(-178776584874023315354484384),(-178776584874023315342979216)⟩,⟨(-309650128205458016436368989),(-309650128205458016434319114)⟩⟩] +lemma amp0_11_15_eq : ∀ k : Fin 16, amp0_1Expr 1 15 k = amp0_11_15 k := by decide +kernel +noncomputable def amp0_11 : Fin 16 → Fin 16 → CBox := ![amp0_11_0,amp0_11_1,amp0_11_2,amp0_11_3,amp0_11_4,amp0_11_5,amp0_11_6,amp0_11_7,amp0_11_8,amp0_11_9,amp0_11_10,amp0_11_11,amp0_11_12,amp0_11_13,amp0_11_14,amp0_11_15] +lemma amp0_11_eq (i k : Fin 16) : amp0_1Expr 1 i k = amp0_11 i k := by + fin_cases i + · exact amp0_11_0_eq k + · exact amp0_11_1_eq k + · exact amp0_11_2_eq k + · exact amp0_11_3_eq k + · exact amp0_11_4_eq k + · exact amp0_11_5_eq k + · exact amp0_11_6_eq k + · exact amp0_11_7_eq k + · exact amp0_11_8_eq k + · exact amp0_11_9_eq k + · exact amp0_11_10_eq k + · exact amp0_11_11_eq k + · exact amp0_11_12_eq k + · exact amp0_11_13_eq k + · exact amp0_11_14_eq k + · exact amp0_11_15_eq k +noncomputable def amp0_12_0 : Fin 16 → CBox := ![⟨⟨178776584874023315345043551,178776584874023315352420050⟩,⟨(-516083547009096694060614982),(-516083547009096694057198524)⟩⟩,⟨⟨629264447029517718456932497,629264447029517718484715427⟩,⟨(-1816529989419765287734937456),(-1816529989419765287717661492)⟩⟩,⟨⟨1014414495963543606899319452,1014414495963543606945491836⟩,⟨(-2928362411572052199892260607),(-2928362411572052199860413868)⟩⟩,⟨⟨1440842106367455813482969064,1440842106367455813548914130⟩,⟨(-4159352889854990063696727991),(-4159352889854990063650445197)⟩⟩,⟨⟨1837153108049314193251390063,1837153108049314193335989206⟩,⟨(-5303404207374145887011630210),(-5303404207374145886951128831)⟩⟩,⟨⟨2256524817754308917888612059,2256524817754308917992772564⟩,⟨(-6514026054817607366941342927),(-6514026054817607366866309934)⟩⟩,⟨⟨2656435792071101113264950449,2656435792071101113387946312⟩,⟨(-7668469598186034814264267358),(-7668469598186034814174852464)⟩⟩,⟨⟨3072133445990435320165445331,3072133445990435320307900926⟩,⟨(-8868485360145152284717966999),(-8868485360145152284613946464)⟩⟩,⟨⟨3473340580412691300444932216,3473340580412691300606286626⟩,⟨(-10026670595442591581713583048),(-10026670595442591581595127046)⟩⟩,⟨⟨3886397599776523265338319014,3886397599776523265518587393⟩,⟨(-11219063502044455816169433770),(-11219063502044455816037683548)⟩⟩,⟨⟨4287805485929443700342645256,4287805485929443700542040610⟩,⟨(-12377828257670592144088338098),(-12377828257670592143941513841)⟩⟩,⟨⟨4698569893355039727456895936,4698569893355039727675567876⟩,⟨(-13563602963674017036776548538),(-13563602963674017036615154012)⟩⟩,⟨⟨5099502883647184281659101791,5099502883647184281896405779⟩,⟨(-14720996813034873395591659908),(-14720996813034873395416572593)⟩⟩,⟨⟨5508052685234101317787702162,5508052685234101318043671018⟩,⟨(-15900378502652747126400926080),(-15900378502652747126212812910)⟩⟩,⟨⟨5908018787060499827685692153,5908018787060499827960800832⟩,⟨(-17054981185433729370571370137),(-17054981185433729370368001668)⟩⟩,⟨⟨6314304889329281698004535867,6314304889329281698298941529⟩,⟨(-18227828137998154550020369747),(-18227828137998154549801924296)⟩⟩] +lemma amp0_12_0_eq : ∀ k : Fin 16, amp0_1Expr 2 0 k = amp0_12_0 k := by decide +kernel +noncomputable def amp0_12_1 : Fin 16 → CBox := ![⟨⟨6712905375084154821591517905,6712905375084154821904686281⟩,⟨(-19378488626746612489096907573),(-19378488626746612488864158882)⟩⟩,⟨⟨7116811458893626802063770103,7116811458893626802395563162⟩,⟨(-20544465057820243452158183025),(-20544465057820243451912060114)⟩⟩,⟨⟨7513700288185479521540467670,7513700288185479521890412036⟩,⟨(-21690184419970276426078355164),(-21690184419970276425819522827)⟩⟩,⟨⟨7915071511567247979426046382,7915071511567247979796124405⟩,⟨(-22848843339292443595823170274),(-22848843339292443595546354198)⟩⟩,⟨⟨8309934963699564221982508264,8309934963699564222370158167⟩,⟨(-23988715941201132046954245460),(-23988715941201132046666190077)⟩⟩,⟨⟨8708593155276932932427908090,8708593155276932932833311204⟩,⟨(-25139543012310348165201504618),(-25139543012310348164902065951)⟩⟩,⟨⟨9101138730168082673484575348,9101138730168082673909876867⟩,⟨(-26272724478973356682546472239),(-26272724478973356682228846381)⟩⟩,⟨⟨9496891073954188850677231605,9496891073954188851119742689⟩,⟨(-27415163090060025285632028068),(-27415163090060025285304297709)⟩⟩,⟨⟨9886841054724459426517622953,9886841054724459426979481450⟩,⟨(-28540851721901050822607348422),(-28540851721901050822262761892)⟩⟩,⟨⟨10279485372927895294463645533,10279485372927895294945388796⟩,⟨(-29674318235953704693155370567),(-29674318235953704692792646094)⟩⟩,⟨⟨10666572908823690776476488447,10666572908823690776974473209⟩,⟨(-30791743701200636930357765413),(-30791743701200636929986864525)⟩⟩,⟨⟨11055901047314695423442775621,11055901047314695423960159589⟩,⟨(-31915637229005024094955224892),(-31915637229005024094567256132)⟩⟩,⟨⟨11439867680844907708743446504,11439867680844907709275832045⟩,⟨(-33024053425147536339850786898),(-33024053425147536339457908990)⟩⟩,⟨⟨11825667778884814561557998458,11825667778884814562110844115⟩,⟨(-34137762377431157503618652492),(-34137762377431157503205291328)⟩⟩,⟨⟨12206261841045965249591186361,12206261841045965250162373993⟩,⟨(-35236442798634725059103185713),(-35236442798634725058674935234)⟩⟩,⟨⟨12588319915260722390540711843,12588319915260722391131049653⟩,⟨(-36339349458604525326671467925),(-36339349458604525326226141451)⟩⟩] +lemma amp0_12_1_eq : ∀ k : Fin 16, amp0_1Expr 2 1 k = amp0_12_1 k := by decide +kernel +noncomputable def amp0_12_2 : Fin 16 → CBox := ![⟨⟨12965295463818583363449180068,12965295463818583364053460907⟩,⟨(-37427584130793464683540494601),(-37427584130793464683092615623)⟩⟩,⟨⟨13343396554569321850761949332,13343396554569321851385864897⟩,⟨(-38519067963422614613546822131),(-38519067963422614613080072692)⟩⟩,⟨⟨13716512663740494235405315775,13716512663740494236047798743⟩,⟨(-39596161393767425467437586120),(-39596161393767425466954548815)⟩⟩,⟨⟨14090441693045962457595386696,14090441693045962458257003962⟩,⟨(-40675601522404063164005546779),(-40675601522404063163504666417)⟩⟩,⟨⟨14459461977215688467364746980,14459461977215688468046189311⟩,⟨(-41740871324413180698551277289),(-41740871324413180698030068925)⟩⟩,⟨⟨14829004411061715033476591211,14829004411061715034169368210⟩,⟨(-42807648442703145243876167110),(-42807648442703145243359192619)⟩⟩,⟨⟨15193696708276728727733043580,15193696708276728728444209873⟩,⟨(-43860424422545501058347671712),(-43860424422545501057814081133)⟩⟩,⟨⟨15558639082871133557380713137,15558639082871133558109122756⟩,⟨(-44913922313599405413758795382),(-44913922313599405413211921845)⟩⟩,⟨⟨15918775249752562214212026728,15918775249752562214958638540⟩,⟨(-45953545878068969524282565434),(-45953545878068969523719160307)⟩⟩,⟨⟨16278905600962081266704429937,16278905600962081267469497918⟩,⟨(-46993152654139820991757141621),(-46993152654139820991176471158)⟩⟩,⟨⟨16634261386743642866780375761,16634261386743642867563636162⟩,⟨(-48018976447035198879767856707),(-48018976447035198879170204831)⟩⟩,⟨⟨16989369609173106073628229986,16989369609173106074419944517⟩,⟨(-49044085586090699300577410363),(-49044085586090699299990864339)⟩⟩,⟨⟨17339724586802453970626691195,17339724586802453971437994950⟩,⟨(-50055473289321845906160934112),(-50055473289321845905552874366)⟩⟩,⟨⟨17689602740734276710807622757,17689602740734276711636928777⟩,⟨(-51065484521102381801834666514),(-51065484521102381801209626522)⟩⟩,⟨⟨18034740279655822663321397188,18034740279655822664169801425⟩,⟨(-52061810776121379278163538194),(-52061810776121379277517880150)⟩⟩,⟨⟨18379182858626920876327483180,18379182858626920877191511090⟩,⟨(-53056130854568041697546853732),(-53056130854568041696890538285)⟩⟩] +lemma amp0_12_2_eq : ∀ k : Fin 16, amp0_1Expr 2 2 k = amp0_12_2 k := by decide +kernel +noncomputable def amp0_12_3 : Fin 16 → CBox := ![⟨⟨18718890128322294124742091272,18718890128322294125623709421⟩,⟨(-54036781272589524416343593922),(-54036781272589524415670470557)⟩⟩,⟨⟨19057694296448717007814968731,19057694296448717008714521551⟩,⟨(-55014824660941311801125686987),(-55014824660941311800434671105)⟩⟩,⟨⟨19391762292844942225631674328,19391762292844942226549272491⟩,⟨(-55979195899176309597688315858),(-55979195899176309596978614357)⟩⟩,⟨⟨19724728098486747676704624787,19724728098486747677623614457⟩,⟨(-56940385386767494549038598812),(-56940385386767494548358176959)⟩⟩,⟨⟨20052951687444352543693019028,20052951687444352544630996635⟩,⟨(-57887885273962785791763009442),(-57887885273962785791060596493)⟩⟩,⟨⟨20379882258044908823671827500,20379882258044908824627232256⟩,⟨(-58831652538675531387730314863),(-58831652538675531387010287126)⟩⟩,⟨⟨20702060231618653077514135938,20702060231618653078486607311⟩,⟨(-59761700237524378291962055058),(-59761700237524378291224978038)⟩⟩,⟨⟨21022761953305465944830905673,21022761953305465945819615946⟩,⟨(-60687486364251667551252835021),(-60687486364251667550500950505)⟩⟩,⟨⟨21338697095528772242817854704,21338697095528772243823597652⟩,⟨(-61599512561297110511742664154),(-61599512561297110510973204058)⟩⟩,⟨⟨21652979780165887256203981659,21652979780165887257222580939⟩,⟨(-62506768524181493585306323643),(-62506768524181493584531178781)⟩⟩,⟨⟨21962478939877190903319791707,21962478939877190904354998591⟩,⟨(-63400215640047914274228418944),(-63400215640047914273436281973)⟩⟩,⟨⟨22270155981605558912172408893,22270155981605558913222432091⟩,⟨(-64288402754374619219763036442),(-64288402754374619218958896163)⟩⟩,⟨⟨22573030150397963506324746398,22573030150397963507390135721⟩,⟨(-65162725168789013936781064745),(-65162725168789013935962853700)⟩⟩,⟨⟨22873918673218157793632791378,22873918673218157794713252775⟩,⟨(-66031315517020554069715103316),(-66031315517020554068883471792)⟩⟩,⟨⟨23169983067012150233402992277,23169983067012150234498695703⟩,⟨(-66885979804292678583255116402),(-66885979804292678582409091370)⟩⟩,⟨⟨23463904064604503189400126034,23463904064604503190510717994⟩,⟨(-67734456639694820210090308617),(-67734456639694820209230696191)⟩⟩] +lemma amp0_12_3_eq : ∀ k : Fin 16, amp0_1Expr 2 3 k = amp0_12_3 k := by decide +kernel +noncomputable def amp0_12_4 : Fin 16 → CBox := ![⟨⟨23752978207657740000471741625,23752978207657740001571770629⟩,⟨(-68568941811232553507890114505),(-68568941811232553507089902119)⟩⟩,⟨⟨24039756676364397076336654404,24039756676364397077455386215⟩,⟨(-69396799941760439164001663619),(-69396799941760439163176138727)⟩⟩,⟨⟨24321664486771101359521816428,24321664486771101360658062134⟩,⟨(-70210597692885282670886311360),(-70210597692885282670038418990)⟩⟩,⟨⟨24601129552458858920050863715,24601129552458858921203476209⟩,⟨(-71017343847404899042482744242),(-71017343847404899041615551529)⟩⟩,⟨⟨24875699428374202213013872461,24875699428374202214182340300⟩,⟨(-71809958806260327012769457566),(-71809958806260327011883951404)⟩⟩,⟨⟨25147684467739387131865356375,25147684467739387133050387176⟩,⟨(-72595111984725529378594121498),(-72595111984725529377688000688)⟩⟩,⟨⟨25414749373705691726594826088,25414749373705691727793705878⟩,⟨(-73366061961479269626971708983),(-73366061961479269626052316073)⟩⟩,⟨⟨25679092130460598064985427706,25679092130460598066199712296⟩,⟨(-74129153770333134321410456297),(-74129153770333134320473027837)⟩⟩,⟨⟨25938489683322627373607501724,25938489683322627374837475606⟩,⟨(-74877970005193248323902188961),(-74877970005193248322945409172)⟩⟩,⟨⟨26195032379608320405503624877,26195032379608320406741567123⟩,⟨(-75618544978989134712556598574),(-75618544978989134711602470369)⟩⟩,⟨⟨26446604933591878656343996663,26446604933591878657597704169⟩,⟨(-76344772387804779790481006927),(-76344772387804779789506525593)⟩⟩,⟨⟨26695194376888032118987289206,26695194376888032120255173898⟩,⟨(-77062388297828446848290061402),(-77062388297828446847299513000)⟩⟩,⟨⟨26938789107485135128082117965,26938789107485135129364796501⟩,⟨(-77765585714245505798026974174),(-77765585714245505797018079097)⟩⟩,⟨⟨27179276793229187798304576163,27179276793229187799598970971⟩,⟨(-78459813864751100475884530408),(-78459813864751100474865862133)⟩⟩,⟨⟨27414745779588332834162075470,27414745779588332835471016601⟩,⟨(-79139554278052403994008191766),(-79139554278052403992971078774)⟩⟩,⟨⟨27646987989670052251449785177,27646987989670052252771286418⟩,⟨(-79809979790591775614989963296),(-79809979790591775613939816612)⟩⟩] +lemma amp0_12_4_eq : ∀ k : Fin 16, amp0_1Expr 2 4 k = amp0_12_4 k := by decide +kernel +noncomputable def amp0_12_5 : Fin 16 → CBox := ![⟨⟨27874188295234711901800549946,27874188295234711903135250219⟩,⟨(-80465850578480383003330092519),(-80465850578480383002264563541)⟩⟩,⟨⟨28098046192495536939936313775,28098046192495536941283930505⟩,⟨(-81112072664699187622550798139),(-81112072664699187621470368352)⟩⟩,⟨⟨28316839943670277253154866425,28316839943670277254515976760⟩,⟨(-81743675820387909213468931074),(-81743675820387909212371427979)⟩⟩,⟨⟨28532179662507527615990998494,28532179662507527617365135880⟩,⟨(-82365308043577433328582289436),(-82365308043577433327468714456)⟩⟩,⟨⟨28742434125160893641861480127,28742434125160893643248730269⟩,⟨(-82972260396633638288678176781),(-82972260396633638287547773981)⟩⟩,⟨⟨28949126858313515181393223547,28949126858313515182742907096⟩,⟨(-83568930922259665945790504721),(-83568930922259665944789216608)⟩⟩,⟨⟨29150714511951410420311156694,29150714511951410421676338440⟩,⟨(-84150864352725385234423203519),(-84150864352725385233397334731)⟩⟩,⟨⟨29348636593525162299239089057,29348636593525162300618229709⟩,⟨(-84722216188101268817802570883),(-84722216188101268816756198410)⟩⟩,⟨⟨29541435202988933493559343004,29541435202988933494951363608⟩,⟨(-85278777833467737960384883144),(-85278777833467737959320609312)⟩⟩,⟨⟨29730468187763879466780408659,29730468187763879468184932941⟩,⟨(-85824469056695405392185944281),(-85824469056695405391104478741)⟩⟩,⟨⟨29914360872324529842068360900,29914360872324529843483925373⟩,⟨(-86355321511360877551632353502),(-86355321511360877550537406944)⟩⟩,⟨⟨30094391611375639619885179925,30094391611375639621311306202⟩,⟨(-86875025489628705059146997311),(-86875025489628705058039564524)⟩⟩,⟨⟨30269266911110177883470346877,30269266911110177884908523456⟩,⟨(-87379846996510465846560382513),(-87379846996510465845435651029)⟩⟩,⟨⟨30440187623762200860594791290,30440187623762200862042227763⟩,⟨(-87873252593809106546798176151),(-87873252593809106545663805728)⟩⟩,⟨⟨30605939563110598317290482364,30605939563110598318748522178⟩,⟨(-88351737227816605519619727411),(-88351737227816605518471322972)⟩⟩,⟨⟨30767647905240686647671097201,30767647905240686649139982855⟩,⟨(-88818549002111678512356932192),(-88818549002111678511193389348)⟩⟩] +lemma amp0_12_5_eq : ∀ k : Fin 16, amp0_1Expr 2 5 k = amp0_12_5 k := by decide +kernel +noncomputable def amp0_12_6 : Fin 16 → CBox := ![⟨⟨30924176053652663074350147956,30924176053652663075824284034⟩,⟨(-89270406845218719925236752568),(-89270406845218719924073705867)⟩⟩,⟨⟨31076575182348133091041024294,31076575182348133092526624436⟩,⟨(-89710345235101690097798170885),(-89710345235101690096617270196)⟩⟩,⟨⟨31223784711938343739131124929,31223784711938343740624622092⟩,⟨(-90135302542782621582978279564),(-90135302542782621581789303092)⟩⟩,⟨⟨31366783346512185481295987957,31366783346512185482800400835⟩,⟨(-90548104043607403861037739204),(-90548104043607403859831551640)⟩⟩,⟨⟨31504585086650592892836119363,31504585086650592894349376320⟩,⟨(-90945903402425945744099418931),(-90945903402425945742881480884)⟩⟩,⟨⟨31638097566013635098402790916,31638097566013635099925627148⟩,⟨(-91331320731928079604184827779),(-91331320731928079602952587994)⟩⟩,⟨⟨31766408054785126235642793834,31766408054785126237157751296⟩,⟨(-91701721208088443914877462899),(-91701721208088443913680798214)⟩⟩,⟨⟨31890354391170951216414018816,31890354391170951217939618993⟩,⟨(-92059523461475563711053744716),(-92059523461475563709838751793)⟩⟩,⟨⟨32009095923644769041000989513,32009095923644769042535293779⟩,⟨(-92402300740164300762855518641),(-92402300740164300761627273330)⟩⟩,⟨⟨32123401852681396181920174651,32123401852681396183461992158⟩,⟨(-92732273534660635462090462589),(-92732273534660635460851959013)⟩⟩,⟨⟨32232502525936830261606082283,32232502525936830263156206759⟩,⟨(-93047220050024606813073277046),(-93047220050024606811821703384)⟩⟩,⟨⟨32337099553057724189831997179,32337099553057724191388212665⟩,⟨(-93349165658848020294159596942),(-93349165658848020292900899750)⟩⟩,⟨⟨32436493307917857221137799118,32436493307917857222700876515⟩,⟨(-93636090714469347692938901950),(-93636090714469347691670335505)⟩⟩,⟨⟨32531318751103864919533728983,32531318751103864921104603339⟩,⟨(-93909828190216683237276397667),(-93909828190216683235994805884)⟩⟩,⟨⟨32620945410534091403613052060,32620945410534091405183152505⟩,⟨(-94168558069959724092914196798),(-94168558069959724091643801766)⟩⟩,⟨⟨32705942439377387421274131431,32705942439377387422850695987⟩,⟨(-94413923357374700799021590985),(-94413923357374700797741035377)⟩⟩] +lemma amp0_12_6_eq : ∀ k : Fin 16, amp0_1Expr 2 6 k = amp0_12_6 k := by decide +kernel +noncomputable def amp0_12_7 : Fin 16 → CBox := ![⟨⟨32785747743509981347056479572,32785747743509981348638333535⟩,⟨(-94644301426493266081663695205),(-94644301426493266080375850924)⟩⟩,⟨⟨32860865414590931772461155351,32860865414590931774049081709⟩,⟨(-94861147464590688555126779087),(-94861147464590688553828917080)⟩⟩,⟨⟨32930801052341203472860147815,32930801052341203474449387627⟩,⟨(-95063034260996026154243155586),(-95063034260996026152948495524)⟩⟩,⟨⟨32995994340909188938019572197,32995994340909188939613537402⟩,⟨(-95251231074516442955670527425),(-95251231074516442954368745661)⟩⟩,⟨⟨33056017978152788407431241770,33056017978152788409026940293⟩,⟨(-95424504390118105957142384760),(-95424504390118105955841601700)⟩⟩,⟨⟨33111247806102404777527897221,33111247806102404779128147404⟩,⟨(-95583939170288144597506339404),(-95583939170288144596197939817)⟩⟩,⟨⟨33161323110387142479252762765,33161323110387142480855145395⟩,⟨(-95728494122330873260226350991),(-95728494122330873258916803089)⟩⟩,⟨⟨33206556370521783190695519961,33206556370521783192299852709⟩,⟨(-95859071296906169172750024775),(-95859071296906169171439370696)⟩⟩,⟨⟨33246653032290985851650385882,33246653032290985853256597457⟩,⟨(-95974820389236441834553560239),(-95974820389236441833241492118)⟩⟩,⟨⟨33281862608866566223890120511,33281862608866566225498416821⟩,⟨(-96076461681806262182657261844),(-96076461681806262181342696567)⟩⟩,⟨⟨33311956359174495039300472962,33311956359174495040909534882⟩,⟨(-96163334856012302606753373030),(-96163334856012302605439607004)⟩⟩,⟨⟨33337121144716975240297671144,33337121144716975241907562915⟩,⟨(-96235979334547553340104943367),(-96235979334547553338791298247)⟩⟩,⟨⟨33357193769420233715579419031,33357193769420233717188908336⟩,⟨(-96293924010926396403530230522),(-96293924010926396402219754483)⟩⟩,⟨⟨33372298677811606172491527150,33372298677811606174100078101⟩,⟨(-96337528125555614028921458148),(-96337528125555614027615201393)⟩⟩,⟨⟨33382338028223777526412142514,33382338028223777528018675150⟩,⟨(-96366509233870394586701310657),(-96366509233870394585401884214)⟩⟩,⟨⟨33387374004052282215607154463,33387374004052282217210280500⟩,⟨(-96381046843871492741396360109),(-96381046843871492740107271266)⟩⟩] +lemma amp0_12_7_eq : ∀ k : Fin 16, amp0_1Expr 2 7 k = amp0_12_7 k := by decide +kernel +noncomputable def amp0_12_8 : Fin 16 → CBox := ![⟨⟨33387374004052282215607154463,33387374004052282217210280500⟩,⟨(-96381046843871492741396360109),(-96381046843871492740107271266)⟩⟩,⟨⟨33382338028223777526412142514,33382338028223777528018675150⟩,⟨(-96366509233870394586701310657),(-96366509233870394585401884214)⟩⟩,⟨⟨33372298677811606172491527150,33372298677811606174100078101⟩,⟨(-96337528125555614028921458148),(-96337528125555614027615201393)⟩⟩,⟨⟨33357193769420233715579419031,33357193769420233717188908336⟩,⟨(-96293924010926396403530230522),(-96293924010926396402219754483)⟩⟩,⟨⟨33337121144716975240297671144,33337121144716975241907562915⟩,⟨(-96235979334547553340104943367),(-96235979334547553338791298247)⟩⟩,⟨⟨33311956359174495039300472962,33311956359174495040909534882⟩,⟨(-96163334856012302606753373030),(-96163334856012302605439607004)⟩⟩,⟨⟨33281862608866566223890120511,33281862608866566225498416821⟩,⟨(-96076461681806262182657261844),(-96076461681806262181342696567)⟩⟩,⟨⟨33246653032290985851650385882,33246653032290985853256597457⟩,⟨(-95974820389236441834553560239),(-95974820389236441833241492118)⟩⟩,⟨⟨33206556370521783190695519961,33206556370521783192299852709⟩,⟨(-95859071296906169172750024775),(-95859071296906169171439370696)⟩⟩,⟨⟨33161323110387142479252762765,33161323110387142480855145395⟩,⟨(-95728494122330873260226350991),(-95728494122330873258916803089)⟩⟩,⟨⟨33111247806102404777527897221,33111247806102404779128147404⟩,⟨(-95583939170288144597506339404),(-95583939170288144596197939817)⟩⟩,⟨⟨33056017978152788407431241770,33056017978152788409026940293⟩,⟨(-95424504390118105957142384760),(-95424504390118105955841601700)⟩⟩,⟨⟨32995994340909188938019572197,32995994340909188939613537402⟩,⟨(-95251231074516442955670527425),(-95251231074516442954368745661)⟩⟩,⟨⟨32930801052341203472860147815,32930801052341203474449387627⟩,⟨(-95063034260996026154243155586),(-95063034260996026152948495524)⟩⟩,⟨⟨32860865414590931772461155351,32860865414590931774049081709⟩,⟨(-94861147464590688555126779087),(-94861147464590688553828917080)⟩⟩,⟨⟨32785747743509981347056479572,32785747743509981348638333535⟩,⟨(-94644301426493266081663695205),(-94644301426493266080375850924)⟩⟩] +lemma amp0_12_8_eq : ∀ k : Fin 16, amp0_1Expr 2 8 k = amp0_12_8 k := by decide +kernel +noncomputable def amp0_12_9 : Fin 16 → CBox := ![⟨⟨32705942439377387421274131431,32705942439377387422850695987⟩,⟨(-94413923357374700799021590985),(-94413923357374700797741035377)⟩⟩,⟨⟨32620945410534091403613052060,32620945410534091405183152505⟩,⟨(-94168558069959724092914196798),(-94168558069959724091643801766)⟩⟩,⟨⟨32531318751103864919533728983,32531318751103864921104603339⟩,⟨(-93909828190216683237276397667),(-93909828190216683235994805884)⟩⟩,⟨⟨32436493307917857221137799118,32436493307917857222700876515⟩,⟨(-93636090714469347692938901950),(-93636090714469347691670335505)⟩⟩,⟨⟨32337099553057724189831997179,32337099553057724191388212665⟩,⟨(-93349165658848020294159596942),(-93349165658848020292900899750)⟩⟩,⟨⟨32232502525936830261606082283,32232502525936830263156206759⟩,⟨(-93047220050024606813073277046),(-93047220050024606811821703384)⟩⟩,⟨⟨32123401852681396181920174651,32123401852681396183461992158⟩,⟨(-92732273534660635462090462589),(-92732273534660635460851959013)⟩⟩,⟨⟨32009095923644769041000989513,32009095923644769042535293779⟩,⟨(-92402300740164300762855518641),(-92402300740164300761627273330)⟩⟩,⟨⟨31890354391170951216414018816,31890354391170951217939618993⟩,⟨(-92059523461475563711053744716),(-92059523461475563709838751793)⟩⟩,⟨⟨31766408054785126235642793834,31766408054785126237157751296⟩,⟨(-91701721208088443914877462899),(-91701721208088443913680798214)⟩⟩,⟨⟨31638097566013635098402790916,31638097566013635099925627148⟩,⟨(-91331320731928079604184827779),(-91331320731928079602952587994)⟩⟩,⟨⟨31504585086650592892836119363,31504585086650592894349376320⟩,⟨(-90945903402425945744099418931),(-90945903402425945742881480884)⟩⟩,⟨⟨31366783346512185481295987957,31366783346512185482800400835⟩,⟨(-90548104043607403861037739204),(-90548104043607403859831551640)⟩⟩,⟨⟨31223784711938343739131124929,31223784711938343740624622092⟩,⟨(-90135302542782621582978279564),(-90135302542782621581789303092)⟩⟩,⟨⟨31076575182348133091041024294,31076575182348133092526624436⟩,⟨(-89710345235101690097798170885),(-89710345235101690096617270196)⟩⟩,⟨⟨30924176053652663074350147956,30924176053652663075824284034⟩,⟨(-89270406845218719925236752568),(-89270406845218719924073705867)⟩⟩] +lemma amp0_12_9_eq : ∀ k : Fin 16, amp0_1Expr 2 9 k = amp0_12_9 k := by decide +kernel +noncomputable def amp0_12_10 : Fin 16 → CBox := ![⟨⟨30767647905240686647671097201,30767647905240686649139982855⟩,⟨(-88818549002111678512356932192),(-88818549002111678511193389348)⟩⟩,⟨⟨30605939563110598317290482364,30605939563110598318748522178⟩,⟨(-88351737227816605519619727411),(-88351737227816605518471322972)⟩⟩,⟨⟨30440187623762200860594791290,30440187623762200862042227763⟩,⟨(-87873252593809106546798176151),(-87873252593809106545663805728)⟩⟩,⟨⟨30269266911110177883470346877,30269266911110177884908523456⟩,⟨(-87379846996510465846560382513),(-87379846996510465845435651029)⟩⟩,⟨⟨30094391611375639619885179925,30094391611375639621311306202⟩,⟨(-86875025489628705059146997311),(-86875025489628705058039564524)⟩⟩,⟨⟨29914360872324529842068360900,29914360872324529843483925373⟩,⟨(-86355321511360877551632353502),(-86355321511360877550537406944)⟩⟩,⟨⟨29730468187763879466780408659,29730468187763879468184932941⟩,⟨(-85824469056695405392185944281),(-85824469056695405391104478741)⟩⟩,⟨⟨29541435202988933493559343004,29541435202988933494951363608⟩,⟨(-85278777833467737960384883144),(-85278777833467737959320609312)⟩⟩,⟨⟨29348636593525162299239089057,29348636593525162300618229709⟩,⟨(-84722216188101268817802570883),(-84722216188101268816756198410)⟩⟩,⟨⟨29150714511951410420311156694,29150714511951410421676338440⟩,⟨(-84150864352725385234423203519),(-84150864352725385233397334731)⟩⟩,⟨⟨28949126858313515181393223547,28949126858313515182742907096⟩,⟨(-83568930922259665945790504721),(-83568930922259665944789216608)⟩⟩,⟨⟨28742434125160893641861480127,28742434125160893643248730269⟩,⟨(-82972260396633638288678176781),(-82972260396633638287547773981)⟩⟩,⟨⟨28532179662507527615990998494,28532179662507527617365135880⟩,⟨(-82365308043577433328582289436),(-82365308043577433327468714456)⟩⟩,⟨⟨28316839943670277253154866425,28316839943670277254515976760⟩,⟨(-81743675820387909213468931074),(-81743675820387909212371427979)⟩⟩,⟨⟨28098046192495536939936313775,28098046192495536941283930505⟩,⟨(-81112072664699187622550798139),(-81112072664699187621470368352)⟩⟩,⟨⟨27874188295234711901800549946,27874188295234711903135250219⟩,⟨(-80465850578480383003330092519),(-80465850578480383002264563541)⟩⟩] +lemma amp0_12_10_eq : ∀ k : Fin 16, amp0_1Expr 2 10 k = amp0_12_10 k := by decide +kernel +noncomputable def amp0_12_11 : Fin 16 → CBox := ![⟨⟨27646987989670052251449785177,27646987989670052252771286418⟩,⟨(-79809979790591775614989963296),(-79809979790591775613939816612)⟩⟩,⟨⟨27414745779588332834162075470,27414745779588332835471016601⟩,⟨(-79139554278052403994008191766),(-79139554278052403992971078774)⟩⟩,⟨⟨27179276793229187798304576163,27179276793229187799598970971⟩,⟨(-78459813864751100475884530408),(-78459813864751100474865862133)⟩⟩,⟨⟨26938789107485135128082117965,26938789107485135129364796501⟩,⟨(-77765585714245505798026974174),(-77765585714245505797018079097)⟩⟩,⟨⟨26695194376888032118987289206,26695194376888032120255173898⟩,⟨(-77062388297828446848290061402),(-77062388297828446847299513000)⟩⟩,⟨⟨26446604933591878656343996663,26446604933591878657597704169⟩,⟨(-76344772387804779790481006927),(-76344772387804779789506525593)⟩⟩,⟨⟨26195032379608320405503624877,26195032379608320406741567123⟩,⟨(-75618544978989134712556598574),(-75618544978989134711602470369)⟩⟩,⟨⟨25938489683322627373607501724,25938489683322627374837475606⟩,⟨(-74877970005193248323902188961),(-74877970005193248322945409172)⟩⟩,⟨⟨25679092130460598064985427706,25679092130460598066199712296⟩,⟨(-74129153770333134321410456297),(-74129153770333134320473027837)⟩⟩,⟨⟨25414749373705691726594826088,25414749373705691727793705878⟩,⟨(-73366061961479269626971708983),(-73366061961479269626052316073)⟩⟩,⟨⟨25147684467739387131865356375,25147684467739387133050387176⟩,⟨(-72595111984725529378594121498),(-72595111984725529377688000688)⟩⟩,⟨⟨24875699428374202213013872461,24875699428374202214182340300⟩,⟨(-71809958806260327012769457566),(-71809958806260327011883951404)⟩⟩,⟨⟨24601129552458858920050863715,24601129552458858921203476209⟩,⟨(-71017343847404899042482744242),(-71017343847404899041615551529)⟩⟩,⟨⟨24321664486771101359521816428,24321664486771101360658062134⟩,⟨(-70210597692885282670886311360),(-70210597692885282670038418990)⟩⟩,⟨⟨24039756676364397076336654404,24039756676364397077455386215⟩,⟨(-69396799941760439164001663619),(-69396799941760439163176138727)⟩⟩,⟨⟨23752978207657740000471741625,23752978207657740001571770629⟩,⟨(-68568941811232553507890114505),(-68568941811232553507089902119)⟩⟩] +lemma amp0_12_11_eq : ∀ k : Fin 16, amp0_1Expr 2 11 k = amp0_12_11 k := by decide +kernel +noncomputable def amp0_12_12 : Fin 16 → CBox := ![⟨⟨23463904064604503189400126034,23463904064604503190510717994⟩,⟨(-67734456639694820210090308617),(-67734456639694820209230696191)⟩⟩,⟨⟨23169983067012150233402992277,23169983067012150234498695703⟩,⟨(-66885979804292678583255116402),(-66885979804292678582409091370)⟩⟩,⟨⟨22873918673218157793632791378,22873918673218157794713252775⟩,⟨(-66031315517020554069715103316),(-66031315517020554068883471792)⟩⟩,⟨⟨22573030150397963506324746398,22573030150397963507390135721⟩,⟨(-65162725168789013936781064745),(-65162725168789013935962853700)⟩⟩,⟨⟨22270155981605558912172408893,22270155981605558913222432091⟩,⟨(-64288402754374619219763036442),(-64288402754374619218958896163)⟩⟩,⟨⟨21962478939877190903319791707,21962478939877190904354998591⟩,⟨(-63400215640047914274228418944),(-63400215640047914273436281973)⟩⟩,⟨⟨21652979780165887256203981659,21652979780165887257222580939⟩,⟨(-62506768524181493585306323643),(-62506768524181493584531178781)⟩⟩,⟨⟨21338697095528772242817854704,21338697095528772243823597652⟩,⟨(-61599512561297110511742664154),(-61599512561297110510973204058)⟩⟩,⟨⟨21022761953305465944830905673,21022761953305465945819615946⟩,⟨(-60687486364251667551252835021),(-60687486364251667550500950505)⟩⟩,⟨⟨20702060231618653077514135938,20702060231618653078486607311⟩,⟨(-59761700237524378291962055058),(-59761700237524378291224978038)⟩⟩,⟨⟨20379882258044908823671827500,20379882258044908824627232256⟩,⟨(-58831652538675531387730314863),(-58831652538675531387010287126)⟩⟩,⟨⟨20052951687444352543693019028,20052951687444352544630996635⟩,⟨(-57887885273962785791763009442),(-57887885273962785791060596493)⟩⟩,⟨⟨19724728098486747676704624787,19724728098486747677623614457⟩,⟨(-56940385386767494549038598812),(-56940385386767494548358176959)⟩⟩,⟨⟨19391762292844942225631674328,19391762292844942226549272491⟩,⟨(-55979195899176309597688315858),(-55979195899176309596978614357)⟩⟩,⟨⟨19057694296448717007814968731,19057694296448717008714521551⟩,⟨(-55014824660941311801125686987),(-55014824660941311800434671105)⟩⟩,⟨⟨18718890128322294124742091272,18718890128322294125623709421⟩,⟨(-54036781272589524416343593922),(-54036781272589524415670470557)⟩⟩] +lemma amp0_12_12_eq : ∀ k : Fin 16, amp0_1Expr 2 12 k = amp0_12_12 k := by decide +kernel +noncomputable def amp0_12_13 : Fin 16 → CBox := ![⟨⟨18379182858626920876327483180,18379182858626920877191511090⟩,⟨(-53056130854568041697546853732),(-53056130854568041696890538285)⟩⟩,⟨⟨18034740279655822663321397188,18034740279655822664169801425⟩,⟨(-52061810776121379278163538194),(-52061810776121379277517880150)⟩⟩,⟨⟨17689602740734276710807622757,17689602740734276711636928777⟩,⟨(-51065484521102381801834666514),(-51065484521102381801209626522)⟩⟩,⟨⟨17339724586802453970626691195,17339724586802453971437994950⟩,⟨(-50055473289321845906160934112),(-50055473289321845905552874366)⟩⟩,⟨⟨16989369609173106073628229986,16989369609173106074419944517⟩,⟨(-49044085586090699300577410363),(-49044085586090699299990864339)⟩⟩,⟨⟨16634261386743642866780375761,16634261386743642867563636162⟩,⟨(-48018976447035198879767856707),(-48018976447035198879170204831)⟩⟩,⟨⟨16278905600962081266704429937,16278905600962081267469497918⟩,⟨(-46993152654139820991757141621),(-46993152654139820991176471158)⟩⟩,⟨⟨15918775249752562214212026728,15918775249752562214958638540⟩,⟨(-45953545878068969524282565434),(-45953545878068969523719160307)⟩⟩,⟨⟨15558639082871133557380713137,15558639082871133558109122756⟩,⟨(-44913922313599405413758795382),(-44913922313599405413211921845)⟩⟩,⟨⟨15193696708276728727733043580,15193696708276728728444209873⟩,⟨(-43860424422545501058347671712),(-43860424422545501057814081133)⟩⟩,⟨⟨14829004411061715033476591211,14829004411061715034169368210⟩,⟨(-42807648442703145243876167110),(-42807648442703145243359192619)⟩⟩,⟨⟨14459461977215688467364746980,14459461977215688468046189311⟩,⟨(-41740871324413180698551277289),(-41740871324413180698030068925)⟩⟩,⟨⟨14090441693045962457595386696,14090441693045962458257003962⟩,⟨(-40675601522404063164005546779),(-40675601522404063163504666417)⟩⟩,⟨⟨13716512663740494235405315775,13716512663740494236047798743⟩,⟨(-39596161393767425467437586120),(-39596161393767425466954548815)⟩⟩,⟨⟨13343396554569321850761949332,13343396554569321851385864897⟩,⟨(-38519067963422614613546822131),(-38519067963422614613080072692)⟩⟩,⟨⟨12965295463818583363449180068,12965295463818583364053460907⟩,⟨(-37427584130793464683540494601),(-37427584130793464683092615623)⟩⟩] +lemma amp0_12_13_eq : ∀ k : Fin 16, amp0_1Expr 2 13 k = amp0_12_13 k := by decide +kernel +noncomputable def amp0_12_14 : Fin 16 → CBox := ![⟨⟨12588319915260722390540711843,12588319915260722391131049653⟩,⟨(-36339349458604525326671467925),(-36339349458604525326226141451)⟩⟩,⟨⟨12206261841045965249591186361,12206261841045965250162373993⟩,⟨(-35236442798634725059103185713),(-35236442798634725058674935234)⟩⟩,⟨⟨11825667778884814561557998458,11825667778884814562110844115⟩,⟨(-34137762377431157503618652492),(-34137762377431157503205291328)⟩⟩,⟨⟨11439867680844907708743446504,11439867680844907709275832045⟩,⟨(-33024053425147536339850786898),(-33024053425147536339457908990)⟩⟩,⟨⟨11055901047314695423442775621,11055901047314695423960159589⟩,⟨(-31915637229005024094955224892),(-31915637229005024094567256132)⟩⟩,⟨⟨10666572908823690776476488447,10666572908823690776974473209⟩,⟨(-30791743701200636930357765413),(-30791743701200636929986864525)⟩⟩,⟨⟨10279485372927895294463645533,10279485372927895294945388796⟩,⟨(-29674318235953704693155370567),(-29674318235953704692792646094)⟩⟩,⟨⟨9886841054724459426517622953,9886841054724459426979481450⟩,⟨(-28540851721901050822607348422),(-28540851721901050822262761892)⟩⟩,⟨⟨9496891073954188850677231605,9496891073954188851119742689⟩,⟨(-27415163090060025285632028068),(-27415163090060025285304297709)⟩⟩,⟨⟨9101138730168082673484575348,9101138730168082673909876867⟩,⟨(-26272724478973356682546472239),(-26272724478973356682228846381)⟩⟩,⟨⟨8708593155276932932427908090,8708593155276932932833311204⟩,⟨(-25139543012310348165201504618),(-25139543012310348164902065951)⟩⟩,⟨⟨8309934963699564221982508264,8309934963699564222370158167⟩,⟨(-23988715941201132046954245460),(-23988715941201132046666190077)⟩⟩,⟨⟨7915071511567247979426046382,7915071511567247979796124405⟩,⟨(-22848843339292443595823170274),(-22848843339292443595546354198)⟩⟩,⟨⟨7513700288185479521540467670,7513700288185479521890412036⟩,⟨(-21690184419970276426078355164),(-21690184419970276425819522827)⟩⟩,⟨⟨7116811458893626802063770103,7116811458893626802395563162⟩,⟨(-20544465057820243452158183025),(-20544465057820243451912060114)⟩⟩,⟨⟨6712905375084154821591517905,6712905375084154821904686281⟩,⟨(-19378488626746612489096907573),(-19378488626746612488864158882)⟩⟩] +lemma amp0_12_14_eq : ∀ k : Fin 16, amp0_1Expr 2 14 k = amp0_12_14 k := by decide +kernel +noncomputable def amp0_12_15 : Fin 16 → CBox := ![⟨⟨6314304889329281698004535867,6314304889329281698298941529⟩,⟨(-18227828137998154550020369747),(-18227828137998154549801924296)⟩⟩,⟨⟨5908018787060499827685692153,5908018787060499827960800832⟩,⟨(-17054981185433729370571370137),(-17054981185433729370368001668)⟩⟩,⟨⟨5508052685234101317787702162,5508052685234101318043671018⟩,⟨(-15900378502652747126400926080),(-15900378502652747126212812910)⟩⟩,⟨⟨5099502883647184281659101791,5099502883647184281896405779⟩,⟨(-14720996813034873395591659908),(-14720996813034873395416572593)⟩⟩,⟨⟨4698569893355039727456895936,4698569893355039727675567876⟩,⟨(-13563602963674017036776548538),(-13563602963674017036615154012)⟩⟩,⟨⟨4287805485929443700342645256,4287805485929443700542040610⟩,⟨(-12377828257670592144088338098),(-12377828257670592143941513841)⟩⟩,⟨⟨3886397599776523265338319014,3886397599776523265518587393⟩,⟨(-11219063502044455816169433770),(-11219063502044455816037683548)⟩⟩,⟨⟨3473340580412691300444932216,3473340580412691300606286626⟩,⟨(-10026670595442591581713583048),(-10026670595442591581595127046)⟩⟩,⟨⟨3072133445990435320165445331,3072133445990435320307900926⟩,⟨(-8868485360145152284717966999),(-8868485360145152284613946464)⟩⟩,⟨⟨2656435792071101113264950449,2656435792071101113387946312⟩,⟨(-7668469598186034814264267358),(-7668469598186034814174852464)⟩⟩,⟨⟨2256524817754308917888612059,2256524817754308917992772564⟩,⟨(-6514026054817607366941342927),(-6514026054817607366866309934)⟩⟩,⟨⟨1837153108049314193251390063,1837153108049314193335989206⟩,⟨(-5303404207374145887011630210),(-5303404207374145886951128831)⟩⟩,⟨⟨1440842106367455813482969064,1440842106367455813548914130⟩,⟨(-4159352889854990063696727991),(-4159352889854990063650445197)⟩⟩,⟨⟨1014414495963543606899319452,1014414495963543606945491836⟩,⟨(-2928362411572052199892260607),(-2928362411572052199860413868)⟩⟩,⟨⟨629264447029517718456932497,629264447029517718484715427⟩,⟨(-1816529989419765287734937456),(-1816529989419765287717661492)⟩⟩,⟨⟨178776584874023315345043551,178776584874023315352420050⟩,⟨(-516083547009096694060614982),(-516083547009096694057198524)⟩⟩] +lemma amp0_12_15_eq : ∀ k : Fin 16, amp0_1Expr 2 15 k = amp0_12_15 k := by decide +kernel +noncomputable def amp0_12 : Fin 16 → Fin 16 → CBox := ![amp0_12_0,amp0_12_1,amp0_12_2,amp0_12_3,amp0_12_4,amp0_12_5,amp0_12_6,amp0_12_7,amp0_12_8,amp0_12_9,amp0_12_10,amp0_12_11,amp0_12_12,amp0_12_13,amp0_12_14,amp0_12_15] +lemma amp0_12_eq (i k : Fin 16) : amp0_1Expr 2 i k = amp0_12 i k := by + fin_cases i + · exact amp0_12_0_eq k + · exact amp0_12_1_eq k + · exact amp0_12_2_eq k + · exact amp0_12_3_eq k + · exact amp0_12_4_eq k + · exact amp0_12_5_eq k + · exact amp0_12_6_eq k + · exact amp0_12_7_eq k + · exact amp0_12_8_eq k + · exact amp0_12_9_eq k + · exact amp0_12_10_eq k + · exact amp0_12_11_eq k + · exact amp0_12_12_eq k + · exact amp0_12_13_eq k + · exact amp0_12_14_eq k + · exact amp0_12_15_eq k +noncomputable def amp0_13_0 : Fin 16 → CBox := ![⟨⟨178776584874023315345043551,178776584874023315352420050⟩,⟨(-103216709401819338812122997),(-103216709401819338811439704)⟩⟩,⟨⟨629264447029517718456932497,629264447029517718484715427⟩,⟨(-363305997883953057546987492),(-363305997883953057543532298)⟩⟩,⟨⟨1014414495963543606899319452,1014414495963543606945491836⟩,⟨(-585672482314410439978452122),(-585672482314410439972082773)⟩⟩,⟨⟨1440842106367455813482969064,1440842106367455813548914130⟩,⟨(-831870577970998012739345599),(-831870577970998012730089039)⟩⟩,⟨⟨1837153108049314193251390063,1837153108049314193335989206⟩,⟨(-1060680841474829177402326042),(-1060680841474829177390225766)⟩⟩,⟨⟨2256524817754308917888612059,2256524817754308917992772564⟩,⟨(-1302805210963521473388268586),(-1302805210963521473373261986)⟩⟩,⟨⟨2656435792071101113264950449,2656435792071101113387946312⟩,⟨(-1533693919637206962852853472),(-1533693919637206962834970492)⟩⟩,⟨⟨3072133445990435320165445331,3072133445990435320307900926⟩,⟨(-1773697072029030456943593400),(-1773697072029030456922789292)⟩⟩,⟨⟨3473340580412691300444932216,3473340580412691300606286626⟩,⟨(-2005334119088518316342716610),(-2005334119088518316319025409)⟩⟩,⟨⟨3886397599776523265338319014,3886397599776523265518587393⟩,⟨(-2243812700408891163233886754),(-2243812700408891163207536709)⟩⟩,⟨⟨4287805485929443700342645256,4287805485929443700542040610⟩,⟨(-2475565651534118428817667620),(-2475565651534118428788302768)⟩⟩,⟨⟨4698569893355039727456895936,4698569893355039727675567876⟩,⟨(-2712720592734803407355309708),(-2712720592734803407323030802)⟩⟩,⟨⟨5099502883647184281659101791,5099502883647184281896405779⟩,⟨(-2944199362606974679118331982),(-2944199362606974679083314518)⟩⟩,⟨⟨5508052685234101317787702162,5508052685234101318043671018⟩,⟨(-3180075700530549425280185216),(-3180075700530549425242562582)⟩⟩,⟨⟨5908018787060499827685692153,5908018787060499827960800832⟩,⟨(-3410996237086745874114274028),(-3410996237086745874073600333)⟩⟩,⟨⟨6314304889329281698004535867,6314304889329281698298941529⟩,⟨(-3645565627599630910004073950),(-3645565627599630909960384859)⟩⟩] +lemma amp0_13_0_eq : ∀ k : Fin 16, amp0_1Expr 3 0 k = amp0_13_0 k := by decide +kernel +noncomputable def amp0_13_1 : Fin 16 → CBox := ![⟨⟨6712905375084154821591517905,6712905375084154821904686281⟩,⟨(-3875697725349322497819381515),(-3875697725349322497772831776)⟩⟩,⟨⟨7116811458893626802063770103,7116811458893626802395563162⟩,⟨(-4108893011564048690431636605),(-4108893011564048690382412022)⟩⟩,⟨⟨7513700288185479521540467670,7513700288185479521890412036⟩,⟨(-4338036883994055285215671033),(-4338036883994055285163904565)⟩⟩,⟨⟨7915071511567247979426046382,7915071511567247979796124405⟩,⟨(-4569768667858488719164634055),(-4569768667858488719109270839)⟩⟩,⟨⟨8309934963699564221982508264,8309934963699564222370158167⟩,⟨(-4797743188240226409390849092),(-4797743188240226409333238015)⟩⟩,⟨⟨8708593155276932932427908090,8708593155276932932833311204⟩,⟨(-5027908602462069633040300924),(-5027908602462069632980413190)⟩⟩,⟨⟨9101138730168082673484575348,9101138730168082673909876867⟩,⟨(-5254544895794671336509294448),(-5254544895794671336445769276)⟩⟩,⟨⟨9496891073954188850677231605,9496891073954188851119742689⟩,⟨(-5483032618012005057126405614),(-5483032618012005057060859541)⟩⟩,⟨⟨9886841054724459426517622953,9886841054724459426979481450⟩,⟨(-5708170344380210164521469685),(-5708170344380210164452552378)⟩⟩,⟨⟨10279485372927895294463645533,10279485372927895294945388796⟩,⟨(-5934863647190740938631074114),(-5934863647190740938558529218)⟩⟩,⟨⟨10666572908823690776476488447,10666572908823690776974473209⟩,⟨(-6158348740240127386071553083),(-6158348740240127385997372905)⟩⟩,⟨⟨11055901047314695423442775621,11055901047314695423960159589⟩,⟨(-6383127445801004818991044979),(-6383127445801004818913451226)⟩⟩,⟨⟨11439867680844907708743446504,11439867680844907709275832045⟩,⟨(-6604810685029507267970157380),(-6604810685029507267891581798)⟩⟩,⟨⟨11825667778884814561557998458,11825667778884814562110844115⟩,⟨(-6827552475486231500723730499),(-6827552475486231500641058265)⟩⟩,⟨⟨12206261841045965249591186361,12206261841045965250162373993⟩,⟨(-7047288559726945011820637143),(-7047288559726945011734987046)⟩⟩,⟨⟨12588319915260722390540711843,12588319915260722391131049653⟩,⟨(-7267869891720905065334293585),(-7267869891720905065245228290)⟩⟩] +lemma amp0_13_1_eq : ∀ k : Fin 16, amp0_1Expr 3 1 k = amp0_13_1 k := by decide +kernel +noncomputable def amp0_13_2 : Fin 16 → CBox := ![⟨⟨12965295463818583363449180068,12965295463818583364053460907⟩,⟨(-7485516826158692936708098921),(-7485516826158692936618523124)⟩⟩,⟨⟨13343396554569321850761949332,13343396554569321851385864897⟩,⟨(-7703813592684522922709364427),(-7703813592684522922616014538)⟩⟩,⟨⟨13716512663740494235405315775,13716512663740494236047798743⟩,⟨(-7919232278753485093487517224),(-7919232278753485093390909763)⟩⟩,⟨⟨14090441693045962457595386696,14090441693045962458257003962⟩,⟨(-8135120304480812632801109356),(-8135120304480812632700933283)⟩⟩,⟨⟨14459461977215688467364746980,14459461977215688468046189311⟩,⟨(-8348174264882636139710255458),(-8348174264882636139606013785)⟩⟩,⟨⟨14829004411061715033476591211,14829004411061715034169368210⟩,⟨(-8561529688540629048775233422),(-8561529688540629048671838523)⟩⟩,⟨⟨15193696708276728727733043580,15193696708276728728444209873⟩,⟨(-8772084884509100211669534343),(-8772084884509100211562816226)⟩⟩,⟨⟨15558639082871133557380713137,15558639082871133558109122756⟩,⟨(-8982784462719881082751759077),(-8982784462719881082642384369)⟩⟩,⟨⟨15918775249752562214212026728,15918775249752562214958638540⟩,⟨(-9190709175613793904856513087),(-9190709175613793904743832061)⟩⟩,⟨⟨16278905600962081266704429937,16278905600962081267469497918⟩,⟨(-9398630530827964198351428325),(-9398630530827964198235294231)⟩⟩,⟨⟨16634261386743642866780375761,16634261386743642867563636162⟩,⟨(-9603795289407039775953571342),(-9603795289407039775834040966)⟩⟩,⟨⟨16989369609173106073628229986,16989369609173106074419944517⟩,⟨(-9808817117218139860115482073),(-9808817117218139859998172867)⟩⟩,⟨⟨17339724586802453970626691195,17339724586802453971437994950⟩,⟨(-10011094657864369181232186823),(-10011094657864369181110574873)⟩⟩,⟨⟨17689602740734276710807622757,17689602740734276711636928777⟩,⟨(-10213096904220476360366933303),(-10213096904220476360241925304)⟩⟩,⟨⟨18034740279655822663321397188,18034740279655822664169801425⟩,⟨(-10412362155224275855632707639),(-10412362155224275855503576030)⟩⟩,⟨⟨18379182858626920876327483180,18379182858626920877191511090⟩,⟨(-10611226170913608339509370747),(-10611226170913608339378107657)⟩⟩] +lemma amp0_13_2_eq : ∀ k : Fin 16, amp0_1Expr 3 2 k = amp0_13_2 k := by decide +kernel +noncomputable def amp0_13_3 : Fin 16 → CBox := ![⟨⟨18718890128322294124742091272,18718890128322294125623709421⟩,⟨(-10807356254517904883268718785),(-10807356254517904883134094111)⟩⟩,⟨⟨19057694296448717007814968731,19057694296448717008714521551⟩,⟨(-11002964932188262360225137398),(-11002964932188262360086934221)⟩⟩,⟨⟨19391762292844942225631674328,19391762292844942226549272491⟩,⟨(-11195839179835261919537663172),(-11195839179835261919395722871)⟩⟩,⟨⟨19724728098486747676704624787,19724728098486747677623614457⟩,⟨(-11388077077353498909807719763),(-11388077077353498909671635391)⟩⟩,⟨⟨20052951687444352543693019028,20052951687444352544630996635⟩,⟨(-11577577054792557158352601889),(-11577577054792557158212119298)⟩⟩,⟨⟨20379882258044908823671827500,20379882258044908824627232256⟩,⟨(-11766330507735106277546062973),(-11766330507735106277402057425)⟩⟩,⟨⟨20702060231618653077514135938,20702060231618653078486607311⟩,⟨(-11952340047504875658392411012),(-11952340047504875658244995607)⟩⟩,⟨⟨21022761953305465944830905673,21022761953305465945819615946⟩,⟨(-12137497272850333510250567005),(-12137497272850333510100190101)⟩⟩,⟨⟨21338697095528772242817854704,21338697095528772243823597652⟩,⟨(-12319902512259422102348532831),(-12319902512259422102194640811)⟩⟩,⟨⟨21652979780165887256203981659,21652979780165887257222580939⟩,⟨(-12501353704836298717061264729),(-12501353704836298716906235756)⟩⟩,⟨⟨21962478939877190903319791707,21962478939877190904354998591⟩,⟨(-12680043128009582854845683789),(-12680043128009582854687256394)⟩⟩,⟨⟨22270155981605558912172408893,22270155981605558913222432091⟩,⟨(-12857680550874923843952607289),(-12857680550874923843791779232)⟩⟩,⟨⟨22573030150397963506324746398,22573030150397963507390135721⟩,⟨(-13032545033757802787356212949),(-13032545033757802787192570740)⟩⟩,⟨⟨22873918673218157793632791378,22873918673218157794713252775⟩,⟨(-13206263103404110813943020664),(-13206263103404110813776694358)⟩⟩,⟨⟨23169983067012150233402992277,23169983067012150234498695703⟩,⟨(-13377195960858535716651023281),(-13377195960858535716481818274)⟩⟩,⟨⟨23463904064604503189400126034,23463904064604503190510717994⟩,⟨(-13546891327938964042018061724),(-13546891327938964041846139238)⟩⟩] +lemma amp0_13_3_eq : ∀ k : Fin 16, amp0_1Expr 3 3 k = amp0_13_3 k := by decide +kernel +noncomputable def amp0_13_4 : Fin 16 → CBox := ![⟨⟨23752978207657740000471741625,23752978207657740001571770629⟩,⟨(-13713788362246510701578022901),(-13713788362246510701417980423)⟩⟩,⟨⟨24039756676364397076336654404,24039756676364397077455386215⟩,⟨(-13879359988352087832800332724),(-13879359988352087832635227745)⟩⟩,⟨⟨24321664486771101359521816428,24321664486771101360658062134⟩,⟨(-14042119538577056534177262272),(-14042119538577056534007683798)⟩⟩,⟨⟨24601129552458858920050863715,24601129552458858921203476209⟩,⟨(-14203468769480979808496548849),(-14203468769480979808323110305)⟩⟩,⟨⟨24875699428374202213013872461,24875699428374202214182340300⟩,⟨(-14361991761252065402553891514),(-14361991761252065402376790280)⟩⟩,⟨⟨25147684467739387131865356375,25147684467739387133050387176⟩,⟨(-14519022396945105875718824300),(-14519022396945105875537600137)⟩⟩,⟨⟨25414749373705691726594826088,25414749373705691727793705878⟩,⟨(-14673212392295853925394341797),(-14673212392295853925210463214)⟩⟩,⟨⟨25679092130460598064985427706,25679092130460598066199712296⟩,⟨(-14825830754066626864282091260),(-14825830754066626864094605567)⟩⟩,⟨⟨25938489683322627373607501724,25938489683322627374837475606⟩,⟨(-14975594001038649664780437793),(-14975594001038649664589081834)⟩⟩,⟨⟨26195032379608320405503624877,26195032379608320406741567123⟩,⟨(-15123708995797826942511319715),(-15123708995797826942320494073)⟩⟩,⟨⟨26446604933591878656343996663,26446604933591878657597704169⟩,⟨(-15268954477560955958096201386),(-15268954477560955957901305118)⟩⟩,⟨⟨26695194376888032118987289206,26695194376888032120255173898⟩,⟨(-15412477659565689369658012281),(-15412477659565689369459902600)⟩⟩,⟨⟨26938789107485135128082117965,26938789107485135129364796501⟩,⟨(-15553117142849101159605394835),(-15553117142849101159403615819)⟩⟩,⟨⟨27179276793229187798304576163,27179276793229187799598970971⟩,⟨(-15691962772950220095176906082),(-15691962772950220094973172426)⟩⟩,⟨⟨27414745779588332834162075470,27414745779588332835471016601⟩,⟨(-15827910855610480798801638354),(-15827910855610480798594215754)⟩⟩,⟨⟨27646987989670052251449785177,27646987989670052252771286418⟩,⟨(-15961995958118355122997992660),(-15961995958118355122787963322)⟩⟩] +lemma amp0_13_4_eq : ∀ k : Fin 16, amp0_1Expr 3 4 k = amp0_13_4 k := by decide +kernel +noncomputable def amp0_13_5 : Fin 16 → CBox := ![⟨⟨27874188295234711901800549946,27874188295234711903135250219⟩,⟨(-16093170115696076600666018504),(-16093170115696076600452912708)⟩⟩,⟨⟨28098046192495536939936313775,28098046192495536941283930505⟩,⟨(-16222414532939837524510159628),(-16222414532939837524294073670)⟩⟩,⟨⟨28316839943670277253154866425,28316839943670277254515976760⟩,⟨(-16348735164077581842693786215),(-16348735164077581842474285595)⟩⟩,⟨⟨28532179662507527615990998494,28532179662507527617365135880⟩,⟨(-16473061608715486665716457888),(-16473061608715486665493742891)⟩⟩,⟨⟨28742434125160893641861480127,28742434125160893643248730269⟩,⟨(-16594452079326727657735635357),(-16594452079326727657509554796)⟩⟩,⟨⟨28949126858313515181393223547,28949126858313515182742907096⟩,⟨(-16713786184451933189158100945),(-16713786184451933188957843321)⟩⟩,⟨⟨29150714511951410420311156694,29150714511951410421676338440⟩,⟨(-16830172870545077046884640704),(-16830172870545077046679466946)⟩⟩,⟨⟨29348636593525162299239089057,29348636593525162300618229709⟩,⟨(-16944443237620253763560514177),(-16944443237620253763351239682)⟩⟩,⟨⟨29541435202988933493559343004,29541435202988933494951363608⟩,⟨(-17055755566693547592076976629),(-17055755566693547591864121862)⟩⟩,⟨⟨29730468187763879466780408659,29730468187763879468184932941⟩,⟨(-17164893811339081078437188857),(-17164893811339081078220895748)⟩⟩,⟨⟨29914360872324529842068360900,29914360872324529843483925373⟩,⟨(-17271064302272175510326470701),(-17271064302272175510107481388)⟩⟩,⟨⟨30094391611375639619885179925,30094391611375639621311306202⟩,⟨(-17375005097925741011829399463),(-17375005097925741011607912904)⟩⟩,⟨⟨30269266911110177883470346877,30269266911110177884908523456⟩,⟨(-17475969399302093169312076503),(-17475969399302093169087130205)⟩⟩,⟨⟨30440187623762200860594791290,30440187623762200862042227763⟩,⟨(-17574650518761821309359635231),(-17574650518761821309132761145)⟩⟩,⟨⟨30605939563110598317290482364,30605939563110598318748522178⟩,⟨(-17670347445563321103923945483),(-17670347445563321103694264594)⟩⟩,⟨⟨30767647905240686647671097201,30767647905240686649139982855⟩,⟨(-17763709800422335702471386439),(-17763709800422335702238677869)⟩⟩] +lemma amp0_13_5_eq : ∀ k : Fin 16, amp0_1Expr 3 5 k = amp0_13_5 k := by decide +kernel +noncomputable def amp0_13_6 : Fin 16 → CBox := ![⟨⟨30924176053652663074350147956,30924176053652663075824284034⟩,⟨(-17854081369043743985047350514),(-17854081369043743984814741173)⟩⟩,⟨⟨31076575182348133091041024294,31076575182348133092526624436⟩,⟨(-17942069047020338019559634177),(-17942069047020338019323454039)⟩⟩,⟨⟨31223784711938343739131124929,31223784711938343740624622092⟩,⟨(-18027060508556524316595655913),(-18027060508556524316357860618)⟩⟩,⟨⟨31366783346512185481295987957,31366783346512185482800400835⟩,⟨(-18109620808721480772207547841),(-18109620808721480771966310328)⟩⟩,⟨⟨31504585086650592892836119363,31504585086650592894349376320⟩,⟨(-18189180680485189148819883787),(-18189180680485189148576296176)⟩⟩,⟨⟨31638097566013635098402790916,31638097566013635099925627148⟩,⟨(-18266264146385615920836965556),(-18266264146385615920590517598)⟩⟩,⟨⟨31766408054785126235642793834,31766408054785126237157751296⟩,⟨(-18340344241617688782975492580),(-18340344241617688782736159642)⟩⟩,⟨⟨31890354391170951216414018816,31890354391170951217939618993⟩,⟨(-18411904692295112742210748944),(-18411904692295112741967750358)⟩⟩,⟨⟨32009095923644769041000989513,32009095923644769042535293779⟩,⟨(-18480460148032860152571103729),(-18480460148032860152325454666)⟩⟩,⟨⟨32123401852681396181920174651,32123401852681396183461992158⟩,⟨(-18546454706932127092418092518),(-18546454706932127092170391802)⟩⟩,⟨⟨32232502525936830261606082283,32232502525936830263156206759⟩,⟨(-18609444010004921362614655410),(-18609444010004921362364340676)⟩⟩,⟨⟨32337099553057724189831997179,32337099553057724191388212665⟩,⟨(-18669833131769604058831919389),(-18669833131769604058580179950)⟩⟩,⟨⟨32436493307917857221137799118,32436493307917857222700876515⟩,⟨(-18727218142893869538587780390),(-18727218142893869538334067101)⟩⟩,⟨⟨32531318751103864919533728983,32531318751103864921104603339⟩,⟨(-18781965638043336647455279534),(-18781965638043336647198961176)⟩⟩,⟨⟨32620945410534091403613052060,32620945410534091405183152505⟩,⟨(-18833711613991944818582839360),(-18833711613991944818328760353)⟩⟩,⟨⟨32705942439377387421274131431,32705942439377387422850695987⟩,⟨(-18882784671474940159804318197),(-18882784671474940159548207075)⟩⟩] +lemma amp0_13_6_eq : ∀ k : Fin 16, amp0_1Expr 3 6 k = amp0_13_6 k := by decide +kernel +noncomputable def amp0_13_7 : Fin 16 → CBox := ![⟨⟨32785747743509981347056479572,32785747743509981348638333535⟩,⟨(-18928860285298653216332739041),(-18928860285298653216075170184)⟩⟩,⟨⟨32860865414590931772461155351,32860865414590931774049081709⟩,⟨(-18972229492918137711025355818),(-18972229492918137710765783416)⟩⟩,⟨⟨32930801052341203472860147815,32930801052341203474449387627⟩,⟨(-19012606852199205230848631118),(-19012606852199205230589699104)⟩⟩,⟨⟨32995994340909188938019572197,32995994340909188939613537402⟩,⟨(-19050246214903288591134105485),(-19050246214903288590873749132)⟩⟩,⟨⟨33056017978152788407431241770,33056017978152788409026940293⟩,⟨(-19084900878023621191428476952),(-19084900878023621191168320340)⟩⟩,⟨⟨33111247806102404777527897221,33111247806102404779128147404⟩,⟨(-19116787834057628919501267881),(-19116787834057628919239587963)⟩⟩,⟨⟨33161323110387142479252762765,33161323110387142480855145395⟩,⟨(-19145698824466174652045270199),(-19145698824466174651783360617)⟩⟩,⟨⟨33206556370521783190695519961,33206556370521783192299852709⟩,⟨(-19171814259381233834550004955),(-19171814259381233834287874139)⟩⟩,⟨⟨33246653032290985851650385882,33246653032290985853256597457⟩,⟨(-19194964077847288366910712048),(-19194964077847288366648298423)⟩⟩,⟨⟨33281862608866566223890120511,33281862608866566225498416821⟩,⟨(-19215292336361252436531452369),(-19215292336361252436268539313)⟩⟩,⟨⟨33311956359174495039300472962,33311956359174495040909534882⟩,⟨(-19232666971202460521350674606),(-19232666971202460521087921400)⟩⟩,⟨⟨33337121144716975240297671144,33337121144716975241907562915⟩,⟨(-19247195866909510668020988674),(-19247195866909510667758259649)⟩⟩,⟨⟨33357193769420233715579419031,33357193769420233717188908336⟩,⟨(-19258784802185279280706046105),(-19258784802185279280443950896)⟩⟩,⟨⟨33372298677811606172491527150,33372298677811606174100078101⟩,⟨(-19267505625111122805784291630),(-19267505625111122805523040278)⟩⟩,⟨⟨33382338028223777526412142514,33382338028223777528018675150⟩,⟨(-19273301846774078917340262132),(-19273301846774078917080376842)⟩⟩,⟨⟨33387374004052282215607154463,33387374004052282217210280500⟩,⟨(-19276209368774298548279272022),(-19276209368774298548021454253)⟩⟩] +lemma amp0_13_7_eq : ∀ k : Fin 16, amp0_1Expr 3 7 k = amp0_13_7 k := by decide +kernel +noncomputable def amp0_13_8 : Fin 16 → CBox := ![⟨⟨33387374004052282215607154463,33387374004052282217210280500⟩,⟨(-19276209368774298548279272022),(-19276209368774298548021454253)⟩⟩,⟨⟨33382338028223777526412142514,33382338028223777528018675150⟩,⟨(-19273301846774078917340262132),(-19273301846774078917080376842)⟩⟩,⟨⟨33372298677811606172491527150,33372298677811606174100078101⟩,⟨(-19267505625111122805784291630),(-19267505625111122805523040278)⟩⟩,⟨⟨33357193769420233715579419031,33357193769420233717188908336⟩,⟨(-19258784802185279280706046105),(-19258784802185279280443950896)⟩⟩,⟨⟨33337121144716975240297671144,33337121144716975241907562915⟩,⟨(-19247195866909510668020988674),(-19247195866909510667758259649)⟩⟩,⟨⟨33311956359174495039300472962,33311956359174495040909534882⟩,⟨(-19232666971202460521350674606),(-19232666971202460521087921400)⟩⟩,⟨⟨33281862608866566223890120511,33281862608866566225498416821⟩,⟨(-19215292336361252436531452369),(-19215292336361252436268539313)⟩⟩,⟨⟨33246653032290985851650385882,33246653032290985853256597457⟩,⟨(-19194964077847288366910712048),(-19194964077847288366648298423)⟩⟩,⟨⟨33206556370521783190695519961,33206556370521783192299852709⟩,⟨(-19171814259381233834550004955),(-19171814259381233834287874139)⟩⟩,⟨⟨33161323110387142479252762765,33161323110387142480855145395⟩,⟨(-19145698824466174652045270199),(-19145698824466174651783360617)⟩⟩,⟨⟨33111247806102404777527897221,33111247806102404779128147404⟩,⟨(-19116787834057628919501267881),(-19116787834057628919239587963)⟩⟩,⟨⟨33056017978152788407431241770,33056017978152788409026940293⟩,⟨(-19084900878023621191428476952),(-19084900878023621191168320340)⟩⟩,⟨⟨32995994340909188938019572197,32995994340909188939613537402⟩,⟨(-19050246214903288591134105485),(-19050246214903288590873749132)⟩⟩,⟨⟨32930801052341203472860147815,32930801052341203474449387627⟩,⟨(-19012606852199205230848631118),(-19012606852199205230589699104)⟩⟩,⟨⟨32860865414590931772461155351,32860865414590931774049081709⟩,⟨(-18972229492918137711025355818),(-18972229492918137710765783416)⟩⟩,⟨⟨32785747743509981347056479572,32785747743509981348638333535⟩,⟨(-18928860285298653216332739041),(-18928860285298653216075170184)⟩⟩] +lemma amp0_13_8_eq : ∀ k : Fin 16, amp0_1Expr 3 8 k = amp0_13_8 k := by decide +kernel +noncomputable def amp0_13_9 : Fin 16 → CBox := ![⟨⟨32705942439377387421274131431,32705942439377387422850695987⟩,⟨(-18882784671474940159804318197),(-18882784671474940159548207075)⟩⟩,⟨⟨32620945410534091403613052060,32620945410534091405183152505⟩,⟨(-18833711613991944818582839360),(-18833711613991944818328760353)⟩⟩,⟨⟨32531318751103864919533728983,32531318751103864921104603339⟩,⟨(-18781965638043336647455279534),(-18781965638043336647198961176)⟩⟩,⟨⟨32436493307917857221137799118,32436493307917857222700876515⟩,⟨(-18727218142893869538587780390),(-18727218142893869538334067101)⟩⟩,⟨⟨32337099553057724189831997179,32337099553057724191388212665⟩,⟨(-18669833131769604058831919389),(-18669833131769604058580179950)⟩⟩,⟨⟨32232502525936830261606082283,32232502525936830263156206759⟩,⟨(-18609444010004921362614655410),(-18609444010004921362364340676)⟩⟩,⟨⟨32123401852681396181920174651,32123401852681396183461992158⟩,⟨(-18546454706932127092418092518),(-18546454706932127092170391802)⟩⟩,⟨⟨32009095923644769041000989513,32009095923644769042535293779⟩,⟨(-18480460148032860152571103729),(-18480460148032860152325454666)⟩⟩,⟨⟨31890354391170951216414018816,31890354391170951217939618993⟩,⟨(-18411904692295112742210748944),(-18411904692295112741967750358)⟩⟩,⟨⟨31766408054785126235642793834,31766408054785126237157751296⟩,⟨(-18340344241617688782975492580),(-18340344241617688782736159642)⟩⟩,⟨⟨31638097566013635098402790916,31638097566013635099925627148⟩,⟨(-18266264146385615920836965556),(-18266264146385615920590517598)⟩⟩,⟨⟨31504585086650592892836119363,31504585086650592894349376320⟩,⟨(-18189180680485189148819883787),(-18189180680485189148576296176)⟩⟩,⟨⟨31366783346512185481295987957,31366783346512185482800400835⟩,⟨(-18109620808721480772207547841),(-18109620808721480771966310328)⟩⟩,⟨⟨31223784711938343739131124929,31223784711938343740624622092⟩,⟨(-18027060508556524316595655913),(-18027060508556524316357860618)⟩⟩,⟨⟨31076575182348133091041024294,31076575182348133092526624436⟩,⟨(-17942069047020338019559634177),(-17942069047020338019323454039)⟩⟩,⟨⟨30924176053652663074350147956,30924176053652663075824284034⟩,⟨(-17854081369043743985047350514),(-17854081369043743984814741173)⟩⟩] +lemma amp0_13_9_eq : ∀ k : Fin 16, amp0_1Expr 3 9 k = amp0_13_9 k := by decide +kernel +noncomputable def amp0_13_10 : Fin 16 → CBox := ![⟨⟨30767647905240686647671097201,30767647905240686649139982855⟩,⟨(-17763709800422335702471386439),(-17763709800422335702238677869)⟩⟩,⟨⟨30605939563110598317290482364,30605939563110598318748522178⟩,⟨(-17670347445563321103923945483),(-17670347445563321103694264594)⟩⟩,⟨⟨30440187623762200860594791290,30440187623762200862042227763⟩,⟨(-17574650518761821309359635231),(-17574650518761821309132761145)⟩⟩,⟨⟨30269266911110177883470346877,30269266911110177884908523456⟩,⟨(-17475969399302093169312076503),(-17475969399302093169087130205)⟩⟩,⟨⟨30094391611375639619885179925,30094391611375639621311306202⟩,⟨(-17375005097925741011829399463),(-17375005097925741011607912904)⟩⟩,⟨⟨29914360872324529842068360900,29914360872324529843483925373⟩,⟨(-17271064302272175510326470701),(-17271064302272175510107481388)⟩⟩,⟨⟨29730468187763879466780408659,29730468187763879468184932941⟩,⟨(-17164893811339081078437188857),(-17164893811339081078220895748)⟩⟩,⟨⟨29541435202988933493559343004,29541435202988933494951363608⟩,⟨(-17055755566693547592076976629),(-17055755566693547591864121862)⟩⟩,⟨⟨29348636593525162299239089057,29348636593525162300618229709⟩,⟨(-16944443237620253763560514177),(-16944443237620253763351239682)⟩⟩,⟨⟨29150714511951410420311156694,29150714511951410421676338440⟩,⟨(-16830172870545077046884640704),(-16830172870545077046679466946)⟩⟩,⟨⟨28949126858313515181393223547,28949126858313515182742907096⟩,⟨(-16713786184451933189158100945),(-16713786184451933188957843321)⟩⟩,⟨⟨28742434125160893641861480127,28742434125160893643248730269⟩,⟨(-16594452079326727657735635357),(-16594452079326727657509554796)⟩⟩,⟨⟨28532179662507527615990998494,28532179662507527617365135880⟩,⟨(-16473061608715486665716457888),(-16473061608715486665493742891)⟩⟩,⟨⟨28316839943670277253154866425,28316839943670277254515976760⟩,⟨(-16348735164077581842693786215),(-16348735164077581842474285595)⟩⟩,⟨⟨28098046192495536939936313775,28098046192495536941283930505⟩,⟨(-16222414532939837524510159628),(-16222414532939837524294073670)⟩⟩,⟨⟨27874188295234711901800549946,27874188295234711903135250219⟩,⟨(-16093170115696076600666018504),(-16093170115696076600452912708)⟩⟩] +lemma amp0_13_10_eq : ∀ k : Fin 16, amp0_1Expr 3 10 k = amp0_13_10 k := by decide +kernel +noncomputable def amp0_13_11 : Fin 16 → CBox := ![⟨⟨27646987989670052251449785177,27646987989670052252771286418⟩,⟨(-15961995958118355122997992660),(-15961995958118355122787963322)⟩⟩,⟨⟨27414745779588332834162075470,27414745779588332835471016601⟩,⟨(-15827910855610480798801638354),(-15827910855610480798594215754)⟩⟩,⟨⟨27179276793229187798304576163,27179276793229187799598970971⟩,⟨(-15691962772950220095176906082),(-15691962772950220094973172426)⟩⟩,⟨⟨26938789107485135128082117965,26938789107485135129364796501⟩,⟨(-15553117142849101159605394835),(-15553117142849101159403615819)⟩⟩,⟨⟨26695194376888032118987289206,26695194376888032120255173898⟩,⟨(-15412477659565689369658012281),(-15412477659565689369459902600)⟩⟩,⟨⟨26446604933591878656343996663,26446604933591878657597704169⟩,⟨(-15268954477560955958096201386),(-15268954477560955957901305118)⟩⟩,⟨⟨26195032379608320405503624877,26195032379608320406741567123⟩,⟨(-15123708995797826942511319715),(-15123708995797826942320494073)⟩⟩,⟨⟨25938489683322627373607501724,25938489683322627374837475606⟩,⟨(-14975594001038649664780437793),(-14975594001038649664589081834)⟩⟩,⟨⟨25679092130460598064985427706,25679092130460598066199712296⟩,⟨(-14825830754066626864282091260),(-14825830754066626864094605567)⟩⟩,⟨⟨25414749373705691726594826088,25414749373705691727793705878⟩,⟨(-14673212392295853925394341797),(-14673212392295853925210463214)⟩⟩,⟨⟨25147684467739387131865356375,25147684467739387133050387176⟩,⟨(-14519022396945105875718824300),(-14519022396945105875537600137)⟩⟩,⟨⟨24875699428374202213013872461,24875699428374202214182340300⟩,⟨(-14361991761252065402553891514),(-14361991761252065402376790280)⟩⟩,⟨⟨24601129552458858920050863715,24601129552458858921203476209⟩,⟨(-14203468769480979808496548849),(-14203468769480979808323110305)⟩⟩,⟨⟨24321664486771101359521816428,24321664486771101360658062134⟩,⟨(-14042119538577056534177262272),(-14042119538577056534007683798)⟩⟩,⟨⟨24039756676364397076336654404,24039756676364397077455386215⟩,⟨(-13879359988352087832800332724),(-13879359988352087832635227745)⟩⟩,⟨⟨23752978207657740000471741625,23752978207657740001571770629⟩,⟨(-13713788362246510701578022901),(-13713788362246510701417980423)⟩⟩] +lemma amp0_13_11_eq : ∀ k : Fin 16, amp0_1Expr 3 11 k = amp0_13_11 k := by decide +kernel +noncomputable def amp0_13_12 : Fin 16 → CBox := ![⟨⟨23463904064604503189400126034,23463904064604503190510717994⟩,⟨(-13546891327938964042018061724),(-13546891327938964041846139238)⟩⟩,⟨⟨23169983067012150233402992277,23169983067012150234498695703⟩,⟨(-13377195960858535716651023281),(-13377195960858535716481818274)⟩⟩,⟨⟨22873918673218157793632791378,22873918673218157794713252775⟩,⟨(-13206263103404110813943020664),(-13206263103404110813776694358)⟩⟩,⟨⟨22573030150397963506324746398,22573030150397963507390135721⟩,⟨(-13032545033757802787356212949),(-13032545033757802787192570740)⟩⟩,⟨⟨22270155981605558912172408893,22270155981605558913222432091⟩,⟨(-12857680550874923843952607289),(-12857680550874923843791779232)⟩⟩,⟨⟨21962478939877190903319791707,21962478939877190904354998591⟩,⟨(-12680043128009582854845683789),(-12680043128009582854687256394)⟩⟩,⟨⟨21652979780165887256203981659,21652979780165887257222580939⟩,⟨(-12501353704836298717061264729),(-12501353704836298716906235756)⟩⟩,⟨⟨21338697095528772242817854704,21338697095528772243823597652⟩,⟨(-12319902512259422102348532831),(-12319902512259422102194640811)⟩⟩,⟨⟨21022761953305465944830905673,21022761953305465945819615946⟩,⟨(-12137497272850333510250567005),(-12137497272850333510100190101)⟩⟩,⟨⟨20702060231618653077514135938,20702060231618653078486607311⟩,⟨(-11952340047504875658392411012),(-11952340047504875658244995607)⟩⟩,⟨⟨20379882258044908823671827500,20379882258044908824627232256⟩,⟨(-11766330507735106277546062973),(-11766330507735106277402057425)⟩⟩,⟨⟨20052951687444352543693019028,20052951687444352544630996635⟩,⟨(-11577577054792557158352601889),(-11577577054792557158212119298)⟩⟩,⟨⟨19724728098486747676704624787,19724728098486747677623614457⟩,⟨(-11388077077353498909807719763),(-11388077077353498909671635391)⟩⟩,⟨⟨19391762292844942225631674328,19391762292844942226549272491⟩,⟨(-11195839179835261919537663172),(-11195839179835261919395722871)⟩⟩,⟨⟨19057694296448717007814968731,19057694296448717008714521551⟩,⟨(-11002964932188262360225137398),(-11002964932188262360086934221)⟩⟩,⟨⟨18718890128322294124742091272,18718890128322294125623709421⟩,⟨(-10807356254517904883268718785),(-10807356254517904883134094111)⟩⟩] +lemma amp0_13_12_eq : ∀ k : Fin 16, amp0_1Expr 3 12 k = amp0_13_12 k := by decide +kernel +noncomputable def amp0_13_13 : Fin 16 → CBox := ![⟨⟨18379182858626920876327483180,18379182858626920877191511090⟩,⟨(-10611226170913608339509370747),(-10611226170913608339378107657)⟩⟩,⟨⟨18034740279655822663321397188,18034740279655822664169801425⟩,⟨(-10412362155224275855632707639),(-10412362155224275855503576030)⟩⟩,⟨⟨17689602740734276710807622757,17689602740734276711636928777⟩,⟨(-10213096904220476360366933303),(-10213096904220476360241925304)⟩⟩,⟨⟨17339724586802453970626691195,17339724586802453971437994950⟩,⟨(-10011094657864369181232186823),(-10011094657864369181110574873)⟩⟩,⟨⟨16989369609173106073628229986,16989369609173106074419944517⟩,⟨(-9808817117218139860115482073),(-9808817117218139859998172867)⟩⟩,⟨⟨16634261386743642866780375761,16634261386743642867563636162⟩,⟨(-9603795289407039775953571342),(-9603795289407039775834040966)⟩⟩,⟨⟨16278905600962081266704429937,16278905600962081267469497918⟩,⟨(-9398630530827964198351428325),(-9398630530827964198235294231)⟩⟩,⟨⟨15918775249752562214212026728,15918775249752562214958638540⟩,⟨(-9190709175613793904856513087),(-9190709175613793904743832061)⟩⟩,⟨⟨15558639082871133557380713137,15558639082871133558109122756⟩,⟨(-8982784462719881082751759077),(-8982784462719881082642384369)⟩⟩,⟨⟨15193696708276728727733043580,15193696708276728728444209873⟩,⟨(-8772084884509100211669534343),(-8772084884509100211562816226)⟩⟩,⟨⟨14829004411061715033476591211,14829004411061715034169368210⟩,⟨(-8561529688540629048775233422),(-8561529688540629048671838523)⟩⟩,⟨⟨14459461977215688467364746980,14459461977215688468046189311⟩,⟨(-8348174264882636139710255458),(-8348174264882636139606013785)⟩⟩,⟨⟨14090441693045962457595386696,14090441693045962458257003962⟩,⟨(-8135120304480812632801109356),(-8135120304480812632700933283)⟩⟩,⟨⟨13716512663740494235405315775,13716512663740494236047798743⟩,⟨(-7919232278753485093487517224),(-7919232278753485093390909763)⟩⟩,⟨⟨13343396554569321850761949332,13343396554569321851385864897⟩,⟨(-7703813592684522922709364427),(-7703813592684522922616014538)⟩⟩,⟨⟨12965295463818583363449180068,12965295463818583364053460907⟩,⟨(-7485516826158692936708098921),(-7485516826158692936618523124)⟩⟩] +lemma amp0_13_13_eq : ∀ k : Fin 16, amp0_1Expr 3 13 k = amp0_13_13 k := by decide +kernel +noncomputable def amp0_13_14 : Fin 16 → CBox := ![⟨⟨12588319915260722390540711843,12588319915260722391131049653⟩,⟨(-7267869891720905065334293585),(-7267869891720905065245228290)⟩⟩,⟨⟨12206261841045965249591186361,12206261841045965250162373993⟩,⟨(-7047288559726945011820637143),(-7047288559726945011734987046)⟩⟩,⟨⟨11825667778884814561557998458,11825667778884814562110844115⟩,⟨(-6827552475486231500723730499),(-6827552475486231500641058265)⟩⟩,⟨⟨11439867680844907708743446504,11439867680844907709275832045⟩,⟨(-6604810685029507267970157380),(-6604810685029507267891581798)⟩⟩,⟨⟨11055901047314695423442775621,11055901047314695423960159589⟩,⟨(-6383127445801004818991044979),(-6383127445801004818913451226)⟩⟩,⟨⟨10666572908823690776476488447,10666572908823690776974473209⟩,⟨(-6158348740240127386071553083),(-6158348740240127385997372905)⟩⟩,⟨⟨10279485372927895294463645533,10279485372927895294945388796⟩,⟨(-5934863647190740938631074114),(-5934863647190740938558529218)⟩⟩,⟨⟨9886841054724459426517622953,9886841054724459426979481450⟩,⟨(-5708170344380210164521469685),(-5708170344380210164452552378)⟩⟩,⟨⟨9496891073954188850677231605,9496891073954188851119742689⟩,⟨(-5483032618012005057126405614),(-5483032618012005057060859541)⟩⟩,⟨⟨9101138730168082673484575348,9101138730168082673909876867⟩,⟨(-5254544895794671336509294448),(-5254544895794671336445769276)⟩⟩,⟨⟨8708593155276932932427908090,8708593155276932932833311204⟩,⟨(-5027908602462069633040300924),(-5027908602462069632980413190)⟩⟩,⟨⟨8309934963699564221982508264,8309934963699564222370158167⟩,⟨(-4797743188240226409390849092),(-4797743188240226409333238015)⟩⟩,⟨⟨7915071511567247979426046382,7915071511567247979796124405⟩,⟨(-4569768667858488719164634055),(-4569768667858488719109270839)⟩⟩,⟨⟨7513700288185479521540467670,7513700288185479521890412036⟩,⟨(-4338036883994055285215671033),(-4338036883994055285163904565)⟩⟩,⟨⟨7116811458893626802063770103,7116811458893626802395563162⟩,⟨(-4108893011564048690431636605),(-4108893011564048690382412022)⟩⟩,⟨⟨6712905375084154821591517905,6712905375084154821904686281⟩,⟨(-3875697725349322497819381515),(-3875697725349322497772831776)⟩⟩] +lemma amp0_13_14_eq : ∀ k : Fin 16, amp0_1Expr 3 14 k = amp0_13_14 k := by decide +kernel +noncomputable def amp0_13_15 : Fin 16 → CBox := ![⟨⟨6314304889329281698004535867,6314304889329281698298941529⟩,⟨(-3645565627599630910004073950),(-3645565627599630909960384859)⟩⟩,⟨⟨5908018787060499827685692153,5908018787060499827960800832⟩,⟨(-3410996237086745874114274028),(-3410996237086745874073600333)⟩⟩,⟨⟨5508052685234101317787702162,5508052685234101318043671018⟩,⟨(-3180075700530549425280185216),(-3180075700530549425242562582)⟩⟩,⟨⟨5099502883647184281659101791,5099502883647184281896405779⟩,⟨(-2944199362606974679118331982),(-2944199362606974679083314518)⟩⟩,⟨⟨4698569893355039727456895936,4698569893355039727675567876⟩,⟨(-2712720592734803407355309708),(-2712720592734803407323030802)⟩⟩,⟨⟨4287805485929443700342645256,4287805485929443700542040610⟩,⟨(-2475565651534118428817667620),(-2475565651534118428788302768)⟩⟩,⟨⟨3886397599776523265338319014,3886397599776523265518587393⟩,⟨(-2243812700408891163233886754),(-2243812700408891163207536709)⟩⟩,⟨⟨3473340580412691300444932216,3473340580412691300606286626⟩,⟨(-2005334119088518316342716610),(-2005334119088518316319025409)⟩⟩,⟨⟨3072133445990435320165445331,3072133445990435320307900926⟩,⟨(-1773697072029030456943593400),(-1773697072029030456922789292)⟩⟩,⟨⟨2656435792071101113264950449,2656435792071101113387946312⟩,⟨(-1533693919637206962852853472),(-1533693919637206962834970492)⟩⟩,⟨⟨2256524817754308917888612059,2256524817754308917992772564⟩,⟨(-1302805210963521473388268586),(-1302805210963521473373261986)⟩⟩,⟨⟨1837153108049314193251390063,1837153108049314193335989206⟩,⟨(-1060680841474829177402326042),(-1060680841474829177390225766)⟩⟩,⟨⟨1440842106367455813482969064,1440842106367455813548914130⟩,⟨(-831870577970998012739345599),(-831870577970998012730089039)⟩⟩,⟨⟨1014414495963543606899319452,1014414495963543606945491836⟩,⟨(-585672482314410439978452122),(-585672482314410439972082773)⟩⟩,⟨⟨629264447029517718456932497,629264447029517718484715427⟩,⟨(-363305997883953057546987492),(-363305997883953057543532298)⟩⟩,⟨⟨178776584874023315345043551,178776584874023315352420050⟩,⟨(-103216709401819338812122997),(-103216709401819338811439704)⟩⟩] +lemma amp0_13_15_eq : ∀ k : Fin 16, amp0_1Expr 3 15 k = amp0_13_15 k := by decide +kernel +noncomputable def amp0_13 : Fin 16 → Fin 16 → CBox := ![amp0_13_0,amp0_13_1,amp0_13_2,amp0_13_3,amp0_13_4,amp0_13_5,amp0_13_6,amp0_13_7,amp0_13_8,amp0_13_9,amp0_13_10,amp0_13_11,amp0_13_12,amp0_13_13,amp0_13_14,amp0_13_15] +lemma amp0_13_eq (i k : Fin 16) : amp0_1Expr 3 i k = amp0_13 i k := by + fin_cases i + · exact amp0_13_0_eq k + · exact amp0_13_1_eq k + · exact amp0_13_2_eq k + · exact amp0_13_3_eq k + · exact amp0_13_4_eq k + · exact amp0_13_5_eq k + · exact amp0_13_6_eq k + · exact amp0_13_7_eq k + · exact amp0_13_8_eq k + · exact amp0_13_9_eq k + · exact amp0_13_10_eq k + · exact amp0_13_11_eq k + · exact amp0_13_12_eq k + · exact amp0_13_13_eq k + · exact amp0_13_14_eq k + · exact amp0_13_15_eq k +noncomputable def amp0_14_0 : Fin 16 → CBox := ![⟨⟨357553169748046630694215770,357553169748046630700711430⟩,⟨0,0⟩⟩,⟨⟨1258528894059035436928397235,1258528894059035436954898614⟩,⟨0,0⟩⟩,⟨⟨2028828991927087213822065804,2028828991927087213867556772⟩,⟨0,0⟩⟩,⟨⟨2881684212734911626999212952,2881684212734911627064553436⟩,⟨0,0⟩⟩,⟨⟨3674306216098628386545207360,3674306216098628386629551179⟩,⟨0,0⟩⟩,⟨⟨4513049635508617835829336327,4513049635508617835933432919⟩,⟨0,0⟩⟩,⟨⟨5312871584142202226591248655,5312871584142202226714544867⟩,⟨0,0⟩⟩,⟨⟨6144266891980870640401838545,6144266891980870640544853969⟩,⟨0,0⟩⟩,⟨⟨6946681160825382600970077797,6946681160825382601132359888⟩,⟨0,0⟩⟩,⟨⟨7772795199553046530766390537,7772795199553046530947422277⟩,⟨0,0⟩⟩,⟨⟨8575610971858887400784313139,8575610971858887400985058594⟩,⟨0,0⟩⟩,⟨⟨9397139786710079455022300696,9397139786710079455242626929⟩,⟨0,0⟩⟩,⟨⟨10199005767294368563435971558,10199005767294368563675043583⟩,⟨0,0⟩⟩,⟨⟨11016105370468202635702607352,11016105370468202635960139008⟩,⟨0,0⟩⟩,⟨⟨11816037574120999655507824155,11816037574120999655785161813⟩,⟨0,0⟩⟩,⟨⟨12628609778658563396154894359,12628609778658563396452060432⟩,⟨0,0⟩⟩] +lemma amp0_14_0_eq : ∀ k : Fin 16, amp0_1Expr 4 0 k = amp0_14_0 k := by decide +kernel +noncomputable def amp0_14_1 : Fin 16 → CBox := ![⟨⟨13425810750168309643338063720,13425810750168309643654344652⟩,⟨0,0⟩⟩,⟨⟨14233622917787253604291895928,14233622917787253604626770603⟩,⟨0,0⟩⟩,⟨⟨15027400576370959043254456816,15027400576370959043607302595⟩,⟨0,0⟩⟩,⟨⟨15830143023134495959034883511,15830143023134495959409458062⟩,⟨0,0⟩⟩,⟨⟨16619869927399128444156926255,16619869927399128444548406607⟩,⟨0,0⟩⟩,⟨⟨17417186310553865865056932525,17417186310553865865465506063⟩,⟨0,0⟩⟩,⟨⟨18202277460336165347179332492,18202277460336165347609571938⟩,⟨0,0⟩⟩,⟨⟨18993782147908377701573784515,18993782147908377702020164072⟩,⟨0,0⟩⟩,⟨⟨19773682109448918853263572721,19773682109448918853730636086⟩,⟨0,0⟩⟩,⟨⟨20558970745855790589164685613,20558970745855790589653383046⟩,⟨0,0⟩⟩,⟨⟨21333145817647381553199310844,21333145817647381553702612468⟩,⟨0,0⟩⟩,⟨⟨22111802094629390847140876340,22111802094629390847664994079⟩,⟨0,0⟩⟩,⟨⟨22879735361689815417751085435,22879735361689815418287471662⟩,⟨0,0⟩⟩,⟨⟨23651335557769629123389099016,23651335557769629123948586131⟩,⟨0,0⟩⟩,⟨⟨24412523682091930499464264266,24412523682091930500042856444⟩,⟨0,0⟩⟩,⟨⟨25176639830521444781372138483,25176639830521444781971384511⟩,⟨0,0⟩⟩] +lemma amp0_14_1_eq : ∀ k : Fin 16, amp0_1Expr 4 1 k = amp0_14_1 k := by decide +kernel +noncomputable def amp0_14_2 : Fin 16 → CBox := ![⟨⟨25930590927637166727197780810,25930590927637166727807501141⟩,⟨0,0⟩⟩,⟨⟨26686793109138643701832051207,26686793109138643702463577249⟩,⟨0,0⟩⟩,⟨⟨27433025327480988471127400841,27433025327480988471778828195⟩,⟨0,0⟩⟩,⟨⟨28180883386091924915516178205,28180883386091924916188603112⟩,⟨0,0⟩⟩,⟨⟨28918923954431376935063420932,28918923954431376935758451650⟩,⟨0,0⟩⟩,⟨⟨29658008822123430067295643610,29658008822123430067996275232⟩,⟨0,0⟩⟩,⟨⟨30387393416553457455816970557,30387393416553457456537536350⟩,⟨0,0⟩⟩,⟨⟨31117278165742267115120737654,31117278165742267115858934133⟩,⟨0,0⟩⟩,⟨⟨31837550499505124428791681823,31837550499505124429549648713⟩,⟨0,0⟩⟩,⟨⟨32557811201924162533784805095,32557811201924162534563050614⟩,⟨0,0⟩⟩,⟨⟨33268522773487285733944903334,33268522773487285734743120511⟩,⟨0,0⟩⟩,⟨⟨33978739218346212147648812658,33978739218346212148447536349⟩,⟨0,0⟩⟩,⟨⟨34679449173604907941653826177,34679449173604907942475546112⟩,⟨0,0⟩⟩,⟨⟨35379205481468553422023769392,35379205481468553422865333677⟩,⟨0,0⟩⟩,⟨⟨36069480559311645327059288863,36069480559311645327923108363⟩,⟨0,0⟩⟩,⟨⟨36758365717253841753079415407,36758365717253841753958573133⟩,⟨0,0⟩⟩] +lemma amp0_14_2_eq : ∀ k : Fin 16, amp0_1Expr 4 2 k = amp0_14_2 k := by decide +kernel +noncomputable def amp0_14_3 : Fin 16 → CBox := ![⟨⟨37437780256644588249916476794,37437780256644588250815124592⟩,⟨0,0⟩⟩,⟨⟨38115388592897434016070056060,38115388592897434016988924505⟩,⟨0,0⟩⟩,⟨⟨38783524585689884451711182224,38783524585689884452650711415⟩,⟨0,0⟩⟩,⟨⟨39449456196973495353864772658,39449456196973495354791705830⟩,⟨0,0⟩⟩,⟨⟨40105903374888705087849141139,40105903374888705088798890188⟩,⟨0,0⟩⟩,⟨⟨40759764516089817647814308222,40759764516089817648783811292⟩,⟨0,0⟩⟩,⟨⟨41404120463237306155506365479,41404120463237306156495121020⟩,⟨0,0⟩⟩,⟨⟨42045523906610931890147311237,42045523906610931891153732001⟩,⟨0,0⟩⟩,⟨⟨42677394191057544486128505509,42677394191057544487154399202⟩,⟨0,0⟩⟩,⟨⟨43305959560331774512908017467,43305959560331774513945107729⟩,⟨0,0⟩⟩,⟨⟨43924957879754381807146785139,43924957879754381808202795457⟩,⟨0,0⟩⟩,⟨⟨44540311963211117824859125008,44540311963211117825930556959⟩,⟨0,0⟩⟩,⟨⟨45146060300795927013170794598,45146060300795927014258969641⟩,⟨0,0⟩⟩,⟨⟨45747837346436315587793833280,45747837346436315588898255025⟩,⟨0,0⟩⟩,⟨⟨46339966134024300467341072392,46339966134024300468462303567⟩,⟨0,0⟩⟩,⟨⟨46927808129209006379342127723,46927808129209006380479560335⟩,⟨0,0⟩⟩] +lemma amp0_14_3_eq : ∀ k : Fin 16, amp0_1Expr 4 3 k = amp0_14_3 k := by decide +kernel +noncomputable def amp0_14_4 : Fin 16 → CBox := ![⟨⟨47505956415315480001492034784,47505956415315480002594989723⟩,⟨0,0⟩⟩,⟨⟨48079513352728794153228483208,48079513352728794154355598030⟩,⟨0,0⟩⟩,⟨⟨48643328973542202719605317639,48643328973542202720754439487⟩,⟨0,0⟩⟩,⟨⟨49202259104917717840669866180,49202259104917717841838813667⟩,⟨0,0⟩⟩,⟨⟨49751398856748404426602224593,49751398856748404427790200929⟩,⟨0,0⟩⟩,⟨⟨50295368935478774264311473647,50295368935478774265520013456⟩,⟨0,0⟩⟩,⟨⟨50829498747411383453776580671,50829498747411383455000483261⟩,⟨0,0⟩⟩,⟨⟨51358184260921196130563888643,51358184260921196131806391362⟩,⟨0,0⟩⟩,⟨⟨51876979366645254747814027209,51876979366645254749075927452⟩,⟨0,0⟩⟩,⟨⟨52390064759216640811612198114,52390064759216640812878185885⟩,⟨0,0⟩⟩,⟨⟨52893209867183757313298751506,52893209867183757314584650158⟩,⟨0,0⟩⟩,⟨⟨53390388753776064238591077519,53390388753776064239893848690⟩,⟨0,0⟩⟩,⟨⟨53877578214970270256786360616,53877578214970270258107468315⟩,⟨0,0⟩⟩,⟨⟨54358553586458375597236830837,54358553586458375598570263431⟩,⟨0,0⟩⟩,⟨⟨54829491559176665668957267376,54829491559176665670308916768⟩,⟨0,0⟩⟩,⟨⟨55293975979340104503538050193,55293975979340104504904092996⟩,⟨0,0⟩⟩] +lemma amp0_14_4_eq : ∀ k : Fin 16, amp0_1Expr 4 4 k = amp0_14_4 k := by decide +kernel +noncomputable def amp0_14_5 : Fin 16 → CBox := ![⟨⟨55748376590469423804244826698,55748376590469423805626773633⟩,⟨0,0⟩⟩,⟨⟨56196092384991073880521524132,56196092384991073881918964427⟩,⟨0,0⟩⟩,⟨⟨56633679887340554506963682257,56633679887340554508378004113⟩,⟨0,0⟩⟩,⟨⟨57064359325015055232640919452,57064359325015055234071349294⟩,⟨0,0⟩⟩,⟨⟨57484868250321787284386738337,57484868250321787285833682453⟩,⟨0,0⟩⟩,⟨⟨57898253716627030363454998543,57898253716627030364817262744⟩,⟨0,0⟩⟩,⟨⟨58301429023902820841295520304,58301429023902820842679469964⟩,⟨0,0⟩⟩,⟨⟨58697273187050324599155955844,58697273187050324600558681688⟩,⟨0,0⟩⟩,⟨⟨59082870405977866987800916230,59082870405977866989220496994⟩,⟨0,0⟩⟩,⟨⟨59460936375527758934247413071,59460936375527758935683270129⟩,⟨0,0⟩⟩,⟨⟨59828721744649059684827564373,59828721744649059686277008174⟩,⟨0,0⟩⟩,⟨⟨60188783222751279240465360054,60188783222751279241927612199⟩,⟨0,0⟩⟩,⟨⟨60538533822220355767639732530,60538533822220355769118008136⟩,⟨0,0⟩⟩,⟨⟨60880375247524401721892568601,60880375247524401723381469504⟩,⟨0,0⟩⟩,⟨⟨61211879126221196635287778626,61211879126221196636790230459⟩,⟨0,0⟩⟩,⟨⟨61535295810481373296052742795,61535295810481373297569417317⟩,⟨0,0⟩⟩] +lemma amp0_14_5_eq : ∀ k : Fin 16, amp0_1Expr 4 5 k = amp0_14_5 k := by decide +kernel +noncomputable def amp0_14_6 : Fin 16 → CBox := ![⟨⟨61848352107305326149414459166,61848352107305326150934404813⟩,⟨0,0⟩⟩,⟨⟨62153150364696266182799731351,62153150364696266184335566110⟩,⟨0,0⟩⟩,⟨⟨62447569423876687478983332279,62447569423876687480528161764⟩,⟨0,0⟩⟩,⟨⟨62733566693024370963316360747,62733566693024370964876416837⟩,⟨0,0⟩⟩,⟨⟨63009170173301185786399805954,63009170173301185787971185413⟩,⟨0,0⟩⟩,⟨⟨63276195132027270197536232397,63276195132027270199120603729⟩,⟨0,0⟩⟩,⟨⟨63532816109570252472019201437,63532816109570252473581888821⟩,⟨0,0⟩⟩,⟨⟨63780708782341902433564513821,63780708782341902435142761798⟩,⟨0,0⟩⟩,⟨⟨64018191847289538082741197432,64018191847289538084331369152⟩,⟨0,0⟩⟩,⟨⟨64246803705362792364582207491,64246803705362792366182126128⟩,⟨0,0⟩⟩,⟨⟨64465005051873660523956542327,64465005051873660525568035757⟩,⟨0,0⟩⟩,⟨⟨64674199106115448380410787683,64674199106115448382029632004⟩,⟨0,0⟩⟩,⟨⟨64872986615835714443024686963,64872986615835714444652664303⟩,⟨0,0⟩⟩,⟨⟨65062637502207729839818736592,65062637502207729841457928051⟩,⟨0,0⟩⟩,⟨⟨65241890821068182807979452584,65241890821068182809612956546⟩,⟨0,0⟩⟩,⟨⟨65411884878754774843303574249,65411884878754774844946080587⟩,⟨0,0⟩⟩] +lemma amp0_14_6_eq : ∀ k : Fin 16, amp0_1Expr 4 6 k = amp0_14_6 k := by decide +kernel +noncomputable def amp0_14_7 : Fin 16 → CBox := ![⟨⟨65571495487019962694870113555,65571495487019962696519512658⟩,⟨0,0⟩⟩,⟨⟨65721730829181863545681199883,65721730829181863547339274238⟩,⟨0,0⟩⟩,⟨⟨65861602104682406946480799904,65861602104682406948138270980⟩,⟨0,0⟩⟩,⟨⟨65991988681818377876801154243,65991988681818377878465064954⟩,⟨0,0⟩⟩,⟨⟨66112035956305576815625879575,66112035956305576817290484550⟩,⟨0,0⟩⟩,⟨⟨66222495612204809555820465955,66222495612204809557491623294⟩,⟨0,0⟩⟩,⟨⟨66322646220774284959271353483,66322646220774284960944462837⟩,⟨0,0⟩⟩,⟨⟨66413112741043566382157912493,66413112741043566383832832847⟩,⟨0,0⟩⟩,⟨⟨66493306064581971704068570327,66493306064581971705745396350⟩,⟨0,0⟩⟩,⟨⟨66563725217733132448548852715,66563725217733132450228221948⟩,⟨0,0⟩⟩,⟨⟨66623912718348990079370252602,66623912718348990081049763085⟩,⟨0,0⟩⟩,⟨⟨66674242289433950481365230124,66674242289433950483045237995⟩,⟨0,0⟩⟩,⟨⟨66714387538840467431929189454,66714387538840467433607465279⟩,⟨0,0⟩⟩,⟨⟨66744597355623212345753754525,66744597355623212347429455977⟩,⟨0,0⟩⟩,⟨⟨66764676056447555053595217103,66764676056447555055266418225⟩,⟨0,0⟩⟩,⟨⟨66774748008104564431985357301,66774748008104564433649512624⟩,⟨0,0⟩⟩] +lemma amp0_14_7_eq : ∀ k : Fin 16, amp0_1Expr 4 7 k = amp0_14_7 k := by decide +kernel +noncomputable def amp0_14_8 : Fin 16 → CBox := ![⟨⟨66774748008104564431985357301,66774748008104564433649512624⟩,⟨0,0⟩⟩,⟨⟨66764676056447555053595217103,66764676056447555055266418225⟩,⟨0,0⟩⟩,⟨⟨66744597355623212345753754525,66744597355623212347429455977⟩,⟨0,0⟩⟩,⟨⟨66714387538840467431929189454,66714387538840467433607465279⟩,⟨0,0⟩⟩,⟨⟨66674242289433950481365230124,66674242289433950483045237995⟩,⟨0,0⟩⟩,⟨⟨66623912718348990079370252602,66623912718348990081049763085⟩,⟨0,0⟩⟩,⟨⟨66563725217733132448548852715,66563725217733132450228221948⟩,⟨0,0⟩⟩,⟨⟨66493306064581971704068570327,66493306064581971705745396350⟩,⟨0,0⟩⟩,⟨⟨66413112741043566382157912493,66413112741043566383832832847⟩,⟨0,0⟩⟩,⟨⟨66322646220774284959271353483,66322646220774284960944462837⟩,⟨0,0⟩⟩,⟨⟨66222495612204809555820465955,66222495612204809557491623294⟩,⟨0,0⟩⟩,⟨⟨66112035956305576815625879575,66112035956305576817290484550⟩,⟨0,0⟩⟩,⟨⟨65991988681818377876801154243,65991988681818377878465064954⟩,⟨0,0⟩⟩,⟨⟨65861602104682406946480799904,65861602104682406948138270980⟩,⟨0,0⟩⟩,⟨⟨65721730829181863545681199883,65721730829181863547339274238⟩,⟨0,0⟩⟩,⟨⟨65571495487019962694870113555,65571495487019962696519512658⟩,⟨0,0⟩⟩] +lemma amp0_14_8_eq : ∀ k : Fin 16, amp0_1Expr 4 8 k = amp0_14_8 k := by decide +kernel +noncomputable def amp0_14_9 : Fin 16 → CBox := ![⟨⟨65411884878754774843303574249,65411884878754774844946080587⟩,⟨0,0⟩⟩,⟨⟨65241890821068182807979452584,65241890821068182809612956546⟩,⟨0,0⟩⟩,⟨⟨65062637502207729839818736592,65062637502207729841457928051⟩,⟨0,0⟩⟩,⟨⟨64872986615835714443024686963,64872986615835714444652664303⟩,⟨0,0⟩⟩,⟨⟨64674199106115448380410787683,64674199106115448382029632004⟩,⟨0,0⟩⟩,⟨⟨64465005051873660523956542327,64465005051873660525568035757⟩,⟨0,0⟩⟩,⟨⟨64246803705362792364582207491,64246803705362792366182126128⟩,⟨0,0⟩⟩,⟨⟨64018191847289538082741197432,64018191847289538084331369152⟩,⟨0,0⟩⟩,⟨⟨63780708782341902433564513821,63780708782341902435142761798⟩,⟨0,0⟩⟩,⟨⟨63532816109570252472019201437,63532816109570252473581888821⟩,⟨0,0⟩⟩,⟨⟨63276195132027270197536232397,63276195132027270199120603729⟩,⟨0,0⟩⟩,⟨⟨63009170173301185786399805954,63009170173301185787971185413⟩,⟨0,0⟩⟩,⟨⟨62733566693024370963316360747,62733566693024370964876416837⟩,⟨0,0⟩⟩,⟨⟨62447569423876687478983332279,62447569423876687480528161764⟩,⟨0,0⟩⟩,⟨⟨62153150364696266182799731351,62153150364696266184335566110⟩,⟨0,0⟩⟩,⟨⟨61848352107305326149414459166,61848352107305326150934404813⟩,⟨0,0⟩⟩] +lemma amp0_14_9_eq : ∀ k : Fin 16, amp0_1Expr 4 9 k = amp0_14_9 k := by decide +kernel +noncomputable def amp0_14_10 : Fin 16 → CBox := ![⟨⟨61535295810481373296052742795,61535295810481373297569417317⟩,⟨0,0⟩⟩,⟨⟨61211879126221196635287778626,61211879126221196636790230459⟩,⟨0,0⟩⟩,⟨⟨60880375247524401721892568601,60880375247524401723381469504⟩,⟨0,0⟩⟩,⟨⟨60538533822220355767639732530,60538533822220355769118008136⟩,⟨0,0⟩⟩,⟨⟨60188783222751279240465360054,60188783222751279241927612199⟩,⟨0,0⟩⟩,⟨⟨59828721744649059684827564373,59828721744649059686277008174⟩,⟨0,0⟩⟩,⟨⟨59460936375527758934247413071,59460936375527758935683270129⟩,⟨0,0⟩⟩,⟨⟨59082870405977866987800916230,59082870405977866989220496994⟩,⟨0,0⟩⟩,⟨⟨58697273187050324599155955844,58697273187050324600558681688⟩,⟨0,0⟩⟩,⟨⟨58301429023902820841295520304,58301429023902820842679469964⟩,⟨0,0⟩⟩,⟨⟨57898253716627030363454998543,57898253716627030364817262744⟩,⟨0,0⟩⟩,⟨⟨57484868250321787284386738337,57484868250321787285833682453⟩,⟨0,0⟩⟩,⟨⟨57064359325015055232640919452,57064359325015055234071349294⟩,⟨0,0⟩⟩,⟨⟨56633679887340554506963682257,56633679887340554508378004113⟩,⟨0,0⟩⟩,⟨⟨56196092384991073880521524132,56196092384991073881918964427⟩,⟨0,0⟩⟩,⟨⟨55748376590469423804244826698,55748376590469423805626773633⟩,⟨0,0⟩⟩] +lemma amp0_14_10_eq : ∀ k : Fin 16, amp0_1Expr 4 10 k = amp0_14_10 k := by decide +kernel +noncomputable def amp0_14_11 : Fin 16 → CBox := ![⟨⟨55293975979340104503538050193,55293975979340104504904092996⟩,⟨0,0⟩⟩,⟨⟨54829491559176665668957267376,54829491559176665670308916768⟩,⟨0,0⟩⟩,⟨⟨54358553586458375597236830837,54358553586458375598570263431⟩,⟨0,0⟩⟩,⟨⟨53877578214970270256786360616,53877578214970270258107468315⟩,⟨0,0⟩⟩,⟨⟨53390388753776064238591077519,53390388753776064239893848690⟩,⟨0,0⟩⟩,⟨⟨52893209867183757313298751506,52893209867183757314584650158⟩,⟨0,0⟩⟩,⟨⟨52390064759216640811612198114,52390064759216640812878185885⟩,⟨0,0⟩⟩,⟨⟨51876979366645254747814027209,51876979366645254749075927452⟩,⟨0,0⟩⟩,⟨⟨51358184260921196130563888643,51358184260921196131806391362⟩,⟨0,0⟩⟩,⟨⟨50829498747411383453776580671,50829498747411383455000483261⟩,⟨0,0⟩⟩,⟨⟨50295368935478774264311473647,50295368935478774265520013456⟩,⟨0,0⟩⟩,⟨⟨49751398856748404426602224593,49751398856748404427790200929⟩,⟨0,0⟩⟩,⟨⟨49202259104917717840669866180,49202259104917717841838813667⟩,⟨0,0⟩⟩,⟨⟨48643328973542202719605317639,48643328973542202720754439487⟩,⟨0,0⟩⟩,⟨⟨48079513352728794153228483208,48079513352728794154355598030⟩,⟨0,0⟩⟩,⟨⟨47505956415315480001492034784,47505956415315480002594989723⟩,⟨0,0⟩⟩] +lemma amp0_14_11_eq : ∀ k : Fin 16, amp0_1Expr 4 11 k = amp0_14_11 k := by decide +kernel +noncomputable def amp0_14_12 : Fin 16 → CBox := ![⟨⟨46927808129209006379342127723,46927808129209006380479560335⟩,⟨0,0⟩⟩,⟨⟨46339966134024300467341072392,46339966134024300468462303567⟩,⟨0,0⟩⟩,⟨⟨45747837346436315587793833280,45747837346436315588898255025⟩,⟨0,0⟩⟩,⟨⟨45146060300795927013170794598,45146060300795927014258969641⟩,⟨0,0⟩⟩,⟨⟨44540311963211117824859125008,44540311963211117825930556959⟩,⟨0,0⟩⟩,⟨⟨43924957879754381807146785139,43924957879754381808202795457⟩,⟨0,0⟩⟩,⟨⟨43305959560331774512908017467,43305959560331774513945107729⟩,⟨0,0⟩⟩,⟨⟨42677394191057544486128505509,42677394191057544487154399202⟩,⟨0,0⟩⟩,⟨⟨42045523906610931890147311237,42045523906610931891153732001⟩,⟨0,0⟩⟩,⟨⟨41404120463237306155506365479,41404120463237306156495121020⟩,⟨0,0⟩⟩,⟨⟨40759764516089817647814308222,40759764516089817648783811292⟩,⟨0,0⟩⟩,⟨⟨40105903374888705087849141139,40105903374888705088798890188⟩,⟨0,0⟩⟩,⟨⟨39449456196973495353864772658,39449456196973495354791705830⟩,⟨0,0⟩⟩,⟨⟨38783524585689884451711182224,38783524585689884452650711415⟩,⟨0,0⟩⟩,⟨⟨38115388592897434016070056060,38115388592897434016988924505⟩,⟨0,0⟩⟩,⟨⟨37437780256644588249916476794,37437780256644588250815124592⟩,⟨0,0⟩⟩] +lemma amp0_14_12_eq : ∀ k : Fin 16, amp0_1Expr 4 12 k = amp0_14_12 k := by decide +kernel +noncomputable def amp0_14_13 : Fin 16 → CBox := ![⟨⟨36758365717253841753079415407,36758365717253841753958573133⟩,⟨0,0⟩⟩,⟨⟨36069480559311645327059288863,36069480559311645327923108363⟩,⟨0,0⟩⟩,⟨⟨35379205481468553422023769392,35379205481468553422865333677⟩,⟨0,0⟩⟩,⟨⟨34679449173604907941653826177,34679449173604907942475546112⟩,⟨0,0⟩⟩,⟨⟨33978739218346212147648812658,33978739218346212148447536349⟩,⟨0,0⟩⟩,⟨⟨33268522773487285733944903334,33268522773487285734743120511⟩,⟨0,0⟩⟩,⟨⟨32557811201924162533784805095,32557811201924162534563050614⟩,⟨0,0⟩⟩,⟨⟨31837550499505124428791681823,31837550499505124429549648713⟩,⟨0,0⟩⟩,⟨⟨31117278165742267115120737654,31117278165742267115858934133⟩,⟨0,0⟩⟩,⟨⟨30387393416553457455816970557,30387393416553457456537536350⟩,⟨0,0⟩⟩,⟨⟨29658008822123430067295643610,29658008822123430067996275232⟩,⟨0,0⟩⟩,⟨⟨28918923954431376935063420932,28918923954431376935758451650⟩,⟨0,0⟩⟩,⟨⟨28180883386091924915516178205,28180883386091924916188603112⟩,⟨0,0⟩⟩,⟨⟨27433025327480988471127400841,27433025327480988471778828195⟩,⟨0,0⟩⟩,⟨⟨26686793109138643701832051207,26686793109138643702463577249⟩,⟨0,0⟩⟩,⟨⟨25930590927637166727197780810,25930590927637166727807501141⟩,⟨0,0⟩⟩] +lemma amp0_14_13_eq : ∀ k : Fin 16, amp0_1Expr 4 13 k = amp0_14_13 k := by decide +kernel +noncomputable def amp0_14_14 : Fin 16 → CBox := ![⟨⟨25176639830521444781372138483,25176639830521444781971384511⟩,⟨0,0⟩⟩,⟨⟨24412523682091930499464264266,24412523682091930500042856444⟩,⟨0,0⟩⟩,⟨⟨23651335557769629123389099016,23651335557769629123948586131⟩,⟨0,0⟩⟩,⟨⟨22879735361689815417751085435,22879735361689815418287471662⟩,⟨0,0⟩⟩,⟨⟨22111802094629390847140876340,22111802094629390847664994079⟩,⟨0,0⟩⟩,⟨⟨21333145817647381553199310844,21333145817647381553702612468⟩,⟨0,0⟩⟩,⟨⟨20558970745855790589164685613,20558970745855790589653383046⟩,⟨0,0⟩⟩,⟨⟨19773682109448918853263572721,19773682109448918853730636086⟩,⟨0,0⟩⟩,⟨⟨18993782147908377701573784515,18993782147908377702020164072⟩,⟨0,0⟩⟩,⟨⟨18202277460336165347179332492,18202277460336165347609571938⟩,⟨0,0⟩⟩,⟨⟨17417186310553865865056932525,17417186310553865865465506063⟩,⟨0,0⟩⟩,⟨⟨16619869927399128444156926255,16619869927399128444548406607⟩,⟨0,0⟩⟩,⟨⟨15830143023134495959034883511,15830143023134495959409458062⟩,⟨0,0⟩⟩,⟨⟨15027400576370959043254456816,15027400576370959043607302595⟩,⟨0,0⟩⟩,⟨⟨14233622917787253604291895928,14233622917787253604626770603⟩,⟨0,0⟩⟩,⟨⟨13425810750168309643338063720,13425810750168309643654344652⟩,⟨0,0⟩⟩] +lemma amp0_14_14_eq : ∀ k : Fin 16, amp0_1Expr 4 14 k = amp0_14_14 k := by decide +kernel +noncomputable def amp0_14_15 : Fin 16 → CBox := ![⟨⟨12628609778658563396154894359,12628609778658563396452060432⟩,⟨0,0⟩⟩,⟨⟨11816037574120999655507824155,11816037574120999655785161813⟩,⟨0,0⟩⟩,⟨⟨11016105370468202635702607352,11016105370468202635960139008⟩,⟨0,0⟩⟩,⟨⟨10199005767294368563435971558,10199005767294368563675043583⟩,⟨0,0⟩⟩,⟨⟨9397139786710079455022300696,9397139786710079455242626929⟩,⟨0,0⟩⟩,⟨⟨8575610971858887400784313139,8575610971858887400985058594⟩,⟨0,0⟩⟩,⟨⟨7772795199553046530766390537,7772795199553046530947422277⟩,⟨0,0⟩⟩,⟨⟨6946681160825382600970077797,6946681160825382601132359888⟩,⟨0,0⟩⟩,⟨⟨6144266891980870640401838545,6144266891980870640544853969⟩,⟨0,0⟩⟩,⟨⟨5312871584142202226591248655,5312871584142202226714544867⟩,⟨0,0⟩⟩,⟨⟨4513049635508617835829336327,4513049635508617835933432919⟩,⟨0,0⟩⟩,⟨⟨3674306216098628386545207360,3674306216098628386629551179⟩,⟨0,0⟩⟩,⟨⟨2881684212734911626999212952,2881684212734911627064553436⟩,⟨0,0⟩⟩,⟨⟨2028828991927087213822065804,2028828991927087213867556772⟩,⟨0,0⟩⟩,⟨⟨1258528894059035436928397235,1258528894059035436954898614⟩,⟨0,0⟩⟩,⟨⟨357553169748046630694215770,357553169748046630700711430⟩,⟨0,0⟩⟩] +lemma amp0_14_15_eq : ∀ k : Fin 16, amp0_1Expr 4 15 k = amp0_14_15 k := by decide +kernel +noncomputable def amp0_14 : Fin 16 → Fin 16 → CBox := ![amp0_14_0,amp0_14_1,amp0_14_2,amp0_14_3,amp0_14_4,amp0_14_5,amp0_14_6,amp0_14_7,amp0_14_8,amp0_14_9,amp0_14_10,amp0_14_11,amp0_14_12,amp0_14_13,amp0_14_14,amp0_14_15] +lemma amp0_14_eq (i k : Fin 16) : amp0_1Expr 4 i k = amp0_14 i k := by + fin_cases i + · exact amp0_14_0_eq k + · exact amp0_14_1_eq k + · exact amp0_14_2_eq k + · exact amp0_14_3_eq k + · exact amp0_14_4_eq k + · exact amp0_14_5_eq k + · exact amp0_14_6_eq k + · exact amp0_14_7_eq k + · exact amp0_14_8_eq k + · exact amp0_14_9_eq k + · exact amp0_14_10_eq k + · exact amp0_14_11_eq k + · exact amp0_14_12_eq k + · exact amp0_14_13_eq k + · exact amp0_14_14_eq k + · exact amp0_14_15_eq k +noncomputable def amp0_15_0 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨206433418803638677622879409,206433418803638677624245993⟩⟩,⟨⟨0,0⟩,⟨726611995767906115087064597,726611995767906115093974983⟩⟩,⟨⟨0,0⟩,⟨1171344964628820879944165547,1171344964628820879956904243⟩⟩,⟨⟨0,0⟩,⟨1663741155941996025460178078,1663741155941996025478691197⟩⟩,⟨⟨0,0⟩,⟨2121361682949658354780451532,2121361682949658354804652084⟩⟩,⟨⟨0,0⟩,⟨2605610421927042946746523973,2605610421927042946776537171⟩⟩,⟨⟨0,0⟩,⟨3067387839274413925669940985,3067387839274413925705706943⟩⟩,⟨⟨0,0⟩,⟨3547394144058060913845578585,3547394144058060913887186800⟩⟩,⟨⟨0,0⟩,⟨4010668238177036632638050818,4010668238177036632685433220⟩⟩,⟨⟨0,0⟩,⟨4487625400817782326415073419,4487625400817782326467773508⟩⟩,⟨⟨0,0⟩,⟨4951131303068236857576605536,4951131303068236857635335239⟩⟩,⟨⟨0,0⟩,⟨5425441185469606814646061604,5425441185469606814710619416⟩⟩,⟨⟨0,0⟩,⟨5888398725213949358166629037,5888398725213949358236663964⟩⟩,⟨⟨0,0⟩,⟨6360151401061098850485125164,6360151401061098850560370432⟩⟩,⟨⟨0,0⟩,⟨6821992474173491748147200667,6821992474173491748228548055⟩⟩,⟨⟨0,0⟩,⟨7291131255199261819920769718,7291131255199261820008147899⟩⟩] +lemma amp0_15_0_eq : ∀ k : Fin 16, amp0_1Expr 5 0 k = amp0_15_0 k := by decide +kernel +noncomputable def amp0_15_1 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨7751395450698644995545663552,7751395450698644995638763029⟩⟩,⟨⟨0,0⟩,⟨8217786023128097380764824045,8217786023128097380863273210⟩⟩,⟨⟨0,0⟩,⟨8676073767988110570327809130,8676073767988110570431342066⟩⟩,⟨⟨0,0⟩,⟨9139537335716977438218541679,9139537335716977438329268110⟩⟩,⟨⟨0,0⟩,⟨9595486376480452818666476030,9595486376480452818781698184⟩⟩,⟨⟨0,0⟩,⟨10055817204924139265960826380,10055817204924139266080601847⟩⟩,⟨⟨0,0⟩,⟨10509089791589342672891538552,10509089791589342673018588896⟩⟩,⟨⟨0,0⟩,⟨10966065236024010114121719083,10966065236024010114252811227⟩⟩,⟨⟨0,0⟩,⟨11416340688760420328905104757,11416340688760420329042939369⟩⟩,⟨⟨0,0⟩,⟨11869727294381481877117058437,11869727294381481877262148227⟩⟩,⟨⟨0,0⟩,⟨12316697480480254771994745810,12316697480480254772143106166⟩⟩,⟨⟨0,0⟩,⟨12766254891602009637826902453,12766254891602009637982089957⟩⟩,⟨⟨0,0⟩,⟨13209621370059014535783163596,13209621370059014535940314759⟩⟩,⟨⟨0,0⟩,⟨13655104950972463001282116531,13655104950972463001447460997⟩⟩,⟨⟨0,0⟩,⟨14094577119453890023469974093,14094577119453890023641274285⟩⟩,⟨⟨0,0⟩,⟨14535739783441810130490456580,14535739783441810130668587170⟩⟩] +lemma amp0_15_1_eq : ∀ k : Fin 16, amp0_1Expr 5 1 k = amp0_15_1 k := by decide +kernel +noncomputable def amp0_15_2 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨14971033652317385873237046249,14971033652317385873416197841⟩⟩,⟨⟨0,0⟩,⟨15407627185369045845232029077,15407627185369045845418728853⟩⟩,⟨⟨0,0⟩,⟨15838464557506970186781819526,15838464557506970186975034448⟩⟩,⟨⟨0,0⟩,⟨16270240608961625265401866566,16270240608961625265602218712⟩⟩,⟨⟨0,0⟩,⟨16696348529765272279212027570,16696348529765272279420510916⟩⟩,⟨⟨0,0⟩,⟨17123059377081258097343677047,17123059377081258097550466844⟩⟩,⟨⟨0,0⟩,⟨17544169769018200423125632453,17544169769018200423339068685⟩⟩,⟨⟨0,0⟩,⟨17965568925439762165284768738,17965568925439762165503518153⟩⟩,⟨⟨0,0⟩,⟨18381418351227587809487664123,18381418351227587809713026174⟩⟩,⟨⟨0,0⟩,⟨18797261061655928396470588463,18797261061655928396702856649⟩⟩,⟨⟨0,0⟩,⟨19207590578814079551668081932,19207590578814079551907142683⟩⟩,⟨⟨0,0⟩,⟨19617634234436279719996345735,19617634234436279720230964146⟩⟩,⟨⟨0,0⟩,⟨20022189315728738362221149746,20022189315728738362464373645⟩⟩,⟨⟨0,0⟩,⟨20426193808440952720483850609,20426193808440952720733866606⟩⟩,⟨⟨0,0⟩,⟨20824724310448551711007152060,20824724310448551711265415278⟩⟩,⟨⟨0,0⟩,⟨21222452341827216678756215314,21222452341827216679018741493⟩⟩] +lemma amp0_15_2_eq : ∀ k : Fin 16, amp0_1Expr 5 2 k = amp0_15_2 k := by decide +kernel +noncomputable def amp0_15_3 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨21614712509035809766268188222,21614712509035809766537437569⟩⟩,⟨⟨0,0⟩,⟨22005929864376524720173868442,22005929864376524720450274795⟩⟩,⟨⟨0,0⟩,⟨22391678359670523838791445742,22391678359670523839075326344⟩⟩,⟨⟨0,0⟩,⟨22776154154706997819343270783,22776154154706997819615439525⟩⟩,⟨⟨0,0⟩,⟨23155154109585114316424238597,23155154109585114316705203777⟩⟩,⟨⟨0,0⟩,⟨23532661015470212554804114850,23532661015470212555092125945⟩⟩,⟨⟨0,0⟩,⟨23904680095009751316489991215,23904680095009751316784822024⟩⟩,⟨⟨0,0⟩,⟨24274994545700667020200380202,24274994545700667020501134009⟩⟩,⟨⟨0,0⟩,⟨24639805024518844204389281623,24639805024518844204697065662⟩⟩,⟨⟨0,0⟩,⟨25002707409672597433812471512,25002707409672597434122529458⟩⟩,⟨⟨0,0⟩,⟨25360086256019165709374512789,25360086256019165709691367578⟩⟩,⟨⟨0,0⟩,⟨25715361101749847687583558465,25715361101749847687905214577⟩⟩,⟨⟨0,0⟩,⟨26065090067515605574385141480,26065090067515605574712425898⟩⟩,⟨⟨0,0⟩,⟨26412526206808221627553388717,26412526206808221627886041327⟩⟩,⟨⟨0,0⟩,⟨26754391921717071432963636548,26754391921717071433302046561⟩⟩,⟨⟨0,0⟩,⟨27093782655877928083692278476,27093782655877928084036123447⟩⟩] +lemma amp0_15_3_eq : ∀ k : Fin 16, amp0_1Expr 5 3 k = amp0_15_3 k := by decide +kernel +noncomputable def amp0_15_4 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨27427576724493021402835960847,27427576724493021403156045802⟩⟩,⟨⟨0,0⟩,⟨27758719976704175665270455490,27758719976704175665600665448⟩⟩,⟨⟨0,0⟩,⟨28084239077154113068015367596,28084239077154113068354524544⟩⟩,⟨⟨0,0⟩,⟨28406937538961959616646220611,28406937538961959616993097697⟩⟩,⟨⟨0,0⟩,⟨28723983522504130804753580561,28723983522504130805107783027⟩⟩,⟨⟨0,0⟩,⟨29038044793890211751075200275,29038044793890211751437648600⟩⟩,⟨⟨0,0⟩,⟨29346424784591707850420926429,29346424784591707850788683594⟩⟩,⟨⟨0,0⟩,⟨29651661508133253728189211135,29651661508133253728564182519⟩⟩,⟨⟨0,0⟩,⟨29951188002077299329178163668,29951188002077299329560875585⟩⟩,⟨⟨0,0⟩,⟨30247417991595653884640988147,30247417991595653885022639430⟩⟩,⟨⟨0,0⟩,⟨30537908955121911915802610237,30537908955121911916192402771⟩⟩,⟨⟨0,0⟩,⟨30824955319131378738919805200,30824955319131378739316024561⟩⟩,⟨⟨0,0⟩,⟨31106234285698202318807231638,31106234285698202319210789670⟩⟩,⟨⟨0,0⟩,⟨31383925545900440189946344853,31383925545900440190353812163⟩⟩,⟨⟨0,0⟩,⟨31655821711220961597188431509,31655821711220961597603276707⟩⟩,⟨⟨0,0⟩,⟨31923991916236710245575926644,31923991916236710245995985319⟩⟩] +lemma amp0_15_4_eq : ∀ k : Fin 16, amp0_1Expr 5 4 k = amp0_15_4 k := by decide +kernel +noncomputable def amp0_15_5 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨32186340231392153200905825416,32186340231392153201332037008⟩⟩,⟨⟨0,0⟩,⟨32444829065879675048588147341,32444829065879675049020319256⟩⟩,⟨⟨0,0⟩,⟨32697470328155163684948571191,32697470328155163685387572430⟩⟩,⟨⟨0,0⟩,⟨32946123217430973330987485782,32946123217430973331432915775⟩⟩,⟨⟨0,0⟩,⟨33188904158653455315019109592,33188904158653455315471270713⟩⟩,⟨⟨0,0⟩,⟨33427572368903866377915686643,33427572368903866378316201889⟩⟩,⟨⟨0,0⟩,⟨33660345741090154093358933892,33660345741090154093769281408⟩⟩,⟨⟨0,0⟩,⟨33888886475240507526702479364,33888886475240507527121028353⟩⟩,⟨⟨0,0⟩,⟨34111511133387095183728243724,34111511133387095184153953258⟩⟩,⟨⟨0,0⟩,⟨34329787622678162156441791496,34329787622678162156874377713⟩⟩,⟨⟨0,0⟩,⟨34542128604544351020214962777,34542128604544351020652941401⟩⟩,⟨⟨0,0⟩,⟨34750010195851482023215825809,34750010195851482023658798925⟩⟩,⟨⟨0,0⟩,⟨34951938798604186338174260411,34951938798604186338624153005⟩⟩,⟨⟨0,0⟩,⟨35149301037523642618265522291,35149301037523642618719270461⟩⟩,⟨⟨0,0⟩,⟨35340694891126642207388529188,35340694891126642207847890965⟩⟩,⟨⟨0,0⟩,⟨35527419600844671404477355739,35527419600844671404942772877⟩⟩] +lemma amp0_15_5_eq : ∀ k : Fin 16, amp0_1Expr 5 5 k = amp0_15_5 k := by decide +kernel +noncomputable def amp0_15_6 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨35708162738087487969629482346,35708162738087487970094701028⟩⟩,⟨⟨0,0⟩,⟨35884138094040676038646908078,35884138094040676039119268354⟩⟩,⟨⟨0,0⟩,⟨36054121017113048632715721236,36054121017113048633191311826⟩⟩,⟨⟨0,0⟩,⟨36219241617442961543932620656,36219241617442961544415095682⟩⟩,⟨⟨0,0⟩,⟨36378361360970378297152592353,36378361360970378297639767573⟩⟩,⟨⟨0,0⟩,⟨36532528292771231841181035197,36532528292771231841673931112⟩⟩,⟨⟨0,0⟩,⟨36680688483235377565472319285,36680688483235377565950985160⟩⟩,⟨⟨0,0⟩,⟨36823809384590225483935500717,36823809384590225484421497887⟩⟩,⟨⟨0,0⟩,⟨36960920296065720304650909332,36960920296065720305142207457⟩⟩,⟨⟨0,0⟩,⟨37092909413864254184340783605,37092909413864254184836185036⟩⟩,⟨⟨0,0⟩,⟨37218888020009842724728681353,37218888020009842725229310819⟩⟩,⟨⟨0,0⟩,⟨37339666263539208117160359900,37339666263539208117663838777⟩⟩,⟨⟨0,0⟩,⟨37454436285787739076668134202,37454436285787739077175560780⟩⟩,⟨⟨0,0⟩,⟨37563931276086673294397922353,37563931276086673294910559067⟩⟩,⟨⟨0,0⟩,⟨37667423227983889636657520706,37667423227983889637165678719⟩⟩,⟨⟨0,0⟩,⟨37765569342949880319096414150,37765569342949880319608636394⟩⟩] +lemma amp0_15_6_eq : ∀ k : Fin 16, amp0_1Expr 5 6 k = amp0_15_6 k := by decide +kernel +noncomputable def amp0_15_7 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨37857720570597306432150340369,37857720570597306432665478082⟩⟩,⟨⟨0,0⟩,⟨37944458985836275421531566832,37944458985836275422050711635⟩⟩,⟨⟨0,0⟩,⟨38025213704398410461179398209,38025213704398410461697262235⟩⟩,⟨⟨0,0⟩,⟨38100492429806577181747498264,38100492429806577182268210970⟩⟩,⟨⟨0,0⟩,⟨38169801756047242382336640680,38169801756047242382856953904⟩⟩,⟨⟨0,0⟩,⟨38233575668115257838479175926,38233575668115257839002535762⟩⟩,⟨⟨0,0⟩,⟨38291397648932349303566721235,38291397648932349304090540397⟩⟩,⟨⟨0,0⟩,⟨38343628518762467668575748278,38343628518762467669100009910⟩⟩,⟨⟨0,0⟩,⟨38389928155694576733296596847,38389928155694576733821424096⟩⟩,⟨⟨0,0⟩,⟨38430584672722504872537078627,38430584672722504873062904738⟩⟩,⟨⟨0,0⟩,⟨38465333942404921042175842801,38465333942404921042701349212⟩⟩,⟨⟨0,0⟩,⟨38494391733819021335516519298,38494391733819021336041977347⟩⟩,⟨⟨0,0⟩,⟨38517569604370558560887901793,38517569604370558561412092209⟩⟩,⟨⟨0,0⟩,⟨38535011250222245611046080557,38535011250222245611568583260⟩⟩,⟨⟨0,0⟩,⟨38546603693548157834160753685,38546603693548157834680524263⟩⟩,⟨⟨0,0⟩,⟨38552418737548597096042908506,38552418737548597096558544044⟩⟩] +lemma amp0_15_7_eq : ∀ k : Fin 16, amp0_1Expr 5 7 k = amp0_15_7 k := by decide +kernel +noncomputable def amp0_15_8 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨38552418737548597096042908506,38552418737548597096558544044⟩⟩,⟨⟨0,0⟩,⟨38546603693548157834160753685,38546603693548157834680524263⟩⟩,⟨⟨0,0⟩,⟨38535011250222245611046080557,38535011250222245611568583260⟩⟩,⟨⟨0,0⟩,⟨38517569604370558560887901793,38517569604370558561412092209⟩⟩,⟨⟨0,0⟩,⟨38494391733819021335516519298,38494391733819021336041977347⟩⟩,⟨⟨0,0⟩,⟨38465333942404921042175842801,38465333942404921042701349212⟩⟩,⟨⟨0,0⟩,⟨38430584672722504872537078627,38430584672722504873062904738⟩⟩,⟨⟨0,0⟩,⟨38389928155694576733296596847,38389928155694576733821424096⟩⟩,⟨⟨0,0⟩,⟨38343628518762467668575748278,38343628518762467669100009910⟩⟩,⟨⟨0,0⟩,⟨38291397648932349303566721235,38291397648932349304090540397⟩⟩,⟨⟨0,0⟩,⟨38233575668115257838479175926,38233575668115257839002535762⟩⟩,⟨⟨0,0⟩,⟨38169801756047242382336640680,38169801756047242382856953904⟩⟩,⟨⟨0,0⟩,⟨38100492429806577181747498264,38100492429806577182268210970⟩⟩,⟨⟨0,0⟩,⟨38025213704398410461179398209,38025213704398410461697262235⟩⟩,⟨⟨0,0⟩,⟨37944458985836275421531566832,37944458985836275422050711635⟩⟩,⟨⟨0,0⟩,⟨37857720570597306432150340369,37857720570597306432665478082⟩⟩] +lemma amp0_15_8_eq : ∀ k : Fin 16, amp0_1Expr 5 8 k = amp0_15_8 k := by decide +kernel +noncomputable def amp0_15_9 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨37765569342949880319096414150,37765569342949880319608636394⟩⟩,⟨⟨0,0⟩,⟨37667423227983889636657520706,37667423227983889637165678719⟩⟩,⟨⟨0,0⟩,⟨37563931276086673294397922353,37563931276086673294910559067⟩⟩,⟨⟨0,0⟩,⟨37454436285787739076668134202,37454436285787739077175560780⟩⟩,⟨⟨0,0⟩,⟨37339666263539208117160359900,37339666263539208117663838777⟩⟩,⟨⟨0,0⟩,⟨37218888020009842724728681353,37218888020009842725229310819⟩⟩,⟨⟨0,0⟩,⟨37092909413864254184340783605,37092909413864254184836185036⟩⟩,⟨⟨0,0⟩,⟨36960920296065720304650909332,36960920296065720305142207457⟩⟩,⟨⟨0,0⟩,⟨36823809384590225483935500717,36823809384590225484421497887⟩⟩,⟨⟨0,0⟩,⟨36680688483235377565472319285,36680688483235377565950985160⟩⟩,⟨⟨0,0⟩,⟨36532528292771231841181035197,36532528292771231841673931112⟩⟩,⟨⟨0,0⟩,⟨36378361360970378297152592353,36378361360970378297639767573⟩⟩,⟨⟨0,0⟩,⟨36219241617442961543932620656,36219241617442961544415095682⟩⟩,⟨⟨0,0⟩,⟨36054121017113048632715721236,36054121017113048633191311826⟩⟩,⟨⟨0,0⟩,⟨35884138094040676038646908078,35884138094040676039119268354⟩⟩,⟨⟨0,0⟩,⟨35708162738087487969629482346,35708162738087487970094701028⟩⟩] +lemma amp0_15_9_eq : ∀ k : Fin 16, amp0_1Expr 5 9 k = amp0_15_9 k := by decide +kernel +noncomputable def amp0_15_10 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨35527419600844671404477355739,35527419600844671404942772877⟩⟩,⟨⟨0,0⟩,⟨35340694891126642207388529188,35340694891126642207847890965⟩⟩,⟨⟨0,0⟩,⟨35149301037523642618265522291,35149301037523642618719270461⟩⟩,⟨⟨0,0⟩,⟨34951938798604186338174260411,34951938798604186338624153005⟩⟩,⟨⟨0,0⟩,⟨34750010195851482023215825809,34750010195851482023658798925⟩⟩,⟨⟨0,0⟩,⟨34542128604544351020214962777,34542128604544351020652941401⟩⟩,⟨⟨0,0⟩,⟨34329787622678162156441791496,34329787622678162156874377713⟩⟩,⟨⟨0,0⟩,⟨34111511133387095183728243724,34111511133387095184153953258⟩⟩,⟨⟨0,0⟩,⟨33888886475240507526702479364,33888886475240507527121028353⟩⟩,⟨⟨0,0⟩,⟨33660345741090154093358933892,33660345741090154093769281408⟩⟩,⟨⟨0,0⟩,⟨33427572368903866377915686643,33427572368903866378316201889⟩⟩,⟨⟨0,0⟩,⟨33188904158653455315019109592,33188904158653455315471270713⟩⟩,⟨⟨0,0⟩,⟨32946123217430973330987485782,32946123217430973331432915775⟩⟩,⟨⟨0,0⟩,⟨32697470328155163684948571191,32697470328155163685387572430⟩⟩,⟨⟨0,0⟩,⟨32444829065879675048588147341,32444829065879675049020319256⟩⟩,⟨⟨0,0⟩,⟨32186340231392153200905825416,32186340231392153201332037008⟩⟩] +lemma amp0_15_10_eq : ∀ k : Fin 16, amp0_1Expr 5 10 k = amp0_15_10 k := by decide +kernel +noncomputable def amp0_15_11 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨31923991916236710245575926644,31923991916236710245995985319⟩⟩,⟨⟨0,0⟩,⟨31655821711220961597188431509,31655821711220961597603276707⟩⟩,⟨⟨0,0⟩,⟨31383925545900440189946344853,31383925545900440190353812163⟩⟩,⟨⟨0,0⟩,⟨31106234285698202318807231638,31106234285698202319210789670⟩⟩,⟨⟨0,0⟩,⟨30824955319131378738919805200,30824955319131378739316024561⟩⟩,⟨⟨0,0⟩,⟨30537908955121911915802610237,30537908955121911916192402771⟩⟩,⟨⟨0,0⟩,⟨30247417991595653884640988147,30247417991595653885022639430⟩⟩,⟨⟨0,0⟩,⟨29951188002077299329178163668,29951188002077299329560875585⟩⟩,⟨⟨0,0⟩,⟨29651661508133253728189211135,29651661508133253728564182519⟩⟩,⟨⟨0,0⟩,⟨29346424784591707850420926429,29346424784591707850788683594⟩⟩,⟨⟨0,0⟩,⟨29038044793890211751075200275,29038044793890211751437648600⟩⟩,⟨⟨0,0⟩,⟨28723983522504130804753580561,28723983522504130805107783027⟩⟩,⟨⟨0,0⟩,⟨28406937538961959616646220611,28406937538961959616993097697⟩⟩,⟨⟨0,0⟩,⟨28084239077154113068015367596,28084239077154113068354524544⟩⟩,⟨⟨0,0⟩,⟨27758719976704175665270455490,27758719976704175665600665448⟩⟩,⟨⟨0,0⟩,⟨27427576724493021402835960847,27427576724493021403156045802⟩⟩] +lemma amp0_15_11_eq : ∀ k : Fin 16, amp0_1Expr 5 11 k = amp0_15_11 k := by decide +kernel +noncomputable def amp0_15_12 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨27093782655877928083692278476,27093782655877928084036123447⟩⟩,⟨⟨0,0⟩,⟨26754391921717071432963636548,26754391921717071433302046561⟩⟩,⟨⟨0,0⟩,⟨26412526206808221627553388717,26412526206808221627886041327⟩⟩,⟨⟨0,0⟩,⟨26065090067515605574385141480,26065090067515605574712425898⟩⟩,⟨⟨0,0⟩,⟨25715361101749847687583558465,25715361101749847687905214577⟩⟩,⟨⟨0,0⟩,⟨25360086256019165709374512789,25360086256019165709691367578⟩⟩,⟨⟨0,0⟩,⟨25002707409672597433812471512,25002707409672597434122529458⟩⟩,⟨⟨0,0⟩,⟨24639805024518844204389281623,24639805024518844204697065662⟩⟩,⟨⟨0,0⟩,⟨24274994545700667020200380202,24274994545700667020501134009⟩⟩,⟨⟨0,0⟩,⟨23904680095009751316489991215,23904680095009751316784822024⟩⟩,⟨⟨0,0⟩,⟨23532661015470212554804114850,23532661015470212555092125945⟩⟩,⟨⟨0,0⟩,⟨23155154109585114316424238597,23155154109585114316705203777⟩⟩,⟨⟨0,0⟩,⟨22776154154706997819343270783,22776154154706997819615439525⟩⟩,⟨⟨0,0⟩,⟨22391678359670523838791445742,22391678359670523839075326344⟩⟩,⟨⟨0,0⟩,⟨22005929864376524720173868442,22005929864376524720450274795⟩⟩,⟨⟨0,0⟩,⟨21614712509035809766268188222,21614712509035809766537437569⟩⟩] +lemma amp0_15_12_eq : ∀ k : Fin 16, amp0_1Expr 5 12 k = amp0_15_12 k := by decide +kernel +noncomputable def amp0_15_13 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨21222452341827216678756215314,21222452341827216679018741493⟩⟩,⟨⟨0,0⟩,⟨20824724310448551711007152060,20824724310448551711265415278⟩⟩,⟨⟨0,0⟩,⟨20426193808440952720483850609,20426193808440952720733866606⟩⟩,⟨⟨0,0⟩,⟨20022189315728738362221149746,20022189315728738362464373645⟩⟩,⟨⟨0,0⟩,⟨19617634234436279719996345735,19617634234436279720230964146⟩⟩,⟨⟨0,0⟩,⟨19207590578814079551668081932,19207590578814079551907142683⟩⟩,⟨⟨0,0⟩,⟨18797261061655928396470588463,18797261061655928396702856649⟩⟩,⟨⟨0,0⟩,⟨18381418351227587809487664123,18381418351227587809713026174⟩⟩,⟨⟨0,0⟩,⟨17965568925439762165284768738,17965568925439762165503518153⟩⟩,⟨⟨0,0⟩,⟨17544169769018200423125632453,17544169769018200423339068685⟩⟩,⟨⟨0,0⟩,⟨17123059377081258097343677047,17123059377081258097550466844⟩⟩,⟨⟨0,0⟩,⟨16696348529765272279212027570,16696348529765272279420510916⟩⟩,⟨⟨0,0⟩,⟨16270240608961625265401866566,16270240608961625265602218712⟩⟩,⟨⟨0,0⟩,⟨15838464557506970186781819526,15838464557506970186975034448⟩⟩,⟨⟨0,0⟩,⟨15407627185369045845232029077,15407627185369045845418728853⟩⟩,⟨⟨0,0⟩,⟨14971033652317385873237046249,14971033652317385873416197841⟩⟩] +lemma amp0_15_13_eq : ∀ k : Fin 16, amp0_1Expr 5 13 k = amp0_15_13 k := by decide +kernel +noncomputable def amp0_15_14 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨14535739783441810130490456580,14535739783441810130668587170⟩⟩,⟨⟨0,0⟩,⟨14094577119453890023469974093,14094577119453890023641274285⟩⟩,⟨⟨0,0⟩,⟨13655104950972463001282116531,13655104950972463001447460997⟩⟩,⟨⟨0,0⟩,⟨13209621370059014535783163596,13209621370059014535940314759⟩⟩,⟨⟨0,0⟩,⟨12766254891602009637826902453,12766254891602009637982089957⟩⟩,⟨⟨0,0⟩,⟨12316697480480254771994745810,12316697480480254772143106166⟩⟩,⟨⟨0,0⟩,⟨11869727294381481877117058437,11869727294381481877262148227⟩⟩,⟨⟨0,0⟩,⟨11416340688760420328905104757,11416340688760420329042939369⟩⟩,⟨⟨0,0⟩,⟨10966065236024010114121719083,10966065236024010114252811227⟩⟩,⟨⟨0,0⟩,⟨10509089791589342672891538552,10509089791589342673018588896⟩⟩,⟨⟨0,0⟩,⟨10055817204924139265960826380,10055817204924139266080601847⟩⟩,⟨⟨0,0⟩,⟨9595486376480452818666476030,9595486376480452818781698184⟩⟩,⟨⟨0,0⟩,⟨9139537335716977438218541679,9139537335716977438329268110⟩⟩,⟨⟨0,0⟩,⟨8676073767988110570327809130,8676073767988110570431342066⟩⟩,⟨⟨0,0⟩,⟨8217786023128097380764824045,8217786023128097380863273210⟩⟩,⟨⟨0,0⟩,⟨7751395450698644995545663552,7751395450698644995638763029⟩⟩] +lemma amp0_15_14_eq : ∀ k : Fin 16, amp0_1Expr 5 14 k = amp0_15_14 k := by decide +kernel +noncomputable def amp0_15_15 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨7291131255199261819920769718,7291131255199261820008147899⟩⟩,⟨⟨0,0⟩,⟨6821992474173491748147200667,6821992474173491748228548055⟩⟩,⟨⟨0,0⟩,⟨6360151401061098850485125164,6360151401061098850560370432⟩⟩,⟨⟨0,0⟩,⟨5888398725213949358166629037,5888398725213949358236663964⟩⟩,⟨⟨0,0⟩,⟨5425441185469606814646061604,5425441185469606814710619416⟩⟩,⟨⟨0,0⟩,⟨4951131303068236857576605536,4951131303068236857635335239⟩⟩,⟨⟨0,0⟩,⟨4487625400817782326415073419,4487625400817782326467773508⟩⟩,⟨⟨0,0⟩,⟨4010668238177036632638050818,4010668238177036632685433220⟩⟩,⟨⟨0,0⟩,⟨3547394144058060913845578585,3547394144058060913887186800⟩⟩,⟨⟨0,0⟩,⟨3067387839274413925669940985,3067387839274413925705706943⟩⟩,⟨⟨0,0⟩,⟨2605610421927042946746523973,2605610421927042946776537171⟩⟩,⟨⟨0,0⟩,⟨2121361682949658354780451532,2121361682949658354804652084⟩⟩,⟨⟨0,0⟩,⟨1663741155941996025460178078,1663741155941996025478691197⟩⟩,⟨⟨0,0⟩,⟨1171344964628820879944165547,1171344964628820879956904243⟩⟩,⟨⟨0,0⟩,⟨726611995767906115087064597,726611995767906115093974983⟩⟩,⟨⟨0,0⟩,⟨206433418803638677622879409,206433418803638677624245993⟩⟩] +lemma amp0_15_15_eq : ∀ k : Fin 16, amp0_1Expr 5 15 k = amp0_15_15 k := by decide +kernel +noncomputable def amp0_15 : Fin 16 → Fin 16 → CBox := ![amp0_15_0,amp0_15_1,amp0_15_2,amp0_15_3,amp0_15_4,amp0_15_5,amp0_15_6,amp0_15_7,amp0_15_8,amp0_15_9,amp0_15_10,amp0_15_11,amp0_15_12,amp0_15_13,amp0_15_14,amp0_15_15] +lemma amp0_15_eq (i k : Fin 16) : amp0_1Expr 5 i k = amp0_15 i k := by + fin_cases i + · exact amp0_15_0_eq k + · exact amp0_15_1_eq k + · exact amp0_15_2_eq k + · exact amp0_15_3_eq k + · exact amp0_15_4_eq k + · exact amp0_15_5_eq k + · exact amp0_15_6_eq k + · exact amp0_15_7_eq k + · exact amp0_15_8_eq k + · exact amp0_15_9_eq k + · exact amp0_15_10_eq k + · exact amp0_15_11_eq k + · exact amp0_15_12_eq k + · exact amp0_15_13_eq k + · exact amp0_15_14_eq k + · exact amp0_15_15_eq k +noncomputable def amp0_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp0_10,amp0_11,amp0_12,amp0_13,amp0_14,amp0_15] +lemma amp0_1_eq (j : Fin 6) (i k : Fin 16) : amp0_1Expr j i k = amp0_1 j i k := by + fin_cases j + · exact amp0_10_eq i k + · exact amp0_11_eq i k + · exact amp0_12_eq i k + · exact amp0_13_eq i k + · exact amp0_14_eq i k + · exact amp0_15_eq i k +lemma amp0_1_contains (j : Fin 6) (i k : Fin 16) : + (amp0_1 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude true 0 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp0_1_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 0 j) (bLookup_contains 0 j) true) +noncomputable def amp1_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 1 j) (bLookup 1 j) false) +noncomputable def amp1_00_0 : Fin 16 → CBox := ![⟨⟨61807075809980497319086715,61807075809980497392039946⟩,⟨93606319881131816186008287,93606319881131816261343699⟩⟩,⟨⟨217622452567858381669678486,217622452567858381927088145⟩,⟨329454183859859827454858376,329454183859859827720974828⟩⟩,⟨⟨351052184343906018586202957,351052184343906019001634365⟩,⟨531021213985451592024849172,531021213985451592454556918⟩⟩,⟨⟨499115216475746477931810643,499115216475746478521984515⟩,⟨754075270951602632818211549,754075270951602633428715382⟩⟩,⟨⟨637235451339344762500092150,637235451339344763252745585⟩,⟨961197924719543986714042187,961197924719543987492687717⟩⟩,⟨⟨783982155445960966779833282,783982155445960967704338525⟩,⟨1180168517784169613273937920,1180168517784169614230380226⟩⟩,⟨⟨924735220695209804499216224,924735220695209805587633491⟩,⟨1388695194947131464411237204,1388695194947131465537271474⟩⟩,⟨⟨1071888806465636004024565523,1071888806465636005283294771⟩,⟨1605161115664026581948186406,1605161115664026583250394037⟩⟩,⟨⟨1215030212771232995943503152,1215030212771232997366610050⟩,⟨1813694339092520910892390816,1813694339092520912364624518⟩⟩,⟨⟨1363497023522419448518982384,1363497023522419450111093785⟩,⟨2028006478273828714490293596,2028006478273828716137225406⟩⟩,⟨⟨1509194149754225627700659047,1509194149754225629457221497⟩,⟨2235783529102243050901586051,2235783529102243052718592977⟩⟩,⟨⟨1659636895855445336011151968,1659636895855445337935848372⟩,⟨2447936219445482034143057085,2447936219445482036133867279⟩⟩,⟨⟨1808194715185831677886860384,1808194715185831679975542521⟩,⟨2654416770198902271418485189,2654416770198902273578739689⟩⟩,⟨⟨1961174422985067259965968439,1961174422985067262221581814⟩,⟨2864265852138096932419667303,2864265852138096934752321627⟩⟩,⟨⟨2112952253765624868899836922,2112952253765624871319113526⟩,⟨3069008905085332607369693806,3069008905085332609871455124⟩⟩,⟨⟨2268976048459290499008724741,2268976048459290501594136235⟩,⟨3276347120733813477836488579,3276347120733813480509841485⟩⟩] +lemma amp1_00_0_eq : ∀ k : Fin 16, amp1_0Expr 0 0 k = amp1_00_0 k := by decide +kernel +noncomputable def amp1_00_1 : Fin 16 → CBox := ![⟨⟨2424354699718827724067729585,2424354699718827726815993537⟩,⟨3478964236115248129503535048,3478964236115248132345006133⟩⟩,⟨⟨2583894907002060993912193697,2583894907002060996825265377⟩,⟨3683553132480533353066521919,3683553132480533356078021574⟩⟩,⟨⟨2743261070260653747306861016,2743261070260653750381731744⟩,⟨3883687729396738506602394550,3883687729396738509780734708⟩⟩,⟨⟨2906763572030138483253411854,2906763572030138486492479507⟩,⟨4085273230009796540780013392,4085273230009796544127855128⟩⟩,⟨⟨3070501230603920209297755364,3070501230603920212697438080⟩,⟨4282590458767819544809533731,4282590458767819548322800218⟩⟩,⟨⟨3238389183974555334932349602,3238389183974555338494102821⟩,⟨4480911350149214402167553772,4480911350149214405847686986⟩⟩,⟨⟨3406874261341373945131257183,3406874261341373948853386903⟩,⟨4675092805467640804431363284,4675092805467640808276856231⟩⟩,⟨⟨3579549604893755315865387777,3579549604893755319748040640⟩,⟨4869885802761709859079899417,4869885802761709863090468086⟩⟩,⟨⟨3753146263507334686236430076,3753146263507334690278033658⟩,⟨5060626664353293747987053193,5060626664353293752161294294⟩⟩,⟨⟨3930990088459011908410628326,3930990088459011912612336930⟩,⟨5251629681473291202258709040,5251629681473291206597773522⟩⟩,⟨⟨4110047942555296306526103654,4110047942555296310884235922⟩,⟨5438637159484464536384523954,5438637159484464540884136385⟩⟩,⟨⟨4293420252680930465628694574,4293420252680930470145222258⟩,⟨5625591570337328758469213738,5625591570337328763131668259⟩⟩,⟨⟨4478272126733734337541307273,4478272126733734342212300868⟩,⟨5808584090911250853091636080,5808584090911250857912348077⟩⟩,⟨⟨4667511260808256205306333370,4667511260808256210134517807⟩,⟨5991236389712338723635313092,5991236389712338728617562521⟩⟩,⟨⟨4858471298017232393379638891,4858471298017232398362027570⟩,⟨6169943217786975310887511820,6169943217786975316027923711⟩⟩,⟨⟨5053893166890991938122199258,5053893166890991943259557968⟩,⟨6348046302403234884509115721,6348046302403234889808444221⟩⟩] +lemma amp1_00_1_eq : ∀ k : Fin 16, amp1_0Expr 0 1 k = amp1_00_1 k := by decide +kernel +noncomputable def amp1_00_2 : Fin 16 → CBox := ![⟨⟨5251255178759393195631335443,5251255178759393200919448337⟩,⟨6522207430371915605406314201,6522207430371915610859675926⟩⟩,⟨⟨5453152406194639425564497338,5453152406194639431005962560⟩,⟨6695521637468797315832991824,6695521637468797321443453136⟩⟩,⟨⟨5657188400228982821898200340,5657188400228982827490510376⟩,⟨6864887838212670994871672330,6864887838212671000636461812⟩⟩,⟨⟨5865829422271475421776457706,5865829422271475427520027519⟩,⟨7033181807190165081421075104,7033181807190165087340537889⟩⟩,⟨⟨6076788270378231112476346243,6076788270378231118369423108⟩,⟨7197514788940299668329023985,7197514788940299674401287576⟩⟩,⟨⟨6292416428427336080526448690,6292416428427336086565502788⟩,⟨7360566202203180000683630422,7360566202203180006904412148⟩⟩,⟨⟨6510522653335354104925691820,6510522653335354111111660731⟩,⟨7519638825309515325573517270,7519638825309515331944128203⟩⟩,⟨⟨6733355304423391471318179849,6733355304423391477650519399⟩,⟨7677235055044664131912827178,7677235055044664138432518728⟩⟩,⟨⟨6958807970262681293749494261,6958807970262681300226602425⟩,⟨7830831584346860424480983617,7830831584346860431148038392⟩⟩,⟨⟨7189035630872744174055297797,7189035630872744180677136317⟩,⟨7982770265394130975957387515,7982770265394130982771636129⟩⟩,⟨⟨7422007329431644345696311611,7422007329431644352460765628⟩,⟨8130686640354154035186984022,8130686640354154042146109070⟩⟩,⟨⟨7659792864603087728868652851,7659792864603087735771085929⟩,⟨8276776182124073163750959919,8276776182124073170849817780⟩⟩,⟨⟨7900428792156239089392438724,7900428792156239096435840318⟩,⟨8418820292296028769090202840,8418820292296028776332044596⟩⟩,⟨⟨8145906658607977461434332498,8145906658607977468617650900⟩,⟨8558880338430821663574644418,8558880338430821670958199359⟩⟩,⟨⟨8394323780343831785828771355,8394323780343831793150530620⟩,⟨8694872295401433742898662211,8694872295401433750422270343⟩⟩,⟨⟨8647599330288870377167336914,8647599330288870384625492906⟩,⟨8828734137087854336766878324,8828734137087854344428274697⟩⟩] +lemma amp1_00_2_eq : ∀ k : Fin 16, amp1_0Expr 0 2 k = amp1_00_2 k := by decide +kernel +noncomputable def amp1_00_3 : Fin 16 → CBox := ![⟨⟨8903885630727711217170263546,8903885630727711224763744213⟩,⟨8958506536417053647157473083,8958506536417053654955413971⟩⟩,⟨⟨9165034481603350068244143590,9165034481603350075972613149⟩,⟨9086013483402380501059137461,9086013483402380508993107801⟩⟩,⟨⟨9429248300261514708045861145,9429248300261514715907394201⟩,⟨9209411651745818261933435387,9209411651745818270001289144⟩⟩,⟨⟨9698315774542769430528505912,9698315774542769438514342272⟩,⟨9330419363854674446735291768,9330419363854674454928384814⟩⟩,⟨⟨9970485226636493510967017706,9970485226636493519083744418⟩,⟨9447301587616115107099902039,9447301587616115115424380974⟩⟩,⟨⟨10247485865101240461368620215,10247485865101240469614822605⟩,⟨9561678368711325847566586647,9561678368711325856020869669⟩⟩,⟨⟨10527608347401967985094609541,10527608347401967993468120740⟩,⟨9671916101415044672956479161,9671916101415044681538185828⟩⟩,⟨⟨10812525498589820695811380796,10812525498589820704311056644⟩,⟨9779543157160454149619333014,9779543157160454158327158924⟩⟩,⟨⟨11100567280711380221070733837,11100567280711380229694986820⟩,⟨9883021203356295241257437220,9883021203356295250089532750⟩⟩,⟨⟨11393352768809079990170156422,11393352768809079998916011805⟩,⟨9983792863738742430782208673,9983792863738742439735657163⟩⟩,⟨⟨11689248670271528400884245104,11689248670271528409751660461⟩,⟨10080409537723725490459462967,10080409537723725499533774925⟩⟩,⟨⟨11989822543229301143028296988,11989822543229301152015464519⟩,⟨10174233445019220158725447978,10174233445019220167918745542⟩⟩,⟨⟨12293475696635137280385306162,12293475696635137289490505108⟩,⟨10263900703025054910315387467,10263900703025054919625690780⟩⟩,⟨⟨12601726055946726475871954127,12601726055946726485094112502⟩,⟨10350697965712873052793987480,10350697965712873062220044705⟩⟩,⟨⟨12913007756543522220791401874,12913007756543522230128599515⟩,⟨10433341510499256411898491314,10433341510499256421438139949⟩⟩,⟨⟨13228790669791017670858247372,13228790669791017680309318839⟩,⟨10513046823511369710338772163,10513046823511369719990671984⟩⟩] +lemma amp1_00_3_eq : ∀ k : Fin 16, amp1_0Expr 0 3 k = amp1_00_3 k := by decide +kernel +noncomputable def amp1_00_4 : Fin 16 → CBox := ![⟨⟨13547540311594870246655303974,13547540311594870256203709224⟩,⟨10588606180541638401572429934,10588606180541638411322985993⟩⟩,⟨⟨13870679808556787436125450507,13870679808556787445786724413⟩,⟨10661167912165665654777705564,10661167912165665664638776040⟩⟩,⟨⟨14196704907083676758298619977,14196704907083676768070098879⟩,⟨10729596476738939804927254882,10729596476738939814896042233⟩⟩,⟨⟨14526993059923276495587272878,14526993059923276505467250081⟩,⟨10794976722458016731380775402,10794976722458016741455468680⟩⟩,⟨⟨14860069361427849812491943694,14860069361427849822478107931⟩,⟨10856241777340714714709284677,10856241777340714724887387961⟩⟩,⟨⟨15197266449213083418854808303,15197266449213083428946500081⟩,⟨10914416380884288097315171803,10914416380884288107595640740⟩⟩,⟨⟨15537138126172045883826857754,15537138126172045894020421725⟩,⟨10968499084131140271981667636,10968499084131140282361051287⟩⟩,⟨⟨15880972883725075911181499446,15880972883725075921476738937⟩,⟨11019457626020161253590704765,11019457626020161264068276546⟩⟩,⟨⟨16227352816129327222754977307,16227352816129327233150050869⟩,⟨11066352968805839603597690518,11066352968805839614171287778⟩⟩,⟨⟨16577522766959766582560625777,16577522766959766593049487932⟩,⟨11110098722699359154566436341,11110098722699359165231336211⟩⟩,⟨⟨16930092908798811837587256630,16930092908798811848172781397⟩,⟨11149815457100347824829558636,11149815457100347835586798569⟩⟩,⟨⟨17286264781638916820835546953,17286264781638916831515507038⟩,⟨11186365314284536919638469907,11186365314284536930485887930⟩⟩,⟨⟨17644676611775328028140767445,17644676611775328038913534115⟩,⟨11218925851059632476637476120,11218925851059632487573039787⟩⟩,⟨⟨18006486840006223550218454954,18006486840006223561080755258⟩,⟨11248310213462072922660052306,11248310213462072933680956908⟩⟩,⟨⟨18370361896448975215495828161,18370361896448975226447500889⟩,⟨11273750489980914291750126097,11273750489980914302855257769⟩⟩,⟨⟨18737417199483850465008194348,18737417199483850476046620420⟩,⟨11296013132140582247952541414,11296013132140582259139516167⟩⟩] +lemma amp1_00_4_eq : ∀ k : Fin 16, amp1_0Expr 0 4 k = amp1_00_4 k := by decide +kernel +noncomputable def amp1_00_5 : Fin 16 → CBox := ![⟨⟨19106347695878775470715963323,19106347695878775481839526767⟩,⟨11314382450704319812540622435,11314382450704319823807409809⟩⟩,⟨⟨19478225741351432864155605154,19478225741351432875362805461⟩,⟨11329580351179425873349857880,11329580351179425884694746017⟩⟩,⟨⟨19851775264316154180319020519,19851775264316154191608232437⟩,⟨11340941188067103654088372838,11340941188067103665509303707⟩⟩,⟨⟨20228025409711111025546526336,20228025409711111036916084488⟩,⟨11349144330817616108520496139,11349144330817616120015645423⟩⟩,⟨⟨20605729695451711992029251614,20605729695451712003477183151⟩,⟨11353572116476826247322970736,11353572116476826258890077156⟩⟩,⟨⟨20985873807605189168710763976,20985873807605189180198983301⟩,⟨11354863262815097435198797557,11354863262815097446816318310⟩⟩,⟨⟨21367241596063550527809177511,21367241596063550539373749970⟩,⟨11352446133696523073125449080,11352446133696523084812041946⟩⟩,⟨⟨21750774946763198889200923079,21750774946763198900839368155⟩,⟨11346920565457163526378252811,11346920565457163538131611443⟩⟩,⟨⟨22135288911358198471083179658,22135288911358198482792677522⟩,⟨11337759088070144803476568555,11337759088070144815293978823⟩⟩,⟨⟨22521681147073459202498997708,22521681147073459214277885882⟩,⟨11325524322708492000306167324,11325524322708492012185768107⟩⟩,⟨⟨22908798897916853147682454864,22908798897916853159527605691⟩,⟨11309731190549000384939523615,11309731190549000396878478762⟩⟩,⟨⟨23297495081501631395519459487,23297495081501631407429065073⟩,⟨11290906668935665523304938597,11290906668935665535301329854⟩⟩,⟨⟨23686650239791094297073970482,23686650239791094309047149333⟩,⟨11268606373009233813515866741,11268606373009233825567974416⟩⟩,⟨⟨24077071961816197273879044767,24077071961816197285912177423⟩,⟨11243323120745824184431178857,11243323120745824196536210801⟩⟩,⟨⟨24467675302934313603038922593,24467675302934313615131043842⟩,⟨11214651594476165240815841046,11214651594476165252972034693⟩⟩,⟨⟨24859221860129145532133282828,24859221860129145544283127398⟩,⟨11183051857613982149621385252,11183051857613982161827048998⟩⟩] +lemma amp1_00_5_eq : ∀ k : Fin 16, amp1_0Expr 0 5 k = amp1_00_5 k := by decide +kernel +noncomputable def amp1_00_6 : Fin 16 → CBox := ![⟨⟨25250662522808687673461153213,25250662522808687685662126012⟩,⟨11148156096993299616196185165,11148156096993299628447035052⟩⟩,⟨⟨25642712160920303488236905223,25642712160920303500492601664⟩,⟨11110392953092266456275457504,11110392953092266468571957784⟩⟩,⟨⟨26034358919673431880902868141,26034358919673431893208338702⟩,⟨11069430612991638086337609970,11069430612991638098676242606⟩⟩,⟨⟨26426270137886539131230920454,26426270137886539143587192807⟩,⟨11025667558510627209496430639,11025667558510627221876458344⟩⟩,⟨⟨26817472735739109604213300121,26817472735739109616616617228⟩,⟨10978806526128320221441428186,10978806526128320233859879734⟩⟩,⟨⟨27208585649643287136728872367,27208585649643287149178390377⟩,⟨10929217041190162840464921185,10929217041190162852920240318⟩⟩,⟨⟨27598676188065708564700084752,27598676188065708577178658839⟩,⟨10876634987672294444769749067,10876634987672294457253735722⟩⟩,⟨⟨27988313948006293661269066915,27988313948006293673791158431⟩,⟨10821402079296846172292162047,10821402079296846184809372864⟩⟩,⟨⟨28376608330789774162730655591,28376608330789774175292570063⟩,⟨10763285990618389566646737026,10763285990618389579194291262⟩⟩,⟨⟨28764078592296864033829620825,28764078592296864046428827988⟩,⟨10702601715564881045050301486,10702601715564881057625973964⟩⟩,⟨⟨29149878019988816252106126007,29149878019988816264741364169⟩,⟨10639147403809585990301263910,10639147403809586002903131864⟩⟩,⟨⟨29534474462844933438695618176,29534474462844933451363364174⟩,⟨10573212372214930087510666981,10573212372214930100136159727⟩⟩,⟨⟨29917066974230152112123040056,29917066974230152124821987744⟩,⟨10504623968440219208778334764,10504623968440219221425529743⟩⟩,⟨⟨30298070866611623242007467027,30298070866611623254737000053⟩,⟨10433646829482808440111854900,10433646829482808452779218924⟩⟩,⟨⟨30676732923606948322376352158,30676732923606948335126475054⟩,⟨10360136259400063438038235225,10360136259400063450720889864⟩⟩,⟨⟨31053414727617214673882451028,31053414727617214686658388505⟩,⟨10284333170258724877314006867,10284333170258724890012427498⟩⟩] +lemma amp1_00_6_eq : ∀ k : Fin 16, amp1_0Expr 0 6 k = amp1_00_6 k := by decide +kernel +noncomputable def amp1_00_7 : Fin 16 → CBox := ![⟨⟨31427412839837072290784774387,31427412839837072303583416046⟩,⟨10206119614000527234892821499,10206119614000527247604495637⟩⟩,⟨⟨31799033854642245717998639641,31799033854642245730819261404⟩,⟨10125713693415573134256931904,10125713693415573146980274793⟩⟩,⟨⟨32167626239791013885717415767,32167626239791013898553445199⟩,⟨10043023030699348447951887548,10043023030699348460683337593⟩⟩,⟨⟨32533440278469252243311068835,32533440278469252256164282330⟩,⟨9958243798476948503692513081,9958243798476948516431282051⟩⟩,⟨⟨32895878554624100163919836488,32895878554624100176785291568⟩,⟨9871308040509020985785678772,9871308040509020998528777353⟩⟩,⟨⟨33255133650751022775923691243,33255133650751022788802691197⟩,⟨9782390844341318617045954765,9782390844341318629792408825⟩⟩,⟨⟨33610664556515969069496619557,33610664556515969082384807579⟩,⟨9691447553836554530159639743,9691447553836554542906681949⟩⟩,⟨⟨33962604696428565047399057933,33962604696428565060294703610⟩,⟨9598632984837958454270326730,9598632984837958467016083271⟩⟩,⟨⟨34310471834867213831303714012,34310471834867213844204760750⟩,⟨9503924685557910371879785075,9503924685557910384622194731⟩⟩,⟨⟨34654338711478692787179230442,34654338711478692800084415509⟩,⟨9407457983942729210529834471,9407457983942729223267158198⟩⟩,⟨⟨34993784313669635289442587105,34993784313669635302348625170⟩,⟨9309231561179438208889395465,9309231561179438221619265167⟩⟩,⟨⟨35328819097647587462075474901,35328819097647587474980899498⟩,⟨9209362013527415732216632633,9209362013527415744937261587⟩⟩,⟨⟨35659085801652974329763371551,35659085801652974342664920539⟩,⟨9107868106980742792230210655,9107868106980742804939278394⟩⟩,⟨⟨35984530925723178374464412339,35984530925723178387360019505⟩,⟨9004848436555031098923618651,9004848436555031111619206389⟩⟩,⟨⟨36304863566717623082002594089,36304863566717623094889183725⟩,⟨8900340827068535302546543054,8900340827068535315226432480⟩⟩,⟨⟨36619964518815973815736571466,36619964518815973828611074625⟩,⟨8794426578665159381861482395,8794426578665159394523534497⟩⟩] +lemma amp1_00_7_eq : ∀ k : Fin 16, amp1_0Expr 0 7 k = amp1_00_7 k := by decide +kernel +noncomputable def amp1_00_8 : Fin 16 → CBox := ![⟨⟨36929611926089865218628330823,36929611926089865231492525974⟩,⟨8687161570299088851191005238,8687161570299088863834193702⟩⟩,⟨⟨37233619047055274849505880444,37233619047055274862362151111⟩,⟨8578610491117965246500548391,8578610491117965259123995401⟩⟩,⟨⟨37531835843583857273431018768,37531835843583857286276041232⟩,⟨8468846290047854252086320283,8468846290047854264687769296⟩⟩,⟨⟨37824006125065671193394552421,37824006125065671206225675205⟩,⟨8357917708082895470109033016,8357917708082895482686432230⟩⟩,⟨⟨38110054525322969650034532568,38110054525322969662849306481⟩,⟨8245913799818552225224663167,8245913799818552237775999870⟩⟩,⟨⟨38389653403567465011636758274,38389653403567465024432388659⟩,⟨8132868001268293342026243341,8132868001268293354549476834⟩⟩,⟨⟨38662805005262343431626271074,38662805005262343444401053259⟩,⟨8018884527690609882965240121,8018884527690609895458567027⟩⟩,⟨⟨38929108146444252383137156425,38929108146444252395888115765⟩,⟨7903982134891120293823152361,7903982134891120306284518126⟩⟩,⟨⟨39188645711864622815460336757,39188645711864622828185864872⟩,⟨7788279272603138577894421861,7788279272603138590322066470⟩⟩,⟨⟨39440940784641322485435380027,39440940784641322498134047778⟩,⟨7671780623981725281881510339,7671780623981725294273724081⟩⟩,⟨⟨39686160007311778555572162395,39686160007311778568242016353⟩,⟨7554617965465760285072149497,7554617965465760297427141199⟩⟩,⟨⟨39923748438299769346716264170,39923748438299769359352978882⟩,⟨7436782499007134079428271548,7436782499007134091743790840⟩⟩,⟨⟨40153959690687680845131993715,40153959690687680857737180565⟩,⟨7318418438071501428248735348,7318418438071501440523682699⟩⟩,⟨⟨40376158398593158127367825088,40376158398593158139936515364⟩,⟨7199504079777677719156334333,7199504079777677731388385248⟩⟩,⟨⟨40590688456638496507148778624,40590688456638496519683469397⟩,⟨7080195202764724601377774724,7080195202764724613565998151⟩⟩,⟨⟨40796831560816104773059290969,40796831560816104785552726041⟩,⟨6960457761575989114236783352,6960457761575989126378486999⟩⟩] +lemma amp1_00_8_eq : ∀ k : Fin 16, amp1_0Expr 0 8 k = amp1_00_8 k := by decide +kernel +noncomputable def amp1_00_9 : Fin 16 → CBox := ![⟨⟨40995025301110911684081080231,40995025301110911696532434915⟩,⟨6840458245787715431205639457,6840458245787715443299329076⟩⟩,⟨⟨41184465800377021985303602342,41184465800377021997710114099⟩,⟨6720150816414533782132008103,6720150816414533794175834887⟩⟩,⟨⟨41365687865881404979736232081,41365687865881404992105427301⟩,⟨6599711837193156465721063230,6599711837193156477714909484⟩⟩,⟨⟨41537799283470313584288053066,41537799283470313596607715014⟩,⟨6479084212287986013272560939,6479084212287986025213051649⟩⟩,⟨⟨41701435713723056435466245703,41701435713723056447735835666⟩,⟨6358453360166392011525396003,6358453360166392023411145258⟩⟩,⟨⟨41855613704346172108441979738,41855613704346172120661229011⟩,⟨6237751453240013987596704313,6237751453240013999426290479⟩⟩,⟨⟨42001073526209366457939351353,42001073526209366470103766790⟩,⟨6117172162551223576811500961,6117172162551223588582986012⟩⟩,⟨⟨42136737441258510892244703402,42136737441258510904353983337⟩,⟨5996637443010511045612633742,5996637443010511057324593771⟩⟩,⟨⟨42263454216326920812073707084,42263454216326920824124581663⟩,⟨5876348433316097782418742233,5876348433316097794069450073⟩⟩,⟨⟨42380048623353053882322582846,42380048623353053894311250707⟩,⟨5756217374969136669310167126,5756217374969136680897756437⟩⟩,⟨⟨42487481948260072364973355703,42487481948260072376923091417⟩,⟨5636452106634096238445395755,5636452106634096249971753404⟩⟩,⟨⟨42584478100957778797923950977,42584478100957778809810153115⟩,⟨5516955650974356812466760522,5516955650974356823927193324⟩⟩,⟨⟨42672115056920672305032493932,42672115056920672316854531898⟩,⟨5397941796180264747497733976,5397941796180264758890956507⟩⟩,⟨⟨42749012311956280095758574247,42749012311956280107512434791⟩,⟨5279304831724161765552178241,5279304831724161776876355402⟩⟩,⟨⟨42816368860023784912864218262,42816368860023784924552538342⟩,⟨5161263762173697552678095772,5161263762173697563932395840⟩⟩,⟨⟨42872696037160660009465662281,42872696037160660021082274489⟩,⟨5043704621085468717070025087,5043704621085468728252362297⟩⟩] +lemma amp1_00_9_eq : ∀ k : Fin 16, amp1_0Expr 0 9 k = amp1_00_9 k := by decide +kernel +noncomputable def amp1_00_10 : Fin 16 → CBox := ![⟨⟨42919318355755731013212520742,42919318355755731024764472990⟩,⟨4926850913609606516566341403,4926850913609606527676375882⟩⟩,⟨⟨42954635037853696228896788979,42954635037853696240375210424⟩,⟨4810580886804078366140384477,4810580886804078377175780392⟩⟩,⟨⟨42980100799343156697112126086,42980100799343156708515922312⟩,⟨4695121848038555017526324760,4695121848038555028485866800⟩⟩,⟨⟨42993998568939656955284833429,42993998568939656966614702194⟩,⟨4580344719906157486646850821,4580344719906157497529290456⟩⟩,⟨⟨42997918152110508835577816924,42997918152110508846828303309⟩,⟨4466479931156336022159978013,4466479931156336032963645578⟩⟩,⟨⟨42990021761428578103491416938,42990021761428578114663555216⟩,⟨4353391535005783230244579408,4353391535005783240968301030⟩⟩,⟨⟨42972039396907675038961412869,42972039396907675050053166058⟩,⟨4241312418368850879303724860,4241312418368850889946261312⟩⟩,⟨⟨42942007868279380513968293657,42942007868279380524976373657⟩,⟨4130100213631344492169855774,4130100213631344502729588877⟩⟩,⟨⟨42901802714098938095537176372,42901802714098938106459564809⟩,⟨4019989620392040574341793617,4019989620392040584817507768⟩⟩,⟨⟨42849330367942142010022479222,42849330367942142020856562719⟩,⟨3910832292576797913346210900,3910832292576797923736422617⟩⟩,⟨⟨42786617512628098973359678685,42786617512628098984101870845⟩,⟨3802864114837687644675595228,3802864114837687654979036398⟩⟩,⟨⟨42711434920268362589740735957,42711434920268362600468714047⟩,⟨3695931199172180277173740895,3695931199172180287395880915⟩⟩,⟨⟨42625966311011907573085841719,42625966311011907583723337917⟩,⟨3590270005622009707218472002,3590270005622009717351589553⟩⟩,⟨⟨42527841169799341079049700606,42527841169799341089595838579⟩,⟨3485721535251655936273686601,3485721535251655946316480731⟩⟩,⟨⟨42419406463464054156511305405,42419406463464054166964174181⟩,⟨3382522231915680823386504002,3382522231915680833337936663⟩⟩,⟨⟨42298144391795944934287012452,42298144391795944944646392651⟩,⟨3280508411477009111162646496,3280508411477009121021454371⟩⟩] +lemma amp1_00_10_eq : ∀ k : Fin 16, amp1_0Expr 0 10 k = amp1_00_10 k := by decide +kernel +noncomputable def amp1_00_11 : Fin 16 → CBox := ![⟨⟨42166571726714147620245561320,42166571726714147630509710544⟩,⟨3179915928231531512839044569,3179915928231531522604204670⟩⟩,⟨⟨42022016976737183259103081670,42022016976737183269272067830⟩,⟨3080576833550168279770924630,3080576833550168289441245184⟩⟩,⟨⟨41867173663459559945863354175,41867173663459559955933012945⟩,⟨2982725837119988768944513310,2982725837119988778518883130⟩⟩,⟨⟨41699209749389120248082288523,41699209749389120258055938304⟩,⟨2886191141720374762024512507,2886191141720374771501940024⟩⟩,⟨⟨41521002878771966927363130450,41521002878771966937234823716⟩,⟨2791205775812629712201092501,2791205775812629721580364569⟩⟩,⟨⟨41329553118928773516131070153,41329553118928773525900845005⟩,⟨2697594504860290108069044468,2697594504860290117348985591⟩⟩,⟨⟨41127930086174088477086808883,41127930086174088486751140316⟩,⟨2605588158021350732600717484,2605588158021350741780378700⟩⟩,⟨⟨40912958056998651181053030357,40912958056998651190623181527⟩,⟨2515008470250995156055760872,2515008470250995165134637636⟩⟩,⟨⟨40687907000504772067199360109,40687907000504772076662050968⟩,⟨2426083571964919952596007257,2426083571964919961572542934⟩⟩,⟨⟨40449416900965345873440292328,40449416900965345882795117260⟩,⟨2338632570078793026811416754,2338632570078793035684443088⟩⟩,⟨⟨40200967055101451277213395671,40200967055101451286461893226⟩,⟨2252880415556413292223665823,2252880415556413300992634055⟩⟩,⟨⟨39939003980058891777878050742,39939003980058891787014895441⟩,⟨2168643985507320731227289012,2168643985507320739890717301⟩⟩,⟨⟨39667225941247487814770821901,39667225941247487823796120495⟩,⟨2086144589544568115418743664,2086144589544568123976016837⟩⟩,⟨⟨39381876062477065827931726713,39381876062477065836843795666⟩,⟨2005197269047037016922557016,2005197269047037025372450422⟩⟩,⟨⟨39086881968257398518407031871,39086881968257398527203148877⟩,⟨1926019249259763427437801693,1926019249259763435779639595⟩⟩,⟨⟨38778272621949003794700483799,38778272621949003803377724867⟩,⟨1848424125801029966833612985,1848424125801029975066095156⟩⟩] +lemma amp1_00_11_eq : ∀ k : Fin 16, amp1_0Expr 0 11 k = amp1_00_11 k := by decide +kernel +noncomputable def amp1_00_12 : Fin 16 → CBox := ![⟨⟨38460216243005038068660294911,38460216243005038077265627021⟩,⟨1772624615471496370090184172,1772624615471496378214940868⟩⟩,⟨⟨38128515922663753400613815470,38128515922663753409104923034⟩,⟨1698433254021623109880687203,1698433254021623117894586210⟩⟩,⟨⟨37787592668138201569444983251,37787592668138201577820550709⟩,⟨1626057844719219432109060327,1626057844719219440011590300⟩⟩,⟨⟨37433010921879802181315172892,37433010921879802189574554954⟩,⟨1555310245266803036479796999,1555310245266803044269767499⟩⟩,⟨⟨37069457758667848377546268021,37069457758667848385688173030⟩,⟨1486392959332582239509140709,1486392959332582247186057669⟩⟩,⟨⟨36692244989938961250280670784,36692244989938961258305223998⟩,⟨1419117544299396708369272552,1419117544299396715932018590⟩⟩,⟨⟨36306340277071639356796067751,36306340277071639364699645611⟩,⟨1353680837210838826407152479,1353680837210838833855237626⟩⟩,⟨⟨35906787447809543942554024975,35906787447809543950342016074⟩,⟨1289894468725546299461645456,1289894468725546306794109555⟩⟩,⟨⟨35498850687510697370691822612,35498850687510697378356475953⟩,⟨1227949261284789797585874234,1227949261284789804802088574⟩⟩,⟨⟨35077288922676154675221870680,35077288922676154682763770479⟩,⟨1167657288222717644709583417,1167657288222717651808465329⟩⟩,⟨⟨34647680430227238035650815036,34647680430227238043068033075⟩,⟨1109203028438482888226780075,1109203028438482895208026270⟩⟩,⟨⟨34204480522472212094944164419,34204480522472212102235168871⟩,⟨1052399363061589154336846566,1052399363061589161199254976⟩⟩,⟨⟨33753601017671970428045023013,33753601017671970435206547663⟩,⟨997424117522348576145800441,997424117522348582889055608⟩⟩,⟨⟨33289172830610727878773154930,33289172830610727885834595221⟩,⟨944091341481054271814721620,944091341481054278438544674⟩⟩,⟨⟨32817462954408717995673086961,32817462954408718002605524750⟩,⟨892571915944851588367441124,892571915944851594870859140⟩⟩,⟨⟨32332254722500828540439240053,32332254722500828547241941132⟩,⟨842681415331583223704401852,842681415331583230086233700⟩⟩] +lemma amp1_00_12_eq : ∀ k : Fin 16, amp1_0Expr 0 12 k = amp1_00_12 k := by decide +kernel +noncomputable def amp1_00_13 : Fin 16 → CBox := ![⟨⟨31840194483367027696819290737,31840194483367027703492334501⟩,⟨794583504186444001550992856,794583504186444007811128588⟩⟩,⟨⟨31334692005730726057252160744,31334692005730726063798206985⟩,⟨748095633259677203976566497,748095633259677210113949917⟩⟩,⟨⟨30822800161573188409364101673,30822800161573188415776831607⟩,⟨703373997437957600995312192,703373997437957607009794318⟩⟩,⟨⟨30297525886035927470328769734,30297525886035927476609154845⟩,⟨660238270565454970124428692,660238270565454976014850694⟩⟩,⟨⟨29766359269103985857149414060,29766359269103985863294338359⟩,⟨618836943425914624386357203,618836943425914630152686610⟩⟩,⟨⟨29221871261330109933285907438,29221871261330109939314093874⟩,⟨578992254726878444771494559,578992254726878450412946757⟩⟩,⟨⟨28672024055703603214020944799,28672024055703603219915179952⟩,⟨540844775349904466574109711,540844775349904472090467394⟩⟩,⟨⟨28108914846118349605786129436,28108914846118349611544991379⟩,⟨504219645448085490672935943,504219645448085496062955873⟩⟩,⟨⟨27541017830326309972011735274,27541017830326309977635449572⟩,⟨469249318722501105611038756,469249318722501110874891451⟩⟩,⟨⟨26959913128480904309212990635,26959913128480904314702433464⟩,⟨435762167956083809972763712,435762167956083815109270932⟩⟩,⟨⟨26374632899886217332291129193,26374632899886217337644270493⟩,⟨403882350770507062635976563,403882350770507067645395264⟩⟩,⟨⟨25776190161419290677275190281,25776190161419290682503610621⟩,⟨373441798139992524772381182,373441798139992529653610427⟩⟩,⟨⟨25174228364824610569738618048,25174228364824610574827178715⟩,⟨344556210927922260857631922,344556210927922265610783295⟩⟩,⟨⟨24559135189546464316503844976,24559135189546464321452857524⟩,⟨317061398000412768763922510,317061398000412773387737782⟩⟩,⟨⟨23941227780934638856051104097,23941227780934638860861745429⟩,⟨291064460826259374386517764,291064460826259378881475855⟩⟩,⟨⟨23310200110631642069358991251,23310200110631642074028287151⟩,⟨266405399753673126148367987,266405399753673130513092680⟩⟩] +lemma amp1_00_13_eq : ∀ k : Fin 16, amp1_0Expr 0 13 k = amp1_00_13 k := by decide +kernel +noncomputable def amp1_00_14 : Fin 16 → CBox := ![⟨⟨22677116699534118856964823479,22677116699534118861503138061⟩,⟨243182592066960779273101654,243182592066960783508219055⟩⟩,⟨⟨22030896768952754478743836652,22030896768952754483140850626⟩,⟨221240536816929511862702373,221240536816929515966754583⟩⟩,⟨⟨21383440102110633499512210154,21383440102110633503769734733⟩,⟨200668779944004747923304328,200668779944004751896971811⟩⟩,⟨⟨20722794073015559522753417787,20722794073015559526866476054⟩,⟨181316619785693725474637806,181316619785693729316428819⟩⟩,⟨⟨20061799751985878424978628328,20061799751985878428957482910⟩,⟨163264681172595938028463618,163264681172595941739210921⟩⟩,⟨⟨19387514922600583544262410834,19387514922600583548097985699⟩,⟨146367355405605192073020363,146367355405605195651163113⟩⟩,⟨⟨18713851496227712879673698279,18713851496227712883372312909⟩,⟨130696273572377447804001387,130696273572377451250486925⟩⟩,⟨⟨18026732916713064960667255770,18026732916713064964221014006⟩,⟨116111206435427027875155240,116111206435427031188329439⟩⟩,⟨⟨17341302569582749714580822045,17341302569582749717991296343⟩,⟨102674735551117052949805298,102674735551117056130686658⟩⟩,⟨⟨16642168789751721057938328125,16642168789751721061208184044⟩,⟨90252290198623870044988222,90252290198623873091931685⟩⟩,⟨⟨15945908985863070530012151670,15945908985863070533137320328⟩,⟨78897363137513934609491708,78897363137513937523677605⟩⟩,⟨⟨15235586477600848862976231338,15235586477600848865959189016⟩,⟨68481313526766470841867052,68481313526766473621488720⟩⟩,⟨⟨14529473166332548088086545682,14529473166332548090928570269⟩,⟨59048522219791194075308043,59048522219791196721733319⟩⟩,⟨⟨13808788625619452981634057207,13808788625619452984328943471⟩,⟨50476541709763955887114387,50476541709763958398373974⟩⟩,⟨⟨13093842083524598544344660219,13093842083524598546897250995⟩,⟨42800633560112768872289699,42800633560112771250007830⟩⟩,⟨⟨12363611164030934046100540668,12363611164030934048508234195⟩,⟨35904798986054575443541121,35904798986054577685550421⟩⟩] +lemma amp1_00_14_eq : ∀ k : Fin 16, amp1_0Expr 0 14 k = amp1_00_14 k := by decide +kernel +noncomputable def amp1_00_15 : Fin 16 → CBox := ![⟨⟨11640906474730461962757351879,11640906474730461965021242049⟩,⟨29815188073350488035467945,29815188073350490143612757⟩⟩,⟨⟨10901916162184254398082166659,10901916162184254400199420929⟩,⟨24422498031291933480246339,24422498031291935452148664⟩⟩,⟨⟨10172602315072406992121879391,10172602315072406994094493291⟩,⟨19743789781400818145146084,19743789781400819983006195⟩⟩,⟨⟨9425581176452244331236685316,9425581176452244333063340767⟩,⟨15676695838757777271719374,15676695838757778972815417⟩⟩,⟨⟨8690917343933110757514464986,8690917343933110759197239857⟩,⟨12229223778246477724150227,12229223778246479291085485⟩⟩,⟨⟨7936480653240993684571317637,7936480653240993686106515561⟩,⟨9306173334082595615922378,9306173334082597045553661⟩⟩,⟨⟨7197909971989378770795483730,7197909971989378772185917244⟩,⟨6906546457326443808507550,6906546457326445104021466⟩⟩,⟨⟨6436446914697699141704419883,6436446914697699142947417679⟩,⟨4942536047449002236383708,4942536047449003393997237⟩⟩,⟨⟨5695762752695653296916446706,5695762752695653298015212457⟩,⟨3404195131147990925991898,3404195131147991949695062⟩⟩,⟨⟨4927169374622884835914524775,4927169374622884836864207108⟩,⟨2211333236794331190457579,2211333236794332075516028⟩⟩,⟨⟨4186952203246164132120349766,4186952203246164132926392120⟩,⟨1345113899161041785228083,1345113899161042536944418⟩⟩,⟨⟨3409858307668758867065504587,3409858307668758867721335283⟩,⟨733193241686197985015606,733193241686198596964974⟩⟩,⟨⟨2674938742797905265965039796,2674938742797905266478589251⟩,⟨347891772871138965917618,347891772871139445806631⟩⟩,⟨⟨1883617619535721157128874699,1883617619535721157489949810⟩,⟨124974050225334591881219,124974050225334929723296⟩⟩,⟨⟨1168594191641463783134676584,1168594191641463783357051979⟩,⟨27910132336248057717426,27910132336248267277283⟩⟩,⟨⟨332022702301807070789393458,332022702301807070851610897⟩,⟨881064552150245318561,881064552150304854201⟩⟩] +lemma amp1_00_15_eq : ∀ k : Fin 16, amp1_0Expr 0 15 k = amp1_00_15 k := by decide +kernel +noncomputable def amp1_00 : Fin 16 → Fin 16 → CBox := ![amp1_00_0,amp1_00_1,amp1_00_2,amp1_00_3,amp1_00_4,amp1_00_5,amp1_00_6,amp1_00_7,amp1_00_8,amp1_00_9,amp1_00_10,amp1_00_11,amp1_00_12,amp1_00_13,amp1_00_14,amp1_00_15] +lemma amp1_00_eq (i k : Fin 16) : amp1_0Expr 0 i k = amp1_00 i k := by + fin_cases i + · exact amp1_00_0_eq k + · exact amp1_00_1_eq k + · exact amp1_00_2_eq k + · exact amp1_00_3_eq k + · exact amp1_00_4_eq k + · exact amp1_00_5_eq k + · exact amp1_00_6_eq k + · exact amp1_00_7_eq k + · exact amp1_00_8_eq k + · exact amp1_00_9_eq k + · exact amp1_00_10_eq k + · exact amp1_00_11_eq k + · exact amp1_00_12_eq k + · exact amp1_00_13_eq k + · exact amp1_00_14_eq k + · exact amp1_00_15_eq k +noncomputable def amp1_01_0 : Fin 16 → CBox := ![⟨⟨(-21200997748146017692560387),(-21200997748146017609336739)⟩,⟨79126252864372438498630117,79126252864372438582660591⟩⟩,⟨⟨(-74602058010201874190083040),(-74602058010201873896937424)⟩,⟨278515354377778840703934318,278515354377778841000509469⟩⟩,⟨⟨(-120192360892399083852970506),(-120192360892399083380249120)⟩,⟨448996920341323833930961074,448996920341323834409660872⟩⟩,⟨⟨(-170566322030367127559880167),(-170566322030367126888424764)⟩,⟨637767312329780873190085136,637767312329780873870152282⟩⟩,⟨⟨(-217224648705536777172615795),(-217224648705536776316456502)⟩,⟨813233281518097448415433124,813233281518097449282744280⟩⟩,⟨⟨(-266416875503616319299484834),(-266416875503616318247926495)⟩,⟨998940926603876333397421039,998940926603876334462764482⟩⟩,⟨⟨(-313075681733514035263992698),(-313075681733514034026124726)⟩,⟨1176074633880924900787218129,1176074633880924902041445561⟩⟩,⟨⟨(-361317038189751186159371076),(-361317038189751184727897867)⟩,⟨1360246022016509626323640711,1360246022016509627774115158⟩⟩,⟨⟨(-407533556144932433823705861),(-407533556144932432205421924)⟩,⟨1538057384426956145571318081,1538057384426956147211197081⟩⟩,⟨⟨(-454777932959963232045696930),(-454777932959963230235206827)⟩,⟨1721179330705583987557937455,1721179330705583989392522033⟩⟩,⟨⟨(-500254512323635366610005300),(-500254512323635364612717846)⟩,⟨1899212786784745668072484090,1899212786784745670096545667⟩⟩,⟨⟨(-546376569734763781589081788),(-546376569734763779400749512)⟩,⟨2081468392157442825902435179,2081468392157442828120194388⟩⟩,⟨⟨(-590867651307883323203693728),(-590867651307883320829001903)⟩,⟨2259453762604975882140278698,2259453762604975884546936018⟩⟩,⟨⟨(-635712588277230058337833601),(-635712588277230055773364035)⟩,⟨2440906172532428501530894809,2440906172532428504129819785⟩⟩,⟨⟨(-678997202608834479643420929),(-678997202608834476893168055)⟩,⟨2618654073209206331449553350,2618654073209206334236994112⟩⟩,⟨⟨(-722398204945136250983949122),(-722398204945136248045092853)⟩,⟨2799309645312332411667031164,2799309645312332414645813537⟩⟩] +lemma amp1_01_0_eq : ∀ k : Fin 16, amp1_0Expr 1 0 k = amp1_01_0 k := by decide +kernel +noncomputable def amp1_01_1 : Fin 16 → CBox := ![⟨⟨(-764269745960762456179550974),(-764269745960762453055801607)⟩,⟨2976671394772112284150917423,2976671394772112287317236192⟩⟩,⟨⟨(-806055577633586230851001360),(-806055577633586227540053496)⟩,⟨3156506113297329180815155243,3156506113297329184171234225⟩⟩,⟨⟨(-846317475743604404814098901),(-846317475743604401319359873)⟩,⟨3333355688471934091352660323,3333355688471934094895011564⟩⟩,⟨⟨(-886316364241138486481218882),(-886316364241138482800537931)⟩,⟨3512327784120728346718245456,3512327784120728350449649194⟩⟩,⟨⟨(-924780146848747180260224237),(-924780146848747176397020702)⟩,⟨3688552722665358536313487004,3688552722665358540229747602⟩⟩,⟨⟨(-962822056073484330224026709),(-962822056073484326176681135)⟩,⟨3866609314988946008570280306,3866609314988946012673055976⟩⟩,⟨⟨(-999306496545248707328118945),(-999306496545248703099357111)⟩,⟨4042105721687455206736378516,4042105721687455211023730666⟩⟩,⟨⟨(-1035224616365930060117098571),(-1035224616365930055705901624)⟩,⟨4219186582780116875307980980,4219186582780116879780016086⟩⟩,⟨⟨(-1069555423906068117541786383),(-1069555423906068112950752620)⟩,⟨4393856201276870411896351178,4393856201276870416551257656⟩⟩,⟨⟨(-1103187243654037576808888300),(-1103187243654037572036896045)⟩,⟨4569896015953293283119710260,4569896015953293287958785239⟩⟩,⟨⟨(-1135197038961059698799377939),(-1135197038961059693849547668)⟩,⟨4743644418268419804787079649,4743644418268419809806043097⟩⟩,⟨⟨(-1166385182190926885520850028),(-1166385182190926880392000296)⟩,⟨4918574206876960892704079811,4918574206876960897905178134⟩⟩,⟨⟨(-1195913630143822122114359103),(-1195913630143822116809602988)⟩,⟨5091309624611818764784424663,5091309624611818770163119589⟩⟩,⟨⟨(-1224506542255692818102623768),(-1224506542255692812620744209)⟩,⟨5265057674610481445666142093,5265057674610481451225510916⟩⟩,⟨⟨(-1251400572213454710929833109),(-1251400572213454705273642020)⟩,⟨5436690217042848174908319541,5436690217042848180644899490⟩⟩,⟨⟨(-1277253110866572787650692502),(-1277253110866572781819644072)⟩,⟨5609182713831998269236368398,5609182713831998275150991257⟩⟩] +lemma amp1_01_1_eq : ∀ k : Fin 16, amp1_0Expr 1 1 k = amp1_01_1 k := by decide +kernel +noncomputable def amp1_01_2 : Fin 16 → CBox := ![⟨⟨(-1301367184982554882020464057),(-1301367184982554876017626737)⟩,⟨5779623829225898708304251664,5779623829225898714392123873⟩⟩,⟨⟨(-1324341141703506710765596514),(-1324341141703506704590098258)⟩,⟨5950785296248705970247936263,5950785296248705976511904201⟩⟩,⟨⟨(-1345537547514930532481009623),(-1345537547514930526135466865)⟩,⟨6119947391728407394762434375,6119947391728407401199586015⟩⟩,⟨⟨(-1365502117203263489910897230),(-1365502117203263483395112414)⟩,⟨6289701006026611583311317283,6289701006026611589922065885⟩⟩,⟨⟨(-1383651269610054827227949932),(-1383651269610054820544342028)⟩,⟨6457497174238602897415720461,6457497174238602904197965788⟩⟩,⟨⟨(-1400483478008096272752115657),(-1400483478008096265901490446)⟩,⟨6625764998716732347046286000,6625764998716732353996256149⟩⟩,⟨⟨(-1415464220912164478339328613),(-1415464220912164471323475811)⟩,⟨6792108818572694577811428424,6792108818572694584929884843⟩⟩,⟨⟨(-1429049316205043879589564299),(-1429049316205043872408723691)⟩,⟨6958811977487692950889181573,6958811977487692958175502773⟩⟩,⟨⟨(-1440749217200764371977453441),(-1440749217200764364633988187)⟩,⟨7123617367739239378932686892,7123617367739239386384926260⟩⟩,⟨⟨(-1450981029550553092716624106),(-1450981029550553085210771467)⟩,⟨7288676182929682771506290725,7288676182929682779124331033⟩⟩,⟨⟨(-1459296663011229587062763441),(-1459296663011229579396992580)⟩,⟨7451857294425257001852402185,7451857294425257009633759273⟩⟩,⟨⟨(-1466077934364034266659341926),(-1466077934364034258834872224)⟩,⟨7615191394130827666580934439,7615191394130827674520897469⟩⟩,⟨⟨(-1470915149533975722930303562),(-1470915149533975714948604701)⟩,⟨7776662531125120367073881218,7776662531125120375175078107⟩⟩,⟨⟨(-1474157835113469807367050283),(-1474157835113469799228749614)⟩,⟨7938190939589940624527402814,7938190939589940632788667888⟩⟩,⟨⟨(-1475432006660776880113466893),(-1475432006660776871820917023)⟩,⟨8097866503423670610400780750,8097866503423670618820246856⟩⟩,⟨⟨(-1475057548970374028944136882),(-1475057548970374020498217372)⟩,⟨8257507717059530600585094864,8257507717059530609160644489⟩⟩] +lemma amp1_01_2_eq : ∀ k : Fin 16, amp1_0Expr 1 2 k = amp1_01_2 k := by decide +kernel +noncomputable def amp1_01_3 : Fin 16 → CBox := ![⟨⟨(-1472693808039142883255004869),(-1472693808039142874657999595)⟩,⟨8415302167490874779876264005,8415302167490874788606419913⟩⟩,⟨⟨(-1468633383815857725046094858),(-1468633383815857716298673982)⟩,⟨8572974221743745251475651376,8572974221743745260359913975⟩⟩,⟨⟨(-1462566828032877796833895967),(-1462566828032877787938501968)⟩,⟨8728802052545642361441533823,8728802052545642370477590227⟩⟩,⟨⟨(-1454761568354611433203162475),(-1454761568354611424161818641)⟩,⟨8884422582484511324424056742,8884422582484511333603658914⟩⟩,⟨⟨(-1444937449552986827111189247),(-1444937449552986817925030152)⟩,⟨9038198308842333547132642140,9038198308842333556461344176⟩⟩,⟨⟨(-1433338633151167607506375010),(-1433338633151167598176399442)⟩,⟨9191684605700923121644060209,9191684605700923131120324056⟩⟩,⟨⟨(-1419712521808274072220821125),(-1419712521808274062749518250)⟩,⟨9343322761589903377987361673,9343322761589903387608651722⟩⟩,⟨⟨(-1404281741549902619619673033),(-1404281741549902610008068518)⟩,⟨9494591826929396445043754725,9494591826929396454808778143⟩⟩,⟨⟨(-1386819667123227710313438965),(-1386819667123227700563951807)⟩,⟨9644006971109064361121231916,9644006971109064371027967275⟩⟩,⟨⟨(-1367528969581152226181600112),(-1367528969581152216295546696)⟩,⟨9792975569862268405375687272,9792975569862268415421247239⟩⟩,⟨⟨(-1346207536078227034922836618),(-1346207536078227024902454073)⟩,⟨9940082299453919842466258595,9940082299453919852649951822⟩⟩,⟨⟨(-1323039534093113964980622398),(-1323039534093113954827148493)⟩,⟨10086667012811142031456452903,10086667012811142041776393285⟩⟩,⟨⟨(-1297846010341133855774288585),(-1297846010341133845490177320)⟩,⟨10231379983662703692146542876,10231379983662703702600584270⟩⟩,⟨⟨(-1270793968484442831695226932),(-1270793968484442821281695916)⟩,⟨10375497262535287443018838428,10375497262535287453605699788⟩⟩,⟨⟨(-1241726352678157535324201351),(-1241726352678157524783737490)⟩,⟨10517731215752051188484129999,10517731215752051199201486130⟩⟩,⟨⟨(-1210794245546516210905074908),(-1210794245546516200238970388)⟩,⟨10659297435379377057557964332,10659297435379377068404437947⟩⟩] +lemma amp1_01_3_eq : ∀ k : Fin 16, amp1_0Expr 1 3 k = amp1_01_3 k := by decide +kernel +noncomputable def amp1_01_4 : Fin 16 → CBox := ![⟨⟨(-1177861303754219811302816219),(-1177861303754219800514840568)⟩,⟨10798967229527006695071365311,10798967229527006706032975247⟩⟩,⟨⟨(-1143063847057745734749870344),(-1143063847057745723839867841)⟩,⟨10937898745661799631456566596,10937898745661799642545328340⟩⟩,⟨⟨(-1106285125457925321848531628),(-1106285125457925310819087508)⟩,⟨11074919394242342481937788371,11074919394242342493150746569⟩⟩,⟨⟨(-1067647779905278892290533307),(-1067647779905278881143114612)⟩,⟨11211132601246841551384490265,11211132601246841562719779369⟩⟩,⟨⟨(-1027053590612907732633098121),(-1027053590612907721370259458)⟩,⟨11345419315118104379908367819,11345419315118104391363332196⟩⟩,⟨⟨(-984612538642019961694182785),(-984612538642019950317367714)⟩,⟨11478830706222580007473765323,11478830706222580019047325183⟩⟩,⟨⟨(-940243919065148520298514671),(-940243919065148508810365908)⟩,⟨11610298940682518590639093468,11610298940682518602327581217⟩⟩,⟨⟨(-894046014519051206940250420),(-894046014519051195342237572)⟩,⟨11740825170592413310994597822,11740825170592413322797264117⟩⟩,⟨⟨(-845954660264327092776893095),(-845954660264327081071555772)⟩,⟨11869390676887742874602646885,11869390676887742886517187675⟩⟩,⟨⟨(-796057351165117016336589916),(-796057351165117004525748513)⟩,⟨11996948626872484288853161405,11996948626872484300874528626⟩⟩,⟨⟨(-744305522585891424615222380),(-744305522585891412701178595)⟩,⟨12122527507917913647350761816,12122527507917913659480085464⟩⟩,⟨⟨(-690776747215659334402110790),(-690776747215659322386547966)⟩,⟨12247034353470363539045223989,12247034353470363551280212792⟩⟩,⟨⟨(-635437149768916189984934267),(-635437149768916177870396723)⟩,⟨12369543123584179444877151423,12369543123584179457215645558⟩⟩,⟨⟨(-578355206323740699854513157),(-578355206323740687642752447)⟩,⟨12490916404702645323972682555,12490916404702645336411657090⟩⟩,⟨⟨(-519510844972550447564347205),(-519510844972550435257860876)⟩,⟨12610272053177684413221380443,12610272053177684425759690203⟩⟩,⟨⟨(-458964235113816234213132257),(-458964235113816221813688836)⟩,⟨12728429747290870346722214894,12728429747290870359357289391⟩⟩] +lemma amp1_01_4_eq : ∀ k : Fin 16, amp1_0Expr 1 4 k = amp1_01_4 k := by decide +kernel +noncomputable def amp1_01_5 : Fin 16 → CBox := ![⟨⟨(-396708243080582517514672772),(-396708243080582505024827621)⟩,⟨12844549805628615328983784208,12844549805628615341713469498⟩⟩,⟨⟨(-332795489766457428905505429),(-332795489766457416327032348)⟩,⟨12959410403156659911844018189,12959410403156659924666485283⟩⟩,⟨⟨(-267230932009016913785791532),(-267230932009016901121251392)⟩,⟨13072213015797350192492229867,13072213015797350205405297592⟩⟩,⟨⟨(-200060372047518437724520908),(-200060372047518424975735532)⟩,⟨13183695598318310286995544268,13183695598318310299997258319⟩⟩,⟨⟨(-131300023895232525660248981),(-131300023895232512829791873)⟩,⟨13293099596702383258177266074,13293099596702383271265218840⟩⟩,⟨⟨(-60989575718594465688668207),(-60989575718594452778499101)⟩,⟨13401123917672504861610498096,13401123917672504874759453645⟩⟩,⟨⟨10844322831049754664395306,10844322831049767652268876⟩,⟨13507048897469016387759915730,13507048897469016400991973603⟩⟩,⟨⟨84167415613325554597955737,84167415613325567663580771⟩,⟨13611535465426379716900963344,13611535465426379730213600841⟩⟩,⟨⟨158943429375429816393344707,158943429375429829534227360⟩,⟨13713901866762786046814897870,13713901866762786060205172872⟩⟩,⟨⟨235142878030640284231371887,235142878030640297445672931⟩,⟨13814772030927031137499701539,13814772030927031150965596956⟩⟩,⟨⟨312720669268858315864706257,312720669268858329149926196⟩,⟨13913501221452239897327682887,13913501221452239910866081287⟩⟩,⟨⟨391651442932367431115559958,391651442932367444469813300⟩,⟨14010677259617772587312587486,14010677259617772600921391498⟩⟩,⟨⟨471882086469988756347426987,471882086469988769768244097⟩,⟨14105691620226997957292359199,14105691620226997970969829148⟩⟩,⟨⟨553390737349356882394736287,553390737349356895880172083⟩,⟨14199096828833113758529612683,14199096828833113772272546666⟩⟩,⟨⟨636117057419228704084499989,636117057419228717632096190⟩,⟨14290319841879049255387913745,14290319841879049269194512931⟩⟩,⟨⟨720042067433924784811287867,720042067433924798419119644⟩,⟨14379878628127616719231525957,14379878628127616733099975936⟩⟩] +lemma amp1_01_5_eq : ∀ k : Fin 16, amp1_0Expr 1 5 k = amp1_01_5 k := by decide +kernel +noncomputable def amp1_01_6 : Fin 16 → CBox := ![⟨⟨805098995476766743352218901,805098995476766757017663853⟩,⟨14467234967937969458757502992,14467234967937969472682768818⟩⟩,⟨⟨891271143504906019733021517,891271143504906033454286184⟩,⟨14552872943817548113132701136,14552872943817548127115738343⟩⟩,⟨⟨978486096073492377776913869,978486096073492391551431908⟩,⟨14636288569334225169178453281,14636288569334225183215184782⟩⟩,⟨⟨1066728844927581711288289354,1066728844927581725114178856⟩,⟨14717932647398650173066699050,14717932647398650187156567216⟩⟩,⟨⟨1155922120804361322853731387,1155922120804361336728463740⟩,⟨14797334896748985680922076975,14797334896748985695061713631⟩⟩,⟨⟨1246052023010540690525965221,1246052023010540704447580628⟩,⟨14874913387488450457501172012,14874913387488450471688932205⟩⟩,⟨⟨1337037218598631683014138491,1337037218598631696979463200⟩,⟨14950231074293923350318231990,14950231074293923364543517359⟩⟩,⟨⟨1428864340008512023626000884,1428864340008512037633763642⟩,⟨15023673784927369909670317857,15023673784927369923939829612⟩⟩,⟨⟨1521448782010739727655651190,1521448782010739741703331030⟩,⟨15094837296150380128637228223,15094837296150380142947683700⟩⟩,⟨⟨1614777142231782613991151744,1614777142231782628076675787⟩,⟨15164075630659516489442648042,15164075630659516503791463654⟩⟩,⟨⟨1708762336589618499069475730,1708762336589618513190466865⟩,⟨15231017025784040859575674983,15231017025784040873960872056⟩⟩,⟨⟨1803390365179201672599441964,1803390365179201686753740975⟩,⟨15295984086001509208370388471,15295984086001509222788882582⟩⟩,⟨⟨1898572461203197761277469692,1898572461203197775462702759⟩,⟨15358637197338913592145364595,15358637197338913606595181258⟩⟩,⟨⟨1994293468533173430067089567,1994293468533173444281271741⟩,⟨15419267884896003669422764922,15419267884896003683902300649⟩⟩,⟨⟨2090463737118857204031235530,2090463737118857218271436604⟩,⟨15477568418803002336220715525,15477568418803002350723586189⟩⟩,⟨⟨2187066398781639939185388133,2187066398781639953449991646⟩,⟨15533799537735820895435019729,15533799537735820909962598455⟩⟩] +lemma amp1_01_6_eq : ∀ k : Fin 16, amp1_0Expr 1 6 k = amp1_01_6 k := by decide +kernel +noncomputable def amp1_01_7 : Fin 16 → CBox := ![⟨⟨2284011723569921220377964914,2284011723569921234664506968⟩,⟨15587685176527595989057702868,15587685176527596003607129923⟩⟩,⟨⟨2381280577164033968349000103,2381280577164033982655480333⟩,⟨15639455536334749117978795750,15639455536334749132548380474⟩⟩,⟨⟨2478783957473054950328073530,2478783957473054964651785241⟩,⟨15688866040672614610040971265,15688866040672614624626168664⟩⟩,⟨⟨2576499910575701803251527623,2576499910575701817590641340⟩,⟨15736116559612223235368546058,15736116559612223249968908407⟩⟩,⟨⟨2674340974901806323059309243,2674340974901806337411237803⟩,⟨15780993871141975061558627550,15780993871141975076170468026⟩⟩,⟨⟨2772281823008508024489255271,2772281823008508038852152345⟩,⟨15823667679551215975749162980,15823667679551215990371752472⟩⟩,⟨⟨2870237351867682603929473136,2870237351867682618300819738⟩,⟨15863956023565484563469697058,15863956023565484578099645893⟩⟩,⟨⟨2968178305054376168596045169,2968178305054376182973733882⟩,⟨15901998566981822785000519610,15901998566981822799635660862⟩⟩,⟨⟨3066022761912183575081166743,3066022761912183589462875429⟩,⟨15937644554877363136876997533,15937644554877363151515084582⟩⟩,⟨⟨3163736978953513801214659631,3163736978953513815598334764⟩,⟨15971003696737210703397604800,15971003696737210718036659199⟩⟩,⟨⟨3261243047971253814305790371,3261243047971253828689031929⟩,⟨16001956428036152246458078035,16001956428036152261095283488⟩⟩,⟨⟨3358502176630126845642128939,3358502176630126860022851326⟩,⟨16030582551723848845574426606,16030582551723848860207733908⟩⟩,⟨⟨3455441305937765934841207224,3455441305937765949217018077⟩,⟨16056793715426502895653444143,16056793715426502910280101623⟩⟩,⟨⟨3552016028125640372408457571,3552016028125640386777221760⟩,⟨16080639825444260639850046202,16080639825444260654467719659⟩⟩,⟨⟨3648158977317992708283411907,3648158977317992722642781114⟩,⟨16102063800480165312023167331,16102063800480165326629207463⟩⟩,⟨⟨3743819557812891022493312287,3743819557812891036841035854⟩,⟨16121085622507949032635790220,16121085622507949047227450608⟩⟩] +lemma amp1_01_7_eq : ∀ k : Fin 16, amp1_0Expr 1 7 k = amp1_01_7 k := by decide +kernel +noncomputable def amp1_01_8 : Fin 16 → CBox := ![⟨⟨3838936948354641364027592539,3838936948354641378361826707⟩,⟨16137679577051435063117967364,16137679577051435077694790408⟩⟩,⟨⟨3933453785754504363645489094,3933453785754504377964582189⟩,⟨16151835656664655962966513608,16151835656664655977528082748⟩⟩,⟨⟨4027316652971965577618335923,4027316652971965591919977649⟩,⟨16163559646081355352579376820,16163559646081355367122957755⟩⟩,⟨⟨4120460831554768154115285615,4120460831554768168397289110⟩,⟨16172811445893734318956820394,16172811445893734333479829646⟩⟩,⟨⟨4212841176887782019469633207,4212841176887782033729789046⟩,⟨16179628509085138213730113480,16179628509085138228230256313⟩⟩,⟨⟨4304385018046793802593585175,4304385018046793816829700653⟩,⟨16183940504084139268428761316,16183940504084139282903388679⟩⟩,⟨⟨4395056360232925790319843759,4395056360232925804529827998⟩,⟨16185816757998551633560030578,16185816757998551648007174449⟩⟩,⟨⟨4484773972155641970556455082,4484773972155641984738084415⟩,⟨16185156528841388479494136997,16185156528841388493911109703⟩⟩,⟨⟨4573511896020794183628211282,4573511896020794197779418195⟩,⟨16182061260921426015781578454,16182061260921426030166510596⟩⟩,⟨⟨4661179720283377523002765875,4661179720283377537121526637⟩,⟨16176399584960796681491792061,16176399584960796695842616863⟩⟩,⟨⟨4747762421818147139848939883,4747762421818147153933194757⟩,⟨16168305343299959955551656446,16168305343299959969866355808⟩⟩,⟨⟨4833159775573701692768232660,4833159775573701706815602528⟩,⟨16157616283110355828229065207,16157616283110355842504431358⟩⟩,⟨⟨4917368601983236253780594692,4917368601983236267789467683⟩,⟨16144498964094147600554669201,16144498964094147614790183023⟩⟩,⟨⟨5000278214431857733952028785,5000278214431857747919964259⟩,⟨16128759953271801577799590352,16128759953271801591991777523⟩⟩,⟨⟨5081898197858587691274445296,5081898197858587705199998189⟩,⟨16110598886482400900646120598,16110598886482400914794797619⟩⟩,⟨⟨5162106739699877460843524154,5162106739699877474723956367⟩,⟨16089790812494670861190507834,16089790812494670875291340265⟩⟩] +lemma amp1_01_8_eq : ∀ k : Fin 16, amp1_0Expr 1 8 k = amp1_01_8 k := by decide +kernel +noncomputable def amp1_01_9 : Fin 16 → CBox := ![⟨⟨5240927123333318056639849161,5240927123333318070473315191⟩,⟨16066568842662290253277649367,16066568842662290267329198220⟩⟩,⟨⟨5318225727917871554588714149,5318225727917871568373059301⟩,⟨16040676126525502145349694321,16040676126525502159349398510⟩⟩,⟨⟨5394040483223651218427155190,5394040483223651232161677998⟩,⟨16012379692314264389980503319,16012379692314264403930147101⟩⟩,⟨⟨5468225258138892841814624957,5468225258138892855495938544⟩,⟨15981390364882744985355548509,15981390364882744999248940985⟩⟩,⟨⟨5540833591960248516754066178,5540833591960248530380439021⟩,⟨15948009574304220330936177206,15948009574304220344772036738⟩⟩,⟨⟨5611706119807830349322315684,5611706119807830362891941163⟩,⟨15911915348957411199241379342,15911915348957411213018130938⟩⟩,⟨⟨5680912970116970100921106632,5680912970116970114431778111⟩,⟨15873444051210859990676750314,15873444051210860004391604268⟩⟩,⟨⟨5748280797263719414371714190,5748280797263719427821620331⟩,⟨15832240392729996299231070402,15832240392729996312882474318⟩⟩,⟨⟨5813897316367642393926506309,5813897316367642407313617850⟩,⟨15788676246274872379934329072,15788676246274872393520034471⟩⟩,⟨⟨5877574428479661448933470542,5877574428479661462255526357⟩,⟨15742362435705703701716758342,15742362435705703715233881830⟩⟩,⟨⟨5939418452515192713920905508,5939418452515192727179631900⟩,⟨15693706972379097946582073092,15693706972379097960038189918⟩⟩,⟨⟨5999225735715103697778808850,5999225735715103710969055421⟩,⟨15642286167682489949228070931,15642286167682489962612617467⟩⟩,⟨⟨6057122239300989960230653364,6057122239300989973350834849⟩,⟨15588544852681940980378758939,15588544852681940993690529291⟩⟩,⟨⟨6112887925821387950175218226,6112887925821387963223061727⟩,⟨15532024144979888134119448523,15532024144979888147355523549⟩⟩,⟨⟨6166669460771249636254626557,6166669460771249649229071387⟩,⟨15473206432540371779164431063,15473206432540371792324791716⟩⟩,⟨⟨6218229558013077280169784610,6218229558013077293068244581⟩,⟨15411596897770927493805594108,15411596897770927506886588266⟩⟩] +lemma amp1_01_9_eq : ∀ k : Fin 16, amp1_0Expr 1 9 k = amp1_01_9 k := by decide +kernel +noncomputable def amp1_01_10 : Fin 16 → CBox := ![⟨⟨6267736675051758998822371229,6267736675051759011644457261⟩,⟨15347716282373875278374863145,15347716282373875291378107168⟩⟩,⟨⟨6314935376994437579610888765,6314935376994437592353652766⟩,⟨15281033028174715430816848543,15281033028174715443737702204⟩⟩,⟨⟨6360017029461777970815376794,6360017029461777983477306274⟩,⟨15212107091136628360673812743,15212107091136628373510968753⟩⟩,⟨⟨6402707109412398759796223193,6402707109412398772375762408⟩,⟨15140369298783346693458359974,15140369298783346706210650665⟩⟩,⟨⟨6443221037982585867838931101,6443221037982585880333946029⟩,⟨15066419750081994061936474317,15066419750081994074601118177⟩⟩,⟨⟨6481264221694148961218659754,6481264221694148973627678466⟩,⟨14989650711313712724696981459,14989650711313712737272907758⟩⟩,⟨⟨6517077319185573877604103975,6517077319185573889925559475⟩,⟨14910703426521076350818066423,14910703426521076363303703627⟩⟩,⟨⟨6550344637419011235561475603,6550344637419011247793244990⟩,⟨14828930575092458552393540791,14828930575092458564786352203⟩⟩,⟨⟨6581333292818818855739265924,6581333292818818867879802432⟩,⟨14745015627295552447125766526,14745015627295552459424271972⟩⟩,⟨⟨6609705412470190916179778096,6609705412470190928227092950⟩,⟨14658270565100727820588554671,14658270565100727832790434256⟩⟩,⟨⟨6635755833349495756758324698,6635755833349495768710689012⟩,⟨14569422251704258992665253858,14569422251704259004768497946⟩⟩,⟨⟨6659123366312126130582506000,6659123366312126142450437127⟩,⟨14477740769324397526827154175,14477740769324397538856724002⟩⟩,⟨⟨6680131878862065306025928883,6680131878862065317796456545⟩,⟨14383997633643022504419905295,14383997633643022516349105827⟩⟩,⟨⟨6698395667843274548117184017,6698395667843274559788617909⟩,⟨14287419725175177233876952928,14287419725175177245704086286⟩⟩,⟨⟨6714268993818673762312049982,6714268993818673773883012906⟩,⟨14188824572737963378526609363,14188824572737963390250308276⟩⟩,⟨⟨6727340374381965542076857411,6727340374381965553545763659⟩,⟨14087394444768172412734725800,14087394444768172424353553310⟩⟩] +lemma amp1_01_10_eq : ∀ k : Fin 16, amp1_0Expr 1 10 k = amp1_01_10 k := by decide +kernel +noncomputable def amp1_01_11 : Fin 16 → CBox := ![⟨⟨6737995884298379449561856318,6737995884298379460927379185⟩,⟨13983994354273938473400991281,13983994354273938484913717074⟩⟩,⟨⟨6745796922454165570838417177,6745796922454165582099058454⟩,⟨13877760428862221618379602467,13877760428862221629784848247⟩⟩,⟨⟨6751162864445427387102927258,6751162864445427398257039967⟩,⟨13769606757741895728206877959,13769606757741895739502611784⟩⟩,⟨⟨6753626569166360599465050447,6753626569166360610511655264⟩,⟨13658621669290438617930135895,13658621669290438629116099610⟩⟩,⟨⟨6753642272973576355976179972,6753642272973576366913368900⟩,⟨13545770053851676373905801337,13545770053851676384979455995⟩⟩,⟨⟨6750712783063954819125215266,6750712783063954829951511565⟩,⟨13430090639729840601692634892,13430090639729840612652624265⟩⟩,⟨⟨6745328838693188032968415793,6745328838693188043682362918⟩,⟨13312600989880204624380780975,13312600989880204635225379728⟩⟩,⟨⟨6736961583495307969141447664,6736961583495307979743415300⟩,⟨13192288274680628010061124470,13192288274680628020792638727⟩⟩,⟨⟨6726139994150162345786369980,6726139994150162356273326479⟩,⟨13070224763249050472086560427,13070224763249050482700194245⟩⟩,⟨⟨6712301827623456977667741567,6712301827623456988038172851⟩,⟨12945343936547491340992437984,12945343936547491351486701657⟩⟩,⟨⟨6696016136590598285170422399,6696016136590598295423807111⟩,⟨12818774983250052345402688754,12818774983250052355777568229⟩⟩,⟨⟨6676685444351346264474697223,6676685444351346274608695484⟩,⟨12689395370737127182256902888,12689395370737127192509387860⟩⟩,⟨⟨6654920835592035193651701615,6654920835592035203665587331⟩,⟨12558393620863077462771084221,12558393620863077472900778861⟩⟩,⟨⟨6630087614551658170456119476,6630087614551658180348187300⟩,⟨12424588648707795321461023112,12424588648707795331466060160⟩⟩,⟨⟨6602840986831060891531460854,6602840986831060901300577849⟩,⟨12289230946636141836703538779,12289230946636141846582639844⟩⟩,⟨⟨6572506897118696865943901354,6572506897118696875588143661⟩,⟨12151078098928051679224738997,12151078098928051688975696008⟩⟩] +lemma amp1_01_11_eq : ∀ k : Fin 16, amp1_0Expr 1 11 k = amp1_01_11 k := by decide +kernel +noncomputable def amp1_01_12 : Fin 16 → CBox := ![⟨⟨6539786911587757505080444764,6539786911587757514607152703⟩,⟨12011445456625111876104199201,12011445456625111885741350419⟩⟩,⟨⟨6503965300486807039144659030,6503965300486807048545271880⟩,⟨11869026225722510358069562712,11869026225722510367578311969⟩⟩,⟨⟨6465792401719725019191877300,6465792401719725028465609169⟩,⟨11725203786418223859437732603,11725203786418223868817327700⟩⟩,⟨⟨6424508299387027296171282359,6424508299387027305316622031⟩,⟨11578603616002317778358167577,11578603616002317787607121590⟩⟩,⟨⟨6380914709972157429794953189,6380914709972157438811156943⟩,⟨11430680613299923005723288070,11430680613299923014840934142⟩⟩,⟨⟨6334204796740548248987955430,6334204796740548257873671019⟩,⟨11279988833896564199811641523,11279988833896564208796704652⟩⟩,⟨⟨6285234485625599930393840030,6285234485625599939147993313⟩,⟨11128058546639388547329117688,11128058546639388556180231256⟩⟩,⟨⟨6233147030713438126284113912,6233147030713438134906256337⟩,⟨10973368303317580907598315111,10973368303317580916315851937⟩⟩,⟨⟨6178855655619645349905988111,6178855655619645358394364383⟩,⟨10817528006622082762643480421,10817528006622082771224902829⟩⟩,⟨⟨6121450427081258560132307007,6121450427081258568485662884⟩,⟨10658936178507251025474199287,10658936178507251033918374942⟩⟩,⟨⟨6061905251429144046823785681,6061905251429144055041453730⟩,⟨10499287091478479191701849119,10499287091478479200008035582⟩⟩,⟨⟨5999253397173679850076377438,5999253397173679858156716781⟩,⟨10336894202622095027647363856,10336894202622095035813830581⟩⟩,⟨⟨5934533182109937821880095837,5934533182109937829822246296⟩,⟨10173541433403865852530314584,10173541433403865860556001453⟩⟩,⟨⟨5866717081786807392413345735,5866717081786807400221132445⟩,⟨10007451554420563639305456084,10007451554420563647197907634⟩⟩,⟨⟨5796911954074452375767680146,5796911954074452383435811092⟩,⟨9840504043408363509449890318,9840504043408363517200338090⟩⟩,⟨⟨5724025041563033591887951082,5724025041563033599414927265⟩,⟨9670824683114651285428086086,9670824683114651293035045145⟩⟩] +lemma amp1_01_12_eq : ∀ k : Fin 16, amp1_0Expr 1 12 k = amp1_01_12 k := by decide +kernel +noncomputable def amp1_01_13 : Fin 16 → CBox := ![⟨⟨5649236338304962619068389071,5649236338304962626454061998⟩,⟨9500395145389383192930241710,9500395145389383200393775139⟩⟩,⟨⟨5571382894442604312271604648,5571382894442604319515099143⟩,⟨9327237131436671779751598935,9327237131436671787071188512⟩⟩,⟨⟨5491722985866013014223568318,5491722985866013021323688183⟩,⟨9153441999783160940826900986,9153441999783160948000719014⟩⟩,⟨⟨5409017900884565058908743458,5409017900884565065864286710⟩,⟨8976919346946421920193223459,8976919346946421927220286909⟩⟩,⟨⟨5324609992740546781741382577,5324609992740546788551774207⟩,⟨8799878717233028378242894545,8799878717233028385122422323⟩⟩,⟨⟨5237178497632684818561989913,5237178497632684825229217582⟩,⟨8620108481557367646191016670,8620108481557367652927225898⟩⟩,⟨⟨5148156415191852927365079363,5148156415191852933886134389⟩,⟨8439946062817799877831593892,8439946062817799884419569047⟩⟩,⟨⟨5056133780857354071343145329,5056133780857354077716379978⟩,⟨8257048179182731769665958602,8257048179182731776103991063⟩⟩,⟨⟨4962641737053548567418165306,4962641737053548573643749306⟩,⟨8073891251526697324595818065,8073891251526697330884245901⟩⟩,⟨⟨4866172939526522693683079521,4866172939526522699759783078⟩,⟨7887988351277483143661266996,7887988351277483149799006580⟩⟩,⟨⟨4768365290585439101872928726,4768365290585439107800614740⟩,⟨7701967735867611909444886153,7701967735867611915431647040⟩⟩,⟨⟨4667604639830390449433976668,4667604639830390455213316001⟩,⟨7513184939854719579523981654,7513184939854719585361817196⟩⟩,⟨⟨4565645632825386015920827209,4565645632825386021549382681⟩,⟨7324434986785622821683086051,7324434986785622827367979977⟩⟩,⟨⟨4460756361378034508926758863,4460756361378034514403148189⟩,⟨7132899667243141766252578712,7132899667243141771783254127⟩⟩,⟨⟨4354819879751416835867144527,4354819879751416841191987163⟩,⟨6941558269502167800757056821,6941558269502167806134310090⟩⟩,⟨⟨4245973685653209032252669462,4245973685653209037423941286⟩,⟨6747399771356555778303898846,6747399771356555783525496874⟩⟩] +lemma amp1_01_13_eq : ∀ k : Fin 16, amp1_0Expr 1 13 k = amp1_01_13 k := by decide +kernel +noncomputable def amp1_01_14 : Fin 16 → CBox := ![⟨⟨4136243001104005919804236075,4136243001104005924824313508⟩,⟨6553608416552974931309486659,6553608416552974936378996062⟩⟩,⟨⟨4023619536781975775492535831,4023619536781975780358034636⟩,⟨6356957724447011209807130003,6356957724447011214720125669⟩⟩,⟨⟨3910287079510016523810720818,3910287079510016528522581976⟩,⟨6160861601363098387420295331,6160861601363098392177927961⟩⟩,⟨⟨3794073373886888807019621575,3794073373886888811575365011⟩,⟨5961850931998991711042204102,5961850931998991715641592118⟩⟩,⟨⟨3677340538784555432128453009,3677340538784555436530673346⟩,⟨5763599117434207255799331269,5763599117434207260244174373⟩⟩,⟨⟨3557730332926508849520292286,3557730332926508853765710301⟩,⟨5562361406207675355372500156,5562361406207675359658665661⟩⟩,⟨⟨3437807348312835884777039013,3437807348312835888867668966⟩,⟨5362107171159859916978999126,5362107171159859921109136803⟩⟩,⟨⟨3315000313463928715923912187,3315000313463928719856603171⟩,⟨5158775404641295801372160414,5158775404641295805342441094⟩⟩,⟨⟨3192106213901878725623207513,3192106213901878729399231785⟩,⟨4956676701445121828485992820,4956676701445121832297854092⟩⟩,⟨⟨3066307001327064536018838879,3066307001327064539636910551⟩,⟨4751383017782577117301594043,4751383017782577120954126117⟩⟩,⟨⟨2940669771791629929079523611,2940669771791629932540051495⟩,⟨4547603248732651618879702792,4547603248732651622372846960⟩⟩,⟨⟨2812086809666075324851135783,2812086809666075328152674905⟩,⟨4340477676223076923659809081,4340477676223076926992526536⟩⟩,⟨⟨2683943814481260424338927427,2683943814481260427483050197⟩,⟨4135186914051686841796360189,4135186914051686844970296910⟩⟩,⟨⟨2552787704241245727507805544,2552787704241245730491333509⟩,⟨3926355522928479234225050013,3926355522928479237236552841⟩⟩,⟨⟨2422386601048110150647150442,2422386601048110153472541897⟩,⟨3719732484985923616657867970,3719732484985923619509774276⟩⟩,⟨⟨2288867844092956757217137060,2288867844092956759881692069⟩,⟨3509314543367761258775404277,3509314543367761261464944999⟩⟩] +lemma amp1_01_14_eq : ∀ k : Fin 16, amp1_0Expr 1 14 k = amp1_01_14 k := by decide +kernel +noncomputable def amp1_01_15 : Fin 16 → CBox := ![⟨⟨2156468356005109232675871254,2156468356005109235181608771⟩,⟨3301549883160338007244111410,3301549883160338009773308982⟩⟩,⟨⟨2020793891701713701303527227,2020793891701713703647483788⟩,⟨3089653229522617469119245059,3089653229522617471485039917⟩⟩,⟨⟨1886671179096717444842467050,1886671179096717447027164342⟩,⟨2880955267010668280012403586,2880955267010668282217345513⟩⟩,⟨⟨1749038661238240341456959242,1749038661238240343479397459⟩,⟨2667668272751396449234807962,2667668272751396451276011026⟩⟩,⟨⟨1613489887008430526711171605,1613489887008430528574301393⟩,⟨2458273575721273437993775416,2458273575721273439874196585⟩⟩,⟨⟨1474077279626811779355458974,1474077279626811781055422989⟩,⟨2243650032411292435451834602,2243650032411292437167523789⟩⟩,⟨⟨1337435151873991548564089653,1337435151873991550104544928⟩,⟨2033844578275865445711167449,2033844578275865447265785630⟩⟩,⟨⟨1196379539691389894353947871,1196379539691389895730611260⟩,⟨1817872262152470695152038098,1817872262152470696541385876⟩⟩,⟨⟨1059043066974508924447838728,1059043066974508925665248076⟩,⟨1608038679975637952398274252,1608038679975637953626863469⟩⟩,⟨⟨916390748773486729501755403,916390748773486730554280073⟩,⟨1390564433741657780080693514,1390564433741657781142842184⟩⟩,⟨⟨778906364526569702886712015,778906364526569703780599541⟩,⟨1181305541838949028000809023,1181305541838949028902815111⟩⟩,⟨⟨634468744668161749790592218,634468744668161750518237054⟩,⟨961817692572005301476634439,961817692572005302210847689⟩⟩,⟨⟨497802445934328672655569484,497802445934328673226068295⟩,⟨754369343679912894522870088,754369343679912895098453850⟩⟩,⟨⟨350580594428963539744008930,350580594428963540145561263⟩,⟨531126854482823631895190308,531126854482823632300275441⟩⟩,⟨⟨217517133608356368431036672,217517133608356368679823165⟩,⟨329477776279697421880459469,329477776279697422131286036⟩⟩,⟨⟨61803751110521223882213066,61803751110521223952714811⟩,⟨93607064644523401942558711,93607064644523402013548019⟩⟩] +lemma amp1_01_15_eq : ∀ k : Fin 16, amp1_0Expr 1 15 k = amp1_01_15 k := by decide +kernel +noncomputable def amp1_01 : Fin 16 → Fin 16 → CBox := ![amp1_01_0,amp1_01_1,amp1_01_2,amp1_01_3,amp1_01_4,amp1_01_5,amp1_01_6,amp1_01_7,amp1_01_8,amp1_01_9,amp1_01_10,amp1_01_11,amp1_01_12,amp1_01_13,amp1_01_14,amp1_01_15] +lemma amp1_01_eq (i k : Fin 16) : amp1_0Expr 1 i k = amp1_01 i k := by + fin_cases i + · exact amp1_01_0_eq k + · exact amp1_01_1_eq k + · exact amp1_01_2_eq k + · exact amp1_01_3_eq k + · exact amp1_01_4_eq k + · exact amp1_01_5_eq k + · exact amp1_01_6_eq k + · exact amp1_01_7_eq k + · exact amp1_01_8_eq k + · exact amp1_01_9_eq k + · exact amp1_01_10_eq k + · exact amp1_01_11_eq k + · exact amp1_01_12_eq k + · exact amp1_01_13_eq k + · exact amp1_01_14_eq k + · exact amp1_01_15_eq k +noncomputable def amp1_02_0 : Fin 16 → CBox := ![⟨⟨3879958785275112038377508,3879958785275112120368229⟩,⟨(-122567471280363286433007116),(-122567471280363286345790498)⟩⟩,⟨⟨13650175150687428798531353,13650175150687429087161918⟩,⟨(-431364070668856703134079243),(-431364070668856702825847264)⟩⟩,⟨⟨21983523651551168359372197,21983523651551168824683819⟩,⟨(-695214108876785738312947195),(-695214108876785737815119313)⟩⟩,⟨⟨31179044355557077368065917,31179044355557078028967751⟩,⟨(-987092899012678169419573390),(-987092899012678168712248762)⟩⟩,⟨⟨39677398895630803493969281,39677398895630804336632899⟩,⟨(-1257973829753348145944472929),(-1257973829753348145042281530)⟩⟩,⟨⟨48615544208752414812181782,48615544208752415847155897⟩,⟨(-1544176903888298843621928285),(-1544176903888298842513681363)⟩⟩,⟨⟨57063171561483148563097024,57063171561483149781428436⟩,⟨(-1816489744758606940432697251),(-1816489744758606939127871433)⟩⟩,⟨⟨65765911859849136301689746,65765911859849137710579818⟩,⟨(-2098922128909745106983859577),(-2098922128909745105474816836)⟩⟩,⟨⟨74061576839334821925915480,74061576839334823518678918⟩,⟨(-2370675397458598664443874599),(-2370675397458598662737707000)⟩⟩,⟨⟨82500375771706863140678145,82500375771706864922689750⟩,⟨(-2649635766322934327767648858),(-2649635766322934325858957262)⟩⟩,⟨⟨90569617020491862860902517,90569617020491864826783519⟩,⟨(-2919670857096353626569598523),(-2919670857096353624463653577)⟩⟩,⟨⟨98701682743287779877127597,98701682743287782031102900⟩,⟨(-3194992965302262005868784534),(-3194992965302262003561255203)⟩⟩,⟨⟨106479847507503672027857403,106479847507503674365351747⟩,⟨(-3462444674511776430659805462),(-3462444674511776428155723333)⟩⟩,⟨⟨114257301548440445218075030,114257301548440447742503446⟩,⟨(-3733783376039664087169019792),(-3733783376039664084464944965)⟩⟩,⟨⟨121684572072040859959215623,121684572072040862666587091⟩,⟨(-3997919240462884169005490567),(-3997919240462884166105133636)⟩⟩,⟨⟨129057702025783011855271548,129057702025783014748398883⟩,⟨(-4264849685296952061738296091),(-4264849685296952058638743346)⟩⟩] +lemma amp1_02_0_eq : ∀ k : Fin 16, amp1_0Expr 2 0 k = amp1_02_0 k := by decide +kernel +noncomputable def amp1_02_1 : Fin 16 → CBox := ![⟨⟨136077282776195069778110576,136077282776195072853382942⟩,⟨(-4525009209521115847032431870),(-4525009209521115843737676972)⟩⟩,⟨⟨142995990074842381641231875,142995990074842384900981115⟩,⟨(-4787069085461776977243489921),(-4787069085461776973751296191)⟩⟩,⟨⟨149553373702972238196462973,149553373702972241637375981⟩,⟨(-5042637101134134527081357296),(-5042637101134134523395379375)⟩⟩,⟨⟨155967942045822866771083452,155967942045822870395146830⟩,⟨(-5299347482185625022177158645),(-5299347482185625018294128684)⟩⟩,⟨⟨162010611149165402228216138,162010611149165406032299269⟩,⟨(-5549741340571017131079205641),(-5549741340571017127003954547)⟩⟩,⟨⟨167872178600500610727004375,167872178600500614712733583⟩,⟨(-5800618248161341848620576215),(-5800618248161341844351368762)⟩⟩,⟨⟨173349505411826659282935112,173349505411826663447443213⟩,⟨(-6045281341110323434097005328),(-6045281341110323429635358760)⟩⟩,⟨⟨178610391771038572707606883,178610391771038577052186051⟩,⟨(-6289842815143717970477863881),(-6289842815143717965824235342)⟩⟩,⟨⟨183473635416527253782452984,183473635416527258304368197⟩,⟨(-6528241263088992430195963175),(-6528241263088992425351750046)⟩⟩,⟨⟨188087591943334410475919343,188087591943334415176279315⟩,⟨(-6766012069971473229390515251),(-6766012069971473224354285499)⟩⟩,⟨⟨192289946439909148061483505,192289946439909152937550279⟩,⟨(-6997633106004553573000699633),(-6997633106004553567777562133)⟩⟩,⟨⟨196212360252700209927743237,196212360252700214980456559⟩,⟨(-7228148112506377877290143816),(-7228148112506377871877162288)⟩⟩,⟨⟨199709029546385544619604791,199709029546385549846296975⟩,⟨(-7452499421993761631562274383),(-7452499421993761625964952208)⟩⟩,⟨⟨202897099326568412720663285,202897099326568418122117425⟩,⟨(-7675306168153303120791084215),(-7675306168153303115005198140)⟩⟩,⟨⟨205645386537749176360271779,205645386537749181933923925⟩,⟨(-7891915786249052717100371927),(-7891915786249052711129874863)⟩⟩,⟨⟨208058278551216333610571074,208058278551216339356944586⟩,⟨(-8106576549529889636543356197),(-8106576549529889630387243919)⟩⟩] +lemma amp1_02_1_eq : ∀ k : Fin 16, amp1_0Expr 2 1 k = amp1_02_1 k := by decide +kernel +noncomputable def amp1_02_2 : Fin 16 → CBox := ![⟨⟨210017682054448930997934365,210017682054448936914466462⟩,⟨(-8314993091186655489039483254),(-8314993091186655482703626783)⟩⟩,⟨⟨211616671566013947484324930,211616671566013953571456080⟩,⟨(-8521086609528128281173109986),(-8521086609528128274653532711)⟩⟩,⟨⟨212748983439329024696918971,212748983439329030952191528⟩,⟨(-8720879698151552971844698536),(-8720879698151552965144578735)⟩⟩,⟨⟨213497584459482971072750434,213497584459482977496369554⟩,⟨(-8918002651777658869988689511),(-8918002651777658863107505520)⟩⟩,⟨⟨213766988463633257474124054,213766988463633264063687474⟩,⟨(-9108763463709258359684144995),(-9108763463709258352623934397)⟩⟩,⟨⟨213631073557620227323525443,213631073557620234078966488⟩,⟨(-9296531777052657535926294395),(-9296531777052657528692367918)⟩⟩,⟨⟨213004240754904453051278447,213004240754904459970310323⟩,⟨(-9477873648727356634691962333),(-9477873648727356627282326590)⟩⟩,⟨⟨211952151935659410950469799,211952151935659418033002718⟩,⟨(-9655923651121575524514048928),(-9655923651121575516929528619)⟩⟩,⟨⟨210398332634527916295306862,210398332634527923538977793⟩,⟨(-9827482713622402164028541376),(-9827482713622402156270977810)⟩⟩,⟨⟨208400983934442232867338259,208400983934442240271953541⟩,⟨(-9995472183599167428698646352),(-9995472183599167420768121727)⟩⟩,⟨⟨205892095009582895509429703,205892095009582903072618872⟩,⟨(-10156908000462491393231218366),(-10156908000462491385130329123)⟩⟩,⟨⟨202923067063906284656274952,202923067063906292377608790⟩,⟨(-10314517109853438205472512705),(-10314517109853438197207529259)⟩⟩,⟨⟨199433773939111559257426715,199433773939111567134680067⟩,⟨(-10465513301118362375637087223),(-10465513301118362367203653128)⟩⟩,⟨⟨195469400750658442736522897,195469400750658450769254604⟩,⟨(-10612445469636159680041860124),(-10612445469636159671441407629)⟩⟩,⟨⟨190977193492842954831099793,190977193492842963016961735⟩,⟨(-10752710309841076392891851244),(-10752710309841076384126160625)⟩⟩,⟨⟨185996641445891656368988277,185996641445891664707418031⟩,⟨(-10888692977215860970226199826),(-10888692977215860961297914961)⟩⟩] +lemma amp1_02_2_eq : ∀ k : Fin 16, amp1_0Expr 2 2 k = amp1_02_2 k := by decide +kernel +noncomputable def amp1_02_3 : Fin 16 → CBox := ![⟨⟨180481904531985215954163878,180481904531985224442821780⟩,⟨(-11017959958234980205272591651),(-11017959958234980196182977618)⟩⟩,⟨⟨174467243660505011750099664,174467243660505020388364443⟩,⟨(-11142745278603371183241219091),(-11142745278603371173990749657)⟩⟩,⟨⟨167913319061886690753072223,167913319061886699538580910⟩,⟨(-11260773630433533244098416554),(-11260773630433533234689474758)⟩⟩,⟨⟨160849586539891015398823990,160849586539891024330721767⟩,⟨(-11374139092090506453020048361),(-11374139092090506443463015340)⟩⟩,⟨⟨153242829832196979990026726,153242829832196989066095860⟩,⟨(-11480714256280876630574792197),(-11480714256280876620861916356)⟩⟩,⟨⟨145118085633601577140586542,145118085633601586360006656⟩,⟨(-11582463228841943747390206339),(-11582463228841943737523251499)⟩⟩,⟨⟨136447914889822788118105967,136447914889822797478499886⟩,⟨(-11677397280418556215698577158),(-11677397280418556205680211141)⟩⟩,⟨⟨127253289556255327748156677,127253289556255337248626523⟩,⟨(-11767359490730520557060686584),(-11767359490730520546892324110)⟩⟩,⟨⟨117512226822329394170612484,117512226822329403808781333⟩,⟨(-11850491505340563950491739893),(-11850491505340563940175409672)⟩⟩,⟨⟨107241961276348509207967457,107241961276348518982840533⟩,⟨(-11928523443012722034475019644),(-11928523443012722024014056609)⟩⟩,⟨⟨96425666463738809400434529,96425666463738819309642877⟩,⟨(-11999719806689291510675780181),(-11999719806689291500070585225)⟩⟩,⟨⟨85077143809515948339385781,85077143809515958381870804⟩,⟨(-12065705059819838062355851496),(-12065705059819838051608509273)⟩⟩,⟨⟨73184440870410263030871777,73184440870410273204238664⟩,⟨(-12124859719306100568866814567),(-12124859719306100557979514536)⟩⟩,⟨⟨60758210132504836907572039,60758210132504847210695628⟩,⟨(-12178709240801132347438461261),(-12178709240801132336412538137)⟩⟩,⟨⟨47791105411493691018045747,47791105411493701448520870⟩,⟨(-12225743892813659150056450436),(-12225743892813659138894313891)⟩⟩,⟨⟨34290897173801398452342094,34290897173801409008972656⟩,⟨(-12267396197604605608271208649),(-12267396197604605596974297548)⟩⟩] +lemma amp1_02_3_eq : ∀ k : Fin 16, amp1_0Expr 2 3 k = amp1_02_3 k := by decide +kernel +noncomputable def amp1_02_4 : Fin 16 → CBox := ![⟨⟨20254589856050157265942233,20254589856050167946291705⟩,⟨(-12302260415786548488745316985),(-12302260415786548477329330040)⟩⟩,⟨⟨5687323776543072962760346,5687323776543083765604514⟩,⟨(-12331681709222448392738657679),(-12331681709222448381189648201)⟩⟩,⟨⟨(-9409791622879204916035277),(-9409791622879193992836570)⟩,⟨(-12354353007857352986794986853),(-12354353007857352975116123372)⟩⟩,⟨⟨(-25034007430938003922260126),(-25034007430937992879840270)⟩,⟨(-12371537245564442609603699559),(-12371537245564442597796974730)⟩⟩,⟨⟨(-41180346568378015739101268),(-41180346568378004579870116)⟩,⟨(-12382021079404164398202845411),(-12382021079404164386271075170)⟩⟩,⟨⟨(-57848224281887259376391650),(-57848224281887248101713505)⟩,⟨(-12386989958954766632542134433),(-12386989958954766620486431109)⟩⟩,⟨⟨(-75029026486201871417547731),(-75029026486201860029845649)⟩,⟨(-12385319658769618638657525506),(-12385319658769618626481786582)⟩⟩,⟨⟨(-92724115420509251632605746),(-92724115420509240133300915)⟩,⟨(-12378122543576607845050365563),(-12378122543576607832755347966)⟩⟩,⟨⟨(-110921465181059587890795874),(-110921465181059576282310711)⟩,⟨(-12364359187269234986996028219),(-12364359187269234974584180521)⟩⟩,⟨⟨(-129624176699714377293269782),(-129624176699714365577121033)⟩,⟨(-12345072963214964901322898334),(-12345072963214964888799439528)⟩⟩,⟨⟨(-148817033106942340245799287),(-148817033106942328424381627)⟩,⟨(-12319305182556303639187393749),(-12319305182556303626551203309)⟩⟩,⟨⟨(-168504673533636032552958996),(-168504673533636020627813901)⟩,⟨(-12288034047971003671264090825),(-12288034047971003658517544462)⟩⟩,⟨⟨(-188668907616950593195463814),(-188668907616950581169022814)⟩,⟨(-12250377771220481943394149836),(-12250377771220481930539566382)⟩⟩,⟨⟨(-209315719072238101113195473),(-209315719072238088987063812)⟩,⟨(-12207252960941082873027917624),(-12207252960941082860068361839)⟩⟩,⟨⟨(-230424158959427080213455651),(-230424158959427067990052092)⟩,⟨(-12157851091806403302539471348),(-12157851091806403289476266525)⟩⟩,⟨⟨(-252001368026594224731445919),(-252001368026594212412418220)⟩,⟨(-12103030536169712871627213414),(-12103030536169712858462967238)⟩⟩] +lemma amp1_02_4_eq : ∀ k : Fin 16, amp1_0Expr 2 4 k = amp1_02_4 k := by decide +kernel +noncomputable def amp1_02_5 : Fin 16 → CBox := ![⟨⟨(-274023851828888854976733351),(-274023851828888842564520985)⟩,⟨(-12042052569745894422931085713),(-12042052569745894409668132285)⟩⟩,⟨⟨(-296499725935113395590693737),(-296499725935113383086974497)⟩,⟨(-11975720489497781959261599781),(-11975720489497781945901821955)⟩⟩,⟨⟨(-319403162242363061850326710),(-319403162242363049257540248)⟩,⟨(-11903362066001848891497694202),(-11903362066001848878043465329)⟩⟩,⟨⟨(-342743073623196827588659576),(-342743073623196814908529076)⟩,⟨(-11825728504234840791717488230),(-11825728504234840778170824323)⟩⟩,⟨⟨(-366491509474366953485994632),(-366491509474366940720967253)⟩,⟨(-11742210901522501522214567156),(-11742210901522501508578070783)⟩⟩,⟨⟨(-390658006571625135234868615),(-390658006571625122387384787)⟩,⟨(-11653511193886496336140931947),(-11653511193886496322436857586)⟩⟩,⟨⟨(-415212702747027497749434242),(-415212702747027484821260976)⟩,⟨(-11559080759900927545108147795),(-11559080759900927531317482556)⟩⟩,⟨⟨(-440165588872478698761634550),(-440165588872478685754586449)⟩,⟨(-11459574944464423395429040361),(-11459574944464423381554317076)⟩⟩,⟨⟨(-465485102335801779128593502),(-465485102335801766045133973)⟩,⟨(-11354502470925237574516140358),(-11354502470925237560560444372)⟩⟩,⟨⟨(-491181521415673110337608551),(-491181521415673097179572396)⟩,⟨(-11244474639196531156438202600),(-11244474639196531142403602741)⟩⟩,⟨⟨(-517221794716025929841920019),(-517221794716025916611777052)⟩,⟨(-11129054677989375503443907981),(-11129054677989375489333596057)⟩⟩,⟨⟨(-543616323914329984536811506),(-543616323914329971236436044)⟩,⟨(-11008812268737794923649171948),(-11008812268737794909465277904)⟩⟩,⟨⟨(-570330781341174631580191907),(-570330781341174618212001462)⟩,⟨(-10883362392611907642103803591),(-10883362392611907627848435553)⟩⟩,⟨⟨(-597375530343283822917145845),(-597375530343283809483088014)⟩,⟨(-10753235430257550917948407957),(-10753235430257550903624541340)⟩⟩,⟨⟨(-624715180610339846806249729),(-624715180610339833308738224)⟩,⟨(-10618095439580003776966322686),(-10618095439580003762576110869)⟩⟩,⟨⟨(-652359897332128809266712162),(-652359897332128795707666737)⟩,⟨(-10478435719046032937902771915),(-10478435719046032923448149615)⟩⟩] +lemma amp1_02_5_eq : ∀ k : Fin 16, amp1_0Expr 2 5 k = amp1_02_5 k := by decide +kernel +noncomputable def amp1_02_6 : Fin 16 → CBox := ![⟨⟨(-680273442550118238246547975),(-680273442550118224628526703)⟩,⟨(-10333966796497269510828318765),(-10333966796497269496313819808)⟩⟩,⟨⟨(-708465625022413967524975673),(-708465625022413953849793934)⟩,⟨(-10185147016540992948352752209),(-10185147016540992933778299638)⟩⟩,⟨⟨(-736899575704910801277799025),(-736899575704910787547965109)⟩,⟨(-10031730831766537427398203132),(-10031730831766537412767598569)⟩⟩,⟨⟨(-765584589867977196195765203),(-765584589867977182413184663)⟩,⟨(-9874143678923797029981613076),(-9874143678923797015295947546)⟩⟩,⟨⟨(-794483385699661734987906161),(-794483385699661721155049673)⟩,⟨(-9712181445281533223227682803),(-9712181445281533208490263587)⟩⟩,⟨⟨(-823604588828041792640901868),(-823604588828041778759747703)⟩,⟨(-9546238630672845000851658519),(-9546238630672844986064326007)⟩⟩,⟨⟨(-852910724910369627137808730),(-852910724910369613211233946)⟩,⟨(-9376150116333900739107404802),(-9376150116333900724277946470)⟩⟩,⟨⟨(-882409594374653807357386513),(-882409594374653793386925543)⟩,⟨(-9202281367689968078570302043),(-9202281367689968063695256629)⟩⟩,⟨⟨(-912063752650362541332191318),(-912063752650362527320297747)⟩,⟨(-9024503863463823825219024302),(-9024503863463823810301611783)⟩⟩,⟨⟨(-941880019709382450061710619),(-941880019709382436010453908)⟩,⟨(-8843155874832078388243910833),(-8843155874832078373286557892)⟩⟩,⟨⟨(-971821205254406145360718097),(-971821205254406131272461910)⟩,⟨(-8658143121192879042053063613),(-8658143121192879027058162146)⟩⟩,⟨⟨(-1001892993559003067387179123),(-1001892993559003053264046443)⟩,⟨(-8469778462885265649525346522),(-8469778462885265634495615837)⟩⟩,⟨⟨(-1032058675418273699367529595),(-1032058675418273685211874640)⟩,⟨(-8277999538776276716178701283),(-8277999538776276701116550975)⟩⟩,⟨⟨(-1062322643896193748852016890),(-1062322643896193734665877136)⟩,⟨(-8083095530211274987284448870),(-8083095530211274972191761274)⟩⟩,⟨⟨(-1092648900128508002922928347),(-1092648900128507988708948441)⟩,⟨(-7885033706297814522895070137),(-7885033706297814507776518938)⟩⟩,⟨⟨(-1123040389909159617484385754),(-1123040389909159603244413200)⟩,⟨(-7684081254476398351835438248),(-7684081254476398336691373422)⟩⟩] +lemma amp1_02_6_eq : ∀ k : Fin 16, amp1_0Expr 2 6 k = amp1_02_6 k := by decide +kernel +noncomputable def amp1_02_7 : Fin 16 → CBox := ![⟨⟨(-1153462056495804001298700870),(-1153462056495803987035124252)⟩,⟨(-7480232813604224353097040951),(-7480232813604224337930342960)⟩⟩,⟨⟨(-1183915241523606801269645927),(-1183915241523606786984529204)⟩,⟨(-7273735220039842627576608889),(-7273735220039842612389217378)⟩⟩,⟨⟨(-1214366064785788516299765225),(-1214366064785788501995609423)⟩,⟨(-7064608247735718456669646736),(-7064608247735718441465148845)⟩⟩,⟨⟨(-1244814105761670554552365002),(-1244814105761670540231153345)⟩,⟨(-6853079986732202824437854909),(-6853079986732202809217647027)⟩⟩,⟨⟨(-1275226897923018343951133658),(-1275226897923018329615293579)⟩,⟨(-6639193134656046175141570076),(-6639193134656046159908822138)⟩⟩,⟨⟨(-1305602099205304587777766794),(-1305602099205304573429301904)⟩,⟨(-6423158605894403155790354402),(-6423158605894403140546611783)⟩⟩,⟨⟨(-1335908896727803493483410098),(-1335908896727803479124705704)⟩,⟨(-6205039831217902900501786954),(-6205039831217902885250029996)⟩⟩,⟨⟨(-1366142865816302827275284927),(-1366142865816302812908471720)⟩,⟨(-5985032089673039411634531051),(-5985032089673039396376928345)⟩⟩,⟨⟨(-1396275090131028167036742088),(-1396275090131028152664098361)⟩,⟨(-5763217373417767346475965349),(-5763217373417767331215051353)⟩⟩,⟨⟨(-1426298899351587792399091238),(-1426298899351587778022730611)⟩,⟨(-5539776839679163592261402218),(-5539776839679163576999241273)⟩⟩,⟨⟨(-1456187519599523437601897565),(-1456187519599523423224124227)⟩,⟨(-5314808887097895782836044627),(-5314808887097895767575317703)⟩⟩,⟨⟨(-1485931869600694450395991280),(-1485931869600694436018934186)⟩,⟨(-5088482041213931499008321688),(-5088482041213931483751148901)⟩⟩,⟨⟨(-1515507566993773335055523832),(-1515507566993773320681467454)⟩,⟨(-4860908967342022023443104214),(-4860908967342022008192141041)⟩⟩,⟨⟨(-1544902951662533289474967584),(-1544902951662533275106066942)⟩,⟨(-4632247029345956292148446528),(-4632247029345956276905849125)⟩⟩,⟨⟨(-1574096285070836606926609555),(-1574096285070836592565116583)⟩,⟨(-4402621032885085140724166388),(-4402621032885085125492477316)⟩⟩,⟨⟨(-1603073157470555460134849135),(-1603073157470555445782967430)⟩,⟨(-4172178633191482125973394500),(-4172178633191482110754885553)⟩⟩] +lemma amp1_02_7_eq : ∀ k : Fin 16, amp1_0Expr 2 7 k = amp1_02_7 k := by decide +kernel +noncomputable def amp1_02_8 : Fin 16 → CBox := ![⟨⟨(-1631814729838361679756419125),(-1631814729838361665416166794)⟩,⟨(-3941054661915855034132121768),(-3941054661915855018928793627)⟩⟩,⟨⟨(-1660303668769385658563342511),(-1660303668769385644236675061)⟩,⟨(-3709388504799454377634686704),(-3709388504799454362448235445)⟩⟩,⟨⟨(-1688524293960479643847552671),(-1688524293960479629536678093)⟩,⟨(-3477322915694507885654097492),(-3477322915694507870487094094)⟩⟩,⟨⟨(-1716456170741849861228102986),(-1716456170741849846935201645)⟩,⟨(-3244990439079095955770945284),(-3244990439079095940625650341)⟩⟩,⟨⟨(-1744087040413192151744623626),(-1744087040413192137471841270)⟩,⟨(-3012539656434915116705990690),(-3012539656434915101584869678)⟩⟩,⟨⟨(-1771393185483115338182655956),(-1771393185483115323932175713)⟩,⟨(-2780097691227619026940529988),(-2780097691227619011845773844)⟩⟩,⟨⟨(-1798366035585636061061956482),(-1798366035585636046835859226)⟩,⟨(-2547816865913584006735273908),(-2547816865913583991669206102)⟩⟩,⟨⟨(-1824978404518385192282440253),(-1824978404518385178082917678)⟩,⟨(-2315820298120161847475540117),(-2315820298120161832440365639)⟩⟩,⟨⟨(-1851225681024307919453583294),(-1851225681024307905282685793)⟩,⟨(-2084261971263796427795915840),(-2084261971263796412793971630)⟩⟩,⟨⟨(-1877077019562249940769975096),(-1877077019562249926629813476)⟩,⟨(-1853262410112932285582461032),(-1853262410112932270615784805)⟩⟩,⟨⟨(-1902532043019967784260202924),(-1902532043019967770152808459)⟩,⟨(-1622975184394542511663996697),(-1622975184394542496734865589)⟩⟩,⟨⟨(-1927556050721390647341893936),(-1927556050721390633269514373)⟩,⟨(-1393519639683891595345593725),(-1393519639683891580456195443)⟩⟩,⟨⟨(-1952153179241507544731188048),(-1952153179241507530695653846)⟩,⟨(-1165046861439384307918431453),(-1165046861439384293070926477)⟩⟩,⟨⟨(-1976284671347843429313897419),(-1976284671347843415317478631)⟩,⟨(-937676433293190030840226536),(-937676433293190016036733632)⟩⟩,⟨⟨(-1999959461627553393980648867),(-1999959461627553380025093270)⟩,⟨(-711554888590493778636681153),(-711554888590493763879306618)⟩⟩,⟨⟨(-2023134528757460753717744367),(-2023134528757460739805431771)⟩,⟨(-486803472788073239104742090),(-486803472788073224395640628)⟩⟩] +lemma amp1_02_8_eq : ∀ k : Fin 16, amp1_0Expr 2 8 k = amp1_02_8 k := by decide +kernel +noncomputable def amp1_02_9 : Fin 16 → CBox := ![⟨⟨(-2045823894754960304082564880),(-2045823894754960290215376522)⟩,⟨(-263562100607910101195344082),(-263562100607910086536718572)⟩⟩,⟨⟨(-2067980060037523117507960906),(-2067980060037523103688043884)⟩,⟨(-41955112604255401340557552),(-41955112604255386734357572)⟩⟩,⟨⟨(-2089622428913628655553702586),(-2089622428913628641782475750)⟩,⟨177886261786289682699020503,177886261786289697256641772⟩⟩,⟨⟨(-2110698802178643207665050588),(-2110698802178643193945131465)⟩,⟨395833141072021068714882414,395833141072021083223203956⟩⟩,⟨⟨(-2131234267129205421907907640),(-2131234267129205408241089146)⟩,⟨611765049514521625710754089,611765049514521640167534055⟩⟩,⟨⟨(-2151171695779136637607845829),(-2151171695779136623996128955)⟩,⟨825547103119635303748972388,825547103119635318152192395⟩⟩,⟨⟨(-2170542165389195932739706070),(-2170542165389195919185044807)⟩,⟨1037071651746580050221727562,1037071651746580064569180907⟩⟩,⟨⟨(-2189283381584877546384323904),(-2189283381584877532888712760)⟩,⟨1246196328331549388223256498,1246196328331549402512878059⟩⟩,⟨⟨(-2207432725343774297339760592),(-2207432725343774283905057703)⟩,⟨1452828385619031172246680936,1452828385619031186476223820⟩⟩,⟨⟨(-2224922489144277988226933477),(-2224922489144277974855299763)⟩,⟨1656816470484195164040967769,1656816470484195178208332924⟩⟩,⟨⟨(-2241796678770103860502461741),(-2241796678770103847194313444)⟩,⟨1858084823329935693128898749,1858084823329935707233065733⟩⟩,⟨⟨(-2257981916876387037504349867),(-2257981916876387024262931668)⟩,⟨2056471575959897863912308364,2056471575959897877950297921⟩⟩,⟨⟨(-2273529163108222216729862114),(-2273529163108222203556812998)⟩,⟨2251920051020218702236645902,2251920051020218716206393914⟩⟩,⟨⟨(-2288359102870154514776152214),(-2288359102870154501673620902)⟩,⟨2444256306414078180045134113,2444256306414078193944510203⟩⟩,⟨⟨(-2302529987397462920807360632),(-2302529987397462907776765345)⟩,⟨2633444854018968525828580903,2633444854018968539655821333⟩⟩,⟨⟨(-2315956285754596635782423764),(-2315956285754596622826019577)⟩,⟨2819298085151350323448446372,2819298085151350337201225373⟩⟩] +lemma amp1_02_9_eq : ∀ k : Fin 16, amp1_0Expr 2 9 k = amp1_02_9 k := by decide +kernel +noncomputable def amp1_02_10 : Fin 16 → CBox := ![⟨⟨(-2328703887964928787637851947),(-2328703887964928774756778292)⟩,⟨3001803823208976888350418401,3001803823208976902027266725⟩⟩,⟨⟨(-2340680755002884021572210629),(-2340680755002884008768850793)⟩,⟨3180759162059836148833930795,3180759162059836162432420666⟩⟩,⟨⟨(-2351960773241646503737628384),(-2351960773241646491013514223)⟩,⟨3356177377460502019046334238,3356177377460502032564571243⟩⟩,⟨⟨(-2362445090058189691362469233),(-2362445090058189678719455131)⟩,⟨3527838592150593748861165760,3527838592150593762297318672⟩⟩,⟨⟨(-2372215957107662523782175407),(-2372215957107662511221991755)⟩,⟨3695783697285085554344442384,3695783697285085567696242536⟩⟩,⟨⟨(-2381167387695425266755780864),(-2381167387695425254280244273)⟩,⟨3859774122958531634413582111,3859774122958531647679315227⟩⟩,⟨⟨(-2389390380194425851492884328),(-2389390380194425839103488344)⟩,⟨4019880565076796300001339658,4019880565076796313179125799⟩⟩,⟨⟨(-2396771477060693177056343141),(-2396771477060693164755132168)⟩,⟨4175843986282035554808799238,4175843986282035567896486509⟩⟩,⟨⟨(-2403410818601281080095416695),(-2403410818601281067883843175)⟩,⟨4327767107534995240017725495,4327767107534995253013371534⟩⟩,⟨⟨(-2409187121859322929058733974),(-2409187121859322916938785544)⟩,⟨4475368589970234208442764878,4475368589970234221344361941⟩⟩,⟨⟨(-2414210079512698834586392356),(-2414210079512698822559558667)⟩,⟨4618785436100077377137763864,4618785436100077389943317501⟩⟩,⟨⟨(-2418350209193668536270587918),(-2418350209193668524334301580)⟩,⟨4757712105708804687945802508,4757712105708804700662146203⟩⟩,⟨⟨(-2421727183233931702796798901),(-2421727183233931690956605809)⟩,⟨4892322181481084229536714112,4892322181481084242153995466⟩⟩,⟨⟨(-2424202924583346359382653688),(-2424202924583346347640412872)⟩,⟨5022283949006873586755000764,5022283949006873599271417320⟩⟩,⟨⟨(-2425907531195030721258546145),(-2425907531195030709615555165)⟩,⟨5147809918611011608598497820,5147809918611011621012337491⟩⟩,⟨⟨(-2426693912733208580756943446),(-2426693912733208569215011731)⟩,⟨5268540147848284064838124018,5268540147848284077147615267⟩⟩] +lemma amp1_02_10_eq : ∀ k : Fin 16, amp1_0Expr 2 10 k = amp1_02_10 k := by decide +kernel +noncomputable def amp1_02_11 : Fin 16 → CBox := ![⟨⟨(-2426703059506517402994851093),(-2426703059506517391555221921)⟩,⟨5384728478631456726551966134,5384728478631456738755372369⟩⟩,⟨⟨(-2425778423647994279197295016),(-2425778423647994267861739476)⟩,⟨5495984596739625927860886695,5495984596739625939956597084⟩⟩,⟨⟨(-2424072377684404572357450951),(-2424072377684404561127296005)⟩,⟨5602606144782335839930100285,5602606144782335851916202233⟩⟩,⟨⟨(-2421418443727190691666203957),(-2421418443727190680543021994)⟩,⟨5704170193164292660186844973,5704170193164292672062090973⟩⟩,⟨⟨(-2417980892197620384729840294),(-2417980892197620373715014640)⟩,⟨5801020729354123579780915854,5801020729354123591543117162⟩⟩,⟨⟨(-2413582811509080767867177800),(-2413582811509080756962451622)⟩,⟨5892699853735738749992004915,5892699853735738761639559159⟩⟩,⟨⟨(-2408400914527138085742972006),(-2408400914527138074949532452)⟩,⟨5979600529148772279458280917,5979600529148772290989427882⟩⟩,⟨⟨(-2402247317769154109236843713),(-2402247317769154098555763950)⟩,⟨6061227407633339044876788330,6061227407633339056291533641⟩⟩,⟨⟨(-2395311753463174161258279186),(-2395311753463174150691269454)⟩,⟨6138025157190511919365833540,6138025157190511930660949732⟩⟩,⟨⟨(-2387394789714916369241899241),(-2387394789714916358790697754)⟩,⟨6209458365200048603374563665,6209458365200048614548440837⟩⟩,⟨⟨(-2378699791404616155800720560),(-2378699791404616145466107569)⟩,⟨6276026248728455316911743254,6276026248728455327963488530⟩⟩,⟨⟨(-2369015159056540804731214598),(-2369015159056540794515210235)⟩,⟨6337150559881646372453003973,6337150559881646383380169876⟩⟩,⟨⟨(-2358558544463308445598935097),(-2358558544463308435502352221)⟩,⟨6393388039878690535051624662,6393388039878690545853078712⟩⟩,⟨⟨(-2347105513770651340410138876),(-2347105513770651330434765196)⟩,⟨6444114661991905430082317559,6444114661991905440756257440⟩⟩,⟨⟨(-2334888706214894733613798850),(-2334888706214894723760554199)⟩,⟨6489947817563698268531737628,6489947817563698279076699147⟩⟩,⟨⟨(-2321670133412686584650161190),(-2321670133412686574920899822)⟩,⟨6530214563095713366226629046,6530214563095713376640528377⟩⟩] +lemma amp1_02_11_eq : ∀ k : Fin 16, amp1_0Expr 2 11 k = amp1_02_11 k := by decide +kernel +noncomputable def amp1_02_12 : Fin 16 → CBox := ![⟨⟨(-2307698174977533044631548057),(-2307698174977533035024156527)⟩,⟨6565596239720875892125388146,6565596239720875902415181636⟩⟩,⟨⟨(-2292720507871634206390838641),(-2292720507871634196909511056)⟩,⟨6595367630112066624915745315,6595367630112066635072846960⟩⟩,⟨⟨(-2277002064539917349583447574),(-2277002064539917340228900352)⟩,⟨6620277525069111311698764966,6620277525069111321722074361⟩⟩,⟨⟨(-2260275339499294545344656690),(-2260275339499294536118583965)⟩,⟨6639544828550017266360909967,6639544828550017276248771532⟩⟩,⟨⟨(-2242822698300631550641561038),(-2242822698300631541544620340)⟩,⟨6653989512042218751684432214,6653989512042218761435740328⟩⟩,⟨⟨(-2224360528584459046397042776),(-2224360528584459037430867878)⟩,⟨6662770714602010412185976613,6662770714602010421799296826⟩⟩,⟨⟨(-2205189586821923080816727416),(-2205189586821923071982050341)⟩,⟨6666783586820205317558242885,6666783586820205327032176135⟩⟩,⟨⟨(-2185009142180270257775699603),(-2185009142180270249073829785)⟩,⟨6665123296129450480901485353,6665123296129450490235508808⟩⟩,⟨⟨(-2164139388842547372628973371),(-2164139388842547364060834552)⟩,⟨6658764480713494465922708131,6658764480713494475114628154⟩⟩,⟨⟨(-2142261366330319255530581308),(-2142261366330319247097763208)⟩,⟨6646733762883445489590365192,6646733762883445498638867280⟩⟩,⟨⟨(-2119715855836485798193190373),(-2119715855836485789896191463)⟩,⟨6630089937481298242646159766,6630089937481298251550273495⟩⟩,⟨⟨(-2096164441775423776364490559),(-2096164441775423768205029962)⟩,⟨6607786086607936756754494702,6607786086607936765512418318⟩⟩,⟨⟨(-2071969760247240128475616634),(-2071969760247240120454210625)⟩,⟨6580970251493499817541882867,6580970251493499826152377423⟩⟩,⟨⟨(-2046772583258113388244832549),(-2046772583258113380361292492)⟩,⟨6548516491970916015277035068,6548516491970916023744440501⟩⟩,⟨⟨(-2020958807571332058362079685),(-2020958807571332050618421787)⟩,⟨6511667677976304901377890190,6511667677976304909696103128⟩⟩,⟨⟨(-1994146882575085238165095679),(-1994146882575085230562986445)⟩,⟨6469212799559737148433355558,6469212799559737156600728427⟩⟩] +lemma amp1_02_12_eq : ∀ k : Fin 16, amp1_0Expr 2 12 k = amp1_02_12 k := by decide +kernel +noncomputable def amp1_02_13 : Fin 16 → CBox := ![⟨⟨(-1966747532510034623434178745),(-1966747532510034615973785523)⟩,⟨6422495716916812293785107699,6422495716916812301801182679⟩⟩,⟨⟨(-1938355195558533561308853051),(-1938355195558533553991628707)⟩,⟨6370213642455437855524094805,6370213642455437863388006551⟩⟩,⟨⟨(-1909407179455943114800525828),(-1909407179455943107626951675)⟩,⟨6313818272542788762621318151,6313818272542788770331480581⟩⟩,⟨⟨(-1879472013194223011234199370),(-1879472013194223004205842517)⟩,⟨6251907558164086776602648590,6251907558164086784157756659⟩⟩,⟨⟨(-1849015567631871918211494725),(-1849015567631871911328563100)⟩,⟨6186048690645079586090062115,6186048690645079593489184903⟩⟩,⟨⟨(-1817578317105888933860176527),(-1817578317105888927123137168)⟩,⟨6114731957924170433098169109,6114731957924170440343775501⟩⟩,⟨⟨(-1785656941255495362996156238),(-1785656941255495356406005889)⟩,⟨6039648676377402697535113450,6039648676377402704623490095⟩⟩,⟨⟨(-1752761419649620965158136731),(-1752761419649620958716610418)⟩,⟨5959171975618640095443803002,5959171975618640102373134442⟩⟩,⟨⟨(-1719421805166915542279082583),(-1719421805166915535986010537)⟩,⟨5875127095561754902900129826,5875127095561754909670340967⟩⟩,⟨⟨(-1685114788864628456601858994),(-1685114788864628450458844316)⟩,⟨5785759198684294963443984465,5785759198684294970053814896⟩⟩,⟨⟨(-1650406746432396898718445925),(-1650406746432396892725362836)⟩,⟨5693038662963567903631815592,5693038662963567910080881344⟩⟩,⟨⟨(-1614737858512345291746696638),(-1614737858512345285904503207)⟩,⟨5595070283507472610584820686,5595070283507472616874089869⟩⟩,⟨⟨(-1578714242533121582243884814),(-1578714242533121576553181356)⟩,⟨5493982521505838010535043509,5493982521505838016661335327⟩⟩,⟨⟨(-1541735823394698531701589456),(-1541735823394698526164064237)⟩,⟨5387725457787697852863230658,5387725457787697858825094906⟩⟩,⟨⟨(-1504452456875062278042215959),(-1504452456875062272657340059)⟩,⟨5278600717010409433208535487,5278600717010409439006483706⟩⟩,⟨⟨(-1466219420058686704185113363),(-1466219420058686698954818967)⟩,⟨5164386912180486540431453731,5164386912180486546063226293⟩⟩] +lemma amp1_02_13_eq : ∀ k : Fin 16, amp1_0Expr 2 13 k = amp1_02_13 k := by decide +kernel +noncomputable def amp1_02_14 : Fin 16 → CBox := ![⟨⟨(-1427735022535455726438331350),(-1427735022535455721361402779)⟩,⟨5047576573863635236936516558,5047576573863635242404712074⟩⟩,⟨⟨(-1388304692841029171330470603),(-1388304692841029166409340937)⟩,⟨4925757083095201916757907491,4925757083095201922058670051⟩⟩,⟨⟨(-1348680815428673163016572323),(-1348680815428673158250438249)⟩,⟨4801632978135981773272365054,4801632978135981778406588597⟩⟩,⟨⟨(-1308112744935633600299912480),(-1308112744935633595690929203)⟩,⟨4672576827644525570788087020,4672576827644525575752962535⟩⟩,⟨⟨(-1267413718493796656133161946),(-1267413718493796651679861956)⟩,⟨4541530576380334127521938188,4541530576380334132320357122⟩⟩,⟨⟨(-1225769473690637198684320620),(-1225769473690637194389181041)⟩,⟨4405623490092420667016148277,4405623490092420671644360539⟩⟩,⟨⟨(-1184062379197272516415713878),(-1184062379197272512277365974)⟩,⟨4268065901036920914161623918,4268065901036920918621834354⟩⟩,⟨⟨(-1141405288495768022497176736),(-1141405288495768018518107858)⟩,⟨4125708856111166400258994832,4125708856111166404547581351⟩⟩,⟨⟨(-1098759963836750401011990611),(-1098759963836750397190971333)⟩,⟨3982069437942472595687918262,3982069437942472599806110369⟩⟩,⟨⟨(-1055154808079998942467984874),(-1055154808079998938806931324)⟩,⟨3833676985522832345941430478,3833676985522832349887982803⟩⟩,⟨⟨(-1011643914289791207977080326),(-1011643914289791204474931400)⟩,⟨3684403659605764697476471617,3684403659605764701251554800⟩⟩,⟨⟨(-967156531134783554108779017),(-967156531134783550767591217)⟩,⟨3530401903468807404845744588,3530401903468807408447900141⟩⟩,⟨⟨(-922855716952742064320220260),(-922855716952742061138381164)⟩,⟨3375961063325344166925602385,3375961063325344170356406780⟩⟩,⟨⟨(-877552468455697323191464513),(-877552468455697320171737389)⟩,⟨3216785108696359717806349862,3216785108696359721062223641⟩⟩,⟨⟨(-832540701852476257013702962),(-832540701852476254153995310)⟩,⟨3057662284067658627543319582,3057662284067658630626944860⟩⟩,⟨⟨(-786487712894928245619574146),(-786487712894928242922623868)⟩,⟨2893752813332920236237589003,2893752813332920239145998640⟩⟩] +lemma amp1_02_14_eq : ∀ k : Fin 16, amp1_0Expr 2 14 k = amp1_02_14 k := by decide +kernel +noncomputable def amp1_02_15 : Fin 16 → CBox := ![⟨⟨(-740847907532440089966640892),(-740847907532440087430293395)⟩,⟨2730454417871979513936330693,2730454417871979516671582097⟩⟩,⟨⟨(-694109896984862770750085690),(-694109896984862768377352884)⟩,⟨2562252729958608316907497136,2562252729958608319466368427⟩⟩,⟨⟨(-647930087912547944448288834),(-647930087912547942236581715)⟩,⟨2395309843151967920295083457,2395309843151967922680239218⟩⟩,⟨⟨(-600568424452937724636942253),(-600568424452937722589527622)⟩,⟨2223249984354933125130628741,2223249984354933127338837078⟩⟩,⟨⟨(-553944039744584080410586415),(-553944039744584078524389934)⟩,⟨2053226209596039719431849339,2053226209596039721466225550⟩⟩,⟨⟨(-506013192423768213909657250),(-506013192423768212188577134)⟩,⟨1877721100066514051720516681,1877721100066514053576848738⟩⟩,⟨⟨(-459051718781122085148919074),(-459051718781122083589184185)⟩,⟨1705229344880351672056984020,1705229344880351673739190128⟩⟩,⟨⟨(-410592008094929308190822613),(-410592008094929306796964344)⟩,⟨1526643086357059702724499744,1526643086357059704227942962⟩⟩,⟨⟨(-363423561467897670238954862),(-363423561467897669006244616)⟩,⟨1352384370115140401379124910,1352384370115140402708664971⟩⟩,⟨⟨(-314444059502586099229536055),(-314444059502586098163727486)⟩,⟨1170967778522800205513376004,1170967778522800206662883708⟩⟩,⟨⟨(-267249234881142829131169439),(-267249234881142828225910324)⟩,⟨995834519116790994138105587,995834519116790995114362773⟩⟩,⟨⟨(-217678350262436311363516077),(-217678350262436310626561117)⟩,⟨811540044256275284720664760,811540044256275285515372466⟩⟩,⟨⟨(-170781598208610637625384310),(-170781598208610637047481007)⟩,⟨636963890694916839732025250,636963890694916840355079264⟩⟩,⟨⟨(-120269695103812263457563588),(-120269695103812263050738192)⟩,⟨448708305135166574597497144,448708305135166575036032851⟩⟩,⟨⟨(-74619328860196489164187204),(-74619328860196488911932099)⟩,⟨278450898688109036885958105,278450898688109037157602305⟩⟩,⟨⟨(-21201542952788275774235175),(-21201542952788275702630515)⟩,⟨79124218132947008905935158,79124218132947008982881223⟩⟩] +lemma amp1_02_15_eq : ∀ k : Fin 16, amp1_0Expr 2 15 k = amp1_02_15 k := by decide +kernel +noncomputable def amp1_02 : Fin 16 → Fin 16 → CBox := ![amp1_02_0,amp1_02_1,amp1_02_2,amp1_02_3,amp1_02_4,amp1_02_5,amp1_02_6,amp1_02_7,amp1_02_8,amp1_02_9,amp1_02_10,amp1_02_11,amp1_02_12,amp1_02_13,amp1_02_14,amp1_02_15] +lemma amp1_02_eq (i k : Fin 16) : amp1_0Expr 2 i k = amp1_02 i k := by + fin_cases i + · exact amp1_02_0_eq k + · exact amp1_02_1_eq k + · exact amp1_02_2_eq k + · exact amp1_02_3_eq k + · exact amp1_02_4_eq k + · exact amp1_02_5_eq k + · exact amp1_02_6_eq k + · exact amp1_02_7_eq k + · exact amp1_02_8_eq k + · exact amp1_02_9_eq k + · exact amp1_02_10_eq k + · exact amp1_02_11_eq k + · exact amp1_02_12_eq k + · exact amp1_02_13_eq k + · exact amp1_02_14_eq k + · exact amp1_02_15_eq k +noncomputable def amp1_03_0 : Fin 16 → CBox := ![⟨⟨28961932684408956566125258,28961932684408956648992532⟩,⟨(-108088421629316623548183305),(-108088421629316623459893183)⟩⟩,⟨⟨101934636156411633697549988,101934636156411633989521445⟩,⟨(-380457469031610618313847872),(-380457469031610618001983861)⟩⟩,⟨⟨164303715798580050240568880,164303715798580050711461710⟩,⟨(-613334122835736609920672734),(-613334122835736609417099007)⟩⟩,⟨⟨233326121558913299028019351,233326121558913299696902148⟩,⟨(-871186651208288426570001556),(-871186651208288425854539000)⟩⟩,⟨⟨297426065127709466011671636,297426065127709466864588213⟩,⟨(-1110855805182812689556355749),(-1110855805182812688643819063)⟩⟩,⟨⟨365201167664663818558066351,365201167664663819605675772⟩,⟨(-1364502516451548233452574466),(-1364502516451548232331624546)⟩⟩,⟨⟨429755452535542680032427145,429755452535542681265695510⟩,⟨(-1606422611371462724536816320),(-1606422611371462723217043095)⟩⟩,⟨⟨496779687860134071241133740,496779687860134072667341055⟩,⟨(-1857937861212912763937059238),(-1857937861212912762410715609)⟩⟩,⟨⟨561363858858550299105813318,561363858858550300718213748⟩,⟨(-2100745591827982120665446987),(-2100745591827982118939701667)⟩⟩,⟨⟨627753677415993116085234673,627753677415993117889201206⟩,⟨(-2350783611667305758719218338),(-2350783611667305756788548680)⟩⟩,⟨⟨692139589723734900516206114,692139589723734902506406892⟩,⟨(-2593845958137972052063673261),(-2593845958137972049933456616)⟩⟩,⟨⟨757901026502040894587802078,757901026502040896768482767⟩,⟨(-2842646229294924351024745585),(-2842646229294924348690556972)⟩⟩,⟨⟨821929235447912045774135169,821929235447912048140646867⟩,⟨(-3085583556042871420061463918),(-3085583556042871417528356049)⟩⟩,⟨⟨887025356064341239402580850,887025356064341241958345988⟩,⟨(-3333221861124225947087246356),(-3333221861124225944351690456)⟩⟩,⟨⟨950567018378215206844214891,950567018378215209585326104⟩,⟨(-3575765080212056900559148709),(-3575765080212056897624943807)⟩⟩,⟨⟨1014941222716878723571847815,1014941222716878726501145367⟩,⟨(-3822239823595647444650875521),(-3822239823595647441515035095)⟩⟩] +lemma amp1_03_0_eq : ∀ k : Fin 16, amp1_0Expr 3 0 k = amp1_03_0 k := by decide +kernel +noncomputable def amp1_03_1 : Fin 16 → CBox := ![⟨⟨1077883602232748619705067808,1077883602232748622818883447⟩,⟨(-4064175658897576025866792760),(-4064175658897576022533314069)⟩⟩,⟨⟨1141469472398106270782708051,1141469472398106274083361969⟩,⟨(-4309443980893408081872218603),(-4309443980893408078338778869)⟩⟩,⟨⟨1203709513037336067994162272,1203709513037336071478293179⟩,⟨(-4550590350097117298862561809),(-4550590350097117295132816577)⟩⟩,⟨⟨1266435608730476309934153821,1266435608730476313604036266⟩,⟨(-4794585396694248918283154060),(-4794585396694248914353891350)⟩⟩,⟨⟨1327876778745353550465621362,1327876778745353554317784340⟩,⟨(-5034779014066831688602009350),(-5034779014066831684477918939)⟩⟩,⟨⟨1389669240966076207240696217,1389669240966076211276803271⟩,⟨(-5277419040692664110868877287),(-5277419040692664106548169494)⟩⟩,⟨⟨1450219875451213456307553556,1450219875451213460525058343⟩,⟨(-5516508625412449267111469189),(-5516508625412449262595804493)⟩⟩,⟨⟨1511003972326829345359082276,1511003972326829349758913329⟩,⟨(-5757702167580947126841545773),(-5757702167580947122131158107)⟩⟩,⟨⟨1570576367321974630942409472,1570576367321974635522152461⟩,⟨(-5995544472595421100262712392),(-5995544472595421095359128267)⟩⟩,⟨⟨1630277484998892582257087666,1630277484998892587017941996⟩,⟨(-6235193461909661495082647876),(-6235193461909661489984393652)⟩⟩,⟨⟨1688787395928877563825700778,1688787395928877568764438998⟩,⟨(-6471650828876508410654069026),(-6471650828876508405366069291)⟩⟩,⟨⟨1747331717944640687985543953,1747331717944640693103565727⟩,⟨(-6709652564294323394494629435),(-6709652564294323389014041623)⟩⟩,⟨⟨1804698087720239808370466235,1804698087720239813664509428⟩,⟨(-6944591354177976140644928113),(-6944591354177976134977051329)⟩⟩,⟨⟨1862013089146079479759612373,1862013089146079485231244300⟩,⟨(-7180839801288695679423502293),(-7180839801288695673564294536)⟩⟩,⟨⟨1918157912262776192744521319,1918157912262776198390904253⟩,⟨(-7414129352478748710613953024),(-7414129352478748704567263504)⟩⟩,⟨⟨1974172737953186971040787226,1974172737953186976862577722⟩,⟨(-7648516030942834537851012709),(-7648516030942834531615801990)⟩⟩] +lemma amp1_03_1_eq : ∀ k : Fin 16, amp1_0Expr 3 1 k = amp1_03_1 k := by decide +kernel +noncomputable def amp1_03_2 : Fin 16 → CBox := ![⟨⟨2029021007614158827972241092,2029021007614158833966170044⟩,⟨(-7880027948563344676317133733),(-7880027948563344669899077818)⟩⟩,⟨⟨2083666774454682874273392243,2083666774454682880440719772⟩,⟨(-8112442557927185204563793108),(-8112442557927185197959050147)⟩⟩,⟨⟨2137146481363943352843832936,2137146481363943359181976673⟩,⟨(-8342050218637644143153637850),(-8342050218637644136365327830)⟩⟩,⟨⟨2190356528382616218463802717,2190356528382616224973069697⟩,⟨(-8572381092874492158748221608),(-8572381092874492151775769065)⟩⟩,⟨⟨2242398691902886485610607760,2242398691902886492288718401⟩,⟨(-8799959294373126732679771119),(-8799959294373126725525196135)⟩⟩,⟨⟨2294108792999918949125877891,2294108792999918955971597818⟩,⟨(-9028093741442792104502219342),(-9028093741442792097170601750)⟩⟩,⟨⟨2344647512366173191644815123,2344647512366173198656873751⟩,⟨(-9253518451934735694631814933),(-9253518451934735687121279339)⟩⟩,⟨⟨2394796061039331725504071826,2394796061039331732682243122⟩,⟨(-9479343014527573368015384405),(-9479343014527573360326673107)⟩⟩,⟨⟨2443768578530119846331156864,2443768578530119853673239422⟩,⟨(-9702491193075080760767119178),(-9702491193075080752902049960)⟩⟩,⟨⟨2492296750695577595455143130,2492296750695577602961004410⟩,⟨(-9925891854410859261787603341),(-9925891854410859253746190044)⟩⟩,⟨⟨2539643521280938662476509837,2539643521280938670143770046⟩,⟨(-10146641322784137644840038454),(-10146641322784137636624832460)⟩⟩,⟨⟨2586495420234720876235450846,2586495420234720884062340860⟩,⟨(-10367503673603066749126022673),(-10367503673603066740743252746)⟩⟩,⟨⟨2632160183892715636698139021,2632160183892715644684024099⟩,⟨(-10585733026427970769446064951),(-10585733026427970760891322103)⟩⟩,⟨⟨2677282970138362623809899678,2677282970138362631954143144⟩,⟨(-10803942404318854572548960903),(-10803942404318854563823610729)⟩⟩,⟨⟨2721212824130579167229960418,2721212824130579175530396536⟩,⟨(-11019530948347429638445035404),(-11019530948347429629550789030)⟩⟩,⟨⟨2764556831933516495097524047,2764556831933516503553130739⟩,⟨(-11234972557258896388068511480),(-11234972557258896379007994672)⟩⟩] +lemma amp1_03_2_eq : ∀ k : Fin 16, amp1_0Expr 3 2 k = amp1_03_2 k := by decide +kernel +noncomputable def amp1_03_3 : Fin 16 → CBox := ![⟨⟨2806702301068682130899360173,2806702301068682139508102667⟩,⟨(-11447800273274370154348105267),(-11447800273274370145122497192)⟩⟩,⟨⟨2848221143020587923608901091,2848221143020587932370234846⟩,⟨(-11660359288828456109353093911),(-11660359288828456099962786309)⟩⟩,⟨⟨2888536246444014351435043542,2888536246444014360346650397⟩,⟨(-11870306811520720517346255449),(-11870306811520720507793563095)⟩⟩,⟨⟨2928186906929899217454901662,2928186906929899226513619203⟩,⟨(-12079868476215849084817813076),(-12079868476215849075113632544)⟩⟩,⟨⟨2966629220334579182292107312,2966629220334579191498216043⟩,⟨(-12286817088624293466475278978),(-12286817088624293456611224924)⟩⟩,⟨⟨3004372138528183201297206395,3004372138528183210649696266⟩,⟨(-12493266799941353461656027111),(-12493266799941353451633843723)⟩⟩,⟨⟨3040902850941148592665062626,3040902850941148602161535510⟩,⟨(-12697098439946643865627859145),(-12697098439946643855450159724)⟩⟩,⟨⟨3076701993770364264684912125,3076701993770364274324383624⟩,⟨(-12900321833607413842755985206),(-12900321833607413832424152750)⟩⟩,⟨⟨3111285958257693438771607340,3111285958257693448551841578⟩,⟨(-13100919110583140011186023191),(-13100919110583140000701969958)⟩⟩,⟨⟨3145108883654880788512281729,3145108883654880798431727816⟩,⟨(-13300802140657279553707851935),(-13300802140657279543075100798)⟩⟩,⟨⟨3177714661431659368868462026,3177714661431659378925306955⟩,⟨(-13498048360845440578563383602),(-13498048360845440567782038021)⟩⟩,⟨⟨3209532572096607501548710174,3209532572096607511741673964⟩,⟨(-13694477377996221575723423474),(-13694477377996221564795621711)⟩⟩,⟨⟨3240132469638297594730665423,3240132469638297605057459939⟩,⟨(-13888256577500092564351041136),(-13888256577500092553278860738)⟩⟩,⟨⟨3269920257482540571170764513,3269920257482540581630253285⟩,⟨(-14081118406356634804093271009),(-14081118406356634792878005742)⟩⟩,⟨⟨3298490356321137199143250479,3298490356321137209733081524⟩,⟨(-14271315390886446209205680396),(-14271315390886446197849649293)⟩⟩,⟨⟨3326226637723369590523230401,3326226637723369601242187894⟩,⟨(-14460497407301863538995502348),(-14460497407301863527500108291)⟩⟩] +lemma amp1_03_3_eq : ∀ k : Fin 16, amp1_0Expr 3 3 k = amp1_03_3 k := by decide +kernel +noncomputable def amp1_03_4 : Fin 16 → CBox := ![⟨⟨3352746816681966790253779767,3352746816681966801095885447⟩,⟨(-14646997797987563447462105131),(-14646997797987563435845474974)⟩⟩,⟨⟨3378413958659882562132571615,3378413958659882573100736881⟩,⟨(-14832388006767633051684858997),(-14832388006767633039930207849)⟩⟩,⟨⟨3402867908337385437937255754,3402867908337385449028915157⟩,⟨(-15015078291485974190547336678),(-15015078291485974178657836357)⟩⟩,⟨⟨3426452045727478392604048776,3426452045727478403817741006⟩,⟨(-15196565405037342938596946107),(-15196565405037342926574623211)⟩⟩,⟨⟨3448827275094380704872636770,3448827275094380716205885011⟩,⟨(-15375332994799783067961472256),(-15375332994799783055809090715)⟩⟩,⟨⟨3470318318825307788210948141,3470318318825307799662488822⟩,⟨(-15552806513040120888822450700),(-15552806513040120876540954539)⟩⟩,⟨⟨3490606153833979771082706546,3490606153833979782649752418⟩,⟨(-15727539803062231951796257875),(-15727539803062231939389781593)⟩⟩,⟨⟨3509997790378983399474899872,3509997790378983411156244989⟩,⟨(-15900890094849810599126182716),(-15900890094849810586595206274)⟩⟩,⟨⟨3528193364529409831842050270,3528193364529409843635311183⟩,⟨(-16071478529978340173729804166),(-16071478529978340161076614770)⟩⟩,⟨⟨3545483046627544266429868957,3545483046627544278332523577⟩,⟨(-16240596916249946041180158688),(-16240596916249946028411041804)⟩⟩,⟨⟨3561585283463094192783679325,3561585283463094204794358584⟩,⟨(-16406931060464956911269234409),(-16406931060464956898381828379)⟩⟩,⟨⟨3576774212206507248907380441,3576774212206507261024339429⟩,⟨(-16571709899214950271192150155),(-16571709899214950258188994196)⟩⟩,⟨⟨3590785799744958395916445255,3590785799744958408137330771⟩,⟨(-16733681508954972304875942212),(-16733681508954972291759130099)⟩⟩,⟨⟨3603878898139419239625024161,3603878898139419251947846447⟩,⟨(-16894014282141810017266076823),(-16894014282141810004039126954)⟩⟩,⟨⟨3615806255272725529791523380,3615806255272725542214218187⟩,⟨(-17051516383222202667602805122),(-17051516383222202654266440638)⟩⟩,⟨⟨3626812133390334594807469672,3626812133390334607328145142⟩,⟨(-17207297785649707781401046144),(-17207297785649707767958158555)⟩⟩] +lemma amp1_03_4_eq : ∀ k : Fin 16, amp1_0Expr 3 4 k = amp1_03_4 k := by decide +kernel +noncomputable def amp1_03_5 : Fin 16 → CBox := ![⟨⟨3636665368312970439604304582,3636665368312970452220598639⟩,⟨(-17360224753560355572373249970),(-17360224753560355558825928922)⟩⟩,⟨⟨3645596280169054789315367637,3645596280169054802025568714⟩,⟨(-17511350783747840150311757826),(-17511350783747840136661881835)⟩⟩,⟨⟨3653389140919529092920403978,3653389140919529105722137209⟩,⟨(-17659598427127333733710436507),(-17659598427127333719960135395)⟩⟩,⟨⟨3660260933219737811241462446,3660260933219737824132947056⟩,⟨(-17805966480154147999869125715),(-17805966480154147986020437752)⟩⟩,⟨⟨3666010750443287903766955417,3666010750443287916745748017⟩,⟨(-17949432127244847819138539406),(-17949432127244847805193903568)⟩⟩,⟨⟨3670842803361557937415181708,3670842803361557950473094721⟩,⟨(-18090941089530117505738427725),(-18090941089530117491731303247)⟩⟩,⟨⟨3674570425424286339453026754,3674570425424286352594369211⟩,⟨(-18229523677422811950357465443),(-18229523677422811936257204692)⟩⟩,⟨⟨3677385585587409286274982890,3677385585587409299497756358⟩,⟨(-18366074023379331825356130842),(-18366074023379331811165523919)⟩⟩,⟨⟨3679115306193341871303839394,3679115306193341884605449233⟩,⟨(-18499674189858254064826385557),(-18499674189858254050548601289)⟩⟩,⟨⟨3679939812063130913790667074,3679939812063130927169229195⟩,⟨(-18631168080340187713355783847),(-18631168080340187698992923330)⟩⟩,⟨⟨3679699290545943955853200549,3679699290545943969306078116⟩,⟨(-18759688258139469148269501305),(-18759688258139469133824974515)⟩⟩,⟨⟨3678562690405316116236197733,3678562690405316129761460503⟩,⟨(-18886029640586245505126620835),(-18886029640586245490602630821)⟩⟩,⟨⟨3676382864885864084645663672,3676382864885864098241037696⟩,⟨(-19009374153867873891087231786),(-19009374153867873876485336208)⟩⟩,⟨⟨3673317927650381341446981202,3673317927650381355110224811⟩,⟨(-19130468864031146362784644004),(-19130468864031146348108530235)⟩⟩,⟨⟨3669232921269698155510830642,3669232921269698169239655761⟩,⟨(-19248544026892494345816627082),(-19248544026892494331067939227)⟩⟩,⟨⟨3664275540361137512023173841,3664275540361137525815673938⟩,⟨(-19364299892018987423959809327),(-19364299892018987409140361272)⟩⟩] +lemma amp1_03_5_eq : ∀ k : Fin 16, amp1_0Expr 3 5 k = amp1_03_5 k := by decide +kernel +noncomputable def amp1_03_6 : Fin 16 → CBox := ![⟨⟨3658322560816306347732704911,3658322560816306361585767093⟩,⟨(-19477014108835248922053854436),(-19477014108835248907169654405)⟩⟩,⟨⟨3651511651349555838789045080,3651511651349555852701445980⟩,⟨(-19587341052165564399876870793),(-19587341052165564384926000836)⟩⟩,⟨⟨3643730883976759514150346236,3643730883976759528119224496⟩,⟨(-19694604919569198005824474877),(-19694604919569197990811660751)⟩⟩,⟨⟨3635108273525679631647808516,3635108273525679645671526841⟩,⟨(-19799415066001035729990514886),(-19799415066001035714915874922)⟩⟩,⟨⟨3625542768190859115584174682,3625542768190859129660053889⟩,⟨(-19901141476296742592240924967),(-19901141476296742577108237835)⟩⟩,⟨⟨3615153081412633106283509953,3615153081412633120409622543⟩,⟨(-20000349259050390001106053487),(-20000349259050389985916900382)⟩⟩,⟨⟨3603848633485493155749341007,3603848633485493169921276921⟩,⟨(-20096453504860393738824870421),(-20096453504860393723592756988)⟩⟩,⟨⟨3591739170896349730267829678,3591739170896349744485665608⟩,⟨(-20189975772974661185695068439),(-20189975772974661170410353980)⟩⟩,⟨⟨3578744196597950559779892965,3578744196597950574040986083⟩,⟨(-20280375652905229758455015567),(-20280375652905229743121380081)⟩⟩,⟨⟨3564964807805920705384963399,3564964807805920719687126962⟩,⟨(-20368131779383182053288488182),(-20368131779383182037908774950)⟩⟩,⟨⟨3550330214233771988007659527,3550330214233772002348572753⟩,⟨(-20452747704499536690286080853),(-20452747704499536674862227516)⟩⟩,⟨⟨3534933165946285983837279657,3534933165946285998214623922⟩,⟨(-20534659694915338562762755594),(-20534659694915338547298278147)⟩⟩,⟨⟨3518712216093701101580018859,3518712216093701115991479967⟩,⟨(-20613414795808417362311684150),(-20613414795808417346808524065)⟩⟩,⟨⟨3501752055229296065464208809,3501752055229296079907798800⟩,⟨(-20689407397179327211011090742),(-20689407397179327195470778456)⟩⟩,⟨⟨3484000228327755658772212182,3484000228327755673244630091⟩,⟨(-20762227631404382290911434847),(-20762227631404382275341839213)⟩⟩,⟨⟨3465533640571906324023903536,3465533640571906338523821981⟩,⟨(-20832228441125359869325510906),(-20832228441125359853724170541)⟩⟩] +lemma amp1_03_6_eq : ∀ k : Fin 16, amp1_0Expr 3 6 k = amp1_03_6 k := by decide +kernel +noncomputable def amp1_03_7 : Fin 16 → CBox := ![⟨⟨3446308488096305390962813305,3446308488096305405487734803⟩,⟨(-20899042700789127722397122997),(-20899042700789127706767188536)⟩⟩,⟨⟨3426394152251373877270558992,3426394152251373891818450912⟩,⟨(-20962982275421640060660513167),(-20962982275421640045003638655)⟩⟩,⟨⟨3405755149938270337357937382,3405755149938270351925953339⟩,⟨(-21023722494691886940251955286),(-21023722494691886924573561650)⟩⟩,⟨⟨3384453588426760859126233656,3384453588426760873712599625⟩,⟨(-21081534458393281328809619538),(-21081534458393281313109697919)⟩⟩,⟨⟨3362461984665090317323388433,3362461984665090331925460715⟩,⟨(-21136135720701933580417199244),(-21136135720701933564700030538)⟩⟩,⟨⟨3339835410553762043488693889,3339835410553762058104625112⟩,⟨(-21187756873077179759250110209),(-21187756873077179743516069040)⟩⟩,⟨⟨3316554071515918833450585317,3316554071515918848077815695⟩,⟨(-21236157517786041359386225884),(-21236157517786041343639207551)⟩⟩,⟨⟨3292666232435827783066325441,3292666232435827797702691954⟩,⟨(-21281527940939713349809397441),(-21281527940939713334051706424)⟩⟩,⟨⟨3268159484324522582830240973,3268159484324522597473437001⟩,⟨(-21323669669235982604693995611),(-21323669669235982588928008112)⟩⟩,⟨⟨3243075503668707968856179861,3243075503668707983504078644⟩,⟨(-21362732833799042441238231940),(-21362732833799042425466006981)⟩⟩,⟨⟨3217408972461584946986196756,3217408972461584961636396373⟩,⟨(-21398560813586495458144115321),(-21398560813586495442368805213)⟩⟩,⟨⟨3191195188247866234496520097,3191195188247866249146870805⟩,⟨(-21431263683489746594543795800),(-21431263683489746578767559160)⟩⟩,⟨⟨3164435637327486820544256069,3164435637327486835192385603⟩,⟨(-21460726653040581553612829761),(-21460726653040581537838744442)⟩⟩,⟨⟨3137159439118677311171926608,3137159439118677325815630803⟩,⟨(-21487019788804570096857704158),(-21487019788804570081088316843)⟩⟩,⟨⟨3109374605180143922464452351,3109374605180143937101405633⟩,⟨(-21510070158936524996056423226),(-21510070158936524980294688875)⟩⟩,⟨⟨3081104269457900090387021061,3081104269457900105014936830⟩,⟨(-21529907819246173811153553258),(-21529907819246173795402574664)⟩⟩] +lemma amp1_03_7_eq : ∀ k : Fin 16, amp1_0Expr 3 7 k = amp1_03_7 k := by decide +kernel +noncomputable def amp1_03_8 : Fin 16 → CBox := ![⟨⟨3052362697090093870765392923,3052362697090093885382379390⟩,⟨(-21546501773789659841623428380),(-21546501773789659825883246047)⟩⟩,⟨⟨3023167221481594870827554410,3023167221481594885431763116⟩,⟨(-21559842015121015646962902949),(-21559842015121015631233518776)⟩⟩,⟨⟨2993538096820730956799077423,2993538096820730971388200875⟩,⟨(-21569939609441664809525611233),(-21569939609441664793810123187)⟩⟩,⟨⟨2963487033579410294371317438,2963487033579410308943092399⟩,⟨(-21576744383507812976830283657),(-21576744383507812961131593063)⟩⟩,⟨⟨2933040017435368533147436555,2933040017435368547699658362⟩,⟨(-21580309640851035962589090324),(-21580309640851035946909721374)⟩⟩,⟨⟨2902203306577993046404891104,2902203306577993060935294357⟩,⟨(-21580544889634482479980025111),(-21580544889634482464322974977)⟩⟩,⟨⟨2871008367434659700192676324,2871008367434659714699145456⟩,⟨(-21577545895060383371241567595),(-21577545895060383355608940288)⟩⟩,⟨⟨2839456169937165557583802412,2839456169937165572064065564⟩,⟨(-21571181643200007947127837068),(-21571181643200007931522687955)⟩⟩,⟨⟨2807583417227822690887190159,2807583417227822705339167416⟩,⟨(-21561590634879316580383036804),(-21561590634879316564807351944)⟩⟩,⟨⟨2775385948681472386163090480,2775385948681472400584629543⟩,⟨(-21548601079181353477176933822),(-21548601079181353461632950940)⟩⟩,⟨⟨2742905466739098847005237288,2742905466739098861394263401⟩,⟨(-21532394536825923738797369317),(-21532394536825923723287289549)⟩⟩,⟨⟨2710132831866718013931475828,2710132831866718028285641844⟩,⟨(-21512758132670314346808705168),(-21512758132670314331336292893)⟩⟩,⟨⟨2677114514946923868946186066,2677114514946923883263690582⟩,⟨(-21489916862875205693693289224),(-21489916862875205678258763809)⟩⟩,⟨⟨2643836543376215424342449692,2643836543376215438620915118⟩,⟨(-21463616407291073907684773729),(-21463616407291073892292264080)⟩⟩,⟨⟨2610349932147427284558155460,2610349932147427298795862286⟩,⟨(-21434125625569291842978914369),(-21434125625569291827628211223)⟩⟩,⟨⟨2576636015834648638542212384,2576636015834648652736648812⟩,⟨(-21401148336756202594158047996),(-21401148336756202578854431657)⟩⟩] +lemma amp1_03_8_eq : ∀ k : Fin 16, amp1_0Expr 3 8 k = amp1_03_8 k := by decide +kernel +noncomputable def amp1_03_9 : Fin 16 → CBox := ![⟨⟨2542750135726105637424031274,2542750135726105651573294647⟩,⟨(-21364997746051829226773510304),(-21364997746051829211518455865)⟩⟩,⟨⟨2508669068418740544185319305,2508669068418740558287205126⟩,⟨(-21325335339126882099623282081),(-21325335339126882084419720741)⟩⟩,⟨⟨2474452270211861158760724338,2474452270211861172813864666⟩,⟨(-21282519204597587931129556310),(-21282519204597587915974696966)⟩⟩,⟨⟨2440072089333331593280502182,2440072089333331607282127314⟩,⟨(-21236167963352248755060591775),(-21236167963352248739962198388)⟩⟩,⟨⟨2405591892376083629314389280,2405591892376083643262681370⟩,⟨(-21186685183218049684845530045),(-21186685183218049669804901076)⟩⟩,⟨⟨2370979723709041495758235518,2370979723709041509651156024⟩,⟨(-21133646027672907029447371393),(-21133646027672907014466146104)⟩⟩,⟨⟨2336302662126107222704458615,2336302662126107236540001015⟩,⟨(-21077500199934525553997010282),(-21077500199934525539078508030)⟩⟩,⟨⟨2301524567663435554725070997,2301524567663435568501202332⟩,⟨(-21017778749484845928502470975),(-21017778749484845913648309157)⟩⟩,⟨⟨2266716039927229240282540396,2266716039927229253997361479⟩,⟨(-20954978234322163655392154880),(-20954978234322163640604947684)⟩⟩,⟨⟨2231836869251584794656994108,2231836869251584808308300479⟩,⟨(-20888584866272174089636261388),(-20888584866272174074919404110)⟩⟩,⟨⟨2196960991470571038419246939,2196960991470571052006565146⟩,⟨(-20819142843941037489580411307),(-20819142843941037474923502860)⟩⟩,⟨⟨2162044237014133813064795015,2162044237014133826584833286⟩,⟨(-20746092747230246859920925437),(-20746092747230246845337559600)⟩⟩,⟨⟨2127163700285434611110579511,2127163700285434624561658784⟩,⟨(-20670027271284326536657494223),(-20670027271284326522148934107)⟩⟩,⟨⟨2092271356811515800648568973,2092271356811515814028504804⟩,⟨(-20590340495214860970101669402),(-20590340495214860955671375556)⟩⟩,⟨⟨2057447288974506885503098126,2057447288974506898810413946⟩,⟨(-20507674540888388065226538139),(-20507674540888388050874218273)⟩⟩,⟨⟨2022639717611827950192953103,2022639717611827963425372941⟩,⟨(-20421376038668206956401959063),(-20421376038668206942132052653)⟩⟩] +lemma amp1_03_9_eq : ∀ k : Fin 16, amp1_0Expr 3 9 k = amp1_03_9 k := by decide +kernel +noncomputable def amp1_03_10 : Fin 16 → CBox := ![⟨⟨1987931549728337533648182157,1987931549728337546804462862⟩,⟨(-20332137546265245982385812498),(-20332137546265245968195875369)⟩⟩,⟨⟨1953267346877153980740751555,1953267346877153993818514721⟩,⟨(-20239257213188160520511183353),(-20239257213188160506406975171)⟩⟩,⟨⟨1918732684752018660622131756,1918732684752018673619803264⟩,⟨(-20143479126334660964177839768),(-20143479126334660950160808171)⟩⟩,⟨⟨1884268556168849024858858978,1884268556168849037774511411⟩,⟨(-20044051832424222626486137455),(-20044051832424222612557448723)⟩⟩,⟨⟨1849963057211983576985986951,1849963057211983589817892749⟩,⟨(-19941772131050466978967650072),(-19941772131050466965130717938)⟩⟩,⟨⟨1815753697566544618934272622,1815753697566544631680536974⟩,⟨(-19835837748000941974840748235),(-19835837748000941961096621611)⟩⟩,⟨⟨1781730953284378172630081778,1781730953284378185289177692⟩,⟨(-19727099475934232925861333374),(-19727099475934232912211841697)⟩⟩,⟨⟨1747828931468450473370454101,1747828931468450485940313462⟩,⟨(-19614702898187926569577925544),(-19614702898187926556026064774)⟩⟩,⟨⟨1714140355858606904935217964,1714140355858606917414358306⟩,⟨(-19499554185248504554739981751),(-19499554185248504541287473351)⟩⟩,⟨⟨1680596006311990908137331962,1680596006311990920523739740⟩,⟨(-19380745345054523382331816525),(-19380745345054523368981379991)⟩⟩,⟨⟨1647290730420484238056744628,1647290730420484250348934978⟩,⟨(-19259239423561871635925971528),(-19259239423561871622680045803)⟩⟩,⟨⟨1614152050723986320978721812,1614152050723986333177729748⟩,⟨(-19134073299866862086911041025),(-19134073299866862073736295489)⟩⟩,⟨⟨1581276823609002936029418645,1581276823609002948131001488⟩,⟨(-19006268515478860216404362440),(-19006268515478860203335881507)⟩⟩,⟨⟨1548589378578545795383926613,1548589378578545807386166009⟩,⟨(-18874805136505160774194891641),(-18874805136505160761234588712)⟩⟩,⟨⟨1516188474909137463643090721,1516188474909137475544663409⟩,⟨(-18740764953329143616083417959),(-18740764953329143603232914058)⟩⟩,⟨⟨1483995307408650713819453291,1483995307408650725618472430⟩,⟨(-18603069392699912655203222908),(-18603069392699912642464092861)⟩⟩] +lemma amp1_03_10_eq : ∀ k : Fin 16, amp1_0Expr 3 10 k = amp1_03_10 k := by decide +kernel +noncomputable def amp1_03_11 : Fin 16 → CBox := ![⟨⟨1452110441910411416539193310,1452110441910411428234383458⟩,⟨(-18462862392632775907149306384),(-18462862392632775894523003059)⟩⟩,⟨⟨1420451990584158330802649721,1420451990584158342392155406⟩,⟨(-18319004758906739871821617508),(-18319004758906739859309648798)⟩⟩,⟨⟨1389122239527252768375420692,1389122239527252779857946641⟩,⟨(-18172704635181060420552397362),(-18172704635181060408157292009)⟩⟩,⟨⟨1358036263634718297440291859,1358036263634718308814094697⟩,⟨(-18022760054661231476973349279),(-18022760054661231464695141582)⟩⟩,⟨⟨1327297993542522896724776092,1327297993542522907988551332⟩,⟨(-17870445599596263105089821849),(-17870445599596263092931722249)⟩⟩,⟨⟨1296819505060955765156335866,1296819505060955776308253676⟩,⟨(-17714494192276883864641550409),(-17714494192276883852605051146)⟩⟩,⟨⟨1266706308800120557973830884,1266706308800120569012732726⟩,⟨(-17556249279257666375732022909),(-17556249279257666363819277035)⟩⟩,⟨⟨1236867511941315310489998776,1236867511941315321414401207⟩,⟨(-17394376127771225308207375308),(-17394376127771225296415050573)⟩⟩,⟨⟨1207410152336318489842889388,1207410152336318500651381841⟩,⟨(-17230289687506447759232226346),(-17230289687506447747566537095)⟩⟩,⟨⟨1178240390605265273251726784,1178240390605265283942495518⟩,⟨(-17062584798927204701159354355),(-17062584798927204689621982053)⟩⟩,⟨⟨1149466751702578891779851215,1149466751702578902352002085⟩,⟨(-16892750790067593225757418327),(-16892750790067593214348289345)⟩⟩,⟨⟨1120992462606217915873384491,1120992462606217926324964990⟩,⟨(-16719309050418805869312868499),(-16719309050418805858035671309)⟩⟩,⟨⟨1092927508695107950919936811,1092927508695107961250062763⟩,⟨(-16543826424653578848983788074),(-16543826424653578837838964609)⟩⟩,⟨⟨1065172186189613302435387253,1065172186189613312642232869⟩,⟨(-16364747545951427029068860689),(-16364747545951427018058600013)⟩⟩,⟨⟨1037837928668444755547729260,1037837928668444765630401266⟩,⟨(-16183720207741975255928634996),(-16183720207741975245054558049)⟩⟩,⟨⟨1010822093413230048328645192,1010822093413230058285292407⟩,⟨(-15999108667388608430611409356),(-15999108667388608419876156021)⟩⟩] +lemma amp1_03_11_eq : ∀ k : Fin 16, amp1_0Expr 3 11 k = amp1_03_11 k := by decide +kernel +noncomputable def amp1_03_12 : Fin 16 → CBox := ![⟨⟨984237565572035147432455910,984237565572035157263511690⟩,⟨(-15812645428547598356539003961),(-15812645428547598345923647148)⟩⟩,⟨⟨957978743038009301727174804,957978743038009311429779516⟩,⟨(-15622610400856905377788965048),(-15622610400856905367312463399)⟩⟩,⟨⟨932159982810118384672232326,932159982810118394245652626⟩,⟨(-15430824930239571219511115035),(-15430824930239571209174425451)⟩⟩,⟨⟨906672689268592786347354325,906672689268592795789815341⟩,⟨(-15235480209839706649563415220),(-15235480209839706639368236275)⟩⟩,⟨⟨881632729986460002559701452,881632729986460011870527192⟩,⟨(-15038490978485002548993310647),(-15038490978485002538940498997)⟩⟩,⟨⟨856928466383461513062733950,856928466383461522240184955⟩,⟨(-14837954895288084934914855247),(-14837954895288084925005835749)⟩⟩,⟨⟨832677335556609198478985126,832677335556609207522406964⟩,⟨(-14635885117434399694670817795),(-14635885117434399684907383712)⟩⟩,⟨⟨808764589255093786816760607,808764589255093795724532108⟩,⟨(-14430280442791656556677015509),(-14430280442791656547058424841)⟩⟩,⟨⟨785309315371561564298906599,785309315371561573070338992⟩,⟨(-14223258013300100159374235876),(-14223258013300100149903833161)⟩⟩,⟨⟨762193569721006549007275210,762193569721006557640655907⟩,⟨(-14012711856863991512138589533),(-14012711856863991502817616533)⟩⟩,⟨⟨739538197058095825954036335,739538197058095834448892819⟩,⟨(-13800869285718909530743521848),(-13800869285718909521572978753)⟩⟩,⟨⟨717221948726958425927900728,717221948726958434282467711⟩,⟨(-13585512982404054946026187793),(-13585512982404054937008100958)⟩⟩,⟨⟨695367560142768073570327504,695367560142768081784171614⟩,⟨(-13368987327135203611967114788),(-13368987327135203603102913739)⟩⟩,⟨⟨673850344124014272428451388,673850344124014280500447334⟩,⟨(-13148956313395641794261932460),(-13148956313395641785541458715)⟩⟩,⟨⟨652795091788750853487745513,652795091788750861417016613⟩,⟨(-12927889110493074366387178700),(-12927889110493074357822007626)⟩⟩,⟨⟨632073513961611676770881760,632073513961611684555682647⟩,⟨(-12703322788898146658968556626),(-12703322788898146650560391210)⟩⟩] +lemma amp1_03_12_eq : ∀ k : Fin 16, amp1_0Expr 3 12 k = amp1_03_12 k := by decide +kernel +noncomputable def amp1_03_13 : Fin 16 → CBox := ![⟨⟨611812657977590215284946059,611812657977590222925062997⟩,⟨(-12477859985588748979491537793),(-12477859985588748971240359982)⟩⟩,⟨⟨591880435079202651080651185,591880435079202658574411807⟩,⟨(-12248901576360430806883807548),(-12248901576360430798790052215)⟩⟩,⟨⟨572406389931761066263188907,572406389931761073610351508⟩,⟨(-12019193464512074887946685245),(-12019193464512074880012835133)⟩⟩,⟨⟨553254396759381066196698379,553254396759381073395541170⟩,⟨(-11785989842249272321674656062),(-11785989842249272313901751177)⟩⟩,⟨⟨534556785538942673357552876,534556785538942680407974626⟩,⟨(-11552190996705267459908551035),(-11552190996705267452297712485)⟩⟩,⟨⟨516173109165466833097712663,516173109165466839998304088⟩,⟨(-11314892509916248288311997378),(-11314892509916248280857438019)⟩⟩,⟨⟨498238825505639999582345181,498238825505640006332850168⟩,⟨(-11077161734298976367258739149),(-11077161734298976359967025193)⟩⟩,⟨⟨480608826245970964868304192,480608826245970971466934447⟩,⟨(-10835922004518573150659356218),(-10835922004518573143532472398)⟩⟩,⟨⟨463422103936756772265041185,463422103936756778711936675⟩,⟨(-10594422288566577740894495915),(-10594422288566577733932125573)⟩⟩,⟨⟨446528482746640281982272909,446528482746640288275676985⟩,⟨(-10349397984639524259668371602),(-10349397984639524252871676100)⟩⟩,⟨⟨430070973009901823074455464,430070973009901829214580423⟩,⟨(-10104296478593671666102038828),(-10104296478593671659471545595)⟩⟩,⟨⟨413893844926907936381114119,413893844926907942366339821⟩,⟨(-9855647059989243414004916723),(-9855647059989243407537662580)⟩⟩,⟨⟨398144701390011665138331696,398144701390011670968756557⟩,⟨(-9607115073633503396352228454),(-9607115073633503390053644465)⟩⟩,⟨⟨382661674529915796436439495,382661674529915802110241636⟩,⟨(-9355002494152378513892070778),(-9355002494152378507763555304)⟩⟩,⟨⟨367597646013606648737983683,367597646013606654255646752⟩,⟨(-9103215531180647034337575128),(-9103215531180647028378266427)⟩⟩,⟨⟨352783905501023192780259708,352783905501023198139864680⟩,⟨(-8847803890694001745598369244),(-8847803890694001739810907508)⟩⟩] +lemma amp1_03_13_eq : ∀ k : Fin 16, amp1_0Expr 3 13 k = amp1_03_13 k := by decide +kernel +noncomputable def amp1_03_14 : Fin 16 → CBox := ![⟨⟨338379436866514910983530964,338379436866514916185809142⟩,⟨(-8592941733663811199223312437),(-8592941733663811193603221595)⟩⟩,⟨⟨324207832883997845045453604,324207832883997850088339783⟩,⟨(-8334396859882911744829783095),(-8334396859882911739382567462)⟩⟩,⟨⟨310435174390837904014170357,310435174390837908898409464⟩,⟨(-8076643728041312620512785540),(-8076643728041312615237161134)⟩⟩,⟨⟨296876313238220663442658051,296876313238220668166199854⟩,⟨(-7815132661565149086256407071),(-7815132661565149081155836499)⟩⟩,⟨⟨283705639198143821916884033,283705639198143826480729969⟩,⟨(-7554677474851569756962733558),(-7554677474851569752032614209)⟩⟩,⟨⟨270727975798331217072214231,270727975798331221474192608⟩,⟨(-7290367816815763960631779995),(-7290367816815763955877198147)⟩⟩,⟨⟨258127513858285655358200754,258127513858285659599420429⟩,⟨(-7027404617116228128354038128),(-7027404617116228123771796047)⟩⟩,⟨⟨245697443409679354655575923,245697443409679358733790133⟩,⟨(-6760463675959846489170764692),(-6760463675959846484765527546)⟩⟩,⟨⟨233633616719040371632382229,233633616719040375548803440⟩,⟨(-6495192286245952079472061864),(-6495192286245952075242248948)⟩⟩,⟨⟨221715561959387854549921611,221715561959387858302348178⟩,⟨(-6225785921507571177150232204),(-6225785921507571173096659097)⟩⟩,⟨⟨210153148075784388529964703,210153148075784392119742504⟩,⟨(-5958412974436369720672714536),(-5958412974436369716795797534)⟩⟩,⟨⟨198709636461404594122337143,198709636461404597547117673⟩,⟨(-5686703967624550075464393219),(-5686703967624550071765084333)⟩⟩,⟨⟨187611949731911378836922390,187611949731911382098348209⟩,⟨(-5417444526625207412898965864),(-5417444526625207409375486878)⟩⟩,⟨⟨176603670878666506600415316,176603670878666509695861045⟩,⟨(-5143590184553662441294705094),(-5143590184553662437951396541)⟩⟩,⟨⟨165932780470787632122270556,165932780470787635053702535⟩,⟨(-4872670352582002517296811697),(-4872670352582002514130383560)⟩⟩,⟨⟨155318606561625304302190511,155318606561625307066807626⟩,⟨(-4596818807493225000095881925),(-4596818807493224997109468057)⟩⟩] +lemma amp1_03_14_eq : ∀ k : Fin 16, amp1_0Expr 3 14 k = amp1_03_14 k := by decide +kernel +noncomputable def amp1_03_15 : Fin 16 → CBox := ![⟨⟨145035613158655621745008196,145035613158655624345049105⟩,⟨(-4324480061443653039855106188),(-4324480061443653037046541282)⟩⟩,⟨⟨134772549321311576130241388,134772549321311578562628095⟩,⟨(-4046764236525468037879156539),(-4046764236525468035251896321)⟩⟩,⟨⟨124837966603352849731782606,124837966603352851999176157⟩,⟨(-3773270955602465725242005377),(-3773270955602465722793268496)⟩⟩,⟨⟨114880963487470649105252422,114880963487470651204211597⟩,⟨(-3493798066189291986852908344),(-3493798066189291984585843293)⟩⟩,⟨⟨105255304014169034296315866,105255304014169036230018160⟩,⟨(-3219451412858754962836318298),(-3219451412858754960747705322)⟩⟩,⟨⟨95556780279474823742174125,95556780279474825506635780⟩,⟨(-2938283203764518819187276534),(-2938283203764518817281552356)⟩⟩,⟨⟨86201582863164167792426855,86201582863164169391537450⟩,⟨(-2663448859237587216640252773),(-2663448859237587214913406944)⟩⟩,⟨⟨76710273924286168986227544,76710273924286170415262069⟩,⟨(-2380560469553496670038387547),(-2380560469553496668495030847)⟩⟩,⟨⟨67590214532387264697933804,67590214532387265961789307⟩,⟨(-2105730519172041089827666772),(-2105730519172041088462864059)⟩⟩,⟨⟨58248221471473432237558392,58248221471473433330321024⟩,⟨(-1820912411232195603670983958),(-1820912411232195602491055341)⟩⟩,⟨⟨49336388574768574612775048,49336388574768575540965230⟩,⟨(-1546867131686620927920487835),(-1546867131686620926918464481)⟩⟩,⟨⟨40070315969642351152580493,40070315969642351908227190⟩,⟨(-1259440216236720542507160759),(-1259440216236720541691537598)⟩⟩,⟨⟨31365478994745584033260439,31365478994745584625864140⟩,⟨(-987788682558420447816118269),(-987788682558420447176743303)⟩⟩,⟨⟨22050497043216618422680666,22050497043216618839881463⟩,⟨(-695464056977236407823835598),(-695464056977236407373875644)⟩⟩,⟨⟨13665132145527715734138466,13665132145527715992913253⟩,⟨(-431419890933529199452410778),(-431419890933529199173884603)⟩⟩,⟨⟨3880430946345568753254372,3880430946345568826761426⟩,⟨(-122569233409467586981283196),(-122569233409467586902507765)⟩⟩] +lemma amp1_03_15_eq : ∀ k : Fin 16, amp1_0Expr 3 15 k = amp1_03_15 k := by decide +kernel +noncomputable def amp1_03 : Fin 16 → Fin 16 → CBox := ![amp1_03_0,amp1_03_1,amp1_03_2,amp1_03_3,amp1_03_4,amp1_03_5,amp1_03_6,amp1_03_7,amp1_03_8,amp1_03_9,amp1_03_10,amp1_03_11,amp1_03_12,amp1_03_13,amp1_03_14,amp1_03_15] +lemma amp1_03_eq (i k : Fin 16) : amp1_0Expr 3 i k = amp1_03 i k := by + fin_cases i + · exact amp1_03_0_eq k + · exact amp1_03_1_eq k + · exact amp1_03_2_eq k + · exact amp1_03_3_eq k + · exact amp1_03_4_eq k + · exact amp1_03_5_eq k + · exact amp1_03_6_eq k + · exact amp1_03_7_eq k + · exact amp1_03_8_eq k + · exact amp1_03_9_eq k + · exact amp1_03_10_eq k + · exact amp1_03_11_eq k + · exact amp1_03_12_eq k + · exact amp1_03_13_eq k + · exact amp1_03_14_eq k + · exact amp1_03_15_eq k +noncomputable def amp1_04_0 : Fin 16 → CBox := ![⟨⟨108087540564764473191846237,108087540564764473263539163⟩,⟨(-1017365712714837437091),(-1017365712714758292094)⟩⟩,⟨⟨380429558899274369864259217,380429558899274370117704342⟩,⟨(-32227844834902053620121),(-32227844834901775044132)⟩⟩,⟨⟨613209148785511274696223723,613209148785511275105624060⟩,⟨(-144307603078629899887889),(-144307603078629450810271)⟩⟩,⟨⟨870838759435417286705375802,870838759435417287287080893⟩,⟨(-401710817432017060196323),(-401710817432016422350763)⟩⟩,⟨⟨1110122611941126490425107202,1110122611941126491167101438⟩,⟨(-846618630911082269625020),(-846618630911081456353648)⟩⟩,⟨⟨1363157402552387190259295865,1363157402552387191170781943⟩,⟨(-1553203743542670148270059),(-1553203743542669149377076)⟩⟩,⟨⟨1604211278134668391688519660,1604211278134668392761719185⟩,⟨(-2553427679062348247412635),(-2553427679062347071528029)⟩⟩,⟨⟨1854533666081764771093653867,1854533666081764772334854764⟩,⟨(-3930825950684613178245854),(-3930825950684611818399860)⟩⟩,⟨⟨2095803055780533116261033168,2095803055780533117664418546⟩,⟨(-5707149034948222221526242),(-5707149034948220684153740)⟩⟩,⟨⟨2343877065209979312485002924,2343877065209979314055004460⟩,⟨(-7974992912616158643436493),(-7974992912616156923317216)⟩⟩,⟨⟨2584539784803889453771167939,2584539784803889455503496903⟩,⟨(-10745843359115809161072763),(-10745843359115807263387592)⟩⟩,⟨⟨2830417005516677870367477039,2830417005516677872265700404⟩,⟨(-14121091280701554314639699),(-14121091280701552235277380)⟩⟩,⟨⟨3069906860204113639606319129,3069906860204113641666307600⟩,⟨(-18101889125021379676113691),(-18101889125021377419457665)⟩⟩,⟨⟨3313478071342825125503825871,3313478071342825127728414411⟩,⟨(-22798164690230291882867348),(-22798164690230289445583053)⟩⟩,⟨⟨3551342582180764963390593385,3551342582180764965776788593⟩,⟨(-28200671625299008627638249),(-28200671625299006013557611)⟩⟩,⟨⟨3792424635522296952673214847,3792424635522296955223430539⟩,⟨(-34427613720176450315029804),(-34427613720176447521396535)⟩⟩] +lemma amp1_04_0_eq : ∀ k : Fin 16, amp1_0Expr 4 0 k = amp1_04_0 k := by decide +kernel +noncomputable def amp1_04_1 : Fin 16 → CBox := ![⟨⟨4028270859911521446232048934,4028270859911521448943015448⟩,⟨(-41459290719596025497566190),(-41459290719596022527823860)⟩⟩,⟨⟨4266643347333295308556667338,4266643347333295311430232707⟩,⟨(-49421914614835278269238005),(-49421914614835275121087034)⟩⟩,⟨⟨4500113808387353338284579247,4500113808387353341317755846⟩,⟨(-58285289887787188497206734),(-58285289887787185173800519)⟩⟩,⟨⟨4735536874474457719265517708,4735536874474457722461106173⟩,⟨(-68183360397692091712108382),(-68183360397692088211499910)⟩⟩,⟨⟨4966297700540065212571753395,4966297700540065215925701268⟩,⟨(-79075409598275567639783995),(-79075409598275563964923320)⟩⟩,⟨⟨5198521677555150170822598531,5198521677555150174336363709⟩,⟨(-91102827691590657543781543),(-91102827691590653693047268)⟩⟩,⟨⟨5426256335213825391383619434,5426256335213825395056104499⟩,⟨(-104214368082311432483847769),(-104214368082311428459974430)⟩⟩,⟨⟨5655027432029830067962547427,5655027432029830071793269472⟩,⟨(-118558572418822141986556925),(-118558572418822137788218959)⟩⟩,⟨⟨5879433266159994066214155039,5879433266159994070202119908⟩,⟨(-134073672582852008083934401),(-134073672582852003713729585)⟩⟩,⟨⟨6104497188337284040859148727,6104497188337284045005594947⟩,⟨(-150915057458186186833623979),(-150915057458186182290417427)⟩⟩,⟨⟨6325283473470903211920955063,6325283473470903216221538224⟩,⟨(-169010464087999571327939195),(-169010464087999566614304100)⟩⟩,⟨⟨6546387883121727449562255197,6546387883121727454019592496⟩,⟨(-188521815248313385121942258),(-188521815248313380236909915)⟩⟩,⟨⟨6763274734392282408028387907,6763274734392282412637763347⟩,⟨(-209366398483646599616003468),(-209366398483646594562087573)⟩⟩,⟨⟨6980171021344690924115945765,6980171021344690928881171954⟩,⟨(-231712348237249838902161324),(-231712348237249833678527521)⟩⟩,⟨⟨7192888815661819191129012683,7192888815661819196046775637⟩,⟨(-255466566973823131866568380),(-255466566973823126475625265)⟩⟩,⟨⟨7405333438875873750716358706,7405333438875873755787573141⟩,⟨(-280803069984181519027667903),(-280803069984181513468828348)⟩⟩] +lemma amp1_04_1_eq : ∀ k : Fin 16, amp1_0Expr 4 1 k = amp1_04_1 k := by decide +kernel +noncomputable def amp1_04_2 : Fin 16 → CBox := ![⟨⟨7613622548809671542074042414,7613622548809671547293627609⟩,⟨(-307618458522706086899085765),(-307618458522706081174788797)⟩⟩,⟨⟨7821378097100925821845312647,7821378097100925827216920415⟩,⟨(-336092289619148271567680168),(-336092289619148265677378748)⟩⟩,⟨⟨8024988820637231365824105831,8024988820637231371345118847⟩,⟨(-366110966970354774081579930),(-366110966970354768027575443)⟩⟩,⟨⟨8227824881946569889090543559,8227824881946569894761475306⟩,⟨(-397859242260386789604248042),(-397859242260386783386248321)⟩⟩,⟨⟨8426517496233134198875365113,8426517496233134204694649333⟩,⟨(-431213445365565146714439798),(-431213445365565140334666648)⟩⟩,⟨⟨8624211390672285032607156485,8624211390672285038569920163⟩,⟨(-466363167876582225088911260),(-466363167876582218547481918)⟩⟩,⟨⟨8817756283978651875171471230,8817756283978651881279875575⟩,⟨(-503174809944199810647046632),(-503174809944199803945970965)⟩⟩,⟨⟨9010093695805072252688864937,9010093695805072258942207186⟩,⟨(-541842440962969027539445403),(-541842440962969020678740543)⟩⟩,⟨⟨9198271547626995260153026336,9198271547626995266549924788⟩,⟨(-582222696060299645369718283),(-582222696060299638351555268)⟩⟩,⟨⟨9385047079060954785046579835,9385047079060954791587041497⟩,⟨(-624513753276140040691184755),(-624513753276140033515645782)⟩⟩,⟨⟨9567649068057259189678847915,9567649068057259196360789623⟩,⟨(-668562668250543288161784796),(-668562668250543280831068657)⟩⟩,⟨⟨9748666730177152114133325024,9748666730177152120950923884⟩,⟨(-714571351742874044108637399),(-714571351742874036623353512)⟩⟩,⟨⟨9925494755862515788494638394,9925494755862515795452367992⟩,⟨(-762377486480516799176545189),(-762377486480516791538421433)⟩⟩,⟨⟨10100568406880896960507315144,10100568406880896967603940599⟩,⟨(-812186333523575934971470944),(-812186333523575927180876097)⟩⟩,⟨⟨10271435315087752423204921752,10271435315087752430439141376⟩,⟨(-863826430484116381533088156),(-863826430484116373592144943)⟩⟩,⟨⟨10440389053072452375039346076,10440389053072452382408772551⟩,⟨(-917506000071359157570654099),(-917506000071359149479930035)⟩⟩] +lemma amp1_04_2_eq : ∀ k : Fin 16, amp1_0Expr 4 2 k = amp1_04_2 k := by decide +kernel +noncomputable def amp1_04_3 : Fin 16 → CBox := ![⟨⟨10605118857942786918952463243,10605118857942786926456289586⟩,⟨(-973044683965568819966855435),(-973044683965568811728431005)⟩⟩,⟨⟨10767787372883604509081752661,10767787372883604516719683218⟩,⟨(-1030653271883720179368791524),(-1030653271883720170983138840)⟩⟩,⟨⟨10926215470039666233417693209,10926215470039666241187858833⟩,⟨(-1090142780287363177475439216),(-1090142780287363168944724051)⟩⟩,⟨⟨11082444358693500496359140596,11082444358693500504251614163⟩,⟨(-1151726165495505757906260906),(-1151726165495505749232031714)⟩⟩,⟨⟨11234417725562704299618526008,11234417725562704307641281522⟩,⟨(-1215206111117198399725963176),(-1215206111117198390909400712)⟩⟩,⟨⟨11384063771502870560704107805,11384063771502870568855626749⟩,⟨(-1280797334109812444107120017),(-1280797334109812435148976337)⟩⟩,⟨⟨11529441151723926207990920440,11529441151723926216269059988⟩,⟨(-1348294499353228948876681729),(-1348294499353228939779159115)⟩⟩,⟨⟨11672372572322624032041982674,11672372572322624040445571180⟩,⟨(-1417913673107950994308256696),(-1417913673107950985072152796)⟩⟩,⟨⟨11811024641857593698397765696,11811024641857593706925295678⟩,⟨(-1489441837489806944925930451),(-1489441837489806935553379460)⟩⟩,⟨⟨11947121303446440713779236841,11947121303446440722427624835⟩,⟨(-1563095991521031548792386725),(-1563095991521031539284505775)⟩⟩,⟨⟨12078930816546043856478307869,12078930816546043865247674396⟩,⟨(-1638655792425954720090423185),(-1638655792425954710449142191)⟩⟩,⟨⟨12208084418663639322306383084,12208084418663639331194902528⟩,⟨(-1716338750384461644902289657),(-1716338750384461635128637126)⟩⟩,⟨⟨12332946332233289513773713891,12332946332233289522779727027⟩,⟨(-1795917577556343217973850062),(-1795917577556343208069989898)⟩⟩,⟨⟨12455060561637415357698492706,12455060561637415366820938861⟩,⟨(-1877609868733088070805302234),(-1877609868733088060772222145)⟩⟩,⟨⟨12572882136864823084853819925,12572882136864823094090822209⟩,⟨(-1961181792819992286992440548),(-1961181792819992276832337477)⟩⟩,⟨⟨12687872791830367154250242682,12687872791830367163600649116⟩,⟨(-2046850597829250587986934089),(-2046850597829250577700869633)⟩⟩] +lemma amp1_04_3_eq : ∀ k : Fin 16, amp1_0Expr 4 3 k = amp1_04_3 k := by decide +kernel +noncomputable def amp1_04_4 : Fin 16 → CBox := ![⟨⟨12798573672186533465808030416,12798573672186533475256147379⟩,⟨(-2134376333215646669751825411),(-2134376333215646659344307568)⟩⟩,⟨⟨12906368757507869609244625129,12906368757507869618805248475⟩,⟨(-2223975464049050686852702495),(-2223975464049050676322251644)⟩⟩,⟨⟨13009881022438937158443972372,13009881022438937168114463531⟩,⟨(-2315402366125218531377492673),(-2315402366125218520726427695)⟩⟩,⟨⟨13110420815492774807821240238,13110420815492774817599906270⟩,⟨(-2408872280684075513674947106),(-2408872280684075502904520879)⟩⟩,⟨⟨13206689009292462321204239220,13206689009292462331088803295⟩,⟨(-2504134377618229009293616294),(-2504134377618228998406106862)⟩⟩,⟨⟨13299926097483707580897038422,13299926097483707590886748522⟩,⟨(-2601402228747062350903827662),(-2601402228747062339900365430)⟩⟩,⟨⟨13388907232983438909115863278,13388907232983438919207275131⟩,⟨(-2700420287741234999310414858),(-2700420287741234988193517384)⟩⟩,⟨⟨13474806522884890630494682413,13474806522884890640687442260⟩,⟨(-2801400006700950701547364635),(-2801400006700950690318132951)⟩⟩,⟨⟨13556470059727345001474740465,13556470059727345011766975067⟩,⟨(-2904081634627201920649478610),(-2904081634627201909310125739)⟩⟩,⟨⟨13635008758228595292222897015,13635008758228595302609363734⟩,⟨(-3008674048861856010536017294),(-3008674048861855999088738018)⟩⟩,⟨⟨13709336555604666786684494835,13709336555604666797167238432⟩,⟨(-3114913827091087454569592138),(-3114913827091087443015758385)⟩⟩,⟨⟨13780504123402320542319029114,13780504123402320552895957029⟩,⟨(-3223006812058119985573108965),(-3223006812058119973914271981)⟩⟩,⟨⟨13847490367234597526025602957,13847490367234597536694997344⟩,⟨(-3332686465209943398335630085),(-3332686465209943386573976043)⟩⟩,⟨⟨13911288445021821231345775228,13911288445021821242104750526⟩,⟨(-3444155129960154748060194437),(-3444155129960154736197521206)⟩⟩,⟨⟨13970939549672034370707323720,13970939549672034381555292401⟩,⟨(-3557143728219029248766659273),(-3557143728219029236804877880)⟩⟩,⟨⟨14027381857418176251291887605,14027381857418176262226487936⟩,⟨(-3671850634329706816218033196),(-3671850634329706804158863909)⟩⟩] +lemma amp1_04_4_eq : ∀ k : Fin 16, amp1_0Expr 4 4 k = amp1_04_4 k := by decide +kernel +noncomputable def amp1_04_5 : Fin 16 → CBox := ![⟨⟨14079716342083346443797476346,14079716342083346454816985997⟩,⟨(-3788004828890165638251013786),(-3788004828890165626096652013)⟩⟩,⟨⟨14128828551832159309371357472,14128828551832159320474250036⟩,⟨(-3905800242272824157845436917),(-3905800242272824145597422846)⟩⟩,⟨⟨14173876891875677779744703760,14173876891875677790929218261⟩,⟨(-4024964533395238309134595344),(-4024964533395238296795124658)⟩⟩,⟨⟨14215696474532138274822856911,14215696474532138286087333055⟩,⟨(-4145686708418613035037844528),(-4145686708418613022608528440)⟩⟩,⟨⟨14253500928072667524004172571,14253500928072667535346592353⟩,⟨(-4267693745496789291465333447),(-4267693745496789278948443417)⟩⟩,⟨⟨14288076974692429843003235387,14288076974692429854397126693⟩,⟨(-4391169240786213748618672728),(-4391169240786213736023473770)⟩⟩,⟨⟨14318691384846014018822549590,14318691384846014030292154132⟩,⟨(-4515840153749391096080218083),(-4515840153749391083401096746)⟩⟩,⟨⟨14346084402987291232699716011,14346084402987291244242773616⟩,⟨(-4641884178945692244901552856),(-4641884178945692232140355481)⟩⟩,⟨⟨14369573976226909554219662004,14369573976226909565833571210⟩,⟨(-4769028940240375252499821446),(-4769028940240375239659005232)⟩⟩,⟨⟨14389855661971336815495488588,14389855661971336827178544387⟩,⟨(-4897445732925117425281927915),(-4897445732925117412363199752)⟩⟩,⟨⟨14406296723133685899352592472,14406296723133685911102021620⟩,⟨(-5026863549246854138024273988),(-5026863549246854125030164259)⟩⟩,⟨⟨14419549709429909464181199059,14419549709429909475995221942⟩,⟨(-5157446781166343523084838113),(-5157446781166343510017123543)⟩⟩,⟨⟨14429029433961716385543910490,14429029433961716397421169276⟩,⟨(-5288926514038202110848884074),(-5288926514038202097709607460)⟩⟩,⟨⟨14435347015992591326254986324,14435347015992591338192578212⟩,⟨(-5421459725686305876406119229),(-5421459725686305863197486866)⟩⟩,⟨⟨14437963140088415960568248672,14437963140088415972564749344⟩,⟨(-5554780339909606559971649865),(-5554780339909606546695720061)⟩⟩,⟨⟨14437448978409380888183108112,14437448978409380900237026307⟩,⟨(-5689037402459319922164563324),(-5689037402459319908823043640)⟩⟩] +lemma amp1_04_5_eq : ∀ k : Fin 16, amp1_0Expr 4 5 k = amp1_04_5 k := by decide +kernel +noncomputable def amp1_04_6 : Fin 16 → CBox := ![⟨⟨14433309487749780185677661958,14433309487749780197784310996⟩,⟨(-5823968441393309574405567095),(-5823968441393309561001809731)⟩⟩,⟨⟨14426077289991866827795402330,14426077289991866839956070402⟩,⟨(-5959714044899289800430434389),(-5959714044899289786965050779)⟩⟩,⟨⟨14415300087845036220777026141,14415300087845036232987995525⟩,⟨(-6096016131460073501370449021),(-6096016131460073487846414460)⟩⟩,⟨⟨14401473269820770962906251215,14401473269820770975167266499⟩,⟨(-6233006298189215742243928633),(-6233006298189215728662461199)⟩⟩,⟨⟨14384185825322385760100735447,14384185825322385772408776169⟩,⟨(-6370431660394543915357241224),(-6370431660394543901721046177)⟩⟩,⟨⟨14363897152416293742902463063,14363897152416293755256201139⟩,⟨(-6508414282079257389061221752),(-6508414282079257375371970299)⟩⟩,⟨⟨14340236129891257049685855200,14340236129891257062075350276⟩,⟨(-6646707301904864100031578043),(-6646707301904864086295202359)⟩⟩,⟨⟨14313627339658563383367742554,14313627339658563395799704617⟩,⟨(-6785422699654169375625544987),(-6785422699654169361840072976)⟩⟩,⟨⟨14283738209894718692858346862,14283738209894718705329838729⟩,⟨(-6924320483909415377139851256),(-6924320483909415363307979816)⟩⟩,⟨⟨14250959616831958456420936519,14250959616831958468929731420⟩,⟨(-7063501989456468226561324376),(-7063501989456468212685170362)⟩⟩,⟨⟨14214996251259522682563879286,14214996251259522695108284957⟩,⟨(-7202734961332202784881187712),(-7202734961332202770962850813)⟩⟩,⟨⟨14176206334748946531046527841,14176206334748946543623848663⟩,⟨(-7342109518243493798313213367),(-7342109518243493784355083005)⟩⟩,⟨⟨14134330583520431328785532229,14134330583520431341394064856⟩,⟨(-7481402028133446268713153087),(-7481402028133446254717340908)⟩⟩,⟨⟨14089695559986170724975832402,14089695559986170737614257903⟩,⟨(-7620690811554857000373621088),(-7620690811554856986341805673)⟩⟩,⟨⟨14042076814989848488413152660,14042076814989848501075748114⟩,⟨(-7759761765703628875802660497),(-7759761765703628861739133989)⟩⟩,⟨⟨13991770195337644417699689597,13991770195337644430387844197⟩,⟨(-7898680819171865505346747963),(-7898680819171865491251739266)⟩⟩] +lemma amp1_04_6_eq : ∀ k : Fin 16, amp1_0Expr 4 6 k = amp1_04_6 k := by decide +kernel +noncomputable def amp1_04_7 : Fin 16 → CBox := ![⟨⟨13938584939213138587690057392,13938584939213138600401238736⟩,⟨(-8037244324657834621120823934),(-8037244324657834606996889746)⟩⟩,⟨⟨13882787072656915438764672119,13882787072656915451497471410⟩,⟨(-8175505212462621455354637402),(-8175505212462621441203507684)⟩⟩,⟨⟨13824218414914209200535871994,13824218414914209213286281766⟩,⟨(-8313271236982902327492475644),(-8313271236982902313317591311)⟩⟩,⟨⟨13763116020321779879960111788,13763116020321779892727811614⟩,⟨(-8450581710525803778700202833),(-8450581710525803764502670390)⟩⟩,⟨⟨13699353221694799480352097775,13699353221694799493133842606⟩,⟨(-8587256755412933335511753754),(-8587256755412933321294600713)⟩⟩,⟨⟨13633138907611419453506140560,13633138907611419466301345848⟩,⟨(-8723321431972879250768894164),(-8723321431972879236533346426)⟩⟩,⟨⟨13564376893804316056802504334,13564376893804316069608197963⟩,⟨(-8858609216839208431589327758),(-8858609216839208417338251239)⟩⟩,⟨⟨13493248668336574751185380058,13493248668336574763999720083⟩,⟨(-8993130269122809613461406922),(-8993130269122809599196837351)⟩⟩,⟨⟨13419687534344862290116947346,13419687534344862302937931462⟩,⟨(-9126732426498762499238210488),(-9126732426498762484962411028)⟩⟩,⟨⟨13343848306108432537497580904,13343848306108432550323533251⟩,⟨(-9259410281325397362126262297),(-9259410281325397347841145652)⟩⟩,⟨⟨13265692812318202095324824407,13265692812318202108153273789⟩,⟨(-9391027059631885643755563404),(-9391027059631885629463703509)⟩⟩,⟨⟨13185349883671194348511342141,13185349883671194361340538788⟩,⟨(-9521561104079381988191975712),(-9521561104079381973895356623)⟩⟩,⟨⟨13102808944957686062685073450,13102808944957686075512593271⟩,⟨(-9650892077252799432758039577),(-9650892077252799418459228971)⟩⟩,⟨⟨13018173498756715823945029820,13018173498756715836768903623⟩,⟨(-9778981370569384269790946406),(-9778981370569384255492093796)⟩⟩,⟨⟨12931459667818559728725591698,12931459667818559741543499352⟩,⟨(-9905726152639809851859475266),(-9905726152639809837563085009)⟩⟩,⟨⟨12842746248947084939132205024,12842746248947084951941842635⟩,⟨(-10031070142211902040404906870),(-10031070142211902026113419361)⟩⟩] +lemma amp1_04_7_eq : ∀ k : Fin 16, amp1_0Expr 4 7 k = amp1_04_7 k := by decide +kernel +noncomputable def amp1_04_8 : Fin 16 → CBox := ![⟨⟨12752075195124500438932336229,12752075195124500451733111185⟩,⟨(-10154929105121458601556750395),(-10154929105121458587271338085)⟩⟩,⟨⟨12659501188052480323588270597,12659501188052480336379711539⟩,⟨(-10277228344774870558846451621),(-10277228344774870544568043762)⟩⟩,⟨⟨12565091172886633689779287245,12565091172886633702558978150⟩,⟨(-10397903337713655829353672242),(-10397903337713655815084807617)⟩⟩,⟨⟨12468876276527070163786449035,12468876276527070176552189157⟩,⟨(-10516860206617878178177188556),(-10516860206617878163920195942)⟩⟩,⟨⟨12370947627323620209571212090,12370947627323620222320923101⟩,⟨(-10634055275149534863332718682),(-10634055275149534849089892585)⟩⟩,⟨⟨12271313328455044250305571234,12271313328455044263037027068⟩,⟨(-10749374695591017532580986040),(-10749374695591017518354696545)⟩⟩,⟨⟨12170087911117654139945748130,12170087911117654152657138361⟩,⟨(-10862796798838857619843376550),(-10862796798838857605635690155)⟩⟩,⟨⟨12067256957642097554505019681,12067256957642097567194082629⟩,⟨(-10974186951129577919900559336),(-10974186951129577905713910404)⟩⟩,⟨⟨11962957650041358105395406341,11962957650041358118060385167⟩,⟨(-11083546675297232720605432539),(-11083546675297232706441854601)⟩⟩,⟨⟨11857153525344798926328793618,11857153525344798938967910649⟩,⟨(-11190719708089349797875146765),(-11190719708089349783736632020)⟩⟩,⟨⟨11750003692484605101094714913,11750003692484605113706118341⟩,⟨(-11295731974597181562529317264),(-11295731974597181548417968678)⟩⟩,⟨⟨11641450092161293340402741722,11641450092161293352983807064⟩,⟨(-11398404708883201008522101126),(-11398404708883200994440747447)⟩⟩,⟨⟨11531673064398257169417929815,11531673064398257181967870588⟩,⟨(-11498789475413175219311223964),(-11498789475413175205260941416)⟩⟩,⟨⟨11420593376591725439192467556,11420593376591725451708494625⟩,⟨(-11596684100503760024026165974),(-11596684100503760010009963332)⟩⟩,⟨⟨11308411932153718688224590117,11308411932153718700706150466⟩,⟨(-11692167053261121770879394930),(-11692167053261121756898059601)⟩⟩,⟨⟨11195028722755675338817014265,11195028722755675351260712686⟩,⟨(-11785011813049447613886247084),(-11785011813049447599943459710)⟩⟩] +lemma amp1_04_8_eq : ∀ k : Fin 16, amp1_0Expr 4 8 k = amp1_04_8 k := by decide +kernel +noncomputable def amp1_04_9 : Fin 16 → CBox := ![⟨⟨11080664575793104329062762865,11080664575793104341467139611⟩,⟨(-11875325048569344309272703763),(-11875325048569344295370199421)⟩⟩,⟨⟨10965199079726818641243589767,10965199079726818653606534608⟩,⟨(-11962854916411658340811105881),(-11962854916411658326951263863)⟩⟩,⟨⟨10848872375114779470729552859,10848872375114779483051810976⟩,⟨(-12047737611262769695294649132),(-12047737611262769681476738345)⟩⟩,⟨⟨10731543994912029526056076076,10731543994912029538333040555⟩,⟨(-12129694951829510857399784628),(-12129694951829510843628943052)⟩⟩,⟨⟨10613472811003119577172771544,10613472811003119589403090434⟩,⟨(-12208894018594742996833242477),(-12208894018594742983111074226)⟩⟩,⟨⟨10494498623863321019050645462,10494498623863321031232868335⟩,⟨(-12285029235075145127218891786),(-12285029235075145113547046536)⟩⟩,⟨⟨10374898484369644488922016752,10374898484369644501053810876⟩,⟨(-12358299963021469195999793545),(-12358299963021469182381001337)⟩⟩,⟨⟨10254492758866456341904343653,10254492758866456353984252597⟩,⟨(-12428372128096910068731665062),(-12428372128096910055167590356)⟩⟩,⟨⟨10133576155025317463225347928,10133576155025317475251380089⟩,⟨(-12495478806982420235724936961),(-12495478806982420222217941239)⟩⟩,⟨⟨10011949878599879625072924056,10011949878599879637042798916⟩,⟨(-12559256276019802226849432550),(-12559256276019802213402200124)⟩⟩,⟨⟨9889925802750874629393379822,9889925802750874641311351419⟩,⟨(-12619972801525971480122735735),(-12619972801525971466729714323)⟩⟩,⟨⟨9767286221101926618843389954,9767286221101926630702266948⟩,⟨(-12677233806482011592597127361),(-12677233806482011579267172432)⟩⟩,⟨⟨9644359712773699307613050801,9644359712773699319411522011⟩,⟨(-12731344265802869011512196330),(-12731344265802868998246835353)⟩⟩,⟨⟨9520909882223222864308533728,9520909882223222876044309617⟩,⟨(-12781877488373212787052303671),(-12781877488373212773854281156)⟩⟩,⟨⟨9397281587796121589588569512,9397281587796121601261090560⟩,⟨(-12829176724540682370013532767),(-12829176724540682356883361267)⟩⟩,⟨⟨9273219941674907320941662516,9273219941674907332548178632⟩,⟨(-12872781847134098508531682978),(-12872781847134098495472757951)⟩⟩] +lemma amp1_04_9_eq : ∀ k : Fin 16, amp1_0Expr 4 9 k = amp1_04_9 k := by decide +kernel +noncomputable def amp1_04_10 : Fin 16 → CBox := ![⟨⟨9149085688651263813597099349,9149085688651263825137983085⟩,⟨(-12913076000709954114314115387),(-12913076000709954101325602252)⟩⟩,⟨⟨9024605618711995260631498557,9024605618711995272103453802⟩,⟨(-12949564233877359610025314314),(-12949564233877359597111404970)⟩⟩,⟨⟨8900156005588836760788561910,8900156005588836772190253110⟩,⟨(-12982671260697089645402624685),(-12982671260697089632564890303)⟩⟩,⟨⟨8775445459414988794120040387,8775445459414988805450208984⟩,⟨(-13011865845697627173829950368),(-13011865845697627161069710000)⟩⟩,⟨⟨8650865462114801436924580511,8650865462114801448181015329⟩,⟨(-13037616009409894498797642970),(-13037616009409894486117766209)⟩⟩,⟨⟨8526106557451941571277195571,8526106557451941582458719387⟩,⟨(-13059352694651544120030856992),(-13059352694651544107432542946)⟩⟩,⟨⟨8401575153225740907047870083,8401575153225740918153010457⟩,⟨(-13077589032858803759543364572),(-13077589032858803747028408072)⟩⟩,⟨⟨8276943810117781747714757158,8276943810117781758741478192⟩,⟨(-13091716523008848069323776286),(-13091716523008848056894691360)⟩⟩,⟨⟨8152633619791341010098354076,8152633619791341021045220748⟩,⟨(-13102295285879987927099288388),(-13102295285879987914757848312)⟩⟩,⟨⟨8028299211358000291069894927,8028299211358000301935043014⟩,⟨(-13108675662500827688622212071),(-13108675662500827676370707947)⟩⟩,⟨⟨7904376160746774182720828549,7904376160746774193502591724⟩,⟨(-13111466722795377670127938179),(-13111466722795377657968580495)⟩⟩,⟨⟨7780501183390035821679495437,7780501183390035832390654065⟩,⟨(-13109975835423449530209330378),(-13109975835423449518119774590)⟩⟩,⟨⟨7657124184661244090108933425,7657124184661244100734407595⟩,⟨(-13104863068938931653707434901),(-13104863068938931641712138691)⟩⟩,⟨⟨7533863948438057102468107002,7533863948438057113006367710⟩,⟨(-13095390895588513068275664816),(-13095390895588513056376372086)⟩⟩,⟨⟨7411184602149717725234055382,7411184602149717735683809376⟩,⟨(-13082272531117872674431380401),(-13082272531117872662629718586)⟩⟩,⟨⟨7288686941995592825304556390,7288686941995592835664382824⟩,⟨(-13064723507257033423318559625),(-13064723507257033411616070661)⟩⟩] +lemma amp1_04_10_eq : ∀ k : Fin 16, amp1_0Expr 4 10 k = amp1_04_10 k := by decide +kernel +noncomputable def amp1_04_11 : Fin 16 → CBox := ![⟨⟨7166849260492193641982403155,7166849260492193652251054664⟩,⟨(-13043512445221825677947503779),(-13043512445221825666345741029)⟩⟩,⟨⟨7045254268925825563003283719,7045254268925825573179407073⟩,⟨(-13017805760334312465840190993),(-13017805760334312454340582652)⟩⟩,⟨⟨6924394421718987480973559288,6924394421718987491055560570⟩,⟨(-12988429859341489305944304923),(-12988429859341489294549104454)⟩⟩,⟨⟨6803834203601598983567524614,6803834203601598993554572329⟩,⟨(-12954499720255460285935337784),(-12954499720255460274644968639)⟩⟩,⟨⟨6684080285311726168837387653,6684080285311726178727629559⟩,⟨(-12916902050911340027803152740),(-12916902050911340016620396626)⟩⟩,⟨⟨6564678735176536023354872776,6564678735176536033146961258⟩,⟨(-12874697911143072125602742618),(-12874697911143072114529021369)⟩⟩,⟨⟨6446150556558307204868173705,6446150556558307214560726473⟩,⟨(-12828836976547584767958244004),(-12828836976547584756995541116)⟩⟩,⟨⟨6328023158965385688469626983,6328023158965385698063025108⟩,⟨(-12778323730974931503579974834),(-12778323730974931492726207298)⟩⟩,⟨⟨6210832061486286489665740190,6210832061486286499157100216⟩,⟨(-12724173653412829163562444624),(-12724173653412829152822613620)⟩⟩,⟨⟨6094085714796064413368826694,6094085714796064422756750323⟩,⟨(-12665331797658554994760997511),(-12665331797658554984136640965)⟩⟩,⟨⟨5978334409183305112800905154,5978334409183305122084870477⟩,⟨(-12602882471102409493850471759),(-12602882471102409483341908846)⟩⟩,⟨⟨5863067273078091139134429038,5863067273078091148312285988⟩,⟨(-12535708225070645795048639067),(-12535708225070645784658953349)⟩⟩,⟨⟨5748849702195562102307150291,5748849702195562111378190875⟩,⟨(-12464965433213760040946657141),(-12464965433213760030676584677)⟩⟩,⟨⟨5635151069212487209022189198,5635151069212487217984836976⟩,⟨(-12389470828282574158827026295),(-12389470828282574148678490905)⟩⟩,⟨⟨5522552295576309586210207759,5522552295576309595063411272⟩,⟨(-12310456327929295119359253329),(-12310456327929295109333826462)⟩⟩,⟨⟨5410502486846970014280568698,5410502486846970023022577623⟩,⟨(-12226669257357300088561378132),(-12226669257357300078661378784)⟩⟩] +lemma amp1_04_11_eq : ∀ k : Fin 16, amp1_0Expr 4 11 k = amp1_04_11 k := by decide +kernel +noncomputable def amp1_04_12 : Fin 16 → CBox := ![⟨⟨5299598605036228631605828837,5299598605036228640242476868⟩,⟨(-12139420827114858746709402176),(-12139420827114858736920690655)⟩⟩,⟨⟨5189268890357648951479991682,5189268890357648960004049397⟩,⟨(-12047385059268084758522952656),(-12047385059268084748860242466)⟩⟩,⟨⟨5080126964526698152492102692,5080126964526698160902804840⟩,⟨(-11951956513609678107835930769),(-11951956513609678098300257038)⟩⟩,⟨⟨4971579506814651725211130265,4971579506814651733507039882⟩,⟨(-11851731667654209177947633529),(-11851731667654209168540578040)⟩⟩,⟨⟨4864257533465782376420515926,4864257533465782384600902520⟩,⟨(-11748192836559880538311679163),(-11748192836559880529034231957)⟩⟩,⟨⟨4757545357564359430799975882,4757545357564359438863526398⟩,⟨(-11639854320292927859452337116),(-11639854320292927850305818168)⟩⟩,⟨⟨4652092253695657250427440409,4652092253695657258373196597⟩,⟨(-11528290994826055295046542999),(-11528290994826055286032622839)⟩⟩,⟨⟨4547259239435361302152881636,4547259239435361309980182834⟩,⟨(-11411929904329072433125699029),(-11411929904329072424244029519)⟩⟩,⟨⟨4443714856139645996686535150,4443714856139646004393931620⟩,⟨(-11292443748676301663867666667),(-11292443748676301655121192687)⟩⟩,⟨⟨4340795755448946826314258354,4340795755448946833900507796⟩,⟨(-11168166729462903624536509111),(-11168166729462903615926390575)⟩⟩,⟨⟨4239190917007583670511060906,4239190917007583677975544182⟩,⟨(-11040875160160211473430327493),(-11040875160160211464957594722)⟩⟩,⟨⟨4138211394787939826465376656,4138211394787939833806564729⟩,⟨(-10908804229451485832928851829),(-10908804229451485824595347728)⟩⟩,⟨⟨4038567963280529152977750805,4038567963280529160194909427⟩,⟨(-10773840262747186156525887296),(-10773840262747186148333025671)⟩⟩,⟨⟨3939544661649823520272047598,3939544661649823527367338467⟩,⟨(-10634112592427048445389528850),(-10634112592427048437329262133)⟩⟩,⟨⟨3841875627090693853481181983,3841875627090693860450884859⟩,⟨(-10491624661005867349965659266),(-10491624661005867342047522592)⟩⟩,⟨⟨3744816252481093000176474186,3744816252481093007019156691⟩,⟨(-10344392320674815748902370605),(-10344392320674815741127948857)⟩⟩] +lemma amp1_04_12_eq : ∀ k : Fin 16, amp1_0Expr 4 12 k = amp1_04_12 k := by decide +kernel +noncomputable def amp1_04_13 : Fin 16 → CBox := ![⟨⟨3649125848500894631302655403,3649125848500894638018096372⟩,⟨(-10194544061302622085062188322),(-10194544061302622077431713693)⟩⟩,⟨⟨3554029280958997052777117026,3554029280958997059364291657⟩,⟨(-10039973720638874089737556631),(-10039973720638874082251513150)⟩⟩,⟨⟨3460313126081253213380785074,3460313126081253219838837397⟩,⟨(-9882943734709660313781168272),(-9882943734709660306441762407)⟩⟩,⟨⟨3367169549953243541811964326,3367169549953243548139642947⟩,⟨(-9721216324032392151192562009),(-9721216324032392144000834624)⟩⟩,⟨⟨3275414814581194285605275458,3275414814581194291802146650⟩,⟨(-9557197913543233295065320895),(-9557197913543233288022398810)⟩⟩,⟨⟨3184205869562094242788024172,3184205869562094248854780240⟩,⟨(-9388508241009929522851228623),(-9388508241009929515952444377)⟩⟩,⟨⟨3094391468904845381186481740,3094391468904845387121231307⟩,⟨(-9217709123208483656335268956),(-9217709123208483649586198629)⟩⟩,⟨⟨3005090420171712716288562181,3005090420171712722089763959⟩,⟨(-9042265446402566969846732928),(-9042265446402566963249197238)⟩⟩,⟨⟨2917187233521913599316797127,2917187233521913604984526708⟩,⟨(-8864907451324136427483891612),(-8864907451324136421037806944)⟩⟩,⟨⟨2829759159330008924657023423,2829759159330008930189992814⟩,⟨(-8682931000002419892034682616),(-8682931000002419885741128949)⟩⟩,⟨⟨2743730276390491656208273682,2743730276390491661606426487⟩,⟨(-8499249756460134725472619170),(-8499249756460134719332151876)⟩⟩,⟨⟨2658132271048943736691453437,2658132271048943741954554237⟩,⟨(-8310974201781988972321226796),(-8310974201781988966331499947)⟩⟩,⟨⟨2573933266443338306177926984,2573933266443338311304629928⟩,⟨(-8121218819281640848481151169),(-8121218819281640842646873941)⟩⟩,⟨⟨2490114655939707510500739538,2490114655939707515489644230⟩,⟨(-7926889682697347371621528866),(-7926889682697347365943999961)⟩⟩,⟨⟨2407693893711849710217646066,2407693893711849715069209371⟩,⟨(-7731322439515148043465988478),(-7731322439515148037944564185)⟩⟩,⟨⟨2325596460322086132141458027,2325596460322086136853892955⟩,⟨(-7531196431271605636099637858),(-7531196431271605630736710049)⟩⟩] +lemma amp1_04_13_eq : ∀ k : Fin 16, amp1_0Expr 4 13 k = amp1_04_13 k := by decide +kernel +noncomputable def amp1_04_14 : Fin 16 → CBox := ![⟨⟨2244895431260576306895433911,2244895431260576311470178767⟩,⟨(-7330092483041432286283153599),(-7330092483041432281075027299)⟩⟩,⟨⟨2164453642095936426361821287,2164453642095936430796346053⟩,⟨(-7124436755348031965737224240),(-7124436755348031960688684810)⟩⟩,⟨⟨2085407338328973889533937688,2085407338328973893828964448⟩,⟨(-6918083884758200756316461274),(-6918083884758200751426467493)⟩⟩,⟨⟨2006548570653898226062622224,2006548570653898230216087833⟩,⟨(-6707175176996376673439008752),(-6707175176996376668710671350)⟩⟩,⟨⟨1929085904514240991627978459,1929085904514240995641518591⟩,⟨(-6495873614970292568609315030),(-6495873614970292564038754721)⟩⟩,⟨⟨1851730657331299417624427714,1851730657331299421495544520⟩,⟨(-6279997256106114466177076074),(-6279997256106114461768772054)⟩⟩,⟨⟨1775774935642936919711749089,1775774935642936923441836843⟩,⟨(-6064059620565666575102428587),(-6064059620565666570853649777)⟩⟩,⟨⟨1699837011606552735045104559,1699837011606552738631699099⟩,⟨(-5843508333865144117627152919),(-5843508333865144113542065962)⟩⟩,⟨⟨1625306483484242214496604696,1625306483484242217940774060⟩,⟨(-5623259758294419901251103838),(-5623259758294419897328390453)⟩⟩,⟨⟨1550693116039930367068260049,1550693116039930370368471192⟩,⟨(-5398332179446450277394264321),(-5398332179446450273634734899)⟩⟩,⟨⟨1477501624287155313099461823,1477501624287155316256439537⟩,⟨(-5174110748446996735370822436),(-5174110748446996731774829327)⟩⟩,⟨⟨1404113508856730525496168495,1404113508856730528508226728⟩,⟨(-4945109508397047028915529349),(-4945109508397047025484046560)⟩⟩,⟨⟨1332171296615410867204931264,1332171296615410870073466593⟩,⟨(-4717267198118655933458880615),(-4717267198118655930190358140)⟩⟩,⟨⟨1259902455156923930028500348,1259902455156923932750903132⟩,⟨(-4484496312031306882049753542),(-4484496312031306878948097447)⟩⟩,⟨⟨1189117220101469159812701269,1189117220101469162390932336⟩,⟨(-4253400785223850298273016747),(-4253400785223850295335312131)⟩⟩,⟨⟨1117854571377976866425406848,1117854571377976868856995737⟩,⟨(-4017161876444438554150805292),(-4017161876444438551379947530)⟩⟩] +lemma amp1_04_14_eq : ∀ k : Fin 16, amp1_0Expr 4 14 k = amp1_04_14 k := by decide +kernel +noncomputable def amp1_04_15 : Fin 16 → CBox := ![⟨⟨1048132940709839558099315969,1048132940709839560386131843⟩,⟨(-3783199784228645035663565304),(-3783199784228645033057620577)⟩⟩,⟨⟨977755331440135426842649138,977755331440135428981990530⟩,⟨(-3543786234992750820158841946),(-3543786234992750817720975272)⟩⟩,⟨⟨909005103464368789404187736,909005103464368791398352341⟩,⟨(-3307369321525166184612487310),(-3307369321525166182340167089)⟩⟩,⟨⟨839381295990389712269640254,839381295990389714115739778⟩,⟨(-3065056473631586440893102284),(-3065056473631586438789276419)⟩⟩,⟨⟨771515193413272925777348967,771515193413272927478102142⟩,⟨(-2826633270511767722802460621),(-2826633270511767720864191630)⟩⟩,⟨⟨702499674662275765624848412,702499674662275767176744471⟩,⟨(-2581660444753823031805492327),(-2581660444753823030036870144)⟩⟩,⟨⟨635442380963758499738577234,635442380963758501144979747⟩,⟨(-2341740172299399887459478958),(-2341740172299399885856810578)⟩⟩,⟨⟨566866130460975756990767604,566866130460975758247637591⟩,⟨(-2094273829805534680441421413),(-2094273829805534679009008007)⟩⟩,⟨⟨500569403508014505973423950,500569403508014507084970057⟩,⟨(-1853480404442691530260007303),(-1853480404442691528993295295)⟩⟩,⟨⟨432217216285064137611753199,432217216285064138572806279⟩,⟨(-1603527089250132360748515592),(-1603527089250132359653356032)⟩⟩,⟨⟨366698613902451313246896094,366698613902451314063165774⟩,⟨(-1362741222863623936228991836),(-1362741222863623935298936100)⟩⟩,⟨⟨298242291517176554653743414,298242291517176555318249484⟩,⟨(-1109895761162676724050461574),(-1109895761162676723293397723)⟩⟩,⟨⟨233713411606817814104612968,233713411606817814625678454⟩,⟨(-870731121346295532237659378),(-870731121346295531644179829)⟩⟩,⟨⟨164442842991784815170253023,164442842991784815537054729⟩,⟨(-613170481679804685291566294),(-613170481679804684873892384)⟩⟩,⟨⟨101965707073669371608130004,101965707073669371835520067⟩,⟨(-380420923474277062623342177),(-380420923474277062364774754)⟩⟩,⟨⟨28962913528335770684994086,28962913528335770749512292⟩,⟨(-108087267962443344220622311),(-108087267962443344147475052)⟩⟩] +lemma amp1_04_15_eq : ∀ k : Fin 16, amp1_0Expr 4 15 k = amp1_04_15 k := by decide +kernel +noncomputable def amp1_04 : Fin 16 → Fin 16 → CBox := ![amp1_04_0,amp1_04_1,amp1_04_2,amp1_04_3,amp1_04_4,amp1_04_5,amp1_04_6,amp1_04_7,amp1_04_8,amp1_04_9,amp1_04_10,amp1_04_11,amp1_04_12,amp1_04_13,amp1_04_14,amp1_04_15] +lemma amp1_04_eq (i k : Fin 16) : amp1_0Expr 4 i k = amp1_04 i k := by + fin_cases i + · exact amp1_04_0_eq k + · exact amp1_04_1_eq k + · exact amp1_04_2_eq k + · exact amp1_04_3_eq k + · exact amp1_04_4_eq k + · exact amp1_04_5_eq k + · exact amp1_04_6_eq k + · exact amp1_04_7_eq k + · exact amp1_04_8_eq k + · exact amp1_04_9_eq k + · exact amp1_04_10_eq k + · exact amp1_04_11_eq k + · exact amp1_04_12_eq k + · exact amp1_04_13_eq k + · exact amp1_04_14_eq k + · exact amp1_04_15_eq k +noncomputable def amp1_05_0 : Fin 16 → CBox := ![⟨⟨1017365712714789582412,1017365712714806656212⟩,⟨(-8649277),8649282⟩⟩,⟨⟨32227844834901885180018,32227844834901945277190⟩,⟨(-30443786),30443938⟩⟩,⟨⟨144307603078629628353343,144307603078629725234573⟩,⟨(-49076495),49077175⟩⟩,⟨⟨401710817432016674520882,401710817432016812129440⟩,⟨(-69704918),69706811⟩⟩,⟨⟨846618630911081777873541,846618630911081953334801⟩,⟨(-88874594),88878584⟩⟩,⟨⟨1553203743542669544274406,1553203743542669759792852⟩,⟨(-109157596),109164916⟩⟩,⟨⟨2553427679062347536387104,2553427679062347790106762⟩,⟨(-128496428),128508463⟩⟩,⟨⟨3930825950684612355971439,3930825950684612649403087⟩,⟨(-148595623),148614150⟩⟩,⟨⟨5707149034948221291888609,5707149034948221623651904⟩,⟨(-167990161),168017060⟩⟩,⟨⟨7974992912616157603273367,7974992912616157974503158⟩,⟨(-187953565),187991153⟩⟩,⟨⟨10745843359115808013509729,10745843359115808423099256⟩,⟨(-207348839),207399486⟩⟩,⟨⟨14121091280701553057183412,14121091280701553506030838⟩,⟨(-227191331),227257887⟩⟩,⟨⟨18101889125021378311407097,18101889125021378798578011⟩,⟨(-246552709),246638028⟩⟩,⟨⟨22798164690230290408885678,22798164690230290935112099⟩,⟨(-266276136),266383589⟩⟩,⟨⟨28200671625299007046688031,28200671625299007611159772⟩,⟨(-285577905),285710821⟩⟩,⟨⟨34427613720176448625434016,34427613720176449228761472⟩,⟨(-305177998),305340263⟩⟩] +lemma amp1_05_0_eq : ∀ k : Fin 16, amp1_0Expr 5 0 k = amp1_05_0 k := by decide +kernel +noncomputable def amp1_05_1 : Fin 16 → CBox := ![⟨⟨41459290719596023701396978,41459290719596024342852285⟩,⟨(-324398995),324594402⟩⟩,⟨⟨49421914614835276365094033,49421914614835277045189338⟩,⟨(-343868277),344101214⟩⟩,⟨⟨58285289887787186486983824,58285289887787187205055019⟩,⟨(-362989933),363264645⟩⟩,⟨⟨68183360397692089594610300,68183360397692090351108873⟩,⟨(-382319110),382640474⟩⟩,⟨⟨79075409598275565416789351,79075409598275566211083119⟩,⟨(-401324468),401697169⟩⟩,⟨⟨91102827691590655214296079,91102827691590656046755579⟩,⟨(-420503170),420932559⟩⟩,⟨⟨104214368082311430049500797,104214368082311430919577461⟩,⟨(-439376357),439867544⟩⟩,⟨⟨118558572418822139446543938,118558572418822140354522327⟩,⟨(-458393565),458952359⟩⟩,⟨⟨134073672582852005439799426,134073672582852006385165105⟩,⟨(-477119484),477751404⟩⟩,⟨⟨150915057458186184084660442,150915057458186185067690711⟩,⟨(-495963786),496675084⟩⟩,⟨⟨169010464087999568475706810,169010464087999569495831432⟩,⟨(-514527932),515324518⟩⟩,⟨⟨188521815248313382165818294,188521815248313383223311190⟩,⟨(-533187700),534076247⟩⟩,⟨⟨209366398483646596557519735,209366398483646597651807019⟩,⟨(-551576044),552562836⟩⟩,⟨⟨231712348237249835740755396,231712348237249836872123012⟩,⟨(-570039541),571131656⟩⟩,⟨⟨255466566973823128603691729,255466566973823129771621321⟩,⟨(-588238459),589442533⟩⟩,⟨⟨280803069984181515662938027,280803069984181516867601337⟩,⟨(-606493926),607817417⟩⟩] +lemma amp1_05_1_eq : ∀ k : Fin 16, amp1_0Expr 5 1 k = amp1_05_1 k := by decide +kernel +noncomputable def amp1_05_2 : Fin 16 → CBox := ![⟨⟨307618458522706083434003884,307618458522706084674813386⟩,⟨(-624490152),625940030⟩⟩,⟨⟨336092289619148268001842143,336092289619148269279051481⟩,⟨(-642525864),644109946⟩⟩,⟨⟨366110966970354770416364258,366110966970354771729493556⟩,⟨(-660306459),662032026⟩⟩,⟨⟨397859242260386785839448420,397859242260386787188609169⟩,⟨(-678110774),679985977⟩⟩,⟨⟨431213445365565142851366494,431213445365565144236135516⟩,⟨(-695663107),697695517⟩⟩,⟨⟨466363167876582221127714333,466363167876582222547898543⟩,⟨(-713224498),715422577⟩⟩,⟨⟨503174809944199806588832842,503174809944199808044203939⟩,⟨(-730536239),732907819⟩⟩,⟨⟨541842440962969023384215113,541842440962969024874778130⟩,⟨(-747843328),750397158⟩⟩,⟨⟨582222696060299641118745460,582222696060299642644098651⟩,⟨(-764902435),767646586⟩⟩,⟨⟨624513753276140036344488249,624513753276140037904663649⟩,⟨(-781944015),784887494⟩⟩,⟨⟨668562668250543283720670392,668562668250543285315230170⟩,⟨(-798738735),801889827⟩⟩,⟨⟨714571351742874039573607259,714571351742874041202143039⟩,⟨(-815503790),818871732⟩⟩,⟨⟨762377486480516794548436625,762377486480516796210976411⟩,⟨(-832022660),835615923⟩⟩,⟨⟨812186333523575930250503951,812186333523575931946962128⟩,⟨(-848500387),852328410⟩⟩,⟨⟨863826430484116376720496000,863826430484116378450503326⟩,⟨(-864732233),868803649⟩⟩,⟨⟨917506000071359152666816133,917506000071359154430166154⟩,⟨(-880912051),885236471⟩⟩] +lemma amp1_05_2_eq : ∀ k : Fin 16, amp1_0Expr 5 2 k = amp1_05_2 k := by decide +kernel +noncomputable def amp1_05_3 : Fin 16 → CBox := ![⟨⟨973044683965568814972962705,973044683965568816769328213⟩,⟨(-896845994),901432181⟩⟩,⟨⟨1030653271883720174285090559,1030653271883720176114434553⟩,⟨(-912717564),917575273⟩⟩,⟨⟨1090142780287363172303205486,1090142780287363174165117053⟩,⟨(-928343020),933481118⟩⟩,⟨⟨1151726165495505752646781654,1151726165495505754540217983⟩,⟨(-943896255),949324609⟩⟩,⟨⟨1215206111117198394379527286,1215206111117198396305065498⟩,⟨(-959202943),964930493⟩⟩,⟨⟨1280797334109812438674184368,1280797334109812440631645328⟩,⟨(-974428020),980464717⟩⟩,⟨⟨1348294499353228943358554610,1348294499353228945347498066⟩,⟨(-989405963),995760790⟩⟩,⟨⟨1417913673107950988705408156,1417913673107950990725673631⟩,⟨(-1004293333),1010976292⟩⟩,⟨⟨1489441837489806939239598145,1489441837489806941290818507⟩,⟨(-1018932866),1025952953⟩⟩,⟨⟨1563095991521031543023329216,1563095991521031545105085916⟩,⟨(-1033473265),1040840501⟩⟩,⟨⟨1638655792425954714239670991,1638655792425954716351806866⟩,⟨(-1047765036),1055488404⟩⟩,⟨⟨1716338750384461638970483115,1716338750384461641112726979⟩,⟨(-1061949492),1070038997⟩⟩,⟨⟨1795917577556343211962250610,1795917577556343214134217455⟩,⟨(-1075884472),1084349051⟩⟩,⟨⟨1877609868733088064714481105,1877609868733088066915996752⟩,⟨(-1089704311),1098553925⟩⟩,⟨⟨1961181792819992280823689030,1961181792819992283054341857⟩,⟨(-1103273794),1112517302⟩⟩,⟨⟨2046850597829250581740870232,2046850597829250584000465972⟩,⟨(-1116720654),1126367938⟩⟩] +lemma amp1_05_3_eq : ∀ k : Fin 16, amp1_0Expr 5 3 k = amp1_05_3 k := by decide +kernel +noncomputable def amp1_05_4 : Fin 16 → CBox := ![⟨⟨2134376333215646663432048323,2134376333215646665717870852⟩,⟨(-1129916262),1139976076⟩⟩,⟨⟨2223975464049050680457263121,2223975464049050682771710882⟩,⟨(-1142982092),1153464208⟩⟩,⟨⟨2315402366125218524907797788,2315402366125218527250350329⟩,⟨(-1155795782),1166708814⟩⟩,⟨⟨2408872280684075507131755406,2408872280684075509502127948⟩,⟨(-1168472853),1179826430⟩⟩,⟨⟨2504134377618229002678290582,2504134377618229005076009938⟩,⟨(-1180896918),1192699488⟩⟩,⟨⟨2601402228747062344216980508,2601402228747062346641931516⟩,⟨(-1193177826),1205438842⟩⟩,⟨⟨2700420287741234992553645583,2700420287741234995005121740⟩,⟨(-1205204900),1217932611⟩⟩,⟨⟨2801400006700950694721233840,2801400006700950697199194443⟩,⟨(-1217082571),1230286223⟩⟩,⟨⟨2904081634627201913755278269,2904081634627201916259327216⟩,⟨(-1228705631),1242393246⟩⟩,⟨⟨3008674048861856003575380190,3008674048861856006104426118⟩,⟨(-1240173328),1254353911⟩⟩,⟨⟨3114913827091087447542966565,3114913827091087450097459922⟩,⟨(-1251385699),1266067015⟩⟩,⟨⟨3223006812058119978481463601,3223006812058119981060997707⟩,⟨(-1262437021),1277627805⟩⟩,⟨⟨3332686465209943391180225147,3332686465209943393784441173⟩,⟨(-1273232378),1288940107⟩⟩,⟨⟨3444155129960154740842225629,3444155129960154743470509532⟩,⟨(-1283861268),1300094375⟩⟩,⟨⟨3557143728219029241487109645,3557143728219029244139382151⟩,⟨(-1294233634),1310999283⟩⟩,⟨⟨3671850634329706808878002201,3671850634329706811553764286⟩,⟨(-1304434380),1321740669⟩⟩] +lemma amp1_05_4_eq : ∀ k : Fin 16, amp1_0Expr 5 4 k = amp1_05_4 k := by decide +kernel +noncomputable def amp1_05_5 : Fin 16 → CBox := ![⟨⟨3788004828890165630851767163,3788004828890165633550658963⟩,⟨(-1314378134),1332231885⟩⟩,⟨⟨3905800242272824150387876314,3905800242272824153109614508⟩,⟨(-1324145369),1342554318⟩⟩,⟨⟨4024964533395238301619985443,4024964533395238304364213006⟩,⟨(-1333655245),1352625842⟩⟩,⟨⟨4145686708418613027467141181,4145686708418613030233537629⟩,⟨(-1342983953),1362523542⟩⟩,⟨⟨4267693745496789283839876158,4267693745496789286628011086⟩,⟨(-1352055038),1372169675⟩⟩,⟨⟨4391169240786213740947055220,4391169240786213743748986484⟩,⟨(-1360940553),1381637159⟩⟩,⟨⟨4515840153749391088355894394,4515840153749391091179078131⟩,⟨(-1369568293),1390852502⟩⟩,⟨⟨4641884178945692237125682973,4641884178945692239969626164⟩,⟨(-1378006299),1399884583⟩⟩,⟨⟨4769028940240375244673929926,4769028940240375247538018886⟩,⟨(-1386186496),1408664042⟩⟩,⟨⟨4897445732925117417407021078,4897445732925117420290931042⟩,⟨(-1394173029),1417255834⟩⟩,⟨⟨5026863549246854130101949885,5026863549246854133004993968⟩,⟨(-1401901838),1425594620⟩⟩,⟨⟨5157446781166343515116159516,5157446781166343518037970301⟩,⟨(-1409433287),1433741538⟩⟩,⟨⟨5288926514038202102834962209,5288926514038202105775339515⟩,⟨(-1416707223),1441635169⟩⟩,⟨⟨5421459725686305868348433875,5421459725686305871306606307⟩,⟨(-1423780327),1449332932⟩⟩,⟨⟨5554780339909606551871328981,5554780339909606554847079070⟩,⟨(-1430596257),1456777233⟩⟩,⟨⟨5689037402459319914022576195,5689037402459319917015655313⟩,⟨(-1437208104),1464021865⟩⟩] +lemma amp1_05_5_eq : ∀ k : Fin 16, amp1_0Expr 5 5 k = amp1_05_5 k := by decide +kernel +noncomputable def amp1_05_6 : Fin 16 → CBox := ![⟨⟨5823968441393309566224337274,5823968441393309569233231363⟩,⟨(-1443563249),1471012972⟩⟩,⟨⟨5959714044899289792209824059,5959714044899289795235403116⟩,⟨(-1449711279),1477800802⟩⟩,⟨⟨6096016131460073493112507015,6096016131460073496153630255⟩,⟨(-1455603211),1484335158⟩⟩,⟨⟨6233006298189215733949113574,6233006298189215737006065350⟩,⟨(-1461285209),1490662823⟩⟩,⟨⟨6370431660394543907027334590,6370431660394543910099239563⟩,⟨(-1466711851),1496737183⟩⟩,⟨⟨6508414282079257380697125845,6508414282079257383783834764⟩,⟨(-1471925948),1502601624⟩⟩,⟨⟨6646707301904864091638304435,6646707301904864094735709485⟩,⟨(-1476885569),1508213052⟩⟩,⟨⟨6785422699654169367200343970,6785422699654169370311957286⟩,⟨(-1481630238),1513611519⟩⟩,⟨⟨6924320483909415368684502808,6924320483909415371809445312⟩,⟨(-1486121451),1518757390⟩⟩,⟨⟨7063501989456468218077159757,7063501989456468221214871297⟩,⟨(-1490395507),1523687441⟩⟩,⟨⟨7202734961332202776369393882,7202734961332202779519585057⟩,⟨(-1494417266),1528365437⟩⟩,⟨⟨7342109518243493789775386880,7342109518243493792937240250⟩,⟨(-1498219859),1532824935⟩⟩,⟨⟨7481402028133446260150497563,7481402028133446263323703240⟩,⟨(-1501771455),1537033050⟩⟩,⟨⟨7620690811554856991787015662,7620690811554856994971480964⟩,⟨(-1505102069),1541020164⟩⟩,⟨⟨7759761765703628867195494500,7759761765703628870388719511⟩,⟨(-1508183129),1544756698⟩⟩,⟨⟨7898680819171865496718444953,7898680819171865499921799258⟩,⟨(-1511041577),1548269904⟩⟩] +lemma amp1_05_6_eq : ∀ k : Fin 16, amp1_0Expr 5 6 k = amp1_05_6 k := by decide +kernel +noncomputable def amp1_05_7 : Fin 16 → CBox := ![⟨⟨8037244324657834612473043526,8037244324657834615685752115⟩,⟨(-1513652056),1551533465⟩⟩,⟨⟨8175505212462621446688298976,8175505212462621449910241662⟩,⟨(-1516038476),1554571540⟩⟩,⟨⟨8313271236982902318810129272,8313271236982902322039635283⟩,⟨(-1518178653),1557361041⟩⟩,⟨⟨8450581710525803770002139851,8450581710525803773239722473⟩,⟨(-1520093505),1559923069⟩⟩,⟨⟨8587256755412933326800117584,8587256755412933330044506892⟩,⟨(-1521763982),1562237728⟩⟩,⟨⟨8723321431972879242044091580,8723321431972879245295690241⟩,⟨(-1523208041),1564323091⟩⟩,⟨⟨8858609216839208422853347847,8858609216839208426111033974⟩,⟨(-1524409733),1566162426⟩⟩,⟨⟨8993130269122809604715462946,8993130269122809607978836940⟩,⟨(-1525384085),1567770807⟩⟩,⟨⟨9126732426498762490483696550,9126732426498762493752224715⟩,⟨(-1526118219),1569134639⟩⟩,⟨⟨9259410281325397353364265890,9259410281325397356637678038⟩,⟨(-1526624256),1570266018⟩⟩,⟨⟨9391027059631885634987797677,9391027059631885638265233776⟩,⟨(-1526892363),1571154466⟩⟩,⟨⟨9521561104079381979419597349,9521561104079381982700721096⟩,⟨(-1526931776),1571809116⟩⟩,⟨⟨9650892077252799423982764241,9650892077252799427266705308⟩,⟨(-1526735687),1572222594⟩⟩,⟨⟨9778981370569384261014094640,9778981370569384264300355387⟩,⟨(-1526310463),1572401085⟩⟩,⟨⟨9905726152639809843082708684,9905726152639809846370464560⟩,⟨(-1525652299),1572340299⟩⟩,⟨⟨10031070142211902031629835846,10031070142211902034918301365⟩,⟨(-1524764713),1572043488⟩⟩] +lemma amp1_05_7_eq : ∀ k : Fin 16, amp1_0Expr 5 7 k = amp1_05_7 k := by decide +kernel +noncomputable def amp1_05_8 : Fin 16 → CBox := ![⟨⟨10154929105121458592783714399,10154929105121458596073378393⟩,⟨(-1523646886),1571509437⟩⟩,⟨⟨10277228344774870550075549360,10277228344774870553367139474⟩,⟨(-1522299493),1570738469⟩⟩,⟨⟨10397903337713655820586619766,10397903337713655823879239003⟩,⟨(-1520724694),1569732439⟩⟩,⟨⟨10516860206617878169415484086,10516860206617878172708461536⟩,⟨(-1518920327),1568488744⟩⟩,⟨⟨10634055275149534854577844719,10634055275149534857870507205⟩,⟨(-1516891519),1567012304⟩⟩,⟨⟨10749374695591017523834482596,10749374695591017527126117883⟩,⟨(-1514633279),1565297591⟩⟩,⟨⟨10862796798838857611106509322,10862796798838857614396650827⟩,⟨(-1512153697),1563352594⟩⟩,⟨⟨10974186951129577911174933568,10974186951129577914462803820⟩,⟨(-1509444947),1561168852⟩⟩,⟨⟨11083546675297232711892292633,11083546675297232715177435657⟩,⟨(-1506518082),1558757425⟩⟩,⟨⟨11190719708089349789175657215,11190719708089349792457735826⟩,⟨(-1503362442),1556106917⟩⟩,⟨⟨11295731974597181553844804040,11295731974597181557123269539⟩,⟨(-1499992043),1553231464⟩⟩,⟨⟨11398404708883200999854567119,11398404708883201003128243019⟩,⟨(-1496393379),1550116722⟩⟩,⟨⟨11498789475413175210660980995,11498789475413175213930321121⟩,⟨(-1492583438),1546779918⟩⟩,⟨⟨11596684100503760015395399226,11596684100503760018659043472⟩,⟨(-1488545861),1543203740⟩⟩,⟨⟨11692167053261121762268140447,11692167053261121765526806324⟩,⟨(-1484300613),1539408525⟩⟩,⟨⟨11785011813049447605297364579,11785011813049447608549015719⟩,⟨(-1479828464),1535373976⟩⟩] +lemma amp1_05_8_eq : ∀ k : Fin 16, amp1_0Expr 5 8 k = amp1_05_8 k := by decide +kernel +noncomputable def amp1_05_9 : Fin 16 → CBox := ![⟨⟨11875325048569344300707190436,11875325048569344303951570644⟩,⟨(-1475152374),1531123553⟩⟩,⟨⟨11962854916411658332270523136,11962854916411658335506892232⟩,⟨(-1470250225),1526633953⟩⟩,⟨⟨12047737611262769686777541922,12047737611262769690008082952⟩,⟨(-1465147984),1521931784⟩⟩,⟨⟨12129694951829510848910476440,12129694951829510852131684649⟩,⟨(-1459820625),1516990709⟩⟩,⟨⟨12208894018594742988372627830,12208894018594742991584323241⟩,⟨(-1454297142),1511840510⟩⟩,⟨⟨12285029235075145118787809592,12285029235075145121989969182⟩,⟨(-1448549574),1506451785⟩⟩,⟨⟨12358299963021469187600279033,12358299963021469190791568208⟩,⟨(-1442609970),1500857522⟩⟩,⟨⟨12428372128096910060364575977,12428372128096910063544949706⟩,⟨(-1436447400),1495025219⟩⟩,⟨⟨12495478806982420227391955176,12495478806982420230560417868⟩,⟨(-1430096998),1488991106⟩⟩,⟨⟨12559256276019802218552440002,12559256276019802221707918946⟩,⟨(-1423524831),1482719537⟩⟩,⟨⟨12619972801525971471855516153,12619972801525971475004899109⟩,⟨(-1416769149),1476250027⟩⟩,⟨⟨12677233806482011584367738452,12677233806482011587503773156⟩,⟨(-1409792979),1469543742⟩⟩,⟨⟨12731344265802869003321517603,12731344265802869006443980801⟩,⟨(-1402637727),1462643524⟩⟩,⟨⟨12781877488373212778902286737,12781877488373212782010028207⟩,⟨(-1395263331),1455507303⟩⟩,⟨⟨12829176724540682361904058657,12829176724540682364997837952⟩,⟨(-1387714397),1448181302⟩⟩,⟨⟨12872781847134098500465359340,12872781847134098503543365893⟩,⟨(-1379947727),1440620153⟩⟩] +lemma amp1_05_9_eq : ∀ k : Fin 16, amp1_0Expr 5 9 k = amp1_05_9 k := by decide +kernel +noncomputable def amp1_05_10 : Fin 16 → CBox := ![⟨⟨12913076000709954106289492960,12913076000709954109353800510⟩,⟨(-1372011176),1432873517⟩⟩,⟨⟨12949564233877359602045802479,12949564233877359605093794187⟩,⟨(-1363858352),1424892671⟩⟩,⟨⟨12982671260697089637469197176,12982671260697089640500507245⟩,⟨(-1355540413),1416730774⟩⟩,⟨⟨13011865845697627165943149194,13011865845697627168958023410⟩,⟨(-1347007717),1408335678⟩⟩,⟨⟨13037616009409894490959757925,13037616009409894493956497456⟩,⟨(-1338314782),1399764110⟩⟩,⟨⟨13059352694651544112242315771,13059352694651544115221275782⟩,⟨(-1329408646),1390960424⟩⟩,⟨⟨13077589032858803751805400248,13077589032858803754765921217⟩,⟨(-1320347258),1381984988⟩⟩,⟨⟨13091716523008848061638137234,13091716523008848064579248553⟩,⟨(-1311074263),1372778579⟩⟩,⟨⟨13102295285879987919467204561,13102295285879987922388231979⟩,⟨(-1301651112),1363405289⟩⟩,⟨⟨13108675662500827681045214785,13108675662500827683945399516⟩,⟨(-1292017977),1353802225⟩⟩,⟨⟨13111466722795377662607713435,13111466722795377665485906897⟩,⟨(-1282239892),1344037296⟩⟩,⟨⟨13109975835423449522722779790,13109975835423449525602847549⟩,⟨(-1272253467),1334043843⟩⟩,⟨⟨13104863068938931646278510902,13104863068938931649137019215⟩,⟨(-1262127411),1323893690⟩⟩,⟨⟨13095390895588513060905363462,13095390895588513063742078019⟩,⟨(-1251794672),1313516306⟩⟩,⟨⟨13082272531117872667120843520,13082272531117872669935122003⟩,⟨(-1241327732),1302987536⟩⟩,⟨⟨13064723507257033416068587328,13064723507257033418860385880⟩,⟨(-1230655773),1292232865⟩⟩] +lemma amp1_05_10_eq : ∀ k : Fin 16, amp1_0Expr 5 10 k = amp1_05_10 k := by decide +kernel +noncomputable def amp1_05_11 : Fin 16 → CBox := ![⟨⟨13043512445221825670759183875,13043512445221825673527894563⟩,⟨(-1219855157),1281332277⟩⟩,⟨⟨13017805760334312458714215862,13017805760334312461459897033⟩,⟨(-1208851185),1270207143⟩⟩,⟨⟨12988429859341489298882482948,12988429859341489301603786002⟩,⟨(-1197724215),1258941717⟩⟩,⟨⟨12954499720255460278937362575,12954499720255460281635339101⟩,⟨(-1186395540),1247453121⟩⟩,⟨⟨12916902050911340020871381825,12916902050911340023544113508⟩,⟨(-1174949644),1235830018⟩⟩,⟨⟨12874697911143072118737873893,12874697911143072121385402544⟩,⟨(-1163303675),1223985132⟩⟩,⟨⟨12828836976547584761161858126,12828836976547584763783021239⟩,⟨(-1151546384),1212011688⟩⟩,⟨⟨12778323730974931496849270651,12778323730974931499447603661⟩,⟨(-1139590624),1199817846⟩⟩,⟨⟨12724173653412829156902042275,12724173653412829159473321634⟩,⟨(-1127529566),1187501567⟩⟩,⟨⟨12665331797658554988171722429,12665331797658554990715851660⟩,⟨(-1115271601),1174966266⟩⟩,⟨⟨12602882471102409487332284349,12602882471102409489849677555⟩,⟨(-1102914494),1162314821⟩⟩,⟨⟨12535708225070645788603915868,12535708225070645791092920286⟩,⟨(-1090361992),1149445711⟩⟩,⟨⟨12464965433213760034575798202,12464965433213760037036365666⟩,⟨(-1077716640),1136466932⟩⟩,⟨⟨12389470828282574152531253659,12389470828282574154962880905⟩,⟨(-1064877342),1123271810⟩⟩,⟨⟨12310456327929295113139825718,12310456327929295115541582712⟩,⟨(-1051951630),1109973684⟩⟩,⟨⟨12226669257357300082419917733,12226669257357300084790896301⟩,⟨(-1038833346),1096460493⟩⟩] +lemma amp1_05_11_eq : ∀ k : Fin 16, amp1_0Expr 5 11 k = amp1_05_11 k := by decide +kernel +noncomputable def amp1_05_12 : Fin 16 → CBox := ![⟨⟨12139420827114858740631480403,12139420827114858742986414025⟩,⟨(-1025635235),1082851159⟩⟩,⟨⟨12047385059268084752522590852,12047385059268084754848167714⟩,⟨(-1012245837),1069027975⟩⟩,⟨⟨11951956513609678101913899585,11951956513609678104209629503⟩,⟨(-998783361),1055115722⟩⟩,⟨⟨11851731667654209172104826855,11851731667654209174370521321⟩,⟨(-985130777),1040990755⟩⟩,⟨⟨11748192836559880532548847602,11748192836559880534784011376⟩,⟨(-971412036),1026784012⟩⟩,⟨⟨11639854320292927853770116583,11639854320292927855974815384⟩,⟨(-957504247),1012365598⟩⟩,⟨⟨11528290994826055289446390298,11528290994826055291619396858⟩,⟨(-943537407),997872934⟩⟩,⟨⟨11411929904329072427606585285,11411929904329072429749626831⟩,⟨(-929382438),983169528⟩⟩,⟨⟨11292443748676301658432349475,11292443748676301660542871341⟩,⟨(-915175727),968399650⟩⟩,⟨⟨11168166729462903619185470390,11168166729462903621263686270⟩,⟨(-900781643),953419820⟩⟩,⟨⟨11040875160160211468164437515,11040875160160211470209652615⟩,⟨(-886343344),938381566⟩⟩,⟨⟨10908804229451485827749277574,10908804229451485829761018421⟩,⟨(-871718247),923133988⟩⟩,⟨⟨10773840262747186151433910629,10773840262747186153411042457⟩,⟨(-857056702),907836326⟩⟩,⟨⟨10634112592427048440376427585,10634112592427048442328364709⟩,⟨(-842208719),892329774⟩⟩,⟨⟨10491624661005867345040865664,10491624661005867346958293535⟩,⟨(-827332323),876781799⟩⟩,⟨⟨10344392320674815744066795359,10344392320674815745949494875⟩,⟨(-812269607),861025143⟩⟩] +lemma amp1_05_12_eq : ∀ k : Fin 16, amp1_0Expr 5 12 k = amp1_05_12 k := by decide +kernel +noncomputable def amp1_05_13 : Fin 16 → CBox := ![⟨⟨10194544061302622080315990889,10194544061302622082163889793⟩,⟨(-797186808),845236074⟩⟩,⟨⟨10039973720638874085080546274,10039973720638874086894527329⟩,⟨(-781917529),829238269⟩⟩,⟨⟨9882943734709660309215510055,9882943734709660310993463640⟩,⟨(-766636826),813217447⟩⟩,⟨⟨9721216324032392146718620296,9721216324032392148460875632⟩,⟨(-751169164),796987526⟩⟩,⟨⟨9557197913543233290684213780,9557197913543233292389675059⟩,⟨(-735699110),780744415⟩⟩,⟨⟨9388508241009929518557609081,9388508241009929520232319771⟩,⟨(-720041250),764291481⟩⟩,⟨⟨9217709123208483652134738547,9217709123208483653773084642⟩,⟨(-704390450),747835665⟩⟩,⟨⟨9042265446402566965740428203,9042265446402566967341973962⟩,⟨(-688550572),731168880⟩⟩,⟨⟨8864907451324136423471790381,8864907451324136425036509019⟩,⟨(-672727689),714510068⟩⟩,⟨⟨8682931000002419888117174303,8682931000002419889645383335⟩,⟨(-656713962),697638643⟩⟩,⟨⟨8499249756460134721650358525,8499249756460134723141315639⟩,⟨(-640727719),680786667⟩⟩,⟨⟨8310974201781988968591168860,8310974201781988970048634148⟩,⟨(-624548288),663719850⟩⟩,⟨⟨8121218819281640844848144777,8121218819281640846267140868⟩,⟨(-608407475),646684675⟩⟩,⟨⟨7926889682697347368086162758,7926889682697347369466826674⟩,⟨(-592070452),629431733⟩⟩,⟨⟨7731322439515148040027801612,7731322439515148041370422108⟩,⟨(-575783933),612223460⟩⟩,⟨⟨7531196431271605632760298313,7531196431271605634063946588⟩,⟨(-559297381),594793668⟩⟩] +lemma amp1_05_13_eq : ∀ k : Fin 16, amp1_0Expr 5 13 k = amp1_05_13 k := by decide +kernel +noncomputable def amp1_05_14 : Fin 16 → CBox := ![⟨⟨7330092483041432283039195297,7330092483041432284307118107⟩,⟨(-542874109),577422546⟩⟩,⟨⟨7124436755348031962592691448,7124436755348031963821600782⟩,⟨(-526246022),559825156⟩⟩,⟨⟨6918083884758200753270591751,6918083884758200754460979582⟩,⟨(-509695057),542301601⟩⟩,⟨⟨6707175176996376670494150650,6707175176996376671644446242⟩,⟨(-492933337),524545820⟩⟩,⟨⟨6495873614970292565761922777,6495873614970292566875345769⟩,⟨(-476263867),506880436⟩⟩,⟨⟨6279997256106114463430839697,6279997256106114464504503748⟩,⟨(-459376293),488975386⟩⟩,⟨⟨6064059620565666572455011167,6064059620565666573490865820⟩,⟨(-442597673),471179002⟩⟩,⟨⟨5843508333865144115081899016,5843508333865144116077436007⟩,⟨(-425591852),453133671⟩⟩,⟨⟨5623259758294419898807156874,5623259758294419899762776785⟩,⟨(-408713652),435217387⟩⟩,⟨⟨5398332179446450275051571754,5398332179446450275968203998⟩,⟨(-391596959),417040558⟩⟩,⟨⟨5174110748446996733130274846,5174110748446996734006495153⟩,⟨(-374629038),399015830⟩⟩,⟨⟨4945109508397047026777186796,4945109508397047027613862763⟩,⟨(-357408524),380715979⟩⟩,⟨⟨4717267198118655931421819464,4717267198118655932219251621⟩,⟨(-340361141),362594723⟩⟩,⟨⟨4484496312031306880116901603,4484496312031306880873153952⟩,⟨(-323043390),344179868⟩⟩,⟨⟨4253400785223850296442189000,4253400785223850297158718540⟩,⟨(-305927380),325974650⟩⟩,⟨⟨4017161876444438552423836692,4017161876444438553099882390⟩,⟨(-288518290),307452112⟩⟩] +lemma amp1_05_14_eq : ∀ k : Fin 16, amp1_0Expr 5 14 k = amp1_05_14 k := by decide +kernel +noncomputable def amp1_05_15 : Fin 16 → CBox := ![⟨⟨3783199784228645034039376375,3783199784228645034675163654⟩,⟨(-271345339),289176443⟩⟩,⟨⟨3543786234992750818639430354,3543786234992750819234142504⟩,⟨(-253849755),270552447⟩⟩,⟨⟨3307369321525166183196329864,3307369321525166183750480160⟩,⟨(-236632890),252221294⟩⟩,⟨⟨3065056473631586439581836846,3065056473631586440095111404⟩,⟨(-219053953),233500279⟩⟩,⟨⟨2826633270511767721594355964,2826633270511767722067276130⟩,⟨(-201808416),215130998⟩⟩,⟨⟨2581660444753823030703131286,2581660444753823031134635965⟩,⟨(-184146342),196314310⟩⟩,⟨⟨2341740172299399886460641342,2341740172299399886851471667⟩,⟨(-166891340),177928508⟩⟩,⟨⟨2094273829805534679548615651,2094273829805534679898071885⟩,⟨(-149140852),159011654⟩⟩,⟨⟨1853480404442691529470536178,1853480404442691529779449487⟩,⟨(-131903444),140639329⟩⟩,⟨⟨1603527089250132360065992741,1603527089250132360333005265⟩,⟨(-114047646),121605443⟩⟩,⟨⟨1362741222863623935649432662,1362741222863623935876050252⟩,⟨(-96872877),103295795⟩⟩,⟨⟨1109895761162676723578741400,1109895761162676723763124558⟩,⟨(-78865429),84096626⟩⟩,⟨⟨870731121346295531867960560,870731121346295532012313602⟩,⟨(-61850197),65954156⟩⟩,⟨⟨613170481679804685031439076,613170481679804685132916841⟩,⟨(-43543935),46433951⟩⟩,⟨⟨380420923474277062462502691,380420923474277062524929798⟩,⟨(-27010779),28803792⟩⟩,⟨⟨108087267962443344175239691,108087267962443344192663167⟩,⟨(-7673799),8183240⟩⟩] +lemma amp1_05_15_eq : ∀ k : Fin 16, amp1_0Expr 5 15 k = amp1_05_15 k := by decide +kernel +noncomputable def amp1_05 : Fin 16 → Fin 16 → CBox := ![amp1_05_0,amp1_05_1,amp1_05_2,amp1_05_3,amp1_05_4,amp1_05_5,amp1_05_6,amp1_05_7,amp1_05_8,amp1_05_9,amp1_05_10,amp1_05_11,amp1_05_12,amp1_05_13,amp1_05_14,amp1_05_15] +lemma amp1_05_eq (i k : Fin 16) : amp1_0Expr 5 i k = amp1_05 i k := by + fin_cases i + · exact amp1_05_0_eq k + · exact amp1_05_1_eq k + · exact amp1_05_2_eq k + · exact amp1_05_3_eq k + · exact amp1_05_4_eq k + · exact amp1_05_5_eq k + · exact amp1_05_6_eq k + · exact amp1_05_7_eq k + · exact amp1_05_8_eq k + · exact amp1_05_9_eq k + · exact amp1_05_10_eq k + · exact amp1_05_11_eq k + · exact amp1_05_12_eq k + · exact amp1_05_13_eq k + · exact amp1_05_14_eq k + · exact amp1_05_15_eq k +noncomputable def amp1_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp1_00,amp1_01,amp1_02,amp1_03,amp1_04,amp1_05] +lemma amp1_0_eq (j : Fin 6) (i k : Fin 16) : amp1_0Expr j i k = amp1_0 j i k := by + fin_cases j + · exact amp1_00_eq i k + · exact amp1_01_eq i k + · exact amp1_02_eq i k + · exact amp1_03_eq i k + · exact amp1_04_eq i k + · exact amp1_05_eq i k +lemma amp1_0_contains (j : Fin 6) (i k : Fin 16) : + (amp1_0 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude false 1 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp1_0_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 1 j) (bLookup_contains 1 j) false) +noncomputable def amp1_1Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 1 j) (bLookup 1 j) true) +noncomputable def amp1_10_0 : Fin 16 → CBox := ![⟨⟨(-178776584874023315364657005),(-178776584874023315333871026)⟩,⟨(-516083547009096694075783434),(-516083547009096694043399675)⟩⟩,⟨⟨(-629264447029517718527787515),(-629264447029517718417607030)⟩,⟨(-1816529989419765287788327935),(-1816529989419765287669091792)⟩⟩,⟨⟨(-1014414495963543607014926794),(-1014414495963543606835924286)⟩,⟨(-2928362411572052199978329472),(-2928362411572052199782116408)⟩⟩,⟨⟨(-1440842106367455813647537337),(-1440842106367455813392924585)⟩,⟨(-4159352889854990063818977471),(-4159352889854990063539233973)⟩⟩,⟨⟨(-1837153108049314193461739232),(-1837153108049314193136578388)⟩,⟨(-5303404207374145887167505036),(-5303404207374145886809328390)⟩⟩,⟨⟨(-2256524817754308918147227874),(-2256524817754308917747592025)⟩,⟨(-6514026054817607367132799704),(-6514026054817607366692140339)⟩⟩,⟨⟨(-2656435792071101113569774852),(-2656435792071101113098938242)⟩,⟨(-7668469598186034814489654923),(-7668469598186034813969815789)⟩⟩,⟨⟨(-3072133445990435320518183268),(-3072133445990435319973454373)⟩,⟨(-8868485360145152284978624787),(-8868485360145152284376824216)⟩⟩,⟨⟨(-3473340580412691300844030919),(-3473340580412691300227868082)⟩,⟨(-10026670595442591582008281598),(-10026670595442591581327037673)⟩⟩,⟨⟨(-3886397599776523265784604740),(-3886397599776523265095441154)⟩,⟨(-11219063502044455816499178496),(-11219063502044455815737712419)⟩⟩,⟨⟨(-4287805485929443700835533649),(-4287805485929443700074681674)⟩,⟨(-12377828257670592144452140619),(-12377828257670592143610560093)⟩⟩,⟨⟨(-4698569893355039727997177044),(-4698569893355039727163261902)⟩,⟨(-13563602963674017037175202716),(-13563602963674017036252495462)⟩⟩,⟨⟨(-5099502883647184282245458132),(-5099502883647184281340411714)⟩,⟨(-14720996813034873396024331589),(-14720996813034873395022968079)⟩⟩,⟨⟨(-5508052685234101318420687915),(-5508052685234101317443480033)⟩,⟨(-15900378502652747126868261518),(-15900378502652747125787674529)⟩⟩,⟨⟨(-5908018787060499828365194732),(-5908018787060499827316474406)⟩,⟨(-17054981185433729371072641040),(-17054981185433729369911991952)⟩⟩,⟨⟨(-6314304889329281698731145026),(-6314304889329281697609927538)⟩,⟨(-18227828137998154550556112341),(-18227828137998154549314555437)⟩⟩] +lemma amp1_10_0_eq : ∀ k : Fin 16, amp1_1Expr 0 0 k = amp1_10_0 k := by decide +kernel +noncomputable def amp1_10_1 : Fin 16 → CBox := ![⟨⟨(-6712905375084154822364173308),(-6712905375084154821171999301)⟩,⟨(-19378488626746612489666469766),(-19378488626746612488346024092)⟩⟩,⟨⟨(-7116811458893626802882696877),(-7116811458893626801619009654)⟩,⟨(-20544465057820243452762014975),(-20544465057820243451362749882)⟩⟩,⟨⟨(-7513700288185479522404712121),(-7513700288185479521070903915)⟩,⟨(-21690184419970276426715861486),(-21690184419970276425239578778)⟩⟩,⟨⟨(-7915071511567247980337897672),(-7915071511567247978931399196)⟩,⟨(-22848843339292443596494731281),(-22848843339292443594935430360)⟩⟩,⟨⟨(-8309934963699564222938959170),(-8309934963699564221463184346)⟩,⟨(-23988715941201132047659308994),(-23988715941201132046024788751)⟩⟩,⟨⟨(-8708593155276932933429399686),(-8708593155276932931883670291)⟩,⟨(-25139543012310348165940392647),(-25139543012310348164229894241)⟩⟩,⟨⟨(-9101138730168082674532834430),(-9101138730168082672915805671)⟩,⟨(-26272724478973356683318666132),(-26272724478973356681526376088)⟩⟩,⟨⟨(-9496891073954188851769788831),(-9496891073954188850083729646)⟩,⟨(-27415163090060025286437799907),(-27415163090060025284571281320)⟩⟩,⟨⟨(-9886841054724459427656219010),(-9886841054724459425899751327)⟩,⟨(-28540851721901050823446205901),(-28540851721901050821499647261)⟩⟩,⟨⟨(-10279485372927895295649002196),(-10279485372927895293821235859)⟩,⟨(-29674318235953704694027542288),(-29674318235953704691999225258)⟩⟩,⟨⟨(-10666572908823690777704582096),(-10666572908823690775809887992)⟩,⟨(-30791743701200636931262779908),(-30791743701200636929163566385)⟩⟩,⟨⟨(-11055901047314695424716917329),(-11055901047314695422751844360)⟩,⟨(-31915637229005024095893272265),(-31915637229005024093713907746)⟩⟩,⟨⟨(-11439867680844907710058871652),(-11439867680844907708028519500)⟩,⟨(-33024053425147536340821412248),(-33024053425147536338574924186)⟩⟩,⟨⟨(-11825667778884814562920291087),(-11825667778884814560818961132)⟩,⟨(-34137762377431157504622011381),(-34137762377431157502292528590)⟩⟩,⟨⟨(-12206261841045965250997871986),(-12206261841045965248828364060)⟩,⟨(-35236442798634725060138836430),(-35236442798634725057732796389)⟩⟩,⟨⟨(-12588319915260722391992698875),(-12588319915260722389754013074)⟩,⟨(-36339349458604525327739534686),(-36339349458604525325254513500)⟩⟩] +lemma amp1_10_1_eq : ∀ k : Fin 16, amp1_1Expr 0 1 k = amp1_10_1 k := by decide +kernel +noncomputable def amp1_10_2 : Fin 16 → CBox := ![⟨⟨(-12965295463818583364940913468),(-12965295463818583362638922459)⟩,⟨(-37427584130793464684640546175),(-37427584130793464682091890860)⟩⟩,⟨⟨(-13343396554569321852299197838),(-13343396554569321849928062544)⟩,⟨(-38519067963422614614678954015),(-38519067963422614612050164242)⟩⟩,⟨⟨(-13716512663740494236986670852),(-13716512663740494234548111341)⟩,⟨(-39596161393767425468601375360),(-39596161393767425465895841443)⟩⟩,⟨⟨(-14090441693045962459221470881),(-14090441693045962456714813814)⟩,⟨(-40675601522404063165201062347),(-40675601522404063162417097378)⟩⟩,⟨⟨(-14459461977215688469035915044),(-14459461977215688466461112418)⟩,⟨(-41740871324413180699778102698),(-41740871324413180696914017100)⟩⟩,⟨⟨(-14829004411061715035184388498),(-14829004411061715032549862338)⟩,⟨(-42807648442703145245134346662),(-42807648442703145242214617706)⟩⟩,⟨⟨(-15193696708276728729484192732),(-15193696708276728726783523502)⟩,⟨(-43860424422545501059636793893),(-43860424422545501056641357489)⟩⟩,⟨⟨(-15558639082871133559174085304),(-15558639082871133556408386226)⟩,⟨(-44913922313599405415078881411),(-44913922313599405412011030169)⟩⟩,⟨⟨(-15918775249752562216048251800),(-15918775249752562213217193343)⟩,⟨(-45953545878068969525633207525),(-45953545878068969522490471564)⟩⟩,⟨⟨(-16278905600962081268583761492),(-16278905600962081265687090443)⟩,⟨(-46993152654139820993138339278),(-46993152654139820989919985797)⟩⟩,⟨⟨(-16634261386743642868702223239),(-16634261386743642865740828541)⟩,⟨(-48018976447035198881179204830),(-48018976447035198877886291376)⟩⟩,⟨⟨(-16989369609173106075582838152),(-16989369609173106072566490512)⟩,⟨(-49044085586090699302018887947),(-49044085586090699298679541899)⟩⟩,⟨⟨(-17339724586802453972624869790),(-17339724586802453969543056517)⟩,⟨(-50055473289321845907632137863),(-50055473289321845904214509820)⟩⟩,⟨⟨(-17689602740734276712847752186),(-17689602740734276709702122674)⟩,⟨(-51065484521102381803335555976),(-51065484521102381799844256673)⟩⟩,⟨⟨(-18034740279655822665404248915),(-18034740279655822662194327961)⟩,⟨(-52061810776121379279693711145),(-52061810776121379276125870902)⟩⟩,⟨⟨(-18379182858626920878449535093),(-18379182858626920875178888241)⟩,⟨(-53056130854568041699106251208),(-53056130854568041695471943278)⟩⟩] +lemma amp1_10_2_eq : ∀ k : Fin 16, amp1_1Expr 0 2 k = amp1_10_2 k := by decide +kernel +noncomputable def amp1_10_3 : Fin 16 → CBox := ![⟨⟨(-18718890128322294126904985812),(-18718890128322294123572266550)⟩,⟨(-54036781272589524417931814152),(-54036781272589524414225655285)⟩⟩,⟨⟨(-19057694296448717010018988515),(-19057694296448717006623970666)⟩,⟨(-55014824660941311802742653347),(-55014824660941311798963705275)⟩⟩,⟨⟨(-19391762292844942227876605844),(-19391762292844942224419798903)⟩,⟨(-55979195899176309599333626502),(-55979195899176309595481863528)⟩⟩,⟨⟨(-19724728098486747678973738757),(-19724728098486747675471940884)⟩,⟨(-56940385386767494550712160225),(-56940385386767494546835726205)⟩⟩,⟨⟨(-20052951687444352546003587285),(-20052951687444352542439823008)⟩,⟨(-57887885273962785793464419265),(-57887885273962785789512811841)⟩⟩,⟨⟨(-20379882258044908826022200751),(-20379882258044908822398200169)⟩,⟨(-58831652538675531389459463390),(-58831652538675531385437268377)⟩⟩,⟨⟨(-20702060231618653079903628344),(-20702060231618653076220374306)⟩,⟨(-59761700237524378293718539051),(-59761700237524378289627092022)⟩⟩,⟨⟨(-21022761953305465947258588470),(-21022761953305465943517101998)⟩,⟨(-60687486364251667553036529225),(-60687486364251667548878311165)⟩⟩,⟨⟨(-21338697095528772245284195401),(-21338697095528772241484306870)⟩,⟨(-61599512561297110513553164146),(-61599512561297110509326179303)⟩⟩,⟨⟨(-21652979780165887258704690808),(-21652979780165887254850792936)⟩,⟨(-62506768524181493587143489217),(-62506768524181493582859896154)⟩⟩,⟨⟨(-21962478939877190905858293154),(-21962478939877190901947261037)⟩,⟨(-63400215640047914276091844239),(-63400215640047914271741110690)⟩⟩,⟨⟨(-22270155981605558914746786627),(-22270155981605558910780650149)⟩,⟨(-64288402754374619221652566859),(-64288402754374619217239976865)⟩⟩,⟨⟨(-22573030150397963508935221483),(-22573030150397963504914059732)⟩,⟨(-65162725168789013938696292779),(-65162725168789013934220557096)⟩⟩,⟨⟨(-22873918673218157796278933847),(-22873918673218157792203300881)⟩,⟨(-66031315517020554071655860494),(-66031315517020554067117951144)⟩⟩,⟨⟨(-23169983067012150236084641882),(-23169983067012150231954999431)⟩,⟨(-66885979804292678585220993416),(-66885979804292678580620719027)⟩⟩,⟨⟨(-23463904064604503192116782569),(-23463904064604503187933764789)⟩,⟨(-67734456639694820212081123610),(-67734456639694820207419637592)⟩⟩] +lemma amp1_10_3_eq : ∀ k : Fin 16, amp1_1Expr 0 3 k = amp1_10_3 k := by decide +kernel +noncomputable def amp1_10_4 : Fin 16 → CBox := ![⟨⟨(-23752978207657740003197621841),(-23752978207657739998987314881)⟩,⟨(-68568941811232553509905456241),(-68568941811232553505256531367)⟩⟩,⟨⟨(-24039756676364397079100866928),(-24039756676364397074834305629)⟩,⟨(-69396799941760439166041337318),(-69396799941760439161320633013)⟩⟩,⟨⟨(-24321664486771101362322838960),(-24321664486771101358001850010)⟩,⟨(-70210597692885282672949903769),(-70210597692885282668161154256)⟩⟩,⟨⟨(-24601129552458858922887381947),(-24601129552458858918513432311)⟩,⟨(-71017343847404899044570048103),(-71017343847404899039716716318)⟩⟩,⟨⟨(-24875699428374202215885039881),(-24875699428374202211459281994)⟩,⟨(-71809958806260327014880057542),(-71809958806260327009963923550)⟩⟩,⟨⟨(-25147684467739387134771703674),(-25147684467739387130293768382)⟩,⟨(-72595111984725529380727798278),(-72595111984725529375746979702)⟩⟩,⟨⟨(-25414749373705691729533302517),(-25414749373705691725006548049)⟩,⟨(-73366061961479269629128045114),(-73366061961479269624090681715)⟩⟩,⟨⟨(-25679092130460598067957402750),(-25679092130460598063380629741)⟩,⟨(-74129153770333134323589220814),(-74129153770333134318490990215)⟩⟩,⟨⟨(-25938489683322627376612921384),(-25938489683322627371986492879)⟩,⟨(-74877970005193248326102962285),(-74877970005193248320943349981)⟩⟩,⟨⟨(-26195032379608320408534572815),(-26195032379608320403866583565)⟩,⟨(-75618544978989134714779138482),(-75618544978989134709580609961)⟩⟩,⟨⟨(-26446604933591878659407929577),(-26446604933591878654691233490)⟩,⟨(-76344772387804779792724891724),(-76344772387804779787465247588)⟩⟩,⟨⟨(-26695194376888032122082414834),(-26695194376888032117318990599)⟩,⟨(-77062388297828446850555037983),(-77062388297828446845239047648)⟩⟩,⟨⟨(-26938789107485135131208711084),(-26938789107485135126398596065)⟩,⟨(-77765585714245505800312618758),(-77765585714245505794938811916)⟩⟩,⟨⟨(-27179276793229187801459346529),(-27179276793229187796606025144)⟩,⟨(-78459813864751100478190579375),(-78459813864751100472768032940)⟩⟩,⟨⟨(-27414745779588332837347509614),(-27414745779588332832448808972)⟩,⟨(-79139554278052403996334219301),(-79139554278052403990855074935)⟩⟩,⟨⟨(-27646987989670052254663676017),(-27646987989670052249722004855)⟩,⟨(-79809979790591775617335695619),(-79809979790591775611805887186)⟩⟩] +lemma amp1_10_4_eq : ∀ k : Fin 16, amp1_1Expr 0 4 k = amp1_10_4 k := by decide +kernel +noncomputable def amp1_10_5 : Fin 16 → CBox := ![⟨⟨(-27874188295234711905043191296),(-27874188295234711900058570890)⟩,⟨(-80465850578480383005695101846),(-80465850578480383000113097687)⟩⟩,⟨⟨(-28098046192495536943207194276),(-28098046192495536938180344867)⟩,⟨(-81112072664699187624934800881),(-81112072664699187619301624054)⟩⟩,⟨⟨(-28316839943670277256454216594),(-28316839943670277251385224146)⟩,⟨(-81743675820387909215871497559),(-81743675820387909210185796111)⟩⟩,⟨⟨(-28532179662507527619318115353),(-28532179662507527614207898700)⟩,⟨(-82365308043577433331003126603),(-82365308043577433325266461617)⟩⟩,⟨⟨(-28742434125160893645216101304),(-28742434125160893640065240619)⟩,⟨(-82972260396633638291116853168),(-82972260396633638285329292677)⟩⟩,⟨⟨(-28949126858313515184724425900),(-28949126858313515179584066913)⟩,⟨(-83568930922259665948246718130),(-83568930922259665942554781751)⟩⟩,⟨⟨(-29150714511951410423671655578),(-29150714511951410418489401972)⟩,⟨(-84150864352725385236896520804),(-84150864352725385231147340355)⟩⟩,⟨⟨(-29348636593525162302627094279),(-29348636593525162297404965325)⟩,⟨(-84722216188101268820292681036),(-84722216188101268814490927443)⟩⟩,⟨⟨(-29541435202988933496973424918),(-29541435202988933491713170449)⟩,⟨(-85278777833467737962891351460),(-85278777833467737957040457206)⟩⟩,⟨⟨(-29730468187763879470219933239),(-29730468187763879464922422613)⟩,⟨(-85824469056695405394708451263),(-85824469056695405388809736147)⟩⟩,⟨⟨(-29914360872324529845531512814),(-29914360872324529840198882602)⟩,⟨(-86355321511360877554170463015),(-86355321511360877548228470616)⟩⟩,⟨⟨(-30094391611375639623371216443),(-30094391611375639618004450723)⟩,⟨(-86875025489628705061700381686),(-86875025489628705055716732545)⟩⟩,⟨⟨(-30269266911110177886980403616),(-30269266911110177881578688959)⟩,⟨(-87379846996510465849128604332),(-87379846996510465843099321321)⟩⟩,⟨⟨(-30440187623762200864125807156),(-30440187623762200858692451794)⟩,⟨(-87873252593809106549380899884),(-87873252593809106543314283526)⟩⟩,⟨⟨(-30605939563110598320843447012),(-30605939563110598315377784310)⟩,⟨(-88351737227816605522216514509),(-88351737227816605516109007226)⟩⟩,⟨⟨(-30767647905240686651245976351),(-30767647905240686645748293291)⟩,⟨(-88818549002111678514967439573),(-88818549002111678508818592163)⟩⟩] +lemma amp1_10_5_eq : ∀ k : Fin 16, amp1_1Expr 0 5 k = amp1_10_5 k := by decide +kernel +noncomputable def amp1_10_6 : Fin 16 → CBox := ![⟨⟨(-30924176053652663077940991617),(-30924176053652663072417561922)⟩,⟨(-89270406845218719927860540713),(-89270406845218719921686827076)⟩⟩,⟨⟨(-31076575182348133094653763482),(-31076575182348133089098914177)⟩,⟨(-89710345235101690100434889464),(-89710345235101690094218628497)⟩⟩,⟨⟨(-31223784711938343742761837382),(-31223784711938343737179815049)⟩,⟨(-90135302542782621585627488262),(-90135302542782621579379299043)⟩⟩,⟨⟨(-31366783346512185484947404139),(-31366783346512185479335741471)⟩,⟨(-90548104043607403863699080743),(-90548104043607403857410510259)⟩⟩,⟨⟨(-31504585086650592896505811921),(-31504585086650592890867261049)⟩,⟨(-90945903402425945746772452376),(-90945903402425945740449803292)⟩⟩,⟨⟨(-31638097566013635102091201452),(-31638097566013635096425588826)⟩,⟨(-91331320731928079606869189205),(-91331320731928079600510605258)⟩⟩,⟨⟨(-31766408054785126239332108236),(-31766408054785126233657573065)⟩,⟨(-91701721208088443917572710938),(-91701721208088443911228911849)⟩⟩,⟨⟨(-31890354391170951220122459851),(-31890354391170951214421052103)⟩,⟨(-92059523461475563713759509088),(-92059523461475563707377298644)⟩⟩,⟨⟨(-32009095923644769044726262294),(-32009095923644769039000602126)⟩,⟨(-92402300740164300765571357739),(-92402300740164300759156655130)⟩⟩,⟨⟨(-32123401852681396185660784721),(-32123401852681396179912643790)⟩,⟨(-92732273534660635464816000072),(-92732273534660635458372518124)⟩⟩,⟨⟨(-32232502525936830265362467078),(-32232502525936830259591733247)⟩,⟨(-93047220050024606815808071269),(-93047220050024606809333841572)⟩⟩,⟨⟨(-32337099553057724193601632473),(-32337099553057724187811111420)⟩,⟨(-93349165658848020296903265788),(-93349165658848020290404964630)⟩⟩,⟨⟨(-32436493307917857224921099658),(-32436493307917857219110701813)⟩,⟨(-93636090714469347695691003945),(-93636090714469347689166728690)⟩⟩,⟨⟨(-32531318751103864923331317123),(-32531318751103864917500705624)⟩,⟨(-93909828190216683240036545208),(-93909828190216683233483879978)⟩⟩,⟨⟨(-32620945410534091407416001083),(-32620945410534091401574427541)⟩,⟨(-94168558069959724095681948789),(-94168558069959724089125958037)⟩⟩,⟨⟨(-32705942439377387425089362468),(-32705942439377387419230195079)⟩,⟨(-94413923357374700801796554622),(-94413923357374700795216631163)⟩⟩] +lemma amp1_10_6_eq : ∀ k : Fin 16, amp1_1Expr 0 6 k = amp1_10_6 k := by decide +kernel +noncomputable def amp1_10_7 : Fin 16 → CBox := ![⟨⟨(-32785747743509981350882462554),(-32785747743509981345007555840)⟩,⟨(-94644301426493266084445429992),(-94644301426493266077845286947)⟩⟩,⟨⟨(-32860865414590931776298352406),(-32860865414590931770407537190)⟩,⟨(-94861147464590688557914887296),(-94861147464590688551292555155)⟩⟩,⟨⟨(-32930801052341203476703445300),(-32930801052341203470802159072)⟩,⟨(-95063034260996026157037197544),(-95063034260996026150406735626)⟩⟩,⟨⟨(-32995994340909188941872057445),(-32995994340909188935957509242)⟩,⟨(-95251231074516442958470100763),(-95251231074516442951821953826)⟩⟩,⟨⟨(-33056017978152788411289568853),(-33056017978152788405365427677)⟩,⟨(-95424504390118105959947050855),(-95424504390118105953290176948)⟩⟩,⟨⟨(-33111247806102404781394556352),(-33111247806102404775458631576)⟩,⟨(-95583939170288144600315691522),(-95583939170288144593642252157)⟩⟩,⟨⟨(-33161323110387142483124981914),(-33161323110387142477180367698)⟩,⟨(-95728494122330873263039951790),(-95728494122330873256357250373)⟩⟩,⟨⟨(-33206556370521783194572785367),(-33206556370521783188620298071)⟩,⟨(-95859071296906169175567463429),(-95859071296906169168876326656)⟩⟩,⟨⟨(-33246653032290985855532274664),(-33246653032290985849572658177)⟩,⟨(-95974820389236441837374400929),(-95974820389236441830675353223)⟩⟩,⟨⟨(-33281862608866566227776504064),(-33281862608866566221810192407)⟩,⟨(-96076461681806262185481089920),(-96076461681806262178773840025)⟩⟩,⟨⟨(-33311956359174495043189681991),(-33311956359174495037218664168)⟩,⟨(-96163334856012302609579754436),(-96163334856012302602868427679)⟩⟩,⟨⟨(-33337121144716975244189432512),(-33337121144716975238214289695)⟩,⟨(-96235979334547553342933459901),(-96235979334547553336218176581)⟩⟩,⟨⟨(-33357193769420233719472151870),(-33357193769420233713494783156)⟩,⟨(-96293924010926396406360450134),(-96293924010926396399645083514)⟩⟩,⟨⟨(-33372298677811606176384355541),(-33372298677811606170405947303)⟩,⟨(-96337528125555614031752959350),(-96337528125555614025039364554)⟩⟩,⟨⟨(-33382338028223777530303639766),(-33382338028223777524325935265)⟩,⟨(-96366509233870394589533663656),(-96366509233870394582825272489)⟩⟩,⟨⟨(-33387374004052282219495589820),(-33387374004052282213520632494)⟩,⟨(-96381046843871492744229140389),(-96381046843871492737530270840)⟩⟩] +lemma amp1_10_7_eq : ∀ k : Fin 16, amp1_1Expr 0 7 k = amp1_10_7 k := by decide +kernel +noncomputable def amp1_10_8 : Fin 16 → CBox := ![⟨⟨(-33387374004052282219495589820),(-33387374004052282213520632494)⟩,⟨(-96381046843871492744229140389),(-96381046843871492737530270840)⟩⟩,⟨⟨(-33382338028223777530303639766),(-33382338028223777524325935265)⟩,⟨(-96366509233870394589533663656),(-96366509233870394582825272489)⟩⟩,⟨⟨(-33372298677811606176384355541),(-33372298677811606170405947303)⟩,⟨(-96337528125555614031752959350),(-96337528125555614025039364554)⟩⟩,⟨⟨(-33357193769420233719472151870),(-33357193769420233713494783156)⟩,⟨(-96293924010926396406360450134),(-96293924010926396399645083514)⟩⟩,⟨⟨(-33337121144716975244189432512),(-33337121144716975238214289695)⟩,⟨(-96235979334547553342933459901),(-96235979334547553336218176581)⟩⟩,⟨⟨(-33311956359174495043189681991),(-33311956359174495037218664168)⟩,⟨(-96163334856012302609579754436),(-96163334856012302602868427679)⟩⟩,⟨⟨(-33281862608866566227776504064),(-33281862608866566221810192407)⟩,⟨(-96076461681806262185481089920),(-96076461681806262178773840025)⟩⟩,⟨⟨(-33246653032290985855532274664),(-33246653032290985849572658177)⟩,⟨(-95974820389236441837374400929),(-95974820389236441830675353223)⟩⟩,⟨⟨(-33206556370521783194572785367),(-33206556370521783188620298071)⟩,⟨(-95859071296906169175567463429),(-95859071296906169168876326656)⟩⟩,⟨⟨(-33161323110387142483124981914),(-33161323110387142477180367698)⟩,⟨(-95728494122330873263039951790),(-95728494122330873256357250373)⟩⟩,⟨⟨(-33111247806102404781394556352),(-33111247806102404775458631576)⟩,⟨(-95583939170288144600315691522),(-95583939170288144593642252157)⟩⟩,⟨⟨(-33056017978152788411289568853),(-33056017978152788405365427677)⟩,⟨(-95424504390118105959947050855),(-95424504390118105953290176948)⟩⟩,⟨⟨(-32995994340909188941872057445),(-32995994340909188935957509242)⟩,⟨(-95251231074516442958470100763),(-95251231074516442951821953826)⟩⟩,⟨⟨(-32930801052341203476703445300),(-32930801052341203470802159072)⟩,⟨(-95063034260996026157037197544),(-95063034260996026150406735626)⟩⟩,⟨⟨(-32860865414590931776298352406),(-32860865414590931770407537190)⟩,⟨(-94861147464590688557914887296),(-94861147464590688551292555155)⟩⟩,⟨⟨(-32785747743509981350882462554),(-32785747743509981345007555840)⟩,⟨(-94644301426493266084445429992),(-94644301426493266077845286947)⟩⟩] +lemma amp1_10_8_eq : ∀ k : Fin 16, amp1_1Expr 0 8 k = amp1_10_8 k := by decide +kernel +noncomputable def amp1_10_9 : Fin 16 → CBox := ![⟨⟨(-32705942439377387425089362468),(-32705942439377387419230195079)⟩,⟨(-94413923357374700801796554622),(-94413923357374700795216631163)⟩⟩,⟨⟨(-32620945410534091407416001083),(-32620945410534091401574427541)⟩,⟨(-94168558069959724095681948789),(-94168558069959724089125958037)⟩⟩,⟨⟨(-32531318751103864923331317123),(-32531318751103864917500705624)⟩,⟨(-93909828190216683240036545208),(-93909828190216683233483879978)⟩⟩,⟨⟨(-32436493307917857224921099658),(-32436493307917857219110701813)⟩,⟨(-93636090714469347695691003945),(-93636090714469347689166728690)⟩⟩,⟨⟨(-32337099553057724193601632473),(-32337099553057724187811111420)⟩,⟨(-93349165658848020296903265788),(-93349165658848020290404964630)⟩⟩,⟨⟨(-32232502525936830265362467078),(-32232502525936830259591733247)⟩,⟨(-93047220050024606815808071269),(-93047220050024606809333841572)⟩⟩,⟨⟨(-32123401852681396185660784721),(-32123401852681396179912643790)⟩,⟨(-92732273534660635464816000072),(-92732273534660635458372518124)⟩⟩,⟨⟨(-32009095923644769044726262294),(-32009095923644769039000602126)⟩,⟨(-92402300740164300765571357739),(-92402300740164300759156655130)⟩⟩,⟨⟨(-31890354391170951220122459851),(-31890354391170951214421052103)⟩,⟨(-92059523461475563713759509088),(-92059523461475563707377298644)⟩⟩,⟨⟨(-31766408054785126239332108236),(-31766408054785126233657573065)⟩,⟨(-91701721208088443917572710938),(-91701721208088443911228911849)⟩⟩,⟨⟨(-31638097566013635102091201452),(-31638097566013635096425588826)⟩,⟨(-91331320731928079606869189205),(-91331320731928079600510605258)⟩⟩,⟨⟨(-31504585086650592896505811921),(-31504585086650592890867261049)⟩,⟨(-90945903402425945746772452376),(-90945903402425945740449803292)⟩⟩,⟨⟨(-31366783346512185484947404139),(-31366783346512185479335741471)⟩,⟨(-90548104043607403863699080743),(-90548104043607403857410510259)⟩⟩,⟨⟨(-31223784711938343742761837382),(-31223784711938343737179815049)⟩,⟨(-90135302542782621585627488262),(-90135302542782621579379299043)⟩⟩,⟨⟨(-31076575182348133094653763482),(-31076575182348133089098914177)⟩,⟨(-89710345235101690100434889464),(-89710345235101690094218628497)⟩⟩,⟨⟨(-30924176053652663077940991617),(-30924176053652663072417561922)⟩,⟨(-89270406845218719927860540713),(-89270406845218719921686827076)⟩⟩] +lemma amp1_10_9_eq : ∀ k : Fin 16, amp1_1Expr 0 9 k = amp1_10_9 k := by decide +kernel +noncomputable def amp1_10_10 : Fin 16 → CBox := ![⟨⟨(-30767647905240686651245976351),(-30767647905240686645748293291)⟩,⟨(-88818549002111678514967439573),(-88818549002111678508818592163)⟩⟩,⟨⟨(-30605939563110598320843447012),(-30605939563110598315377784310)⟩,⟨(-88351737227816605522216514509),(-88351737227816605516109007226)⟩⟩,⟨⟨(-30440187623762200864125807156),(-30440187623762200858692451794)⟩,⟨(-87873252593809106549380899884),(-87873252593809106543314283526)⟩⟩,⟨⟨(-30269266911110177886980403616),(-30269266911110177881578688959)⟩,⟨(-87379846996510465849128604332),(-87379846996510465843099321321)⟩⟩,⟨⟨(-30094391611375639623371216443),(-30094391611375639618004450723)⟩,⟨(-86875025489628705061700381686),(-86875025489628705055716732545)⟩⟩,⟨⟨(-29914360872324529845531512814),(-29914360872324529840198882602)⟩,⟨(-86355321511360877554170463015),(-86355321511360877548228470616)⟩⟩,⟨⟨(-29730468187763879470219933239),(-29730468187763879464922422613)⟩,⟨(-85824469056695405394708451263),(-85824469056695405388809736147)⟩⟩,⟨⟨(-29541435202988933496973424918),(-29541435202988933491713170449)⟩,⟨(-85278777833467737962891351460),(-85278777833467737957040457206)⟩⟩,⟨⟨(-29348636593525162302627094279),(-29348636593525162297404965325)⟩,⟨(-84722216188101268820292681036),(-84722216188101268814490927443)⟩⟩,⟨⟨(-29150714511951410423671655578),(-29150714511951410418489401972)⟩,⟨(-84150864352725385236896520804),(-84150864352725385231147340355)⟩⟩,⟨⟨(-28949126858313515184724425900),(-28949126858313515179584066913)⟩,⟨(-83568930922259665948246718130),(-83568930922259665942554781751)⟩⟩,⟨⟨(-28742434125160893645216101304),(-28742434125160893640065240619)⟩,⟨(-82972260396633638291116853168),(-82972260396633638285329292677)⟩⟩,⟨⟨(-28532179662507527619318115353),(-28532179662507527614207898700)⟩,⟨(-82365308043577433331003126603),(-82365308043577433325266461617)⟩⟩,⟨⟨(-28316839943670277256454216594),(-28316839943670277251385224146)⟩,⟨(-81743675820387909215871497559),(-81743675820387909210185796111)⟩⟩,⟨⟨(-28098046192495536943207194276),(-28098046192495536938180344867)⟩,⟨(-81112072664699187624934800881),(-81112072664699187619301624054)⟩⟩,⟨⟨(-27874188295234711905043191296),(-27874188295234711900058570890)⟩,⟨(-80465850578480383005695101846),(-80465850578480383000113097687)⟩⟩] +lemma amp1_10_10_eq : ∀ k : Fin 16, amp1_1Expr 0 10 k = amp1_10_10 k := by decide +kernel +noncomputable def amp1_10_11 : Fin 16 → CBox := ![⟨⟨(-27646987989670052254663676017),(-27646987989670052249722004855)⟩,⟨(-79809979790591775617335695619),(-79809979790591775611805887186)⟩⟩,⟨⟨(-27414745779588332837347509614),(-27414745779588332832448808972)⟩,⟨(-79139554278052403996334219301),(-79139554278052403990855074935)⟩⟩,⟨⟨(-27179276793229187801459346529),(-27179276793229187796606025144)⟩,⟨(-78459813864751100478190579375),(-78459813864751100472768032940)⟩⟩,⟨⟨(-26938789107485135131208711084),(-26938789107485135126398596065)⟩,⟨(-77765585714245505800312618758),(-77765585714245505794938811916)⟩⟩,⟨⟨(-26695194376888032122082414834),(-26695194376888032117318990599)⟩,⟨(-77062388297828446850555037983),(-77062388297828446845239047648)⟩⟩,⟨⟨(-26446604933591878659407929577),(-26446604933591878654691233490)⟩,⟨(-76344772387804779792724891724),(-76344772387804779787465247588)⟩⟩,⟨⟨(-26195032379608320408534572815),(-26195032379608320403866583565)⟩,⟨(-75618544978989134714779138482),(-75618544978989134709580609961)⟩⟩,⟨⟨(-25938489683322627376612921384),(-25938489683322627371986492879)⟩,⟨(-74877970005193248326102962285),(-74877970005193248320943349981)⟩⟩,⟨⟨(-25679092130460598067957402750),(-25679092130460598063380629741)⟩,⟨(-74129153770333134323589220814),(-74129153770333134318490990215)⟩⟩,⟨⟨(-25414749373705691729533302517),(-25414749373705691725006548049)⟩,⟨(-73366061961479269629128045114),(-73366061961479269624090681715)⟩⟩,⟨⟨(-25147684467739387134771703674),(-25147684467739387130293768382)⟩,⟨(-72595111984725529380727798278),(-72595111984725529375746979702)⟩⟩,⟨⟨(-24875699428374202215885039881),(-24875699428374202211459281994)⟩,⟨(-71809958806260327014880057542),(-71809958806260327009963923550)⟩⟩,⟨⟨(-24601129552458858922887381947),(-24601129552458858918513432311)⟩,⟨(-71017343847404899044570048103),(-71017343847404899039716716318)⟩⟩,⟨⟨(-24321664486771101362322838960),(-24321664486771101358001850010)⟩,⟨(-70210597692885282672949903769),(-70210597692885282668161154256)⟩⟩,⟨⟨(-24039756676364397079100866928),(-24039756676364397074834305629)⟩,⟨(-69396799941760439166041337318),(-69396799941760439161320633013)⟩⟩,⟨⟨(-23752978207657740003197621841),(-23752978207657739998987314881)⟩,⟨(-68568941811232553509905456241),(-68568941811232553505256531367)⟩⟩] +lemma amp1_10_11_eq : ∀ k : Fin 16, amp1_1Expr 0 11 k = amp1_10_11 k := by decide +kernel +noncomputable def amp1_10_12 : Fin 16 → CBox := ![⟨⟨(-23463904064604503192116782569),(-23463904064604503187933764789)⟩,⟨(-67734456639694820212081123610),(-67734456639694820207419637592)⟩⟩,⟨⟨(-23169983067012150236084641882),(-23169983067012150231954999431)⟩,⟨(-66885979804292678585220993416),(-66885979804292678580620719027)⟩⟩,⟨⟨(-22873918673218157796278933847),(-22873918673218157792203300881)⟩,⟨(-66031315517020554071655860494),(-66031315517020554067117951144)⟩⟩,⟨⟨(-22573030150397963508935221483),(-22573030150397963504914059732)⟩,⟨(-65162725168789013938696292779),(-65162725168789013934220557096)⟩⟩,⟨⟨(-22270155981605558914746786627),(-22270155981605558910780650149)⟩,⟨(-64288402754374619221652566859),(-64288402754374619217239976865)⟩⟩,⟨⟨(-21962478939877190905858293154),(-21962478939877190901947261037)⟩,⟨(-63400215640047914276091844239),(-63400215640047914271741110690)⟩⟩,⟨⟨(-21652979780165887258704690808),(-21652979780165887254850792936)⟩,⟨(-62506768524181493587143489217),(-62506768524181493582859896154)⟩⟩,⟨⟨(-21338697095528772245284195401),(-21338697095528772241484306870)⟩,⟨(-61599512561297110513553164146),(-61599512561297110509326179303)⟩⟩,⟨⟨(-21022761953305465947258588470),(-21022761953305465943517101998)⟩,⟨(-60687486364251667553036529225),(-60687486364251667548878311165)⟩⟩,⟨⟨(-20702060231618653079903628344),(-20702060231618653076220374306)⟩,⟨(-59761700237524378293718539051),(-59761700237524378289627092022)⟩⟩,⟨⟨(-20379882258044908826022200751),(-20379882258044908822398200169)⟩,⟨(-58831652538675531389459463390),(-58831652538675531385437268377)⟩⟩,⟨⟨(-20052951687444352546003587285),(-20052951687444352542439823008)⟩,⟨(-57887885273962785793464419265),(-57887885273962785789512811841)⟩⟩,⟨⟨(-19724728098486747678973738757),(-19724728098486747675471940884)⟩,⟨(-56940385386767494550712160225),(-56940385386767494546835726205)⟩⟩,⟨⟨(-19391762292844942227876605844),(-19391762292844942224419798903)⟩,⟨(-55979195899176309599333626502),(-55979195899176309595481863528)⟩⟩,⟨⟨(-19057694296448717010018988515),(-19057694296448717006623970666)⟩,⟨(-55014824660941311802742653347),(-55014824660941311798963705275)⟩⟩,⟨⟨(-18718890128322294126904985812),(-18718890128322294123572266550)⟩,⟨(-54036781272589524417931814152),(-54036781272589524414225655285)⟩⟩] +lemma amp1_10_12_eq : ∀ k : Fin 16, amp1_1Expr 0 12 k = amp1_10_12 k := by decide +kernel +noncomputable def amp1_10_13 : Fin 16 → CBox := ![⟨⟨(-18379182858626920878449535093),(-18379182858626920875178888241)⟩,⟨(-53056130854568041699106251208),(-53056130854568041695471943278)⟩⟩,⟨⟨(-18034740279655822665404248915),(-18034740279655822662194327961)⟩,⟨(-52061810776121379279693711145),(-52061810776121379276125870902)⟩⟩,⟨⟨(-17689602740734276712847752186),(-17689602740734276709702122674)⟩,⟨(-51065484521102381803335555976),(-51065484521102381799844256673)⟩⟩,⟨⟨(-17339724586802453972624869790),(-17339724586802453969543056517)⟩,⟨(-50055473289321845907632137863),(-50055473289321845904214509820)⟩⟩,⟨⟨(-16989369609173106075582838152),(-16989369609173106072566490512)⟩,⟨(-49044085586090699302018887947),(-49044085586090699298679541899)⟩⟩,⟨⟨(-16634261386743642868702223239),(-16634261386743642865740828541)⟩,⟨(-48018976447035198881179204830),(-48018976447035198877886291376)⟩⟩,⟨⟨(-16278905600962081268583761492),(-16278905600962081265687090443)⟩,⟨(-46993152654139820993138339278),(-46993152654139820989919985797)⟩⟩,⟨⟨(-15918775249752562216048251800),(-15918775249752562213217193343)⟩,⟨(-45953545878068969525633207525),(-45953545878068969522490471564)⟩⟩,⟨⟨(-15558639082871133559174085304),(-15558639082871133556408386226)⟩,⟨(-44913922313599405415078881411),(-44913922313599405412011030169)⟩⟩,⟨⟨(-15193696708276728729484192732),(-15193696708276728726783523502)⟩,⟨(-43860424422545501059636793893),(-43860424422545501056641357489)⟩⟩,⟨⟨(-14829004411061715035184388498),(-14829004411061715032549862338)⟩,⟨(-42807648442703145245134346662),(-42807648442703145242214617706)⟩⟩,⟨⟨(-14459461977215688469035915044),(-14459461977215688466461112418)⟩,⟨(-41740871324413180699778102698),(-41740871324413180696914017100)⟩⟩,⟨⟨(-14090441693045962459221470881),(-14090441693045962456714813814)⟩,⟨(-40675601522404063165201062347),(-40675601522404063162417097378)⟩⟩,⟨⟨(-13716512663740494236986670852),(-13716512663740494234548111341)⟩,⟨(-39596161393767425468601375360),(-39596161393767425465895841443)⟩⟩,⟨⟨(-13343396554569321852299197838),(-13343396554569321849928062544)⟩,⟨(-38519067963422614614678954015),(-38519067963422614612050164242)⟩⟩,⟨⟨(-12965295463818583364940913468),(-12965295463818583362638922459)⟩,⟨(-37427584130793464684640546175),(-37427584130793464682091890860)⟩⟩] +lemma amp1_10_13_eq : ∀ k : Fin 16, amp1_1Expr 0 13 k = amp1_10_13 k := by decide +kernel +noncomputable def amp1_10_14 : Fin 16 → CBox := ![⟨⟨(-12588319915260722391992698875),(-12588319915260722389754013074)⟩,⟨(-36339349458604525327739534686),(-36339349458604525325254513500)⟩⟩,⟨⟨(-12206261841045965250997871986),(-12206261841045965248828364060)⟩,⟨(-35236442798634725060138836430),(-35236442798634725057732796389)⟩⟩,⟨⟨(-11825667778884814562920291087),(-11825667778884814560818961132)⟩,⟨(-34137762377431157504622011381),(-34137762377431157502292528590)⟩⟩,⟨⟨(-11439867680844907710058871652),(-11439867680844907708028519500)⟩,⟨(-33024053425147536340821412248),(-33024053425147536338574924186)⟩⟩,⟨⟨(-11055901047314695424716917329),(-11055901047314695422751844360)⟩,⟨(-31915637229005024095893272265),(-31915637229005024093713907746)⟩⟩,⟨⟨(-10666572908823690777704582096),(-10666572908823690775809887992)⟩,⟨(-30791743701200636931262779908),(-30791743701200636929163566385)⟩⟩,⟨⟨(-10279485372927895295649002196),(-10279485372927895293821235859)⟩,⟨(-29674318235953704694027542288),(-29674318235953704691999225258)⟩⟩,⟨⟨(-9886841054724459427656219010),(-9886841054724459425899751327)⟩,⟨(-28540851721901050823446205901),(-28540851721901050821499647261)⟩⟩,⟨⟨(-9496891073954188851769788831),(-9496891073954188850083729646)⟩,⟨(-27415163090060025286437799907),(-27415163090060025284571281320)⟩⟩,⟨⟨(-9101138730168082674532834430),(-9101138730168082672915805671)⟩,⟨(-26272724478973356683318666132),(-26272724478973356681526376088)⟩⟩,⟨⟨(-8708593155276932933429399686),(-8708593155276932931883670291)⟩,⟨(-25139543012310348165940392647),(-25139543012310348164229894241)⟩⟩,⟨⟨(-8309934963699564222938959170),(-8309934963699564221463184346)⟩,⟨(-23988715941201132047659308994),(-23988715941201132046024788751)⟩⟩,⟨⟨(-7915071511567247980337897672),(-7915071511567247978931399196)⟩,⟨(-22848843339292443596494731281),(-22848843339292443594935430360)⟩⟩,⟨⟨(-7513700288185479522404712121),(-7513700288185479521070903915)⟩,⟨(-21690184419970276426715861486),(-21690184419970276425239578778)⟩⟩,⟨⟨(-7116811458893626802882696877),(-7116811458893626801619009654)⟩,⟨(-20544465057820243452762014975),(-20544465057820243451362749882)⟩⟩,⟨⟨(-6712905375084154822364173308),(-6712905375084154821171999301)⟩,⟨(-19378488626746612489666469766),(-19378488626746612488346024092)⟩⟩] +lemma amp1_10_14_eq : ∀ k : Fin 16, amp1_1Expr 0 14 k = amp1_10_14 k := by decide +kernel +noncomputable def amp1_10_15 : Fin 16 → CBox := ![⟨⟨(-6314304889329281698731145026),(-6314304889329281697609927538)⟩,⟨(-18227828137998154550556112341),(-18227828137998154549314555437)⟩⟩,⟨⟨(-5908018787060499828365194732),(-5908018787060499827316474406)⟩,⟨(-17054981185433729371072641040),(-17054981185433729369911991952)⟩⟩,⟨⟨(-5508052685234101318420687915),(-5508052685234101317443480033)⟩,⟨(-15900378502652747126868261518),(-15900378502652747125787674529)⟩⟩,⟨⟨(-5099502883647184282245458132),(-5099502883647184281340411714)⟩,⟨(-14720996813034873396024331589),(-14720996813034873395022968079)⟩⟩,⟨⟨(-4698569893355039727997177044),(-4698569893355039727163261902)⟩,⟨(-13563602963674017037175202716),(-13563602963674017036252495462)⟩⟩,⟨⟨(-4287805485929443700835533649),(-4287805485929443700074681674)⟩,⟨(-12377828257670592144452140619),(-12377828257670592143610560093)⟩⟩,⟨⟨(-3886397599776523265784604740),(-3886397599776523265095441154)⟩,⟨(-11219063502044455816499178496),(-11219063502044455815737712419)⟩⟩,⟨⟨(-3473340580412691300844030919),(-3473340580412691300227868082)⟩,⟨(-10026670595442591582008281598),(-10026670595442591581327037673)⟩⟩,⟨⟨(-3072133445990435320518183268),(-3072133445990435319973454373)⟩,⟨(-8868485360145152284978624787),(-8868485360145152284376824216)⟩⟩,⟨⟨(-2656435792071101113569774852),(-2656435792071101113098938242)⟩,⟨(-7668469598186034814489654923),(-7668469598186034813969815789)⟩⟩,⟨⟨(-2256524817754308918147227874),(-2256524817754308917747592025)⟩,⟨(-6514026054817607367132799704),(-6514026054817607366692140339)⟩⟩,⟨⟨(-1837153108049314193461739232),(-1837153108049314193136578388)⟩,⟨(-5303404207374145887167505036),(-5303404207374145886809328390)⟩⟩,⟨⟨(-1440842106367455813647537337),(-1440842106367455813392924585)⟩,⟨(-4159352889854990063818977471),(-4159352889854990063539233973)⟩⟩,⟨⟨(-1014414495963543607014926794),(-1014414495963543606835924286)⟩,⟨(-2928362411572052199978329472),(-2928362411572052199782116408)⟩⟩,⟨⟨(-629264447029517718527787515),(-629264447029517718417607030)⟩,⟨(-1816529989419765287788327935),(-1816529989419765287669091792)⟩⟩,⟨⟨(-178776584874023315364657005),(-178776584874023315333871026)⟩,⟨(-516083547009096694075783434),(-516083547009096694043399675)⟩⟩] +lemma amp1_10_15_eq : ∀ k : Fin 16, amp1_1Expr 0 15 k = amp1_10_15 k := by decide +kernel +noncomputable def amp1_10 : Fin 16 → Fin 16 → CBox := ![amp1_10_0,amp1_10_1,amp1_10_2,amp1_10_3,amp1_10_4,amp1_10_5,amp1_10_6,amp1_10_7,amp1_10_8,amp1_10_9,amp1_10_10,amp1_10_11,amp1_10_12,amp1_10_13,amp1_10_14,amp1_10_15] +lemma amp1_10_eq (i k : Fin 16) : amp1_1Expr 0 i k = amp1_10 i k := by + fin_cases i + · exact amp1_10_0_eq k + · exact amp1_10_1_eq k + · exact amp1_10_2_eq k + · exact amp1_10_3_eq k + · exact amp1_10_4_eq k + · exact amp1_10_5_eq k + · exact amp1_10_6_eq k + · exact amp1_10_7_eq k + · exact amp1_10_8_eq k + · exact amp1_10_9_eq k + · exact amp1_10_10_eq k + · exact amp1_10_11_eq k + · exact amp1_10_12_eq k + · exact amp1_10_13_eq k + · exact amp1_10_14_eq k + · exact amp1_10_15_eq k +noncomputable def amp1_11_0 : Fin 16 → CBox := ![⟨⟨27656833929615362261842843,27656833929615362287386726⟩,⟨(-158530377261050063375886837),(-158530377261050063348734071)⟩⟩,⟨⟨97347548738388396573839292,97347548738388396664030973⟩,⟨(-558001095360729850836297400),(-558001095360729850739111216)⟩⟩,⟨⟨156930468665277272954098492,156930468665277273099707431⟩,⟨(-899533419644964986115396225),(-899533419644964985957498156)⟩⟩,⟨⟨222899049574540211848314004,222899049574540212055188512⟩,⟨(-1277668677120078436760991142),(-1277668677120078436536395606)⟩⟩,⟨⟨284208574900344161364713227,284208574900344161628569383⟩,⟨(-1629097991275517500546327281),(-1629097991275517500259498428)⟩⟩,⟨⟨349085604172734028656047471,349085604172734028980173385⟩,⟨(-2000976419308989531209651633),(-2000976419308989530857126195)⟩⟩,⟨⟨410952047203312812167350815,410952047203312812548977813⟩,⟨(-2355598014043832587787217628),(-2355598014043832587371883071)⟩⟩,⟨⟨475260698067625593405306007,475260698067625593846685537⟩,⟨(-2724218468164281644447773067),(-2724218468164281643967255638)⟩⟩,⟨⟨537327657764345331882400123,537327657764345332381467477⟩,⟨(-3079989434617208980891752592),(-3079989434617208980348220336)⟩⟩,⟨⟨601227801041259060729084625,601227801041259061287459640⟩,⟨(-3446268302491409285569469742),(-3446268302491409284961543017)⟩⟩,⟨⟨663325817138793156850381311,663325817138793157466506848⟩,⟨(-3802217285811704743486625095),(-3802217285811704742815458076)⟩⟩,⟨⟨726871292114567086768840492,726871292114567087444016849⟩,⟨(-4166463176963937581953991051),(-4166463176963937581218372332)⟩⟩,⟨⟨788895841566765076051335362,788895841566765076784120854⟩,⟨(-4521991045740504832372530651),(-4521991045740504831574165269)⟩⟩,⟨⟨852098715826997532204683026,852098715826997532996122413⟩,⟨(-4884273132184544490933227255),(-4884273132184544490071207941)⟩⟩,⟨⟨913973687112991919932988328,913973687112991920781983424⟩,⟨(-5238943611312729715314406947),(-5238943611312729714389302175)⟩⟩,⟨⟨976826365869980121351368078,976826365869980122258805867⟩,⟨(-5599218359339591154132831411),(-5599218359339591153143773168)⟩⟩] +lemma amp1_11_0_eq : ∀ k : Fin 16, amp1_1Expr 1 0 k = amp1_11_0 k := by decide +kernel +noncomputable def amp1_11_1 : Fin 16 → CBox := ![⟨⟨1038490075614490173353621829,1038490075614490174318370583⟩,⟨(-5952677876578302846042721367),(-5952677876578302844991069513)⟩⟩,⟨⟨1100974564234470578064397449,1100974564234470579087160022⟩,⟨(-6310842140032989848167681559),(-6310842140032989847052946796)⟩⟩,⟨⟨1162373479802631048115180043,1162373479802631049194925359⟩,⟨(-6662783843599317383142805028),(-6662783843599317381966216161)⟩⟩,⟨⟨1224465824149729458084427969,1224465824149729459222074538⟩,⟨(-7018700316157947637121348736),(-7018700316157947635880631127)⟩⟩,⟨⟨1285551412780888595940576702,1285551412780888597134839914⟩,⟨(-7368846013802003603148777623),(-7368846013802003601846953227)⟩⟩,⟨⟨1347224049647206332753864017,1347224049647206334005289901⟩,⟨(-7722356701756482300514578834),(-7722356701756482299151049353)⟩⟩,⟨⟨1407951061421259998592792547,1407951061421259999900878603⟩,⟨(-8070447018637191335750575599),(-8070447018637191334324143519)⟩⟩,⟨⟨1469174162069821262594913565,1469174162069821263959681547⟩,⟨(-8421380942151647584460921009),(-8421380942151647582973600945)⟩⟩,⟨⟨1529499634035960901503023702,1529499634035960902924012322⟩,⟨(-8767169612452131969760632314),(-8767169612452131968211197496)⟩⟩,⟨⟨1590241921453586581733829585,1590241921453586583211489744⟩,⟨(-9115347490097914104421011346),(-9115347490097914102808674639)⟩⟩,⟨⟨1650124571656563994564045924,1650124571656563996097055516⟩,⟨(-9458597883553255377608783821),(-9458597883553255375937416553)⟩⟩,⟨⟨1710353844287314213395086835,1710353844287314214984240197⟩,⟨(-9803835134375633248278669056),(-9803835134375633246545212802)⟩⟩,⟨⟨1769753689214106826016328166,1769753689214106827660213145⟩,⟨(-10144318063457720922586081509),(-10144318063457720920795054018)⟩⟩,⟨⟨1829437172087648438666216199,1829437172087648440365927499⟩,⟨(-10486426819661528380727324583),(-10486426819661528378873674099)⟩⟩,⟨⟨1888315278407924772786838634,1888315278407924774541337961⟩,⟨(-10823919116542794560151614001),(-10823919116542794558237819007)⟩⟩,⟨⟨1947419868181087738823617446,1947419868181087740633229666⟩,⟨(-11162709628083080545825525544),(-11162709628083080543850700574)⟩⟩] +lemma amp1_11_1_eq : ∀ k : Fin 16, amp1_1Expr 1 1 k = amp1_11_1 k := by decide +kernel +noncomputable def amp1_11_2 : Fin 16 → CBox := ![⟨⟨2005738188498802508628015370,2005738188498802510491241177⟩,⟨(-11496993203156297956892138591),(-11496993203156297954861487070)⟩⟩,⟨⟨2064230630799723993276404726,2064230630799723995194278263⟩,⟨(-11832274854283970912276193643),(-11832274854283970910184538686)⟩⟩,⟨⟨2121951893766475950149450471,2121951893766475952121126180⟩,⟨(-12163136066286436996885064639),(-12163136066286436994733927427)⟩⟩,⟨⟨2179798915915662806545975606,2179798915915662808571652149⟩,⟨(-12494718136312138249076681013),(-12494718136312138246865465127)⟩⟩,⟨⟨2236886552549583810553764469,2236886552549583812632878671⟩,⟨(-12821947369981803764085554756),(-12821947369981803761814213601)⟩⟩,⟨⟨2294054966019543062540511148,2294054966019543064671820813⟩,⟨(-13149639620579715177205659448),(-13149639620579715174881661695)⟩⟩,⟨⟨2350473060741471694033389501,2350473060741471696217323947⟩,⟨(-13473031005992043603168507766),(-13473031005992043600786156900)⟩⟩,⟨⟨2406929842568628606512209175,2406929842568628608748625255⟩,⟨(-13796644147857138299290860844),(-13796644147857138296851144223)⟩⟩,⟨⟨2462643101475025593851573869,2462643101475025596139963881⟩,⟨(-14115995378563845096156113816),(-14115995378563845093658735283)⟩⟩,⟨⟨2518355460693847128309878420,2518355460693847130650280860⟩,⟨(-14435341452215658458649485079),(-14435341452215658456094220093)⟩⟩,⟨⟨2573329192070436683399636609,2573329192070436685791358953⟩,⟨(-14750453673547913146511900383),(-14750453673547913143899533295)⟩⟩,⟨⟨2628264625263173644848278876,2628264625263173647289780815⟩,⟨(-15065346367744487153648786184),(-15065346367744487150987980978)⟩⟩,⟨⟨2682464728926284390043279585,2682464728926284392535634912⟩,⟨(-15376024115716937965235623193),(-15376024115716937962517053825)⟩⟩,⟨⟨2736591067706676008093749447,2736591067706676010636647573⟩,⟨(-15686279039633828380550848425),(-15686279039633828377775977108)⟩⟩,⟨⟨2789984030792729046072401116,2789984030792729048665364500⟩,⟨(-15992330216809733951852801985),(-15992330216809733949021203439)⟩⟩,⟨⟨2843269483200295800784565197,2843269483200295803426961463⟩,⟨(-16297765137314199945231447188),(-16297765137314199942346282592)⟩⟩] +lemma amp1_11_2_eq : ∀ k : Fin 16, amp1_1Expr 1 2 k = amp1_11_2 k := by decide +kernel +noncomputable def amp1_11_3 : Fin 16 → CBox := ![⟨⟨2895822380713515639851540444,2895822380713515642543027458⟩,⟨(-16599001015944936167202006999),(-16599001015944936164262078448)⟩⟩,⟨⟨2948235567927807710654034424,2948235567927807713394542197⟩,⟨(-16899436068043877785840590492),(-16899436068043877782845696680)⟩⟩,⟨⟨2999916066825581611425021036,2999916066825581614213920211⟩,⟨(-17195671313486425146771299361),(-17195671313486425143721888197)⟩⟩,⟨⟨3051426056220250140874109127,3051426056220250143708672897⟩,⟨(-17490929189793999196010356268),(-17490929189793999192921322637)⟩⟩,⟨⟨3102202422140761770937320438,3102202422140761773819623677⟩,⟨(-17781981899074080704756926937),(-17781981899074080701613213924)⟩⟩,⟨⟨3152778757425303729309141628,3152778757425303732238766385⟩,⟨(-18071888022585713740768540050),(-18071888022585713737571680763)⟩⟩,⟨⟨3202619863391098237123888124,3202619863391098240100129902⟩,⟨(-18357579774287072137317774413),(-18357579774287072134068636493)⟩⟩,⟨⟨3252232592395201073488818006,3252232592395201076511347251⟩,⟨(-18641962457640735661978615309),(-18641962457640735658678102936)⟩⟩,⟨⟨3301107928990071959662507436,3301107928990071962730796314⟩,⟨(-18922118370239566026496023006),(-18922118370239566023143981853)⟩⟩,⟨⟨3349727629506710175671455235,3349727629506710178784632107⟩,⟨(-19200808963849719073297071996),(-19200808963849719069897395955)⟩⟩,⟨⟨3397607316141974804089999255,3397607316141974807247991499⟩,⟨(-19475257760293532467989149933),(-19475257760293532464539064065)⟩⟩,⟨⟨3445205120144288773418903539,3445205120144288776621185326⟩,⟨(-19748090791163501395823513390),(-19748090791163501392324816201)⟩⟩,⟨⟨3492059917117642066041054498,3492059917117642069287055299⟩,⟨(-20016664867993086924540207076),(-20016664867993086920992964756)⟩⟩,⟨⟨3538607533590063831874339837,3538607533590063835163743125⟩,⟨(-20283478170584238482861860804),(-20283478170584238479266563035)⟩⟩,⟨⟨3584408854704921197487901409,3584408854704921200820074989⟩,⟨(-20546013670268378116864294594),(-20546013670268378113221346855)⟩⟩,⟨⟨3629878591273424892193115963,3629878591273424895567712579⟩,⟨(-20806648510485813831708507661),(-20806648510485813828018470532)⟩⟩] +lemma amp1_11_3_eq : ∀ k : Fin 16, amp1_1Expr 1 3 k = amp1_11_3 k := by decide +kernel +noncomputable def amp1_11_4 : Fin 16 → CBox := ![⟨⟨3674598516835281400239322718,3674598516835281403651743422⟩,⟨(-21062985395917073507418728453),(-21062985395917073503704729883)⟩⟩,⟨⟨3718963300339778586783249922,3718963300339778590237708789⟩,⟨(-21317286589031645011795308310),(-21317286589031645008031661521)⟩⟩,⟨⟨3762574590383011706317781063,3762574590383011709813429329⟩,⟨(-21567268719343079952306318190),(-21567268719343079948494639002)⟩⟩,⟨⟨3805807986503100694394586376,3805807986503100697930913152⟩,⟨(-21815084742487181202843362097),(-21815084742487181198984949339)⟩⟩,⟨⟨3848284094129928589514375078,3848284094129928593090633057⟩,⟨(-22058559949511922587203235717),(-22058559949511922583299107293)⟩⟩,⟨⟨3890360326150824616960179610,3890360326150824620576125435⟩,⟨(-22299743049246755115322403586),(-22299743049246755111372230028)⟩⟩,⟨⟨3931675410886016121552544931,3931675410886016125207087158⟩,⟨(-22536563214067886174243397852),(-22536563214067886170250153033)⟩⟩,⟨⟨3972569377672655660906580415,3972569377672655664599588160⟩,⟨(-22770969509411938191899870279),(-22770969509411938187862488429)⟩⟩,⟨⟨4012698318754671953250253716,4012698318754671956981095977⟩,⟨(-23000990638547993577145257949),(-23000990638547993573064056938)⟩⟩,⟨⟨4052385611987333476794005218,4052385611987333480561097879⟩,⟨(-23228480219772493902020344989),(-23228480219772493897902500507)⟩⟩,⟨⟨4091304021530033257092750316,4091304021530033260896621145⟩,⟨(-23451562520621022478260780582),(-23451562520621022474099951741)⟩⟩,⟨⟨4129760942243346617544414395,4129760942243346621384410525⟩,⟨(-23671999544052382610782861337),(-23671999544052382606580800293)⟩⟩,⟨⟨4167445178213067188315220551,4167445178213067192190755610⟩,⟨(-23888007499275235542327932749),(-23888007499275235538084668536)⟩⟩,⟨⟨4204648752671252389210361994,4204648752671252393120535772⟩,⟨(-24101260278292724879744194351),(-24101260278292724875462814230)⟩⟩,⟨⟨4241075931632628760573884733,4241075931632628764518449995⟩,⟨(-24310062718875738326150254166),(-24310062718875738321828827205)⟩⟩,⟨⟨4277003926566657991652894212,4277003926566657995631103241⟩,⟨(-24516003811251671112557612776),(-24516003811251671108198272275)⟩⟩] +lemma amp1_11_4_eq : ∀ k : Fin 16, amp1_1Expr 1 4 k = amp1_11_4 k := by decide +kernel +noncomputable def amp1_11_5 : Fin 16 → CBox := ![⟨⟨4312151936157441296611703305,4312151936157441300622966729⟩,⟨(-24717473988010959200195373905),(-24717473988010959195798134595)⟩⟩,⟨⟨4346782873384138106138235497,4346782873384138110182053369⟩,⟨(-24915980279708113743143902451),(-24915980279708113738709400261)⟩⟩,⟨⟨4380630384484886429260533822,4380630384484886433336304178⟩,⟨(-25109995933047354707622556667),(-25109995933047354703150863670)⟩⟩,⟨⟨4413943554923445712444052461,4413943554923445716551231655⟩,⟨(-25300948718562378097061822012),(-25300948718562378092553750149)⟩⟩,⟨⟨4446470033492561670586385671,4446470033492561674724292832⟩,⟨(-25487392146311851005414173720),(-25487392146311851000870233286)⟩⟩,⟨⟨4478445510590351193932728960,4478445510590351198093037795⟩,⟨(-25670677205632635583561400461),(-25670677205632635579026942079)⟩⟩,⟨⟨4509631229138743670440009412,4509631229138743674630232236⟩,⟨(-25849435328822564394349914716),(-25849435328822564389778471691)⟩⟩,⟨⟨4540249881715345224837916786,4540249881715345229057315125⟩,⟨(-26024943001050944219867765318),(-26024943001050944215261125231)⟩⟩,⟨⟨4570075930398161687526179801,4570075930398161691773887395⟩,⟨(-26195907427489870973805499180),(-26195907427489870969165209494)⟩⟩,⟨⟨4599319434914282687001751384,4599319434914282691277196020⟩,⟨(-26363532681167646459160687426),(-26363532681167646454487515953)⟩⟩,⟨⟨4627767732219821175470519732,4627767732219821179772773365⟩,⟨(-26526599766711817868029799285),(-26526599766711817863325636413)⟩⟩,⟨⟨4655618584475842400638458530,4655618584475842404966920004⟩,⟨(-26686242266877425819909934479),(-26686242266877425815175649673)⟩⟩,⟨⟨4682671887494008451996082167,4682671887494008456350278043⟩,⟨(-26841313174290110080148558239),(-26841313174290110075383425955)⟩⟩,⟨⟨4709113413761441754947609390,4709113413761441759326568195⟩,⟨(-26992877346284704826138171450),(-26992877346284704821345122023)⟩⟩,⟨⟨4734755328016043887360097358,4734755328016043891763321395⟩,⟨(-27139858101595408885565780589),(-27139858101595408880744218636)⟩⟩,⟨⟨4759771695603984754053842949,4759771695603984758480817787⟩,⟨(-27283253191630305217538255833),(-27283253191630305212688432517)⟩⟩] +lemma amp1_11_5_eq : ∀ k : Fin 16, amp1_1Expr 1 5 k = amp1_11_5 k := by decide +kernel +noncomputable def amp1_11_6 : Fin 16 → CBox := ![⟨⟨4783986684434824892512916090,4783986684434824896962069028⟩,⟨(-27422054737913393777067082905),(-27422054737913393772194557206)⟩⟩,⟨⟨4807562911692542944825832145,4807562911692542949297560831⟩,⟨(-27557194870405423916240964968),(-27557194870405423911340702980)⟩⟩,⟨⟨4830336305174704890791375582,4830336305174704895284419819⟩,⟨(-27687733118905934105241639067),(-27687733118905934100317402192)⟩⟩,⟨⟨4852458270930776059830619587,4852458270930776064344871588⟩,⟨(-27814537350583032898965628238),(-27814537350583032894015225131)⟩⟩,⟨⟨4873776274319785401498132395,4873776274319785406032562309⟩,⟨(-27936733229124759958944859372),(-27936733229124759953970726223)⟩⟩,⟨⟨4894430726757596739947959913,4894430726757596744502095998⟩,⟨(-28055125599900809407892786411),(-28055125599900809402894765804)⟩⟩,⟨⟨4914280428450251326987762669,4914280428450251331558194092⟩,⟨(-28168905098518191444135607869),(-28168905098518191439129780503)⟩⟩,⟨⟨4933454993419274264668631113,4933454993419274269257627458⟩,⟨(-28278814679133661278762097968),(-28278814679133661273732543045)⟩⟩,⟨⟨4951824372420951260786446638,4951824372420951265392997550⟩,⟨(-28384108892874762681385880468),(-28384108892874762676334917144)⟩⟩,⟨⟨4969507561182857999546910181,4969507561182858004170225981⟩,⟨(-28485469829297843098780286812),(-28485469829297843093709482465)⟩⟩,⟨⟨4986385494073012460239140357,4986385494073012464878633327⟩,⟨(-28582214998150946290386945641),(-28582214998150946285296196561)⟩⟩,⟨⟨5002566710481483924435546956,5002566710481483929090259545⟩,⟨(-28674966552732571915021020649),(-28674966552732571909912811078)⟩⟩,⟨⟨5017942977869881852628627741,5017942977869881857297968969⟩,⟨(-28763104098633633251186179526),(-28763104098633633246060425766)⟩⟩,⟨⟨5032612524982808371954003123,5032612524982808376637494074⟩,⟨(-28847190688008953398726889238),(-28847190688008953393583288828)⟩⟩,⟨⟨5046477817449798230126260568,5046477817449798234821865698⟩,⟨(-28926667248891541286217672827),(-28926667248891541281064425378)⟩⟩,⟨⟨5059626903572492894896470968,5059626903572492899604678065⟩,⟨(-29002038478619925956999542021),(-29002038478619925951830762971)⟩⟩] +lemma amp1_11_6_eq : ∀ k : Fin 16, amp1_1Expr 1 6 k = amp1_11_6 k := by decide +kernel +noncomputable def amp1_11_7 : Fin 16 → CBox := ![⟨⟨5071972827087325082160909814,5071972827087325086880828489⟩,⟨(-29072805939473303388075349058),(-29072805939473303382892678645)⟩⟩,⟨⟨5083593571245343646130740612,5083593571245343650861852138⟩,⟨(-29139416635408825010725387156),(-29139416635408825005528671516)⟩⟩,⟨⟨5094412652057206985373323217,5094412652057206990114184044⟩,⟨(-29201432156313619209049019416),(-29201432156313619203843075995)⟩⟩,⟨⟨5104498088897388240776166821,5104498088897388245526657454⟩,⟨(-29259242392698065080155425801),(-29259242392698065074937775818)⟩⟩,⟨⟨5113783777894453971948270063,5113783777894453976707221977⟩,⟨(-29312468433812529142807229874),(-29312468433812529137581122578)⟩⟩,⟨⟨5122327862012853057989209103,5122327862012853062756403949⟩,⟨(-29361443558083335042974983525),(-29361443558083335037738472439)⟩⟩,⟨⟨5130074538545206821347409225,5130074538545206826121769165⟩,⟨(-29405847901556588302246632484),(-29405847901556588297002457128)⟩⟩,⟨⟨5137072148240684474909632590,5137072148240684479690468486⟩,⟨(-29445958555862602791885980279),(-29445958555862602786634860587)⟩⟩,⟨⟨5143275123403590878672028266,5143275123403590883458627952⟩,⟨(-29481514324654470131780537029),(-29481514324654470126523128429)⟩⟩,⟨⟨5148722063855938645669625635,5148722063855938650461353885⟩,⟨(-29512736464073129735404560901),(-29512736464073129730141244250)⟩⟩,⟨⟨5153377583230425999895345229,5153377583230426004691299670⟩,⟨(-29539422137663312528681821443),(-29539422137663312523414356295)⟩⟩,⟨⟨5157270589102046092236572349,5157270589102046097036090124⟩,⟨(-29561737045113602860040166693),(-29561737045113602854769064357)⟩⟩,⟨⟨5160375834950324842324411298,5160375834950324847126606694⟩,⟨(-29579536472085928972905021131),(-29579536472085928967631961453)⟩⟩,⟨⟨5162712572410639435569130687,5162712572410639440373242716⟩,⟨(-29592930769932401684475608494),(-29592930769932401679201639416)⟩⟩,⟨⟨5164265665324380304762290349,5164265665324380309567460500⟩,⟨(-29601833177422839534419396309),(-29601833177422839529146059511)⟩⟩,⟨⟨5165044733496314877448982713,5165044733496314882254313264⟩,⟨(-29606298835766928310731801597),(-29606298835766928305460904994)⟩⟩] +lemma amp1_11_7_eq : ∀ k : Fin 16, amp1_1Expr 1 7 k = amp1_11_7 k := by decide +kernel +noncomputable def amp1_11_8 : Fin 16 → CBox := ![⟨⟨5165044733496314877448982713,5165044733496314882254313264⟩,⟨(-29606298835766928310731801597),(-29606298835766928305460904994)⟩⟩,⟨⟨5164265665324380304762290349,5164265665324380309567460500⟩,⟨(-29601833177422839534419396309),(-29601833177422839529146059511)⟩⟩,⟨⟨5162712572410639435569130687,5162712572410639440373242716⟩,⟨(-29592930769932401684475608494),(-29592930769932401679201639416)⟩⟩,⟨⟨5160375834950324842324411298,5160375834950324847126606694⟩,⟨(-29579536472085928972905021131),(-29579536472085928967631961453)⟩⟩,⟨⟨5157270589102046092236572349,5157270589102046097036090124⟩,⟨(-29561737045113602860040166693),(-29561737045113602854769064357)⟩⟩,⟨⟨5153377583230425999895345229,5153377583230426004691299670⟩,⟨(-29539422137663312528681821443),(-29539422137663312523414356295)⟩⟩,⟨⟨5148722063855938645669625635,5148722063855938650461353885⟩,⟨(-29512736464073129735404560901),(-29512736464073129730141244250)⟩⟩,⟨⟨5143275123403590878672028266,5143275123403590883458627952⟩,⟨(-29481514324654470131780537029),(-29481514324654470126523128429)⟩⟩,⟨⟨5137072148240684474909632590,5137072148240684479690468486⟩,⟨(-29445958555862602791885980279),(-29445958555862602786634860587)⟩⟩,⟨⟨5130074538545206821347409225,5130074538545206826121769165⟩,⟨(-29405847901556588302246632484),(-29405847901556588297002457128)⟩⟩,⟨⟨5122327862012853057989209103,5122327862012853062756403949⟩,⟨(-29361443558083335042974983525),(-29361443558083335037738472439)⟩⟩,⟨⟨5113783777894453971948270063,5113783777894453976707221977⟩,⟨(-29312468433812529142807229874),(-29312468433812529137581122578)⟩⟩,⟨⟨5104498088897388240776166821,5104498088897388245526657454⟩,⟨(-29259242392698065080155425801),(-29259242392698065074937775818)⟩⟩,⟨⟨5094412652057206985373323217,5094412652057206990114184044⟩,⟨(-29201432156313619209049019416),(-29201432156313619203843075995)⟩⟩,⟨⟨5083593571245343646130740612,5083593571245343650861852138⟩,⟨(-29139416635408825010725387156),(-29139416635408825005528671516)⟩⟩,⟨⟨5071972827087325082160909814,5071972827087325086880828489⟩,⟨(-29072805939473303388075349058),(-29072805939473303382892678645)⟩⟩] +lemma amp1_11_8_eq : ∀ k : Fin 16, amp1_1Expr 1 8 k = amp1_11_8 k := by decide +kernel +noncomputable def amp1_11_9 : Fin 16 → CBox := ![⟨⟨5059626903572492894896470968,5059626903572492899604678065⟩,⟨(-29002038478619925956999542021),(-29002038478619925951830762971)⟩⟩,⟨⟨5046477817449798230126260568,5046477817449798234821865698⟩,⟨(-28926667248891541286217672827),(-28926667248891541281064425378)⟩⟩,⟨⟨5032612524982808371954003123,5032612524982808376637494074⟩,⟨(-28847190688008953398726889238),(-28847190688008953393583288828)⟩⟩,⟨⟨5017942977869881852628627741,5017942977869881857297968969⟩,⟨(-28763104098633633251186179526),(-28763104098633633246060425766)⟩⟩,⟨⟨5002566710481483924435546956,5002566710481483929090259545⟩,⟨(-28674966552732571915021020649),(-28674966552732571909912811078)⟩⟩,⟨⟨4986385494073012460239140357,4986385494073012464878633327⟩,⟨(-28582214998150946290386945641),(-28582214998150946285296196561)⟩⟩,⟨⟨4969507561182857999546910181,4969507561182858004170225981⟩,⟨(-28485469829297843098780286812),(-28485469829297843093709482465)⟩⟩,⟨⟨4951824372420951260786446638,4951824372420951265392997550⟩,⟨(-28384108892874762681385880468),(-28384108892874762676334917144)⟩⟩,⟨⟨4933454993419274264668631113,4933454993419274269257627458⟩,⟨(-28278814679133661278762097968),(-28278814679133661273732543045)⟩⟩,⟨⟨4914280428450251326987762669,4914280428450251331558194092⟩,⟨(-28168905098518191444135607869),(-28168905098518191439129780503)⟩⟩,⟨⟨4894430726757596739947959913,4894430726757596744502095998⟩,⟨(-28055125599900809407892786411),(-28055125599900809402894765804)⟩⟩,⟨⟨4873776274319785401498132395,4873776274319785406032562309⟩,⟨(-27936733229124759958944859372),(-27936733229124759953970726223)⟩⟩,⟨⟨4852458270930776059830619587,4852458270930776064344871588⟩,⟨(-27814537350583032898965628238),(-27814537350583032894015225131)⟩⟩,⟨⟨4830336305174704890791375582,4830336305174704895284419819⟩,⟨(-27687733118905934105241639067),(-27687733118905934100317402192)⟩⟩,⟨⟨4807562911692542944825832145,4807562911692542949297560831⟩,⟨(-27557194870405423916240964968),(-27557194870405423911340702980)⟩⟩,⟨⟨4783986684434824892512916090,4783986684434824896962069028⟩,⟨(-27422054737913393777067082905),(-27422054737913393772194557206)⟩⟩] +lemma amp1_11_9_eq : ∀ k : Fin 16, amp1_1Expr 1 9 k = amp1_11_9 k := by decide +kernel +noncomputable def amp1_11_10 : Fin 16 → CBox := ![⟨⟨4759771695603984754053842949,4759771695603984758480817787⟩,⟨(-27283253191630305217538255833),(-27283253191630305212688432517)⟩⟩,⟨⟨4734755328016043887360097358,4734755328016043891763321395⟩,⟨(-27139858101595408885565780589),(-27139858101595408880744218636)⟩⟩,⟨⟨4709113413761441754947609390,4709113413761441759326568195⟩,⟨(-26992877346284704826138171450),(-26992877346284704821345122023)⟩⟩,⟨⟨4682671887494008451996082167,4682671887494008456350278043⟩,⟨(-26841313174290110080148558239),(-26841313174290110075383425955)⟩⟩,⟨⟨4655618584475842400638458530,4655618584475842404966920004⟩,⟨(-26686242266877425819909934479),(-26686242266877425815175649673)⟩⟩,⟨⟨4627767732219821175470519732,4627767732219821179772773365⟩,⟨(-26526599766711817868029799285),(-26526599766711817863325636413)⟩⟩,⟨⟨4599319434914282687001751384,4599319434914282691277196020⟩,⟨(-26363532681167646459160687426),(-26363532681167646454487515953)⟩⟩,⟨⟨4570075930398161687526179801,4570075930398161691773887395⟩,⟨(-26195907427489870973805499180),(-26195907427489870969165209494)⟩⟩,⟨⟨4540249881715345224837916786,4540249881715345229057315125⟩,⟨(-26024943001050944219867765318),(-26024943001050944215261125231)⟩⟩,⟨⟨4509631229138743670440009412,4509631229138743674630232236⟩,⟨(-25849435328822564394349914716),(-25849435328822564389778471691)⟩⟩,⟨⟨4478445510590351193932728960,4478445510590351198093037795⟩,⟨(-25670677205632635583561400461),(-25670677205632635579026942079)⟩⟩,⟨⟨4446470033492561670586385671,4446470033492561674724292832⟩,⟨(-25487392146311851005414173720),(-25487392146311851000870233286)⟩⟩,⟨⟨4413943554923445712444052461,4413943554923445716551231655⟩,⟨(-25300948718562378097061822012),(-25300948718562378092553750149)⟩⟩,⟨⟨4380630384484886429260533822,4380630384484886433336304178⟩,⟨(-25109995933047354707622556667),(-25109995933047354703150863670)⟩⟩,⟨⟨4346782873384138106138235497,4346782873384138110182053369⟩,⟨(-24915980279708113743143902451),(-24915980279708113738709400261)⟩⟩,⟨⟨4312151936157441296611703305,4312151936157441300622966729⟩,⟨(-24717473988010959200195373905),(-24717473988010959195798134595)⟩⟩] +lemma amp1_11_10_eq : ∀ k : Fin 16, amp1_1Expr 1 10 k = amp1_11_10 k := by decide +kernel +noncomputable def amp1_11_11 : Fin 16 → CBox := ![⟨⟨4277003926566657991652894212,4277003926566657995631103241⟩,⟨(-24516003811251671112557612776),(-24516003811251671108198272275)⟩⟩,⟨⟨4241075931632628760573884733,4241075931632628764518449995⟩,⟨(-24310062718875738326150254166),(-24310062718875738321828827205)⟩⟩,⟨⟨4204648752671252389210361994,4204648752671252393120535772⟩,⟨(-24101260278292724879744194351),(-24101260278292724875462814230)⟩⟩,⟨⟨4167445178213067188315220551,4167445178213067192190755610⟩,⟨(-23888007499275235542327932749),(-23888007499275235538084668536)⟩⟩,⟨⟨4129760942243346617544414395,4129760942243346621384410525⟩,⟨(-23671999544052382610782861337),(-23671999544052382606580800293)⟩⟩,⟨⟨4091304021530033257092750316,4091304021530033260896621145⟩,⟨(-23451562520621022478260780582),(-23451562520621022474099951741)⟩⟩,⟨⟨4052385611987333476794005218,4052385611987333480561097879⟩,⟨(-23228480219772493902020344989),(-23228480219772493897902500507)⟩⟩,⟨⟨4012698318754671953250253716,4012698318754671956981095977⟩,⟨(-23000990638547993577145257949),(-23000990638547993573064056938)⟩⟩,⟨⟨3972569377672655660906580415,3972569377672655664599588160⟩,⟨(-22770969509411938191899870279),(-22770969509411938187862488429)⟩⟩,⟨⟨3931675410886016121552544931,3931675410886016125207087158⟩,⟨(-22536563214067886174243397852),(-22536563214067886170250153033)⟩⟩,⟨⟨3890360326150824616960179610,3890360326150824620576125435⟩,⟨(-22299743049246755115322403586),(-22299743049246755111372230028)⟩⟩,⟨⟨3848284094129928589514375078,3848284094129928593090633057⟩,⟨(-22058559949511922587203235717),(-22058559949511922583299107293)⟩⟩,⟨⟨3805807986503100694394586376,3805807986503100697930913152⟩,⟨(-21815084742487181202843362097),(-21815084742487181198984949339)⟩⟩,⟨⟨3762574590383011706317781063,3762574590383011709813429329⟩,⟨(-21567268719343079952306318190),(-21567268719343079948494639002)⟩⟩,⟨⟨3718963300339778586783249922,3718963300339778590237708789⟩,⟨(-21317286589031645011795308310),(-21317286589031645008031661521)⟩⟩,⟨⟨3674598516835281400239322718,3674598516835281403651743422⟩,⟨(-21062985395917073507418728453),(-21062985395917073503704729883)⟩⟩] +lemma amp1_11_11_eq : ∀ k : Fin 16, amp1_1Expr 1 11 k = amp1_11_11 k := by decide +kernel +noncomputable def amp1_11_12 : Fin 16 → CBox := ![⟨⟨3629878591273424892193115963,3629878591273424895567712579⟩,⟨(-20806648510485813831708507661),(-20806648510485813828018470532)⟩⟩,⟨⟨3584408854704921197487901409,3584408854704921200820074989⟩,⟨(-20546013670268378116864294594),(-20546013670268378113221346855)⟩⟩,⟨⟨3538607533590063831874339837,3538607533590063835163743125⟩,⟨(-20283478170584238482861860804),(-20283478170584238479266563035)⟩⟩,⟨⟨3492059917117642066041054498,3492059917117642069287055299⟩,⟨(-20016664867993086924540207076),(-20016664867993086920992964756)⟩⟩,⟨⟨3445205120144288773418903539,3445205120144288776621185326⟩,⟨(-19748090791163501395823513390),(-19748090791163501392324816201)⟩⟩,⟨⟨3397607316141974804089999255,3397607316141974807247991499⟩,⟨(-19475257760293532467989149933),(-19475257760293532464539064065)⟩⟩,⟨⟨3349727629506710175671455235,3349727629506710178784632107⟩,⟨(-19200808963849719073297071996),(-19200808963849719069897395955)⟩⟩,⟨⟨3301107928990071959662507436,3301107928990071962730796314⟩,⟨(-18922118370239566026496023006),(-18922118370239566023143981853)⟩⟩,⟨⟨3252232592395201073488818006,3252232592395201076511347251⟩,⟨(-18641962457640735661978615309),(-18641962457640735658678102936)⟩⟩,⟨⟨3202619863391098237123888124,3202619863391098240100129902⟩,⟨(-18357579774287072137317774413),(-18357579774287072134068636493)⟩⟩,⟨⟨3152778757425303729309141628,3152778757425303732238766385⟩,⟨(-18071888022585713740768540050),(-18071888022585713737571680763)⟩⟩,⟨⟨3102202422140761770937320438,3102202422140761773819623677⟩,⟨(-17781981899074080704756926937),(-17781981899074080701613213924)⟩⟩,⟨⟨3051426056220250140874109127,3051426056220250143708672897⟩,⟨(-17490929189793999196010356268),(-17490929189793999192921322637)⟩⟩,⟨⟨2999916066825581611425021036,2999916066825581614213920211⟩,⟨(-17195671313486425146771299361),(-17195671313486425143721888197)⟩⟩,⟨⟨2948235567927807710654034424,2948235567927807713394542197⟩,⟨(-16899436068043877785840590492),(-16899436068043877782845696680)⟩⟩,⟨⟨2895822380713515639851540444,2895822380713515642543027458⟩,⟨(-16599001015944936167202006999),(-16599001015944936164262078448)⟩⟩] +lemma amp1_11_12_eq : ∀ k : Fin 16, amp1_1Expr 1 12 k = amp1_11_12 k := by decide +kernel +noncomputable def amp1_11_13 : Fin 16 → CBox := ![⟨⟨2843269483200295800784565197,2843269483200295803426961463⟩,⟨(-16297765137314199945231447188),(-16297765137314199942346282592)⟩⟩,⟨⟨2789984030792729046072401116,2789984030792729048665364500⟩,⟨(-15992330216809733951852801985),(-15992330216809733949021203439)⟩⟩,⟨⟨2736591067706676008093749447,2736591067706676010636647573⟩,⟨(-15686279039633828380550848425),(-15686279039633828377775977108)⟩⟩,⟨⟨2682464728926284390043279585,2682464728926284392535634912⟩,⟨(-15376024115716937965235623193),(-15376024115716937962517053825)⟩⟩,⟨⟨2628264625263173644848278876,2628264625263173647289780815⟩,⟨(-15065346367744487153648786184),(-15065346367744487150987980978)⟩⟩,⟨⟨2573329192070436683399636609,2573329192070436685791358953⟩,⟨(-14750453673547913146511900383),(-14750453673547913143899533295)⟩⟩,⟨⟨2518355460693847128309878420,2518355460693847130650280860⟩,⟨(-14435341452215658458649485079),(-14435341452215658456094220093)⟩⟩,⟨⟨2462643101475025593851573869,2462643101475025596139963881⟩,⟨(-14115995378563845096156113816),(-14115995378563845093658735283)⟩⟩,⟨⟨2406929842568628606512209175,2406929842568628608748625255⟩,⟨(-13796644147857138299290860844),(-13796644147857138296851144223)⟩⟩,⟨⟨2350473060741471694033389501,2350473060741471696217323947⟩,⟨(-13473031005992043603168507766),(-13473031005992043600786156900)⟩⟩,⟨⟨2294054966019543062540511148,2294054966019543064671820813⟩,⟨(-13149639620579715177205659448),(-13149639620579715174881661695)⟩⟩,⟨⟨2236886552549583810553764469,2236886552549583812632878671⟩,⟨(-12821947369981803764085554756),(-12821947369981803761814213601)⟩⟩,⟨⟨2179798915915662806545975606,2179798915915662808571652149⟩,⟨(-12494718136312138249076681013),(-12494718136312138246865465127)⟩⟩,⟨⟨2121951893766475950149450471,2121951893766475952121126180⟩,⟨(-12163136066286436996885064639),(-12163136066286436994733927427)⟩⟩,⟨⟨2064230630799723993276404726,2064230630799723995194278263⟩,⟨(-11832274854283970912276193643),(-11832274854283970910184538686)⟩⟩,⟨⟨2005738188498802508628015370,2005738188498802510491241177⟩,⟨(-11496993203156297956892138591),(-11496993203156297954861487070)⟩⟩] +lemma amp1_11_13_eq : ∀ k : Fin 16, amp1_1Expr 1 13 k = amp1_11_13 k := by decide +kernel +noncomputable def amp1_11_14 : Fin 16 → CBox := ![⟨⟨1947419868181087738823617446,1947419868181087740633229666⟩,⟨(-11162709628083080545825525544),(-11162709628083080543850700574)⟩⟩,⟨⟨1888315278407924772786838634,1888315278407924774541337961⟩,⟨(-10823919116542794560151614001),(-10823919116542794558237819007)⟩⟩,⟨⟨1829437172087648438666216199,1829437172087648440365927499⟩,⟨(-10486426819661528380727324583),(-10486426819661528378873674099)⟩⟩,⟨⟨1769753689214106826016328166,1769753689214106827660213145⟩,⟨(-10144318063457720922586081509),(-10144318063457720920795054018)⟩⟩,⟨⟨1710353844287314213395086835,1710353844287314214984240197⟩,⟨(-9803835134375633248278669056),(-9803835134375633246545212802)⟩⟩,⟨⟨1650124571656563994564045924,1650124571656563996097055516⟩,⟨(-9458597883553255377608783821),(-9458597883553255375937416553)⟩⟩,⟨⟨1590241921453586581733829585,1590241921453586583211489744⟩,⟨(-9115347490097914104421011346),(-9115347490097914102808674639)⟩⟩,⟨⟨1529499634035960901503023702,1529499634035960902924012322⟩,⟨(-8767169612452131969760632314),(-8767169612452131968211197496)⟩⟩,⟨⟨1469174162069821262594913565,1469174162069821263959681547⟩,⟨(-8421380942151647584460921009),(-8421380942151647582973600945)⟩⟩,⟨⟨1407951061421259998592792547,1407951061421259999900878603⟩,⟨(-8070447018637191335750575599),(-8070447018637191334324143519)⟩⟩,⟨⟨1347224049647206332753864017,1347224049647206334005289901⟩,⟨(-7722356701756482300514578834),(-7722356701756482299151049353)⟩⟩,⟨⟨1285551412780888595940576702,1285551412780888597134839914⟩,⟨(-7368846013802003603148777623),(-7368846013802003601846953227)⟩⟩,⟨⟨1224465824149729458084427969,1224465824149729459222074538⟩,⟨(-7018700316157947637121348736),(-7018700316157947635880631127)⟩⟩,⟨⟨1162373479802631048115180043,1162373479802631049194925359⟩,⟨(-6662783843599317383142805028),(-6662783843599317381966216161)⟩⟩,⟨⟨1100974564234470578064397449,1100974564234470579087160022⟩,⟨(-6310842140032989848167681559),(-6310842140032989847052946796)⟩⟩,⟨⟨1038490075614490173353621829,1038490075614490174318370583⟩,⟨(-5952677876578302846042721367),(-5952677876578302844991069513)⟩⟩] +lemma amp1_11_14_eq : ∀ k : Fin 16, amp1_1Expr 1 14 k = amp1_11_14 k := by decide +kernel +noncomputable def amp1_11_15 : Fin 16 → CBox := ![⟨⟨976826365869980121351368078,976826365869980122258805867⟩,⟨(-5599218359339591154132831411),(-5599218359339591153143773168)⟩⟩,⟨⟨913973687112991919932988328,913973687112991920781983424⟩,⟨(-5238943611312729715314406947),(-5238943611312729714389302175)⟩⟩,⟨⟨852098715826997532204683026,852098715826997532996122413⟩,⟨(-4884273132184544490933227255),(-4884273132184544490071207941)⟩⟩,⟨⟨788895841566765076051335362,788895841566765076784120854⟩,⟨(-4521991045740504832372530651),(-4521991045740504831574165269)⟩⟩,⟨⟨726871292114567086768840492,726871292114567087444016849⟩,⟨(-4166463176963937581953991051),(-4166463176963937581218372332)⟩⟩,⟨⟨663325817138793156850381311,663325817138793157466506848⟩,⟨(-3802217285811704743486625095),(-3802217285811704742815458076)⟩⟩,⟨⟨601227801041259060729084625,601227801041259061287459640⟩,⟨(-3446268302491409285569469742),(-3446268302491409284961543017)⟩⟩,⟨⟨537327657764345331882400123,537327657764345332381467477⟩,⟨(-3079989434617208980891752592),(-3079989434617208980348220336)⟩⟩,⟨⟨475260698067625593405306007,475260698067625593846685537⟩,⟨(-2724218468164281644447773067),(-2724218468164281643967255638)⟩⟩,⟨⟨410952047203312812167350815,410952047203312812548977813⟩,⟨(-2355598014043832587787217628),(-2355598014043832587371883071)⟩⟩,⟨⟨349085604172734028656047471,349085604172734028980173385⟩,⟨(-2000976419308989531209651633),(-2000976419308989530857126195)⟩⟩,⟨⟨284208574900344161364713227,284208574900344161628569383⟩,⟨(-1629097991275517500546327281),(-1629097991275517500259498428)⟩⟩,⟨⟨222899049574540211848314004,222899049574540212055188512⟩,⟨(-1277668677120078436760991142),(-1277668677120078436536395606)⟩⟩,⟨⟨156930468665277272954098492,156930468665277273099707431⟩,⟨(-899533419644964986115396225),(-899533419644964985957498156)⟩⟩,⟨⟨97347548738388396573839292,97347548738388396664030973⟩,⟨(-558001095360729850836297400),(-558001095360729850739111216)⟩⟩,⟨⟨27656833929615362261842843,27656833929615362287386726⟩,⟨(-158530377261050063375886837),(-158530377261050063348734071)⟩⟩] +lemma amp1_11_15_eq : ∀ k : Fin 16, amp1_1Expr 1 15 k = amp1_11_15 k := by decide +kernel +noncomputable def amp1_11 : Fin 16 → Fin 16 → CBox := ![amp1_11_0,amp1_11_1,amp1_11_2,amp1_11_3,amp1_11_4,amp1_11_5,amp1_11_6,amp1_11_7,amp1_11_8,amp1_11_9,amp1_11_10,amp1_11_11,amp1_11_12,amp1_11_13,amp1_11_14,amp1_11_15] +lemma amp1_11_eq (i k : Fin 16) : amp1_1Expr 1 i k = amp1_11 i k := by + fin_cases i + · exact amp1_11_0_eq k + · exact amp1_11_1_eq k + · exact amp1_11_2_eq k + · exact amp1_11_3_eq k + · exact amp1_11_4_eq k + · exact amp1_11_5_eq k + · exact amp1_11_6_eq k + · exact amp1_11_7_eq k + · exact amp1_11_8_eq k + · exact amp1_11_9_eq k + · exact amp1_11_10_eq k + · exact amp1_11_11_eq k + · exact amp1_11_12_eq k + · exact amp1_11_13_eq k + · exact amp1_11_14_eq k + · exact amp1_11_15_eq k +noncomputable def amp1_12_0 : Fin 16 → CBox := ![⟨⟨385210003677661992959706116,385210003677661992983599170⟩,⟨47903041542588614251592822,47903041542588614272386485⟩⟩,⟨⟨1355876442797423833515075140,1355876442797423833603093890⟩,⟨168610900407176264268572200,168610900407176264342249863⟩⟩,⟨⟨2185759460592364486796860961,2185759460592364486941736049⟩,⟨271811544983855893858699856,271811544983855893977843938⟩⟩,⟨⟨3104583262309451838876923841,3104583262309451839083482569⟩,⟨386072478821917588742021454,386072478821917588911347261⟩⟩,⟨⟨3958514790998972547947403235,3958514790998972548211887856⟩,⟨492263691674140854289197787,492263691674140854505235665⟩⟩,⟨⟨4862135239681351864531422709,4862135239681351864856819938⟩,⟨604634002618053415604739073,604634002618053415870159384⟩⟩,⟨⟨5723823631345515038812797592,5723823631345515039196672391⟩,⟨711789825230581337962950776,711789825230581338275510648⟩⟩,⟨⟨6619527590048496233869823975,6619527590048496234314228017⟩,⟨823175675893779269490775900,823175675893779269852304261⟩⟩,⟨⟨7484008818589727932923343000,7484008818589727933426419335⟩,⟨930678803559827651851671493,930678803559827652260492845⟩⟩,⟨⟨8374023000594305591574767669,8374023000594305592137079139⟩,⟨1041357098326373040963264617,1041357098326373041420630281⟩⟩,⟨⟨9238936788997680557722176709,9238936788997680558343661072⟩,⟨1148914017256532114220244409,1148914017256532114724985330⟩⟩,⟨⟨10124011078824646541887004098,10124011078824646542568402353⟩,⟨1258978008505669232834968637,1258978008505669233388109724⟩⟩,⟨⟨10987901608861133639591349894,10987901608861133640330833371⟩,⟨1366407679473444525949165774,1366407679473444526549499516⟩⟩,⟨⟨11868204086295200168019668818,11868204086295200168817649033⟩,⟨1475878268876554359719081015,1475878268876554360367417915⟩⟩,⟨⟨12730011261233991575561351260,12730011261233991576418467540⟩,⟨1583048862860762033012606897,1583048862860762033708170742⟩⟩,⟨⟨13605436144528543517635090496,13605436144528543518551964247⟩,⟨1691912895859670665980452306,1691912895859670666723950418⟩⟩] +lemma amp1_12_0_eq : ∀ k : Fin 16, amp1_1Expr 2 0 k = amp1_12_0 k := by decide +kernel +noncomputable def amp1_12_1 : Fin 16 → CBox := ![⟨⟨14464300825782799816828646082,14464300825782799817803782239⟩,⟨1798717574120342149707766680,1798717574120342150498246951⟩⟩,⟨⟨15334597482021724182501494634,15334597482021724183534833168⟩,⟨1906943883095107532814097477,1906943883095107533652081365⟩⟩,⟨⟨16189774056173590091522935669,16189774056173590092613142628⟩,⟨2013289924388793187413746005,2013289924388793188298368066⟩⟩,⟨⟨17054608847284225417280799295,17054608847284225418432346603⟩,⟨2120837019559029801339430947,2120837019559029802271694145⟩⟩,⟨⟨17905421340180017040267047002,17905421340180017041474123625⟩,⟨2226640362678449215771231506,2226640362678449216749764440⟩⟩,⟨⟨18764410360201072197988474239,18764410360201072199251640673⟩,⟨2333460503167656965711195335,2333460503167656966736446007⟩⟩,⟨⟨19610228521757425345957811675,19610228521757425347281416680⟩,⟨2438642772952151337419294047,2438642772952151338491193877⟩⟩,⟨⟨20462956309978198964362459082,20462956309978198965740852490⟩,⟨2544684293872362529950093327,2544684293872362531068259372⟩⟩,⟨⟨21303181743484879754968313407,21303181743484879756405842028⟩,⟨2649171076308288359446690588,2649171076308288360611084953⟩⟩,⟨⟨22149212667309377171108243135,22149212667309377172606185356⟩,⟨2754379804283567773011635375,2754379804283567774222685637⟩⟩,⟨⟨22983270389303945547980982288,22983270389303945549531239335⟩,⟨2858099596926999394711750067,2858099596926999395967895135⟩⟩,⟨⟨23822155938916705060761531989,23822155938916705062371008026⟩,⟨2962419757226376389886997045,2962419757226376391189318860⟩⟩,⟨⟨24649489050903922244000816323,24649489050903922245659795880⟩,⟨3065303306601293613544979905,3065303306601293614891735799⟩⟩,⟨⟨25480772729857277562296589251,25480772729857277564016915887⟩,⟨3168678131310934620916644401,3168678131310934622309489968⟩⟩,⟨⟨26300838960499855272500142033,26300838960499855274277018858⟩,⟨3270658002911095463692345435,3270658002911095465130165159⟩⟩,⟨⟨27124059698702532520452590029,27124059698702532522287823982⟩,⟨3373030155358729585051750050,3373030155358729586534914582⟩⟩] +lemma amp1_12_1_eq : ∀ k : Fin 16, amp1_1Expr 2 1 k = amp1_12_1 k := by decide +kernel +noncomputable def amp1_12_2 : Fin 16 → CBox := ![⟨⟨27936329116135969236090321551,27936329116135969237972465381⟩,⟨3474040449161087916739998075,3474040449161087918266577203⟩⟩,⟨⟨28751023739938367695380695540,28751023739938367697322063507⟩,⟨3575352331085074933364232153,3575352331085074934935869432⟩⟩,⟨⟨29554977221247464421556703446,29554977221247464423554772750⟩,⟨3675328491220533190317565578,3675328491220533191933450325⟩⟩,⟨⟨30360682302007587722349635059,30360682302007587724405663561⟩,⟨3775522472649487016758904087,3775522472649487018419273765⟩⟩,⟨⟨31155810506980960745912195611,31155810506980960748027452075⟩,⟨3874401159783468515573765018,3874401159783468517278288046⟩⟩,⟨⟨31952063788142973130138704585,31952063788142973132294918113⟩,⟨3973419756501542920591348935,3973419756501542922337805279⟩⟩,⟨⟨32737866477294929150160350546,32737866477294929152372504735⟩,⟨4071138763026156820422803509,4071138763026156822212572948⟩⟩,⟨⟨33524208008310895721950383079,33524208008310895724216019903⟩,⟨4168924777582623866470915298,4168924777582623868303717093⟩⟩,⟨⟨34300193600980150022968039647,34300193600980150025289010135⟩,⟨4265422972663742713820788749,4265422972663742715696373950⟩⟩,⟨⟨35076166662618009662426815055,35076166662618009664803666189⟩,⟨4361919609440269938322798139,4361919609440269940241234187⟩⟩,⟨⟨35841851965557722417683921654,35841851965557722420115871507⟩,⟨4457136905266166405670150572,4457136905266166407630864248⟩⟩,⟨⟨36607003843609385792843718367,36607003843609385795309772763⟩,⟨4552287866691792566865170089,4552287866691792568865525969⟩⟩,⟨⟨37361913902531192332050880737,37361913902531192334574819798⟩,⟨4646165200011800397516704268,4646165200011800399559185688⟩⟩,⟨⟨38115796549175229430478432228,38115796549175229433056815198⟩,⟨4739914768807124340476345013,4739914768807124342560476561⟩⟩,⟨⟨38859464590104374373499645062,38859464590104374376134621284⟩,⟨4832394093638817759710881324,4832394093638817761836457686⟩⟩,⟨⟨39601635200454137554238963201,39601635200454137556923014979⟩,⟨4924687204513016734091414283,4924687204513016736257431310⟩⟩] +lemma amp1_12_2_eq : ∀ k : Fin 16, amp1_1Expr 2 2 k = amp1_12_2 k := by decide +kernel +noncomputable def amp1_12_3 : Fin 16 → CBox := ![⟨⟨40333602637358103890149930737,40333602637358103892887083561⟩,⟨5015711493090873599644737549,5015711493090873601851223766⟩⟩,⟨⟨41063624160825241727112916460,41063624160825241729903872069⟩,⟨5106493796332646934924059676,5106493796332646937171012316⟩⟩,⟨⟨41783440652515466063531845082,41783440652515466066376630035⟩,⟨5196007046184098692623303064,5196007046184098694910253276⟩⟩,⟨⟨42500882253193745495141316966,42500882253193745498003997917⟩,⟨5285224964912998623933690308,5285224964912998626256059699⟩⟩,⟨⟨43208105797029466859195593363,43208105797029466862113873174⟩,⟨5373172210511033612281361706,5373172210511033614643366083⟩⟩,⟨⟨43912543273515121377539251861,43912543273515121380509709645⟩,⟨5460772992884498814661529104,5460772992884498817062614159⟩⟩,⟨⟨44606740326628404393052628872,44606740326628404396074275150⟩,⟨5547100320722679179809807259,5547100320722679182249376152⟩⟩,⟨⟨45297756499006132964065047652,45297756499006132967136032892⟩,⟨5633032088059931358870273551,5633032088059931361347949114⟩⟩,⟨⟨45978502120047616446226377244,45978502120047616449348198519⟩,⟨5717686654279278178553441103,5717686654279278181068934320⟩⟩,⟨⟨46655687189838484689021249176,46655687189838484692184833787⟩,⟨5801898445822878361183570394,5801898445822878363735588288⟩⟩,⟨⟨47322565195896356611684875447,47322565195896356614898092235⟩,⟨5884828495725633242064900503,5884828495725633244653944735⟩⟩,⟨⟨47985517083355406598732397002,47985517083355406601991304745⟩,⟨5967270310586346292449380843,5967270310586346295074779650⟩⟩,⟨⟨48638120217913569079672396964,48638120217913569082977965449⟩,⟨6048425199522518650544607981,6048425199522518653206003159⟩⟩,⟨⟨49286444880026379420134859884,49286444880026379423486366677⟩,⟨6129048036223983145401300106,6129048036223983148098403865⟩⟩,⟨⟨49924374988729221665301701043,49924374988729221668699296501⟩,⟨6208378251448693316819415843,6208378251448693319551765958⟩⟩,⟨⟨50557686720482431272013967672,50557686720482431275456794218⟩,⟨6287134145392114252713856208,6287134145392114255481132357⟩⟩] +lemma amp1_12_3_eq : ∀ k : Fin 16, amp1_1Expr 2 3 k = amp1_12_3 k := by decide +kernel +noncomputable def amp1_12_4 : Fin 16 → CBox := ![⟨⟨51180554932150761402215979344,51180554932150761405648979782⟩,⟨6364591328575947896134812768,6364591328575947898929685089⟩⟩,⟨⟨51798476653068572740502205991,51798476653068572743988336558⟩,⟨6441433387672530654206198911,6441433387672530657036267511⟩⟩,⟨⟨52405903563925214426419323207,52405903563925214429955804230⟩,⟨6516970357811033116452571102,6516970357811033119317004750⟩⟩,⟨⟨53008067091420818535566378868,53008067091420818539150629381⟩,⟨6591852796474778414557859498,6591852796474778417456093718⟩⟩,⟨⟨53599682950878333016624127914,53599682950878333020254826885⟩,⟨6665423572992208218316424736,6665423572992208221247807244⟩⟩,⟨⟨54185729261629598881784730695,54185729261629598885463287177⟩,⟨6738301744643456636530611031,6738301744643456639495059364⟩⟩,⟨⟨54761174158297399575847651850,54761174158297399579567997907⟩,⟨6809861570523821676964724167,6809861570523821679960993250⟩⟩,⟨⟨55330753638593851791994388578,55330753638593851795759754717⟩,⟨6880691998721315537087326861,6880691998721315540115547053⟩⟩,⟨⟨55889677685399926701593492822,55889677685399926705404270779⟩,⟨6950197363529305752841988102,6950197363529305755901715124⟩⟩,⟨⟨56442450371203974288940649360,56442450371203974292780075113⟩,⟨7018937771823159983434006368,7018937771823159986522870916⟩⟩,⟨⟨56984513888713790570931080578,56984513888713790574815731726⟩,⟨7086346434500889438366441558,7086346434500889441486009671⟩⟩,⟨⟨57520149696019410856680142533,57520149696019410860606463784⟩,⟨7152955775078996128971428619,7152955775078996132120960787⟩⟩,⟨⟨58045023393183337445651201745,58045023393183337449620298333⟩,⟨7218226786422966777324257544,7218226786422966780503393282⟩⟩,⟨⟨58563202339129627987001719976,58563202339129627991006821640⟩,⟨7282665267607715311054887747,7282665267607715314262475389⟩⟩,⟨⟨59070567490809294430090483426,59070567490809294434137463528⟩,⟨7345758992345223271901257214,7345758992345223275137526826⟩⟩,⟨⟨59570979905906762495755014062,59570979905906762499839448532⟩,⟨7407988104985039133890010119,7407988104985039137154089864⟩⟩] +lemma amp1_12_4_eq : ∀ k : Fin 16, amp1_1Expr 2 4 k = amp1_12_4 k := by decide +kernel +noncomputable def amp1_12_5 : Fin 16 → CBox := ![⟨⟨60060528526626865101425235130,60060528526626865105548275070⟩,⟨7468866243381194001591385444,7468866243381194004882915833⟩⟩,⟨⟨60542875258375211987233032033,60542875258375211991393919028⟩,⟨7528848786171561306334202216,7528848786171561309652755730⟩⟩,⟨⟨61014310271825440936801952439,61014310271825440941001703489⟩,⟨7587474395107808978225562011,7587474395107808981570760269⟩⟩,⟨⟨61478302879938500945667101756,61478302879938500949904557035⟩,⟨7645174498868595234834425199,7645174498868595238205779632⟩⟩,⟨⟨61931338283814348955559543583,61931338283814348959834660233⟩,⟨7701512012341604310523042448,7701512012341604313920040774⟩⟩,⟨⟨62376699227217381557978364141,62376699227217381562181783979⟩,⟨7756895163271230795236836592,7756895163271230798645524429⟩⟩,⟨⟨62811060253041564512330279260,62811060253041564516576112605⟩,⟨7810910412267589699903124116,7810910412267589703337182797⟩⟩,⟨⟨63237523068765669824592660295,63237523068765669828877426429⟩,⟨7863943474189563307739048344,7863943474189563311197679598⟩⟩,⟨⟨63652946336376028675929817283,63652946336376028680250962148⟩,⟨7915603705897224210836407060,7915603705897224214318782510⟩⟩,⟨⟨64060255810442041621855742466,64060255810442041626212286817⟩,⟨7966254941510515698203802020,7966254941510515701709424492⟩⟩,⟨⟨64456489476868880860908414000,64456489476868880865296974472⟩,⟨8015528837832533153115654934,8015528837832533156643591247⟩⟩,⟨⟨64844401807227121641717821568,64844401807227121646137194590⟩,⟨8063767928974056204243793980,8063767928974056207793509461⟩⟩,⟨⟨65221205709714364220253385587,65221205709714364224706547758⟩,⟨8110625624314076258972391928,8110625624314076262543742783⟩⟩,⟨⟨65589488661285843477461236103,65589488661285843481941997989⟩,⟨8156423691238937793080396236,8156423691238937796672218536⟩⟩,⟨⟨65946634454237240523272315862,65946634454237240527783340928⟩,⟨8200836789531233322783397053,8200836789531233326395506735⟩⟩,⟨⟨66295067506085358050734324888,66295067506085358055275954723⟩,⟨8244166409214366187907610351,8244166409214366191539646784⟩⟩] +lemma amp1_12_5_eq : ∀ k : Fin 16, amp1_1Expr 2 5 k = amp1_12_5 k := by decide +kernel +noncomputable def amp1_12_6 : Fin 16 → CBox := ![⟨⟨66632338791740151042558307977,66632338791740151047118254364⟩,⟨8286108000174094193533866375,8286108000174094197183785030⟩⟩,⟨⟨66960713276388809128259605551,66960713276388809132851072278⟩,⟨8326943223635252123385921312,8326943223635252127054952528⟩⟩,⟨⟨67277905729051392370411753370,67277905729051392375026822333⟩,⟨8366387898207114528459464900,8366387898207114532146106660⟩⟩,⟨⟨67586024963955147023786943381,67586024963955147028431930556⟩,⟨8404704266859928645960502223,8404704266859928649665120166⟩⟩,⟨⟨67882946447620971188540712907,67882946447620971193210922016⟩,⟨8441628131845618339207589255,8441628131845618342929081288⟩⟩,⟨⟨68170625858784866938129690866,68170625858784866942826514125⟩,⟨8477402692870422434295150031,8477402692870422438033261683⟩⟩,⟨⟨68447096538020503799655080526,68447096538020503804340668326⟩,⟨8511783384717186122335233160,8511783384717186126084739026⟩⟩,⟨⟨68714163775761176698883790178,68714163775761176703597855508⟩,⟨8544994705456564206180016324,8544994705456564209945419873⟩⟩,⟨⟨68970016219710489344180711947,68970016219710489348918844775⟩,⟨8576811403190957624278071695,8576811403190957628058305641⟩⟩,⟨⟨69216311266545650364784517683,69216311266545650369543953627⟩,⟨8607439584566411086578961051,8607439584566411090373239437⟩⟩,⟨⟨69451390545946672984853308630,69451390545946672989635525040⟩,⟨8636673021858896435366381745,8636673021858896439174369372⟩⟩,⟨⟨69676765816596932305506094633,69676765816596932310306115277⟩,⟨8664699710806636203168250948,8664699710806636206988880019⟩⟩,⟨⟨69890929593705596296315102586,69890929593705596301134355716⟩,⟨8691332187154105826515872123,8691332187154105830348801530⟩⟩,⟨⟨70095250027190538212436462281,70095250027190538217276758249⟩,⟨8716740588077719896710835063,8716740588077719900555834514⟩⟩,⟨⟨70288368638517981038771264332,70288368638517981043613902876⟩,⟨8740755979092348351477990539,8740755979092348355332216278⟩⟩,⟨⟨70471511782327267738867330555,70471511782327267743727700299⟩,⟨8763530864329954363139824086,8763530864329954367004728243⟩⟩] +lemma amp1_12_6_eq : ∀ k : Fin 16, amp1_1Expr 2 6 k = amp1_12_6 k := by decide +kernel +noncomputable def amp1_12_7 : Fin 16 → CBox := ![⟨⟨70643468314107287777699936940,70643468314107287782575274462⟩,⟨8784914631124003045121767259,8784914631124003048996488618⟩⟩,⟨⟨70805324400427207192482386660,70805324400427207197374169324⟩,⟨8805042350427450411857524820,8805042350427450415741779785⟩⟩,⟨⟨70956014756739613932525996152,70956014756739613937423738013⟩,⟨8823781548084791253182129396,8823781548084791257074097378⟩⟩,⟨⟨71096486770715766118250524206,71096486770715766123161364781⟩,⟨8841250037108512102647305549,8841250037108512106547401618⟩⟩,⟨⟨71225819734200030788248577417,71225819734200030793165838381⟩,⟨8857333322234713240585529274,8857333322234713244492407573⟩⟩,⟨⟨71344823474217662614485229667,71344823474217662619414769216⟩,⟨8872132110031922796563747463,8872132110031922800477658593⟩⟩,⟨⟨71452720759319491781295338983,71452720759319491786231713810⟩,⟨8885549747375761002380991125,8885549747375761006300744321⟩⟩,⟨⟨71550184889284250857745044232,71550184889284250862687644827⟩,⟨8897669962899864877751908572,8897669962899864881676945328⟩⟩,⟨⟨71636581187985562583418915818,71636581187985562588367358748⟩,⟨8908413831040106602579431139,8908413831040106606509191700⟩⟩,⟨⟨71712447281589071094897513940,71712447281589071099852024215⟩,⟨8917848208649375138197355439,8917848208649375142131380589⟩⟩,⟨⟨71777290301579416079945247411,71777290301579416084902753815⟩,⟨8925911804741608514559211267,8925911804741608518496609080⟩⟩,⟨⟨71831512878535996574281965479,71831512878535996579242385897⟩,⟨8932654688705418476542005186,8932654688705418480482274077⟩⟩,⟨⟨71874763373790792274934173292,71874763373790792279894624616⟩,⟨8938033132284629589047958440,8938033132284629592990232235⟩⟩,⟨⟨71907309928033851782003765930,71907309928033851786962871215⟩,⟨8942080480289843927634553770,8942080480289843931578166002⟩⟩,⟨⟨71928941721771935359038592999,71928941721771935363993798602⟩,⟨8944770516125318300803540347,8944770516125318304747668465⟩⟩,⟨⟨71939792741600879310115528308,71939792741600879315063619033⟩,⟨8946119901781668786370214401,8946119901781668790313959786⟩⟩] +lemma amp1_12_7_eq : ∀ k : Fin 16, amp1_1Expr 2 7 k = amp1_12_7 k := by decide +kernel +noncomputable def amp1_12_8 : Fin 16 → CBox := ![⟨⟨71939792741600879310115528308,71939792741600879315063619033⟩,⟨8946119901781668786370214401,8946119901781668790313959786⟩⟩,⟨⟨71928941721771935359038592999,71928941721771935363993798602⟩,⟨8944770516125318300803540347,8944770516125318304747668465⟩⟩,⟨⟨71907309928033851782003765930,71907309928033851786962871215⟩,⟨8942080480289843927634553770,8942080480289843931578166002⟩⟩,⟨⟨71874763373790792274934173292,71874763373790792279894624616⟩,⟨8938033132284629589047958440,8938033132284629592990232235⟩⟩,⟨⟨71831512878535996574281965479,71831512878535996579242385897⟩,⟨8932654688705418476542005186,8932654688705418480482274077⟩⟩,⟨⟨71777290301579416079945247411,71777290301579416084902753815⟩,⟨8925911804741608514559211267,8925911804741608518496609080⟩⟩,⟨⟨71712447281589071094897513940,71712447281589071099852024215⟩,⟨8917848208649375138197355439,8917848208649375142131380589⟩⟩,⟨⟨71636581187985562583418915818,71636581187985562588367358748⟩,⟨8908413831040106602579431139,8908413831040106606509191700⟩⟩,⟨⟨71550184889284250857745044232,71550184889284250862687644827⟩,⟨8897669962899864877751908572,8897669962899864881676945328⟩⟩,⟨⟨71452720759319491781295338983,71452720759319491786231713810⟩,⟨8885549747375761002380991125,8885549747375761006300744321⟩⟩,⟨⟨71344823474217662614485229667,71344823474217662619414769216⟩,⟨8872132110031922796563747463,8872132110031922800477658593⟩⟩,⟨⟨71225819734200030788248577417,71225819734200030793165838381⟩,⟨8857333322234713240585529274,8857333322234713244492407573⟩⟩,⟨⟨71096486770715766118250524206,71096486770715766123161364781⟩,⟨8841250037108512102647305549,8841250037108512106547401618⟩⟩,⟨⟨70956014756739613932525996152,70956014756739613937423738013⟩,⟨8823781548084791253182129396,8823781548084791257074097378⟩⟩,⟨⟨70805324400427207192482386660,70805324400427207197374169324⟩,⟨8805042350427450411857524820,8805042350427450415741779785⟩⟩,⟨⟨70643468314107287777699936940,70643468314107287782575274462⟩,⟨8784914631124003045121767259,8784914631124003048996488618⟩⟩] +lemma amp1_12_8_eq : ∀ k : Fin 16, amp1_1Expr 2 8 k = amp1_12_8 k := by decide +kernel +noncomputable def amp1_12_9 : Fin 16 → CBox := ![⟨⟨70471511782327267738867330555,70471511782327267743727700299⟩,⟨8763530864329954363139824086,8763530864329954367004728243⟩⟩,⟨⟨70288368638517981038771264332,70288368638517981043613902876⟩,⟨8740755979092348351477990539,8740755979092348355332216278⟩⟩,⟨⟨70095250027190538212436462281,70095250027190538217276758249⟩,⟨8716740588077719896710835063,8716740588077719900555834514⟩⟩,⟨⟨69890929593705596296315102586,69890929593705596301134355716⟩,⟨8691332187154105826515872123,8691332187154105830348801530⟩⟩,⟨⟨69676765816596932305506094633,69676765816596932310306115277⟩,⟨8664699710806636203168250948,8664699710806636206988880019⟩⟩,⟨⟨69451390545946672984853308630,69451390545946672989635525040⟩,⟨8636673021858896435366381745,8636673021858896439174369372⟩⟩,⟨⟨69216311266545650364784517683,69216311266545650369543953627⟩,⟨8607439584566411086578961051,8607439584566411090373239437⟩⟩,⟨⟨68970016219710489344180711947,68970016219710489348918844775⟩,⟨8576811403190957624278071695,8576811403190957628058305641⟩⟩,⟨⟨68714163775761176698883790178,68714163775761176703597855508⟩,⟨8544994705456564206180016324,8544994705456564209945419873⟩⟩,⟨⟨68447096538020503799655080526,68447096538020503804340668326⟩,⟨8511783384717186122335233160,8511783384717186126084739026⟩⟩,⟨⟨68170625858784866938129690866,68170625858784866942826514125⟩,⟨8477402692870422434295150031,8477402692870422438033261683⟩⟩,⟨⟨67882946447620971188540712907,67882946447620971193210922016⟩,⟨8441628131845618339207589255,8441628131845618342929081288⟩⟩,⟨⟨67586024963955147023786943381,67586024963955147028431930556⟩,⟨8404704266859928645960502223,8404704266859928649665120166⟩⟩,⟨⟨67277905729051392370411753370,67277905729051392375026822333⟩,⟨8366387898207114528459464900,8366387898207114532146106660⟩⟩,⟨⟨66960713276388809128259605551,66960713276388809132851072278⟩,⟨8326943223635252123385921312,8326943223635252127054952528⟩⟩,⟨⟨66632338791740151042558307977,66632338791740151047118254364⟩,⟨8286108000174094193533866375,8286108000174094197183785030⟩⟩] +lemma amp1_12_9_eq : ∀ k : Fin 16, amp1_1Expr 2 9 k = amp1_12_9 k := by decide +kernel +noncomputable def amp1_12_10 : Fin 16 → CBox := ![⟨⟨66295067506085358050734324888,66295067506085358055275954723⟩,⟨8244166409214366187907610351,8244166409214366191539646784⟩⟩,⟨⟨65946634454237240523272315862,65946634454237240527783340928⟩,⟨8200836789531233322783397053,8200836789531233326395506735⟩⟩,⟨⟨65589488661285843477461236103,65589488661285843481941997989⟩,⟨8156423691238937793080396236,8156423691238937796672218536⟩⟩,⟨⟨65221205709714364220253385587,65221205709714364224706547758⟩,⟨8110625624314076258972391928,8110625624314076262543742783⟩⟩,⟨⟨64844401807227121641717821568,64844401807227121646137194590⟩,⟨8063767928974056204243793980,8063767928974056207793509461⟩⟩,⟨⟨64456489476868880860908414000,64456489476868880865296974472⟩,⟨8015528837832533153115654934,8015528837832533156643591247⟩⟩,⟨⟨64060255810442041621855742466,64060255810442041626212286817⟩,⟨7966254941510515698203802020,7966254941510515701709424492⟩⟩,⟨⟨63652946336376028675929817283,63652946336376028680250962148⟩,⟨7915603705897224210836407060,7915603705897224214318782510⟩⟩,⟨⟨63237523068765669824592660295,63237523068765669828877426429⟩,⟨7863943474189563307739048344,7863943474189563311197679598⟩⟩,⟨⟨62811060253041564512330279260,62811060253041564516576112605⟩,⟨7810910412267589699903124116,7810910412267589703337182797⟩⟩,⟨⟨62376699227217381557978364141,62376699227217381562181783979⟩,⟨7756895163271230795236836592,7756895163271230798645524429⟩⟩,⟨⟨61931338283814348955559543583,61931338283814348959834660233⟩,⟨7701512012341604310523042448,7701512012341604313920040774⟩⟩,⟨⟨61478302879938500945667101756,61478302879938500949904557035⟩,⟨7645174498868595234834425199,7645174498868595238205779632⟩⟩,⟨⟨61014310271825440936801952439,61014310271825440941001703489⟩,⟨7587474395107808978225562011,7587474395107808981570760269⟩⟩,⟨⟨60542875258375211987233032033,60542875258375211991393919028⟩,⟨7528848786171561306334202216,7528848786171561309652755730⟩⟩,⟨⟨60060528526626865101425235130,60060528526626865105548275070⟩,⟨7468866243381194001591385444,7468866243381194004882915833⟩⟩] +lemma amp1_12_10_eq : ∀ k : Fin 16, amp1_1Expr 2 10 k = amp1_12_10 k := by decide +kernel +noncomputable def amp1_12_11 : Fin 16 → CBox := ![⟨⟨59570979905906762495755014062,59570979905906762499839448532⟩,⟨7407988104985039133890010119,7407988104985039137154089864⟩⟩,⟨⟨59070567490809294430090483426,59070567490809294434137463528⟩,⟨7345758992345223271901257214,7345758992345223275137526826⟩⟩,⟨⟨58563202339129627987001719976,58563202339129627991006821640⟩,⟨7282665267607715311054887747,7282665267607715314262475389⟩⟩,⟨⟨58045023393183337445651201745,58045023393183337449620298333⟩,⟨7218226786422966777324257544,7218226786422966780503393282⟩⟩,⟨⟨57520149696019410856680142533,57520149696019410860606463784⟩,⟨7152955775078996128971428619,7152955775078996132120960787⟩⟩,⟨⟨56984513888713790570931080578,56984513888713790574815731726⟩,⟨7086346434500889438366441558,7086346434500889441486009671⟩⟩,⟨⟨56442450371203974288940649360,56442450371203974292780075113⟩,⟨7018937771823159983434006368,7018937771823159986522870916⟩⟩,⟨⟨55889677685399926701593492822,55889677685399926705404270779⟩,⟨6950197363529305752841988102,6950197363529305755901715124⟩⟩,⟨⟨55330753638593851791994388578,55330753638593851795759754717⟩,⟨6880691998721315537087326861,6880691998721315540115547053⟩⟩,⟨⟨54761174158297399575847651850,54761174158297399579567997907⟩,⟨6809861570523821676964724167,6809861570523821679960993250⟩⟩,⟨⟨54185729261629598881784730695,54185729261629598885463287177⟩,⟨6738301744643456636530611031,6738301744643456639495059364⟩⟩,⟨⟨53599682950878333016624127914,53599682950878333020254826885⟩,⟨6665423572992208218316424736,6665423572992208221247807244⟩⟩,⟨⟨53008067091420818535566378868,53008067091420818539150629381⟩,⟨6591852796474778414557859498,6591852796474778417456093718⟩⟩,⟨⟨52405903563925214426419323207,52405903563925214429955804230⟩,⟨6516970357811033116452571102,6516970357811033119317004750⟩⟩,⟨⟨51798476653068572740502205991,51798476653068572743988336558⟩,⟨6441433387672530654206198911,6441433387672530657036267511⟩⟩,⟨⟨51180554932150761402215979344,51180554932150761405648979782⟩,⟨6364591328575947896134812768,6364591328575947898929685089⟩⟩] +lemma amp1_12_11_eq : ∀ k : Fin 16, amp1_1Expr 2 11 k = amp1_12_11 k := by decide +kernel +noncomputable def amp1_12_12 : Fin 16 → CBox := ![⟨⟨50557686720482431272013967672,50557686720482431275456794218⟩,⟨6287134145392114252713856208,6287134145392114255481132357⟩⟩,⟨⟨49924374988729221665301701043,49924374988729221668699296501⟩,⟨6208378251448693316819415843,6208378251448693319551765958⟩⟩,⟨⟨49286444880026379420134859884,49286444880026379423486366677⟩,⟨6129048036223983145401300106,6129048036223983148098403865⟩⟩,⟨⟨48638120217913569079672396964,48638120217913569082977965449⟩,⟨6048425199522518650544607981,6048425199522518653206003159⟩⟩,⟨⟨47985517083355406598732397002,47985517083355406601991304745⟩,⟨5967270310586346292449380843,5967270310586346295074779650⟩⟩,⟨⟨47322565195896356611684875447,47322565195896356614898092235⟩,⟨5884828495725633242064900503,5884828495725633244653944735⟩⟩,⟨⟨46655687189838484689021249176,46655687189838484692184833787⟩,⟨5801898445822878361183570394,5801898445822878363735588288⟩⟩,⟨⟨45978502120047616446226377244,45978502120047616449348198519⟩,⟨5717686654279278178553441103,5717686654279278181068934320⟩⟩,⟨⟨45297756499006132964065047652,45297756499006132967136032892⟩,⟨5633032088059931358870273551,5633032088059931361347949114⟩⟩,⟨⟨44606740326628404393052628872,44606740326628404396074275150⟩,⟨5547100320722679179809807259,5547100320722679182249376152⟩⟩,⟨⟨43912543273515121377539251861,43912543273515121380509709645⟩,⟨5460772992884498814661529104,5460772992884498817062614159⟩⟩,⟨⟨43208105797029466859195593363,43208105797029466862113873174⟩,⟨5373172210511033612281361706,5373172210511033614643366083⟩⟩,⟨⟨42500882253193745495141316966,42500882253193745498003997917⟩,⟨5285224964912998623933690308,5285224964912998626256059699⟩⟩,⟨⟨41783440652515466063531845082,41783440652515466066376630035⟩,⟨5196007046184098692623303064,5196007046184098694910253276⟩⟩,⟨⟨41063624160825241727112916460,41063624160825241729903872069⟩,⟨5106493796332646934924059676,5106493796332646937171012316⟩⟩,⟨⟨40333602637358103890149930737,40333602637358103892887083561⟩,⟨5015711493090873599644737549,5015711493090873601851223766⟩⟩] +lemma amp1_12_12_eq : ∀ k : Fin 16, amp1_1Expr 2 12 k = amp1_12_12 k := by decide +kernel +noncomputable def amp1_12_13 : Fin 16 → CBox := ![⟨⟨39601635200454137554238963201,39601635200454137556923014979⟩,⟨4924687204513016734091414283,4924687204513016736257431310⟩⟩,⟨⟨38859464590104374373499645062,38859464590104374376134621284⟩,⟨4832394093638817759710881324,4832394093638817761836457686⟩⟩,⟨⟨38115796549175229430478432228,38115796549175229433056815198⟩,⟨4739914768807124340476345013,4739914768807124342560476561⟩⟩,⟨⟨37361913902531192332050880737,37361913902531192334574819798⟩,⟨4646165200011800397516704268,4646165200011800399559185688⟩⟩,⟨⟨36607003843609385792843718367,36607003843609385795309772763⟩,⟨4552287866691792566865170089,4552287866691792568865525969⟩⟩,⟨⟨35841851965557722417683921654,35841851965557722420115871507⟩,⟨4457136905266166405670150572,4457136905266166407630864248⟩⟩,⟨⟨35076166662618009662426815055,35076166662618009664803666189⟩,⟨4361919609440269938322798139,4361919609440269940241234187⟩⟩,⟨⟨34300193600980150022968039647,34300193600980150025289010135⟩,⟨4265422972663742713820788749,4265422972663742715696373950⟩⟩,⟨⟨33524208008310895721950383079,33524208008310895724216019903⟩,⟨4168924777582623866470915298,4168924777582623868303717093⟩⟩,⟨⟨32737866477294929150160350546,32737866477294929152372504735⟩,⟨4071138763026156820422803509,4071138763026156822212572948⟩⟩,⟨⟨31952063788142973130138704585,31952063788142973132294918113⟩,⟨3973419756501542920591348935,3973419756501542922337805279⟩⟩,⟨⟨31155810506980960745912195611,31155810506980960748027452075⟩,⟨3874401159783468515573765018,3874401159783468517278288046⟩⟩,⟨⟨30360682302007587722349635059,30360682302007587724405663561⟩,⟨3775522472649487016758904087,3775522472649487018419273765⟩⟩,⟨⟨29554977221247464421556703446,29554977221247464423554772750⟩,⟨3675328491220533190317565578,3675328491220533191933450325⟩⟩,⟨⟨28751023739938367695380695540,28751023739938367697322063507⟩,⟨3575352331085074933364232153,3575352331085074934935869432⟩⟩,⟨⟨27936329116135969236090321551,27936329116135969237972465381⟩,⟨3474040449161087916739998075,3474040449161087918266577203⟩⟩] +lemma amp1_12_13_eq : ∀ k : Fin 16, amp1_1Expr 2 13 k = amp1_12_13 k := by decide +kernel +noncomputable def amp1_12_14 : Fin 16 → CBox := ![⟨⟨27124059698702532520452590029,27124059698702532522287823982⟩,⟨3373030155358729585051750050,3373030155358729586534914582⟩⟩,⟨⟨26300838960499855272500142033,26300838960499855274277018858⟩,⟨3270658002911095463692345435,3270658002911095465130165159⟩⟩,⟨⟨25480772729857277562296589251,25480772729857277564016915887⟩,⟨3168678131310934620916644401,3168678131310934622309489968⟩⟩,⟨⟨24649489050903922244000816323,24649489050903922245659795880⟩,⟨3065303306601293613544979905,3065303306601293614891735799⟩⟩,⟨⟨23822155938916705060761531989,23822155938916705062371008026⟩,⟨2962419757226376389886997045,2962419757226376391189318860⟩⟩,⟨⟨22983270389303945547980982288,22983270389303945549531239335⟩,⟨2858099596926999394711750067,2858099596926999395967895135⟩⟩,⟨⟨22149212667309377171108243135,22149212667309377172606185356⟩,⟨2754379804283567773011635375,2754379804283567774222685637⟩⟩,⟨⟨21303181743484879754968313407,21303181743484879756405842028⟩,⟨2649171076308288359446690588,2649171076308288360611084953⟩⟩,⟨⟨20462956309978198964362459082,20462956309978198965740852490⟩,⟨2544684293872362529950093327,2544684293872362531068259372⟩⟩,⟨⟨19610228521757425345957811675,19610228521757425347281416680⟩,⟨2438642772952151337419294047,2438642772952151338491193877⟩⟩,⟨⟨18764410360201072197988474239,18764410360201072199251640673⟩,⟨2333460503167656965711195335,2333460503167656966736446007⟩⟩,⟨⟨17905421340180017040267047002,17905421340180017041474123625⟩,⟨2226640362678449215771231506,2226640362678449216749764440⟩⟩,⟨⟨17054608847284225417280799295,17054608847284225418432346603⟩,⟨2120837019559029801339430947,2120837019559029802271694145⟩⟩,⟨⟨16189774056173590091522935669,16189774056173590092613142628⟩,⟨2013289924388793187413746005,2013289924388793188298368066⟩⟩,⟨⟨15334597482021724182501494634,15334597482021724183534833168⟩,⟨1906943883095107532814097477,1906943883095107533652081365⟩⟩,⟨⟨14464300825782799816828646082,14464300825782799817803782239⟩,⟨1798717574120342149707766680,1798717574120342150498246951⟩⟩] +lemma amp1_12_14_eq : ∀ k : Fin 16, amp1_1Expr 2 14 k = amp1_12_14 k := by decide +kernel +noncomputable def amp1_12_15 : Fin 16 → CBox := ![⟨⟨13605436144528543517635090496,13605436144528543518551964247⟩,⟨1691912895859670665980452306,1691912895859670666723950418⟩⟩,⟨⟨12730011261233991575561351260,12730011261233991576418467540⟩,⟨1583048862860762033012606897,1583048862860762033708170742⟩⟩,⟨⟨11868204086295200168019668818,11868204086295200168817649033⟩,⟨1475878268876554359719081015,1475878268876554360367417915⟩⟩,⟨⟨10987901608861133639591349894,10987901608861133640330833371⟩,⟨1366407679473444525949165774,1366407679473444526549499516⟩⟩,⟨⟨10124011078824646541887004098,10124011078824646542568402353⟩,⟨1258978008505669232834968637,1258978008505669233388109724⟩⟩,⟨⟨9238936788997680557722176709,9238936788997680558343661072⟩,⟨1148914017256532114220244409,1148914017256532114724985330⟩⟩,⟨⟨8374023000594305591574767669,8374023000594305592137079139⟩,⟨1041357098326373040963264617,1041357098326373041420630281⟩⟩,⟨⟨7484008818589727932923343000,7484008818589727933426419335⟩,⟨930678803559827651851671493,930678803559827652260492845⟩⟩,⟨⟨6619527590048496233869823975,6619527590048496234314228017⟩,⟨823175675893779269490775900,823175675893779269852304261⟩⟩,⟨⟨5723823631345515038812797592,5723823631345515039196672391⟩,⟨711789825230581337962950776,711789825230581338275510648⟩⟩,⟨⟨4862135239681351864531422709,4862135239681351864856819938⟩,⟨604634002618053415604739073,604634002618053415870159384⟩⟩,⟨⟨3958514790998972547947403235,3958514790998972548211887856⟩,⟨492263691674140854289197787,492263691674140854505235665⟩⟩,⟨⟨3104583262309451838876923841,3104583262309451839083482569⟩,⟨386072478821917588742021454,386072478821917588911347261⟩⟩,⟨⟨2185759460592364486796860961,2185759460592364486941736049⟩,⟨271811544983855893858699856,271811544983855893977843938⟩⟩,⟨⟨1355876442797423833515075140,1355876442797423833603093890⟩,⟨168610900407176264268572200,168610900407176264342249863⟩⟩,⟨⟨385210003677661992959706116,385210003677661992983599170⟩,⟨47903041542588614251592822,47903041542588614272386485⟩⟩] +lemma amp1_12_15_eq : ∀ k : Fin 16, amp1_1Expr 2 15 k = amp1_12_15 k := by decide +kernel +noncomputable def amp1_12 : Fin 16 → Fin 16 → CBox := ![amp1_12_0,amp1_12_1,amp1_12_2,amp1_12_3,amp1_12_4,amp1_12_5,amp1_12_6,amp1_12_7,amp1_12_8,amp1_12_9,amp1_12_10,amp1_12_11,amp1_12_12,amp1_12_13,amp1_12_14,amp1_12_15] +lemma amp1_12_eq (i k : Fin 16) : amp1_1Expr 2 i k = amp1_12 i k := by + fin_cases i + · exact amp1_12_0_eq k + · exact amp1_12_1_eq k + · exact amp1_12_2_eq k + · exact amp1_12_3_eq k + · exact amp1_12_4_eq k + · exact amp1_12_5_eq k + · exact amp1_12_6_eq k + · exact amp1_12_7_eq k + · exact amp1_12_8_eq k + · exact amp1_12_9_eq k + · exact amp1_12_10_eq k + · exact amp1_12_11_eq k + · exact amp1_12_12_eq k + · exact amp1_12_13_eq k + · exact amp1_12_14_eq k + · exact amp1_12_15_eq k +noncomputable def amp1_13_0 : Fin 16 → CBox := ![⟨⟨(-27656833929615362284877102),(-27656833929615362266068417)⟩,⟨47903041542588614252482915,47903041542588614270523424⟩⟩,⟨⟨(-97347548738388396655197505),(-97347548738388396588712624)⟩,⟨168610900407176264271705180,168610900407176264335692192⟩⟩,⟨⟨(-156930468665277273085467316),(-156930468665277272978075253)⟩,⟨271811544983855893863750419,271811544983855893967272553⟩⟩,⟨⟨(-222899049574540212034962306),(-222899049574540211882369834)⟩,⟨386072478821917588749195113,386072478821917588896332001⟩⟩,⟨⟨(-284208574900344161602779856),(-284208574900344161408136287)⟩,⟨492263691674140854298344597,492263691674140854486090382⟩⟩,⟨⟨(-349085604172734028948496816),(-349085604172734028709382827)⟩,⟨604634002618053415615973849,604634002618053415846643757⟩⟩,⟨⟨(-410952047203312812511687385),(-410952047203312812230138490)⟩,⟨711789825230581337976176628,711789825230581338247827482⟩⟩,⟨⟨(-475260698067625593803559643),(-475260698067625593477919136)⟩,⟨823175675893779269506071425,823175675893779269820289038⟩⟩,⟨⟨(-537327657764345332332709531),(-537327657764345331964496208)⟩,⟨930678803559827651868964547,930678803559827652224296575⟩⟩,⟨⟨(-601227801041259061232903296),(-601227801041259060820943751)⟩,⟨1041357098326373040982614198,1041357098326373041380129474⟩⟩,⟨⟨(-663325817138793157406315633),(-663325817138793156951728137)⟩,⟨1148914017256532114241592518,1148914017256532114680301383⟩⟩,⟨⟨(-726871292114567087378059419),(-726871292114567086879896170)⟩,⟨1258978008505669232858361858,1258978008505669233339145132⟩⟩,⟨⟨(-788895841566765076712535220),(-788895841566765076171867516)⟩,⟨1366407679473444525974555158,1366407679473444526496356734⟩⟩,⟨⟨(-852098715826997532918801653),(-852098715826997532334871688)⟩,⟨1475878268876554359746504486,1475878268876554360310017566⟩⟩,⟨⟨(-913973687112991920699048032),(-913973687112991920072630612)⟩,⟨1583048862860762033042021717,1583048862860762033646602278⟩⟩,⟨⟨(-976826365869980122170167126),(-976826365869980121500613365)⟩,⟨1691912895859670666011889942,1691912895859670666658147978⟩⟩] +lemma amp1_13_0_eq : ∀ k : Fin 16, amp1_1Expr 3 0 k = amp1_13_0 k := by decide +kernel +noncomputable def amp1_13_1 : Fin 16 → CBox := ![⟨⟨(-1038490075614490174224136381),(-1038490075614490173512288460)⟩,⟨1798717574120342149741188866,1798717574120342150428290629⟩⟩,⟨⟨(-1100974564234470578987255880),(-1100974564234470578232610829)⟩,⟨1906943883095107532849530630,1906943883095107533577915868⟩⟩,⟨⟨(-1162373479802631049089449784),(-1162373479802631048292774312)⟩,⟨2013289924388793187451155186,2013289924388793188220066525⟩⟩,⟨⟨(-1224465824149729459110964607),(-1224465824149729458271509072)⟩,⟨2120837019559029801378838473,2120837019559029802189209846⟩⟩,⟨⟨(-1285551412780888597018186982),(-1285551412780888596136990820)⟩,⟨2226640362678449215812604977,2226640362678449216663165202⟩⟩,⟨⟨(-1347224049647206333883040699),(-1347224049647206332959700844)⟩,⟨2333460503167656965754553643,2333460503167656966645692284⟩⟩,⟨⟨(-1407951061421259999773118937),(-1407951061421259998807907605)⟩,⟨2438642772952151337464606760,2438642772952151338396349371⟩⟩,⟨⟨(-1469174162069821263826366401),(-1469174162069821262819382649)⟩,⟨2544684293872362529997376410,2544684293872362530969290663⟩⟩,⟨⟨(-1529499634035960902785223149),(-1529499634035960901736709667)⟩,⟨2649171076308288359495915152,2649171076308288360508052509⟩⟩,⟨⟨(-1590241921453586583067188723),(-1590241921453586581976796114)⟩,⟨2754379804283567773062814836,2754379804283567774115561381⟩⟩,⟨⟨(-1650124571656563995947320650),(-1650124571656563994816161678)⟩,⟨2858099596926999394764856757,2858099596926999395856736974⟩⟩,⟨⟨(-1710353844287314214829040033),(-1710353844287314213656404772)⟩,⟨2962419757226376389942042121,2962419757226376391074103445⟩⟩,⟨⟨(-1769753689214106827499622946),(-1769753689214106826286721561)⟩,⟨3065303306601293613601936672,3065303306601293614772519002⟩⟩,⟨⟨(-1829437172087648440199921529),(-1829437172087648438945728388)⟩,⟨3168678131310934620975521989,3168678131310934622186252683⟩⟩,⟨⟨(-1888315278407924774369989300),(-1888315278407924773075346567)⟩,⟨3270658002911095463753117923,3270658002911095465002961639⟩⟩,⟨⟨(-1947419868181087740456517763),(-1947419868181087739121155726)⟩,⟨3373030155358729585114424727,3373030155358729586403729571⟩⟩] +lemma amp1_13_1_eq : ∀ k : Fin 16, amp1_1Expr 3 1 k = amp1_13_1 k := by decide +kernel +noncomputable def amp1_13_2 : Fin 16 → CBox := ![⟨⟨(-2005738188498802510309237379),(-2005738188498802508934463868)⟩,⟨3474040449161087916804549636,3474040449161087918131463666⟩⟩,⟨⟨(-2064230630799723995006966770),(-2064230630799723993591790043)⟩,⟨3575352331085074933430666203,3575352331085074934796815639⟩⟩,⟨⟨(-2121951893766475951928576969),(-2121951893766475950473654782)⟩,⟨3675328491220533190385857297,3675328491220533191790508226⟩⟩,⟨⟨(-2179798915915662808373853810),(-2179798915915662806879018127)⟩,⟨3775522472649487016829057522,3775522472649487018272434888⟩⟩,⟨⟨(-2236886552549583812429900111),(-2236886552549583810895529175)⟩,⟨3874401159783468515645755729,3874401159783468517127603547⟩⟩,⟨⟨(-2294054966019543064463654703),(-2294054966019543062891010381)⟩,⟨3973419756501542920665179523,3973419756501542922183269715⟩⟩,⟨⟨(-2350473060741471696004038371),(-2350473060741471694392508623)⟩,⟨4071138763026156820498449825,4071138763026156822054236864⟩⟩,⟨⟨(-2406929842568628608530216703),(-2406929842568628606879954096)⟩,⟨4168924777582623866548378588,4168924777582623868141577883⟩⟩,⟨⟨(-2462643101475025595916499821),(-2462643101475025594227830990)⟩,⟨4265422972663742713900045083,4265422972663742715530481700⟩⟩,⟨⟨(-2518355460693847130421761374),(-2518355460693847128694647604)⟩,⟨4361919609440269938403847489,4361919609440269940071588957⟩⟩,⟨⟨(-2573329192070436685557851066),(-2573329192070436683792805003)⟩,⟨4457136905266166405752969166,4457136905266166407457515796⟩⟩,⟨⟨(-2628264625263173647051288001),(-2628264625263173645249840630)⟩,⟨4552287866691792566949756694,4552287866691792568688476874⟩⟩,⟨⟨(-2682464728926284392292223897),(-2682464728926284390453122350)⟩,⟨4646165200011800397603035219,4646165200011800399378485484⟩⟩,⟨⟨(-2736591067706676010388325050),(-2736591067706676008511861953)⟩,⟨4739914768807124340564417936,4739914768807124342376130218⟩⟩,⟨⟨(-2789984030792729048412197016),(-2789984030792729046498671314)⟩,⟨4832394093638817759800672617,4832394093638817761648514607⟩⟩,⟨⟨(-2843269483200295803168958774),(-2843269483200295801218976660)⟩,⟨4924687204513016734182920485,4924687204513016736065898736⟩⟩] +lemma amp1_13_2_eq : ∀ k : Fin 16, amp1_1Expr 3 2 k = amp1_13_2 k := by decide +kernel +noncomputable def amp1_13_3 : Fin 16 → CBox := ![⟨⟨(-2895822380713515642280256037),(-2895822380713515640293981248)⟩,⟨5015711493090873599737935085,5015711493090873601656151045⟩⟩,⟨⟨(-2948235567927807713127014723),(-2948235567927807711104483223)⟩,⟨5106493796332646935018944048,5106493796332646936972408859⟩⟩,⟨⟨(-2999916066825581613941703168),(-2999916066825581611883365887)⟩,⟨5196007046184098692719850693,5196007046184098694708168441⟩⟩,⟨⟨(-3051426056220250143431781758),(-3051426056220250141340323977)⟩,⟨5285224964912998624031895706,5285224964912998626050504971⟩⟩,⟨⟨(-3102202422140761773538125011),(-3102202422140761771411293201)⟩,⟨5373172210511033612381201261,5373172210511033614434390881⟩⟩,⟨⟨(-3152778757425303731952678344),(-3152778757425303729790841741)⟩,⟨5460772992884498814762996381,5460772992884498816850231958⟩⟩,⟨⟨(-3202619863391098239809519201),(-3202619863391098237613203254)⟩,⟨5547100320722679179912878593,5547100320722679182033636480⟩⟩,⟨⟨(-3252232592395201076216234615),(-3252232592395201073985713262)⟩,⟨5633032088059931358974941594,5633032088059931361128867355⟩⟩,⟨⟨(-3301107928990071962431248654),(-3301107928990071960166870154)⟩,⟨5717686654279278178659682123,5717686654279278180846560148⟩⟩,⟨⟨(-3349727629506710178480672619),(-3349727629506710176183246357)⟩,⟨5801898445822878361291376163,5801898445822878363509938922⟩⟩,⟨⟨(-3397607316141974806939687334),(-3397607316141974804609105717)⟩,⟨5884828495725633242174247205,5884828495725633244425070026⟩⟩,⟨⟨(-3445205120144288776308562062),(-3445205120144288773945282274)⟩,⟨5967270310586346292560259406,5967270310586346294842698587⟩⟩,⟨⟨(-3492059917117642068970180358),(-3492059917117642066574591985)⟩,⟨6048425199522518650656994493,6048425199522518652970765793⟩⟩,⟨⟨(-3538607533590063834842644382),(-3538607533590063832414989144)⟩,⟨6129048036223983145515184681,6129048036223983147860030888⟩⟩,⟨⟨(-3584408854704921200494820162),(-3584408854704921198035548511)⟩,⟨6208378251448693316934774462,6208378251448693319310307644⟩⟩,⟨⟨(-3629878591273424895238331758),(-3629878591273424892747710199)⟩,⟨6287134145392114252830678199,6287134145392114255236611043⟩⟩] +lemma amp1_13_3_eq : ∀ k : Fin 16, amp1_1Expr 3 3 k = amp1_13_3 k := by decide +kernel +noncomputable def amp1_13_4 : Fin 16 → CBox := ![⟨⟨(-3674598516835281403318304646),(-3674598516835281400800749528)⟩,⟨6364591328575947896253074001,6364591328575947898682151284⟩⟩,⟨⟨(-3718963300339778589900244283),(-3718963300339778587351455045)⟩,⟨6441433387672530654325887956,6441433387672530656785745139⟩⟩,⟨⟨(-3762574590383011709472007467),(-3762574590383011706892649376)⟩,⟨6516970357811033116573663708,6516970357811033119063544570⟩⟩,⟨⟨(-3805807986503100697585568225),(-3805807986503100694976060142)⟩,⟨6591852796474778414680343504,6591852796474778417199721185⟩⟩,⟨⟨(-3848284094129928592741433782),(-3848284094129928590102338594)⟩,⟨6665423572992208218440275769,6665423572992208220988573371⟩⟩,⟨⟨(-3890360326150824620223108097),(-3890360326150824617554571781)⟩,⟨6738301744643456636655816222,6738301744643456639232991090⟩⟩,⟨⟨(-3931675410886016124850320825),(-3931675410886016122153249463)⟩,⟨6809861570523821677091259019,6809861570523821679696141847⟩⟩,⟨⟨(-3972569377672655664239111044),(-3972569377672655661513532968)⟩,⟨6880691998721315537215177822,6880691998721315539847940889⟩⟩,⟨⟨(-4012698318754671956616977499),(-4012698318754671953863337406)⟩,⟨6950197363529305752971130551,6950197363529305755631405735⟩⟩,⟨⟨(-4052385611987333480193378115),(-4052385611987333477413152566)⟩,⟨7018937771823159983564426090,7018937771823159986249888051⟩⟩,⟨⟨(-4091304021530033260525369864),(-4091304021530033257717843848)⟩,⟨7086346434500889438498113808,7086346434500889441210405127⟩⟩,⟨⟨(-4129760942243346621009669603),(-4129760942243346618175383602)⟩,⟨7152955775078996129104338545,7152955775078996131842765650⟩⟩,⟨⟨(-4167445178213067191812595161),(-4167445178213067188951947378)⟩,⟨7218226786422966777458380280,7218226786422966780222659603⟩⟩,⟨⟨(-4204648752671252392738999414),(-4204648752671252389852773002)⟩,⟨7282665267607715311190207821,7282665267607715313979235547⟩⟩,⟨⟨(-4241075931632628764133608178),(-4241075931632628761221861300)⟩,⟨7345758992345223272037749640,7345758992345223274851833122⟩⟩,⟨⟨(-4277003926566657995243001262),(-4277003926566657992306360070)⟩,⟨7407988104985039134027658832,7407988104985039136865975924⟩⟩] +lemma amp1_13_4_eq : ∀ k : Fin 16, amp1_1Expr 3 4 k = amp1_13_4 k := by decide +kernel +noncomputable def amp1_13_5 : Fin 16 → CBox := ![⟨⟨(-4312151936157441300231675365),(-4312151936157441297270539282)⟩,⟨7468866243381194001730165341,7468866243381194004592434201⟩⟩,⟨⟨(-4346782873384138109787619540),(-4346782873384138106802362593)⟩,⟨7528848786171561306474096656,7528848786171561309359941237⟩⟩,⟨⟨(-4380630384484886432938798974),(-4380630384484886429929832340)⟩,⟨7587474395107808978366545781,7587474395107808981275665689⟩⟩,⟨⟨(-4413943554923445716150703561),(-4413943554923445713118440761)⟩,⟨7645174498868595234976481101,7645174498868595237908440961⟩⟩,⟨⟨(-4446470033492561674320813235),(-4446470033492561671265743559)⟩,⟨7701512012341604310666145164,7701512012341604313620511005⟩⟩,⟨⟨(-4478445510590351197686656694),(-4478445510590351194616972250)⟩,⟨7756895163271230795380968389,7756895163271230798343840681⟩⟩,⟨⟨(-4509631229138743674221021294),(-4509631229138743671129017440)⟩,⟨7810910412267589700048259577,7810910412267589703033398269⟩⟩,⟨⟨(-4540249881715345228645325799),(-4540249881715345225531602911)⟩,⟨7863943474189563307885169218,7863943474189563310891832490⟩⟩,⟨⟨(-4570075930398161691359191607),(-4570075930398161688224422926)⟩,⟨7915603705897224210983487839,7915603705897224214010926216⟩⟩,⟨⟨(-4599319434914282690859846631),(-4599319434914282687704462504)⟩,⟨7966254941510515698351823956,7966254941510515701399598254⟩⟩,⟨⟨(-4627767732219821179352842534),(-4627767732219821176177577350)⟩,⟨8015528837832533153264592434,8015528837832533156331848631⟩⟩,⟨⟨(-4655618584475842404544461943),(-4655618584475842401349771366)⟩,⟨8063767928974056204393627817,8063767928974056207479890715⟩⟩,⟨⟨(-4682671887494008455925365123),(-4682671887494008452711528365)⟩,⟨8110625624314076259123096433,8110625624314076262228301631⟩⟩,⟨⟨(-4709113413761441758899255930),(-4709113413761441755667095481)⟩,⟨8156423691238937793231951720,8156423691238937796354996191⟩⟩,⟨⟨(-4734755328016043891333682343),(-4734755328016043888083501172)⟩,⟨8200836789531233322935777782,8200836789531233326076557061⟩⟩,⟨⟨(-4759771695603984758048908711),(-4759771695603984754781068910)⟩,⟨8244166409214366188060796193,8244166409214366191219011919⟩⟩] +lemma amp1_13_5_eq : ∀ k : Fin 16, amp1_1Expr 3 5 k = amp1_13_5 k := by decide +kernel +noncomputable def amp1_13_6 : Fin 16 → CBox := ![⟨⟨(-4783986684434824896527962646),(-4783986684434824893243841760)⟩,⟨8286108000174094193687831539,8286108000174094196861518960⟩⟩,⟨⟨(-4807562911692542948861315105),(-4807562911692542945560359930)⟩,⟨8326943223635252123540645240,8326943223635252126731098280⟩⟩,⟨⟨(-4830336305174704894846107601),(-4830336305174704891529382821)⟩,⟨8366387898207114528614921754,8366387898207114531820718317⟩⟩,⟨⟨(-4852458270930776063904551988),(-4852458270930776060572006749)⟩,⟨8404704266859928646116671038,8404704266859928649338241610⟩⟩,⟨⟨(-4873776274319785405590308281),(-4873776274319785402242776647)⟩,⟨8441628131845618339364444157,8441628131845618342600766677⟩⟩,⟨⟨(-4894430726757596744057967752),(-4894430726757596740695759874)⟩,⟨8477402692870422434452669664,8477402692870422437703555715⟩⟩,⟨⟨(-4914280428450251331112264654),(-4914280428450251327738595385)⟩,⟨8511783384717186122493391625,8511783384717186125753695914⟩⟩,⟨⟨(-4933454993419274268809958089),(-4933454993419274265422393432)⟩,⟨8544994705456564206338791893,8544994705456564209613085094⟩⟩,⟨⟨(-4951824372420951264943661315),(-4951824372420951261543015539)⟩,⟨8576811403190957624437438454,8576811403190957627724733437⟩⟩,⟨⟨(-4969507561182858003719285147),(-4969507561182858000306180824)⟩,⟨8607439584566411086738896915,8607439584566411090038476032⟩⟩,⟨⟨(-4986385494073012464426160963),(-4986385494073012461000989710)⟩,⟨8636673021858896435526860799,8636673021858896438838469010⟩⟩,⟨⟨(-5002566710481483928636318872),(-5002566710481483925199868571)⟩,⟨8664699710806636203329250769,8664699710806636206651889634⟩⟩,⟨⟨(-5017942977869881856842633029),(-5017942977869881853395298632)⟩,⟨8691332187154105826677366806,8691332187154105830010775346⟩⟩,⟨⟨(-5032612524982808376180826997),(-5032612524982808372722915314)⟩,⟨8716740588077719896872801863,8716740588077719900216820138⟩⟩,⟨⟨(-5046477817449798234363940463),(-5046477817449798230897291180)⟩,⟨8740755979092348351640403571,8740755979092348354992267887⟩⟩,⟨⟨(-5059626903572492899145559661),(-5059626903572492895669510574)⟩,⟨8763530864329954363302660301,8763530864329954366663894084⟩⟩] +lemma amp1_13_6_eq : ∀ k : Fin 16, amp1_1Expr 3 6 k = amp1_13_6 k := by decide +kernel +noncomputable def amp1_13_7 : Fin 16 → CBox := ![⟨⟨(-5071972827087325086420589797),(-5071972827087325082935835704)⟩,⟨8784914631124003045285000808,8784914631124003048654822794⟩⟩,⟨⟨(-5083593571245343650400558962),(-5083593571245343646907441988)⟩,⟨8805042350427450412021132365,8805042350427450415399331147⟩⟩,⟨⟨(-5094412652057206989651909128),(-5094412652057206986151677595)⟩,⟨8823781548084791253346085137,8823781548084791256730919929⟩⟩,⟨⟨(-5104498088897388245063467369),(-5104498088897388241556062112)⟩,⟨8841250037108512102811585874,8841250037108512106203544778⟩⟩,⟨⟨(-5113783777894453976243189295),(-5113783777894453972729584076)⟩,⟨8857333322234713240750108444,8857333322234713244147925217⟩⟩,⟨⟨(-5122327862012853062291595963),(-5122327862012853058771828531)⟩,⟨8872132110031922796728601611,8872132110031922800132600678⟩⟩,⟨⟨(-5130074538545206825656258234),(-5130074538545206822131212236)⟩,⟨8885549747375761002546094588,8885549747375761005955164563⟩⟩,⟨⟨(-5137072148240684479224322581),(-5137072148240684475694504737)⟩,⟨8897669962899864877917237241,8897669962899864881330894186⟩⟩,⟨⟨(-5143275123403590882991919179),(-5143275123403590879457848141)⟩,⟨8908413831040106602744959442,8908413831040106606162722704⟩⟩,⟨⟨(-5148722063855938649994150848),(-5148722063855938646456277726)⟩,⟨8917848208649375138363059043,8917848208649375141784544668⟩⟩,⟨⟨(-5153377583230426004223674184),(-5153377583230426000682708617)⟩,⟨8925911804741608514725064702,8925911804741608518149459547⟩⟩,⟨⟨(-5157270589102046096568111381),(-5157270589102046093024530533)⟩,⟨8932654688705418476707983911,8932654688705418480134862298⟩⟩,⟨⟨(-5160375834950324846658346176),(-5160375834950324843112843920)⟩,⟨8938033132284629589214037102,8938033132284629592642611275⟩⟩,⟨⟨(-5162712572410639439904770159),(-5162712572410639436357920329)⟩,⟨8942080480289843927800707637,8942080480289843931230387631⟩⟩,⟨⟨(-5164265665324380309098847013),(-5164265665324380305551317282)⟩,⟨8944770516125318300969744197,8944770516125318304399785472⟩⟩,⟨⟨(-5165044733496314881785629083),(-5165044733496314878238128677)⟩,⟨8946119901781668786536443325,8946119901781668789966024312⟩⟩] +lemma amp1_13_7_eq : ∀ k : Fin 16, amp1_1Expr 3 7 k = amp1_13_7 k := by decide +kernel +noncomputable def amp1_13_8 : Fin 16 → CBox := ![⟨⟨(-5165044733496314881785629083),(-5165044733496314878238128677)⟩,⟨8946119901781668786536443325,8946119901781668789966024312⟩⟩,⟨⟨(-5164265665324380309098847013),(-5164265665324380305551317282)⟩,⟨8944770516125318300969744197,8944770516125318304399785472⟩⟩,⟨⟨(-5162712572410639439904770159),(-5162712572410639436357920329)⟩,⟨8942080480289843927800707637,8942080480289843931230387631⟩⟩,⟨⟨(-5160375834950324846658346176),(-5160375834950324843112843920)⟩,⟨8938033132284629589214037102,8938033132284629592642611275⟩⟩,⟨⟨(-5157270589102046096568111381),(-5157270589102046093024530533)⟩,⟨8932654688705418476707983911,8932654688705418480134862298⟩⟩,⟨⟨(-5153377583230426004223674184),(-5153377583230426000682708617)⟩,⟨8925911804741608514725064702,8925911804741608518149459547⟩⟩,⟨⟨(-5148722063855938649994150848),(-5148722063855938646456277726)⟩,⟨8917848208649375138363059043,8917848208649375141784544668⟩⟩,⟨⟨(-5143275123403590882991919179),(-5143275123403590879457848141)⟩,⟨8908413831040106602744959442,8908413831040106606162722704⟩⟩,⟨⟨(-5137072148240684479224322581),(-5137072148240684475694504737)⟩,⟨8897669962899864877917237241,8897669962899864881330894186⟩⟩,⟨⟨(-5130074538545206825656258234),(-5130074538545206822131212236)⟩,⟨8885549747375761002546094588,8885549747375761005955164563⟩⟩,⟨⟨(-5122327862012853062291595963),(-5122327862012853058771828531)⟩,⟨8872132110031922796728601611,8872132110031922800132600678⟩⟩,⟨⟨(-5113783777894453976243189295),(-5113783777894453972729584076)⟩,⟨8857333322234713240750108444,8857333322234713244147925217⟩⟩,⟨⟨(-5104498088897388245063467369),(-5104498088897388241556062112)⟩,⟨8841250037108512102811585874,8841250037108512106203544778⟩⟩,⟨⟨(-5094412652057206989651909128),(-5094412652057206986151677595)⟩,⟨8823781548084791253346085137,8823781548084791256730919929⟩⟩,⟨⟨(-5083593571245343650400558962),(-5083593571245343646907441988)⟩,⟨8805042350427450412021132365,8805042350427450415399331147⟩⟩,⟨⟨(-5071972827087325086420589797),(-5071972827087325082935835704)⟩,⟨8784914631124003045285000808,8784914631124003048654822794⟩⟩] +lemma amp1_13_8_eq : ∀ k : Fin 16, amp1_1Expr 3 8 k = amp1_13_8 k := by decide +kernel +noncomputable def amp1_13_9 : Fin 16 → CBox := ![⟨⟨(-5059626903572492899145559661),(-5059626903572492895669510574)⟩,⟨8763530864329954363302660301,8763530864329954366663894084⟩⟩,⟨⟨(-5046477817449798234363940463),(-5046477817449798230897291180)⟩,⟨8740755979092348351640403571,8740755979092348354992267887⟩⟩,⟨⟨(-5032612524982808376180826997),(-5032612524982808372722915314)⟩,⟨8716740588077719896872801863,8716740588077719900216820138⟩⟩,⟨⟨(-5017942977869881856842633029),(-5017942977869881853395298632)⟩,⟨8691332187154105826677366806,8691332187154105830010775346⟩⟩,⟨⟨(-5002566710481483928636318872),(-5002566710481483925199868571)⟩,⟨8664699710806636203329250769,8664699710806636206651889634⟩⟩,⟨⟨(-4986385494073012464426160963),(-4986385494073012461000989710)⟩,⟨8636673021858896435526860799,8636673021858896438838469010⟩⟩,⟨⟨(-4969507561182858003719285147),(-4969507561182858000306180824)⟩,⟨8607439584566411086738896915,8607439584566411090038476032⟩⟩,⟨⟨(-4951824372420951264943661315),(-4951824372420951261543015539)⟩,⟨8576811403190957624437438454,8576811403190957627724733437⟩⟩,⟨⟨(-4933454993419274268809958089),(-4933454993419274265422393432)⟩,⟨8544994705456564206338791893,8544994705456564209613085094⟩⟩,⟨⟨(-4914280428450251331112264654),(-4914280428450251327738595385)⟩,⟨8511783384717186122493391625,8511783384717186125753695914⟩⟩,⟨⟨(-4894430726757596744057967752),(-4894430726757596740695759874)⟩,⟨8477402692870422434452669664,8477402692870422437703555715⟩⟩,⟨⟨(-4873776274319785405590308281),(-4873776274319785402242776647)⟩,⟨8441628131845618339364444157,8441628131845618342600766677⟩⟩,⟨⟨(-4852458270930776063904551988),(-4852458270930776060572006749)⟩,⟨8404704266859928646116671038,8404704266859928649338241610⟩⟩,⟨⟨(-4830336305174704894846107601),(-4830336305174704891529382821)⟩,⟨8366387898207114528614921754,8366387898207114531820718317⟩⟩,⟨⟨(-4807562911692542948861315105),(-4807562911692542945560359930)⟩,⟨8326943223635252123540645240,8326943223635252126731098280⟩⟩,⟨⟨(-4783986684434824896527962646),(-4783986684434824893243841760)⟩,⟨8286108000174094193687831539,8286108000174094196861518960⟩⟩] +lemma amp1_13_9_eq : ∀ k : Fin 16, amp1_1Expr 3 9 k = amp1_13_9 k := by decide +kernel +noncomputable def amp1_13_10 : Fin 16 → CBox := ![⟨⟨(-4759771695603984758048908711),(-4759771695603984754781068910)⟩,⟨8244166409214366188060796193,8244166409214366191219011919⟩⟩,⟨⟨(-4734755328016043891333682343),(-4734755328016043888083501172)⟩,⟨8200836789531233322935777782,8200836789531233326076557061⟩⟩,⟨⟨(-4709113413761441758899255930),(-4709113413761441755667095481)⟩,⟨8156423691238937793231951720,8156423691238937796354996191⟩⟩,⟨⟨(-4682671887494008455925365123),(-4682671887494008452711528365)⟩,⟨8110625624314076259123096433,8110625624314076262228301631⟩⟩,⟨⟨(-4655618584475842404544461943),(-4655618584475842401349771366)⟩,⟨8063767928974056204393627817,8063767928974056207479890715⟩⟩,⟨⟨(-4627767732219821179352842534),(-4627767732219821176177577350)⟩,⟨8015528837832533153264592434,8015528837832533156331848631⟩⟩,⟨⟨(-4599319434914282690859846631),(-4599319434914282687704462504)⟩,⟨7966254941510515698351823956,7966254941510515701399598254⟩⟩,⟨⟨(-4570075930398161691359191607),(-4570075930398161688224422926)⟩,⟨7915603705897224210983487839,7915603705897224214010926216⟩⟩,⟨⟨(-4540249881715345228645325799),(-4540249881715345225531602911)⟩,⟨7863943474189563307885169218,7863943474189563310891832490⟩⟩,⟨⟨(-4509631229138743674221021294),(-4509631229138743671129017440)⟩,⟨7810910412267589700048259577,7810910412267589703033398269⟩⟩,⟨⟨(-4478445510590351197686656694),(-4478445510590351194616972250)⟩,⟨7756895163271230795380968389,7756895163271230798343840681⟩⟩,⟨⟨(-4446470033492561674320813235),(-4446470033492561671265743559)⟩,⟨7701512012341604310666145164,7701512012341604313620511005⟩⟩,⟨⟨(-4413943554923445716150703561),(-4413943554923445713118440761)⟩,⟨7645174498868595234976481101,7645174498868595237908440961⟩⟩,⟨⟨(-4380630384484886432938798974),(-4380630384484886429929832340)⟩,⟨7587474395107808978366545781,7587474395107808981275665689⟩⟩,⟨⟨(-4346782873384138109787619540),(-4346782873384138106802362593)⟩,⟨7528848786171561306474096656,7528848786171561309359941237⟩⟩,⟨⟨(-4312151936157441300231675365),(-4312151936157441297270539282)⟩,⟨7468866243381194001730165341,7468866243381194004592434201⟩⟩] +lemma amp1_13_10_eq : ∀ k : Fin 16, amp1_1Expr 3 10 k = amp1_13_10 k := by decide +kernel +noncomputable def amp1_13_11 : Fin 16 → CBox := ![⟨⟨(-4277003926566657995243001262),(-4277003926566657992306360070)⟩,⟨7407988104985039134027658832,7407988104985039136865975924⟩⟩,⟨⟨(-4241075931632628764133608178),(-4241075931632628761221861300)⟩,⟨7345758992345223272037749640,7345758992345223274851833122⟩⟩,⟨⟨(-4204648752671252392738999414),(-4204648752671252389852773002)⟩,⟨7282665267607715311190207821,7282665267607715313979235547⟩⟩,⟨⟨(-4167445178213067191812595161),(-4167445178213067188951947378)⟩,⟨7218226786422966777458380280,7218226786422966780222659603⟩⟩,⟨⟨(-4129760942243346621009669603),(-4129760942243346618175383602)⟩,⟨7152955775078996129104338545,7152955775078996131842765650⟩⟩,⟨⟨(-4091304021530033260525369864),(-4091304021530033257717843848)⟩,⟨7086346434500889438498113808,7086346434500889441210405127⟩⟩,⟨⟨(-4052385611987333480193378115),(-4052385611987333477413152566)⟩,⟨7018937771823159983564426090,7018937771823159986249888051⟩⟩,⟨⟨(-4012698318754671956616977499),(-4012698318754671953863337406)⟩,⟨6950197363529305752971130551,6950197363529305755631405735⟩⟩,⟨⟨(-3972569377672655664239111044),(-3972569377672655661513532968)⟩,⟨6880691998721315537215177822,6880691998721315539847940889⟩⟩,⟨⟨(-3931675410886016124850320825),(-3931675410886016122153249463)⟩,⟨6809861570523821677091259019,6809861570523821679696141847⟩⟩,⟨⟨(-3890360326150824620223108097),(-3890360326150824617554571781)⟩,⟨6738301744643456636655816222,6738301744643456639232991090⟩⟩,⟨⟨(-3848284094129928592741433782),(-3848284094129928590102338594)⟩,⟨6665423572992208218440275769,6665423572992208220988573371⟩⟩,⟨⟨(-3805807986503100697585568225),(-3805807986503100694976060142)⟩,⟨6591852796474778414680343504,6591852796474778417199721185⟩⟩,⟨⟨(-3762574590383011709472007467),(-3762574590383011706892649376)⟩,⟨6516970357811033116573663708,6516970357811033119063544570⟩⟩,⟨⟨(-3718963300339778589900244283),(-3718963300339778587351455045)⟩,⟨6441433387672530654325887956,6441433387672530656785745139⟩⟩,⟨⟨(-3674598516835281403318304646),(-3674598516835281400800749528)⟩,⟨6364591328575947896253074001,6364591328575947898682151284⟩⟩] +lemma amp1_13_11_eq : ∀ k : Fin 16, amp1_1Expr 3 11 k = amp1_13_11 k := by decide +kernel +noncomputable def amp1_13_12 : Fin 16 → CBox := ![⟨⟨(-3629878591273424895238331758),(-3629878591273424892747710199)⟩,⟨6287134145392114252830678199,6287134145392114255236611043⟩⟩,⟨⟨(-3584408854704921200494820162),(-3584408854704921198035548511)⟩,⟨6208378251448693316934774462,6208378251448693319310307644⟩⟩,⟨⟨(-3538607533590063834842644382),(-3538607533590063832414989144)⟩,⟨6129048036223983145515184681,6129048036223983147860030888⟩⟩,⟨⟨(-3492059917117642068970180358),(-3492059917117642066574591985)⟩,⟨6048425199522518650656994493,6048425199522518652970765793⟩⟩,⟨⟨(-3445205120144288776308562062),(-3445205120144288773945282274)⟩,⟨5967270310586346292560259406,5967270310586346294842698587⟩⟩,⟨⟨(-3397607316141974806939687334),(-3397607316141974804609105717)⟩,⟨5884828495725633242174247205,5884828495725633244425070026⟩⟩,⟨⟨(-3349727629506710178480672619),(-3349727629506710176183246357)⟩,⟨5801898445822878361291376163,5801898445822878363509938922⟩⟩,⟨⟨(-3301107928990071962431248654),(-3301107928990071960166870154)⟩,⟨5717686654279278178659682123,5717686654279278180846560148⟩⟩,⟨⟨(-3252232592395201076216234615),(-3252232592395201073985713262)⟩,⟨5633032088059931358974941594,5633032088059931361128867355⟩⟩,⟨⟨(-3202619863391098239809519201),(-3202619863391098237613203254)⟩,⟨5547100320722679179912878593,5547100320722679182033636480⟩⟩,⟨⟨(-3152778757425303731952678344),(-3152778757425303729790841741)⟩,⟨5460772992884498814762996381,5460772992884498816850231958⟩⟩,⟨⟨(-3102202422140761773538125011),(-3102202422140761771411293201)⟩,⟨5373172210511033612381201261,5373172210511033614434390881⟩⟩,⟨⟨(-3051426056220250143431781758),(-3051426056220250141340323977)⟩,⟨5285224964912998624031895706,5285224964912998626050504971⟩⟩,⟨⟨(-2999916066825581613941703168),(-2999916066825581611883365887)⟩,⟨5196007046184098692719850693,5196007046184098694708168441⟩⟩,⟨⟨(-2948235567927807713127014723),(-2948235567927807711104483223)⟩,⟨5106493796332646935018944048,5106493796332646936972408859⟩⟩,⟨⟨(-2895822380713515642280256037),(-2895822380713515640293981248)⟩,⟨5015711493090873599737935085,5015711493090873601656151045⟩⟩] +lemma amp1_13_12_eq : ∀ k : Fin 16, amp1_1Expr 3 12 k = amp1_13_12 k := by decide +kernel +noncomputable def amp1_13_13 : Fin 16 → CBox := ![⟨⟨(-2843269483200295803168958774),(-2843269483200295801218976660)⟩,⟨4924687204513016734182920485,4924687204513016736065898736⟩⟩,⟨⟨(-2789984030792729048412197016),(-2789984030792729046498671314)⟩,⟨4832394093638817759800672617,4832394093638817761648514607⟩⟩,⟨⟨(-2736591067706676010388325050),(-2736591067706676008511861953)⟩,⟨4739914768807124340564417936,4739914768807124342376130218⟩⟩,⟨⟨(-2682464728926284392292223897),(-2682464728926284390453122350)⟩,⟨4646165200011800397603035219,4646165200011800399378485484⟩⟩,⟨⟨(-2628264625263173647051288001),(-2628264625263173645249840630)⟩,⟨4552287866691792566949756694,4552287866691792568688476874⟩⟩,⟨⟨(-2573329192070436685557851066),(-2573329192070436683792805003)⟩,⟨4457136905266166405752969166,4457136905266166407457515796⟩⟩,⟨⟨(-2518355460693847130421761374),(-2518355460693847128694647604)⟩,⟨4361919609440269938403847489,4361919609440269940071588957⟩⟩,⟨⟨(-2462643101475025595916499821),(-2462643101475025594227830990)⟩,⟨4265422972663742713900045083,4265422972663742715530481700⟩⟩,⟨⟨(-2406929842568628608530216703),(-2406929842568628606879954096)⟩,⟨4168924777582623866548378588,4168924777582623868141577883⟩⟩,⟨⟨(-2350473060741471696004038371),(-2350473060741471694392508623)⟩,⟨4071138763026156820498449825,4071138763026156822054236864⟩⟩,⟨⟨(-2294054966019543064463654703),(-2294054966019543062891010381)⟩,⟨3973419756501542920665179523,3973419756501542922183269715⟩⟩,⟨⟨(-2236886552549583812429900111),(-2236886552549583810895529175)⟩,⟨3874401159783468515645755729,3874401159783468517127603547⟩⟩,⟨⟨(-2179798915915662808373853810),(-2179798915915662806879018127)⟩,⟨3775522472649487016829057522,3775522472649487018272434888⟩⟩,⟨⟨(-2121951893766475951928576969),(-2121951893766475950473654782)⟩,⟨3675328491220533190385857297,3675328491220533191790508226⟩⟩,⟨⟨(-2064230630799723995006966770),(-2064230630799723993591790043)⟩,⟨3575352331085074933430666203,3575352331085074934796815639⟩⟩,⟨⟨(-2005738188498802510309237379),(-2005738188498802508934463868)⟩,⟨3474040449161087916804549636,3474040449161087918131463666⟩⟩] +lemma amp1_13_13_eq : ∀ k : Fin 16, amp1_1Expr 3 13 k = amp1_13_13 k := by decide +kernel +noncomputable def amp1_13_14 : Fin 16 → CBox := ![⟨⟨(-1947419868181087740456517763),(-1947419868181087739121155726)⟩,⟨3373030155358729585114424727,3373030155358729586403729571⟩⟩,⟨⟨(-1888315278407924774369989300),(-1888315278407924773075346567)⟩,⟨3270658002911095463753117923,3270658002911095465002961639⟩⟩,⟨⟨(-1829437172087648440199921529),(-1829437172087648438945728388)⟩,⟨3168678131310934620975521989,3168678131310934622186252683⟩⟩,⟨⟨(-1769753689214106827499622946),(-1769753689214106826286721561)⟩,⟨3065303306601293613601936672,3065303306601293614772519002⟩⟩,⟨⟨(-1710353844287314214829040033),(-1710353844287314213656404772)⟩,⟨2962419757226376389942042121,2962419757226376391074103445⟩⟩,⟨⟨(-1650124571656563995947320650),(-1650124571656563994816161678)⟩,⟨2858099596926999394764856757,2858099596926999395856736974⟩⟩,⟨⟨(-1590241921453586583067188723),(-1590241921453586581976796114)⟩,⟨2754379804283567773062814836,2754379804283567774115561381⟩⟩,⟨⟨(-1529499634035960902785223149),(-1529499634035960901736709667)⟩,⟨2649171076308288359495915152,2649171076308288360508052509⟩⟩,⟨⟨(-1469174162069821263826366401),(-1469174162069821262819382649)⟩,⟨2544684293872362529997376410,2544684293872362530969290663⟩⟩,⟨⟨(-1407951061421259999773118937),(-1407951061421259998807907605)⟩,⟨2438642772952151337464606760,2438642772952151338396349371⟩⟩,⟨⟨(-1347224049647206333883040699),(-1347224049647206332959700844)⟩,⟨2333460503167656965754553643,2333460503167656966645692284⟩⟩,⟨⟨(-1285551412780888597018186982),(-1285551412780888596136990820)⟩,⟨2226640362678449215812604977,2226640362678449216663165202⟩⟩,⟨⟨(-1224465824149729459110964607),(-1224465824149729458271509072)⟩,⟨2120837019559029801378838473,2120837019559029802189209846⟩⟩,⟨⟨(-1162373479802631049089449784),(-1162373479802631048292774312)⟩,⟨2013289924388793187451155186,2013289924388793188220066525⟩⟩,⟨⟨(-1100974564234470578987255880),(-1100974564234470578232610829)⟩,⟨1906943883095107532849530630,1906943883095107533577915868⟩⟩,⟨⟨(-1038490075614490174224136381),(-1038490075614490173512288460)⟩,⟨1798717574120342149741188866,1798717574120342150428290629⟩⟩] +lemma amp1_13_14_eq : ∀ k : Fin 16, amp1_1Expr 3 14 k = amp1_13_14 k := by decide +kernel +noncomputable def amp1_13_15 : Fin 16 → CBox := ![⟨⟨(-976826365869980122170167126),(-976826365869980121500613365)⟩,⟨1691912895859670666011889942,1691912895859670666658147978⟩⟩,⟨⟨(-913973687112991920699048032),(-913973687112991920072630612)⟩,⟨1583048862860762033042021717,1583048862860762033646602278⟩⟩,⟨⟨(-852098715826997532918801653),(-852098715826997532334871688)⟩,⟨1475878268876554359746504486,1475878268876554360310017566⟩⟩,⟨⟨(-788895841566765076712535220),(-788895841566765076171867516)⟩,⟨1366407679473444525974555158,1366407679473444526496356734⟩⟩,⟨⟨(-726871292114567087378059419),(-726871292114567086879896170)⟩,⟨1258978008505669232858361858,1258978008505669233339145132⟩⟩,⟨⟨(-663325817138793157406315633),(-663325817138793156951728137)⟩,⟨1148914017256532114241592518,1148914017256532114680301383⟩⟩,⟨⟨(-601227801041259061232903296),(-601227801041259060820943751)⟩,⟨1041357098326373040982614198,1041357098326373041380129474⟩⟩,⟨⟨(-537327657764345332332709531),(-537327657764345331964496208)⟩,⟨930678803559827651868964547,930678803559827652224296575⟩⟩,⟨⟨(-475260698067625593803559643),(-475260698067625593477919136)⟩,⟨823175675893779269506071425,823175675893779269820289038⟩⟩,⟨⟨(-410952047203312812511687385),(-410952047203312812230138490)⟩,⟨711789825230581337976176628,711789825230581338247827482⟩⟩,⟨⟨(-349085604172734028948496816),(-349085604172734028709382827)⟩,⟨604634002618053415615973849,604634002618053415846643757⟩⟩,⟨⟨(-284208574900344161602779856),(-284208574900344161408136287)⟩,⟨492263691674140854298344597,492263691674140854486090382⟩⟩,⟨⟨(-222899049574540212034962306),(-222899049574540211882369834)⟩,⟨386072478821917588749195113,386072478821917588896332001⟩⟩,⟨⟨(-156930468665277273085467316),(-156930468665277272978075253)⟩,⟨271811544983855893863750419,271811544983855893967272553⟩⟩,⟨⟨(-97347548738388396655197505),(-97347548738388396588712624)⟩,⟨168610900407176264271705180,168610900407176264335692192⟩⟩,⟨⟨(-27656833929615362284877102),(-27656833929615362266068417)⟩,⟨47903041542588614252482915,47903041542588614270523424⟩⟩] +lemma amp1_13_15_eq : ∀ k : Fin 16, amp1_1Expr 3 15 k = amp1_13_15 k := by decide +kernel +noncomputable def amp1_13 : Fin 16 → Fin 16 → CBox := ![amp1_13_0,amp1_13_1,amp1_13_2,amp1_13_3,amp1_13_4,amp1_13_5,amp1_13_6,amp1_13_7,amp1_13_8,amp1_13_9,amp1_13_10,amp1_13_11,amp1_13_12,amp1_13_13,amp1_13_14,amp1_13_15] +lemma amp1_13_eq (i k : Fin 16) : amp1_1Expr 3 i k = amp1_13 i k := by + fin_cases i + · exact amp1_13_0_eq k + · exact amp1_13_1_eq k + · exact amp1_13_2_eq k + · exact amp1_13_3_eq k + · exact amp1_13_4_eq k + · exact amp1_13_5_eq k + · exact amp1_13_6_eq k + · exact amp1_13_7_eq k + · exact amp1_13_8_eq k + · exact amp1_13_9_eq k + · exact amp1_13_10_eq k + · exact amp1_13_11_eq k + · exact amp1_13_12_eq k + · exact amp1_13_13_eq k + · exact amp1_13_14_eq k + · exact amp1_13_15_eq k +noncomputable def amp1_14_0 : Fin 16 → CBox := ![⟨⟨(-206433418803638677632338361),(-206433418803638677616131501)⟩,⟨151119750944407953066122587,151119750944407953080341243⟩⟩,⟨⟨(-726611995767906115122458798),(-726611995767906115063313059)⟩,⟨531916898291129321822981006,531916898291129321874565835⟩⟩,⟨⟨(-1171344964628820880002821974),(-1171344964628820879905876550)⟩,⟨857484027298266333848316253,857484027298266333932644633⟩⟩,⟨⟨(-1663741155941996025543911282),(-1663741155941996025405793605)⟩,⟨1217943056792915601497014695,1217943056792915601617099125⟩⟩,⟨⟨(-2121361682949658354887811289),(-2121361682949658354711108330)⟩,⟨1552944533148970031711177783,1552944533148970031864727845⟩⟩,⟨⟨(-2605610421927042946878679343),(-2605610421927042946661351619)⟩,⟨1907439213581574889017003910,1907439213581574889205816310⟩⟩,⟨⟨(-3067387839274413925825951188),(-3067387839274413925569674022)⟩,⟨2245483744867788300843836372,2245483744867788301066428397⟩⟩,⟨⟨(-3547394144058060914026247705),(-3547394144058060913729621147)⟩,⟨2596872747922809726466665412,2596872747922809726724269803⟩⟩,⟨⟨(-4010668238177036632842654868),(-4010668238177036632506949847)⟩,⟨2936012922648345968230731777,2936012922648345968522227313⟩⟩,⟨⟨(-4487625400817782326643692288),(-4487625400817782326268381643)⟩,⟨3285169798735264204237975676,3285169798735264204563904326⟩⟩,⟨⟨(-4951131303068236857829423850),(-4951131303068236857414762651)⟩,⟨3624479668790650543082659652,3624479668790650543442681276⟩⟩,⟨⟨(-5425441185469606814923301381),(-5425441185469606814468714448)⟩,⟨3971698601240472640239211762,3971698601240472640633870643⟩⟩,⟨⟨(-5888398725213949358467494264),(-5888398725213949357974148696)⟩,⟨4310607042080419205120622532,4310607042080419205548934818⟩⟩,⟨⟨(-6360151401061098850809693844),(-6360151401061098850277224142)⟩,⟨4655953969407103785056847406,4655953969407103785519180971⟩⟩,⟨⟨(-6821992474173491748495976034),(-6821992474173491747924202956)⟩,⟨4994045099947507907188324245,4994045099947507907684697260⟩⟩,⟨⟨(-7291131255199261820293966522),(-7291131255199261819682436770)⟩,⟨5337478523459301576049976622,5337478523459301576580804156⟩⟩] +lemma amp1_14_0_eq : ∀ k : Fin 16, amp1_1Expr 4 0 k = amp1_14_0 k := by decide +kernel +noncomputable def amp1_14_1 : Fin 16 → CBox := ![⟨⟨(-7751395450698644995942624405),(-7751395450698644995292285459)⟩,⟨5674415299469664647596627514,5674415299469664648161114746⟩⟩,⟨⟨(-8217786023128097381185417498),(-8217786023128097380496200549)⟩,⟨6015836894659156223319519863,6015836894659156223917787039⟩⟩,⟨⟨(-8676073767988110570771451628),(-8676073767988110570044205096)⟩,⟨6351326808382848472707520949,6351326808382848473338854569⟩⟩,⟨⟨(-9139537335716977438687545843),(-9139537335716977437919787918)⟩,⟨6690605687417518520585509657,6690605687417518521251785560⟩⟩,⟨⟨(-9595486376480452819157849512),(-9595486376480452818352818180)⟩,⟨7024383550918675625248102400,7024383550918675625946864513⟩⟩,⟨⟨(-10055817204924139266474798540),(-10055817204924139265632121207)⟩,⟨7361369105629726598842132002,7361369105629726599573703058⟩⟩,⟨⟨(-10509089791589342673430554264),(-10509089791589342672548016776)⟩,⟨7693187668746822674022371745,7693187668746822674788292116⟩⟩,⟨⟨(-10966065236024010114682690427),(-10966065236024010113763259666)⟩,⟨8027716911884367587175101663,8027716911884367587973241673⟩⟩,⟨⟨(-11416340688760420329490469754),(-11416340688760420328531926708)⟩,⟨8357341420688498524070131841,8357341420688498524902039505⟩⟩,⟨⟨(-11869727294381481877727451757),(-11869727294381481876729060059)⟩,⟨8689243451474308711747840121,8689243451474308712614089980⟩⟩,⟨⟨(-12316697480480254772625931312),(-12316697480480254771592136842)⟩,⟨9016448337167126780893489105,9016448337167126781790753367⟩⟩,⟨⟨(-12766254891602009638482538141),(-12766254891602009637409598325)⟩,⟨9345547203027381208991543737,9345547203027381209922591667⟩⟩,⟨⟨(-13209621370059014536458143291),(-13209621370059014535351366677)⟩,⟨9670113991630800881634293831,9670113991630800882595168692⟩⟩,⟨⟨(-13655104950972463001982752869),(-13655104950972463000835757617)⟩,⟨9996230606797166121762103148,9996230606797166122757500916⟩⟩,⟨⟨(-14094577119453890024193793844),(-14094577119453890023009249687)⟩,⟨10317946562638040475638311332,10317946562638040476666209069⟩⟩,⟨⟨(-14535739783441810131238400685),(-14535739783441810130015311421)⟩,⟨10640900047079634650514560864,10640900047079634651575707118⟩⟩] +lemma amp1_14_1_eq : ∀ k : Fin 16, amp1_1Expr 4 1 k = amp1_14_1 k := by decide +kernel +noncomputable def amp1_14_2 : Fin 16 → CBox := ![⟨⟨(-14971033652317385874003075250),(-14971033652317385872747672177)⟩,⟨10959557275319780853582619549,10959557275319780854672385758⟩⟩,⟨⟨(-15407627185369045846022721105),(-15407627185369045844728383608)⟩,⟨11279165923769597856210880320,11279165923769597857334127935⟩⟩,⟨⟨(-15838464557506970187595915896),(-15838464557506970186264090819)⟩,⟨11594560769974018283945558087,11594560769974018285101162295⟩⟩,⟨⟨(-16270240608961625266240026153),(-16270240608961625264870023937)⟩,⟨11910642777130299649703383284,11910642777130299650891859581⟩⟩,⟨⟨(-16696348529765272280075022154),(-16696348529765272278666256299)⟩,⟨12222575424666104655429703038,12222575424666104656651416128⟩⟩,⟨⟨(-17123059377081258098221705515),(-17123059377081258096783957426)⟩,⟨12534949445042171969519499042,12534949445042171970767295315⟩⟩,⟨⟨(-17544169769018200424026815246),(-17544169769018200422552147549)⟩,⟨12843223647535257032248234834,12843223647535257033527860977⟩⟩,⟨⟨(-17965568925439762166207783923),(-17965568925439762164697509112)⟩,⟨13151709240302504949382222604,13151709240302504950692721098⟩⟩,⟨⟨(-18381418351227587810433593600),(-18381418351227587808886811185)⟩,⟨13456132148277536618839768512,13456132148277536620181735265⟩⟩,⟨⟨(-18797261061655928397439725467),(-18797261061655928395856142433)⟩,⟨13760550140268234136839464737,13760550140268234138213114175⟩⟩,⟨⟨(-19207590578814079552660096772),(-19207590578814079551040223026)⟩,⟨14060932194673206181791706044,14060932194673206183196602010⟩⟩,⟨⟨(-19617634234436279720999992299),(-19617634234436279719355083297)⟩,⟨14361104983909932427156995322,14361104983909932428584894991⟩⟩,⟨⟨(-20022189315728738363249260706),(-20022189315728738361566663186)⟩,⟨14657259857876169578926987209,14657259857876169580387090812⟩⟩,⟨⟨(-20426193808440952721534590990),(-20426193808440952719816157925)⟩,⟨14953011673027600701024025846,14953011673027600702514970635⟩⟩,⟨⟨(-20824724310448551712081762401),(-20824724310448551710326432186)⟩,⟨15244756248863093615526178405,15244756248863093617048679094⟩⟩,⟨⟨(-21222452341827216679850679898),(-21222452341827216678062494482)⟩,⟨15535913375426625073787196500,15535913375426625075338285027⟩⟩] +lemma amp1_14_2_eq : ∀ k : Fin 16, amp1_1Expr 4 2 k = amp1_14_2 k := by decide +kernel +noncomputable def amp1_14_3 : Fin 16 → CBox := ![⟨⟨(-21614712509035809767384752910),(-21614712509035809765561645166)⟩,⟨15823067747608778483102377884,15823067747608778484683505128⟩⟩,⟨⟨(-22005929864376524721312926193),(-22005929864376524719454537248)⟩,⟨16109458728520909295340396173,16109458728520909296951812955⟩⟩,⟨⟨(-22391678359670523839953099415),(-22391678359670523838059505178)⟩,⟨16391846226019360612354202402,16391846226019360613995790778⟩⟩,⟨⟨(-22776154154706997820508284379),(-22776154154706997818598762451)⟩,⟨16673302042266497533946257306,16673302042266497535603890578⟩⟩,⟨⟨(-23155154109585114317612905755),(-23155154109585114315667341490)⟩,⟨16950749265303590770840085783,16950749265303590772528426441⟩⟩,⟨⟨(-23532661015470212556014626519),(-23532661015470212554034877774)⟩,⟨17227103500619605092415842133,17227103500619605094133513101⟩⟩,⟨⟨(-23904680095009751317721906066),(-23904680095009751315708593557)⟩,⟨17499440368227554838412627147,17499440368227554840159111442⟩⟩,⟨⟨(-24274994545700667021452734696),(-24274994545700667019406877682)⟩,⟨17770529360910264869333831094,17770529360910264871108363125⟩⟩,⟨⟨(-24639805024518844205662967234),(-24639805024518844203583854156)⟩,⟨18037589166538700281116910131,18037589166538700282919948020⟩⟩,⟨⟨(-25002707409672597435102657116),(-25002707409672597432995181469)⟩,⟨18303252150659177078464066577,18303252150659177080292006276⟩⟩,⟨⟨(-25360086256019165710685504795),(-25360086256019165708545540724)⟩,⟨18564871623735216097131766856,18564871623735216098987565702⟩⟩,⟨⟨(-25715361101749847688913278874),(-25715361101749847686742973154)⟩,⟨18824950861461270136626088070,18824950861461270138508150520⟩⟩,⟨⟨(-26065090067515605575734199871),(-26065090067515605573533124207)⟩,⟨19080970233280321438127341738,19080970233280321440035918073⟩⟩,⟨⟨(-26412526206808221628921435096),(-26412526206808221626690014430)⟩,⟨19335311139628093959573358182,19335311139628093961508111173⟩⟩,⟨⟨(-26754391921717071434350841760),(-26754391921717071432089087333)⟩,⟨19585574212307229033701715153,19585574212307229035662573039⟩⟩,⟨⟨(-27093782655877928085098223056),(-27093782655877928082806635237)⟩,⟨19834025473331078294965556753,19834025473331078296952125011⟩⟩] +lemma amp1_14_3_eq : ∀ k : Fin 16, amp1_1Expr 4 3 k = amp1_14_3 k := by decide +kernel +noncomputable def amp1_14_4 : Fin 16 → CBox := ![⟨⟨(-27427576724493021404231230426),(-27427576724493021401939406527)⟩,⟨20078379690822458597963350993,20078379690822458599953899057⟩⟩,⟨⟨(-27758719976704175666688831172),(-27758719976704175664363076739)⟩,⟨20320793376024618487256941274,20320793376024618489276104962⟩⟩,⟨⟨(-28084239077154113069455450897),(-28084239077154113067097348255)⟩,⟨20559089896388089650880642146,20559089896388089652927198971⟩⟩,⟨⟨(-28406937538961959618106674107),(-28406937538961959615717652884)⟩,⟨20795321565955758223306187458,20795321565955758225379058690⟩⟩,⟨⟨(-28723983522504130806233787912),(-28723983522504130803814649215)⟩,⟨21027415334244273621123178468,21027415334244273623221713188⟩⟩,⟨⟨(-29038044793890211752575964958),(-29038044793890211750126002875)⟩,⟨21257324141588562512502875739,21257324141588562514627556670⟩⟩,⟨⟨(-29346424784591707851939088713),(-29346424784591707849461648684)⟩,⟨21483073962819675602614468028,21483073962819675604762781342⟩⟩,⟨⟨(-29651661508133253729726553181),(-29651661508133253727219955793)⟩,⟨21706522752787942401625782101,21706522752787942403798921364⟩⟩,⟨⟨(-29951188002077299330734987943),(-29951188002077299328199117387)⟩,⟨21925791364567955417879403161,21925791364567955420077388025⟩⟩,⟨⟨(-30247417991595653886208364259),(-30247417991595653883652258681)⟩,⟨22142646767620986926207267872,22142646767620986928423444356⟩⟩,⟨⟨(-30537908955121911917389515096),(-30537908955121911914804385184)⟩,⟨22355300912061845396724862407,22355300912061845398965599281⟩⟩,⟨⟨(-30824955319131378740524389351),(-30824955319131378737912197158)⟩,⟨22565433434644685498892743687,22565433434644685501156565343⟩⟩,⟨⟨(-31106234285698202320430180837),(-31106234285698202317790429132)⟩,⟨22771343929272067937193496240,22771343929272067939480700897⟩⟩,⟨⟨(-31383925545900440191584089067),(-31383925545900440188920465158)⟩,⟨22974628040557935406497839754,22974628040557935408805687196⟩⟩,⟨⟨(-31655821711220961598844212174),(-31655821711220961596153664056)⟩,⟨23173669847955704070969322507,23173669847955704073299980864⟩⟩,⟨⟨(-31923991916236710247247433289),(-31923991916236710244532393226)⟩,⟨23369984063103394257155837165,23369984063103394259507483400⟩⟩] +lemma amp1_14_4_eq : ∀ k : Fin 16, amp1_1Expr 4 4 k = amp1_14_4 k := by decide +kernel +noncomputable def amp1_14_5 : Fin 16 → CBox := ![⟨⟨(-32186340231392153202593769258),(-32186340231392153199853716340)⟩,⟨23562036359077270602526088914,23562036359077270604899037960⟩⟩,⟨⟨(-32444829065879675050292184491),(-32444829065879675047527588766)⟩,⟨23751263319111398831113935916,23751263319111398833507799656⟩⟩,⟨⟨(-32697470328155163686669341420),(-32697470328155163683879754263)⟩,⟨23936209559185390821189289372,23936209559185390823604329529⟩⟩,⟨⟨(-32946123217430973332724432172),(-32946123217430973329910540873)⟩,⟨24118236107584081900821331889,24118236107584081903256999845⟩⟩,⟨⟨(-33188904158653455316772304332),(-33188904158653455313934228645)⟩,⟨24295964091668331968529395181,24295964091668331970985536300⟩⟩,⟨⟨(-33427572368903866379626591507),(-33427572368903866376823004095)⟩,⟨24470681347723163984695050427,24470681347723163987128666431⟩⟩,⟨⟨(-33660345741090154095088795943),(-33660345741090154092258642433)⟩,⟨24641083282812666747086445912,24641083282812666749542164472⟩⟩,⟨⟨(-33888886475240507528449501882),(-33888886475240507525594717351)⟩,⟨24808386711809817071597563856,24808386711809817074073920123⟩⟩,⟨⟨(-34111511133387095185491153865),(-34111511133387095182613204543)⟩,⟨24971359272590771803211137175,24971359272590771805706990321⟩⟩,⟨⟨(-34329787622678162158220134946),(-34329787622678162155319617279)⟩,⟨25131148752849596776938573357,25131148752849596779453437161⟩⟩,⟨⟨(-34542128604544351022007022584),(-34542128604544351019085847546)⟩,⟨25286593140104708663740190401,25286593140104708666272598238⟩⟩,⟨⟨(-34750010195851482025021029245),(-34750010195851482022079915331)⟩,⟨25438773026899797216371872700,25438773026899797218921247735⟩⟩,⟨⟨(-34951938798604186339994299100),(-34951938798604186337031749279)⟩,⟨25586595023616169428582710577,25586595023616169431150080819⟩⟩,⟨⟨(-35149301037523642620097153325),(-35149301037523642617116559770)⟩,⟨25731074210000759102739300100,25731074210000759105322130224⟩⟩,⟨⟨(-35340694891126642209233276633),(-35340694891126642206233310373)⟩,⟨25871184235094554427006669301,25871184235094554429605864111⟩⟩,⟨⟨(-35527419600844671406335478315),(-35527419600844671403316033254)⟩,⟨26007876209636701890678090918,26007876209636701893293674830⟩⟩] +lemma amp1_14_5_eq : ∀ k : Fin 16, amp1_1Expr 4 5 k = amp1_14_5 k := by decide +kernel +noncomputable def amp1_14_6 : Fin 16 → CBox := ![⟨⟨(-35708162738087487971494491752),(-35708162738087487968462251719)⟩,⟨26140189369217838178883115754,26140189369217838181510127643⟩⟩,⟨⟨(-35884138094040676040525957464),(-35884138094040676037473925157)⟩,⟨26269012270655590143246517695,26269012270655590145890025566⟩⟩,⟨⟨(-36054121017113048634604664413),(-36054121017113048631537181903)⟩,⟨26393448406763638845357012302,26393448406763638848013769192⟩⟩,⟨⟨(-36219241617442961545834921139),(-36219241617442961542748683850)⟩,⟨26514325075581409418468970992,26514325075581409421141340563⟩⟩,⟨⟨(-36378361360970378299065830660),(-36378361360970378295963454232)⟩,⟨26630808812330807488328425703,26630808812330807491014424736⟩⟩,⟨⟨(-36532528292771231843106037676),(-36532528292771231839986857658)⟩,⟨26743666839256038355432515594,26743666839256038358132574010⟩⟩,⟨⟨(-36680688483235377567388899731),(-36680688483235377564273298677)⟩,⟨26852127626334874905620458547,26852127626334874908319586774⟩⟩,⟨⟨(-36823809384590225485865022921),(-36823809384590225482731801763)⟩,⟨26956899397751676948698974775,26956899397751676951412634132⟩⟩,⟨⟨(-36960920296065720306591107356),(-36960920296065720303442728488)⟩,⟨27057271551223817777156786838,27057271551223817779883106185⟩⟩,⟨⟨(-37092909413864254186290259023),(-37092909413864254183128288293)⟩,⟨27153894291498538179304589049,27153894291498538182042363689⟩⟩,⟨⟨(-37218888020009842726688323275),(-37218888020009842723512068045)⟩,⟨27246117031863817798287844365,27246117031863817801037512794⟩⟩,⟨⟨(-37339666263539208119127585845),(-37339666263539208115939798584)⟩,⟨27334532842576240262307360746,27334532842576240265066848705⟩⟩,⟨⟨(-37454436285787739078643806932),(-37454436285787739075443821277)⟩,⟨27418550330047975365410587042,27418550330047975368180313818⟩⟩,⟨⟨(-37563931276086673296383097517),(-37563931276086673293170030249)⟩,⟨27498706226121056544472083066,27498706226121056547252635057⟩⟩,⟨⟨(-37667423227983889638642274142),(-37667423227983889635426245651)⟩,⟨27574467593084293170370586867,27574467593084293173154486970⟩⟩,⟨⟨(-37765569342949880321089079229),(-37765569342949880317861930889)⟩,⟨27646315535804894523253336266,27646315535804894526046496038⟩⟩] +lemma amp1_14_6_eq : ∀ k : Fin 16, amp1_1Expr 4 6 k = amp1_14_6 k := by decide +kernel +noncomputable def amp1_14_7 : Fin 16 → CBox := ![⟨⟨(-37857720570597306434149533325),(-37857720570597306430912844863)⟩,⟨27713774916422656261763621941,27713774916422656264564816568⟩⟩,⟨⟨(-37944458985836275423538167098),(-37944458985836275420291236015)⟩,⟨27777271843345588123191291103,27777271843345588126000973117⟩⟩,⟨⟨(-38025213704398410463187883352),(-38025213704398410459936427677)⟩,⟨27836388400283996484341020169,27836388400283996487154935437⟩⟩,⟨⟨(-38100492429806577183761783079),(-38100492429806577180502067016)⟩,⟨27891496252011800694091373181,27891496252011800696912194040⟩⟩,⟨⟨(-38169801756047242384353242998),(-38169801756047242381088943844)⟩,⟨27942234200258334432325205591,27942234200258334435150171990⟩⟩,⟨⟨(-38233575668115257840501324848),(-38233575668115257837229394445)⟩,⟨27988919944089551716375646022,27988919944089551719206926236⟩⟩,⟨⟨(-38291397648932349305591596154),(-38291397648932349302315049666)⟩,⟨28031248571841935654737527864,28031248571841935657572846758⟩⟩,⟨⟨(-38343628518762467670603113163),(-38343628518762467667322369383)⟩,⟨28069484222281098712613740665,28069484222281098715452727893⟩⟩,⟨⟨(-38389928155694576735326342334),(-38389928155694576732041704506)⟩,⟨28103377908887394969802380567,28103377908887394972644746491⟩⟩,⟨⟨(-38430584672722504874569416746),(-38430584672722504871280857303)⟩,⟨28133140545010627575041154336,28133140545010627577886854776⟩⟩,⟨⟨(-38465333942404921044209223422),(-38465333942404921040918485591)⟩,⟨28158578775944069036222912406,28158578775944069039070603859⟩⟩,⟨⟨(-38494391733819021337550990647),(-38494391733819021334258212246)⟩,⟨28179850555614929144876479534,28179850555614929147725996197⟩⟩,⟨⟨(-38517569604370558562922014102),(-38517569604370558559628837100)⟩,⟨28196817934469908870068470979,28196817934469908872918543786⟩⟩,⟨⟨(-38535011250222245613079188880),(-38535011250222245609786445731)⟩,⟨28209586105400966733734416772,28209586105400966736584370902⟩⟩,⟨⟨(-38546603693548157836191584317),(-38546603693548157832900739925)⟩,⟨28218072362899397218460913438,28218072362899397221309609796⟩⟩,⟨⟨(-38552418737548597098069832053),(-38552418737548597094782704663)⟩,⟨28222329270555967334968751947,28222329270555967337814793592⟩⟩] +lemma amp1_14_7_eq : ∀ k : Fin 16, amp1_1Expr 4 7 k = amp1_14_7 k := by decide +kernel +noncomputable def amp1_14_8 : Fin 16 → CBox := ![⟨⟨(-38552418737548597098069832053),(-38552418737548597094782704663)⟩,⟨28222329270555967334968751947,28222329270555967337814793592⟩⟩,⟨⟨(-38546603693548157836191584317),(-38546603693548157832900739925)⟩,⟨28218072362899397218460913438,28218072362899397221309609796⟩⟩,⟨⟨(-38535011250222245613079188880),(-38535011250222245609786445731)⟩,⟨28209586105400966733734416772,28209586105400966736584370902⟩⟩,⟨⟨(-38517569604370558562922014102),(-38517569604370558559628837100)⟩,⟨28196817934469908870068470979,28196817934469908872918543786⟩⟩,⟨⟨(-38494391733819021337550990647),(-38494391733819021334258212246)⟩,⟨28179850555614929144876479534,28179850555614929147725996197⟩⟩,⟨⟨(-38465333942404921044209223422),(-38465333942404921040918485591)⟩,⟨28158578775944069036222912406,28158578775944069039070603859⟩⟩,⟨⟨(-38430584672722504874569416746),(-38430584672722504871280857303)⟩,⟨28133140545010627575041154336,28133140545010627577886854776⟩⟩,⟨⟨(-38389928155694576735326342334),(-38389928155694576732041704506)⟩,⟨28103377908887394969802380567,28103377908887394972644746491⟩⟩,⟨⟨(-38343628518762467670603113163),(-38343628518762467667322369383)⟩,⟨28069484222281098712613740665,28069484222281098715452727893⟩⟩,⟨⟨(-38291397648932349305591596154),(-38291397648932349302315049666)⟩,⟨28031248571841935654737527864,28031248571841935657572846758⟩⟩,⟨⟨(-38233575668115257840501324848),(-38233575668115257837229394445)⟩,⟨27988919944089551716375646022,27988919944089551719206926236⟩⟩,⟨⟨(-38169801756047242384353242998),(-38169801756047242381088943844)⟩,⟨27942234200258334432325205591,27942234200258334435150171990⟩⟩,⟨⟨(-38100492429806577183761783079),(-38100492429806577180502067016)⟩,⟨27891496252011800694091373181,27891496252011800696912194040⟩⟩,⟨⟨(-38025213704398410463187883352),(-38025213704398410459936427677)⟩,⟨27836388400283996484341020169,27836388400283996487154935437⟩⟩,⟨⟨(-37944458985836275423538167098),(-37944458985836275420291236015)⟩,⟨27777271843345588123191291103,27777271843345588126000973117⟩⟩,⟨⟨(-37857720570597306434149533325),(-37857720570597306430912844863)⟩,⟨27713774916422656261763621941,27713774916422656264564816568⟩⟩] +lemma amp1_14_8_eq : ∀ k : Fin 16, amp1_1Expr 4 8 k = amp1_14_8 k := by decide +kernel +noncomputable def amp1_14_9 : Fin 16 → CBox := ![⟨⟨(-37765569342949880321089079229),(-37765569342949880317861930889)⟩,⟨27646315535804894523253336266,27646315535804894526046496038⟩⟩,⟨⟨(-37667423227983889638642274142),(-37667423227983889635426245651)⟩,⟨27574467593084293170370586867,27574467593084293173154486970⟩⟩,⟨⟨(-37563931276086673296383097517),(-37563931276086673293170030249)⟩,⟨27498706226121056544472083066,27498706226121056547252635057⟩⟩,⟨⟨(-37454436285787739078643806932),(-37454436285787739075443821277)⟩,⟨27418550330047975365410587042,27418550330047975368180313818⟩⟩,⟨⟨(-37339666263539208119127585845),(-37339666263539208115939798584)⟩,⟨27334532842576240262307360746,27334532842576240265066848705⟩⟩,⟨⟨(-37218888020009842726688323275),(-37218888020009842723512068045)⟩,⟨27246117031863817798287844365,27246117031863817801037512794⟩⟩,⟨⟨(-37092909413864254186290259023),(-37092909413864254183128288293)⟩,⟨27153894291498538179304589049,27153894291498538182042363689⟩⟩,⟨⟨(-36960920296065720306591107356),(-36960920296065720303442728488)⟩,⟨27057271551223817777156786838,27057271551223817779883106185⟩⟩,⟨⟨(-36823809384590225485865022921),(-36823809384590225482731801763)⟩,⟨26956899397751676948698974775,26956899397751676951412634132⟩⟩,⟨⟨(-36680688483235377567388899731),(-36680688483235377564273298677)⟩,⟨26852127626334874905620458547,26852127626334874908319586774⟩⟩,⟨⟨(-36532528292771231843106037676),(-36532528292771231839986857658)⟩,⟨26743666839256038355432515594,26743666839256038358132574010⟩⟩,⟨⟨(-36378361360970378299065830660),(-36378361360970378295963454232)⟩,⟨26630808812330807488328425703,26630808812330807491014424736⟩⟩,⟨⟨(-36219241617442961545834921139),(-36219241617442961542748683850)⟩,⟨26514325075581409418468970992,26514325075581409421141340563⟩⟩,⟨⟨(-36054121017113048634604664413),(-36054121017113048631537181903)⟩,⟨26393448406763638845357012302,26393448406763638848013769192⟩⟩,⟨⟨(-35884138094040676040525957464),(-35884138094040676037473925157)⟩,⟨26269012270655590143246517695,26269012270655590145890025566⟩⟩,⟨⟨(-35708162738087487971494491752),(-35708162738087487968462251719)⟩,⟨26140189369217838178883115754,26140189369217838181510127643⟩⟩] +lemma amp1_14_9_eq : ∀ k : Fin 16, amp1_1Expr 4 9 k = amp1_14_9 k := by decide +kernel +noncomputable def amp1_14_10 : Fin 16 → CBox := ![⟨⟨(-35527419600844671406335478315),(-35527419600844671403316033254)⟩,⟨26007876209636701890678090918,26007876209636701893293674830⟩⟩,⟨⟨(-35340694891126642209233276633),(-35340694891126642206233310373)⟩,⟨25871184235094554427006669301,25871184235094554429605864111⟩⟩,⟨⟨(-35149301037523642620097153325),(-35149301037523642617116559770)⟩,⟨25731074210000759102739300100,25731074210000759105322130224⟩⟩,⟨⟨(-34951938798604186339994299100),(-34951938798604186337031749279)⟩,⟨25586595023616169428582710577,25586595023616169431150080819⟩⟩,⟨⟨(-34750010195851482025021029245),(-34750010195851482022079915331)⟩,⟨25438773026899797216371872700,25438773026899797218921247735⟩⟩,⟨⟨(-34542128604544351022007022584),(-34542128604544351019085847546)⟩,⟨25286593140104708663740190401,25286593140104708666272598238⟩⟩,⟨⟨(-34329787622678162158220134946),(-34329787622678162155319617279)⟩,⟨25131148752849596776938573357,25131148752849596779453437161⟩⟩,⟨⟨(-34111511133387095185491153865),(-34111511133387095182613204543)⟩,⟨24971359272590771803211137175,24971359272590771805706990321⟩⟩,⟨⟨(-33888886475240507528449501882),(-33888886475240507525594717351)⟩,⟨24808386711809817071597563856,24808386711809817074073920123⟩⟩,⟨⟨(-33660345741090154095088795943),(-33660345741090154092258642433)⟩,⟨24641083282812666747086445912,24641083282812666749542164472⟩⟩,⟨⟨(-33427572368903866379626591507),(-33427572368903866376823004095)⟩,⟨24470681347723163984695050427,24470681347723163987128666431⟩⟩,⟨⟨(-33188904158653455316772304332),(-33188904158653455313934228645)⟩,⟨24295964091668331968529395181,24295964091668331970985536300⟩⟩,⟨⟨(-32946123217430973332724432172),(-32946123217430973329910540873)⟩,⟨24118236107584081900821331889,24118236107584081903256999845⟩⟩,⟨⟨(-32697470328155163686669341420),(-32697470328155163683879754263)⟩,⟨23936209559185390821189289372,23936209559185390823604329529⟩⟩,⟨⟨(-32444829065879675050292184491),(-32444829065879675047527588766)⟩,⟨23751263319111398831113935916,23751263319111398833507799656⟩⟩,⟨⟨(-32186340231392153202593769258),(-32186340231392153199853716340)⟩,⟨23562036359077270602526088914,23562036359077270604899037960⟩⟩] +lemma amp1_14_10_eq : ∀ k : Fin 16, amp1_1Expr 4 10 k = amp1_14_10 k := by decide +kernel +noncomputable def amp1_14_11 : Fin 16 → CBox := ![⟨⟨(-31923991916236710247247433289),(-31923991916236710244532393226)⟩,⟨23369984063103394257155837165,23369984063103394259507483400⟩⟩,⟨⟨(-31655821711220961598844212174),(-31655821711220961596153664056)⟩,⟨23173669847955704070969322507,23173669847955704073299980864⟩⟩,⟨⟨(-31383925545900440191584089067),(-31383925545900440188920465158)⟩,⟨22974628040557935406497839754,22974628040557935408805687196⟩⟩,⟨⟨(-31106234285698202320430180837),(-31106234285698202317790429132)⟩,⟨22771343929272067937193496240,22771343929272067939480700897⟩⟩,⟨⟨(-30824955319131378740524389351),(-30824955319131378737912197158)⟩,⟨22565433434644685498892743687,22565433434644685501156565343⟩⟩,⟨⟨(-30537908955121911917389515096),(-30537908955121911914804385184)⟩,⟨22355300912061845396724862407,22355300912061845398965599281⟩⟩,⟨⟨(-30247417991595653886208364259),(-30247417991595653883652258681)⟩,⟨22142646767620986926207267872,22142646767620986928423444356⟩⟩,⟨⟨(-29951188002077299330734987943),(-29951188002077299328199117387)⟩,⟨21925791364567955417879403161,21925791364567955420077388025⟩⟩,⟨⟨(-29651661508133253729726553181),(-29651661508133253727219955793)⟩,⟨21706522752787942401625782101,21706522752787942403798921364⟩⟩,⟨⟨(-29346424784591707851939088713),(-29346424784591707849461648684)⟩,⟨21483073962819675602614468028,21483073962819675604762781342⟩⟩,⟨⟨(-29038044793890211752575964958),(-29038044793890211750126002875)⟩,⟨21257324141588562512502875739,21257324141588562514627556670⟩⟩,⟨⟨(-28723983522504130806233787912),(-28723983522504130803814649215)⟩,⟨21027415334244273621123178468,21027415334244273623221713188⟩⟩,⟨⟨(-28406937538961959618106674107),(-28406937538961959615717652884)⟩,⟨20795321565955758223306187458,20795321565955758225379058690⟩⟩,⟨⟨(-28084239077154113069455450897),(-28084239077154113067097348255)⟩,⟨20559089896388089650880642146,20559089896388089652927198971⟩⟩,⟨⟨(-27758719976704175666688831172),(-27758719976704175664363076739)⟩,⟨20320793376024618487256941274,20320793376024618489276104962⟩⟩,⟨⟨(-27427576724493021404231230426),(-27427576724493021401939406527)⟩,⟨20078379690822458597963350993,20078379690822458599953899057⟩⟩] +lemma amp1_14_11_eq : ∀ k : Fin 16, amp1_1Expr 4 11 k = amp1_14_11 k := by decide +kernel +noncomputable def amp1_14_12 : Fin 16 → CBox := ![⟨⟨(-27093782655877928085098223056),(-27093782655877928082806635237)⟩,⟨19834025473331078294965556753,19834025473331078296952125011⟩⟩,⟨⟨(-26754391921717071434350841760),(-26754391921717071432089087333)⟩,⟨19585574212307229033701715153,19585574212307229035662573039⟩⟩,⟨⟨(-26412526206808221628921435096),(-26412526206808221626690014430)⟩,⟨19335311139628093959573358182,19335311139628093961508111173⟩⟩,⟨⟨(-26065090067515605575734199871),(-26065090067515605573533124207)⟩,⟨19080970233280321438127341738,19080970233280321440035918073⟩⟩,⟨⟨(-25715361101749847688913278874),(-25715361101749847686742973154)⟩,⟨18824950861461270136626088070,18824950861461270138508150520⟩⟩,⟨⟨(-25360086256019165710685504795),(-25360086256019165708545540724)⟩,⟨18564871623735216097131766856,18564871623735216098987565702⟩⟩,⟨⟨(-25002707409672597435102657116),(-25002707409672597432995181469)⟩,⟨18303252150659177078464066577,18303252150659177080292006276⟩⟩,⟨⟨(-24639805024518844205662967234),(-24639805024518844203583854156)⟩,⟨18037589166538700281116910131,18037589166538700282919948020⟩⟩,⟨⟨(-24274994545700667021452734696),(-24274994545700667019406877682)⟩,⟨17770529360910264869333831094,17770529360910264871108363125⟩⟩,⟨⟨(-23904680095009751317721906066),(-23904680095009751315708593557)⟩,⟨17499440368227554838412627147,17499440368227554840159111442⟩⟩,⟨⟨(-23532661015470212556014626519),(-23532661015470212554034877774)⟩,⟨17227103500619605092415842133,17227103500619605094133513101⟩⟩,⟨⟨(-23155154109585114317612905755),(-23155154109585114315667341490)⟩,⟨16950749265303590770840085783,16950749265303590772528426441⟩⟩,⟨⟨(-22776154154706997820508284379),(-22776154154706997818598762451)⟩,⟨16673302042266497533946257306,16673302042266497535603890578⟩⟩,⟨⟨(-22391678359670523839953099415),(-22391678359670523838059505178)⟩,⟨16391846226019360612354202402,16391846226019360613995790778⟩⟩,⟨⟨(-22005929864376524721312926193),(-22005929864376524719454537248)⟩,⟨16109458728520909295340396173,16109458728520909296951812955⟩⟩,⟨⟨(-21614712509035809767384752910),(-21614712509035809765561645166)⟩,⟨15823067747608778483102377884,15823067747608778484683505128⟩⟩] +lemma amp1_14_12_eq : ∀ k : Fin 16, amp1_1Expr 4 12 k = amp1_14_12 k := by decide +kernel +noncomputable def amp1_14_13 : Fin 16 → CBox := ![⟨⟨(-21222452341827216679850679898),(-21222452341827216678062494482)⟩,⟨15535913375426625073787196500,15535913375426625075338285027⟩⟩,⟨⟨(-20824724310448551712081762401),(-20824724310448551710326432186)⟩,⟨15244756248863093615526178405,15244756248863093617048679094⟩⟩,⟨⟨(-20426193808440952721534590990),(-20426193808440952719816157925)⟩,⟨14953011673027600701024025846,14953011673027600702514970635⟩⟩,⟨⟨(-20022189315728738363249260706),(-20022189315728738361566663186)⟩,⟨14657259857876169578926987209,14657259857876169580387090812⟩⟩,⟨⟨(-19617634234436279720999992299),(-19617634234436279719355083297)⟩,⟨14361104983909932427156995322,14361104983909932428584894991⟩⟩,⟨⟨(-19207590578814079552660096772),(-19207590578814079551040223026)⟩,⟨14060932194673206181791706044,14060932194673206183196602010⟩⟩,⟨⟨(-18797261061655928397439725467),(-18797261061655928395856142433)⟩,⟨13760550140268234136839464737,13760550140268234138213114175⟩⟩,⟨⟨(-18381418351227587810433593600),(-18381418351227587808886811185)⟩,⟨13456132148277536618839768512,13456132148277536620181735265⟩⟩,⟨⟨(-17965568925439762166207783923),(-17965568925439762164697509112)⟩,⟨13151709240302504949382222604,13151709240302504950692721098⟩⟩,⟨⟨(-17544169769018200424026815246),(-17544169769018200422552147549)⟩,⟨12843223647535257032248234834,12843223647535257033527860977⟩⟩,⟨⟨(-17123059377081258098221705515),(-17123059377081258096783957426)⟩,⟨12534949445042171969519499042,12534949445042171970767295315⟩⟩,⟨⟨(-16696348529765272280075022154),(-16696348529765272278666256299)⟩,⟨12222575424666104655429703038,12222575424666104656651416128⟩⟩,⟨⟨(-16270240608961625266240026153),(-16270240608961625264870023937)⟩,⟨11910642777130299649703383284,11910642777130299650891859581⟩⟩,⟨⟨(-15838464557506970187595915896),(-15838464557506970186264090819)⟩,⟨11594560769974018283945558087,11594560769974018285101162295⟩⟩,⟨⟨(-15407627185369045846022721105),(-15407627185369045844728383608)⟩,⟨11279165923769597856210880320,11279165923769597857334127935⟩⟩,⟨⟨(-14971033652317385874003075250),(-14971033652317385872747672177)⟩,⟨10959557275319780853582619549,10959557275319780854672385758⟩⟩] +lemma amp1_14_13_eq : ∀ k : Fin 16, amp1_1Expr 4 13 k = amp1_14_13 k := by decide +kernel +noncomputable def amp1_14_14 : Fin 16 → CBox := ![⟨⟨(-14535739783441810131238400685),(-14535739783441810130015311421)⟩,⟨10640900047079634650514560864,10640900047079634651575707118⟩⟩,⟨⟨(-14094577119453890024193793844),(-14094577119453890023009249687)⟩,⟨10317946562638040475638311332,10317946562638040476666209069⟩⟩,⟨⟨(-13655104950972463001982752869),(-13655104950972463000835757617)⟩,⟨9996230606797166121762103148,9996230606797166122757500916⟩⟩,⟨⟨(-13209621370059014536458143291),(-13209621370059014535351366677)⟩,⟨9670113991630800881634293831,9670113991630800882595168692⟩⟩,⟨⟨(-12766254891602009638482538141),(-12766254891602009637409598325)⟩,⟨9345547203027381208991543737,9345547203027381209922591667⟩⟩,⟨⟨(-12316697480480254772625931312),(-12316697480480254771592136842)⟩,⟨9016448337167126780893489105,9016448337167126781790753367⟩⟩,⟨⟨(-11869727294381481877727451757),(-11869727294381481876729060059)⟩,⟨8689243451474308711747840121,8689243451474308712614089980⟩⟩,⟨⟨(-11416340688760420329490469754),(-11416340688760420328531926708)⟩,⟨8357341420688498524070131841,8357341420688498524902039505⟩⟩,⟨⟨(-10966065236024010114682690427),(-10966065236024010113763259666)⟩,⟨8027716911884367587175101663,8027716911884367587973241673⟩⟩,⟨⟨(-10509089791589342673430554264),(-10509089791589342672548016776)⟩,⟨7693187668746822674022371745,7693187668746822674788292116⟩⟩,⟨⟨(-10055817204924139266474798540),(-10055817204924139265632121207)⟩,⟨7361369105629726598842132002,7361369105629726599573703058⟩⟩,⟨⟨(-9595486376480452819157849512),(-9595486376480452818352818180)⟩,⟨7024383550918675625248102400,7024383550918675625946864513⟩⟩,⟨⟨(-9139537335716977438687545843),(-9139537335716977437919787918)⟩,⟨6690605687417518520585509657,6690605687417518521251785560⟩⟩,⟨⟨(-8676073767988110570771451628),(-8676073767988110570044205096)⟩,⟨6351326808382848472707520949,6351326808382848473338854569⟩⟩,⟨⟨(-8217786023128097381185417498),(-8217786023128097380496200549)⟩,⟨6015836894659156223319519863,6015836894659156223917787039⟩⟩,⟨⟨(-7751395450698644995942624405),(-7751395450698644995292285459)⟩,⟨5674415299469664647596627514,5674415299469664648161114746⟩⟩] +lemma amp1_14_14_eq : ∀ k : Fin 16, amp1_1Expr 4 14 k = amp1_14_14 k := by decide +kernel +noncomputable def amp1_14_15 : Fin 16 → CBox := ![⟨⟨(-7291131255199261820293966522),(-7291131255199261819682436770)⟩,⟨5337478523459301576049976622,5337478523459301576580804156⟩⟩,⟨⟨(-6821992474173491748495976034),(-6821992474173491747924202956)⟩,⟨4994045099947507907188324245,4994045099947507907684697260⟩⟩,⟨⟨(-6360151401061098850809693844),(-6360151401061098850277224142)⟩,⟨4655953969407103785056847406,4655953969407103785519180971⟩⟩,⟨⟨(-5888398725213949358467494264),(-5888398725213949357974148696)⟩,⟨4310607042080419205120622532,4310607042080419205548934818⟩⟩,⟨⟨(-5425441185469606814923301381),(-5425441185469606814468714448)⟩,⟨3971698601240472640239211762,3971698601240472640633870643⟩⟩,⟨⟨(-4951131303068236857829423850),(-4951131303068236857414762651)⟩,⟨3624479668790650543082659652,3624479668790650543442681276⟩⟩,⟨⟨(-4487625400817782326643692288),(-4487625400817782326268381643)⟩,⟨3285169798735264204237975676,3285169798735264204563904326⟩⟩,⟨⟨(-4010668238177036632842654868),(-4010668238177036632506949847)⟩,⟨2936012922648345968230731777,2936012922648345968522227313⟩⟩,⟨⟨(-3547394144058060914026247705),(-3547394144058060913729621147)⟩,⟨2596872747922809726466665412,2596872747922809726724269803⟩⟩,⟨⟨(-3067387839274413925825951188),(-3067387839274413925569674022)⟩,⟨2245483744867788300843836372,2245483744867788301066428397⟩⟩,⟨⟨(-2605610421927042946878679343),(-2605610421927042946661351619)⟩,⟨1907439213581574889017003910,1907439213581574889205816310⟩⟩,⟨⟨(-2121361682949658354887811289),(-2121361682949658354711108330)⟩,⟨1552944533148970031711177783,1552944533148970031864727845⟩⟩,⟨⟨(-1663741155941996025543911282),(-1663741155941996025405793605)⟩,⟨1217943056792915601497014695,1217943056792915601617099125⟩⟩,⟨⟨(-1171344964628820880002821974),(-1171344964628820879905876550)⟩,⟨857484027298266333848316253,857484027298266333932644633⟩⟩,⟨⟨(-726611995767906115122458798),(-726611995767906115063313059)⟩,⟨531916898291129321822981006,531916898291129321874565835⟩⟩,⟨⟨(-206433418803638677632338361),(-206433418803638677616131501)⟩,⟨151119750944407953066122587,151119750944407953080341243⟩⟩] +lemma amp1_14_15_eq : ∀ k : Fin 16, amp1_1Expr 4 15 k = amp1_14_15 k := by decide +kernel +noncomputable def amp1_14 : Fin 16 → Fin 16 → CBox := ![amp1_14_0,amp1_14_1,amp1_14_2,amp1_14_3,amp1_14_4,amp1_14_5,amp1_14_6,amp1_14_7,amp1_14_8,amp1_14_9,amp1_14_10,amp1_14_11,amp1_14_12,amp1_14_13,amp1_14_14,amp1_14_15] +lemma amp1_14_eq (i k : Fin 16) : amp1_1Expr 4 i k = amp1_14 i k := by + fin_cases i + · exact amp1_14_0_eq k + · exact amp1_14_1_eq k + · exact amp1_14_2_eq k + · exact amp1_14_3_eq k + · exact amp1_14_4_eq k + · exact amp1_14_5_eq k + · exact amp1_14_6_eq k + · exact amp1_14_7_eq k + · exact amp1_14_8_eq k + · exact amp1_14_9_eq k + · exact amp1_14_10_eq k + · exact amp1_14_11_eq k + · exact amp1_14_12_eq k + · exact amp1_14_13_eq k + · exact amp1_14_14_eq k + · exact amp1_14_15_eq k +noncomputable def amp1_15_0 : Fin 16 → CBox := ![⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩] +lemma amp1_15_0_eq : ∀ k : Fin 16, amp1_1Expr 5 0 k = amp1_15_0 k := by decide +kernel +noncomputable def amp1_15_1 : Fin 16 → CBox := ![⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩] +lemma amp1_15_1_eq : ∀ k : Fin 16, amp1_1Expr 5 1 k = amp1_15_1 k := by decide +kernel +noncomputable def amp1_15_2 : Fin 16 → CBox := ![⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩] +lemma amp1_15_2_eq : ∀ k : Fin 16, amp1_1Expr 5 2 k = amp1_15_2 k := by decide +kernel +noncomputable def amp1_15_3 : Fin 16 → CBox := ![⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩] +lemma amp1_15_3_eq : ∀ k : Fin 16, amp1_1Expr 5 3 k = amp1_15_3 k := by decide +kernel +noncomputable def amp1_15_4 : Fin 16 → CBox := ![⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩] +lemma amp1_15_4_eq : ∀ k : Fin 16, amp1_1Expr 5 4 k = amp1_15_4 k := by decide +kernel +noncomputable def amp1_15_5 : Fin 16 → CBox := ![⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩] +lemma amp1_15_5_eq : ∀ k : Fin 16, amp1_1Expr 5 5 k = amp1_15_5 k := by decide +kernel +noncomputable def amp1_15_6 : Fin 16 → CBox := ![⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩] +lemma amp1_15_6_eq : ∀ k : Fin 16, amp1_1Expr 5 6 k = amp1_15_6 k := by decide +kernel +noncomputable def amp1_15_7 : Fin 16 → CBox := ![⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩] +lemma amp1_15_7_eq : ∀ k : Fin 16, amp1_1Expr 5 7 k = amp1_15_7 k := by decide +kernel +noncomputable def amp1_15_8 : Fin 16 → CBox := ![⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩] +lemma amp1_15_8_eq : ∀ k : Fin 16, amp1_1Expr 5 8 k = amp1_15_8 k := by decide +kernel +noncomputable def amp1_15_9 : Fin 16 → CBox := ![⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩] +lemma amp1_15_9_eq : ∀ k : Fin 16, amp1_1Expr 5 9 k = amp1_15_9 k := by decide +kernel +noncomputable def amp1_15_10 : Fin 16 → CBox := ![⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩] +lemma amp1_15_10_eq : ∀ k : Fin 16, amp1_1Expr 5 10 k = amp1_15_10 k := by decide +kernel +noncomputable def amp1_15_11 : Fin 16 → CBox := ![⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩] +lemma amp1_15_11_eq : ∀ k : Fin 16, amp1_1Expr 5 11 k = amp1_15_11 k := by decide +kernel +noncomputable def amp1_15_12 : Fin 16 → CBox := ![⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩] +lemma amp1_15_12_eq : ∀ k : Fin 16, amp1_1Expr 5 12 k = amp1_15_12 k := by decide +kernel +noncomputable def amp1_15_13 : Fin 16 → CBox := ![⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩] +lemma amp1_15_13_eq : ∀ k : Fin 16, amp1_1Expr 5 13 k = amp1_15_13 k := by decide +kernel +noncomputable def amp1_15_14 : Fin 16 → CBox := ![⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩] +lemma amp1_15_14_eq : ∀ k : Fin 16, amp1_1Expr 5 14 k = amp1_15_14 k := by decide +kernel +noncomputable def amp1_15_15 : Fin 16 → CBox := ![⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩] +lemma amp1_15_15_eq : ∀ k : Fin 16, amp1_1Expr 5 15 k = amp1_15_15 k := by decide +kernel +noncomputable def amp1_15 : Fin 16 → Fin 16 → CBox := ![amp1_15_0,amp1_15_1,amp1_15_2,amp1_15_3,amp1_15_4,amp1_15_5,amp1_15_6,amp1_15_7,amp1_15_8,amp1_15_9,amp1_15_10,amp1_15_11,amp1_15_12,amp1_15_13,amp1_15_14,amp1_15_15] +lemma amp1_15_eq (i k : Fin 16) : amp1_1Expr 5 i k = amp1_15 i k := by + fin_cases i + · exact amp1_15_0_eq k + · exact amp1_15_1_eq k + · exact amp1_15_2_eq k + · exact amp1_15_3_eq k + · exact amp1_15_4_eq k + · exact amp1_15_5_eq k + · exact amp1_15_6_eq k + · exact amp1_15_7_eq k + · exact amp1_15_8_eq k + · exact amp1_15_9_eq k + · exact amp1_15_10_eq k + · exact amp1_15_11_eq k + · exact amp1_15_12_eq k + · exact amp1_15_13_eq k + · exact amp1_15_14_eq k + · exact amp1_15_15_eq k +noncomputable def amp1_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp1_10,amp1_11,amp1_12,amp1_13,amp1_14,amp1_15] +lemma amp1_1_eq (j : Fin 6) (i k : Fin 16) : amp1_1Expr j i k = amp1_1 j i k := by + fin_cases j + · exact amp1_10_eq i k + · exact amp1_11_eq i k + · exact amp1_12_eq i k + · exact amp1_13_eq i k + · exact amp1_14_eq i k + · exact amp1_15_eq i k +lemma amp1_1_contains (j : Fin 6) (i k : Fin 16) : + (amp1_1 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude true 1 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp1_1_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 1 j) (bLookup_contains 1 j) true) +noncomputable def amp3_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 3 j) (bLookup 3 j) false) +noncomputable def amp3_00_0 : Fin 16 → CBox := ![⟨⟨61807075809980497310863593,61807075809980497399028168⟩,⟨(-93606319881131816265436004),(-93606319881131816182389210)⟩⟩,⟨⟨217622452567858381640735242,217622452567858381951684591⟩,⟨(-329454183859859827735378325),(-329454183859859827442120442)⟩⟩,⟨⟨351052184343906018539547184,351052184343906019041282326⟩,⟨(-531021213985451592477773857),(-531021213985451592004316832)⟩⟩,⟨⟨499115216475746477865547776,499115216475746478578292650⟩,⟨(-754075270951602633461686834),(-754075270951602632789052376)⟩⟩,⟨⟨637235451339344762415612709,637235451339344763324530398⟩,⟨(-961197924719543987534719381),(-961197924719543986676869961)⟩⟩,⟨⟨783982155445960966676083876,783982155445960967792492710⟩,⟨(-1180168517784169614281993127),(-1180168517784169613228291541)⟩⟩,⟨⟨924735220695209804377100209,924735220695209805691386538⟩,⟨(-1388695194947131465598012454),(-1388695194947131464357517063)⟩⟩,⟨⟨1071888806465636003883367327,1071888806465636005403251182⟩,⟨(-1605161115664026583320614591),(-1605161115664026581886081186)⟩⟩,⟨⟨1215030212771232995783900465,1215030212771232997502190083⟩,⟨(-1813694339092520912443982502),(-1813694339092520910822202599)⟩⟩,⟨⟨1363497023522419448340443915,1363497023522419450262744238⟩,⟨(-2028006478273828716225979205),(-2028006478273828714411793266)⟩⟩,⟨⟨1509194149754225627503734708,1509194149754225629624470224⟩,⟨(-2235783529102243052816462766),(-2235783529102243050815020451)⟩⟩,⟨⟨1659636895855445335795428317,1659636895855445338119040937⟩,⟨(-2447936219445482036241051410),(-2447936219445482034048250047)⟩⟩,⟨⟨1808194715185831677652806595,1808194715185831680174274408⟩,⟨(-2654416770198902273694997261),(-2654416770198902271315649004)⟩⟩,⟨⟨1961174422985067259713254201,1961174422985067262436126878⟩,⟨(-2864265852138096934877808263),(-2864265852138096932308663456)⟩⟩,⟨⟨2112952253765624868628876839,2112952253765624871549112660⟩,⟨(-3069008905085332610005955847),(-3069008905085332607250711536)⟩⟩,⟨⟨2268976048459290498719251203,2268976048459290501839808966⟩,⟨(-3276347120733813480653479381),(-3276347120733813477709418010)⟩⟩] +lemma amp3_00_0_eq : ∀ k : Fin 16, amp3_0Expr 0 0 k = amp3_00_0 k := by decide +kernel +noncomputable def amp3_00_1 : Fin 16 → CBox := ![⟨⟨2424354699718827723760118645,2424354699718827727077012577⟩,⟨(-3478964236115248132497584203),(-3478964236115248129368549397)⟩⟩,⟨⟨2583894907002060993586227389,2583894907002060997101807044⟩,⟨(-3683553132480533356239636896),(-3683553132480533352923534178)⟩⟩,⟨⟨2743261070260653746962887338,2743261070260653750673491671⟩,⟨(-3883687729396738509951203068),(-3883687729396738506451566511)⟩⟩,⟨⟨2906763572030138482891253611,2906763572030138486799598369⟩,⟨(-4085273230009796544307252043),(-4085273230009796540621276984)⟩⟩,⟨⟨3070501230603920208917739732,3070501230603920213019628316⟩,⟨(-4282590458767819548510950697),(-4282590458767819544643042475)⟩⟩,⟨⟨3238389183974555334534333834,3238389183974555338831474865⟩,⟨(-4480911350149214406044648170),(-4480911350149214401993255724)⟩⟩,⟨⟨3406874261341373944715552803,3406874261341373949205665630⟩,⟨(-4675092805467640808482459814),(-4675092805467640804249405940)⟩⟩,⟨⟨3579549604893755315431881810,3579549604893755320115310255⟩,⟨(-4869885802761709863304755202),(-4869885802761709858890244868)⟩⟩,⟨⟨3753146263507334685785422205,3753146263507334690660028267⟩,⟨(-5060626664353293752384101467),(-5060626664353293747789844555)⟩⟩,⟨⟨3930990088459011907942031768,3930990088459011913009117581⟩,⟨(-5251629681473291206829127705),(-5251629681473291202053920829)⟩⟩,⟨⟨4110047942555296306040209124,4110047942555296311295543545⟩,⟨(-5438637159484464541123877549),(-5438637159484464536172296136)⟩⟩,⟨⟨4293420252680930465125438671,4293420252680930470571097174⟩,⟨(-5625591570337328763379810621),(-5625591570337328758249531979)⟩⟩,⟨⟨4478272126733734337020973948,4478272126733734342652488996⟩,⟨(-5808584090911250858168734005),(-5808584090911250852864638128)⟩⟩,⟨⟨4667511260808256204768880341,4667511260808256210589040701⟩,⟨(-5991236389712338728882194677),(-5991236389712338723400994725)⟩⟩,⟨⟨4858471298017232392825345061,4858471298017232398830634722⟩,⟨(-6169943217786975316300646057),(-6169943217786975310646009285)⟩⟩,⟨⟨5053893166890991937551041605,5053893166890991943742253790⟩,⟨(-6348046302403234890089248843),(-6348046302403234884260434048)⟩⟩] +lemma amp3_00_1_eq : ∀ k : Fin 16, amp3_0Expr 0 1 k = amp3_00_1 k := by decide +kernel +noncomputable def amp3_00_2 : Fin 16 → CBox := ![⟨⟨5251255178759393195043589165,5251255178759393201415984790⟩,⟨(-6522207430371915611148407763),(-6522207430371915605150588683)⟩⟩,⟨⟨5453152406194639424960157115,5453152406194639431516328285⟩,⟨(-6695521637468797321740094534),(-6695521637468797315570236012)⟩⟩,⟨⟨5657188400228982821277538733,5657188400228982828014458945⟩,⟨(-6864887838212671000940858216),(-6864887838212670994602020987)⟩⟩,⟨⟨5865829422271475421139485765,5865829422271475428057532976⟩,⟨(-7033181807190165087652662626),(-7033181807190165081144549670)⟩⟩,⟨⟨6076788270378231111823334734,6076788270378231118920239969⟩,⟨(-7197514788940299674720986237),(-7197514788940299668045759018)⟩⟩,⟨⟨6292416428427336079857423884,6292416428427336087129591529⟩,⟨(-7360566202203180007231649677),(-7360566202203180000393654692)⟩⟩,⟨⟨6510522653335354104240923355,6510522653335354111688776289⟩,⟨(-7519638825309515332278750068),(-7519638825309515325276965374)⟩⟩,⟨⟨6733355304423391470617708205,6733355304423391478240609598⟩,⟨(-7677235055044664138774482062),(-7677235055044664131609734719)⟩⟩,⟨⟨6958807970262681293033588473,6958807970262681300829422225⟩,⟨(-7830831584346860431497188339),(-7830831584346860424171485415)⟩⟩,⟨⟨7189035630872744173324011653,7189035630872744181292621711⟩,⟨(-7982770265394130983127922532),(-7982770265394130975641525554)⟩⟩,⟨⟨7422007329431644344949913958,7422007329431644353088671304⟩,⟨(-8130686640354154042509376613),(-8130686640354154034864893472)⟩⟩,⟨⟨7659792864603087728107209966,7659792864603087736411336793⟩,⟨(-8276776182124073171220009488),(-8276776182124073163422688730)⟩⟩,⟨⟨7900428792156239088616219583,7900428792156239097088190571⟩,⟨(-8418820292296028776709004605),(-8418820292296028768755886619)⟩⟩,⟨⟨8145906658607977460643415125,8145906658607977469282015055⟩,⟨(-8558880338430821671341864323),(-8558880338430821663234336698)⟩⟩,⟨⟨8394323780343831785023425094,8394323780343831793826662241⟩,⟨(-8694872295401433750812483802),(-8694872295401433742552499083)⟩⟩,⟨⟨8647599330288870376347650851,8647599330288870385313296752⟩,⟨(-8828734137087854344824967350),(-8828734137087854336414918541)⟩⟩] +lemma amp3_00_2_eq : ∀ k : Fin 16, amp3_0Expr 0 2 k = amp3_00_2 k := by decide +kernel +noncomputable def amp3_00_3 : Fin 16 → CBox := ![⟨⟨8903885630727711216336507560,8903885630727711225462973127⟩,⟨(-8958506536417053655358428749),(-8958506536417053646799853240)⟩⟩,⟨⟨9165034481603350067396417196,9165034481603350076683162737⟩,⟨(-9086013483402380509402369841),(-9086013483402380500695921192)⟩⟩,⟨⟨9429248300261514707184434870,9429248300261514716629016544⟩,⟨(-9209411651745818270416640787),(-9209411651745818261564759782)⟩⟩,⟨⟨9698315774542769429653489100,9698315774542769439246924394⟩,⟨(-9330419363854674455349746012),(-9330419363854674446361225016)⟩⟩,⟨⟨9970485226636493510078681603,9970485226636493519827037642⟩,⟨(-9447301587616115115851593521),(-9447301587616115106720581695)⟩⟩,⟨⟨10247485865101240460467083427,10247485865101240470368705916⟩,⟨(-9561678368711325856453848692),(-9561678368711325847182085144)⟩⟩,⟨⟨10527608347401967984180144053,10527608347401967994232344740⟩,⟨(-9671916101415044681976772639),(-9671916101415044672566934471)⟩⟩,⟨⟨10812525498589820694884113945,10812525498589820705085492798⟩,⟨(-9779543157160454158771264174),(-9779543157160454149224821514)⟩⟩,⟨⟨11100567280711380220130938337,11100567280711380230479385083⟩,⟨(-9883021203356295250538997350),(-9883021203356295240858097230)⟩⟩,⟨⟨11393352768809079989217967826,11393352768809079999710236619⟩,⟨(-9983792863738742440190387628),(-9983792863738742430378120227)⟩⟩,⟨⟨11689248670271528399919936811,11689248670271528410555461231⟩,⟨(-10080409537723725499993611866),(-10080409537723725490050764654)⟩⟩,⟨⟨11989822543229301142052012275,11989822543229301152828699149⟩,⟨(-10174233445019220168383591664),(-10174233445019220158312223203)⟩⟩,⟨⟨12293475696635137279397319046,12293475696635137290312922575⟩,⟨(-10263900703025054920095386506),(-10263900703025054909897774998)⟩⟩,⟨⟨12601726055946726474872415134,12601726055946726485925564642⟩,⟨(-10350697965712873062694489251),(-10350697965712873052372073821)⟩⟩,⟨⟨12913007756543522219780585544,12913007756543522230968835013⟩,⟨(-10433341510499256421917173677),(-10433341510499256411472415306)⟩⟩,⟨⟨13228790669791017669836311022,13228790669791017681158183919⟩,⟨(-10513046823511369720474190932),(-10513046823511369709908623139)⟩⟩] +lemma amp3_00_3_eq : ∀ k : Fin 16, amp3_0Expr 0 3 k = amp3_00_3 k := by decide +kernel +noncomputable def amp3_00_4 : Fin 16 → CBox := ![⟨⟨13547540311594870245622522554,13547540311594870257060952442⟩,⟨(-10588606180541638411810830599),(-10588606180541638401138346698)⟩⟩,⟨⟨13870679808556787435081987682,13870679808556787446652186824⟩,⟨(-10661167912165665665130839470),(-10661167912165665654339780019)⟩⟩,⟨⟨14196704907083676757244750973,14196704907083676768943529082⟩,⟨(-10729596476738939815392165142),(-10729596476738939804485625675)⟩⟩,⟨⟨14526993059923276494523167275,14526993059923276506348484395⟩,⟨(-10794976722458016741955541666),(-10794976722458016730935536745)⟩⟩,⟨⟨14860069361427849811417876850,14860069361427849823366895184⟩,⟨(-10856241777340714725391252049),(-10856241777340714714260574936)⟩⟩,⟨⟨15197266449213083417770955289,15197266449213083429842672282⟩,⟨(-10914416380884288108103184249),(-10914416380884288096863087250)⟩⟩,⟨⟨15537138126172045882733493900,15537138126172045894923728129⟩,⟨(-10968499084131140282872115770),(-10968499084131140271526346221)⟩⟩,⟨⟨15880972883725075910078804904,15880972883725075922387007658⟩,⟨(-11019457626020161264582748333),(-11019457626020161253132244575)⟩⟩,⟨⟨16227352816129327221643227208,16227352816129327234067031792⟩,⟨(-11066352968805839614689009114),(-11066352968805839603136228951)⟩⟩,⟨⟨16577522766959766581440004951,16577522766959766593973005682⟩,⟨(-11110098722699359165752191719),(-11110098722699359154102073056)⟩⟩,⟨⟨16930092908798811836458039828,16930092908798811849102586705⟩,⟨(-11149815457100347836110631351),(-11149815457100347824362430343)⟩⟩,⟨⟨17286264781638916819697923293,17286264781638916832451421439⟩,⟨(-11186365314284536931012581182),(-11186365314284536919168677598)⟩⟩,⟨⟨17644676611775328026995011107,17644676611775328039855309405⟩,⟨(-11218925851059632488102437637),(-11218925851059632476165155670)⟩⟩,⟨⟨18006486840006223549064758958,18006486840006223562028210268⟩,⟨(-11248310213462072934212941396),(-11248310213462072922185305812)⟩⟩,⟨⟨18370361896448975214334465922,18370361896448975227400388708⟩,⟨(-11273750489980914303389674220),(-11273750489980914291273088459)⟩⟩,⟨⟨18737417199483850463839362413,18737417199483850477004757558⟩,⟨(-11296013132140582259676245732),(-11296013132140582247473315602)⟩⟩] +lemma amp3_00_4_eq : ∀ k : Fin 16, amp3_0Expr 0 4 k = amp3_00_4 k := by decide +kernel +noncomputable def amp3_00_5 : Fin 16 → CBox := ![⟨⟨19106347695878775469539934139,19106347695878775482802667830⟩,⟨(-11314382450704319824346299184),(-11314382450704319812059342226)⟩⟩,⟨⟨19478225741351432862972578429,19478225741351432876330765013⟩,⟨(-11329580351179425885235675724),(-11329580351179425872866626897)⟩⟩,⟨⟨19851775264316154179129267527,19851775264316154192580766831⟩,⟨(-11340941188067103666052121986),(-11340941188067103653603323591)⟩⟩,⟨⟨20228025409711111024350249584,20228025409711111037893006708⟩,⟨(-11349144330817616120560232422),(-11349144330817616108033732683)⟩⟩,⟨⟨20605729695451711990826720993,20605729695451712004458251528⟩,⟨(-11353572116476826259436282831),(-11353572116476826246834624168)⟩⟩,⟨⟨20985873807605189167502184443,20985873807605189181184009594⟩,⟨(-11354863262815097447364022686),(-11354863262815097434708972153)⟩⟩,⟨⟨21367241596063550526594817364,21367241596063550540362494722⟩,⟨(-11352446133696523085361096866),(-11352446133696523072634274378)⟩⟩,⟨⟨21750774946763198887980989382,21750774946763198901831642246⟩,⟨(-11346920565457163538681897052),(-11346920565457163525885833103)⟩⟩,⟨⟨22135288911358198469857938903,22135288911358198483788243938⟩,⟨(-11337759088070144815845349022),(-11337759088070144802983031674)⟩⟩,⟨⟨22521681147073459201268658728,22521681147073459215276554968⟩,⟨(-11325524322708492012738103396),(-11325524322708491999811617373)⟩⟩,⟨⟨22908798897916853146447282134,22908798897916853160529143101⟩,⟨(-11309731190549000397431635268),(-11309731190549000384444086584)⟩⟩,⟨⟨23297495081501631394279663284,23297495081501631408433280946⟩,⟨(-11290906668935665535855188663),(-11290906668935665522808718200)⟩⟩,⟨⟨23686650239791094295829813050,23686650239791094310053812222⟩,⟨(-11268606373009233826122394046),(-11268606373009233813018986988)⟩⟩,⟨⟨24077071961816197272630737509,24077071961816197286921097579⟩,⟨(-11243323120745824197091073147),(-11243323120745824183933742884)⟩⟩,⟨⟨24467675302934313601786725309,24467675302934313616141992940⟩,⟨(-11214651594476165253527200823),(-11214651594476165240317970741)⟩⟩,⟨⟨24859221860129145530877407740,24859221860129145545295916117⟩,⟨(-11183051857613982162382401835),(-11183051857613982149123182989)⟩⟩] +lemma amp3_00_5_eq : ∀ k : Fin 16, amp3_0Expr 0 5 k = amp3_00_5 k := by decide +kernel +noncomputable def amp3_00_6 : Fin 16 → CBox := ![⟨⟨25250662522808687672201857469,25250662522808687686676529365⟩,⟨(-11148156096993299629002438373),(-11148156096993299615697770579)⟩⟩,⟨⟨25642712160920303486974401559,25642712160920303501508431062⟩,⟨(-11110392953092266469127295745),(-11110392953092266455776932029)⟩⟩,⟨⟨26034358919673431879637410848,26034358919673431894225372710⟩,⟨(-11069430612991638099231381846),(-11069430612991638085839090854)⟩⟩,⟨⟨26426270137886539129962722491,26426270137886539144605243857⟩,⟨(-11025667558510627222431284457),(-11025667558510627208998018203)⟩⟩,⟨⟨26817472735739109602942612718,26817472735739109617635467650⟩,⟨(-10978806526128320234414262366),(-10978806526128320220943237170)⟩⟩,⟨⟨27208585649643287135455908425,27208585649643287150197853906⟩,⟨(-10929217041190162853474066695),(-10929217041190162839967050628)⟩⟩,⟨⟨27598676188065708563425092237,27598676188065708578198521771⟩,⟨(-10876634987672294457806878640),(-10876634987672294444272311079)⟩⟩,⟨⟨27988313948006293659992258395,27988313948006293674811236076⟩,⟨(-10821402079296846185361721366),(-10821402079296846171795254229)⟩⟩,⟨⟨28376608330789774161452275579,28376608330789774176312652880⟩,⟨(-10763285990618389579745721432),(-10763285990618389566150468737)⟩⟩,⟨⟨28764078592296864032549881291,28764078592296864047448733122⟩,⟨(-10702601715564881058176376839),(-10702601715564881044554768737)⟩⟩,⟨⟨29149878019988816250825267817,29149878019988816265760886433⟩,⟨(-10639147403809586003452386944),(-10639147403809585989806573202)⟩⟩,⟨⟨29534474462844933437413852449,29534474462844933452382322797⟩,⟨(-10573212372214930100684160214),(-10573212372214930087016912586)⟩⟩,⟨⟨29917066974230152110840603828,29917066974230152125840182072⟩,⟨(-10504623968440219221972158678),(-10504623968440219208285620218)⟩⟩,⟨⟨30298070866611623240724570321,30298070866611623255754251638⟩,⟨(-10433646829482808453324371833),(-10433646829482808439620272602)⟩⟩,⟨⟨30676732923606948321093228002,30676732923606948336142587951⟩,⟨(-10360136259400063451264453444),(-10360136259400063437547885643)⟩⟩,⟨⟨31053414727617214672599308114,31053414727617214687673186814⟩,⟨(-10284333170258724890554299752),(-10284333170258724876824980394)⟩⟩] +lemma amp3_00_6_eq : ∀ k : Fin 16, amp3_0Expr 0 6 k = amp3_00_6 k := by decide +kernel +noncomputable def amp3_00_7 : Fin 16 → CBox := ![⟨⟨31427412839837072289501841559,31427412839837072304596708695⟩,⟨(-10206119614000527248144567030),(-10206119614000527234405215445)⟩⟩,⟨⟨31799033854642245716716124041,31799033854642245731830875258⟩,⟨(-10125713693415573147518445945),(-10125713693415573133770834534)⟩⟩,⟨⟨32167626239791013884435541891,32167626239791013899563194214⟩,⟨(-10043023030699348461219502838),(-10043023030699348447467392923)⟩⟩,⟨⟨32533440278469252242030042057,32533440278469252257171996337⟩,⟨(-9958243798476948516965344760),(-9958243798476948503209707222)⟩⟩,⟨⟨32895878554624100162639876798,32895878554624100177790789698⟩,⟨(-9871308040509020999060635824),(-9871308040509020985304652410)⟩⟩,⟨⟨33255133650751022774645002047,33255133650751022789805806438⟩,⟨(-9782390844341318630321969306),(-9782390844341318616566791570)⟩⟩,⟨⟨33610664556515969068219416186,33610664556515969083385364377⟩,⟨(-9691447553836554543433846787),(-9691447553836554529682427040)⟩⟩,⟨⟨33962604696428565046123541631,33962604696428565061292538286⟩,⟨(-9598632984837958467540761701),(-9598632984837958453795145741)⟩⟩,⟨⟨34310471834867213830030095310,34310471834867213845199703188⟩,⟨(-9503924685557910385144293230),(-9503924685557910371406719650)⟩⟩,⟨⟨34654338711478692785907708244,34654338711478692801076305532⟩,⟨(-9407457983942729223786589095),(-9407457983942729210058963291)⟩⟩,⟨⟨34993784313669635288173367002,34993784313669635303337298220⟩,⟨(-9309231561179438222135939137),(-9309231561179438208420798844)⟩⟩,⟨⟨35328819097647587460808753285,35328819097647587475966199047⟩,⟨(-9209362013527415745451094149),(-9209362013527415731750386629)⟩⟩,⟨⟨35659085801652974328499348950,35659085801652974343646687696⟩,⟨(-9107868106980742805450184482),(-9107868106980742791766391994)⟩⟩,⟨⟨35984530925723178373203282474,35984530925723178388338101533⟩,⟨(-9004848436555031112127104794),(-9004848436555031098462300691)⟩⟩,⟨⟨36304863566717623080744552304,36304863566717623095863427492⟩,⟨(-8900340827068535315731242449),(-8900340827068535302087798882)⟩⟩,⟨⟨36619964518815973814481808667,36619964518815973829581331312⟩,⟨(-8794426578665159395025178173),(-8794426578665159381405382606)⟩⟩] +lemma amp3_00_7_eq : ∀ k : Fin 16, amp3_0Expr 0 7 k = amp3_00_7 k := by decide +kernel +noncomputable def amp3_00_8 : Fin 16 → CBox := ![⟨⟨36929611926089865217377037055,36929611926089865232458648298⟩,⟨(-8687161570299088864332594686),(-8687161570299088850737619240)⟩⟩,⟨⟨37233619047055274848258243661,37233619047055274863323994280⟩,⟨(-8578610491117965259619079250),(-8578610491117965246049943958)⟩⟩,⟨⟨37531835843583857272187223619,37531835843583857287233463886⟩,⟨(-8468846290047854265179464002),(-8468846290047854251638563114)⟩⟩,⟨⟨37824006125065671192154783783,37824006125065671207178536685⟩,⟨(-8357917708082895483174666820),(-8357917708082895469664188012)⟩⟩,⟨⟨38110054525322969648798969596,38110054525322969663797471410⟩,⟨(-8245913799818552238260706755),(-8245913799818552224782792291)⟩⟩,⟨⟨38389653403567465010405582659,38389653403567465025375720596⟩,⟨(-8132868001268293355030588555),(-8132868001268293341587408582)⟩⟩,⟨⟨38662805005262343430399656391,38662805005262343445339422867⟩,⟨(-8018884527690609895936020429),(-8018884527690609882529499687)⟩⟩,⟨⟨38929108146444252381915281076,38929108146444252396821390894⟩,⟨(-7903982134891120306758249303),(-7903982134891120293390565295)⟩⟩,⟨⟨39188645711864622814243368664,39188645711864622829113922265⟩,⟨(-7788279272603138590792016709),(-7788279272603138577465042609)⟩⟩,⟨⟨39440940784641322484223494213,39440940784641322499056759640⟩,⟨(-7671780623981725294739833051),(-7671780623981725281455394974)⟩⟩,⟨⟨39686160007311778554365521059,39686160007311778569159265536⟩,⟨(-7554617965465760297889354631),(-7554617965465760284649348695)⟩⟩,⟨⟨39923748438299769345515038878,39923748438299769360264641992⟩,⟨(-7436782499007134092202051994),(-7436782499007134079008838397)⟩⟩,⟨⟨40153959690687680843936340886,40153959690687680858643146588⟩,⟨(-7318418438071501440977941741),(-7318418438071501427832716762)⟩⟩,⟨⟨40376158398593158126177912766,40376158398593158140836665341⟩,⟨(-7199504079777677731838589034),(-7199504079777677718743780405)⟩⟩,⟨⟨40590688456638496505964757395,40590688456638496520577698454⟩,⟨(-7080195202764724614012101263),(-7080195202764724600968728616)⟩⟩,⟨⟨40796831560816104771881325301,40796831560816104786440919677⟩,⟨(-6960457761575989126820439887),(-6960457761575989113831292164)⟩⟩] +lemma amp3_00_8_eq : ∀ k : Fin 16, amp3_0Expr 0 8 k = amp3_00_8 k := by decide +kernel +noncomputable def amp3_00_9 : Fin 16 → CBox := ![⟨⟨40995025301110911682909314837,40995025301110911697414494395⟩,⟨(-6840458245787715443737090713),(-6840458245787715430803742617)⟩⟩,⟨⟨41184465800377021984138198068,41184465800377021998585929390⟩,⟨(-6720150816414533794609359299),(-6720150816414533781733749727)⟩⟩,⟨⟨41365687865881404978577327733,41365687865881404992974905795⟩,⟨(-6599711837193156478144160001),(-6599711837193156465326479038)⟩⟩,⟨⟨41537799283470313583135805839,41537799283470313597470751141⟩,⟨(-6479084212287986025637985854),(-6479084212287986012881692079)⟩⟩,⟨⟨41701435713723056434320788471,41701435713723056448592342925⟩,⟨(-6358453360166392023831730792),(-6358453360166392011138274518)⟩⟩,⟨⟨41855613704346172107303466023,41855613704346172121511106280⟩,⟨(-6237751453240013999842488448),(-6237751453240013987213368408)⟩⟩,⟨⟨42001073526209366456807908080,42001073526209366470946933639⟩,⟨(-6117172162551223588994768318),(-6117172162551223576431979043)⟩⟩,⟨⟨42136737441258510891120480411,42136737441258510905190343062⟩,⟨(-5996637443010511057731925001),(-5996637443010511045236961105)⟩⟩,⟨⟨42263454216326920810956825340,42263454216326920824954059868⟩,⟨(-5876348433316097794472306332),(-5876348433316097782046943693)⟩⟩,⟨⟨42380048623353053881213188511,42380048623353053895133755066⟩,⟨(-5756217374969136681296105743),(-5756217374969136668942275104)⟩⟩,⟨⟨42487481948260072363871563782,42487481948260072377738553511⟩,⟨(-5636452106634096250365575995),(-5636452106634096238081431532)⟩⟩,⟨⟨42584478100957778796829903963,42584478100957778810618484947⟩,⟨(-5516955650974356824316460591),(-5516955650974356812106753694)⟩⟩,⟨⟨42672115056920672303946300878,42672115056920672317655670968⟩,⟨(-5397941796180264759275652747),(-5397941796180264747141702344)⟩⟩,⟨⟨42749012311956280094680374003,42749012311956280108306297361⟩,⟨(-5279304831724161777256455308),(-5279304831724161765200148630)⟩⟩,⟨⟨42816368860023784911794113937,42816368860023784925339067761⟩,⟨(-5161263762173697564307887690),(-5161263762173697552330082569)⟩⟩,⟨⟨42872696037160660008403789116,42872696037160660021861391207⟩,⟨(-5043704621085468728623224010),(-5043704621085468716726052410)⟩⟩] +lemma amp3_00_9_eq : ∀ k : Fin 16, amp3_0Expr 0 9 k = amp3_00_9 k := by decide +kernel +noncomputable def amp3_00_10 : Fin 16 → CBox := ![⟨⟨42919318355755731012158975925,42919318355755731025536126125⟩,⟨(-4926850913609606528042599626),(-4926850913609606516226420293)⟩⟩,⟨⟨42954635037853696227851704187,42954635037853696241139324527⟩,⟨(-4810580886804078377537347228),(-4810580886804078365804536411)⟩⟩,⟨⟨42980100799343156696075592610,42980100799343156709272452184⟩,⟨(-4695121848038555028842772689),(-4695121848038555017194557514)⟩⟩,⟨⟨42993998568939656954256979438,42993998568939656967363576387⟩,⟨(-4580344719906157497881519511),(-4580344719906157486319183306)⟩⟩,⟨⟨42997918152110508834558727845,42997918152110508847569482214⟩,⟨(-4466479931156336033311197453),(-4466479931156336021836414815)⟩⟩,⟨⟨42990021761428578102481217495,42990021761428578115396971280⟩,⟨(-4353391535005783241311162786),(-4353391535005783229925136957)⟩⟩,⟨⟨42972039396907675037960182662,42972039396907675050778785159⟩,⟨(-4241312418368850890284436189),(-4241312418368850878988404641)⟩⟩,⟨⟨42942007868279380512976154043,42942007868279380525694132016⟩,⟨(-4130100213631344503063066780),(-4130100213631344491858671820)⟩⟩,⟨⟨42901802714098938094554201164,42901802714098938107169433686⟩,⟨(-4019989620392040585146295406),(-4019989620392040574034744404)⟩⟩,⟨⟨42849330367942142009048786497,42849330367942142021558481981⟩,⟨(-3910832292576797924060512628),(-3910832292576797913043308159)⟩⟩,⟨⟨42786617512628098972395336517,42786617512628098984795817017⟩,⟨(-3802864114837687655298438842),(-3802864114837687644376834520)⟩⟩,⟨⟨42711434920268362588785859236,42711434920268362601154630505⟩,⟨(-3695931199172180287710591039),(-3695931199172180276879131746)⟩⟩,⟨⟨42625966311011907572140492831,42625966311011907584401206333⟩,⟨(-3590270005622009717661620648),(-3590270005622009706928007159)⟩⟩,⟨⟨42527841169799341078113991359,42527841169799341090265605687⟩,⟨(-3485721535251655946621830523),(-3485721535251655935987373492)⟩⟩,⟨⟨42419406463464054155585292551,42419406463464054167625826676⟩,⟨(-3382522231915680833638621545),(-3382522231915680823104332660)⟩⟩,⟨⟨42298144391795944933370804833,42298144391795944945299880471⟩,⟨(-3280508411477009121317474419),(-3280508411477009110884622362)⟩⟩] +lemma amp3_00_10_eq : ∀ k : Fin 16, amp3_0Expr 0 10 k = amp3_00_10 k := by decide +kernel +noncomputable def amp3_00_11 : Fin 16 → CBox := ![⟨⟨42166571726714147619339210109,42166571726714147631155025275⟩,⟨(-3179915928231531522895579247),(-3179915928231531512565155067)⟩⟩,⟨⟨42022016976737183258206692865,42022016976737183269909162449⟩,⟨(-3080576833550168289727976575),(-3080576833550168279501173327)⟩⟩,⟨⟨41867173663459559944976973431,41867173663459559956561883796⟩,⟨(-2982725837119988778800993534),(-2982725837119988768678885135)⟩⟩,⟨⟨41699209749389120247206019129,41699209749389120258676541229⟩,⟨(-2886191141720374771779433791),(-2886191141720374761763009271)⟩⟩,⟨⟨41521002878771966926497012600,41521002878771966937847159684⟩,⟨(-2791205775812629721853266594),(-2791205775812629711943696746)⟩⟩,⟨⟨41329553118928773515275204570,41329553118928773526504872537⟩,⟨(-2697594504860290117617302142),(-2697594504860290107815756376)⟩⟩,⟨⟨41127930086174088476241230362,41127930086174088487346864866⟩,⟨(-2605588158021350742044137227),(-2605588158021350732351517323)⟩⟩,⟨⟨40912958056998651180217837207,40912958056998651191210564110⟩,⟨(-2515008470250995165393846169),(-2515008470250995155810647321)⟩⟩,⟨⟨40687907000504772066374581784,40687907000504772077241101384⟩,⟨(-2426083571964919961827231338),(-2426083571964919952354958426)⟩⟩,⟨⟨40449416900965345872626024885,40449416900965345883365798814⟩,⟨(-2338632570078793035934620996),(-2338632570078793026574429953)⟩⟩,⟨⟨40200967055101451276409663282,40200967055101451287024219928⟩,⟨(-2252880415556413301238333600),(-2252880415556413291990717118)⟩⟩,⟨⟨39939003980058891777084947383,39939003980058891787568832681⟩,⟨(-2168643985507320740131949559),(-2168643985507320730998374479)⟩⟩,⟨⟨39667225941247487813988366517,39667225941247487824341686351⟩,⟨(-2086144589544568124212816066),(-2086144589544568115193837442)⟩⟩,⟨⟨39381876062477065827160011380,39381876062477065837380957402⟩,⟨(-2005197269047037025604828972),(-2005197269047037016701654089)⟩⟩,⟨⟨39086881968257398517646070362,39086881968257398527731928500⟩,⟨(-1926019249259763436007633701),(-1926019249259763427220874388)⟩⟩,⟨⟨38778272621949003793950366479,38778272621949003803898091294⟩,⟨(-1848424125801029975289718275),(-1848424125801029966620655333)⟩⟩] +lemma amp3_00_11_eq : ∀ k : Fin 16, amp3_0Expr 0 11 k = amp3_00_11 k := by decide +kernel +noncomputable def amp3_00_12 : Fin 16 → CBox := ![⟨⟨38460216243005038067921030428,38460216243005038077777606053⟩,⟨(-1772624615471496378434231070),(-1772624615471496369881166808)⟩⟩,⟨⟨38128515922663753399885492681,38128515922663753409608485011⟩,⟨(-1698433254021623118109557881),(-1698433254021623109675603351)⟩⟩,⟨⟨37787592668138201568727605720,37787592668138201578315725096⟩,⟨(-1626057844719219440222283203),(-1626057844719219431907879043)⟩⟩,⟨⟨37433010921879802180608828179,37433010921879802190061313279⟩,⟨(-1555310245266803044476196773),(-1555310245266803036282510851)⟩⟩,⟨⟨37069457758667848376850954642,37069457758667848386166548294⟩,⟨(-1486392959332582247388264625),(-1486392959332582239315717283)⟩⟩,⟨⟨36692244989938961249596475227,36692244989938961258775188672⟩,⟨(-1419117544299396716130018944),(-1419117544299396708179703913)⟩⟩,⟨⟨36306340277071639356122983507,36306340277071639365161236111⟩,⟨(-1353680837210838834049074095),(-1353680837210838826221404858)⟩⟩,⟨⟨35906787447809543941892137695,35906787447809543950795205564⟩,⟨(-1289894468725546306983798249),(-1289894468725546299279710568)⟩⟩,⟨⟨35498850687510697370041120778,35498850687510697378801304153⟩,⟨(-1227949261284789804987673483),(-1227949261284789797407717059)⟩⟩,⟨⟨35077288922676154674582439356,35077288922676154683200210984⟩,⟨(-1167657288222717651989962769),(-1167657288222717644535195479)⟩⟩,⟨⟨34647680430227238035022637694,34647680430227238043496128803⟩,⟨(-1109203028438482895385481371),(-1109203028438482888056125210)⟩⟩,⟨⟨34204480522472212094327325803,34204480522472212102654893581⟩,⟨(-1052399363061589161372684075),(-1052399363061589154169916266)⟩⟩,⟨⟨33753601017671970427439501572,33753601017671970435617947379⟩,⟨(-997424117522348583058504846),(-997424117522348575982557495)⟩⟩,⟨⟨33289172830610727878179035367,33289172830610727886237643584⟩,⟨(-944091341481054278604030216),(-944091341481054271655157652)⟩⟩,⟨⟨32817462954408717995090342665,32817462954408718003000270811⟩,⟨(-892571915944851595032428020),(-892571915944851588211517969)⟩⟩,⟨⟨32332254722500828539867955992,32332254722500828547628358126⟩,⟨(-842681415331583230243901715),(-842681415331583223552111436)⟩⟩] +lemma amp3_00_12_eq : ∀ k : Fin 16, amp3_0Expr 0 12 k = amp3_00_12 k := by decide +kernel +noncomputable def amp3_00_13 : Fin 16 → CBox := ![⟨⟨31840194483367027696259435183,31840194483367027703870474443⟩,⟨(-794583504186444007964943551),(-794583504186444001402296145)⟩⟩,⟨⟨31334692005730726056703819251,31334692005730726064168042397⟩,⟨(-748095633259677210263927061),(-748095633259677203831455889)⟩⟩,⟨⟨30822800161573188408827237319,30822800161573188416138417426⟩,⟨(-703373997437957607155982129),(-703373997437957600853747864)⟩⟩,⟨⟨30297525886035927469803469005,30297525886035927476962462561⟩,⟨(-660238270565454976157263636),(-660238270565454969986403690)⟩⟩,⟨⟨29766359269103985856635634722,29766359269103985863639425806⟩,⟨(-618836943425914630291373748),(-618836943425914624251830982)⟩⟩,⟨⟨29221871261330109932783737294,29221871261330109939650931175⟩,⟨(-578992254726878450547921582),(-578992254726878444640460993)⟩⟩,⟨⟨28672024055703603213530336155,28672024055703603220243827844⟩,⟨(-540844775349904472221779465),(-540844775349904466446527595)⟩⟩,⟨⟨28108914846118349605307171821,28108914846118349611865418260⟩,⟨(-504219645448085496190617494),(-504219645448085490548800166)⟩⟩,⟨⟨27541017830326309971544375341,27541017830326309977947719114⟩,⟨(-469249318722501110998952606),(-469249318722501105490307493)⟩⟩,⟨⟨26959913128480904308757320100,26959913128480904315006511959⟩,⟨(-435762167956083815229742518),(-435762167956083809855433067)⟩⟩,⟨⟨26374632899886217331847088806,26374632899886217337940224621⟩,⟨(-403882350770507067762327638),(-403882350770507062522004121)⟩⟩,⟨⟨25776190161419290676842874455,25776190161419290682791404148⟩,⟨(-373441798139992529767012847),(-373441798139992524661764464)⟩⟩,⟨⟨25174228364824610569317961319,25174228364824610575106881449⟩,⟨(-344556210927922265720706455),(-344556210927922260750327934)⟩⟩,⟨⟨24559135189546464316094945029,24559135189546464321724430256⟩,⟨(-317061398000412773494189060),(-317061398000412768659930411)⟩⟩,⟨⟨23941227780934638855653888865,23941227780934638861125261263⟩,⟨(-291064460826259378984506275),(-291064460826259374285793971)⟩⟩,⟨⟨23310200110631642068973562344,23310200110631642074283703396⟩,⟨(-266405399753673130612707483),(-266405399753673126050913528)⟩⟩] +lemma amp3_00_13_eq : ∀ k : Fin 16, amp3_0Expr 0 13 k = amp3_00_13 k := by decide +kernel +noncomputable def amp3_00_14 : Fin 16 → CBox := ![⟨⟨22677116699534118856591101736,22677116699534118861750531358⟩,⟨(-243182592066960783604469607),(-243182592066960779178872319)⟩⟩,⟨⟨22030896768952754478381928367,22030896768952754483380174239⟩,⟨(-221240536816929516059643711),(-221240536816929511771701320)⟩⟩,⟨⟨21383440102110633499162028462,21383440102110633504001069160⟩,⟨(-200668779944004751986551277),(-200668779944004747835486644)⟩⟩,⟨⟨20722794073015559522415074549,20722794073015559527089769866⟩,⟨(-181316619785693729402698728),(-181316619785693725390009062)⟩⟩,⟨⟨20061799751985878424652028208,20061799751985878429172820889⟩,⟨(-163264681172595941822223527),(-163264681172595937946978090)⟩⟩,⟨⟨19387514922600583543947672314,19387514922600583548305310973⟩,⟨(-146367355405605195730915458),(-146367355405605191994686352)⟩⟩,⟨⟨18713851496227712879370716581,18713851496227712883571715106⟩,⟨(-130696273572377451327031903),(-130696273572377447728772192)⟩⟩,⟨⟨18026732916713064960376157270,18026732916713064964412429918⟩,⟨(-116111206435427031261660639),(-116111206435427027803042265)⟩⟩,⟨⟨17341302569582749714301491290,17341302569582749718174821185⟩,⟨(-102674735551117056200857829),(-102674735551117052880760632)⟩⟩,⟨⟨16642168789751721057670900957,16642168789751721061383747189⟩,⟨(-90252290198623873158932506),(-90252290198623869979026807)⟩⟩,⟨⟨15945908985863070529756500364,15945908985863070533305023556⟩,⟨(-78897363137513937587562993),(-78897363137513934546564100)⟩⟩,⟨⟨15235586477600848862732503184,15235586477600848866118952936⟩,⟨(-68481313526766473682243892),(-68481313526766470781992265)⟩⟩,⟨⟨14529473166332548087854598592,14529473166332548091080504531⟩,⟨(-59048522219791196779414798),(-59048522219791194018434650)⟩⟩,⟨⟨13808788625619452981414052479,13808788625619452984472958204⟩,⟨(-50476541709763958452961824),(-50476541709763955833266143)⟩⟩,⟨⟨13093842083524598544136438601,13093842083524598547033465490⟩,⟨(-42800633560112771301560795),(-42800633560112768821412571)⟩⟩,⟨⟨12363611164030934045904280875,12363611164030934048636545837⟩,⟨(-35904798986054577734042527),(-35904798986054575395664471)⟩⟩] +lemma amp3_00_14_eq : ∀ k : Fin 16, amp3_0Expr 0 14 k = amp3_00_14 k := by decide +kernel +noncomputable def amp3_00_15 : Fin 16 → CBox := ![⟨⟨11640906474730461962572873640,11640906474730461965141782231⟩,⟨(-29815188073350490189105844),(-29815188073350487990534254)⟩⟩,⟨⟨10901916162184254397909670804,10901916162184254400312071191⟩,⟨(-24422498031291935494609526),(-24422498031291933438291749)⟩⟩,⟨⟨10172602315072406991961159149,10172602315072406994199400654⟩,⟨(-19743789781400820022501047),(-19743789781400818106108313)⟩⟩,⟨⟨9425581176452244331087970377,9425581176452244333160366502⟩,⟨(-15676695838757779009302131),(-15676695838757777235643005)⟩⟩,⟨⟨8690917343933110757377513942,8690917343933110759286551866⟩,⟨(-12229223778246479324636582),(-12229223778246477690966290)⟩⟩,⟨⟨7936480653240993684446399260,7936480653240993686187948164⟩,⟨(-9306173334082597076115566),(-9306173334082595585686394)⟩⟩,⟨⟨7197909971989378770682309162,7197909971989378772259667529⟩,⟨(-6906546457326445131676078),(-6906546457326443781140812)⟩⟩,⟨⟨6436446914697699141603313597,6436446914697699143013282174⟩,⟨(-4942536047449003418675457),(-4942536047449002211956700)⟩⟩,⟨⟨5695762752695653296827050540,5695762752695653298073431626⟩,⟨(-3404195131147991971493444),(-3404195131147990904410941)⟩⟩,⟨⟨4927169374622884835837248698,4927169374622884836914520281⟩,⟨(-2211333236794332094342684),(-2211333236794331171815318)⟩⟩,⟨⟨4186952203246164132054724400,4186952203246164132969110381⟩,⟨(-1345113899161042552920708),(-1345113899161041769405798)⟩⟩,⟨⟨3409858307668758867012087301,3409858307668758867756100470⟩,⟨(-733193241686198609961153),(-733193241686197972143026)⟩⟩,⟨⟨2674938742797905265923153042,2674938742797905266505846131⟩,⟨(-347891772871139455992406),(-347891772871138955827660)⟩⟩,⟨⟨1883617619535721157099388512,1883617619535721157509135196⟩,⟨(-124974050225334936890890),(-124974050225334584780491)⟩⟩,⟨⟨1168594191641463783116387234,1168594191641463783368951200⟩,⟨(-27910132336248271722006),(-27910132336248053313938)⟩⟩,⟨⟨332022702301807070784197607,332022702301807070854991242⟩,⟨(-881064552150306116751),(-881064552150244067690)⟩⟩] +lemma amp3_00_15_eq : ∀ k : Fin 16, amp3_0Expr 0 15 k = amp3_00_15 k := by decide +kernel +noncomputable def amp3_00 : Fin 16 → Fin 16 → CBox := ![amp3_00_0,amp3_00_1,amp3_00_2,amp3_00_3,amp3_00_4,amp3_00_5,amp3_00_6,amp3_00_7,amp3_00_8,amp3_00_9,amp3_00_10,amp3_00_11,amp3_00_12,amp3_00_13,amp3_00_14,amp3_00_15] +lemma amp3_00_eq (i k : Fin 16) : amp3_0Expr 0 i k = amp3_00 i k := by + fin_cases i + · exact amp3_00_0_eq k + · exact amp3_00_1_eq k + · exact amp3_00_2_eq k + · exact amp3_00_3_eq k + · exact amp3_00_4_eq k + · exact amp3_00_5_eq k + · exact amp3_00_6_eq k + · exact amp3_00_7_eq k + · exact amp3_00_8_eq k + · exact amp3_00_9_eq k + · exact amp3_00_10_eq k + · exact amp3_00_11_eq k + · exact amp3_00_12_eq k + · exact amp3_00_13_eq k + · exact amp3_00_14_eq k + · exact amp3_00_15_eq k +noncomputable def amp3_01_0 : Fin 16 → CBox := ![⟨⟨(-21200997748146017699919933),(-21200997748146017602695084)⟩,⟨(-79126252864372438589919292),(-79126252864372438492196027)⟩⟩,⟨⟨(-74602058010201874215986980),(-74602058010201873873560483)⟩,⟨(-278515354377778841026058144),(-278515354377778840681288044)⟩⟩,⟨⟨(-120192360892399083894727815),(-120192360892399083342565935)⟩,⟨(-448996920341323834450844485),(-448996920341323833894456015)⟩⟩,⟨⟨(-170566322030367127619187733),(-170566322030367126834904895)⟩,⟨(-637767312329780873928642890),(-637767312329780873138239158)⟩⟩,⟨⟨(-217224648705536777248230791),(-217224648705536776248222738)⟩,⟨(-813233281518097449357314040),(-813233281518097448349334546)⟩⟩,⟨⟨(-266416875503616319392352343),(-266416875503616318164127607)⟩,⟨(-998940926603876334554342678),(-998940926603876333316246096)⟩⟩,⟨⟨(-313075681733514035373306836),(-313075681733514033927489855)⟩,⟨(-1176074633880924902149234150),(-1176074633880924900691674146)⟩⟩,⟨⟨(-361317038189751186285775610),(-361317038189751184613848445)⟩,⟨(-1360246022016509627898744976),(-1360246022016509626213168440)⟩⟩,⟨⟨(-407533556144932433966597805),(-407533556144932432076504655)⟩,⟨(-1538057384426956147352069059),(-1538057384426956145446448459)⟩⟩,⟨⟨(-454777932959963232205556135),(-454777932959963230090991797)⟩,⟨(-1721179330705583989550104091),(-1721179330705583987418255621)⟩⟩,⟨⟨(-500254512323635366786344064),(-500254512323635364453648385)⟩,⟨(-1899212786784745670270351304),(-1899212786784745667918421177)⟩⟩,⟨⟨(-546376569734763781782275489),(-546376569734763779226490703)⟩,⟨(-2081468392157442828310587254),(-2081468392157442825733668730)⟩⟩,⟨⟨(-590867651307883323413327830),(-590867651307883320639931700)⟩,⟨(-2259453762604975884753500660),(-2259453762604975881957176851)⟩⟩,⟨⟨(-635712588277230058564210067),(-635712588277230055569214486)⟩,⟨(-2440906172532428504352846231),(-2440906172532428501333200341)⟩⟩,⟨⟨(-678997202608834479886174955),(-678997202608834476674272872)⟩,⟨(-2618654073209206334476114861),(-2618654073209206331237591874)⟩⟩,⟨⟨(-722398204945136251243327519),(-722398204945136247811234546)⟩,⟨(-2799309645312332414901263036),(-2799309645312332411440594704)⟩⟩] +lemma amp3_01_0_eq : ∀ k : Fin 16, amp3_0Expr 1 0 k = amp3_01_0 k := by decide +kernel +noncomputable def amp3_01_1 : Fin 16 → CBox := ![⟨⟨(-764269745960762456455224313),(-764269745960762452807282593)⟩,⟨(-2976671394772112287588680757),(-2976671394772112283910301596)⟩⟩,⟨⟨(-806055577633586231143172967),(-806055577633586227276696206)⟩,⟨(-3156506113297329184458864254),(-3156506113297329180560191100)⟩⟩,⟨⟨(-846317475743604405122465305),(-846317475743604401041443909)⟩,⟨(-3333355688471934095198517928),(-3333355688471934091083621694)⟩⟩,⟨⟨(-886316364241138486805947839),(-886316364241138482507918485)⟩,⟨(-3512327784120728350769186078),(-3512327784120728346434995470)⟩⟩,⟨⟨(-924780146848747180601031740),(-924780146848747176089960403)⟩,⟨(-3688552722665358540565024059),(-3688552722665358536016283358)⟩⟩,⟨⟨(-962822056073484330581050574),(-962822056073484325855062836)⟩,⟨(-3866609314988946013024195563),(-3866609314988946008259013256)⟩⟩,⟨⟨(-999306496545248707701089971),(-999306496545248702763430654)⟩,⟨(-4042105721687455211390456057),(-4042105721687455206411293668)⟩⟩,⟨⟨(-1035224616365930060506128792),(-1035224616365930055355573745)⟩,⟨(-4219186582780116880162424351),(-4219186582780116874968992049)⟩⟩,⟨⟨(-1069555423906068117946617965),(-1069555423906068112586263458)⟩,⟨(-4393856201276870416949081734),(-4393856201276870411543694655)⟩⟩,⟨⟨(-1103187243654037577229610666),(-1103187243654037571658173338)⟩,⟨(-4569896015953293288372098877),(-4569896015953293282753320514)⟩⟩,⟨⟨(-1135197038961059699235742015),(-1135197038961059693456824173)⟩,⟨(-4743644418268419810234586971),(-4743644418268419804407186296)⟩⟩,⟨⟨(-1166385182190926885972925106),(-1166385182190926879985222493)⟩,⟨(-4918574206876960898349005158),(-4918574206876960892310635669)⟩⟩,⟨⟨(-1195913630143822122581902867),(-1195913630143822116388998042)⟩,⟨(-5091309624611818770621976239),(-5091309624611818764377654192)⟩⟩,⟨⟨(-1224506542255692818585687363),(-1224506542255692812186275516)⟩,⟨(-5265057674610481451699431280),(-5265057674610481445246014781)⟩⟩,⟨⟨(-1251400572213454711428179402),(-1251400572213454704825532545)⟩,⟨(-5436690217042848181133634338),(-5436690217042848174475056027)⟩⟩,⟨⟨(-1277253110866572788164356120),(-1277253110866572781357872636)⟩,⟨(-5609182713831998275654557502),(-5609182713831998268789953379)⟩⟩] +lemma amp3_01_1_eq : ∀ k : Fin 16, amp3_0Expr 1 1 k = amp3_01_1 k := by decide +kernel +noncomputable def amp3_01_2 : Fin 16 → CBox := ![⟨⟨(-1301367184982554882549211806),(-1301367184982554875542413197)⟩,⟨(-5779623829225898714910275402),(-5779623829225898707844903000)⟩⟩,⟨⟨(-1324341141703506711309447855),(-1324341141703506704101435607)⟩,⟨(-5950785296248705977044642137),(-5950785296248705969775652632)⟩⟩,⟨⟨(-1345537547514930533039734308),(-1345537547514930525633572723)⟩,⟨(-6119947391728407401746666433),(-6119947391728407394277431687)⟩⟩,⟨⟨(-1365502117203263490484500695),(-1365502117203263482879992880)⟩,⟨(-6289701006026611590483475301),(-6289701006026611582813607147)⟩⟩,⟨⟨(-1383651269610054827816204079),(-1383651269610054820016213171)⟩,⟨(-6457497174238602904773461732),(-6457497174238602896905517487)⟩⟩,⟨⟨(-1400483478008096273355012885),(-1400483478008096265360370553)⟩,⟨(-6625764998716732354585811559),(-6625764998716732346523613820)⟩⟩,⟨⟨(-1415464220912164478956642329),(-1415464220912164470769579948)⟩,⟨(-6792108818572694585533258123),(-6792108818572694577276500860)⟩⟩,⟨⟨(-1429049316205043880221274722),(-1429049316205043871842081522)⟩,⟨(-6958811977487692958792654190),(-6958811977487692950342033479)⟩⟩,⟨⟨(-1440749217200764372623334963),(-1440749217200764364054814209)⟩,⟨(-7123617367739239387015614638),(-7123617367739239378373531706)⟩⟩,⟨⟨(-1450981029550553093376645524),(-1450981029550553084619106002)⟩,⟨(-7288676182929682779768504777),(-7288676182929682770935173806)⟩⟩,⟨⟨(-1459296663011229587736699719),(-1459296663011229578793049900)⟩,⟨(-7451857294425257010291177274),(-7451857294425257001269536902)⟩⟩,⟨⟨(-1466077934364034267347151114),(-1466077934364034258218702657)⟩,⟨(-7615191394130827675191497001),(-7615191394130827665986376008)⟩⟩,⟨⟨(-1470915149533975723631760859),(-1470915149533975714320422560)⟩,⟨(-7776662531125120375858617862),(-7776662531125120366467843175)⟩⟩,⟨⟨(-1474157835113469808082103606),(-1474157835113469798588614645)⟩,⟨(-7938190939589940633485074678),(-7938190939589940623909949640)⟩⟩,⟨⟨(-1475432006660776880841891415),(-1475432006660776871169043778)⟩,⟨(-8097866503423670619529278978),(-8097866503423670609772126328)⟩⟩,⟨⟨(-1475057548970374029685870944),(-1475057548970374019834674474)⟩,⟨(-8257507717059530609882218908),(-8257507717059530599945312393)⟩⟩] +lemma amp3_01_2_eq : ∀ k : Fin 16, amp3_0Expr 1 2 k = amp3_01_2 k := by decide +kernel +noncomputable def amp3_01_3 : Fin 16 → CBox := ![⟨⟨(-1472693808039142884009823409),(-1472693808039142873983001983)⟩,⟨(-8415302167490874789340294395),(-8415302167490874779225567835)⟩⟩,⟨⟨(-1468633383815857725813927156),(-1468633383815857715612298651)⟩,⟨(-8572974221743745261105996214),(-8572974221743745250814122916)⟩⟩,⟨⟨(-1462566828032877797614516572),(-1462566828032877787240964346)⟩,⟨(-8728802052545642371235637369),(-8728802052545642360769387968)⟩⟩,⟨⟨(-1454761568354611433996492083),(-1454761568354611423453203623)⟩,⟨(-8884422582484511334373569926),(-8884422582484511323741382635)⟩⟩,⟨⟨(-1444937449552986827917001906),(-1444937449552986817205553719)⟩,⟨(-9038198308842333557242875536),(-9038198308842333546439655262)⟩⟩,⟨⟨(-1433338633151167608324583278),(-1433338633151167597446153943)⟩,⟨(-9191684605700923131913366516),(-9191684605700923120940856982)⟩⟩,⟨⟨(-1419712521808274073051198469),(-1419712521808274062008720248)⟩,⟨(-9343322761589903388412961087),(-9343322761589903377274158175)⟩⟩,⟨⟨(-1404281741549902620462124295),(-1404281741549902609256817395)⟩,⟨(-9494591826929396455624237436),(-9494591826929396444320654223)⟩⟩,⟨⟨(-1386819667123227711167736988),(-1386819667123227699802464710)⟩,⟨(-9644006971109064371854331652),(-9644006971109064360388451063)⟩⟩,⟨⟨(-1367528969581152227047642418),(-1367528969581152215523929636)⟩,⟨(-9792975569862268416258392463),(-9792975569862268404633335773)⟩⟩,⟨⟨(-1346207536078227035800395407),(-1346207536078227024120924757)⟩,⟨(-9940082299453919853497632449),(-9940082299453919841714553634)⟩⟩,⟨⟨(-1323039534093113965869588255),(-1323039534093113954035819175)⟩,⟨(-10086667012811142042634478264),(-10086667012811142030695510223)⟩⟩,⟨⟨(-1297846010341133856674433071),(-1297846010341133844689266221)⟩,⟨(-10231379983662703703468827637),(-10231379983662703691376580127)⟩⟩,⟨⟨(-1270793968484442832606434058),(-1270793968484442820471321161)⟩,⟨(-10375497262535287454483964113),(-10375497262535287442239977008)⟩⟩,⟨⟨(-1241726352678157536246242065),(-1241726352678157523964117750)⟩,⟨(-10517731215752051200089525020),(-10517731215752051187696587939)⟩⟩,⟨⟨(-1210794245546516211837826995),(-1210794245546516199410229300)⟩,⟨(-10659297435379377069302108014),(-10659297435379377056761868318)⟩⟩] +lemma amp3_01_3_eq : ∀ k : Fin 16, amp3_0Expr 1 3 k = amp3_01_3 k := by decide +kernel +noncomputable def amp3_01_4 : Fin 16 → CBox := ![⟨⟨(-1177861303754219812246050061),(-1177861303754219799677197170)⟩,⟨(-10798967229527006706940029787),(-10798967229527006694266933654)⟩⟩,⟨⟨(-1143063847057745735703457837),(-1143063847057745722993450935)⟩,⟨(-10937898745661799643461618412),(-10937898745661799630643930908)⟩⟩,⟨⟨(-1106285125457925322812242647),(-1106285125457925309964116404)⟩,⟨(-11074919394242342494076025286),(-11074919394242342481117167131)⟩⟩,⟨⟨(-1067647779905278893264234186),(-1067647779905278880279722939)⟩,⟨(-11211132601246841563653892636),(-11211132601246841550556019659)⟩⟩,⟨⟨(-1027053590612907733616558301),(-1027053590612907720498666690)⟩,⟨(-11345419315118104392306033086),(-11345419315118104379072266369)⟩⟩,⟨⟨(-984612538642019962687263357),(-984612538642019949437711977)⟩,⟨(-11478830706222580019998454833),(-11478830706222580006630173448)⟩⟩,⟨⟨(-940243919065148521300984728),(-940243919065148507922866721)⟩,⟨(-11610298940682518603286892816),(-11610298940682518589788229595)⟩⟩,⟨⟨(-894046014519051207951966112),(-894046014519051194447037237)⟩,⟨(-11740825170592413323764594412),(-11740825170592413310136606271)⟩⟩,⟨⟨(-845954660264327093797623268),(-845954660264327080168873726)⟩,⟨(-11869390676887742887492290135),(-11869390676887742873737745845)⟩⟩,⟨⟨(-796057351165117017366186083),(-796057351165117003615730920)⟩,⟨(-11996948626872484301857235978),(-11996948626872484287981498769)⟩⟩,⟨⟨(-744305522585891425653453243),(-744305522585891411784044675)⟩,⟨(-12122527507917913660470151630),(-12122527507917913646472555381)⟩⟩,⟨⟨(-690776747215659335448823513),(-690776747215659321462447438)⟩,⟨(-12247034353470363552277466838),(-12247034353470363538160624905)⟩⟩,⟨⟨(-635437149768916191039897526),(-635437149768916176939548445)⟩,⟨(-12369543123584179458219842042),(-12369543123584179443986376937)⟩⟩,⟨⟨(-578355206323740700917570056),(-578355206323740686705309397)⟩,⟨(-12490916404702645337422621771),(-12490916404702645323075886760)⟩⟩,⟨⟨(-519510844972550448635266512),(-519510844972550434314041402)⟩,⟨(-12610272053177684426777178457),(-12610272053177684412318779872)⟩⟩,⟨⟨(-458964235113816235291753293),(-458964235113816220863648879)⟩,⟨(-12728429747290870360381124018),(-12728429747290870345813966279)⟩⟩] +lemma amp3_01_4_eq : ∀ k : Fin 16, amp3_0Expr 1 4 k = amp3_01_4 k := by decide +kernel +noncomputable def amp3_01_5 : Fin 16 → CBox := ![⟨⟨(-396708243080582518600764528),(-396708243080582504068784867)⟩,⟨(-12844549805628615342743406884),(-12844549805628615328070103201)⟩⟩,⟨⟨(-332795489766457429998903714),(-332795489766457415365145416)⟩,⟨(-12959410403156659925702345604),(-12959410403156659910925063860)⟩⟩,⟨⟨(-267230932009016914886265692),(-267230932009016900153737149)⟩,⟨(-13072213015797350206446838440),(-13072213015797350191568216818)⟩⟩,⟨⟨(-200060372047518438831903508),(-200060372047518424002754995)⟩,⟨(-13183695598318310301044297578),(-13183695598318310286066633618)⟩⟩,⟨⟨(-131300023895232526774309858),(-131300023895232511851560929)⟩,⟨(-13293099596702383272317515502),(-13293099596702383257243671198)⟩⟩,⟨⟨(-60989575718594466809236943),(-60989575718594451795180891)⟩,⟨(-13401123917672504875816823625),(-13401123917672504860672381877)⟩⟩,⟨⟨10844322831049753537548240,10844322831049768640459605⟩,⟨(-13507048897469016402054177492),(-13507048897469016386817490143)⟩⟩,⟨⟨84167415613325553465003490,84167415613325568656479022⟩,⟨(-13611535465426379731280452901),(-13611535465426379715954392755)⟩⟩,⟨⟨158943429375429815254516031,158943429375429830531619689⟩,⟨(-13713901866762786061276435493),(-13713901866762786045864392679)⟩⟩,⟨⟨235142878030640283086842411,235142878030640298447392746⟩,⟨(-13814772030927031152041083054),(-13814772030927031136545427326)⟩⟩,⟨⟨312720669268858314714703809,312720669268858330155761520⟩,⟨(-13913501221452239911945555248),(-13913501221452239896369848302)⟩⟩,⟨⟨391651442932367429960262407,391651442932367445479596201⟩,⟨(-14010677259617772602004665193),(-14010677259617772586351359056)⟩⟩,⟨⟨471882086469988755187061090,471882086469988770781764230⟩,⟨(-14105691620226997972056669159),(-14105691620226997956327943648)⟩⟩,⟨⟨553390737349356881229481910,553390737349356896897260421⟩,⟨(-14199096828833113773362764111),(-14199096828833113757562177227)⟩⟩,⟨⟨636117057419228702914582672,636117057419228718652544185⟩,⟨(-14290319841879049270287876782),(-14290319841879049254417663011)⟩⟩,⟨⟨720042067433924783636889244,720042067433924799442757419⟩,⟨(-14379878628127616734196296844),(-14379878628127616718258627600)⟩⟩] +lemma amp3_01_5_eq : ∀ k : Fin 16, amp3_0Expr 1 5 k = amp3_01_5 k := by decide +kernel +noncomputable def amp3_01_6 : Fin 16 → CBox := ![⟨⟨805098995476766742173563144,805098995476766758044284813⟩,⟨(-14467234967937969473781818339),(-14467234967937969457782159369)⟩⟩,⟨⟨891271143504906018550291802,891271143504906034483719839⟩,⟨(-14552872943817548128217326935),(-14552872943817548112155080097)⟩⟩,⟨⟨978486096073492376590332850,978486096073492392583473781⟩,⟨(-14636288569334225184319086779),(-14636288569334225168198754746)⟩⟩,⟨⟨1066728844927581710098041527,1066728844927581726148658066⟩,⟨(-14717932647398650188262593151),(-14717932647398650172085090826)⟩⟩,⟨⟨1155922120804361321660037742,1155922120804361337765178087⟩,⟨(-14797334896748985696169640801),(-14797334896748985679938756379)⟩⟩,⟨⟨1246052023010540689329011361,1246052023010540705486359065⟩,⟨(-14874913387488450472798571478),(-14874913387488450456516306580)⟩⟩,⟨⟨1337037218598631681814143592,1337037218598631698020105956⟩,⟨(-14950231074293923365654649180),(-14950231074293923349332016274)⟩⟩,⟨⟨1428864340008512022423151448,1428864340008512038676099720⟩,⟨(-15023673784927369925052265433),(-15023673784927369908682918902)⟩⟩,⟨⟨1521448782010739726450164433,1521448782010739742747163241⟩,⟨(-15094837296150380144061207292),(-15094837296150380127648837658)⟩⟩,⟨⟨1614777142231782612783214862,1614777142231782629121833390⟩,⟨(-15164075630659516504905887296),(-15164075630659516488453432205)⟩⟩,⟨⟨1708762336589618497859303836,1708762336589618514236755400⟩,⟨(-15231017025784040875075983019),(-15231017025784040858585822427)⟩⟩,⟨⟨1803390365179201671387222753,1803390365179201687800990158⟩,⟨(-15295984086001509223904494203),(-15295984086001509207380064626)⟩⟩,⟨⟨1898572461203197760063416033,1898572461203197776510721007⟩,⟨(-15358637197338913607711084477),(-15358637197338913591154754787)⟩⟩,⟨⟨1994293468533173428851389459,1994293468533173445329889415⟩,⟨(-15419267884896003685018310084),(-15419267884896003668432033474)⟩⟩,⟨⟨2090463737118857202814099458,2090463737118857219320465138⟩,⟨(-15477568418803002351839496611),(-15477568418803002335230044394)⟩⟩,⟨⟨2187066398781639937967004221,2187066398781639954499262234⟩,⟨(-15533799537735820911078225975),(-15533799537735820894444571944)⟩⟩] +lemma amp3_01_6_eq : ∀ k : Fin 16, amp3_0Expr 1 6 k = amp3_01_6 k := by decide +kernel +noncomputable def amp3_01_7 : Fin 16 → CBox := ![⟨⟨2284011723569921219158541123,2284011723569921235713834196⟩,⟨(-15587685176527596004722273301),(-15587685176527595988067656877)⟩⟩,⟨⟨2381280577164033967128724502,2381280577164033983704696403⟩,⟨(-15639455536334749133662857516),(-15639455536334749116989313110)⟩⟩,⟨⟨2478783957473054949107151424,2478783957473054965700708024⟩,⟨(-15688866040672614625739782269),(-15688866040672614609052226782)⟩⟩,⟨⟨2576499910575701802030146856,2576499910575701818639104215⟩,⟨(-15736116559612223251081478270),(-15736116559612223234380699644)⟩⟩,⟨⟨2674340974901806321837672332,2674340974901806338459062050⟩,⟨(-15780993871141975077281801327),(-15780993871141975060571850246)⟩⟩,⟨⟨2772281823008508023267549668,2772281823008508039899172681⟩,⟨(-15823667679551215991481670978),(-15823667679551215974763612893)⟩⟩,⟨⟨2870237351867682602707898445,2870237351867682619346860975⟩,⟨(-15863956023565484579207961201),(-15863956023565484562485541340)⟩⟩,⟨⟨2968178305054376167374788294,2968178305054376184018632226⟩,⟨(-15901998566981822800742196982),(-15901998566981822784017914409)⟩⟩,⟨⟨3066022761912183573860424247,3066022761912183590506459339⟩,⟨(-15937644554877363152619657656),(-15937644554877363135896106002)⟩⟩,⟨⟨3163736978953513799994617720,3163736978953513816640442080⟩,⟨(-15971003696737210719139095644),(-15971003696737210702418580984)⟩⟩,⟨⟨3261243047971253813086642448,3261243047971253829729494864⟩,⟨(-16001956428036152262195404111),(-16001956428036152245481080980)⟩⟩,⟨⟨3358502176630126844424060367,3358502176630126861061509490⟩,⟨(-16030582551723848861305367684),(-16030582551723848844599608122)⟩⟩,⟨⟨3455441305937765933624408132,3455441305937765950253707543⟩,⟨(-16056793715426502911375074136),(-16056793715426502894680959069)⟩⟩,⟨⟨3552016028125640371193112340,3552016028125640387811784035⟩,⟨(-16080639825444260655559862585),(-16080639825444260638880043986)⟩⟩,⟨⟨3648158977317992707069707279,3648158977317992723675056226⟩,⟨(-16102063800480165327718351266),(-16102063800480165311055798513)⟩⟩,⟨⟨3743819557812891021281431533,3743819557812891037870867325⟩,⟨(-16121085622507949048313429792),(-16121085622507949031671201773)⟩⟩] +lemma amp3_01_7_eq : ∀ k : Fin 16, amp3_0Expr 1 7 k = amp3_01_7 k := by decide +kernel +noncomputable def amp3_01_8 : Fin 16 → CBox := ![⟨⟨3838936948354641362817718907,3838936948354641379389058615⟩,⟨(-16137679577051435078777440417),(-16137679577051435062156305442)⟩⟩,⟨⟨3933453785754504362437804620,3933453785754504378989060179⟩,⟨(-16151835656664655978607241033),(-16151835656664655962007922602)⟩⟩,⟨⟨4027316652971965576413020257,4027316652971965592941549934⟩,⟨(-16163559646081355368198464826),(-16163559646081355351623998421)⟩⟩,⟨⟨4120460831554768152912519445,4120460831554768169415803559⟩,⟨(-16172811445893734334551526012),(-16172811445893734318004796316)⟩⟩,⟨⟨4212841176887782018269592486,4212841176887782034745098082⟩,⟨(-16179628509085138229297987627),(-16179628509085138212781580882)⟩⟩,⟨⟨4304385018046793801396449133,4304385018046793817841654465⟩,⟨(-16183940504084139283966998604),(-16183940504084139267483859145)⟩⟩,⟨⟨4395056360232925789125784557,4395056360232925805538283292⟩,⟨(-16185816757998551649066513855),(-16185816757998551632618891396)⟩⟩,⟨⟨4484773972155641969365650392,4484773972155641985742893782⟩,⟨(-16185156528841388494966025492),(-16185156528841388478556896911)⟩⟩,⟨⟨4573511896020794182440829385,4573511896020794198780442692⟩,⟨(-16182061260921426031216858918),(-16182061260921426014848365373)⟩⟩,⟨⟨4661179720283377521818982790,4661179720283377538118621329⟩,⟨(-16176399584960796696888247936),(-16176399584960796680562739184)⟩⟩,⟨⟨4747762421818147138668919923,4747762421818147154926225109⟩,⟨(-16168305343299959970907131112),(-16168305343299959954626886982)⟩⟩,⟨⟨4833159775573701691592150106,4833159775573701707804426148⟩,⟨(-16157616283110355843540204493),(-16157616283110355827308709387)⟩⟩,⟨⟨4917368601983236252608609811,4917368601983236268773954498⟩,⟨(-16144498964094147615820820846),(-16144498964094147599638845494)⟩⟩,⟨⟨5000278214431857732784314040,5000278214431857748899974477⟩,⟨(-16128759953271801593017137067),(-16128759953271801576888425974)⟩⟩,⟨⟨5081898197858587690111156830,5081898197858587706175406243⟩,⟨(-16110598886482400915814751157),(-16110598886482400899739729243)⟩⟩,⟨⟨5162106739699877459684832542,5162106739699877475694625113⟩,⟨(-16089790812494670876305748305),(-16089790812494670860289013667)⟩⟩] +lemma amp3_01_8_eq : ∀ k : Fin 16, amp3_0Expr 1 8 k = amp3_01_8 k := by decide +kernel +noncomputable def amp3_01_9 : Fin 16 → CBox := ![⟨⟨5240927123333318055485906351,5240927123333318071439123612⟩,⟨(-16066568842662290268337938479),(-16066568842662290252381161279)⟩⟩,⟨⟨5318225727917871553439688760,5318225727917871569333872937⟩,⟨(-16040676126525502160352335006),(-16040676126525502144458333396)⟩⟩,⟨⟨5394040483223651217283194910,5394040483223651233117380415⟩,⟨(-16012379692314264404927163013),(-16012379692314264389094373628)⟩⟩,⟨⟨5468225258138892840675896396,5468225258138892856446398001⟩,⟨(-15981390364882745000239903861),(-15981390364882744984474768036)⟩⟩,⟨⟨5540833591960248515620712698,5540833591960248531325543693⟩,⟨(-15948009574304220345756835233),(-15948009574304220330060845190)⟩⟩,⟨⟨5611706119807830348194501835,5611706119807830363831562049⟩,⟨(-15911915348957411213996636141),(-15911915348957411198371610656)⟩⟩,⟨⟨5680912970116970099798971395,5680912970116970115365808017⟩,⟨(-15873444051210860005363710313),(-15873444051210859989812639360)⟩⟩,⟨⟨5748280797263719413255420011,5748280797263719428749933010⟩,⟨(-15832240392729996313848055835),(-15832240392729996298372728941)⟩⟩,⟨⟨5813897316367642392816187731,5813897316367642408236110757⟩,⟨(-15788676246274872394478991072),(-15788676246274872379081846672)⟩⟩,⟨⟨5877574428479661447829287878,5877574428479661463172076003⟩,⟨(-15742362435705703716186091674),(-15742362435705703700870243659)⟩⟩,⟨⟨5939418452515192712822988811,5939418452515192728090140397⟩,⟨(-15693706972379097960983558085),(-15693706972379097945741610868)⟩⟩,⟨⟨5999225735715103696687316271,5999225735715103711873402036⟩,⟨(-15642286167682489963551025624),(-15642286167682489948393766737)⟩⟩,⟨⟨6057122239300989959145710421,6057122239300989974248926357⟩,⟨(-15588544852681940994621887969),(-15588544852681940979550692703)⟩⟩,⟨⟨6112887925821387949096980887,6112887925821387964114780139⟩,⟨(-15532024144979888148279717893),(-15532024144979888133297722758)⟩⟩,⟨⟨6166669460771249635183215762,6166669460771249650114328141⟩,⟨(-15473206432540371793241737679),(-15473206432540371778349120906)⟩⟩,⟨⟨6218229558013077279105354134,6218229558013077293946924412⟩,⟨(-15411596897770927507796174433),(-15411596897770927492996799045)⟩⟩] +lemma amp3_01_9_eq : ∀ k : Fin 16, amp3_0Expr 1 9 k = amp3_01_9 k := by decide +kernel +noncomputable def amp3_01_10 : Fin 16 → CBox := ![⟨⟨6267736675051758997765037393,6267736675051759012516476263⟩,⟨(-15347716282373875292280254886),(-15347716282373875277572653549)⟩⟩,⟨⟨6314935376994437578560803144,6314935376994437593218898371⟩,⟨(-15281033028174715444632303444),(-15281033028174715430021320920)⟩⟩,⟨⟨6360017029461777969772651055,6360017029461777984335699224⟩,⟨(-15212107091136628374397950219),(-15212107091136628359885032731)⟩⟩,⟨⟨6402707109412398758761006716,6402707109412398773227192794⟩,⟨(-15140369298783346707089907654),(-15140369298783346692676421153)⟩⟩,⟨⟨6443221037982585866811330863,6443221037982585881178339228⟩,⟨(-15066419750081994075472582706),(-15066419750081994061161437626)⟩⟩,⟨⟨6481264221694148960198822949,6481264221694148974464927185⟩,⟨(-14989650711313712738136478382),(-14989650711313712723928937612)⟩⟩,⟨⟨6517077319185573876592132862,6517077319185573890755593705⟩,⟨(-14910703426521076364159317628),(-14910703426521076350057071704)⟩⟩,⟨⟨6550344637419011234557515204,6550344637419011248615960003⟩,⟨(-14828930575092458565633911314),(-14828930575092458551639683115)⟩⟩,⟨⟨6581333292818818854743413750,6581333292818818868695132812⟩,⟨(-14745015627295552460263718685),(-14745015627295552446379097567)⟩⟩,⟨⟨6609705412470190915192177026,6609705412470190929034936474⟩,⟨(-14658270565100727833621673393),(-14658270565100727819849159622)⟩⟩,⟨⟨6635755833349495755779067466,6635755833349495769510984833⟩,⟨(-14569422251704259005591477155),(-14569422251704258991933179833)⟩⟩,⟨⟨6659123366312126129611733375,6659123366312126143243085458⟩,⟨(-14477740769324397539671351098),(-14477740769324397526102483733)⟩⟩,⟨⟨6680131878862065305063728795,6680131878862065318581401082⟩,⟨(-14383997633643022517155333547),(-14383997633643022503702681043)⟩⟩,⟨⟨6698395667843274547163695163,6698395667843274560565761227⟩,⟨(-14287419725175177246501825333),(-14287419725175177233167254880)⟩⟩,⟨⟨6714268993818673761367355465,6714268993818673774652303211⟩,⟨(-14188824572737963391039516414),(-14188824572737963377824475676)⟩⟩,⟨⟨6727340374381965541141093906,6727340374381965554307105806⟩,⟨(-14087394444768172425134144014),(-14087394444768172412040234044)⟩⟩] +lemma amp3_01_10_eq : ∀ k : Fin 16, amp3_0Expr 1 10 k = amp3_01_10 k := by decide +kernel +noncomputable def amp3_01_11 : Fin 16 → CBox := ![⟨⟨6737995884298379448635102076,6737995884298379461680725859⟩,⟨(-13983994354273938485685653065),(-13983994354273938472714175223)⟩⟩,⟨⟨6745796922454165569920806903,6745796922454165582844316702⟩,⟨(-13877760428862221630548045650),(-13877760428862221617700537341)⟩⟩,⟨⟨6751162864445427386194534328,6751162864445427398994166919⟩,⟨(-13769606757741895740257038208),(-13769606757741895727535593200)⟩⟩,⟨⟨6753626569166360598566007660,6753626569166360611240560058⟩,⟨(-13658621669290438629861673698),(-13658621669290438617266704516)⟩⟩,⟨⟨6753642272973576355086555802,6753642272973576367634013082⟩,⟨(-13545770053851676385716150172),(-13545770053851676373250248505)⟩⟩,⟨⟨6750712783063954818245140679,6750712783063954830663806258⟩,⟨(-13430090639729840613380359551),(-13430090639729840601045031524)⟩⟩,⟨⟨6745328838693188032097954335,6745328838693188044386274047⟩,⟨(-13312600989880204635944133292),(-13312600989880204623741148030)⟩⟩,⟨⟨6736961583495307968280728546,6736961583495307980438855863⟩,⟨(-13192288274680628021502333818),(-13192288274680628009429530897)⟩⟩,⟨⟨6726139994150162344935451791,6726139994150162356960266747⟩,⟨(-13070224763249050483400812703),(-13070224763249050471463023041)⟩⟩,⟨⟨6712301827623456976826751854,6712301827623456988716527578⟩,⟨(-12945343936547491352178168805),(-12945343936547491340377023905)⟩⟩,⟨⟨6696016136590598284339414764,6696016136590598296093550880⟩,⟨(-12818774983250052356459870506),(-12818774983250052344795410714)⟩⟩,⟨⟨6676685444351346263653797642,6676685444351346275269744676⟩,⟨(-12689395370737127193182452498),(-12689395370737127181657826321)⟩⟩,⟨⟨6654920835592035192840958668,6654920835592035204317920815⟩,⟨(-12558393620863077473564596828),(-12558393620863077462180217838)⟩⟩,⟨⟨6630087614551658169655657678,6630087614551658180991722947⟩,⟨(-12424588648707795332120560423),(-12424588648707795320878430814)⟩⟩,⟨⟨6602840986831060890741323724,6602840986831060901935298786⟩,⟨(-12289230946636141847227817832),(-12289230946636141836129225311)⟩⟩,⟨⟨6572506897118696865164212059,6572506897118696876213969107⟩,⟨(-12151078098928051689611482243),(-12151078098928051678658766888)⟩⟩] +lemma amp3_01_11_eq : ∀ k : Fin 16, amp3_0Expr 1 11 k = amp3_01_11 k := by decide +kernel +noncomputable def amp3_01_12 : Fin 16 → CBox := ![⟨⟨6539786911587757504311241717,6539786911587757515224070019⟩,⟨(-12011445456625111886367744728),(-12011445456625111875546569286)⟩⟩,⟨⟨6503965300486807038386064180,6503965300486807049153201478⟩,⟨(-11869026225722510368195246236),(-11869026225722510357520336314)⟩⟩,⟨⟨6465792401719725018443923903,6465792401719725029064542630⟩,⟨(-11725203786418223869424806093),(-11725203786418223858896906697)⟩⟩,⟨⟨6424508299387027295434091284,6424508299387027305906480799⟩,⟨(-11578603616002317788205077157),(-11578603616002317777825802457)⟩⟩,⟨⟨6380914709972157429068552473,6380914709972157439391936804⟩,⟨(-11430680613299923015429375337),(-11430680613299923005199376895)⟩⟩,⟨⟨6334204796740548248272465012,6334204796740548258445294279⟩,⟨(-11279988833896564209375565478),(-11279988833896564199296243741)⟩⟩,⟨⟨6285234485625599929689282661,6285234485625599939710459962⟩,⟨(-11128058546639388556749524409),(-11128058546639388546822222681)⟩⟩,⟨⟨6233147030713438125590608766,6233147030713438135459489361⟩,⟨(-10973368303317580916875512153),(-10973368303317580907099981675)⟩⟩,⟨⟨6178855655619645349223552571,6178855655619645358938367980⟩,⟨(-10817528006622082771774947012),(-10817528006622082762153694190)⟩⟩,⟨⟨6121450427081258559461059660,6121450427081258569020360523⟩,⟨(-10658936178507251034458738332),(-10658936178507251024993018610)⟩⟩,⟨⟨6061905251429144046163738449,6061905251429144055566853837⟩,⟨(-10499287091478479200538739266),(-10499287091478479191229255899)⟩⟩,⟨⟨5999253397173679849427648518,5999253397173679858672743104⟩,⟨(-10336894202622095036334810057),(-10336894202622095027183416210)⟩⟩,⟨⟨5934533182109937821242691576,5934533182109937830328911517⟩,⟨(-10173541433403865861067281983),(-10173541433403865852074990693)⟩⟩,⟨⟨5866717081786807391787384158,5866717081786807400718360369⟩,⟨(-10007451554420563647699424716),(-10007451554420563638858814061)⟩⟩,⟨⟨5796911954074452375153161896,5796911954074452383923618704⟩,⟨(-9840504043408363517692121164),(-9840504043408363509011904612)⟩⟩,⟨⟨5724025041563033591284994246,5724025041563033599893238189⟩,⟨(-9670824683114651293517029436),(-9670824683114651284998815050)⟩⟩] +lemma amp3_01_12_eq : ∀ k : Fin 16, amp3_0Expr 1 12 k = amp3_01_12 k := by decide +kernel +noncomputable def amp3_01_13 : Fin 16 → CBox := ![⟨⟨5649236338304962618476988437,5649236338304962626922897586⟩,⟨(-9500395145389383200865994292),(-9500395145389383192509656037)⟩⟩,⟨⟨5571382894442604311691878628,5571382894442604319974382583⟩,⟨(-9327237131436671787533577186),(-9327237131436671779339757476)⟩⟩,⟨⟨5491722985866013013655505664,5491722985866013021773445279⟩,⟨(-9153441999783160948453315106),(-9153441999783160940423770635)⟩⟩,⟨⟨5409017900884565058352463203,5409017900884565066304439936⟩,⟨(-8976919346946421927663024199),(-8976919346946421919798863840)⟩⟩,⟨⟨5324609992740546781196867223,5324609992740546788982353931⟩,⟨(-8799878717233028385555343029),(-8799878717233028377857268687)⟩⟩,⟨⟨5237178497632684818029359437,5237178497632684825650145259⟩,⟨(-8620108481557367653350262588),(-8620108481557367645814185268)⟩⟩,⟨⟨5148156415191852926844309772,5148156415191852934297445096⟩,⟨(-8439946062817799884832768366),(-8439946062817799877463516014)⟩⟩,⟨⟨5056133780857354070834357910,5056133780857354078117993816⟩,⟨(-8257048179182731776507283995),(-8257048179182731769306696342)⟩⟩,⟨⟨4962641737053548566921329277,4962641737053548574035706237⟩,⟨(-8073891251526697331277683664),(-8073891251526697324245326402)⟩⟩,⟨⟨4866172939526522693198317894,4866172939526522700142001481⟩,⟨(-7887988351277483150182518169),(-7887988351277483143319609779)⟩⟩,⟨⟨4768365290585439101400203581,4768365290585439108173139686⟩,⟨(-7701967735867611915805288432),(-7701967735867611909112014101)⟩⟩,⟨⟨4667604639830390448973413215,4667604639830390455576063729⟩,⟨(-7513184939854719585725514953),(-7513184939854719579199960769)⟩⟩,⟨⟨4565645632825386015472379974,4565645632825386021902403648⟩,⟨(-7324434986785622827721795076),(-7324434986785622821367862575)⟩⟩,⟨⟨4460756361378034508490555804,4460756361378034514746356027⟩,⟨(-7132899667243141772127110199),(-7132899667243141765946221241)⟩⟩,⟨⟨4354819879751416835443132114,4354819879751416841525438057⟩,⟨(-6941558269502167806468273420),(-6941558269502167800459506846)⟩⟩,⟨⟨4245973685653209031840979034,4245973685653209037747545721⟩,⟨(-6747399771356555783849487594),(-6747399771356555778015228059)⟩⟩] +lemma amp3_01_13_eq : ∀ k : Fin 16, amp3_0Expr 1 13 k = amp3_01_13 k := by decide +kernel +noncomputable def amp3_01_14 : Fin 16 → CBox := ![⟨⟨4136243001104005919404805451,4136243001104005925138133824⟩,⟨(-6553608416552974936693086158),(-6553608416552974931029631446)⟩⟩,⟨⟨4023619536781975775105500478,4023619536781975780661977546⟩,⟨(-6356957724447011215024231126),(-6356957724447011209536165734)⟩⟩,⟨⟨3910287079510016523436009171,3910287079510016528816716501⟩,⟨(-6160861601363098392472126958),(-6160861601363098387158152844)⟩⟩,⟨⟨3794073373886888806657374120,3794073373886888811859593361⟩,⟨(-5961850931998991715925795734),(-5961850931998991710788963116)⟩⟩,⟨⟨3677340538784555431778587903,3677340538784555436805071881⟩,⟨(-5763599117434207260518467611),(-5763599117434207255554916517)⟩⟩,⟨⟨3557730332926508849182956109,3557730332926508854030175854⟩,⟨(-5562361406207675359922953796),(-5562361406207675355136996502)⟩⟩,⟨⟨3437807348312835884452138533,3437807348312835889122286063⟩,⟨(-5362107171159859921363512456),(-5362107171159859916752324485)⟩⟩,⟨⟨3315000313463928715611601394,3315000313463928720101262205⟩,⟨(-5158775404641295805586802656),(-5158775404641295801154405762)⟩⟩,⟨⟨3192106213901878725323380395,3192106213901878729634026499⟩,⟨(-4956676701445121832532302823),(-4956676701445121828277068342)⟩⟩,⟨⟨3066307001327064535731658477,3066307001327064539861723587⟩,⟨(-4751383017782577121178552193),(-4751383017782577117101598007)⟩⟩,⟨⟨2940669771791629928804869355,2940669771791629932754987166⟩,⟨(-4547603248732651622587361604),(-4547603248732651618688536474)⟩⟩,⟨⟨2812086809666075324589181851,2812086809666075328357606442⟩,⟨(-4340477676223076927197010036),(-4340477676223076923477579534)⟩⟩,⟨⟨2683943814481260424089536384,2683943814481260427678094253⟩,⟨(-4135186914051686845164872192),(-4135186914051686841622958225)⟩⟩,⟨⟨2552787704241245727271165425,2552787704241245730676351757⟩,⟨(-3926355522928479237421088147),(-3926355522928479234060593394)⟩⟩,⟨⟨2422386601048110150423103871,2422386601048110153647665700⟩,⟨(-3719732484985923619684406572),(-3719732484985923616502234960)⟩⟩,⟨⟨2288867844092956757005889564,2288867844092956760046768680⟩,⟨(-3509314543367761261629527615),(-3509314543367761258628725898)⟩⟩] +lemma amp3_01_14_eq : ∀ k : Fin 16, amp3_0Expr 1 14 k = amp3_01_14 k := by decide +kernel +noncomputable def amp3_01_15 : Fin 16 → CBox := ![⟨⟨2156468356005109232477241316,2156468356005109235336787510⟩,⟨(-3301549883160338009927996139),(-3301549883160338007106250512)⟩⟩,⟨⟨2020793891701713701117742896,2020793891701713703792593545⟩,⟨(-3089653229522617471629666090),(-3089653229522617468990349438)⟩⟩,⟨⟨1886671179096717444669316714,1886671179096717447162377017⟩,⟨(-2880955267010668282352086764),(-2880955267010668279892316592)⟩⟩,⟨⟨1749038661238240341296700718,1749038661238240343604517904⟩,⟨(-2667668272751396451400677311),(-2667668272751396449123699210)⟩⟩,⟨⟨1613489887008430526563554369,1613489887008430528689530942⟩,⟨(-2458273575721273439988992615),(-2458273575721273437891462684)⟩⟩,⟨⟨1474077279626811779220781611,1474077279626811781160533863⟩,⟨(-2243650032411292437272226433),(-2243650032411292435358516966)⟩⟩,⟨⟨1337435151873991548442048867,1337435151873991550199778684⟩,⟨(-2033844578275865447360638977),(-2033844578275865445626627552)⟩⟩,⟨⟨1196379539691389894244900931,1196379539691389895815693503⟩,⟨(-1817872262152470696626119775),(-1817872262152470695076516891)⟩⟩,⟨⟨1059043066974508924351405950,1059043066974508925740478985⟩,⟨(-1608038679975637953701779691),(-1608038679975637952331502928)⟩⟩,⟨⟨916390748773486729418384875,916390748773486730619313564⟩,⟨(-1390564433741657781207598588),(-1390564433741657780022977153)⟩⟩,⟨⟨778906364526569702815902415,778906364526569703835829693⟩,⟨(-1181305541838949028957806263),(-1181305541838949027951796076)⟩⟩,⟨⟨634468744668161749732949247,634468744668161750563193995⟩,⟨(-961817692572005302255607585),(-961817692572005301436740348)⟩⟩,⟨⟨497802445934328672610365515,497802445934328673261321612⟩,⟨(-754369343679912895133551083),(-754369343679912894491588155)⟩⟩,⟨⟨350580594428963539712185647,350580594428963540170378199⟩,⟨(-531126854482823632324981672),(-531126854482823631873169761)⟩⟩,⟨⟨217517133608356368411296891,217517133608356368695216474⟩,⟨(-329477776279697422146610334),(-329477776279697421866800976)⟩⟩,⟨⟨61803751110521223876605046,61803751110521223957087941⟩,⟨(-93607064644523402017901496),(-93607064644523401938678469)⟩⟩] +lemma amp3_01_15_eq : ∀ k : Fin 16, amp3_0Expr 1 15 k = amp3_01_15 k := by decide +kernel +noncomputable def amp3_01 : Fin 16 → Fin 16 → CBox := ![amp3_01_0,amp3_01_1,amp3_01_2,amp3_01_3,amp3_01_4,amp3_01_5,amp3_01_6,amp3_01_7,amp3_01_8,amp3_01_9,amp3_01_10,amp3_01_11,amp3_01_12,amp3_01_13,amp3_01_14,amp3_01_15] +lemma amp3_01_eq (i k : Fin 16) : amp3_0Expr 1 i k = amp3_01 i k := by + fin_cases i + · exact amp3_01_0_eq k + · exact amp3_01_1_eq k + · exact amp3_01_2_eq k + · exact amp3_01_3_eq k + · exact amp3_01_4_eq k + · exact amp3_01_5_eq k + · exact amp3_01_6_eq k + · exact amp3_01_7_eq k + · exact amp3_01_8_eq k + · exact amp3_01_9_eq k + · exact amp3_01_10_eq k + · exact amp3_01_11_eq k + · exact amp3_01_12_eq k + · exact amp3_01_13_eq k + · exact amp3_01_14_eq k + · exact amp3_01_15_eq k +noncomputable def amp3_02_0 : Fin 16 → CBox := ![⟨⟨3879958785275112030872829,3879958785275112126017444⟩,⟨122567471280363286346014081,122567471280363286432562813⟩⟩,⟨⟨13650175150687428772116661,13650175150687429107045981⟩,⟨431364070668856702826634357,431364070668856703132515093⟩⟩,⟨⟨21983523651551168316791814,21983523651551168856737384⟩,⟨695214108876785737816388538,695214108876785738310424790⟩⟩,⟨⟨31179044355557077307589902,31179044355557078074493878⟩,⟨987092899012678168714052340,987092899012678169415988735⟩⟩,⟨⟨39677398895630803416865500,39677398895630804394678268⟩,⟨1257973829753348145044582570,1257973829753348145939899050⟩⟩,⟨⟨48615544208752414717487257,48615544208752415918446900⟩,⟨1544176903888298842516509784,1544176903888298843616305330⟩⟩,⟨⟨57063171561483148451634363,57063171561483149865347534⟩,⟨1816489744758606939131204107,1816489744758606940426070732⟩⟩,⟨⟨65765911859849136172803554,65765911859849137807622528⟩,⟨2098922128909745105478675063,2098922128909745106976186599⟩⟩,⟨⟨74061576839334821780221764,74061576839334823628383826⟩,⟨2370675397458598662742074301,2370675397458598664435187301⟩⟩,⟨⟨82500375771706862977688982,82500375771706865045426964⟩,⟨2649635766322934325863850484,2649635766322934327757913017⟩⟩,⟨⟨90569617020491862681116652,90569617020491864962180493⟩,⟨2919670857096353624469060225,2919670857096353626558838205⟩⟩,⟨⟨98701682743287779680163958,98701682743287782179449955⟩,⟨3194992965302262003567189471,3194992965302262005856970618⟩⟩,⟨⟨106479847507503671814140416,106479847507503674526332870⟩,⟨3462444674511776428162175421,3462444674511776430646956501⟩⟩,⟨⟨114257301548440444987298805,114257301548440447916353006⟩,⟨3733783376039664084471927350,3733783376039664087155109909⟩⟩,⟨⟨121684572072040859711754156,121684572072040862853027610⟩,⟨3997919240462884166112638494,3997919240462884168990534237⟩⟩,⟨⟨129057702025783011590875496,129057702025783014947622789⟩,⟨4264849685296952058646781980,4264849685296952061722269602⟩⟩] +lemma amp3_02_0_eq : ∀ k : Fin 16, amp3_0Expr 2 0 k = amp3_02_0 k := by decide +kernel +noncomputable def amp3_02_1 : Fin 16 → CBox := ![⟨⟨136077282776195069497118141,136077282776195073065140269⟩,⟨4525009209521115843746243089,4525009209521115847015346508⟩⟩,⟨⟨142995990074842381343438358,142995990074842385125431294⟩,⟨4787069085461776973760400264,4787069085461776977225323462⟩⟩,⟨⟨149553373702972237882180379,149553373702972241874289317⟩,⟨5042637101134134523405016343,5042637101134134527062118432⟩⟩,⟨⟨155967942045822866440143647,155967942045822870644655826⟩,⟨5299347482185625018304308418,5299347482185625022156826189⟩⟩,⟨⟨162010611149165401880911543,162010611149165406294189507⟩,⟨5549741340571017127014673006,5549741340571017131057786114⟩⟩,⟨⟨167872178600500610363197672,167872178600500614987114947⟩,⟨5800618248161341844362635374,5800618248161341848598049163⟩⟩,⟨⟨173349505411826658902903879,173349505411826663734112975⟩,⟨6045281341110323429647170349,6045281341110323434073375414⟩⟩,⟨⟨178610391771038572311240365,178610391771038577351234657⟩,⟨6289842815143717965836601002,6289842815143717970453111167⟩⟩,⟨⟨183473635416527253370017417,183473635416527258615601955⟩,⟨6528241263088992425364667348,6528241263088992430170090712⟩⟩,⟨⟨188087591943334410047327296,188087591943334415499771653⟩,⟨6766012069971473224367763280,6766012069971473229363503463⟩⟩,⟨⟨192289946439909147616992511,192289946439909153273114532⟩,⟨6997633106004553567791598615,6997633106004553572972550154⟩⟩,⟨⟨196212360252700209467286648,196212360252700215328151025⟩,⟨7228148112506377871891766110,7228148112506377877260837329⟩⟩,⟨⟨199709029546385544143433478,199709029546385550205940458⟩,⟨7452499421993761625980122162,7452499421993761631531811266⟩⟩,⟨⟨202897099326568412228729342,202897099326568418493754605⟩,⟨7675306168153303115020942709,7675306168153303120759445334⟩⟩,⟨⟨205645386537749175852821004,205645386537749182317377858⟩,⟨7891915786249052711146193343,7891915786249052717067556543⟩⟩,⟨⟨208058278551216333087572636,208058278551216339752247559⟩,⟨8106576549529889630404144666,8106576549529889636509345310⟩⟩] +lemma amp3_02_1_eq : ∀ k : Fin 16, amp3_0Expr 2 1 k = amp3_02_1 k := by decide +kernel +noncomputable def amp3_02_2 : Fin 16 → CBox := ![⟨⟨210017682054448930459630244,210017682054448937321444812⟩,⟨8314993091186655482721109536,8314993091186655489004275134⟩⟩,⟨⟨211616671566013946930699976,211616671566013953990130727⟩,⟨8521086609528128274671605717,8521086609528128281136685732⟩⟩,⟨⟨212748983439329024128212348,212748983439329031382391308⟩,⟨8720879698151552965163242128,8720879698151552971807055537⟩⟩,⟨⟨213497584459482970488961493,213497584459482977938104880⟩,⟨8918002651777658863126767448,8918002651777658869949808951⟩⟩,⟨⟨213766988463633256875489939,213766988463633264516789051⟩,⟨9108763463709258352643795343,9108763463709258359644023479⟩⟩,⟨⟨213631073557620226710058989,213631073557620234543434961⟩,⟨9296531777052657528712835938,9296531777052657535884913191⟩⟩,⟨⟨213004240754904452423215420,213004240754904460445977753⟩,⟨9477873648727356627303402470,9477873648727356634649317358⟩⟩,⟨⟨211952151935659410307835625,211952151935659418519860617⟩,⟨9655923651121575516951220324,9655923651121575524470121538⟩⟩,⟨⟨210398332634527915638336445,210398332634527924036859164⟩,⟨9827482713622402156293286391,9827482713622402163983326885⟩⟩,⟨⟨208400983934442232196068829,208400983934442240780841326⟩,⟨9995472183599167420791055054,9995472183599167428652126222⟩⟩,⟨⟨205892095009582894824095711,205892095009582903592346674⟩,⟨10156908000462491385153888474,10156908000462491393183387392⟩⟩,⟨⟨202923067063906283956924723,202923067063906292908151480⟩,⟨10314517109853438197231722404,10314517109853438205423352474⟩⟩,⟨⟨199433773939111558544294571,199433773939111567675871573⟩,⟨10465513301118362367228481533,10465513301118362375586592093⟩⟩,⟨⟨195469400750658442009667618,195469400750658451321062172⟩,⟨10612445469636159671466878956,10612445469636159679990011834⟩⟩,⟨⟨190977193492842954090755827,190977193492842963579219392⟩,⟨10752710309841076384152276494,10752710309841076392838643794⟩⟩,⟨⟨185996641445891655615224270,185996641445891665280085807⟩,⟨10888692977215860961324682913,10888692977215860970171615139⟩⟩] +lemma amp3_02_2_eq : ∀ k : Fin 16, amp3_0Expr 2 2 k = amp3_02_2 k := by decide +kernel +noncomputable def amp3_02_3 : Fin 16 → CBox := ![⟨⟨180481904531985215187214596,180481904531985225025733625⟩,⟨11017959958234980196210399396,11017959958234980205216623443⟩⟩,⟨⟨174467243660505010970043080,174467243660505020981473539⟩,⟨11142745278603371174018832665,11142745278603371183183849507⟩⟩,⟨⟨167913319061886689960143559,167913319061886700141720988⟩,⟨11260773630433533234718220828,11260773630433533244039639101⟩⟩,⟨⟨160849586539891014593110043,160849586539891024943839507⟩,⟨11374139092090506443492431727,11374139092090506452959845446⟩⟩,⟨⟨153242829832196979171763274,153242829832196989689024663⟩,⟨11480714256280876620892004949,11480714256280876630513157189⟩⟩,⟨⟨145118085633601576309868727,145118085633601586992687018⟩,⟨11582463228841943737554019387,11582463228841943747327121952⟩⟩,⟨⟨136447914889822787275170186,136447914889822798120764797⟩,⟨11677397280418556205711660237,11677397280418556215634036696⟩⟩,⟨⟨127253289556255326893105973,127253289556255337900410595⟩,⟨11767359490730520546924461317,11767359490730520556994673109⟩⟩,⟨⟨117512226822329393303683898,117512226822329404469917088⟩,⟨11850491505340563940208236900,11850491505340563950424246716⟩⟩,⟨⟨107241961276348508329271505,107241961276348519653256978⟩,⟨11928523443012722024047580557,11928523443012722034406030227⟩⟩,⟨⟨96425666463738808510208901,96425666463738819989172028⟩,⟨11999719806689291500104807767,11999719806689291510605287909⟩⟩,⟨⟨85077143809515947437748059,85077143809515959070436334⟩,⟨12065705059819838051643436885,12065705059819838062283840281⟩⟩,⟨⟨73184440870410262118060273,73184440870410273901672062⟩,⟨12124859719306100558015149028,12124859719306100568793277935⟩⟩,⟨⟨60758210132504835983711014,60758210132504847916915486⟩,⟨12178709240801132336448885740,12178709240801132347363383626⟩⟩,⟨⟨47791105411493690083374091,47791105411493702163358149⟩,⟨12225743892813659138931376320,12225743892813659149979825534⟩⟩,⟨⟨34290897173801397506990368,34290897173801409732341109⟩,⟨12267396197604605597012080769,12267396197604605608193021447⟩⟩] +lemma amp3_02_3_eq : ∀ k : Fin 16, amp3_0Expr 2 3 k = amp3_02_3 k := by decide +kernel +noncomputable def amp3_02_4 : Fin 16 → CBox := ![⟨⟨20254589856050156310149841,20254589856050168678021775⟩,⟨12302260415786548477367835649,12302260415786548488665561497⟩⟩,⟨⟨5687323776543071996663787,5687323776543084505605351⟩,⟨12331681709222448381228881874,12331681709222448392657319477⟩⟩,⟨⟨(-9409791622879205892196163),(-9409791622879193244735018)⟩,⟨12354353007857352975156086554,12354353007857352986712060294⟩⟩,⟨⟨(-25034007430938004908343255),(-25034007430937992123733234)⟩,⟨12371537245564442597837672790,12371537245564442609519170875⟩⟩,⟨⟨(-41180346568378016734866460),(-41180346568378003815928107)⟩,⟨12382021079404164386312509375,12382021079404164398116709366⟩⟩,⟨⟨(-57848224281887260381691576),(-57848224281887247330035915)⟩,⟨12386989958954766620528606495,12386989958954766632454377974⟩⟩,⟨⟨(-75029026486201872432141978),(-75029026486201859250603407)⟩,⟨12385319658769618626524704213,12385319658769618638568143867⟩⟩,⟨⟨(-92724115420509252656342073),(-92724115420509239346597364)⟩,⟨12378122543576607832799012526,12378122543576607844959346460⟩⟩,⟨⟨(-110921465181059588923433749),(-110921465181059575488317144)⟩,⟨12364359187269234974628592841,12364359187269234986903367415⟩⟩,⟨⟨(-129624176699714378334652380),(-129624176699714364775944535)⟩,⟨12345072963214964888844603918,12345072963214964901228584372⟩⟩,⟨⟨(-148817033106942341295686085),(-148817033106942327616193802)⟩,⟨12319305182556303626597120344,12319305182556303639091422983⟩⟩,⟨⟨(-168504673533636033611188898),(-168504673533636019812725377)⟩,⟨12288034047971003658564218052,12288034047971003671166452675⟩⟩,⟨⟨(-188668907616950594261796443),(-188668907616950580347205432)⟩,⟨12250377771220481930586996823,12250377771220481943294841307⟩⟩,⟨⟨(-209315719072238102187465772),(-209315719072238088158631553)⟩,⟨12207252960941082860116552622,12207252960941082872926929066⟩⟩,⟨⟨(-230424158959427081295423525),(-230424158959427067155176965)⟩,⟨12157851091806403289525217639,12157851091806403302436800476⟩⟩,⟨⟨(-252001368026594225820942656),(-252001368026594211571217363)⟩,⟨12103030536169712858512681734,12103030536169712871522851561⟩⟩] +lemma amp3_02_4_eq : ∀ k : Fin 16, amp3_0Expr 2 4 k = amp3_02_4 k := by decide +kernel +noncomputable def amp3_02_5 : Fin 16 → CBox := ![⟨⟨(-274023851828888856073519288),(-274023851828888841717166501)⟩,⟨12042052569745894409718609823,12042052569745894422825031356⟩⟩,⟨⟨(-296499725935113396694596800),(-296499725935113382233586497)⟩,⟨11975720489497781945953065122,11975720489497781959153845290⟩⟩,⟨⟨(-319403162242363062961107820),(-319403162242363048398290844)⟩,⟨11903362066001848878095473436,11903362066001848891388238871⟩⟩,⟨⟨(-342743073623196828706143586),(-342743073623196814043541171)⟩,⟨11825728504234840778223599474,11825728504234840791606325515⟩⟩,⟨⟨(-366491509474366954609943203),(-366491509474366939850412885)⟩,⟨11742210901522501508631611916,11742210901522501522101697219⟩⟩,⟨⟨(-390658006571625136365103809),(-390658006571625121511389471)⟩,⟨11653511193886496322491166300,11653511193886496336026349380⟩⟩,⟨⟨(-415212702747027498885718620),(-415212702747027483939996587)⟩,⟨11559080759900927531372557396,11559080759900927544991853678⟩⟩,⟨⟨(-440165588872478699903787662),(-440165588872478684868180942)⟩,⟨11459574944464423381610159119,11459574944464423395311030471⟩⟩,⟨⟨(-465485102335801780276378968),(-465485102335801765153758968)⟩,⟨11354502470925237560617051749,11354502470925237574396416738⟩⟩,⟨⟨(-491181521415673111490843676),(-491181521415673096283358115)⟩,⟨11244474639196531142460975987,11244474639196531156316762257⟩⟩,⟨⟨(-517221794716025931000369648),(-517221794716025915710894767)⟩,⟨11129054677989375489391732871,11129054677989375503320753971⟩⟩,⟨⟨(-543616323914329985700290965),(-543616323914329970331018082)⟩,⟨11008812268737794909524178262,11008812268737794923524302551⟩⟩,⟨⟨(-570330781341174632748467429),(-570330781341174617302218649)⟩,⟨10883362392611907627908096702,10883362392611907641977222914⟩⟩,⟨⟨(-597375530343283824090031032),(-597375530343283808569074614)⟩,⟨10753235430257550903684962680,10753235430257550917820115600⟩⟩,⟨⟨(-624715180610339847983512365),(-624715180610339832390664521)⟩,⟨10618095439580003762637289181,10618095439580003776836323848⟩⟩,⟨⟨(-652359897332128810448164379),(-652359897332128794785668777)⟩,⟨10478435719046032923510083704,10478435719046032937771067551⟩⟩] +lemma amp3_02_5_eq : ∀ k : Fin 16, amp3_0Expr 2 5 k = amp3_02_5 k := by decide +kernel +noncomputable def amp3_02_6 : Fin 16 → CBox := ![⟨⟨(-680273442550118239431959274),(-680273442550118223702774127)⟩,⟨10333966796497269496376505974,10333966796497269510694915205⟩⟩,⟨⟨(-708465625022413968714156959),(-708465625022413952920424410)⟩,⟨10185147016540992933841736076,10185147016540992948217651804⟩⟩,⟨⟨(-736899575704910802470521677),(-736899575704910786615147540)⟩,⟨10031730831766537412831781082,10031730831766537427261413377⟩⟩,⟨⟨(-765584589867977197391839139),(-765584589867977181477058186)⟩,⟨9874143678923797015360873706,9874143678923797029843137754⟩⟩,⟨⟨(-794483385699661736187104800),(-794483385699661720215782351)⟩,⟨9712181445281533208555928689,9712181445281533223087530603⟩⟩,⟨⟨(-823604588828041793843034370),(-823604588828041777817479994)⟩,⟨9546238630672844986130726984,9546238630672845000709834690⟩⟩,⟨⟨(-852910724910369628342650718),(-852910724910369612266132971)⟩,⟨9376150116333900724345078097,9376150116333900738963919258⟩⟩,⟨⟨(-882409594374653808564746611),(-882409594374653792439132936)⟩,⟨9202281367689968063763115188,9202281367689968078425161528⟩⟩,⟨⟨(-912063752650362542541847510),(-912063752650362526369979587)⟩,⟨9024503863463823810370191519,9024503863463823825072239980⟩⟩,⟨⟨(-941880019709382451273471214),(-941880019709382435057752864)⟩,⟨8843155874832078373355854426,8843155874832078388095490973⟩⟩,⟨⟨(-971821205254406146574363593),(-971821205254406130317542918)⟩,⟨8658143121192879027128169180,8658143121192879041903020650⟩⟩,⟨⟨(-1001892993559003068602517725),(-1001892993559003052307053066)⟩,⟨8469778462885265634566328324,8469778462885265649373690274⟩⟩,⟨⟨(-1032058675418273700584344467),(-1032058675418273684252970573)⟩,⟨8277999538776276701187962068,8277999538776276716025445478⟩⟩,⟨⟨(-1062322643896193750070116336),(-1062322643896193733705206702)⟩,⟨8083095530211274972263865246,8083095530211274987129604897⟩⟩,⟨⟨(-1092648900128508004142098348),(-1092648900128507987746673995)⟩,⟨7885033706297814507849308389,7885033706297814522738653032⟩⟩,⟨⟨(-1123040389909159618704434907),(-1123040389909159602280679694)⟩,⟨7684081254476398336764841936,7684081254476398351677460990⟩⟩] +lemma amp3_02_6_eq : ∀ k : Fin 16, amp3_0Expr 2 6 k = amp3_02_6 k := by decide +kernel +noncomputable def amp3_02_7 : Fin 16 → CBox := ![⟨⟨(-1153462056495804002519418118),(-1153462056495803986070092601)⟩,⟨7480232813604224338004482578,7480232813604224352937519896⟩⟩,⟨⟨(-1183915241523606802490840350),(-1183915241523606786018344861)⟩,⟨7273735220039842612464020989,7273735220039842627415558624⟩⟩,⟨⟨(-1214366064785788517521228869),(-1214366064785788501028431767)⟩,⟨7064608247735718441540607929,7064608247735718456507084945⟩⟩,⟨⟨(-1244814105761670555773907610),(-1244814105761670539263128209)⟩,⟨6853079986732202809293753775,6853079986732202824273797801⟩⟩,⟨⟨(-1275226897923018345172550516),(-1275226897923018328646578709)⟩,⟨6639193134656046159985567465,6639193134656046174976036669⟩⟩,⟨⟨(-1305602099205304588998868482),(-1305602099205304572460043391)⟩,⟨6423158605894403140623987176,6423158605894403155623362536⟩⟩,⟨⟨(-1335908896727803494703995277),(-1335908896727803478155059567)⟩,⟨6205039831217902885328025807,6205039831217902900333356983⟩⟩,⟨⟨(-1366142865816302828495165177),(-1366142865816302811938584194)⟩,⟨5985032089673039396455535357,5985032089673039411464682453⟩⟩,⟨⟨(-1396275090131028168255719570),(-1396275090131028151694123643)⟩,⟨5763217373417767331294259354,5763217373417767346304719811⟩⟩,⟨⟨(-1426298899351587793616978693),(-1426298899351587777052814967)⟩,⟨5539776839679163577079040339,5539776839679163592088780862⟩⟩,⟨⟨(-1456187519599523438818500777),(-1456187519599523422254419945)⟩,⟨5314808887097895767655697062,5314808887097895782662070469⟩⟩,⟨⟨(-1485931869600694451611124297),(-1485931869600694435049587456)⟩,⟨5088482041213931483832097924,5088482041213931498833017491⟩⟩,⟨⟨(-1515507566993773336268996182),(-1515507566993773319712628561)⟩,⟨4860908967342022008273648401,4860908967342022023266494315⟩⟩,⟨⟨(-1544902951662533290686594766),(-1544902951662533274137881896)⟩,⟨4632247029345956276987903489,4632247029345956291970555329⟩⟩,⟨⟨(-1574096285070836608136204949),(-1574096285070836591597733580)⟩,⟨4402621032885085125575066805,4402621032885085140545019533⟩⟩,⟨⟨(-1603073157470555461342229822),(-1603073157470555444816532203)⟩,⟨4172178633191482110837998135,4172178633191482125793018026⟩⟩] +lemma amp3_02_7_eq : ∀ k : Fin 16, amp3_0Expr 2 7 k = amp3_02_7 k := by decide +kernel +noncomputable def amp3_02_8 : Fin 16 → CBox := ![⟨⟨(-1631814729838361680961402450),(-1631814729838361664450825362)⟩,⟨3941054661915855019012416882,3941054661915855033950542611⟩⟩,⟨⟨(-1660303668769385659765747260),(-1660303668769385643272572784)⟩,⟨3709388504799454362532356643,3709388504799454377451932523⟩⟩,⟨⟨(-1688524293960479645047200252),(-1688524293960479628573958731)⟩,⟨3477322915694507870571700281,3477322915694507885470196493⟩⟩,⟨⟨(-1716456170741849862424814011),(-1716456170741849845974010093)⟩,⟨3244990439079095940710728098,3244990439079095955585926739⟩⟩,⟨⟨(-1744087040413192152938223661),(-1744087040413192136512318947)⟩,⟨3012539656434915101670405529,3012539656434915116519884053⟩⟩,⟨⟨(-1771393185483115339372967546),(-1771393185483115322974466964)⟩,⟨2780097691227619011931753688,2780097691227619026753366125⟩⟩,⟨⟨(-1798366035585636062248809443),(-1798366035585636045880103047)⟩,⟨2547816865913583991755615951,2547816865913584006547083492⟩⟩,⟨⟨(-1824978404518385193465659160),(-1824978404518385177129257782)⟩,⟨2315820298120161832527190718,2315820298120161847286355592⟩⟩,⟨⟨(-1851225681024307920633002299),(-1851225681024307904331258679)⟩,⟨2084261971263796412881197456,2084261971263796427605769068⟩⟩,⟨⟨(-1877077019562249941945420897),(-1877077019562249925680762146)⟩,⟨1853262410112932270703395938,1853262410112932285391386011⟩⟩,⟨⟨(-1902532043019967785431514085),(-1902532043019967769206266836)⟩,⟨1622975184394542496822847064,1622975184394542511472026442⟩⟩,⟨⟨(-1927556050721390648508899364),(-1927556050721390632325624677)⟩,⟨1393519639683891580544531168,1393519639683891595152763762⟩⟩,⟨⟨(-1952153179241507545893730792),(-1952153179241507529754547353)⟩,⟨1165046861439384293159601024,1165046861439384307724775913⟩⟩,⟨⟨(-1976284671347843430471808665),(-1976284671347843414379296709)⟩,⟨937676433293190016125730269,937676433293190030645782446⟩⟩,⟨⟨(-1999959461627553395133776220),(-1999959461627553379089964476)⟩,⟨711554888590493763968609471,711554888590493778441483715⟩⟩,⟨⟨(-2023134528757460754865921359),(-2023134528757460738873496556)⟩,⟨486803472788073224485232339,486803472788073238908829801⟩⟩] +lemma amp3_02_8_eq : ∀ k : Fin 16, amp3_0Expr 2 8 k = amp3_02_8 k := by decide +kernel +noncomputable def amp3_02_9 : Fin 16 → CBox := ![⟨⟨(-2045823894754960305225643732),(-2045823894754960289286760657)⟩,⟨263562100607910086626582840,263562100607910100998753172⟩⟩,⟨⟨(-2067980060037523118645777553),(-2067980060037523102762886843)⟩,⟨41955112604255386824476429,41955112604255401143327951⟩⟩,⟨⟨(-2089622428913628656686113923),(-2089622428913628640860900451)⟩,⟨(-177886261786289697166285029),(-177886261786289682896851586)⟩⟩,⟨⟨(-2110698802178643208791895002),(-2110698802178643193027276351)⟩,⟨(-395833141072021083132627891),(-395833141072021068913273653)⟩⟩,⟨⟨(-2131234267129205423029046750),(-2131234267129205407327074216)⟩,⟨(-611765049514521640076755754),(-611765049514521625909667349)⟩⟩,⟨⟨(-2151171695779136638723120514),(-2151171695779136623086091571)⟩,⟨(-825547103119635318061230997),(-825547103119635303948364986)⟩⟩,⟨⟨(-2170542165389195933848982719),(-2170542165389195918279101985)⟩,⟨(-1037071651746580064478053854),(-1037071651746580050421560493)⟩⟩,⟨⟨(-2189283381584877547487445921),(-2189283381584877531987000737)⟩,⟨(-1246196328331549402421605049),(-1246196328331549388423485766)⟩⟩,⟨⟨(-2207432725343774298436599178),(-2207432725343774283007690452)⟩,⟨(-1452828385619031186384822627),(-1452828385619031172447266723)⟩⟩,⟨⟨(-2224922489144277989317334583),(-2224922489144277973962412354)⟩,⟨(-1656816470484195178116823784),(-1656816470484195164241864813)⟩⟩,⟨⟨(-2241796678770103861586301414),(-2241796678770103846306016748)⟩,⟨(-1858084823329935707141466723),(-1858084823329935693330066482)⟩⟩,⟨⟨(-2257981916876387038581476621),(-2257981916876387023379359550)⟩,⟨(-2056471575959897877858629794),(-2056471575959897864113700306)⟩⟩,⟨⟨(-2273529163108222217800156875),(-2273529163108222202678073175)⟩,⟨(-2251920051020218716114675024),(-2251920051020218702438220799)⟩⟩,⟨⟨(-2288359102870154515839466067),(-2288359102870154500799846000)⟩,⟨(-2444256306414078193852761798),(-2444256306414078180246844316)⟩⟩,⟨⟨(-2302529987397462921863579405),(-2302529987397462906908059867)⟩,⟨(-2633444854018968539564062014),(-2633444854018968526030384545)⟩⟩,⟨⟨(-2315956285754596636831401112),(-2315956285754596621962514888)⟩,⟨(-2819298085151350337109476860),(-2819298085151350323650294685)⟩⟩] +lemma amp3_02_9_eq : ∀ k : Fin 16, amp3_0Expr 2 9 k = amp3_02_9 k := by decide +kernel +noncomputable def amp3_02_10 : Fin 16 → CBox := ![⟨⟨(-2328703887964928788679478626),(-2328703887964928773898575628)⟩,⟨(-3001803823208976901935547833),(-3001803823208976888552268974)⟩⟩,⟨⟨(-2340680755002884022606342850),(-2340680755002884007916080234)⟩,⟨(-3180759162059836162340753566),(-3180759162059836149035733797)⟩⟩,⟨⟨(-2351960773241646504764161850),(-2351960773241646490166273685)⟩,⟨(-3356177377460502032472974933),(-3356177377460502019248046790)⟩⟩,⟨⟨(-2362445090058189692381262696),(-2362445090058189677877873393)⟩,⟨(-3527838592150593762205815746),(-3527838592150593749062737025)⟩⟩,⟨⟨(-2372215957107662524793129531),(-2372215957107662510386163362)⟩,⟨(-3695783697285085567604852141),(-3695783697285085554545829090)⟩⟩,⟨⟨(-2381167387695425267758756916),(-2381167387695425253450296691)⟩,⟨(-3859774122958531647588060358),(-3859774122958531634614732473)⟩⟩,⟨⟨(-2389390380194425852487787942),(-2389390380194425838279512696)⟩,⟨(-4019880565076796313088025718),(-4019880565076796300202210091)⟩⟩,⟨⟨(-2396771477060693178043038067),(-2396771477060693163937254599)⟩,⟨(-4175843986282035567805564586),(-4175843986282035555009337068)⟩⟩,⟨⟨(-2403410818601281081073813546),(-2403410818601281067072151338)⟩,⟨(-4327767107534995252922647109),(-4327767107534995240217886907)⟩⟩,⟨⟨(-2409187121859322930028698940),(-2409187121859322916133404261)⟩,⟨(-4475368589970234221253858732),(-4475368589970234208642496372)⟩⟩,⟨⟨(-2414210079512698835547841035),(-2414210079512698821760572070)⟩,⟨(-4618785436100077389853054890),(-4618785436100077377337021477)⟩⟩,⟨⟨(-2418350209193668537223388890),(-2418350209193668523541833174)⟩,⟨(-4757712105708804700572148230),(-4757712105708804688144531976)⟩⟩,⟨⟨(-2421727183233931703740872754),(-2421727183233931690170736157)⟩,⟨(-4892322181481084242064281518),(-4892322181481084229734871414)⟩⟩,⟨⟨(-2424202924583346360317871332),(-2424202924583346346861264167)⟩,⟨(-5022283949006873599182011730),(-5022283949006873586952530931)⟩⟩,⟨⟨(-2425907531195030722184833160),(-2425907531195030708843204352)⟩,⟨(-5147809918611011620923259612),(-5147809918611011608795356865)⟩⟩,⟨⟨(-2426693912733208581674173007),(-2426693912733208568449579707)⟩,⟨(-5268540147848284077058889701),(-5268540147848284065034256332)⟩⟩] +lemma amp3_02_10_eq : ∀ k : Fin 16, amp3_0Expr 2 10 k = amp3_02_10 k := by decide +kernel +noncomputable def amp3_02_11 : Fin 16 → CBox := ![⟨⟨(-2426703059506517403902953774),(-2426703059506517390796781965)⟩,⟨(-5384728478631456738667018394),(-5384728478631456726747327852)⟩⟩,⟨⟨(-2425778423647994280096146181),(-2425778423647994267110411208)⟩,⟨(-5495984596739625939868639540),(-5495984596739625928055421634)⟩⟩,⟨⟨(-2424072377684404573246986168),(-2424072377684404560383148987)⟩,⟨(-5602606144782335851828660284),(-5602606144782335840123764798)⟩⟩,⟨⟨(-2421418443727190692546300699),(-2421418443727190679806174594)⟩,⟨(-5704170193164292671974989673),(-5704170193164292660379582365)⟩⟩,⟨⟨(-2417980892197620385600439121),(-2417980892197620372985532651)⟩,⟨(-5801020729354123591456475518),(-5801020729354123579972682792)⟩⟩,⟨⟨(-2413582811509080768728158206),(-2413582811509080756240452195)⟩,⟨(-5892699853735738761553402410),(-5892699853735738750182744256)⟩⟩,⟨⟨(-2408400914527138086594279543),(-2408400914527138074235077557)⟩,⟨(-5979600529148772290903774836),(-5979600529148772279647949740)⟩⟩,⟨⟨(-2402247317769154110078359793),(-2402247317769154097848969557)⟩,⟨(-6061227407633339056206409695),(-6061227407633339045065329109)⟩⟩,⟨⟨(-2395311753463174162089954361),(-2395311753463174149992193658)⟩,⟨(-6138025157190511930576373451),(-6138025157190511919553203865)⟩⟩,⟨⟨(-2387394789714916370063616732),(-2387394789714916358099455386)⟩,⟨(-6209458365200048614464437750),(-6209458365200048603560705690)⟩⟩,⟨⟨(-2378699791404616156612435922),(-2378699791404616144782752790)⟩,⟨(-6276026248728455327880076914),(-6276026248728455317096615185)⟩⟩,⟨⟨(-2369015159056540805532812746),(-2369015159056540793839856793)⟩,⟨(-6337150559881646383297375366),(-6337150559881646372636547702)⟩⟩,⟨⟨(-2358558544463308446390376597),(-2358558544463308434835050281)⟩,⟨(-6393388039878690545770919254),(-6393388039878690535233799115)⟩⟩,⟨⟨(-2347105513770651341191310211),(-2347105513770651329775627480)⟩,⟨(-6444114661991905440674758747),(-6444114661991905430263064429)⟩⟩,⟨⟨(-2334888706214894734384665606),(-2334888706214894723109626811)⟩,⟨(-6489947817563698278995878786),(-6489947817563698268711016667)⟩⟩,⟨⟨(-2321670133412686585410611285),(-2321670133412686574278294526)⟩,⟨(-6530214563095713376560412117),(-6530214563095713366404381807)⟩⟩] +lemma amp3_02_11_eq : ∀ k : Fin 16, amp3_0Expr 2 11 k = amp3_02_11 k := by decide +kernel +noncomputable def amp3_02_12 : Fin 16 → CBox := ![⟨⟨(-2307698174977533045381552118),(-2307698174977533034389915298)⟩,⟨(-6565596239720875902335786619),(-6565596239720875892301575314)⟩⟩,⟨⟨(-2292720507871634207130285869),(-2292720507871634196283744775)⟩,⟨(-6595367630112066634994198987),(-6595367630112066625090308358)⟩⟩,⟨⟨(-2277002064539917350312313662),(-2277002064539917339611646786)⟩,⟨(-6620277525069111321644190100),(-6620277525069111311871665614)⟩⟩,⟨⟨(-2260275339499294546062831965),(-2260275339499294535509953198)⟩,⟨(-6639544828550017276171676791),(-6639544828550017266532089658)⟩⟩,⟨⟨(-2242822698300631551349026292),(-2242822698300631540944645852)⟩,⟨(-6653989512042218761359451254),(-6653989512042218751853853834)⟩⟩,⟨⟨(-2224360528584459047093689293),(-2224360528584459036839659050)⟩,⟨(-6662770714602010421723839215),(-6662770714602010412353581621)⟩⟩,⟨⟨(-2205189586821923081502541125),(-2205189586821923071399636272)⟩,⟨(-6666783586820205326957565562),(-6666783586820205317723995440)⟩⟩,⟨⟨(-2185009142180270258450572565),(-2185009142180270248500319264)⟩,⟨(-6665123296129450490161771036),(-6665123296129450481065326979)⟩⟩,⟨⟨(-2164139388842547373292896706),(-2164139388842547363496252197)⟩,⟨(-6658764480713494475041778134),(-6658764480713494466084604377)⟩⟩,⟨⟨(-2142261366330319256183447655),(-2142261366330319246542217332)⟩,⟨(-6646733762883445498566930727),(-6646733762883445489750257693)⟩⟩,⟨⟨(-2119715855836485798834996109),(-2119715855836485789349702093)⟩,⟨(-6630089937481298251479264684),(-6630089937481298242804015581)⟩⟩,⟨⟨(-2096164441775423776995128688),(-2096164441775423767667705071)⟩,⟨(-6607786086607936765442362896),(-6607786086607936756910255612)⟩⟩,⟨⟨(-2071969760247240129095088873),(-2071969760247240119926065524)⟩,⟨(-6580970251493499826083288937),(-6580970251493499817695517566)⟩⟩,⟨⟨(-2046772583258113388853032033),(-2046772583258113379842434962)⟩,⟨(-6548516491970916023676344522),(-6548516491970916015428485516)⟩⟩,⟨⟨(-2020958807571332058959013573),(-2020958807571332050108862282)⟩,⟨(-6511667677976304909629012416),(-6511667677976304901527126845)⟩⟩,⟨⟨(-1994146882575085238750656985),(-1994146882575085230062832727)⟩,⟨(-6469212799559737156534668465),(-6469212799559737148580320581)⟩⟩] +lemma amp3_02_12_eq : ∀ k : Fin 16, amp3_0Expr 2 12 k = amp3_02_12 k := by decide +kernel +noncomputable def amp3_02_13 : Fin 16 → CBox := ![⟨⟨(-1966747532510034624008380193),(-1966747532510034615483043028)⟩,⟨(-6422495716916812301736165382),(-6422495716916812293929773445)⟩⟩,⟨⟨(-1938355195558533561871587260),(-1938355195558533553510405367)⟩,⟨(-6370213642455437863324057310),(-6370213642455437855666403654)⟩⟩,⟨⟨(-1909407179455943115351811232),(-1909407179455943107155247729)⟩,⟨(-6313818272542788770268610407),(-6313818272542788762761244492)⟩⟩,⟨⟨(-1879472013194223011773927890),(-1879472013194223003743766284)⟩,⟨(-6251907558164086784095990848),(-6251907558164086776740135029)⟩⟩,⟨⟨(-1849015567631871918739690688),(-1849015567631871910876109414)⟩,⟨(-6186048690645079593428533497),(-6186048690645079586225085221)⟩⟩,⟨⟨(-1817578317105888934376730816),(-1817578317105888926680414978)⟩,⟨(-6114731957924170440284263703),(-6114731957924170433230671712)⟩⟩,⟨⟨(-1785656941255495363501099289),(-1785656941255495355973004388)⟩,⟨(-6039648676377402704565126914),(-6039648676377402697665074452)⟩⟩,⟨⟨(-1752761419649620965651358017),(-1752761419649620958293439464)⟩,⟨(-5959171975618640102315944998),(-5959171975618640095571165436)⟩⟩,⟨⟨(-1719421805166915542760618912),(-1719421805166915535572653408)⟩,⟨(-5875127095561754909614333160),(-5875127095561754903024875091)⟩⟩,⟨⟨(-1685114788864628457071598003),(-1685114788864628450055412100)⟩,⟨(-5785759198684294969999013778),(-5785759198684294963566055771)⟩⟩,⟨⟨(-1650406746432396899176431109),(-1650406746432396892331832576)⟩,⟨(-5693038662963567910027293631),(-5693038662963567903751197007)⟩⟩,⟨⟨(-1614737858512345292192813324),(-1614737858512345285520987591)⟩,⟨(-5595070283507472616821740570),(-5595070283507472610701455544)⟩⟩,⟨⟨(-1578714242533121582678183563),(-1578714242533121576179650816)⟩,⟨(-5493982521505838016610229890),(-5493982521505838010648918740)⟩⟩,⟨⟨(-1541735823394698532123952736),(-1541735823394698525800633497)⟩,⟨(-5387725457787697858775258326),(-5387725457787697852974289649)⟩⟩,⟨⟨(-1504452456875062278452701859),(-1504452456875062272303972496)⟩,⟨(-5278600717010409438957920073),(-5278600717010409433316768238)⟩⟩,⟨⟨(-1466219420058686704583600861),(-1466219420058686698611631845)⟩,⟨(-5164386912180486546015960636),(-5164386912180486540536803587)⟩⟩] +lemma amp3_02_13_eq : ∀ k : Fin 16, amp3_0Expr 2 13 k = amp3_02_13 k := by decide +kernel +noncomputable def amp3_02_14 : Fin 16 → CBox := ![⟨⟨(-1427735022535455726824886623),(-1427735022535455721028351897)⟩,⟨(-5047576573863635242358747018),(-5047576573863635237038976819)⟩⟩,⟨⟨(-1388304692841029171704968398),(-1388304692841029166086546702)⟩,⟨(-4925757083095201922014030720),(-4925757083095201916857421330)⟩⟩,⟨⟨(-1348680815428673163379087591),(-1348680815428673157937848242)⟩,⟨(-4801632978135981778363276033),(-4801632978135981773368929338)⟩⟩,⟨⟨(-1308112744935633600650314861),(-1308112744935633595388667699)⟩,⟨(-4672576827644525575711002033),(-4672576827644525570881644574)⟩⟩,⟨⟨(-1267413718493796656471536011),(-1267413718493796651387867550)⟩,⟨(-4541530576380334132279748009),(-4541530576380334127612489753)⟩⟩,⟨⟨(-1225769473690637199010529850),(-1225769473690637194107582753)⟩,⟨(-4405623490092420671605128381),(-4405623490092420667103636109)⟩⟩,⟨⟨(-1184062379197272516729853516),(-1184062379197272512006092461)⟩,⟨(-4268065901036920918583976603),(-4268065901036920914246052989)⟩⟩,⟨⟨(-1141405288495768022799102818),(-1141405288495768018257293969)⟩,⟨(-4125708856111166404511123978),(-4125708856111166400340306533)⟩⟩,⟨⟨(-1098759963836750401301810382),(-1098759963836750396940534600)⟩,⟨(-3982069437942472599771048757),(-3982069437942472595766122229)⟩⟩,⟨⟨(-1055154808079998942745545327),(-1055154808079998938567013778)⟩,⟨(-3833676985522832349854343499),(-3833676985522832346016466857)⟩⟩,⟨⟨(-1011643914289791208242502406),(-1011643914289791204245437947)⟩,⟨(-3684403659605764701219330882),(-3684403659605764697548355234)⟩⟩,⟨⟨(-967156531134783554361898644),(-967156531134783550548672799)⟩,⟨(-3530401903468807408417118962),(-3530401903468807404914413840)⟩⟩,⟨⟨(-922855716952742064561174299),(-922855716952742060929928106)⟩,⟨(-3375961063325344170327058815),(-3375961063325344166991077956)⟩⟩,⟨⟨(-877552468455697323420075175),(-877552468455697319973911807)⟩,⟨(-3216785108696359721034337349),(-3216785108696359717868567722)⟩⟩,⟨⟨(-832540701852476257230125981),(-832540701852476253966670359)⟩,⟨(-3057662284067658630600507728),(-3057662284067658627602307138)⟩⟩,⟨⟨(-786487712894928245823614506),(-786487712894928242745975868)⟩,⟨(-2893752813332920239121040650),(-2893752813332920236293278874)⟩⟩] +lemma amp3_02_14_eq : ∀ k : Fin 16, amp3_0Expr 2 14 k = amp3_02_14 k := by decide +kernel +noncomputable def amp3_02_15 : Fin 16 → CBox := ![⟨⟨(-740847907532440090158477242),(-740847907532440087264174798)⟩,⟨(-2730454417871979516648087227),(-2730454417871979513988758172)⟩⟩,⟨⟨(-694109896984862770929500919),(-694109896984862768221958409)⟩,⟨(-2562252729958608319444368765),(-2562252729958608316956590188)⟩⟩,⟨⟨(-647930087912547944615490242),(-647930087912547942091738118)⟩,⟨(-2395309843151967922659714505),(-2395309843151967920340886886)⟩⟩,⟨⟨(-600568424452937724791683631),(-600568424452937722455454075)⟩,⟨(-2223249984354933127319822358),(-2223249984354933125173063966)⟩⟩,⟨⟨(-553944039744584080553112217),(-553944039744584078400880100)⟩,⟨(-2053226209596039721448695260),(-2053226209596039719470973057)⟩⟩,⟨⟨(-506013192423768214039681544),(-506013192423768212075883840)⟩,⟨(-1877721100066514053560842177),(-1877721100066514051756240862)⟩⟩,⟨⟨(-459051718781122085266736832),(-459051718781122083487056390)⟩,⟨(-1705229344880351673724674762),(-1705229344880351672089380977)⟩⟩,⟨⟨(-410592008094929308296090886),(-410592008094929306705703514)⟩,⟨(-1526643086357059704214964474),(-1526643086357059702753467254)⟩⟩,⟨⟨(-363423561467897670332041928),(-363423561467897668925535230)⟩,⟨(-1352384370115140402697181028),(-1352384370115140401404757218)⟩⟩,⟨⟨(-314444059502586099310010924),(-314444059502586098093946545)⟩,⟨(-1170967778522800206652950198),(-1170967778522800205535548153)⟩⟩,⟨⟨(-267249234881142829199517365),(-267249234881142828166639937)⟩,⟨(-995834519116790995105922156),(-995834519116790994156945827)⟩⟩,⟨⟨(-217678350262436311419153555),(-217678350262436310578309732)⟩,⟨(-811540044256275285508498802),(-811540044256275284736007629)⟩⟩,⟨⟨(-170781598208610637669014585),(-170781598208610637009640736)⟩,⟨(-636963890694916840349687307),(-636963890694916839744060899)⟩⟩,⟨⟨(-120269695103812263488278487),(-120269695103812263024098245)⟩,⟨(-448708305135166575032236111),(-448708305135166574605972101)⟩⟩,⟨⟨(-74619328860196489183239248),(-74619328860196488895407238)⟩,⟨(-278450898688109037155246865),(-278450898688109036891215870)⟩⟩,⟨⟨(-21201542952788275779647781),(-21201542952788275697935807)⟩,⟨(-79124218132947008982212000),(-79124218132947008907428989)⟩⟩] +lemma amp3_02_15_eq : ∀ k : Fin 16, amp3_0Expr 2 15 k = amp3_02_15 k := by decide +kernel +noncomputable def amp3_02 : Fin 16 → Fin 16 → CBox := ![amp3_02_0,amp3_02_1,amp3_02_2,amp3_02_3,amp3_02_4,amp3_02_5,amp3_02_6,amp3_02_7,amp3_02_8,amp3_02_9,amp3_02_10,amp3_02_11,amp3_02_12,amp3_02_13,amp3_02_14,amp3_02_15] +lemma amp3_02_eq (i k : Fin 16) : amp3_0Expr 2 i k = amp3_02 i k := by + fin_cases i + · exact amp3_02_0_eq k + · exact amp3_02_1_eq k + · exact amp3_02_2_eq k + · exact amp3_02_3_eq k + · exact amp3_02_4_eq k + · exact amp3_02_5_eq k + · exact amp3_02_6_eq k + · exact amp3_02_7_eq k + · exact amp3_02_8_eq k + · exact amp3_02_9_eq k + · exact amp3_02_10_eq k + · exact amp3_02_11_eq k + · exact amp3_02_12_eq k + · exact amp3_02_13_eq k + · exact amp3_02_14_eq k + · exact amp3_02_15_eq k +noncomputable def amp3_03_0 : Fin 16 → CBox := ![⟨⟨28961932684408956581308931,28961932684408956632853570⟩,⟨108088421629316623483349573,108088421629316623525110095⟩⟩,⟨⟨101934636156411633750993427,101934636156411633932715304⟩,⟨380457469031610618084545754,380457469031610618232634552⟩⟩,⟨⟨164303715798580050326721135,164303715798580050619887796⟩,⟨613334122835736609550191544,613334122835736609789753666⟩⟩,⟨⟨233326121558913299150383050,233326121558913299566836057⟩,⟨871186651208288426043574064,871186651208288426384052520⟩⟩,⟨⟨297426065127709466167684916,297426065127709466698751174⟩,⟨1110855805182812688884840102,1110855805182812689319267696⟩⟩,⟨⟨365201167664663818749682164,365201167664663819401989431⟩,⟨1364502516451548232627650135,1364502516451548233161376788⟩⟩,⟨⟨429755452535542680257986362,429755452535542681025920536⟩,⟨1606422611371462723565511905,1606422611371462724194026993⟩⟩,⟨⟨496779687860134071501969041,496779687860134072390057271⟩,⟨1857937861212912762813688687,1857937861212912763540648946⟩⟩,⟨⟨561363858858550299400685440,561363858858550300404734526⟩,⟨2100745591827982119395266942,2100745591827982120217294513⟩⟩,⟨⟨627753677415993116415139485,627753677415993117538463264⟩,⟨2350783611667305757298247562,2350783611667305758217804924⟩⟩,⟨⟨692139589723734900880143439,692139589723734902119468464⟩,⟨2593845958137972050495747010,2593845958137972051510513223⟩⟩,⟨⟨757901026502040894986553595,757901026502040896344507143⟩,⟨2842646229294924349306650080,2842646229294924350418644400⟩⟩,⟨⟨821929235447912046206852881,821929235447912047680529536⟩,⟨3085583556042871418196945484,3085583556042871419403703516⟩⟩,⟨⟨887025356064341239869896296,887025356064341241461408752⟩,⟨3333221861124225945073756142,3333221861124225946376859141⟩⟩,⟨⟨950567018378215207345383880,950567018378215209052353139⟩,⟨3575765080212056898399340328,3575765080212056899797257754⟩⟩,⟨⟨1014941222716878724107389407,1014941222716878725931576975⟩,⟨3822239823595647442342569267,3822239823595647443836682950⟩⟩] +lemma amp3_03_0_eq : ∀ k : Fin 16, amp3_0Expr 3 0 k = amp3_03_0 k := by decide +kernel +noncomputable def amp3_03_1 : Fin 16 → CBox := ![⟨⟨1077883602232748620274311972,1077883602232748622213424026⟩,⟨4064175658897576023412955632,4064175658897576025001307863⟩⟩,⟨⟨1141469472398106271386085405,1141469472398106273441544797⟩,⟨4309443980893408079271198649,4309443980893408080954776725⟩⟩,⟨⟨1203709513037336068631057488,1203709513037336070800763579⟩,⟨4550590350097117296117069398,4550590350097117297894088053⟩⟩,⟨⟨1266435608730476310604925372,1266435608730476312890403196⟩,⟨4794585396694248915390537212,4794585396694248917263092253⟩⟩,⟨⟨1327876778745353551169695189,1327876778745353553568648353⟩,⟨5034779014066831685566076979,5034779014066831687531220852⟩⟩,⟨⟨1389669240966076207978370230,1389669240966076210491836727⟩,⟨5277419040692664107688306752,5277419040692664109746896849⟩⟩,⟨⟨1450219875451213457078285320,1450219875451213459704827309⟩,⟨5516508625412449263787089503,5516508625412449265939109118⟩⟩,⟨⟨1511003972326829346163117673,1511003972326829348903144523⟩,⟨5757702167580947123373978119,5757702167580947125618418803⟩⟩,⟨⟨1570576367321974631779230555,1570576367321974634631385082⟩,⟨5995544472595421096652690167,5995544472595421098989592662⟩⟩,⟨⟨1630277484998892583126894784,1630277484998892586091950251⟩,⟨6235193461909661491329014912,6235193461909661493759216277⟩⟩,⟨⟨1688787395928877564727995058,1688787395928877567803741012⟩,⟨6471650828876508406760986758,6471650828876508409281069795⟩⟩,⟨⟨1747331717944640688920485281,1747331717944640692107977845⟩,⟨6709652564294323390459510801,6709652564294323393071803959⟩⟩,⟨⟨1804698087720239809337570621,1804698087720239812634533187⟩,⟨6944591354177976136472332535,6944591354177976139172997135⟩⟩,⟨⟨1862013089146079480759003292,1862013089146079484166733925⟩,⟨7180839801288695675109587533,7180839801288695677902261590⟩⟩,⟨⟨1918157912262776193775726373,1918157912262776197292348231⟩,⟨7414129352478748706161846968,7414129352478748709044104894⟩⟩,⟨⟨1974172737953186972103896774,1974172737953186975729864693⟩,⟨7648516030942834533259825013,7648516030942834536232402358⟩⟩] +lemma amp3_03_1_eq : ∀ k : Fin 16, amp3_0Expr 3 1 k = amp3_03_1 k := by decide +kernel +noncomputable def amp3_03_2 : Fin 16 → CBox := ![⟨⟨2029021007614158829066791709,2029021007614158832799778275⟩,⟨7880027948563344671591833362,7880027948563344674650449043⟩⟩,⟨⟨2083666774454682875399443906,2083666774454682879240569460⟩,⟨8112442557927185199700640826,8112442557927185202848924611⟩⟩,⟨⟨2137146481363943354000929087,2137146481363943357948538145⟩,⟨8342050218637644138155057610,8342050218637644141391262263⟩⟩,⟨⟨2190356528382616219651975254,2190356528382616223706292308⟩,⟨8572381092874492153613697610,8572381092874492156938271348⟩⟩,⟨⟨2242398691902886486829405290,2242398691902886490989066400⟩,⟨8799959294373126727410635755,8799959294373126730822914382⟩⟩,⟨⟨2294108792999918950375306199,2294108792999918954639047674⟩,⟨9028093741442792099103572166,9028093741442792102598427494⟩⟩,⟨⟨2344647512366173192924426591,2344647512366173197291885158⟩,⟨9253518451934735689101099029,9253518451934735692681749814⟩⟩,⟨⟨2394796061039331726813847835,2394796061039331731284817907⟩,⟨9479343014527573362353324452,9479343014527573366019053802⟩⟩,⟨⟨2443768578530119847670652436,2443768578530119852243833980⟩,⟨9702491193075080754974855824,9702491193075080758725180355⟩⟩,⟨⟨2492296750695577596824316736,2492296750695577601499644389⟩,⟨9925891854410859255865097744,9925891854410859259700098293⟩⟩,⟨⟨2539643521280938663874918215,2539643521280938668650909578⟩,⟨10146641322784137638789167784,10146641322784137642707621340⟩⟩,⟨⟨2586495420234720877663030883,2586495420234720882538028061⟩,⟨10367503673603066742952929961,10367503673603066746948767745⟩⟩,⟨⟨2632160183892715638154448417,2632160183892715643128711697⟩,⟨10585733026427970763145668717,10585733026427970767224624470⟩⟩,⟨⟨2677282970138362625294854925,2677282970138362630367900516⟩,⟨10803942404318854566122509763,10803942404318854570283439636⟩⟩,⟨⟨2721212824130579168743119563,2721212824130579173913675715⟩,⟨11019530948347429631893568731,11019530948347429636136084713⟩⟩,⟨⟨2764556831933516496638784267,2764556831933516501906021276⟩,⟨11234972557258896381394508441,11234972557258896385716265079⟩⟩] +lemma amp3_03_2_eq : ∀ k : Fin 16, amp3_0Expr 3 2 k = amp3_03_2 k := by decide +kernel +noncomputable def amp3_03_3 : Fin 16 → CBox := ![⟨⟨2806702301068682132468279366,2806702301068682137831056484⟩,⟨11447800273274370147552073216,11447800273274370151953214433⟩⟩,⟨⟨2848221143020587925205358104,2848221143020587930663360684⟩,⟨11660359288828456102435249852,11660359288828456106915719878⟩⟩,⟨⟨2888536246444014353058595730,2888536246444014358610400541⟩,⟨11870306811520720510308241639,11870306811520720514867050076⟩⟩,⟨⟨2928186906929899219105410448,2928186906929899224748120682⟩,⟨12079868476215849077670324580,12079868476215849082296963811⟩⟩,⟨⟨2966629220334579183969129204,2966629220334579189703921893⟩,⟨12286817088624293459209256716,12286817088624293463913438797⟩⟩,⟨⟨3004372138528183203000586234,3004372138528183208826750973⟩,⟨12493266799941353454272988251,12493266799941353459053408465⟩⟩,⟨⟨3040902850941148594394355836,3040902850941148600310393171⟩,⟨12697098439946643858129741635,12697098439946643862985116554⟩⟩,⟨⟨3076701993770364266439947755,3076701993770364272445205406⟩,⟨12900321833607413835143920691,12900321833607413840073355000⟩⟩,⟨⟨3111285958257693440551939561,3111285958257693446645082881⟩,⟨13100919110583140003461246659,13100919110583140008464161760⟩⟩,⟨⟨3145108883654880790317724539,3145108883654880796497565766⟩,⟨13300802140657279545873611679,13300802140657279550947018437⟩⟩,⟨⟨3177714661431659370698568230,3177714661431659376964198437⟩,⟨13498048360845440570619103679,13498048360845440575764236542⟩⟩,⟨⟨3209532572096607503403279419,3209532572096607509753811384⟩,⟨13694477377996221567670945384,13694477377996221572886243846⟩⟩,⟨⟨3240132469638297596609249081,3240132469638297603043301800⟩,⟨13888256577500092556191760749,13888256577500092561476489730⟩⟩,⟨⟨3269920257482540573073148553,3269920257482540579590006627⟩,⟨14081118406356634795828164135,14081118406356634801181649714⟩⟩,⟨⟨3298490356321137201068984815,3298490356321137207667206556⟩,⟨14271315390886446200836382046,14271315390886446206257652397⟩⟩,⟨⟨3326226637723369592472087959,3326226637723369599150905679⟩,⟨14460497407301863530523077201,14460497407301863536011389535⟩⟩] +lemma amp3_03_3_eq : ∀ k : Fin 16, amp3_0Expr 3 3 k = amp3_03_3 k := by decide +kernel +noncomputable def amp3_03_4 : Fin 16 → CBox := ![⟨⟨3352746816681966792225309020,3352746816681966798979657947⟩,⟨14646997797987563438903993653,14646997797987563444442573131⟩⟩,⟨⟨3378413958659882564126533060,3378413958659882570959798596⟩,⟨14832388006767633043023918752,14832388006767633048630248848⟩⟩,⟨⟨3402867908337385439953196468,3402867908337385446863729816⟩,⟨15015078291485974181786050765,15015078291485974187458316449⟩⟩,⟨⟨3426452045727478394641717417,3426452045727478401628555986⟩,⟨15196565405037342929736965110,15196565405037342935473875160⟩⟩,⟨⟨3448827275094380706931579097,3448827275094380713993165786⟩,⟨15375332994799783059004869134,15375332994799783064805021059⟩⟩,⟨⟨3470318318825307790290901545,3470318318825307797426495109⟩,⟨15552806513040120879769775831,15552806513040120885632996151⟩⟩,⟨⟨3490606153833979773183215567,3490606153833979780390951390⟩,⟨15727539803062231942650952656,15727539803062231948574472753⟩⟩,⟨⟨3509997790378983401595691187,3509997790378983408874908178⟩,⟨15900890094849810589888316645,15900890094849810595872460690⟩⟩,⟨⟨3528193364529409833982667327,3528193364529409841331907391⟩,⟨16071478529978340164400969368,16071478529978340170444820208⟩⟩,⟨⟨3545483046627544268590028253,3545483046627544276007335648⟩,⟨16240596916249946031766214136,16240596916249946037864322496⟩⟩,⟨⟨3561585283463094194962923363,3561585283463094202447856853⟩,⟨16406931060464956901767121575,16406931060464956907923222997⟩⟩,⟨⟨3576774212206507251105416063,3576774212206507258656817561⟩,⟨16571709899214950261603966501,16571709899214950267816388530⟩⟩,⟨⟨3590785799744958398132814179,3590785799744958405749260522⟩,⟨16733681508954972295203083067,16733681508954972301471109249⟩⟩,⟨⟨3603878898139419241859424080,3603878898139419249539531826⟩,⟨16894014282141810007511604312,16894014282141810013832612139⟩⟩,⟨⟨3615806255272725532043495410,3615806255272725539786132237⟩,⟨17051516383222202657766742608,17051516383222202664141389248⟩⟩,⟨⟨3626812133390334597076702856,3626812133390334604880601751⟩,⟨17207297785649707771485815077,17207297785649707777912132622⟩⟩] +lemma amp3_03_4_eq : ∀ k : Fin 16, amp3_0Expr 3 4 k = amp3_03_4 k := by decide +kernel +noncomputable def amp3_03_5 : Fin 16 → CBox := ![⟨⟨3636665368312970441890339625,3636665368312970449754071991⟩,⟨17360224753560355562380239146,17360224753560355568857520758⟩⟩,⟨⟨3645596280169054791617885417,3645596280169054799540382121⟩,⟨17511350783747840140242362624,17511350783747840146769679727⟩⟩,⟨⟨3653389140919529095238944993,3653389140919529103218765833⟩,⟨17659598427127333723566085111,17659598427127333730142692656⟩⟩,⟨⟨3660260933219737813575699885,3660260933219737821611723190⟩,⟨17805966480154147989651360877,17805966480154147996276195523⟩⟩,⟨⟨3666010750443287906116429790,3666010750443287914207147623⟩,⟨17949432127244847808849097978,17949432127244847815521106919⟩⟩,⟨⟨3670842803361557939779558976,3670842803361557947917458639⟩,⟨18090941089530117495410261723,18090941089530117502096984323⟩⟩,⟨⟨3674570425424286341831847665,3674570425424286350022174017⟩,⟨18229523677422811939959224939,18229523677422811946692695801⟩⟩,⟨⟨3677385585587409288667906634,3677385585587409296909351013⟩,⟨18366074023379331814890087685,18366074023379331821668537683⟩⟩,⟨⟨3679115306193341873710407189,3679115306193341882001310728⟩,⟨18499674189858254054295006438,18499674189858254061116653886⟩⟩,⟨⟨3679939812063130916210531784,3679939812063130924549714195⟩,⟨18631168080340187702760641229,18631168080340187709624427119⟩⟩,⟨⟨3679699290545943958285904104,3679699290545943966671663819⟩,⟨18759688258139469137613303529,18759688258139469144517204543⟩⟩,⟨⟨3678562690405316118681387106,3678562690405316127112510868⟩,⟨18886029640586245494411032576,18886029640586245501353907625⟩⟩,⟨⟨3676382864885864087102881751,3676382864885864095578029915⟩,⟨19009374153867873880313109924,19009374153867873887294786848⟩⟩,⟨⟨3673317927650381343915869497,3673317927650381352433529732⟩,⟨19130468864031146351955128425,19130468864031146358973000465⟩⟩,⟨⟨3669232921269698157990933252,3669232921269698166549750345⟩,⟨19248544026892494334932662324,19248544026892494341986469030⟩⟩,⟨⟨3664275540361137514514127228,3664275540361137523112935533⟩,⟨19364299892018987413022653291,19364299892018987420111678849⟩⟩] +lemma amp3_03_5_eq : ∀ k : Fin 16, amp3_0Expr 3 5 k = amp3_03_5 k := by decide +kernel +noncomputable def amp3_03_6 : Fin 16 → CBox := ![⟨⟨3658322560816306350234054642,3658322560816306358870672198⟩,⟨19477014108835248911068817364,19477014108835248918188434644⟩⟩,⟨⟨3651511651349555841300422978,3651511651349555849974378050⟩,⟨19587341052165564388841470853,19587341052165564395994712169⟩⟩,⟨⟨3643730883976759516671299593,3643730883976759525380659337⟩,⟨19694604919569197994742741802,19694604919569198001926259211⟩⟩,⟨⟨3635108273525679634177964917,3635108273525679642921853636⟩,⟨19799415066001035718861995819,19799415066001035726076800497⟩⟩,⟨⟨3625542768190859118123083404,3625542768190859126899747506⟩,⟨19901141476296742581068704894,19901141476296742588312391969⟩⟩,⟨⟨3615153081412633108830794736,3615153081412633117639077521⟩,⟨20000349259050389989891135686,20000349259050389997163267488⟩⟩,⟨⟨3603848633485493158304553374,3603848633485493167140966948⟩,⟨20096453504860393727580069576,20096453504860393734868509500⟩⟩,⟨⟨3591739170896349732830589907,3591739170896349741695990209⟩,⟨20189975772974661174410159776,20189975772974661181725704958⟩⟩,⟨⟨3578744196597950562349755088,3578744196597950571242417518⟩,⟨20280375652905229747132991231,20280375652905229754473325205⟩⟩,⟨⟨3564964807805920707961544602,3564964807805920716880069382⟩,⟨20368131779383182041931601771,20368131779383182049295049529⟩⟩,⟨⟨3550330214233771990590516617,3550330214233771999533496738⟩,⟨20452747704499536678895585652,20452747704499536686281566821⟩⟩,⟨⟨3534933165946285986426027093,3534933165946285995391937897⟩,⟨20534659694915338551341572850,20534659694915338558747750487⟩⟩,⟨⟨3518712216093701104174216484,3518712216093701113161652577⟩,⟨20613414795808417350861074867,20613414795808417358286857741⟩⟩,⟨⟨3501752055229296068063468711,3501752055229296077071242399⟩,⟨20689407397179327199531986073,20689407397179327206977032545⟩⟩,⟨⟨3484000228327755661376097501,3484000228327755670401811132⟩,⟨20762227631404382279411027457,20762227631404382286868811125⟩⟩,⟨⟨3465533640571906326632024334,3465533640571906335675156405⟩,⟨20832228441125359857800736107,20832228441125359865274915889⟩⟩] +lemma amp3_03_6_eq : ∀ k : Fin 16, amp3_0Expr 3 6 k = amp3_03_6 k := by decide +kernel +noncomputable def amp3_03_7 : Fin 16 → CBox := ![⟨⟨3446308488096305393574736279,3446308488096305402633686616⟩,⟨20899042700789127710850459904,20899042700789127718339219064⟩⟩,⟨⟨3426394152251373879885892515,3426394152251373888959439310⟩,⟨20962982275421640049093009005,20962982275421640056595898780⟩⟩,⟨⟨3405755149938270339976251966,3405755149938270349062439620⟩,⟨21023722494691886928668364520,21023722494691886936181288566⟩⟩,⟨⟨3384453588426760861747136311,3384453588426760870845005914⟩,⟨21081534458393281317209323465,21081534458393281324733502707⟩⟩,⟨⟨3362461984665090319946453741,3362461984665090329054245345⟩,⟨21136135720701933568803817742,21136135720701933576336285793⟩⟩,⟨⟨3339835410553762046113527816,3339835410553762055230212818⟩,⟨21187756873077179747623405514,21187756873077179755165005659⟩⟩,⟨⟨3316554071515918836076766766,3316554071515918845200661583⟩,⟨21236157517786041347749438104,21236157517786041355297578720⟩⟩,⟨⟨3292666232435827785693459639,3292666232435827794823223059⟩,⟨21281527940939713338164216589,21281527940939713345717816035⟩⟩,⟨⟨3268159484324522585457911397,3268159484324522594592104945⟩,⟨21323669669235982593042148909,21323669669235982600600123067⟩⟩,⟨⟨3243075503668707971483991296,3243075503668707980621312454⟩,⟨21362732833799042429581162314,21362732833799042437142679044⟩⟩,⟨⟨3217408972461584949613737497,3217408972461584958752643927⟩,⟨21398560813586495446484332691,21398560813586495454047519426⟩⟩,⟨⟨3191195188247866237123394774,3191195188247866246262562829⟩,⟨21431263683489746582882841497,21431263683489746590446769677⟩⟩,⟨⟨3164435637327486823170058035,3164435637327486832307965971⟩,⟨21460726653040581541953146210,21460726653040581549516004646⟩⟩,⟨⟨3137159439118677313796260617,3137159439118677322931531648⟩,⟨21487019788804570085201219991,21487019788804570092761694391⟩⟩,⟨⟨3109374605180143925086917053,3109374605180143934218066569⟩,⟨21510070158936524984405465309,21510070158936524991961853556⟩⟩,⟨⟨3081104269457900093007221598,3081104269457900102132791118⟩,⟨21529907819246173799510605978,21529907819246173807061039193⟩⟩] +lemma amp3_03_7_eq : ∀ k : Fin 16, amp3_0Expr 3 7 k = amp3_03_7 k := by decide +kernel +noncomputable def amp3_03_8 : Fin 16 → CBox := ![⟨⟨3052362697090093873382933476,3052362697090093882501862125⟩,⟨21546501773789659829987911845,21546501773789659837533587818⟩⟩,⟨⟨3023167221481594873442040765,3023167221481594882553308413⟩,⟨21559842015121015635334200694,21559842015121015642876352176⟩⟩,⟨⟨2993538096820730959410119519,2993538096820730968512239055⟩,⟨21569939609441664797906208890,21569939609441664805442960933⟩⟩,⟨⟨2963487033579410296978521950,2963487033579410306070058165⟩,⟨21576744383507812965222464609,21576744383507812972752150515⟩⟩,⟨⟨2933040017435368535750419406,2933040017435368544829977008⟩,⟨21580309640851035950994774844,21580309640851035958516077455⟩⟩,⟨⟨2902203306577993049003260092,2902203306577993058069400916⟩,⟨21580544889634482468401593219,21580544889634482475912749231⟩⟩,⟨⟨2871008367434659702786053573,2871008367434659711837459942⟩,⟨21577545895060383359680528151,21577545895060383367180623893⟩⟩,⟨⟨2839456169937165560171797067,2839456169937165569207023092⟩,⟨21571181643200007935586629427,21571181643200007943073841941⟩⟩,⟨⟨2807583417227822693469430760,2807583417227822702487182469⟩,⟨21561590634879316568863060986,21561590634879316576336577161⟩⟩,⟨⟨2775385948681472388739187732,2775385948681472397738137076⟩,⟨21548601079181353465679813021,21548601079181353473138625403⟩⟩,⟨⟨2742905466739098849574826354,2742905466739098858553672118⟩,⟨21532394536825923727324728080,21532394536825923734767790403⟩⟩,⟨⟨2710132831866718016494169173,2710132831866718025451386308⟩,⟨21512758132670314335363695143,21512758132670314342788470513⟩⟩,⟨⟨2677114514946923871501625682,2677114514946923880436173472⟩,⟨21489916862875205682275562975,21489916862875205689682968140⟩⟩,⟨⟨2643836543376215426890249993,2643836543376215435800570382⟩,⟨21463616407291073896297849539,21463616407291073903684979672⟩⟩,⟨⟨2610349932147427287097965466,2610349932147427295983086328⟩,⟨21434125625569291831622026285,21434125625569291838990207338⟩⟩,⟨⟨2576636015834648641073648636,2576636015834648649931874754⟩,⟨21401148336756202582835868098,21401148336756202590181039848⟩⟩] +lemma amp3_03_8_eq : ∀ k : Fin 16, amp3_0Expr 3 8 k = amp3_03_8 k := by decide +kernel +noncomputable def amp3_03_9 : Fin 16 → CBox := ![⟨⟨2542750135726105639946750014,2542750135726105648776912379⟩,⟨21364997746051829215486967429,21364997746051829222808751390⟩⟩,⟨⟨2508669068418740546698939369,2508669068418740555499646733⟩,⟨21325335339126882088374701877,21325335339126882095671382376⟩⟩,⟨⟨2474452270211861161264909376,2474452270211861170035513283⟩,⟨21282519204597587919915612172,21282519204597587927191056183⟩⟩,⟨⟨2440072089333331595774873481,2440072089333331604513413798⟩,⟨21236167963352248743888445046,21236167963352248751136099047⟩⟩,⟨⟨2405591892376083631798618084,2405591892376083640503981857⟩,⟨21186685183218049673715954746,21186685183218049680935574772⟩⟩,⟨⟨2370979723709041498231945707,2370979723709041506902899956⟩,⟨21133646027672907018361407342,21133646027672907025552558986⟩⟩,⟨⟨2336302662126107225167329206,2336302662126107233802557295⟩,⟨21077500199934525542957463769,21077500199934525550117860160⟩⟩,⟨⟨2301524567663435557176728595,2301524567663435565774998808⟩,⟨21017778749484845917510363352,21017778749484845924639585897⟩⟩,⟨⟨2266716039927229242722671967,2266716039927229251282759585⟩,⟨20954978234322163644449598938,20954978234322163651546043302⟩⟩,⟨⟨2231836869251584797085229098,2231836869251584805605726305⟩,⟨20888584866272174078746059989,20888584866272174085807523190⟩⟩,⟨⟨2196960991470571040835280434,2196960991470571049316372420⟩,⟨20819142843941037478731673937,20819142843941037485769543665⟩⟩,⟨⟨2162044237014133815468259413,2162044237014133823907446183⟩,⟨20746092747230246849126657241,20746092747230246856128525140⟩⟩,⟨⟨2127163700285434613501178183,2127163700285434621897423094⟩,⟨20670027271284326525918481145,20670027271284326532884046848⟩⟩,⟨⟨2092271356811515803025937364,2092271356811515811377842641⟩,⟨20590340495214860959420787332,20590340495214860966347768454⟩⟩,⟨⟨2057447288974506887866948053,2057447288974506896173662929⟩,⟨20507674540888388054603030171,20507674540888388061492657278⟩⟩,⟨⟨2022639717611827952542923143,2022639717611827960802952989⟩,⟨20421376038668206945839684147,20421376038668206952688688330⟩⟩] +lemma amp3_03_9_eq : ∀ k : Fin 16, amp3_0Expr 3 9 k = amp3_03_9 k := by decide +kernel +noncomputable def amp3_03_10 : Fin 16 → CBox := ![⟨⟨1987931549728337535983992732,1987931549728337544196703190⟩,⟨20332137546265245971881874676,20332137546265245978693613325⟩⟩,⟨⟨1953267346877153983062044443,1953267346877153991225832928⟩,⟨20239257213188160510070766040,20239257213188160516840642153⟩⟩,⟨⟨1918732684752018662928636144,1918732684752018671042519932⟩,⟨20143479126334660953801951933,20143479126334660960529405433⟩⟩,⟨⟨1884268556168849027150219899,1884268556168849035213041708⟩,⟨20044051832424222616175373519,20044051832424222622860392625⟩⟩,⟨⟨1849963057211983579261942509,1849963057211983587272548387⟩,⟨19941772131050466968724998498,19941772131050466975365030786⟩⟩,⟨⟨1815753697566544621194471153,1815753697566544629151730591⟩,⟨19835837748000941964666690568,19835837748000941971261833232⟩⟩,⟨⟨1781730953284378174874270456,1781730953284378182777211902⟩,⟨19727099475934232915757287457,19727099475934232922306545528⟩⟩,⟨⟨1747828931468450475598284597,1747828931468450483445598283⟩,⟨19614702898187926559546324549,19614702898187926566047839582⟩⟩,⟨⟨1714140355858606907146446670,1714140355858606914937187019⟩,⟨19499554185248504544782149498,19499554185248504551235007072⟩⟩,⟨⟨1680596006311990910331613901,1680596006311990918064519667⟩,⟨19380745345054523372449914362,19380745345054523378852523751⟩⟩,⟨⟨1647290730420484240233845562,1647290730420484247907949835⟩,⟨19259239423561871626122054987,19259239423561871632472756270⟩⟩,⟨⟨1614152050723986323138300120,1614152050723986330755384097⟩,⟨19134073299866862077151226022,19134073299866862083484469726⟩⟩,⟨⟨1581276823609002938171249608,1581276823609002945727569244⟩,⟨19006268515478860206723364486,19006268515478860213004816606⟩⟩,⟨⟨1548589378578545797507671957,1548589378578545805002048924⟩,⟨18874805136505160764594075379,18874805136505160770822933486⟩⟩,⟨⟨1516188474909137465748535397,1516188474909137473180125357⟩,⟨18740764953329143606564050301,18740764953329143612739414563⟩⟩,⟨⟨1483995307408650715906262347,1483995307408650723273912321⟩,⟨18603069392699912645766334629,18603069392699912651887732224⟩⟩] +lemma amp3_03_10_eq : ∀ k : Fin 16, amp3_0Expr 3 10 k = amp3_03_10 k := by decide +kernel +noncomputable def amp3_03_11 : Fin 16 → CBox := ![⟨⟨1452110441910411418607161517,1452110441910411425910054880⟩,⟨18462862392632775897796011315,18462862392632775903862680743⟩⟩,⟨⟨1420451990584158332851445413,1420451990584158340088454408⟩,⟨18319004758906739862552884174,18319004758906739868564410589⟩⟩,⟨⟨1389122239527252770404848615,1389122239527252777575116277⟩,⟨18172704635181060411370430836,18172704635181060417324946420⟩⟩,⟨⟨1358036263634718299450023575,1358036263634718306552528151⟩,⟨18022760054661231467877649128,18022760054661231473776203731⟩⟩,⟨⟨1327297993542522898714626480,1327297993542522905748480872⟩,⟨17870445599596263096083290510,17870445599596263101923303533⟩⟩,⟨⟨1296819505060955767125979647,1296819505060955774090069633⟩,⟨17714494192276883855725149956,17714494192276883861506204521⟩⟩,⟨⟨1266706308800120559923093234,1266706308800120566816656321⟩,⟨17556249279257666366907614359,17556249279257666372628155522⟩⟩,⟨⟨1236867511941315312418557486,1236867511941315319240819951⟩,⟨17394376127771225299471100714,17394376127771225305135527457⟩⟩,⟨⟨1207410152336318491750580098,1207410152336318498500505639⟩,⟨17230289687506447750590024303,17230289687506447756192687983⟩⟩,⟨⟨1178240390605265275138230251,1178240390605265281814709111⟩,⟨17062584798927204692612384975,17062584798927204698152662444⟩⟩,⟨⟨1149466751702578893645013718,1149466751702578900247503783⟩,⟨16892750790067593217305348846,16892750790067593222783846328⟩⟩,⟨⟨1120992462606217917716889629,1120992462606217924244136835⟩,⟨16719309050418805860958870227,16719309050418805866372949424⟩⟩,⟨⟨1092927508695107952741641689,1092927508695107959193091183⟩,⟨16543826424653578840728060766,16543826424653578846077778501⟩⟩,⟨⟨1065172186189613304234978166,1065172186189613310609497300⟩,⟨16364747545951427020913080251,16364747545951427026197289830⟩⟩,⟨⟨1037837928668444757325074338,1037837928668444763622075946⟩,⟨16183720207741975247874197510,16183720207741975253091742140⟩⟩,⟨⟨1010822093413230050083433257,1010822093413230056301754286⟩,⟨15999108667388608422660445331,15999108667388608427809720102⟩⟩] +lemma amp3_03_11_eq : ∀ k : Fin 16, amp3_0Expr 3 11 k = amp3_03_11 k := by decide +kernel +noncomputable def amp3_03_12 : Fin 16 → CBox := ![⟨⟨984237565572035149164566326,984237565572035155304922500⟩,⟨15812645428547598348672379155,15812645428547598353772739880⟩⟩,⟨⟨957978743038009303436298733,957978743038009309496513863⟩,⟨15622610400856905370025132252,15622610400856905375058648349⟩⟩,⟨⟨932159982810118386358260592,932159982810118392337859397⟩,⟨15430824930239571211850842115,15430824930239571216816949116⟩⟩,⟨⟨906672689268592788009980213,906672689268592793907866973⟩,⟨15235480209839706642007898125,15235480209839706646905919162⟩⟩,⟨⟨881632729986460004198827490,881632729986460010014559366⟩,⟨15038490978485002541543235555,15038490978485002546372669190⟩⟩,⟨⟨856928466383461514678055301,856928466383461520410568144⟩,⟨14837954895288084927571147270,14837954895288084932331584655⟩⟩,⟨⟨832677335556609200070416293,832677335556609205719263261⟩,⟨14635885117434399687435118749,14635885117434399692125083628⟩⟩,⟨⟨808764589255093788383998356,808764589255093793948230265⟩,⟨14430280442791656549548086138,14430280442791656554169331577⟩⟩,⟨⟨785309315371561565841877698,785309315371561571320987095⟩,⟨14223258013300100152355288820,14223258013300100156904747993⟩⟩,⟨⟨762193569721006550525677716,762193569721006555918621270⟩,⟨14012711856863991505230371333,14012711856863991509707809472⟩⟩,⟨⟨739538197058095827447809609,739538197058095832754269076⟩,⟨13800869285718909523946920913,13800869285718909528351575067⟩⟩,⟨⟨717221948726958427396743768,717221948726958432615621063⟩,⟨13585512982404054939342736779,13585512982404054943673584507⟩⟩,⟨⟨695367560142768075014192623,695367560142768080145180751⟩,⟨13368987327135203605398152180,13368987327135203609653959431⟩⟩,⟨⟨673850344124014273847038128,673850344124014278889677727⟩,⟨13148956313395641787796807012,13148956313395641791988734247⟩⟩,⟨⟨652795091788750854881019544,652795091788750859834531470⟩,⟨12927889110493074360037396169,12927889110493074364154020301⟩⟩,⟨⟨632073513961611678138542723,632073513961611683001847147⟩,⟨12703322788898146652735327505,12703322788898146656775946891⟩⟩] +lemma amp3_03_12_eq : ∀ k : Fin 16, amp3_0Expr 3 12 k = amp3_03_12 k := by decide +kernel +noncomputable def amp3_03_13 : Fin 16 → CBox := ![⟨⟨611812657977590216626973433,611812657977590221399924273⟩,⟨12477859985588748973374796616,12477859985588748977339536814⟩⟩,⟨⟨591880435079202652396744206,591880435079202657078335254⟩,⟨12248901576360430800883496201,12248901576360430804772924545⟩⟩,⟨⟨572406389931761067553341374,572406389931761072143367524⟩,⟨12019193464512074882065262122,12019193464512074885876956821⟩⟩,⟨⟨553254396759381067460608547,553254396759381071958015952⟩,⟨11785989842249272315912666816,11785989842249272319646592653⟩⟩,⟨⟨534556785538942674595229450,534556785538942678999921098⟩,⟨11552190996705267454267116462,11552190996705267457922164731⟩⟩,⟨⟨516173109165466834308852265,516173109165466838620089932⟩,⟨11314892509916248282784833612,11314892509916248286367800812⟩⟩,⟨⟨498238825505640000766972085,498238825505640004984469999⟩,⟨11077161734298976361852437240,11077161734298976365356718738⟩⟩,⟨⟨480608826245970966026112637,480608826245970970148758220⟩,⟨10835922004518573145375400652,10835922004518573148800027924⟩⟩,⟨⟨463422103936756773396071789,463422103936756777423939747⟩,⟨10594422288566577735732621288,10594422288566577739077819168⟩⟩,⟨⟨446528482746640283086216659,446528482746640287018232513⟩,⟨10349397984639524254629234170,10349397984639524257894867010⟩⟩,⟨⟨430070973009901824151370213,430070973009901827987643417⟩,⟨10104296478593671661186245154,10104296478593671664371637318⟩⟩,⟨⟨413893844926907937430686607,413893844926907941170287722⟩,⟨9855647059989243409208992103,9855647059989243412318145093⟩⟩,⟨⟨398144701390011666160638049,398144701390011669803522771⟩,⟨9607115073633503391681712671,9607115073633503394708987373⟩⟩,⟨⟨382661674529915797431161034,382661674529915800976209165⟩,⟨9355002494152378509347842418,9355002494152378512292895053⟩⟩,⟨⟨367597646013606649705216039,367597646013606653152725930⟩,⟨9103215531180647029918912751,9103215531180647032782333118⟩⟩,⟨⟨352783905501023193719677405,352783905501023197068445588⟩,⟨8847803890694001741307382857,8847803890694001744087605917⟩⟩] +lemma amp3_03_13_eq : ∀ k : Fin 16, amp3_0Expr 3 13 k = amp3_03_13 k := by decide +kernel +noncomputable def amp3_03_14 : Fin 16 → CBox := ![⟨⟨338379436866514911895250598,338379436866514915145777315⟩,⟨8592941733663811195055700220,8592941733663811197756861420⟩⟩,⟨⟨324207832883997845929141264,324207832883997849080094199⟩,⟨8334396859882911740790506190,8334396859882911743408202098⟩⟩,⟨⟨310435174390837904869965354,310435174390837907921808793⟩,⟨8076643728041312616600770994,8076643728041312619135870567⟩⟩,⟨⟨296876313238220664270216072,296876313238220667221654171⟩,⟨7815132661565149082474558223,7815132661565149084924731685⟩⟩,⟨⟨283705639198143822716369234,283705639198143825568068594⟩,⟨7554677474851569753306699033,7554677474851569755676052648⟩⟩,⟨⟨270727975798331217843269501,270727975798331220593839400⟩,⟨7290367816815763957106066921,7290367816815763959390686780⟩⟩,⟨⟨258127513858285656101017704,258127513858285658751172314⟩,⟨7027404617116228124955744414,7027404617116228127158242109⟩⟩,⟨⟨245697443409679355369781694,245697443409679357918088088⟩,⟨6760463675959846485903951791,6760463675959846488020883451⟩⟩,⟨⟨233633616719040372318199152,233633616719040374765408214⟩,⟨6495192286245952076335494356,6495192286245952078367754199⟩⟩,⟨⟨221715561959387855206957370,221715561959387857551722061⟩,⟨6225785921507571174144091506,6225785921507571176092145982⟩⟩,⟨⟨210153148075784389158476489,210153148075784391401605289⟩,⟨5958412974436369717797818502,5958412974436369719660451128⟩⟩,⟨⟨198709636461404594721908454,198709636461404596861958331⟩,⟨5686703967624550072721021730,5686703967624550074498638358⟩⟩,⟨⟨187611949731911379407850629,187611949731911381445839410⟩,⟨5417444526625207410285807104,5417444526625207411979254810⟩⟩,⟨⟨176603670878666507142253616,176603670878666509076525474⟩,⟨5143590184553662438815379662,5143590184553662440421771367⟩⟩,⟨⟨165932780470787632635363633,165932780470787634467157575⟩,⟨4872670352582002514948572166,4872670352582002516470112955⟩⟩,⟨⟨155318606561625304786052839,155318606561625306513619132⟩,⟨4596818807493224997881081204,4596818807493224999316212807⟩⟩] +lemma amp3_03_14_eq : ∀ k : Fin 16, amp3_0Expr 3 14 k = amp3_03_14 k := by decide +kernel +noncomputable def amp3_03_15 : Fin 16 → CBox := ![⟨⟨145035613158655622200041490,145035613158655623824768052⟩,⟨4324480061443653037772213228,4324480061443653039121831090⟩⟩,⟨⟨134772549321311576555909974,134772549321311578075876624⟩,⟨4046764236525468035930766799,4046764236525468037193149709⟩⟩,⟨⟨124837966603352850128558894,124837966603352851545423132⟩,⟨3773270955602465723426085298,3773270955602465724602515828⟩⟩,⟨⟨114880963487470649472534008,114880963487470650784154391⟩,⟨3493798066189291985171640400,3493798066189291986260916639⟩⟩,⟨⟨105255304014169034634666122,105255304014169035843020307⟩,⟨3219451412858754961287376407,3219451412858754962290925356⟩⟩,⟨⟨95556780279474824050898717,95556780279474825153498696⟩,⟨2938283203764518817773985455,2938283203764518818689609842⟩⟩,⟨⟨86201582863164168072211934,86201582863164169071482907⟩,⟨2663448859237587215359692391,2663448859237587216189213821⟩⟩,⟨⟨76710273924286169236245794,76710273924286170129242475⟩,⟨2380560469553496668893845260,2380560469553496669635316910⟩⟩,⟨⟨67590214532387264919048343,67590214532387265708822653⟩,⟨2105730519172041088815580885,2105730519172041089471179118⟩⟩,⟨⟨58248221471473432428735241,58248221471473433111595003⟩,⟨1820912411232195602796022244,1820912411232195603362751743⟩⟩,⟨⟨49336388574768574775158108,49336388574768575355175237⟩,⟨1546867131686620927177503656,1546867131686620927658671482⟩⟩,⟨⟨40070315969642351284775932,40070315969642351756971480⟩,⟨1259440216236720541902423379,1259440216236720542294011599⟩⟩,⟨⟨31365478994745584136933022,31365478994745584507240788⟩,⟨987788682558420447342129639,987788682558420447648955345⟩⟩,⟨⟨22050497043216618495667626,22050497043216618756367368⟩,⟨695464056977236407490310937,695464056977236407706148737⟩⟩,⟨⟨13665132145527715779412712,13665132145527715941108309⟩,⟨431419890933529199246110514,431419890933529199379408170⟩⟩,⟨⟨3880430946345568766116794,3880430946345568812043538⟩,⟨122569233409467586923027218,122569233409467586960543035⟩⟩] +lemma amp3_03_15_eq : ∀ k : Fin 16, amp3_0Expr 3 15 k = amp3_03_15 k := by decide +kernel +noncomputable def amp3_03 : Fin 16 → Fin 16 → CBox := ![amp3_03_0,amp3_03_1,amp3_03_2,amp3_03_3,amp3_03_4,amp3_03_5,amp3_03_6,amp3_03_7,amp3_03_8,amp3_03_9,amp3_03_10,amp3_03_11,amp3_03_12,amp3_03_13,amp3_03_14,amp3_03_15] +lemma amp3_03_eq (i k : Fin 16) : amp3_0Expr 3 i k = amp3_03 i k := by + fin_cases i + · exact amp3_03_0_eq k + · exact amp3_03_1_eq k + · exact amp3_03_2_eq k + · exact amp3_03_3_eq k + · exact amp3_03_4_eq k + · exact amp3_03_5_eq k + · exact amp3_03_6_eq k + · exact amp3_03_7_eq k + · exact amp3_03_8_eq k + · exact amp3_03_9_eq k + · exact amp3_03_10_eq k + · exact amp3_03_11_eq k + · exact amp3_03_12_eq k + · exact amp3_03_13_eq k + · exact amp3_03_14_eq k + · exact amp3_03_15_eq k +noncomputable def amp3_04_0 : Fin 16 → CBox := ![⟨⟨108087540564764473198763762,108087540564764473256621629⟩,⟨1017365712714780646405,1017365712714816101665⟩⟩,⟨⟨380429558899274369888607467,380429558899274370093355807⟩,⟨32227844834901853726999,32227844834901978523393⟩⟩,⟨⟨613209148785511274735473659,613209148785511275066372849⟩,⟨144307603078629577649943,144307603078629778828760⟩⟩,⟨⟨870838759435417286761123034,870838759435417287231330110⟩,⟨401710817432016602505246,401710817432016888251182⟩⟩,⟨⟨1110122611941126490496184379,1110122611941126491096016779⟩,⟨846618630911081686052803,846618630911082050391262⟩⟩,⟨⟨1363157402552387190346592460,1363157402552387191083471621⟩,⟨1553203743542669431498369,1553203743542669879000107⟩⟩,⟨⟨1604211278134668391791279488,1604211278134668392658936791⟩,⟨2553427679062347403631280,2553427679062347930434031⟩⟩,⟨⟨1854533666081764771212483692,1854533666081764772215990199⟩,⟨3930825950684612202450313,3930825950684612811681108⟩⟩,⟨⟨2095803055780533116395367982,2095803055780533117530033292⟩,⟨5707149034948221118330257,5707149034948221807111561⟩⟩,⟨⟨2343877065209979312635295927,2343877065209979313904640975⟩,⟨7974992912616157409090134,7974992912616158179766183⟩⟩,⟨⟨2584539784803889453936962939,2584539784803889455337606932⟩,⟨10745843359115807799288651,10745843359115808649545735⟩⟩,⟨⟨2830417005516677870549129536,2830417005516677872083923105⟩,⟨14121091280701552822462534,14121091280701553754149771⟩⟩,⟨⟨3069906860204113639803442158,3069906860204113641469024587⟩,⟨18101889125021378056683568,18101889125021379067844616⟩⟩,⟨⟨3313478071342825125716706413,3313478071342825127515332379⟩,⟨22798164690230290133785551,22798164690230291225922479⟩⟩,⟨⟨3551342582180764963618891665,3551342582180764965548241076⟩,⟨28200671625299006751647043,28200671625299007923054175⟩⟩,⟨⟨3792424635522296952917166490,3792424635522296954979174626⟩,⟨34427613720176448310144072,34427613720176449562066525⟩⟩] +lemma amp3_04_0_eq : ∀ k : Fin 16, amp3_0Expr 4 0 k = amp3_04_0 k := by decide +kernel +noncomputable def amp3_04_1 : Fin 16 → CBox := ![⟨⟨4028270859911521446491347849,4028270859911521448683350118⟩,⟨41459290719596023366249858,41459290719596024697154814⟩⟩,⟨⟨4266643347333295308831508745,4266643347333295311154954511⟩,⟨49421914614835276009833354,49421914614835277420761432⟩⟩,⟨⟨4500113808387353338574681878,4500113808387353341027138091⟩,⟨58285289887787186111968868,58285289887787187601517969⟩⟩,⟨⟨4735536874474457719571043809,4735536874474457722154977469⟩,⟨68183360397692089199626814,68183360397692090768690359⟩⟩,⟨⟨4966297700540065212892440403,4966297700540065215604315394⟩,⟨79075409598275565002172033,79075409598275566649430526⟩⟩,⟨⟨5198521677555150171158580994,5198521677555150173999576081⟩,⟨91102827691590654779866000,91102827691590656506059365⟩⟩,⟨⟨5426256335213825391734649104,5426256335213825394704153785⟩,⟨104214368082311429595573759,104214368082311431399505093⟩⟩,⟨⟨5655027432029830068328735050,5655027432029830071426034032⟩,⟨118558572418822138972971322,118558572418822140855232338⟩⟩,⟨⟨5879433266159994066595263432,5879433266159994069819826577⟩,⟨134073672582852004946882346,134073672582852006906340586⟩⟩,⟨⟨6104497188337284041255267794,6104497188337284044608142097⟩,⟨150915057458186183572276781,150915057458186185609462294⟩⟩,⟨⟨6325283473470903212331856225,6325283473470903215809143353⟩,⟨169010464087999567944146193,169010464087999570057894450⟩⟩,⟨⟨6546387883121727449988009833,6546387883121727453592171711⟩,⟨188521815248313381614982133,188521815248313383805771511⟩⟩,⟨⟨6763274734392282408468774134,6763274734392282412195526746⟩,⟨209366398483646595987688644,209366398483646598254369591⟩⟩,⟨⟨6980171021344690924571018285,6980171021344690928424051566⟩,⟨231712348237249835151851945,231712348237249837494871437⟩⟩,⟨⟨7192888815661819191598554820,7192888815661819195574975695⟩,⟨255466566973823127995989473,255466566973823130414268099⟩⟩,⟨⟨7405333438875873751200409988,7405333438875873755301040130⟩,⟨280803069984181515036378769,280803069984181517530209836⟩⟩] +lemma amp3_04_1_eq : ∀ k : Fin 16, amp3_0Expr 4 1 k = amp3_04_1 k := by decide +kernel +noncomputable def amp3_04_2 : Fin 16 → CBox := ![⟨⟨7613622548809671542572390181,7613622548809671546792561120⟩,⟨307618458522706082788855673,307618458522706085357102008⟩⟩,⟨⟨7821378097100925822357982506,7821378097100925826701280182⟩,⟨336092289619148267338064422,336092289619148269981065037⟩⟩,⟨⟨8024988820637231366350888181,8024988820637231370815100819⟩,⟨366110966970354769734220825,366110966970354772450955019⟩⟩,⟨⟨8227824881946569889631451144,8227824881946569894217051453⟩,⟨397859242260386785138915018,397859242260386787929546204⟩⟩,⟨⟨8426517496233134199430190620,8426517496233134204136012775⟩,⟨431213445365565142132703688,431213445365565144996274584⟩⟩,⟨⟨8624211390672285033175900692,8624211390672285037997054252⟩,⟨466363167876582220390913024,466363167876582223327251364⟩⟩,⟨⟨8817756283978651875753928488,8817756283978651880692971273⟩,⟨503174809944199805834151197,503174809944199808842499577⟩⟩,⟨⟨9010093695805072253285024842,9010093695805072258341258494⟩,⟨541842440962969022611658204,541842440962969025692013395⟩⟩,⟨⟨9198271547626995260762684390,9198271547626995265935121067⟩,⟨582222696060299640328569738,582222696060299643480004479⟩⟩,⟨⟨9385047079060954785669715139,9385047079060954790958386759⟩,⟨624513753276140035536712096,624513753276140038759222848⟩⟩,⟨⟨9567649068057259190315256706,9567649068057259195718472096⟩,⟨668562668250543282895549105,668562668250543286188174946⟩⟩,⟨⟨9748666730177152114782976520,9748666730177152120294957028⟩,⟨714571351742874038731171768,714571351742874042093442995⟩⟩,⟨⟨9925494755862515789157329228,9925494755862515794782939289⟩,⟨762377486480516793688941536,762377486480516797120364531⟩⟩,⟨⟨10100568406880896961183005198,10100568406880896966921072467⟩,⟨812186333523575929373992059,812186333523575932874395522⟩⟩,⟨⟨10271435315087752423893407783,10271435315087752429743020873⟩,⟨863826430484116375827221601,863826430484116379395715347⟩⟩,⟨⟨10440389053072452375740579128,10440389053072452381699430609⟩,⟨917506000071359151756833275,917506000071359155393102061⟩⟩] +lemma amp3_04_2_eq : ∀ k : Fin 16, amp3_0Expr 4 2 k = amp3_04_2 k := by decide +kernel +noncomputable def amp3_04_3 : Fin 16 → CBox := ![⟨⟨10605118857942786919666239975,10605118857942786925733913114⟩,⟨973044683965568814046525680,973044683965568817749721393⟩⟩,⟨⟨10767787372883604509808015736,10767787372883604515984311261⟩,⟨1030653271883720173342264106,1030653271883720177112219001⟩⟩,⟨⟨10926215470039666234156239016,10926215470039666240439678377⟩,⟨1090142780287363171344244149,1090142780287363175180025916⟩⟩,⟨⟨11082444358693500497109903834,11082444358693500503490672003⟩,⟨1151726165495505751671760350,1151726165495505755572174527⟩⟩,⟨⟨11234417725562704300381302665,11234417725562704306867764911⟩,⟨1215206111117198393388701010,1215206111117198397353802412⟩⟩,⟨⟨11384063771502870561478825007,11384063771502870568069589899⟩,⟨1280797334109812437667637738,1280797334109812441697075641⟩⟩,⟨⟨11529441151723926208777373671,11529441151723926215470690571⟩,⟨1348294499353228942336543229,1348294499353228946429353836⟩⟩,⟨⟨11672372572322624032840091855,11672372572322624039634930521⟩,⟨1417913673107950987668025903,1417913673107950991823858111⟩⟩,⟨⟨11811024641857593699207325737,11811024641857593706102571996⟩,⟨1489441837489806938187101351,1489441837489806942405062991⟩⟩,⟨⟨11947121303446440714600160801,11947121303446440721592886281⟩,⟨1563095991521031541955820606,1563095991521031546235284312⟩⟩,⟨⟨12078930816546043857310390038,12078930816546043864401109837⟩,⟨1638655792425954713157407709,1638655792425954717497689601⟩⟩,⟨⟨12208084418663639323149529988,12208084418663639330336586674⟩,⟨1716338750384461637873576341,1716338750384461642274179021⟩⟩,⟨⟨12332946332233289514627719178,12332946332233289521909849475⟩,⟨1795917577556343210850958363,1795917577556343215310968297⟩⟩,⟨⟨12455060561637415358563256678,12455060561637415365939580630⟩,⟨1877609868733088063588922646,1877609868733088068107922809⟩⟩,⟨⟨12572882136864823085729135583,12572882136864823093198173686⟩,⟨1961181792819992279684123287,1961181792819992284261171641⟩⟩,⟨⟨12687872791830367155136004404,12687872791830367162696797391⟩,⟨2046850597829250580587424195,2046850597829250585222067709⟩⟩] +lemma amp3_04_3_eq : ∀ k : Fin 16, amp3_0Expr 4 3 k = amp3_04_3 k := by decide +kernel +noncomputable def amp3_04_4 : Fin 16 → CBox := ![⟨⟨12798573672186533466704030569,12798573672186533474341283673⟩,⟨2134376333215646662264981840,2134376333215646666953972055⟩⟩,⟨⟨12906368757507869610150752453,12906368757507869617879465723⟩,⟨2223975464049050679276710571,2223975464049050684022171940⟩⟩,⟨⟨13009881022438937159360018628,13009881022438937167177953819⟩,⟨2315402366125218523714019933,2315402366125218528514897753⟩⟩,⟨⟨13110420815492774808747088806,13110420815492774816652768163⟩,⟨2408872280684075505924893688,2408872280684075510780614625⟩⟩,⟨⟨13206689009292462322139681296,13206689009292462330131229756⟩,⟨2504134377618229001458606653,2504134377618229006368161401⟩⟩,⟨⟨13299926097483707581841952289,13299926097483707589918843541⟩,⟨2601402228747062342984622560,2601402228747062347947593472⟩⟩,⟨⟨13388907232983438910070039622,13388907232983438918229232554⟩,⟨2700420287741234991308876117,2700420287741234996324018773⟩⟩,⟨⟨13474806522884890631457994681,13474806522884890639699371304⟩,⟨2801400006700950693464207493,2801400006700950698531165396⟩⟩,⟨⟨13556470059727345002446978896,13556470059727345010769070451⟩,⟨2904081634627201912486258339,2904081634627201917604095777⟩⟩,⟨⟨13635008758228595293203930471,13635008758228595301601739708⟩,⟨3008674048861856002294527466,3008674048861856007461824567⟩⟩,⟨⟨13709336555604666787674113181,13709336555604666796150090573⟩,⟨3114913827091087446250545073,3114913827091087451467211111⟩⟩,⟨⟨13780504123402320543317096872,13780504123402320551869404435⟩,⟨3223006812058119977177639996,3223006812058119982442927649⟩⟩,⟨⟨13847490367234597527031909696,13847490367234597535659236423⟩,⟨3332686465209943389865264110,3332686465209943395178271958⟩⟩,⟨⟨13911288445021821232360181371,13911288445021821241059905045⟩,⟨3444155129960154739516299402,3444155129960154744876061193⟩⟩,⟨⟨13970939549672034371729618630,13970939549672034380501559563⟩,⟨3557143728219029240150483474,3557143728219029245556376099⟩⟩,⟨⟨14027381857418176252321927836,14027381857418176261163996000⟩,⟨3671850634329706807530853644,3671850634329706812982014855⟩⟩] +lemma amp3_04_4_eq : ∀ k : Fin 16, amp3_0Expr 4 4 k = amp3_04_4 k := by decide +kernel +noncomputable def amp3_04_5 : Fin 16 → CBox := ![⟨⟨14079716342083346444835051150,14079716342083346453745932921⟩,⟨3788004828890165629494361940,3788004828890165634989886979⟩⟩,⟨⟨14128828551832159310416319762,14128828551832159319394768402⟩,⟨3905800242272824149020397031,3905800242272824154559628875⟩⟩,⟨⟨14173876891875677780796842776,14173876891875677789841506730⟩,⟨4024964533395238300242698189,4024964533395238305824734069⟩⟩,⟨⟨14215696474532138275882022149,14215696474532138284991528364⟩,⟨4145686708418613026080233354,4145686708418613031704369133⟩⟩,⟨⟨14253500928072667525070153362,14253500928072667534242893814⟩,⟨4267693745496789282443614106,4267693745496789288108873002⟩⟩,⟨⟨14288076974692429844075878028,14288076974692429853285675031⟩,⟨4391169240786213739541630877,4391169240786213745239677655⟩⟩,⟨⟨14318691384846014019901643613,14318691384846014029173149250⟩,⟨4515840153749391086941574252,4515840153749391092679318274⟩⟩,⟨⟨14346084402987291233785104725,14346084402987291243116360069⟩,⟨4641884178945692235702663254,4641884178945692241479209477⟩⟩,⟨⟨14369573976226909555311135255,14369573976226909564699949426⟩,⟨4769028940240375243242477146,4769028940240375249056664950⟩⟩,⟨⟨14389855661971336816592886908,14389855661971336826037862590⟩,⟨4897445732925117415967335502,4897445732925117421818429663⟩⟩,⟨⟨14406296723133685900455706133,14406296723133685909954480691⟩,⟨5026863549246854128654297924,5026863549246854134541064719⟩⟩,⟨⟨14419549709429909465289866020,14419549709429909474840973623⟩,⟨5157446781166343513660745243,5157446781166343519582398841⟩⟩,⟨⟨14429029433961716386657921567,14429029433961716396260414825⟩,⟨5288926514038202101372051801,5288926514038202107327845541⟩⟩,⟨⟨14435347015992591327374177103,14435347015992591337025472735⟩,⟨5421459725686305866878234975,5421459725686305872866971573⟩⟩,⟨⟨14437963140088415961692410636,14437963140088415971391494400⟩,⟨5554780339909606550394107401,5554780339909606556415023531⟩⟩,⟨⟨14437448978409380889312074666,14437448978409380899057780212⟩,⟨5689037402459319912538542919,5689037402459319918590957055⟩⟩] +lemma amp3_04_5_eq : ∀ k : Fin 16, amp3_0Expr 4 5 k = amp3_04_5 k := by decide +kernel +noncomputable def amp3_04_6 : Fin 16 → CBox := ![⟨⟨14433309487749780186811225371,14433309487749780196599275527⟩,⟨5823968441393309564733757611,5823968441393309570815610740⟩⟩,⟨⟨14426077289991866828933394020,14426077289991866838765406939⟩,⟨5959714044899289790712912108,5959714044899289796824634779⟩⟩,⟨⟨14415300087845036221919239284,14415300087845036231791905976⟩,⟨6096016131460073491609527442,6096016131460073497749435099⟩⟩,⟨⟨14401473269820770964052515431,14401473269820770973965915162⟩,⟨6233006298189215732440283373,6233006298189215738608214816⟩⟩,⟨⟨14384185825322385761250844940,14384185825322385771202364994⟩,⟨6370431660394543905512917645,6370431660394543911707455234⟩⟩,⟨⟨14363897152416293744056245837,14363897152416293754044897197⟩,⟨6508414282079257379177341826,6508414282079257385397885097⟩⟩,⟨⟨14340236129891257050843106611,14340236129891257060859355466⟩,⟨6646707301904864090113416301,6646707301904864096355316896⟩⟩,⟨⟨14313627339658563384528289168,14313627339658563394579188643⟩,⟨6785422699654169365670573858,6785422699654169371936887468⟩⟩,⟨⟨14283738209894718694021985313,14283738209894718704105003343⟩,⟨6924320483909415367150112603,6924320483909415373439421661⟩⟩,⟨⟨14250959616831958457587492107,14250959616831958467700748816⟩,⟨7063501989456468216538373856,7063501989456468222849656958⟩⟩,⟨⟨14214996251259522683733150042,14214996251259522693875356646⟩,⟨7202734961332202774826472953,7202734961332202781158904561⟩⟩,⟨⟨14176206334748946532218337972,14176206334748946542387149190⟩,⟨7342109518243493788228557375,7342109518243493794580854399⟩⟩,⟨⟨14134330583520431329959681288,14134330583520431340153795392⟩,⟨7481402028133446258600018787,7481402028133446264971337851⟩⟩,⟨⟨14089695559986170726152143664,14089695559986170736370595206⟩,⟨7620690811554856990233115924,7620690811554856996622894709⟩⟩,⟨⟨14042076814989848489591427321,14042076814989848499828892913⟩,⟨7759761765703628865638431595,7759761765703628872043639642⟩⟩,⟨⟨13991770195337644418879750164,13991770195337644429137975329⟩,⟨7898680819171865495158448851,7898680819171865501579982517⟩⟩] +lemma amp3_04_6_eq : ∀ k : Fin 16, amp3_0Expr 4 6 k = amp3_04_6 k := by decide +kernel +noncomputable def amp3_04_7 : Fin 16 → CBox := ![⟨⟨13938584939213138588871706823,13938584939213138599148556383⟩,⟨8037244324657834610910370365,8037244324657834617346927343⟩⟩,⟨⟨13882787072656915439947732306,13882787072656915450242156355⟩,⟨8175505212462621445123180199,8175505212462621451574163868⟩⟩,⟨⟨13824218414914209201720147779,13824218414914209212028533542⟩,⟨8313271236982902317242819213,8313271236982902323706035054⟩⟩,⟨⟨13763116020321779881145424600,13763116020321779891467812816⟩,⟨8450581710525803768432871241,8450581710525803774908353277⟩⟩,⟨⟨13699353221694799481538254456,13699353221694799491871792010⟩,⟨8587256755412933325229142806,8587256755412933331715101211⟩⟩,⟨⟨13633138907611419454692962222,13633138907611419465037427734⟩,⟨8723321431972879240471644470,8723321431972879246968000194⟩⟩,⟨⟨13564376893804316057989799936,13564376893804316068342610241⟩,⟨8858609216839208421279678696,8858609216839208427784794092⟩⟩,⟨⟨13493248668336574752372970537,13493248668336574762732648591⟩,⟨8993130269122809603140806519,8993130269122809609653798175⟩⟩,⟨⟨13419687534344862291304643889,13419687534344862301669573134⟩,⟨9126732426498762488908300897,9126732426498762495428123801⟩⟩,⟨⟨13343848306108432538685204412,13343848306108432549054075355⟩,⟨9259410281325397351788366536,9259410281325397358314264938⟩⟩,⟨⟨13265692812318202096512188409,13265692812318202106882912175⟩,⟨9391027059631885633411640287,9391027059631885639942247578⟩⟩,⟨⟨13185349883671194349698267630,13185349883671194360069462029⟩,⟨9521561104079381977843418041,9521561104079381984377910952⟩⟩,⟨⟨13102808944957686063871376409,13102808944957686074240996020⟩,⟨9650892077252799422406806154,9650892077252799428943812810⟩⟩,⟨⟨13018173498756715825130531462,13018173498756715835496975640⟩,⟨9778981370569384259438594323,9778981370569384265977129044⟩⟩,⟨⟨12931459667818559729910110563,12931459667818559740271433979⟩,⟨9905726152639809841507906606,9905726152639809848046648620⟩⟩,⟨⟨12842746248947084940315562668,12842746248947084950669830696⟩,⟨10031070142211902030055968834,10031070142211902036593643858⟩⟩] +lemma amp3_04_7_eq : ∀ k : Fin 16, amp3_0Expr 4 7 k = amp3_04_7 k := by decide +kernel +noncomputable def amp3_04_8 : Fin 16 → CBox := ![⟨⟨12752075195124500440114353858,12752075195124500450461344600⟩,⟨10154929105121458591211020112,10154929105121458597747626373⟩⟩,⟨⟨12659501188052480324768770225,12659501188052480335108382078⟩,⟨10277228344774870548504264750,10277228344774870555040040652⟩⟩,⟨⟨12565091172886633690958092845,12565091172886633701288276195⟩,⟨10397903337713655819016979544,10397903337713655825550543386⟩⟩,⟨⟨12468876276527070164963383189,12468876276527070175282307311⟩,⟨10516860206617878167847725182,10516860206617878174377916673⟩⟩,⟨⟨12370947627323620210746101640,12370947627323620221052050092⟩,⟨10634055275149534853012198760,10634055275149534859537866200⟩⟩,⟨⟨12271313328455044251478239437,12271313328455044261769356217⟩,⟨10749374695591017522271186352,10749374695591017528791128274⟩⟩,⟨⟨12170087911117654141116024793,12170087911117654151390856628⟩,⟨10862796798838857609545791198,10862796798838857616059068962⟩⟩,⟨⟨12067256957642097555672728837,12067256957642097565929383941⟩,⟨10974186951129577909617030037,10974186951129577916122377366⟩⟩,⟨⟨11962957650041358106560380857,11962957650041358116797454600⟩,⟨11083546675297232710337428746,11083546675297232716833924354⟩⟩,⟨⟨11857153525344798927490858399,11857153525344798937706942627⟩,⟨11190719708089349787624069018,11190719708089349794110887610⟩⟩,⟨⟨11750003692484605102253705977,11750003692484605112447295939⟩,⟨11295731974597181552296713101,11295731974597181558772847680⟩⟩,⟨⟨11641450092161293341558484933,11641450092161293351727325097⟩,⟨11398404708883200998310208932,11398404708883201004773995857⟩⟩,⟨⟨11531673064398257170570264436,11531673064398257180713910013⟩,⟨11498789475413175209120573510,11498789475413175215572015600⟩⟩,⟨⟨11420593376591725440341220495,11420593376591725450457250544⟩,⟨11596684100503760013859177269,11596684100503760020296428463⟩⟩,⟨⟨11308411932153718689369603966,11308411932153718699457801599⟩,⟨11692167053261121760736318227,11692167053261121767159652582⟩⟩,⟨⟨11195028722755675339958117053,11195028722755675350015454320⟩,⟨11785011813049447603770176136,11785011813049447610177072770⟩⟩] +lemma amp3_04_8_eq : ∀ k : Fin 16, amp3_0Expr 4 8 k = amp3_04_8 k := by decide +kernel +noncomputable def amp3_04_9 : Fin 16 → CBox := ![⟨⟨11080664575793104330199800599,11080664575793104340225148114⟩,⟨11875325048569344299184846109,11875325048569344305574613193⟩⟩,⟨⟨10965199079726818642376391672,10965199079726818652368005353⟩,⟨11962854916411658330753256076,11962854916411658337124670575⟩⟩,⟨⟨10848872375114779471857968437,10848872375114779481816917857⟩,⟨12047737611262769685265558474,12047737611262769691620375881⟩⟩,⟨⟨10731543994912029527179935816,10731543994912029537101978938⟩,⟨12129694951829510847404008764,12129694951829510853738243343⟩⟩,⟨⟨10613472811003119578291928522,10613472811003119588176031619⟩,⟨12208894018594742986871878152,12208894018594742993184930712⟩⟩,⟨⟨10494498623863321020164931491,10494498623863321030010007588⟩,⟨12285029235075145117293008986,12285029235075145123584377595⟩⟩,⟨⟨10374898484369644490031288561,10374898484369644499835316785⟩,⟨12358299963021469186111625488,12358299963021469192379564931⟩⟩,⟨⟨10254492758866456343008434435,10254492758866456352770320237⟩,⟨12428372128096910058882299390,12428372128096910065126287991⟩⟩,⟨⟨10133576155025317464324118136,10133576155025317474042175217⟩,⟨12495478806982420225916249178,12495478806982420232134889570⟩⟩,⟨⟨10011949878599879626166208316,10011949878599879635838516329⟩,⟨12559256276019802217083533231,12559256276019802223275278493⟩⟩,⟨⟨9889925802750874630481042383,9889925802750874640112153920⟩,⟨12619972801525971470393597766,12619972801525971476564942976⟩⟩,⟨⟨9767286221101926619925266918,9767286221101926629508348976⟩,⟨12677233806482011582913035749,12677233806482011589056257037⟩⟩,⟨⟨9644359712773699308689010284,9644359712773699318223043293⟩,⟨12731344265802869001874215149,12731344265802869007988705918⟩⟩,⟨⟨9520909882223222865378413346,9520909882223222874861464153⟩,⟨12781877488373212777462610425,12781877488373212783546751600⟩⟩,⟨⟨9397281587796121590652241316,9397281587796121600084034880⟩,⟨12829176724540682360472188346,12829176724540682366526365721⟩⟩,⟨⟨9273219941674907321998965669,9273219941674907331377106223⟩,⟨12872781847134098499041519452,12872781847134098505063456494⟩⟩] +lemma amp3_04_9_eq : ∀ k : Fin 16, amp3_0Expr 4 9 k = amp3_04_9 k := by decide +kernel +noncomputable def amp3_04_10 : Fin 16 → CBox := ![⟨⟨9149085688651263814647909904,9149085688651263823973047155⟩,⟨12913076000709954104873858530,12913076000709954110865265050⟩⟩,⟨⟨9024605618711995261675657249,9024605618711995270944847253⟩,⟨12949564233877359600638596402,12949564233877359606596392608⟩⟩,⟨⟨8900156005588836761825948857,8900156005588836771038125708⟩,⟨12982671260697089636070589554,12982671260697089641994055787⟩⟩,⟨⟨8775445459414988795150497918,8775445459414988804304752975⟩,⟨13011865845697627164553361339,13011865845697627170442283560⟩⟩,⟨⟨8650865462114801437947992874,8650865462114801447042376910⟩,⟨13037616009409894489578954893,13037616009409894495431290715⟩⟩,⟨⟨8526106557451941572293406704,8526106557451941581327090089⟩,⟨13059352694651544110870717252,13059352694651544116686365236⟩⟩,⟨⟨8401575153225740908056768423,8401575153225740917028532782⟩,⟨13077589032858803750443166136,13077589032858803756221133755⟩⟩,⟨⟨8276943810117781748716188259,8276943810117781757624342896⟩,⟨13091716523008848060285485559,13091716523008848066024348901⟩⟩,⟨⟨8152633619791341011092210627,8152633619791341019935566507⟩,⟨13102295285879987918124289946,13102295285879987923823052545⟩⟩,⟨⟨8028299211358000292056024103,8028299211358000300833059760⟩,⟨13108675662500827679712253571,13108675662500827685369706707⟩⟩,⟨⟨7904376160746774183699127347,7904376160746774192408414180⟩,⟨13111466722795377661284854859,13111466722795377666899538764⟩⟩,⟨⟨7780501183390035822649812649,7780501183390035831304471284⟩,⟨13109975835423449521410238483,13109975835423449527005572210⟩⟩,⟨⟨7657124184661244091071170418,7657124184661244099656350218⟩,⟨13104863068938931644976430602,13104863068938931650528680495⟩⟩,⟨⟨7533863948438057103422114173,7533863948438057111936623871⟩,⟨13095390895588513059613957076,13095390895588513065122445768⟩⟩,⟨⟨7411184602149717726179738529,7411184602149717734622505500⟩,⟨13082272531117872665840249172,13082272531117872671304045952⟩⟩,⟨⟨7288686941995592826241767497,7288686941995592834611706086⟩,⟨13064723507257033414799016194,13064723507257033420217637622⟩⟩] +lemma amp3_04_10_eq : ∀ k : Fin 16, amp3_0Expr 4 10 k = amp3_04_10 k := by decide +kernel +noncomputable def amp3_04_11 : Fin 16 → CBox := ![⟨⟨7166849260492193642911052511,7166849260492193651207127140⟩,⟨13043512445221825669500768351,13043512445221825674873329866⟩⟩,⟨⟨7045254268925825563923224871,7045254268925825572144414947⟩,⟨13017805760334312457467165399,13017805760334312462793289242⟩⟩,⟨⟨6924394421718987481884707077,6924394421718987490029621430⟩,⟨12988429859341489297646924092,12988429859341489302924997057⟩⟩,⟨⟨6803834203601598984469734120,6803834203601598992537871347⟩,⟨12954499720255460277713503062,12954499720255460282944144090⟩⟩,⟨⟨6684080285311726169730578331,6684080285311726177720279692⟩,⟨12916902050911340019659342233,12916902050911340024840380681⟩⟩,⟨⟨6564678735176536024238901199,6564678735176536032149146645⟩,⟨12874697911143072117537860264,12874697911143072122668908719⟩⟩,⟨⟨6446150556558307205742964006,6446150556558307213572555298⟩,⟨12828836976547584759973984946,12828836976547584765053641121⟩⟩,⟨⟨6328023158965385689335037183,6328023158965385697084680469⟩,⟨12778323730974931495673742299,12778323730974931500705115769⟩⟩,⟨⟨6210832061486286490521699170,6210832061486286498188685373⟩,⟨12724173653412829155738967014,12724173653412829160717607272⟩⟩,⟨⟨6094085714796064414215193866,6094085714796064421798447332⟩,⟨12665331797658554987021303020,12665331797658554991946691014⟩⟩,⟨⟨5978334409183305113637614216,5978334409183305121136777521⟩,⟨12602882471102409486194622699,12602882471102409491066958683⟩⟩,⟨⟨5863067273078091139961340729,5863067273078091147374584086⟩,⟨12535708225070645787479213170,12535708225070645792296424991⟩⟩,⟨⟨5748849702195562103124203204,5748849702195562110450972975⟩,⟨12464965433213760033464149870,12464965433213760038225988914⟩⟩,⟨⟨5635151069212487209829245327,5635151069212487217068283079⟩,⟨12389470828282574151432859383,12389470828282574156138406055⟩⟩,⟨⟨5522552295576309587007210667,5522552295576309594157608923⟩,⟨12310456327929295112054774271,12310456327929295116702911810⟩⟩,⟨⟨5410502486846970015067381555,5410502486846970022127705833⟩,⟨12226669257357300081348407383,12226669257357300085937814185⟩⟩] +lemma amp3_04_11_eq : ∀ k : Fin 16, amp3_0Expr 4 11 k = amp3_04_11 k := by decide +kernel +noncomputable def amp3_04_12 : Fin 16 → CBox := ![⟨⟨5299598605036228632382400262,5299598605036228639358617609⟩,⟨12139420827114858739573593125,12139420827114858744118829993⟩⟩,⟨⟨5189268890357648952246185927,5189268890357648959131380727⟩,⟨12047385059268084751478523584,12047385059268084755965867992⟩⟩,⟨⟨5080126964526698153247873526,5080126964526698160041402976⟩,⟨11951956513609678100883727340,11951956513609678105312530828⟩⟩,⟨⟨4971579506814651725956342916,4971579506814651732657081986⟩,⟨11851731667654209171088745351,11851731667654209175458411200⟩⟩,⟨⟨4864257533465782377155129414,4864257533465782383762458859⟩,⟨11748192836559880531546924713,11748192836559880535856814184⟩⟩,⟨⟨4757545357564359431523856294,4757545357564359438036773306⟩,⟨11639854320292927852782546931,11639854320292927857032319780⟩⟩,⟨⟨4652092253695657251140552129,4652092253695657257558198189⟩,⟨11528290994826055288473234429,11528290994826055292661535070⟩⟩,⟨⟨4547259239435361302855091478,4547259239435361309177114700⟩,⟨11411929904329072426648036872,11411929904329072430776188524⟩⟩,⟨⟨4443714856139645997377812984,4443714856139646003602851510⟩,⟨11292443748676301657488461528,11292443748676301661553796823⟩⟩,⟨⟨4340795755448946826994471575,4340795755448946833121590654⟩,⟨11168166729462903618256435801,11168166729462903622258766042⟩⟩,⟨⟨4239190917007583671180185006,4239190917007583677208841160⟩,⟨11040875160160211467250301530,11040875160160211471188835318⟩⟩,⟨⟨4138211394787939827123279448,4138211394787939833052250255⟩,⟨10908804229451485826850232497,10908804229451485830724095192⟩⟩,⟨⟨4038567963280529153624413556,4038567963280529159453027802⟩,⟨10773840262747186150549993698,10773840262747186154357970545⟩⟩,⟨⟨3939544661649823520907338351,3939544661649823526638063749⟩,⟨10634112592427048439507830733,10634112592427048443258935662⟩⟩,⟨⟨3841875627090693854105087953,3841875627090693859734254227⟩,⟨10491624661005867344187617848,10491624661005867347872473510⟩⟩,⟨⟨3744816252481093000788863443,3744816252481093006315344008⟩,⟨10344392320674815743229088393,10344392320674815746847075567⟩⟩] +lemma amp3_04_12_eq : ∀ k : Fin 16, amp3_0Expr 4 12 k = amp3_04_12 k := by decide +kernel +noncomputable def amp3_04_13 : Fin 16 → CBox := ![⟨⟨3649125848500894631903521302,3649125848500894637327131400⟩,⟨10194544061302622079493845145,10194544061302622083044846604⟩⟩,⟨⟨3554029280958997053366327430,3554029280958997058686348269⟩,⟨10039973720638874084274153733,10039973720638874087758651803⟩⟩,⟨⟨3460313126081253213958339702,3460313126081253219173937612⟩,⟨9882943734709660308424882165,9882943734709660311840740794⟩⟩,⟨⟨3367169549953243542377730566,3367169549953243547487960890⟩,⟨9721216324032392145943949538,9721216324032392149291096511⟩⟩,⟨⟨3275414814581194286159259648,3275414814581194291163696234⟩,⟨9557197913543233289925502296,9557197913543233293202834716⟩⟩,⟨⟨3184205869562094243330092927,3184205869562094248229736134⟩,⟨9388508241009929517815050230,9388508241009929521028208353⟩⟩,⟨⟨3094391468904845381716648303,3094391468904845386509598909⟩,⟨9217709123208483651408324729,9217709123208483654551707709⟩⟩,⟨⟨3005090420171712716806692056,3005090420171712721491718815⟩,⟨9042265446402566965030354097,9042265446402566968103120298⟩⟩,⟨⟨2917187233521913599822910799,2917187233521913604400065252⟩,⟨8864907451324136422778038152,8864907451324136425780195234⟩⟩,⟨⟨2829759159330008925150984889,2829759159330008929619291867⟩,⟨8682931000002419887439940457,8682931000002419890371396310⟩⟩,⟨⟨2743730276390491656690111061,2743730276390491661049472995⟩,⟨8499249756460134720989614421,8499249756460134723849683652⟩⟩,⟨⟨2658132271048943737161028766,2658132271048943741411526770⟩,⟨8310974201781988967947113428,8310974201781988970739141545⟩⟩,⟨⟨2573933266443338306635276477,2573933266443338310775505350⟩,⟨8121218819281640844220737907,8121218819281640846939828315⟩⟩,⟨⟨2490114655939707510945722739,2490114655939707514974603419⟩,⟨7926889682697347367475606505,7926889682697347370121475238⟩⟩,⟨⟨2407693893711849710650307825,2407693893711849714568218419⟩,⟨7731322439515148039434043619,7731322439515148042007085681⟩⟩,⟨⟨2325596460322086132561654777,2325596460322086136367135718⟩,⟨7531196431271605632183544588,7531196431271605634682402078⟩⟩] +lemma amp3_04_13_eq : ∀ k : Fin 16, amp3_0Expr 4 13 k = amp3_04_13 k := by decide +kernel +noncomputable def amp3_04_14 : Fin 16 → CBox := ![⟨⟨2244895431260576307303219785,2244895431260576310997609759⟩,⟨7330092483041432282479380321,7330092483041432284907433624⟩⟩,⟨⟨2164453642095936426757048867,2164453642095936430338152917⟩,⟨7124436755348031962050026170,7124436755348031964403548018⟩⟩,⟨⟨2085407338328973889916671164,2085407338328973893385089155⟩,⟨6918083884758200752744996393,6918083884758200755024642048⟩⟩,⟨⟨2006548570653898226432709445,2006548570653898229786722801⟩,⟨6707175176996376669985842295,6707175176996376672189589141⟩⟩,⟨⟨1929085904514240991985494618,1929085904514240995226592097⟩,⟨6495873614970292565270806063,6495873614970292567402069442⟩⟩,⟨⟨1851730657331299417969214849,1851730657331299421095254958⟩,⟨6279997256106114462957139298,6279997256106114465012565352⟩⟩,⟨⟨1775774935642936920043894561,1775774935642936923056097396⟩,⟨6064059620565666571998614509,6064059620565666573980384277⟩⟩,⟨⟨1699837011606552735364443269,1699837011606552738260715640⟩,⟨5843508333865144114643040167,5843508333865144116548158500⟩⟩,⟨⟨1625306483484242214803237623,1625306483484242217584442933⟩,⟨5623259758294419898385704026,5623259758294419900214842991⟩⟩,⟨⟨1550693116039930367362013300,1550693116039930370027007645⟩,⟨5398332179446450274647770631,5398332179446450276401348703⟩⟩,⟨⟨1477501624287155313380451839,1477501624287155315929720887⟩,⟨5174110748446996732743971847,5174110748446996734420881543⟩⟩,⟨⟨1404113508856730525764210469,1404113508856730528196480027⟩,⟨4945109508397047026408642200,4945109508397047028009210123⟩⟩,⟨⟨1332171296615410867460159490,1332171296615410869776547302⟩,⟨4717267198118655931070854566,4717267198118655932595750201⟩⟩,⟨⟨1259902455156923930270716338,1259902455156923932469053300⟩,⟨4484496312031306879783795023,4484496312031306881230503472⟩⟩,⟨⟨1189117220101469160042060337,1189117220101469162123981840⟩,⟨4253400785223850296126732554,4253400785223850297497141020⟩⟩,⟨⟨1117854571377976866641693117,1117854571377976868605205913⟩,⟨4017161876444438552126332431,4017161876444438553419052531⟩⟩] +lemma amp3_04_14_eq : ∀ k : Fin 16, amp3_0Expr 4 14 k = amp3_04_14 k := by decide +kernel +noncomputable def amp3_04_15 : Fin 16 → CBox := ![⟨⟨1048132940709839558302710099,1048132940709839560149301907⟩,⟨3783199784228645033759580662,3783199784228645034975341652⟩⟩,⟨⟨977755331440135427032912723,977755331440135428760407069⟩,⟨3543786234992750818377675732,3543786234992750819514970471⟩⟩,⟨⟨909005103464368789581532901,909005103464368791191776747⟩,⟨3307369321525166182952328806,3307369321525166184012265524⟩⟩,⟨⟨839381295990389712433798650,839381295990389713924492506⟩,⟨3065056473631586439355962578,3065056473631586440337452758⟩⟩,⟨⟨771515193413272925928573235,771515193413272927301896175⟩,⟨2826633270511767721386264593,2826633270511767722290541527⟩⟩,⟨⟨702499674662275765762828998,702499674662275767015947248⟩,⟨2581660444753823030513252215,2581660444753823031338363851⟩⟩,⟨⟨635442380963758499863621513,635442380963758500999239239⟩,⟨2341740172299399886288554730,2341740172299399887036111734⟩⟩,⟨⟨566866130460975757102506468,566866130460975758117389598⟩,⟨2094273829805534679394832324,2094273829805534680063075349⟩⟩,⟨⟨500569403508014506072243722,500569403508014506969769282⟩,⟨1853480404442691529334527010,1853480404442691529925383455⟩⟩,⟨⟨432217216285064137697192286,432217216285064138473195269⟩,⟨1603527089250132359948395301,1603527089250132360459185090⟩⟩,⟨⟨366698613902451313319466160,366698613902451313978551842⟩,⟨1362741222863623935549544665,1362741222863623935983228995⟩⟩,⟨⟨298242291517176554712821922,298242291517176555249361751⟩,⟨1109895761162676723497421391,1109895761162676723850380602⟩⟩,⟨⟨233713411606817814150944212,233713411606817814571651714⟩,⟨870731121346295531804185402,870731121346295532080744439⟩⟩,⟨⟨164442842991784815202870703,164442842991784815499017867⟩,⟨613170481679804684986539947,613170481679804685181093855⟩⟩,⟨⟨101965707073669371628362875,101965707073669371811925047⟩,⟨380420923474277062434651280,380420923474277062554814592⟩⟩,⟨⟨28962913528335770690742239,28962913528335770742808867⟩,⟨108087267962443344167327069,108087267962443344201153486⟩⟩] +lemma amp3_04_15_eq : ∀ k : Fin 16, amp3_0Expr 4 15 k = amp3_04_15 k := by decide +kernel +noncomputable def amp3_04 : Fin 16 → Fin 16 → CBox := ![amp3_04_0,amp3_04_1,amp3_04_2,amp3_04_3,amp3_04_4,amp3_04_5,amp3_04_6,amp3_04_7,amp3_04_8,amp3_04_9,amp3_04_10,amp3_04_11,amp3_04_12,amp3_04_13,amp3_04_14,amp3_04_15] +lemma amp3_04_eq (i k : Fin 16) : amp3_0Expr 4 i k = amp3_04 i k := by + fin_cases i + · exact amp3_04_0_eq k + · exact amp3_04_1_eq k + · exact amp3_04_2_eq k + · exact amp3_04_3_eq k + · exact amp3_04_4_eq k + · exact amp3_04_5_eq k + · exact amp3_04_6_eq k + · exact amp3_04_7_eq k + · exact amp3_04_8_eq k + · exact amp3_04_9_eq k + · exact amp3_04_10_eq k + · exact amp3_04_11_eq k + · exact amp3_04_12_eq k + · exact amp3_04_13_eq k + · exact amp3_04_14_eq k + · exact amp3_04_15_eq k +noncomputable def amp3_05_0 : Fin 16 → CBox := ![⟨⟨1017365712714789582412,1017365712714806656212⟩,⟨(-8649277),8649282⟩⟩,⟨⟨32227844834901885180018,32227844834901945277190⟩,⟨(-30443786),30443938⟩⟩,⟨⟨144307603078629628353343,144307603078629725234573⟩,⟨(-49076495),49077175⟩⟩,⟨⟨401710817432016674520882,401710817432016812129440⟩,⟨(-69704918),69706811⟩⟩,⟨⟨846618630911081777873541,846618630911081953334801⟩,⟨(-88874594),88878584⟩⟩,⟨⟨1553203743542669544274406,1553203743542669759792852⟩,⟨(-109157596),109164916⟩⟩,⟨⟨2553427679062347536387104,2553427679062347790106762⟩,⟨(-128496428),128508463⟩⟩,⟨⟨3930825950684612355971439,3930825950684612649403087⟩,⟨(-148595623),148614150⟩⟩,⟨⟨5707149034948221291888609,5707149034948221623651904⟩,⟨(-167990161),168017060⟩⟩,⟨⟨7974992912616157603273367,7974992912616157974503158⟩,⟨(-187953565),187991153⟩⟩,⟨⟨10745843359115808013509729,10745843359115808423099256⟩,⟨(-207348839),207399486⟩⟩,⟨⟨14121091280701553057183412,14121091280701553506030838⟩,⟨(-227191331),227257887⟩⟩,⟨⟨18101889125021378311407097,18101889125021378798578011⟩,⟨(-246552709),246638028⟩⟩,⟨⟨22798164690230290408885678,22798164690230290935112099⟩,⟨(-266276136),266383589⟩⟩,⟨⟨28200671625299007046688031,28200671625299007611159772⟩,⟨(-285577905),285710821⟩⟩,⟨⟨34427613720176448625434016,34427613720176449228761472⟩,⟨(-305177998),305340263⟩⟩] +lemma amp3_05_0_eq : ∀ k : Fin 16, amp3_0Expr 5 0 k = amp3_05_0 k := by decide +kernel +noncomputable def amp3_05_1 : Fin 16 → CBox := ![⟨⟨41459290719596023701396978,41459290719596024342852285⟩,⟨(-324398995),324594402⟩⟩,⟨⟨49421914614835276365094033,49421914614835277045189338⟩,⟨(-343868277),344101214⟩⟩,⟨⟨58285289887787186486983824,58285289887787187205055019⟩,⟨(-362989933),363264645⟩⟩,⟨⟨68183360397692089594610300,68183360397692090351108873⟩,⟨(-382319110),382640474⟩⟩,⟨⟨79075409598275565416789351,79075409598275566211083119⟩,⟨(-401324468),401697169⟩⟩,⟨⟨91102827691590655214296079,91102827691590656046755579⟩,⟨(-420503170),420932559⟩⟩,⟨⟨104214368082311430049500797,104214368082311430919577461⟩,⟨(-439376357),439867544⟩⟩,⟨⟨118558572418822139446543938,118558572418822140354522327⟩,⟨(-458393565),458952359⟩⟩,⟨⟨134073672582852005439799426,134073672582852006385165105⟩,⟨(-477119484),477751404⟩⟩,⟨⟨150915057458186184084660442,150915057458186185067690711⟩,⟨(-495963786),496675084⟩⟩,⟨⟨169010464087999568475706810,169010464087999569495831432⟩,⟨(-514527932),515324518⟩⟩,⟨⟨188521815248313382165818294,188521815248313383223311190⟩,⟨(-533187700),534076247⟩⟩,⟨⟨209366398483646596557519735,209366398483646597651807019⟩,⟨(-551576044),552562836⟩⟩,⟨⟨231712348237249835740755396,231712348237249836872123012⟩,⟨(-570039541),571131656⟩⟩,⟨⟨255466566973823128603691729,255466566973823129771621321⟩,⟨(-588238459),589442533⟩⟩,⟨⟨280803069984181515662938027,280803069984181516867601337⟩,⟨(-606493926),607817417⟩⟩] +lemma amp3_05_1_eq : ∀ k : Fin 16, amp3_0Expr 5 1 k = amp3_05_1 k := by decide +kernel +noncomputable def amp3_05_2 : Fin 16 → CBox := ![⟨⟨307618458522706083434003884,307618458522706084674813386⟩,⟨(-624490152),625940030⟩⟩,⟨⟨336092289619148268001842143,336092289619148269279051481⟩,⟨(-642525864),644109946⟩⟩,⟨⟨366110966970354770416364258,366110966970354771729493556⟩,⟨(-660306459),662032026⟩⟩,⟨⟨397859242260386785839448420,397859242260386787188609169⟩,⟨(-678110774),679985977⟩⟩,⟨⟨431213445365565142851366494,431213445365565144236135516⟩,⟨(-695663107),697695517⟩⟩,⟨⟨466363167876582221127714333,466363167876582222547898543⟩,⟨(-713224498),715422577⟩⟩,⟨⟨503174809944199806588832842,503174809944199808044203939⟩,⟨(-730536239),732907819⟩⟩,⟨⟨541842440962969023384215113,541842440962969024874778130⟩,⟨(-747843328),750397158⟩⟩,⟨⟨582222696060299641118745460,582222696060299642644098651⟩,⟨(-764902435),767646586⟩⟩,⟨⟨624513753276140036344488249,624513753276140037904663649⟩,⟨(-781944015),784887494⟩⟩,⟨⟨668562668250543283720670392,668562668250543285315230170⟩,⟨(-798738735),801889827⟩⟩,⟨⟨714571351742874039573607259,714571351742874041202143039⟩,⟨(-815503790),818871732⟩⟩,⟨⟨762377486480516794548436625,762377486480516796210976411⟩,⟨(-832022660),835615923⟩⟩,⟨⟨812186333523575930250503951,812186333523575931946962128⟩,⟨(-848500387),852328410⟩⟩,⟨⟨863826430484116376720496000,863826430484116378450503326⟩,⟨(-864732233),868803649⟩⟩,⟨⟨917506000071359152666816133,917506000071359154430166154⟩,⟨(-880912051),885236471⟩⟩] +lemma amp3_05_2_eq : ∀ k : Fin 16, amp3_0Expr 5 2 k = amp3_05_2 k := by decide +kernel +noncomputable def amp3_05_3 : Fin 16 → CBox := ![⟨⟨973044683965568814972962705,973044683965568816769328213⟩,⟨(-896845994),901432181⟩⟩,⟨⟨1030653271883720174285090559,1030653271883720176114434553⟩,⟨(-912717564),917575273⟩⟩,⟨⟨1090142780287363172303205486,1090142780287363174165117053⟩,⟨(-928343020),933481118⟩⟩,⟨⟨1151726165495505752646781654,1151726165495505754540217983⟩,⟨(-943896255),949324609⟩⟩,⟨⟨1215206111117198394379527286,1215206111117198396305065498⟩,⟨(-959202943),964930493⟩⟩,⟨⟨1280797334109812438674184368,1280797334109812440631645328⟩,⟨(-974428020),980464717⟩⟩,⟨⟨1348294499353228943358554610,1348294499353228945347498066⟩,⟨(-989405963),995760790⟩⟩,⟨⟨1417913673107950988705408156,1417913673107950990725673631⟩,⟨(-1004293333),1010976292⟩⟩,⟨⟨1489441837489806939239598145,1489441837489806941290818507⟩,⟨(-1018932866),1025952953⟩⟩,⟨⟨1563095991521031543023329216,1563095991521031545105085916⟩,⟨(-1033473265),1040840501⟩⟩,⟨⟨1638655792425954714239670991,1638655792425954716351806866⟩,⟨(-1047765036),1055488404⟩⟩,⟨⟨1716338750384461638970483115,1716338750384461641112726979⟩,⟨(-1061949492),1070038997⟩⟩,⟨⟨1795917577556343211962250610,1795917577556343214134217455⟩,⟨(-1075884472),1084349051⟩⟩,⟨⟨1877609868733088064714481105,1877609868733088066915996752⟩,⟨(-1089704311),1098553925⟩⟩,⟨⟨1961181792819992280823689030,1961181792819992283054341857⟩,⟨(-1103273794),1112517302⟩⟩,⟨⟨2046850597829250581740870232,2046850597829250584000465972⟩,⟨(-1116720654),1126367938⟩⟩] +lemma amp3_05_3_eq : ∀ k : Fin 16, amp3_0Expr 5 3 k = amp3_05_3 k := by decide +kernel +noncomputable def amp3_05_4 : Fin 16 → CBox := ![⟨⟨2134376333215646663432048323,2134376333215646665717870852⟩,⟨(-1129916262),1139976076⟩⟩,⟨⟨2223975464049050680457263121,2223975464049050682771710882⟩,⟨(-1142982092),1153464208⟩⟩,⟨⟨2315402366125218524907797788,2315402366125218527250350329⟩,⟨(-1155795782),1166708814⟩⟩,⟨⟨2408872280684075507131755406,2408872280684075509502127948⟩,⟨(-1168472853),1179826430⟩⟩,⟨⟨2504134377618229002678290582,2504134377618229005076009938⟩,⟨(-1180896918),1192699488⟩⟩,⟨⟨2601402228747062344216980508,2601402228747062346641931516⟩,⟨(-1193177826),1205438842⟩⟩,⟨⟨2700420287741234992553645583,2700420287741234995005121740⟩,⟨(-1205204900),1217932611⟩⟩,⟨⟨2801400006700950694721233840,2801400006700950697199194443⟩,⟨(-1217082571),1230286223⟩⟩,⟨⟨2904081634627201913755278269,2904081634627201916259327216⟩,⟨(-1228705631),1242393246⟩⟩,⟨⟨3008674048861856003575380190,3008674048861856006104426118⟩,⟨(-1240173328),1254353911⟩⟩,⟨⟨3114913827091087447542966565,3114913827091087450097459922⟩,⟨(-1251385699),1266067015⟩⟩,⟨⟨3223006812058119978481463601,3223006812058119981060997707⟩,⟨(-1262437021),1277627805⟩⟩,⟨⟨3332686465209943391180225147,3332686465209943393784441173⟩,⟨(-1273232378),1288940107⟩⟩,⟨⟨3444155129960154740842225629,3444155129960154743470509532⟩,⟨(-1283861268),1300094375⟩⟩,⟨⟨3557143728219029241487109645,3557143728219029244139382151⟩,⟨(-1294233634),1310999283⟩⟩,⟨⟨3671850634329706808878002201,3671850634329706811553764286⟩,⟨(-1304434380),1321740669⟩⟩] +lemma amp3_05_4_eq : ∀ k : Fin 16, amp3_0Expr 5 4 k = amp3_05_4 k := by decide +kernel +noncomputable def amp3_05_5 : Fin 16 → CBox := ![⟨⟨3788004828890165630851767163,3788004828890165633550658963⟩,⟨(-1314378134),1332231885⟩⟩,⟨⟨3905800242272824150387876314,3905800242272824153109614508⟩,⟨(-1324145369),1342554318⟩⟩,⟨⟨4024964533395238301619985443,4024964533395238304364213006⟩,⟨(-1333655245),1352625842⟩⟩,⟨⟨4145686708418613027467141181,4145686708418613030233537629⟩,⟨(-1342983953),1362523542⟩⟩,⟨⟨4267693745496789283839876158,4267693745496789286628011086⟩,⟨(-1352055038),1372169675⟩⟩,⟨⟨4391169240786213740947055220,4391169240786213743748986484⟩,⟨(-1360940553),1381637159⟩⟩,⟨⟨4515840153749391088355894394,4515840153749391091179078131⟩,⟨(-1369568293),1390852502⟩⟩,⟨⟨4641884178945692237125682973,4641884178945692239969626164⟩,⟨(-1378006299),1399884583⟩⟩,⟨⟨4769028940240375244673929926,4769028940240375247538018886⟩,⟨(-1386186496),1408664042⟩⟩,⟨⟨4897445732925117417407021078,4897445732925117420290931042⟩,⟨(-1394173029),1417255834⟩⟩,⟨⟨5026863549246854130101949885,5026863549246854133004993968⟩,⟨(-1401901838),1425594620⟩⟩,⟨⟨5157446781166343515116159516,5157446781166343518037970301⟩,⟨(-1409433287),1433741538⟩⟩,⟨⟨5288926514038202102834962209,5288926514038202105775339515⟩,⟨(-1416707223),1441635169⟩⟩,⟨⟨5421459725686305868348433875,5421459725686305871306606307⟩,⟨(-1423780327),1449332932⟩⟩,⟨⟨5554780339909606551871328981,5554780339909606554847079070⟩,⟨(-1430596257),1456777233⟩⟩,⟨⟨5689037402459319914022576195,5689037402459319917015655313⟩,⟨(-1437208104),1464021865⟩⟩] +lemma amp3_05_5_eq : ∀ k : Fin 16, amp3_0Expr 5 5 k = amp3_05_5 k := by decide +kernel +noncomputable def amp3_05_6 : Fin 16 → CBox := ![⟨⟨5823968441393309566224337274,5823968441393309569233231363⟩,⟨(-1443563249),1471012972⟩⟩,⟨⟨5959714044899289792209824059,5959714044899289795235403116⟩,⟨(-1449711279),1477800802⟩⟩,⟨⟨6096016131460073493112507015,6096016131460073496153630255⟩,⟨(-1455603211),1484335158⟩⟩,⟨⟨6233006298189215733949113574,6233006298189215737006065350⟩,⟨(-1461285209),1490662823⟩⟩,⟨⟨6370431660394543907027334590,6370431660394543910099239563⟩,⟨(-1466711851),1496737183⟩⟩,⟨⟨6508414282079257380697125845,6508414282079257383783834764⟩,⟨(-1471925948),1502601624⟩⟩,⟨⟨6646707301904864091638304435,6646707301904864094735709485⟩,⟨(-1476885569),1508213052⟩⟩,⟨⟨6785422699654169367200343970,6785422699654169370311957286⟩,⟨(-1481630238),1513611519⟩⟩,⟨⟨6924320483909415368684502808,6924320483909415371809445312⟩,⟨(-1486121451),1518757390⟩⟩,⟨⟨7063501989456468218077159757,7063501989456468221214871297⟩,⟨(-1490395507),1523687441⟩⟩,⟨⟨7202734961332202776369393882,7202734961332202779519585057⟩,⟨(-1494417266),1528365437⟩⟩,⟨⟨7342109518243493789775386880,7342109518243493792937240250⟩,⟨(-1498219859),1532824935⟩⟩,⟨⟨7481402028133446260150497563,7481402028133446263323703240⟩,⟨(-1501771455),1537033050⟩⟩,⟨⟨7620690811554856991787015662,7620690811554856994971480964⟩,⟨(-1505102069),1541020164⟩⟩,⟨⟨7759761765703628867195494500,7759761765703628870388719511⟩,⟨(-1508183129),1544756698⟩⟩,⟨⟨7898680819171865496718444953,7898680819171865499921799258⟩,⟨(-1511041577),1548269904⟩⟩] +lemma amp3_05_6_eq : ∀ k : Fin 16, amp3_0Expr 5 6 k = amp3_05_6 k := by decide +kernel +noncomputable def amp3_05_7 : Fin 16 → CBox := ![⟨⟨8037244324657834612473043526,8037244324657834615685752115⟩,⟨(-1513652056),1551533465⟩⟩,⟨⟨8175505212462621446688298976,8175505212462621449910241662⟩,⟨(-1516038476),1554571540⟩⟩,⟨⟨8313271236982902318810129272,8313271236982902322039635283⟩,⟨(-1518178653),1557361041⟩⟩,⟨⟨8450581710525803770002139851,8450581710525803773239722473⟩,⟨(-1520093505),1559923069⟩⟩,⟨⟨8587256755412933326800117584,8587256755412933330044506892⟩,⟨(-1521763982),1562237728⟩⟩,⟨⟨8723321431972879242044091580,8723321431972879245295690241⟩,⟨(-1523208041),1564323091⟩⟩,⟨⟨8858609216839208422853347847,8858609216839208426111033974⟩,⟨(-1524409733),1566162426⟩⟩,⟨⟨8993130269122809604715462946,8993130269122809607978836940⟩,⟨(-1525384085),1567770807⟩⟩,⟨⟨9126732426498762490483696550,9126732426498762493752224715⟩,⟨(-1526118219),1569134639⟩⟩,⟨⟨9259410281325397353364265890,9259410281325397356637678038⟩,⟨(-1526624256),1570266018⟩⟩,⟨⟨9391027059631885634987797677,9391027059631885638265233776⟩,⟨(-1526892363),1571154466⟩⟩,⟨⟨9521561104079381979419597349,9521561104079381982700721096⟩,⟨(-1526931776),1571809116⟩⟩,⟨⟨9650892077252799423982764241,9650892077252799427266705308⟩,⟨(-1526735687),1572222594⟩⟩,⟨⟨9778981370569384261014094640,9778981370569384264300355387⟩,⟨(-1526310463),1572401085⟩⟩,⟨⟨9905726152639809843082708684,9905726152639809846370464560⟩,⟨(-1525652299),1572340299⟩⟩,⟨⟨10031070142211902031629835846,10031070142211902034918301365⟩,⟨(-1524764713),1572043488⟩⟩] +lemma amp3_05_7_eq : ∀ k : Fin 16, amp3_0Expr 5 7 k = amp3_05_7 k := by decide +kernel +noncomputable def amp3_05_8 : Fin 16 → CBox := ![⟨⟨10154929105121458592783714399,10154929105121458596073378393⟩,⟨(-1523646886),1571509437⟩⟩,⟨⟨10277228344774870550075549360,10277228344774870553367139474⟩,⟨(-1522299493),1570738469⟩⟩,⟨⟨10397903337713655820586619766,10397903337713655823879239003⟩,⟨(-1520724694),1569732439⟩⟩,⟨⟨10516860206617878169415484086,10516860206617878172708461536⟩,⟨(-1518920327),1568488744⟩⟩,⟨⟨10634055275149534854577844719,10634055275149534857870507205⟩,⟨(-1516891519),1567012304⟩⟩,⟨⟨10749374695591017523834482596,10749374695591017527126117883⟩,⟨(-1514633279),1565297591⟩⟩,⟨⟨10862796798838857611106509322,10862796798838857614396650827⟩,⟨(-1512153697),1563352594⟩⟩,⟨⟨10974186951129577911174933568,10974186951129577914462803820⟩,⟨(-1509444947),1561168852⟩⟩,⟨⟨11083546675297232711892292633,11083546675297232715177435657⟩,⟨(-1506518082),1558757425⟩⟩,⟨⟨11190719708089349789175657215,11190719708089349792457735826⟩,⟨(-1503362442),1556106917⟩⟩,⟨⟨11295731974597181553844804040,11295731974597181557123269539⟩,⟨(-1499992043),1553231464⟩⟩,⟨⟨11398404708883200999854567119,11398404708883201003128243019⟩,⟨(-1496393379),1550116722⟩⟩,⟨⟨11498789475413175210660980995,11498789475413175213930321121⟩,⟨(-1492583438),1546779918⟩⟩,⟨⟨11596684100503760015395399226,11596684100503760018659043472⟩,⟨(-1488545861),1543203740⟩⟩,⟨⟨11692167053261121762268140447,11692167053261121765526806324⟩,⟨(-1484300613),1539408525⟩⟩,⟨⟨11785011813049447605297364579,11785011813049447608549015719⟩,⟨(-1479828464),1535373976⟩⟩] +lemma amp3_05_8_eq : ∀ k : Fin 16, amp3_0Expr 5 8 k = amp3_05_8 k := by decide +kernel +noncomputable def amp3_05_9 : Fin 16 → CBox := ![⟨⟨11875325048569344300707190436,11875325048569344303951570644⟩,⟨(-1475152374),1531123553⟩⟩,⟨⟨11962854916411658332270523136,11962854916411658335506892232⟩,⟨(-1470250225),1526633953⟩⟩,⟨⟨12047737611262769686777541922,12047737611262769690008082952⟩,⟨(-1465147984),1521931784⟩⟩,⟨⟨12129694951829510848910476440,12129694951829510852131684649⟩,⟨(-1459820625),1516990709⟩⟩,⟨⟨12208894018594742988372627830,12208894018594742991584323241⟩,⟨(-1454297142),1511840510⟩⟩,⟨⟨12285029235075145118787809592,12285029235075145121989969182⟩,⟨(-1448549574),1506451785⟩⟩,⟨⟨12358299963021469187600279033,12358299963021469190791568208⟩,⟨(-1442609970),1500857522⟩⟩,⟨⟨12428372128096910060364575977,12428372128096910063544949706⟩,⟨(-1436447400),1495025219⟩⟩,⟨⟨12495478806982420227391955176,12495478806982420230560417868⟩,⟨(-1430096998),1488991106⟩⟩,⟨⟨12559256276019802218552440002,12559256276019802221707918946⟩,⟨(-1423524831),1482719537⟩⟩,⟨⟨12619972801525971471855516153,12619972801525971475004899109⟩,⟨(-1416769149),1476250027⟩⟩,⟨⟨12677233806482011584367738452,12677233806482011587503773156⟩,⟨(-1409792979),1469543742⟩⟩,⟨⟨12731344265802869003321517603,12731344265802869006443980801⟩,⟨(-1402637727),1462643524⟩⟩,⟨⟨12781877488373212778902286737,12781877488373212782010028207⟩,⟨(-1395263331),1455507303⟩⟩,⟨⟨12829176724540682361904058657,12829176724540682364997837952⟩,⟨(-1387714397),1448181302⟩⟩,⟨⟨12872781847134098500465359340,12872781847134098503543365893⟩,⟨(-1379947727),1440620153⟩⟩] +lemma amp3_05_9_eq : ∀ k : Fin 16, amp3_0Expr 5 9 k = amp3_05_9 k := by decide +kernel +noncomputable def amp3_05_10 : Fin 16 → CBox := ![⟨⟨12913076000709954106289492960,12913076000709954109353800510⟩,⟨(-1372011176),1432873517⟩⟩,⟨⟨12949564233877359602045802479,12949564233877359605093794187⟩,⟨(-1363858352),1424892671⟩⟩,⟨⟨12982671260697089637469197176,12982671260697089640500507245⟩,⟨(-1355540413),1416730774⟩⟩,⟨⟨13011865845697627165943149194,13011865845697627168958023410⟩,⟨(-1347007717),1408335678⟩⟩,⟨⟨13037616009409894490959757925,13037616009409894493956497456⟩,⟨(-1338314782),1399764110⟩⟩,⟨⟨13059352694651544112242315771,13059352694651544115221275782⟩,⟨(-1329408646),1390960424⟩⟩,⟨⟨13077589032858803751805400248,13077589032858803754765921217⟩,⟨(-1320347258),1381984988⟩⟩,⟨⟨13091716523008848061638137234,13091716523008848064579248553⟩,⟨(-1311074263),1372778579⟩⟩,⟨⟨13102295285879987919467204561,13102295285879987922388231979⟩,⟨(-1301651112),1363405289⟩⟩,⟨⟨13108675662500827681045214785,13108675662500827683945399516⟩,⟨(-1292017977),1353802225⟩⟩,⟨⟨13111466722795377662607713435,13111466722795377665485906897⟩,⟨(-1282239892),1344037296⟩⟩,⟨⟨13109975835423449522722779790,13109975835423449525602847549⟩,⟨(-1272253467),1334043843⟩⟩,⟨⟨13104863068938931646278510902,13104863068938931649137019215⟩,⟨(-1262127411),1323893690⟩⟩,⟨⟨13095390895588513060905363462,13095390895588513063742078019⟩,⟨(-1251794672),1313516306⟩⟩,⟨⟨13082272531117872667120843520,13082272531117872669935122003⟩,⟨(-1241327732),1302987536⟩⟩,⟨⟨13064723507257033416068587328,13064723507257033418860385880⟩,⟨(-1230655773),1292232865⟩⟩] +lemma amp3_05_10_eq : ∀ k : Fin 16, amp3_0Expr 5 10 k = amp3_05_10 k := by decide +kernel +noncomputable def amp3_05_11 : Fin 16 → CBox := ![⟨⟨13043512445221825670759183875,13043512445221825673527894563⟩,⟨(-1219855157),1281332277⟩⟩,⟨⟨13017805760334312458714215862,13017805760334312461459897033⟩,⟨(-1208851185),1270207143⟩⟩,⟨⟨12988429859341489298882482948,12988429859341489301603786002⟩,⟨(-1197724215),1258941717⟩⟩,⟨⟨12954499720255460278937362575,12954499720255460281635339101⟩,⟨(-1186395540),1247453121⟩⟩,⟨⟨12916902050911340020871381825,12916902050911340023544113508⟩,⟨(-1174949644),1235830018⟩⟩,⟨⟨12874697911143072118737873893,12874697911143072121385402544⟩,⟨(-1163303675),1223985132⟩⟩,⟨⟨12828836976547584761161858126,12828836976547584763783021239⟩,⟨(-1151546384),1212011688⟩⟩,⟨⟨12778323730974931496849270651,12778323730974931499447603661⟩,⟨(-1139590624),1199817846⟩⟩,⟨⟨12724173653412829156902042275,12724173653412829159473321634⟩,⟨(-1127529566),1187501567⟩⟩,⟨⟨12665331797658554988171722429,12665331797658554990715851660⟩,⟨(-1115271601),1174966266⟩⟩,⟨⟨12602882471102409487332284349,12602882471102409489849677555⟩,⟨(-1102914494),1162314821⟩⟩,⟨⟨12535708225070645788603915868,12535708225070645791092920286⟩,⟨(-1090361992),1149445711⟩⟩,⟨⟨12464965433213760034575798202,12464965433213760037036365666⟩,⟨(-1077716640),1136466932⟩⟩,⟨⟨12389470828282574152531253659,12389470828282574154962880905⟩,⟨(-1064877342),1123271810⟩⟩,⟨⟨12310456327929295113139825718,12310456327929295115541582712⟩,⟨(-1051951630),1109973684⟩⟩,⟨⟨12226669257357300082419917733,12226669257357300084790896301⟩,⟨(-1038833346),1096460493⟩⟩] +lemma amp3_05_11_eq : ∀ k : Fin 16, amp3_0Expr 5 11 k = amp3_05_11 k := by decide +kernel +noncomputable def amp3_05_12 : Fin 16 → CBox := ![⟨⟨12139420827114858740631480403,12139420827114858742986414025⟩,⟨(-1025635235),1082851159⟩⟩,⟨⟨12047385059268084752522590852,12047385059268084754848167714⟩,⟨(-1012245837),1069027975⟩⟩,⟨⟨11951956513609678101913899585,11951956513609678104209629503⟩,⟨(-998783361),1055115722⟩⟩,⟨⟨11851731667654209172104826855,11851731667654209174370521321⟩,⟨(-985130777),1040990755⟩⟩,⟨⟨11748192836559880532548847602,11748192836559880534784011376⟩,⟨(-971412036),1026784012⟩⟩,⟨⟨11639854320292927853770116583,11639854320292927855974815384⟩,⟨(-957504247),1012365598⟩⟩,⟨⟨11528290994826055289446390298,11528290994826055291619396858⟩,⟨(-943537407),997872934⟩⟩,⟨⟨11411929904329072427606585285,11411929904329072429749626831⟩,⟨(-929382438),983169528⟩⟩,⟨⟨11292443748676301658432349475,11292443748676301660542871341⟩,⟨(-915175727),968399650⟩⟩,⟨⟨11168166729462903619185470390,11168166729462903621263686270⟩,⟨(-900781643),953419820⟩⟩,⟨⟨11040875160160211468164437515,11040875160160211470209652615⟩,⟨(-886343344),938381566⟩⟩,⟨⟨10908804229451485827749277574,10908804229451485829761018421⟩,⟨(-871718247),923133988⟩⟩,⟨⟨10773840262747186151433910629,10773840262747186153411042457⟩,⟨(-857056702),907836326⟩⟩,⟨⟨10634112592427048440376427585,10634112592427048442328364709⟩,⟨(-842208719),892329774⟩⟩,⟨⟨10491624661005867345040865664,10491624661005867346958293535⟩,⟨(-827332323),876781799⟩⟩,⟨⟨10344392320674815744066795359,10344392320674815745949494875⟩,⟨(-812269607),861025143⟩⟩] +lemma amp3_05_12_eq : ∀ k : Fin 16, amp3_0Expr 5 12 k = amp3_05_12 k := by decide +kernel +noncomputable def amp3_05_13 : Fin 16 → CBox := ![⟨⟨10194544061302622080315990889,10194544061302622082163889793⟩,⟨(-797186808),845236074⟩⟩,⟨⟨10039973720638874085080546274,10039973720638874086894527329⟩,⟨(-781917529),829238269⟩⟩,⟨⟨9882943734709660309215510055,9882943734709660310993463640⟩,⟨(-766636826),813217447⟩⟩,⟨⟨9721216324032392146718620296,9721216324032392148460875632⟩,⟨(-751169164),796987526⟩⟩,⟨⟨9557197913543233290684213780,9557197913543233292389675059⟩,⟨(-735699110),780744415⟩⟩,⟨⟨9388508241009929518557609081,9388508241009929520232319771⟩,⟨(-720041250),764291481⟩⟩,⟨⟨9217709123208483652134738547,9217709123208483653773084642⟩,⟨(-704390450),747835665⟩⟩,⟨⟨9042265446402566965740428203,9042265446402566967341973962⟩,⟨(-688550572),731168880⟩⟩,⟨⟨8864907451324136423471790381,8864907451324136425036509019⟩,⟨(-672727689),714510068⟩⟩,⟨⟨8682931000002419888117174303,8682931000002419889645383335⟩,⟨(-656713962),697638643⟩⟩,⟨⟨8499249756460134721650358525,8499249756460134723141315639⟩,⟨(-640727719),680786667⟩⟩,⟨⟨8310974201781988968591168860,8310974201781988970048634148⟩,⟨(-624548288),663719850⟩⟩,⟨⟨8121218819281640844848144777,8121218819281640846267140868⟩,⟨(-608407475),646684675⟩⟩,⟨⟨7926889682697347368086162758,7926889682697347369466826674⟩,⟨(-592070452),629431733⟩⟩,⟨⟨7731322439515148040027801612,7731322439515148041370422108⟩,⟨(-575783933),612223460⟩⟩,⟨⟨7531196431271605632760298313,7531196431271605634063946588⟩,⟨(-559297381),594793668⟩⟩] +lemma amp3_05_13_eq : ∀ k : Fin 16, amp3_0Expr 5 13 k = amp3_05_13 k := by decide +kernel +noncomputable def amp3_05_14 : Fin 16 → CBox := ![⟨⟨7330092483041432283039195297,7330092483041432284307118107⟩,⟨(-542874109),577422546⟩⟩,⟨⟨7124436755348031962592691448,7124436755348031963821600782⟩,⟨(-526246022),559825156⟩⟩,⟨⟨6918083884758200753270591751,6918083884758200754460979582⟩,⟨(-509695057),542301601⟩⟩,⟨⟨6707175176996376670494150650,6707175176996376671644446242⟩,⟨(-492933337),524545820⟩⟩,⟨⟨6495873614970292565761922777,6495873614970292566875345769⟩,⟨(-476263867),506880436⟩⟩,⟨⟨6279997256106114463430839697,6279997256106114464504503748⟩,⟨(-459376293),488975386⟩⟩,⟨⟨6064059620565666572455011167,6064059620565666573490865820⟩,⟨(-442597673),471179002⟩⟩,⟨⟨5843508333865144115081899016,5843508333865144116077436007⟩,⟨(-425591852),453133671⟩⟩,⟨⟨5623259758294419898807156874,5623259758294419899762776785⟩,⟨(-408713652),435217387⟩⟩,⟨⟨5398332179446450275051571754,5398332179446450275968203998⟩,⟨(-391596959),417040558⟩⟩,⟨⟨5174110748446996733130274846,5174110748446996734006495153⟩,⟨(-374629038),399015830⟩⟩,⟨⟨4945109508397047026777186796,4945109508397047027613862763⟩,⟨(-357408524),380715979⟩⟩,⟨⟨4717267198118655931421819464,4717267198118655932219251621⟩,⟨(-340361141),362594723⟩⟩,⟨⟨4484496312031306880116901603,4484496312031306880873153952⟩,⟨(-323043390),344179868⟩⟩,⟨⟨4253400785223850296442189000,4253400785223850297158718540⟩,⟨(-305927380),325974650⟩⟩,⟨⟨4017161876444438552423836692,4017161876444438553099882390⟩,⟨(-288518290),307452112⟩⟩] +lemma amp3_05_14_eq : ∀ k : Fin 16, amp3_0Expr 5 14 k = amp3_05_14 k := by decide +kernel +noncomputable def amp3_05_15 : Fin 16 → CBox := ![⟨⟨3783199784228645034039376375,3783199784228645034675163654⟩,⟨(-271345339),289176443⟩⟩,⟨⟨3543786234992750818639430354,3543786234992750819234142504⟩,⟨(-253849755),270552447⟩⟩,⟨⟨3307369321525166183196329864,3307369321525166183750480160⟩,⟨(-236632890),252221294⟩⟩,⟨⟨3065056473631586439581836846,3065056473631586440095111404⟩,⟨(-219053953),233500279⟩⟩,⟨⟨2826633270511767721594355964,2826633270511767722067276130⟩,⟨(-201808416),215130998⟩⟩,⟨⟨2581660444753823030703131286,2581660444753823031134635965⟩,⟨(-184146342),196314310⟩⟩,⟨⟨2341740172299399886460641342,2341740172299399886851471667⟩,⟨(-166891340),177928508⟩⟩,⟨⟨2094273829805534679548615651,2094273829805534679898071885⟩,⟨(-149140852),159011654⟩⟩,⟨⟨1853480404442691529470536178,1853480404442691529779449487⟩,⟨(-131903444),140639329⟩⟩,⟨⟨1603527089250132360065992741,1603527089250132360333005265⟩,⟨(-114047646),121605443⟩⟩,⟨⟨1362741222863623935649432662,1362741222863623935876050252⟩,⟨(-96872877),103295795⟩⟩,⟨⟨1109895761162676723578741400,1109895761162676723763124558⟩,⟨(-78865429),84096626⟩⟩,⟨⟨870731121346295531867960560,870731121346295532012313602⟩,⟨(-61850197),65954156⟩⟩,⟨⟨613170481679804685031439076,613170481679804685132916841⟩,⟨(-43543935),46433951⟩⟩,⟨⟨380420923474277062462502691,380420923474277062524929798⟩,⟨(-27010779),28803792⟩⟩,⟨⟨108087267962443344175239691,108087267962443344192663167⟩,⟨(-7673799),8183240⟩⟩] +lemma amp3_05_15_eq : ∀ k : Fin 16, amp3_0Expr 5 15 k = amp3_05_15 k := by decide +kernel +noncomputable def amp3_05 : Fin 16 → Fin 16 → CBox := ![amp3_05_0,amp3_05_1,amp3_05_2,amp3_05_3,amp3_05_4,amp3_05_5,amp3_05_6,amp3_05_7,amp3_05_8,amp3_05_9,amp3_05_10,amp3_05_11,amp3_05_12,amp3_05_13,amp3_05_14,amp3_05_15] +lemma amp3_05_eq (i k : Fin 16) : amp3_0Expr 5 i k = amp3_05 i k := by + fin_cases i + · exact amp3_05_0_eq k + · exact amp3_05_1_eq k + · exact amp3_05_2_eq k + · exact amp3_05_3_eq k + · exact amp3_05_4_eq k + · exact amp3_05_5_eq k + · exact amp3_05_6_eq k + · exact amp3_05_7_eq k + · exact amp3_05_8_eq k + · exact amp3_05_9_eq k + · exact amp3_05_10_eq k + · exact amp3_05_11_eq k + · exact amp3_05_12_eq k + · exact amp3_05_13_eq k + · exact amp3_05_14_eq k + · exact amp3_05_15_eq k +noncomputable def amp3_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp3_00,amp3_01,amp3_02,amp3_03,amp3_04,amp3_05] +lemma amp3_0_eq (j : Fin 6) (i k : Fin 16) : amp3_0Expr j i k = amp3_0 j i k := by + fin_cases j + · exact amp3_00_eq i k + · exact amp3_01_eq i k + · exact amp3_02_eq i k + · exact amp3_03_eq i k + · exact amp3_04_eq i k + · exact amp3_05_eq i k +lemma amp3_0_contains (j : Fin 6) (i k : Fin 16) : + (amp3_0 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude false 3 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp3_0_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 3 j) (bLookup_contains 3 j) false) +noncomputable def amp3_1Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 3 j) (bLookup 3 j) true) +noncomputable def amp3_10_0 : Fin 16 → CBox := ![⟨⟨178776584874023315329347999,178776584874023315370061539⟩,⟨(-516083547009096694081565204),(-516083547009096694036509008)⟩⟩,⟨⟨629264447029517718401686713,629264447029517718546810596⟩,⟨(-1816529989419765287808678824),(-1816529989419765287644837768)⟩⟩,⟨⟨1014414495963543606810259718,1014414495963543607045593215⟩,⟨(-2928362411572052200011136404),(-2928362411572052199743017371)⟩⟩,⟨⟨1440842106367455813356471448,1440842106367455813691094947⟩,⟨(-4159352889854990063865575394),(-4159352889854990063483698944)⟩⟩,⟨⟨1837153108049314193090098629,1837153108049314193517277586⟩,⟨(-5303404207374145887226919957),(-5303404207374145886738518167)⟩⟩,⟨⟨2256524817754308917690502211,2256524817754308918215444112⟩,⟨(-6514026054817607367205777424),(-6514026054817607366605166082)⟩⟩,⟨⟨2656435792071101113031730727,2656435792071101113650080664⟩,⟨(-7668469598186034814575566066),(-7668469598186034813867427582)⟩⟩,⟨⟨3072133445990435319895729756,3072133445990435320611055895⟩,⟨(-8868485360145152285077979907),(-8868485360145152284258413586)⟩⟩,⟨⟨3473340580412691300139992971,3473340580412691300949032302⟩,⟨(-10026670595442591582120612060),(-10026670595442591581193163135)⟩⟩,⟨⟨3886397599776523264997115749,3886397599776523265902093110⟩,⟨(-11219063502044455816624867534),(-11219063502044455815587917238)⟩⟩,⟨⟨4287805485929443699966200696,4287805485929443700965156846⟩,⟨(-12377828257670592144590811492),(-12377828257670592143445293266)⟩⟩,⟨⟨4698569893355039727044388633,4698569893355039728139217921⟩,⟨(-13563602963674017037327158021),(-13563602963674017036071396357)⟩⟩,⟨⟨5099502883647184281211394888,5099502883647184282399619479⟩,⟨(-14720996813034873396189253370),(-14720996813034873394826415632)⟩⟩,⟨⟨5508052685234101317304126944,5508052685234101318587199992⟩,⟨(-15900378502652747127046396108),(-15900378502652747125575375162)⟩⟩,⟨⟨5908018787060499827167002222,5908018787060499828543798049⟩,⟨(-17054981185433729371263710837),(-17054981185433729369684276511)⟩⟩,⟨⟨6314304889329281697450176362,6314304889329281698922030641⟩,⟨(-18227828137998154550760321738),(-18227828137998154549071180326)⟩⟩] +lemma amp3_10_0_eq : ∀ k : Fin 16, amp3_1Expr 0 0 k = amp3_10_0 k := by decide +kernel +noncomputable def amp3_10_1 : Fin 16 → CBox := ![⟨⟨6712905375084154821002163580,6712905375084154822567108879⟩,⟨(-19378488626746612489883570204),(-19378488626746612488087285542)⟩⟩,⟨⟨7116811458893626801438955157,7116811458893626803097842796⟩,⟨(-20544465057820243452992178041),(-20544465057820243451088443398)⟩⟩,⟨⟨7513700288185479520880808176,7513700288185479522631856252⟩,⟨(-21690184419970276426958860238),(-21690184419970276424949974828)⟩⟩,⟨⟨7915071511567247978731148812,7915071511567247980577175520⟩,⟨(-22848843339292443596750710681),(-22848843339292443594630356177)⟩⟩,⟨⟨8309934963699564221252943963,8309934963699564223190174002⟩,⟨(-23988715941201132047928058577),(-23988715941201132045704495168)⟩⟩,⟨⟨8708593155276932931663343903,8708593155276932933692666219⟩,⟨(-25139543012310348166222035137),(-25139543012310348163894234995)⟩⟩,⟨⟨9101138730168082672685547926,9101138730168082674807967876⟩,⟨(-26272724478973356683613003844),(-26272724478973356681175586780)⟩⟩,⟨⟨9496891073954188849843459412,9496891073954188852056886132⟩,⟨(-27415163090060025286744936549),(-27415163090060025284205238350)⟩⟩,⟨⟨9886841054724459425649615405,9886841054724459427955104756⟩,⟨(-28540851721901050823765953820),(-28540851721901050821118574272)⟩⟩,⟨⟨10279485372927895293561166081,10279485372927895295959757839⟩,⟨(-29674318235953704694359988622),(-29674318235953704691603018402)⟩⟩,⟨⟨10666572908823690775540024945,10666572908823690778027039652⟩,⟨(-30791743701200636931607744945),(-30791743701200636928752439838)⟩⟩,⟨⟨11055901047314695422472131356,11055901047314695425051144532⟩,⟨(-31915637229005024096250828468),(-31915637229005024093287775150)⟩⟩,⟨⟨11439867680844907707739092186,11439867680844907710404706421⟩,⟨(-33024053425147536341191386223),(-33024053425147536338133992189)⟩⟩,⟨⟨11825667778884814560519773120,11825667778884814563277788848⟩,⟨(-34137762377431157505004462423),(-34137762377431157501836726525)⟩⟩,⟨⟨12206261841045965248519547062,12206261841045965251366875357⟩,⟨(-35236442798634725060533596172),(-35236442798634725057262324916)⟩⟩,⟨⟨12588319915260722389435530052,12588319915260722392373252115⟩,⟨(-36339349458604525328146650475),(-36339349458604525324769316189)⟩⟩] +lemma amp3_10_1_eq : ∀ k : Fin 16, amp3_1Expr 0 1 k = amp3_10_1 k := by decide +kernel +noncomputable def amp3_10_2 : Fin 16 → CBox := ![⟨⟨12965295463818583362310902000,12965295463818583365332862928⟩,⟨(-37427584130793464685059853638),(-37427584130793464681592163610)⟩⟩,⟨⟨13343396554569321849590476171,13343396554569321852702577544⟩,⟨(-38519067963422614615110489554),(-38519067963422614611535863671)⟩⟩,⟨⟨13716512663740494234201085175,13716512663740494237401330105⟩,⟨(-39596161393767425469044977756),(-39596161393767425465367159689)⟩⟩,⟨⟨14090441693045962456358327287,14090441693045962459647434256⟩,⟨(-40675601522404063165656757890),(-40675601522404063161874003108)⟩⟩,⟨⟨14459461977215688466095289721,14459461977215688469473034146⟩,⟨(-41740871324413180700245732637),(-41740871324413180696356699514)⟩⟩,⟨⟨14829004411061715032174690260,14829004411061715035632679113⟩,⟨(-42807648442703145245613927883),(-42807648442703145241643056679)⟩⟩,⟨⟨15193696708276728726399124752,15193696708276728729943508236⟩,⟨(-43860424422545501060128169539),(-43860424422545501056055739962)⟩⟩,⟨⟨15558639082871133556014754476,15558639082871133559644433258⟩,⟨(-44913922313599405415582059569),(-44913922313599405411411346502)⟩⟩,⟨⟨15918775249752562212814450191,15918775249752562216529486908⟩,⟨(-45953545878068969526148032759),(-45953545878068969521876907006)⟩⟩,⟨⟨16278905600962081265275236035,16278905600962081269075883579⟩,⟨(-46993152654139820993664811401),(-46993152654139820989292540572)⟩⟩,⟨⟨16634261386743642865319983673,16634261386743642869205087966⟩,⟨(-48018976447035198881717169427),(-48018976447035198877245149513)⟩⟩,⟨⟨16989369609173106072136661447,16989369609173106076096438036⟩,⟨(-49044085586090699302568337013),(-49044085586090699298024712938)⟩⟩,⟨⟨17339724586802453969104363512,17339724586802453973149061137⟩,⟨(-50055473289321845908192917673),(-50055473289321845903546176969)⟩⟩,⟨⟨17689602740734276709254577793,17689602740734276713382520581⟩,⟨(-51065484521102381803907651111),(-51065484521102381799162438310)⟩⟩,⟨⟨18034740279655822661738051141,18034740279655822665949451046⟩,⟨(-52061810776121379280276968289),(-52061810776121379275430749747)⟩⟩,⟨⟨18379182858626920874713897063,18379182858626920879005149951⟩,⟨(-53056130854568041699700647886),(-53056130854568041694763546116)⟩⟩] +lemma amp3_10_2_eq : ∀ k : Fin 16, amp3_1Expr 0 2 k = amp3_10_2 k := by decide +kernel +noncomputable def amp3_10_3 : Fin 16 → CBox := ![⟨⟨18718890128322294123098680819,18718890128322294127470870246⟩,⟨(-54036781272589524418537197220),(-54036781272589524413504164633)⟩⟩,⟨⟨19057694296448717006141813229,19057694296448717010595115222⟩,⟨(-55014824660941311803358993598),(-55014824660941311798229155940)⟩⟩,⟨⟨19391762292844942223929189585,19391762292844942228462831649⟩,⟨(-55979195899176309599960770765),(-55979195899176309594734438060)⟩⟩,⟨⟨19724728098486747674972907570,19724728098486747679570030338⟩,⟨(-56940385386767494551350072853),(-56940385386767494546075467084)⟩⟩,⟨⟨20052951687444352541932485675,20052951687444352546609801282⟩,⟨(-57887885273962785794112946893),(-57887885273962785788739901850)⟩⟩,⟨⟨20379882258044908821882591531,20379882258044908826638298076⟩,⟨(-58831652538675531390118564200),(-58831652538675531384651757354)⟩⟩,⟨⟨20702060231618653075696614603,20702060231618653080529465321⟩,⟨(-59761700237524378294388059340),(-59761700237524378288829163147)⟩⟩,⟨⟨21022761953305465942985228578,21022761953305465947894120473⟩,⟨(-60687486364251667553716421251),(-60687486364251667548068021338)⟩⟩,⟨⟨21338697095528772240944440329,21338697095528772245929278333⟩,⟨(-61599512561297110514243273752),(-61599512561297110508503712245)⟩⟩,⟨⟨21652979780165887254302975079,21652979780165887259359274712⟩,⟨(-62506768524181493587843762964),(-62506768524181493582025315556)⟩⟩,⟨⟨21962478939877190901391612888,21962478939877190906522233423⟩,⟨(-63400215640047914276802127423),(-63400215640047914270894600927)⟩⟩,⟨⟨22270155981605558910217217806,22270155981605558915420028177⟩,⟨(-64288402754374619222372800551),(-64288402754374619216381608166)⟩⟩,⟨⟨22573030150397963504342964709,22573030150397963509617619119⟩,⟨(-65162725168789013939426321651),(-65162725168789013933350514581)⟩⟩,⟨⟨22873918673218157791624593414,22873918673218157796970427542⟩,⟨(-66031315517020554072395620328),(-66031315517020554066236311347)⟩⟩,⟨⟨23169983067012150231368801569,23169983067012150236785085800⟩,⟨(-66885979804292678585970328197),(-66885979804292678579727667886)⟩⟩,⟨⟨23463904064604503187340130760,23463904064604503192826111913⟩,⟨(-67734456639694820212839964018),(-67734456639694820206515257721)⟩⟩] +lemma amp3_10_3_eq : ∀ k : Fin 16, amp3_1Expr 0 3 k = amp3_10_3 k := by decide +kernel +noncomputable def amp3_10_4 : Fin 16 → CBox := ![⟨⟨23752978207657739998386367310,23752978207657740003915690087⟩,⟨(-68568941811232553510673645525),(-68568941811232553504341009580)⟩⟩,⟨⟨24039756676364397074226102596,24039756676364397079827604678⟩,⟨(-69396799941760439166818801235),(-69396799941760439160394057794)⟩⟩,⟨⟨24321664486771101357386514743,24321664486771101363058098970⟩,⟨(-70210597692885282673736484798),(-70210597692885282667223713336)⟩⟩,⟨⟨24601129552458858917891026610,24601129552458858923631090370⟩,⟨(-71017343847404899045365667243),(-71017343847404899038768503850)⟩⟩,⟨⟨24875699428374202210829929707,24875699428374202216637048733⟩,⟨(-71809958806260327015684556480),(-71809958806260327009005128211)⟩⟩,⟨⟨25147684467739387129657534906,25147684467739387135531934814⟩,⟨(-72595111984725529381541093418),(-72595111984725529374777701121)⟩⟩,⟨⟨25414749373705691724363557861,25414749373705691730301607206⟩,⟨(-73366061961479269629949977335),(-73366061961479269623111109530)⟩⟩,⟨⟨25679092130460598062730951712,25679092130460598068733698695⟩,⟨(-74129153770333134324419702080),(-74129153770333134317501229348)⟩⟩,⟨⟨25938489683322627371330252123,25938489683322627377397059089⟩,⟨(-74877970005193248326941832664),(-74877970005193248319943591036)⟩⟩,⟨⟨26195032379608320403203852309,26195032379608320409326465975⟩,⟨(-75618544978989134715626305646),(-75618544978989134708570962975)⟩⟩,⟨⟨26446604933591878654022137478,26446604933591878660207427942⟩,⟨(-76344772387804779793580194934),(-76344772387804779786445904127)⟩⟩,⟨⟨26695194376888032116643605303,26695194376888032122889428222⟩,⟨(-77062388297828446851418380764),(-77062388297828446844210122692)⟩⟩,⟨⟨26938789107485135125717047851,26938789107485135132023088502⟩,⟨(-77765585714245505801183839577),(-77765585714245505793900497978)⟩⟩,⟨⟨27179276793229187795918392619,27179276793229187802280994049⟩,⟨(-78459813864751100479069577747),(-78459813864751100471720449776)⟩⟩,⟨⟨27414745779588332831755219110,27414745779588332838176275517⟩,⟨(-79139554278052403997220832919),(-79139554278052403989798415984)⟩⟩,⟨⟨27646987989670052249022539291,27646987989670052255499462756⟩,⟨(-79809979790591775618229820126),(-79809979790591775610740276818)⟩⟩] +lemma amp3_10_4_eq : ∀ k : Fin 16, amp3_1Expr 0 4 k = amp3_10_4 k := by decide +kernel +noncomputable def amp3_10_5 : Fin 16 → CBox := ![⟨⟨27874188295234711899353357186,27874188295234711905885846450⟩,⟨(-80465850578480383006596574182),(-80465850578480382999038730234)⟩⟩,⟨⟨28098046192495536937469467584,28098046192495536944056616802⟩,⟨(-81112072664699187625843512951),(-81112072664699187618218628345)⟩⟩,⟨⟨28316839943670277250668811406,28316839943670277257310253400⟩,⟨(-81743675820387909216787285584),(-81743675820387909209094367336)⟩⟩,⟨⟨28532179662507527613486037891,28532179662507527620180662022⟩,⟨(-82365308043577433331925878878),(-82365308043577433324166732906)⟩⟩,⟨⟨28742434125160893639338060396,28742434125160893646085004105⟩,⟨(-82972260396633638292046405231),(-82972260396633638284221460033)⟩⟩,⟨⟨28949126858313515178851657389,28949126858313515185599577158⟩,⟨(-83568930922259665949182954792),(-83568930922259665941438982455)⟩⟩,⟨⟨29150714511951410417751892304,29150714511951410424552900964⟩,⟨(-84150864352725385237839276964),(-84150864352725385230023771175)⟩⟩,⟨⟨29348636593525162296662448251,29348636593525162303514322981⟩,⟨(-84722216188101268821241838146),(-84722216188101268813359729662)⟩⟩,⟨⟨29541435202988933490965775593,29541435202988933497866482049⟩,⟨(-85278777833467737963846743822),(-85278777833467737955901828302)⟩⟩,⟨⟨29730468187763879464170245244,29730468187763879471118704962⟩,⟨(-85824469056695405395669957095),(-85824469056695405387663821259)⟩⟩,⟨⟨29914360872324529839442052770,29914360872324529846435843735⟩,⟨(-86355321511360877555137916076),(-86355321511360877547075467869)⟩⟩,⟨⟨30094391611375639617243066134,30094391611375639624280989812⟩,⟨(-86875025489628705062673657077),(-86875025489628705054556790792)⟩⟩,⟨⟨30269266911110177880812880045,30269266911110177887895463581⟩,⟨(-87379846996510465850107535323),(-87379846996510465841932639270)⟩⟩,⟨⟨30440187623762200857922318607,30440187623762200865046034168⟩,⟨(-87873252593809106550365358580),(-87873252593809106542141013601)⟩⟩,⟨⟨30605939563110598314603457618,30605939563110598321768684815⟩,⟨(-88351737227816605523206333748),(-88351737227816605514929348649)⟩⟩,⟨⟨30767647905240686644969875397,30767647905240686652176102704⟩,⟨(-88818549002111678515962488582),(-88818549002111678507632700788)⟩⟩] +lemma amp3_10_5_eq : ∀ k : Fin 16, amp3_1Expr 0 5 k = amp3_10_5 k := by decide +kernel +noncomputable def amp3_10_6 : Fin 16 → CBox := ![⟨⟨30924176053652663071635183883,30924176053652663078875849920⟩,⟨(-89270406845218719928860651961),(-89270406845218719920494902565)⟩⟩,⟨⟨31076575182348133088312680459,31076575182348133095593228911⟩,⟨(-89710345235101690101439929415),(-89710345235101690093020829998)⟩⟩,⟨⟨31223784711938343736389856947,31223784711938343743705753052⟩,⟨(-90135302542782621586637289081),(-90135302542782621578175826580)⟩⟩,⟨⟨31366783346512185478542165521,31366783346512185485895642753⟩,⟨(-90548104043607403864713506245),(-90548104043607403856201526135)⟩⟩,⟨⟨31504585086650592890070198730,31504585086650592897458216372⟩,⟨(-90945903402425945747791334491),(-90945903402425945739235507813)⟩⟩,⟨⟨31638097566013635095625148657,31638097566013635103047642074⟩,⟨(-91331320731928079607892389214),(-91331320731928079599291163748)⟩⟩,⟨⟨31766408054785126232853886656,31766408054785126240292427769⟩,⟨(-91701721208088443918600060606),(-91701721208088443910004524809)⟩⟩,⟨⟨31890354391170951213614229866,31890354391170951221086526363⟩,⟨(-92059523461475563714790867274),(-92059523461475563706148134285)⟩⟩,⟨⟨32009095923644769038190775742,32009095923644769045693918441⟩,⟨(-92402300740164300766606556116),(-92402300740164300757922914062)⟩⟩,⟨⟨32123401852681396179099925479,32123401852681396186631896412⟩,⟨(-92732273534660635465854895190),(-92732273534660635457134371310)⟩⟩,⟨⟨32232502525936830258776254702,32232502525936830266336876955⟩,⟨(-93047220050024606816850494785),(-93047220050024606808091489643)⟩⟩,⟨⟨32337099553057724186992986583,32337099553057724194579204388⟩,⟨(-93349165658848020297949072051),(-93349165658848020289158581169)⟩⟩,⟨⟨32436493307917857218290062325,32436493307917857225901676311⟩,⟨(-93636090714469347696740024677),(-93636090714469347687916514251)⟩⟩,⟨⟨32531318751103864916677667063,32531318751103864924314760413⟩,⟨(-93909828190216683241088632667),(-93909828190216683232230010639)⟩⟩,⟨⟨32620945410534091400749121437,32620945410534091408402153846⟩,⟨(-94168558069959724096736934841),(-94168558069959724087868634178)⟩⟩,⟨⟨32705942439377387418402738560,32705942439377387426078084747⟩,⟨(-94413923357374700802854289543),(-94413923357374700793956031224)⟩⟩] +lemma amp3_10_6_eq : ∀ k : Fin 16, amp3_1Expr 0 6 k = amp3_10_6 k := by decide +kernel +noncomputable def amp3_10_7 : Fin 16 → CBox := ![⟨⟨32785747743509981344178080255,32785747743509981351873597400⟩,⟨(-94644301426493266085505745876),(-94644301426493266076581611037)⟩⟩,⟨⟨32860865414590931769576161138,32860865414590931777291758109⟩,⟨(-94861147464590688558977632543),(-94861147464590688550025983950)⟩⟩,⟨⟨32930801052341203469969013656,32930801052341203477698965204⟩,⟨(-95063034260996026158102204562),(-95063034260996026149137468860)⟩⟩,⟨⟨32995994340909188935122714444,32995994340909188942869548185⟩,⟨(-95251231074516442959537216182),(-95251231074516442950550174286)⟩⟩,⟨⟨33056017978152788404529114288,33056017978152788412288874147⟩,⟨(-95424504390118105961016107483),(-95424504390118105952016083890)⟩⟩,⟨⟨33111247806102404774620920879,33111247806102404782395531280⟩,⟨(-95583939170288144601386534324),(-95583939170288144592366030350)⟩⟩,⟨⟨33161323110387142476341390101,33161323110387142484127470651⟩,⟨(-95728494122330873264112414066),(-95728494122330873255079098491)⟩⟩,⟨⟨33206556370521783187780176078,33206556370521783195576641536⟩,⟨(-95859071296906169176641388583),(-95859071296906169167596431328)⟩⟩,⟨⟨33246653032290985848731521743,33246653032290985856537342982⟩,⟨(-95974820389236441838449622839),(-95974820389236441829393912431)⟩⟩,⟨⟨33281862608866566220968165174,33281862608866566228782636791⟩,⟨(-96076461681806262186557450534),(-96076461681806262177491042135)⟩⟩,⟨⟨33311956359174495036375875568,33311956359174495044196724472⟩,⟨(-96163334856012302610657088305),(-96163334856012302601584469871)⟩⟩,⟨⟨33337121144716975237370864428,33337121144716975245197235741⟩,⟨(-96235979334547553344011607618),(-96235979334547553334933248836)⟩⟩,⟨⟨33357193769420233712650850054,33357193769420233720480561907⟩,⟨(-96293924010926396407439247016),(-96293924010926396398359382100)⟩⟩,⟨⟨33372298677811606169561632049,33372298677811606177393222210⟩,⟨(-96337528125555614032832244735),(-96337528125555614023753080945)⟩⟩,⟨⟨33382338028223777523481366017,33382338028223777531312809931⟩,⟨(-96366509233870394590613273721),(-96366509233870394581538601929)⟩⟩,⟨⟨33387374004052282212675935835,33387374004052282220504912226⟩,⟨(-96381046843871492745308913322),(-96381046843871492736243406176)⟩⟩] +lemma amp3_10_7_eq : ∀ k : Fin 16, amp3_1Expr 0 7 k = amp3_10_7 k := by decide +kernel +noncomputable def amp3_10_8 : Fin 16 → CBox := ![⟨⟨33387374004052282212675935835,33387374004052282220504912226⟩,⟨(-96381046843871492745308913322),(-96381046843871492736243406176)⟩⟩,⟨⟨33382338028223777523481366017,33382338028223777531312809931⟩,⟨(-96366509233870394590613273721),(-96366509233870394581538601929)⟩⟩,⟨⟨33372298677811606169561632049,33372298677811606177393222210⟩,⟨(-96337528125555614032832244735),(-96337528125555614023753080945)⟩⟩,⟨⟨33357193769420233712650850054,33357193769420233720480561907⟩,⟨(-96293924010926396407439247016),(-96293924010926396398359382100)⟩⟩,⟨⟨33337121144716975237370864428,33337121144716975245197235741⟩,⟨(-96235979334547553344011607618),(-96235979334547553334933248836)⟩⟩,⟨⟨33311956359174495036375875568,33311956359174495044196724472⟩,⟨(-96163334856012302610657088305),(-96163334856012302601584469871)⟩⟩,⟨⟨33281862608866566220968165174,33281862608866566228782636791⟩,⟨(-96076461681806262186557450534),(-96076461681806262177491042135)⟩⟩,⟨⟨33246653032290985848731521743,33246653032290985856537342982⟩,⟨(-95974820389236441838449622839),(-95974820389236441829393912431)⟩⟩,⟨⟨33206556370521783187780176078,33206556370521783195576641536⟩,⟨(-95859071296906169176641388583),(-95859071296906169167596431328)⟩⟩,⟨⟨33161323110387142476341390101,33161323110387142484127470651⟩,⟨(-95728494122330873264112414066),(-95728494122330873255079098491)⟩⟩,⟨⟨33111247806102404774620920879,33111247806102404782395531280⟩,⟨(-95583939170288144601386534324),(-95583939170288144592366030350)⟩⟩,⟨⟨33056017978152788404529114288,33056017978152788412288874147⟩,⟨(-95424504390118105961016107483),(-95424504390118105952016083890)⟩⟩,⟨⟨32995994340909188935122714444,32995994340909188942869548185⟩,⟨(-95251231074516442959537216182),(-95251231074516442950550174286)⟩⟩,⟨⟨32930801052341203469969013656,32930801052341203477698965204⟩,⟨(-95063034260996026158102204562),(-95063034260996026149137468860)⟩⟩,⟨⟨32860865414590931769576161138,32860865414590931777291758109⟩,⟨(-94861147464590688558977632543),(-94861147464590688550025983950)⟩⟩,⟨⟨32785747743509981344178080255,32785747743509981351873597400⟩,⟨(-94644301426493266085505745876),(-94644301426493266076581611037)⟩⟩] +lemma amp3_10_8_eq : ∀ k : Fin 16, amp3_1Expr 0 8 k = amp3_10_8 k := by decide +kernel +noncomputable def amp3_10_9 : Fin 16 → CBox := ![⟨⟨32705942439377387418402738560,32705942439377387426078084747⟩,⟨(-94413923357374700802854289543),(-94413923357374700793956031224)⟩⟩,⟨⟨32620945410534091400749121437,32620945410534091408402153846⟩,⟨(-94168558069959724096736934841),(-94168558069959724087868634178)⟩⟩,⟨⟨32531318751103864916677667063,32531318751103864924314760413⟩,⟨(-93909828190216683241088632667),(-93909828190216683232230010639)⟩⟩,⟨⟨32436493307917857218290062325,32436493307917857225901676311⟩,⟨(-93636090714469347696740024677),(-93636090714469347687916514251)⟩⟩,⟨⟨32337099553057724186992986583,32337099553057724194579204388⟩,⟨(-93349165658848020297949072051),(-93349165658848020289158581169)⟩⟩,⟨⟨32232502525936830258776254702,32232502525936830266336876955⟩,⟨(-93047220050024606816850494785),(-93047220050024606808091489643)⟩⟩,⟨⟨32123401852681396179099925479,32123401852681396186631896412⟩,⟨(-92732273534660635465854895190),(-92732273534660635457134371310)⟩⟩,⟨⟨32009095923644769038190775742,32009095923644769045693918441⟩,⟨(-92402300740164300766606556116),(-92402300740164300757922914062)⟩⟩,⟨⟨31890354391170951213614229866,31890354391170951221086526363⟩,⟨(-92059523461475563714790867274),(-92059523461475563706148134285)⟩⟩,⟨⟨31766408054785126232853886656,31766408054785126240292427769⟩,⟨(-91701721208088443918600060606),(-91701721208088443910004524809)⟩⟩,⟨⟨31638097566013635095625148657,31638097566013635103047642074⟩,⟨(-91331320731928079607892389214),(-91331320731928079599291163748)⟩⟩,⟨⟨31504585086650592890070198730,31504585086650592897458216372⟩,⟨(-90945903402425945747791334491),(-90945903402425945739235507813)⟩⟩,⟨⟨31366783346512185478542165521,31366783346512185485895642753⟩,⟨(-90548104043607403864713506245),(-90548104043607403856201526135)⟩⟩,⟨⟨31223784711938343736389856947,31223784711938343743705753052⟩,⟨(-90135302542782621586637289081),(-90135302542782621578175826580)⟩⟩,⟨⟨31076575182348133088312680459,31076575182348133095593228911⟩,⟨(-89710345235101690101439929415),(-89710345235101690093020829998)⟩⟩,⟨⟨30924176053652663071635183883,30924176053652663078875849920⟩,⟨(-89270406845218719928860651961),(-89270406845218719920494902565)⟩⟩] +lemma amp3_10_9_eq : ∀ k : Fin 16, amp3_1Expr 0 9 k = amp3_10_9 k := by decide +kernel +noncomputable def amp3_10_10 : Fin 16 → CBox := ![⟨⟨30767647905240686644969875397,30767647905240686652176102704⟩,⟨(-88818549002111678515962488582),(-88818549002111678507632700788)⟩⟩,⟨⟨30605939563110598314603457618,30605939563110598321768684815⟩,⟨(-88351737227816605523206333748),(-88351737227816605514929348649)⟩⟩,⟨⟨30440187623762200857922318607,30440187623762200865046034168⟩,⟨(-87873252593809106550365358580),(-87873252593809106542141013601)⟩⟩,⟨⟨30269266911110177880812880045,30269266911110177887895463581⟩,⟨(-87379846996510465850107535323),(-87379846996510465841932639270)⟩⟩,⟨⟨30094391611375639617243066134,30094391611375639624280989812⟩,⟨(-86875025489628705062673657077),(-86875025489628705054556790792)⟩⟩,⟨⟨29914360872324529839442052770,29914360872324529846435843735⟩,⟨(-86355321511360877555137916076),(-86355321511360877547075467869)⟩⟩,⟨⟨29730468187763879464170245244,29730468187763879471118704962⟩,⟨(-85824469056695405395669957095),(-85824469056695405387663821259)⟩⟩,⟨⟨29541435202988933490965775593,29541435202988933497866482049⟩,⟨(-85278777833467737963846743822),(-85278777833467737955901828302)⟩⟩,⟨⟨29348636593525162296662448251,29348636593525162303514322981⟩,⟨(-84722216188101268821241838146),(-84722216188101268813359729662)⟩⟩,⟨⟨29150714511951410417751892304,29150714511951410424552900964⟩,⟨(-84150864352725385237839276964),(-84150864352725385230023771175)⟩⟩,⟨⟨28949126858313515178851657389,28949126858313515185599577158⟩,⟨(-83568930922259665949182954792),(-83568930922259665941438982455)⟩⟩,⟨⟨28742434125160893639338060396,28742434125160893646085004105⟩,⟨(-82972260396633638292046405231),(-82972260396633638284221460033)⟩⟩,⟨⟨28532179662507527613486037891,28532179662507527620180662022⟩,⟨(-82365308043577433331925878878),(-82365308043577433324166732906)⟩⟩,⟨⟨28316839943670277250668811406,28316839943670277257310253400⟩,⟨(-81743675820387909216787285584),(-81743675820387909209094367336)⟩⟩,⟨⟨28098046192495536937469467584,28098046192495536944056616802⟩,⟨(-81112072664699187625843512951),(-81112072664699187618218628345)⟩⟩,⟨⟨27874188295234711899353357186,27874188295234711905885846450⟩,⟨(-80465850578480383006596574182),(-80465850578480382999038730234)⟩⟩] +lemma amp3_10_10_eq : ∀ k : Fin 16, amp3_1Expr 0 10 k = amp3_10_10 k := by decide +kernel +noncomputable def amp3_10_11 : Fin 16 → CBox := ![⟨⟨27646987989670052249022539291,27646987989670052255499462756⟩,⟨(-79809979790591775618229820126),(-79809979790591775610740276818)⟩⟩,⟨⟨27414745779588332831755219110,27414745779588332838176275517⟩,⟨(-79139554278052403997220832919),(-79139554278052403989798415984)⟩⟩,⟨⟨27179276793229187795918392619,27179276793229187802280994049⟩,⟨(-78459813864751100479069577747),(-78459813864751100471720449776)⟩⟩,⟨⟨26938789107485135125717047851,26938789107485135132023088502⟩,⟨(-77765585714245505801183839577),(-77765585714245505793900497978)⟩⟩,⟨⟨26695194376888032116643605303,26695194376888032122889428222⟩,⟨(-77062388297828446851418380764),(-77062388297828446844210122692)⟩⟩,⟨⟨26446604933591878654022137478,26446604933591878660207427942⟩,⟨(-76344772387804779793580194934),(-76344772387804779786445904127)⟩⟩,⟨⟨26195032379608320403203852309,26195032379608320409326465975⟩,⟨(-75618544978989134715626305646),(-75618544978989134708570962975)⟩⟩,⟨⟨25938489683322627371330252123,25938489683322627377397059089⟩,⟨(-74877970005193248326941832664),(-74877970005193248319943591036)⟩⟩,⟨⟨25679092130460598062730951712,25679092130460598068733698695⟩,⟨(-74129153770333134324419702080),(-74129153770333134317501229348)⟩⟩,⟨⟨25414749373705691724363557861,25414749373705691730301607206⟩,⟨(-73366061961479269629949977335),(-73366061961479269623111109530)⟩⟩,⟨⟨25147684467739387129657534906,25147684467739387135531934814⟩,⟨(-72595111984725529381541093418),(-72595111984725529374777701121)⟩⟩,⟨⟨24875699428374202210829929707,24875699428374202216637048733⟩,⟨(-71809958806260327015684556480),(-71809958806260327009005128211)⟩⟩,⟨⟨24601129552458858917891026610,24601129552458858923631090370⟩,⟨(-71017343847404899045365667243),(-71017343847404899038768503850)⟩⟩,⟨⟨24321664486771101357386514743,24321664486771101363058098970⟩,⟨(-70210597692885282673736484798),(-70210597692885282667223713336)⟩⟩,⟨⟨24039756676364397074226102596,24039756676364397079827604678⟩,⟨(-69396799941760439166818801235),(-69396799941760439160394057794)⟩⟩,⟨⟨23752978207657739998386367310,23752978207657740003915690087⟩,⟨(-68568941811232553510673645525),(-68568941811232553504341009580)⟩⟩] +lemma amp3_10_11_eq : ∀ k : Fin 16, amp3_1Expr 0 11 k = amp3_10_11 k := by decide +kernel +noncomputable def amp3_10_12 : Fin 16 → CBox := ![⟨⟨23463904064604503187340130760,23463904064604503192826111913⟩,⟨(-67734456639694820212839964018),(-67734456639694820206515257721)⟩⟩,⟨⟨23169983067012150231368801569,23169983067012150236785085800⟩,⟨(-66885979804292678585970328197),(-66885979804292678579727667886)⟩⟩,⟨⟨22873918673218157791624593414,22873918673218157796970427542⟩,⟨(-66031315517020554072395620328),(-66031315517020554066236311347)⟩⟩,⟨⟨22573030150397963504342964709,22573030150397963509617619119⟩,⟨(-65162725168789013939426321651),(-65162725168789013933350514581)⟩⟩,⟨⟨22270155981605558910217217806,22270155981605558915420028177⟩,⟨(-64288402754374619222372800551),(-64288402754374619216381608166)⟩⟩,⟨⟨21962478939877190901391612888,21962478939877190906522233423⟩,⟨(-63400215640047914276802127423),(-63400215640047914270894600927)⟩⟩,⟨⟨21652979780165887254302975079,21652979780165887259359274712⟩,⟨(-62506768524181493587843762964),(-62506768524181493582025315556)⟩⟩,⟨⟨21338697095528772240944440329,21338697095528772245929278333⟩,⟨(-61599512561297110514243273752),(-61599512561297110508503712245)⟩⟩,⟨⟨21022761953305465942985228578,21022761953305465947894120473⟩,⟨(-60687486364251667553716421251),(-60687486364251667548068021338)⟩⟩,⟨⟨20702060231618653075696614603,20702060231618653080529465321⟩,⟨(-59761700237524378294388059340),(-59761700237524378288829163147)⟩⟩,⟨⟨20379882258044908821882591531,20379882258044908826638298076⟩,⟨(-58831652538675531390118564200),(-58831652538675531384651757354)⟩⟩,⟨⟨20052951687444352541932485675,20052951687444352546609801282⟩,⟨(-57887885273962785794112946893),(-57887885273962785788739901850)⟩⟩,⟨⟨19724728098486747674972907570,19724728098486747679570030338⟩,⟨(-56940385386767494551350072853),(-56940385386767494546075467084)⟩⟩,⟨⟨19391762292844942223929189585,19391762292844942228462831649⟩,⟨(-55979195899176309599960770765),(-55979195899176309594734438060)⟩⟩,⟨⟨19057694296448717006141813229,19057694296448717010595115222⟩,⟨(-55014824660941311803358993598),(-55014824660941311798229155940)⟩⟩,⟨⟨18718890128322294123098680819,18718890128322294127470870246⟩,⟨(-54036781272589524418537197220),(-54036781272589524413504164633)⟩⟩] +lemma amp3_10_12_eq : ∀ k : Fin 16, amp3_1Expr 0 12 k = amp3_10_12 k := by decide +kernel +noncomputable def amp3_10_13 : Fin 16 → CBox := ![⟨⟨18379182858626920874713897063,18379182858626920879005149951⟩,⟨(-53056130854568041699700647886),(-53056130854568041694763546116)⟩⟩,⟨⟨18034740279655822661738051141,18034740279655822665949451046⟩,⟨(-52061810776121379280276968289),(-52061810776121379275430749747)⟩⟩,⟨⟨17689602740734276709254577793,17689602740734276713382520581⟩,⟨(-51065484521102381803907651111),(-51065484521102381799162438310)⟩⟩,⟨⟨17339724586802453969104363512,17339724586802453973149061137⟩,⟨(-50055473289321845908192917673),(-50055473289321845903546176969)⟩⟩,⟨⟨16989369609173106072136661447,16989369609173106076096438036⟩,⟨(-49044085586090699302568337013),(-49044085586090699298024712938)⟩⟩,⟨⟨16634261386743642865319983673,16634261386743642869205087966⟩,⟨(-48018976447035198881717169427),(-48018976447035198877245149513)⟩⟩,⟨⟨16278905600962081265275236035,16278905600962081269075883579⟩,⟨(-46993152654139820993664811401),(-46993152654139820989292540572)⟩⟩,⟨⟨15918775249752562212814450191,15918775249752562216529486908⟩,⟨(-45953545878068969526148032759),(-45953545878068969521876907006)⟩⟩,⟨⟨15558639082871133556014754476,15558639082871133559644433258⟩,⟨(-44913922313599405415582059569),(-44913922313599405411411346502)⟩⟩,⟨⟨15193696708276728726399124752,15193696708276728729943508236⟩,⟨(-43860424422545501060128169539),(-43860424422545501056055739962)⟩⟩,⟨⟨14829004411061715032174690260,14829004411061715035632679113⟩,⟨(-42807648442703145245613927883),(-42807648442703145241643056679)⟩⟩,⟨⟨14459461977215688466095289721,14459461977215688469473034146⟩,⟨(-41740871324413180700245732637),(-41740871324413180696356699514)⟩⟩,⟨⟨14090441693045962456358327287,14090441693045962459647434256⟩,⟨(-40675601522404063165656757890),(-40675601522404063161874003108)⟩⟩,⟨⟨13716512663740494234201085175,13716512663740494237401330105⟩,⟨(-39596161393767425469044977756),(-39596161393767425465367159689)⟩⟩,⟨⟨13343396554569321849590476171,13343396554569321852702577544⟩,⟨(-38519067963422614615110489554),(-38519067963422614611535863671)⟩⟩,⟨⟨12965295463818583362310902000,12965295463818583365332862928⟩,⟨(-37427584130793464685059853638),(-37427584130793464681592163610)⟩⟩] +lemma amp3_10_13_eq : ∀ k : Fin 16, amp3_1Expr 0 13 k = amp3_10_13 k := by decide +kernel +noncomputable def amp3_10_14 : Fin 16 → CBox := ![⟨⟨12588319915260722389435530052,12588319915260722392373252115⟩,⟨(-36339349458604525328146650475),(-36339349458604525324769316189)⟩⟩,⟨⟨12206261841045965248519547062,12206261841045965251366875357⟩,⟨(-35236442798634725060533596172),(-35236442798634725057262324916)⟩⟩,⟨⟨11825667778884814560519773120,11825667778884814563277788848⟩,⟨(-34137762377431157505004462423),(-34137762377431157501836726525)⟩⟩,⟨⟨11439867680844907707739092186,11439867680844907710404706421⟩,⟨(-33024053425147536341191386223),(-33024053425147536338133992189)⟩⟩,⟨⟨11055901047314695422472131356,11055901047314695425051144532⟩,⟨(-31915637229005024096250828468),(-31915637229005024093287775150)⟩⟩,⟨⟨10666572908823690775540024945,10666572908823690778027039652⟩,⟨(-30791743701200636931607744945),(-30791743701200636928752439838)⟩⟩,⟨⟨10279485372927895293561166081,10279485372927895295959757839⟩,⟨(-29674318235953704694359988622),(-29674318235953704691603018402)⟩⟩,⟨⟨9886841054724459425649615405,9886841054724459427955104756⟩,⟨(-28540851721901050823765953820),(-28540851721901050821118574272)⟩⟩,⟨⟨9496891073954188849843459412,9496891073954188852056886132⟩,⟨(-27415163090060025286744936549),(-27415163090060025284205238350)⟩⟩,⟨⟨9101138730168082672685547926,9101138730168082674807967876⟩,⟨(-26272724478973356683613003844),(-26272724478973356681175586780)⟩⟩,⟨⟨8708593155276932931663343903,8708593155276932933692666219⟩,⟨(-25139543012310348166222035137),(-25139543012310348163894234995)⟩⟩,⟨⟨8309934963699564221252943963,8309934963699564223190174002⟩,⟨(-23988715941201132047928058577),(-23988715941201132045704495168)⟩⟩,⟨⟨7915071511567247978731148812,7915071511567247980577175520⟩,⟨(-22848843339292443596750710681),(-22848843339292443594630356177)⟩⟩,⟨⟨7513700288185479520880808176,7513700288185479522631856252⟩,⟨(-21690184419970276426958860238),(-21690184419970276424949974828)⟩⟩,⟨⟨7116811458893626801438955157,7116811458893626803097842796⟩,⟨(-20544465057820243452992178041),(-20544465057820243451088443398)⟩⟩,⟨⟨6712905375084154821002163580,6712905375084154822567108879⟩,⟨(-19378488626746612489883570204),(-19378488626746612488087285542)⟩⟩] +lemma amp3_10_14_eq : ∀ k : Fin 16, amp3_1Expr 0 14 k = amp3_10_14 k := by decide +kernel +noncomputable def amp3_10_15 : Fin 16 → CBox := ![⟨⟨6314304889329281697450176362,6314304889329281698922030641⟩,⟨(-18227828137998154550760321738),(-18227828137998154549071180326)⟩⟩,⟨⟨5908018787060499827167002222,5908018787060499828543798049⟩,⟨(-17054981185433729371263710837),(-17054981185433729369684276511)⟩⟩,⟨⟨5508052685234101317304126944,5508052685234101318587199992⟩,⟨(-15900378502652747127046396108),(-15900378502652747125575375162)⟩⟩,⟨⟨5099502883647184281211394888,5099502883647184282399619479⟩,⟨(-14720996813034873396189253370),(-14720996813034873394826415632)⟩⟩,⟨⟨4698569893355039727044388633,4698569893355039728139217921⟩,⟨(-13563602963674017037327158021),(-13563602963674017036071396357)⟩⟩,⟨⟨4287805485929443699966200696,4287805485929443700965156846⟩,⟨(-12377828257670592144590811492),(-12377828257670592143445293266)⟩⟩,⟨⟨3886397599776523264997115749,3886397599776523265902093110⟩,⟨(-11219063502044455816624867534),(-11219063502044455815587917238)⟩⟩,⟨⟨3473340580412691300139992971,3473340580412691300949032302⟩,⟨(-10026670595442591582120612060),(-10026670595442591581193163135)⟩⟩,⟨⟨3072133445990435319895729756,3072133445990435320611055895⟩,⟨(-8868485360145152285077979907),(-8868485360145152284258413586)⟩⟩,⟨⟨2656435792071101113031730727,2656435792071101113650080664⟩,⟨(-7668469598186034814575566066),(-7668469598186034813867427582)⟩⟩,⟨⟨2256524817754308917690502211,2256524817754308918215444112⟩,⟨(-6514026054817607367205777424),(-6514026054817607366605166082)⟩⟩,⟨⟨1837153108049314193090098629,1837153108049314193517277586⟩,⟨(-5303404207374145887226919957),(-5303404207374145886738518167)⟩⟩,⟨⟨1440842106367455813356471448,1440842106367455813691094947⟩,⟨(-4159352889854990063865575394),(-4159352889854990063483698944)⟩⟩,⟨⟨1014414495963543606810259718,1014414495963543607045593215⟩,⟨(-2928362411572052200011136404),(-2928362411572052199743017371)⟩⟩,⟨⟨629264447029517718401686713,629264447029517718546810596⟩,⟨(-1816529989419765287808678824),(-1816529989419765287644837768)⟩⟩,⟨⟨178776584874023315329347999,178776584874023315370061539⟩,⟨(-516083547009096694081565204),(-516083547009096694036509008)⟩⟩] +lemma amp3_10_15_eq : ∀ k : Fin 16, amp3_1Expr 0 15 k = amp3_10_15 k := by decide +kernel +noncomputable def amp3_10 : Fin 16 → Fin 16 → CBox := ![amp3_10_0,amp3_10_1,amp3_10_2,amp3_10_3,amp3_10_4,amp3_10_5,amp3_10_6,amp3_10_7,amp3_10_8,amp3_10_9,amp3_10_10,amp3_10_11,amp3_10_12,amp3_10_13,amp3_10_14,amp3_10_15] +lemma amp3_10_eq (i k : Fin 16) : amp3_1Expr 0 i k = amp3_10 i k := by + fin_cases i + · exact amp3_10_0_eq k + · exact amp3_10_1_eq k + · exact amp3_10_2_eq k + · exact amp3_10_3_eq k + · exact amp3_10_4_eq k + · exact amp3_10_5_eq k + · exact amp3_10_6_eq k + · exact amp3_10_7_eq k + · exact amp3_10_8_eq k + · exact amp3_10_9_eq k + · exact amp3_10_10_eq k + · exact amp3_10_11_eq k + · exact amp3_10_12_eq k + · exact amp3_10_13_eq k + · exact amp3_10_14_eq k + · exact amp3_10_15_eq k +noncomputable def amp3_11_0 : Fin 16 → CBox := ![⟨⟨(-27656833929615362292264311),(-27656833929615362256294169)⟩,⟨(-158530377261050063379232069),(-158530377261050063344401428)⟩⟩,⟨⟨(-97347548738388396681199278),(-97347548738388396554308863)⟩,⟨(-558001095360729850848072071),(-558001095360729850723861018)⟩⟩,⟨⟨(-156930468665277273127383836),(-156930468665277272922614193)⟩,⟨(-899533419644964986134377747),(-899533419644964985932913863)⟩⟩,⟨⟨(-222899049574540212094499198),(-222899049574540211803594707)⟩,⟨(-1277668677120078436787951893),(-1277668677120078436501476857)⟩⟩,⟨⟨(-284208574900344161678692675),(-284208574900344161307693658)⟩,⟨(-1629097991275517500580703724),(-1629097991275517500214975098)⟩⟩,⟨⟨(-349085604172734029041738452),(-349085604172734028586011898)⟩,⟨(-2000976419308989531251875276),(-2000976419308989530802439409)⟩⟩,⟨⟨(-410952047203312812621453703),(-410952047203312812084903237)⟩,⟨(-2355598014043832587836924325),(-2355598014043832587307504459)⟩⟩,⟨⟨(-475260698067625593930502961),(-475260698067625593309956456)⟩,⟨(-2724218468164281644505258217),(-2724218468164281643892802611)⟩⟩,⟨⟨(-537327657764345332476231089),(-537327657764345331774598339)⟩,⟨(-3079989434617208980956745049),(-3079989434617208980264044069)⟩⟩,⟨⟨(-601227801041259061393492741),(-601227801041259060608462826)⟩,⟨(-3446268302491409285642191240),(-3446268302491409284867356331)⟩⟩,⟨⟨(-663325817138793157583491614),(-663325817138793156717301047)⟩,⟨(-3802217285811704743566857657),(-3802217285811704742711543286)⟩⟩,⟨⟨(-726871292114567087572208555),(-726871292114567086623011368)⟩,⟨(-4166463176963937582041909755),(-4166463176963937581104502683)⟩⟩,⟨⟨(-788895841566765076923251268),(-788895841566765075893062514)⟩,⟨(-4521991045740504832467951534),(-4521991045740504831450579026)⟩⟩,⟨⟨(-852098715826997533146399346),(-852098715826997532033730052)⟩,⟨(-4884273132184544491036292840),(-4884273132184544489937720511)⟩⟩,⟨⟨(-913973687112991920943172685),(-913973687112991919749621639)⟩,⟨(-5238943611312729715424956618),(-5238943611312729714246121583)⟩⟩,⟨⟨(-976826365869980122431079886),(-976826365869980121155391521)⟩,⟨(-5599218359339591154250983426),(-5599218359339591152990746248)⟩⟩] +lemma amp3_11_0_eq : ∀ k : Fin 16, amp3_1Expr 1 0 k = amp3_11_0 k := by decide +kernel +noncomputable def amp3_11_1 : Fin 16 → CBox := ![⟨⟨(-1038490075614490174501519672),(-1038490075614490173145273941)⟩,⟨(-5952677876578302846168331915),(-5952677876578302844828382527)⟩⟩,⟨⟨(-1100974564234470579281328934),(-1100974564234470577843513562)⟩,⟨(-6310842140032989848300849918),(-6310842140032989846880471163)⟩⟩,⟨⟨(-1162373479802631049399922641),(-1162373479802631047881977951)⟩,⟨(-6662783843599317383283399891),(-6662783843599317381784121944)⟩⟩,⟨⟨(-1224465824149729459438022484),(-1224465824149729457838768552)⟩,⟨(-7018700316157947637269453978),(-7018700316157947635688809694)⟩⟩,⟨⟨(-1285551412780888597361560973),(-1285551412780888595682661940)⟩,⟨(-7368846013802003603304271471),(-7368846013802003601645562295)⟩⟩,⟨⟨(-1347224049647206334242887604),(-1347224049647206332483576134)⟩,⟨(-7722356701756482300677532294),(-7722356701756482298939996956)⟩⟩,⟨⟨(-1407951061421260000149186178),(-1407951061421259998310321259)⟩,⟨(-8070447018637191335920874295),(-8070447018637191334103577796)⟩⟩,⟨⟨(-1469174162069821264218786486),(-1469174162069821262300159345)⟩,⟨(-8421380942151647584638624944),(-8421380942151647582743444180)⟩⟩,⟨⟨(-1529499634035960903193756318),(-1529499634035960901196166636)⟩,⟨(-8767169612452131969945632915),(-8767169612452131967971590310)⟩⟩,⟨⟨(-1590241921453586583491946308),(-1590241921453586581414786050)⟩,⟨(-9115347490097914104613359029),(-9115347490097914102559551734)⟩⟩,⟨⟨(-1650124571656563996388073041),(-1650124571656563994232988386)⟩,⟨(-9458597883553255377808374609),(-9458597883553255375678912598)⟩⟩,⟨⟨(-1710353844287314215285879813),(-1710353844287314213051945751)⟩,⟨(-9803835134375633248485544875),(-9803835134375633246277273494)⟩⟩,⟨⟨(-1769753689214106827972328573),(-1769753689214106825661269942)⟩,⟨(-10144318063457720922800142035),(-10144318063457720920517809295)⟩⟩,⟨⟨(-1829437172087648440688568763),(-1829437172087648438299183930)⟩,⟨(-10486426819661528380948604124),(-10486426819661528378587079526)⟩⟩,⟨⟨(-1888315278407924774874363023),(-1888315278407924772407993898)⟩,⟨(-10823919116542794560380015142),(-10823919116542794557942000753)⟩⟩,⟨⟨(-1947419868181087740976678469),(-1947419868181087738432914805)⟩,⟨(-11162709628083080546061075680),(-11162709628083080543545623159)⟩⟩] +lemma amp3_11_1_eq : ∀ k : Fin 16, amp3_1Expr 1 1 k = amp3_11_1 k := by decide +kernel +noncomputable def amp3_11_2 : Fin 16 → CBox := ![⟨⟨(-2005738188498802510844975054),(-2005738188498802508225612571)⟩,⟨(-11496993203156297957134742618),(-11496993203156297954547273668)⟩⟩,⟨⟨(-2064230630799723995558327922),(-2064230630799723992862266835)⟩,⟨(-11832274854283970912525872622),(-11832274854283970909861162019)⟩⟩,⟨⟨(-2121951893766475952495355615),(-2121951893766475949723732205)⟩,⟨(-12163136066286436997141725293),(-12163136066286436994401508306)⟩⟩,⟨⟨(-2179798915915662808956083540),(-2179798915915662806108651737)⟩,⟨(-12494718136312138249340338552),(-12494718136312138246523983851)⟩⟩,⟨⟨(-2236886552549583813027378091),(-2236886552549583810104987347)⟩,⟨(-12821947369981803764356117329),(-12821947369981803761463789135)⟩⟩,⟨⟨(-2294054966019543065076402509),(-2294054966019543062080264569)⟩,⟨(-13149639620579715177483136826),(-13149639620579715174522281382)⟩⟩,⟨⟨(-2350473060741471696631855591),(-2350473060741471693561823997)⟩,⟨(-13473031005992043603452809193),(-13473031005992043600417938285)⟩⟩,⟨⟨(-2406929842568628609173113670),(-2406929842568628606029316985)⟩,⟨(-13796644147857138299581991000),(-13796644147857138296474081245)⟩⟩,⟨⟨(-2462643101475025596574277939),(-2462643101475025593357504163)⟩,⟨(-14115995378563845096453982768),(-14115995378563845093272944419)⟩⟩,⟨⟨(-2518355460693847131094420402),(-2518355460693847127804631378)⟩,⟨(-14435341452215658458954092719),(-14435341452215658455699701485)⟩⟩,⟨⟨(-2573329192070436686245193715),(-2573329192070436682883360419)⟩,⟨(-14750453673547913146823157370),(-14750453673547913143496402654)⟩⟩,⟨⟨(-2628264625263173647753304041),(-2628264625263173644320981222)⟩,⟨(-15065346367744487153966687885),(-15065346367744487150576244304)⟩⟩,⟨⟨(-2682464728926284393008716920),(-2682464728926284389505107992)⟩,⟨(-15376024115716937965560080667),(-15376024115716937962096826313)⟩⟩,⟨⟨(-2736591067706676011119275353),(-2736591067706676007544718715)⟩,⟨(-15686279039633828380881852749),(-15686279039633828377347270313)⟩⟩,⟨⟨(-2789984030792729049157408712),(-2789984030792729045512658379)⟩,⟨(-15992330216809733952190264454),(-15992330216809733948584132249)⟩⟩,⟨⟨(-2843269483200295803928403148),(-2843269483200295800214132024)⟩,⟨(-16297765137314199945575354797),(-16297765137314199941900863851)⟩⟩] +lemma amp3_11_2_eq : ∀ k : Fin 16, amp3_1Expr 1 2 k = amp3_11_2 k := by decide +kernel +noncomputable def amp3_11_3 : Fin 16 → CBox := ![⟨⟨(-2895822380713515643053737421),(-2895822380713515639270563804)⟩,⟨(-16599001015944936167552271144),(-16599001015944936163808426916)⟩⟩,⟨⟨(-2948235567927807713914495800),(-2948235567927807710062542347)⟩,⟨(-16899436068043877786197194272),(-16899436068043877782383834243)⟩⟩,⟨⟨(-2999916066825581614742988236),(-2999916066825581610823160519)⟩,⟨(-17195671313486425147134154155),(-17195671313486425143251929635)⟩⟩,⟨⟨(-3051426056220250144246825272),(-3051426056220250140261914377)⟩,⟨(-17490929189793999196379441452),(-17490929189793999192443294663)⟩⟩,⟨⟨(-3102202422140761774366731019),(-3102202422140761770314938641)⟩,⟨(-17781981899074080705132153776),(-17781981899074080701127231465)⟩⟩,⟨⟨(-3152778757425303732794793418),(-3152778757425303728676612914)⟩,⟨(-18071888022585713741149884348),(-18071888022585713737077775154)⟩⟩,⟨⟨(-3202619863391098240664946959),(-3202619863391098236481359998)⟩,⟨(-18357579774287072137705147242),(-18357579774287072133566922915)⟩⟩,⟨⟨(-3252232592395201077084914056),(-3252232592395201072836336288)⟩,⟨(-18641962457640735662371989044),(-18641962457640735658168617164)⟩⟩,⟨⟨(-3301107928990071963312982819),(-3301107928990071959000220065)⟩,⟨(-18922118370239566026895308457),(-18922118370239566022626839406)⟩⟩,⟨⟨(-3349727629506710179375393228),(-3349727629506710174999413499)⟩,⟨(-19200808963849719073702238242),(-19200808963849719069372636880)⟩⟩,⟨⟨(-3397607316141974807847196727),(-3397607316141974803408351619)⟩,⟨(-19475257760293532468400107466),(-19475257760293532464006804290)⟩⟩,⟨⟨(-3445205120144288777228784947),(-3445205120144288772727706556)⟩,⟨(-19748090791163501396240228114),(-19748090791163501391785099886)⟩⟩,⟨⟨(-3492059917117642069902918276),(-3492059917117642065340457234)⟩,⟨(-20016664867993086924962589121),(-20016664867993086920445908299)⟩⟩,⟨⟨(-3538607533590063835787815284),(-3538607533590063831164403922)⟩,⟨(-20283478170584238483289873015),(-20283478170584238478712214556)⟩⟩,⟨⟨(-3584408854704921201452224712),(-3584408854704921196768776567)⟩,⟨(-20546013670268378117297846703),(-20546013670268378112659823267)⟩⟩,⟨⟨(-3629878591273424896207881388),(-3629878591273424891464868720)⟩,⟨(-20806648510485813832147559561),(-20806648510485813827449823782)⟩⟩] +lemma amp3_11_3_eq : ∀ k : Fin 16, amp3_1Expr 1 3 k = amp3_11_3 k := by decide +kernel +noncomputable def amp3_11_4 : Fin 16 → CBox := ![⟨⟨(-3674598516835281404299799079),(-3674598516835281399502103504)⟩,⟨(-21062985395917073507863189451),(-21062985395917073503129077433)⟩⟩,⟨⟨(-3718963300339778590893588661),(-3718963300339778586037129989)⟩,⟨(-21317286589031645012245135450),(-21317286589031645007449059006)⟩⟩,⟨⟨(-3762574590383011710477000529),(-3762574590383011705562911581)⟩,⟨(-21567268719343079952761420333),(-21567268719343079947905204463)⟩⟩,⟨⟨(-3805807986503100698602109035),(-3805807986503100693631043160)⟩,⟨(-21815084742487181203303693534),(-21815084742487181198388741976)⟩⟩,⟨⟨(-3848284094129928593769320067),(-3848284094129928588742310060)⟩,⟨(-22058559949511922587668704851),(-22058559949511922582696245740)⟩⟩,⟨⟨(-3890360326150824621262233048),(-3890360326150824616179673014)⟩,⟨(-22299743049246755115792962050),(-22299743049246755110762776928)⟩⟩,⟨⟨(-3931675410886016125900481138),(-3931675410886016120763749464)⟩,⟨(-22536563214067886174718953581),(-22536563214067886169634227627)⟩⟩,⟨⟨(-3972569377672655665300194238),(-3972569377672655660109580563)⟩,⟨(-22770969509411938192380372337),(-22770969509411938187240156687)⟩⟩,⟨⟨(-4012698318754671957688779233),(-4012698318754671952445202964)⟩,⟨(-23000990638547993577630613802),(-23000990638547993572435438707)⟩⟩,⟨⟨(-4052385611987333481275780424),(-4052385611987333475980992172)⟩,⟨(-23228480219772493902510501219),(-23228480219772493897267664974)⟩⟩,⟨⟨(-4091304021530033261618167377),(-4091304021530033256271929234)⟩,⟨(-23451562520621022478755644187),(-23451562520621022473459019357)⟩⟩,⟨⟨(-4129760942243346622112739056),(-4129760942243346616715877862)⟩,⟨(-23671999544052382611282376498),(-23671999544052382605933843355)⟩⟩,⟨⟨(-4167445178213067192925730168),(-4167445178213067187479123589)⟩,⟨(-23888007499275235542832006006),(-23888007499275235537431808090)⟩⟩,⟨⟨(-4204648752671252393862071588),(-4204648752671252388366801036)⟩,⟨(-24101260278292724880252767566),(-24101260278292724874804125574)⟩⟩,⟨⟨(-4241075931632628765266410143),(-4241075931632628759723015543)⟩,⟨(-24310062718875738326663233430),(-24310062718875738321164431968)⟩⟩,⟨⟨(-4277003926566657996385399684),(-4277003926566657990794816940)⟩,⟨(-24516003811251671113074937710),(-24516003811251671107528248658)⟩⟩] +lemma amp3_11_4_eq : ∀ k : Fin 16, amp3_1Expr 1 4 k = amp3_11_4 k := by decide +kernel +noncomputable def amp3_11_5 : Fin 16 → CBox := ![⟨⟨(-4312151936157441301383461908),(-4312151936157441295746574436)⟩,⟨(-24717473988010959200716950166),(-24717473988010959195122604787)⟩⟩,⟨⟨(-4346782873384138110948656092),(-4346782873384138105266158769)⟩,⟨(-24915980279708113743669667496),(-24915980279708113738028445267)⟩⟩,⟨⟨(-4380630384484886434108876281),(-4380630384484886428381666411)⟩,⟨(-25109995933047354708152415737),(-25109995933047354702464606218)⟩⟩,⟨⟨(-4413943554923445717329678899),(-4413943554923445711558501568)⟩,⟨(-25300948718562378097595710476),(-25300948718562378091862273948)⟩⟩,⟨⟨(-4446470033492561675508476477),(-4446470033492561669694309128)⟩,⟨(-25487392146311851005951996424),(-25487392146311851000173661577)⟩⟩,⟨⟨(-4478445510590351198882860665),(-4478445510590351193034237312)⟩,⟨(-25670677205632635584103090758),(-25670677205632635578325361180)⟩⟩,⟨⟨(-4509631229138743675425555049),(-4509631229138743669535261105)⟩,⟨(-25849435328822564394895377081),(-25849435328822564389072005323)⟩⟩,⟨⟨(-4540249881715345229858037873),(-4540249881715345223927025588)⟩,⟨(-26024943001050944220416931162),(-26024943001050944214549862230)⟩⟩,⟨⟨(-4570075930398161692579870292),(-4570075930398161686609304728)⟩,⟨(-26195907427489870974358272632),(-26195907427489870968449274026)⟩⟩,⟨⟨(-4599319434914282692088336330),(-4599319434914282686079009310)⟩,⟨(-26363532681167646459716998026),(-26363532681167646453766999279)⟩⟩,⟨⟨(-4627767732219821180588930843),(-4627767732219821174542070196)⟩,⟨(-26526599766711817868589550848),(-26526599766711817862600663107)⟩⟩,⟨⟨(-4655618584475842405787989285),(-4655618584475842399704421395)⟩,⟨(-26686242266877425820473054742),(-26686242266877425814446313329)⟩⟩,⟨⟨(-4682671887494008457176118469),(-4682671887494008451056617442)⟩,⟨(-26841313174290110080714950734),(-26841313174290110074649851516)⟩⟩,⟨⟨(-4709113413761441760157071875),(-4709113413761441754002839813)⟩,⟨(-26992877346284704826707762179),(-26992877346284704820607405327)⟩⟩,⟨⟨(-4734755328016043892598347307),(-4734755328016043886410183352)⟩,⟨(-27139858101595408886138472835),(-27139858101595408880002484949)⟩⟩,⟨⟨(-4759771695603984759320255609),(-4759771695603984753098910014)⟩,⟨(-27283253191630305218113973933),(-27283253191630305211942779835)⟩⟩] +lemma amp3_11_5_eq : ∀ k : Fin 16, amp3_1Expr 1 5 k = amp3_11_5 k := by decide +kernel +noncomputable def amp3_11_6 : Fin 16 → CBox := ![⟨⟨(-4783986684434824897805777427),(-4783986684434824891553125004)⟩,⟨(-27422054737913393777645729930),(-27422054737913393771445111071)⟩⟩,⟨⟨(-4807562911692542950145427156),(-4807562911692542943861311060)⟩,⟨(-27557194870405423916822463655),(-27557194870405423910587563458)⟩⟩,⟨⟨(-4830336305174704896136302482),(-4830336305174704889822285567)⟩,⟨(-27687733118905934105825892309),(-27687733118905934099560695053)⟩⟩,⟨⟨(-4852458270930776065200655701),(-4852458270930776058857091335)⟩,⟨(-27814537350583032899552557242),(-27814537350583032893255052426)⟩⟩,⟨⟨(-4873776274319785406892106086),(-4873776274319785400520327202)⟩,⟨(-27936733229124759959534366894),(-27936733229124759953207213898)⟩⟩,⟨⟨(-4894430726757596745365282413),(-4894430726757596738966010904)⟩,⟨(-28055125599900809408484792192),(-28055125599900809402128017811)⟩⟩,⟨⟨(-4914280428450251332424881219),(-4914280428450251326001831298)⟩,⟨(-28168905098518191444730014571),(-28168905098518191438359922910)⟩⟩,⟨⟨(-4933454993419274270127696229),(-4933454993419274263678852830)⟩,⟨(-28278814679133661279358823928),(-28278814679133661272959681617)⟩⟩,⟨⟨(-4951824372420951266266305962),(-4951824372420951259792982984)⟩,⟨(-28384108892874762681984828297),(-28384108892874762675559178020)⟩⟩,⟨⟨(-4969507561182858005046653018),(-4969507561182857998549898823)⟩,⟨(-28485469829297843099381373510),(-28485469829297843092930973142)⟩⟩,⟨⟨(-4986385494073012465758036972),(-4986385494073012459238742851)⟩,⟨(-28582214998150946290990073810),(-28582214998150946284515043187)⟩⟩,⟨⟨(-5002566710481483929972516924),(-5002566710481483923431903081)⟩,⟨(-28674966552732571915626106016),(-28674966552732571909129122799)⟩⟩,⟨⟨(-5017942977869881858182938121),(-5017942977869881851621898990)⟩,⟨(-28763104098633633251793124729),(-28763104098633633245274328684)⟩⟩,⟨⟨(-5032612524982808377525050361),(-5032612524982808370944331283)⟩,⟨(-28847190688008953399335608797),(-28847190688008953392794893655)⟩⟩,⟨⟨(-5046477817449798235711867281),(-5046477817449798229113806992)⟩,⟨(-28926667248891541286828069462),(-28926667248891541280273858107)⟩⟩,⟨⟨(-5059626903572492900496998633),(-5059626903572492893881379346)⟩,⟨(-29002038478619925957611529103),(-29002038478619925951038135800)⟩⟩] +lemma amp3_11_6_eq : ∀ k : Fin 16, amp3_1Expr 1 6 k = amp3_11_6 k := by decide +kernel +noncomputable def amp3_11_7 : Fin 16 → CBox := ![⟨⟨(-5071972827087325087775326396),(-5071972827087325081143341282)⟩,⟨(-29072805939473303388688829441),(-29072805939473303382098117396)⟩⟩,⟨⟨(-5083593571245343651758399491),(-5083593571245343645110840659)⟩,⟨(-29139416635408825011340273126),(-29139416635408825004732289793)⟩⟩,⟨⟨(-5094412652057206991012639460),(-5094412652057206984351252677)⟩,⟨(-29201432156313619209665214007),(-29201432156313619203044999385)⟩⟩,⟨⟨(-5104498088897388246426891547),(-5104498088897388239752072883)⟩,⟨(-29259242392698065080772840276),(-29259242392698065074138119252)⟩⟩,⟨⟨(-5113783777894453977609093703),(-5113783777894453970922313176)⟩,⟨(-29312468433812529143425767500),(-29312468433812529136780011341)⟩⟩,⟨⟨(-5122327862012853063659782518),(-5122327862012853056961538052)⟩,⟨(-29361443558083335043594554600),(-29361443558083335036936022710)⟩⟩,⟨⟨(-5130074538545206827026513945),(-5130074538545206820318183991)⟩,⟨(-29405847901556588302867140558),(-29405847901556588296198793826)⟩⟩,⟨⟨(-5137072148240684480596447371),(-5137072148240684473879003455)⟩,⟨(-29445958555862602792507334750),(-29445958555862602785830101058)⟩⟩,⟨⟨(-5143275123403590884365700799),(-5143275123403590877640154655)⟩,⟨(-29481514324654470132402641780),(-29481514324654470125717397159)⟩⟩,⟨⟨(-5148722063855938651369387360),(-5148722063855938644636659227)⟩,⟨(-29512736464073129736027324486),(-29512736464073129729334659678)⟩⟩,⟨⟨(-5153377583230426005600154197),(-5153377583230425998861444804)⟩,⟨(-29539422137663312529305148137),(-29539422137663312522607042402)⟩⟩,⟨⟨(-5157270589102046097945631225),(-5157270589102046091201890887)⟩,⟨(-29561737045113602860663964266),(-29561737045113602853961140596)⟩⟩,⟨⟨(-5160375834950324848036695439),(-5160375834950324841289106843)⟩,⟨(-29579536472085928973529194298),(-29579536472085928966823551233)⟩⟩,⟨⟨(-5162712572410639441283743570),(-5162712572410639434533357422)⟩,⟨(-29592930769932401685100064301),(-29592930769932401678392863129)⟩⟩,⟨⟨(-5164265665324380310478235259),(-5164265665324380303726205494)⟩,⟨(-29601833177422839535044039971),(-29601833177422839528337039922)⟩⟩,⟨⟨(-5165044733496314883165225420),(-5165044733496314876412741557)⟩,⟨(-29606298835766928311356539491),(-29606298835766928304651763357)⟩⟩] +lemma amp3_11_7_eq : ∀ k : Fin 16, amp3_1Expr 1 7 k = amp3_11_7 k := by decide +kernel +noncomputable def amp3_11_8 : Fin 16 → CBox := ![⟨⟨(-5165044733496314883165225420),(-5165044733496314876412741557)⟩,⟨(-29606298835766928311356539491),(-29606298835766928304651763357)⟩⟩,⟨⟨(-5164265665324380310478235259),(-5164265665324380303726205494)⟩,⟨(-29601833177422839535044039971),(-29601833177422839528337039922)⟩⟩,⟨⟨(-5162712572410639441283743570),(-5162712572410639434533357422)⟩,⟨(-29592930769932401685100064301),(-29592930769932401678392863129)⟩⟩,⟨⟨(-5160375834950324848036695439),(-5160375834950324841289106843)⟩,⟨(-29579536472085928973529194298),(-29579536472085928966823551233)⟩⟩,⟨⟨(-5157270589102046097945631225),(-5157270589102046091201890887)⟩,⟨(-29561737045113602860663964266),(-29561737045113602853961140596)⟩⟩,⟨⟨(-5153377583230426005600154197),(-5153377583230425998861444804)⟩,⟨(-29539422137663312529305148137),(-29539422137663312522607042402)⟩⟩,⟨⟨(-5148722063855938651369387360),(-5148722063855938644636659227)⟩,⟨(-29512736464073129736027324486),(-29512736464073129729334659678)⟩⟩,⟨⟨(-5143275123403590884365700799),(-5143275123403590877640154655)⟩,⟨(-29481514324654470132402641780),(-29481514324654470125717397159)⟩⟩,⟨⟨(-5137072148240684480596447371),(-5137072148240684473879003455)⟩,⟨(-29445958555862602792507334750),(-29445958555862602785830101058)⟩⟩,⟨⟨(-5130074538545206827026513945),(-5130074538545206820318183991)⟩,⟨(-29405847901556588302867140558),(-29405847901556588296198793826)⟩⟩,⟨⟨(-5122327862012853063659782518),(-5122327862012853056961538052)⟩,⟨(-29361443558083335043594554600),(-29361443558083335036936022710)⟩⟩,⟨⟨(-5113783777894453977609093703),(-5113783777894453970922313176)⟩,⟨(-29312468433812529143425767500),(-29312468433812529136780011341)⟩⟩,⟨⟨(-5104498088897388246426891547),(-5104498088897388239752072883)⟩,⟨(-29259242392698065080772840276),(-29259242392698065074138119252)⟩⟩,⟨⟨(-5094412652057206991012639460),(-5094412652057206984351252677)⟩,⟨(-29201432156313619209665214007),(-29201432156313619203044999385)⟩⟩,⟨⟨(-5083593571245343651758399491),(-5083593571245343645110840659)⟩,⟨(-29139416635408825011340273126),(-29139416635408825004732289793)⟩⟩,⟨⟨(-5071972827087325087775326396),(-5071972827087325081143341282)⟩,⟨(-29072805939473303388688829441),(-29072805939473303382098117396)⟩⟩] +lemma amp3_11_8_eq : ∀ k : Fin 16, amp3_1Expr 1 8 k = amp3_11_8 k := by decide +kernel +noncomputable def amp3_11_9 : Fin 16 → CBox := ![⟨⟨(-5059626903572492900496998633),(-5059626903572492893881379346)⟩,⟨(-29002038478619925957611529103),(-29002038478619925951038135800)⟩⟩,⟨⟨(-5046477817449798235711867281),(-5046477817449798229113806992)⟩,⟨(-28926667248891541286828069462),(-28926667248891541280273858107)⟩⟩,⟨⟨(-5032612524982808377525050361),(-5032612524982808370944331283)⟩,⟨(-28847190688008953399335608797),(-28847190688008953392794893655)⟩⟩,⟨⟨(-5017942977869881858182938121),(-5017942977869881851621898990)⟩,⟨(-28763104098633633251793124729),(-28763104098633633245274328684)⟩⟩,⟨⟨(-5002566710481483929972516924),(-5002566710481483923431903081)⟩,⟨(-28674966552732571915626106016),(-28674966552732571909129122799)⟩⟩,⟨⟨(-4986385494073012465758036972),(-4986385494073012459238742851)⟩,⟨(-28582214998150946290990073810),(-28582214998150946284515043187)⟩⟩,⟨⟨(-4969507561182858005046653018),(-4969507561182857998549898823)⟩,⟨(-28485469829297843099381373510),(-28485469829297843092930973142)⟩⟩,⟨⟨(-4951824372420951266266305962),(-4951824372420951259792982984)⟩,⟨(-28384108892874762681984828297),(-28384108892874762675559178020)⟩⟩,⟨⟨(-4933454993419274270127696229),(-4933454993419274263678852830)⟩,⟨(-28278814679133661279358823928),(-28278814679133661272959681617)⟩⟩,⟨⟨(-4914280428450251332424881219),(-4914280428450251326001831298)⟩,⟨(-28168905098518191444730014571),(-28168905098518191438359922910)⟩⟩,⟨⟨(-4894430726757596745365282413),(-4894430726757596738966010904)⟩,⟨(-28055125599900809408484792192),(-28055125599900809402128017811)⟩⟩,⟨⟨(-4873776274319785406892106086),(-4873776274319785400520327202)⟩,⟨(-27936733229124759959534366894),(-27936733229124759953207213898)⟩⟩,⟨⟨(-4852458270930776065200655701),(-4852458270930776058857091335)⟩,⟨(-27814537350583032899552557242),(-27814537350583032893255052426)⟩⟩,⟨⟨(-4830336305174704896136302482),(-4830336305174704889822285567)⟩,⟨(-27687733118905934105825892309),(-27687733118905934099560695053)⟩⟩,⟨⟨(-4807562911692542950145427156),(-4807562911692542943861311060)⟩,⟨(-27557194870405423916822463655),(-27557194870405423910587563458)⟩⟩,⟨⟨(-4783986684434824897805777427),(-4783986684434824891553125004)⟩,⟨(-27422054737913393777645729930),(-27422054737913393771445111071)⟩⟩] +lemma amp3_11_9_eq : ∀ k : Fin 16, amp3_1Expr 1 9 k = amp3_11_9 k := by decide +kernel +noncomputable def amp3_11_10 : Fin 16 → CBox := ![⟨⟨(-4759771695603984759320255609),(-4759771695603984753098910014)⟩,⟨(-27283253191630305218113973933),(-27283253191630305211942779835)⟩⟩,⟨⟨(-4734755328016043892598347307),(-4734755328016043886410183352)⟩,⟨(-27139858101595408886138472835),(-27139858101595408880002484949)⟩⟩,⟨⟨(-4709113413761441760157071875),(-4709113413761441754002839813)⟩,⟨(-26992877346284704826707762179),(-26992877346284704820607405327)⟩⟩,⟨⟨(-4682671887494008457176118469),(-4682671887494008451056617442)⟩,⟨(-26841313174290110080714950734),(-26841313174290110074649851516)⟩⟩,⟨⟨(-4655618584475842405787989285),(-4655618584475842399704421395)⟩,⟨(-26686242266877425820473054742),(-26686242266877425814446313329)⟩⟩,⟨⟨(-4627767732219821180588930843),(-4627767732219821174542070196)⟩,⟨(-26526599766711817868589550848),(-26526599766711817862600663107)⟩⟩,⟨⟨(-4599319434914282692088336330),(-4599319434914282686079009310)⟩,⟨(-26363532681167646459716998026),(-26363532681167646453766999279)⟩⟩,⟨⟨(-4570075930398161692579870292),(-4570075930398161686609304728)⟩,⟨(-26195907427489870974358272632),(-26195907427489870968449274026)⟩⟩,⟨⟨(-4540249881715345229858037873),(-4540249881715345223927025588)⟩,⟨(-26024943001050944220416931162),(-26024943001050944214549862230)⟩⟩,⟨⟨(-4509631229138743675425555049),(-4509631229138743669535261105)⟩,⟨(-25849435328822564394895377081),(-25849435328822564389072005323)⟩⟩,⟨⟨(-4478445510590351198882860665),(-4478445510590351193034237312)⟩,⟨(-25670677205632635584103090758),(-25670677205632635578325361180)⟩⟩,⟨⟨(-4446470033492561675508476477),(-4446470033492561669694309128)⟩,⟨(-25487392146311851005951996424),(-25487392146311851000173661577)⟩⟩,⟨⟨(-4413943554923445717329678899),(-4413943554923445711558501568)⟩,⟨(-25300948718562378097595710476),(-25300948718562378091862273948)⟩⟩,⟨⟨(-4380630384484886434108876281),(-4380630384484886428381666411)⟩,⟨(-25109995933047354708152415737),(-25109995933047354702464606218)⟩⟩,⟨⟨(-4346782873384138110948656092),(-4346782873384138105266158769)⟩,⟨(-24915980279708113743669667496),(-24915980279708113738028445267)⟩⟩,⟨⟨(-4312151936157441301383461908),(-4312151936157441295746574436)⟩,⟨(-24717473988010959200716950166),(-24717473988010959195122604787)⟩⟩] +lemma amp3_11_10_eq : ∀ k : Fin 16, amp3_1Expr 1 10 k = amp3_11_10 k := by decide +kernel +noncomputable def amp3_11_11 : Fin 16 → CBox := ![⟨⟨(-4277003926566657996385399684),(-4277003926566657990794816940)⟩,⟨(-24516003811251671113074937710),(-24516003811251671107528248658)⟩⟩,⟨⟨(-4241075931632628765266410143),(-4241075931632628759723015543)⟩,⟨(-24310062718875738326663233430),(-24310062718875738321164431968)⟩⟩,⟨⟨(-4204648752671252393862071588),(-4204648752671252388366801036)⟩,⟨(-24101260278292724880252767566),(-24101260278292724874804125574)⟩⟩,⟨⟨(-4167445178213067192925730168),(-4167445178213067187479123589)⟩,⟨(-23888007499275235542832006006),(-23888007499275235537431808090)⟩⟩,⟨⟨(-4129760942243346622112739056),(-4129760942243346616715877862)⟩,⟨(-23671999544052382611282376498),(-23671999544052382605933843355)⟩⟩,⟨⟨(-4091304021530033261618167377),(-4091304021530033256271929234)⟩,⟨(-23451562520621022478755644187),(-23451562520621022473459019357)⟩⟩,⟨⟨(-4052385611987333481275780424),(-4052385611987333475980992172)⟩,⟨(-23228480219772493902510501219),(-23228480219772493897267664974)⟩⟩,⟨⟨(-4012698318754671957688779233),(-4012698318754671952445202964)⟩,⟨(-23000990638547993577630613802),(-23000990638547993572435438707)⟩⟩,⟨⟨(-3972569377672655665300194238),(-3972569377672655660109580563)⟩,⟨(-22770969509411938192380372337),(-22770969509411938187240156687)⟩⟩,⟨⟨(-3931675410886016125900481138),(-3931675410886016120763749464)⟩,⟨(-22536563214067886174718953581),(-22536563214067886169634227627)⟩⟩,⟨⟨(-3890360326150824621262233048),(-3890360326150824616179673014)⟩,⟨(-22299743049246755115792962050),(-22299743049246755110762776928)⟩⟩,⟨⟨(-3848284094129928593769320067),(-3848284094129928588742310060)⟩,⟨(-22058559949511922587668704851),(-22058559949511922582696245740)⟩⟩,⟨⟨(-3805807986503100698602109035),(-3805807986503100693631043160)⟩,⟨(-21815084742487181203303693534),(-21815084742487181198388741976)⟩⟩,⟨⟨(-3762574590383011710477000529),(-3762574590383011705562911581)⟩,⟨(-21567268719343079952761420333),(-21567268719343079947905204463)⟩⟩,⟨⟨(-3718963300339778590893588661),(-3718963300339778586037129989)⟩,⟨(-21317286589031645012245135450),(-21317286589031645007449059006)⟩⟩,⟨⟨(-3674598516835281404299799079),(-3674598516835281399502103504)⟩,⟨(-21062985395917073507863189451),(-21062985395917073503129077433)⟩⟩] +lemma amp3_11_11_eq : ∀ k : Fin 16, amp3_1Expr 1 11 k = amp3_11_11 k := by decide +kernel +noncomputable def amp3_11_12 : Fin 16 → CBox := ![⟨⟨(-3629878591273424896207881388),(-3629878591273424891464868720)⟩,⟨(-20806648510485813832147559561),(-20806648510485813827449823782)⟩⟩,⟨⟨(-3584408854704921201452224712),(-3584408854704921196768776567)⟩,⟨(-20546013670268378117297846703),(-20546013670268378112659823267)⟩⟩,⟨⟨(-3538607533590063835787815284),(-3538607533590063831164403922)⟩,⟨(-20283478170584238483289873015),(-20283478170584238478712214556)⟩⟩,⟨⟨(-3492059917117642069902918276),(-3492059917117642065340457234)⟩,⟨(-20016664867993086924962589121),(-20016664867993086920445908299)⟩⟩,⟨⟨(-3445205120144288777228784947),(-3445205120144288772727706556)⟩,⟨(-19748090791163501396240228114),(-19748090791163501391785099886)⟩⟩,⟨⟨(-3397607316141974807847196727),(-3397607316141974803408351619)⟩,⟨(-19475257760293532468400107466),(-19475257760293532464006804290)⟩⟩,⟨⟨(-3349727629506710179375393228),(-3349727629506710174999413499)⟩,⟨(-19200808963849719073702238242),(-19200808963849719069372636880)⟩⟩,⟨⟨(-3301107928990071963312982819),(-3301107928990071959000220065)⟩,⟨(-18922118370239566026895308457),(-18922118370239566022626839406)⟩⟩,⟨⟨(-3252232592395201077084914056),(-3252232592395201072836336288)⟩,⟨(-18641962457640735662371989044),(-18641962457640735658168617164)⟩⟩,⟨⟨(-3202619863391098240664946959),(-3202619863391098236481359998)⟩,⟨(-18357579774287072137705147242),(-18357579774287072133566922915)⟩⟩,⟨⟨(-3152778757425303732794793418),(-3152778757425303728676612914)⟩,⟨(-18071888022585713741149884348),(-18071888022585713737077775154)⟩⟩,⟨⟨(-3102202422140761774366731019),(-3102202422140761770314938641)⟩,⟨(-17781981899074080705132153776),(-17781981899074080701127231465)⟩⟩,⟨⟨(-3051426056220250144246825272),(-3051426056220250140261914377)⟩,⟨(-17490929189793999196379441452),(-17490929189793999192443294663)⟩⟩,⟨⟨(-2999916066825581614742988236),(-2999916066825581610823160519)⟩,⟨(-17195671313486425147134154155),(-17195671313486425143251929635)⟩⟩,⟨⟨(-2948235567927807713914495800),(-2948235567927807710062542347)⟩,⟨(-16899436068043877786197194272),(-16899436068043877782383834243)⟩⟩,⟨⟨(-2895822380713515643053737421),(-2895822380713515639270563804)⟩,⟨(-16599001015944936167552271144),(-16599001015944936163808426916)⟩⟩] +lemma amp3_11_12_eq : ∀ k : Fin 16, amp3_1Expr 1 12 k = amp3_11_12 k := by decide +kernel +noncomputable def amp3_11_13 : Fin 16 → CBox := ![⟨⟨(-2843269483200295803928403148),(-2843269483200295800214132024)⟩,⟨(-16297765137314199945575354797),(-16297765137314199941900863851)⟩⟩,⟨⟨(-2789984030792729049157408712),(-2789984030792729045512658379)⟩,⟨(-15992330216809733952190264454),(-15992330216809733948584132249)⟩⟩,⟨⟨(-2736591067706676011119275353),(-2736591067706676007544718715)⟩,⟨(-15686279039633828380881852749),(-15686279039633828377347270313)⟩⟩,⟨⟨(-2682464728926284393008716920),(-2682464728926284389505107992)⟩,⟨(-15376024115716937965560080667),(-15376024115716937962096826313)⟩⟩,⟨⟨(-2628264625263173647753304041),(-2628264625263173644320981222)⟩,⟨(-15065346367744487153966687885),(-15065346367744487150576244304)⟩⟩,⟨⟨(-2573329192070436686245193715),(-2573329192070436682883360419)⟩,⟨(-14750453673547913146823157370),(-14750453673547913143496402654)⟩⟩,⟨⟨(-2518355460693847131094420402),(-2518355460693847127804631378)⟩,⟨(-14435341452215658458954092719),(-14435341452215658455699701485)⟩⟩,⟨⟨(-2462643101475025596574277939),(-2462643101475025593357504163)⟩,⟨(-14115995378563845096453982768),(-14115995378563845093272944419)⟩⟩,⟨⟨(-2406929842568628609173113670),(-2406929842568628606029316985)⟩,⟨(-13796644147857138299581991000),(-13796644147857138296474081245)⟩⟩,⟨⟨(-2350473060741471696631855591),(-2350473060741471693561823997)⟩,⟨(-13473031005992043603452809193),(-13473031005992043600417938285)⟩⟩,⟨⟨(-2294054966019543065076402509),(-2294054966019543062080264569)⟩,⟨(-13149639620579715177483136826),(-13149639620579715174522281382)⟩⟩,⟨⟨(-2236886552549583813027378091),(-2236886552549583810104987347)⟩,⟨(-12821947369981803764356117329),(-12821947369981803761463789135)⟩⟩,⟨⟨(-2179798915915662808956083540),(-2179798915915662806108651737)⟩,⟨(-12494718136312138249340338552),(-12494718136312138246523983851)⟩⟩,⟨⟨(-2121951893766475952495355615),(-2121951893766475949723732205)⟩,⟨(-12163136066286436997141725293),(-12163136066286436994401508306)⟩⟩,⟨⟨(-2064230630799723995558327922),(-2064230630799723992862266835)⟩,⟨(-11832274854283970912525872622),(-11832274854283970909861162019)⟩⟩,⟨⟨(-2005738188498802510844975054),(-2005738188498802508225612571)⟩,⟨(-11496993203156297957134742618),(-11496993203156297954547273668)⟩⟩] +lemma amp3_11_13_eq : ∀ k : Fin 16, amp3_1Expr 1 13 k = amp3_11_13 k := by decide +kernel +noncomputable def amp3_11_14 : Fin 16 → CBox := ![⟨⟨(-1947419868181087740976678469),(-1947419868181087738432914805)⟩,⟨(-11162709628083080546061075680),(-11162709628083080543545623159)⟩⟩,⟨⟨(-1888315278407924774874363023),(-1888315278407924772407993898)⟩,⟨(-10823919116542794560380015142),(-10823919116542794557942000753)⟩⟩,⟨⟨(-1829437172087648440688568763),(-1829437172087648438299183930)⟩,⟨(-10486426819661528380948604124),(-10486426819661528378587079526)⟩⟩,⟨⟨(-1769753689214106827972328573),(-1769753689214106825661269942)⟩,⟨(-10144318063457720922800142035),(-10144318063457720920517809295)⟩⟩,⟨⟨(-1710353844287314215285879813),(-1710353844287314213051945751)⟩,⟨(-9803835134375633248485544875),(-9803835134375633246277273494)⟩⟩,⟨⟨(-1650124571656563996388073041),(-1650124571656563994232988386)⟩,⟨(-9458597883553255377808374609),(-9458597883553255375678912598)⟩⟩,⟨⟨(-1590241921453586583491946308),(-1590241921453586581414786050)⟩,⟨(-9115347490097914104613359029),(-9115347490097914102559551734)⟩⟩,⟨⟨(-1529499634035960903193756318),(-1529499634035960901196166636)⟩,⟨(-8767169612452131969945632915),(-8767169612452131967971590310)⟩⟩,⟨⟨(-1469174162069821264218786486),(-1469174162069821262300159345)⟩,⟨(-8421380942151647584638624944),(-8421380942151647582743444180)⟩⟩,⟨⟨(-1407951061421260000149186178),(-1407951061421259998310321259)⟩,⟨(-8070447018637191335920874295),(-8070447018637191334103577796)⟩⟩,⟨⟨(-1347224049647206334242887604),(-1347224049647206332483576134)⟩,⟨(-7722356701756482300677532294),(-7722356701756482298939996956)⟩⟩,⟨⟨(-1285551412780888597361560973),(-1285551412780888595682661940)⟩,⟨(-7368846013802003603304271471),(-7368846013802003601645562295)⟩⟩,⟨⟨(-1224465824149729459438022484),(-1224465824149729457838768552)⟩,⟨(-7018700316157947637269453978),(-7018700316157947635688809694)⟩⟩,⟨⟨(-1162373479802631049399922641),(-1162373479802631047881977951)⟩,⟨(-6662783843599317383283399891),(-6662783843599317381784121944)⟩⟩,⟨⟨(-1100974564234470579281328934),(-1100974564234470577843513562)⟩,⟨(-6310842140032989848300849918),(-6310842140032989846880471163)⟩⟩,⟨⟨(-1038490075614490174501519672),(-1038490075614490173145273941)⟩,⟨(-5952677876578302846168331915),(-5952677876578302844828382527)⟩⟩] +lemma amp3_11_14_eq : ∀ k : Fin 16, amp3_1Expr 1 14 k = amp3_11_14 k := by decide +kernel +noncomputable def amp3_11_15 : Fin 16 → CBox := ![⟨⟨(-976826365869980122431079886),(-976826365869980121155391521)⟩,⟨(-5599218359339591154250983426),(-5599218359339591152990746248)⟩⟩,⟨⟨(-913973687112991920943172685),(-913973687112991919749621639)⟩,⟨(-5238943611312729715424956618),(-5238943611312729714246121583)⟩⟩,⟨⟨(-852098715826997533146399346),(-852098715826997532033730052)⟩,⟨(-4884273132184544491036292840),(-4884273132184544489937720511)⟩⟩,⟨⟨(-788895841566765076923251268),(-788895841566765075893062514)⟩,⟨(-4521991045740504832467951534),(-4521991045740504831450579026)⟩⟩,⟨⟨(-726871292114567087572208555),(-726871292114567086623011368)⟩,⟨(-4166463176963937582041909755),(-4166463176963937581104502683)⟩⟩,⟨⟨(-663325817138793157583491614),(-663325817138793156717301047)⟩,⟨(-3802217285811704743566857657),(-3802217285811704742711543286)⟩⟩,⟨⟨(-601227801041259061393492741),(-601227801041259060608462826)⟩,⟨(-3446268302491409285642191240),(-3446268302491409284867356331)⟩⟩,⟨⟨(-537327657764345332476231089),(-537327657764345331774598339)⟩,⟨(-3079989434617208980956745049),(-3079989434617208980264044069)⟩⟩,⟨⟨(-475260698067625593930502961),(-475260698067625593309956456)⟩,⟨(-2724218468164281644505258217),(-2724218468164281643892802611)⟩⟩,⟨⟨(-410952047203312812621453703),(-410952047203312812084903237)⟩,⟨(-2355598014043832587836924325),(-2355598014043832587307504459)⟩⟩,⟨⟨(-349085604172734029041738452),(-349085604172734028586011898)⟩,⟨(-2000976419308989531251875276),(-2000976419308989530802439409)⟩⟩,⟨⟨(-284208574900344161678692675),(-284208574900344161307693658)⟩,⟨(-1629097991275517500580703724),(-1629097991275517500214975098)⟩⟩,⟨⟨(-222899049574540212094499198),(-222899049574540211803594707)⟩,⟨(-1277668677120078436787951893),(-1277668677120078436501476857)⟩⟩,⟨⟨(-156930468665277273127383836),(-156930468665277272922614193)⟩,⟨(-899533419644964986134377747),(-899533419644964985932913863)⟩⟩,⟨⟨(-97347548738388396681199278),(-97347548738388396554308863)⟩,⟨(-558001095360729850848072071),(-558001095360729850723861018)⟩⟩,⟨⟨(-27656833929615362292264311),(-27656833929615362256294169)⟩,⟨(-158530377261050063379232069),(-158530377261050063344401428)⟩⟩] +lemma amp3_11_15_eq : ∀ k : Fin 16, amp3_1Expr 1 15 k = amp3_11_15 k := by decide +kernel +noncomputable def amp3_11 : Fin 16 → Fin 16 → CBox := ![amp3_11_0,amp3_11_1,amp3_11_2,amp3_11_3,amp3_11_4,amp3_11_5,amp3_11_6,amp3_11_7,amp3_11_8,amp3_11_9,amp3_11_10,amp3_11_11,amp3_11_12,amp3_11_13,amp3_11_14,amp3_11_15] +lemma amp3_11_eq (i k : Fin 16) : amp3_1Expr 1 i k = amp3_11 i k := by + fin_cases i + · exact amp3_11_0_eq k + · exact amp3_11_1_eq k + · exact amp3_11_2_eq k + · exact amp3_11_3_eq k + · exact amp3_11_4_eq k + · exact amp3_11_5_eq k + · exact amp3_11_6_eq k + · exact amp3_11_7_eq k + · exact amp3_11_8_eq k + · exact amp3_11_9_eq k + · exact amp3_11_10_eq k + · exact amp3_11_11_eq k + · exact amp3_11_12_eq k + · exact amp3_11_13_eq k + · exact amp3_11_14_eq k + · exact amp3_11_15_eq k +noncomputable def amp3_12_0 : Fin 16 → CBox := ![⟨⟨(-385210003677661992985603661),(-385210003677661992958854988)⟩,⟨47903041542588614247597182,47903041542588614274209493⟩⟩,⟨⟨(-1355876442797423833610149372),(-1355876442797423833512079310)⟩,⟨168610900407176264254508195,168610900407176264348666555⟩⟩,⟨⟨(-2185759460592364486953109937),(-2185759460592364486792031491)⟩,⟨271811544983855893836027781,271811544983855893988188054⟩⟩,⟨⟨(-3104583262309451839099637679),(-3104583262309451838870064215)⟩,⟨386072478821917588709818760,386072478821917588926039715⟩⟩,⟨⟨(-3958514790998972548232486511),(-3958514790998972547938656834)⟩,⟨492263691674140854248137577,492263691674140854523969355⟩⟩,⟨⟨(-4862135239681351864882120702),(-4862135239681351864520679744)⟩,⟨604634002618053415554305942,604634002618053415893169462⟩⟩,⟨⟨(-5723823631345515039226457064),(-5723823631345515038800150713)⟩,⟨711789825230581337903579670,711789825230581338302598670⟩⟩,⟨⟨(-6619527590048496234348673604),(-6619527590048496233855198024)⟩,⟨823175675893779269422113988,823175675893779269883631206⟩⟩,⟨⟨(-7484008818589727933465363364),(-7484008818589727932906806965)⟩,⟨930678803559827651774042637,930678803559827652295910952⟩⟩,⟨⟨(-8374023000594305592180654475),(-8374023000594305591556265132)⟩,⟨1041357098326373040876403974,1041357098326373041460260384⟩⟩,⟨⟨(-9238936788997680558391737101),(-9238936788997680557701763132)⟩,⟨1148914017256532114124412335,1148914017256532114768708641⟩⟩,⟨⟨(-10124011078824646542621083983),(-10124011078824646541864634935)⟩,⟨1258978008505669232729956015,1258978008505669233436021653⟩⟩,⟨⟨(-10987901608861133640388010369),(-10987901608861133639567071951)⟩,⟨1366407679473444525835192334,1366407679473444526601499812⟩⟩,⟨⟨(-11868204086295200168879406802),(-11868204086295200167993445834)⟩,⟨1475878268876554359595976523,1475878268876554360423584246⟩⟩,⟨⟨(-12730011261233991576484709836),(-12730011261233991575533224099)⟩,⟨1583048862860762032880563198,1583048862860762033768415579⟩⟩,⟨⟨(-13605436144528543518622761932),(-13605436144528543517605029070)⟩,⟨1691912895859670665839328149,1691912895859670666788338208⟩⟩] +lemma amp3_12_0_eq : ∀ k : Fin 16, amp3_1Expr 2 0 k = amp3_12_0 k := by decide +kernel +noncomputable def amp3_12_1 : Fin 16 → CBox := ![⟨⟨(-14464300825782799817879049141),(-14464300825782799816796686981)⟩,⟨1798717574120342149557733837,1798717574120342150566699322⟩⟩,⟨⟨(-15334597482021724183614628773),(-15334597482021724182467612598)⟩,⟨1906943883095107532655037369,1906943883095107533724652418⟩⟩,⟨⟨(-16189774056173590092697388257),(-16189774056173590091487164107)⟩,⟨2013289924388793187245815467,2013289924388793188374986247⟩⟩,⟨⟨(-17054608847284225418521092515),(-17054608847284225417243116867)⟩,⟨2120837019559029801162529797,2120837019559029802352405161⟩⟩,⟨⟨(-17905421340180017041567296852),(-17905421340180017040227484690)⟩,⟨2226640362678449215585505192,2226640362678449216834501930⟩⟩,⟨⟨(-18764410360201072199349283763),(-18764410360201072197947013978)⟩,⟨2333460503167656965516559046,2333460503167656966825248666⟩⟩,⟨⟨(-19610228521757425347383461096),(-19610228521757425345914482565)⟩,⟨2438642772952151337215884399,2438642772952151338583999375⟩⟩,⟨⟨(-20462956309978198965847334188),(-20462956309978198964317245856)⟩,⟨2544684293872362529737838650,2544684293872362531165100408⟩⟩,⟨⟨(-21303181743484879756516695950),(-21303181743484879754921243690)⟩,⟨2649171076308288359225720562,2649171076308288360711902359⟩⟩,⟨⟨(-22149212667309377172721441712),(-22149212667309377171059304100)⟩,⟨2754379804283567772781889784,2754379804283567774327506889⟩⟩,⟨⟨(-22983270389303945549650835820),(-22983270389303945547930200389)⟩,⟨2858099596926999394473353103,2858099596926999396076663569⟩⟩,⟨⟨(-23822155938916705062494969763),(-23822155938916705060708896559)⟩,⟨2962419757226376389639898632,2962419757226376391302057324⟩⟩,⟨⟨(-24649489050903922245788062755),(-24649489050903922243946352887)⟩,⟨3065303306601293613289299871,3065303306601293615008389620⟩⟩,⟨⟨(-25480772729857277564149508456),(-25480772729857277562240289081)⟩,⟨3168678131310934620652341769,3168678131310934622430077843⟩⟩,⟨⟨(-26300838960499855274413878750),(-26300838960499855272442029913)⟩,⟨3270658002911095463419536560,3270658002911095465254634001⟩⟩,⟨⟨(-27124059698702532522428967612),(-27124059698702532520392658990)⟩,⟨3373030155358729584770402210,3373030155358729586663279321⟩⟩] +lemma amp3_12_1_eq : ∀ k : Fin 16, amp3_1Expr 2 1 k = amp3_12_1 k := by decide +kernel +noncomputable def amp3_12_2 : Fin 16 → CBox := ![⟨⟨(-27936329116135969238117835762),(-27936329116135969236028595790)⟩,⟨3474040449161087916450224865,3474040449161087918398786010⟩⟩,⟨⟨(-28751023739938367697471673259),(-28751023739938367695317169698)⟩,⟨3575352331085074933066008417,3575352331085074935071933786⟩⟩,⟨⟨(-29554977221247464423708565981),(-29554977221247464421491401256)⟩,⟨3675328491220533190011002730,3675328491220533192073319392⟩⟩,⟨⟨(-30360682302007587724563649384),(-30360682302007587722282552651)⟩,⟨3775522472649487016443983958,3775522472649487018562955835⟩⟩,⟨⟨(-31155810506980960748189575453),(-31155810506980960745843356355)⟩,⟨3874401159783468515250597318,3874401159783468517425733064⟩⟩,⟨⟨(-31952063788142973132461184901),(-31952063788142973130068105995)⟩,⟨3973419756501542920259921995,3973419756501542922489018570⟩⟩,⟨⟨(-32737866477294929152542860551),(-32737866477294929150088015712)⟩,⟨4071138763026156820083225728,4071138763026156822367505053⟩⟩,⟨⟨(-33524208008310895724390467550),(-33524208008310895721876310811)⟩,⟨4168924777582623866123181087,4168924777582623868462370563⟩⟩,⟨⟨(-34300193600980150025467495726),(-34300193600980150022892252826)⟩,⟨4265422972663742713465005526,4265422972663742715858699776⟩⟩,⟨⟨(-35076166662618009664986189659),(-35076166662618009662349313710)⟩,⟨4361919609440269937958966035,4361919609440269940407232309⟩⟩,⟨⟨(-35841851965557722420302379321),(-35841851965557722417604728515)⟩,⟨4457136905266166405298376297,4457136905266166407800485979⟩⟩,⟨⟨(-36607003843609385795500262146),(-36607003843609385792762834613)⟩,⟨4552287866691792566485459177,4552287866691792569038768785⟩⟩,⟨⟨(-37361913902531192334769237456),(-37361913902531192331968328997)⟩,⟨4646165200011800397129162953,4646165200011800399736001119⟩⟩,⟨⟨(-38115796549175229433255155783),(-38115796549175229430394214773)⟩,⟨4739914768807124340080983952,4739914768807124342740859746⟩⟩,⟨⟨(-38859464590104374376336831644),(-38859464590104374373413784460)⟩,⟨4832394093638817759307806469,4832394093638817762020360283⟩⟩,⟨⟨(-39601635200454137557129087322),(-39601635200454137554151462762)⟩,⟨4924687204513016733680641167,4924687204513016736444846232⟩⟩] +lemma amp3_12_2_eq : ∀ k : Fin 16, amp3_1Expr 2 2 k = amp3_12_2 k := by decide +kernel +noncomputable def amp3_12_3 : Fin 16 → CBox := ![⟨⟨(-40333602637358103893096964793),(-40333602637358103890060813004)⟩,⟨5015711493090873599226372006,5015711493090873602042102728⟩⟩,⟨⟨(-41063624160825241730117552065),(-41063624160825241727022185732)⟩,⟨5106493796332646934498121890,5106493796332646937365346108⟩⟩,⟨⟨(-41783440652515466066594055692),(-41783440652515466063439523909)⟩,⟨5196007046184098692189898888,5196007046184098695107993603⟩⟩,⟨⟨(-42500882253193745498225156875),(-42500882253193745495047410594)⟩,⟨5285224964912998623492844375,5285224964912998626457195322⟩⟩,⟨⟨(-43208105797029466862338712263),(-43208105797029466859100124370)⟩,⟨5373172210511033611833180004,5373172210511033614847848644⟩⟩,⟨⟨(-43912543273515121380738214368),(-43912543273515121377442226401)⟩,⟨5460772992884498814206040534,5460772992884498817270430474⟩⟩,⟨⟨(-44606740326628404396306392219),(-44606740326628404392954069573)⟩,⟨5547100320722679179347118039,5547100320722679182460477758⟩⟩,⟨⟨(-45297756499006132967371745755),(-45297756499006132963964961543)⟩,⟨5633032088059931358400416676,5633032088059931361562320957⟩⟩,⟨⟨(-45978502120047616449587453732),(-45978502120047616446124787016)⟩,⟨5717686654279278178076523105,5717686654279278181286527795⟩⟩,⟨⟨(-46655687189838484692427612822),(-46655687189838484688918162697)⟩,⟨5801898445822878360699628206,5801898445822878363956386544⟩⟩,⟨⟨(-47322565195896356615144341458),(-47322565195896356611580315490)⟩,⟨5884828495725633241574041036,5884828495725633244877898994⟩⟩,⟨⟨(-47985517083355406602241003726),(-47985517083355406598626372243)⟩,⟨5967270310586346291951644821,5967270310586346295301871333⟩⟩,⟨⟨(-48638120217913569083231060336),(-48638120217913569079564930268)⟩,⟨6048425199522518650040102748,6048425199522518653436183289⟩⟩,⟨⟨(-49286444880026379423742835208),(-49286444880026379420025960705)⟩,⟨6129048036223983144890070041,6129048036223983148331652194⟩⟩,⟨⟨(-49924374988729221668959084586),(-49924374988729221665191392347)⟩,⟨6208378251448693316301568765,6208378251448693319788033294⟩⟩,⟨⟨(-50557686720482431275719877824),(-50557686720482431271902259663)⟩,⟨6287134145392114252189440022,6287134145392114255720396844⟩⟩] +lemma amp3_12_3_eq : ∀ k : Fin 16, amp3_1Expr 2 3 k = amp3_12_3 k := by decide +kernel +noncomputable def amp3_12_4 : Fin 16 → CBox := ![⟨⟨(-51180554932150761405915304564),(-51180554932150761402102895098)⟩,⟨6364591328575947895603935800,6364591328575947899171897303⟩⟩,⟨⟨(-51798476653068572744257876778),(-51798476653068572740387756437)⟩,⟨6441433387672530653668912470,6441433387672530657281404042⟩⟩,⟨⟨(-52405903563925214430228505276),(-52405903563925214426303531534)⟩,⟨6516970357811033115908984046,6516970357811033119565015932⟩⟩,⟨⟨(-53008067091420818539426463865),(-53008067091420818535449256705)⟩,⟨6591852796474778414008026423,6591852796474778417706954642⟩⟩,⟨⟨(-53599682950878333020533739921),(-53599682950878333016505698566)⟩,⟨6665423572992208217760455048,6665423572992208221501467992⟩⟩,⟨⟨(-54185729261629598885745249781),(-54185729261629598881665006469)⟩,⟨6738301744643456635968562502,6738301744643456639751493580⟩⟩,⟨⟨(-54761174158297399579852954915),(-54761174158297399575726656169)⟩,⟨6809861570523821676396706760,6809861570523821680220150761⟩⟩,⟨⟨(-55330753638593851796047675607),(-55330753638593851791872134402)⟩,⟨6880691998721315536513401417,6880691998721315540377400101⟩⟩,⟨⟨(-55889677685399926705695100104),(-55889677685399926701470003695)⟩,⟨6950197363529305752262265146,6950197363529305756166213284⟩⟩,⟨⟨(-56442450371203974293073780864),(-56442450371203974288815938873)⟩,⟨7018937771823159982848549705,7018937771823159986789985074⟩⟩,⟨⟨(-56984513888713790575112258176),(-56984513888713790570805172393)⟩,⟨7086346434500889437775362270,7086346434500889441755689148⟩⟩,⟨⟨(-57520149696019410860905777485),(-57520149696019410856553050852)⟩,⟨7152955775078996128374793379,7152955775078996132393175163⟩⟩,⟨⟨(-58045023393183337449922343284),(-58045023393183337445522950347)⟩,⟨7218226786422966776722177984,7218226786422966780778091625⟩⟩,⟨⟨(-58563202339129627991311563005),(-58563202339129627986872323654)⟩,⟨7282665267607715310447433308,7282665267607715314539626016⟩⟩,⟨⟨(-59070567490809294434444845034),(-59070567490809294429959966073)⟩,⟨7345758992345223271288540064,7345758992345223275417078562⟩⟩,⟨⟨(-59570979905906762500149434000),(-59570979905906762495623391039)⟩,⟨7407988104985039133272102376,7407988104985039137436009803⟩⟩] +lemma amp3_12_4_eq : ∀ k : Fin 16, amp3_1Expr 2 4 k = amp3_12_4 k := by decide +kernel +noncomputable def amp3_12_5 : Fin 16 → CBox := ![⟨⟨(-60060528526626865105860807969),(-60060528526626865101292530442)⟩,⟨7468866243381194000968399794,7468866243381194005167152564⟩⟩,⟨⟨(-60542875258375211991708961882),(-60542875258375211987099261592)⟩,⟨7528848786171561305706213363,7528848786171561309939275169⟩⟩,⟨⟨(-61014310271825440941319199518),(-61014310271825440936667140355)⟩,⟨7587474395107808977592683137,7587474395107808981859510776⟩⟩,⟨⟨(-61478302879938500950224467511),(-61478302879938500945531264473)⟩,⟨7645174498868595234196733500,7645174498868595238496725987⟩⟩,⟨⟨(-61931338283814348960156928138),(-61931338283814348955422705311)⟩,⟨7701512012341604309880651581,7701512012341604314213131120⟩⟩,⟨⟨(-62376699227217381562506369379),(-62376699227217381557840541837)⟩,⟨7756895163271230794589826160,7756895163271230798940722448⟩⟩,⟨⟨(-62811060253041564516902958259),(-62811060253041564512191497229)⟩,⟨7810910412267589699251608218,7810910412267589703634436432⟩⟩,⟨⟨(-63237523068765669829206491239),(-63237523068765669824452935987)⟩,⟨7863943474189563307083108905,7863943474189563311496951469⟩⟩,⟨⟨(-63652946336376028680582188668),(-63652946336376028675789175091)⟩,⟨7915603705897224210176158589,7915603705897224214620020374⟩⟩,⟨⟨(-64060255810442041626545632826),(-64060255810442041621714200317)⟩,⟨7966254941510515697539328678,7966254941510515702012589951⟩⟩,⟨⟨(-64456489476868880865632382335),(-64456489476868880860765996367)⟩,⟨8015528837832533152447071607,8015528837832533156948631883⟩⟩,⟨⟨(-64844401807227121646474621006),(-64844401807227121641574546837)⟩,⟨8063767928974056203571186983,8063767928974056208100385894⟩⟩,⟨⟨(-65221205709714364225045934923),(-65221205709714364220109278301)⟩,⟨8110625624314076258295876483,8110625624314076262852402442⟩⟩,⟨⟨(-65589488661285843482283301563),(-65589488661285843477316315090)⟩,⟨8156423691238937792400060728,8156423691238937796982621096⟩⟩,⟨⟨(-65946634454237240528126502958),(-65946634454237240523126605730)⟩,⟨8200836789531233322099357003,8200836789531233326707599489⟩⟩,⟨⟨(-66295067506085358055620929869),(-66295067506085358050587844888)⟩,⟨8244166409214366187219956134,8244166409214366191853388499⟩⟩] +lemma amp3_12_5_eq : ∀ k : Fin 16, amp3_1Expr 2 5 k = amp3_12_5 k := by decide +kernel +noncomputable def amp3_12_6 : Fin 16 → CBox := ![⟨⟨(-66632338791740151047464984547),(-66632338791740151042411082771)⟩,⟨8286108000174094192842713769,8286108000174094197499122883⟩⟩,⟨⟨(-66960713276388809133199511200),(-66960713276388809128111654796)⟩,⟨8326943223635252122691362598,8326943223635252127371844415⟩⟩,⟨⟨(-67277905729051392375376911809),(-67277905729051392370263101773)⟩,⟨8366387898207114527761616066,8366387898207114532464499662⟩⟩,⟨⟨(-67586024963955147028783623371),(-67586024963955147023637610990)⟩,⟨8404704266859928645259457382,8404704266859928649984971343⟩⟩,⟨⟨(-67882946447620971193564159901),(-67882946447620971188390724463)⟩,⟨8441628131845618338503464558,8441628131845618343250337648⟩⟩,⟨⟨(-68170625858784866943181248988),(-68170625858784866937979066790)⟩,⟨8477402692870422433588041341,8477402692870422438355879487⟩⟩,⟨⟨(-68447096538020503804696841840),(-68447096538020503799503845584)⟩,⟨8511783384717186121625256742,8511783384717186126408665229⟩⟩,⟨⟨(-68714163775761176703955418742),(-68714163775761176698731965146)⟩,⟨8544994705456564205467269717,8544994705456564210270609972⟩⟩,⟨⟨(-68970016219710489349277739371),(-68970016219710489344028321605)⟩,⟨8576811403190957623562671225,8576811403190957628384706563⟩⟩,⟨⟨(-69216311266545650369904129852),(-69216311266545650364631583149)⟩,⟨8607439584566411085861005853,8607439584566411090700805952⟩⟩,⟨⟨(-69451390545946672989996924531),(-69451390545946672984699854684)⟩,⟨8636673021858896434645988157,8636673021858896439503048400⟩⟩,⟨⟨(-69676765816596932310668687538),(-69676765816596932305352142717)⟩,⟨8664699710806636202445519625,8664699710806636207318625637⟩⟩,⟨⟨(-69890929593705596301498042406),(-69890929593705596296160677472)⟩,⟨8691332187154105825790919359,8691332187154105830679560680⟩⟩,⟨⟨(-70095250027190538217641508148),(-70095250027190538212281585717)⟩,⟨8716740588077719895983762959,8716740588077719900887560611⟩⟩,⟨⟨(-70288368638517981043979657693),(-70288368638517981038615961070)⟩,⟨8740755979092348350748915286,8740755979092348355664856309⟩⟩,⟨⟨(-70471511782327267744094408126),(-70471511782327267738711622634)⟩,⟨8763530864329954362408849158,8763530864329954367338235000⟩⟩] +lemma amp3_12_6_eq : ∀ k : Fin 16, amp3_1Expr 2 6 k = amp3_12_6 k := by decide +kernel +noncomputable def amp3_12_7 : Fin 16 → CBox := ![⟨⟨(-70643468314107287782942877087),(-70643468314107287777543849079)⟩,⟨8784914631124003044389008689,8784914631124003049330809160⟩⟩,⟨⟨(-70805324400427207197742614188),(-70805324400427207192325941175)⟩,⟨8805042350427450411123087376,8805042350427450416076866312⟩⟩,⟨⟨(-70956014756739613937792967015),(-70956014756739613932369217715)⟩,⟨8823781548084791252446128898,8823781548084791257409897048⟩⟩,⟨⟨(-71096486770715766123531324748),(-71096486770715766118093435394)⟩,⟨8841250037108512101909847986,8841250037108512106883866072⟩⟩,⟨⟨(-71225819734200030793536471349),(-71225819734200030788091202841)⟩,⟨8857333322234713239846730188,8857333322234713244829484096⟩⟩,⟨⟨(-71344823474217662619786021435),(-71344823474217662614327592151)⟩,⟨8872132110031922795823713995,8872132110031922800815298302⟩⟩,⟨⟨(-71452720759319491786603527487),(-71452720759319491781137463066)⟩,⟨8885549747375761001639838479,8885549747375761006638894654⟩⟩,⟨⟨(-71550184889284250863059965671),(-71550184889284250857586952966)⟩,⟨8897669962899864877009744966,8897669962899864882015556910⟩⟩,⟨⟨(-71636581187985562588740129167),(-71636581187985562583260633659)⟩,⟨8908413831040106601836371376,8908413831040106606848212154⟩⟩,⟨⟨(-71712447281589071100225189413),(-71712447281589071094739064154)⟩,⟨8917848208649375137453508745,8917848208649375142470760079⟩⟩,⟨⟨(-71777290301579416085276256432),(-71777290301579416079786654353)⟩,⟨8925911804741608513814691981,8925911804741608518836295440⟩⟩,⟨⟨(-71831512878535996579616170669),(-71831512878535996574123252615)⟩,⟨8932654688705418475796923469,8932654688705418480822217046⟩⟩,⟨⟨(-71874763373790792280268634447),(-71874763373790792274775364865)⟩,⟨8938033132284629588302428101,8938033132284629593330379887⟩⟩,⟨⟨(-71907309928033851787337050407),(-71907309928033851781844885591)⟩,⟨8942080480289843926888685838,8942080480289843931918467680⟩⟩,⟨⟨(-71928941721771935364368090358),(-71928941721771935358879664865)⟩,⟨8944770516125318300057448036,8944770516125318305088072516⟩⟩,⟨⟨(-71939792741600879315437967254),(-71939792741600879309956576197)⟩,⟨8946119901781668785624009537,8946119901781668790654415189⟩⟩] +lemma amp3_12_7_eq : ∀ k : Fin 16, amp3_1Expr 2 7 k = amp3_12_7 k := by decide +kernel +noncomputable def amp3_12_8 : Fin 16 → CBox := ![⟨⟨(-71939792741600879315437967254),(-71939792741600879309956576197)⟩,⟨8946119901781668785624009537,8946119901781668790654415189⟩⟩,⟨⟨(-71928941721771935364368090358),(-71928941721771935358879664865)⟩,⟨8944770516125318300057448036,8944770516125318305088072516⟩⟩,⟨⟨(-71907309928033851787337050407),(-71907309928033851781844885591)⟩,⟨8942080480289843926888685838,8942080480289843931918467680⟩⟩,⟨⟨(-71874763373790792280268634447),(-71874763373790792274775364865)⟩,⟨8938033132284629588302428101,8938033132284629593330379887⟩⟩,⟨⟨(-71831512878535996579616170669),(-71831512878535996574123252615)⟩,⟨8932654688705418475796923469,8932654688705418480822217046⟩⟩,⟨⟨(-71777290301579416085276256432),(-71777290301579416079786654353)⟩,⟨8925911804741608513814691981,8925911804741608518836295440⟩⟩,⟨⟨(-71712447281589071100225189413),(-71712447281589071094739064154)⟩,⟨8917848208649375137453508745,8917848208649375142470760079⟩⟩,⟨⟨(-71636581187985562588740129167),(-71636581187985562583260633659)⟩,⟨8908413831040106601836371376,8908413831040106606848212154⟩⟩,⟨⟨(-71550184889284250863059965671),(-71550184889284250857586952966)⟩,⟨8897669962899864877009744966,8897669962899864882015556910⟩⟩,⟨⟨(-71452720759319491786603527487),(-71452720759319491781137463066)⟩,⟨8885549747375761001639838479,8885549747375761006638894654⟩⟩,⟨⟨(-71344823474217662619786021435),(-71344823474217662614327592151)⟩,⟨8872132110031922795823713995,8872132110031922800815298302⟩⟩,⟨⟨(-71225819734200030793536471349),(-71225819734200030788091202841)⟩,⟨8857333322234713239846730188,8857333322234713244829484096⟩⟩,⟨⟨(-71096486770715766123531324748),(-71096486770715766118093435394)⟩,⟨8841250037108512101909847986,8841250037108512106883866072⟩⟩,⟨⟨(-70956014756739613937792967015),(-70956014756739613932369217715)⟩,⟨8823781548084791252446128898,8823781548084791257409897048⟩⟩,⟨⟨(-70805324400427207197742614188),(-70805324400427207192325941175)⟩,⟨8805042350427450411123087376,8805042350427450416076866312⟩⟩,⟨⟨(-70643468314107287782942877087),(-70643468314107287777543849079)⟩,⟨8784914631124003044389008689,8784914631124003049330809160⟩⟩] +lemma amp3_12_8_eq : ∀ k : Fin 16, amp3_1Expr 2 8 k = amp3_12_8 k := by decide +kernel +noncomputable def amp3_12_9 : Fin 16 → CBox := ![⟨⟨(-70471511782327267744094408126),(-70471511782327267738711622634)⟩,⟨8763530864329954362408849158,8763530864329954367338235000⟩⟩,⟨⟨(-70288368638517981043979657693),(-70288368638517981038615961070)⟩,⟨8740755979092348350748915286,8740755979092348355664856309⟩⟩,⟨⟨(-70095250027190538217641508148),(-70095250027190538212281585717)⟩,⟨8716740588077719895983762959,8716740588077719900887560611⟩⟩,⟨⟨(-69890929593705596301498042406),(-69890929593705596296160677472)⟩,⟨8691332187154105825790919359,8691332187154105830679560680⟩⟩,⟨⟨(-69676765816596932310668687538),(-69676765816596932305352142717)⟩,⟨8664699710806636202445519625,8664699710806636207318625637⟩⟩,⟨⟨(-69451390545946672989996924531),(-69451390545946672984699854684)⟩,⟨8636673021858896434645988157,8636673021858896439503048400⟩⟩,⟨⟨(-69216311266545650369904129852),(-69216311266545650364631583149)⟩,⟨8607439584566411085861005853,8607439584566411090700805952⟩⟩,⟨⟨(-68970016219710489349277739371),(-68970016219710489344028321605)⟩,⟨8576811403190957623562671225,8576811403190957628384706563⟩⟩,⟨⟨(-68714163775761176703955418742),(-68714163775761176698731965146)⟩,⟨8544994705456564205467269717,8544994705456564210270609972⟩⟩,⟨⟨(-68447096538020503804696841840),(-68447096538020503799503845584)⟩,⟨8511783384717186121625256742,8511783384717186126408665229⟩⟩,⟨⟨(-68170625858784866943181248988),(-68170625858784866937979066790)⟩,⟨8477402692870422433588041341,8477402692870422438355879487⟩⟩,⟨⟨(-67882946447620971193564159901),(-67882946447620971188390724463)⟩,⟨8441628131845618338503464558,8441628131845618343250337648⟩⟩,⟨⟨(-67586024963955147028783623371),(-67586024963955147023637610990)⟩,⟨8404704266859928645259457382,8404704266859928649984971343⟩⟩,⟨⟨(-67277905729051392375376911809),(-67277905729051392370263101773)⟩,⟨8366387898207114527761616066,8366387898207114532464499662⟩⟩,⟨⟨(-66960713276388809133199511200),(-66960713276388809128111654796)⟩,⟨8326943223635252122691362598,8326943223635252127371844415⟩⟩,⟨⟨(-66632338791740151047464984547),(-66632338791740151042411082771)⟩,⟨8286108000174094192842713769,8286108000174094197499122883⟩⟩] +lemma amp3_12_9_eq : ∀ k : Fin 16, amp3_1Expr 2 9 k = amp3_12_9 k := by decide +kernel +noncomputable def amp3_12_10 : Fin 16 → CBox := ![⟨⟨(-66295067506085358055620929869),(-66295067506085358050587844888)⟩,⟨8244166409214366187219956134,8244166409214366191853388499⟩⟩,⟨⟨(-65946634454237240528126502958),(-65946634454237240523126605730)⟩,⟨8200836789531233322099357003,8200836789531233326707599489⟩⟩,⟨⟨(-65589488661285843482283301563),(-65589488661285843477316315090)⟩,⟨8156423691238937792400060728,8156423691238937796982621096⟩⟩,⟨⟨(-65221205709714364225045934923),(-65221205709714364220109278301)⟩,⟨8110625624314076258295876483,8110625624314076262852402442⟩⟩,⟨⟨(-64844401807227121646474621006),(-64844401807227121641574546837)⟩,⟨8063767928974056203571186983,8063767928974056208100385894⟩⟩,⟨⟨(-64456489476868880865632382335),(-64456489476868880860765996367)⟩,⟨8015528837832533152447071607,8015528837832533156948631883⟩⟩,⟨⟨(-64060255810442041626545632826),(-64060255810442041621714200317)⟩,⟨7966254941510515697539328678,7966254941510515702012589951⟩⟩,⟨⟨(-63652946336376028680582188668),(-63652946336376028675789175091)⟩,⟨7915603705897224210176158589,7915603705897224214620020374⟩⟩,⟨⟨(-63237523068765669829206491239),(-63237523068765669824452935987)⟩,⟨7863943474189563307083108905,7863943474189563311496951469⟩⟩,⟨⟨(-62811060253041564516902958259),(-62811060253041564512191497229)⟩,⟨7810910412267589699251608218,7810910412267589703634436432⟩⟩,⟨⟨(-62376699227217381562506369379),(-62376699227217381557840541837)⟩,⟨7756895163271230794589826160,7756895163271230798940722448⟩⟩,⟨⟨(-61931338283814348960156928138),(-61931338283814348955422705311)⟩,⟨7701512012341604309880651581,7701512012341604314213131120⟩⟩,⟨⟨(-61478302879938500950224467511),(-61478302879938500945531264473)⟩,⟨7645174498868595234196733500,7645174498868595238496725987⟩⟩,⟨⟨(-61014310271825440941319199518),(-61014310271825440936667140355)⟩,⟨7587474395107808977592683137,7587474395107808981859510776⟩⟩,⟨⟨(-60542875258375211991708961882),(-60542875258375211987099261592)⟩,⟨7528848786171561305706213363,7528848786171561309939275169⟩⟩,⟨⟨(-60060528526626865105860807969),(-60060528526626865101292530442)⟩,⟨7468866243381194000968399794,7468866243381194005167152564⟩⟩] +lemma amp3_12_10_eq : ∀ k : Fin 16, amp3_1Expr 2 10 k = amp3_12_10 k := by decide +kernel +noncomputable def amp3_12_11 : Fin 16 → CBox := ![⟨⟨(-59570979905906762500149434000),(-59570979905906762495623391039)⟩,⟨7407988104985039133272102376,7407988104985039137436009803⟩⟩,⟨⟨(-59070567490809294434444845034),(-59070567490809294429959966073)⟩,⟨7345758992345223271288540064,7345758992345223275417078562⟩⟩,⟨⟨(-58563202339129627991311563005),(-58563202339129627986872323654)⟩,⟨7282665267607715310447433308,7282665267607715314539626016⟩⟩,⟨⟨(-58045023393183337449922343284),(-58045023393183337445522950347)⟩,⟨7218226786422966776722177984,7218226786422966780778091625⟩⟩,⟨⟨(-57520149696019410860905777485),(-57520149696019410856553050852)⟩,⟨7152955775078996128374793379,7152955775078996132393175163⟩⟩,⟨⟨(-56984513888713790575112258176),(-56984513888713790570805172393)⟩,⟨7086346434500889437775362270,7086346434500889441755689148⟩⟩,⟨⟨(-56442450371203974293073780864),(-56442450371203974288815938873)⟩,⟨7018937771823159982848549705,7018937771823159986789985074⟩⟩,⟨⟨(-55889677685399926705695100104),(-55889677685399926701470003695)⟩,⟨6950197363529305752262265146,6950197363529305756166213284⟩⟩,⟨⟨(-55330753638593851796047675607),(-55330753638593851791872134402)⟩,⟨6880691998721315536513401417,6880691998721315540377400101⟩⟩,⟨⟨(-54761174158297399579852954915),(-54761174158297399575726656169)⟩,⟨6809861570523821676396706760,6809861570523821680220150761⟩⟩,⟨⟨(-54185729261629598885745249781),(-54185729261629598881665006469)⟩,⟨6738301744643456635968562502,6738301744643456639751493580⟩⟩,⟨⟨(-53599682950878333020533739921),(-53599682950878333016505698566)⟩,⟨6665423572992208217760455048,6665423572992208221501467992⟩⟩,⟨⟨(-53008067091420818539426463865),(-53008067091420818535449256705)⟩,⟨6591852796474778414008026423,6591852796474778417706954642⟩⟩,⟨⟨(-52405903563925214430228505276),(-52405903563925214426303531534)⟩,⟨6516970357811033115908984046,6516970357811033119565015932⟩⟩,⟨⟨(-51798476653068572744257876778),(-51798476653068572740387756437)⟩,⟨6441433387672530653668912470,6441433387672530657281404042⟩⟩,⟨⟨(-51180554932150761405915304564),(-51180554932150761402102895098)⟩,⟨6364591328575947895603935800,6364591328575947899171897303⟩⟩] +lemma amp3_12_11_eq : ∀ k : Fin 16, amp3_1Expr 2 11 k = amp3_12_11 k := by decide +kernel +noncomputable def amp3_12_12 : Fin 16 → CBox := ![⟨⟨(-50557686720482431275719877824),(-50557686720482431271902259663)⟩,⟨6287134145392114252189440022,6287134145392114255720396844⟩⟩,⟨⟨(-49924374988729221668959084586),(-49924374988729221665191392347)⟩,⟨6208378251448693316301568765,6208378251448693319788033294⟩⟩,⟨⟨(-49286444880026379423742835208),(-49286444880026379420025960705)⟩,⟨6129048036223983144890070041,6129048036223983148331652194⟩⟩,⟨⟨(-48638120217913569083231060336),(-48638120217913569079564930268)⟩,⟨6048425199522518650040102748,6048425199522518653436183289⟩⟩,⟨⟨(-47985517083355406602241003726),(-47985517083355406598626372243)⟩,⟨5967270310586346291951644821,5967270310586346295301871333⟩⟩,⟨⟨(-47322565195896356615144341458),(-47322565195896356611580315490)⟩,⟨5884828495725633241574041036,5884828495725633244877898994⟩⟩,⟨⟨(-46655687189838484692427612822),(-46655687189838484688918162697)⟩,⟨5801898445822878360699628206,5801898445822878363956386544⟩⟩,⟨⟨(-45978502120047616449587453732),(-45978502120047616446124787016)⟩,⟨5717686654279278178076523105,5717686654279278181286527795⟩⟩,⟨⟨(-45297756499006132967371745755),(-45297756499006132963964961543)⟩,⟨5633032088059931358400416676,5633032088059931361562320957⟩⟩,⟨⟨(-44606740326628404396306392219),(-44606740326628404392954069573)⟩,⟨5547100320722679179347118039,5547100320722679182460477758⟩⟩,⟨⟨(-43912543273515121380738214368),(-43912543273515121377442226401)⟩,⟨5460772992884498814206040534,5460772992884498817270430474⟩⟩,⟨⟨(-43208105797029466862338712263),(-43208105797029466859100124370)⟩,⟨5373172210511033611833180004,5373172210511033614847848644⟩⟩,⟨⟨(-42500882253193745498225156875),(-42500882253193745495047410594)⟩,⟨5285224964912998623492844375,5285224964912998626457195322⟩⟩,⟨⟨(-41783440652515466066594055692),(-41783440652515466063439523909)⟩,⟨5196007046184098692189898888,5196007046184098695107993603⟩⟩,⟨⟨(-41063624160825241730117552065),(-41063624160825241727022185732)⟩,⟨5106493796332646934498121890,5106493796332646937365346108⟩⟩,⟨⟨(-40333602637358103893096964793),(-40333602637358103890060813004)⟩,⟨5015711493090873599226372006,5015711493090873602042102728⟩⟩] +lemma amp3_12_12_eq : ∀ k : Fin 16, amp3_1Expr 2 12 k = amp3_12_12 k := by decide +kernel +noncomputable def amp3_12_13 : Fin 16 → CBox := ![⟨⟨(-39601635200454137557129087322),(-39601635200454137554151462762)⟩,⟨4924687204513016733680641167,4924687204513016736444846232⟩⟩,⟨⟨(-38859464590104374376336831644),(-38859464590104374373413784460)⟩,⟨4832394093638817759307806469,4832394093638817762020360283⟩⟩,⟨⟨(-38115796549175229433255155783),(-38115796549175229430394214773)⟩,⟨4739914768807124340080983952,4739914768807124342740859746⟩⟩,⟨⟨(-37361913902531192334769237456),(-37361913902531192331968328997)⟩,⟨4646165200011800397129162953,4646165200011800399736001119⟩⟩,⟨⟨(-36607003843609385795500262146),(-36607003843609385792762834613)⟩,⟨4552287866691792566485459177,4552287866691792569038768785⟩⟩,⟨⟨(-35841851965557722420302379321),(-35841851965557722417604728515)⟩,⟨4457136905266166405298376297,4457136905266166407800485979⟩⟩,⟨⟨(-35076166662618009664986189659),(-35076166662618009662349313710)⟩,⟨4361919609440269937958966035,4361919609440269940407232309⟩⟩,⟨⟨(-34300193600980150025467495726),(-34300193600980150022892252826)⟩,⟨4265422972663742713465005526,4265422972663742715858699776⟩⟩,⟨⟨(-33524208008310895724390467550),(-33524208008310895721876310811)⟩,⟨4168924777582623866123181087,4168924777582623868462370563⟩⟩,⟨⟨(-32737866477294929152542860551),(-32737866477294929150088015712)⟩,⟨4071138763026156820083225728,4071138763026156822367505053⟩⟩,⟨⟨(-31952063788142973132461184901),(-31952063788142973130068105995)⟩,⟨3973419756501542920259921995,3973419756501542922489018570⟩⟩,⟨⟨(-31155810506980960748189575453),(-31155810506980960745843356355)⟩,⟨3874401159783468515250597318,3874401159783468517425733064⟩⟩,⟨⟨(-30360682302007587724563649384),(-30360682302007587722282552651)⟩,⟨3775522472649487016443983958,3775522472649487018562955835⟩⟩,⟨⟨(-29554977221247464423708565981),(-29554977221247464421491401256)⟩,⟨3675328491220533190011002730,3675328491220533192073319392⟩⟩,⟨⟨(-28751023739938367697471673259),(-28751023739938367695317169698)⟩,⟨3575352331085074933066008417,3575352331085074935071933786⟩⟩,⟨⟨(-27936329116135969238117835762),(-27936329116135969236028595790)⟩,⟨3474040449161087916450224865,3474040449161087918398786010⟩⟩] +lemma amp3_12_13_eq : ∀ k : Fin 16, amp3_1Expr 2 13 k = amp3_12_13 k := by decide +kernel +noncomputable def amp3_12_14 : Fin 16 → CBox := ![⟨⟨(-27124059698702532522428967612),(-27124059698702532520392658990)⟩,⟨3373030155358729584770402210,3373030155358729586663279321⟩⟩,⟨⟨(-26300838960499855274413878750),(-26300838960499855272442029913)⟩,⟨3270658002911095463419536560,3270658002911095465254634001⟩⟩,⟨⟨(-25480772729857277564149508456),(-25480772729857277562240289081)⟩,⟨3168678131310934620652341769,3168678131310934622430077843⟩⟩,⟨⟨(-24649489050903922245788062755),(-24649489050903922243946352887)⟩,⟨3065303306601293613289299871,3065303306601293615008389620⟩⟩,⟨⟨(-23822155938916705062494969763),(-23822155938916705060708896559)⟩,⟨2962419757226376389639898632,2962419757226376391302057324⟩⟩,⟨⟨(-22983270389303945549650835820),(-22983270389303945547930200389)⟩,⟨2858099596926999394473353103,2858099596926999396076663569⟩⟩,⟨⟨(-22149212667309377172721441712),(-22149212667309377171059304100)⟩,⟨2754379804283567772781889784,2754379804283567774327506889⟩⟩,⟨⟨(-21303181743484879756516695950),(-21303181743484879754921243690)⟩,⟨2649171076308288359225720562,2649171076308288360711902359⟩⟩,⟨⟨(-20462956309978198965847334188),(-20462956309978198964317245856)⟩,⟨2544684293872362529737838650,2544684293872362531165100408⟩⟩,⟨⟨(-19610228521757425347383461096),(-19610228521757425345914482565)⟩,⟨2438642772952151337215884399,2438642772952151338583999375⟩⟩,⟨⟨(-18764410360201072199349283763),(-18764410360201072197947013978)⟩,⟨2333460503167656965516559046,2333460503167656966825248666⟩⟩,⟨⟨(-17905421340180017041567296852),(-17905421340180017040227484690)⟩,⟨2226640362678449215585505192,2226640362678449216834501930⟩⟩,⟨⟨(-17054608847284225418521092515),(-17054608847284225417243116867)⟩,⟨2120837019559029801162529797,2120837019559029802352405161⟩⟩,⟨⟨(-16189774056173590092697388257),(-16189774056173590091487164107)⟩,⟨2013289924388793187245815467,2013289924388793188374986247⟩⟩,⟨⟨(-15334597482021724183614628773),(-15334597482021724182467612598)⟩,⟨1906943883095107532655037369,1906943883095107533724652418⟩⟩,⟨⟨(-14464300825782799817879049141),(-14464300825782799816796686981)⟩,⟨1798717574120342149557733837,1798717574120342150566699322⟩⟩] +lemma amp3_12_14_eq : ∀ k : Fin 16, amp3_1Expr 2 14 k = amp3_12_14 k := by decide +kernel +noncomputable def amp3_12_15 : Fin 16 → CBox := ![⟨⟨(-13605436144528543518622761932),(-13605436144528543517605029070)⟩,⟨1691912895859670665839328149,1691912895859670666788338208⟩⟩,⟨⟨(-12730011261233991576484709836),(-12730011261233991575533224099)⟩,⟨1583048862860762032880563198,1583048862860762033768415579⟩⟩,⟨⟨(-11868204086295200168879406802),(-11868204086295200167993445834)⟩,⟨1475878268876554359595976523,1475878268876554360423584246⟩⟩,⟨⟨(-10987901608861133640388010369),(-10987901608861133639567071951)⟩,⟨1366407679473444525835192334,1366407679473444526601499812⟩⟩,⟨⟨(-10124011078824646542621083983),(-10124011078824646541864634935)⟩,⟨1258978008505669232729956015,1258978008505669233436021653⟩⟩,⟨⟨(-9238936788997680558391737101),(-9238936788997680557701763132)⟩,⟨1148914017256532114124412335,1148914017256532114768708641⟩⟩,⟨⟨(-8374023000594305592180654475),(-8374023000594305591556265132)⟩,⟨1041357098326373040876403974,1041357098326373041460260384⟩⟩,⟨⟨(-7484008818589727933465363364),(-7484008818589727932906806965)⟩,⟨930678803559827651774042637,930678803559827652295910952⟩⟩,⟨⟨(-6619527590048496234348673604),(-6619527590048496233855198024)⟩,⟨823175675893779269422113988,823175675893779269883631206⟩⟩,⟨⟨(-5723823631345515039226457064),(-5723823631345515038800150713)⟩,⟨711789825230581337903579670,711789825230581338302598670⟩⟩,⟨⟨(-4862135239681351864882120702),(-4862135239681351864520679744)⟩,⟨604634002618053415554305942,604634002618053415893169462⟩⟩,⟨⟨(-3958514790998972548232486511),(-3958514790998972547938656834)⟩,⟨492263691674140854248137577,492263691674140854523969355⟩⟩,⟨⟨(-3104583262309451839099637679),(-3104583262309451838870064215)⟩,⟨386072478821917588709818760,386072478821917588926039715⟩⟩,⟨⟨(-2185759460592364486953109937),(-2185759460592364486792031491)⟩,⟨271811544983855893836027781,271811544983855893988188054⟩⟩,⟨⟨(-1355876442797423833610149372),(-1355876442797423833512079310)⟩,⟨168610900407176264254508195,168610900407176264348666555⟩⟩,⟨⟨(-385210003677661992985603661),(-385210003677661992958854988)⟩,⟨47903041542588614247597182,47903041542588614274209493⟩⟩] +lemma amp3_12_15_eq : ∀ k : Fin 16, amp3_1Expr 2 15 k = amp3_12_15 k := by decide +kernel +noncomputable def amp3_12 : Fin 16 → Fin 16 → CBox := ![amp3_12_0,amp3_12_1,amp3_12_2,amp3_12_3,amp3_12_4,amp3_12_5,amp3_12_6,amp3_12_7,amp3_12_8,amp3_12_9,amp3_12_10,amp3_12_11,amp3_12_12,amp3_12_13,amp3_12_14,amp3_12_15] +lemma amp3_12_eq (i k : Fin 16) : amp3_1Expr 2 i k = amp3_12 i k := by + fin_cases i + · exact amp3_12_0_eq k + · exact amp3_12_1_eq k + · exact amp3_12_2_eq k + · exact amp3_12_3_eq k + · exact amp3_12_4_eq k + · exact amp3_12_5_eq k + · exact amp3_12_6_eq k + · exact amp3_12_7_eq k + · exact amp3_12_8_eq k + · exact amp3_12_9_eq k + · exact amp3_12_10_eq k + · exact amp3_12_11_eq k + · exact amp3_12_12_eq k + · exact amp3_12_13_eq k + · exact amp3_12_14_eq k + · exact amp3_12_15_eq k +noncomputable def amp3_13_0 : Fin 16 → CBox := ![⟨⟨27656833929615362270524295,27656833929615362279267860⟩,⟨47903041542588614256916260,47903041542588614267809321⟩⟩,⟨⟨97347548738388396604396587,97347548738388396635453890⟩,⟨168610900407176264287309834,168610900407176264326138992⟩⟩,⟨⟨156930468665277273003358805,156930468665277273053639347⟩,⟨271811544983855893888906119,271811544983855893951872183⟩⟩,⟨⟨222899049574540211918281786,222899049574540211989754870⟩,⟨386072478821917588784925470,386072478821917588874457807⟩⟩,⟨⟨284208574900344161453926006,284208574900344161545137883⟩,⟨492263691674140854343902772,492263691674140854458199578⟩⟩,⟨⟨349085604172734028765625084,349085604172734028877696760⟩,⟨604634002618053415671931707,604634002618053415812386247⟩⟩,⟨⟨410952047203312812296348240,410952047203312812428339841⟩,⟨711789825230581338042051577,711789825230581338207498709⟩⟩,⟨⟨475260698067625593554489851,475260698067625593707169292⟩,⟨823175675893779269582254947,823175675893779269773649337⟩⟩,⟨⟨537327657764345332051066722,537327657764345332223731024⟩,⟨930678803559827651955097302,930678803559827652171565934⟩⟩,⟨⟨601227801041259060917809414,601227801041259061110964833⟩,⟨1041357098326373041078990043,1041357098326373041321127993⟩⟩,⟨⟨663325817138793157058598602,663325817138793157271782716⟩,⟨1148914017256532114347922574,1148914017256532114615205914⟩⟩,⟨⟨726871292114567086997004643,726871292114567087230638479⟩,⟨1258978008505669232974878152,1258978008505669233267813629⟩⟩,⟨⟨788895841566765076298968955,788895841566765076552534725⟩,⟨1366407679473444526101013887,1366407679473444526418938453⟩⟩,⟨⟨852098715826997532472155937,852098715826997532745982620⟩,⟨1475878268876554359883094532,1475878268876554360226396872⟩⟩,⟨⟨913973687112991920219883728,913973687112991920513679781⟩,⟨1583048862860762033188530222,1583048862860762033556909485⟩⟩,⟨⟨976826365869980121657992870,976826365869980121972051362⟩,⟨1691912895859670666168473630,1691912895859670666562287138⟩⟩] +lemma amp3_13_0_eq : ∀ k : Fin 16, amp3_1Expr 3 0 k = amp3_13_0 k := by decide +kernel +noncomputable def amp3_13_1 : Fin 16 → CBox := ![⟨⟨1038490075614490173679602795,1038490075614490174013514247⟩,⟨1798717574120342149907657147,1798717574120342150326378421⟩⟩,⟨⟨1100974564234470578409992232,1100974564234470578763960908⟩,⟨1906943883095107533026015073,1906943883095107533469871746⟩⟩,⟨⟨1162373479802631048480047883,1162373479802631048853702145⟩,⟨2013289924388793187637481776,2013289924388793188105997021⟩⟩,⟨⟨1224465824149729458468786532,1224465824149729458862623663⟩,⟨2120837019559029801575118365,2120837019559029802069046911⟩⟩,⟨⟨1285551412780888596344109968,1285551412780888596757456919⟩,⟨2226640362678449216018676790,2226640362678449216537007634⟩⟩,⟨⟨1347224049647206333176756261,1347224049647206333609802454⟩,⟨2333460503167656965970511481,2333460503167656966513482473⟩⟩,⟨⟨1407951061421259999034746937,1407951061421259999487564298⟩,⟨2438642772952151337690299039,2438642772952151338258180115⟩⟩,⟨⟨1469174162069821263056085824,1469174162069821263528394755⟩,⟨2544684293872362530232882654,2544684293872362530825113279⟩⟩,⟨⟨1529499634035960901983132064,1529499634035960902475016547⟩,⟨2649171076308288359741091471,2649171076308288360357955086⟩⟩,⟨⟨1590241921453586582233004888,1590241921453586582744662628⟩,⟨2754379804283567773317728045,2754379804283567773959503014⟩⟩,⟨⟨1650124571656563995082018330,1650124571656563995612649412⟩,⟨2858099596926999395029369059,2858099596926999395694802025⟩⟩,⟨⟨1710353844287314213931965147,1710353844287314214482153350⟩,⟨2962419757226376390216209077,2962419757226376390906257896⟩⟩,⟨⟨1769753689214106826571852029,1769753689214106827140689040⟩,⟨3065303306601293613885625328,3065303306601293614598844251⟩⟩,⟨⟨1829437172087648439240474646,1829437172087648439828882873⟩,⟨3168678131310934621268777810,3168678131310934622006720894⟩⟩,⟨⟨1888315278407924773379578858,1888315278407924773987009237⟩,⟨3270658002911095464055811810,3270658002911095464817651848⟩⟩,⟨⟨1947419868181087739434910540,1947419868181087740061550358⟩,⟨3373030155358729585426592984,3373030155358729586212619552⟩⟩] +lemma amp3_13_1_eq : ∀ k : Fin 16, amp3_1Expr 3 1 k = amp3_13_1 k := by decide +kernel +noncomputable def amp3_13_2 : Fin 16 → CBox := ![⟨⟨2005738188498802509257614525,2005738188498802509902442101⟩,⟨3474040449161087917126066225,3474040449161087917934630579⟩⟩,⟨⟨2064230630799723993924364598,2064230630799723994588308304⟩,⟨3575352331085074933761559036,3575352331085074934594242398⟩⟩,⟨⟨2121951893766475950815528988,2121951893766475951498211723⟩,⟨3675328491220533190726002755,3675328491220533191582270510⟩⟩,⟨⟨2179798915915662807230212244,2179798915915662807931756277⟩,⟨3775522472649487017178475764,3775522472649487018058520355⟩⟩,⟨⟨2236886552549583811255920857,2236886552549583811976224306⟩,⟨3874401159783468516004325028,3874401159783468516908086720⟩⟩,⟨⟨2294054966019543063260612643,2294054966019543063998384244⟩,⟨3973419756501542921032912826,3973419756501542921958142667⟩⟩,⟨⟨2350473060741471694771200578,2350473060741471695527325435⟩,⟨4071138763026156820875226857,4071138763026156821823573227⟩⟩,⟨⟨2406929842568628607267741977,2406929842568628608042053443⟩,⟨4168924777582623866934205551,4168924777582623867905373860⟩⟩,⟨⟨2462643101475025594624595006,2462643101475025595417037035⟩,⟨4265422972663742714294802791,4265422972663742715288810257⟩⟩,⟨⟨2518355460693847129100387609,2518355460693847129910999245⟩,⟨4361919609440269938807535798,4361919609440269939824450183⟩⟩,⟨⟨2573329192070436684207401996,2573329192070436685035939398⟩,⟨4457136905266166406165469676,4457136905266166407204982175⟩⟩,⟨⟨2628264625263173645673288439,2628264625263173646518234563⟩,⟨4552287866691792567371063265,4552287866691792568430552166⟩⟩,⟨⟨2682464728926284390885302505,2682464728926284391748177824⟩,⟨4646165200011800398033029979,4646165200011800399115241850⟩⟩,⟨⟨2736591067706676008952762569,2736591067706676009833301304⟩,⟨4739914768807124341003089061,4739914768807124342107574896⟩⟩,⟨⟨2789984030792729046948174234,2789984030792729047846344336⟩,⟨4832394093638817760247902547,4832394093638817761374719567⟩⟩,⟨⟨2843269483200295801677064564,2843269483200295802592298966⟩,⟨4924687204513016734638691987,4924687204513016735786874529⟩⟩] +lemma amp3_13_2_eq : ∀ k : Fin 16, amp3_1Expr 3 2 k = amp3_13_2 k := by decide +kernel +noncomputable def amp3_13_3 : Fin 16 → CBox := ![⟨⟨2895822380713515640760536111,2895822380713515641692937674⟩,⟨5015711493090873600202130731,5015711493090873601371969560⟩⟩,⟨⟨2948235567927807711579482536,2948235567927807712529066141⟩,⟨5106493796332646935491541444,5106493796332646936683083807⟩⟩,⟨⟨2999916066825581612366691605,2999916066825581613333272967⟩,⟨5196007046184098693200732389,5196007046184098694413771724⟩⟩,⟨⟨3051426056220250141831948627,3051426056220250142812904520⟩,⟨5285224964912998624521034370,5285224964912998625751053322⟩⟩,⟨⟨3102202422140761771911098588,3102202422140761772908949527⟩,⟨5373172210511033612878479295,5373172210511033614129956294⟩⟩,⟨⟨3152778757425303730298795638,3152778757425303731313245183⟩,⟨5460772992884498815268381719,5460772992884498816540834063⟩⟩,⟨⟨3202619863391098238129187205,3202619863391098239159977479⟩,⟨5547100320722679180426253381,5547100320722679181719347429⟩⟩,⟨⟨3252232592395201074509690472,3252232592395201075556630650⟩,⟨5633032088059931359496269221,5633032088059931360809709559⟩⟩,⟨⟨3301107928990071960698721820,3301107928990071961761732002⟩,⟨5717686654279278179188844388,5717686654279278180522605972⟩⟩,⟨⟨3349727629506710176722931293,3349727629506710177801295126⟩,⟨5801898445822878361828332087,5801898445822878363181213453⟩⟩,⟨⟨3397607316141974805156504697,3397607316141974806250599088⟩,⟨5884828495725633242718878166,5884828495725633244091645884⟩⟩,⟨⟨3445205120144288774500349883,3445205120144288775609820232⟩,⟨5967270310586346293112520218,5967270310586346294504603435⟩⟩,⟨⟨3492059917117642067137208514,3492059917117642068261935637⟩,⟨6048425199522518651216766053,6048425199522518652628072546⟩⟩,⟨⟨3538607533590063832985105103,3538607533590063834124959071⟩,⟨6129048036223983146082417748,6129048036223983147512769692⟩⟩,⟨⟨3584408854704921198613043662,3584408854704921199767845623⟩,⟨6208378251448693317509349407,6208378251448693318958551736⟩⟩,⟨⟨3629878591273424893332531120,3629878591273424894502135240⟩,⟨6287134145392114253412541870,6287134145392114254880392963⟩⟩] +lemma amp3_13_3_eq : ∀ k : Fin 16, amp3_1Expr 3 3 k = amp3_13_3 k := by decide +kernel +noncomputable def amp3_13_4 : Fin 16 → CBox := ![⟨⟨3674598516835281401392775413,3674598516835281402573038224⟩,⟨6364591328575947896842106203,6364591328575947898321544616⟩⟩,⟨⟨3718963300339778587950628677,3718963300339778589145979984⟩,⟨6441433387672530654922031761,6441433387672530656420784733⟩⟩,⟨⟨3762574590383011707498849358,3762574590383011708708898112⟩,⟨6516970357811033117176798333,6516970357811033118694304370⟩⟩,⟨⟨3805807986503100695589225589,3805807986503100696813690456⟩,⟨6591852796474778415290408372,6591852796474778416826238277⟩⟩,⟨⟨3848284094129928590722347498,3848284094129928591960941190⟩,⟨6665423572992208219057149489,6665423572992208220610922071⟩⟩,⟨⟨3890360326150824618181359716,3890360326150824619434081784⟩,⟨6738301744643456637279434694,6738301744643456638851210639⟩⟩,⟨⟨3931675410886016122786693799,3931675410886016124052915162⟩,⟨6809861570523821677721500232,6809861570523821679310306941⟩⟩,⟨⟨3972569377672655662153565857,3972569377672655663433411441⟩,⟨6880691998721315537851974272,6880691998721315539458092854⟩⟩,⟨⟨4012698318754671954509835592,4012698318754671955803139115⟩,⟨6950197363529305753614359605,6950197363529305755237619647⟩⟩,⟨⟨4052385611987333478066044894,4052385611987333479371490523⟩,⟨7018937771823159984214016953,7018937771823159985852207252⟩⟩,⟨⟨4091304021530033258377006441,4091304021530033259695589006⟩,⟨7086346434500889439153943230,7086346434500889440808905070⟩⟩,⟨⟨4129760942243346618840742107,4129760942243346620172089076⟩,⟨7152955775078996129766332549,7152955775078996131437491624⟩⟩,⟨⟨4167445178213067189623377307,4167445178213067190967371678⟩,⟨7218226786422966778126415005,7218226786422966779813687435⟩⟩,⟨⟨4204648752671252390530196914,4204648752671252391886230460⟩,⟨7282665267607715311864206220,7282665267607715313566612406⟩⟩,⟨⟨4241075931632628761905154106,4241075931632628763273451219⟩,⟨7345758992345223272717587257,7345758992345223274435635201⟩⟩,⟨⟨4277003926566657992995441346,4277003926566657994375557540⟩,⟨7407988104985039134713255648,7407988104985039136446252210⟩⟩] +lemma amp3_13_4_eq : ∀ k : Fin 16, amp3_1Expr 3 4 k = amp3_13_4 k := by decide +kernel +noncomputable def amp3_13_5 : Fin 16 → CBox := ![⟨⟨4312151936157441297965283363,4312151936157441299357103074⟩,⟨7468866243381194002421396326,7468866243381194004169261237⟩⟩,⟨⟨4346782873384138107502686170,4346782873384138108906023549⟩,⟨7528848786171561307170878925,7528848786171561308933369767⟩⟩,⟨⟨4380630384484886430635609195,4380630384484886432050338175⟩,⟨7587474395107808979068753751,7587474395107808980845772594⟩⟩,⟨⟨4413943554923445713829584803,4413943554923445715255486327⟩,⟨7645174498868595235684029118,7645174498868595237475278678⟩⟩,⟨⟨4446470033492561671982128042,4446470033492561673418999119⟩,⟨7701512012341604311378907123,7701512012341604313184156737⟩⟩,⟨⟨4478445510590351195338508400,4478445510590351196778357447⟩,⟨7756895163271230796098855965,7756895163271230797904348500⟩⟩,⟨⟨4509631229138743671855578017,4509631229138743673306397094⟩,⟨7810910412267589700771146173,7810910412267589702590845678⟩⟩,⟨⟨4540249881715345226263096555,4540249881715345227724491654⟩,⟨7863943474189563308612963935,7863943474189563310446275138⟩⟩,⟨⟨4570075930398161688960721936,4570075930398161690432308269⟩,⟨7915603705897224211716063624,7915603705897224213562441885⟩⟩,⟨⟨4599319434914282688445473024,4599319434914282689927032250⟩,⟨7966254941510515699089087427,7966254941510515700948244112⟩⟩,⟨⟨4627767732219821176923171264,4627767732219821178414258390⟩,⟨8015528837832533154006416121,8015528837832533155877702716⟩⟩,⟨⟨4655618584475842402099852416,4655618584475842403600229208⟩,⟨8063767928974056205139915950,8063767928974056207023011657⟩⟩,⟨⟨4682671887494008453465968056,4682671887494008454975645553⟩,⟨8110625624314076259873721167,8110625624314076261768767698⟩⟩,⟨⟨4709113413761441756425795248,4709113413761441757944173602⟩,⟨8156423691238937793986814989,8156423691238937795892867419⟩⟩,⟨⟨4734755328016043888846332186,4734755328016043890373399431⟩,⟨8200836789531233323694751408,8200836789531233325611911920⟩⟩,⟨⟨4759771695603984755547930389,4759771695603984757083552086⟩,⟨8244166409214366188823779902,8244166409214366190751911797⟩⟩] +lemma amp3_13_5_eq : ∀ k : Fin 16, amp3_1Expr 3 5 k = amp3_13_5 k := by decide +kernel +noncomputable def amp3_13_6 : Fin 16 → CBox := ![⟨⟨4783986684434824894014604590,4783986684434824895557694840⟩,⟨8286108000174094194454696872,8286108000174094196392042500⟩⟩,⟨⟨4807562911692542946334921199,4807562911692542947886265669⟩,⟨8326943223635252124311289804,8326943223635252126259308168⟩⟩,⟨⟨4830336305174704892307613181,4830336305174704893866439362⟩,⟨8366387898207114529389216856,8366387898207114531346693338⟩⟩,⟨⟨4852458270930776061353801247,4852458270930776062920397067⟩,⟨8404704266859928646894512256,8404704266859928648862045692⟩⟩,⟨⟨4873776274319785403028005755,4873776274319785404601829732⟩,⟨8441628131845618340145702616,8441628131845618342122478717⟩⟩,⟨⟨4894430726757596741484316684,4894430726757596743065300156⟩,⟨8477402692870422435237238998,8477402692870422437223240831⟩⟩,⟨⟨4914280428450251328530350242,4914280428450251330115571225⟩,⟨8511783384717186123281142835,8511783384717186125271433080⟩⟩,⟨⟨4933454993419274266217237562,4933454993419274267809375757⟩,⟨8544994705456564207129616754,8544994705456564209128940564⟩⟩,⟨⟨4951824372420951262340819216,4951824372420951263939353384⟩,⟨8576811403190957625231207896,8576811403190957627238786228⟩⟩,⟨⟨4969507561182858001106833494,4969507561182858002711390787⟩,⟨8607439584566411087535500944,8607439584566411089550793484⟩⟩,⟨⟨4986385494073012461804361636,4986385494073012463414843493⟩,⟨8636673021858896436326170334,8636673021858896438349130146⟩⟩,⟨⟨5002566710481483926005847502,5002566710481483927621719596⟩,⟨8664699710806636204131154127,8664699710806636206160962827⟩⟩,⟨⟨5017942977869881854203754881,5017942977869881855824915204⟩,⟨8691332187154105827481734954,8691332187154105829518339589⟩⟩,⟨⟨5032612524982808373533735019,5032612524982808375160133957⟩,⟨8716740588077719897679521516,8716740588077719899722944785⟩⟩,⟨⟨5046477817449798231710344765,5046477817449798233340435323⟩,⟨8740755979092348352449345808,8740755979092348354497031864⟩⟩,⟨⟨5059626903572492896484682649,5059626903572492898119387680⟩,⟨8763530864329954364113710316,8763530864329954366167367676⟩⟩] +lemma amp3_13_6_eq : ∀ k : Fin 16, amp3_1Expr 3 6 k = amp3_13_6 k := by decide +kernel +noncomputable def amp3_13_7 : Fin 16 → CBox := ![⟨⟨5071972827087325083752996869,5071972827087325085391913868⟩,⟨8784914631124003046098029854,8784914631124003048157084819⟩⟩,⟨⟨5083593571245343647726475406,5083593571245343649369526163⟩,⟨8805042350427450412836024197,8805042350427450414900452770⟩⟩,⟨⟨5094412652057206986972454109,5094412652057206988618682049⟩,⟨8823781548084791254162711250,8823781548084791256230979822⟩⟩,⟨⟨5104498088897388242378463521,5104498088897388244028194805⟩,⟨8841250037108512103629828666,8841250037108512105702614937⟩⟩,⟨⟨5113783777894453973553481531,5113783777894453975206033447⟩,⟨8857333322234713241569839717,8857333322234713243646084125⟩⟩,⟨⟨5122327862012853059597102550,5122327862012853061252707241⟩,⟨8872132110031922797549702487,8872132110031922799629921112⟩⟩,⟨⟨5130074538545206822957734347,5130074538545206824615798364⟩,⟨8885549747375761003368437244,8885549747375761005451724777⟩⟩,⟨⟨5137072148240684476522154254,5137072148240684478182443485⟩,⟨8897669962899864878740701603,8897669962899864880826767690⟩⟩,⟨⟨5143275123403590880286497038,5143275123403590881948782022⟩,⟨8908413831040106603569418130,8908413831040106605657987479⟩⟩,⟨⟨5148722063855938647285804196,5148722063855938648949908966⟩,⟨8917848208649375139188390867,8917848208649375141279274907⟩⟩,⟨⟨5153377583230426001512985152,5153377583230426003178488089⟩,⟨8925911804741608515551142798,8925911804741608517643732917⟩⟩,⟨⟨5157270589102046093855434283,5157270589102046095522135723⟩,⟨8932654688705418477534686050,8932654688705418479628753628⟩⟩,⟨⟨5160375834950324843944247965,5160375834950324845611740725⟩,⟨8938033132284629590041237007,8938033132284629592136197872⟩⟩,⟨⟨5162712572410639437189700854,5162712572410639438857690781⟩,⟨8942080480289843928628282117,8942080480289843930723744912⟩⟩,⟨⟨5164265665324380306383348030,5164265665324380308051452643⟩,⟨8944770516125318301797567636,8944770516125318303892990341⟩⟩,⟨⟨5165044733496314879070284943,5165044733496314880738076706⟩,⟨8946119901781668787364391647,8946119901781668789459152727⟩⟩] +lemma amp3_13_7_eq : ∀ k : Fin 16, amp3_1Expr 3 7 k = amp3_13_7 k := by decide +kernel +noncomputable def amp3_13_8 : Fin 16 → CBox := ![⟨⟨5165044733496314879070284943,5165044733496314880738076706⟩,⟨8946119901781668787364391647,8946119901781668789459152727⟩⟩,⟨⟨5164265665324380306383348030,5164265665324380308051452643⟩,⟨8944770516125318301797567636,8944770516125318303892990341⟩⟩,⟨⟨5162712572410639437189700854,5162712572410639438857690781⟩,⟨8942080480289843928628282117,8942080480289843930723744912⟩⟩,⟨⟨5160375834950324843944247965,5160375834950324845611740725⟩,⟨8938033132284629590041237007,8938033132284629592136197872⟩⟩,⟨⟨5157270589102046093855434283,5157270589102046095522135723⟩,⟨8932654688705418477534686050,8932654688705418479628753628⟩⟩,⟨⟨5153377583230426001512985152,5153377583230426003178488089⟩,⟨8925911804741608515551142798,8925911804741608517643732917⟩⟩,⟨⟨5148722063855938647285804196,5148722063855938648949908966⟩,⟨8917848208649375139188390867,8917848208649375141279274907⟩⟩,⟨⟨5143275123403590880286497038,5143275123403590881948782022⟩,⟨8908413831040106603569418130,8908413831040106605657987479⟩⟩,⟨⟨5137072148240684476522154254,5137072148240684478182443485⟩,⟨8897669962899864878740701603,8897669962899864880826767690⟩⟩,⟨⟨5130074538545206822957734347,5130074538545206824615798364⟩,⟨8885549747375761003368437244,8885549747375761005451724777⟩⟩,⟨⟨5122327862012853059597102550,5122327862012853061252707241⟩,⟨8872132110031922797549702487,8872132110031922799629921112⟩⟩,⟨⟨5113783777894453973553481531,5113783777894453975206033447⟩,⟨8857333322234713241569839717,8857333322234713243646084125⟩⟩,⟨⟨5104498088897388242378463521,5104498088897388244028194805⟩,⟨8841250037108512103629828666,8841250037108512105702614937⟩⟩,⟨⟨5094412652057206986972454109,5094412652057206988618682049⟩,⟨8823781548084791254162711250,8823781548084791256230979822⟩⟩,⟨⟨5083593571245343647726475406,5083593571245343649369526163⟩,⟨8805042350427450412836024197,8805042350427450414900452770⟩⟩,⟨⟨5071972827087325083752996869,5071972827087325085391913868⟩,⟨8784914631124003046098029854,8784914631124003048157084819⟩⟩] +lemma amp3_13_8_eq : ∀ k : Fin 16, amp3_1Expr 3 8 k = amp3_13_8 k := by decide +kernel +noncomputable def amp3_13_9 : Fin 16 → CBox := ![⟨⟨5059626903572492896484682649,5059626903572492898119387680⟩,⟨8763530864329954364113710316,8763530864329954366167367676⟩⟩,⟨⟨5046477817449798231710344765,5046477817449798233340435323⟩,⟨8740755979092348352449345808,8740755979092348354497031864⟩⟩,⟨⟨5032612524982808373533735019,5032612524982808375160133957⟩,⟨8716740588077719897679521516,8716740588077719899722944785⟩⟩,⟨⟨5017942977869881854203754881,5017942977869881855824915204⟩,⟨8691332187154105827481734954,8691332187154105829518339589⟩⟩,⟨⟨5002566710481483926005847502,5002566710481483927621719596⟩,⟨8664699710806636204131154127,8664699710806636206160962827⟩⟩,⟨⟨4986385494073012461804361636,4986385494073012463414843493⟩,⟨8636673021858896436326170334,8636673021858896438349130146⟩⟩,⟨⟨4969507561182858001106833494,4969507561182858002711390787⟩,⟨8607439584566411087535500944,8607439584566411089550793484⟩⟩,⟨⟨4951824372420951262340819216,4951824372420951263939353384⟩,⟨8576811403190957625231207896,8576811403190957627238786228⟩⟩,⟨⟨4933454993419274266217237562,4933454993419274267809375757⟩,⟨8544994705456564207129616754,8544994705456564209128940564⟩⟩,⟨⟨4914280428450251328530350242,4914280428450251330115571225⟩,⟨8511783384717186123281142835,8511783384717186125271433080⟩⟩,⟨⟨4894430726757596741484316684,4894430726757596743065300156⟩,⟨8477402692870422435237238998,8477402692870422437223240831⟩⟩,⟨⟨4873776274319785403028005755,4873776274319785404601829732⟩,⟨8441628131845618340145702616,8441628131845618342122478717⟩⟩,⟨⟨4852458270930776061353801247,4852458270930776062920397067⟩,⟨8404704266859928646894512256,8404704266859928648862045692⟩⟩,⟨⟨4830336305174704892307613181,4830336305174704893866439362⟩,⟨8366387898207114529389216856,8366387898207114531346693338⟩⟩,⟨⟨4807562911692542946334921199,4807562911692542947886265669⟩,⟨8326943223635252124311289804,8326943223635252126259308168⟩⟩,⟨⟨4783986684434824894014604590,4783986684434824895557694840⟩,⟨8286108000174094194454696872,8286108000174094196392042500⟩⟩] +lemma amp3_13_9_eq : ∀ k : Fin 16, amp3_1Expr 3 9 k = amp3_13_9 k := by decide +kernel +noncomputable def amp3_13_10 : Fin 16 → CBox := ![⟨⟨4759771695603984755547930389,4759771695603984757083552086⟩,⟨8244166409214366188823779902,8244166409214366190751911797⟩⟩,⟨⟨4734755328016043888846332186,4734755328016043890373399431⟩,⟨8200836789531233323694751408,8200836789531233325611911920⟩⟩,⟨⟨4709113413761441756425795248,4709113413761441757944173602⟩,⟨8156423691238937793986814989,8156423691238937795892867419⟩⟩,⟨⟨4682671887494008453465968056,4682671887494008454975645553⟩,⟨8110625624314076259873721167,8110625624314076261768767698⟩⟩,⟨⟨4655618584475842402099852416,4655618584475842403600229208⟩,⟨8063767928974056205139915950,8063767928974056207023011657⟩⟩,⟨⟨4627767732219821176923171264,4627767732219821178414258390⟩,⟨8015528837832533154006416121,8015528837832533155877702716⟩⟩,⟨⟨4599319434914282688445473024,4599319434914282689927032250⟩,⟨7966254941510515699089087427,7966254941510515700948244112⟩⟩,⟨⟨4570075930398161688960721936,4570075930398161690432308269⟩,⟨7915603705897224211716063624,7915603705897224213562441885⟩⟩,⟨⟨4540249881715345226263096555,4540249881715345227724491654⟩,⟨7863943474189563308612963935,7863943474189563310446275138⟩⟩,⟨⟨4509631229138743671855578017,4509631229138743673306397094⟩,⟨7810910412267589700771146173,7810910412267589702590845678⟩⟩,⟨⟨4478445510590351195338508400,4478445510590351196778357447⟩,⟨7756895163271230796098855965,7756895163271230797904348500⟩⟩,⟨⟨4446470033492561671982128042,4446470033492561673418999119⟩,⟨7701512012341604311378907123,7701512012341604313184156737⟩⟩,⟨⟨4413943554923445713829584803,4413943554923445715255486327⟩,⟨7645174498868595235684029118,7645174498868595237475278678⟩⟩,⟨⟨4380630384484886430635609195,4380630384484886432050338175⟩,⟨7587474395107808979068753751,7587474395107808980845772594⟩⟩,⟨⟨4346782873384138107502686170,4346782873384138108906023549⟩,⟨7528848786171561307170878925,7528848786171561308933369767⟩⟩,⟨⟨4312151936157441297965283363,4312151936157441299357103074⟩,⟨7468866243381194002421396326,7468866243381194004169261237⟩⟩] +lemma amp3_13_10_eq : ∀ k : Fin 16, amp3_1Expr 3 10 k = amp3_13_10 k := by decide +kernel +noncomputable def amp3_13_11 : Fin 16 → CBox := ![⟨⟨4277003926566657992995441346,4277003926566657994375557540⟩,⟨7407988104985039134713255648,7407988104985039136446252210⟩⟩,⟨⟨4241075931632628761905154106,4241075931632628763273451219⟩,⟨7345758992345223272717587257,7345758992345223274435635201⟩⟩,⟨⟨4204648752671252390530196914,4204648752671252391886230460⟩,⟨7282665267607715311864206220,7282665267607715313566612406⟩⟩,⟨⟨4167445178213067189623377307,4167445178213067190967371678⟩,⟨7218226786422966778126415005,7218226786422966779813687435⟩⟩,⟨⟨4129760942243346618840742107,4129760942243346620172089076⟩,⟨7152955775078996129766332549,7152955775078996131437491624⟩⟩,⟨⟨4091304021530033258377006441,4091304021530033259695589006⟩,⟨7086346434500889439153943230,7086346434500889440808905070⟩⟩,⟨⟨4052385611987333478066044894,4052385611987333479371490523⟩,⟨7018937771823159984214016953,7018937771823159985852207252⟩⟩,⟨⟨4012698318754671954509835592,4012698318754671955803139115⟩,⟨6950197363529305753614359605,6950197363529305755237619647⟩⟩,⟨⟨3972569377672655662153565857,3972569377672655663433411441⟩,⟨6880691998721315537851974272,6880691998721315539458092854⟩⟩,⟨⟨3931675410886016122786693799,3931675410886016124052915162⟩,⟨6809861570523821677721500232,6809861570523821679310306941⟩⟩,⟨⟨3890360326150824618181359716,3890360326150824619434081784⟩,⟨6738301744643456637279434694,6738301744643456638851210639⟩⟩,⟨⟨3848284094129928590722347498,3848284094129928591960941190⟩,⟨6665423572992208219057149489,6665423572992208220610922071⟩⟩,⟨⟨3805807986503100695589225589,3805807986503100696813690456⟩,⟨6591852796474778415290408372,6591852796474778416826238277⟩⟩,⟨⟨3762574590383011707498849358,3762574590383011708708898112⟩,⟨6516970357811033117176798333,6516970357811033118694304370⟩⟩,⟨⟨3718963300339778587950628677,3718963300339778589145979984⟩,⟨6441433387672530654922031761,6441433387672530656420784733⟩⟩,⟨⟨3674598516835281401392775413,3674598516835281402573038224⟩,⟨6364591328575947896842106203,6364591328575947898321544616⟩⟩] +lemma amp3_13_11_eq : ∀ k : Fin 16, amp3_1Expr 3 11 k = amp3_13_11 k := by decide +kernel +noncomputable def amp3_13_12 : Fin 16 → CBox := ![⟨⟨3629878591273424893332531120,3629878591273424894502135240⟩,⟨6287134145392114253412541870,6287134145392114254880392963⟩⟩,⟨⟨3584408854704921198613043662,3584408854704921199767845623⟩,⟨6208378251448693317509349407,6208378251448693318958551736⟩⟩,⟨⟨3538607533590063832985105103,3538607533590063834124959071⟩,⟨6129048036223983146082417748,6129048036223983147512769692⟩⟩,⟨⟨3492059917117642067137208514,3492059917117642068261935637⟩,⟨6048425199522518651216766053,6048425199522518652628072546⟩⟩,⟨⟨3445205120144288774500349883,3445205120144288775609820232⟩,⟨5967270310586346293112520218,5967270310586346294504603435⟩⟩,⟨⟨3397607316141974805156504697,3397607316141974806250599088⟩,⟨5884828495725633242718878166,5884828495725633244091645884⟩⟩,⟨⟨3349727629506710176722931293,3349727629506710177801295126⟩,⟨5801898445822878361828332087,5801898445822878363181213453⟩⟩,⟨⟨3301107928990071960698721820,3301107928990071961761732002⟩,⟨5717686654279278179188844388,5717686654279278180522605972⟩⟩,⟨⟨3252232592395201074509690472,3252232592395201075556630650⟩,⟨5633032088059931359496269221,5633032088059931360809709559⟩⟩,⟨⟨3202619863391098238129187205,3202619863391098239159977479⟩,⟨5547100320722679180426253381,5547100320722679181719347429⟩⟩,⟨⟨3152778757425303730298795638,3152778757425303731313245183⟩,⟨5460772992884498815268381719,5460772992884498816540834063⟩⟩,⟨⟨3102202422140761771911098588,3102202422140761772908949527⟩,⟨5373172210511033612878479295,5373172210511033614129956294⟩⟩,⟨⟨3051426056220250141831948627,3051426056220250142812904520⟩,⟨5285224964912998624521034370,5285224964912998625751053322⟩⟩,⟨⟨2999916066825581612366691605,2999916066825581613333272967⟩,⟨5196007046184098693200732389,5196007046184098694413771724⟩⟩,⟨⟨2948235567927807711579482536,2948235567927807712529066141⟩,⟨5106493796332646935491541444,5106493796332646936683083807⟩⟩,⟨⟨2895822380713515640760536111,2895822380713515641692937674⟩,⟨5015711493090873600202130731,5015711493090873601371969560⟩⟩] +lemma amp3_13_12_eq : ∀ k : Fin 16, amp3_1Expr 3 12 k = amp3_13_12 k := by decide +kernel +noncomputable def amp3_13_13 : Fin 16 → CBox := ![⟨⟨2843269483200295801677064564,2843269483200295802592298966⟩,⟨4924687204513016734638691987,4924687204513016735786874529⟩⟩,⟨⟨2789984030792729046948174234,2789984030792729047846344336⟩,⟨4832394093638817760247902547,4832394093638817761374719567⟩⟩,⟨⟨2736591067706676008952762569,2736591067706676009833301304⟩,⟨4739914768807124341003089061,4739914768807124342107574896⟩⟩,⟨⟨2682464728926284390885302505,2682464728926284391748177824⟩,⟨4646165200011800398033029979,4646165200011800399115241850⟩⟩,⟨⟨2628264625263173645673288439,2628264625263173646518234563⟩,⟨4552287866691792567371063265,4552287866691792568430552166⟩⟩,⟨⟨2573329192070436684207401996,2573329192070436685035939398⟩,⟨4457136905266166406165469676,4457136905266166407204982175⟩⟩,⟨⟨2518355460693847129100387609,2518355460693847129910999245⟩,⟨4361919609440269938807535798,4361919609440269939824450183⟩⟩,⟨⟨2462643101475025594624595006,2462643101475025595417037035⟩,⟨4265422972663742714294802791,4265422972663742715288810257⟩⟩,⟨⟨2406929842568628607267741977,2406929842568628608042053443⟩,⟨4168924777582623866934205551,4168924777582623867905373860⟩⟩,⟨⟨2350473060741471694771200578,2350473060741471695527325435⟩,⟨4071138763026156820875226857,4071138763026156821823573227⟩⟩,⟨⟨2294054966019543063260612643,2294054966019543063998384244⟩,⟨3973419756501542921032912826,3973419756501542921958142667⟩⟩,⟨⟨2236886552549583811255920857,2236886552549583811976224306⟩,⟨3874401159783468516004325028,3874401159783468516908086720⟩⟩,⟨⟨2179798915915662807230212244,2179798915915662807931756277⟩,⟨3775522472649487017178475764,3775522472649487018058520355⟩⟩,⟨⟨2121951893766475950815528988,2121951893766475951498211723⟩,⟨3675328491220533190726002755,3675328491220533191582270510⟩⟩,⟨⟨2064230630799723993924364598,2064230630799723994588308304⟩,⟨3575352331085074933761559036,3575352331085074934594242398⟩⟩,⟨⟨2005738188498802509257614525,2005738188498802509902442101⟩,⟨3474040449161087917126066225,3474040449161087917934630579⟩⟩] +lemma amp3_13_13_eq : ∀ k : Fin 16, amp3_1Expr 3 13 k = amp3_13_13 k := by decide +kernel +noncomputable def amp3_13_14 : Fin 16 → CBox := ![⟨⟨1947419868181087739434910540,1947419868181087740061550358⟩,⟨3373030155358729585426592984,3373030155358729586212619552⟩⟩,⟨⟨1888315278407924773379578858,1888315278407924773987009237⟩,⟨3270658002911095464055811810,3270658002911095464817651848⟩⟩,⟨⟨1829437172087648439240474646,1829437172087648439828882873⟩,⟨3168678131310934621268777810,3168678131310934622006720894⟩⟩,⟨⟨1769753689214106826571852029,1769753689214106827140689040⟩,⟨3065303306601293613885625328,3065303306601293614598844251⟩⟩,⟨⟨1710353844287314213931965147,1710353844287314214482153350⟩,⟨2962419757226376390216209077,2962419757226376390906257896⟩⟩,⟨⟨1650124571656563995082018330,1650124571656563995612649412⟩,⟨2858099596926999395029369059,2858099596926999395694802025⟩⟩,⟨⟨1590241921453586582233004888,1590241921453586582744662628⟩,⟨2754379804283567773317728045,2754379804283567773959503014⟩⟩,⟨⟨1529499634035960901983132064,1529499634035960902475016547⟩,⟨2649171076308288359741091471,2649171076308288360357955086⟩⟩,⟨⟨1469174162069821263056085824,1469174162069821263528394755⟩,⟨2544684293872362530232882654,2544684293872362530825113279⟩⟩,⟨⟨1407951061421259999034746937,1407951061421259999487564298⟩,⟨2438642772952151337690299039,2438642772952151338258180115⟩⟩,⟨⟨1347224049647206333176756261,1347224049647206333609802454⟩,⟨2333460503167656965970511481,2333460503167656966513482473⟩⟩,⟨⟨1285551412780888596344109968,1285551412780888596757456919⟩,⟨2226640362678449216018676790,2226640362678449216537007634⟩⟩,⟨⟨1224465824149729458468786532,1224465824149729458862623663⟩,⟨2120837019559029801575118365,2120837019559029802069046911⟩⟩,⟨⟨1162373479802631048480047883,1162373479802631048853702145⟩,⟨2013289924388793187637481776,2013289924388793188105997021⟩⟩,⟨⟨1100974564234470578409992232,1100974564234470578763960908⟩,⟨1906943883095107533026015073,1906943883095107533469871746⟩⟩,⟨⟨1038490075614490173679602795,1038490075614490174013514247⟩,⟨1798717574120342149907657147,1798717574120342150326378421⟩⟩] +lemma amp3_13_14_eq : ∀ k : Fin 16, amp3_1Expr 3 14 k = amp3_13_14 k := by decide +kernel +noncomputable def amp3_13_15 : Fin 16 → CBox := ![⟨⟨976826365869980121657992870,976826365869980121972051362⟩,⟨1691912895859670666168473630,1691912895859670666562287138⟩⟩,⟨⟨913973687112991920219883728,913973687112991920513679781⟩,⟨1583048862860762033188530222,1583048862860762033556909485⟩⟩,⟨⟨852098715826997532472155937,852098715826997532745982620⟩,⟨1475878268876554359883094532,1475878268876554360226396872⟩⟩,⟨⟨788895841566765076298968955,788895841566765076552534725⟩,⟨1366407679473444526101013887,1366407679473444526418938453⟩⟩,⟨⟨726871292114567086997004643,726871292114567087230638479⟩,⟨1258978008505669232974878152,1258978008505669233267813629⟩⟩,⟨⟨663325817138793157058598602,663325817138793157271782716⟩,⟨1148914017256532114347922574,1148914017256532114615205914⟩⟩,⟨⟨601227801041259060917809414,601227801041259061110964833⟩,⟨1041357098326373041078990043,1041357098326373041321127993⟩⟩,⟨⟨537327657764345332051066722,537327657764345332223731024⟩,⟨930678803559827651955097302,930678803559827652171565934⟩⟩,⟨⟨475260698067625593554489851,475260698067625593707169292⟩,⟨823175675893779269582254947,823175675893779269773649337⟩⟩,⟨⟨410952047203312812296348240,410952047203312812428339841⟩,⟨711789825230581338042051577,711789825230581338207498709⟩⟩,⟨⟨349085604172734028765625084,349085604172734028877696760⟩,⟨604634002618053415671931707,604634002618053415812386247⟩⟩,⟨⟨284208574900344161453926006,284208574900344161545137883⟩,⟨492263691674140854343902772,492263691674140854458199578⟩⟩,⟨⟨222899049574540211918281786,222899049574540211989754870⟩,⟨386072478821917588784925470,386072478821917588874457807⟩⟩,⟨⟨156930468665277273003358805,156930468665277273053639347⟩,⟨271811544983855893888906119,271811544983855893951872183⟩⟩,⟨⟨97347548738388396604396587,97347548738388396635453890⟩,⟨168610900407176264287309834,168610900407176264326138992⟩⟩,⟨⟨27656833929615362270524295,27656833929615362279267860⟩,⟨47903041542588614256916260,47903041542588614267809321⟩⟩] +lemma amp3_13_15_eq : ∀ k : Fin 16, amp3_1Expr 3 15 k = amp3_13_15 k := by decide +kernel +noncomputable def amp3_13 : Fin 16 → Fin 16 → CBox := ![amp3_13_0,amp3_13_1,amp3_13_2,amp3_13_3,amp3_13_4,amp3_13_5,amp3_13_6,amp3_13_7,amp3_13_8,amp3_13_9,amp3_13_10,amp3_13_11,amp3_13_12,amp3_13_13,amp3_13_14,amp3_13_15] +lemma amp3_13_eq (i k : Fin 16) : amp3_1Expr 3 i k = amp3_13 i k := by + fin_cases i + · exact amp3_13_0_eq k + · exact amp3_13_1_eq k + · exact amp3_13_2_eq k + · exact amp3_13_3_eq k + · exact amp3_13_4_eq k + · exact amp3_13_5_eq k + · exact amp3_13_6_eq k + · exact amp3_13_7_eq k + · exact amp3_13_8_eq k + · exact amp3_13_9_eq k + · exact amp3_13_10_eq k + · exact amp3_13_11_eq k + · exact amp3_13_12_eq k + · exact amp3_13_13_eq k + · exact amp3_13_14_eq k + · exact amp3_13_15_eq k +noncomputable def amp3_14_0 : Fin 16 → CBox := ![⟨⟨206433418803638677619696514,206433418803638677627559241⟩,⟨151119750944407953068355965,151119750944407953079932317⟩⟩,⟨⟨726611995767906115075861325,726611995767906115105637076⟩,⟨531916898291129321830842133,531916898291129321873126483⟩⟩,⟨⟨1171344964628820879926105157,1171344964628820879975704283⟩,⟨857484027298266333860988893,857484027298266333930324305⟩⟩,⟨⟨1663741155941996025434525674,1663741155941996025505394176⟩,⟨1217943056792915601515014509,1217943056792915601613803405⟩⟩,⟨⟨2121361682949658354747743303,2121361682949658354838699855⟩,⟨1552944533148970031734128538,1552944533148970031860525620⟩⟩,⟨⟨2605610421927042946706349352,2605610421927042946818357115⟩,⟨1907439213581574889045193694,1907439213581574889200654832⟩⟩,⟨⟨3067387839274413925622646446,3067387839274413925754938396⟩,⟨2245483744867788300877022070,2245483744867788301060352180⟩⟩,⟨⟨3547394144058060913790883065,3547394144058060913944122335⟩,⟨2596872747922809726505044240,2596872747922809726717242737⟩⟩,⟨⟨4010668238177036632576212303,4010668238177036632749804285⟩,⟨2936012922648345968274122711,2936012922648345968514282543⟩⟩,⟨⟨4487625400817782326345880937,4487625400817782326539799717⟩,⟨3285169798735264204286526753,3285169798735264204555014747⟩⟩,⟨⟨4951131303068236857500266485,4951131303068236857714800700⟩,⟨3624479668790650543136225343,3624479668790650543432873534⟩⟩,⟨⟨5425441185469606814562409403,5425441185469606814797697531⟩,⟨3971698601240472640297908954,3971698601240472640623123336⟩⟩,⟨⟨5888398725213949358075838722,5888398725213949358331172529⟩,⟨4310607042080419205184328405,4310607042080419205537270434⟩⟩,⟨⟨6360151401061098850387061127,6360151401061098850662450609⟩,⟨4655953969407103785125657114,4655953969407103785506582088⟩⟩,⟨⟨6821992474173491748042015731,6821992474173491748338040763⟩,⟨4994045099947507907262130556,4994045099947507907671183512⟩⟩,⟨⟨7291131255199261819808351362,7291131255199261820125170266⟩,⟨5337478523459301576128858489,5337478523459301576566361087⟩⟩] +lemma amp3_14_0_eq : ∀ k : Fin 16, amp3_1Expr 4 0 k = amp3_14_0 k := by decide +kernel +noncomputable def amp3_14_1 : Fin 16 → CBox := ![⟨⟨7751395450698644995426148610,7751395450698644995763172618⟩,⟨5674415299469664647680488923,5674415299469664648145759936⟩⟩,⟨⟨8217786023128097380638118057,8217786023128097380995168349⟩,⟨6015836894659156223408427096,6015836894659156223901508351⟩⟩,⟨⟨8676073767988110570194037029,8676073767988110570570592705⟩,⟨6351326808382848472801386342,6351326808382848473321668054⟩⟩,⟨⟨9139537335716977438077623661,9139537335716977438475957321⟩,⟨6690605687417518520684389205,6690605687417518521233680966⟩⟩,⟨⟨9595486376480452818518527960,9595486376480452818935705359⟩,⟨7024383550918675625351914805,7024383550918675625927856726⟩⟩,⟨⟨10055817204924139265805780696,10055817204924139266241997314⟩,⟨7361369105629726598950924671,7361369105629726599553783397⟩⟩,⟨⟨10509089791589342672729504081,10509089791589342673187259369⟩,⟨7693187668746822674136068315,7693187668746822674767474563⟩⟩,⟨⟨10966065236024010113952638733,10966065236024010114428816138⟩,⟨8027716911884367587293742196,8027716911884367587951518893⟩⟩,⟨⟨11416340688760420328729081832,11416340688760420329226171183⟩,⟨8357341420688498524193643850,8357341420688498524879424771⟩⟩,⟨⟨11869727294381481876934044968,11869727294381481877452656878⟩,⟨8689243451474308711876257264,8689243451474308712590577127⟩⟩,⟨⟨12316697480480254771804840728,12316697480480254772340788670⟩,⟨9016448337167126781026741964,9016448337167126781766355108⟩⟩,⟨⟨12766254891602009637630065866,12766254891602009638186987840⟩,⟨9345547203027381209129660304,9345547203027381209897302875⟩⟩,⟨⟨13209621370059014535579490960,13209621370059014536152328657⟩,⟨9670113991630800881777207126,9670113991630800882569001631⟩⟩,⟨⟨13655104950972463001071575204,13655104950972463001666624888⟩,⟨9996230606797166121909836076,9996230606797166122730451393⟩⟩,⟨⟨14094577119453890023252656762,14094577119453890023867491687⟩,⟨10317946562638040475790798857,10317946562638040476638288990⟩⟩,⟨⟨14535739783441810130266337179,14535739783441810130901885215⟩,⟨10640900047079634650671821274,10640900047079634651546913137⟩⟩] +lemma amp3_14_1_eq : ∀ k : Fin 16, amp3_1Expr 4 1 k = amp3_14_1 k := by decide +kernel +noncomputable def amp3_14_2 : Fin 16 → CBox := ![⟨⟨14971033652317385873006215267,14971033652317385873656482335⟩,⟨10959557275319780853744589350,10959557275319780854642729499⟩⟩,⟨⟨15407627185369045844994466474,15407627185369045845666020656⟩,⟨11279165923769597856377573575,11279165923769597857303606824⟩⟩,⟨⟨15838464557506970186537614054,15838464557506970187229241175⟩,⟨11594560769974018284116912518,11594560769974018285069787734⟩⟩,⟨⟨16270240608961625265151003753,16270240608961625265863355427⟩,⟨11910642777130299649879409048,11910642777130299650859629711⟩⟩,⟨⟨16696348529765272278954594808,16696348529765272279688486646⟩,⟨12222575424666104655610338813,12222575424666104656618342177⟩⟩,⟨⟨17123059377081258097079665042,17123059377081258097825291266⟩,⟨12534949445042171969704751350,12534949445042171970733376089⟩⟩,⟨⟨17544169769018200422855127554,17544169769018200423620651912⟩,⟨12843223647535257032438043084,12843223647535257033493107569⟩⟩,⟨⟨17965568925439762165007766494,17965568925439762165791864819⟩,⟨13151709240302504949576589920,13151709240302504950657132936⟩⟩,⟨⟨18381418351227587809204250101,18381418351227587810008047207⟩,⟨13456132148277536619038634853,13456132148277536620145323344⟩⟩,⟨⟨18797261061655928396180762768,18797261061655928397004551941⟩,⟨13760550140268234137042830030,13760550140268234138175878507⟩⟩,⟨⟨19207590578814079551371929569,19207590578814079552215423748⟩,⟨14060932194673206181999510642,14060932194673206183158553517⟩⟩,⟨⟨19617634234436279719693871111,19617634234436279720545826395⟩,⟨14361104983909932427369236133,14361104983909932428546034238⟩⟩,⟨⟨20022189315728738361912437487,20022189315728738362785728987⟩,⟨14657259857876169579143604852,14657259857876169580347428672⟩⟩,⟨⟨20426193808440952720168909203,20426193808440952721061706204⟩,⟨14953011673027600701245014366,14953011673027600702474508199⟩⟩,⟨⟨20824724310448551710686065909,20824724310448551711599651274⟩,⟨15244756248863093615751478577,15244756248863093617007427205⟩⟩,⟨⟨21222452341827216678428996791,21222452341827216679359361009⟩,⟨15535913375426625074016799644,15535913375426625075296245275⟩⟩] +lemma amp3_14_2_eq : ∀ k : Fin 16, amp3_1Expr 4 2 k = amp3_14_2 k := by decide +kernel +noncomputable def amp3_14_3 : Fin 16 → CBox := ![⟨⟨21614712509035809765934921633,21614712509035809766884352845⟩,⟨15823067747608778483336224843,15823067747608778484640688344⟩⟩,⟨⟨22005929864376524719834569865,22005929864376524720803469094⟩,⟨16109458728520909295578475665,16109458728520909296908221205⟩⟩,⟨⟨22391678359670523838446199500,22391678359670523839434711890⟩,⟨16391846226019360612596455261,16391846226019360613951434895⟩⟩,⟨⟨22776154154706997818992096498,22776154154706997819980995893⟩,⟨16673302042266497534192669762,16673302042266497535558773084⟩⟩,⟨⟨23155154109585114316067220699,23155154109585114317076843079⟩,⟨16950749265303590771090598594,16950749265303590772482558182⟩⟩,⟨⟨23532661015470212554441276359,23532661015470212555469824219⟩,⟨17227103500619605092670439145,17227103500619605094086897036⟩⟩,⟨⟨23904680095009751316121416745,23904680095009751317168491188⟩,⟨17499440368227554838671248988,17499440368227554840111758440⟩⟩,⟨⟨24274994545700667019826096036,24274994545700667020890746705⟩,⟨17770529360910264869596459322,17770529360910264871060276563⟩⟩,⟨⟨24639805024518844204009372625,24639805024518844205092533552⟩,⟨18037589166538700281383485200,18037589166538700282871138803⟩⟩,⟨⟨25002707409672597433426967101,25002707409672597434523821917⟩,⟨18303252150659177078734567843,18303252150659177080242478182⟩⟩,⟨⟨25360086256019165708983498130,25360086256019165710098395953⟩,⟨18564871623735216097406134560,18564871623735216098937329673⟩⟩,⟨⟨25715361101749847687187065998,25715361101749847688317945100⟩,⟨18824950861461270136904299450,18824950861461270138457210724⟩⟩,⟨⟨26065090067515605573983256714,26065090067515605575130769557⟩,⟨19080970233280321438409336793,19080970233280321439984285495⟩⟩,⟨⟨26412526206808221627146147005,26412526206808221628309961322⟩,⟨19335311139628093959859112107,19335311139628093961455790356⟩⟩,⟨⟨26754391921717071432551123777,26754391921717071433731453487⟩,⟨19585574212307229033991167681,19585574212307229035609575017⟩⟩,⟨⟨27093782655877928083274532808,27093782655877928084470977581⟩,⟨19834025473331078295258681109,19834025473331078296898454686⟩⟩] +lemma amp3_14_3_eq : ∀ k : Fin 16, amp3_1Expr 4 3 k = amp3_14_3 k := by decide +kernel +noncomputable def amp3_14_4 : Fin 16 → CBox := ![⟨⟨27427576724493021402413068572,27427576724493021403596257318⟩,⟨20078379690822458598260086627,20078379690822458599899567517⟩⟩,⟨⟨27758719976704175664842457481,27758719976704175666046191799⟩,⟨20320793376024618487557259507,20320793376024618489221117457⟩⟩,⟨⟨28084239077154113067582350568,28084239077154113068805275464⟩,⟨20559089896388089651184482131,20559089896388089652871566642⟩⟩,⟨⟨28406937538961959616208228055,28406937538961959617449027914⟩,⟨20795321565955758223613518678,20795321565955758225322787125⟩⟩,⟨⟨28723983522504130804310699630,28723983522504130805568801819⟩,⟨21027415334244273621433939770,21027415334244273623164813584⟩⟩,⟨⟨29038044793890211750627476988,29038044793890211751903708063⟩,⟨21257324141588562512817034832,21257324141588562514570034939⟩⟩,⟨⟨29346424784591707849968448383,29346424784591707851259692544⟩,⟨21483073962819675602931963447,21483073962819675604704648738⟩⟩,⟨⟨29651661508133253727732026794,29651661508133253729040090507⟩,⟨21706522752787942401946579839,21706522752787942403740184114⟩⟩,⟨⟨29951188002077299328716361076,29951188002077299330041590961⟩,⟨21925791364567955418203441439,21925791364567955420018057439⟩⟩,⟨⟨30247417991595653884174618131,30247417991595653885508109285⟩,⟨22142646767620986926534511027,22142646767620986928363526967⟩⟩,⟨⟨30537908955121911915331761284,30537908955121911916682534995⟩,⟨22355300912061845397055248348,22355300912061845398905106455⟩⟩,⟨⟨30824955319131378738444530420,30824955319131378739810763868⟩,⟨22565433434644685499226235149,22565433434644685501095503904⟩⟩,⟨⟨31106234285698202318327619958,31106234285698202319710043493⟩,⟨22771343929272067937530030825,22771343929272067939419082270⟩⟩,⟨⟨31383925545900440189462451588,31383925545900440190857522920⟩,⟨22974628040557935406837378646,22974628040557935408743518488⟩⟩,⟨⟨31655821711220961596700346011,31655821711220961598111351386⟩,⟨23173669847955704071311803012,23173669847955704073237273554⟩⟩,⟨⟨31923991916236710245083706362,31923991916236710246508364119⟩,⟨23369984063103394257501218970,23369984063103394259444244869⟩⟩] +lemma amp3_14_4_eq : ∀ k : Fin 16, amp3_1Expr 4 4 k = amp3_14_4 k := by decide +kernel +noncomputable def amp3_14_5 : Fin 16 → CBox := ![⟨⟨32186340231392153200409560115,32186340231392153201848626488⟩,⟨23562036359077270602874309034,23562036359077270604835279741⟩⟩,⟨⟨32444829065879675048087896527,32444829065879675049541057472⟩,⟨23751263319111398831464952595,23751263319111398833443529394⟩⟩,⟨⟨32697470328155163684444425027,32697470328155163685912365528⟩,⟨23936209559185390821543039346,23936209559185390823539558808⟩⟩,⟨⟨32946123217430973330479505761,32946123217430973331961699742⟩,⟨24118236107584081901177772009,24118236107584081903191736565⟩⟩,⟨⟨33188904158653455314507386252,33188904158653455316003951304⟩,⟨24295964091668331968888461919,24295964091668331970919792093⟩⟩,⟨⟨33427572368903866377400283396,33427572368903866378852713096⟩,⟨24470681347723163985056699287,24470681347723163987062449444⟩⟩,⟨⟨33660345741090154092839941627,33660345741090154094309528618⟩,⟨24641083282812666747450613119,24641083282812666749475486382⟩⟩,⟨⟨33888886475240507526179963342,33888886475240507527664943633⟩,⟨24808386711809817071964203618,24808386711809817074006789315⟩⟩,⟨⟨34111511133387095183202295162,34111511133387095184701441654⟩,⟨24971359272590771803580185486,24971359272590771805639418513⟩⟩,⟨⟨34329787622678162155912477436,34329787622678162157425369438⟩,⟨25131148752849596777309983175,25131148752849596779385432968⟩⟩,⟨⟨34542128604544351019682374737,34542128604544351021207341191⟩,⟨25286593140104708664113897510,25286593140104708666204173417⟩⟩,⟨⟨34750010195851482022680032545,34750010195851482024216535206⟩,⟨25438773026899797216747828855,25438773026899797218852411119⟩⟩,⟨⟨34951938798604186337635353710,34951938798604186339185130233⟩,⟨25586595023616169428960851373,25586595023616169431080844200⟩⟩,⟨⟨35149301037523642617723572559,35149301037523642619283415344⟩,⟨25731074210000759103119576135,25731074210000759105252502649⟩⟩,⟨⟨35340694891126642206843628448,35340694891126642208415107712⟩,⟨25871184235094554427389016002,25871184235094554429535857402⟩⟩,⟨⟨35527419600844671403929575983,35527419600844671405512986548⟩,⟨26007876209636701891062457772,26007876209636701893223298236⟩⟩] +lemma amp3_14_5_eq : ∀ k : Fin 16, amp3_1Expr 4 5 k = amp3_14_5 k := by decide +kernel +noncomputable def amp3_14_6 : Fin 16 → CBox := ![⟨⟨35708162738087487969078915801,35708162738087487970667815619⟩,⟨26140189369217838179269438045,26140189369217838181439393014⟩⟩,⟨⟨35884138094040676038093628255,35884138094040676039695207343⟩,⟨26269012270655590143634743843,26269012270655590145818942345⟩⟩,⟨⟨36054121017113048632159820531,36054121017113048633769979034⟩,⟨26393448406763638845747077475,26393448406763638847942349251⟩⟩,⟨⟨36219241617442961543374174037,36219241617442961544996413069⟩,⟨26514325075581409418860822584,26514325075581409421069593533⟩⟩,⟨⟨36378361360970378296591692346,36378361360970378298223638825⟩,⟨26630808812330807488721998793,26630808812330807490942362503⟩⟩,⟨⟨36532528292771231840617758166,36532528292771231842260276737⟩,⟨26743666839256038355827756597,26743666839256038358060206387⟩⟩,⟨⟨36680688483235377564906757845,36680688483235377566539708751⟩,⟨26852127626334874906017302478,26852127626334874908246925659⟩⟩,⟨⟨36823809384590225483367732566,36823809384590225485012518562⟩,⟨26956899397751676949097367112,26956899397751676951339689507⟩⟩,⟨⟨36960920296065720304081027135,36960920296065720305735428757⟩,⟨27057271551223817777556662562,27057271551223817779809889956⟩⟩,⟨⟨37092909413864254183768866334,37092909413864254185431524756⟩,⟨27153894291498538179705892747,27153894291498538181968886001⟩⟩,⟨⟨37218888020009842724154821680,37218888020009842725826672491⟩,⟨27246117031863817798690511011,27246117031863817800963785555⟩⟩,⟨⟨37339666263539208116584638006,37339666263539208118263138935⟩,⟨27334532842576240262711334077,27334532842576240264992882215⟩⟩,⟨⟨37454436285787739076090642726,37454436285787739077776702993⟩,⟨27418550330047975365815802056,27418550330047975368106119979⟩⟩,⟨⟨37563931276086673293818742628,37563931276086673295513458670⟩,⟨27498706226121056544878482693,27498706226121056547178224319⟩⟩,⟨⟨37667423227983889636076745290,37667423227983889637770239364⟩,⟨27574467593084293170778106161,27574467593084293173079871223⟩⟩,⟨⟨37765569342949880318514125468,37765569342949880320214772280⟩,⟨27646315535804894523661917391,27646315535804894525971685873⟩⟩] +lemma amp3_14_6_eq : ∀ k : Fin 16, amp3_1Expr 4 6 k = amp3_14_6 k := by decide +kernel +noncomputable def amp3_14_7 : Fin 16 → CBox := ![⟨⟨37857720570597306431566630852,37857720570597306433273092992⟩,⟨27713774916422656262173200039,27713774916422656264489823860⟩⟩,⟨⟨37944458985836275420946519938,37944458985836275422659718692⟩,⟨27777271843345588123601807613,27777271843345588125925808587⟩⟩,⟨⟨38025213704398410460593106198,38025213704398410462307565402⟩,⟨27836388400283996484752410355,27836388400283996487079610939⟩⟩,⟨⟨38100492429806577181160045567,38100492429806577182879722358⟩,⟨27891496252011800694503577799,27891496252011800696836720422⟩⟩,⟨⟨38169801756047242381748119337,38169801756047242383469577704⟩,⟨27942234200258334432738160057,27942234200258334435074561077⟩⟩,⟨⟨38233575668115257837889671285,38233575668115257839616183130⟩,⟨27988919944089551716789290451,27988919944089551719131188993⟩⟩,⟨⟨38291397648932349302976325065,38291397648932349304705115805⟩,⟨28031248571841935655151797862,28031248571841935657496994975⟩⟩,⟨⟨38343628518762467667984546786,38343628518762467669715423623⟩,⟨28069484222281098713028575742,28069484222281098715376772645⟩⟩,⟨⟨38389928155694576732704681484,38389928155694576734437580916⟩,⟨28103377908887394970217716554,28103377908887394972568699527⟩⟩,⟨⟨38430584672722504871944536401,38430584672722504873679714093⟩,⟨28133140545010627575456930181,28133140545010627577810727276⟩⟩,⟨⟨38465333942404921041582764793,38465333942404921043318716292⟩,⟨28158578775944069036639064199,28158578775944069038994407523⟩⟩,⟨⟨38494391733819021334922993263,38494391733819021336659810803⟩,⟨28179850555614929145292945700,28179850555614929147649742301⟩⟩,⟨⟨38517569604370558560294018389,38517569604370558562030297669⟩,⟨28196817934469908870485187904,28196817934469908872842243977⟩⟩,⟨⟨38535011250222245610451928229,38535011250222245612187068657⟩,⟨28209586105400966734151322396,28209586105400966736508036542⟩⟩,⟨⟨38546603693548157833566422619,38546603693548157835299195719⟩,⟨28218072362899397218877944479,28218072362899397221233252472⟩⟩,⟨⟨38552418737548597095448487781,38552418737548597097177308831⟩,⟨28222329270555967335385845901,28222329270555967337738424749⟩⟩] +lemma amp3_14_7_eq : ∀ k : Fin 16, amp3_1Expr 4 7 k = amp3_14_7 k := by decide +kernel +noncomputable def amp3_14_8 : Fin 16 → CBox := ![⟨⟨38552418737548597095448487781,38552418737548597097177308831⟩,⟨28222329270555967335385845901,28222329270555967337738424749⟩⟩,⟨⟨38546603693548157833566422619,38546603693548157835299195719⟩,⟨28218072362899397218877944479,28218072362899397221233252472⟩⟩,⟨⟨38535011250222245610451928229,38535011250222245612187068657⟩,⟨28209586105400966734151322396,28209586105400966736508036542⟩⟩,⟨⟨38517569604370558560294018389,38517569604370558562030297669⟩,⟨28196817934469908870485187904,28196817934469908872842243977⟩⟩,⟨⟨38494391733819021334922993263,38494391733819021336659810803⟩,⟨28179850555614929145292945700,28179850555614929147649742301⟩⟩,⟨⟨38465333942404921041582764793,38465333942404921043318716292⟩,⟨28158578775944069036639064199,28158578775944069038994407523⟩⟩,⟨⟨38430584672722504871944536401,38430584672722504873679714093⟩,⟨28133140545010627575456930181,28133140545010627577810727276⟩⟩,⟨⟨38389928155694576732704681484,38389928155694576734437580916⟩,⟨28103377908887394970217716554,28103377908887394972568699527⟩⟩,⟨⟨38343628518762467667984546786,38343628518762467669715423623⟩,⟨28069484222281098713028575742,28069484222281098715376772645⟩⟩,⟨⟨38291397648932349302976325065,38291397648932349304705115805⟩,⟨28031248571841935655151797862,28031248571841935657496994975⟩⟩,⟨⟨38233575668115257837889671285,38233575668115257839616183130⟩,⟨27988919944089551716789290451,27988919944089551719131188993⟩⟩,⟨⟨38169801756047242381748119337,38169801756047242383469577704⟩,⟨27942234200258334432738160057,27942234200258334435074561077⟩⟩,⟨⟨38100492429806577181160045567,38100492429806577182879722358⟩,⟨27891496252011800694503577799,27891496252011800696836720422⟩⟩,⟨⟨38025213704398410460593106198,38025213704398410462307565402⟩,⟨27836388400283996484752410355,27836388400283996487079610939⟩⟩,⟨⟨37944458985836275420946519938,37944458985836275422659718692⟩,⟨27777271843345588123601807613,27777271843345588125925808587⟩⟩,⟨⟨37857720570597306431566630852,37857720570597306433273092992⟩,⟨27713774916422656262173200039,27713774916422656264489823860⟩⟩] +lemma amp3_14_8_eq : ∀ k : Fin 16, amp3_1Expr 4 8 k = amp3_14_8 k := by decide +kernel +noncomputable def amp3_14_9 : Fin 16 → CBox := ![⟨⟨37765569342949880318514125468,37765569342949880320214772280⟩,⟨27646315535804894523661917391,27646315535804894525971685873⟩⟩,⟨⟨37667423227983889636076745290,37667423227983889637770239364⟩,⟨27574467593084293170778106161,27574467593084293173079871223⟩⟩,⟨⟨37563931276086673293818742628,37563931276086673295513458670⟩,⟨27498706226121056544878482693,27498706226121056547178224319⟩⟩,⟨⟨37454436285787739076090642726,37454436285787739077776702993⟩,⟨27418550330047975365815802056,27418550330047975368106119979⟩⟩,⟨⟨37339666263539208116584638006,37339666263539208118263138935⟩,⟨27334532842576240262711334077,27334532842576240264992882215⟩⟩,⟨⟨37218888020009842724154821680,37218888020009842725826672491⟩,⟨27246117031863817798690511011,27246117031863817800963785555⟩⟩,⟨⟨37092909413864254183768866334,37092909413864254185431524756⟩,⟨27153894291498538179705892747,27153894291498538181968886001⟩⟩,⟨⟨36960920296065720304081027135,36960920296065720305735428757⟩,⟨27057271551223817777556662562,27057271551223817779809889956⟩⟩,⟨⟨36823809384590225483367732566,36823809384590225485012518562⟩,⟨26956899397751676949097367112,26956899397751676951339689507⟩⟩,⟨⟨36680688483235377564906757845,36680688483235377566539708751⟩,⟨26852127626334874906017302478,26852127626334874908246925659⟩⟩,⟨⟨36532528292771231840617758166,36532528292771231842260276737⟩,⟨26743666839256038355827756597,26743666839256038358060206387⟩⟩,⟨⟨36378361360970378296591692346,36378361360970378298223638825⟩,⟨26630808812330807488721998793,26630808812330807490942362503⟩⟩,⟨⟨36219241617442961543374174037,36219241617442961544996413069⟩,⟨26514325075581409418860822584,26514325075581409421069593533⟩⟩,⟨⟨36054121017113048632159820531,36054121017113048633769979034⟩,⟨26393448406763638845747077475,26393448406763638847942349251⟩⟩,⟨⟨35884138094040676038093628255,35884138094040676039695207343⟩,⟨26269012270655590143634743843,26269012270655590145818942345⟩⟩,⟨⟨35708162738087487969078915801,35708162738087487970667815619⟩,⟨26140189369217838179269438045,26140189369217838181439393014⟩⟩] +lemma amp3_14_9_eq : ∀ k : Fin 16, amp3_1Expr 4 9 k = amp3_14_9 k := by decide +kernel +noncomputable def amp3_14_10 : Fin 16 → CBox := ![⟨⟨35527419600844671403929575983,35527419600844671405512986548⟩,⟨26007876209636701891062457772,26007876209636701893223298236⟩⟩,⟨⟨35340694891126642206843628448,35340694891126642208415107712⟩,⟨25871184235094554427389016002,25871184235094554429535857402⟩⟩,⟨⟨35149301037523642617723572559,35149301037523642619283415344⟩,⟨25731074210000759103119576135,25731074210000759105252502649⟩⟩,⟨⟨34951938798604186337635353710,34951938798604186339185130233⟩,⟨25586595023616169428960851373,25586595023616169431080844200⟩⟩,⟨⟨34750010195851482022680032545,34750010195851482024216535206⟩,⟨25438773026899797216747828855,25438773026899797218852411119⟩⟩,⟨⟨34542128604544351019682374737,34542128604544351021207341191⟩,⟨25286593140104708664113897510,25286593140104708666204173417⟩⟩,⟨⟨34329787622678162155912477436,34329787622678162157425369438⟩,⟨25131148752849596777309983175,25131148752849596779385432968⟩⟩,⟨⟨34111511133387095183202295162,34111511133387095184701441654⟩,⟨24971359272590771803580185486,24971359272590771805639418513⟩⟩,⟨⟨33888886475240507526179963342,33888886475240507527664943633⟩,⟨24808386711809817071964203618,24808386711809817074006789315⟩⟩,⟨⟨33660345741090154092839941627,33660345741090154094309528618⟩,⟨24641083282812666747450613119,24641083282812666749475486382⟩⟩,⟨⟨33427572368903866377400283396,33427572368903866378852713096⟩,⟨24470681347723163985056699287,24470681347723163987062449444⟩⟩,⟨⟨33188904158653455314507386252,33188904158653455316003951304⟩,⟨24295964091668331968888461919,24295964091668331970919792093⟩⟩,⟨⟨32946123217430973330479505761,32946123217430973331961699742⟩,⟨24118236107584081901177772009,24118236107584081903191736565⟩⟩,⟨⟨32697470328155163684444425027,32697470328155163685912365528⟩,⟨23936209559185390821543039346,23936209559185390823539558808⟩⟩,⟨⟨32444829065879675048087896527,32444829065879675049541057472⟩,⟨23751263319111398831464952595,23751263319111398833443529394⟩⟩,⟨⟨32186340231392153200409560115,32186340231392153201848626488⟩,⟨23562036359077270602874309034,23562036359077270604835279741⟩⟩] +lemma amp3_14_10_eq : ∀ k : Fin 16, amp3_1Expr 4 10 k = amp3_14_10 k := by decide +kernel +noncomputable def amp3_14_11 : Fin 16 → CBox := ![⟨⟨31923991916236710245083706362,31923991916236710246508364119⟩,⟨23369984063103394257501218970,23369984063103394259444244869⟩⟩,⟨⟨31655821711220961596700346011,31655821711220961598111351386⟩,⟨23173669847955704071311803012,23173669847955704073237273554⟩⟩,⟨⟨31383925545900440189462451588,31383925545900440190857522920⟩,⟨22974628040557935406837378646,22974628040557935408743518488⟩⟩,⟨⟨31106234285698202318327619958,31106234285698202319710043493⟩,⟨22771343929272067937530030825,22771343929272067939419082270⟩⟩,⟨⟨30824955319131378738444530420,30824955319131378739810763868⟩,⟨22565433434644685499226235149,22565433434644685501095503904⟩⟩,⟨⟨30537908955121911915331761284,30537908955121911916682534995⟩,⟨22355300912061845397055248348,22355300912061845398905106455⟩⟩,⟨⟨30247417991595653884174618131,30247417991595653885508109285⟩,⟨22142646767620986926534511027,22142646767620986928363526967⟩⟩,⟨⟨29951188002077299328716361076,29951188002077299330041590961⟩,⟨21925791364567955418203441439,21925791364567955420018057439⟩⟩,⟨⟨29651661508133253727732026794,29651661508133253729040090507⟩,⟨21706522752787942401946579839,21706522752787942403740184114⟩⟩,⟨⟨29346424784591707849968448383,29346424784591707851259692544⟩,⟨21483073962819675602931963447,21483073962819675604704648738⟩⟩,⟨⟨29038044793890211750627476988,29038044793890211751903708063⟩,⟨21257324141588562512817034832,21257324141588562514570034939⟩⟩,⟨⟨28723983522504130804310699630,28723983522504130805568801819⟩,⟨21027415334244273621433939770,21027415334244273623164813584⟩⟩,⟨⟨28406937538961959616208228055,28406937538961959617449027914⟩,⟨20795321565955758223613518678,20795321565955758225322787125⟩⟩,⟨⟨28084239077154113067582350568,28084239077154113068805275464⟩,⟨20559089896388089651184482131,20559089896388089652871566642⟩⟩,⟨⟨27758719976704175664842457481,27758719976704175666046191799⟩,⟨20320793376024618487557259507,20320793376024618489221117457⟩⟩,⟨⟨27427576724493021402413068572,27427576724493021403596257318⟩,⟨20078379690822458598260086627,20078379690822458599899567517⟩⟩] +lemma amp3_14_11_eq : ∀ k : Fin 16, amp3_1Expr 4 11 k = amp3_14_11 k := by decide +kernel +noncomputable def amp3_14_12 : Fin 16 → CBox := ![⟨⟨27093782655877928083274532808,27093782655877928084470977581⟩,⟨19834025473331078295258681109,19834025473331078296898454686⟩⟩,⟨⟨26754391921717071432551123777,26754391921717071433731453487⟩,⟨19585574212307229033991167681,19585574212307229035609575017⟩⟩,⟨⟨26412526206808221627146147005,26412526206808221628309961322⟩,⟨19335311139628093959859112107,19335311139628093961455790356⟩⟩,⟨⟨26065090067515605573983256714,26065090067515605575130769557⟩,⟨19080970233280321438409336793,19080970233280321439984285495⟩⟩,⟨⟨25715361101749847687187065998,25715361101749847688317945100⟩,⟨18824950861461270136904299450,18824950861461270138457210724⟩⟩,⟨⟨25360086256019165708983498130,25360086256019165710098395953⟩,⟨18564871623735216097406134560,18564871623735216098937329673⟩⟩,⟨⟨25002707409672597433426967101,25002707409672597434523821917⟩,⟨18303252150659177078734567843,18303252150659177080242478182⟩⟩,⟨⟨24639805024518844204009372625,24639805024518844205092533552⟩,⟨18037589166538700281383485200,18037589166538700282871138803⟩⟩,⟨⟨24274994545700667019826096036,24274994545700667020890746705⟩,⟨17770529360910264869596459322,17770529360910264871060276563⟩⟩,⟨⟨23904680095009751316121416745,23904680095009751317168491188⟩,⟨17499440368227554838671248988,17499440368227554840111758440⟩⟩,⟨⟨23532661015470212554441276359,23532661015470212555469824219⟩,⟨17227103500619605092670439145,17227103500619605094086897036⟩⟩,⟨⟨23155154109585114316067220699,23155154109585114317076843079⟩,⟨16950749265303590771090598594,16950749265303590772482558182⟩⟩,⟨⟨22776154154706997818992096498,22776154154706997819980995893⟩,⟨16673302042266497534192669762,16673302042266497535558773084⟩⟩,⟨⟨22391678359670523838446199500,22391678359670523839434711890⟩,⟨16391846226019360612596455261,16391846226019360613951434895⟩⟩,⟨⟨22005929864376524719834569865,22005929864376524720803469094⟩,⟨16109458728520909295578475665,16109458728520909296908221205⟩⟩,⟨⟨21614712509035809765934921633,21614712509035809766884352845⟩,⟨15823067747608778483336224843,15823067747608778484640688344⟩⟩] +lemma amp3_14_12_eq : ∀ k : Fin 16, amp3_1Expr 4 12 k = amp3_14_12 k := by decide +kernel +noncomputable def amp3_14_13 : Fin 16 → CBox := ![⟨⟨21222452341827216678428996791,21222452341827216679359361009⟩,⟨15535913375426625074016799644,15535913375426625075296245275⟩⟩,⟨⟨20824724310448551710686065909,20824724310448551711599651274⟩,⟨15244756248863093615751478577,15244756248863093617007427205⟩⟩,⟨⟨20426193808440952720168909203,20426193808440952721061706204⟩,⟨14953011673027600701245014366,14953011673027600702474508199⟩⟩,⟨⟨20022189315728738361912437487,20022189315728738362785728987⟩,⟨14657259857876169579143604852,14657259857876169580347428672⟩⟩,⟨⟨19617634234436279719693871111,19617634234436279720545826395⟩,⟨14361104983909932427369236133,14361104983909932428546034238⟩⟩,⟨⟨19207590578814079551371929569,19207590578814079552215423748⟩,⟨14060932194673206181999510642,14060932194673206183158553517⟩⟩,⟨⟨18797261061655928396180762768,18797261061655928397004551941⟩,⟨13760550140268234137042830030,13760550140268234138175878507⟩⟩,⟨⟨18381418351227587809204250101,18381418351227587810008047207⟩,⟨13456132148277536619038634853,13456132148277536620145323344⟩⟩,⟨⟨17965568925439762165007766494,17965568925439762165791864819⟩,⟨13151709240302504949576589920,13151709240302504950657132936⟩⟩,⟨⟨17544169769018200422855127554,17544169769018200423620651912⟩,⟨12843223647535257032438043084,12843223647535257033493107569⟩⟩,⟨⟨17123059377081258097079665042,17123059377081258097825291266⟩,⟨12534949445042171969704751350,12534949445042171970733376089⟩⟩,⟨⟨16696348529765272278954594808,16696348529765272279688486646⟩,⟨12222575424666104655610338813,12222575424666104656618342177⟩⟩,⟨⟨16270240608961625265151003753,16270240608961625265863355427⟩,⟨11910642777130299649879409048,11910642777130299650859629711⟩⟩,⟨⟨15838464557506970186537614054,15838464557506970187229241175⟩,⟨11594560769974018284116912518,11594560769974018285069787734⟩⟩,⟨⟨15407627185369045844994466474,15407627185369045845666020656⟩,⟨11279165923769597856377573575,11279165923769597857303606824⟩⟩,⟨⟨14971033652317385873006215267,14971033652317385873656482335⟩,⟨10959557275319780853744589350,10959557275319780854642729499⟩⟩] +lemma amp3_14_13_eq : ∀ k : Fin 16, amp3_1Expr 4 13 k = amp3_14_13 k := by decide +kernel +noncomputable def amp3_14_14 : Fin 16 → CBox := ![⟨⟨14535739783441810130266337179,14535739783441810130901885215⟩,⟨10640900047079634650671821274,10640900047079634651546913137⟩⟩,⟨⟨14094577119453890023252656762,14094577119453890023867491687⟩,⟨10317946562638040475790798857,10317946562638040476638288990⟩⟩,⟨⟨13655104950972463001071575204,13655104950972463001666624888⟩,⟨9996230606797166121909836076,9996230606797166122730451393⟩⟩,⟨⟨13209621370059014535579490960,13209621370059014536152328657⟩,⟨9670113991630800881777207126,9670113991630800882569001631⟩⟩,⟨⟨12766254891602009637630065866,12766254891602009638186987840⟩,⟨9345547203027381209129660304,9345547203027381209897302875⟩⟩,⟨⟨12316697480480254771804840728,12316697480480254772340788670⟩,⟨9016448337167126781026741964,9016448337167126781766355108⟩⟩,⟨⟨11869727294381481876934044968,11869727294381481877452656878⟩,⟨8689243451474308711876257264,8689243451474308712590577127⟩⟩,⟨⟨11416340688760420328729081832,11416340688760420329226171183⟩,⟨8357341420688498524193643850,8357341420688498524879424771⟩⟩,⟨⟨10966065236024010113952638733,10966065236024010114428816138⟩,⟨8027716911884367587293742196,8027716911884367587951518893⟩⟩,⟨⟨10509089791589342672729504081,10509089791589342673187259369⟩,⟨7693187668746822674136068315,7693187668746822674767474563⟩⟩,⟨⟨10055817204924139265805780696,10055817204924139266241997314⟩,⟨7361369105629726598950924671,7361369105629726599553783397⟩⟩,⟨⟨9595486376480452818518527960,9595486376480452818935705359⟩,⟨7024383550918675625351914805,7024383550918675625927856726⟩⟩,⟨⟨9139537335716977438077623661,9139537335716977438475957321⟩,⟨6690605687417518520684389205,6690605687417518521233680966⟩⟩,⟨⟨8676073767988110570194037029,8676073767988110570570592705⟩,⟨6351326808382848472801386342,6351326808382848473321668054⟩⟩,⟨⟨8217786023128097380638118057,8217786023128097380995168349⟩,⟨6015836894659156223408427096,6015836894659156223901508351⟩⟩,⟨⟨7751395450698644995426148610,7751395450698644995763172618⟩,⟨5674415299469664647680488923,5674415299469664648145759936⟩⟩] +lemma amp3_14_14_eq : ∀ k : Fin 16, amp3_1Expr 4 14 k = amp3_14_14 k := by decide +kernel +noncomputable def amp3_14_15 : Fin 16 → CBox := ![⟨⟨7291131255199261819808351362,7291131255199261820125170266⟩,⟨5337478523459301576128858489,5337478523459301576566361087⟩⟩,⟨⟨6821992474173491748042015731,6821992474173491748338040763⟩,⟨4994045099947507907262130556,4994045099947507907671183512⟩⟩,⟨⟨6360151401061098850387061127,6360151401061098850662450609⟩,⟨4655953969407103785125657114,4655953969407103785506582088⟩⟩,⟨⟨5888398725213949358075838722,5888398725213949358331172529⟩,⟨4310607042080419205184328405,4310607042080419205537270434⟩⟩,⟨⟨5425441185469606814562409403,5425441185469606814797697531⟩,⟨3971698601240472640297908954,3971698601240472640623123336⟩⟩,⟨⟨4951131303068236857500266485,4951131303068236857714800700⟩,⟨3624479668790650543136225343,3624479668790650543432873534⟩⟩,⟨⟨4487625400817782326345880937,4487625400817782326539799717⟩,⟨3285169798735264204286526753,3285169798735264204555014747⟩⟩,⟨⟨4010668238177036632576212303,4010668238177036632749804285⟩,⟨2936012922648345968274122711,2936012922648345968514282543⟩⟩,⟨⟨3547394144058060913790883065,3547394144058060913944122335⟩,⟨2596872747922809726505044240,2596872747922809726717242737⟩⟩,⟨⟨3067387839274413925622646446,3067387839274413925754938396⟩,⟨2245483744867788300877022070,2245483744867788301060352180⟩⟩,⟨⟨2605610421927042946706349352,2605610421927042946818357115⟩,⟨1907439213581574889045193694,1907439213581574889200654832⟩⟩,⟨⟨2121361682949658354747743303,2121361682949658354838699855⟩,⟨1552944533148970031734128538,1552944533148970031860525620⟩⟩,⟨⟨1663741155941996025434525674,1663741155941996025505394176⟩,⟨1217943056792915601515014509,1217943056792915601613803405⟩⟩,⟨⟨1171344964628820879926105157,1171344964628820879975704283⟩,⟨857484027298266333860988893,857484027298266333930324305⟩⟩,⟨⟨726611995767906115075861325,726611995767906115105637076⟩,⟨531916898291129321830842133,531916898291129321873126483⟩⟩,⟨⟨206433418803638677619696514,206433418803638677627559241⟩,⟨151119750944407953068355965,151119750944407953079932317⟩⟩] +lemma amp3_14_15_eq : ∀ k : Fin 16, amp3_1Expr 4 15 k = amp3_14_15 k := by decide +kernel +noncomputable def amp3_14 : Fin 16 → Fin 16 → CBox := ![amp3_14_0,amp3_14_1,amp3_14_2,amp3_14_3,amp3_14_4,amp3_14_5,amp3_14_6,amp3_14_7,amp3_14_8,amp3_14_9,amp3_14_10,amp3_14_11,amp3_14_12,amp3_14_13,amp3_14_14,amp3_14_15] +lemma amp3_14_eq (i k : Fin 16) : amp3_1Expr 4 i k = amp3_14 i k := by + fin_cases i + · exact amp3_14_0_eq k + · exact amp3_14_1_eq k + · exact amp3_14_2_eq k + · exact amp3_14_3_eq k + · exact amp3_14_4_eq k + · exact amp3_14_5_eq k + · exact amp3_14_6_eq k + · exact amp3_14_7_eq k + · exact amp3_14_8_eq k + · exact amp3_14_9_eq k + · exact amp3_14_10_eq k + · exact amp3_14_11_eq k + · exact amp3_14_12_eq k + · exact amp3_14_13_eq k + · exact amp3_14_14_eq k + · exact amp3_14_15_eq k +noncomputable def amp3_15_0 : Fin 16 → CBox := ![⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩] +lemma amp3_15_0_eq : ∀ k : Fin 16, amp3_1Expr 5 0 k = amp3_15_0 k := by decide +kernel +noncomputable def amp3_15_1 : Fin 16 → CBox := ![⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩] +lemma amp3_15_1_eq : ∀ k : Fin 16, amp3_1Expr 5 1 k = amp3_15_1 k := by decide +kernel +noncomputable def amp3_15_2 : Fin 16 → CBox := ![⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩] +lemma amp3_15_2_eq : ∀ k : Fin 16, amp3_1Expr 5 2 k = amp3_15_2 k := by decide +kernel +noncomputable def amp3_15_3 : Fin 16 → CBox := ![⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩] +lemma amp3_15_3_eq : ∀ k : Fin 16, amp3_1Expr 5 3 k = amp3_15_3 k := by decide +kernel +noncomputable def amp3_15_4 : Fin 16 → CBox := ![⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩] +lemma amp3_15_4_eq : ∀ k : Fin 16, amp3_1Expr 5 4 k = amp3_15_4 k := by decide +kernel +noncomputable def amp3_15_5 : Fin 16 → CBox := ![⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩] +lemma amp3_15_5_eq : ∀ k : Fin 16, amp3_1Expr 5 5 k = amp3_15_5 k := by decide +kernel +noncomputable def amp3_15_6 : Fin 16 → CBox := ![⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩] +lemma amp3_15_6_eq : ∀ k : Fin 16, amp3_1Expr 5 6 k = amp3_15_6 k := by decide +kernel +noncomputable def amp3_15_7 : Fin 16 → CBox := ![⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩] +lemma amp3_15_7_eq : ∀ k : Fin 16, amp3_1Expr 5 7 k = amp3_15_7 k := by decide +kernel +noncomputable def amp3_15_8 : Fin 16 → CBox := ![⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩] +lemma amp3_15_8_eq : ∀ k : Fin 16, amp3_1Expr 5 8 k = amp3_15_8 k := by decide +kernel +noncomputable def amp3_15_9 : Fin 16 → CBox := ![⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩] +lemma amp3_15_9_eq : ∀ k : Fin 16, amp3_1Expr 5 9 k = amp3_15_9 k := by decide +kernel +noncomputable def amp3_15_10 : Fin 16 → CBox := ![⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩] +lemma amp3_15_10_eq : ∀ k : Fin 16, amp3_1Expr 5 10 k = amp3_15_10 k := by decide +kernel +noncomputable def amp3_15_11 : Fin 16 → CBox := ![⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩] +lemma amp3_15_11_eq : ∀ k : Fin 16, amp3_1Expr 5 11 k = amp3_15_11 k := by decide +kernel +noncomputable def amp3_15_12 : Fin 16 → CBox := ![⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩] +lemma amp3_15_12_eq : ∀ k : Fin 16, amp3_1Expr 5 12 k = amp3_15_12 k := by decide +kernel +noncomputable def amp3_15_13 : Fin 16 → CBox := ![⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩] +lemma amp3_15_13_eq : ∀ k : Fin 16, amp3_1Expr 5 13 k = amp3_15_13 k := by decide +kernel +noncomputable def amp3_15_14 : Fin 16 → CBox := ![⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩] +lemma amp3_15_14_eq : ∀ k : Fin 16, amp3_1Expr 5 14 k = amp3_15_14 k := by decide +kernel +noncomputable def amp3_15_15 : Fin 16 → CBox := ![⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩] +lemma amp3_15_15_eq : ∀ k : Fin 16, amp3_1Expr 5 15 k = amp3_15_15 k := by decide +kernel +noncomputable def amp3_15 : Fin 16 → Fin 16 → CBox := ![amp3_15_0,amp3_15_1,amp3_15_2,amp3_15_3,amp3_15_4,amp3_15_5,amp3_15_6,amp3_15_7,amp3_15_8,amp3_15_9,amp3_15_10,amp3_15_11,amp3_15_12,amp3_15_13,amp3_15_14,amp3_15_15] +lemma amp3_15_eq (i k : Fin 16) : amp3_1Expr 5 i k = amp3_15 i k := by + fin_cases i + · exact amp3_15_0_eq k + · exact amp3_15_1_eq k + · exact amp3_15_2_eq k + · exact amp3_15_3_eq k + · exact amp3_15_4_eq k + · exact amp3_15_5_eq k + · exact amp3_15_6_eq k + · exact amp3_15_7_eq k + · exact amp3_15_8_eq k + · exact amp3_15_9_eq k + · exact amp3_15_10_eq k + · exact amp3_15_11_eq k + · exact amp3_15_12_eq k + · exact amp3_15_13_eq k + · exact amp3_15_14_eq k + · exact amp3_15_15_eq k +noncomputable def amp3_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp3_10,amp3_11,amp3_12,amp3_13,amp3_14,amp3_15] +lemma amp3_1_eq (j : Fin 6) (i k : Fin 16) : amp3_1Expr j i k = amp3_1 j i k := by + fin_cases j + · exact amp3_10_eq i k + · exact amp3_11_eq i k + · exact amp3_12_eq i k + · exact amp3_13_eq i k + · exact amp3_14_eq i k + · exact amp3_15_eq i k +lemma amp3_1_contains (j : Fin 6) (i k : Fin 16) : + (amp3_1 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude true 3 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp3_1_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 3 j) (bLookup_contains 3 j) true) +noncomputable def amp4_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 4 j) (bLookup 4 j) false) +noncomputable def amp4_00_0 : Fin 16 → CBox := ![⟨⟨378311542062827993378771716,378311542062827993491113088⟩,⟨(-280818959643395448722507762),(-280818959643395448621882354)⟩⟩,⟨⟨1331666599228979130028161315,1331666599228979130427427901⟩,⟨(-988362551579579482946375602),(-988362551579579482589340287)⟩⟩,⟨⟨2146962531497788175538645192,2146962531497788176185200501⟩,⟨(-1593063641956354777014590518),(-1593063641956354776436874259)⟩⟩,⟨⟨3049969189616626461810074290,3049969189616626462729151724⟩,⟨(-2262225812854807899790345833),(-2262225812854807898969252749)⟩⟩,⟨⟨3889714875854835023479841869,3889714875854835024652743140⟩,⟨(-2883593774158631961845928084),(-2883593774158631960798260226)⟩⟩,⟨⟨4778913502483939792391163767,4778913502483939793832236151⟩,⟨(-3540505553352508841914764303),(-3540505553352508840627674441)⟩⟩,⟨⟨5627665378449837345864288370,5627665378449837347561409947⟩,⟨(-4166085584841394395697926950),(-4166085584841394394182319302)⟩⟩,⟨⟨6510766371253528027762640395,6510766371253528029725601914⟩,⟨(-4815483346992079748694393250),(-4815483346992079746941515819)⟩⟩,⟨⟨7364201298529060706714183674,7364201298529060708933881876⟩,⟨(-5441083017277562735899214939),(-5441083017277562733917262957)⟩⟩,⟨⟨8243940560523596548839160614,8243940560523596551321942814⟩,⟨(-6084019434821486147075125229),(-6084019434821486144858289707)⟩⟩,⟨⟨9100286616793075456212121674,9100286616793075458952043185⟩,⟨(-6707350587306729156681401102),(-6707350587306729154235275192)⟩⟩,⟨⟨9977942994475396344657736196,9977942994475396347660059388⟩,⟨(-7343808658336446106786245314),(-7343808658336446104106079245)⟩⟩,⟨⟨10836308992460680809202134349,10836308992460680812460058525⟩,⟨(-7963250310596706818983335387),(-7963250310596706816075183440)⟩⟩,⟨⟨11712581613479463384501762188,11712581613479463388019337700⟩,⟨(-8592797556414290802364013401),(-8592797556414290799224200194)⟩⟩,⟨⟨12572455852226421908442225367,12572455852226421912215686865⟩,⟨(-9207026715255997827584379581),(-9207026715255997824216614855)⟩⟩,⟨⟨13447764927121316311878299520,13447764927121316315911241234⟩,⟨(-9829041362201440439360422257),(-9829041362201440435761510962)⟩⟩] +lemma amp4_00_0_eq : ∀ k : Fin 16, amp4_0Expr 0 0 k = amp4_00_0 k := by decide +kernel +noncomputable def amp4_00_1 : Fin 16 → CBox := ![⟨⟨14308822311873111076742461143,14308822311873111081029438518⟩,⟨(-10436892708345744394729535317),(-10436892708345744390904338030)⟩⟩,⟨⟨15183434235972487696852427187,15183434235972487701395834892⟩,⟨(-11050659397441600065790479748),(-11050659397441600061736790159)⟩⟩,⟨⟨16045448831436297200507859359,16045448831436297205302722765⟩,⟨(-11651063188190215526763033582),(-11651063188190215522485304765)⟩⟩,⟨⟨16919535355801448298784138424,16919535355801448303836916598⟩,⟨(-12255819690029389629667383243),(-12255819690029389625160557647)⟩⟩,⟨⟨17782335736979317987523504247,17782335736979317992825017350⟩,⟨(-12847771376303458642117558409),(-12847771376303458637389093060)⟩⟩,⟨⟨18656004585714032498607413012,18656004585714032504159877335⟩,⟨(-13442734050447643214556380562),(-13442734050447643209604371731)⟩⟩,⟨⟨19519448836556444544405466939,19519448836556444550209972429⟩,⟨(-14025278416402922421710275806),(-14025278416402922416534729162)⟩⟩,⟨⟨20392760588543402483995074316,20392760588543402490047350350⟩,⟨(-14609657408285129586016534128),(-14609657408285129580620291052)⟩⟩,⟨⟨21256721204025116436978374280,21256721204025116443279655969⟩,⟨(-15181879993059881253096564173),(-15181879993059881247479518532)⟩⟩,⟨⟨22129699016728950109715965067,22129699016728950116268615789⟩,⟨(-15754889044419873616272775415),(-15754889044419873610433084609)⟩⟩,⟨⟨22994053180899398034539522948,22994053180899398041332461499⟩,⟨(-16315911478453393619000691076),(-16315911478453393612947020119)⟩⟩,⟨⟨23866688543885904274901230064,23866688543885904281942200102⟩,⟨(-16876774711011986285611502149),(-16876774711011986279338241761)⟩⟩,⟨⟨24731311510389197927875943657,24731311510389197935152300761⟩,⟨(-17425752272733752569823752284),(-17425752272733752563340615296)⟩⟩,⟨⟨25603567686077201652754851663,25603567686077201660279097131⟩,⟨(-17973709169137016181809144412),(-17973709169137016175107260561)⟩⟩,⟨⟨26468328045561050642621203675,26468328045561050650385686614⟩,⟨(-18509829653360925943911926954),(-18509829653360925936997473372)⟩⟩,⟨⟨27340142110550102086601080088,27340142110550102094608046841⟩,⟨(-19044138907209704665124861822),(-19044138907209704657996269525)⟩⟩] +lemma amp4_00_1_eq : ∀ k : Fin 16, amp4_0Expr 0 1 k = amp4_00_1 k := by decide +kernel +noncomputable def amp4_00_2 : Fin 16 → CBox := ![⟨⟨28204898260586856217312539107,28204898260586856225547651566⟩,⟨(-19566622291115746828151845898),(-19566622291115746820819889005)⟩⟩,⟨⟨29076182276017907750217136360,29076182276017907758693061084⟩,⟨(-20086564912406391959776265915),(-20086564912406391952232185375)⟩⟩,⟨⟨29940779691262844412969338610,29940779691262844421680782387⟩,⟨(-20594663514638012997230269813),(-20594663514638012989478558358)⟩⟩,⟨⟨30811421321048063674235737542,30811421321048063683184057346⟩,⟨(-21099545421570495257217390939),(-21099545421570495249257218966)⟩⟩,⟨⟨31675690378430352249468387660,31675690378430352258652162394⟩,⟨(-21592544366820899018276403018),(-21592544366820899010109607105)⟩⟩,⟨⟨32545553154869964854894229551,32545553154869964864294786730⟩,⟨(-22081698606609540015662562264),(-22081698606609540007301978407)⟩⟩,⟨⟨33409307359673668450354934236,33409307359673668459984812347⟩,⟨(-22558916475928545990660352221),(-22558916475928545982098295596)⟩⟩,⟨⟨34278230725412291624928588335,34278230725412291634785056637⟩,⟨(-23031705165133992410004288538),(-23031705165133992401242789349)⟩⟩,⟨⟨35141265238770782229335876194,35141265238770782239418142851⟩,⟨(-23492494753040581288031459126),(-23492494753040581279071938072)⟩⟩,⟨⟨36009064450886533003130218626,36009064450886533013438493825⟩,⟨(-23948310796182392942783081120),(-23948310796182392933625639783)⟩⟩,⟨⟨36871154853038013019926740688,36871154853038013030457555165⟩,⟨(-24392059921062462120789169785),(-24392059921062462111437041564)⟩⟩,⟨⟨37737620807858560757546850262,37737620807858560768278085074⟩,⟨(-24830328546372219506783271650),(-24830328546372219497251300972)⟩⟩,⟨⟨38598522052996473283575299574,38598522052996473294528769172⟩,⟨(-25256460876888086323114766013),(-25256460876888086313389487432)⟩⟩,⟨⟨39463421072625266666585741975,39463421072625266677757304919⟩,⟨(-25676641015292465006878433844),(-25676641015292464996962903223)⟩⟩,⟨⟨40322866605140757560991853380,40322866605140757572381083830⟩,⟨(-26084616886204301245157687978),(-26084616886204301235053174833)⟩⟩,⟨⟨41185940214987332200052283237,41185940214987332211650669585⟩,⟨(-26486202411263563027063211060),(-26486202411263563016775593245)⟩⟩] +lemma amp4_00_2_eq : ∀ k : Fin 16, amp4_0Expr 0 2 k = amp4_00_2 k := by decide +kernel +noncomputable def amp4_00_3 : Fin 16 → CBox := ![⟨⟨42043641226155267997075163662,42043641226155268008884223145⟩,⟨(-26875519609251160958533977852),(-26875519609251160948063273932)⟩⟩,⟨⟨42904605944822856756415137076,42904605944822856768434793671⟩,⟨(-27258040450207141520536952204),(-27258040450207141509883637988)⟩⟩,⟨⟨43760250755218848578255878423,43760250755218848590483507960⟩,⟨(-27628234955237454803453230799),(-27628234955237454792620026581)⟩⟩,⟨⟨44618797912588186049075968000,44618797912588186061472944629⟩,⟨(-27991258091564023358126867478),(-27991258091564023347138491585)⟩⟩,⟨⟨45472051469783390766633383191,45472051469783390779236549282⟩,⟨(-28341904762848345339509051178),(-28341904762848345328343338463)⟩⟩,⟨⟨46327847065219614773911285614,46327847065219614786716051509⟩,⟨(-28685035106133977561193395215),(-28685035106133977549853739527)⟩⟩,⟨⟨47178350549239536330647656325,47178350549239536343650317118⟩,⟨(-29015748304245134037642071819),(-29015748304245134026131879887)⟩⟩,⟨⟨48031035159014761740149186220,48031035159014761753346692479⟩,⟨(-29338629471481362467906466234),(-29338629471481362456228168937)⟩⟩,⟨⟨48878405690090595135520229954,48878405690090595148911497322⟩,⟨(-29649063610068885743092918169),(-29649063610068885731248319329)⟩⟩,⟨⟨49727594431017382774717672580,49727594431017382788291866306⟩,⟨(-29951378591216227311931429954),(-29951378591216227299927672810)⟩⟩,⟨⟨50571424875580975777204140603,50571424875580975790966955202⟩,⟨(-30241228613171176491227782573),(-30241228613171176479062579371)⟩⟩,⟨⟨51416707430266351701369689145,51416707430266351715315654583⟩,⟨(-30522700335057660496285559909),(-30522700335057660483962819104)⟩⟩,⟨⟨52256566302127791377821059197,52256566302127791391948521996⟩,⟨(-30791702109075164751311127453),(-30791702109075164738833020876)⟩⟩,⟨⟨53097507010032401748720665704,53097507010032401763027519279⟩,⟨(-31052093897138619178999842394),(-31052093897138619166368287786)⟩⟩,⟨⟨53932938464358250322560434962,53932938464358250337044152504⟩,⟨(-31300024531497769256561653123),(-31300024531497769243779358759)⟩⟩,⟨⟨54769076481877509086498427017,54769076481877509101156681754⟩,⟨(-31539140470534109152127747982),(-31539140470534109139196789618)⟩⟩] +lemma amp4_00_3_eq : ∀ k : Fin 16, amp4_0Expr 0 3 k = amp4_00_3 k := by decide +kernel +noncomputable def amp4_00_4 : Fin 16 → CBox := ![⟨⟨55599600400044430272958562926,55599600400044430287728847230⟩,⟨(-31765818541624915226035065859),(-31765818541624915212992437953)⟩⟩,⟨⟨56430449932046836982682615310,56430449932046836997631720426⟩,⟨(-31983503736496996985893835366),(-31983503736496996972701916618)⟩⟩,⟨⟨57255562095740320687308531217,57255562095740320702430779701⟩,⟨(-32188789430216819436578915313),(-32188789430216819423242297414)⟩⟩,⟨⟨58080612700352613167860531751,58080612700352613183151612133⟩,⟨(-32384930167374050216171546733),(-32384930167374050202693519011)⟩⟩,⟨⟨58899785053456634280290203342,58899785053456634295745990071⟩,⟨(-32568725332022144166383543090),(-32568725332022144152767782670)⟩⟩,⟨⟨59718502021340807275123214738,59718502021340807290743710117⟩,⟨(-32743249142652864314425655353),(-32743249142652864300673059973)⟩⟩,⟨⟨60531183018252352418132431031,60531183018252352433908266820⟩,⟨(-32905497252393420838641131212),(-32905497252393420824758234397)⟩⟩,⟨⟨61343007827150606221744863440,61343007827150606237677990791⟩,⟨(-33058372878060483783683208906),(-33058372878060483769669868081)⟩⟩,⟨⟨62148622866175471725814916848,62148622866175471741903091248⟩,⟨(-33199058906417518833914538005),(-33199058906417518819773414412)⟩⟩,⟨⟨62952973711087682689879537793,62952973711087682706102423924⟩,⟨(-33330296168098077487018176345),(-33330296168098077472761033912)⟩⟩,⟨⟨63750925651547277105250656225,63750925651547277121624026979⟩,⟨(-33449446371301043498009952382),(-33449446371301043483629846044)⟩⟩,⟨⟨64547198050538409948398005954,64547198050538409964916188900⟩,⟨(-33559095942853610782633844720),(-33559095942853610768134777893)⟩⟩,⟨⟨65336867812153771327870254446,65336867812153771344531810636⟩,⟨(-33656777553178897453823822088),(-33656777553178897439208054956)⟩⟩,⟨⟨66124435287456140995698371947,66124435287456141012493934777⟩,⟨(-33744930640386218792077365963),(-33744930640386218777350756753)⟩⟩,⟨⟨66905182530484269059026503214,66905182530484269075960023297⟩,⟨(-33821251469942742899531959338),(-33821251469942742884694009730)⟩⟩,⟨⟨67683397364254630705576509128,67683397364254630722641195639⟩,⟨(-33888039396421746768317729282),(-33888039396421746753372966264)⟩⟩] +lemma amp4_00_4_eq : ∀ k : Fin 16, amp4_0Expr 0 4 k = amp4_00_4 k := by decide +kernel +noncomputable def amp4_00_5 : Fin 16 → CBox := ![⟨⟨68454561248740610746048927933,68454561248740610763243401770⟩,⟨(-33943147352112959462256303043),(-33943147352112959447206977104)⟩⟩,⟨⟨69222755312549499241994777147,69222755312549499259316373213⟩,⟨(-33988741053538277644854539569),(-33988741053538277629703096449)⟩⟩,⟨⟨69983655334931225527679091100,69983655334931225545126316594⟩,⟨(-34022823564201310987236337451),(-34022823564201310971985111274)⟩⟩,⟨⟨70741140991797938931613338872,70741140991797938949183030414⟩,⟨(-34047432992452848350694851507),(-34047432992452848335346564655)⟩⟩,⟨⟨71491077896962809037449582254,71491077896962809055139035096⟩,⟨(-34060716349430478767259530327),(-34060716349430478751817129560)⟩⟩,⟨⟨72237148974501104269734186012,72237148974501104287414913786⟩,⟨(-34064589788445292330981028501),(-34064589788445292315506334961)⟩⟩,⟨⟨72975405741249243418762248571,72975405741249243436563384883⟩,⟨(-34057338401089569244912865579),(-34057338401089569229346073791)⟩⟩,⟨⟨73709338574254111145901134033,73709338574254111163816789417⟩,⟨(-34040761696371490604817656331),(-34040761696371490589162825330)⟩⟩,⟨⟨74435181471973219688831646533,74435181471973219706856221037⟩,⟨(-34013277264210434436252727861),(-34013277264210434420514174938)⟩⟩,⟨⟨75156236012556517640857695639,75156236012556517658988172692⟩,⟨(-33976572968125476026877504236),(-33976572968125476011057903877)⟩⟩,⟨⟨75868915726761529178598031928,75868915726761529196827830951⟩,⟨(-33929193571647001180906926419),(-33929193571647001165010971178)⟩⟩,⟨⟨76576336719932691814235273864,76576336719932691832561049087⟩,⟨(-33872720006806996596128230189),(-33872720006806996580158720849)⟩⟩,⟨⟨77275089544170907703030414015,77275089544170907721453065918⟩,⟨(-33805819119027701466882789500),(-33805819119027701450841080645)⟩⟩,⟨⟨77968107766557648946492166474,77968107766557648965002442627⟩,⟨(-33729969362237472579743603832),(-33729969362237472563635076535)⟩⟩,⟨⟨78652156858028397923686851153,78652156858028397942285321001⟩,⟨(-33643954783428495749009048117),(-33643954783428495732835199215)⟩⟩,⟨⟨79329990417240758861485786182,79329990417240758880170920073⟩,⟨(-33549155572841946475533560646),(-33549155572841946459296431803)⟩⟩] +lemma amp4_00_5_eq : ∀ k : Fin 16, amp4_0Expr 0 5 k = amp4_00_5 k := by decide +kernel +noncomputable def amp4_00_6 : Fin 16 → CBox := ![⟨⟨79998547113329202154349914495,79998547113329202173104377703⟩,⟨(-33444468290979898875354847015),(-33444468290979898859063515122)⟩⟩,⟨⟨80660402805288127025335560801,80660402805288127044173255814⟩,⟨(-33331178859276799395692456090),(-33331178859276799379342461014)⟩⟩,⟨⟨81312667998066685690282137034,81312667998066685709190976639⟩,⟨(-33208291838974914285970000034),(-33208291838974914269568139051)⟩⟩,⟨⟨81957742719445335920805067680,81957742719445335939790731527⟩,⟨(-33077002675531881655536863332),(-33077002675531881639082250148)⟩⟩,⟨⟨82592908285054303992971579132,82592908285054304012025831587⟩,⟨(-32936419578384960691455181032),(-32936419578384960674952992929)⟩⟩,⟨⟨83220390497816444441232199252,83220390497816444460354807931⟩,⟨(-32787651123570488548605855160),(-32787651123570488532057635345)⟩⟩,⟨⟨83837640777498492320352516451,83837640777498492339494630306⟩,⟨(-32629904963016883361577758896),(-32629904963016883345004393875)⟩⟩,⟨⟨84446712022363487004696337060,84446712022363487023904520708⟩,⟨(-32464206237890538544217637272),(-32464206237890538527602307455)⟩⟩,⟨⟨85045225351795677429038136458,85045225351795677448304477652⟩,⟨(-32289857971855168727347171117),(-32289857971855168710694830033)⟩⟩,⟨⟨85635061807313951470750910785,85635061807313951490070088002⟩,⟨(-32107805146694643162618556273),(-32107805146694643145932708881)⟩⟩,⟨⟨86214012090756224579691863981,86214012090756224599063248749⟩,⟨(-31917442211428757998428164136),(-31917442211428757981710917301)⟩⟩,⟨⟨86783786174542563203705111886,86783786174542563223120579819⟩,⟨(-31719637116644790290106947700),(-31719637116644790273362825113)⟩⟩,⟨⟨87342344500203965537868004775,87342344500203965557326856821⟩,⟨(-31513871905320657653956539115),(-31513871905320657637187676536)⟩⟩,⟨⟨87891226508748835860250785054,87891226508748835879753387865⟩,⟨(-31300940488448425348000659725),(-31300940488448425331208453622)⟩⟩,⟨⟨88428562801662577371955311441,88428562801662577391475752957⟩,⟨(-31080408778200190341810490169),(-31080408778200190325005975659)⟩⟩,⟨⟨88955722585023898038648771518,88955722585023898058204424683⟩,⟨(-30852999510776174659671496813),(-30852999510776174642850032870)⟩⟩] +lemma amp4_00_6_eq : ∀ k : Fin 16, amp4_0Expr 0 6 k = amp4_00_6 k := by decide +kernel +noncomputable def amp4_00_7 : Fin 16 → CBox := ![⟨⟨89471007293620074299268686903,89471007293620074318853634310⟩,⟨(-30618358842001581732435841591),(-30618358842001581715601399464)⟩⟩,⟨⟨89975615961189654853983798931,89975615961189654873598044061⟩,⟨(-30377141080246719430552898524),(-30377141080246719413707008656)⟩⟩,⟨⟨90468021773660573972685283616,90468021773660573992313117559⟩,⟨(-30129069092098045371653533982),(-30129069092098045354803351094)⟩⟩,⟨⟨90949253427100935863291152741,90949253427100935882939741696⟩,⟨(-29874731395430845538890395129),(-29874731395430845522035053925)⟩⟩,⟨⟨91417957013568803466280072739,91417957013568803485938482358⟩,⟨(-29613924121527062985177616308),(-29613924121527062968322592962)⟩⟩,⟨⟨91874990502927410896732384626,91874990502927410916406265759⟩,⟨(-29347172533023955878964826989),(-29347172533023955862109810426)⟩⟩,⟨⟨92319174279347974805267737303,92319174279347974824947772521⟩,⟨(-29074342661509663618305648990),(-29074342661509663601455489849)⟩⟩,⟨⟨92751194978277172125969624374,92751194978277172145653127753⟩,⟨(-28795898954513875390633435559),(-28795898954513875373790520919)⟩⟩,⟨⟨93170048887946097638088428725,93170048887946097657772557317⟩,⟨(-28511774056673731143453016753),(-28511774056673731126620121389)⟩⟩,⟨⟨93576250483888385765151630812,93576250483888385784834863593⟩,⟨(-28222373951828187659390731697),(-28222373951828187642569839991)⟩⟩,⟨⟨93968973792359875149459146832,93968973792359875169135220928⟩,⟨(-27927694683538314654451518198),(-27927694683538314637646370066)⟩⟩,⟨⟨94348560087499663873669247555,94348560087499663893336197844⟩,⟨(-27628086040582247224411547352),(-27628086040582247207624274217)⟩⟩,⟨⟨94714363186679370142996656048,94714363186679370162648414904⟩,⟨(-27323604320942228404425254580),(-27323604320942228387659499988)⟩⟩,⟨⟨95066549905414100944299378995,95066549905414100963932330045⟩,⟨(-27014545309665093324474265109),(-27014545309665093307732562967)⟩⟩,⟨⟨95404656122550905989937189293,95404656122550906009545739815⟩,⟨(-26701022481205605935306761758),(-26701022481205605918592497591)⟩⟩,⟨⟨95728672721196517270712493435,95728672721196517290290526680⟩,⟨(-26383279735995478173210450276),(-26383279735995478156526827180)⟩⟩] +lemma amp4_00_7_eq : ∀ k : Fin 16, amp4_0Expr 0 7 k = amp4_00_7 k := by decide +kernel +noncomputable def amp4_00_8 : Fin 16 → CBox := ![⟨⟨96038320128470408673610240105,96038320128470408693164979587⟩,⟨(-26061484710897266581156376185),(-26061484710897266564503254037)⟩⟩,⟨⟨96333411602888557757458433976,96333411602888557776997716092⟩,⟨(-25735831473353895767041286985),(-25735831473353895750418095911)⟩⟩,⟨⟨96613854823274779843295903965,96613854823274779862813380624⟩,⟨(-25406538870143562783749653302),(-25406538870143562767159996059)⟩⟩,⟨⟨96879283510092067006669697612,96879283510092067026160239494⟩,⟨(-25073753124248686437764236493),(-25073753124248686421211077775)⟩⟩,⟨⟨97129795515175046061682082926,97129795515175046081141745211⟩,⟨(-24737741399455656703053044968),(-24737741399455656686539310024)⟩⟩,⟨⟨97364842882257704871718980203,97364842882257704891142233262⟩,⟨(-24398604003804880053395122583),(-24398604003804880036923757328)⟩⟩,⟨⟨97584716777672036409676178767,97584716777672036429060904678⟩,⟨(-24056653583071829676145522454),(-24056653583071829659718879852)⟩⟩,⟨⟨97788685199523136190011176652,97788685199523136209351525014⟩,⟨(-23711946404673360908648036759),(-23711946404673360892269120611)⟩⟩,⟨⟨97977235993713229894131953430,97977235993713229913426173542⟩,⟨(-23364837817809415760786795963),(-23364837817809415744457886562)⟩⟩,⟨⟨98149450507473328221319231441,98149450507473328240565240729⟩,⟨(-23015341871945175872669404403),(-23015341871945175856392489053)⟩⟩,⟨⟨98306016859488166676505205493,98306016859488166695700241173⟩,⟨(-22663853896397280882158714353),(-22663853896397280865936225858)⟩⟩,⟨⟨98445826897244472649212390646,98445826897244472668347330473⟩,⟨(-22310347497021402265139232264),(-22310347497021402248974799527)⟩⟩,⟨⟨98569772839319364465259427260,98569772839319364484340406065⟩,⟨(-21955255314214504311510868894),(-21955255314214504295404910417)⟩⟩,⟨⟨98676553932462718214494412335,98676553932462718233510663989⟩,⟨(-21598512239333033184138436231),(-21598512239333033168094824408)⟩⟩,⟨⟨98767270563185905643303932512,98767270563185905662263548977⟩,⟨(-21240585608294173830706095052),(-21240585608294173814724805101)⟩⟩,⟨⟨98840426014599106781724369675,98840426014599106800611182991⟩,⟨(-20881373284727967369179867935),(-20881373284727967353265898137)⟩⟩] +lemma amp4_00_8_eq : ∀ k : Fin 16, amp4_0Expr 0 8 k = amp4_00_8 k := by decide +kernel +noncomputable def amp4_00_9 : Fin 16 → CBox := ![⟨⟨98897333158517595049039630758,98897333158517595067853777483⟩,⟨(-20521374737363146319980028603),(-20521374737363146304135107381)⟩⟩,⟨⟨98936295678432651035085738149,98936295678432651053821903275⟩,⟨(-20160452449243601372648653683),(-20160452449243601356875272654)⟩⟩,⟨⟨98958843508018617598193552499,98958843508018617616871672261⟩,⟨(-19799135511579469423306280236),(-19799135511579469407602103198)⟩⟩,⟨⟨98963076809444127010257715161,98963076809444127028849940097⟩,⟨(-19437252636863958065842569144),(-19437252636863958050214691294)⟩⟩,⟨⟨98950747425420686200710998620,98950747425420686219218061817⟩,⟨(-19075360080499176060479973882),(-19075360080499176044929930075)⟩⟩,⟨⟨98919747775113580436273394610,98919747775113580454695947079⟩,⟨(-18713254359720041988569979056),(-18713254359720041973099030371)⟩⟩,⟨⟨98872056741226453895116590590,98872056741226453913445853128⟩,⟨(-18351516487653670756085862451),(-18351516487653670740697267812)⟩⟩,⟨⟨98805354462264414158818248818,98805354462264414177054893721⟩,⟨(-17989912329031533162357913633),(-17989912329031533147052967930)⟩⟩,⟨⟨98721852290684114155776999985,98721852290684114173915306799⟩,⟨(-17629045299948293372640902942),(-17629045299948293357422301512)⟩⟩,⟨⟨98619013212785837638260825759,98619013212785837656293143513⟩,⟨(-17268652124907410033175658678),(-17268652124907410018046051542)⟩⟩,⟨⟨98499286796433229669772113875,98499286796433229687754185609⟩,⟨(-16909356319902288740448643380),(-16909356319902288725399953999)⟩⟩,⟨⟨98359913650272973186987099306,98359913650272973204863012199⟩,⟨(-16550866952923070462367357991),(-16550866952923070447410745498)⟩⟩,⟨⟨98203587638479469094920769272,98203587638479469112690892933⟩,⟨(-16193825388540794267312163682),(-16193825388540794252449139812)⟩⟩,⟨⟨98027321390349533905461036090,98027321390349533923117299349⟩,⟨(-15837914495172485321323262100),(-15837914495172485306556440936)⟩⟩,⟨⟨97834059504391608450294942035,97834059504391608467845045028⟩,⟨(-15483791286521092682547370074),(-15483791286521092667876974784)⟩⟩,⟨⟨97620580627681174490695161529,97620580627681174508126244804⟩,⟨(-15131113863256406175564626024),(-15131113863256406160994052427)⟩⟩] +lemma amp4_00_9_eq : ∀ k : Fin 16, amp4_0Expr 0 9 k = amp4_00_9 k := by decide +kernel +noncomputable def amp4_00_10 : Fin 16 → CBox := ![⟨⟨97390086912867344342914232406,97390086912867344360244083484⟩,⟨(-14780552740828819573895071439),(-14780552740828819559423140785)⟩⟩,⟨⟨97139116592947780549902179636,97139116592947780567111657725⟩,⟨(-14431742660412235122453043719),(-14431742660412235108083932182)⟩⟩,⟨⟨96871136604084608370090754962,96871136604084608387178953944⟩,⟨(-14085365544115665076444072467),(-14085365544115665062179302320)⟩⟩,⟨⟨96582437873319470361614602015,96582437873319470378584247049⟩,⟨(-13741034159718472483636451122),(-13741034159718472469476967075)⟩⟩,⟨⟨96276759790541569254674556811,96276759790541569271515031582⟩,⟨(-13399439793469008090002597202),(-13399439793469008075951360325)⟩⟩,⟨⟨95950138590273254134795282620,95950138590273254151509918153⟩,⟨(-13060174605017349714080966464),(-13060174605017349700138728137)⟩⟩,⟨⟨95606594262390733477715536985,95606594262390733494301247594⟩,⟨(-12723937255106552661080185067),(-12723937255106552647248691795)⟩⟩,⟨⟨95241900428894401732119077274,95241900428894401748569657673⟩,⟨(-12390300640894033499496811762),(-12390300640894033485778178546)⟩⟩,⟨⟨94860366341589850352646361590,94860366341589850368958944735⟩,⟨(-12059968861176121745828108685),(-12059968861176121732224088910)⟩⟩,⟨⟨94457494513127834901390925910,94457494513127834917560673877⟩,⟨(-11732496877730393762653683856),(-11732496877730393749166019090)⟩⟩,⟨⟨94037892679524014074804637830,94037892679524014090825075550⟩,⟨(-11408592344513062956451213067),(-11408592344513062943081892946)⟩⟩,⟨⟨93596783121779459635588500413,93596783121779459651630947676⟩,⟨(-11087793597516540853772709122),(-11087793597516540840502647074)⟩⟩,⟨⟨93139081893098735479585738712,93139081893098735495484060613⟩,⟨(-10770810016866029143711615383),(-10770810016866029130562240348)⟩⟩,⟨⟨92659721240414412426848233443,92659721240414412442601413511⟩,⟨(-10457164605754967830679328351),(-10457164605754967817651895030)⟩⟩,⟨⟨92163936034662120534794065889,92163936034662120550399240762⟩,⟨(-10147566695747042491817513622),(-10147566695747042478913481793)⟩⟩,⟨⟨91646357944657780210068411441,91646357944657780225526102228⟩,⟨(-9841525234431027354943128023),(-9841525234431027342163669294)⟩⟩] +lemma amp4_00_10_eq : ∀ k : Fin 16, amp4_0Expr 0 10 k = amp4_00_10 k := by decide +kernel +noncomputable def amp4_00_11 : Fin 16 → CBox := ![⟨⟨91112551891484927861266900007,91112551891484927876574755735⟩,⟨(-9539747784694594559767178043),(-9539747784694594547113788630)⟩⟩,⟨⟨90556837610772477103091082878,90556837610772477118250031401⟩,⟨(-9241730500650504860355327533),(-9241730500650504847828993698)⟩⟩,⟨⟨89985122110909477391804639142,89985122110909477406806909233⟩,⟨(-8948177511359966327665966566),(-8948177511359966315268531735)⟩⟩,⟨⟨89391400949767563548276891692,89391400949767563563130550409⟩,⟨(-8658573425161124306694076684),(-8658573425161124294425955123)⟩⟩,⟨⟨88781936147671460055394190045,88781936147671460070087768290⟩,⟨(-8373617327437889157008945985),(-8373617327437889144872370613)⟩⟩,⟨⟨88150385861677238784266255393,88150385861677238798800630361⟩,⟨(-8092783514580870344395604822),(-8092783514580870332391569512)⟩⟩,⟨⟨87503381030302004584880425243,87503381030302004599249204477⟩,⟨(-7816764474064052217771194706),(-7816764474064052205901224487)⟩⟩,⟨⟨86834228107044795684590288416,86834228107044795698818294422⟩,⟨(-7545025410752985487916568561),(-7545025410752985476179671335)⟩⟩,⟨⟨86149941943930302378242388624,86149941943930302392302633144⟩,⟨(-7278250715894759877313454403),(-7278250715894759865713063958)⟩⟩,⟨⟨85443461793045652408227567061,85443461793045652422119911748⟩,⟨(-7015897710236379099733498273),(-7015897710236379088270639454)⟩⟩,⟨⟨84722202627229175133965271286,84722202627229175147693986401⟩,⟨(-6758641246669239895742945116),(-6758641246669239884418114970)⟩⟩,⟨⟨83978719672087676246161234287,83978719672087676259715960331⟩,⟨(-6505931956521962212523229899),(-6505931956521962201338418588)⟩⟩,⟨⟨83220845581676824487530189930,83220845581676824500912279874⟩,⟨(-6258433768633704364865651221),(-6258433768633704353821643129)⟩⟩,⟨⟨82440733251133709757428616031,82440733251133709770635258149⟩,⟨(-6015591807141111069142624174),(-6015591807141111058240661059)⟩⟩,⟨⟨81646652091747448065451774763,81646652091747448078478225210⟩,⟨(-5778057747779290300452308137),(-5778057747779290289693445484)⟩⟩,⟨⟨80830332710398563821491601795,80830332710398563834332614794⟩,⟨(-5545272377403089918400929975),(-5545272377403089907786657837)⟩⟩] +lemma amp4_00_11_eq : ∀ k : Fin 16, amp4_0Expr 0 11 k = amp4_00_11 k := by decide +kernel +noncomputable def amp4_00_12 : Fin 16 → CBox := ![⟨⟨80000502055091529484788347004,80000502055091529497542726187⟩,⟨(-5317873846414489127937122491),(-5317873846414489117461669193)⟩⟩,⟨⟨79148446630478481502870413229,79148446630478481515450572030⟩,⟨(-5095299762064869347066842750),(-5095299762064869336737214113)⟩⟩,⟨⟨78283373622223876842780686352,78283373622223876855184723429⟩,⟨(-4878173534157658313508994800),(-4878173534157658303325936300)⟩⟩,⟨⟨77396101527372456279237021592,77396101527372456291464384937⟩,⟨(-4665930735800409126375786197),(-4665930735800409116340496160)⟩⟩,⟨⟨76496342645704898936372597622,76496342645704898948421530010⟩,⟨(-4459178877997746735217226640),(-4459178877997746725330492739)⟩⟩,⟨⟨75574421195248408627084021845,75574421195248408638955417795⟩,⟨(-4257352632898190141548791663),(-4257352632898190131811608676)⟩⟩,⟨⟨74640581939279942141825299069,74640581939279942153512433486⟩,⟨(-4061042511632516495412394928),(-4061042511632516485825634142)⟩⟩,⟨⟨73684625857188758857483171810,73684625857188758868997873034⟩,⟨(-3869683406176638914324062757),(-3869683406176638904888260434)⟩⟩,⟨⟨72717360347935638415506960475,72717360347935638426834168032⟩,⟨(-3683847783854369408443268599),(-3683847783854369399159810229)⟩⟩,⟨⟨71728031124513723021249607756,71728031124513723032391111451⟩,⟨(-3502971864668152949558768480),(-3502971864668152940428568293)⟩⟩,⟨⟨70728041630345612348665280280,70728041630345612359617785155⟩,⟨(-3327609085315448679853989469),(-3327609085315448670877556989)⟩⟩,⟨⟨69706046765619109351079116134,69706046765619109361840253236⟩,⟨(-3157198089184767477925311070),(-3157198089184767469103926107)⟩⟩,⟨⟨68674083155717387047057615812,68674083155717387057621468606⟩,⟨(-2992272352567045743092467623),(-2992272352567045734426779120)⟩⟩,⟨⟨67620175285568061749444525443,67620175285568061759871442977⟩,⟨(-2832274024443162829839784988),(-2832274024443162821328307138)⟩⟩,⟨⟨66557034417628224684301421557,66557034417628224694533128955⟩,⟨(-2677715747834554779235647009),(-2677715747834554770881107020)⟩⟩,⟨⟨65472010317928385320797148889,65472010317928385330832907787⟩,⟨(-2528044245994749684981784909),(-2528044245994749676785403939)⟩⟩] +lemma amp4_00_12_eq : ∀ k : Fin 16, amp4_0Expr 0 12 k = amp4_00_12 k := by decide +kernel +noncomputable def amp4_00_13 : Fin 16 → CBox := ![⟨⟨64378535368065489520152686878,64378535368065489529993327707⟩,⟨(-2383750512559332018256499994),(-2383750512559332010218525536)⟩⟩,⟨⟨63263234830527651832858815549,63263234830527651842510277387⟩,⟨(-2244286899779031625266092220),(-2244286899779031617387366528)⟩⟩,⟨⟨62140314575590477614953989409,62140314575590477624403957696⟩,⟨(-2110121992313872816054715830),(-2110121992313872808335716561)⟩⟩,⟨⟨60995619146876161664944698726,60995619146876161674195879540⟩,⟨(-1980714811696364923172077783),(-1980714811696364915613946181)⟩⟩,⟨⟨59844187212359458886255061939,59844187212359458895301699725⟩,⟨(-1856510830277743885687684449),(-1856510830277743878290666095)⟩⟩,⟨⟨58671018784936478607937856613,58671018784936478616818177515⟩,⟨(-1736976764180635346571673520),(-1736976764180635339335772640)⟩⟩,⟨⟨57492052875717392043511258652,57492052875717392052190993371⟩,⟨(-1622534326049713411707291701),(-1622534326049713404633430933)⟩⟩,⟨⟨56291372114626450541781467826,56291372114626450550258511283⟩,⟨(-1512658936344256483728933466),(-1512658936344256476818472323)⟩⟩,⟨⟨55085893251315210126024478746,55085893251315210134299705984⟩,⟨(-1407747956167503328268702948),(-1407747956167503321521529036)⟩⟩,⟨⟨53858697834819218655037640523,53858697834819218663113401679⟩,⟨(-1307286503868251441076938025),(-1307286503868251434494188179)⟩⟩,⟨⟨52627769626328846107047217885,52627769626328846114919669655⟩,⟨(-1211647052311521198790129612),(-1211647052311521192371567449)⟩⟩,⟨⟨51375092269471411814648137461,51375092269471411822341117245⟩,⟨(-1120325394419977584920745411),(-1120325394419977578667239965)⟩⟩,⟨⟨50119820263601198822571243253,50119820263601198830054813066⟩,⟨(-1033668632783766792897887984),(-1033668632783766786809782415)⟩⟩,⟨⟨48842726480580325907940469493,48842726480580325915215920418⟩,⟨(-951184194001238316335549620),(-951184194001238310414139401)⟩⟩,⟨⟨47564257650757907181061226788,47564257650757907188130988879⟩,⟨(-873193382478778132923142830),(-873193382478778127167822126)⟩⟩,⟨⟨46263843192459105091389380960,46263843192459105098248334226⟩,⟨(-799216199261019387925574428),(-799216199261019382337936046)⟩⟩] +lemma amp4_00_13_eq : ∀ k : Fin 16, amp4_0Expr 0 13 k = amp4_00_13 k := by decide +kernel +noncomputable def amp4_00_14 : Fin 16 → CBox := ![⟨⟨44963365643193229005784465285,44963365643193229012453318661⟩,⟨(-729547776200882347018037203),(-729547776200882341597198200)⟩⟩,⟨⟨43640753516496572728317445824,43640753516496572734776390034⟩,⟨(-663721610450788544501963924),(-663721610450788539249692275)⟩⟩,⟨⟨42319496527379578947283946059,42319496527379578953536511851⟩,⟨(-602006339832014252400353414),(-602006339832014247315781329)⟩⟩,⟨⟨40975833456671023113402156704,40975833456671023119439328163⟩,⟨(-543949859357081184767740778),(-543949859357081179852652000)⟩⟩,⟨⟨39635068043190852234556059706,39635068043190852240398074422⟩,⟨(-489794043517787822144428221),(-489794043517787817397693083)⟩⟩,⟨⟨38271520160944685272571233779,38271520160944685278200920220⟩,⟨(-439102066216815583989955833),(-439102066216815579413460335)⟩⟩,⟨⟨36912560424497651081264875024,36912560424497651086694479455⟩,⟨(-392088820717132350896820335),(-392088820717132346489306755)⟩⟩,⟨⟨35530307857230846711685192690,35530307857230846716900034290⟩,⟨(-348333619306281090820633667),(-348333619306281086584139094)⟩⟩,⟨⟨34154513553232396882976604532,34154513553232396887979572148⟩,⟨(-308024206653351165757097985),(-308024206653351161690392771)⟩⟩,⟨⟨32754743364966791657468454280,32754743364966791662265634326⟩,⟨(-270756870595871616751695603),(-270756870595871612856631158)⟩⟩,⟨⟨31363524387602547693932926475,31363524387602547698515888007⟩,⟨(-236692089412541810156771860),(-236692089412541806431907444)⟩⟩,⟨⟨29947420983976246641437203154,29947420983976246645811821193⟩,⟨(-205443940580299418561608999),(-205443940580299415009084479)⟩⟩,⟨⟨28542244950103857903842007861,28542244950103857908010318678⟩,⟨(-177145566659373587972571197),(-177145566659373584590700299)⟩⟩,⟨⟨27110976386795096435049017539,27110976386795096438999838864⟩,⟨(-151429625129291873114406092),(-151429625129291869905570794)⟩⟩,⟨⟨25693381412495025247488113049,25693381412495025251230281736⟩,⟨(-128401900680338311779866706),(-128401900680338308741985035)⟩⟩,⟨⟨24248078776185217398967456745,24248078776185217402497038771⟩,⟨(-107714396958163731198889196),(-107714396958163728334625295)⟩⟩] +lemma amp4_00_14_eq : ∀ k : Fin 16, amp4_0Expr 0 14 k = amp4_00_14 k := by decide +kernel +noncomputable def amp4_00_15 : Fin 16 → CBox := ![⟨⟨22819695353392487775808141415,22819695353392487779126528966⟩,⟨(-89445564220051468683901473),(-89445564220051465990963687)⟩⟩,⟨⟨21361419760645051437794497676,21361419760645051440897352004⟩,⟨(-73267494093875804722365451),(-73267494093875802203645942)⟩⟩,⟨⟨19924009505566803116816448531,19924009505566803119706659994⟩,⟨(-59231369344202458425956826),(-59231369344202456078655953)⟩⟩,⟨⟨18453695453727093462699248342,18453695453727093465375693714⟩,⟨(-47030087516273335508693266),(-47030087516273333336198535)⟩⟩,⟨⟨17009223442553061766297005385,17009223442553061768762534591⟩,⟨(-36687671334739436574629057),(-36687671334739434573653175)⟩⟩,⟨⟨15527573120279843513207057665,15527573120279843515456072033⟩,⟨(-27918520002247789951804933),(-27918520002247788126262053)⟩⟩,⟨⟨14078353508990555871228475615,14078353508990555873264900788⟩,⟨(-20719639371979334238328772),(-20719639371979332584156778)⟩⟩,⟨⟨12585618000455526852576061222,12585618000455526854396678549⟩,⟨(-14827608142347009222535596),(-14827608142347007744503207)⟩⟩,⟨⟨11134640317483545320743928365,11134640317483545322353013904⟩,⟨(-10212585393443975000582080),(-10212585393443973693624287)⟩⟩,⟨⟨9630099532377512377356987609,9630099532377512378747523234⟩,⟨(-6633999710382995492953159),(-6633999710382994363039867)⟩⟩,⟨⟨8181883550284142957797479756,8181883550284142958977378100⟩,⟨(-4035341697483126987746135),(-4035341697483126028110123)⟩⟩,⟨⟨6662337732184249128098865478,6662337732184249129058667877⟩,⟨(-2199579725058595283654659),(-2199579725058594502462398)⟩⟩,⟨⟨5225792715938785249885374961,5225792715938785250636579957⟩,⟨(-1043675318613417939631129),(-1043675318613417327054134)⟩⟩,⟨⟨3679527966689603314110950474,3679527966689603314638877930⟩,⟨(-374922150676004509125174),(-374922150676004077876550)⟩⟩,⟨⟨2282638338302584531511547311,2282638338302584531835898510⟩,⟨(-83730397008744628120179),(-83730397008744360628618)⟩⟩,⟨⟨648527168554654566854303322,648527168554654566944576807⟩,⟨(-2643193656450865211327),(-2643193656450789217675)⟩⟩] +lemma amp4_00_15_eq : ∀ k : Fin 16, amp4_0Expr 0 15 k = amp4_00_15 k := by decide +kernel +noncomputable def amp4_00 : Fin 16 → Fin 16 → CBox := ![amp4_00_0,amp4_00_1,amp4_00_2,amp4_00_3,amp4_00_4,amp4_00_5,amp4_00_6,amp4_00_7,amp4_00_8,amp4_00_9,amp4_00_10,amp4_00_11,amp4_00_12,amp4_00_13,amp4_00_14,amp4_00_15] +lemma amp4_00_eq (i k : Fin 16) : amp4_0Expr 0 i k = amp4_00 i k := by + fin_cases i + · exact amp4_00_0_eq k + · exact amp4_00_1_eq k + · exact amp4_00_2_eq k + · exact amp4_00_3_eq k + · exact amp4_00_4_eq k + · exact amp4_00_5_eq k + · exact amp4_00_6_eq k + · exact amp4_00_7_eq k + · exact amp4_00_8_eq k + · exact amp4_00_9_eq k + · exact amp4_00_10_eq k + · exact amp4_00_11_eq k + · exact amp4_00_12_eq k + · exact amp4_00_13_eq k + · exact amp4_00_14_eq k + · exact amp4_00_15_eq k +noncomputable def amp4_01_0 : Fin 16 → CBox := ![⟨⟨216178096704881190102196580,216178096704881190225294808⟩,⟨(-374427922718183715782205705),(-374427922718183715668823068)⟩⟩,⟨⟨760954644405476281481517998,760954644405476281916998131⟩,⟨(-1317900465836448055060158609),(-1317900465836448054657266198)⟩⟩,⟨⟨1226846039970384573695020458,1226846039970384574398700759⟩,⟨(-2124459778092482373598949635),(-2124459778092482372946579143)⟩⟩,⟨⟨1742868230553603122001437274,1742868230553603123001328231⟩,⟨(-3017344759125023950619944440),(-3017344759125023949692614648)⟩⟩,⟨⟨2222754687533542233258532970,2222754687533542234534015816⟩,⟨(-3846991278603234543935352103),(-3846991278603234542751939389)⟩⟩,⟨⟨2730918658829647214554586940,2730918658829647216121442473⟩,⟨(-4724709412834161582289212479),(-4724709412834161580835233782)⟩⟩,⟨⟨3215991175376982936333684029,3215991175376982938178555948⟩,⟨(-5561414779498908855734985385),(-5561414779498908854022677848)⟩⟩,⟨⟨3720718699712779201983859762,3720718699712779204117521577⟩,⟨(-6430857048049550305796842696),(-6430857048049550303816322503)⟩⟩,⟨⟨4208522681233388133389290000,4208522681233388135801741645⟩,⟨(-7269604964512430656187869903),(-7269604964512430653948325887)⟩⟩,⟨⟨4711392819792956324275960364,4711392819792956326974703667⟩,⟨(-8132745552467294195997820532),(-8132745552467294193492822388)⟩⟩,⟨⟨5200931341264551389170365474,5200931341264551392148135309⟩,⟨(-8971052636411219997748921460),(-8971052636411219994984501609)⟩⟩,⟨⟨5702690360505990878578667968,5702690360505990881841517955⟩,⟨(-9828432549116667577738386306),(-9828432549116667574709220616)⟩⟩,⟨⟨6193469559200747702917146847,6193469559200747706457915322⟩,⟨(-10664697168311882426164557207),(-10664697168311882422877496112)⟩⟩,⟨⟨6694532219466138382460541693,6694532219466138386284009778⟩,⟨(-11516294777896590193483444149),(-11516294777896590189934381480)⟩⟩,⟨⟨7186274820674048161552935451,7186274820674048165654081335⟩,⟨(-12349303114435206239969888798),(-12349303114435206236162669665)⟩⟩,⟨⟨7686896216477907637851931404,7686896216477907642234841864⟩,⟨(-13194834047155305386194075309),(-13194834047155305382125065395)⟩⟩] +lemma amp4_01_0_eq : ∀ k : Fin 16, amp4_0Expr 1 0 k = amp4_01_0 k := by decide +kernel +noncomputable def amp4_01_1 : Fin 16 → CBox := ![⟨⟨8179431270407463187360854702,8179431270407463192019838077⟩,⟨(-14023571341419156255764346849),(-14023571341419156251439028094)⟩⟩,⟨⟨8679778271599624059694279528,8679778271599624064632396369⟩,⟨(-14862614430602471730988400936),(-14862614430602471726404331256)⟩⟩,⟨⟨9172991138669868912444673957,9172991138669868917656715529⟩,⟨(-15686180542716245906849895238),(-15686180542716245902012080449)⟩⟩,⟨⟨9673176157629234175905296900,9673176157629234181396370044⟩,⟨(-16518238486698559758809599248),(-16518238486698559753711641831)⟩⟩,⟨⟨10166982950388058531968336301,10166982950388058537730990338⟩,⟨(-17335805775651577605896160660),(-17335805775651577600547163915)⟩⟩,⟨⟨10667081393814560758940225540,10667081393814560764976909121⟩,⟨(-18160337490009399427306114515),(-18160337490009399421703834813)⟩⟩,⟨⟨11161414647180990554681016326,11161414647180990560990275238⟩,⟨(-18971128092466434843337402082),(-18971128092466434837480924271)⟩⟩,⟨⟨11661474520054717285056650924,11661474520054717291637025270⟩,⟨(-19787567417700190611314840137),(-19787567417700190605208245892)⟩⟩,⟨⟨12156274521770270248557919612,12156274521770270255408135428⟩,⟨(-20590840276719456092383434136),(-20590840276719456086025673648)⟩⟩,⟨⟨12656321942234984788536376467,12656321942234984795658593192⟩,⟨(-21398607546610297169925629890),(-21398607546610297163314361722)⟩⟩,⟨⟨13151531136520227415832443850,13151531136520227423218419849⟩,⟨(-22193650704154673739888356601),(-22193650704154673733034450973)⟩⟩,⟨⟨13651573583309681968385653140,13651573583309681976040470234⟩,⟨(-22992160324867102866755719977),(-22992160324867102859651646914)⟩⟩,⟨⟨14147132748685516428197282135,14147132748685516436111863379⟩,⟨(-23778286223002084608228375685),(-23778286223002084600886473770)⟩⟩,⟨⟨14647160988346775930867606810,14647160988346775939049617001⟩,⟨(-24566951898681369158407446328),(-24566951898681369150815649258)⟩⟩,⟨⟨15143006495104444874508730092,15143006495104444882951995320⟩,⟨(-25343494481598689799879900238),(-25343494481598689792045736288)⟩⟩,⟨⟨15642995711027499870085710055,15642995711027499878791902886⟩,⟨(-26121732985813821897246661629),(-26121732985813821889167952917)⟩⟩] +lemma amp4_01_1_eq : ∀ k : Fin 16, amp4_0Expr 1 1 k = amp4_01_1 k := by decide +kernel +noncomputable def amp4_01_2 : Fin 16 → CBox := ![⟨⟨16139057467372682556703844983,16139057467372682565663000881⟩,⟨(-26888045920748681822091369106),(-26888045920748681813781989031)⟩⟩,⟨⟨16638967892697315017203418165,16638967892697315026423056138⟩,⟨(-27655279932353967409155823526),(-27655279932353967400603664122)⟩⟩,⟨⟨17135167749790936431748636260,17135167749790936441223995458⟩,⟨(-28410735546851922309075683323),(-28410735546851922300285991363)⟩⟩,⟨⟨17634944986474635439231076023,17634944986474635448963097506⟩,⟨(-29166395861544427132189442608),(-29166395861544427123160930455)⟩⟩,⟨⟨18131195462343455936237102105,18131195462343455946223262614⟩,⟨(-29910384550181176272193946176),(-29910384550181176262928191214)⟩⟩,⟨⟨18630770600488307216300956227,18630770600488307226530631855⟩,⟨(-30653911861124241215814448243),(-30653911861124241206329063436)⟩⟩,⟨⟨19126973834809539098327305665,19126973834809539108805979502⟩,⟨(-31385841805106312758002285091),(-31385841805106312748285661462)⟩⟩,⟨⟨19626263446018664427799234063,19626263446018664438525314478⟩,⟨(-32116688176346159870889898958),(-32116688176346159860944621447)⟩⟩,⟨⟨20122310329016182674386834288,20122310329016182685358185761⟩,⟨(-32835985273731698196957931526),(-32835985273731698186784990313)⟩⟩,⟨⟨20621216382883457430445039909,20621216382883457441661667387⟩,⟨(-33553615387626237331176794027),(-33553615387626237320776035861)⟩⟩,⟨⟨21116985820896760529087460831,21116985820896760540545703732⟩,⟨(-34259723325597251503288670382),(-34259723325597251492663603041)⟩⟩,⟨⟨21615395558186525718806083770,21615395558186525730493075116⟩,⟨(-34963615558774036556969615755),(-34963615558774036546140793751)⟩⟩,⟨⟨22110753850746593073267543759,22110753850746593085194108563⟩,⟨(-35655995980880480016136428520),(-35655995980880480005083884291)⟩⟩,⟨⟨22608539636751836373199366120,22608539636751836385362856749⟩,⟨(-36345643346037159487277925932),(-36345643346037159476005572625)⟩⟩,⟨⟨23103339947972155487555786479,23103339947972155499954292865⟩,⟨(-37023776081384766614103289602),(-37023776081384766602611839643)⟩⟩,⟨⟨23600359122855001193820296593,23600359122855001206448592624⟩,⟨(-37698687060910749382876249428),(-37698687060910749371173608952)⟩⟩] +lemma amp4_01_2_eq : ∀ k : Fin 16, amp4_0Expr 1 2 k = amp4_01_2 k := by decide +kernel +noncomputable def amp4_01_3 : Fin 16 → CBox := ![⟨⟨24094441035229122339375558601,24094441035229122352232847567⟩,⟨(-38362070391662964291471998405),(-38362070391662964279557096330)⟩⟩,⟨⟨24590535773604755298898361459,24590535773604755311984180689⟩,⟨(-39021769681444076801639612823),(-39021769681444076789512638573)⟩⟩,⟨⟨25083724915859867982615681263,25083724915859867995926859952⟩,⟨(-39669920631426435896042909691),(-39669920631426435883706610712)⟩⟩,⟨⟨25578722104728642435916110868,25578722104728642449430020340⟩,⟨(-40313949807985743548771541732),(-40313949807985743536260967742)⟩⟩,⟨⟨26070829847813166034595033393,26070829847813166048331122832⟩,⟨(-40946404439649227925359332361),(-40946404439649227912641473118)⟩⟩,⟨⟨26564540989704766470440350353,26564540989704766484395439400⟩,⟨(-41574322560160752089446263683),(-41574322560160752076525427406)⟩⟩,⟨⟨27055364206662108538861996781,27055364206662108553032288161⟩,⟨(-42190636270328331660996069381),(-42190636270328331647875981507)⟩⟩,⟨⟨27547585353230431776054205554,27547585353230431790437340601⟩,⟨(-42802020412496186026813631209),(-42802020412496186013497198594)⟩⟩,⟨⟨28036906239872469141257459468,28036906239872469155851138890⟩,⟨(-43401768219601819899524479274),(-43401768219601819886013085551)⟩⟩,⟨⟨28527417959975720978165372908,28527417959975720992962713756⟩,⟨(-43996213966587486238979483793),(-43996213966587486225282934318)⟩⟩,⟨⟨29015003914076697206055860216,29015003914076697221058446571⟩,⟨(-44578990783793092124094006765),(-44578990783793092110207681785)⟩⟩,⟨⟨29503571299465376800157203496,29503571299465376815361173919⟩,⟨(-45156112658074627391089636524),(-45156112658074627377018581172)⟩⟩,⟨⟨29989174856755619584727031466,29989174856755619600129749257⟩,⟨(-45721533547900628788866717634),(-45721533547900628774612833842)⟩⟩,⟨⟨30475547567785164428964829110,30475547567785164444564309552⟩,⟨(-46280965397009150546169918515),(-46280965397009150531735297351)⟩⟩,⟨⟨30958906393406142486551882254,30958906393406142502344981825⟩,⟨(-46828665804061895016396226998),(-46828665804061895001783552221)⟩⟩,⟨⟨31442818746632094515967457728,31442818746632094531952014558⟩,⟨(-47370061140459967991274599573),(-47370061140459967976486166708)⟩⟩] +lemma amp4_01_3_eq : ∀ k : Fin 16, amp4_0Expr 1 3 k = amp4_01_3 k := by decide +kernel +noncomputable def amp4_01_4 : Fin 16 → CBox := ![⟨⟨31923655680969363485451782135,31923655680969363501590207382⟩,⟨(-47899697099569643546869057369),(-47899697099569643531959231156)⟩⟩,⟨⟨32404826780030267606468338460,32404826780030267622798103742⟩,⟨(-48422729396441952941987066813),(-48422729396441952926898440165)⟩⟩,⟨⟨32882849938003413140817152266,32882849938003413157333294050⟩,⟨(-48933977714096870311513447268),(-48933977714096870296251478325)⟩⟩,⟨⟨33360983848821784342679415028,33360983848821784359378537536⟩,⟨(-49438340658465771313283273137),(-49438340658465771297852016927)⟩⟩,⟨⟨33835886771805093085138489284,33835886771805093102016513392⟩,⟨(-49930899065884821094481103206),(-49930899065884821078884654313)⟩⟩,⟨⟨34310672742819537177970802964,34310672742819537195026766428⟩,⟨(-50416306770206392308348654495),(-50416306770206392292587407515)⟩⟩,⟨⟨34782134602411432448818764189,34782134602411432466045569887⟩,⟨(-50889894046760940211219230106),(-50889894046760940195301696399)⟩⟩,⟨⟨35253247330278985743856969044,35253247330278985761254732043⟩,⟨(-51356081219975404915448750644),(-51356081219975404899373693285)⟩⟩,⟨⟨35720933183145069690362238862,35720933183145069707927949742⟩,⟨(-51810437285976343926288065580),(-51810437285976343910057999464)⟩⟩,⟨⟨36188033124111665533349624650,36188033124111665551070548565⟩,⟨(-52257159364861488860209488356),(-52257159364861488843841762343)⟩⟩,⟨⟨36651594217104950302380651916,36651594217104950320264130826⟩,⟨(-52692045342982261668085932231),(-52692045342982261651568062194)⟩⟩,⟨⟨37114327944026099964925110710,37114327944026099982966799567⟩,⟨(-53119078584576036860128270797),(-53119078584576036843465427943)⟩⟩,⟨⟨37573402068745722425496069401,37573402068745722443693412767⟩,⟨(-53534276829399654237998186256),(-53534276829399654221192236290)⟩⟩,⟨⟨38031402673543520189196864784,38031402673543520207543355737⟩,⟨(-53941418365208258043240513844),(-53941418365208258026299626214)⟩⟩,⟨⟨38485614569435227261111557408,38485614569435227279607736524⟩,⟨(-54336732460574162052469453159),(-54336732460574162035391099117)⟩⟩,⟨⟨38938502110597625171064018519,38938502110597625189704824610⟩,⟨(-54723800313256923576863323909),(-54723800313256923559653552811)⟩⟩] +lemma amp4_01_4_eq : ∀ k : Fin 16, amp4_0Expr 1 4 k = amp4_01_4 k := by decide +kernel +noncomputable def amp4_01_5 : Fin 16 → CBox := ![⟨⟨39387463915629646538586034115,39387463915629646557368939070⟩,⟨(-55099055037248306630559378504),(-55099055037248306613220020576)⟩⟩,⟨⟨39834845910190629859062175377,39834845910190629877984458327⟩,⟨(-55465888100464746010834395952),(-55465888100464745993368166422)⟩⟩,⟨⟨40278157658060360175939410936,40278157658060360194998476568⟩,⟨(-55820929358023382472809355274),(-55820929358023382455218209173)⟩⟩,⟨⟨40719629617343008887146839097,40719629617343008906339648177⟩,⟨(-56167387340136493603724675394),(-56167387340136493586011742632)⟩⟩,⟨⟨41156879780085661537336635580,41156879780085661556659893285⟩,⟨(-56502082063423845869144747628),(-56502082063423845851312958247)⟩⟩,⟨⟨41592025788342503416978553679,41592025788342503436357033894⟩,⟨(-56828045395773452723392335318),(-56828045395773452705543424197)⟩⟩,⟨⟨42022791863124524169781968060,42022791863124524189288274501⟩,⟨(-57142281412516486081445463849),(-57142281412516486063478222024)⟩⟩,⟨⟨42451185198069898667317960548,42451185198069898686947426814⟩,⟨(-57447651123004775877768807952),(-57447651123004775859688556426)⟩⟩,⟨⟨42875034336859009478077031023,42875034336859009497824693602⟩,⟨(-57741336993174612739961211934),(-57741336993174612721773161428)⟩⟩,⟨⟨43296238130955518462975949537,43296238130955518482838769533⟩,⟨(-58026034545940520688988970089),(-58026034545940520670696180341)⟩⟩,⟨⟨43712727811667077678281135651,43712727811667077698253584566⟩,⟨(-58299099367213351280641478374),(-58299099367213351262249884702)⟩⟩,⟨⟨44126295752901991283265137886,44126295752901991303343961032⟩,⟨(-58563066469211670210138387347),(-58563066469211670191651277063)⟩⟩,⟨⟨44534974490528961690247667155,44534974490528961710431647127⟩,⟨(-58815459651755407764726310870),(-58815459651755407746143863980)⟩⟩,⟨⟨44940451561296249812597097926,44940451561296249832879552826⟩,⟨(-59058658027098961841297452613),(-59058658027098961822627471334)⟩⟩,⟨⟨45340859657438342134081133229,45340859657438342154460657550⟩,⟨(-59290349038316896112943958023),(-59290349038316896094186890746)⟩⟩,⟨⟨45737782910027527910098850842,45737782910027527930573191401⟩,⟨(-59512760171284748199703368939),(-59512760171284748180861161809)⟩⟩] +lemma amp4_01_5_eq : ∀ k : Fin 16, amp4_0Expr 1 5 k = amp4_01_5 k := by decide +kernel +noncomputable def amp4_01_6 : Fin 16 → CBox := ![⟨⟨46129453239144780481158255521,46129453239144780501715686417⟩,⟨(-59723738251229604667753804947),(-59723738251229604648840324497)⟩⟩,⟨⟨46517352606228878994986603131,46517352606228879015633749259⟩,⟨(-59925363098890158535140362418),(-59925363098890158516146027324)⟩⟩,⟨⟨46899811436856682782144676796,46899811436856682802872841570⟩,⟨(-60115636947139037694241181185),(-60115636947139037675175902651)⟩⟩,⟨⟨47278210575267993073913765789,47278210575267993094724814738⟩,⟨(-60296495622583303132941905309),(-60296495622583303113802329283)⟩⟩,⟨⟨47650978424344926841782980091,47650978424344926862670441473⟩,⟨(-60466093057436351375845373109),(-60466093057436351356638511298)⟩⟩,⟨⟨48019395590329343774606052253,48019395590329343795568364949⟩,⟨(-60626224484662940130085933479),(-60626224484662940110812844142)⟩⟩,⟨⟨48381988108706628756297725509,48381988108706628777304983981⟩,⟨(-60775192075596587840068422961),(-60775192075596587820765511384)⟩⟩,⟨⟨48739937062754433238447867636,48739937062754433259525497430⟩,⟨(-60914653617135678089680952605),(-60914653617135678070315231272)⟩⟩,⟨⟨49091865949876773909592106375,49091865949876773930733833013⟩,⟨(-61043056291505091456865989545),(-61043056291505091437444161936)⟩⟩,⟨⟨49438856889140577136942492967,49438856889140577158143787225⟩,⟨(-61161923349913194964252336798),(-61161923349913194944779166377)⟩⟩,⟨⟨49779630834812999953345476436,49779630834812999974604275887⟩,⟨(-61269843974958385977780400759),(-61269843974958385958257335956)⟩⟩,⟨⟨50115171351041714239441458223,50115171351041714260751600272⟩,⟨(-61368209569358896438561127182),(-61368209569358896418994891664)⟩⟩,⟨⟨50444297002126083606835837477,50444297002126083628195226616⟩,⟨(-61455748510624834929023436756),(-61455748510624834909415509040)⟩⟩,⟨⟨50767893062967538843303819963,50767893062967538864711185313⟩,⟨(-61533722829510703211847494601),(-61533722829510703192198615101)⟩⟩,⟨⟨51084876012786017698225884520,51084876012786017719664576370⟩,⟨(-61600997486843855152905771215),(-61600997486843855133235042309)⟩⟩,⟨⟨51396032964240217838436231232,51396032964240217859914790206⟩,⟨(-61658707418398045857355869080),(-61658707418398045837652125158)⟩⟩] +lemma amp4_01_6_eq : ∀ k : Fin 16, amp4_0Expr 1 6 k = amp4_01_6 k := by decide +kernel +noncomputable def amp4_01_7 : Fin 16 → CBox := ![⟨⟨51700378762401316352764751940,51700378762401316374278087660⟩,⟨(-61705851740730076336880142708),(-61705851740730076317148495851)⟩⟩,⟨⟨51998602350141418586467008439,51998602350141418608013620111⟩,⟨(-61743440381956466395869049564),(-61743440381956466376110536472)⟩⟩,⟨⟨52289817530447678145155595011,52289817530447678166724744682⟩,⟨(-61770604362130427004076808357),(-61770604362130426984303213391)⟩⟩,⟨⟨52574614937666663614866708782,52574614937666663636461025482⟩,⟨(-61788230508122298354407576032),(-61788230508122298334615011882)⟩⟩,⟨⟨52852208061711668642055061999,52852208061711668663666577226⟩,⟨(-61795579659057486236396049751),(-61795579659057486216592945729)⟩⟩,⟨⟨53123088961099440453397936815,53123088961099440475028398544⟩,⟨(-61793417273762555378443608296),(-61793417273762555358627196911)⟩⟩,⟨⟨53386571675115929056900846884,53386571675115929078543234578⟩,⟨(-61781132087291394021388511224),(-61781132087291394001566092136)⟩⟩,⟨⟨53643049292524299038860567190,53643049292524299060511801544⟩,⟨(-61759369757161249605924046558),(-61759369757161249586098466367)⟩⟩,⟨⟨53891937395004824537624019083,53891937395004824559280835648⟩,⟨(-61727645146905002424193808540),(-61727645146905002404367964422)⟩⟩,⟨⟨54133529582316605957578739395,54133529582316605979238728764⟩,⟨(-61686485518842746546258665160),(-61686485518842746526434659552)⟩⟩,⟨⟨54367344099893634768726899252,54367344099893634790384834724⟩,⟨(-61635530248522632916907738867),(-61635530248522632897090727226)⟩⟩,⟨⟨54593574414576906635735002637,54593574414576906657388212382⟩,⟨(-61575189453565319659832128378),(-61575189453565319640024483294)⟩⟩,⟨⟨54811842683620554321391705816,54811842683620554343035090194⟩,⟨(-61505225552171657634549368600),(-61505225552171657614756052437)⟩⟩,⟨⟨55022241472420156553354191826,55022241472420156574984121022⟩,⟨(-61425932616363687207255925284),(-61425932616363687187480384830)⟩⟩,⟨⟨55224498223789075549582994412,55224498223789075571194660565⟩,⟨(-61337194781628037004981370963),(-61337194781628036985228217587)⟩⟩,⟨⟨55418603707984574294925279440,55418603707984574316513601508⟩,⟨(-61239191025557904136293220038),(-61239191025557904116567458690)⟩⟩] +lemma amp4_01_7_eq : ∀ k : Fin 16, amp4_0Expr 1 7 k = amp4_01_7 k := by decide +kernel +noncomputable def amp4_01_8 : Fin 16 → CBox := ![⟨⟨55604392152348909136667322826,55604392152348909158234928368⟩,⟨(-61131926017191833605601735168),(-61131926017191833585899727816)⟩⟩,⟨⟨55781751511991666610105925325,55781751511991666631655813698⟩,⟨(-61015464445677466948872502948),(-61015464445677466929190460118)⟩⟩,⟨⟨55950624423136563892769073505,55950624423136563914296037020⟩,⟨(-60889930469856510360313774263),(-60889930469856510340656809613)⟩⟩,⟨⟨56110794877668172439619269804,56110794877668172461118798973⟩,⟨(-60755275153273810312281531983),(-60755275153273810292654075620)⟩⟩,⟨⟨56262315671182135948573201003,56262315671182135970041497248⟩,⟨(-60611741239856456152651608688),(-60611741239856456133057180792)⟩⟩,⟨⟨56404865553832332602120036075,56404865553832332623552359153⟩,⟨(-60459166688611488049814436683),(-60459166688611488030257693293)⟩⟩,⟨⟨56538609358586796344337422295,56538609358586796365731053025⟩,⟨(-60297912062590627218422318361),(-60297912062590627198905616557)⟩⟩,⟨⟨56663119181951047668828312677,56663119181951047690178324677⟩,⟨(-60127702596238212345824151337),(-60127702596238212326352294702)⟩⟩,⟨⟨56778673901785933699815269850,56778673901785933721119176101⟩,⟨(-59949016044926429729193843336),(-59949016044926429709768911605)⟩⟩,⟨⟨56884737411991141106595674226,56884737411991141127850735497⟩,⟨(-59761465157436564772715183058),(-59761465157436564753339671841)⟩⟩,⟨⟨56981704775035893921332147614,56981704775035893942535314344⟩,⟨(-59565644394886997046033810627),(-59565644394886997026710428845)⟩⟩,⟨⟨57068929991917070151891515605,57068929991917070173035969403⟩,⟨(-59361054117555599329562400502),(-59361054117555599310297869152)⟩⟩,⟨⟨57146926584997720776131234948,57146926584997720797219105473⟩,⟨(-59148405147716851278447210289),(-59148405147716851259238821045)⟩⟩,⟨⟨57214936825728964690331081447,57214936825728964711354602058⟩,⟨(-58927085411208756274725018072),(-58927085411208756255580462196)⟩⟩,⟨⟨57273595111339169060155491917,57273595111339169081117953553⟩,⟨(-58697921891305617862393897295),(-58697921891305617843309353065)⟩⟩,⟨⟨57322029994988735842340900304,57322029994988735863231406219⟩,⟨(-58460189888305538215589257860),(-58460189888305538196575555705)⟩⟩] +lemma amp4_01_8_eq : ∀ k : Fin 16, amp4_0Expr 1 8 k = amp4_01_8 k := by decide +kernel +noncomputable def amp4_01_9 : Fin 16 → CBox := ![⟨⟨57360999308336436044779759745,57360999308336436065597010286⟩,⟨(-58214832493927036410573932448),(-58214832493927036391631930557)⟩⟩,⟨⟨57389515738848061896219361228,57389515738848061916958759576⟩,⟨(-57961012043858325496287958055),(-57961012043858325477422008972)⟩⟩,⟨⟨57408463262529407886190840423,57408463262529407906862600966⟩,⟨(-57699787837221051236706550199),(-57699787837221051217905982865)⟩⟩,⟨⟨57416736387670180490397088789,57416736387670180510983546717⟩,⟨(-57430208754472601732730493791),(-57430208754472601714012800267)⟩⟩,⟨⟨57415348101568588037778404920,57415348101568588058278659113⟩,⟨(-57153450557310358361751865616),(-57153450557310358343117530279)⟩⟩,⟨⟨57403072245427413467433717305,57403072245427413487846644560⟩,⟨(-56868448024388813974215581668),(-56868448024388813955665464378)⟩⟩,⟨⟨57381053849488078591707048771,57381053849488078612026257189⟩,⟨(-56576493796899537495117692567),(-56576493796899537476657765645)⟩⟩,⟨⟨57347943416158015947611058048,57347943416158015967835442526⟩,⟨(-56276407743897212934901013461),(-56276407743897212916532098157)⟩⟩,⟨⟨57305021223746809529252796911,57305021223746809549377765685⟩,⟨(-55969599971154929698842185155),(-55969599971154929680568418631)⟩⟩,⟨⟨57250811569879035947204793613,57250811569879035967224420068⟩,⟨(-55654774462893430063610093739),(-55654774462893430045437026423)⟩⟩,⟨⟨57186733369499414911897539055,57186733369499414931842945348⟩,⟨(-55333459550106873527031651648),(-55333459550106873508928828264)⟩⟩,⟨⟨57111181643476128358365182497,57111181643476128378202430965⟩,⟨(-55004242182282387965803511992),(-55004242182282387947803682257)⟩⟩,⟨⟨57025717526688472978561327677,57025717526688472998289420170⟩,⟨(-54668769860252940669843913158),(-54668769860252940651947718104)⟩⟩,⟨⟨56928603472226391711435297799,56928603472226391731048079605⟩,⟨(-54325511165871561372325557520),(-54325511165871561354538714300)⟩⟩,⟨⟨56821546625690967850150546558,56821546625690967869651308935⟩,⟨(-53976233907971589630381885759),(-53976233907971589612700979901)⟩⟩,⟨⟨56702673347755963883158635025,56702673347755963902538449355⟩,⟨(-53619286775321773767437112803),(-53619286775321773749870455412)⟩⟩] +lemma amp4_01_9_eq : ∀ k : Fin 16, amp4_0Expr 1 9 k = amp4_01_9 k := by decide +kernel +noncomputable def amp4_01_10 : Fin 16 → CBox := ![⟨⟨56573840807403479199153953363,56573840807403479218422000066⟩,⟨(-53256559227280372565427643176),(-53256559227280372547966294163)⟩⟩,⟨⟨56433035498389971710013045799,56433035498389971729156759127⟩,⟨(-52886278330644809237019695367),(-52886278330644809219675396257)⟩⟩,⟨⟨56282268863812425466963528831,56282268863812425485981264683⟩,⟨(-52510456754391692673116219290),(-52510456754391692655890269464)⟩⟩,⟨⟨56119383488018099285609891260,56119383488018099304501793319⟩,⟨(-52127197998652331436553937978),(-52127197998652331419446086223)⟩⟩,⟨⟨55946549595267317747744729150,55946549595267317766503541957⟩,⟨(-51738639731432340707664292391),(-51738639731432340690681040848)⟩⟩,⟨⟨55761461529774112652219683155,55761461529774112670845914827⟩,⟨(-51342759711670134124592253208),(-51342759711670134107733042203)⟩⟩,⟨⟨55566453080856047965314899122,55566453080856047983805704927⟩,⟨(-50941822641600879566607859875),(-50941822641600879549875113472)⟩⟩,⟨⟨55359065711011718704277641855,55359065711011718722627996545⟩,⟨(-50533678118735812427252751038),(-50533678118735812410650984828)⟩⟩,⟨⟨55141801858471342191597024927,55141801858471342209804241662⟩,⟨(-50120720177939652924308249244),(-50120720177939652907839687110)⟩⟩,⟨⟨54912045126251679059594732500,54912045126251679077654593356⟩,⟨(-49700667571396760920221097140),(-49700667571396760903889509926)⟩⟩,⟨⟨54672472011356249300259876960,54672472011356249318167634226⟩,⟨(-49276046247796042931404099577),(-49276046247796042915213574122)⟩⟩,⟨⟨54420302914975651896462382667,54420302914975651914316249842⟩,⟨(-48844441146119199897497485929),(-48844441146119199881359785383)⟩⟩,⟨⟨54158394158123486816175879651,54158394158123486833878318507⟩,⟨(-48408513014940887200905530552),(-48408513014940887184908367329)⟩⟩,⟨⟨53883797201350272315689546723,53883797201350272333238582557⟩,⟨(-47965709705207934753459517519),(-47965709705207934737604638480)⟩⟩,⟨⟨53599554343458202634993306073,53599554343458202652386362863⟩,⟨(-47518829981201000959318736096),(-47518829981201000943608279410)⟩⟩,⟨⟨53302541933179948217252029754,53302541933179948234488036139⟩,⟨(-47065180998020995927612837237),(-47065180998020995912047734232)⟩⟩] +lemma amp4_01_10_eq : ∀ k : Fin 16, amp4_0Expr 1 10 k = amp4_01_10 k := by decide +kernel +noncomputable def amp4_01_11 : Fin 16 → CBox := ![⟨⟨52995994826935803464735161287,52995994826935803481811873467⟩,⟨(-46607703109347872840165783059),(-46607703109347872824747850703)⟩⟩,⟨⟨52676607617608152087809653237,52676607617608152104726250684⟩,⟨(-46143558804143416038891670571),(-46143558804143416023621665760)⟩⟩,⟨⟨52347814767615522027122265232,52347814767615522043873391697⟩,⟨(-45675833988866173887913222674),(-45675833988866173872795709245)⟩⟩,⟨⟨52006121951313997758003817467,52006121951313997774592813945⟩,⟨(-45201542120060396521760526861),(-45201542120060396506792613939)⟩⟩,⟨⟨51655170802305930029388562889,51655170802305930045807957899⟩,⟨(-44723919046104129651054940019),(-44723919046104129636242990049)⟩⟩,⟨⟨51291270343182927310057559372,51291270343182927326306524187⟩,⟨(-44239824390742203949679171259),(-44239824390742203935023948469)⟩⟩,⟨⟨50918277515640258670619360259,50918277515640258686693417661⟩,⟨(-43752648800183480436588537654),(-43752648800183480422093782690)⟩⟩,⟨⟨50532296327666664065898147430,50532296327666664081810411972⟩,⟨(-43259092787421499477080486103),(-43259092787421499462735008101)⟩⟩,⟨⟨50137407800346803438027500193,50137407800346803453761547157⟩,⟨(-42762707165920163612781247587),(-42762707165920163598599010135)⟩⟩,⟨⟨49729501867287412443149016983,49729501867287412458703448589⟩,⟨(-42260027532708592964370123029),(-42260027532708592950352394183)⟩⟩,⟨⟨49312893106352557893550210539,49312893106352557908926836384⟩,⟨(-41754770804878517501572515902),(-41754770804878517487717661028)⟩⟩,⟨⟨48883247542983718264936106463,48883247542983718280127587038⟩,⟨(-41243301274051427109310779700),(-41243301274051427095625085395)⟩⟩,⟨⟨48445123577616311134756880701,48445123577616311149763367512⟩,⟨(-40729508525552322695629744004),(-40729508525552322682112955596)⟩⟩,⟨⟨47993952631239446583165366684,47993952631239446597983925017⟩,⟨(-40209578506404967521815467003),(-40209578506404967508470149426)⟩⟩,⟨⟨47534548075850634256406337926,47534548075850634271033615306⟩,⟨(-39687580733536050712953327047),(-39687580733536050699782180477)⟩⟩,⟨⟨47062095067181843614848268578,47062095067181843629279919655⟩,⟨(-39159515044829035110437462601),(-39159515044829035097444187258)⟩⟩] +lemma amp4_01_11_eq : ∀ k : Fin 16, amp4_0Expr 1 11 k = amp4_01_11 k := by decide +kernel +noncomputable def amp4_01_12 : Fin 16 → CBox := ![⟨⟨46581674090560506755218080445,46581674090560506769511085465⟩,⟨(-38629638932420094649324159726),(-38629638932420094636461357916)⟩⟩,⟨⟨46088211293078281195014365398,46088211293078281209116449730⟩,⟨(-38093757547584261712678074743),(-38093757547584261699989386136)⟩⟩,⟨⟨45587067535100049485677012654,45587067535100049499586568428⟩,⟨(-37556325276015496923787070840),(-37556325276015496911273745332)⟩⟩,⟨⟨45072895991902418525852272019,45072895991902418539567703889⟩,⟨(-37012943090142376913336721893),(-37012943090142376901000207592)⟩⟩,⟨⟨44551352428728505141433954876,44551352428728505154953783096⟩,⟨(-36468272172387989470183290954),(-36468272172387989458024706864)⟩⟩,⟨⟨44016801705877156916257954884,44016801705877156929581435920⟩,⟨(-35917698790368763340319123400),(-35917698790368763328339244616)⟩⟩,⟨⟨43475210464933256598703127749,43475210464933256611825938153⟩,⟨(-35366101940059582632926560471),(-35366101940059582621128833076)⟩⟩,⟨⟨42920638340131367374707232791,42920638340131367387635001732⟩,⟨(-34808641484971070956057291577),(-34808641484971070944437301812)⟩⟩,⟨⟨42359380466582957781539563630,42359380466582957794263158482⟩,⟨(-34250426516620521673117626539),(-34250426516620521661682684483)⟩⟩,⟨⟨41785172551826620553492362810,41785172551826620566011573377⟩,⟨(-33686377457136004631096360723),(-33686377457136004619846818520)⟩⟩,⟨⟨41204657728780365015560303160,41204657728780365027872902986⟩,⟨(-33121847219887909128464467205),(-33121847219887909117402027790)⟩⟩,⟨⟨40611227025314597185528206738,40611227025314597197631563926⟩,⟨(-32551502215094701970966404090),(-32551502215094701960093350569)⟩⟩,⟨⟨40011893250606163034968873521,40011893250606163046859283916⟩,⟨(-31980954561653417676565647686),(-31980954561653417665884824349)⟩⟩,⟨⟨39399679634069395885590501247,39399679634069395897301880484⟩,⟨(-31404600321161671904314953108),(-31404600321161671893799512210)⟩⟩,⟨⟨38781992857287976055889488658,38781992857287976067387682802⟩,⟨(-30828328113986547887353588803),(-30828328113986547877030717206)⟩⟩,⟨⟨38151462490292992733865649365,38151462490292992745148979636⟩,⟨(-30246245270577493866440594219),(-30246245270577493856311812871)⟩⟩] +lemma amp4_01_12_eq : ∀ k : Fin 16, amp4_0Expr 1 12 k = amp4_01_12 k := by decide +kernel +noncomputable def amp4_01_13 : Fin 16 → CBox := ![⟨⟨37515916214701895586134853068,37515916214701895597203655666⟩,⟨(-29664536428009339046098511961),(-29664536428009339036163420160)⟩⟩,⟨⟨36867560883204292050927512322,36867560883204292061784001783⟩,⟨(-29076999419243010073636124302),(-29076999419243010063893203589)⟩⟩,⟨⟨36214675738530962942468974036,36214675738530962953105887315⟩,⟨(-28490137005044295423172500382),(-28490137005044295413627363283)⟩⟩,⟨⟨35549012107074406102334774647,35549012107074406112752436110⟩,⟨(-27897413959149906215664151489),(-27897413959149906206316751494)⟩⟩,⟨⟨34879335400887064596273416411,34879335400887064606468443612⟩,⟨(-27305676320075878016119413163),(-27305676320075878006972255650)⟩⟩,⟨⟨34196904180035839882133172929,34196904180035839892126589920⟩,⟨(-26708028939969975911404560332),(-26708028939969975902441458028)⟩⟩,⟨⟨33511009437781972854909231825,33511009437781972864681102855⟩,⟨(-26111689897582010820346871681),(-26111689897582010811583292117)⟩⟩,⟨⟨32812374454529583662086107014,32812374454529583671633938425⟩,⟨(-25509373334832923261726400352),(-25509373334832923253164524351)⟩⟩,⟨⟨32110860961560415528684931044,32110860961560415538009334855⟩,⟨(-24908702440023996843188194196),(-24908702440023996834827377574)⟩⟩,⟨⟨31396608119896869221361163603,31396608119896869230462234008⟩,⟨(-24301965147752881241025831100),(-24301965147752881232866274915)⟩⟩,⟨⟨30680100483363635967812957211,30680100483363635976688628816⟩,⟨(-23697228009691568276416377045),(-23697228009691568268459520097)⟩⟩,⟨⟨29950836596968091675560962284,29950836596968091684223837984⟩,⟨(-23086311559380869127309865418),(-23086311559380869119546263723)⟩⟩,⟨⟨29219984352006516528444102275,29219984352006516536876977102⟩,⟨(-22477770265282184310325991807),(-22477770265282184302768734754)⟩⟩,⟨⟨28476335823381425328938580737,28476335823381425337140895033⟩,⟨(-21862909106639664081696077463),(-21862909106639664074345884173)⟩⟩,⟨⟨27731813117541314675912600135,27731813117541314683886100307⟩,⟨(-21250822755711429466465830164),(-21250822755711429459321162039)⟩⟩,⟨⟨26974424426496031881347972254,26974424426496031889088333535⟩,⟨(-20632243890130439341619741188),(-20632243890130439334684208806)⟩⟩] +lemma amp4_01_13_eq : ∀ k : Fin 16, amp4_0Expr 1 13 k = amp4_01_13 k := by decide +kernel +noncomputable def amp4_01_14 : Fin 16 → CBox := ![⟨⟨26216929830613376021788985507,26216929830613376029308695801⟩,⟨(-20016869275477547790824408834),(-20016869275477547784088240398)⟩⟩,⟨⟨25446461777665758126114776569,25446461777665758133400916821⟩,⟨(-19394791800628643999699824921),(-19394791800628643993173230230)⟩⟩,⟨⟨24676718293128202307768359002,24676718293128202314823496465⟩,⟨(-18776384288913035181571110325),(-18776384288913035175251895184)⟩⟩,⟨⟨23893845916454611539691136389,23893845916454611546508602699⟩,⟨(-18151018751876527479519975275),(-18151018751876527473413549247)⟩⟩,⟨⟨23112601282892650744351456295,23112601282892650750943661107⟩,⟨(-17529833435702370045254078417),(-17529833435702370039350747606)⟩⟩,⟨⟨22318011324547399758818992704,22318011324547399765174464315⟩,⟨(-16901380900075814394549598308),(-16901380900075814388858444257)⟩⟩,⟨⟨21526038786896205371627821287,21526038786896205377754423470⟩,⟨(-16277674138709383414475983047),(-16277674138709383408990764254)⟩⟩,⟨⟨20720426513693708413538525142,20720426513693708419426175803⟩,⟨(-15646324818801589371311635380),(-15646324818801589366040369089)⟩⟩,⟨⟨19918526298868113924596471115,19918526298868113930247700678⟩,⟨(-15020356350489597804259768874),(-15020356350489597799200205681)⟩⟩,⟨⟨19102591364227198822663938006,19102591364227198828080701633⟩,⟨(-14386287577197417908060833030),(-14386287577197417903211933920)⟩⟩,⟨⟨18291593274947669876274875674,18291593274947669881453245927⟩,⟨(-13758323502997698958894115073),(-13758323502997698954258476592)⟩⟩,⟨⟨17466034098586215724449949730,17466034098586215729391662552⟩,⟨(-13121696630410524531110615055),(-13121696630410524526687390190)⟩⟩,⟨⟨16646801914210679939067465323,16646801914210679943774860068⟩,⟨(-12492013778908554411322998878),(-12492013778908554407110019070)⟩⟩,⟨⟨15812307671885148453290705946,15812307671885148457755452774⟩,⟨(-11852969355029271355390914011),(-11852969355029271351394941189)⟩⟩,⟨⟨14985746577513146590190936008,14985746577513146594419533571⟩,⟨(-11221861931682051146087613677),(-11221861931682051142303312460)⟩⟩,⟨⟨14142985148994726980804839218,14142985148994726984793032059⟩,⟨(-10580511904289962701036069228),(-10580511904289962697467186096)⟩⟩] +lemma amp4_01_14_eq : ∀ k : Fin 16, amp4_0Expr 1 14 k = amp4_01_14 k := by decide +kernel +noncomputable def amp4_01_15 : Fin 16 → CBox := ![⟨⟨13310054472240610516312602783,13310054472240610520062776722⟩,⟨(-9948302114494842395762952979),(-9948302114494842392407165038)⟩⟩,⟨⟨12459653165725225879260672662,12459653165725225882768139977⟩,⟨(-9304716707381165565489725343),(-9304716707381165562351172106)⟩⟩,⟨⟨11621388954718542221939394455,11621388954718542225207701392⟩,⟨(-8671772715539894078657270727),(-8671772715539894075732687964)⟩⟩,⟨⟨10763901435960595295098942344,10763901435960595298125011648⟩,⟨(-8025957093951737931505888236),(-8025957093951737928798289407)⟩⟩,⟨⟨9921458629352590131639329741,9921458629352590134427049543⟩,⟨(-7392725553449432020846918159),(-7392725553449432018352674654)⟩⟩,⟨⟨9057303243356612223437804340,9057303243356612225981123567⟩,⟨(-6744575280643059542031377997),(-6744575280643059539755841970)⟩⟩,⟨⟨8212040588873131917773525585,8212040588873131920077453759⟩,⟨(-6111645620650791924924217651),(-6111645620650791922862782141)⟩⟩,⟨⟨7341372702389267820963671047,7341372702389267823023016686⟩,⟨(-5460853161467358747181088220),(-5460853161467358745338627872)⟩⟩,⟨⟨6495043067450789577823334814,6495043067450789579644020605⟩,⟨(-4829100127516671714464126856),(-4829100127516671712835137442)⟩⟩,⟨⟨5617451667733587955273191554,5617451667733587956846988691⟩,⟨(-4174930917788571722245516078),(-4174930917788571720837396079)⟩⟩,⟨⟨4772700687509769113835691199,4772700687509769115171767965⟩,⟨(-3545886008949153010572213652),(-3545886008949153009376705114)⟩⟩,⟨⟨3886328401331190696060349839,3886328401331190697147620139⟩,⟨(-2886526547125376755020431021),(-2886526547125376754047503386)⟩⟩,⟨⟨3048362346346898394870476283,3048362346346898395722281417⟩,⟨(-2263617379946292456621969741),(-2263617379946292455859618241)⟩⟩,⟨⟨2146385301085473656855208701,2146385301085473657454352086⟩,⟨(-1593563538157256116063504145),(-1593563538157256115527203615)⟩⟩,⟨⟨1331537687849639522381977308,1331537687849639522751807877⟩,⟨(-988474192108924475599876297),(-988474192108924475268559480)⟩⟩,⟨⟨378307472599977134190478545,378307472599977134294454107⟩,⟨(-280822483901604049823845166),(-280822483901604049730529902)⟩⟩] +lemma amp4_01_15_eq : ∀ k : Fin 16, amp4_0Expr 1 15 k = amp4_01_15 k := by decide +kernel +noncomputable def amp4_01 : Fin 16 → Fin 16 → CBox := ![amp4_01_0,amp4_01_1,amp4_01_2,amp4_01_3,amp4_01_4,amp4_01_5,amp4_01_6,amp4_01_7,amp4_01_8,amp4_01_9,amp4_01_10,amp4_01_11,amp4_01_12,amp4_01_13,amp4_01_14,amp4_01_15] +lemma amp4_01_eq (i k : Fin 16) : amp4_0Expr 1 i k = amp4_01 i k := by + fin_cases i + · exact amp4_01_0_eq k + · exact amp4_01_1_eq k + · exact amp4_01_2_eq k + · exact amp4_01_3_eq k + · exact amp4_01_4_eq k + · exact amp4_01_5_eq k + · exact amp4_01_6_eq k + · exact amp4_01_7_eq k + · exact amp4_01_8_eq k + · exact amp4_01_9_eq k + · exact amp4_01_10_eq k + · exact amp4_01_11_eq k + · exact amp4_01_12_eq k + · exact amp4_01_13_eq k + · exact amp4_01_14_eq k + · exact amp4_01_15_eq k +noncomputable def amp4_02_0 : Fin 16 → CBox := ![⟨⟨(-54041599249796242541476366),(-54041599249796242446742918)⟩,⟨(-280822483901604049821582058),(-280822483901604049733813243)⟩⟩,⟨⟨(-190146006047468727577665833),(-190146006047468727243673363)⟩,⟨(-988474192108924475591911333),(-988474192108924475280124750)⟩⟩,⟨⟨(-306296625633745083447668447),(-306296625633745082908844953)⟩,⟨(-1593563538157256116050656637),(-1593563538157256115545869526)⟩⟩,⟨⟨(-434562139038283732852985871),(-434562139038283732087574271)⟩,⟨(-2263617379946292456603705093),(-2263617379946292455886167105)⟩⟩,⟨⟨(-553254643319516198575522433),(-553254643319516197599469150)⟩,⟨(-2886526547125376754997102368),(-2886526547125376754081419496)⟩⟩,⟨⟨(-678264203944726629156134447),(-678264203944726627957267731)⟩,⟨(-3545886008949153010543505267),(-3545886008949153009418447036)⟩⟩,⟨⟨(-796656689266941485454660882),(-796656689266941484043309259)⟩,⟨(-4174930917788571722211632638),(-4174930917788571720886656184)⟩⟩,⟨⟨(-918878550319976540595104435),(-918878550319976538962960940)⟩,⟨(-4829100127516671714424827982),(-4829100127516671712892256345)⟩⟩,⟨⟨(-1035722616832870897836956495),(-1035722616832870895991742288)⟩,⟨(-5460853161467358747136491073),(-5460853161467358745403412684)⟩⟩,⟨⟨(-1154920100324467628746840388),(-1154920100324467626682482674)⟩,⟨(-6111645620650791924874124553),(-6111645620650791922935507154)⟩⟩,⟨⟨(-1269338535658679900122267153),(-1269338535658679897844800213)⟩,⟨(-6744575280643059541975861291),(-6744575280643059539836374200)⟩⟩,⟨⟨(-1385074452694480755556783726),(-1385074452694480753061400546)⟩,⟨(-7392725553449432020785791036),(-7392725553449432018441262110)⟩⟩,⟨⟨(-1496324458565750464116398829),(-1496324458565750461408460845)⟩,⟨(-8025957093951737931439175074),(-8025957093951737928894856307)⟩⟩,⟨⟨(-1608088331382122511804259561),(-1608088331382122508879907733)⟩,⟨(-8671772715539894078584800977),(-8671772715539894075837454922)⟩⟩,⟨⟨(-1715491774245777396324377454),(-1715491774245777393188013205)⟩,⟨(-9304716707381165565411499818),(-9304716707381165562464092888)⟩⟩,⟨⟨(-1822744664673969620942085255),(-1822744664673969617590500761)⟩,⟨(-9948302114494842395678796466),(-9948302114494842392528456303)⟩⟩] +lemma amp4_02_0_eq : ∀ k : Fin 16, amp4_0Expr 2 0 k = amp4_02_0 k := by decide +kernel +noncomputable def amp4_02_1 : Fin 16 → CBox := ![⟨⟨(-1925662356783027230056078878),(-1925662356783027226493518499)⟩,⟨(-10580511904289962700945940379),(-10580511904289962697596847752)⟩⟩,⟨⟨(-2027856563382254596812328216),(-2027856563382254593036206723)⟩,⟨(-11221861931682051145991351118),(-11221861931682051142441540309)⟩⟩,⟨⟨(-2125677576240079068478955079),(-2125677576240079064493163262)⟩,⟨(-11852969355029271355288467129),(-11852969355029271351541747077)⟩⟩,⟨⟨(-2222266878263943787990443733),(-2222266878263943783792237816)⟩,⟨(-12492013778908554411214190185),(-12492013778908554407265608981)⟩⟩,⟨⟨(-2314403935001972384096135641),(-2314403935001972379689742940)⟩,⟨(-13121696630410524530995359470),(-13121696630410524526851812204)⟩⟩,⟨⟨(-2404849718840317057750625917),(-2404849718840317053134175856)⟩,⟨(-13758323502997698958772243802),(-13758323502997698954431922842)⟩⟩,⟨⟨(-2490737353558602279113272646),(-2490737353558602274289490071)⟩,⟨(-14386287577197417907932253964),(-14386287577197417903394460633)⟩⟩,⟨⟨(-2574512734309565672269085430),(-2574512734309565667237207901)⟩,⟨(-15020356350489597804124296723),(-15020356350489597799392016900)⟩⟩,⟨⟨(-2653606821766868048491546459),(-2653606821766868043254161867)⟩,⟨(-15646324818801589371169140768),(-15646324818801589366241558951)⟩⟩,⟨⟨(-2730199695366460919960445677),(-2730199695366460914516195776)⟩,⟨(-16277674138709383414326294173),(-16277674138709383409201519166)⟩⟩,⟨⟨(-2801977699877058096736304505),(-2801977699877058091089209048)⟩,⟨(-16901380900075814394392587887),(-16901380900075814389078856547)⟩⟩,⟨⟨(-2870893176988519520592742591),(-2870893176988519514740995765)⟩,⟨(-17529833435702370045089551348),(-17529833435702370039581023183)⟩⟩,⟨⟨(-2934854791530895144244411786),(-2934854791530895138192114083)⟩,⟨(-18151018751876527479347772367),(-18151018751876527473653812353)⟩⟩,⟨⟨(-2995617245904600707336684396),(-2995617245904600701081681330)⟩,⟨(-18776384288913035181391047079),(-18776384288913035175502337610)⟩⟩,⟨⟨(-3051285243726369726340824735),(-3051285243726369719886557519)⟩,⟨(-19394791800628643999511743759),(-19394791800628643993433974404)⟩⟩,⟨⟨(-3103440101552353112514843369),(-3103440101552353105860566035)⟩,⟨(-20016869275477547790628104597),(-20016869275477547784359495485)⟩⟩] +lemma amp4_02_1_eq : ∀ k : Fin 16, amp4_0Expr 2 1 k = amp4_02_1 k := by decide +kernel +noncomputable def amp4_02_2 : Fin 16 → CBox := ![⟨⟨(-3150361298590390651900262325),(-3150361298590390645050092565)⟩,⟨(-20632243890130439341415018242),(-20632243890130439334966134929)⟩⟩,⟨⟨(-3193476640519277486466746302),(-3193476640519277479418929957)⟩,⟨(-21250822755711429466252502439),(-21250822755711429459613946185)⟩⟩,⟨⟨(-3231222907407964145734036588),(-3231222907407964138491642665)⟩,⟨(-21862909106639664081473961305),(-21862909106639664074649674001)⟩⟩,⟨⟨(-3264890925120046853336108976),(-3264890925120046845898821373)⟩,⟨(-22477770265282184310094872871),(-22477770265282184303083742612)⟩⟩,⟨⟨(-3293060210159864201250207908),(-3293060210159864193620656630)⟩,⟨(-23086311559380869127069529745),(-23086311559380869119872666991)⟩⟩,⟨⟨(-3316898542476902921291515105),(-3316898542476902913471586249)⟩,⟨(-23697228009691568276166624572),(-23697228009691568268797514081)⟩⟩,⟨⟨(-3335115880112810333667714735),(-3335115880112810325658563692)⟩,⟨(-24301965147752881240766456103),(-24301965147752881233216028109)⟩⟩,⟨⟨(-3348768843736130167818891134),(-3348768843736130159620891365)⟩,⟨(-24908702440023996842918974679),(-24908702440023996835189104595)⟩⟩,⟨⟨(-3356687331080684203548023093),(-3356687331080684195163714071)⟩,⟨(-25509373334832923261447095341),(-25509373334832923253538428238)⟩⟩,⟨⟨(-3359827055051961756357403872),(-3359827055051961747787000361)⟩,⟨(-26111689897582010820057281260),(-26111689897582010811969562911)⟩⟩,⟨⟨(-3357128784003878194879144085),(-3357128784003878186125445727)⟩,⟨(-26708028939969975911104460590),(-26708028939969975902840280969)⟩⟩,⟨⟨(-3349456253285868569297070962),(-3349456253285868560362400544)⟩,⟨(-27305676320075878015808576549),(-27305676320075878007383846038)⟩⟩,⟨⟨(-3335853189055162487426370300),(-3335853189055162478311237710)⟩,⟨(-27897413959149906215342325904),(-27897413959149906206741321999)⟩⟩,⟨⟨(-3317099200307678297331814331),(-3317099200307678288037059866)⟩,⟨(-28490137005044295422839476583),(-28490137005044295414065108631)⟩⟩,⟨⟨(-3292333999351204292384689389),(-3292333999351204282912858489)⟩,⟨(-29076999419243010073291664112),(-29076999419243010064344321760)⟩⟩,⟨⟨(-3262260030508592738169141901),(-3262260030508592728521512526)⟩,⟨(-29664536428009339045742384707),(-29664536428009339036628125154)⟩⟩] +lemma amp4_02_2_eq : ∀ k : Fin 16, amp4_0Expr 2 2 k = amp4_02_2 k := by decide +kernel +noncomputable def amp4_02_3 : Fin 16 → CBox := ![⟨⟨(-3226106792406270245491001938),(-3226106792406270235669965566)⟩,⟨(-30246245270577493866072527014),(-30246245270577493856790336613)⟩⟩,⟨⟨(-3184505786735493327412191126),(-3184505786735493317418450417)⟩,⟨(-30828328113986547886973379027),(-30828328113986547877523243588)⟩⟩,⟨⟨(-3136770735638797879101163966),(-3136770735638797868937463855)⟩,⟨(-31404600321161671903922352220),(-31404600321161671894306248059)⟩⟩,⟨⟨(-3083467800382581573997141581),(-3083467800382581563666963016)⟩,⟨(-31980954561653417676160424678),(-31980954561653417666405979989)⟩⟩,⟨⟨(-3023989892491346128745556418),(-3023989892491346118248840752)⟩,⟨(-32551502215094701970548285086),(-32551502215094701960629157428)⟩⟩,⟨⟨(-2958842911860480860419326316),(-2958842911860480849757291071)⟩,⟨(-33121847219887909128033243476),(-33121847219887909117952672060)⟩⟩,⟨⟨(-2887494366024993926615539943),(-2887494366024993915791018929)⟩,⟨(-33686377457136004630651777363),(-33686377457136004620412511950)⟩⟩,⟨⟨(-2810394528122248855599101761),(-2810394528122248844613278240)⟩,⟨(-34250426516620521672659455151),(-34250426516620521662263631171)⟩⟩,⟨⟨(-2727081277184922339170774768),(-2727081277184922328026336169)⟩,⟨(-34808641484971070955585247150),(-34808641484971070945033742937)⟩⟩,⟨⟨(-2637953514370964562575090939),(-2637953514370964551273712169)⟩,⟨(-35366101940059582632440445163),(-35366101940059582621740940521)⟩⟩,⟨⟨(-2542615575294554502355600780),(-2542615575294554490899609333)⟩,⟨(-35917698790368763339818679902),(-35917698790368763328967231217)⟩⟩,⟨⟨(-2441418917511016992333910205),(-2441418917511016980724759078)⟩,⟨(-36468272172387989469668296662),(-36468272172387989458668767702)⟩⟩,⟨⟨(-2334030678714418166177989454),(-2334030678714418154418427888)⟩,⟨(-37012943090142376912806897660),(-37012943090142376901660576746)⟩⟩,⟨⟨(-2220758519338662925627064045),(-2220758519338662913718447144)⟩,⟨(-37556325276015496923242220073),(-37556325276015496911950590397)⟩⟩,⟨⟨(-2101328943994057818760983384),(-2101328943994057806706119685)⟩,⟨(-38093757547584261712117941739),(-38093757547584261700682917199)⟩⟩,⟨⟨(-1976009217898928211028409087),(-1976009217898928198828741539)⟩,⟨(-38629638932420094648748530917),(-38629638932420094637171758172)⟩⟩] +lemma amp4_02_3_eq : ∀ k : Fin 16, amp4_0Expr 2 3 k = amp4_02_3 k := by decide +kernel +noncomputable def amp4_02_4 : Fin 16 → CBox := ![⟨⟨(-1844581962247356718584622665),(-1844581962247356706244973392)⟩,⟨(-39159515044829035109846054013),(-39159515044829035098171694567)⟩⟩,⟨⟨(-1707277235866546199940254262),(-1707277235866546187459691449)⟩,⟨(-39687580733536050712345961162),(-39687580733536050700526940700)⟩⟩,⟨⟨(-1563930681890850030779838435),(-1563930681890850018161346741)⟩,⟨(-40209578506404967521191893650),(-40209578506404967509232366178)⟩⟩,⟨⟨(-1414738155238729007398360363),(-1414738155238728994643607656)⟩,⟨(-40729508525552322694989762029),(-40729508525552322682892797188)⟩⟩,⟨⟨(-1259585357298864893362428870),(-1259585357298864880474343442)⟩,⟨(-41243301274051427108654121022),(-41243301274051427096422772969)⟩⟩,⟨⟨(-1098636778057080059691615961),(-1098636778057080046671816240)⟩,⟨(-41754770804878517500899008801),(-41754770804878517488533332366)⟩⟩,⟨⟨(-931825323346807513479204130),(-931825323346807500330708818)⟩,⟨(-42260027532708592963679526793),(-42260027532708592951186242734)⟩⟩,⟨⟨(-759286813304513193549715251),(-759286813304513180274177001)⟩,⟨(-42762707165920163612073376813),(-42762707165920163599451186364)⟩⟩,⟨⟨(-580998596233061925494711585),(-580998596233061912095054502)⟩,⟨(-43259092787421499476355077927),(-43259092787421499463605727353)⟩⟩,⟨⟨(-397070390550080378049369056),(-397070390550080364527495540)⟩,⟨(-43752648800183480435845443931),(-43752648800183480422983157265)⟩⟩,⟨⟨(-207521301389361168939853929),(-207521301389361155298534791)⟩,⟨(-44239824390742203948918164513),(-44239824390742203935932158131)⟩⟩,⟨⟨(-12437401339430058166463025),(-12437401339430044407559585)⟩,⟨(-44723919046104129650275853985),(-44723919046104129637170164408)⟩⟩,⟨⟨188123070292156638159253386,188123070292156652038866793⟩,⟨(-45201542120060396520963120260),(-45201542120060396507738946435)⟩⟩,⟨⟨394095330249564827472363379,394095330249564841471415082⟩,⟨(-45675833988866173887097361724),(-45675833988866173873761296287)⟩⟩,⟨⟨605384576270902248808889848,605384576270902262924712422⟩,⟨(-46143558804143416038057144717),(-46143558804143416024606670007)⟩⟩,⟨⟨821945046048500777531507853,821945046048500791762358267⟩,⟨(-46607703109347872839312448454),(-46607703109347872825752378007)⟩⟩] +lemma amp4_02_4_eq : ∀ k : Fin 16, amp4_0Expr 2 4 k = amp4_02_4 k := by decide +kernel +noncomputable def amp4_02_5 : Fin 16 → CBox := ![⟨⟨1043647904151814548788595587,1043647904151814563131766131⟩,⟨(-47065180998020995926740464069),(-47065180998020995913071966526)⟩⟩,⟨⟨1270464218986711962299668126,1270464218986711976753411665⟩,⟨(-47518829981201000958427221836),(-47518829981201000944652280695)⟩⟩,⟨⟨1502233618996220067837566173,1502233618996220082399200330⟩,⟨(-47965709705207934752548672004),(-47965709705207934738668551124)⟩⟩,⟨⟨1738941882367760226811968099,1738941882367760241479681781⟩,⟨(-48408513014940887199975235598),(-48408513014940887185992270553)⟩⟩,⟨⟨1980399573281853801302915752,1980399573281853816073992027⟩,⟨(-48844441146119199896547541586),(-48844441146119199882463831498)⟩⟩,⟨⟨2226605120174738645543167917,2226605120174738660411895844⟩,⟨(-49276046247796042930434422795),(-49276046247796042916337806871)⟩⟩,⟨⟨2477342476248368331111414053,2477342476248368346078778629⟩,⟨(-49700667571396760919231521464),(-49700667571396760905034048357)⟩⟩,⟨⟨2732620714951390509410067337,2732620714951390524474102001⟩,⟨(-50120720177939652923298685211),(-50120720177939652909004581126)⟩⟩,⟨⟨2992199618976326453392111242,2992199618976326468549996062⟩,⟨(-50533678118735812426223018523),(-50533678118735812411836367449)⟩⟩,⟨⟨3256096949420832953746455166,3256096949420832968996270813⟩,⟨(-50941822641600879565557911469),(-50941822641600879551080992383)⟩⟩,⟨⟨3524050751167936198890604149,3524050751167936214229466784⟩,⟨(-51342759711670134123521949201),(-51342759711670134108959510389)⟩⟩,⟨⟨3796085557627739779533828126,3796085557627739794959722379⟩,⟨(-51738639731432340706573574978),(-51738639731432340691928116319)⟩⟩,⟨⟨4071920105227590617454209842,4071920105227590632964579974⟩,⟨(-52127197998652331435442661335),(-52127197998652331420713868524)⟩⟩,⟨⟨4351583821024066912693396729,4351583821024066928285897590⟩,⟨(-52510456754391692671984362958),(-52510456754391692657178739276)⟩⟩,⟨⟨4634778562880533297427104388,4634778562880533313099185489⟩,⟨(-52886278330644809235867149183),(-52886278330644809220984617989)⟩⟩,⟨⟨4921536804563662769584770552,4921536804563662785334459531⟩,⟨(-53256559227280372564254383692),(-53256559227280372549296251586)⟩⟩] +lemma amp4_02_5_eq : ∀ k : Fin 16, amp4_0Expr 2 5 k = amp4_02_5 k := by decide +kernel +noncomputable def amp4_02_6 : Fin 16 → CBox := ![⟨⟨5211545959219569876878316213,5211545959219569892701924261⟩,⟨(-53619286775321773766243018412),(-53619286775321773751221224973)⟩⟩,⟨⟨5504839727528238398108712791,5504839727528238414005243210⟩,⟨(-53976233907971589629166978245),(-53976233907971589614072500331)⟩⟩,⟨⟨5801093518733540591394684455,5801093518733540607360774894⟩,⟨(-54325511165871561371089758736),(-54325511165871561355931019251)⟩⟩,⟨⟨6100340463476996960838815341,6100340463476996976872956408⟩,⟨(-54668769860252940668587236520),(-54668769860252940653360754949)⟩⟩,⟨⟨6402246417548082016453617100,6402246417548082032552665378⟩,⟨(-55004242182282387964525876332),(-55004242182282387949237488403)⟩⟩,⟨⟨6706842163395529020031607976,6706842163395529036193647347⟩,⟨(-55333459550106873525733109484),(-55333459550106873510383312342)⟩⟩,⟨⟨7013786465799827068548740149,7013786465799827084767205627⟩,⟨(-55654774462893430062290601115),(-55654774462893430046912189430)⟩⟩,⟨⟨7323105995817128615237124953,7323105995817128631513865414⟩,⟨(-55969599971154929697501794557),(-55969599971154929682064169669)⟩⟩,⟨⟨7634454903770375701704123246,7634454903770375718035963276⟩,⟨(-56276407743897212933539673961),(-56276407743897212918048446069)⟩⟩,⟨⟨7947853997402201836857415817,7947853997402201853241972265⟩,⟨(-56576493796899537493735501661),(-56576493796899537478194575039)⟩⟩,⟨⟨8262955305126832987834879195,8262955305126833004269635026⟩,⟨(-56868448024388813972812531393),(-56868448024388813957222702069)⟩⟩,⟨⟨8579772027189616079842052548,8579772027189616096324282215⟩,⟨(-57153450557310358360328049471),(-57153450557310358344695065466)⟩⟩,⟨⟨8897956580352137090311865860,8897956580352137106839019121⟩,⟨(-57430208754472601731285903116),(-57430208754472601715610601465)⟩⟩,⟨⟨9217512817478329134640730208,9217512817478329151210933063⟩,⟨(-57699787837221051235241318860),(-57699787837221051219523879576)⟩⟩,⟨⟨9538096073201428562701476829,9538096073201428579309540006⟩,⟨(-57961012043858325494802115531),(-57961012043858325479059932634)⟩⟩,⟨⟨9859699114059058837520166198,9859699114059058854165959391⟩,⟨(-58214832493927036409067614860),(-58214832493927036393289709158)⟩⟩] +lemma amp4_02_6_eq : ∀ k : Fin 16, amp4_0Expr 2 6 k = amp4_02_6 k := by decide +kernel +noncomputable def amp4_02_7 : Fin 16 → CBox := ![⟨⟨10181982742790945416726305112,10181982742790945433406728406⟩,⟨(-58460189888305538214062488687),(-58460189888305538198253127806)⟩⟩,⟨⟨10504926898294682006664307028,10504926898294682023377451649⟩,⟨(-58697921891305617860846859591),(-58697921891305617845006500536)⟩⟩,⟨⟨10828200423713924624338122214,10828200423713924641079746213⟩,⟨(-58927085411208756273157779799),(-58927085411208756257297080296)⟩⟩,⟨⟨11151768683345019929083982572,11151768683345019945852961881⟩,⟨(-59148405147716851276859951483),(-59148405147716851260974695538)⟩⟩,⟨⟨11475311156384266148078669524,11475311156384266164871244948⟩,⟨(-59361054117555599327955189821),(-59361054117555599312052895837)⟩⟩,⟨⟨11798776876647167701567873444,11798776876647167718382820688⟩,⟨(-59565644394886997044406869240),(-59565644394886997028484353298)⟩⟩,⟨⟨12121858579633741945518223151,12121858579633741962351995578⟩,⟨(-59761465157436564771068618067),(-59761465157436564755132352707)⟩⟩,⟨⟨12444487200597002847882246253,12444487200597002864732518965⟩,⟨(-59949016044926429727527879615),(-59949016044926429711580091759)⟩⟩,⟨⟨12766371377432736019776381815,12766371377432736036640385401⟩,⟨(-60127702596238212344138892125),(-60127702596238212328181837990)⟩⟩,⟨⟨13087422163231365895571570318,13087422163231365912447185042⟩,⟨(-60297912062590627216718034723),(-60297912062590627200753220728)⟩⟩,⟨⟨13407366771468262502455356635,13407366771468262519339391847⟩,⟨(-60459166688611488048091275091),(-60459166688611488032123180346)⟩⟩,⟨⟨13726094570583996525948829344,13726094570583996542839042860⟩,⟨(-60611741239856456150909839421),(-60611741239856456134940250381)⟩⟩,⟨⟨14043354051196659757658758975,14043354051196659774551926390⟩,⟨(-60755275153273810310521302575),(-60755275153273810294554550113)⟩⟩,⟨⟨14359011072281940606139111732,14359011072281940623032769923⟩,⟨(-60889930469856510358535396363),(-60889930469856510342574348463)⟩⟩,⟨⟨14672838132892184405535986842,14672838132892184422426998850⟩,⟨(-61015464445677466947076162217),(-61015464445677466931124849038)⟩⟩,⟨⟨14984675731863074761281111328,14984675731863074778166554009⟩,⟨(-61131926017191833603787747469),(-61131926017191833587850623268)⟩⟩] +lemma amp4_02_7_eq : ∀ k : Fin 16, amp4_0Expr 2 7 k = amp4_02_7 k := by decide +kernel +noncomputable def amp4_02_8 : Fin 16 → CBox := ![⟨⟨15294323139136966164171601866,15294323139136966181050285307⟩,⟨(-61239191025557904134461765793),(-61239191025557904118534653136)⟩⟩,⟨⟨15601593613229836173035467505,15601593613229836189906804707⟩,⟨(-61337194781628037003132813407),(-61337194781628036987211321379)⟩⟩,⟨⟨15906315990142619505099377887,15906315990142619521960184530⟩,⟨(-61425932616363687205390488662),(-61425932616363687189479148155)⟩⟩,⟨⟨16208274374609356621281068814,16208274374609356638128621469⟩,⟨(-61505225552171657632667414157),(-61505225552171657616770088944)⟩⟩,⟨⟨16507329998259378713896490552,16507329998259378730727928215⟩,⟨(-61575189453565319657933880709),(-61575189453565319642053544395)⟩⟩,⟨⟨16803235861366092224635612808,16803235861366092241448159284⟩,⟨(-61635530248522632914993600296),(-61635530248522632899134386839)⟩⟩,⟨⟨17095888457015016540002185760,17095888457015016556793337323⟩,⟨(-61686485518842746544328897481),(-61686485518842746528492633494)⟩⟩,⟨⟨17385007689009774571590898791,17385007689009774588357747660⟩,⟨(-61727645146905002422248817794),(-61727645146905002406439824275)⟩⟩,⟨⟨17670528216033060615922110724,17670528216033060632662159820⟩,⟨(-61759369757161249603964089265),(-61759369757161249588183934852)⟩⟩,⟨⟨17952134807759095361433093338,17952134807759095378144164383⟩,⟨(-61781132087291394019414039023),(-61781132087291394003664696648)⟩⟩,⟨⟨18229803233207923481189992665,18229803233207923497869497802⟩,⟨(-61793417273762555376454919090),(-61793417273762555360738620440)⟩⟩,⟨⟨18503181040059935330846299635,18503181040059935347490678808⟩,⟨(-61795579659057486234393593398),(-61795579659057486218716718893)⟩⟩,⟨⟨18772288095563448530873681425,18772288095563448547481970369⟩,⟨(-61788230508122298352391649006),(-61788230508122298336750820765)⟩⟩,⟨⟨19036732582516068865954896052,19036732582516068882523256197⟩,⟨(-61770604362130427002047900762),(-61770604362130426986450549829)⟩⟩,⟨⟨19296581500290932795778421112,19296581500290932812306393020⟩,⟨(-61743440381956466393827493548),(-61743440381956466378269052558)⟩⟩,⟨⟨19551401463769977898962429335,19551401463769977915445025884⟩,⟨(-61705851740730076334826430597),(-61705851740730076319317682685)⟩⟩] +lemma amp4_02_8_eq : ∀ k : Fin 16, amp4_0Expr 2 8 k = amp4_02_8 k := by decide +kernel +noncomputable def amp4_02_9 : Fin 16 → CBox := ![⟨⟨19801309687552755847678058413,19801309687552755864113206361⟩,⟨(-61658707418398045855290324213),(-61658707418398045839831645332)⟩⟩,⟨⟨20045828949971502225585670269,20045828949971502241970547998⟩,⟨(-61600997486843855150828931659),(-61600997486843855135424342684)⟩⟩,⟨⟨20285129816748110872324144324,20285129816748110888660851711⟩,⟨(-61533722829510703209759724502),(-61533722829510703194397319161)⟩⟩,⟨⟨20518688889592298562429261473,20518688889592298578710310405⟩,⟨(-61455748510624834926925269176),(-61455748510624834911623070164)⟩⟩,⟨⟨20746733278067739076562824437,20746733278067739092786339632⟩,⟨(-61368209569358896436452922054),(-61368209569358896421210939252)⟩⟩,⟨⟨20968690989484188844118669592,20968690989484188860283052816⟩,⟨(-61269843974958385975662730023),(-61269843974958385960481286030)⟩⟩,⟨⟨21184848931314704260912906110,21184848931314704277014375702⟩,⟨(-61161923349913194962125593947),(-61161923349913194947010616478)⟩⟩,⟨⟨21394584014239112431161787215,21394584014239112447198693047⟩,⟨(-61043056291505091454730746308),(-61043056291505091439682529825)⟩⟩,⟨⟨21598246264137755765983270958,21598246264137755781952397196⟩,⟨(-60914653617135678087537591323),(-60914653617135678072560127340)⟩⟩,⟨⟨21795158901087172386110669730,21795158901087172402008633455⟩,⟨(-60775192075596587837917558572),(-60775192075596587823016311710)⟩⟩,⟨⟨21985738462012314248213484131,21985738462012314264050847640⟩,⟨(-60626224484662940127927985827),(-60626224484662940113069123303)⟩⟩,⟨⟨22169251782766751210099660688,22169251782766751225862294489⟩,⟨(-60466093057436351373680950167),(-60466093057436351358899653864)⟩⟩,⟨⟨22346185382511130134573819447,22346185382511130150259914442⟩,⟨(-60296495622583303130771419025),(-60296495622583303116067919405)⟩⟩,⟨⟨22515746911016388806181900188,22515746911016388821787941785⟩,⟨(-60115636947139037692065276528),(-60115636947139037677445289425)⟩⟩,⟨⟨22678496426631719822665654634,22678496426631719838191630353⟩,⟨(-59925363098890158532959482210),(-59925363098890158518418765686)⟩⟩,⟨⟨22833579473571542212810616804,22833579473571542228251824624⟩,⟨(-59723738251229604665568590698),(-59723738251229604651115768510)⟩⟩] +lemma amp4_02_9_eq : ∀ k : Fin 16, amp4_0Expr 2 9 k = amp4_02_9 k := by decide +kernel +noncomputable def amp4_02_10 : Fin 16 → CBox := ![⟨⟨22981633300190248250590004971,22981633300190248265948782488⟩,⟨(-59512760171284748197514246515),(-59512760171284748183138885011)⟩⟩,⟨⟨23121738297799915923209218155,23121738297799915938479472450⟩,⟨(-59290349038316896110751611742),(-59290349038316896096466205888)⟩⟩,⟨⟨23254612658551026335849020533,23254612658551026351028826396⟩,⟨(-59058658027098961839102344614),(-59058658027098961824907917303)⟩⟩,⟨⟨23379268434376153275585958525,23379268434376153290674293775⟩,⟨(-58815459651755407762529113176),(-58815459651755407748424767301)⟩⟩,⟨⟨23496508628236617219511460627,23496508628236617234504015784⟩,⟨(-58563066469211670207939549772),(-58563066469211670193932190541)⟩⟩,⟨⟨23605273614679661154617280912,23605273614679661169513275325⟩,⟨(-58299099367213351278441707558),(-58299099367213351264530101704)⟩⟩,⟨⟨23706455199255048790125072438,23706455199255048804922127967⟩,⟨(-58026034545940520686788743474),(-58026034545940520672975227612)⟩⟩,⟨⟨23798918575897508496191967119,23798918575897508510886893076⟩,⟨(-57741336993174612737761228826),(-57741336993174612724050341104)⟩⟩,⟨⟨23883648482287129715659651660,23883648482287129730250034696⟩,⟨(-57447651123004775875569525287),(-57447651123004775861963417287)⟩⟩,⟨⟨23959431248126959813236690231,23959431248126959827719765037⟩,⟨(-57142281412516486079247619957),(-57142281412516486065750028592)⟩⟩,⟨⟨24027348825197648450102751364,24027348825197648464475303319⟩,⟨(-56828045395773452721196418686),(-56828045395773452707811695200)⟩⟩,⟨⟨24086104798098504398923819215,24086104798098504413228288300⟩,⟨(-56502082063423845866951481371),(-56502082063423845853576974797)⟩⟩,⟨⟨24136882783668556774259505130,24136882783668556788451852333⟩,⟨(-56167387340136493601534530680),(-56167387340136493588271042235)⟩⟩,⟨⟨24178299524479406966475328256,24178299524479406980553771443⟩,⟨(-55820929358023382470623087022),(-55820929358023382457472042480)⟩⟩,⟨⟨24211644941099333254561364033,24211644941099333268523697410⟩,⟨(-55465888100464746008652499146),(-55465888100464745995616048540)⟩⟩,⟨⟨24235444600068984012264613442,24235444600068984026109394337⟩,⟨(-55099055037248306628382596460),(-55099055037248306615461215064)⟩⟩] +lemma amp4_02_10_eq : ∀ k : Fin 16, amp4_0Expr 2 10 k = amp4_02_10 k := by decide +kernel +noncomputable def amp4_02_11 : Fin 16 → CBox := ![⟨⟨24251099573278797932672870948,24251099573278797946397958389⟩,⟨(-54723800313256923574692124215),(-54723800313256923561887603545)⟩⟩,⟨⟨24257039656559110292319227755,24257039656559110305923427645⟩,⟨(-54336732460574162050304616853),(-54336732460574162037617233200)⟩⟩,⟨⟨24254782153702901223019490466,24254782153702901236499360162⟩,⟨(-53941418365208258041082537663),(-53941418365208258028517359697)⟩⟩,⟨⟨24242656207905948858002208018,24242656207905948871358385674⟩,⟨(-53534276829399654235847829954),(-53534276829399654223400818783)⟩⟩,⟨⟨24222300695793620048262015074,24222300695793620061489999185⟩,⟨(-53119078584576036857986008433),(-53119078584576036845664399448)⟩⟩,⟨⟨24191938908740600509507289176,24191938908740600522605873816⟩,⟨(-52692045342982261665952552184),(-52692045342982261653756644876)⟩⟩,⟨⟨24153336928664241516382489708,24153336928664241529348648672⟩,⟨(-52257159364861488858085484101),(-52257159364861488846019478009)⟩⟩,⟨⟨24104606644636262032711462415,24104606644636262045550564171⟩,⟨(-51810437285976343924174209537),(-51810437285976343912224087367)⟩⟩,⟨⟨24047647303475182962378514646,24047647303475182975081770951⟩,⟨(-51356081219975404913345504628),(-51356081219975404901527708060)⟩⟩,⟨⟨23980453451446492476046792618,23980453451446492488612773693⟩,⟨(-50889894046760940209127399737),(-50889894046760940197442845176)⟩⟩,⟨⟨23905063827831287798581725711,23905063827831287811010470282⟩,⟨(-50416306770206392306268724822),(-50416306770206392294715222802)⟩⟩,⟨⟨23819349261332177071940455761,23819349261332177084227559839⟩,⟨(-49930899065884821092413855497),(-49930899065884821080998368619)⟩⟩,⟨⟨23725494726085482311703952043,23725494726085482323848592892⟩,⟨(-49438340658465771311229164231),(-49438340658465771299951192021)⟩⟩,⟨⟨23621240473502539038773933750,23621240473502539050773924857⟩,⟨(-48933977714096870309473283624),(-48933977714096870298335322495)⟩⟩,⟨⟨23508924923834064882263744297,23508924923834064894116657408⟩,⟨(-48422729396441952939961319651),(-48422729396441952928966501787)⟩⟩,⟨⟨23386150348106776829384569196,23386150348106776841087419251⟩,⟨(-47899697099569643544858513107),(-47899697099569643534010739473)⟩⟩] +lemma amp4_02_11_eq : ∀ k : Fin 16, amp4_0Expr 2 11 k = amp4_02_11 k := by decide +kernel +noncomputable def amp4_02_12 : Fin 16 → CBox := ![⟨⟨23255416355315092186701616748,23255416355315092198281979648⟩,⟨(-47370061140459967989279690189),(-47370061140459967978520710259)⟩⟩,⟨⟨23114179222126173360991374480,23114179222126173372422598889⟩,⟨(-46828665804061895014417770669),(-46828665804061895003800329348)⟩⟩,⟨⟨22965108092852812167877801096,22965108092852812179158397577⟩,⟨(-46280965397009150544208367090),(-46280965397009150533733877578)⟩⟩,⟨⟨22805504546530246734685601438,22805504546530246745813989035⟩,⟨(-45721533547900628786922859092),(-45721533547900628776592446506)⟩⟩,⟨⟨22638216297927530242119603241,22638216297927530253094302661⟩,⟨(-45156112658074627389163888954),(-45156112658074627378978830349)⟩⟩,⟨⟨22460380744372878346978233434,22460380744372878357798191052⟩,⟨(-44578990783793092122187179821),(-44578990783793092112147775867)⟩⟩,⟨⟨22275033993891594803989846383,22275033993891594814652247107⟩,⟨(-43996213966587486237092004152),(-43996213966587486227202469516)⟩⟩,⟨⟨22079138889913241382253615248,22079138889913241392760597032⟩,⟨(-43401768219601819897657133195),(-43401768219601819887911294323)⟩⟩,⟨⟨21875930660798627819223949768,21875930660798627829570142673⟩,⟨(-42802020412496186024966802495),(-42802020412496186015373720677)⟩⟩,⟨⟨21662186209249192763455930210,21662186209249192773640586911⟩,⟨(-42190636270328331659170570697),(-42190636270328331649730023559)⟩⟩,⟨⟨21441351653265516713808516591,21441351653265516723829948292⟩,⟨(-41574322560160752087642490552),(-41574322560160752078356618028)⟩⟩,⟨⟨21210005403344372455178607304,21210005403344372465034700960⟩,⟨(-40946404439649227923578066365),(-40946404439649227914449050589)⟩⟩,⟨⟨20971817442746619423467467564,20971817442746619433155701035⟩,⟨(-40313949807985743547013139108),(-40313949807985743538044600459)⟩⟩,⟨⟨20723153794710415291578113284,20723153794710415301115666468⟩,⟨(-39669920631426435894308170405),(-39669920631426435885465519042)⟩⟩,⟨⟨20467922686069874599969969182,20467922686069874609338479451⟩,⟨(-39021769681444076799928894925),(-39021769681444076791246489544)⟩⟩,⟨⟨20202262299366847077732429775,20202262299366847086930279705⟩,⟨(-38362070391662964289786076409),(-38362070391662964281265136164)⟩⟩] +lemma amp4_02_12_eq : ∀ k : Fin 16, amp4_0Expr 2 12 k = amp4_02_12 k := by decide +kernel +noncomputable def amp4_02_13 : Fin 16 → CBox := ![⟨⟨19930335122569564581438516312,19930335122569564590465358334⟩,⟨(-37698687060910749381215431607),(-37698687060910749372855554820)⟩⟩,⟨⟨19648034226035689978996009543,19648034226035689987852418360⟩,⟨(-37023776081384766612468375264),(-37023776081384766604266913313)⟩⟩,⟨⟨19359794302657532650556193299,19359794302657532659237932057⟩,⟨(-36345643346037159485669229000),(-36345643346037159477633485911)⟩⟩,⟨⟨19061243904824525893469327168,19061243904824525901975846375⟩,⟨(-35655995980880480014554714712),(-35655995980880480006683892820)⟩⟩,⟨⟨18757110151215029558943825534,18757110151215029567272903909⟩,⟨(-34963615558774036555415154045),(-34963615558774036547712654509)⟩⟩,⟨⟨18442735147894587392673593520,18442735147894587400835926537⟩,⟨(-34259723325597251501762242324),(-34259723325597251494206556021)⟩⟩,⟨⟨18123161369778897283572424244,18123161369778897291557013223⟩,⟨(-33553615387626237329678662142),(-33553615387626237322289844648)⟩⟩,⟨⟨17793419544774984108453785610,17793419544774984116258565419⟩,⟨(-32835985273731698195488852041),(-32835985273731698188268920361)⟩⟩,⟨⟨17458893682166788332840836495,17458893682166788340465812441⟩,⟨(-32116688176346159869450080602),(-32116688176346159862398490209)⟩⟩,⟨⟨17114274595032739870586980013,17114274595032739878031589036⟩,⟨(-31385841805106312756592505139),(-31385841805106312749708713410)⟩⟩,⟨⟨16765317928981978330441491171,16765317928981978337704432633⟩,⟨(-30653911861124241214434909769),(-30653911861124241207721121682)⟩⟩,⟨⟨16406341680881195363519517176,16406341680881195370606976734⟩,⟨(-29910384550181176270845396531),(-29910384550181176264288530149)⟩⟩,⟨⟨16043508017433088294597529216,16043508017433088301499902081⟩,⟨(-29166395861544427130872033394),(-29166395861544427124489424597)⟩⟩,⟨⟨15670723881909517348843858261,15670723881909517355560177139⟩,⟨(-28410735546851922307790177057),(-28410735546851922301581899869)⟩⟩,⟨⟨15294598734220721943992964926,15294598734220721950524119846⟩,⟨(-27655279932353967407902354464),(-27655279932353967401866878713)⟩⟩,⟨⟨14908583633281858221801121569,14908583633281858228143988275⟩,⟨(-26888045920748681820870678319),(-26888045920748681815011790176)⟩⟩] +lemma amp4_02_13_eq : ∀ k : Fin 16, amp4_0Expr 2 13 k = amp4_02_13 k := by decide +kernel +noncomputable def amp4_02_14 : Fin 16 → CBox := ![⟨⟨14519783431090773806303477667,14519783431090773812464864537⟩,⟨(-26121732985813821896058821042),(-26121732985813821890364294461)⟩⟩,⟨⟨14121140227209152358999803591,14121140227209152364971910221⟩,⟨(-25343494481598689798725674092),(-25343494481598689793207875326)⟩⟩,⟨⟨13720311595397776586846504922,13720311595397776592630807656⟩,⟨(-24566951898681369157286888703),(-24566951898681369151943557203)⟩⟩,⟨⟨13309667154750930040945391854,13309667154750930046537413227⟩,⟨(-23778286223002084607142226805),(-23778286223002084601979431470)⟩⟩,⟨⟨12897486322316428438736615383,12897486322316428444143331110⟩,⟨(-22992160324867102865703972884),(-22992160324867102860709686473)⟩⟩,⟨⟨12475489280168229140980071450,12475489280168229146194359361⟩,⟨(-22193650704154673738871770677),(-22193650704154673734056833752)⟩⟩,⟨⟨12052661712402240051284112794,12052661712402240056310563995⟩,⟨(-21398607546610297168944164216),(-21398607546610297164301153373)⟩⟩,⟨⟨11619979831438862225921276318,11619979831438862230753430710⟩,⟨(-20590840276719456091437838108),(-20590840276719456086976145129)⟩⟩,⟨⟨11187240230379428726428929888,11187240230379428731068404710⟩,⟨(-19787567417700190610404999802),(-19787567417700190606122535413)⟩⟩,⟨⟨10744557174851744833677605228,10744557174851744838124718987⟩,⟨(-18971128092466434842464096376),(-18971128092466434838358272797)⟩⟩,⟨⟨10302670083048198137313404696,10302670083048198141566308546⟩,⟨(-18160337490009399426469186736),(-18160337490009399422544422766)⟩⟩,⟨⟨9850681311994956269567650613,9850681311994956273626421877⟩,⟨(-17335805775651577605096387045),(-17335805775651577601350234451)⟩⟩,⟨⟨9400442716038465816829061282,9400442716038465820695434834⟩,⟨(-16518238486698559758046741991),(-16518238486698559754477455872)⟩⟩,⟨⟨8939849979118720165835031017,8939849979118720169503392197⟩,⟨(-15686180542716245906124767464),(-15686180542716245902739843696)⟩⟩,⟨⟨8482090613140282953607821100,8482090613140282957082415533⟩,⟨(-14862614430602471730300697892),(-14862614430602471727094370922)⟩⟩,⟨⟨8013594107529079091965262939,8013594107529079095242647311⟩,⟨(-14023571341419156255114903708),(-14023571341419156252090527214)⟩⟩] +lemma amp4_02_14_eq : ∀ k : Fin 16, amp4_0Expr 2 14 k = amp4_02_14 k := by decide +kernel +noncomputable def amp4_02_15 : Fin 16 → CBox := ![⟨⟨7549185761597201842795785296,7549185761597201845877964967⟩,⟨(-13194834047155305385582480569),(-13194834047155305382738457210)⟩⟩,⟨⟨7073472134172852132847855003,7073472134172852135731091171⟩,⟨(-12349303114435206239397042398),(-12349303114435206236737071771)⟩⟩,⟨⟨6603339560705217220342147616,6603339560705217223029321313⟩,⟨(-11516294777896590192948836648),(-11516294777896590190470324288)⟩⟩,⟨⟨6121062002700662189224772716,6121062002700662191712864784⟩,⟨(-10664697168311882425669145757),(-10664697168311882423374039283)⟩⟩,⟨⟨5646205995383184665938607698,5646205995383184668230872643⟩,⟨(-9828432549116667577281513810),(-9828432549116667575167041392)⟩⟩,⟨⟨5157947967828088156741151996,5157947967828088158832721107⟩,⟨(-8971052636411219997331659459),(-8971052636411219995402544493)⟩⟩,⟨⟨4679492848142491693522992666,4679492848142491695418060909⟩,⟨(-8132745552467294195619336262),(-8132745552467294193871939414)⟩⟩,⟨⟨4185694085093595247918097759,4185694085093595249611977956⟩,⟨(-7269604964512430655849387807),(-7269604964512430654287307843)⟩⟩,⟨⟨3704995395910040752291532470,3704995395910040753789299931⟩,⟨(-6430857048049550305497265703),(-6430857048049550304116284807)⟩⟩,⟨⟨3205777464660733545956072107,3205777464660733547250909566⟩,⟨(-5561414779498908855475806991),(-5561414779498908854282141382)⟩⟩,⟨⟨2724705843855476536180409635,2724705843855476537279870405⟩,⟨(-4724709412834161582068943720),(-4724709412834161581055704885)⟩⟩,⟨⟨2219368213009897905986601444,2219368213009897906881462896⟩,⟨(-3846991278603234543755947880),(-3846991278603234542931476653)⟩⟩,⟨⟨1741261387283875055177546376,1741261387283875055878832357⟩,⟨(-3017344759125023950479188000),(-3017344759125023949833451174)⟩⟩,⟨⟨1226268809558070055093029449,1226268809558070055586448814⟩,⟨(-2124459778092482373499824147),(-2124459778092482373045744363)⟩⟩,⟨⟨760825733026136673885849161,760825733026136674190878901⟩,⟨(-1317900465836448054998654648),(-1317900465836448054718784744)⟩⟩,⟨⟨216174027242030330928252908,216174027242030331014287871⟩,⟨(-374427922718183715764729704),(-374427922718183715686300430)⟩⟩] +lemma amp4_02_15_eq : ∀ k : Fin 16, amp4_0Expr 2 15 k = amp4_02_15 k := by decide +kernel +noncomputable def amp4_02 : Fin 16 → Fin 16 → CBox := ![amp4_02_0,amp4_02_1,amp4_02_2,amp4_02_3,amp4_02_4,amp4_02_5,amp4_02_6,amp4_02_7,amp4_02_8,amp4_02_9,amp4_02_10,amp4_02_11,amp4_02_12,amp4_02_13,amp4_02_14,amp4_02_15] +lemma amp4_02_eq (i k : Fin 16) : amp4_0Expr 2 i k = amp4_02 i k := by + fin_cases i + · exact amp4_02_0_eq k + · exact amp4_02_1_eq k + · exact amp4_02_2_eq k + · exact amp4_02_3_eq k + · exact amp4_02_4_eq k + · exact amp4_02_5_eq k + · exact amp4_02_6_eq k + · exact amp4_02_7_eq k + · exact amp4_02_8_eq k + · exact amp4_02_9_eq k + · exact amp4_02_10_eq k + · exact amp4_02_11_eq k + · exact amp4_02_12_eq k + · exact amp4_02_13_eq k + · exact amp4_02_14_eq k + · exact amp4_02_15_eq k +noncomputable def amp4_03_0 : Fin 16 → CBox := ![⟨⟨(-108087776645299701635849792),(-108087776645299701528516207)⟩,⟨(-187215282955920083326247305),(-187215282955920083228521381)⟩⟩,⟨⟨(-380437037396694513637856667),(-380437037396694513258963554)⟩,⟨(-658992098116728399853081106),(-658992098116728399507199471)⟩⟩,⟨⟨(-613242635481344000221670607),(-613242635481343999610044316)⟩,⟨(-1062417350121579189068454904),(-1062417350121579188509429328)⟩⟩,⟨⟨(-870931976755011540739550774),(-870931976755011539870619365)⟩,⟨(-1509194217221818684300271307),(-1509194217221818683505884940)⟩⟩,⟨⟨(-1110319070478132265149259258),(-1110319070478132264041050898)⟩,⟨(-1924595429164146569635611743),(-1924595429164146568622212895)⟩⟩,⟨⟨(-1363517824735395271258832934),(-1363517824735395269897559521)⟩,⟨(-2364372377265822354670544236),(-2364372377265822353425594888)⟩⟩,⟨⟨(-1604803803089663534819993577),(-1604803803089663533217326539)⟩,⟨(-2784024389604645925651696762),(-2784024389604645924185778233)⟩⟩,⟨⟨(-1855445817418033836788629156),(-1855445817418033834935150567)⟩,⟨(-3220534816721497140442323413),(-3220534816721497138746865353)⟩⟩,⟨⟨(-2097127404323008791483639222),(-2097127404323008789388072932)⟩,⟨(-3642216286327388832754453066),(-3642216286327388830837370328)⟩⟩,⟨⟨(-2345727668755707966704347912),(-2345727668755707964359922506)⟩,⟨(-4076732595919636765173136095),(-4076732595919636763028488359)⟩⟩,⟨⟨(-2587033366433380936301047395),(-2587033366433380933714396539)⟩,⟨(-4499485578206733893911034493),(-4499485578206733891544503085)⟩⟩,⟨⟨(-2833693816152118499866442076),(-2833693816152118497032161167)⟩,⟨(-4932560110225703507222911458),(-4932560110225703504629679312)⟩⟩,⟨⟨(-3074107418194097130629580350),(-3074107418194097127553786404)⟩,⟨(-5355863627914077880908564265),(-5355863627914077878094305865)⟩⟩,⟨⟨(-3318768403870281330443913851),(-3318768403870281327122286383)⟩,⟨(-5787763073620396326032281011),(-5787763073620396322993187316)⟩⟩,⟨⟨(-3557886570805400324354317857),(-3557886570805400320791592860)⟩,⟨(-6211285304264541022429173356),(-6211285304264541019169122983)⟩⟩,⟨⟨(-3800413591088733260694223550),(-3800413591088733256886764886)⟩,⟨(-6642139805687678427527573175),(-6642139805687678424043287519)⟩⟩] +lemma amp4_03_0_eq : ∀ k : Fin 16, amp4_0Expr 3 0 k = amp4_03_0 k := by decide +kernel +noncomputable def amp4_03_1 : Fin 16 → CBox := ![⟨⟨(-4037891521804236566764266229),(-4037891521804236562716912585)⟩,⟨(-7065642869188659993575547189),(-7065642869188659989871521374)⟩⟩,⟨⟨(-4278111742531267937263701135),(-4278111742531267932973589779)⟩,⟨(-7495508165641405021483483566),(-7495508165641405017557269480)⟩⟩,⟨⟨(-4513638956975200476145852365),(-4513638956975200471617411283)⟩,⟨(-7918805083922768890086749771),(-7918805083922768885942450927)⟩⟩,⟨⟨(-4751358878317501979153708060),(-4751358878317501974383286803)⟩,⟨(-8347692026678966673500974235),(-8347692026678966669134330189)⟩⟩,⟨⟨(-4984647213196184812565480991),(-4984647213196184807558479111)⟩,⟨(-8770624858115938512343871988),(-8770624858115938507760939540)⟩⟩,⟨⟨(-5219662162292792063963929385),(-5219662162292792058718184612)⟩,⟨(-9198514789710970618851574613),(-9198514789710970614050347742)⟩⟩,⟨⟨(-5450439363487605993448567573),(-5450439363487605987966439275)⟩,⟨(-9620942481531153230169649123),(-9620942481531153225151024878)⟩⟩,⟨⟨(-5682539044503830972047787589),(-5682539044503830966329183079)⟩,⟨(-10047795812176770888666054909),(-10047795812176770883431363412)⟩⟩,⟨⟨(-5910545170156570121463521314),(-5910545170156570115510637896)⟩,⟨(-10469586948012868591736897580),(-10469586948012868586286891227)⟩⟩,⟨⟨(-6139517149294759668304526932),(-6139517149294759662115647463)⟩,⟨(-10895348183663714760550900827),(-10895348183663714754883761507)⟩⟩,⟨⟨(-6364502488150114251617195955),(-6364502488150114245197841371)⟩,⟨(-11316376385185744662083460220),(-11316376385185744656205946719)⟩⟩,⟨⟨(-6590134522594449260937173093),(-6590134522594449254284333046)⟩,⟨(-11740977184192445344599004262),(-11740977184192445338506756261)⟩⟩,⟨⟨(-6811858376238199973004582345),(-6811858376238199966124119316)⟩,⟨(-12161118041179582896651401580),(-12161118041179582890351895904)⟩⟩,⟨⟨(-7033940058876825675515693440),(-7033940058876825668403475151)⟩,⟨(-12584479119256691705561669653),(-12584479119256691699048305055)⟩⟩,⟨⟨(-7252170038834943531409195883),(-7252170038834943524069645926)⟩,⟨(-13003608046024739172352934370),(-13003608046024739165630693792)⟩⟩,⟨⟨(-7470494018033523045526091070),(-7470494018033523037958070895)⟩,⟨(-13425640381007352122298566546),(-13425640381007352115365980121)⟩⟩] +lemma amp4_03_1_eq : ∀ k : Fin 16, amp4_0Expr 3 1 k = amp4_03_1 k := by decide +kernel +noncomputable def amp4_03_2 : Fin 16 → CBox := ![⟨⟨(-7685005660532958679268618743),(-7685005660532958671478316109)⟩,⟨(-13843631060004850605178667703),(-13843631060004850598043967410)⟩⟩,⟨⟨(-7899368584324722178959511831),(-7899368584324722170943095792)⟩,⟨(-14264236657416372771213669182),(-14264236657416372763870349442)⟩⟩,⟨⟨(-8109945166182524758362185318),(-8109945166182524750123341107)⟩,⟨(-14680959870426580312883587789),(-14680959870426580305335416984)⟩⟩,⟨⟨(-8320148440411834242973211220),(-8320148440411834234511338010)⟩,⟨(-15100032247164096962725391255),(-15100032247164096954971491465)⟩⟩,⟨⟨(-8526580924464771545358360786),(-8526580924464771536676068840)⟩,⟨(-15515354972300576928742588170),(-15515354972300576920784810986)⟩⟩,⟨⟨(-8732431340398425837686877270),(-8732431340398425828789077751)⟩,⟨(-15932779456717881207491038741),(-15932779456717881199338383000)⟩⟩,⟨⟨(-8934518404974519797017819885),(-8934518404974519787903342647)⟩,⟨(-16346564154487282099731653436),(-16346564154487282091379118079)⟩⟩,⟨⟨(-9135828671805620940902931853),(-9135828671805620931572522940)⟩,⟨(-16762218066256831599774593203),(-16762218066256831591223434284)⟩⟩,⟨⟨(-9333376794432716792170500551),(-9333376794432716782626567377)⟩,⟨(-17174322105037977340541716282),(-17174322105037977331793452456)⟩⟩,⟨⟨(-9529965999846553676309284679),(-9529965999846553666551905449)⟩,⟨(-17588074856837975371643309262),(-17588074856837975362697819732)⟩⟩,⟨⟨(-9722789575135201166549970568),(-9722789575135201156582259111)⟩,⟨(-17998350044888943425134195646),(-17998350044888943415994301360)⟩⟩,⟨⟨(-9914483589414670316726813392),(-9914483589414670306554825174)⟩,⟨(-18410063194525890221535380177),(-18410063194525890212211911698)⟩⟩,⟨⟨(-10102405067272650550377215661),(-10102405067272650539997397471)⟩,⟨(-18818355396288422469863429041),(-18818355396288422460346861613)⟩⟩,⟨⟨(-10289036901471448280852416378),(-10289036901471448270266203755)⟩,⟨(-19227882669175516151877917784),(-19227882669175516142170366682)⟩⟩,⟨⟨(-10471886935880932280078647418),(-10471886935880932269288354017)⟩,⟨(-19634031490581899119898474690),(-19634031490581899110001269850)⟩⟩,⟨⟨(-10653297061338301663411000631),(-10653297061338301652419282867)⟩,⟨(-20041218786735040700782286797),(-20041218786735040690699719873)⟩⟩] +lemma amp4_03_2_eq : ∀ k : Fin 16, amp4_0Expr 3 2 k = amp4_03_2 k := by decide +kernel +noncomputable def amp4_03_3 : Fin 16 → CBox := ![⟨⟨(-10830914662657600158438088048),(-10830914662657600147246755034)⟩,⟨(-20445057318828856988444650716),(-20445057318828856978177103790)⟩⟩,⟨⟨(-11006951296947727439191089879),(-11006951296947727427800705862)⟩,⟨(-20849742714639315790657216740),(-20849742714639315780204925776)⟩⟩,⟨⟨(-11179183982570730033656924833),(-11179183982570730022070381838)⟩,⟨(-21251097327934799363162520293),(-21251097327934799352527885661)⟩⟩,⟨⟨(-11349703345494939034997247358),(-11349703345494939023225010828)⟩,⟨(-21653111080276394646154699113),(-21653111080276394635356714278)⟩⟩,⟨⟨(-11516407285010085032298486018),(-11516407285010085020333376814)⟩,⟨(-22051801264416997701866260694),(-22051801264416997690888163258)⟩⟩,⟨⟨(-11681273827215117694978903040),(-11681273827215117682822812804)⟩,⟨(-22450965822738100384875274651),(-22450965822738100373719586550)⟩⟩,⟨⟨(-11842313979139518098458121480),(-11842313979139518086114226401)⟩,⟨(-22846804067498242305503528584),(-22846804067498242294173178180)⟩⟩,⟨⟨(-12001400585230277160493242349),(-12001400585230277147963115759)⟩,⟨(-23242934098175277717855451830),(-23242934098175277706352255276)⟩⟩,⟨⟨(-12156650823073975905048147556),(-12156650823073975892334315136)⟩,⟨(-23635725812889229407151873306),(-23635725812889229395477493012)⟩⟩,⟨⟨(-12309838990586571068890211784),(-12309838990586571055996250831)⟩,⟨(-24028628239110001367424112510),(-24028628239110001355584169286)⟩⟩,⟨⟨(-12459182216505905218932908510),(-12459182216505905205859671122)⟩,⟨(-24418171708345641133049891513),(-24418171708345641121042775674)⟩⟩,⟨⟨(-12606362211752111360185997311),(-12606362211752111346935798422)⟩,⟨(-24807645768036187063382170549),(-24807645768036187051210948795)⟩⟩,⟨⟨(-12749690456432380786345413363),(-12749690456432380772920939718)⟩,⟨(-25193732141850518957849951819),(-25193732141850518945516571614)⟩⟩,⟨⟨(-12890761447976222142637077003),(-12890761447976222129039885561)⟩,⟨(-25579569465583404430068076229),(-25579569465583404417574020290)⟩⟩,⟨⟨(-13027975955678080901405202446),(-13027975955678080887638207088)⟩,⟨(-25961982783063382181959820082),(-25961982783063382169307464201)⟩⟩,⟨⟨(-13162846126029484040076372706),(-13162846126029484026141253274)⟩,⟨(-26343967493437228559833737607),(-26343967493437228547024709038)⟩⟩] +lemma amp4_03_3_eq : ∀ k : Fin 16, amp4_0Expr 3 3 k = amp4_03_3 k := by decide +kernel +noncomputable def amp4_03_4 : Fin 16 → CBox := ![⟨⟨(-13293857423965123422798130038),(-13293857423965123408712153477)⟩,⟨(-26722484738486366732862162241),(-26722484738486366719927670782)⟩⟩,⟨⟨(-13422444059953820462133758630),(-13422444059953820447882082579)⟩,⟨(-27100393572110621621446117891),(-27100393572110621608354590201)⟩⟩,⟨⟨(-13547172011345183423851139910),(-13547172011345183409437470216)⟩,⟨(-27474784760618990690553473486),(-27474784760618990677308817558)⟩⟩,⟨⟨(-13669401573555797797106662487),(-13669401573555797782533292274)⟩,⟨(-27848387213549737839298832702),(-27848387213549737825903706378)⟩⟩,⟨⟨(-13787775413879760299005020501),(-13787775413879760284275284104)⟩,⟨(-28218415511203391653725183581),(-28218415511203391640182751625)⟩⟩,⟨⟨(-13903583585475940668598982257),(-13903583585475940653714217413)⟩,⟨(-28587474008437816102267421102),(-28587474008437816088578308659)⟩⟩,⟨⟨(-14015541941529172493699730108),(-14015541941529172478664495739)⟩,⟨(-28952895878498659655696336777),(-28952895878498659641866223900)⟩⟩,⟨⟨(-14124873656763304513606544855),(-14124873656763304498421784875)⟩,⟨(-29317165967935082396599352835),(-29317165967935082382627965799)⟩⟩,⟨⟨(-14230364548288532463161903180),(-14230364548288532447830533525)⟩,⟨(-29677731348364664707318552620),(-29677731348364664693208168917)⟩⟩,⟨⟨(-14333174000978512772470214815),(-14333174000978512756998335274)⟩,⟨(-30036961919462770539204530511),(-30036961919462770524965552184)⟩⟩,⟨⟨(-14432154824688615852118188147),(-14432154824688615836504603097)⟩,⟨(-30392414428781566006452661390),(-30392414428781565992078771452)⟩⟩,⟨⟨(-14528405456940400019807022491),(-14528405456940400004054541762)⟩,⟨(-30746347956006963008778134021),(-30746347956006962994272768076)⟩⟩,⟨⟨(-14620842952860431984307029989),(-14620842952860431968418407662)⟩,⟨(-31096425127280389272553011546),(-31096425127280389257918077512)⟩⟩,⟨⟨(-14710507424321566679164850645),(-14710507424321566663143758764)⟩,⟨(-31444797938284112185657436379),(-31444797938284112170898155654)⟩⟩,⟨⟨(-14796377624443827089400465943),(-14796377624443827073248465481)⟩,⟨(-31789231480612333456613658460),(-31789231480612333441729383140)⟩⟩,⟨⟨(-14879437762386679085219956520),(-14879437762386679068940185917)⟩,⟨(-32131774048975759068513523686),(-32131774048975759053508276757)⟩⟩] +lemma amp4_03_4_eq : ∀ k : Fin 16, amp4_0Expr 3 4 k = amp4_03_4 k := by decide +kernel +noncomputable def amp4_03_5 : Fin 16 → CBox := ![⟨⟨(-14958725921702116241593894526),(-14958725921702116225189112226)⟩,⟨(-32470290135839666992946248548),(-32470290135839666977821922932)⟩⟩,⟨⟨(-15035172652254284752490351706),(-15035172652254284735962830710)⟩,⟨(-32806727398105894251517648764),(-32806727398105894236276338368)⟩⟩,⟨⟨(-15107873162286132221965579008),(-15107873162286132205318117752)⟩,⟨(-33139046981889175151932497549),(-33139046981889175136576159887)⟩⟩,⟨⟨(-15177706423148238170335348139),(-15177706423148238153570376227)⟩,⟨(-33469098678501261373902700692),(-33469098678501261358433694046)⟩⟩,⟨⟨(-15243822708171844175037286788),(-15243822708171844158157873415)⟩,⟨(-33794937830470193361639420943),(-33794937830470193346060282401)⟩⟩,⟨⟨(-15307051343188484543518904463),(-15307051343188484526554077560)⟩,⟨(-34118318870143257840098574441),(-34118318870143257824470882888)⟩⟩,⟨⟨(-15366595739375523235730245438),(-15366595739375523218654985252)⟩,⟨(-34437389145123439922222253920),(-34437389145123439906486237289)⟩⟩,⟨⟨(-15423237375352834048604312227),(-15423237375352834031421718514)⟩,⟨(-34753809992090448811966962413),(-34753809992090448796126324289)⟩⟩,⟨⟨(-15476230993129035694614192908),(-15476230993129035677327956244)⟩,⟨(-35065818817034323119893080464),(-35065818817034323103951735940)⟩⟩,⟨⟨(-15526311899321362471211158004),(-15526311899321362453823801077)⟩,⟨(-35374985900523536675194195312),(-35374985900523536659154517432)⟩⟩,⟨⟨(-15572784469274971188056118314),(-15572784469274971170571521310)⟩,⟨(-35679636986115350497516172167),(-35679636986115350481382540281)⟩⟩,⟨⟨(-15616339399993066259339528898),(-15616339399993066241760308472)⟩,⟨(-35981253131340339150220725924),(-35981253131340339133995687959)⟩⟩,⟨⟨(-15656329102716728228240162056),(-15656329102716728210568663624)⟩,⟨(-36278246905736940124326659661),(-36278246905736940108011079202)⟩⟩,⟨⟨(-15693401123540242582577834469),(-15693401123540242564817906845)⟩,⟨(-36572011785607313459011070097),(-36572011785607313442610295061)⟩⟩,⟨⟨(-15726954403832162888969659934),(-15726954403832162871123718579)⟩,⟨(-36861045849364565617833632605),(-36861045849364565601348689323)⟩⟩,⟨⟨(-15757594701939614074341355931),(-15757594701939614056411724708)⟩,⟨(-37146656456056783886929136822),(-37146656456056783870361771436)⟩⟩] +lemma amp4_03_5_eq : ∀ k : Fin 16, amp4_0Expr 3 5 k = amp4_03_5 k := by decide +kernel +noncomputable def amp4_03_6 : Fin 16 → CBox := ![⟨⟨(-15784766067830753294665837440),(-15784766067830753276658485812)⟩,⟨(-37427426057243005421783682903),(-37427426057243005405143305671)⟩⟩,⟨⟨(-15809033746990327269146636954),(-15809033746990327251060864943)⟩,⟨(-37704577192705625608962886110),(-37704577192705625592244046516)⟩⟩,⟨⟨(-15829885554103249536641941353),(-15829885554103249518482662890)⟩,⟨(-37976775721155761507895603073),(-37976775721155761491105257479)⟩⟩,⟨⟨(-15847847414897476881525188576),(-15847847414897476863293387784)⟩,⟨(-38245160505562048700234748201),(-38245160505562048683371322176)⟩⟩,⟨⟨(-15862449636679283549153393099),(-15862449636679283530853215160)⟩,⟨(-38508480005179710919208202406),(-38508480005179710902276848696)⟩⟩,⟨⟨(-15874179942565600173517726422),(-15874179942565600155151341820)⟩,⟨(-38767790402282614435363250173),(-38767790402282614418365182427)⟩⟩,⟨⟨(-15882609926972234275716367489),(-15882609926972234257295589738)⟩,⟨(-39021922100251998936711951770),(-39021922100251998919671225762)⟩⟩,⟨⟨(-15888190156809504922375731696),(-15888190156809504903893847117)⟩,⟨(-39271849458541985731244769625),(-39271849458541985714140821872)⟩⟩,⟨⟨(-15890532370051617756126509893),(-15890532370051617737587566642)⟩,⟨(-39516484310268312309689525434),(-39516484310268312292527353403)⟩⟩,⟨⟨(-15890050957749703308092415004),(-15890050957749703289499594542)⟩,⟨(-39756719918783432860240424280),(-39756719918783432843023651592)⟩⟩,⟨⟨(-15886396715741246518458538669),(-15886396715741246499814506448)⟩,⟨(-39991549167339213983240106052),(-39991549167339213965970346696)⟩⟩,⟨⟨(-15879948777716489894776128445),(-15879948777716489876084594640)⟩,⟨(-40221784824929036249579051815),(-40221784824929036232261241670)⟩⟩,⟨⟨(-15870395965896233990529915796),(-15870395965896233971793548099)⟩,⟨(-40446500573744396497484915108),(-40446500573744396480120697065)⟩⟩,⟨⟨(-15858083017040198194242449514),(-15858083017040198175463424642)⟩,⟨(-40666429170545086317622233910),(-40666429170545086300212630704)⟩⟩,⟨⟨(-15842735799263472777460937884),(-15842735799263472758646448650)⟩,⟨(-40880724968043728262815851341),(-40880724968043728245374171160)⟩⟩,⟨⟨(-15824665458155277060682246662),(-15824665458155277041831421600)⟩,⟨(-41090041077880596088699886561),(-41090041077880596071219297902)⟩⟩] +lemma amp4_03_6_eq : ∀ k : Fin 16, amp4_0Expr 3 6 k = amp4_03_6 k := by decide +kernel +noncomputable def amp4_03_7 : Fin 16 → CBox := ![⟨⟨(-15803633975378364923170563641),(-15803633975378364904286987316)⟩,⟨(-41293612512729021853055079150),(-41293612512729021835539635888)⟩⟩,⟨⟨(-15779919659492432497268540574),(-15779919659492432478354497930)⟩,⟨(-41492012995125320113305825161),(-41492012995125320095756756625)⟩⟩,⟨⟨(-15753319718995211186472253270),(-15753319718995211167533010728)⟩,⟨(-41684558300731730094118930437),(-41684558300731730076544803150)⟩⟩,⟨⟨(-15724080330676077107349375723),(-15724080330676077088385978060)⟩,⟨(-41871742911168401332963605857),(-41871742911168401315362356893)⟩⟩,⟨⟨(-15692033086589667674954327383),(-15692033086589667655971168165)⟩,⟨(-42052963578039444250764963871),(-42052963578039444233142944604)⟩⟩,⟨⟨(-15657392690583621186578616593),(-15657392690583621167577040631)⟩,⟨(-42228635585079918130291472039),(-42228635585079918112647344791)⟩⟩,⟨⟨(-15620024316508954012323289656),(-15620024316508953993307379882)⟩,⟨(-42398236979618284947012151512),(-42398236979618284929351520569)⟩⟩,⟨⟨(-15580111809858637525978443342),(-15580111809858637506950983210)⟩,⟨(-42562103787485332683331532026),(-42562103787485332665656903135)⟩⟩,⟨⟨(-15537553164378959168150919854),(-15537553164378959149114864561)⟩,⟨(-42719795775789181666389829460),(-42719795775789181648703818567)⟩⟩,⟨⟨(-15492501939501556299526940300),(-15492501939501556280484889101)⟩,⟨(-42871569550957288111163863809),(-42871569550957288093468462920)⟩⟩,⟨⟨(-15444888225406960353068525252),(-15444888225406960334023976476)⟩,⟨(-43017067126163756485105978363),(-43017067126163756467405371349)⟩⟩,⟨⟨(-15394835827189225856028013748),(-15394835827189225836983646859)⟩,⟨(-43156465426510488181389960659),(-43156465426510488163686348620)⟩⟩,⟨⟨(-15342306245244277893145212868),(-15342306245244277874104460200)⟩,⟨(-43289489338210172036096907658),(-43289489338210172018394369852)⟩⟩,⟨⟨(-15287394022998347962828095380),(-15287394022998347943793902826)⟩,⟨(-43416235743253624995435701163),(-43416235743253624977737208989)⟩⟩,⟨⟨(-15230091421094775483345255579),(-15230091421094775464320937183)⟩,⟨(-43536513127490966385936981634),(-43536513127490966368246391351)⟩⟩,⟨⟨(-15170464176227409620318634364),(-15170464176227409601307528538)⟩,⟨(-43650337868227585358643255242),(-43650337868227585340964680965)⟩⟩] +lemma amp4_03_7_eq : ∀ k : Fin 16, amp4_0Expr 3 7 k = amp4_03_7 k := by decide +kernel +noncomputable def amp4_03_8 : Fin 16 → CBox := ![⟨⟨(-15108534694772631339733245088),(-15108534694772631320736607138)⟩,⟨(-43757602876593655889317273566),(-43757602876593655871648710833)⟩⟩,⟨⟨(-15044340325027245129823470040),(-15044340325027245110842467379)⟩,⟨(-43858243463441536441993632824),(-43858243463441536424332863691)⟩⟩,⟨⟨(-14977933039426212182999551242),(-14977933039426212164037583687)⟩,⟨(-43952237889760801842290793462),(-43952237889760801824642008681)⟩⟩,⟨⟨(-14909322180561738520369672814),(-14909322180561738501429947484)⟩,⟨(-44039439737108019358243019240),(-44039439737108019340609908683)⟩⟩,⟨⟨(-14838588741654149418372839503),(-14838588741654149399458341499)⟩,⟨(-44119913640219351688414001947),(-44119913640219351670799642635)⟩⟩,⟨⟨(-14765714407427394408552317730),(-14765714407427394389666298440)⟩,⟨(-44193430686074901352008303568),(-44193430686074901334416577842)⟩⟩,⟨⟨(-14690808680744826170546184573),(-14690808680744826151691309549)⟩,⟨(-44260143007209407438774726567),(-44260143007209407421207875686)⟩⟩,⟨⟨(-14613825902063551457678989458),(-14613825902063551438858547969)⟩,⟨(-44319738326455971744499755129),(-44319738326455971726961804853)⟩⟩,⟨⟨(-14534903606771425972247103287),(-14534903606771425953463674749)⟩,⟨(-44372457499720152559767741677),(-44372457499720152542260746228)⟩⟩,⟨⟨(-14453969070883883329002676465),(-14453969070883883310258976522)⟩,⟨(-44417903909473114195357572468),(-44417903909473114177883864511)⟩⟩,⟨⟨(-14371187419271470030502360135),(-14371187419271470011801084269)⟩,⟨(-44456408463955476462339521889),(-44456408463955476444901611932)⟩⟩,⟨⟨(-14286459109854533838234957678),(-14286459109854533819579845224)⟩,⟨(-44487489119541331157203367448),(-44487489119541331139806767660)⟩⟩,⟨⟨(-14199976448232391386811553151),(-14199976448232391368203972873)⟩,⟨(-44511568271573848408495303380),(-44511568271573848391138482121)⟩⟩,⟨⟨(-14111613287234782337955214197),(-14111613287234782319399122264)⟩,⟨(-44528077251653400823009051401),(-44528077251653400805698272683)⟩⟩,⟨⟨(-14021588739093182339238164079),(-14021588739093182320734631236)⟩,⟨(-44537531485776168646286459118),(-44537531485776168629019308647)⟩⟩,⟨⟨(-13929750231182558426502284846),(-13929750231182558408056013722)⟩,⟨(-44539274365153559973819021060),(-44539274365153559956604190767)⟩⟩] +lemma amp4_03_8_eq : ∀ k : Fin 16, amp4_0Expr 3 8 k = amp4_03_8 k := by decide +kernel +noncomputable def amp4_03_9 : Fin 16 → CBox := ![⟨⟨(-13836343343456537658416201949),(-13836343343456537640029360864)⟩,⟨(-44533916002351605534922595914),(-44533916002351605517761234077)⟩⟩,⟨⟨(-13741189223909458044636433791),(-13741189223909458026312154023)⟩,⟨(-44520710411029257918842667470),(-44520710411029257901738581210)⟩⟩,⟨⟨(-13644559617186241846444558729),(-13644559617186241828182239160)⟩,⟨(-44500364162834738292140639553),(-44500364162834738275086070289)⟩⟩,⟨⟨(-13546249504048201695832405158),(-13546249504048201677638292414)⟩,⟨(-44472040329896629693124281168),(-44472040329896629676133165764)⟩⟩,⟨⟨(-13446556527540865295145217724),(-13446556527540865277021323939)⟩,⟨(-44436543836977574325703924398),(-44436543836977574308777115456)⟩⟩,⟨⟨(-13345249578869775346902409526),(-13345249578869775328851027074)⟩,⟨(-44392945117908785986090304683),(-44392945117908785969228930657)⟩⟩,⟨⟨(-13242651970967202822969680607),(-13242651970967202804994067582)⟩,⟨(-44342149471797090328630516566),(-44342149471797090311839693031)⟩⟩,⟨⟨(-13138506547957870409911198970),(-13138506547957870392013638952)⟩,⟨(-44283132857876190830880597780),(-44283132857876190814161437159)⟩⟩,⟨⟨(-13033162103145379491890875757),(-13033162103145379474074168844)⟩,⟨(-44216903104522734121280566391),(-44216903104522734104636779542)⟩⟩,⟨⟨(-12926335439914765211856891301),(-12926335439914765194124398572)⟩,⟨(-44142339712955156712338909226),(-44142339712955156695775348041)⟩⟩,⟨⟨(-12818400682842243127521226263),(-12818400682842243109867674838)⟩,⟨(-44060555336838681037558126516),(-44060555336838681021050993388)⟩⟩,⟨⟨(-12709048563635549710052870265),(-12709048563635549692487940204)⟩,⟨(-43970330880333674328363276242),(-43970330880333674311939014156)⟩⟩,⟨⟨(-12598678431090650246395827419),(-12598678431090650228921425762)⟩,⟨(-43872886267892411162418930706),(-43872886267892411146078486632)⟩⟩,⟨⟨(-12486954875646679893291538429),(-12486954875646679875911038537)⟩,⟨(-43766901502423237828871120865),(-43766901502423237812619527653)⟩⟩,⟨⟨(-12374302407169630983831592262),(-12374302407169630966545919516)⟩,⟨(-43653706383624194512755390075),(-43653706383624194496590311871)⟩⟩,⟨⟨(-12260359364960358827065658418),(-12260359364960358809878777073)⟩,⟨(-43531877533150836321109255188),(-43531877533150836305037849208)⟩⟩] +lemma amp4_03_9_eq : ∀ k : Fin 16, amp4_0Expr 3 9 k = amp4_03_9 k := by decide +kernel +noncomputable def amp4_03_10 : Fin 16 → CBox := ![⟨⟨(-12145575402814296977716045995),(-12145575402814296960627601190)⟩,⟨(-43402857400061159520188999644),(-43402857400061159504204404862)⟩⟩,⟨⟨(-12029562456848286363379323971),(-12029562456848286346394031045)⟩,⟨(-43265116557036652492718095164),(-43265116557036652476830277222)⟩⟩,⟨⟨(-11912795356034850697503367023),(-11912795356034850680623150160)⟩,⟨(-43120213058314582626129051754),(-43120213058314582610339473087)⟩⟩,⟨⟨(-11794859436887015696161131401),(-11794859436887015679387973554)⟩,⟨(-42966508558840016451413111502),(-42966508558840016435721977978)⟩⟩,⟨⟨(-11676254785871290770882595284),(-11676254785871290754219567306)⟩,⟨(-42805679869119668651586700718),(-42805679869119668635999762181)⟩⟩,⟨⟨(-11556539896572626196440729669),(-11556539896572626179889720051)⟩,⟨(-42635976641658567652435930524),(-42635976641658567636953131596)⟩⟩,⟨⟨(-11436240249354519303457062365),(-11436240249354519287020160981)⟩,⟨(-42459197804863177796425027317),(-42459197804863177781048752662)⟩⟩,⟨⟨(-11314887201744799285568016968),(-11314887201744799269248253241)⟩,⟨(-42273477691473123431431290766),(-42273477691473123416165709595)⟩⟩,⟨⟨(-11193031821885686206860691911),(-11193031821885686190660076618)⟩,⟨(-42080740937155571764237802489),(-42080740937155571749085160450)⟩⟩,⟨⟨(-11070177984999804938804445744),(-11070177984999804922725805911)⟩,⟨(-41879002986243165082238352413),(-41879002986243165067202217524)⟩⟩,⟨⟨(-10946902602183902582099727855),(-10946902602183902566145420503)⟩,⟨(-41670318018120667630860570333),(-41670318018120667615944771217)⟩⟩,⟨⟨(-10822681663208514054991489575),(-10822681663208514039143951083)⟩,⟨(-41452578747774839332043360728),(-41452578747774839317173425700)⟩⟩,⟨⟨(-10698118242888078860317793968),(-10698118242888078844597925427)⟩,⟨(-41227973003696867775461995774),(-41227973003696867760712465729)⟩⟩,⟨⟨(-10572659981189494841703848237),(-10572659981189494826114001393)⟩,⟨(-40994266634704622870006912568),(-40994266634704622855379651243)⟩⟩,⟨⟨(-10446936507831760493498074975),(-10446936507831760478040075192)⟩,⟨(-40753785517369639301742926074),(-40753785517369639287240106214)⟩⟩,⟨⟨(-10320366582518682348353217727),(-10320366582518682333029237126)⟩,⟨(-40504164175066977694588380940),(-40504164175066977680211171469)⟩⟩] +lemma amp4_03_10_eq : ∀ k : Fin 16, amp4_0Expr 3 10 k = amp4_03_10 k := by decide +kernel +noncomputable def amp4_03_11 : Fin 16 → CBox := ![⟨⟨(-10193606856940619653641021206),(-10193606856940619638452781914)⟩,⟨(-40247871252884809803893199447),(-40247871252884809789643502295)⟩⟩,⟨⟨(-10066046608386185480142757937),(-10066046608386185465092362556)⟩,⟨(-39982405137043079468861130596),(-39982405137043079454739946332)⟩⟩,⟨⟨(-9938370059630899399495454144),(-9938370059630899384585150675)⟩,⟨(-39710382314626196339642612318),(-39710382314626196325654219064)⟩⟩,⟨⟨(-9809936325337673539773965730),(-9809936325337673525005069119)⟩,⟨(-39429159836619646987437721240),(-39429159836619646973579949859)⟩⟩,⟨⟨(-9681457837513789997953244808),(-9681457837513789983328350628)⟩,⟨(-39141507494478870216488288470),(-39141507494478870202767003116)⟩⟩,⟨⟨(-9552262782662623515857875355),(-9552262782662623501379064076)⟩,⟨(-38844635381021623723487049061),(-38844635381021623709903258197)⟩⟩,⟨⟨(-9423092537135648393010735615),(-9423092537135648378679957611)⟩,⟨(-38541472484140778961444570681),(-38541472484140778948001872927)⟩⟩,⟨⟨(-9293243500114667670944206848),(-9293243500114667656760974837)⟩,⟨(-38229075846919509155137684230),(-38229075846919509141826528930)⟩⟩,⟨⟨(-9163486833407365281842798799),(-9163486833407365267811224334)⟩,⟨(-37910540021990323697871480649),(-37910540021990323684704487496)⟩⟩,⟨⟨(-9033086186570512495215059929),(-9033086186570512481337300188)⟩,⟨(-37582762392551006901144209721),(-37582762392551006888122826342)⟩⟩,⟨⟨(-8902843464298267096363467919),(-8902843464298267082640203315)⟩,⟨(-37249009973765690907637137123),(-37249009973765690894760199096)⟩⟩,⟨⟨(-8771988490153551905363061181),(-8771988490153551891797526781)⟩,⟨(-36906013303036785637484918057),(-36906013303036785624758347275)⟩⟩,⟨⟨(-8641354997290955532704439032),(-8641354997290955519297563804)⟩,⟨(-36557219346463186455538234905),(-36557219346463186442962101211)⟩⟩,⟨⟨(-8510137780266505609358671954),(-8510137780266505596112867280)⟩,⟨(-36199183968310893478834863461),(-36199183968310893466411773875)⟩⟩,⟨⟨(-8379203628013698245111809855),(-8379203628013698232028552792)⟩,⟨(-35835542235016523849061476381),(-35835542235016523836794151287)⟩⟩,⟨⟨(-8247710961894296712624273710),(-8247710961894296699706215017)⟩,⟨(-35462666793226975167874621336),(-35462666793226975155766715689)⟩⟩] +lemma amp4_03_11_eq : ∀ k : Fin 16, amp4_0Expr 3 11 k = amp4_03_11 k := by decide +kernel +noncomputable def amp4_03_12 : Fin 16 → CBox := ![⟨⟨(-8116561011386679959945976418),(-8116561011386679947184018989)⟩,⟨(-35084389701477101900364896879),(-35084389701477101888373661125)⟩⟩,⟨⟨(-7984874322454034664871305108),(-7984874322454034652276483345)⟩,⟨(-34696891039541015484259649011),(-34696891039541015472424876350)⟩⟩,⟨⟨(-7853588125537927123353999256),(-7853588125537927110927355908)⟩,⟨(-34304209586577058051034223245),(-34304209586577058039357307471)⟩⟩,⟨⟨(-7721783411383447805592205276),(-7721783411383447793335900212)⟩,⟨(-33902322599608770831965913251),(-33902322599608770820448441374)⟩⟩,⟨⟨(-7590435168664401912716761192),(-7590435168664401900631757126)⟩,⟨(-33495486253722824982877762840),(-33495486253722824971521011441)⟩⟩,⟨⟨(-7458582952572418648489780441),(-7458582952572418636578072809)⟩,⟨(-33079463701769969915418391431),(-33079463701769969904223320323)⟩⟩,⟨⟨(-7327241488934059195003681035),(-7327241488934059183266629026)⟩,⟨(-32658740265637904972075671499),(-32658740265637904961045698281)⟩⟩,⟨⟨(-7195406789654343160192098271),(-7195406789654343148630632131)⟩,⟨(-32228852547519978349223759352),(-32228852547519978338355044398)⟩⟩,⟨⟨(-7064135547446101824960969646),(-7064135547446101813577194079)⟩,⟨(-31794527994050942070162799174),(-31794527994050942059462344782)⟩⟩,⟨⟨(-6932377864084680759879837729),(-6932377864084680748675642126)⟩,⟨(-31351062880690569334022321918),(-31351062880690569323490689789)⟩⟩,⟨⟨(-6801234914189918179573461540),(-6801234914189918168549692902)⟩,⟨(-30903441163010943344484521727),(-30903441163010943334123532518)⟩⟩,⟨⟨(-6669608225842941314958301353),(-6669608225842941304117262467)⟩,⟨(-30446703488971523654896041973),(-30446703488971523644708056419)⟩⟩,⟨⟨(-6538646296869098834954092511),(-6538646296869098824296799375)⟩,⟨(-29986106326608720517007413543),(-29986106326608720506995334748)⟩⟩,⟨⟨(-6407199076500887398972523865),(-6407199076500887388495314744)⟩,⟨(-29516417638199563353548338479),(-29516417638199563343687156645)⟩⟩,⟨⟨(-6276465602386653853171601277),(-6276465602386653842880372459)⟩,⟨(-29043184282096844703612732639),(-29043184282096844693928171732)⟩⟩,⟨⟨(-6145240844302976693256134821),(-6145240844302976683153029909)⟩,⟨(-28560882439914327412158200112),(-28560882439914327402651903341)⟩⟩] +lemma amp4_03_12_eq : ∀ k : Fin 16, amp4_0Expr 3 12 k = amp4_03_12 k := by decide +kernel +noncomputable def amp4_03_13 : Fin 16 → CBox := ![⟨⟨(-6014778030722670198958168596),(-6014778030722670189043382619)⟩,⟨(-28075369419636451036255333697),(-28075369419636451026927149539)⟩⟩,⟨⟨(-5883813290803553425277065233),(-5883813290803553415552108975)⟩,⟨(-27580808152723655659075185842),(-27580808152723655649923861403)⟩⟩,⟨⟨(-5753658200878406090756228761),(-5753658200878406081222407052)⟩,⟨(-27083389010168380214707670201),(-27083389010168380205738743961)⟩⟩,⟨⟨(-5622985648496712873686424379),(-5622985648496712864345572984)⟩,⟨(-26576937418018996269075817850),(-26576937418018996260289432434)⟩⟩,⟨⟨(-5493170308514490690574499570),(-5493170308514490681427215130)⟩,⟨(-26068002433224048761141957673),(-26068002433224048752540720168)⟩⟩,⟨⟨(-5362816788755508048540651944),(-5362816788755508039585524447)⟩,⟨(-25550044430516219015791977379),(-25550044430516219007360576412)⟩⟩,⟨⟨(-5233368314880381867832283911),(-5233368314880381859072407099)⟩,⟨(-25030000346882201881264690144),(-25030000346882201873018101469)⟩⟩,⟨⟨(-5103355419261583129287206604),(-5103355419261583120724889238)⟩,⟨(-24500934043936752274583472983),(-24500934043936752266523944579)⟩⟩,⟨⟨(-4974296166625037240296311049),(-4974296166625037231931324624)⟩,⟨(-23970203802578994626305699126),(-23970203802578994618432819899)⟩⟩,⟨⟨(-4844640309945409755700549478),(-4844640309945409747534807291)⟩,⟨(-23430440811840713615557702472),(-23430440811840713607871803380)⟩⟩,⟨⟨(-4715988046106649586882743866),(-4715988046106649578916308576)⟩,⟨(-22889463308150554145759323938),(-22889463308150554138261990600)⟩⟩,⟨⟨(-4586700546256559631954379905),(-4586700546256559624187293268)⟩,⟨(-22339427963100884072518454956),(-22339427963100884065200674145)⟩⟩,⟨⟨(-4458468651901207212946051068),(-4458468651901207205380592629)⟩,⟨(-21788657843426339783502551778),(-21788657843426339776377173450)⟩⟩,⟨⟨(-4329555808319028459015914048),(-4329555808319028451654160961)⟩,⟨(-21228786310638838539199803541),(-21228786310638838532267642851)⟩⟩,⟨⟨(-4201753509376722292446659146),(-4201753509376722285287847636)⟩,⟨(-20668693834058910712863521207),(-20668693834058910706123281970)⟩⟩,⟨⟨(-4073216674158508904117745934),(-4073216674158508897164579447)⟩,⟨(-20099433090623093084634327780),(-20099433090623093078089622657)⟩⟩] +lemma amp4_03_13_eq : ∀ k : Fin 16, amp4_0Expr 3 13 k = amp4_03_13 k := by decide +kernel +noncomputable def amp4_03_14 : Fin 16 → CBox := ![⟨⟨(-3945849311504897661360989051),(-3945849311504897654610969387)⟩,⟨(-19530504091343626227729282991),(-19530504091343626221370779097)⟩⟩,⟨⟨(-3817684944647839113950270526),(-3817684944647839107407433579)⟩,⟨(-18952310726994784971566864703),(-18952310726994784965404594714)⟩⟩,⟨⟨(-3690754290616350216298846103),(-3690754290616350209962030035)⟩,⟨(-18375046729025025681457511276),(-18375046729025025675489524648)⟩⟩,⟨⟨(-3562953986981834935597771050),(-3562953986981834929470139934)⟩,⟨(-17788385512305140024445856017),(-17788385512305140018677515021)⟩⟩,⟨⟨(-3436458622733459668712659835),(-3436458622733459662791439577)⟩,⟨(-17203304073357178165213425798),(-17203304073357178159635419551)⟩⟩,⟨⟨(-3309009092141056803726783341),(-3309009092141056798015920028)⟩,⟨(-16608646189264604006562643010),(-16608646189264604001183923924)⟩⟩,⟨⟨(-3182944867741019473719344812),(-3182944867741019468216563011)⟩,⟨(-16016281591564628515168770870),(-16016281591564628509983395714)⟩⟩,⟨⟨(-3055827839515424066256673529),(-3055827839515424060965811312)⟩,⟨(-15414102405930735312005594919),(-15414102405930735307021477405)⟩⟩,⟨⟨(-2930188451566032091995845197),(-2930188451566032086915232329)⟩,⟨(-14815006879387363694946757987),(-14815006879387363690161881925)⟩⟩,⟨⟨(-2803380457805536570589755237),(-2803380457805536565721559666)⟩,⟨(-14205782996800170164701491534),(-14205782996800170160114837042)⟩⟩,⟨⟨(-2678158201915089024662883635),(-2678158201915089020006152031)⟩,⟨(-13600528776722671086548517546),(-13600528776722671082162847666)⟩⟩,⟨⟨(-2551630163796799081556633905),(-2551630163796799077113729305)⟩,⟨(-12984734003356991586444899562),(-12984734003356991582259361787)⟩⟩,⟨⟨(-2426816959457020057925858703),(-2426816959457020053694662321)⟩,⟨(-12373916734468972020333526041),(-12373916734468972016346177080)⟩⟩,⟨⟨(-2300533445903440629032115976),(-2300533445903440625016639541)⟩,⟨(-11752016271609743440923050107),(-11752016271609743437140547546)⟩⟩,⟨⟨(-2176122307226760426941278746),(-2176122307226760423138488935)⟩,⟨(-11136260664561825605792830341),(-11136260664561825602210100093)⟩⟩,⟨⟨(-2050040228941815302134524938),(-2050040228941815298548085887)⟩,⟨(-10508702306317853547744510518),(-10508702306317853544365200836)⟩⟩] +lemma amp4_03_14_eq : ∀ k : Fin 16, amp4_0Expr 3 14 k = amp4_03_14 k := by decide +kernel +noncomputable def amp4_03_15 : Fin 16 → CBox := ![⟨⟨(-1926027505834498967734107630),(-1926027505834498964361233609)⟩,⟨(-9888671738348141417431257278),(-9888671738348141414253288426)⟩⟩,⟨⟨(-1800093789121674418320653704),(-1800093789121674415165370291)⟩,⟨(-9255871711318581696414715936),(-9255871711318581693442101866)⟩⟩,⟨⟨(-1676482825452813383828645281),(-1676482825452813380887543223)⟩,⟨(-8632285135977092440396316682),(-8632285135977092437626056682)⟩⟩,⟨⟨(-1550630125940814599788750447),(-1550630125940814597066045417)⟩,⟨(-7994603702274222375138534948),(-7994603702274222372573488842)⟩⟩,⟨⟨(-1427437726536585415408053887),(-1427437726536585412899720431)⟩,⟨(-7368267105892939063718634232),(-7368267105892939061355458595)⟩⟩,⟨⟨(-1301576065736027324782786713),(-1301576065736027322494033285)⟩,⟨(-6725962933974894349266832661),(-6725962933974894347110673379)⟩⟩,⟨⟨(-1178845079062316102118351815),(-1178845079062316100044214932)⟩,⟨(-6097832527736139035918347803),(-6097832527736139033964920618)⟩⟩,⟨⟨(-1052844063937715562214417891),(-1052844063937715560360813810)⟩,⟨(-5450968089372460741467349799),(-5450968089372460739721265487)⟩⟩,⟨⟨(-930671028172030378106687322),(-930671028172030376467416902)⟩,⟨(-4822291737254375731514761133),(-4822291737254375729970893815)⟩⟩,⟨⟨(-804316972304128528447340651),(-804316972304128527030035931)⟩,⟨(-4170508251314983058915871114),(-4170508251314983057581263431)⟩⟩,⟨⟨(-682923815175354638114653163),(-682923815175354636910888386)⟩,⟨(-3543195781150830926195982689),(-3543195781150830925062852737)⟩⟩,⟨⟨(-555794499212249444174253640),(-555794499212249443194315823)⟩,⟨(-2885060160642004358394457255),(-2885060160642004357472270052)⟩⟩,⟨⟨(-435767271490579783084432711),(-435767271490579782316046234)⟩,⟨(-2262921596400550178175754213),(-2262921596400550177453169009)⟩⟩,⟨⟨(-306729548442980972479071586),(-306729548442980971938187678)⟩,⟨(-1593313590056805446517622414),(-1593313590056805446009304165)⟩⟩,⟨⟨(-190242689581973433323979175),(-190242689581973432988724353)⟩,⟨(-988418371844251979259824421),(-988418371844251978945859466)⟩⟩,⟨⟨(-54044651346934386936012270),(-54044651346934386840922134)⟩,⟨(-280820721772499749269394951),(-280820721772499749181008568)⟩⟩] +lemma amp4_03_15_eq : ∀ k : Fin 16, amp4_0Expr 3 15 k = amp4_03_15 k := by decide +kernel +noncomputable def amp4_03 : Fin 16 → Fin 16 → CBox := ![amp4_03_0,amp4_03_1,amp4_03_2,amp4_03_3,amp4_03_4,amp4_03_5,amp4_03_6,amp4_03_7,amp4_03_8,amp4_03_9,amp4_03_10,amp4_03_11,amp4_03_12,amp4_03_13,amp4_03_14,amp4_03_15] +lemma amp4_03_eq (i k : Fin 16) : amp4_0Expr 3 i k = amp4_03 i k := by + fin_cases i + · exact amp4_03_0_eq k + · exact amp4_03_1_eq k + · exact amp4_03_2_eq k + · exact amp4_03_3_eq k + · exact amp4_03_4_eq k + · exact amp4_03_5_eq k + · exact amp4_03_6_eq k + · exact amp4_03_7_eq k + · exact amp4_03_8_eq k + · exact amp4_03_9_eq k + · exact amp4_03_10_eq k + · exact amp4_03_11_eq k + · exact amp4_03_12_eq k + · exact amp4_03_13_eq k + · exact amp4_03_14_eq k + · exact amp4_03_15_eq k +noncomputable def amp4_04_0 : Fin 16 → CBox := ![⟨⟨(-108088285328156059031156926),(-108088285328156058932982980)⟩,⟨(-1762129104300596960335),(-1762129104300508032807)⟩⟩,⟨⟨(-380453151319111964582263056),(-380453151319111964235609658)⟩,⟨(-55820264672496489687900),(-55820264672496176678880)⟩⟩,⟨⟨(-613314789282883315038776764),(-613314789282883314479120551)⟩,⟨(-249948100450669787112830),(-249948100450669282526487)⟩⟩,⟨⟨(-871132832163727549080975046),(-871132832163727548285855187)⟩,⟨(-695783545742278788859215),(-695783545742278072169847)⟩⟩,⟨⟨(-1110742379793587806043510117),(-1110742379793587805029406814)⟩,⟨(-1466386483372397062865472),(-1466386483372396149062126)⟩⟩,⟨⟨(-1364294426607166606037504898),(-1364294426607166604791804757)⟩,⟨(-2690227798322084912847777),(-2690227798322083790471444)⟩⟩,⟨⟨(-1606080516929194708595890859),(-1606080516929194707129260468)⟩,⟨(-4422666473588663961347776),(-4422666473588662640091641)⟩⟩,⟨⟨(-1857411230393376142975538735),(-1857411230393376141279359151)⟩,⟨(-6808390262295983679893106),(-6808390262295982151921583)⟩⟩,⟨⟨(-2099980978840482902139691764),(-2099980978840482900221933853)⟩,⟨(-9885072094898006539624875),(-9885072094898004812163455)⟩⟩,⟨⟨(-2349715165212016045517318266),(-2349715165212016043371805349)⟩,⟨(-13813092914652889929908989),(-13813092914652887997087053)⟩⟩,⟨⟨(-2592406288112938840320336045),(-2592406288112938837953090975)⟩,⟨(-18612346668165193783939162),(-18612346668165191651571173)⟩⟩,⟨⟨(-2840754361792469276408803471),(-2840754361792469273814885435)⟩,⟨(-24458447556492958245224389),(-24458447556492955908684210)⟩⟩,⟨⟨(-3083158362756607819800269899),(-3083158362756607816985276594)⟩,⟨(-31353391677515557579466567),(-31353391677515555043672747)⟩⟩,⟨⟨(-3330167486215396475664590965),(-3330167486215396472624574119)⟩,⟨(-39487579562801639570009737),(-39487579562801636831208105)⟩⟩,⟨⟨(-3571986906618049827895132045),(-3571986906618049824634367507)⟩,⟨(-48844996062583870478922462),(-48844996062583867541408148)⟩⟩,⟨⟨(-3817627397948821485025677132),(-3817627397948821481540831028)⟩,⟨(-59630376146700979831918811),(-59630376146700976692585330)⟩⟩] +lemma amp4_04_0_eq : ∀ k : Fin 16, amp4_0Expr 4 0 k = amp4_04_0 k := by decide +kernel +noncomputable def amp4_04_1 : Fin 16 → CBox := ![⟨⟨(-4058621167164034578634957248),(-4058621167164034574930453680)⟩,⟨(-71809597972109154886212587),(-71809597972109151548920169)⟩⟩,⟨⟨(-4302822699838685575467524665),(-4302822699838685571540749551)⟩,⟨(-85601267120225541985071079),(-85601267120225538447226535)⟩⟩,⟨⟨(-4542781601919094069411897258),(-4542781601919094065266896155)⟩,⟨(-100953083419527916252057542),(-100953083419527912517194485)⟩⟩,⟨⟨(-4785450558516348023974878397),(-4785450558516348019608196083)⟩,⟨(-118097044439582392868571523),(-118097044439582388934481305)⟩⟩,⟨⟨(-5024184917995322595299039666),(-5024184917995322590715725652)⟩,⟨(-136962627053532946638104957),(-136962627053532942508102288)⟩⟩,⟨⟨(-5265213576138587391597567412),(-5265213576138587386795624885)⟩,⟨(-157794726275027874412105435),(-157794726275027870084356171)⟩⟩,⟨⟨(-5502546547528761708501145609),(-5502546547528761703482579207)⟩,⟨(-180504580397247745518440325),(-180504580397247740995988517)⟩⟩,⟨⟨(-5741818330713242041800236444),(-5741818330713242036565101611)⟩,⟨(-205349471102234111565380740),(-205349471102234106846742157)⟩⟩,⟨⟨(-5977582006447996124213962935),(-5977582006447996118764113914)⟩,⟨(-232222412870854061650220560),(-232222412870854056738282287)⟩⟩,⟨⟨(-6214974678023852760378796009),(-6214974678023852754712614715)⟩,⟨(-261392547144754901743753326),(-261392547144754896637219408)⟩⟩,⟨⟨(-6449007720194114035888362920),(-6449007720194114030011077592)⟩,⟨(-292734710811210390514448387),(-292734710811210385216225968)⟩⟩,⟨⟨(-6684395430218605952054822041),(-6684395430218605945963476232)⟩,⟨(-326529362345191882659533347),(-326529362345191877168488300)⟩⟩,⟨⟨(-6916541575480023271319476333),(-6916541575480023265019659124)⟩,⟨(-362633239571387457783018417),(-362633239571387452102004086)⟩⟩,⟨⟨(-7149796232995450593423676245),(-7149796232995450586911261199)⟩,⟨(-401337559888009502912848701),(-401337559888009497040850384)⟩⟩,⟨⟨(-7379903322321855095750107524),(-7379903322321855089029230788)⟩,⟨(-442481073633859031021221965),(-442481073633859024960949674)⟩⟩,⟨⟨(-7610895553025613803398123516),(-7610895553025613796467671182)⟩,⟨(-486365184133921566072637319),(-486365184133921559823401630)⟩⟩] +lemma amp4_04_1_eq : ∀ k : Fin 16, amp4_0Expr 4 1 k = amp4_04_1 k := by decide +kernel +noncomputable def amp4_04_2 : Fin 16 → CBox := ![⟨⟨(-7838814889794311721027632194),(-7838814889794311713893549624)⟩,⟨(-532810799507346260050859587),(-532810799507346253615453505)⟩⟩,⟨⟨(-8067414729134296313003986310),(-8067414729134296305662391307)⟩,⟨(-582128921652518756755840913),(-582128921652518750133550064)⟩⟩,⟨⟨(-8293000649667702143615463331),(-8293000649667702136069753111)⟩,⟨(-634122796000825545736594340),(-634122796000825538929996812)⟩⟩,⟨⟨(-8519078061542027635939611308),(-8519078061542027628189172397)⟩,⟨(-689112421855844530150619762),(-689112421855844523159355420)⟩⟩,⟨⟨(-8742187647147554116832326216),(-8742187647147554108879458416)⟩,⟨(-746883596279985058204164937),(-746883596279985051030691989)⟩⟩,⟨⟨(-8965612924336716948300521741),(-8965612924336716940150245957)⟩,⟨(-807764701541014134155378790),(-807764701541014126799965096)⟩⟩,⟨⟨(-9186105809946619700363650455),(-9186105809946619692014393209)⟩,⟨(-871524335912167629050750126),(-871524335912167621515500230)⟩⟩,⟨⟨(-9406749892287105452648091109),(-9406749892287105444100580918)⟩,⟨(-938498637445002220549339058),(-938498637445002212834271597)⟩⟩,⟨⟨(-9624488142462866612784596352),(-9624488142462866604040926761)⟩,⟨(-1008439290896170990892724107),(-1008439290896170983000232472)⟩⟩,⟨⟨(-9842222876484623694537959255),(-9842222876484623685598151440)⟩,⟨(-1081689550699808942914792592),(-1081689550699808934844936869)⟩⟩,⟨⟨(-10057070909260472808468458402),(-10057070909260472799335332579)⟩,⟨(-1157984509453756899526742213),(-1157984509453756891281970477)⟩⟩,⟨⟨(-10271769265286107336573319031),(-10271769265286107327253068820)⟩,⟨(-1237673886851829258972962735),(-1237673886851829250554181060)⟩⟩,⟨⟨(-10483593810512908947712932866),(-10483593810512908938201479126)⟩,⟨(-1320476541130909950663923726),(-1320476541130909942072768616)⟩⟩,⟨⟨(-10695130068233236246040963095),(-10695130068233236236339695190)⟩,⟨(-1406747994875915212620245124),(-1406747994875915203857142281)⟩⟩,⟨⟨(-10903800151122990468504034654),(-10903800151122990458614939521)⟩,⟨(-1496191266519354418794913082),(-1496191266519354409862184877)⟩⟩,⟨⟨(-11112050061373981239811341164),(-11112050061373981229737067048)⟩,⟨(-1589167008372888014155399312),(-1589167008372888005053755360)⟩⟩] +lemma amp4_04_2_eq : ∀ k : Fin 16, amp4_0Expr 4 2 k = amp4_04_2 k := by decide +kernel +noncomputable def amp4_04_3 : Fin 16 → CBox := ![⟨⟨(-11317437004640384565993365320),(-11317437004640384555735372510)⟩,⟨(-1685362830663166458671594126),(-1685362830663166449403283887)⟩⟩,⟨⟨(-11522277932889587526404337130),(-11522277932889587515963076762)⟩,⟨(-1785143831889703188206670410),(-1785143831889703178772180907)⟩⟩,⟨⟨(-11724255372714411619881164103),(-11724255372714411609259220947)⟩,⟨(-1888182682962108555307773469),(-1888182682962108545709500731)⟩⟩,⟨⟨(-11925566428242691911394758251),(-11925566428242691900602967109)⟩,⟨(-1994848235044697164174322890),(-1994848235044697154414563579)⟩⟩,⟨⟨(-12124010340568684229564376819),(-12124010340568684218594755151)⟩,⟨(-2104798726123178320760106920),(-2104798726123178310839548675)⟩⟩,⟨⟨(-12321672494270023914394118418),(-12321672494270023903248477365)⟩,⟨(-2218406056876965788742885418),(-2218406056876965778662393363)⟩⟩,⟨⟨(-12516461228816132570217533308),(-12516461228816132558898753390)⟩,⟨(-2335314576445435301908896527),(-2335314576445435291670924445)⟩⟩,⟨⟨(-12710357421784252654928098984),(-12710357421784252643437645142)⟩,⟨(-2455898522569579607861096783),(-2455898522569579597466538953)⟩⟩,⟨⟨(-12901371741818879374752170617),(-12901371741818879363092233083)⟩,⟨(-2579788937451092611809930323),(-2579788937451092601261118707)⟩⟩,⟨⟨(-13091386986347086840488056513),(-13091386986347086828662217530)⟩,⟨(-2707361674421677665896868426),(-2707361674421677655195203035)⟩⟩,⟨⟨(-13278510112718882576141039041),(-13278510112718882564149709318)⟩,⟨(-2838235088598793430015005980),(-2838235088598793419162460523)⟩⟩,⟨⟨(-13464531586944342179761615054),(-13464531586944342167607023515)⟩,⟨(-2972785918665164492487508139),(-2972785918665164481485283551)⟩⟩,⟨⟨(-13647649245210552392419042627),(-13647649245210552380103544849)⟩,⟨(-3110620490533606086619201717),(-3110620490533606075469672187)⟩⟩,⟨⟨(-13829566382342766175088970224),(-13829566382342766162613974749)⟩,⟨(-3252115689438438878067028201),(-3252115689438438866771280356)⟩⟩,⟨⟨(-14008566852088077041913882111),(-14008566852088077029281983860)⟩,⟨(-3396866508043246233797097078),(-3396866508043246222357557296)⟩⟩,⟨⟨(-14186271424944109331045843513),(-14186271424944109318258568170)⟩,⟨(-3545249230942992754401762079),(-3545249230942992742819603171)⟩⟩] +lemma amp4_04_3_eq : ∀ k : Fin 16, amp4_0Expr 4 3 k = amp4_04_3 k := by decide +kernel +noncomputable def amp4_04_4 : Fin 16 → CBox := ![⟨⟨(-14361045590572946754614274213),(-14361045590572946741689717292)⟩,⟨(-3696848251602059948067864779),(-3696848251602059936349510831)⟩⟩,⟨⟨(-14534431791978345802464914005),(-14534431791978345789386771108)⟩,⟨(-3852038498519526869458703190),(-3852038498519526857600885464)⟩⟩,⟨⟨(-14704873194407792686409948113),(-14704873194407792673181655462)⟩,⟨(-4010394538094074048607978639),(-4010394538094074036613324380)⟩⟩,⟨⟨(-14873837713897835550779819747),(-14873837713897835537403534921)⟩,⟨(-4172289179089136245778677161),(-4172289179089136233648612129)⟩⟩,⟨⟨(-15039842602688874800453823215),(-15039842602688874786932582502)⟩,⟨(-4337287971014641477571509829),(-4337287971014641465308585428)⟩⟩,⟨⟨(-15204284699849471840819581730),(-15204284699849471827154492481)⟩,⟨(-4505760831112826599738748698),(-4505760831112826587344141864)⟩⟩,⟨⟨(-15365752085399789990091004915),(-15365752085399789976286444369)⟩,⟨(-4677265140157586069085689917),(-4677265140157586056562361954)⟩⟩,⟨⟨(-15525573660113779861084073997),(-15525573660113779847140704704)⟩,⟨(-4852167143929839920825160972),(-4852167143929839908174202817)⟩⟩,⟨⟨(-15682405365602133420158963782),(-15682405365602133406079358914)⟩,⟨(-5030016940501990327912491601),(-5030016940501990315136332378)⟩⟩,⟨⟨(-15837511025409440774379430849),(-15837511025409440760169926664)⟩,⟨(-5211176316042701481167138763),(-5211176316042701468268730237)⟩⟩,⟨⟨(-15989611738234159576013773550),(-15989611738234159561672409392)⟩,⟨(-5395189009720580232267453978),(-5395189009720580219247764043)⟩⟩,⟨⟨(-16139908862969460009174376364),(-16139908862969459994703842627)⟩,⟨(-5582411551625259440693301138),(-5582411551625259427554134810)⟩⟩,⟨⟨(-16287186185465403680026354432),(-16287186185465403665429039059)⟩,⟨(-5772382283440749540499445178),(-5772382283440749527243176608)⟩⟩,⟨⟨(-16432584989301644049717607732),(-16432584989301644034997160864)⟩,⟨(-5965451674239977554496376618),(-5965451674239977541125207314)⟩⟩,⟨⟨(-16574949488553341710278306347),(-16574949488553341695435784286)⟩,⟨(-6161153667100336576304105835),(-6161153667100336562819929738)⟩⟩,⟨⟨(-16715363079551532489795790246),(-16715363079551532474834239710)⟩,⟨(-6359831856463063042593060406),(-6359831856463063028997915354)⟩⟩] +lemma amp4_04_4_eq : ∀ k : Fin 16, amp4_0Expr 4 4 k = amp4_04_4 k := by decide +kernel +noncomputable def amp4_04_5 : Fin 16 → CBox := ![⟨⟨(-16852728336147199057159229985),(-16852728336147199042081037669)⟩,⟨(-6561016822954018239390510658),(-6561016822954018225686779972)⟩⟩,⟨⟨(-16988072773390696827826375584),(-16988072773390696812633611873)⟩,⟨(-6765044463831361663986536921),(-6765044463831361650175918634)⟩⟩,⟨⟨(-17120355428983751372920363144),(-17120355428983751357615456696)⟩,⟨(-6971443070503311889906674567),(-6971443070503311875991549804)⟩⟩,⟨⟨(-17250549777357544684216417816),(-17250549777357544668801601277)⟩,⟨(-7180540011244019431940018135),(-7180540011244019417922181402)⟩⟩,⟨⟨(-17377669580920238817107470109),(-17377669580920238801585472781)⟩,⟨(-7391862398344360571991687709),(-7391862398344360557873649239)⟩⟩,⟨⟨(-17502635963581591414141615190),(-17502635963581591398545076782)⟩,⟨(-7605728229675375307121228322),(-7605728229675375292918014165)⟩⟩,⟨⟨(-17624515816250218780060293600),(-17624515816250218764359914625)⟩,⟨(-7821664585153595844599250400),(-7821664585153595830299712159)⟩⟩,⟨⟨(-17744179464825680167322094082),(-17744179464825680151520850049)⟩,⟨(-8039979240784081166724795665),(-8039979240784081152331085929)⟩⟩,⟨⟨(-17860745463249223317108887049),(-17860745463249223301210214902)⟩,⟨(-8260200427262689002512316993),(-8260200427262688988027265184)⟩⟩,⟨⟨(-17975034765783921180075191076),(-17975034765783921164081406529)⟩,⟨(-8482624836737701776909225020),(-8482624836737701762334719509)⟩⟩,⟨⟨(-18086216243898398253270318826),(-18086216243898398237185091175)⟩,⟨(-8706783070011566478916923503),(-8706783070011566464255920153)⟩⟩,⟨⟨(-18195062790576238017063526387),(-18195062790576238000889273994)⟩,⟨(-8932959862312672062871408801),(-8932959862312672048125895499)⟩⟩,⟨⟨(-18300792359735829279826410094),(-18300792359735829263565016029)⟩,⟨(-9160689439812314991966528791),(-9160689439812314977138617214)⟩⟩,⟨⟨(-18404130986383395516923453174),(-18404130986383395500578772155)⟩,⟨(-9390243696077110053843756759),(-9390243696077110038936158604)⟩⟩,⟨⟨(-18504344573786966165079506292),(-18504344573786966148653506273)⟩,⟨(-9621161773608156751187754411),(-9621161773608156736202609237)⟩⟩,⟨⟨(-18602113403169274031529658238),(-18602113403169274015024396385)⟩,⟨(-9853701827219213052153347456),(-9853701827219213037092484095)⟩⟩] +lemma amp4_04_5_eq : ∀ k : Fin 16, amp4_0Expr 4 5 k = amp4_04_5 k := by decide +kernel +noncomputable def amp4_04_6 : Fin 16 → CBox := ![⟨⟨(-18696750288527408077957355208),(-18696750288527408061378990507)⟩,⟨(-10087409242170937453269783968),(-10087409242170937438137584784)⟩⟩,⟨⟨(-18788890769439972165433840811),(-18788890769439972148780854104)⟩,⟨(-10322527524347395124594628684),(-10322527524347395109391006100)⟩⟩,⟨⟨(-18877893619833286283383113495),(-18877893619833286266660431787)⟩,⟨(-10558609663448323550447462799),(-10558609663448323535176148786)⟩⟩,⟨⟨(-18964350563992084748687612260),(-18964350563992084731895679613)⟩,⟨(-10795883592360529514441868479),(-10795883592360529499103809490)⟩⟩,⟨⟨(-19047665466876555502857697247),(-19047665466876555486000529470)⟩,⟨(-11033911301948713644479665255),(-11033911301948713629078128706)⟩⟩,⟨⟨(-19128387083605228864059797098),(-19128387083605228847139248179)⟩,⟨(-11272904213268192496534465916),(-11272904213268192481071167515)⟩⟩,⟨⟨(-19205963577924666321730099067),(-19205963577924666304759478895)⟩,⟨(-11512434749938273358352334484),(-11512434749938273342836134731)⟩⟩,⟨⟨(-19280901506636589606173491770),(-19280901506636589589143927885)⟩,⟨(-11752696866632195584661931668),(-11752696866632195569088221411)⟩⟩,⟨⟨(-19352692612006325440669179879),(-19352692612006325423584589105)⟩,⟨(-11993274886021022111138584511),(-11993274886021022095510625233)⟩⟩,⟨⟨(-19421801952477937417334138747),(-19421801952477937400197591693)⟩,⟨(-12234344325102447173622161461),(-12234344325102447157942412891)⟩⟩,⟨⟨(-19487764196407347906849214373),(-19487764196407347889662964358)⟩,⟨(-12475502906480027995275791413),(-12475502906480027979546486046)⟩⟩,⟨⟨(-19551003536838236789872408753),(-19551003536838236772640169064)⟩,⟨(-12716906720332784043212930098),(-12716906720332784027436987444)⟩⟩,⟨⟨(-19611096979962957120816464825),(-19611096979962957103540489547)⟩,⟨(-12958168424575972046784385879),(-12958168424575972030964065314)⟩⟩,⟨⟨(-19668428422817626690350100505),(-19668428422817626673032218669)⟩,⟨(-13199423674386312951756222008),(-13199423674386312935893200547)⟩⟩,⟨⟨(-19722616682115287211274674851),(-19722616682115287193922774020)⟩,⟨(-13440301632829067584646469803),(-13440301632829067568746790500)⟩⟩,⟨⟨(-19774005867741209809260172147),(-19774005867741209791872289407)⟩,⟨(-13680916491575430882862325318),(-13680916491575430866925144016)⟩⟩] +lemma amp4_04_6_eq : ∀ k : Fin 16, amp4_0Expr 4 6 k = amp4_04_6 k := by decide +kernel +noncomputable def amp4_04_7 : Fin 16 → CBox := ![⟨⟨(-19822256137707282229628376416),(-19822256137707282212207911535)⟩,⟨(-13920915523151978248989758898),(-13920915523151978233018120491)⟩⟩,⟨⟨(-19867672265723743220836681556),(-19867672265723743203385591197)⟩,⟨(-14160390405529449223334450725),(-14160390405529449207330101707)⟩⟩,⟨⟨(-19909955337486662346103426946),(-19909955337486662328627260308)⟩,⟨(-14399008159555355458949219793),(-14399008159555355442916745061)⟩⟩,⟨⟨(-19949371185938978992579110045),(-19949371185938978975078249268)⟩,⟨(-14636836876143002877190342732),(-14636836876143002861130400644)⟩⟩,⟨⟨(-19985661464296134338585230552),(-19985661464296134321064137469)⟩,⟨(-14873564998014268179601399333),(-14873564998014268163517868027)⟩⟩,⟨⟨(-20019053406570060807834060739),(-20019053406570060790293489443)⟩,⟨(-15109235930931520590939542865),(-15109235930931520574833280175)⟩⟩,⟨⟨(-20049328924928558223985605833),(-20049328924928558206429651166)⟩,⟨(-15343561247963450584604525943),(-15343561247963450568479140164)⟩⟩,⟨⟨(-20076676944420042328574040814),(-20076676944420042311005282310)⟩,⟨(-15576558545206277176673624708),(-15576558545206277160531369952)⟩⟩,⟨⟨(-20100919377628340413632851946),(-20100919377628340396053942738)⟩,⟨(-15807964269782240608571293927),(-15807964269782240592414745314)⟩⟩,⟨⟨(-20122207080164254976451407452),(-20122207080164254958864701799)⟩,⟨(-16037769055381219786892833190),(-16037769055381219770724026270)⟩⟩,⟨⟨(-20140401755222903170806827484),(-20140401755222903153215709296)⟩,⟨(-16265736002536586705048517648),(-16265736002536586688870577421)⟩⟩,⟨⟨(-20155616379228916845984294313),(-20155616379228916828391211220)⟩,⟨(-16491827599637104471476088821),(-16491827599637104455291169830)⟩⟩,⟨⟨(-20167752283870677605384977571),(-20167752283870677587793235835)⟩,⟨(-16715835416165790961271889025),(-16715835416165790945083117803)⟩⟩,⟨⟨(-20176884708283040093585343589),(-20176884708283040075997759710)⟩,⟨(-16937692580095708525250227718),(-16937692580095708509060041666)⟩⟩,⟨⟨(-20182954497414680405138463154),(-20182954497414680387558224629)⟩,⟨(-17157220982235930514098815931),(-17157220982235930497910245047)⟩⟩,⟨⟨(-20185999247333360636386839775),(-20185999247333360618817282856)⟩,⟨(-17374323140598177723496071957),(-17374323140598177707312054582)⟩⟩] +lemma amp4_04_7_eq : ∀ k : Fin 16, amp4_0Expr 4 7 k = amp4_04_7 k := by decide +kernel +noncomputable def amp4_04_8 : Fin 16 → CBox := ![⟨⟨(-20185999247333360636380327572),(-20185999247333360618821899050)⟩,⟨(-17588853157330318784852058684),(-17588853157330318768673331792)⟩⟩,⟨⟨(-20182954497414680405118930471),(-20182954497414680387572070426)⟩,⟨(-17800681654137070626235963753),(-17800681654137070610062846240)⟩⟩,⟨⟨(-20176884708283040093552802174),(-20176884708283040076020826782)⟩,⟨(-18009696873110062219000138778),(-18009696873110062202835748836)⟩⟩,⟨⟨(-20167752283870677605339447069),(-20167752283870677587825510259)⟩,⟨(-18215736213961485605619695690),(-18215736213961485589466774985)⟩⟩,⟨⟨(-20155616379228916845925802070),(-20155616379228916828432673610)⟩,⟨(-18418724027054831485595578553),(-18418724027054831469456837593)⟩⟩,⟨⟨(-20140401755222903170735408864),(-20140401755222903153266334586)⟩,⟨(-18618463122358876438940355698),(-18618463122358876422818607186)⟩⟩,⟨⟨(-20122207080164254976367105282),(-20122207080164254958924459628)⟩,⟨(-18814915967885458442217474545),(-18814915967885458426115050233)⟩⟩,⟨⟨(-20100919377628340413535717273),(-20100919377628340396122796924)⟩,⟨(-19007849371115820764909726986),(-19007849371115820748829551133)⟩⟩,⟨⟨(-20076676944420042328464131795),(-20076676944420042311083191626)⟩,⟨(-19197265969675916929680220613),(-19197265969675916913624584775)⟩⟩,⟨⟨(-20049328924928558223862989126),(-20049328924928558206516568363)⟩,⟨(-19382895107673109081445057969),(-19382895107673109065416121497)⟩⟩,⟨⟨(-20019053406570060807698809638),(-20019053406570060790389362565)⟩,⟨(-19564781688682637255200756707),(-19564781688682637239200949059)⟩⟩,⟨⟨(-19985661464296134338437427218),(-19985661464296134321168908277)⟩,⟨(-19742616081018041992658644358),(-19742616081018041976691575462)⟩⟩,⟨⟨(-19949371185938978992418842682),(-19949371185938978975191855238)⟩,⟨(-19916487596953897028449391700),(-19916487596953897012515731007)⟩⟩,⟨⟨(-19909955337486662345930793070),(-19909955337486662328749632315)⟩,⟨(-20086046061398696916940212644),(-20086046061398696901043884185)⟩⟩,⟨⟨(-19867672265723743220651784015),(-19867672265723743203516656337)⟩,⟨(-20251427386831146289521441008),(-20251427386831146273662633078)⟩⟩,⟨⟨(-19822256137707282229431327901),(-19822256137707282212347589928)⟩,⟨(-20412239228001054490758198959),(-20412239228001054474942002213)⟩⟩] +lemma amp4_04_8_eq : ∀ k : Fin 16, amp4_0Expr 4 8 k = amp4_04_8 k := by decide +kernel +noncomputable def amp4_04_9 : Fin 16 → CBox := ![⟨⟨(-19774005867741209809051089849),(-19774005867741209792020497981)⟩,⟨(-20568666340517449775562991075),(-20568666340517449759791255021)⟩⟩,⟨⟨(-19722616682115287211053686418),(-19722616682115287194079422290)⟩,⟨(-20720272518800126896969884082),(-20720272518800126881245448896)⟩⟩,⟨⟨(-19668428422817626690117337133),(-19668428422817626673197213638)⟩,⟨(-20867293658965616901077190127),(-20867293658965616885397654294)⟩⟩,⟨⟨(-19611096979962957120572068869),(-19611096979962957103713730306)⟩,⟨(-21009247936880438438361475855),(-21009247936880438422734461834)⟩⟩,⟨⟨(-19551003536838236789616525040),(-19551003536838236772821552952)⟩,⟨(-21146424744429860195775057341),(-21146424744429860180202229522)⟩⟩,⟨⟨(-19487764196407347906581999680),(-19487764196407347889852380243)⟩,⟨(-21278294807619172001302403578),(-21278294807619171985785347143)⟩⟩,⟨⟨(-19421801952477937417055751125),(-19421801952477937400394927540)⟩,⟨(-21405203431129762110742200816),(-21405203431129762095284552226)⟩⟩,⟨⟨(-19352692612006325440379790207),(-19352692612006325423789723785)⟩,⟨(-21526571981236779153874015256),(-21526571981236779138477390452)⟩⟩,⟨⟨(-19280901506636589605873270884),(-19280901506636589589356740302)⟩,⟨(-21642804158593692365100033966),(-21642804158593692349767453640)⟩⟩,⟨⟨(-19205963577924666321419231598),(-19205963577924666304979838172)⟩,⟨(-21753269975344588909985755480),(-21753269975344588894720607653)⟩⟩,⟨⟨(-19128387083605228863738466189),(-19128387083605228847367024494)⟩,⟨(-21858434082380325701316498422),(-21858434082380325686108120022)⟩⟩,⟨⟨(-19047665466876555502526100903),(-19047665466876555486235582468)⟩,⟨(-21957613052256640463194624758),(-21957613052256640448057098656)⟩⟩,⟨⟨(-18964350563992084748345945428),(-18964350563992084732137871106)⟩,⟨(-22051335117021254439227339344),(-22051335117021254424162288915)⟩⟩,⟨⟨(-18877893619833286283031587138),(-18877893619833286266909612231)⟩,⟨(-22138861225983276192827640716),(-22138861225983276177838570851)⟩⟩,⟨⟨(-18788890769439972165072661143),(-18788890769439972149036877325)⟩,⟨(-22220785906184532932620563682),(-22220785906184532917707364504)⟩⟩,⟨⟨(-18696750288527408077586745714),(-18696750288527408061641698086)⟩,⟨(-22296312193986599252373367510),(-22296312193986599237540678294)⟩⟩] +lemma amp4_04_9_eq : ∀ k : Fin 16, amp4_0Expr 4 9 k = amp4_04_9 k := by decide +kernel +noncomputable def amp4_04_10 : Fin 16 → CBox := ![⟨⟨(-18602113403169274031149835828),(-18602113403169274015293634565)⟩,⟨(-22366103715227964319136759170),(-22366103715227964304382162036)⟩⟩,⟨⟨(-18504344573786966164690706510),(-18504344573786966148929108089)⟩,⟨(-22429303188952330501431325149),(-22429303188952330486760846101)⟩⟩,⟨⟨(-18404130986383395516525903030),(-18404130986383395500860576689)⟩,⟨(-22486646241491648388565048108),(-22486646241491648373980462131)⟩⟩,⟨⟨(-18300792359735829279420356695),(-18300792359735829263852848120)⟩,⟨(-22537212746018467646635141257),(-22537212746018467632137506015)⟩⟩,⟨⟨(-18195062790576238016649206222),(-18195062790576238001182966004)⟩,⟨(-22581813337871331066109159216),(-22581813337871331051702525270)⟩⟩,⟨⟨(-18086216243898398252847990050),(-18086216243898398237484460112)⟩,⟨(-22619462381098000789272017933),(-22619462381098000774957243060)⟩⟩,⟨⟨(-17975034765783921179645099003),(-17975034765783921164386278502)⟩,⟨(-22651048645416984019895944156),(-22651048645416984005675244691)⟩⟩,⟨⟨(-17860745463249223316671300344),(-17860745463249223301520399465)⟩,⟨(-22675518176140289626122942150),(-22675518176140289611999461482)⟩⟩,⟨⟨(-17744179464825680166877266208),(-17744179464825680151836167536)⟩,⟨(-22693841130914327071809520366),(-22693841130914327057785465487)⟩⟩,⟨⟨(-17624515816250218779608503172),(-17624515816250218764680167537)⟩,⟨(-22704892267393046165182991800),(-22704892267393046151261128295)⟩⟩,⟨⟨(-17502635963581591413683123121),(-17502635963581591398870080170)⟩,⟨(-22709726525630194889204945862),(-22709726525630194875388266662)⟩⟩,⟨⟨(-17377669580920238816642564386),(-17377669580920238801915022507)⟩,⟨(-22707144232953652513367122806),(-22707144232953652499615731790)⟩⟩,⟨⟨(-17250549777357544683745366075),(-17250549777357544669135507624)⟩,⟨(-22698288661635232235633666865),(-22698288661635232221989119579)⟩⟩,⟨⟨(-17120355428983751372443462148),(-17120355428983751357953509304)⟩,⟨(-22681882376134207326637703924),(-22681882376134207313101835271)⟩⟩,⟨⟨(-16988072773390696827343898951),(-16988072773390696812975616787)⟩,⟨(-22659160702358851765026097582),(-22659160702358851751600949997)⟩⟩,⟨⟨(-16852728336147199056671482641),(-16852728336147199042426778742)⟩,⟨(-22628764901408639643270215951),(-22628764901408639629957283218)⟩⟩] +lemma amp4_04_10_eq : ∀ k : Fin 16, amp4_0Expr 4 10 k = amp4_04_10 k := by decide +kernel +noncomputable def amp4_04_11 : Fin 16 → CBox := ![⟨⟨(-16715363079551532489303051023),(-16715363079551532475183519291)⟩,⟨(-22592026264281164513953946510),(-22592026264281164500755173507)⟩⟩,⟨⟨(-16574949488553341709780887708),(-16574949488553341695788380884)⟩,⟨(-22547500979961828601406297304),(-22547500979961828588322989543)⟩⟩,⟨⟨(-16432584989301644049215792941),(-16432584989301644035352873686)⟩,⟨(-22496620426924145863079342502),(-22496620426924145850114688916)⟩⟩,⟨⟨(-16287186185465403679520462853),(-16287186185465403665787641723)⟩,⟨(-22437851702119264970886455504),(-22437851702119264958040030069)⟩⟩,⟨⟨(-16139908862969460008664694889),(-16139908862969459995065131770)⟩,⟨(-22372730628569073856735827667),(-22372730628569073844011766442)⟩⟩,⟨⟨(-15989611738234159575500627799),(-15989611738234159562036154197)⟩,⟨(-22299630914200695666962676128),(-22299630914200695654362291005)⟩⟩,⟨⟨(-15837511025409440773863110526),(-15837511025409440760535921773)⟩,⟨(-22220197445398718326277541421),(-22220197445398718313803618848)⟩⟩,⟨⟨(-15682405365602133419639800107),(-15682405365602133406447369540)⟩,⟨(-22132705937611679224184548295),(-22132705937611679211832338148)⟩⟩,⟨⟨(-15525573660113779860562358651),(-15525573660113779847510524090)⟩,⟨(-22038915252040322524006325147),(-22038915252040322511783874362)⟩⟩,⟨⟨(-15365752085399789989567074063),(-15365752085399789976657834223)⟩,⟨(-21936998168262280560621049034),(-21936998168262280548529887516)⟩⟩,⟨⟨(-15204284699849471840293728182),(-15204284699849471827527245243)⟩,⟨(-21828832761768576211120141189),(-21828832761768576199160240909)⟩⟩,⟨⟨(-15039842602688874799926387419),(-15039842602688874787306456845)⟩,⟨(-21712483554681429445734870834),(-21712483554681429433910446971)⟩⟩,⟨⟨(-14873837713897835550251094785),(-14873837713897835537778323093)⟩,⟨(-21589953444916033478902947429),(-21589953444916033467214729360)⟩⟩,⟨⟨(-14704873194407792685880278053),(-14704873194407792673557113569)⟩,⟨(-21459192953477879625817378224),(-21459192953477879614267580250)⟩⟩,⟨⟨(-14534431791978345801934591331),(-14534431791978345789762691822)⟩,⟨(-21322335824331331325336836515),(-21322335824331331313927671169)⟩⟩,⟨⟨(-14361045590572946754083645955),(-14361045590572946742065854620)⟩,⟨(-21177212361083276818740572371),(-21177212361083276807474945906)⟩⟩] +lemma amp4_04_11_eq : ∀ k : Fin 16, amp4_0Expr 4 11 k = amp4_04_11 k := by decide +kernel +noncomputable def amp4_04_12 : Fin 16 → CBox := ![⟨⟨(-14186271424944109330515200675),(-14186271424944109318634715833)⟩,⟨(-21026093647022739436111887826),(-21026093647022739424964837423)⟩⟩,⟨⟨(-14008566852088077041383574033),(-14008566852088077029657894228)⟩,⟨(-20866683020998512839044153464),(-20866683020998512828040060329)⟩⟩,⟨⟨(-13829566382342766174559285538),(-13829566382342766162989443224)⟩,⟨(-20701395931425746120645959726),(-20701395931425746109786182722)⟩⟩,⟨⟨(-13647649245210552391890332337),(-13647649245210552380478322620)⟩,⟨(-20527801406050109835496572533),(-20527801406050109824782754553)⟩⟩,⟨⟨(-13464531586944342179234164523),(-13464531586944342167980908303)⟩,⟨(-20348466890038440332122602764),(-20348466890038440321556063742)⟩⟩,⟨⟨(-13278510112718882575615200305),(-13278510112718882564522451581)⟩,⟨(-20160819075447450995393948184),(-20160819075447450984975883421)⟩⟩,⟨⟨(-13091386986347086839964110755),(-13091386986347086829033617950)⟩,⟨(-19967585727477484875839617829),(-19967585727477484865572566181)⟩⟩,⟨⟨(-12901371741818879374230470286),(-12901371741818879363462041825)⟩,⟨(-19766042406712590496590592629),(-19766042406712590486472865268)⟩⟩,⟨⟨(-12710357421784252654408920168),(-12710357421784252643805666502)⟩,⟨(-19559086314320908313109603429),(-19559086314320908303145987938)⟩⟩,⟨⟨(-12516461228816132569701228269),(-12516461228816132559264737665)⟩,⟨(-19343832202830089359576786855),(-19343832202830089349768210706)⟩⟩,⟨⟨(-12321672494270023913880957223),(-12321672494270023903612233117)⟩,⟨(-19123356737422651708587845233),(-19123356737422651698935822687)⟩⟩,⟨⟨(-12124010340568684229054710966),(-12124010340568684218956033220)⟩,⟨(-18894603175232230227441868037),(-18894603175232230217948512819)⟩⟩,⟨⟨(-11925566428242691910888850854),(-11925566428242691900961580986)⟩,⟨(-18660838727709348906497361999),(-18660838727709348897164896811)⟩⟩,⟨⟨(-11724255372714411619379365343),(-11724255372714411609614922406)⟩,⟨(-18418823303491636536692004276),(-18418823303491636527505414177)⟩⟩,⟨⟨(-11522277932889587525906902226),(-11522277932889587516315684889)⟩,⟨(-18172026966804761014724969261),(-18172026966804761005700589297)⟩⟩,⟨⟨(-11317437004640384565500642615),(-11317437004640384556084640382)⟩,⟨(-17917013072834107306700207333),(-17917013072834107297839707272)⟩⟩] +lemma amp4_04_12_eq : ∀ k : Fin 16, amp4_0Expr 4 12 k = amp4_04_12 k := by decide +kernel +noncomputable def amp4_04_13 : Fin 16 → CBox := ![⟨⟨(-11112050061373981239323577027),(-11112050061373981230082820025)⟩,⟨(-17657468274175708685696954122),(-17657468274175708677000603374)⟩⟩,⟨⟨(-10903800151122990468021575109),(-10903800151122990458956932323)⟩,⟨(-17389744590802867497737320566),(-17389744590802867489204881453)⟩⟩,⟨⟨(-10695130068233236245564044695),(-10695130068233236236677760136)⟩,⟨(-17117760676861643338861970527),(-17117760676861643330497181467)⟩⟩,⟨⟨(-10483593810512908947241898871),(-10483593810512908938535372894)⟩,⟨(-16837640584592057549663738244),(-16837640584592057541467323553)⟩⟩,⟨⟨(-10271769265286107336108395196),(-10271769265286107327582631384)⟩,⟨(-16553552364248146338753695363),(-16553552364248146330727575091)⟩⟩,⟨⟨(-10057070909260472808009984836),(-10057070909260472799660322853)⟩,⟨(-16261373280708308081402008848),(-16261373280708308073537015690)⟩⟩,⟨⟨(-9842222876484623694086149906),(-9842222876484623685918417764)⟩,⟨(-15965540530788261962709121867),(-15965540530788261955014936302)⟩⟩,⟨⟨(-9624488142462866612339787845),(-9624488142462866604356230519)⟩,⟨(-15661663168693720859519258412),(-15661663168693720851997944127)⟩⟩,⟨⟨(-9406749892287105452210484559),(-9406749892287105444410779548)⟩,⟨(-15354470110089328274145779681),(-15354470110089328266797271146)⟩⟩,⟨⟨(-9186105809946619699933578735),(-9186105809946619692319250754)⟩,⟨(-15039277650619030661227878476),(-15039277650619030654052946755)⟩⟩,⟨⟨(-8965612924336716947878172068),(-8965612924336716940449629707)⟩,⟨(-14721132404406360011207552411),(-14721132404406360004207298809)⟩⟩,⟨⟨(-8742187647147554116418027528),(-8742187647147554109173135203)⟩,⟨(-14395029577880599346261673118),(-14395029577880599339430922001)⟩⟩,⟨⟨(-8519078061542027635533535813),(-8519078061542027628477020150)⟩,⟨(-14066363614380330172200676567),(-14066363614380330165547787625)⟩⟩,⟨⟨(-8293000649667702143217935943),(-8293000649667702136351541515)⟩,⟨(-13729775676425341998854326099),(-13729775676425341992380419723)⟩⟩,⟨⟨(-8067414729134296312615163064),(-8067414729134296305938009755)⟩,⟨(-13391043274937594640530219227),(-13391043274937594634234451747)⟩⟩,⟨⟨(-7838814889794311720647834003),(-7838814889794311714162770637)⟩,⟨(-13044414860743831219425836246),(-13044414860743831213311200314)⟩⟩] +lemma amp4_04_13_eq : ∀ k : Fin 16, amp4_0Expr 4 13 k = amp4_04_13 k := by decide +kernel +noncomputable def amp4_04_14 : Fin 16 → CBox := ![⟨⟨(-7610895553025613803027488994),(-7610895553025613796730396502)⟩,⟨(-12696092604806469777386539733),(-12696092604806469771446979952)⟩⟩,⟨⟨(-7379903322321855095388953750),(-7379903322321855089285235654)⟩,⟨(-12339886435573950629889978087),(-12339886435573950624132606182)⟩⟩,⟨⟨(-7149796232995450593072123064),(-7149796232995450587160460657)⟩,⟨(-11982472779424677455133707027),(-11982472779424677449557143351)⟩⟩,⟨⟨(-6916541575480023270977837324),(-6916541575480023265261830893)⟩,⟨(-11617168181822501713788999180),(-11617168181822501708397421811)⟩⟩,⟨⟨(-6684395430218605951723196798),(-6684395430218605946198549716)⟩,⟨(-11251183140674657524293223532),(-11251183140674657519080423810)⟩⟩,⟨⟨(-6449007720194114035567062072),(-6449007720194114030238832600)⟩,⟨(-10877274318968929079865057087),(-10877274318968929074837542271)⟩⟩,⟨⟨(-6214974678023852760067897225),(-6214974678023852754932996190)⟩,⟨(-10503259362946582411359037724),(-10503259362946582406512683570)⟩⟩,⟨⟨(-5977582006447996123913774723),(-5977582006447996118976903170)⟩,⟨(-10121253328706587502554084117),(-10121253328706587497894805563)⟩⟩,⟨⟨(-5741818330713242041510812621),(-5741818330713242036770260500)⟩,⟨(-9739771605523419724480114640),(-9739771605523419720006341323)⟩⟩,⟨⟨(-5502546547528761708222793748),(-5502546547528761703679889704)⟩,⟨(-9350185610935281614921936273),(-9350185610935281610633706546)⟩⟩,⟨⟨(-5265213576138587391330315197),(-5265213576138587386985067367)⟩,⟨(-8961822700298428810132252012),(-8961822700298428806031010114)⟩⟩,⟨⟨(-5024184917995322595043195408),(-5024184917995322590897081572)⟩,⟨(-8565180917535639095152494016),(-8565180917535639091238482381)⟩⟩,⟨⟨(-4785450558516348023730440857),(-4785450558516348019781466319)⟩,⟨(-8170546460019593086832083757),(-8170546460019593083103590899)⟩⟩,⟨⟨(-4542781601919094069179177830),(-4542781601919094065431859975)⟩,⟨(-7767375458793477018208761401),(-7767375458793477014671008067)⟩⟩,⟨⟨(-4302822699838685575246489664),(-4302822699838685571697430831)⟩,⟨(-7367106264961066710873603503),(-7367106264961066707522677555)⟩⟩,⟨⟨(-4058621167164034578425924459),(-4058621167164034575078627159)⟩,⟨(-6957928472230496263479325852),(-6957928472230496260318569313)⟩⟩] +lemma amp4_04_14_eq : ∀ k : Fin 16, amp4_0Expr 4 14 k = amp4_04_14 k := by decide +kernel +noncomputable def amp4_04_15 : Fin 16 → CBox := ![⟨⟨(-3817627397948821484828575793),(-3817627397948821481680546864)⟩,⟨(-6552694241467626959879907745),(-6552694241467626956907304091)⟩⟩,⟨⟨(-3571986906618049827710291092),(-3571986906618049824765392535)⟩,⟨(-6138017810170665218675660909),(-6138017810170665215894852179)⟩⟩,⟨⟨(-3330167486215396475491896188),(-3330167486215396472746989295)⟩,⟨(-5728531704276193868508906350),(-5728531704276193865917083468)⟩⟩,⟨⟨(-3083158362756607819640068425),(-3083158362756607817098835858)⟩,⟨(-5308833540397804546234981416),(-5308833540397804543835187232)⟩⟩,⟨⟨(-2840754361792469276260928410),(-2840754361792469273919707088)⟩,⟨(-4895872438890964071417195372),(-4895872438890964069206229392)⟩⟩,⟨⟨(-2592406288112938840185163597),(-2592406288112938838048908344)⟩,⟨(-4471567058204486104660553621),(-4471567058204486102643128278)⟩⟩,⟨⟨(-2349715165212016045394614560),(-2349715165212016043458784216)⟩,⟨(-4056012956547657431570128727),(-4056012956547657429742154412)⟩⟩,⟨⟨(-2099980978840482902029879999),(-2099980978840482900299774230)⟩,⟨(-3627388678185041824099476219),(-3627388678185041822465583702)⟩⟩,⟨⟨(-1857411230393376142878293908),(-1857411230393376141348291419)⟩,⟨(-3210322231328053165943484742),(-3210322231328053164498697030)⟩⟩,⟨⟨(-1606080516929194708511715551),(-1606080516929194707188928371)⟩,⟨(-2777390389894262930592457448),(-2777390389894262929343392596)⟩⟩,⟨⟨(-1364294426607166605965936937),(-1364294426607166604842535907)⟩,⟨(-2360337035568339228051094637),(-2360337035568339226990448381)⟩⟩,⟨⟨(-1110742379793587805985199006),(-1110742379793587805070740809)⟩,⟨(-1922395849439087974651742527),(-1922395849439087973788444825)⟩⟩,⟨⟨(-871132832163727549035215238),(-871132832163727548318292155)⟩,⟨(-1508150541903205266595688464),(-1508150541903205265919078680)⟩⟩,⟨⟨(-613314789282883315006545336),(-613314789282883314501967889)⟩,⟨(-1062042427970903184724795881),(-1062042427970903184248706801)⟩⟩,⟨⟨(-380453151319111964562263142),(-380453151319111964249786653)⟩,⟨(-658908367719719655327590365),(-658908367719719655033168755)⟩⟩,⟨⟨(-108088285328156059025474013),(-108088285328156058937011328)⟩,⟨(-187212639762263632490193310),(-187212639762263632407088370)⟩⟩] +lemma amp4_04_15_eq : ∀ k : Fin 16, amp4_0Expr 4 15 k = amp4_04_15 k := by decide +kernel +noncomputable def amp4_04 : Fin 16 → Fin 16 → CBox := ![amp4_04_0,amp4_04_1,amp4_04_2,amp4_04_3,amp4_04_4,amp4_04_5,amp4_04_6,amp4_04_7,amp4_04_8,amp4_04_9,amp4_04_10,amp4_04_11,amp4_04_12,amp4_04_13,amp4_04_14,amp4_04_15] +lemma amp4_04_eq (i k : Fin 16) : amp4_0Expr 4 i k = amp4_04 i k := by + fin_cases i + · exact amp4_04_0_eq k + · exact amp4_04_1_eq k + · exact amp4_04_2_eq k + · exact amp4_04_3_eq k + · exact amp4_04_4_eq k + · exact amp4_04_5_eq k + · exact amp4_04_6_eq k + · exact amp4_04_7_eq k + · exact amp4_04_8_eq k + · exact amp4_04_9_eq k + · exact amp4_04_10_eq k + · exact amp4_04_11_eq k + · exact amp4_04_12_eq k + · exact amp4_04_13_eq k + · exact amp4_04_14_eq k + · exact amp4_04_15_eq k +noncomputable def amp4_05_0 : Fin 16 → CBox := ![⟨⟨(-1017365712714798119321),(-1017365712714798119303)⟩,⟨0,0⟩⟩,⟨⟨(-32227844834901915228914),(-32227844834901915228293)⟩,⟨0,0⟩⟩,⟨⟨(-144307603078629676795440),(-144307603078629676792476)⟩,⟨0,0⟩⟩,⟨⟨(-401710817432016743329331),(-401710817432016743320991)⟩,⟨0,0⟩⟩,⟨⟨(-846618630911081865613070),(-846618630911081865595272)⟩,⟨0,0⟩⟩,⟨⟨(-1553203743542669652050032),(-1553203743542669652017226)⟩,⟨0,0⟩⟩,⟨⟨(-2553427679062347663274071),(-2553427679062347663219796)⟩,⟨0,0⟩⟩,⟨⟨(-3930825950684612502729165),(-3930825950684612502645361)⟩,⟨0,0⟩⟩,⟨⟨(-5707149034948221457831324),(-5707149034948221457709189)⟩,⟨0,0⟩⟩,⟨⟨(-7974992912616157788973303),(-7974992912616157788803222)⟩,⟨0,0⟩⟩,⟨⟨(-10745843359115808218419703),(-10745843359115808218189282)⟩,⟨0,0⟩⟩,⟨⟨(-14121091280701553281758774),(-14121091280701553281455476)⟩,⟨0,0⟩⟩,⟨⟨(-18101889125021378555186890),(-18101889125021378554798218)⟩,⟨0,0⟩⟩,⟨⟨(-22798164690230290672242914),(-22798164690230290671754863)⟩,⟨0,0⟩⟩,⟨⟨(-28200671625299007329227057),(-28200671625299007328620746)⟩,⟨0,0⟩⟩,⟨⟨(-34427613720176448927468864),(-34427613720176448926726625)⟩,⟨0,0⟩⟩] +lemma amp4_05_0_eq : ∀ k : Fin 16, amp4_0Expr 5 0 k = amp4_05_0 k := by decide +kernel +noncomputable def amp4_05_1 : Fin 16 → CBox := ![⟨⟨(-41459290719596024022572080),(-41459290719596024021677183)⟩,⟨0,0⟩⟩,⟨⟨(-49421914614835276705674313),(-49421914614835276704609058)⟩,⟨0,0⟩⟩,⟨⟨(-58285289887787186846646188),(-58285289887787186845392655)⟩,⟨0,0⟩⟩,⟨⟨(-68183360397692089973599004),(-68183360397692089972120169)⟩,⟨0,0⟩⟩,⟨⟨(-79075409598275565814789512),(-79075409598275565813082958)⟩,⟨0,0⟩⟩,⟨⟨(-91102827691590655631504501),(-91102827691590655629547156)⟩,⟨0,0⟩⟩,⟨⟨(-104214368082311430485667936),(-104214368082311430483410322)⟩,⟨0,0⟩⟩,⟨⟨(-118558572418822139901809339),(-118558572418822139899256927)⟩,⟨0,0⟩⟩,⟨⟨(-134073672582852005913933433),(-134073672582852005911031098)⟩,⟨0,0⟩⟩,⟨⟨(-150915057458186184577820425),(-150915057458186184574530728)⟩,⟨0,0⟩⟩,⟨⟨(-169010464087999568987596133),(-169010464087999568983942109)⟩,⟨0,0⟩⟩,⟨⟨(-188521815248313382696613204),(-188521815248313382692516281)⟩,⟨0,0⟩⟩,⟨⟨(-209366398483646597106911142),(-209366398483646597102415613)⟩,⟨0,0⟩⟩,⟨⟨(-231712348237249836308951574),(-231712348237249836303926834)⟩,⟨0,0⟩⟩,⟨⟨(-255466566973823129190432188),(-255466566973823129184880861)⟩,⟨0,0⟩⟩,⟨⟨(-280803069984181516268335015),(-280803069984181516262204349)⟩,⟨0,0⟩⟩] +lemma amp4_05_1_eq : ∀ k : Fin 16, amp4_0Expr 5 1 k = amp4_05_1 k := by decide +kernel +noncomputable def amp4_05_2 : Fin 16 → CBox := ![⟨⟨(-307618458522706084057722309),(-307618458522706084051094961)⟩,⟨0,0⟩⟩,⟨⟨(-336092289619148268644092817),(-336092289619148268636800808)⟩,⟨0,0⟩⟩,⟨⟨(-366110966970354771076915514),(-366110966970354771068942300)⟩,⟨0,0⟩⟩,⟨⟨(-397859242260386786518384314),(-397859242260386786509673275)⟩,⟨0,0⟩⟩,⟨⟨(-431213445365565143548508820),(-431213445365565143538993191)⟩,⟨0,0⟩⟩,⟨⟨(-466363167876582221842856889),(-466363167876582221832755987)⟩,⟨0,0⟩⟩,⟨⟨(-503174809944199807321989869),(-503174809944199807311046913)⟩,⟨0,0⟩⟩,⟨⟨(-541842440962969024135391917),(-541842440962969024123601326)⟩,⟨0,0⟩⟩,⟨⟨(-582222696060299641887781073),(-582222696060299641875063038)⟩,⟨0,0⟩⟩,⟨⟨(-624513753276140037131427559),(-624513753276140037117724339)⟩,⟨0,0⟩⟩,⟨⟨(-668562668250543284525315132),(-668562668250543284510585430)⟩,⟨0,0⟩⟩,⟨⟨(-714571351742874040395573774),(-714571351742874040380176524)⟩,⟨0,0⟩⟩,⟨⟨(-762377486480516795387991724),(-762377486480516795371421312)⟩,⟨0,0⟩⟩,⟨⟨(-812186333523575931107597971),(-812186333523575931089868108)⟩,⟨0,0⟩⟩,⟨⟨(-863826430484116377594998124),(-863826430484116377576001202)⟩,⟨0,0⟩⟩,⟨⟨(-917506000071359153558566515),(-917506000071359153538415772)⟩,⟨0,0⟩⟩] +lemma amp4_05_2_eq : ∀ k : Fin 16, amp4_0Expr 5 2 k = amp4_05_2 k := by decide +kernel +noncomputable def amp4_05_3 : Fin 16 → CBox := ![⟨⟨(-973044683965568815881872493),(-973044683965568815860418425)⟩,⟨0,0⟩⟩,⟨⟨(-1030653271883720175211179501),(-1030653271883720175188345611)⟩,⟨0,0⟩⟩,⟨⟨(-1090142780287363173246301208),(-1090142780287363173222021331)⟩,⟨0,0⟩⟩,⟨⟨(-1151726165495505753605907759),(-1151726165495505753581091878)⟩,⟨0,0⟩⟩,⟨⟨(-1215206111117198395355499826),(-1215206111117198395329092959)⟩,⟨0,0⟩⟩,⟨⟨(-1280797334109812439666899848),(-1280797334109812439638929848)⟩,⟨0,0⟩⟩,⟨⟨(-1348294499353228944367812267),(-1348294499353228944338240409)⟩,⟨0,0⟩⟩,⟨⟨(-1417913673107950989731131974),(-1417913673107950989699949813)⟩,⟨0,0⟩⟩,⟨⟨(-1489441837489806940281661168),(-1489441837489806940248755484)⟩,⟨0,0⟩⟩,⟨⟨(-1563095991521031544081405797),(-1563095991521031544047009336)⟩,⟨0,0⟩⟩,⟨⟨(-1638655792425954715313844930),(-1638655792425954715277632927)⟩,⟨0,0⟩⟩,⟨⟨(-1716338750384461640060584209),(-1716338750384461640022625884)⟩,⟨0,0⟩⟩,⟨⟨(-1795917577556343213068135676),(-1795917577556343213028332389)⟩,⟨0,0⟩⟩,⟨⟨(-1877609868733088065836084692),(-1877609868733088065794393165)⟩,⟨0,0⟩⟩,⟨⟨(-1961181792819992281960842248),(-1961181792819992281917188640)⟩,⟨0,0⟩⟩,⟨⟨(-2046850597829250582893494965),(-2046850597829250582847841239)⟩,⟨0,0⟩⟩] +lemma amp4_05_3_eq : ∀ k : Fin 16, amp4_0Expr 5 3 k = amp4_05_3 k := by decide +kernel +noncomputable def amp4_05_4 : Fin 16 → CBox := ![⟨⟨(-2134376333215646664597672115),(-2134376333215646664552247059)⟩,⟨0,0⟩⟩,⟨⟨(-2223975464049050681638407685),(-2223975464049050681590566318)⟩,⟨0,0⟩⟩,⟨⟨(-2315402366125218526104187284),(-2315402366125218526053960833)⟩,⟨0,0⟩⟩,⟨⟨(-2408872280684075508343235146),(-2408872280684075508290648207)⟩,⟨0,0⟩⟩,⟨⟨(-2504134377618229003904632930),(-2504134377618229003849667590)⟩,⟨0,0⟩⟩,⟨⟨(-2601402228747062345458206934),(-2601402228747062345400705091)⟩,⟨0,0⟩⟩,⟨⟨(-2700420287741234993809296048),(-2700420287741234993749471276)⟩,⟨0,0⟩⟩,⟨⟨(-2801400006700950695991410538),(-2801400006700950695929017744)⟩,⟨0,0⟩⟩,⟨⟨(-2904081634627201915039832444),(-2904081634627201914974773042)⟩,⟨0,0⟩⟩,⟨⟨(-3008674048861856004873369378),(-3008674048861856004806436930)⟩,⟨0,0⟩⟩,⟨⟨(-3114913827091087448855089391),(-3114913827091087448785337097)⟩,⟨0,0⟩⟩,⟨⟨(-3223006812058119979807468030),(-3223006812058119979734993278)⟩,⟨0,0⟩⟩,⟨⟨(-3332686465209943392520001300),(-3332686465209943392444665021)⟩,⟨0,0⟩⟩,⟨⟨(-3444155129960154742195319605),(-3444155129960154742117415557)⟩,⟨0,0⟩⟩,⟨⟨(-3557143728219029242853691824),(-3557143728219029242772799972)⟩,⟨0,0⟩⟩,⟨⟨(-3671850634329706810257738954),(-3671850634329706810174027533)⟩,⟨0,0⟩⟩] +lemma amp4_05_4_eq : ∀ k : Fin 16, amp4_0Expr 5 4 k = amp4_05_4 k := by decide +kernel +noncomputable def amp4_05_5 : Fin 16 → CBox := ![⟨⟨(-3788004828890165632244548911),(-3788004828890165632157877215)⟩,⟨0,0⟩⟩,⟨⟨(-3905800242272824151793590144),(-3905800242272824151703900678)⟩,⟨0,0⟩⟩,⟨⟨(-4024964533395238303038525162),(-4024964533395238302945673287)⟩,⟨0,0⟩⟩,⟨⟨(-4145686708418613028898361495),(-4145686708418613028802317316)⟩,⟨0,0⟩⟩,⟨⟨(-4267693745496789285283597948),(-4267693745496789285184289296)⟩,⟨0,0⟩⟩,⟨⟨(-4391169240786213742395516085),(-4391169240786213742300525619)⟩,⟨0,0⟩⟩,⟨⟨(-4515840153749391089816802117),(-4515840153749391089718170409)⟩,⟨0,0⟩⟩,⟨⟨(-4641884178945692238598728609),(-4641884178945692238496580528)⟩,⟨0,0⟩⟩,⟨⟨(-4769028940240375246158751690),(-4769028940240375246053197123)⟩,⟨0,0⟩⟩,⟨⟨(-4897445732925117418903482392),(-4897445732925117418794469729)⟩,⟨0,0⟩⟩,⟨⟨(-5026863549246854131609615911),(-5026863549246854131497327942)⟩,⟨0,0⟩⟩,⟨⟨(-5157446781166343516634854923),(-5157446781166343516519274895)⟩,⟨0,0⟩⟩,⟨⟨(-5288926514038202104364738897),(-5288926514038202104245562827)⟩,⟨0,0⟩⟩,⟨⟨(-5421459725686305869888716221),(-5421459725686305869766323961)⟩,⟨0,0⟩⟩,⟨⟨(-5554780339909606553422151517),(-5554780339909606553296256534)⟩,⟨0,0⟩⟩,⟨⟨(-5689037402459319915583889545),(-5689037402459319915454341963)⟩,⟨0,0⟩⟩] +lemma amp4_05_5_eq : ∀ k : Fin 16, amp4_0Expr 5 5 k = amp4_05_5 k := by decide +kernel +noncomputable def amp4_05_6 : Fin 16 → CBox := ![⟨⟨(-5823968441393309567794879179),(-5823968441393309567662689457)⟩,⟨0,0⟩⟩,⟨⟨(-5959714044899289793790667047),(-5959714044899289793654560129)⟩,⟨0,0⟩⟩,⟨⟨(-6096016131460073494702761775),(-6096016131460073494563375495)⟩,⟨0,0⟩⟩,⟨⟨(-6233006298189215735549270065),(-6233006298189215735405908859)⟩,⟨0,0⟩⟩,⟨⟨(-6370431660394543908636768498),(-6370431660394543908489805655)⟩,⟨0,0⟩⟩,⟨⟨(-6508414282079257382315896408),(-6508414282079257382165064201)⟩,⟨0,0⟩⟩,⟨⟨(-6646707301904864093262554284),(-6646707301904864093111459636)⟩,⟨0,0⟩⟩,⟨⟨(-6785422699654169368833796417),(-6785422699654169368678504840)⟩,⟨0,0⟩⟩,⟨⟨(-6924320483909415370326528512),(-6924320483909415370167419608)⟩,⟨0,0⟩⟩,⟨⟨(-7063501989456468219727412243),(-7063501989456468219564618811)⟩,⟨0,0⟩⟩,⟨⟨(-7202734961332202778027832648),(-7202734961332202777861146291)⟩,⟨0,0⟩⟩,⟨⟨(-7342109518243493791441410473),(-7342109518243493791271216656)⟩,⟨0,0⟩⟩,⟨⟨(-7481402028133446261824044022),(-7481402028133446261650156780)⟩,⟨0,0⟩⟩,⟨⟨(-7620690811554856993468210426),(-7620690811554856993290286200)⟩,⟨0,0⟩⟩,⟨⟨(-7759761765703628868882084470),(-7759761765703628868702129542)⟩,⟨0,0⟩⟩,⟨⟨(-7898680819171865498412019786),(-7898680819171865498228224425)⟩,⟨0,0⟩⟩] +lemma amp4_05_6_eq : ∀ k : Fin 16, amp4_0Expr 5 6 k = amp4_05_6 k := by decide +kernel +noncomputable def amp4_05_7 : Fin 16 → CBox := ![⟨⟨(-8037244324657834614173073787),(-8037244324657834613985721855)⟩,⟨0,0⟩⟩,⟨⟨(-8175505212462621448394886328),(-8175505212462621448203654310)⟩,⟨0,0⟩⟩,⟨⟨(-8313271236982902320521847138),(-8313271236982902320327917417)⟩,⟨0,0⟩⟩,⟨⟨(-8450581710525803771719724974),(-8450581710525803771522137350)⟩,⟨0,0⟩⟩,⟨⟨(-8587256755412933328522542717),(-8587256755412933328322081758)⟩,⟨0,0⟩⟩,⟨⟨(-8723321431972879243771984286),(-8723321431972879243567797535)⟩,⟨0,0⟩⟩,⟨⟨(-8858609216839208424585827262),(-8858609216839208424378554559)⟩,⟨0,0⟩⟩,⟨⟨(-8993130269122809606452355642),(-8993130269122809606241944244)⟩,⟨0,0⟩⟩,⟨⟨(-9126732426498762492224708064),(-9126732426498762492011213200)⟩,⟨0,0⟩⟩,⟨⟨(-9259410281325397355109353318),(-9259410281325397354892590610)⟩,⟨0,0⟩⟩,⟨⟨(-9391027059631885636736338293),(-9391027059631885636516693161)⟩,⟨0,0⟩⟩,⟨⟨(-9521561104079381981171483090),(-9521561104079381980948835355)⟩,⟨0,0⟩⟩,⟨⟨(-9650892077252799425737360020),(-9650892077252799425512109529)⟩,⟨0,0⟩⟩,⟨⟨(-9778981370569384262771131863),(-9778981370569384262543318164)⟩,⟨0,0⟩⟩,⟨⟨(-9905726152639809844841595839),(-9905726152639809844611577405)⟩,⟨0,0⟩⟩,⟨⟨(-10031070142211902033390017148),(-10031070142211902033158120063)⟩,⟨0,0⟩⟩] +lemma amp4_05_7_eq : ∀ k : Fin 16, amp4_0Expr 5 7 k = amp4_05_7 k := by decide +kernel +noncomputable def amp4_05_8 : Fin 16 → CBox := ![⟨⟨(-10154929105121458594545909382),(-10154929105121458594311183409)⟩,⟨0,0⟩⟩,⟨⟨(-10277228344774870551840715881),(-10277228344774870551601972953)⟩,⟨0,0⟩⟩,⟨⟨(-10397903337713655822354089057),(-10397903337713655822111769712)⟩,⟨0,0⟩⟩,⟨⟨(-10516860206617878171184815819),(-10516860206617878170939129804)⟩,⟨0,0⟩⟩,⟨⟨(-10634055275149534856348591337),(-10634055275149534856099760587)⟩,⟨0,0⟩⟩,⟨⟨(-10749374695591017525606162680),(-10749374695591017525354437800)⟩,⟨0,0⟩⟩,⟨⟨(-10862796798838857612878879168),(-10862796798838857612624280982)⟩,⟨0,0⟩⟩,⟨⟨(-10974186951129577912947446620),(-10974186951129577912690290769)⟩,⟨0,0⟩⟩,⟨⟨(-11083546675297232713664712919),(-11083546675297232713405015370)⟩,⟨0,0⟩⟩,⟨⟨(-11190719708089349790947878441),(-11190719708089349790685514600)⟩,⟨0,0⟩⟩,⟨⟨(-11295731974597181555616494500),(-11295731974597181555351579078)⟩,⟨0,0⟩⟩,⟨⟨(-11398404708883201001624781067),(-11398404708883201001358029071)⟩,⟨0,0⟩⟩,⟨⟨(-11498789475413175212430386109),(-11498789475413175212160916007)⟩,⟨0,0⟩⟩,⟨⟨(-11596684100503760017162865871),(-11596684100503760016891576827)⟩,⟨0,0⟩⟩,⟨⟨(-11692167053261121764034596716),(-11692167053261121763760350055)⟩,⟨0,0⟩⟩,⟨⟨(-11785011813049447607061004192),(-11785011813049447606785376106)⟩,⟨0,0⟩⟩] +lemma amp4_05_8_eq : ∀ k : Fin 16, amp4_0Expr 5 8 k = amp4_05_8 k := by decide +kernel +noncomputable def amp4_05_9 : Fin 16 → CBox := ![⟨⟨(-11875325048569344302467964378),(-11875325048569344302190796702)⟩,⟨0,0⟩⟩,⟨⟨(-11962854916411658334027920822),(-11962854916411658333749494545)⟩,⟨0,0⟩⟩,⟨⟨(-12047737611262769688533950049),(-12047737611262769688251674825)⟩,⟨0,0⟩⟩,⟨⟨(-12129694951829510850662619250),(-12129694951829510850379541840)⟩,⟨0,0⟩⟩,⟨⟨(-12208894018594742990120525336),(-12208894018594742989836425735)⟩,⟨0,0⟩⟩,⟨⟨(-12285029235075145120531667071),(-12285029235075145120246111703)⟩,⟨0,0⟩⟩,⟨⟨(-12358299963021469189338958095),(-12358299963021469189052889147)⟩,⟨0,0⟩⟩,⟨⟨(-12428372128096910062098259099),(-12428372128096910061811266584)⟩,⟨0,0⟩⟩,⟨⟨(-12495478806982420229119839057),(-12495478806982420228832533987)⟩,⟨0,0⟩⟩,⟨⟨(-12559256276019802220273678557),(-12559256276019802219986680391)⟩,⟨0,0⟩⟩,⟨⟨(-12619972801525971473577185392),(-12619972801525971473283229869)⟩,⟨0,0⟩⟩,⟨⟨(-12677233806482011586082811773),(-12677233806482011585788699835)⟩,⟨0,0⟩⟩,⟨⟨(-12731344265802869005029955834),(-12731344265802869004735542569)⟩,⟨0,0⟩⟩,⟨⟨(-12781877488373212780603164274),(-12781877488373212780309150670)⟩,⟨0,0⟩⟩,⟨⟨(-12829176724540682363598314845),(-12829176724540682363303581764)⟩,⟨0,0⟩⟩,⟨⟨(-12872781847134098502151407110),(-12872781847134098501857318123)⟩,⟨0,0⟩⟩] +lemma amp4_05_9_eq : ∀ k : Fin 16, amp4_0Expr 5 9 k = amp4_05_9 k := by decide +kernel +noncomputable def amp4_05_10 : Fin 16 → CBox := ![⟨⟨(-12913076000709954107969581428),(-12913076000709954107673712042)⟩,⟨0,0⟩⟩,⟨⟨(-12949564233877359603717537120),(-12949564233877359603422059547)⟩,⟨0,0⟩⟩,⟨⟨(-12982671260697089639132383026),(-12982671260697089638837321395)⟩,⟨0,0⟩⟩,⟨⟨(-13011865845697627167598253108),(-13011865845697627167302919496)⟩,⟨0,0⟩⟩,⟨⟨(-13037616009409894492605247238),(-13037616009409894492311008143)⟩,⟨0,0⟩⟩,⟨⟨(-13059352694651544113878765415),(-13059352694651544113584826138)⟩,⟨0,0⟩⟩,⟨⟨(-13077589032858803753432312078),(-13077589032858803753139009388)⟩,⟨0,0⟩⟩,⟨⟨(-13091716523008848063254759055),(-13091716523008848062962626732)⟩,⟨0,0⟩⟩,⟨⟨(-13102295285879987921073018582),(-13102295285879987920782417958)⟩,⟨0,0⟩⟩,⟨⟨(-13108675662500827682639679242),(-13108675662500827682350935059)⟩,⟨0,0⟩⟩,⟨⟨(-13111466722795377664189831159),(-13111466722795377663903789173)⟩,⟨0,0⟩⟩,⟨⟨(-13109975835423449524316631941),(-13109975835423449524008995398)⟩,⟨0,0⟩⟩,⟨⟨(-13104863068938931647860809977),(-13104863068938931647554720140)⟩,⟨0,0⟩⟩,⟨⟨(-13095390895588513062476089290),(-13095390895588513062171352192)⟩,⟨0,0⟩⟩,⟨⟨(-13082272531117872668679494720),(-13082272531117872668376470803)⟩,⟨0,0⟩⟩,⟨⟨(-13064723507257033417615332703),(-13064723507257033417313640504)⟩,⟨0,0⟩⟩] +lemma amp4_05_10_eq : ∀ k : Fin 16, amp4_0Expr 5 10 k = amp4_05_10 k := by decide +kernel +noncomputable def amp4_05_11 : Fin 16 → CBox := ![⟨⟨(-13043512445221825672293550996),(-13043512445221825671993527441)⟩,⟨0,0⟩⟩,⟨⟨(-13017805760334312460236474248),(-13017805760334312459937638647)⟩,⟨0,0⟩⟩,⟨⟨(-12988429859341489300391413932),(-12988429859341489300094855018)⟩,⟨0,0⟩⟩,⟨⟨(-12954499720255460280434227424),(-12954499720255460280138474253)⟩,⟨0,0⟩⟩,⟨⟨(-12916902050911340022354386450),(-12916902050911340022061108882)⟩,⟨0,0⟩⟩,⟨⟨(-12874697911143072120207268295),(-12874697911143072119916008142)⟩,⟨0,0⟩⟩,⟨⟨(-12828836976547584762616598180),(-12828836976547584762328281186)⟩,⟨0,0⟩⟩,⟨⟨(-12778323730974931498293098503),(-12778323730974931498003775809)⟩,⟨0,0⟩⟩,⟨⟨(-12724173653412829158330846765),(-12724173653412829158044517143)⟩,⟨0,0⟩⟩,⟨⟨(-12665331797658554989585612343),(-12665331797658554989301961746)⟩,⟨0,0⟩⟩,⟨⟨(-12602882471102409488731780035),(-12602882471102409488450181869)⟩,⟨0,0⟩⟩,⟨⟨(-12535708225070645789987568409),(-12535708225070645789709267745)⟩,⟨0,0⟩⟩,⟨⟨(-12464965433213760035943659374),(-12464965433213760035668504494)⟩,⟨0,0⟩⟩,⟨⟨(-12389470828282574153883022678),(-12389470828282574153611111885)⟩,⟨0,0⟩⟩,⟨⟨(-12310456327929295114474666028),(-12310456327929295114206742402)⟩,⟨0,0⟩⟩,⟨⟨(-12226669257357300083737122331),(-12226669257357300083473691703)⟩,⟨0,0⟩⟩] +lemma amp4_05_11_eq : ∀ k : Fin 16, amp4_0Expr 5 11 k = amp4_05_11 k := by decide +kernel +noncomputable def amp4_05_12 : Fin 16 → CBox := ![⟨⟨(-12139420827114858741945869610),(-12139420827114858741672024818)⟩,⟨0,0⟩⟩,⟨⟨(-12047385059268084753821052791),(-12047385059268084753549705776)⟩,⟨0,0⟩⟩,⟨⟨(-11951956513609678103196024092),(-11951956513609678102927504996)⟩,⟨0,0⟩⟩,⟨⟨(-11851731667654209173370624215),(-11851731667654209173104723961)⟩,⟨0,0⟩⟩,⟨⟨(-11748192836559880533797895581),(-11748192836559880533534963397)⟩,⟨0,0⟩⟩,⟨⟨(-11639854320292927855002678655),(-11639854320292927854742253311)⟩,⟨0,0⟩⟩,⟨⟨(-11528290994826055290661304981),(-11528290994826055290404482175)⟩,⟨0,0⟩⟩,⟨⟨(-11411929904329072428805776649),(-11411929904329072428550435466)⟩,⟨0,0⟩⟩,⟨⟨(-11292443748676301659613321193),(-11292443748676301659361899622)⟩,⟨0,0⟩⟩,⟨⟨(-11168166729462903620348632239),(-11168166729462903620100524422)⟩,⟨0,0⟩⟩,⟨⟨(-11040875160160211469309145351),(-11040875160160211469064944779)⟩,⟨0,0⟩⟩,⟨⟨(-10908804229451485828875253413),(-10908804229451485828635042582)⟩,⟨0,0⟩⟩,⟨⟨(-10773840262747186152540062408),(-10773840262747186152304890678)⟩,⟨0,0⟩⟩,⟨⟨(-10634112592427048441472364715),(-10634112592427048441232427579)⟩,⟨0,0⟩⟩,⟨⟨(-10491624661005867346117308060),(-10491624661005867345881851139)⟩,⟨0,0⟩⟩,⟨⟨(-10344392320674815745123718853),(-10344392320674815744892571381)⟩,⟨0,0⟩⟩] +lemma amp4_05_12_eq : ∀ k : Fin 16, amp4_0Expr 5 12 k = amp4_05_12 k := by decide +kernel +noncomputable def amp4_05_13 : Fin 16 → CBox := ![⟨⟨(-10194544061302622081353349131),(-10194544061302622081126531551)⟩,⟨0,0⟩⟩,⟨⟨(-10039973720638874086099417068),(-10039973720638874085875656535)⟩,⟨0,0⟩⟩,⟨⟨(-9882943734709660310213800777),(-9882943734709660309995172919)⟩,⟨0,0⟩⟩,⟨⟨(-9721216324032392147696855621),(-9721216324032392147482640307)⟩,⟨0,0⟩⟩,⟨⟨(-9557197913543233291641305592),(-9557197913543233291432583248)⟩,⟨0,0⟩⟩,⟨⟨(-9388508241009929519499797078),(-9388508241009929519290131775)⟩,⟨0,0⟩⟩,⟨⟨(-9217709123208483653056406661),(-9217709123208483652851416528)⟩,⟨0,0⟩⟩,⟨⟨(-9042265446402566966641338117),(-9042265446402566966441064048)⟩,⟨0,0⟩⟩,⟨⟨(-8864907451324136424351902989),(-8864907451324136424156396412)⟩,⟨0,0⟩⟩,⟨⟨(-8682931000002419888977006228),(-8682931000002419888785551411)⟩,⟨0,0⟩⟩,⟨⟨(-8499249756460134722489144291),(-8499249756460134722302529873)⟩,⟨0,0⟩⟩,⟨⟨(-8310974201781988969412869924),(-8310974201781988969226933084)⟩,⟨0,0⟩⟩,⟨⟨(-8121218819281640845647749096),(-8121218819281640845467536550)⟩,⟨0,0⟩⟩,⟨⟨(-7926889682697347368864011650),(-7926889682697347368688977782)⟩,⟨0,0⟩⟩,⟨⟨(-7731322439515148040784136865),(-7731322439515148040614086854)⟩,⟨0,0⟩⟩,⟨⟨(-7531196431271605633494399164),(-7531196431271605633329845737)⟩,⟨0,0⟩⟩] +lemma amp4_05_13_eq : ∀ k : Fin 16, amp4_0Expr 5 13 k = amp4_05_13 k := by decide +kernel +noncomputable def amp4_05_14 : Fin 16 → CBox := ![⟨⟨(-7330092483041432283754248319),(-7330092483041432283592065085)⟩,⟨0,0⟩⟩,⟨⟨(-7124436755348031963285621370),(-7124436755348031963128670860)⟩,⟨0,0⟩⟩,⟨⟨(-6918083884758200753941816049),(-6918083884758200753789755284)⟩,⟨0,0⟩⟩,⟨⟨(-6707175176996376671142317200),(-6707175176996376670996279692)⟩,⟨0,0⟩⟩,⟨⟨(-6495873614970292566390161081),(-6495873614970292566247107465)⟩,⟨0,0⟩⟩,⟨⟨(-6279997256106114464036489326),(-6279997256106114463898854120)⟩,⟨0,0⟩⟩,⟨⟨(-6064059620565666573039914267),(-6064059620565666572905962720)⟩,⟨0,0⟩⟩,⟨⟨(-5843508333865144115643782304),(-5843508333865144115515552720)⟩,⟨0,0⟩⟩,⟨⟨(-5623259758294419899346294264),(-5623259758294419899223639395)⟩,⟨0,0⟩⟩,⟨⟨(-5398332179446450275569138937),(-5398332179446450275450636815)⟩,⟨0,0⟩⟩,⟨⟨(-5174110748446996733624699071),(-5174110748446996733512070928)⟩,⟨0,0⟩⟩,⟨⟨(-4945109508397047027249596088),(-4945109508397047027141453471)⟩,⟨0,0⟩⟩,⟨⟨(-4717267198118655931872340776),(-4717267198118655931768730310)⟩,⟨0,0⟩⟩,⟨⟨(-4484496312031306880543877255),(-4484496312031306880446178299)⟩,⟨0,0⟩⟩,⟨⟨(-4253400785223850296846872977),(-4253400785223850296754034564)⟩,⟨0,0⟩⟩,⟨⟨(-4017161876444438552805769194),(-4017161876444438552717949888)⟩,⟨0,0⟩⟩] +lemma amp4_05_14_eq : ∀ k : Fin 16, amp4_0Expr 5 14 k = amp4_05_14 k := by decide +kernel +noncomputable def amp4_05_15 : Fin 16 → CBox := ![⟨⟨(-3783199784228645034398544459),(-3783199784228645034315995570)⟩,⟨0,0⟩⟩,⟨⟨(-3543786234992750818975348432),(-3543786234992750818898224426)⟩,⟨0,0⟩⟩,⟨⟨(-3307369321525166183509229142),(-3307369321525166183437580882)⟩,⟨0,0⟩⟩,⟨⟨(-3065056473631586439871774522),(-3065056473631586439805173728)⟩,⟨0,0⟩⟩,⟨⟨(-2826633270511767721861515268),(-2826633270511767721800116826)⟩,⟨0,0⟩⟩,⟨⟨(-2581660444753823030946877483),(-2581660444753823030890889768)⟩,⟨0,0⟩⟩,⟨⟨(-2341740172299399886681302029),(-2341740172299399886630810980)⟩,⟨0,0⟩⟩,⟨⟨(-2094273829805534679745997692),(-2094273829805534679700689844)⟩,⟨0,0⟩⟩,⟨⟨(-1853480404442691529644948805),(-1853480404442691529605036860)⟩,⟨0,0⟩⟩,⟨⟨(-1603527089250132360216709753),(-1603527089250132360182288253)⟩,⟨0,0⟩⟩,⟨⟨(-1362741222863623935777266407),(-1362741222863623935748216507)⟩,⟨0,0⟩⟩,⟨⟨(-1109895761162676723682702291),(-1109895761162676723659163666)⟩,⟨0,0⟩⟩,⟨⟨(-870731121346295531949241768),(-870731121346295531931032395)⟩,⟨0,0⟩⟩,⟨⟨(-613170481679804685088512483),(-613170481679804685075843434)⟩,⟨0,0⟩⟩,⟨⟨(-380420923474277062497385139),(-380420923474277062490047351)⟩,⟨0,0⟩⟩,⟨⟨(-108087267962443344184837671),(-108087267962443344183065187)⟩,⟨0,0⟩⟩] +lemma amp4_05_15_eq : ∀ k : Fin 16, amp4_0Expr 5 15 k = amp4_05_15 k := by decide +kernel +noncomputable def amp4_05 : Fin 16 → Fin 16 → CBox := ![amp4_05_0,amp4_05_1,amp4_05_2,amp4_05_3,amp4_05_4,amp4_05_5,amp4_05_6,amp4_05_7,amp4_05_8,amp4_05_9,amp4_05_10,amp4_05_11,amp4_05_12,amp4_05_13,amp4_05_14,amp4_05_15] +lemma amp4_05_eq (i k : Fin 16) : amp4_0Expr 5 i k = amp4_05 i k := by + fin_cases i + · exact amp4_05_0_eq k + · exact amp4_05_1_eq k + · exact amp4_05_2_eq k + · exact amp4_05_3_eq k + · exact amp4_05_4_eq k + · exact amp4_05_5_eq k + · exact amp4_05_6_eq k + · exact amp4_05_7_eq k + · exact amp4_05_8_eq k + · exact amp4_05_9_eq k + · exact amp4_05_10_eq k + · exact amp4_05_11_eq k + · exact amp4_05_12_eq k + · exact amp4_05_13_eq k + · exact amp4_05_14_eq k + · exact amp4_05_15_eq k +noncomputable def amp4_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp4_00,amp4_01,amp4_02,amp4_03,amp4_04,amp4_05] +lemma amp4_0_eq (j : Fin 6) (i k : Fin 16) : amp4_0Expr j i k = amp4_0 j i k := by + fin_cases j + · exact amp4_00_eq i k + · exact amp4_01_eq i k + · exact amp4_02_eq i k + · exact amp4_03_eq i k + · exact amp4_04_eq i k + · exact amp4_05_eq i k +lemma amp4_0_contains (j : Fin 6) (i k : Fin 16) : + (amp4_0 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude false 4 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp4_0_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 4 j) (bLookup_contains 4 j) false) +noncomputable def amp4_1Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 4 j) (bLookup 4 j) true) +noncomputable def amp4_10_0 : Fin 16 → CBox := ![⟨⟨536329754622069946021849373,536329754622069946070723655⟩,⟨(-516083547009096694085762376),(-516083547009096694031735501)⟩⟩,⟨⟨1887793341088553155324049553,1887793341088553155501535634⟩,⟨(-1816529989419765287823452187),(-1816529989419765287628035800)⟩⟩,⟨⟨3043243487890630820622597692,3043243487890630820912870172⟩,⟨(-2928362411572052200034952009),(-2928362411572052199715931526)⟩⟩,⟨⟨4322526319102367440341867300,4322526319102367440755250943⟩,⟨(-4159352889854990063899402323),(-4159352889854990063445227070)⟩⟩,⟨⟨5511459324147942579617688424,5511459324147942580146322007⟩,⟨(-5303404207374145887270051156),(-5303404207374145886689464407)⟩⟩,⟨⟨6769574453262926753498199366,6769574453262926754148254594⟩,⟨(-6514026054817607367258754293),(-6514026054817607366544914693)⟩⟩,⟨⟨7969307376213303339597505222,7969307376213303340363892783⟩,⟨(-7668469598186034814637931722),(-7668469598186034813796498185)⟩⟩,⟨⟨9216400337971305960268107767,9216400337971305961155062451⟩,⟨(-8868485360145152285150104978),(-8868485360145152284176384661)⟩⟩,⟨⟨10420021741238073901076762818,10420021741238073902080434109⟩,⟨(-10026670595442591582202156348),(-10026670595442591581100421593)⟩⟩,⟨⟨11659192799329569795726237284,11659192799329569796848443369⟩,⟨(-11219063502044455816716109242),(-11219063502044455815484146674)⟩⟩,⟨⟨12863416457788331100709395492,12863416457788331101949032698⟩,⟨(-12377828257670592144691477130),(-12377828257670592143330804725)⟩⟩,⟨⟨14095709680065119182021631920,14095709680065119183380548803⟩,⟨(-13563602963674017037437467255),(-13563602963674017035945940010)⟩⟩,⟨⟨15298508650941552844598464248,15298508650941552846073256423⟩,⟨(-14720996813034873396308975385),(-14720996813034873394690253988)⟩⟩,⟨⟨16524158055702303952953914269,16524158055702303954545819667⟩,⟨(-15900378502652747127175709726),(-15900378502652747125428304844)⟩⟩,⟨⟨17724056361181499482618170834,17724056361181499484327330203⟩,⟨(-17054981185433729371402414536),(-17054981185433729369526526713)⟩⟩,⟨⟨18942914667987845093544519057,18942914667987845095372349345⟩,⟨(-18227828137998154550908563895),(-18227828137998154548902582297)⟩⟩] +lemma amp4_10_0_eq : ∀ k : Fin 16, amp4_1Expr 0 0 k = amp4_10_0 k := by decide +kernel +noncomputable def amp4_10_1 : Fin 16 → CBox := ![⟨⟨20138716125252464464275853215,20138716125252464466219601854⟩,⟨(-19378488626746612490041170381),(-19378488626746612487908044496)⟩⟩,⟨⟨21350434376680880405662603702,21350434376680880407722650309⟩,⟨(-20544465057820243453159260800),(-20544465057820243450898417670)⟩⟩,⟨⟨22541100864556438564063211604,22541100864556438566237086280⟩,⟨(-21690184419970276427135260832),(-21690184419970276424749351785)⟩⟩,⟨⟨23745214534701743937690129946,23745214534701743939984450301⟩,⟨(-22848843339292443596936534346),(-22848843339292443594419016136)⟩⟩,⟨⟨24929804891098692665330181258,24929804891098692667736288410⟩,⟨(-23988715941201132048123152527),(-23988715941201132045482611891)⟩⟩,⟨⟨26125779465830798796636764494,26125779465830798799155770118⟩,⟨(-25139543012310348166426488462),(-25139543012310348163661707161)⟩⟩,⟨⟨27303416190504248019777604129,27303416190504248022415029370⟩,⟨(-26272724478973356683826673037),(-26272724478973356680932577600)⟩⟩,⟨⟨28490673221862566551326172531,28490673221862566554074430597⟩,⟨(-27415163090060025286967896897),(-27415163090060025283951662201)⟩⟩,⟨⟨29660523164173378278818377264,29660523164173378281683013671⟩,⟨(-28540851721901050823998069099),(-28540851721901050820854586083)⟩⟩,⟨⟨30838456118783685882627275530,30838456118783685885610305408⟩,⟨(-29674318235953704694601322087),(-29674318235953704691328546230)⟩⟩,⟨⟨31999718726471072328637047611,31999718726471072331726709869⟩,⟨(-30791743701200636931858166139),(-30791743701200636928467632057)⟩⟩,⟨⟨33167703141944086269506986015,33167703141944086272713088969⟩,⟨(-31915637229005024096510389995),(-31915637229005024092992571931)⟩⟩,⟨⟨34319603042534723125380473854,34319603042534723128689022528⟩,⟨(-33024053425147536341459962208),(-33024053425147536337828536692)⟩⟩,⟨⟨35477003336654443683795468700,35477003336654443687223113006⟩,⟨(-34137762377431157505282095912),(-34137762377431157501520969793)⟩⟩,⟨⟨36618785523137895747866758147,36618785523137895751406364845⟩,⟨(-35236442798634725060820164941),(-35236442798634725056936405955)⟩⟩,⟨⟨37764959745782167170686951569,37764959745782167174341164283⟩,⟨(-36339349458604525328442188896),(-36339349458604525324433195909)⟩⟩] +lemma amp4_10_1_eq : ∀ k : Fin 16, amp4_1Expr 0 1 k = amp4_10_1 k := by decide +kernel +noncomputable def amp4_10_2 : Fin 16 → CBox := ![⟨⟨38895886391455750089384350799,38895886391455750093136787743⟩,⟨(-37427584130793464685364242387),(-37427584130793464681245977720)⟩⟩,⟨⟨40030189663707965551294569530,40030189663707965555162474171⟩,⟨(-38519067963422614615423755055),(-38519067963422614611179582117)⟩⟩,⟨⟨41149537991221482705196950132,41149537991221482709176374758⟩,⟨(-39596161393767425469367002975),(-39596161393767425465000915575)⟩⟩,⟨⟨42271325079137887371739383777,42271325079137887375832150682⟩,⟨(-40675601522404063165987561914),(-40675601522404063161497774728)⟩⟩,⟨⟨43378385931647065401020050181,43378385931647065405227497321⟩,⟨(-41740871324413180700585200221),(-41740871324413180695970617937)⟩⟩,⟨⟨44487013233185145099328129634,44487013233185145103624863935⟩,⟨(-42807648442703145245962071286),(-42807648442703145241247107962)⟩⟩,⟨⟨45581090124830186182070393819,45581090124830186186476853581⟩,⟨(-43860424422545501060484874894),(-43860424422545501055650053609)⟩⟩,⟨⟨46675917248613400670986290989,46675917248613400675499075720⟩,⟨(-44913922313599405415947332747),(-44913922313599405410995915837)⟩⟩,⟨⟨47756325749257686641453477310,47756325749257686646074744611⟩,⟨(-45953545878068969526521760923),(-45953545878068969521451860358)⟩⟩,⟨⟨48836716802886243798903932920,48836716802886243803634443845⟩,⟨(-46993152654139820994046994415),(-46993152654139820988857878096)⟩⟩,⟨⟨49902784160230928599105371076,49902784160230928603943620109⟩,⟨(-48018976447035198882107695198),(-48018976447035198876800998695)⟩⟩,⟨⟨50968108827519318219622552829,50968108827519318224539288064⟩,⟨(-49044085586090699302967199727),(-49044085586090699297571080388)⟩⟩,⟨⟨52019173760407361910591908648,52019173760407361915619824287⟩,⟨(-50055473289321845908600005740),(-50055473289321845903083189603)⟩⟩,⟨⟨53068808222202830131108710952,53068808222202830136242974786⟩,⟨(-51065484521102381804322953334),(-51065484521102381798690108860)⟩⟩,⟨⟨54104220838967467988624394040,54104220838967467993867584736⟩,⟨(-52061810776121379280700373373),(-52061810776121379274949204792)⟩⟩,⟨⟨55137548575880762627617063439,55137548575880762632958653400⟩,⟨(-53056130854568041700132139515),(-53056130854568041694272804212)⟩⟩] +lemma amp4_10_2_eq : ∀ k : Fin 16, amp4_1Expr 0 2 k = amp4_10_2 k := by decide +kernel +noncomputable def amp4_10_3 : Fin 16 → CBox := ![⟨⟨56156670384966882372835650925,56156670384966882378280831449⟩,⟨(-54036781272589524418976664222),(-54036781272589524413004352217)⟩⟩,⟨⟨57173082889346151022029113604,57173082889346151027578782883⟩,⟨(-55014824660941311803806414771),(-55014824660941311797720297126)⟩⟩,⟨⟨58175286878534826675454412544,58175286878534826681108194070⟩,⟨(-55979195899176309600416034917),(-55979195899176309594216659308)⟩⟩,⟨⟨59174184295460243028648527955,59174184295460243034356295330⟩,⟨(-56940385386767494551813154108),(-56940385386767494545548797825)⟩⟩,⟨⟨60158855062333057629589327007,60158855062333057635403160096⟩,⟨(-57887885273962785794583733917),(-57887885273962785788204468705)⟩⟩,⟨⟨61139646774134726469501464812,61139646774134726475416487813⟩,⟨(-58831652538675531390597026635),(-58831652538675531384107594847)⟩⟩,⟨⟨62106180694855959231004455583,62106180694855959237018875918⟩,⟨(-59761700237524378294874085610),(-59761700237524378288276398177)⟩⟩,⟨⟨63068285859916397832930939915,63068285859916397839042053589⟩,⟨(-60687486364251667554209976697),(-60687486364251667547506693323)⟩⟩,⟨⟨64016091286586316726868316246,64016091286586316733077791503⟩,⟨(-61599512561297110514744246470),(-61599512561297110507933948457)⟩⟩,⟨⟨64958939340497661767003349108,64958939340497661773298409719⟩,⟨(-62506768524181493588352114157),(-62506768524181493581447160118)⟩⟩,⟨⟨65887436819631572708327786616,65887436819631572714718970786⟩,⟨(-63400215640047914277317744787),(-63400215640047914270308181562)⟩⟩,⟨⟨66810467944816676734862780903,66810467944816676741344442171⟩,⟨(-64288402754374619222895641308),(-64288402754374619215786973528)⟩⟩,⟨⟨67719090451193890517297292954,67719090451193890523870362251⟩,⟨(-65162725168789013939956273044),(-65162725168789013932747792910)⟩⟩,⟨⟨68621756019654473379199074939,68621756019654473385862373063⟩,⟨(-66031315517020554072932635739),(-66031315517020554065625555662)⟩⟩,⟨⟨69509949201036450698487683067,69509949201036450705240998196⟩,⟨(-66885979804292678586514294369),(-66885979804292678579109006997)⟩⟩,⟨⟨70391712193813509566457249004,70391712193813509573299200002⟩,⟨(-67734456639694820213390830630),(-67734456639694820205888748858)⟩⟩] +lemma amp4_10_3_eq : ∀ k : Fin 16, amp4_1Expr 0 3 k = amp4_10_3 k := by decide +kernel +noncomputable def amp4_10_4 : Fin 16 → CBox := ![⟨⟨71258934622973219999650620509,71258934622973220006504127827⟩,⟨(-68568941811232553511231298787),(-68568941811232553503706782158)⟩⟩,⟨⟨72119270029093191227224054128,72119270029093191234176571620⟩,⟨(-69396799941760439167383187251),(-69396799941760439159752173111)⟩⟩,⟨⟨72964993460313304076758597322,72964993460313304083805829607⟩,⟨(-70210597692885282674307489217),(-70210597692885282666574301443)⟩⟩,⟨⟨73803388657376576758324977773,73803388657376576765463118100⟩,⟨(-71017343847404899045943232718),(-71017343847404899038111629970)⟩⟩,⟨⟨74627098285122606637193606266,74627098285122606644420387989⟩,⟨(-71809958806260327016268568085),(-71809958806260327008340923051)⟩⟩,⟨⟨75443053403218161393727852291,75443053403218161401045011573⟩,⟨(-72595111984725529382131490469),(-72595111984725529374106233697)⟩⟩,⟨⟨76244248121117075177896421225,76244248121117075185295080103⟩,⟨(-73366061961479269630546644319),(-73366061961479269622432511216)⟩⟩,⟨⟨77037276391381794193048588107,77037276391381794200533006778⟩,⟨(-74129153770333134325022575091),(-74129153770333134316815572827)⟩⟩,⟨⟨77815469049967882118895539565,77815469049967882126465831710⟩,⟨(-74877970005193248327550795601),(-74877970005193248319251008351)⟩⟩,⟨⟨78585097138824961214564850513,78585097138824961222197426264⟩,⟨(-75618544978989134716241291485),(-75618544978989134707871530353)⟩⟩,⟨⟨79339814800775635967067276594,79339814800775635974784783111⟩,⟨(-76344772387804779794201086991),(-76344772387804779785739754275)⟩⟩,⟨⟨80085583130664096354978686557,80085583130664096362775913352⟩,⟨(-77062388297828446852045109003),(-77062388297828446843497335262)⟩⟩,⟨⟨80816367322455405382245076226,80816367322455405390123126064⟩,⟨(-77765585714245505801816286737),(-77765585714245505793181206333)⟩⟩,⟨⟨81537830379687563392894585034,81537830379687563400843760392⟩,⟨(-78459813864751100479707670883),(-78459813864751100470994736878)⟩⟩,⟨⟨82244237338764998500449590010,82244237338764998508477630246⟩,⟨(-79139554278052403997864454205),(-79139554278052403989066415837)⟩⟩,⟨⟨82940963969010156752295465899,82940963969010156760395929651⟩,⟨(-79809979790591775618878893808),(-79809979790591775610002075580)⟩⟩] +lemma amp4_10_4_eq : ∀ k : Fin 16, amp4_1Expr 0 4 k = amp4_10_4 k := by decide +kernel +noncomputable def amp4_10_5 : Fin 16 → CBox := ![⟨⟨83622564885704135703330881538,83622564885704135711504931312⟩,⟨(-80465850578480383007250981890),(-80465850578480382998294462530)⟩⟩,⟨⟨84294138577486610817721542663,84294138577486610825967830710⟩,⟨(-81112072664699187626503176214),(-81112072664699187617468383419)⟩⟩,⟨⟨84950519831010831757360946465,84950519831010831765680446642⟩,⟨(-81743675820387909217452085510),(-81743675820387909208338280405)⟩⟩,⟨⟨85596538987522582845853345122,85596538987522582854244141045⟩,⟨(-82365308043577433332595734377),(-82365308043577433323404896197)⟩⟩,⟨⟨86227302375482680923449170256,86227302375482680931910758291⟩,⟨(-82972260396633638292721196914),(-82972260396633638283454009328)⟩⟩,⟨⟨86847380574940545542029045354,86847380574940545550408854622⟩,⟨(-83568930922259665949862599041),(-83568930922259665940666012855)⟩⟩,⟨⟨87452143535854231258767868884,87452143535854231267224330042⟩,⟨(-84150864352725385238523653924),(-84150864352725385229245418989)⟩⟩,⟨⟨88045909780575486895536962379,88045909780575486904064909189⟩,⟨(-84722216188101268821930861761),(-84722216188101268812576092766)⟩⟩,⟨⟨88624305608966800478483401245,88624305608966800487078830381⟩,⟨(-85278777833467737964540293808),(-85278777833467737955113043497)⟩⟩,⟨⟨89191404563291638398132554986,89191404563291638406793774287⟩,⟨(-85824469056695405396367945044),(-85824469056695405386869989091)⟩⟩,⟨⟨89743082616973589523982750356,89743082616973589532704600380⟩,⟨(-86355321511360877555840221310),(-86355321511360877546276725589)⟩⟩,⟨⟨90283174834126918857419832978,90283174834126918866200300823⟩,⟨(-86875025489628705063380188927),(-86875025489628705053753241518)⟩⟩,⟨⟨90807800733330533648162342381,90807800733330533657005122292⟩,⟨(-87379846996510465850818172754),(-87379846996510465841124420657)⟩⟩,⟨⟨91320562871286602579522977952,91320562871286602588419107099⟩,⟨(-87873252593809106551080008750),(-87873252593809106541328231240)⟩⟩,⟨⟨91817818689331794949597737494,91817818689331794958550472980⟩,⟨(-88351737227816605523924875308),(-88351737227816605514112140551)⟩⟩,⟨⟨92302943715722059940727568723,92302943715722059949737033122⟩,⟨(-88818549002111678516684826600),(-88818549002111678506811174922)⟩⟩] +lemma amp4_10_5_eq : ∀ k : Fin 16, amp4_1Expr 0 5 k = amp4_10_5 k := by decide +kernel +noncomputable def amp4_10_6 : Fin 16 → CBox := ![⟨⟨92772528160957989220753092538,92772528160957989229801724658⟩,⟨(-89270406845218719929586664821),(-89270406845218719919669197247)⟩⟩,⟨⟨93229725547044399270814399851,93229725547044399279920222908⟩,⟨(-89710345235101690102169520179),(-89710345235101690092191055475)⟩⟩,⟨⟨93671354135815031215073765588,93671354135815031224225302098⟩,⟨(-90135302542782621587370335911),(-90135302542782621577342121422)⟩⟩,⟨⟨94100350039536556441557731329,94100350039536556450763407427⟩,⟨(-90548104043607403865449910282),(-90548104043607403855364002775)⟩⟩,⟨⟨94513755259951778676167888282,94513755259951778685420711611⟩,⟨(-90945903402425945748530973726),(-90945903402425945738394305014)⟩⟩,⟨⟨94914292698040905292857984321,94914292698040905302159518801⟩,⟨(-91331320731928079608635162948),(-91331320731928079598446396036)⟩⟩,⟨⟨95299224164355378704568460913,95299224164355378713865554195⟩,⟨(-91701721208088443919345846710),(-91701721208088443909156331084)⟩⟩,⟨⟨95671063173512853646872927910,95671063173512853656220491577⟩,⟨(-92059523461475563715539563290),(-92059523461475563705296631073)⟩⟩,⟨⟨96027287770934307120625018714,96027287770934307130016458256⟩,⟨(-92402300740164300767358039850),(-92402300740164300757068240337)⟩⟩,⟨⟨96370205558044188543374082362,96370205558044188552805161672⟩,⟨(-92732273534660635466609062505),(-92732273534660635456276645507)⟩⟩,⟨⟨96697507577810490782423700189,96697507577810490791896021750⟩,⟨(-93047220050024606817607223478),(-93047220050024606807230850746)⟩⟩,⟨⟨97011298659173172567093674381,97011298659173172576599916578⟩,⟨(-93349165658848020298708256389),(-93349165658848020288295149431)⟩⟩,⟨⟨97309479923753571661003696257,97309479923753571670545393384⟩,⟨(-93636090714469347697501542502),(-93636090714469347687050428604)⟩⟩,⟨⟨97593956253311594756184441286,97593956253311594765763715077⟩,⟨(-93909828190216683241852376726),(-93909828190216683231361393061)⟩⟩,⟨⟨97862836231602274208415752169,97862836231602274218006112282⟩,⟨(-94168558069959724097502783083),(-94168558069959724086997623481)⟩⟩,⟨⟨98117827318132162261392675869,98117827318132162271015143779⟩,⟨(-94413923357374700803622133276),(-94413923357374700793082751025)⟩⟩] +lemma amp4_10_6_eq : ∀ k : Fin 16, amp4_1Expr 0 6 k = amp4_10_6 k := by decide +kernel +noncomputable def amp4_10_7 : Fin 16 → CBox := ![⟨⟨98357243230529944038733791569,98357243230529944048384066490⟩,⟨(-94644301426493266086275463214),(-94644301426493266075706199959)⟩⟩,⟨⟨98582596243772795314942238431,98582596243772795324621968058⟩,⟨(-94861147464590688559749113434),(-94861147464590688549148567158)⟩⟩,⟨⟨98792403157023610416134020315,98792403157023610425828152605⟩,⟨(-95063034260996026158875327345),(-95063034260996026148258184719)⟩⟩,⟨⟨98987983022727566811607450265,98987983022727566821325511577⟩,⟨(-95251231074516442960311869520),(-95251231074516442949669149421)⟩⟩,⟨⟨99168053934458365219837999838,99168053934458365229570240578⟩,⟨(-95424504390118105961792170008),(-95424504390118105951133456336)⟩⟩,⟨⟨99333743418307214330123863177,99333743418307214339878021221⟩,⟨(-95583939170288144602163893491),(-95583939170288144591481928107)⟩⟩,⟨⟨99483969331161427435294739725,99483969331161427445062786323⟩,⟨(-95728494122330873264890948860),(-95728494122330873254193659189)⟩⟩,⟨⟨99619669111565349569619650942,99619669111565349579400314740⟩,⟨(-95859071296906169177420985327),(-95859071296906169166709784254)⟩⟩,⟨⟨99739959096872957552481269931,99739959096872957562273568629⟩,⟨(-95974820389236441839230160940),(-95974820389236441828506194738)⟩⟩,⟨⟨99845587826599698669197858104,99845587826599698679001678324⟩,⟨(-96076461681806262187338815257),(-96076461681806262176602384312)⟩⟩,⟨⟨99935869077523485115426679798,99935869077523485125237298840⟩,⟨(-96163334856012302611439159545),(-96163334856012302600695008516)⟩⟩,⟨⟨100011363434150925718416404860,100011363434150925728233278078⟩,⟨(-96235979334547553344794269656),(-96235979334547553334043115557)⟩⟩,⟨⟨100071581308260701144260157327,100071581308260701154078825992⟩,⟨(-96293924010926396408222380303),(-96293924010926396397468712863)⟩⟩,⟨⟨100116896033434818514995359543,100116896033434818524813472826⟩,⟨(-96337528125555614033615732643),(-96337528125555614022862008392)⟩⟩,⟨⟨100147014084671332576756459816,100147014084671332586570020026⟩,⟨(-96366509233870394591396997325),(-96366509233870394580647261315)⟩⟩,⟨⟨100162122012156846644341121539,100162122012156846654145215330⟩,⟨(-96381046843871492746092755157),(-96381046843871492735351931097)⟩⟩] +lemma amp4_10_7_eq : ∀ k : Fin 16, amp4_1Expr 0 7 k = amp4_10_7 k := by decide +kernel +noncomputable def amp4_10_8 : Fin 16 → CBox := ![⟨⟨100162122012156846644341121539,100162122012156846654145215330⟩,⟨(-96381046843871492746092755157),(-96381046843871492735351931097)⟩⟩,⟨⟨100147014084671332576756459816,100147014084671332586570020026⟩,⟨(-96366509233870394591396997325),(-96366509233870394580647261315)⟩⟩,⟨⟨100116896033434818514995359543,100116896033434818524813472826⟩,⟨(-96337528125555614033615732643),(-96337528125555614022862008392)⟩⟩,⟨⟨100071581308260701144260157327,100071581308260701154078825992⟩,⟨(-96293924010926396408222380303),(-96293924010926396397468712863)⟩⟩,⟨⟨100011363434150925718416404860,100011363434150925728233278078⟩,⟨(-96235979334547553344794269656),(-96235979334547553334043115557)⟩⟩,⟨⟨99935869077523485115426679798,99935869077523485125237298840⟩,⟨(-96163334856012302611439159545),(-96163334856012302600695008516)⟩⟩,⟨⟨99845587826599698669197858104,99845587826599698679001678324⟩,⟨(-96076461681806262187338815257),(-96076461681806262176602384312)⟩⟩,⟨⟨99739959096872957552481269931,99739959096872957562273568629⟩,⟨(-95974820389236441839230160940),(-95974820389236441828506194738)⟩⟩,⟨⟨99619669111565349569619650942,99619669111565349579400314740⟩,⟨(-95859071296906169177420985327),(-95859071296906169166709784254)⟩⟩,⟨⟨99483969331161427435294739725,99483969331161427445062786323⟩,⟨(-95728494122330873264890948860),(-95728494122330873254193659189)⟩⟩,⟨⟨99333743418307214330123863177,99333743418307214339878021221⟩,⟨(-95583939170288144602163893491),(-95583939170288144591481928107)⟩⟩,⟨⟨99168053934458365219837999838,99168053934458365229570240578⟩,⟨(-95424504390118105961792170008),(-95424504390118105951133456336)⟩⟩,⟨⟨98987983022727566811607450265,98987983022727566821325511577⟩,⟨(-95251231074516442960311869520),(-95251231074516442949669149421)⟩⟩,⟨⟨98792403157023610416134020315,98792403157023610425828152605⟩,⟨(-95063034260996026158875327345),(-95063034260996026148258184719)⟩⟩,⟨⟨98582596243772795314942238431,98582596243772795324621968058⟩,⟨(-94861147464590688559749113434),(-94861147464590688549148567158)⟩⟩,⟨⟨98357243230529944038733791569,98357243230529944048384066490⟩,⟨(-94644301426493266086275463214),(-94644301426493266075706199959)⟩⟩] +lemma amp4_10_8_eq : ∀ k : Fin 16, amp4_1Expr 0 8 k = amp4_10_8 k := by decide +kernel +noncomputable def amp4_10_9 : Fin 16 → CBox := ![⟨⟨98117827318132162261392675869,98117827318132162271015143779⟩,⟨(-94413923357374700803622133276),(-94413923357374700793082751025)⟩⟩,⟨⟨97862836231602274208415752169,97862836231602274218006112282⟩,⟨(-94168558069959724097502783083),(-94168558069959724086997623481)⟩⟩,⟨⟨97593956253311594756184441286,97593956253311594765763715077⟩,⟨(-93909828190216683241852376726),(-93909828190216683231361393061)⟩⟩,⟨⟨97309479923753571661003696257,97309479923753571670545393384⟩,⟨(-93636090714469347697501542502),(-93636090714469347687050428604)⟩⟩,⟨⟨97011298659173172567093674381,97011298659173172576599916578⟩,⟨(-93349165658848020298708256389),(-93349165658848020288295149431)⟩⟩,⟨⟨96697507577810490782423700189,96697507577810490791896021750⟩,⟨(-93047220050024606817607223478),(-93047220050024606807230850746)⟩⟩,⟨⟨96370205558044188543374082362,96370205558044188552805161672⟩,⟨(-92732273534660635466609062505),(-92732273534660635456276645507)⟩⟩,⟨⟨96027287770934307120625018714,96027287770934307130016458256⟩,⟨(-92402300740164300767358039850),(-92402300740164300757068240337)⟩⟩,⟨⟨95671063173512853646872927910,95671063173512853656220491577⟩,⟨(-92059523461475563715539563290),(-92059523461475563705296631073)⟩⟩,⟨⟨95299224164355378704568460913,95299224164355378713865554195⟩,⟨(-91701721208088443919345846710),(-91701721208088443909156331084)⟩⟩,⟨⟨94914292698040905292857984321,94914292698040905302159518801⟩,⟨(-91331320731928079608635162948),(-91331320731928079598446396036)⟩⟩,⟨⟨94513755259951778676167888282,94513755259951778685420711611⟩,⟨(-90945903402425945748530973726),(-90945903402425945738394305014)⟩⟩,⟨⟨94100350039536556441557731329,94100350039536556450763407427⟩,⟨(-90548104043607403865449910282),(-90548104043607403855364002775)⟩⟩,⟨⟨93671354135815031215073765588,93671354135815031224225302098⟩,⟨(-90135302542782621587370335911),(-90135302542782621577342121422)⟩⟩,⟨⟨93229725547044399270814399851,93229725547044399279920222908⟩,⟨(-89710345235101690102169520179),(-89710345235101690092191055475)⟩⟩,⟨⟨92772528160957989220753092538,92772528160957989229801724658⟩,⟨(-89270406845218719929586664821),(-89270406845218719919669197247)⟩⟩] +lemma amp4_10_9_eq : ∀ k : Fin 16, amp4_1Expr 0 9 k = amp4_10_9 k := by decide +kernel +noncomputable def amp4_10_10 : Fin 16 → CBox := ![⟨⟨92302943715722059940727568723,92302943715722059949737033122⟩,⟨(-88818549002111678516684826600),(-88818549002111678506811174922)⟩⟩,⟨⟨91817818689331794949597737494,91817818689331794958550472980⟩,⟨(-88351737227816605523924875308),(-88351737227816605514112140551)⟩⟩,⟨⟨91320562871286602579522977952,91320562871286602588419107099⟩,⟨(-87873252593809106551080008750),(-87873252593809106541328231240)⟩⟩,⟨⟨90807800733330533648162342381,90807800733330533657005122292⟩,⟨(-87379846996510465850818172754),(-87379846996510465841124420657)⟩⟩,⟨⟨90283174834126918857419832978,90283174834126918866200300823⟩,⟨(-86875025489628705063380188927),(-86875025489628705053753241518)⟩⟩,⟨⟨89743082616973589523982750356,89743082616973589532704600380⟩,⟨(-86355321511360877555840221310),(-86355321511360877546276725589)⟩⟩,⟨⟨89191404563291638398132554986,89191404563291638406793774287⟩,⟨(-85824469056695405396367945044),(-85824469056695405386869989091)⟩⟩,⟨⟨88624305608966800478483401245,88624305608966800487078830381⟩,⟨(-85278777833467737964540293808),(-85278777833467737955113043497)⟩⟩,⟨⟨88045909780575486895536962379,88045909780575486904064909189⟩,⟨(-84722216188101268821930861761),(-84722216188101268812576092766)⟩⟩,⟨⟨87452143535854231258767868884,87452143535854231267224330042⟩,⟨(-84150864352725385238523653924),(-84150864352725385229245418989)⟩⟩,⟨⟨86847380574940545542029045354,86847380574940545550408854622⟩,⟨(-83568930922259665949862599041),(-83568930922259665940666012855)⟩⟩,⟨⟨86227302375482680923449170256,86227302375482680931910758291⟩,⟨(-82972260396633638292721196914),(-82972260396633638283454009328)⟩⟩,⟨⟨85596538987522582845853345122,85596538987522582854244141045⟩,⟨(-82365308043577433332595734377),(-82365308043577433323404896197)⟩⟩,⟨⟨84950519831010831757360946465,84950519831010831765680446642⟩,⟨(-81743675820387909217452085510),(-81743675820387909208338280405)⟩⟩,⟨⟨84294138577486610817721542663,84294138577486610825967830710⟩,⟨(-81112072664699187626503176214),(-81112072664699187617468383419)⟩⟩,⟨⟨83622564885704135703330881538,83622564885704135711504931312⟩,⟨(-80465850578480383007250981890),(-80465850578480382998294462530)⟩⟩] +lemma amp4_10_10_eq : ∀ k : Fin 16, amp4_1Expr 0 10 k = amp4_10_10 k := by decide +kernel +noncomputable def amp4_10_11 : Fin 16 → CBox := ![⟨⟨82940963969010156752295465899,82940963969010156760395929651⟩,⟨(-79809979790591775618878893808),(-79809979790591775610002075580)⟩⟩,⟨⟨82244237338764998500449590010,82244237338764998508477630246⟩,⟨(-79139554278052403997864454205),(-79139554278052403989066415837)⟩⟩,⟨⟨81537830379687563392894585034,81537830379687563400843760392⟩,⟨(-78459813864751100479707670883),(-78459813864751100470994736878)⟩⟩,⟨⟨80816367322455405382245076226,80816367322455405390123126064⟩,⟨(-77765585714245505801816286737),(-77765585714245505793181206333)⟩⟩,⟨⟨80085583130664096354978686557,80085583130664096362775913352⟩,⟨(-77062388297828446852045109003),(-77062388297828446843497335262)⟩⟩,⟨⟨79339814800775635967067276594,79339814800775635974784783111⟩,⟨(-76344772387804779794201086991),(-76344772387804779785739754275)⟩⟩,⟨⟨78585097138824961214564850513,78585097138824961222197426264⟩,⟨(-75618544978989134716241291485),(-75618544978989134707871530353)⟩⟩,⟨⟨77815469049967882118895539565,77815469049967882126465831710⟩,⟨(-74877970005193248327550795601),(-74877970005193248319251008351)⟩⟩,⟨⟨77037276391381794193048588107,77037276391381794200533006778⟩,⟨(-74129153770333134325022575091),(-74129153770333134316815572827)⟩⟩,⟨⟨76244248121117075177896421225,76244248121117075185295080103⟩,⟨(-73366061961479269630546644319),(-73366061961479269622432511216)⟩⟩,⟨⟨75443053403218161393727852291,75443053403218161401045011573⟩,⟨(-72595111984725529382131490469),(-72595111984725529374106233697)⟩⟩,⟨⟨74627098285122606637193606266,74627098285122606644420387989⟩,⟨(-71809958806260327016268568085),(-71809958806260327008340923051)⟩⟩,⟨⟨73803388657376576758324977773,73803388657376576765463118100⟩,⟨(-71017343847404899045943232718),(-71017343847404899038111629970)⟩⟩,⟨⟨72964993460313304076758597322,72964993460313304083805829607⟩,⟨(-70210597692885282674307489217),(-70210597692885282666574301443)⟩⟩,⟨⟨72119270029093191227224054128,72119270029093191234176571620⟩,⟨(-69396799941760439167383187251),(-69396799941760439159752173111)⟩⟩,⟨⟨71258934622973219999650620509,71258934622973220006504127827⟩,⟨(-68568941811232553511231298787),(-68568941811232553503706782158)⟩⟩] +lemma amp4_10_11_eq : ∀ k : Fin 16, amp4_1Expr 0 11 k = amp4_10_11 k := by decide +kernel +noncomputable def amp4_10_12 : Fin 16 → CBox := ![⟨⟨70391712193813509566457249004,70391712193813509573299200002⟩,⟨(-67734456639694820213390830630),(-67734456639694820205888748858)⟩⟩,⟨⟨69509949201036450698487683067,69509949201036450705240998196⟩,⟨(-66885979804292678586514294369),(-66885979804292678579109006997)⟩⟩,⟨⟨68621756019654473379199074939,68621756019654473385862373063⟩,⟨(-66031315517020554072932635739),(-66031315517020554065625555662)⟩⟩,⟨⟨67719090451193890517297292954,67719090451193890523870362251⟩,⟨(-65162725168789013939956273044),(-65162725168789013932747792910)⟩⟩,⟨⟨66810467944816676734862780903,66810467944816676741344442171⟩,⟨(-64288402754374619222895641308),(-64288402754374619215786973528)⟩⟩,⟨⟨65887436819631572708327786616,65887436819631572714718970786⟩,⟨(-63400215640047914277317744787),(-63400215640047914270308181562)⟩⟩,⟨⟨64958939340497661767003349108,64958939340497661773298409719⟩,⟨(-62506768524181493588352114157),(-62506768524181493581447160118)⟩⟩,⟨⟨64016091286586316726868316246,64016091286586316733077791503⟩,⟨(-61599512561297110514744246470),(-61599512561297110507933948457)⟩⟩,⟨⟨63068285859916397832930939915,63068285859916397839042053589⟩,⟨(-60687486364251667554209976697),(-60687486364251667547506693323)⟩⟩,⟨⟨62106180694855959231004455583,62106180694855959237018875918⟩,⟨(-59761700237524378294874085610),(-59761700237524378288276398177)⟩⟩,⟨⟨61139646774134726469501464812,61139646774134726475416487813⟩,⟨(-58831652538675531390597026635),(-58831652538675531384107594847)⟩⟩,⟨⟨60158855062333057629589327007,60158855062333057635403160096⟩,⟨(-57887885273962785794583733917),(-57887885273962785788204468705)⟩⟩,⟨⟨59174184295460243028648527955,59174184295460243034356295330⟩,⟨(-56940385386767494551813154108),(-56940385386767494545548797825)⟩⟩,⟨⟨58175286878534826675454412544,58175286878534826681108194070⟩,⟨(-55979195899176309600416034917),(-55979195899176309594216659308)⟩⟩,⟨⟨57173082889346151022029113604,57173082889346151027578782883⟩,⟨(-55014824660941311803806414771),(-55014824660941311797720297126)⟩⟩,⟨⟨56156670384966882372835650925,56156670384966882378280831449⟩,⟨(-54036781272589524418976664222),(-54036781272589524413004352217)⟩⟩] +lemma amp4_10_12_eq : ∀ k : Fin 16, amp4_1Expr 0 12 k = amp4_10_12 k := by decide +kernel +noncomputable def amp4_10_13 : Fin 16 → CBox := ![⟨⟨55137548575880762627617063439,55137548575880762632958653400⟩,⟨(-53056130854568041700132139515),(-53056130854568041694272804212)⟩⟩,⟨⟨54104220838967467988624394040,54104220838967467993867584736⟩,⟨(-52061810776121379280700373373),(-52061810776121379274949204792)⟩⟩,⟨⟨53068808222202830131108710952,53068808222202830136242974786⟩,⟨(-51065484521102381804322953334),(-51065484521102381798690108860)⟩⟩,⟨⟨52019173760407361910591908648,52019173760407361915619824287⟩,⟨(-50055473289321845908600005740),(-50055473289321845903083189603)⟩⟩,⟨⟨50968108827519318219622552829,50968108827519318224539288064⟩,⟨(-49044085586090699302967199727),(-49044085586090699297571080388)⟩⟩,⟨⟨49902784160230928599105371076,49902784160230928603943620109⟩,⟨(-48018976447035198882107695198),(-48018976447035198876800998695)⟩⟩,⟨⟨48836716802886243798903932920,48836716802886243803634443845⟩,⟨(-46993152654139820994046994415),(-46993152654139820988857878096)⟩⟩,⟨⟨47756325749257686641453477310,47756325749257686646074744611⟩,⟨(-45953545878068969526521760923),(-45953545878068969521451860358)⟩⟩,⟨⟨46675917248613400670986290989,46675917248613400675499075720⟩,⟨(-44913922313599405415947332747),(-44913922313599405410995915837)⟩⟩,⟨⟨45581090124830186182070393819,45581090124830186186476853581⟩,⟨(-43860424422545501060484874894),(-43860424422545501055650053609)⟩⟩,⟨⟨44487013233185145099328129634,44487013233185145103624863935⟩,⟨(-42807648442703145245962071286),(-42807648442703145241247107962)⟩⟩,⟨⟨43378385931647065401020050181,43378385931647065405227497321⟩,⟨(-41740871324413180700585200221),(-41740871324413180695970617937)⟩⟩,⟨⟨42271325079137887371739383777,42271325079137887375832150682⟩,⟨(-40675601522404063165987561914),(-40675601522404063161497774728)⟩⟩,⟨⟨41149537991221482705196950132,41149537991221482709176374758⟩,⟨(-39596161393767425469367002975),(-39596161393767425465000915575)⟩⟩,⟨⟨40030189663707965551294569530,40030189663707965555162474171⟩,⟨(-38519067963422614615423755055),(-38519067963422614611179582117)⟩⟩,⟨⟨38895886391455750089384350799,38895886391455750093136787743⟩,⟨(-37427584130793464685364242387),(-37427584130793464681245977720)⟩⟩] +lemma amp4_10_13_eq : ∀ k : Fin 16, amp4_1Expr 0 13 k = amp4_10_13 k := by decide +kernel +noncomputable def amp4_10_14 : Fin 16 → CBox := ![⟨⟨37764959745782167170686951569,37764959745782167174341164283⟩,⟨(-36339349458604525328442188896),(-36339349458604525324433195909)⟩⟩,⟨⟨36618785523137895747866758147,36618785523137895751406364845⟩,⟨(-35236442798634725060820164941),(-35236442798634725056936405955)⟩⟩,⟨⟨35477003336654443683795468700,35477003336654443687223113006⟩,⟨(-34137762377431157505282095912),(-34137762377431157501520969793)⟩⟩,⟨⟨34319603042534723125380473854,34319603042534723128689022528⟩,⟨(-33024053425147536341459962208),(-33024053425147536337828536692)⟩⟩,⟨⟨33167703141944086269506986015,33167703141944086272713088969⟩,⟨(-31915637229005024096510389995),(-31915637229005024092992571931)⟩⟩,⟨⟨31999718726471072328637047611,31999718726471072331726709869⟩,⟨(-30791743701200636931858166139),(-30791743701200636928467632057)⟩⟩,⟨⟨30838456118783685882627275530,30838456118783685885610305408⟩,⟨(-29674318235953704694601322087),(-29674318235953704691328546230)⟩⟩,⟨⟨29660523164173378278818377264,29660523164173378281683013671⟩,⟨(-28540851721901050823998069099),(-28540851721901050820854586083)⟩⟩,⟨⟨28490673221862566551326172531,28490673221862566554074430597⟩,⟨(-27415163090060025286967896897),(-27415163090060025283951662201)⟩⟩,⟨⟨27303416190504248019777604129,27303416190504248022415029370⟩,⟨(-26272724478973356683826673037),(-26272724478973356680932577600)⟩⟩,⟨⟨26125779465830798796636764494,26125779465830798799155770118⟩,⟨(-25139543012310348166426488462),(-25139543012310348163661707161)⟩⟩,⟨⟨24929804891098692665330181258,24929804891098692667736288410⟩,⟨(-23988715941201132048123152527),(-23988715941201132045482611891)⟩⟩,⟨⟨23745214534701743937690129946,23745214534701743939984450301⟩,⟨(-22848843339292443596936534346),(-22848843339292443594419016136)⟩⟩,⟨⟨22541100864556438564063211604,22541100864556438566237086280⟩,⟨(-21690184419970276427135260832),(-21690184419970276424749351785)⟩⟩,⟨⟨21350434376680880405662603702,21350434376680880407722650309⟩,⟨(-20544465057820243453159260800),(-20544465057820243450898417670)⟩⟩,⟨⟨20138716125252464464275853215,20138716125252464466219601854⟩,⟨(-19378488626746612490041170381),(-19378488626746612487908044496)⟩⟩] +lemma amp4_10_14_eq : ∀ k : Fin 16, amp4_1Expr 0 14 k = amp4_10_14 k := by decide +kernel +noncomputable def amp4_10_15 : Fin 16 → CBox := ![⟨⟨18942914667987845093544519057,18942914667987845095372349345⟩,⟨(-18227828137998154550908563895),(-18227828137998154548902582297)⟩⟩,⟨⟨17724056361181499482618170834,17724056361181499484327330203⟩,⟨(-17054981185433729371402414536),(-17054981185433729369526526713)⟩⟩,⟨⟨16524158055702303952953914269,16524158055702303954545819667⟩,⟨(-15900378502652747127175709726),(-15900378502652747125428304844)⟩⟩,⟨⟨15298508650941552844598464248,15298508650941552846073256423⟩,⟨(-14720996813034873396308975385),(-14720996813034873394690253988)⟩⟩,⟨⟨14095709680065119182021631920,14095709680065119183380548803⟩,⟨(-13563602963674017037437467255),(-13563602963674017035945940010)⟩⟩,⟨⟨12863416457788331100709395492,12863416457788331101949032698⟩,⟨(-12377828257670592144691477130),(-12377828257670592143330804725)⟩⟩,⟨⟨11659192799329569795726237284,11659192799329569796848443369⟩,⟨(-11219063502044455816716109242),(-11219063502044455815484146674)⟩⟩,⟨⟨10420021741238073901076762818,10420021741238073902080434109⟩,⟨(-10026670595442591582202156348),(-10026670595442591581100421593)⟩⟩,⟨⟨9216400337971305960268107767,9216400337971305961155062451⟩,⟨(-8868485360145152285150104978),(-8868485360145152284176384661)⟩⟩,⟨⟨7969307376213303339597505222,7969307376213303340363892783⟩,⟨(-7668469598186034814637931722),(-7668469598186034813796498185)⟩⟩,⟨⟨6769574453262926753498199366,6769574453262926754148254594⟩,⟨(-6514026054817607367258754293),(-6514026054817607366544914693)⟩⟩,⟨⟨5511459324147942579617688424,5511459324147942580146322007⟩,⟨(-5303404207374145887270051156),(-5303404207374145886689464407)⟩⟩,⟨⟨4322526319102367440341867300,4322526319102367440755250943⟩,⟨(-4159352889854990063899402323),(-4159352889854990063445227070)⟩⟩,⟨⟨3043243487890630820622597692,3043243487890630820912870172⟩,⟨(-2928362411572052200034952009),(-2928362411572052199715931526)⟩⟩,⟨⟨1887793341088553155324049553,1887793341088553155501535634⟩,⟨(-1816529989419765287823452187),(-1816529989419765287628035800)⟩⟩,⟨⟨536329754622069946021849373,536329754622069946070723655⟩,⟨(-516083547009096694085762376),(-516083547009096694031735501)⟩⟩] +lemma amp4_10_15_eq : ∀ k : Fin 16, amp4_1Expr 0 15 k = amp4_10_15 k := by decide +kernel +noncomputable def amp4_10 : Fin 16 → Fin 16 → CBox := ![amp4_10_0,amp4_10_1,amp4_10_2,amp4_10_3,amp4_10_4,amp4_10_5,amp4_10_6,amp4_10_7,amp4_10_8,amp4_10_9,amp4_10_10,amp4_10_11,amp4_10_12,amp4_10_13,amp4_10_14,amp4_10_15] +lemma amp4_10_eq (i k : Fin 16) : amp4_1Expr 0 i k = amp4_10 i k := by + fin_cases i + · exact amp4_10_0_eq k + · exact amp4_10_1_eq k + · exact amp4_10_2_eq k + · exact amp4_10_3_eq k + · exact amp4_10_4_eq k + · exact amp4_10_5_eq k + · exact amp4_10_6_eq k + · exact amp4_10_7_eq k + · exact amp4_10_8_eq k + · exact amp4_10_9_eq k + · exact amp4_10_10_eq k + · exact amp4_10_11_eq k + · exact amp4_10_12_eq k + · exact amp4_10_13_eq k + · exact amp4_10_14_eq k + · exact amp4_10_15_eq k +noncomputable def amp4_11_0 : Fin 16 → CBox := ![⟨⟨178776584874023315329293846,178776584874023315368230497⟩,⟨(-309650128205458016457116449),(-309650128205458016413466445)⟩⟩,⟨⟨629264447029517718401496104,629264447029517718540365625⟩,⟨(-1089917993651859172713990150),(-1089917993651859172557198899)⟩⟩,⟨⟨1014414495963543606809952444,1014414495963543607035203511⟩,⟨(-1757017446943231320053081645),(-1757017446943231319797926060)⟩⟩,⟨⟨1440842106367455813356035006,1440842106367455813676337741⟩,⟨(-2495611733912994038385250041),(-2495611733912994038022205940)⟩⟩,⟨⟨1837153108049314193089542142,1837153108049314193498461335⟩,⟨(-3182042524424487532420184232),(-3182042524424487531956390033)⟩⟩,⟨⟨2256524817754308917689818693,2256524817754308918192332627⟩,⟨(-3908415632890564420426680974),(-3908415632890564419856582785)⟩⟩,⟨⟨2656435792071101113030926072,2656435792071101113622873263⟩,⟨(-4601081758911620888866846277),(-4601081758911620888195062311)⟩⟩,⟨⟨3072133445990435319894799183,3072133445990435320579590889⟩,⟨(-5321091216087091371187308791),(-5321091216087091370410031346)⟩⟩,⟨⟨3473340580412691300138940870,3473340580412691300913458106⟩,⟨(-6016002357265554949431239488),(-6016002357265554948551942517)⟩⟩,⟨⟨3886397599776523264995938529,3886397599776523265862288355⟩,⟨(-6731438101226673490152686197),(-6731438101226673489169297060)⟩⟩,⟨⟨4287805485929443699964901888,4287805485929443700921240842⟩,⟨(-7426696954602355286950613160),(-7426696954602355285864774643)⟩⟩,⟨⟨4698569893355039727042965401,4698569893355039728091094840⟩,⟨(-8138161778204410222611209637),(-8138161778204410221421046798)⟩⟩,⟨⟨5099502883647184281209850210,5099502883647184282347390014⟩,⟨(-8832598087820924037946805712),(-8832598087820924036655132746)⟩⟩,⟨⟨5508052685234101317302458514,5508052685234101318530786131⟩,⟨(-9540227101591648276479778617),(-9540227101591648275085223303)⟩⟩,⟨⟨5908018787060499827165212638,5908018787060499828483287708⟩,⟨(-10232988711260237623028462095),(-10232988711260237621531684137)⟩⟩,⟨⟨6314304889329281697448263712,6314304889329281698857359089⟩,⟨(-10936696882798892730745012355),(-10936696882798892729144648120)⟩⟩] +lemma amp4_11_0_eq : ∀ k : Fin 16, amp4_1Expr 1 0 k = amp4_11_0 k := by decide +kernel +noncomputable def amp4_11_1 : Fin 16 → CBox := ![⟨⟨6712905375084154821000130190,6712905375084154822498354833⟩,⟨(-11627093176047967494237193610),(-11627093176047967492535495736)⟩⟩,⟨⟨7116811458893626801436799420,7116811458893626803024951916⟩,⟨(-12326679034692146072120833169),(-12326679034692146070317124491)⟩⟩,⟨⟨7513700288185479520878532219,7513700288185479522554900409⟩,⟨(-13014110651982165856518996371),(-13014110651982165854615308632)⟩⟩,⟨⟨7915071511567247978728751277,7915071511567247980496108805⟩,⟨(-13709306003575466158412465548),(-13709306003575466156404591138)⟩⟩,⟨⟨8309934963699564221250426821,8309934963699564223105063068⟩,⟨(-14393229564720679229136935528),(-14393229564720679227030435421)⟩⟩,⟨⟨8708593155276932931660706004,8708593155276932933603472200⟩,⟨(-15083725807386208900131556280),(-15083725807386208897925461080)⟩⟩,⟨⟨9101138730168082672682791122,9101138730168082674714753377⟩,⟨(-15763634687384014010584092725),(-15763634687384014008275742453)⟩⟩,⟨⟨9496891073954188849840582732,9496891073954188851959618310⟩,⟨(-16449097854036015172481354248),(-16449097854036015170074852325)⟩⟩,⟨⟨9886841054724459425646620606,9886841054724459427853843040⟩,⟨(-17124511033140630494711801109),(-17124511033140630492204446702)⟩⟩,⟨⟨10279485372927895293558052347,10279485372927895295854474632⟩,⟨(-17804590941572222817086181728),(-17804590941572222814476578821)⟩⟩,⟨⟨10666572908823690775536793959,10666572908823690777917791868⟩,⟨(-18475046220720382159452541090),(-18475046220720382156747959626)⟩⟩,⟨⟨11055901047314695422468782440,11055901047314695424937909222⟩,⟨(-19149382337403014458256199259),(-19149382337403014455450782990)⟩⟩,⟨⟨11439867680844907707735626963,11439867680844907710287538497⟩,⟨(-19814432055088521805238096728),(-19814432055088521802340388475)⟩⟩,⟨⟨11825667778884814560516191036,11825667778884814563156669533⟩,⟨(-20482657426458694503543589128),(-20482657426458694500543817792)⟩⟩,⟨⟨12206261841045965248515849693,12206261841045965251241857971⟩,⟨(-21141865679180835036878477931),(-21141865679180835033781211287)⟩⟩,⟨⟨12588319915260722389431716954,12588319915260722392244321663⟩,⟨(-21803609675162715197463786031),(-21803609675162715194267371404)⟩⟩] +lemma amp4_11_1_eq : ∀ k : Fin 16, amp4_1Expr 1 1 k = amp4_11_1 k := by decide +kernel +noncomputable def amp4_11_2 : Fin 16 → CBox := ![⟨⟨12965295463818583362306974714,12965295463818583365200071467⟩,⟨(-22456550478476078811628950970),(-22456550478476078808343285125)⟩⟩,⟨⟨13343396554569321849586434356,13343396554569321852565913545⟩,⟨(-23111440778053568769676627044),(-23111440778053568766291657300)⟩⟩,⟨⟨13716512663740494234196930340,13716512663740494237260844624⟩,⟨(-23757696836260455282054386473),(-23757696836260455278572822360)⟩⟩,⟨⟨14090441693045962456354059185,14090441693045962459503118968⟩,⟨(-24405360913442437900038558246),(-24405360913442437896459277487)⟩⟩,⟨⟨14459461977215688466090909841,14459461977215688469324939327⟩,⟨(-25044522794647908420808822257),(-25044522794647908417131476120)⟩⟩,⟨⟨14829004411061715032170198443,14829004411061715035480799414⟩,⟨(-25684589065621887148046642452),(-25684589065621887144285846559)⟩⟩,⟨⟨15193696708276728726394522467,15193696708276728729787893334⟩,⟨(-26316254653527300636771868645),(-26316254653527300632916241615)⟩⟩,⟨⟨15558639082871133556010041647,15558639082871133559485080589⟩,⟨(-26948353388159643250060895301),(-26948353388159643246112378821)⟩⟩,⟨⟨15918775249752562212809628273,15918775249752562216366445700⟩,⟨(-27572127526841381716416952014),(-27572127526841381712374715277)⟩⟩,⟨⟨16278905600962081265270305031,16278905600962081268909153891⟩,⟨(-28195891592483892596943491733),(-28195891592483892592807095845)⟩⟩,⟨⟨16634261386743642865314945029,16634261386743642869034718699⟩,⟨(-28811385868221119329791160692),(-28811385868221119325561887016)⟩⟩,⟨⟨16989369609173106072131515239,16989369609173106075922431726⟩,⟨(-29426451351654419582318104062),(-29426451351654419578012862564)⟩⟩,⟨⟨17339724586802453969099111178,17339724586802453972971466467⟩,⟨(-30033283973593107545708877862),(-30033283973593107541309202846)⟩⟩,⟨⟨17689602740734276709249219479,17689602740734276713201342434⟩,⟨(-30639290712661429083153721518),(-30639290712661429078662444023)⟩⟩,⟨⟨18034740279655822661732588282,18034740279655822665764737977⟩,⟨(-31237086465672827568991098580),(-31237086465672827564407139033)⟩⟩,⟨⟨18379182858626920874708329870,18379182858626920878816909076⟩,⟨(-31833678512740825020661061306),(-31833678512740825015990557808)⟩⟩] +lemma amp4_11_2_eq : ∀ k : Fin 16, amp4_1Expr 1 2 k = amp4_11_2 k := by decide +kernel +noncomputable def amp4_11_3 : Fin 16 → CBox := ![⟨⟨18718890128322294123093010726,18718890128322294127279150066⟩,⟨(-32422068763553714651978529278),(-32422068763553714647218893396)⟩⟩,⟨⟨19057694296448717006136040509,19057694296448717010399924986⟩,⟨(-33008894796564787082887104169),(-33008894796564787078037895288)⟩⟩,⟨⟨19391762292844942223923315673,19391762292844942228264219865⟩,⟨(-33587517539505785760863450899),(-33587517539505785755925295234)⟩⟩,⟨⟨19724728098486747674966932800,19724728098486747679368008295⟩,⟨(-34164231232060496731712262166),(-34164231232060496726714195351)⟩⟩,⟨⟨20052951687444352541926411484,20052951687444352546404417550⟩,⟨(-34732731164377671477384999693),(-34732731164377671472297362763)⟩⟩,⟨⟨20379882258044908821876418310,20379882258044908826429565898⟩,⟨(-35298991523205318835003324037),(-35298991523205318829829043654)⟩⟩,⟨⟨20702060231618653075690343792,20702060231618653080317433375⟩,⟨(-35857020142514626977579757695),(-35857020142514626972320279060)⟩⟩,⟨⟨21022761953305465942978860625,21022761953305465947678803877⟩,⟨(-36412491818551000533191443891),(-36412491818551000527848455589)⟩⟩,⟨⟨21338697095528772240937976676,21338697095528772245710725907⟩,⟨(-36959707536778266309522006416),(-36959707536778266304094956750)⟩⟩,⟨⟨21652979780165887254296416228,21652979780165887259137503381⟩,⟨(-37504061114508896153696675383),(-37504061114508896148193083355)⟩⟩,⟨⟨21962478939877190901384960287,21962478939877190906297292180⟩,⟨(-38040129384028748567085850696),(-38040129384028748561500044998)⟩⟩,⟨⟨22270155981605558910210472008,22270155981605558915191935684⟩,⟨(-38573041652624771534442327868),(-38573041652624771528777725772)⟩⟩,⟨⟨22573030150397963504336127167,22573030150397963509386424568⟩,⟨(-39097635101273408364688294136),(-39097635101273408358944772767)⟩⟩,⟨⟨22873918673218157791617664731,22873918673218157796736151270⟩,⟨(-39618789310212332444483636127),(-39618789310212332438662047702)⟩⟩,⟨⟨23169983067012150231361783205,23169983067012150236547777216⟩,⟨(-40131587882575607152642002975),(-40131587882575607146742886220)⟩⟩,⟨⟨23463904064604503187333023366,23463904064604503192585792969⟩,⟨(-40640673983816892128777228554),(-40640673983816892122801565891)⟩⟩] +lemma amp4_11_3_eq : ∀ k : Fin 16, amp4_1Expr 1 3 k = amp4_11_3 k := by decide +kernel +noncomputable def amp4_11_4 : Fin 16 → CBox := ![⟨⟨23752978207657739998379172353,23752978207657740003672410426⟩,⟨(-41141365086739532107490659847),(-41141365086739532101483371568)⟩⟩,⟨⟨24039756676364397074218820772,24039756676364397079581387811⟩,⟨(-41638079965056263501190870657),(-41638079965056263495101663422)⟩⟩,⟨⟨24321664486771101357379147526,24321664486771101362808994783⟩,⟨(-42126358615731169605354375392),(-42126358615731169599186149588)⟩⟩,⟨⟨24601129552458858917883574742,24601129552458858923379123883⟩,⟨(-42610406308442939428344667724),(-42610406308442939422099832044)⟩⟩,⟨⟨24875699428374202210822394669,24875699428374202216382270082⟩,⟨(-43085975283756196210548560223),(-43085975283756196204228845880)⟩⟩,⟨⟨25147684467739387129649917482,25147684467739387135274370473⟩,⟨(-43557067190835317630074923111),(-43557067190835317623679550860)⟩⟩,⟨⟨25414749373705691724355859541,25414749373705691730041307568⟩,⟨(-44019637176887561779132469137),(-44019637176887561772666989390)⟩⟩,⟨⟨25679092130460598062723173321,25679092130460598068470691640⟩,⟨(-44477492262199880595826395148),(-44477492262199880589288583261)⟩⟩,⟨⟨25938489683322627371322395159,25938489683322627377131395266⟩,⟨(-44926782003115948997351538466),(-44926782003115948990741755687)⟩⟩,⟨⟨26195032379608320403195917635,26195032379608320409058174624⟩,⟨(-45371126987393480830573956640),(-45371126987393480823906069024)⟩⟩,⟨⟨26446604933591878654014126601,26446604933591878659936559967⟩,⟨(-45806863432682867877357797261),(-45806863432682867870619158500)⟩⟩,⟨⟨26695194376888032116635519127,26695194376888032122616014177⟩,⟨(-46237432978697068112072079359),(-46237432978697068105265955237)⟩⟩,⟨⟨26938789107485135125708887888,26938789107485135131747179542⟩,⟨(-46659351428547303481942496785),(-46659351428547303475068681777)⟩⟩,⟨⟨27179276793229187795910159810,27179276793229187802002621998⟩,⟨(-47075888318850660288684939709),(-47075888318850660281749300889)⟩⟩,⟨⟨27414745779588332831746914976,27414745779588332837895491776⟩,⟨(-47483732566831442399586463275),(-47483732566831442392584965550)⟩⟩,⟨⟨27646987989670052249014164809,27646987989670052255216300374⟩,⟨(-47885987874355065372202478469),(-47885987874355065365139119303)⟩⟩] +lemma amp4_11_4_eq : ∀ k : Fin 16, amp4_1Expr 1 4 k = amp4_11_4 k := by decide +kernel +noncomputable def amp4_11_5 : Fin 16 → CBox := ![⟨⟨27874188295234711899344913883,27874188295234711905600357067⟩,⟨(-48279510347088229805232923153),(-48279510347088229798107466603)⟩⟩,⟨⟨28098046192495536937460956473,28098046192495536943768834651⟩,⟨(-48667243598819512576791325781),(-48667243598819512569604838494)⟩⟩,⟨⟨28316839943670277250660234021,28316839943670277257020230348⟩,⟨(-49046205492232745531367597091),(-49046205492232745524119953962)⟩⟩,⟨⟨28532179662507527613477395278,28532179662507527619888433445⟩,⟨(-49419184826146460000460602809),(-49419184826146459993153208420)⟩⟩,⟨⟨28742434125160893639329354096,28742434125160893645790622087⟩,⟨(-49783356237980182976542535760),(-49783356237980182969176119857)⟩⟩,⟨⟨28949126858313515178842888479,28949126858313515185303078179⟩,⟨(-50141358553355799570833919720),(-50141358553355799563496876599)⟩⟩,⟨⟨29150714511951410417743062332,29150714511951410424254337310⟩,⟨(-50490518611635231144036933738),(-50490518611635231136638234099)⟩⟩,⟨⟨29348636593525162296653558327,29348636593525162303213732196⟩,⟨(-50833329712860761294087523498),(-50833329712860761286630466490)⟩⟩,⟨⟨29541435202988933490956827269,29541435202988933497563916607⟩,⟨(-51167266700080642779659285604),(-51167266700080642772146624819)⟩⟩,⟨⟨29730468187763879464161239660,29730468187763879470814203431⟩,⟨(-51494681434017243238761860026),(-51494681434017243231194897492)⟩⟩,⟨⟨29914360872324529839432991483,29914360872324529846129458762⟩,⟨(-51813192906816526534451046754),(-51813192906816526526833204998)⟩⟩,⟨⟨30094391611375639617233950316,30094391611375639623972760951⟩,⟨(-52125015293777223038980726046),(-52125015293777223031313500591)⟩⟩,⟨⟨30269266911110177880803711255,30269266911110177887585443636⟩,⟨(-52427908197906279511449051873),(-52427908197906279503730754875)⟩⟩,⟨⟨30440187623762200857913098044,30440187623762200864734263640⟩,⟨(-52723951556285463931611563822),(-52723951556285463923847711342)⟩⟩,⟨⟨30605939563110598314594186847,30605939563110598321455216644⟩,⟨(-53011042336689963315323730496),(-53011042336689963307512888226)⟩⟩,⟨⟨30767647905240686644960555643,30767647905240686651860978305⟩,⟨(-53291129401267007110984820013),(-53291129401267007103127266239)⟩⟩] +lemma amp4_11_5_eq : ∀ k : Fin 16, amp4_1Expr 1 5 k = amp4_11_5 k := by decide +kernel +noncomputable def amp4_11_6 : Fin 16 → CBox := ![⟨⟨30924176053652663071625816717,30924176053652663078559122349⟩,⟨(-53562244107131231958730877712),(-53562244107131231950837198560)⟩⟩,⟨⟨31076575182348133088303267129,31076575182348133095274940457⟩,⟨(-53826207141061014062285414993),(-53826207141061014054345561180)⟩⟩,⟨⟨31223784711938343736380399027,31223784711938343743385956869⟩,⟨(-54081181525669572953410564227),(-54081181525669572945431610259)⟩⟩,⟨⟨31366783346512185478532664285,31366783346512185485574381967⟩,⟨(-54328862426164442320262835351),(-54328862426164442312240279893)⟩⟩,⟨⟨31504585086650592890060655753,31504585086650592897135544212⟩,⟨(-54567542041455567450115835416),(-54567542041455567442054164115)⟩⟩,⟨⟨31638097566013635095615565238,31638097566013635102723602469⟩,⟨(-54798792439156847766182575174),(-54798792439156847758081255360)⟩⟩,⟨⟨31766408054785126232844264370,31766408054785126239967073999⟩,⟨(-55021032724853066352613046992),(-55021032724853066344503215236)⟩⟩,⟨⟨31890354391170951213604570036,31890354391170951220759903126⟩,⟨(-55235714076885338230333200357),(-55235714076885338222183530166)⟩⟩,⟨⟨32009095923644769038181079944,32009095923644769045366079045⟩,⟨(-55441380444098580461428044957),(-55441380444098580453242792964)⟩⟩,⟨⟨32123401852681396179090195058,32123401852681396186302886287⟩,⟨(-55639364120796381280982276808),(-55639364120796381272764271623)⟩⟩,⟨⟨32232502525936830258766491233,32232502525936830266006749413⟩,⟨(-55828332030014764091584626882),(-55828332030014764083333392641)⟩⟩,⟨⟨32337099553057724186983191431,32337099553057724194248005556⟩,⟨(-56009499395308812180248557560),(-56009499395308812171968710165)⟩⟩,⟨⟨32436493307917857218280237066,32436493307917857225569459482⟩,⟨(-56181654428681608619527675453),(-56181654428681608611218778237)⟩⟩,⟨⟨32531318751103864916667813081,32531318751103864923981572374⟩,⟨(-56345896914130009946141177608),(-56345896914130009937802399935)⟩⟩,⟨⟨32620945410534091400739240306,32620945410534091408068047845⟩,⟨(-56501134841975834459534258478),(-56501134841975834451181343327)⟩⟩,⟨⟨32705942439377387418392831682,32705942439377387425743108200⟩,⟨(-56648354014424820483208559104),(-56648354014424820474829769360)⟩⟩] +lemma amp4_11_6_eq : ∀ k : Fin 16, amp4_1Expr 1 6 k = amp4_11_6 k := by decide +kernel +noncomputable def amp4_11_7 : Fin 16 → CBox := ![⟨⟨32785747743509981344168149204,32785747743509981351537803482⟩,⟨(-56786580855895959652803083236),(-56786580855895959644401350122)⟩⟩,⟨⟨32860865414590931769566207333,32860865414590931776955194830⟩,⟨(-56916688478754413136889651155),(-56916688478754413128464428020)⟩⟩,⟨⟨32930801052341203469959038667,32930801052341203477361685640⟩,⟨(-57037820556597615696367593256),(-57037820556597615687928017729)⟩⟩,⟨⟨32995994340909188935112719708,32995994340909188942531600906⟩,⟨(-57150738644709865777231582199),(-57150738644709865768772563604)⟩⟩,⟨⟨33056017978152788404519101370,33056017978152788411950312102⟩,⟨(-57254702634070863578121662490),(-57254702634070863569649276014)⟩⟩,⟨⟨33111247806102404774610891231,33111247806102404782056403568⟩,⟨(-57350363502172886762346444833),(-57350363502172886753856636825)⟩⟩,⟨⟨33161323110387142476331345285,33161323110387142483787830064⟩,⟨(-57437096473398523959984263146),(-57437096473398523951482113958)⟩⟩,⟨⟨33206556370521783187770117561,33206556370521783195236537667⟩,⟨(-57515442778143701507503716848),(-57515442778143701498990378472)⟩⟩,⟨⟨33246653032290985848721451080,33246653032290985856196828440⟩,⟨(-57584892233541865104590491442),(-57584892233541865096066974413)⟩⟩,⟨⟨33281862608866566220958083846,33281862608866566228441761630⟩,⟨(-57645877009083757313456798561),(-57645877009083757304923590204)⟩⟩,⟨⟨33311956359174495036365785124,33311956359174495043855541089⟩,⟨(-57698000913607381567917957727),(-57698000913607381559378226303)⟩⟩,⟨⟨33337121144716975237360766362,33337121144716975244855794618⟩,⟨(-57741587600728532007931820364),(-57741587600728531999386305805)⟩⟩,⟨⟨33357193769420233712640745907,33357193769420233720138915199⟩,⟨(-57776354406555837845989322133),(-57776354406555837837441038256)⟩⟩,⟨⟨33372298677811606169551523327,33372298677811606177051420796⟩,⟨(-57802516875333368421225811671),(-57802516875333368412676544552)⟩⟩,⟨⟨33382338028223777523471254254,33382338028223777530970905693⟩,⟨(-57819905540322236755894888267),(-57819905540322236747347383245)⟩⟩,⟨⟨33387374004052282212665822547,33387374004052282220162956409⟩,⟨(-57828628106322895648712502376),(-57828628106322895640170028076)⟩⟩] +lemma amp4_11_7_eq : ∀ k : Fin 16, amp4_1Expr 1 7 k = amp4_11_7 k := by decide +kernel +noncomputable def amp4_11_8 : Fin 16 → CBox := ![⟨⟨33387374004052282212665822547,33387374004052282220162956409⟩,⟨(-57828628106322895648712502376),(-57828628106322895640170028076)⟩⟩,⟨⟨33382338028223777523471254254,33382338028223777530970905693⟩,⟨(-57819905540322236755894888267),(-57819905540322236747347383245)⟩⟩,⟨⟨33372298677811606169551523327,33372298677811606177051420796⟩,⟨(-57802516875333368421225811671),(-57802516875333368412676544552)⟩⟩,⟨⟨33357193769420233712640745907,33357193769420233720138915199⟩,⟨(-57776354406555837845989322133),(-57776354406555837837441038256)⟩⟩,⟨⟨33337121144716975237360766362,33337121144716975244855794618⟩,⟨(-57741587600728532007931820364),(-57741587600728531999386305805)⟩⟩,⟨⟨33311956359174495036365785124,33311956359174495043855541089⟩,⟨(-57698000913607381567917957727),(-57698000913607381559378226303)⟩⟩,⟨⟨33281862608866566220958083846,33281862608866566228441761630⟩,⟨(-57645877009083757313456798561),(-57645877009083757304923590204)⟩⟩,⟨⟨33246653032290985848721451080,33246653032290985856196828440⟩,⟨(-57584892233541865104590491442),(-57584892233541865096066974413)⟩⟩,⟨⟨33206556370521783187770117561,33206556370521783195236537667⟩,⟨(-57515442778143701507503716848),(-57515442778143701498990378472)⟩⟩,⟨⟨33161323110387142476331345285,33161323110387142483787830064⟩,⟨(-57437096473398523959984263146),(-57437096473398523951482113958)⟩⟩,⟨⟨33111247806102404774610891231,33111247806102404782056403568⟩,⟨(-57350363502172886762346444833),(-57350363502172886753856636825)⟩⟩,⟨⟨33056017978152788404519101370,33056017978152788411950312102⟩,⟨(-57254702634070863578121662490),(-57254702634070863569649276014)⟩⟩,⟨⟨32995994340909188935112719708,32995994340909188942531600906⟩,⟨(-57150738644709865777231582199),(-57150738644709865768772563604)⟩⟩,⟨⟨32930801052341203469959038667,32930801052341203477361685640⟩,⟨(-57037820556597615696367593256),(-57037820556597615687928017729)⟩⟩,⟨⟨32860865414590931769566207333,32860865414590931776955194830⟩,⟨(-56916688478754413136889651155),(-56916688478754413128464428020)⟩⟩,⟨⟨32785747743509981344168149204,32785747743509981351537803482⟩,⟨(-56786580855895959652803083236),(-56786580855895959644401350122)⟩⟩] +lemma amp4_11_8_eq : ∀ k : Fin 16, amp4_1Expr 1 8 k = amp4_11_8 k := by decide +kernel +noncomputable def amp4_11_9 : Fin 16 → CBox := ![⟨⟨32705942439377387418392831682,32705942439377387425743108200⟩,⟨(-56648354014424820483208559104),(-56648354014424820474829769360)⟩⟩,⟨⟨32620945410534091400739240306,32620945410534091408068047845⟩,⟨(-56501134841975834459534258478),(-56501134841975834451181343327)⟩⟩,⟨⟨32531318751103864916667813081,32531318751103864923981572374⟩,⟨(-56345896914130009946141177608),(-56345896914130009937802399935)⟩⟩,⟨⟨32436493307917857218280237066,32436493307917857225569459482⟩,⟨(-56181654428681608619527675453),(-56181654428681608611218778237)⟩⟩,⟨⟨32337099553057724186983191431,32337099553057724194248005556⟩,⟨(-56009499395308812180248557560),(-56009499395308812171968710165)⟩⟩,⟨⟨32232502525936830258766491233,32232502525936830266006749413⟩,⟨(-55828332030014764091584626882),(-55828332030014764083333392641)⟩⟩,⟨⟨32123401852681396179090195058,32123401852681396186302886287⟩,⟨(-55639364120796381280982276808),(-55639364120796381272764271623)⟩⟩,⟨⟨32009095923644769038181079944,32009095923644769045366079045⟩,⟨(-55441380444098580461428044957),(-55441380444098580453242792964)⟩⟩,⟨⟨31890354391170951213604570036,31890354391170951220759903126⟩,⟨(-55235714076885338230333200357),(-55235714076885338222183530166)⟩⟩,⟨⟨31766408054785126232844264370,31766408054785126239967073999⟩,⟨(-55021032724853066352613046992),(-55021032724853066344503215236)⟩⟩,⟨⟨31638097566013635095615565238,31638097566013635102723602469⟩,⟨(-54798792439156847766182575174),(-54798792439156847758081255360)⟩⟩,⟨⟨31504585086650592890060655753,31504585086650592897135544212⟩,⟨(-54567542041455567450115835416),(-54567542041455567442054164115)⟩⟩,⟨⟨31366783346512185478532664285,31366783346512185485574381967⟩,⟨(-54328862426164442320262835351),(-54328862426164442312240279893)⟩⟩,⟨⟨31223784711938343736380399027,31223784711938343743385956869⟩,⟨(-54081181525669572953410564227),(-54081181525669572945431610259)⟩⟩,⟨⟨31076575182348133088303267129,31076575182348133095274940457⟩,⟨(-53826207141061014062285414993),(-53826207141061014054345561180)⟩⟩,⟨⟨30924176053652663071625816717,30924176053652663078559122349⟩,⟨(-53562244107131231958730877712),(-53562244107131231950837198560)⟩⟩] +lemma amp4_11_9_eq : ∀ k : Fin 16, amp4_1Expr 1 9 k = amp4_11_9 k := by decide +kernel +noncomputable def amp4_11_10 : Fin 16 → CBox := ![⟨⟨30767647905240686644960555643,30767647905240686651860978305⟩,⟨(-53291129401267007110984820013),(-53291129401267007103127266239)⟩⟩,⟨⟨30605939563110598314594186847,30605939563110598321455216644⟩,⟨(-53011042336689963315323730496),(-53011042336689963307512888226)⟩⟩,⟨⟨30440187623762200857913098044,30440187623762200864734263640⟩,⟨(-52723951556285463931611563822),(-52723951556285463923847711342)⟩⟩,⟨⟨30269266911110177880803711255,30269266911110177887585443636⟩,⟨(-52427908197906279511449051873),(-52427908197906279503730754875)⟩⟩,⟨⟨30094391611375639617233950316,30094391611375639623972760951⟩,⟨(-52125015293777223038980726046),(-52125015293777223031313500591)⟩⟩,⟨⟨29914360872324529839432991483,29914360872324529846129458762⟩,⟨(-51813192906816526534451046754),(-51813192906816526526833204998)⟩⟩,⟨⟨29730468187763879464161239660,29730468187763879470814203431⟩,⟨(-51494681434017243238761860026),(-51494681434017243231194897492)⟩⟩,⟨⟨29541435202988933490956827269,29541435202988933497563916607⟩,⟨(-51167266700080642779659285604),(-51167266700080642772146624819)⟩⟩,⟨⟨29348636593525162296653558327,29348636593525162303213732196⟩,⟨(-50833329712860761294087523498),(-50833329712860761286630466490)⟩⟩,⟨⟨29150714511951410417743062332,29150714511951410424254337310⟩,⟨(-50490518611635231144036933738),(-50490518611635231136638234099)⟩⟩,⟨⟨28949126858313515178842888479,28949126858313515185303078179⟩,⟨(-50141358553355799570833919720),(-50141358553355799563496876599)⟩⟩,⟨⟨28742434125160893639329354096,28742434125160893645790622087⟩,⟨(-49783356237980182976542535760),(-49783356237980182969176119857)⟩⟩,⟨⟨28532179662507527613477395278,28532179662507527619888433445⟩,⟨(-49419184826146460000460602809),(-49419184826146459993153208420)⟩⟩,⟨⟨28316839943670277250660234021,28316839943670277257020230348⟩,⟨(-49046205492232745531367597091),(-49046205492232745524119953962)⟩⟩,⟨⟨28098046192495536937460956473,28098046192495536943768834651⟩,⟨(-48667243598819512576791325781),(-48667243598819512569604838494)⟩⟩,⟨⟨27874188295234711899344913883,27874188295234711905600357067⟩,⟨(-48279510347088229805232923153),(-48279510347088229798107466603)⟩⟩] +lemma amp4_11_10_eq : ∀ k : Fin 16, amp4_1Expr 1 10 k = amp4_11_10 k := by decide +kernel +noncomputable def amp4_11_11 : Fin 16 → CBox := ![⟨⟨27646987989670052249014164809,27646987989670052255216300374⟩,⟨(-47885987874355065372202478469),(-47885987874355065365139119303)⟩⟩,⟨⟨27414745779588332831746914976,27414745779588332837895491776⟩,⟨(-47483732566831442399586463275),(-47483732566831442392584965550)⟩⟩,⟨⟨27179276793229187795910159810,27179276793229187802002621998⟩,⟨(-47075888318850660288684939709),(-47075888318850660281749300889)⟩⟩,⟨⟨26938789107485135125708887888,26938789107485135131747179542⟩,⟨(-46659351428547303481942496785),(-46659351428547303475068681777)⟩⟩,⟨⟨26695194376888032116635519127,26695194376888032122616014177⟩,⟨(-46237432978697068112072079359),(-46237432978697068105265955237)⟩⟩,⟨⟨26446604933591878654014126601,26446604933591878659936559967⟩,⟨(-45806863432682867877357797261),(-45806863432682867870619158500)⟩⟩,⟨⟨26195032379608320403195917635,26195032379608320409058174624⟩,⟨(-45371126987393480830573956640),(-45371126987393480823906069024)⟩⟩,⟨⟨25938489683322627371322395159,25938489683322627377131395266⟩,⟨(-44926782003115948997351538466),(-44926782003115948990741755687)⟩⟩,⟨⟨25679092130460598062723173321,25679092130460598068470691640⟩,⟨(-44477492262199880595826395148),(-44477492262199880589288583261)⟩⟩,⟨⟨25414749373705691724355859541,25414749373705691730041307568⟩,⟨(-44019637176887561779132469137),(-44019637176887561772666989390)⟩⟩,⟨⟨25147684467739387129649917482,25147684467739387135274370473⟩,⟨(-43557067190835317630074923111),(-43557067190835317623679550860)⟩⟩,⟨⟨24875699428374202210822394669,24875699428374202216382270082⟩,⟨(-43085975283756196210548560223),(-43085975283756196204228845880)⟩⟩,⟨⟨24601129552458858917883574742,24601129552458858923379123883⟩,⟨(-42610406308442939428344667724),(-42610406308442939422099832044)⟩⟩,⟨⟨24321664486771101357379147526,24321664486771101362808994783⟩,⟨(-42126358615731169605354375392),(-42126358615731169599186149588)⟩⟩,⟨⟨24039756676364397074218820772,24039756676364397079581387811⟩,⟨(-41638079965056263501190870657),(-41638079965056263495101663422)⟩⟩,⟨⟨23752978207657739998379172353,23752978207657740003672410426⟩,⟨(-41141365086739532107490659847),(-41141365086739532101483371568)⟩⟩] +lemma amp4_11_11_eq : ∀ k : Fin 16, amp4_1Expr 1 11 k = amp4_11_11 k := by decide +kernel +noncomputable def amp4_11_12 : Fin 16 → CBox := ![⟨⟨23463904064604503187333023366,23463904064604503192585792969⟩,⟨(-40640673983816892128777228554),(-40640673983816892122801565891)⟩⟩,⟨⟨23169983067012150231361783205,23169983067012150236547777216⟩,⟨(-40131587882575607152642002975),(-40131587882575607146742886220)⟩⟩,⟨⟨22873918673218157791617664731,22873918673218157796736151270⟩,⟨(-39618789310212332444483636127),(-39618789310212332438662047702)⟩⟩,⟨⟨22573030150397963504336127167,22573030150397963509386424568⟩,⟨(-39097635101273408364688294136),(-39097635101273408358944772767)⟩⟩,⟨⟨22270155981605558910210472008,22270155981605558915191935684⟩,⟨(-38573041652624771534442327868),(-38573041652624771528777725772)⟩⟩,⟨⟨21962478939877190901384960287,21962478939877190906297292180⟩,⟨(-38040129384028748567085850696),(-38040129384028748561500044998)⟩⟩,⟨⟨21652979780165887254296416228,21652979780165887259137503381⟩,⟨(-37504061114508896153696675383),(-37504061114508896148193083355)⟩⟩,⟨⟨21338697095528772240937976676,21338697095528772245710725907⟩,⟨(-36959707536778266309522006416),(-36959707536778266304094956750)⟩⟩,⟨⟨21022761953305465942978860625,21022761953305465947678803877⟩,⟨(-36412491818551000533191443891),(-36412491818551000527848455589)⟩⟩,⟨⟨20702060231618653075690343792,20702060231618653080317433375⟩,⟨(-35857020142514626977579757695),(-35857020142514626972320279060)⟩⟩,⟨⟨20379882258044908821876418310,20379882258044908826429565898⟩,⟨(-35298991523205318835003324037),(-35298991523205318829829043654)⟩⟩,⟨⟨20052951687444352541926411484,20052951687444352546404417550⟩,⟨(-34732731164377671477384999693),(-34732731164377671472297362763)⟩⟩,⟨⟨19724728098486747674966932800,19724728098486747679368008295⟩,⟨(-34164231232060496731712262166),(-34164231232060496726714195351)⟩⟩,⟨⟨19391762292844942223923315673,19391762292844942228264219865⟩,⟨(-33587517539505785760863450899),(-33587517539505785755925295234)⟩⟩,⟨⟨19057694296448717006136040509,19057694296448717010399924986⟩,⟨(-33008894796564787082887104169),(-33008894796564787078037895288)⟩⟩,⟨⟨18718890128322294123093010726,18718890128322294127279150066⟩,⟨(-32422068763553714651978529278),(-32422068763553714647218893396)⟩⟩] +lemma amp4_11_12_eq : ∀ k : Fin 16, amp4_1Expr 1 12 k = amp4_11_12 k := by decide +kernel +noncomputable def amp4_11_13 : Fin 16 → CBox := ![⟨⟨18379182858626920874708329870,18379182858626920878816909076⟩,⟨(-31833678512740825020661061306),(-31833678512740825015990557808)⟩⟩,⟨⟨18034740279655822661732588282,18034740279655822665764737977⟩,⟨(-31237086465672827568991098580),(-31237086465672827564407139033)⟩⟩,⟨⟨17689602740734276709249219479,17689602740734276713201342434⟩,⟨(-30639290712661429083153721518),(-30639290712661429078662444023)⟩⟩,⟨⟨17339724586802453969099111178,17339724586802453972971466467⟩,⟨(-30033283973593107545708877862),(-30033283973593107541309202846)⟩⟩,⟨⟨16989369609173106072131515239,16989369609173106075922431726⟩,⟨(-29426451351654419582318104062),(-29426451351654419578012862564)⟩⟩,⟨⟨16634261386743642865314945029,16634261386743642869034718699⟩,⟨(-28811385868221119329791160692),(-28811385868221119325561887016)⟩⟩,⟨⟨16278905600962081265270305031,16278905600962081268909153891⟩,⟨(-28195891592483892596943491733),(-28195891592483892592807095845)⟩⟩,⟨⟨15918775249752562212809628273,15918775249752562216366445700⟩,⟨(-27572127526841381716416952014),(-27572127526841381712374715277)⟩⟩,⟨⟨15558639082871133556010041647,15558639082871133559485080589⟩,⟨(-26948353388159643250060895301),(-26948353388159643246112378821)⟩⟩,⟨⟨15193696708276728726394522467,15193696708276728729787893334⟩,⟨(-26316254653527300636771868645),(-26316254653527300632916241615)⟩⟩,⟨⟨14829004411061715032170198443,14829004411061715035480799414⟩,⟨(-25684589065621887148046642452),(-25684589065621887144285846559)⟩⟩,⟨⟨14459461977215688466090909841,14459461977215688469324939327⟩,⟨(-25044522794647908420808822257),(-25044522794647908417131476120)⟩⟩,⟨⟨14090441693045962456354059185,14090441693045962459503118968⟩,⟨(-24405360913442437900038558246),(-24405360913442437896459277487)⟩⟩,⟨⟨13716512663740494234196930340,13716512663740494237260844624⟩,⟨(-23757696836260455282054386473),(-23757696836260455278572822360)⟩⟩,⟨⟨13343396554569321849586434356,13343396554569321852565913545⟩,⟨(-23111440778053568769676627044),(-23111440778053568766291657300)⟩⟩,⟨⟨12965295463818583362306974714,12965295463818583365200071467⟩,⟨(-22456550478476078811628950970),(-22456550478476078808343285125)⟩⟩] +lemma amp4_11_13_eq : ∀ k : Fin 16, amp4_1Expr 1 13 k = amp4_11_13 k := by decide +kernel +noncomputable def amp4_11_14 : Fin 16 → CBox := ![⟨⟨12588319915260722389431716954,12588319915260722392244321663⟩,⟨(-21803609675162715197463786031),(-21803609675162715194267371404)⟩⟩,⟨⟨12206261841045965248515849693,12206261841045965251241857971⟩,⟨(-21141865679180835036878477931),(-21141865679180835033781211287)⟩⟩,⟨⟨11825667778884814560516191036,11825667778884814563156669533⟩,⟨(-20482657426458694503543589128),(-20482657426458694500543817792)⟩⟩,⟨⟨11439867680844907707735626963,11439867680844907710287538497⟩,⟨(-19814432055088521805238096728),(-19814432055088521802340388475)⟩⟩,⟨⟨11055901047314695422468782440,11055901047314695424937909222⟩,⟨(-19149382337403014458256199259),(-19149382337403014455450782990)⟩⟩,⟨⟨10666572908823690775536793959,10666572908823690777917791868⟩,⟨(-18475046220720382159452541090),(-18475046220720382156747959626)⟩⟩,⟨⟨10279485372927895293558052347,10279485372927895295854474632⟩,⟨(-17804590941572222817086181728),(-17804590941572222814476578821)⟩⟩,⟨⟨9886841054724459425646620606,9886841054724459427853843040⟩,⟨(-17124511033140630494711801109),(-17124511033140630492204446702)⟩⟩,⟨⟨9496891073954188849840582732,9496891073954188851959618310⟩,⟨(-16449097854036015172481354248),(-16449097854036015170074852325)⟩⟩,⟨⟨9101138730168082672682791122,9101138730168082674714753377⟩,⟨(-15763634687384014010584092725),(-15763634687384014008275742453)⟩⟩,⟨⟨8708593155276932931660706004,8708593155276932933603472200⟩,⟨(-15083725807386208900131556280),(-15083725807386208897925461080)⟩⟩,⟨⟨8309934963699564221250426821,8309934963699564223105063068⟩,⟨(-14393229564720679229136935528),(-14393229564720679227030435421)⟩⟩,⟨⟨7915071511567247978728751277,7915071511567247980496108805⟩,⟨(-13709306003575466158412465548),(-13709306003575466156404591138)⟩⟩,⟨⟨7513700288185479520878532219,7513700288185479522554900409⟩,⟨(-13014110651982165856518996371),(-13014110651982165854615308632)⟩⟩,⟨⟨7116811458893626801436799420,7116811458893626803024951916⟩,⟨(-12326679034692146072120833169),(-12326679034692146070317124491)⟩⟩,⟨⟨6712905375084154821000130190,6712905375084154822498354833⟩,⟨(-11627093176047967494237193610),(-11627093176047967492535495736)⟩⟩] +lemma amp4_11_14_eq : ∀ k : Fin 16, amp4_1Expr 1 14 k = amp4_11_14 k := by decide +kernel +noncomputable def amp4_11_15 : Fin 16 → CBox := ![⟨⟨6314304889329281697448263712,6314304889329281698857359089⟩,⟨(-10936696882798892730745012355),(-10936696882798892729144648120)⟩⟩,⟨⟨5908018787060499827165212638,5908018787060499828483287708⟩,⟨(-10232988711260237623028462095),(-10232988711260237621531684137)⟩⟩,⟨⟨5508052685234101317302458514,5508052685234101318530786131⟩,⟨(-9540227101591648276479778617),(-9540227101591648275085223303)⟩⟩,⟨⟨5099502883647184281209850210,5099502883647184282347390014⟩,⟨(-8832598087820924037946805712),(-8832598087820924036655132746)⟩⟩,⟨⟨4698569893355039727042965401,4698569893355039728091094840⟩,⟨(-8138161778204410222611209637),(-8138161778204410221421046798)⟩⟩,⟨⟨4287805485929443699964901888,4287805485929443700921240842⟩,⟨(-7426696954602355286950613160),(-7426696954602355285864774643)⟩⟩,⟨⟨3886397599776523264995938529,3886397599776523265862288355⟩,⟨(-6731438101226673490152686197),(-6731438101226673489169297060)⟩⟩,⟨⟨3473340580412691300138940870,3473340580412691300913458106⟩,⟨(-6016002357265554949431239488),(-6016002357265554948551942517)⟩⟩,⟨⟨3072133445990435319894799183,3072133445990435320579590889⟩,⟨(-5321091216087091371187308791),(-5321091216087091370410031346)⟩⟩,⟨⟨2656435792071101113030926072,2656435792071101113622873263⟩,⟨(-4601081758911620888866846277),(-4601081758911620888195062311)⟩⟩,⟨⟨2256524817754308917689818693,2256524817754308918192332627⟩,⟨(-3908415632890564420426680974),(-3908415632890564419856582785)⟩⟩,⟨⟨1837153108049314193089542142,1837153108049314193498461335⟩,⟨(-3182042524424487532420184232),(-3182042524424487531956390033)⟩⟩,⟨⟨1440842106367455813356035006,1440842106367455813676337741⟩,⟨(-2495611733912994038385250041),(-2495611733912994038022205940)⟩⟩,⟨⟨1014414495963543606809952444,1014414495963543607035203511⟩,⟨(-1757017446943231320053081645),(-1757017446943231319797926060)⟩⟩,⟨⟨629264447029517718401496104,629264447029517718540365625⟩,⟨(-1089917993651859172713990150),(-1089917993651859172557198899)⟩⟩,⟨⟨178776584874023315329293846,178776584874023315368230497⟩,⟨(-309650128205458016457116449),(-309650128205458016413466445)⟩⟩] +lemma amp4_11_15_eq : ∀ k : Fin 16, amp4_1Expr 1 15 k = amp4_11_15 k := by decide +kernel +noncomputable def amp4_11 : Fin 16 → Fin 16 → CBox := ![amp4_11_0,amp4_11_1,amp4_11_2,amp4_11_3,amp4_11_4,amp4_11_5,amp4_11_6,amp4_11_7,amp4_11_8,amp4_11_9,amp4_11_10,amp4_11_11,amp4_11_12,amp4_11_13,amp4_11_14,amp4_11_15] +lemma amp4_11_eq (i k : Fin 16) : amp4_1Expr 1 i k = amp4_11 i k := by + fin_cases i + · exact amp4_11_0_eq k + · exact amp4_11_1_eq k + · exact amp4_11_2_eq k + · exact amp4_11_3_eq k + · exact amp4_11_4_eq k + · exact amp4_11_5_eq k + · exact amp4_11_6_eq k + · exact amp4_11_7_eq k + · exact amp4_11_8_eq k + · exact amp4_11_9_eq k + · exact amp4_11_10_eq k + · exact amp4_11_11_eq k + · exact amp4_11_12_eq k + · exact amp4_11_13_eq k + · exact amp4_11_14_eq k + · exact amp4_11_15_eq k +noncomputable def amp4_12_0 : Fin 16 → CBox := ![⟨⟨(-178776584874023315358765569),(-178776584874023315336812836)⟩,⟨(-516083547009096694073668717),(-516083547009096694047199623)⟩⟩,⟨⟨(-629264447029517718507050623),(-629264447029517718427961722)⟩,⟨(-1816529989419765287780884478),(-1816529989419765287682466990)⟩⟩,⟨⟨(-1014414495963543606981497599),(-1014414495963543606852616712)⟩,⟨(-2928362411572052199966330142),(-2928362411572052199803678082)⟩⟩,⟨⟨(-1440842106367455813600055571),(-1440842106367455813416633976)⟩,⟨(-4159352889854990063801934004),(-4159352889854990063569859490)⟩⟩,⟨⟨(-1837153108049314193401197363),(-1837153108049314193166809168)⟩,⟨(-5303404207374145887145773677),(-5303404207374145886848377612)⟩⟩,⟨⟨(-2256524817754308918072865955),(-2256524817754308917784723664)⟩,⟨(-6514026054817607367106107671),(-6514026054817607366740103428)⟩⟩,⟨⟨(-2656435792071101113482234197),(-2656435792071101113142650508)⟩,⟨(-7668469598186034814458232414),(-7668469598186034814026279102)⟩⟩,⟨⟨(-3072133445990435320416943639),(-3072133445990435320024007041)⟩,⟨(-8868485360145152284942285064),(-8868485360145152284442123303)⟩⟩,⟨⟨(-3473340580412691300729569838),(-3473340580412691300285022706)⟩,⟨(-10026670595442591581967196067),(-10026670595442591581400864534)⟩⟩,⟨⟨(-3886397599776523265656531705),(-3886397599776523265159392727)⟩,⟨(-11219063502044455816453206986),(-11219063502044455815820318927)⟩⟩,⟨⟨(-4287805485929443700694232548),(-4287805485929443700145238507)⟩,⟨(-12377828257670592144401420926),(-12377828257670592143701698642)⟩⟩,⟨⟨(-4698569893355039727842339540),(-4698569893355039727240577959)⟩,⟨(-13563602963674017037119624164),(-13563602963674017036352364928)⟩⟩,⟨⟨(-5099502883647184282077408212),(-5099502883647184281424325216)⟩,⟨(-14720996813034873395964010471),(-14720996813034873395131359491)⟩⟩,⟨⟨(-5508052685234101318239174571),(-5508052685234101317534116317)⟩,⟨(-15900378502652747126803107737),(-15900378502652747125904749786)⟩⟩,⟨⟨(-5908018787060499828170500835),(-5908018787060499827413692225)⟩,⟨(-17054981185433729371002756131),(-17054981185433729370037568605)⟩⟩,⟨⟨(-6314304889329281698523062305),(-6314304889329281697713830888)⟩,⟨(-18227828137998154550481421546),(-18227828137998154549448767818)⟩⟩] +lemma amp4_12_0_eq : ∀ k : Fin 16, amp4_1Expr 2 0 k = amp4_12_0 k := by decide +kernel +noncomputable def amp4_12_1 : Fin 16 → CBox := ![⟨⟨(-6712905375084154822142955036),(-6712905375084154821282461715)⟩,⟨(-19378488626746612489587063996),(-19378488626746612488488708842)⟩⟩,⟨⟨(-7116811458893626802648168213),(-7116811458893626801736118436)⟩,⟨(-20544465057820243452677831471),(-20544465057820243451514019773)⟩⟩,⟨⟨(-7513700288185479522157104311),(-7513700288185479521194543595)⟩,⟨(-21690184419970276426626983255),(-21690184419970276425399284656)⟩⟩,⟨⟨(-7915071511567247980077063004),(-7915071511567247979061643533)⟩,⟨(-22848843339292443596401105301),(-22848843339292443595103667500)⟩⟩,⟨⟨(-8309934963699564222665112102),(-8309934963699564221599926252)⟩,⟨(-23988715941201132047561012243),(-23988715941201132046201418828)⟩⟩,⟨⟨(-8708593155276932933142415166),(-8708593155276932932026972210)⟩,⟨(-25139543012310348165837380239),(-25139543012310348164414997914)⟩⟩,⟨⟨(-9101138730168082674232913894),(-9101138730168082673065567019)⟩,⟨(-26272724478973356683211010373),(-26272724478973356681719823431)⟩⟩,⟨⟨(-9496891073954188851456826602),(-9496891073954188850240003190)⟩,⟨(-27415163090060025286325462863),(-27415163090060025284773140493)⟩⟩,⟨⟨(-9886841054724459427330406299),(-9886841054724459426062441589)⟩,⟨(-28540851721901050823329256207),(-28540851721901050821709794934)⟩⟩,⟨⟨(-10279485372927895295310250215),(-10279485372927895293990387173)⟩,⟨(-29674318235953704693905948075),(-29674318235953704692217718700)⟩⟩,⟨⟨(-10666572908823690777353073964),(-10666572908823690775985408922)⟩,⟨(-30791743701200636931136606904),(-30791743701200636929390287484)⟩⟩,⟨⟨(-11055901047314695424352579208),(-11055901047314695422933771774)⟩,⟨(-31915637229005024095762493967),(-31915637229005024093948904129)⟩⟩,⟨⟨(-11439867680844907709681880227),(-11439867680844907708216765175)⟩,⟨(-33024053425147536340686092077),(-33024053425147536338818081890)⟩⟩,⟨⟨(-11825667778884814562530585938),(-11825667778884814561013555236)⟩,⟨(-34137762377431157504482127650),(-34137762377431157502543886587)⟩⟩,⟨⟨(-12206261841045965250595624672),(-12206261841045965249029220928)⟩,⟨(-35236442798634725059994450719),(-35236442798634725057992244024)⟩⟩,⟨⟨(-12588319915260722391577861152),(-12588319915260722389961156796)⟩,⟨(-36339349458604525327590629677),(-36339349458604525325522081889)⟩⟩] +lemma amp4_12_1_eq : ∀ k : Fin 16, amp4_1Expr 2 1 k = amp4_12_1 k := by decide +kernel +noncomputable def amp4_12_2 : Fin 16 → CBox := ![⟨⟨(-12965295463818583364513652826),(-12965295463818583362852269401)⟩,⟨(-37427584130793464684487181989),(-37427584130793464682367471974)⟩⟩,⟨⟨(-13343396554569321851859477186),(-13343396554569321850147631227)⟩,⟨(-38519067963422614614521117339),(-38519067963422614612333782005)⟩⟩,⟨⟨(-13716512663740494236534654465),(-13716512663740494234773819737)⟩,⟨(-39596161393767425468439125158),(-39596161393767425466187389897)⟩⟩,⟨⟨(-14090441693045962458757131971),(-14090441693045962456946675298)⟩,⟨(-40675601522404063165034389005),(-40675601522404063162716593801)⟩⟩,⟨⟨(-14459461977215688468559415374),(-14459461977215688466699046217)⟩,⟨(-41740871324413180699607064281),(-41740871324413180697221357157)⟩⟩,⟨⟨(-14829004411061715034695710861),(-14829004411061715032793877043)⟩,⟨(-42807648442703145244958936993),(-42807648442703145242529812494)⟩⟩,⟨⟨(-15193696708276728728983496961),(-15193696708276728727033539304)⟩,⟨(-43860424422545501059457070344),(-43860424422545501056964303918)⟩⟩,⟨⟨(-15558639082871133558661363157),(-15558639082871133556664407238)⟩,⟨(-44913922313599405414894841022),(-44913922313599405412341733553)⟩⟩,⟨⟨(-15918775249752562215523661662),(-15918775249752562213479140480)⟩,⟨(-45953545878068969525444907149),(-45953545878068969522828829747)⟩⟩,⟨⟨(-16278905600962081268047303555),(-16278905600962081265954963608)⟩,⟨(-46993152654139820992945778984),(-46993152654139820990265998656)⟩⟩,⟨⟨(-16634261386743642868154054844),(-16634261386743642866014549168)⟩,⟨(-48018976447035198880982441095),(-48018976447035198878239857425)⟩⟩,⟨⟨(-16989369609173106075022967458),(-16989369609173106072846054527)⟩,⟨(-49044085586090699301817923700),(-49044085586090699299040655876)⟩⟩,⟨⟨(-17339724586802453972053453436),(-17339724586802453969828385704)⟩,⟨(-50055473289321845907427029329),(-50055473289321845904583070693)⟩⟩,⟨⟨(-17689602740734276712264805885),(-17689602740734276709993209188)⟩,⟨(-51065484521102381803126308795),(-51065484521102381800220254308)⟩⟩,⟨⟨(-18034740279655822664809928891),(-18034740279655822662491093793)⟩,⟨(-52061810776121379279480381393),(-52061810776121379276509204535)⟩⟩,⟨⟨(-18379182858626920877843864247),(-18379182858626920875481321955)⟩,⟨(-53056130854568041698888847106),(-53056130854568041695862598138)⟩⟩] +lemma amp4_12_2_eq : ∀ k : Fin 16, amp4_1Expr 2 2 k = amp4_12_2 k := by decide +kernel +noncomputable def amp4_12_3 : Fin 16 → CBox := ![⟨⟨(-18718890128322294126288120193),(-18718890128322294123880290226)⟩,⟨(-54036781272589524417710391713),(-54036781272589524414623530722)⟩⟩,⟨⟨(-19057694296448717009390957883),(-19057694296448717006937569444)⟩,⟨(-55014824660941311802517223253),(-55014824660941311799368782092)⟩⟩,⟨⟨(-19391762292844942227237566277),(-19391762292844942224738894847)⟩,⟨(-55979195899176309599104244777),(-55979195899176309595894041058)⟩⟩,⟨⟨(-19724728098486747678323726575),(-19724728098486747675796515857)⟩,⟨(-56940385386767494550478839906),(-56940385386767494547254981019)⟩⟩,⟨⟨(-20052951687444352545342758765),(-20052951687444352542769798976)⟩,⟨(-57887885273962785793227216448),(-57887885273962785789939043143)⟩⟩,⟨⟨(-20379882258044908825350598503),(-20379882258044908822733555855)⟩,⟨(-58831652538675531389218393369),(-58831652538675531385870448684)⟩⟩,⟨⟨(-20702060231618653079221408986),(-20702060231618653076561031506)⟩,⟨(-59761700237524378293473658043),(-59761700237524378290067120314)⟩⟩,⟨⟨(-21022761953305465946565800651),(-21022761953305465943863036419)⟩,⟨(-60687486364251667552787854694),(-60687486364251667549325156065)⟩⟩,⟨⟨(-21338697095528772244580996200),(-21338697095528772241835440077)⟩,⟨(-61599512561297110513300752473),(-61599512561297110509779739496)⟩⟩,⟨⟨(-21652979780165887257991134678),(-21652979780165887255207097737)⟩,⟨(-62506768524181493586887359951),(-62506768524181493583320136517)⟩⟩,⟨⟨(-21962478939877190905134537735),(-21962478939877190902308658719)⟩,⟨(-63400215640047914275832053962),(-63400215640047914272207929548)⟩⟩,⟨⟨(-22270155981605558914012891964),(-22270155981605558911147110727)⟩,⟨(-64288402754374619221389137124),(-64288402754374619217713335488)⟩⟩,⟨⟨(-22573030150397963508191345851),(-22573030150397963505285504176)⟩,⟨(-65162725168789013938429280400),(-65162725168789013934700353397)⟩⟩,⟨⟨(-22873918673218157795525142681),(-22873918673218157792579696515)⟩,⟨(-66031315517020554071385288958),(-66031315517020554067604142918)⟩⟩,⟨⟨(-23169983067012150235321094158),(-23169983067012150232336266873)⟩,⟨(-66885979804292678584946919786),(-66885979804292678581113203735)⟩⟩,⟨⟨(-23463904064604503191343548921),(-23463904064604503188319868770)⟩,⟨(-67734456639694820211803573241),(-67734456639694820207918369676)⟩⟩] +lemma amp4_12_3_eq : ∀ k : Fin 16, amp4_1Expr 2 3 k = amp4_12_3 k := by decide +kernel +noncomputable def amp4_12_4 : Fin 16 → CBox := ![⟨⟨(-23752978207657740002414861991),(-23752978207657739999378175643)⟩,⟨(-68568941811232553509624486465),(-68568941811232553505761407806)⟩⟩,⟨⟨(-24039756676364397078308656530),(-24039756676364397075229885397)⟩,⟨(-69396799941760439165756975290),(-69396799941760439161831605012)⟩⟩,⟨⟨(-24321664486771101361521338523),(-24321664486771101358402068637)⟩,⟨(-70210597692885282672662207103),(-70210597692885282668678118286)⟩⟩,⟨⟨(-24601129552458858922076671968),(-24601129552458858918918249600)⟩,⟨(-71017343847404899044279045694),(-71017343847404899040239620459)⟩⟩,⟨⟨(-24875699428374202215065281678),(-24875699428374202211868617394)⟩,⟨(-71809958806260327014585807295),(-71809958806260327010492663754)⟩⟩,⟨⟨(-25147684467739387133942982428),(-25147684467739387130707579359)⟩,⟨(-72595111984725529380430330769),(-72595111984725529376281501027)⟩⟩,⟨⟨(-25414749373705691728695780367),(-25414749373705691725424753641)⟩,⟨(-73366061961479269628827418540),(-73366061961479269624630879581)⟩⟩,⟨⟨(-25679092130460598067111169402),(-25679092130460598063803185154)⟩,⟨(-74129153770333134323285467377),(-74129153770333134319036806764)⟩⟩,⟨⟨(-25938489683322627375758139803),(-25938489683322627372413316740)⟩,⟨(-74877970005193248325796140480),(-74877970005193248321494680100)⟩⟩,⟨⟨(-26195032379608320407671337080),(-26195032379608320404297628895)⟩,⟨(-75618544978989134714469282079),(-75618544978989134710137392969)⟩⟩,⟨⟨(-26446604933591878658536403476),(-26446604933591878655126418505)⟩,⟨(-76344772387804779792412059513),(-76344772387804779788027377844)⟩⟩,⟨⟨(-26695194376888032121202696672),(-26695194376888032117758266210)⟩,⟨(-77062388297828446850239265252),(-77062388297828446845806461745)⟩⟩,⟨⟨(-26938789107485135130320965458),(-26938789107485135126841880085)⟩,⟨(-77765585714245505799993964588),(-77765585714245505795511403689)⟩⟩,⟨⟨(-27179276793229187800563675830),(-27179276793229187797053266443)⟩,⟨(-78459813864751100477869080519),(-78459813864751100473345736348)⟩⟩,⟨⟨(-27414745779588332836444079228),(-27414745779588332832899924969)⟩,⟨(-79139554278052403996009935124),(-79139554278052403991437783305)⟩⟩,⟨⟨(-27646987989670052253752592280),(-27646987989670052250176942450)⟩,⟨(-79809979790591775617008664290),(-79809979790591775612393531931)⟩⟩] +lemma amp4_12_4_eq : ∀ k : Fin 16, amp4_1Expr 2 4 k = amp4_12_4 k := by decide +kernel +noncomputable def amp4_12_5 : Fin 16 → CBox := ![⟨⟨(-27874188295234711904124620360),(-27874188295234711900517247120)⟩,⟨(-80465850578480383005365383005),(-80465850578480383000705571641)⟩⟩,⟨⟨(-28098046192495536942281246287),(-28098046192495536938642704730)⟩,⟨(-81112072664699187624602434064),(-81112072664699187619898856172)⟩⟩,⟨⟨(-28316839943670277255521058437),(-28316839943670277251851184311)⟩,⟨(-81743675820387909215536542669),(-81743675820387909210787678754)⟩⟩,⟨⟨(-28532179662507527618377860853),(-28532179662507527614677402330)⟩,⟨(-82365308043577433330665624499),(-82365308043577433325872921369)⟩⟩,⟨⟨(-28742434125160893644268918042),(-28742434125160893640538204035)⟩,⟨(-82972260396633638290776864000),(-82972260396633638285940221448)⟩⟩,⟨⟨(-28949126858313515183770431249),(-28949126858313515180060431506)⟩,⟨(-83568930922259665947904284030),(-83568930922259665943170103836)⟩⟩,⟨⟨(-29150714511951410422711017771),(-29150714511951410418969083737)⟩,⟨(-84150864352725385236551702160),(-84150864352725385231766947244)⟩⟩,⟨⟨(-29348636593525162301659934113),(-29348636593525162297887903943)⟩,⟨(-84722216188101268819945521207),(-84722216188101268815114741223)⟩⟩,⟨⟨(-29541435202988933495999911232),(-29541435202988933492199281613)⟩,⟨(-85278777833467737962541911050),(-85278777833467737957668368977)⟩⟩,⟨⟨(-29730468187763879469240190126),(-29730468187763879465411644358)⟩,⟨(-85824469056695405394356774815),(-85824469056695405389441665869)⟩⟩,⟨⟨(-29914360872324529844545709670),(-29914360872324529840691130344)⟩,⟨(-86355321511360877553816611333),(-86355321511360877548864309030)⟩⟩,⟨⟨(-30094391611375639622379480534),(-30094391611375639618499660913)⟩,⟨(-86875025489628705061344400452),(-86875025489628705056356397564)⟩⟩,⟨⟨(-30269266911110177885982904835),(-30269266911110177882076776762)⟩,⟨(-87379846996510465848770554529),(-87379846996510465843742703366)⟩⟩,⟨⟨(-30440187623762200863122675824),(-30440187623762200859193352137)⟩,⟨(-87873252593809106549020828290),(-87873252593809106543961298540)⟩⟩,⟨⟨(-30605939563110598319834853461),(-30605939563110598315881412140)⟩,⟨(-88351737227816605521854482265),(-88351737227816605516759545345)⟩⟩,⟨⟨(-30767647905240686650232053835),(-30767647905240686646254582069)⟩,⟨(-88818549002111678514603494510),(-88818549002111678509472567440)⟩⟩] +lemma amp4_12_5_eq : ∀ k : Fin 16, amp4_1Expr 2 5 k = amp4_12_5 k := by decide +kernel +noncomputable def amp4_12_6 : Fin 16 → CBox := ![⟨⟨(-30924176053652663076921910845),(-30924176053652663072926426407)⟩,⟨(-89270406845218719927494744106),(-89270406845218719922344129404)⟩⟩,⟨⟨(-31076575182348133093629660522),(-31076575182348133089610286425)⟩,⟨(-89710345235101690100067290155),(-89710345235101690094879170112)⟩⟩,⟨⟨(-31223784711938343741732883253),(-31223784711938343737693609664)⟩,⟨(-90135302542782621585258147638),(-90135302542782621580042969640)⟩⟩,⟨⟨(-31366783346512185483913737608),(-31366783346512185479851889162)⟩,⟨(-90548104043607403863328048613),(-90548104043607403858077220333)⟩⟩,⟨⟨(-31504585086650592895467604247),(-31504585086650592891385676299)⟩,⟨(-90945903402425945746399790214),(-90945903402425945741119442382)⟩⟩,⟨⟨(-31638097566013635101048593984),(-31638097566013635096946201055)⟩,⟨(-91331320731928079606494947747),(-91331320731928079601183082195)⟩⟩,⟨⟨(-31766408054785126238285272401),(-31766408054785126234180296673)⟩,⟨(-91701721208088443917196951718),(-91701721208088443911904116062)⟩⟩,⟨⟨(-31890354391170951219071539466),(-31890354391170951214945815276)⟩,⟨(-92059523461475563713382283729),(-92059523461475563708055137373)⟩⟩,⟨⟨(-32009095923644769043671428880),(-32009095923644769039527319219)⟩,⟨(-92402300740164300765192727807),(-92402300740164300759837017744)⟩⟩,⟨⟨(-32123401852681396184602184449),(-32123401852681396180441241813)⟩,⟨(-92732273534660635464436018036),(-92732273534660635459055310344)⟩⟩,⟨⟨(-32232502525936830264300271483),(-32232502525936830260122126548)⟩,⟨(-93047220050024606815426798700),(-93047220050024606810018952759)⟩⟩,⟨⟨(-32337099553057724192535989970),(-32337099553057724188343225889)⟩,⟨(-93349165658848020296520755960),(-93349165658848020291092299056)⟩⟩,⟨⟨(-32436493307917857223852181715),(-32436493307917857219644451829)⟩,⟨(-93636090714469347695307318405),(-93636090714469347689856175760)⟩⟩,⟨⟨(-32531318751103864922259274286),(-32531318751103864918036016014)⟩,⟨(-93909828190216683239651737995),(-93909828190216683234175342590)⟩⟩,⟨⟨(-32620945410534091406341004673),(-32620945410534091402111212759)⟩,⟨(-94168558069959724095296081398),(-94168558069959724089819325690)⟩⟩,⟨⟨(-32705942439377387424011565051),(-32705942439377387419768378943)⟩,⟨(-94413923357374700801409681816),(-94413923357374700795911805452)⟩⟩] +lemma amp4_12_6_eq : ∀ k : Fin 16, amp4_1Expr 2 6 k = amp4_12_6 k := by decide +kernel +noncomputable def amp4_12_7 : Fin 16 → CBox := ![⟨⟨(-32785747743509981349802035219),(-32785747743509981345547052918)⟩,⟨(-94644301426493266084057613183),(-94644301426493266078542157521)⟩⟩,⟨⟨(-32860865414590931775215449629),(-32860865414590931770948270348)⟩,⟨(-94861147464590688557526181934),(-94861147464590688551991022377)⟩⟩,⟨⟨(-32930801052341203475618237852),(-32930801052341203471344043036)⟩,⟨(-95063034260996026156647664925),(-95063034260996026151106689350)⟩⟩,⟨⟨(-32995994340909188940784701606),(-32995994340909188936500465978)⟩,⟨(-95251231074516442958079796984),(-95251231074516442952523293253)⟩⟩,⟨⟨(-33056017978152788410200234984),(-33056017978152788405909372116)⟩,⟨(-95424504390118105959556037067),(-95424504390118105953992792195)⟩⟩,⟨⟨(-33111247806102404780303402430),(-33111247806102404776003484834)⟩,⟨(-95583939170288144599924024430),(-95583939170288144594346041330)⟩⟩,⟨⟨(-33161323110387142482032177801),(-33161323110387142477726044956)⟩,⟨(-95728494122330873262647692366),(-95728494122330873257062103910)⟩⟩,⟨⟨(-33206556370521783193478490630),(-33206556370521783189166719653)⟩,⟨(-95859071296906169175174668949),(-95859071296906169169582141640)⟩⟩,⟨⟨(-33246653032290985854436658574),(-33246653032290985850119739559)⟩,⟨(-95974820389236441836981132153),(-95974820389236441831382020472)⟩⟩,⟨⟨(-33281862608866566226679727672),(-33281862608866566222357853170)⟩,⟨(-96076461681806262185087404656),(-96076461681806262179481255664)⟩⟩,⟨⟨(-33311956359174495042091913884),(-33311956359174495037766820132)⟩,⟨(-96163334856012302609185713199),(-96163334856012302603576482969)⟩⟩,⟨⟨(-33337121144716975243090835120),(-33337121144716975238762859751)⟩,⟨(-96235979334547553342539120993),(-96235979334547553336926766757)⟩⟩,⟨⟨(-33357193769420233718372893001),(-33357193769420233714043683511)⟩,⟨(-96293924010926396405965873791),(-96293924010926396400354100339)⟩⟩,⟨⟨(-33372298677811606175284598902),(-33372298677811606170955096213)⟩,⟨(-96337528125555614031358204334),(-96337528125555614025748702438)⟩⟩,⟨⟨(-33382338028223777529203552288),(-33382338028223777524875249376)⟩,⟨(-96366509233870394589138789886),(-96366509233870394583534823762)⟩⟩,⟨⟨(-33387374004052282218395336386),(-33387374004052282214070029472)⟩,⟨(-96381046843871492743834207050),(-96381046843871492738239929154)⟩⟩] +lemma amp4_12_7_eq : ∀ k : Fin 16, amp4_1Expr 2 7 k = amp4_12_7 k := by decide +kernel +noncomputable def amp4_12_8 : Fin 16 → CBox := ![⟨⟨(-33387374004052282218395336386),(-33387374004052282214070029472)⟩,⟨(-96381046843871492743834207050),(-96381046843871492738239929154)⟩⟩,⟨⟨(-33382338028223777529203552288),(-33382338028223777524875249376)⟩,⟨(-96366509233870394589138789886),(-96366509233870394583534823762)⟩⟩,⟨⟨(-33372298677811606175284598902),(-33372298677811606170955096213)⟩,⟨(-96337528125555614031358204334),(-96337528125555614025748702438)⟩⟩,⟨⟨(-33357193769420233718372893001),(-33357193769420233714043683511)⟩,⟨(-96293924010926396405965873791),(-96293924010926396400354100339)⟩⟩,⟨⟨(-33337121144716975243090835120),(-33337121144716975238762859751)⟩,⟨(-96235979334547553342539120993),(-96235979334547553336926766757)⟩⟩,⟨⟨(-33311956359174495042091913884),(-33311956359174495037766820132)⟩,⟨(-96163334856012302609185713199),(-96163334856012302603576482969)⟩⟩,⟨⟨(-33281862608866566226679727672),(-33281862608866566222357853170)⟩,⟨(-96076461681806262185087404656),(-96076461681806262179481255664)⟩⟩,⟨⟨(-33246653032290985854436658574),(-33246653032290985850119739559)⟩,⟨(-95974820389236441836981132153),(-95974820389236441831382020472)⟩⟩,⟨⟨(-33206556370521783193478490630),(-33206556370521783189166719653)⟩,⟨(-95859071296906169175174668949),(-95859071296906169169582141640)⟩⟩,⟨⟨(-33161323110387142482032177801),(-33161323110387142477726044956)⟩,⟨(-95728494122330873262647692366),(-95728494122330873257062103910)⟩⟩,⟨⟨(-33111247806102404780303402430),(-33111247806102404776003484834)⟩,⟨(-95583939170288144599924024430),(-95583939170288144594346041330)⟩⟩,⟨⟨(-33056017978152788410200234984),(-33056017978152788405909372116)⟩,⟨(-95424504390118105959556037067),(-95424504390118105953992792195)⟩⟩,⟨⟨(-32995994340909188940784701606),(-32995994340909188936500465978)⟩,⟨(-95251231074516442958079796984),(-95251231074516442952523293253)⟩⟩,⟨⟨(-32930801052341203475618237852),(-32930801052341203471344043036)⟩,⟨(-95063034260996026156647664925),(-95063034260996026151106689350)⟩⟩,⟨⟨(-32860865414590931775215449629),(-32860865414590931770948270348)⟩,⟨(-94861147464590688557526181934),(-94861147464590688551991022377)⟩⟩,⟨⟨(-32785747743509981349802035219),(-32785747743509981345547052918)⟩,⟨(-94644301426493266084057613183),(-94644301426493266078542157521)⟩⟩] +lemma amp4_12_8_eq : ∀ k : Fin 16, amp4_1Expr 2 8 k = amp4_12_8 k := by decide +kernel +noncomputable def amp4_12_9 : Fin 16 → CBox := ![⟨⟨(-32705942439377387424011565051),(-32705942439377387419768378943)⟩,⟨(-94413923357374700801409681816),(-94413923357374700795911805452)⟩⟩,⟨⟨(-32620945410534091406341004673),(-32620945410534091402111212759)⟩,⟨(-94168558069959724095296081398),(-94168558069959724089819325690)⟩⟩,⟨⟨(-32531318751103864922259274286),(-32531318751103864918036016014)⟩,⟨(-93909828190216683239651737995),(-93909828190216683234175342590)⟩⟩,⟨⟨(-32436493307917857223852181715),(-32436493307917857219644451829)⟩,⟨(-93636090714469347695307318405),(-93636090714469347689856175760)⟩⟩,⟨⟨(-32337099553057724192535989970),(-32337099553057724188343225889)⟩,⟨(-93349165658848020296520755960),(-93349165658848020291092299056)⟩⟩,⟨⟨(-32232502525936830264300271483),(-32232502525936830260122126548)⟩,⟨(-93047220050024606815426798700),(-93047220050024606810018952759)⟩⟩,⟨⟨(-32123401852681396184602184449),(-32123401852681396180441241813)⟩,⟨(-92732273534660635464436018036),(-92732273534660635459055310344)⟩⟩,⟨⟨(-32009095923644769043671428880),(-32009095923644769039527319219)⟩,⟨(-92402300740164300765192727807),(-92402300740164300759837017744)⟩⟩,⟨⟨(-31890354391170951219071539466),(-31890354391170951214945815276)⟩,⟨(-92059523461475563713382283729),(-92059523461475563708055137373)⟩⟩,⟨⟨(-31766408054785126238285272401),(-31766408054785126234180296673)⟩,⟨(-91701721208088443917196951718),(-91701721208088443911904116062)⟩⟩,⟨⟨(-31638097566013635101048593984),(-31638097566013635096946201055)⟩,⟨(-91331320731928079606494947747),(-91331320731928079601183082195)⟩⟩,⟨⟨(-31504585086650592895467604247),(-31504585086650592891385676299)⟩,⟨(-90945903402425945746399790214),(-90945903402425945741119442382)⟩⟩,⟨⟨(-31366783346512185483913737608),(-31366783346512185479851889162)⟩,⟨(-90548104043607403863328048613),(-90548104043607403858077220333)⟩⟩,⟨⟨(-31223784711938343741732883253),(-31223784711938343737693609664)⟩,⟨(-90135302542782621585258147638),(-90135302542782621580042969640)⟩⟩,⟨⟨(-31076575182348133093629660522),(-31076575182348133089610286425)⟩,⟨(-89710345235101690100067290155),(-89710345235101690094879170112)⟩⟩,⟨⟨(-30924176053652663076921910845),(-30924176053652663072926426407)⟩,⟨(-89270406845218719927494744106),(-89270406845218719922344129404)⟩⟩] +lemma amp4_12_9_eq : ∀ k : Fin 16, amp4_1Expr 2 9 k = amp4_12_9 k := by decide +kernel +noncomputable def amp4_12_10 : Fin 16 → CBox := ![⟨⟨(-30767647905240686650232053835),(-30767647905240686646254582069)⟩,⟨(-88818549002111678514603494510),(-88818549002111678509472567440)⟩⟩,⟨⟨(-30605939563110598319834853461),(-30605939563110598315881412140)⟩,⟨(-88351737227816605521854482265),(-88351737227816605516759545345)⟩⟩,⟨⟨(-30440187623762200863122675824),(-30440187623762200859193352137)⟩,⟨(-87873252593809106549020828290),(-87873252593809106543961298540)⟩⟩,⟨⟨(-30269266911110177885982904835),(-30269266911110177882076776762)⟩,⟨(-87379846996510465848770554529),(-87379846996510465843742703366)⟩⟩,⟨⟨(-30094391611375639622379480534),(-30094391611375639618499660913)⟩,⟨(-86875025489628705061344400452),(-86875025489628705056356397564)⟩⟩,⟨⟨(-29914360872324529844545709670),(-29914360872324529840691130344)⟩,⟨(-86355321511360877553816611333),(-86355321511360877548864309030)⟩⟩,⟨⟨(-29730468187763879469240190126),(-29730468187763879465411644358)⟩,⟨(-85824469056695405394356774815),(-85824469056695405389441665869)⟩⟩,⟨⟨(-29541435202988933495999911232),(-29541435202988933492199281613)⟩,⟨(-85278777833467737962541911050),(-85278777833467737957668368977)⟩⟩,⟨⟨(-29348636593525162301659934113),(-29348636593525162297887903943)⟩,⟨(-84722216188101268819945521207),(-84722216188101268815114741223)⟩⟩,⟨⟨(-29150714511951410422711017771),(-29150714511951410418969083737)⟩,⟨(-84150864352725385236551702160),(-84150864352725385231766947244)⟩⟩,⟨⟨(-28949126858313515183770431249),(-28949126858313515180060431506)⟩,⟨(-83568930922259665947904284030),(-83568930922259665943170103836)⟩⟩,⟨⟨(-28742434125160893644268918042),(-28742434125160893640538204035)⟩,⟨(-82972260396633638290776864000),(-82972260396633638285940221448)⟩⟩,⟨⟨(-28532179662507527618377860853),(-28532179662507527614677402330)⟩,⟨(-82365308043577433330665624499),(-82365308043577433325872921369)⟩⟩,⟨⟨(-28316839943670277255521058437),(-28316839943670277251851184311)⟩,⟨(-81743675820387909215536542669),(-81743675820387909210787678754)⟩⟩,⟨⟨(-28098046192495536942281246287),(-28098046192495536938642704730)⟩,⟨(-81112072664699187624602434064),(-81112072664699187619898856172)⟩⟩,⟨⟨(-27874188295234711904124620360),(-27874188295234711900517247120)⟩,⟨(-80465850578480383005365383005),(-80465850578480383000705571641)⟩⟩] +lemma amp4_12_10_eq : ∀ k : Fin 16, amp4_1Expr 2 10 k = amp4_12_10 k := by decide +kernel +noncomputable def amp4_12_11 : Fin 16 → CBox := ![⟨⟨(-27646987989670052253752592280),(-27646987989670052250176942450)⟩,⟨(-79809979790591775617008664290),(-79809979790591775612393531931)⟩⟩,⟨⟨(-27414745779588332836444079228),(-27414745779588332832899924969)⟩,⟨(-79139554278052403996009935124),(-79139554278052403991437783305)⟩⟩,⟨⟨(-27179276793229187800563675830),(-27179276793229187797053266443)⟩,⟨(-78459813864751100477869080519),(-78459813864751100473345736348)⟩⟩,⟨⟨(-26938789107485135130320965458),(-26938789107485135126841880085)⟩,⟨(-77765585714245505799993964588),(-77765585714245505795511403689)⟩⟩,⟨⟨(-26695194376888032121202696672),(-26695194376888032117758266210)⟩,⟨(-77062388297828446850239265252),(-77062388297828446845806461745)⟩⟩,⟨⟨(-26446604933591878658536403476),(-26446604933591878655126418505)⟩,⟨(-76344772387804779792412059513),(-76344772387804779788027377844)⟩⟩,⟨⟨(-26195032379608320407671337080),(-26195032379608320404297628895)⟩,⟨(-75618544978989134714469282079),(-75618544978989134710137392969)⟩⟩,⟨⟨(-25938489683322627375758139803),(-25938489683322627372413316740)⟩,⟨(-74877970005193248325796140480),(-74877970005193248321494680100)⟩⟩,⟨⟨(-25679092130460598067111169402),(-25679092130460598063803185154)⟩,⟨(-74129153770333134323285467377),(-74129153770333134319036806764)⟩⟩,⟨⟨(-25414749373705691728695780367),(-25414749373705691725424753641)⟩,⟨(-73366061961479269628827418540),(-73366061961479269624630879581)⟩⟩,⟨⟨(-25147684467739387133942982428),(-25147684467739387130707579359)⟩,⟨(-72595111984725529380430330769),(-72595111984725529376281501027)⟩⟩,⟨⟨(-24875699428374202215065281678),(-24875699428374202211868617394)⟩,⟨(-71809958806260327014585807295),(-71809958806260327010492663754)⟩⟩,⟨⟨(-24601129552458858922076671968),(-24601129552458858918918249600)⟩,⟨(-71017343847404899044279045694),(-71017343847404899040239620459)⟩⟩,⟨⟨(-24321664486771101361521338523),(-24321664486771101358402068637)⟩,⟨(-70210597692885282672662207103),(-70210597692885282668678118286)⟩⟩,⟨⟨(-24039756676364397078308656530),(-24039756676364397075229885397)⟩,⟨(-69396799941760439165756975290),(-69396799941760439161831605012)⟩⟩,⟨⟨(-23752978207657740002414861991),(-23752978207657739999378175643)⟩,⟨(-68568941811232553509624486465),(-68568941811232553505761407806)⟩⟩] +lemma amp4_12_11_eq : ∀ k : Fin 16, amp4_1Expr 2 11 k = amp4_12_11 k := by decide +kernel +noncomputable def amp4_12_12 : Fin 16 → CBox := ![⟨⟨(-23463904064604503191343548921),(-23463904064604503188319868770)⟩,⟨(-67734456639694820211803573241),(-67734456639694820207918369676)⟩⟩,⟨⟨(-23169983067012150235321094158),(-23169983067012150232336266873)⟩,⟨(-66885979804292678584946919786),(-66885979804292678581113203735)⟩⟩,⟨⟨(-22873918673218157795525142681),(-22873918673218157792579696515)⟩,⟨(-66031315517020554071385288958),(-66031315517020554067604142918)⟩⟩,⟨⟨(-22573030150397963508191345851),(-22573030150397963505285504176)⟩,⟨(-65162725168789013938429280400),(-65162725168789013934700353397)⟩⟩,⟨⟨(-22270155981605558914012891964),(-22270155981605558911147110727)⟩,⟨(-64288402754374619221389137124),(-64288402754374619217713335488)⟩⟩,⟨⟨(-21962478939877190905134537735),(-21962478939877190902308658719)⟩,⟨(-63400215640047914275832053962),(-63400215640047914272207929548)⟩⟩,⟨⟨(-21652979780165887257991134678),(-21652979780165887255207097737)⟩,⟨(-62506768524181493586887359951),(-62506768524181493583320136517)⟩⟩,⟨⟨(-21338697095528772244580996200),(-21338697095528772241835440077)⟩,⟨(-61599512561297110513300752473),(-61599512561297110509779739496)⟩⟩,⟨⟨(-21022761953305465946565800651),(-21022761953305465943863036419)⟩,⟨(-60687486364251667552787854694),(-60687486364251667549325156065)⟩⟩,⟨⟨(-20702060231618653079221408986),(-20702060231618653076561031506)⟩,⟨(-59761700237524378293473658043),(-59761700237524378290067120314)⟩⟩,⟨⟨(-20379882258044908825350598503),(-20379882258044908822733555855)⟩,⟨(-58831652538675531389218393369),(-58831652538675531385870448684)⟩⟩,⟨⟨(-20052951687444352545342758765),(-20052951687444352542769798976)⟩,⟨(-57887885273962785793227216448),(-57887885273962785789939043143)⟩⟩,⟨⟨(-19724728098486747678323726575),(-19724728098486747675796515857)⟩,⟨(-56940385386767494550478839906),(-56940385386767494547254981019)⟩⟩,⟨⟨(-19391762292844942227237566277),(-19391762292844942224738894847)⟩,⟨(-55979195899176309599104244777),(-55979195899176309595894041058)⟩⟩,⟨⟨(-19057694296448717009390957883),(-19057694296448717006937569444)⟩,⟨(-55014824660941311802517223253),(-55014824660941311799368782092)⟩⟩,⟨⟨(-18718890128322294126288120193),(-18718890128322294123880290226)⟩,⟨(-54036781272589524417710391713),(-54036781272589524414623530722)⟩⟩] +lemma amp4_12_12_eq : ∀ k : Fin 16, amp4_1Expr 2 12 k = amp4_12_12 k := by decide +kernel +noncomputable def amp4_12_13 : Fin 16 → CBox := ![⟨⟨(-18379182858626920877843864247),(-18379182858626920875481321955)⟩,⟨(-53056130854568041698888847106),(-53056130854568041695862598138)⟩⟩,⟨⟨(-18034740279655822664809928891),(-18034740279655822662491093793)⟩,⟨(-52061810776121379279480381393),(-52061810776121379276509204535)⟩⟩,⟨⟨(-17689602740734276712264805885),(-17689602740734276709993209188)⟩,⟨(-51065484521102381803126308795),(-51065484521102381800220254308)⟩⟩,⟨⟨(-17339724586802453972053453436),(-17339724586802453969828385704)⟩,⟨(-50055473289321845907427029329),(-50055473289321845904583070693)⟩⟩,⟨⟨(-16989369609173106075022967458),(-16989369609173106072846054527)⟩,⟨(-49044085586090699301817923700),(-49044085586090699299040655876)⟩⟩,⟨⟨(-16634261386743642868154054844),(-16634261386743642866014549168)⟩,⟨(-48018976447035198880982441095),(-48018976447035198878239857425)⟩⟩,⟨⟨(-16278905600962081268047303555),(-16278905600962081265954963608)⟩,⟨(-46993152654139820992945778984),(-46993152654139820990265998656)⟩⟩,⟨⟨(-15918775249752562215523661662),(-15918775249752562213479140480)⟩,⟨(-45953545878068969525444907149),(-45953545878068969522828829747)⟩⟩,⟨⟨(-15558639082871133558661363157),(-15558639082871133556664407238)⟩,⟨(-44913922313599405414894841022),(-44913922313599405412341733553)⟩⟩,⟨⟨(-15193696708276728728983496961),(-15193696708276728727033539304)⟩,⟨(-43860424422545501059457070344),(-43860424422545501056964303918)⟩⟩,⟨⟨(-14829004411061715034695710861),(-14829004411061715032793877043)⟩,⟨(-42807648442703145244958936993),(-42807648442703145242529812494)⟩⟩,⟨⟨(-14459461977215688468559415374),(-14459461977215688466699046217)⟩,⟨(-41740871324413180699607064281),(-41740871324413180697221357157)⟩⟩,⟨⟨(-14090441693045962458757131971),(-14090441693045962456946675298)⟩,⟨(-40675601522404063165034389005),(-40675601522404063162716593801)⟩⟩,⟨⟨(-13716512663740494236534654465),(-13716512663740494234773819737)⟩,⟨(-39596161393767425468439125158),(-39596161393767425466187389897)⟩⟩,⟨⟨(-13343396554569321851859477186),(-13343396554569321850147631227)⟩,⟨(-38519067963422614614521117339),(-38519067963422614612333782005)⟩⟩,⟨⟨(-12965295463818583364513652826),(-12965295463818583362852269401)⟩,⟨(-37427584130793464684487181989),(-37427584130793464682367471974)⟩⟩] +lemma amp4_12_13_eq : ∀ k : Fin 16, amp4_1Expr 2 13 k = amp4_12_13 k := by decide +kernel +noncomputable def amp4_12_14 : Fin 16 → CBox := ![⟨⟨(-12588319915260722391577861152),(-12588319915260722389961156796)⟩,⟨(-36339349458604525327590629677),(-36339349458604525325522081889)⟩⟩,⟨⟨(-12206261841045965250595624672),(-12206261841045965249029220928)⟩,⟨(-35236442798634725059994450719),(-35236442798634725057992244024)⟩⟩,⟨⟨(-11825667778884814562530585938),(-11825667778884814561013555236)⟩,⟨(-34137762377431157504482127650),(-34137762377431157502543886587)⟩⟩,⟨⟨(-11439867680844907709681880227),(-11439867680844907708216765175)⟩,⟨(-33024053425147536340686092077),(-33024053425147536338818081890)⟩⟩,⟨⟨(-11055901047314695424352579208),(-11055901047314695422933771774)⟩,⟨(-31915637229005024095762493967),(-31915637229005024093948904129)⟩⟩,⟨⟨(-10666572908823690777353073964),(-10666572908823690775985408922)⟩,⟨(-30791743701200636931136606904),(-30791743701200636929390287484)⟩⟩,⟨⟨(-10279485372927895295310250215),(-10279485372927895293990387173)⟩,⟨(-29674318235953704693905948075),(-29674318235953704692217718700)⟩⟩,⟨⟨(-9886841054724459427330406299),(-9886841054724459426062441589)⟩,⟨(-28540851721901050823329256207),(-28540851721901050821709794934)⟩⟩,⟨⟨(-9496891073954188851456826602),(-9496891073954188850240003190)⟩,⟨(-27415163090060025286325462863),(-27415163090060025284773140493)⟩⟩,⟨⟨(-9101138730168082674232913894),(-9101138730168082673065567019)⟩,⟨(-26272724478973356683211010373),(-26272724478973356681719823431)⟩⟩,⟨⟨(-8708593155276932933142415166),(-8708593155276932932026972210)⟩,⟨(-25139543012310348165837380239),(-25139543012310348164414997914)⟩⟩,⟨⟨(-8309934963699564222665112102),(-8309934963699564221599926252)⟩,⟨(-23988715941201132047561012243),(-23988715941201132046201418828)⟩⟩,⟨⟨(-7915071511567247980077063004),(-7915071511567247979061643533)⟩,⟨(-22848843339292443596401105301),(-22848843339292443595103667500)⟩⟩,⟨⟨(-7513700288185479522157104311),(-7513700288185479521194543595)⟩,⟨(-21690184419970276426626983255),(-21690184419970276425399284656)⟩⟩,⟨⟨(-7116811458893626802648168213),(-7116811458893626801736118436)⟩,⟨(-20544465057820243452677831471),(-20544465057820243451514019773)⟩⟩,⟨⟨(-6712905375084154822142955036),(-6712905375084154821282461715)⟩,⟨(-19378488626746612489587063996),(-19378488626746612488488708842)⟩⟩] +lemma amp4_12_14_eq : ∀ k : Fin 16, amp4_1Expr 2 14 k = amp4_12_14 k := by decide +kernel +noncomputable def amp4_12_15 : Fin 16 → CBox := ![⟨⟨(-6314304889329281698523062305),(-6314304889329281697713830888)⟩,⟨(-18227828137998154550481421546),(-18227828137998154549448767818)⟩⟩,⟨⟨(-5908018787060499828170500835),(-5908018787060499827413692225)⟩,⟨(-17054981185433729371002756131),(-17054981185433729370037568605)⟩⟩,⟨⟨(-5508052685234101318239174571),(-5508052685234101317534116317)⟩,⟨(-15900378502652747126803107737),(-15900378502652747125904749786)⟩⟩,⟨⟨(-5099502883647184282077408212),(-5099502883647184281424325216)⟩,⟨(-14720996813034873395964010471),(-14720996813034873395131359491)⟩⟩,⟨⟨(-4698569893355039727842339540),(-4698569893355039727240577959)⟩,⟨(-13563602963674017037119624164),(-13563602963674017036352364928)⟩⟩,⟨⟨(-4287805485929443700694232548),(-4287805485929443700145238507)⟩,⟨(-12377828257670592144401420926),(-12377828257670592143701698642)⟩⟩,⟨⟨(-3886397599776523265656531705),(-3886397599776523265159392727)⟩,⟨(-11219063502044455816453206986),(-11219063502044455815820318927)⟩⟩,⟨⟨(-3473340580412691300729569838),(-3473340580412691300285022706)⟩,⟨(-10026670595442591581967196067),(-10026670595442591581400864534)⟩⟩,⟨⟨(-3072133445990435320416943639),(-3072133445990435320024007041)⟩,⟨(-8868485360145152284942285064),(-8868485360145152284442123303)⟩⟩,⟨⟨(-2656435792071101113482234197),(-2656435792071101113142650508)⟩,⟨(-7668469598186034814458232414),(-7668469598186034814026279102)⟩⟩,⟨⟨(-2256524817754308918072865955),(-2256524817754308917784723664)⟩,⟨(-6514026054817607367106107671),(-6514026054817607366740103428)⟩⟩,⟨⟨(-1837153108049314193401197363),(-1837153108049314193166809168)⟩,⟨(-5303404207374145887145773677),(-5303404207374145886848377612)⟩⟩,⟨⟨(-1440842106367455813600055571),(-1440842106367455813416633976)⟩,⟨(-4159352889854990063801934004),(-4159352889854990063569859490)⟩⟩,⟨⟨(-1014414495963543606981497599),(-1014414495963543606852616712)⟩,⟨(-2928362411572052199966330142),(-2928362411572052199803678082)⟩⟩,⟨⟨(-629264447029517718507050623),(-629264447029517718427961722)⟩,⟨(-1816529989419765287780884478),(-1816529989419765287682466990)⟩⟩,⟨⟨(-178776584874023315358765569),(-178776584874023315336812836)⟩,⟨(-516083547009096694073668717),(-516083547009096694047199623)⟩⟩] +lemma amp4_12_15_eq : ∀ k : Fin 16, amp4_1Expr 2 15 k = amp4_12_15 k := by decide +kernel +noncomputable def amp4_12 : Fin 16 → Fin 16 → CBox := ![amp4_12_0,amp4_12_1,amp4_12_2,amp4_12_3,amp4_12_4,amp4_12_5,amp4_12_6,amp4_12_7,amp4_12_8,amp4_12_9,amp4_12_10,amp4_12_11,amp4_12_12,amp4_12_13,amp4_12_14,amp4_12_15] +lemma amp4_12_eq (i k : Fin 16) : amp4_1Expr 2 i k = amp4_12 i k := by + fin_cases i + · exact amp4_12_0_eq k + · exact amp4_12_1_eq k + · exact amp4_12_2_eq k + · exact amp4_12_3_eq k + · exact amp4_12_4_eq k + · exact amp4_12_5_eq k + · exact amp4_12_6_eq k + · exact amp4_12_7_eq k + · exact amp4_12_8_eq k + · exact amp4_12_9_eq k + · exact amp4_12_10_eq k + · exact amp4_12_11_eq k + · exact amp4_12_12_eq k + · exact amp4_12_13_eq k + · exact amp4_12_14_eq k + · exact amp4_12_15_eq k +noncomputable def amp4_13_0 : Fin 16 → CBox := ![⟨⟨(-178776584874023315358765569),(-178776584874023315336812836)⟩,⟨(-103216709401819338825176732),(-103216709401819338801440803)⟩⟩,⟨⟨(-629264447029517718507050623),(-629264447029517718427961722)⟩,⟨(-363305997883953057592934514),(-363305997883953057508337796)⟩⟩,⟨⟨(-1014414495963543606981497599),(-1014414495963543606852616712)⟩,⟨(-585672482314410440052521657),(-585672482314410439915346987)⟩⟩,⟨⟨(-1440842106367455813600055571),(-1440842106367455813416633976)⟩,⟨(-831870577970998012844551612),(-831870577970998012649503332)⟩⟩,⟨⟨(-1837153108049314193401197363),(-1837153108049314193166809168)⟩,⟨(-1060680841474829177536469509),(-1060680841474829177287474547)⟩⟩,⟨⟨(-2256524817754308918072865955),(-2256524817754308917784723664)⟩,⟨(-1302805210963521473553033330),(-1302805210963521473247055480)⟩⟩,⟨⟨(-2656435792071101113482234197),(-2656435792071101113142650508)⟩,⟨(-1533693919637206963046818528),(-1533693919637206962686397130)⟩⟩,⟨⟨(-3072133445990435320416943639),(-3072133445990435320024007041)⟩,⟨(-1773697072029030457167911465),(-1773697072029030456750966131)⟩⟩,⟨⟨(-3473340580412691300729569838),(-3473340580412691300285022706)⟩,⟨(-2005334119088518316596329629),(-2005334119088518316124762897)⟩⟩,⟨⟨(-3886397599776523265656531705),(-3886397599776523265159392727)⟩,⟨(-2243812700408891163517659971),(-2243812700408891162990172088)⟩⟩,⟨⟨(-4287805485929443700694232548),(-4287805485929443700145238507)⟩,⟨(-2475565651534118429130750448),(-2475565651534118428548487569)⟩⟩,⟨⟨(-4698569893355039727842339540),(-4698569893355039727240577959)⟩,⟨(-2712720592734803407698385334),(-2712720592734803407060241718)⟩⟩,⟨⟨(-5099502883647184282077408212),(-5099502883647184281424325216)⟩,⟨(-2944199362606974679490682545),(-2944199362606974678798101417)⟩⟩,⟨⟨(-5508052685234101318239174571),(-5508052685234101317534116317)⟩,⟨(-3180075700530549425682366873),(-3180075700530549424934499458)⟩⟩,⟨⟨(-5908018787060499828170500835),(-5908018787060499827413692225)⟩,⟨(-3410996237086745874545660022),(-3410996237086745873743167270)⟩⟩,⟨⟨(-6314304889329281698523062305),(-6314304889329281697713830888)⟩,⟨(-3645565627599630910465125749),(-3645565627599630909607228380)⟩⟩] +lemma amp4_13_0_eq : ∀ k : Fin 16, amp4_1Expr 3 0 k = amp4_13_0 k := by decide +kernel +noncomputable def amp4_13_1 : Fin 16 → CBox := ![⟨⟨(-6712905375084154822142955036),(-6712905375084154821282461715)⟩,⟨(-3875697725349322498309537938),(-3875697725349322497397381736)⟩⟩,⟨⟨(-7116811458893626802648168213),(-7116811458893626801736118436)⟩,⟨(-4108893011564048690951285052),(-4108893011564048689984371681)⟩⟩,⟨⟨(-7513700288185479522157104311),(-7513700288185479521194543595)⟩,⟨(-4338036883994055285764299124),(-4338036883994055284743666395)⟩⟩,⟨⟨(-7915071511567247980077063004),(-7915071511567247979061643533)⟩,⟨(-4569768667858488719742569082),(-4569768667858488718666584141)⟩⟩,⟨⟨(-8309934963699564222665112102),(-8309934963699564221599926252)⟩,⟨(-4797743188240226409997615876),(-4797743188240226408868466766)⟩⟩,⟨⟨(-8708593155276932933142415166),(-8708593155276932932026972210)⟩,⟨(-5027908602462069633676176545),(-5027908602462069632493345152)⟩⟩,⟨⟨(-9101138730168082674232913894),(-9101138730168082673065567019)⟩,⟨(-5254544895794671337173832582),(-5254544895794671335936746325)⟩⟩,⟨⟨(-9496891073954188851456826602),(-9496891073954188850240003190)⟩,⟨(-5483032618012005057819840409),(-5483032618012005056529702325)⟩⟩,⟨⟨(-9886841054724459427330406299),(-9886841054724459426062441589)⟩,⟨(-5708170344380210165243377470),(-5708170344380210163899585420)⟩⟩,⟨⟨(-10279485372927895295310250215),(-10279485372927895293990387173)⟩,⟨(-5934863647190740939381651622),(-5934863647190740937983601824)⟩⟩,⟨⟨(-10666572908823690777353073964),(-10666572908823690775985408922)⟩,⟨(-6158348740240127386850394574),(-6158348740240127385400795864)⟩⟩,⟨⟨(-11055901047314695424352579208),(-11055901047314695422933771774)⟩,⟨(-6383127445801004819798314054),(-6383127445801004818295099222)⟩⟩,⟨⟨(-11439867680844907709681880227),(-11439867680844907708216765175)⟩,⟨(-6604810685029507268805462559),(-6604810685029507267251754698)⟩⟩,⟨⟨(-11825667778884814562530585938),(-11825667778884814561013555236)⟩,⟨(-6827552475486231501587205656),(-6827552475486231499979653524)⟩⟩,⟨⟨(-12206261841045965250595624672),(-12206261841045965249029220928)⟩,⟨(-7047288559726945012711902149),(-7047288559726945011052295836)⟩⟩,⟨⟨(-12588319915260722391577861152),(-12588319915260722389961156796)⟩,⟨(-7267869891720905066253455338),(-7267869891720905064541168728)⟩⟩] +lemma amp4_13_1_eq : ∀ k : Fin 16, amp4_1Expr 3 1 k = amp4_13_1 k := by decide +kernel +noncomputable def amp4_13_2 : Fin 16 → CBox := ![⟨⟨(-12965295463818583364513652826),(-12965295463818583362852269401)⟩,⟨(-7485516826158692937654786308),(-7485516826158692935893379475)⟩⟩,⟨⟨(-13343396554569321851859477186),(-13343396554569321850147631227)⟩,⟨(-7703813592684522923683659634),(-7703813592684522921869723850)⟩⟩,⟨⟨(-13716512663740494236534654465),(-13716512663740494234773819737)⟩,⟨(-7919232278753485094489056262),(-7919232278753485092623750844)⟩⟩,⟨⟨(-14090441693045962458757131971),(-14090441693045962456946675298)⟩,⟨(-8135120304480812633829951582),(-8135120304480812631912860668)⟩⟩,⟨⟨(-14459461977215688468559415374),(-14459461977215688466699046217)⟩,⟨(-8348174264882636140766042450),(-8348174264882636138797302016)⟩⟩,⟨⟨(-14829004411061715034695710861),(-14829004411061715032793877043)⟩,⟨(-8561529688540629049858003305),(-8561529688540629047842458399)⟩⟩,⟨⟨(-15193696708276728728983496961),(-15193696708276728727033539304)⟩,⟨(-8772084884509100212778932975),(-8772084884509100210713039011)⟩⟩,⟨⟨(-15558639082871133558661363157),(-15558639082871133556664407238)⟩,⟨(-8982784462719881083887804717),(-8982784462719881081772196077)⟩⟩,⟨⟨(-15918775249752562215523661662),(-15918775249752562213479140480)⟩,⟨(-9190709175613793906018854802),(-9190709175613793903853501501)⟩⟩,⟨⟨(-16278905600962081268047303555),(-16278905600962081265954963608)⟩,⟨(-9398630530827964199540065688),(-9398630530827964197324821729)⟩⟩,⟨⟨(-16634261386743642868154054844),(-16634261386743642866014549168)⟩,⟨(-9603795289407039777168155730),(-9603795289407039774903693560)⟩⟩,⟨⟨(-16989369609173106075022967458),(-16989369609173106072846054527)⟩,⟨(-9808817117218139861355995410),(-9808817117218139859047964405)⟩⟩,⟨⟨(-17339724586802453972053453436),(-17339724586802453969828385704)⟩,⟨(-10011094657864369182498282040),(-10011094657864369180140771200)⟩⟩,⟨⟨(-17689602740734276712264805885),(-17689602740734276709993209188)⟩,⟨(-10213096904220476361658575585),(-10213096904220476359252553090)⟩⟩,⟨⟨(-18034740279655822664809928891),(-18034740279655822662491093793)⟩,⟨(-10412362155224275856949550839),(-10412362155224275854494900415)⟩⟩,⟨⟨(-18379182858626920877843864247),(-18379182858626920875481321955)⟩,⟨(-10611226170913608340851364121),(-10611226170913608338350167510)⟩⟩] +lemma amp4_13_2_eq : ∀ k : Fin 16, amp4_1Expr 3 2 k = amp4_13_2 k := by decide +kernel +noncomputable def amp4_13_3 : Fin 16 → CBox := ![⟨⟨(-18718890128322294126288120193),(-18718890128322294123880290226)⟩,⟨(-10807356254517904884635516576),(-10807356254517904882087154276)⟩⟩,⟨⟨(-19057694296448717009390957883),(-19057694296448717006937569444)⟩,⟨(-11002964932188262361616673664),(-11002964932188262359021045208)⟩⟩,⟨⟨(-19391762292844942227237566277),(-19391762292844942224738894847)⟩,⟨(-11195839179835261920953592091),(-11195839179835261918311149572)⟩⟩,⟨⟨(-19724728098486747678323726575),(-19724728098486747675796515857)⟩,⟨(-11388077077353498911247960857),(-11388077077353498908568439452)⟩⟩,⟨⟨(-20052951687444352545342758765),(-20052951687444352542769798976)⟩,⟨(-11577577054792557159816808895),(-11577577054792557157090565948)⟩⟩,⟨⟨(-20379882258044908825350598503),(-20379882258044908822733555855)⟩,⟨(-11766330507735106279034141479),(-11766330507735106276262218982)⟩⟩,⟨⟨(-20702060231618653079221408986),(-20702060231618653076561031506)⟩,⟨(-11952340047504875659904013997),(-11952340047504875657087137883)⟩⟩,⟨⟨(-21022761953305465946565800651),(-21022761953305465943863036419)⟩,⟨(-12137497272850333511785586677),(-12137497272850333508924395661)⟩⟩,⟨⟨(-21338697095528772244580996200),(-21338697095528772241835440077)⟩,⟨(-12319902512259422103906621150),(-12319902512259422101001176249)⟩⟩,⟨⟨(-21652979780165887257991134678),(-21652979780165887255207097737)⟩,⟨(-12501353704836298718642301037),(-12501353704836298715695193492)⟩⟩,⟨⟨(-21962478939877190905134537735),(-21962478939877190902308658719)⟩,⟨(-12680043128009582856449318807),(-12680043128009582853458903970)⟩⟩,⟨⟨(-22270155981605558914012891964),(-22270155981605558911147110727)⟩,⟨(-12857680550874923845578707971),(-12857680550874923842546218557)⟩⟩,⟨⟨(-22573030150397963508191345851),(-22573030150397963505285504176)⟩,⟨(-13032545033757802789004428604),(-13032545033757802785930070437)⟩⟩,⟨⟨(-22873918673218157795525142681),(-22873918673218157792579696515)⟩,⟨(-13206263103404110815613206305),(-13206263103404110812497365484)⟩⟩,⟨⟨(-23169983067012150235321094158),(-23169983067012150232336266873)⟩,⟨(-13377195960858535718342826665),(-13377195960858535715185930639)⟩⟩,⟨⟨(-23463904064604503191343548921),(-23463904064604503188319868770)⟩,⟨(-13546891327938964043731326347),(-13546891327938964040533812723)⟩⟩] +lemma amp4_13_3_eq : ∀ k : Fin 16, amp4_1Expr 3 3 k = amp4_13_3 k := by decide +kernel +noncomputable def amp4_13_4 : Fin 16 → CBox := ![⟨⟨(-23752978207657740002414861991),(-23752978207657739999378175643)⟩,⟨(-13713788362246510703312394861),(-13713788362246510700089486110)⟩⟩,⟨⟨(-24039756676364397078308656530),(-24039756676364397075229885397)⟩,⟨(-13879359988352087834555644396),(-13879359988352087831290694030)⟩⟩,⟨⟨(-24321664486771101361521338523),(-24321664486771101358402068637)⟩,⟨(-14042119538577056535953158015),(-14042119538577056532647383094)⟩⟩,⟨⟨(-24601129552458858922076671968),(-24601129552458858918918249600)⟩,⟨(-14203468769480979810292850301),(-14203468769480979806947179236)⟩⟩,⟨⟨(-24875699428374202215065281678),(-24875699428374202211868617394)⟩,⟨(-14361991761252065404370241243),(-14361991761252065400985502631)⟩⟩,⟨⟨(-25147684467739387133942982428),(-25147684467739387130707579359)⟩,⟨(-14519022396945105877555033570),(-14519022396945105874131100476)⟩⟩,⟨⟨(-25414749373705691728695780367),(-25414749373705691725424753641)⟩,⟨(-14673212392295853927250051354),(-14673212392295853923789026722)⟩⟩,⟨⟨(-25679092130460598067111169402),(-25679092130460598063803185154)⟩,⟨(-14825830754066626866157102340),(-14825830754066626862658384494)⟩⟩,⟨⟨(-25938489683322627375758139803),(-25938489683322627372413316740)⟩,⟨(-14975594001038649666674389312),(-14975594001038649663138352762)⟩⟩,⟨⟨(-26195032379608320407671337080),(-26195032379608320404297628895)⟩,⟨(-15123708995797826944424003221),(-15123708995797826940855416674)⟩⟩,⟨⟨(-26446604933591878658536403476),(-26446604933591878655126418505)⟩,⟨(-15268954477560955960027253972),(-15268954477560955956422157369)⟩⟩,⟨⟨(-26695194376888032121202696672),(-26695194376888032117758266210)⟩,⟨(-15412477659565689371607216131),(-15412477659565689367966851345)⟩⟩,⟨⟨(-26938789107485135130320965458),(-26938789107485135126841880085)⟩,⟨(-15553117142849101161572385249),(-15553117142849101157896940411)⟩⟩,⟨⟨(-27179276793229187800563675830),(-27179276793229187797053266443)⟩,⟨(-15691962772950220097161456193),(-15691962772950220093453046641)⟩⟩,⟨⟨(-27414745779588332836444079228),(-27414745779588332832899924969)⟩,⟨(-15827910855610480800803381711),(-15827910855610480797060920285)⟩⟩,⟨⟨(-27646987989670052253752592280),(-27646987989670052250176942450)⟩,⟨(-15961995958118355125016693654),(-15961995958118355121241678641)⟩⟩] +lemma amp4_13_4_eq : ∀ k : Fin 16, amp4_1Expr 3 4 k = amp4_13_4 k := by decide +kernel +noncomputable def amp4_13_5 : Fin 16 → CBox := ![⟨⟨(-27874188295234711904124620360),(-27874188295234711900517247120)⟩,⟨(-16093170115696076602701308990),(-16093170115696076598893920808)⟩⟩,⟨⟨(-28098046192495536942281246287),(-28098046192495536938642704730)⟩,⟨(-16222414532939837526561795553),(-16222414532939837522722561490)⟩⟩,⟨⟨(-28316839943670277255521058437),(-28316839943670277251851184311)⟩,⟨(-16348735164077581844761397811),(-16348735164077581840890536370)⟩⟩,⟨⟨(-28532179662507527618377860853),(-28532179662507527614677402330)⟩,⟨(-16473061608715486667799792950),(-16473061608715486663897949804)⟩⟩,⟨⟨(-28742434125160893644268918042),(-28742434125160893640538204035)⟩,⟨(-16594452079326727659834322576),(-16594452079326727655902002263)⟩⟩,⟨⟨(-28949126858313515183770431249),(-28949126858313515180060431506)⟩,⟨(-16713786184451933191271880254),(-16713786184451933187338730549)⟩⟩,⟨⟨(-29150714511951410422711017771),(-29150714511951410418969083737)⟩,⟨(-16830172870545077049013139345),(-16830172870545077045049079459)⟩⟩,⟨⟨(-29348636593525162301659934113),(-29348636593525162297887903943)⟩,⟨(-16944443237620253765703464501),(-16944443237620253761709782494)⟩⟩,⟨⟨(-29541435202988933495999911232),(-29541435202988933492199281613)⟩,⟨(-17055755566693547594234004535),(-17055755566693547590211881527)⟩⟩,⟨⟨(-29730468187763879469240190126),(-29730468187763879465411644358)⟩,⟨(-17164893811339081080608019390),(-17164893811339081076558082876)⟩⟩,⟨⟨(-29914360872324529844545709670),(-29914360872324529840691130344)⟩,⟨(-17271064302272175512510728532),(-17271064302272175508434383474)⟩⟩,⟨⟨(-30094391611375639622379480534),(-30094391611375639618499660913)⟩,⟨(-17375005097925741014026802604),(-17375005097925741009924745945)⟩⟩,⟨⟨(-30269266911110177885982904835),(-30269266911110177882076776762)⟩,⟨(-17475969399302093171522248520),(-17475969399302093167394182542)⟩⟩,⟨⟨(-30440187623762200863122675824),(-30440187623762200859193352137)⟩,⟨(-17574650518761821311582287370),(-17574650518761821307430253957)⟩⟩,⟨⟨(-30605939563110598319834853461),(-30605939563110598315881412140)⟩,⟨(-17670347445563321106158700337),(-17670347445563321101982486968)⟩⟩,⟨⟨(-30767647905240686650232053835),(-30767647905240686646254582069)⟩,⟨(-17763709800422335704717948757),(-17763709800422335700517855962)⟩⟩] +lemma amp4_13_5_eq : ∀ k : Fin 16, amp4_1Expr 3 5 k = amp4_13_5 k := by decide +kernel +noncomputable def amp4_13_6 : Fin 16 → CBox := ![⟨⟨(-30924176053652663076921910845),(-30924176053652663072926426407)⟩,⟨(-17854081369043743987305342052),(-17854081369043743983085164710)⟩⟩,⟨⟨(-31076575182348133093629660522),(-31076575182348133089610286425)⟩,⟨(-17942069047020338021828753448),(-17942069047020338017585353956)⟩⟩,⟨⟨(-31223784711938343741732883253),(-31223784711938343737693609664)⟩,⟨(-18027060508556524318875523987),(-18027060508556524314611527166)⟩⟩,⟨⟨(-31366783346512185483913737608),(-31366783346512185479851889162)⟩,⟨(-18109620808721480774497857250),(-18109620808721480770211979021)⟩⟩,⟨⟨(-31504585086650592895467604247),(-31504585086650592891385676299)⟩,⟨(-18189180680485189151120255070),(-18189180680485189146814257675)⟩⟩,⟨⟨(-31638097566013635101048593984),(-31638097566013635096946201055)⟩,⟨(-18266264146385615923147085524),(-18266264146385615918821011799)⟩⟩,⟨⟨(-31766408054785126238285272401),(-31766408054785126234180296673)⟩,⟨(-18340344241617688785294981399),(-18340344241617688780959477490)⟩⟩,⟨⟨(-31890354391170951219071539466),(-31890354391170951214945815276)⟩,⟨(-18411904692295112744539287956),(-18411904692295112740184135938)⟩⟩,⟨⟨(-32009095923644769043671428880),(-32009095923644769039527319219)⟩,⟨(-18480460148032860154908312895),(-18480460148032860150535199080)⟩⟩,⟨⟨(-32123401852681396184602184449),(-32123401852681396180441241813)⟩,⟨(-18546454706932127094763647965),(-18546454706932127090373743133)⟩⟩,⟨⟨(-32232502525936830264300271483),(-32232502525936830260122126548)⟩,⟨(-18609444010004921364968177063),(-18609444010004921360561590052)⟩⟩,⟨⟨(-32337099553057724192535989970),(-32337099553057724188343225889)⟩,⟨(-18669833131769604061193078407),(-18669833131769604056771579256)⟩⟩,⟨⟨(-32436493307917857223852181715),(-32436493307917857219644451829)⟩,⟨(-18727218142893869540956196846),(-18727218142893869536519907355)⟩⟩,⟨⟨(-32531318751103864922259274286),(-32531318751103864918036016014)⟩,⟨(-18781965638043336649830619861),(-18781965638043336645379497883)⟩⟩,⟨⟨(-32620945410534091406341004673),(-32620945410534091402111212759)⟩,⟨(-18833711613991944820964723960),(-18833711613991944816504284277)⟩⟩,⟨⟨(-32705942439377387424011565051),(-32705942439377387419768378943)⟩,⟨(-18882784671474940162192409028),(-18882784671474940157718977150)⟩⟩] +lemma amp4_13_6_eq : ∀ k : Fin 16, amp4_1Expr 3 6 k = amp4_13_6 k := by decide +kernel +noncomputable def amp4_13_7 : Fin 16 → CBox := ![⟨⟨(-32785747743509981349802035219),(-32785747743509981345547052918)⟩,⟨(-18928860285298653218726657019),(-18928860285298653214241476782)⟩⟩,⟨⟨(-32860865414590931775215449629),(-32860865414590931770948270348)⟩,⟨(-18972229492918137713424758664),(-18972229492918137708927888713)⟩⟩,⟨⟨(-32930801052341203475618237852),(-32930801052341203471344043036)⟩,⟨(-19012606852199205233253140457),(-19012606852199205228747892930)⟩⟩,⟨⟨(-32995994340909188940784701606),(-32995994340909188936500465978)⟩,⟨(-19050246214903288593543375045),(-19050246214903288589028296724)⟩⟩,⟨⟨(-33056017978152788410200234984),(-33056017978152788405909372116)⟩,⟨(-19084900878023621193842129260),(-19084900878023621189319510834)⟩⟩,⟨⟨(-33111247806102404780303402430),(-33111247806102404776003484834)⟩,⟨(-19116787834057628921918952907),(-19116787834057628917387689476)⟩⟩,⟨⟨(-33161323110387142482032177801),(-33161323110387142477726044956)⟩,⟨(-19145698824466174654466611574),(-19145698824466174649928661439)⟩⟩,⟨⟨(-33206556370521783193478490630),(-33206556370521783189166719653)⟩,⟨(-19171814259381233836974649130),(-19171814259381233832430645083)⟩⟩,⟨⟨(-33246653032290985854436658574),(-33246653032290985850119739559)⟩,⟨(-19194964077847288369338283962),(-19194964077847288364788826777)⟩⟩,⟨⟨(-33281862608866566226679727672),(-33281862608866566222357853170)⟩,⟨(-19215292336361252438961595181),(-19215292336361252434407098410)⟩⟩,⟨⟨(-33311956359174495042091913884),(-33311956359174495037766820132)⟩,⟨(-19232666971202460523783014775),(-19232666971202460519224797366)⟩⟩,⟨⟨(-33337121144716975243090835120),(-33337121144716975238762859751)⟩,⟨(-19247195866909510670455166300),(-19247195866909510665893728159)⟩⟩,⟨⟨(-33357193769420233718372893001),(-33357193769420233714043683511)⟩,⟨(-19258784802185279283141689374),(-19258784802185279278578296752)⟩⟩,⟨⟨(-33372298677811606175284598902),(-33372298677811606170955096213)⟩,⟨(-19267505625111122808221037815),(-19267505625111122803656541323)⟩⟩,⟨⟨(-33382338028223777529203552288),(-33382338028223777524875249376)⟩,⟨(-19273301846774078919777741361),(-19273301846774078915213316390)⟩⟩,⟨⟨(-33387374004052282218395336386),(-33387374004052282214070029472)⟩,⟨(-19276209368774298550717118963),(-19276209368774298546154112141)⟩⟩] +lemma amp4_13_7_eq : ∀ k : Fin 16, amp4_1Expr 3 7 k = amp4_13_7 k := by decide +kernel +noncomputable def amp4_13_8 : Fin 16 → CBox := ![⟨⟨(-33387374004052282218395336386),(-33387374004052282214070029472)⟩,⟨(-19276209368774298550717118963),(-19276209368774298546154112141)⟩⟩,⟨⟨(-33382338028223777529203552288),(-33382338028223777524875249376)⟩,⟨(-19273301846774078919777741361),(-19273301846774078915213316390)⟩⟩,⟨⟨(-33372298677811606175284598902),(-33372298677811606170955096213)⟩,⟨(-19267505625111122808221037815),(-19267505625111122803656541323)⟩⟩,⟨⟨(-33357193769420233718372893001),(-33357193769420233714043683511)⟩,⟨(-19258784802185279283141689374),(-19258784802185279278578296752)⟩⟩,⟨⟨(-33337121144716975243090835120),(-33337121144716975238762859751)⟩,⟨(-19247195866909510670455166300),(-19247195866909510665893728159)⟩⟩,⟨⟨(-33311956359174495042091913884),(-33311956359174495037766820132)⟩,⟨(-19232666971202460523783014775),(-19232666971202460519224797366)⟩⟩,⟨⟨(-33281862608866566226679727672),(-33281862608866566222357853170)⟩,⟨(-19215292336361252438961595181),(-19215292336361252434407098410)⟩⟩,⟨⟨(-33246653032290985854436658574),(-33246653032290985850119739559)⟩,⟨(-19194964077847288369338283962),(-19194964077847288364788826777)⟩⟩,⟨⟨(-33206556370521783193478490630),(-33206556370521783189166719653)⟩,⟨(-19171814259381233836974649130),(-19171814259381233832430645083)⟩⟩,⟨⟨(-33161323110387142482032177801),(-33161323110387142477726044956)⟩,⟨(-19145698824466174654466611574),(-19145698824466174649928661439)⟩⟩,⟨⟨(-33111247806102404780303402430),(-33111247806102404776003484834)⟩,⟨(-19116787834057628921918952907),(-19116787834057628917387689476)⟩⟩,⟨⟨(-33056017978152788410200234984),(-33056017978152788405909372116)⟩,⟨(-19084900878023621193842129260),(-19084900878023621189319510834)⟩⟩,⟨⟨(-32995994340909188940784701606),(-32995994340909188936500465978)⟩,⟨(-19050246214903288593543375045),(-19050246214903288589028296724)⟩⟩,⟨⟨(-32930801052341203475618237852),(-32930801052341203471344043036)⟩,⟨(-19012606852199205233253140457),(-19012606852199205228747892930)⟩⟩,⟨⟨(-32860865414590931775215449629),(-32860865414590931770948270348)⟩,⟨(-18972229492918137713424758664),(-18972229492918137708927888713)⟩⟩,⟨⟨(-32785747743509981349802035219),(-32785747743509981345547052918)⟩,⟨(-18928860285298653218726657019),(-18928860285298653214241476782)⟩⟩] +lemma amp4_13_8_eq : ∀ k : Fin 16, amp4_1Expr 3 8 k = amp4_13_8 k := by decide +kernel +noncomputable def amp4_13_9 : Fin 16 → CBox := ![⟨⟨(-32705942439377387424011565051),(-32705942439377387419768378943)⟩,⟨(-18882784671474940162192409028),(-18882784671474940157718977150)⟩⟩,⟨⟨(-32620945410534091406341004673),(-32620945410534091402111212759)⟩,⟨(-18833711613991944820964723960),(-18833711613991944816504284277)⟩⟩,⟨⟨(-32531318751103864922259274286),(-32531318751103864918036016014)⟩,⟨(-18781965638043336649830619861),(-18781965638043336645379497883)⟩⟩,⟨⟨(-32436493307917857223852181715),(-32436493307917857219644451829)⟩,⟨(-18727218142893869540956196846),(-18727218142893869536519907355)⟩⟩,⟨⟨(-32337099553057724192535989970),(-32337099553057724188343225889)⟩,⟨(-18669833131769604061193078407),(-18669833131769604056771579256)⟩⟩,⟨⟨(-32232502525936830264300271483),(-32232502525936830260122126548)⟩,⟨(-18609444010004921364968177063),(-18609444010004921360561590052)⟩⟩,⟨⟨(-32123401852681396184602184449),(-32123401852681396180441241813)⟩,⟨(-18546454706932127094763647965),(-18546454706932127090373743133)⟩⟩,⟨⟨(-32009095923644769043671428880),(-32009095923644769039527319219)⟩,⟨(-18480460148032860154908312895),(-18480460148032860150535199080)⟩⟩,⟨⟨(-31890354391170951219071539466),(-31890354391170951214945815276)⟩,⟨(-18411904692295112744539287956),(-18411904692295112740184135938)⟩⟩,⟨⟨(-31766408054785126238285272401),(-31766408054785126234180296673)⟩,⟨(-18340344241617688785294981399),(-18340344241617688780959477490)⟩⟩,⟨⟨(-31638097566013635101048593984),(-31638097566013635096946201055)⟩,⟨(-18266264146385615923147085524),(-18266264146385615918821011799)⟩⟩,⟨⟨(-31504585086650592895467604247),(-31504585086650592891385676299)⟩,⟨(-18189180680485189151120255070),(-18189180680485189146814257675)⟩⟩,⟨⟨(-31366783346512185483913737608),(-31366783346512185479851889162)⟩,⟨(-18109620808721480774497857250),(-18109620808721480770211979021)⟩⟩,⟨⟨(-31223784711938343741732883253),(-31223784711938343737693609664)⟩,⟨(-18027060508556524318875523987),(-18027060508556524314611527166)⟩⟩,⟨⟨(-31076575182348133093629660522),(-31076575182348133089610286425)⟩,⟨(-17942069047020338021828753448),(-17942069047020338017585353956)⟩⟩,⟨⟨(-30924176053652663076921910845),(-30924176053652663072926426407)⟩,⟨(-17854081369043743987305342052),(-17854081369043743983085164710)⟩⟩] +lemma amp4_13_9_eq : ∀ k : Fin 16, amp4_1Expr 3 9 k = amp4_13_9 k := by decide +kernel +noncomputable def amp4_13_10 : Fin 16 → CBox := ![⟨⟨(-30767647905240686650232053835),(-30767647905240686646254582069)⟩,⟨(-17763709800422335704717948757),(-17763709800422335700517855962)⟩⟩,⟨⟨(-30605939563110598319834853461),(-30605939563110598315881412140)⟩,⟨(-17670347445563321106158700337),(-17670347445563321101982486968)⟩⟩,⟨⟨(-30440187623762200863122675824),(-30440187623762200859193352137)⟩,⟨(-17574650518761821311582287370),(-17574650518761821307430253957)⟩⟩,⟨⟨(-30269266911110177885982904835),(-30269266911110177882076776762)⟩,⟨(-17475969399302093171522248520),(-17475969399302093167394182542)⟩⟩,⟨⟨(-30094391611375639622379480534),(-30094391611375639618499660913)⟩,⟨(-17375005097925741014026802604),(-17375005097925741009924745945)⟩⟩,⟨⟨(-29914360872324529844545709670),(-29914360872324529840691130344)⟩,⟨(-17271064302272175512510728532),(-17271064302272175508434383474)⟩⟩,⟨⟨(-29730468187763879469240190126),(-29730468187763879465411644358)⟩,⟨(-17164893811339081080608019390),(-17164893811339081076558082876)⟩⟩,⟨⟨(-29541435202988933495999911232),(-29541435202988933492199281613)⟩,⟨(-17055755566693547594234004535),(-17055755566693547590211881527)⟩⟩,⟨⟨(-29348636593525162301659934113),(-29348636593525162297887903943)⟩,⟨(-16944443237620253765703464501),(-16944443237620253761709782494)⟩⟩,⟨⟨(-29150714511951410422711017771),(-29150714511951410418969083737)⟩,⟨(-16830172870545077049013139345),(-16830172870545077045049079459)⟩⟩,⟨⟨(-28949126858313515183770431249),(-28949126858313515180060431506)⟩,⟨(-16713786184451933191271880254),(-16713786184451933187338730549)⟩⟩,⟨⟨(-28742434125160893644268918042),(-28742434125160893640538204035)⟩,⟨(-16594452079326727659834322576),(-16594452079326727655902002263)⟩⟩,⟨⟨(-28532179662507527618377860853),(-28532179662507527614677402330)⟩,⟨(-16473061608715486667799792950),(-16473061608715486663897949804)⟩⟩,⟨⟨(-28316839943670277255521058437),(-28316839943670277251851184311)⟩,⟨(-16348735164077581844761397811),(-16348735164077581840890536370)⟩⟩,⟨⟨(-28098046192495536942281246287),(-28098046192495536938642704730)⟩,⟨(-16222414532939837526561795553),(-16222414532939837522722561490)⟩⟩,⟨⟨(-27874188295234711904124620360),(-27874188295234711900517247120)⟩,⟨(-16093170115696076602701308990),(-16093170115696076598893920808)⟩⟩] +lemma amp4_13_10_eq : ∀ k : Fin 16, amp4_1Expr 3 10 k = amp4_13_10 k := by decide +kernel +noncomputable def amp4_13_11 : Fin 16 → CBox := ![⟨⟨(-27646987989670052253752592280),(-27646987989670052250176942450)⟩,⟨(-15961995958118355125016693654),(-15961995958118355121241678641)⟩⟩,⟨⟨(-27414745779588332836444079228),(-27414745779588332832899924969)⟩,⟨(-15827910855610480800803381711),(-15827910855610480797060920285)⟩⟩,⟨⟨(-27179276793229187800563675830),(-27179276793229187797053266443)⟩,⟨(-15691962772950220097161456193),(-15691962772950220093453046641)⟩⟩,⟨⟨(-26938789107485135130320965458),(-26938789107485135126841880085)⟩,⟨(-15553117142849101161572385249),(-15553117142849101157896940411)⟩⟩,⟨⟨(-26695194376888032121202696672),(-26695194376888032117758266210)⟩,⟨(-15412477659565689371607216131),(-15412477659565689367966851345)⟩⟩,⟨⟨(-26446604933591878658536403476),(-26446604933591878655126418505)⟩,⟨(-15268954477560955960027253972),(-15268954477560955956422157369)⟩⟩,⟨⟨(-26195032379608320407671337080),(-26195032379608320404297628895)⟩,⟨(-15123708995797826944424003221),(-15123708995797826940855416674)⟩⟩,⟨⟨(-25938489683322627375758139803),(-25938489683322627372413316740)⟩,⟨(-14975594001038649666674389312),(-14975594001038649663138352762)⟩⟩,⟨⟨(-25679092130460598067111169402),(-25679092130460598063803185154)⟩,⟨(-14825830754066626866157102340),(-14825830754066626862658384494)⟩⟩,⟨⟨(-25414749373705691728695780367),(-25414749373705691725424753641)⟩,⟨(-14673212392295853927250051354),(-14673212392295853923789026722)⟩⟩,⟨⟨(-25147684467739387133942982428),(-25147684467739387130707579359)⟩,⟨(-14519022396945105877555033570),(-14519022396945105874131100476)⟩⟩,⟨⟨(-24875699428374202215065281678),(-24875699428374202211868617394)⟩,⟨(-14361991761252065404370241243),(-14361991761252065400985502631)⟩⟩,⟨⟨(-24601129552458858922076671968),(-24601129552458858918918249600)⟩,⟨(-14203468769480979810292850301),(-14203468769480979806947179236)⟩⟩,⟨⟨(-24321664486771101361521338523),(-24321664486771101358402068637)⟩,⟨(-14042119538577056535953158015),(-14042119538577056532647383094)⟩⟩,⟨⟨(-24039756676364397078308656530),(-24039756676364397075229885397)⟩,⟨(-13879359988352087834555644396),(-13879359988352087831290694030)⟩⟩,⟨⟨(-23752978207657740002414861991),(-23752978207657739999378175643)⟩,⟨(-13713788362246510703312394861),(-13713788362246510700089486110)⟩⟩] +lemma amp4_13_11_eq : ∀ k : Fin 16, amp4_1Expr 3 11 k = amp4_13_11 k := by decide +kernel +noncomputable def amp4_13_12 : Fin 16 → CBox := ![⟨⟨(-23463904064604503191343548921),(-23463904064604503188319868770)⟩,⟨(-13546891327938964043731326347),(-13546891327938964040533812723)⟩⟩,⟨⟨(-23169983067012150235321094158),(-23169983067012150232336266873)⟩,⟨(-13377195960858535718342826665),(-13377195960858535715185930639)⟩⟩,⟨⟨(-22873918673218157795525142681),(-22873918673218157792579696515)⟩,⟨(-13206263103404110815613206305),(-13206263103404110812497365484)⟩⟩,⟨⟨(-22573030150397963508191345851),(-22573030150397963505285504176)⟩,⟨(-13032545033757802789004428604),(-13032545033757802785930070437)⟩⟩,⟨⟨(-22270155981605558914012891964),(-22270155981605558911147110727)⟩,⟨(-12857680550874923845578707971),(-12857680550874923842546218557)⟩⟩,⟨⟨(-21962478939877190905134537735),(-21962478939877190902308658719)⟩,⟨(-12680043128009582856449318807),(-12680043128009582853458903970)⟩⟩,⟨⟨(-21652979780165887257991134678),(-21652979780165887255207097737)⟩,⟨(-12501353704836298718642301037),(-12501353704836298715695193492)⟩⟩,⟨⟨(-21338697095528772244580996200),(-21338697095528772241835440077)⟩,⟨(-12319902512259422103906621150),(-12319902512259422101001176249)⟩⟩,⟨⟨(-21022761953305465946565800651),(-21022761953305465943863036419)⟩,⟨(-12137497272850333511785586677),(-12137497272850333508924395661)⟩⟩,⟨⟨(-20702060231618653079221408986),(-20702060231618653076561031506)⟩,⟨(-11952340047504875659904013997),(-11952340047504875657087137883)⟩⟩,⟨⟨(-20379882258044908825350598503),(-20379882258044908822733555855)⟩,⟨(-11766330507735106279034141479),(-11766330507735106276262218982)⟩⟩,⟨⟨(-20052951687444352545342758765),(-20052951687444352542769798976)⟩,⟨(-11577577054792557159816808895),(-11577577054792557157090565948)⟩⟩,⟨⟨(-19724728098486747678323726575),(-19724728098486747675796515857)⟩,⟨(-11388077077353498911247960857),(-11388077077353498908568439452)⟩⟩,⟨⟨(-19391762292844942227237566277),(-19391762292844942224738894847)⟩,⟨(-11195839179835261920953592091),(-11195839179835261918311149572)⟩⟩,⟨⟨(-19057694296448717009390957883),(-19057694296448717006937569444)⟩,⟨(-11002964932188262361616673664),(-11002964932188262359021045208)⟩⟩,⟨⟨(-18718890128322294126288120193),(-18718890128322294123880290226)⟩,⟨(-10807356254517904884635516576),(-10807356254517904882087154276)⟩⟩] +lemma amp4_13_12_eq : ∀ k : Fin 16, amp4_1Expr 3 12 k = amp4_13_12 k := by decide +kernel +noncomputable def amp4_13_13 : Fin 16 → CBox := ![⟨⟨(-18379182858626920877843864247),(-18379182858626920875481321955)⟩,⟨(-10611226170913608340851364121),(-10611226170913608338350167510)⟩⟩,⟨⟨(-18034740279655822664809928891),(-18034740279655822662491093793)⟩,⟨(-10412362155224275856949550839),(-10412362155224275854494900415)⟩⟩,⟨⟨(-17689602740734276712264805885),(-17689602740734276709993209188)⟩,⟨(-10213096904220476361658575585),(-10213096904220476359252553090)⟩⟩,⟨⟨(-17339724586802453972053453436),(-17339724586802453969828385704)⟩,⟨(-10011094657864369182498282040),(-10011094657864369180140771200)⟩⟩,⟨⟨(-16989369609173106075022967458),(-16989369609173106072846054527)⟩,⟨(-9808817117218139861355995410),(-9808817117218139859047964405)⟩⟩,⟨⟨(-16634261386743642868154054844),(-16634261386743642866014549168)⟩,⟨(-9603795289407039777168155730),(-9603795289407039774903693560)⟩⟩,⟨⟨(-16278905600962081268047303555),(-16278905600962081265954963608)⟩,⟨(-9398630530827964199540065688),(-9398630530827964197324821729)⟩⟩,⟨⟨(-15918775249752562215523661662),(-15918775249752562213479140480)⟩,⟨(-9190709175613793906018854802),(-9190709175613793903853501501)⟩⟩,⟨⟨(-15558639082871133558661363157),(-15558639082871133556664407238)⟩,⟨(-8982784462719881083887804717),(-8982784462719881081772196077)⟩⟩,⟨⟨(-15193696708276728728983496961),(-15193696708276728727033539304)⟩,⟨(-8772084884509100212778932975),(-8772084884509100210713039011)⟩⟩,⟨⟨(-14829004411061715034695710861),(-14829004411061715032793877043)⟩,⟨(-8561529688540629049858003305),(-8561529688540629047842458399)⟩⟩,⟨⟨(-14459461977215688468559415374),(-14459461977215688466699046217)⟩,⟨(-8348174264882636140766042450),(-8348174264882636138797302016)⟩⟩,⟨⟨(-14090441693045962458757131971),(-14090441693045962456946675298)⟩,⟨(-8135120304480812633829951582),(-8135120304480812631912860668)⟩⟩,⟨⟨(-13716512663740494236534654465),(-13716512663740494234773819737)⟩,⟨(-7919232278753485094489056262),(-7919232278753485092623750844)⟩⟩,⟨⟨(-13343396554569321851859477186),(-13343396554569321850147631227)⟩,⟨(-7703813592684522923683659634),(-7703813592684522921869723850)⟩⟩,⟨⟨(-12965295463818583364513652826),(-12965295463818583362852269401)⟩,⟨(-7485516826158692937654786308),(-7485516826158692935893379475)⟩⟩] +lemma amp4_13_13_eq : ∀ k : Fin 16, amp4_1Expr 3 13 k = amp4_13_13 k := by decide +kernel +noncomputable def amp4_13_14 : Fin 16 → CBox := ![⟨⟨(-12588319915260722391577861152),(-12588319915260722389961156796)⟩,⟨(-7267869891720905066253455338),(-7267869891720905064541168728)⟩⟩,⟨⟨(-12206261841045965250595624672),(-12206261841045965249029220928)⟩,⟨(-7047288559726945012711902149),(-7047288559726945011052295836)⟩⟩,⟨⟨(-11825667778884814562530585938),(-11825667778884814561013555236)⟩,⟨(-6827552475486231501587205656),(-6827552475486231499979653524)⟩⟩,⟨⟨(-11439867680844907709681880227),(-11439867680844907708216765175)⟩,⟨(-6604810685029507268805462559),(-6604810685029507267251754698)⟩⟩,⟨⟨(-11055901047314695424352579208),(-11055901047314695422933771774)⟩,⟨(-6383127445801004819798314054),(-6383127445801004818295099222)⟩⟩,⟨⟨(-10666572908823690777353073964),(-10666572908823690775985408922)⟩,⟨(-6158348740240127386850394574),(-6158348740240127385400795864)⟩⟩,⟨⟨(-10279485372927895295310250215),(-10279485372927895293990387173)⟩,⟨(-5934863647190740939381651622),(-5934863647190740937983601824)⟩⟩,⟨⟨(-9886841054724459427330406299),(-9886841054724459426062441589)⟩,⟨(-5708170344380210165243377470),(-5708170344380210163899585420)⟩⟩,⟨⟨(-9496891073954188851456826602),(-9496891073954188850240003190)⟩,⟨(-5483032618012005057819840409),(-5483032618012005056529702325)⟩⟩,⟨⟨(-9101138730168082674232913894),(-9101138730168082673065567019)⟩,⟨(-5254544895794671337173832582),(-5254544895794671335936746325)⟩⟩,⟨⟨(-8708593155276932933142415166),(-8708593155276932932026972210)⟩,⟨(-5027908602462069633676176545),(-5027908602462069632493345152)⟩⟩,⟨⟨(-8309934963699564222665112102),(-8309934963699564221599926252)⟩,⟨(-4797743188240226409997615876),(-4797743188240226408868466766)⟩⟩,⟨⟨(-7915071511567247980077063004),(-7915071511567247979061643533)⟩,⟨(-4569768667858488719742569082),(-4569768667858488718666584141)⟩⟩,⟨⟨(-7513700288185479522157104311),(-7513700288185479521194543595)⟩,⟨(-4338036883994055285764299124),(-4338036883994055284743666395)⟩⟩,⟨⟨(-7116811458893626802648168213),(-7116811458893626801736118436)⟩,⟨(-4108893011564048690951285052),(-4108893011564048689984371681)⟩⟩,⟨⟨(-6712905375084154822142955036),(-6712905375084154821282461715)⟩,⟨(-3875697725349322498309537938),(-3875697725349322497397381736)⟩⟩] +lemma amp4_13_14_eq : ∀ k : Fin 16, amp4_1Expr 3 14 k = amp4_13_14 k := by decide +kernel +noncomputable def amp4_13_15 : Fin 16 → CBox := ![⟨⟨(-6314304889329281698523062305),(-6314304889329281697713830888)⟩,⟨(-3645565627599630910465125749),(-3645565627599630909607228380)⟩⟩,⟨⟨(-5908018787060499828170500835),(-5908018787060499827413692225)⟩,⟨(-3410996237086745874545660022),(-3410996237086745873743167270)⟩⟩,⟨⟨(-5508052685234101318239174571),(-5508052685234101317534116317)⟩,⟨(-3180075700530549425682366873),(-3180075700530549424934499458)⟩⟩,⟨⟨(-5099502883647184282077408212),(-5099502883647184281424325216)⟩,⟨(-2944199362606974679490682545),(-2944199362606974678798101417)⟩⟩,⟨⟨(-4698569893355039727842339540),(-4698569893355039727240577959)⟩,⟨(-2712720592734803407698385334),(-2712720592734803407060241718)⟩⟩,⟨⟨(-4287805485929443700694232548),(-4287805485929443700145238507)⟩,⟨(-2475565651534118429130750448),(-2475565651534118428548487569)⟩⟩,⟨⟨(-3886397599776523265656531705),(-3886397599776523265159392727)⟩,⟨(-2243812700408891163517659971),(-2243812700408891162990172088)⟩⟩,⟨⟨(-3473340580412691300729569838),(-3473340580412691300285022706)⟩,⟨(-2005334119088518316596329629),(-2005334119088518316124762897)⟩⟩,⟨⟨(-3072133445990435320416943639),(-3072133445990435320024007041)⟩,⟨(-1773697072029030457167911465),(-1773697072029030456750966131)⟩⟩,⟨⟨(-2656435792071101113482234197),(-2656435792071101113142650508)⟩,⟨(-1533693919637206963046818528),(-1533693919637206962686397130)⟩⟩,⟨⟨(-2256524817754308918072865955),(-2256524817754308917784723664)⟩,⟨(-1302805210963521473553033330),(-1302805210963521473247055480)⟩⟩,⟨⟨(-1837153108049314193401197363),(-1837153108049314193166809168)⟩,⟨(-1060680841474829177536469509),(-1060680841474829177287474547)⟩⟩,⟨⟨(-1440842106367455813600055571),(-1440842106367455813416633976)⟩,⟨(-831870577970998012844551612),(-831870577970998012649503332)⟩⟩,⟨⟨(-1014414495963543606981497599),(-1014414495963543606852616712)⟩,⟨(-585672482314410440052521657),(-585672482314410439915346987)⟩⟩,⟨⟨(-629264447029517718507050623),(-629264447029517718427961722)⟩,⟨(-363305997883953057592934514),(-363305997883953057508337796)⟩⟩,⟨⟨(-178776584874023315358765569),(-178776584874023315336812836)⟩,⟨(-103216709401819338825176732),(-103216709401819338801440803)⟩⟩] +lemma amp4_13_15_eq : ∀ k : Fin 16, amp4_1Expr 3 15 k = amp4_13_15 k := by decide +kernel +noncomputable def amp4_13 : Fin 16 → Fin 16 → CBox := ![amp4_13_0,amp4_13_1,amp4_13_2,amp4_13_3,amp4_13_4,amp4_13_5,amp4_13_6,amp4_13_7,amp4_13_8,amp4_13_9,amp4_13_10,amp4_13_11,amp4_13_12,amp4_13_13,amp4_13_14,amp4_13_15] +lemma amp4_13_eq (i k : Fin 16) : amp4_1Expr 3 i k = amp4_13 i k := by + fin_cases i + · exact amp4_13_0_eq k + · exact amp4_13_1_eq k + · exact amp4_13_2_eq k + · exact amp4_13_3_eq k + · exact amp4_13_4_eq k + · exact amp4_13_5_eq k + · exact amp4_13_6_eq k + · exact amp4_13_7_eq k + · exact amp4_13_8_eq k + · exact amp4_13_9_eq k + · exact amp4_13_10_eq k + · exact amp4_13_11_eq k + · exact amp4_13_12_eq k + · exact amp4_13_13_eq k + · exact amp4_13_14_eq k + · exact amp4_13_15_eq k +noncomputable def amp4_14_0 : Fin 16 → CBox := ![⟨⟨(-357553169748046630706226828),(-357553169748046630686875920)⟩,⟨(-10853768),7693724⟩⟩,⟨⟨(-1258528894059035436974311917),(-1258528894059035436902562157)⟩,⟨(-38203495),27080655⟩⟩,⟨⟨(-2028828991927087213898852256),(-2028828991927087213780418009)⟩,⟨(-61586475),43655745⟩⟩,⟨⟨(-2881684212734911627109004548),(-2881684212734911626940057747)⟩,⟨(-87475471),62007233⟩⟩,⟨⟨(-3674306216098628386686228796),(-3674306216098628386469781212)⟩,⟨(-111536047),79062640⟩⟩,⟨⟨(-4513049635508617836003048483),(-4513049635508617835736692457)⟩,⟨(-136996670),97110474⟩⟩,⟨⟨(-5312871584142202226796497999),(-5312871584142202226482186041)⟩,⟨(-161275805),114320807⟩⟩,⟨⟨(-6144266891980870640639631701),(-6144266891980870640275709051)⟩,⟨(-186513372),132210527⟩⟩,⟨⟨(-6946681160825382601239515175),(-6946681160825382600827476345)⟩,⟨(-210871199),149476641⟩⟩,⟨⟨(-7772795199553046531067320698),(-7772795199553046530606830619)⟩,⟨(-235948448),167252719⟩⟩,⟨⟨(-8575610971858887401117340764),(-8575610971858887400608273021)⟩,⟨(-260318463),184527473⟩⟩,⟨⟨(-9397139786710079455387581503),(-9397139786710079454829396237)⟩,⟨(-285256525),202204888⟩⟩,⟨⟨(-10199005767294368563832367256),(-10199005767294368563226606396)⟩,⟨(-309597708),219459204⟩⟩,⟨⟨(-11016105370468202636130066763),(-11016105370468202635476468771)⟩,⟨(-334401319),237041313⟩⟩,⟨⟨(-11816037574120999655967428837),(-11816037574120999655265264569)⟩,⟨(-358683801),254254018⟩⟩,⟨⟨(-12628609778658563396646861701),(-12628609778658563395895654293)⟩,⟨(-383349979),271738708⟩⟩] +lemma amp4_14_0_eq : ∀ k : Fin 16, amp4_1Expr 4 0 k = amp4_14_0 k := by decide +kernel +noncomputable def amp4_14_1 : Fin 16 → CBox := ![⟨⟨(-13425810750168309643861443060),(-13425810750168309643062458714)⟩,⟨(-407549553),288892644⟩⟩,⟨⟨(-14233622917787253604846329830),(-14233622917787253603999708156)⟩,⟨(-432071237),306274908⟩⟩,⟨⟨(-15027400576370959043839106155),(-15027400576370959042945974379)⟩,⟨(-456166894),323355182⟩⟩,⟨⟨(-15830143023134495959653644239),(-15830143023134495958709922379)⟩,⟨(-480534683),340628358⟩⟩,⟨⟨(-16619869927399128444804774632),(-16619869927399128443815753612)⟩,⟨(-504507376),357621469⟩⟩,⟨⟨(-17417186310553865865734173007),(-17417186310553865864699392573)⟩,⟨(-528710454),374777888⟩⟩,⟨⟨(-18202277460336165347890349221),(-18202277460336165346805676191)⟩,⟨(-552542426),391671248⟩⟩,⟨⟨(-18993782147908377702313150627),(-18993782147908377701183880207)⟩,⟨(-576569085),408702613⟩⟩,⟨⟨(-19773682109448918854035652904),(-19773682109448918852857658629)⟩,⟨(-600243475),425484271⟩⟩,⟨⟨(-20558970745855790589970513249),(-20558970745855790588742651118)⟩,⟨(-624081442),442381880⟩⟩,⟨⟨(-21333145817647381554031684626),(-21333145817647381552761384086)⟩,⟨(-647582049),459040352⟩⟩,⟨⟨(-22111802094629390848006077317),(-22111802094629390846686965327)⟩,⟨(-671218686),475795248⟩⟩,⟨⟨(-22879735361689815418640400572),(-22879735361689815417281410291)⟩,⟨(-694529819),492319410⟩⟩,⟨⟨(-23651335557769629124313417277),(-23651335557769629122903584466)⟩,⟨(-717952264),508922476⟩⟩,⟨⟨(-24412523682091930500419429216),(-24412523682091930498963124047)⟩,⟨(-741058644),525301498⟩⟩,⟨⟨(-25176639830521444782359744075),(-25176639830521444780855312490)⟩,⟨(-764253906),541743524⟩⟩] +lemma amp4_14_1_eq : ∀ k : Fin 16, amp4_1Expr 4 1 k = amp4_14_1 k := by decide +kernel +noncomputable def amp4_14_2 : Fin 16 → CBox := ![⟨⟨(-25930590927637166728207490697),(-25930590927637166726665477711)⟩,⟨(-787140600),557966822⟩⟩,⟨⟨(-26686793109138643702875231521),(-26686793109138643701284224792)⟩,⟨(-810095628),574238558⟩⟩,⟨⟨(-27433025327480988472201993392),(-27433025327480988470564255773)⟩,⟨(-832748011),590295763⟩⟩,⟨⟨(-28180883386091924916623304313),(-28180883386091924914937681108)⟩,⟨(-855449748),606387953⟩⟩,⟨⟨(-28918923954431376936204537417),(-28918923954431376934469773341)⟩,⟨(-877853468),622268892⟩⟩,⟨⟨(-29658008822123430068453761674),(-29658008822123430066686824087)⟩,⟨(-900288888),638172303⟩⟩,⟨⟨(-30387393416553457457006273836),(-30387393416553457455193178229)⟩,⟨(-922429850),653866986⟩⟩,⟨⟨(-31117278165742267116338930378),(-31117278165742267114481962254)⟩,⟨(-944585994),669572431⟩⟩,⟨⟨(-31837550499505124430040755442),(-31837550499505124428138120675)⟩,⟨(-966450347),685071039⟩⟩,⟨⟨(-32557811201924162535065267647),(-32557811201924162533116458437)⟩,⟨(-988314347),700569397⟩⟩,⟨⟨(-33268522773487285735256300550),(-33268522773487285733261967190)⟩,⟨(-1009888477),715862279⟩⟩,⟨⟨(-33978739218346212148971671756),(-33978739218346212146951297193)⟩,⟨(-1031447577),731144508⟩⟩,⟨⟨(-34679449173604907943010490245),(-34679449173604907940941926540)⟩,⟨(-1052718101),746222178⟩⟩,⟨⟨(-35379205481468553423411071826),(-35379205481468553421297505160)⟩,⟨(-1073959676),761279328⟩⟩,⟨⟨(-36069480559311645328479494277),(-36069480559311645326318854666)⟩,⟨(-1094913442),776132464⟩⟩,⟨⟨(-36758365717253841754525585371),(-36758365717253841752324839777)⟩,⟨(-1115825017),790955692⟩⟩] +lemma amp4_14_2_eq : ∀ k : Fin 16, amp4_1Expr 4 2 k = amp4_14_2 k := by decide +kernel +noncomputable def amp4_14_3 : Fin 16 → CBox := ![⟨⟨(-37437780256644588251392617066),(-37437780256644588249147954145)⟩,⟨(-1136449104),805575134⟩⟩,⟨⟨(-38115388592897434017576869354),(-38115388592897434015287623469)⟩,⟨(-1157018362),820155711⟩⟩,⟨⟨(-38783524585689884453248962524),(-38783524585689884450915034138)⟩,⟨(-1177300082),834532465⟩⟩,⟨⟨(-39449456196973495355400229196),(-39449456196973495353054954331)⟩,⟨(-1197514886),848861785⟩⟩,⟨⟨(-40105903374888705089417539509),(-40105903374888705087025847266)⟩,⟨(-1217441783),862987022⟩⟩,⟨⟨(-40759764516089817649412546678),(-40759764516089817646977591889)⟩,⟨(-1237290179),877056614⟩⟩,⟨⟨(-41404120463237306157133795850),(-41404120463237306154656421808)⟩,⟨(-1256850039),890921675⟩⟩,⟨⟨(-42045523906610931891802300732),(-42045523906610931889284200838)⟩,⟨(-1276320274),904723206⟩⟩,⟨⟨(-42677394191057544487812714780),(-42677394191057544485252424079)⟩,⟨(-1295501123),918319605⟩⟩,⟨⟨(-43305959560331774514613119175),(-43305959560331774512019032849)⟩,⟨(-1314581650),931844889⟩⟩,⟨⟨(-43924957879754381808880355195),(-43924957879754381806245093726)⟩,⟨(-1333371762),945164313⟩⟩,⟨⟨(-44540311963211117826617608775),(-44540311963211117823944801607)⟩,⟨(-1352051250),958405321⟩⟩,⟨⟨(-45146060300795927014955365364),(-45146060300795927012244036398)⟩,⟨(-1370439150),971439635⟩⟩,⟨⟨(-45747837346436315589603933396),(-45747837346436315586854721801)⟩,⟨(-1388706499),984388496⟩⟩,⟨⟨(-46339966134024300469177115757),(-46339966134024300466389805696)⟩,⟨(-1406680968),997129749⟩⟩,⟨⟨(-46927808129209006381203440218),(-46927808129209006378378793807)⟩,⟨(-1424525309),1009778760⟩⟩] +lemma amp4_14_3_eq : ∀ k : Fin 16, amp4_1Expr 4 3 k = amp4_14_3 k := by decide +kernel +noncomputable def amp4_14_4 : Fin 16 → CBox := ![⟨⟨(-47505956415315480003327787771),(-47505956415315480000516832642)⟩,⟨(-1442075391),1022219185⟩⟩,⟨⟨(-48079513352728794155097243419),(-48079513352728794152241507091)⟩,⟨(-1459486099),1034560814⟩⟩,⟨⟨(-48643328973542202721504781953),(-48643328973542202718606767516)⟩,⟨(-1476601103),1046692833⟩⟩,⟨⟨(-49202259104917717842597777851),(-49202259104917717839659842342)⟩,⟨(-1493567804),1058719727⟩⟩,⟨⟨(-49751398856748404428557635809),(-49751398856748404425580928015)⟩,⟨(-1510237312),1070535954⟩⟩,⟨⟨(-50295368935478774266295839288),(-50295368935478774263279010453)⟩,⟨(-1526749892),1082240942⟩⟩,⟨⟨(-50829498747411383455784548255),(-50829498747411383452733152862)⟩,⟨(-1542963763),1093734190⟩⟩,⟨⟨(-51358184260921196132598611539),(-51358184260921196129509607979)⟩,⟨(-1559012368),1105110290⟩⟩,⟨⟨(-51876979366645254749876150247),(-51876979366645254746749096720)⟩,⟨(-1574760744),1116273570⟩⟩,⟨⟨(-52390064759216640813686323224),(-52390064759216640810536735010)⟩,⟨(-1590335798),1127313990⟩⟩,⟨⟨(-52893209867183757315400548708),(-52893209867183757312212959841)⟩,⟨(-1605609107),1138140519⟩⟩,⟨⟨(-53390388753776064240717416419),(-53390388753776064237495079766)⟩,⟨(-1620701308),1148838668⟩⟩,⟨⟨(-53877578214970270258938551134),(-53877578214970270255680361839)⟩,⟨(-1635490273),1159321867⟩⟩,⟨⟨(-54358553586458375599408765483),(-54358553586458375596120958599)⟩,⟨(-1650090606),1169671354⟩⟩,⟨⟨(-54829491559176665671154683224),(-54829491559176665667831727725)⟩,⟨(-1664386246),1179804858⟩⟩,⟨⟨(-55293975979340104505757024307),(-55293975979340104502402975607)⟩,⟨(-1678485984),1189799497⟩⟩] +lemma amp4_14_4_eq : ∀ k : Fin 16, amp4_1Expr 4 4 k = amp4_14_4 k := by decide +kernel +noncomputable def amp4_14_5 : Fin 16 → CBox := ![⟨⟨(-55748376590469423806486714252),(-55748376590469423803100424178)⟩,⟨(-1692279622),1199577156⟩⟩,⟨⟨(-56196092384991073882785811238),(-56196092384991073879367930903)⟩,⟨(-1705870337),1209210972⟩⟩,⟨⟨(-56633679887340554509251600883),(-56633679887340554505801106234)⟩,⟨(-1719153601),1218626851⟩⟩,⟨⟨(-57064359325015055234951589464),(-57064359325015055231469502442)⟩,⟨(-1732227166),1227894085⟩⟩,⟨⟨(-57484868250321787286720409138),(-57484868250321787283206689121)⟩,⟨(-1744991999),1236942472⟩⟩,⟨⟨(-57898253716627030365710366062),(-57898253716627030362266463351)⟩,⟨(-1757540594),1245837579⟩⟩,⟨⟨(-58301429023902820843578792420),(-58301429023902820840098708730)⟩,⟨(-1769779252),1254512986⟩⟩,⟨⟨(-58697273187050324601464110196),(-58697273187050324597951018383)⟩,⟨(-1781795369),1263030645⟩⟩,⟨⟨(-59082870405977866990131873490),(-59082870405977866986588063230)⟩,⟨(-1793500433),1271327812⟩⟩,⟨⟨(-59460936375527758936600478441),(-59460936375527758933026799134)⟩,⟨(-1804976881),1279462924⟩⟩,⟨⟨(-59828721744649059687199889720),(-59828721744649059683599400539)⟩,⟨(-1816141254),1287376822⟩⟩,⟨⟨(-60188783222751279242856047835),(-60188783222751279239229804878)⟩,⟨(-1827071164),1295124518⟩⟩,⟨⟨(-60538533822220355770051838813),(-60538533822220355766396997676)⟩,⟨(-1837688079),1302650349⟩⟩,⟨⟨(-60880375247524401724320573219),(-60880375247524401720642816426)⟩,⟨(-1848064907),1310005992⟩⟩,⟨⟨(-61211879126221196637734447751),(-61211879126221196634031221341)⟩,⟨(-1858127931),1317139195⟩⟩,⟨⟨(-61535295810481373298518623439),(-61535295810481373294789546413)⟩,⟨(-1867945463),1324098380⟩⟩] +lemma amp4_14_5_eq : ∀ k : Fin 16, amp4_1Expr 4 5 k = amp4_14_5 k := by decide +kernel +noncomputable def amp4_14_6 : Fin 16 → CBox := ![⟨⟨(-61848352107305326151888439951),(-61848352107305326148144836366)⟩,⟨(-1877448498),1330834633⟩⟩,⟨⟨(-62153150364696266185294302881),(-62153150364696266181523851652)⟩,⟨(-1886700855),1337393192⟩⟩,⟨⟨(-62447569423876687481491440065),(-62447569423876687477701408747)⟩,⟨(-1895638144),1343728415⟩⟩,⟨⟨(-62733566693024370965844106758),(-62733566693024370962028566264)⟩,⟨(-1904319785),1349882420⟩⟩,⟨⟨(-63009170173301185788943126626),(-63009170173301185785106353884)⟩,⟨(-1912685914),1355812775⟩⟩,⟨⟨(-63276195132027270200096663907),(-63276195132027270196237298839)⟩,⟨(-1920791637),1361558539⟩⟩,⟨⟨(-63532816109570252474561907479),(-63532816109570252470714999964)⟩,⟨(-1928581540),1367080434⟩⟩,⟨⟨(-63780708782341902436126604298),(-63780708782341902432255223607)⟩,⟨(-1936106490),1372414515⟩⟩,⟨⟨(-64018191847289538085318874921),(-64018191847289538081427032167)⟩,⟨(-1943315449),1377524606⟩⟩,⟨⟨(-64246803705362792367173158324),(-64246803705362792363263349283)⟩,⟨(-1950255116),1382443809⟩⟩,⟨⟨(-64465005051873660526562433795),(-64465005051873660522633204882)⟩,⟨(-1956878765),1387139001⟩⟩,⟨⟨(-64674199106115448383027256942),(-64674199106115448379083155903)⟩,⟨(-1963228992),1391640377⟩⟩,⟨⟨(-64872986615835714445653355617),(-64872986615835714441692974473)⟩,⟨(-1969263321),1395917828⟩⟩,⟨⟨(-65062637502207729842461544805),(-65062637502207729838483130950)⟩,⟨(-1975020302),1399998680⟩⟩,⟨⟨(-65241890821068182810619338352),(-65241890821068182806640167230)⟩,⟨(-1980461657),1403855800⟩⟩,⟨⟨(-65411884878754774845955084619),(-65411884878754774841960799258)⟩,⟨(-1985621942),1407513682⟩⟩] +lemma amp4_14_6_eq : ∀ k : Fin 16, amp4_1Expr 4 6 k = amp4_14_6 k := by decide +kernel +noncomputable def amp4_14_7 : Fin 16 → CBox := ![⟨⟨(-65571495487019962697530978746),(-65571495487019962693524062077)⟩,⟨(-1990467030),1410948136⟩⟩,⟨⟨(-65721730829181863548353057765),(-65721730829181863544332064374)⟩,⟨(-1995027525),1414180856⟩⟩,⟨⟨(-65861602104682406949154212077),(-65861602104682406945128793118)⟩,⟨(-1999273412),1417190565⟩⟩,⟨⟨(-65991988681818377879483017315),(-65991988681818377875446470882)⟩,⟨(-2003231385),1419996185⟩⟩,⟨⟨(-66112035956305576818310288688),(-66112035956305576814268731884)⟩,⟨(-2006875501),1422579327⟩⟩,⟨⟨(-66222495612204809558513131315),(-66222495612204809554461050748)⟩,⟨(-2010228578),1424956165⟩⟩,⟨⟨(-66322646220774284961967515721),(-66322646220774284957909882386)⟩,⟨(-2013268718),1427111177⟩⟩,⟨⟨(-66413112741043566384857281212),(-66413112741043566380794584298)⟩,⟨(-2016014890),1429057809⟩⟩,⟨⟨(-66493306064581971706771081729),(-66493306064581971702703595925)⟩,⟨(-2018449212),1430783385⟩⟩,⟨⟨(-66563725217733132451254993570),(-66563725217733132447182432748)⟩,⟨(-2020586833),1432298644⟩⟩,⟨⟨(-66623912718348990082077463122),(-66623912718348990078002597107)⟩,⟨(-2022413866),1433593740⟩⟩,⟨⟨(-66674242289433950484073714386),(-66674242289433950479996541463)⟩,⟨(-2023941654),1434676717⟩⟩,⟨⟨(-66714387538840467434636560927),(-66714387538840467430559676692)⟩,⟨(-2025160290),1435540551⟩⟩,⟨⟨(-66744597355623212348459017623),(-66744597355623212344383621615)⟩,⟨(-2026077329),1436190597⟩⟩,⟨⟨(-66764676056447555056296289593),(-66764676056447555052224672018)⟩,⟨(-2026686832),1436622645⟩⟩,⟨⟨(-66774748008104564434679539355),(-66774748008104564430614605459)⟩,⟨(-2026992573),1436839370⟩⟩] +lemma amp4_14_7_eq : ∀ k : Fin 16, amp4_1Expr 4 7 k = amp4_14_7 k := by decide +kernel +noncomputable def amp4_14_8 : Fin 16 → CBox := ![⟨⟨(-66774748008104564434679539355),(-66774748008104564430614605459)⟩,⟨(-2026992573),1436839370⟩⟩,⟨⟨(-66764676056447555056296289593),(-66764676056447555052224672018)⟩,⟨(-2026686832),1436622645⟩⟩,⟨⟨(-66744597355623212348459017623),(-66744597355623212344383621615)⟩,⟨(-2026077329),1436190597⟩⟩,⟨⟨(-66714387538840467434636560927),(-66714387538840467430559676692)⟩,⟨(-2025160290),1435540551⟩⟩,⟨⟨(-66674242289433950484073714386),(-66674242289433950479996541463)⟩,⟨(-2023941654),1434676717⟩⟩,⟨⟨(-66623912718348990082077463122),(-66623912718348990078002597107)⟩,⟨(-2022413866),1433593740⟩⟩,⟨⟨(-66563725217733132451254993570),(-66563725217733132447182432748)⟩,⟨(-2020586833),1432298644⟩⟩,⟨⟨(-66493306064581971706771081729),(-66493306064581971702703595925)⟩,⟨(-2018449212),1430783385⟩⟩,⟨⟨(-66413112741043566384857281212),(-66413112741043566380794584298)⟩,⟨(-2016014890),1429057809⟩⟩,⟨⟨(-66322646220774284961967515721),(-66322646220774284957909882386)⟩,⟨(-2013268718),1427111177⟩⟩,⟨⟨(-66222495612204809558513131315),(-66222495612204809554461050748)⟩,⟨(-2010228578),1424956165⟩⟩,⟨⟨(-66112035956305576818310288688),(-66112035956305576814268731884)⟩,⟨(-2006875501),1422579327⟩⟩,⟨⟨(-65991988681818377879483017315),(-65991988681818377875446470882)⟩,⟨(-2003231385),1419996185⟩⟩,⟨⟨(-65861602104682406949154212077),(-65861602104682406945128793118)⟩,⟨(-1999273412),1417190565⟩⟩,⟨⟨(-65721730829181863548353057765),(-65721730829181863544332064374)⟩,⟨(-1995027525),1414180856⟩⟩,⟨⟨(-65571495487019962697530978746),(-65571495487019962693524062077)⟩,⟨(-1990467030),1410948136⟩⟩] +lemma amp4_14_8_eq : ∀ k : Fin 16, amp4_1Expr 4 8 k = amp4_14_8 k := by decide +kernel +noncomputable def amp4_14_9 : Fin 16 → CBox := ![⟨⟨(-65411884878754774845955084619),(-65411884878754774841960799258)⟩,⟨(-1985621942),1407513682⟩⟩,⟨⟨(-65241890821068182810619338352),(-65241890821068182806640167230)⟩,⟨(-1980461657),1403855800⟩⟩,⟨⟨(-65062637502207729842461544805),(-65062637502207729838483130950)⟩,⟨(-1975020302),1399998680⟩⟩,⟨⟨(-64872986615835714445653355617),(-64872986615835714441692974473)⟩,⟨(-1969263321),1395917828⟩⟩,⟨⟨(-64674199106115448383027256942),(-64674199106115448379083155903)⟩,⟨(-1963228992),1391640377⟩⟩,⟨⟨(-64465005051873660526562433795),(-64465005051873660522633204882)⟩,⟨(-1956878765),1387139001⟩⟩,⟨⟨(-64246803705362792367173158324),(-64246803705362792363263349283)⟩,⟨(-1950255116),1382443809⟩⟩,⟨⟨(-64018191847289538085318874921),(-64018191847289538081427032167)⟩,⟨(-1943315449),1377524606⟩⟩,⟨⟨(-63780708782341902436126604298),(-63780708782341902432255223607)⟩,⟨(-1936106490),1372414515⟩⟩,⟨⟨(-63532816109570252474561907479),(-63532816109570252470714999964)⟩,⟨(-1928581540),1367080434⟩⟩,⟨⟨(-63276195132027270200096663907),(-63276195132027270196237298839)⟩,⟨(-1920791637),1361558539⟩⟩,⟨⟨(-63009170173301185788943126626),(-63009170173301185785106353884)⟩,⟨(-1912685914),1355812775⟩⟩,⟨⟨(-62733566693024370965844106758),(-62733566693024370962028566264)⟩,⟨(-1904319785),1349882420⟩⟩,⟨⟨(-62447569423876687481491440065),(-62447569423876687477701408747)⟩,⟨(-1895638144),1343728415⟩⟩,⟨⟨(-62153150364696266185294302881),(-62153150364696266181523851652)⟩,⟨(-1886700855),1337393192⟩⟩,⟨⟨(-61848352107305326151888439951),(-61848352107305326148144836366)⟩,⟨(-1877448498),1330834633⟩⟩] +lemma amp4_14_9_eq : ∀ k : Fin 16, amp4_1Expr 4 9 k = amp4_14_9 k := by decide +kernel +noncomputable def amp4_14_10 : Fin 16 → CBox := ![⟨⟨(-61535295810481373298518623439),(-61535295810481373294789546413)⟩,⟨(-1867945463),1324098380⟩⟩,⟨⟨(-61211879126221196637734447751),(-61211879126221196634031221341)⟩,⟨(-1858127931),1317139195⟩⟩,⟨⟨(-60880375247524401724320573219),(-60880375247524401720642816426)⟩,⟨(-1848064907),1310005992⟩⟩,⟨⟨(-60538533822220355770051838813),(-60538533822220355766396997676)⟩,⟨(-1837688079),1302650349⟩⟩,⟨⟨(-60188783222751279242856047835),(-60188783222751279239229804878)⟩,⟨(-1827071164),1295124518⟩⟩,⟨⟨(-59828721744649059687199889720),(-59828721744649059683599400539)⟩,⟨(-1816141254),1287376822⟩⟩,⟨⟨(-59460936375527758936600478441),(-59460936375527758933026799134)⟩,⟨(-1804976881),1279462924⟩⟩,⟨⟨(-59082870405977866990131873490),(-59082870405977866986588063230)⟩,⟨(-1793500433),1271327812⟩⟩,⟨⟨(-58697273187050324601464110196),(-58697273187050324597951018383)⟩,⟨(-1781795369),1263030645⟩⟩,⟨⟨(-58301429023902820843578792420),(-58301429023902820840098708730)⟩,⟨(-1769779252),1254512986⟩⟩,⟨⟨(-57898253716627030365710366062),(-57898253716627030362266463351)⟩,⟨(-1757540594),1245837579⟩⟩,⟨⟨(-57484868250321787286720409138),(-57484868250321787283206689121)⟩,⟨(-1744991999),1236942472⟩⟩,⟨⟨(-57064359325015055234951589464),(-57064359325015055231469502442)⟩,⟨(-1732227166),1227894085⟩⟩,⟨⟨(-56633679887340554509251600883),(-56633679887340554505801106234)⟩,⟨(-1719153601),1218626851⟩⟩,⟨⟨(-56196092384991073882785811238),(-56196092384991073879367930903)⟩,⟨(-1705870337),1209210972⟩⟩,⟨⟨(-55748376590469423806486714252),(-55748376590469423803100424178)⟩,⟨(-1692279622),1199577156⟩⟩] +lemma amp4_14_10_eq : ∀ k : Fin 16, amp4_1Expr 4 10 k = amp4_14_10 k := by decide +kernel +noncomputable def amp4_14_11 : Fin 16 → CBox := ![⟨⟨(-55293975979340104505757024307),(-55293975979340104502402975607)⟩,⟨(-1678485984),1189799497⟩⟩,⟨⟨(-54829491559176665671154683224),(-54829491559176665667831727725)⟩,⟨(-1664386246),1179804858⟩⟩,⟨⟨(-54358553586458375599408765483),(-54358553586458375596120958599)⟩,⟨(-1650090606),1169671354⟩⟩,⟨⟨(-53877578214970270258938551134),(-53877578214970270255680361839)⟩,⟨(-1635490273),1159321867⟩⟩,⟨⟨(-53390388753776064240717416419),(-53390388753776064237495079766)⟩,⟨(-1620701308),1148838668⟩⟩,⟨⟨(-52893209867183757315400548708),(-52893209867183757312212959841)⟩,⟨(-1605609107),1138140519⟩⟩,⟨⟨(-52390064759216640813686323224),(-52390064759216640810536735010)⟩,⟨(-1590335798),1127313990⟩⟩,⟨⟨(-51876979366645254749876150247),(-51876979366645254746749096720)⟩,⟨(-1574760744),1116273570⟩⟩,⟨⟨(-51358184260921196132598611539),(-51358184260921196129509607979)⟩,⟨(-1559012368),1105110290⟩⟩,⟨⟨(-50829498747411383455784548255),(-50829498747411383452733152862)⟩,⟨(-1542963763),1093734190⟩⟩,⟨⟨(-50295368935478774266295839288),(-50295368935478774263279010453)⟩,⟨(-1526749892),1082240942⟩⟩,⟨⟨(-49751398856748404428557635809),(-49751398856748404425580928015)⟩,⟨(-1510237312),1070535954⟩⟩,⟨⟨(-49202259104917717842597777851),(-49202259104917717839659842342)⟩,⟨(-1493567804),1058719727⟩⟩,⟨⟨(-48643328973542202721504781953),(-48643328973542202718606767516)⟩,⟨(-1476601103),1046692833⟩⟩,⟨⟨(-48079513352728794155097243419),(-48079513352728794152241507091)⟩,⟨(-1459486099),1034560814⟩⟩,⟨⟨(-47505956415315480003327787771),(-47505956415315480000516832642)⟩,⟨(-1442075391),1022219185⟩⟩] +lemma amp4_14_11_eq : ∀ k : Fin 16, amp4_1Expr 4 11 k = amp4_14_11 k := by decide +kernel +noncomputable def amp4_14_12 : Fin 16 → CBox := ![⟨⟨(-46927808129209006381203440218),(-46927808129209006378378793807)⟩,⟨(-1424525309),1009778760⟩⟩,⟨⟨(-46339966134024300469177115757),(-46339966134024300466389805696)⟩,⟨(-1406680968),997129749⟩⟩,⟨⟨(-45747837346436315589603933396),(-45747837346436315586854721801)⟩,⟨(-1388706499),984388496⟩⟩,⟨⟨(-45146060300795927014955365364),(-45146060300795927012244036398)⟩,⟨(-1370439150),971439635⟩⟩,⟨⟨(-44540311963211117826617608775),(-44540311963211117823944801607)⟩,⟨(-1352051250),958405321⟩⟩,⟨⟨(-43924957879754381808880355195),(-43924957879754381806245093726)⟩,⟨(-1333371762),945164313⟩⟩,⟨⟨(-43305959560331774514613119175),(-43305959560331774512019032849)⟩,⟨(-1314581650),931844889⟩⟩,⟨⟨(-42677394191057544487812714780),(-42677394191057544485252424079)⟩,⟨(-1295501123),918319605⟩⟩,⟨⟨(-42045523906610931891802300732),(-42045523906610931889284200838)⟩,⟨(-1276320274),904723206⟩⟩,⟨⟨(-41404120463237306157133795850),(-41404120463237306154656421808)⟩,⟨(-1256850039),890921675⟩⟩,⟨⟨(-40759764516089817649412546678),(-40759764516089817646977591889)⟩,⟨(-1237290179),877056614⟩⟩,⟨⟨(-40105903374888705089417539509),(-40105903374888705087025847266)⟩,⟨(-1217441783),862987022⟩⟩,⟨⟨(-39449456196973495355400229196),(-39449456196973495353054954331)⟩,⟨(-1197514886),848861785⟩⟩,⟨⟨(-38783524585689884453248962524),(-38783524585689884450915034138)⟩,⟨(-1177300082),834532465⟩⟩,⟨⟨(-38115388592897434017576869354),(-38115388592897434015287623469)⟩,⟨(-1157018362),820155711⟩⟩,⟨⟨(-37437780256644588251392617066),(-37437780256644588249147954145)⟩,⟨(-1136449104),805575134⟩⟩] +lemma amp4_14_12_eq : ∀ k : Fin 16, amp4_1Expr 4 12 k = amp4_14_12 k := by decide +kernel +noncomputable def amp4_14_13 : Fin 16 → CBox := ![⟨⟨(-36758365717253841754525585371),(-36758365717253841752324839777)⟩,⟨(-1115825017),790955692⟩⟩,⟨⟨(-36069480559311645328479494277),(-36069480559311645326318854666)⟩,⟨(-1094913442),776132464⟩⟩,⟨⟨(-35379205481468553423411071826),(-35379205481468553421297505160)⟩,⟨(-1073959676),761279328⟩⟩,⟨⟨(-34679449173604907943010490245),(-34679449173604907940941926540)⟩,⟨(-1052718101),746222178⟩⟩,⟨⟨(-33978739218346212148971671756),(-33978739218346212146951297193)⟩,⟨(-1031447577),731144508⟩⟩,⟨⟨(-33268522773487285735256300550),(-33268522773487285733261967190)⟩,⟨(-1009888477),715862279⟩⟩,⟨⟨(-32557811201924162535065267647),(-32557811201924162533116458437)⟩,⟨(-988314347),700569397⟩⟩,⟨⟨(-31837550499505124430040755442),(-31837550499505124428138120675)⟩,⟨(-966450347),685071039⟩⟩,⟨⟨(-31117278165742267116338930378),(-31117278165742267114481962254)⟩,⟨(-944585994),669572431⟩⟩,⟨⟨(-30387393416553457457006273836),(-30387393416553457455193178229)⟩,⟨(-922429850),653866986⟩⟩,⟨⟨(-29658008822123430068453761674),(-29658008822123430066686824087)⟩,⟨(-900288888),638172303⟩⟩,⟨⟨(-28918923954431376936204537417),(-28918923954431376934469773341)⟩,⟨(-877853468),622268892⟩⟩,⟨⟨(-28180883386091924916623304313),(-28180883386091924914937681108)⟩,⟨(-855449748),606387953⟩⟩,⟨⟨(-27433025327480988472201993392),(-27433025327480988470564255773)⟩,⟨(-832748011),590295763⟩⟩,⟨⟨(-26686793109138643702875231521),(-26686793109138643701284224792)⟩,⟨(-810095628),574238558⟩⟩,⟨⟨(-25930590927637166728207490697),(-25930590927637166726665477711)⟩,⟨(-787140600),557966822⟩⟩] +lemma amp4_14_13_eq : ∀ k : Fin 16, amp4_1Expr 4 13 k = amp4_14_13 k := by decide +kernel +noncomputable def amp4_14_14 : Fin 16 → CBox := ![⟨⟨(-25176639830521444782359744075),(-25176639830521444780855312490)⟩,⟨(-764253906),541743524⟩⟩,⟨⟨(-24412523682091930500419429216),(-24412523682091930498963124047)⟩,⟨(-741058644),525301498⟩⟩,⟨⟨(-23651335557769629124313417277),(-23651335557769629122903584466)⟩,⟨(-717952264),508922476⟩⟩,⟨⟨(-22879735361689815418640400572),(-22879735361689815417281410291)⟩,⟨(-694529819),492319410⟩⟩,⟨⟨(-22111802094629390848006077317),(-22111802094629390846686965327)⟩,⟨(-671218686),475795248⟩⟩,⟨⟨(-21333145817647381554031684626),(-21333145817647381552761384086)⟩,⟨(-647582049),459040352⟩⟩,⟨⟨(-20558970745855790589970513249),(-20558970745855790588742651118)⟩,⟨(-624081442),442381880⟩⟩,⟨⟨(-19773682109448918854035652904),(-19773682109448918852857658629)⟩,⟨(-600243475),425484271⟩⟩,⟨⟨(-18993782147908377702313150627),(-18993782147908377701183880207)⟩,⟨(-576569085),408702613⟩⟩,⟨⟨(-18202277460336165347890349221),(-18202277460336165346805676191)⟩,⟨(-552542426),391671248⟩⟩,⟨⟨(-17417186310553865865734173007),(-17417186310553865864699392573)⟩,⟨(-528710454),374777888⟩⟩,⟨⟨(-16619869927399128444804774632),(-16619869927399128443815753612)⟩,⟨(-504507376),357621469⟩⟩,⟨⟨(-15830143023134495959653644239),(-15830143023134495958709922379)⟩,⟨(-480534683),340628358⟩⟩,⟨⟨(-15027400576370959043839106155),(-15027400576370959042945974379)⟩,⟨(-456166894),323355182⟩⟩,⟨⟨(-14233622917787253604846329830),(-14233622917787253603999708156)⟩,⟨(-432071237),306274908⟩⟩,⟨⟨(-13425810750168309643861443060),(-13425810750168309643062458714)⟩,⟨(-407549553),288892644⟩⟩] +lemma amp4_14_14_eq : ∀ k : Fin 16, amp4_1Expr 4 14 k = amp4_14_14 k := by decide +kernel +noncomputable def amp4_14_15 : Fin 16 → CBox := ![⟨⟨(-12628609778658563396646861701),(-12628609778658563395895654293)⟩,⟨(-383349979),271738708⟩⟩,⟨⟨(-11816037574120999655967428837),(-11816037574120999655265264569)⟩,⟨(-358683801),254254018⟩⟩,⟨⟨(-11016105370468202636130066763),(-11016105370468202635476468771)⟩,⟨(-334401319),237041313⟩⟩,⟨⟨(-10199005767294368563832367256),(-10199005767294368563226606396)⟩,⟨(-309597708),219459204⟩⟩,⟨⟨(-9397139786710079455387581503),(-9397139786710079454829396237)⟩,⟨(-285256525),202204888⟩⟩,⟨⟨(-8575610971858887401117340764),(-8575610971858887400608273021)⟩,⟨(-260318463),184527473⟩⟩,⟨⟨(-7772795199553046531067320698),(-7772795199553046530606830619)⟩,⟨(-235948448),167252719⟩⟩,⟨⟨(-6946681160825382601239515175),(-6946681160825382600827476345)⟩,⟨(-210871199),149476641⟩⟩,⟨⟨(-6144266891980870640639631701),(-6144266891980870640275709051)⟩,⟨(-186513372),132210527⟩⟩,⟨⟨(-5312871584142202226796497999),(-5312871584142202226482186041)⟩,⟨(-161275805),114320807⟩⟩,⟨⟨(-4513049635508617836003048483),(-4513049635508617835736692457)⟩,⟨(-136996670),97110474⟩⟩,⟨⟨(-3674306216098628386686228796),(-3674306216098628386469781212)⟩,⟨(-111536047),79062640⟩⟩,⟨⟨(-2881684212734911627109004548),(-2881684212734911626940057747)⟩,⟨(-87475471),62007233⟩⟩,⟨⟨(-2028828991927087213898852256),(-2028828991927087213780418009)⟩,⟨(-61586475),43655745⟩⟩,⟨⟨(-1258528894059035436974311917),(-1258528894059035436902562157)⟩,⟨(-38203495),27080655⟩⟩,⟨⟨(-357553169748046630706226828),(-357553169748046630686875920)⟩,⟨(-10853768),7693724⟩⟩] +lemma amp4_14_15_eq : ∀ k : Fin 16, amp4_1Expr 4 15 k = amp4_14_15 k := by decide +kernel +noncomputable def amp4_14 : Fin 16 → Fin 16 → CBox := ![amp4_14_0,amp4_14_1,amp4_14_2,amp4_14_3,amp4_14_4,amp4_14_5,amp4_14_6,amp4_14_7,amp4_14_8,amp4_14_9,amp4_14_10,amp4_14_11,amp4_14_12,amp4_14_13,amp4_14_14,amp4_14_15] +lemma amp4_14_eq (i k : Fin 16) : amp4_1Expr 4 i k = amp4_14 i k := by + fin_cases i + · exact amp4_14_0_eq k + · exact amp4_14_1_eq k + · exact amp4_14_2_eq k + · exact amp4_14_3_eq k + · exact amp4_14_4_eq k + · exact amp4_14_5_eq k + · exact amp4_14_6_eq k + · exact amp4_14_7_eq k + · exact amp4_14_8_eq k + · exact amp4_14_9_eq k + · exact amp4_14_10_eq k + · exact amp4_14_11_eq k + · exact amp4_14_12_eq k + · exact amp4_14_13_eq k + · exact amp4_14_14_eq k + · exact amp4_14_15_eq k +noncomputable def amp4_15_0 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨206433418803638677622879409,206433418803638677624245993⟩⟩,⟨⟨0,0⟩,⟨726611995767906115087064597,726611995767906115093974983⟩⟩,⟨⟨0,0⟩,⟨1171344964628820879944165547,1171344964628820879956904243⟩⟩,⟨⟨0,0⟩,⟨1663741155941996025460178078,1663741155941996025478691197⟩⟩,⟨⟨0,0⟩,⟨2121361682949658354780451532,2121361682949658354804652084⟩⟩,⟨⟨0,0⟩,⟨2605610421927042946746523973,2605610421927042946776537171⟩⟩,⟨⟨0,0⟩,⟨3067387839274413925669940985,3067387839274413925705706943⟩⟩,⟨⟨0,0⟩,⟨3547394144058060913845578585,3547394144058060913887186800⟩⟩,⟨⟨0,0⟩,⟨4010668238177036632638050818,4010668238177036632685433220⟩⟩,⟨⟨0,0⟩,⟨4487625400817782326415073419,4487625400817782326467773508⟩⟩,⟨⟨0,0⟩,⟨4951131303068236857576605536,4951131303068236857635335239⟩⟩,⟨⟨0,0⟩,⟨5425441185469606814646061604,5425441185469606814710619416⟩⟩,⟨⟨0,0⟩,⟨5888398725213949358166629037,5888398725213949358236663964⟩⟩,⟨⟨0,0⟩,⟨6360151401061098850485125164,6360151401061098850560370432⟩⟩,⟨⟨0,0⟩,⟨6821992474173491748147200667,6821992474173491748228548055⟩⟩,⟨⟨0,0⟩,⟨7291131255199261819920769718,7291131255199261820008147899⟩⟩] +lemma amp4_15_0_eq : ∀ k : Fin 16, amp4_1Expr 5 0 k = amp4_15_0 k := by decide +kernel +noncomputable def amp4_15_1 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨7751395450698644995545663552,7751395450698644995638763029⟩⟩,⟨⟨0,0⟩,⟨8217786023128097380764824045,8217786023128097380863273210⟩⟩,⟨⟨0,0⟩,⟨8676073767988110570327809130,8676073767988110570431342066⟩⟩,⟨⟨0,0⟩,⟨9139537335716977438218541679,9139537335716977438329268110⟩⟩,⟨⟨0,0⟩,⟨9595486376480452818666476030,9595486376480452818781698184⟩⟩,⟨⟨0,0⟩,⟨10055817204924139265960826380,10055817204924139266080601847⟩⟩,⟨⟨0,0⟩,⟨10509089791589342672891538552,10509089791589342673018588896⟩⟩,⟨⟨0,0⟩,⟨10966065236024010114121719083,10966065236024010114252811227⟩⟩,⟨⟨0,0⟩,⟨11416340688760420328905104757,11416340688760420329042939369⟩⟩,⟨⟨0,0⟩,⟨11869727294381481877117058437,11869727294381481877262148227⟩⟩,⟨⟨0,0⟩,⟨12316697480480254771994745810,12316697480480254772143106166⟩⟩,⟨⟨0,0⟩,⟨12766254891602009637826902453,12766254891602009637982089957⟩⟩,⟨⟨0,0⟩,⟨13209621370059014535783163596,13209621370059014535940314759⟩⟩,⟨⟨0,0⟩,⟨13655104950972463001282116531,13655104950972463001447460997⟩⟩,⟨⟨0,0⟩,⟨14094577119453890023469974093,14094577119453890023641274285⟩⟩,⟨⟨0,0⟩,⟨14535739783441810130490456580,14535739783441810130668587170⟩⟩] +lemma amp4_15_1_eq : ∀ k : Fin 16, amp4_1Expr 5 1 k = amp4_15_1 k := by decide +kernel +noncomputable def amp4_15_2 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨14971033652317385873237046249,14971033652317385873416197841⟩⟩,⟨⟨0,0⟩,⟨15407627185369045845232029077,15407627185369045845418728853⟩⟩,⟨⟨0,0⟩,⟨15838464557506970186781819526,15838464557506970186975034448⟩⟩,⟨⟨0,0⟩,⟨16270240608961625265401866566,16270240608961625265602218712⟩⟩,⟨⟨0,0⟩,⟨16696348529765272279212027570,16696348529765272279420510916⟩⟩,⟨⟨0,0⟩,⟨17123059377081258097343677047,17123059377081258097550466844⟩⟩,⟨⟨0,0⟩,⟨17544169769018200423125632453,17544169769018200423339068685⟩⟩,⟨⟨0,0⟩,⟨17965568925439762165284768738,17965568925439762165503518153⟩⟩,⟨⟨0,0⟩,⟨18381418351227587809487664123,18381418351227587809713026174⟩⟩,⟨⟨0,0⟩,⟨18797261061655928396470588463,18797261061655928396702856649⟩⟩,⟨⟨0,0⟩,⟨19207590578814079551668081932,19207590578814079551907142683⟩⟩,⟨⟨0,0⟩,⟨19617634234436279719996345735,19617634234436279720230964146⟩⟩,⟨⟨0,0⟩,⟨20022189315728738362221149746,20022189315728738362464373645⟩⟩,⟨⟨0,0⟩,⟨20426193808440952720483850609,20426193808440952720733866606⟩⟩,⟨⟨0,0⟩,⟨20824724310448551711007152060,20824724310448551711265415278⟩⟩,⟨⟨0,0⟩,⟨21222452341827216678756215314,21222452341827216679018741493⟩⟩] +lemma amp4_15_2_eq : ∀ k : Fin 16, amp4_1Expr 5 2 k = amp4_15_2 k := by decide +kernel +noncomputable def amp4_15_3 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨21614712509035809766268188222,21614712509035809766537437569⟩⟩,⟨⟨0,0⟩,⟨22005929864376524720173868442,22005929864376524720450274795⟩⟩,⟨⟨0,0⟩,⟨22391678359670523838791445742,22391678359670523839075326344⟩⟩,⟨⟨0,0⟩,⟨22776154154706997819343270783,22776154154706997819615439525⟩⟩,⟨⟨0,0⟩,⟨23155154109585114316424238597,23155154109585114316705203777⟩⟩,⟨⟨0,0⟩,⟨23532661015470212554804114850,23532661015470212555092125945⟩⟩,⟨⟨0,0⟩,⟨23904680095009751316489991215,23904680095009751316784822024⟩⟩,⟨⟨0,0⟩,⟨24274994545700667020200380202,24274994545700667020501134009⟩⟩,⟨⟨0,0⟩,⟨24639805024518844204389281623,24639805024518844204697065662⟩⟩,⟨⟨0,0⟩,⟨25002707409672597433812471512,25002707409672597434122529458⟩⟩,⟨⟨0,0⟩,⟨25360086256019165709374512789,25360086256019165709691367578⟩⟩,⟨⟨0,0⟩,⟨25715361101749847687583558465,25715361101749847687905214577⟩⟩,⟨⟨0,0⟩,⟨26065090067515605574385141480,26065090067515605574712425898⟩⟩,⟨⟨0,0⟩,⟨26412526206808221627553388717,26412526206808221627886041327⟩⟩,⟨⟨0,0⟩,⟨26754391921717071432963636548,26754391921717071433302046561⟩⟩,⟨⟨0,0⟩,⟨27093782655877928083692278476,27093782655877928084036123447⟩⟩] +lemma amp4_15_3_eq : ∀ k : Fin 16, amp4_1Expr 5 3 k = amp4_15_3 k := by decide +kernel +noncomputable def amp4_15_4 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨27427576724493021402835960847,27427576724493021403156045802⟩⟩,⟨⟨0,0⟩,⟨27758719976704175665270455490,27758719976704175665600665448⟩⟩,⟨⟨0,0⟩,⟨28084239077154113068015367596,28084239077154113068354524544⟩⟩,⟨⟨0,0⟩,⟨28406937538961959616646220611,28406937538961959616993097697⟩⟩,⟨⟨0,0⟩,⟨28723983522504130804753580561,28723983522504130805107783027⟩⟩,⟨⟨0,0⟩,⟨29038044793890211751075200275,29038044793890211751437648600⟩⟩,⟨⟨0,0⟩,⟨29346424784591707850420926429,29346424784591707850788683594⟩⟩,⟨⟨0,0⟩,⟨29651661508133253728189211135,29651661508133253728564182519⟩⟩,⟨⟨0,0⟩,⟨29951188002077299329178163668,29951188002077299329560875585⟩⟩,⟨⟨0,0⟩,⟨30247417991595653884640988147,30247417991595653885022639430⟩⟩,⟨⟨0,0⟩,⟨30537908955121911915802610237,30537908955121911916192402771⟩⟩,⟨⟨0,0⟩,⟨30824955319131378738919805200,30824955319131378739316024561⟩⟩,⟨⟨0,0⟩,⟨31106234285698202318807231638,31106234285698202319210789670⟩⟩,⟨⟨0,0⟩,⟨31383925545900440189946344853,31383925545900440190353812163⟩⟩,⟨⟨0,0⟩,⟨31655821711220961597188431509,31655821711220961597603276707⟩⟩,⟨⟨0,0⟩,⟨31923991916236710245575926644,31923991916236710245995985319⟩⟩] +lemma amp4_15_4_eq : ∀ k : Fin 16, amp4_1Expr 5 4 k = amp4_15_4 k := by decide +kernel +noncomputable def amp4_15_5 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨32186340231392153200905825416,32186340231392153201332037008⟩⟩,⟨⟨0,0⟩,⟨32444829065879675048588147341,32444829065879675049020319256⟩⟩,⟨⟨0,0⟩,⟨32697470328155163684948571191,32697470328155163685387572430⟩⟩,⟨⟨0,0⟩,⟨32946123217430973330987485782,32946123217430973331432915775⟩⟩,⟨⟨0,0⟩,⟨33188904158653455315019109592,33188904158653455315471270713⟩⟩,⟨⟨0,0⟩,⟨33427572368903866377915686643,33427572368903866378316201889⟩⟩,⟨⟨0,0⟩,⟨33660345741090154093358933892,33660345741090154093769281408⟩⟩,⟨⟨0,0⟩,⟨33888886475240507526702479364,33888886475240507527121028353⟩⟩,⟨⟨0,0⟩,⟨34111511133387095183728243724,34111511133387095184153953258⟩⟩,⟨⟨0,0⟩,⟨34329787622678162156441791496,34329787622678162156874377713⟩⟩,⟨⟨0,0⟩,⟨34542128604544351020214962777,34542128604544351020652941401⟩⟩,⟨⟨0,0⟩,⟨34750010195851482023215825809,34750010195851482023658798925⟩⟩,⟨⟨0,0⟩,⟨34951938798604186338174260411,34951938798604186338624153005⟩⟩,⟨⟨0,0⟩,⟨35149301037523642618265522291,35149301037523642618719270461⟩⟩,⟨⟨0,0⟩,⟨35340694891126642207388529188,35340694891126642207847890965⟩⟩,⟨⟨0,0⟩,⟨35527419600844671404477355739,35527419600844671404942772877⟩⟩] +lemma amp4_15_5_eq : ∀ k : Fin 16, amp4_1Expr 5 5 k = amp4_15_5 k := by decide +kernel +noncomputable def amp4_15_6 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨35708162738087487969629482346,35708162738087487970094701028⟩⟩,⟨⟨0,0⟩,⟨35884138094040676038646908078,35884138094040676039119268354⟩⟩,⟨⟨0,0⟩,⟨36054121017113048632715721236,36054121017113048633191311826⟩⟩,⟨⟨0,0⟩,⟨36219241617442961543932620656,36219241617442961544415095682⟩⟩,⟨⟨0,0⟩,⟨36378361360970378297152592353,36378361360970378297639767573⟩⟩,⟨⟨0,0⟩,⟨36532528292771231841181035197,36532528292771231841673931112⟩⟩,⟨⟨0,0⟩,⟨36680688483235377565472319285,36680688483235377565950985160⟩⟩,⟨⟨0,0⟩,⟨36823809384590225483935500717,36823809384590225484421497887⟩⟩,⟨⟨0,0⟩,⟨36960920296065720304650909332,36960920296065720305142207457⟩⟩,⟨⟨0,0⟩,⟨37092909413864254184340783605,37092909413864254184836185036⟩⟩,⟨⟨0,0⟩,⟨37218888020009842724728681353,37218888020009842725229310819⟩⟩,⟨⟨0,0⟩,⟨37339666263539208117160359900,37339666263539208117663838777⟩⟩,⟨⟨0,0⟩,⟨37454436285787739076668134202,37454436285787739077175560780⟩⟩,⟨⟨0,0⟩,⟨37563931276086673294397922353,37563931276086673294910559067⟩⟩,⟨⟨0,0⟩,⟨37667423227983889636657520706,37667423227983889637165678719⟩⟩,⟨⟨0,0⟩,⟨37765569342949880319096414150,37765569342949880319608636394⟩⟩] +lemma amp4_15_6_eq : ∀ k : Fin 16, amp4_1Expr 5 6 k = amp4_15_6 k := by decide +kernel +noncomputable def amp4_15_7 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨37857720570597306432150340369,37857720570597306432665478082⟩⟩,⟨⟨0,0⟩,⟨37944458985836275421531566832,37944458985836275422050711635⟩⟩,⟨⟨0,0⟩,⟨38025213704398410461179398209,38025213704398410461697262235⟩⟩,⟨⟨0,0⟩,⟨38100492429806577181747498264,38100492429806577182268210970⟩⟩,⟨⟨0,0⟩,⟨38169801756047242382336640680,38169801756047242382856953904⟩⟩,⟨⟨0,0⟩,⟨38233575668115257838479175926,38233575668115257839002535762⟩⟩,⟨⟨0,0⟩,⟨38291397648932349303566721235,38291397648932349304090540397⟩⟩,⟨⟨0,0⟩,⟨38343628518762467668575748278,38343628518762467669100009910⟩⟩,⟨⟨0,0⟩,⟨38389928155694576733296596847,38389928155694576733821424096⟩⟩,⟨⟨0,0⟩,⟨38430584672722504872537078627,38430584672722504873062904738⟩⟩,⟨⟨0,0⟩,⟨38465333942404921042175842801,38465333942404921042701349212⟩⟩,⟨⟨0,0⟩,⟨38494391733819021335516519298,38494391733819021336041977347⟩⟩,⟨⟨0,0⟩,⟨38517569604370558560887901793,38517569604370558561412092209⟩⟩,⟨⟨0,0⟩,⟨38535011250222245611046080557,38535011250222245611568583260⟩⟩,⟨⟨0,0⟩,⟨38546603693548157834160753685,38546603693548157834680524263⟩⟩,⟨⟨0,0⟩,⟨38552418737548597096042908506,38552418737548597096558544044⟩⟩] +lemma amp4_15_7_eq : ∀ k : Fin 16, amp4_1Expr 5 7 k = amp4_15_7 k := by decide +kernel +noncomputable def amp4_15_8 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨38552418737548597096042908506,38552418737548597096558544044⟩⟩,⟨⟨0,0⟩,⟨38546603693548157834160753685,38546603693548157834680524263⟩⟩,⟨⟨0,0⟩,⟨38535011250222245611046080557,38535011250222245611568583260⟩⟩,⟨⟨0,0⟩,⟨38517569604370558560887901793,38517569604370558561412092209⟩⟩,⟨⟨0,0⟩,⟨38494391733819021335516519298,38494391733819021336041977347⟩⟩,⟨⟨0,0⟩,⟨38465333942404921042175842801,38465333942404921042701349212⟩⟩,⟨⟨0,0⟩,⟨38430584672722504872537078627,38430584672722504873062904738⟩⟩,⟨⟨0,0⟩,⟨38389928155694576733296596847,38389928155694576733821424096⟩⟩,⟨⟨0,0⟩,⟨38343628518762467668575748278,38343628518762467669100009910⟩⟩,⟨⟨0,0⟩,⟨38291397648932349303566721235,38291397648932349304090540397⟩⟩,⟨⟨0,0⟩,⟨38233575668115257838479175926,38233575668115257839002535762⟩⟩,⟨⟨0,0⟩,⟨38169801756047242382336640680,38169801756047242382856953904⟩⟩,⟨⟨0,0⟩,⟨38100492429806577181747498264,38100492429806577182268210970⟩⟩,⟨⟨0,0⟩,⟨38025213704398410461179398209,38025213704398410461697262235⟩⟩,⟨⟨0,0⟩,⟨37944458985836275421531566832,37944458985836275422050711635⟩⟩,⟨⟨0,0⟩,⟨37857720570597306432150340369,37857720570597306432665478082⟩⟩] +lemma amp4_15_8_eq : ∀ k : Fin 16, amp4_1Expr 5 8 k = amp4_15_8 k := by decide +kernel +noncomputable def amp4_15_9 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨37765569342949880319096414150,37765569342949880319608636394⟩⟩,⟨⟨0,0⟩,⟨37667423227983889636657520706,37667423227983889637165678719⟩⟩,⟨⟨0,0⟩,⟨37563931276086673294397922353,37563931276086673294910559067⟩⟩,⟨⟨0,0⟩,⟨37454436285787739076668134202,37454436285787739077175560780⟩⟩,⟨⟨0,0⟩,⟨37339666263539208117160359900,37339666263539208117663838777⟩⟩,⟨⟨0,0⟩,⟨37218888020009842724728681353,37218888020009842725229310819⟩⟩,⟨⟨0,0⟩,⟨37092909413864254184340783605,37092909413864254184836185036⟩⟩,⟨⟨0,0⟩,⟨36960920296065720304650909332,36960920296065720305142207457⟩⟩,⟨⟨0,0⟩,⟨36823809384590225483935500717,36823809384590225484421497887⟩⟩,⟨⟨0,0⟩,⟨36680688483235377565472319285,36680688483235377565950985160⟩⟩,⟨⟨0,0⟩,⟨36532528292771231841181035197,36532528292771231841673931112⟩⟩,⟨⟨0,0⟩,⟨36378361360970378297152592353,36378361360970378297639767573⟩⟩,⟨⟨0,0⟩,⟨36219241617442961543932620656,36219241617442961544415095682⟩⟩,⟨⟨0,0⟩,⟨36054121017113048632715721236,36054121017113048633191311826⟩⟩,⟨⟨0,0⟩,⟨35884138094040676038646908078,35884138094040676039119268354⟩⟩,⟨⟨0,0⟩,⟨35708162738087487969629482346,35708162738087487970094701028⟩⟩] +lemma amp4_15_9_eq : ∀ k : Fin 16, amp4_1Expr 5 9 k = amp4_15_9 k := by decide +kernel +noncomputable def amp4_15_10 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨35527419600844671404477355739,35527419600844671404942772877⟩⟩,⟨⟨0,0⟩,⟨35340694891126642207388529188,35340694891126642207847890965⟩⟩,⟨⟨0,0⟩,⟨35149301037523642618265522291,35149301037523642618719270461⟩⟩,⟨⟨0,0⟩,⟨34951938798604186338174260411,34951938798604186338624153005⟩⟩,⟨⟨0,0⟩,⟨34750010195851482023215825809,34750010195851482023658798925⟩⟩,⟨⟨0,0⟩,⟨34542128604544351020214962777,34542128604544351020652941401⟩⟩,⟨⟨0,0⟩,⟨34329787622678162156441791496,34329787622678162156874377713⟩⟩,⟨⟨0,0⟩,⟨34111511133387095183728243724,34111511133387095184153953258⟩⟩,⟨⟨0,0⟩,⟨33888886475240507526702479364,33888886475240507527121028353⟩⟩,⟨⟨0,0⟩,⟨33660345741090154093358933892,33660345741090154093769281408⟩⟩,⟨⟨0,0⟩,⟨33427572368903866377915686643,33427572368903866378316201889⟩⟩,⟨⟨0,0⟩,⟨33188904158653455315019109592,33188904158653455315471270713⟩⟩,⟨⟨0,0⟩,⟨32946123217430973330987485782,32946123217430973331432915775⟩⟩,⟨⟨0,0⟩,⟨32697470328155163684948571191,32697470328155163685387572430⟩⟩,⟨⟨0,0⟩,⟨32444829065879675048588147341,32444829065879675049020319256⟩⟩,⟨⟨0,0⟩,⟨32186340231392153200905825416,32186340231392153201332037008⟩⟩] +lemma amp4_15_10_eq : ∀ k : Fin 16, amp4_1Expr 5 10 k = amp4_15_10 k := by decide +kernel +noncomputable def amp4_15_11 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨31923991916236710245575926644,31923991916236710245995985319⟩⟩,⟨⟨0,0⟩,⟨31655821711220961597188431509,31655821711220961597603276707⟩⟩,⟨⟨0,0⟩,⟨31383925545900440189946344853,31383925545900440190353812163⟩⟩,⟨⟨0,0⟩,⟨31106234285698202318807231638,31106234285698202319210789670⟩⟩,⟨⟨0,0⟩,⟨30824955319131378738919805200,30824955319131378739316024561⟩⟩,⟨⟨0,0⟩,⟨30537908955121911915802610237,30537908955121911916192402771⟩⟩,⟨⟨0,0⟩,⟨30247417991595653884640988147,30247417991595653885022639430⟩⟩,⟨⟨0,0⟩,⟨29951188002077299329178163668,29951188002077299329560875585⟩⟩,⟨⟨0,0⟩,⟨29651661508133253728189211135,29651661508133253728564182519⟩⟩,⟨⟨0,0⟩,⟨29346424784591707850420926429,29346424784591707850788683594⟩⟩,⟨⟨0,0⟩,⟨29038044793890211751075200275,29038044793890211751437648600⟩⟩,⟨⟨0,0⟩,⟨28723983522504130804753580561,28723983522504130805107783027⟩⟩,⟨⟨0,0⟩,⟨28406937538961959616646220611,28406937538961959616993097697⟩⟩,⟨⟨0,0⟩,⟨28084239077154113068015367596,28084239077154113068354524544⟩⟩,⟨⟨0,0⟩,⟨27758719976704175665270455490,27758719976704175665600665448⟩⟩,⟨⟨0,0⟩,⟨27427576724493021402835960847,27427576724493021403156045802⟩⟩] +lemma amp4_15_11_eq : ∀ k : Fin 16, amp4_1Expr 5 11 k = amp4_15_11 k := by decide +kernel +noncomputable def amp4_15_12 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨27093782655877928083692278476,27093782655877928084036123447⟩⟩,⟨⟨0,0⟩,⟨26754391921717071432963636548,26754391921717071433302046561⟩⟩,⟨⟨0,0⟩,⟨26412526206808221627553388717,26412526206808221627886041327⟩⟩,⟨⟨0,0⟩,⟨26065090067515605574385141480,26065090067515605574712425898⟩⟩,⟨⟨0,0⟩,⟨25715361101749847687583558465,25715361101749847687905214577⟩⟩,⟨⟨0,0⟩,⟨25360086256019165709374512789,25360086256019165709691367578⟩⟩,⟨⟨0,0⟩,⟨25002707409672597433812471512,25002707409672597434122529458⟩⟩,⟨⟨0,0⟩,⟨24639805024518844204389281623,24639805024518844204697065662⟩⟩,⟨⟨0,0⟩,⟨24274994545700667020200380202,24274994545700667020501134009⟩⟩,⟨⟨0,0⟩,⟨23904680095009751316489991215,23904680095009751316784822024⟩⟩,⟨⟨0,0⟩,⟨23532661015470212554804114850,23532661015470212555092125945⟩⟩,⟨⟨0,0⟩,⟨23155154109585114316424238597,23155154109585114316705203777⟩⟩,⟨⟨0,0⟩,⟨22776154154706997819343270783,22776154154706997819615439525⟩⟩,⟨⟨0,0⟩,⟨22391678359670523838791445742,22391678359670523839075326344⟩⟩,⟨⟨0,0⟩,⟨22005929864376524720173868442,22005929864376524720450274795⟩⟩,⟨⟨0,0⟩,⟨21614712509035809766268188222,21614712509035809766537437569⟩⟩] +lemma amp4_15_12_eq : ∀ k : Fin 16, amp4_1Expr 5 12 k = amp4_15_12 k := by decide +kernel +noncomputable def amp4_15_13 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨21222452341827216678756215314,21222452341827216679018741493⟩⟩,⟨⟨0,0⟩,⟨20824724310448551711007152060,20824724310448551711265415278⟩⟩,⟨⟨0,0⟩,⟨20426193808440952720483850609,20426193808440952720733866606⟩⟩,⟨⟨0,0⟩,⟨20022189315728738362221149746,20022189315728738362464373645⟩⟩,⟨⟨0,0⟩,⟨19617634234436279719996345735,19617634234436279720230964146⟩⟩,⟨⟨0,0⟩,⟨19207590578814079551668081932,19207590578814079551907142683⟩⟩,⟨⟨0,0⟩,⟨18797261061655928396470588463,18797261061655928396702856649⟩⟩,⟨⟨0,0⟩,⟨18381418351227587809487664123,18381418351227587809713026174⟩⟩,⟨⟨0,0⟩,⟨17965568925439762165284768738,17965568925439762165503518153⟩⟩,⟨⟨0,0⟩,⟨17544169769018200423125632453,17544169769018200423339068685⟩⟩,⟨⟨0,0⟩,⟨17123059377081258097343677047,17123059377081258097550466844⟩⟩,⟨⟨0,0⟩,⟨16696348529765272279212027570,16696348529765272279420510916⟩⟩,⟨⟨0,0⟩,⟨16270240608961625265401866566,16270240608961625265602218712⟩⟩,⟨⟨0,0⟩,⟨15838464557506970186781819526,15838464557506970186975034448⟩⟩,⟨⟨0,0⟩,⟨15407627185369045845232029077,15407627185369045845418728853⟩⟩,⟨⟨0,0⟩,⟨14971033652317385873237046249,14971033652317385873416197841⟩⟩] +lemma amp4_15_13_eq : ∀ k : Fin 16, amp4_1Expr 5 13 k = amp4_15_13 k := by decide +kernel +noncomputable def amp4_15_14 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨14535739783441810130490456580,14535739783441810130668587170⟩⟩,⟨⟨0,0⟩,⟨14094577119453890023469974093,14094577119453890023641274285⟩⟩,⟨⟨0,0⟩,⟨13655104950972463001282116531,13655104950972463001447460997⟩⟩,⟨⟨0,0⟩,⟨13209621370059014535783163596,13209621370059014535940314759⟩⟩,⟨⟨0,0⟩,⟨12766254891602009637826902453,12766254891602009637982089957⟩⟩,⟨⟨0,0⟩,⟨12316697480480254771994745810,12316697480480254772143106166⟩⟩,⟨⟨0,0⟩,⟨11869727294381481877117058437,11869727294381481877262148227⟩⟩,⟨⟨0,0⟩,⟨11416340688760420328905104757,11416340688760420329042939369⟩⟩,⟨⟨0,0⟩,⟨10966065236024010114121719083,10966065236024010114252811227⟩⟩,⟨⟨0,0⟩,⟨10509089791589342672891538552,10509089791589342673018588896⟩⟩,⟨⟨0,0⟩,⟨10055817204924139265960826380,10055817204924139266080601847⟩⟩,⟨⟨0,0⟩,⟨9595486376480452818666476030,9595486376480452818781698184⟩⟩,⟨⟨0,0⟩,⟨9139537335716977438218541679,9139537335716977438329268110⟩⟩,⟨⟨0,0⟩,⟨8676073767988110570327809130,8676073767988110570431342066⟩⟩,⟨⟨0,0⟩,⟨8217786023128097380764824045,8217786023128097380863273210⟩⟩,⟨⟨0,0⟩,⟨7751395450698644995545663552,7751395450698644995638763029⟩⟩] +lemma amp4_15_14_eq : ∀ k : Fin 16, amp4_1Expr 5 14 k = amp4_15_14 k := by decide +kernel +noncomputable def amp4_15_15 : Fin 16 → CBox := ![⟨⟨0,0⟩,⟨7291131255199261819920769718,7291131255199261820008147899⟩⟩,⟨⟨0,0⟩,⟨6821992474173491748147200667,6821992474173491748228548055⟩⟩,⟨⟨0,0⟩,⟨6360151401061098850485125164,6360151401061098850560370432⟩⟩,⟨⟨0,0⟩,⟨5888398725213949358166629037,5888398725213949358236663964⟩⟩,⟨⟨0,0⟩,⟨5425441185469606814646061604,5425441185469606814710619416⟩⟩,⟨⟨0,0⟩,⟨4951131303068236857576605536,4951131303068236857635335239⟩⟩,⟨⟨0,0⟩,⟨4487625400817782326415073419,4487625400817782326467773508⟩⟩,⟨⟨0,0⟩,⟨4010668238177036632638050818,4010668238177036632685433220⟩⟩,⟨⟨0,0⟩,⟨3547394144058060913845578585,3547394144058060913887186800⟩⟩,⟨⟨0,0⟩,⟨3067387839274413925669940985,3067387839274413925705706943⟩⟩,⟨⟨0,0⟩,⟨2605610421927042946746523973,2605610421927042946776537171⟩⟩,⟨⟨0,0⟩,⟨2121361682949658354780451532,2121361682949658354804652084⟩⟩,⟨⟨0,0⟩,⟨1663741155941996025460178078,1663741155941996025478691197⟩⟩,⟨⟨0,0⟩,⟨1171344964628820879944165547,1171344964628820879956904243⟩⟩,⟨⟨0,0⟩,⟨726611995767906115087064597,726611995767906115093974983⟩⟩,⟨⟨0,0⟩,⟨206433418803638677622879409,206433418803638677624245993⟩⟩] +lemma amp4_15_15_eq : ∀ k : Fin 16, amp4_1Expr 5 15 k = amp4_15_15 k := by decide +kernel +noncomputable def amp4_15 : Fin 16 → Fin 16 → CBox := ![amp4_15_0,amp4_15_1,amp4_15_2,amp4_15_3,amp4_15_4,amp4_15_5,amp4_15_6,amp4_15_7,amp4_15_8,amp4_15_9,amp4_15_10,amp4_15_11,amp4_15_12,amp4_15_13,amp4_15_14,amp4_15_15] +lemma amp4_15_eq (i k : Fin 16) : amp4_1Expr 5 i k = amp4_15 i k := by + fin_cases i + · exact amp4_15_0_eq k + · exact amp4_15_1_eq k + · exact amp4_15_2_eq k + · exact amp4_15_3_eq k + · exact amp4_15_4_eq k + · exact amp4_15_5_eq k + · exact amp4_15_6_eq k + · exact amp4_15_7_eq k + · exact amp4_15_8_eq k + · exact amp4_15_9_eq k + · exact amp4_15_10_eq k + · exact amp4_15_11_eq k + · exact amp4_15_12_eq k + · exact amp4_15_13_eq k + · exact amp4_15_14_eq k + · exact amp4_15_15_eq k +noncomputable def amp4_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp4_10,amp4_11,amp4_12,amp4_13,amp4_14,amp4_15] +lemma amp4_1_eq (j : Fin 6) (i k : Fin 16) : amp4_1Expr j i k = amp4_1 j i k := by + fin_cases j + · exact amp4_10_eq i k + · exact amp4_11_eq i k + · exact amp4_12_eq i k + · exact amp4_13_eq i k + · exact amp4_14_eq i k + · exact amp4_15_eq i k +lemma amp4_1_contains (j : Fin 6) (i k : Fin 16) : + (amp4_1 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude true 4 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp4_1_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 4 j) (bLookup_contains 4 j) true) +noncomputable def amp7_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 7 j) (bLookup 7 j) false) +noncomputable def amp7_00_0 : Fin 16 → CBox := ![⟨⟨1559522290940923961266002621,1559522290940923961467376560⟩,⟨93606319881131816135819496,93606319881131816324769281⟩⟩,⟨⟨5489335956442995593551614987,5489335956442995594276275675⟩,⟨329454183859859827278205697,329454183859859827944219672⟩⟩,⟨⟨8849391192914736850387618597,8849391192914736851567866322⟩,⟨531021213985451591740085661,531021213985451592814432615⟩⟩,⟨⟨12569885820067326834906148947,12569885820067326836585641899⟩,⟨754075270951602632413767847,754075270951602633939851669⟩⟩,⟨⟨16028133338719027728431900088,16028133338719027730577737781⟩,⟨961197924719543986198397243,961197924719543988144381145⟩⟩,⟨⟨19688200262379251460926909481,19688200262379251463564598906⟩,⟨1180168517784169612640651477,1180168517784169615030785962⟩⟩,⟨⟨23179239671638022549666673686,23179239671638022552774873253⟩,⟨1388695194947131463665810398,1388695194947131466479455887⟩⟩,⟨⟨26808933779188429187984079062,26808933779188429191580216120⟩,⟨1605161115664026581086235932,1605161115664026584339920066⟩⟩,⟨⟨30313220215010751626324497156,30313220215010751630392446671⟩,⟨1813694339092520909918036055,1813694339092520913596311295⟩⟩,⟨⟨33922105419220902004037583642,33922105419220902008586402739⟩,⟨2028006478273828713400271168,2028006478273828717515227732⟩⟩,⟨⟨37430629388735435997067915392,37430629388735436002090378547⟩,⟨2235783529102243049699231062,2235783529102243054238727609⟩⟩,⟨⟨41022283987435101553377672958,41022283987435101558882064707⟩,⟨2447936219445482032825820668,2447936219445482037799393119⟩⟩,⟨⟨44529690171788392486768386315,44529690171788392492741356088⟩,⟨2654416770198902269989205360,2654416770198902275386108100⟩⟩,⟨⟨48105328693697031301232704624,48105328693697031307680147351⟩,⟨2864265852138096930876297900,2864265852138096936704163173⟩⟩,⟨⟨51607854703631617557070240531,51607854703631617563989506382⟩,⟨3069008905085332605714735533,3069008905085332611964653739⟩⟩,⟨⟨55167572989373913989909965788,55167572989373913997307009254⟩,⟨3276347120733813476068273367,3276347120733813482746556735⟩⟩] +lemma amp7_00_0_eq : ∀ k : Fin 16, amp7_0Expr 0 0 k = amp7_00_0 k := by decide +kernel +noncomputable def amp7_00_1 : Fin 16 → CBox := ![⟨⟨58662259261339671042505161810,58662259261339671050369175889⟩,⟨3478964236115248127624324163,3478964236115248134722430700⟩⟩,⟨⟨62205555163652398986582425403,62205555163652398994915972742⟩,⟨3683553132480533351074945788,3683553132480533358597944466⟩⟩,⟨⟨65689889407964693191112696448,65689889407964693199905981004⟩,⟨3883687729396738504500539173,3883687729396738512440576101⟩⟩,⟨⟨69215911607703542287262832900,69215911607703542296536293020⟩,⟨4085273230009796538566753660,4085273230009796546929101581⟩⟩,⟨⟨72687649587317296508357670168,72687649587317296518083609374⟩,⟨4282590458767819542486824621,4282590458767819551263043318⟩⟩,⟨⟨76195328596562208774337701370,76195328596562208784520248025⟩,⟨4480911350149214399734476190,4480911350149214408928159238⟩⟩,⟨⟨79652395792001608790025411700,79652395792001608800678316807⟩,⟨4675092805467640801889772882,4675092805467640811495280381⟩⟩,⟨⟨83140518217898985963931728682,83140518217898985975033525305⟩,⟨4869885802761709856429054695,4869885802761709866447858291⟩⟩,⟨⟨86580952196126867157908306595,86580952196126867169472901483⟩,⟨5060626664353293745228733880,5060626664353293755655474674⟩⟩,⟨⟨90048205369189710369591327622,90048205369189710381625076767⟩,⟨5251629681473291199392329553,5251629681473291210229567053⟩⟩,⟨⟨93470120180796412024293046934,93470120180796412036759388852⟩,⟨5438637159484464533411805784,5438637159484464544651445985⟩⟩,⟨⟨96915120276839725674319596513,96915120276839725687247467227⟩,⟨5625591570337328755389710226,5625591570337328767035146944⟩⟩,⟨⟨100316683497884847661581130907,100316683497884847674927455633⟩,⟨5808584090911250849907024099,5808584090911250861949960105⟩⟩,⟨⟨103737993975309751819485303316,103737993975309751833298875370⟩,⟨5991236389712338720345271282,5991236389712338732789807906⟩⟩,⟨⟨107117411371679709628856039291,107117411371679709643113864159⟩,⟨6169943217786975307493683073,6169943217786975320332814349⟩⟩,⟨⟨110513555478414122632350870540,110513555478414122647060667570⟩,⟨6348046302403234881011292817,6348046302403234894246340943⟩⟩] +lemma amp7_00_1_eq : ∀ k : Fin 16, amp7_0Expr 0 1 k = amp7_00_1 k := by decide +kernel +noncomputable def amp7_00_2 : Fin 16 → CBox := ![⟨⟨113869060460768812976431041901,113869060460768812991542738753⟩,⟨6522207430371915601806114452,6522207430371915615428627368⟩⟩,⟨⟨117238529978915546547218994939,117238529978915546562782911571⟩,⟨6695521637468797312130312840,6695521637468797326143692418⟩⟩,⟨⟨120568376179638323120399204118,120568376179638323136401679483⟩,⟨6864887838212670991068112533,6864887838212671005466065567⟩⟩,⟨⟨123909637712160872980760881248,123909637712160872997206985865⟩,⟨7033181807190165077516629033,7033181807190165092299621195⟩⟩,⟨⟨127212093663662906286789927700,127212093663662906303681498240⟩,⟨7197514788940299664325276526,7197514788940299679487947991⟩⟩,⟨⟨130523593276006329180499715078,130523593276006329197761875630⟩,⟨7360566202203179996580666234,7360566202203180012118654985⟩⟩,⟨⟨133796938545584940362666632848,133796938545584940380357233127⟩,⟨7519638825309515321372911997,7519638825309515337284066202⟩⟩,⟨⟨137077105284698035362842516906,137077105284698035380951079924⟩,⟨7677235055044664127614749645,7677235055044664143898054618⟩⟩,⟨⟨140319627646981816029469850121,140319627646981816048000623040⟩,⟨7830831584346860420087003667,7830831584346860436737295416⟩⟩,⟨⟨143566876282777311349931286831,143566876282777311368885918777⟩,⟨7982770265394130971467752873,7982770265394130988484420739⟩⟩,⟨⟨146776869650728164122491318849,146776869650728164141863302998⟩,⟨8130686640354154030603261471,8130686640354154047980551202⟩⟩,⟨⟨149989602873402892438610586561,149989602873402892458313161541⟩,⟨8276776182124073159073471357,8276776182124073176805633212⟩⟩,⟨⟨153165365797939979018430308563,153165365797939979038557565455⟩,⟨8418820292296028764320514164,8418820292296028782407366860⟩⟩,⟨⟨156341976032508445798212823771,156341976032508445818749779076⟩,⟨8558880338430821658713147420,8558880338430821677152658593⟩⟩,⟨⟨159481810638921607041520201191,159481810638921607062472373832⟩,⟨8694872295401433737946923595,8694872295401433756734001174⟩⟩,⟨⟨162620681590677643897965169200,162620681590677643919300680138⟩,⟨8828734137087854331725355854,8828734137087854350856826190⟩⟩] +lemma amp7_00_2_eq : ∀ k : Fin 16, amp7_0Expr 0 2 k = amp7_00_2 k := by decide +kernel +noncomputable def amp7_00_3 : Fin 16 → CBox := ![⟨⟨165722892858705901260669946884,165722892858705901282402008149⟩,⟨8958506536417053642027735562,8958506536417053661498919843⟩⟩,⟨⟨168822400871159063610770730318,168822400871159063632901080450⟩,⟨9086013483402380495841705005,9086013483402380515651040222⟩⟩,⟨⟨171885296191891475361682569853,171885296191891475384208014333⟩,⟨9209411651745818256629879851,9209411651745818276771779340⟩⟩,⟨⟨174943811476575137912250165595,174943811476575137935021534500⟩,⟨9330419363854674441346192245,9330419363854674461810831920⟩⟩,⟨⟨177965700437479761811510702165,177965700437479761834679795925⟩,⟨9447301587616115101626834096,9447301587616115122416912506⟩⟩,⟨⟨180981588219498180353541373947,180981588219498180377092736282⟩,⟨9561678368711325842010185190,9561678368711325863122815317⟩⟩,⟨⟨183960782581606165189126823820,183960782581606165213053059323⟩,⟨9671916101415044667318323881,9671916101415044688747668484⟩⟩,⟨⟨186932404193713723974357138266,186932404193713723998649131796⟩,⟨9779543157160454143900111637,9779543157160454165643442196⟩⟩,⟨⟨189867218034020844997699236660,189867218034020845022359836535⟩,⟨9883021203356295235458733754,9883021203356295257510734263⟩⟩,⟨⟨192792931984002380232173278098,192792931984002380257163418651⟩,⟨9983792863738742424904760827,9983792863738742447260977614⟩⟩,⟨⟨195681681982641483710940497977,195681681982641483736289343751⟩,⟨10080409537723725484504859075,10080409537723725507161326263⟩⟩,⟨⟨198559845012858139645390193373,198559845012858139671079764007⟩,⟨10174233445019220152694473012,10174233445019220175647668554⟩⟩,⟨⟨201400850869304864561501929980,201400850869304864587532886226⟩,⟨10263900703025054904209633934,10263900703025054927454091531⟩⟩,⟨⟨204229819022860206368487137705,204229819022860206394854719550⟩,⟨10350697965712873046614285014,10350697965712873070147006939⟩⟩,⟨⟨207021403988877594705170164534,207021403988877594731871646843⟩,⟨10433341510499256405646436296,10433341510499256429461763816⟩⟩,⟨⟨209799533693516875095365893001,209799533693516875122395869316⟩,⟨10513046823511369704015236377,10513046823511369728109986923⟩⟩] +lemma amp7_00_3_eq : ∀ k : Fin 16, amp7_0Expr 0 3 k = amp7_00_3 k := by decide +kernel +noncomputable def amp7_00_4 : Fin 16 → CBox := ![⟨⟨212540025213077564280501836398,212540025213077564307628312743⟩,⟨10588606180541638395179013218,10588606180541638419536086368⟩⟩,⟨⟨215265674391363652892614509374,215265674391363652920096865950⟩,⟨10661167912165665648315319427,10661167912165665672944639618⟩⟩,⟨⟨217953404839659306050600110338,217953404839659306078423489056⟩,⟨10729596476738939798397502090,10729596476738939823292757855⟩⟩,⟨⟨220624934051964634188732816306,220624934051964634216884521709⟩,⟨10794976722458016724784604837,10794976722458016749941964983⟩⟩,⟨⟨223258241566996417093451731086,223258241566996417121922932033⟩,⟨10856241777340714708048301410,10856241777340714733461748647⟩⟩,⟨⟨225874015192264305799056210586,225874015192264305827850752515⟩,⟨10914416380884288090590359807,10914416380884288116256747769⟩⟩,⟨⟨228451244593530978813673750975,228451244593530978842763007140⟩,⟨10968499084131140265194633578,10968499084131140291106983719⟩⟩,⟨⟨231009632051486375360887511673,231009632051486375390282855064⟩,⟨11019457626020161246742465489,11019457626020161272897872043⟩⟩,⟨⟨233529135841038683529462292395,233529135841038683559162031774⟩,⟨11066352968805839596689853507,11066352968805839623082621347⟩⟩,⟨⟨236028512858491124931003002936,236028512858491124960934908084⟩,⟨11110098722699359147600049145,11110098722699359174223203531⟩⟩,⟨⟨238488652300169018919220473637,238488652300169018949450507760⟩,⟨11149815457100347817806228714,11149815457100347844657271265⟩⟩,⟨⟨240927402223193583086993763774,240927402223193583117504858735⟩,⟨11186365314284536912559273398,11186365314284536939633721949⟩⟩,⟨⟨243326548496255444004899421611,243326548496255444035692889592⟩,⟨11218925851059632469504019562,11218925851059632496796304120⟩⟩,⟨⟨245703063649319210775480931566,245703063649319210806526148915⟩,⟨11248310213462072915473438364,11248310213462072942978369967⟩⟩,⟨⟨248039599072946296520816160964,248039599072946296552134456633⟩,⟨11273750489980914284511959450,11273750489980914312224886722⟩⟩,⟨⟨250352282165437670800031757059,250352282165437670831602275797⟩,⟨11296013132140582240663949234,11296013132140582268580044035⟩⟩] +lemma amp7_00_4_eq : ∀ k : Fin 16, amp7_0Expr 0 4 k = amp7_00_4 k := by decide +kernel +noncomputable def amp7_00_5 : Fin 16 → CBox := ![⟨⟨252624601490780038413672854250,252624601490780038445497121909⟩,⟨11314382450704319805203206558,11314382450704319833316902806⟩⟩,⟨⟨254871867070873140176967890106,254871867070873140209040416953⟩,⟨11329580351179425865964768011,11329580351179425894271853865⟩⟩,⟨⟨257078378837416307792439561405,257078378837416307824761356184⟩,⟨11340941188067103646657206961,11340941188067103675152092589⟩⟩,⟨⟨259258654792745124244973944960,259258654792745124277537789285⟩,⟨11349144330817616101044424561,11349144330817616129722733809⟩⟩,⟨⟨261397782745835816552828210808,261397782745835816585630660116⟩,⟨11353572116476826239803586547,11353572116476826268659532159⟩⟩,⟨⟨263509511850049750616778613279,263509511850049750649355347603⟩,⟨11354863262815097427637289782,11354863262815097456646729155⟩⟩,⟨⟨265579696416436686482630182801,265579696416436686515459645443⟩,⟨11352446133696523065523404854,11352446133696523094701477675⟩⟩,⟨⟨267621337920350464673171005196,267621337920350464706236139230⟩,⟨11346920565457163518736878034,11346920565457163548078633995⟩⟩,⟨⟨269621037738582027375021275070,269621037738582027408308059908⟩,⟨11337759088070144795797443329,11337759088070144825296660204⟩⟩,⟨⟨271591069004310945450975654126,271591069004310945484477580023⟩,⟨11325524322708491992590512620,11325524322708492022242644889⟩⟩,⟨⟨273518762506793391166440175281,273518762506793391200139708961⟩,⟨11309731190549000377188911418,11309731190549000406987626973⟩⟩,⟨⟨275415680682973656299840762822,275415680682973656333730382234⟩,⟨11290906668935665515520603185,11290906668935665545461262579⟩⟩,⟨⟨277269867726437355277601375334,277269867726437355311690542177⟩,⟨11268606373009233805699370890,11268606373009233835776772786⟩⟩,⟨⟨279092191462366264684140421966,279092191462366264718400424608⟩,⟨11243323120745824176583768436,11243323120745824206792366250⟩⟩,⟨⟨280871395003418211494267618068,280871395003418211528706639375⟩,⟨11214651594476165232939068523,11214651594476165263273634555⟩⟩,⟨⟨282617666199706564372029592201,282617666199706564406646676807⟩,⟨11183051857613982141716506412,11183051857613982172172564857⟩⟩] +lemma amp7_00_5_eq : ∀ k : Fin 16, amp7_0Expr 0 5 k = amp7_00_5 k := by decide +kernel +noncomputable def amp7_00_6 : Fin 16 → CBox := ![⟨⟨284320434012068981187547348006,284320434012068981222286939772⟩,⟨11148156096993299608264741075,11148156096993299638834561559⟩⟩,⟨⟨285989219605175727814229786148,285989219605175727849145810225⟩,⟨11110392953092266448318712233,11110392953092266478999948429⟩⟩,⟨⟨287614126035126229694754872879,287614126035126229729810434980⟩,⟨11069430612991638078357092091,11069430612991638109142800477⟩⟩,⟨⟨289204019812940810627607181241,289204019812940810662826871359⟩,⟨11025667558510627201493410918,11025667558510627232380020560⟩⟩,⟨⟨290749667569381942332038446206,290749667569381942367399115519⟩,⟨10978806526128320213417421624,10978806526128320244398558948⟩⟩,⟨⟨292259292014831432585386805035,292259292014831432620892042619⟩,⟨10929217041190162832421203698,10929217041190162863492458958⟩⟩,⟨⟨293724313990328606576840344644,293724313990328606612324739724⟩,⟨10876634987672294436707821015,10876634987672294467857617140⟩⟩,⟨⟨295152322149813397124247871215,295152322149813397159879327159⟩,⟨10821402079296846164213303001,10821402079296846195443326435⟩⟩,⟨⟨296535383268852184147197807540,296535383268852184182954407410⟩,⟨10763285990618389558552431647,10763285990618389589856452167⟩⟩,⟨⟨297880460642154538172621945341,297880460642154538208489464397⟩,⟨10702601715564881036941831547,10702601715564881068314740124⟩⟩,⟨⟨299180259732782416088133258151,299180259732782416124115132603⟩,⟨10639147403809585982180097338,10639147403809586013616651420⟩⟩,⟨⟨300441126180946087213561628362,300441126180946087249634059862⟩,⟨10573212372214930079378086344,10573212372214930110872820705⟩⟩,⟨⟨301656397865881435855825723091,301656397865881435891991943504⟩,⟨10504623968440219200635790238,10504623968440219232183494366⟩⟩,⟨⟨302831809533427061926794564429,302831809533427061963060089260⟩,⟨10433646829482808431960628493,10433646829482808463556866838⟩⟩,⟨⟨303961326136640504037102534879,303961326136640504073383678055⟩,⟨10360136259400063429879758364,10360136259400063461516398493⟩⟩,⟨⟨305050077384360259802713463846,305050077384360259839074396708⟩,⟨10284333170258724869149559691,10284333170258724900824169582⟩⟩] +lemma amp7_00_6_eq : ∀ k : Fin 16, amp7_0Expr 0 6 k = amp7_00_6 k := by decide +kernel +noncomputable def amp7_00_7 : Fin 16 → CBox := ![⟨⟨306092650849061334069859471039,306092650849061334106285388772⟩,⟨10206119614000527226723815718,10206119614000527258430664906⟩⟩,⟨⟨307093576193527009681611338705,307093576193527009718106399241⟩,⟨10125713693415573126084644529,10125713693415573157819238511⟩⟩,⟨⟨308048060007423432753332553338,308048060007423432789848498156⟩,⟨10043023030699348439777709625,10043023030699348471533306890⟩⟩,⟨⟨308960036063244451348652699054,308960036063244451385218225473⟩,⟨9958243798476948495517717286,9958243798476948527290620107⟩⟩,⟨⟨309825327186882581401992687362,309825327186882581438576005724⟩,⟨9871308040509020977611634573,9871308040509021009395713776⟩⟩,⟨⟨310647274607664285404802501575,310647274607664285441426879525⟩,⟨9782390844341318608873929343,9782390844341318640665304053⟩⟩,⟨⟨311422315401608446257453533715,311422315401608446294092604527⟩,⟨9691447553836554521990980102,9691447553836554553783785133⟩⟩,⟨⟨312153200815486117757614244683,312153200815486117794263121813⟩,⟨9598632984837958446106293455,9598632984837958477895753405⟩⟩,⟨⟨312836980962051704678380614947,312836980962051704715034941034⟩,⟨9503924685557910363721701847,9503924685557910395502701558⟩⟩,⟨⟨313475818897612118479152026648,313475818897612118515810654669⟩,⟨9407457983942729202378954227,9407457983942729234146860522⟩⟩,⟨⟨314067377312833340300336103740,314067377312833340336983034098⟩,⟨9309231561179438200747017742,9309231561179438232496454350⟩⟩,⟨⟨314613232111183074977542050963,314613232111183075014174766790⟩,⟨9209362013527415724084001722,9209362013527415755810297451⟩⟩,⟨⟨315111658842671186723729764597,315111658842671186760333058117⟩,⟨9107868106980742784108601163,9107868106980742815806474926⟩⟩,⟨⟨315563646551369344187265199231,315563646551369344223830948211⟩,⟨9004848436555031090814265276,9004848436555031122478925592⟩⟩,⟨⟨315968084657701632063471267895,315968084657701632099985769689⟩,⟨8900340827068535294450694718,8900340827068535326077011953⟩⟩,⟨⟨316325374902243945741335489287,316325374902243945777782501122⟩,⟨8794426578665159373780363315,8794426578665159405363339539⟩⟩] +lemma amp7_00_7_eq : ∀ k : Fin 16, amp7_0Expr 0 7 k = amp7_00_7 k := by decide +kernel +noncomputable def amp7_00_8 : Fin 16 → CBox := ![⟨⟨316635022309517837144241448968,316635022309517837180649752148⟩,⟨8687161570299088843125837934,8687161570299088874661586487⟩⟩,⟨⟨316896840138039283831017146656,316896840138039283867416144669⟩,⟨8578610491117965238452545763,8578610491117965269937345588⟩⟩,⟨⟨317110951469230023086302764530,317110951469230023122676011067⟩,⟨8468846290047854244056677770,8468846290047854275485464578⟩⟩,⟨⟨317276579166083883587460227967,317276579166083883623794530284⟩,⟨8357917708082895462098951422,8357917708082895493466847645⟩⟩,⟨⟨317394467538858457165628655129,317394467538858457201915627275⟩,⟨8245913799818552217235310205,8245913799818552248537549545⟩⟩,⟨⟨317463246402731170022686008296,317463246402731170058911064200⟩,⟨8132868001268293334058806996,8132868001268293365290542156⟩⟩,⟨⟨317484285191395769123782894163,317484285191395769159943465536⟩,⟨8018884527690609875020859772,8018884527690609906177589450⟩⟩,⟨⟨317455617273628743230425866430,317455617273628743266506486980⟩,⟨7903982134891120285903002508,7903982134891120316979886307⟩⟩,⟨⟨317379241830922175525915187947,317379241830922175561914618634⟩,⟨7788279272603138569999612983,7788279272603138600992250060⟩⟩,⟨⟨317252591629733799673659668644,317252591629733799709574470268⟩,⟨7671780623981725274013202839,7671780623981725304917119872⟩⟩,⟨⟨317078300964225041184745897380,317078300964225041220571280028⟩,⟨7554617965465760277231424422,7554617965465760308042247886⟩⟩,⟨⟨316853197070558250585111410736,316853197070558250620821397347⟩,⟨7436782499007134071616274648,7436782499007134102329014171⟩⟩,⟨⟨316580555475462879950823098329,316580555475462879986441649313⟩,⟨7318418438071501420466517748,7318418438071501451077551228⟩⟩,⟨⟨316256592166225576995359403116,316256592166225577030855127864⟩,⟨7199504079777677711405026633,7199504079777677741909314450⟩⟩,⟨⟨315885230795523260471164659938,315885230795523260506567424983⟩,⟨7080195202764724593658397670,7080195202764724624052547233⟩⟩,⟨⟨315462069570040366552563665935,315462069570040366587825020453⟩,⟨6960457761575989106550451952,6960457761575989136829081880⟩⟩] +lemma amp7_00_8_eq : ∀ k : Fin 16, amp7_0Expr 0 8 k = amp7_00_8 k := by decide +kernel +noncomputable def amp7_00_9 : Fin 16 → CBox := ![⟨⟨314991687957853956813368011884,314991687957853956848492524283⟩,⟨6840458245787715423553343661,6840458245787715453712560387⟩⟩,⟨⟨314469059013410577700511666072,314469059013410577735485436091⟩,⟨6720150816414533774514846943,6720150816414533804550139656⟩⟩,⟨⟨313899426532696843665030886586,313899426532696843699920959406⟩,⟨6599711837193156458139995478,6599711837193156488048910509⟩⟩,⟨⟨313277130175121597328523658880,313277130175121597363244747995⟩,⟨6479084212287986005728669323,6479084212287986035505197683⟩⟩,⟨⟨312608087431824210210890228539,312608087431824210245448558703⟩,⟨6358453360166392004019607771,6358453360166392033660091987⟩⟩,⟨⟨311885995417139771945051792542,311885995417139771979452316785⟩,⟨6237751453240013980130085616,6237751453240014009630498942⟩⟩,⟨⟨311117455576067040597338719895,311117455576067040631557359173⟩,⟨6117172162551223569384947214,6117172162551223598741145482⟩⟩,⟨⟨310295512379320920877342890130,310295512379320920911384785904⟩,⟨5996637443010511038227194303,5996637443010511067435178083⟩⟩,⟨⟨309427462418134024275707164398,309427462418134024309558097377⟩,⟨5876348433316097775075280408,5876348433316097804131182761⟩⟩,⟨⟨308505686425615951895140711385,308505686425615951928779462945⟩,⟨5756217374969136662009715320,5756217374969136690909124589⟩⟩,⟨⟨307538188313448217814331973290,307538188313448217847936058739⟩,⟨5636452106634096231188784922,5636452106634096259931515469⟩⟩,⟨⟨306516672934600611526472166495,306516672934600611559869581972⟩,⟨5516955650974356805255006009,5516955650974356833833850046⟩⟩,⟨⟨305449864731974943802153783569,305449864731974943835349181600⟩,⟨5397941796180264740331634172,5397941796180264768743301883⟩⟩,⟨⟨304328779427409077910377107231,304328779427409077943348002825⟩,⟨5279304831724161758432731387,5279304831724161786672904183⟩⟩,⟨⟨303162876304279209239644677165,303162876304279209272418168924⟩,⟨5161263762173697545606067511,5161263762173697573671978187⟩⟩,⟨⟨301942467526420953524359997458,301942467526420953556898947864⟩,⟨5043704621085468710046396559,5043704621085468737933507262⟩⟩] +lemma amp7_00_9_eq : ∀ k : Fin 16, amp7_0Expr 0 9 k = amp7_00_9 k := by decide +kernel +noncomputable def amp7_00_10 : Fin 16 → CBox := ![⟨⟨300677762695333149853937059917,300677762695333149886299792596⟩,⟨4926850913609606509591845350,4926850913609606537297950389⟩⟩,⟨⟨299358354738337594120973290057,299358354738337594153103000353⟩,⟨4810580886804078359215985000,4810580886804078386736328032⟩⟩,⟨⟨297995220299893224108240389673,297995220299893224140137283108⟩,⟨4695121848038555010652721575,4695121848038555037984291842⟩⟩,⟨⟨296577216055585917936697666623,296577216055585917968372666697⟩,⟨4580344719906157479824991103,4580344719906157506964151218⟩⟩,⟨⟨295116103753582533740802574873,295116103753582533772226165856⟩,⟨4466479931156336015390528348,4466479931156336042333884243⟩⟩,⟨⟨293599985370305116123170055316,293599985370305116154354740525⟩,⟨4353391535005783223528470216,4353391535005783250272490770⟩⟩,⟨⟨292041427254145161288375915671,292041427254145161319315013816⟩,⟨4241312418368850872641589516,4241312418368850899183382783⟩⟩,⟨⟨290427756695503209418860578031,290427756695503209449537567081⟩,⟨4130100213631344485562608164,4130100213631344511898230181⟩⟩,⟨⟨288772365687686203880477237335,288772365687686203910886357038⟩,⟨4019989620392040567790033846,4019989620392040593916688578⟩⟩,⟨⟨287061785188315277965828645702,287061785188315277995957297003⟩,⟨3910832292576797906850836599,3910832292576797932764745981⟩⟩,⟨⟨285310255555072660422427302581,285310255555072660452258460552⟩,⟨3802864114837687638237173185,3802864114837687663935561551⟩⟩,⟨⟨283503487970652467151553455176,283503487970652467181608430987⟩,⟨3695931199172180270793152815,3695931199172180296279225804⟩⟩,⟨⟨281656595694045920793540422194,281656595694045920823317880862⟩,⟨3590270005622009700896251328,3590270005622009726160853520⟩⟩,⟨⟨279754444742899494692210158060,279754444742899494721709045757⟩,⟨3485721535251655930010699498,3485721535251655955050296516⟩⟩,⟨⟨277813047792985761470375665000,277813047792985761499589711030⟩,⟨3382522231915680817183250546,3382522231915680841995444251⟩⟩,⟨⟨275816398186697207878307471185,275816398186697207907240419987⟩,⟨3280508411477009105019977749,3280508411477009129601301134⟩⟩] +lemma amp7_00_10_eq : ∀ k : Fin 16, amp7_0Expr 0 10 k = amp7_00_10 k := by decide +kernel +noncomputable def amp7_00_11 : Fin 16 → CBox := ![⟨⟨273781436692667967956343576986,273781436692667967984990912967⟩,⟨3179915928231531506757427229,3179915928231531531105571785⟩⟩,⟨⟨271691254153234504565508071225,271691254153234504593874366821⟩,⟨3080576833550168273751195148,3080576833550168297862794420⟩⟩,⟨⟨269563750472772547172220073663,269563750472772547200284163725⟩,⟨2982725837119988762987105000,2982725837119988786859837407⟩⟩,⟨⟨267381081633869236225944075289,267381081633869236253732161179⟩,⟨2886191141720374756130247755,2886191141720374779760975220⟩⟩,⟨⟨265162140320326633194632744010,265162140320326633222112778674⟩,⟨2791205775812629706370371224,2791205775812629729756745911⟩⟩,⟨⟨262888112510298980598883237997,262888112510298980626059620530⟩,⟨2697594504860290102302675592,2697594504860290125441402702⟩⟩,⟨⟨260578920177705446826655059263,260578920177705446853510687247⟩,⟨2605588158021350726899067517,2605588158021350749788139700⟩⟩,⟨⟨258214741081908007488892418795,258214741081908007515503089081⟩,⟨2515008470250995150419625937,2515008470250995173056445458⟩⟩,⟨⟨255816566168266071518043009787,255816566168266071544330529643⟩,⟨2426083571964919947025720428,2426083571964919969407749201⟩⟩,⟨⟨253363523368324278804429654069,253363523368324278830395234154⟩,⟨2338632570078793021307762071,2338632570078793043431763535⟩⟩,⟨⟨250877715798152673658561459048,250877715798152673684219484566⟩,⟨2252880415556413286786942884,2252880415556413308651464442⟩⟩,⟨⟨248337176185627459059987949434,248337176185627459085309608243⟩,⟨2168643985507320725858270551,2168643985507320747459785580⟩⟩,⟨⟨245765166933288845509069287746,245765166933288845534060469705⟩,⟨2086144589544568110117695744,2086144589544568131454763585⟩⟩,⟨⟨243138575995052695121388200346,243138575995052695146042202571⟩,⟨2005197269047037011690241905,2005197269047037032759615133⟩⟩,⟨⟨240481876551064263976052497079,240481876551064264000356884072⟩,⟨1926019249259763422274451830,1926019249259763443074708379⟩⟩,⟨⟨237770757523431697829704088913,237770757523431697853645255696⟩,⟨1848424125801029961739981076,1848424125801029982267818293⟩⟩] +lemma amp7_00_11_eq : ∀ k : Fin 16, amp7_0Expr 0 11 k = amp7_00_11 k := by decide +kernel +noncomputable def amp7_00_12 : Fin 16 → CBox := ![⟨⟨235030959266730895494325045023,235030959266730895518195073015⟩,⟨1772624615471496365066468908,1772624615471496385322850780⟩⟩,⟨⟨232236912154997825886148952646,232236912154997825909691595846⟩,⟨1698433254021623104927632706,1698433254021623124907443101⟩⟩,⟨⟨229415685635051681463215181993,229415685635051681486426142592⟩,⟨1626057844719219427226831370,1626057844719219446928973744⟩⟩,⟨⟨226540386094549529463584687133,226540386094549529486464045649⟩,⟨1555310245266803031669130171,1555310245266803051090446660⟩⟩,⟨⟨223639480228296686881058307835,223639480228296686903602329088⟩,⟨1486392959332582234770166642,1486392959332582253909660191⟩⟩,⟨⟨220684678302308916561483552453,220684678302308916583696278492⟩,⟨1419117544299396703702721434,1419117544299396722557321518⟩⟩,⟨⟨217705919492264939599941690450,217705919492264939621804551433⟩,⟨1353680837210838821813120520,1353680837210838840381917683⟩⟩,⟨⟨214673438201119008720320132508,214673438201119008741869261079⟩,⟨1289894468725546294940857657,1289894468725546313220950457⟩⟩,⟨⟨211618729382634600650369686450,211618729382634600671562444737⟩,⟨1227949261284789793138392022,1227949261284789811128817240⟩⟩,⟨⟨208510463156880351880379924852,208510463156880351901222869170⟩,⟨1167657288222717640336127925,1167657288222717658033870796⟩⟩,⟨⟨205381782784624177928942553283,205381782784624177949426962236⟩,⟨1109203028438482883927377496,1109203028438482901331886896⟩⟩,⟨⟨202199695733315480396599211551,202199695733315480416719857705⟩,⟨1052399363061589150112215589,1052399363061589167220363606⟩⟩,⟨⟨198999096719704338910869849789,198999096719704338930610572798⟩,⟨997424117522348571995931469,997424117522348588807243428⟩⟩,⟨⟨195745220722240688533504071556,195745220722240688553041007435⟩,⟨944091341481054267740332445,944091341481054284252606644⟩⟩,⟨⟨192474829343964431539284365909,192474829343964431558449299830⟩,⟨892571915944851584368485675,892571915944851600580680841⟩⟩,⟨⟨189151261950479018585013340326,189151261950479018603805788134⟩,⟨842681415331583219781598710,842681415331583235690610302⟩⟩] +lemma amp7_00_12_eq : ∀ k : Fin 16, amp7_0Expr 0 12 k = amp7_00_12 k := by decide +kernel +noncomputable def amp7_00_13 : Fin 16 → CBox := ![⟨⟨185813276743755801218680727446,185813276743755801237103917310⟩,⟨794583504186443997704258648,794583504186444013310001841⟩⟩,⟨⟨182422178864308501313995627962,182422178864308501332068012814⟩,⟨748095633259677200206622437,748095633259677215506113059⟩⟩,⟨⟨179018869535473656747182547469,179018869535473656764869005260⟩,⟨703373997437957597302036603,703373997437957612295247281⟩⟩,⟨⟨175562462891819667400393762728,175562462891819667417703756826⟩,⟨660238270565454966508547452,660238270565454981192382363⟩⟩,⟨⟨172096169277903790567905147287,172096169277903790584822614453⟩,⟨618836943425914620847709115,618836943425914635222357407⟩⟩,⟨⟨168576733582626629711080648924,168576733582626629727716896995⟩,⟨578992254726878441310812416,578992254726878455373538464⟩⟩,⟨⟨165049864707608170390882136280,165049864707608170407138759965⟩,⟨540844775349904463191191339,540844775349904476942103574⟩⟩,⟨⟨161469734522837484342476421909,161469734522837484358349075380⟩,⟨504219645448085487368523559,504219645448085500804408070⟩⟩,⟨⟨157884767810600953864490304564,157884767810600953879981777862⟩,⟨469249318722501102384887448,469249318722501115506349439⟩⟩,⟨⟨154246329020730490567891733664,154246329020730490583010203859⟩,⟨435762167956083806825627943,435762167956083819629492413⟩⟩,⟨⟨150605809747465210433185359109,150605809747465210447919679807⟩,⟨403882350770507059567566567,403882350770507072054639801⟩⟩,⟨⟨146911495554703965852492179520,146911495554703965866912277970⟩,⟨373441798139992521783466863,373441798139992533950617716⟩⟩,⟨⟨143218036654714008129608518113,143218036654714008143628660539⟩,⟨344556210927922257947876108,344556210927922269795886879⟩⟩,⟨⟨139470322968955804615871685520,139470322968955804629497189865⟩,⟨317061398000412765934114206,317061398000412777459654504⟩⟩,⟨⟨135726605353655545978553458464,135726605353655545991790837674⟩,⟨291064460826259371636269300,291064460826259382840618194⟩⟩,⟨⟨131928005392641061850986874702,131928005392641061863823400575⟩,⟨266405399753673123478491700,266405399753673134358148930⟩⟩] +lemma amp7_00_13_eq : ∀ k : Fin 16, amp7_0Expr 0 13 k = amp7_00_13 k := by decide +kernel +noncomputable def amp7_00_14 : Fin 16 → CBox := ![⟨⟨128136779011057249552001689720,128136779011057249564496052704⟩,⟨243182592066960776683155617,243182592066960787239686533⟩⟩,⟨⟨124289836842615231715007758567,124289836842615231727105165700⟩,⟨221240536816929509353527208,221240536816929519583286278⟩⟩,⟨⟨120453922816612129114457766837,120453922816612129126167505559⟩,⟨200668779944004745494399249,200668779944004755399156981⟩⟩,⟨⟨116561205444166672847538209600,116561205444166672858836662640⟩,⟨181316619785693723126877587,181316619785693732702877039⟩⟩,⟨⟨112683499776144673634392662717,112683499776144673645336595428⟩,⟨163264681172595935761282946,163264681172595945010612031⟩⟩,⟨⟨108747587160841699262729973486,108747587160841699273272519258⟩,⟨146367355405605189887335213,146367355405605198806073431⟩⟩,⟨⟨104831066776958411341532334505,104831066776958411351707115815⟩,⟨130696273572377445699174851,130696273572377454289707505⟩⟩,⟨⟨100854538849332597432993714055,100854538849332597442761300065⟩,⟨116111206435427025852153113,116111206435427034110351213⟩⟩,⟨⟨96902271182587980363278272199,96902271182587980372645671760⟩,⟨102674735551117051007910171,102674735551117058936435178⟩⟩,⟨⟨92887690320411955903439448689,92887690320411955912426147902⟩,⟨90252290198623868185226414,90252290198623875779817306⟩⟩,⟨⟨88902848398450723970000265917,88902848398450723978580703052⟩,⟨78897363137513932831053911,78897363137513940094767247⟩⟩,⟨⟨84852734834314225162594032760,84852734834314225170787473693⟩,⟨68481313526766469145853703,68481313526766476074092771⟩⟩,⟨⟨80838621202005951892628980185,80838621202005951900439370326⟩,⟨59048522219791192460803082,59048522219791199057081923⟩⟩,⟨⟨76755416963323492425947353919,76755416963323492433345731449⟩,⟨50476541709763954355310027,50476541709763960614652234⟩⟩,⟨⟨72715502340174936537496874481,72715502340174936544505975803⟩,⟨42800633560112767422143341,42800633560112773348638101⟩⟩,⟨⟨68601515725651777364993783770,68601515725651777371605605670⟩,⟨35904798986054574076360342,35904798986054579664558581⟩⟩] +lemma amp7_00_14_eq : ∀ k : Fin 16, amp7_0Expr 0 14 k = amp7_00_14 k := by decide +kernel +noncomputable def amp7_00_15 : Fin 16 → CBox := ![⟨⟨64539503415645085454088386427,64539503415645085460304321568⟩,⟨29815188073350486750056506,29815188073350492004652938⟩⟩,⟨⟨60396818612050247086655629125,60396818612050247092466754929⟩,⟨24422498031291932278059773,24422498031291937193040499⟩⟩,⟨⟨56316756585784371033765188830,56316756585784371039176485574⟩,⟨19743789781400817024796080,19743789781400821605691569⟩⟩,⟨⟨52147076633054805140467541965,52147076633054805145479823616⟩,⟨15676695838757776234856344,15676695838757780474839885⟩⟩,⟨⟨48053564435512766975203438075,48053564435512766979821004093⟩,⟨12229223778246476769136808,12229223778246480674761519⟩⟩,⟨⟨43857915892222204054233327126,43857915892222204058444919466⟩,⟨9306173334082594744675073,9306173334082598308049664⟩⟩,⟨⟨39756518367687861326581649156,39756518367687861330393662031⟩,⟨6906546457326443019050369,6906546457326446248150579⟩⟩,⟨⟨35534636916937217772324866257,35534636916937217775733801930⟩,⟨4942536047449001531015118,4942536047449004416382836⟩⟩,⟨⟨31432807725418446481088009511,31432807725418446484100084539⟩,⟨3404195131147990302244622,3404195131147992853872494⟩⟩,⟨⟨27181673825565697581265532488,27181673825565697583867896619⟩,⟨2211333236794330651219917,2211333236794332857262339⟩⟩,⟨⟨23091170310179454626423484999,23091170310179454628630593466⟩,⟨1345113899161041327248829,1345113899161043200941651⟩⟩,⟨⟨18800756195048441833124464053,18800756195048441834919175950⟩,⟨733193241686197612204926,733193241686199137517448⟩⟩,⟨⟨14745709346389485623039160617,14745709346389485624442464118⟩,⟨347891772871138673563503,347891772871139869724744⟩⟩,⟨⟨10381956628106551989000573263,10381956628106551989985898844⟩,⟨124974050225334386069252,124974050225335228165906⟩⟩,⟨⟨6440307695516600995060224320,6440307695516600995662628273⟩,⟨27910132336247930054947,27910132336248452402300⟩⟩,⟨⟨1829737917432750534748701359,1829737917432750534914555516⟩,⟨881064552150209050180,881064552150357448154⟩⟩] +lemma amp7_00_15_eq : ∀ k : Fin 16, amp7_0Expr 0 15 k = amp7_00_15 k := by decide +kernel +noncomputable def amp7_00 : Fin 16 → Fin 16 → CBox := ![amp7_00_0,amp7_00_1,amp7_00_2,amp7_00_3,amp7_00_4,amp7_00_5,amp7_00_6,amp7_00_7,amp7_00_8,amp7_00_9,amp7_00_10,amp7_00_11,amp7_00_12,amp7_00_13,amp7_00_14,amp7_00_15] +lemma amp7_00_eq (i k : Fin 16) : amp7_0Expr 0 i k = amp7_00 i k := by + fin_cases i + · exact amp7_00_0_eq k + · exact amp7_00_1_eq k + · exact amp7_00_2_eq k + · exact amp7_00_3_eq k + · exact amp7_00_4_eq k + · exact amp7_00_5_eq k + · exact amp7_00_6_eq k + · exact amp7_00_7_eq k + · exact amp7_00_8_eq k + · exact amp7_00_9_eq k + · exact amp7_00_10_eq k + · exact amp7_00_11_eq k + · exact amp7_00_12_eq k + · exact amp7_00_13_eq k + · exact amp7_00_14_eq k + · exact amp7_00_15_eq k +noncomputable def amp7_01_0 : Fin 16 → CBox := ![⟨⟨1102088937858270181353729715,1102088937858270181570029962⟩,⟨295300788789259126809265857,295300788789259127017755049⟩⟩,⟨⟨3879294710425496027321461331,3879294710425496028094009067⟩,⟨1039357201326332965488688429,1039357201326332966225531778⟩⟩,⟨⟨6254061791736625378961052330,6254061791736625380214963705⟩,⟨1675337883700933203767742245,1675337883700933204957838384⟩⟩,⟨⟨8883903197754802696880416638,8883903197754802698663629191⟩,⟨2379229555022371936604860185,2379229555022371938295772482⟩⟩,⟨⟨11328881539795970240295064114,11328881539795970242571864471⟩,⟨3033024803843450895163456592,3033024803843450897320208048⟩⟩,⟨⟨13917127160292995719776969248,13917127160292995722574929107⟩,⟨3724423372331124204193371929,3724423372331124206842699673⟩⟩,⟨⟨16386647989420772849933853486,16386647989420772853229839319⟩,⟨4383128812381189620327203136,4383128812381189623446445304⟩⟩,⟨⟨18955083471876935667319193872,18955083471876935671132058011⟩,⟨5067206830901892684580119186,5067206830901892688187521510⟩⟩,⟨⟨21435879089724502549948765274,21435879089724502554261118767⟩,⟨5726605044038025503894657197,5726605044038025507973254322⟩⟩,⟨⟨23991804549643204462111686218,23991804549643204466934835607⟩,⟨6404659675304383759613391088,6404659675304383764176064897⟩⟩,⟨⟨26478046610248602795400173652,26478046610248602800724199276⟩,⟨7062533676292391728523640226,7062533676292391733557788001⟩⟩,⟨⟨29024525644062964295095697128,29024525644062964300930329711⟩,⟨7734734933180978268044703473,7734734933180978273560654473⟩⟩,⟨⟨31512960724499068395544313114,31512960724499068401876052489⟩,⟨8389566709868148760168461087,8389566709868148766154163264⟩⟩,⟨⟨34051378273882346248434042833,34051378273882346255270209607⟩,⟨9055644815582760866697332445,9055644815582760873160978200⟩⟩,⟨⟨36539869626915827773883173197,36539869626915827781218356838⟩,⟨9706226543194707967413468515,9706226543194707974346185047⟩⟩,⟨⟨39070810253034233323052091794,39070810253034233330893122385⟩,⟨10365709213769622478340745629,10365709213769622485749469609⟩⟩] +lemma amp7_01_0_eq : ∀ k : Fin 16, amp7_0Expr 1 0 k = amp7_01_0 k := by decide +kernel +noncomputable def amp7_01_1 : Fin 16 → CBox := ![⟨⟨41557777871199088338377166293,41557777871199088346713230741⟩,⟨11010995147660989387505316484,11010995147660989395380470740⟩⟩,⟨⟨44081392149094618343334754573,44081392149094618352169861436⟩,⟨11663307683745029772116854033,11663307683745029780463744113⟩⟩,⟨⟨46565559944373481006018279714,46565559944373481015342605554⟩,⟨12302348312534547849916067997,12302348312534547858725922211⟩⟩,⟨⟨49081738751393079147495281130,49081738751393079157325169198⟩,⟨12946862180358040207802825691,12946862180358040217083483209⟩⟩,⟨⟨51562006374793350932305359616,51562006374793350942618505000⟩,⟨13578771739459452588021758036,13578771739459452597761559841⟩⟩,⟨⟨54070471955917311492908513428,54070471955917311503709409863⟩,⟨14214830811882939472896867958,14214830811882939483099921362⟩⟩,⟨⟨56545843812244422911897440920,56545843812244422923193349197⟩,⟨14838770080580355754819216660,14838770080580355765481958522⟩⟩,⟨⟨59046200785592461143343108442,59046200785592461155120116452⟩,⟨15465706099368956670814995433,15465706099368956681936172778⟩⟩,⟨⟨61515743851300289353557544070,61515743851300289365823161082⟩,⟨16080872869007158639867360966,16080872869007158651443704236⟩⟩,⟨⟨64007509311183496066372817529,64007509311183496079132682879⟩,⟨16698015257084626425750882323,16698015257084626437785799044⟩⟩,⟨⟨66470326561342197864130263541,66470326561342197877356126706⟩,⟨17303638930480648729285266770,17303638930480648741766330449⟩⟩,⟨⟨68952948560618553279657615156,68952948560618553293370981952⟩,⟨17910321436817546021779366572,17910321436817546034713713213⟩⟩,⟨⟨71408161377362287779591511708,71408161377362287793759553626⟩,⟨18505659978604572103240527752,18505659978604572116614716406⟩⟩,⟨⟨73881030613396447891235142700,73881030613396447905893354265⟩,⟨19101225444126882949591122907,19101225444126882963415522656⟩⟩,⟨⟨76327766630301121270368694503,76327766630301121285498601266⟩,⟨19685563727738912097394863013,19685563727738912111659870145⟩⟩,⟨⟨78790223991043618357584952669,78790223991043618373192674427⟩,⟨20269367679914862832533040897,20269367679914862847241060329⟩⟩] +lemma amp7_01_1_eq : ∀ k : Fin 16, amp7_0Expr 1 1 k = amp7_01_1 k := by decide +kernel +noncomputable def amp7_01_2 : Fin 16 → CBox := ![⟨⟨81227608375539202465872956356,81227608375539202481920733871⟩,⟨20842016691769109970961660514,20842016691769109986098250640⟩⟩,⟨⟨83678949881142211135951381267,83678949881142211152475579981⟩,⟨21413430175279002047358664684,21413430175279002062933689957⟩⟩,⟨⟨86106098879043725774607845102,86106098879043725791596718948⟩,⟨21973726757123102127909540344,21973726757123102143915300936⟩⟩,⟨⟨88545578943925473731143571413,88545578943925473748601101731⟩,⟨22532138644589893269901953719,22532138644589893286339693804⟩⟩,⟨⟨90961594967913421661208420367,90961594967913421679133965662⟩,⟨23079445577802580831413351116,23079445577802580848278246739⟩⟩,⟨⟨93388428560758176811609174023,93388428560758176829949415328⟩,⟨23624264511637001787083179142,23624264511637001804361692190⟩⟩,⟨⟨95792396370099360463919052865,95792396370099360482713422291⟩,⟨24157970818577534350704169836,24157970818577534368401682338⟩⟩,⟨⟨98205760443890943470784011074,98205760443890943490025138335⟩,⟨24688626880135965794413414955,24688626880135965812527785239⟩⟩,⟨⟨100596744122130928652013244368,100596744122130928671702261207⟩,⟨25208148260544373306917848447,25208148260544373325444752101⟩⟩,⟨⟨102995778560777490165218256420,102995778560777490185356382077⟩,⟨25724094429346650072203770176,25724094429346650091142986356⟩⟩,⟨⟨105372819096868674034571473428,105372819096868674055152156110⟩,⟨26228873776445116035320655347,26228873776445116054665934421⟩⟩,⟨⟨107756627345939477773364437194,107756627345939477794325288509⟩,⟨26729587221217294244227588355,26729587221217294263962702673⟩⟩,⟨⟨110118740687065649114736505907,110118740687065649136143216546⟩,⟨27219095179189904656715925914,27219095179189904676852597988⟩⟩,⟨⟨112486390185063711859807387165,112486390185063711881649047142⟩,⟨27704078409009261239089969690,27704078409009261259624530893⟩⟩,⟨⟨114832565670311263388387269006,114832565670311263410665999133⟩,⟨28177813944701418776621506389,28177813944701418797549844067⟩⟩,⟨⟨117183088163066982128900328411,117183088163066982151592941625⟩,⟨28646595839664774757205057398,28646595839664774778520320926⟩⟩] +lemma amp7_01_2_eq : ∀ k : Fin 16, amp7_0Expr 1 2 k = amp7_01_2 k := by decide +kernel +noncomputable def amp7_01_3 : Fin 16 → CBox := ![⟨⟨119512287274270832555443857700,119512287274270832578558015619⟩,⟨29104086808840506263927599388,29104086808840506285627030329⟩⟩,⟨⟨121844679072130333796789194019,121844679072130333820325846762⟩,⟨29556223543755479937405133779,29556223543755479959487602551⟩⟩,⟨⟨124155834456613809792335086501,124155834456613809816290094677⟩,⟨29997027237399739237973501974,29997027237399739260433334132⟩⟩,⟨⟨126469056678259059244564287145,126469056678259059268829441072⟩,⟨30432103107978883623002705858,30432103107978883645812308896⟩⟩,⟨⟨128761071410825821027746695188,128761071410825821052429822198⟩,⟨30855806767745305198275151968,30855806767745305221455873780⟩⟩,⟨⟨131054050246400468876842151092,131054050246400468901931629524⟩,⟨31273434926021346053550362721,31273434926021346077097685663⟩⟩,⟨⟨133325797306735744422160477160,133325797306735744447649123357⟩,⟨31679656220515710611870571478,31679656220515710635778065581⟩⟩,⟨⟨135597424324932184042358317909,135597424324932184068239004547⟩,⟨32079479324281999757355999456,32079479324281999781620085339⟩⟩,⟨⟨137847746272761056082934113737,137847746272761056109207073950⟩,⟨32467866779767209211718665902,32467866779767209236334658459⟩⟩,⟨⟨140096878790657178274082341346,140096878790657178300718614579⟩,⟨32849557559514378979589857368,32849557559514379004548908280⟩⟩,⟨⟨142324587625396826294430943606,142324587625396826321449874864⟩,⟨33219790940039775545266389343,33219790940039775570568288690⟩⟩,⟨⟨144550049155458843883362516028,144550049155458843910750378425⟩,⟨33583052685930903091753062728,33583052685930903117392409138⟩⟩,⟨⟨146753926350228373764716157214,146753926350228373792471587591⟩,⟨33934843318971122031495567426,33934843318971122057467258766⟩⟩,⟨⟨148954507135577544830133873792,148954507135577544858252697948⟩,⟨34279410289754643641926957166,34279410289754643668227686149⟩⟩,⟨⟨151133303837658889281609628655,151133303837658889310088021483⟩,⟨34612501334288220688551974043,34612501334288220715176040968⟩⟩,⟨⟨153307761484133862352157971002,153307761484133862380991224004⟩,⟨34938139089609094533786505296,34938139089609094560730343872⟩⟩] +lemma amp7_01_3_eq : ∀ k : Fin 16, amp7_0Expr 1 3 k = amp7_01_3 k := by decide +kernel +noncomputable def amp7_01_4 : Fin 16 → CBox := ![⟨⟨155460198875561920595929364495,155460198875561920624945947229⟩,⟨35252305744241606854821168389,35252305744241606882041024532⟩⟩,⟨⟨157607259087086457082072535273,157607259087086457111461224275⟩,⟨35558811401520389852591108832,35558811401520389880127327275⟩⟩,⟨⟨159732028900161944729961532182,159732028900161944759709652250⟩,⟨35853861050807490781801513816,35853861050807490809646303684⟩⟩,⟨⟨161850386322304011854325416382,161850386322304011884422832140⟩,⟨36141063467674361615284266017,36141063467674361643432560035⟩⟩,⟨⟨163946151505592800668263660638,163946151505592800698702068619⟩,⟨36416835765259395951812799186,36416835765259395980257805059⟩⟩,⟨⟨166034470680872050007803922889,166034470680872050038585270149⟩,⟨36684595648427398976783964268,36684595648427399005523203771⟩⟩,⟨⟨168099866211769223299966991741,168099866211769223331068406488⟩,⟨36940962535999628561578610699,36940962535999628590602074342⟩⟩,⟨⟨170156782649161603206538945330,170156782649161603237967853825⟩,⟨37189172477418071619345882926,37189172477418071648652188511⟩⟩,⟨⟨172190416489421670777471132597,172190416489421670809224459272⟩,⟨37426038138837605862800995904,37426038138837605892384473564⟩⟩,⟨⟨174214537849568804691569600580,174214537849568804723593077533⟩,⟨37654622579967653805629937756,37654622579967653835475705469⟩⟩,⟨⟨176214992040382924335232398595,176214992040382924367572843716⟩,⟨37871923330204057879234237876,37871923330204057909347448266⟩⟩,⟨⟨178204899437200859230540858543,178204899437200859263184651804⟩,⟨38080838455293043575151115824,38080838455293043605525585267⟩⟩,⟨⟨180170731330472669857373223652,180170731330472669890319496457⟩,⟨38278542564095099997071871208,38278542564095100027702371841⟩⟩,⟨⟨182124980749140954811730907906,182124980749140954844955928264⟩,⟨38467776123385623916015212192,38467776123385623946893365841⟩⟩,⟨⟨184054724371601113667537209145,184054724371601113701054939712⟩,⟨38645883573846309324886361561,38645883573846309356010072445⟩⟩,⟨⟨185971848202277675085603663652,185971848202277675119397538681⟩,⟨38815454637734521682436888998,38815454637734521713799228108⟩⟩] +lemma amp7_01_4_eq : ∀ k : Fin 16, amp7_0Expr 1 4 k = amp7_01_4 k := by decide +kernel +noncomputable def amp7_01_5 : Fin 16 → CBox := ![⟨⟨187864015749003401151709603030,187864015749003401185778895707⟩,⟨38973996820142682155278504075,38973996820142682186874247405⟩⟩,⟨⟨189742524435037546366766889361,189742524435037546401106404594⟩,⟨39123955465392405240205212123,39123955465392405272029743062⟩⟩,⟨⟨191595607888822722058075251326,191595607888822722092683900894⟩,⟨39262994806974376308385839002,39262994806974376340433836012⟩⟩,⟨⟨193433991687716030323552637551,193433991687716030358423894269⟩,⟨39393421736196173573599628484,39393421736196173605866109351⟩⟩,⟨⟨195246464560581567021621081863,195246464560581567056750526820⟩,⟨39513051267549282297635527355,39513051267549282330114469737⟩⟩,⟨⟨197043195415465577217204001934,197043195415465577252243274339⟩,⟨39624057363263260180805037333,39624057363263260213422654161⟩⟩,⟨⟨198813514608418093392454550847,198813514608418093427759213946⟩,⟨39724400222470671743797275122,39724400222470671776620352866⟩⟩,⟨⟨200567048127371937208381287345,200567048127371937243937400460⟩,⟨39816126037186355549750952565,39816126037186355582772857432⟩⟩,⟨⟨202293655904318679481611588621,202293655904318679517406802610⟩,⟨39897334912780482163976865233,39897334912780482197189979062⟩⟩,⟨⟨204002433444434158506533430516,204002433444434158542561656431⟩,⟨39969950096644638634967092019,39969950096644638668366324960⟩⟩,⟨⟨205683759515949394769782872698,205683759515949394806029096839⟩,⟨40032206610755328115641197537,40032206610755328149218462533⟩⟩,⟨⟨207346210368661730217007684017,207346210368661730253464981060⟩,⟨40085909278437561563034134777,40085909278437561596784141922⟩⟩,⟨⟨208980674081079314457478814856,208980674081079314494152446478⟩,⟨40129423311622252282955273038,40129423311622252316873882296⟩⟩,⟨⟨210595217754916127529479313178,210595217754916127566346368694⟩,⟨40164439350227293027220024538,40164439350227293061298829795⟩⟩,⟨⟨212181230379998465606483020655,212181230379998465643547814389⟩,⟨40189448309633768453208319535,40189448309633768487443008554⟩⟩,⟨⟨213746278976555415000544178510,213746278976555415037804689027⟩,⟨40206030629547524925516968394,40206030629547524959903072603⟩⟩] +lemma amp7_01_5_eq : ∀ k : Fin 16, amp7_0Expr 1 5 k = amp7_01_5 k := by decide +kernel +noncomputable def amp7_01_6 : Fin 16 → CBox := ![⟨⟨215282246096763861766869565001,215282246096763861804281866265⟩,⟨40212798662206166453373767622,40212798662206166487897905318⟩⟩,⟨⟨216796206775391264494737395934,216796206775391264532340993687⟩,⟨40211226392898912830606271659,40211226392898912865271724961⟩⟩,⟨⟨218280530759559737820294022204,218280530759559737858059098455⟩,⟨40200043546080650720629749867,40200043546080650755425846461⟩⟩,⟨⟨219741808285939344343600324628,219741808285939344381544197657⟩,⟨40180621179004388173338611655,40180621179004388208264351633⟩⟩,⟨⟨221172890849933913138745422670,221172890849933913176848642801⟩,⟨40151802509713008843269982033,40151802509713008878316651762⟩⟩,⟨⟨222579890223438034751070963878,222579890223438034789334927112⟩,⟨40114858990540393394809027295,40114858990540393429972647197⟩⟩,⟨⟨223956135070172351889741403536,223956135070172351928038157719⟩,⟨40068743626333527781005669923,40068743626333527816258201461⟩⟩,⟨⟨225307264224628230771025200395,225307264224628230809481274405⟩,⟨40014631398892210358023412711,40014631398892210393383342039⟩⟩,⟨⟨226627079757599591419052726321,226627079757599591457649533597⟩,⟨39951581552344200242923574119,39951581552344200278382448690⟩⟩,⟨⟨227920752329829932546030736767,227920752329829932584756048925⟩,⟨39880675556702454858189247673,39880675556702454893740601687⟩⟩,⟨⟨229182554434144874347276331223,229182554434144874386130933645⟩,⟨39801075495934331090687497298,39801075495934331126326372052⟩⟩,⟨⟨230417192594420635070747708349,230417192594420635109711962496⟩,⟨39713772123190995178642903059,39713772123190995214361534512⟩⟩,⟨⟨231619407479093604643136619285,231619407479093604682211117669⟩,⟨39618027100997935283485974524,39618027100997935319279392060⟩⟩,⟨⟨232793444817417378327625259117,232793444817417378366812855850⟩,⟨39514743107421543036490755060,39514743107421543072355063741⟩⟩,⟨⟨233934511912552159139776322068,233934511912552159179010789645⟩,⟨39403278251626318994269201526,39403278251626319030188170550⟩⟩,⟨⟨235046396374489785531889429513,235046396374489785571218668997⟩,⟨39284449634874509490352266299,39284449634874509526329613337⟩⟩] +lemma amp7_01_6_eq : ∀ k : Fin 16, amp7_0Expr 1 6 k = amp7_01_6 k := by decide +kernel +noncomputable def amp7_01_7 : Fin 16 → CBox := ![⟨⟨236124771276792074032972343983,236124771276792074072383060506⟩,⟨39157708802626491193152047344,39157708802626491229180512886⟩⟩,⟨⟨237172968142386505367990655152,237172968142386505407484658126⟩,⟨39023789642856992636012276152,39023789642856992672087744336⟩⟩,⟨⟨238187125602308079999162665921,238187125602308080038700814470⟩,⟨38882234241680134634327804520,38882234241680134670438879997⟩⟩,⟨⟨239170120501443106866824301465,239170120501443106906427300440⟩,⟨38733695510438573650186264898,38733695510438573686331910648⟩⟩,⟨⟨240118557445124203590969458680,240118557445124203630610797665⟩,⟨38577803288908377054764515400,38577803288908377090935496304⟩⟩,⟨⟨241034859402556496158146893547,241034859402556496197843160399⟩,⟨38415131628745579076937362543,38415131628745579113131917024⟩⟩,⟨⟨241916097981613941644197644410,241916097981613941683926530444⟩,⟨38245395439744184135322655705,38245395439744184171532329547⟩⟩,⟨⟨242764242484760095034670777162,242764242484760095074426989682⟩,⟨38069091917576288202290679060,38069091917576288238510188556⟩⟩,⟨⟨243576833146865032907575388784,243576833146865032947353627816⟩,⟨37886018457136518952737615880,37886018457136518988961260961⟩⟩,⟨⟨244355385229316022624003973540,244355385229316022663801902029⟩,⟨37696597294414925919127371420,37696597294414925955350350352⟩⟩,⟨⟨245097909802417205962581430304,245097909802417206002384721886⟩,⟨37500705819218187287650963689,37500705819218187323866265799⟩⟩,⟨⟨245805467136055951405189581043,245805467136055951444994762151⟩,⟨37298693102022918548262073244,37298693102022918584464708934⟩⟩,⟨⟨246476541919033007132846344720,246476541919033007172639629186⟩,⟨37090514128662259228025601685,37090514128662259264208713026⟩⟩,⟨⟨247111737907551681762490310084,247111737907551681802263860468⟩,⟨36876446500871572274574523541,36876446500871572310732511947⟩⟩,⟨⟨247710016760027860452561772339,247710016760027860492302985512⟩,⟨36656520490029906405736686195,36656520490029906441862998991⟩⟩,⟨⟨248271523626580225393666303010,248271523626580225433360888894⟩,⟨36430943832750866211777669659,36430943832750866247865777947⟩⟩] +lemma amp7_01_7_eq : ∀ k : Fin 16, amp7_0Expr 1 7 k = amp7_01_7 k := by decide +kernel +noncomputable def amp7_01_8 : Fin 16 → CBox := ![⟨⟨248795701050586257857925251441,248795701050586257897593874547⟩,⟨36199819861475239119965285334,36199819861475239156013560074⟩⟩,⟨⟨249282232912266652332235391913,249282232912266652371899746135⟩,⟨35963287961944275642733558859,35963287961944275678740690484⟩⟩,⟨⟨249731047118426714355262165205,249731047118426714394907544542⟩,⟨35721522387220123868224265249,35721522387220123904183470150⟩⟩,⟨⟨250141363040241398640902515957,250141363040241398680517061106⟩,⟨35474595600399333160554948580,35474595600399333196460030413⟩⟩,⟨⟨250513598991149060607367406497,250513598991149060646942667455⟩,⟨35222750717243902166218914910,35222750717243902202064069295⟩⟩,⟨⟨250846506012137325418788465999,250846506012137325458311494189⟩,⟨34965994623347910532071749579,34965994623347910567850716992⟩⟩,⟨⟨251140998435603911923918568750,251140998435603911963385543357⟩,⟨34704637320649346333974784705,34704637320649346369682534332⟩⟩,⟨⟨251395354559775651615911817146,251395354559775651655309004472⟩,⟨34438621381838913454167389882,34438621381838913489797580271⟩⟩,⟨⟨251610990924665792555925047657,251610990924665792595249601552⟩,⟨34168321799167045218939070907,34168321799167045254486847884⟩⟩,⟨⟨251785708069448953557184699267,251785708069448953596432469068⟩,⟨33893618018639213520946507613,33893618018639213556406920194⟩⟩,⟨⟨251921431516868368602285816305,251921431516868368641451227604⟩,⟨33614948207245718433410307704,33614948207245718468778241106⟩⟩,⟨⟨252015478411803646587073771601,252015478411803646626134676192⟩,⟨33332129793936222475623001377,33332129793936222510891105044⟩⟩,⟨⟨252070290634472429620176049522,252070290634472429659149672118⟩,⟨33045662385145755134376892677,33045662385145755169543123834⟩⟩,⟨⟨252082695662953565699096933662,252082695662953565737956846919⟩,⟨32755302427237606209262768029,32755302427237606244319311887⟩⟩,⟨⟨252055659725684453223641177917,252055659725684453262409441112⟩,⟨32461609311407643787891558022,32461609311407643822837056995⟩⟩,⟨⟨251985513702620182757349625511,251985513702620182795986087595⟩,⟨32164279461810340080032114344,32164279461810340114857032126⟩⟩] +lemma amp7_01_8_eq : ∀ k : Fin 16, amp7_0Expr 1 8 k = amp7_01_8 k := by decide +kernel +noncomputable def amp7_01_9 : Fin 16 → CBox := ![⟨⟨251875756796925501435143977371,251875756796925501473650430644⟩,⟨31863930481006021240637710809,31863930481006021275338111943⟩⟩,⟨⟨251722215675293292115402846843,251722215675293292153766752173⟩,⟨31560199657932759873692200858,31560199657932759908262239947⟩⟩,⟨⟨251528931801266464015069783557,251528931801266464053343109839⟩,⟨31253761315423978367535291747,31253761315423978401977392211⟩⟩,⟨⟨251291219300638232507293894667,251291219300638232545406840288⟩,⟨30944194421149637499667273673,30944194421149637533968426371⟩⟩,⟨⟨251013671869395834220515872542,251013671869395834258471612371⟩,⟨30632228610791207904528561476,30632228610791207938685170753⟩⟩,⟨⟨250691082019641374210093627050,250691082019641374247894714750⟩,⟨30317385271621816746053337752,30317385271621816780061492788⟩⟩,⟨⟨250328606369769749907735330561,250328606369769749945360692198⟩,⟨30000448030123796420936641591,30000448030123796454789921831⟩⟩,⟨⟨249920505963284085191796251088,249920505963284085229248520580⟩,⟨29680881360548827030738755072,29680881360548827064433255391⟩⟩,⟨⟨249472511784910354702781617248,249472511784910354740047537549⟩,⟨29359521645583211108507668908,29359521645583211142037975279⟩⟩,⟨⟨248978342730866012759530584116,248978342730866012796591629080⟩,⟨29035777039515431879200632976,29035777039515431912560455560⟩⟩,⟨⟨248444316391166953184644108130,248444316391166953221641965252⟩,⟨28710535536537612702218991803,28710535536537612735421041361⟩⟩,⟨⟨247863597965460509151736070983,247863597965460509188530424260⟩,⟨28383149488471577757561486894,28383149488471577790585256475⟩⟩,⟨⟨247243104729634202442770547160,247243104729634202479363408444⟩,⟨28054557449060372442592613846,28054557449060372475434683126⟩⟩,⟨⟨246575435714377538678131270609,246575435714377538714503032290⟩,⟨27724056407900035114697594877,27724056407900035147351671939⟩⟩,⟨⟨245868121856331883728008951015,245868121856331883764179925178⟩,⟨27392634522338951357975449103,27392634522338951390440304846⟩⟩,⟨⟨245113182562931495902613611735,245113182562931495938552210885⟩,⟨27059533780557546620684526889,27059533780557546652952547251⟩⟩] +lemma amp7_01_9_eq : ∀ k : Fin 16, amp7_0Expr 1 9 k = amp7_01_9 k := by decide +kernel +noncomputable def amp7_01_10 : Fin 16 → CBox := ![⟨⟨244318777360190751749257902126,244318777360190751785009760023⟩,⟨26725791087292515100889923271,26725791087292515132962630681⟩⟩,⟨⟨243476331530262021983252081444,243476331530262022018769727528⟩,⟨26390593707993928529069644924,26390593707993928560937825937⟩⟩,⟨⟨242594649137857625288117599254,242594649137857625323399598089⟩,⟨26055026542509240091921727609,26055026542509240123581911613⟩⟩,⟨⟨241664545716434029771057187201,241664545716434029806110991248⟩,⟨25718222326859750893720863467,25718222326859750925169815016⟩⟩,⟨⟨240695486914829266661018796501,240695486914829266695818697128⟩,⟨25381313312414681086803596641,25381313312414681118035298750⟩⟩,⟨⟨239677661690547554036676553277,239677661690547554071231392687⟩,⟨25043377809807420979578476434,25043377809807421010589932955⟩⟩,⟨⟨238621215502947656586726814081,238621215502947656621029599834⟩,⟨24705594892371311180353118250,24705594892371311211140471795⟩⟩,⟨⟨237515692610117462148866145864,237515692610117462182901943879⟩,⟨24366988455573209036506421254,24366988455573209067064175630⟩⟩,⟨⟨236371937784837922320575740771,236371937784837922354338190972⟩,⟨24028783985186936916186812813,24028783985186936946511237467⟩⟩,⟨⟨235178831062536135196039409966,235178831062536135229516876922⟩,⟨23689950872599509992155212675,23689950872599510022241306387⟩⟩,⟨⟨233947937416443306604739394248,233947937416443306637916406308⟩,⟨23351760733276686469459989066,23351760733276686499303322593⟩⟩,⟨⟨232667451620007509561496696265,232667451620007509594799634652⟩,⟨23013128260317976089453857630,23013128260317976119092764529⟩⟩,⟨⟨231349681239408039675586518054,231349681239408039708602736208⟩,⟨22675371050480248554348046781,22675371050480248583738487764⟩⟩,⟨⟨229982113099936804394349153853,229982113099936804427076477011⟩,⟨22337348791965653832158206267,22337348791965653861296191211⟩⟩,⟨⟨228577821395677657760985619585,228577821395677657793417462505⟩,⟨22000425057283611674391578319,22000425057283611703273785068⟩⟩,⟨⟨227123560523375192019993938838,227123560523375192052131991803⟩,⟨21663404102548503669575956948,21663404102548503698198738319⟩⟩] +lemma amp7_01_10_eq : ∀ k : Fin 16, amp7_0Expr 1 10 k = amp7_01_10 k := by decide +kernel +noncomputable def amp7_01_11 : Fin 16 → CBox := ![⟨⟨225633197137326073713045603903,225633197137326073744884626858⟩,⟨21327695622933352086343713817,21327695622933352114703902746⟩⟩,⟨⟨224092726764750813737099085617,224092726764750813768641610734⟩,⟨20992047885300280096590037662,20992047885300280124684178300⟩⟩,⟨⟨222516836325278459516820842775,222516836325278459548048058778⟩,⟨20657917017662205205177496983,20657917017662205233001367512⟩⟩,⟨⟨220890733886764977508570853196,220890733886764977539503030596⟩,⟨20323994599710325395627230178,20323994599710325423178958511⟩⟩,⟨⟨219229956611277723753988769194,219229956611277723784598023466⟩,⟨19991783677967916326256318360,19991783677967916353530919896⟩⟩,⟨⟨217518894154993001449356579518,217518894154993001479645289389⟩,⟨19659918293912015492217573633,19659918293912015519211626380⟩⟩,⟨⟨215773966298139143432099394653,215773966298139143462052122019⟩,⟨19329949087603916627022360163,19329949087603916653732258048⟩⟩,⟨⟨213978710727400683632936495005,213978710727400683662614692056⟩,⟨19000451543935031833114817369,19000451543935031859542349179⟩⟩,⟨⟨212150464874051781966640097566,212150464874051781995977630873⟩,⟨18673024776650951857124907602,18673024776650951883261977236⟩⟩,⟨⟨210271878014667217782023583172,210271878014667217811020247231⟩,⟨18346184512029961321748790082,18346184512029961347591828383⟩⟩,⟨⟨208361243217416167478455986045,208361243217416167507122527322⟩,⟨18021579440744177029539232455,18021579440744177055087203874⟩⟩,⟨⟨206400281707890630602730442358,206400281707890630631041606880⟩,⟨17697664125973585183370075598,17697664125973585208617171018⟩⟩,⟨⟨204408283469455120407555066087,204408283469455120435514481159⟩,⟨17376138182231228472845551321,17376138182231228497790180729⟩⟩,⟨⟨202365998470939139377729736211,202365998470939139405330610791⟩,⟨17055393380958232367142374718,17055393380958232391780442128⟩⟩,⟨⟨200293758572598872621162336215,200293758572598872648393198037⟩,⟨16737181874734243193538903575,16737181874734243217867751283⟩⟩,⟨⟨198171295295397271015581690683,198171295295397271042429877508⟩,⟨16419830765359345002065229690,16419830765359345026080249818⟩⟩] +lemma amp7_01_11_eq : ∀ k : Fin 16, amp7_0Expr 1 11 k = amp7_01_11 k := by decide +kernel +noncomputable def amp7_01_12 : Fin 16 → CBox := ![⟨⟨196020031473427629432586977315,196020031473427629459294855009⟩,⟨16105146652283613035618203759,16105146652283613059337666650⟩⟩,⟨⟨193818628516734387067595965907,193818628516734387093948827341⟩,⟨15791389811362494915805480776,15791389811362494939208132848⟩⟩,⟨⟨191589653989756327167202659982,191589653989756327193195919848⟩,⟨15480423523884399985011735201,15480423523884400008095760162⟩⟩,⟨⟨189310642490989542415439076440,189310642490989542441071526621⟩,⟨15170438771115004198484672071,15170438771115004221246420956⟩⟩,⟨⟨187005365342270666958430093757,187005365342270666983697561231⟩,⟨14863358114068846279923459445,14863358114068846302361222163⟩⟩,⟨⟨184650167931912916710118155480,184650167931912916735022862268⟩,⟨14557300418748473624607804810,14557300418748473646718293711⟩⟩,⟨⟨182270090351975544851561260646,182270090351975544876086773687⟩,⟨14254250529681451629750378784,14254250529681451651531147928⟩⟩,⟨⟨179840219909120717690102757835,179840219909120717714278076618⟩,⟨13952251978297194782510351542,13952251978297194803960132926⟩⟩,⟨⟨177386937305604389423389526044,177386937305604389447177965581⟩,⟨13653355352837984736545565651,13653355352837984757660406379⟩⟩,⟨⟨174883995508394585170853733042,174883995508394585194259663318⟩,⟨13355525177213708908741403925,13355525177213708929518227526⟩⟩,⟨⟨172359195492072152371863629695,172359195492072152394878949163⟩,⟨13060881759698104065659244161,13060881759698104086096594678⟩⟩,⟨⟨169784871155770591519295487384,169784871155770591541914546904⟩,⟨12767306424856491813074830163,12767306424856491833168772852⟩⟩,⟨⟨167190332414052911985290406843,167190332414052912007498794381⟩,⟨12476993764394877354551791140,12476993764394877374300504137⟩⟩,⟨⟨164546399607492550945313833223,164546399607492550967258444408⟩,⟨12187737114995289980699694143,12187737114995290000110636724⟩⟩,⟨⟨161883990679850759551598123706,161883990679850759573136958705⟩,⟨11901810587175803854867853895,11901810587175803873929930875⟩⟩,⟨⟨159172306608214890727596557722,159172306608214890748727948987⟩,⟨11616914051045788912282207742,11616914051045788930991780325⟩⟩] +lemma amp7_01_12_eq : ∀ k : Fin 16, amp7_0Expr 1 12 k = amp7_01_12 k := by decide +kernel +noncomputable def amp7_01_13 : Fin 16 → CBox := ![⟨⟨156443984581947960120941928925,156443984581947960141667851468⟩,⟨11335407145532101495232550281,11335407145532101513589331071⟩⟩,⟨⟨153666487219981670739591338068,153666487219981670759926223195⟩,⟨11054889992404904530222151869,11054889992404904548223743361⟩⟩,⟨⟨150874296370014650934810148301,150874296370014650954723881969⟩,⟨10777814666830312798418330104,10777814666830312816062411455⟩⟩,⟨⟨148033001824406485095495002687,148033001824406485114994297506⟩,⟨10501674319907455506441847001,10501674319907455523725342614⟩⟩,⟨⟨145179072227836692982240656384,145179072227836693001311403026⟩,⟨10229021420718776454603170154,10229021420718776471525051292⟩⟩,⟨⟨142276071800021690804832322779,142276071800021690823567290526⟩,⟨9957233818058454210907164914,9957233818058454227470415970⟩⟩,⟨⟨139362617965696802225764061304,139362617965696802244079850878⟩,⟨9688973569370079947857029901,9688973569370079964056011279⟩⟩,⟨⟨136400074875784146833451394190,136400074875784146851343066865⟩,⟨9421493571303331049302047921,9421493571303331065132782530⟩⟩,⟨⟨133429394442438188025837831008,133429394442438188043307315539⟩,⟨9157576133452635368824904514,9157576133452635384287878824⟩⟩,⟨⟨130409540159951773701134222949,130409540159951773718187281381⟩,⟨8894337971165882754362094654,8894337971165882769454104466⟩⟩,⟨⟨127384012735082403941164602808,127384012735082403957791594260⟩,⟨8634694071620776349285812348,8634694071620776364006859295⟩⟩,⟨⟨124309142840555095514783600196,124309142840555095531042403457⟩,⟨8375611830585849862875062160,8375611830585849877225290103⟩⟩,⟨⟨121231229079003094521862804616,121231229079003094537680674067⟩,⟨8120153471306396391073006048,8120153471306396405048323705⟩⟩,⟨⟨118103698548785723723024793221,118103698548785723738405006571⟩,⟨7865121601183851304859500994,7865121601183851318456367466⟩⟩,⟨⟨114975939609167286450891868549,114975939609167286465839900940⟩,⟨7613742848740464334597851109,7613742848740464347817779383⟩⟩,⟨⟨111798157368647936299641144749,111798157368647936314144879593⟩,⟨7362636688401967943072486975,7362636688401967955910743457⟩⟩] +lemma amp7_01_13_eq : ∀ k : Fin 16, amp7_0Expr 1 13 k = amp7_01_13 k := by decide +kernel +noncomputable def amp7_01_14 : Fin 16 → CBox := ![⟨⟨108623174944359293488387622088,108623174944359293502496752423⟩,⟨7115214556521337960599160391,7115214556521337973060334222⟩⟩,⟨⟨105397597463176734955232408902,105397597463176734968899257965⟩,⟨6867890858394657465042059158,6867890858394657477119050098⟩⟩,⟨⟨102178094674235493138276457035,102178094674235493151509071008⟩,⟨6624286297837598056992749092,6624286297837598068687788350⟩⟩,⟨⟨98907218265895227221409184318,98907218265895227234186129429⟩,⟨6380583728966284902312193887,6380583728966284913619696445⟩⟩,⟨⟨95645981838252966881220538162,95645981838252966893590199100⟩,⟨6140642747930834018349551667,6140642747930834029274601212⟩⟩,⟨⟨92332333149545203791779568146,92332333149545203803700810331⟩,⟨5900382334383674490606744694,5900382334383674501142376871⟩⟩,⟨⟨89032237534754024547793589635,89032237534754024559295380342⟩,⟨5663937286076232283494932783,5663937286076232293645371964⟩⟩,⟨⟨85678361420341753069417407833,85678361420341753080464764939⟩,⟨5426922749806999810662842727,5426922749806999820421272077⟩⟩,⟨⟨82342375884702641155480884615,82342375884702641166080225670⟩,⟨5193793846282766105854139095,5193793846282766115223674045⟩⟩,⟨⟨78950819371192803894594921360,78950819371192803904761331852⟩,⟨4959811753947199975940331097,4959811753947199984917142803⟩⟩,⟨⟨75582019731829227624177584502,75582019731829227633890052391⟩,⟨4729808904115832927912099161,4729808904115832936498086413⟩⟩,⟨⟨72155309912272385734946474454,72155309912272385744219723112⟩,⟨4498628495419628053162062931,4498628495419628061352978453⟩⟩,⟨⟨68756897761275499446719428154,68756897761275499455557649136⟩,⟨4271553634847071019718455309,4271553634847071027518246823⟩⟩,⟨⟨65297509875106229342710555234,65297509875106229351087409806⟩,⟨4042926102704053605996944107,4042926102704053613398454862⟩⟩,⟨⟨61872844323457997063043330585,61872844323457997070979256840⟩,⟨3818576314215594168250235372,3818576314215594175259074655⟩⟩,⟨⟨58383153209769581769369389226,58383153209769581776855667994⟩,⟨3592233124806953305105603040,3592233124806953311715158828⟩⟩] +lemma amp7_01_14_eq : ∀ k : Fin 16, amp7_0Expr 1 14 k = amp7_01_14 k := by decide +kernel +noncomputable def amp7_01_15 : Fin 16 → CBox := ![⟨⟨54935804544626330767194368872,54935804544626330774233458051⟩,⟨3370405110600690903486714253,3370405110600690909702158599⟩⟩,⟨⟨51418006349442538651586748004,51418006349442538658169026086⟩,⟨3146054572773215482269748906,3146054572773215488083823909⟩⟩,⟨⟨47951850290683078209832603730,47951850290683078215963945491⟩,⟨2926551596391128859951617958,2926551596391128865370661900⟩⟩,⟨⟨44407827334485770037831085529,44407827334485770043509835108⟩,⟨2703872051001439205044629836,2703872051001439210060956922⟩⟩,⟨⟨40927220083475100830030798248,40927220083475100835262589326⟩,⟨2486515758282676543359453516,2486515758282676547980517993⟩⟩,⟨⟨37358287825271691763385100667,37358287825271691768157689782⟩,⟨2265141719129524050795913974,2265141719129524055012236512⟩⟩,⟨⟨33868417361743168326244646956,33868417361743168330565985722⟩,⟨2049794564101097760298977067,2049794564101097764119749222⟩⟩,⟨⟨30274799397741112513462790811,30274799397741112517326698936⟩,⟨1829286560222367137183046442,1829286560222367140597422618⟩⟩,⟨⟨26782471259172710142646130630,26782471259172710146061080603⟩,⟨1615900331877007176621496163,1615900331877007179640929225⟩⟩,⟨⟨23162049866769122148128878440,23162049866769122151079971566⟩,⟨1395671289099782474731010291,1395671289099782477341516685⟩⟩,⟨⟨19677744015863216028382433002,19677744015863216030886298220⟩,⟨1184411949326034366730612431,1184411949326034368947740094⟩⟩,⟨⟨16022433859081099922552794840,16022433859081099924589463652⟩,⟨963510929833827464740383503,963510929833827466545224863⟩⟩,⟨⟨12567181482434424472802095977,12567181482434424474395776988⟩,⟨755172765314776927642967694,755172765314776929058149490⟩⟩,⟨⟨8848419706798893032499164498,8848419706798893033618925427⟩,⟨531415469688980890990742434,531415469688980891986914174⟩⟩,⟨⟨5489118996954148587661105487,5489118996954148588348201334⟩,⟨329542231969367225550871395,329542231969367226168345803⟩⟩,⟨⟨1559515441983256086728251044,1559515441983256086918948455⟩,⟨93609099375948831493331814,93609099375948831668485773⟩⟩] +lemma amp7_01_15_eq : ∀ k : Fin 16, amp7_0Expr 1 15 k = amp7_01_15 k := by decide +kernel +noncomputable def amp7_01 : Fin 16 → Fin 16 → CBox := ![amp7_01_0,amp7_01_1,amp7_01_2,amp7_01_3,amp7_01_4,amp7_01_5,amp7_01_6,amp7_01_7,amp7_01_8,amp7_01_9,amp7_01_10,amp7_01_11,amp7_01_12,amp7_01_13,amp7_01_14,amp7_01_15] +lemma amp7_01_eq (i k : Fin 16) : amp7_0Expr 1 i k = amp7_01 i k := by + fin_cases i + · exact amp7_01_0_eq k + · exact amp7_01_1_eq k + · exact amp7_01_2_eq k + · exact amp7_01_3_eq k + · exact amp7_01_4_eq k + · exact amp7_01_5_eq k + · exact amp7_01_6_eq k + · exact amp7_01_7_eq k + · exact amp7_01_8_eq k + · exact amp7_01_9_eq k + · exact amp7_01_10_eq k + · exact amp7_01_11_eq k + · exact amp7_01_12_eq k + · exact amp7_01_13_eq k + · exact amp7_01_14_eq k + · exact amp7_01_15_eq k +noncomputable def amp7_02_0 : Fin 16 → CBox := ![⟨⟨752741090608955445073285556,752741090608955445304534963⟩,⟨309783635300835519830550883,309783635300835520061352353⟩⟩,⟨⟨2649618567617601027252602229,2649618567617601028074214568⟩,⟨1090384078917921350429210686,1090384078917921351244737831⟩⟩,⟨⟨4271652924137867923082648340,4271652924137867924412950046⟩,⟨1757756433048590260978429737,1757756433048590262295484471⟩⟩,⟨⟨6067955913242831812365333751,6067955913242831814256340049⟩,⟨2496635008007367991272149650,2496635008007367993143425935⟩⟩,⟨⟨7738059115552217079224347406,7738059115552217081637585245⟩,⟨3183302452159180911761903872,3183302452159180914148682616⟩⟩,⟨⟨9506105053272041830039447672,9506105053272041833004505069⟩,⟨3909894395053282237862636406,3909894395053282240794538162⟩⟩,⟨⟨11193160729980066847101277220,11193160729980066850593244498⟩,⟨4602725467600047194666837495,4602725467600047198118788240⟩⟩,⟨⟨12947905178745837693365034149,12947905178745837697404138694⟩,⟨5322861140762390235336016116,5322861140762390239328242610⟩⟩,⟨⟨14642926722148890147622266089,14642926722148890152189837077⟩,⟨6017834219833436496024601454,6017834219833436500538347035⟩⟩,⟨⟨16389430759450253917880450978,16389430759450253922989715434⟩,⟨6733274908699897532934670663,6733274908699897537984273105⟩⟩,⟨⟨18088511929847427431935765762,18088511929847427437574475768⟩,⟨7428462608637170111887741112,7428462608637170117459220151⟩⟩,⟨⟨19828942123646101801569995691,19828942123646101807749130336⟩,⟨8139782299306211986204336864,8139782299306211992309190446⟩⟩,⟨⟨21529934359163815187849832192,21529934359163815194555540027⟩,⟨8833984998264612083836092717,8833984998264612090461042488⟩⟩,⟨⟨23265309596030025740911258688,23265309596030025748152052719⟩,⟨9541290239441461225943257889,9541290239441461233097446392⟩⟩,⟨⟨24966825789130204940625959645,24966825789130204948394091755⟩,⟨10233627042758717119119702301,10233627042758717126793283468⟩⟩,⟨⟨26697616924776496712292687659,26697616924776496720595723671⟩,⟨10936804679057980971108401584,10936804679057980979309120807⟩⟩] +lemma amp7_02_0_eq : ∀ k : Fin 16, amp7_0Expr 2 0 k = amp7_02_0 k := by decide +kernel +noncomputable def amp7_02_1 : Fin 16 → CBox := ![⟨⟨28398648759530835033797208668,28398648759530835042624122364⟩,⟨11626556877695830409469014235,11626556877695830418186344466⟩⟩,⟨⟨30125028652640462456675569950,30125028652640462466031518722⟩,⟨12325377884663294760622921190,12325377884663294769862829283⟩⟩,⟨⟨31824773709394047787038949972,31824773709394047796913889470⟩,⟨13011918726766667365692510242,13011918726766667375445362576⟩⟩,⟨⟨33546736048761689548651445861,33546736048761689559058573031⟩,⟨13706088031084382881997225922,13706088031084382892271627873⟩⟩,⟨⟨35244510043612919438880885721,35244510043612919449801857404⟩,⟨14388847512213722106125879880,14388847512213722116909176218⟩⟩,⟨⟨36961931337444383072805637872,36961931337444383084245224618⟩,⟨15078030401009826393556336880,15078030401009826404853147140⟩⟩,⟨⟨38657119431536439566028378525,38657119431536439577988625295⟩,⟨15756476112840100525402301406,15756476112840100537208576823⟩⟩,⟨⟨40369793640478122112840560928,40369793640478122125313375642⟩,⟨16440313362871605902802471152,16440313362871605915117117267⟩⟩,⟨⟨42061821427468001605599646819,42061821427468001618587384952⟩,⟨17113939417537288040136842845,17113939417537288052956151339⟩⟩,⟨⟨43769480326598193436944423140,43769480326598193450452115237⟩,⟨17792056527207565427691370902,17792056527207565441019180688⟩⟩,⟨⟨45457795487182887780078687430,45457795487182887794084346797⟩,⟨18460376846595903416731977931,18460376846595903430554849758⟩⟩,⟨⟨47160121097022481571409530125,47160121097022481585928820144⟩,⟨19132389977871419149114253887,19132389977871419163439983162⟩⟩,⟨⟨48844181194264717113739550228,48844181194264717128747435814⟩,⟨19794934082959038242519670438,19794934082959038257333729429⟩⟩,⟨⟨50540813576353335216884947921,50540813576353335232406468536⟩,⟨20460454067353999562731570048,20460454067353999578045213575⟩⟩,⟨⟨52220077570636705847109167380,52220077570636705863129173561⟩,⟨21116764369090721389404505870,21116764369090721405207319006⟩⟩,⟨⟨53910619802580624803556513591,53910619802580624820079776662⟩,⟨21775399522604202525834299441,21775399522604202542129016044⟩⟩] +lemma amp7_02_1_eq : ∀ k : Fin 16, amp7_0Expr 2 1 k = amp7_02_1 k := by decide +kernel +noncomputable def amp7_02_2 : Fin 16 → CBox := ![⟨⟨55584541922073851331908158062,55584541922073851348906382239⟩,⟨22425029550945179207730611495,22425029550945179224501605434⟩⟩,⟨⟨57268563301231505011953018736,57268563301231505029451509423⟩,⟨23076387727770760413771954881,23076387727770760431029972562⟩⟩,⟨⟨58936588465145650255275315272,58936588465145650273263618849⟩,⟨23718900966578546040132306962,23718900966578546057868982856⟩⟩,⟨⟨60613626573115870800445269206,60613626573115870818926383289⟩,⟨24362591109869678079852093304,24362591109869678098068907237⟩⟩,⟨⟨62275186877665940950346281698,62275186877665940969317385729⟩,⟨24997560234149827799123626984,24997560234149827817815328824⟩⟩,⟨⟨63944748900429145034656521718,63944748900429145054081241807⟩,⟨25633193584541045791636476691,25633193584541045810788515729⟩⟩,⟨⟨65599260858704032828790336370,65599260858704032848693311102⟩,⟨26260199971170722529631160148,26260199971170722549249343804⟩⟩,⟨⟨67260824416962985786309914301,67260824416962985806686098803⟩,⟨26887391036100908214788376306,26887391036100908234870501364⟩⟩,⟨⟨68907686752786437254174541529,68907686752786437275022371292⟩,⟨27506024464108464979789152886,27506024464108465000330526939⟩⟩,⟨⟨70560700411286343694603582127,70560700411286343715923773482⟩,⟨28124391815787047251119435416,28124391815787047272119946740⟩⟩,⟨⟨72199292274565356570667753190,72199292274565356592453492146⟩,⟨28734250300078313247003079525,28734250300078313268455948209⟩⟩,⟨⟨73843175845167467144920847677,73843175845167467167129147096⟩,⟨29343417247805243034940523145,29343417247805243056828070122⟩⟩,⟨⟨75472855359092801412294230658,75472855359092801434967784847⟩,⟨29944106967972239798837438677,29944106967972239821172588418⟩⟩,⟨⟨77107000077452723023299274763,77107000077452723046430264790⟩,⟨30543702136249633415797522938,30543702136249633438576383259⟩⟩,⟨⟨78727103155820439406946021128,78727103155820439430533589883⟩,⟨31134837433682652699322360226,31134837433682652722540519033⟩⟩,⟨⟨80350871788386054431505611826,80350871788386054455533416521⟩,⟨31724495268137345654795098494,31724495268137345678445129772⟩⟩] +lemma amp7_02_2_eq : ∀ k : Fin 16, amp7_0Expr 2 2 k = amp7_02_2 k := by decide +kernel +noncomputable def amp7_02_3 : Fin 16 → CBox := ![⟨⟨81960711179847413141224855185,81960711179847413165695837992⟩,⟨32305698692395420399339079575,32305698692395420423418072577⟩⟩,⟨⟨83573438102217768145355813139,83573438102217768170270082711⟩,⟨32885059909187538543865981833,32885059909187538568372840532⟩⟩,⟨⟨85172302630801084113870986924,85172302630801084139223394807⟩,⟨33455962299849386860363209509,33455962299849386885291811329⟩⟩,⟨⟨86773293907645469570051480200,86773293907645469595767145954⟩,⟨34024674289889249656325080671,34024674289889249681644757589⟩⟩,⟨⟨88360447887500187756984527582,88360447887500187783135111215⟩,⟨34584914883759463467474915394,34584914883759463493209699561⟩⟩,⟨⟨89948981376586003085675764383,89948981376586003112252567194⟩,⟨35142632080018527000886176703,35142632080018527027031197848⟩⟩,⟨⟨91523664184882791978679248026,91523664184882792005675023496⟩,⟨35691858636139516146008096473,35691858636139516172556391881⟩⟩,⟨⟨93098989682257366167236015060,93098989682257366194645060229⟩,⟨36238242850190588052304282990,36238242850190588079252021270⟩⟩,⟨⟨94660415478379246990366433491,94660415478379247018186586298⟩,⟨36776111786955339636617104692,36776111786955339663959294943⟩⟩,⟨⟨96221754917716353946036196457,96221754917716353974246676609⟩,⟨37310832519333562207536765997,37310832519333562235263591136⟩⟩,⟨⟨97769112499846303308265384722,97769112499846303336877148369⟩,⟨37837009059334329331042845764,37837009059334329359154391746⟩⟩,⟨⟨99315660215954264168077900786,99315660215954264197080549213⟩,⟨38359743787188607343917754692,38359743787188607372408109087⟩⟩,⟨⟨100848113008272486060189330481,100848113008272486089579590321⟩,⟨38873902106423422541593993263,38873902106423422570457703454⟩⟩,⟨⟨102379036072466122522491745401,102379036072466122552265705248⟩,⟨39384336551103756187742771134,39384336551103756216976307891⟩⟩,⟨⟨103895722237665022383728482063,103895722237665022413881169745⟩,⟨39886159929898664419758646820,39886159929898664449355881451⟩⟩,⟨⟨105410160870922715602222607376,105410160870922715632749672232⟩,⟨40383988306513330515794497492,40383988306513330545751610606⟩⟩] +lemma amp7_02_3_eq : ∀ k : Fin 16, amp7_0Expr 2 3 k = amp7_02_3 k := by decide +kernel +noncomputable def amp7_02_4 : Fin 16 → CBox := ![⟨⟨106910193543801517052835457477,106910193543801517083616587066⟩,⟨40873169280073945165825054371,40873169280073945196091806851⟩⟩,⟨⟨108407261612219029522425618480,108407261612219029553589435671⟩,⟨41358094530592833418745672047,41358094530592833449369041151⟩⟩,⟨⟨109889729250853083520546081345,109889729250853083552081515241⟩,⟨41834335037523380671140297103,41834335037523380702111770985⟩⟩,⟨⟨111368514846768013316100024347,111368514846768013347998860196⟩,⟨42306069048658748540941462844,42306069048658748572255505911⟩⟩,⟨⟨112832481698245188561576514668,112832481698245188593830675331⟩,⟨42769080576114876759532379775,42769080576114876791181626763⟩⟩,⟨⟨114292047809469377111696690111,114292047809469377144306211907⟩,⟨43227344382948996003168936263,43227344382948996035150879022⟩⟩,⟨⟨115736554487508436712978951677,115736554487508436745925719341⟩,⟨43676848107347071297069185159,43676848107347071329372654624⟩⟩,⟨⟨117175939756319820295980618115,117175939756319820329268378976⟩,⟨44121372083476610169918352039,44121372083476610202542142798⟩⟩,⟨⟨118600003928277599202209511173,118600003928277599235833769305⟩,⟨44557099005884894825816388238,44557099005884894858754466952⟩⟩,⟨⟨120018223501151367740000716471,120018223501151367773922668157⟩,⟨44987623040699086148363244059,44987623040699086181598323433⟩⟩,⟨⟨121420840682019321645661745988,121420840682019321679911254996⟩,⟨45409314116198159728725752342,45409314116198159762264688418⟩⟩,⟨⟨122816887150494215962289077137,122816887150494215996855284622⟩,⟨45825587779790596367047354771,45825587779790596400883253201⟩⟩,⟨⟨124197031601504606456382807634,124197031601504606491262723804⟩,⟨46232994040221245952567268863,46232994040221245986694637859⟩⟩,⟨⟨125569876034064210600538117385,125569876034064210635713856319⟩,⟨46634776736345183802025294258,46634776736345183836434552958⟩⟩,⟨⟨126926501763489906704911996299,126926501763489906740390787547⟩,⟨47027659405968905013119907029,47027659405968905047809351461⟩⟩,⟨⟨128275094827876442007656471899,128275094827876442043425316050⟩,⟨47414720513377003426982679936,47414720513377003461944476856⟩⟩] +lemma amp7_02_4_eq : ∀ k : Fin 16, amp7_0Expr 2 4 k = amp7_02_4 k := by decide +kernel +noncomputable def amp7_02_5 : Fin 16 → CBox := ![⟨⟨129607136691529779074809134623,129607136691529779110865126970⟩,⟨47792851117062570500854076992,47792851117062570536082753413⟩⟩,⟨⟨130930409866488463568153807995,130930409866488463604491743885⟩,⟨48164970119519357007794977989,48164970119519357043285504950⟩⟩,⟨⟨132236784765314337503230901628,132236784765314337539847625937⟩,⟨48528130583142679953152455607,48528130583142679988899248516⟩⟩,⟨⟨133533651640381848625057682265,133533651640381848661947024752⟩,⟨48885097188358111846110923094,48885097188358111882108524208⟩⟩,⟨⟨134813259812406406449798133346,134813259812406406486954635239⟩,⟨49233079931164875134128705460,49233079931164875170370684451⟩⟩,⟨⟨136082617474001406181819889098,136082617474001406219001259663⟩,⟨49574694178867441793928556232,49574694178867441830323362178⟩⟩,⟨⟨137334343877746732147492099951,137334343877746732184941443337⟩,⟨49907302197601165353523622300,49907302197601165390155572151⟩⟩,⟨⟨138575074379489316505163004197,138575074379489316542868947883⟩,⟨50233374556946912754424524441,50233374556946912791286117234⟩⟩,⟨⟨139797790165801490656216878457,139797790165801490694168480056⟩,⟨50550421501590905159112383147,50550421501590905196195198492⟩⟩,⟨⟨141008762080678473545935531031,141008762080678473584126801442⟩,⟨50860772958088918683320346190,50860772958088918720618783598⟩⟩,⟨⟨142201326149745376015456271930,142201326149745376053874423043⟩,⟨51162083199110509203447200027,51162083199110509240952191585⟩⟩,⟨⟨143381396201447026571324225992,143381396201447026609962647997⟩,⟨51456545331234470068135304924,51456545331234470105840988934⟩⟩,⟨⟨144542656841606585820449133027,144542656841606585859309052617⟩,⟨51741954018255005225048423302,51741954018255005262950790378⟩⟩,⟨⟨145690671612085969967612964680,145690671612085970006676682937⟩,⟨52020369063903419366330783771,52020369063903419404419939975⟩⟩,⟨⟨146819468216847922578777827789,146819468216847922618045919781⟩,⟨52289722175748647732662165624,52289722175748647770933868358⟩⟩,⟨⟨147934265926895006692467291147,147934265926895006731936473078⟩,⟨52551943088712423313000461059,52551943088712423351449923862⟩⟩] +lemma amp7_02_5_eq : ∀ k : Fin 16, amp7_0Expr 2 5 k = amp7_02_5 k := by decide +kernel +noncomputable def amp7_02_6 : Fin 16 → CBox := ![⟨⟨149029430786421903402707509794,149029430786421903442344967606⟩,⟨52805097474825743621178350370,52805097474825743659789495350⟩⟩,⟨⟨150109843145800088421923255368,150109843145800088461754421717⟩,⟨53050987971420316081378475821,53050987971420316120156646036⟩⟩,⟨⟨151170203308918135183702852892,151170203308918135223704680761⟩,⟨53287811384646460672129657849,53287811384646460711062264107⟩⟩,⟨⟨152215057432380217557933906071,152215057432380217598116446480⟩,⟨53517245980666110448896040901,53517245980666110487982901181⟩⟩,⟨⟨153239436635019181894845034100,153239436635019181935192417129⟩,⟨53737617101435600925991062900,53737617101435600965222165893⟩⟩,⟨⟨154247557020302415901623629133,154247557020302415942134857101⟩,⟨53950481139589555645658049715,53950481139589555685029258227⟩⟩,⟨⟨155234777676097626072425145436,155234777676097626113009141878⟩,⟨54154289591555036316068155985,54154289591555036355543261216⟩⟩,⟨⟨156204988239793289070155721472,156204988239793289110898182709⟩,⟨54350479259548051563089096388,54350479259548051602694234633⟩⟩,⟨⟨157153873488422886649795228181,157153873488422886690680885613⟩,⟨54537625616742647151301029980,54537625616742647191026480403⟩⟩,⟨⟨158084999655424348943116055077,158084999655424348984134419352⟩,⟨54717047956166734796006065165,54717047956166734835844307572⟩⟩,⟨⟨158994375464102449739665486411,158994375464102449780814729947⟩,⟨54887443741772106983534165747,54887443741772107023480174415⟩⟩,⟨⟨159885246306157141882861162458,159885246306157141924125626527⟩,⟨55050016647980693881215555280,55050016647980693921260021588⟩⟩,⟨⟨160753943619559312242373704669,160753943619559312283751432544⟩,⟨55203584324808659197467110679,55203584324808659237605008342⟩⟩,⟨⟨161603394038284151473308992283,161603394038284151514799916908⟩,⟨55349236537949517741106491829,55349236537949517781333840585⟩⟩,⟨⟨162430250972046404999932506562,162430250972046405041488295205⟩,⟨55485909490756076538287101278,55485909490756076578583027466⟩⟩,⟨⟨163237123921613224688796964929,163237123921613224730448800579⟩,⟨55614580578144709842143794710,55614580578144709882515007680⟩⟩] +lemma amp7_02_6_eq : ∀ k : Fin 16, amp7_0Expr 2 6 k = amp7_02_6 k := by decide +kernel +noncomputable def amp7_02_7 : Fin 16 → CBox := ![⟨⟨164020987994420283362305890790,164020987994420283404042195509⟩,⟨55734303087909235290756930384,55734303087909235331195183539⟩⟩,⟨⟨164784136738977673603242232528,164784136738977673645062184003⟩,⟨55845943417929887312596303380,55845943417929887353097297117⟩⟩,⟨⟨165523867138141131811399472131,165523867138141131853273546675⟩,⟨55948670628245126240260815619,55948670628245126280810268163⟩⟩,⟨⟨166242157538911934728449242747,166242157538911934770389726421⟩,⟨56043241335972105555944920569,56043241335972105596542974572⟩⟩,⟨⟨166936627414234758610201424645,166936627414234758652187571984⟩,⟨56128939211702624475617429478,56128939211702624516252861191⟩⟩,⟨⟨167608940241114367884417941971,167608940241114367926459177053⟩,⟨56206412156440081541424374390,56206412156440081582096298006⟩⟩,⟨⟨168257039021745336245551040250,168257039021745336287629553816⟩,⟨56275057434817913099661750851,56275057434817913140359977617⟩⟩,⟨⟨168882272284125027856999545533,168882272284125027899109532244⟩,⟨56335415149761510643127005460,56335415149761510683845538823⟩⟩,⟨⟨169482908013025698449441198660,169482908013025698491576684363⟩,⟨56386995284098069276960344639,56386995284098069317693041157⟩⟩,⟨⟨170059979304477564603149693077,170059979304477564645306926087⟩,⟨56430230918327061556670473628,56430230918327061597411987838⟩⟩,⟨⟨170612080985055502453703362992,170612080985055502495870110885⟩,⟨56464744014529945580263169715,56464744014529945621005310654⟩⟩,⟨⟨171139929836441258226038812979,171139929836441258268210517396⟩,⟨56490861267542971875936710116,56490861267542971916673883772⟩⟩,⟨⟨171642449785846914760213600247,171642449785846914802378413767⟩,⟨56508316013635089499987869827,56508316013635089540712100423⟩⟩,⟨⟨172120040021351966643164504463,172120040021351966685314826596⟩,⟨56517329062647435510039081933,56517329062647435550743760325⟩⟩,⟨⟨172571956224893028887745221005,172571956224893028929870048792⟩,⟨56517744651494016743565956464,56517744651494016784243442019⟩⟩,⟨⟨172998278315439785925402468074,172998278315439785967489690392⟩,⟨56509678071718156306253515374,56509678071718156346895757109⟩⟩] +lemma amp7_02_7_eq : ∀ k : Fin 16, amp7_0Expr 2 7 k = amp7_02_7 k := by decide +kernel +noncomputable def amp7_02_8 : Fin 16 → CBox := ![⟨⟨173398596776536261828506222707,173398596776536261870568029382⟩,⟨56493084117174670275797747267,56493084117174670316404770731⟩⟩,⟨⟨173772670184996760060422054962,173772670184996760102471425338⟩,⟨56467972795309526092701794719,56467972795309526133273667911⟩⟩,⟨⟨174120427265082727676357262194,174120427265082727718381777582⟩,⟨56434409242010340797441682746,56434409242010340837970394776⟩⟩,⟨⟨174441302777690227522827856018,174441302777690227564817098384⟩,⟨56392298283167858076869073233,56392298283167858117347106656⟩⟩,⟨⟨174735567520464214553046577608,174735567520464214594992502105⟩,⟨56341815310181682508018165038,56341815310181682548439031817⟩⟩,⟨⟨175002329558816490021049289623,175002329558816490062940718847⟩,⟨56282759938481958558582022221,56282759938481958598937965256⟩⟩,⟨⟨175242205993251993645305018669,175242205993251993687137165813⟩,⟨56215417857065720626849823028,56215417857065720667135458157⟩⟩,⟨⟨175453974901305501737066772087,175453974901305501778827901149⟩,⟨56139483310134043934736993760,56139483310134043974944431711⟩⟩,⟨⟨175638604317856302271054788439,175638604317856302312740808837⟩,⟨56055352455821907412791539142,56055352455821907452915719664⟩⟩,⟨⟨175794538618330206792191021313,175794538618330206833796893826⟩,⟨55962613873422600982136755757,55962613873422601022171920405⟩⟩,⟨⟨175923101812801938016728836124,175923101812801938058248603154⟩,⟨55861774492691337562170210097,55861774492691337602110738639⟩⟩,⟨⟨176022400427443933933221436759,176022400427443933974637482104⟩,⟨55752316799734243709546198140,55752316799734243749382389304⟩⟩,⟨⟨176094119907053886041109781076,176094119907053886082432090868⟩,⟨55634858931490181191408548143,55634858931490181231139934209⟩⟩,⟨⟨176136024335265759814713603717,176136024335265759855921579604⟩,⟨55508776715645939273202071453,55508776715645939312818015194⟩⟩,⟨⟨176150166481477121143275570776,176150166481477121184382621452⟩,⟨55374800067782235530678579718,55374800067782235570179711810⟩⟩,⟨⟨176133962931856779093819054133,176133962931856779134794981128⟩,⟨55232197451942160419422976980,55232197451942160458795709069⟩⟩] +lemma amp7_02_8_eq : ∀ k : Fin 16, amp7_0Expr 2 8 k = amp7_02_8 k := by decide +kernel +noncomputable def amp7_02_9 : Fin 16 → CBox := ![⟨⟨176089840114651461788020539755,176089840114651461828864608239⟩,⟨55081811273218240485148818689,55081811273218240524389446429⟩⟩,⟨⟨176014861584079508510439370516,176014861584079508551140689238⟩,⟨54922801783033576730054033855,54922801783033576769155046452⟩⟩,⟨⟨175911834222425324465715980137,175911834222425324506308951294⟩,⟨54756124730531257021492409684,54756124730531257060461075458⟩⟩,⟨⟨175777462517407875517721641459,175777462517407875558155324887⟩,⟨54580831157264827805247731764,54580831157264827844064115703⟩⟩,⟨⟨175614941080781091833980405850,175614941080781091874255103723⟩,⟨54397991159677982759687158090,54397991159677982798348021049⟩⟩,⟨⟨175420608775856007260010398202,175420608775856007300125786059⟩,⟨54206545418598736644951778933,54206545418598736683452949720⟩⟩,⟨⟨175198055721799165335241304715,175198055721799165375180763219⟩,⟨54007679535615391295900584658,54007679535615391334233636450⟩⟩,⟨⟨174943248049919885730800232858,174943248049919885770563492787⟩,⟨53800222520163030981880402044,53800222520163031020041233837⟩⟩,⟨⟨174660179692747162141659892660,174660179692747162181235825647⟩,⟨53585476798200549094042225920,53585476798200549132024241894⟩⟩,⟨⟨174344436362676348815237405739,174344436362676348854610947744⟩,⟨53362158230143255965929921745,53362158230143256003724473752⟩⟩,⟨⟨174000424668584620243973485107,174000424668584620283242066348⟩,⟨53131687554698908157879868564,53131687554698908195513588265⟩⟩,⟨⟨173623341604458310230428307311,173623341604458310269491578846⟩,⟨52892665830502096659029395029,52892665830502096696467598222⟩⟩,⟨⟨173218015908461422387662719435,173218015908461422426520321186⟩,⟨52646633775382819642969147964,52646633775382819680208706276⟩⟩,⟨⟨172779246906822796755679325147,172779246906822796794315447590⟩,⟨52392075809000797708613790102,52392075809000797745645914350⟩⟩,⟨⟨172312295547099315085427629779,172312295547099315123854787265⟩,⟨52130654482697492416811016808,52130654482697492453636533162⟩⟩,⟨⟨171811553846848748604135683884,171811553846848748642329669768⟩,⟨51860735544992785587632748680,51860735544992785624240397995⟩⟩] +lemma amp7_02_9_eq : ∀ k : Fin 16, amp7_0Expr 2 9 k = amp7_02_9 k := by decide +kernel +noncomputable def amp7_02_10 : Fin 16 → CBox := ![⟨⟨171282725712279709248837386724,171282725712279709286828499794⟩,⟨51584105434466164755396979658,51584105434466164791793056455⟩⟩,⟨⟨170719785473143725905293890678,170719785473143725943046811997⟩,⟨51299008989452981558809470832,51299008989452981594979366867⟩⟩,⟨⟨170128891460016683957050195778,170128891460016683994562283864⟩,⟨51007358801599904765798306405,51007358801599904801738434861⟩⟩,⟨⟨169503589145301876070837309340,169503589145301876108111747907⟩,⟨50707276339698656490528607341,50707276339698656526236030772⟩⟩,⟨⟨168850503519371012039408061413,168850503519371012076425217643⟩,⟨50400802840770248595191131364,50400802840770248630657302447⟩⟩,⟨⟨168162739178938845300124290500,168162739178938845336888347067⟩,⟨50085933709249036377790071524,50085933709249036413012345740⟩⟩,⟨⟨167447400839258285291643671380,167447400839258285328148177702⟩,⟨49764841562494873471745632328,49764841562494873506719469769⟩⟩,⟨⟨166697139288831800506418850685,166697139288831800542651309981⟩,⟨49435392793261232655307764361,49435392793261232690025618090⟩⟩,⟨⟨165919552930021005934926095856,165919552930021005970880529442⟩,⟨49099894395077740026003117779,49099894395077740060460744331⟩⟩,⟨⟨165106824823113337358296392302,165106824823113337393962641917⟩,⟨48756080529969453922526595912,48756080529969453956717147190⟩⟩,⟨⟨164267061992969971647602023313,164267061992969971682967771092⟩,⟨48406395844835687664732589824,48406395844835687698650019586⟩⟩,⟨⟨163391964781905688750696948890,163391964781905688786059630335⟩,⟨48048438758542860867363597513,48048438758542860901091610853⟩⟩,⟨⟨162490164831553539358185056535,162490164831553539393253514998⟩,⟨47684795153033399630596272979,47684795153033399664046784629⟩⟩,⟨⟨161552863614235145080123108271,161552863614235145114893853485⟩,⟨47312923873764852913701146167,47312923873764852946869346279⟩⟩,⟨⟨160589234538283526445542127059,160589234538283526480009179217⟩,⟨46935555949938053543068412215,46935555949938053575950321804⟩⟩,⟨⟨159589962787534702157778141806,159589962787534702191940729385⟩,⟨46550006477923013419080518122,46550006477923013451672187949⟩⟩] +lemma amp7_02_10_eq : ∀ k : Fin 16, amp7_0Expr 2 10 k = amp7_02_10 k := by decide +kernel +noncomputable def amp7_02_11 : Fin 16 → CBox := ![⟨⟨158564781952032721773117713826,158564781952032721806970837079⟩,⟨46159155906393935302301540336,46159155906393935334599430998⟩⟩,⟨⟨157503842124524323557146304821,157503842124524323590689816059⟩,⟨45760171030284367809978281988,45760171030284367841978600040⟩⟩,⟨⟨156417456880820380747486445327,156417456880820380780705873259⟩,⟨45356086383305933399825525747,45356086383305933431522039813⟩⟩,⟨⟨155295220902751397219721126770,155295220902751397252628792329⟩,⟨44943915494514986781565228474,44943915494514986812957837528⟩⟩,⟨⟨154148049085717860443244131153,154148049085717860475819223256⟩,⟨44526852079409283534253100264,44526852079409283565333892624⟩⟩,⟨⟨152964958712577414088487381505,152964958712577414120729669760⟩,⟨44101750984386232776464236194,44101750984386232807229467692⟩⟩,⟨⟨151757489022035977722839753373,151757489022035977754737239029⟩,⟨43671970677691365814928858811,43671970677691365845373259657⟩⟩,⟨⟨150514056069908882474476027704,150514056069908882506070035057⟩,⟨43234201408092009692462661910,43234201408092009722594492433⟩⟩,⟨⟨149246848334498120593795593070,149246848334498120625038506876⟩,⟨42791972490819973010941501434,42791972490819973040745410871⟩⟩,⟨⟨147943654780489111199311649957,147943654780489111230201454621⟩,⟨42341803111482098548839924321,42341803111482098578311700519⟩⟩,⟨⟨146617340103658147439127244803,146617340103658147469670474560⟩,⟨41887400105921523667371898522,41887400105921523696511815901⟩⟩,⟨⟨145255038053090601710011146919,145255038053090601740188159328⟩,⟨41425104520495853959322134951,41425104520495853988121017655⟩⟩,⟨⟨143870318841389437341778846703,143870318841389437371591212777⟩,⟨40958808029042512631698399511,40958808029042512660155259457⟩⟩,⟨⟨142449630359472922540583854075,142449630359472922570024946944⟩,⟨40484665783057927833764414593,40484665783057927861873789732⟩⟩,⟨⟨141007280233851200628725749589,141007280233851200657786584470⟩,⟨40006762329618491215648704931,40006762329618491243406685988⟩⟩,⟨⟨139528997039495214053392745301,139528997039495214082062558957⟩,⟨39521058410672900183822914900,39521058410672900211222942909⟩⟩] +lemma amp7_02_11_eq : ∀ k : Fin 16, amp7_0Expr 2 11 k = amp7_02_11 k := by decide +kernel +noncomputable def amp7_02_12 : Fin 16 → CBox := ![⟨⟨138029860630930874523653831621,138029860630930874552102423207⟩,⟨39031840285267595699399572333,39031840285267595726488485644⟩⟩,⟨⟨136494843650292427697908813205,136494843650292427725983195648⟩,⟨38534864919928205252323157075,38534864919928205279054067860⟩⟩,⟨⟨134939836281768314822254134727,134939836281768314849950299101⟩,⟨38034630027220819773471299509,38034630027220819799841948203⟩⟩,⟨⟨133349015058935788750662891874,133349015058935788777978165795⟩,⟨37526678474083808457525831444,37526678474083808483531980690⟩⟩,⟨⟨131739122316590668349460586868,131739122316590668376391304680⟩,⟨37015730186699826371789288817,37015730186699826397428941989⟩⟩,⟨⟨130093494278495420584315949373,130093494278495420610861877796⟩,⟨36497102524891684975829288552,36497102524891685001098872531⟩⟩,⟨⟨128429771475729696776986235361,128429771475729696803135150217⟩,⟨35975749542556442067707493663,35975749542556442092602705373⟩⟩,⟨⟨126730401047899643109062724635,126730401047899643134833257692⟩,⟨35446750454746823092255067452,35446750454746823116777668158⟩⟩,⟨⟨125013972587361220878435425322,125013972587361220903801133968⟩,⟨34915306670497901736809396074,34915306670497901760951292017⟩⟩,⟨⟨123261990156431958051441311980,123261990156431958076403495750⟩,⟨34376245219222168500614438283,34376245219222168524372504403⟩⟩,⟨⟨121494048796207287551103348641,121494048796207287575655792279⟩,⟨33835029594240970932908828187,33835029594240970956280727482⟩⟩,⟨⟨119690649514110670815060634235,119690649514110670839197564740⟩,⟨33286218989979701989026455112,33286218989979702012007150563⟩⟩,⟨⟨117872455546187641911888294748,117872455546187641935599108149⟩,⟨32735555438969895130269860062,32735555438969895152855982331⟩⟩,⟨⟨116018897969540139998675165177,116018897969540140022061658718⟩,⟨32177312797974465584533659363,32177312797974465606749983448⟩⟩,⟨⟨114151778320816046729308502701,114151778320816046752270209120⟩,⟨31617530087522920287908429665,31617530087522920309726740148⟩⟩,⟨⟨112249382877082224384184209240,112249382877082224406718166735⟩,⟨31050176176771643895784832553,31050176176771643917200883889⟩⟩] +lemma amp7_02_12_eq : ∀ k : Fin 16, amp7_0Expr 2 12 k = amp7_02_12 k := by decide +kernel +noncomputable def amp7_02_13 : Fin 16 → CBox := ![⟨⟨110334730146035769495799525732,110334730146035769517906837072⟩,⟨30481607839807493064427439079,30481607839807493085441419885⟩⟩,⟨⟨108384877415336089049692599413,108384877415336089071381673728⟩,⟨29905466805669651531927516312,29905466805669651552538261105⟩⟩,⟨⟨106424148861217577719240708415,106424148861217577740490115701⟩,⟨29328451076056413101431540486,29328451076056413121633123874⟩⟩,⟨⟨104428277658881762040787410840,104428277658881762061600095304⟩,⟨28743850152150938247627748695,28743850152150938267417538669⟩⟩,⟨⟨102422994165264323102592561462,102422994165264323122958454515⟩,⟨28158729924703042325163456028,28158729924703042344538871679⟩⟩,⟨⟨100382599404958987105999067705,100382599404958987125981835611⟩,⟨27565999112946202604523200723,27565999112946202623498229114⟩⟩,⟨⟨98334344446273312139267886512,98334344446273312158808679529⟩,⟨26973121935898930146625855953,26973121935898930165184641294⟩⟩,⟨⟨96250974756097388110901172340,96250974756097388129994697222⟩,⟨26372593652664972590859215831,26372593652664972608996814014⟩⟩,⟨⟨94161393405149062941187777251,94161393405149062959835464754⟩,⟨25772311762061903842855890065,25772311762061903860573239469⟩⟩,⟨⟨92036648458498225984390305058,92036648458498226002594412484⟩,⟨25164320438465933965524918112,25164320438465933982819060760⟩⟩,⟨⟨89907446486169819663604005967,89907446486169819681357915012⟩,⟨24556990847390166230950172058,24556990847390166247819988877⟩⟩,⟨⟨87742973993891190978097984845,87742973993891190995440704205⟩,⟨23941872468533711118695015392,23941872468533711135147572169⟩⟩,⟨⟨85575917131172237532073792543,85575917131172237548954259802⟩,⟨23327857129110666843126646906,23327857129110666859148926873⟩⟩,⟨⟨83373409419160655605942177808,83373409419160655622360844321⟩,⟨22705948691063811670253823894,22705948691063811685842283490⟩⟩,⟨⟨81170322879360580554789017409,81170322879360580570750155500⟩,⟨22085614754517298584839212534,22085614754517298599996126204⟩⟩,⟨⟨78931512942433685616273345642,78931512942433685631766494075⟩,⟨21457253608814522139270748162,21457253608814522153989557922⟩⟩] +lemma amp7_02_13_eq : ∀ k : Fin 16, amp7_0Expr 2 13 k = amp7_02_13 k := by decide +kernel +noncomputable def amp7_02_14 : Fin 16 → CBox := ![⟨⟨76694281342839049166908070108,76694281342839049181968831614⟩,⟨20830973819883225865263826147,20830973819883225879555588408⟩⟩,⟨⟨74420938215138110697910941218,74420938215138110712503717981⟩,⟨20196496861686558355969898711,20196496861686558369821089953⟩⟩,⟨⟨72151506100671429546325424054,72151506100671429560456561427⟩,⟨19564650140601382622402702056,19564650140601382635816639167⟩⟩,⟨⟨69845429304284926481551592403,69845429304284926495203949926⟩,⟨18924392775571865297646977752,18924392775571865310615092466⟩⟩,⟨⟨67545802574934915989309371570,67545802574934916002517918476⟩,⟨18287365067314172787363500664,18287365067314172799897163196⟩⟩,⟨⟨65208815283367778812707967247,65208815283367778825441591571⟩,⟨17641659858656647867449194224,17641659858656647879535885322⟩⟩,⟨⟨62881063987061241529932053486,62881063987061241542212183625⟩,⟨16999845372000998795092550805,16999845372000998806740242757⟩⟩,⟨⟨60515004335227173211756783130,60515004335227173223556556124⟩,⟨16349020214172862651878075634,16349020214172862663075264883⟩⟩,⟨⟨58161267553712704365559270347,58161267553712704376884357244⟩,⟨15702823244206600950797869728,15702823244206600961548641627⟩⟩,⟨⟨55767977179120681703667570351,55767977179120681714526376555⟩,⟨15047198816744978615965604485,15047198816744978626267738853⟩⟩,⟨⟨53390471192600893126104754274,53390471192600893136483789182⟩,⟨14397036467266120784330435989,14397036467266120794183202209⟩⟩,⟨⟨50971779482293182780109931230,50971779482293182790017203576⟩,⟨13736922558656003719816825682,13736922558656003729217657831⟩⟩,⟨⟨48572811220923146005999015608,48572811220923146015439064103⟩,⟨13083228901153424387910140537,13083228901153424396863640536⟩⟩,⟨⟨46130512617983276430054306263,46130512617983276439005974269⟩,⟨12418918892310122223763638821,12418918892310122232259021966⟩⟩,⟨⟨43712501956394826156262409403,43712501956394826164741992228⟩,⟨11762151512974700325676357968,11762151512974700333721902162⟩⟩,⟨⟨41248321512376485936024774336,41248321512376485944023343638⟩,⟨11093913729100181435692014225,11093913729100181443279819943⟩⟩] +lemma amp7_02_14_eq : ∀ k : Fin 16, amp7_0Expr 2 14 k = amp7_02_14 k := by decide +kernel +noncomputable def amp7_02_15 : Fin 16 → CBox := ![⟨⟨38813839045860125570981214578,38813839045860125578502682780⟩,⟨10434564441209975376330441820,10434564441209975383466114720⟩⟩,⟨⟨36329376948289464006699460512,36329376948289464013733993657⟩,⟨9762627886445305982199421642,9762627886445305988874235633⟩⟩,⟨⟨33881210455995821809487496898,33881210455995821816041833238⟩,⟨9101241144963221448161918199,9101241144963221454383008221⟩⟩,⟨⟨31377846384643951768833819581,31377846384643951774903376314⟩,⟨8425770488118191517391078961,8425770488118191523150408994⟩⟩,⟨⟨28919124383827172167938058500,28919124383827172173529917119⟩,⟨7762977115742381374712541366,7762977115742381380018371700⟩⟩,⟨⟨26397838543475809177203770959,26397838543475809182305362561⟩,⟨7084025363010623345056433056,7084025363010623349897539351⟩⟩,⟨⟨23932278392163434053131261744,23932278392163434057752006029⟩,⟨6420609661129616075278932160,6420609661129616079665568590⟩⟩,⟨⟨21393280349394913652857386324,21393280349394913656988254277⟩,⟨5738019342107921946889103116,5738019342107921950809518407⟩⟩,⟨⟨18925743387549605251557766004,18925743387549605255209541400⟩,⟨5075068482803261909655656715,5075068482803261913122471143⟩⟩,⟨⟨16367588945757346132749695973,16367588945757346135906041046⟩,⟨4388235667739314315714646209,4388235667739314318711814450⟩⟩,⟨⟨13905533889722180872525298863,13905533889722180875204346417⟩,⟨3727529779818209543549418119,3727529779818209546094676767⟩⟩,⟨⟨11322562292305581119669433402,11322562292305581121849248214⟩,⟨3034718041105273058937122647,3034718041105273061008894528⟩⟩,⟨⟨8880904787393590073084331478,8880904787393590074791327763⟩,⟨2380032976657235970124897733,2380032976657235971749002515⟩⟩,⟨⟨6252984665123409521211165118,6252984665123409522411359543⟩,⟨1675626498907090463144882681,1675626498907090464287860206⟩⟩,⟨⟨3879054158516811427010884405,3879054158516811427750075940⟩,⟨1039421657016002769333775510,1039421657016002770041355198⟩⟩,⟨⟨1102081344137210721061001850,1102081344137210721267822061⟩,⟨295302823520684556409663744,295302823520684556609834147⟩⟩] +lemma amp7_02_15_eq : ∀ k : Fin 16, amp7_0Expr 2 15 k = amp7_02_15 k := by decide +kernel +noncomputable def amp7_02 : Fin 16 → Fin 16 → CBox := ![amp7_02_0,amp7_02_1,amp7_02_2,amp7_02_3,amp7_02_4,amp7_02_5,amp7_02_6,amp7_02_7,amp7_02_8,amp7_02_9,amp7_02_10,amp7_02_11,amp7_02_12,amp7_02_13,amp7_02_14,amp7_02_15] +lemma amp7_02_eq (i k : Fin 16) : amp7_0Expr 2 i k = amp7_02 i k := by + fin_cases i + · exact amp7_02_0_eq k + · exact amp7_02_1_eq k + · exact amp7_02_2_eq k + · exact amp7_02_3_eq k + · exact amp7_02_4_eq k + · exact amp7_02_5_eq k + · exact amp7_02_6_eq k + · exact amp7_02_7_eq k + · exact amp7_02_8_eq k + · exact amp7_02_9_eq k + · exact amp7_02_10_eq k + · exact amp7_02_11_eq k + · exact amp7_02_12_eq k + · exact amp7_02_13_eq k + · exact amp7_02_14_eq k + · exact amp7_02_15_eq k +noncomputable def amp7_03_0 : Fin 16 → CBox := ![⟨⟨403394260725353423614639549,403394260725353423815008765⟩,⟨108090183758420923956948487,108090183758420924159041336⟩⟩,⟨⟨1419974652654540929182316308,1419974652654540929891683364⟩,⟨380513289296283114140024604,380513289296283114852453291⟩⟩,⟨⟨2289388364142189097015391531,2289388364142189098162048201⟩,⟨613584070936187278637341198,613584070936187279786643374⟩⟩,⟨⟨3252410339548292944784399508,3252410339548292946413867332⟩,⟨871882434754030703838248285,871882434754030705470867141⟩⟩,⟨⟨4148083309939375000262532403,4148083309939375002341312299⟩,⟨1112322191666185084680099418,1112322191666185086762034229⟩⟩,⟨⟨5096636149994630610252775602,5096636149994630612806578632⟩,⟨1367192744249870315983585073,1367192744249870318540833573⟩⟩,⟨⟨6002226898218423192283693105,6002226898218423195290843027⟩,⟨1610845277845051385694098699,1610845277845051388704659782⟩⟩,⟨⟨6944657711565424332320312620,6944657711565424335798391450⟩,⟨1864746251475208744374118315,1864746251475208747855758157⟩⟩,⟨⟨7855681503608225967213358992,7855681503608225971146156990⟩,⟨2110630663922880123538765489,2110630663922880127475059805⟩⟩,⟨⟨8795031962169919531952547701,8795031962169919536352208302⟩,⟨2364596704581958644547242887,2364596704581958648951216693⟩⟩,⟨⟨9709723092805367877257164762,9709723092805367882112135031⟩,⟨2612458304806137241322072555,2612458304806137246180895699⟩⟩,⟨⟨10647479694509940861947678583,10647479694509940867267829514⟩,⟨2867104676851417304311167690,2867104676851417309635172190⟩⟩,⟨⟨11565009882953583359385070498,11565009882953583365158761748⟩,⟨3116936947720386972259459421,3116936947720386978037285037⟩⟩,⟨⟨12502039082867935524789131425,12502039082867935531024164815⟩,⟨3372709440687027580845387686,3372709440687027587085352343⟩⟩,⟨⟨13421982622969881115479093223,13421982622969881122167636893⟩,⟨3624610076274640764804448447,3624610076274640771497239123⟩⟩,⟨⟨14358851210238936551295374945,14358851210238936558444168295⟩,⟨3881870199742348417820961660,3881870199742348424973522116⟩⟩] +lemma amp7_03_0_eq : ∀ k : Fin 16, amp7_0Expr 3 0 k = amp7_03_0 k := by decide +kernel +noncomputable def amp7_03_1 : Fin 16 → CBox := ![⟨⟨15280978938582177754126890989,15280978938582177761726720964⟩,⟨4135985256869685173671316978,4135985256869685181274692404⟩⟩,⟨⟨16218087070801141847662231828,16218087070801141855718107773⟩,⟨4395045248013633616350532599,4395045248013633624410344876⟩⟩,⟨⟨17142272764302401755898570406,17142272764302401764402087892⟩,⟨4651543433516645207190441397,4651543433516645215698493710⟩⟩,⟨⟨18079916706527992040826173139,18079916706527992049786321354⟩,⟨4912682441133831302804462832,4912682441133831311766763576⟩⟩,⟨⟨19006089122030763512367932293,19006089122030763521772049111⟩,⟨5171741641120364626478201524,5171741641120364635885806210⟩⟩,⟨⟨19944493546663045309483212998,19944493546663045319335451584⟩,⟨5435213766967691976100598114,5435213766967691985957619161⟩⟩,⟨⟨20872609418910767651845256089,20872609418910767662144115025⟩,⟨5697013205809697003036166409,5697013205809697013337011135⟩⟩,⟨⟨21811945067782605223491816379,21811945067782605234234256353⟩,⟨5963051638683181228398415751,5963051638683181239144737861⟩⟩,⟨⟨22741972676218565864858541868,22741972676218565876043364367⟩,⟨6227766885466275151494460554,6227766885466275162680998458⟩⟩,⟨⟨23682366399471076993447855648,23682366399471077005078894011⟩,⟨6496586009054416385995073066,6496586009054416397624925214⟩⟩,⟨⟨24614274877111577266419113531,24614274877111577278482107651⟩,⟨6764385539687718789932545183,6764385539687718801997063134⟩⟩,⟨⟨25555815448674723247313042613,25555815448674723259817386855⟩,⟨7036181926639515265509475886,7036181926639515278012898944⟩⟩,⟨⟨26489567409650793046499359351,26489567409650793059429207368⟩,⟨7307224593749363586383067782,7307224593749363599316451210⟩⟩,⟨⟨27432308887547472380398509609,27432308887547472393768179794⟩,⟨7582177361176705169886157449,7582177361176705183254760944⟩⟩,⟨⟨28367855077946113554644096505,28367855077946113568443165177⟩,⟨7856610426112607728786589002,7856610426112607742583080085⟩⟩,⟨⟨29311818684101812767449749696,29311818684101812781681394518⟩,⟨8134881215076756090674901682,8134881215076756104901157991⟩⟩] +lemma amp7_03_1_eq : ∀ k : Fin 16, amp7_0Expr 3 1 k = amp7_03_1 k := by decide +kernel +noncomputable def amp7_03_2 : Fin 16 → CBox := ![⟨⟨30249093927131206283703106510,30249093927131206298349787699⟩,⟨8412838748070690922727909353,8412838748070690937374703354⟩⟩,⟨⟨31194269010939947158349392475,31194269010939947173425315930⟩,⟨8694571479579703947283640283,8694571479579703962355627242⟩⟩,⟨⟨32133189018217929508818243461,32133189018217929524315617978⟩,⟨8976173014638469674464380534,8976173014638469689955115131⟩⟩,⟨⟨33079533444566654658111795591,33079533444566654674032567851⟩,⟨9261493514730336674082199662,9261493514730336689992670572⟩⟩,⟨⟨34019992232784025384926236100,34019992232784025401266810117⟩,⟨9546842890653111775681333567,9546842890653111792006323744⟩⟩,⟨⟨34967432407976695481487688831,34967432407976695498228370405⟩,⟨9835858442983806223074405913,9835858442983806239808577987⟩⟩,⟨⟨35909300157252905002971004932,35909300157252905020123220488⟩,⟨10125042787846903307719361369,10125042787846903324861753648⟩⟩,⟨⟨36857730830997997128005012973,36857730830997997145566075264⟩,⟨10417841651972575572222311164,10417841651972575589772133084⟩⟩,⟨⟨37800852079502245500303067386,37800852079502245518270111260⟩,⟨10710930483971251734942781532,10710930483971251752895093724⟩⟩,⟨⟨38750136015071337263245315207,38750136015071337281618706740⟩,⟨11007581405110668187610817983,11007581405110668205965479384⟩⟩,⟨⟨39694328120512582393459137285,39694328120512582412233151484⟩,⟨11304625832237894526906033412,11304625832237894545657319203⟩⟩,⟨⟨40644295696138330559087701903,40644295696138330578238553229⟩,⟨11605177560454895990276279372,11605177560454896009416952242⟩⟩,⟨⟨41589347517600470507498712468,41589347517600470527047910828⟩,⟨11906209567558880701922898719,11906209567558880721455007388⟩⟩,⟨⟨42539796303365310120201315626,42539796303365310140144339579⟩,⟨12210690399194769766619614537,12210690399194769786541231839⟩⟩,⟨⟨43485467071813731805445329959,43485467071813731825779756864⟩,⟨12515722214866784038332236572,12515722214866784058638605829⟩⟩,⟨⟨44436161413776485890057987831,44436161413776485910774483807⟩,⟨12824139565631784382961519455,12824139565631784403649137793⟩⟩] +lemma amp7_03_2_eq : ∀ k : Fin 16, amp7_0Expr 3 2 k = amp7_03_2 k := by decide +kernel +noncomputable def amp7_03_3 : Fin 16 → CBox := ![⟨⟨45382179769389562545318390089,45382179769389562566416632148⟩,⟨13133163103937536593406405406,13133163103937536614471120785⟩⟩,⟨⟨46332850404188922671606161584,46332850404188922693085826123⟩,⟨13445503120718159277596565787,13445503120718159299037301934⟩⟩,⟨⟨47278913585275721611166877251,47278913585275721633023178992⟩,⟨13758489494482829052345985513,13758489494482829074157307335⟩⟩,⟨⟨48229257302527385651700114074,48229257302527385673890976750⟩,⟨14074716711260546228352573231,14074716711260546250521061449⟩⟩,⟨⟨49175030475291752884173501142,49175030475291752906736780815⟩,⟨14391615814747471766256955854,14391615814747471788789582499⟩⟩,⟨⟨50124709840881349736811824740,50124709840881349759742152499⟩,⟨14711672856818319229084369047,14711672856818319251978271607⟩⟩,⟨⟨51069825562383068482240562794,51069825562383068505531979495⟩,⟨15032413016392079145891516489,15032413016392079169140900437⟩⟩,⟨⟨52018468712690499284558496970,52018468712690499308207214642⟩,⟨15356220356176993428643580522,15356220356176993452245889515⟩⟩,⟨⟨52962526521487244840832190453,52962526521487244864835080306⟩,⟨15680708048034232600698785590,15680708048034232624649045912⟩⟩,⟨⟨53909727036296561164861311136,53909727036296561189206067936⟩,⟨16008163815078957196988975948,16008163815078957221281960991⟩⟩,⟨⟨54852293166721735040240590678,54852293166721735064931425914⟩,⟨16336283449444233985646498391,16336283449444234010279399252⟩⟩,⟨⟨55797610026834146095717624359,55797610026834146120747969166⟩,⟨16667263296661386044966410256,16667263296661386069935560505⟩⟩,⟨⟨56738217243872941571630440970,56738217243872941596996534319⟩,⟨16998877068033698627417896495,16998877068033698652718110306⟩⟩,⟨⟨57681174878087788283621184856,57681174878087788309320033763⟩,⟨17333234095795073658302695400,17333234095795073683931242733⟩⟩,⟨⟨58619322430491147770778577164,58619322430491147796805464794⟩,⟨17668181898929692418845015858,17668181898929692444796414817⟩⟩,⟨⟨59559410855540819438185673932,59559410855540819464537297473⟩,⟨18005746638244856268942117028,18005746638244856295213420898⟩⟩] +lemma amp7_03_3_eq : ∀ k : Fin 16, amp7_0Expr 3 3 k = amp7_03_3 k := by decide +kernel +noncomputable def amp7_03_4 : Fin 16 → CBox := ![⟨⟨60494564545256760177380228498,60494564545256760203986598002⟩,⟨18343846049589623370802342595,18343846049589623397368261580⟩⟩,⟨⟨61431239601400652647491179025,61431239601400652674424098539⟩,⟨18684426505287159896123606285,18684426505287159923003802617⟩⟩,⟨⟨62362831967669440840341286213,62362831967669440867592595870⟩,⟨19025472829580048213849185380,19025472829580048241037118839⟩⟩,⟨⟨63295515651916090289356378614,63295515651916090316920485772⟩,⟨19368854584126479158786984703,19368854584126479186278792127⟩⟩,⟨⟨64222946268515805461963839163,64222946268515805489834253426⟩,⟨19712620965814424519667506125,19712620965814424547457128844⟩⟩,⟨⟨65151027166813766564248271671,65151027166813766592424037408⟩,⟨20058567344152947462421227627,20058567344152947490506115400⟩⟩,⟨⟨66073663050988885123031097933,66073663050988885151499989677⟩,⟨20404804943219817994474932147,20404804943219818022847243821⟩⟩,⟨⟨66996496870178988084674214127,66996496870178988113437339095⟩,⟨20753057238779650493279082763,20753057238779650521936800583⟩⟩,⟨⟨67913673001760729545277056165,67913673001760729574329947569⟩,⟨21101495470480330474709862074,21101495470480330503647522548⟩⟩,⟨⟨68830583201595786796623719039,68830583201595786825943069049⟩,⟨21451773232292647495164162494,21451773232292647524372064835⟩⟩,⟨⟨69741603150746806408292232275,69741603150746806437893251972⟩,⟨21802120070185537116101814432,21802120070185537145580603669⟩⟩,⟨⟨70651881675845692677217995961,70651881675845692707093345617⟩,⟨22154121450840209684203422946,22154121450840209713948275440⟩⟩,⟨⟨71556018337746486451311962860,71556018337746486481458028526⟩,⟨22506063792395721817451028240,22506063792395721847456726019⟩⟩,⟨⟨72458926448947621134966386398,72458926448947621165371718422⟩,⟨22859465956381787543601729396,22859465956381787573862058133⟩⟩,⟨⟨73355422883597728988591257961,73355422883597729019258133675⟩,⟨23212670050322539215512794179,23212670050322539246024385721⟩⟩,⟨⟨74250192087804915743442537377,74250192087804915774362266663⟩,⟨23567129642112770795371777555,23567129642112770826129193932⟩⟩] +lemma amp7_03_4_eq : ∀ k : Fin 16, amp7_0Expr 3 4 k = amp7_03_4 k := by decide +kernel +noncomputable def amp7_03_5 : Fin 16 → CBox := ![⟨⟨75138262462946322633652620048,75138262462946322664821624265⟩,⟨23921241576514373782918046645,23921241576514373813916063112⟩⟩,⟨⟨76024095540212204924857062287,76024095540212204956271121779⟩,⟨24276395247579201785233028217,24276395247579201816467546184⟩⟩,⟨⟨76902926175201191254970309563,76902926175201191286625712063⟩,⟨24631041497630645594337156150,24631041497630645625802912524⟩⟩,⟨⟨77778998301466279959028276991,77778998301466279990920200704⟩,⟨24986506491398167402318593480,24986506491398167434011220808⟩⟩,⟨⟨78647748809728035166847145729,78647748809728035198970530615⟩,⟨25341294525589208361434382420,25341294525589208393348179321⟩⟩,⟨⟨79513208773323448892447899611,79513208773323448924659927175⟩,⟨25696669319205492783007266337,25696669319205492815093200968⟩⟩,⟨⟨80371013300824761995982633753,80371013300824762028423275605⟩,⟨26051188262576407764906335455,26051188262576407797205452023⟩⟩,⟨⟨81224984810552388044198808552,81224984810552388076860142263⟩,⟨26406053264163412961837765591,26406053264163412994344563709⟩⟩,⟨⟨82070953367524677080654855718,82070953367524677113528602987⟩,⟨26759874617120943036909107928,26759874617120943069616838249⟩⟩,⟨⟨82912536449847906007933040603,82912536449847906041014391295⟩,⟨27113792917077889459653240490,27113792917077889492557345439⟩⟩,⟨⟨83745756332788211396448678659,83745756332788211429728254121⟩,⟨27466471328151035596399195044,27466471328151035629492558804⟩⟩,⟨⟨84574028815398666446001918564,84574028815398666479474488240⟩,⟨27818989502898917537039802528,27818989502898917570317656352⟩⟩,⟨⟨85393566116172059291526377990,85393566116172059325190802999⟩,⟨28170063593680188851928549695,28170063593680188885386475791⟩⟩,⟨⟨86207585194942118279393239149,86207585194942118313237717754⟩,⟨28520712560108256385342880518,28520712560108256418973893001⟩⟩,⟨⟨87012486393606986108267418900,87012486393606986142290436958⟩,⟨28869705800500651065562677234,28869705800500651099362245916⟩⟩,⟨⟨87811290279693918303760939891,87811290279693918337959183477⟩,⟨29218001719238200444519188422,29218001719238200478483075447⟩⟩] +lemma amp7_03_5_eq : ∀ k : Fin 16, amp7_0Expr 3 5 k = amp7_03_5 k := by decide +kernel +noncomputable def amp7_03_6 : Fin 16 → CBox := ![⟨⟨88600583917473254610141299938,88600583917473254644493417412⟩,⟨29564423351006186343588135414,29564423351006186377705206019⟩⟩,⟨⟨89383193561108202146713222929,89383193561108202181232947213⟩,⟨29909868576512959492592735008,29909868576512959526864391927⟩⟩,⟨⟨90155891989736606045640296270,90155891989736606080312071047⟩,⟨30253214583017521524258705293,30253214583017521558675749391⟩⟩,⟨⟨90921312877010306511653745802,90921312877010306546482163505⟩,⟨30595298658361565212286027653,30595298658361565246846784354⟩⟩,⟨⟨91676414080498994563429212363,91676414080498994598402963036⟩,⟨30935052778245456204448489808,30935052778245456239145174813⟩⟩,⟨⟨92423638099246054438349947836,92423638099246054473467034642⟩,⟨31273253472318582465246251764,31273253472318582500074952014⟩⟩,⟨⟨93160127583927764352242066611,93160127583927764387446030560⟩,⟨31608888254798667064683465189,31608888254798667099621079950⟩⟩,⟨⟨93888134954612516741999007590,93888134954612516777339786331⟩,⟨31942672639606856737749819475,31942672639606856772809976702⟩⟩,⟨⟨94604987703155597254751255939,94604987703155597290217862404⟩,⟨32273650538926251836880245235,32273650538926251872055272912⟩⟩,⟨⟨95312748970475233563823349158,95312748970475233599408051166⟩,⟨32602476104485629194096704718,32602476104485629229380672809⟩⟩,⟨⟨96008931455392227913983704647,96008931455392227949683606932⟩,⟨32928250610979564652651828606,32928250610979564688039840920⟩⟩,⟨⟨96695409536137142490323709314,96695409536137142526127908929⟩,⟨33251566415248122572976259711,33251566415248122608461249187⟩⟩,⟨⟨97369881788158466107348095379,97369881788158466143253602174⟩,⟨33571583220384389376011779543,33571583220384389411588824189⟩⟩,⟨⟨98034034070705781616378827685,98034034070705781652384167897⟩,⟨33888831071565640129601645608,33888831071565640165266902458⟩⟩,⟨⟨98685751797244279732894621635,98685751797244279768968673081⟩,⟨34202529264233449842325085260,34202529264233449878063926603⟩⟩,⟨⟨99326532287908529348043901859,99326532287908529384204118570⟩,⟨34513144932700790718884838633,34513144932700790754699931110⟩⟩] +lemma amp7_03_6_eq : ∀ k : Fin 16, amp7_0Expr 3 6 k = amp7_03_6 k := by decide +kernel +noncomputable def amp7_03_7 : Fin 16 → CBox := ![⟨⟨99954449036706327309743034885,99954449036706327345980585506⟩,⟨34819958223941105938020209450,34819958223941105973904647488⟩⟩,⟨⟨100570810548031463290821425575,100570810548031463327134366462⟩,⟨35123372680951089250568295627,35123372680951089286518036950⟩⟩,⟨⟨101173879910957085948093570514,101173879910957085984462117011⟩,⟨35422730654247242365724819743,35422730654247242401729154666⟩⟩,⟨⟨101764776286906566365730494139,101764776286906566402160667146⟩,⟨35718371334536284172474846498,35718371334536284208532481479⟩⟩,⟨⟨102341954138758246961893776170,102341954138758246998371104778⟩,⟨36009700718716201726453179227,36009700718716201762555257976⟩⟩,⟨⟨102906342511645118858398604890,102906342511645118894927400911⟩,⟨36296992804008700316585438122,36296992804008700352730082351⟩⟩,⟨⟨103456589278715939275427659761,103456589278715939311995256905⟩,⟨36579718765749491910355537395,36579718765749491946534553271⟩⟩,⟨⟨103993432352612770289717159511,103993432352612770326318496311⟩,⟨36858086486145990492821640484,36858086486145990529029822300⟩⟩,⟨⟨104515715305685126487466700687,104515715305685126524096345421⟩,⟨37131633939018223179582979006,37131633939018223215814692624⟩⟩,⟨⟨105023983660964503941337438296,105023983660964503977991616650⟩,⟨37400501889180262194432191861,37400501889180262230682694796⟩⟩,⟨⟨105517279227325684585491732096,105517279227325684622161179731⟩,⟨37664296816123082129483755654,37664296816123082165746095605⟩⟩,⟨⟨105995953640905947031986309122,105995953640905947068666713672⟩,⟨37923091283126851032305585660,37923091283126851068574801225⟩⟩,⟨⟨106459249729913621817241438916,106459249729913621853923738419⟩,⟨38176562069206372481171478108,38176562069206372517440698136⟩⟩,⟨⟨106907323505721635790528912105,106907323505721635827206916240⟩,⟨38424712368900278588401000278,38424712368900278624664592570⟩⟩,⟨⟨107339621842398007171684930297,107339621842398007208350110632⟩,⟨38667291141172455476460871142,38667291141172455512712192583⟩⟩,⟨⟨107756103146511248494438600993,107756103146511248531081913401⟩,⟨38904230959844351500974125910,38904230959844351537206487811⟩⟩] +lemma amp7_03_7_eq : ∀ k : Fin 16, amp7_0Expr 3 7 k = amp7_03_7 k := by decide +kernel +noncomputable def amp7_03_8 : Fin 16 → CBox := ![⟨⟨108156421607607724397536764228,108156421607607724434164092461⟩,⟨39135354931119978592819897338,39135354931119978629031873059⟩⟩,⟨⟨108540335802501738344344993432,108540335802501738380963005070⟩,⟨39360523669258086239563768439,39360523669258086275754390613⟩⟩,⟨⟨108907710749452396823693729676,108907710749452396860293056015⟩,⟨39579636482551726994917616463,39579636482551727031080029135⟩⟩,⟨⟨109258102721756934579816602057,109258102721756934616389271137⟩,⟨39792480597469298548874711519,39792480597469298585002626511⟩⟩,⟨⟨109591591324928903358943852130,109591591324928903395483189668⟩,⟨39999033667905867414647752129,39999033667905867450735304681⟩⟩,⟨⟨109907527801086672152776338477,109907527801086672189273901313⟩,⟨40199008011993358885427879803,40199008011993358921468616616⟩⟩,⟨⟨110206210349738932983420381783,110206210349738933019871567076⟩,⟨40392461862945841780015636735,40392461862945841816004502084⟩⟩,⟨⟨110486782193964929775008873982,110486782193964929811404839886⟩,⟨40579031014315828678649485292,40579031014315828714579858260⟩⟩,⟨⟨110749764386344044703678034192,110749764386344044740014583266⟩,⟨40758856604555233476735020329,40758856604555233512602013787⟩⟩,⟨⟨110994088875300809821962361739,110994088875300809858234900657⟩,⟨40931496186854462525358241369,40931496186854462561156819432⟩⟩,⟨⟨111220504083332688990593372028,111220504083332689026796580913⟩,⟨41097176225508560960803723489,41097176225508560996528656840⟩⟩,⟨⟨111427727151967422284786883883,111427727151967422320908170510⟩,⟨41255374213688356306349913484,41255374213688356341993191818⟩⟩,⟨⟨111616738655048517678253426413,111616738655048517714297536903⟩,⟨41406404459829102689103323934,41406404459829102724663470836⟩⟩,⟨⟨111786037108081713951259478119,111786037108081713987211947448⟩,⟨41549662468689770791672001950,41549662468689770827140331609⟩⟩,⟨⟨111936840290530910830696010220,111936840290530910866563832969⟩,⟨41685553012400438099633939316,41685553012400438135009896558⟩⟩,⟨⟨112067423974142823041087011762,112067423974142823076849565282⟩,⟨41813387564757257052147006984,41813387564757257087419591392⟩⟩] +lemma amp7_03_8_eq : ∀ k : Fin 16, amp7_0Expr 3 8 k = amp7_03_8 k := by decide +kernel +noncomputable def amp7_03_9 : Fin 16 → CBox := ![⟨⟨112179248480946766447087957975,112179248480946766482743216381⟩,⟨41933664086569278969667971803,41933664086569279004833294406⟩⟩,⟨⟨112270362409277383243211744235,112270362409277383278751377990⟩,⟨42045607857927008964031351241,42045607857927008999083014898⟩⟩,⟨⟨112342474254846954608585964187,112342474254846954644030456520⟩,⟨42149812863563204799746656122,42149812863563204834689301168⟩⟩,⟨⟨112393400686007029382486193044,112393400686007029417801608173⟩,⟨42245415900232687161079317279,42245415900232687195896935473⟩⟩,⟨⟨112425104310761092441223250157,112425104310761092476408273800⟩,⟨42333109927647909848398335228,42333109927647909883087423823⟩⟩,⟨⟨112435164767145785434099185073,112435164767145785469152232290⟩,⟨42411940835292078998651470385,42411940835292079033208187300⟩⟩,⟨⟨112425805036850049955709574320,112425805036850049990618552651⟩,⟨42482703631064287632771998033,42482703631064287667188860239⟩⟩,⟨⟨112394362264652596335507789746,112394362264652596370271114807⟩,⟨42544350730721625050543818924,42544350730721625084816979847⟩⟩,⟨⟨112343326407566389813245408194,112343326407566389847854461371⟩,⟨42597782392915855988799883012,42597782392915856022923193532⟩⟩,⟨⟨112269786270506487094787415141,112269786270506487129231146528⟩,⟨42641854841616762968077072663,42641854841616763002043140826⟩⟩,⟨⟨112176505747528258780423908095,112176505747528258814763723997⟩,⟨42677576926321363159478436495,42677576926321363193307825476⟩⟩,⟨⟨112060319049938122898727775925,112060319049938122932897658111⟩,⟨42703705799486887291851437351,42703705799486887325515866637⟩⟩,⟨⟨111924271353091511341089202964,111924271353091511375087509861⟩,⟨42721362388305580944778133734,42721362388305580978274229391⟩⟩,⟨⟨111764935587641267617314946903,111764935587641267651130123421⟩,⟨42729201721198137131987197435,42729201721198137165307395091⟩⟩,⟨⟨111585645962407428809907487356,111585645962407428843546290602⟩,⟨42728460447072920967069332872,42728460447072921000213561043⟩⟩,⟨⟨111382706977900099811251267567,111382706977900099844696657926⟩,⟨42717688232654806178171184751,42717688232654806211129770830⟩⟩] +lemma amp7_03_9_eq : ∀ k : Fin 16, amp7_0Expr 3 9 k = amp7_03_9 k := by decide +kernel +noncomputable def amp7_03_10 : Fin 16 → CBox := ![⟨⟨111159750065078620859804918769,111159750065078620893075181151⟩,⟨42698241261493210271087346263,42698241261493210303864692720⟩⟩,⟨⟨110912803649902789434449657090,110912803649902789467520593846⟩,⟨42668560402140490991688185802,42668560402140491024271918297⟩⟩,⟨⟨110645805042872832268489132460,110645805042872832301357743202⟩,⟨42630125367826309322672834434,42630125367826309355059285083⟩⟩,⟨⟨110354498419867349541565915595,110354498419867349574232936949⟩,⟨42581264578442690243237915100,42581264578442690275424276578⟩⟩,⟨⟨110043136133322651913730017407,110043136133322651946181371234⟩,⟨42523585468921798015387736316,42523585468921798047366113646⟩⟩,⟨⟨109707169361981680680754084431,109707169361981680712991213953⟩,⟨42455300129098942734620083212,42455300129098942766387991689⟩⟩,⟨⟨109351175208427717753271902564,109351175208427717785289381169⟩,⟨42378148121351216916465159466,42378148121351216948018137462⟩⟩,⟨⟨108970302490554986930481114643,108970302490554986962269465907⟩,⟨42290221074328216166615642685,42290221074328216197946978254⟩⟩,⟨⟨108569463361084077473579969618,108569463361084077505134026737⟩,⟨42193395316162831597675220313,42193395316162831628780584228⟩⟩,⟨⟨108143494246191367206399017441,108143494246191367237710882728⟩,⟨42085637612447569518857139825,42085637612447569549730479855⟩⟩,⟨⟨107697653292292014357836371113,107697653292292014388896798923⟩,⟨41968965949192066496695408366,41968965949192066527330907197⟩⟩,⟨⟨107226453779227317467346791777,107226453779227317498349667988⟩,⟨41841217532820514571991768853,41841217532820514602462091533⟩⟩,⟨⟨106735511492637970691751204776,106735511492637970722504457366⟩,⟨41704557177114092423977495248,41704557177114092454205631958⟩⟩,⟨⟨106219005024121998831453047532,106219005024121998861953155173⟩,⟨41556687512639368073001848436,41556687512639368102983494627⟩⟩,⟨⟨105682920212007267801831125417,105682920212007267832073060476⟩,⟨41399925655687995353512318351,41399925655687995383243456534⟩⟩,⟨⟨105121088558951245716202845849,105121088558951245746184838041⟩,⟨41231834294108552271113034427,41231834294108552300590045156⟩⟩] +lemma amp7_03_10_eq : ∀ k : Fin 16, amp7_0Expr 3 10 k = amp7_03_10 k := by decide +kernel +noncomputable def amp7_03_11 : Fin 16 → CBox := ![⟨⟨104539879211961195508480711877,104539879211961195538198342628⟩,⟨41054888656913940393983131174,41054888656913940423202278755⟩⟩,⟨⟨103932763244632145840398481297,103932763244632145869850476448⟩,⟨40866505738868568446351060046,40866505738868568475308985589⟩⟩,⟨⟨103306507295703791281483854603,103306507295703791310659641915⟩,⟨40669325062105206257003954614,40669325062105206285694618834⟩⟩,⟨⟨102654207638993277214215921917,102654207638993277243122407574⟩,⟨40460611756780496421480864926,40460611756780496449904119325⟩⟩,⟨⟨101983043611069337157735435881,101983043611069337186357829573⟩,⟨40243176228165336935702979142,40243176228165336963851172210⟩⟩,⟨⟨101285721181304898850677279259,101285721181304898879014254847⟩,⟨40014125106477579505740794294,40014125106477579533610586830⟩⟩,⟨⟨100569848722480396779019441711,100569848722480396807062099991⟩,⟨39776446724656384676410380027,39776446724656384703996544392⟩⟩,⟨⟨99827725143392012817097817154,99827725143392012844872350038⟩,⟨39527082065382904507049066460,39527082065382904534359154968⟩⟩,⟨⟨99067405448357288382041242667,99067405448357288409515108363⟩,⟨39269204939546770258166345841,39269204939546770285185826226⟩⟩,⟨⟨98280763343969559608913947559,98280763343969559636084672750⟩,⟨38999582967189485236982219442,38999582967189485263707355112⟩⟩,⟨⟨97476319461002536891227326876,97476319461002536918098381615⟩,⟨38721583551836169412353351425,38721583551836169438783990499⟩⟩,⟨⟨96645502623361218609945613402,96645502623361218636502751985⟩,⟨38431792605100235290805567030,38431792605100235316933285275⟩⟩,⟨⟨95797319646537514314581236078,95797319646537514340824613101⟩,⟨38133779869569612303927818875,38133779869569612329751209197⟩⟩,⟨⟨94922733076289279859924282586,94922733076289279885848359619⟩,⟨37823940499429306631215135246,37823940499429306656729278102⟩⟩,⟨⟨94031258223032823753335973442,94031258223032823778933964213⟩,⟨37506056032073306557886055631,37506056032073306583086899844⟩⟩,⟨⟨93113368040950457177481917254,93113368040950457202745466963⟩,⟨37176321028471885226269951545,37176321028471885251151438936⟩⟩] +lemma amp7_03_11_eq : ∀ k : Fin 16, amp7_0Expr 3 11 k = amp7_03_11 k := by decide +kernel +noncomputable def amp7_03_12 : Fin 16 → CBox := ![⟨⟨92179110615548978359161286590,92179110615548978384202954116⟩,⟨36838739075570337769822391523,36838739075570337794428212730⟩⟩,⟨⟨91218443843118553084503584145,91218443843118553109220198966⟩,⟨36489293421855418194301637869,36489293421855418218587944827⟩⟩,⟨⟨90241975087389980582928785268,90241975087389980607316968288⟩,⟨36132220861665317317924956401,36132220861665317341889252880⟩⟩,⟨⟨89239119294536244261650050068,89239119294536244285706875889⟩,⟨35763281615889816463130721326,35763281615889816486769161114⟩⟩,⟨⟨88221072127470550276647439779,88221072127470550300369747884⟩,⟨35386957868523442859491695151,35386957868523442882801940406⟩⟩,⟨⟨87176674945370852315839668559,87176674945370852339226228160⟩,⟨34998773970735535908992400269,34998773970735535931971329165⟩⟩,⟨⟨86117743594309903995361488587,86117743594309904018403498127⟩,⟨34603470844911884549506192030,34603470844911884572149330858⟩⟩,⟨⟨85032512091007640959080548075,85032512091007640981789384215⟩,⟨34196322849504247032573238932,34196322849504247054882519473⟩⟩,⟨⟨83933451617794353995312138691,83933451617794354017669434026⟩,⟨33782344327621008452107481620,33782344327621008474074650307⟩⟩,⟨⟨82808151533932234554559325641,82808151533932234576564902807⟩,⟨33356544059694080851659344277,33356544059694080873281734949⟩⟩,⟨⟨81669777260502634201798807205,81669777260502634223447974802⟩,⟨32924226023141561219598172599,32924226023141561240873170040⟩⟩,⟨⟨80505232101902235941812007112,80505232101902235963099770449⟩,⟨32480116157636285154061983372,32480116157636285174984952121⟩⟩,⟨⟨79328418941069557993102554961,79328418941069558014021258796⟩,⟨32029826054844552499389168685,32029826054844552519956377025⟩⟩,⟨⟨78125508924014777495540209532,78125508924014777516157340001⟩,⟨31567779616887278312184363728,31567779616887278332420490604⟩⟩,⟨⟨76911190622787201255131751994,76911190622787201275379276383⟩,⟨31099916077297835362676202945,31099916077297835382553280396⟩⟩,⟨⟨75670851466624373787854690901,75670851466624373807729506088⟩,⟨30620335861732253947569964074,30620335861732253967084125039⟩⟩] +lemma amp7_03_12_eq : ∀ k : Fin 16, amp7_0Expr 3 12 k = amp7_03_12 k := by decide +kernel +noncomputable def amp7_03_13 : Fin 16 → CBox := ![⟨⟨74420019771426200953933105936,74420019771426200973435525620⟩,⟨30135328259764457647427063234,30135328259764457666578021501⟩⟩,⟨⟨73143241331329381447777666982,73143241331329381466912333999⟩,⟨29638646167163298287197412851,29638646167163298305984476262⟩⟩,⟨⟨71856945087130164815733265661,71856945087130164834485416316⟩,⟨29136954141373718209728841847,29136954141373718228145777924⟩⟩,⟨⟨70544769817389431135587461401,70544769817389431153957977237⟩,⟨28623630426841329854604392149,28623630426841329872648940011⟩⟩,⟨⟨69224114016235186516360230642,69224114016235186534342013605⟩,⟨28105743360953413782277055733,28105743360953413799946187405⟩⟩,⟨⟨67877635250906212928396804974,67877635250906212946031844359⟩,⟨27576265790624556353662820297,27576265790624556370970991002⟩⟩,⟨⟨66523780050058305707521694684,66523780050058305724770032488⟩,⟨27042702265087238314266876609,27042702265087238331197878432⟩⟩,⟨⟨65144140082813196356647784234,65144140082813196373504728684⟩,⟨26497585173212293994832029987,26497585173212294011381311397⟩⟩,⟨⟨63758299819184074282507145582,63758299819184074298973485911⟩,⟨25948892398655906000047649803,25948892398655906016215658625⟩⟩,⟨⟨62346687757047098158201712707,62346687757047098174277923482⟩,⟨25388675635258554906259668133,25388675635258554922043963518⟩⟩,⟨⟨60930129993717370110072542340,60930129993717370125754091740⟩,⟨24825428883000031663030613903,24825428883000031678429661090⟩⟩,⟨⟨59487779349009275412322221108,59487779349009275427634429277⟩,⟨24250676637869842746337234317,24250676637869842761358656742⟩⟩,⟨⟨58041824002623021389391661249,58041824002623021404299896053⟩,⟨23673478688013833554986884327,23673478688013833569617015258⟩⟩,⟨⟨56570009972232934859143787750,56570009972232934873647254553⟩,⟨23084778170577720499546390013,23084778170577720513782186454⟩⟩,⟨⟨55096028589069022700851546304,55096028589069022714953240514⟩,⟨22494258806118241662032007780,22494258806118241675875331231⟩⟩,⟨⟨53596064947491040567742198185,53596064947491040581433856212⟩,⟨21892218751437832952558437439,21892218751437832966003119685⟩⟩] +lemma amp7_03_13_eq : ∀ k : Fin 16, amp7_0Expr 3 13 k = amp7_03_13 k := by decide +kernel +noncomputable def amp7_03_14 : Fin 16 → CBox := ![⟨⟨52095480224360237130483078263,52095480224360237143789002580⟩,⟨21289034338470280964503471881,21289034338470280977560234944⟩⟩,⟨⟨50568715722447518405135782591,50568715722447518418030672168⟩,⟨20674283295456862362985556291,20674283295456862375641234945⟩⟩,⟨⟨49043001411865566709537141090,49043001411865566722025574047⟩,⟨20059116507465990064281688033,20059116507465990076539173812⟩⟩,⟨⟨47490815519671002414018069214,47490815519671002426087176722⟩,⟨19432300843387650789057821814,19432300843387650800908907803⟩⟩,⟨⟨45941496926587157664928149595,45941496926587157676602035585⟩,⟨18805860615526227270634656774,18805860615526227282090422989⟩⟩,⟨⟨44365294673296468298772523444,44365294673296468310028814807⟩,⟨18167642135784693030253602442,18167642135784693041301868139⟩⟩,⟨⟨42793950059934125086168547334,42793950059934125097022290967⟩,⟨17530663980062810529840445436,17530663980062810540488846484⟩⟩,⟨⟨41195155583977737470757935650,41195155583977737481189548373⟩,⟨16881717004666433982233601532,16881717004666433992470944797⟩⟩,⟨⟨39603418981017187475962025606,39603418981017187485975903322⟩,⟨16234963891769371794839005200,16234963891769371804668806134⟩⟩,⟨⟨37983467166495009789245454144,37983467166495009798846002817⟩,⟨15575971532442852783338138949,15575971532442852792758898691⟩⟩,⟨⟨36373033401819555362552865820,36373033401819555371731607521⟩,⟨14920235674734798522451764218,14920235674734798531462043916⟩⟩,⟨⟨34733358560711026853377309129,34733358560711026862138259693⟩,⟨14251884885160189162645934359,14251884885160189171243854968⟩⟩,⟨⟨33105991878689448497963868056,33105991878689448506310950603⟩,⟨13587990986644800492138659257,13587990986644800500328198254⟩⟩,⟨⟨31448011672891630398714113074,31448011672891630406631401017⟩,⟨12910965643347139452299447406,12910965643347139460070309093⟩⟩,⟨⟨29805560374555505547059289944,29805560374555505554558919615⟩,⟨12239776617543069221347341704,12239776617543069228707293767⟩⟩,⟨⟨28130651691427828656174980456,28130651691427828663249203196⟩,⟨11554747279723721257139827887,11554747279723721264081596600⟩⟩] +lemma amp7_03_14_eq : ∀ k : Fin 16, amp7_0Expr 3 14 k = amp7_03_14 k := by decide +kernel +noncomputable def amp7_03_15 : Fin 16 → CBox := ![⟨⟨26475073331322565409814670043,26475073331322565416467352710⟩,⟨10877174302911279993682890309,10877174302911280000211316696⟩⟩,⟨⟨24784533782129140181393889074,24784533782129140187616534483⟩,⟨10184782046696133250893351522,10184782046696133257000457664⟩⟩,⟨⟨23117939942833731593217093364,23117939942833731599015778752⟩,⟨9501802659878659588474217492,9501802659878659594166369169⟩⟩,⟨⟨21412921908433719940231508405,21412921908433719945601064494⟩,⟨8802631606587096528202503655,8802631606587096533472519837⟩⟩,⟨⟨19737661954691011228188775405,19737661954691011233135814204⟩,⟨8115323851749719029752667796,8115323851749719034607893529⟩⟩,⟨⟨18019049706433749622409110476,18019049706433749626922729345⟩,⟨7409850261969004919741075204,7409850261969004924171220726⟩⟩,⟨⟨16337879594883099667098004685,16337879594883099671186853939⟩,⟨6719461815785244644489198832,6719461815785244648503490697⟩⟩,⟨⟨14606035130854249472354194504,14606035130854249476009327206⟩,⟨6007949147738538490811977327,6007949147738538494399815047⟩⟩,⟨⟨12922495920369191890429549765,12922495920369191893661136788⟩,⟨5316052750500094252830127498,5316052750500094256002840385⟩⟩,⟨⟨11176655113995702477859838678,11176655113995702480653275467⟩,⟨4598302801126458531720825033,4598302801126458534463776653⟩⟩,⟨⟨9496064986444769652677178320,9496064986444769655048621664⟩,⟨3907204167254960153812414233,3907204167254960156141756043⟩⟩,⟨⟨7732586486692739040657552298,7732586486692739042587359746⟩,⟨3181836065675808515401430816,3181836065675808517297448749⟩⟩,⟨⟨6065359213699051205464107723,6065359213699051206975838361⟩,⟨2495939224461625713034223638,2495939224461625714520464134⟩⟩,⟨⟨4270720105127730695116234305,4270720105127730696179463695⟩,⟨1757506484948139591579218849,1757506484948139592625130406⟩⟩,⟨⟨2649410243553751328923426496,2649410243553751329579338141⟩,⟨1090328258653248854180155699,1090328258653248854827454951⟩⟩,⟨⟨752734514253608699597476477,752734514253608699781646922⟩,⟨309781873171731219301954652,309781873171731219484958294⟩⟩] +lemma amp7_03_15_eq : ∀ k : Fin 16, amp7_0Expr 3 15 k = amp7_03_15 k := by decide +kernel +noncomputable def amp7_03 : Fin 16 → Fin 16 → CBox := ![amp7_03_0,amp7_03_1,amp7_03_2,amp7_03_3,amp7_03_4,amp7_03_5,amp7_03_6,amp7_03_7,amp7_03_8,amp7_03_9,amp7_03_10,amp7_03_11,amp7_03_12,amp7_03_13,amp7_03_14,amp7_03_15] +lemma amp7_03_eq (i k : Fin 16) : amp7_0Expr 3 i k = amp7_03 i k := by + fin_cases i + · exact amp7_03_0_eq k + · exact amp7_03_1_eq k + · exact amp7_03_2_eq k + · exact amp7_03_3_eq k + · exact amp7_03_4_eq k + · exact amp7_03_5_eq k + · exact amp7_03_6_eq k + · exact amp7_03_7_eq k + · exact amp7_03_8_eq k + · exact amp7_03_9_eq k + · exact amp7_03_10_eq k + · exact amp7_03_11_eq k + · exact amp7_03_12_eq k + · exact amp7_03_13_eq k + · exact amp7_03_14_eq k + · exact amp7_03_15_eq k +noncomputable def amp7_04_0 : Fin 16 → CBox := ![⟨⟨108091064822973074233599717,108091064822973074431771967⟩,⟨1017365712714695577821,1017365712714901170273⟩⟩,⟨⟨380541199428619362308033535,380541199428619363006663585⟩,⟨32227844834901554302036,32227844834902277949113⟩⟩,⟨⟨613709044986412613407032205,613709044986412614534094212⟩,⟨144307603078629094966123,144307603078630261515967⟩⟩,⟨⟨872230326526901843056738234,872230326526901844657776585⟩,⟨401710817432015916934284,401710817432017573831573⟩⟩,⟨⟨1113055384907871282987190477,1113055384907871285028873360⟩,⟨846618630911080811942279,846618630911082924521657⟩⟩,⟨⟨1368537858149031358164442590,1368537858149031360672273660⟩,⟨1553203743542668357898792,1553203743542670952636141⟩⟩,⟨⟨1613056611081845717350349735,1613056611081845720302767946⟩,⟨2553427679062346139829361,2553427679062349194295883⟩⟩,⟨⟨1868150446606356735838847921,1868150446606356739253290089⟩,⟨3930825950684610740968262,3930825950684614273255421⟩⟩,⟨⟨2115573199970329126384325345,2115573199970329130244703030⟩,⟨5707149034948219466099291,5707149034948223459476482⟩⟩,⟨⟨2371503251039285089037449968,2371503251039285093356549499⟩,⟨7974992912616155560516080,7974992912616160028527420⟩⟩,⟨⟨2621764478140219837690207461,2621764478140219842455478050⟩,⟨10745843359115805759960101,10745843359115810689126505⟩⟩,⟨⟨2879333900629663782859699747,2879333900629663788081294893⟩,⟨14121091280701550587981961,14121091280701555988961786⟩⟩,⟨⟨3132613643559144750426051810,3132613643559144756092853545⟩,⟨18101889125021375631783897,18101889125021381493169162⟩⟩,⟨⟨3392453230468428399957242953,3392453230468428406077433013⟩,⟨22798164690230287514907123,22798164690230293845336012⟩⟩,⟨⟨3649032574305932699321777382,3649032574305932705886265816⟩,⟨28200671625299003942938177,28200671625299010732424949⟩⟩,⟨⟨3911685387815698906965012412,3911685387815698913980641255⟩,⟨34427613720176445308672034,34427613720176452564346626⟩⟩] +lemma amp7_04_0_eq : ∀ k : Fin 16, amp7_0Expr 4 0 k = amp7_04_0 k := by decide +kernel +noncomputable def amp7_04_1 : Fin 16 → CBox := ![⟨⟨4171890055855739750293655679,4171890055855739757751674215⟩,⟨41459290719596020175744534,41459290719596027888633244⟩⟩,⟨⟨4437845881573746386472770917,4437845881573746394378724358⟩,⟨49421914614835272627854334,49421914614835280803900453⟩⟩,⟨⟨4702019975226409164397477319,4702019975226409172743361828⟩,⟨58285289887787182541936689,58285289887787191172918184⟩⟩,⟨⟨4971730963353622498270472364,4971730963353622507062257173⟩,⟨68183360397692085439502160,68183360397692094530415370⟩⟩,⟨⟨5240222954647131098780478858,5240222954647131108009390295⟩,⟨79075409598275561055141442,79075409598275570598317125⟩⟩,⟨⟨5514111130105205912240884251,5514111130105205921911001201⟩,⟨91102827691590650644226474,91102827691590660643837200⟩⟩,⟨⟨5787265496008320874681323282,5787265496008320884787258334⟩,⟨104214368082311425274331957,104214368082311435723192949⟩⟩,⟨⟨6065726374234298283018349324,6065726374234298293561713370⟩,⟨118558572418822134464712824,118558572418822145366273569⟩⟩,⟨⟨6343878091901702181108771784,6343878091901702192084508858⟩,⟨134073672582852000254474029,134073672582852011601895796⟩⟩,⟨⟨6627282282626793835607736276,6627282282626793847018952865⟩,⟨150915057458186178694556526,150915057458186190490724733⟩⟩,⟨⟨6910752895093323983882829805,6910752895093323995721012191⟩,⟨169010464087999562883871539,169010464087999575122136012⟩⟩,⟨⟨7199446607812111205484223772,7199446607812111217753667216⟩,⟨188521815248313376371214972,188521815248313389053963537⟩⟩,⟨⟨7488541213535057313872161195,7488541213535057326564035065⟩,⟨209366398483646590563100759,209366398483646603683871592⟩⟩,⟨⟨7782846141120709919892419857,7782846141120709933012096032⟩,⟨231712348237249829545706687,231712348237249843106455303⟩⟩,⟨⟨8077850962929537242799918427,8077850962929537256340213171⟩,⟨255466566973823122210891431,255466566973823136205362291⟩⟩,⟨⟨8378063807143716872166581908,8378063807143716886129427839⟩,⟨280803069984181509071774412,280803069984181523501405026⟩⟩] +lemma amp7_04_1_eq : ∀ k : Fin 16, amp7_0Expr 4 1 k = amp7_04_1 k := by decide +kernel +noncomputable def amp7_04_2 : Fin 16 → CBox := ![⟨⟨8679244147824364051162024025,8679244147824364065538272181⟩,⟨307618458522706076647297207,307618458522706091505880701⟩⟩,⟨⟨8985635940405963324023272592,8985635940405963338817742424⟩,⟨336092289619148261019166259,336092289619148276307851748⟩⟩,⟨⟨9293234412638882445647998363,9293234412638882460854408620⟩,⟨366110966970354763240494722,366110966970354778953274249⟩⟩,⟨⟨9606049725658258937426276705,9606049725658258953045692523⟩,⟨397859242260386778470130579,397859242260386794607668945⟩⟩,⟨⟨9920284688793104303006158237,9920284688793104319033570061⟩,⟨431213445365565135291341919,431213445365565151847757525⟩⟩,⟨⟨10239740793754313288328924183,10239740793754313304758840237⟩,⟨466363167876582213376887849,466363167876582230352222723⟩⟩,⟨⟨10560804955802987120376008349,10560804955802987137207839169⟩,⟨503174809944199798649920798,503174809944199816038540180⟩⟩,⟨⟨10887090970695076680582645251,10887090970695076697815648182⟩,⟨541842440962969015257271437,541842440962969033059117949⟩⟩,⟨⟨11215150129419337228429704641,11215150129419337246059159643⟩,⟨582222696060299632806468466,582222696060299651015771317⟩⟩,⟨⟨11548426180460572657063607057,11548426180460572675089473197⟩,⟨624513753276140027847071897,624513753276140046463521241⟩⟩,⟨⟨11883618086964772974620161997,11883618086964772993036900922⟩,⟨668562668250543275040800877,668562668250543294058615258⟩⟩,⟨⟨12224014503880810617669208119,12224014503880810636469328377⟩,⟨714571351742874030711610549,714571351742874050129776184⟩⟩,⟨⟨12566447838124335675117125807,12566447838124335694303265262⟩,⟨762377486480516785506991660,762377486480516805320208453⟩⟩,⟨⟨12914064396632727370747874041,12914064396632727390318156513⟩,⟨812186333523575921030061539,812186333523575941237389170⟩⟩,⟨⟨13263817848126461245504172584,13263817848126461265454086461⟩,⟨863826430484116367323731817,863826430484116387919480323⟩⟩,⟨⟨13618723069818228387770207513,13618723069818228408096220459⟩,⟨917506000071359143094299362,917506000071359164077171099⟩⟩] +lemma amp7_04_2_eq : ∀ k : Fin 16, amp7_0Expr 4 2 k = amp7_04_2 k := by decide +kernel +noncomputable def amp7_04_3 : Fin 16 → CBox := ![⟨⟨13975844519269119820430133457,13975844519269119841128375396⟩,⟨973044683965568805227369014,973044683965568826591716753⟩⟩,⟨⟨14338075036663010869344801821,14338075036663010890414336692⟩,⟨1030653271883720164367101616,1030653271883720186111572338⟩⟩,⟨⟨14702580835963883327602248675,14702580835963883349037851766⟩,⟨1090142780287363162215499593,1090142780287363184334357619⟩⟩,⟨⟨15072140828782894808000492389,15072140828782894829788035309⟩,⟨1151726165495505742390147560,1151726165495505764880819911⟩⟩,⟨⟨15444015177809060924155798339,15444015177809060946303320383⟩,⟨1215206111117198383956648034,1215206111117198406814377943⟩⟩,⟨⟨15820875885256802120932796993,15820875885256802143437495125⟩,⟨1280797334109812428085950785,1280797334109812451308824665⟩⟩,⟨⟨16200070304614796794281677525,16200070304614796817137944849⟩,⟨1348294499353228932607656135,1348294499353228956189887253⟩⟩,⟨⟨16584169617461783229968724972,16584169617461783253174100354⟩,⟨1417913673107950977792833037,1417913673107951001732331358⟩⟩,⟨⟨16970602516759778903957698588,16970602516759778927507460847⟩,⟨1489441837489806928168043477,1489441837489806952459080109⟩⟩,⟨⟨17361844652289796027251095886,17361844652289796051139908713⟩,⟨1563095991521031531793876300,1563095991521031556433916627⟩⟩,⟨⟨17755400993743630697927712380,17755400993743630722153202892⟩,⟨1638655792425954702855025496,1638655792425954727838533315⟩⟩,⟨⟨18153656255993968288444165829,18153656255993968313002703162⟩,⟨1716338750384461627431815269,1716338750384461652756224919⟩⟩,⟨⟨18554187313300501667922275019,18554187313300501692808913706⟩,⟨1795917577556343200272275282,1795917577556343225931804029⟩⟩,⟨⟨18959291940514293094491951178,18959291940514293119704097502⟩,⟨1877609868733088052874453540,1877609868733088078866461996⟩⟩,⟨⟨19366615152951315532860779946,19366615152951315558393170936⟩,⟨1961181792819992268836333651,1961181792819992295154992906⟩⟩,⟨⟨19778371253716352643221899275,19778371253716352669071723025⟩,⟨2046850597829250569607523577,2046850597829250596250010720⟩⟩] +lemma amp7_04_3_eq : ∀ k : Fin 16, amp7_0Expr 4 3 k = amp7_04_3 k := by decide +kernel +noncomputable def amp7_04_4 : Fin 16 → CBox := ![⟨⟨20192270175390653341879368804,20192270175390653368019560211⟩,⟨2134376333215646651155444495,2134376333215646678113606142⟩⟩,⟨⟨20610445754546923327858217199,20610445754546923354310833712⟩,⟨2223975464049050668038816383,2223975464049050695312265884⟩⟩,⟨⟨21030670098627085235121206474,21030670098627085261879835466⟩,⟨2315402366125218512350251848,2315402366125218539933011510⟩⟩,⟨⟨21454999173671047278607430526,21454999173671047305668294561⟩,⟨2408872280684075494436598823,2408872280684075522325449029⟩⟩,⟨⟨21881264951321745255348011431,21881264951321745282705221598⟩,⟨2504134377618228989848276408,2504134377618229018037267117⟩⟩,⟨⟨22311447759709360759149157962,22311447759709360786800410105⟩,⟨2601402228747062331253668295,2601402228747062359739606218⟩⟩,⟨⟨22743437513298611025840910226,22743437513298611053778331925⟩,⟨2700420287741234979459797305,2700420287741235008236480156⟩⟩,⟨⟨23179140810744570450479477735,23179140810744570478701374517⟩,⟨2801400006700950681498476845,2801400006700950710562648747⟩⟩,⟨⟨23616503940731325635419108379,23616503940731325663920255111⟩,⟨2904081634627201900406382889,2904081634627201929752134008⟩⟩,⟨⟨24057361390313998232466938748,24057361390313998261237060001⟩,⟨3008674048861855990102038472,3008674048861856019724931270⟩⟩,⟨⟨24499714575045827228920728226,24499714575045827257961441083⟩,⟨3114913827091087433947956503,3114913827091087463842910983⟩⟩,⟨⟨24945327226652839401201673825,24945327226652839430508184214⟩,⟨3223006812058119964766538929,3223006812058119994929677109⟩⟩,⟨⟨25392254934116096584319241217,25392254934116096613886602655⟩,⟨3332686465209943377348170715,3332686465209943407773588078⟩⟩,⟨⟨25842191793501776317435917456,25842191793501776347257776161⟩,⟨3444155129960154726894853924,3444155129960154757578345719⟩⟩,⟨⟨26293246883872707500218592928,26293246883872707530292094340⟩,⟨3557143728219029227427211462,3557143728219029258363139156⟩⟩,⟨⟨26747045570344302313190325443,26747045570344302343510001618⟩,⟨3671850634329706794707445922,3671850634329706825891605950⟩⟩] +lemma amp7_04_4_eq : ∀ k : Fin 16, amp7_0Expr 4 4 k = amp7_04_4 k := by decide +kernel +noncomputable def amp7_04_5 : Fin 16 → CBox := ![⟨⟨27201749987991382899104073558,27201749987991382929664970045⟩,⟨3788004828890165616573348527,3788004828890165647999810063⟩⟩,⟨⟨27658917479494882613686167186,27658917479494882644484351432⟩,⟨3905800242272824136003516803,3905800242272824167668183595⟩⟩,⟨⟨28116763032882301535719944859,28116763032882301566750425905⟩,⟨4024964533395238287132484656,4024964533395238319029419043⟩⟩,⟨⟨28576776497020177114688018123,28576776497020177145946570917⟩,⟨4145686708418613012878470970,4145686708418613045003436474⟩⟩,⟨⟨29037225724761388643800154011,29037225724761388675281284809⟩,⟨4267693745496789269152838829,4267693745496789301499816908⟩⟩,⟨⟨29499533434043180432915310168,29499533434043180464563536887⟩,⟨4391169240786213726163670318,4391169240786213758720704982⟩⟩,⟨⟨29962020555153205683524612847,29962020555153205715388015993⟩,⟨4515840153749391073478965715,4515840153749391106247919777⟩⟩,⟨⟨30426042884555453541490582726,30426042884555453573563670088⟩,⟨4641884178945692222157275138,4641884178945692255133548985⟩⟩,⟨⟨30889974830752287534428164671,30889974830752287566704232897⟩,⟨4769028940240375229616846943,4769028940240375262794230807⟩⟩,⟨⟨31355105335446740344343634980,31355105335446740376818287054⟩,⟨4897445732925117402263370079,4897445732925117435637344858⟩⟩,⟨⟨31819862863156818832067100340,31819862863156818864733201064⟩,⟨5026863549246854114874533763,5026863549246854148438816266⟩⟩,⟨⟨32285469434055253564659059640,32285469434055253597511969963⟩,⟨5157446781166343499807125402,5157446781166343533557071037⟩⟩,⟨⟨32750408313586346344069834935,32750408313586346377105536840⟩,⟨5288926514038202087447110512,5288926514038202121376925194⟩⟩,⟨⟨33215834408146811408398051165,33215834408146811441609344095⟩,⟨5421459725686305852883949256,5421459725686305886988506393⟩⟩,⟨⟨33680286687304729437265494722,33680286687304729470648230590⟩,⟨5554780339909606536333007961,5554780339909606570606501289⟩⟩,⟨⟨34144852632847806966680806797,34144852632847807000230990721⟩,⟨5689037402459319898412638546,5689037402459319932850390943⟩⟩] +lemma amp7_04_5_eq : ∀ k : Fin 16, amp7_0Expr 4 5 k = amp7_04_5 k := by decide +kernel +noncomputable def amp7_04_6 : Fin 16 → CBox := ![⟨⟨34608127972091655066285478543,34608127972091655099991231916⟩,⟨5823968441393309550545574192,5823968441393309585140490691⟩⟩,⟨⟨35071132338686657050929400324,35071132338686657084793341975⟩,⟨5959714044899289776464488054,5959714044899289811212941500⟩⟩,⟨⟨35532519414741683295499869026,35532519414741683329512375809⟩,⟨6096016131460073477303382489,6096016131460073512198661916⟩⟩,⟨⟨35993240454541829965502381794,35993240454541829999662491859⟩,⟨6233006298189215718078483454,6233006298189215753116311947⟩⟩,⟨⟨36452008429219813022662684205,36452008429219813056962415334⟩,⟨6370431660394543891097974997,6370431660394543926271920655⟩⟩,⟨⟨36909705578952678709467075714,36909705578952678743902855350⟩,⟨6508414282079257364711347841,6508414282079257400016640498⟩⟩,⟨⟨37365105629767803739796208989,37365105629767803774341934915⟩,⟨6646707301904864075598874354,6646707301904864111025866185⟩⟩,⟨⟨37819021072922954525997469517,37819021072922954560670283812⟩,⟨6785422699654169351109598779,6785422699654169386657125730⟩⟩,⟨⟨38270287981936762888347292128,38270287981936762923139312950⟩,⟨6924320483909415352545197528,6924320483909415388206860041⟩⟩,⟨⟨38719648267036852776787264822,38719648267036852811692551822⟩,⟨7063501989456468201891655073,7063501989456468237662165827⟩⟩,⟨⟨39166002064219578646151383097,39166002064219578681165336063⟩,⟨7202734961332202760140431975,7202734961332202796014003613⟩⟩,⟨⟨39610019775414514590427445534,39610019775414514625542766053⟩,⟨7342109518243493773505350013,7342109518243493809476391148⟩⟩,⟨⟨40050667432672375395232230188,40050667432672375430444269282⟩,⟨7481402028133446243842113534,7481402028133446279904841877⟩⟩,⟨⟨40488542908758796601291811546,40488542908758796636597123869⟩,⟨7620690811554856975442686219,7620690811554857011592192486⟩⟩,⟨⟨40922680080647983630446546360,40922680080647983665828875019⟩,⟨7759761765703628850817931516,7759761765703628887046271980⟩⟩,⟨⟨41353603178488506156099397999,41353603178488506191563074464⟩,⟨7898680819171865480310067614,7898680819171865516613756632⟩⟩] +lemma amp7_04_6_eq : ∀ k : Fin 16, amp7_0Expr 4 6 k = amp7_04_6 k := by decide +kernel +noncomputable def amp7_04_7 : Fin 16 → CBox := ![⟨⟨41780415985517095058284538743,41780415985517095093822516164⟩,⟨8037244324657834596036546235,8037244324657834632409396628⟩⟩,⟨⟨42203567883715813857991318619,42203567883715813893599929773⟩,⟨8175505212462621430226116360,8175505212462621466663118035⟩⟩,⟨⟨42622234734024920090943235770,42622234734024920126610847698⟩,⟨8313271236982902302324936719,8313271236982902338819041433⟩⟩,⟨⟨43036789772607785606801583677,43036789772607785642527826475⟩,⟨8450581710525803753496385482,8450581710525803790043185787⟩⟩,⟨⟨43446483217723335811974520216,43446483217723335847749954885⟩,⟨8587256755412933310276456230,8587256755412933346869342488⟩⟩,⟨⟨43851610769474460607764778412,43851610769474460643588354074⟩,⟨8723321431972879225504982954,8723321431972879262139410037⟩⟩,⟨⟨44251499389731217198357486546,44251499389731217234220547964⟩,⟨8858609216839208406301424696,8858609216839208442970971809⟩⟩,⟨⟨44646365758749129076848808096,44646365758749129112746281365⟩,⟨8993130269122809588153194720,8993130269122809624852491084⟩⟩,⟨⟨45035616073909343479550332766,45035616073909343515476624523⟩,⟨9126732426498762473913692383,9126732426498762510636949250⟩⟩,⟨⟨45419386416870872083552111322,45419386416870872119502721752⟩,⟨9259410281325397336789003176,9259410281325397373530959365⟩⟩,⟨⟨45797164817391375477674280444,45797164817391375513642007890⟩,⟨9391027059631885618409860423,9391027059631885655164447736⟩⟩,⟨⟨46169005082945403263703165663,46169005082945403299683232568⟩,⟨9521561104079381962841469140,9521561104079381999603343959⟩⟩,⟨⟨46534479777289267957461205624,46534479777289267993446474752⟩,⟨9650892077252799407407002455,9650892077252799444170136191⟩⟩,⟨⟨46893558658948132846674795427,46893558658948132882659676785⟩,⟨9778981370569384244443187358,9778981370569384281202062123⟩⟩,⟨⟨47245901632290420729154798533,47245901632290420765132414472⟩,⟨9905726152639809826519185164,9905726152639809863267871050⟩⟩,⟨⟨47591392530143440358363424114,47591392530143440394326876621⟩,⟨10031070142211902015076187023,10031070142211902051808868652⟩⟩] +lemma amp7_04_7_eq : ∀ k : Fin 16, amp7_0Expr 4 7 k = amp7_04_7 k := by decide +kernel +noncomputable def amp7_04_8 : Fin 16 → CBox := ![⟨⟨47929781509785137980883735707,47929781509785138016832492658⟩,⟨10154929105121458576242439938,10154929105121458612954556669⟩⟩,⟨⟨48260864496326621548315704783,48260864496326621584249897338⟩,⟨10277228344774870533549141461,10277228344774870570236384595⟩⟩,⟨⟨48584484919106758100048791354,48584484919106758135961249270⟩,⟨10397903337713655804077547041,10397903337713655840734028950⟩⟩,⟨⟨48900348704450041347313629978,48900348704450041383197949564⟩,⟨10516860206617878152926238466,10516860206617878189546248533⟩⟩,⟨⟨49208395681433283153073390170,49208395681433283188923577313⟩,⟨10634055275149534838110862322,10634055275149534874688798510⟩⟩,⟨⟨49508239573172797100525538551,49508239573172797136334985520⟩,⟨10749374695591017507392253604,10749374695591017543922363598⟩⟩,⟨⟨49799919846888570996752122281,49799919846888571032515813766⟩,⟨10862796798838857594691435938,10862796798838857631168388971⟩⟩,⟨⟨50082955699873739056733278894,50082955699873739092444379654⟩,⟨10974186951129577894789502803,10974186951129577931207483829⟩⟩,⟨⟨50357489589393191937205869578,50357489589393191972859532705⟩,⟨11083546675297232695538871369,11083546675297232731892627782⟩⟩,⟨⟨50622943740691017061713855127,50622943740691017097305208071⟩,⟨11190719708089349772856727925,11190719708089349809140890254⟩⟩,⟨⟨50879567069849879584040240516,50879567069849879619564004269⟩,⟨11295731974597181537562696902,11295731974597181573771990211⟩⟩,⟨⟨51126682254197377298319695778,51126682254197377333767292647⟩,⟨11398404708883200983611758761,11398404708883201019739982230⟩⟩,⟨⟨51364648258306051198972641774,51364648258306051234343404043⟩,⟨11498789475413175194459763524,11498789475413175230502717956⟩⟩,⟨⟨51592685499389119245792322232,51592685499389119281076833608⟩,⟨11596684100503759999238242178,11596684100503760035189553646⟩⟩,⟨⟨51811266705816011240050078212,51811266705816011275248810543⟩,⟨11692167053261121746157296512,11692167053261121782013105505⟩⟩,⟨⟨52019507178757784293188748416,52019507178757784328289380879⟩,⟨11785011813049447589235295010,11785011813049447624988564297⟩⟩] +lemma amp7_04_8_eq : ∀ k : Fin 16, amp7_0Expr 4 8 k = amp7_04_8 k := by decide +kernel +noncomputable def amp7_04_9 : Fin 16 → CBox := ![⟨⟨52217997256828003853119788751,52217997256828003888118605916⟩,⟨11875325048569344284696107179,11875325048569344320342082300⟩⟩,⟨⟨52405744117327072408195193960,52405744117327072443085596372⟩,⟨11962854916411658316312878036,11962854916411658351845833238⟩⟩,⟨⟨52583459693046013245971074555,52583459693046013280759978121⟩,⟨12047737611262769670875504872,12047737611262769706293206419⟩⟩,⟨⟨52750039868672906375956098316,52750039868672906410624893693⟩,⟨12129694951829510833066488813,12129694951829510868360463882⟩⟩,⟨⟨52906322299862839941992516359,52906322299862839976537919346⟩,⟨12208894018594742972588816173,12208894018594743007754552189⟩⟩,⟨⟨53051088239101664995020218644,53051088239101665029438796593⟩,⟨12285029235075145103066603803,12285029235075145138099129274⟩⟩,⟨⟨53185305346629168683872927984,53185305346629168718156405727⟩,⟨12358299963021469171943761047,12358299963021469206837495634⟩⟩,⟨⟨53307636721340014623223245591,53307636721340014657368162074⟩,⟨12428372128096910044775163274,12428372128096910079525135057⟩⟩,⟨⟨53419184472212702167106003296,53419184472212702201105699934⟩,⟨12495478806982420211871683822,12495478806982420246472740963⟩⟩,⟨⟨53518489829289057418840936917,53518489829289057452687512323⟩,⟨12559256276019802203103714188,12559256276019802237549880518⟩⟩,⟨⟨53606793967511526005916822063,53606793967511526039637146066⟩,⟨12619972801525971456480324837,12619972801525971490774423986⟩⟩,⟨⟨53682512325615207519244588883,53682512325615207552804514849⟩,⟨12677233806482011569068471726,12677233806482011603198373135⟩⟩,⟨⟨53747029946816208160203769103,53747029946816208193600060228⟩,⟨12731344265802868988100116095,12731344265802869022061627095⟩⟩,⟨⟨53798632334189775224230380633,53798632334189775257454885845⟩,⟨12781877488373212763761125698,12781877488373212797548244534⟩⟩,⟨⟨53838853400165187429225945849,53838853400165187462279570595⟩,⟨12829176724540682346845029172,12829176724540682380454643279⟩⟩,⟨⟨53865844329648105800223012407,53865844329648105833094920349⟩,⟨12872781847134098485490821149,12872781847134098518916296654⟩⟩] +lemma amp7_04_9_eq : ∀ k : Fin 16, amp7_0Expr 4 9 k = amp7_04_9 k := by decide +kernel +noncomputable def amp7_04_10 : Fin 16 → CBox := ![⟨⟨53881293119107192426538113823,53881293119107192459234811022⟩,⟨12913076000709954091401286402,12913076000709954124640924794⟩⟩,⟨⟨53883211996616656238306024955,53883211996616656270813269904⟩,⟨12949564233877359587246271180,12949564233877359620292661876⟩⟩,⟨⟨53873448488572133512877865684,53873448488572133545191969813⟩,⟨12982671260697089622760129541,12982671260697089655609236912⟩⟩,⟨⟨53849870951451924062498390593,53849870951451924094617153321⟩,⟨13011865845697627151326872199,13011865845697627183974179049⟩⟩,⟨⟨53814492137857463544407312641,53814492137857463576321652171⟩,⟨13037616009409894476438006860,13037616009409894508878249489⟩⟩,⟨⟨53765031319647943125243154519,53765031319647943156951282425⟩,⟨13059352694651544097817400505,13059352694651544130046202913⟩⟩,⟨⟨53703672444059708922423051061,53703672444059708953920207173⟩,⟨13077589032858803737479001769,13077589032858803769492247084⟩⟩,⟨⟨53627980162398360975711013642,53627980162398361006990028970⟩,⟨13091716523008848047412547923,13091716523008848079204567091⟩⟩,⟨⟨53540315881619995129638662204,53540315881619995160694884327⟩,⟨13102295285879987905344049926,13102295285879987936910821417⟩⟩,⟨⟨53438083746144092597533040084,53438083746144092628360138047⟩,⟨13108675662500827667026769413,13108675662500827698362869474⟩⟩,⟨⟨53323829212007163937409217402,53323829212007163968000627919⟩,⟨13111466722795377648695546168,13111466722795377679796591574⟩⟩,⟨⟨53194789649297340824793214524,53194789649297340855242644170⟩,⟨13109975835423449508919147196,13109975835423449539804372623⟩⟩,⟨⟨53053701507931708537939266265,53053701507931708568149647644⟩,⟨13104863068938931632584923966,13104863068938931663227776252⟩⟩,⟨⟨52897628700706471732493179550,52897628700706471762460373552⟩,⟨13095390895588513047324060591,13095390895588513077719709050⟩⟩,⟨⟨52729506006867421232226151293,52729506006867421261945808622⟩,⟨13082272531117872653653276641,13082272531117872683798077374⟩⟩,⟨⟨52546216744812872088977555425,52546216744812872118446382127⟩,⟨13064723507257033402716976626,13064723507257033432606324180⟩⟩] +lemma amp7_04_10_eq : ∀ k : Fin 16, amp7_0Expr 4 10 k = amp7_04_10 k := by decide +kernel +noncomputable def amp7_04_11 : Fin 16 → CBox := ![⟨⟨52350901789054522647218875888,52350901789054522676432821964⟩,⟨13043512445221825657524921002,13043512445221825687155326354⟩⟩,⟨⟨52140256228849482743342574345,52140256228849482772298690140⟩,⟨13017805760334312445599502819,13017805760334312474966497589⟩⟩,⟨⟨51917635275567279184862952288,51917635275567279213554230406⟩,⟨12988429859341489285888649865,12988429859341489314988127558⟩⟩,⟨⟨51679537607840128903273755684,51679537607840128931701312405⟩,⟨12954499720255460266066593396,12954499720255460294895113643⟩⟩,⟨⟨51429541542449873860452747789,51429541542449873888607457640⟩,⟨12916902050911340008124943893,12916902050911340036677956441⟩⟩,⟨⟨51163940563577927335636429354,51163940563577927363515338946⟩,⟨12874697911143072106117933319,12874697911143072134391022494⟩⟩,⟨⟨50886545447355743835997085498,50886545447355743863594135216⟩,⟨12828836976547584748669618157,12828836976547584776659118320⟩⟩,⟨⟨50593435034188744115620137869,50593435034188744142946287109⟩,⟨12778323730974931484486879901,12778323730974931512191902962⟩⟩,⟨⟨50288662565566931516683009258,50288662565566931543720230166⟩,⟨12724173653412829144670638545,12724173653412829172084589559⟩⟩,⟨⟨49968082051320625513841318233,49968082051320625540586131885⟩,⟨12665331797658554976073437278,12665331797658555003191829476⟩⟩,⟨⟨49635999932720457514496888680,49635999932720457540949651147⟩,⟨12602882471102409475368188730,12602882471102409502189199600⟩⟩,⟨⟨49288034382440950010293078788,49288034382440950036444271850⟩,⟨12535708225070645776776124846,12535708225070645803293743591⟩⟩,⟨⟨48928756592027629040036191738,48928756592027629065884503008⟩,⟨12464965433213760022885314419,12464965433213760049097394211⟩⟩,⟨⟨48553536976168246440818267649,48553536976168246466358675475⟩,⟨12389470828282574140980176375,12389470828282574166881886948⟩⟩,⟨⟨48167223944238972217287431623,48167223944238972242515202776⟩,⟨12310456327929295101729087721,12310456327929295127317541666⟩⟩,⟨⟨47764927209013523632412781347,47764927209013523657321401528⟩,⟨12226669257357300071151603311,12226669257357300096421594965⟩⟩] +lemma amp7_04_11_eq : ∀ k : Fin 16, amp7_0Expr 4 11 k = amp7_04_11 k := by decide +kernel +noncomputable def amp7_04_12 : Fin 16 → CBox := ![⟨⟨47351785899081707484677863298,47351785899081707509323892905⟩,⟨12139420827114858729506450858,12139420827114858754470901127⟩⟩,⟨⟨46922634932354674610662039366,46922634932354674634990429299⟩,⟨12047385059268084741542916480,12047385059268084766184243758⟩⟩,⟨⟨46482918827378190375125633038,46482918827378190399133559390⟩,⟨11951956513609678091080368469,11951956513609678115396418521⟩⟩,⟨⟨46027182318914871377796523196,46027182318914871401480301122⟩,⟨11851731667654209161419496446,11851731667654209185405836513⟩⟩,⟨⟨45561191313542663022510902701,45561191313542663045867848756⟩,⟨11748192836559880522012430907,11748192836559880545667054199⟩⟩,⟨⟨45079183508459261403687896975,45079183508459261426715268516⟩,⟨11639854320292927843384659537,11639854320292927866703410530⟩⟩,⟨⟨44587263708650626984466337513,44587263708650627007158667512⟩,⟨11528290994826055279212528832,11528290994826055302192825479⟩⟩,⟨⟨44079344052860542277949471943,44079344052860542300310508321⟩,⟨11411929904329072417526355351,11411929904329072440165723702⟩⟩,⟨⟨43561887484781462605786158602,43561887484781462627805490902⟩,⟨11292443748676301648506307757,11292443748676301670800999747⟩⟩,⟨⟨43028460161109125528614647670,43028460161109125550290113602⟩,⟨11168166729462903609415644621,11168166729462903631361689422⟩⟩,⟨⟨42485904391852887071102758528,42485904391852887092431182398⟩,⟨11040875160160211458551302767,11040875160160211480146978574⟩⟩,⟨⟨41927417745252400265038024510,41927417745252400286014678588⟩,⟨10908804229451485818294855377,10908804229451485839535516919⟩⟩,⟨⟨41360245418699226949938490696,41360245418699226970558687154⟩,⟨10773840262747186142138591846,10773840262747186163022249215⟩⟩,⟨⟨40777191268633096577868667439,40777191268633096598165555532⟩,⟨10634112592427048431242229852,10634112592427048451774133760⟩⟩,⟨⟨40185929560700215867422813591,40185929560700215887360370367⟩,⟨10491624661005867336068092768,10491624661005867356238251419⟩⟩,⟨⟨39578842398149307598350487037,39578842398149307617924973049⟩,⟨10344392320674815735257463686,10344392320674815755061497358⟩⟩] +lemma amp7_04_12_eq : ∀ k : Fin 16, amp7_0Expr 4 12 k = amp7_04_12 k := by decide +kernel +noncomputable def amp7_04_13 : Fin 16 → CBox := ![⟨⟨38964062396852311987752402036,38964062396852312006963464732⟩,⟨10194544061302622071670313962,10194544061302622091107657728⟩⟩,⟨⟨38333518462564732033588891444,38333518462564732052436921276⟩,⟨10039973720638874076600542253,10039973720638874095667915245⟩⟩,⟨⟨37695834479804539876730504317,37695834479804539895207422144⟩,⟨9882943734709660300901298632,9882943734709660319596290581⟩⟩,⟨⟨37042450719137358627054790608,37042450719137358645158940260⟩,⟨9721216324032392138572224885,9721216324032392156890991453⟩⟩,⟨⟨36382519543077486949321297340,36382519543077486967048665676⟩,⟨9557197913543233282705656220,9557197913543233300647001344⟩⟩,⟨⟨35706952430978710392075127773,35706952430978710409445725715⟩,⟨9388508241009929510748922042,9388508241009929528314697713⟩⟩,⟨⟨35025472530481369293381562480,35025472530481369310374266906⟩,⟨9217709123208483644495841455,9217709123208483661680543267⟩⟩,⟨⟨34328416757559154422401262036,34328416757559154439011469184⟩,⟨9042265446402566958273367607,9042265446402566975072341167⟩⟩,⟨⟨33626127453700570134979681145,33626127453700570151207744343⟩,⟨8864907451324136416176378086,8864907451324136432589926844⟩⟩,⟨⟨32908314460568070234782291949,32908314460568070250626374750⟩,⟨8682931000002419880995476104,8682931000002419897019660971⟩⟩,⟨⟨32185995085203211666593284018,32185995085203211682051118590⟩,⟨8499249756460134714702072605,8499249756460134730336714524⟩⟩,⟨⟨31448191426810142417474198434,31448191426810142432556999479⟩,⟨8310974201781988961818386525,8310974201781988977062938419⟩⟩,⟨⟨30706660495203998639144902633,30706660495203998653834582664⟩,⟨8121218819281640838250443624,8121218819281640853100738749⟩⟩,⟨⟨29949666008790391497082949448,29949666008790391511376925966⟩,⟨7926889682697347361665666965,7926889682697347376117469757⟩⟩,⟨⟨29189780443587038980457972191,29189780443587038994358225194⟩,⟨7731322439515148033783960032,7731322439515148047838634016⟩⟩,⟨⟨28414426181809748560484758409,28414426181809748573984665691⟩,⟨7531196431271605626695276708,7531196431271605640347437474⟩⟩] +lemma amp7_04_13_eq : ∀ k : Fin 16, amp7_0Expr 4 13 k = amp7_04_13 k := by decide +kernel +noncomputable def amp7_04_14 : Fin 16 → CBox := ![⟨⟨27637080640873515851459855602,27637080640873515864572796448⟩,⟨7330092483041432277152304129,7330092483041432290406557146⟩⟩,⟨⟨26844226513243837676246506677,26844226513243837688956829202⟩,⟨7124436755348031956886148468,7124436755348031969734646028⟩⟩,⟨⟨26050352897178328790216880236,26050352897178328802527722657⟩,⟨6918083884758200747743557500,6918083884758200760188457864⟩⟩,⟨⟨25240884934298901644374691661,25240884934298901656276860379⟩,⟨6707175176996376665148907416,6707175176996376677183950627⟩⟩,⟨⟨24431452185863556031254817511,24431452185863556042761974222⟩,⟨6495873614970292560597467237,6495873614970292572227875337⟩⟩,⟨⟨23606279295269157568713658730,23606279295269157579811512219⟩,⟨6279997256106114458449533994,6279997256106114469667570811⟩⟩,⟨⟨22782293661536101734099695394,22782293661536101744797333127⟩,⟨6064059620565666567655671021,6064059620565666578465659567⟩⟩,⟨⟨21942343669019727732145059126,21942343669019727742429523892⟩,⟨5843508333865144110466985371,5843508333865144120861368456⟩⟩,⟨⟨21104849694531081655767703538,21104849694531081665642587144⟩,⟨5623259758294419894375283230,5623259758294419904357249411⟩⟩,⟨⟨20251064337910493589541488506,20251064337910493599006528375⟩,⟨5398332179446450270805321658,5398332179446450280370503941⟩⟩,⟨⟨19401147024884012926315105407,19401147024884012935367320204⟩,⟨5174110748446996729068032657,5174110748446996738218264214⟩⟩,⟨⟨18534475343928008709073812955,18534475343928008717712535062⟩,⟨4945109508397047022901689128,4945109508397047031632231702⟩⟩,⟨⟨17673264216654597034460316775,17673264216654597042689430394⟩,⟨4717267198118655927731186743,4717267198118655936046138758⟩⟩,⟨⟨16794653372743877960365456891,16794653372743877968173485527⟩,⟨4484496312031306876614063361,4484496312031306884505492418⟩⟩,⟨⟨15923329750023602575800314341,15923329750023602583195881379⟩,⟨4253400785223850293124955675,4253400785223850300598751052⟩⟩,⟨⟨15033711515838969387951239603,15033711515838969394926953311⟩,⟨4017161876444438549295384252,4017161876444438556344289012⟩⟩] +lemma amp7_04_14_eq : ∀ k : Fin 16, amp7_0Expr 4 14 k = amp7_04_14 k := by decide +kernel +noncomputable def amp7_04_15 : Fin 16 → CBox := ![⟨⟨14153521423645093472749722252,14153521423645093479310149233⟩,⟨3783199784228645031097142490,3783199784228645037726576715⟩⟩,⟨⟨13253790951781465859414305684,13253790951781465865551360159⟩,⟨3543786234992750815886911653,3543786234992750822088912077⟩⟩,⟨⟨12366068512016756521967288102,12366068512016756527687231611⟩,⟨3307369321525166180630502535,3307369321525166186411720293⟩⟩,⟨⟨11457048376785998800614830469,11457048376785998805910886859⟩,⟨3065056473631586437206625344,3065056473631586442558731074⟩⟩,⟨⟨10563260071195201064811492862,10563260071195201069690807776⟩,⟨2826633270511767719406143804,2826633270511767724337007279⟩⟩,⟨⟨9645633791071247971478404612,9645633791071247975930552069⟩,⟨2581660444753823028706433691,2581660444753823033205777488⟩⟩,⟨⟨8747468294059073359737032062,8747468294059073363771091196⟩,⟨2341740172299399884651043232,2341740172299399888728587089⟩⟩,⟨⟨7821643486831059402381412608,7821643486831059405987112430⟩,⟨2094273829805534677931488493,2094273829805534681575574661⟩⟩,⟨⟨6921213866164120835377178607,6921213866164120838565578946⟩,⟨1853480404442691528040315711,1853480404442691531263098482⟩⟩,⟨⟨5986997996073589996649899451,5986997996073589999406360114⟩,⟨1603527089250132358829383266,1603527089250132361615834107⟩⟩,⟨⟨5087372685039129767526239442,5087372685039129769866908463⟩,⟨1362741222863623934599049084,1362741222863623936965709983⟩⟩,⟨⟨4143033990395352502473607003,4143033990395352504378760599⟩,⟨1109895761162676722723611767,1109895761162676724650241003⟩⟩,⟨⟨3250014495413228346133315618,3250014495413228347626510091⟩,⟨870731121346295531197325850,870731121346295532708041245⟩⟩,⟨⟨2288527698933591183801816459,2288527698933591184852496656⟩,⟨613170481679804684559297382,613170481679804685622728372⟩⟩,⟨⟨1419782442513108681757680380,1419782442513108682407487931⟩,⟨380420923474277062169628155,380420923474277062828766719⟩⟩,⟨⟨403388193052863035522811825,403388193052863035706257914⟩,⟨108087267962443344092033658,108087267962443344278983853⟩⟩] +lemma amp7_04_15_eq : ∀ k : Fin 16, amp7_0Expr 4 15 k = amp7_04_15 k := by decide +kernel +noncomputable def amp7_04 : Fin 16 → Fin 16 → CBox := ![amp7_04_0,amp7_04_1,amp7_04_2,amp7_04_3,amp7_04_4,amp7_04_5,amp7_04_6,amp7_04_7,amp7_04_8,amp7_04_9,amp7_04_10,amp7_04_11,amp7_04_12,amp7_04_13,amp7_04_14,amp7_04_15] +lemma amp7_04_eq (i k : Fin 16) : amp7_0Expr 4 i k = amp7_04 i k := by + fin_cases i + · exact amp7_04_0_eq k + · exact amp7_04_1_eq k + · exact amp7_04_2_eq k + · exact amp7_04_3_eq k + · exact amp7_04_4_eq k + · exact amp7_04_5_eq k + · exact amp7_04_6_eq k + · exact amp7_04_7_eq k + · exact amp7_04_8_eq k + · exact amp7_04_9_eq k + · exact amp7_04_10_eq k + · exact amp7_04_11_eq k + · exact amp7_04_12_eq k + · exact amp7_04_13_eq k + · exact amp7_04_14_eq k + · exact amp7_04_15_eq k +noncomputable def amp7_05_0 : Fin 16 → CBox := ![⟨⟨1017365712714789582412,1017365712714806656212⟩,⟨(-8649277),8649282⟩⟩,⟨⟨32227844834901885180018,32227844834901945277190⟩,⟨(-30443786),30443938⟩⟩,⟨⟨144307603078629628353343,144307603078629725234573⟩,⟨(-49076495),49077175⟩⟩,⟨⟨401710817432016674520882,401710817432016812129440⟩,⟨(-69704918),69706811⟩⟩,⟨⟨846618630911081777873541,846618630911081953334801⟩,⟨(-88874594),88878584⟩⟩,⟨⟨1553203743542669544274406,1553203743542669759792852⟩,⟨(-109157596),109164916⟩⟩,⟨⟨2553427679062347536387104,2553427679062347790106762⟩,⟨(-128496428),128508463⟩⟩,⟨⟨3930825950684612355971439,3930825950684612649403087⟩,⟨(-148595623),148614150⟩⟩,⟨⟨5707149034948221291888609,5707149034948221623651904⟩,⟨(-167990161),168017060⟩⟩,⟨⟨7974992912616157603273367,7974992912616157974503158⟩,⟨(-187953565),187991153⟩⟩,⟨⟨10745843359115808013509729,10745843359115808423099256⟩,⟨(-207348839),207399486⟩⟩,⟨⟨14121091280701553057183412,14121091280701553506030838⟩,⟨(-227191331),227257887⟩⟩,⟨⟨18101889125021378311407097,18101889125021378798578011⟩,⟨(-246552709),246638028⟩⟩,⟨⟨22798164690230290408885678,22798164690230290935112099⟩,⟨(-266276136),266383589⟩⟩,⟨⟨28200671625299007046688031,28200671625299007611159772⟩,⟨(-285577905),285710821⟩⟩,⟨⟨34427613720176448625434016,34427613720176449228761472⟩,⟨(-305177998),305340263⟩⟩] +lemma amp7_05_0_eq : ∀ k : Fin 16, amp7_0Expr 5 0 k = amp7_05_0 k := by decide +kernel +noncomputable def amp7_05_1 : Fin 16 → CBox := ![⟨⟨41459290719596023701396978,41459290719596024342852285⟩,⟨(-324398995),324594402⟩⟩,⟨⟨49421914614835276365094033,49421914614835277045189338⟩,⟨(-343868277),344101214⟩⟩,⟨⟨58285289887787186486983824,58285289887787187205055019⟩,⟨(-362989933),363264645⟩⟩,⟨⟨68183360397692089594610300,68183360397692090351108873⟩,⟨(-382319110),382640474⟩⟩,⟨⟨79075409598275565416789351,79075409598275566211083119⟩,⟨(-401324468),401697169⟩⟩,⟨⟨91102827691590655214296079,91102827691590656046755579⟩,⟨(-420503170),420932559⟩⟩,⟨⟨104214368082311430049500797,104214368082311430919577461⟩,⟨(-439376357),439867544⟩⟩,⟨⟨118558572418822139446543938,118558572418822140354522327⟩,⟨(-458393565),458952359⟩⟩,⟨⟨134073672582852005439799426,134073672582852006385165105⟩,⟨(-477119484),477751404⟩⟩,⟨⟨150915057458186184084660442,150915057458186185067690711⟩,⟨(-495963786),496675084⟩⟩,⟨⟨169010464087999568475706810,169010464087999569495831432⟩,⟨(-514527932),515324518⟩⟩,⟨⟨188521815248313382165818294,188521815248313383223311190⟩,⟨(-533187700),534076247⟩⟩,⟨⟨209366398483646596557519735,209366398483646597651807019⟩,⟨(-551576044),552562836⟩⟩,⟨⟨231712348237249835740755396,231712348237249836872123012⟩,⟨(-570039541),571131656⟩⟩,⟨⟨255466566973823128603691729,255466566973823129771621321⟩,⟨(-588238459),589442533⟩⟩,⟨⟨280803069984181515662938027,280803069984181516867601337⟩,⟨(-606493926),607817417⟩⟩] +lemma amp7_05_1_eq : ∀ k : Fin 16, amp7_0Expr 5 1 k = amp7_05_1 k := by decide +kernel +noncomputable def amp7_05_2 : Fin 16 → CBox := ![⟨⟨307618458522706083434003884,307618458522706084674813386⟩,⟨(-624490152),625940030⟩⟩,⟨⟨336092289619148268001842143,336092289619148269279051481⟩,⟨(-642525864),644109946⟩⟩,⟨⟨366110966970354770416364258,366110966970354771729493556⟩,⟨(-660306459),662032026⟩⟩,⟨⟨397859242260386785839448420,397859242260386787188609169⟩,⟨(-678110774),679985977⟩⟩,⟨⟨431213445365565142851366494,431213445365565144236135516⟩,⟨(-695663107),697695517⟩⟩,⟨⟨466363167876582221127714333,466363167876582222547898543⟩,⟨(-713224498),715422577⟩⟩,⟨⟨503174809944199806588832842,503174809944199808044203939⟩,⟨(-730536239),732907819⟩⟩,⟨⟨541842440962969023384215113,541842440962969024874778130⟩,⟨(-747843328),750397158⟩⟩,⟨⟨582222696060299641118745460,582222696060299642644098651⟩,⟨(-764902435),767646586⟩⟩,⟨⟨624513753276140036344488249,624513753276140037904663649⟩,⟨(-781944015),784887494⟩⟩,⟨⟨668562668250543283720670392,668562668250543285315230170⟩,⟨(-798738735),801889827⟩⟩,⟨⟨714571351742874039573607259,714571351742874041202143039⟩,⟨(-815503790),818871732⟩⟩,⟨⟨762377486480516794548436625,762377486480516796210976411⟩,⟨(-832022660),835615923⟩⟩,⟨⟨812186333523575930250503951,812186333523575931946962128⟩,⟨(-848500387),852328410⟩⟩,⟨⟨863826430484116376720496000,863826430484116378450503326⟩,⟨(-864732233),868803649⟩⟩,⟨⟨917506000071359152666816133,917506000071359154430166154⟩,⟨(-880912051),885236471⟩⟩] +lemma amp7_05_2_eq : ∀ k : Fin 16, amp7_0Expr 5 2 k = amp7_05_2 k := by decide +kernel +noncomputable def amp7_05_3 : Fin 16 → CBox := ![⟨⟨973044683965568814972962705,973044683965568816769328213⟩,⟨(-896845994),901432181⟩⟩,⟨⟨1030653271883720174285090559,1030653271883720176114434553⟩,⟨(-912717564),917575273⟩⟩,⟨⟨1090142780287363172303205486,1090142780287363174165117053⟩,⟨(-928343020),933481118⟩⟩,⟨⟨1151726165495505752646781654,1151726165495505754540217983⟩,⟨(-943896255),949324609⟩⟩,⟨⟨1215206111117198394379527286,1215206111117198396305065498⟩,⟨(-959202943),964930493⟩⟩,⟨⟨1280797334109812438674184368,1280797334109812440631645328⟩,⟨(-974428020),980464717⟩⟩,⟨⟨1348294499353228943358554610,1348294499353228945347498066⟩,⟨(-989405963),995760790⟩⟩,⟨⟨1417913673107950988705408156,1417913673107950990725673631⟩,⟨(-1004293333),1010976292⟩⟩,⟨⟨1489441837489806939239598145,1489441837489806941290818507⟩,⟨(-1018932866),1025952953⟩⟩,⟨⟨1563095991521031543023329216,1563095991521031545105085916⟩,⟨(-1033473265),1040840501⟩⟩,⟨⟨1638655792425954714239670991,1638655792425954716351806866⟩,⟨(-1047765036),1055488404⟩⟩,⟨⟨1716338750384461638970483115,1716338750384461641112726979⟩,⟨(-1061949492),1070038997⟩⟩,⟨⟨1795917577556343211962250610,1795917577556343214134217455⟩,⟨(-1075884472),1084349051⟩⟩,⟨⟨1877609868733088064714481105,1877609868733088066915996752⟩,⟨(-1089704311),1098553925⟩⟩,⟨⟨1961181792819992280823689030,1961181792819992283054341857⟩,⟨(-1103273794),1112517302⟩⟩,⟨⟨2046850597829250581740870232,2046850597829250584000465972⟩,⟨(-1116720654),1126367938⟩⟩] +lemma amp7_05_3_eq : ∀ k : Fin 16, amp7_0Expr 5 3 k = amp7_05_3 k := by decide +kernel +noncomputable def amp7_05_4 : Fin 16 → CBox := ![⟨⟨2134376333215646663432048323,2134376333215646665717870852⟩,⟨(-1129916262),1139976076⟩⟩,⟨⟨2223975464049050680457263121,2223975464049050682771710882⟩,⟨(-1142982092),1153464208⟩⟩,⟨⟨2315402366125218524907797788,2315402366125218527250350329⟩,⟨(-1155795782),1166708814⟩⟩,⟨⟨2408872280684075507131755406,2408872280684075509502127948⟩,⟨(-1168472853),1179826430⟩⟩,⟨⟨2504134377618229002678290582,2504134377618229005076009938⟩,⟨(-1180896918),1192699488⟩⟩,⟨⟨2601402228747062344216980508,2601402228747062346641931516⟩,⟨(-1193177826),1205438842⟩⟩,⟨⟨2700420287741234992553645583,2700420287741234995005121740⟩,⟨(-1205204900),1217932611⟩⟩,⟨⟨2801400006700950694721233840,2801400006700950697199194443⟩,⟨(-1217082571),1230286223⟩⟩,⟨⟨2904081634627201913755278269,2904081634627201916259327216⟩,⟨(-1228705631),1242393246⟩⟩,⟨⟨3008674048861856003575380190,3008674048861856006104426118⟩,⟨(-1240173328),1254353911⟩⟩,⟨⟨3114913827091087447542966565,3114913827091087450097459922⟩,⟨(-1251385699),1266067015⟩⟩,⟨⟨3223006812058119978481463601,3223006812058119981060997707⟩,⟨(-1262437021),1277627805⟩⟩,⟨⟨3332686465209943391180225147,3332686465209943393784441173⟩,⟨(-1273232378),1288940107⟩⟩,⟨⟨3444155129960154740842225629,3444155129960154743470509532⟩,⟨(-1283861268),1300094375⟩⟩,⟨⟨3557143728219029241487109645,3557143728219029244139382151⟩,⟨(-1294233634),1310999283⟩⟩,⟨⟨3671850634329706808878002201,3671850634329706811553764286⟩,⟨(-1304434380),1321740669⟩⟩] +lemma amp7_05_4_eq : ∀ k : Fin 16, amp7_0Expr 5 4 k = amp7_05_4 k := by decide +kernel +noncomputable def amp7_05_5 : Fin 16 → CBox := ![⟨⟨3788004828890165630851767163,3788004828890165633550658963⟩,⟨(-1314378134),1332231885⟩⟩,⟨⟨3905800242272824150387876314,3905800242272824153109614508⟩,⟨(-1324145369),1342554318⟩⟩,⟨⟨4024964533395238301619985443,4024964533395238304364213006⟩,⟨(-1333655245),1352625842⟩⟩,⟨⟨4145686708418613027467141181,4145686708418613030233537629⟩,⟨(-1342983953),1362523542⟩⟩,⟨⟨4267693745496789283839876158,4267693745496789286628011086⟩,⟨(-1352055038),1372169675⟩⟩,⟨⟨4391169240786213740947055220,4391169240786213743748986484⟩,⟨(-1360940553),1381637159⟩⟩,⟨⟨4515840153749391088355894394,4515840153749391091179078131⟩,⟨(-1369568293),1390852502⟩⟩,⟨⟨4641884178945692237125682973,4641884178945692239969626164⟩,⟨(-1378006299),1399884583⟩⟩,⟨⟨4769028940240375244673929926,4769028940240375247538018886⟩,⟨(-1386186496),1408664042⟩⟩,⟨⟨4897445732925117417407021078,4897445732925117420290931042⟩,⟨(-1394173029),1417255834⟩⟩,⟨⟨5026863549246854130101949885,5026863549246854133004993968⟩,⟨(-1401901838),1425594620⟩⟩,⟨⟨5157446781166343515116159516,5157446781166343518037970301⟩,⟨(-1409433287),1433741538⟩⟩,⟨⟨5288926514038202102834962209,5288926514038202105775339515⟩,⟨(-1416707223),1441635169⟩⟩,⟨⟨5421459725686305868348433875,5421459725686305871306606307⟩,⟨(-1423780327),1449332932⟩⟩,⟨⟨5554780339909606551871328981,5554780339909606554847079070⟩,⟨(-1430596257),1456777233⟩⟩,⟨⟨5689037402459319914022576195,5689037402459319917015655313⟩,⟨(-1437208104),1464021865⟩⟩] +lemma amp7_05_5_eq : ∀ k : Fin 16, amp7_0Expr 5 5 k = amp7_05_5 k := by decide +kernel +noncomputable def amp7_05_6 : Fin 16 → CBox := ![⟨⟨5823968441393309566224337274,5823968441393309569233231363⟩,⟨(-1443563249),1471012972⟩⟩,⟨⟨5959714044899289792209824059,5959714044899289795235403116⟩,⟨(-1449711279),1477800802⟩⟩,⟨⟨6096016131460073493112507015,6096016131460073496153630255⟩,⟨(-1455603211),1484335158⟩⟩,⟨⟨6233006298189215733949113574,6233006298189215737006065350⟩,⟨(-1461285209),1490662823⟩⟩,⟨⟨6370431660394543907027334590,6370431660394543910099239563⟩,⟨(-1466711851),1496737183⟩⟩,⟨⟨6508414282079257380697125845,6508414282079257383783834764⟩,⟨(-1471925948),1502601624⟩⟩,⟨⟨6646707301904864091638304435,6646707301904864094735709485⟩,⟨(-1476885569),1508213052⟩⟩,⟨⟨6785422699654169367200343970,6785422699654169370311957286⟩,⟨(-1481630238),1513611519⟩⟩,⟨⟨6924320483909415368684502808,6924320483909415371809445312⟩,⟨(-1486121451),1518757390⟩⟩,⟨⟨7063501989456468218077159757,7063501989456468221214871297⟩,⟨(-1490395507),1523687441⟩⟩,⟨⟨7202734961332202776369393882,7202734961332202779519585057⟩,⟨(-1494417266),1528365437⟩⟩,⟨⟨7342109518243493789775386880,7342109518243493792937240250⟩,⟨(-1498219859),1532824935⟩⟩,⟨⟨7481402028133446260150497563,7481402028133446263323703240⟩,⟨(-1501771455),1537033050⟩⟩,⟨⟨7620690811554856991787015662,7620690811554856994971480964⟩,⟨(-1505102069),1541020164⟩⟩,⟨⟨7759761765703628867195494500,7759761765703628870388719511⟩,⟨(-1508183129),1544756698⟩⟩,⟨⟨7898680819171865496718444953,7898680819171865499921799258⟩,⟨(-1511041577),1548269904⟩⟩] +lemma amp7_05_6_eq : ∀ k : Fin 16, amp7_0Expr 5 6 k = amp7_05_6 k := by decide +kernel +noncomputable def amp7_05_7 : Fin 16 → CBox := ![⟨⟨8037244324657834612473043526,8037244324657834615685752115⟩,⟨(-1513652056),1551533465⟩⟩,⟨⟨8175505212462621446688298976,8175505212462621449910241662⟩,⟨(-1516038476),1554571540⟩⟩,⟨⟨8313271236982902318810129272,8313271236982902322039635283⟩,⟨(-1518178653),1557361041⟩⟩,⟨⟨8450581710525803770002139851,8450581710525803773239722473⟩,⟨(-1520093505),1559923069⟩⟩,⟨⟨8587256755412933326800117584,8587256755412933330044506892⟩,⟨(-1521763982),1562237728⟩⟩,⟨⟨8723321431972879242044091580,8723321431972879245295690241⟩,⟨(-1523208041),1564323091⟩⟩,⟨⟨8858609216839208422853347847,8858609216839208426111033974⟩,⟨(-1524409733),1566162426⟩⟩,⟨⟨8993130269122809604715462946,8993130269122809607978836940⟩,⟨(-1525384085),1567770807⟩⟩,⟨⟨9126732426498762490483696550,9126732426498762493752224715⟩,⟨(-1526118219),1569134639⟩⟩,⟨⟨9259410281325397353364265890,9259410281325397356637678038⟩,⟨(-1526624256),1570266018⟩⟩,⟨⟨9391027059631885634987797677,9391027059631885638265233776⟩,⟨(-1526892363),1571154466⟩⟩,⟨⟨9521561104079381979419597349,9521561104079381982700721096⟩,⟨(-1526931776),1571809116⟩⟩,⟨⟨9650892077252799423982764241,9650892077252799427266705308⟩,⟨(-1526735687),1572222594⟩⟩,⟨⟨9778981370569384261014094640,9778981370569384264300355387⟩,⟨(-1526310463),1572401085⟩⟩,⟨⟨9905726152639809843082708684,9905726152639809846370464560⟩,⟨(-1525652299),1572340299⟩⟩,⟨⟨10031070142211902031629835846,10031070142211902034918301365⟩,⟨(-1524764713),1572043488⟩⟩] +lemma amp7_05_7_eq : ∀ k : Fin 16, amp7_0Expr 5 7 k = amp7_05_7 k := by decide +kernel +noncomputable def amp7_05_8 : Fin 16 → CBox := ![⟨⟨10154929105121458592783714399,10154929105121458596073378393⟩,⟨(-1523646886),1571509437⟩⟩,⟨⟨10277228344774870550075549360,10277228344774870553367139474⟩,⟨(-1522299493),1570738469⟩⟩,⟨⟨10397903337713655820586619766,10397903337713655823879239003⟩,⟨(-1520724694),1569732439⟩⟩,⟨⟨10516860206617878169415484086,10516860206617878172708461536⟩,⟨(-1518920327),1568488744⟩⟩,⟨⟨10634055275149534854577844719,10634055275149534857870507205⟩,⟨(-1516891519),1567012304⟩⟩,⟨⟨10749374695591017523834482596,10749374695591017527126117883⟩,⟨(-1514633279),1565297591⟩⟩,⟨⟨10862796798838857611106509322,10862796798838857614396650827⟩,⟨(-1512153697),1563352594⟩⟩,⟨⟨10974186951129577911174933568,10974186951129577914462803820⟩,⟨(-1509444947),1561168852⟩⟩,⟨⟨11083546675297232711892292633,11083546675297232715177435657⟩,⟨(-1506518082),1558757425⟩⟩,⟨⟨11190719708089349789175657215,11190719708089349792457735826⟩,⟨(-1503362442),1556106917⟩⟩,⟨⟨11295731974597181553844804040,11295731974597181557123269539⟩,⟨(-1499992043),1553231464⟩⟩,⟨⟨11398404708883200999854567119,11398404708883201003128243019⟩,⟨(-1496393379),1550116722⟩⟩,⟨⟨11498789475413175210660980995,11498789475413175213930321121⟩,⟨(-1492583438),1546779918⟩⟩,⟨⟨11596684100503760015395399226,11596684100503760018659043472⟩,⟨(-1488545861),1543203740⟩⟩,⟨⟨11692167053261121762268140447,11692167053261121765526806324⟩,⟨(-1484300613),1539408525⟩⟩,⟨⟨11785011813049447605297364579,11785011813049447608549015719⟩,⟨(-1479828464),1535373976⟩⟩] +lemma amp7_05_8_eq : ∀ k : Fin 16, amp7_0Expr 5 8 k = amp7_05_8 k := by decide +kernel +noncomputable def amp7_05_9 : Fin 16 → CBox := ![⟨⟨11875325048569344300707190436,11875325048569344303951570644⟩,⟨(-1475152374),1531123553⟩⟩,⟨⟨11962854916411658332270523136,11962854916411658335506892232⟩,⟨(-1470250225),1526633953⟩⟩,⟨⟨12047737611262769686777541922,12047737611262769690008082952⟩,⟨(-1465147984),1521931784⟩⟩,⟨⟨12129694951829510848910476440,12129694951829510852131684649⟩,⟨(-1459820625),1516990709⟩⟩,⟨⟨12208894018594742988372627830,12208894018594742991584323241⟩,⟨(-1454297142),1511840510⟩⟩,⟨⟨12285029235075145118787809592,12285029235075145121989969182⟩,⟨(-1448549574),1506451785⟩⟩,⟨⟨12358299963021469187600279033,12358299963021469190791568208⟩,⟨(-1442609970),1500857522⟩⟩,⟨⟨12428372128096910060364575977,12428372128096910063544949706⟩,⟨(-1436447400),1495025219⟩⟩,⟨⟨12495478806982420227391955176,12495478806982420230560417868⟩,⟨(-1430096998),1488991106⟩⟩,⟨⟨12559256276019802218552440002,12559256276019802221707918946⟩,⟨(-1423524831),1482719537⟩⟩,⟨⟨12619972801525971471855516153,12619972801525971475004899109⟩,⟨(-1416769149),1476250027⟩⟩,⟨⟨12677233806482011584367738452,12677233806482011587503773156⟩,⟨(-1409792979),1469543742⟩⟩,⟨⟨12731344265802869003321517603,12731344265802869006443980801⟩,⟨(-1402637727),1462643524⟩⟩,⟨⟨12781877488373212778902286737,12781877488373212782010028207⟩,⟨(-1395263331),1455507303⟩⟩,⟨⟨12829176724540682361904058657,12829176724540682364997837952⟩,⟨(-1387714397),1448181302⟩⟩,⟨⟨12872781847134098500465359340,12872781847134098503543365893⟩,⟨(-1379947727),1440620153⟩⟩] +lemma amp7_05_9_eq : ∀ k : Fin 16, amp7_0Expr 5 9 k = amp7_05_9 k := by decide +kernel +noncomputable def amp7_05_10 : Fin 16 → CBox := ![⟨⟨12913076000709954106289492960,12913076000709954109353800510⟩,⟨(-1372011176),1432873517⟩⟩,⟨⟨12949564233877359602045802479,12949564233877359605093794187⟩,⟨(-1363858352),1424892671⟩⟩,⟨⟨12982671260697089637469197176,12982671260697089640500507245⟩,⟨(-1355540413),1416730774⟩⟩,⟨⟨13011865845697627165943149194,13011865845697627168958023410⟩,⟨(-1347007717),1408335678⟩⟩,⟨⟨13037616009409894490959757925,13037616009409894493956497456⟩,⟨(-1338314782),1399764110⟩⟩,⟨⟨13059352694651544112242315771,13059352694651544115221275782⟩,⟨(-1329408646),1390960424⟩⟩,⟨⟨13077589032858803751805400248,13077589032858803754765921217⟩,⟨(-1320347258),1381984988⟩⟩,⟨⟨13091716523008848061638137234,13091716523008848064579248553⟩,⟨(-1311074263),1372778579⟩⟩,⟨⟨13102295285879987919467204561,13102295285879987922388231979⟩,⟨(-1301651112),1363405289⟩⟩,⟨⟨13108675662500827681045214785,13108675662500827683945399516⟩,⟨(-1292017977),1353802225⟩⟩,⟨⟨13111466722795377662607713435,13111466722795377665485906897⟩,⟨(-1282239892),1344037296⟩⟩,⟨⟨13109975835423449522722779790,13109975835423449525602847549⟩,⟨(-1272253467),1334043843⟩⟩,⟨⟨13104863068938931646278510902,13104863068938931649137019215⟩,⟨(-1262127411),1323893690⟩⟩,⟨⟨13095390895588513060905363462,13095390895588513063742078019⟩,⟨(-1251794672),1313516306⟩⟩,⟨⟨13082272531117872667120843520,13082272531117872669935122003⟩,⟨(-1241327732),1302987536⟩⟩,⟨⟨13064723507257033416068587328,13064723507257033418860385880⟩,⟨(-1230655773),1292232865⟩⟩] +lemma amp7_05_10_eq : ∀ k : Fin 16, amp7_0Expr 5 10 k = amp7_05_10 k := by decide +kernel +noncomputable def amp7_05_11 : Fin 16 → CBox := ![⟨⟨13043512445221825670759183875,13043512445221825673527894563⟩,⟨(-1219855157),1281332277⟩⟩,⟨⟨13017805760334312458714215862,13017805760334312461459897033⟩,⟨(-1208851185),1270207143⟩⟩,⟨⟨12988429859341489298882482948,12988429859341489301603786002⟩,⟨(-1197724215),1258941717⟩⟩,⟨⟨12954499720255460278937362575,12954499720255460281635339101⟩,⟨(-1186395540),1247453121⟩⟩,⟨⟨12916902050911340020871381825,12916902050911340023544113508⟩,⟨(-1174949644),1235830018⟩⟩,⟨⟨12874697911143072118737873893,12874697911143072121385402544⟩,⟨(-1163303675),1223985132⟩⟩,⟨⟨12828836976547584761161858126,12828836976547584763783021239⟩,⟨(-1151546384),1212011688⟩⟩,⟨⟨12778323730974931496849270651,12778323730974931499447603661⟩,⟨(-1139590624),1199817846⟩⟩,⟨⟨12724173653412829156902042275,12724173653412829159473321634⟩,⟨(-1127529566),1187501567⟩⟩,⟨⟨12665331797658554988171722429,12665331797658554990715851660⟩,⟨(-1115271601),1174966266⟩⟩,⟨⟨12602882471102409487332284349,12602882471102409489849677555⟩,⟨(-1102914494),1162314821⟩⟩,⟨⟨12535708225070645788603915868,12535708225070645791092920286⟩,⟨(-1090361992),1149445711⟩⟩,⟨⟨12464965433213760034575798202,12464965433213760037036365666⟩,⟨(-1077716640),1136466932⟩⟩,⟨⟨12389470828282574152531253659,12389470828282574154962880905⟩,⟨(-1064877342),1123271810⟩⟩,⟨⟨12310456327929295113139825718,12310456327929295115541582712⟩,⟨(-1051951630),1109973684⟩⟩,⟨⟨12226669257357300082419917733,12226669257357300084790896301⟩,⟨(-1038833346),1096460493⟩⟩] +lemma amp7_05_11_eq : ∀ k : Fin 16, amp7_0Expr 5 11 k = amp7_05_11 k := by decide +kernel +noncomputable def amp7_05_12 : Fin 16 → CBox := ![⟨⟨12139420827114858740631480403,12139420827114858742986414025⟩,⟨(-1025635235),1082851159⟩⟩,⟨⟨12047385059268084752522590852,12047385059268084754848167714⟩,⟨(-1012245837),1069027975⟩⟩,⟨⟨11951956513609678101913899585,11951956513609678104209629503⟩,⟨(-998783361),1055115722⟩⟩,⟨⟨11851731667654209172104826855,11851731667654209174370521321⟩,⟨(-985130777),1040990755⟩⟩,⟨⟨11748192836559880532548847602,11748192836559880534784011376⟩,⟨(-971412036),1026784012⟩⟩,⟨⟨11639854320292927853770116583,11639854320292927855974815384⟩,⟨(-957504247),1012365598⟩⟩,⟨⟨11528290994826055289446390298,11528290994826055291619396858⟩,⟨(-943537407),997872934⟩⟩,⟨⟨11411929904329072427606585285,11411929904329072429749626831⟩,⟨(-929382438),983169528⟩⟩,⟨⟨11292443748676301658432349475,11292443748676301660542871341⟩,⟨(-915175727),968399650⟩⟩,⟨⟨11168166729462903619185470390,11168166729462903621263686270⟩,⟨(-900781643),953419820⟩⟩,⟨⟨11040875160160211468164437515,11040875160160211470209652615⟩,⟨(-886343344),938381566⟩⟩,⟨⟨10908804229451485827749277574,10908804229451485829761018421⟩,⟨(-871718247),923133988⟩⟩,⟨⟨10773840262747186151433910629,10773840262747186153411042457⟩,⟨(-857056702),907836326⟩⟩,⟨⟨10634112592427048440376427585,10634112592427048442328364709⟩,⟨(-842208719),892329774⟩⟩,⟨⟨10491624661005867345040865664,10491624661005867346958293535⟩,⟨(-827332323),876781799⟩⟩,⟨⟨10344392320674815744066795359,10344392320674815745949494875⟩,⟨(-812269607),861025143⟩⟩] +lemma amp7_05_12_eq : ∀ k : Fin 16, amp7_0Expr 5 12 k = amp7_05_12 k := by decide +kernel +noncomputable def amp7_05_13 : Fin 16 → CBox := ![⟨⟨10194544061302622080315990889,10194544061302622082163889793⟩,⟨(-797186808),845236074⟩⟩,⟨⟨10039973720638874085080546274,10039973720638874086894527329⟩,⟨(-781917529),829238269⟩⟩,⟨⟨9882943734709660309215510055,9882943734709660310993463640⟩,⟨(-766636826),813217447⟩⟩,⟨⟨9721216324032392146718620296,9721216324032392148460875632⟩,⟨(-751169164),796987526⟩⟩,⟨⟨9557197913543233290684213780,9557197913543233292389675059⟩,⟨(-735699110),780744415⟩⟩,⟨⟨9388508241009929518557609081,9388508241009929520232319771⟩,⟨(-720041250),764291481⟩⟩,⟨⟨9217709123208483652134738547,9217709123208483653773084642⟩,⟨(-704390450),747835665⟩⟩,⟨⟨9042265446402566965740428203,9042265446402566967341973962⟩,⟨(-688550572),731168880⟩⟩,⟨⟨8864907451324136423471790381,8864907451324136425036509019⟩,⟨(-672727689),714510068⟩⟩,⟨⟨8682931000002419888117174303,8682931000002419889645383335⟩,⟨(-656713962),697638643⟩⟩,⟨⟨8499249756460134721650358525,8499249756460134723141315639⟩,⟨(-640727719),680786667⟩⟩,⟨⟨8310974201781988968591168860,8310974201781988970048634148⟩,⟨(-624548288),663719850⟩⟩,⟨⟨8121218819281640844848144777,8121218819281640846267140868⟩,⟨(-608407475),646684675⟩⟩,⟨⟨7926889682697347368086162758,7926889682697347369466826674⟩,⟨(-592070452),629431733⟩⟩,⟨⟨7731322439515148040027801612,7731322439515148041370422108⟩,⟨(-575783933),612223460⟩⟩,⟨⟨7531196431271605632760298313,7531196431271605634063946588⟩,⟨(-559297381),594793668⟩⟩] +lemma amp7_05_13_eq : ∀ k : Fin 16, amp7_0Expr 5 13 k = amp7_05_13 k := by decide +kernel +noncomputable def amp7_05_14 : Fin 16 → CBox := ![⟨⟨7330092483041432283039195297,7330092483041432284307118107⟩,⟨(-542874109),577422546⟩⟩,⟨⟨7124436755348031962592691448,7124436755348031963821600782⟩,⟨(-526246022),559825156⟩⟩,⟨⟨6918083884758200753270591751,6918083884758200754460979582⟩,⟨(-509695057),542301601⟩⟩,⟨⟨6707175176996376670494150650,6707175176996376671644446242⟩,⟨(-492933337),524545820⟩⟩,⟨⟨6495873614970292565761922777,6495873614970292566875345769⟩,⟨(-476263867),506880436⟩⟩,⟨⟨6279997256106114463430839697,6279997256106114464504503748⟩,⟨(-459376293),488975386⟩⟩,⟨⟨6064059620565666572455011167,6064059620565666573490865820⟩,⟨(-442597673),471179002⟩⟩,⟨⟨5843508333865144115081899016,5843508333865144116077436007⟩,⟨(-425591852),453133671⟩⟩,⟨⟨5623259758294419898807156874,5623259758294419899762776785⟩,⟨(-408713652),435217387⟩⟩,⟨⟨5398332179446450275051571754,5398332179446450275968203998⟩,⟨(-391596959),417040558⟩⟩,⟨⟨5174110748446996733130274846,5174110748446996734006495153⟩,⟨(-374629038),399015830⟩⟩,⟨⟨4945109508397047026777186796,4945109508397047027613862763⟩,⟨(-357408524),380715979⟩⟩,⟨⟨4717267198118655931421819464,4717267198118655932219251621⟩,⟨(-340361141),362594723⟩⟩,⟨⟨4484496312031306880116901603,4484496312031306880873153952⟩,⟨(-323043390),344179868⟩⟩,⟨⟨4253400785223850296442189000,4253400785223850297158718540⟩,⟨(-305927380),325974650⟩⟩,⟨⟨4017161876444438552423836692,4017161876444438553099882390⟩,⟨(-288518290),307452112⟩⟩] +lemma amp7_05_14_eq : ∀ k : Fin 16, amp7_0Expr 5 14 k = amp7_05_14 k := by decide +kernel +noncomputable def amp7_05_15 : Fin 16 → CBox := ![⟨⟨3783199784228645034039376375,3783199784228645034675163654⟩,⟨(-271345339),289176443⟩⟩,⟨⟨3543786234992750818639430354,3543786234992750819234142504⟩,⟨(-253849755),270552447⟩⟩,⟨⟨3307369321525166183196329864,3307369321525166183750480160⟩,⟨(-236632890),252221294⟩⟩,⟨⟨3065056473631586439581836846,3065056473631586440095111404⟩,⟨(-219053953),233500279⟩⟩,⟨⟨2826633270511767721594355964,2826633270511767722067276130⟩,⟨(-201808416),215130998⟩⟩,⟨⟨2581660444753823030703131286,2581660444753823031134635965⟩,⟨(-184146342),196314310⟩⟩,⟨⟨2341740172299399886460641342,2341740172299399886851471667⟩,⟨(-166891340),177928508⟩⟩,⟨⟨2094273829805534679548615651,2094273829805534679898071885⟩,⟨(-149140852),159011654⟩⟩,⟨⟨1853480404442691529470536178,1853480404442691529779449487⟩,⟨(-131903444),140639329⟩⟩,⟨⟨1603527089250132360065992741,1603527089250132360333005265⟩,⟨(-114047646),121605443⟩⟩,⟨⟨1362741222863623935649432662,1362741222863623935876050252⟩,⟨(-96872877),103295795⟩⟩,⟨⟨1109895761162676723578741400,1109895761162676723763124558⟩,⟨(-78865429),84096626⟩⟩,⟨⟨870731121346295531867960560,870731121346295532012313602⟩,⟨(-61850197),65954156⟩⟩,⟨⟨613170481679804685031439076,613170481679804685132916841⟩,⟨(-43543935),46433951⟩⟩,⟨⟨380420923474277062462502691,380420923474277062524929798⟩,⟨(-27010779),28803792⟩⟩,⟨⟨108087267962443344175239691,108087267962443344192663167⟩,⟨(-7673799),8183240⟩⟩] +lemma amp7_05_15_eq : ∀ k : Fin 16, amp7_0Expr 5 15 k = amp7_05_15 k := by decide +kernel +noncomputable def amp7_05 : Fin 16 → Fin 16 → CBox := ![amp7_05_0,amp7_05_1,amp7_05_2,amp7_05_3,amp7_05_4,amp7_05_5,amp7_05_6,amp7_05_7,amp7_05_8,amp7_05_9,amp7_05_10,amp7_05_11,amp7_05_12,amp7_05_13,amp7_05_14,amp7_05_15] +lemma amp7_05_eq (i k : Fin 16) : amp7_0Expr 5 i k = amp7_05 i k := by + fin_cases i + · exact amp7_05_0_eq k + · exact amp7_05_1_eq k + · exact amp7_05_2_eq k + · exact amp7_05_3_eq k + · exact amp7_05_4_eq k + · exact amp7_05_5_eq k + · exact amp7_05_6_eq k + · exact amp7_05_7_eq k + · exact amp7_05_8_eq k + · exact amp7_05_9_eq k + · exact amp7_05_10_eq k + · exact amp7_05_11_eq k + · exact amp7_05_12_eq k + · exact amp7_05_13_eq k + · exact amp7_05_14_eq k + · exact amp7_05_15_eq k +noncomputable def amp7_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp7_00,amp7_01,amp7_02,amp7_03,amp7_04,amp7_05] +lemma amp7_0_eq (j : Fin 6) (i k : Fin 16) : amp7_0Expr j i k = amp7_0 j i k := by + fin_cases j + · exact amp7_00_eq i k + · exact amp7_01_eq i k + · exact amp7_02_eq i k + · exact amp7_03_eq i k + · exact amp7_04_eq i k + · exact amp7_05_eq i k +lemma amp7_0_contains (j : Fin 6) (i k : Fin 16) : + (amp7_0 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude false 7 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp7_0_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 7 j) (bLookup_contains 7 j) false) +noncomputable def amp7_1Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 7 j) (bLookup 7 j) true) +noncomputable def amp7_10_0 : Fin 16 → CBox := ![⟨⟨(-178776584874023315385344282),(-178776584874023315307284498)⟩,⟨(-516083547009096694099450847),(-516083547009096694019732261)⟩⟩,⟨⟨(-629264447029517718600603359),(-629264447029517718324026786)⟩,⟨(-1816529989419765287871633375),(-1816529989419765287585786352)⟩⟩,⟨⟨(-1014414495963543607132310588),(-1014414495963543606685066953)⟩,⟨(-2928362411572052200112623163),(-2928362411572052199647822717)⟩⟩,⟨⟨(-1440842106367455813814265547),(-1440842106367455813178651625)⟩,⟨(-4159352889854990064009723961),(-4159352889854990063348487483)⟩⟩,⟨⟨(-1837153108049314193674326890),(-1837153108049314192863368553)⟩,⟨(-5303404207374145887410717325),(-5303404207374145886566116101)⟩⟩,⟨⟨(-2256524817754308918408343468),(-2256524817754308917412015872)⟩,⟨(-6514026054817607367431530694),(-6514026054817607366393409348)⟩⟩,⟨⟨(-2656435792071101113877166469),(-2656435792071101112703889848)⟩,⟨(-7668469598186034814841328296),(-7668469598186034813618142415)⟩⟩,⟨⟨(-3072133445990435320873677675),(-3072133445990435319516586043)⟩,⟨(-8868485360145152285385330470),(-8868485360145152283970118533)⟩⟩,⟨⟨(-3473340580412691301245951334),(-3473340580412691299711334755)⟩,⟨(-10026670595442591582468101257),(-10026670595442591580867218014)⟩⟩,⟨⟨(-3886397599776523266234322382),(-3886397599776523264517480589)⟩,⟨(-11219063502044455817013680882),(-11219063502044455815223210032)⟩⟩,⟨⟨(-4287805485929443701331700529),(-4287805485929443699437026258)⟩,⟨(-12377828257670592145019783558),(-12377828257670592143042917154)⟩⟩,⟨⟨(-4698569893355039728540875860),(-4698569893355039726464520191)⟩,⟨(-13563602963674017037797224875),(-13563602963674017035630473304)⟩⟩,⟨⟨(-5099502883647184282835551234),(-5099502883647184280582045775)⟩,⟨(-14720996813034873396699431430),(-14720996813034873394347868238)⟩⟩,⟨⟨(-5508052685234101319058056687),(-5508052685234101316624357142)⟩,⟨(-15900378502652747127597447397),(-15900378502652747125058488649)⟩⟩,⟨⟨(-5908018787060499829048845905),(-5908018787060499826437871076)⟩,⟨(-17054981185433729371854776601),(-17054981185433729369129856392)⟩⟩,⟨⟨(-6314304889329281699461809925),(-6314304889329281696670903898)⟩,⟨(-18227828137998154551392034259),(-18227828137998154548478633519)⟩⟩] +lemma amp7_10_0_eq : ∀ k : Fin 16, amp7_1Expr 0 0 k = amp7_10_0 k := by decide +kernel +noncomputable def amp7_10_1 : Fin 16 → CBox := ![⟨⟨(-6712905375084154823140962584),(-6712905375084154820173698309)⟩,⟨(-19378488626746612490555160577),(-19378488626746612487457333280)⟩⟩,⟨⟨(-7116811458893626803706224473),(-7116811458893626800560642294)⟩,⟨(-20544465057820243453704177063),(-20544465057820243450420587794)⟩⟩,⟨⟨(-7513700288185479523274166028),(-7513700288185479519953513748)⟩,⟨(-21690184419970276427710565870),(-21690184419970276424244874394)⟩⟩,⟨⟨(-7915071511567247981253796575),(-7915071511567247977754319630)⟩,⟨(-22848843339292443597542571364),(-22848843339292443593887590277)⟩⟩,⟨⟨(-8309934963699564223900550017),(-8309934963699564220227383176)⟩,⟨(-23988715941201132048759423241),(-23988715941201132044924674504)⟩⟩,⟨⟨(-8708593155276932934437121588),(-8708593155276932930588583186)⟩,⟨(-25139543012310348167093283427),(-25139543012310348163077003461)⟩⟩,⟨⟨(-9101138730168082675585980061),(-9101138730168082671562341662)⟩,⟨(-26272724478973356684523524224),(-26272724478973356680321517996)⟩⟩,⟨⟨(-9496891073954188852868729265),(-9496891073954188848671411841)⟩,⟨(-27415163090060025287695049840),(-27415163090060025283314031387)⟩⟩,⟨⟨(-9886841054724459428800282821),(-9886841054724459424429442618)⟩,⟨(-28540851721901050824755079527),(-28540851721901050820190773635)⟩⟩,⟨⟨(-10279485372927895296838501161),(-10279485372927895292292535561)⟩,⟨(-29674318235953704695388396298),(-29674318235953704690638371248)⟩⟩,⟨⟨(-10666572908823690778938873209),(-10666572908823690774223622474)⟩,⟨(-30791743701200636932674878664),(-30791743701200636927751467628)⟩⟩,⟨⟨(-11055901047314695425996259863),(-11055901047314695421107680414)⟩,⟨(-31915637229005024097356912391),(-31915637229005024092250267620)⟩⟩,⟨⟨(-11439867680844907711382645195),(-11439867680844907706327254457)⟩,⟨(-33024053425147536342335883959),(-33024053425147536337060452475)⟩⟩,⟨⟨(-11825667778884814564288707801),(-11825667778884814559060322328)⟩,⟨(-34137762377431157506187557401),(-34137762377431157500726982570)⟩⟩,⟨⟨(-12206261841045965252410329449),(-12206261841045965247013125705)⟩,⟨(-35236442798634725061754767556),(-35236442798634725056116865264)⟩⟩,⟨⟨(-12588319915260722393449366498),(-12588319915260722387881957449)⟩,⟨(-36339349458604525329406044731),(-36339349458604525323588003455)⟩⟩] +lemma amp7_10_1_eq : ∀ k : Fin 16, amp7_1Expr 0 1 k = amp7_10_1 k := by decide +kernel +noncomputable def amp7_10_2 : Fin 16 → CBox := ![⟨⟨(-12965295463818583366441203121),(-12965295463818583360710805407)⟩,⟨(-37427584130793464686356962287),(-37427584130793464680375474748)⟩⟩,⟨⟨(-13343396554569321853843239765),(-13343396554569321847943716679)⟩,⟨(-38519067963422614616445425200),(-38519067963422614610283693057)⟩⟩,⟨⟨(-13716512663740494238573888211),(-13716512663740494232508278000)⟩,⟨(-39596161393767425470417241678),(-39596161393767425464079975125)⟩⟩,⟨⟨(-14090441693045962460851957740),(-14090441693045962454619372103)⟩,⟨(-40675601522404063167066431417),(-40675601522404063160551728307)⟩⟩,⟨⟨(-14459461977215688470709103384),(-14459461977215688464310792336)⟩,⟨(-41740871324413180701692324674),(-41740871324413180694999795123)⟩⟩,⟨⟨(-14829004411061715036900338740),(-14829004411061715030344586233)⟩,⟨(-42807648442703145247097490669),(-42807648442703145240251473698)⟩⟩,⟨⟨(-15193696708276728731242343638),(-15193696708276728724524012657)⟩,⟨(-43860424422545501061648217845),(-43860424422545501054629933537)⟩⟩,⟨⟨(-15558639082871133560974465812),(-15558639082871133554094603450)⟩,⟨(-44913922313599405417138618412),(-44913922313599405409951293167)⟩⟩,⟨⟨(-15918775249752562217890305756),(-15918775249752562210849853385)⟩,⟨(-45953545878068969527740621305),(-45953545878068969520383057784)⟩⟩,⟨⟨(-16278905600962081270467488223),(-16278905600962081263266194168)⟩,⟨(-46993152654139820995293429067),(-46993152654139820987764896009)⟩⟩,⟨⟨(-16634261386743642870627070252),(-16634261386743642863267085993)⟩,⟨(-48018976447035198883381338544),(-48018976447035198875684157662)⟩⟩,⟨⟨(-16989369609173106077548776800),(-16989369609173106070039938506)⟩,⟨(-49044085586090699304268032813),(-49044085586090699296430397033)⟩⟩,⟨⟨(-17339724586802453974631350048),(-17339724586802453966964401926)⟩,⟨(-50055473289321845909927664620),(-50055473289321845901918983062)⟩⟩,⟨⟨(-17689602740734276714894718877),(-17689602740734276707071436409)⟩,⟨(-51065484521102381805677401501),(-51065484521102381797502411148)⟩⟩,⟨⟨(-18034740279655822667491153476),(-18034740279655822659512315016)⟩,⟨(-52061810776121379282081247849),(-52061810776121379273738334198)⟩⟩,⟨⟨(-18379182858626920880576297106),(-18379182858626920872445651965)⟩,⟨(-53056130854568041701539387088),(-53056130854568041693038807398)⟩⟩] +lemma amp7_10_2_eq : ∀ k : Fin 16, amp7_1Expr 0 2 k = amp7_10_2 k := by decide +kernel +noncomputable def amp7_10_3 : Fin 16 → CBox := ![⟨⟨(-18718890128322294129071057326),(-18718890128322294120788511150)⟩,⟨(-54036781272589524420409922322),(-54036781272589524411747547115)⟩⟩,⟨⟨(-19057694296448717012224265028),(-19057694296448717003789830445)⟩,⟨(-55014824660941311805265614250),(-55014824660941311796440744372)⟩⟩,⟨⟨(-19391762292844942230120539306),(-19391762292844942221535978194)⟩,⟨(-55979195899176309601900813138),(-55979195899176309592914676893)⟩⟩,⟨⟨(-19724728098486747681256201626),(-19724728098486747672538603598)⟩,⟨(-56940385386767494553323426679),(-56940385386767494544224459750)⟩⟩,⟨⟨(-20052951687444352548324030812),(-20052951687444352539457674377)⟩,⟨(-57887885273962785796119137738),(-57887885273962785786858093369)⟩⟩,⟨⟨(-20379882258044908828380475313),(-20379882258044908819367432484)⟩,⟨(-58831652538675531392157462704),(-58831652538675531382739269063)⟩⟩,⟨⟨(-20702060231618653082299183991),(-20702060231618653073141694343)⟩,⟨(-59761700237524378296459190032),(-59761700237524378286886441040)⟩⟩,⟨⟨(-21022761953305465949691254376),(-21022761953305465940390729295)⟩,⟨(-60687486364251667555819636439),(-60687486364251667546095203951)⟩⟩,⟨⟨(-21338697095528772247753419998),(-21338697095528772238310950284)⟩,⟨(-61599512561297110516378096567),(-61599512561297110506501246881)⟩⟩,⟨⟨(-21652979780165887261210282880),(-21652979780165887251630698209)⟩,⟨(-62506768524181493590010028084),(-62506768524181493579993357287)⟩⟩,⟨⟨(-21962478939877190908399699172),(-21962478939877190898681139545)⟩,⟨(-63400215640047914278999356283),(-63400215640047914268833598647)⟩⟩,⟨⟨(-22270155981605558917323795742),(-22270155981605558907468772865)⟩,⟨(-64288402754374619224600810858),(-64288402754374619214291732866)⟩⟩,⟨⟨(-22573030150397963511547277927),(-22573030150397963501557140911)⟩,⟨(-65162725168789013941684632902),(-65162725168789013931232216973)⟩⟩,⟨⟨(-22873918673218157798925807851),(-22873918673218157788801635815)⟩,⟨(-66031315517020554074684033872),(-66031315517020554064089777767)⟩⟩,⟨⟨(-23169983067012150238765775217),(-23169983067012150228509305533)⟩,⟨(-66885979804292678588288361403),(-66885979804292678577553351040)⟩⟩,⟨⟨(-23463904064604503194831927210),(-23463904064604503184444360813)⟩,⟨(-67734456639694820215187402453),(-67734456639694820204313358750)⟩⟩] +lemma amp7_10_3_eq : ∀ k : Fin 16, amp7_1Expr 0 3 k = amp7_10_3 k := by decide +kernel +noncomputable def amp7_10_4 : Fin 16 → CBox := ![⟨⟨(-23752978207657740005946216929),(-23752978207657739995454921619)⟩,⟨(-68568941811232553513050004286),(-68568941811232553502111983322)⟩⟩,⟨⟨(-24039756676364397081882646819),(-24039756676364397071259264480)⟩,⟨(-69396799941760439169223850652),(-69396799941760439158138119680)⟩⟩,⟨⟨(-24321664486771101365137240042),(-24321664486771101354384885308)⟩,⟨(-70210597692885282676169737587),(-70210597692885282664941320438)⟩⟩,⟨⟨(-24601129552458858925734121554),(-24601129552458858914854907325)⟩,⟨(-71017343847404899047826879021),(-71017343847404899036459885399)⟩⟩,⟨⟨(-24875699428374202218763551564),(-24875699428374202207759924706)⟩,⟨(-71809958806260327018173237510),(-71809958806260327006670743583)⟩⟩,⟨⟨(-25147684467739387137681688326),(-25147684467739387126553963193)⟩,⟨(-72595111984725529384056985100),(-72595111984725529372417792880)⟩⟩,⟨⟨(-25414749373705691732474190801),(-25414749373705691721227026649)⟩,⟨(-73366061961479269632492587436),(-73366061961479269620726139392)⟩⟩,⟨⟨(-25679092130460598070928879670),(-25679092130460598059561796952)⟩,⟨(-74129153770333134326988758264),(-74129153770333134315091452766)⟩⟩,⟨⟨(-25938489683322627379614414702),(-25938489683322627368129084121)⟩,⟨(-74877970005193248329536840189),(-74877970005193248317509472077)⟩⟩,⟨⟨(-26195032379608320411565752178),(-26195032379608320399971023393)⟩,⟨(-75618544978989134718246978899),(-75618544978989134706112769544)⟩⟩,⟨⟨(-26446604933591878662468219861),(-26446604933591878650758261033)⟩,⟨(-76344772387804779796226036680),(-76344772387804779783964102632)⟩⟩,⟨⟨(-26695194376888032125171470847),(-26695194376888032113349049486)⟩,⟨(-77062388297828446854089092557),(-77062388297828446841704993074)⟩⟩,⟨⟨(-26938789107485135134325954858),(-26938789107485135122392429079)⟩,⟨(-77765585714245505803878921723),(-77765585714245505791372508950)⟩⟩,⟨⟨(-27179276793229187804604418531),(-27179276793229187792564094344)⟩,⟨(-78459813864751100481788719404),(-78459813864751100469169892910)⟩⟩,⟨⟨(-27414745779588332840519829100),(-27414745779588332828371860708)⟩,⟨(-79139554278052403999963531991),(-79139554278052403987225762245)⟩⟩,⟨⟨(-27646987989670052257862869598),(-27646987989670052245610518992)⟩,⟨(-79809979790591775620995753792),(-79809979790591775608145829012)⟩⟩] +lemma amp7_10_4_eq : ∀ k : Fin 16, amp7_1Expr 0 4 k = amp7_10_4 k := by decide +kernel +noncomputable def amp7_10_5 : Fin 16 → CBox := ![⟨⟨(-27874188295234711908268675544),(-27874188295234711895913297230)⟩,⟨(-80465850578480383009385238027),(-80465850578480382996422961505)⟩⟩,⟨⟨(-28098046192495536946458582421),(-28098046192495536934001780471)⟩,⟨(-81112072664699187628654572585),(-81112072664699187615581852349)⟩⟩,⟨⟨(-28316839943670277259730922635),(-28316839943670277247174122121)⟩,⟨(-81743675820387909219620234366),(-81743675820387909206437059304)⟩⟩,⟨⟨(-28532179662507527622619739604),(-28532179662507527609964772709)⟩,⟨(-82365308043577433334780371250),(-82365308043577433321489216971)⟩⟩,⟨⟨(-28742434125160893648542055321),(-28742434125160893635790846909)⟩,⟨(-82972260396633638294921932440),(-82972260396633638281524213405)⟩⟩,⟨⟨(-28949126858313515188074297534),(-28949126858313515175278935163)⟩,⟨(-83568930922259665952079160507),(-83568930922259665938722339374)⟩⟩,⟨⟨(-29150714511951410427044854090),(-29150714511951410414154291376)⟩,⟨(-84150864352725385240755650447),(-84150864352725385227288210711)⟩⟩,⟨⟨(-29348636593525162306023195505),(-29348636593525162293040421004)⟩,⟨(-84722216188101268824178012678),(-84722216188101268810605595800)⟩⟩,⟨⟨(-29541435202988933500391835990),(-29541435202988933487319954333)⟩,⟨(-85278777833467737966802206827),(-85278777833467737953129601839)⟩⟩,⟨⟨(-29730468187763879473660218416),(-29730468187763879460501094702)⟩,⟨(-85824469056695405398644331841),(-85824469056695405384873855568)⟩⟩,⟨⟨(-29914360872324529848993077282),(-29914360872324529835750207330)⟩,⟨(-86355321511360877558130688304),(-86355321511360877544268245326)⟩⟩,⟨⟨(-30094391611375639626853613313),(-30094391611375639613529002414)⟩,⟨(-86875025489628705065684440421),(-86875025489628705051732673810)⟩⟩,⟨⟨(-30269266911110177890483036324),(-30269266911110177877077234297)⟩,⟨(-87379846996510465853135814007),(-87379846996510465839092111646)⟩⟩,⟨⟨(-30440187623762200867648218092),(-30440187623762200854165578881)⟩,⟨(-87873252593809106553410736969),(-87873252593809106539284446440)⟩⟩,⟨⟨(-30605939563110598324385038068),(-30605939563110598310826261813)⟩,⟨(-88351737227816605526268294735),(-88351737227816605512057227000)⟩⟩,⟨⟨(-30767647905240686654806279619),(-30767647905240686641172722548)⟩,⟨(-88818549002111678519040627626),(-88818549002111678504745404110)⟩⟩] +lemma amp7_10_5_eq : ∀ k : Fin 16, amp7_1Expr 0 5 k = amp7_10_5 k := by decide +kernel +noncomputable def amp7_10_6 : Fin 16 → CBox := ![⟨⟨(-30924176053652663081519407666),(-30924176053652663067818713299)⟩,⟨(-89270406845218719931954450811),(-89270406845218719917592916977)⟩⟩,⟨⟨(-31076575182348133098249814520),(-31076575182348133084477401716)⟩,⟨(-89710345235101690104548974986),(-89710345235101690090104542975)⟩⟩,⟨⟨(-31223784711938343746374922889),(-31223784711938343732536410514)⟩,⟨(-90135302542782621589761062179),(-90135302542782621575245725126)⟩⟩,⟨⟨(-31366783346512185488577036849),(-31366783346512185474671071080)⟩,⟨(-90548104043607403867851585594),(-90548104043607403853258005407)⟩⟩,⟨⟨(-31504585086650592900151390471),(-31504585086650592886182097651)⟩,⟨(-90945903402425945750943200169),(-90945903402425945736279055499)⟩⟩,⟨⟨(-31638097566013635105752229506),(-31638097566013635091720570294)⟩,⟨(-91331320731928079611057612104),(-91331320731928079596322182359)⟩⟩,⟨⟨(-31766408054785126243007983842),(-31766408054785126228933473005)⟩,⟨(-91701721208088443921778120276),(-91701721208088443907023502511)⟩⟩,⟨⟨(-31890354391170951223812678008),(-31890354391170951209678519525)⟩,⟨(-92059523461475563717981327114),(-92059523461475563703155480619)⟩⟩,⟨⟨(-32009095923644769048430220723),(-32009095923644769034240411055)⟩,⟨(-92402300740164300769808895412),(-92402300740164300754919117456)⟩⟩,⟨⟨(-32123401852681396189377970153),(-32123401852681396175135453862)⟩,⟨(-92732273534660635469068670184),(-92732273534660635454119848012)⟩⟩,⟨⟨(-32232502525936830269092277183),(-32232502525936830254798318554)⟩,⟨(-93047220050024606820075184719),(-93047220050024606805066728122)⟩⟩,⟨⟨(-32337099553057724197343546108),(-32337099553057724183002141717)⟩,⟨(-93349165658848020301184226361),(-93349165658848020286124004057)⟩⟩,⟨⟨(-32436493307917857228674514721),(-32436493307917857214286950896)⟩,⟨(-93636090714469347699985122802),(-93636090714469347684872609833)⟩⟩,⟨⟨(-32531318751103864927095704990),(-32531318751103864912662852865)⟩,⟨(-93909828190216683244343217571),(-93909828190216683229177207615)⟩⟩,⟨⟨(-32620945410534091411190760171),(-32620945410534091396723246070)⟩,⟨(-94168558069959724100000486415),(-94168558069959724084807420411)⟩⟩,⟨⟨(-32705942439377387428873957056),(-32705942439377387414366373385)⟩,⟨(-94413923357374700806126344615),(-94413923357374700790886841169)⟩⟩] +lemma amp7_10_6_eq : ∀ k : Fin 16, amp7_1Expr 0 6 k = amp7_10_6 k := by decide +kernel +noncomputable def amp7_10_7 : Fin 16 → CBox := ![⟨⟨(-32785747743509981354676291877),(-32785747743509981340131866004)⟩,⟨(-94644301426493266088785785044),(-94644301426493266073504931895)⟩⟩,⟨⟨(-32860865414590931780100874031),(-32860865414590931765520676328)⟩,⟨(-94861147464590688562265186833),(-94861147464590688546942255618)⟩⟩,⟨⟨(-32930801052341203480514059584),(-32930801052341203465904897822)⟩,⟨(-95063034260996026161396755540),(-95063034260996026146047177630)⟩⟩,⟨⟨(-32995994340909188945690215623),(-32995994340909188931050552857)⟩,⟨(-95251231074516442962838289400),(-95251231074516442947453765189)⟩⟩,⟨⟨(-33056017978152788415114672715),(-33056017978152788400449544955)⟩,⟨(-95424504390118105964323185746),(-95424504390118105948914042057)⟩⟩,⟨⟨(-33111247806102404785226051178),(-33111247806102404770534535422)⟩,⟨(-95583939170288144604699138037),(-95583939170288144589258805642)⟩⟩,⟨⟨(-33161323110387142486962271244),(-33161323110387142472248824660)⟩,⟨(-95728494122330873267430027545),(-95728494122330873251967174617)⟩⟩,⟨⟨(-33206556370521783198415308901),(-33206556370521783183682028227)⟩,⟨(-95859071296906169179963527409),(-95859071296906169164480262676)⟩⟩,⟨⟨(-33246653032290985859379438015),(-33246653032290985844628425411)⟩,⟨(-95974820389236441841775773122),(-95974820389236441826273981029)⟩⟩,⟨⟨(-33281862608866566231627741720),(-33281862608866566216860723494)⟩,⟨(-96076461681806262189887123348),(-96076461681806262174367806597)⟩⟩,⟨⟨(-33311956359174495047044401970),(-33311956359174495032264719903)⟩,⟨(-96163334856012302613989771838),(-96163334856012302598458410277)⟩⟩,⟨⟨(-33337121144716975248047064454),(-33337121144716975233256603081)⟩,⟨(-96235979334547553347346808753),(-96235979334547553331804827728)⟩⟩,⟨⟨(-33357193769420233723332106532),(-33357193769420233708534111467)⟩,⟨(-96293924010926396410776456310),(-96293924010926396395229077338)⟩⟩,⟨⟨(-33372298677811606180246058080),(-33372298677811606165443029308)⟩,⟨(-96337528125555614036170965195),(-96337528125555614020621358708)⟩⟩,⟨⟨(-33382338028223777534166504016),(-33382338028223777519361524281)⟩,⟨(-96366509233870394593952998564),(-96366509233870394578405937580)⟩⟩,⟨⟨(-33387374004052282223359036812),(-33387374004052282208555472591)⟩,⟨(-96381046843871492748649141988),(-96381046843871492733110269241)⟩⟩] +lemma amp7_10_7_eq : ∀ k : Fin 16, amp7_1Expr 0 7 k = amp7_10_7 k := by decide +kernel +noncomputable def amp7_10_8 : Fin 16 → CBox := ![⟨⟨(-33387374004052282223359036812),(-33387374004052282208555472591)⟩,⟨(-96381046843871492748649141988),(-96381046843871492733110269241)⟩⟩,⟨⟨(-33382338028223777534166504016),(-33382338028223777519361524281)⟩,⟨(-96366509233870394593952998564),(-96366509233870394578405937580)⟩⟩,⟨⟨(-33372298677811606180246058080),(-33372298677811606165443029308)⟩,⟨(-96337528125555614036170965195),(-96337528125555614020621358708)⟩⟩,⟨⟨(-33357193769420233723332106532),(-33357193769420233708534111467)⟩,⟨(-96293924010926396410776456310),(-96293924010926396395229077338)⟩⟩,⟨⟨(-33337121144716975248047064454),(-33337121144716975233256603081)⟩,⟨(-96235979334547553347346808753),(-96235979334547553331804827728)⟩⟩,⟨⟨(-33311956359174495047044401970),(-33311956359174495032264719903)⟩,⟨(-96163334856012302613989771838),(-96163334856012302598458410277)⟩⟩,⟨⟨(-33281862608866566231627741720),(-33281862608866566216860723494)⟩,⟨(-96076461681806262189887123348),(-96076461681806262174367806597)⟩⟩,⟨⟨(-33246653032290985859379438015),(-33246653032290985844628425411)⟩,⟨(-95974820389236441841775773122),(-95974820389236441826273981029)⟩⟩,⟨⟨(-33206556370521783198415308901),(-33206556370521783183682028227)⟩,⟨(-95859071296906169179963527409),(-95859071296906169164480262676)⟩⟩,⟨⟨(-33161323110387142486962271244),(-33161323110387142472248824660)⟩,⟨(-95728494122330873267430027545),(-95728494122330873251967174617)⟩⟩,⟨⟨(-33111247806102404785226051178),(-33111247806102404770534535422)⟩,⟨(-95583939170288144604699138037),(-95583939170288144589258805642)⟩⟩,⟨⟨(-33056017978152788415114672715),(-33056017978152788400449544955)⟩,⟨(-95424504390118105964323185746),(-95424504390118105948914042057)⟩⟩,⟨⟨(-32995994340909188945690215623),(-32995994340909188931050552857)⟩,⟨(-95251231074516442962838289400),(-95251231074516442947453765189)⟩⟩,⟨⟨(-32930801052341203480514059584),(-32930801052341203465904897822)⟩,⟨(-95063034260996026161396755540),(-95063034260996026146047177630)⟩⟩,⟨⟨(-32860865414590931780100874031),(-32860865414590931765520676328)⟩,⟨(-94861147464590688562265186833),(-94861147464590688546942255618)⟩⟩,⟨⟨(-32785747743509981354676291877),(-32785747743509981340131866004)⟩,⟨(-94644301426493266088785785044),(-94644301426493266073504931895)⟩⟩] +lemma amp7_10_8_eq : ∀ k : Fin 16, amp7_1Expr 0 8 k = amp7_10_8 k := by decide +kernel +noncomputable def amp7_10_9 : Fin 16 → CBox := ![⟨⟨(-32705942439377387428873957056),(-32705942439377387414366373385)⟩,⟨(-94413923357374700806126344615),(-94413923357374700790886841169)⟩⟩,⟨⟨(-32620945410534091411190760171),(-32620945410534091396723246070)⟩,⟨(-94168558069959724100000486415),(-94168558069959724084807420411)⟩⟩,⟨⟨(-32531318751103864927095704990),(-32531318751103864912662852865)⟩,⟨(-93909828190216683244343217571),(-93909828190216683229177207615)⟩⟩,⟨⟨(-32436493307917857228674514721),(-32436493307917857214286950896)⟩,⟨(-93636090714469347699985122802),(-93636090714469347684872609833)⟩⟩,⟨⟨(-32337099553057724197343546108),(-32337099553057724183002141717)⟩,⟨(-93349165658848020301184226361),(-93349165658848020286124004057)⟩⟩,⟨⟨(-32232502525936830269092277183),(-32232502525936830254798318554)⟩,⟨(-93047220050024606820075184719),(-93047220050024606805066728122)⟩⟩,⟨⟨(-32123401852681396189377970153),(-32123401852681396175135453862)⟩,⟨(-92732273534660635469068670184),(-92732273534660635454119848012)⟩⟩,⟨⟨(-32009095923644769048430220723),(-32009095923644769034240411055)⟩,⟨(-92402300740164300769808895412),(-92402300740164300754919117456)⟩⟩,⟨⟨(-31890354391170951223812678008),(-31890354391170951209678519525)⟩,⟨(-92059523461475563717981327114),(-92059523461475563703155480619)⟩⟩,⟨⟨(-31766408054785126243007983842),(-31766408054785126228933473005)⟩,⟨(-91701721208088443921778120276),(-91701721208088443907023502511)⟩⟩,⟨⟨(-31638097566013635105752229506),(-31638097566013635091720570294)⟩,⟨(-91331320731928079611057612104),(-91331320731928079596322182359)⟩⟩,⟨⟨(-31504585086650592900151390471),(-31504585086650592886182097651)⟩,⟨(-90945903402425945750943200169),(-90945903402425945736279055499)⟩⟩,⟨⟨(-31366783346512185488577036849),(-31366783346512185474671071080)⟩,⟨(-90548104043607403867851585594),(-90548104043607403853258005407)⟩⟩,⟨⟨(-31223784711938343746374922889),(-31223784711938343732536410514)⟩,⟨(-90135302542782621589761062179),(-90135302542782621575245725126)⟩⟩,⟨⟨(-31076575182348133098249814520),(-31076575182348133084477401716)⟩,⟨(-89710345235101690104548974986),(-89710345235101690090104542975)⟩⟩,⟨⟨(-30924176053652663081519407666),(-30924176053652663067818713299)⟩,⟨(-89270406845218719931954450811),(-89270406845218719917592916977)⟩⟩] +lemma amp7_10_9_eq : ∀ k : Fin 16, amp7_1Expr 0 9 k = amp7_10_9 k := by decide +kernel +noncomputable def amp7_10_10 : Fin 16 → CBox := ![⟨⟨(-30767647905240686654806279619),(-30767647905240686641172722548)⟩,⟨(-88818549002111678519040627626),(-88818549002111678504745404110)⟩⟩,⟨⟨(-30605939563110598324385038068),(-30605939563110598310826261813)⟩,⟨(-88351737227816605526268294735),(-88351737227816605512057227000)⟩⟩,⟨⟨(-30440187623762200867648218092),(-30440187623762200854165578881)⟩,⟨(-87873252593809106553410736969),(-87873252593809106539284446440)⟩⟩,⟨⟨(-30269266911110177890483036324),(-30269266911110177877077234297)⟩,⟨(-87379846996510465853135814007),(-87379846996510465839092111646)⟩⟩,⟨⟨(-30094391611375639626853613313),(-30094391611375639613529002414)⟩,⟨(-86875025489628705065684440421),(-86875025489628705051732673810)⟩⟩,⟨⟨(-29914360872324529848993077282),(-29914360872324529835750207330)⟩,⟨(-86355321511360877558130688304),(-86355321511360877544268245326)⟩⟩,⟨⟨(-29730468187763879473660218416),(-29730468187763879460501094702)⟩,⟨(-85824469056695405398644331841),(-85824469056695405384873855568)⟩⟩,⟨⟨(-29541435202988933500391835990),(-29541435202988933487319954333)⟩,⟨(-85278777833467737966802206827),(-85278777833467737953129601839)⟩⟩,⟨⟨(-29348636593525162306023195505),(-29348636593525162293040421004)⟩,⟨(-84722216188101268824178012678),(-84722216188101268810605595800)⟩⟩,⟨⟨(-29150714511951410427044854090),(-29150714511951410414154291376)⟩,⟨(-84150864352725385240755650447),(-84150864352725385227288210711)⟩⟩,⟨⟨(-28949126858313515188074297534),(-28949126858313515175278935163)⟩,⟨(-83568930922259665952079160507),(-83568930922259665938722339374)⟩⟩,⟨⟨(-28742434125160893648542055321),(-28742434125160893635790846909)⟩,⟨(-82972260396633638294921932440),(-82972260396633638281524213405)⟩⟩,⟨⟨(-28532179662507527622619739604),(-28532179662507527609964772709)⟩,⟨(-82365308043577433334780371250),(-82365308043577433321489216971)⟩⟩,⟨⟨(-28316839943670277259730922635),(-28316839943670277247174122121)⟩,⟨(-81743675820387909219620234366),(-81743675820387909206437059304)⟩⟩,⟨⟨(-28098046192495536946458582421),(-28098046192495536934001780471)⟩,⟨(-81112072664699187628654572585),(-81112072664699187615581852349)⟩⟩,⟨⟨(-27874188295234711908268675544),(-27874188295234711895913297230)⟩,⟨(-80465850578480383009385238027),(-80465850578480382996422961505)⟩⟩] +lemma amp7_10_10_eq : ∀ k : Fin 16, amp7_1Expr 0 10 k = amp7_10_10 k := by decide +kernel +noncomputable def amp7_10_11 : Fin 16 → CBox := ![⟨⟨(-27646987989670052257862869598),(-27646987989670052245610518992)⟩,⟨(-79809979790591775620995753792),(-79809979790591775608145829012)⟩⟩,⟨⟨(-27414745779588332840519829100),(-27414745779588332828371860708)⟩,⟨(-79139554278052403999963531991),(-79139554278052403987225762245)⟩⟩,⟨⟨(-27179276793229187804604418531),(-27179276793229187792564094344)⟩,⟨(-78459813864751100481788719404),(-78459813864751100469169892910)⟩⟩,⟨⟨(-26938789107485135134325954858),(-26938789107485135122392429079)⟩,⟨(-77765585714245505803878921723),(-77765585714245505791372508950)⟩⟩,⟨⟨(-26695194376888032125171470847),(-26695194376888032113349049486)⟩,⟨(-77062388297828446854089092557),(-77062388297828446841704993074)⟩⟩,⟨⟨(-26446604933591878662468219861),(-26446604933591878650758261033)⟩,⟨(-76344772387804779796226036680),(-76344772387804779783964102632)⟩⟩,⟨⟨(-26195032379608320411565752178),(-26195032379608320399971023393)⟩,⟨(-75618544978989134718246978899),(-75618544978989134706112769544)⟩⟩,⟨⟨(-25938489683322627379614414702),(-25938489683322627368129084121)⟩,⟨(-74877970005193248329536840189),(-74877970005193248317509472077)⟩⟩,⟨⟨(-25679092130460598070928879670),(-25679092130460598059561796952)⟩,⟨(-74129153770333134326988758264),(-74129153770333134315091452766)⟩⟩,⟨⟨(-25414749373705691732474190801),(-25414749373705691721227026649)⟩,⟨(-73366061961479269632492587436),(-73366061961479269620726139392)⟩⟩,⟨⟨(-25147684467739387137681688326),(-25147684467739387126553963193)⟩,⟨(-72595111984725529384056985100),(-72595111984725529372417792880)⟩⟩,⟨⟨(-24875699428374202218763551564),(-24875699428374202207759924706)⟩,⟨(-71809958806260327018173237510),(-71809958806260327006670743583)⟩⟩,⟨⟨(-24601129552458858925734121554),(-24601129552458858914854907325)⟩,⟨(-71017343847404899047826879021),(-71017343847404899036459885399)⟩⟩,⟨⟨(-24321664486771101365137240042),(-24321664486771101354384885308)⟩,⟨(-70210597692885282676169737587),(-70210597692885282664941320438)⟩⟩,⟨⟨(-24039756676364397081882646819),(-24039756676364397071259264480)⟩,⟨(-69396799941760439169223850652),(-69396799941760439158138119680)⟩⟩,⟨⟨(-23752978207657740005946216929),(-23752978207657739995454921619)⟩,⟨(-68568941811232553513050004286),(-68568941811232553502111983322)⟩⟩] +lemma amp7_10_11_eq : ∀ k : Fin 16, amp7_1Expr 0 11 k = amp7_10_11 k := by decide +kernel +noncomputable def amp7_10_12 : Fin 16 → CBox := ![⟨⟨(-23463904064604503194831927210),(-23463904064604503184444360813)⟩,⟨(-67734456639694820215187402453),(-67734456639694820204313358750)⟩⟩,⟨⟨(-23169983067012150238765775217),(-23169983067012150228509305533)⟩,⟨(-66885979804292678588288361403),(-66885979804292678577553351040)⟩⟩,⟨⟨(-22873918673218157798925807851),(-22873918673218157788801635815)⟩,⟨(-66031315517020554074684033872),(-66031315517020554064089777767)⟩⟩,⟨⟨(-22573030150397963511547277927),(-22573030150397963501557140911)⟩,⟨(-65162725168789013941684632902),(-65162725168789013931232216973)⟩⟩,⟨⟨(-22270155981605558917323795742),(-22270155981605558907468772865)⟩,⟨(-64288402754374619224600810858),(-64288402754374619214291732866)⟩⟩,⟨⟨(-21962478939877190908399699172),(-21962478939877190898681139545)⟩,⟨(-63400215640047914278999356283),(-63400215640047914268833598647)⟩⟩,⟨⟨(-21652979780165887261210282880),(-21652979780165887251630698209)⟩,⟨(-62506768524181493590010028084),(-62506768524181493579993357287)⟩⟩,⟨⟨(-21338697095528772247753419998),(-21338697095528772238310950284)⟩,⟨(-61599512561297110516378096567),(-61599512561297110506501246881)⟩⟩,⟨⟨(-21022761953305465949691254376),(-21022761953305465940390729295)⟩,⟨(-60687486364251667555819636439),(-60687486364251667546095203951)⟩⟩,⟨⟨(-20702060231618653082299183991),(-20702060231618653073141694343)⟩,⟨(-59761700237524378296459190032),(-59761700237524378286886441040)⟩⟩,⟨⟨(-20379882258044908828380475313),(-20379882258044908819367432484)⟩,⟨(-58831652538675531392157462704),(-58831652538675531382739269063)⟩⟩,⟨⟨(-20052951687444352548324030812),(-20052951687444352539457674377)⟩,⟨(-57887885273962785796119137738),(-57887885273962785786858093369)⟩⟩,⟨⟨(-19724728098486747681256201626),(-19724728098486747672538603598)⟩,⟨(-56940385386767494553323426679),(-56940385386767494544224459750)⟩⟩,⟨⟨(-19391762292844942230120539306),(-19391762292844942221535978194)⟩,⟨(-55979195899176309601900813138),(-55979195899176309592914676893)⟩⟩,⟨⟨(-19057694296448717012224265028),(-19057694296448717003789830445)⟩,⟨(-55014824660941311805265614250),(-55014824660941311796440744372)⟩⟩,⟨⟨(-18718890128322294129071057326),(-18718890128322294120788511150)⟩,⟨(-54036781272589524420409922322),(-54036781272589524411747547115)⟩⟩] +lemma amp7_10_12_eq : ∀ k : Fin 16, amp7_1Expr 0 12 k = amp7_10_12 k := by decide +kernel +noncomputable def amp7_10_13 : Fin 16 → CBox := ![⟨⟨(-18379182858626920880576297106),(-18379182858626920872445651965)⟩,⟨(-53056130854568041701539387088),(-53056130854568041693038807398)⟩⟩,⟨⟨(-18034740279655822667491153476),(-18034740279655822659512315016)⟩,⟨(-52061810776121379282081247849),(-52061810776121379273738334198)⟩⟩,⟨⟨(-17689602740734276714894718877),(-17689602740734276707071436409)⟩,⟨(-51065484521102381805677401501),(-51065484521102381797502411148)⟩⟩,⟨⟨(-17339724586802453974631350048),(-17339724586802453966964401926)⟩,⟨(-50055473289321845909927664620),(-50055473289321845901918983062)⟩⟩,⟨⟨(-16989369609173106077548776800),(-16989369609173106070039938506)⟩,⟨(-49044085586090699304268032813),(-49044085586090699296430397033)⟩⟩,⟨⟨(-16634261386743642870627070252),(-16634261386743642863267085993)⟩,⟨(-48018976447035198883381338544),(-48018976447035198875684157662)⟩⟩,⟨⟨(-16278905600962081270467488223),(-16278905600962081263266194168)⟩,⟨(-46993152654139820995293429067),(-46993152654139820987764896009)⟩⟩,⟨⟨(-15918775249752562217890305756),(-15918775249752562210849853385)⟩,⟨(-45953545878068969527740621305),(-45953545878068969520383057784)⟩⟩,⟨⟨(-15558639082871133560974465812),(-15558639082871133554094603450)⟩,⟨(-44913922313599405417138618412),(-44913922313599405409951293167)⟩⟩,⟨⟨(-15193696708276728731242343638),(-15193696708276728724524012657)⟩,⟨(-43860424422545501061648217845),(-43860424422545501054629933537)⟩⟩,⟨⟨(-14829004411061715036900338740),(-14829004411061715030344586233)⟩,⟨(-42807648442703145247097490669),(-42807648442703145240251473698)⟩⟩,⟨⟨(-14459461977215688470709103384),(-14459461977215688464310792336)⟩,⟨(-41740871324413180701692324674),(-41740871324413180694999795123)⟩⟩,⟨⟨(-14090441693045962460851957740),(-14090441693045962454619372103)⟩,⟨(-40675601522404063167066431417),(-40675601522404063160551728307)⟩⟩,⟨⟨(-13716512663740494238573888211),(-13716512663740494232508278000)⟩,⟨(-39596161393767425470417241678),(-39596161393767425464079975125)⟩⟩,⟨⟨(-13343396554569321853843239765),(-13343396554569321847943716679)⟩,⟨(-38519067963422614616445425200),(-38519067963422614610283693057)⟩⟩,⟨⟨(-12965295463818583366441203121),(-12965295463818583360710805407)⟩,⟨(-37427584130793464686356962287),(-37427584130793464680375474748)⟩⟩] +lemma amp7_10_13_eq : ∀ k : Fin 16, amp7_1Expr 0 13 k = amp7_10_13 k := by decide +kernel +noncomputable def amp7_10_14 : Fin 16 → CBox := ![⟨⟨(-12588319915260722393449366498),(-12588319915260722387881957449)⟩,⟨(-36339349458604525329406044731),(-36339349458604525323588003455)⟩⟩,⟨⟨(-12206261841045965252410329449),(-12206261841045965247013125705)⟩,⟨(-35236442798634725061754767556),(-35236442798634725056116865264)⟩⟩,⟨⟨(-11825667778884814564288707801),(-11825667778884814559060322328)⟩,⟨(-34137762377431157506187557401),(-34137762377431157500726982570)⟩⟩,⟨⟨(-11439867680844907711382645195),(-11439867680844907706327254457)⟩,⟨(-33024053425147536342335883959),(-33024053425147536337060452475)⟩⟩,⟨⟨(-11055901047314695425996259863),(-11055901047314695421107680414)⟩,⟨(-31915637229005024097356912391),(-31915637229005024092250267620)⟩⟩,⟨⟨(-10666572908823690778938873209),(-10666572908823690774223622474)⟩,⟨(-30791743701200636932674878664),(-30791743701200636927751467628)⟩⟩,⟨⟨(-10279485372927895296838501161),(-10279485372927895292292535561)⟩,⟨(-29674318235953704695388396298),(-29674318235953704690638371248)⟩⟩,⟨⟨(-9886841054724459428800282821),(-9886841054724459424429442618)⟩,⟨(-28540851721901050824755079527),(-28540851721901050820190773635)⟩⟩,⟨⟨(-9496891073954188852868729265),(-9496891073954188848671411841)⟩,⟨(-27415163090060025287695049840),(-27415163090060025283314031387)⟩⟩,⟨⟨(-9101138730168082675585980061),(-9101138730168082671562341662)⟩,⟨(-26272724478973356684523524224),(-26272724478973356680321517996)⟩⟩,⟨⟨(-8708593155276932934437121588),(-8708593155276932930588583186)⟩,⟨(-25139543012310348167093283427),(-25139543012310348163077003461)⟩⟩,⟨⟨(-8309934963699564223900550017),(-8309934963699564220227383176)⟩,⟨(-23988715941201132048759423241),(-23988715941201132044924674504)⟩⟩,⟨⟨(-7915071511567247981253796575),(-7915071511567247977754319630)⟩,⟨(-22848843339292443597542571364),(-22848843339292443593887590277)⟩⟩,⟨⟨(-7513700288185479523274166028),(-7513700288185479519953513748)⟩,⟨(-21690184419970276427710565870),(-21690184419970276424244874394)⟩⟩,⟨⟨(-7116811458893626803706224473),(-7116811458893626800560642294)⟩,⟨(-20544465057820243453704177063),(-20544465057820243450420587794)⟩⟩,⟨⟨(-6712905375084154823140962584),(-6712905375084154820173698309)⟩,⟨(-19378488626746612490555160577),(-19378488626746612487457333280)⟩⟩] +lemma amp7_10_14_eq : ∀ k : Fin 16, amp7_1Expr 0 14 k = amp7_10_14 k := by decide +kernel +noncomputable def amp7_10_15 : Fin 16 → CBox := ![⟨⟨(-6314304889329281699461809925),(-6314304889329281696670903898)⟩,⟨(-18227828137998154551392034259),(-18227828137998154548478633519)⟩⟩,⟨⟨(-5908018787060499829048845905),(-5908018787060499826437871076)⟩,⟨(-17054981185433729371854776601),(-17054981185433729369129856392)⟩⟩,⟨⟨(-5508052685234101319058056687),(-5508052685234101316624357142)⟩,⟨(-15900378502652747127597447397),(-15900378502652747125058488649)⟩⟩,⟨⟨(-5099502883647184282835551234),(-5099502883647184280582045775)⟩,⟨(-14720996813034873396699431430),(-14720996813034873394347868238)⟩⟩,⟨⟨(-4698569893355039728540875860),(-4698569893355039726464520191)⟩,⟨(-13563602963674017037797224875),(-13563602963674017035630473304)⟩⟩,⟨⟨(-4287805485929443701331700529),(-4287805485929443699437026258)⟩,⟨(-12377828257670592145019783558),(-12377828257670592143042917154)⟩⟩,⟨⟨(-3886397599776523266234322382),(-3886397599776523264517480589)⟩,⟨(-11219063502044455817013680882),(-11219063502044455815223210032)⟩⟩,⟨⟨(-3473340580412691301245951334),(-3473340580412691299711334755)⟩,⟨(-10026670595442591582468101257),(-10026670595442591580867218014)⟩⟩,⟨⟨(-3072133445990435320873677675),(-3072133445990435319516586043)⟩,⟨(-8868485360145152285385330470),(-8868485360145152283970118533)⟩⟩,⟨⟨(-2656435792071101113877166469),(-2656435792071101112703889848)⟩,⟨(-7668469598186034814841328296),(-7668469598186034813618142415)⟩⟩,⟨⟨(-2256524817754308918408343468),(-2256524817754308917412015872)⟩,⟨(-6514026054817607367431530694),(-6514026054817607366393409348)⟩⟩,⟨⟨(-1837153108049314193674326890),(-1837153108049314192863368553)⟩,⟨(-5303404207374145887410717325),(-5303404207374145886566116101)⟩⟩,⟨⟨(-1440842106367455813814265547),(-1440842106367455813178651625)⟩,⟨(-4159352889854990064009723961),(-4159352889854990063348487483)⟩⟩,⟨⟨(-1014414495963543607132310588),(-1014414495963543606685066953)⟩,⟨(-2928362411572052200112623163),(-2928362411572052199647822717)⟩⟩,⟨⟨(-629264447029517718600603359),(-629264447029517718324026786)⟩,⟨(-1816529989419765287871633375),(-1816529989419765287585786352)⟩⟩,⟨⟨(-178776584874023315385344282),(-178776584874023315307284498)⟩,⟨(-516083547009096694099450847),(-516083547009096694019732261)⟩⟩] +lemma amp7_10_15_eq : ∀ k : Fin 16, amp7_1Expr 0 15 k = amp7_10_15 k := by decide +kernel +noncomputable def amp7_10 : Fin 16 → Fin 16 → CBox := ![amp7_10_0,amp7_10_1,amp7_10_2,amp7_10_3,amp7_10_4,amp7_10_5,amp7_10_6,amp7_10_7,amp7_10_8,amp7_10_9,amp7_10_10,amp7_10_11,amp7_10_12,amp7_10_13,amp7_10_14,amp7_10_15] +lemma amp7_10_eq (i k : Fin 16) : amp7_1Expr 0 i k = amp7_10 i k := by + fin_cases i + · exact amp7_10_0_eq k + · exact amp7_10_1_eq k + · exact amp7_10_2_eq k + · exact amp7_10_3_eq k + · exact amp7_10_4_eq k + · exact amp7_10_5_eq k + · exact amp7_10_6_eq k + · exact amp7_10_7_eq k + · exact amp7_10_8_eq k + · exact amp7_10_9_eq k + · exact amp7_10_10_eq k + · exact amp7_10_11_eq k + · exact amp7_10_12_eq k + · exact amp7_10_13_eq k + · exact amp7_10_14_eq k + · exact amp7_10_15_eq k +noncomputable def amp7_11_0 : Fin 16 → CBox := ![⟨⟨(-385210003677661993001841233),(-385210003677661992936859914)⟩,⟨(-873636716757143324791863454),(-873636716757143324722854824)⟩⟩,⟨⟨(-1355876442797423833667302980),(-1355876442797423833434660233)⟩,⟨(-3075058883478800724797321485),(-3075058883478800724545534046)⟩⟩,⟨⟨(-2185759460592364487045245205),(-2185759460592364486667226994)⟩,⟨(-4957191403499139413933090736),(-4957191403499139413520427464)⟩⟩,⟨⟨(-3104583262309451839230503685),(-3104583262309451838692795874)⟩,⟨(-7041037102589901691007393396),(-7041037102589901690419484343)⟩⟩,⟨⟨(-3958514790998972548399347882),(-3958514790998972547712629927)⟩,⟨(-8977710423472774273954987717),(-8977710423472774273202851900)⟩⟩,⟨⟨(-4862135239681351865087071951),(-4862135239681351864243057089)⟩,⟨(-11027075690326225203260215559),(-11027075690326225202335167549)⟩⟩,⟨⟨(-5723823631345515039467730650),(-5723823631345515038473326584)⟩,⟨(-12981341182328237041432561211),(-12981341182328237040341736829)⟩⟩,⟨⟨(-6619527590048496234627703368),(-6619527590048496233477230170)⟩,⟨(-15012752252126022925787575770),(-15012752252126022924525013227)⟩⟩,⟨⟨(-7484008818589727933780833190),(-7484008818589727932479478168)⟩,⟨(-16973351756267974183439228409),(-16973351756267974182010340420)⟩⟩,⟨⟨(-8374023000594305592533640641),(-8374023000594305591078117491)⟩,⟨(-18991858701597502347780696286),(-18991858701597502346183224010)⟩⟩,⟨⟨(-9238936788997680558781181562),(-9238936788997680557174229850)⟩,⟨(-20953439229529479545805801894),(-20953439229529479544040852196)⟩⟩,⟨⟨(-10124011078824646543047836555),(-10124011078824646541286564870)⟩,⟨(-22960742750384096492821743830),(-22960742750384096490886860515)⟩⟩,⟨⟨(-10987901608861133640851178104),(-10987901608861133638939674672)⟩,⟨(-24920002580329241960137755701),(-24920002580329241958037901113)⟩⟩,⟨⟨(-11868204086295200169379681504),(-11868204086295200167315784237)⟩,⟨(-26916483873120949763301902179),(-26916483873120949761035511597)⟩⟩,⟨⟨(-12730011261233991577021311881),(-12730011261233991574806354246)⟩,⟨(-28871018759554729027365687731),(-28871018759554729024932022774)⟩⟩,⟨⟨(-13605436144528543519196265342),(-13605436144528543516828173405)⟩,⟨(-30856437916656717947550984177),(-30856437916656717944948111604)⟩⟩] +lemma amp7_11_0_eq : ∀ k : Fin 16, amp7_1Expr 1 0 k = amp7_11_0 k := by decide +kernel +noncomputable def amp7_11_1 : Fin 16 → CBox := ![⟨⟨(-14464300825782799818488755860),(-14464300825782799815970791072)⟩,⟨(-32804299376914922133897891650),(-32804299376914922131129839321)⟩⟩,⟨⟨(-15334597482021724184261020689),(-15334597482021724181592023693)⟩,⟨(-34778087975607497058000584736),(-34778087975607497055067048967)⟩⟩,⟨⟨(-16189774056173590093379828021),(-16189774056173590090562745547)⟩,⟨(-36717584996341235470969081925),(-36717584996341235467873669775)⟩⟩,⟨⟨(-17054608847284225419239987243),(-17054608847284225416269317177)⟩,⟨(-38678986362426939556584611203),(-38678986362426939553316808989)⟩⟩,⟨⟨(-17905421340180017042322055470),(-17905421340180017039205104528)⟩,⟨(-40608585868600260492922082034),(-40608585868600260489495608373)⟩⟩,⟨⟨(-18764410360201072200140250932),(-18764410360201072196875586473)⟩,⟨(-42556729322864214032154535932),(-42556729322864214028567805071)⟩⟩,⟨⟨(-19610228521757425348210081632),(-19610228521757425344794759760)⟩,⟨(-44475001939309522031710620608),(-44475001939309522027954276507)⟩⟩,⟨⟨(-20462956309978198966709899348),(-20462956309978198963148833218)⟩,⟨(-46408945237968402989274367505),(-46408945237968402985360958619)⟩⟩,⟨⟨(-21303181743484879757414678730),(-21303181743484879753704855090)⟩,⟨(-48314533831349969678026767697),(-48314533831349969673946916694)⟩⟩,⟨⟨(-22149212667309377173655086826),(-22149212667309377169794608050)⟩,⟨(-50233288981809495284564604849),(-50233288981809495280315189053)⟩⟩,⟨⟨(-22983270389303945550619638569),(-22983270389303945546617880547)⟩,⟨(-52124889518848018485882348004),(-52124889518848018481482195676)⟩⟩,⟨⟨(-23822155938916705063499133651),(-23822155938916705059348677261)⟩,⟨(-54027439323634414944508690701),(-54027439323634414939941957803)⟩⟩,⟨⟨(-24649489050903922246827100817),(-24649489050903922242538893764)⟩,⟨(-55903788786837351760092316091),(-55903788786837351755381481278)⟩⟩,⟨⟨(-25480772729857277565223587220),(-25480772729857277560785364561)⟩,⟨(-57789097935200786629587195133),(-57789097935200786624705245824)⟩⟩,⟨⟨(-26300838960499855275522525371),(-26300838960499855270940280500)⟩,⟨(-59648966480726655561231008395),(-59648966480726655556189255269)⟩⟩,⟨⟨(-27124059698702532523572315062),(-27124059698702532518843904565)⟩,⟨(-61515989289125970110793078472),(-61515989289125970105587302116)⟩⟩] +lemma amp7_11_1_eq : ∀ k : Fin 16, amp7_1Expr 1 1 k = amp7_11_1 k := by decide +kernel +noncomputable def amp7_11_2 : Fin 16 → CBox := ![⟨⟨(-27936329116135969239295422414),(-27936329116135969234433461661)⟩,⟨(-63358175058430631413562613425),(-63358175058430631408219196959)⟩⟩,⟨⟨(-28751023739938367698683601342),(-28751023739938367693675517388)⟩,⟨(-65205861072561258318289600964),(-65205861072561258312780522966)⟩⟩,⟨⟨(-29554977221247464424954382728),(-29554977221247464419803844073)⟩,⟨(-67029186721248413941559348309),(-67029186721248413935890743610)⟩⟩,⟨⟨(-30360682302007587725843428630),(-30360682302007587720548990581)⟩,⟨(-68856484908495988082600955151),(-68856484908495988076769903600)⟩⟩,⟨⟨(-31155810506980960749502871356),(-31155810506980960744064393326)⟩,⟨(-70659795278844557636779566998),(-70659795278844557630783598029)⟩⟩,⟨⟨(-31952063788142973133808044886),(-31952063788142973128243677766)⟩,⟨(-72465657264826575314405402386),(-72465657264826575308285910182)⟩⟩,⟨⟨(-32737866477294929153922844099),(-32737866477294929148218719000)⟩,⟨(-74247817839098958517480461636),(-74247817839098958511203866231)⟩⟩,⟨⟨(-33524208008310895725803597375),(-33524208008310895719962114850)⟩,⟨(-76031200479341672532275319333),(-76031200479341672525847174679)⟩⟩,⟨⟨(-34300193600980150026913335299),(-34300193600980150020933748928)⟩,⟨(-77791096377574093956551319257),(-77791096377574093949967825736)⟩⟩,⟨⟨(-35076166662618009666464738450),(-35076166662618009660346502591)⟩,⟨(-79550963856063983529100811642),(-79550963856063983522360729216)⟩⟩,⟨⟨(-35841851965557722421813203677),(-35841851965557722415558197595)⟩,⟨(-81287499220522484617352295374),(-81287499220522484610457793218)⟩⟩,⟨⟨(-36607003843609385797043339582),(-36607003843609385790672614349)⟩,⟨(-83022824804436911451926921330),(-83022824804436911444925633689)⟩⟩,⟨⟨(-37361913902531192336344136252),(-37361913902531192329835004187)⟩,⟨(-84734922462926753851598299396),(-84734922462926753844436688202)⟩⟩,⟨⟨(-38115796549175229434861832633),(-38115796549175229428217844080)⟩,⟨(-86444690002570935227721582471),(-86444690002570935220407490713)⟩⟩,⟨⟨(-38859464590104374377974855975),(-38859464590104374371194951128)⟩,⟨(-88131291335433024609167182194),(-88131291335433024601696128263)⟩⟩,⟨⟨(-39601635200454137558798396014),(-39601635200454137551890252291)⟩,⟨(-89814496571821883454644797153),(-89814496571821883447033888412)⟩⟩] +lemma amp7_11_2_eq : ∀ k : Fin 16, amp7_1Expr 1 2 k = amp7_11_2 k := by decide +kernel +noncomputable def amp7_11_3 : Fin 16 → CBox := ![⟨⟨(-40333602637358103894797127756),(-40333602637358103887757807986)⟩,⟨(-91474561529234112670356114608),(-91474561529234112662596614004)⟩⟩,⟨⟨(-41063624160825241731848487274),(-41063624160825241724677497276)⟩,⟨(-93130213253838745821369879133),(-93130213253838745813460270022)⟩⟩,⟨⟨(-41783440652515466068355332979),(-41783440652515466061053734711)⟩,⟨(-94762720484866194053651357469),(-94762720484866194045591972241)⟩⟩,⟨⟨(-42500882253193745500016676134),(-42500882253193745492620656258)⟩,⟨(-96389841583740989907199509128),(-96389841583740989899071934157)⟩⟩,⟨⟨(-43208105797029466864160042776),(-43208105797029466856632988335)⟩,⟨(-97993788648851490883987168381),(-97993788648851490875706288618)⟩⟩,⟨⟨(-43912543273515121382589238696),(-43912543273515121374934867750)⟩,⟨(-99591417054765349039995238308),(-99591417054765349031568919338)⟩⟩,⟨⟨(-44606740326628404398186678701),(-44606740326628404390407073022)⟩,⟨(-101165820700761684451993319838),(-101165820700761684443424199737)⟩⟩,⟨⟨(-45297756499006132969281160310),(-45297756499006132961378508717)⟩,⟨(-102733010270862599445997490229),(-102733010270862599437289886022)⟩⟩,⟨⟨(-45978502120047616451525563430),(-45978502120047616443499464353)⟩,⟨(-104276906752354655002541951824),(-104276906752354654993692863366)⟩⟩,⟨⟨(-46655687189838484694394267576),(-46655687189838484686254173500)⟩,⟨(-105812728084513268102950002843),(-105812728084513268093980143544)⟩⟩,⟨⟨(-47322565195896356617139106800),(-47322565195896356608878248281)⟩,⟨(-107325173519802296086182651794),(-107325173519802296077074572073)⟩⟩,⟨⟨(-47985517083355406604263714160),(-47985517083355406595886451200)⟩,⟨(-108828714717585737049497585479),(-108828714717585737040260374878)⟩⟩,⟨⟨(-48638120217913569085281279637),(-48638120217913569076787746292)⟩,⟨(-110308785469584940954895760764),(-110308785469584940945527618008)⟩⟩,⟨⟨(-49286444880026379425820383026),(-49286444880026379417211758093)⟩,⟨(-111779152863456869662520479849),(-111779152863456869653023207991)⟩⟩,⟨⟨(-49924374988729221671063522765),(-49924374988729221662340764617)⟩,⟨(-113225945938316979055675112591),(-113225945938316979046048770541)⟩⟩,⟨⟨(-50557686720482431277851011688),(-50557686720482431269015470520)⟩,⟨(-114662264768903826594577766573),(-114662264768903826584824476961)⟩⟩] +lemma amp7_11_3_eq : ∀ k : Fin 16, amp7_1Expr 1 3 k = amp7_11_3 k := by decide +kernel +noncomputable def amp7_11_4 : Fin 16 → CBox := ![⟨⟨(-51180554932150761408072693893),(-51180554932150761399180540855)⟩,⟨(-116074898226548033514542378951),(-116074898226548033504787410500)⟩⟩,⟨⟨(-51798476653068572746441313064),(-51798476653068572737430119532)⟩,⟨(-117476313294489233322463521346),(-117476313294489233312564282815)⟩⟩,⟨⟨(-52405903563925214432437546137),(-52405903563925214423311211211)⟩,⟨(-118853926666427485395795163555),(-118853926666427485385758362876)⟩⟩,⟨⟨(-53008067091420818541660887435),(-53008067091420818532422553497)⟩,⟨(-120219602952322616888523706380),(-120219602952322616878355399553)⟩⟩,⟨⟨(-53599682950878333022793101590),(-53599682950878333013445214733)⟩,⟨(-121561357663008731444808706576),(-121561357663008731434512295440)⟩⟩,⟨⟨(-54185729261629598888029314779),(-54185729261629598878571060026)⟩,⟨(-122890480920204303648409641127),(-122890480920204303637982144304)⟩⟩,⟨⟨(-54761174158297399582161276365),(-54761174158297399572599852447)⟩,⟨(-124195560708890653086313316094),(-124195560708890653075768903228)⟩⟩,⟨⟨(-55330753638593851798380006267),(-55330753638593851788712808308)⟩,⟨(-125487338031254330457603124213),(-125487338031254330446934694341)⟩⟩,⟨⟨(-55889677685399926708050990821),(-55889677685399926698278763644)⟩,⟨(-126754949371838503077408700974),(-126754949371838503066615775612)⟩⟩,⟨⟨(-56442450371203974295452972342),(-56442450371203974285593136100)⟩,⟨(-128008609738205775529909189386),(-128008609738205775519030025147)⟩⟩,⟨⟨(-56984513888713790577514298997),(-56984513888713790567551418380)⟩,⟨(-129237982254988537109583033422),(-129237982254988537098580445173)⟩⟩,⟨⟨(-57520149696019410863330396705),(-57520149696019410853268712615)⟩,⟨(-130452777051604511092743748290),(-130452777051604511081626046552)⟩⟩,⟨⟨(-58045023393183337452369087252),(-58045023393183337442208642391)⟩,⟨(-131643163929215776060735889396),(-131643163929215776049500981610)⟩⟩,⟨⟨(-58563202339129627993780149521),(-58563202339129627983528428241)⟩,⟨(-132818367451209476079097318735),(-132818367451209476067760817080)⟩⟩,⟨⟨(-59070567490809294436934818269),(-59070567490809294426587100659)⟩,⟨(-133969045837229069668999854172),(-133969045837229069657548854207)⟩⟩,⟨⟨(-59570979905906762502660500880),(-59570979905906762492221952618)⟩,⟨(-135103955769931880124616471500),(-135103955769931880113061274284)⟩⟩] +lemma amp7_11_4_eq : ∀ k : Fin 16, amp7_1Expr 1 4 k = amp7_11_4 k := by decide +kernel +noncomputable def amp7_11_5 : Fin 16 → CBox := ![⟨⟨(-60060528526626865108392510556),(-60060528526626865097863139326)⟩,⟨(-136214227168949806813718089717),(-136214227168949806802056502583)⟩⟩,⟨⟨(-60542875258375211994260996599),(-60542875258375211983642329000)⟩,⟨(-137308165049690261509269223567),(-137308165049690261497503243642)⟩⟩,⟨⟨(-61014310271825440943891106408),(-61014310271825440933183289334)⟩,⟨(-138377355707728463726683768611),(-138377355707728463714811509201)⟩⟩,⟨⟨(-61478302879938500952815932859),(-61478302879938500942020919977)⟩,⟨(-139429667368592488567527254591),(-139429667368592488555551632460)⟩⟩,⟨⟨(-61931338283814348962767490069),(-61931338283814348951886492984)⟩,⟨(-140457128646955425579421388912),(-140457128646955425567342922825)⟩⟩,⟨⟨(-62376699227217381565135704396),(-62376699227217381554278899883)⟩,⟨(-141467184638886696315552602577),(-141467184638886696303619606597)⟩⟩,⟨⟨(-62811060253041564519550602688),(-62811060253041564508605053731)⟩,⟨(-142452293376628206082081942023),(-142452293376628206070036042953)⟩⟩,⟨⟨(-63237523068765669831872112150),(-63237523068765669820842141924)⟩,⟨(-143419489375151593423374328420),(-143419489375151593411223724220)⟩⟩,⟨⟨(-63652946336376028683265320716),(-63652946336376028672154660809)⟩,⟨(-144361648239445604954651388148),(-144361648239445604942402296026)⟩⟩,⟨⟨(-64060255810442041629245933994),(-64060255810442041618056429105)⟩,⟨(-145285405432223164332947511372),(-145285405432223164320602464370)⟩⟩,⟨⟨(-64456489476868880868349385751),(-64456489476868880857085600642)⟩,⟨(-146184043256009937243019069567),(-146184043256009937230586167112)⟩⟩,⟨⟨(-64844401807227121649207975904),(-64844401807227121637872001738)⟩,⟨(-147063808712379984306215068668),(-147063808712379984293697360551)⟩⟩,⟨⟨(-65221205709714364227795173054),(-65221205709714364216385218108)⟩,⟨(-147918380818730821620848720467),(-147918380818730821608239883291)⟩⟩,⟨⟨(-65589488661285843485048063748),(-65589488661285843473571226339)⟩,⟨(-148753627841333508275379170645),(-148753627841333508262693569563)⟩⟩,⟨⟨(-65946634454237240530906319738),(-65946634454237240519361124342)⟩,⟨(-149563616354037802161637795147),(-149563616354037802148869818042)⟩⟩,⟨⟨(-66295067506085358058415433981),(-66295067506085358046802468349)⟩,⟨(-150353844812593051815181808384),(-150353844812593051802331015760)⟩⟩] +lemma amp7_11_5_eq : ∀ k : Fin 16, amp7_1Expr 1 5 k = amp7_11_5 k := by decide +kernel +noncomputable def amp7_11_6 : Fin 16 → CBox := ![⟨⟨(-66632338791740151050273705493),(-66632338791740151038606448407)⟩,⟨(-151118758952524046081453353016),(-151118758952524046068548043357)⟩⟩,⟨⟨(-66960713276388809136022073958),(-66960713276388809124288270605)⟩,⟨(-151863495599797956287441964108),(-151863495599797956274452534185)⟩⟩,⟨⟨(-67277905729051392378212845027),(-67277905729051392366421606237)⟩,⟨(-152582871966659309068839813478),(-152582871966659309055784651361)⟩⟩,⟨⟨(-67586024963955147031632544591),(-67586024963955147019778522179)⟩,⟨(-153281670736631774831271953959),(-153281670736631774818137084417)⟩⟩,⟨⟨(-67882946447620971196425597110),(-67882946447620971184514681757)⟩,⟨(-153955073575727131537451940343),(-153955073575727131524248445109)⟩⟩,⟨⟨(-68170625858784866946054812609),(-68170625858784866934086597901)⟩,⟨(-154607515863955349808709572934),(-154607515863955349795434650110)⟩⟩,⟨⟨(-68447096538020503807582059397),(-68447096538020503795595590519)⟩,⟨(-155234537317658696393885410015),(-155234537317658696380625331834)⟩⟩,⟨⟨(-68714163775761176706851893856),(-68714163775761176694808460831)⟩,⟨(-155840232243817466151643736231),(-155840232243817466138308797430)⟩⟩,⟨⟨(-68970016219710489352184999310),(-68970016219710489340090208393)⟩,⟨(-156420492587453838852654399893),(-156420492587453838839255033678)⟩⟩,⟨⟨(-69216311266545650372821771748),(-69216311266545650360679406756)⟩,⟨(-156979077240023427833759625550),(-156979077240023427820302469105)⟩⟩,⟨⟨(-69451390545946672992924475610),(-69451390545946672980734255519)⟩,⟨(-157512225101898267344146985254),(-157512225101898267330629119534)⟩⟩,⟨⟨(-69676765816596932313605738753),(-69676765816596932301373674868)⟩,⟨(-158023364764963468681712767739),(-158023364764963468668145851933)⟩⟩,⟨⟨(-69890929593705596304444121164),(-69890929593705596292169981104)⟩,⟨(-158509077330305062143132082614),(-158509077330305062129513308866)⟩⟩,⟨⟨(-70095250027190538220596199526),(-70095250027190538208279222873)⟩,⟨(-158972465692424413084291039328),(-158972465692424413070616680556)⟩⟩,⟨⟨(-70288368638517981046942489507),(-70288368638517981034602571362)⟩,⟨(-159410448891027906908099176189),(-159410448891027906894412074617)⟩⟩,⟨⟨(-70471511782327267747064959885),(-70471511782327267734687775652)⟩,⟨(-159825808236129475649554212862),(-159825808236129475635819851660)⟩⟩] +lemma amp7_11_6_eq : ∀ k : Fin 16, amp7_1Expr 1 6 k = amp7_11_6 k := by decide +kernel +noncomputable def amp7_11_7 : Fin 16 → CBox := ![⟨⟨(-70643468314107287785920677247),(-70643468314107287773510183565)⟩,⟨(-160215796913513228783783380794),(-160215796913513228770008457655)⟩⟩,⟨⟨(-70805324400427207200727236991),(-70805324400427207188283033854)⟩,⟨(-160582878293772552108079057195),(-160582878293772552094260610129)⟩⟩,⟨⟨(-70956014756739613940783941795),(-70956014756739613928317706138)⟩,⟨(-160924636365678433108006376226),(-160924636365678433094168616411)⟩⟩,⟨⟨(-71096486770715766126528220778),(-71096486770715766114033903017)⟩,⟨(-161243219756334820839771677783),(-161243219756334820825898806291)⟩⟩,⟨⟨(-71225819734200030796538819089),(-71225819734200030784024285692)⟩,⟨(-161536540346423682780079207424),(-161536540346423682766186798916)⟩⟩,⟨⟨(-71344823474217662622793385482),(-71344823474217662610253880017)⟩,⟨(-161806434782492954160653734685),(-161806434782492954146728900475)⟩⟩,⟨⟨(-71452720759319491789615439677),(-71452720759319491777057590114)⟩,⟨(-162051140343105158226835139237),(-162051140343105158212890651771)⟩⟩,⟨⟨(-71550184889284250866075986220),(-71550184889284250853501514918)⟩,⟨(-162272184037949735562254909379),(-162272184037949735548292552397)⟩⟩,⟨⟨(-71636581187985562591759791537),(-71636581187985562579170262475)⟩,⟨(-162468126453818413545977857306),(-162468126453818413531998926232)⟩⟩,⟨⟨(-71712447281589071103248049730),(-71712447281589071090644361099)⟩,⟨(-162640186899539394638570398698),(-162640186899539394624574788357)⟩⟩,⟨⟨(-71777290301579416088301850046),(-71777290301579416075688248831)⟩,⟨(-162787247574361292693493191370),(-162787247574361292679488291219)⟩⟩,⟨⟨(-71831512878535996582644049902),(-71831512878535996570021751044)⟩,⟨(-162910221623981503828844535045),(-162910221623981503814830939922)⟩⟩,⟨⟨(-71874763373790792283298336797),(-71874763373790792270671393737)⟩,⟨(-163008311549766863842835478113),(-163008311549766863828820148896)⟩⟩,⟨⟨(-71907309928033851790368124675),(-71907309928033851777739056090)⟩,⟨(-163082125481178826382051276525),(-163082125481178826368037747875)⟩⟩,⟨⟨(-71928941721771935367400076461),(-71928941721771935354772600212)⟩,⟨(-163131185290317949647669806115),(-163131185290317949633664289494)⟩⟩,⟨⟨(-71939792741600879318470410755),(-71939792741600879305848891963)⟩,⟨(-163155794851976057180748810168),(-163155794851976057166759012249)⟩⟩] +lemma amp7_11_7_eq : ∀ k : Fin 16, amp7_1Expr 1 7 k = amp7_11_7 k := by decide +kernel +noncomputable def amp7_11_8 : Fin 16 → CBox := ![⟨⟨(-71939792741600879318470410755),(-71939792741600879305848891963)⟩,⟨(-163155794851976057180748810168),(-163155794851976057166759012249)⟩⟩,⟨⟨(-71928941721771935367400076461),(-71928941721771935354772600212)⟩,⟨(-163131185290317949647669806115),(-163131185290317949633664289494)⟩⟩,⟨⟨(-71907309928033851790368124675),(-71907309928033851777739056090)⟩,⟨(-163082125481178826382051276525),(-163082125481178826368037747875)⟩⟩,⟨⟨(-71874763373790792283298336797),(-71874763373790792270671393737)⟩,⟨(-163008311549766863842835478113),(-163008311549766863828820148896)⟩⟩,⟨⟨(-71831512878535996582644049902),(-71831512878535996570021751044)⟩,⟨(-162910221623981503828844535045),(-162910221623981503814830939922)⟩⟩,⟨⟨(-71777290301579416088301850046),(-71777290301579416075688248831)⟩,⟨(-162787247574361292693493191370),(-162787247574361292679488291219)⟩⟩,⟨⟨(-71712447281589071103248049730),(-71712447281589071090644361099)⟩,⟨(-162640186899539394638570398698),(-162640186899539394624574788357)⟩⟩,⟨⟨(-71636581187985562591759791537),(-71636581187985562579170262475)⟩,⟨(-162468126453818413545977857306),(-162468126453818413531998926232)⟩⟩,⟨⟨(-71550184889284250866075986220),(-71550184889284250853501514918)⟩,⟨(-162272184037949735562254909379),(-162272184037949735548292552397)⟩⟩,⟨⟨(-71452720759319491789615439677),(-71452720759319491777057590114)⟩,⟨(-162051140343105158226835139237),(-162051140343105158212890651771)⟩⟩,⟨⟨(-71344823474217662622793385482),(-71344823474217662610253880017)⟩,⟨(-161806434782492954160653734685),(-161806434782492954146728900475)⟩⟩,⟨⟨(-71225819734200030796538819089),(-71225819734200030784024285692)⟩,⟨(-161536540346423682780079207424),(-161536540346423682766186798916)⟩⟩,⟨⟨(-71096486770715766126528220778),(-71096486770715766114033903017)⟩,⟨(-161243219756334820839771677783),(-161243219756334820825898806291)⟩⟩,⟨⟨(-70956014756739613940783941795),(-70956014756739613928317706138)⟩,⟨(-160924636365678433108006376226),(-160924636365678433094168616411)⟩⟩,⟨⟨(-70805324400427207200727236991),(-70805324400427207188283033854)⟩,⟨(-160582878293772552108079057195),(-160582878293772552094260610129)⟩⟩,⟨⟨(-70643468314107287785920677247),(-70643468314107287773510183565)⟩,⟨(-160215796913513228783783380794),(-160215796913513228770008457655)⟩⟩] +lemma amp7_11_8_eq : ∀ k : Fin 16, amp7_1Expr 1 8 k = amp7_11_8 k := by decide +kernel +noncomputable def amp7_11_9 : Fin 16 → CBox := ![⟨⟨(-70471511782327267747064959885),(-70471511782327267734687775652)⟩,⟨(-159825808236129475649554212862),(-159825808236129475635819851660)⟩⟩,⟨⟨(-70288368638517981046942489507),(-70288368638517981034602571362)⟩,⟨(-159410448891027906908099176189),(-159410448891027906894412074617)⟩⟩,⟨⟨(-70095250027190538220596199526),(-70095250027190538208279222873)⟩,⟨(-158972465692424413084291039328),(-158972465692424413070616680556)⟩⟩,⟨⟨(-69890929593705596304444121164),(-69890929593705596292169981104)⟩,⟨(-158509077330305062143132082614),(-158509077330305062129513308866)⟩⟩,⟨⟨(-69676765816596932313605738753),(-69676765816596932301373674868)⟩,⟨(-158023364764963468681712767739),(-158023364764963468668145851933)⟩⟩,⟨⟨(-69451390545946672992924475610),(-69451390545946672980734255519)⟩,⟨(-157512225101898267344146985254),(-157512225101898267330629119534)⟩⟩,⟨⟨(-69216311266545650372821771748),(-69216311266545650360679406756)⟩,⟨(-156979077240023427833759625550),(-156979077240023427820302469105)⟩⟩,⟨⟨(-68970016219710489352184999310),(-68970016219710489340090208393)⟩,⟨(-156420492587453838852654399893),(-156420492587453838839255033678)⟩⟩,⟨⟨(-68714163775761176706851893856),(-68714163775761176694808460831)⟩,⟨(-155840232243817466151643736231),(-155840232243817466138308797430)⟩⟩,⟨⟨(-68447096538020503807582059397),(-68447096538020503795595590519)⟩,⟨(-155234537317658696393885410015),(-155234537317658696380625331834)⟩⟩,⟨⟨(-68170625858784866946054812609),(-68170625858784866934086597901)⟩,⟨(-154607515863955349808709572934),(-154607515863955349795434650110)⟩⟩,⟨⟨(-67882946447620971196425597110),(-67882946447620971184514681757)⟩,⟨(-153955073575727131537451940343),(-153955073575727131524248445109)⟩⟩,⟨⟨(-67586024963955147031632544591),(-67586024963955147019778522179)⟩,⟨(-153281670736631774831271953959),(-153281670736631774818137084417)⟩⟩,⟨⟨(-67277905729051392378212845027),(-67277905729051392366421606237)⟩,⟨(-152582871966659309068839813478),(-152582871966659309055784651361)⟩⟩,⟨⟨(-66960713276388809136022073958),(-66960713276388809124288270605)⟩,⟨(-151863495599797956287441964108),(-151863495599797956274452534185)⟩⟩,⟨⟨(-66632338791740151050273705493),(-66632338791740151038606448407)⟩,⟨(-151118758952524046081453353016),(-151118758952524046068548043357)⟩⟩] +lemma amp7_11_9_eq : ∀ k : Fin 16, amp7_1Expr 1 9 k = amp7_11_9 k := by decide +kernel +noncomputable def amp7_11_10 : Fin 16 → CBox := ![⟨⟨(-66295067506085358058415433981),(-66295067506085358046802468349)⟩,⟨(-150353844812593051815181808384),(-150353844812593051802331015760)⟩⟩,⟨⟨(-65946634454237240530906319738),(-65946634454237240519361124342)⟩,⟨(-149563616354037802161637795147),(-149563616354037802148869818042)⟩⟩,⟨⟨(-65589488661285843485048063748),(-65589488661285843473571226339)⟩,⟨(-148753627841333508275379170645),(-148753627841333508262693569563)⟩⟩,⟨⟨(-65221205709714364227795173054),(-65221205709714364216385218108)⟩,⟨(-147918380818730821620848720467),(-147918380818730821608239883291)⟩⟩,⟨⟨(-64844401807227121649207975904),(-64844401807227121637872001738)⟩,⟨(-147063808712379984306215068668),(-147063808712379984293697360551)⟩⟩,⟨⟨(-64456489476868880868349385751),(-64456489476868880857085600642)⟩,⟨(-146184043256009937243019069567),(-146184043256009937230586167112)⟩⟩,⟨⟨(-64060255810442041629245933994),(-64060255810442041618056429105)⟩,⟨(-145285405432223164332947511372),(-145285405432223164320602464370)⟩⟩,⟨⟨(-63652946336376028683265320716),(-63652946336376028672154660809)⟩,⟨(-144361648239445604954651388148),(-144361648239445604942402296026)⟩⟩,⟨⟨(-63237523068765669831872112150),(-63237523068765669820842141924)⟩,⟨(-143419489375151593423374328420),(-143419489375151593411223724220)⟩⟩,⟨⟨(-62811060253041564519550602688),(-62811060253041564508605053731)⟩,⟨(-142452293376628206082081942023),(-142452293376628206070036042953)⟩⟩,⟨⟨(-62376699227217381565135704396),(-62376699227217381554278899883)⟩,⟨(-141467184638886696315552602577),(-141467184638886696303619606597)⟩⟩,⟨⟨(-61931338283814348962767490069),(-61931338283814348951886492984)⟩,⟨(-140457128646955425579421388912),(-140457128646955425567342922825)⟩⟩,⟨⟨(-61478302879938500952815932859),(-61478302879938500942020919977)⟩,⟨(-139429667368592488567527254591),(-139429667368592488555551632460)⟩⟩,⟨⟨(-61014310271825440943891106408),(-61014310271825440933183289334)⟩,⟨(-138377355707728463726683768611),(-138377355707728463714811509201)⟩⟩,⟨⟨(-60542875258375211994260996599),(-60542875258375211983642329000)⟩,⟨(-137308165049690261509269223567),(-137308165049690261497503243642)⟩⟩,⟨⟨(-60060528526626865108392510556),(-60060528526626865097863139326)⟩,⟨(-136214227168949806813718089717),(-136214227168949806802056502583)⟩⟩] +lemma amp7_11_10_eq : ∀ k : Fin 16, amp7_1Expr 1 10 k = amp7_11_10 k := by decide +kernel +noncomputable def amp7_11_11 : Fin 16 → CBox := ![⟨⟨(-59570979905906762502660500880),(-59570979905906762492221952618)⟩,⟨(-135103955769931880124616471500),(-135103955769931880113061274284)⟩⟩,⟨⟨(-59070567490809294436934818269),(-59070567490809294426587100659)⟩,⟨(-133969045837229069668999854172),(-133969045837229069657548854207)⟩⟩,⟨⟨(-58563202339129627993780149521),(-58563202339129627983528428241)⟩,⟨(-132818367451209476079097318735),(-132818367451209476067760817080)⟩⟩,⟨⟨(-58045023393183337452369087252),(-58045023393183337442208642391)⟩,⟨(-131643163929215776060735889396),(-131643163929215776049500981610)⟩⟩,⟨⟨(-57520149696019410863330396705),(-57520149696019410853268712615)⟩,⟨(-130452777051604511092743748290),(-130452777051604511081626046552)⟩⟩,⟨⟨(-56984513888713790577514298997),(-56984513888713790567551418380)⟩,⟨(-129237982254988537109583033422),(-129237982254988537098580445173)⟩⟩,⟨⟨(-56442450371203974295452972342),(-56442450371203974285593136100)⟩,⟨(-128008609738205775529909189386),(-128008609738205775519030025147)⟩⟩,⟨⟨(-55889677685399926708050990821),(-55889677685399926698278763644)⟩,⟨(-126754949371838503077408700974),(-126754949371838503066615775612)⟩⟩,⟨⟨(-55330753638593851798380006267),(-55330753638593851788712808308)⟩,⟨(-125487338031254330457603124213),(-125487338031254330446934694341)⟩⟩,⟨⟨(-54761174158297399582161276365),(-54761174158297399572599852447)⟩,⟨(-124195560708890653086313316094),(-124195560708890653075768903228)⟩⟩,⟨⟨(-54185729261629598888029314779),(-54185729261629598878571060026)⟩,⟨(-122890480920204303648409641127),(-122890480920204303637982144304)⟩⟩,⟨⟨(-53599682950878333022793101590),(-53599682950878333013445214733)⟩,⟨(-121561357663008731444808706576),(-121561357663008731434512295440)⟩⟩,⟨⟨(-53008067091420818541660887435),(-53008067091420818532422553497)⟩,⟨(-120219602952322616888523706380),(-120219602952322616878355399553)⟩⟩,⟨⟨(-52405903563925214432437546137),(-52405903563925214423311211211)⟩,⟨(-118853926666427485395795163555),(-118853926666427485385758362876)⟩⟩,⟨⟨(-51798476653068572746441313064),(-51798476653068572737430119532)⟩,⟨(-117476313294489233322463521346),(-117476313294489233312564282815)⟩⟩,⟨⟨(-51180554932150761408072693893),(-51180554932150761399180540855)⟩,⟨(-116074898226548033514542378951),(-116074898226548033504787410500)⟩⟩] +lemma amp7_11_11_eq : ∀ k : Fin 16, amp7_1Expr 1 11 k = amp7_11_11 k := by decide +kernel +noncomputable def amp7_11_12 : Fin 16 → CBox := ![⟨⟨(-50557686720482431277851011688),(-50557686720482431269015470520)⟩,⟨(-114662264768903826594577766573),(-114662264768903826584824476961)⟩⟩,⟨⟨(-49924374988729221671063522765),(-49924374988729221662340764617)⟩,⟨(-113225945938316979055675112591),(-113225945938316979046048770541)⟩⟩,⟨⟨(-49286444880026379425820383026),(-49286444880026379417211758093)⟩,⟨(-111779152863456869662520479849),(-111779152863456869653023207991)⟩⟩,⟨⟨(-48638120217913569085281279637),(-48638120217913569076787746292)⟩,⟨(-110308785469584940954895760764),(-110308785469584940945527618008)⟩⟩,⟨⟨(-47985517083355406604263714160),(-47985517083355406595886451200)⟩,⟨(-108828714717585737049497585479),(-108828714717585737040260374878)⟩⟩,⟨⟨(-47322565195896356617139106800),(-47322565195896356608878248281)⟩,⟨(-107325173519802296086182651794),(-107325173519802296077074572073)⟩⟩,⟨⟨(-46655687189838484694394267576),(-46655687189838484686254173500)⟩,⟨(-105812728084513268102950002843),(-105812728084513268093980143544)⟩⟩,⟨⟨(-45978502120047616451525563430),(-45978502120047616443499464353)⟩,⟨(-104276906752354655002541951824),(-104276906752354654993692863366)⟩⟩,⟨⟨(-45297756499006132969281160310),(-45297756499006132961378508717)⟩,⟨(-102733010270862599445997490229),(-102733010270862599437289886022)⟩⟩,⟨⟨(-44606740326628404398186678701),(-44606740326628404390407073022)⟩,⟨(-101165820700761684451993319838),(-101165820700761684443424199737)⟩⟩,⟨⟨(-43912543273515121382589238696),(-43912543273515121374934867750)⟩,⟨(-99591417054765349039995238308),(-99591417054765349031568919338)⟩⟩,⟨⟨(-43208105797029466864160042776),(-43208105797029466856632988335)⟩,⟨(-97993788648851490883987168381),(-97993788648851490875706288618)⟩⟩,⟨⟨(-42500882253193745500016676134),(-42500882253193745492620656258)⟩,⟨(-96389841583740989907199509128),(-96389841583740989899071934157)⟩⟩,⟨⟨(-41783440652515466068355332979),(-41783440652515466061053734711)⟩,⟨(-94762720484866194053651357469),(-94762720484866194045591972241)⟩⟩,⟨⟨(-41063624160825241731848487274),(-41063624160825241724677497276)⟩,⟨(-93130213253838745821369879133),(-93130213253838745813460270022)⟩⟩,⟨⟨(-40333602637358103894797127756),(-40333602637358103887757807986)⟩,⟨(-91474561529234112670356114608),(-91474561529234112662596614004)⟩⟩] +lemma amp7_11_12_eq : ∀ k : Fin 16, amp7_1Expr 1 12 k = amp7_11_12 k := by decide +kernel +noncomputable def amp7_11_13 : Fin 16 → CBox := ![⟨⟨(-39601635200454137558798396014),(-39601635200454137551890252291)⟩,⟨(-89814496571821883454644797153),(-89814496571821883447033888412)⟩⟩,⟨⟨(-38859464590104374377974855975),(-38859464590104374371194951128)⟩,⟨(-88131291335433024609167182194),(-88131291335433024601696128263)⟩⟩,⟨⟨(-38115796549175229434861832633),(-38115796549175229428217844080)⟩,⟨(-86444690002570935227721582471),(-86444690002570935220407490713)⟩⟩,⟨⟨(-37361913902531192336344136252),(-37361913902531192329835004187)⟩,⟨(-84734922462926753851598299396),(-84734922462926753844436688202)⟩⟩,⟨⟨(-36607003843609385797043339582),(-36607003843609385790672614349)⟩,⟨(-83022824804436911451926921330),(-83022824804436911444925633689)⟩⟩,⟨⟨(-35841851965557722421813203677),(-35841851965557722415558197595)⟩,⟨(-81287499220522484617352295374),(-81287499220522484610457793218)⟩⟩,⟨⟨(-35076166662618009666464738450),(-35076166662618009660346502591)⟩,⟨(-79550963856063983529100811642),(-79550963856063983522360729216)⟩⟩,⟨⟨(-34300193600980150026913335299),(-34300193600980150020933748928)⟩,⟨(-77791096377574093956551319257),(-77791096377574093949967825736)⟩⟩,⟨⟨(-33524208008310895725803597375),(-33524208008310895719962114850)⟩,⟨(-76031200479341672532275319333),(-76031200479341672525847174679)⟩⟩,⟨⟨(-32737866477294929153922844099),(-32737866477294929148218719000)⟩,⟨(-74247817839098958517480461636),(-74247817839098958511203866231)⟩⟩,⟨⟨(-31952063788142973133808044886),(-31952063788142973128243677766)⟩,⟨(-72465657264826575314405402386),(-72465657264826575308285910182)⟩⟩,⟨⟨(-31155810506980960749502871356),(-31155810506980960744064393326)⟩,⟨(-70659795278844557636779566998),(-70659795278844557630783598029)⟩⟩,⟨⟨(-30360682302007587725843428630),(-30360682302007587720548990581)⟩,⟨(-68856484908495988082600955151),(-68856484908495988076769903600)⟩⟩,⟨⟨(-29554977221247464424954382728),(-29554977221247464419803844073)⟩,⟨(-67029186721248413941559348309),(-67029186721248413935890743610)⟩⟩,⟨⟨(-28751023739938367698683601342),(-28751023739938367693675517388)⟩,⟨(-65205861072561258318289600964),(-65205861072561258312780522966)⟩⟩,⟨⟨(-27936329116135969239295422414),(-27936329116135969234433461661)⟩,⟨(-63358175058430631413562613425),(-63358175058430631408219196959)⟩⟩] +lemma amp7_11_13_eq : ∀ k : Fin 16, amp7_1Expr 1 13 k = amp7_11_13 k := by decide +kernel +noncomputable def amp7_11_14 : Fin 16 → CBox := ![⟨⟨(-27124059698702532523572315062),(-27124059698702532518843904565)⟩,⟨(-61515989289125970110793078472),(-61515989289125970105587302116)⟩⟩,⟨⟨(-26300838960499855275522525371),(-26300838960499855270940280500)⟩,⟨(-59648966480726655561231008395),(-59648966480726655556189255269)⟩⟩,⟨⟨(-25480772729857277565223587220),(-25480772729857277560785364561)⟩,⟨(-57789097935200786629587195133),(-57789097935200786624705245824)⟩⟩,⟨⟨(-24649489050903922246827100817),(-24649489050903922242538893764)⟩,⟨(-55903788786837351760092316091),(-55903788786837351755381481278)⟩⟩,⟨⟨(-23822155938916705063499133651),(-23822155938916705059348677261)⟩,⟨(-54027439323634414944508690701),(-54027439323634414939941957803)⟩⟩,⟨⟨(-22983270389303945550619638569),(-22983270389303945546617880547)⟩,⟨(-52124889518848018485882348004),(-52124889518848018481482195676)⟩⟩,⟨⟨(-22149212667309377173655086826),(-22149212667309377169794608050)⟩,⟨(-50233288981809495284564604849),(-50233288981809495280315189053)⟩⟩,⟨⟨(-21303181743484879757414678730),(-21303181743484879753704855090)⟩,⟨(-48314533831349969678026767697),(-48314533831349969673946916694)⟩⟩,⟨⟨(-20462956309978198966709899348),(-20462956309978198963148833218)⟩,⟨(-46408945237968402989274367505),(-46408945237968402985360958619)⟩⟩,⟨⟨(-19610228521757425348210081632),(-19610228521757425344794759760)⟩,⟨(-44475001939309522031710620608),(-44475001939309522027954276507)⟩⟩,⟨⟨(-18764410360201072200140250932),(-18764410360201072196875586473)⟩,⟨(-42556729322864214032154535932),(-42556729322864214028567805071)⟩⟩,⟨⟨(-17905421340180017042322055470),(-17905421340180017039205104528)⟩,⟨(-40608585868600260492922082034),(-40608585868600260489495608373)⟩⟩,⟨⟨(-17054608847284225419239987243),(-17054608847284225416269317177)⟩,⟨(-38678986362426939556584611203),(-38678986362426939553316808989)⟩⟩,⟨⟨(-16189774056173590093379828021),(-16189774056173590090562745547)⟩,⟨(-36717584996341235470969081925),(-36717584996341235467873669775)⟩⟩,⟨⟨(-15334597482021724184261020689),(-15334597482021724181592023693)⟩,⟨(-34778087975607497058000584736),(-34778087975607497055067048967)⟩⟩,⟨⟨(-14464300825782799818488755860),(-14464300825782799815970791072)⟩,⟨(-32804299376914922133897891650),(-32804299376914922131129839321)⟩⟩] +lemma amp7_11_14_eq : ∀ k : Fin 16, amp7_1Expr 1 14 k = amp7_11_14 k := by decide +kernel +noncomputable def amp7_11_15 : Fin 16 → CBox := ![⟨⟨(-13605436144528543519196265342),(-13605436144528543516828173405)⟩,⟨(-30856437916656717947550984177),(-30856437916656717944948111604)⟩⟩,⟨⟨(-12730011261233991577021311881),(-12730011261233991574806354246)⟩,⟨(-28871018759554729027365687731),(-28871018759554729024932022774)⟩⟩,⟨⟨(-11868204086295200169379681504),(-11868204086295200167315784237)⟩,⟨(-26916483873120949763301902179),(-26916483873120949761035511597)⟩⟩,⟨⟨(-10987901608861133640851178104),(-10987901608861133638939674672)⟩,⟨(-24920002580329241960137755701),(-24920002580329241958037901113)⟩⟩,⟨⟨(-10124011078824646543047836555),(-10124011078824646541286564870)⟩,⟨(-22960742750384096492821743830),(-22960742750384096490886860515)⟩⟩,⟨⟨(-9238936788997680558781181562),(-9238936788997680557174229850)⟩,⟨(-20953439229529479545805801894),(-20953439229529479544040852196)⟩⟩,⟨⟨(-8374023000594305592533640641),(-8374023000594305591078117491)⟩,⟨(-18991858701597502347780696286),(-18991858701597502346183224010)⟩⟩,⟨⟨(-7484008818589727933780833190),(-7484008818589727932479478168)⟩,⟨(-16973351756267974183439228409),(-16973351756267974182010340420)⟩⟩,⟨⟨(-6619527590048496234627703368),(-6619527590048496233477230170)⟩,⟨(-15012752252126022925787575770),(-15012752252126022924525013227)⟩⟩,⟨⟨(-5723823631345515039467730650),(-5723823631345515038473326584)⟩,⟨(-12981341182328237041432561211),(-12981341182328237040341736829)⟩⟩,⟨⟨(-4862135239681351865087071951),(-4862135239681351864243057089)⟩,⟨(-11027075690326225203260215559),(-11027075690326225202335167549)⟩⟩,⟨⟨(-3958514790998972548399347882),(-3958514790998972547712629927)⟩,⟨(-8977710423472774273954987717),(-8977710423472774273202851900)⟩⟩,⟨⟨(-3104583262309451839230503685),(-3104583262309451838692795874)⟩,⟨(-7041037102589901691007393396),(-7041037102589901690419484343)⟩⟩,⟨⟨(-2185759460592364487045245205),(-2185759460592364486667226994)⟩,⟨(-4957191403499139413933090736),(-4957191403499139413520427464)⟩⟩,⟨⟨(-1355876442797423833667302980),(-1355876442797423833434660233)⟩,⟨(-3075058883478800724797321485),(-3075058883478800724545534046)⟩⟩,⟨⟨(-385210003677661993001841233),(-385210003677661992936859914)⟩,⟨(-873636716757143324791863454),(-873636716757143324722854824)⟩⟩] +lemma amp7_11_15_eq : ∀ k : Fin 16, amp7_1Expr 1 15 k = amp7_11_15 k := by decide +kernel +noncomputable def amp7_11 : Fin 16 → Fin 16 → CBox := ![amp7_11_0,amp7_11_1,amp7_11_2,amp7_11_3,amp7_11_4,amp7_11_5,amp7_11_6,amp7_11_7,amp7_11_8,amp7_11_9,amp7_11_10,amp7_11_11,amp7_11_12,amp7_11_13,amp7_11_14,amp7_11_15] +lemma amp7_11_eq (i k : Fin 16) : amp7_1Expr 1 i k = amp7_11 i k := by + fin_cases i + · exact amp7_11_0_eq k + · exact amp7_11_1_eq k + · exact amp7_11_2_eq k + · exact amp7_11_3_eq k + · exact amp7_11_4_eq k + · exact amp7_11_5_eq k + · exact amp7_11_6_eq k + · exact amp7_11_7_eq k + · exact amp7_11_8_eq k + · exact amp7_11_9_eq k + · exact amp7_11_10_eq k + · exact amp7_11_11_eq k + · exact amp7_11_12_eq k + · exact amp7_11_13_eq k + · exact amp7_11_14_eq k + · exact amp7_11_15_eq k +noncomputable def amp7_12_0 : Fin 16 → CBox := ![⟨⟨(-27656833929615362301610970),(-27656833929615362243014461)⟩,⟨(-667203297953504647164066679),(-667203297953504647102051385)⟩⟩,⟨⟨(-97347548738388396714097994),(-97347548738388396507566454)⟩,⟨(-2348446887710894609690848324),(-2348446887710894609465776528)⟩⟩,⟨⟨(-156930468665277273180418668),(-156930468665277272847262443)⟩,⟨(-3785846438870318533956038631),(-3785846438870318533588041395)⟩⟩,⟨⟨(-222899049574540212169828187),(-222899049574540211696567476)⟩,⟨(-5377295946647905665500084817),(-5377295946647905664976037460)⟩⟩,⟨⟨(-284208574900344161774741289),(-284208574900344161171228039)⟩,⟨(-6856348740523115919113846891),(-6856348740523115918443733564)⟩⟩,⟨⟨(-349085604172734029159712332),(-349085604172734028418394918)⟩,⟨(-8421465268399182256438860267),(-8421465268399182255614846557)⟩⟩,⟨⟨(-410952047203312812760335419),(-410952047203312811887580460)⟩,⟨(-9913953343053823115674093288),(-9913953343053823114702642628)⟩⟩,⟨⟨(-475260698067625594091117859),(-475260698067625593081755230)⟩,⟨(-11465358108067962011839371583),(-11465358108067962010715108547)⟩⟩,⟨⟨(-537327657764345332657821588),(-537327657764345331516595036)⟩,⟨(-12962683518090937550684809200),(-12962683518090937549412622364)⟩⟩,⟨⟨(-601227801041259061596678366),(-601227801041259060319777222)⟩,⟨(-14504233300779720021235732828),(-14504233300779720019813279810)⟩⟩,⟨⟨(-663325817138793157807663335),(-663325817138793156398798454)⟩,⟨(-16002307926461242688085304115),(-16002307926461242686514037066)⟩⟩,⟨⟨(-726871292114567087817855541),(-726871292114567086273996773)⟩,⟨(-17535301564914489678017803450),(-17535301564914489676295359152)⟩⟩,⟨⟨(-788895841566765077189859522),(-788895841566765075514266205)⟩,⟨(-19031603855115292601799807614),(-19031603855115292599930487989)⟩⟩,⟨⟨(-852098715826997533434367084),(-852098715826997531624586244)⟩,⟨(-20556332472059850912632133184),(-20556332472059850910614346466)⟩⟩,⟨⟨(-913973687112991921252051141),(-913973687112991919310767938)⟩,⟨(-22049026285381237279019797160),(-22049026285381237276853426584)⟩⟩,⟨⟨(-976826365869980122761199476),(-976826365869980120686358472)⟩,⟨(-23565306661457456127417424283),(-23565306661457456125100664196)⟩⟩] +lemma amp7_12_0_eq : ∀ k : Fin 16, amp7_1Expr 2 0 k = amp7_12_0 k := by decide +kernel +noncomputable def amp7_12_1 : Fin 16 → CBox := ![⟨⟨(-1038490075614490174852478584),(-1038490075614490172646632439)⟩,⟨(-25052903926216277138125799795),(-25052903926216277135662126666)⟩⟩,⟨⟨(-1100974564234470579653404551),(-1100974564234470577314869501)⟩,⟨(-26560301952479399676995960492),(-26560301952479399674384866015)⟩⟩,⟨⟨(-1162373479802631049792748092),(-1162373479802631047323852580)⟩,⟨(-28041511228353124900388505991),(-28041511228353124897633110449)⟩⟩,⟨⟨(-1224465824149729459851832114),(-1224465824149729457250828914)⟩,⟨(-29539449026709962118098137362),(-29539449026709962115190177875)⟩⟩,⟨⟨(-1285551412780888597796014547),(-1285551412780888595065391440)⟩,⟨(-31013099492119807673975335512),(-31013099492119807670925628100)⟩⟩,⟨⟨(-1347224049647206334698183517),(-1347224049647206331836692895)⟩,⟨(-32500912117940074765900967770),(-32500912117940074762708103704)⟩⟩,⟨⟨(-1407951061421260000625004855),(-1407951061421259997634279331)⟩,⟨(-33965912147720179358511268828),(-33965912147720179355168421246)⟩⟩,⟨⟨(-1469174162069821264715295580),(-1469174162069821261594720527)⟩,⟨(-35442880001944392874832933130),(-35442880001944392871349518340)⟩⟩,⟨⟨(-1529499634035960903710652474),(-1529499634035960900461761934)⟩,⟨(-36898193142589549348787460163),(-36898193142589549345156618878)⟩⟩,⟨⟨(-1590241921453586584029370389),(-1590241921453586580651215324)⟩,⟨(-38363561687428013407098289925),(-38363561687428013403317496980)⟩⟩,⟨⟨(-1650124571656563996945734532),(-1650124571656563993440664401)⟩,⟨(-39808192038367763713527386976),(-39808192038367763709611311128)⟩⟩,⟨⟨(-1710353844287314215863895856),(-1710353844287314212230702072)⟩,⟨(-41261184432032405306307013214),(-41261184432032405302243437527)⟩⟩,⟨⟨(-1769753689214106828570418862),(-1769753689214106824811504827)⟩,⟨(-42694167416778337223924787623),(-42694167416778337219731158516)⟩⟩,⟨⟨(-1829437172087648441306829153),(-1829437172087648437420761187)⟩,⟨(-44133992984228323627904857832),(-44133992984228323623560450075)⟩⟩,⟨⟨(-1888315278407924775512521337),(-1888315278407924771501300238)⟩,⟨(-45554389361272765537347298611),(-45554389361272765532861021451)⟩⟩,⟨⟨(-1947419868181087741634811247),(-1947419868181087737497841479)⟩,⟨(-46980249505684159979874467531),(-46980249505684159975243022307)⟩⟩] +lemma amp7_12_1_eq : ∀ k : Fin 16, amp7_1Expr 2 1 k = amp7_12_1 k := by decide +kernel +noncomputable def amp7_12_2 : Fin 16 → CBox := ![⟨⟨(-2005738188498802511522816576),(-2005738188498802507262537114)⟩,⟨(-48387141406113245539888904487),(-48387141406113245535132704957)⟩⟩,⟨⟨(-2064230630799723996255937032),(-2064230630799723991871105641)⟩,⟨(-49798233887192212472605851334),(-49798233887192212467703438682)⟩⟩,⟨⟨(-2121951893766475953212471692),(-2121951893766475948704855564)⟩,⟨(-51190722163741443754311882413),(-51190722163741443749268201537)⟩⟩,⟨⟨(-2179798915915662809692749084),(-2179798915915662805061999263)⟩,⟨(-52586244299534362816718878175),(-52586244299534362811531656585)⟩⟩,⟨⟨(-2236886552549583813783336467),(-2236886552549583809030923668)⟩,⟨(-53963446749079285357071868495),(-53963446749079285351739475110)⟩⟩,⟨⟨(-2294054966019543065851681016),(-2294054966019543060978750899)⟩,⟨(-55342597887745317216560408264),(-55342597887745317211114428947)⟩⟩,⟨⟨(-2350473060741471697426200658),(-2350473060741471692433220609)⟩,⟨(-56703648070080758093839622311),(-56703648070080758088254664432)⟩⟩,⟨⟨(-2406929842568628609986538371),(-2406929842568628604873605302)⟩,⟨(-58065631553901910366462782214),(-58065631553901910360743074341)⟩⟩,⟨⟨(-2462643101475025597406531000),(-2462643101475025592175041196)⟩,⟨(-59409678026346506146522121247),(-59409678026346506140665011949)⟩⟩,⟨⟨(-2518355460693847131945501519),(-2518355460693847126595417559)⟩,⟨(-60753702794408055132074630404),(-60753702794408055126079172956)⟩⟩,⟨⟨(-2573329192070436687114853267),(-2573329192070436681647750407)⟩,⟨(-62079908641708405065114770179),(-62079908641708405058982869914)⟩⟩,⟨⟨(-2628264625263173648641529086),(-2628264625263173643058993407)⟩,⟨(-63405190570000631731358521666),(-63405190570000631725126570133)⟩⟩,⟨⟨(-2682464728926284393915258951),(-2682464728926284388217095450)⟩,⟨(-64712733147198015488789531634),(-64712733147198015482416888991)⟩⟩,⟨⟨(-2736591067706676012044109443),(-2736591067706676006230716864)⟩,⟨(-66018496194129982506636372618),(-66018496194129982500129053457)⟩⟩,⟨⟨(-2789984030792729050100287016),(-2789984030792729044173019357)⟩,⟨(-67306567024984472897543568697),(-67306567024984472890898397326)⟩⟩,⟨⟨(-2843269483200295804889289331),(-2843269483200295798848907454)⟩,⟨(-68592044229994666775261016271),(-68592044229994666768491093921)⟩⟩] +lemma amp7_12_2_eq : ∀ k : Fin 16, amp7_1Expr 2 2 k = amp7_12_2 k := by decide +kernel +noncomputable def amp7_12_3 : Fin 16 → CBox := ![⟨⟨(-2895822380713515644032383916),(-2895822380713515637880105430)⟩,⟨(-69859849020198302903446890531),(-69859849020198302896545791318)⟩⟩,⟨⟨(-2948235567927807714910855392),(-2948235567927807708646917251)⟩,⟨(-71124283389462221100541088648),(-71124283389462221093507701343)⟩⟩,⟨⟨(-2999916066825581615756813311),(-2999916066825581609382720510)⟩,⟨(-72371042125195670214190880321),(-72371042125195670207025705491)⟩⟩,⟨⟨(-3051426056220250145278058207),(-3051426056220250138796741326)⟩,⟨(-73613687429033992087192305575),(-73613687429033992079957708797)⟩⟩,⟨⟨(-3102202422140761775415123886),(-3102202422140761768825384804)⟩,⟨(-74838634539266376566883681541),(-74838634539266376559514906807)⟩⟩,⟨⟨(-3152778757425303733860278615),(-3152778757425303727162774339)⟩,⟨(-76058756039295136484498335947),(-76058756039295136477001457623)⟩⟩,⟨⟨(-3202619863391098241747276015),(-3202619863391098234943589712)⟩,⟨(-77261140605751933134797322439),(-77261140605751933127174602818)⟩⟩,⟨⟨(-3252232592395201078184009791),(-3252232592395201071274743949)⟩,⟨(-78458015725161932425078811205),(-78458015725161932417333624136)⟩⟩,⟨⟨(-3301107928990071964428596030),(-3301107928990071957415159740)⟩,⟨(-79637101727835810797421066180),(-79637101727835810789551368728)⟩⟩,⟨⟨(-3349727629506710180507437522),(-3349727629506710173391007933)⟩,⟨(-80810020674840670668397411256),(-80810020674840670660419108498)⟩⟩,⟨⟨(-3397607316141974808995422016),(-3397607316141974801776956137)⟩,⟨(-81965087263783130376055074949),(-81965087263783130367955089683)⟩⟩,⟨⟨(-3445205120144288778393095969),(-3445205120144288771073456508)⟩,⟨(-83113353615835889361150050685),(-83113353615835889352935419587)⟩⟩,⟨⟨(-3492059917117642071083063931),(-3492059917117642063663709382)⟩,⟨(-84243695402069335379734999094),(-84243695402069335371404596706)⟩⟩,⟨⟨(-3538607533590063836983691759),(-3538607533590063829465305761)⟩,⟨(-85366626656648648034180126633),(-85366626656648648025735433398)⟩⟩,⟨⟨(-3584408854704921202663579795),(-3584408854704921195047686439)⟩,⟨(-86471554016599907621912873837),(-86471554016599907613354186046)⟩⟩,⟨⟨(-3629878591273424897434603021),(-3629878591273424889721945839)⟩,⟨(-87568482113025898510075613201),(-87568482113025898501404663575)⟩⟩] +lemma amp7_12_3_eq : ∀ k : Fin 16, amp7_1Expr 2 3 k = amp7_12_3 k := by decide +kernel +noncomputable def amp7_12_4 : Fin 16 → CBox := ![⟨⟨(-3674598516835281405541633863),(-3674598516835281397737707899)⟩,⟨(-88647321502055012110914561758),(-88647321502055012102227271500)⟩⟩,⟨⟨(-3718963300339778592150416574),(-3718963300339778584251432185)⟩,⟨(-89717593317785057656385388637),(-89717593317785057647572979270)⟩⟩,⟨⟨(-3762574590383011711748566928),(-3762574590383011703756273375)⟩,⟨(-90769687589273372326957572619),(-90769687589273372318025420767)⟩⟩,⟨⟨(-3805807986503100699888286209),(-3805807986503100691803646003)⟩,⟨(-91812665413360657271041991677),(-91812665413360657261994849603)⟩⟩,⟨⟨(-3848284094129928595069852090),(-3848284094129928586894517570)⟩,⟨(-92837374140504600639206853155),(-92837374140504600630047573871)⟩⟩,⟨⟨(-3890360326150824622576984783),(-3890360326150824614311677197)⟩,⟨(-93852436126314091896472520084),(-93852436126314091887198961338)⟩⟩,⟨⟨(-3931675410886016127229195353),(-3931675410886016118875915790)⟩,⟨(-94849135924298945235019855729),(-94849135924298945225643095291)⟩⟩,⟨⟨(-3972569377672655666642728616),(-3972569377672655658202111239)⟩,⟨(-95835676523121076728528914661),(-95835676523121076719043671272)⟩⟩,⟨⟨(-4012698318754671959044875233),(-4012698318754671950518465323)⟩,⟨(-96803761369761203747332646315),(-96803761369761203737738812158)⟩⟩,⟨⟨(-4052385611987333482645288790),(-4052385611987333474035198276)⟩,⟨(-97761191746610121644366275541),(-97761191746610121634693216212)⟩⟩,⟨⟨(-4091304021530033263000828264),(-4091304021530033254307448270)⟩,⟨(-98700073299866625192865359610),(-98700073299866625183084935434)⟩⟩,⟨⟨(-4129760942243346623508396504),(-4129760942243346614732931420)⟩,⟨(-99627821732473132352897515312),(-99627821732473132343016228495)⟩⟩,⟨⟨(-4167445178213067194334123046),(-4167445178213067185478082680)⟩,⟨(-100536929643517573740990053136),(-100536929643517573731006565759)⟩⟩,⟨⟨(-4204648752671252395283037457),(-4204648752671252386347896455)⟩,⟨(-101434441905309035888203683519),(-101434441905309035878130080580)⟩⟩,⟨⟨(-4241075931632628766699686618),(-4241075931632628757686620084)⟩,⟨(-102313224126008108070852077629),(-102313224126008108060678765339)⟩⟩,⟨⟨(-4277003926566657997830818066),(-4277003926566657988741170291)⟩,⟨(-103179963853695169878071373651),(-103179963853695169867806387100)⟩⟩] +lemma amp7_12_4_eq : ∀ k : Fin 16, amp7_1Expr 2 4 k = amp7_12_4 k := by decide +kernel +noncomputable def amp7_12_5 : Fin 16 → CBox := ![⟨⟨(-4312151936157441302840758601),(-4312151936157441293676051115)⟩,⟨(-104027886937557653611832427624),(-104027886937557653601474354899)⟩⟩,⟨⟨(-4346782873384138112417656350),(-4346782873384138103179007054)⟩,⟨(-104863335983810586459690833058),(-104863335983810586449241373492)⟩⟩,⟨⟨(-4380630384484886435589315344),(-4380630384484886426278262471)⟩,⟨(-105679885379573300040733779341),(-105679885379573300030191755855)⟩⟩,⟨⟨(-4413943554923445718821376187),(-4413943554923445709439101973)⟩,⟨(-106483544151161515235527644991),(-106483544151161515224895465068)⟩⟩,⟨⟨(-4446470033492561677011166125),(-4446470033492561667559291616)⟩,⟨(-107268224488301970263379248391),(-107268224488301970252657573117)⟩⟩,⟨⟨(-4478445510590351200396356462),(-4478445510590351190883866452)⟩,⟨(-108039612269982829936661425638),(-108039612269982829926040079975)⟩⟩,⟨⟨(-4509631229138743676949590095),(-4509631229138743667369916106)⟩,⟨(-108791947635538051987733681718),(-108791947635538051977015609937)⟩⟩,⟨⟨(-4540249881715345231392420528),(-4540249881715345221746978733)⟩,⟨(-109530602899911085895670390127),(-109530602899911085884862044022)⟩⟩,⟨⟨(-4570075930398161694124332695),(-4570075930398161684414936595)⟩,⟨(-110250137106058509769910695668),(-110250137106058509759017090263)⟩⟩,⟨⟨(-4599319434914282693642681608),(-4599319434914282683870599613)⟩,⟨(-110955617809545002175482639945),(-110955617809545002164505905905)⟩⟩,⟨⟨(-4627767732219821182152890256),(-4627767732219821172320000762)⟩,⟨(-111641914651465586221771982055),(-111641914651465586210718572745)⟩⟩,⟨⟨(-4655618584475842407361360925),(-4655618584475842397468979093)⟩,⟨(-112313798516528502281958547940),(-112313798516528502270830993686)⟩⟩,⟨⟨(-4682671887494008458758632805),(-4682671887494008448808185222)⟩,⟨(-112966442020126635281623372361),(-112966442020126635270417112493)⟩⟩,⟨⟨(-4709113413761441761748522154),(-4709113413761441751741711428)⟩,⟨(-113604326803809865656055310330),(-113604326803809865644781521632)⟩⟩,⟨⟨(-4734755328016043894198463300),(-4734755328016043884136742742)⟩,⟨(-114222921462911159953182022235),(-114222921462911159941836687941)⟩⟩,⟨⟨(-4759771695603984760928825912),(-4759771695603984750813457543)⟩,⟨(-114826425211748380409627941777),(-114826425211748380398210936882)⟩⟩] +lemma amp7_12_5_eq : ∀ k : Fin 16, amp7_1Expr 2 5 k = amp7_12_5 k := by decide +kernel +noncomputable def amp7_12_6 : Fin 16 → CBox := ![⟨⟨(-4783986684434824899422531215),(-4783986684434824889256045461)⟩,⟨(-115410596214436558110744449365),(-115410596214436558099277655491)⟩⟩,⟨⟨(-4807562911692542951770148556),(-4807562911692542941552911154)⟩,⟨(-115979357505757280247705466244),(-115979357505757280236166490261)⟩⟩,⟨⟨(-4830336305174704897768720176),(-4830336305174704887502950786)⟩,⟨(-116528750949546260435028348331),(-116528750949546260423431503689)⟩⟩,⟨⟨(-4852458270930776066840549540),(-4852458270930776056527134468)⟩,⟨(-117062429119188813286233864779),(-117062429119188813274568697839)⟩⟩,⟨⟨(-4873776274319785408539204368),(-4873776274319785398180134280)⟩,⟨(-117576712214756753239186442313),(-117576712214756753227461687001)⟩⟩,⟨⟨(-4894430726757596747019360891),(-4894430726757596736615900539)⟩,⟨(-118074987571184117966407259597),(-118074987571184117954620999518)⟩⟩,⟨⟨(-4914280428450251334085667927),(-4914280428450251323642189898)⟩,⟨(-118553848834423318827303494183),(-118553848834423318815521887107)⟩⟩,⟨⟨(-4933454993419274271794963003),(-4933454993419274261310004569)⟩,⟨(-119016422859227240666588845904),(-119016422859227240654743610549)⟩⟩,⟨⟨(-4951824372420951267939780688),(-4951824372420951257415314480)⟩,⟨(-119459572291388118546876441603),(-119459572291388118534975817020)⟩⟩,⟨⟨(-4969507561182858006726103798),(-4969507561182857996163739557)⟩,⟨(-119886167826159173648285419386),(-119886167826159173636334705505)⟩⟩,⟨⟨(-4986385494073012467443191669),(-4986385494073012456844479475)⟩,⟨(-120293337081888424618277486396),(-120293337081888424606274725073)⟩⟩,⟨⟨(-5002566710481483931663140081),(-5002566710481483921029870130)⟩,⟨(-120683698501424260563406663463),(-120683698501424260551360993516)⟩⟩,⟨⟨(-5017942977869881859878757705),(-5017942977869881849212482970)⟩,⟨(-121054641044517323065312282218),(-121054641044517323053221830316)⟩⟩,⟨⟨(-5032612524982808379225827536),(-5032612524982808368527871531)⟩,⟨(-121408534416337739788734357263),(-121408534416337739776596514978)⟩⟩,⟨⟨(-5046477817449798237417330248),(-5046477817449798226690689680)⟩,⟨(-121743025663044017270285594346),(-121743025663044017258133351438)⟩⟩,⟨⟨(-5059626903572492902206905349),(-5059626903572492891451948368)⟩,⟨(-122060238893179595329295985170),(-122060238893179595317103222031)⟩⟩] +lemma amp7_12_6_eq : ∀ k : Fin 16, amp7_1Expr 2 6 k = amp7_12_6 k := by decide +kernel +noncomputable def amp7_12_7 : Fin 16 → CBox := ![⟨⟨(-5071972827087325089489405431),(-5071972827087325078707982284)⟩,⟨(-122358076342915922350466726355),(-122358076342915922338238828514)⟩⟩,⟨⟨(-5083593571245343653476405769),(-5083593571245343642669901843)⟩,⟨(-122638419307936276685375677249),(-122638419307936276673110626799)⟩⟩,⟨⟨(-5094412652057206992734302059),(-5094412652057206981905118970)⟩,⟨(-122899422661280022645655056649),(-122899422661280022633371613802)⟩⟩,⟨⟨(-5104498088897388248151962531),(-5104498088897388237301096551)⟩,⟨(-123142727326528243656848114629),(-123142727326528243644534460659)⟩⟩,⟨⟨(-5113783777894453979337302796),(-5113783777894453968466878227)⟩,⟨(-123366738590376440396565709172),(-123366738590376440384234007869)⟩⟩,⟨⟨(-5122327862012853065390879094),(-5122327862012853054502000575)⟩,⟨(-123572859114377696320993557625),(-123572859114377696308634215515)⟩⟩,⟨⟨(-5130074538545206828760228520),(-5130074538545206817854926869)⟩,⟨(-123759742694172808922085962969),(-123759742694172808909709002981)⟩⟩,⟨⟨(-5137072148240684482332526795),(-5137072148240684471412386360)⟩,⟨(-123928555519187267892495365193),(-123928555519187267880102401817)⟩⟩,⟨⟨(-5143275123403590886103876527),(-5143275123403590875170559139)⟩,⟨(-124078198298123836811496102552),(-124078198298123836799088392689)⟩⟩,⟨⟨(-5148722063855938653109403887),(-5148722063855938642164448307)⟩,⟨(-124209602226816889764846463985),(-124209602226816889752424181891)⟩⟩,⟨⟨(-5153377583230426007341744062),(-5153377583230425996386998489)⟩,⟨(-124321913631956371650130214473),(-124321913631956371637699270030)⟩⟩,⟨⟨(-5157270589102046099688536735),(-5157270589102046088725575306)⟩,⟨(-124415829890162482492140430202),(-124415829890162482479701534452)⟩⟩,⟨⟨(-5160375834950324849780650371),(-5160375834950324838811300247)⟩,⟨(-124490741945396305280760859734),(-124490741945396305268319594017)⟩⟩,⟨⟨(-5162712572410639443028488205),(-5162712572410639432054428818)⟩,⟨(-124547114230956580769819867088),(-124547114230956580757379189632)⟩⟩,⟨⟨(-5164265665324380312223504764),(-5164265665324380301246531157)⟩,⟨(-124584581596769791812326256277),(-124584581596769791799891174700)⟩⟩,⟨⟨(-5165044733496314884910758212),(-5165044733496314873932693142)⟩,⟨(-124603376114427460083527140526),(-124603376114427460071103801112)⟩⟩] +lemma amp7_12_7_eq : ∀ k : Fin 16, amp7_1Expr 2 7 k = amp7_12_7 k := by decide +kernel +noncomputable def amp7_12_8 : Fin 16 → CBox := ![⟨⟨(-5165044733496314884910758212),(-5165044733496314873932693142)⟩,⟨(-124603376114427460083527140526),(-124603376114427460071103801112)⟩⟩,⟨⟨(-5164265665324380312223504764),(-5164265665324380301246531157)⟩,⟨(-124584581596769791812326256277),(-124584581596769791799891174700)⟩⟩,⟨⟨(-5162712572410639443028488205),(-5162712572410639432054428818)⟩,⟨(-124547114230956580769819867088),(-124547114230956580757379189632)⟩⟩,⟨⟨(-5160375834950324849780650371),(-5160375834950324838811300247)⟩,⟨(-124490741945396305280760859734),(-124490741945396305268319594017)⟩⟩,⟨⟨(-5157270589102046099688536735),(-5157270589102046088725575306)⟩,⟨(-124415829890162482492140430202),(-124415829890162482479701534452)⟩⟩,⟨⟨(-5153377583230426007341744062),(-5153377583230425996386998489)⟩,⟨(-124321913631956371650130214473),(-124321913631956371637699270030)⟩⟩,⟨⟨(-5148722063855938653109403887),(-5148722063855938642164448307)⟩,⟨(-124209602226816889764846463985),(-124209602226816889752424181891)⟩⟩,⟨⟨(-5143275123403590886103876527),(-5143275123403590875170559139)⟩,⟨(-124078198298123836811496102552),(-124078198298123836799088392689)⟩⟩,⟨⟨(-5137072148240684482332526795),(-5137072148240684471412386360)⟩,⟨(-123928555519187267892495365193),(-123928555519187267880102401817)⟩⟩,⟨⟨(-5130074538545206828760228520),(-5130074538545206817854926869)⟩,⟨(-123759742694172808922085962969),(-123759742694172808909709002981)⟩⟩,⟨⟨(-5122327862012853065390879094),(-5122327862012853054502000575)⟩,⟨(-123572859114377696320993557625),(-123572859114377696308634215515)⟩⟩,⟨⟨(-5113783777894453979337302796),(-5113783777894453968466878227)⟩,⟨(-123366738590376440396565709172),(-123366738590376440384234007869)⟩⟩,⟨⟨(-5104498088897388248151962531),(-5104498088897388237301096551)⟩,⟨(-123142727326528243656848114629),(-123142727326528243644534460659)⟩⟩,⟨⟨(-5094412652057206992734302059),(-5094412652057206981905118970)⟩,⟨(-122899422661280022645655056649),(-122899422661280022633371613802)⟩⟩,⟨⟨(-5083593571245343653476405769),(-5083593571245343642669901843)⟩,⟨(-122638419307936276685375677249),(-122638419307936276673110626799)⟩⟩,⟨⟨(-5071972827087325089489405431),(-5071972827087325078707982284)⟩,⟨(-122358076342915922350466726355),(-122358076342915922338238828514)⟩⟩] +lemma amp7_12_8_eq : ∀ k : Fin 16, amp7_1Expr 2 8 k = amp7_12_8 k := by decide +kernel +noncomputable def amp7_12_9 : Fin 16 → CBox := ![⟨⟨(-5059626903572492902206905349),(-5059626903572492891451948368)⟩,⟨(-122060238893179595329295985170),(-122060238893179595317103222031)⟩⟩,⟨⟨(-5046477817449798237417330248),(-5046477817449798226690689680)⟩,⟨(-121743025663044017270285594346),(-121743025663044017258133351438)⟩⟩,⟨⟨(-5032612524982808379225827536),(-5032612524982808368527871531)⟩,⟨(-121408534416337739788734357263),(-121408534416337739776596514978)⟩⟩,⟨⟨(-5017942977869881859878757705),(-5017942977869881849212482970)⟩,⟨(-121054641044517323065312282218),(-121054641044517323053221830316)⟩⟩,⟨⟨(-5002566710481483931663140081),(-5002566710481483921029870130)⟩,⟨(-120683698501424260563406663463),(-120683698501424260551360993516)⟩⟩,⟨⟨(-4986385494073012467443191669),(-4986385494073012456844479475)⟩,⟨(-120293337081888424618277486396),(-120293337081888424606274725073)⟩⟩,⟨⟨(-4969507561182858006726103798),(-4969507561182857996163739557)⟩,⟨(-119886167826159173648285419386),(-119886167826159173636334705505)⟩⟩,⟨⟨(-4951824372420951267939780688),(-4951824372420951257415314480)⟩,⟨(-119459572291388118546876441603),(-119459572291388118534975817020)⟩⟩,⟨⟨(-4933454993419274271794963003),(-4933454993419274261310004569)⟩,⟨(-119016422859227240666588845904),(-119016422859227240654743610549)⟩⟩,⟨⟨(-4914280428450251334085667927),(-4914280428450251323642189898)⟩,⟨(-118553848834423318827303494183),(-118553848834423318815521887107)⟩⟩,⟨⟨(-4894430726757596747019360891),(-4894430726757596736615900539)⟩,⟨(-118074987571184117966407259597),(-118074987571184117954620999518)⟩⟩,⟨⟨(-4873776274319785408539204368),(-4873776274319785398180134280)⟩,⟨(-117576712214756753239186442313),(-117576712214756753227461687001)⟩⟩,⟨⟨(-4852458270930776066840549540),(-4852458270930776056527134468)⟩,⟨(-117062429119188813286233864779),(-117062429119188813274568697839)⟩⟩,⟨⟨(-4830336305174704897768720176),(-4830336305174704887502950786)⟩,⟨(-116528750949546260435028348331),(-116528750949546260423431503689)⟩⟩,⟨⟨(-4807562911692542951770148556),(-4807562911692542941552911154)⟩,⟨(-115979357505757280247705466244),(-115979357505757280236166490261)⟩⟩,⟨⟨(-4783986684434824899422531215),(-4783986684434824889256045461)⟩,⟨(-115410596214436558110744449365),(-115410596214436558099277655491)⟩⟩] +lemma amp7_12_9_eq : ∀ k : Fin 16, amp7_1Expr 2 9 k = amp7_12_9 k := by decide +kernel +noncomputable def amp7_12_10 : Fin 16 → CBox := ![⟨⟨(-4759771695603984760928825912),(-4759771695603984750813457543)⟩,⟨(-114826425211748380409627941777),(-114826425211748380398210936882)⟩⟩,⟨⟨(-4734755328016043894198463300),(-4734755328016043884136742742)⟩,⟨(-114222921462911159953182022235),(-114222921462911159941836687941)⟩⟩,⟨⟨(-4709113413761441761748522154),(-4709113413761441751741711428)⟩,⟨(-113604326803809865656055310330),(-113604326803809865644781521632)⟩⟩,⟨⟨(-4682671887494008458758632805),(-4682671887494008448808185222)⟩,⟨(-112966442020126635281623372361),(-112966442020126635270417112493)⟩⟩,⟨⟨(-4655618584475842407361360925),(-4655618584475842397468979093)⟩,⟨(-112313798516528502281958547940),(-112313798516528502270830993686)⟩⟩,⟨⟨(-4627767732219821182152890256),(-4627767732219821172320000762)⟩,⟨(-111641914651465586221771982055),(-111641914651465586210718572745)⟩⟩,⟨⟨(-4599319434914282693642681608),(-4599319434914282683870599613)⟩,⟨(-110955617809545002175482639945),(-110955617809545002164505905905)⟩⟩,⟨⟨(-4570075930398161694124332695),(-4570075930398161684414936595)⟩,⟨(-110250137106058509769910695668),(-110250137106058509759017090263)⟩⟩,⟨⟨(-4540249881715345231392420528),(-4540249881715345221746978733)⟩,⟨(-109530602899911085895670390127),(-109530602899911085884862044022)⟩⟩,⟨⟨(-4509631229138743676949590095),(-4509631229138743667369916106)⟩,⟨(-108791947635538051987733681718),(-108791947635538051977015609937)⟩⟩,⟨⟨(-4478445510590351200396356462),(-4478445510590351190883866452)⟩,⟨(-108039612269982829936661425638),(-108039612269982829926040079975)⟩⟩,⟨⟨(-4446470033492561677011166125),(-4446470033492561667559291616)⟩,⟨(-107268224488301970263379248391),(-107268224488301970252657573117)⟩⟩,⟨⟨(-4413943554923445718821376187),(-4413943554923445709439101973)⟩,⟨(-106483544151161515235527644991),(-106483544151161515224895465068)⟩⟩,⟨⟨(-4380630384484886435589315344),(-4380630384484886426278262471)⟩,⟨(-105679885379573300040733779341),(-105679885379573300030191755855)⟩⟩,⟨⟨(-4346782873384138112417656350),(-4346782873384138103179007054)⟩,⟨(-104863335983810586459690833058),(-104863335983810586449241373492)⟩⟩,⟨⟨(-4312151936157441302840758601),(-4312151936157441293676051115)⟩,⟨(-104027886937557653611832427624),(-104027886937557653601474354899)⟩⟩] +lemma amp7_12_10_eq : ∀ k : Fin 16, amp7_1Expr 2 10 k = amp7_12_10 k := by decide +kernel +noncomputable def amp7_12_11 : Fin 16 → CBox := ![⟨⟨(-4277003926566657997830818066),(-4277003926566657988741170291)⟩,⟨(-103179963853695169878071373651),(-103179963853695169867806387100)⟩⟩,⟨⟨(-4241075931632628766699686618),(-4241075931632628757686620084)⟩,⟨(-102313224126008108070852077629),(-102313224126008108060678765339)⟩⟩,⟨⟨(-4204648752671252395283037457),(-4204648752671252386347896455)⟩,⟨(-101434441905309035888203683519),(-101434441905309035878130080580)⟩⟩,⟨⟨(-4167445178213067194334123046),(-4167445178213067185478082680)⟩,⟨(-100536929643517573740990053136),(-100536929643517573731006565759)⟩⟩,⟨⟨(-4129760942243346623508396504),(-4129760942243346614732931420)⟩,⟨(-99627821732473132352897515312),(-99627821732473132343016228495)⟩⟩,⟨⟨(-4091304021530033263000828264),(-4091304021530033254307448270)⟩,⟨(-98700073299866625192865359610),(-98700073299866625183084935434)⟩⟩,⟨⟨(-4052385611987333482645288790),(-4052385611987333474035198276)⟩,⟨(-97761191746610121644366275541),(-97761191746610121634693216212)⟩⟩,⟨⟨(-4012698318754671959044875233),(-4012698318754671950518465323)⟩,⟨(-96803761369761203747332646315),(-96803761369761203737738812158)⟩⟩,⟨⟨(-3972569377672655666642728616),(-3972569377672655658202111239)⟩,⟨(-95835676523121076728528914661),(-95835676523121076719043671272)⟩⟩,⟨⟨(-3931675410886016127229195353),(-3931675410886016118875915790)⟩,⟨(-94849135924298945235019855729),(-94849135924298945225643095291)⟩⟩,⟨⟨(-3890360326150824622576984783),(-3890360326150824614311677197)⟩,⟨(-93852436126314091896472520084),(-93852436126314091887198961338)⟩⟩,⟨⟨(-3848284094129928595069852090),(-3848284094129928586894517570)⟩,⟨(-92837374140504600639206853155),(-92837374140504600630047573871)⟩⟩,⟨⟨(-3805807986503100699888286209),(-3805807986503100691803646003)⟩,⟨(-91812665413360657271041991677),(-91812665413360657261994849603)⟩⟩,⟨⟨(-3762574590383011711748566928),(-3762574590383011703756273375)⟩,⟨(-90769687589273372326957572619),(-90769687589273372318025420767)⟩⟩,⟨⟨(-3718963300339778592150416574),(-3718963300339778584251432185)⟩,⟨(-89717593317785057656385388637),(-89717593317785057647572979270)⟩⟩,⟨⟨(-3674598516835281405541633863),(-3674598516835281397737707899)⟩,⟨(-88647321502055012110914561758),(-88647321502055012102227271500)⟩⟩] +lemma amp7_12_11_eq : ∀ k : Fin 16, amp7_1Expr 2 11 k = amp7_12_11 k := by decide +kernel +noncomputable def amp7_12_12 : Fin 16 → CBox := ![⟨⟨(-3629878591273424897434603021),(-3629878591273424889721945839)⟩,⟨(-87568482113025898510075613201),(-87568482113025898501404663575)⟩⟩,⟨⟨(-3584408854704921202663579795),(-3584408854704921195047686439)⟩,⟨(-86471554016599907621912873837),(-86471554016599907613354186046)⟩⟩,⟨⟨(-3538607533590063836983691759),(-3538607533590063829465305761)⟩,⟨(-85366626656648648034180126633),(-85366626656648648025735433398)⟩⟩,⟨⟨(-3492059917117642071083063931),(-3492059917117642063663709382)⟩,⟨(-84243695402069335379734999094),(-84243695402069335371404596706)⟩⟩,⟨⟨(-3445205120144288778393095969),(-3445205120144288771073456508)⟩,⟨(-83113353615835889361150050685),(-83113353615835889352935419587)⟩⟩,⟨⟨(-3397607316141974808995422016),(-3397607316141974801776956137)⟩,⟨(-81965087263783130376055074949),(-81965087263783130367955089683)⟩⟩,⟨⟨(-3349727629506710180507437522),(-3349727629506710173391007933)⟩,⟨(-80810020674840670668397411256),(-80810020674840670660419108498)⟩⟩,⟨⟨(-3301107928990071964428596030),(-3301107928990071957415159740)⟩,⟨(-79637101727835810797421066180),(-79637101727835810789551368728)⟩⟩,⟨⟨(-3252232592395201078184009791),(-3252232592395201071274743949)⟩,⟨(-78458015725161932425078811205),(-78458015725161932417333624136)⟩⟩,⟨⟨(-3202619863391098241747276015),(-3202619863391098234943589712)⟩,⟨(-77261140605751933134797322439),(-77261140605751933127174602818)⟩⟩,⟨⟨(-3152778757425303733860278615),(-3152778757425303727162774339)⟩,⟨(-76058756039295136484498335947),(-76058756039295136477001457623)⟩⟩,⟨⟨(-3102202422140761775415123886),(-3102202422140761768825384804)⟩,⟨(-74838634539266376566883681541),(-74838634539266376559514906807)⟩⟩,⟨⟨(-3051426056220250145278058207),(-3051426056220250138796741326)⟩,⟨(-73613687429033992087192305575),(-73613687429033992079957708797)⟩⟩,⟨⟨(-2999916066825581615756813311),(-2999916066825581609382720510)⟩,⟨(-72371042125195670214190880321),(-72371042125195670207025705491)⟩⟩,⟨⟨(-2948235567927807714910855392),(-2948235567927807708646917251)⟩,⟨(-71124283389462221100541088648),(-71124283389462221093507701343)⟩⟩,⟨⟨(-2895822380713515644032383916),(-2895822380713515637880105430)⟩,⟨(-69859849020198302903446890531),(-69859849020198302896545791318)⟩⟩] +lemma amp7_12_12_eq : ∀ k : Fin 16, amp7_1Expr 2 12 k = amp7_12_12 k := by decide +kernel +noncomputable def amp7_12_13 : Fin 16 → CBox := ![⟨⟨(-2843269483200295804889289331),(-2843269483200295798848907454)⟩,⟨(-68592044229994666775261016271),(-68592044229994666768491093921)⟩⟩,⟨⟨(-2789984030792729050100287016),(-2789984030792729044173019357)⟩,⟨(-67306567024984472897543568697),(-67306567024984472890898397326)⟩⟩,⟨⟨(-2736591067706676012044109443),(-2736591067706676006230716864)⟩,⟨(-66018496194129982506636372618),(-66018496194129982500129053457)⟩⟩,⟨⟨(-2682464728926284393915258951),(-2682464728926284388217095450)⟩,⟨(-64712733147198015488789531634),(-64712733147198015482416888991)⟩⟩,⟨⟨(-2628264625263173648641529086),(-2628264625263173643058993407)⟩,⟨(-63405190570000631731358521666),(-63405190570000631725126570133)⟩⟩,⟨⟨(-2573329192070436687114853267),(-2573329192070436681647750407)⟩,⟨(-62079908641708405065114770179),(-62079908641708405058982869914)⟩⟩,⟨⟨(-2518355460693847131945501519),(-2518355460693847126595417559)⟩,⟨(-60753702794408055132074630404),(-60753702794408055126079172956)⟩⟩,⟨⟨(-2462643101475025597406531000),(-2462643101475025592175041196)⟩,⟨(-59409678026346506146522121247),(-59409678026346506140665011949)⟩⟩,⟨⟨(-2406929842568628609986538371),(-2406929842568628604873605302)⟩,⟨(-58065631553901910366462782214),(-58065631553901910360743074341)⟩⟩,⟨⟨(-2350473060741471697426200658),(-2350473060741471692433220609)⟩,⟨(-56703648070080758093839622311),(-56703648070080758088254664432)⟩⟩,⟨⟨(-2294054966019543065851681016),(-2294054966019543060978750899)⟩,⟨(-55342597887745317216560408264),(-55342597887745317211114428947)⟩⟩,⟨⟨(-2236886552549583813783336467),(-2236886552549583809030923668)⟩,⟨(-53963446749079285357071868495),(-53963446749079285351739475110)⟩⟩,⟨⟨(-2179798915915662809692749084),(-2179798915915662805061999263)⟩,⟨(-52586244299534362816718878175),(-52586244299534362811531656585)⟩⟩,⟨⟨(-2121951893766475953212471692),(-2121951893766475948704855564)⟩,⟨(-51190722163741443754311882413),(-51190722163741443749268201537)⟩⟩,⟨⟨(-2064230630799723996255937032),(-2064230630799723991871105641)⟩,⟨(-49798233887192212472605851334),(-49798233887192212467703438682)⟩⟩,⟨⟨(-2005738188498802511522816576),(-2005738188498802507262537114)⟩,⟨(-48387141406113245539888904487),(-48387141406113245535132704957)⟩⟩] +lemma amp7_12_13_eq : ∀ k : Fin 16, amp7_1Expr 2 13 k = amp7_12_13 k := by decide +kernel +noncomputable def amp7_12_14 : Fin 16 → CBox := ![⟨⟨(-1947419868181087741634811247),(-1947419868181087737497841479)⟩,⟨(-46980249505684159979874467531),(-46980249505684159975243022307)⟩⟩,⟨⟨(-1888315278407924775512521337),(-1888315278407924771501300238)⟩,⟨(-45554389361272765537347298611),(-45554389361272765532861021451)⟩⟩,⟨⟨(-1829437172087648441306829153),(-1829437172087648437420761187)⟩,⟨(-44133992984228323627904857832),(-44133992984228323623560450075)⟩⟩,⟨⟨(-1769753689214106828570418862),(-1769753689214106824811504827)⟩,⟨(-42694167416778337223924787623),(-42694167416778337219731158516)⟩⟩,⟨⟨(-1710353844287314215863895856),(-1710353844287314212230702072)⟩,⟨(-41261184432032405306307013214),(-41261184432032405302243437527)⟩⟩,⟨⟨(-1650124571656563996945734532),(-1650124571656563993440664401)⟩,⟨(-39808192038367763713527386976),(-39808192038367763709611311128)⟩⟩,⟨⟨(-1590241921453586584029370389),(-1590241921453586580651215324)⟩,⟨(-38363561687428013407098289925),(-38363561687428013403317496980)⟩⟩,⟨⟨(-1529499634035960903710652474),(-1529499634035960900461761934)⟩,⟨(-36898193142589549348787460163),(-36898193142589549345156618878)⟩⟩,⟨⟨(-1469174162069821264715295580),(-1469174162069821261594720527)⟩,⟨(-35442880001944392874832933130),(-35442880001944392871349518340)⟩⟩,⟨⟨(-1407951061421260000625004855),(-1407951061421259997634279331)⟩,⟨(-33965912147720179358511268828),(-33965912147720179355168421246)⟩⟩,⟨⟨(-1347224049647206334698183517),(-1347224049647206331836692895)⟩,⟨(-32500912117940074765900967770),(-32500912117940074762708103704)⟩⟩,⟨⟨(-1285551412780888597796014547),(-1285551412780888595065391440)⟩,⟨(-31013099492119807673975335512),(-31013099492119807670925628100)⟩⟩,⟨⟨(-1224465824149729459851832114),(-1224465824149729457250828914)⟩,⟨(-29539449026709962118098137362),(-29539449026709962115190177875)⟩⟩,⟨⟨(-1162373479802631049792748092),(-1162373479802631047323852580)⟩,⟨(-28041511228353124900388505991),(-28041511228353124897633110449)⟩⟩,⟨⟨(-1100974564234470579653404551),(-1100974564234470577314869501)⟩,⟨(-26560301952479399676995960492),(-26560301952479399674384866015)⟩⟩,⟨⟨(-1038490075614490174852478584),(-1038490075614490172646632439)⟩,⟨(-25052903926216277138125799795),(-25052903926216277135662126666)⟩⟩] +lemma amp7_12_14_eq : ∀ k : Fin 16, amp7_1Expr 2 14 k = amp7_12_14 k := by decide +kernel +noncomputable def amp7_12_15 : Fin 16 → CBox := ![⟨⟨(-976826365869980122761199476),(-976826365869980120686358472)⟩,⟨(-23565306661457456127417424283),(-23565306661457456125100664196)⟩⟩,⟨⟨(-913973687112991921252051141),(-913973687112991919310767938)⟩,⟨(-22049026285381237279019797160),(-22049026285381237276853426584)⟩⟩,⟨⟨(-852098715826997533434367084),(-852098715826997531624586244)⟩,⟨(-20556332472059850912632133184),(-20556332472059850910614346466)⟩⟩,⟨⟨(-788895841566765077189859522),(-788895841566765075514266205)⟩,⟨(-19031603855115292601799807614),(-19031603855115292599930487989)⟩⟩,⟨⟨(-726871292114567087817855541),(-726871292114567086273996773)⟩,⟨(-17535301564914489678017803450),(-17535301564914489676295359152)⟩⟩,⟨⟨(-663325817138793157807663335),(-663325817138793156398798454)⟩,⟨(-16002307926461242688085304115),(-16002307926461242686514037066)⟩⟩,⟨⟨(-601227801041259061596678366),(-601227801041259060319777222)⟩,⟨(-14504233300779720021235732828),(-14504233300779720019813279810)⟩⟩,⟨⟨(-537327657764345332657821588),(-537327657764345331516595036)⟩,⟨(-12962683518090937550684809200),(-12962683518090937549412622364)⟩⟩,⟨⟨(-475260698067625594091117859),(-475260698067625593081755230)⟩,⟨(-11465358108067962011839371583),(-11465358108067962010715108547)⟩⟩,⟨⟨(-410952047203312812760335419),(-410952047203312811887580460)⟩,⟨(-9913953343053823115674093288),(-9913953343053823114702642628)⟩⟩,⟨⟨(-349085604172734029159712332),(-349085604172734028418394918)⟩,⟨(-8421465268399182256438860267),(-8421465268399182255614846557)⟩⟩,⟨⟨(-284208574900344161774741289),(-284208574900344161171228039)⟩,⟨(-6856348740523115919113846891),(-6856348740523115918443733564)⟩⟩,⟨⟨(-222899049574540212169828187),(-222899049574540211696567476)⟩,⟨(-5377295946647905665500084817),(-5377295946647905664976037460)⟩⟩,⟨⟨(-156930468665277273180418668),(-156930468665277272847262443)⟩,⟨(-3785846438870318533956038631),(-3785846438870318533588041395)⟩⟩,⟨⟨(-97347548738388396714097994),(-97347548738388396507566454)⟩,⟨(-2348446887710894609690848324),(-2348446887710894609465776528)⟩⟩,⟨⟨(-27656833929615362301610970),(-27656833929615362243014461)⟩,⟨(-667203297953504647164066679),(-667203297953504647102051385)⟩⟩] +lemma amp7_12_15_eq : ∀ k : Fin 16, amp7_1Expr 2 15 k = amp7_12_15 k := by decide +kernel +noncomputable def amp7_12 : Fin 16 → Fin 16 → CBox := ![amp7_12_0,amp7_12_1,amp7_12_2,amp7_12_3,amp7_12_4,amp7_12_5,amp7_12_6,amp7_12_7,amp7_12_8,amp7_12_9,amp7_12_10,amp7_12_11,amp7_12_12,amp7_12_13,amp7_12_14,amp7_12_15] +lemma amp7_12_eq (i k : Fin 16) : amp7_1Expr 2 i k = amp7_12 i k := by + fin_cases i + · exact amp7_12_0_eq k + · exact amp7_12_1_eq k + · exact amp7_12_2_eq k + · exact amp7_12_3_eq k + · exact amp7_12_4_eq k + · exact amp7_12_5_eq k + · exact amp7_12_6_eq k + · exact amp7_12_7_eq k + · exact amp7_12_8_eq k + · exact amp7_12_9_eq k + · exact amp7_12_10_eq k + · exact amp7_12_11_eq k + · exact amp7_12_12_eq k + · exact amp7_12_13_eq k + · exact amp7_12_14_eq k + · exact amp7_12_15_eq k +noncomputable def amp7_13_0 : Fin 16 → CBox := ![⟨⟨385210003677661992952149995,385210003677661992997475379⟩,⟨(-667203297953504647154747600),(-667203297953504647108451558)⟩⟩,⟨⟨1355876442797423833488478828,1355876442797423833651935883⟩,⟨(-2348446887710894609658046685),(-2348446887710894609488304091)⟩⟩,⟨⟨2185759460592364486753986006,2185759460592364487020472462⟩,⟨(-3785846438870318533903160293),(-3785846438870318533624357266)⟩⟩,⟨⟨3104583262309451838816025618,3104583262309451839195317269⟩,⟨(-5377295946647905665424978107),(-5377295946647905665027619369)⟩⟩,⟨⟨3958514790998972547869754643,3958514790998972548354483262⟩,⟨(-6856348740523115919018081696),(-6856348740523115918509503341)⟩⟩,⟨⟨4862135239681351864436049071,4862135239681351865031965968⟩,⟨(-8421465268399182256321234501),(-8421465268399182255695629772)⟩⟩,⟨⟨5723823631345515038700521431,5723823631345515039402858549⟩,⟨(-9913953343053823115535621381),(-9913953343053823114797742590)⟩⟩,⟨⟨6619527590048496233739978055,6619527590048496234552679627⟩,⟨(-11465358108067962011679230624),(-11465358108067962010825090416)⟩⟩,⟨⟨7484008818589727932776539773,7484008818589727933696011678⟩,⟨(-12962683518090937550503754536),(-12962683518090937549536967381)⟩⟩,⟨⟨8374023000594305591410506291,8374023000594305592438731974⟩,⟨(-14504233300779720021033146759),(-14504233300779720019952412201)⟩⟩,⟨⟨9238936788997680557540949540,9238936788997680558676470222⟩,⟨(-16002307926461242687861793876),(-16002307926461242686667539792)⟩⟩,⟨⟨10124011078824646541688415677,10124011078824646542933094048⟩,⟨(-17535301564914489677772881313),(-17535301564914489676463567176)⟩⟩,⟨⟨10987901608861133639375815753,10987901608861133640726644521⟩,⟨(-19031603855115292601533986062),(-19031603855115292600113049348)⟩⟩,⟨⟨11868204086295200167786867027,11868204086295200169245170836⟩,⟨(-20556332472059850912345015175),(-20556332472059850910811533840)⟩⟩,⟨⟨12730011261233991575311644616,12730011261233991576877033750⟩,⟨(-22049026285381237278711830136),(-22049026285381237277064932678)⟩⟩,⟨⟨13605436144528543517368211879,13605436144528543519042065407⟩,⟨(-23565306661457456127088278802),(-23565306661457456125326715265)⟩⟩] +lemma amp7_13_0_eq : ∀ k : Fin 16, amp7_1Expr 3 0 k = amp7_13_0 k := by decide +kernel +noncomputable def amp7_13_1 : Fin 16 → CBox := ![⟨⟨14464300825782799816544920329,14464300825782799818324821811⟩,⟨(-25052903926216277137775876485),(-25052903926216277135902447567)⟩⟩,⟨⟨15334597482021724182200697501,15334597482021724184087222958⟩,⟨(-26560301952479399676624982788),(-26560301952479399674639646687)⟩⟩,⟨⟨16189774056173590091205363746,16189774056173590093196337975⟩,⟨(-28041511228353124899996839682),(-28041511228353124897902099675)⟩⟩,⟨⟨17054608847284225416946263130,17054608847284225419046695419⟩,⟨(-29539449026709962117685548794),(-29539449026709962115473536125)⟩⟩,⟨⟨17905421340180017039915821650,17905421340180017042119120792⟩,⟨(-31013099492119807673542163914),(-31013099492119807671223122395)⟩⟩,⟨⟨18764410360201072197620399313,18764410360201072199927580730⟩,⟨(-32500912117940074765447015335),(-32500912117940074763019869897)⟩⟩,⟨⟨19610228521757425345573145529,19610228521757425347987825180⟩,⟨(-33965912147720179358036854187),(-33965912147720179355494240505)⟩⟩,⟨⟨20462956309978198963961066180,20462956309978198966477978336⟩,⟨(-35442880001944392874337889126),(-35442880001944392871689505468)⟩⟩,⟨⟨21303181743484879754550438990,21303181743484879757173234854⟩,⟨(-36898193142589549348272089254),(-36898193142589549345510566151)⟩⟩,⟨⟨22149212667309377170673773325,22149212667309377173404054290⟩,⟨(-38363561687428013406562451664),(-38363561687428013403685500855)⟩⟩,⟨⟨22983270389303945547530151946,22983270389303945550359153072⟩,⟨(-39808192038367763712971371021),(-39808192038367763709993172672)⟩⟩,⟨⟨23822155938916705060294246414,23822155938916705063229140477⟩,⟨(-41261184432032405305730702769),(-41261184432032405302639236954)⟩⟩,⟨⟨24649489050903922243517302123,24649489050903922246547730898⟩,⟨(-42694167416778337223328462166),(-42694167416778337220140703885)⟩⟩,⟨⟨25480772729857277561796768934,25480772729857277564934795781⟩,⟨(-44133992984228323627288421791),(-44133992984228323623983807023)⟩⟩,⟨⟨26300838960499855271984235635,26300838960499855275224439547⟩,⟨(-45554389361272765536711023361),(-45554389361272765533298003604)⟩⟩,⟨⟨27124059698702532519920535674,27124059698702532523264899100⟩,⟨(-46980249505684159979218276757),(-46980249505684159975693682076)⟩⟩] +lemma amp7_13_1_eq : ∀ k : Fin 16, amp7_1Expr 3 1 k = amp7_13_1 k := by decide +kernel +noncomputable def amp7_13_2 : Fin 16 → CBox := ![⟨⟨27936329116135969235542334054,27936329116135969238978800435⟩,⟨(-48387141406113245539213063127),(-48387141406113245535596860388)⟩⟩,⟨⟨28751023739938367694816727329,28751023739938367698357745858⟩,⟨(-49798233887192212471910300715),(-49798233887192212468181130070)⟩⟩,⟨⟨29554977221247464420976965216,29554977221247464424619415477⟩,⟨(-51190722163741443753596882388),(-51190722163741443749759250420)⟩⟩,⟨⟨30360682302007587721754092451,30360682302007587725499329759⟩,⟨(-52586244299534362815984386368),(-52586244299534362812036092065)⟩⟩,⟨⟨31155810506980960745301056096,31155810506980960749149760740⟩,⟨(-53963446749079285356318140786),(-53963446749079285352257121455)⟩⟩,⟨⟨31952063788142973129511946095,31952063788142973133445909773⟩,⟨(-55342597887745317215787417433),(-55342597887745317211645304850)⟩⟩,⟨⟨32737866477294929149518178074,32737866477294929153551802935⟩,⟨(-56703648070080758093047621182),(-56703648070080758088798596259)⟩⟩,⟨⟨33524208008310895721292786057,33524208008310895725423644051⟩,⟨(-58065631553901910365651757749),(-58065631553901910361300071044)⟩⟩,⟨⟨34300193600980150022295221211,34300193600980150026524587187⟩,⟨(-59409678026346506145692323982),(-59409678026346506141234901468)⟩⟩,⟨⟨35076166662618009661738775453,35076166662618009666067195693⟩,⟨(-60753702794408055131226060641),(-60753702794408055126661955082)⟩⟩,⟨⟨35841851965557722416980862685,35841851965557722421406982872⟩,⟨(-62079908641708405064247676800),(-62079908641708405059578373718)⟩⟩,⟨⟨36607003843609385792125650494,36607003843609385796628446774⟩,⟨(-63405190570000631730472917578),(-63405190570000631725734786752)⟩⟩,⟨⟨37361913902531192331318004861,37361913902531192335920687520⟩,⟨(-64712733147198015487885664607),(-64712733147198015483037648260)⟩⟩,⟨⟨38115796549175229429730768501,38115796549175229434429839621⟩,⟨(-66018496194129982505714267510),(-66018496194129982500762338307)⟩⟩,⟨⟨38859464590104374372737393850,38859464590104374377534434452⟩,⟨(-67306567024984472896603472620),(-67306567024984472891544038043)⟩⟩,⟨⟨39601635200454137553462153876,39601635200454137558349562952⟩,⟨(-68592044229994666774302965451),(-68592044229994666769149065625)⟩⟩] +lemma amp7_13_2_eq : ∀ k : Fin 16, amp7_1Expr 3 2 k = amp7_13_2 k := by decide +kernel +noncomputable def amp7_13_3 : Fin 16 → CBox := ![⟨⟨40333602637358103889358763441,40333602637358103894339998795⟩,⟨(-69859849020198302902471131806),(-69859849020198302897215924486)⟩⟩,⟨⟨41063624160825241726307429363,41063624160825241731383084468⟩,⟨(-71124283389462221099547669093),(-71124283389462221094189963644)⟩⟩,⟨⟨41783440652515466062712238362,41783440652515466067881771989⟩,⟨(-72371042125195670213180046820),(-72371042125195670207719927371)⟩⟩,⟨⟨42500882253193745494307637208,42500882253193745499534983876⟩,⟨(-73613687429033992086164115581),(-73613687429033992080663850797)⟩⟩,⟨⟨43208105797029466858348041000,43208105797029466863670335058⟩,⟨(-74838634539266376565838382250),(-74838634539266376560232799158)⟩⟩,⟨⟨43912543273515121376677881543,43912543273515121382091547094⟩,⟨(-76058756039295136483435994761),(-76058756039295136477731054034)⟩⟩,⟨⟨44606740326628404392177641471,44606740326628404397681119279⟩,⟨(-77261140605751933133718187097),(-77261140605751933127915733147)⟩⟩,⟨⟨45297756499006132963176505564,45297756499006132968767769117⟩,⟨(-78458015725161932423982958660),(-78458015725161932418086235533)⟩⟩,⟨⟨45978502120047616445324481930,45978502120047616451004456870⟩,⟨(-79637101727835810796308744897),(-79637101727835810790315290551)⟩⟩,⟨⟨46655687189838484688106070480,46655687189838484693865486004⟩,⟨(-80810020674840670667268707375),(-80810020674840670661194281589)⟩⟩,⟨⟨47322565195896356610756615547,47322565195896356616602767033⟩,⟨(-81965087263783130374910237819),(-81965087263783130368741342793)⟩⟩,⟨⟨47985517083355406597791132912,47985517083355406603719860695⟩,⟨(-83113353615835889359989175288),(-83113353615835889353732687484)⟩⟩,⟨⟨48638120217913569078718331680,48638120217913569084730029763⟩,⟨(-84243695402069335378558335789),(-84243695402069335372212707449)⟩⟩,⟨⟨49286444880026379419168077331,49286444880026379425261785235⟩,⟨(-85366626656648648032987778926),(-85366626656648648026554315900)⟩⟩,⟨⟨49924374988729221664322405117,49924374988729221670497694866⟩,⟨(-86471554016599907620705093195),(-86471554016599907614183667604)⟩⟩,⟨⟨50557686720482431271022248964,50557686720482431277278006023⟩,⟨(-87568482113025898508852511353),(-87568482113025898502244667456)⟩⟩] +lemma amp7_13_3_eq : ∀ k : Fin 16, amp7_1Expr 3 3 k = amp7_13_3 k := by decide +kernel +noncomputable def amp7_13_4 : Fin 16 → CBox := ![⟨⟨51180554932150761401212042711,51180554932150761407492628826⟩,⟨(-88647321502055012109676391355),(-88647321502055012103077624187)⟩⟩,⟨⟨51798476653068572739486148460,51798476653068572745854244658⟩,⟨(-89717593317785057655132269346),(-89717593317785057648433598579)⟩⟩,⟨⟨52405903563925214425391350641,52405903563925214431843593336⟩,⟨(-90769687589273372325689758332),(-90769687589273372318896132329)⟩⟩,⟨⟨53008067091420818534526594511,53008067091420818541060109894⟩,⟨(-91812665413360657269759609728),(-91812665413360657262875565968)⟩⟩,⟨⟨53599682950878333015572738664,53599682950878333022185618851⟩,⟨(-92837374140504600637910158715),(-92837374140504600630938119793)⟩⟩,⟨⟨54185729261629598880721845802,54185729261629598887415189967⟩,⟨(-93852436126314091895161647892),(-93852436126314091888099244279)⟩⟩,⟨⟨54761174158297399574773479268,54761174158297399581540629633⟩,⟨(-94849135924298945233695062257),(-94849135924298945226552939112)⟩⟩,⟨⟨55330753638593851790909043360,55330753638593851797752904092⟩,⟨(-95835676523121076727190341806),(-95835676523121076719962978519)⟩⟩,⟨⟨55889677685399926700497183981,55889677685399926707417553969⟩,⟨(-96803761369761203745980551855),(-96803761369761203738667405795)⟩⟩,⟨⟨56442450371203974287833497558,56442450371203974294813270530⟩,⟨(-97761191746610121643000808292),(-97761191746610121635630994035)⟩⟩,⟨⟨56984513888713790569813295882,56984513888713790576868453600⟩,⟨(-98700073299866625191486778651),(-98700073299866625184031719512)⟩⟩,⟨⟨57520149696019410855551851026,57520149696019410862678480572⟩,⟨(-99627821732473132351505976142),(-99627821732473132343971912034)⟩⟩,⟨⟨58045023393183337444512614532,58045023393183337451711222358⟩,⟨(-100536929643517573739585816114),(-100536929643517573731970969949)⟩⟩,⟨⟨58563202339129627985852968379,58563202339129627993116411741⟩,⟨(-101434441905309035886786910607),(-101434441905309035879103094189)⟩⟩,⟨⟨59070567490809294428931779564,59070567490809294436265330166⟩,⟨(-102313224126008108069423030436),(-102313224126008108061660208699)⟩⟩,⟨⟨59570979905906762494586494316,59570979905906762501985341252⟩,⟨(-103179963853695169876630220379),(-103179963853695169868796144693)⟩⟩] +lemma amp7_13_4_eq : ∀ k : Fin 16, amp7_1Expr 3 4 k = amp7_13_4 k := by decide +kernel +noncomputable def amp7_13_5 : Fin 16 → CBox := ![⟨⟨60060528526626865100247112601,60060528526626865107711802530⟩,⟨(-104027886937557653610379431093),(-104027886937557653602472246225)⟩⟩,⟨⟨60542875258375211986045447989,60542875258375211993574821800⟩,⟨(-104863335983810586458226167496),(-104863335983810586450247278894)⟩⟩,⟨⟨61014310271825440935605120921,61014310271825440943199588507⟩,⟨(-105679885379573300039257708727),(-105679885379573300031205494037)⟩⟩,⟨⟨61478302879938500944461168750,61478302879938500952119156204⟩,⟨(-106483544151161515234040349374),(-106483544151161515225916912376)⟩⟩,⟨⟨61931338283814348954344724022,61931338283814348962065578847⟩,⟨(-107268224488301970261880992849),(-107268224488301970253686547501)⟩⟩,⟨⟨62376699227217381556754808564,62376699227217381564428745586⟩,⟨(-108039612269982829935152395833),(-108039612269982829927076453923)⟩⟩,⟨⟨62811060253041564511098203437,62811060253041564518838720961⟩,⟨(-108791947635538051986214143763),(-108791947635538051978059200691)⟩⟩,⟨⟨63237523068765669823352219152,63237523068765669831155397021⟩,⟨(-109530602899911085894140535096),(-109530602899911085885912720353)⟩⟩,⟨⟨63652946336376028674681227369,63652946336376028682543897304⟩,⟨(-110250137106058509768370790633),(-110250137106058509760074668753)⟩⟩,⟨⟨64060255810442041620599162938,64060255810442041628519894259⟩,⟨(-110955617809545002173932881197),(-110955617809545002165570251744)⟩⟩,⟨⟨64456489476868880859644062116,64456489476868880867618855222⟩,⟨(-111641914651465586220212637542),(-111641914651465586211789501911)⟩⟩,⟨⟨64844401807227121640445860556,64844401807227121648473048893⟩,⟨(-112313798516528502280389818972),(-112313798516528502271908367924)⟩⟩,⟨⟨65221205709714364218974033345,65221205709714364227055975461⟩,⟨(-112966442020126635280045527676),(-112966442020126635271500747237)⟩⟩,⟨⟨65589488661285843476174659775,65589488661285843484304692146⟩,⟨(-113604326803809865654468556069),(-113604326803809865645871275309)⟩⟩,⟨⟨65946634454237240521978733910,65946634454237240530158900353⟩,⟨(-114222921462911159951586627830),(-114222921462911159942932375511)⟩⟩,⟨⟨66295067506085358049433908217,66295067506085358057664065560⟩,⟨(-114826425211748380408024118010),(-114826425211748380399312413583)⟩⟩] +lemma amp7_13_5_eq : ∀ k : Fin 16, amp7_1Expr 3 5 k = amp7_13_5 k := by decide +kernel +noncomputable def amp7_13_6 : Fin 16 → CBox := ![⟨⟨66632338791740151041251275531,66632338791740151049518514540⟩,⟨(-115410596214436558109132466261),(-115410596214436558100384735874)⟩⟩,⟨⟨66960713276388809126946131847,66960713276388809135263161307⟩,⟨(-115979357505757280246085539038),(-115979357505757280237279026507)⟩⟩,⟨⟨67277905729051392369092057750,67277905729051392377450337412⟩,⟨(-116528750949546260433400747541),(-116528750949546260424549310013)⟩⟩,⟨⟨67586024963955147022461203821,67586024963955147030866544845⟩,⟨(-117062429119188813284598809905),(-117062429119188813275691623490)⟩⟩,⟨⟨67882946447620971187209149058,67882946447620971195656232145⟩,⟨(-117576712214756753237544204254),(-117576712214756753228589545931)⟩⟩,⟨⟨68170625858784866936792484016,68170625858784866945282187172⟩,⟨(-118074987571184117964758061940),(-118074987571184117955753638173)⟩⟩,⟨⟨68447096538020503798312450542,68447096538020503806806300524⟩,⟨(-118553848834423318825647608091),(-118553848834423318816659119256)⟩⟩,⟨⟨68714163775761176697535921512,68714163775761176706073108123⟩,⟨(-119016422859227240664926498867),(-119016422859227240655885279956)⟩⟩,⟨⟨68970016219710489342827824586,68970016219710489351403313822⟩,⟨(-119459572291388118545207904931),(-119459572291388118536121737355)⟩⟩,⟨⟨69216311266545650363426799100,69216311266545650372037294825⟩,⟨(-119886167826159173646610924294),(-119886167826159173637484717973)⟩⟩,⟨⟨69451390545946672983490978829,69451390545946672992137334370⟩,⟨(-120293337081888424616597304219),(-120293337081888424607428643327)⟩⟩,⟨⟨69676765816596932304139343964,69676765816596932312816043177⟩,⟨(-120683698501424260561721028961),(-120683698501424260552518656327)⟩⟩,⟨⟨69890929593705596294944150969,69890929593705596303651998320⟩,⟨(-121054641044517323063621466623),(-121054641044517323054383051407)⟩⟩,⟨⟨70095250027190538211061502798,70095250027190538219801760976⟩,⟨(-121408534416337739787038598706),(-121408534416337739777761130803)⟩⟩,⟨⟨70288368638517981037392516714,70288368638517981046145862208⟩,⟨(-121743025663044017268585163825),(-121743025663044017259301175884)⟩⟩,⟨⟨70471511782327267737484990476,70471511782327267746266256897⟩,⟨(-122060238893179595327591124012),(-122060238893179595318274089355)⟩⟩] +lemma amp7_13_6_eq : ∀ k : Fin 16, amp7_1Expr 3 6 k = amp7_13_6 k := by decide +kernel +noncomputable def amp7_13_7 : Fin 16 → CBox := ![⟨⟨70643468314107287776314223834,70643468314107287785120025355⟩,⟨(-122358076342915922348757705190),(-122358076342915922339412552855)⟩⟩,⟨⟨70805324400427207191093498651,70805324400427207199924750670⟩,⟨(-122638419307936276683662740428),(-122638419307936276674287040340)⟩⟩,⟨⟨70956014756739613931134152264,70956014756739613939979747595⟩,⟨(-122899422661280022643938474297),(-122899422661280022634550531028)⟩⟩,⟨⟨71096486770715766116855924877,71096486770715766125722434510⟩,⟨(-123142727326528243655128133949),(-123142727326528243645715711794)⟩⟩,⟨⟨71225819734200030786851441145,71225819734200030795731567000⟩,⟨(-123366738590376440394842599643),(-123366738590376440385417407840)⟩⟩,⟨⟨71344823474217662613085759067,71344823474217662621984784641⟩,⟨(-123572859114377696319267569133),(-123572859114377696309819592705)⟩⟩,⟨⟨71452720759319491779893751914,71452720759319491788805615960⟩,⟨(-123759742694172808920357364204),(-123759742694172808910896172858)⟩⟩,⟨⟨71550184889284250856341545347,71550184889284250865265057874⟩,⟨(-123928555519187267890764408556),(-123928555519187267881291191037)⟩⟩,⟨⟨71636581187985562582013722220,71636581187985562590947884001⟩,⟨(-124078198298123836809763055798),(-124078198298123836800278617364)⟩⟩,⟨⟨71712447281589071093490832184,71712447281589071102435282351⟩,⟨(-124209602226816889763111581863),(-124209602226816889753615667063)⟩⟩,⟨⟨71777290301579416078537293721,71777290301579416087488347755⟩,⟨(-124321913631956371648393763656),(-124321913631956371638891832553)⟩⟩,⟨⟨71831512878535996572872948181,71831512878535996581829933068⟩,⟨(-124415829890162482490402667620),(-124415829890162482480894997870)⟩⟩,⟨⟨71874763373790792273524307610,71874763373790792282483729775⟩,⟨(-124490741945396305279022050828),(-124490741945396305269513776031)⟩⟩,⟨⟨71907309928033851780593261828,71907309928033851789553148781⟩,⟨(-124547114230956580768080270809),(-124547114230956580758573912400)⟩⟩,⟨⟨71928941721771935357627664577,71928941721771935366584855399⟩,⟨(-124584581596769791810586136678),(-124584581596769791801086256875)⟩⟩,⟨⟨71939792741600879308704387036,71939792741600879317655066710⟩,⟨(-124603376114427460081786758417),(-124603376114427460072299063574)⟩⟩] +lemma amp7_13_7_eq : ∀ k : Fin 16, amp7_1Expr 3 7 k = amp7_13_7 k := by decide +kernel +noncomputable def amp7_13_8 : Fin 16 → CBox := ![⟨⟨71939792741600879308704387036,71939792741600879317655066710⟩,⟨(-124603376114427460081786758417),(-124603376114427460072299063574)⟩⟩,⟨⟨71928941721771935357627664577,71928941721771935366584855399⟩,⟨(-124584581596769791810586136678),(-124584581596769791801086256875)⟩⟩,⟨⟨71907309928033851780593261828,71907309928033851789553148781⟩,⟨(-124547114230956580768080270809),(-124547114230956580758573912400)⟩⟩,⟨⟨71874763373790792273524307610,71874763373790792282483729775⟩,⟨(-124490741945396305279022050828),(-124490741945396305269513776031)⟩⟩,⟨⟨71831512878535996572872948181,71831512878535996581829933068⟩,⟨(-124415829890162482490402667620),(-124415829890162482480894997870)⟩⟩,⟨⟨71777290301579416078537293721,71777290301579416087488347755⟩,⟨(-124321913631956371648393763656),(-124321913631956371638891832553)⟩⟩,⟨⟨71712447281589071093490832184,71712447281589071102435282351⟩,⟨(-124209602226816889763111581863),(-124209602226816889753615667063)⟩⟩,⟨⟨71636581187985562582013722220,71636581187985562590947884001⟩,⟨(-124078198298123836809763055798),(-124078198298123836800278617364)⟩⟩,⟨⟨71550184889284250856341545347,71550184889284250865265057874⟩,⟨(-123928555519187267890764408556),(-123928555519187267881291191037)⟩⟩,⟨⟨71452720759319491779893751914,71452720759319491788805615960⟩,⟨(-123759742694172808920357364204),(-123759742694172808910896172858)⟩⟩,⟨⟨71344823474217662613085759067,71344823474217662621984784641⟩,⟨(-123572859114377696319267569133),(-123572859114377696309819592705)⟩⟩,⟨⟨71225819734200030786851441145,71225819734200030795731567000⟩,⟨(-123366738590376440394842599643),(-123366738590376440385417407840)⟩⟩,⟨⟨71096486770715766116855924877,71096486770715766125722434510⟩,⟨(-123142727326528243655128133949),(-123142727326528243645715711794)⟩⟩,⟨⟨70956014756739613931134152264,70956014756739613939979747595⟩,⟨(-122899422661280022643938474297),(-122899422661280022634550531028)⟩⟩,⟨⟨70805324400427207191093498651,70805324400427207199924750670⟩,⟨(-122638419307936276683662740428),(-122638419307936276674287040340)⟩⟩,⟨⟨70643468314107287776314223834,70643468314107287785120025355⟩,⟨(-122358076342915922348757705190),(-122358076342915922339412552855)⟩⟩] +lemma amp7_13_8_eq : ∀ k : Fin 16, amp7_1Expr 3 8 k = amp7_13_8 k := by decide +kernel +noncomputable def amp7_13_9 : Fin 16 → CBox := ![⟨⟨70471511782327267737484990476,70471511782327267746266256897⟩,⟨(-122060238893179595327591124012),(-122060238893179595318274089355)⟩⟩,⟨⟨70288368638517981037392516714,70288368638517981046145862208⟩,⟨(-121743025663044017268585163825),(-121743025663044017259301175884)⟩⟩,⟨⟨70095250027190538211061502798,70095250027190538219801760976⟩,⟨(-121408534416337739787038598706),(-121408534416337739777761130803)⟩⟩,⟨⟨69890929593705596294944150969,69890929593705596303651998320⟩,⟨(-121054641044517323063621466623),(-121054641044517323054383051407)⟩⟩,⟨⟨69676765816596932304139343964,69676765816596932312816043177⟩,⟨(-120683698501424260561721028961),(-120683698501424260552518656327)⟩⟩,⟨⟨69451390545946672983490978829,69451390545946672992137334370⟩,⟨(-120293337081888424616597304219),(-120293337081888424607428643327)⟩⟩,⟨⟨69216311266545650363426799100,69216311266545650372037294825⟩,⟨(-119886167826159173646610924294),(-119886167826159173637484717973)⟩⟩,⟨⟨68970016219710489342827824586,68970016219710489351403313822⟩,⟨(-119459572291388118545207904931),(-119459572291388118536121737355)⟩⟩,⟨⟨68714163775761176697535921512,68714163775761176706073108123⟩,⟨(-119016422859227240664926498867),(-119016422859227240655885279956)⟩⟩,⟨⟨68447096538020503798312450542,68447096538020503806806300524⟩,⟨(-118553848834423318825647608091),(-118553848834423318816659119256)⟩⟩,⟨⟨68170625858784866936792484016,68170625858784866945282187172⟩,⟨(-118074987571184117964758061940),(-118074987571184117955753638173)⟩⟩,⟨⟨67882946447620971187209149058,67882946447620971195656232145⟩,⟨(-117576712214756753237544204254),(-117576712214756753228589545931)⟩⟩,⟨⟨67586024963955147022461203821,67586024963955147030866544845⟩,⟨(-117062429119188813284598809905),(-117062429119188813275691623490)⟩⟩,⟨⟨67277905729051392369092057750,67277905729051392377450337412⟩,⟨(-116528750949546260433400747541),(-116528750949546260424549310013)⟩⟩,⟨⟨66960713276388809126946131847,66960713276388809135263161307⟩,⟨(-115979357505757280246085539038),(-115979357505757280237279026507)⟩⟩,⟨⟨66632338791740151041251275531,66632338791740151049518514540⟩,⟨(-115410596214436558109132466261),(-115410596214436558100384735874)⟩⟩] +lemma amp7_13_9_eq : ∀ k : Fin 16, amp7_1Expr 3 9 k = amp7_13_9 k := by decide +kernel +noncomputable def amp7_13_10 : Fin 16 → CBox := ![⟨⟨66295067506085358049433908217,66295067506085358057664065560⟩,⟨(-114826425211748380408024118010),(-114826425211748380399312413583)⟩⟩,⟨⟨65946634454237240521978733910,65946634454237240530158900353⟩,⟨(-114222921462911159951586627830),(-114222921462911159942932375511)⟩⟩,⟨⟨65589488661285843476174659775,65589488661285843484304692146⟩,⟨(-113604326803809865654468556069),(-113604326803809865645871275309)⟩⟩,⟨⟨65221205709714364218974033345,65221205709714364227055975461⟩,⟨(-112966442020126635280045527676),(-112966442020126635271500747237)⟩⟩,⟨⟨64844401807227121640445860556,64844401807227121648473048893⟩,⟨(-112313798516528502280389818972),(-112313798516528502271908367924)⟩⟩,⟨⟨64456489476868880859644062116,64456489476868880867618855222⟩,⟨(-111641914651465586220212637542),(-111641914651465586211789501911)⟩⟩,⟨⟨64060255810442041620599162938,64060255810442041628519894259⟩,⟨(-110955617809545002173932881197),(-110955617809545002165570251744)⟩⟩,⟨⟨63652946336376028674681227369,63652946336376028682543897304⟩,⟨(-110250137106058509768370790633),(-110250137106058509760074668753)⟩⟩,⟨⟨63237523068765669823352219152,63237523068765669831155397021⟩,⟨(-109530602899911085894140535096),(-109530602899911085885912720353)⟩⟩,⟨⟨62811060253041564511098203437,62811060253041564518838720961⟩,⟨(-108791947635538051986214143763),(-108791947635538051978059200691)⟩⟩,⟨⟨62376699227217381556754808564,62376699227217381564428745586⟩,⟨(-108039612269982829935152395833),(-108039612269982829927076453923)⟩⟩,⟨⟨61931338283814348954344724022,61931338283814348962065578847⟩,⟨(-107268224488301970261880992849),(-107268224488301970253686547501)⟩⟩,⟨⟨61478302879938500944461168750,61478302879938500952119156204⟩,⟨(-106483544151161515234040349374),(-106483544151161515225916912376)⟩⟩,⟨⟨61014310271825440935605120921,61014310271825440943199588507⟩,⟨(-105679885379573300039257708727),(-105679885379573300031205494037)⟩⟩,⟨⟨60542875258375211986045447989,60542875258375211993574821800⟩,⟨(-104863335983810586458226167496),(-104863335983810586450247278894)⟩⟩,⟨⟨60060528526626865100247112601,60060528526626865107711802530⟩,⟨(-104027886937557653610379431093),(-104027886937557653602472246225)⟩⟩] +lemma amp7_13_10_eq : ∀ k : Fin 16, amp7_1Expr 3 10 k = amp7_13_10 k := by decide +kernel +noncomputable def amp7_13_11 : Fin 16 → CBox := ![⟨⟨59570979905906762494586494316,59570979905906762501985341252⟩,⟨(-103179963853695169876630220379),(-103179963853695169868796144693)⟩⟩,⟨⟨59070567490809294428931779564,59070567490809294436265330166⟩,⟨(-102313224126008108069423030436),(-102313224126008108061660208699)⟩⟩,⟨⟨58563202339129627985852968379,58563202339129627993116411741⟩,⟨(-101434441905309035886786910607),(-101434441905309035879103094189)⟩⟩,⟨⟨58045023393183337444512614532,58045023393183337451711222358⟩,⟨(-100536929643517573739585816114),(-100536929643517573731970969949)⟩⟩,⟨⟨57520149696019410855551851026,57520149696019410862678480572⟩,⟨(-99627821732473132351505976142),(-99627821732473132343971912034)⟩⟩,⟨⟨56984513888713790569813295882,56984513888713790576868453600⟩,⟨(-98700073299866625191486778651),(-98700073299866625184031719512)⟩⟩,⟨⟨56442450371203974287833497558,56442450371203974294813270530⟩,⟨(-97761191746610121643000808292),(-97761191746610121635630994035)⟩⟩,⟨⟨55889677685399926700497183981,55889677685399926707417553969⟩,⟨(-96803761369761203745980551855),(-96803761369761203738667405795)⟩⟩,⟨⟨55330753638593851790909043360,55330753638593851797752904092⟩,⟨(-95835676523121076727190341806),(-95835676523121076719962978519)⟩⟩,⟨⟨54761174158297399574773479268,54761174158297399581540629633⟩,⟨(-94849135924298945233695062257),(-94849135924298945226552939112)⟩⟩,⟨⟨54185729261629598880721845802,54185729261629598887415189967⟩,⟨(-93852436126314091895161647892),(-93852436126314091888099244279)⟩⟩,⟨⟨53599682950878333015572738664,53599682950878333022185618851⟩,⟨(-92837374140504600637910158715),(-92837374140504600630938119793)⟩⟩,⟨⟨53008067091420818534526594511,53008067091420818541060109894⟩,⟨(-91812665413360657269759609728),(-91812665413360657262875565968)⟩⟩,⟨⟨52405903563925214425391350641,52405903563925214431843593336⟩,⟨(-90769687589273372325689758332),(-90769687589273372318896132329)⟩⟩,⟨⟨51798476653068572739486148460,51798476653068572745854244658⟩,⟨(-89717593317785057655132269346),(-89717593317785057648433598579)⟩⟩,⟨⟨51180554932150761401212042711,51180554932150761407492628826⟩,⟨(-88647321502055012109676391355),(-88647321502055012103077624187)⟩⟩] +lemma amp7_13_11_eq : ∀ k : Fin 16, amp7_1Expr 3 11 k = amp7_13_11 k := by decide +kernel +noncomputable def amp7_13_12 : Fin 16 → CBox := ![⟨⟨50557686720482431271022248964,50557686720482431277278006023⟩,⟨(-87568482113025898508852511353),(-87568482113025898502244667456)⟩⟩,⟨⟨49924374988729221664322405117,49924374988729221670497694866⟩,⟨(-86471554016599907620705093195),(-86471554016599907614183667604)⟩⟩,⟨⟨49286444880026379419168077331,49286444880026379425261785235⟩,⟨(-85366626656648648032987778926),(-85366626656648648026554315900)⟩⟩,⟨⟨48638120217913569078718331680,48638120217913569084730029763⟩,⟨(-84243695402069335378558335789),(-84243695402069335372212707449)⟩⟩,⟨⟨47985517083355406597791132912,47985517083355406603719860695⟩,⟨(-83113353615835889359989175288),(-83113353615835889353732687484)⟩⟩,⟨⟨47322565195896356610756615547,47322565195896356616602767033⟩,⟨(-81965087263783130374910237819),(-81965087263783130368741342793)⟩⟩,⟨⟨46655687189838484688106070480,46655687189838484693865486004⟩,⟨(-80810020674840670667268707375),(-80810020674840670661194281589)⟩⟩,⟨⟨45978502120047616445324481930,45978502120047616451004456870⟩,⟨(-79637101727835810796308744897),(-79637101727835810790315290551)⟩⟩,⟨⟨45297756499006132963176505564,45297756499006132968767769117⟩,⟨(-78458015725161932423982958660),(-78458015725161932418086235533)⟩⟩,⟨⟨44606740326628404392177641471,44606740326628404397681119279⟩,⟨(-77261140605751933133718187097),(-77261140605751933127915733147)⟩⟩,⟨⟨43912543273515121376677881543,43912543273515121382091547094⟩,⟨(-76058756039295136483435994761),(-76058756039295136477731054034)⟩⟩,⟨⟨43208105797029466858348041000,43208105797029466863670335058⟩,⟨(-74838634539266376565838382250),(-74838634539266376560232799158)⟩⟩,⟨⟨42500882253193745494307637208,42500882253193745499534983876⟩,⟨(-73613687429033992086164115581),(-73613687429033992080663850797)⟩⟩,⟨⟨41783440652515466062712238362,41783440652515466067881771989⟩,⟨(-72371042125195670213180046820),(-72371042125195670207719927371)⟩⟩,⟨⟨41063624160825241726307429363,41063624160825241731383084468⟩,⟨(-71124283389462221099547669093),(-71124283389462221094189963644)⟩⟩,⟨⟨40333602637358103889358763441,40333602637358103894339998795⟩,⟨(-69859849020198302902471131806),(-69859849020198302897215924486)⟩⟩] +lemma amp7_13_12_eq : ∀ k : Fin 16, amp7_1Expr 3 12 k = amp7_13_12 k := by decide +kernel +noncomputable def amp7_13_13 : Fin 16 → CBox := ![⟨⟨39601635200454137553462153876,39601635200454137558349562952⟩,⟨(-68592044229994666774302965451),(-68592044229994666769149065625)⟩⟩,⟨⟨38859464590104374372737393850,38859464590104374377534434452⟩,⟨(-67306567024984472896603472620),(-67306567024984472891544038043)⟩⟩,⟨⟨38115796549175229429730768501,38115796549175229434429839621⟩,⟨(-66018496194129982505714267510),(-66018496194129982500762338307)⟩⟩,⟨⟨37361913902531192331318004861,37361913902531192335920687520⟩,⟨(-64712733147198015487885664607),(-64712733147198015483037648260)⟩⟩,⟨⟨36607003843609385792125650494,36607003843609385796628446774⟩,⟨(-63405190570000631730472917578),(-63405190570000631725734786752)⟩⟩,⟨⟨35841851965557722416980862685,35841851965557722421406982872⟩,⟨(-62079908641708405064247676800),(-62079908641708405059578373718)⟩⟩,⟨⟨35076166662618009661738775453,35076166662618009666067195693⟩,⟨(-60753702794408055131226060641),(-60753702794408055126661955082)⟩⟩,⟨⟨34300193600980150022295221211,34300193600980150026524587187⟩,⟨(-59409678026346506145692323982),(-59409678026346506141234901468)⟩⟩,⟨⟨33524208008310895721292786057,33524208008310895725423644051⟩,⟨(-58065631553901910365651757749),(-58065631553901910361300071044)⟩⟩,⟨⟨32737866477294929149518178074,32737866477294929153551802935⟩,⟨(-56703648070080758093047621182),(-56703648070080758088798596259)⟩⟩,⟨⟨31952063788142973129511946095,31952063788142973133445909773⟩,⟨(-55342597887745317215787417433),(-55342597887745317211645304850)⟩⟩,⟨⟨31155810506980960745301056096,31155810506980960749149760740⟩,⟨(-53963446749079285356318140786),(-53963446749079285352257121455)⟩⟩,⟨⟨30360682302007587721754092451,30360682302007587725499329759⟩,⟨(-52586244299534362815984386368),(-52586244299534362812036092065)⟩⟩,⟨⟨29554977221247464420976965216,29554977221247464424619415477⟩,⟨(-51190722163741443753596882388),(-51190722163741443749759250420)⟩⟩,⟨⟨28751023739938367694816727329,28751023739938367698357745858⟩,⟨(-49798233887192212471910300715),(-49798233887192212468181130070)⟩⟩,⟨⟨27936329116135969235542334054,27936329116135969238978800435⟩,⟨(-48387141406113245539213063127),(-48387141406113245535596860388)⟩⟩] +lemma amp7_13_13_eq : ∀ k : Fin 16, amp7_1Expr 3 13 k = amp7_13_13 k := by decide +kernel +noncomputable def amp7_13_14 : Fin 16 → CBox := ![⟨⟨27124059698702532519920535674,27124059698702532523264899100⟩,⟨(-46980249505684159979218276757),(-46980249505684159975693682076)⟩⟩,⟨⟨26300838960499855271984235635,26300838960499855275224439547⟩,⟨(-45554389361272765536711023361),(-45554389361272765533298003604)⟩⟩,⟨⟨25480772729857277561796768934,25480772729857277564934795781⟩,⟨(-44133992984228323627288421791),(-44133992984228323623983807023)⟩⟩,⟨⟨24649489050903922243517302123,24649489050903922246547730898⟩,⟨(-42694167416778337223328462166),(-42694167416778337220140703885)⟩⟩,⟨⟨23822155938916705060294246414,23822155938916705063229140477⟩,⟨(-41261184432032405305730702769),(-41261184432032405302639236954)⟩⟩,⟨⟨22983270389303945547530151946,22983270389303945550359153072⟩,⟨(-39808192038367763712971371021),(-39808192038367763709993172672)⟩⟩,⟨⟨22149212667309377170673773325,22149212667309377173404054290⟩,⟨(-38363561687428013406562451664),(-38363561687428013403685500855)⟩⟩,⟨⟨21303181743484879754550438990,21303181743484879757173234854⟩,⟨(-36898193142589549348272089254),(-36898193142589549345510566151)⟩⟩,⟨⟨20462956309978198963961066180,20462956309978198966477978336⟩,⟨(-35442880001944392874337889126),(-35442880001944392871689505468)⟩⟩,⟨⟨19610228521757425345573145529,19610228521757425347987825180⟩,⟨(-33965912147720179358036854187),(-33965912147720179355494240505)⟩⟩,⟨⟨18764410360201072197620399313,18764410360201072199927580730⟩,⟨(-32500912117940074765447015335),(-32500912117940074763019869897)⟩⟩,⟨⟨17905421340180017039915821650,17905421340180017042119120792⟩,⟨(-31013099492119807673542163914),(-31013099492119807671223122395)⟩⟩,⟨⟨17054608847284225416946263130,17054608847284225419046695419⟩,⟨(-29539449026709962117685548794),(-29539449026709962115473536125)⟩⟩,⟨⟨16189774056173590091205363746,16189774056173590093196337975⟩,⟨(-28041511228353124899996839682),(-28041511228353124897902099675)⟩⟩,⟨⟨15334597482021724182200697501,15334597482021724184087222958⟩,⟨(-26560301952479399676624982788),(-26560301952479399674639646687)⟩⟩,⟨⟨14464300825782799816544920329,14464300825782799818324821811⟩,⟨(-25052903926216277137775876485),(-25052903926216277135902447567)⟩⟩] +lemma amp7_13_14_eq : ∀ k : Fin 16, amp7_1Expr 3 14 k = amp7_13_14 k := by decide +kernel +noncomputable def amp7_13_15 : Fin 16 → CBox := ![⟨⟨13605436144528543517368211879,13605436144528543519042065407⟩,⟨(-23565306661457456127088278802),(-23565306661457456125326715265)⟩⟩,⟨⟨12730011261233991575311644616,12730011261233991576877033750⟩,⟨(-22049026285381237278711830136),(-22049026285381237277064932678)⟩⟩,⟨⟨11868204086295200167786867027,11868204086295200169245170836⟩,⟨(-20556332472059850912345015175),(-20556332472059850910811533840)⟩⟩,⟨⟨10987901608861133639375815753,10987901608861133640726644521⟩,⟨(-19031603855115292601533986062),(-19031603855115292600113049348)⟩⟩,⟨⟨10124011078824646541688415677,10124011078824646542933094048⟩,⟨(-17535301564914489677772881313),(-17535301564914489676463567176)⟩⟩,⟨⟨9238936788997680557540949540,9238936788997680558676470222⟩,⟨(-16002307926461242687861793876),(-16002307926461242686667539792)⟩⟩,⟨⟨8374023000594305591410506291,8374023000594305592438731974⟩,⟨(-14504233300779720021033146759),(-14504233300779720019952412201)⟩⟩,⟨⟨7484008818589727932776539773,7484008818589727933696011678⟩,⟨(-12962683518090937550503754536),(-12962683518090937549536967381)⟩⟩,⟨⟨6619527590048496233739978055,6619527590048496234552679627⟩,⟨(-11465358108067962011679230624),(-11465358108067962010825090416)⟩⟩,⟨⟨5723823631345515038700521431,5723823631345515039402858549⟩,⟨(-9913953343053823115535621381),(-9913953343053823114797742590)⟩⟩,⟨⟨4862135239681351864436049071,4862135239681351865031965968⟩,⟨(-8421465268399182256321234501),(-8421465268399182255695629772)⟩⟩,⟨⟨3958514790998972547869754643,3958514790998972548354483262⟩,⟨(-6856348740523115919018081696),(-6856348740523115918509503341)⟩⟩,⟨⟨3104583262309451838816025618,3104583262309451839195317269⟩,⟨(-5377295946647905665424978107),(-5377295946647905665027619369)⟩⟩,⟨⟨2185759460592364486753986006,2185759460592364487020472462⟩,⟨(-3785846438870318533903160293),(-3785846438870318533624357266)⟩⟩,⟨⟨1355876442797423833488478828,1355876442797423833651935883⟩,⟨(-2348446887710894609658046685),(-2348446887710894609488304091)⟩⟩,⟨⟨385210003677661992952149995,385210003677661992997475379⟩,⟨(-667203297953504647154747600),(-667203297953504647108451558)⟩⟩] +lemma amp7_13_15_eq : ∀ k : Fin 16, amp7_1Expr 3 15 k = amp7_13_15 k := by decide +kernel +noncomputable def amp7_13 : Fin 16 → Fin 16 → CBox := ![amp7_13_0,amp7_13_1,amp7_13_2,amp7_13_3,amp7_13_4,amp7_13_5,amp7_13_6,amp7_13_7,amp7_13_8,amp7_13_9,amp7_13_10,amp7_13_11,amp7_13_12,amp7_13_13,amp7_13_14,amp7_13_15] +lemma amp7_13_eq (i k : Fin 16) : amp7_1Expr 3 i k = amp7_13 i k := by + fin_cases i + · exact amp7_13_0_eq k + · exact amp7_13_1_eq k + · exact amp7_13_2_eq k + · exact amp7_13_3_eq k + · exact amp7_13_4_eq k + · exact amp7_13_5_eq k + · exact amp7_13_6_eq k + · exact amp7_13_7_eq k + · exact amp7_13_8_eq k + · exact amp7_13_9_eq k + · exact amp7_13_10_eq k + · exact amp7_13_11_eq k + · exact amp7_13_12_eq k + · exact amp7_13_13_eq k + · exact amp7_13_14_eq k + · exact amp7_13_15_eq k +noncomputable def amp7_14_0 : Fin 16 → CBox := ![⟨⟨206433418803638677605872232,206433418803638677646228799⟩,⟨(-563986588551685308340424636),(-563986588551685308299317030)⟩⟩,⟨⟨726611995767906115027202103,726611995767906115171350879⟩,⟨(-1985140889826941552103315667),(-1985140889826941551952885640)⟩⟩,⟨⟨1171344964628820879847663382,1171344964628820880081639132⟩,⟨(-3200173956555908093912225111),(-3200173956555908093665354533)⟩⟩,⟨⟨1663741155941996025323109471,1663741155941996025655860668⟩,⟨(-4545425368676907652667901965),(-4545425368676907652316108804)⟩⟩,⟨⟨2121361682949658354605681502,2121361682949658355030552926⟩,⟨(-5795667899048286741593148234),(-5795667899048286741142966154)⟩⟩,⟨⟨2605610421927042946531858735,2605610421927042947054004985⟩,⟨(-7118660057435660782905197842),(-7118660057435660782351463817)⟩⟩,⟨⟨3067387839274413925417231856,3067387839274413926032348789⟩,⟨(-8380259423416616152650078659),(-8380259423416616151997024653)⟩⟩,⟨⟨3547394144058060913553323763,3547394144058060914264943846⟩,⟨(-9691661036038931554697832531),(-9691661036038931553941913758)⟩⟩,⟨⟨4010668238177036632307628800,4010668238177036633112523676⟩,⟨(-10957349399002419234118296105),(-10957349399002419233262727844)⟩⟩,⟨⟨4487625400817782326045356914,4487625400817782326945654467⟩,⟨(-12260420600370828857751435237),(-12260420600370828856794987394)⟩⟩,⟨⟨4951131303068236857168702738,4951131303068236858162574294⟩,⟨(-13526742274927124258991361890),(-13526742274927124257934524751)⟩⟩,⟨⟨5425441185469606814199082418,5425441185469606815288367067⟩,⟨(-14822580972179686270359752504),(-14822580972179686269201120570)⟩⟩,⟨⟨5888398725213949357681508734,5888398725213949358863711317⟩,⟨(-16087404492508317922352901226),(-16087404492508317921095488727)⟩⟩,⟨⟨6360151401061098849961139150,6360151401061098851237654069⟩,⟨(-17376256771529301486997049621),(-17376256771529301485639993069)⟩⟩,⟨⟨6821992474173491747585165518,6821992474173491748955012502⟩,⟨(-18638030048294491404524853915),(-18638030048294491403067511390)⟩⟩,⟨⟨7291131255199261819320084206,7291131255199261820784570279⟩,⟨(-19919741033857825217006503032),(-19919741033857825215447748177)⟩⟩] +lemma amp7_14_0_eq : ∀ k : Fin 16, amp7_1Expr 4 0 k = amp7_14_0 k := by decide +kernel +noncomputable def amp7_14_1 : Fin 16 → CBox := ![⟨⟨7751395450698644994907058817,7751395450698644996464198301⟩,⟨(-21177206200866954639873888100),(-21177206200866954638216173187)⟩⟩,⟨⟨8217786023128097380087795360,8217786023128097381738373762⟩,⟨(-22451408940915350986105768973),(-22451408940915350984349000097)⟩⟩,⟨⟨8676073767988110569613024053,8676073767988110571355245039⟩,⟨(-23703474344359069614688707451),(-23703474344359069612835078099)⟩⟩,⟨⟨9139537335716977437465573796,9139537335716977439302524671⟩,⟨(-24969680358851473398423514395),(-24969680358851473396466323626)⟩⟩,⟨⟨9595486376480452817875944431,9595486376480452819803508122⟩,⟨(-26215356303879581264049055414),(-26215356303879581261997034160)⟩⟩,⟨⟨10055817204924139265132370068,10055817204924139267151431772⟩,⟨(-27473003515478005132299549244),(-27473003515478005130151746857)⟩⟩,⟨⟨10509089791589342672025739026,10509089791589342674137687184⟩,⟨(-28711367251925508021415564031),(-28711367251925508019165822932)⟩⟩,⟨⟨10966065236024010113218271280,10966065236024010115420572192⟩,⟨(-29959847383932387817094617802),(-29959847383932387814751100530)⟩⟩,⟨⟨11416340688760420327964560661,11416340688760420330258649538⟩,⟨(-31190022798209339183628955259),(-31190022798209339181185496460)⟩⟩,⟨⟨11869727294381481876139161733,11869727294381481878526138902⟩,⟨(-32428698040237272467804881484),(-32428698040237272465259517150)⟩⟩,⟨⟨12316697480480254770980025120,12316697480480254773454694071⟩,⟨(-33649843298127636326768558496),(-33649843298127636324133336456)⟩⟩,⟨⟨12766254891602009636775144626,12766254891602009639341550603⟩,⟨(-34878056986231400486603607401),(-34878056986231400483868342483)⟩⟩,⟨⟨13209621370059014534694878678,13209621370059014537346988882⟩,⟨(-36089356731748829955217529426),(-36089356731748829952396629777)⟩⟩,⟨⟨13655104950972463000157130102,13655104950972463002901574044⟩,⟨(-37306440508742092126419168399),(-37306440508742092123495231023)⟩⟩,⟨⟨14094577119453890022308781408,14094577119453890025142186110⟩,⟨(-38507100801545820524740179856),(-38507100801545820521720406270)⟩⟩,⟨⟨14535739783441810129292918366,14535739783441810132216477790⟩,⟨(-39712379613963254913729075325),(-39712379613963254910610769823)⟩⟩] +lemma amp7_14_1_eq : ∀ k : Fin 16, amp7_1Expr 4 1 k = amp7_14_1 k := by decide +kernel +noncomputable def amp7_14_2 : Fin 16 → CBox := ![⟨⟨14971033652317385872003646012,14971033652317385875010442297⟩,⟨(-40901624579954552602345417419),(-40901624579954552599145514091)⟩⟩,⟨⟨15407627185369045843962659742,15407627185369045847059465544⟩,⟨(-42094420294507689549036736710),(-42094420294507689545737167661)⟩⟩,⟨⟨15838464557506970185476955320,15838464557506970188661650409⟩,⟨(-43271489884987958659940574137),(-43271489884987958656545203812)⟩⟩,⟨⟨16270240608961625264061430155,16270240608961625267334813901⟩,⟨(-44451123995053550183009884534),(-44451123995053550179516843445)⟩⟩,⟨⟨16696348529765272277836485926,16696348529765272281198481743⟩,⟨(-45615272484196649216429951804),(-45615272484196649212837550546)⟩⟩,⟨⟨17123059377081258095932980499,17123059377081258099373877513⟩,⟨(-46781068199204688166829703015),(-46781068199204688163164674149)⟩⟩,⟨⟨17544169769018200421680242398,17544169769018200425207322811⟩,⟨(-47931563185571657881191118057),(-47931563185571657877431690262)⟩⟩,⟨⟨17965568925439762163804661386,17965568925439762167416646486⟩,⟨(-49082847091182029282708539026),(-49082847091182029278858302536)⟩⟩,⟨⟨18381418351227587807973296693,18381418351227587811670437732⟩,⟨(-50218968850732712240639919527),(-50218968850732712236696328928)⟩⟩,⟨⟨18797261061655928394921961508,18797261061655928398704550715⟩,⟨(-51355072263580090932674309300),(-51355072263580090928636563956)⟩⟩,⟨⟨19207590578814079550085649661,19207590578814079553952532167⟩,⟨(-52476113352301365288089409547),(-52476113352301365283958817879)⟩⟩,⟨⟨19617634234436279718380131699,19617634234436279722320018605⟩,⟨(-53596373452782491870148369745),(-53596373452782491865955677840)⟩⟩,⟨⟨20022189315728738360571606126,20022189315728738364596508610⟩,⟨(-54701638489333646306440100668),(-54701638489333646302150654882)⟩⟩,⟨⟨20426193808440952718801022764,20426193808440952722909023445⟩,⟨(-55805399289909506145129651601),(-55805399289909506140748505889)⟩⟩,⟨⟨20824724310448551709291490971,20824724310448551713483011073⟩,⟨(-56894204869760197040748835223),(-56894204869760197036273005164)⟩⟩,⟨⟨21222452341827216677007787092,21222452341827216681278690791⟩,⟨(-57980818059081058434567426346),(-57980818059081058430007942422)⟩⟩] +lemma amp7_14_2_eq : ∀ k : Fin 16, amp7_1Expr 4 2 k = amp7_14_2 k := by decide +kernel +noncomputable def amp7_14_3 : Fin 16 → CBox := ![⟨⟨21614712509035809764487443342,21614712509035809768839158104⟩,⟨(-59052492765680398018972064334),(-59052492765680398014323195075)⟩⟩,⟨⟨22005929864376524718360892815,22005929864376524722793655520⟩,⟨(-60121318457273958739088013792),(-60121318457273958734348762725)⟩⟩,⟨⟨22391678359670523836946689927,22391678359670523841459784886⟩,⟨(-61175202945360408293403754811),(-61175202945360408288574245334)⟩⟩,⟨⟨22776154154706997817466839630,22776154154706997822040840358⟩,⟨(-62225610351680493176113669610),(-62225610351680493171246549560)⟩⟩,⟨⟨23155154109585114314516583238,23155154109585114319170963786⟩,⟨(-63261057484473819407239015139),(-63261057484473819402279246187)⟩⟩,⟨⟨23532661015470212552865358292,23532661015470212557598086137⟩,⟨(-64292425531560030205639143462),(-64292425531560030200591778438)⟩⟩,⟨⟨23904680095009751314520585576,23904680095009751319330398007⟩,⟨(-65308800558247057475071023139),(-65308800558247057469937673589)⟩⟩,⟨⟨24274994545700667018200465919,24274994545700667023086144261⟩,⟨(-66320518452311598913473692256),(-66320518452311598908257116666)⟩⟩,⟨⟨24639805024518844202359312146,24639805024518844207320924072⟩,⟨(-67317199215576388693697624870),(-67317199215576388688395794698)⟩⟩,⟨⟨25002707409672597431752604040,25002707409672597436785032836⟩,⟨(-68308666970004371949940987987),(-68308666970004371944567243208)⟩⟩,⟨⟨25360086256019165707285202382,25360086256019165712391927730⟩,⟨(-69285044135773547519794290774),(-69285044135773547514337274511)⟩⟩,⟨⟨25715361101749847685464978464,25715361101749847690643607451⟩,⟨(-70255673064960965515762518568),(-70255673064960965510228063606)⟩⟩,⟨⟨26065090067515605572237748787,26065090067515605577488060921⟩,⟨(-71211150368311532590924346335),(-71211150368311532585311197377)⟩⟩,⟨⟨26412526206808221625377372227,26412526206808221630698674339⟩,⟨(-72160363553244537218763279120),(-72160363553244537213072561920)⟩⟩,⟨⟨26754391921717071430759455186,26754391921717071436151084375⟩,⟨(-73094358055741371903768947498),(-73094358055741371898000607215)⟩⟩,⟨⟨27093782655877928081460136145,27093782655877928086921302506⟩,⟨(-74021590785086934466545710314),(-74021590785086934460701075973)⟩⟩] +lemma amp7_14_3_eq : ∀ k : Fin 16, amp7_1Expr 4 3 k = amp7_14_3 k := by decide +kernel +noncomputable def amp7_14_4 : Fin 16 → CBox := ![⟨⟨27427576724493021400576318633,27427576724493021406076770126⟩,⟨(-74933533139808501407806071885),(-74933533139808501401965918892)⟩⟩,⟨⟨27758719976704175662983531782,27758719976704175668556652753⟩,⟨(-75838233329432969822036111049),(-75838233329432969816108343735)⟩⟩,⟨⟨28084239077154113065701625743,28084239077154113071345175924⟩,⟨(-76727568050696315791213201420),(-76727568050696315785202056402)⟩⟩,⟨⟨28406937538961959614305892995,28406937538961959620018112785⟩,⟨(-77609196643879677460960327231),(-77609196643879677454869667005)⟩⟩,⟨⟨28723983522504130802387132866,28723983522504130808166559898⟩,⟨(-78475382379252535235050154784),(-78475382379252535228882081208)⟩⟩,⟨⟨29038044793890211748682878397,29038044793890211754529869417⟩,⟨(-79333413729368986019133364213),(-79333413729368986012885902861)⟩⟩,⟨⟨29346424784591707848003198426,29346424784591707853913743366⟩,⟨(-80175923532003091307987974666),(-80175923532003091301670178199)⟩⟩,⟨⟨29651661508133253725746335967,29651661508133253731721746523⟩,⟨(-81009845769054449862592251834),(-81009845769054449856199483735)⟩⟩,⟨⟨29951188002077299326710611778,29951188002077299332750335747⟩,⟨(-81828167368722554080880923288),(-81828167368722554074412779463)⟩⟩,⟨⟨30247417991595653882149031120,30247417991595653888243644710⟩,⟨(-82637482750812294700167140869),(-82637482750812294693648263371)⟩⟩,⟨⟨30537908955121911913286720885,30537908955121911919444342028⟩,⟨(-83431118822305669233065133786),(-83431118822305669226471421624)⟩⟩,⟨⟨30824955319131378736380267310,30824955319131378742598530984⟩,⟨(-84215344072907442981519461320),(-84215344072907442974856222021)⟩⟩,⟨⟨31106234285698202316244520363,31106234285698202322523249097⟩,⟨(-84983812500668472579648921139),(-84983812500668472572914707671)⟩⟩,⟨⟨31383925545900440187360755768,31383925545900440193695842545⟩,⟨(-85742479132358815791275545020),(-85742479132358815784480376195)⟩⟩,⟨⟨31655821711220961594580442047,31655821711220961600974260931⟩,⟨(-86485313270397627270284034971),(-86485313270397627263419483555)⟩⟩,⟨⟨31923991916236710242945843771,31923991916236710249395526613⟩,⟨(-87217967895576814753292012710),(-87217967895576814746364666554)⟩⟩] +lemma amp7_14_4_eq : ∀ k : Fin 16, amp7_1Expr 4 4 k = amp7_14_4 k := by decide +kernel +noncomputable def amp7_14_5 : Fin 16 → CBox := ![⟨⟨32186340231392153198254128773,32186340231392153204759515408⟩,⟨(-87934716821861577009370401724),(-87934716821861577002378748262)⟩⟩,⟨⟨32444829065879675045915154895,32444829065879675052475323771⟩,⟨(-88640921450870748933370242279),(-88640921450870748926315506432)⟩⟩,⟨⟨32697470328155163682254764699,32697470328155163688869480360⟩,⟨(-89331150215495718196215464517),(-89331150215495718189096330815)⟩⟩,⟨⟨32946123217430973328273193828,32946123217430973334941302403⟩,⟨(-90010482542446028567972783590),(-90010482542446028560791068488)⟩⟩,⟨⟨33188904158653455312284815941,33188904158653455319005510745⟩,⟨(-90673772408975242603791662271),(-90673772408975242596547602766)⟩⟩,⟨⟨33427572368903866375161730126,33427572368903866381875857365⟩,⟨(-91325826085530896745638056173),(-91325826085530896738491885796)⟩⟩,⟨⟨33660345741090154090585800160,33660345741090154097353724595⟩,⟨(-91961774764992974938970783670),(-91961774764992974931755608245)⟩⟩,⟨⟨33888886475240507523910517126,33888886475240507530729808524⟩,⟨(-92586159662290832130218865965),(-92586159662290832122939907215)⟩⟩,⟨⟨34111511133387095180917940381,34111511133387095187786440417⟩,⟨(-93194381539364962175930286531),(-93194381539364962168591459413)⟩⟩,⟨⟨34329787622678162153613505275,34329787622678162160530108831⟩,⟨(-93790723998205921095129838688),(-93790723998205921087732705944)⟩⟩,⟨⟨34542128604544351017369182679,34542128604544351024331284413⟩,⟨(-94370850349193410709518050264),(-94370850349193410702067741616)⟩⟩,⟨⟨34750010195851482020352919225,34750010195851482027359278957⟩,⟨(-94938793418602761268190087532),(-94938793418602761260688497460)⟩⟩,⟨⟨34951938798604186335294717782,34951938798604186342346136133⟩,⟨(-95490472620824542110360967235),(-95490472620824542102803914346)⟩⟩,⟨⟨35149301037523642615369719821,35149301037523642622462270417⟩,⟨(-96029676285048044344734333605),(-96029676285048044337131015361)⟩⟩,⟨⟨35340694891126642204476958587,35340694891126642211611272185⟩,⟨(-96552574017347838847286055424),(-96552574017347838839632749348)⟩⟩,⟨⟨35527419600844671401550401677,35527419600844671408726038151⟩,⟨(-97062715411326044705174114716),(-97062715411326044697470459242)⟩⟩] +lemma amp7_14_5_eq : ∀ k : Fin 16, amp7_1Expr 4 5 k = amp7_14_5 k := by decide +kernel +noncomputable def amp7_14_6 : Fin 16 → CBox := ![⟨⟨35708162738087487966687637621,35708162738087487973897213386⟩,⟨(-97556514845392814123704572707),(-97556514845392814115968736530)⟩⟩,⟨⟨35884138094040676035690565486,35884138094040676042940520082⟩,⟨(-98037288458736942226143486446),(-98037288458736942218356279360)⟩⟩,⟨⟨36054121017113048629745374469,36054121017113048637030664798⟩,⟨(-98501690440989736116420861698),(-98501690440989736108594054432)⟩⟩,⟨⟨36219241617442961540948670299,36219241617442961548272032116⟩,⟨(-98952808310467332512005272439),(-98952808310467332504129762049)⟩⟩,⟨⟨36378361360970378294155532793,36378361360970378301513648446⟩,⟨(-99387531534271564088336635099),(-99387531534271564080419475482)⟩⟩,⟨⟨36532528292771231838171274475,36532528292771231845564229006⟩,⟨(-99808723424798502043531768053),(-99808723424798502035571067835)⟩⟩,⟨⟨36680688483235377562450352271,36680688483235377569857060426⟩,⟨(-100213504592805630042281208232),(-100213504592805630034332561333)⟩⟩,⟨⟨36823809384590225480901742576,36823809384590225488342813897⟩,⟨(-100604518166932127922323317401),(-100604518166932127914328729503)⟩⟩,⟨⟨36960920296065720301605855201,36960920296065720309078124217⟩,⟨(-100979112143355258392242907485),(-100979112143355258384209013669)⟩⟩,⟨⟨37092909413864254181284855448,37092909413864254188786157133⟩,⟨(-101339713119227046553797531446),(-101339713119227046545728531031)⟩⟩,⟨⟨37218888020009842721662374352,37218888020009842729192698201⟩,⟨(-101683893071883503253586005921),(-101683893071883503245479914275)⟩⟩,⟨⟨37339666263539208114084102489,37339666263539208121640087666⟩,⟨(-102013865369654656502491179546),(-102013865369654656494355436693)⟩⟩,⟨⟨37454436285787739073582421373,37454436285787739081164031369⟩,⟨(-102327422901623453524634533098),(-102327422901623453516467226223)⟩⟩,⟨⟨37563931276086673291303188695,37563931276086673298910689624⟩,⟨(-102626568778294403139182999146),(-102626568778294403130981634240)⟩⟩,⟨⟨37667423227983889633554260783,37667423227983889641176829989⟩,⟨(-102909314049052072449600901522),(-102909314049052072441393035806)⟩⟩,⟨⟨37765569342949880315985068383,37765569342949880323630239107⟩,⟨(-103177454221704655167384336926),(-103177454221704655159147598523)⟩⟩] +lemma amp7_14_6_eq : ∀ k : Fin 16, amp7_1Expr 4 6 k = amp7_14_6 k := by decide +kernel +noncomputable def amp7_14_7 : Fin 16 → CBox := ![⟨⟨37857720570597306429031402652,37857720570597306436696893851⟩,⟨(-103429216057617269132021515201),(-103429216057617269123760127937)⟩⟩,⟨⟨37944458985836275418405483102,37944458985836275426091364056⟩,⟨(-103666189815018138972233009289),(-103666189815018138963944970771)⟩⟩,⟨⟨38025213704398410458046661440,38025213704398410465746514113⟩,⟨(-103886815809080817412684607252),(-103886815809080817404385447533)⟩⟩,⟨⟨38100492429806577178608559598,38100492429806577186325479175⟩,⟨(-104092481111624955063587990289),(-104092481111624955055267418885)⟩⟩,⟨⟨38169801756047242379191991911,38169801756047242386921602762⟩,⟨(-104281837712352819203007345884),(-104281837712352819194675317679)⟩⟩,⟨⟨38233575668115257835329273095,38233575668115257843073975815⟩,⟨(-104456071280320067399358844804),(-104456071280320067391006947064)⟩⟩,⟨⟨38291397648932349300412054695,38291397648932349308168137831⟩,⟨(-104614043869706634267904021347),(-104614043869706634259540400243)⟩⟩,⟨⟨38343628518762467665416778657,38343628518762467673183169337⟩,⟨(-104756741259806034055805774316),(-104756741259806034047431488146)⟩⟩,⟨⟨38389928155694576730133812794,38389928155694576737909513906⟩,⟨(-104883234220276548442443221048),(-104883234220276548434059007202)⟩⟩,⟨⟨38430584672722504869370945055,38430584672722504877155324004⟩,⟨(-104994309890455637326170573515),(-104994309890455637317776270009)⟩⟩,⟨⟨38465333942404921039006846384,38465333942404921046797468880⟩,⟨(-105089246660753911126633162747),(-105089246660753911118233441446)⟩⟩,⟨⟨38494391733819021332345128933,38494391733819021340141191338⟩,⟨(-105168634023252971821971442974),(-105168634023252971813566592994)⟩⟩,⟨⟨38517569604370558557714601900,38517569604370558565513774379⟩,⟨(-105231957143211025997905521743),(-105231957143211025989499938728)⟩⟩,⟨⟨38535011250222245607871343721,38535011250222245615672122766⟩,⟨(-105279608605845457961885310323),(-105279608605845457953481180480)⟩⟩,⟨⟨38546603693548157830985061797,38546603693548157838785298233⟩,⟨(-105311279749995712892835082149),(-105311279749995712884436317840)⟩⟩,⟨⟨38552418737548597092866737541,38552418737548597100663937249⟩,⟨(-105327166745653161533096632026),(-105327166745653161524708112063)⟩⟩] +lemma amp7_14_7_eq : ∀ k : Fin 16, amp7_1Expr 4 7 k = amp7_14_7 k := by decide +kernel +noncomputable def amp7_14_8 : Fin 16 → CBox := ![⟨⟨38552418737548597092866737541,38552418737548597100663937249⟩,⟨(-105327166745653161533096632026),(-105327166745653161524708112063)⟩⟩,⟨⟨38546603693548157830985061797,38546603693548157838785298233⟩,⟨(-105311279749995712892835082149),(-105311279749995712884436317840)⟩⟩,⟨⟨38535011250222245607871343721,38535011250222245615672122766⟩,⟨(-105279608605845457961885310323),(-105279608605845457953481180480)⟩⟩,⟨⟨38517569604370558557714601900,38517569604370558565513774379⟩,⟨(-105231957143211025997905521743),(-105231957143211025989499938728)⟩⟩,⟨⟨38494391733819021332345128933,38494391733819021340141191338⟩,⟨(-105168634023252971821971442974),(-105168634023252971813566592994)⟩⟩,⟨⟨38465333942404921039006846384,38465333942404921046797468880⟩,⟨(-105089246660753911126633162747),(-105089246660753911118233441446)⟩⟩,⟨⟨38430584672722504869370945055,38430584672722504877155324004⟩,⟨(-104994309890455637326170573515),(-104994309890455637317776270009)⟩⟩,⟨⟨38389928155694576730133812794,38389928155694576737909513906⟩,⟨(-104883234220276548442443221048),(-104883234220276548434059007202)⟩⟩,⟨⟨38343628518762467665416778657,38343628518762467673183169337⟩,⟨(-104756741259806034055805774316),(-104756741259806034047431488146)⟩⟩,⟨⟨38291397648932349300412054695,38291397648932349308168137831⟩,⟨(-104614043869706634267904021347),(-104614043869706634259540400243)⟩⟩,⟨⟨38233575668115257835329273095,38233575668115257843073975815⟩,⟨(-104456071280320067399358844804),(-104456071280320067391006947064)⟩⟩,⟨⟨38169801756047242379191991911,38169801756047242386921602762⟩,⟨(-104281837712352819203007345884),(-104281837712352819194675317679)⟩⟩,⟨⟨38100492429806577178608559598,38100492429806577186325479175⟩,⟨(-104092481111624955063587990289),(-104092481111624955055267418885)⟩⟩,⟨⟨38025213704398410458046661440,38025213704398410465746514113⟩,⟨(-103886815809080817412684607252),(-103886815809080817404385447533)⟩⟩,⟨⟨37944458985836275418405483102,37944458985836275426091364056⟩,⟨(-103666189815018138972233009289),(-103666189815018138963944970771)⟩⟩,⟨⟨37857720570597306429031402652,37857720570597306436696893851⟩,⟨(-103429216057617269132021515201),(-103429216057617269123760127937)⟩⟩] +lemma amp7_14_8_eq : ∀ k : Fin 16, amp7_1Expr 4 8 k = amp7_14_8 k := by decide +kernel +noncomputable def amp7_14_9 : Fin 16 → CBox := ![⟨⟨37765569342949880315985068383,37765569342949880323630239107⟩,⟨(-103177454221704655167384336926),(-103177454221704655159147598523)⟩⟩,⟨⟨37667423227983889633554260783,37667423227983889641176829989⟩,⟨(-102909314049052072449600901522),(-102909314049052072441393035806)⟩⟩,⟨⟨37563931276086673291303188695,37563931276086673298910689624⟩,⟨(-102626568778294403139182999146),(-102626568778294403130981634240)⟩⟩,⟨⟨37454436285787739073582421373,37454436285787739081164031369⟩,⟨(-102327422901623453524634533098),(-102327422901623453516467226223)⟩⟩,⟨⟨37339666263539208114084102489,37339666263539208121640087666⟩,⟨(-102013865369654656502491179546),(-102013865369654656494355436693)⟩⟩,⟨⟨37218888020009842721662374352,37218888020009842729192698201⟩,⟨(-101683893071883503253586005921),(-101683893071883503245479914275)⟩⟩,⟨⟨37092909413864254181284855448,37092909413864254188786157133⟩,⟨(-101339713119227046553797531446),(-101339713119227046545728531031)⟩⟩,⟨⟨36960920296065720301605855201,36960920296065720309078124217⟩,⟨(-100979112143355258392242907485),(-100979112143355258384209013669)⟩⟩,⟨⟨36823809384590225480901742576,36823809384590225488342813897⟩,⟨(-100604518166932127922323317401),(-100604518166932127914328729503)⟩⟩,⟨⟨36680688483235377562450352271,36680688483235377569857060426⟩,⟨(-100213504592805630042281208232),(-100213504592805630034332561333)⟩⟩,⟨⟨36532528292771231838171274475,36532528292771231845564229006⟩,⟨(-99808723424798502043531768053),(-99808723424798502035571067835)⟩⟩,⟨⟨36378361360970378294155532793,36378361360970378301513648446⟩,⟨(-99387531534271564088336635099),(-99387531534271564080419475482)⟩⟩,⟨⟨36219241617442961540948670299,36219241617442961548272032116⟩,⟨(-98952808310467332512005272439),(-98952808310467332504129762049)⟩⟩,⟨⟨36054121017113048629745374469,36054121017113048637030664798⟩,⟨(-98501690440989736116420861698),(-98501690440989736108594054432)⟩⟩,⟨⟨35884138094040676035690565486,35884138094040676042940520082⟩,⟨(-98037288458736942226143486446),(-98037288458736942218356279360)⟩⟩,⟨⟨35708162738087487966687637621,35708162738087487973897213386⟩,⟨(-97556514845392814123704572707),(-97556514845392814115968736530)⟩⟩] +lemma amp7_14_9_eq : ∀ k : Fin 16, amp7_1Expr 4 9 k = amp7_14_9 k := by decide +kernel +noncomputable def amp7_14_10 : Fin 16 → CBox := ![⟨⟨35527419600844671401550401677,35527419600844671408726038151⟩,⟨(-97062715411326044705174114716),(-97062715411326044697470459242)⟩⟩,⟨⟨35340694891126642204476958587,35340694891126642211611272185⟩,⟨(-96552574017347838847286055424),(-96552574017347838839632749348)⟩⟩,⟨⟨35149301037523642615369719821,35149301037523642622462270417⟩,⟨(-96029676285048044344734333605),(-96029676285048044337131015361)⟩⟩,⟨⟨34951938798604186335294717782,34951938798604186342346136133⟩,⟨(-95490472620824542110360967235),(-95490472620824542102803914346)⟩⟩,⟨⟨34750010195851482020352919225,34750010195851482027359278957⟩,⟨(-94938793418602761268190087532),(-94938793418602761260688497460)⟩⟩,⟨⟨34542128604544351017369182679,34542128604544351024331284413⟩,⟨(-94370850349193410709518050264),(-94370850349193410702067741616)⟩⟩,⟨⟨34329787622678162153613505275,34329787622678162160530108831⟩,⟨(-93790723998205921095129838688),(-93790723998205921087732705944)⟩⟩,⟨⟨34111511133387095180917940381,34111511133387095187786440417⟩,⟨(-93194381539364962175930286531),(-93194381539364962168591459413)⟩⟩,⟨⟨33888886475240507523910517126,33888886475240507530729808524⟩,⟨(-92586159662290832130218865965),(-92586159662290832122939907215)⟩⟩,⟨⟨33660345741090154090585800160,33660345741090154097353724595⟩,⟨(-91961774764992974938970783670),(-91961774764992974931755608245)⟩⟩,⟨⟨33427572368903866375161730126,33427572368903866381875857365⟩,⟨(-91325826085530896745638056173),(-91325826085530896738491885796)⟩⟩,⟨⟨33188904158653455312284815941,33188904158653455319005510745⟩,⟨(-90673772408975242603791662271),(-90673772408975242596547602766)⟩⟩,⟨⟨32946123217430973328273193828,32946123217430973334941302403⟩,⟨(-90010482542446028567972783590),(-90010482542446028560791068488)⟩⟩,⟨⟨32697470328155163682254764699,32697470328155163688869480360⟩,⟨(-89331150215495718196215464517),(-89331150215495718189096330815)⟩⟩,⟨⟨32444829065879675045915154895,32444829065879675052475323771⟩,⟨(-88640921450870748933370242279),(-88640921450870748926315506432)⟩⟩,⟨⟨32186340231392153198254128773,32186340231392153204759515408⟩,⟨(-87934716821861577009370401724),(-87934716821861577002378748262)⟩⟩] +lemma amp7_14_10_eq : ∀ k : Fin 16, amp7_1Expr 4 10 k = amp7_14_10 k := by decide +kernel +noncomputable def amp7_14_11 : Fin 16 → CBox := ![⟨⟨31923991916236710242945843771,31923991916236710249395526613⟩,⟨(-87217967895576814753292012710),(-87217967895576814746364666554)⟩⟩,⟨⟨31655821711220961594580442047,31655821711220961600974260931⟩,⟨(-86485313270397627270284034971),(-86485313270397627263419483555)⟩⟩,⟨⟨31383925545900440187360755768,31383925545900440193695842545⟩,⟨(-85742479132358815791275545020),(-85742479132358815784480376195)⟩⟩,⟨⟨31106234285698202316244520363,31106234285698202322523249097⟩,⟨(-84983812500668472579648921139),(-84983812500668472572914707671)⟩⟩,⟨⟨30824955319131378736380267310,30824955319131378742598530984⟩,⟨(-84215344072907442981519461320),(-84215344072907442974856222021)⟩⟩,⟨⟨30537908955121911913286720885,30537908955121911919444342028⟩,⟨(-83431118822305669233065133786),(-83431118822305669226471421624)⟩⟩,⟨⟨30247417991595653882149031120,30247417991595653888243644710⟩,⟨(-82637482750812294700167140869),(-82637482750812294693648263371)⟩⟩,⟨⟨29951188002077299326710611778,29951188002077299332750335747⟩,⟨(-81828167368722554080880923288),(-81828167368722554074412779463)⟩⟩,⟨⟨29651661508133253725746335967,29651661508133253731721746523⟩,⟨(-81009845769054449862592251834),(-81009845769054449856199483735)⟩⟩,⟨⟨29346424784591707848003198426,29346424784591707853913743366⟩,⟨(-80175923532003091307987974666),(-80175923532003091301670178199)⟩⟩,⟨⟨29038044793890211748682878397,29038044793890211754529869417⟩,⟨(-79333413729368986019133364213),(-79333413729368986012885902861)⟩⟩,⟨⟨28723983522504130802387132866,28723983522504130808166559898⟩,⟨(-78475382379252535235050154784),(-78475382379252535228882081208)⟩⟩,⟨⟨28406937538961959614305892995,28406937538961959620018112785⟩,⟨(-77609196643879677460960327231),(-77609196643879677454869667005)⟩⟩,⟨⟨28084239077154113065701625743,28084239077154113071345175924⟩,⟨(-76727568050696315791213201420),(-76727568050696315785202056402)⟩⟩,⟨⟨27758719976704175662983531782,27758719976704175668556652753⟩,⟨(-75838233329432969822036111049),(-75838233329432969816108343735)⟩⟩,⟨⟨27427576724493021400576318633,27427576724493021406076770126⟩,⟨(-74933533139808501407806071885),(-74933533139808501401965918892)⟩⟩] +lemma amp7_14_11_eq : ∀ k : Fin 16, amp7_1Expr 4 11 k = amp7_14_11 k := by decide +kernel +noncomputable def amp7_14_12 : Fin 16 → CBox := ![⟨⟨27093782655877928081460136145,27093782655877928086921302506⟩,⟨(-74021590785086934466545710314),(-74021590785086934460701075973)⟩⟩,⟨⟨26754391921717071430759455186,26754391921717071436151084375⟩,⟨(-73094358055741371903768947498),(-73094358055741371898000607215)⟩⟩,⟨⟨26412526206808221625377372227,26412526206808221630698674339⟩,⟨(-72160363553244537218763279120),(-72160363553244537213072561920)⟩⟩,⟨⟨26065090067515605572237748787,26065090067515605577488060921⟩,⟨(-71211150368311532590924346335),(-71211150368311532585311197377)⟩⟩,⟨⟨25715361101749847685464978464,25715361101749847690643607451⟩,⟨(-70255673064960965515762518568),(-70255673064960965510228063606)⟩⟩,⟨⟨25360086256019165707285202382,25360086256019165712391927730⟩,⟨(-69285044135773547519794290774),(-69285044135773547514337274511)⟩⟩,⟨⟨25002707409672597431752604040,25002707409672597436785032836⟩,⟨(-68308666970004371949940987987),(-68308666970004371944567243208)⟩⟩,⟨⟨24639805024518844202359312146,24639805024518844207320924072⟩,⟨(-67317199215576388693697624870),(-67317199215576388688395794698)⟩⟩,⟨⟨24274994545700667018200465919,24274994545700667023086144261⟩,⟨(-66320518452311598913473692256),(-66320518452311598908257116666)⟩⟩,⟨⟨23904680095009751314520585576,23904680095009751319330398007⟩,⟨(-65308800558247057475071023139),(-65308800558247057469937673589)⟩⟩,⟨⟨23532661015470212552865358292,23532661015470212557598086137⟩,⟨(-64292425531560030205639143462),(-64292425531560030200591778438)⟩⟩,⟨⟨23155154109585114314516583238,23155154109585114319170963786⟩,⟨(-63261057484473819407239015139),(-63261057484473819402279246187)⟩⟩,⟨⟨22776154154706997817466839630,22776154154706997822040840358⟩,⟨(-62225610351680493176113669610),(-62225610351680493171246549560)⟩⟩,⟨⟨22391678359670523836946689927,22391678359670523841459784886⟩,⟨(-61175202945360408293403754811),(-61175202945360408288574245334)⟩⟩,⟨⟨22005929864376524718360892815,22005929864376524722793655520⟩,⟨(-60121318457273958739088013792),(-60121318457273958734348762725)⟩⟩,⟨⟨21614712509035809764487443342,21614712509035809768839158104⟩,⟨(-59052492765680398018972064334),(-59052492765680398014323195075)⟩⟩] +lemma amp7_14_12_eq : ∀ k : Fin 16, amp7_1Expr 4 12 k = amp7_14_12 k := by decide +kernel +noncomputable def amp7_14_13 : Fin 16 → CBox := ![⟨⟨21222452341827216677007787092,21222452341827216681278690791⟩,⟨(-57980818059081058434567426346),(-57980818059081058430007942422)⟩⟩,⟨⟨20824724310448551709291490971,20824724310448551713483011073⟩,⟨(-56894204869760197040748835223),(-56894204869760197036273005164)⟩⟩,⟨⟨20426193808440952718801022764,20426193808440952722909023445⟩,⟨(-55805399289909506145129651601),(-55805399289909506140748505889)⟩⟩,⟨⟨20022189315728738360571606126,20022189315728738364596508610⟩,⟨(-54701638489333646306440100668),(-54701638489333646302150654882)⟩⟩,⟨⟨19617634234436279718380131699,19617634234436279722320018605⟩,⟨(-53596373452782491870148369745),(-53596373452782491865955677840)⟩⟩,⟨⟨19207590578814079550085649661,19207590578814079553952532167⟩,⟨(-52476113352301365288089409547),(-52476113352301365283958817879)⟩⟩,⟨⟨18797261061655928394921961508,18797261061655928398704550715⟩,⟨(-51355072263580090932674309300),(-51355072263580090928636563956)⟩⟩,⟨⟨18381418351227587807973296693,18381418351227587811670437732⟩,⟨(-50218968850732712240639919527),(-50218968850732712236696328928)⟩⟩,⟨⟨17965568925439762163804661386,17965568925439762167416646486⟩,⟨(-49082847091182029282708539026),(-49082847091182029278858302536)⟩⟩,⟨⟨17544169769018200421680242398,17544169769018200425207322811⟩,⟨(-47931563185571657881191118057),(-47931563185571657877431690262)⟩⟩,⟨⟨17123059377081258095932980499,17123059377081258099373877513⟩,⟨(-46781068199204688166829703015),(-46781068199204688163164674149)⟩⟩,⟨⟨16696348529765272277836485926,16696348529765272281198481743⟩,⟨(-45615272484196649216429951804),(-45615272484196649212837550546)⟩⟩,⟨⟨16270240608961625264061430155,16270240608961625267334813901⟩,⟨(-44451123995053550183009884534),(-44451123995053550179516843445)⟩⟩,⟨⟨15838464557506970185476955320,15838464557506970188661650409⟩,⟨(-43271489884987958659940574137),(-43271489884987958656545203812)⟩⟩,⟨⟨15407627185369045843962659742,15407627185369045847059465544⟩,⟨(-42094420294507689549036736710),(-42094420294507689545737167661)⟩⟩,⟨⟨14971033652317385872003646012,14971033652317385875010442297⟩,⟨(-40901624579954552602345417419),(-40901624579954552599145514091)⟩⟩] +lemma amp7_14_13_eq : ∀ k : Fin 16, amp7_1Expr 4 13 k = amp7_14_13 k := by decide +kernel +noncomputable def amp7_14_14 : Fin 16 → CBox := ![⟨⟨14535739783441810129292918366,14535739783441810132216477790⟩,⟨(-39712379613963254913729075325),(-39712379613963254910610769823)⟩⟩,⟨⟨14094577119453890022308781408,14094577119453890025142186110⟩,⟨(-38507100801545820524740179856),(-38507100801545820521720406270)⟩⟩,⟨⟨13655104950972463000157130102,13655104950972463002901574044⟩,⟨(-37306440508742092126419168399),(-37306440508742092123495231023)⟩⟩,⟨⟨13209621370059014534694878678,13209621370059014537346988882⟩,⟨(-36089356731748829955217529426),(-36089356731748829952396629777)⟩⟩,⟨⟨12766254891602009636775144626,12766254891602009639341550603⟩,⟨(-34878056986231400486603607401),(-34878056986231400483868342483)⟩⟩,⟨⟨12316697480480254770980025120,12316697480480254773454694071⟩,⟨(-33649843298127636326768558496),(-33649843298127636324133336456)⟩⟩,⟨⟨11869727294381481876139161733,11869727294381481878526138902⟩,⟨(-32428698040237272467804881484),(-32428698040237272465259517150)⟩⟩,⟨⟨11416340688760420327964560661,11416340688760420330258649538⟩,⟨(-31190022798209339183628955259),(-31190022798209339181185496460)⟩⟩,⟨⟨10966065236024010113218271280,10966065236024010115420572192⟩,⟨(-29959847383932387817094617802),(-29959847383932387814751100530)⟩⟩,⟨⟨10509089791589342672025739026,10509089791589342674137687184⟩,⟨(-28711367251925508021415564031),(-28711367251925508019165822932)⟩⟩,⟨⟨10055817204924139265132370068,10055817204924139267151431772⟩,⟨(-27473003515478005132299549244),(-27473003515478005130151746857)⟩⟩,⟨⟨9595486376480452817875944431,9595486376480452819803508122⟩,⟨(-26215356303879581264049055414),(-26215356303879581261997034160)⟩⟩,⟨⟨9139537335716977437465573796,9139537335716977439302524671⟩,⟨(-24969680358851473398423514395),(-24969680358851473396466323626)⟩⟩,⟨⟨8676073767988110569613024053,8676073767988110571355245039⟩,⟨(-23703474344359069614688707451),(-23703474344359069612835078099)⟩⟩,⟨⟨8217786023128097380087795360,8217786023128097381738373762⟩,⟨(-22451408940915350986105768973),(-22451408940915350984349000097)⟩⟩,⟨⟨7751395450698644994907058817,7751395450698644996464198301⟩,⟨(-21177206200866954639873888100),(-21177206200866954638216173187)⟩⟩] +lemma amp7_14_14_eq : ∀ k : Fin 16, amp7_1Expr 4 14 k = amp7_14_14 k := by decide +kernel +noncomputable def amp7_14_15 : Fin 16 → CBox := ![⟨⟨7291131255199261819320084206,7291131255199261820784570279⟩,⟨(-19919741033857825217006503032),(-19919741033857825215447748177)⟩⟩,⟨⟨6821992474173491747585165518,6821992474173491748955012502⟩,⟨(-18638030048294491404524853915),(-18638030048294491403067511390)⟩⟩,⟨⟨6360151401061098849961139150,6360151401061098851237654069⟩,⟨(-17376256771529301486997049621),(-17376256771529301485639993069)⟩⟩,⟨⟨5888398725213949357681508734,5888398725213949358863711317⟩,⟨(-16087404492508317922352901226),(-16087404492508317921095488727)⟩⟩,⟨⟨5425441185469606814199082418,5425441185469606815288367067⟩,⟨(-14822580972179686270359752504),(-14822580972179686269201120570)⟩⟩,⟨⟨4951131303068236857168702738,4951131303068236858162574294⟩,⟨(-13526742274927124258991361890),(-13526742274927124257934524751)⟩⟩,⟨⟨4487625400817782326045356914,4487625400817782326945654467⟩,⟨(-12260420600370828857751435237),(-12260420600370828856794987394)⟩⟩,⟨⟨4010668238177036632307628800,4010668238177036633112523676⟩,⟨(-10957349399002419234118296105),(-10957349399002419233262727844)⟩⟩,⟨⟨3547394144058060913553323763,3547394144058060914264943846⟩,⟨(-9691661036038931554697832531),(-9691661036038931553941913758)⟩⟩,⟨⟨3067387839274413925417231856,3067387839274413926032348789⟩,⟨(-8380259423416616152650078659),(-8380259423416616151997024653)⟩⟩,⟨⟨2605610421927042946531858735,2605610421927042947054004985⟩,⟨(-7118660057435660782905197842),(-7118660057435660782351463817)⟩⟩,⟨⟨2121361682949658354605681502,2121361682949658355030552926⟩,⟨(-5795667899048286741593148234),(-5795667899048286741142966154)⟩⟩,⟨⟨1663741155941996025323109471,1663741155941996025655860668⟩,⟨(-4545425368676907652667901965),(-4545425368676907652316108804)⟩⟩,⟨⟨1171344964628820879847663382,1171344964628820880081639132⟩,⟨(-3200173956555908093912225111),(-3200173956555908093665354533)⟩⟩,⟨⟨726611995767906115027202103,726611995767906115171350879⟩,⟨(-1985140889826941552103315667),(-1985140889826941551952885640)⟩⟩,⟨⟨206433418803638677605872232,206433418803638677646228799⟩,⟨(-563986588551685308340424636),(-563986588551685308299317030)⟩⟩] +lemma amp7_14_15_eq : ∀ k : Fin 16, amp7_1Expr 4 15 k = amp7_14_15 k := by decide +kernel +noncomputable def amp7_14 : Fin 16 → Fin 16 → CBox := ![amp7_14_0,amp7_14_1,amp7_14_2,amp7_14_3,amp7_14_4,amp7_14_5,amp7_14_6,amp7_14_7,amp7_14_8,amp7_14_9,amp7_14_10,amp7_14_11,amp7_14_12,amp7_14_13,amp7_14_14,amp7_14_15] +lemma amp7_14_eq (i k : Fin 16) : amp7_1Expr 4 i k = amp7_14 i k := by + fin_cases i + · exact amp7_14_0_eq k + · exact amp7_14_1_eq k + · exact amp7_14_2_eq k + · exact amp7_14_3_eq k + · exact amp7_14_4_eq k + · exact amp7_14_5_eq k + · exact amp7_14_6_eq k + · exact amp7_14_7_eq k + · exact amp7_14_8_eq k + · exact amp7_14_9_eq k + · exact amp7_14_10_eq k + · exact amp7_14_11_eq k + · exact amp7_14_12_eq k + · exact amp7_14_13_eq k + · exact amp7_14_14_eq k + · exact amp7_14_15_eq k +noncomputable def amp7_15_0 : Fin 16 → CBox := ![⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩] +lemma amp7_15_0_eq : ∀ k : Fin 16, amp7_1Expr 5 0 k = amp7_15_0 k := by decide +kernel +noncomputable def amp7_15_1 : Fin 16 → CBox := ![⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩] +lemma amp7_15_1_eq : ∀ k : Fin 16, amp7_1Expr 5 1 k = amp7_15_1 k := by decide +kernel +noncomputable def amp7_15_2 : Fin 16 → CBox := ![⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩] +lemma amp7_15_2_eq : ∀ k : Fin 16, amp7_1Expr 5 2 k = amp7_15_2 k := by decide +kernel +noncomputable def amp7_15_3 : Fin 16 → CBox := ![⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩] +lemma amp7_15_3_eq : ∀ k : Fin 16, amp7_1Expr 5 3 k = amp7_15_3 k := by decide +kernel +noncomputable def amp7_15_4 : Fin 16 → CBox := ![⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩] +lemma amp7_15_4_eq : ∀ k : Fin 16, amp7_1Expr 5 4 k = amp7_15_4 k := by decide +kernel +noncomputable def amp7_15_5 : Fin 16 → CBox := ![⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩] +lemma amp7_15_5_eq : ∀ k : Fin 16, amp7_1Expr 5 5 k = amp7_15_5 k := by decide +kernel +noncomputable def amp7_15_6 : Fin 16 → CBox := ![⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩] +lemma amp7_15_6_eq : ∀ k : Fin 16, amp7_1Expr 5 6 k = amp7_15_6 k := by decide +kernel +noncomputable def amp7_15_7 : Fin 16 → CBox := ![⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩] +lemma amp7_15_7_eq : ∀ k : Fin 16, amp7_1Expr 5 7 k = amp7_15_7 k := by decide +kernel +noncomputable def amp7_15_8 : Fin 16 → CBox := ![⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩] +lemma amp7_15_8_eq : ∀ k : Fin 16, amp7_1Expr 5 8 k = amp7_15_8 k := by decide +kernel +noncomputable def amp7_15_9 : Fin 16 → CBox := ![⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩] +lemma amp7_15_9_eq : ∀ k : Fin 16, amp7_1Expr 5 9 k = amp7_15_9 k := by decide +kernel +noncomputable def amp7_15_10 : Fin 16 → CBox := ![⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩] +lemma amp7_15_10_eq : ∀ k : Fin 16, amp7_1Expr 5 10 k = amp7_15_10 k := by decide +kernel +noncomputable def amp7_15_11 : Fin 16 → CBox := ![⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩] +lemma amp7_15_11_eq : ∀ k : Fin 16, amp7_1Expr 5 11 k = amp7_15_11 k := by decide +kernel +noncomputable def amp7_15_12 : Fin 16 → CBox := ![⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩] +lemma amp7_15_12_eq : ∀ k : Fin 16, amp7_1Expr 5 12 k = amp7_15_12 k := by decide +kernel +noncomputable def amp7_15_13 : Fin 16 → CBox := ![⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩] +lemma amp7_15_13_eq : ∀ k : Fin 16, amp7_1Expr 5 13 k = amp7_15_13 k := by decide +kernel +noncomputable def amp7_15_14 : Fin 16 → CBox := ![⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩] +lemma amp7_15_14_eq : ∀ k : Fin 16, amp7_1Expr 5 14 k = amp7_15_14 k := by decide +kernel +noncomputable def amp7_15_15 : Fin 16 → CBox := ![⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩] +lemma amp7_15_15_eq : ∀ k : Fin 16, amp7_1Expr 5 15 k = amp7_15_15 k := by decide +kernel +noncomputable def amp7_15 : Fin 16 → Fin 16 → CBox := ![amp7_15_0,amp7_15_1,amp7_15_2,amp7_15_3,amp7_15_4,amp7_15_5,amp7_15_6,amp7_15_7,amp7_15_8,amp7_15_9,amp7_15_10,amp7_15_11,amp7_15_12,amp7_15_13,amp7_15_14,amp7_15_15] +lemma amp7_15_eq (i k : Fin 16) : amp7_1Expr 5 i k = amp7_15 i k := by + fin_cases i + · exact amp7_15_0_eq k + · exact amp7_15_1_eq k + · exact amp7_15_2_eq k + · exact amp7_15_3_eq k + · exact amp7_15_4_eq k + · exact amp7_15_5_eq k + · exact amp7_15_6_eq k + · exact amp7_15_7_eq k + · exact amp7_15_8_eq k + · exact amp7_15_9_eq k + · exact amp7_15_10_eq k + · exact amp7_15_11_eq k + · exact amp7_15_12_eq k + · exact amp7_15_13_eq k + · exact amp7_15_14_eq k + · exact amp7_15_15_eq k +noncomputable def amp7_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp7_10,amp7_11,amp7_12,amp7_13,amp7_14,amp7_15] +lemma amp7_1_eq (j : Fin 6) (i k : Fin 16) : amp7_1Expr j i k = amp7_1 j i k := by + fin_cases j + · exact amp7_10_eq i k + · exact amp7_11_eq i k + · exact amp7_12_eq i k + · exact amp7_13_eq i k + · exact amp7_14_eq i k + · exact amp7_15_eq i k +lemma amp7_1_contains (j : Fin 6) (i k : Fin 16) : + (amp7_1 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude true 7 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp7_1_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 7 j) (bLookup_contains 7 j) true) +noncomputable def amp9_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 9 j) (bLookup 9 j) false) +noncomputable def amp9_00_0 : Fin 16 → CBox := ![⟨⟨1559522290940923961292996524,1559522290940923961442714443⟩,⟨(-93606319881131816285424308),(-93606319881131816155341825)⟩⟩,⟨⟨5489335956442995593646628198,5489335956442995594189469816⟩,⟨(-329454183859859827805732339),(-329454183859859827346919611)⟩⟩,⟨⟨8849391192914736850540782970,8849391192914736851427932230⟩,⟨(-531021213985451592591183999),(-531021213985451591850852033)⟩⟩,⟨⟨12569885820067326835123692372,12569885820067326836386889288⟩,⟨(-754075270951602633622760294),(-754075270951602632571086556)⟩⟩,⟨⟨16028133338719027728709269099,16028133338719027730324326297⟩,⟨(-961197924719543987740078730),(-961197924719543986398969717)⟩⟩,⟨⟨19688200262379251461267577586,19688200262379251463253354418⟩,⟨(-1180168517784169614534202466),(-1180168517784169612886982209)⟩⟩,⟨⟨23179239671638022550067692933,23179239671638022552408488307⟩,⟨(-1388695194947131465894879977),(-1388695194947131463955758866)⟩⟩,⟨⟨26808933779188429188447820890,26808933779188429191156523159⟩,⟨(-1605161115664026583663884831),(-1605161115664026581421506245)⟩⟩,⟨⟨30313220215010751626848760663,30313220215010751629913455453⟩,⟨(-1813694339092520912832013628),(-1813694339092520910297024911)⟩⟩,⟨⟨33922105419220902004624142130,33922105419220902008050491880⟩,⟨(-2028006478273828716660069373),(-2028006478273828713824246776)⟩⟩,⟨⟨37430629388735435997714993613,37430629388735436001499168653⟩,⟨(-2235783529102243053295282168),(-2235783529102243050166894939)⟩⟩,⟨⟨41022283987435101554086664072,41022283987435101558234281409⟩,⟨(-2447936219445482036765613289),(-2447936219445482033338162824)⟩⟩,⟨⟨44529690171788392487537786209,44529690171788392492038372013⟩,⟨(-2654416770198902274264169462),(-2654416770198902270545120423)⟩⟩,⟨⟨48105328693697031302063640173,48105328693697031306920931129⟩,⟨(-2864265852138096935492403475),(-2864265852138096931476580073)⟩⟩,⟨⟨51607854703631617557961392753,51607854703631617563175261244⟩,⟨(-3069008905085332610664975943),(-3069008905085332606358410411)⟩⟩,⟨⟨55167572989373913990862262214,55167572989373913996436885671⟩,⟨(-3276347120733813481357586132),(-3276347120733813476755987823)⟩⟩] +lemma amp9_00_0_eq : ∀ k : Fin 16, amp9_0Expr 0 0 k = amp9_00_0 k := by decide +kernel +noncomputable def amp9_00_1 : Fin 16 → CBox := ![⟨⟨58662259261339671043517415866,58662259261339671049444255869⟩,⟨(-3478964236115248133245874535),(-3478964236115248128355196693)⟩⟩,⟨⟨62205555163652398987655407998,62205555163652398993935549577⟩,⟨(-3683553132480533357032653368),(-3683553132480533351849506903)⟩⟩,⟨⟨65689889407964693192245318812,65689889407964693198871047098⟩,⟨(-3883687729396738510788112111),(-3883687729396738505317975314)⟩⟩,⟨⟨69215911607703542288455738280,69215911607703542295446258033⟩,⟨(-4085273230009796545188498535),(-4085273230009796539427499998)⟩⟩,⟨⟨72687649587317296509609843697,72687649587317296516939397952⟩,⟨(-4282590458767819549435752960),(-4282590458767819543390118340)⟩⟩,⟨⟨76195328596562208775649679199,76195328596562208783321367413⟩,⟨(-4480911350149214407013368721),(-4480911350149214400680672086)⟩⟩,⟨⟨79652395792001608791396235704,79652395792001608799425639580⟩,⟨(-4675092805467640809494356254),(-4675092805467640802878146559)⟩⟩,⟨⟨83140518217898985965361843075,83140518217898985973726642453⟩,⟨(-4869885802761709864360119015),(-4869885802761709857459891636)⟩⟩,⟨⟨86580952196126867159396797285,86580952196126867168112645127⟩,⟨(-5060626664353293753482220223),(-5060626664353293746301339014)⟩⟩,⟨⟨90048205369189710371138558413,90048205369189710380211111121⟩,⟨(-5251629681473291207970230504),(-5251629681473291200506927491)⟩⟩,⟨⟨93470120180796412025898138118,93470120180796412035292514413⟩,⟨(-5438637159484464542307274894),(-5438637159484464534567723910)⟩⟩,⟨⟨96915120276839725675982840476,96915120276839725685727413224⟩,⟨(-5625591570337328764605676006),(-5625591570337328756587118899)⟩⟩,⟨⟨100316683497884847663301674856,100316683497884847673354997769⟩,⟨(-5808584090911250859436395458),(-5808584090911250851145267869)⟩⟩,⟨⟨103737993975309751821263375392,103737993975309751831673801352⟩,⟨(-5991236389712338730191775525),(-5991236389712338721624471566)⟩⟩,⟨⟨107117411371679709630690807741,107117411371679709641436930272⟩,⟨(-6169943217786975317651487627),(-6169943217786975308813197458)⟩⟩,⟨⟨110513555478414122634242505098,110513555478414122645331714679⟩,⟨(-6348046302403234891481428754),(-6348046302403234882371198130)⟩⟩] +lemma amp9_00_1_eq : ∀ k : Fin 16, amp9_0Expr 0 1 k = amp9_00_1 k := by decide +kernel +noncomputable def amp9_00_2 : Fin 16 → CBox := ![⟨⟨113869060460768812978378727171,113869060460768812989762508015⟩,⟨(-6522207430371915612581277311),(-6522207430371915603205778062)⟩⟩,⟨⟨117238529978915546549222847076,117238529978915546560951292603⟩,⟨(-6695521637468797323213689352),(-6695521637468797313569770614)⟩⟩,⟨⟨120568376179638323122458420319,120568376179638323134519401772⟩,⟨(-6864887838212671002454536918),(-6864887838212670992546739032)⟩⟩,⟨⟨123909637712160872982875528155,123909637712160872995273984080⟩,⟨(-7033181807190165089206422021),(-7033181807190165079034422250)⟩⟩,⟨⟨127212093663662906288959212038,127212093663662906301698493004⟩,⟨(-7197514788940299676314190141),(-7197514788940299665881616141)⟩⟩,⟨⟨130523593276006329182723657448,130523593276006329195728843508⟩,⟨(-7360566202203180008864258802),(-7360566202203179998175515029)⟩⟩,⟨⟨133796938545584940364944447009,133796938545584940378274888173⟩,⟨(-7519638825309515333950131737),(-7519638825309515323005653112)⟩⟩,⟨⟨137077105284698035365174180416,137077105284698035378819437870⟩,⟨(-7677235055044664140484563279),(-7677235055044664129285312980)⟩⟩,⟨⟨140319627646981816031854581726,140319627646981816045820393253⟩,⟨(-7830831584346860433245338582),(-7830831584346860421794774496)⟩⟩,⟨⟨143566876282777311352369023675,143566876282777311366657153775⟩,⟨(-7982770265394130984914037211),(-7982770265394130973212630275)⟩⟩,⟨⟨146776869650728164124981282989,146776869650728164139586709005⟩,⟨(-8130686640354154044332826284),(-8130686640354154032384631804)⟩⟩,⟨⟨149989602873402892441152677049,149989602873402892455988825749⟩,⟨(-8276776182124073173080659869),(-8276776182124073160891204730)⟩⟩,⟨⟨153165365797939979021023749391,153165365797939979036186192219⟩,⟨(-8418820292296028778606226480),(-8418820292296028766173997185)⟩⟩,⟨⟨156341976032508445800857477982,156341976032508445816331488377⟩,⟨(-8558880338430821673275495443),(-8558880338430821660602222908)⟩⟩,⟨⟨159481810638921607044215293588,159481810638921607060007869198⟩,⟨(-8694872295401433752781894525),(-8694872295401433739870977764)⟩⟩,⟨⟨162620681590677643900710528696,162620681590677643916790112636⟩,⟨(-8828734137087854346829969037),(-8828734137087854333684205774)⟩⟩] +lemma amp9_00_2_eq : ∀ k : Fin 16, amp9_0Expr 0 2 k = amp9_00_2 k := by decide +kernel +noncomputable def amp9_00_3 : Fin 16 → CBox := ![⟨⟨165722892858705901263464798179,165722892858705901279846081329⟩,⟨(-8958506536417053657398390836),(-8958506536417053644020766564)⟩⟩,⟨⟨168822400871159063613614869911,168822400871159063630299974916⟩,⟨(-9086013483402380511477078763),(-9086013483402380497868709832)⟩⟩,⟨⟨171885296191891475364575221606,171885296191891475381562434343⟩,⟨(-9209411651745818272525464697),(-9209411651745818258690242594)⟩⟩,⟨⟨174943811476575137915191095168,174943811476575137932331688772⟩,⟨(-9330419363854674457492447780),(-9330419363854674443439682650)⟩⟩,⟨⟨177965700437479761814499132001,177965700437479761831946389975⟩,⟨(-9447301587616115118027539775),(-9447301587616115103752834774)⟩⟩,⟨⟨180981588219498180356577040328,180981588219498180374316005622⟩,⟨(-9561678368711325858662780022),(-9561678368711325844168444134)⟩⟩,⟨⟨183960782581606165192208947316,183960782581606165210233711156⟩,⟨(-9671916101415044684218053998),(-9671916101415044669508222075)⟩⟩,⟨⟨186932404193713723977485427145,186932404193713723995787427202⟩,⟨(-9779543157160454161044615082),(-9779543157160454146121376503)⟩⟩,⟨⟨189867218034020845000872909283,189867218034020845019456484727⟩,⟨(-9883021203356295252843781034),(-9883021203356295237710744590)⟩⟩,⟨⟨192792931984002380235392015996,192792931984002380254218705124⟩,⟨(-9983792863738742442526303688),(-9983792863738742427187225603)⟩⟩,⟨⟨195681681982641483714203517061,195681681982641483733303979966⟩,⟨(-10080409537723725502360021817),(-10080409537723725486817155414)⟩⟩,⟨⟨198559845012858139648697149650,198559845012858139668054058787⟩,⟨(-10174233445019220170780176291),(-10174233445019220155036290507)⟩⟩,⟨⟨201400850869304864564852036756,201400850869304864584467553436⟩,⟨(-10263900703025054922521505692),(-10263900703025054906580348607)⟩⟩,⟨⟨204229819022860206371880026609,204229819022860206391750090310⟩,⟨(-10350697965712873065149806025),(-10350697965712873049013569110)⟩⟩,⟨⟨207021403988877594708605046191,207021403988877594728728437510⟩,⟨(-10433341510499256424401046429),(-10433341510499256408073664369)⟩⟩,⟨⟨209799533693516875098842375757,209799533693516875119214432322⟩,⟨(-10513046823511369722986265956),(-10513046823511369706470064315)⟩⟩] +lemma amp9_00_3_eq : ∀ k : Fin 16, amp9_0Expr 0 3 k = amp9_00_3 k := by decide +kernel +noncomputable def amp9_00_4 : Fin 16 → CBox := ![⟨⟨212540025213077564284019128183,212540025213077564304409366966⟩,⟨(-10588606180541638414350464977),(-10588606180541638397660814285)⟩⟩,⟨⟨215265674391363652896172196304,215265674391363652916840784195⟩,⟨(-10661167912165665667697663750),(-10661167912165665650823734115)⟩⟩,⟨⟨217953404839659306054197397694,217953404839659306075130992694⟩,⟨(-10729596476738939817985535332),(-10729596476738939800931902593)⟩⟩,⟨⟨220624934051964634192369268983,220624934051964634213556003010⟩,⟨(-10794976722458016744575073520),(-10794976722458016727344617183)⟩⟩,⟨⟨223258241566996417097126551816,223258241566996417118559114791⟩,⟨(-10856241777340714728036300768),(-10856241777340714710633296982)⟩⟩,⟨⟨225874015192264305802768944018,225874015192264305824452047592⟩,⟨(-10914416380884288110773351729),(-10914416380884288093199951071)⟩⟩,⟨⟨228451244593530978817423597434,228451244593530978839330140634⟩,⟨(-10968499084131140285566756706),(-10968499084131140267828191397)⟩⟩,⟨⟨231009632051486375364673996507,231009632051486375386816255587⟩,⟨(-11019457626020161267301451667),(-11019457626020161249399589650)⟩⟩,⟨⟨233529135841038683533284613710,233529135841038683555662427576⟩,⟨(-11066352968805839617431129365),(-11066352968805839599369914669)⟩⟩,⟨⟨236028512858491124934860667692,236028512858491124957402744707⟩,⟨(-11110098722699359168517305759),(-11110098722699359150302635271)⟩⟩,⟨⟨238488652300169018923112677944,238488652300169018945886515417⟩,⟨(-11149815457100347838898093877),(-11149815457100347820530710605)⟩⟩,⟨⟨240927402223193583090919997093,240927402223193583113909499101⟩,⟨(-11186365314284536933821957858),(-11186365314284536915305228034)⟩⟩,⟨⟨243326548496255444008858878312,243326548496255444032066894628⟩,⟨(-11218925851059632490933083715),(-11218925851059632472270818246)⟩⟩,⟨⟨245703063649319210779473084479,245703063649319210802869995656⟩,⟨(-11248310213462072937064412176),(-11248310213462072918260647912)⟩⟩,⟨⟨248039599072946296524840203002,248039599072946296548448878542⟩,⟨(-11273750489980914306261325902),(-11273750489980914287318952047)⟩⟩,⟨⟨250352282165437670804087145267,250352282165437670827887764513⟩,⟨(-11296013132140582262567624075),(-11296013132140582243490282332)⟩⟩] +lemma amp9_00_4_eq : ∀ k : Fin 16, amp9_0Expr 0 4 k = amp9_00_4 k := by decide +kernel +noncomputable def amp9_00_5 : Fin 16 → CBox := ![⟨⟨252624601490780038417758780392,252624601490780038441754412130⟩,⟨(-11314382450704319827256761745),(-11314382450704319808048253622)⟩⟩,⟨⟨254871867070873140181083796269,254871867070873140205270014181⟩,⟨(-11329580351179425888164759526),(-11329580351179425868828077912)⟩⟩,⟨⟨257078378837416307796584638539,257078378837416307820963996066⟩,⟨(-11340941188067103668999186365),(-11340941188067103649538154850)⟩⟩,⟨⟨259258654792745124249147620999,259258654792745124273713990465⟩,⟨(-11349144330817616123524806454),(-11349144330817616103942551494)⟩⟩,⟨⟨261397782745835816557029676241,261397782745835816581781158878⟩,⟨(-11353572116476826262417728062),(-11353572116476826242718269779)⟩⟩,⟨⟨263509511850049750621007282678,263509511850049750645480675028⟩,⟨(-11354863262815097450361861016),(-11354863262815097430568063302)⟩⟩,⟨⟨265579696416436686486885246563,265579696416436686511560538129⟩,⟨(-11352446133696523088374692489),(-11352446133696523068469648447)⟩⟩,⟨⟨267621337920350464677451865309,267621337920350464702313140003⟩,⟨(-11346920565457163541710765442),(-11346920565457163521698119352)⟩⟩,⟨⟨269621037738582027379327122222,269621037738582027404361905340⟩,⟨(-11337759088070144818888857469),(-11337759088070144798773065119)⟩⟩,⟨⟨271591069004310945455305878477,271591069004310945480508824008⟩,⟨(-11325524322708492015795761686),(-11325524322708491995580036914)⟩⟩,⟨⟨273518762506793391170793968213,273518762506793391196149087692⟩,⟨(-11309731190549000400502814233),(-11309731190549000380191724358)⟩⟩,⟨⟨275415680682973656304217503408,275415680682973656329718460007⟩,⟨(-11290906668935665538939393119),(-11290906668935665518536221881)⟩⟩,⟨⟨277269867726437355282000256063,277269867726437355307658054446⟩,⟨(-11268606373009233829218998817),(-11268606373009233808727185316)⟩⟩,⟨⟨279092191462366264688560811553,279092191462366264714347945419⟩,⟨(-11243323120745824200199578782),(-11243323120745824179623291460)⟩⟩,⟨⟨280871395003418211498708710525,280871395003418211524634903067⟩,⟨(-11214651594476165256646986588),(-11214651594476165235989694390)⟩⟩,⟨⟨282617666199706564376490746602,282617666199706564402556266538⟩,⟨(-11183051857613982165512964692),(-11183051857613982144777744412)⟩⟩] +lemma amp9_00_5_eq : ∀ k : Fin 16, amp9_0Expr 0 5 k = amp9_00_5 k := by decide +kernel +noncomputable def amp9_00_6 : Fin 16 → CBox := ![⟨⟨284320434012068981192027760317,284320434012068981218178588388⟩,⟨(-11148156096993299632143162483),(-11148156096993299611335990158)⟩⟩,⟨⟨285989219605175727818728806497,285989219605175727845020109369⟩,⟨(-11110392953092266472277675149),(-11110392953092266451399478759)⟩⟩,⟨⟨287614126035126229699271699626,287614126035126229725668115616⟩,⟨(-11069430612991638102390806044),(-11069430612991638081446780150)⟩⟩,⟨⟨289204019812940810632141156251,289204019812940810658668532999⟩,⟨(-11025667558510627225599245215),(-11025667558510627204591524567)⟩⟩,⟨⟨290749667569381942336588770672,290749667569381942363225486852⟩,⟨(-10978806526128320237590154966),(-10978806526128320216523370523)⟩⟩,⟨⟨292259292014831432589952813234,292259292014831432616703730428⟩,⟨(-10929217041190162856657381258),(-10929217041190162835534490211)⟩⟩,⟨⟨293724313990328606581421241046,293724313990328606608122470022⟩,⟨(-10876634987672294460997016667),(-10876634987672294439827860795)⟩⟩,⟨⟨295152322149813397128842983166,295152322149813397155663713410⟩,⟨(-10821402079296846188558171942),(-10821402079296846167339597315)⟩⟩,⟨⟨296535383268852184151806343236,296535383268852184178726172551⟩,⟨(-10763285990618389582947892705),(-10763285990618389561684402558)⟩⟩,⟨⟨297880460642154538177243225836,297880460642154538204249227996⟩,⟨(-10702601715564881061383757447),(-10702601715564881040078979797)⟩⟩,⟨⟨299180259732782416092766495822,299180259732782416119863614115⟩,⟨(-10639147403809586006664392108),(-10639147403809585985321851813)⟩⟩,⟨⟨300441126180946087218206138598,300441126180946087245371884395⟩,⟨(-10573212372214930103900278696),(-10573212372214930082523947814)⟩⟩,⟨⟨301656397865881435860480722898,301656397865881435887719826627⟩,⟨(-10504623968440219225191813181),(-10504623968440219203785194813)⟩⟩,⟨⟨302831809533427061931459364148,302831809533427061958778661068⟩,⟨(-10433646829482808456547051793),(-10433646829482808435113077510)⟩⟩,⟨⟨303961326136640504041776356596,303961326136640504069093649822⟩,⟨(-10360136259400063454489589454),(-10360136259400063433034695549)⟩⟩,⟨⟨305050077384360259807395613450,305050077384360259834776402979⟩,⟨(-10284333170258724893781382452),(-10284333170258724872306487460)⟩⟩] +lemma amp9_00_6_eq : ∀ k : Fin 16, amp9_0Expr 0 6 k = amp9_00_6 k := by decide +kernel +noncomputable def amp9_00_7 : Fin 16 → CBox := ![⟨⟨306092650849061334074549176150,306092650849061334101980136120⟩,⟨(-10206119614000527251373035293),(-10206119614000527229882185797)⟩⟩,⟨⟨307093576193527009686307901341,307093576193527009713794526132⟩,⟨(-10125713693415573150747792124),(-10125713693415573129243960912)⟩⟩,⟨⟨308048060007423432758035207103,308048060007423432785530706056⟩,⟨(-10043023030699348464449174467),(-10043023030699348442937432408)⟩⟩,⟨⟨308960036063244451353360742664,308960036063244451380895156257⟩,⟨(-9958243798476948520194836394),(-9958243798476948498677352513)⟩⟩,⟨⟨309825327186882581406705360849,309825327186882581434248355346⟩,⟨(-9871308040509021002289404028),(-9871308040509020980770651068)⟩⟩,⟨⟨310647274607664285409519100907,310647274607664285437095292769⟩,⟨(-9782390844341318633549511301),(-9782390844341318612031835659)⟩⟩,⟨⟨311422315401608446262173305798,311422315401608446289757771431⟩,⟨(-9691447553836554546659628524),(-9691447553836554525147254139)⟩⟩,⟨⟨312153200815486117762336483274,312153200815486117789925689583⟩,⟨(-9598632984837958470764283516),(-9598632984837958449260446705)⟩⟩,⟨⟨312836980962051704683104574263,312836980962051704710695593392⟩,⟨(-9503924685557910388365030802),(-9503924685557910366873221621)⟩⟩,⟨⟨313475818897612118483876998757,313475818897612118511470040769⟩,⟨(-9407457983942729227004046294),(-9407457983942729205527355367)⟩⟩,⟨⟨314067377312833340305061350608,314067377312833340332641830948⟩,⟨(-9309231561179438225349601699),(-9309231561179438203891797291)⟩⟩,⟨⟨314613232111183074982266863473,314613232111183075009833625036⟩,⟨(-9209362013527415748660469879),(-9209362013527415727224678264)⟩⟩,⟨⟨315111658842671186728453412893,315111658842671186755992647659⟩,⟨(-9107868106980742808654769485),(-9107868106980742787244681777)⟩⟩,⟨⟨315563646551369344191986973500,315563646551369344219491920737⟩,⟨(-9004848436555031115326411191),(-9004848436555031093945272657)⟩⟩,⟨⟨315968084657701632068190446887,315968084657701632095648787601⟩,⟨(-8900340827068535318924777012),(-8900340827068535297576146273)⟩⟩,⟨⟨316325374902243945746051362967,316325374902243945773448216722⟩,⟨(-8794426578665159398212457688),(-8794426578665159376899786196)⟩⟩] +lemma amp9_00_7_eq : ∀ k : Fin 16, amp9_0Expr 0 7 k = amp9_00_7 k := by decide +kernel +noncomputable def amp9_00_8 : Fin 16 → CBox := ![⟨⟨316635022309517837148953305109,316635022309517837176318819954⟩,⟨(-8687161570299088867513136879),(-8687161570299088846238760153)⟩⟩,⟨⟨316896840138039283835724275455,316896840138039283863089217179⟩,⟨(-8578610491117965262792405907),(-8578610491117965241558499255)⟩⟩,⟨⟨317110951469230023091004463201,317110951469230023118353734534⟩,⟨(-8468846290047854268345104065),(-8468846290047854247155201413)⟩⟩,⟨⟨317276579166083883592155787376,317276579166083883619477556998⟩,⟨(-8357917708082895486332147386),(-8357917708082895465189582233)⟩⟩,⟨⟨317394467538858457170317382334,317394467538858457197604594849⟩,⟨(-8245913799818552241409568234),(-8245913799818552220317598177)⟩⟩,⟨⟨317463246402731170027367195259,317463246402731170054606624330⟩,⟨(-8132868001268293358170363638),(-8132868001268293337132294508)⟩⟩,⟨⟨317484285191395769128455858189,317484285191395769155646246820⟩,⟨(-8018884527690609899066261231),(-8018884527690609878085108161)⟩⟩,⟨⟨317455617273628743235089900977,317455617273628743262217140150⟩,⟨(-7903982134891120309878494369),(-7903982134891120288957559772)⟩⟩,⟨⟨317379241830922175530569620960,317379241830922175557633762909⟩,⟨(-7788279272603138593901830079),(-7788279272603138573044052018)⟩⟩,⟨⟨317252591629733799678303795463,317252591629733799705302755055⟩,⟨(-7671780623981725297838759364),(-7671780623981725277047077497)⟩⟩,⟨⟨317078300964225041189379056980,317078300964225041216309314806⟩,⟨(-7554617965465760300976970052),(-7554617965465760280254319358)⟩⟩,⟨⟨316853197070558250589732900709,316853197070558250616569829861⟩,⟨(-7436782499007134095277907474),(-7436782499007134074627749778)⟩⟩,⟨⟨316580555475462879955432269058,316580555475462879982201078943⟩,⟨(-7318418438071501444041625755),(-7318418438071501423466169672)⟩⟩,⟨⟨316256592166225576999955554794,316256592166225577026626200367⟩,⟨(-7199504079777677734889659034),(-7199504079777677714392421518)⟩⟩,⟨⟨315885230795523260475747154732,315885230795523260502350729292⟩,⟨(-7080195202764724617050158208),(-7080195202764724596633144228)⟩⟩,⟨⟨315462069570040366557131806969,315462069570040366583621200024⟩,⟨(-6960457761575989129845047897),(-6960457761575989109512122769)⟩⟩] +lemma amp9_00_8_eq : ∀ k : Fin 16, amp9_0Expr 0 8 k = amp9_00_8 k := by decide +kernel +noncomputable def amp9_00_9 : Fin 16 → CBox := ![⟨⟨314991687957853956817921173473,314991687957853956844302157260⟩,⟨(-6840458245787715446747863383),(-6840458245787715426501559713)⟩⟩,⟨⟨314469059013410577705049154588,314469059013410577731309163337⟩,⟨(-6720150816414533797605867564),(-6720150816414533777449187379)⟩⟩,⟨⟨313899426532696843669552088853,313899426532696843695759347933⟩,⟨(-6599711837193156481126030231),(-6599711837193156461060093677)⟩⟩,⟨⟨313277130175121597333027884809,313277130175121597359098435797⟩,⟨(-6479084212287986028604795917),(-6479084212287986008634111114)⟩⟩,⟨⟨312608087431824210215376877817,312608087431824210241318101326⟩,⟨(-6358453360166392026783119958),(-6358453360166392006910039061)⟩⟩,⟨⟨311885995417139771949520178894,311885995417139771975338349096⟩,⟨(-6237751453240014002778041617),(-6237751453240013983005099012)⟩⟩,⟨⟨311117455576067040601788256217,311117455576067040627460424920⟩,⟨(-6117172162551223591914137768),(-6117172162551223572244201260)⟩⟩,⟨⟨310295512379320920881772894217,310295512379320920907305516582⟩,⟨(-5996637443010511060634702738),(-5996637443010511041070288461)⟩⟩,⟨⟨309427462418134024280117062697,309427462418134024305497024615⟩,⟨(-5876348433316097797358157735),(-5876348433316097777901885952)⟩⟩,⟨⟨308505686425615951899529825996,308505686425615951924737214641⟩,⟨(-5756217374969136684164629974),(-5756217374969136664819438617)⟩⟩,⟨⟨307538188313448217818699744545,307538188313448217843913154080⟩,⟨(-5636452106634096253216451616),(-5636452106634096233981310059)⟩⟩,⟨⟨306516672934600611530817921017,306516672934600611555866645048⟩,⟨(-5516955650974356827149293947),(-5516955650974356808029946290)⟩⟩,⟨⟨305449864731974943806476975903,305449864731974943831366718844⟩,⟨(-5397941796180264762090135648),(-5397941796180264743088686565)⟩⟩,⟨⟨304328779427409077914677068718,304328779427409077939386634329⟩,⟨(-5279304831724161780052201292),(-5279304831724161761171516140)⟩⟩,⟨⟨303162876304279209243920876890,303162876304279209268478388053⟩,⟨(-5161263762173697567084601864),(-5161263762173697548326294529)⟩⟩,⟨⟨301942467526420953528611771654,301942467526420953552981370540⟩,⟨(-5043704621085468731380527087),(-5043704621085468712747693022)⟩⟩] +lemma amp9_00_9_eq : ∀ k : Fin 16, amp9_0Expr 0 9 k = amp9_00_9 k := by decide +kernel +noncomputable def amp9_00_10 : Fin 16 → CBox := ![⟨⟨300677762695333149858163892527,300677762695333149882404898806⟩,⟨(-4926850913609606530780210055),(-4926850913609606512273934144)⟩⟩,⟨⟨299358354738337594125174522362,299358354738337594149231401695⟩,⟨(-4810580886804078380254892854),(-4810580886804078361878500199)⟩⟩,⟨⟨297995220299893224112415520794,297995220299893224136289445883⟩,⟨(-4695121848038555031539985334),(-4695121848038555013295399080)⟩⟩,⟨⟨296577216055585917940846043019,296577216055585917964549198045⟩,⟨(-4580344719906157500558034090),(-4580344719906157482447471825)⟩⟩,⟨⟨295116103753582533744923711155,295116103753582533768427518090⟩,⟨(-4466479931156336035966759178),(-4466479931156336017992561226)⟩⟩,⟨⟨293599985370305116127263303234,293599985370305116150581516210⟩,⟨(-4353391535005783243945413560),(-4353391535005783226109702921)⟩⟩,⟨⟨292041427254145161292440805638,292041427254145161315567650971⟩,⟨(-4241312418368850892897134623),(-4241312418368850875201784038)⟩⟩,⟨⟨290427756695503209422896467176,290427756695503209445816663602⟩,⟨(-4130100213631344505653861658),(-4130100213631344488101418834)⟩⟩,⟨⟨288772365687686203884483672186,288772365687686203907192336347⟩,⟨(-4019989620392040587714958741),(-4019989620392040570307235710)⟩⟩,⟨⟨287061785188315277969804988832,287061785188315277992290752252⟩,⟨(-3910832292576797926606699953),(-3910832292576797909346090524)⟩⟩,⟨⟨285310255555072660426373116942,285310255555072660448619800261⟩,⟨(-3802864114837687657821935566),(-3802864114837687640710267275)⟩⟩,⟨⟨283503487970652467155468108828,283503487970652467177998243510⟩,⟨(-3695931199172180290211059297),(-3695931199172180273243754330)⟩⟩,⟨⟨281656595694045920797423494824,281656595694045920819736559513⟩,⟨(-3590270005622009720138859230),(-3590270005622009703324161421)⟩⟩,⟨⟨279754444742899494696061023235,279754444742899494718157174057⟩,⟨(-3485721535251655949075507995),(-3485721535251655932415591659)⟩⟩,⟨⟨277813047792985761474193919457,277813047792985761496067666780⟩,⟨(-3382522231915680836068550059),(-3382522231915680819564938964)⟩⟩,⟨⟨275816398186697207882092493989,275816398186697207903748781868⟩,⟨(-3280508411477009123723328777),(-3280508411477009107378141960)⟩⟩] +lemma amp9_00_10_eq : ∀ k : Fin 16, amp9_0Expr 0 10 k = amp9_00_10 k := by decide +kernel +noncomputable def amp9_00_11 : Fin 16 → CBox := ![⟨⟨273781436692667967960094982241,273781436692667967981530042951⟩,⟨(-3179915928231531525277184945),(-3179915928231531509091894442)⟩⟩,⟨⟨271691254153234504569225243464,271691254153234504590444838763⟩,⟨(-3080576833550168292085014434),(-3080576833550168276061650738)⟩⟩,⟨⟨269563750472772547175902644683,269563750472772547196886323453⟩,⟨(-2982725837119988781133302369),(-2982725837119988765273389180)⟩⟩,⟨⟨267381081633869236229591435027,267381081633869236250366577759⟩,⟨(-2886191141720374774086700207),(-2886191141720374758392051509)⟩⟩,⟨⟨265162140320326633198244542286,265162140320326633218779781462⟩,⟨(-2791205775812629724135342700),(-2791205775812629708607547752)⟩⟩,⟨⟨262888112510298980602458870064,262888112510298980622759773870⟩,⟨(-2697594504860290119873880066),(-2697594504860290104514921240)⟩⟩,⟨⟨260578920177705446830194193306,260578920177705446850244303689⟩,⟨(-2605588158021350744275082350),(-2605588158021350729086248454)⟩⟩,⟨⟨258214741081908007492394455265,258214741081908007512270728339⟩,⟨(-2515008470250995167598855861),(-2515008470250995152581443597)⟩⟩,⟨⟨255816566168266071521507635587,255816566168266071541132487115⟩,⟨(-2426083571964919964006184234),(-2426083571964919949162053939)⟩⟩,⟨⟨253363523368324278807856274694,253363523368324278827232065045⟩,⟨(-2338632570078793038087219401),(-2338632570078793023418317662)⟩⟩,⟨⟨250877715798152673661949780487,250877715798152673681091466762⟩,⟨(-2252880415556413303364469388),(-2252880415556413288871612632)⟩⟩,⟨⟨248337176185627459063337382043,248337176185627459082217292594⟩,⟨(-2168643985507320742231329641),(-2168643985507320727916765163)⟩⟩,⟨⟨245765166933288845512379556985,245765166933288845531004116207⟩,⟨(-2086144589544568126285345552),(-2086144589544568112149920249)⟩⟩,⟨⟨243138575995052695124658721209,243138575995052695143022357907⟩,⟨(-2005197269047037027650219023),(-2005197269047037013695911144)⟩⟩,⟨⟨240481876551064263979283014902,240481876551064263997373789951⟩,⟨(-1926019249259763438025802670),(-1926019249259763424253483796)⟩⟩,⟨⟨237770757523431697832894023069,237770757523431697850699454857⟩,⟨(-1848424125801029977280381195),(-1848424125801029963692094379)⟩⟩] +lemma amp9_00_11_eq : ∀ k : Fin 16, amp9_0Expr 0 11 k = amp9_00_11 k := by decide +kernel +noncomputable def amp9_00_12 : Fin 16 → CBox := ![⟨⟨235030959266730895497474161155,235030959266730895515286788463⟩,⟨(-1772624615471496380397319551),(-1772624615471496366991594527)⟩⟩,⟨⟨232236912154997825889256674200,232236912154997825906821366635⟩,⟨(-1698433254021623120044790422),(-1698433254021623106825492627)⟩⟩,⟨⟨229415685635051681466281295381,229415685635051681483594172578⟩,⟨(-1626057844719219442129604708),(-1626057844719219429097369601)⟩⟩,⟨⟨226540386094549529466608619521,226540386094549529483670870507⟩,⟨(-1555310245266803046355328770),(-1555310245266803033512071649)⟩⟩,⟨⟨223639480228296686884039866901,223639480228296686900848133046⟩,⟨(-1486392959332582249239165370),(-1486392959332582236585468468)⟩⟩,⟨⟨220684678302308916564422168682,220684678302308916580981594201⟩,⟨(-1419117544299396717952412525),(-1419117544299396705490111042)⟩⟩,⟨⟨217705919492264939602837193317,217705919492264939619129542975⟩,⟨(-1353680837210838835842932203),(-1353680837210838823572568188)⟩⟩,⟨⟨214673438201119008723171955359,214673438201119008739234458490⟩,⟨(-1289894468725546308748847029),(-1289894468725546296672092832)⟩⟩,⟨⟨211618729382634600653177681142,211618729382634600668967991393⟩,⟨(-1227949261284789806723898168),(-1227949261284789794841398272)⟩⟩,⟨⟨208510463156880351883143527065,208510463156880351898669292955⟩,⟨(-1167657288222717653697091025),(-1167657288222717642010636187)⟩⟩,⟨⟨205381782784624177931661637896,205381782784624177946914385210⟩,⟨(-1109203028438482897063512120),(-1109203028438482885573384780)⟩⟩,⟨⟨202199695733315480399273215982,202199695733315480414248806134⟩,⟨(-1052399363061589163021345920),(-1052399363061589151729453754)⟩⟩,⟨⟨198999096719704338913498672641,198999096719704338928181146756⟩,⟨(-997424117522348584677810588),(-997424117522348573584411156)⟩⟩,⟨⟨195745220722240688536087151306,195745220722240688550653732179⟩,⟨(-944091341481054280193708767),(-944091341481054269299785824)⟩⟩,⟨⟨192474829343964431541821625669,192474829343964431556104252702⟩,⟨(-892571915944851596592506292),(-892571915944851585898937259)⟩⟩,⟨⟨189151261950479018587504218860,189151261950479018601503494079⟩,⟨(-842681415331583231774108246),(-842681415331583221282780316)⟩⟩] +lemma amp9_00_12_eq : ∀ k : Fin 16, amp9_0Expr 0 12 k = amp9_00_12 k := by decide +kernel +noncomputable def amp9_00_13 : Fin 16 → CBox := ![⟨⟨185813276743755801221125173243,185813276743755801234844430113⟩,⟨(-794583504186444009465319663),(-794583504186443999176208953)⟩⟩,⟨⟨182422178864308501316393079194,182422178864308501329851857906⟩,⟨(-748095633259677211734200173),(-748095633259677201649072181)⟩⟩,⟨⟨179018869535473656749532978983,179018869535473656762696211940⟩,⟨(-703373997437957608596208334),(-703373997437957598715038989)⟩⟩,⟨⟨175562462891819667402696611094,175562462891819667415574851927⟩,⟨(-660238270565454977567168420),(-660238270565454967891831347)⟩⟩,⟨⟨172096169277903790570160414822,172096169277903790582737601746⟩,⟨(-618836943425914631671028418),(-618836943425914622201342691)⟩⟩,⟨⟨168576733582626629713287769440,168576733582626629725676305762⟩,⟨(-578992254726878451897048789),(-578992254726878442634521789)⟩⟩,⟨⟨165049864707608170393041140819,165049864707608170405142567266⟩,⟨(-540844775349904473540466273),(-540844775349904464485060188)⟩⟩,⟨⟨161469734522837484344586740202,161469734522837484356397814160⟩,⟨(-504219645448085497478582718),(-504219645448085488632274267)⟩⟩,⟨⟨157884767810600953866551997825,157884767810600953878075397113⟩,⟨(-469249318722501112256299725),(-469249318722501103618619853)⟩⟩,⟨⟨154246329020730490569904225999,154246329020730490581149241598⟩,⟨(-435762167956083816456185389),(-435762167956083808029059604)⟩⟩,⟨⟨150605809747465210435148743574,150605809747465210446104055396⟩,⟨(-403882350770507068957986953),(-403882350770507060740814268)⟩⟩,⟨⟨146911495554703965854405872803,146911495554703965865142536139⟩,⟨(-373441798139992530931596238),(-373441798139992522926242099)⟩⟩,⟨⟨143218036654714008131472647055,143218036654714008141904689207⟩,⟨(-344556210927922266854352798),(-344556210927922259060313565)⟩⟩,⟨⟨139470322968955804617685657294,139470322968955804627819542404⟩,⟨(-317061398000412774596598316),(-317061398000412767015917901)⟩⟩,⟨⟨135726605353655545980317435974,135726605353655545990159368433⟩,⟨(-291064460826259380055836680),(-291064460826259372687592985)⟩⟩,⟨⟨131928005392641061852700253122,131928005392641061862238673848⟩,⟨(-266405399753673131652649659),(-266405399753673124499030280)⟩⟩] +lemma amp9_00_13_eq : ∀ k : Fin 16, amp9_0Expr 0 13 k = amp9_00_13 k := by decide +kernel +noncomputable def amp9_00_14 : Fin 16 → CBox := ![⟨⟨128136779011057249553664670721,128136779011057249562957886755⟩,⟨(-243182592066960784613202593),(-243182592066960777673083327)⟩⟩,⟨⟨124289836842615231716619722367,124289836842615231725614138469⟩,⟨(-221240536816929517036846841),(-221240536816929510312527933)⟩⟩,⟨⟨120453922816612129116018957105,120453922816612129124723396219⟩,⟨(-200668779944004752932426159),(-200668779944004746422669450)⟩⟩,⟨⟨116561205444166672849047988038,116561205444166672857440066057⟩,⟨(-181316619785693730316911109),(-181316619785693724024087875)⟩⟩,⟨⟨112683499776144673635851318907,112683499776144673643987248045⟩,⟨(-163264681172595942704999770),(-163264681172595936627654153)⟩⟩,⟨⟨108747587160841699264136846271,108747587160841699271971036877⟩,⟨(-146367355405605196581904959),(-146367355405605190722521970)⟩⟩,⟨⟨104831066776958411342887764186,104831066776958411350453187687⟩,⟨(-130696273572377452146488509),(-130696273572377446503425047)⟩⟩,⟨⟨100854538849332597434297011250,100854538849332597441555567878⟩,⟨(-116111206435427032049214026),(-116111206435427026625102093)⟩⟩,⟨⟨96902271182587980364529833914,96902271182587980371487772024⟩,⟨(-102674735551117056956792776),(-102674735551117051749836268)⟩⟩,⟨⟨92887690320411955904638550581,92887690320411955911316754415⟩,⟨(-90252290198623873882854785),(-90252290198623868895741586)⟩⟩,⟨⟨88902848398450723971147369278,88902848398450723977519392554⟩,⟨(-78897363137513938279792732),(-78897363137513933510471275)⟩⟩,⟨⟨84852734834314225163688369671,84852734834314225169774960051⟩,⟨(-68481313526766474342357658),(-68481313526766469793756626)⟩⟩,⟨⟨80838621202005951893671086032,80838621202005951899475161424⟩,⟨(-59048522219791197407773828),(-59048522219791193077545125)⟩⟩,⟨⟨76755416963323492426936405942,76755416963323492432430591642⟩,⟨(-50476541709763959049106599),(-50476541709763954940439214)⟩⟩,⟨⟨72715502340174936538433495145,72715502340174936543639332088⟩,⟨(-42800633560112771865901343),(-42800633560112767976061220)⟩⟩,⟨⟨68601515725651777365877080355,68601515725651777370788286871⟩,⟨(-35904798986054578266074049),(-35904798986054574598570576)⟩⟩] +lemma amp9_00_14_eq : ∀ k : Fin 16, amp9_0Expr 0 14 k = amp9_00_14 k := by decide +kernel +noncomputable def amp9_00_15 : Fin 16 → CBox := ![⟨⟨64539503415645085454919086187,64539503415645085459535657401⟩,⟨(-29815188073350490689297692),(-29815188073350487241018970)⟩⟩,⟨⟨60396818612050247087432748414,60396818612050247091747658079⟩,⟨(-24422498031291935962398932),(-24422498031291932737221313)⟩⟩,⟨⟨56316756585784371034489584723,56316756585784371038506165304⟩,⟨(-19743789781400820458431625),(-19743789781400817452689563)⟩⟩,⟨⟨52147076633054805141138109628,52147076633054805144859304470⟩,⟨(-15676695838757779412734879),(-15676695838757776630853876)⟩⟩,⟨⟨48053564435512766975821201425,48053564435512766979249340609⟩,⟨(-12229223778246479696211530),(-12229223778246477133865998)⟩⟩,⟨⟨43857915892222204054797014138,43857915892222204057923290619⟩,⟨(-9306173334082597415089766),(-9306173334082595077406084)⟩⟩,⟨⟨39756518367687861327092508708,39756518367687861329920913839⟩,⟨(-6906546457326445438820815),(-6906546457326443320539753)⟩⟩,⟨⟨35534636916937217772781384184,35534636916937217775311337154⟩,⟨(-4942536047449003693098753),(-4942536047449001800386842)⟩⟩,⟨⟨31432807725418446481491758612,31432807725418446483726449094⟩,⟨(-3404195131147992214157218),(-3404195131147990540442466)⟩⟩,⟨⟨27181673825565697581614621917,27181673825565697583544841554⟩,⟨(-2211333236794332304125055),(-2211333236794330857142271)⟩⟩,⟨⟨23091170310179454626720001068,23091170310179454628356189131⟩,⟨(-1345113899161042731088065),(-1345113899161041502138448)⟩⟩,⟨⟨18800756195048441833365859505,18800756195048441834695780555⟩,⟨(-733193241686198754993644),(-733193241686197754569640)⟩⟩,⟨⟨14745709346389485623228473691,14745709346389485624267266717⟩,⟨(-347891772871139569724195),(-347891772871138785203510)⟩⟩,⟨⟨10381956628106551989133853274,10381956628106551989862556125⟩,⟨(-124974050225335016955402),(-124974050225334464661324)⟩⟩,⟨⟨6440307695516600995142899093,6440307695516600995586117522⟩,⟨(-27910132336248321384732),(-27910132336247978804395)⟩⟩,⟨⟨1829737917432750534772189334,1829737917432750534892818721⟩,⟨(-881064552150320225691),(-881064552150222899669)⟩⟩] +lemma amp9_00_15_eq : ∀ k : Fin 16, amp9_0Expr 0 15 k = amp9_00_15 k := by decide +kernel +noncomputable def amp9_00 : Fin 16 → Fin 16 → CBox := ![amp9_00_0,amp9_00_1,amp9_00_2,amp9_00_3,amp9_00_4,amp9_00_5,amp9_00_6,amp9_00_7,amp9_00_8,amp9_00_9,amp9_00_10,amp9_00_11,amp9_00_12,amp9_00_13,amp9_00_14,amp9_00_15] +lemma amp9_00_eq (i k : Fin 16) : amp9_0Expr 0 i k = amp9_00 i k := by + fin_cases i + · exact amp9_00_0_eq k + · exact amp9_00_1_eq k + · exact amp9_00_2_eq k + · exact amp9_00_3_eq k + · exact amp9_00_4_eq k + · exact amp9_00_5_eq k + · exact amp9_00_6_eq k + · exact amp9_00_7_eq k + · exact amp9_00_8_eq k + · exact amp9_00_9_eq k + · exact amp9_00_10_eq k + · exact amp9_00_11_eq k + · exact amp9_00_12_eq k + · exact amp9_00_13_eq k + · exact amp9_00_14_eq k + · exact amp9_00_15_eq k +noncomputable def amp9_01_0 : Fin 16 → CBox := ![⟨⟨1102088937858270181394552454,1102088937858270181533202117⟩,⟨(-295300788789259126971737208),(-295300788789259126840886379)⟩⟩,⟨⟨3879294710425496027465148781,3879294710425496027964382549⟩,⟨(-1039357201326332966063557275),(-1039357201326332965599985274)⟩⟩,⟨⟨6254061791736625379192679436,6254061791736625380006002298⟩,⟨(-1675337883700933204696727710),(-1675337883700933203947152659)⟩⟩,⟨⟨8883903197754802697209399117,8883903197754802698366837324⟩,⟨(-2379229555022371937924904668),(-2379229555022371936859673673)⟩⟩,⟨⟨11328881539795970240714512299,11328881539795970242193455945⟩,⟨(-3033024803843450896847340468),(-3033024803843450895488331723)⟩⟩,⟨⟨13917127160292995720292131254,13917127160292995722110167092⟩,⟨(-3724423372331124206261903698),(-3724423372331124204592367069)⟩⟩,⟨⟨16386647989420772850540265691,16386647989420772852682748053⟩,⟨(-4383128812381189622762738401),(-4383128812381189620796853294)⟩⟩,⟨⟨18955083471876935668020435590,18955083471876935670499405142⟩,⟨(-5067206830901892687396850639),(-5067206830901892685123187137)⟩⟩,⟨⟨21435879089724502550741500692,21435879089724502553545910167⟩,⟨(-5726605044038025507079360529),(-5726605044038025504508548822)⟩⟩,⟨⟨23991804549643204462998587970,23991804549643204466134655875⟩,⟨(-6404659675304383763175911679),(-6404659675304383760300163924)⟩⟩,⟨⟨26478046610248602796378547705,26478046610248602799841474396⟩,⟨(-7062533676292391732454387922),(-7062533676292391729281194589)⟩⟩,⟨⟨29024525644062964296167639137,29024525644062964299963163807⟩,⟨(-7734734933180978272351615979),(-7734734933180978268874647079)⟩⟩,⟨⟨31512960724499068396707537179,31512960724499068400826502452⟩,⟨(-8389566709868148764842033893),(-8389566709868148761069007751)⟩⟩,⟨⟨34051378273882346249690239845,34051378273882346254136743742⟩,⟨(-9055644815582760871743817304),(-9055644815582760867669773503)⟩⟩,⟨⟨36539869626915827775230335360,36539869626915827780002780264⟩,⟨(-9706226543194707972826221803),(-9706226543194707968456230605)⟩⟩,⟨⟨39070810253034233324491606512,39070810253034233329594176240⟩,⟨(-10365709213769622484125100213),(-10365709213769622479454882210)⟩⟩] +lemma amp9_01_0_eq : ∀ k : Fin 16, amp9_0Expr 1 0 k = amp9_01_0 k := by decide +kernel +noncomputable def amp9_01_1 : Fin 16 → CBox := ![⟨⟨41557777871199088339907224183,41557777871199088345332540283⟩,⟨(-11010995147660989393653695945),(-11010995147660989388689405351)⟩⟩,⟨⟨44081392149094618344956504202,44081392149094618350706382332⟩,⟨(-11663307683745029778633224198),(-11663307683745029773371760908)⟩⟩,⟨⟨46565559944373481007730057826,46565559944373481013797830394⟩,⟨(-12302348312534547856793488567),(-12302348312534547851240481392)⟩⟩,⟨⟨49081738751393079149298041303,49081738751393079155698228646⟩,⟨(-12946862180358040215048010905),(-12946862180358040209197457625)⟩⟩,⟨⟨51562006374793350934197548630,51562006374793350940910791563⟩,⟨(-13578771739459452595624751724),(-13578771739459452589485379855)⟩⟩,⟨⟨54070471955917311494890921031,54070471955917311501920201117⟩,⟨(-14214830811882939480860832313),(-14214830811882939474430062194)⟩⟩,⟨⟨56545843812244422913968598028,56545843812244422921323960955⟩,⟨(-14838770080580355763142192189),(-14838770080580355756420817512)⟩⟩,⟨⟨59046200785592461145503663966,59046200785592461153169952494⟩,⟨(-15465706099368956679494938101),(-15465706099368956672485473840)⟩⟩,⟨⟨61515743851300289355806093903,61515743851300289363793477840⟩,⟨(-16080872869007158648902527422),(-16080872869007158641605599228)⟩⟩,⟨⟨64007509311183496068709887242,64007509311183496077022994582⟩,⟨(-16698015257084626435144023546),(-16698015257084626427557253434)⟩⟩,⟨⟨66470326561342197866554499484,66470326561342197875167643538⟩,⟨(-17303638930480648739025421579),(-17303638930480648731158689974)⟩⟩,⟨⟨68952948560618553282169433230,68952948560618553291103316294⟩,⟨(-17910321436817546031873133717),(-17910321436817546023720127610)⟩⟩,⟨⟨71408161377362287782189597499,71408161377362287791413879571⟩,⟨(-18505659978604572113675883540),(-18505659978604572105247574224)⟩⟩,⟨⟨73881030613396447893919813363,73881030613396447903469372526⟩,⟨(-19101225444126882960378006349),(-19101225444126882951664661872)⟩⟩,⟨⟨76327766630301121273138666053,76327766630301121282997457828⟩,⟨(-19685563727738912108525049726),(-19685563727738912099533863709)⟩⟩,⟨⟨78790223991043618360440452429,78790223991043618370614150334⟩,⟨(-20269367679914862844008603081),(-20269367679914862834737638719)⟩⟩] +lemma amp9_01_1_eq : ∀ k : Fin 16, amp9_0Expr 1 1 k = amp9_01_1 k := by decide +kernel +noncomputable def amp9_01_2 : Fin 16 → CBox := ![⟨⟨81227608375539202468812723768,81227608375539202479265953354⟩,⟨(-20842016691769109982769506070),(-20842016691769109973230841032)⟩⟩,⟨⟨83678949881142211138975561217,83678949881142211149744397787⟩,⟨(-21413430175279002059508414596),(-21413430175279002049692497481)⟩⟩,⟨⟨86106098879043725777715194846,86106098879043725788790242656⟩,⟨(-21973726757123102140394821023),(-21973726757123102130307023092)⟩⟩,⟨⟨88545578943925473734334159640,88545578943925473745719254205⟩,⟨(-22532138644589893282723848324),(-22532138644589893272363095152)⟩⟩,⟨⟨90961594967913421664481017613,90961594967913421676177841968⟩,⟨(-23079445577802580844568344010),(-23079445577802580833937157620)⟩⟩,⟨⟨93388428560758176814963778124,93388428560758176826919001670⟩,⟨(-23624264511637001800557647881),(-23624264511637001789669602874)⟩⟩,⟨⟨95792396370099360467354443953,95792396370099360479609804585⟩,⟨(-24157970818577534364504791244),(-24157970818577534353352223177)⟩⟩,⟨⟨98205760443890943474300120771,98205760443890943486848361989⟩,⟨(-24688626880135965808538034746),(-24688626880135965797122997219)⟩⟩,⟨⟨100596744122130928655608859409,100596744122130928668453405737⟩,⟨(-25208148260544373321363427111),(-25208148260544373309687975824)⟩⟩,⟨⟨102995778560777490168893246289,102995778560777490182035548468⟩,⟨(-25724094429346650086970141654),(-25724094429346650075034292441)⟩⟩,⟨⟨105372819096868674038324629027,105372819096868674051760419720⟩,⟨(-26228873776445116050402848023),(-26228873776445116038210590755)⟩⟩,⟨⟨107756627345939477777195569495,107756627345939477790862802682⟩,⟨(-26729587221217294259609492957),(-26729587221217294247176740099)⟩⟩,⟨⟨110118740687065649118644408002,110118740687065649132611054315⟩,⟨(-27219095179189904672410538586),(-27219095179189904659723312929)⟩⟩,⟨⟨112486390185063711863791814773,112486390185063711878047411319⟩,⟨(-27704078409009261255093800394),(-27704078409009261242155351264)⟩⟩,⟨⟨114832565670311263392447015819,114832565670311263406995961918⟩,⟨(-28177813944701418792931713794),(-28177813944701418779743901053)⟩⟩,⟨⟨117183088163066982133035097851,117183088163066982147854752684⟩,⟨(-28646595839664774773815026641),(-28646595839664774760384182989)⟩⟩] +lemma amp9_01_2_eq : ∀ k : Fin 16, amp9_0Expr 1 2 k = amp9_01_2 k := by decide +kernel +noncomputable def amp9_01_3 : Fin 16 → CBox := ![⟨⟨119512287274270832559652442787,119512287274270832574752747513⟩,⟨(-29104086808840506280835842769),(-29104086808840506267162473198)⟩⟩,⟨⟨121844679072130333801071248589,121844679072130333816453793625⟩,⟨(-29556223543755479954610811903),(-29556223543755479940695434453)⟩⟩,⟨⟨124155834456613809796689401903,124155834456613809812352330386⟩,⟨(-29997027237399739255472211962),(-29997027237399739241318244951)⟩⟩,⟨⟨126469056678259059248990470133,126469056678259059264826302025⟩,⟨(-30432103107978883640767197306),(-30432103107978883626401532699)⟩⟩,⟨⟨128761071410825821032243534674,128761071410825821048362384333⟩,⟨(-30855806767745305216328046328),(-30855806767745305201727075820)⟩⟩,⟨⟨131054050246400468881409209078,131054050246400468897800269460⟩,⟨(-31273434926021346071887534057),(-31273434926021346057054990034)⟩⟩,⟨⟨133325797306735744426796539554,133325797306735744443454919660⟩,⟨(-31679656220515710630486866312),(-31679656220515710615426912831)⟩⟩,⟨⟨135597424324932184047062904147,135597424324932184063982372141⟩,⟨(-32079479324281999776248277579),(-32079479324281999760963628051)⟩⟩,⟨⟨137847746272761056087706006327,137847746272761056104889094441⟩,⟨(-32467866779767209230883522383),(-32467866779767209215376589608)⟩⟩,⟨⟨140096878790657178278921019220,140096878790657178296339739398⟩,⟨(-32849557559514378999018928528),(-32849557559514378983297617911)⟩⟩,⟨⟨142324587625396826299335185628,142324587625396826317011188933⟩,⟨(-33219790940039775564960749706),(-33219790940039775549022991854)⟩⟩,⟨⟨144550049155458843888331762581,144550049155458843906252367977⟩,⟨(-33583052685930903111707839154),(-33583052685930903095558019147)⟩⟩,⟨⟨146753926350228373769749183406,146753926350228373787915341024⟩,⟨(-33934843318971122051706946932),(-33934843318971122035347880226)⟩⟩,⟨⟨148954507135577544835230083319,148954507135577544853638734674⟩,⟨(-34279410289754643662392202521),(-34279410289754643645826110119)⟩⟩,⟨⟨151133303837658889286767792869,151133303837658889305417433431⟩,⟨(-34612501334288220709266679715),(-34612501334288220692496967131)⟩⟩,⟨⟨153307761484133862357377458699,153307761484133862376264562217⟩,⟨(-34938139089609094554747715191),(-34938139089609094537776795685)⟩⟩] +lemma amp9_01_3_eq : ∀ k : Fin 16, amp9_0Expr 1 3 k = amp9_01_3 k := by decide +kernel +noncomputable def amp9_01_4 : Fin 16 → CBox := ![⟨⟨155460198875561920601208943373,155460198875561920620164307130⟩,⟨(-35252305744241606875986427811),(-35252305744241606858855753813)⟩⟩,⟨⟨157607259087086457087411540942,157607259087086457106625187052⟩,⟨(-35558811401520389874001411253),(-35558811401520389856669421355)⟩⟩,⟨⟨159732028900161944735358728877,159732028900161944754820316707⟩,⟨(-35853861050807490803450373061),(-35853861050807490785922549242)⟩⟩,⟨⟨161850386322304011859780108187,161850386322304011879480808174⟩,⟨(-36141063467674361637167300560),(-36141063467674361619447432769)⟩⟩,⟨⟨163946151505592800673774608590,163946151505592800693708458228⟩,⟨(-36416835765259395973924526755),(-36416835765259395956017091506)⟩⟩,⟨⟨166034470680872050013370401145,166034470680872050033540710555⟩,⟨(-36684595648427398999122627922),(-36684595648427398981028768358)⟩⟩,⟨⟨168099866211769223305587758481,168099866211769223325974002637⟩,⟨(-36940962535999628584135516222),(-36940962535999628565862919666)⟩⟩,⟨⟨170156782649161603212213246336,170156782649161603232824268922⟩,⟨(-37189172477418071642120403518),(-37189172477418071623669062128)⟩⟩,⟨⟨172190416489421670783197723590,172190416489421670804032800906⟩,⟨(-37426038138837605885788782079),(-37426038138837605867162037785)⟩⟩,⟨⟨174214537849568804697347700479,174214537849568804718354033589⟩,⟨(-37654622579967653828816895630),(-37654622579967653810028188174)⟩⟩,⟨⟨176214992040382924341060761114,176214992040382924362287524071⟩,⟨(-37871923330204057902626845352),(-37871923330204057883668689123)⟩⟩,⟨⟨178204899437200859236418677208,178204899437200859257853767757⟩,⟨(-38080838455293043598744008826),(-38080838455293043579621095570)⟩⟩,⟨⟨180170731330472669863299250671,180170731330472669884944159777⟩,⟨(-38278542564095100020861151781),(-38278542564095100001576372137)⟩⟩,⟨⟨182124980749140954817704312844,182124980749140954839536872428⟩,⟨(-38467776123385623939993351822),(-38467776123385623920553545067)⟩⟩,⟨⟨184054724371601113673556743244,184054724371601113695593277945⟩,⟨(-38645883573846309349052598688),(-38645883573846309329457520036)⟩⟩,⟨⟨185971848202277675091668473920,185971848202277675113894025433⟩,⟨(-38815454637734521706785173121),(-38815454637734521687040168177)⟩⟩] +lemma amp9_01_4_eq : ∀ k : Fin 16, amp9_0Expr 1 4 k = amp9_01_4 k := by decide +kernel +noncomputable def amp9_01_5 : Fin 16 → CBox := ![⟨⟨187864015749003401157818440319,187864015749003401180234645189⟩,⟨(-38973996820142682179804949356),(-38973996820142682159912899179)⟩⟩,⟨⟨189742524435037546372918879486,189742524435037546395522191048⟩,⟨(-39123955465392405264906108072),(-39123955465392405244870003824)⟩⟩,⟨⟨191595607888822722064269145365,191595607888822722087060839021⟩,⟨(-39262994806974376333257205788),(-39262994806974376313080024711)⟩⟩,⟨⟨193433991687716030329787541462,193433991687716030352762776953⟩,⟨(-39393421736196173598637416424),(-39393421736196173578322475636)⟩⟩,⟨⟨195246464560581567027895747584,195246464560581567051052468722⟩,⟨(-39513051267549282322835058905),(-39513051267549282302386036186)⟩⟩,⟨⟨197043195415465577223517516878,197043195415465577246509085861⟩,⟨(-39624057363263260206093483180),(-39624057363263260185582463213)⟩⟩,⟨⟨198813514608418093398805668472,198813514608418093421990009160⟩,⟨(-39724400222470671769242769144),(-39724400222470671748600621764)⟩⟩,⟨⟨200567048127371937214769077799,200567048127371937238134006179⟩,⟨(-39816126037186355575347842797),(-39816126037186355554579464418)⟩⟩,⟨⟨202293655904318679488034807562,202293655904318679511570331751⟩,⟨(-39897334912780482189718883015),(-39897334912780482168829550150)⟩⟩,⟨⟨204002433444434158512991132081,204002433444434158536692951141⟩,⟨(-39969950096644638660850152261),(-39969950096644638639843184644)⟩⟩,⟨⟨205683759515949394776273815443,205683759515949394800129268292⟩,⟨(-40032206610755328141658564237),(-40032206610755328120539710533)⟩⟩,⟨⟨207346210368661730223530907292,207346210368661730247534885678⟩,⟨(-40085909278437561589181544610),(-40085909278437561567954294075)⟩⟩,⟨⟨208980674081079314464033080830,208980674081079314488193193096⟩,⟨(-40129423311622252309229938001),(-40129423311622252287896096785)⟩⟩,⟨⟨210595217754916127536063647612,210595217754916127560358826971⟩,⟨(-40164439350227293053614585825),(-40164439350227293032180731021)⟩⟩,⟨⟨212181230379998465613096190049,212181230379998465637533090210⟩,⟨(-40189448309633768479719817332),(-40189448309633768458187933059)⟩⟩,⟨⟨213746278976555415007185196214,213746278976555415031763664276⟩,⟨(-40206030629547524952142001085),(-40206030629547524930514700640)⟩⟩] +lemma amp9_01_5_eq : ∀ k : Fin 16, amp9_0Expr 1 5 k = amp9_01_5 k := by decide +kernel +noncomputable def amp9_01_6 : Fin 16 → CBox := ![⟨⟨215282246096763861773537202575,215282246096763861798215643256⟩,⟨(-40212798662206166480100305703),(-40212798662206166458388649734)⟩⟩,⟨⟨216796206775391264501430655462,216796206775391264526250465535⟩,⟨(-40211226392898912857438682794),(-40211226392898912835637509727)⟩⟩,⟨⟨218280530759559737827011681042,218280530759559737851945363277⟩,⟨(-40200043546080650747558713087),(-40200043546080650725676382542)⟩⟩,⟨⟨219741808285939344350341374718,219741808285939344375408158828⟩,⟨(-40180621179004388200364230142),(-40180621179004388178399840422)⟩⟩,⟨⟨221172890849933913145508647900,221172890849933913170691393607⟩,⟨(-40151802509713008870384891995),(-40151802509713008848344853726)⟩⟩,⟨⟨222579890223438034757855347140,222579890223438034783157380240⟩,⟨(-40114858990540393422010368768),(-40114858990540393399896739750)⟩⟩,⟨⟨223956135070172351896545735994,223956135070172351921841400988⟩,⟨(-40068743626333527808266752042),(-40068743626333527786105278817)⟩⟩,⟨⟨225307264224628230777848456958,225307264224628230803266228884⟩,⟨(-40014631398892210385363856761),(-40014631398892210363134113167)⟩⟩,⟨⟨226627079757599591425893706166,226627079757599591451417280999⟩,⟨(-39951581552344200270336272379),(-39951581552344200248044431311)⟩⟩,⟨⟨227920752329829932552888407860,227920752329829932578507517799⟩,⟨(-39880675556702454885668883999),(-39880675556702454863319454913)⟩⟩,⟨⟨229182554434144874354149501490,229182554434144874379867198959⟩,⟨(-39801075495934331118230454276),(-39801075495934331095826129904)⟩⟩,⟨⟨230417192594420635077635339830,230417192594420635103433959394⟩,⟨(-39713772123190995206242579856),(-39713772123190995183789153404)⟩⟩,⟨⟨231619407479093604650037529385,231619407479093604675919913737⟩,⟨(-39618027100997935311138737580),(-39618027100997935288638928702)⟩⟩,⟨⟨232793444817417378334538404934,232793444817417378360509391964⟩,⟨(-39514743107421543064193885237),(-39514743107421543041649605354)⟩⟩,⟨⟨233934511912552159146700531211,233934511912552159172696125377⟩,⟨(-39403278251626319022007800137),(-39403278251626318999433045424)⟩⟩,⟨⟨235046396374489785538823655098,235046396374489785564893750115⟩,⟨(-39284449634874509518131238466),(-39284449634874509495520296810)⟩⟩] +lemma amp9_01_6_eq : ∀ k : Fin 16, amp9_0Expr 1 6 k = amp9_01_6 k := by decide +kernel +noncomputable def amp9_01_7 : Fin 16 → CBox := ![⟨⟨236124771276792074039915424541,236124771276792074066048937936⟩,⟨(-39157708802626491220965460013),(-39157708802626491198323373957)⟩⟩,⟨⟨237172968142386505374941540744,237172968142386505401142281716⟩,⟨(-39023789642856992663857211639),(-39023789642856992641186093385)⟩⟩,⟨⟨238187125602308080006120206712,238187125602308080032351225872⟩,⟨(-38882234241680134662194187554),(-38882234241680134639503234455)⟩⟩,⟨⟨239170120501443106873787445360,239170120501443106900071452786⟩,⟨(-38733695510438573678074266455),(-38733695510438573655362504314)⟩⟩,⟨⟨240118557445124203597937068174,240118557445124203624249722717⟩,⟨(-38577803288908377082666213332),(-38577803288908377059940699547)⟩⟩,⟨⟨241034859402556496165117915263,241034859402556496191477813804⟩,⟨(-38415131628745579104852212198),(-38415131628745579082112691187)⟩⟩,⟨⟨241916097981613941651170953860,241916097981613941677557933462⟩,⟨(-38245395439744184163243507997),(-38245395439744184140496277815)⟩⟩,⟨⟨242764242484760095041645320527,242764242484760095068056099729⟩,⟨(-38069091917576288230213475264),(-38069091917576288207461798081)⟩⟩,⟨⟨243576833146865032914550055271,243576833146865032940981455044⟩,⟨(-37886018457136518980657952484),(-37886018457136518957905395038)⟩⟩,⟨⟨244355385229316022630977709699,244355385229316022657429404904⟩,⟨(-37696597294414925947041678869),(-37696597294414925924291018498)⟩⟩,⟨⟨245097909802417205969553139696,245097909802417205996012898854⟩,⟨(-37500705819218187315553518555),(-37500705819218187292809656691)⟩⟩,⟨⟨245805467136055951412158211367,245805467136055951438624572033⟩,⟨(-37298693102022918576149124472),(-37298693102022918553415024913)⟩⟩,⟨⟨246476541919033007139810814542,246476541919033007166272058137⟩,⟨(-37090514128662259255891568538),(-37090514128662259233172005298)⟩⟩,⟨⟨247111737907551681769449568998,247111737907551681795899866993⟩,⟨(-36876446500871572302415051518),(-36876446500871572279713597399)⟩⟩,⟨⟨247710016760027860459514754551,247710016760027860485943542898⟩,⟨(-36656520490029906433546489022),(-36656520490029906410867639323)⟩⟩,⟨⟨248271523626580225400611960728,248271523626580225427006954682⟩,⟨(-36430943832750866239551467263),(-36430943832750866216899726475)⟩⟩] +lemma amp9_01_7_eq : ∀ k : Fin 16, amp9_0Expr 1 7 k = amp9_01_7 k := by decide +kernel +noncomputable def amp9_01_8 : Fin 16 → CBox := ![⟨⟨248795701050586257864862535126,248795701050586257891246408593⟩,⟨(-36199819861475239147702703543),(-36199819861475239125077671068)⟩⟩,⟨⟨249282232912266652339163257075,249282232912266652365559704394⟩,⟨(-35963287961944275670434540891),(-35963287961944275647835504572)⟩⟩,⟨⟨249731047118426714362179579161,249731047118426714388575872885⟩,⟨(-35721522387220123895883270089),(-35721522387220123873315012806)⟩⟩,⟨⟨250141363040241398647808438171,250141363040241398674194713311⟩,⟨(-35474595600399333188167035865),(-35474595600399333165633736180)⟩⟩,⟨⟨250513598991149060614260821729,250513598991149060640630574863⟩,⟨(-35222750717243902193779509840),(-35222750717243902171285001465)⟩⟩,⟨⟨250846506012137325425668338288,250846506012137325452010607831⟩,⟨(-34965994623347910559575851066),(-34965994623347910537124380881)⟩⟩,⟨⟨251140998435603911930783900868,251140998435603911957096779515⟩,⟨(-34704637320649346361418577760),(-34704637320649346339013237103)⟩⟩,⟨⟨251395354559775651622761578296,251395354559775651649033310890⟩,⟨(-34438621381838913481545793223),(-34438621381838913459190917186)⟩⟩,⟨⟨251610990924665792562758259171,251610990924665792588987878932⟩,⟨(-34168321799167045246248431693),(-34168321799167045223946967266)⟩⟩,⟨⟨251785708069448953564000336068,251785708069448953590185661353⟩,⟨(-33893618018639213548183136059),(-33893618018639213525938035245)⟩⟩,⟨⟨251921431516868368609082918823,251921431516868368635220219410⟩,⟨(-33614948207245718460570275133),(-33614948207245718438384778904)⟩⟩,⟨⟨252015478411803646593851320998,252015478411803646619920407174⟩,⟨(-33332129793936222502700218785),(-33332129793936222480579687126)⟩⟩,⟨⟨252070290634472429626933105842,252070290634472429652953010313⟩,⟨(-33045662385145755161370487428),(-33045662385145755139315123731)⟩⟩,⟨⟨252082695662953565705832484797,252082695662953565731778727231⟩,⟨(-32755302427237606236166186582),(-32755302427237606214181824456)⟩⟩,⟨⟨252055659725684453230354304025,252055659725684453256250714519⟩,⟨(-32461609311407643814704596236),(-32461609311407643792790789337)⟩⟩,⟨⟨251985513702620182764039321665,251985513702620182789847683819⟩,⟨(-32164279461810340106746496217),(-32164279461810340084910809985)⟩⟩] +lemma amp9_01_8_eq : ∀ k : Fin 16, amp9_0Expr 1 8 k = amp9_01_8 k := by decide +kernel +noncomputable def amp9_01_9 : Fin 16 → CBox := ![⟨⟨251875756796925501441809344326,251875756796925501467533183134⟩,⟨(-31863930481006021267250636903),(-31863930481006021245495239328)⟩⟩,⟨⟨251722215675293292122042887275,251722215675293292147671585066⟩,⟨(-31560199657932759900199084526),(-31560199657932759878527861314)⟩⟩,⟨⟨251528931801266464021683619286,251528931801266464047270838594⟩,⟨(-31253761315423978393939674273),(-31253761315423978372348471982)⟩⟩,⟨⟨251291219300638232513880536355,251291219300638232539358383082⟩,⟨(-30944194421149637525957402523),(-30944194421149637504457282582)⟩⟩,⟨⟨251013671869395834227074463522,251013671869395834252447766230⟩,⟨(-30632228610791207930701939977),(-30632228610791207909294806422)⟩⟩,⟨⟨250691082019641374216623186324,250691082019641374241896391542⟩,⟨(-30317385271621816772107308984),(-30317385271621816750795137651)⟩⟩,⟨⟨250328606369769749914235023408,250328606369769749939388670082⟩,⟨(-30000448030123796446865864373),(-30000448030123796425653423537)⟩⟩,⟨⟨249920505963284085198265105166,249920505963284085223303704798⟩,⟨(-29680881360548827056540574934),(-29680881360548827035429848147)⟩⟩,⟨⟨249472511784910354709218820202,249472511784910354734130686967⟩,⟨(-29359521645583211134177730866),(-29359521645583211113172520129)⟩⟩,⟨⟨248978342730866012765935172538,248978342730866012790703642025⟩,⟨(-29035777039515431904733894084),(-29035777039515431883838581705)⟩⟩,⟨⟨248444316391166953191015292436,248444316391166953215783580887⟩,⟨(-28710535536537612727629200813),(-28710535536537612706829505147)⟩⟩,⟨⟨247863597965460509158072896947,247863597965460509182702533736⟩,⟨(-28383149488471577782829379502),(-28383149488471577762143914578)⟩⟩,⟨⟨247243104729634202449072248356,247243104729634202473566730816⟩,⟨(-28054557449060372467715785941),(-28054557449060372447146443218)⟩⟩,⟨⟨246575435714377538684396902206,246575435714377538708738451303⟩,⟨(-27724056407900035139670992484),(-27724056407900035119222186066)⟩⟩,⟨⟨245868121856331883734237770121,245868121856331883758448139387⟩,⟨(-27392634522338951382798836834),(-27392634522338951362470309834)⟩⟩,⟨⟨245113182562931495908804683088,245113182562931495932854096428⟩,⟨(-27059533780557546645351523487),(-27059533780557546625149027707)⟩⟩] +lemma amp9_01_9_eq : ∀ k : Fin 16, amp9_0Expr 1 9 k = amp9_01_9 k := by decide +kernel +noncomputable def amp9_01_10 : Fin 16 → CBox := ![⟨⟨244318777360190751755410506734,244318777360190751779345994568⟩,⟨(-26725791087292515125403021658),(-26725791087292515105323592393)⟩⟩,⟨⟨243476331530262021989365293751,243476331530262022013141179438⟩,⟨(-26390593707993928553420858920),(-26390593707993928533471863290)⟩⟩,⟨⟨242594649137857625294190724525,242594649137857625317806923767⟩,⟨(-26055026542509240116108533147),(-26055026542509240096292044028)⟩⟩,⟨⟨241664545716434029777089309688,241664545716434029800555051140⟩,⟨(-25718222326859750917741246456),(-25718222326859750898058669217)⟩⟩,⟨⟨240695486914829266667009246067,240695486914829266690300126000⟩,⟨(-25381313312414681110652461967),(-25381313312414681091108461209)⟩⟩,⟨⟨239677661690547554042624424050,239677661690547554065751042963⟩,⟨(-25043377809807421003254043055),(-25043377809807420983849801346)⟩⟩,⟨⟨238621215502947656592631460861,238621215502947656615588084274⟩,⟨(-24705594892371311203852425241),(-24705594892371311184590493747)⟩⟩,⟨⟨237515692610117462154726672684,237515692610117462177500106808⟩,⟨(-24366988455573209059825180973),(-24366988455573209040709258984)⟩⟩,⟨⟨236371937784837922326391527695,236371937784837922348976622783⟩,⟨(-24028783985186936939322165027),(-24028783985186936920354723832)⟩⟩,⟨⟨235178831062536135201809570924,235178831062536135224196413796⟩,⟨(-23689950872599510015103357886),(-23689950872599509996287618600)⟩⟩,⟨⟨233947937416443306610463334894,233947937416443306632637615908⟩,⟨(-23351760733276686492217341466),(-23351760733276686473556521818)⟩⟩,⟨⟨232667451620007509567173540378,232667451620007509589563345007⟩,⟨(-23013128260317976112059945432),(-23013128260317976093513948602)⟩⟩,⟨⟨231349681239408039681215697204,231349681239408039703409491888⟩,⟨(-22675371050480248576759646494),(-22675371050480248558371348804)⟩⟩,⟨⟨229982113099936804399929801581,229982113099936804421927097915⟩,⟨(-22337348791965653854372515162),(-22337348791965653836144160289)⟩⟩,⟨⟨228577821395677657766517193696,228577821395677657788312469749⟩,⟨(-22000425057283611696406061639),(-22000425057283611678339858119)⟩⟩,⟨⟨227123560523375192025475582511,227123560523375192047072197218⟩,⟨(-21663404102548503691388147482),(-21663404102548503673486012771)⟩⟩] +lemma amp9_01_10_eq : ∀ k : Fin 16, amp9_0Expr 1 10 k = amp9_01_10 k := by decide +kernel +noncomputable def amp9_01_11 : Fin 16 → CBox := ![⟨⟨225633197137326073718476801504,225633197137326073739870527736⟩,⟨(-21327695622933352107951202725),(-21327695622933352090215240421)⟩⟩,⟨⟨224092726764750813742478989797,224092726764750813763674010932⟩,⟨(-20992047885300280117990541529),(-20992047885300280100422494299)⟩⟩,⟨⟨222516836325278459522148964787,222516836325278459543127431393⟩,⟨(-20657917017662205226367522253),(-20657917017662205208970599424)⟩⟩,⟨⟨220890733886764977513846354954,220890733886764977534630171644⟩,⟨(-20323994599710325416606069590),(-20323994599710325399380446356)⟩⟩,⟨⟨219229956611277723759211189177,219229956611277723779773381467⟩,⟨(-19991783677967916347019684800),(-19991783677967916329969385091)⟩⟩,⟨⟨217518894154993001454525088647,217518894154993001474869652690⟩,⟨(-19659918293912015512763202307),(-19659918293912015495889967172)⟩⟩,⟨⟨215773966298139143437213558984,215773966298139143457325914171⟩,⟨(-19329949087603916647347310882),(-19329949087603916630653838407)⟩⟩,⟨⟨213978710727400683637995494168,213978710727400683657938693951⟩,⟨(-19000451543935031853222028516),(-19000451543935031836704864498)⟩⟩,⟨⟨212150464874051781971643525552,212150464874051781991352240683⟩,⟨(-18673024776650951877006916503),(-18673024776650951860673302640)⟩⟩,⟨⟨210271878014667217786970627974,210271878014667217806446238649⟩,⟨(-18346184512029961341403169654),(-18346184512029961325255024701)⟩⟩,⟨⟨208361243217416167483346269973,208361243217416167502600272717⟩,⟨(-18021579440744177048965547238),(-18021579440744177033003106859)⟩⟩,⟨⟨206400281707890630607563161371,206400281707890630626571873049⟩,⟨(-17697664125973585202563651171),(-17697664125973585186791088481)⟩⟩,⟨⟨204408283469455120412329871216,204408283469455120431097614219⟩,⟨(-17376138182231228491805363501),(-17376138182231228476223524134)⟩⟩,⟨⟨202365998470939139382445830931,202365998470939139400967370994⟩,⟨(-17055393380958232385865455043),(-17055393380958232370476812666)⟩⟩,⟨⟨200293758572598872625819400714,200293758572598872644083904771⟩,⟨(-16737181874734243212023124953),(-16737181874734243196829649445)⟩⟩,⟨⟨198171295295397271020178935440,198171295295397271038175284888⟩,⟨(-16419830765359345020307104876),(-16419830765359345005311794645)⟩⟩] +lemma amp9_01_11_eq : ∀ k : Fin 16, amp9_0Expr 1 11 k = amp9_01_11 k := by decide +kernel +noncomputable def amp9_01_12 : Fin 16 → CBox := ![⟨⟨196020031473427629437124112143,196020031473427629455095255181⟩,⟨(-16105146652283613053636497481),(-16105146652283613038820452026)⟩⟩,⟨⟨193818628516734387072072207718,193818628516734387089804968749⟩,⟨(-15791389811362494933580053546),(-15791389811362494918962928885)⟩⟩,⟨⟨191589653989756327171617748725,191589653989756327189108066848⟩,⟨(-15480423523884400002541227830),(-15480423523884399988124268957)⟩⟩,⟨⟨189310642490989542419792234824,189310642490989542437040422507⟩,⟨(-15170438771115004215766543587),(-15170438771115004201551812722)⟩⟩,⟨⟨187005365342270666962721092424,187005365342270666979723441979⟩,⟨(-14863358114068846296956418450),(-14863358114068846282945114545)⟩⟩,⟨⟨184650167931912916714346222221,184650167931912916731106466614⟩,⟨(-14557300418748473641389666083),(-14557300418748473627583499632)⟩⟩,⟨⟨182270090351975544855726197417,182270090351975544872228308580⟩,⟨(-14254250529681451646279075474),(-14254250529681451632680042843)⟩⟩,⟨⟨179840219909120717694203796712,179840219909120717710478276908⟩,⟨(-13952251978297194798785713145),(-13952251978297194785393513382)⟩⟩,⟨⟨177386937305604389427426500982,177386937305604389443437008475⟩,⟨(-13653355352837984752563977472),(-13653355352837984739382177009)⟩⟩,⟨⟨174883995508394585174825879521,174883995508394585190578280536⟩,⟨(-13355525177213708924500882824),(-13355525177213708911530995802)⟩⟩,⟨⟨172359195492072152375770814432,172359195492072152391257287385⟩,⟨(-13060881759698104081158630104),(-13060881759698104068401790828)⟩⟩,⟨⟨169784871155770591523136948276,169784871155770591538353335572⟩,⟨(-12767306424856491828311278460),(-12767306424856491815769864200)⟩⟩,⟨⟨167190332414052911989066044230,167190332414052912003998148773⟩,⟨(-12476993764394877369523732076),(-12476993764394877357199309739)⟩⟩,⟨⟨164546399607492550949022886315,164546399607492550963819092644⟩,⟨(-12187737114995289995415674810),(-12187737114995289983299230494)⟩⟩,⟨⟨161883990679850759555240527440,161883990679850759569758983688⟩,⟨(-11901810587175803869316985841),(-11901810587175803857419428577)⟩⟩,⟨⟨159172306608214890731171551384,159172306608214890745412078601⟩,⟨(-11616914051045788926461938971),(-11616914051045788914785353508)⟩⟩] +lemma amp9_01_12_eq : ∀ k : Fin 16, amp9_0Expr 1 12 k = amp9_01_12 k := by decide +kernel +noncomputable def amp9_01_13 : Fin 16 → CBox := ![⟨⟨156443984581947960124449483156,156443984581947960138414135140⟩,⟨(-11335407145532101509142752906),(-11335407145532101497687311652)⟩⟩,⟨⟨153666487219981670743030690840,153666487219981670756735389796⟩,⟨(-11054889992404904543861515586),(-11054889992404904532628060008)⟩⟩,⟨⟨150874296370014650938181307217,150874296370014650951595946212⟩,⟨(-10777814666830312811784644363),(-10777814666830312800775454144)⟩⟩,⟨⟨148033001824406485098797202841,148033001824406485111929990643⟩,⟨(-10501674319907455519533125458),(-10501674319907455508749715242)⟩⟩,⟨⟨145179072227836692985473943787,145179072227836692998310703640⟩,⟨(-10229021420718776467418442917),(-10229021420718776456861877142)⟩⟩,⟨⟨142276071800021690807995927872,142276071800021690820630933837⟩,⟨(-9957233818058454223450509611),(-9957233818058454213116234671)⟩⟩,⟨⟨139362617965696802228858070175,139362617965696802241207777723⟩,⟨(-9688973569370079960122811832),(-9688973569370079950016583349)⟩⟩,⟨⟨136400074875784146836475030606,136400074875784146848536018251⟩,⟨(-9421493571303331061287389463),(-9421493571303331051411603227)⟩⟩,⟨⟨133429394442438188028791223066,133429394442438188040565192692⟩,⟨(-9157576133452635380530240248),(-9157576133452635370884610121)⟩⟩,⟨⟨130409540159951773704016585424,130409540159951773715510833189⟩,⟨(-8894337971165882765785328720),(-8894337971165882756371461093)⟩⟩,⟨⟨127384012735082403943976108066,127384012735082403955180680180⟩,⟨(-8634694071620776360426834466),(-8634694071620776351245016963)⟩⟩,⟨⟨124309142840555095517523451349,124309142840555095528497782686⟩,⟨(-8375611830585849873735136512),(-8375611830585849864783605828)⟩⟩,⟨⟨121231229079003094524531220944,121231229079003094535202161762⟩,⟨(-8120153471306396401647865679),(-8120153471306396392931096670)⟩⟩,⟨⟨118103698548785723725620963063,118103698548785723735993375077⟩,⟨(-7865121601183851315146740986),(-7865121601183851306666627474)⟩⟩,⟨⟨114975939609167286453416061240,114975939609167286463494918138⟩,⟨(-7613742848740464344598740672),(-7613742848740464336354253904)⟩⟩,⟨⟨111798157368647936302092530208,111798157368647936311867334317⟩,⟨(-7362636688401967952783448536),(-7362636688401967944777640335)⟩⟩] +lemma amp9_01_13_eq : ∀ k : Fin 16, amp9_0Expr 1 13 k = amp9_01_13 k := by decide +kernel +noncomputable def amp9_01_14 : Fin 16 → CBox := ![⟨⟨108623174944359293490766523444,108623174944359293500286361741⟩,⟨(-7115214556521337970024466100),(-7115214556521337962253339752)⟩⟩,⟨⟨105397597463176734957537973328,105397597463176734966756831168⟩,⟨(-6867890858394657474175790098),(-6867890858394657466644720971)⟩⟩,⟨⟨102178094674235493140509065964,102178094674235493149434270103⟩,⟨(-6624286297837598065836740189),(-6624286297837598058544206735)⟩⟩,⟨⟨98907218265895227223567956993,98907218265895227232179788939⟩,⟨(-6380583728966284910862073126),(-6380583728966284903811882283)⟩⟩,⟨⟨95645981838252966883305919808,95645981838252966891651920816⟩,⟨(-6140642747930834026609919839),(-6140642747930834019797825779)⟩⟩,⟨⟨92332333149545203793790643786,92332333149545203801831459812⟩,⟨(-5900382334383674498571889937),(-5900382334383674492003013429)⟩⟩,⟨⟨89032237534754024549730875045,89032237534754024557494492826⟩,⟨(-5663937286076232291168501019),(-5663937286076232284839597224)⟩⟩,⟨⟨85678361420341753071279946072,85678361420341753078733244182⟩,⟨(-5426922749806999818039318796),(-5426922749806999811955280276)⟩⟩,⟨⟨82342375884702641157269270457,82342375884702641164417532449⟩,⟨(-5193793846282766112935953336),(-5193793846282766107094802668)⟩⟩,⟨⟨78950819371192803896308146207,78950819371192803903168417100⟩,⟨(-4959811753947199982725017733),(-4959811753947199977128559762)⟩⟩,⟨⟨75582019731829227625816332862,75582019731829227632366292392⟩,⟨(-4729808904115832934400751238),(-4729808904115832929048404968)⟩⟩,⟨⟨72155309912272385736509673700,72155309912272385742766127447⟩,⟨(-4498628495419628059351873289),(-4498628495419628054245737943)⟩⟩,⟨⟨68756897761275499448207866443,68756897761275499454173496614⟩,⟨(-4271553634847071025612427207),(-4271553634847071020750080219)⟩⟩,⟨⟨65297509875106229344123079765,65297509875106229349773783641⟩,⟨(-4042926102704053611589458476),(-4042926102704053606975752701)⟩⟩,⟨⟨61872844323457997064380851621,61872844323457997069735321152⟩,⟨(-3818576314215594173545794433),(-3818576314215594169176889647)⟩⟩,⟨⟨58383153209769581770630652150,58383153209769581775682599733⟩,⟨(-3592233124806953310099257606),(-3592233124806953305979263440)⟩⟩] +lemma amp9_01_14_eq : ∀ k : Fin 16, amp9_0Expr 1 14 k = amp9_01_14 k := by decide +kernel +noncomputable def amp9_01_15 : Fin 16 → CBox := ![⟨⟨54935804544626330768380431260,54935804544626330773130283168⟩,⟨(-3370405110600690908182334186),(-3370405110600690904308141415)⟩⟩,⟨⟨51418006349442538652696223449,51418006349442538657137043124⟩,⟨(-3146054572773215486661902588),(-3146054572773215483038009116)⟩⟩,⟨⟨47951850290683078210866732775,47951850290683078215002009026⟩,⟨(-2926551596391128864045100445),(-2926551596391128860667595067)⟩⟩,⟨⟨44407827334485770038788306747,44407827334485770042619405475⟩,⟨(-2703872051001439208833800390),(-2703872051001439205707265988)⟩⟩,⟨⟨40927220083475100830912587925,40927220083475100834442300595⟩,⟨(-2486515758282676546849914258),(-2486515758282676543969792204)⟩⟩,⟨⟨37358287825271691764189656661,37358287825271691767409225180⟩,⟨(-2265141719129524053980533568),(-2265141719129524051352727699)⟩⟩,⟨⟨33868417361743168326973764187,33868417361743168329887681668⟩,⟨(-2049794564101097763184679564),(-2049794564101097760803526225)⟩⟩,⟨⟨30274799397741112514114319436,30274799397741112516720561071⟩,⟨(-1829286560222367139761774341),(-1829286560222367137633859835)⟩⟩,⟨⟨26782471259172710143222325364,26782471259172710145525016332⟩,⟨(-1615900331877007178901838210),(-1615900331877007177020148674)⟩⟩,⟨⟨23162049866769122148627049736,23162049866769122150616487577⟩,⟨(-1395671289099782476702457405),(-1395671289099782475075654168)⟩⟩,⟨⟨19677744015863216028805565869,19677744015863216030492621212⟩,⟨(-1184411949326034368404904650),(-1184411949326034367023324090)⟩⟩,⟨⟨16022433859081099922897260850,16022433859081099924268972744⟩,⟨(-963510929833827466103286216),(-963510929833827464978662513)⟩⟩,⟨⟨12567181482434424473072235984,12567181482434424474144436133⟩,⟨(-755172765314776928711553243),(-755172765314776927829824634)⟩⟩,⟨⟨8848419706798893032689345258,8848419706798893033441977944⟩,⟨(-531415469688980891742899448),(-531415469688980891122286900)⟩⟩,⟨⟨5489118996954148587779075076,5489118996954148588238439767⟩,⟨(-329542231969367226016979502),(-329542231969367225632466954)⟩⟩,⟨⟨1559515441983256086761766133,1559515441983256086887765173⟩,⟨(-93609099375948831625482219),(-93609099375948831516512808)⟩⟩] +lemma amp9_01_15_eq : ∀ k : Fin 16, amp9_0Expr 1 15 k = amp9_01_15 k := by decide +kernel +noncomputable def amp9_01 : Fin 16 → Fin 16 → CBox := ![amp9_01_0,amp9_01_1,amp9_01_2,amp9_01_3,amp9_01_4,amp9_01_5,amp9_01_6,amp9_01_7,amp9_01_8,amp9_01_9,amp9_01_10,amp9_01_11,amp9_01_12,amp9_01_13,amp9_01_14,amp9_01_15] +lemma amp9_01_eq (i k : Fin 16) : amp9_0Expr 1 i k = amp9_01 i k := by + fin_cases i + · exact amp9_01_0_eq k + · exact amp9_01_1_eq k + · exact amp9_01_2_eq k + · exact amp9_01_3_eq k + · exact amp9_01_4_eq k + · exact amp9_01_5_eq k + · exact amp9_01_6_eq k + · exact amp9_01_7_eq k + · exact amp9_01_8_eq k + · exact amp9_01_9_eq k + · exact amp9_01_10_eq k + · exact amp9_01_11_eq k + · exact amp9_01_12_eq k + · exact amp9_01_13_eq k + · exact amp9_01_14_eq k + · exact amp9_01_15_eq k +noncomputable def amp9_02_0 : Fin 16 → CBox := ![⟨⟨752741090608955445123022508,752741090608955445258801442⟩,⟨(-309783635300835520001932605),(-309783635300835519880043380)⟩⟩,⟨⟨2649618567617601027427666349,2649618567617601027913241870⟩,⟨(-1090384078917921351035591453),(-1090384078917921350603413577)⟩⟩,⟨⟨4271652924137867923364856934,4271652924137867924153457717⟩,⟨(-1757756433048590261958331823),(-1757756433048590261259247431)⟩⟩,⟨⟨6067955913242831812766161186,6067955913242831813887778059⟩,⟨(-2496635008007367992664554995),(-2496635008007367991670996077)⟩⟩,⟨⟨7738059115552217079735402925,7738059115552217081167669922⟩,⟨(-3183302452159180913538112706),(-3183302452159180912270424286)⟩⟩,⟨⟨9506105053272041830667130072,9506105053272041832427354002⟩,⟨(-3909894395053282240044617870),(-3909894395053282238487190871)⟩⟩,⟨⟨11193160729980066847840153447,11193160729980066849913854925⟩,⟨(-4602725467600047197236000583),(-4602725467600047195402011476)⟩⟩,⟨⟨12947905178745837694219471869,12947905178745837696618496441⟩,⟨(-5322861140762390238307359685),(-5322861140762390236186145305)⟩⟩,⟨⟨14642926722148890148588208212,14642926722148890151301674706⟩,⟨(-6017834219833436499384205246),(-6017834219833436496985637589)⟩⟩,⟨⟨16389430759450253918961162550,16389430759450253921996033221⟩,⟨(-6733274908699897536692958809),(-6733274908699897534009849051)⟩⟩,⟨⟨18088511929847427433127973482,18088511929847427436478286110⟩,⟨(-7428462608637170116034630633),(-7428462608637170113073790526)⟩⟩,⟨⟨19828942123646101802876263657,19828942123646101806548078613⟩,⟨(-8139782299306211990748246497),(-8139782299306211987503791964)⟩⟩,⟨⟨21529934359163815189267386195,21529934359163815193252180240⟩,⟨(-8833984998264612088767042435),(-8833984998264612085246176058)⟩⟩,⟨⟨23265309596030025742442171664,23265309596030025746744482443⟩,⟨(-9541290239441461231267894876),(-9541290239441461227466012289)⟩⟩,⟨⟨24966825789130204942267798020,24966825789130204946884552288⟩,⟨(-10233627042758717124831069211),(-10233627042758717120752686473)⟩⟩,⟨⟨26697616924776496714047156565,26697616924776496718982651345⟩,⟨(-10936804679057980977212184989),(-10936804679057980972853289312)⟩⟩] +lemma amp9_02_0_eq : ∀ k : Fin 16, amp9_0Expr 2 0 k = amp9_02_0 k := by decide +kernel +noncomputable def amp9_02_1 : Fin 16 → CBox := ![⟨⟨28398648759530835035662118034,28398648759530835040909535078⟩,⟨(-11626556877695830415957282302),(-11626556877695830411323603794)⟩⟩,⟨⟨30125028652640462458652335827,30125028652640462464214119162⟩,⟨(-12325377884663294767499924504),(-12325377884663294762588595738)⟩⟩,⟨⟨31824773709394047789125562044,31824773709394047794995530740⟩,⟨(-13011918726766667372950993117),(-13011918726766667367767244252)⟩⟩,⟨⟨33546736048761689550849084470,33546736048761689557038175085⟩,⟨(-13706088031084382889644356325),(-13706088031084382884182165109)⟩⟩,⟨⟨35244510043612919441187676284,35244510043612919447681149013⟩,⟨(-14388847512213722114151215902),(-14388847512213722108419131185)⟩⟩,⟨⟨36961931337444383075222562931,36961931337444383082023308130⟩,⟨(-15078030401009826401963294301),(-15078030401009826395958846388)⟩⟩,⟨⟨38657119431536439568553667622,38657119431536439575667134199⟩,⟨(-15756476112840100534188918009),(-15756476112840100527912277158)⟩⟩,⟨⟨40369793640478122115475026754,40369793640478122122891568960⟩,⟨(-16440313362871605911966649074),(-16440313362871605905420687508)⟩⟩,⟨⟨42061821427468001608341599638,42061821427468001616066822394⟩,⟨(-17113939417537288049676861591),(-17113939417537288042861585755)⟩⟩,⟨⟨43769480326598193439794527046,43769480326598193447832192938⟩,⟨(-17792056527207565437610241038),(-17792056527207565430523264250)⟩⟩,⟨⟨45457795487182887783035315651,45457795487182887791366566995⟩,⟨(-18460376846595903427018170617),(-18460376846595903419669368006)⟩⟩,⟨⟨47160121097022481574473214745,47160121097022481583112700819⟩,⟨(-19132389977871419159774891532),(-19132389977871419152157630713)⟩⟩,⟨⟨48844181194264717116908713696,48844181194264717125834434349⟩,⟨(-19794934082959038253542074826),(-19794934082959038245667427077)⟩⟩,⟨⟨50540813576353335220160003545,50540813576353335229396212562⟩,⟨(-20460454067353999574126462649),(-20460454067353999565984075952)⟩⟩,⟨⟨52220077570636705850488576026,52220077570636705860023085521⟩,⟨(-21116764369090721401163273401),(-21116764369090721392760190239)⟩⟩,⟨⟨53910619802580624807040580565,53910619802580624816877583907⟩,⟨(-21775399522604202537959269299),(-21775399522604202529293422004)⟩⟩] +lemma amp9_02_1_eq : ∀ k : Fin 16, amp9_0Expr 2 1 k = amp9_02_1 k := by decide +kernel +noncomputable def amp9_02_2 : Fin 16 → CBox := ![⟨⟨55584541922073851335495374040,55584541922073851345609480162⟩,⟨(-22425029550945179220207921720),(-22425029550945179211291629146)⟩⟩,⟨⟨57268563301231505015643589952,57268563301231505026059716865⟩,⟨(-23076387727770760426612061773),(-23076387727770760417435026641)⟩⟩,⟨⟨58936588465145650259067755286,58936588465145650269778310496⟩,⟨(-23718900966578546053328580082),(-23718900966578546043895910662)⟩⟩,⟨⟨60613626573115870804339692691,60613626573115870815347462535⟩,⟨(-24362591109869678093405829882),(-24362591109869678083716294871)⟩⟩,⟨⟨62275186877665940954341219488,62275186877665940965646211692⟩,⟨(-24997560234149827813031289731),(-24997560234149827803086919734)⟩⟩,⟨⟨63944748900429145038752003343,63944748900429145050317796507⟩,⟨(-25633193584541045805883432285),(-25633193584541045795698839991)⟩⟩,⟨⟨65599260858704032832984905358,65599260858704032844838942268⟩,⟨(-26260199971170722544224912208),(-26260199971170722533791098389)⟩⟩,⟨⟨67260824416962985790603520591,67260824416962985802740861950⟩,⟨(-26887391036100908229726732494),(-26887391036100908219045787969)⟩⟩,⟨⟨68907686752786437258565737604,68907686752786437270987606174⟩,⟨(-27506024464108464995069104961),(-27506024464108464984142549859)⟩⟩,⟨⟨70560700411286343699092243200,70560700411286343711799604605⟩,⟨(-28124391815787047266740970358),(-28124391815787047255568640297)⟩⟩,⟨⟨72199292274565356575252437633,72199292274565356588241254081⟩,⟨(-28734250300078313262961093364),(-28734250300078313251546608799)⟩⟩,⟨⟨73843175845167467149601360290,73843175845167467162829029344⟩,⟨(-29343417247805243051217518345),(-29343417247805243039578127979)⟩⟩,⟨⟨75472855359092801417069133192,75472855359092801430581119075⟩,⟨(-29944106967972239815448010572),(-29944106967972239803567637817)⟩⟩,⟨⟨77107000077452723028168305468,77107000077452723041957301910⟩,⟨(-30543702136249633432738039248),(-30543702136249633420620000132)⟩⟩,⟨⟨78727103155820439411907743090,78727103155820439425975660507⟩,⟨(-31134837433682652716590077232),(-31134837433682652704235634606)⟩⟩,⟨⟨80350871788386054436559700239,80350871788386054450890829732⟩,⟨(-31724495268137345672382924452),(-31724495268137345659798790039)⟩⟩] +lemma amp9_02_2_eq : ∀ k : Fin 16, amp9_0Expr 2 2 k = amp9_02_2 k := by decide +kernel +noncomputable def amp9_02_3 : Fin 16 → CBox := ![⟨⟨81960711179847413146369872814,81960711179847413160969924837⟩,⟨(-32305698692395420417245771758),(-32305698692395420404431706320)⟩⟩,⟨⟨83573438102217768150591375310,83573438102217768165461207478⟩,⟨(-32885059909187538562090849205),(-32885059909187538549047103335)⟩⟩,⟨⟨85172302630801084119195654757,85172302630801084134332890169⟩,⟨(-33455962299849386878901798907),(-33455962299849386865631341562)⟩⟩,⟨⟨86773293907645469575464812089,86773293907645469590795428670⟩,⟨(-34024674289889249675147196448),(-34024674289889249661679725508)⟩⟩,⟨⟨88360447887500187762485081955,88360447887500187778083516512⟩,⟨(-34584914883759463486606261915),(-34584914883759463472914585695)⟩⟩,⟨⟨89948981376586003091263045422,89948981376586003107121561768⟩,⟨(-35142632080018527020322420379),(-35142632080018527006410320273)⟩⟩,⟨⟨91523664184882791984351810667,91523664184882792000465945834⟩,⟨(-35691858636139516165743950728),(-35691858636139516151615222255)⟩⟩,⟨⟨93098989682257366172993311818,93098989682257366189358424592⟩,⟨(-36238242850190588072336514560),(-36238242850190588057993787076)⟩⟩,⟨⟨94660415478379246996207015214,94660415478379247012823734943⟩,⟨(-36776111786955339656942403618),(-36776111786955339642387491873)⟩⟩,⟨⟨96221754917716353951959466382,96221754917716353968808169131⟩,⟨(-37310832519333562228145972089),(-37310832519333562213387383217)⟩⟩,⟨⟨97769112499846303314269889199,97769112499846303331364331146⟩,⟨(-37837009059334329351937731381),(-37837009059334329336972193432)⟩⟩,⟨⟨99315660215954264174162996032,99315660215954264191494025058⟩,⟨(-38359743787188607365093120544),(-38359743787188607349925133043)⟩⟩,⟨⟨100848113008272486066353558095,100848113008272486083920709933⟩,⟨(-38873902106423422563046079073),(-38873902106423422547677898250)⟩⟩,⟨⟨102379036072466122528734416729,102379036072466122546535112647⟩,⟨(-39384336551103756209468814672),(-39384336551103756193902458613)⟩⟩,⟨⟨103895722237665022390048133837,103895722237665022408080220023⟩,⟨(-39886159929898664441754217976),(-39886159929898664425992608351)⟩⟩,⟨⟨105410160870922715608618508124,105410160870922715626879048697⟩,⟨(-40383988306513330538056595467),(-40383988306513330522101946785)⟩⟩] +lemma amp9_02_3_eq : ∀ k : Fin 16, amp9_0Expr 2 3 k = amp9_02_3 k := by decide +kernel +noncomputable def amp9_02_4 : Fin 16 → CBox := ![⟨⟨106910193543801517059306139072,106910193543801517077677649160⟩,⟨(-40873169280073945188305145035),(-40873169280073945172204478785)⟩⟩,⟨⟨108407261612219029528970308599,108407261612219029547582904147⟩,⟨(-41358094530592833441491600672),(-41358094530592833425196245296)⟩⟩,⟨⟨109889729250853083527163307118,109889729250853083546008753753⟩,⟨(-41834335037523380694145263263),(-41834335037523380677660502638)⟩⟩,⟨⟨111368514846768013322788974494,111368514846768013341860625161⟩,⟨(-42306069048658748564200846305),(-42306069048658748547530436459)⟩⟩,⟨⟨112832481698245188568335711787,112832481698245188587628334390⟩,⟨(-42769080576114876783040533045),(-42769080576114876766188601403)⟩⟩,⟨⟨114292047809469377118525285793,114292047809469377138040555427⟩,⟨(-43227344382948996026924311891),(-43227344382948996009891505790)⟩⟩,⟨⟨115736554487508436719875464286,115736554487508436739598118640⟩,⟨(-43676848107347071321062338016),(-43676848107347071303856579476)⟩⟩,⟨⟨117175939756319820302944163883,117175939756319820322879656711⟩,⟨(-44121372083476610194149080816),(-44121372083476610176769637073)⟩⟩,⟨⟨118600003928277599209238604604,118600003928277599229385300097⟩,⟨(-44557099005884894850280389419),(-44557099005884894832730038383)⟩⟩,⟨⟨120018223501151367747094440154,120018223501151367767415305335⟩,⟨(-44987623040699086173044275985),(-44987623040699086155338293183)⟩⟩,⟨⟨121420840682019321652818611005,121420840682019321673346376051⟩,⟨(-45409314116198159753632406404),(-45409314116198159735760672954)⟩⟩,⟨⟨122816887150494215969508134108,122816887150494215990233771984⟩,⟨(-45825587779790596392173821968),(-45825587779790596374141150530)⟩⟩,⟨⟨124197031601504606463662564717,124197031601504606484585957341⟩,⟨(-46232994040221245977909797848),(-46232994040221245959718411059)⟩⟩,⟨⟨125569876034064210607877594858,125569876034064210628982746034⟩,⟨(-46634776736345183827575427458),(-46634776736345183809232758148)⟩⟩,⟨⟨126926501763489906712309699950,126926501763489906733606715148⟩,⟨(-47027659405968905038877685506),(-47027659405968905020382163402)⟩⟩,⟨⟨128275094827876442015111393253,128275094827876442036589217617⟩,⟨(-47414720513377003452941429948),(-47414720513377003434298677405)⟩⟩] +lemma amp9_02_4_eq : ∀ k : Fin 16, amp9_0Expr 2 4 k = amp9_02_4 k := by decide +kernel +noncomputable def amp9_02_5 : Fin 16 → CBox := ![⟨⟨129607136691529779082319777693,129607136691529779103978385469⟩,⟨(-47792851117062570527010074620),(-47792851117062570508222286606)⟩⟩,⟨⟨130930409866488463575719137108,130930409866488463597555320013⟩,⟨(-48164970119519357034144388303),(-48164970119519357015214323443)⟩⟩,⟨⟨132236784765314337510849419662,132236784765314337532862903303⟩,⟨(-48528130583142679979691446506),(-48528130583142679960621409005)⟩⟩,⟨⟨133533651640381848632728327863,133533651640381848654914987242⟩,⟨(-48885097188358111872835263743),(-48885097188358111853628384895)⟩⟩,⟨⟨134813259812406406457519408930,134813259812406406479876666454⟩,⟨(-49233079931164875161033720784),(-49233079931164875141693149655)⟩⟩,⟨⟨136082617474001406189590709113,136082617474001406211878365283⟩,⟨(-49574694178867441820923953485),(-49574694178867441801538861692)⟩⟩,⟨⟨137334343877746732155310967070,137334343877746732177775006273⟩,⟨(-49907302197601165380695475742),(-49907302197601165361178265755)⟩⟩,⟨⟨138575074379489316513028810120,138575074379489316535659994243⟩,⟨(-50233374556946912781766620971),(-50233374556946912762122364788)⟩⟩,⟨⟨139797790165801490664128126843,139797790165801490686918391361⟩,⟨(-50550421501590905186618061004),(-50550421501590905166851900733)⟩⟩,⟨⟨141008762080678473553891092260,141008762080678473576836622886⟩,⟨(-50860772958088918710985320883),(-50860772958088918691100381514)⟩⟩,⟨⟨142201326149745376023454651407,142201326149745376046545534034⟩,⟨(-51162083199110509231264162814),(-51162083199110509211266237951)⟩⟩,⟨⟨143381396201447026579364274172,143381396201447026602596111504⟩,⟨(-51456545331234470096099736719),(-51456545331234470075992169089)⟩⟩,⟨⟨144542656841606585828529357841,144542656841606585851906245192⟩,⟨(-51741954018255005253158073630),(-51741954018255005232941603996)⟩⟩,⟨⟨145690671612085969975732198025,145690671612085969999238684042⟩,⟨(-52020369063903419394577126427),(-52020369063903419374259089286)⟩⟩,⟨⟨146819468216847922586934580918,146819468216847922610574102354⟩,⟨(-52289722175748647761042715827),(-52289722175748647740624092593)⟩⟩,⟨⟨147934265926895006700660378739,147934265926895006724431931817⟩,⟨(-52551943088712423341511823740),(-52551943088712423320994803898)⟩⟩] +lemma amp9_02_5_eq : ∀ k : Fin 16, amp9_0Expr 2 5 k = amp9_02_5 k := by decide +kernel +noncomputable def amp9_02_6 : Fin 16 → CBox := ![⟨⟨149029430786421903410935447234,149029430786421903434809071069⟩,⟨(-52805097474825743649806203505),(-52805097474825743629203612987)⟩⟩,⟨⟨150109843145800088430184841426,150109843145800088454188278607⟩,⟨(-53050987971420316110129576080),(-53050987971420316089433440197)⟩⟩,⟨⟨151170203308918135191996607912,151170203308918135216109654477⟩,⟨(-53287811384646460700993169083),(-53287811384646460680212836097)⟩⟩,⟨⟨152215057432380217566258614196,152215057432380217590493658528⟩,⟨(-53517245980666110477873215507),(-53517245980666110457006203972)⟩⟩,⟨⟨153239436635019181903199221462,153239436635019181927543224965⟩,⟨(-53737617101435600955073638896),(-53737617101435600934126732046)⟩⟩,⟨⟨154247557020302415910006066507,154247557020302415934460393857⟩,⟨(-53950481139589555674843343746),(-53950481139589555653817986228)⟩⟩,⟨⟨155234777676097626080834365580,155234777676097626105310758280⟩,⟨(-54154289591555036345321703951),(-54154289591555036324250891187)⟩⟩,⟨⟨156204988239793289078590483020,156204988239793289103177022361⟩,⟨(-54350479259548051592438506483),(-54350479259548051571293383246)⟩⟩,⟨⟨157153873488422886658254071359,157153873488422886682938291719⟩,⟨(-54537625616742647180738320522),(-54537625616742647159525410815)⟩⟩,⟨⟨158084999655424348951597727579,158084999655424348976371544869⟩,⟨(-54717047956166734825525204585),(-54717047956166734804249285920)⟩⟩,⟨⟨158994375464102449748168536777,158994375464102449773032909767⟩,⟨(-54887443741772107013131860994),(-54887443741772106991794780662)⟩⟩,⟨⟨159885246306157141891384328613,159885246306157141916326021861⟩,⟨(-55050016647980693910884001776),(-55050016647980693889492304538)⟩⟩,⟨⟨160753943619559312250915544310,160753943619559312275935369181⟩,⟨(-55203584324808659227203007390),(-55203584324808659205758561351)⟩⟩,⟨⟨161603394038284151481868234712,161603394038284151506968563248⟩,⟨(-55349236537949517770907376671),(-55349236537949517749411379565)⟩⟩,⟨⟨162430250972046405008507719479,162430250972046405033642967145⟩,⟨(-55485909490756076568133817471),(-55485909490756076546604006884)⟩⟩,⟨⟨163237123921613224697386870126,163237123921613224722590672667⟩,⟨(-55614580578144709872044582658),(-55614580578144709850471450493)⟩⟩] +lemma amp9_02_6_eq : ∀ k : Fin 16, amp9_0Expr 2 6 k = amp9_02_6 k := by decide +kernel +noncomputable def amp9_02_7 : Fin 16 → CBox := ![⟨⟨164020987994420283370909066807,164020987994420283396172572970⟩,⟨(-55734303087909235320705251052),(-55734303087909235299093931773)⟩⟩,⟨⟨164784136738977673611857394737,164784136738977673637182246518⟩,⟨(-55845943417929887342589399864),(-55845943417929887320941380491)⟩⟩,⟨⟨165523867138141131820025210748,165523867138141131845384588022⟩,⟨(-55948670628245126270286103430),(-55948670628245126248612579381)⟩⟩,⟨⟨166242157538911934737084267779,166242157538911934762492930433⟩,⟨(-56043241335972105586004095497),(-56043241335972105564302100019)⟩⟩,⟨⟨166936627414234758618844338814,166936627414234758644284220221⟩,⟨(-56128939211702624505700953827),(-56128939211702624483978651907)⟩⟩,⟨⟨167608940241114367893067450946,167608940241114367918550456545⟩,⟨(-56206412156440081571532924754),(-56206412156440081549788368829)⟩⟩,⟨⟨168257039021745336254205760080,168257039021745336279716733147⟩,⟨(-56275057434817913129786812337),(-56275057434817913108027161794)⟩⟩,⟨⟨168882272284125027865658178547,168882272284125027891193800715⟩,⟨(-56335415149761510673264152031),(-56335415149761510651492562972)⟩⟩,⟨⟨169482908013025698458102375048,169482908013025698483659296830⟩,⟨(-56386995284098069307105093562),(-56386995284098069285324711239)⟩⟩,⟨⟨170059979304477564611812112793,170059979304477564637389073231⟩,⟨(-56430230918327061586819056947),(-56430230918327061565032381409)⟩⟩,⟨⟨170612080985055502462365671170,170612080985055502487953033094⟩,⟨(-56464744014529945610409043072),(-56464744014529945588621300027)⟩⟩,⟨⟨171139929836441258234699708135,171139929836441258260295405861⟩,⟨(-56490861267542971906075862901),(-56490861267542971884289798033)⟩⟩,⟨⟨171642449785846914768871743251,171642449785846914794466493684⟩,⟨(-56508316013635089530113957811),(-56508316013635089508334616313)⟩⟩,⟨⟨172120040021351966651818593296,172120040021351966677407288837⟩,⟨(-56517329062647435540147084205),(-56517329062647435518378225958)⟩⟩,⟨⟨172571956224893028896393933054,172571956224893028921968102639⟩,⟨(-56517744651494016773649847934),(-56517744651494016751896219371)⟩⟩,⟨⟨172998278315439785934044501656,172998278315439785959594525596⟩,⟨(-56509678071718156336306837085),(-56509678071718156314573640898)⟩⟩] +lemma amp9_02_7_eq : ∀ k : Fin 16, amp9_0Expr 2 7 k = amp9_02_7 k := by decide +kernel +noncomputable def amp9_02_8 : Fin 16 → CBox := ![⟨⟨173398596776536261837140272498,173398596776536261862680838612⟩,⟨(-56493084117174670305822123363),(-56493084117174670284106477867)⟩⟩,⟨⟨173772670184996760069046820452,173772670184996760094593396453⟩,⟨(-56467972795309526122698888013),(-56467972795309526100997879727)⟩⟩,⟨⟨174120427265082727684971456103,174120427265082727710514085948⟩,⟨(-56434409242010340827405063055),(-56434409242010340805723886454)⟩⟩,⟨⟨174441302777690227531430179817,174441302777690227556960929230⟩,⟨(-56392298283167858106792819735),(-56392298283167858085136151356)⟩⟩,⟨⟨174735567520464214561635762804,174735567520464214587149012818⟩,⟨(-56341815310181682537897351588),(-56341815310181682516268904395)⟩⟩,⟨⟨175002329558816490029624040440,175002329558816490055111091320⟩,⟨(-56282759938481958588410489205),(-56282759938481958566815185655)⟩⟩,⟨⟨175242205993251993653864086129,175242205993251993679322538796⟩,⟨(-56215417857065720656623728434),(-56215417857065720635064220553)⟩⟩,⟨⟨175453974901305501745608863905,175453974901305501771029452526⟩,⟨(-56139483310134043964450045752),(-56139483310134043942931396046)⟩⟩,⟨⟨175638604317856302279578675869,175638604317856302304959658075⟩,⟨(-56055352455821907442440198957),(-56055352455821907420964780044)⟩⟩,⟨⟨175794538618330206800695416266,175794538618330206826034214162⟩,⟨(-55962613873422601011716861454),(-55962613873422600990287614431)⟩⟩,⟨⟨175923101812801938025212530785,175923101812801938050505494141⟩,⟨(-55861774492691337591677641361),(-55861774492691337570297544858)⟩⟩,⟨⟨176022400427443933941683147905,176022400427443933966915111723⟩,⟨(-55752316799734243738972848421),(-55752316799734243717648797242)⟩⟩,⟨⟨176094119907053886049548322511,176094119907053886074731538144⟩,⟨(-55634858931490181220755427163),(-55634858931490181199485294958)⟩⟩,⟨⟨176136024335265759823127697716,176136024335265759848244006693⟩,⟨(-55508776715645939302460134109),(-55508776715645939281251763902)⟩⟩,⟨⟨176150166481477121151664053434,176150166481477121176729086251⟩,⟨(-55374800067782235559849910759),(-55374800067782235538700126799)⟩⟩,⟨⟨176133962931856779102180653824,176133962931856779127166639428⟩,⟨(-55232197451942160448495576792),(-55232197451942160427415186808)⟩⟩] +lemma amp9_02_8_eq : ∀ k : Fin 16, amp9_0Expr 2 8 k = amp9_02_8 k := by decide +kernel +noncomputable def amp9_02_9 : Fin 16 → CBox := ![⟨⟨176089840114651461796354115521,176089840114651461821262496224⟩,⟨(-55081811273218240514120412745),(-55081811273218240493110626436)⟩⟩,⟨⟨176014861584079508518743657393,176014861584079508543565955831⟩,⟨(-54922801783033576758918695970),(-54922801783033576737984258310)⟩⟩,⟨⟨175911834222425324473989860760,175911834222425324498762610396⟩,⟨(-54756124730531257050258812861),(-54756124730531257029390012714)⟩⟩,⟨⟨175777462517407875525963858050,175777462517407875550638518087⟩,⟨(-54580831157264827833897520756),(-54580831157264827813111543267)⟩⟩,⟨⟨175614941080781091842189865264,175614941080781091866768822082⟩,⟨(-54397991159677982788218472429),(-54397991159677982767516167130)⟩⟩,⟨⟨175420608775856007268185850341,175420608775856007292671163398⟩,⟨(-54206545418598736673362021668),(-54206545418598736652744826907)⟩⟩,⟨⟨175198055721799165343381681272,175198055721799165367758767220⟩,⟨(-54007679535615391324182680772),(-54007679535615391303656688305)⟩⟩,⟨⟨174943248049919885738904291865,174943248049919885763175249104⟩,⟨(-53800222520163031010031818611),(-53800222520163030989598414604)⟩⟩,⟨⟨174660179692747162149726591252,174660179692747162173882278053⟩,⟨(-53585476798200549122057691195),(-53585476798200549101721192259)⟩⟩,⟨⟨174344436362676348823265510494,174344436362676348847293213367⟩,⟨(-53362158230143255993802348892),(-53362158230143255973568707249)⟩⟩,⟨⟨174000424668584620251961979189,174000424668584620275961064537⟩,⟨(-53131687554698908185637184737),(-53131687554698908165477546663)⟩⟩,⟨⟨173623341604458310238375966225,173623341604458310262248417879⟩,⟨(-52892665830502096686638470006),(-52892665830502096666584843506)⟩⟩,⟨⟨173218015908461422395568552957,173218015908461422419315895484⟩,⟨(-52646633775382819670428119435),(-52646633775382819650481469226)⟩⟩,⟨⟨172779246906822796763542118044,172779246906822796787150856291⟩,⟨(-52392075809000797735915415007),(-52392075809000797716081874542)⟩⟩,⟨⟨172312295547099315093246419007,172312295547099315116730899371⟩,⟨(-52130654482697492443957357108),(-52130654482697492424233996203)⟩⟩,⟨⟨171811553846848748611909263774,171811553846848748635247575026⟩,⟨(-51860735544992785614614083008),(-51860735544992785595009526195)⟩⟩] +lemma amp9_02_9_eq : ∀ k : Fin 16, amp9_0Expr 2 9 k = amp9_02_9 k := by decide +kernel +noncomputable def amp9_02_10 : Fin 16 → CBox := ![⟨⟨171282725712279709256564821973,171282725712279709279789041305⟩,⟨(-51584105434466164782220807215),(-51584105434466164762726716820)⟩⟩,⟨⟨170719785473143725912973985440,170719785473143725936051069906⟩,⟨(-51299008989452981585462712364),(-51299008989452981566091083696)⟩⟩,⟨⟨170128891460016683964682043042,170128891460016683987611074896⟩,⟨(-51007358801599904792278547825),(-51007358801599904773030986607)⟩⟩,⟨⟨169503589145301876078419723305,169503589145301876101206142427⟩,⟨(-50707276339698656516834431004),(-50707276339698656497711283897)⟩⟩,⟨⟨168850503519371012046940163905,168850503519371012069566005538⟩,⟨(-50400802840770248621315129891),(-50400802840770248602323026368)⟩⟩,⟨⟨168162739178938845307604905940,168162739178938845330076588784⟩,⟨(-50085933709249036403731110648),(-50085933709249036384870126978)⟩⟩,⟨⟨167447400839258285299071950973,167447400839258285321384635830⟩,⟨(-49764841562494873497500278461),(-49764841562494873478773101120)⟩⟩,⟨⟨166697139288831800513793629212,166697139288831800535937034955⟩,⟨(-49435392793261232680869970957),(-49435392793261232662281601458)⟩⟩,⟨⟨165919552930021005942246554436,165919552930021005964216256095⟩,⟨(-49099894395077740051369713230),(-49099894395077740032922607184)⟩⟩,⟨⟨165106824823113337365561376169,165106824823113337387349410614⟩,⟨(-48756080529969453947692222383),(-48756080529969453929390705488)⟩⟩,⟨⟨164267061992969971654810744040,164267061992969971676406288459⟩,⟨(-48406395844835687689692237620),(-48406395844835687671540635007)⟩⟩,⟨⟨163391964781905688757848262214,163391964781905688779550926652⟩,⟨(-48048438758542860892202451645),(-48048438758542860874114558946)⟩⟩,⟨⟨162490164831553539365278205017,162490164831553539386798268230⟩,⟨(-47684795153033399655227248563),(-47684795153033399637289497841)⟩⟩,⟨⟨161552863614235145087156958155,161552863614235145108493083855⟩,⟨(-47312923873764852938120902761),(-47312923873764852920335627716)⟩⟩,⟨⟨160589234538283526452515952436,160589234538283526473663535574⟩,⟨(-46935555949938053567273934191),(-46935555949938053549643529681)⟩⟩,⟨⟨159589962787534702164690819387,159589962787534702185651221964⟩,⟨(-46550006477923013443069315022),(-46550006477923013425595277161)⟩⟩] +lemma amp9_02_10_eq : ∀ k : Fin 16, amp9_0Expr 2 10 k = amp9_02_10 k := by decide +kernel +noncomputable def amp9_02_11 : Fin 16 → CBox := ![⟨⟨158564781952032721779968549776,158564781952032721800738085154⟩,⟨(-46159155906393935326070998212),(-46159155906393935308755352539)⟩⟩,⟨⟨157503842124524323563934186226,157503842124524323584514819992⟩,⟨(-45760171030284367833526055494),(-45760171030284367816370165146)⟩⟩,⟨⟨156417456880820380754210710987,156417456880820380774589222282⟩,⟨(-45356086383305933423146270164),(-45356086383305933406154924123)⟩⟩,⟨⟨155295220902751397226380674005,155295220902751397246571477095⟩,⟨(-44943915494514986804660280194),(-44943915494514986787831171675)⟩⟩,⟨⟨154148049085717860449838331962,154148049085717860469821802477⟩,⟨(-44526852079409283557115394553),(-44526852079409283540455065544)⟩⟩,⟨⟨152964958712577414095015143249,152964958712577414114793124590⟩,⟨(-44101750984386232799091455685),(-44101750984386232782601264606)⟩⟩,⟨⟨151757489022035977729300481840,151757489022035977748862097165⟩,⟨(-43671970677691365837316540014),(-43671970677691365821000460931)⟩⟩,⟨⟨150514056069908882480868640045,150514056069908882500257268417⟩,⟨(-43234201408092009714620481466),(-43234201408092009698467889810)⟩⟩,⟨⟨149246848334498120600119529466,149246848334498120619288611635⟩,⟨(-42791972490819973032854873265),(-42791972490819973016879899362)⟩⟩,⟨⟨147943654780489111205565837041,147943654780489111224515393776⟩,⟨(-42341803111482098570506042297),(-42341803111482098554710554882)⟩⟩,⟨⟨146617340103658147445311157785,146617340103658147464048712226⟩,⟨(-41887400105921523688791759126),(-41887400105921523673174340001)⟩⟩,⟨⟨145255038053090601716123721543,145255038053090601734631649955⟩,⟨(-41425104520495853980487958341),(-41425104520495853965055459943)⟩⟩,⟨⟨143870318841389437347819593872,143870318841389437366100387861⟩,⟨(-40958808029042512652609875999),(-40958808029042512637362220733)⟩⟩,⟨⟨142449630359472922546551718204,142449630359472922564600752822⟩,⟨(-40484665783057927854417468491),(-40484665783057927839357814021)⟩⟩,⟨⟨141007280233851200634620277977,141007280233851200652429419421⟩,⟨(-40006762329618491236040060597),(-40006762329618491221171330142)⟩⟩,⟨⟨139528997039495214059212890527,139528997039495214076773361707⟩,⟨(-39521058410672900203947390524),(-39521058410672900189273856572)⟩⟩] +lemma amp9_02_11_eq : ∀ k : Fin 16, amp9_0Expr 2 11 k = amp9_02_11 k := by decide +kernel +noncomputable def amp9_02_12 : Fin 16 → CBox := ![⟨⟨138029860630930874529399178125,138029860630930874546881558180⟩,⟨(-39031840285267595719304593980),(-39031840285267595704778513372)⟩⟩,⟨⟨136494843650292427703578321141,136494843650292427720831594530⟩,⟨(-38534864919928205271963205414),(-38534864919928205257629196107)⟩⟩,⟨⟨134939836281768314827847426480,134939836281768314844868291777⟩,⟨(-38034630027220819792844655553),(-38034630027220819778704155288)⟩⟩,⟨⟨133349015058935788756178934497,133349015058935788772966677559⟩,⟨(-37526678474083808476629618323),(-37526678474083808462684609712)⟩⟩,⟨⟨131739122316590668354899041556,131739122316590668371450630136⟩,⟨(-37015730186699826390622002041),(-37015730186699826376873744750)⟩⟩,⟨⟨130093494278495420589675789309,130093494278495420605992936583⟩,⟨(-36497102524891684994388708256),(-36497102524891684980838534089)⟩⟩,⟨⟨128429771475729696782267161487,128429771475729696798338200846⟩,⟨(-35975749542556442085989759069),(-35975749542556442072641321046)⟩⟩,⟨⟨126730401047899643114263715395,126730401047899643130109214976⟩,⟨(-35446750454746823110263286747),(-35446750454746823097112593800)⟩⟩,⟨⟨125013972587361220883556222427,125013972587361220899150219439⟩,⟨(-34915306670497901754535866458),(-34915306670497901741590451422)⟩⟩,⟨⟨123261990156431958056480898144,123261990156431958071826620331⟩,⟨(-34376245219222168518057376334),(-34376245219222168505318143805)⟩⟩,⟨⟨121494048796207287556061507474,121494048796207287571153139540⟩,⟨(-33835029594240970950066234897),(-33835029594240970937535052533)⟩⟩,⟨⟨119690649514110670819936351598,119690649514110670834770042767⟩,⟨(-33286218989979702005894631033),(-33286218989979701993574322268)⟩⟩,⟨⟨117872455546187641916681397397,117872455546187641931246861463⟩,⟨(-32735555438969895146845719102),(-32735555438969895134739278226)⟩⟩,⟨⟨116018897969540140003384640852,116018897969540140017785593757⟩,⟨(-32177312797974465600843311435),(-32177312797974465588923753954)⟩⟩,⟨⟨114151778320816046733934222687,114151778320816046748070430135⟩,⟨(-31617530087522920303923885896),(-31617530087522920292219149493)⟩⟩,⟨⟨112249382877082224388725161716,112249382877082224402595579862⟩,⟨(-31050176176771643911503181281),(-31050176176771643900015302937)⟩⟩] +lemma amp9_02_12_eq : ∀ k : Fin 16, amp9_0Expr 2 12 k = amp9_02_12 k := by decide +kernel +noncomputable def amp9_02_13 : Fin 16 → CBox := ![⟨⟨110334730146035769500255628068,110334730146035769513861504924⟩,⟨(-30481607839807493079849036605),(-30481607839807493068577650665)⟩⟩,⟨⟨108384877415336089054062838589,108384877415336089067414503658⟩,⟨(-29905466805669651547052531879),(-29905466805669651535996592604)⟩⟩,⟨⟨106424148861217577723525049633,106424148861217577736601127137⟩,⟨(-29328451076056413116254155121),(-29328451076056413105419515375)⟩⟩,⟨⟨104428277658881762044984838013,104428277658881762057790198544⟩,⟨(-28743850152150938262146668128),(-28743850152150938251533741947)⟩⟩,⟨⟨102422994165264323106703089611,102422994165264323119227624043⟩,⟨(-28158729924703042339376141807),(-28158729924703042328987546409)⟩⟩,⟨⟨100382599404958987110021675544,100382599404958987122330986638⟩,⟨(-27565999112946202618444983174),(-27565999112946202608264502095)⟩⟩,⟨⟨98334344446273312143202641139,98334344446273312155237739580⟩,⟨(-26973121935898930160240854738),(-26973121935898930150284493847)⟩⟩,⟨⟨96250974756097388114747044817,96250974756097388126504588682⟩,⟨(-26372593652664972604163838543),(-26372593652664972594434295751)⟩⟩,⟨⟨94161393405149062944944889354,94161393405149062956426065867⟩,⟨(-25772311762061903855850980067),(-25772311762061903846347586516)⟩⟩,⟨⟨92036648458498225988057617362,92036648458498225999266655412⟩,⟨(-25164320438465933978208880968),(-25164320438465933968932325435)⟩⟩,⟨⟨89907446486169819667181697936,89907446486169819678111626026⟩,⟨(-24556990847390166243321719240),(-24556990847390166234273516324)⟩⟩,⟨⟨87742973993891190981585003276,87742973993891190992276828258⟩,⟨(-23941872468533711130762592049),(-23941872468533711121933376560)⟩⟩,⟨⟨85575917131172237535470378090,85575917131172237545872568049⟩,⟨(-23327857129110666854876987781),(-23327857129110666846280305671)⟩⟩,⟨⟨83373409419160655609247259640,83373409419160655619362298031⟩,⟨(-22705948691063811681684785309),(-22705948691063811673321842099)⟩⟩,⟨⟨81170322879360580558002901493,81170322879360580567834467008⟩,⟨(-22085614754517298595952736042),(-22085614754517298587821929133)⟩⟩,⟨⟨78931512942433685619394938969,78931512942433685628934645116⟩,⟨(-21457253608814522150061701762),(-21457253608814522142167202514)⟩⟩] +lemma amp9_02_13_eq : ∀ k : Fin 16, amp9_0Expr 2 13 k = amp9_02_13 k := by decide +kernel +noncomputable def amp9_02_14 : Fin 16 → CBox := ![⟨⟨76694281342839049169937748850,76694281342839049179220471300⟩,⟨(-20830973819883225875742842627),(-20830973819883225868074419816)⟩⟩,⟨⟨74420938215138110700847584779,74420938215138110709839853450⟩,⟨(-20196496861686558366124913308),(-20196496861686558358693643409)⟩⟩,⟨⟨72151506100671429549169484670,72151506100671429557876773283⟩,⟨(-19564650140601382632236509759),(-19564650140601382625040067217)⟩⟩,⟨⟨69845429304284926484301915380,69845429304284926492709276641⟩,⟨(-18924392775571865307152509897),(-18924392775571865300196941267)⟩⟩,⟨⟨67545802574934915991966492313,67545802574934916000107865733⟩,⟨(-18287365067314172796551498183),(-18287365067314172789826606253)⟩⟩,⟨⟨65208815283367778815270689031,65208815283367778823117236394⟩,⟨(-17641659858656647876308688180),(-17641659858656647869824378483)⟩⟩,⟨⟨62881063987061241532401003613,62881063987061241539972948892⟩,⟨(-16999845372000998803630765675),(-16999845372000998797380439661)⟩⟩,⟨⟨60515004335227173214130713050,60515004335227173221403566312⟩,⟨(-16349020214172862660085121113),(-16349020214172862654077555198)⟩⟩,⟨⟨58161267553712704367838910133,58161267553712704374816942591⟩,⟨(-15702823244206600958676950984),(-15702823244206600952909658052)⟩⟩,⟨⟨55767977179120681705851607345,55767977179120681712545720154⟩,⟨(-15047198816744978623516192902),(-15047198816744978617988525704)⟩⟩,⟨⟨53390471192600893128194035106,53390471192600893134589116159⟩,⟨(-14397036467266120791550770880),(-14397036467266120786265312901)⟩⟩,⟨⟨50971779482293182782103063423,50971779482293182788209769900⟩,⟨(-13736922558656003726706130703),(-13736922558656003721662405807)⟩⟩,⟨⟨48572811220923146007896980185,48572811220923146013717973638⟩,⟨(-13083228901153424394471815047),(-13083228901153424389667367791)⟩⟩,⟨⟨46130512617983276431855610401,46130512617983276437372574495⟩,⟨(-12418918892310122229988811498),(-12418918892310122225431165016)⟩⟩,⟨⟨43712501956394826157968192148,43712501956394826163195244343⟩,⟨(-11762151512974700331571901751),(-11762151512974700327255269879)⟩⟩,⟨⟨41248321512376485937633414969,41248321512376485942564711627⟩,⟨(-11093913729100181441252101429),(-11093913729100181437180842380)⟩⟩] +lemma amp9_02_14_eq : ∀ k : Fin 16, amp9_0Expr 2 14 k = amp9_02_14 k := by decide +kernel +noncomputable def amp9_02_15 : Fin 16 → CBox := ![⟨⟨38813839045860125572494042396,38813839045860125577130955975⟩,⟨(-10434564441209975381559029992),(-10434564441209975377730445557)⟩⟩,⟨⟨36329376948289464008114688712,36329376948289464012450787184⟩,⟨(-9762627886445305987090063071),(-9762627886445305983508974801)⟩⟩,⟨⟨33881210455995821810806690594,33881210455995821814845723274⟩,⟨(-9101241144963221452719799013),(-9101241144963221449382494724)⟩⟩,⟨⟨31377846384643951770054970766,31377846384643951773796179113⟩,⟨(-8425770488118191521610717504),(-8425770488118191518520844958)⟩⟩,⟨⟨28919124383827172169063035507,28919124383827172172509934606⟩,⟨(-7762977115742381378599863322),(-7762977115742381375753247632)⟩⟩,⟨⟨26397838543475809178230260793,26397838543475809181374688089⟩,⟨(-7084025363010623348603150048),(-7084025363010623346005960417)⟩⟩,⟨⟨23932278392163434054061541781,23932278392163434056908571349⟩,⟨(-6420609661129616078492444422),(-6420609661129616076139406049)⟩⟩,⟨⟨21393280349394913653688702094,21393280349394913656234553588⟩,⟨(-5738019342107921949761149026),(-5738019342107921947657992815)⟩⟩,⟨⟨18925743387549605252292984109,18925743387549605254542972935⟩,⟨(-5075068482803261912195255955),(-5075068482803261910335628847)⟩⟩,⟨⟨16367588945757346133385375474,16367588945757346135329721973⟩,⟨(-4388235667739314317910105765),(-4388235667739314316302531915)⟩⟩,⟨⟨13905533889722180873065240814,13905533889722180874714828479⟩,⟨(-3727529779818209545413691854),(-3727529779818209544048744392)⟩⟩,⟨⟨11322562292305581120109001023,11322562292305581121450733346⟩,⟨(-3034718041105273060454490792),(-3034718041105273059343611442)⟩⟩,⟨⟨8880904787393590073429058586,8880904787393590074478797481⟩,⟨(-2380032976657235971314208136),(-2380032976657235970443674563)⟩⟩,⟨⟨6252984665123409521453858824,6252984665123409522191333768⟩,⟨(-1675626498907090463981753373),(-1675626498907090463369302466)⟩⟩,⟨⟨3879054158516811427161429153,3879054158516811427613592622⟩,⟨(-1039421657016002769851473050),(-1039421657016002769472982950)⟩⟩,⟨⟨1102081344137210721103771700,1102081344137210721229047120⟩,⟨(-295302823520684556555888269),(-295302823520684556449212394)⟩⟩] +lemma amp9_02_15_eq : ∀ k : Fin 16, amp9_0Expr 2 15 k = amp9_02_15 k := by decide +kernel +noncomputable def amp9_02 : Fin 16 → Fin 16 → CBox := ![amp9_02_0,amp9_02_1,amp9_02_2,amp9_02_3,amp9_02_4,amp9_02_5,amp9_02_6,amp9_02_7,amp9_02_8,amp9_02_9,amp9_02_10,amp9_02_11,amp9_02_12,amp9_02_13,amp9_02_14,amp9_02_15] +lemma amp9_02_eq (i k : Fin 16) : amp9_0Expr 2 i k = amp9_02 i k := by + fin_cases i + · exact amp9_02_0_eq k + · exact amp9_02_1_eq k + · exact amp9_02_2_eq k + · exact amp9_02_3_eq k + · exact amp9_02_4_eq k + · exact amp9_02_5_eq k + · exact amp9_02_6_eq k + · exact amp9_02_7_eq k + · exact amp9_02_8_eq k + · exact amp9_02_9_eq k + · exact amp9_02_10_eq k + · exact amp9_02_11_eq k + · exact amp9_02_12_eq k + · exact amp9_02_13_eq k + · exact amp9_02_14_eq k + · exact amp9_02_15_eq k +noncomputable def amp9_03_0 : Fin 16 → CBox := ![⟨⟨403394260725353423646563270,403394260725353423785059235⟩,⟨(-108090183758420924117826072),(-108090183758420923992706562)⟩⟩,⟨⟨1419974652654540929294681928,1419974652654540929786267112⟩,⟨(-380513289296283114707382832),(-380513289296283114265885463)⟩⟩,⟨⟨2289388364142189097196529907,2289388364142189097992114383⟩,⟨(-613584070936187279552782311),(-613584070936187278840231338)⟩⟩,⟨⟨3252410339548292945041678052,3252410339548292946172507081⟩,⟨(-871882434754030705138702127),(-871882434754030704126415048)⟩⟩,⟨⟨4148083309939375000590568827,4148083309939375002033578854⟩,⟨(-1112322191666185086338511998),(-1112322191666185085047507625)⟩⟩,⟨⟨5096636149994630610655681623,5096636149994630612428619840⟩,⟨(-1367192744249870318020642754),(-1367192744249870316434831344)⟩⟩,⟨⟨6002226898218423192757986724,6002226898218423194845931501⟩,⟨(-1610845277845051388092292550),(-1610845277845051386225272755)⟩⟩,⟨⟨6944657711565424332868803919,6944657711565424335283898518⟩,⟨(-1864746251475208747147582336),(-1864746251475208744988354845)⟩⟩,⟨⟨7855681503608225967833451005,7855681503608225970564527093⟩,⟨(-2110630663922880126674423769),(-2110630663922880124233141944)⟩⟩,⟨⟨8795031962169919532646344823,8795031962169919535701477127⟩,⟨(-2364596704581958648055398071),(-2364596704581958645324099594)⟩⟩,⟨⟨9709723092805367878022574948,9709723092805367881394275428⟩,⟨(-2612458304806137245192589822),(-2612458304806137242179048970)⟩⟩,⟨⟨10647479694509940862786358326,10647479694509940866481299659⟩,⟨(-2867104676851417308552233694),(-2867104676851417305250098574)⟩⟩,⟨⟨11565009882953583360295249916,11565009882953583364305234327⟩,⟨(-3116936947720386976861992179),(-3116936947720386973278341577)⟩⟩,⟨⟨12502039082867935525772153731,12502039082867935530102394156⟩,⟨(-3372709440687027585815962983),(-3372709440687027581945701164)⟩⟩,⟨⟨13421982622969881116533408958,13421982622969881121179090928⟩,⟨(-3624610076274640770135745817),(-3624610076274640765984433500)⟩⟩,⟨⟨14358851210238936552422093178,14358851210238936557387823223⟩,⟨(-3881870199742348423518483798),(-3881870199742348419081832341)⟩⟩] +lemma amp9_03_0_eq : ∀ k : Fin 16, amp9_0Expr 3 0 k = amp9_03_0 k := by decide +kernel +noncomputable def amp9_03_1 : Fin 16 → CBox := ![⟨⟨15280978938582177755324620303,15280978938582177760603898440⟩,⟨(-4135985256869685179727896492),(-4135985256869685175011487193)⟩⟩,⟨⟨16218087070801141848931897637,16218087070801141854527958449⟩,⟨(-4395045248013633622770586226),(-4395045248013633617771007038)⟩⟩,⟨⟨17142272764302401757238898371,17142272764302401763145825527⟩,⟨(-4651543433516645213967407512),(-4651543433516645208689761820)⟩⟩,⟨⟨18079916706527992042237939224,18079916706527992048463238908⟩,⟨(-4912682441133831309943336477),(-4912682441133831304383462978)⟩⟩,⟨⟨19006089122030763513849950935,19006089122030763520383278945⟩,⟨(-5171741641120364633971557747),(-5171741641120364628135519397)⟩⟩,⟨⟨19944493546663045311036134991,19944493546663045317880406124⟩,⟨(-5435213766967691983951696459),(-5435213766967691977836923802)⟩⟩,⟨⟨20872609418910767653467964300,20872609418910767660623864257⟩,⟨(-5697013205809697011240844379),(-5697013205809697004850211480)⟩⟩,⟨⟨21811945067782605225184854310,21811945067782605232648315328⟩,⟨(-5963051638683181236957611608),(-5963051638683181230290746782)⟩⟩,⟨⟨22741972676218565866620845738,22741972676218565874392754776⟩,⟨(-6227766885466275160404273046),(-6227766885466275153463845903)⟩⟩,⟨⟨23682366399471076995279875243,23682366399471077003363220720⟩,⟨(-6496586009054416395258005149),(-6496586009054416388041971132)⟩⟩,⟨⟨24614274877111577268319826959,24614274877111577276702354733⟩,⟨(-6764385539687718799541253744),(-6764385539687718792055768398)⟩⟩,⟨⟨25555815448674723249282816520,25555815448674723257973238991⟩,⟨(-7036181926639515275467711074),(-7036181926639515267709386453)⟩⟩,⟨⟨26489567409650793048537204843,26489567409650793057521619275⟩,⟨(-7307224593749363596683146703),(-7307224593749363588658512382)⟩⟩,⟨⟨27432308887547472382504718610,27432308887547472391796907982⟩,⟨(-7582177361176705180532946160),(-7582177361176705172237411665)⟩⟩,⟨⟨28367855077946113556817706112,28367855077946113566409141499⟩,⟨(-7856610426112607739773982474),(-7856610426112607731212526058)⟩⟩,⟨⟨29311818684101812769690983950,29311818684101812779584440806⟩,⟨(-8134881215076756102004470655),(-8134881215076756093175718351)⟩⟩] +lemma amp9_03_1_eq : ∀ k : Fin 16, amp9_0Expr 3 1 k = amp9_03_1 k := by decide +kernel +noncomputable def amp9_03_2 : Fin 16 → CBox := ![⟨⟨30249093927131206286011022892,30249093927131206296190818111⟩,⟨(-8412838748070690934391626635),(-8412838748070690925302499276)⟩⟩,⟨⟨31194269010939947160724152788,31194269010939947171204212229⟩,⟨(-8694571479579703959285933745),(-8694571479579703949932127912)⟩⟩,⟨⟨32133189018217929511258921046,32133189018217929522033280778⟩,⟨(-8976173014638469686799983988),(-8976173014638469677185675015)⟩⟩,⟨⟨33079533444566654660618494744,33079533444566654671688934305⟩,⟨(-9261493514730336686751947836),(-9261493514730336676876358600)⟩⟩,⟨⟨34019992232784025387498042333,34019992232784025398862770656⟩,⟨(-9546842890653111788681172153),(-9546842890653111778547277649)⟩⟩,⟨⟨34967432407976695484124652961,34967432407976695495763913688⟩,⟨(-9835858442983806236398911904),(-9835858442983806226012130581)⟩⟩,⟨⟨35909300157252905005672221614,35909300157252905017599229503⟩,⟨(-10125042787846903321368723383),(-10125042787846903310727795634)⟩⟩,⟨⟨36857730830997997130770483011,36857730830997997142982586813⟩,⟨(-10417841651972575586195716895),(-10417841651972575575301392380)⟩⟩,⟨⟨37800852079502245503131892081,37800852079502245515628003121⟩,⟨(-10710930483971251749236432773),(-10710930483971251738091444418)⟩⟩,⟨⟨38750136015071337266137448373,38750136015071337278918060908⟩,⟨(-11007581405110668202224611984),(-11007581405110668190828945383)⟩⟩,⟨⟨39694328120512582396413684806,39694328120512582409474842354⟩,⟨(-11304625832237894541835380096),(-11304625832237894530192563628)⟩⟩,⟨⟨40644295696138330562104573268,40644295696138330575422705371⟩,⟨(-11605177560454896005514036421),(-11605177560454895993631043922)⟩⟩,⟨⟨41589347517600470510577016431,41589347517600470524175396744⟩,⟨(-11906209567558880717472245446),(-11906209567558880705344837766)⟩⟩,⟨⟨42539796303365310123340919723,42539796303365310137215324067⟩,⟨(-12210690399194769782478772454),(-12210690399194769770108511137)⟩⟩,⟨⟨43485467071813731808645344402,43485467071813731822795111743⟩,⟨(-12515722214866784054497577336),(-12515722214866784041887031362)⟩⟩,⟨⟨44436161413776485893318240336,44436161413776485907734411977⟩,⟨(-12824139565631784399429739870),(-12824139565631784386581949629)⟩⟩] +lemma amp9_03_2_eq : ∀ k : Fin 16, amp9_0Expr 3 2 k = amp9_03_2 k := by decide +kernel +noncomputable def amp9_03_3 : Fin 16 → CBox := ![⟨⟨45382179769389562548637991156,45382179769389562563322005722⟩,⟨(-13133163103937536610174481085),(-13133163103937536597091410970)⟩⟩,⟨⟨46332850404188922674984901041,46332850404188922689936884159⟩,⟨(-13445503120718159294663668706),(-13445503120718159281345840456)⟩⟩,⟨⟨47278913585275721614603864930,47278913585275721629820794671⟩,⟨(-13758489494482829069707808854),(-13758489494482829056158467799)⟩⟩,⟨⟨48229257302527385655195103687,48229257302527385670635423501⟩,⟨(-14074716711260546245995992328),(-14074716711260546232227915571)⟩⟩,⟨⟨49175030475291752887725601071,49175030475291752903428933494⟩,⟨(-14391615814747471784190072706),(-14391615814747471770194094602)⟩⟩,⟨⟨50124709840881349740420754209,50124709840881349756382317240⟩,⟨(-14711672856818319247304660086),(-14711672856818319233082917414)⟩⟩,⟨⟨51069825562383068485905428112,51069825562383068502121033293⟩,⟨(-15032413016392079164394319733),(-15032413016392079149950408184)⟩⟩,⟨⟨52018468712690499288278984387,52018468712690499304745494783⟩,⟨(-15356220356176993447426721020),(-15356220356176993432762391457)⟩⟩,⟨⟨52962526521487244844607403708,52962526521487244861323466254⟩,⟨(-15680708048034232619758425453),(-15680708048034232604876446490)⟩⟩,⟨⟨53909727036296561168690904921,53909727036296561185644926664⟩,⟨(-16008163815078957216320310661),(-16008163815078957201225027238)⟩⟩,⟨⟨54852293166721735044123665785,54852293166721735061321639585⟩,⟨(-16336283449444234005247858720),(-16336283449444233989939867612)⟩⟩,⟨⟨55797610026834146099653805252,55797610026834146117089933055⟩,⟨(-16667263296661386064834590923),(-16667263296661386049316604071)⟩⟩,⟨⟨56738217243872941575618825216,56738217243872941593291133416⟩,⟨(-16998877068033698647548855614),(-16998877068033698631823839167)⟩⟩,⟨⟨57681174878087788287661367947,57681174878087788305567690327⟩,⟨(-17333234095795073678694201595),(-17333234095795073662763861472)⟩⟩,⟨⟨58619322430491147774869653257,58619322430491147793007066687⟩,⟨(-17668181898929692439492735759),(-17668181898929692423360326327)⟩⟩,⟨⟨59559410855540819442327210740,59559410855540819460693292678⟩,⟨(-18005746638244856289843638631),(-18005746638244856273511015892)⟩⟩] +lemma amp9_03_3_eq : ∀ k : Fin 16, amp9_0Expr 3 3 k = amp9_03_3 k := by decide +kernel +noncomputable def amp9_03_4 : Fin 16 → CBox := ![⟨⟨60494564545256760181571316655,60494564545256760200097877225⟩,⟨(-18343846049589623391933529430),(-18343846049589623375423747684)⟩⟩,⟨⟨61431239601400652651731359610,61431239601400652670491134278⟩,⟨(-18684426505287159917504689948),(-18684426505287159900796932563)⟩⟩,⟨⟨62362831967669440844629646297,62362831967669440863616281583⟩,⟨(-19025472829580048235474783900),(-19025472829580048218573347687)⟩⟩,⟨⟨63295515651916090293692433731,63295515651916090312901317306⟩,⟨(-19368854584126479180653837599),(-19368854584126479163561370432)⟩⟩,⟨⟨64222946268515805466346672845,64222946268515805485773126841⟩,⟨(-19712620965814424541770717944),(-19712620965814424524491027368)⟩⟩,⟨⟨65151027166813766568677374959,65151027166813766588321470774⟩,⟨(-20058567344152947484758882846),(-20058567344152947467293245618)⟩⟩,⟨⟨66073663050988885127505550898,66073663050988885147356881451⟩,⟨(-20404804943219818017040357767),(-20404804943219817999394356538)⟩⟩,⟨⟨66996496870178988089193484331,66996496870178988109254228484⟩,⟨(-20753057238779650516070926551),(-20753057238779650498245250001)⟩⟩,⟨⟨67913673001760729549840220342,67913673001760729570107735180⟩,⟨(-21101495470480330497723833538),(-21101495470480330479721679726)⟩⟩,⟨⟨68830583201595786801230222259,68830583201595786821682314164⟩,⟨(-21451773232292647518391255978),(-21451773232292647500220943553)⟩⟩,⟨⟨69741603150746806412941148106,69741603150746806433594857065⟩,⟨(-21802120070185537139543852659),(-21802120070185537121202464788)⟩⟩,⟨⟨70651881675845692681908747929,70651881675845692702757889012⟩,⟨(-22154121450840209707856305862),(-22154121450840209689347233433)⟩⟩,⟨⟨71556018337746486456043621583,71556018337746486477086414239⟩,⟨(-22506063792395721841310720058),(-22506063792395721822636903521)⟩⟩,⟨⟨72458926448947621139738354787,72458926448947621160964542819⟩,⟨(-22859465956381787567662766703),(-22859465956381787548828939411)⟩⟩,⟨⟨73355422883597728993402603927,73355422883597729014816301961⟩,⟨(-23212670050322539239772995245),(-23212670050322539220780242844)⟩⟩,⟨⟨74250192087804915748292644122,74250192087804915769886392263⟩,⟨(-23567129642112770819826481559),(-23567129642112770800678715155)⟩⟩] +lemma amp9_03_4_eq : ∀ k : Fin 16, amp9_0Expr 3 4 k = amp9_03_4 k := by decide +kernel +noncomputable def amp9_03_5 : Fin 16 → CBox := ![⟨⟨75138262462946322638540553055,75138262462946322660312613191⟩,⟨(-23921241576514373807563219210),(-23921241576514373788263376864)⟩⟩,⟨⟨76024095540212204929782185932,76024095540212204951729603559⟩,⟨(-24276395247579201810065373070),(-24276395247579201790615982891)⟩⟩,⟨⟨76902926175201191259931687210,76902926175201191282052593110⟩,⟨(-24631041497630645619352604174),(-24631041497630645599756639274)⟩⟩,⟨⟨77778998301466279964025255052,77778998301466279986316125712⟩,⟨(-24986506491398167427513603660),(-24986506491398167407773819624)⟩⟩,⟨⟨78647748809728035171878785783,78647748809728035194336405973⟩,⟨(-25341294525589208386804450593),(-25341294525589208366924256456)⟩⟩,⟨⟨79513208773323448897513530952,79513208773323448919996411826⟩,⟨(-25696669319205492808504210197),(-25696669319205492788530986721)⟩⟩,⟨⟨80371013300824762001081316535,80371013300824762023731275466⟩,⟨(-26051188262576407790572399267),(-26051188262576407770462808524)⟩⟩,⟨⟨81224984810552388049329855777,81224984810552388072140329630⟩,⟨(-26406053264163412987668320598),(-26406053264163412967426174819)⟩⟩,⟨⟨82070953367524677085817326493,82070953367524677108781882845⟩,⟨(-26759874617120943062898607251),(-26759874617120943042528361722)⟩⟩,⟨⟨82912536449847906013126232454,82912536449847906036241448415⟩,⟨(-27113792917077889485798019294),(-27113792917077889465302508448)⟩⟩,⟨⟨83745756332788211401671650042,83745756332788211424929992078⟩,⟨(-27466471328151035622693341930),(-27466471328151035602077388258)⟩⟩,⟨⟨84574028815398666451253952324,84574028815398666474651603422⟩,⟨(-27818989502898917563479461634),(-27818989502898917542746077803)⟩⟩,⟨⟨85393566116172059296806532350,85393566116172059320344197085⟩,⟨(-28170063593680188878510509113),(-28170063593680188857661821440)⟩⟩,⟨⟨86207585194942118284700783056,86207585194942118308368097905⟩,⟨(-28520712560108256412061086439),(-28520712560108256391102293803)⟩⟩,⟨⟨87012486393606986113601410773,87012486393606986137398702461⟩,⟨(-28869705800500651092413806318),(-28869705800500651071347150424)⟩⟩,⟨⟨87811290279693918309120635548,87811290279693918333046051442⟩,⟨(-29218001719238200471499953145),(-29218001719238200450327855888)⟩⟩] +lemma amp9_03_5_eq : ∀ k : Fin 16, amp9_0Expr 3 5 k = amp9_03_5 k := by decide +kernel +noncomputable def amp9_03_6 : Fin 16 → CBox := ![⟨⟨88600583917473254615525758440,88600583917473254639559784230⟩,⟨(-29564423351006186370688608300),(-29564423351006186349419920123)⟩⟩,⟨⟨89383193561108202152121687719,89383193561108202176279539137⟩,⟨(-29909868576512959519815286458),(-29909868576512959498446761644)⟩⟩,⟨⟨90155891989736606051071827504,90155891989736606075339781061⟩,⟨(-30253214583017521551595343353),(-30253214583017521530133902072)⟩⟩,⟨⟨90921312877010306517107575294,90921312877010306541491726215⟩,⟨(-30595298658361565239736061843),(-30595298658361565218181510561)⟩⟩,⟨⟨91676414080498994568904401831,91676414080498994593395267506⟩,⟨(-30935052778245456232005342347),(-30935052778245456210363192966)⟩⟩,⟨⟨92423638099246054443845718190,92423638099246054468442823059⟩,⟨(-31273253472318582492907009222),(-31273253472318582471179283425)⟩⟩,⟨⟨93160127583927764357757481609,93160127583927764382406187549⟩,⟨(-31608888254798667092426232110),(-31608888254798667070633766029)⟩⟩,⟨⟨93888134954612516747533277955,93888134954612516772285060908⟩,⟨(-31942672639606856765589238100),(-31942672639606856743716490956)⟩⟩,⟨⟨94604987703155597260303447951,94604987703155597285149134237⟩,⟨(-32273650538926251864809846996),(-32273650538926251842862235241)⟩⟩,⟨⟨95312748970475233569392664058,95312748970475233594326075360⟩,⟨(-32602476104485629222111587656),(-32602476104485629200093108837)⟩⟩,⟨⟨96008931455392227919569211727,96008931455392227944589257682⟩,⟨(-32928250610979564680748297550),(-32928250610979564658661602580)⟩⟩,⟨⟨96695409536137142495924601024,96695409536137142521021946711⟩,⟨(-33251566415248122601148288612),(-33251566415248122578998494145)⟩⟩,⟨⟨97369881788158466112963444519,97369881788158466138136895188⟩,⟨(-33571583220384389404255644389),(-33571583220384389382045438681)⟩⟩,⟨⟨98034034070705781622007818590,98034034070705781647257481293⟩,⟨(-33888831071565640157914556543),(-33888831071565640135645815941)⟩⟩,⟨⟨98685751797244279738536331116,98685751797244279763832868549⟩,⟨(-34202529264233449870693608889),(-34202529264233449848378740173)⟩⟩,⟨⟨99326532287908529353697506803,99326532287908529379059965249⟩,⟨(-34513144932700790747312705976),(-34513144932700790724947061348)⟩⟩] +lemma amp9_03_6_eq : ∀ k : Fin 16, amp9_0Expr 3 6 k = amp9_03_6 k := by decide +kernel +noncomputable def amp9_03_7 : Fin 16 → CBox := ![⟨⟨99954449036706327315407616616,99954449036706327340828938065⟩,⟨(-34819958223941105966501704959),(-34819958223941105944089983123)⟩⟩,⟨⟨100570810548031463296496154184,100570810548031463321975997366⟩,⟨(-35123372680951089279100451861),(-35123372680951089256644701028)⟩⟩,⟨⟨101173879910957085953777532349,101173879910957085979297873397⟩,⟨(-35422730654247242394298112112),(-35422730654247242371806850423)⟩⟩,⟨⟨101764776286906566371422853132,101764776286906566396991324162⟩,⟨(-35718371334536284201089065951),(-35718371334536284178561581567)⟩⟩,⟨⟨102341954138758246967593624201,102341954138758246993197501528⟩,⟨(-36009700718716201755100648994),(-36009700718716201732543623246)⟩⟩,⟨⟨102906342511645118864105100360,102906342511645118889750314597⟩,⟨(-36296992804008700345265373275),(-36296992804008700322678669305)⟩⟩,⟨⟨103456589278715939281139900593,103456589278715939306815518098⟩,⟨(-36579718765749491939060917396),(-36579718765749491916450571917)⟩⟩,⟨⟨103993432352612770295434299189,103993432352612770321136883665⟩,⟨(-36858086486145990521548361079),(-36858086486145990498917556403)⟩⟩,⟨⟨104515715305685126493187843691,104515715305685126518913680484⟩,⟨(-37131633939018223208326572473),(-37131633939018223185678804703)⟩⟩,⟨⟨105023983660964503947061733787,105023983660964503972808678939⟩,⟨(-37400501889180262223189024504),(-37400501889180262200527005949)⟩⟩,⟨⟨105517279227325684591218291623,105517279227325684616978781284⟩,⟨(-37664296816123082158248034047),(-37664296816123082135576599300)⟩⟩,⟨⟨105995953640905947037714278112,105995953640905947063485634306⟩,⟨(-37923091283126851061073463781),(-37923091283126851038395538719)⟩⟩,⟨⟨106459249729913621822969936499,106459249729913621848744780187⟩,⟨(-38176562069206372509937235478),(-38176562069206372487257595099)⟩⟩,⟨⟨106907323505721635796257080544,106907323505721635822030858711⟩,⟨(-38424712368900278617160125935),(-38424712368900278594482362954)⟩⟩,⟨⟨107339621842398007177411896813,107339621842398007203177745405⟩,⟨(-38667291141172455505207863773),(-38667291141172455482536547930)⟩⟩,⟨⟨107756103146511248500163505242,107756103146511248525914019272⟩,⟨(-38904230959844351529703423205),(-38904230959844351507043201088)⟩⟩] +lemma amp9_03_7_eq : ∀ k : Fin 16, amp9_0Expr 3 7 k = amp9_03_7 k := by decide +kernel +noncomputable def amp9_03_8 : Fin 16 → CBox := ![⟨⟨108156421607607724403258742033,108156421607607724429001450114⟩,⟨(-39135354931119978621531204922),(-39135354931119978598881453780)⟩⟩,⟨⟨108540335802501738350063182382,108540335802501738375806392025⟩,⟨(-39360523669258086268257249764),(-39360523669258086245616893551)⟩⟩,⟨⟨108907710749452396829407274706,108907710749452396855143241591⟩,⟨(-39579636482551727023587537630),(-39579636482551727000961408090)⟩⟩,⟨⟨109258102721756934585524639216,109258102721756934611247031093⟩,⟨(-39792480597469298577515918924),(-39792480597469298554908260766)⟩⟩,⟨⟨109591591324928903364645535970,109591591324928903390349281519⟩,⟨(-39999033667905867443255492185),(-39999033667905867420670172323)⟩⟩,⟨⟨109907527801086672158470804018,109907527801086672184149098594⟩,⟨(-40199008011993358913996836870),(-40199008011993358891438266291)⟩⟩,⟨⟨110206210349738932989106793698,110206210349738933014756615063⟩,⟨(-40392461862945841808541854706),(-40392461862945841786013118821)⟩⟩,⟨⟨110486782193964929780686366760,110486782193964929806300509452⟩,⟨(-40579031014315828707127483342),(-40579031014315828684633163077)⟩⟩,⟨⟨110749764386344044709345783129,110749764386344044734921607027⟩,⟨(-40758856604555233505160998715),(-40758856604555233482704039575)⟩⟩,⟨⟨110994088875300809827619501270,110994088875300809853154046404⟩,⟨(-40931496186854462553728306092),(-40931496186854462531311707416)⟩⟩,⟨⟨111220504083332688996239088572,111220504083332689021728568191⟩,⟨(-41097176225508560989113719712),(-41097176225508560966740799019)⟩⟩,⟨⟨111427727151967422290420312286,111427727151967422315853763632⟩,⟨(-41255374213688356334592973965),(-41255374213688356312269709530)⟩⟩,⟨⟨111616738655048517683873764712,111616738655048517709257441940⟩,⟨(-41406404459829102717279033158),(-41406404459829102695005020546)⟩⟩,⟨⟨111786037108081713956865862016,111786037108081713982186924860⟩,⟨(-41549662468689770819772817741),(-41549662468689770797554716280)⟩⟩,⟨⟨111936840290530910836287649865,111936840290530910861554574962⟩,⟨(-41685553012400438127660353142),(-41685553012400438105496869216)⟩⟩,⟨⟨112067423974142823046663044144,112067423974142823071856828114⟩,⟨(-41813387564757257080089162053),(-41813387564757257057989276115)⟩⟩] +lemma amp9_03_8_eq : ∀ k : Fin 16, amp9_0Expr 3 8 k = amp9_03_8 k := by decide +kernel +noncomputable def amp9_03_9 : Fin 16 → CBox := ![⟨⟨112179248480946766452647605847,112179248480946766477767678009⟩,⟨(-41933664086569278997523010854),(-41933664086569278975488796239)⟩⟩,⟨⟨112270362409277383248754146285,112270362409277383273793790139⟩,⟨(-42045607857927008991794020183),(-42045607857927008969829861515)⟩⟩,⟨⟨112342474254846954614110356257,112342474254846954639091482526⟩,⟨(-42149812863563204827422611390),(-42149812863563204805522086931)⟩⟩,⟨⟨112393400686007029387991715917,112393400686007029412881994924⟩,⟨(-42245415900232687188653692562),(-42245415900232687166830806363)⟩⟩,⟨⟨112425104310761092446709153250,112425104310761092471508669649⟩,⟨(-42333109927647909875868627593),(-42333109927647909854125136292)⟩⟩,⟨⟨112435164767145785439564611639,112435164767145785464273379005⟩,⟨(-42411940835292079026014978037),(-42411940835292079004352728681)⟩⟩,⟨⟨112425805036850049961153787832,112425805036850049985761083248⟩,⟨(-42482703631064287660022220794),(-42482703631064287638446986645)⟩⟩,⟨⟨112394362264652596340929936286,112394362264652596365435765673⟩,⟨(-42544350730721625077678048355),(-42544350730721625056191690885)⟩⟩,⟨⟨112343326407566389818644765773,112343326407566389843041849841⟩,⟨(-42597782392915856015812935205),(-42597782392915855994419931149)⟩⟩,⟨⟨112269786270506487100163133008,112269786270506487124442003374⟩,⟨(-42641854841616762994962691167),(-42641854841616762973668458029)⟩⟩,⟨⟨112176505747528258785775279275,112176505747528258809998650538⟩,⟨(-42677576926321363186258131376),(-42677576926321363165040472002)⟩⟩,⟨⟨112060319049938122904053953154,112060319049938122928157379292⟩,⟨(-42703705799486887318498060509),(-42703705799486887297383292283)⟩⟩,⟨⟨111924271353091511346389494756,111924271353091511370372610653⟩,⟨(-42721362388305580971289239124),(-42721362388305580950279141423)⟩⟩,⟨⟨111764935587641267622588509781,111764935587641267646441322754⟩,⟨(-42729201721198137158356349569),(-42729201721198137137456535572)⟩⟩,⟨⟨111585645962407428815153645800,111585645962407428838884156783⟩,⟨(-42728460447072920993297368476),(-42728460447072920972506355527)⟩⟩,⟨⟨111382706977900099816469182162,111382706977900099840061903709⟩,⟨(-42717688232654806204249556157),(-42717688232654806183575078170)⟩⟩] +lemma amp9_03_9_eq : ∀ k : Fin 16, amp9_0Expr 3 9 k = amp9_03_9 k := by decide +kernel +noncomputable def amp9_03_10 : Fin 16 → CBox := ![⟨⟨111159750065078620864993930435,111159750065078620888468357859⟩,⟨(-42698241261493210297021343786),(-42698241261493210276457485567)⟩⟩,⟨⟨110912803649902789439608930734,110912803649902789462942407917⟩,⟨(-42668560402140491017466555709),(-42668560402140490997023765904)⟩⟩,⟨⟨110645805042872832273618025914,110645805042872832296808728673⟩,⟨(-42630125367826309348292775635),(-42630125367826309327973251805)⟩⟩,⟨⟨110354498419867349546663598323,110354498419867349569713793826⟩,⟨(-42581264578442690268697736183),(-42581264578442690248502373403)⟩⟩,⟨⟨110043136133322651918795864629,110043136133322651941692615961⟩,⟨(-42523585468921798040680387353),(-42523585468921798020615653663)⟩⟩,⟨⟨109707169361981680685787270379,109707169361981680708533540020⟩,⟨(-42455300129098942759744190384),(-42455300129098942739810672067)⟩⟩,⟨⟨109351175208427717758271820321,109351175208427717780863287130⟩,⟨(-42378148121351216941417083753),(-42378148121351216921617859865)⟩⟩,⟨⟨108970302490554986935446943399,108970302490554986957875638670⟩,⟨(-42290221074328216191389777690),(-42290221074328216171729675909)⟩⟩,⟨⟨108569463361084077478511120799,108569463361084077500772946669⟩,⟨(-42193395316162831622268036278),(-42193395316162831602750048601)⟩⟩,⟨⟨108143494246191367211294675357,108143494246191367233383230123⟩,⟨(-42085637612447569543263684455),(-42085637612447569523891993261)⟩⟩,⟨⟨107697653292292014362695966017,107697653292292014384603035663⟩,⟨(-41968965949192066520910639963),(-41968965949192066501689771662)⟩⟩,⟨⟨107226453779227317472169513235,107226453779227317494090467742⟩,⟨(-41841217532820514596089446546),(-41841217532820514576944880845)⟩⟩,⟨⟨106735511492637970696536502353,106735511492637970718280263242⟩,⟨(-41704557177114092447881360264),(-41704557177114092428888863397)⟩⟩,⟨⟨106219005024121998836200116166,106219005024121998857764634235⟩,⟨(-41556687512639368096708684237),(-41556687512639368077870720243)⟩⟩,⟨⟨105682920212007267806539434479,105682920212007267827920636757⟩,⟨(-41399925655687995377018833195),(-41399925655687995358338224295)⟩⟩,⟨⟨105121088558951245720871595729,105121088558951245742069172047⟩,⟨(-41231834294108552294416690635),(-41231834294108552275895230556)⟩⟩] +lemma amp9_03_10_eq : ∀ k : Fin 16, amp9_0Expr 3 10 k = amp9_03_10 k := by decide +kernel +noncomputable def amp9_03_11 : Fin 16 → CBox := ![⟨⟨104539879211961195513109392252,104539879211961195534119839021⟩,⟨(-41054888656913940417080892757),(-41054888656913940398721171255)⟩⟩,⟨⟨103932763244632145844986298064,103932763244632145865809789254⟩,⟨(-40866505738868568469240643497),(-40866505738868568451044208521)⟩⟩,⟨⟨103306507295703791286030318258,103306507295703791306657156120⟩,⟨(-40669325062105206279679993557),(-40669325062105206261651788813)⟩⟩,⟨⟨102654207638993277218720243884,102654207638993277239158770832⟩,⟨(-40460611756780496443944279762),(-40460611756780496426082657490)⟩⟩,⟨⟨101983043611069337162197147997,101983043611069337182433406883⟩,⟨(-40243176228165336957946763699),(-40243176228165336940258331247)⟩⟩,⟨⟨101285721181304898855095598466,101285721181304898875129687628⟩,⟨(-40014125106477579527762671729),(-40014125106477579510248986550)⟩⟩,⟨⟨100569848722480396783393921722,100569848722480396803217732937⟩,⟨(-39776446724656384698205739676),(-39776446724656384680871037747)⟩⟩,⟨⟨99827725143392012821427680384,99827725143392012841068818509⟩,⟨(-39527082065382904528626516442),(-39527082065382904511461477951)⟩⟩,⟨⟨99067405448357288386326065257,99067405448357288405752736413⟩,⟨(-39269204939546770279511941684),(-39269204939546770262530160858)⟩⟩,⟨⟨98280763343969559613152957309,98280763343969559632364089886⟩,⟨(-38999582967189485258093273848),(-38999582967189485241296733675)⟩⟩,⟨⟨97476319461002536895420122931,97476319461002536914419890905⟩,⟨(-38721583551836169433230270279),(-38721583551836169416618239388)⟩⟩,⟨⟨96645502623361218614091428824,96645502623361218632866977332⟩,⟨(-38431792605100235311440968973),(-38431792605100235295020131442)⟩⟩,⟨⟨95797319646537514318679693610,95797319646537514337231836219⟩,⟨(-38133779869569612324320823675),(-38133779869569612308091759353)⟩⟩,⟨⟨94922733076289279863974620380,94922733076289279882299199093⟩,⟨(-37823940499429306651361859962),(-37823940499429306635327761129)⟩⟩,⟨⟨94031258223032823757337838465,94031258223032823775428680015⟩,⟨(-37506056032073306577782944134),(-37506056032073306561947092003)⟩⟩,⟨⟨93113368040950457181434552527,93113368040950457199284672688⟩,⟨(-37176321028471885245911976199),(-37176321028471885230278713911)⟩⟩] +lemma amp9_03_11_eq : ∀ k : Fin 16, amp9_0Expr 3 11 k = amp9_03_11 k := by decide +kernel +noncomputable def amp9_03_12 : Fin 16 → CBox := ![⟨⟨92179110615548978363064363962,92179110615548978380786887580⟩,⟨(-36838739075570337789253705241),(-36838739075570337773778630830)⟩⟩,⟨⟨91218443843118553088356351235,91218443843118553105849469150⟩,⟨(-36489293421855418213479417356),(-36489293421855418198204675282)⟩⟩,⟨⟨90241975087389980586730939496,90241975087389980603991790407⟩,⟨(-36132220861665317336847133923),(-36132220861665317321774569161)⟩⟩,⟨⟨89239119294536244265400843323,89239119294536244282427854737⟩,⟨(-35763281615889816481794470028),(-35763281615889816466926235687)⟩⟩,⟨⟨88221072127470550280346595790,88221072127470550297137075588⟩,⟨(-35386957868523442877895070844),(-35386957868523442863232915123)⟩⟩,⟨⟨87176674945370852319486443090,87176674945370852336040505811⟩,⟨(-34998773970735535927133295518),(-34998773970735535912678656563)⟩⟩,⟨⟨86117743594309903998955632459,86117743594309904015264894237⟩,⟨(-34603470844911884567380490803),(-34603470844911884553137315952)⟩⟩,⟨⟨85032512091007640962621320463,85032512091007640978698496714⟩,⟨(-34196322849504247050183882979),(-34196322849504247036148564946)⟩⟩,⟨⟨83933451617794353998799318355,83933451617794354014626407236⟩,⟨(-33782344327621008469446537868),(-33782344327621008455626868912)⟩⟩,⟨⟨82808151533932234557992174618,82808151533932234573570332110⟩,⟨(-33356544059694080868725152760),(-33356544059694080855122130280)⟩⟩,⟨⟨81669777260502634205177133111,81669777260502634220501979688⟩,⟨(-32924226023141561236388400111),(-32924226023141561223004245035)⟩⟩,⟨⟨80505232101902235945135074208,80505232101902235960202944445⟩,⟨(-32480116157636285170572997646),(-32480116157636285157410681774)⟩⟩,⟨⟨79328418941069557996370200711,79328418941069558011173695847⟩,⟨(-32029826054844552515617480122),(-32029826054844552502680410047)⟩⟩,⟨⟨78125508924014777498751699680,78125508924014777513359632560⟩,⟨(-31567779616887278328155652377),(-31567779616887278315417488707)⟩⟩,⟨⟨76911190622787201258286954943,76911190622787201272631492056⟩,⟨(-31099916077297835378362701539),(-31099916077297835365851158645)⟩⟩,⟨⟨75670851466624373790952873020,75670851466624373805032237134⟩,⟨(-30620335861732253962968805635),(-30620335861732253950686091191)⟩⟩] +lemma amp9_03_12_eq : ∀ k : Fin 16, amp9_0Expr 3 12 k = amp9_03_12 k := by decide +kernel +noncomputable def amp9_03_13 : Fin 16 → CBox := ![⟨⟨74420019771426200956974167767,74420019771426200970788812412⟩,⟨(-30135328259764457662538119138),(-30135328259764457650484339930)⟩⟩,⟨⟨73143241331329381450760874520,73143241331329381464316769599⟩,⟨(-29638646167163298302020991258),(-29638646167163298290195178639)⟩⟩,⟨⟨71856945087130164818658552924,71856945087130164831941012855⟩,⟨(-29136954141373718224258822904),(-29136954141373718212667107034)⟩⟩,⟨⟨70544769817389431138454092855,70544769817389431151465329709⟩,⟨(-28623630426841329868839516993),(-28623630426841329857482493690)⟩⟩,⟨⟨69224114016235186519168175271,69224114016235186531901104750⟩,⟨(-28105743360953413796214361989),(-28105743360953413785095037329)⟩⟩,⟨⟨67877635250906212931145324371,67877635250906212943643272396⟩,⟨(-27576265790624556367317768624),(-27576265790624556356420014787)⟩⟩,⟨⟨66523780050058305710210794483,66523780050058305722433749448⟩,⟨(-27042702265087238327623275351),(-27042702265087238316963362530)⟩⟩,⟨⟨65144140082813196359276721588,65144140082813196371221337491⟩,⟨(-26497585173212294007886338479),(-26497585173212293997467134293)⟩⟩,⟨⟨63758299819184074285075964683,63758299819184074296742906369⟩,⟨(-25948892398655906012800280173),(-25948892398655906002621487538)⟩⟩,⟨⟨62346687757047098160709664442,62346687757047098172100764924⟩,⟨(-25388675635258554918709198198),(-25388675635258554908771558338)⟩⟩,⟨⟨60930129993717370112519711645,60930129993717370123630239985⟩,⟨(-24825428883000031675175418265),(-24825428883000031665480710086)⟩⟩,⟨⟨59487779349009275414707850454,59487779349009275425564502041⟩,⟨(-24250676637869842758185965674),(-24250676637869842748724845267)⟩⟩,⟨⟨58041824002623021391715878841,58041824002623021402283743117⟩,⟨(-23673478688013833566525726936),(-23673478688013833557312204313)⟩⟩,⟨⟨56570009972232934861405825108,56570009972232934871685504320⟩,⟨(-23084778170577720510773344051),(-23084778170577720501808714854)⟩⟩,⟨⟨55096028589069022703051577843,55096028589069022713045704303⟩,⟨(-22494258806118241672948723379),(-22494258806118241664231575231)⟩⟩,⟨⟨53596064947491040569879441459,53596064947491040579581175836⟩,⟨(-21892218751437832963159807421),(-21892218751437832954694527161)⟩⟩] +lemma amp9_03_13_eq : ∀ k : Fin 16, amp9_0Expr 3 13 k = amp9_03_13 k := by decide +kernel +noncomputable def amp9_03_14 : Fin 16 → CBox := ![⟨⟨52095480224360237132557757364,52095480224360237141990948016⟩,⟨(-21289034338470280974799939864),(-21289034338470280966576368364)⟩⟩,⟨⟨50568715722447518407147097488,50568715722447518416287901865⟩,⟨(-20674283295456862372965040708),(-20674283295456862364994519262)⟩⟩,⟨⟨49043001411865566711485369681,49043001411865566720337813187⟩,⟨(-20059116507465990073946729415),(-20059116507465990066227052636)⟩⟩,⟨⟨47490815519671002415902389510,47490815519671002424455104273⟩,⟨(-19432300843387650798401325300),(-19432300843387650790938823319)⟩⟩,⟨⟨45941496926587157666748898276,45941496926587157675025327738⟩,⟨(-18805860615526227279667272093),(-18805860615526227272451685749)⟩⟩,⟨⟨44365294673296468300528851207,44365294673296468308508175771⟩,⟨(-18167642135784693038964296380),(-18167642135784693032005864210)⟩⟩,⟨⟨42793950059934125087860855727,42793950059934125095557342787⟩,⟨(-17530663980062810538236336125),(-17530663980062810531528391873)⟩⟩,⟨⟨41195155583977737472385341417,41195155583977737479781026326⟩,⟨(-16881717004666433990304687636),(-16881717004666433983856401262)⟩⟩,⟨⟨39603418981017187477525002718,39603418981017187484623368872⟩,⟨(-16234963891769371802588186874),(-16234963891769371796397178756)⟩⟩,⟨⟨37983467166495009790743077038,37983467166495009797550229611⟩,⟨(-15575971532442852790765164482),(-15575971532442852784830809802)⟩⟩,⟨⟨36373033401819555363985690436,36373033401819555370492088286⟩,⟨(-14920235674734798529554469130),(-14920235674734798523879530906)⟩⟩,⟨⟨34733358560711026854744356884,34733358560711026860955815776⟩,⟨(-14251884885160189169423756331),(-14251884885160189164007864415)⟩⟩,⟨⟨33105991878689448499265789187,33105991878689448505184995430⟩,⟨(-13587990986644800498594723346),(-13587990986644800493435441338)⟩⟩,⟨⟨31448011672891630399949861951,31448011672891630405562815824⟩,⟨(-12910965643347139458424862862),(-12910965643347139453530079039)⟩⟩,⟨⟨29805560374555505548229627394,29805560374555505553547024527⟩,⟨(-12239776617543069227148875253),(-12239776617543069222512617738)⟩⟩,⟨⟨28130651691427828657278774947,28130651691427828662294955693⟩,⟨(-11554747279723721262611724050),(-11554747279723721258238656984)⟩⟩] +lemma amp9_03_14_eq : ∀ k : Fin 16, amp9_0Expr 3 14 k = amp9_03_14 k := by decide +kernel +noncomputable def amp9_03_15 : Fin 16 → CBox := ![⟨⟨26475073331322565410852815190,26475073331322565415569960511⟩,⟨(-10877174302911279998828811007),(-10877174302911279994716195460)⟩⟩,⟨⟨24784533782129140182365141275,24784533782129140186777053973⟩,⟨(-10184782046696133255706985207),(-10184782046696133251859926409)⟩⟩,⟨⟨23117939942833731594122510365,23117939942833731598233278234⟩,⟨(-9501802659878659592960530906),(-9501802659878659589375144305)⟩⟩,⟨⟨21412921908433719941069696739,21412921908433719944876731957⟩,⟨(-8802631606587096532356180582),(-8802631606587096529036423427)⟩⟩,⟨⟨19737661954691011228961003288,19737661954691011232468538567⟩,⟨(-8115323851749719033579372557),(-8115323851749719030520867893)⟩⟩,⟨⟨18019049706433749623113777082,18019049706433749626313879905⟩,⟨(-7409850261969004923232657855),(-7409850261969004920441986775)⟩⟩,⟨⟨16337879594883099667736661410,16337879594883099670635077479⟩,⟨(-6719461815785244647652826625),(-6719461815785244645124386618)⟩⟩,⟨⟨14606035130854249472924939481,14606035130854249475516255284⟩,⟨(-6007949147738538493639589370),(-6007949147738538491379569395)⟩⟩,⟨⟨12922495920369191890934341339,12922495920369191893225067192⟩,⟨(-5316052750500094255330450333),(-5316052750500094253332088939)⟩⟩,⟨⟨11176655113995702478296305731,11176655113995702480276247332⟩,⟨(-4598302801126458533882385651),(-4598302801126458532154813556)⟩⟩,⟨⟨9496064986444769653047923244,9496064986444769654728379035⟩,⟨(-3907204167254960155647901993),(-3907204167254960154181030923)⟩⟩,⟨⟨7732586486692739040959384967,7732586486692739042326651444⟩,⟨(-3181836065675808516895384810),(-3181836065675808515701515285)⟩⟩,⟨⟨6065359213699051205700822797,6065359213699051206771381222⟩,⟨(-2495939224461625714205138576),(-2495939224461625713269557909)⟩⟩,⟨⟨4270720105127730695282888573,4270720105127730696035522994⟩,⟨(-1757506484948139592403130400),(-1757506484948139591744895838)⟩⟩,⟨⟨2649410243553751329026804586,2649410243553751329490050871⟩,⟨(-1090328258653248854689744393),(-1090328258653248854282925436)⟩⟩,⟨⟨752734514253608699626846419,752734514253608699756280391⟩,⟨(-309781873171731219445834323),(-309781873171731219331151458)⟩⟩] +lemma amp9_03_15_eq : ∀ k : Fin 16, amp9_0Expr 3 15 k = amp9_03_15 k := by decide +kernel +noncomputable def amp9_03 : Fin 16 → Fin 16 → CBox := ![amp9_03_0,amp9_03_1,amp9_03_2,amp9_03_3,amp9_03_4,amp9_03_5,amp9_03_6,amp9_03_7,amp9_03_8,amp9_03_9,amp9_03_10,amp9_03_11,amp9_03_12,amp9_03_13,amp9_03_14,amp9_03_15] +lemma amp9_03_eq (i k : Fin 16) : amp9_0Expr 3 i k = amp9_03 i k := by + fin_cases i + · exact amp9_03_0_eq k + · exact amp9_03_1_eq k + · exact amp9_03_2_eq k + · exact amp9_03_3_eq k + · exact amp9_03_4_eq k + · exact amp9_03_5_eq k + · exact amp9_03_6_eq k + · exact amp9_03_7_eq k + · exact amp9_03_8_eq k + · exact amp9_03_9_eq k + · exact amp9_03_10_eq k + · exact amp9_03_11_eq k + · exact amp9_03_12_eq k + · exact amp9_03_13_eq k + · exact amp9_03_14_eq k + · exact amp9_03_15_eq k +noncomputable def amp9_04_0 : Fin 16 → CBox := ![⟨⟨108091064822973074257489822,108091064822973074407881881⟩,⟨(-1017365712714861902748),(-1017365712714733826413)⟩⟩,⟨⟨380541199428619362392122440,380541199428619362922575269⟩,⟨(-32227844834902139734263),(-32227844834901688929233)⟩⟩,⟨⟨613709044986412613542587695,613709044986412614398541358⟩,⟨(-144307603078630038706214),(-144307603078629311988558)⟩⟩,⟨⟨872230326526901843249274391,872230326526901844465247765⟩,⟨(-401710817432017257362698),(-401710817432016225174959)⟩⟩,⟨⟨1113055384907871283232680353,1113055384907871284783398947⟩,⟨(-846618630911082521011522),(-846618630911081204947274)⟩⟩,⟨⟨1368537858149031358465964419,1368537858149031360370780199⟩,⟨(-1553203743542670457023568),(-1553203743542668840587112)⟩⟩,⟨⟨1613056611081845717705299149,1613056611081845719947865169⟩,⟨(-2553427679062348610859842),(-2553427679062346708020889)⟩⟩,⟨⟨1868150446606356736249329620,1868150446606356738842880185⟩,⟨(-3930825950684613598534215),(-3930825950684611398019237)⟩⟩,⟨⟨2115573199970329126848397770,2115573199970329129780734843⟩,⟨(-5707149034948222696659008),(-5707149034948220208887020)⟩⟩,⟨⟨2371503251039285089556690257,2371503251039285092837454869⟩,⟨(-7974992912616159175018433),(-7974992912616156391548091)⟩⟩,⟨⟨2621764478140219838263052403,2621764478140219841882829374⟩,⟨(-10745843359115809747492398),(-10745843359115806676715736)⟩⟩,⟨⟨2879333900629663783487391826,2879333900629663787453860728⟩,⟨(-14121091280701554957156703),(-14121091280701551592428935)⟩⟩,⟨⟨3132613643559144751107269388,3132613643559144755411966588⟩,⟨(-18101889125021380373361814),(-18101889125021376721784667)⟩⟩,⟨⟨3392453230468428400692994594,3392453230468428405342097768⟩,⟨(-22798164690230292635864363),(-22798164690230288692050933)⟩⟩,⟨⟨3649032574305932700110906875,3649032574305932705097651392⟩,⟨(-28200671625299009435185199),(-28200671625299005205348753)⟩⟩,⟨⟨3911685387815698907808353614,3911685387815698913137928854⟩,⟨(-34427613720176451177963248),(-34427613720176446657655028)⟩⟩] +lemma amp9_04_0_eq : ∀ k : Fin 16, amp9_0Expr 4 0 k = amp9_04_0 k := by decide +kernel +noncomputable def amp9_04_1 : Fin 16 → CBox := ![⟨⟨4171890055855739751190171115,4171890055855739756855916010⟩,⟨(-41459290719596026414806687),(-41459290719596021609610256)⟩⟩,⟨⟨4437845881573746387423157505,4437845881573746393429240433⟩,⟨(-49421914614835279241479633),(-49421914614835274147685405)⟩⟩,⟨⟨4702019975226409165400785652,4702019975226409171741118043⟩,⟨(-58285289887787189523458218),(-58285289887787184146180999)⟩⟩,⟨⟨4971730963353622499327288010,4971730963353622506006686858⟩,⟨(-68183360397692092792947577),(-68183360397692087129060358)⟩⟩,⟨⟨5240222954647131099889919284,5240222954647131106901394138⟩,⟨(-79075409598275568774286145),(-79075409598275562828565162)⟩⟩,⟨⟨5514111130105205913403441825,5514111130105205920750107569⟩,⟨(-91102827691590658732426936),(-91102827691590652502263566)⟩⟩,⟨⟨5787265496008320875896167108,5787265496008320883574317924⟩,⟨(-104214368082311433725762629),(-104214368082311427215613516)⟩⟩,⟨⟨6065726374234298284285891939,6065726374234298292296336161⟩,⟨(-118558572418822143282137732),(-118558572418822136489855419)⟩⟩,⟨⟨6343878091901702182428222624,6343878091901702190767506799⟩,⟨(-134073672582852009432346854),(-134073672582852002362170239)⟩⟩,⟨⟨6627282282626793836979438186,6627282282626793845650007333⟩,⟨(-150915057458186188235191215),(-150915057458186180885308007)⟩⟩,⟨⟨6910752895093323985306023962,6910752895093323994300904916⟩,⟨(-169010464087999572781857662),(-169010464087999565156418725)⟩⟩,⟨⟨7199446607812111206959191224,7199446607812111216282143009⟩,⟨(-188521815248313386628469918),(-188521815248313378725957390)⟩⟩,⟨⟨7488541213535057315398168186,7488541213535057325041852033⟩,⟨(-209366398483646601174360771),(-209366398483646592998816153)⟩⟩,⟨⟨7782846141120709921469691922,7782846141120709931439056063⟩,⟨(-231712348237249840512547579),(-231712348237249832062702660)⟩⟩,⟨⟨8077850962929537244427741611,8077850962929537254717055939⟩,⟨(-255466566973823133528222733),(-255466566973823124807974760)⟩⟩,⟨⟨8378063807143716873845131328,8378063807143716884456007129⟩,⟨(-280803069984181520740736322),(-280803069984181511749169095)⟩⟩] +lemma amp9_04_1_eq : ∀ k : Fin 16, amp9_0Expr 4 1 k = amp9_04_1 k := by decide +kernel +noncomputable def amp9_04_2 : Fin 16 → CBox := ![⟨⟨8679244147824364052890601315,8679244147824364063815313369⟩,⟨(-307618458522706088662821873),(-307618458522706079403832462)⟩⟩,⟨⟨8985635940405963325802006649,8985635940405963337045146903⟩,⟨(-336092289619148273382180994),(-336092289619148263854989375)⟩⟩,⟨⟨9293234412638882447476203001,9293234412638882459032890792⟩,⟨(-366110966970354775946110179),(-366110966970354766154452067)⟩⟩,⟨⟨9606049725658258939304038123,9606049725658258951175197780⟩,⟨(-397859242260386791518859514),(-397859242260386781462298546)⟩⟩,⟨⟨9920284688793104304932799644,9920284688793104317114804524⟩,⟨(-431213445365565148678405533),(-431213445365565138360579741)⟩⟩,⟨⟨10239740793754313290304492067,10239740793754313302791790213⟩,⟨(-466363167876582227102241001),(-466363167876582216523205994)⟩⟩,⟨⟨10560804955802987122399833025,10560804955802987135193204697⟩,⟨(-503174809944199812709019514),(-503174809944199801872187880)⟩⟩,⟨⟨10887090970695076682654736064,10887090970695076695753453816⟩,⟨(-541842440962969029650031857),(-541842440962969018555436303)⟩⟩,⟨⟨11215150129419337230549397119,11215150129419337243950101134⟩,⟨(-582222696060299647528201712),(-582222696060299636179406273)⟩⟩,⟨⟨11548426180460572659230875640,11548426180460572672933611006⟩,⟨(-624513753276140042897498689),(-624513753276140031294673653)⟩⟩,⟨⟨11883618086964772976834345855,11883618086964772990834927985⟩,⟨(-668562668250543290415215413),(-668562668250543278561945956)⟩⟩,⟨⟨12224014503880810619930248751,12224014503880810634221338989⟩,⟨(-714571351742874046409083462),(-714571351742874034306135479)⟩⟩,⟨⟨12566447838124335677424364717,12566447838124335692009950748⟩,⟨(-762377486480516801523294434),(-762377486480516789173778143)⟩⟩,⟨⟨12914064396632727373101221536,12914064396632727387979643144⟩,⟨(-812186333523575937364389282),(-812186333523575924768894631)⟩⟩,⟨⟨13263817848126461247902971419,13263817848126461263071064930⟩,⟨(-863826430484116383971463890),(-863826430484116371133494017)⟩⟩,⟨⟨13618723069818228390214338366,13618723069818228405668847336⟩,⟨(-917506000071359160054322026),(-917506000071359146974726983)⟩⟩] +lemma amp9_04_2_eq : ∀ k : Fin 16, amp9_0Expr 4 2 k = amp9_04_2 k := by decide +kernel +noncomputable def amp9_04_3 : Fin 16 → CBox := ![⟨⟨13975844519269119822918939431,13975844519269119838657341536⟩,⟨(-973044683965568822495103625),(-973044683965568809177344121)⟩⟩,⟨⟨14338075036663010871878135386,14338075036663010887899827428⟩,⟨(-1030653271883720181941425243),(-1030653271883720168386314274)⟩⟩,⟨⟨14702580835963883330179452535,14702580835963883346480558749⟩,⟨(-1090142780287363180091745668),(-1090142780287363166302830452)⟩⟩,⟨⟨15072140828782894810621392099,15072140828782894827188171228⟩,⟨(-1151726165495505760566017288),(-1151726165495505746545242738)⟩⟩,⟨⟨15444015177809060926819735594,15444015177809060943661578184⟩,⟨(-1215206111117198402428455326),(-1215206111117198388178386006)⟩⟩,⟨⟨15820875885256802123639571620,15820875885256802140754113539⟩,⟨(-1280797334109812446852098419),(-1280797334109812432373935863)⟩⟩,⟨⟨16200070304614796797030629709,16200070304614796814413618504⟩,⟨(-1348294499353228951663430478),(-1348294499353228936960764043)⟩⟩,⟨⟨16584169617461783232759629918,16584169617461783250409092803⟩,⟨(-1417913673107950997136500833),(-1417913673107950982210628279)⟩⟩,⟨⟨16970602516759778906789894571,16970602516759778924702468679⟩,⟨(-1489441837489806947794952051),(-1489441837489806932649398615)⟩⟩,⟨⟨17361844652289796030124334513,17361844652289796048295219154⟩,⟨(-1563095991521031551701886578),(-1563095991521031536338317914)⟩⟩,⟨⟨17755400993743630700841329706,17755400993743630719269514691⟩,⟨(-1638655792425954723039681165),(-1638655792425954707461422711)⟩⟩,⟨⟨18153656255993968291397890825,18153656255993968310080326127⟩,⟨(-1716338750384461647890983430),(-1716338750384461632099658527)⟩⟩,⟨⟨18554187313300501670915441281,18554187313300501689848548866⟩,⟨(-1795917577556343221001257190),(-1795917577556343205000430119)⟩⟩,⟨⟨18959291940514293097524265951,18959291940514293116706076216⟩,⟨(-1877609868733088073871078339),(-1877609868733088057662375959)⟩⟩,⟨⟨19366615152951315535931574196,19366615152951315555358196567⟩,⟨(-1961181792819992290095860842),(-1961181792819992273682885555)⟩⟩,⟨⟨19778371253716352646330859380,19778371253716352666000147492⟩,⟨(-2046850597829250591127633175),(-2046850597829250574512128154)⟩⟩] +lemma amp9_04_3_eq : ∀ k : Fin 16, amp9_0Expr 4 3 k = amp9_04_3 k := by decide +kernel +noncomputable def amp9_04_4 : Fin 16 → CBox := ![⟨⟨20192270175390653345025822990,20192270175390653364912089206⟩,⟨(-2134376333215646672929076169),(-2134376333215646656116960068)⟩⟩,⟨⟨20610445754546923331041831800,20610445754546923351167838771⟩,⟨(-2223975464049050690066119498),(-2223975464049050673056634884)⟩⟩,⟨⟨21030670098627085238341306910,21030670098627085258702024549⟩,⟨(-2315402366125218534626346546),(-2315402366125218517423228151)⟩⟩,⟨⟨21454999173671047281863663874,21454999173671047302456057908⟩,⟨(-2408872280684075516958833339),(-2408872280684075499564095108)⟩⟩,⟨⟨21881264951321745258639700296,21881264951321745279459269337⟩,⟨(-2504134377618229012611803377),(-2504134377618228995029144308)⟩⟩,⟨⟨22311447759709360762475930913,22311447759709360783521150299⟩,⟨(-2601402228747062354255892920),(-2601402228747062336487241691)⟩⟩,⟨⟨22743437513298611029202087080,22743437513298611050466476726⟩,⟨(-2700420287741235002695624813),(-2700420287741234984744924859)⟩⟩,⟨⟨23179140810744570453874669286,23179140810744570475357348959⟩,⟨(-2801400006700950704965279334),(-2801400006700950686834465548)⟩⟩,⟨⟨23616503940731325638847631719,23616503940731325660544773186⟩,⟨(-2904081634627201924099362804),(-2904081634627201905792078763)⟩⟩,⟨⟨24057361390313998235928387596,24057361390313998257830562890⟩,⟨(-3008674048861856014017414620),(-3008674048861855995536722983)⟩⟩,⟨⟨24499714575045827232414417050,24499714575045827254524644405⟩,⟨(-3114913827091087458081765807),(-3114913827091087439430473414)⟩⟩,⟨⟨24945327226652839404727179952,24945327226652839427041544491⟩,⟨(-3223006812058119989115587040),(-3223006812058119970296145513)⟩⟩,⟨⟨25392254934116096587875876618,25392254934116096610390836895⟩,⟨(-3332686465209943401907674502),(-3332686465209943382923708900)⟩⟩,⟨⟨25842191793501776321023243729,25842191793501776343733355441⟩,⟨(-3444155129960154751661318506),(-3444155129960154732515558090)⟩⟩,⟨⟨26293246883872707503835919705,26293246883872707526739736789⟩,⟨(-3557143728219029252396123940),(-3557143728219029233091922168)⟩⟩,⟨⟨26747045570344302316837199240,26747045570344302339930192104⟩,⟨(-3671850634329706819875337816),(-3671850634329706800415375916)⟩⟩] +lemma amp9_04_4_eq : ∀ k : Fin 16, amp9_0Expr 4 4 k = amp9_04_4 k := by decide +kernel +noncomputable def amp9_04_5 : Fin 16 → CBox := ![⟨⟨27201749987991382902779801847,27201749987991382926058427530⟩,⟨(-3788004828890165641935418626),(-3788004828890165622323337501)⟩⟩,⟨⟨27658917479494882617390282031,27658917479494882640851573828⟩,⟨(-3905800242272824161556428157),(-3905800242272824141794757113)⟩⟩,⟨⟨28116763032882301539451751778,28116763032882301563092132696⟩,⟨(-4024964533395238312871432903),(-4024964533395238292963815658)⟩⟩,⟨⟨28576776497020177118447035344,28576776497020177142263272329⟩,⟨(-4145686708418613038800002174),(-4145686708418613018749065837)⟩⟩,⟨⟨29037225724761388647585685319,29037225724761388671573700523⟩,⟨(-4267693745496789295252071098),(-4267693745496789275061537136)⟩⟩,⟨⟨29499533434043180436726860559,29499533434043180460832188728⟩,⟨(-4391169240786213752429452487),(-4391169240786213732109627242)⟩⟩,⟨⟨29962020555153205687361484619,29962020555153205711633623497⟩,⟨(-4515840153749391099914300230),(-4515840153749391079461021633)⟩⟩,⟨⟨30426042884555453545352268236,30426042884555453569786765977⟩,⟨(-4641884178945692248758388559),(-4641884178945692228174568385)⟩⟩,⟨⟨30889974830752287538313964986,30889974830752287562905536209⟩,⟨(-4769028940240375256378671723),(-4769028940240375235668219300)⟩⟩,⟨⟨31355105335446740348253030397,31355105335446740372998340724⟩,⟨(-4897445732925117429182233717),(-4897445732925117408347944177)⟩⟩,⟨⟨31819862863156818835999390971,31819862863156818860892723264⟩,⟨(-5026863549246854141945297456),(-5026863549246854120991153405)⟩⟩,⟨⟨32285469434055253568613714293,32285469434055253593651513169⟩,⟨(-5157446781166343527026010680),(-5157446781166343505954898621)⟩⟩,⟨⟨32750408313586346348046153056,32750408313586346373225817983⟩,⟨(-5288926514038202114809469403),(-5288926514038202093624883767)⟩⟩,⟨⟨33215834408146811412395490633,33215834408146811437710924534⟩,⟨(-5421459725686305880385539923),(-5421459725686305859090817073)⟩⟩,⟨⟨33680286687304729441283354616,33680286687304729466731825630⟩,⟨(-5554780339909606563969171509),(-5554780339909606542567820098)⟩⟩,⟨⟨34144852632847806970718534620,34144852632847806996297169961⟩,⟨(-5689037402459319926179600365),(-5689037402459319904674477083)⟩⟩] +lemma amp9_04_5_eq : ∀ k : Fin 16, amp9_0Expr 4 5 k = amp9_04_5 k := by decide +kernel +noncomputable def amp9_04_6 : Fin 16 → CBox := ![⟨⟨34608127972091655070342373319,34608127972091655096040708643⟩,⟨(-5823968441393309578437387454),(-5823968441393309556833292839)⟩⟩,⟨⟨35071132338686657055004899722,35071132338686657080826693396⟩,⟨(-5959714044899289804478445010),(-5959714044899289782777157491)⟩⟩,⟨⟨35532519414741683299593272336,35532519414741683325530312799⟩,⟨(-6096016131460073505433920577),(-6096016131460073483639861038)⟩⟩,⟨⟨35993240454541829969613117385,35993240454541829995665598616⟩,⟨(-6233006298189215746322261211),(-6233006298189215724437831408)⟩⟩,⟨⟨36452008429219813026790051966,36452008429219813052951399919⟩,⟨(-6370431660394543919449708668),(-6370431660394543897479055960)⟩⟩,⟨⟨36909705578952678713610495238,36909705578952678739878308347⟩,⟨(-6508414282079257393167217920),(-6508414282079257371113212715)⟩⟩,⟨⟨37365105629767803743954981102,37365105629767803770304561167⟩,⟨(-6646707301904864104150380370),(-6646707301904864082020392688)⟩⟩,⟨⟨37819021072922954530171005554,37819021072922954556620679698⟩,⟨(-6785422699654169379756541720),(-6785422699654169357549813060)⟩⟩,⟨⟨38270287981936762892534894200,38270287981936762919078179691⟩,⟨(-6924320483909415381282323844),(-6924320483909415359002983922)⟩⟩,⟨⟨38719648267036852780988336514,38719648267036852807620491015⟩,⟨(-7063501989456468230714656054),(-7063501989456468208366048599)⟩⟩,⟨⟨39166002064219578650365228157,39166002064219578677083044900⟩,⟨(-7202734961332202789044664366),(-7202734961332202766630316083)⟩⟩,⟨⟨39610019775414514594653460299,39610019775414514621450850783⟩,⟨(-7342109518243493802486213805),(-7342109518243493780009753179)⟩⟩,⟨⟨40050667432672375399469720402,40050667432672375426343422662⟩,⟨(-7481402028133446272894968058),(-7481402028133446250359927163)⟩⟩,⟨⟨40488542908758796605540166789,40488542908758796632487956250⟩,⟨(-7620690811554857004563625544),(-7620690811554856981972933145)⟩⟩,⟨⟨40922680080647983634705074739,40922680080647983661712074318⟩,⟨(-7759761765703628880000150467),(-7759761765703628857359511761)⟩⟩,⟨⟨41353603178488506160367482820,41353603178488506187439254599⟩,⟨(-7898680819171865509551095100),(-7898680819171865486861999249)⟩⟩] +lemma amp9_04_6_eq : ∀ k : Fin 16, amp9_0Expr 4 6 k = amp9_04_6 k := by decide +kernel +noncomputable def amp9_04_7 : Fin 16 → CBox := ![⟨⟨41780415985517095062561490842,41780415985517095089692359805⟩,⟨(-8037244324657834625331329968),(-8037244324657834602597738557)⟩⟩,⟨⟨42203567883715813862276515506,42203567883715813889464053882⟩,⟨(-8175505212462621459570671228),(-8175505212462621436795583530)⟩⟩,⟨⟨42622234734024920095235991384,42622234734024920122469929299⟩,⟨(-8313271236982902331713345107),(-8313271236982902308901597962)⟩⟩,⟨⟨43036789772607785611101270201,43036789772607785638382485065⟩,⟨(-8450581710525803782925274597),(-8450581710525803760079251876)⟩⟩,⟨⟨43446483217723335816280455065,43446483217723335843600861442⟩,⟨(-8587256755412933339740342188),(-8587256755412933316864457578)⟩⟩,⟨⟨43851610769474460612076328901,43851610769474460639436130137⟩,⟨(-8723321431972879255000364211),(-8723321431972879232097128053)⟩⟩,⟨⟨44251499389731217202673973946,44251499389731217230065858071⟩,⟨(-8858609216839208435823000720),(-8858609216839208412896654561)⟩⟩,⟨⟨44646365758749129081169595304,44646365758749129108589748616⟩,⟨(-8993130269122809617696646516),(-8993130269122809594750516647)⟩⟩,⟨⟨45035616073909343483874745290,45035616073909343511318906625⟩,⟨(-9126732426498762503474345350),(-9126732426498762480512059230)⟩⟩,⟨⟨45419386416870872087879508085,45419386416870872115344442902⟩,⟨(-9259410281325397366362655395),(-9259410281325397343387421487)⟩⟩,⟨⟨45797164817391375482003991573,45797164817391375509483818579⟩,⟨(-9391027059631885647991551103),(-9391027059631885625007295516)⟩⟩,⟨⟨46169005082945403268034546540,46169005082945403295525757641⟩,⟨(-9521561104079381992426920695),(-9521561104079381969436927534)⟩⟩,⟨⟨46534479777289267961793591381,46534479777289267989290357103⟩,⟨(-9650892077252799436991286328),(-9650892077252799413999462537)⟩⟩,⟨⟨46893558658948132851007538327,46893558658948132878505541472⟩,⟨(-9778981370569384274021857768),(-9778981370569384251031656320)⟩⟩,⟨⟨47245901632290420733487239098,47245901632290420760980896414⟩,⟨(-9905726152639809856087404225),(-9905726152639809833102655062)⟩⟩,⟨⟨47591392530143440362694911906,47591392530143440390178600674⟩,⟨(-10031070142211902044629216857),(-10031070142211902021653666390)⟩⟩] +lemma amp9_04_7_eq : ∀ k : Fin 16, amp9_0Expr 4 7 k = amp9_04_7 k := by decide +kernel +noncomputable def amp9_04_8 : Fin 16 → CBox := ![⟨⟨47929781509785137985213617024,47929781509785138012688085399⟩,⟨(-10154929105121458605776803275),(-10154929105121458582812935082)⟩⟩,⟨⟨48260864496326621552643326893,48260864496326621580109983014⟩,⟨(-10277228344774870563061611826),(-10277228344774870540111662903)⟩⟩,⟨⟨48584484919106758104373506715,48584484919106758131826445754⟩,⟨(-10397903337713655833563310883),(-10397903337713655810631115914)⟩⟩,⟨⟨48900348704450041351634783960,48900348704450041379068880109⟩,⟨(-10516860206617878182380671461),(-10516860206617878159469867894)⟩⟩,⟨⟨49208395681433283157390341782,49208395681433283184800850730⟩,⟨(-10634055275149534867529426570),(-10634055275149534844643588824)⟩⟩,⟨⟨49508239573172797104837631649,49508239573172797132219223695⟩,⟨(-10749374695591017536770286513),(-10749374695591017513913093494)⟩⟩,⟨⟨49799919846888571001058722810,49799919846888571028407616101⟩,⟨(-10862796798838857624024660288),(-10862796798838857601199441668)⟩⟩,⟨⟨50082955699873739061033729576,50082955699873739088344366315⟩,⟨(-10974186951129577924073196074),(-10974186951129577901283694437)⟩⟩,⟨⟨50357489589393191941499543680,50357489589393191968768293339⟩,⟨(-11083546675297232724768823263),(-11083546675297232702018317825)⟩⟩,⟨⟨50622943740691017066000094602,50622943740691017093223360787⟩,⟨(-11190719708089349802028663686),(-11190719708089349779320453549)⟩⟩,⟨⟨50879567069849879588318426342,50879567069849879615492128624⟩,⟨(-11295731974597181566672372012),(-11295731974597181544009787597)⟩⟩,⟨⟨51126682254197377302589169494,51126682254197377329706004372⟩,⟨(-11398404708883201012654068712),(-11398404708883200990041243658)⟩⟩,⟨⟨51364648258306051203232792453,51364648258306051230293272276⟩,⟨(-11498789475413175223431526992),(-11498789475413175200870746017)⟩⟩,⟨⟨51592685499389119250042491346,51592685499389119277038471396⟩,⟨(-11596684100503760028134182561),(-11596684100503760005629756654)⟩⟩,⟨⟨51811266705816011244289663315,51811266705816011271222776285⟩,⟨(-11692167053261121774974558973),(-11692167053261121752528464351)⟩⟩,⟨⟨52019507178757784297417091245,52019507178757784324276284652⟩,⟨(-11785011813049447617967940094),(-11785011813049447595585156298)⟩⟩] +lemma amp9_04_8_eq : ∀ k : Fin 16, amp9_0Expr 4 8 k = amp9_04_8 k := by decide +kernel +noncomputable def amp9_04_9 : Fin 16 → CBox := ![⟨⟨52217997256828003857336295726,52217997256828003884118995063⟩,⟨(-11875325048569344313340371245),(-11875325048569344291023801762)⟩⟩,⟨⟨52405744117327072412399207406,52405744117327072439100077732⟩,⟨(-11962854916411658344864133010),(-11962854916411658322617452111)⟩⟩,⟨⟨52583459693046013250162010144,52583459693046013276789087672⟩,⟨(-12047737611262769699332493324),(-12047737611262769677156117216)⟩⟩,⟨⟨52750039868672906380133299270,52750039868672906406669234784⟩,⟨(-12129694951829510861421834974),(-12129694951829510839322192119)⟩⟩,⟨⟨52906322299862839946155407985,52906322299862839972598016290⟩,⟨(-12208894018594743000838968603),(-12208894018594742978818788602)⟩⟩,⟨⟨53051088239101664999168145363,53051088239101665025515249012⟩,⟨(-12285029235075145131207686927),(-12285029235075145109269904898)⟩⟩,⟨⟨53185305346629168688005325121,53185305346629168714249725977⟩,⟨(-12358299963021469199971139829),(-12358299963021469178119588792)⟩⟩,⟨⟨53307636721340014627339459047,53307636721340014653478945834⟩,⟨(-12428372128096910072684960083),(-12428372128096910050922584384)⟩⟩,⟨⟨53419184472212702171205478799,53419184472212702197234447311⟩,⟨(-12495478806982420239659675628),(-12495478806982420217989916534)⟩⟩,⟨⟨53518489829289057422923022124,53518489829289057448834814856⟩,⟨(-12559256276019802230765017010),(-12559256276019802209191832681)⟩⟩,⟨⟨53606793967511526009980973489,53606793967511526035803491333⟩,⟨(-12619972801525971484018673958),(-12619972801525971462537568018)⟩⟩,⟨⟨53682512325615207523290156198,53682512325615207548990490067⟩,⟨(-12677233806482011596472826219),(-12677233806482011575093921498)⟩⟩,⟨⟨53747029946816208164230219992,53747029946816208189806140170⟩,⟨(-12731344265802869015367177121),(-12731344265802868994093032439)⟩⟩,⟨⟨53798632334189775228237067027,53798632334189775253681653243⟩,⟨(-12781877488373212790885978149),(-12781877488373212769720598472)⟩⟩,⟨⟨53838853400165187433212346985,53838853400165187458527487144⟩,⟨(-12829176724540682373825435821),(-12829176724540682352770339828)⟩⟩,⟨⟨53865844329648105804188482709,53865844329648105829364564157⟩,⟨(-12872781847134098512321231377),(-12872781847134098491381067695)⟩⟩] +lemma amp9_04_9_eq : ∀ k : Fin 16, amp9_0Expr 4 9 k = amp9_04_9 k := by decide +kernel +noncomputable def amp9_04_10 : Fin 16 → CBox := ![⟨⟨53881293119107192430482144467,53881293119107192455526630437⟩,⟨(-12913076000709954118080857873),(-12913076000709954097255772150)⟩⟩,⟨⟨53883211996616656242227973070,53883211996616656267127838285⟩,⟨(-12949564233877359613768672786),(-12949564233877359593064102453)⟩⟩,⟨⟨53873448488572133516777234775,53873448488572133541529721900⟩,⟨(-12982671260697089649122161987),(-12982671260697089628540631889)⟩⟩,⟨⟨53849870951451924066374540695,53849870951451924090978657618⟩,⟨(-13011865845697627177525093623),(-13011865845697627157069160395)⟩⟩,⟨⟨53814492137857463548259759974,53814492137857463572707329551⟩,⟨(-13037616009409894502467969378),(-13037616009409894482141429060)⟩⟩,⟨⟨53765031319647943129071262210,53765031319647943153361696454⟩,⟨(-13059352694651544123675798973),(-13059352694651544103481080034)⟩⟩,⟨⟨53703672444059708926226348435,53703672444059708950355764596⟩,⟨(-13077589032858803763162513925),(-13077589032858803743102309756)⟩⟩,⟨⟨53627980162398360979488867087,53627980162398361003451288352⟩,⟨(-13091716523008848072916570782),(-13091716523008848052994616310)⟩⟩,⟨⟨53540315881619995133390614543,53540315881619995157182238030⟩,⟨(-13102295285879987930665334670),(-13102295285879987910884273177)⟩⟩,⟨⟨53438083746144092601258461117,53438083746144092624874139591⟩,⟨(-13108675662500827692160953289),(-13108675662500827672524288119)⟩⟩,⟨⟨53323829212007163941107663846,53323829212007163964541655028⟩,⟨(-13111466722795377673638996066),(-13111466722795377654149778490)⟩⟩,⟨⟨53194789649297340828464059720,53194789649297340851811245296⟩,⟨(-13109975835423449533692153471),(-13109975835423449514329242371)⟩⟩,⟨⟨53053701507931708541582081233,53053701507931708564746185618⟩,⟨(-13104863068938931657161660263),(-13104863068938931637950324207)⟩⟩,⟨⟨52897628700706471736107341282,52897628700706471759085391757⟩,⟨(-13095390895588513071700746362),(-13095390895588513052643923744)⟩⟩,⟨⟨52729506006867421235811245516,52729506006867421258599654738⟩,⟨(-13082272531117872677826970765),(-13082272531117872658927069331)⟩⟩,⟨⟨52546216744812872092532962877,52546216744812872115129594490⟩,⟨(-13064723507257033426684118060),(-13064723507257033407943865235)⟩⟩] +lemma amp9_04_10_eq : ∀ k : Fin 16, amp9_0Expr 4 10 k = amp9_04_10 k := by decide +kernel +noncomputable def amp9_04_11 : Fin 16 → CBox := ![⟨⟨52350901789054522650744197416,52350901789054522673145732842⟩,⟨(-13043512445221825681282698741),(-13043512445221825662704396928)⟩⟩,⟨⟨52140256228849482746837194504,52140256228849482769041832870⟩,⟨(-13017805760334312469144487011),(-13017805760334312450730740866)⟩⟩,⟨⟨51917635275567279188326487470,51917635275567279210327921579⟩,⟨(-12988429859341489309217386525),(-12988429859341489290971166578)⟩⟩,⟨⟨51679537607840128906705594303,51679537607840128928506080425⟩,⟨(-12954499720255460289176674688),(-12954499720255460271099571847)⟩⟩,⟨⟨51429541542449873863852522217,51429541542449873885443603152⟩,⟨(-12916902050911340031012445801),(-12916902050911340013107926145)⟩⟩,⟨⟨51163940563577927339003531888,51163940563577927360383385517⟩,⟨(-12874697911143072128779466634),(-12874697911143072111050110524)⟩⟩,⟨⟨50886545447355743839331164932,50886545447355743860494367263⟩,⟨(-12828836976547584771102116419),(-12828836976547584753550558290)⟩⟩,⟨⟨50593435034188744118920590377,50593435034188744139879223485⟩,⟨(-12778323730974931506690475385),(-12778323730974931489315781952)⟩⟩,⟨⟨50288662565566931519949500513,50288662565566931540686138775⟩,⟨(-12724173653412829166639307622),(-12724173653412829149447096804)⟩⟩,⟨⟨49968082051320625517073248256,49968082051320625537585527012⟩,⟨(-12665331797658554997803707460),(-12665331797658554980796658297)⟩⟩,⟨⟨49635999932720457517693940496,49635999932720457537982783880⟩,⟨(-12602882471102409496858780122),(-12602882471102409480037793535)⟩⟩,⟨⟨49288034382440950013454656197,49288034382440950033511652089⟩,⟨(-12535708225070645798022034920),(-12535708225070645781391327221)⟩⟩,⟨⟨48928756592027629043161995610,48928756592027629062986364707⟩,⟨(-12464965433213760043884909399),(-12464965433213760027445762572)⟩⟩,⟨⟨48553536976168246443907705467,48553536976168246463495524362⟩,⟨(-12389470828282574161729628372),(-12389470828282574145485090944)⟩⟩,⟨⟨48167223944238972220340222613,48167223944238972239687255336⟩,⟨(-12310456327929295122225991914),(-12310456327929295106178144572)⟩⟩,⟨⟨47764927209013523635428336540,47764927209013523654529159562⟩,⟨(-12226669257357300091391750709),(-12226669257357300075544029500)⟩⟩] +lemma amp9_04_11_eq : ∀ k : Fin 16, amp9_0Expr 4 11 k = amp9_04_11 k := by decide +kernel +noncomputable def amp9_04_12 : Fin 16 → CBox := ![⟨⟨47351785899081707487655920813,47351785899081707506567555072⟩,⟨(-12139420827114858749503213549),(-12139420827114858733841950415)⟩⟩,⟨⟨46922634932354674613602013606,46922634932354674632270493760⟩,⟨(-12047385059268084761279704073),(-12047385059268084745820722387)⟩⟩,⟨⟨46482918827378190378027281584,46482918827378190396450206597⟩,⟨(-11951956513609678110555445517),(-11951956513609678095300213468)⟩⟩,⟨⟨46027182318914871380659263602,46027182318914871398834025918⟩,⟨(-11851731667654209180629416275),(-11851731667654209165580618886)⟩⟩,⟨⟨45561191313542663025334512606,45561191313542663043258812975⟩,⟨(-11748192836559880540955572073),(-11748192836559880526114592837)⟩⟩,⟨⟨45079183508459261406471796819,45079183508459261424143964054⟩,⟨(-11639854320292927862057847882),(-11639854320292927847427104045)⟩⟩,⟨⟨44587263708650626987210325631,44587263708650627004625237135⟩,⟨(-11528290994826055297613533103),(-11528290994826055283195047924)⟩⟩,⟨⟨44079344052860542280652971335,44079344052860542297815441400⟩,⟨(-11411929904329072435653678743),(-11411929904329072421448196148)⟩⟩,⟨⟨43561887484781462608448988981,43561887484781462625348910647⟩,⟨(-11292443748676301666356517262),(-11292443748676301652367292939)⟩⟩,⟨⟨43028460161109125531236234210,43028460161109125547872507335⟩,⟨(-11168166729462903626985742941),(-11168166729462903613215024544)⟩⟩,⟨⟨42485904391852887073682943056,42485904391852887090052653235⟩,⟨(-11040875160160211475839846146),(-11040875160160211462288931576)⟩⟩,⟨⟨41927417745252400267576233920,41927417745252400283675712341⟩,⟨(-10908804229451485835298169177),(-10908804229451485821969985772)⟩⟩,⟨⟨41360245418699226952434589724,41360245418699226968259366250⟩,⟨(-10773840262747186158854925824),(-10773840262747186145751110325)⟩⟩,⟨⟨40777191268633096580322084162,40777191268633096595906364884⟩,⟨(-10634112592427048447677803315),(-10634112592427048434791390451)⟩⟩,⟨⟨40185929560700215869833436525,40185929560700215885141371047⟩,⟨(-10491624661005867352213113705),(-10491624661005867339553815324)⟩⟩,⟨⟨39578842398149307600717744817,39578842398149307615746649768⟩,⟨(-10344392320674815751108519936),(-10344392320674815738679002441)⟩⟩] +lemma amp9_04_12_eq : ∀ k : Fin 16, amp9_0Expr 4 12 k = amp9_04_12 k := by decide +kernel +noncomputable def amp9_04_13 : Fin 16 → CBox := ![⟨⟨38964062396852311990076207908,38964062396852312004825856463⟩,⟨(-10194544061302622087226998867),(-10194544061302622075027623208)⟩⟩,⟨⟨38333518462564732035868673871,38333518462564732050340513314⟩,⟨(-10039973720638874091860542660),(-10039973720638874079892875159)⟩⟩,⟨⟨37695834479804539878966202331,37695834479804539893152230529⟩,⟨(-9882943734709660315862319218),(-9882943734709660304128645208)⟩⟩,⟨⟨37042450719137358629245831643,37042450719137358643145451764⟩,⟨(-9721216324032392153231390571),(-9721216324032392141733835774)⟩⟩,⟨⟨36382519543077486951467647392,36382519543077486965076872460⟩,⟨(-9557197913543233297061840560),(-9557197913543233285801558593)⟩⟩,⟨⟨35706952430978710394176212248,35706952430978710407516117054⟩,⟨(-9388508241009929524804949462),(-9388508241009929513778362364)⟩⟩,⟨⟨35025472530481369295437375655,35025472530481369308486809995⟩,⟨(-9217709123208483658246229593),(-9217709123208483647458885708)⟩⟩,⟨⟨34328416757559154424411226121,34328416757559154437166656982⟩,⟨(-9042265446402566971714439596),(-9042265446402566961169256189)⟩⟩,⟨⟨33626127453700570136943820193,33626127453700570149405517835⟩,⟨(-8864907451324136429308409312),(-8864907451324136419005217699)⟩⟩,⟨⟨32908314460568070236700023603,32908314460568070248867231939⟩,⟨(-8682931000002419893815512354),(-8682931000002419883756498903)⟩⟩,⟨⟨32185995085203211668464663808,32185995085203211680334972809⟩,⟨(-8499249756460134727209853764),(-8499249756460134717395428225)⟩⟩,⟨⟨31448191426810142419298637818,31448191426810142430884355357⟩,⟨(-8310974201781988974014360412),(-8310974201781988964443296361)⟩⟩,⟨⟨30706660495203998640922490582,30706660495203998652205324202⟩,⟨(-8121218819281640850130306124),(-8121218819281640840807102834)⟩⟩,⟨⟨29949666008790391498813089323,29949666008790391509791566266⟩,⟨(-7926889682697347373226190599),(-7926889682697347364153283247)⟩⟩,⟨⟨29189780443587038982140788681,29189780443587038992816616953⟩,⟨(-7731322439515148045026310792),(-7731322439515148036202777122)⟩⟩,⟨⟨28414426181809748562119644494,28414426181809748572487332667⟩,⟨(-7531196431271605637615095243),(-7531196431271605629044485148)⟩⟩] +lemma amp9_04_13_eq : ∀ k : Fin 16, amp9_0Expr 4 13 k = amp9_04_13 k := by decide +kernel +noncomputable def amp9_04_14 : Fin 16 → CBox := ![⟨⟨27637080640873515853046974373,27637080640873515863119557687⟩,⟨(-7330092483041432287753933698),(-7330092483041432279432199869)⟩⟩,⟨⟨26844226513243837677785237988,26844226513243837687548221715⟩,⟨(-7124436755348031967162787954),(-7124436755348031959095900787)⟩⟩,⟨⟨26050352897178328791707428767,26050352897178328801163529030⟩,⟨(-6918083884758200757697032914),(-6918083884758200749883518929)⟩⟩,⟨⟨25240884934298901645816420814,25240884934298901654957634002⟩,⟨(-6707175176996376674774032457),(-6707175176996376667218221039)⟩⟩,⟨⟨24431452185863556032647977388,24431452185863556041487457817⟩,⟨(-6495873614970292569899055213),(-6495873614970292562596547470)⟩⟩,⟨⟨23606279295269157570057592204,23606279295269157578582279358⟩,⟨(-6279997256106114467420956247),(-6279997256106114460377491727)⟩⟩,⟨⟨22782293661536101735394702674,22782293661536101743613082480⟩,⟨(-6064059620565666576300757485),(-6064059620565666569512989078)⟩⟩,⟨⟨21942343669019727733390457492,21942343669019727741290853913⟩,⟨(-5843508333865144118779328666),(-5843508333865144112252735054)⟩⟩,⟨⟨21104849694531081656963849112,21104849694531081664549147242⟩,⟨(-5623259758294419902357484753),(-5623259758294419896090023915)⟩⟩,⟨⟨20251064337910493590687666600,20251064337910493597958947777⟩,⟨(-5398332179446450278454217165),(-5398332179446450272448075789)⟩⟩,⟨⟨19401147024884012927411735385,19401147024884012934365192445⟩,⟨(-5174110748446996736384761788),(-5174110748446996730639446494)⟩⟩,⟨⟨18534475343928008710120139976,18534475343928008716756527681⟩,⟨(-4945109508397047029882782978),(-4945109508397047024400724424)⟩⟩,⟨⟨17673264216654597035456832903,17673264216654597041779072494⟩,⟨(-4717267198118655934379928000),(-4717267198118655929158590020)⟩⟩,⟨⟨16794653372743877961311356410,16794653372743877967309492806⟩,⟨(-4484496312031306882923873489),(-4484496312031306877968720216)⟩⟩,⟨⟨15923329750023602576696174509,15923329750023602582377707180⟩,⟨(-4253400785223850299100765092),(-4253400785223850294407730633)⟩⟩,⟨⟨15033711515838969388796189407,15033711515838969394155374706⟩,⟨(-4017161876444438554931398499),(-4017161876444438550505066021)⟩⟩] +lemma amp9_04_14_eq : ∀ k : Fin 16, amp9_0Expr 4 14 k = amp9_04_14 k := by decide +kernel +noncomputable def amp9_04_15 : Fin 16 → CBox := ![⟨⟨14153521423645093473544441153,14153521423645093478584528344⟩,⟨(-3783199784228645036397651192),(-3783199784228645032234737798)⟩⟩,⟨⟨13253790951781465860157837352,13253790951781465864872553750⟩,⟨(-3543786234992750820845556104),(-3543786234992750816951083588)⟩⟩,⟨⟨12366068512016756522660438219,12366068512016756527054488731⟩,⟨(-3307369321525166185252591638),(-3307369321525166181622434264)⟩⟩,⟨⟨11457048376785998801256528456,11457048376785998805325170401⟩,⟨(-3065056473631586441485624743),(-3065056473631586438124812877)⟩⟩,⟨⟨10563260071195201065402706113,10563260071195201069151221389⟩,⟨(-2826633270511767723348309889),(-2826633270511767720251997401)⟩⟩,⟨⟨9645633791071247972017904294,9645633791071247975438204961⟩,⟨(-2581660444753823032303548081),(-2581660444753823029478219277)⟩⟩,⟨⟨8747468294059073360226002964,8747468294059073363324890859⟩,⟨(-2341740172299399887910847985),(-2341740172299399885350477696)⟩⟩,⟨⟨7821643486831059402818395918,7821643486831059405588379851⟩,⟨(-2094273829805534680844768885),(-2094273829805534678556505055)⟩⟩,⟨⟨6921213866164120835763671290,6921213866164120838212939039⟩,⟨(-1853480404442691530616725532),(-1853480404442691528593073337)⟩⟩,⟨⟨5986997996073589996984083927,5986997996073589999101463158⟩,⟨(-1603527089250132361056936371),(-1603527089250132359307298272)⟩⟩,⟨⟨5087372685039129767810106400,5087372685039129769607931206⟩,⟨(-1362741222863623936490960493),(-1362741222863623935004982037)⟩⟩,⟨⟨4143033990395352502704712296,4143033990395352504167926926⟩,⟨(-1109895761162676724263729390),(-1109895761162676723054079131)⟩⟩,⟨⟨3250014495413228346314563434,3250014495413228347461165688⟩,⟨(-870731121346295532404912008),(-870731121346295531456489945)⟩⟩,⟨⟨2288527698933591183929420881,2288527698933591184736091448⟩,⟨(-613170481679804685409314541),(-613170481679804684741752184)⟩⟩,⟨⟨1419782442513108681836835570,1419782442513108682335280915⟩,⟨(-380420923474277062696382130),(-380420923474277062282805799)⟩⟩,⟨⟨403388193052863035545300030,403388193052863035685743862⟩,⟨(-108087267962443344241372979),(-108087267962443344124187428)⟩⟩] +lemma amp9_04_15_eq : ∀ k : Fin 16, amp9_0Expr 4 15 k = amp9_04_15 k := by decide +kernel +noncomputable def amp9_04 : Fin 16 → Fin 16 → CBox := ![amp9_04_0,amp9_04_1,amp9_04_2,amp9_04_3,amp9_04_4,amp9_04_5,amp9_04_6,amp9_04_7,amp9_04_8,amp9_04_9,amp9_04_10,amp9_04_11,amp9_04_12,amp9_04_13,amp9_04_14,amp9_04_15] +lemma amp9_04_eq (i k : Fin 16) : amp9_0Expr 4 i k = amp9_04 i k := by + fin_cases i + · exact amp9_04_0_eq k + · exact amp9_04_1_eq k + · exact amp9_04_2_eq k + · exact amp9_04_3_eq k + · exact amp9_04_4_eq k + · exact amp9_04_5_eq k + · exact amp9_04_6_eq k + · exact amp9_04_7_eq k + · exact amp9_04_8_eq k + · exact amp9_04_9_eq k + · exact amp9_04_10_eq k + · exact amp9_04_11_eq k + · exact amp9_04_12_eq k + · exact amp9_04_13_eq k + · exact amp9_04_14_eq k + · exact amp9_04_15_eq k +noncomputable def amp9_05_0 : Fin 16 → CBox := ![⟨⟨1017365712714789582412,1017365712714806656212⟩,⟨(-8649277),8649282⟩⟩,⟨⟨32227844834901885180018,32227844834901945277190⟩,⟨(-30443786),30443938⟩⟩,⟨⟨144307603078629628353343,144307603078629725234573⟩,⟨(-49076495),49077175⟩⟩,⟨⟨401710817432016674520882,401710817432016812129440⟩,⟨(-69704918),69706811⟩⟩,⟨⟨846618630911081777873541,846618630911081953334801⟩,⟨(-88874594),88878584⟩⟩,⟨⟨1553203743542669544274406,1553203743542669759792852⟩,⟨(-109157596),109164916⟩⟩,⟨⟨2553427679062347536387104,2553427679062347790106762⟩,⟨(-128496428),128508463⟩⟩,⟨⟨3930825950684612355971439,3930825950684612649403087⟩,⟨(-148595623),148614150⟩⟩,⟨⟨5707149034948221291888609,5707149034948221623651904⟩,⟨(-167990161),168017060⟩⟩,⟨⟨7974992912616157603273367,7974992912616157974503158⟩,⟨(-187953565),187991153⟩⟩,⟨⟨10745843359115808013509729,10745843359115808423099256⟩,⟨(-207348839),207399486⟩⟩,⟨⟨14121091280701553057183412,14121091280701553506030838⟩,⟨(-227191331),227257887⟩⟩,⟨⟨18101889125021378311407097,18101889125021378798578011⟩,⟨(-246552709),246638028⟩⟩,⟨⟨22798164690230290408885678,22798164690230290935112099⟩,⟨(-266276136),266383589⟩⟩,⟨⟨28200671625299007046688031,28200671625299007611159772⟩,⟨(-285577905),285710821⟩⟩,⟨⟨34427613720176448625434016,34427613720176449228761472⟩,⟨(-305177998),305340263⟩⟩] +lemma amp9_05_0_eq : ∀ k : Fin 16, amp9_0Expr 5 0 k = amp9_05_0 k := by decide +kernel +noncomputable def amp9_05_1 : Fin 16 → CBox := ![⟨⟨41459290719596023701396978,41459290719596024342852285⟩,⟨(-324398995),324594402⟩⟩,⟨⟨49421914614835276365094033,49421914614835277045189338⟩,⟨(-343868277),344101214⟩⟩,⟨⟨58285289887787186486983824,58285289887787187205055019⟩,⟨(-362989933),363264645⟩⟩,⟨⟨68183360397692089594610300,68183360397692090351108873⟩,⟨(-382319110),382640474⟩⟩,⟨⟨79075409598275565416789351,79075409598275566211083119⟩,⟨(-401324468),401697169⟩⟩,⟨⟨91102827691590655214296079,91102827691590656046755579⟩,⟨(-420503170),420932559⟩⟩,⟨⟨104214368082311430049500797,104214368082311430919577461⟩,⟨(-439376357),439867544⟩⟩,⟨⟨118558572418822139446543938,118558572418822140354522327⟩,⟨(-458393565),458952359⟩⟩,⟨⟨134073672582852005439799426,134073672582852006385165105⟩,⟨(-477119484),477751404⟩⟩,⟨⟨150915057458186184084660442,150915057458186185067690711⟩,⟨(-495963786),496675084⟩⟩,⟨⟨169010464087999568475706810,169010464087999569495831432⟩,⟨(-514527932),515324518⟩⟩,⟨⟨188521815248313382165818294,188521815248313383223311190⟩,⟨(-533187700),534076247⟩⟩,⟨⟨209366398483646596557519735,209366398483646597651807019⟩,⟨(-551576044),552562836⟩⟩,⟨⟨231712348237249835740755396,231712348237249836872123012⟩,⟨(-570039541),571131656⟩⟩,⟨⟨255466566973823128603691729,255466566973823129771621321⟩,⟨(-588238459),589442533⟩⟩,⟨⟨280803069984181515662938027,280803069984181516867601337⟩,⟨(-606493926),607817417⟩⟩] +lemma amp9_05_1_eq : ∀ k : Fin 16, amp9_0Expr 5 1 k = amp9_05_1 k := by decide +kernel +noncomputable def amp9_05_2 : Fin 16 → CBox := ![⟨⟨307618458522706083434003884,307618458522706084674813386⟩,⟨(-624490152),625940030⟩⟩,⟨⟨336092289619148268001842143,336092289619148269279051481⟩,⟨(-642525864),644109946⟩⟩,⟨⟨366110966970354770416364258,366110966970354771729493556⟩,⟨(-660306459),662032026⟩⟩,⟨⟨397859242260386785839448420,397859242260386787188609169⟩,⟨(-678110774),679985977⟩⟩,⟨⟨431213445365565142851366494,431213445365565144236135516⟩,⟨(-695663107),697695517⟩⟩,⟨⟨466363167876582221127714333,466363167876582222547898543⟩,⟨(-713224498),715422577⟩⟩,⟨⟨503174809944199806588832842,503174809944199808044203939⟩,⟨(-730536239),732907819⟩⟩,⟨⟨541842440962969023384215113,541842440962969024874778130⟩,⟨(-747843328),750397158⟩⟩,⟨⟨582222696060299641118745460,582222696060299642644098651⟩,⟨(-764902435),767646586⟩⟩,⟨⟨624513753276140036344488249,624513753276140037904663649⟩,⟨(-781944015),784887494⟩⟩,⟨⟨668562668250543283720670392,668562668250543285315230170⟩,⟨(-798738735),801889827⟩⟩,⟨⟨714571351742874039573607259,714571351742874041202143039⟩,⟨(-815503790),818871732⟩⟩,⟨⟨762377486480516794548436625,762377486480516796210976411⟩,⟨(-832022660),835615923⟩⟩,⟨⟨812186333523575930250503951,812186333523575931946962128⟩,⟨(-848500387),852328410⟩⟩,⟨⟨863826430484116376720496000,863826430484116378450503326⟩,⟨(-864732233),868803649⟩⟩,⟨⟨917506000071359152666816133,917506000071359154430166154⟩,⟨(-880912051),885236471⟩⟩] +lemma amp9_05_2_eq : ∀ k : Fin 16, amp9_0Expr 5 2 k = amp9_05_2 k := by decide +kernel +noncomputable def amp9_05_3 : Fin 16 → CBox := ![⟨⟨973044683965568814972962705,973044683965568816769328213⟩,⟨(-896845994),901432181⟩⟩,⟨⟨1030653271883720174285090559,1030653271883720176114434553⟩,⟨(-912717564),917575273⟩⟩,⟨⟨1090142780287363172303205486,1090142780287363174165117053⟩,⟨(-928343020),933481118⟩⟩,⟨⟨1151726165495505752646781654,1151726165495505754540217983⟩,⟨(-943896255),949324609⟩⟩,⟨⟨1215206111117198394379527286,1215206111117198396305065498⟩,⟨(-959202943),964930493⟩⟩,⟨⟨1280797334109812438674184368,1280797334109812440631645328⟩,⟨(-974428020),980464717⟩⟩,⟨⟨1348294499353228943358554610,1348294499353228945347498066⟩,⟨(-989405963),995760790⟩⟩,⟨⟨1417913673107950988705408156,1417913673107950990725673631⟩,⟨(-1004293333),1010976292⟩⟩,⟨⟨1489441837489806939239598145,1489441837489806941290818507⟩,⟨(-1018932866),1025952953⟩⟩,⟨⟨1563095991521031543023329216,1563095991521031545105085916⟩,⟨(-1033473265),1040840501⟩⟩,⟨⟨1638655792425954714239670991,1638655792425954716351806866⟩,⟨(-1047765036),1055488404⟩⟩,⟨⟨1716338750384461638970483115,1716338750384461641112726979⟩,⟨(-1061949492),1070038997⟩⟩,⟨⟨1795917577556343211962250610,1795917577556343214134217455⟩,⟨(-1075884472),1084349051⟩⟩,⟨⟨1877609868733088064714481105,1877609868733088066915996752⟩,⟨(-1089704311),1098553925⟩⟩,⟨⟨1961181792819992280823689030,1961181792819992283054341857⟩,⟨(-1103273794),1112517302⟩⟩,⟨⟨2046850597829250581740870232,2046850597829250584000465972⟩,⟨(-1116720654),1126367938⟩⟩] +lemma amp9_05_3_eq : ∀ k : Fin 16, amp9_0Expr 5 3 k = amp9_05_3 k := by decide +kernel +noncomputable def amp9_05_4 : Fin 16 → CBox := ![⟨⟨2134376333215646663432048323,2134376333215646665717870852⟩,⟨(-1129916262),1139976076⟩⟩,⟨⟨2223975464049050680457263121,2223975464049050682771710882⟩,⟨(-1142982092),1153464208⟩⟩,⟨⟨2315402366125218524907797788,2315402366125218527250350329⟩,⟨(-1155795782),1166708814⟩⟩,⟨⟨2408872280684075507131755406,2408872280684075509502127948⟩,⟨(-1168472853),1179826430⟩⟩,⟨⟨2504134377618229002678290582,2504134377618229005076009938⟩,⟨(-1180896918),1192699488⟩⟩,⟨⟨2601402228747062344216980508,2601402228747062346641931516⟩,⟨(-1193177826),1205438842⟩⟩,⟨⟨2700420287741234992553645583,2700420287741234995005121740⟩,⟨(-1205204900),1217932611⟩⟩,⟨⟨2801400006700950694721233840,2801400006700950697199194443⟩,⟨(-1217082571),1230286223⟩⟩,⟨⟨2904081634627201913755278269,2904081634627201916259327216⟩,⟨(-1228705631),1242393246⟩⟩,⟨⟨3008674048861856003575380190,3008674048861856006104426118⟩,⟨(-1240173328),1254353911⟩⟩,⟨⟨3114913827091087447542966565,3114913827091087450097459922⟩,⟨(-1251385699),1266067015⟩⟩,⟨⟨3223006812058119978481463601,3223006812058119981060997707⟩,⟨(-1262437021),1277627805⟩⟩,⟨⟨3332686465209943391180225147,3332686465209943393784441173⟩,⟨(-1273232378),1288940107⟩⟩,⟨⟨3444155129960154740842225629,3444155129960154743470509532⟩,⟨(-1283861268),1300094375⟩⟩,⟨⟨3557143728219029241487109645,3557143728219029244139382151⟩,⟨(-1294233634),1310999283⟩⟩,⟨⟨3671850634329706808878002201,3671850634329706811553764286⟩,⟨(-1304434380),1321740669⟩⟩] +lemma amp9_05_4_eq : ∀ k : Fin 16, amp9_0Expr 5 4 k = amp9_05_4 k := by decide +kernel +noncomputable def amp9_05_5 : Fin 16 → CBox := ![⟨⟨3788004828890165630851767163,3788004828890165633550658963⟩,⟨(-1314378134),1332231885⟩⟩,⟨⟨3905800242272824150387876314,3905800242272824153109614508⟩,⟨(-1324145369),1342554318⟩⟩,⟨⟨4024964533395238301619985443,4024964533395238304364213006⟩,⟨(-1333655245),1352625842⟩⟩,⟨⟨4145686708418613027467141181,4145686708418613030233537629⟩,⟨(-1342983953),1362523542⟩⟩,⟨⟨4267693745496789283839876158,4267693745496789286628011086⟩,⟨(-1352055038),1372169675⟩⟩,⟨⟨4391169240786213740947055220,4391169240786213743748986484⟩,⟨(-1360940553),1381637159⟩⟩,⟨⟨4515840153749391088355894394,4515840153749391091179078131⟩,⟨(-1369568293),1390852502⟩⟩,⟨⟨4641884178945692237125682973,4641884178945692239969626164⟩,⟨(-1378006299),1399884583⟩⟩,⟨⟨4769028940240375244673929926,4769028940240375247538018886⟩,⟨(-1386186496),1408664042⟩⟩,⟨⟨4897445732925117417407021078,4897445732925117420290931042⟩,⟨(-1394173029),1417255834⟩⟩,⟨⟨5026863549246854130101949885,5026863549246854133004993968⟩,⟨(-1401901838),1425594620⟩⟩,⟨⟨5157446781166343515116159516,5157446781166343518037970301⟩,⟨(-1409433287),1433741538⟩⟩,⟨⟨5288926514038202102834962209,5288926514038202105775339515⟩,⟨(-1416707223),1441635169⟩⟩,⟨⟨5421459725686305868348433875,5421459725686305871306606307⟩,⟨(-1423780327),1449332932⟩⟩,⟨⟨5554780339909606551871328981,5554780339909606554847079070⟩,⟨(-1430596257),1456777233⟩⟩,⟨⟨5689037402459319914022576195,5689037402459319917015655313⟩,⟨(-1437208104),1464021865⟩⟩] +lemma amp9_05_5_eq : ∀ k : Fin 16, amp9_0Expr 5 5 k = amp9_05_5 k := by decide +kernel +noncomputable def amp9_05_6 : Fin 16 → CBox := ![⟨⟨5823968441393309566224337274,5823968441393309569233231363⟩,⟨(-1443563249),1471012972⟩⟩,⟨⟨5959714044899289792209824059,5959714044899289795235403116⟩,⟨(-1449711279),1477800802⟩⟩,⟨⟨6096016131460073493112507015,6096016131460073496153630255⟩,⟨(-1455603211),1484335158⟩⟩,⟨⟨6233006298189215733949113574,6233006298189215737006065350⟩,⟨(-1461285209),1490662823⟩⟩,⟨⟨6370431660394543907027334590,6370431660394543910099239563⟩,⟨(-1466711851),1496737183⟩⟩,⟨⟨6508414282079257380697125845,6508414282079257383783834764⟩,⟨(-1471925948),1502601624⟩⟩,⟨⟨6646707301904864091638304435,6646707301904864094735709485⟩,⟨(-1476885569),1508213052⟩⟩,⟨⟨6785422699654169367200343970,6785422699654169370311957286⟩,⟨(-1481630238),1513611519⟩⟩,⟨⟨6924320483909415368684502808,6924320483909415371809445312⟩,⟨(-1486121451),1518757390⟩⟩,⟨⟨7063501989456468218077159757,7063501989456468221214871297⟩,⟨(-1490395507),1523687441⟩⟩,⟨⟨7202734961332202776369393882,7202734961332202779519585057⟩,⟨(-1494417266),1528365437⟩⟩,⟨⟨7342109518243493789775386880,7342109518243493792937240250⟩,⟨(-1498219859),1532824935⟩⟩,⟨⟨7481402028133446260150497563,7481402028133446263323703240⟩,⟨(-1501771455),1537033050⟩⟩,⟨⟨7620690811554856991787015662,7620690811554856994971480964⟩,⟨(-1505102069),1541020164⟩⟩,⟨⟨7759761765703628867195494500,7759761765703628870388719511⟩,⟨(-1508183129),1544756698⟩⟩,⟨⟨7898680819171865496718444953,7898680819171865499921799258⟩,⟨(-1511041577),1548269904⟩⟩] +lemma amp9_05_6_eq : ∀ k : Fin 16, amp9_0Expr 5 6 k = amp9_05_6 k := by decide +kernel +noncomputable def amp9_05_7 : Fin 16 → CBox := ![⟨⟨8037244324657834612473043526,8037244324657834615685752115⟩,⟨(-1513652056),1551533465⟩⟩,⟨⟨8175505212462621446688298976,8175505212462621449910241662⟩,⟨(-1516038476),1554571540⟩⟩,⟨⟨8313271236982902318810129272,8313271236982902322039635283⟩,⟨(-1518178653),1557361041⟩⟩,⟨⟨8450581710525803770002139851,8450581710525803773239722473⟩,⟨(-1520093505),1559923069⟩⟩,⟨⟨8587256755412933326800117584,8587256755412933330044506892⟩,⟨(-1521763982),1562237728⟩⟩,⟨⟨8723321431972879242044091580,8723321431972879245295690241⟩,⟨(-1523208041),1564323091⟩⟩,⟨⟨8858609216839208422853347847,8858609216839208426111033974⟩,⟨(-1524409733),1566162426⟩⟩,⟨⟨8993130269122809604715462946,8993130269122809607978836940⟩,⟨(-1525384085),1567770807⟩⟩,⟨⟨9126732426498762490483696550,9126732426498762493752224715⟩,⟨(-1526118219),1569134639⟩⟩,⟨⟨9259410281325397353364265890,9259410281325397356637678038⟩,⟨(-1526624256),1570266018⟩⟩,⟨⟨9391027059631885634987797677,9391027059631885638265233776⟩,⟨(-1526892363),1571154466⟩⟩,⟨⟨9521561104079381979419597349,9521561104079381982700721096⟩,⟨(-1526931776),1571809116⟩⟩,⟨⟨9650892077252799423982764241,9650892077252799427266705308⟩,⟨(-1526735687),1572222594⟩⟩,⟨⟨9778981370569384261014094640,9778981370569384264300355387⟩,⟨(-1526310463),1572401085⟩⟩,⟨⟨9905726152639809843082708684,9905726152639809846370464560⟩,⟨(-1525652299),1572340299⟩⟩,⟨⟨10031070142211902031629835846,10031070142211902034918301365⟩,⟨(-1524764713),1572043488⟩⟩] +lemma amp9_05_7_eq : ∀ k : Fin 16, amp9_0Expr 5 7 k = amp9_05_7 k := by decide +kernel +noncomputable def amp9_05_8 : Fin 16 → CBox := ![⟨⟨10154929105121458592783714399,10154929105121458596073378393⟩,⟨(-1523646886),1571509437⟩⟩,⟨⟨10277228344774870550075549360,10277228344774870553367139474⟩,⟨(-1522299493),1570738469⟩⟩,⟨⟨10397903337713655820586619766,10397903337713655823879239003⟩,⟨(-1520724694),1569732439⟩⟩,⟨⟨10516860206617878169415484086,10516860206617878172708461536⟩,⟨(-1518920327),1568488744⟩⟩,⟨⟨10634055275149534854577844719,10634055275149534857870507205⟩,⟨(-1516891519),1567012304⟩⟩,⟨⟨10749374695591017523834482596,10749374695591017527126117883⟩,⟨(-1514633279),1565297591⟩⟩,⟨⟨10862796798838857611106509322,10862796798838857614396650827⟩,⟨(-1512153697),1563352594⟩⟩,⟨⟨10974186951129577911174933568,10974186951129577914462803820⟩,⟨(-1509444947),1561168852⟩⟩,⟨⟨11083546675297232711892292633,11083546675297232715177435657⟩,⟨(-1506518082),1558757425⟩⟩,⟨⟨11190719708089349789175657215,11190719708089349792457735826⟩,⟨(-1503362442),1556106917⟩⟩,⟨⟨11295731974597181553844804040,11295731974597181557123269539⟩,⟨(-1499992043),1553231464⟩⟩,⟨⟨11398404708883200999854567119,11398404708883201003128243019⟩,⟨(-1496393379),1550116722⟩⟩,⟨⟨11498789475413175210660980995,11498789475413175213930321121⟩,⟨(-1492583438),1546779918⟩⟩,⟨⟨11596684100503760015395399226,11596684100503760018659043472⟩,⟨(-1488545861),1543203740⟩⟩,⟨⟨11692167053261121762268140447,11692167053261121765526806324⟩,⟨(-1484300613),1539408525⟩⟩,⟨⟨11785011813049447605297364579,11785011813049447608549015719⟩,⟨(-1479828464),1535373976⟩⟩] +lemma amp9_05_8_eq : ∀ k : Fin 16, amp9_0Expr 5 8 k = amp9_05_8 k := by decide +kernel +noncomputable def amp9_05_9 : Fin 16 → CBox := ![⟨⟨11875325048569344300707190436,11875325048569344303951570644⟩,⟨(-1475152374),1531123553⟩⟩,⟨⟨11962854916411658332270523136,11962854916411658335506892232⟩,⟨(-1470250225),1526633953⟩⟩,⟨⟨12047737611262769686777541922,12047737611262769690008082952⟩,⟨(-1465147984),1521931784⟩⟩,⟨⟨12129694951829510848910476440,12129694951829510852131684649⟩,⟨(-1459820625),1516990709⟩⟩,⟨⟨12208894018594742988372627830,12208894018594742991584323241⟩,⟨(-1454297142),1511840510⟩⟩,⟨⟨12285029235075145118787809592,12285029235075145121989969182⟩,⟨(-1448549574),1506451785⟩⟩,⟨⟨12358299963021469187600279033,12358299963021469190791568208⟩,⟨(-1442609970),1500857522⟩⟩,⟨⟨12428372128096910060364575977,12428372128096910063544949706⟩,⟨(-1436447400),1495025219⟩⟩,⟨⟨12495478806982420227391955176,12495478806982420230560417868⟩,⟨(-1430096998),1488991106⟩⟩,⟨⟨12559256276019802218552440002,12559256276019802221707918946⟩,⟨(-1423524831),1482719537⟩⟩,⟨⟨12619972801525971471855516153,12619972801525971475004899109⟩,⟨(-1416769149),1476250027⟩⟩,⟨⟨12677233806482011584367738452,12677233806482011587503773156⟩,⟨(-1409792979),1469543742⟩⟩,⟨⟨12731344265802869003321517603,12731344265802869006443980801⟩,⟨(-1402637727),1462643524⟩⟩,⟨⟨12781877488373212778902286737,12781877488373212782010028207⟩,⟨(-1395263331),1455507303⟩⟩,⟨⟨12829176724540682361904058657,12829176724540682364997837952⟩,⟨(-1387714397),1448181302⟩⟩,⟨⟨12872781847134098500465359340,12872781847134098503543365893⟩,⟨(-1379947727),1440620153⟩⟩] +lemma amp9_05_9_eq : ∀ k : Fin 16, amp9_0Expr 5 9 k = amp9_05_9 k := by decide +kernel +noncomputable def amp9_05_10 : Fin 16 → CBox := ![⟨⟨12913076000709954106289492960,12913076000709954109353800510⟩,⟨(-1372011176),1432873517⟩⟩,⟨⟨12949564233877359602045802479,12949564233877359605093794187⟩,⟨(-1363858352),1424892671⟩⟩,⟨⟨12982671260697089637469197176,12982671260697089640500507245⟩,⟨(-1355540413),1416730774⟩⟩,⟨⟨13011865845697627165943149194,13011865845697627168958023410⟩,⟨(-1347007717),1408335678⟩⟩,⟨⟨13037616009409894490959757925,13037616009409894493956497456⟩,⟨(-1338314782),1399764110⟩⟩,⟨⟨13059352694651544112242315771,13059352694651544115221275782⟩,⟨(-1329408646),1390960424⟩⟩,⟨⟨13077589032858803751805400248,13077589032858803754765921217⟩,⟨(-1320347258),1381984988⟩⟩,⟨⟨13091716523008848061638137234,13091716523008848064579248553⟩,⟨(-1311074263),1372778579⟩⟩,⟨⟨13102295285879987919467204561,13102295285879987922388231979⟩,⟨(-1301651112),1363405289⟩⟩,⟨⟨13108675662500827681045214785,13108675662500827683945399516⟩,⟨(-1292017977),1353802225⟩⟩,⟨⟨13111466722795377662607713435,13111466722795377665485906897⟩,⟨(-1282239892),1344037296⟩⟩,⟨⟨13109975835423449522722779790,13109975835423449525602847549⟩,⟨(-1272253467),1334043843⟩⟩,⟨⟨13104863068938931646278510902,13104863068938931649137019215⟩,⟨(-1262127411),1323893690⟩⟩,⟨⟨13095390895588513060905363462,13095390895588513063742078019⟩,⟨(-1251794672),1313516306⟩⟩,⟨⟨13082272531117872667120843520,13082272531117872669935122003⟩,⟨(-1241327732),1302987536⟩⟩,⟨⟨13064723507257033416068587328,13064723507257033418860385880⟩,⟨(-1230655773),1292232865⟩⟩] +lemma amp9_05_10_eq : ∀ k : Fin 16, amp9_0Expr 5 10 k = amp9_05_10 k := by decide +kernel +noncomputable def amp9_05_11 : Fin 16 → CBox := ![⟨⟨13043512445221825670759183875,13043512445221825673527894563⟩,⟨(-1219855157),1281332277⟩⟩,⟨⟨13017805760334312458714215862,13017805760334312461459897033⟩,⟨(-1208851185),1270207143⟩⟩,⟨⟨12988429859341489298882482948,12988429859341489301603786002⟩,⟨(-1197724215),1258941717⟩⟩,⟨⟨12954499720255460278937362575,12954499720255460281635339101⟩,⟨(-1186395540),1247453121⟩⟩,⟨⟨12916902050911340020871381825,12916902050911340023544113508⟩,⟨(-1174949644),1235830018⟩⟩,⟨⟨12874697911143072118737873893,12874697911143072121385402544⟩,⟨(-1163303675),1223985132⟩⟩,⟨⟨12828836976547584761161858126,12828836976547584763783021239⟩,⟨(-1151546384),1212011688⟩⟩,⟨⟨12778323730974931496849270651,12778323730974931499447603661⟩,⟨(-1139590624),1199817846⟩⟩,⟨⟨12724173653412829156902042275,12724173653412829159473321634⟩,⟨(-1127529566),1187501567⟩⟩,⟨⟨12665331797658554988171722429,12665331797658554990715851660⟩,⟨(-1115271601),1174966266⟩⟩,⟨⟨12602882471102409487332284349,12602882471102409489849677555⟩,⟨(-1102914494),1162314821⟩⟩,⟨⟨12535708225070645788603915868,12535708225070645791092920286⟩,⟨(-1090361992),1149445711⟩⟩,⟨⟨12464965433213760034575798202,12464965433213760037036365666⟩,⟨(-1077716640),1136466932⟩⟩,⟨⟨12389470828282574152531253659,12389470828282574154962880905⟩,⟨(-1064877342),1123271810⟩⟩,⟨⟨12310456327929295113139825718,12310456327929295115541582712⟩,⟨(-1051951630),1109973684⟩⟩,⟨⟨12226669257357300082419917733,12226669257357300084790896301⟩,⟨(-1038833346),1096460493⟩⟩] +lemma amp9_05_11_eq : ∀ k : Fin 16, amp9_0Expr 5 11 k = amp9_05_11 k := by decide +kernel +noncomputable def amp9_05_12 : Fin 16 → CBox := ![⟨⟨12139420827114858740631480403,12139420827114858742986414025⟩,⟨(-1025635235),1082851159⟩⟩,⟨⟨12047385059268084752522590852,12047385059268084754848167714⟩,⟨(-1012245837),1069027975⟩⟩,⟨⟨11951956513609678101913899585,11951956513609678104209629503⟩,⟨(-998783361),1055115722⟩⟩,⟨⟨11851731667654209172104826855,11851731667654209174370521321⟩,⟨(-985130777),1040990755⟩⟩,⟨⟨11748192836559880532548847602,11748192836559880534784011376⟩,⟨(-971412036),1026784012⟩⟩,⟨⟨11639854320292927853770116583,11639854320292927855974815384⟩,⟨(-957504247),1012365598⟩⟩,⟨⟨11528290994826055289446390298,11528290994826055291619396858⟩,⟨(-943537407),997872934⟩⟩,⟨⟨11411929904329072427606585285,11411929904329072429749626831⟩,⟨(-929382438),983169528⟩⟩,⟨⟨11292443748676301658432349475,11292443748676301660542871341⟩,⟨(-915175727),968399650⟩⟩,⟨⟨11168166729462903619185470390,11168166729462903621263686270⟩,⟨(-900781643),953419820⟩⟩,⟨⟨11040875160160211468164437515,11040875160160211470209652615⟩,⟨(-886343344),938381566⟩⟩,⟨⟨10908804229451485827749277574,10908804229451485829761018421⟩,⟨(-871718247),923133988⟩⟩,⟨⟨10773840262747186151433910629,10773840262747186153411042457⟩,⟨(-857056702),907836326⟩⟩,⟨⟨10634112592427048440376427585,10634112592427048442328364709⟩,⟨(-842208719),892329774⟩⟩,⟨⟨10491624661005867345040865664,10491624661005867346958293535⟩,⟨(-827332323),876781799⟩⟩,⟨⟨10344392320674815744066795359,10344392320674815745949494875⟩,⟨(-812269607),861025143⟩⟩] +lemma amp9_05_12_eq : ∀ k : Fin 16, amp9_0Expr 5 12 k = amp9_05_12 k := by decide +kernel +noncomputable def amp9_05_13 : Fin 16 → CBox := ![⟨⟨10194544061302622080315990889,10194544061302622082163889793⟩,⟨(-797186808),845236074⟩⟩,⟨⟨10039973720638874085080546274,10039973720638874086894527329⟩,⟨(-781917529),829238269⟩⟩,⟨⟨9882943734709660309215510055,9882943734709660310993463640⟩,⟨(-766636826),813217447⟩⟩,⟨⟨9721216324032392146718620296,9721216324032392148460875632⟩,⟨(-751169164),796987526⟩⟩,⟨⟨9557197913543233290684213780,9557197913543233292389675059⟩,⟨(-735699110),780744415⟩⟩,⟨⟨9388508241009929518557609081,9388508241009929520232319771⟩,⟨(-720041250),764291481⟩⟩,⟨⟨9217709123208483652134738547,9217709123208483653773084642⟩,⟨(-704390450),747835665⟩⟩,⟨⟨9042265446402566965740428203,9042265446402566967341973962⟩,⟨(-688550572),731168880⟩⟩,⟨⟨8864907451324136423471790381,8864907451324136425036509019⟩,⟨(-672727689),714510068⟩⟩,⟨⟨8682931000002419888117174303,8682931000002419889645383335⟩,⟨(-656713962),697638643⟩⟩,⟨⟨8499249756460134721650358525,8499249756460134723141315639⟩,⟨(-640727719),680786667⟩⟩,⟨⟨8310974201781988968591168860,8310974201781988970048634148⟩,⟨(-624548288),663719850⟩⟩,⟨⟨8121218819281640844848144777,8121218819281640846267140868⟩,⟨(-608407475),646684675⟩⟩,⟨⟨7926889682697347368086162758,7926889682697347369466826674⟩,⟨(-592070452),629431733⟩⟩,⟨⟨7731322439515148040027801612,7731322439515148041370422108⟩,⟨(-575783933),612223460⟩⟩,⟨⟨7531196431271605632760298313,7531196431271605634063946588⟩,⟨(-559297381),594793668⟩⟩] +lemma amp9_05_13_eq : ∀ k : Fin 16, amp9_0Expr 5 13 k = amp9_05_13 k := by decide +kernel +noncomputable def amp9_05_14 : Fin 16 → CBox := ![⟨⟨7330092483041432283039195297,7330092483041432284307118107⟩,⟨(-542874109),577422546⟩⟩,⟨⟨7124436755348031962592691448,7124436755348031963821600782⟩,⟨(-526246022),559825156⟩⟩,⟨⟨6918083884758200753270591751,6918083884758200754460979582⟩,⟨(-509695057),542301601⟩⟩,⟨⟨6707175176996376670494150650,6707175176996376671644446242⟩,⟨(-492933337),524545820⟩⟩,⟨⟨6495873614970292565761922777,6495873614970292566875345769⟩,⟨(-476263867),506880436⟩⟩,⟨⟨6279997256106114463430839697,6279997256106114464504503748⟩,⟨(-459376293),488975386⟩⟩,⟨⟨6064059620565666572455011167,6064059620565666573490865820⟩,⟨(-442597673),471179002⟩⟩,⟨⟨5843508333865144115081899016,5843508333865144116077436007⟩,⟨(-425591852),453133671⟩⟩,⟨⟨5623259758294419898807156874,5623259758294419899762776785⟩,⟨(-408713652),435217387⟩⟩,⟨⟨5398332179446450275051571754,5398332179446450275968203998⟩,⟨(-391596959),417040558⟩⟩,⟨⟨5174110748446996733130274846,5174110748446996734006495153⟩,⟨(-374629038),399015830⟩⟩,⟨⟨4945109508397047026777186796,4945109508397047027613862763⟩,⟨(-357408524),380715979⟩⟩,⟨⟨4717267198118655931421819464,4717267198118655932219251621⟩,⟨(-340361141),362594723⟩⟩,⟨⟨4484496312031306880116901603,4484496312031306880873153952⟩,⟨(-323043390),344179868⟩⟩,⟨⟨4253400785223850296442189000,4253400785223850297158718540⟩,⟨(-305927380),325974650⟩⟩,⟨⟨4017161876444438552423836692,4017161876444438553099882390⟩,⟨(-288518290),307452112⟩⟩] +lemma amp9_05_14_eq : ∀ k : Fin 16, amp9_0Expr 5 14 k = amp9_05_14 k := by decide +kernel +noncomputable def amp9_05_15 : Fin 16 → CBox := ![⟨⟨3783199784228645034039376375,3783199784228645034675163654⟩,⟨(-271345339),289176443⟩⟩,⟨⟨3543786234992750818639430354,3543786234992750819234142504⟩,⟨(-253849755),270552447⟩⟩,⟨⟨3307369321525166183196329864,3307369321525166183750480160⟩,⟨(-236632890),252221294⟩⟩,⟨⟨3065056473631586439581836846,3065056473631586440095111404⟩,⟨(-219053953),233500279⟩⟩,⟨⟨2826633270511767721594355964,2826633270511767722067276130⟩,⟨(-201808416),215130998⟩⟩,⟨⟨2581660444753823030703131286,2581660444753823031134635965⟩,⟨(-184146342),196314310⟩⟩,⟨⟨2341740172299399886460641342,2341740172299399886851471667⟩,⟨(-166891340),177928508⟩⟩,⟨⟨2094273829805534679548615651,2094273829805534679898071885⟩,⟨(-149140852),159011654⟩⟩,⟨⟨1853480404442691529470536178,1853480404442691529779449487⟩,⟨(-131903444),140639329⟩⟩,⟨⟨1603527089250132360065992741,1603527089250132360333005265⟩,⟨(-114047646),121605443⟩⟩,⟨⟨1362741222863623935649432662,1362741222863623935876050252⟩,⟨(-96872877),103295795⟩⟩,⟨⟨1109895761162676723578741400,1109895761162676723763124558⟩,⟨(-78865429),84096626⟩⟩,⟨⟨870731121346295531867960560,870731121346295532012313602⟩,⟨(-61850197),65954156⟩⟩,⟨⟨613170481679804685031439076,613170481679804685132916841⟩,⟨(-43543935),46433951⟩⟩,⟨⟨380420923474277062462502691,380420923474277062524929798⟩,⟨(-27010779),28803792⟩⟩,⟨⟨108087267962443344175239691,108087267962443344192663167⟩,⟨(-7673799),8183240⟩⟩] +lemma amp9_05_15_eq : ∀ k : Fin 16, amp9_0Expr 5 15 k = amp9_05_15 k := by decide +kernel +noncomputable def amp9_05 : Fin 16 → Fin 16 → CBox := ![amp9_05_0,amp9_05_1,amp9_05_2,amp9_05_3,amp9_05_4,amp9_05_5,amp9_05_6,amp9_05_7,amp9_05_8,amp9_05_9,amp9_05_10,amp9_05_11,amp9_05_12,amp9_05_13,amp9_05_14,amp9_05_15] +lemma amp9_05_eq (i k : Fin 16) : amp9_0Expr 5 i k = amp9_05 i k := by + fin_cases i + · exact amp9_05_0_eq k + · exact amp9_05_1_eq k + · exact amp9_05_2_eq k + · exact amp9_05_3_eq k + · exact amp9_05_4_eq k + · exact amp9_05_5_eq k + · exact amp9_05_6_eq k + · exact amp9_05_7_eq k + · exact amp9_05_8_eq k + · exact amp9_05_9_eq k + · exact amp9_05_10_eq k + · exact amp9_05_11_eq k + · exact amp9_05_12_eq k + · exact amp9_05_13_eq k + · exact amp9_05_14_eq k + · exact amp9_05_15_eq k +noncomputable def amp9_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp9_00,amp9_01,amp9_02,amp9_03,amp9_04,amp9_05] +lemma amp9_0_eq (j : Fin 6) (i k : Fin 16) : amp9_0Expr j i k = amp9_0 j i k := by + fin_cases j + · exact amp9_00_eq i k + · exact amp9_01_eq i k + · exact amp9_02_eq i k + · exact amp9_03_eq i k + · exact amp9_04_eq i k + · exact amp9_05_eq i k +lemma amp9_0_contains (j : Fin 6) (i k : Fin 16) : + (amp9_0 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude false 9 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp9_0_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 9 j) (bLookup_contains 9 j) false) +noncomputable def amp9_1Expr (j : Fin 6) (i k : Fin 16) : CBox := (rcast (weightRows i k)).mul (waveAmplitudeBox (gridRows j i k) (aLookup 9 j) (bLookup 9 j) true) +noncomputable def amp9_10_0 : Fin 16 → CBox := ![⟨⟨178776584874023315318119029,178776584874023315381290509⟩,⟨(-516083547009096694092754891),(-516083547009096694025319321)⟩⟩,⟨⟨629264447029517718362162568,629264447029517718586334740⟩,⟨(-1816529989419765287848064699),(-1816529989419765287605451892)⟩⟩,⟨⟨1014414495963543606746544271,1014414495963543607109308662⟩,⟨(-2928362411572052200074628951),(-2928362411572052199679524823)⟩⟩,⟨⟨1440842106367455813265972053,1440842106367455813781594343⟩,⟨(-4159352889854990063955758191),(-4159352889854990063393516147)⟩⟩,⟨⟨1837153108049314192974706911,1837153108049314193632669304⟩,⟨(-5303404207374145887341907994),(-5303404207374145886623530130)⟩⟩,⟨⟨2256524817754308917548769726,2256524817754308918357176597⟩,⟨(-6514026054817607367347014078),(-6514026054817607366463929427)⟩⟩,⟨⟨2656435792071101112864879805,2656435792071101113816931586⟩,⟨(-7668469598186034814741833284),(-7668469598186034813701160364)⟩⟩,⟨⟨3072133445990435319702768835,3072133445990435320804016816⟩,⟨(-8868485360145152285270265782),(-8868485360145152284066127711)⟩⟩,⟨⟨3473340580412691299921832201,3473340580412691301167193072⟩,⟨(-10026670595442591582338009626),(-10026670595442591580975765569)⟩⟩,⟨⟨3886397599776523264753010838,3886397599776523266146198021⟩,⟨(-11219063502044455816868118479),(-11219063502044455815344666293)⟩⟩,⟨⟨4287805485929443699696883328,4287805485929443701234474214⟩,⟨(-12377828257670592144859186692),(-12377828257670592143176918065)⟩⟩,⟨⟨4698569893355039726749271123,4698569893355039728434335431⟩,⟨(-13563602963674017037621243105),(-13563602963674017035777311273)⟩⟩,⟨⟨5099502883647184280891094747,5099502883647184282719919619⟩,⟨(-14720996813034873396508432986),(-14720996813034873394507236016)⟩⟩,⟨⟨5508052685234101316958165762,5508052685234101318933161174⟩,⟨(-15900378502652747127391146995),(-15900378502652747125230624275)⟩⟩,⟨⟨5908018787060499826795919140,5908018787060499828914881131⟩,⟨(-17054981185433729371633495738),(-17054981185433729369314491610)⟩⟩,⟨⟨6314304889329281697053574421,6314304889329281699318632582⟩,⟨(-18227828137998154551155536224),(-18227828137998154548675965840)⟩⟩] +lemma amp9_10_0_eq : ∀ k : Fin 16, amp9_1Expr 0 0 k = amp9_10_0 k := by decide +kernel +noncomputable def amp9_10_1 : Fin 16 → CBox := ![⟨⟨6712905375084154820580525514,6712905375084154822988746945⟩,⟨(-19378488626746612490303733230),(-19378488626746612487667122516)⟩⟩,⟨⟨7116811458893626800991947720,7116811458893626803544850233⟩,⟨(-20544465057820243453437621686),(-20544465057820243450642999753)⟩⟩,⟨⟨7513700288185479520408872124,7513700288185479523103792304⟩,⟨(-21690184419970276427429145289),(-21690184419970276424479689777)⟩⟩,⟨⟨7915071511567247978234002605,7915071511567247981074321727⟩,⟨(-22848843339292443597246117694),(-22848843339292443594134949165)⟩⟩,⟨⟨8309934963699564220730996355,8309934963699564223712121611⟩,⟨(-23988715941201132048448180227),(-23988715941201132045184373518)⟩⟩,⟨⟨8708593155276932931116356545,8708593155276932934239653577⟩,⟨(-25139543012310348166767108939),(-25139543012310348163349161194)⟩⟩,⟨⟨9101138730168082672113904752,9101138730168082675379611050⟩,⟨(-26272724478973356684182647206),(-26272724478973356680605943418)⟩⟩,⟨⟨9496891073954188849246959006,9496891073954188852653386539⟩,⟨(-27415163090060025287339350184),(-27415163090060025283610824714)⟩⟩,⟨⟨9886841054724459425028622212,9886841054724459428576097949⟩,⟨(-28540851721901050824384774557),(-28540851721901050820499753535)⟩⟩,⟨⟨10279485372927895292915510870,10279485372927895296605413050⟩,⟨(-29674318235953704695003385100),(-29674318235953704690959621923)⟩⟩,⟨⟨10666572908823690774870056738,10666572908823690778697007859⟩,⟨(-30791743701200636932275369363),(-30791743701200636928084815420)⟩⟩,⟨⟨11055901047314695421777709421,11055901047314695425745566467⟩,⟨(-31915637229005024096942821067),(-31915637229005024092595782551)⟩⟩,⟨⟨11439867680844907707020553280,11439867680844907711123245327⟩,⟨(-33024053425147536341907411424),(-33024053425147536337417966988)⟩⟩,⟨⟨11825667778884814559777002082,11825667778884814564020559886⟩,⟨(-34137762377431157505744634983),(-34137762377431157501096553966)⟩⟩,⟨⟨12206261841045965247752870884,12206261841045965252133551535⟩,⟨(-35236442798634725061297590244),(-35236442798634725056498330844)⟩⟩,⟨⟨12588319915260722388644856779,12588319915260722393163925388⟩,⟨(-36339349458604525328934557691),(-36339349458604525323981408973)⟩⟩] +lemma amp9_10_1_eq : ∀ k : Fin 16, amp9_1Expr 0 1 k = amp9_10_1 k := by decide +kernel +noncomputable def amp9_10_2 : Fin 16 → CBox := ![⟨⟨12965295463818583361496550866,12965295463818583366147214062⟩,⟨(-37427584130793464685871355882),(-37427584130793464680780661366)⟩⟩,⟨⟨13343396554569321848752376481,13343396554569321853540677235⟩,⟨(-38519067963422614615945657273),(-38519067963422614610700695952)⟩⟩,⟨⟨13716512663740494233339550035,13716512663740494238262865245⟩,⟨(-39596161393767425469903498939),(-39596161393767425464508638506)⟩⟩,⟨⟨14090441693045962455473305638,14090441693045962460532455905⟩,⟨(-40675601522404063166538683418),(-40675601522404063160992077580)⟩⟩,⟨⟨14459461977215688465187089882,14459461977215688470381233986⟩,⟨(-41740871324413180701150755270),(-41740871324413180695451676882)⟩⟩,⟨⟨14829004411061715031243279434,14829004411061715036564089939⟩,⟨(-42807648442703145246542080302),(-42807648442703145240714904260)⟩⟩,⟨⟨15193696708276728725444807577,15193696708276728730897825412⟩,⟨(-43860424422545501061079148173),(-43860424422545501055104761328)⟩⟩,⟨⟨15558639082871133555037515244,15558639082871133560621672490⟩,⟨(-44913922313599405416555880070),(-44913922313599405410437526001)⟩⟩,⟨⟨15918775249752562211814590780,15918775249752562217529346319⟩,⟨(-45953545878068969527144394305),(-45953545878068969520880545460)⟩⟩,⟨⟨16278905600962081264252756811,16278905600962081270098362802⟩,⟨(-46993152654139820994683713627),(-46993152654139820988273638346)⟩⟩,⟨⟨16634261386743642864275184527,16634261386743642870249887112⟩,⟨(-48018976447035198882758313493),(-48018976447035198876204005447)⟩⟩,⟨⟨16989369609173106071069557929,16989369609173106077163541554⟩,⟨(-49044085586090699303631707423),(-49044085586090699296961342528)⟩⟩,⟨⟨17339724586802453968015254172,17339724586802453974238170477⟩,⟨(-50055473289321845909278216920),(-50055473289321845902460877722)⟩⟩,⟨⟨17689602740734276708143492582,17689602740734276714493605792⟩,⟨(-51065484521102381805014849350),(-51065484521102381798055240071)⟩⟩,⟨⟨18034740279655822660605287816,18034740279655822667082214371⟩,⟨(-52061810776121379281405768804),(-52061810776121379274301949232)⟩⟩,⟨⟨18379182858626920873559499275,18379182858626920880159547739⟩,⟨(-53056130854568041700851007179),(-53056130854568041693613186823)⟩⟩] +lemma amp9_10_2_eq : ∀ k : Fin 16, amp9_1Expr 0 2 k = amp9_10_2 k := by decide +kernel +noncomputable def amp9_10_3 : Fin 16 → CBox := ![⟨⟨18718890128322294121922945993,18718890128322294128646605072⟩,⟨(-54036781272589524419708818906),(-54036781272589524412332542946)⟩⟩,⟨⟨19057694296448717004944798089,19057694296448717011792130362⟩,⟨(-55014824660941311804551821152),(-55014824660941311797036328386)⟩⟩,⟨⟨19391762292844942222711191610,19391762292844942229680829623⟩,⟨(-55979195899176309601174507748),(-55979195899176309593520701076)⟩⟩,⟨⟨19724728098486747673733995989,19724728098486747680808941918⟩,⟨(-56940385386767494552584650279),(-56940385386767494544840889658)⟩⟩,⟨⟨20052951687444352540672958347,20052951687444352547869328610⟩,⟨(-57887885273962785795368067945),(-57887885273962785787484780798)⟩⟩,⟨⟨20379882258044908820602529671,20379882258044908827918359936⟩,⟨(-58831652538675531391394147947),(-58831652538675531383376173606)⟩⟩,⟨⟨20702060231618653074396316721,20702060231618653081829763203⟩,⟨(-59761700237524378295683808316),(-59761700237524378287533414170)⟩⟩,⟨⟨21022761953305465941664787399,21022761953305465949214561653⟩,⟨(-60687486364251667555032243056),(-60687486364251667546752199532)⟩⟩,⟨⟨21338697095528772239604155240,21338697095528772247269563422⟩,⟨(-61599512561297110515578870046),(-61599512561297110507168115951)⟩⟩,⟨⟨21652979780165887252942949872,21652979780165887260719299919⟩,⟨(-62506768524181493589199030318),(-62506768524181493580670048203)⟩⟩,⟨⟨21962478939877190900012148017,21962478939877190907901698294⟩,⟨(-63400215640047914278176766433),(-63400215640047914269519961916)⟩⟩,⟨⟨22270155981605558908818427718,22270155981605558916818818265⟩,⟨(-64288402754374619223766697172),(-64288402754374619214987711545)⟩⟩,⟨⟨22573030150397963502925151073,22573030150397963511035432755⟩,⟨(-65162725168789013940839175269),(-65162725168789013931937660962)⟩⟩,⟨⟨22873918673218157790187880948,22873918673218157798407140008⟩,⟨(-66031315517020554073827306662),(-66031315517020554064804625014)⟩⟩,⟨⟨23169983067012150229913493277,23169983067012150238240394092⟩,⟨(-66885979804292678587420545301),(-66885979804292678578277450782)⟩⟩,⟨⟨23463904064604503185866361270,23463904064604503194299881403⟩,⟨(-67734456639694820214308577737),(-67734456639694820205046644002)⟩⟩] +lemma amp9_10_3_eq : ∀ k : Fin 16, amp9_1Expr 0 3 k = amp9_10_3 k := by decide +kernel +noncomputable def amp9_10_4 : Fin 16 → CBox := ![⟨⟨23752978207657739996894441052,23752978207657740005407616345⟩,⟨(-68568941811232553512160352493),(-68568941811232553502854302612)⟩⟩,⟨⟨24039756676364397072716163762,24039756676364397081337543511⟩,⟨(-69396799941760439168323457765),(-69396799941760439158889401265)⟩⟩,⟨⟨24321664486771101355858869259,24321664486771101364585744453⟩,⟨(-70210597692885282675258786033),(-70210597692885282665701412101)⟩⟩,⟨⟨24601129552458858916345827906,24601129552458858925176289074⟩,⟨(-71017343847404899046905460291),(-71017343847404899037228710802)⟩⟩,⟨⟨24875699428374202209267485249,24875699428374202218199493191⟩,⟨(-71809958806260327017241534951),(-71809958806260327007448149741)⟩⟩,⟨⟨25147684467739387128078007048,25147684467739387137111462671⟩,⟨(-72595111984725529383115095524),(-72595111984725529373203699015)⟩⟩,⟨⟨25414749373705691722767255638,25414749373705691731897909429⟩,⟨(-73366061961479269631540695124),(-73366061961479269621520391741)⟩⟩,⟨⟨25679092130460598061118046102,25679092130460598070346604306⟩,⟨(-74129153770333134326026965172),(-74129153770333134315893966256)⟩⟩,⟨⟨25938489683322627369701053734,25938489683322627379026257479⟩,⟨(-74877970005193248328565331537),(-74877970005193248318320092163)⟩⟩,⟨⟨26195032379608320401558540454,26195032379608320410971777830⟩,⟨(-75618544978989134717265861613),(-75618544978989134706931407008)⟩⟩,⟨⟨26446604933591878652361024333,26446604933591878661868541087⟩,⟨(-76344772387804779795235496913),(-76344772387804779784790602149)⟩⟩,⟨⟨26695194376888032114966878237,26695194376888032124566155287⟩,⟨(-77062388297828446853089242040),(-77062388297828446842539261416)⟩⟩,⟨⟨26938789107485135124025020583,26938789107485135133715115770⟩,⟨(-77765585714245505802869947530),(-77765585714245505792214390024)⟩⟩,⟨⟨27179276793229187794211260302,27179276793229187803988126366⟩,⟨(-78459813864751100480770737907),(-78459813864751100470019289617)⟩⟩,⟨⟨27414745779588332830033296969,27414745779588332839898197658⟩,⟨(-79139554278052403998936731162),(-79139554278052403988082517741)⟩⟩,⟨⟨27646987989670052247286030001,27646987989670052257235972046⟩,⟨(-79809979790591775619960254487),(-79809979790591775609009842456)⟩⟩] +lemma amp9_10_4_eq : ∀ k : Fin 16, amp9_1Expr 0 4 k = amp9_10_4 k := by decide +kernel +noncomputable def amp9_10_5 : Fin 16 → CBox := ![⟨⟨27874188295234711897602577428,27874188295234711907636626208⟩,⟨(-80465850578480383008341229088),(-80465850578480382997294075329)⟩⟩,⟨⟨28098046192495536935704627296,28098046192495536945821457091⟩,⟨(-81112072664699187627602179199),(-81112072664699187616459962097)⟩⟩,⟨⟨28316839943670277248890228667,28316839943670277259088836140⟩,⟨(-81743675820387909218559646207),(-81743675820387909207322006713)⟩⟩,⟨⟨28532179662507527611693929648,28532179662507527621972770264⟩,⟨(-82365308043577433333711717687),(-82365308043577433322380894097)⟩⟩,⟨⟨28742434125160893637532746056,28742434125160893647890318445⟩,⟨(-82972260396633638293845403938),(-82972260396633638282422461326)⟩⟩,⟨⟨28949126858313515177033360663,28949126858313515187417873884⟩,⟨(-83568930922259665950994890468),(-83568930922259665939627046780)⟩⟩,⟨⟨29150714511951410415920933843,29150714511951410426383859425⟩,⟨(-84150864352725385239663830079),(-84150864352725385228199218060)⟩⟩,⟨⟨29348636593525162294819058290,29348636593525162305357712942⟩,⟨(-84722216188101268823078779271),(-84722216188101268811522788537)⟩⟩,⟨⟨29541435202988933489110275938,29541435202988933499721981704⟩,⟨(-85278777833467737965695752278),(-85278777833467737954052819846)⟩⟩,⟨⟨29730468187763879462302872413,29730468187763879472986077793⟩,⟨(-85824469056695405397530797189),(-85824469056695405385802981165)⟩⟩,⟨⟨29914360872324529837563129626,29914360872324529848314766878⟩,⟨(-86355321511360877557010266076),(-86355321511360877545203117869)⟩⟩,⟨⟨30094391611375639615352835248,30094391611375639626171220699⟩,⟨(-86875025489628705064557275262),(-86875025489628705052673172607)⟩⟩,⟨⟨30269266911110177878911665229,30269266911110177889796678398⟩,⟨(-87379846996510465852002099012),(-87379846996510465840038075581)⟩⟩,⟨⟨30440187623762200856010368248,30440187623762200866957984527⟩,⟨(-87873252593809106552270620254),(-87873252593809106540235751926)⟩⟩,⟨⟨30605939563110598312681096368,30605939563110598323691046065⟩,⟨(-88351737227816605525121969893),(-88351737227816605513013712504)⟩⟩,⟨⟨30767647905240686643037357234,30767647905240686654108620866⟩,⟨(-88818549002111678517888246107),(-88818549002111678505706943263)⟩⟩] +lemma amp9_10_5_eq : ∀ k : Fin 16, amp9_1Expr 0 5 k = amp9_10_5 k := by decide +kernel +noncomputable def amp9_10_6 : Fin 16 → CBox := ![⟨⟨30924176053652663069692834177,30924176053652663080818199626⟩,⟨(-89270406845218719930796206636),(-89270406845218719918559347890)⟩⟩,⟨⟨31076575182348133086360758552,31076575182348133097545150818⟩,⟨(-89710345235101690103385022803),(-89710345235101690091075736609)⟩⟩,⟨⟨31223784711938343734428688799,31223784711938343745666921200⟩,⟨(-90135302542782621588591596363),(-90135302542782621576221519298)⟩⟩,⟨⟨31366783346512185476572015618,31366783346512185487865792655⟩,⟨(-90548104043607403866676763861),(-90548104043607403854238268520)⟩⟩,⟨⟨31504585086650592888091393490,31504585086650592899437021612⟩,⟨(-90945903402425945749763217165),(-90945903402425945737263625140)⟩⟩,⟨⟨31638097566013635093637957490,31638097566013635105034833242⟩,⟨(-91331320731928079609872628479),(-91331320731928079597310924483)⟩⟩,⟨⟨31766408054785126230858636297,31766408054785126242287678128⟩,⟨(-91701721208088443920588330868),(-91701721208088443908016254547)⟩⟩,⟨⟨31890354391170951211611194428,31890354391170951223089561801⟩,⟨(-92059523461475563716786895379),(-92059523461475563704152106180)⟩⟩,⟨⟨32009095923644769036180282140,32009095923644769047704412043⟩,⟨(-92402300740164300768610016294),(-92402300740164300755919453884)⟩⟩,⟨⟨32123401852681396177082252314,32123401852681396188649569577⟩,⟨(-92732273534660635467865509814),(-92732273534660635455123756686)⟩⟩,⟨⟨32232502525936830256751728916,32232502525936830268361402741⟩,⟨(-93047220050024606818867938057),(-93047220050024606806074046370)⟩⟩,⟨⟨32337099553057724184961891050,32337099553057724196610299921⟩,⟨(-93349165658848020299973062087),(-93349165658848020287134591133)⟩⟩,⟨⟨32436493307917857216252723863,32436493307917857227939014773⟩,⟨(-93636090714469347698770235802),(-93636090714469347685886303126)⟩⟩,⟨⟨32531318751103864914634372609,32531318751103864926358054867⟩,⟨(-93909828190216683243124778948),(-93909828190216683230193864358)⟩⟩,⟨⟨32620945410534091398700197525,32620945410534091410451077757⟩,⟨(-94168558069959724098778690886),(-94168558069959724085826878133)⟩⟩,⟨⟨32705942439377387416348475979,32705942439377387428132347328⟩,⟨(-94413923357374700804901365580),(-94413923357374700791908955187)⟩⟩] +lemma amp9_10_6_eq : ∀ k : Fin 16, amp9_1Expr 0 6 k = amp9_10_6 k := by decide +kernel +noncomputable def amp9_10_7 : Fin 16 → CBox := ![⟨⟨32785747743509981342118805098,32785747743509981353932872558⟩,⟨(-94644301426493266087557816955),(-94644301426493266074529539958)⟩⟩,⟨⟨32860865414590931767512167834,32860865414590931779355751413⟩,⟨(-94861147464590688561034405262),(-94861147464590688547969211231)⟩⟩,⟨⟨32930801052341203467900627689,32930801052341203479767351170⟩,⟨(-95063034260996026160163354577),(-95063034260996026147076318845)⟩⟩,⟨⟨32995994340909188933050233682,32995994340909188944942028946⟩,⟨(-95251231074516442961602446666),(-95251231074516442948484943801)⟩⟩,⟨⟨33056017978152788402452863438,33056017978152788414365124997⟩,⟨(-95424504390118105963085094868),(-95424504390118105949947096505)⟩⟩,⟨⟨33111247806102404772541201039,33111247806102404784475251120⟩,⟨(-95583939170288144603458978563),(-95583939170288144590293586112)⟩⟩,⟨⟨33161323110387142474258525027,33161323110387142486210335725⟩,⟨(-95728494122330873266187992534),(-95728494122330873253003520022)⟩⟩,⟨⟨33206556370521783185694469900,33206556370521783197662347714⟩,⟨(-95859071296906169178719798217),(-95859071296906169165518021695)⟩⟩,⟨⟨33246653032290985846643297091,33246653032290985858625567634⟩,⟨(-95974820389236441840530542136),(-95974820389236441827312993134)⟩⟩,⟨⟨33281862608866566218877729007,33281862608866566230873072959⟩,⟨(-96076461681806262188640573611),(-96076461681806262175407919058)⟩⟩,⟨⟨33311956359174495034283549209,33311956359174495046289050830⟩,⟨(-96163334856012302612742094960),(-96163334856012302599499463217)⟩⟩,⟨⟨33337121144716975235276957468,33337121144716975247291142701⟩,⟨(-96235979334547553346098189345),(-96235979334547553332846667109)⟩⟩,⟨⟨33357193769420233710555682330,33357193769420233722575729631⟩,⟨(-96293924010926396409527085095),(-96293924010926396396271544021)⟩⟩,⟨⟨33372298677811606167465515585,33372298677811606179489338673⟩,⟨(-96337528125555614034921028236),(-96337528125555614021664297444)⟩⟩,⟨⟨33382338028223777521384618981,33382338028223777533409556967⟩,⟨(-96366509233870394592702685588),(-96366509233870394579449190062)⟩⟩,⟨⟨33387374004052282210578872489,33387374004052282222601975572⟩,⟨(-96381046843871492747398640393),(-96381046843871492734153679105)⟩⟩] +lemma amp9_10_7_eq : ∀ k : Fin 16, amp9_1Expr 0 7 k = amp9_10_7 k := by decide +kernel +noncomputable def amp9_10_8 : Fin 16 → CBox := ![⟨⟨33387374004052282210578872489,33387374004052282222601975572⟩,⟨(-96381046843871492747398640393),(-96381046843871492734153679105)⟩⟩,⟨⟨33382338028223777521384618981,33382338028223777533409556967⟩,⟨(-96366509233870394592702685588),(-96366509233870394579449190062)⟩⟩,⟨⟨33372298677811606167465515585,33372298677811606179489338673⟩,⟨(-96337528125555614034921028236),(-96337528125555614021664297444)⟩⟩,⟨⟨33357193769420233710555682330,33357193769420233722575729631⟩,⟨(-96293924010926396409527085095),(-96293924010926396396271544021)⟩⟩,⟨⟨33337121144716975235276957468,33337121144716975247291142701⟩,⟨(-96235979334547553346098189345),(-96235979334547553332846667109)⟩⟩,⟨⟨33311956359174495034283549209,33311956359174495046289050830⟩,⟨(-96163334856012302612742094960),(-96163334856012302599499463217)⟩⟩,⟨⟨33281862608866566218877729007,33281862608866566230873072959⟩,⟨(-96076461681806262188640573611),(-96076461681806262175407919058)⟩⟩,⟨⟨33246653032290985846643297091,33246653032290985858625567634⟩,⟨(-95974820389236441840530542136),(-95974820389236441827312993134)⟩⟩,⟨⟨33206556370521783185694469900,33206556370521783197662347714⟩,⟨(-95859071296906169178719798217),(-95859071296906169165518021695)⟩⟩,⟨⟨33161323110387142474258525027,33161323110387142486210335725⟩,⟨(-95728494122330873266187992534),(-95728494122330873253003520022)⟩⟩,⟨⟨33111247806102404772541201039,33111247806102404784475251120⟩,⟨(-95583939170288144603458978563),(-95583939170288144590293586112)⟩⟩,⟨⟨33056017978152788402452863438,33056017978152788414365124997⟩,⟨(-95424504390118105963085094868),(-95424504390118105949947096505)⟩⟩,⟨⟨32995994340909188933050233682,32995994340909188944942028946⟩,⟨(-95251231074516442961602446666),(-95251231074516442948484943801)⟩⟩,⟨⟨32930801052341203467900627689,32930801052341203479767351170⟩,⟨(-95063034260996026160163354577),(-95063034260996026147076318845)⟩⟩,⟨⟨32860865414590931767512167834,32860865414590931779355751413⟩,⟨(-94861147464590688561034405262),(-94861147464590688547969211231)⟩⟩,⟨⟨32785747743509981342118805098,32785747743509981353932872558⟩,⟨(-94644301426493266087557816955),(-94644301426493266074529539958)⟩⟩] +lemma amp9_10_8_eq : ∀ k : Fin 16, amp9_1Expr 0 8 k = amp9_10_8 k := by decide +kernel +noncomputable def amp9_10_9 : Fin 16 → CBox := ![⟨⟨32705942439377387416348475979,32705942439377387428132347328⟩,⟨(-94413923357374700804901365580),(-94413923357374700791908955187)⟩⟩,⟨⟨32620945410534091398700197525,32620945410534091410451077757⟩,⟨(-94168558069959724098778690886),(-94168558069959724085826878133)⟩⟩,⟨⟨32531318751103864914634372609,32531318751103864926358054867⟩,⟨(-93909828190216683243124778948),(-93909828190216683230193864358)⟩⟩,⟨⟨32436493307917857216252723863,32436493307917857227939014773⟩,⟨(-93636090714469347698770235802),(-93636090714469347685886303126)⟩⟩,⟨⟨32337099553057724184961891050,32337099553057724196610299921⟩,⟨(-93349165658848020299973062087),(-93349165658848020287134591133)⟩⟩,⟨⟨32232502525936830256751728916,32232502525936830268361402741⟩,⟨(-93047220050024606818867938057),(-93047220050024606806074046370)⟩⟩,⟨⟨32123401852681396177082252314,32123401852681396188649569577⟩,⟨(-92732273534660635467865509814),(-92732273534660635455123756686)⟩⟩,⟨⟨32009095923644769036180282140,32009095923644769047704412043⟩,⟨(-92402300740164300768610016294),(-92402300740164300755919453884)⟩⟩,⟨⟨31890354391170951211611194428,31890354391170951223089561801⟩,⟨(-92059523461475563716786895379),(-92059523461475563704152106180)⟩⟩,⟨⟨31766408054785126230858636297,31766408054785126242287678128⟩,⟨(-91701721208088443920588330868),(-91701721208088443908016254547)⟩⟩,⟨⟨31638097566013635093637957490,31638097566013635105034833242⟩,⟨(-91331320731928079609872628479),(-91331320731928079597310924483)⟩⟩,⟨⟨31504585086650592888091393490,31504585086650592899437021612⟩,⟨(-90945903402425945749763217165),(-90945903402425945737263625140)⟩⟩,⟨⟨31366783346512185476572015618,31366783346512185487865792655⟩,⟨(-90548104043607403866676763861),(-90548104043607403854238268520)⟩⟩,⟨⟨31223784711938343734428688799,31223784711938343745666921200⟩,⟨(-90135302542782621588591596363),(-90135302542782621576221519298)⟩⟩,⟨⟨31076575182348133086360758552,31076575182348133097545150818⟩,⟨(-89710345235101690103385022803),(-89710345235101690091075736609)⟩⟩,⟨⟨30924176053652663069692834177,30924176053652663080818199626⟩,⟨(-89270406845218719930796206636),(-89270406845218719918559347890)⟩⟩] +lemma amp9_10_9_eq : ∀ k : Fin 16, amp9_1Expr 0 9 k = amp9_10_9 k := by decide +kernel +noncomputable def amp9_10_10 : Fin 16 → CBox := ![⟨⟨30767647905240686643037357234,30767647905240686654108620866⟩,⟨(-88818549002111678517888246107),(-88818549002111678505706943263)⟩⟩,⟨⟨30605939563110598312681096368,30605939563110598323691046065⟩,⟨(-88351737227816605525121969893),(-88351737227816605513013712504)⟩⟩,⟨⟨30440187623762200856010368248,30440187623762200866957984527⟩,⟨(-87873252593809106552270620254),(-87873252593809106540235751926)⟩⟩,⟨⟨30269266911110177878911665229,30269266911110177889796678398⟩,⟨(-87379846996510465852002099012),(-87379846996510465840038075581)⟩⟩,⟨⟨30094391611375639615352835248,30094391611375639626171220699⟩,⟨(-86875025489628705064557275262),(-86875025489628705052673172607)⟩⟩,⟨⟨29914360872324529837563129626,29914360872324529848314766878⟩,⟨(-86355321511360877557010266076),(-86355321511360877545203117869)⟩⟩,⟨⟨29730468187763879462302872413,29730468187763879472986077793⟩,⟨(-85824469056695405397530797189),(-85824469056695405385802981165)⟩⟩,⟨⟨29541435202988933489110275938,29541435202988933499721981704⟩,⟨(-85278777833467737965695752278),(-85278777833467737954052819846)⟩⟩,⟨⟨29348636593525162294819058290,29348636593525162305357712942⟩,⟨(-84722216188101268823078779271),(-84722216188101268811522788537)⟩⟩,⟨⟨29150714511951410415920933843,29150714511951410426383859425⟩,⟨(-84150864352725385239663830079),(-84150864352725385228199218060)⟩⟩,⟨⟨28949126858313515177033360663,28949126858313515187417873884⟩,⟨(-83568930922259665950994890468),(-83568930922259665939627046780)⟩⟩,⟨⟨28742434125160893637532746056,28742434125160893647890318445⟩,⟨(-82972260396633638293845403938),(-82972260396633638282422461326)⟩⟩,⟨⟨28532179662507527611693929648,28532179662507527621972770264⟩,⟨(-82365308043577433333711717687),(-82365308043577433322380894097)⟩⟩,⟨⟨28316839943670277248890228667,28316839943670277259088836140⟩,⟨(-81743675820387909218559646207),(-81743675820387909207322006713)⟩⟩,⟨⟨28098046192495536935704627296,28098046192495536945821457091⟩,⟨(-81112072664699187627602179199),(-81112072664699187616459962097)⟩⟩,⟨⟨27874188295234711897602577428,27874188295234711907636626208⟩,⟨(-80465850578480383008341229088),(-80465850578480382997294075329)⟩⟩] +lemma amp9_10_10_eq : ∀ k : Fin 16, amp9_1Expr 0 10 k = amp9_10_10 k := by decide +kernel +noncomputable def amp9_10_11 : Fin 16 → CBox := ![⟨⟨27646987989670052247286030001,27646987989670052257235972046⟩,⟨(-79809979790591775619960254487),(-79809979790591775609009842456)⟩⟩,⟨⟨27414745779588332830033296969,27414745779588332839898197658⟩,⟨(-79139554278052403998936731162),(-79139554278052403988082517741)⟩⟩,⟨⟨27179276793229187794211260302,27179276793229187803988126366⟩,⟨(-78459813864751100480770737907),(-78459813864751100470019289617)⟩⟩,⟨⟨26938789107485135124025020583,26938789107485135133715115770⟩,⟨(-77765585714245505802869947530),(-77765585714245505792214390024)⟩⟩,⟨⟨26695194376888032114966878237,26695194376888032124566155287⟩,⟨(-77062388297828446853089242040),(-77062388297828446842539261416)⟩⟩,⟨⟨26446604933591878652361024333,26446604933591878661868541087⟩,⟨(-76344772387804779795235496913),(-76344772387804779784790602149)⟩⟩,⟨⟨26195032379608320401558540454,26195032379608320410971777830⟩,⟨(-75618544978989134717265861613),(-75618544978989134706931407008)⟩⟩,⟨⟨25938489683322627369701053734,25938489683322627379026257479⟩,⟨(-74877970005193248328565331537),(-74877970005193248318320092163)⟩⟩,⟨⟨25679092130460598061118046102,25679092130460598070346604306⟩,⟨(-74129153770333134326026965172),(-74129153770333134315893966256)⟩⟩,⟨⟨25414749373705691722767255638,25414749373705691731897909429⟩,⟨(-73366061961479269631540695124),(-73366061961479269621520391741)⟩⟩,⟨⟨25147684467739387128078007048,25147684467739387137111462671⟩,⟨(-72595111984725529383115095524),(-72595111984725529373203699015)⟩⟩,⟨⟨24875699428374202209267485249,24875699428374202218199493191⟩,⟨(-71809958806260327017241534951),(-71809958806260327007448149741)⟩⟩,⟨⟨24601129552458858916345827906,24601129552458858925176289074⟩,⟨(-71017343847404899046905460291),(-71017343847404899037228710802)⟩⟩,⟨⟨24321664486771101355858869259,24321664486771101364585744453⟩,⟨(-70210597692885282675258786033),(-70210597692885282665701412101)⟩⟩,⟨⟨24039756676364397072716163762,24039756676364397081337543511⟩,⟨(-69396799941760439168323457765),(-69396799941760439158889401265)⟩⟩,⟨⟨23752978207657739996894441052,23752978207657740005407616345⟩,⟨(-68568941811232553512160352493),(-68568941811232553502854302612)⟩⟩] +lemma amp9_10_11_eq : ∀ k : Fin 16, amp9_1Expr 0 11 k = amp9_10_11 k := by decide +kernel +noncomputable def amp9_10_12 : Fin 16 → CBox := ![⟨⟨23463904064604503185866361270,23463904064604503194299881403⟩,⟨(-67734456639694820214308577737),(-67734456639694820205046644002)⟩⟩,⟨⟨23169983067012150229913493277,23169983067012150238240394092⟩,⟨(-66885979804292678587420545301),(-66885979804292678578277450782)⟩⟩,⟨⟨22873918673218157790187880948,22873918673218157798407140008⟩,⟨(-66031315517020554073827306662),(-66031315517020554064804625014)⟩⟩,⟨⟨22573030150397963502925151073,22573030150397963511035432755⟩,⟨(-65162725168789013940839175269),(-65162725168789013931937660962)⟩⟩,⟨⟨22270155981605558908818427718,22270155981605558916818818265⟩,⟨(-64288402754374619223766697172),(-64288402754374619214987711545)⟩⟩,⟨⟨21962478939877190900012148017,21962478939877190907901698294⟩,⟨(-63400215640047914278176766433),(-63400215640047914269519961916)⟩⟩,⟨⟨21652979780165887252942949872,21652979780165887260719299919⟩,⟨(-62506768524181493589199030318),(-62506768524181493580670048203)⟩⟩,⟨⟨21338697095528772239604155240,21338697095528772247269563422⟩,⟨(-61599512561297110515578870046),(-61599512561297110507168115951)⟩⟩,⟨⟨21022761953305465941664787399,21022761953305465949214561653⟩,⟨(-60687486364251667555032243056),(-60687486364251667546752199532)⟩⟩,⟨⟨20702060231618653074396316721,20702060231618653081829763203⟩,⟨(-59761700237524378295683808316),(-59761700237524378287533414170)⟩⟩,⟨⟨20379882258044908820602529671,20379882258044908827918359936⟩,⟨(-58831652538675531391394147947),(-58831652538675531383376173606)⟩⟩,⟨⟨20052951687444352540672958347,20052951687444352547869328610⟩,⟨(-57887885273962785795368067945),(-57887885273962785787484780798)⟩⟩,⟨⟨19724728098486747673733995989,19724728098486747680808941918⟩,⟨(-56940385386767494552584650279),(-56940385386767494544840889658)⟩⟩,⟨⟨19391762292844942222711191610,19391762292844942229680829623⟩,⟨(-55979195899176309601174507748),(-55979195899176309593520701076)⟩⟩,⟨⟨19057694296448717004944798089,19057694296448717011792130362⟩,⟨(-55014824660941311804551821152),(-55014824660941311797036328386)⟩⟩,⟨⟨18718890128322294121922945993,18718890128322294128646605072⟩,⟨(-54036781272589524419708818906),(-54036781272589524412332542946)⟩⟩] +lemma amp9_10_12_eq : ∀ k : Fin 16, amp9_1Expr 0 12 k = amp9_10_12 k := by decide +kernel +noncomputable def amp9_10_13 : Fin 16 → CBox := ![⟨⟨18379182858626920873559499275,18379182858626920880159547739⟩,⟨(-53056130854568041700851007179),(-53056130854568041693613186823)⟩⟩,⟨⟨18034740279655822660605287816,18034740279655822667082214371⟩,⟨(-52061810776121379281405768804),(-52061810776121379274301949232)⟩⟩,⟨⟨17689602740734276708143492582,17689602740734276714493605792⟩,⟨(-51065484521102381805014849350),(-51065484521102381798055240071)⟩⟩,⟨⟨17339724586802453968015254172,17339724586802453974238170477⟩,⟨(-50055473289321845909278216920),(-50055473289321845902460877722)⟩⟩,⟨⟨16989369609173106071069557929,16989369609173106077163541554⟩,⟨(-49044085586090699303631707423),(-49044085586090699296961342528)⟩⟩,⟨⟨16634261386743642864275184527,16634261386743642870249887112⟩,⟨(-48018976447035198882758313493),(-48018976447035198876204005447)⟩⟩,⟨⟨16278905600962081264252756811,16278905600962081270098362802⟩,⟨(-46993152654139820994683713627),(-46993152654139820988273638346)⟩⟩,⟨⟨15918775249752562211814590780,15918775249752562217529346319⟩,⟨(-45953545878068969527144394305),(-45953545878068969520880545460)⟩⟩,⟨⟨15558639082871133555037515244,15558639082871133560621672490⟩,⟨(-44913922313599405416555880070),(-44913922313599405410437526001)⟩⟩,⟨⟨15193696708276728725444807577,15193696708276728730897825412⟩,⟨(-43860424422545501061079148173),(-43860424422545501055104761328)⟩⟩,⟨⟨14829004411061715031243279434,14829004411061715036564089939⟩,⟨(-42807648442703145246542080302),(-42807648442703145240714904260)⟩⟩,⟨⟨14459461977215688465187089882,14459461977215688470381233986⟩,⟨(-41740871324413180701150755270),(-41740871324413180695451676882)⟩⟩,⟨⟨14090441693045962455473305638,14090441693045962460532455905⟩,⟨(-40675601522404063166538683418),(-40675601522404063160992077580)⟩⟩,⟨⟨13716512663740494233339550035,13716512663740494238262865245⟩,⟨(-39596161393767425469903498939),(-39596161393767425464508638506)⟩⟩,⟨⟨13343396554569321848752376481,13343396554569321853540677235⟩,⟨(-38519067963422614615945657273),(-38519067963422614610700695952)⟩⟩,⟨⟨12965295463818583361496550866,12965295463818583366147214062⟩,⟨(-37427584130793464685871355882),(-37427584130793464680780661366)⟩⟩] +lemma amp9_10_13_eq : ∀ k : Fin 16, amp9_1Expr 0 13 k = amp9_10_13 k := by decide +kernel +noncomputable def amp9_10_14 : Fin 16 → CBox := ![⟨⟨12588319915260722388644856779,12588319915260722393163925388⟩,⟨(-36339349458604525328934557691),(-36339349458604525323981408973)⟩⟩,⟨⟨12206261841045965247752870884,12206261841045965252133551535⟩,⟨(-35236442798634725061297590244),(-35236442798634725056498330844)⟩⟩,⟨⟨11825667778884814559777002082,11825667778884814564020559886⟩,⟨(-34137762377431157505744634983),(-34137762377431157501096553966)⟩⟩,⟨⟨11439867680844907707020553280,11439867680844907711123245327⟩,⟨(-33024053425147536341907411424),(-33024053425147536337417966988)⟩⟩,⟨⟨11055901047314695421777709421,11055901047314695425745566467⟩,⟨(-31915637229005024096942821067),(-31915637229005024092595782551)⟩⟩,⟨⟨10666572908823690774870056738,10666572908823690778697007859⟩,⟨(-30791743701200636932275369363),(-30791743701200636928084815420)⟩⟩,⟨⟨10279485372927895292915510870,10279485372927895296605413050⟩,⟨(-29674318235953704695003385100),(-29674318235953704690959621923)⟩⟩,⟨⟨9886841054724459425028622212,9886841054724459428576097949⟩,⟨(-28540851721901050824384774557),(-28540851721901050820499753535)⟩⟩,⟨⟨9496891073954188849246959006,9496891073954188852653386539⟩,⟨(-27415163090060025287339350184),(-27415163090060025283610824714)⟩⟩,⟨⟨9101138730168082672113904752,9101138730168082675379611050⟩,⟨(-26272724478973356684182647206),(-26272724478973356680605943418)⟩⟩,⟨⟨8708593155276932931116356545,8708593155276932934239653577⟩,⟨(-25139543012310348166767108939),(-25139543012310348163349161194)⟩⟩,⟨⟨8309934963699564220730996355,8309934963699564223712121611⟩,⟨(-23988715941201132048448180227),(-23988715941201132045184373518)⟩⟩,⟨⟨7915071511567247978234002605,7915071511567247981074321727⟩,⟨(-22848843339292443597246117694),(-22848843339292443594134949165)⟩⟩,⟨⟨7513700288185479520408872124,7513700288185479523103792304⟩,⟨(-21690184419970276427429145289),(-21690184419970276424479689777)⟩⟩,⟨⟨7116811458893626800991947720,7116811458893626803544850233⟩,⟨(-20544465057820243453437621686),(-20544465057820243450642999753)⟩⟩,⟨⟨6712905375084154820580525514,6712905375084154822988746945⟩,⟨(-19378488626746612490303733230),(-19378488626746612487667122516)⟩⟩] +lemma amp9_10_14_eq : ∀ k : Fin 16, amp9_1Expr 0 14 k = amp9_10_14 k := by decide +kernel +noncomputable def amp9_10_15 : Fin 16 → CBox := ![⟨⟨6314304889329281697053574421,6314304889329281699318632582⟩,⟨(-18227828137998154551155536224),(-18227828137998154548675965840)⟩⟩,⟨⟨5908018787060499826795919140,5908018787060499828914881131⟩,⟨(-17054981185433729371633495738),(-17054981185433729369314491610)⟩⟩,⟨⟨5508052685234101316958165762,5508052685234101318933161174⟩,⟨(-15900378502652747127391146995),(-15900378502652747125230624275)⟩⟩,⟨⟨5099502883647184280891094747,5099502883647184282719919619⟩,⟨(-14720996813034873396508432986),(-14720996813034873394507236016)⟩⟩,⟨⟨4698569893355039726749271123,4698569893355039728434335431⟩,⟨(-13563602963674017037621243105),(-13563602963674017035777311273)⟩⟩,⟨⟨4287805485929443699696883328,4287805485929443701234474214⟩,⟨(-12377828257670592144859186692),(-12377828257670592143176918065)⟩⟩,⟨⟨3886397599776523264753010838,3886397599776523266146198021⟩,⟨(-11219063502044455816868118479),(-11219063502044455815344666293)⟩⟩,⟨⟨3473340580412691299921832201,3473340580412691301167193072⟩,⟨(-10026670595442591582338009626),(-10026670595442591580975765569)⟩⟩,⟨⟨3072133445990435319702768835,3072133445990435320804016816⟩,⟨(-8868485360145152285270265782),(-8868485360145152284066127711)⟩⟩,⟨⟨2656435792071101112864879805,2656435792071101113816931586⟩,⟨(-7668469598186034814741833284),(-7668469598186034813701160364)⟩⟩,⟨⟨2256524817754308917548769726,2256524817754308918357176597⟩,⟨(-6514026054817607367347014078),(-6514026054817607366463929427)⟩⟩,⟨⟨1837153108049314192974706911,1837153108049314193632669304⟩,⟨(-5303404207374145887341907994),(-5303404207374145886623530130)⟩⟩,⟨⟨1440842106367455813265972053,1440842106367455813781594343⟩,⟨(-4159352889854990063955758191),(-4159352889854990063393516147)⟩⟩,⟨⟨1014414495963543606746544271,1014414495963543607109308662⟩,⟨(-2928362411572052200074628951),(-2928362411572052199679524823)⟩⟩,⟨⟨629264447029517718362162568,629264447029517718586334740⟩,⟨(-1816529989419765287848064699),(-1816529989419765287605451892)⟩⟩,⟨⟨178776584874023315318119029,178776584874023315381290509⟩,⟨(-516083547009096694092754891),(-516083547009096694025319321)⟩⟩] +lemma amp9_10_15_eq : ∀ k : Fin 16, amp9_1Expr 0 15 k = amp9_10_15 k := by decide +kernel +noncomputable def amp9_10 : Fin 16 → Fin 16 → CBox := ![amp9_10_0,amp9_10_1,amp9_10_2,amp9_10_3,amp9_10_4,amp9_10_5,amp9_10_6,amp9_10_7,amp9_10_8,amp9_10_9,amp9_10_10,amp9_10_11,amp9_10_12,amp9_10_13,amp9_10_14,amp9_10_15] +lemma amp9_10_eq (i k : Fin 16) : amp9_1Expr 0 i k = amp9_10 i k := by + fin_cases i + · exact amp9_10_0_eq k + · exact amp9_10_1_eq k + · exact amp9_10_2_eq k + · exact amp9_10_3_eq k + · exact amp9_10_4_eq k + · exact amp9_10_5_eq k + · exact amp9_10_6_eq k + · exact amp9_10_7_eq k + · exact amp9_10_8_eq k + · exact amp9_10_9_eq k + · exact amp9_10_10_eq k + · exact amp9_10_11_eq k + · exact amp9_10_12_eq k + · exact amp9_10_13_eq k + · exact amp9_10_14_eq k + · exact amp9_10_15_eq k +noncomputable def amp9_11_0 : Fin 16 → CBox := ![⟨⟨385210003677661992952978527,385210003677661992996084261⟩,⟨(-873636716757143324777906610),(-873636716757143324733635349)⟩⟩,⟨⟨1355876442797423833491395123,1355876442797423833647039375⟩,⟨(-3075058883478800724748195665),(-3075058883478800724583479737)⟩⟩,⟨⟨2185759460592364486758687261,2185759460592364487012578979⟩,⟨(-4957191403499139413853896777),(-4957191403499139413581598341)⟩⟩,⟨⟨3104583262309451838822703131,3104583262309451839184105615⟩,⟨(-7041037102589901690894908814),(-7041037102589901690506369512)⟩⟩,⟨⟨3958514790998972547878268840,3958514790998972548340187786⟩,⟨(-8977710423472774273811563673),(-8977710423472774273313635280)⟩⟩,⟨⟨4862135239681351864446506826,4862135239681351865014407226⟩,⟨(-11027075690326225203084051736),(-11027075690326225202471239739)⟩⟩,⟨⟨5723823631345515038712832553,5723823631345515039382187972⟩,⟨(-12981341182328237041225176883),(-12981341182328237040501924314)⟩⟩,⟨⟨6619527590048496233754215709,6619527590048496234528774374⟩,⟨(-15012752252126022925547738492),(-15012752252126022924710267970)⟩⟩,⟨⟨7484008818589727932792636802,7484008818589727933668984504⟩,⟨(-16973351756267974183168069436),(-16973351756267974182219788620)⟩⟩,⟨⟨8374023000594305591428517612,8374023000594305592408490671⟩,⟨(-18991858701597502347477290513),(-18991858701597502346417580233)⟩⟩,⟨⟨9238936788997680557560821166,9238936788997680558643105436⟩,⟨(-20953439229529479545471058754),(-20953439229529479544299413981)⟩⟩,⟨⟨10124011078824646541710190971,10124011078824646542896532973⟩,⟨(-22960742750384096492454932872),(-22960742750384096491170192075)⟩⟩,⟨⟨10987901608861133639399449151,10987901608861133640686963658⟩,⟨(-24920002580329241959739644449),(-24920002580329241958345409597)⟩⟩,⟨⟨11868204086295200167812393830,11868204086295200169202310916⟩,⟨(-26916483873120949762871896000),(-26916483873120949761367656312)⟩⟩,⟨⟨12730011261233991575339025042,12730011261233991576831061566⟩,⟨(-28871018759554729026904456743),(-28871018759554729025288286109)⟩⟩,⟨⟨13605436144528543517397475218,13605436144528543518992931781⟩,⟨(-30856437916656717947058034985),(-30856437916656717945328874665)⟩⟩] +lemma amp9_11_0_eq : ∀ k : Fin 16, amp9_1Expr 1 0 k = amp9_11_0 k := by decide +kernel +noncomputable def amp9_11_1 : Fin 16 → CBox := ![⟨⟨14464300825782799816576030964,14464300825782799818272586547⟩,⟨(-32804299376914922133373824261),(-32804299376914922131534638653)⟩⟩,⟨⟨15334597482021724182233680019,15334597482021724184031844771⟩,⟨(-34778087975607497057444984948),(-34778087975607497055496204506)⟩⟩,⟨⟨16189774056173590091240185625,16189774056173590093137871469⟩,⟨(-36717584996341235470382497567),(-36717584996341235468326758369)⟩⟩,⟨⟨17054608847284225416982945145,17054608847284225418985105716⟩,⟨(-38678986362426939555966692339),(-38678986362426939553794100933)⟩⟩,⟨⟨17905421340180017039954333640,17905421340180017042054458530⟩,⟨(-40608585868600260492273336717),(-40608585868600260489996711238)⟩⟩,⟨⟨18764410360201072197660758866,18764410360201072199859816381⟩,⟨(-42556729322864214031474667913),(-42556729322864214029092947686)⟩⟩,⟨⟨19610228521757425345615324315,19610228521757425347917006309⟩,⟨(-44475001939309522031000107091),(-44475001939309522028503090272)⟩⟩,⟨⟨20462956309978198964005079061,20462956309978198966404079988⟩,⟨(-46408945237968402988532958140),(-46408945237968402985933636907)⟩⟩,⟨⟨21303181743484879754596259075,21303181743484879757096302181⟩,⟨(-48314533831349969677254915468),(-48314533831349969674543109613)⟩⟩,⟨⟨22149212667309377170721413101,22149212667309377173324066326⟩,⟨(-50233288981809495283762099412),(-50233288981809495280935059076)⟩⟩,⟨⟨22983270389303945547579585661,22983270389303945550276153056⟩,⟨(-52124889518848018485049623170),(-52124889518848018482125407719)⟩⟩,⟨⟨23822155938916705060345484451,23822155938916705063143110974⟩,⟨(-54027439323634414943645571549),(-54027439323634414940608646979)⟩⟩,⟨⟨24649489050903922243570319635,24649489050903922246458713628⟩,⟨(-55903788786837351759199221186),(-55903788786837351756071324279)⟩⟩,⟨⟨25480772729857277561851574418,25480772729857277564842776477⟩,⟨(-57789097935200786628663981339),(-57789097935200786625418353211)⟩⟩,⟨⟨26300838960499855272040804964,26300838960499855275129458719⟩,⟨(-59648966480726655560278082141),(-59648966480726655556925313109)⟩⟩,⟨⟨27124059698702532519978875632,27124059698702532523166945356⟩,⟨(-61515989289125970109810325464),(-61515989289125970106346398692)⟩⟩] +lemma amp9_11_1_eq : ∀ k : Fin 16, amp9_1Expr 1 1 k = amp9_11_1 k := by decide +kernel +noncomputable def amp9_11_2 : Fin 16 → CBox := ![⟨⟨27936329116135969235602421087,27936329116135969238877913323⟩,⟨(-63358175058430631412550430448),(-63358175058430631409001025786)⟩⟩,⟨⟨28751023739938367694878566653,28751023739938367698253916621⟩,⟨(-65205861072561258317247900150),(-65205861072561258313585151916)⟩⟩,⟨⟨29554977221247464421040533728,29554977221247464424512682904⟩,⟨(-67029186721248413940488518828),(-67029186721248413936717872081)⟩⟩,⟨⟨30360682302007587721819393919,30360682302007587725389687525⟩,⟨(-68856484908495988081500933540),(-68856484908495988077619580611)⟩⟩,⟨⟨31155810506980960745368067771,31155810506980960749037247041⟩,⟨(-70659795278844557635650736475),(-70659795278844557631655527576)⟩⟩,⟨⟨31952063788142973129580670396,31952063788142973133330520546⟩,⟨(-72465657264826575313247722188),(-72465657264826575309180123750)⟩⟩,⟨⟨32737866477294929149588592525,32737866477294929153433575920⟩,⟨(-74247817839098958516294310406),(-74247817839098958512120071350)⟩⟩,⟨⟨33524208008310895721364891815,33524208008310895725302577304⟩,⟨(-76031200479341672531060677549),(-76031200479341672526785386428)⟩⟩,⟨⟨34300193600980150022368996003,34300193600980150026400718104⟩,⟨(-77791096377574093955308562132),(-77791096377574093950927754294)⟩⟩,⟨⟨35076166662618009661814219251,35076166662618009665940524321⟩,⟨(-79550963856063983527829939631),(-79550963856063983523342374232)⟩⟩,⟨⟨35841851965557722417057953362,35841851965557722421277546363⟩,⟨(-81287499220522484616053681220),(-81287499220522484611460866777)⟩⟩,⟨⟨36607003843609385792204386904,36607003843609385796496247055⟩,⟨(-83022824804436911450600584361),(-83022824804436911445950120863)⟩⟩,⟨⟨37361913902531192331398364973,37361913902531192335785761576⟩,⟨(-84734922462926753850244610690),(-84734922462926753845482302363)⟩⟩,⟨⟨38115796549175229429812750107,38115796549175229434292191163⟩,⟨(-86444690002570935226340579253),(-86444690002570935221474203107)⟩⟩,⟨⟨38859464590104374372820974979,38859464590104374377394100369⟩,⟨(-88131291335433024607759234559),(-88131291335433024602783653023)⟩⟩,⟨⟨39601635200454137553547331308,39601635200454137558206548651⟩,⟨(-89814496571821883453209959353),(-89814496571821883448142183630)⟩⟩] +lemma amp9_11_2_eq : ∀ k : Fin 16, amp9_1Expr 1 2 k = amp9_11_2 k := by decide +kernel +noncomputable def amp9_11_3 : Fin 16 → CBox := ![⟨⟨40333602637358103889445515230,40333602637358103894194341123⟩,⟨(-91474561529234112668894756324),(-91474561529234112663725394135)⟩⟩,⟨⟨41063624160825241726395751323,41063624160825241731234790452⟩,⟨(-93130213253838745819882070869),(-93130213253838745814609480606)⟩⟩,⟨⟨41783440652515466062802108544,41783440652515466067730878483⟩,⟨(-94762720484866194052137468971),(-94762720484866194046761327680)⟩⟩,⟨⟨42500882253193745494399050503,42500882253193745499381499457⟩,⟨(-96389841583740989905659626443),(-96389841583740989900261367986)⟩⟩,⟨⟨43208105797029466858440975432,43208105797029466863514296626⟩,⟨(-97993788648851490882421661726),(-97993788648851490876915514874)⟩⟩,⟨⟨43912543273515121376772331118,43912543273515121381932964711⟩,⟨(-99591417054765349038404208629),(-99591417054765349032797860050)⟩⟩,⟨⟨44606740326628404392273584165,44606740326628404397520029926⟩,⟨(-101165820700761684450377138163),(-101165820700761684444672568315)⟩⟩,⟨⟨45297756499006132963273934534,45297756499006132968604184281⟩,⟨(-102733010270862599444356271807),(-102733010270862599438557593446)⟩⟩,⟨⟨45978502120047616445423375087,45978502120047616450838413642⟩,⟨(-104276906752354655000876068775),(-104276906752354654994979622204)⟩⟩,⟨⟨46655687189838484688206420164,46655687189838484693696997242⟩,⟨(-105812728084513268101259584172),(-105812728084513268095285854149)⟩⟩,⟨⟨47322565195896356610858399590,47322565195896356616431869958⟩,⟨(-107325173519802296084468070945),(-107325173519802296078398945990)⟩⟩,⟨⟨47985517083355406597894342870,47985517083355406603546569487⟩,⟨(-108828714717585737047758984702),(-108828714717585737041603302231)⟩⟩,⟨⟨48638120217913569078822945293,48638120217913569084554381794⟩,⟨(-110308785469584940953133515013),(-110308785469584940946888809176)⟩⟩,⟨⟨49286444880026379419274085398,49286444880026379425083795957⟩,⟨(-111779152863456869660734744141),(-111779152863456869654402543236)⟩⟩,⟨⟨49924374988729221664429785279,49924374988729221670317401816⟩,⟨(-113225945938316979053866263538),(-113225945938316979047445958961)⟩⟩,⟨⟨50557686720482431271130991289,50557686720482431277095425880⟩,⟨(-114662264768903826592745971508),(-114662264768903826586239389304)⟩⟩] +lemma amp9_11_3_eq : ∀ k : Fin 16, amp9_1Expr 1 3 k = amp9_11_3 k := by decide +kernel +noncomputable def amp9_11_4 : Fin 16 → CBox := ![⟨⟨51180554932150761401322124736,51180554932150761407307799305⟩,⟨(-116074898226548033512688016261),(-116074898226548033506219754494)⟩⟩,⟨⟨51798476653068572739597559546,51798476653068572745667183621⟩,⟨(-117476313294489233320586770250),(-117476313294489233314013920026)⟩⟩,⟨⟨52405903563925214425504068215,52405903563925214431654338684⟩,⟨(-118853926666427485393896404300),(-118853926666427485387224999596)⟩⟩,⟨⟨53008067091420818534640607252,53008067091420818540868680635⟩,⟨(-120219602952322616886603129668),(-120219602952322616879838888480)⟩⟩,⟨⟨53599682950878333015688023886,53599682950878333021992053077⟩,⟨(-121561357663008731442866694567),(-121561357663008731436012341386)⟩⟩,⟨⟨54185729261629598880838391526,54185729261629598887219507790⟩,⟨(-122890480920204303646446395617),(-122890480920204303639498591399)⟩⟩,⟨⟨54761174158297399574891262691,54761174158297399581342869338⟩,⟨(-124195560708890653084329221190),(-124195560708890653077301454780)⟩⟩,⟨⟨55330753638593851791028051867,55330753638593851797553086862⟩,⟨(-125487338031254330455598392429),(-125487338031254330448483186200)⟩⟩,⟨⟨55889677685399926700617394654,55889677685399926707215718283⟩,⟨(-126754949371838503075383718377),(-126754949371838503068179909574)⟩⟩,⟨⟨56442450371203974287954897165,56442450371203974294609438603⟩,⟨(-128008609738205775527864178849),(-128008609738205775520609629059)⟩⟩,⟨⟨56984513888713790569935861389,56984513888713790576662664107⟩,⟨(-129237982254988537107518382958),(-129237982254988537100175219327)⟩⟩,⟨⟨57520149696019410855675568609,57520149696019410862470756725⟩,⟨(-130452777051604511090659690787),(-130452777051604511083235811063)⟩⟩,⟨⟨58045023393183337444637461044,58045023393183337451501603023⟩,⟨(-131643163929215776058632814783),(-131643163929215776051125435287)⟩⟩,⟨⟨58563202339129627985978929419,58563202339129627992904921094⟩,⟨(-132818367451209476076975469576),(-132818367451209476069399772563)⟩⟩,⟨⟨59070567490809294429058831874,59070567490809294436052007259⟩,⟨(-133969045837229069666859622269),(-133969045837229069659202008860)⟩⟩,⟨⟨59570979905906762494714622941,59570979905906762501770211194⟩,⟨(-135103955769931880122458108764),(-135103955769931880114728433529)⟩⟩] +lemma amp9_11_4_eq : ∀ k : Fin 16, amp9_1Expr 1 4 k = amp9_11_4 k := by decide +kernel +noncomputable def amp9_11_5 : Fin 16 → CBox := ![⟨⟨60060528526626865100376294174,60060528526626865107494904555⟩,⟨(-136214227168949806811541989762),(-136214227168949806803737362383)⟩⟩,⟨⟨60542875258375211986175667021,60542875258375211993356181915⟩,⟨(-137308165049690261507075647331),(-137308165049690261499197602444)⟩⟩,⟨⟨61014310271825440935736353942,61014310271825440942979246117⟩,⟨(-138377355707728463724473111445),(-138377355707728463716519061630)⟩⟩,⟨⟨61478302879938500944593399753,61478302879938500951897138187⟩,⟨(-139429667368592488565299786145),(-139429667368592488557272170231)⟩⟩,⟨⟨61931338283814348954477929438,61931338283814348961841924772⟩,⟨(-140457128646955425577177506186),(-140457128646955425569076139288)⟩⟩,⟨⟨62376699227217381556888971888,62376699227217381564203483170⟩,⟨(-141467184638886696313292583631),(-141467184638886696305365286975)⟩⟩,⟨⟨62811060253041564511233301009,62811060253041564518611889926⟩,⟨(-142452293376628206079806185403),(-142452293376628206071793879402)⟩⟩,⟨⟨63237523068765669823488233985,63237523068765669830927025891⟩,⟨(-143419489375151593421083120293),(-143419489375151593412993495698)⟩⟩,⟨⟨63652946336376028674818135718,63652946336376028682314025947⟩,⟨(-144361648239445604952345128496),(-144361648239445604944183693580)⟩⟩,⟨⟨64060255810442041620736947350,64060255810442041628288551975⟩,⟨(-145285405432223164330626494172),(-145285405432223164322395260927)⟩⟩,⟨⟨64456489476868880859782698770,64456489476868880867386082011⟩,⟨(-146184043256009937240683696116),(-146184043256009937232390052703)⟩⟩,⟨⟨64844401807227121640585331554,64844401807227121648238874805⟩,⟨(-147063808712379984303865640462),(-147063808712379984295512102294)⟩⟩,⟨⟨65221205709714364219114314794,65221205709714364226820440612⟩,⟨(-147918380818730821618485639984),(-147918380818730821610065170305)⟩⟩,⟨⟨65589488661285843476315733348,65589488661285843484067827309⟩,⟨(-148753627841333508273002746614),(-148753627841333508264529163379)⟩⟩,⟨⟨65946634454237240522120575652,65946634454237240529920745747⟩,⟨(-149563616354037802159248431088),(-149563616354037802150715406975)⟩⟩,⟨⟨66295067506085358049576499388,66295067506085358057424652649⟩,⟨(-150353844812593051812779819974),(-150353844812593051804186355975)⟩⟩] +lemma amp9_11_5_eq : ∀ k : Fin 16, amp9_1Expr 1 5 k = amp9_11_5 k := by decide +kernel +noncomputable def amp9_11_6 : Fin 16 → CBox := ![⟨⟨66632338791740151041394592125,66632338791740151049277883634⟩,⟨(-151118758952524046079039144667),(-151118758952524046070412822478)⟩⟩,⟨⟨66960713276388809127090154727,66960713276388809135021344535⟩,⟨(-151863495599797956285015858166),(-151863495599797956276326503227)⟩⟩,⟨⟨67277905729051392369236762865,67277905729051392377207375155⟩,⟨(-152582871966659309066402215089),(-152582871966659309057667497382)⟩⟩,⟨⟨67586024963955147022606571657,67586024963955147030622469870⟩,⟨(-153281670736631774828823191861),(-153281670736631774820028553492)⟩⟩,⟨⟨67882946447620971187355155529,67882946447620971195411084891⟩,⟨(-153955073575727131534992420250),(-153955073575727131526148223858)⟩⟩,⟨⟨68170625858784866936939109245,68170625858784866945036001014⟩,⟨(-154607515863955349806239629703),(-154607515863955349797342479884)⟩⟩,⟨⟨68447096538020503798459670419,68447096538020503806559115941⟩,⟨(-155234537317658696391405449759),(-155234537317658696382540898943)⟩⟩,⟨⟨68714163775761176697683715813,68714163775761176705824959074⟩,⟨(-155840232243817466149154099654),(-155840232243817466140231838709)⟩⟩,⟨⟨68970016219710489342976169188,68970016219710489351154240807⟩,⟨(-156420492587453838850155493326),(-156420492587453838841185235268)⟩⟩,⟨⟨69216311266545650363575673448,69216311266545650371787332360⟩,⟨(-156979077240023427831251795275),(-156979077240023427822239563532)⟩⟩,⟨⟨69451390545946672983640358799,69451390545946672991886522957⟩,⟨(-157512225101898267341630637637),(-157512225101898267332572792913)⟩⟩,⟨⟨69676765816596932304289208683,69676765816596932312564417861⟩,⟨(-158023364764963468679188254375),(-158023364764963468670095832686)⟩⟩,⟨⟨69890929593705596295094476324,69890929593705596303399599589⟩,⟨(-158509077330305062140599809715),(-158509077330305062131469283227)⟩⟩,⟨⟨70095250027190538211212267616,70095250027190538219548624378⟩,⟨(-158972465692424413081751363535),(-158972465692424413072578373049)⟩⟩,⟨⟨70288368638517981037543696903,70288368638517981045892028197⟩,⟨(-159410448891027906905552503365),(-159410448891027906896379171746)⟩⟩,⟨⟨70471511782327267737636564580,70471511782327267746011761496⟩,⟨(-159825808236129475647000904436),(-159825808236129475637792074250)⟩⟩] +lemma amp9_11_6_eq : ∀ k : Fin 16, amp9_1Expr 1 6 k = amp9_11_6 k := by decide +kernel +noncomputable def amp9_11_7 : Fin 16 → CBox := ![⟨⟨70643468314107287776466167791,70643468314107287784864908964⟩,⟨(-160215796913513228781223842076),(-160215796913513228771985492638)⟩⟩,⟨⟨70805324400427207191245790738,70805324400427207199669049764⟩,⟨(-160582878293772552105513654143),(-160582878293772552096242174832)⟩⟩,⟨⟨70956014756739613931286768464,70956014756739613939723502498⟩,⟨(-160924636365678433105435513394),(-160924636365678433096154398349)⟩⟩,⟨⟨71096486770715766117008843212,71096486770715766125465682123⟩,⟨(-161243219756334820837195725399),(-161243219756334820827888519493)⟩⟩,⟨⟨71225819734200030787004637657,71225819734200030795474347550⟩,⟨(-161536540346423682777498569076),(-161536540346423682768180131643)⟩⟩,⟨⟨71344823474217662613239211539,71344823474217662621727135430⟩,⟨(-161806434782492954158068784620),(-161806434782492954148725563652)⟩⟩,⟨⟨71452720759319491780047436458,71452720759319491788547577097⟩,⟨(-162051140343105158224246279862),(-162051140343105158214890334572)⟩⟩,⟨⟨71550184889284250856495439522,71550184889284250865006667036⟩,⟨(-162272184037949735559662518704),(-162272184037949735550294962838)⟩⟩,⟨⟨71636581187985562582167802220,71636581187985562590689181159⟩,⟨(-162468126453818413543382336339),(-162468126453818413534003754569)⟩⟩,⟨⟨71712447281589071093645075362,71712447281589071102176305531⟩,⟨(-162640186899539394635972128968),(-162640186899539394626581739889)⟩⟩,⟨⟨71777290301579416078691676367,71777290301579416087229136767⟩,⟨(-162787247574361292690892572262),(-162787247574361292681497057454)⟩⟩,⟨⟨71831512878535996573027447452,71831512878535996581570526264⟩,⟨(-162910221623981503826241951356),(-162910221623981503816841223635)⟩⟩,⟨⟨71874763373790792273678899906,71874763373790792282224166780⟩,⟨(-163008311549766863840231327382),(-163008311549766863830831643022)⟩⟩,⟨⟨71907309928033851780747924128,71907309928033851789293468250⟩,⟨(-163082125481178826379445946574),(-163082125481178826370050152853)⟩⟩,⟨⟨71928941721771935357782373404,71928941721771935366325096748⟩,⟨(-163131185290317949645063692405),(-163131185290317949635677299861)⟩⟩,⟨⟨71939792741600879308859119202,71939792741600879317395268872⟩,⟨(-163155794851976057178142303306),(-163155794851976057168772326293)⟩⟩] +lemma amp9_11_7_eq : ∀ k : Fin 16, amp9_1Expr 1 7 k = amp9_11_7 k := by decide +kernel +noncomputable def amp9_11_8 : Fin 16 → CBox := ![⟨⟨71939792741600879308859119202,71939792741600879317395268872⟩,⟨(-163155794851976057178142303306),(-163155794851976057168772326293)⟩⟩,⟨⟨71928941721771935357782373404,71928941721771935366325096748⟩,⟨(-163131185290317949645063692405),(-163131185290317949635677299861)⟩⟩,⟨⟨71907309928033851780747924128,71907309928033851789293468250⟩,⟨(-163082125481178826379445946574),(-163082125481178826370050152853)⟩⟩,⟨⟨71874763373790792273678899906,71874763373790792282224166780⟩,⟨(-163008311549766863840231327382),(-163008311549766863830831643022)⟩⟩,⟨⟨71831512878535996573027447452,71831512878535996581570526264⟩,⟨(-162910221623981503826241951356),(-162910221623981503816841223635)⟩⟩,⟨⟨71777290301579416078691676367,71777290301579416087229136767⟩,⟨(-162787247574361292690892572262),(-162787247574361292681497057454)⟩⟩,⟨⟨71712447281589071093645075362,71712447281589071102176305531⟩,⟨(-162640186899539394635972128968),(-162640186899539394626581739889)⟩⟩,⟨⟨71636581187985562582167802220,71636581187985562590689181159⟩,⟨(-162468126453818413543382336339),(-162468126453818413534003754569)⟩⟩,⟨⟨71550184889284250856495439522,71550184889284250865006667036⟩,⟨(-162272184037949735559662518704),(-162272184037949735550294962838)⟩⟩,⟨⟨71452720759319491780047436458,71452720759319491788547577097⟩,⟨(-162051140343105158224246279862),(-162051140343105158214890334572)⟩⟩,⟨⟨71344823474217662613239211539,71344823474217662621727135430⟩,⟨(-161806434782492954158068784620),(-161806434782492954148725563652)⟩⟩,⟨⟨71225819734200030787004637657,71225819734200030795474347550⟩,⟨(-161536540346423682777498569076),(-161536540346423682768180131643)⟩⟩,⟨⟨71096486770715766117008843212,71096486770715766125465682123⟩,⟨(-161243219756334820837195725399),(-161243219756334820827888519493)⟩⟩,⟨⟨70956014756739613931286768464,70956014756739613939723502498⟩,⟨(-160924636365678433105435513394),(-160924636365678433096154398349)⟩⟩,⟨⟨70805324400427207191245790738,70805324400427207199669049764⟩,⟨(-160582878293772552105513654143),(-160582878293772552096242174832)⟩⟩,⟨⟨70643468314107287776466167791,70643468314107287784864908964⟩,⟨(-160215796913513228781223842076),(-160215796913513228771985492638)⟩⟩] +lemma amp9_11_8_eq : ∀ k : Fin 16, amp9_1Expr 1 8 k = amp9_11_8 k := by decide +kernel +noncomputable def amp9_11_9 : Fin 16 → CBox := ![⟨⟨70471511782327267737636564580,70471511782327267746011761496⟩,⟨(-159825808236129475647000904436),(-159825808236129475637792074250)⟩⟩,⟨⟨70288368638517981037543696903,70288368638517981045892028197⟩,⟨(-159410448891027906905552503365),(-159410448891027906896379171746)⟩⟩,⟨⟨70095250027190538211212267616,70095250027190538219548624378⟩,⟨(-158972465692424413081751363535),(-158972465692424413072578373049)⟩⟩,⟨⟨69890929593705596295094476324,69890929593705596303399599589⟩,⟨(-158509077330305062140599809715),(-158509077330305062131469283227)⟩⟩,⟨⟨69676765816596932304289208683,69676765816596932312564417861⟩,⟨(-158023364764963468679188254375),(-158023364764963468670095832686)⟩⟩,⟨⟨69451390545946672983640358799,69451390545946672991886522957⟩,⟨(-157512225101898267341630637637),(-157512225101898267332572792913)⟩⟩,⟨⟨69216311266545650363575673448,69216311266545650371787332360⟩,⟨(-156979077240023427831251795275),(-156979077240023427822239563532)⟩⟩,⟨⟨68970016219710489342976169188,68970016219710489351154240807⟩,⟨(-156420492587453838850155493326),(-156420492587453838841185235268)⟩⟩,⟨⟨68714163775761176697683715813,68714163775761176705824959074⟩,⟨(-155840232243817466149154099654),(-155840232243817466140231838709)⟩⟩,⟨⟨68447096538020503798459670419,68447096538020503806559115941⟩,⟨(-155234537317658696391405449759),(-155234537317658696382540898943)⟩⟩,⟨⟨68170625858784866936939109245,68170625858784866945036001014⟩,⟨(-154607515863955349806239629703),(-154607515863955349797342479884)⟩⟩,⟨⟨67882946447620971187355155529,67882946447620971195411084891⟩,⟨(-153955073575727131534992420250),(-153955073575727131526148223858)⟩⟩,⟨⟨67586024963955147022606571657,67586024963955147030622469870⟩,⟨(-153281670736631774828823191861),(-153281670736631774820028553492)⟩⟩,⟨⟨67277905729051392369236762865,67277905729051392377207375155⟩,⟨(-152582871966659309066402215089),(-152582871966659309057667497382)⟩⟩,⟨⟨66960713276388809127090154727,66960713276388809135021344535⟩,⟨(-151863495599797956285015858166),(-151863495599797956276326503227)⟩⟩,⟨⟨66632338791740151041394592125,66632338791740151049277883634⟩,⟨(-151118758952524046079039144667),(-151118758952524046070412822478)⟩⟩] +lemma amp9_11_9_eq : ∀ k : Fin 16, amp9_1Expr 1 9 k = amp9_11_9 k := by decide +kernel +noncomputable def amp9_11_10 : Fin 16 → CBox := ![⟨⟨66295067506085358049576499388,66295067506085358057424652649⟩,⟨(-150353844812593051812779819974),(-150353844812593051804186355975)⟩⟩,⟨⟨65946634454237240522120575652,65946634454237240529920745747⟩,⟨(-149563616354037802159248431088),(-149563616354037802150715406975)⟩⟩,⟨⟨65589488661285843476315733348,65589488661285843484067827309⟩,⟨(-148753627841333508273002746614),(-148753627841333508264529163379)⟩⟩,⟨⟨65221205709714364219114314794,65221205709714364226820440612⟩,⟨(-147918380818730821618485639984),(-147918380818730821610065170305)⟩⟩,⟨⟨64844401807227121640585331554,64844401807227121648238874805⟩,⟨(-147063808712379984303865640462),(-147063808712379984295512102294)⟩⟩,⟨⟨64456489476868880859782698770,64456489476868880867386082011⟩,⟨(-146184043256009937240683696116),(-146184043256009937232390052703)⟩⟩,⟨⟨64060255810442041620736947350,64060255810442041628288551975⟩,⟨(-145285405432223164330626494172),(-145285405432223164322395260927)⟩⟩,⟨⟨63652946336376028674818135718,63652946336376028682314025947⟩,⟨(-144361648239445604952345128496),(-144361648239445604944183693580)⟩⟩,⟨⟨63237523068765669823488233985,63237523068765669830927025891⟩,⟨(-143419489375151593421083120293),(-143419489375151593412993495698)⟩⟩,⟨⟨62811060253041564511233301009,62811060253041564518611889926⟩,⟨(-142452293376628206079806185403),(-142452293376628206071793879402)⟩⟩,⟨⟨62376699227217381556888971888,62376699227217381564203483170⟩,⟨(-141467184638886696313292583631),(-141467184638886696305365286975)⟩⟩,⟨⟨61931338283814348954477929438,61931338283814348961841924772⟩,⟨(-140457128646955425577177506186),(-140457128646955425569076139288)⟩⟩,⟨⟨61478302879938500944593399753,61478302879938500951897138187⟩,⟨(-139429667368592488565299786145),(-139429667368592488557272170231)⟩⟩,⟨⟨61014310271825440935736353942,61014310271825440942979246117⟩,⟨(-138377355707728463724473111445),(-138377355707728463716519061630)⟩⟩,⟨⟨60542875258375211986175667021,60542875258375211993356181915⟩,⟨(-137308165049690261507075647331),(-137308165049690261499197602444)⟩⟩,⟨⟨60060528526626865100376294174,60060528526626865107494904555⟩,⟨(-136214227168949806811541989762),(-136214227168949806803737362383)⟩⟩] +lemma amp9_11_10_eq : ∀ k : Fin 16, amp9_1Expr 1 10 k = amp9_11_10 k := by decide +kernel +noncomputable def amp9_11_11 : Fin 16 → CBox := ![⟨⟨59570979905906762494714622941,59570979905906762501770211194⟩,⟨(-135103955769931880122458108764),(-135103955769931880114728433529)⟩⟩,⟨⟨59070567490809294429058831874,59070567490809294436052007259⟩,⟨(-133969045837229069666859622269),(-133969045837229069659202008860)⟩⟩,⟨⟨58563202339129627985978929419,58563202339129627992904921094⟩,⟨(-132818367451209476076975469576),(-132818367451209476069399772563)⟩⟩,⟨⟨58045023393183337444637461044,58045023393183337451501603023⟩,⟨(-131643163929215776058632814783),(-131643163929215776051125435287)⟩⟩,⟨⟨57520149696019410855675568609,57520149696019410862470756725⟩,⟨(-130452777051604511090659690787),(-130452777051604511083235811063)⟩⟩,⟨⟨56984513888713790569935861389,56984513888713790576662664107⟩,⟨(-129237982254988537107518382958),(-129237982254988537100175219327)⟩⟩,⟨⟨56442450371203974287954897165,56442450371203974294609438603⟩,⟨(-128008609738205775527864178849),(-128008609738205775520609629059)⟩⟩,⟨⟨55889677685399926700617394654,55889677685399926707215718283⟩,⟨(-126754949371838503075383718377),(-126754949371838503068179909574)⟩⟩,⟨⟨55330753638593851791028051867,55330753638593851797553086862⟩,⟨(-125487338031254330455598392429),(-125487338031254330448483186200)⟩⟩,⟨⟨54761174158297399574891262691,54761174158297399581342869338⟩,⟨(-124195560708890653084329221190),(-124195560708890653077301454780)⟩⟩,⟨⟨54185729261629598880838391526,54185729261629598887219507790⟩,⟨(-122890480920204303646446395617),(-122890480920204303639498591399)⟩⟩,⟨⟨53599682950878333015688023886,53599682950878333021992053077⟩,⟨(-121561357663008731442866694567),(-121561357663008731436012341386)⟩⟩,⟨⟨53008067091420818534640607252,53008067091420818540868680635⟩,⟨(-120219602952322616886603129668),(-120219602952322616879838888480)⟩⟩,⟨⟨52405903563925214425504068215,52405903563925214431654338684⟩,⟨(-118853926666427485393896404300),(-118853926666427485387224999596)⟩⟩,⟨⟨51798476653068572739597559546,51798476653068572745667183621⟩,⟨(-117476313294489233320586770250),(-117476313294489233314013920026)⟩⟩,⟨⟨51180554932150761401322124736,51180554932150761407307799305⟩,⟨(-116074898226548033512688016261),(-116074898226548033506219754494)⟩⟩] +lemma amp9_11_11_eq : ∀ k : Fin 16, amp9_1Expr 1 11 k = amp9_11_11 k := by decide +kernel +noncomputable def amp9_11_12 : Fin 16 → CBox := ![⟨⟨50557686720482431271130991289,50557686720482431277095425880⟩,⟨(-114662264768903826592745971508),(-114662264768903826586239389304)⟩⟩,⟨⟨49924374988729221664429785279,49924374988729221670317401816⟩,⟨(-113225945938316979053866263538),(-113225945938316979047445958961)⟩⟩,⟨⟨49286444880026379419274085398,49286444880026379425083795957⟩,⟨(-111779152863456869660734744141),(-111779152863456869654402543236)⟩⟩,⟨⟨48638120217913569078822945293,48638120217913569084554381794⟩,⟨(-110308785469584940953133515013),(-110308785469584940946888809176)⟩⟩,⟨⟨47985517083355406597894342870,47985517083355406603546569487⟩,⟨(-108828714717585737047758984702),(-108828714717585737041603302231)⟩⟩,⟨⟨47322565195896356610858399590,47322565195896356616431869958⟩,⟨(-107325173519802296084468070945),(-107325173519802296078398945990)⟩⟩,⟨⟨46655687189838484688206420164,46655687189838484693696997242⟩,⟨(-105812728084513268101259584172),(-105812728084513268095285854149)⟩⟩,⟨⟨45978502120047616445423375087,45978502120047616450838413642⟩,⟨(-104276906752354655000876068775),(-104276906752354654994979622204)⟩⟩,⟨⟨45297756499006132963273934534,45297756499006132968604184281⟩,⟨(-102733010270862599444356271807),(-102733010270862599438557593446)⟩⟩,⟨⟨44606740326628404392273584165,44606740326628404397520029926⟩,⟨(-101165820700761684450377138163),(-101165820700761684444672568315)⟩⟩,⟨⟨43912543273515121376772331118,43912543273515121381932964711⟩,⟨(-99591417054765349038404208629),(-99591417054765349032797860050)⟩⟩,⟨⟨43208105797029466858440975432,43208105797029466863514296626⟩,⟨(-97993788648851490882421661726),(-97993788648851490876915514874)⟩⟩,⟨⟨42500882253193745494399050503,42500882253193745499381499457⟩,⟨(-96389841583740989905659626443),(-96389841583740989900261367986)⟩⟩,⟨⟨41783440652515466062802108544,41783440652515466067730878483⟩,⟨(-94762720484866194052137468971),(-94762720484866194046761327680)⟩⟩,⟨⟨41063624160825241726395751323,41063624160825241731234790452⟩,⟨(-93130213253838745819882070869),(-93130213253838745814609480606)⟩⟩,⟨⟨40333602637358103889445515230,40333602637358103894194341123⟩,⟨(-91474561529234112668894756324),(-91474561529234112663725394135)⟩⟩] +lemma amp9_11_12_eq : ∀ k : Fin 16, amp9_1Expr 1 12 k = amp9_11_12 k := by decide +kernel +noncomputable def amp9_11_13 : Fin 16 → CBox := ![⟨⟨39601635200454137553547331308,39601635200454137558206548651⟩,⟨(-89814496571821883453209959353),(-89814496571821883448142183630)⟩⟩,⟨⟨38859464590104374372820974979,38859464590104374377394100369⟩,⟨(-88131291335433024607759234559),(-88131291335433024602783653023)⟩⟩,⟨⟨38115796549175229429812750107,38115796549175229434292191163⟩,⟨(-86444690002570935226340579253),(-86444690002570935221474203107)⟩⟩,⟨⟨37361913902531192331398364973,37361913902531192335785761576⟩,⟨(-84734922462926753850244610690),(-84734922462926753845482302363)⟩⟩,⟨⟨36607003843609385792204386904,36607003843609385796496247055⟩,⟨(-83022824804436911450600584361),(-83022824804436911445950120863)⟩⟩,⟨⟨35841851965557722417057953362,35841851965557722421277546363⟩,⟨(-81287499220522484616053681220),(-81287499220522484611460866777)⟩⟩,⟨⟨35076166662618009661814219251,35076166662618009665940524321⟩,⟨(-79550963856063983527829939631),(-79550963856063983523342374232)⟩⟩,⟨⟨34300193600980150022368996003,34300193600980150026400718104⟩,⟨(-77791096377574093955308562132),(-77791096377574093950927754294)⟩⟩,⟨⟨33524208008310895721364891815,33524208008310895725302577304⟩,⟨(-76031200479341672531060677549),(-76031200479341672526785386428)⟩⟩,⟨⟨32737866477294929149588592525,32737866477294929153433575920⟩,⟨(-74247817839098958516294310406),(-74247817839098958512120071350)⟩⟩,⟨⟨31952063788142973129580670396,31952063788142973133330520546⟩,⟨(-72465657264826575313247722188),(-72465657264826575309180123750)⟩⟩,⟨⟨31155810506980960745368067771,31155810506980960749037247041⟩,⟨(-70659795278844557635650736475),(-70659795278844557631655527576)⟩⟩,⟨⟨30360682302007587721819393919,30360682302007587725389687525⟩,⟨(-68856484908495988081500933540),(-68856484908495988077619580611)⟩⟩,⟨⟨29554977221247464421040533728,29554977221247464424512682904⟩,⟨(-67029186721248413940488518828),(-67029186721248413936717872081)⟩⟩,⟨⟨28751023739938367694878566653,28751023739938367698253916621⟩,⟨(-65205861072561258317247900150),(-65205861072561258313585151916)⟩⟩,⟨⟨27936329116135969235602421087,27936329116135969238877913323⟩,⟨(-63358175058430631412550430448),(-63358175058430631409001025786)⟩⟩] +lemma amp9_11_13_eq : ∀ k : Fin 16, amp9_1Expr 1 13 k = amp9_11_13 k := by decide +kernel +noncomputable def amp9_11_14 : Fin 16 → CBox := ![⟨⟨27124059698702532519978875632,27124059698702532523166945356⟩,⟨(-61515989289125970109810325464),(-61515989289125970106346398692)⟩⟩,⟨⟨26300838960499855272040804964,26300838960499855275129458719⟩,⟨(-59648966480726655560278082141),(-59648966480726655556925313109)⟩⟩,⟨⟨25480772729857277561851574418,25480772729857277564842776477⟩,⟨(-57789097935200786628663981339),(-57789097935200786625418353211)⟩⟩,⟨⟨24649489050903922243570319635,24649489050903922246458713628⟩,⟨(-55903788786837351759199221186),(-55903788786837351756071324279)⟩⟩,⟨⟨23822155938916705060345484451,23822155938916705063143110974⟩,⟨(-54027439323634414943645571549),(-54027439323634414940608646979)⟩⟩,⟨⟨22983270389303945547579585661,22983270389303945550276153056⟩,⟨(-52124889518848018485049623170),(-52124889518848018482125407719)⟩⟩,⟨⟨22149212667309377170721413101,22149212667309377173324066326⟩,⟨(-50233288981809495283762099412),(-50233288981809495280935059076)⟩⟩,⟨⟨21303181743484879754596259075,21303181743484879757096302181⟩,⟨(-48314533831349969677254915468),(-48314533831349969674543109613)⟩⟩,⟨⟨20462956309978198964005079061,20462956309978198966404079988⟩,⟨(-46408945237968402988532958140),(-46408945237968402985933636907)⟩⟩,⟨⟨19610228521757425345615324315,19610228521757425347917006309⟩,⟨(-44475001939309522031000107091),(-44475001939309522028503090272)⟩⟩,⟨⟨18764410360201072197660758866,18764410360201072199859816381⟩,⟨(-42556729322864214031474667913),(-42556729322864214029092947686)⟩⟩,⟨⟨17905421340180017039954333640,17905421340180017042054458530⟩,⟨(-40608585868600260492273336717),(-40608585868600260489996711238)⟩⟩,⟨⟨17054608847284225416982945145,17054608847284225418985105716⟩,⟨(-38678986362426939555966692339),(-38678986362426939553794100933)⟩⟩,⟨⟨16189774056173590091240185625,16189774056173590093137871469⟩,⟨(-36717584996341235470382497567),(-36717584996341235468326758369)⟩⟩,⟨⟨15334597482021724182233680019,15334597482021724184031844771⟩,⟨(-34778087975607497057444984948),(-34778087975607497055496204506)⟩⟩,⟨⟨14464300825782799816576030964,14464300825782799818272586547⟩,⟨(-32804299376914922133373824261),(-32804299376914922131534638653)⟩⟩] +lemma amp9_11_14_eq : ∀ k : Fin 16, amp9_1Expr 1 14 k = amp9_11_14 k := by decide +kernel +noncomputable def amp9_11_15 : Fin 16 → CBox := ![⟨⟨13605436144528543517397475218,13605436144528543518992931781⟩,⟨(-30856437916656717947058034985),(-30856437916656717945328874665)⟩⟩,⟨⟨12730011261233991575339025042,12730011261233991576831061566⟩,⟨(-28871018759554729026904456743),(-28871018759554729025288286109)⟩⟩,⟨⟨11868204086295200167812393830,11868204086295200169202310916⟩,⟨(-26916483873120949762871896000),(-26916483873120949761367656312)⟩⟩,⟨⟨10987901608861133639399449151,10987901608861133640686963658⟩,⟨(-24920002580329241959739644449),(-24920002580329241958345409597)⟩⟩,⟨⟨10124011078824646541710190971,10124011078824646542896532973⟩,⟨(-22960742750384096492454932872),(-22960742750384096491170192075)⟩⟩,⟨⟨9238936788997680557560821166,9238936788997680558643105436⟩,⟨(-20953439229529479545471058754),(-20953439229529479544299413981)⟩⟩,⟨⟨8374023000594305591428517612,8374023000594305592408490671⟩,⟨(-18991858701597502347477290513),(-18991858701597502346417580233)⟩⟩,⟨⟨7484008818589727932792636802,7484008818589727933668984504⟩,⟨(-16973351756267974183168069436),(-16973351756267974182219788620)⟩⟩,⟨⟨6619527590048496233754215709,6619527590048496234528774374⟩,⟨(-15012752252126022925547738492),(-15012752252126022924710267970)⟩⟩,⟨⟨5723823631345515038712832553,5723823631345515039382187972⟩,⟨(-12981341182328237041225176883),(-12981341182328237040501924314)⟩⟩,⟨⟨4862135239681351864446506826,4862135239681351865014407226⟩,⟨(-11027075690326225203084051736),(-11027075690326225202471239739)⟩⟩,⟨⟨3958514790998972547878268840,3958514790998972548340187786⟩,⟨(-8977710423472774273811563673),(-8977710423472774273313635280)⟩⟩,⟨⟨3104583262309451838822703131,3104583262309451839184105615⟩,⟨(-7041037102589901690894908814),(-7041037102589901690506369512)⟩⟩,⟨⟨2185759460592364486758687261,2185759460592364487012578979⟩,⟨(-4957191403499139413853896777),(-4957191403499139413581598341)⟩⟩,⟨⟨1355876442797423833491395123,1355876442797423833647039375⟩,⟨(-3075058883478800724748195665),(-3075058883478800724583479737)⟩⟩,⟨⟨385210003677661992952978527,385210003677661992996084261⟩,⟨(-873636716757143324777906610),(-873636716757143324733635349)⟩⟩] +lemma amp9_11_15_eq : ∀ k : Fin 16, amp9_1Expr 1 15 k = amp9_11_15 k := by decide +kernel +noncomputable def amp9_11 : Fin 16 → Fin 16 → CBox := ![amp9_11_0,amp9_11_1,amp9_11_2,amp9_11_3,amp9_11_4,amp9_11_5,amp9_11_6,amp9_11_7,amp9_11_8,amp9_11_9,amp9_11_10,amp9_11_11,amp9_11_12,amp9_11_13,amp9_11_14,amp9_11_15] +lemma amp9_11_eq (i k : Fin 16) : amp9_1Expr 1 i k = amp9_11 i k := by + fin_cases i + · exact amp9_11_0_eq k + · exact amp9_11_1_eq k + · exact amp9_11_2_eq k + · exact amp9_11_3_eq k + · exact amp9_11_4_eq k + · exact amp9_11_5_eq k + · exact amp9_11_6_eq k + · exact amp9_11_7_eq k + · exact amp9_11_8_eq k + · exact amp9_11_9_eq k + · exact amp9_11_10_eq k + · exact amp9_11_11_eq k + · exact amp9_11_12_eq k + · exact amp9_11_13_eq k + · exact amp9_11_14_eq k + · exact amp9_11_15_eq k +noncomputable def amp9_12_0 : Fin 16 → CBox := ![⟨⟨27656833929615362262006167,27656833929615362291156451⟩,⟨(-667203297953504647150760243),(-667203297953504647115341545)⟩⟩,⟨⟨97347548738388396574414167,97347548738388396677299791⟩,⟨(-2348446887710894609644011839),(-2348446887710894609512555725)⟩⟩,⟨⟨156930468665277272955025228,156930468665277273121097613⟩,⟨(-3785846438870318533880535224),(-3785846438870318533663452448)⟩⟩,⟨⟨222899049574540211849630310,222899049574540212085570447⟩,⟨(-5377295946647905665392842177),(-5377295946647905665083148924)⟩⟩,⟨⟨284208574900344161366391589,284208574900344161667308026⟩,⟨(-6856348740523115918977106615),(-6856348740523115918580306585)⟩⟩,⟨⟨349085604172734028658108958,349085604172734029027754998⟩,⟨(-8421465268399182256270905932),(-8421465268399182255782595456)⟩⟩,⟨⟨410952047203312812169777647,410952047203312812604992042⟩,⟨(-9913953343053823115476373368),(-9913953343053823114900120704)⟩⟩,⟨⟨475260698067625593408112606,475260698067625593911465265⟩,⟨(-11465358108067962011610711067),(-11465358108067962010943489374)⟩⟩,⟨⟨537327657764345331885573252,537327657764345332454707154⟩,⟨(-12962683518090937550426286625),(-12962683518090937549670828723)⟩⟩,⟨⟨601227801041259060732635110,601227801041259061369409134⟩,⟨(-14504233300779720020946466201),(-14504233300779720020102192617)⟩⟩,⟨⟨663325817138793156854298508,663325817138793157556920523⟩,⟨(-16002307926461242687766160487),(-16002307926461242686832790329)⟩⟩,⟨⟨726871292114567086773132950,726871292114567087543091998⟩,⟨(-17535301564914489677668086410),(-17535301564914489676644648431)⟩⟩,⟨⟨788895841566765076055994100,788895841566765076891650171⟩,⟨(-19031603855115292601420248920),(-19031603855115292600309582421)⟩⟩,⟨⟨852098715826997532209715001,852098715826997533112266508⟩,⟨(-20556332472059850912222165912),(-20556332472059850911023812280)⟩⟩,⟨⟨913973687112991919938385699,913973687112991920906561298⟩,⟨(-22049026285381237278580060199),(-22049026285381237277292625674)⟩⟩,⟨⟨976826365869980121357136619,976826365869980122391950785⟩,⟨(-23565306661457456126947447233),(-23565306661457456125570066386)⟩⟩] +lemma amp9_12_0_eq : ∀ k : Fin 16, amp9_1Expr 2 0 k = amp9_12_0 k := by decide +kernel +noncomputable def amp9_12_1 : Fin 16 → CBox := ![⟨⟨1038490075614490173359754517,1038490075614490174459920485⟩,⟨(-25052903926216277137626154700),(-25052903926216277136161160612)⟩⟩,⟨⟨1100974564234470578070899133,1100974564234470579237226782⟩,⟨(-26560301952479399676466252454),(-26560301952479399674913926132)⟩⟩,⟨⟨1162373479802631048122044312,1162373479802631049353361010⟩,⟨(-28041511228353124899829257308),(-28041511228353124898191675079)⟩⟩,⟨⟨1224465824149729458091658917,1224465824149729459388973597⟩,⟨(-29539449026709962117509014407),(-29539449026709962115778580236)⟩⟩,⟨⟨1285551412780888595948168384,1285551412780888597310065157⟩,⟨(-31013099492119807673356822661),(-31013099492119807671543384407)⟩⟩,⟨⟨1347224049647206332761819900,1347224049647206334188921344⟩,⟨(-32500912117940074765252782580),(-32500912117940074763355496057)⟩⟩,⟨⟨1407951061421259998601107047,1407951061421260000092787354⟩,⟨(-33965912147720179357833866262),(-33965912147720179355844995236)⟩⟩,⟨⟨1469174162069821262603589611,1469174162069821264159935225⟩,⟨(-35442880001944392874126074509),(-35442880001944392872055512357)⟩⟩,⟨⟨1529499634035960901512055994,1529499634035960903132488577⟩,⟨(-36898193142589549348051577358),(-36898193142589549345891601576)⟩⟩,⟨⟨1590241921453586581743220583,1590241921453586583428245390⟩,⟨(-38363561687428013406333182396),(-38363561687428013404081668656)⟩⟩,⟨⟨1650124571656563994573790553,1650124571656563996321973381⟩,⟨(-39808192038367763712733468318),(-39808192038367763710404258693)⟩⟩,⟨⟨1710353844287314213405187141,1710353844287314215217367526⟩,⟨(-41261184432032405305484116657),(-41261184432032405303065327546)⟩⟩,⟨⟨1769753689214106826026779252,1769753689214106827901436885⟩,⟨(-42694167416778337223073312226),(-42694167416778337220581592418)⟩⟩,⟨⟨1829437172087648438677019739,1829437172087648440615286311⟩,⟨(-44133992984228323627024667130),(-44133992984228323624439564159)⟩⟩,⟨⟨1888315278407924772797989872,1888315278407924774798722069⟩,⟨(-45554389361272765536438780091),(-45554389361272765533768428703)⟩⟩,⟨⟨1947419868181087738835117720,1947419868181087740898669940⟩,⟨(-46980249505684159978937512227),(-46980249505684159976178831560)⟩⟩] +lemma amp9_12_1_eq : ∀ k : Fin 16, amp9_1Expr 2 1 k = amp9_12_1 k := by decide +kernel +noncomputable def amp9_12_2 : Fin 16 → CBox := ![⟨⟨2005738188498802508639860037,2005738188498802510764630447⟩,⟨(-48387141406113245538923890694),(-48387141406113245536096538379)⟩⟩,⟨⟨2064230630799723993288594813,2064230630799723995475640261⟩,⟨(-49798233887192212471612695277),(-49798233887192212468695379945)⟩⟩,⟨⟨2121951893766475950161981424,2121951893766475952410355792⟩,⟨(-51190722163741443753290955126),(-51190722163741443750287880061)⟩⟩,⟨⟨2179798915915662806558848169,2179798915915662808868766516⟩,⟨(-52586244299534362815670119153),(-52586244299534362812579132802)⟩⟩,⟨⟨2236886552549583810566974156,2236886552549583812937774286⟩,⟨(-53963446749079285355995643099),(-53963446749079285352814384105)⟩⟩,⟨⟨2294054966019543062554058438,2294054966019543064984508688⟩,⟨(-55342597887745317215456677629),(-55342597887745317212216809538)⟩⟩,⟨⟨2350473060741471694047269961,2350473060741471696537701809⟩,⟨(-56703648070080758092708747436),(-56703648070080758089384156061)⟩⟩,⟨⟨2406929842568628606526423034,2406929842568628609076698378⟩,⟨(-58065631553901910365304744484),(-58065631553901910361899695599)⟩⟩,⟨⟨2462643101475025593866116737,2462643101475025596475630919⟩,⟨(-59409678026346506145337278393),(-59409678026346506141848405546)⟩⟩,⟨⟨2518355460693847128324750291,2518355460693847130993541692⟩,⟨(-60753702794408055130862982858),(-60753702794408055127289338458)⟩⟩,⟨⟨2573329192070436683414833121,2573329192070436686142112901⟩,⟨(-62079908641708405063876673313),(-62079908641708405060219452383)⟩⟩,⟨⟨2628264625263173644863799804,2628264625263173647648022658⟩,⟨(-63405190570000631730093993908),(-63405190570000631726389551165)⟩⟩,⟨⟨2682464728926284390059120586,2682464728926284392901264423⟩,⟨(-64712733147198015487498926769),(-64712733147198015483705915233)⟩⟩,⟨⟨2736591067706676008109910085,2736591067706676011009654697⟩,⟨(-66018496194129982505319726138),(-66018496194129982501444089462)⟩⟩,⟨⟨2789984030792729046088877060,2789984030792729049045649274⟩,⟨(-67306567024984472896201233447),(-67306567024984472892239090679)⟩⟩,⟨⟨2843269483200295800801355812,2843269483200295803814509235⟩,⟨(-68592044229994666773893043978),(-68592044229994666769857392958)⟩⟩] +lemma amp9_12_2_eq : ∀ k : Fin 16, amp9_1Expr 2 2 k = amp9_12_2 k := by decide +kernel +noncomputable def amp9_12_3 : Fin 16 → CBox := ![⟨⟨2895822380713515639868641404,2895822380713515642937738377⟩,⟨(-69859849020198302902053633646),(-69859849020198302897937344020)⟩⟩,⟨⟨2948235567927807710671444904,2948235567927807713796397221⟩,⟨(-71124283389462221099122614390),(-71124283389462221094924440573)⟩⟩,⟨⟨2999916066825581611442736711,2999916066825581614622819471⟩,⟨(-72371042125195670212747541206),(-72371042125195670208467279165)⟩⟩,⟨⟨3051426056220250140892128987,3051426056220250144124593152⟩,⟨(-73613687429033992085724183639),(-73613687429033992081424034978)⟩⟩,⟨⟨3102202422140761770955640153,3102202422140761774242464932⟩,⟨(-74838634539266376565391129750),(-74838634539266376561005632962)⟩⟩,⟨⟨3152778757425303729327760016,3152778757425303732668501375⟩,⟨(-76058756039295136482981450540),(-76058756039295136478516487629)⟩⟩,⟨⟨3202619863391098237142800843,3202619863391098240536658412⟩,⟨(-77261140605751933133256457155),(-77261140605751933128713583369)⟩⟩,⟨⟨3252232592395201073508023708,3252232592395201076954638154⟩,⟨(-78458015725161932423514075923),(-78458015725161932418896445488)⟩⟩,⟨⟨3301107928990071959682001766,3301107928990071963180749099⟩,⟨(-79637101727835810795832815678),(-79637101727835810791137676537)⟩⟩,⟨⟨3349727629506710175691236683,3349727629506710179241211930⟩,⟨(-80810020674840670666785768528),(-80810020674840670662028779921)⟩⟩,⟨⟨3397607316141974804110063451,3397607316141974807711097495⟩,⟨(-81965087263783130374420396035),(-81965087263783130369587769115)⟩⟩,⟨⟨3445205120144288773439248819,3445205120144288777090779072⟩,⟨(-83113353615835889359492471207),(-83113353615835889354590971573)⟩⟩,⟨⟨3492059917117642066061676473,3492059917117642069763035521⟩,⟨(-84243695402069335378054876530),(-84243695402069335373082664202)⟩⟩,⟨⟨3538607533590063831895236695,3538607533590063835646067953⟩,⟨(-85366626656648648032477608778),(-85366626656648648027435868793)⟩⟩,⟨⟨3584408854704921197509068741,3584408854704921201308642700⟩,⟨(-86471554016599907620188319753),(-86471554016599907615076630716)⟩⟩,⟨⟨3629878591273424892214551811,3629878591273424896062477978⟩,⟨(-87568482113025898508329182421),(-87568482113025898503148958182)⟩⟩] +lemma amp9_12_3_eq : ∀ k : Fin 16, amp9_1Expr 2 3 k = amp9_12_3 k := by decide +kernel +noncomputable def amp9_12_4 : Fin 16 → CBox := ![⟨⟨3674598516835281400261022655,3674598516835281404152604307⟩,⟨(-88647321502055012109146615037),(-88647321502055012103993055730)⟩⟩,⟨⟨3718963300339778586805211851,3718963300339778590744616751⟩,⟨(-89717593317785057654596096843),(-89717593317785057649360082465)⟩⟩,⟨⟨3762574590383011706340000533,3762574590383011710326281666⟩,⟨(-90769687589273372325147298278),(-90769687589273372319833480844)⟩⟩,⟨⟨3805807986503100694417061157,3805807986503100698449658355⟩,⟨(-91812665413360657269210916604),(-91812665413360657263823684970)⟩⟩,⟨⟨3848284094129928589537100697,3848284094129928593615167906⟩,⟨(-92837374140504600637355341701),(-92837374140504600631896820622)⟩⟩,⟨⟨3890360326150824616983153705,3890360326150824621106395424⟩,⟨(-93852436126314091894600764639),(-93852436126314091889068427317)⟩⟩,⟨⟨3931675410886016121575763007,3931675410886016125742988540⟩,⟨(-94849135924298945233128222502),(-94849135924298945227532414739)⟩⟩,⟨⟨3972569377672655660930039986,3972569377672655665141063535⟩,⟨(-95835676523121076726617606263),(-95835676523121076720952641824)⟩⟩,⟨⟨4012698318754671953273950264,4012698318754671957528041070⟩,⟨(-96803761369761203745402030820),(-96803761369761203739667066192)⟩⟩,⟨⟨4052385611987333476817936135,4052385611987333481113452492⟩,⟨(-97761191746610121642416565437),(-97761191746610121636640541499)⟩⟩,⟨⟨4091304021530033257116911062,4091304021530033261454280476⟩,⟨(-98700073299866625190896924829),(-98700073299866625185050962494)⟩⟩,⟨⟨4129760942243346617568802244,4129760942243346621947311672⟩,⟨(-99627821732473132350910577887),(-99627821732473132345000735567)⟩⟩,⟨⟨4167445178213067188339830940,4167445178213067192758793252⟩,⟨(-100536929643517573738984984826),(-100536929643517573733009181539)⟩⟩,⟨⟨4204648752671252389235192085,4204648752671252393693644394⟩,⟨(-101434441905309035886180715584),(-101434441905309035880150574091)⟩⟩,⟨⟨4241075931632628760598929940,4241075931632628765096523772⟩,⟨(-102313224126008108068811583613),(-102313224126008108062716763494)⟩⟩,⟨⟨4277003926566657991678151588,4277003926566657996214074132⟩,⟨(-103179963853695169876013593724),(-103179963853695169869861650022)⟩⟩] +lemma amp9_12_4_eq : ∀ k : Fin 16, amp9_1Expr 2 4 k = amp9_12_4 k := by decide +kernel +noncomputable def amp9_12_5 : Fin 16 → CBox := ![⟨⟨4312151936157441296637168244,4312151936157441301210728419⟩,⟨(-104027886937557653609757737059),(-104027886937557653603546507776)⟩⟩,⟨⟨4346782873384138106163904945,4346782873384138110774535378⟩,⟨(-104863335983810586457599480631),(-104863335983810586451330167850)⟩⟩,⟨⟨4380630384484886429286403153,4380630384484886433933399725⟩,⟨(-105679885379573300038626141979),(-105679885379573300032296815228)⟩⟩,⟨⟨4413943554923445712470118519,4413943554923445717152867905⟩,⟨(-106483544151161515233403979780),(-106483544151161515227016532686)⟩⟩,⟨⟨4446470033492561670612643810,4446470033492561675330362557⟩,⟨(-107268224488301970261239933829),(-107268224488301970254794270944)⟩⟩,⟨⟨4478445510590351193959175927,4478445510590351198703465892⟩,⟨(-108039612269982829934506726827),(-108039612269982829928192143233)⟩⟩,⟨⟨4509631229138743670466640543,4509631229138743675244911058⟩,⟨(-108791947635538051985563978631),(-108791947635538051979182659119)⟩⟩,⟨⟨4540249881715345224864728732,4540249881715345229676167378⟩,⟨(-109530602899911085893485955595),(-109530602899911085887043806630)⟩⟩,⟨⟨4570075930398161687553167882,4570075930398161692396805045⟩,⟨(-110250137106058509767711911034),(-110250137106058509761213185421)⟩⟩,⟨⟨4599319434914282687028912159,4599319434914282691904099664⟩,⟨(-110955617809545002173269785486),(-110955617809545002166716053678)⟩⟩,⟨⟨4627767732219821175497848505,4627767732219821180403554613⟩,⟨(-111641914651465586219545440367),(-111641914651465586212942391005)⟩⟩,⟨⟨4655618584475842400665951774,4655618584475842405601497423⟩,⟨(-112313798516528502279718606468),(-112313798516528502273068195340)⟩⟩,⟨⟨4682671887494008452023735170,4682671887494008456988542923⟩,⟨(-112966442020126635279370414828),(-112966442020126635272667314286)⟩⟩,⟨⟨4709113413761441754975418541,4709113413761441759968437150⟩,⟨(-113604326803809865653789631078),(-113604326803809865647044429584)⟩⟩,⟨⟨4734755328016043887388057935,4734755328016043892408685434⟩,⟨(-114222921462911159950904005979),(-114222921462911159944111917808)⟩⟩,⟨⟨4759771695603984754081951257,4759771695603984759129591646⟩,⟨(-114826425211748380407337889484),(-114826425211748380400498188064)⟩⟩] +lemma amp9_12_5_eq : ∀ k : Fin 16, amp9_1Expr 2 5 k = amp9_12_5 k := by decide +kernel +noncomputable def amp9_12_6 : Fin 16 → CBox := ![⟨⟨4783986684434824892541167397,4783986684434824897614143476⟩,⟨(-115410596214436558108442746599),(-115410596214436558101576542895)⟩⟩,⟨⟨4807562911692542944854222679,4807562911692542949952848803⟩,⟨(-115979357505757280245392420330),(-115979357505757280238476706938)⟩⟩,⟨⟨4830336305174704890819900602,4830336305174704895942811887⟩,⟨(-116528750949546260432704345534),(-116528750949546260425752663848)⟩⟩,⟨⟨4852458270930776059859275245,4852458270930776065006278958⟩,⟨(-117062429119188813283899218518),(-117062429119188813276900488443)⟩⟩,⟨⟨4873776274319785401526913944,4873776274319785406696875399⟩,⟨(-117576712214756753236841539396),(-117576712214756753229803721715)⟩⟩,⟨⟨4894430726757596739976863435,4894430726757596745169224364⟩,⟨(-118074987571184117964052419276),(-118074987571184117956972959481)⟩⟩,⟨⟨4914280428450251327016783411,4914280428450251332228028043⟩,⟨(-118553848834423318824939103644),(-118553848834423318817883385606)⟩⟩,⟨⟨4933454993419274264697765089,4933454993419274269930074970⟩,⟨(-119016422859227240664215229974),(-119016422859227240657114323155)⟩⟩,⟨⟨4951824372420951260815689092,4951824372420951266067948874⟩,⟨(-119459572291388118544493987677),(-119459572291388118537355356811)⟩⟩,⟨⟨4969507561182857999576257061,4969507561182858004847587587⟩,⟨(-119886167826159173645894457610),(-119886167826159173638722742740)⟩⟩,⟨⟨4986385494073012460268586908,4986385494073012465558295456⟩,⟨(-120293337081888424615878404199),(-120293337081888424608670872797)⟩⟩,⟨⟨5002566710481483924465089063,5002566710481483929772127231⟩,⟨(-120683698501424260560999796054),(-120683698501424260553764916929)⟩⟩,⟨⟨5017942977869881852658260651,5017942977869881857981932494⟩,⟨(-121054641044517323062898016879),(-121054641044517323055633142610)⟩⟩,⟨⟨5032612524982808371983722663,5032612524982808377323457111⟩,⟨(-121408534416337739786313034016),(-121408534416337739779014876546)⟩⟩,⟨⟨5046477817449798230156061987,5046477817449798235509718624⟩,⟨(-121743025663044017267857600140),(-121743025663044017260558375807)⟩⟩,⟨⟨5059626903572492894926350038,5059626903572492900294323259⟩,⟨(-122060238893179595326861664590),(-122060238893179595319534565035)⟩⟩] +lemma amp9_12_6_eq : ∀ k : Fin 16, amp9_1Expr 2 6 k = amp9_12_6 k := by decide +kernel +noncomputable def amp9_12_7 : Fin 16 → CBox := ![⟨⟨5071972827087325082190861792,5071972827087325087572156476⟩,⟨(-122358076342915922348026465824),(-122358076342915922340676104203)⟩⟩,⟨⟨5083593571245343646160761215,5083593571245343651554764074⟩,⟨(-122638419307936276682929825670),(-122638419307936276675553486697)⟩⟩,⟨⟨5094412652057206985403407710,5094412652057206990808570659⟩,⟨(-122899422661280022643203999724),(-122899422661280022635819672681)⟩⟩,⟨⟨5104498088897388240806310873,5104498088897388246222418750⟩,⟨(-123142727326528243654392205333),(-123142727326528243646987365973)⟩⟩,⟨⟨5113783777894453971978468950,5113783777894453977404248946⟩,⟨(-123366738590376440394105332285),(-123366738590376440386691375309)⟩⟩,⟨⟨5122327862012853058019458446,5122327862012853063454595507⟩,⟨(-123572859114377696318529069952),(-123572859114377696311095688712)⟩⟩,⟨⟨5130074538545206821377704316,5130074538545206826821016623⟩,⟨(-123759742694172808919617748165),(-123759742694172808912174198751)⟩⟩,⟨⟨5137072148240684474939969004,5137072148240684480390669743⟩,⟨(-123928555519187267890023783654),(-123928555519187267882570960204)⟩⟩,⟨⟨5143275123403590878702401312,5143275123403590884159674696⟩,⟨(-124078198298123836809021536596),(-124078198298123836801559931842)⟩⟩,⟨⟨5148722063855938645700030847,5148722063855938651163143066⟩,⟨(-124209602226816889762369277362),(-124209602226816889754898338506)⟩⟩,⟨⟨5153377583230425999925777933,5153377583230426005393723416⟩,⟨(-124321913631956371647650787957),(-124321913631956371640175663799)⟩⟩,⟨⟨5157270589102046092267028043,5157270589102046097739044500⟩,⟨(-124415829890162482489659130657),(-124415829890162482482179798958)⟩⟩,⟨⟨5160375834950324842354885330,5160375834950324847829984326⟩,⟨(-124490741945396305278278066173),(-124490741945396305270799350711)⟩⟩,⟨⟨5162712572410639435599618518,5162712572410639441076938854⟩,⟨(-124547114230956580767335949261),(-124547114230956580759860069218)⟩⟩,⟨⟨5164265665324380304792787352,5164265665324380310271368330⟩,⟨(-124584581596769791809841591216),(-124584581596769791802372800605)⟩⟩,⟨⟨5165044733496314877479484316,5165044733496314882958327284⟩,⟨(-124603376114427460081042100635),(-124603376114427460073585801390)⟩⟩] +lemma amp9_12_7_eq : ∀ k : Fin 16, amp9_1Expr 2 7 k = amp9_12_7 k := by decide +kernel +noncomputable def amp9_12_8 : Fin 16 → CBox := ![⟨⟨5165044733496314877479484316,5165044733496314882958327284⟩,⟨(-124603376114427460081042100635),(-124603376114427460073585801390)⟩⟩,⟨⟨5164265665324380304792787352,5164265665324380310271368330⟩,⟨(-124584581596769791809841591216),(-124584581596769791802372800605)⟩⟩,⟨⟨5162712572410639435599618518,5162712572410639441076938854⟩,⟨(-124547114230956580767335949261),(-124547114230956580759860069218)⟩⟩,⟨⟨5160375834950324842354885330,5160375834950324847829984326⟩,⟨(-124490741945396305278278066173),(-124490741945396305270799350711)⟩⟩,⟨⟨5157270589102046092267028043,5157270589102046097739044500⟩,⟨(-124415829890162482489659130657),(-124415829890162482482179798958)⟩⟩,⟨⟨5153377583230425999925777933,5153377583230426005393723416⟩,⟨(-124321913631956371647650787957),(-124321913631956371640175663799)⟩⟩,⟨⟨5148722063855938645700030847,5148722063855938651163143066⟩,⟨(-124209602226816889762369277362),(-124209602226816889754898338506)⟩⟩,⟨⟨5143275123403590878702401312,5143275123403590884159674696⟩,⟨(-124078198298123836809021536596),(-124078198298123836801559931842)⟩⟩,⟨⟨5137072148240684474939969004,5137072148240684480390669743⟩,⟨(-123928555519187267890023783654),(-123928555519187267882570960204)⟩⟩,⟨⟨5130074538545206821377704316,5130074538545206826821016623⟩,⟨(-123759742694172808919617748165),(-123759742694172808912174198751)⟩⟩,⟨⟨5122327862012853058019458446,5122327862012853063454595507⟩,⟨(-123572859114377696318529069952),(-123572859114377696311095688712)⟩⟩,⟨⟨5113783777894453971978468950,5113783777894453977404248946⟩,⟨(-123366738590376440394105332285),(-123366738590376440386691375309)⟩⟩,⟨⟨5104498088897388240806310873,5104498088897388246222418750⟩,⟨(-123142727326528243654392205333),(-123142727326528243646987365973)⟩⟩,⟨⟨5094412652057206985403407710,5094412652057206990808570659⟩,⟨(-122899422661280022643203999724),(-122899422661280022635819672681)⟩⟩,⟨⟨5083593571245343646160761215,5083593571245343651554764074⟩,⟨(-122638419307936276682929825670),(-122638419307936276675553486697)⟩⟩,⟨⟨5071972827087325082190861792,5071972827087325087572156476⟩,⟨(-122358076342915922348026465824),(-122358076342915922340676104203)⟩⟩] +lemma amp9_12_8_eq : ∀ k : Fin 16, amp9_1Expr 2 8 k = amp9_12_8 k := by decide +kernel +noncomputable def amp9_12_9 : Fin 16 → CBox := ![⟨⟨5059626903572492894926350038,5059626903572492900294323259⟩,⟨(-122060238893179595326861664590),(-122060238893179595319534565035)⟩⟩,⟨⟨5046477817449798230156061987,5046477817449798235509718624⟩,⟨(-121743025663044017267857600140),(-121743025663044017260558375807)⟩⟩,⟨⟨5032612524982808371983722663,5032612524982808377323457111⟩,⟨(-121408534416337739786313034016),(-121408534416337739779014876546)⟩⟩,⟨⟨5017942977869881852658260651,5017942977869881857981932494⟩,⟨(-121054641044517323062898016879),(-121054641044517323055633142610)⟩⟩,⟨⟨5002566710481483924465089063,5002566710481483929772127231⟩,⟨(-120683698501424260560999796054),(-120683698501424260553764916929)⟩⟩,⟨⟨4986385494073012460268586908,4986385494073012465558295456⟩,⟨(-120293337081888424615878404199),(-120293337081888424608670872797)⟩⟩,⟨⟨4969507561182857999576257061,4969507561182858004847587587⟩,⟨(-119886167826159173645894457610),(-119886167826159173638722742740)⟩⟩,⟨⟨4951824372420951260815689092,4951824372420951266067948874⟩,⟨(-119459572291388118544493987677),(-119459572291388118537355356811)⟩⟩,⟨⟨4933454993419274264697765089,4933454993419274269930074970⟩,⟨(-119016422859227240664215229974),(-119016422859227240657114323155)⟩⟩,⟨⟨4914280428450251327016783411,4914280428450251332228028043⟩,⟨(-118553848834423318824939103644),(-118553848834423318817883385606)⟩⟩,⟨⟨4894430726757596739976863435,4894430726757596745169224364⟩,⟨(-118074987571184117964052419276),(-118074987571184117956972959481)⟩⟩,⟨⟨4873776274319785401526913944,4873776274319785406696875399⟩,⟨(-117576712214756753236841539396),(-117576712214756753229803721715)⟩⟩,⟨⟨4852458270930776059859275245,4852458270930776065006278958⟩,⟨(-117062429119188813283899218518),(-117062429119188813276900488443)⟩⟩,⟨⟨4830336305174704890819900602,4830336305174704895942811887⟩,⟨(-116528750949546260432704345534),(-116528750949546260425752663848)⟩⟩,⟨⟨4807562911692542944854222679,4807562911692542949952848803⟩,⟨(-115979357505757280245392420330),(-115979357505757280238476706938)⟩⟩,⟨⟨4783986684434824892541167397,4783986684434824897614143476⟩,⟨(-115410596214436558108442746599),(-115410596214436558101576542895)⟩⟩] +lemma amp9_12_9_eq : ∀ k : Fin 16, amp9_1Expr 2 9 k = amp9_12_9 k := by decide +kernel +noncomputable def amp9_12_10 : Fin 16 → CBox := ![⟨⟨4759771695603984754081951257,4759771695603984759129591646⟩,⟨(-114826425211748380407337889484),(-114826425211748380400498188064)⟩⟩,⟨⟨4734755328016043887388057935,4734755328016043892408685434⟩,⟨(-114222921462911159950904005979),(-114222921462911159944111917808)⟩⟩,⟨⟨4709113413761441754975418541,4709113413761441759968437150⟩,⟨(-113604326803809865653789631078),(-113604326803809865647044429584)⟩⟩,⟨⟨4682671887494008452023735170,4682671887494008456988542923⟩,⟨(-112966442020126635279370414828),(-112966442020126635272667314286)⟩⟩,⟨⟨4655618584475842400665951774,4655618584475842405601497423⟩,⟨(-112313798516528502279718606468),(-112313798516528502273068195340)⟩⟩,⟨⟨4627767732219821175497848505,4627767732219821180403554613⟩,⟨(-111641914651465586219545440367),(-111641914651465586212942391005)⟩⟩,⟨⟨4599319434914282687028912159,4599319434914282691904099664⟩,⟨(-110955617809545002173269785486),(-110955617809545002166716053678)⟩⟩,⟨⟨4570075930398161687553167882,4570075930398161692396805045⟩,⟨(-110250137106058509767711911034),(-110250137106058509761213185421)⟩⟩,⟨⟨4540249881715345224864728732,4540249881715345229676167378⟩,⟨(-109530602899911085893485955595),(-109530602899911085887043806630)⟩⟩,⟨⟨4509631229138743670466640543,4509631229138743675244911058⟩,⟨(-108791947635538051985563978631),(-108791947635538051979182659119)⟩⟩,⟨⟨4478445510590351193959175927,4478445510590351198703465892⟩,⟨(-108039612269982829934506726827),(-108039612269982829928192143233)⟩⟩,⟨⟨4446470033492561670612643810,4446470033492561675330362557⟩,⟨(-107268224488301970261239933829),(-107268224488301970254794270944)⟩⟩,⟨⟨4413943554923445712470118519,4413943554923445717152867905⟩,⟨(-106483544151161515233403979780),(-106483544151161515227016532686)⟩⟩,⟨⟨4380630384484886429286403153,4380630384484886433933399725⟩,⟨(-105679885379573300038626141979),(-105679885379573300032296815228)⟩⟩,⟨⟨4346782873384138106163904945,4346782873384138110774535378⟩,⟨(-104863335983810586457599480631),(-104863335983810586451330167850)⟩⟩,⟨⟨4312151936157441296637168244,4312151936157441301210728419⟩,⟨(-104027886937557653609757737059),(-104027886937557653603546507776)⟩⟩] +lemma amp9_12_10_eq : ∀ k : Fin 16, amp9_1Expr 2 10 k = amp9_12_10 k := by decide +kernel +noncomputable def amp9_12_11 : Fin 16 → CBox := ![⟨⟨4277003926566657991678151588,4277003926566657996214074132⟩,⟨(-103179963853695169876013593724),(-103179963853695169869861650022)⟩⟩,⟨⟨4241075931632628760598929940,4241075931632628765096523772⟩,⟨(-102313224126008108068811583613),(-102313224126008108062716763494)⟩⟩,⟨⟨4204648752671252389235192085,4204648752671252393693644394⟩,⟨(-101434441905309035886180715584),(-101434441905309035880150574091)⟩⟩,⟨⟨4167445178213067188339830940,4167445178213067192758793252⟩,⟨(-100536929643517573738984984826),(-100536929643517573733009181539)⟩⟩,⟨⟨4129760942243346617568802244,4129760942243346621947311672⟩,⟨(-99627821732473132350910577887),(-99627821732473132345000735567)⟩⟩,⟨⟨4091304021530033257116911062,4091304021530033261454280476⟩,⟨(-98700073299866625190896924829),(-98700073299866625185050962494)⟩⟩,⟨⟨4052385611987333476817936135,4052385611987333481113452492⟩,⟨(-97761191746610121642416565437),(-97761191746610121636640541499)⟩⟩,⟨⟨4012698318754671953273950264,4012698318754671957528041070⟩,⟨(-96803761369761203745402030820),(-96803761369761203739667066192)⟩⟩,⟨⟨3972569377672655660930039986,3972569377672655665141063535⟩,⟨(-95835676523121076726617606263),(-95835676523121076720952641824)⟩⟩,⟨⟨3931675410886016121575763007,3931675410886016125742988540⟩,⟨(-94849135924298945233128222502),(-94849135924298945227532414739)⟩⟩,⟨⟨3890360326150824616983153705,3890360326150824621106395424⟩,⟨(-93852436126314091894600764639),(-93852436126314091889068427317)⟩⟩,⟨⟨3848284094129928589537100697,3848284094129928593615167906⟩,⟨(-92837374140504600637355341701),(-92837374140504600631896820622)⟩⟩,⟨⟨3805807986503100694417061157,3805807986503100698449658355⟩,⟨(-91812665413360657269210916604),(-91812665413360657263823684970)⟩⟩,⟨⟨3762574590383011706340000533,3762574590383011710326281666⟩,⟨(-90769687589273372325147298278),(-90769687589273372319833480844)⟩⟩,⟨⟨3718963300339778586805211851,3718963300339778590744616751⟩,⟨(-89717593317785057654596096843),(-89717593317785057649360082465)⟩⟩,⟨⟨3674598516835281400261022655,3674598516835281404152604307⟩,⟨(-88647321502055012109146615037),(-88647321502055012103993055730)⟩⟩] +lemma amp9_12_11_eq : ∀ k : Fin 16, amp9_1Expr 2 11 k = amp9_12_11 k := by decide +kernel +noncomputable def amp9_12_12 : Fin 16 → CBox := ![⟨⟨3629878591273424892214551811,3629878591273424896062477978⟩,⟨(-87568482113025898508329182421),(-87568482113025898503148958182)⟩⟩,⟨⟨3584408854704921197509068741,3584408854704921201308642700⟩,⟨(-86471554016599907620188319753),(-86471554016599907615076630716)⟩⟩,⟨⟨3538607533590063831895236695,3538607533590063835646067953⟩,⟨(-85366626656648648032477608778),(-85366626656648648027435868793)⟩⟩,⟨⟨3492059917117642066061676473,3492059917117642069763035521⟩,⟨(-84243695402069335378054876530),(-84243695402069335373082664202)⟩⟩,⟨⟨3445205120144288773439248819,3445205120144288777090779072⟩,⟨(-83113353615835889359492471207),(-83113353615835889354590971573)⟩⟩,⟨⟨3397607316141974804110063451,3397607316141974807711097495⟩,⟨(-81965087263783130374420396035),(-81965087263783130369587769115)⟩⟩,⟨⟨3349727629506710175691236683,3349727629506710179241211930⟩,⟨(-80810020674840670666785768528),(-80810020674840670662028779921)⟩⟩,⟨⟨3301107928990071959682001766,3301107928990071963180749099⟩,⟨(-79637101727835810795832815678),(-79637101727835810791137676537)⟩⟩,⟨⟨3252232592395201073508023708,3252232592395201076954638154⟩,⟨(-78458015725161932423514075923),(-78458015725161932418896445488)⟩⟩,⟨⟨3202619863391098237142800843,3202619863391098240536658412⟩,⟨(-77261140605751933133256457155),(-77261140605751933128713583369)⟩⟩,⟨⟨3152778757425303729327760016,3152778757425303732668501375⟩,⟨(-76058756039295136482981450540),(-76058756039295136478516487629)⟩⟩,⟨⟨3102202422140761770955640153,3102202422140761774242464932⟩,⟨(-74838634539266376565391129750),(-74838634539266376561005632962)⟩⟩,⟨⟨3051426056220250140892128987,3051426056220250144124593152⟩,⟨(-73613687429033992085724183639),(-73613687429033992081424034978)⟩⟩,⟨⟨2999916066825581611442736711,2999916066825581614622819471⟩,⟨(-72371042125195670212747541206),(-72371042125195670208467279165)⟩⟩,⟨⟨2948235567927807710671444904,2948235567927807713796397221⟩,⟨(-71124283389462221099122614390),(-71124283389462221094924440573)⟩⟩,⟨⟨2895822380713515639868641404,2895822380713515642937738377⟩,⟨(-69859849020198302902053633646),(-69859849020198302897937344020)⟩⟩] +lemma amp9_12_12_eq : ∀ k : Fin 16, amp9_1Expr 2 12 k = amp9_12_12 k := by decide +kernel +noncomputable def amp9_12_13 : Fin 16 → CBox := ![⟨⟨2843269483200295800801355812,2843269483200295803814509235⟩,⟨(-68592044229994666773893043978),(-68592044229994666769857392958)⟩⟩,⟨⟨2789984030792729046088877060,2789984030792729049045649274⟩,⟨(-67306567024984472896201233447),(-67306567024984472892239090679)⟩⟩,⟨⟨2736591067706676008109910085,2736591067706676011009654697⟩,⟨(-66018496194129982505319726138),(-66018496194129982501444089462)⟩⟩,⟨⟨2682464728926284390059120586,2682464728926284392901264423⟩,⟨(-64712733147198015487498926769),(-64712733147198015483705915233)⟩⟩,⟨⟨2628264625263173644863799804,2628264625263173647648022658⟩,⟨(-63405190570000631730093993908),(-63405190570000631726389551165)⟩⟩,⟨⟨2573329192070436683414833121,2573329192070436686142112901⟩,⟨(-62079908641708405063876673313),(-62079908641708405060219452383)⟩⟩,⟨⟨2518355460693847128324750291,2518355460693847130993541692⟩,⟨(-60753702794408055130862982858),(-60753702794408055127289338458)⟩⟩,⟨⟨2462643101475025593866116737,2462643101475025596475630919⟩,⟨(-59409678026346506145337278393),(-59409678026346506141848405546)⟩⟩,⟨⟨2406929842568628606526423034,2406929842568628609076698378⟩,⟨(-58065631553901910365304744484),(-58065631553901910361899695599)⟩⟩,⟨⟨2350473060741471694047269961,2350473060741471696537701809⟩,⟨(-56703648070080758092708747436),(-56703648070080758089384156061)⟩⟩,⟨⟨2294054966019543062554058438,2294054966019543064984508688⟩,⟨(-55342597887745317215456677629),(-55342597887745317212216809538)⟩⟩,⟨⟨2236886552549583810566974156,2236886552549583812937774286⟩,⟨(-53963446749079285355995643099),(-53963446749079285352814384105)⟩⟩,⟨⟨2179798915915662806558848169,2179798915915662808868766516⟩,⟨(-52586244299534362815670119153),(-52586244299534362812579132802)⟩⟩,⟨⟨2121951893766475950161981424,2121951893766475952410355792⟩,⟨(-51190722163741443753290955126),(-51190722163741443750287880061)⟩⟩,⟨⟨2064230630799723993288594813,2064230630799723995475640261⟩,⟨(-49798233887192212471612695277),(-49798233887192212468695379945)⟩⟩,⟨⟨2005738188498802508639860037,2005738188498802510764630447⟩,⟨(-48387141406113245538923890694),(-48387141406113245536096538379)⟩⟩] +lemma amp9_12_13_eq : ∀ k : Fin 16, amp9_1Expr 2 13 k = amp9_12_13 k := by decide +kernel +noncomputable def amp9_12_14 : Fin 16 → CBox := ![⟨⟨1947419868181087738835117720,1947419868181087740898669940⟩,⟨(-46980249505684159978937512227),(-46980249505684159976178831560)⟩⟩,⟨⟨1888315278407924772797989872,1888315278407924774798722069⟩,⟨(-45554389361272765536438780091),(-45554389361272765533768428703)⟩⟩,⟨⟨1829437172087648438677019739,1829437172087648440615286311⟩,⟨(-44133992984228323627024667130),(-44133992984228323624439564159)⟩⟩,⟨⟨1769753689214106826026779252,1769753689214106827901436885⟩,⟨(-42694167416778337223073312226),(-42694167416778337220581592418)⟩⟩,⟨⟨1710353844287314213405187141,1710353844287314215217367526⟩,⟨(-41261184432032405305484116657),(-41261184432032405303065327546)⟩⟩,⟨⟨1650124571656563994573790553,1650124571656563996321973381⟩,⟨(-39808192038367763712733468318),(-39808192038367763710404258693)⟩⟩,⟨⟨1590241921453586581743220583,1590241921453586583428245390⟩,⟨(-38363561687428013406333182396),(-38363561687428013404081668656)⟩⟩,⟨⟨1529499634035960901512055994,1529499634035960903132488577⟩,⟨(-36898193142589549348051577358),(-36898193142589549345891601576)⟩⟩,⟨⟨1469174162069821262603589611,1469174162069821264159935225⟩,⟨(-35442880001944392874126074509),(-35442880001944392872055512357)⟩⟩,⟨⟨1407951061421259998601107047,1407951061421260000092787354⟩,⟨(-33965912147720179357833866262),(-33965912147720179355844995236)⟩⟩,⟨⟨1347224049647206332761819900,1347224049647206334188921344⟩,⟨(-32500912117940074765252782580),(-32500912117940074763355496057)⟩⟩,⟨⟨1285551412780888595948168384,1285551412780888597310065157⟩,⟨(-31013099492119807673356822661),(-31013099492119807671543384407)⟩⟩,⟨⟨1224465824149729458091658917,1224465824149729459388973597⟩,⟨(-29539449026709962117509014407),(-29539449026709962115778580236)⟩⟩,⟨⟨1162373479802631048122044312,1162373479802631049353361010⟩,⟨(-28041511228353124899829257308),(-28041511228353124898191675079)⟩⟩,⟨⟨1100974564234470578070899133,1100974564234470579237226782⟩,⟨(-26560301952479399676466252454),(-26560301952479399674913926132)⟩⟩,⟨⟨1038490075614490173359754517,1038490075614490174459920485⟩,⟨(-25052903926216277137626154700),(-25052903926216277136161160612)⟩⟩] +lemma amp9_12_14_eq : ∀ k : Fin 16, amp9_1Expr 2 14 k = amp9_12_14 k := by decide +kernel +noncomputable def amp9_12_15 : Fin 16 → CBox := ![⟨⟨976826365869980121357136619,976826365869980122391950785⟩,⟨(-23565306661457456126947447233),(-23565306661457456125570066386)⟩⟩,⟨⟨913973687112991919938385699,913973687112991920906561298⟩,⟨(-22049026285381237278580060199),(-22049026285381237277292625674)⟩⟩,⟨⟨852098715826997532209715001,852098715826997533112266508⟩,⟨(-20556332472059850912222165912),(-20556332472059850911023812280)⟩⟩,⟨⟨788895841566765076055994100,788895841566765076891650171⟩,⟨(-19031603855115292601420248920),(-19031603855115292600309582421)⟩⟩,⟨⟨726871292114567086773132950,726871292114567087543091998⟩,⟨(-17535301564914489677668086410),(-17535301564914489676644648431)⟩⟩,⟨⟨663325817138793156854298508,663325817138793157556920523⟩,⟨(-16002307926461242687766160487),(-16002307926461242686832790329)⟩⟩,⟨⟨601227801041259060732635110,601227801041259061369409134⟩,⟨(-14504233300779720020946466201),(-14504233300779720020102192617)⟩⟩,⟨⟨537327657764345331885573252,537327657764345332454707154⟩,⟨(-12962683518090937550426286625),(-12962683518090937549670828723)⟩⟩,⟨⟨475260698067625593408112606,475260698067625593911465265⟩,⟨(-11465358108067962011610711067),(-11465358108067962010943489374)⟩⟩,⟨⟨410952047203312812169777647,410952047203312812604992042⟩,⟨(-9913953343053823115476373368),(-9913953343053823114900120704)⟩⟩,⟨⟨349085604172734028658108958,349085604172734029027754998⟩,⟨(-8421465268399182256270905932),(-8421465268399182255782595456)⟩⟩,⟨⟨284208574900344161366391589,284208574900344161667308026⟩,⟨(-6856348740523115918977106615),(-6856348740523115918580306585)⟩⟩,⟨⟨222899049574540211849630310,222899049574540212085570447⟩,⟨(-5377295946647905665392842177),(-5377295946647905665083148924)⟩⟩,⟨⟨156930468665277272955025228,156930468665277273121097613⟩,⟨(-3785846438870318533880535224),(-3785846438870318533663452448)⟩⟩,⟨⟨97347548738388396574414167,97347548738388396677299791⟩,⟨(-2348446887710894609644011839),(-2348446887710894609512555725)⟩⟩,⟨⟨27656833929615362262006167,27656833929615362291156451⟩,⟨(-667203297953504647150760243),(-667203297953504647115341545)⟩⟩] +lemma amp9_12_15_eq : ∀ k : Fin 16, amp9_1Expr 2 15 k = amp9_12_15 k := by decide +kernel +noncomputable def amp9_12 : Fin 16 → Fin 16 → CBox := ![amp9_12_0,amp9_12_1,amp9_12_2,amp9_12_3,amp9_12_4,amp9_12_5,amp9_12_6,amp9_12_7,amp9_12_8,amp9_12_9,amp9_12_10,amp9_12_11,amp9_12_12,amp9_12_13,amp9_12_14,amp9_12_15] +lemma amp9_12_eq (i k : Fin 16) : amp9_1Expr 2 i k = amp9_12 i k := by + fin_cases i + · exact amp9_12_0_eq k + · exact amp9_12_1_eq k + · exact amp9_12_2_eq k + · exact amp9_12_3_eq k + · exact amp9_12_4_eq k + · exact amp9_12_5_eq k + · exact amp9_12_6_eq k + · exact amp9_12_7_eq k + · exact amp9_12_8_eq k + · exact amp9_12_9_eq k + · exact amp9_12_10_eq k + · exact amp9_12_11_eq k + · exact amp9_12_12_eq k + · exact amp9_12_13_eq k + · exact amp9_12_14_eq k + · exact amp9_12_15_eq k +noncomputable def amp9_13_0 : Fin 16 → CBox := ![⟨⟨(-385210003677661992984944041),(-385210003677661992956144145)⟩,⟨(-667203297953504647149870151),(-667203297953504647117204606)⟩⟩,⟨⟨(-1355876442797423833607827616),(-1355876442797423833502537585)⟩,⟨(-2348446887710894609640878859),(-2348446887710894609519113396)⟩⟩,⟨⟨(-2185759460592364486949367117),(-2185759460592364486776649622)⟩,⟨(-3785846438870318533875484661),(-3785846438870318533674023833)⟩⟩,⟨⟨(-3104583262309451839094321497),(-3104583262309451838848216296)⟩,⟨(-5377295946647905665385668519),(-5377295946647905665098164183)⟩⟩,⟨⟨(-3958514790998972548225708086),(-3958514790998972547910799533)⟩,⟨(-6856348740523115918967959804),(-6856348740523115918599451868)⟩⟩,⟨⟨(-4862135239681351864873794948),(-4862135239681351864486463384)⟩,⟨(-8421465268399182256259671155),(-8421465268399182255806111082)⟩⟩,⟨⟨(-5723823631345515039216655785),(-5723823631345515038759870384)⟩,⟨(-9913953343053823115463147516),(-9913953343053823114927803871)⟩⟩,⟨⟨(-6619527590048496234337338552),(-6619527590048496233808614348)⟩,⟨(-11465358108067962011595415541),(-11465358108067962010975504596)⟩⟩,⟨⟨(-7484008818589727933452548005),(-7484008818589727932854139664)⟩,⟨(-12962683518090937550408993571),(-12962683518090937549707024993)⟩⟩,⟨⟨(-8374023000594305592166315085),(-8374023000594305591497334525)⟩,⟨(-14504233300779720020927116620),(-14504233300779720020142693424)⟩⟩,⟨⟨(-9238936788997680558375916662),(-9238936788997680557636745857)⟩,⟨(-16002307926461242687744812378),(-16002307926461242686877474275)⟩⟩,⟨⟨(-10124011078824646542603747974),(-10124011078824646541793389118)⟩,⟨(-17535301564914489677644693189),(-17535301564914489676693613022)⟩⟩,⟨⟨(-10987901608861133640369195064),(-10987901608861133639489746667)⟩,⟨(-19031603855115292601394859535),(-19031603855115292600362725203)⟩⟩,⟨⟨(-11868204086295200168859084097),(-11868204086295200167909925586)⟩,⟨(-20556332472059850912194742442),(-20556332472059850911081212629)⟩⟩,⟨⟨(-12730011261233991576462911402),(-12730011261233991575443639047)⟩,⟨(-22049026285381237278550645379),(-22049026285381237277354194137)⟩⟩,⟨⟨(-13605436144528543518599464450),(-13605436144528543517509283380)⟩,⟨(-23565306661457456126916009597),(-23565306661457456125635868826)⟩⟩] +lemma amp9_13_0_eq : ∀ k : Fin 16, amp9_1Expr 3 0 k = amp9_13_0 k := by decide +kernel +noncomputable def amp9_13_1 : Fin 16 → CBox := ![⟨⟨(-14464300825782799817854280969),(-14464300825782799816694897192)⟩,⟨(-25052903926216277137592732514),(-25052903926216277136231116935)⟩⟩,⟨⟨(-15334597482021724183588370334),(-15334597482021724182359698261)⟩,⟨(-26560301952479399676430819301),(-26560301952479399674988091628)⟩⟩,⟨⟨(-16189774056173590092669665444),(-16189774056173590091373231626)⟩,⟨(-28041511228353124899791848127),(-28041511228353124898269976620)⟩⟩,⟨⟨(-17054608847284225418491888788),(-17054608847284225417123098275)⟩,⟨(-29539449026709962117469606880),(-29539449026709962115861064535)⟩⟩,⟨⟨(-17905421340180017041536636223),(-17905421340180017040101478665)⟩,⟨(-31013099492119807673315449190),(-31013099492119807671629983645)⟩⟩,⟨⟨(-18764410360201072199317152231),(-18764410360201072197814962980)⟩,⟨(-32500912117940074765209424271),(-32500912117940074763446249780)⟩⟩,⟨⟨(-19610228521757425347349881214),(-19610228521757425345776479281)⟩,⟨(-33965912147720179357788553549),(-33965912147720179355939839742)⟩⟩,⟨⟨(-20462956309978198965812294124),(-20462956309978198964173241661)⟩,⟨(-35442880001944392874078791426),(-35442880001944392872154481065)⟩⟩,⟨⟨(-21303181743484879756480217113),(-21303181743484879754771326568)⟩,⟨(-36898193142589549348002352794),(-36898193142589549345994634020)⟩⟩,⟨⟨(-22149212667309377172683514161),(-22149212667309377170903433194)⟩,⟨(-38363561687428013406282002936),(-38363561687428013404188792912)⟩⟩,⟨⟨(-22983270389303945549611480057),(-22983270389303945547768459959)⟩,⟨(-39808192038367763712680361627),(-39808192038367763710515416854)⟩⟩,⟨⟨(-23822155938916705062454177521),(-23822155938916705060541252630)⟩,⟨(-41261184432032405305429071581),(-41261184432032405303180542961)⟩⟩,⟨⟨(-24649489050903922245745853816),(-24649489050903922243772886758)⟩,⟨(-42694167416778337223016355458),(-42694167416778337220700809215)⟩⟩,⟨⟨(-25480772729857277564105876056),(-25480772729857277562060972950)⟩,⟨(-44133992984228323626965789542),(-44133992984228323624562801443)⟩⟩,⟨⟨(-26300838960499855274368842096),(-26300838960499855272256942721)⟩,⟨(-45554389361272765536378007604),(-45554389361272765533895632222)⟩⟩,⟨⟨(-27124059698702532522382521303),(-27124059698702532520201778537)⟩,⟨(-46980249505684159978874837550),(-46980249505684159976310016571)⟩⟩] +lemma amp9_13_1_eq : ∀ k : Fin 16, amp9_1Expr 3 1 k = amp9_13_1 k := by decide +kernel +noncomputable def amp9_13_2 : Fin 16 → CBox := ![⟨⟨(-27936329116135969238069998551),(-27936329116135969235831999145)⟩,⟨(-48387141406113245538859339133),(-48387141406113245536231651917)⟩⟩,⟨⟨(-28751023739938367697422440993),(-28751023739938367695114839792)⟩,⟨(-49798233887192212471546261227),(-49798233887192212468834433738)⟩⟩,⟨⟨(-29554977221247464423657957053),(-29554977221247464421283413680)⟩,⟨(-51190722163741443753222663408),(-51190722163741443750430822160)⟩⟩,⟨⟨(-30360682302007587724511660794),(-30360682302007587722068895077)⟩,⟨(-52586244299534362815599965718),(-52586244299534362812725971678)⟩⟩,⟨⟨(-31155810506980960748136225313),(-31155810506980960745624103216)⟩,⟨(-53963446749079285355923652388),(-53963446749079285352965068605)⟩⟩,⟨⟨(-31952063788142973132406471284),(-31952063788142973129843249374)⟩,⟨(-55342597887745317215382847041),(-55342597887745317212371345102)⟩⟩,⟨⟨(-32737866477294929152486801352),(-32737866477294929149857629153)⟩,⟨(-56703648070080758092633101120),(-56703648070080758089542492145)⟩⟩,⟨⟨(-33524208008310895724333061847),(-33524208008310895721640390522)⟩,⟨(-58065631553901910365227281194),(-58065631553901910362061834809)⟩⟩,⟨⟨(-34300193600980150025408761252),(-34300193600980150022650871685)⟩,⟨(-59409678026346506145258022058),(-59409678026346506142014297796)⟩⟩,⟨⟨(-35076166662618009664926126435),(-35076166662618009662102471805)⟩,⟨(-60753702794408055130781933508),(-60753702794408055127458983688)⟩⟩,⟨⟨(-35841851965557722420241004964),(-35841851965557722417352498244)⟩,⟨(-62079908641708405063793854719),(-62079908641708405060392800836)⟩⟩,⟨⟨(-36607003843609385795437577570),(-36607003843609385792505219730)⟩,⟨(-63405190570000631730009407302),(-63405190570000631726566600260)⟩⟩,⟨⟨(-37361913902531192334705260197),(-37361913902531192331705401577)⟩,⟨(-64712733147198015487412595818),(-64712733147198015483886615436)⟩⟩,⟨⟨(-38115796549175229433189887602),(-38115796549175229430125982045)⟩,⟨(-66018496194129982505231653215),(-66018496194129982501628435805)⟩⟩,⟨⟨(-38859464590104374376270290031),(-38859464590104374373140318310)⟩,⟨(-67306567024984472896111442155),(-67306567024984472892427033758)⟩⟩,⟨⟨(-39601635200454137557061274842),(-39601635200454137553872773725)⟩,⟨(-68592044229994666773801537776),(-68592044229994666770048925532)⟩⟩] +lemma amp9_13_2_eq : ∀ k : Fin 16, amp9_1Expr 3 2 k = amp9_13_2 k := by decide +kernel +noncomputable def amp9_13_3 : Fin 16 → CBox := ![⟨⟨(-40333602637358103893027898917),(-40333602637358103889776972885)⟩,⟨(-69859849020198302901960436111),(-69859849020198302898132416741)⟩⟩,⟨⟨(-41063624160825241730047236124),(-41063624160825241726733208224)⟩,⟨(-71124283389462221099027730018),(-71124283389462221095123044029)⟩⟩,⟨⟨(-41783440652515466066522507162),(-41783440652515466063145480828)⟩,⟨(-72371042125195670212650993578),(-72371042125195670208669364000)⟩⟩,⟨⟨(-42500882253193745498152379824),(-42500882253193745494748318653)⟩,⟨(-73613687429033992085625978242),(-73613687429033992081629589706)⟩⟩,⟨⟨(-43208105797029466862264724186),(-43208105797029466858796055477)⟩,⟨(-74838634539266376565291290194),(-74838634539266376561214608164)⟩⟩,⟨⟨(-43912543273515121380663020037),(-43912543273515121377133200163)⟩,⟨(-76058756039295136482879983264),(-76058756039295136478728869830)⟩⟩,⟨⟨(-44606740326628404396230009169),(-44606740326628404392640158054)⟩,⟨(-77261140605751933133153385821),(-77261140605751933128929323042)⟩⟩,⟨⟨(-45297756499006132967294179432),(-45297756499006132963646187127)⟩,⟨(-78458015725161932423409407880),(-78458015725161932419115527247)⟩⟩,⟨⟨(-45978502120047616449508721724),(-45978502120047616445801221982)⟩,⟨(-79637101727835810795726574658),(-79637101727835810791360050710)⟩⟩,⟨⟨(-46655687189838484692347721225),(-46655687189838484688589832100)⟩,⟨(-80810020674840670666677962759),(-80810020674840670662254429286)⟩⟩,⟨⟨(-47322565195896356615063307922),(-47322565195896356611247291866)⟩,⟨(-81965087263783130374311049332),(-81965087263783130369816643824)⟩⟩,⟨⟨(-47985517083355406602158834974),(-47985517083355406598288683220)⟩,⟨(-83113353615835889359381592643),(-83113353615835889354823052636)⟩⟩,⟨⟨(-48638120217913569083147774089),(-48638120217913569079222648673)⟩,⟨(-84243695402069335377942490018),(-84243695402069335373317901569)⟩⟩,⟨⟨(-49286444880026379423658438792),(-49286444880026379419679116647)⟩,⟨(-85366626656648648032363724203),(-85366626656648648027674241769)⟩⟩,⟨⟨(-49924374988729221668873595800),(-49924374988729221664840058976)⟩,⟨(-86471554016599907620072961134),(-86471554016599907615318089030)⟩⟩,⟨⟨(-50557686720482431275633304576),(-50557686720482431271546469481)⟩,⟨(-87568482113025898508212360430),(-87568482113025898503393479496)⟩⟩] +lemma amp9_13_3_eq : ∀ k : Fin 16, amp9_1Expr 3 3 k = amp9_13_3 k := by decide +kernel +noncomputable def amp9_13_4 : Fin 16 → CBox := ![⟨⟨(-51180554932150761405827664739),(-51180554932150761401742721599)⟩,⟨(-88647321502055012109028353804),(-88647321502055012104240589535)⟩⟩,⟨⟨(-51798476653068572744169178845),(-51798476653068572740023234430)⟩,⟨(-89717593317785057654476407799),(-89717593317785057649610604837)⟩⟩,⟨⟨(-52405903563925214430138767206),(-52405903563925214425934734875)⟩,⟨(-90769687589273372325026205672),(-90769687589273372320086941025)⟩⟩,⟨⟨(-53008067091420818539335694671),(-53008067091420818535076222434)⟩,⟨(-91812665413360657269088432598),(-91812665413360657264080057503)⟩⟩,⟨⟨(-53599682950878333020441957663),(-53599682950878333016128500910)⟩,⟨(-92837374140504600637231490668),(-92837374140504600632156054494)⟩⟩,⟨⟨(-54185729261629598885652463998),(-54185729261629598881283684621)⟩,⟨(-93852436126314091894475559449),(-93852436126314091889330495592)⟩⟩,⟨⟨(-54761174158297399579759183760),(-54761174158297399575341284738)⟩,⟨(-94849135924298945233001687650),(-94849135924298945227797266142)⟩⟩,⟨⟨(-55330753638593851795952929124),(-55330753638593851791482754662)⟩,⟨(-95835676523121076726489755302),(-95835676523121076721220247988)⟩⟩,⟨⟨(-55889677685399926705599396539),(-55889677685399926701076690633)⟩,⟨(-96803761369761203745272888371),(-96803761369761203739937375581)⟩⟩,⟨⟨(-56442450371203974292977130750),(-56442450371203974288418735777)⟩,⟨(-97761191746610121642286145715),(-97761191746610121636913524363)⟩⟩,⟨⟨(-56984513888713790575014679851),(-56984513888713790570404154627)⟩,⟨(-98700073299866625190765252578),(-98700073299866625185326567039)⟩⟩,⟨⟨(-57520149696019410860807281956),(-57520149696019410856148263650)⟩,⟨(-99627821732473132350777667960),(-99627821732473132345278930704)⟩⟩,⟨⟨(-58045023393183337449822948979),(-58045023393183337445114469446)⟩,⟨(-100536929643517573738850862091),(-100536929643517573733289915218)⟩⟩,⟨⟨(-58563202339129627991211281387),(-58563202339129627986460196166)⟩,⟨(-101434441905309035886045395509),(-101434441905309035880433813933)⟩⟩,⟨⟨(-59070567490809294434343694622),(-59070567490809294429544268099)⟩,⟨(-102313224126008108068675091186),(-102313224126008108063002457198)⟩⟩,⟨⟨(-59570979905906762500047426700),(-59570979905906762495204171507)⟩,⟨(-103179963853695169875875945011),(-103179963853695169870149763962)⟩⟩] +lemma amp9_13_4_eq : ∀ k : Fin 16, amp9_1Expr 3 4 k = amp9_13_4 k := by decide +kernel +noncomputable def amp9_13_5 : Fin 16 → CBox := ![⟨⟨(-60060528526626865105757962381),(-60060528526626865100869865803)⟩,⟨(-104027886937557653609618957162),(-104027886937557653603836989408)⟩⟩,⟨⟨(-60542875258375211991605290341),(-60542875258375211986673202529)⟩,⟨(-104863335983810586457459586191),(-104863335983810586451622982343)⟩⟩,⟨⟨(-61014310271825440941214720707),(-61014310271825440936237763657)⟩,⟨(-105679885379573300038485158210),(-105679885379573300032591909808)⟩⟩,⟨⟨(-61478302879938500950119194175),(-61478302879938500945098622515)⟩,⟨(-106483544151161515233261923878),(-106483544151161515227313871357)⟩⟩,⟨⟨(-61931338283814348960050879040),(-61931338283814348954986875202)⟩,⟨(-107268224488301970261096831113),(-107268224488301970255093800713)⟩⟩,⟨⟨(-62376699227217381562399557660),(-62376699227217381557401577584)⟩,⟨(-108039612269982829934362595030),(-108039612269982829928493826982)⟩⟩,⟨⟨(-62811060253041564516795402756),(-62811060253041564511749476242)⟩,⟨(-108791947635538051985418843171),(-108791947635538051979486443646)⟩⟩,⟨⟨(-63237523068765669829098205475),(-63237523068765669824007913849)⟩,⟨(-109530602899911085893339834721),(-109530602899911085887349653737)⟩⟩,⟨⟨(-63652946336376028680473191548),(-63652946336376028675341229490)⟩,⟨(-110250137106058509767564830254),(-110250137106058509761521041715)⟩⟩,⟨⟨(-64060255810442041626435938243),(-64060255810442041621263388352)⟩,⟨(-110955617809545002173121763551),(-110955617809545002167025879917)⟩⟩,⟨⟨(-64456489476868880865522009256),(-64456489476868880860312395982)⟩,⟨(-111641914651465586219396502867),(-111641914651465586213254133621)⟩⟩,⟨⟨(-64844401807227121646363583678),(-64844401807227121641118216593)⟩,⟨(-112313798516528502279568772632),(-112313798516528502273381814086)⟩⟩,⟨⟨(-65221205709714364224934252369),(-65221205709714364219650296371)⟩,⟨(-112966442020126635279219710323),(-112966442020126635272982755438)⟩⟩,⟨⟨(-65589488661285843482170988374),(-65589488661285843476854741438)⟩,⟨(-113604326803809865653638075594),(-113604326803809865647361651929)⟩⟩,⟨⟨(-65946634454237240528013578205),(-65946634454237240522662518732)⟩,⟨(-114222921462911159950751625249),(-114222921462911159944430867482)⟩⟩,⟨⟨(-66295067506085358055507408472),(-66295067506085358050121305857)⟩,⟨(-114826425211748380407184703642),(-114826425211748380400818822928)⟩⟩] +lemma amp9_13_5_eq : ∀ k : Fin 16, amp9_1Expr 3 5 k = amp9_13_5 k := by decide +kernel +noncomputable def amp9_13_6 : Fin 16 → CBox := ![⟨⟨(-66632338791740151047350885617),(-66632338791740151041942170257)⟩,⟨(-115410596214436558108288781435),(-115410596214436558101898808965)⟩⟩,⟨⟨(-66960713276388809133084849974),(-66960713276388809127640431409)⟩,⟨(-115979357505757280245237696402),(-115979357505757280238800561185)⟩⟩,⟨⟨(-67277905729051392375261707432),(-67277905729051392369789646204)⟩,⟨(-116528750949546260432548888679),(-116528750949546260426078052191)⟩⟩,⟨⟨(-67586024963955147028667891382),(-67586024963955147023161987090)⟩,⟨(-117062429119188813283743049702),(-117062429119188813277227366999)⟩⟩,⟨⟨(-67882946447620971193447919474),(-67882946447620971187913011034)⟩,⟨(-117576712214756753236684684494),(-117576712214756753230132036326)⟩⟩,⟨⟨(-68170625858784866943064515948),(-68170625858784866937499328871)⟩,⟨(-118074987571184117963894899642),(-118074987571184117957302665449)⟩⟩,⟨⟨(-68447096538020503804579635382),(-68447096538020503799022162055)⟩,⟨(-118553848834423318824780945178),(-118553848834423318818214428719)⟩⟩,⟨⟨(-68714163775761176703837754967),(-68714163775761176698248402182)⟩,⟨(-119016422859227240664056454405),(-119016422859227240657446657934)⟩⟩,⟨⟨(-68970016219710489349159637483),(-68970016219710489343542958128)⟩,⟨(-119459572291388118544334620919),(-119459572291388118537688929015)⟩⟩,⟨⟨(-69216311266545650369785606217),(-69216311266545650364144486416)⟩,⟨(-119886167826159173645734521745),(-119886167826159173639057506146)⟩⟩,⟨⟨(-69451390545946672989877998354),(-69451390545946672984211103626)⟩,⟨(-120293337081888424615717925144),(-120293337081888424609006773159)⟩⟩,⟨⟨(-69676765816596932310549375436),(-69676765816596932304861805623)⟩,⟨(-120683698501424260560838796232),(-120683698501424260554101907314)⟩⟩,⟨⟨(-69890929593705596301378363578),(-69890929593705596295668833240)⟩,⟨(-121054641044517323062736522196),(-121054641044517323055971168795)⟩⟩,⟨⟨(-70095250027190538217521479448),(-70095250027190538211788303619)⟩,⟨(-121408534416337739786151067217),(-121408534416337739779353890923)⟩⟩,⟨⟨(-70288368638517981043859298303),(-70288368638517981038121319936)⟩,⟨(-121743025663044017267695187108),(-121743025663044017260898324198)⟩⟩,⟨⟨(-70471511782327267743973735128),(-70471511782327267738215692665)⟩,⟨(-122060238893179595326698828375),(-122060238893179595319875399194)⟩⟩] +lemma amp9_13_6_eq : ∀ k : Fin 16, amp9_1Expr 3 6 k = amp9_13_6 k := by decide +kernel +noncomputable def amp9_13_7 : Fin 16 → CBox := ![⟨⟨(-70643468314107287782821909637),(-70643468314107287777046708999)⟩,⟨(-122358076342915922347863232275),(-122358076342915922341017770028)⟩⟩,⟨⟨(-70805324400427207197621369582),(-70805324400427207191827662063)⟩,⟨(-122638419307936276682766218125),(-122638419307936276675895935336)⟩⟩,⟨⟨(-70956014756739613937671464371),(-70956014756739613931869878148)⟩,⟨(-122899422661280022643040043984),(-122899422661280022636162850130)⟩⟩,⟨⟨(-71096486770715766123409581564),(-71096486770715766117593107281)⟩,⟨(-123142727326528243654227925009),(-123142727326528243647331222812)⟩⟩,⟨⟨(-71225819734200030793414506700),(-71225819734200030787589964572)⟩,⟨(-123366738590376440393940753115),(-123366738590376440387035857665)⟩⟩,⟨⟨(-71344823474217662619663853008),(-71344823474217662613825516415)⟩,⟨(-123572859114377696318364215804),(-123572859114377696311440746628)⟩⟩,⟨⟨(-71452720759319491786481174301),(-71452720759319491780634628024)⟩,⟨(-123759742694172808919452644702),(-123759742694172808912519778509)⟩⟩,⟨⟨(-71550184889284250862937445591),(-71550184889284250857083432039)⟩,⟨(-123928555519187267889858454984),(-123928555519187267882917011346)⟩⟩,⟨⟨(-71636581187985562588617461144),(-71636581187985562582756504733)⟩,⟨(-124078198298123836808856008294),(-124078198298123836801906400838)⟩⟩,⟨⟨(-71712447281589071100102391480),(-71712447281589071094234401335)⟩,⟨(-124209602226816889762203573758),(-124209602226816889755245174427)⟩⟩,⟨⟨(-71777290301579416085153347465),(-71777290301579416079281535214)⟩,⟨(-124321913631956371647484934522),(-124321913631956371640522813332)⟩⟩,⟨⟨(-71831512878535996579493168853),(-71831512878535996573617751895)⟩,⟨(-124415829890162482489493151932),(-124415829890162482482527210737)⟩⟩,⟨⟨(-71874763373790792280145558570),(-71874763373790792274269559778)⟩,⟨(-124490741945396305278111987510),(-124490741945396305271146971671)⟩⟩,⟨⟨(-71907309928033851787213918798),(-71907309928033851781338851464)⟩,⟨(-124547114230956580767169795394),(-124547114230956580760207847588)⟩⟩,⟨⟨(-71928941721771935364244921708),(-71928941721771935358373478507)⟩,⟨(-124584581596769791809675387365),(-124584581596769791802720683598)⟩⟩,⟨⟨(-71939792741600879315314780022),(-71939792741600879309450313478)⟩,⟨(-124603376114427460080875871711),(-124603376114427460073933736863)⟩⟩] +lemma amp9_13_7_eq : ∀ k : Fin 16, amp9_1Expr 3 7 k = amp9_13_7 k := by decide +kernel +noncomputable def amp9_13_8 : Fin 16 → CBox := ![⟨⟨(-71939792741600879315314780022),(-71939792741600879309450313478)⟩,⟨(-124603376114427460080875871711),(-124603376114427460073933736863)⟩⟩,⟨⟨(-71928941721771935364244921708),(-71928941721771935358373478507)⟩,⟨(-124584581596769791809675387365),(-124584581596769791802720683598)⟩⟩,⟨⟨(-71907309928033851787213918798),(-71907309928033851781338851464)⟩,⟨(-124547114230956580767169795394),(-124547114230956580760207847588)⟩⟩,⟨⟨(-71874763373790792280145558570),(-71874763373790792274269559778)⟩,⟨(-124490741945396305278111987510),(-124490741945396305271146971671)⟩⟩,⟨⟨(-71831512878535996579493168853),(-71831512878535996573617751895)⟩,⟨(-124415829890162482489493151932),(-124415829890162482482527210737)⟩⟩,⟨⟨(-71777290301579416085153347465),(-71777290301579416079281535214)⟩,⟨(-124321913631956371647484934522),(-124321913631956371640522813332)⟩⟩,⟨⟨(-71712447281589071100102391480),(-71712447281589071094234401335)⟩,⟨(-124209602226816889762203573758),(-124209602226816889755245174427)⟩⟩,⟨⟨(-71636581187985562588617461144),(-71636581187985562582756504733)⟩,⟨(-124078198298123836808856008294),(-124078198298123836801906400838)⟩⟩,⟨⟨(-71550184889284250862937445591),(-71550184889284250857083432039)⟩,⟨(-123928555519187267889858454984),(-123928555519187267882917011346)⟩⟩,⟨⟨(-71452720759319491786481174301),(-71452720759319491780634628024)⟩,⟨(-123759742694172808919452644702),(-123759742694172808912519778509)⟩⟩,⟨⟨(-71344823474217662619663853008),(-71344823474217662613825516415)⟩,⟨(-123572859114377696318364215804),(-123572859114377696311440746628)⟩⟩,⟨⟨(-71225819734200030793414506700),(-71225819734200030787589964572)⟩,⟨(-123366738590376440393940753115),(-123366738590376440387035857665)⟩⟩,⟨⟨(-71096486770715766123409581564),(-71096486770715766117593107281)⟩,⟨(-123142727326528243654227925009),(-123142727326528243647331222812)⟩⟩,⟨⟨(-70956014756739613937671464371),(-70956014756739613931869878148)⟩,⟨(-122899422661280022643040043984),(-122899422661280022636162850130)⟩⟩,⟨⟨(-70805324400427207197621369582),(-70805324400427207191827662063)⟩,⟨(-122638419307936276682766218125),(-122638419307936276675895935336)⟩⟩,⟨⟨(-70643468314107287782821909637),(-70643468314107287777046708999)⟩,⟨(-122358076342915922347863232275),(-122358076342915922341017770028)⟩⟩] +lemma amp9_13_8_eq : ∀ k : Fin 16, amp9_1Expr 3 8 k = amp9_13_8 k := by decide +kernel +noncomputable def amp9_13_9 : Fin 16 → CBox := ![⟨⟨(-70471511782327267743973735128),(-70471511782327267738215692665)⟩,⟨(-122060238893179595326698828375),(-122060238893179595319875399194)⟩⟩,⟨⟨(-70288368638517981043859298303),(-70288368638517981038121319936)⟩,⟨(-121743025663044017267695187108),(-121743025663044017260898324198)⟩⟩,⟨⟨(-70095250027190538217521479448),(-70095250027190538211788303619)⟩,⟨(-121408534416337739786151067217),(-121408534416337739779353890923)⟩⟩,⟨⟨(-69890929593705596301378363578),(-69890929593705596295668833240)⟩,⟨(-121054641044517323062736522196),(-121054641044517323055971168795)⟩⟩,⟨⟨(-69676765816596932310549375436),(-69676765816596932304861805623)⟩,⟨(-120683698501424260560838796232),(-120683698501424260554101907314)⟩⟩,⟨⟨(-69451390545946672989877998354),(-69451390545946672984211103626)⟩,⟨(-120293337081888424615717925144),(-120293337081888424609006773159)⟩⟩,⟨⟨(-69216311266545650369785606217),(-69216311266545650364144486416)⟩,⟨(-119886167826159173645734521745),(-119886167826159173639057506146)⟩⟩,⟨⟨(-68970016219710489349159637483),(-68970016219710489343542958128)⟩,⟨(-119459572291388118544334620919),(-119459572291388118537688929015)⟩⟩,⟨⟨(-68714163775761176703837754967),(-68714163775761176698248402182)⟩,⟨(-119016422859227240664056454405),(-119016422859227240657446657934)⟩⟩,⟨⟨(-68447096538020503804579635382),(-68447096538020503799022162055)⟩,⟨(-118553848834423318824780945178),(-118553848834423318818214428719)⟩⟩,⟨⟨(-68170625858784866943064515948),(-68170625858784866937499328871)⟩,⟨(-118074987571184117963894899642),(-118074987571184117957302665449)⟩⟩,⟨⟨(-67882946447620971193447919474),(-67882946447620971187913011034)⟩,⟨(-117576712214756753236684684494),(-117576712214756753230132036326)⟩⟩,⟨⟨(-67586024963955147028667891382),(-67586024963955147023161987090)⟩,⟨(-117062429119188813283743049702),(-117062429119188813277227366999)⟩⟩,⟨⟨(-67277905729051392375261707432),(-67277905729051392369789646204)⟩,⟨(-116528750949546260432548888679),(-116528750949546260426078052191)⟩⟩,⟨⟨(-66960713276388809133084849974),(-66960713276388809127640431409)⟩,⟨(-115979357505757280245237696402),(-115979357505757280238800561185)⟩⟩,⟨⟨(-66632338791740151047350885617),(-66632338791740151041942170257)⟩,⟨(-115410596214436558108288781435),(-115410596214436558101898808965)⟩⟩] +lemma amp9_13_9_eq : ∀ k : Fin 16, amp9_1Expr 3 9 k = amp9_13_9 k := by decide +kernel +noncomputable def amp9_13_10 : Fin 16 → CBox := ![⟨⟨(-66295067506085358055507408472),(-66295067506085358050121305857)⟩,⟨(-114826425211748380407184703642),(-114826425211748380400818822928)⟩⟩,⟨⟨(-65946634454237240528013578205),(-65946634454237240522662518732)⟩,⟨(-114222921462911159950751625249),(-114222921462911159944430867482)⟩⟩,⟨⟨(-65589488661285843482170988374),(-65589488661285843476854741438)⟩,⟨(-113604326803809865653638075594),(-113604326803809865647361651929)⟩⟩,⟨⟨(-65221205709714364224934252369),(-65221205709714364219650296371)⟩,⟨(-112966442020126635279219710323),(-112966442020126635272982755438)⟩⟩,⟨⟨(-64844401807227121646363583678),(-64844401807227121641118216593)⟩,⟨(-112313798516528502279568772632),(-112313798516528502273381814086)⟩⟩,⟨⟨(-64456489476868880865522009256),(-64456489476868880860312395982)⟩,⟨(-111641914651465586219396502867),(-111641914651465586213254133621)⟩⟩,⟨⟨(-64060255810442041626435938243),(-64060255810442041621263388352)⟩,⟨(-110955617809545002173121763551),(-110955617809545002167025879917)⟩⟩,⟨⟨(-63652946336376028680473191548),(-63652946336376028675341229490)⟩,⟨(-110250137106058509767564830254),(-110250137106058509761521041715)⟩⟩,⟨⟨(-63237523068765669829098205475),(-63237523068765669824007913849)⟩,⟨(-109530602899911085893339834721),(-109530602899911085887349653737)⟩⟩,⟨⟨(-62811060253041564516795402756),(-62811060253041564511749476242)⟩,⟨(-108791947635538051985418843171),(-108791947635538051979486443646)⟩⟩,⟨⟨(-62376699227217381562399557660),(-62376699227217381557401577584)⟩,⟨(-108039612269982829934362595030),(-108039612269982829928493826982)⟩⟩,⟨⟨(-61931338283814348960050879040),(-61931338283814348954986875202)⟩,⟨(-107268224488301970261096831113),(-107268224488301970255093800713)⟩⟩,⟨⟨(-61478302879938500950119194175),(-61478302879938500945098622515)⟩,⟨(-106483544151161515233261923878),(-106483544151161515227313871357)⟩⟩,⟨⟨(-61014310271825440941214720707),(-61014310271825440936237763657)⟩,⟨(-105679885379573300038485158210),(-105679885379573300032591909808)⟩⟩,⟨⟨(-60542875258375211991605290341),(-60542875258375211986673202529)⟩,⟨(-104863335983810586457459586191),(-104863335983810586451622982343)⟩⟩,⟨⟨(-60060528526626865105757962381),(-60060528526626865100869865803)⟩,⟨(-104027886937557653609618957162),(-104027886937557653603836989408)⟩⟩] +lemma amp9_13_10_eq : ∀ k : Fin 16, amp9_1Expr 3 10 k = amp9_13_10 k := by decide +kernel +noncomputable def amp9_13_11 : Fin 16 → CBox := ![⟨⟨(-59570979905906762500047426700),(-59570979905906762495204171507)⟩,⟨(-103179963853695169875875945011),(-103179963853695169870149763962)⟩⟩,⟨⟨(-59070567490809294434343694622),(-59070567490809294429544268099)⟩,⟨(-102313224126008108068675091186),(-102313224126008108063002457198)⟩⟩,⟨⟨(-58563202339129627991211281387),(-58563202339129627986460196166)⟩,⟨(-101434441905309035886045395509),(-101434441905309035880433813933)⟩⟩,⟨⟨(-58045023393183337449822948979),(-58045023393183337445114469446)⟩,⟨(-100536929643517573738850862091),(-100536929643517573733289915218)⟩⟩,⟨⟨(-57520149696019410860807281956),(-57520149696019410856148263650)⟩,⟨(-99627821732473132350777667960),(-99627821732473132345278930704)⟩⟩,⟨⟨(-56984513888713790575014679851),(-56984513888713790570404154627)⟩,⟨(-98700073299866625190765252578),(-98700073299866625185326567039)⟩⟩,⟨⟨(-56442450371203974292977130750),(-56442450371203974288418735777)⟩,⟨(-97761191746610121642286145715),(-97761191746610121636913524363)⟩⟩,⟨⟨(-55889677685399926705599396539),(-55889677685399926701076690633)⟩,⟨(-96803761369761203745272888371),(-96803761369761203739937375581)⟩⟩,⟨⟨(-55330753638593851795952929124),(-55330753638593851791482754662)⟩,⟨(-95835676523121076726489755302),(-95835676523121076721220247988)⟩⟩,⟨⟨(-54761174158297399579759183760),(-54761174158297399575341284738)⟩,⟨(-94849135924298945233001687650),(-94849135924298945227797266142)⟩⟩,⟨⟨(-54185729261629598885652463998),(-54185729261629598881283684621)⟩,⟨(-93852436126314091894475559449),(-93852436126314091889330495592)⟩⟩,⟨⟨(-53599682950878333020441957663),(-53599682950878333016128500910)⟩,⟨(-92837374140504600637231490668),(-92837374140504600632156054494)⟩⟩,⟨⟨(-53008067091420818539335694671),(-53008067091420818535076222434)⟩,⟨(-91812665413360657269088432598),(-91812665413360657264080057503)⟩⟩,⟨⟨(-52405903563925214430138767206),(-52405903563925214425934734875)⟩,⟨(-90769687589273372325026205672),(-90769687589273372320086941025)⟩⟩,⟨⟨(-51798476653068572744169178845),(-51798476653068572740023234430)⟩,⟨(-89717593317785057654476407799),(-89717593317785057649610604837)⟩⟩,⟨⟨(-51180554932150761405827664739),(-51180554932150761401742721599)⟩,⟨(-88647321502055012109028353804),(-88647321502055012104240589535)⟩⟩] +lemma amp9_13_11_eq : ∀ k : Fin 16, amp9_1Expr 3 11 k = amp9_13_11 k := by decide +kernel +noncomputable def amp9_13_12 : Fin 16 → CBox := ![⟨⟨(-50557686720482431275633304576),(-50557686720482431271546469481)⟩,⟨(-87568482113025898508212360430),(-87568482113025898503393479496)⟩⟩,⟨⟨(-49924374988729221668873595800),(-49924374988729221664840058976)⟩,⟨(-86471554016599907620072961134),(-86471554016599907615318089030)⟩⟩,⟨⟨(-49286444880026379423658438792),(-49286444880026379419679116647)⟩,⟨(-85366626656648648032363724203),(-85366626656648648027674241769)⟩⟩,⟨⟨(-48638120217913569083147774089),(-48638120217913569079222648673)⟩,⟨(-84243695402069335377942490018),(-84243695402069335373317901569)⟩⟩,⟨⟨(-47985517083355406602158834974),(-47985517083355406598288683220)⟩,⟨(-83113353615835889359381592643),(-83113353615835889354823052636)⟩⟩,⟨⟨(-47322565195896356615063307922),(-47322565195896356611247291866)⟩,⟨(-81965087263783130374311049332),(-81965087263783130369816643824)⟩⟩,⟨⟨(-46655687189838484692347721225),(-46655687189838484688589832100)⟩,⟨(-80810020674840670666677962759),(-80810020674840670662254429286)⟩⟩,⟨⟨(-45978502120047616449508721724),(-45978502120047616445801221982)⟩,⟨(-79637101727835810795726574658),(-79637101727835810791360050710)⟩⟩,⟨⟨(-45297756499006132967294179432),(-45297756499006132963646187127)⟩,⟨(-78458015725161932423409407880),(-78458015725161932419115527247)⟩⟩,⟨⟨(-44606740326628404396230009169),(-44606740326628404392640158054)⟩,⟨(-77261140605751933133153385821),(-77261140605751933128929323042)⟩⟩,⟨⟨(-43912543273515121380663020037),(-43912543273515121377133200163)⟩,⟨(-76058756039295136482879983264),(-76058756039295136478728869830)⟩⟩,⟨⟨(-43208105797029466862264724186),(-43208105797029466858796055477)⟩,⟨(-74838634539266376565291290194),(-74838634539266376561214608164)⟩⟩,⟨⟨(-42500882253193745498152379824),(-42500882253193745494748318653)⟩,⟨(-73613687429033992085625978242),(-73613687429033992081629589706)⟩⟩,⟨⟨(-41783440652515466066522507162),(-41783440652515466063145480828)⟩,⟨(-72371042125195670212650993578),(-72371042125195670208669364000)⟩⟩,⟨⟨(-41063624160825241730047236124),(-41063624160825241726733208224)⟩,⟨(-71124283389462221099027730018),(-71124283389462221095123044029)⟩⟩,⟨⟨(-40333602637358103893027898917),(-40333602637358103889776972885)⟩,⟨(-69859849020198302901960436111),(-69859849020198302898132416741)⟩⟩] +lemma amp9_13_12_eq : ∀ k : Fin 16, amp9_1Expr 3 12 k = amp9_13_12 k := by decide +kernel +noncomputable def amp9_13_13 : Fin 16 → CBox := ![⟨⟨(-39601635200454137557061274842),(-39601635200454137553872773725)⟩,⟨(-68592044229994666773801537776),(-68592044229994666770048925532)⟩⟩,⟨⟨(-38859464590104374376270290031),(-38859464590104374373140318310)⟩,⟨(-67306567024984472896111442155),(-67306567024984472892427033758)⟩⟩,⟨⟨(-38115796549175229433189887602),(-38115796549175229430125982045)⟩,⟨(-66018496194129982505231653215),(-66018496194129982501628435805)⟩⟩,⟨⟨(-37361913902531192334705260197),(-37361913902531192331705401577)⟩,⟨(-64712733147198015487412595818),(-64712733147198015483886615436)⟩⟩,⟨⟨(-36607003843609385795437577570),(-36607003843609385792505219730)⟩,⟨(-63405190570000631730009407302),(-63405190570000631726566600260)⟩⟩,⟨⟨(-35841851965557722420241004964),(-35841851965557722417352498244)⟩,⟨(-62079908641708405063793854719),(-62079908641708405060392800836)⟩⟩,⟨⟨(-35076166662618009664926126435),(-35076166662618009662102471805)⟩,⟨(-60753702794408055130781933508),(-60753702794408055127458983688)⟩⟩,⟨⟨(-34300193600980150025408761252),(-34300193600980150022650871685)⟩,⟨(-59409678026346506145258022058),(-59409678026346506142014297796)⟩⟩,⟨⟨(-33524208008310895724333061847),(-33524208008310895721640390522)⟩,⟨(-58065631553901910365227281194),(-58065631553901910362061834809)⟩⟩,⟨⟨(-32737866477294929152486801352),(-32737866477294929149857629153)⟩,⟨(-56703648070080758092633101120),(-56703648070080758089542492145)⟩⟩,⟨⟨(-31952063788142973132406471284),(-31952063788142973129843249374)⟩,⟨(-55342597887745317215382847041),(-55342597887745317212371345102)⟩⟩,⟨⟨(-31155810506980960748136225313),(-31155810506980960745624103216)⟩,⟨(-53963446749079285355923652388),(-53963446749079285352965068605)⟩⟩,⟨⟨(-30360682302007587724511660794),(-30360682302007587722068895077)⟩,⟨(-52586244299534362815599965718),(-52586244299534362812725971678)⟩⟩,⟨⟨(-29554977221247464423657957053),(-29554977221247464421283413680)⟩,⟨(-51190722163741443753222663408),(-51190722163741443750430822160)⟩⟩,⟨⟨(-28751023739938367697422440993),(-28751023739938367695114839792)⟩,⟨(-49798233887192212471546261227),(-49798233887192212468834433738)⟩⟩,⟨⟨(-27936329116135969238069998551),(-27936329116135969235831999145)⟩,⟨(-48387141406113245538859339133),(-48387141406113245536231651917)⟩⟩] +lemma amp9_13_13_eq : ∀ k : Fin 16, amp9_1Expr 3 13 k = amp9_13_13 k := by decide +kernel +noncomputable def amp9_13_14 : Fin 16 → CBox := ![⟨⟨(-27124059698702532522382521303),(-27124059698702532520201778537)⟩,⟨(-46980249505684159978874837550),(-46980249505684159976310016571)⟩⟩,⟨⟨(-26300838960499855274368842096),(-26300838960499855272256942721)⟩,⟨(-45554389361272765536378007604),(-45554389361272765533895632222)⟩⟩,⟨⟨(-25480772729857277564105876056),(-25480772729857277562060972950)⟩,⟨(-44133992984228323626965789542),(-44133992984228323624562801443)⟩⟩,⟨⟨(-24649489050903922245745853816),(-24649489050903922243772886758)⟩,⟨(-42694167416778337223016355458),(-42694167416778337220700809215)⟩⟩,⟨⟨(-23822155938916705062454177521),(-23822155938916705060541252630)⟩,⟨(-41261184432032405305429071581),(-41261184432032405303180542961)⟩⟩,⟨⟨(-22983270389303945549611480057),(-22983270389303945547768459959)⟩,⟨(-39808192038367763712680361627),(-39808192038367763710515416854)⟩⟩,⟨⟨(-22149212667309377172683514161),(-22149212667309377170903433194)⟩,⟨(-38363561687428013406282002936),(-38363561687428013404188792912)⟩⟩,⟨⟨(-21303181743484879756480217113),(-21303181743484879754771326568)⟩,⟨(-36898193142589549348002352794),(-36898193142589549345994634020)⟩⟩,⟨⟨(-20462956309978198965812294124),(-20462956309978198964173241661)⟩,⟨(-35442880001944392874078791426),(-35442880001944392872154481065)⟩⟩,⟨⟨(-19610228521757425347349881214),(-19610228521757425345776479281)⟩,⟨(-33965912147720179357788553549),(-33965912147720179355939839742)⟩⟩,⟨⟨(-18764410360201072199317152231),(-18764410360201072197814962980)⟩,⟨(-32500912117940074765209424271),(-32500912117940074763446249780)⟩⟩,⟨⟨(-17905421340180017041536636223),(-17905421340180017040101478665)⟩,⟨(-31013099492119807673315449190),(-31013099492119807671629983645)⟩⟩,⟨⟨(-17054608847284225418491888788),(-17054608847284225417123098275)⟩,⟨(-29539449026709962117469606880),(-29539449026709962115861064535)⟩⟩,⟨⟨(-16189774056173590092669665444),(-16189774056173590091373231626)⟩,⟨(-28041511228353124899791848127),(-28041511228353124898269976620)⟩⟩,⟨⟨(-15334597482021724183588370334),(-15334597482021724182359698261)⟩,⟨(-26560301952479399676430819301),(-26560301952479399674988091628)⟩⟩,⟨⟨(-14464300825782799817854280969),(-14464300825782799816694897192)⟩,⟨(-25052903926216277137592732514),(-25052903926216277136231116935)⟩⟩] +lemma amp9_13_14_eq : ∀ k : Fin 16, amp9_1Expr 3 14 k = amp9_13_14 k := by decide +kernel +noncomputable def amp9_13_15 : Fin 16 → CBox := ![⟨⟨(-13605436144528543518599464450),(-13605436144528543517509283380)⟩,⟨(-23565306661457456126916009597),(-23565306661457456125635868826)⟩⟩,⟨⟨(-12730011261233991576462911402),(-12730011261233991575443639047)⟩,⟨(-22049026285381237278550645379),(-22049026285381237277354194137)⟩⟩,⟨⟨(-11868204086295200168859084097),(-11868204086295200167909925586)⟩,⟨(-20556332472059850912194742442),(-20556332472059850911081212629)⟩⟩,⟨⟨(-10987901608861133640369195064),(-10987901608861133639489746667)⟩,⟨(-19031603855115292601394859535),(-19031603855115292600362725203)⟩⟩,⟨⟨(-10124011078824646542603747974),(-10124011078824646541793389118)⟩,⟨(-17535301564914489677644693189),(-17535301564914489676693613022)⟩⟩,⟨⟨(-9238936788997680558375916662),(-9238936788997680557636745857)⟩,⟨(-16002307926461242687744812378),(-16002307926461242686877474275)⟩⟩,⟨⟨(-8374023000594305592166315085),(-8374023000594305591497334525)⟩,⟨(-14504233300779720020927116620),(-14504233300779720020142693424)⟩⟩,⟨⟨(-7484008818589727933452548005),(-7484008818589727932854139664)⟩,⟨(-12962683518090937550408993571),(-12962683518090937549707024993)⟩⟩,⟨⟨(-6619527590048496234337338552),(-6619527590048496233808614348)⟩,⟨(-11465358108067962011595415541),(-11465358108067962010975504596)⟩⟩,⟨⟨(-5723823631345515039216655785),(-5723823631345515038759870384)⟩,⟨(-9913953343053823115463147516),(-9913953343053823114927803871)⟩⟩,⟨⟨(-4862135239681351864873794948),(-4862135239681351864486463384)⟩,⟨(-8421465268399182256259671155),(-8421465268399182255806111082)⟩⟩,⟨⟨(-3958514790998972548225708086),(-3958514790998972547910799533)⟩,⟨(-6856348740523115918967959804),(-6856348740523115918599451868)⟩⟩,⟨⟨(-3104583262309451839094321497),(-3104583262309451838848216296)⟩,⟨(-5377295946647905665385668519),(-5377295946647905665098164183)⟩⟩,⟨⟨(-2185759460592364486949367117),(-2185759460592364486776649622)⟩,⟨(-3785846438870318533875484661),(-3785846438870318533674023833)⟩⟩,⟨⟨(-1355876442797423833607827616),(-1355876442797423833502537585)⟩,⟨(-2348446887710894609640878859),(-2348446887710894609519113396)⟩⟩,⟨⟨(-385210003677661992984944041),(-385210003677661992956144145)⟩,⟨(-667203297953504647149870151),(-667203297953504647117204606)⟩⟩] +lemma amp9_13_15_eq : ∀ k : Fin 16, amp9_1Expr 3 15 k = amp9_13_15 k := by decide +kernel +noncomputable def amp9_13 : Fin 16 → Fin 16 → CBox := ![amp9_13_0,amp9_13_1,amp9_13_2,amp9_13_3,amp9_13_4,amp9_13_5,amp9_13_6,amp9_13_7,amp9_13_8,amp9_13_9,amp9_13_10,amp9_13_11,amp9_13_12,amp9_13_13,amp9_13_14,amp9_13_15] +lemma amp9_13_eq (i k : Fin 16) : amp9_1Expr 3 i k = amp9_13 i k := by + fin_cases i + · exact amp9_13_0_eq k + · exact amp9_13_1_eq k + · exact amp9_13_2_eq k + · exact amp9_13_3_eq k + · exact amp9_13_4_eq k + · exact amp9_13_5_eq k + · exact amp9_13_6_eq k + · exact amp9_13_7_eq k + · exact amp9_13_8_eq k + · exact amp9_13_9_eq k + · exact amp9_13_10_eq k + · exact amp9_13_11_eq k + · exact amp9_13_12_eq k + · exact amp9_13_13_eq k + · exact amp9_13_14_eq k + · exact amp9_13_15_eq k +noncomputable def amp9_14_0 : Fin 16 → CBox := ![⟨⟨(-206433418803638677634588326),(-206433418803638677609036260)⟩,⟨(-563986588551685308337747155),(-563986588551685308305764901)⟩⟩,⟨⟨(-726611995767906115130378309),(-726611995767906115038338967)⟩,⟨(-1985140889826941552093891368),(-1985140889826941551975581097)⟩⟩,⟨⟨(-1171344964628820880015588732),(-1171344964628820879865616719)⟩,⟨(-3200173956555908093897032540),(-3200173956555908093701941060)⟩⟩,⟨⟨(-1663741155941996025562044779),(-1663741155941996025348609820)⟩,⟨(-4545425368676907652646322920),(-4545425368676907652368075144)⟩⟩,⟨⟨(-2121361682949658354910932497),(-2121361682949658354638195853)⟩,⟨(-5795667899048286741565633762),(-5795667899048286741209226102)⟩⟩,⟨⟨(-2605610421927042946907078489),(-2605610421927042946571795221)⟩,⟨(-7118660057435660782871402570),(-7118660057435660782432849096)⟩⟩,⟨⟨(-3067387839274413925859383352),(-3067387839274413925464246056)⟩,⟨(-8380259423416616152610294045),(-8380259423416616152092833378)⟩⟩,⟨⟨(-3547394144058060914064911568),(-3547394144058060913607695075)⟩,⟨(-9691661036038931554651822142),(-9691661036038931554052715303)⟩⟩,⟨⟨(-4010668238177036632886368061),(-4010668238177036632369100766)⟩,⟨(-10957349399002419234066276962),(-10957349399002419233387999583)⟩⟩,⟨⟨(-4487625400817782326692603947),(-4487625400817782326114139257)⟩,⟨(-12260420600370828857693229866),(-12260420600370828856935156714)⟩⟩,⟨⟨(-4951131303068236857883387366),(-4951131303068236857244589288)⟩,⟨(-13526742274927124258927144759),(-13526742274927124258089171507)⟩⟩,⟨⟨(-5425441185469606814982434510),(-5425441185469606814282238769)⟩,⟨(-14822580972179686270289383481),(-14822580972179686269370582220)⟩⟩,⟨⟨(-5888398725213949358531673273),(-5888398725213949357771760888)⟩,⟨(-16087404492508317922276527554),(-16087404492508317921279410685)⟩⟩,⟨⟨(-6360151401061098850879014593),(-6360151401061098850058621910)⟩,⟨(-17376256771529301486914557226),(-17376256771529301485838650047)⟩⟩,⟨⟨(-6821992474173491748570330495),(-6821992474173491747689726969)⟩,⟨(-18638030048294491404436371352),(-18638030048294491403280593803)⟩⟩,⟨⟨(-7291131255199261820373434234),(-7291131255199261819431836200)⟩,⟨(-19919741033857825216911935648),(-19919741033857825215675483966)⟩⟩] +lemma amp9_14_0_eq : ∀ k : Fin 16, amp9_1Expr 4 0 k = amp9_14_0 k := by decide +kernel +noncomputable def amp9_14_1 : Fin 16 → CBox := ![⟨⟨(-7751395450698644996027108643),(-7751395450698644995025865332)⟩,⟨(-21177206200866954639773351000),(-21177206200866954638458285158)⟩⟩,⟨⟨(-8217786023128097381274985033),(-8217786023128097380213750297)⟩,⟨(-22451408940915350985999182696),(-22451408940915350984605679605)⟩⟩,⟨⟨(-8676073767988110570866014147),(-8676073767988110569746003218)⟩,⟨(-23703474344359069614576177094),(-23703474344359069613106072055)⟩⟩,⟨⟨(-9139537335716977438787159757),(-9139537335716977437605656519)⟩,⟨(-24969680358851473398304972826),(-24969680358851473396751793696)⟩⟩,⟨⟨(-9595486376480452819262432920),(-9595486376480452818023015537)⟩,⟨(-26215356303879581263924600098),(-26215356303879581262296745630)⟩⟩,⟨⟨(-10055817204924139266584399199),(-10055817204924139265286496717)⟩,⟨(-27473003515478005132169123347),(-27473003515478005130465836590)⟩⟩,⟨⟨(-10509089791589342673545095245),(-10509089791589342672186813035)⟩,⟨(-28711367251925508021279259101),(-28711367251925508019494070466)⟩⟩,⟨⟨(-10966065236024010114802212088),(-10966065236024010113386349404)⟩,⟨(-29959847383932387816952385812),(-29959847383932387815093621523)⟩⟩,⟨⟨(-11416340688760420329614899070),(-11416340688760420328139540207)⟩,⟨(-31190022798209339183480883109),(-31190022798209339181542081641)⟩⟩,⟨⟨(-11869727294381481877856822638),(-11869727294381481876321090388)⟩,⟨(-32428698040237272467650928822),(-32428698040237272465630263693)⟩⟩,⟨⟨(-12316697480480254772760173824),(-12316697480480254771168804537)⟩,⟨(-33649843298127636326608808545),(-33649843298127636324518043948)⟩⟩,⟨⟨(-12766254891602009638621680482),(-12766254891602009636970814460)⟩,⟨(-34878056986231400486438026602),(-34878056986231400484267091735)⟩⟩,⟨⟨(-13209621370059014536602117985),(-13209621370059014534897344040)⟩,⟨(-36089356731748829955046198079),(-36089356731748829952809227417)⟩⟩,⟨⟨(-13655104950972463002131582991),(-13655104950972463000366423442)⟩,⟨(-37306440508742092126242059044),(-37306440508742092123921743178)⟩⟩,⟨⟨(-14094577119453890024347413874),(-14094577119453890022524810588)⟩,⟨(-38507100801545820524557370461),(-38507100801545820522160645175)⟩⟩,⟨⟨(-14535739783441810131396829048),(-14535739783441810129515709296)⟩,⟨(-39712379613963254913540543965),(-39712379613963254911064788281)⟩⟩] +lemma amp9_14_1_eq : ∀ k : Fin 16, amp9_1Expr 4 1 k = amp9_14_1 k := by decide +kernel +noncomputable def amp9_14_2 : Fin 16 → CBox := ![⟨⟨(-14971033652317385874166247981),(-14971033652317385872233108740)⟩,⟨(-40901624579954552602151240213),(-40901624579954552599613128792)⟩⟩,⟨⟨(-15407627185369045846190652369),(-15407627185369045844198814188)⟩,⟨(-42094420294507689548836896801),(-42094420294507689546218419200)⟩⟩,⟨⟨(-15838464557506970187768542956),(-15838464557506970185719713259)⟩,⟨(-43271489884987958659735146184),(-43271489884987958657039912397)⟩⟩,⟨⟨(-16270240608961625266417359238),(-16270240608961625264310805975)⟩,⟨(-44451123995053550182798856363),(-44451123995053550180025038395)⟩⟩,⟨⟨(-16696348529765272280256999488),(-16696348529765272278092392750)⟩,⟨(-45615272484196649216213396930),(-45615272484196649213359054820)⟩⟩,⟨⟨(-17123059377081258098408333668),(-17123059377081258096195427569)⟩,⟨(-46781068199204688166607613619),(-46781068199204688163699506578)⟩⟩,⟨⟨(-17544169769018200424218033178),(-17544169769018200421949143874)⟩,⟨(-47931563185571657880963566777),(-47931563185571657877979675918)⟩⟩,⟨⟨(-17965568925439762166403594781),(-17965568925439762164080021695)⟩,⟨(-49082847091182029282475522118),(-49082847091182029279419450440)⟩⟩,⟨⟨(-18381418351227587810633936896),(-18381418351227587808255030773)⟩,⟨(-50218968850732712240401508971),(-50218968850732712237270465734)⟩⟩,⟨⟨(-18797261061655928397644601128),(-18797261061655928395210069257)⟩,⟨(-51355072263580090932430505184),(-51355072263580090929223689456)⟩⟩,⟨⟨(-19207590578814079552869444709),(-19207590578814079550380046577)⟩,⟨(-52476113352301365287840283378),(-52476113352301365284558759869)⟩⟩,⟨⟨(-19617634234436279721213809395),(-19617634234436279718680813400)⟩,⟨(-53596373452782491869893925230),(-53596373452782491866568427392)⟩⟩,⟨⟨(-20022189315728738363467487141),(-20022189315728738360878488488)⟩,⟨(-54701638489333646306180408995),(-54701638489333646302776040563)⟩⟩,⟨⟨(-20426193808440952721757220763),(-20426193808440952719114097349)⟩,⟨(-55805399289909506144864719912),(-55805399289909506141386510501)⟩⟩,⟨⟨(-20824724310448551712308735850),(-20824724310448551709610673878)⟩,⟨(-56894204869760197040478734516),(-56894204869760197036923457728)⟩⟩,⟨⟨(-21222452341827216680081988275),(-21222452341827216677333066022)⟩,⟨(-57980818059081058434292167029),(-57980818059081058430670817875)⟩⟩] +lemma amp9_14_2_eq : ∀ k : Fin 16, amp9_1Expr 4 2 k = amp9_14_2 k := by decide +kernel +noncomputable def amp9_14_3 : Fin 16 → CBox := ![⟨⟨(-21614712509035809767620336621),(-21614712509035809764818734488)⟩,⟨(-59052492765680398018691717327),(-59052492765680398014998322629)⟩⟩,⟨⟨(-22005929864376524721552773872),(-22005929864376524718698180194)⟩,⟨(-60121318457273958738802592620),(-60121318457273958735036109808)⟩⟩,⟨⟨(-22391678359670523840197151455),(-22391678359670523837289889716)⟩,⟨(-61175202945360408293113330406),(-61175202945360408289273641129)⟩⟩,⟨⟨(-22776154154706997820756526909),(-22776154154706997817815932324)⟩,⟨(-62225610351680493175818258479),(-62225610351680493171957954315)⟩⟩,⟨⟨(-23155154109585114317865279093),(-23155154109585114314871484907)⟩,⟨(-63261057484473819406938688306),(-63261057484473819403002488865)⟩⟩,⟨⟨(-23532661015470212556271114391),(-23532661015470212553226046052)⟩,⟨(-64292425531560030205333920292),(-64292425531560030201326812404)⟩⟩,⟨⟨(-23904680095009751317982448659),(-23904680095009751314886975314)⟩,⟨(-65308800558247057474760974809),(-65308800558247057470684327434)⟩⟩,⟨⟨(-24274994545700667021717313431),(-24274994545700667018572531509)⟩,⟨(-66320518452311598913158840876),(-66320518452311598909015337146)⟩⟩,⟨⟨(-24639805024518844205931522123),(-24639805024518844202736969227)⟩,⟨(-67317199215576388693378041827),(-67317199215576388689165409898)⟩⟩,⟨⟨(-25002707409672597435375167361),(-25002707409672597432135823367)⟩,⟨(-68308666970004371949616698030),(-68308666970004371945348193530)⟩⟩,⟨⟨(-25360086256019165710961910193),(-25360086256019165707673899296)⟩,⟨(-69285044135773547519465365544),(-69285044135773547515129387429)⟩⟩,⟨⟨(-25715361101749847689193556495),(-25715361101749847685859120715)⟩,⟨(-70255673064960965515428985355),(-70255673064960965511031273403)⟩⟩,⟨⟨(-26065090067515605576018289269),(-26065090067515605572637251373)⟩,⟨(-71211150368311532590586277069),(-71211150368311532586125330829)⟩⟩,⟨⟨(-26412526206808221629209311279),(-26412526206808221625782200007)⟩,⟨(-72160363553244537218420703540),(-72160363553244537213897547411)⟩⟩,⟨⟨(-26754391921717071434642444017),(-26754391921717071431169522780)⟩,⟨(-73094358055741371903421937854),(-73094358055741371898836270756)⟩⟩,⟨⟨(-27093782655877928085393524409),(-27093782655877928081875405620)⟩,⟨(-74021590785086934466194298706),(-74021590785086934461547340258)⟩⟩] +lemma amp9_14_3_eq : ∀ k : Fin 16, amp9_1Expr 4 3 k = amp9_14_3 k := by decide +kernel +noncomputable def amp9_14_4 : Fin 16 → CBox := ![⟨⟨(-27427576724493021404530169878),(-27427576724493021400996704206)⟩,⟨(-74933533139808501407450330903),(-74933533139808501402822609111)⟩⟩,⟨⟨(-27758719976704175666991379830),(-27758719976704175663408992826)⟩,⟨(-75838233329432969821676075076),(-75838233329432969816975377091)⟩⟩,⟨⟨(-28084239077154113069761547463),(-28084239077154113066132076055)⟩,⟨(-76727568050696315790848943400),(-76727568050696315786079257227)⟩⟩,⟨⟨(-28406937538961959618416287837),(-28406937538961959614741289343)⟩,⟨(-77609196643879677460591883750),(-77609196643879677455756947197)⟩⟩,⟨⟨(-28723983522504130806546857199),(-28723983522504130802827388613)⟩,⟨(-78475382379252535234677599155),(-78475382379252535229779264214)⟩⟩,⟨⟨(-29038044793890211752892457271),(-29038044793890211749127947798)⟩,⟨(-79333413729368986018756735149),(-79333413729368986013792895454)⟩⟩,⟨⟨(-29346424784591707852258942130),(-29346424784591707848452994402)⟩,⟨(-80175923532003091307607345853),(-80175923532003091302586802927)⟩⟩,⟨⟨(-29651661508133253730049733443),(-29651661508133253726200810341)⟩,⟨(-81009845769054449862207664042),(-81009845769054449857125642420)⟩⟩,⟨⟨(-29951188002077299331061432813),(-29951188002077299327169677028)⟩,⟨(-81828167368722554080492450579),(-81828167368722554075348293747)⟩⟩,⟨⟨(-30247417991595653886538037807),(-30247417991595653882612636720)⟩,⟨(-82637482750812294699774826001),(-82637482750812294694593030289)⟩⟩,⟨⟨(-30537908955121911917722354772),(-30537908955121911913754778874)⟩,⟨(-83431118822305669232669051193),(-83431118822305669227425261920)⟩⟩,⟨⟨(-30824955319131378740860357611),(-30824955319131378736852724890)⟩,⟨(-84215344072907442981119655680),(-84215344072907442975819028104)⟩⟩,⟨⟨(-31106234285698202320769214822),(-31106234285698202316721289138)⟩,⟨(-84983812500668472579245467256),(-84983812500668472573886299398)⟩⟩,⟨⟨(-31383925545900440191926149672),(-31383925545900440187841780748)⟩,⟨(-85742479132358815790868489428),(-85742479132358815785460641506)⟩⟩,⟨⟨(-31655821711220961599189236238),(-31655821711220961595065634411)⟩,⟨(-86485313270397627269873452833),(-86485313270397627264408241443)⟩⟩,⟨⟨(-31923991916236710247595380202),(-31923991916236710243435146410)⟩,⟨(-87217967895576814752877952352),(-87217967895576814747361800639)⟩⟩] +lemma amp9_14_4_eq : ∀ k : Fin 16, amp9_1Expr 4 4 k = amp9_14_4 k := by decide +kernel +noncomputable def amp9_14_5 : Fin 16 → CBox := ![⟨⟨(-32186340231392153202944575565),(-32186340231392153198747452454)⟩,⟨(-87934716821861577008952938658),(-87934716821861577003384076699)⟩⟩,⟨⟨(-32444829065879675050645808127),(-32444829065879675046412440463)⟩,⟨(-88640921450870748932949426563),(-88640921450870748927328908672)⟩⟩,⟨⟨(-32697470328155163687025718651),(-32697470328155163682755922528)⟩,⟨(-89331150215495718195791371995),(-89331150215495718190117624212)⟩⟩,⟨⟨(-32946123217430973333083519528),(-32946123217430973328778162788)⟩,⟨(-90010482542446028567545465991),(-90010482542446028561820128466)⟩⟩,⟨⟨(-33188904158653455317134037813),(-33188904158653455312793506033)⟩,⟨(-90673772408975242603361195757),(-90673772408975242597584245917)⟩⟩,⟨⟨(-33427572368903866379990926289),(-33427572368903866375674078313)⟩,⟨(-91325826085530896745204494086),(-91325826085530896739535983660)⟩⟩,⟨⟨(-33660345741090154095455667774),(-33660345741090154091101716090)⟩,⟨(-91961774764992974938534202467),(-91961774764992974932806976700)⟩⟩,⟨⟨(-33888886475240507528818864632),(-33888886475240507524429935926)⟩,⟨(-92586159662290832129779320544),(-92586159662290832123998414055)⟩⟩,⟨⟨(-34111511133387095185862943051),(-34111511133387095181440771375)⟩,⟨(-93194381539364962175487853626),(-93194381539364962169656919852)⟩⟩,⟨⟨(-34329787622678162158594303178),(-34329787622678162154139681816)⟩,⟨(-93790723998205921094684574694),(-93790723998205921088804984169)⟩⟩,⟨⟨(-34542128604544351022383505169),(-34542128604544351017898613795)⟩,⟨(-94370850349193410709070032166),(-94370850349193410703146652232)⟩⟩,⟨⟨(-34750010195851482025399777579),(-34750010195851482020885536566)⟩,⟨(-94938793418602761267739373170),(-94938793418602761261773901181)⟩⟩,⟨⟨(-34951938798604186340375248301),(-34951938798604186335830430105)⟩,⟨(-95490472620824542109907633821),(-95490472620824542103895625232)⟩⟩,⟨⟨(-35149301037523642620480253622),(-35149301037523642615908457137)⟩,⟨(-96029676285048044344278440364),(-96029676285048044338228890783)⟩⟩,⟨⟨(-35340694891126642209618462976),(-35340694891126642205018629419)⟩,⟨(-96552574017347838846827679767),(-96552574017347838840736602887)⟩⟩,⟨⟨(-35527419600844671406722699813),(-35527419600844671402094934459)⟩,⟨(-97062715411326044704713317203),(-97062715411326044698580145058)⟩⟩] +lemma amp9_14_5_eq : ∀ k : Fin 16, amp9_1Expr 4 5 k = amp9_14_5 k := by decide +kernel +noncomputable def amp9_14_6 : Fin 16 → CBox := ![⟨⟨(-35708162738087487971883683211),(-35708162738087487967234940674)⟩,⟨(-97556514845392814123241430921),(-97556514845392814117084067792)⟩⟩,⟨⟨(-35884138094040676040917066919),(-35884138094040676036240565733)⟩,⟨(-98037288458736942225678062225),(-98037288458736942219477107146)⟩⟩,⟨⟨(-36054121017113048634997626551),(-36054121017113048630297980064)⟩,⟨(-98501690440989736115953232767),(-98501690440989736109720191572)⟩⟩,⟨⟨(-36219241617442961546229682963),(-36219241617442961541503806716)⟩,⟨(-98952808310467332511535501862),(-98952808310467332505261056670)⟩⟩,⟨⟨(-36378361360970378299462326768),(-36378361360970378294713108057)⟩,⟨(-99387531534271564087864800708),(-99387531534271564081555740149)⟩⟩,⟨⟨(-36532528292771231843504214084),(-36532528292771231838731212672)⟩,⟨(-99808723424798502043057934087),(-99808723424798502036712147850)⟩⟩,⟨⟨(-36680688483235377567788690971),(-36680688483235377563012561336)⟩,⟨(-100213504592805630041805452599),(-100213504592805630035478269076)⟩⟩,⟨⟨(-36823809384590225486266374068),(-36823809384590225481466145271)⟩,⟨(-100604518166932127921845705462),(-100604518166932127915478907575)⟩⟩,⟨⟨(-36960920296065720306993952907),(-36960920296065720302172359411)⟩,⟨(-100979112143355258391763517191),(-100979112143355258385363474349)⟩⟩,⟨⟨(-37092909413864254186694543153),(-37092909413864254181853382671)⟩,⟨(-101339713119227046553316429227),(-101339713119227046546887114343)⟩⟩,⟨⟨(-37218888020009842727093980475),(-37218888020009842722232832462)⟩,⟨(-101683893071883503253103269735),(-101683893071883503246642432482)⟩⟩,⟨⟨(-37339666263539208119534559435),(-37339666263539208114656411781)⟩,⟨(-102013865369654656502006876844),(-102013865369654656495521727364)⟩⟩,⟨⟨(-37454436285787739079052031427),(-37454436285787739074156489759)⟩,⟨(-102327422901623453524148741807),(-102327422901623453517637101694)⟩⟩,⟨⟨(-37563931276086673296792515422),(-37563931276086673291878935322)⟩,⟨(-102626568778294403138695787683),(-102626568778294403132154929746)⟩⟩,⟨⟨(-37667423227983889639052820031),(-37667423227983889634131593643)⟩,⟨(-102909314049052072449112347748),(-102909314049052072442569563845)⟩⟩,⟨⟨(-37765569342949880321500694835),(-37765569342949880316563905540)⟩,⟨(-103177454221704655166894510178),(-103177454221704655160327192119)⟩⟩] +lemma amp9_14_6_eq : ∀ k : Fin 16, amp9_1Expr 4 6 k = amp9_14_6 k := by decide +kernel +noncomputable def amp9_14_7 : Fin 16 → CBox := ![⟨⟨(-37857720570597306434562153308),(-37857720570597306429611652221)⟩,⟨(-103429216057617269131530493234),(-103429216057617269124942599843)⟩⟩,⟨⟨(-37944458985836275423951732463),(-37944458985836275418987062121)⟩,⟨(-103666189815018138971740862307),(-103666189815018138965130151919)⟩⟩,⟨⟨(-38025213704398410463602328881),(-38025213704398410458629478196)⟩,⟨(-103886815809080817412191412866),(-103886815809080817405573151025)⟩⟩,⟨⟨(-38100492429806577184177049088),(-38100492429806577179192530159)⟩,⟨(-104092481111624955063093819524),(-104092481111624955056457473680)⟩⟩,⟨⟨(-38169801756047242384769264425),(-38169801756047242379777024784)⟩,⟨(-104281837712352819202512276163),(-104281837712352819195867537325)⟩⟩,⟨⟨(-38233575668115257840918041362),(-38233575668115257835915283438)⟩,⟨(-104456071280320067398862947923),(-104456071280320067392201158664)⟩⟩,⟨⟨(-38291397648932349306008942883),(-38291397648932349300998951282)⟩,⟨(-104614043869706634267407374504),(-104614043869706634260736417892)⟩⟩,⟨⟨(-38343628518762467671021029168),(-38343628518762467666004475792)⟩,⟨(-104756741259806034055308450029),(-104756741259806034048629137207)⟩⟩,⟨⟨(-38389928155694576735744762970),(-38389928155694576730722219569)⟩,⟨(-104883234220276548441945296246),(-104883234220276548435258102414)⟩⟩,⟨⟨(-38430584672722504874988280506),(-38430584672722504869959974977)⟩,⟨(-104994309890455637325672121389),(-104994309890455637318976635113)⟩⟩,⟨⟨(-38465333942404921044628465923),(-38465333942404921039596408912)⟩,⟨(-105089246660753911126134259916),(-105089246660753911119434891931)⟩⟩,⟨⟨(-38494391733819021337970549855),(-38494391733819021332935136833)⟩,⟨(-105168634023252971821472163259),(-105168634023252971814768951088)⟩⟩,⟨⟨(-38517569604370558563341825931),(-38517569604370558558304965050)⟩,⟨(-105231957143211025997405941406),(-105231957143211025990703020775)⟩⟩,⟨⟨(-38535011250222245613499190809),(-38535011250222245608461974201)⟩,⟨(-105279608605845457961385503765),(-105279608605845457954684807309)⟩⟩,⟨⟨(-38546603693548157836611712595),(-38546603693548157831575869956)⟩,⟨(-105311279749995712892335125234),(-105311279749995712885640306755)⟩⟩,⟨⟨(-38552418737548597098490023710),(-38552418737548597093457634827)⟩,⟨(-105327166745653161532596599689),(-105327166745653161525912282610)⟩⟩] +lemma amp9_14_7_eq : ∀ k : Fin 16, amp9_1Expr 4 7 k = amp9_14_7 k := by decide +kernel +noncomputable def amp9_14_8 : Fin 16 → CBox := ![⟨⟨(-38552418737548597098490023710),(-38552418737548597093457634827)⟩,⟨(-105327166745653161532596599689),(-105327166745653161525912282610)⟩⟩,⟨⟨(-38546603693548157836611712595),(-38546603693548157831575869956)⟩,⟨(-105311279749995712892335125234),(-105311279749995712885640306755)⟩⟩,⟨⟨(-38535011250222245613499190809),(-38535011250222245608461974201)⟩,⟨(-105279608605845457961385503765),(-105279608605845457954684807309)⟩⟩,⟨⟨(-38517569604370558563341825931),(-38517569604370558558304965050)⟩,⟨(-105231957143211025997405941406),(-105231957143211025990703020775)⟩⟩,⟨⟨(-38494391733819021337970549855),(-38494391733819021332935136833)⟩,⟨(-105168634023252971821472163259),(-105168634023252971814768951088)⟩⟩,⟨⟨(-38465333942404921044628465923),(-38465333942404921039596408912)⟩,⟨(-105089246660753911126134259916),(-105089246660753911119434891931)⟩⟩,⟨⟨(-38430584672722504874988280506),(-38430584672722504869959974977)⟩,⟨(-104994309890455637325672121389),(-104994309890455637318976635113)⟩⟩,⟨⟨(-38389928155694576735744762970),(-38389928155694576730722219569)⟩,⟨(-104883234220276548441945296246),(-104883234220276548435258102414)⟩⟩,⟨⟨(-38343628518762467671021029168),(-38343628518762467666004475792)⟩,⟨(-104756741259806034055308450029),(-104756741259806034048629137207)⟩⟩,⟨⟨(-38291397648932349306008942883),(-38291397648932349300998951282)⟩,⟨(-104614043869706634267407374504),(-104614043869706634260736417892)⟩⟩,⟨⟨(-38233575668115257840918041362),(-38233575668115257835915283438)⟩,⟨(-104456071280320067398862947923),(-104456071280320067392201158664)⟩⟩,⟨⟨(-38169801756047242384769264425),(-38169801756047242379777024784)⟩,⟨(-104281837712352819202512276163),(-104281837712352819195867537325)⟩⟩,⟨⟨(-38100492429806577184177049088),(-38100492429806577179192530159)⟩,⟨(-104092481111624955063093819524),(-104092481111624955056457473680)⟩⟩,⟨⟨(-38025213704398410463602328881),(-38025213704398410458629478196)⟩,⟨(-103886815809080817412191412866),(-103886815809080817405573151025)⟩⟩,⟨⟨(-37944458985836275423951732463),(-37944458985836275418987062121)⟩,⟨(-103666189815018138971740862307),(-103666189815018138965130151919)⟩⟩,⟨⟨(-37857720570597306434562153308),(-37857720570597306429611652221)⟩,⟨(-103429216057617269131530493234),(-103429216057617269124942599843)⟩⟩] +lemma amp9_14_8_eq : ∀ k : Fin 16, amp9_1Expr 4 8 k = amp9_14_8 k := by decide +kernel +noncomputable def amp9_14_9 : Fin 16 → CBox := ![⟨⟨(-37765569342949880321500694835),(-37765569342949880316563905540)⟩,⟨(-103177454221704655166894510178),(-103177454221704655160327192119)⟩⟩,⟨⟨(-37667423227983889639052820031),(-37667423227983889634131593643)⟩,⟨(-102909314049052072449112347748),(-102909314049052072442569563845)⟩⟩,⟨⟨(-37563931276086673296792515422),(-37563931276086673291878935322)⟩,⟨(-102626568778294403138695787683),(-102626568778294403132154929746)⟩⟩,⟨⟨(-37454436285787739079052031427),(-37454436285787739074156489759)⟩,⟨(-102327422901623453524148741807),(-102327422901623453517637101694)⟩⟩,⟨⟨(-37339666263539208119534559435),(-37339666263539208114656411781)⟩,⟨(-102013865369654656502006876844),(-102013865369654656495521727364)⟩⟩,⟨⟨(-37218888020009842727093980475),(-37218888020009842722232832462)⟩,⟨(-101683893071883503253103269735),(-101683893071883503246642432482)⟩⟩,⟨⟨(-37092909413864254186694543153),(-37092909413864254181853382671)⟩,⟨(-101339713119227046553316429227),(-101339713119227046546887114343)⟩⟩,⟨⟨(-36960920296065720306993952907),(-36960920296065720302172359411)⟩,⟨(-100979112143355258391763517191),(-100979112143355258385363474349)⟩⟩,⟨⟨(-36823809384590225486266374068),(-36823809384590225481466145271)⟩,⟨(-100604518166932127921845705462),(-100604518166932127915478907575)⟩⟩,⟨⟨(-36680688483235377567788690971),(-36680688483235377563012561336)⟩,⟨(-100213504592805630041805452599),(-100213504592805630035478269076)⟩⟩,⟨⟨(-36532528292771231843504214084),(-36532528292771231838731212672)⟩,⟨(-99808723424798502043057934087),(-99808723424798502036712147850)⟩⟩,⟨⟨(-36378361360970378299462326768),(-36378361360970378294713108057)⟩,⟨(-99387531534271564087864800708),(-99387531534271564081555740149)⟩⟩,⟨⟨(-36219241617442961546229682963),(-36219241617442961541503806716)⟩,⟨(-98952808310467332511535501862),(-98952808310467332505261056670)⟩⟩,⟨⟨(-36054121017113048634997626551),(-36054121017113048630297980064)⟩,⟨(-98501690440989736115953232767),(-98501690440989736109720191572)⟩⟩,⟨⟨(-35884138094040676040917066919),(-35884138094040676036240565733)⟩,⟨(-98037288458736942225678062225),(-98037288458736942219477107146)⟩⟩,⟨⟨(-35708162738087487971883683211),(-35708162738087487967234940674)⟩,⟨(-97556514845392814123241430921),(-97556514845392814117084067792)⟩⟩] +lemma amp9_14_9_eq : ∀ k : Fin 16, amp9_1Expr 4 9 k = amp9_14_9 k := by decide +kernel +noncomputable def amp9_14_10 : Fin 16 → CBox := ![⟨⟨(-35527419600844671406722699813),(-35527419600844671402094934459)⟩,⟨(-97062715411326044704713317203),(-97062715411326044698580145058)⟩⟩,⟨⟨(-35340694891126642209618462976),(-35340694891126642205018629419)⟩,⟨(-96552574017347838846827679767),(-96552574017347838840736602887)⟩⟩,⟨⟨(-35149301037523642620480253622),(-35149301037523642615908457137)⟩,⟨(-96029676285048044344278440364),(-96029676285048044338228890783)⟩⟩,⟨⟨(-34951938798604186340375248301),(-34951938798604186335830430105)⟩,⟨(-95490472620824542109907633821),(-95490472620824542103895625232)⟩⟩,⟨⟨(-34750010195851482025399777579),(-34750010195851482020885536566)⟩,⟨(-94938793418602761267739373170),(-94938793418602761261773901181)⟩⟩,⟨⟨(-34542128604544351022383505169),(-34542128604544351017898613795)⟩,⟨(-94370850349193410709070032166),(-94370850349193410703146652232)⟩⟩,⟨⟨(-34329787622678162158594303178),(-34329787622678162154139681816)⟩,⟨(-93790723998205921094684574694),(-93790723998205921088804984169)⟩⟩,⟨⟨(-34111511133387095185862943051),(-34111511133387095181440771375)⟩,⟨(-93194381539364962175487853626),(-93194381539364962169656919852)⟩⟩,⟨⟨(-33888886475240507528818864632),(-33888886475240507524429935926)⟩,⟨(-92586159662290832129779320544),(-92586159662290832123998414055)⟩⟩,⟨⟨(-33660345741090154095455667774),(-33660345741090154091101716090)⟩,⟨(-91961774764992974938534202467),(-91961774764992974932806976700)⟩⟩,⟨⟨(-33427572368903866379990926289),(-33427572368903866375674078313)⟩,⟨(-91325826085530896745204494086),(-91325826085530896739535983660)⟩⟩,⟨⟨(-33188904158653455317134037813),(-33188904158653455312793506033)⟩,⟨(-90673772408975242603361195757),(-90673772408975242597584245917)⟩⟩,⟨⟨(-32946123217430973333083519528),(-32946123217430973328778162788)⟩,⟨(-90010482542446028567545465991),(-90010482542446028561820128466)⟩⟩,⟨⟨(-32697470328155163687025718651),(-32697470328155163682755922528)⟩,⟨(-89331150215495718195791371995),(-89331150215495718190117624212)⟩⟩,⟨⟨(-32444829065879675050645808127),(-32444829065879675046412440463)⟩,⟨(-88640921450870748932949426563),(-88640921450870748927328908672)⟩⟩,⟨⟨(-32186340231392153202944575565),(-32186340231392153198747452454)⟩,⟨(-87934716821861577008952938658),(-87934716821861577003384076699)⟩⟩] +lemma amp9_14_10_eq : ∀ k : Fin 16, amp9_1Expr 4 10 k = amp9_14_10 k := by decide +kernel +noncomputable def amp9_14_11 : Fin 16 → CBox := ![⟨⟨(-31923991916236710247595380202),(-31923991916236710243435146410)⟩,⟨(-87217967895576814752877952352),(-87217967895576814747361800639)⟩⟩,⟨⟨(-31655821711220961599189236238),(-31655821711220961595065634411)⟩,⟨(-86485313270397627269873452833),(-86485313270397627264408241443)⟩⟩,⟨⟨(-31383925545900440191926149672),(-31383925545900440187841780748)⟩,⟨(-85742479132358815790868489428),(-85742479132358815785460641506)⟩⟩,⟨⟨(-31106234285698202320769214822),(-31106234285698202316721289138)⟩,⟨(-84983812500668472579245467256),(-84983812500668472573886299398)⟩⟩,⟨⟨(-30824955319131378740860357611),(-30824955319131378736852724890)⟩,⟨(-84215344072907442981119655680),(-84215344072907442975819028104)⟩⟩,⟨⟨(-30537908955121911917722354772),(-30537908955121911913754778874)⟩,⟨(-83431118822305669232669051193),(-83431118822305669227425261920)⟩⟩,⟨⟨(-30247417991595653886538037807),(-30247417991595653882612636720)⟩,⟨(-82637482750812294699774826001),(-82637482750812294694593030289)⟩⟩,⟨⟨(-29951188002077299331061432813),(-29951188002077299327169677028)⟩,⟨(-81828167368722554080492450579),(-81828167368722554075348293747)⟩⟩,⟨⟨(-29651661508133253730049733443),(-29651661508133253726200810341)⟩,⟨(-81009845769054449862207664042),(-81009845769054449857125642420)⟩⟩,⟨⟨(-29346424784591707852258942130),(-29346424784591707848452994402)⟩,⟨(-80175923532003091307607345853),(-80175923532003091302586802927)⟩⟩,⟨⟨(-29038044793890211752892457271),(-29038044793890211749127947798)⟩,⟨(-79333413729368986018756735149),(-79333413729368986013792895454)⟩⟩,⟨⟨(-28723983522504130806546857199),(-28723983522504130802827388613)⟩,⟨(-78475382379252535234677599155),(-78475382379252535229779264214)⟩⟩,⟨⟨(-28406937538961959618416287837),(-28406937538961959614741289343)⟩,⟨(-77609196643879677460591883750),(-77609196643879677455756947197)⟩⟩,⟨⟨(-28084239077154113069761547463),(-28084239077154113066132076055)⟩,⟨(-76727568050696315790848943400),(-76727568050696315786079257227)⟩⟩,⟨⟨(-27758719976704175666991379830),(-27758719976704175663408992826)⟩,⟨(-75838233329432969821676075076),(-75838233329432969816975377091)⟩⟩,⟨⟨(-27427576724493021404530169878),(-27427576724493021400996704206)⟩,⟨(-74933533139808501407450330903),(-74933533139808501402822609111)⟩⟩] +lemma amp9_14_11_eq : ∀ k : Fin 16, amp9_1Expr 4 11 k = amp9_14_11 k := by decide +kernel +noncomputable def amp9_14_12 : Fin 16 → CBox := ![⟨⟨(-27093782655877928085393524409),(-27093782655877928081875405620)⟩,⟨(-74021590785086934466194298706),(-74021590785086934461547340258)⟩⟩,⟨⟨(-26754391921717071434642444017),(-26754391921717071431169522780)⟩,⟨(-73094358055741371903421937854),(-73094358055741371898836270756)⟩⟩,⟨⟨(-26412526206808221629209311279),(-26412526206808221625782200007)⟩,⟨(-72160363553244537218420703540),(-72160363553244537213897547411)⟩⟩,⟨⟨(-26065090067515605576018289269),(-26065090067515605572637251373)⟩,⟨(-71211150368311532590586277069),(-71211150368311532586125330829)⟩⟩,⟨⟨(-25715361101749847689193556495),(-25715361101749847685859120715)⟩,⟨(-70255673064960965515428985355),(-70255673064960965511031273403)⟩⟩,⟨⟨(-25360086256019165710961910193),(-25360086256019165707673899296)⟩,⟨(-69285044135773547519465365544),(-69285044135773547515129387429)⟩⟩,⟨⟨(-25002707409672597435375167361),(-25002707409672597432135823367)⟩,⟨(-68308666970004371949616698030),(-68308666970004371945348193530)⟩⟩,⟨⟨(-24639805024518844205931522123),(-24639805024518844202736969227)⟩,⟨(-67317199215576388693378041827),(-67317199215576388689165409898)⟩⟩,⟨⟨(-24274994545700667021717313431),(-24274994545700667018572531509)⟩,⟨(-66320518452311598913158840876),(-66320518452311598909015337146)⟩⟩,⟨⟨(-23904680095009751317982448659),(-23904680095009751314886975314)⟩,⟨(-65308800558247057474760974809),(-65308800558247057470684327434)⟩⟩,⟨⟨(-23532661015470212556271114391),(-23532661015470212553226046052)⟩,⟨(-64292425531560030205333920292),(-64292425531560030201326812404)⟩⟩,⟨⟨(-23155154109585114317865279093),(-23155154109585114314871484907)⟩,⟨(-63261057484473819406938688306),(-63261057484473819403002488865)⟩⟩,⟨⟨(-22776154154706997820756526909),(-22776154154706997817815932324)⟩,⟨(-62225610351680493175818258479),(-62225610351680493171957954315)⟩⟩,⟨⟨(-22391678359670523840197151455),(-22391678359670523837289889716)⟩,⟨(-61175202945360408293113330406),(-61175202945360408289273641129)⟩⟩,⟨⟨(-22005929864376524721552773872),(-22005929864376524718698180194)⟩,⟨(-60121318457273958738802592620),(-60121318457273958735036109808)⟩⟩,⟨⟨(-21614712509035809767620336621),(-21614712509035809764818734488)⟩,⟨(-59052492765680398018691717327),(-59052492765680398014998322629)⟩⟩] +lemma amp9_14_12_eq : ∀ k : Fin 16, amp9_1Expr 4 12 k = amp9_14_12 k := by decide +kernel +noncomputable def amp9_14_13 : Fin 16 → CBox := ![⟨⟨(-21222452341827216680081988275),(-21222452341827216677333066022)⟩,⟨(-57980818059081058434292167029),(-57980818059081058430670817875)⟩⟩,⟨⟨(-20824724310448551712308735850),(-20824724310448551709610673878)⟩,⟨(-56894204869760197040478734516),(-56894204869760197036923457728)⟩⟩,⟨⟨(-20426193808440952721757220763),(-20426193808440952719114097349)⟩,⟨(-55805399289909506144864719912),(-55805399289909506141386510501)⟩⟩,⟨⟨(-20022189315728738363467487141),(-20022189315728738360878488488)⟩,⟨(-54701638489333646306180408995),(-54701638489333646302776040563)⟩⟩,⟨⟨(-19617634234436279721213809395),(-19617634234436279718680813400)⟩,⟨(-53596373452782491869893925230),(-53596373452782491866568427392)⟩⟩,⟨⟨(-19207590578814079552869444709),(-19207590578814079550380046577)⟩,⟨(-52476113352301365287840283378),(-52476113352301365284558759869)⟩⟩,⟨⟨(-18797261061655928397644601128),(-18797261061655928395210069257)⟩,⟨(-51355072263580090932430505184),(-51355072263580090929223689456)⟩⟩,⟨⟨(-18381418351227587810633936896),(-18381418351227587808255030773)⟩,⟨(-50218968850732712240401508971),(-50218968850732712237270465734)⟩⟩,⟨⟨(-17965568925439762166403594781),(-17965568925439762164080021695)⟩,⟨(-49082847091182029282475522118),(-49082847091182029279419450440)⟩⟩,⟨⟨(-17544169769018200424218033178),(-17544169769018200421949143874)⟩,⟨(-47931563185571657880963566777),(-47931563185571657877979675918)⟩⟩,⟨⟨(-17123059377081258098408333668),(-17123059377081258096195427569)⟩,⟨(-46781068199204688166607613619),(-46781068199204688163699506578)⟩⟩,⟨⟨(-16696348529765272280256999488),(-16696348529765272278092392750)⟩,⟨(-45615272484196649216213396930),(-45615272484196649213359054820)⟩⟩,⟨⟨(-16270240608961625266417359238),(-16270240608961625264310805975)⟩,⟨(-44451123995053550182798856363),(-44451123995053550180025038395)⟩⟩,⟨⟨(-15838464557506970187768542956),(-15838464557506970185719713259)⟩,⟨(-43271489884987958659735146184),(-43271489884987958657039912397)⟩⟩,⟨⟨(-15407627185369045846190652369),(-15407627185369045844198814188)⟩,⟨(-42094420294507689548836896801),(-42094420294507689546218419200)⟩⟩,⟨⟨(-14971033652317385874166247981),(-14971033652317385872233108740)⟩,⟨(-40901624579954552602151240213),(-40901624579954552599613128792)⟩⟩] +lemma amp9_14_13_eq : ∀ k : Fin 16, amp9_1Expr 4 13 k = amp9_14_13 k := by decide +kernel +noncomputable def amp9_14_14 : Fin 16 → CBox := ![⟨⟨(-14535739783441810131396829048),(-14535739783441810129515709296)⟩,⟨(-39712379613963254913540543965),(-39712379613963254911064788281)⟩⟩,⟨⟨(-14094577119453890024347413874),(-14094577119453890022524810588)⟩,⟨(-38507100801545820524557370461),(-38507100801545820522160645175)⟩⟩,⟨⟨(-13655104950972463002131582991),(-13655104950972463000366423442)⟩,⟨(-37306440508742092126242059044),(-37306440508742092123921743178)⟩⟩,⟨⟨(-13209621370059014536602117985),(-13209621370059014534897344040)⟩,⟨(-36089356731748829955046198079),(-36089356731748829952809227417)⟩⟩,⟨⟨(-12766254891602009638621680482),(-12766254891602009636970814460)⟩,⟨(-34878056986231400486438026602),(-34878056986231400484267091735)⟩⟩,⟨⟨(-12316697480480254772760173824),(-12316697480480254771168804537)⟩,⟨(-33649843298127636326608808545),(-33649843298127636324518043948)⟩⟩,⟨⟨(-11869727294381481877856822638),(-11869727294381481876321090388)⟩,⟨(-32428698040237272467650928822),(-32428698040237272465630263693)⟩⟩,⟨⟨(-11416340688760420329614899070),(-11416340688760420328139540207)⟩,⟨(-31190022798209339183480883109),(-31190022798209339181542081641)⟩⟩,⟨⟨(-10966065236024010114802212088),(-10966065236024010113386349404)⟩,⟨(-29959847383932387816952385812),(-29959847383932387815093621523)⟩⟩,⟨⟨(-10509089791589342673545095245),(-10509089791589342672186813035)⟩,⟨(-28711367251925508021279259101),(-28711367251925508019494070466)⟩⟩,⟨⟨(-10055817204924139266584399199),(-10055817204924139265286496717)⟩,⟨(-27473003515478005132169123347),(-27473003515478005130465836590)⟩⟩,⟨⟨(-9595486376480452819262432920),(-9595486376480452818023015537)⟩,⟨(-26215356303879581263924600098),(-26215356303879581262296745630)⟩⟩,⟨⟨(-9139537335716977438787159757),(-9139537335716977437605656519)⟩,⟨(-24969680358851473398304972826),(-24969680358851473396751793696)⟩⟩,⟨⟨(-8676073767988110570866014147),(-8676073767988110569746003218)⟩,⟨(-23703474344359069614576177094),(-23703474344359069613106072055)⟩⟩,⟨⟨(-8217786023128097381274985033),(-8217786023128097380213750297)⟩,⟨(-22451408940915350985999182696),(-22451408940915350984605679605)⟩⟩,⟨⟨(-7751395450698644996027108643),(-7751395450698644995025865332)⟩,⟨(-21177206200866954639773351000),(-21177206200866954638458285158)⟩⟩] +lemma amp9_14_14_eq : ∀ k : Fin 16, amp9_1Expr 4 14 k = amp9_14_14 k := by decide +kernel +noncomputable def amp9_14_15 : Fin 16 → CBox := ![⟨⟨(-7291131255199261820373434234),(-7291131255199261819431836200)⟩,⟨(-19919741033857825216911935648),(-19919741033857825215675483966)⟩⟩,⟨⟨(-6821992474173491748570330495),(-6821992474173491747689726969)⟩,⟨(-18638030048294491404436371352),(-18638030048294491403280593803)⟩⟩,⟨⟨(-6360151401061098850879014593),(-6360151401061098850058621910)⟩,⟨(-17376256771529301486914557226),(-17376256771529301485838650047)⟩⟩,⟨⟨(-5888398725213949358531673273),(-5888398725213949357771760888)⟩,⟨(-16087404492508317922276527554),(-16087404492508317921279410685)⟩⟩,⟨⟨(-5425441185469606814982434510),(-5425441185469606814282238769)⟩,⟨(-14822580972179686270289383481),(-14822580972179686269370582220)⟩⟩,⟨⟨(-4951131303068236857883387366),(-4951131303068236857244589288)⟩,⟨(-13526742274927124258927144759),(-13526742274927124258089171507)⟩⟩,⟨⟨(-4487625400817782326692603947),(-4487625400817782326114139257)⟩,⟨(-12260420600370828857693229866),(-12260420600370828856935156714)⟩⟩,⟨⟨(-4010668238177036632886368061),(-4010668238177036632369100766)⟩,⟨(-10957349399002419234066276962),(-10957349399002419233387999583)⟩⟩,⟨⟨(-3547394144058060914064911568),(-3547394144058060913607695075)⟩,⟨(-9691661036038931554651822142),(-9691661036038931554052715303)⟩⟩,⟨⟨(-3067387839274413925859383352),(-3067387839274413925464246056)⟩,⟨(-8380259423416616152610294045),(-8380259423416616152092833378)⟩⟩,⟨⟨(-2605610421927042946907078489),(-2605610421927042946571795221)⟩,⟨(-7118660057435660782871402570),(-7118660057435660782432849096)⟩⟩,⟨⟨(-2121361682949658354910932497),(-2121361682949658354638195853)⟩,⟨(-5795667899048286741565633762),(-5795667899048286741209226102)⟩⟩,⟨⟨(-1663741155941996025562044779),(-1663741155941996025348609820)⟩,⟨(-4545425368676907652646322920),(-4545425368676907652368075144)⟩⟩,⟨⟨(-1171344964628820880015588732),(-1171344964628820879865616719)⟩,⟨(-3200173956555908093897032540),(-3200173956555908093701941060)⟩⟩,⟨⟨(-726611995767906115130378309),(-726611995767906115038338967)⟩,⟨(-1985140889826941552093891368),(-1985140889826941551975581097)⟩⟩,⟨⟨(-206433418803638677634588326),(-206433418803638677609036260)⟩,⟨(-563986588551685308337747155),(-563986588551685308305764901)⟩⟩] +lemma amp9_14_15_eq : ∀ k : Fin 16, amp9_1Expr 4 15 k = amp9_14_15 k := by decide +kernel +noncomputable def amp9_14 : Fin 16 → Fin 16 → CBox := ![amp9_14_0,amp9_14_1,amp9_14_2,amp9_14_3,amp9_14_4,amp9_14_5,amp9_14_6,amp9_14_7,amp9_14_8,amp9_14_9,amp9_14_10,amp9_14_11,amp9_14_12,amp9_14_13,amp9_14_14,amp9_14_15] +lemma amp9_14_eq (i k : Fin 16) : amp9_1Expr 4 i k = amp9_14 i k := by + fin_cases i + · exact amp9_14_0_eq k + · exact amp9_14_1_eq k + · exact amp9_14_2_eq k + · exact amp9_14_3_eq k + · exact amp9_14_4_eq k + · exact amp9_14_5_eq k + · exact amp9_14_6_eq k + · exact amp9_14_7_eq k + · exact amp9_14_8_eq k + · exact amp9_14_9_eq k + · exact amp9_14_10_eq k + · exact amp9_14_11_eq k + · exact amp9_14_12_eq k + · exact amp9_14_13_eq k + · exact amp9_14_14_eq k + · exact amp9_14_15_eq k +noncomputable def amp9_15_0 : Fin 16 → CBox := ![⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩] +lemma amp9_15_0_eq : ∀ k : Fin 16, amp9_1Expr 5 0 k = amp9_15_0 k := by decide +kernel +noncomputable def amp9_15_1 : Fin 16 → CBox := ![⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩] +lemma amp9_15_1_eq : ∀ k : Fin 16, amp9_1Expr 5 1 k = amp9_15_1 k := by decide +kernel +noncomputable def amp9_15_2 : Fin 16 → CBox := ![⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩] +lemma amp9_15_2_eq : ∀ k : Fin 16, amp9_1Expr 5 2 k = amp9_15_2 k := by decide +kernel +noncomputable def amp9_15_3 : Fin 16 → CBox := ![⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩] +lemma amp9_15_3_eq : ∀ k : Fin 16, amp9_1Expr 5 3 k = amp9_15_3 k := by decide +kernel +noncomputable def amp9_15_4 : Fin 16 → CBox := ![⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩] +lemma amp9_15_4_eq : ∀ k : Fin 16, amp9_1Expr 5 4 k = amp9_15_4 k := by decide +kernel +noncomputable def amp9_15_5 : Fin 16 → CBox := ![⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩] +lemma amp9_15_5_eq : ∀ k : Fin 16, amp9_1Expr 5 5 k = amp9_15_5 k := by decide +kernel +noncomputable def amp9_15_6 : Fin 16 → CBox := ![⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩] +lemma amp9_15_6_eq : ∀ k : Fin 16, amp9_1Expr 5 6 k = amp9_15_6 k := by decide +kernel +noncomputable def amp9_15_7 : Fin 16 → CBox := ![⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩] +lemma amp9_15_7_eq : ∀ k : Fin 16, amp9_1Expr 5 7 k = amp9_15_7 k := by decide +kernel +noncomputable def amp9_15_8 : Fin 16 → CBox := ![⟨⟨(-166228924),347935474⟩,⟨(-38552418737548597096812285730),(-38552418737548597095789166820)⟩⟩,⟨⟨(-166203851),347882993⟩,⟨(-38546603693548157834934227676),(-38546603693548157833907050273)⟩⟩,⟨⟨(-166153867),347778371⟩,⟨(-38535011250222245611822210374),(-38535011250222245610792453443)⟩⟩,⟨⟨(-166078663),347620960⟩,⟨(-38517569604370558561665604527),(-38517569604370558560634389475)⟩⟩,⟨⟨(-165978726),347411780⟩,⟨(-38494391733819021336295337115),(-38494391733819021335263159531)⟩⟩,⟨⟨(-165853435),347149534⟩,⟨(-38465333942404921042954517729),(-38465333942404921041922674284)⟩⟩,⟨⟨(-165703605),346835922⟩,⟨(-38430584672722504873315844544),(-38430584672722504872284138820)⟩⟩,⟨⟨(-165528303),346468997⟩,⟨(-38389928155694576734074096312),(-38389928155694576733043924631)⟩⟩,⟨⟨(-165328670),346051143⟩,⟨(-38343628518762467669352377395),(-38343628518762467668323380793)⟩⟩,⟨⟨(-165103463),345579759⟩,⟨(-38291397648932349304342564111),(-38291397648932349303314697520)⟩⟩,⟨⟨(-164854148),345057916⟩,⟨(-38233575668115257839254178908),(-38233575668115257838227532780)⟩⟩,⟨⟨(-164579170),344482356⟩,⟨(-38169801756047242383108177307),(-38169801756047242382085417276)⟩⟩,⟨⟨(-164280325),343856840⟩,⟨(-38100492429806577182518978198),(-38100492429806577181496731036)⟩⟩,⟨⟨(-163955741),343177450⟩,⟨(-38025213704398410461947533998),(-38025213704398410460929126446)⟩⟩,⟨⟨(-163607546),342448639⟩,⟨(-37944458985836275422300451893),(-37944458985836275421281826574)⟩⟩,⟨⟨(-163233550),341665825⟩,⟨(-37857720570597306432914647451),(-37857720570597306431901171000)⟩⟩] +lemma amp9_15_8_eq : ∀ k : Fin 16, amp9_1Expr 5 8 k = amp9_15_8 k := by decide +kernel +noncomputable def amp9_15_9 : Fin 16 → CBox := ![⟨⟨(-162836216),340834160⟩,⟨(-37765569342949880319857199248),(-37765569342949880318847851296)⟩⟩,⟨⟨(-162413033),339948392⟩,⟨(-37667423227983889637413595602),(-37667423227983889636409603823)⟩⟩,⟨⟨(-161966800),339014377⟩,⟨(-37563931276086673295157794793),(-37563931276086673294150686627)⟩⟩,⟨⟨(-161494683),338026185⟩,⟨(-37454436285787739077422075840),(-37454436285787739076421619142)⟩⟩,⟨⟨(-160999822),336990386⟩,⟨(-37339666263539208117909598451),(-37339666263539208116914600225)⟩⟩,⟨⟨(-160479055),335900363⟩,⟨(-37218888020009842725474275563),(-37218888020009842724483716609)⟩⟩,⟨⟨(-159935865),334763406⟩,⟨(-37092909413864254185080320622),(-37092909413864254184096648018)⟩⟩,⟨⟨(-159366759),333572205⟩,⟨(-36960920296065720305385474326),(-36960920296065720304407642462)⟩⟩,⟨⟨(-158775569),332334779⟩,⟨(-36823809384590225484663862329),(-36823809384590225483693136274)⟩⟩,⟨⟨(-158158466),331043113⟩,⟨(-36680688483235377566192407619),(-36680688483235377565230896826)⟩⟩,⟨⟨(-157519634),329705968⟩,⟨(-36532528292771231841914378420),(-36532528292771231840940587889)⟩⟩,⟨⟨(-156854903),328314612⟩,⟨(-36378361360970378297879200195),(-36378361360970378296913159730)⟩⟩,⟨⟨(-156168816),326878557⟩,⟨(-36219241617442961544653481021),(-36219241617442961543694235316)⟩⟩,⟨⟨(-155456855),325388344⟩,⟨(-36054121017113048633428610386),(-36054121017113048632478422676)⟩⟩,⟨⟨(-154723929),323854248⟩,⟨(-35884138094040676039355448132),(-35884138094040676038410728300)⟩⟩,⟨⟨(-153965164),322266071⟩,⟨(-35708162738087487970329722583),(-35708162738087487969394460791)⟩⟩] +lemma amp9_15_9_eq : ∀ k : Fin 16, amp9_1Expr 5 9 k = amp9_15_9 k := by decide +kernel +noncomputable def amp9_15_10 : Fin 16 → CBox := ![⟨⟨(-153185843),320634865⟩,⟨(-35527419600844671405176604829),(-35527419600844671404243523786)⟩⟩,⟨⟨(-152380730),318949675⟩,⟨(-35340694891126642208080493945),(-35340694891126642207155926208)⟩⟩,⟨⟨(-151555485),317222346⟩,⟨(-35149301037523642618950613738),(-35149301037523642618034179014)⟩⟩,⟨⟨(-150704505),315441152⟩,⟨(-34951938798604186338854197297),(-34951938798604186337944216119)⟩⟩,⟨⟨(-149833837),313618747⟩,⟨(-34750010195851482023887514177),(-34750010195851482022987110557)⟩⟩,⟨⟨(-148937501),311742616⟩,⟨(-34542128604544351020880288432),(-34542128604544351019987615746)⟩⟩,⟨⟨(-148021936),309826239⟩,⟨(-34329787622678162157100327172),(-34329787622678162156215842036)⟩⟩,⟨⟨(-147080780),307856295⟩,⟨(-34111511133387095184378466080),(-34111511133387095183503730902)⟩⟩,⟨⟨(-146120875),305847108⟩,⟨(-33888886475240507527344075920),(-33888886475240507526479431797)⟩⟩,⟨⟨(-145135461),303784528⟩,⟨(-33660345741090154093990824780),(-33660345741090154093137390519)⟩⟩,⟨⟨(-144131797),301683749⟩,⟨(-33427572368903866378536213210),(-33427572368903866377695675322)⟩⟩,⟨⟨(-143102716),299529769⟩,⟨(-33188904158653455315689711183),(-33188904158653455314800669121)⟩⟩,⟨⟨(-142055902),297338672⟩,⟨(-32946123217430973331649758326),(-32946123217430973330770643230)⟩⟩,⟨⟨(-140983770),295094580⟩,⟨(-32697470328155163685602778415),(-32697470328155163684733365206)⟩⟩,⟨⟨(-139894440),292814494⟩,⟨(-32444829065879675049233862424),(-32444829065879675048374604173)⟩⟩,⟨⟨(-138779898),290481633⟩,⟨(-32186340231392153201543878871),(-32186340231392153200693983553)⟩⟩] +lemma amp9_15_10_eq : ∀ k : Fin 16, amp9_1Expr 5 10 k = amp9_15_10 k := by decide +kernel +noncomputable def amp9_15_11 : Fin 16 → CBox := ![⟨⟨(-137648714),288113940⟩,⟨(-31923991916236710246206100476),(-31923991916236710245365811487)⟩⟩,⟨⟨(-136492427),285693704⟩,⟨(-31655821711220961597811626840),(-31655821711220961596980081377)⟩⟩,⟨⟨(-135320075),283239842⟩,⟨(-31383925545900440190560372748),(-31383925545900440189739784268)⟩⟩,⟨⟨(-134122736),280733679⟩,⟨(-31106234285698202319415522566),(-31106234285698202318602498743)⟩⟩,⟨⟨(-132909927),278195138⟩,⟨(-30824955319131378739518906154),(-30824955319131378738716923607)⟩⟩,⟨⟨(-131672251),275604545⟩,⟨(-30537908955121911916393395102),(-30537908955121911915601617906)⟩⟩,⟨⟨(-130419723),272982865⟩,⟨(-30247417991595653885221719827),(-30247417991595653884441907750)⟩⟩,⟨⟨(-129142449),270309390⟩,⟨(-29951188002077299329758006275),(-29951188002077299328981032978)⟩⟩,⟨⟨(-127850962),267606164⟩,⟨(-29651661508133253728759341807),(-29651661508133253727994051847)⟩⟩,⟨⟨(-126534853),264851404⟩,⟨(-29346424784591707850981833895),(-29346424784591707850227776128)⟩⟩,⟨⟨(-125205191),262068275⟩,⟨(-29038044793890211751628769227),(-29038044793890211750884079648)⟩⟩,⟨⟨(-123851033),259233873⟩,⟨(-28723983522504130805296836586),(-28723983522504130804564527001)⟩⟩,⟨⟨(-122484006),256372534⟩,⟨(-28406937538961959617180064545),(-28406937538961959616459253763)⟩⟩,⟨⟨(-121092606),253460181⟩,⟨(-28084239077154113068539367478),(-28084239077154113067830524662)⟩⟩,⟨⟨(-119689045),250522372⟩,⟨(-27758719976704175665783365902),(-27758719976704175665087755036)⟩⟩,⟨⟨(-118261233),247533805⟩,⟨(-27427576724493021403336566760),(-27427576724493021402655439889)⟩⟩] +lemma amp9_15_11_eq : ∀ k : Fin 16, amp9_1Expr 5 11 k = amp9_15_11 k := by decide +kernel +noncomputable def amp9_15_12 : Fin 16 → CBox := ![⟨⟨(-116821992),244521315⟩,⟨(-27093782655877928084214447462),(-27093782655877928083513954461)⟩⟩,⟨⟨(-115358619),241458314⟩,⟨(-26754391921717071433478136797),(-26754391921717071432787546312)⟩⟩,⟨⟨(-113884575),238372977⟩,⟨(-26412526206808221628059881494),(-26412526206808221627379548549)⟩⟩,⟨⟨(-112386513),235237367⟩,⟨(-26065090067515605574883979334),(-26065090067515605574213588044)⟩⟩,⟨⟨(-110878564),232081064⟩,⟨(-25715361101749847688074466191),(-25715361101749847687414306851)⟩⟩,⟨⟨(-109346703),228874709⟩,⟨(-25360086256019165709858280868),(-25360086256019165709207599499)⟩⟩,⟨⟨(-107805769),225649366⟩,⟨(-25002707409672597434287090576),(-25002707409672597433647910394)⟩⟩,⟨⟨(-106241020),222374173⟩,⟨(-24639805024518844204859238254),(-24639805024518844204227109031)⟩⟩,⟨⟨(-104668043),219081760⟩,⟨(-24274994545700667020660905516),(-24274994545700667020040608695)⟩⟩,⟨⟨(-103071335),215739673⟩,⟨(-23904680095009751316942156220),(-23904680095009751316332657018)⟩⟩,⟨⟨(-101467277),212382202⟩,⟨(-23532661015470212555247011612),(-23532661015470212554649229183)⟩⟩,⟨⟨(-99839556),208975203⟩,⟨(-23155154109585114316857604795),(-23155154109585114316271837580)⟩⟩,⟨⟨(-98205398),205554729⟩,⟨(-22776154154706997819765346066),(-22776154154706997819193364242)⟩⟩,⟨⟨(-96547629),202084836⟩,⟨(-22391678359670523839222702368),(-22391678359670523838644069718)⟩⟩,⟨⟨(-94884373),198603457⟩,⟨(-22005929864376524720595111927),(-22005929864376524720029031310)⟩⟩,⟨⟨(-93197536),195072722⟩,⟨(-21614712509035809766679699813),(-21614712509035809766125925979)⟩⟩] +lemma amp9_15_12_eq : ∀ k : Fin 16, amp9_1Expr 5 12 k = amp9_15_12 k := by decide +kernel +noncomputable def amp9_15_13 : Fin 16 → CBox := ![⟨⟨(-91506202),191532575⟩,⟨(-21222452341827216679158421985),(-21222452341827216678616534821)⟩⟩,⟨⟨(-89791293),187943080⟩,⟨(-20824724310448551711402478031),(-20824724310448551710870089307)⟩⟩,⟨⟨(-88072924),184346344⟩,⟨(-20426193808440952720868306338),(-20426193808440952720349410876)⟩⟩,⟨⟨(-86330952),180700204⟩,⟨(-20022189315728738362596154328),(-20022189315728738362089369063)⟩⟩,⟨⟨(-84586606),177049096⟩,⟨(-19617634234436279720360082155),(-19617634234436279719867227725)⟩⟩,⟨⟨(-82818594),173348453⟩,⟨(-19207590578814079552033561895),(-19207590578814079551541662720)⟩⟩,⟨⟨(-81049350),169645230⟩,⟨(-18797261061655928396826575182),(-18797261061655928396346869929)⟩⟩,⟨⟨(-79256335),165892251⟩,⟨(-18381418351227587809834007742),(-18381418351227587809366682554)⟩⟩,⟨⟨(-77463290),162139211⟩,⟨(-17965568925439762165621762712),(-17965568925439762165166524179)⟩⟩,⟨⟨(-75646317),158336084⟩,⟨(-17544169769018200423454539707),(-17544169769018200423010161430)⟩⟩,⟨⟨(-73830588),154535564⟩,⟨(-17123059377081258097663166231),(-17123059377081258097230977660)⟩⟩,⟨⟨(-71990712),150684500⟩,⟨(-16696348529765272279530401806),(-16696348529765272279102136679)⟩⟩,⟨⟨(-70153435),146838877⟩,⟨(-16270240608961625265709305074),(-16270240608961625265294780204)⟩⟩,⟨⟨(-68291719),142942100⟩,⟨(-15838464557506970187079278976),(-15838464557506970186677574998)⟩⟩,⟨⟨(-66434050),139053794⟩,⟨(-15407627185369045845520137725),(-15407627185369045845130620205)⟩⟩,⟨⟨(-64551562),135113538⟩,⟨(-14971033652317385873514733171),(-14971033652317385873138510918)⟩⟩] +lemma amp9_15_13_eq : ∀ k : Fin 16, amp9_1Expr 5 13 k = amp9_15_13 k := by decide +kernel +noncomputable def amp9_15_14 : Fin 16 → CBox := ![⟨⟨(-62674677),131185012⟩,⟨(-14535739783441810130764257513),(-14535739783441810130394786237)⟩⟩,⟨⟨(-60772488),127203520⟩,⟨(-14094577119453890023734041014),(-14094577119453890023377207365)⟩⟩,⟨⟨(-58877588),123237285⟩,⟨(-13655104950972463001537335238),(-13655104950972463001192242290)⟩⟩,⟨⟨(-56956768),119216797⟩,⟨(-13209621370059014536027256946),(-13209621370059014535696221409)⟩⟩,⟨⟨(-55045076),115215416⟩,⟨(-12766254891602009638066114025),(-12766254891602009637742878385)⟩⟩,⟨⟨(-53106691),111158161⟩,⟨(-12316697480480254772224171367),(-12316697480480254771913680609)⟩⟩,⟨⟨(-51179461),107124257⟩,⟨(-11869727294381481877340271590),(-11869727294381481877038935074)⟩⟩,⟨⟨(-49224565),103032444⟩,⟨(-11416340688760420329118078663),(-11416340688760420328829965462)⟩⟩,⟨⟨(-47283084),98968709⟩,⟨(-10966065236024010114324986929),(-10966065236024010114049543382)⟩⟩,⟨⟨(-45312714),94844507⟩,⟨(-10509089791589342673087756908),(-10509089791589342672822370540)⟩⟩,⟨⟨(-43358309),90753723⟩,⟨(-10055817204924139266146786541),(-10055817204924139265894641687)⟩⟩,⟨⟨(-41373471),86599239⟩,⟨(-9595486376480452818844853103),(-9595486376480452818603321111)⟩⟩,⟨⟨(-39407527),82484300⟩,⟨(-9139537335716977438389422095),(-9139537335716977438158387694)⟩⟩,⟨⟨(-37409181),78301542⟩,⟨(-8676073767988110570488445658),(-8676073767988110570270705539)⟩⟩,⟨⟨(-35433153),74165497⟩,⟨(-8217786023128097380917360475),(-8217786023128097380710736781)⟩⟩,⟨⟨(-33422187),69956323⟩,⟨(-7751395450698644995689780636),(-7751395450698644995494645945)⟩⟩] +lemma amp9_15_14_eq : ∀ k : Fin 16, amp9_1Expr 5 14 k = amp9_15_14 k := by decide +kernel +noncomputable def amp9_15_15 : Fin 16 → CBox := ![⟨⟨(-31437636),65802440⟩,⟨(-7291131255199261820056136170),(-7291131255199261819872781447)⟩⟩,⟨⟨(-29414821),61568464⟩,⟨(-6821992474173491748273448581),(-6821992474173491748102300141)⟩⟩,⟨⟨(-27423471),57400349⟩,⟨(-6360151401061098850602231244),(-6360151401061098850443264352)⟩⟩,⟨⟨(-25389385),53142783⟩,⟨(-5888398725213949358275419826),(-5888398725213949358127873175)⟩⟩,⟨⟨(-23393221),48964592⟩,⟨(-5425441185469606814746328215),(-5425441185469606814610352805)⟩⟩,⟨⟨(-21348109),44683947⟩,⟨(-4951131303068236857667922258),(-4951131303068236857544018517)⟩⟩,⟨⟨(-19349581),40500807⟩,⟨(-4487625400817782326497309856),(-4487625400817782326385537071)⟩⟩,⟨⟨(-17293055),36196270⟩,⟨(-4010668238177036632711830363),(-4010668238177036632611653675)⟩⟩,⟨⟨(-15295526),32015223⟩,⟨(-3547394144058060913910534797),(-3547394144058060913822230588)⟩⟩,⟨⟨(-13225852),27683167⟩,⟨(-3067387839274413925725895668),(-3067387839274413925649752261)⟩⟩,⟨⟨(-11234777),23515627⟩,⟨(-2605610421927042946793686601),(-2605610421927042946729374544)⟩⟩,⟨⟨(-9146811),19145284⟩,⟨(-2121361682949658354818614318),(-2121361682949658354766489298)⟩⟩,⟨⟨(-7173659),15015260⟩,⟨(-1663741155941996025489641495),(-1663741155941996025449227780)⟩⟩,⟨⟨(-5050563),10571386⟩,⟨(-1171344964628820879964613722),(-1171344964628820879936456068)⟩⟩,⟨⟨(-3132980),6557672⟩,⟨(-726611995767906115098757348),(-726611995767906115082282231)⟩⟩,⟨⟨(-890093),1863062⟩,⟨(-206433418803638677625604682),(-206433418803638677621520720)⟩⟩] +lemma amp9_15_15_eq : ∀ k : Fin 16, amp9_1Expr 5 15 k = amp9_15_15 k := by decide +kernel +noncomputable def amp9_15 : Fin 16 → Fin 16 → CBox := ![amp9_15_0,amp9_15_1,amp9_15_2,amp9_15_3,amp9_15_4,amp9_15_5,amp9_15_6,amp9_15_7,amp9_15_8,amp9_15_9,amp9_15_10,amp9_15_11,amp9_15_12,amp9_15_13,amp9_15_14,amp9_15_15] +lemma amp9_15_eq (i k : Fin 16) : amp9_1Expr 5 i k = amp9_15 i k := by + fin_cases i + · exact amp9_15_0_eq k + · exact amp9_15_1_eq k + · exact amp9_15_2_eq k + · exact amp9_15_3_eq k + · exact amp9_15_4_eq k + · exact amp9_15_5_eq k + · exact amp9_15_6_eq k + · exact amp9_15_7_eq k + · exact amp9_15_8_eq k + · exact amp9_15_9_eq k + · exact amp9_15_10_eq k + · exact amp9_15_11_eq k + · exact amp9_15_12_eq k + · exact amp9_15_13_eq k + · exact amp9_15_14_eq k + · exact amp9_15_15_eq k +noncomputable def amp9_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![amp9_10,amp9_11,amp9_12,amp9_13,amp9_14,amp9_15] +lemma amp9_1_eq (j : Fin 6) (i k : Fin 16) : amp9_1Expr j i k = amp9_1 j i k := by + fin_cases j + · exact amp9_10_eq i k + · exact amp9_11_eq i k + · exact amp9_12_eq i k + · exact amp9_13_eq i k + · exact amp9_14_eq i k + · exact amp9_15_eq i k +lemma amp9_1_contains (j : Fin 6) (i k : Fin 16) : + (amp9_1 j i k).Contains ((fejerWeight (16*i.val+k.val):ℂ)*waveAmplitude true 9 j.val (quadraturePoint j.val (16*i.val+k.val))) := by + rw [← amp9_1_eq] + exact CBox.contains_mul (rcast_contains (weightRows_contains i k)) + (waveAmplitudeBox_contains (gridRows_contains j i k) (aLookup_contains 9 j) (bLookup_contains 9 j) true) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/AtomKernels.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/AtomKernels.lean new file mode 100644 index 0000000000000000000000000000000000000000..a6f61b3c8f582bbf100c497bff54afcf224dc68d --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/AtomKernels.lean @@ -0,0 +1,1388 @@ +import OAI.Analysis.PlanarPacking.MomentRecurrence +import OAI.Analysis.PlanarPacking.Grid + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid +noncomputable def atomPoint0 : PointBox := ⟨⟨0,0⟩,⟨⟨2886751345948128822491487805010,2886751345948128822591487805032⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨2933333333333333333333333333333,2933333333333333333333333333334⟩⟩,⟨⟨999999999999999999999999999989,1000000000000000000000000000015⟩,⟨(-15),15⟩⟩,⟨⟨99875126068614995128859923084,99875126068614995129850328303⟩,⟨(-2),2⟩⟩⟩ +lemma atomPoint0_contains : atomPoint0.Contains (0/6:ℝ) := by + have ht : atomPoint0.t.Contains (0/6:ℝ) := by + convert RBox.contains_rat 0 6 (by norm_num) using 1 <;> norm_num [atomPoint0] + decide +kernel + have he : PointBox.calc atomPoint0.t = atomPoint0 := by decide +kernel + rw [← he] + exact PointBox.calc_contains ht (by decide +kernel) +noncomputable def atomPoint1 : PointBox := ⟨⟨166666666666666666666666666666,166666666666666666666666666667⟩,⟨⟨2459717123174736984844818011358,2459717123174736984930025111996⟩,⟨1024882134656140410352007504727,1024882134656140410387510463337⟩⟩,⟨⟨(-1183431952662721893491124260363),(-1183431952662721893491124260348)⟩,⟨2440236686390532544378698224848,2440236686390532544378698224864⟩⟩,⟨⟨866025403784438646763098939526,866025403784438646763954632529⟩,⟨(-500000000000000000001210408427),(-499999999999999999999469888220)⟩⟩,⟨⟨88011921021907828079523012267,88011921021907828081313061486⟩,⟨(-117881300351469008776578899699),(-117881300351469008774941580239)⟩⟩⟩ +lemma atomPoint1_contains : atomPoint1.Contains (1/6:ℝ) := by + have ht : atomPoint1.t.Contains (1/6:ℝ) := by + convert RBox.contains_rat 1 6 (by norm_num) using 1 <;> norm_num [atomPoint1] + decide +kernel + have he : PointBox.calc atomPoint1.t = atomPoint1 := by decide +kernel + rw [← he] + exact PointBox.calc_contains ht (by decide +kernel) +noncomputable def atomPoint2 : PointBox := ⟨⟨333333333333333333333333333333,333333333333333333333333333334⟩,⟨⟨1703656532034961272290058376722,1703656532034961272349074770188⟩,⟨1419713776695801060241715313933,1419713776695801060290895641830⟩⟩,⟨⟨(-1639344262295081967213114754110),(-1639344262295081967213114754090)⟩,⟨1567213114754098360655737704910,1567213114754098360655737704927⟩⟩,⟨⟨499999999999999999997708137538,500000000000000000000931269165⟩,⟨(-866025403784438646766051325440),(-866025403784438646762180554973)⟩⟩,⟨⟨81619205305569481307151807559,81619205305569481310396378569⟩,⟨(-280396055793447804630865756591),(-280396055793447804627615754177)⟩⟩⟩ +lemma atomPoint2_contains : atomPoint2.Contains (2/6:ℝ) := by + have ht : atomPoint2.t.Contains (2/6:ℝ) := by + convert RBox.contains_rat 2 6 (by norm_num) using 1 + norm_num [atomPoint2] + decide +kernel + have he : PointBox.calc atomPoint2.t = atomPoint2 := by decide +kernel + rw [← he] + exact PointBox.calc_contains ht (by decide +kernel) +noncomputable def atomPoint3 : PointBox := ⟨⟨500000000000000000000000000000,500000000000000000000000000000⟩,⟨⟨1126537110613903930728385484882,1126537110613903930767409875134⟩,⟨1408171388267379913410481856103,1408171388267379913459262343918⟩⟩,⟨⟨(-1626016260162601626016260162603),(-1626016260162601626016260162601)⟩,⟨900813008130081300813008130080,900813008130081300813008130083⟩⟩,⟨⟨(-4444983321),2088366603⟩,⟨(-1000000000000000000003266674962),(-999999999999999999996733325039)⟩⟩,⟨⟨142697957066396950735325887717,142697957066396950739297566444⟩,⟨(-471767338116830861279282785979),(-471767338116830861275221116079)⟩⟩⟩ +lemma atomPoint3_contains : atomPoint3.Contains (3/6:ℝ) := by + have ht : atomPoint3.t.Contains (3/6:ℝ) := by + convert RBox.contains_rat 3 6 (by norm_num) using 1 + norm_num [atomPoint3] + decide +kernel + have he : PointBox.calc atomPoint3.t = atomPoint3 := by decide +kernel + rw [← he] + exact PointBox.calc_contains ht (by decide +kernel) +noncomputable def atomPoint4 : PointBox := ⟨⟨666666666666666666666666666666,666666666666666666666666666667⟩,⟨⟨764140062162739982424217360149,764140062162739982450687948391⟩,⟨1273566770271233304040362266913,1273566770271233304084479913987⟩⟩,⟨⟨(-1470588235294117647058823529418),(-1470588235294117647058823529408)⟩,⟨482352941176470588235294117645,482352941176470588235294117651⟩⟩,⟨⟨(-500000000000000000006328835244),(-499999999999999999996392351351)⟩,⟨(-866025403784438646767669145432),(-866025403784438646758206118258)⟩⟩,⟨⟨276546840654658619933702465609,276546840654658619937500463543⟩,⟨(-626318886933968865987490837754),(-626318886933968865983439240032)⟩⟩⟩ +lemma atomPoint4_contains : atomPoint4.Contains (4/6:ℝ) := by + have ht : atomPoint4.t.Contains (4/6:ℝ) := by + convert RBox.contains_rat 4 6 (by norm_num) using 1 + norm_num [atomPoint4] + decide +kernel + have he : PointBox.calc atomPoint4.t = atomPoint4 := by decide +kernel + rw [← he] + exact PointBox.calc_contains ht (by decide +kernel) +noncomputable def atomPoint5 : PointBox := ⟨⟨833333333333333333333333333333,833333333333333333333333333334⟩,⟨⟨540562020567660013574478860754,540562020567660013593204478445⟩,⟨1126170876182625028280164293239,1126170876182625028319175996763⟩⟩,⟨⟨(-1300390117035110533159947984400),(-1300390117035110533159947984390)⟩,⟨224187256176853055916775032508,224187256176853055916775032512⟩⟩,⟨⟨(-866025403784438646770926677365),(-866025403784438646758483511404)⟩,⟨(-500000000000000000004285885012),(-499999999999999999992312631744)⟩⟩,⟨⟨437924188962394509423764780759,437924188962394509426958319345⟩,⟨(-715119061161322533370337011021),(-715119061161322533366664758504)⟩⟩⟩ +lemma atomPoint5_contains : atomPoint5.Contains (5/6:ℝ) := by + have ht : atomPoint5.t.Contains (5/6:ℝ) := by + convert RBox.contains_rat 5 6 (by norm_num) using 1 + norm_num [atomPoint5] + decide +kernel + have he : PointBox.calc atomPoint5.t = atomPoint5 := by decide +kernel + rw [← he] + exact PointBox.calc_contains ht (by decide +kernel) +noncomputable def atomPoint6 : PointBox := ⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨⟨398172599441121216895377628277,398172599441121216909170731728⟩,⟨995431498602803042238444070694,995431498602803042272926829319⟩⟩,⟨⟨(-1149425287356321839080459770116),(-1149425287356321839080459770114)⟩,⟨59770114942528735632183908045,59770114942528735632183908047⟩⟩,⟨⟨(-1000000000000000000006553197785),(-999999999999999999993446802219)⟩,⟨(-4196581061),8909814505⟩⟩,⟨⟨591041363234240777970266834369,591041363234240777972775244344⟩,⟨(-749036735415657815476580310485),(-749036735415657815473358766432)⟩⟩⟩ +lemma atomPoint6_contains : atomPoint6.Contains (6/6:ℝ) := by + have ht : atomPoint6.t.Contains (6/6:ℝ) := by + convert RBox.contains_rat 6 6 (by norm_num) using 1 + norm_num [atomPoint6] + decide +kernel + have he : PointBox.calc atomPoint6.t = atomPoint6 := by decide +kernel + rw [← he] + exact PointBox.calc_contains ht (by decide +kernel) +noncomputable def atomPoints : Fin 7 → PointBox := ![atomPoint0,atomPoint1,atomPoint2,atomPoint3,atomPoint4,atomPoint5,atomPoint6] +lemma atomPoints_contains (j : Fin 7) : (atomPoints j).Contains ((j.val:ℝ)/6) := by + fin_cases j + · simpa [atomPoints] using atomPoint0_contains + · simpa [atomPoints] using atomPoint1_contains + · simpa [atomPoints] using atomPoint2_contains + · simpa [atomPoints] using atomPoint3_contains + · simpa [atomPoints] using atomPoint4_contains + · simpa [atomPoints] using atomPoint5_contains + · simpa [atomPoints] using atomPoint6_contains +noncomputable def atomKernel0_0 : Fin 7 → CBox := ![⟨⟨2886751345948128822491487805010,2886751345948128822591487805032⟩,⟨0,0⟩⟩,⟨⟨2459717123174736984844818011358,2459717123174736984930025111996⟩,⟨1024882134656140410352007504727,1024882134656140410387510463337⟩⟩,⟨⟨1703656532034961272290058376722,1703656532034961272349074770188⟩,⟨1419713776695801060241715313933,1419713776695801060290895641830⟩⟩,⟨⟨1126537110613903930728385484882,1126537110613903930767409875134⟩,⟨1408171388267379913410481856103,1408171388267379913459262343918⟩⟩,⟨⟨764140062162739982424217360149,764140062162739982450687948391⟩,⟨1273566770271233304040362266913,1273566770271233304084479913987⟩⟩,⟨⟨540562020567660013574478860754,540562020567660013593204478445⟩,⟨1126170876182625028280164293239,1126170876182625028319175996763⟩⟩,⟨⟨398172599441121216895377628277,398172599441121216909170731728⟩,⟨995431498602803042238444070694,995431498602803042272926829319⟩⟩] +lemma atomKernel0_0_eq (j : Fin 7) : atomKernel0_0 j = kernel0Box (atomPoints j) 0 := by + fin_cases j <;> decide +kernel +lemma atomKernel0_0_contains (j : Fin 7) : (atomKernel0_0 j).Contains + (complexTransformedFactor 0 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel0_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=0) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel0_1 : Fin 7 → CBox := ![⟨⟨(-26602390675435195142530321043993),(-26602390675435195141524109159245)⟩,⟨0,0⟩⟩,⟨⟨(-15046386883137311960977771542034),(-15046386883137311960120407568771)⟩,⟨(-17001868484744399809876351294364),(-17001868484744399809233270664782)⟩⟩,⟨⟨(-1076288362329791189253868592463),(-1076288362329791188660038627375)⟩,⟨(-15764114872167322034205686079730),(-15764114872167322033609422385277)⟩⟩,⟨⟨4005248804305423355782453862022,4005248804305423356175121914620⟩,⟨(-9739775289205357801899857956194),(-9739775289205357801531459575359)⟩⟩,⟨⟨4725920142797114330304028335327,4725920142797114330570378540195⟩,⟨(-5460226459805430899811586813878),(-5460226459805430899605058580158)⟩⟩,⟨⟨4220020865203592699679309874866,4220020865203592699867729265570⟩,⟨(-3001523701832900019824858424479),(-3001523701832900019711328446699)⟩⟩,⟨⟨3519762856635247957323462123219,3519762856635247957462249969389⟩,⟨(-1624727135620028673173671104732),(-1624727135620028673112217238669)⟩⟩] +lemma atomKernel0_1_eq (j : Fin 7) : atomKernel0_1 j = (kernel0Box (atomPoints j) 0).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel0_1_contains (j : Fin 7) : (atomKernel0_1 j).Contains + (complexTransformedFactor 0 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel0_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=0) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel1_0 : Fin 7 → CBox := ![⟨⟨287235913262267589131245569,287235913262267589152589145⟩,⟨(-3),3⟩⟩,⟨⟨(-1227594407139841125053370123),(-1227594407139841124878361402)⟩,⟨225258927663398569617556379,225258927663398569785347626⟩⟩,⟨⟨(-4099475087999640329578559768),(-4099475087999640327343491894)⟩,⟨15600083655785914278280280272,15600083655785914280549783452⟩⟩,⟨⟨(-51036477369635067913459257139),(-51036477369635067901487188489)⟩,⟨93385323635182926762172010361,93385323635182926773837146635⟩⟩,⟨⟨(-294139142057855203281176399137),(-294139142057855203251857742481)⟩,⟨141367692329865808421293419379,141367692329865808447103276276⟩⟩,⟨⟨(-607731118347857408150380104706),(-607731118347857408104316711950)⟩,⟨(-110320451301813891842385438936),(-110320451301813891798653618696)⟩⟩,⟨⟨(-667529588463563842466349351680),(-667529588463563842419653782517)⟩,⟨(-586481159748591935787351906668),(-586481159748591935733302259315)⟩⟩] +lemma atomKernel1_0_eq (j : Fin 7) : atomKernel1_0 j = kernel0Box (atomPoints j) 1 := by + fin_cases j <;> decide +kernel +lemma atomKernel1_0_contains (j : Fin 7) : (atomKernel1_0 j).Contains + (complexTransformedFactor 1 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel1_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=1) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel1_1 : Fin 7 → CBox := ![⟨⟨(-2646976155858891764422936308),(-2646976155858891764217822444)⟩,⟨(-28),28⟩⟩,⟨⟨10248502049497462764170562060,10248502049497462766168665657⟩,⟨2837138858378663619951611366,2837138858378663621908620316⟩⟩,⟨⟨100526751266157010641267391192,100526751266157010664280121597⟩,⟨(-55694797749507294492877899648),(-55694797749507294469881268035)⟩⟩,⟨⟨621471044354675043360749079671,621471044354675043456196879347⟩,⟨(-3570646982377401830921203437),(-3570646982377401735081237023)⟩⟩,⟨⟨1098842859300173353297675724200,1098842859300173353464842925351⟩,⟨1144697213258281395037408564524,1144697213258281395216979041672⟩⟩,⟨⟨(-22663614851943702239959505301),(-22663614851943702026062341800)⟩,⟨2560460779786166905954461002828,2560460779786166906181594339863⟩⟩,⟨⟨(-1992454469280585019061246880751),(-1992454469280585018850163867175)⟩,⟨2520592259912149515844324457216,2520592259912149516031115751282⟩⟩] +lemma atomKernel1_1_eq (j : Fin 7) : atomKernel1_1 j = (kernel0Box (atomPoints j) 1).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel1_1_contains (j : Fin 7) : (atomKernel1_1 j).Contains + (complexTransformedFactor 1 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel1_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=1) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel3_0 : Fin 7 → CBox := ![⟨⟨2843789610077025929,2843789610077025936⟩,⟨(-3),3⟩⟩,⟨⟨(-64228312723007910724),(-64228312723007910558)⟩,⟨266166603357464236131,266166603357464236302⟩⟩,⟨⟨(-494776904616736031147973),(-494776904616736030744849)⟩,⟨(-695181898442626142129027),(-695181898442626141728600)⟩⟩,⟨⟨(-106555917680778035558591732),(-106555917680778035421458844)⟩,⟨(-354976034124043666142003790),(-354976034124043666003755425)⟩⟩,⟨⟨15213751127784570539427089845,15213751127784570544253007311⟩,⟨(-4099688160756901354180537737),(-4099688160756901349483904669)⟩⟩,⟨⟨20629052952773211972690043554,20629052952773211997040008897⟩,⟨149592350264871972775750070482,149592350264871972801712808839⟩⟩,⟨⟨(-595922937275834702091915645087),(-595922937275834701979420127280)⟩,⟨132015435447815391188745737182,132015435447815391291484111950⟩⟩] +lemma atomKernel3_0_eq (j : Fin 7) : atomKernel3_0 j = kernel0Box (atomPoints j) 3 := by + fin_cases j <;> decide +kernel +lemma atomKernel3_0_contains (j : Fin 7) : (atomKernel3_0 j).Contains + (complexTransformedFactor 3 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel3_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=3) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel3_1 : Fin 7 → CBox := ![⟨⟨(-26206483738960704163),(-26206483738960704098)⟩,⟨(-28),28⟩⟩,⟨⟨1481959463502825266027,1481959463502825267941⟩,⟨(-1801702358473668140785),(-1801702358473668138848)⟩⟩,⟨⟨(-1144235911228454129864486),(-1144235911228454125798275)⟩,⟨5970935715710382851586040,5970935715710382855652717⟩⟩,⟨⟨(-1511765319270662542217988349),(-1511765319270662541116960688)⟩,⟨1548895291282867661132607122,1548895291282867662229291849⟩⟩,⟨⟨(-41994771009654300602998834631),(-41994771009654300573853781897)⟩,⟨(-64074876924145524496005170041),(-64074876924145524466348903640)⟩⟩,⟨⟨596599890019863798301114245875,596599890019863798426321053128⟩,⟨(-189634434098775036919004515716),(-189634434098775036800638386208)⟩⟩,⟨⟨588609623562744722558957134694,588609623562744722952945344464⟩,⟨2127104262412552993036337815244,2127104262412552993468782183206⟩⟩] +lemma atomKernel3_1_eq (j : Fin 7) : atomKernel3_1 j = (kernel0Box (atomPoints j) 3).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel3_1_contains (j : Fin 7) : (atomKernel3_1 j).Contains + (complexTransformedFactor 3 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel3_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=3) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel4_0 : Fin 7 → CBox := ![⟨⟨282961158716610,282961158716614⟩,⟨(-3),3⟩⟩,⟨⟨(-42706143494991529),(-42706143494991525)⟩,⟨(-120926048035417579),(-120926048035417575)⟩⟩,⟨⟨3053947772385296866737,3053947772385296871889⟩,⟨(-5402739214956985245174),(-5402739214956985240000)⟩⟩,⟨⟨16903170382964137658517564,16903170382964137671935629⟩,⟨(-13880229317351426973322715),(-13880229317351426960021447)⟩⟩,⟨⟨588535793916102761833935025,588535793916102762958836647⟩,⟨3411772456086199165686422228,3411772456086199166834991902⟩⟩,⟨⟨(-65878528817845185855981007311),(-65878528817845185832427874592)⟩,⟨(-35143520097970271640063878406),(-35143520097970271616257367065)⟩⟩,⟨⟨390977274694468298190061327583,390977274694468298307974382443⟩,⟨(-321010859534684108975007802739),(-321010859534684108863412052127)⟩⟩] +lemma atomKernel4_0_eq (j : Fin 7) : atomKernel4_0 j = kernel0Box (atomPoints j) 4 := by + fin_cases j <;> decide +kernel +lemma atomKernel4_0_contains (j : Fin 7) : (atomKernel4_0 j).Contains + (complexTransformedFactor 4 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel4_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=4) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel4_1 : Fin 7 → CBox := ![⟨⟨(-2607582845927753),(-2607582845927715)⟩,⟨(-28),28⟩⟩,⟨⟨(-122191150045355554),(-122191150045355508)⟩,⟨1085822365390366632,1085822365390366679⟩⟩,⟨⟨(-42861177505166100888659),(-42861177505166100836508)⟩,⟨10872335876083759744346,10872335876083759796489⟩⟩,⟨⟨(-118739869432107462448785546),(-118739869432107462342488016)⟩,⟨(-47065263808519467727174204),(-47065263808519467620588654)⟩⟩,⟨⟨14870510372727659189857152835,14870510372727659196921171202⟩,⟨(-7889080428845410359742320073),(-7889080428845410352779682537)⟩⟩,⟨⟨(-97173103755644446269075637291),(-97173103755644446154625706676)⟩,⟨293885051024413729859965615305,293885051024413729973889646122⟩⟩,⟨⟨(-1232593686666143723165478075673),(-1232593686666143722736438517056)⟩,⟨(-1351551833658380839059320879344),(-1351551833658380838607893199339)⟩⟩] +lemma atomKernel4_1_eq (j : Fin 7) : atomKernel4_1 j = (kernel0Box (atomPoints j) 4).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel4_1_contains (j : Fin 7) : (atomKernel4_1 j).Contains + (complexTransformedFactor 4 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel4_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=4) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel7_0 : Fin 7 → CBox := ![⟨⟨277,281⟩,⟨(-3),3⟩⟩,⟨⟨11580277,11580282⟩,⟨(-6288733),(-6288728)⟩⟩,⟨⟨(-1665710323167166),(-1665710323167162)⟩,⟨1710986465904294,1710986465904298⟩⟩,⟨⟨(-4288482058811659370282),(-4288482058811659363575)⟩,⟨1347241831520230599839,1347241831520230606532⟩⟩,⟨⟨36521831631557482951131335,36521831631557482985427878⟩,⟨3899877544961305718935797,3899877544961305753146455⟩⟩,⟨⟨(-6285013554969111273878743515),(-6285013554969111268462701209)⟩,⟨(-6478261771340776764017300108),(-6478261771340776758509615976)⟩⟩,⟨⟨144338024383918188411416917775,144338024383918188519066263138⟩,⟨249223963933666164018182252952,249223963933666164130533379093⟩⟩] +lemma atomKernel7_0_eq (j : Fin 7) : atomKernel7_0 j = kernel0Box (atomPoints j) 7 := by + fin_cases j <;> decide +kernel +lemma atomKernel7_0_contains (j : Fin 7) : (atomKernel7_0 j).Contains + (complexTransformedFactor 7 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel7_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=7) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel7_1 : Fin 7 → CBox := ![⟨⟨(-2590),(-2552)⟩,⟨(-28),28⟩⟩,⟨⟨(-112157738),(-112157680)⟩,⟨5156952,5157010⟩⟩,⟨⟨17013040262490527,17013040262490568⟩,⟨154541955914585,154541955914626⟩⟩,⟨⟨19018440239828876646774,19018440239828876700006⟩,⟨18094092713122343905337,18094092713122343958622⟩⟩,⟨⟨(-37326201238580442081012481),(-37326201238580441870754607)⟩,⟨(-174640172189637644844922541),(-174640172189637644634075644)⟩⟩,⟨⟨(-22039050446094185125438974516),(-22039050446094185099025575597)⟩,⟨30238813374675442746566322808,30238813374675442772667801795⟩⟩,⟨⟨872851388260399717489646974695,872851388260399717918514409563⟩,⟨(-568005984018613276009284490086),(-568005984018613275597655333954)⟩⟩] +lemma atomKernel7_1_eq (j : Fin 7) : atomKernel7_1 j = (kernel0Box (atomPoints j) 7).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel7_1_contains (j : Fin 7) : (atomKernel7_1 j).Contains + (complexTransformedFactor 7 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel7_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=7) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel9_0 : Fin 7 → CBox := ![⟨⟨0,3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-13055430470),(-13055430466)⟩,⟨(-125645570149),(-125645570145)⟩⟩,⟨⟨7154252614161620552,7154252614161620589⟩,⟨(-13924345974453591569),(-13924345974453591532)⟩⟩,⟨⟨(-1698695877854235861304740),(-1698695877854235858983332)⟩,⟨(-509093624274864032090577),(-509093624274864029767916)⟩⟩,⟨⟨(-1026692507277594175516071066),(-1026692507277594173128666505)⟩,⟨1953323598494588998753708432,1953323598494589001134169251⟩⟩,⟨⟨196702530130659703536642999895,196702530130659703684165160486⟩,⟨21124309294066164671702566946,21124309294066164817617441453⟩⟩] +lemma atomKernel9_0_eq (j : Fin 7) : atomKernel9_0 j = kernel0Box (atomPoints j) 9 := by + fin_cases j <;> decide +kernel +lemma atomKernel9_0_contains (j : Fin 7) : (atomKernel9_0 j).Contains + (complexTransformedFactor 9 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel9_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=9) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel9_1 : Fin 7 → CBox := ![⟨⟨(-28),0⟩,⟨(-28),28⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-582814768607),(-582814768566)⟩,⟨685859094687,685859094729⟩⟩,⟨⟨(-91375913998733273822),(-91375913998733273527)⟩,⟨2859794631161188478,2859794631161188773⟩⟩,⟨⟨222122721895776563286434,222122721895776577550545⟩,⟨8619414914226240484798227,8619414914226240499070203⟩⟩,⟨⟨8703009863156394059139731164,8703009863156394070573781917⟩,⟨2818607183340039793692065116,2818607183340039805139620169⟩⟩,⟨⟨39344937084074217692613206192,39344937084074218247576725826⟩,⟨(-714264540569317372231588285146),(-714264540569317371669209421945)⟩⟩] +lemma atomKernel9_1_eq (j : Fin 7) : atomKernel9_1 j = (kernel0Box (atomPoints j) 9).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel9_1_contains (j : Fin 7) : (atomKernel9_1 j).Contains + (complexTransformedFactor 9 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel9_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=9) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel12_0 : Fin 7 → CBox := ![⟨⟨0,3⟩,⟨(-3),3⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨(-7456),(-7452)⟩,⟨48027,48031⟩⟩,⟨⟨(-2433521169088633),(-2433521169088629)⟩,⟨2104633841203363,2104633841203366⟩⟩,⟨⟨(-10126433418478817995544),(-10126433418478817959972)⟩,⟨15855193807734678938298,15855193807734678973769⟩⟩,⟨⟨(-190318804329798986529500314),(-190318804329798986262853704)⟩,⟨186919098208693442779401710,186919098208693443043376098⟩⟩,⟨⟨(-29985267079005839469470031008),(-29985267079005839367492391446)⟩,⟨108564951811294072989478110531,108564951811294073091885636862⟩⟩] +lemma atomKernel12_0_eq (j : Fin 7) : atomKernel12_0 j = kernel0Box (atomPoints j) 12 := by + fin_cases j <;> decide +kernel +lemma atomKernel12_0_contains (j : Fin 7) : (atomKernel12_0 j).Contains + (complexTransformedFactor 12 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel12_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=12) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel12_1 : Fin 7 → CBox := ![⟨⟨(-28),0⟩,⟨(-28),28⟩⟩,⟨⟨(-42),8⟩,⟨(-31),23⟩⟩,⟨⟨284036,284077⟩,⟨(-198104),(-198063)⟩⟩,⟨⟨17637895069707079,17637895069707107⟩,⟨6475021789587754,6475021789587784⟩⟩,⟨⟨88595980360819229063312,88595980360819229281375⟩,⟨22757742687381368101870,22757742687381368320190⟩⟩,⟨⟨897662343959606823409130490,897662343959606824678201911⟩,⟨645860594990278562951585548,645860594990278564229728316⟩⟩,⟨⟨397661302041150198906510073424,397661302041150199296720796209⟩,⟨87891975067646749052475051597,87891975067646749440357915747⟩⟩] +lemma atomKernel12_1_eq (j : Fin 7) : atomKernel12_1 j = (kernel0Box (atomPoints j) 12).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel12_1_contains (j : Fin 7) : (atomKernel12_1 j).Contains + (complexTransformedFactor 12 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel12_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=12) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel13_0 : Fin 7 → CBox := ![⟨⟨0,3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),0⟩,⟨(-2),3⟩⟩,⟨⟨(-341),(-337)⟩,⟨98,102⟩⟩,⟨⟨(-169976153021903),(-169976153021900)⟩,⟨(-84606803526621),(-84606803526617)⟩⟩,⟨⟨(-3263693326028840015143),(-3263693326028840004989)⟩,⟨(-2537037848528971869479),(-2537037848528971859297)⟩⟩,⟨⟨(-19618607417581830024810844),(-19618607417581829855857605)⟩,⟨(-130432011910631655003953346),(-130432011910631654833571214)⟩⟩,⟨⟨(-18541242464926204931798182214),(-18541242464926204806447611936)⟩,⟨(-91487929281433214680992385330),(-91487929281433214554185512444)⟩⟩] +lemma atomKernel13_0_eq (j : Fin 7) : atomKernel13_0 j = kernel0Box (atomPoints j) 13 := by + fin_cases j <;> decide +kernel +lemma atomKernel13_0_contains (j : Fin 7) : (atomKernel13_0 j).Contains + (complexTransformedFactor 13 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel13_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=13) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel13_1 : Fin 7 → CBox := ![⟨⟨(-28),0⟩,⟨(-28),28⟩⟩,⟨⟨(-8),42⟩,⟨(-23),31⟩⟩,⟨⟨2163,2205⟩,⟨1233,1274⟩⟩,⟨⟨48835088491071,48835088491101⟩,⟨1107722107138669,1107722107138696⟩⟩,⟨⟨(-6775428697773202029332),(-6775428697773201966850)⟩,⟨18922744590791917501633,18922744590791917564035⟩⟩,⟨⟨(-519035897525465939974967179),(-519035897525465939158171005)⟩,⟨172011742142599044405582776,172011742142599045216355299⟩⟩,⟨⟨(-326883743568561696968067370144),(-326883743568561696485564285752)⟩,⟨84131904661401513556648150900,84131904661401514033371076133⟩⟩] +lemma atomKernel13_1_eq (j : Fin 7) : atomKernel13_1 j = (kernel0Box (atomPoints j) 13).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel13_1_contains (j : Fin 7) : (atomKernel13_1 j).Contains + (complexTransformedFactor 13 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel13_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=13) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel15_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨0,4⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨625573895434,625573895437⟩,⟨(-214227081645),(-214227081642)⟩⟩,⟨⟨132384326353275230385,132384326353275230804⟩,⟨149359938803361118801,149359938803361119222⟩⟩,⟨⟨(-28810067062832780021385073),(-28810067062832779936816669)⟩,⟨14486376964375100047519274,14486376964375100131573904⟩⟩,⟨⟨(-58231720871487424966415309699),(-58231720871487424854159620381)⟩,⟨(-26845578778470410410385226492),(-26845578778470410298096885403)⟩⟩] +lemma atomKernel15_0_eq (j : Fin 7) : atomKernel15_0 j = kernel0Box (atomPoints j) 15 := by + fin_cases j <;> decide +kernel +lemma atomKernel15_0_contains (j : Fin 7) : (atomKernel15_0 j).Contains + (complexTransformedFactor 15 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel15_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=15) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel15_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-23),31⟩,⟨(-42),8⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-2864698396932),(-2864698396907)⟩,⟨(-2589347110637),(-2589347110612)⟩⟩,⟨⟨489431859984239291916,489431859984239294500⟩,⟨(-837947705130953727508),(-837947705130953724930)⟩⟩,⟨⟨79472213774095043298203588,79472213774095043701406556⟩,⟨107494824575706493716140980,107494824575706494121235166⟩⟩,⟨⟨(-86005718452907319310299713598),(-86005718452907318883401587765)⟩,⟨215317144707460205231342483657,215317144707460205658470834949⟩⟩] +lemma atomKernel15_1_eq (j : Fin 7) : atomKernel15_1 j = (kernel0Box (atomPoints j) 15).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel15_1_contains (j : Fin 7) : (atomKernel15_1 j).Contains + (complexTransformedFactor 15 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel15_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=15) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel16_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩,⟨⟨25900948433,25900948436⟩,⟨29186647703,29186647707⟩⟩,⟨⟨(-35362811819921003609),(-35362811819921003509)⟩,⟨25936559903539299125,25936559903539299225⟩⟩,⟨⟨2558988247663461789901146,2558988247663461822219051⟩,⟨(-15737954547823165151092270),(-15737954547823165118709214)⟩⟩,⟨⟨53107114358929705735138510744,53107114358929705810825491739⟩,⟨(-1990265249209479056273496423),(-1990265249209478981209968663)⟩⟩] +lemma atomKernel16_0_eq (j : Fin 7) : atomKernel16_0 j = kernel0Box (atomPoints j) 16 := by + fin_cases j <;> decide +kernel +lemma atomKernel16_0_contains (j : Fin 7) : (atomKernel16_0 j).Contains + (complexTransformedFactor 16 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel16_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=16) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel16_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-30),11⟩,⟨(-31),10⟩⟩,⟨⟨75794229201,75794229231⟩,⟨(-214907164993),(-214907164965)⟩⟩,⟨⟨173413891756673643302,173413891756673643917⟩,⟨124072675056722227766,124072675056722228381⟩⟩,⟨⟨(-66096511680512424745057204),(-66096511680512424589790778)⟩,⟨630096109946563809592209,630096109946563964496528⟩⟩,⟨⟨(-17159000623478874601575700458),(-17159000623478874316252730094)⟩,⟨(-191397454004269867419843465767),(-191397454004269867131829260053)⟩⟩] +lemma atomKernel16_1_eq (j : Fin 7) : atomKernel16_1 j = (kernel0Box (atomPoints j) 16).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel16_1_contains (j : Fin 7) : (atomKernel16_1 j).Contains + (complexTransformedFactor 16 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel16_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=16) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel19_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-4),0⟩,⟨(-2),2⟩⟩,⟨⟨(-2694941),(-2694938)⟩,⟨(-7553494),(-7553491)⟩⟩,⟨⟨161985630457654811,161985630457654815⟩,⟨436136473825194671,436136473825194675⟩⟩,⟨⟨875795745701851962050983,875795745701851969854345⟩,⟨(-1717008702880404811713990),(-1717008702880404803916317)⟩⟩,⟨⟨(-3773270257214874982714516262),(-3773270257214874921032772599)⟩,⟨30019734216488397017839289471,30019734216488397079757731725⟩⟩] +lemma atomKernel19_0_eq (j : Fin 7) : atomKernel19_0 j = kernel0Box (atomPoints j) 19 := by + fin_cases j <;> decide +kernel +lemma atomKernel19_0_contains (j : Fin 7) : (atomKernel19_0 j).Contains + (complexTransformedFactor 19 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel19_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=19) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel19_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-11),30⟩,⟨(-10),31⟩⟩,⟨⟨(-30958727),(-30958703)⟩,⟨35142785,35142810⟩⟩,⟨⟨1769479826288535701,1769479826288535726⟩,⟨(-1409274084194273722),(-1409274084194273697)⟩⟩,⟨⟨(-7631316207020498734798912),(-7631316207020498697422870)⟩,⟨(-2368587012362611643398018),(-2368587012362611606011795)⟩⟩,⟨⟨109110561539634485129127268825,109110561539634485364645873668⟩,⟨7988470969262919066081260666,7988470969262919300503590470⟩⟩] +lemma atomKernel19_1_eq (j : Fin 7) : atomKernel19_1 j = (kernel0Box (atomPoints j) 19).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel19_1_contains (j : Fin 7) : (atomKernel19_1 j).Contains + (complexTransformedFactor 19 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel19_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=19) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel21_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩,⟨⟨25312,25315⟩,⟨11801,11804⟩⟩,⟨⟨(-3818447111475508),(-3818447111475505)⟩,⟨(-22135735523014202),(-22135735523014199)⟩⟩,⟨⟨(-465579338219423601664417),(-465579338219423599382689)⟩,⟨(-72777510407062961050706),(-72777510407062958771017)⟩⟩,⟨⟨15107785144520704772910159032,15107785144520704814094127433⟩,⟨14272246381970123218210380229,14272246381970123259587922189⟩⟩] +lemma atomKernel21_0_eq (j : Fin 7) : atomKernel21_0 j = kernel0Box (atomPoints j) 21 := by + fin_cases j <;> decide +kernel +lemma atomKernel21_0_contains (j : Fin 7) : (atomKernel21_0 j).Contains + (complexTransformedFactor 21 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel21_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=21) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel21_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-30),11⟩,⟨(-31),10⟩⟩,⟨⟨(-11359),(-11334)⟩,⟨(-162722),(-162697)⟩⟩,⟨⟨(-96480550487984323),(-96480550487984304)⟩,⟨51184714145044773,51184714145044792⟩⟩,⟨⟨30592198090449795242469,30592198090449806164697⟩,⟨1953286993187611677087887,1953286993187611688021236⟩⟩,⟨⟨48700613826522762890528929747,48700613826522763047850641807⟩,⟨(-57234553114940164290854633226),(-57234553114940164134186467881)⟩⟩] +lemma atomKernel21_1_eq (j : Fin 7) : atomKernel21_1 j = (kernel0Box (atomPoints j) 21).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel21_1_contains (j : Fin 7) : (atomKernel21_1 j).Contains + (complexTransformedFactor 21 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel21_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=21) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel24_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-4),0⟩,⟨(-2),2⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-236955311709037),(-236955311709034)⟩,⟨(-25302583633154),(-25302583633151)⟩⟩,⟨⟨(-50902692348634872196574),(-50902692348634872055211)⟩,⟨(-25572105302796923445599),(-25572105302796923304077)⟩⟩,⟨⟨(-9409877970793072962720468375),(-9409877970793072933272212257)⟩,⟨7173247941176577457230122546,7173247941176577486520048649⟩⟩] +lemma atomKernel24_0_eq (j : Fin 7) : atomKernel24_0 j = kernel0Box (atomPoints j) 24 := by + fin_cases j <;> decide +kernel +lemma atomKernel24_0_contains (j : Fin 7) : (atomKernel24_0 j).Contains + (complexTransformedFactor 24 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel24_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=24) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel24_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-11),30⟩,⟨(-10),31⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨242174098457843,242174098457862⟩,⟨1133073413611544,1133073413611563⟩⟩,⟨⟨(-68618597869347544447143),(-68618597869347543768973)⟩,⟨225963129972071328187395,225963129972071328865300⟩⟩,⟨⟨27669709444365382060075635835,27669709444365382171459994905⟩,⟨32632369547623298580507136818,32632369547623298692457871091⟩⟩] +lemma atomKernel24_1_eq (j : Fin 7) : atomKernel24_1 j = (kernel0Box (atomPoints j) 24).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel24_1_contains (j : Fin 7) : (atomKernel24_1 j).Contains + (complexTransformedFactor 24 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel24_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=24) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel25_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨10340074628317,10340074628320⟩,⟨(-51331061870575),(-51331061870572)⟩⟩,⟨⟨25007424357324989033834,25007424357324989135643⟩,⟨(-12960697545205626522481),(-12960697545205626421114)⟩⟩,⟨⟨4265780981286296484845899622,4265780981286296520258313301⟩,⟨(-8830170284357607012539510376),(-8830170284357606977137540426)⟩⟩] +lemma atomKernel25_0_eq (j : Fin 7) : atomKernel25_0 j = kernel0Box (atomPoints j) 25 := by + fin_cases j <;> decide +kernel +lemma atomKernel25_0_contains (j : Fin 7) : (atomKernel25_0 j).Contains + (complexTransformedFactor 25 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel25_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=25) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel25_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-252817850132719),(-252817850132700)⟩,⟨30013822947977,30013822947997⟩⟩,⟨⟨(-70561141275445737041550),(-70561141275445736555506)⟩,⟨(-93034447094966848163873),(-93034447094966847676205)⟩⟩,⟨⟨(-32686974824484623380691466343),(-32686974824484623246100477472)⟩,⟨(-13745775507675035894603552736),(-13745775507675035760026548446)⟩⟩] +lemma atomKernel25_1_eq (j : Fin 7) : atomKernel25_1 j = (kernel0Box (atomPoints j) 25).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel25_1_contains (j : Fin 7) : (atomKernel25_1 j).Contains + (complexTransformedFactor 25 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel25_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=25) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel27_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-946122032372),(-946122032369)⟩,⟨2344393842845,2344393842848⟩⟩,⟨⟨(-4914715484280113312030),(-4914715484280113277429)⟩,⟨(-4823446996496663396948),(-4823446996496663362281)⟩⟩,⟨⟨(-3163347492825092488356998232),(-3163347492825092453738357979)⟩,⟨(-5947311263201831421663297862),(-5947311263201831386929852948)⟩⟩] +lemma atomKernel27_0_eq (j : Fin 7) : atomKernel27_0 j = kernel0Box (atomPoints j) 27 := by + fin_cases j <;> decide +kernel +lemma atomKernel27_0_contains (j : Fin 7) : (atomKernel27_0 j).Contains + (complexTransformedFactor 27 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel27_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=27) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel27_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-30),11⟩,⟨(-31),10⟩⟩,⟨⟨(-6),21⟩,⟨(-19),11⟩⟩,⟨⟨12264786356508,12264786356528⟩,⟨818481221881,818481221900⟩⟩,⟨⟨(-16243750035431970811935),(-16243750035431970645865)⟩,⟨23475245713674834422464,23475245713674834588311⟩⟩,⟨⟨(-20881903462514637627417506508),(-20881903462514637495423423685)⟩,⟨12539676748978747560769434746,12539676748978747692340176601⟩⟩] +lemma atomKernel27_1_eq (j : Fin 7) : atomKernel27_1 j = (kernel0Box (atomPoints j) 27).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel27_1_contains (j : Fin 7) : (atomKernel27_1 j).Contains + (complexTransformedFactor 27 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel27_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=27) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel28_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),2⟩,⟨0,4⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-493754047503),(-493754047500)⟩,⟨(-254534926262),(-254534926259)⟩⟩,⟨⟨3357153827198104502458,3357153827198104516477⟩,⟨(-568253757477525623876),(-568253757477525609895)⟩⟩,⟨⟨4568030054686774396541880045,4568030054686774407918970971⟩,⟨3209886730187197181988549093,3209886730187197193397127950⟩⟩] +lemma atomKernel28_0_eq (j : Fin 7) : atomKernel28_0 j = kernel0Box (atomPoints j) 28 := by + fin_cases j <;> decide +kernel +lemma atomKernel28_0_contains (j : Fin 7) : (atomKernel28_0 j).Contains + (complexTransformedFactor 28 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel28_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=28) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel28_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-10),31⟩,⟨(-30),11⟩⟩,⟨⟨(-6),21⟩,⟨(-19),11⟩⟩,⟨⟨(-427735225680),(-427735225661)⟩,⟨2666849509051,2666849509071⟩⟩,⟨⟨(-4685945174865765828890),(-4685945174865765761884)⟩,⟨(-13314743247109872706579),(-13314743247109872639414)⟩⟩,⟨⟨10733230239114978357051547456,10733230239114978400424162862⟩,⟨(-17098006669934193027518235080),(-17098006669934192984238611740)⟩⟩] +lemma atomKernel28_1_eq (j : Fin 7) : atomKernel28_1 j = (kernel0Box (atomPoints j) 28).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel28_1_contains (j : Fin 7) : (atomKernel28_1 j).Contains + (complexTransformedFactor 28 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel28_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=28) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel31_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨0,3⟩,⟨(-2),2⟩⟩,⟨⟨(-4030720336),(-4030720333)⟩,⟨4299209323,4299209326⟩⟩,⟨⟨407412577843147764126,407412577843147767566⟩,⟨58579429178108479865,58579429178108483303⟩⟩,⟨⟨(-2224103963996790476325329693),(-2224103963996790455774833313)⟩,⟨2270745127693704504337839885,2270745127693704524857452908⟩⟩] +lemma atomKernel31_0_eq (j : Fin 7) : atomKernel31_0 j = kernel0Box (atomPoints j) 31 := by + fin_cases j <;> decide +kernel +lemma atomKernel31_0_contains (j : Fin 7) : (atomKernel31_0 j).Contains + (complexTransformedFactor 31 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel31_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=31) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel31_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-19),11⟩,⟨(-21),6⟩⟩,⟨⟨25970278706,25970278725⟩,⟨12107049782,12107049802⟩⟩,⟨⟨(-47628420768149630847),(-47628420768149614376)⟩,⟨(-1705658777325531325301),(-1705658777325531308820)⟩⟩,⟨⟨8617347244127811818499525611,8617347244127811896482648040⟩,⟨7604911897842197952003746458,7604911897842198030092082194⟩⟩] +lemma atomKernel31_1_eq (j : Fin 7) : atomKernel31_1 j = (kernel0Box (atomPoints j) 31).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel31_1_contains (j : Fin 7) : (atomKernel31_1 j).Contains + (complexTransformedFactor 31 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel31_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=31) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel33_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨229435537,229435540⟩,⟨(-168277587),(-168277584)⟩⟩,⟨⟨(-17402041971918504781),(-17402041971918504071)⟩,⟨(-99113638007083976860),(-99113638007083976149)⟩⟩,⟨⟨356134034453168626612634853,356134034453168633806136668⟩,⟨2154120630586429646770321740,2154120630586429653996527604⟩⟩] +lemma atomKernel33_0_eq (j : Fin 7) : atomKernel33_0 j = kernel0Box (atomPoints j) 33 := by + fin_cases j <;> decide +kernel +lemma atomKernel33_0_contains (j : Fin 7) : (atomKernel33_0 j).Contains + (complexTransformedFactor 33 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel33_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=33) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel33_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-6),21⟩,⟨(-19),11⟩⟩,⟨⟨(-1125117261),(-1125117242)⟩,⟨(-804989193),(-804989174)⟩⟩,⟨⟨(-392652206894016658349),(-392652206894016654942)⟩,⟨140898727616430839872,140898727616430843274⟩⟩,⟨⟨7711713205226792022808918861,7711713205226792050278657229⟩,⟨(-1690495727387573553837620386),(-1690495727387573526499428095)⟩⟩] +lemma atomKernel33_1_eq (j : Fin 7) : atomKernel33_1 j = (kernel0Box (atomPoints j) 33).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel33_1_contains (j : Fin 7) : (atomKernel33_1 j).Contains + (complexTransformedFactor 33 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel33_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=33) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel36_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-1050972),(-1050969)⟩,⟨(-2829675),(-2829672)⟩⟩,⟨⟨1657458069911691374,1657458069911691465⟩,⟨(-12051186734807603617),(-12051186734807603525)⟩⟩,⟨⟨(-1243020940282687197299659347),(-1243020940282687190617026701)⟩,⟨1676392578950671605784059,1676392578950678274948786⟩⟩] +lemma atomKernel36_0_eq (j : Fin 7) : atomKernel36_0 j = kernel0Box (atomPoints j) 36 := by + fin_cases j <;> decide +kernel +lemma atomKernel36_0_contains (j : Fin 7) : (atomKernel36_0 j).Contains + (complexTransformedFactor 36 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel36_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=36) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel36_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-11480476),(-11480456)⟩,⟨9143427,9143446⟩⟩,⟨⟨(-50400021493982320839),(-50400021493982320398)⟩,⟨1716504632604075338,1716504632604075776⟩⟩,⟨⟨239459708312164333399207818,239459708312164358737317874⟩,⟨4488266200039790625597273898,4488266200039790650995014418⟩⟩] +lemma atomKernel36_1_eq (j : Fin 7) : atomKernel36_1 j = (kernel0Box (atomPoints j) 36).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel36_1_contains (j : Fin 7) : (atomKernel36_1 j).Contains + (complexTransformedFactor 36 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel36_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=36) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel37_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨0,3⟩,⟨(-2),2⟩⟩,⟨⟨640417,640420⟩,⟨(-172576),(-172573)⟩⟩,⟨⟨4344109497548861007,4344109497548861053⟩,⟨4160151813898398136,4160151813898398182⟩⟩,⟨⟨918146183807522803526732868,918146183807522811268423752⟩,⟨(-467290594442411598540061168),(-467290594442411590816352397)⟩⟩] +lemma atomKernel37_0_eq (j : Fin 7) : atomKernel37_0 j = kernel0Box (atomPoints j) 37 := by + fin_cases j <;> decide +kernel +lemma atomKernel37_0_contains (j : Fin 7) : (atomKernel37_0 j).Contains + (complexTransformedFactor 37 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel37_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=37) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel37_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-19),11⟩,⟨(-21),6⟩⟩,⟨⟨(-1767764),(-1767745)⟩,⟨(-2697224),(-2697205)⟩⟩,⟨⟨13935873524237933494,13935873524237933716⟩,⟨(-20676989198405546918),(-20676989198405546696)⟩⟩,⟨⟨(-1859801892531483976917095203),(-1859801892531483947566978519)⟩,⟨(-3227705054763723539994758263),(-3227705054763723510578171492)⟩⟩] +lemma atomKernel37_1_eq (j : Fin 7) : atomKernel37_1 j = (kernel0Box (atomPoints j) 37).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel37_1_contains (j : Fin 7) : (atomKernel37_1 j).Contains + (complexTransformedFactor 37 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel37_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=37) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel39_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-31926),(-31923)⟩,⟨2507,2510⟩⟩,⟨⟨635863206902312638,635863206902312662⟩,⟨(-1325938779881954263),(-1325938779881954239)⟩⟩,⟨⟨113546669637062691669758862,113546669637062697375502405⟩,⟨(-698503320922647562276889979),(-698503320922647556566360541)⟩⟩] +lemma atomKernel39_0_eq (j : Fin 7) : atomKernel39_0 j = kernel0Box (atomPoints j) 39 := by + fin_cases j <;> decide +kernel +lemma atomKernel39_0_contains (j : Fin 7) : (atomKernel39_0 j).Contains + (complexTransformedFactor 39 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel39_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=39) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel39_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-11),19⟩,⟨(-6),21⟩⟩,⟨⟨59957,59976⟩,⟨143680,143699⟩⟩,⟨⟨(-5864694104202136490),(-5864694104202136374)⟩,⟨(-1663824078702990933),(-1663824078702990817)⟩⟩,⟨⟨(-2543634718900661190487942318),(-2543634718900661168787588579)⟩,⟨(-278859669301624039056922852),(-278859669301624017379326452)⟩⟩] +lemma atomKernel39_1_eq (j : Fin 7) : atomKernel39_1 j = (kernel0Box (atomPoints j) 39).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel39_1_contains (j : Fin 7) : (atomKernel39_1 j).Contains + (complexTransformedFactor 39 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel39_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=39) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel40_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨97,100⟩,⟨(-7038),(-7035)⟩⟩,⟨⟨346384015365736346,346384015365736351⟩,⟨639293806035028343,639293806035028348⟩⟩,⟨⟨177965390395636590606821606,177965390395636592442449226⟩,⟨558868935012030951364803856,558868935012030953210918094⟩⟩] +lemma atomKernel40_0_eq (j : Fin 7) : atomKernel40_0 j = kernel0Box (atomPoints j) 40 := by + fin_cases j <;> decide +kernel +lemma atomKernel40_0_contains (j : Fin 7) : (atomKernel40_0 j).Contains + (complexTransformedFactor 40 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel40_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=40) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel40_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-11),19⟩,⟨(-6),21⟩⟩,⟨⟨(-32668),(-32648)⟩,⟨10198,10217⟩⟩,⟨⟨2367744446448568917,2367744446448568942⟩,⟨(-1865339093500727158),(-1865339093500727133)⟩⟩,⟨⟨1984673118246228857746059855,1984673118246228864763638546⟩,⟨(-747578353067753521244344664),(-747578353067753514266814852)⟩⟩] +lemma atomKernel40_1_eq (j : Fin 7) : atomKernel40_1 j = (kernel0Box (atomPoints j) 40).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel40_1_contains (j : Fin 7) : (atomKernel40_1 j).Contains + (complexTransformedFactor 40 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel40_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=40) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel43_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-73),(-70)⟩,⟨(-24),(-21)⟩⟩,⟨⟨16259798808128842,16259798808128846⟩,⟨86378826263974455,86378826263974459⟩⟩,⟨⟨(-330372957935110601859926653),(-330372957935110598947142807)⟩,⟨48509138613335145931700031,48509138613335148839683869⟩⟩] +lemma atomKernel43_0_eq (j : Fin 7) : atomKernel43_0 j = kernel0Box (atomPoints j) 43 := by + fin_cases j <;> decide +kernel +lemma atomKernel43_0_contains (j : Fin 7) : (atomKernel43_0 j).Contains + (complexTransformedFactor 43 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel43_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=43) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel43_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-6),21⟩,⟨(-19),11⟩⟩,⟨⟨(-5),14⟩,⟨355,374⟩⟩,⟨⟨341431218542899030,341431218542899050⟩,⟨(-127263134088074692),(-127263134088074672)⟩⟩,⟨⟨237203001028153647116588586,237203001028153658165092179⟩,⟨1183876629898497547286430368,1183876629898497558354436945⟩⟩] +lemma atomKernel43_1_eq (j : Fin 7) : atomKernel43_1 j = (kernel0Box (atomPoints j) 43).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel43_1_contains (j : Fin 7) : (atomKernel43_1 j).Contains + (complexTransformedFactor 43 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel43_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=43) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel45_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨2,5⟩,⟨1,4⟩⟩,⟨⟨18830809875395978,18830809875395981⟩,⟨(-10352733558348000),(-10352733558347997)⟩⟩,⟨⟨(-107165896840389841321838953),(-107165896840389839088330843)⟩,⟨202796730022409554673157723,202796730022409556906216278⟩⟩] +lemma atomKernel45_0_eq (j : Fin 7) : atomKernel45_0 j = kernel0Box (atomPoints j) 45 := by + fin_cases j <;> decide +kernel +lemma atomKernel45_0_contains (j : Fin 7) : (atomKernel45_0 j).Contains + (complexTransformedFactor 45 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel45_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=45) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel45_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-11),19⟩,⟨(-6),21⟩⟩,⟨⟨(-3),16⟩,⟨(-30),(-10)⟩⟩,⟨⟨(-55556615640004652),(-55556615640004636)⟩,⟨(-69637950593080931),(-69637950593080915)⟩⟩,⟨⟨752427172540631380285593794,752427172540631388771014742⟩,⟨348899021763434204543123126,348899021763434213029040968⟩⟩] +lemma atomKernel45_1_eq (j : Fin 7) : atomKernel45_1 j = (kernel0Box (atomPoints j) 45).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel45_1_contains (j : Fin 7) : (atomKernel45_1 j).Contains + (complexTransformedFactor 45 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel45_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=45) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel48_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨0,3⟩,⟨(-2),2⟩⟩,⟨⟨(-1),2⟩,⟨(-3),0⟩⟩,⟨⟨2549875219752031,2549875219752034⟩,⟨(-496182088842491),(-496182088842488)⟩⟩,⟨⟨(-104063906274990395845241810),(-104063906274990395052490689)⟩,⟨(-78886104748897649066142166),(-78886104748897648272540146)⟩⟩] +lemma atomKernel48_0_eq (j : Fin 7) : atomKernel48_0 j = kernel0Box (atomPoints j) 48 := by + fin_cases j <;> decide +kernel +lemma atomKernel48_0_contains (j : Fin 7) : (atomKernel48_0 j).Contains + (complexTransformedFactor 48 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel48_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=48) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel48_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-19),11⟩,⟨(-21),6⟩⟩,⟨⟨(-17),2⟩,⟨(-10),10⟩⟩,⟨⟨(-3822940682990759),(-3822940682990743)⟩,⟨(-10067531589409261),(-10067531589409245)⟩⟩,⟨⟨(-265319349620308840886986549),(-265319349620308837871442516)⟩,⟨390590183711652991010880853,390590183711652994023786395⟩⟩] +lemma atomKernel48_1_eq (j : Fin 7) : atomKernel48_1 j = (kernel0Box (atomPoints j) 48).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel48_1_contains (j : Fin 7) : (atomKernel48_1 j).Contains + (complexTransformedFactor 48 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel48_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=48) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel49_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨0,3⟩,⟨(-1),2⟩⟩,⟨⟨(-541164345766439),(-541164345766436)⟩,⟨1164871767201477,1164871767201480⟩⟩,⟨⟨106495610180144283951438661,106495610180144284840827478⟩,⟨19291243679728066472327862,19291243679728067361043383⟩⟩] +lemma atomKernel49_0_eq (j : Fin 7) : atomKernel49_0 j = kernel0Box (atomPoints j) 49 := by + fin_cases j <;> decide +kernel +lemma atomKernel49_0_contains (j : Fin 7) : (atomKernel49_0 j).Contains + (complexTransformedFactor 49 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel49_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=49) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel49_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-10),10⟩,⟨(-17),2⟩⟩,⟨⟨5139990790469704,5139990790469719⟩,⟨1390391504787011,1390391504787026⟩⟩,⟨⟨49664145334029922136449977,49664145334029925512913778⟩,⟨(-388180802886771933709335300),(-388180802886771930329616411)⟩⟩] +lemma atomKernel49_1_eq (j : Fin 7) : atomKernel49_1 j = (kernel0Box (atomPoints j) 49).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel49_1_contains (j : Fin 7) : (atomKernel49_1 j).Contains + (complexTransformedFactor 49 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel49_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=49) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel51_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),1⟩⟩,⟨⟨311828906300556,311828906300558⟩,⟨37060368709048,37060368709051⟩⟩,⟨⟨53904277469795663176536190,53904277469795664246312225⟩,⟨(-51198948346911017898515124),(-51198948346911016829532955)⟩⟩] +lemma atomKernel51_0_eq (j : Fin 7) : atomKernel51_0 j = kernel0Box (atomPoints j) 51 := by + fin_cases j <;> decide +kernel +lemma atomKernel51_0_contains (j : Fin 7) : (atomKernel51_0 j).Contains + (complexTransformedFactor 51 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel51_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=51) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel51_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-17),10⟩,⟨(-11),19⟩⟩,⟨⟨(-68220091928561),(-68220091928546)⟩,⟨(-1300015199948792),(-1300015199948781)⟩⟩,⟨⟨(-195002522605954123780304968),(-195002522605954119718686374)⟩,⟨(-185035951283069611197523655),(-185035951283069607133157977)⟩⟩] +lemma atomKernel51_1_eq (j : Fin 7) : atomKernel51_1 j = (kernel0Box (atomPoints j) 51).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel51_1_contains (j : Fin 7) : (atomKernel51_1 j).Contains + (complexTransformedFactor 51 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel51_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=51) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel52_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨0,3⟩,⟨(-1),2⟩⟩,⟨⟨(-105312484749326),(-105312484749324)⟩,⟨114096081268131,114096081268134⟩⟩,⟨⟨(-20646909703251340773450717),(-20646909703251340282135772)⟩,⟨58054105314515772666001100,58054105314515773157431688⟩⟩] +lemma atomKernel52_0_eq (j : Fin 7) : atomKernel52_0 j = kernel0Box (atomPoints j) 52 := by + fin_cases j <;> decide +kernel +lemma atomKernel52_0_contains (j : Fin 7) : (atomKernel52_0 j).Contains + (complexTransformedFactor 52 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel52_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=52) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel52_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-10),10⟩,⟨(-17),2⟩⟩,⟨⟨540288382282069,540288382282084⟩,⟨349874232005769,349874232005780⟩⟩,⟨⟨213511825423736055546754853,213511825423736057414258988⟩,⟨63655514486427655666285289,63655514486427657532985939⟩⟩] +lemma atomKernel52_1_eq (j : Fin 7) : atomKernel52_1 j = (kernel0Box (atomPoints j) 52).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel52_1_contains (j : Fin 7) : (atomKernel52_1 j).Contains + (complexTransformedFactor 52 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel52_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=52) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel55_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-1),2⟩,⟨(-3),0⟩⟩,⟨⟨(-16335865291838),(-16335865291835)⟩,⟨9243578969829,9243578969832⟩⟩,⟨⟨(-30714034438307723652198978),(-30714034438307722796076532)⟩,⟨(-16946837666584302430922347),(-16946837666584301574712951)⟩⟩] +lemma atomKernel55_0_eq (j : Fin 7) : atomKernel55_0 j = kernel0Box (atomPoints j) 55 := by + fin_cases j <;> decide +kernel +lemma atomKernel55_0_contains (j : Fin 7) : (atomKernel55_0 j).Contains + (complexTransformedFactor 55 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel55_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=55) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel55_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-17),2⟩,⟨(-10),10⟩⟩,⟨⟨49268188756146,49268188756161⟩,⟨60226546533177,60226546533192⟩⟩,⟨⟨(-55428194824526991733240576),(-55428194824526988480476019)⟩,⟨114091342655939419980830988,114091342655939423233447907⟩⟩] +lemma atomKernel55_1_eq (j : Fin 7) : atomKernel55_1 j = (kernel0Box (atomPoints j) 55).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel55_1_contains (j : Fin 7) : (atomKernel55_1 j).Contains + (complexTransformedFactor 55 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel55_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=55) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel57_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-2),1⟩,⟨0,3⟩⟩,⟨⟨3391042084770,3391042084773⟩,⟨3091717459698,3091717459701⟩⟩,⟨⟨(-21855590582580566140865624),(-21855590582580565938327545)⟩,⟨10147279730891965438020305,10147279730891965640119812⟩⟩] +lemma atomKernel57_0_eq (j : Fin 7) : atomKernel57_0 j = kernel0Box (atomPoints j) 57 := by + fin_cases j <;> decide +kernel +lemma atomKernel57_0_contains (j : Fin 7) : (atomKernel57_0 j).Contains + (complexTransformedFactor 57 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel57_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=57) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel57_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-2),17⟩,⟨(-10),10⟩⟩,⟨⟨10242253069099,10242253069114⟩,⟨(-16030922975189),(-16030922975174)⟩⟩,⟨⟨40745988876809292236146413,40745988876809293004093949⟩,⟨77015717933751555155819035,77015717933751555925395494⟩⟩] +lemma atomKernel57_1_eq (j : Fin 7) : atomKernel57_1 j = (kernel0Box (atomPoints j) 57).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel57_1_contains (j : Fin 7) : (atomKernel57_1 j).Contains + (complexTransformedFactor 57 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel57_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=57) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel60_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨0,3⟩,⟨(-1),2⟩⟩,⟨⟨276141132453,276141132456⟩,⟨481112337745,481112337747⟩⟩,⟨⟨(-3687892951764255580220410),(-3687892951764255439615550)⟩,⟨(-13213433696955863833376530),(-13213433696955863692536649)⟩⟩] +lemma atomKernel60_0_eq (j : Fin 7) : atomKernel60_0 j = kernel0Box (atomPoints j) 60 := by + fin_cases j <;> decide +kernel +lemma atomKernel60_0_contains (j : Fin 7) : (atomKernel60_0 j).Contains + (complexTransformedFactor 60 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel60_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=60) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel60_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-10),10⟩,⟨(-17),2⟩⟩,⟨⟨1770998736931,1770998736943⟩,⟨(-1466968117338),(-1466968117323)⟩⟩,⟨⟨(-47021565110366643310598364),(-47021565110366642775465957)⟩,⟨15798208239658489099154911,15798208239658489633378987⟩⟩] +lemma atomKernel60_1_eq (j : Fin 7) : atomKernel60_1 j = (kernel0Box (atomPoints j) 60).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel60_1_contains (j : Fin 7) : (atomKernel60_1 j).Contains + (complexTransformedFactor 60 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel60_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=60) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel61_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-2),1⟩,⟨0,3⟩⟩,⟨⟨(-272745757303),(-272745757300)⟩,⟨(-29030202555),(-29030202552)⟩⟩,⟨⟨7680066386702458508481384,7680066386702458647801409⟩,⟨8383946322022811120249854,8383946322022811259696890⟩⟩] +lemma atomKernel61_0_eq (j : Fin 7) : atomKernel61_0 j = kernel0Box (atomPoints j) 61 := by + fin_cases j <;> decide +kernel +lemma atomKernel61_0_contains (j : Fin 7) : (atomKernel61_0 j).Contains + (complexTransformedFactor 61 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel61_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=61) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel61_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-2),17⟩,⟨(-10),10⟩⟩,⟨⟨73499239201,73499239217⟩,⟨1134693279692,1134693279708⟩⟩,⟨⟨28832536650691517300184176,28832536650691517829992601⟩,⟨(-29307201421334448060540620),(-29307201421334447531174655)⟩⟩] +lemma atomKernel61_1_eq (j : Fin 7) : atomKernel61_1 j = (kernel0Box (atomPoints j) 61).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel61_1_contains (j : Fin 7) : (atomKernel61_1 j).Contains + (complexTransformedFactor 61 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel61_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=61) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel63_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-1),2⟩,⟨(-3),0⟩⟩,⟨⟨14016533948,14016533950⟩,⟨65577083170,65577083173⟩⟩,⟨⟨7763190550023462404344915,7763190550023462585911865⟩,⟨(-854893022145203587180632),(-854893022145203405719207)⟩⟩] +lemma atomKernel63_0_eq (j : Fin 7) : atomKernel63_0 j = kernel0Box (atomPoints j) 63 := by + fin_cases j <;> decide +kernel +lemma atomKernel63_0_contains (j : Fin 7) : (atomKernel63_0 j).Contains + (complexTransformedFactor 63 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel63_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=63) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel63_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-17),2⟩,⟨(-10),10⟩⟩,⟨⟨258029882626,258029882641⟩,⟨(-103447960612),(-103447960601)⟩⟩,⟨⟨(-4544761290569955933404665),(-4544761290569955244034832)⟩,⟨(-27872557088731765363058055),(-27872557088731764673251706)⟩⟩] +lemma atomKernel63_1_eq (j : Fin 7) : atomKernel63_1 j = (kernel0Box (atomPoints j) 63).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel63_1_contains (j : Fin 7) : (atomKernel63_1 j).Contains + (complexTransformedFactor 63 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel63_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=63) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel64_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨0,3⟩,⟨(-1),2⟩⟩,⟨⟨(-30322265718),(-30322265715)⟩,⟨(-13414726933),(-13414726930)⟩⟩,⟨⟨(-5417607093436297299550652),(-5417607093436297234620271)⟩,⟨3542579624932083293148638,3542579624932083357981311⟩⟩] +lemma atomKernel64_0_eq (j : Fin 7) : atomKernel64_0 j = kernel0Box (atomPoints j) 64 := by + fin_cases j <;> decide +kernel +lemma atomKernel64_0_contains (j : Fin 7) : (atomKernel64_0 j).Contains + (complexTransformedFactor 64 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel64_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=64) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel64_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-10),10⟩,⟨(-17),2⟩⟩,⟨⟨(-33447006320),(-33447006304)⟩,⟨133323491750,133323491765⟩⟩,⟨⟨13809629524105563278775466,13809629524105563525124090⟩,⟨18897918223338345978367614,18897918223338346225071149⟩⟩] +lemma atomKernel64_1_eq (j : Fin 7) : atomKernel64_1 j = (kernel0Box (atomPoints j) 64).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel64_1_contains (j : Fin 7) : (atomKernel64_1 j).Contains + (complexTransformedFactor 64 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel64_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=64) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel67_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-1),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2994806832),(-2994806830)⟩,⟨(-2663982706),(-2663982703)⟩⟩,⟨⟨(-1491288608414460994055002),(-1491288608414460949634509)⟩,⟨(-3369987193263265566741046),(-3369987193263265522252121)⟩⟩] +lemma atomKernel67_0_eq (j : Fin 7) : atomKernel67_0 j = kernel0Box (atomPoints j) 67 := by + fin_cases j <;> decide +kernel +lemma atomKernel67_0_contains (j : Fin 7) : (atomKernel67_0 j).Contains + (complexTransformedFactor 67 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel67_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=67) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel67_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-17),2⟩,⟨(-10),10⟩⟩,⟨⟨(-8773900461),(-8773900446)⟩,⟨14110928914,14110928926⟩⟩,⟨⟨(-11889087240856962074595714),(-11889087240856961905564435)⟩,⟨6017875794307459362748221,6017875794307459531524769⟩⟩] +lemma atomKernel67_1_eq (j : Fin 7) : atomKernel67_1 j = (kernel0Box (atomPoints j) 67).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel67_1_contains (j : Fin 7) : (atomKernel67_1 j).Contains + (complexTransformedFactor 67 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel67_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=67) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel69_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),1⟩⟩,⟨⟨(-390964209),(-390964206)⟩,⟨898566756,898566758⟩⟩,⟨⟨(-2472967857929847675126881),(-2472967857929847620472772)⟩,⟨(-540845680360740571625389),(-540845680360740516984804)⟩⟩] +lemma atomKernel69_0_eq (j : Fin 7) : atomKernel69_0 j = kernel0Box (atomPoints j) 69 := by + fin_cases j <;> decide +kernel +lemma atomKernel69_0_contains (j : Fin 7) : (atomKernel69_0 j).Contains + (complexTransformedFactor 69 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel69_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=69) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel69_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-10),10⟩,⟨(-2),17⟩⟩,⟨⟨3946269268,3946269279⟩,⟨964339428,964339442⟩⟩,⟨⟨(-1488650365615171334974520),(-1488650365615171127395664)⟩,⟨9031507735029591659109512,9031507735029591866755718⟩⟩] +lemma atomKernel69_1_eq (j : Fin 7) : atomKernel69_1 j = (kernel0Box (atomPoints j) 69).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel69_1_contains (j : Fin 7) : (atomKernel69_1 j).Contains + (complexTransformedFactor 69 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel69_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=69) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel72_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-2),1⟩,⟨0,3⟩⟩,⟨⟨(-78188356),(-78188354)⟩,⟨88990295,88990297⟩⟩,⟨⟨531628501514138473100772,531628501514138493147184⟩,⟨(-1339538026650656465365006),(-1339538026650656445317450)⟩⟩] +lemma atomKernel72_0_eq (j : Fin 7) : atomKernel72_0 j = kernel0Box (atomPoints j) 72 := by + fin_cases j <;> decide +kernel +lemma atomKernel72_0_contains (j : Fin 7) : (atomKernel72_0 j).Contains + (complexTransformedFactor 72 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel72_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=72) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel72_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-2),17⟩,⟨(-10),10⟩⟩,⟨⟨418620151,418620161⟩,⟨256746258,256746269⟩⟩,⟨⟨(-4936932360757759705282210),(-4936932360757759629110065)⟩,⟨(-1668194813749212036209059),(-1668194813749211960049634)⟩⟩] +lemma atomKernel72_1_eq (j : Fin 7) : atomKernel72_1 j = (kernel0Box (atomPoints j) 72).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel72_1_contains (j : Fin 7) : (atomKernel72_1 j).Contains + (complexTransformedFactor 72 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel72_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=72) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel73_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),1⟩⟩,⟨⟨(-12943923),(-12943920)⟩,⟨(-57124493),(-57124490)⟩⟩,⟨⟨109287676979571211948290,109287676979571227649066⟩,⟨1189440891031047220487264,1189440891031047236203926⟩⟩] +lemma atomKernel73_0_eq (j : Fin 7) : atomKernel73_0 j = kernel0Box (atomPoints j) 73 := by + fin_cases j <;> decide +kernel +lemma atomKernel73_0_contains (j : Fin 7) : (atomKernel73_0 j).Contains + (complexTransformedFactor 73 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel73_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=73) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel73_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-10),10⟩,⟨(-2),17⟩⟩,⟨⟨(-224253997),(-224253982)⟩,⟨93112811,93112826⟩⟩,⟨⟨4274580715241190966150627,4274580715241191025865828⟩,⟨(-617985952775082751425094),(-617985952775082691776045)⟩⟩] +lemma atomKernel73_1_eq (j : Fin 7) : atomKernel73_1 j = (kernel0Box (atomPoints j) 73).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel73_1_contains (j : Fin 7) : (atomKernel73_1 j).Contains + (complexTransformedFactor 73 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel73_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=73) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel75_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨0,3⟩,⟨(-1),2⟩⟩,⟨⟨(-12286520),(-12286517)⟩,⟨7355538,7355541⟩⟩,⟨⟨703608085078664601370298,703608085078664619181865⟩,⟨422055543839951182722930,422055543839951200537419⟩⟩] +lemma atomKernel75_0_eq (j : Fin 7) : atomKernel75_0 j = kernel0Box (atomPoints j) 75 := by + fin_cases j <;> decide +kernel +lemma atomKernel75_0_contains (j : Fin 7) : (atomKernel75_0 j).Contains + (complexTransformedFactor 75 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel75_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=75) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel75_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-10),10⟩,⟨(-17),2⟩⟩,⟨⟨38703006,38703021⟩,⟨45013514,45013530⟩⟩,⟨⟨1391934708503196287668457,1391934708503196355346851⟩,⟨(-2619997901239201881920850),(-2619997901239201814249391)⟩⟩] +lemma atomKernel75_1_eq (j : Fin 7) : atomKernel75_1 j = (kernel0Box (atomPoints j) 75).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel75_1_contains (j : Fin 7) : (atomKernel75_1 j).Contains + (complexTransformedFactor 75 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel75_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=75) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel76_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-2),1⟩,⟨0,3⟩⟩,⟨⟨619843,619845⟩,⟨(-7053373),(-7053371)⟩⟩,⟨⟨(-678312739500487052041191),(-678312739500487041764779)⟩,⟨(-48153947454543726886191),(-48153947454543716615960)⟩⟩] +lemma atomKernel76_0_eq (j : Fin 7) : atomKernel76_0 j = kernel0Box (atomPoints j) 76 := by + fin_cases j <;> decide +kernel +lemma atomKernel76_0_contains (j : Fin 7) : (atomKernel76_0 j).Contains + (complexTransformedFactor 76 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel76_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=76) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel76_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-2),17⟩,⟨(-10),10⟩⟩,⟨⟨(-29251677),(-29251667)⟩,⟨2435474,2435484⟩⟩,⟨⟨(-46516099958030390332757),(-46516099958030351316090)⟩,⟨2458446992878682192858732,2458446992878682231903426⟩⟩] +lemma atomKernel76_1_eq (j : Fin 7) : atomKernel76_1 j = (kernel0Box (atomPoints j) 76).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel76_1_contains (j : Fin 7) : (atomKernel76_1 j).Contains + (complexTransformedFactor 76 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel76_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=76) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel79_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨0,3⟩,⟨(-1),2⟩⟩,⟨⟨331845,331848⟩,⟨(-788988),(-788986)⟩⟩,⟨⟨89529674993727874189181,89529674993727886667074⟩,⟨(-376651654647634047610591),(-376651654647634035130828)⟩⟩] +lemma atomKernel79_0_eq (j : Fin 7) : atomKernel79_0 j = kernel0Box (atomPoints j) 79 := by + fin_cases j <;> decide +kernel +lemma atomKernel79_0_contains (j : Fin 7) : (atomKernel79_0 j).Contains + (complexTransformedFactor 79 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel79_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=79) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel79_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-10),10⟩,⟨(-17),2⟩⟩,⟨⟨(-3456972),(-3456961)⟩,⟨(-800011),(-799996)⟩⟩,⟨⟨(-1376910219774543734492856),(-1376910219774543687080707)⟩,⟨(-252568843144825406234940),(-252568843144825358832321)⟩⟩] +lemma atomKernel79_1_eq (j : Fin 7) : atomKernel79_1 j = (kernel0Box (atomPoints j) 79).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel79_1_contains (j : Fin 7) : (atomKernel79_1 j).Contains + (complexTransformedFactor 79 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel79_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=79) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel81_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),0⟩,⟨(-2),1⟩⟩,⟨⟨(-208567),(-208565)⟩,⟨(-17042),(-17039)⟩⟩,⟨⟨(-172436430715579443954493),(-172436430715579440303708)⟩,⟨(-202453859519989861406243),(-202453859519989857752274)⟩⟩] +lemma atomKernel81_0_eq (j : Fin 7) : atomKernel81_0 j = kernel0Box (atomPoints j) 81 := by + fin_cases j <;> decide +kernel +lemma atomKernel81_0_contains (j : Fin 7) : (atomKernel81_0 j).Contains + (complexTransformedFactor 81 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel81_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=81) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel81_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-10),10⟩,⟨(-2),17⟩⟩,⟨⟨77271,77286⟩,⟨864050,864061⟩⟩,⟨⟨(-698687191394988581642740),(-698687191394988567760212)⟩,⟨660687881552612128250917,660687881552612142122219⟩⟩] +lemma atomKernel81_1_eq (j : Fin 7) : atomKernel81_1 j = (kernel0Box (atomPoints j) 81).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel81_1_contains (j : Fin 7) : (atomKernel81_1 j).Contains + (complexTransformedFactor 81 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel81_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=81) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel84_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-2),1⟩,⟨0,3⟩⟩,⟨⟨(-23379),(-23376)⟩,⟨(-9665),(-9663)⟩⟩,⟨⟨129624059787215343467447,129624059787215345689455⟩,⟨(-78230506048611033060433),(-78230506048611030840833)⟩⟩] +lemma atomKernel84_0_eq (j : Fin 7) : atomKernel84_0 j = kernel0Box (atomPoints j) 84 := by + fin_cases j <;> decide +kernel +lemma atomKernel84_0_contains (j : Fin 7) : (atomKernel84_0 j).Contains + (complexTransformedFactor 84 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel84_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=84) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel84_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-2),17⟩,⟨(-10),10⟩⟩,⟨⟨(-23021),(-23010)⟩,⟨102303,102318⟩⟩,⟨⟨(-306832338821425630953193),(-306832338821425622519948)⟩,⟨(-453386250615374248059790),(-453386250615374239617742)⟩⟩] +lemma atomKernel84_1_eq (j : Fin 7) : atomKernel84_1 j = (kernel0Box (atomPoints j) 84).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel84_1_contains (j : Fin 7) : (atomKernel84_1 j).Contains + (complexTransformedFactor 84 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel84_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=84) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel85_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),1⟩⟩,⟨⟨10651,10653⟩,⟨(-6557),(-6555)⟩⟩,⟨⟨(-66479865675897499458536),(-66479865675897497215962)⟩,⟨106424352074323537274067,106424352074323539516148⟩⟩] +lemma atomKernel85_0_eq (j : Fin 7) : atomKernel85_0 j = kernel0Box (atomPoints j) 85 := by + fin_cases j <;> decide +kernel +lemma atomKernel85_0_contains (j : Fin 7) : (atomKernel85_0 j).Contains + (complexTransformedFactor 85 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel85_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=85) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel85_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-17),10⟩,⟨(-11),19⟩⟩,⟨⟨(-34291),(-34280)⟩,⟨(-38904),(-38894)⟩⟩,⟨⟨396784253834411909373238,396784253834411917891811⟩,⟨220076868461803344191588,220076868461803352711413⟩⟩] +lemma atomKernel85_1_eq (j : Fin 7) : atomKernel85_1 j = (kernel0Box (atomPoints j) 85).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel85_1_contains (j : Fin 7) : (atomKernel85_1 j).Contains + (complexTransformedFactor 85 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel85_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=85) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel87_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-2),1⟩,⟨0,3⟩⟩,⟨⟨(-2335),(-2332)⟩,⟨(-1977),(-1975)⟩⟩,⟨⟨32012112202517490930319,32012112202517492431184⟩,⟨80030280506293728395916,80030280506293729898451⟩⟩] +lemma atomKernel87_0_eq (j : Fin 7) : atomKernel87_0 j = kernel0Box (atomPoints j) 87 := by + fin_cases j <;> decide +kernel +lemma atomKernel87_0_contains (j : Fin 7) : (atomKernel87_0 j).Contains + (complexTransformedFactor 87 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel87_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=87) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel87_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-2),17⟩,⟨(-10),10⟩⟩,⟨⟨(-6435),(-6423)⟩,⟨10917,10932⟩⟩,⟨⟨282980405108269099955578,282980405108269105664034⟩,⟨(-130624124907003306108101),(-130624124907003300405886)⟩⟩] +lemma atomKernel87_1_eq (j : Fin 7) : atomKernel87_1 j = (kernel0Box (atomPoints j) 87).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel87_1_contains (j : Fin 7) : (atomKernel87_1 j).Contains + (complexTransformedFactor 87 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel87_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=87) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel88_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),0⟩,⟨(-2),1⟩⟩,⟨⟨1466,1469⟩,⟨(-363),(-360)⟩⟩,⟨⟨(-53667761454177673217850),(-53667761454177671809334)⟩,⟨(-47151664169976977915978),(-47151664169976976506861)⟩⟩] +lemma atomKernel88_0_eq (j : Fin 7) : atomKernel88_0 j = kernel0Box (atomPoints j) 88 := by + fin_cases j <;> decide +kernel +lemma atomKernel88_0_contains (j : Fin 7) : (atomKernel88_0 j).Contains + (complexTransformedFactor 88 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel88_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=88) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel88_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-10),10⟩,⟨(-2),17⟩⟩,⟨⟨(-2518),(-2503)⟩,⟨(-5748),(-5733)⟩⟩,⟨⟨(-160188511511197630997088),(-160188511511197625643673)⟩,⟨202649510173129374133916,202649510173129379485345⟩⟩] +lemma atomKernel88_1_eq (j : Fin 7) : atomKernel88_1 j = (kernel0Box (atomPoints j) 88).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel88_1_contains (j : Fin 7) : (atomKernel88_1 j).Contains + (complexTransformedFactor 88 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel88_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=88) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel91_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-2),1⟩,⟨0,3⟩⟩,⟨⟨181,184⟩,⟨11,14⟩⟩,⟨⟨31433625527526022583414,31433625527526024155485⟩,⟨(-25808495280877464698778),(-25808495280877463127214)⟩⟩] +lemma atomKernel91_0_eq (j : Fin 7) : atomKernel91_0 j = kernel0Box (atomPoints j) 91 := by + fin_cases j <;> decide +kernel +lemma atomKernel91_0_contains (j : Fin 7) : (atomKernel91_0 j).Contains + (complexTransformedFactor 91 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel91_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=91) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel91_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-2),17⟩,⟨(-10),10⟩⟩,⟨⟨(-85),(-70)⟩,⟨(-762),(-747)⟩⟩,⟨⟨(-99097545770489476463551),(-99097545770489470493083)⟩,⟨(-108661492546998332529326),(-108661492546998326557061)⟩⟩] +lemma atomKernel91_1_eq (j : Fin 7) : atomKernel91_1 j = (kernel0Box (atomPoints j) 91).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel91_1_contains (j : Fin 7) : (atomKernel91_1 j).Contains + (complexTransformedFactor 91 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel91_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=91) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel93_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-1),3⟩,⟨(-3),2⟩⟩,⟨⟨(-12),(-9)⟩,⟨(-45),(-43)⟩⟩,⟨⟨(-1550134697257742362828),(-1550134697257741337808)⟩,⟨(-27894603629501960600858),(-27894603629501959575495)⟩⟩] +lemma atomKernel93_0_eq (j : Fin 7) : atomKernel93_0 j = kernel0Box (atomPoints j) 93 := by + fin_cases j <;> decide +kernel +lemma atomKernel93_0_contains (j : Fin 7) : (atomKernel93_0 j).Contains + (complexTransformedFactor 93 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel93_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=93) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel93_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-19),11⟩,⟨(-17),10⟩⟩,⟨⟨(-178),(-167)⟩,⟨67,81⟩⟩,⟨⟨(-100437066051539775915596),(-100437066051539772020190)⟩,⟨10835440037374908526648,10835440037374912420593⟩⟩] +lemma atomKernel93_1_eq (j : Fin 7) : atomKernel93_1 j = (kernel0Box (atomPoints j) 93).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel93_1_contains (j : Fin 7) : (atomKernel93_1 j).Contains + (complexTransformedFactor 93 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel93_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=93) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel96_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),1⟩,⟨(-2),3⟩⟩,⟨⟨0,2⟩,⟨(-7),(-4)⟩⟩,⟨⟨15814406802226201521746,15814406802226201786124⟩,⟨1698343281962387932152,1698343281962388196402⟩⟩] +lemma atomKernel96_0_eq (j : Fin 7) : atomKernel96_0 j = kernel0Box (atomPoints j) 96 := by + fin_cases j <;> decide +kernel +lemma atomKernel96_0_contains (j : Fin 7) : (atomKernel96_0 j).Contains + (complexTransformedFactor 96 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel96_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=96) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel96_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),16⟩,⟨(-21),19⟩⟩,⟨⟨(-11),19⟩,⟨(-10),17⟩⟩,⟨⟨(-31),(-16)⟩,⟨(-6),5⟩⟩,⟨⟨3163237606767119156122,3163237606767120160009⟩,⟨(-57425138362303901024255),(-57425138362303900019776)⟩⟩] +lemma atomKernel96_1_eq (j : Fin 7) : atomKernel96_1 j = (kernel0Box (atomPoints j) 96).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel96_1_contains (j : Fin 7) : (atomKernel96_1 j).Contains + (complexTransformedFactor 96 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel96_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=96) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel97_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),3⟩,⟨(-3),2⟩⟩,⟨⟨0,3⟩,⟨0,3⟩⟩,⟨⟨(-12325932838736401844278),(-12325932838736401506904)⟩,⟨4674042778858330868088,4674042778858331205212⟩⟩] +lemma atomKernel97_0_eq (j : Fin 7) : atomKernel97_0 j = kernel0Box (atomPoints j) 97 := by + fin_cases j <;> decide +kernel +lemma atomKernel97_0_contains (j : Fin 7) : (atomKernel97_0 j).Contains + (complexTransformedFactor 97 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel97_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=97) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel97_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-19),11⟩,⟨(-17),10⟩⟩,⟨⟨(-3),13⟩,⟨(-15),0⟩⟩,⟨⟨19192571930432366632996,19192571930432367913771⟩,⟨43631603741460833699467,43631603741460834981181⟩⟩] +lemma atomKernel97_1_eq (j : Fin 7) : atomKernel97_1 j = (kernel0Box (atomPoints j) 97).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel97_1_contains (j : Fin 7) : (atomKernel97_1 j).Contains + (complexTransformedFactor 97 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel97_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=97) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel99_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-2),3⟩⟩,⟨⟨(-1),2⟩,⟨(-2),0⟩⟩,⟨⟨(-2410742817318172851508),(-2410742817318172628096)⟩,⟨8728359067203883702675,8728359067203883926122⟩⟩] +lemma atomKernel99_0_eq (j : Fin 7) : atomKernel99_0 j = kernel0Box (atomPoints j) 99 := by + fin_cases j <;> decide +kernel +lemma atomKernel99_0_contains (j : Fin 7) : (atomKernel99_0 j).Contains + (complexTransformedFactor 99 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel99_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=99) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel99_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-11),19⟩,⟨(-10),17⟩⟩,⟨⟨(-10),1⟩,⟨(-9),6⟩⟩,⟨⟨31971005130459540601775,31971005130459541450702⟩,⟨7066301828693344635646,7066301828693345484384⟩⟩] +lemma atomKernel99_1_eq (j : Fin 7) : atomKernel99_1 j = (kernel0Box (atomPoints j) 99).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel99_1_contains (j : Fin 7) : (atomKernel99_1 j).Contains + (complexTransformedFactor 99 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel99_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=99) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +noncomputable def atomKernel100_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-2),3⟩⟩,⟨⟨0,2⟩,⟨(-1),2⟩⟩,⟨⟨(-1490670967802415506034),(-1490670967802415341050)⟩,⟨(-7355407834301021603761),(-7355407834301021438660)⟩⟩] +lemma atomKernel100_0_eq (j : Fin 7) : atomKernel100_0 j = kernel0Box (atomPoints j) 100 := by + fin_cases j <;> decide +kernel +lemma atomKernel100_0_contains (j : Fin 7) : (atomKernel100_0 j).Contains + (complexTransformedFactor 100 1 0 ((j.val:ℝ)/6)) := by + rw [atomKernel100_0_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=100) (by decide) + have h0 := transformed_factor_zero_contains hh + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using h0 +noncomputable def atomKernel100_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-11),19⟩,⟨(-10),17⟩⟩,⟨⟨(-6),9⟩,⟨(-10),1⟩⟩,⟨⟨(-26280660926903198384712),(-26280660926903197757462)⟩,⟨6764001278873901214272,6764001278873901841058⟩⟩] +lemma atomKernel100_1_eq (j : Fin 7) : atomKernel100_1 j = (kernel0Box (atomPoints j) 100).mul (piI.mul (atomPoints j).z) := by + fin_cases j <;> decide +kernel +lemma atomKernel100_1_contains (j : Fin 7) : (atomKernel100_1 j).Contains + (complexTransformedFactor 100 1 1 ((j.val:ℝ)/6)) := by + rw [atomKernel100_1_eq] + have hh := kernel0Box_contains (atomPoints_contains j) (m:=100) (by decide) + have h0 := transformed_factor_zero_contains hh + rw [transformed_factor_step] + have hzz : complexZ ((j.val:ℂ)/6) = z ((j.val:ℝ)/6) := by + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat] using + complexZ_ofReal ((j.val:ℝ)/6) + have hz := (atomPoints_contains j).2.2.1 + rw [pointZ_eq] at hz + simpa only [Nat.zero_add,Nat.cast_one,div_one,hzz,complexZ_ofReal,Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using + CBox.contains_mul h0 (CBox.contains_mul piI_contains hz) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/Bernstein0.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/Bernstein0.lean new file mode 100644 index 0000000000000000000000000000000000000000..5813ea23b826a218621e64695bfe5fe1f17c8cda --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/Bernstein0.lean @@ -0,0 +1,321 @@ +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_0 +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_4 +import OAI.Analysis.PlanarPacking.BernsteinBoxes +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_1 +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_2 +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_3 +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_5 +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_6 +import OAI.Analysis.PlanarPacking.Certificate.HighMoments0_7 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.Bernstein0 +open IntegerIntervals IntegerBasis Numerical CachedData +namespace N1_right +noncomputable def t0 : RBox := {lo := 3010659550390303898621260289067, hi := 3010659550390480643209021776036} +lemma t0_checked : ((hm0_1_0_0.realAnswer).add hm0_0_1_0.realAnswer).scale (1) 1=t0 := by decide +kernel +lemma t0_contains : t0.Contains (sourcePower true 0 (1/2) 0 0) := by + rw [← t0_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_0.realContains hm0_0_1_0.realContains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t1 : RBox := {lo := -1157514538053939177724331753156, hi := -1157514538053536044087787283906} +lemma t1_checked : ((hm0_1_0_1.realAnswer).add hm0_0_1_1.realAnswer).scale (1) 2=t1 := by decide +kernel +lemma t1_contains : t1.Contains (sourcePower true 0 (1/2) 0 1) := by + rw [← t1_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_1.realContains hm0_0_1_1.realContains) (1) 2 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t2 : RBox := {lo := -4083980829144199815552047121103, hi := -4083980829143671848176401706360} +lemma t2_checked : ((hm0_1_0_2.realAnswer).add hm0_0_1_2.realAnswer).scale (1) 4=t2 := by decide +kernel +lemma t2_contains : t2.Contains (sourcePower true 0 (1/2) 0 2) := by + rw [← t2_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_2.realContains hm0_0_1_2.realContains) (1) 4 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t3 : RBox := {lo := 5721821381827118436337229302358, hi := 5721821381827687689264449589910} +lemma t3_checked : ((hm0_1_0_3.realAnswer).add hm0_0_1_3.realAnswer).scale (1) 8=t3 := by decide +kernel +lemma t3_contains : t3.Contains (sourcePower true 0 (1/2) 0 3) := by + rw [← t3_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_3.realContains hm0_0_1_3.realContains) (1) 8 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t4 : RBox := {lo := -5382937070567010163413286437938, hi := -5382937070566575703506296564245} +lemma t4_checked : ((hm0_1_0_4.realAnswer).add hm0_0_1_4.realAnswer).scale (1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 0 (1/2) 0 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_4.realContains hm0_0_1_4.realContains) (1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t5 : RBox := {lo := 5253869407757627792877906430708, hi := 5253869407757964053467863760797} +lemma t5_checked : ((hm0_1_0_5.realAnswer).add hm0_0_1_5.realAnswer).scale (1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 0 (1/2) 0 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_5.realContains hm0_0_1_5.realContains) (1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t6 : RBox := {lo := -4661177298176000350739551351826, hi := -4661177298175791351040369632539} +lemma t6_checked : ((hm0_1_0_6.realAnswer).add hm0_0_1_6.realAnswer).scale (1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 0 (1/2) 0 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_6.realContains hm0_0_1_6.realContains) (1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t7 : RBox := {lo := 3374880889767393803869957738866, hi := 3374880889767507686009309906298} +lemma t7_checked : ((hm0_1_0_7.realAnswer).add hm0_0_1_7.realAnswer).scale (1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 0 (1/2) 0 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_7.realContains hm0_0_1_7.realContains) (1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t8 : RBox := {lo := -2010835960397130498414037786335, hi := -2010835960397074580873968573056} +lemma t8_checked : ((hm0_1_0_8.realAnswer).add hm0_0_1_8.realAnswer).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 0 (1/2) 0 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_8.realContains hm0_0_1_8.realContains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t9 : RBox := {lo := 1018772257458285554425588694868, hi := 1018772257458309724068594789857} +lemma t9_checked : ((hm0_1_0_9.realAnswer).add hm0_0_1_9.realAnswer).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 0 (1/2) 0 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_9.realContains hm0_0_1_9.realContains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t10 : RBox := {lo := -448722651349900756596575570102, hi := -448722651349891193108893116955} +lemma t10_checked : ((hm0_1_0_10.realAnswer).add hm0_0_1_10.realAnswer).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 0 (1/2) 0 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_10.realContains hm0_0_1_10.realContains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := 173606185176861026422696113900, hi := 173606185176864469860234569222} +lemma t11_checked : ((hm0_1_0_11.realAnswer).add hm0_0_1_11.realAnswer).scale (1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 0 (1/2) 0 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_11.realContains hm0_0_1_11.realContains) (1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -59507280908054413476215557022, hi := -59507280908053273606054575733} +lemma t12_checked : ((hm0_1_0_12.realAnswer).add hm0_0_1_12.realAnswer).scale (1) 4096=t12 := by decide +kernel +lemma t12_contains : t12.Contains (sourcePower true 0 (1/2) 0 12) := by + rw [← t12_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_12.realContains hm0_0_1_12.realContains) (1) 4096 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t13 : RBox := {lo := 18383711669706433117720700424, hi := 18383711669706782326150549042} +lemma t13_checked : ((hm0_1_0_13.realAnswer).add hm0_0_1_13.realAnswer).scale (1) 8192=t13 := by decide +kernel +lemma t13_contains : t13.Contains (sourcePower true 0 (1/2) 0 13) := by + rw [← t13_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_13.realContains hm0_0_1_13.realContains) (1) 8192 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t14 : RBox := {lo := -5280308198453700154466861404, hi := -5280308198453600612036277149} +lemma t14_checked : ((hm0_1_0_14.realAnswer).add hm0_0_1_14.realAnswer).scale (1) 16384=t14 := by decide +kernel +lemma t14_contains : t14.Contains (sourcePower true 0 (1/2) 0 14) := by + rw [← t14_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_14.realContains hm0_0_1_14.realContains) (1) 16384 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t15 : RBox := {lo := 1468750860697749988104331417, hi := 1468750860697776464442125617} +lemma t15_checked : ((hm0_1_0_15.realAnswer).add hm0_0_1_15.realAnswer).scale (1) 32768=t15 := by decide +kernel +lemma t15_contains : t15.Contains (sourcePower true 0 (1/2) 0 15) := by + rw [← t15_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_15.realContains hm0_0_1_15.realContains) (1) 32768 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t16 : RBox := {lo := -408586155659153146991480533, hi := -408586155659146522856268285} +lemma t16_checked : ((hm0_1_0_16.realAnswer).add hm0_0_1_16.realAnswer).scale (1) 65536=t16 := by decide +kernel +lemma t16_contains : t16.Contains (sourcePower true 0 (1/2) 0 16) := by + rw [← t16_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_16.realContains hm0_0_1_16.realContains) (1) 65536 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t17 : RBox := {lo := 114108058606255134053354090, hi := 114108058606256695231919493} +lemma t17_checked : ((hm0_1_0_17.realAnswer).add hm0_0_1_17.realAnswer).scale (1) 131072=t17 := by decide +kernel +lemma t17_contains : t17.Contains (sourcePower true 0 (1/2) 0 17) := by + rw [← t17_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_17.realContains hm0_0_1_17.realContains) (1) 131072 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t18 : RBox := {lo := -31289156184766260600739793, hi := -31289156184765912884567838} +lemma t18_checked : ((hm0_1_0_18.realAnswer).add hm0_0_1_18.realAnswer).scale (1) 262144=t18 := by decide +kernel +lemma t18_contains : t18.Contains (sourcePower true 0 (1/2) 0 18) := by + rw [← t18_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_18.realContains hm0_0_1_18.realContains) (1) 262144 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t19 : RBox := {lo := 8193300540967235684014113, hi := 8193300540967309215535189} +lemma t19_checked : ((hm0_1_0_19.realAnswer).add hm0_0_1_19.realAnswer).scale (1) 524288=t19 := by decide +kernel +lemma t19_contains : t19.Contains (sourcePower true 0 (1/2) 0 19) := by + rw [← t19_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_19.realContains hm0_0_1_19.realContains) (1) 524288 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t20 : RBox := {lo := -2010567823212377569297526, hi := -2010567823212362778860796} +lemma t20_checked : ((hm0_1_0_20.realAnswer).add hm0_0_1_20.realAnswer).scale (1) 1048576=t20 := by decide +kernel +lemma t20_contains : t20.Contains (sourcePower true 0 (1/2) 0 20) := by + rw [← t20_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_20.realContains hm0_0_1_20.realContains) (1) 1048576 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t21 : RBox := {lo := 458686901207641578218607, hi := 458686901207644417814637} +lemma t21_checked : ((hm0_1_0_21.realAnswer).add hm0_0_1_21.realAnswer).scale (1) 2097152=t21 := by decide +kernel +lemma t21_contains : t21.Contains (sourcePower true 0 (1/2) 0 21) := by + rw [← t21_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_21.realContains hm0_0_1_21.realContains) (1) 2097152 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t22 : RBox := {lo := -97262997565299989711617, hi := -97262997565299469091222} +lemma t22_checked : ((hm0_1_0_22.realAnswer).add hm0_0_1_22.realAnswer).scale (1) 4194304=t22 := by decide +kernel +lemma t22_contains : t22.Contains (sourcePower true 0 (1/2) 0 22) := by + rw [← t22_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_22.realContains hm0_0_1_22.realContains) (1) 4194304 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t23 : RBox := {lo := 19253022017069823168490, hi := 19253022017069914774625} +lemma t23_checked : ((hm0_1_0_23.realAnswer).add hm0_0_1_23.realAnswer).scale (1) 8388608=t23 := by decide +kernel +lemma t23_contains : t23.Contains (sourcePower true 0 (1/2) 0 23) := by + rw [← t23_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_23.realContains hm0_0_1_23.realContains) (1) 8388608 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t24 : RBox := {lo := -3582895898254668588208, hi := -3582895898254653101891} +lemma t24_checked : ((hm0_1_0_24.realAnswer).add hm0_0_1_24.realAnswer).scale (1) 16777216=t24 := by decide +kernel +lemma t24_contains : t24.Contains (sourcePower true 0 (1/2) 0 24) := by + rw [← t24_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_24.realContains hm0_0_1_24.realContains) (1) 16777216 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t25 : RBox := {lo := 632382829782203366350, hi := 632382829782205884770} +lemma t25_checked : ((hm0_1_0_25.realAnswer).add hm0_0_1_25.realAnswer).scale (1) 33554432=t25 := by decide +kernel +lemma t25_contains : t25.Contains (sourcePower true 0 (1/2) 0 25) := by + rw [← t25_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_25.realContains hm0_0_1_25.realContains) (1) 33554432 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t26 : RBox := {lo := -106912686730081946069, hi := -106912686730081550688} +lemma t26_checked : ((hm0_1_0_26.realAnswer).add hm0_0_1_26.realAnswer).scale (1) 67108864=t26 := by decide +kernel +lemma t26_contains : t26.Contains (sourcePower true 0 (1/2) 0 26) := by + rw [← t26_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_26.realContains hm0_0_1_26.realContains) (1) 67108864 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t27 : RBox := {lo := 17487194279363975319, hi := 17487194279364035379} +lemma t27_checked : ((hm0_1_0_27.realAnswer).add hm0_0_1_27.realAnswer).scale (1) 134217728=t27 := by decide +kernel +lemma t27_contains : t27.Contains (sourcePower true 0 (1/2) 0 27) := by + rw [← t27_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_27.realContains hm0_0_1_27.realContains) (1) 134217728 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t28 : RBox := {lo := -2791162666881053465, hi := -2791162666881044618} +lemma t28_checked : ((hm0_1_0_28.realAnswer).add hm0_0_1_28.realAnswer).scale (1) 268435456=t28 := by decide +kernel +lemma t28_contains : t28.Contains (sourcePower true 0 (1/2) 0 28) := by + rw [← t28_checked] + convert RBox.contains_scale (RBox.contains_add hm0_1_0_28.realContains hm0_0_1_28.realContains) (1) 268435456 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 0 (1/2) 0 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (37:ℝ)/50 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -20540279013060288964123, hi := 20540279013060288964123} +lemma t13_contains : t13.Contains (sourcePower false 12 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 13 coarse_12_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -2370812092565497112264, hi := 2370812092565497112264} +lemma t14_contains : t14.Contains (sourcePower false 12 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 14 coarse_12_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -263953881363605769697, hi := 263953881363605769697} +lemma t15_contains : t15.Contains (sourcePower false 12 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 15 coarse_12_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -28365989397522196385, hi := 28365989397522196385} +lemma t16_contains : t16.Contains (sourcePower false 12 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 16 coarse_12_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -2943072604808163227, hi := 2943072604808163227} +lemma t17_contains : t17.Contains (sourcePower false 12 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 17 coarse_12_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -294818953479539848, hi := 294818953479539848} +lemma t18_contains : t18.Contains (sourcePower false 12 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 18 coarse_12_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -28516436648066880, hi := 28516436648066880} +lemma t19_contains : t19.Contains (sourcePower false 12 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 19 coarse_12_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -2663938389153873, hi := 2663938389153873} +lemma t20_contains : t20.Contains (sourcePower false 12 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 20 coarse_12_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -240457452818595, hi := 240457452818595} +lemma t21_contains : t21.Contains (sourcePower false 12 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 21 coarse_12_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -20985905895579, hi := 20985905895579} +lemma t22_contains : t22.Contains (sourcePower false 12 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 22 coarse_12_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -1772419477128, hi := 1772419477128} +lemma t23_contains : t23.Contains (sourcePower false 12 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 23 coarse_12_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -145009275090, hi := 145009275090} +lemma t24_contains : t24.Contains (sourcePower false 12 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 24 coarse_12_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -11505508624, hi := 11505508624} +lemma t25_contains : t25.Contains (sourcePower false 12 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 25 coarse_12_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -886376938, hi := 886376938} +lemma t26_contains : t26.Contains (sourcePower false 12 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 26 coarse_12_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -66385150, hi := 66385150} +lemma t27_contains : t27.Contains (sourcePower false 12 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 27 coarse_12_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -4839517, hi := 4839517} +lemma t28_contains : t28.Contains (sourcePower false 12 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (1/2) 2 28 coarse_12_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 12 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -20540279013060288964123, hi := 20540279013060288964123} +lemma t13_contains : t13.Contains (sourcePower true 12 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 13 coarse_12_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -2370812092565497112264, hi := 2370812092565497112264} +lemma t14_contains : t14.Contains (sourcePower true 12 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 14 coarse_12_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -263953881363605769697, hi := 263953881363605769697} +lemma t15_contains : t15.Contains (sourcePower true 12 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 15 coarse_12_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -28365989397522196385, hi := 28365989397522196385} +lemma t16_contains : t16.Contains (sourcePower true 12 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 16 coarse_12_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -2943072604808163227, hi := 2943072604808163227} +lemma t17_contains : t17.Contains (sourcePower true 12 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 17 coarse_12_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -294818953479539848, hi := 294818953479539848} +lemma t18_contains : t18.Contains (sourcePower true 12 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 18 coarse_12_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -28516436648066880, hi := 28516436648066880} +lemma t19_contains : t19.Contains (sourcePower true 12 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 19 coarse_12_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -2663938389153873, hi := 2663938389153873} +lemma t20_contains : t20.Contains (sourcePower true 12 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 20 coarse_12_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -240457452818595, hi := 240457452818595} +lemma t21_contains : t21.Contains (sourcePower true 12 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 21 coarse_12_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -20985905895579, hi := 20985905895579} +lemma t22_contains : t22.Contains (sourcePower true 12 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 22 coarse_12_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -1772419477128, hi := 1772419477128} +lemma t23_contains : t23.Contains (sourcePower true 12 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 23 coarse_12_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -145009275090, hi := 145009275090} +lemma t24_contains : t24.Contains (sourcePower true 12 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 24 coarse_12_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -11505508624, hi := 11505508624} +lemma t25_contains : t25.Contains (sourcePower true 12 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 25 coarse_12_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -886376938, hi := 886376938} +lemma t26_contains : t26.Contains (sourcePower true 12 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 26 coarse_12_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -66385150, hi := 66385150} +lemma t27_contains : t27.Contains (sourcePower true 12 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 27 coarse_12_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -4839517, hi := 4839517} +lemma t28_contains : t28.Contains (sourcePower true 12 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (1/2) 2 28 coarse_12_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 12 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -32747839256939319082147225590, hi := 32747839256939319082147225590} +lemma t13_contains : t13.Contains (sourcePower false 12 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 13 coarse_12_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -11339520743565903157545117223, hi := 11339520743565903157545117223} +lemma t14_contains : t14.Contains (sourcePower false 12 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 14 coarse_12_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -3787449695975412374043620960, hi := 3787449695975412374043620960} +lemma t15_contains : t15.Contains (sourcePower false 12 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 15 coarse_12_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1221062831484096079059057587, hi := 1221062831484096079059057587} +lemma t16_contains : t16.Contains (sourcePower false 12 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 16 coarse_12_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -380068875905760782769548654, hi := 380068875905760782769548654} +lemma t17_contains : t17.Contains (sourcePower false 12 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 17 coarse_12_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -114218903123511579077843282, hi := 114218903123511579077843282} +lemma t18_contains : t18.Contains (sourcePower false 12 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 18 coarse_12_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -33143555492194773979714580, hi := 33143555492194773979714580} +lemma t19_contains : t19.Contains (sourcePower false 12 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 19 coarse_12_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -9288578820526788622989364, hi := 9288578820526788622989364} +lemma t20_contains : t20.Contains (sourcePower false 12 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 20 coarse_12_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -2515269886776208955260010, hi := 2515269886776208955260010} +lemma t21_contains : t21.Contains (sourcePower false 12 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 21 coarse_12_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -658559963858000548233917, hi := 658559963858000548233917} +lemma t22_contains : t22.Contains (sourcePower false 12 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 22 coarse_12_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -166861203791677917241811, hi := 166861203791677917241811} +lemma t23_contains : t23.Contains (sourcePower false 12 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 23 coarse_12_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -40954902349054626329048, hi := 40954902349054626329048} +lemma t24_contains : t24.Contains (sourcePower false 12 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 24 coarse_12_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -9748486402679208977336, hi := 9748486402679208977336} +lemma t25_contains : t25.Contains (sourcePower false 12 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 25 coarse_12_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -2253051248616112321678, hi := 2253051248616112321678} +lemma t26_contains : t26.Contains (sourcePower false 12 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 26 coarse_12_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -506226427008888682575, hi := 506226427008888682575} +lemma t27_contains : t27.Contains (sourcePower false 12 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 27 coarse_12_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -110712622742236369478, hi := 110712622742236369478} +lemma t28_contains : t28.Contains (sourcePower false 12 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 12 (-3/2) 2 28 coarse_12_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 12 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -32747839256939319082147225590, hi := 32747839256939319082147225590} +lemma t13_contains : t13.Contains (sourcePower true 12 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 13 coarse_12_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -11339520743565903157545117223, hi := 11339520743565903157545117223} +lemma t14_contains : t14.Contains (sourcePower true 12 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 14 coarse_12_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -3787449695975412374043620960, hi := 3787449695975412374043620960} +lemma t15_contains : t15.Contains (sourcePower true 12 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 15 coarse_12_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1221062831484096079059057587, hi := 1221062831484096079059057587} +lemma t16_contains : t16.Contains (sourcePower true 12 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 16 coarse_12_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -380068875905760782769548654, hi := 380068875905760782769548654} +lemma t17_contains : t17.Contains (sourcePower true 12 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 17 coarse_12_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -114218903123511579077843282, hi := 114218903123511579077843282} +lemma t18_contains : t18.Contains (sourcePower true 12 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 18 coarse_12_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -33143555492194773979714580, hi := 33143555492194773979714580} +lemma t19_contains : t19.Contains (sourcePower true 12 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 19 coarse_12_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -9288578820526788622989364, hi := 9288578820526788622989364} +lemma t20_contains : t20.Contains (sourcePower true 12 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 20 coarse_12_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -2515269886776208955260010, hi := 2515269886776208955260010} +lemma t21_contains : t21.Contains (sourcePower true 12 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 21 coarse_12_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -658559963858000548233917, hi := 658559963858000548233917} +lemma t22_contains : t22.Contains (sourcePower true 12 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 22 coarse_12_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -166861203791677917241811, hi := 166861203791677917241811} +lemma t23_contains : t23.Contains (sourcePower true 12 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 23 coarse_12_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -40954902349054626329048, hi := 40954902349054626329048} +lemma t24_contains : t24.Contains (sourcePower true 12 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 24 coarse_12_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -9748486402679208977336, hi := 9748486402679208977336} +lemma t25_contains : t25.Contains (sourcePower true 12 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 25 coarse_12_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -2253051248616112321678, hi := 2253051248616112321678} +lemma t26_contains : t26.Contains (sourcePower true 12 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 26 coarse_12_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -506226427008888682575, hi := 506226427008888682575} +lemma t27_contains : t27.Contains (sourcePower true 12 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 27 coarse_12_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -110712622742236369478, hi := 110712622742236369478} +lemma t28_contains : t28.Contains (sourcePower true 12 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 12 (-3/2) 2 28 coarse_12_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 12 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -617291382224693317143528265, hi := 617291382224693317143528265} +lemma t12_contains : t12.Contains (sourcePower false 13 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 12 coarse_13_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -144478140411823014312463399, hi := 144478140411823014312463399} +lemma t13_contains : t13.Contains (sourcePower false 13 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 13 coarse_13_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -32567611871130225775617023, hi := 32567611871130225775617023} +lemma t14_contains : t14.Contains (sourcePower false 13 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 14 coarse_13_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -7086462145518744700765859, hi := 7086462145518744700765859} +lemma t15_contains : t15.Contains (sourcePower false 13 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 15 coarse_13_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1490272985556831369284206, hi := 1490272985556831369284206} +lemma t16_contains : t16.Contains (sourcePower false 13 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 16 coarse_13_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -303042818377332642491714, hi := 303042818377332642491714} +lemma t17_contains : t17.Contains (sourcePower false 13 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 17 coarse_13_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -59589010613871900078267, hi := 59589010613871900078267} +lemma t18_contains : t18.Contains (sourcePower false 13 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 18 coarse_13_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -11329372415748521439348, hi := 11329372415748521439348} +lemma t19_contains : t19.Contains (sourcePower false 13 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 19 coarse_13_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -2082539517045679030472, hi := 2082539517045679030472} +lemma t20_contains : t20.Contains (sourcePower false 13 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 20 coarse_13_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -370140407122910181103, hi := 370140407122910181103} +lemma t21_contains : t21.Contains (sourcePower false 13 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 21 coarse_13_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -63628917450002357168, hi := 63628917450002357168} +lemma t22_contains : t22.Contains (sourcePower false 13 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 22 coarse_13_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -10584744548565259465, hi := 10584744548565259465} +lemma t23_contains : t23.Contains (sourcePower false 13 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 23 coarse_13_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1705111562507517738, hi := 1705111562507517738} +lemma t24_contains : t24.Contains (sourcePower false 13 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 24 coarse_13_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -266227122488009142, hi := 266227122488009142} +lemma t25_contains : t25.Contains (sourcePower false 13 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 25 coarse_13_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -40328799510286982, hi := 40328799510286982} +lemma t26_contains : t26.Contains (sourcePower false 13 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 26 coarse_13_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -5933603166316064, hi := 5933603166316064} +lemma t27_contains : t27.Contains (sourcePower false 13 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 27 coarse_13_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -848915492766886, hi := 848915492766886} +lemma t28_contains : t28.Contains (sourcePower false 13 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (1/1) 2 28 coarse_13_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 13 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -617291382224693317143528265, hi := 617291382224693317143528265} +lemma t12_contains : t12.Contains (sourcePower true 13 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 12 coarse_13_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -144478140411823014312463399, hi := 144478140411823014312463399} +lemma t13_contains : t13.Contains (sourcePower true 13 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 13 coarse_13_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -32567611871130225775617023, hi := 32567611871130225775617023} +lemma t14_contains : t14.Contains (sourcePower true 13 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 14 coarse_13_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -7086462145518744700765859, hi := 7086462145518744700765859} +lemma t15_contains : t15.Contains (sourcePower true 13 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 15 coarse_13_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1490272985556831369284206, hi := 1490272985556831369284206} +lemma t16_contains : t16.Contains (sourcePower true 13 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 16 coarse_13_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -303042818377332642491714, hi := 303042818377332642491714} +lemma t17_contains : t17.Contains (sourcePower true 13 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 17 coarse_13_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -59589010613871900078267, hi := 59589010613871900078267} +lemma t18_contains : t18.Contains (sourcePower true 13 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 18 coarse_13_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -11329372415748521439348, hi := 11329372415748521439348} +lemma t19_contains : t19.Contains (sourcePower true 13 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 19 coarse_13_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -2082539517045679030472, hi := 2082539517045679030472} +lemma t20_contains : t20.Contains (sourcePower true 13 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 20 coarse_13_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -370140407122910181103, hi := 370140407122910181103} +lemma t21_contains : t21.Contains (sourcePower true 13 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 21 coarse_13_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -63628917450002357168, hi := 63628917450002357168} +lemma t22_contains : t22.Contains (sourcePower true 13 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 22 coarse_13_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -10584744548565259465, hi := 10584744548565259465} +lemma t23_contains : t23.Contains (sourcePower true 13 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 23 coarse_13_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1705111562507517738, hi := 1705111562507517738} +lemma t24_contains : t24.Contains (sourcePower true 13 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 24 coarse_13_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -266227122488009142, hi := 266227122488009142} +lemma t25_contains : t25.Contains (sourcePower true 13 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 25 coarse_13_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -40328799510286982, hi := 40328799510286982} +lemma t26_contains : t26.Contains (sourcePower true 13 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 26 coarse_13_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -5933603166316064, hi := 5933603166316064} +lemma t27_contains : t27.Contains (sourcePower true 13 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 27 coarse_13_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -848915492766886, hi := 848915492766886} +lemma t28_contains : t28.Contains (sourcePower true 13 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (1/1) 2 28 coarse_13_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 13 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -150705903863450516880745, hi := 150705903863450516880745} +lemma t12_contains : t12.Contains (sourcePower false 13 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 12 coarse_13_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -17636491749490114051815, hi := 17636491749490114051815} +lemma t13_contains : t13.Contains (sourcePower false 13 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 13 coarse_13_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -1987769279243788194313, hi := 1987769279243788194313} +lemma t14_contains : t14.Contains (sourcePower false 13 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 14 coarse_13_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -216261662155723410058, hi := 216261662155723410058} +lemma t15_contains : t15.Contains (sourcePower false 13 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 15 coarse_13_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -22739761132153798970, hi := 22739761132153798970} +lemma t16_contains : t16.Contains (sourcePower false 13 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 16 coarse_13_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -2312033221262608662, hi := 2312033221262608662} +lemma t17_contains : t17.Contains (sourcePower false 13 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 17 coarse_13_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -227314035850036240, hi := 227314035850036240} +lemma t18_contains : t18.Contains (sourcePower false 13 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 18 coarse_13_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -21609062987801593, hi := 21609062987801593} +lemma t19_contains : t19.Contains (sourcePower false 13 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 19 coarse_13_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1986064450307540, hi := 1986064450307540} +lemma t20_contains : t20.Contains (sourcePower false 13 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 20 coarse_13_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -176496699868637, hi := 176496699868637} +lemma t21_contains : t21.Contains (sourcePower false 13 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 21 coarse_13_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -15170316088201, hi := 15170316088201} +lemma t22_contains : t22.Contains (sourcePower false 13 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 22 coarse_13_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -1261799877711, hi := 1261799877711} +lemma t23_contains : t23.Contains (sourcePower false 13 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 23 coarse_13_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -101632568986, hi := 101632568986} +lemma t24_contains : t24.Contains (sourcePower false 13 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 24 coarse_13_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -7934186533, hi := 7934186533} +lemma t25_contains : t25.Contains (sourcePower false 13 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 25 coarse_13_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -600945943, hi := 600945943} +lemma t26_contains : t26.Contains (sourcePower false 13 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 26 coarse_13_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -44208789, hi := 44208789} +lemma t27_contains : t27.Contains (sourcePower false 13 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 27 coarse_13_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -3162457, hi := 3162457} +lemma t28_contains : t28.Contains (sourcePower false 13 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 13 (-1/2) 2 28 coarse_13_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 13 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -150705903863450516880745, hi := 150705903863450516880745} +lemma t12_contains : t12.Contains (sourcePower true 13 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 12 coarse_13_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -17636491749490114051815, hi := 17636491749490114051815} +lemma t13_contains : t13.Contains (sourcePower true 13 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 13 coarse_13_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -1987769279243788194313, hi := 1987769279243788194313} +lemma t14_contains : t14.Contains (sourcePower true 13 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 14 coarse_13_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -216261662155723410058, hi := 216261662155723410058} +lemma t15_contains : t15.Contains (sourcePower true 13 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 15 coarse_13_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -22739761132153798970, hi := 22739761132153798970} +lemma t16_contains : t16.Contains (sourcePower true 13 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 16 coarse_13_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -2312033221262608662, hi := 2312033221262608662} +lemma t17_contains : t17.Contains (sourcePower true 13 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 17 coarse_13_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -227314035850036240, hi := 227314035850036240} +lemma t18_contains : t18.Contains (sourcePower true 13 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 18 coarse_13_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -21609062987801593, hi := 21609062987801593} +lemma t19_contains : t19.Contains (sourcePower true 13 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 19 coarse_13_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1986064450307540, hi := 1986064450307540} +lemma t20_contains : t20.Contains (sourcePower true 13 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 20 coarse_13_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -176496699868637, hi := 176496699868637} +lemma t21_contains : t21.Contains (sourcePower true 13 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 21 coarse_13_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -15170316088201, hi := 15170316088201} +lemma t22_contains : t22.Contains (sourcePower true 13 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 22 coarse_13_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -1261799877711, hi := 1261799877711} +lemma t23_contains : t23.Contains (sourcePower true 13 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 23 coarse_13_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -101632568986, hi := 101632568986} +lemma t24_contains : t24.Contains (sourcePower true 13 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 24 coarse_13_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -7934186533, hi := 7934186533} +lemma t25_contains : t25.Contains (sourcePower true 13 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 25 coarse_13_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -600945943, hi := 600945943} +lemma t26_contains : t26.Contains (sourcePower true 13 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 26 coarse_13_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -44208789, hi := 44208789} +lemma t27_contains : t27.Contains (sourcePower true 13 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 27 coarse_13_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -3162457, hi := 3162457} +lemma t28_contains : t28.Contains (sourcePower true 13 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 13 (-1/2) 2 28 coarse_13_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 13 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -124676864188939402959787, hi := 124676864188939402959787} +lemma t12_contains : t12.Contains (sourcePower false 15 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 12 coarse_15_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14011371607662972651343, hi := 14011371607662972651343} +lemma t13_contains : t13.Contains (sourcePower false 15 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 13 coarse_15_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -1513738773311503444352, hi := 1513738773311503444352} +lemma t14_contains : t14.Contains (sourcePower false 15 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 14 coarse_15_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -157824026550899286770, hi := 157824026550899286770} +lemma t15_contains : t15.Contains (sourcePower false 15 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 15 coarse_15_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -15922942750219540366, hi := 15922942750219540366} +lemma t16_contains : t16.Contains (sourcePower false 15 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 16 coarse_15_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1557074307019053506, hi := 1557074307019053506} +lemma t17_contains : t17.Contains (sourcePower false 15 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 17 coarse_15_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -147690407521422312, hi := 147690407521422312} +lemma t18_contains : t18.Contains (sourcePower false 15 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 18 coarse_15_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -13589382730293059, hi := 13589382730293059} +lemma t19_contains : t19.Contains (sourcePower false 15 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 19 coarse_15_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1212674233406933, hi := 1212674233406933} +lemma t20_contains : t20.Contains (sourcePower false 15 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 20 coarse_15_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -104912039047631, hi := 104912039047631} +lemma t21_contains : t21.Contains (sourcePower false 15 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 21 coarse_15_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -8796397165936, hi := 8796397165936} +lemma t22_contains : t22.Contains (sourcePower false 15 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 22 coarse_15_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -714679113149, hi := 714679113149} +lemma t23_contains : t23.Contains (sourcePower false 15 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 23 coarse_15_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -56267812699, hi := 56267812699} +lemma t24_contains : t24.Contains (sourcePower false 15 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 24 coarse_15_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -4293965936, hi := 4293965936} +lemma t25_contains : t25.Contains (sourcePower false 15 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 25 coarse_15_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -317759162, hi := 317759162} +lemma t26_contains : t26.Contains (sourcePower false 15 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 26 coarse_15_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -22816166, hi := 22816166} +lemma t27_contains : t27.Contains (sourcePower false 15 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 27 coarse_15_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1590803, hi := 1590803} +lemma t28_contains : t28.Contains (sourcePower false 15 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (1/2) 2 28 coarse_15_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 15 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -124676864188939402959787, hi := 124676864188939402959787} +lemma t12_contains : t12.Contains (sourcePower true 15 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 12 coarse_15_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14011371607662972651343, hi := 14011371607662972651343} +lemma t13_contains : t13.Contains (sourcePower true 15 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 13 coarse_15_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -1513738773311503444352, hi := 1513738773311503444352} +lemma t14_contains : t14.Contains (sourcePower true 15 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 14 coarse_15_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -157824026550899286770, hi := 157824026550899286770} +lemma t15_contains : t15.Contains (sourcePower true 15 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 15 coarse_15_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -15922942750219540366, hi := 15922942750219540366} +lemma t16_contains : t16.Contains (sourcePower true 15 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 16 coarse_15_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1557074307019053506, hi := 1557074307019053506} +lemma t17_contains : t17.Contains (sourcePower true 15 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 17 coarse_15_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -147690407521422312, hi := 147690407521422312} +lemma t18_contains : t18.Contains (sourcePower true 15 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 18 coarse_15_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -13589382730293059, hi := 13589382730293059} +lemma t19_contains : t19.Contains (sourcePower true 15 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 19 coarse_15_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1212674233406933, hi := 1212674233406933} +lemma t20_contains : t20.Contains (sourcePower true 15 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 20 coarse_15_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -104912039047631, hi := 104912039047631} +lemma t21_contains : t21.Contains (sourcePower true 15 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 21 coarse_15_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -8796397165936, hi := 8796397165936} +lemma t22_contains : t22.Contains (sourcePower true 15 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 22 coarse_15_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -714679113149, hi := 714679113149} +lemma t23_contains : t23.Contains (sourcePower true 15 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 23 coarse_15_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -56267812699, hi := 56267812699} +lemma t24_contains : t24.Contains (sourcePower true 15 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 24 coarse_15_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -4293965936, hi := 4293965936} +lemma t25_contains : t25.Contains (sourcePower true 15 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 25 coarse_15_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -317759162, hi := 317759162} +lemma t26_contains : t26.Contains (sourcePower true 15 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 26 coarse_15_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -22816166, hi := 22816166} +lemma t27_contains : t27.Contains (sourcePower true 15 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 27 coarse_15_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1590803, hi := 1590803} +lemma t28_contains : t28.Contains (sourcePower true 15 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (1/2) 2 28 coarse_15_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 15 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -510676435717895794523285937, hi := 510676435717895794523285937} +lemma t12_contains : t12.Contains (sourcePower false 15 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 12 coarse_15_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -114781156209975071959800993, hi := 114781156209975071959800993} +lemma t13_contains : t13.Contains (sourcePower false 15 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 13 coarse_15_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -24801096061935672432257826, hi := 24801096061935672432257826} +lemma t14_contains : t14.Contains (sourcePower false 15 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 14 coarse_15_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -5171577702019867828849372, hi := 5171577702019867828849372} +lemma t15_contains : t15.Contains (sourcePower false 15 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 15 coarse_15_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1043525976078387797403047, hi := 1043525976078387797403047} +lemma t16_contains : t16.Contains (sourcePower false 15 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 16 coarse_15_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -204088843569601381051700, hi := 204088843569601381051700} +lemma t17_contains : t17.Contains (sourcePower false 15 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 17 coarse_15_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -38716154189295730443609, hi := 38716154189295730443609} +lemma t18_contains : t18.Contains (sourcePower false 15 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 18 coarse_15_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -7124750292899887013175, hi := 7124750292899887013175} +lemma t19_contains : t19.Contains (sourcePower false 15 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 19 coarse_15_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1271581096968907241704, hi := 1271581096968907241704} +lemma t20_contains : t20.Contains (sourcePower false 15 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 20 coarse_15_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -220016492512816141698, hi := 220016492512816141698} +lemma t21_contains : t21.Contains (sourcePower false 15 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 21 coarse_15_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -36894763818673297662, hi := 36894763818673297662} +lemma t22_contains : t22.Contains (sourcePower false 15 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 22 coarse_15_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -5995162925987219398, hi := 5995162925987219398} +lemma t23_contains : t23.Contains (sourcePower false 15 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 23 coarse_15_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -944017247492413777, hi := 944017247492413777} +lemma t24_contains : t24.Contains (sourcePower false 15 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 24 coarse_15_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -144081587984564201, hi := 144081587984564201} +lemma t25_contains : t25.Contains (sourcePower false 15 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 25 coarse_15_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -21324456348662756, hi := 21324456348662756} +lemma t26_contains : t26.Contains (sourcePower false 15 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 26 coarse_15_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -3062333875518606, hi := 3062333875518606} +lemma t27_contains : t27.Contains (sourcePower false 15 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 27 coarse_15_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -427027912874177, hi := 427027912874177} +lemma t28_contains : t28.Contains (sourcePower false 15 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 15 (-1/1) 2 28 coarse_15_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 15 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -510676435717895794523285937, hi := 510676435717895794523285937} +lemma t12_contains : t12.Contains (sourcePower true 15 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 12 coarse_15_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -114781156209975071959800993, hi := 114781156209975071959800993} +lemma t13_contains : t13.Contains (sourcePower true 15 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 13 coarse_15_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -24801096061935672432257826, hi := 24801096061935672432257826} +lemma t14_contains : t14.Contains (sourcePower true 15 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 14 coarse_15_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -5171577702019867828849372, hi := 5171577702019867828849372} +lemma t15_contains : t15.Contains (sourcePower true 15 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 15 coarse_15_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1043525976078387797403047, hi := 1043525976078387797403047} +lemma t16_contains : t16.Contains (sourcePower true 15 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 16 coarse_15_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -204088843569601381051700, hi := 204088843569601381051700} +lemma t17_contains : t17.Contains (sourcePower true 15 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 17 coarse_15_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -38716154189295730443609, hi := 38716154189295730443609} +lemma t18_contains : t18.Contains (sourcePower true 15 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 18 coarse_15_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -7124750292899887013175, hi := 7124750292899887013175} +lemma t19_contains : t19.Contains (sourcePower true 15 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 19 coarse_15_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1271581096968907241704, hi := 1271581096968907241704} +lemma t20_contains : t20.Contains (sourcePower true 15 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 20 coarse_15_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -220016492512816141698, hi := 220016492512816141698} +lemma t21_contains : t21.Contains (sourcePower true 15 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 21 coarse_15_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -36894763818673297662, hi := 36894763818673297662} +lemma t22_contains : t22.Contains (sourcePower true 15 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 22 coarse_15_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -5995162925987219398, hi := 5995162925987219398} +lemma t23_contains : t23.Contains (sourcePower true 15 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 23 coarse_15_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -944017247492413777, hi := 944017247492413777} +lemma t24_contains : t24.Contains (sourcePower true 15 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 24 coarse_15_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -144081587984564201, hi := 144081587984564201} +lemma t25_contains : t25.Contains (sourcePower true 15 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 25 coarse_15_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -21324456348662756, hi := 21324456348662756} +lemma t26_contains : t26.Contains (sourcePower true 15 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 26 coarse_15_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -3062333875518606, hi := 3062333875518606} +lemma t27_contains : t27.Contains (sourcePower true 15 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 27 coarse_15_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -427027912874177, hi := 427027912874177} +lemma t28_contains : t28.Contains (sourcePower true 15 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 15 (-1/1) 2 28 coarse_15_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 15 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -20500998507632111319484518539, hi := 20500998507632111319484518539} +lemma t13_contains : t13.Contains (sourcePower false 16 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 13 coarse_16_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -6523208948461922490851005092, hi := 6523208948461922490851005092} +lemma t14_contains : t14.Contains (sourcePower false 16 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 14 coarse_16_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2001108592322595368095247195, hi := 2001108592322595368095247195} +lemma t15_contains : t15.Contains (sourcePower false 16 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 15 coarse_16_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -593882974596011604139733432, hi := 593882974596011604139733432} +lemma t16_contains : t16.Contains (sourcePower false 16 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 16 coarse_16_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -170914791314823074313359263, hi := 170914791314823074313359263} +lemma t17_contains : t17.Contains (sourcePower false 16 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 17 coarse_16_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -47763463222836881166984422, hi := 47763463222836881166984422} +lemma t18_contains : t18.Contains (sourcePower false 16 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 18 coarse_16_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -12968152058503371238596043, hi := 12968152058503371238596043} +lemma t19_contains : t19.Contains (sourcePower false 16 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 19 coarse_16_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -3420604834478252576726273, hi := 3420604834478252576726273} +lemma t20_contains : t20.Contains (sourcePower false 16 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 20 coarse_16_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -876206515302459865725797, hi := 876206515302459865725797} +lemma t21_contains : t21.Contains (sourcePower false 16 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 21 coarse_16_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -217861827796249410693090, hi := 217861827796249410693090} +lemma t22_contains : t22.Contains (sourcePower false 16 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 22 coarse_16_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -52558745128403565729773, hi := 52558745128403565729773} +lemma t23_contains : t23.Contains (sourcePower false 16 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 23 coarse_16_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -12299393946913104075874, hi := 12299393946913104075874} +lemma t24_contains : t24.Contains (sourcePower false 16 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 24 coarse_16_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -2791704545697118689729, hi := 2791704545697118689729} +lemma t25_contains : t25.Contains (sourcePower false 16 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 25 coarse_16_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -614700496900798892964, hi := 614700496900798892964} +lemma t26_contains : t26.Contains (sourcePower false 16 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 26 coarse_16_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -131343900200550587389, hi := 131343900200550587389} +lemma t27_contains : t27.Contains (sourcePower false 16 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 27 coarse_16_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -27247313584658673303, hi := 27247313584658673303} +lemma t28_contains : t28.Contains (sourcePower false 16 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (3/2) 2 28 coarse_16_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 16 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -20500998507632111319484518539, hi := 20500998507632111319484518539} +lemma t13_contains : t13.Contains (sourcePower true 16 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 13 coarse_16_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -6523208948461922490851005092, hi := 6523208948461922490851005092} +lemma t14_contains : t14.Contains (sourcePower true 16 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 14 coarse_16_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2001108592322595368095247195, hi := 2001108592322595368095247195} +lemma t15_contains : t15.Contains (sourcePower true 16 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 15 coarse_16_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -593882974596011604139733432, hi := 593882974596011604139733432} +lemma t16_contains : t16.Contains (sourcePower true 16 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 16 coarse_16_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -170914791314823074313359263, hi := 170914791314823074313359263} +lemma t17_contains : t17.Contains (sourcePower true 16 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 17 coarse_16_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -47763463222836881166984422, hi := 47763463222836881166984422} +lemma t18_contains : t18.Contains (sourcePower true 16 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 18 coarse_16_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -12968152058503371238596043, hi := 12968152058503371238596043} +lemma t19_contains : t19.Contains (sourcePower true 16 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 19 coarse_16_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -3420604834478252576726273, hi := 3420604834478252576726273} +lemma t20_contains : t20.Contains (sourcePower true 16 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 20 coarse_16_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -876206515302459865725797, hi := 876206515302459865725797} +lemma t21_contains : t21.Contains (sourcePower true 16 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 21 coarse_16_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -217861827796249410693090, hi := 217861827796249410693090} +lemma t22_contains : t22.Contains (sourcePower true 16 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 22 coarse_16_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -52558745128403565729773, hi := 52558745128403565729773} +lemma t23_contains : t23.Contains (sourcePower true 16 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 23 coarse_16_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -12299393946913104075874, hi := 12299393946913104075874} +lemma t24_contains : t24.Contains (sourcePower true 16 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 24 coarse_16_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -2791704545697118689729, hi := 2791704545697118689729} +lemma t25_contains : t25.Contains (sourcePower true 16 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 25 coarse_16_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -614700496900798892964, hi := 614700496900798892964} +lemma t26_contains : t26.Contains (sourcePower true 16 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 26 coarse_16_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -131343900200550587389, hi := 131343900200550587389} +lemma t27_contains : t27.Contains (sourcePower true 16 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 27 coarse_16_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -27247313584658673303, hi := 27247313584658673303} +lemma t28_contains : t28.Contains (sourcePower true 16 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (3/2) 2 28 coarse_16_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 16 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -12858748514342521132471, hi := 12858748514342521132471} +lemma t13_contains : t13.Contains (sourcePower false 16 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 13 coarse_16_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -1363840942406677210505, hi := 1363840942406677210505} +lemma t14_contains : t14.Contains (sourcePower false 16 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 14 coarse_16_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -139460698457561636444, hi := 139460698457561636444} +lemma t15_contains : t15.Contains (sourcePower false 16 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 15 coarse_16_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -13796241869293868031, hi := 13796241869293868031} +lemma t16_contains : t16.Contains (sourcePower false 16 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 16 coarse_16_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1323482852618229035, hi := 1323482852618229035} +lemma t17_contains : t17.Contains (sourcePower false 16 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 17 coarse_16_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -123285847235706941, hi := 123285847235706941} +lemma t18_contains : t18.Contains (sourcePower false 16 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 18 coarse_16_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -11157689062837503, hi := 11157689062837503} +lemma t19_contains : t19.Contains (sourcePower false 16 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 19 coarse_16_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -981019885685285, hi := 981019885685285} +lemma t20_contains : t20.Contains (sourcePower false 16 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 20 coarse_16_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -83764524801244, hi := 83764524801244} +lemma t21_contains : t21.Contains (sourcePower false 16 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 21 coarse_16_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -6942462444250, hi := 6942462444250} +lemma t22_contains : t22.Contains (sourcePower false 16 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 22 coarse_16_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -558285218147, hi := 558285218147} +lemma t23_contains : t23.Contains (sourcePower false 16 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 23 coarse_16_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -43548539931, hi := 43548539931} +lemma t24_contains : t24.Contains (sourcePower false 16 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 24 coarse_16_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -3294868496, hi := 3294868496} +lemma t25_contains : t25.Contains (sourcePower false 16 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 25 coarse_16_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -241830427, hi := 241830427} +lemma t26_contains : t26.Contains (sourcePower false 16 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 26 coarse_16_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -17224080, hi := 17224080} +lemma t27_contains : t27.Contains (sourcePower false 16 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 27 coarse_16_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1191047, hi := 1191047} +lemma t28_contains : t28.Contains (sourcePower false 16 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 16 (-1/2) 2 28 coarse_16_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 16 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -12858748514342521132471, hi := 12858748514342521132471} +lemma t13_contains : t13.Contains (sourcePower true 16 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 13 coarse_16_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -1363840942406677210505, hi := 1363840942406677210505} +lemma t14_contains : t14.Contains (sourcePower true 16 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 14 coarse_16_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -139460698457561636444, hi := 139460698457561636444} +lemma t15_contains : t15.Contains (sourcePower true 16 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 15 coarse_16_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -13796241869293868031, hi := 13796241869293868031} +lemma t16_contains : t16.Contains (sourcePower true 16 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 16 coarse_16_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1323482852618229035, hi := 1323482852618229035} +lemma t17_contains : t17.Contains (sourcePower true 16 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 17 coarse_16_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -123285847235706941, hi := 123285847235706941} +lemma t18_contains : t18.Contains (sourcePower true 16 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 18 coarse_16_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -11157689062837503, hi := 11157689062837503} +lemma t19_contains : t19.Contains (sourcePower true 16 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 19 coarse_16_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -981019885685285, hi := 981019885685285} +lemma t20_contains : t20.Contains (sourcePower true 16 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 20 coarse_16_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -83764524801244, hi := 83764524801244} +lemma t21_contains : t21.Contains (sourcePower true 16 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 21 coarse_16_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -6942462444250, hi := 6942462444250} +lemma t22_contains : t22.Contains (sourcePower true 16 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 22 coarse_16_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -558285218147, hi := 558285218147} +lemma t23_contains : t23.Contains (sourcePower true 16 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 23 coarse_16_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -43548539931, hi := 43548539931} +lemma t24_contains : t24.Contains (sourcePower true 16 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 24 coarse_16_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -3294868496, hi := 3294868496} +lemma t25_contains : t25.Contains (sourcePower true 16 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 25 coarse_16_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -241830427, hi := 241830427} +lemma t26_contains : t26.Contains (sourcePower true 16 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 26 coarse_16_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -17224080, hi := 17224080} +lemma t27_contains : t27.Contains (sourcePower true 16 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 27 coarse_16_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1191047, hi := 1191047} +lemma t28_contains : t28.Contains (sourcePower true 16 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 16 (-1/2) 2 28 coarse_16_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 16 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -88441022552632104701542875, hi := 88441022552632104701542875} +lemma t13_contains : t13.Contains (sourcePower false 19 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 13 coarse_19_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -17961769109023805605644033, hi := 17961769109023805605644033} +lemma t14_contains : t14.Contains (sourcePower false 19 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 14 coarse_19_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -3499152986883578905581056, hi := 3499152986883578905581056} +lemma t15_contains : t15.Contains (sourcePower false 19 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 15 coarse_19_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -657025204371517831247787, hi := 657025204371517831247787} +lemma t16_contains : t16.Contains (sourcePower false 19 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 16 coarse_19_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -119404930671123464551117, hi := 119404930671123464551117} +lemma t17_contains : t17.Contains (sourcePower false 19 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 17 coarse_19_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -21074327843674396260647, hi := 21074327843674396260647} +lemma t18_contains : t18.Contains (sourcePower false 19 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 18 coarse_19_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3621158106959460131472, hi := 3621158106959460131472} +lemma t19_contains : t19.Contains (sourcePower false 19 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 19 coarse_19_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -606685585115109330584, hi := 606685585115109330584} +lemma t20_contains : t20.Contains (sourcePower false 19 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 20 coarse_19_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -99171959366183814819, hi := 99171959366183814819} +lemma t21_contains : t21.Contains (sourcePower false 19 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 21 coarse_19_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -15816651699858251513, hi := 15816651699858251513} +lemma t22_contains : t22.Contains (sourcePower false 19 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 22 coarse_19_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -2460008358849052878, hi := 2460008358849052878} +lemma t23_contains : t23.Contains (sourcePower false 19 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 23 coarse_19_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -372867321116342342, hi := 372867321116342342} +lemma t24_contains : t24.Contains (sourcePower false 19 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 24 coarse_19_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -55036650600723914, hi := 55036650600723914} +lemma t25_contains : t25.Contains (sourcePower false 19 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 25 coarse_19_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -7905972890555824, hi := 7905972890555824} +lemma t26_contains : t26.Contains (sourcePower false 19 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 26 coarse_19_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1104748937734647, hi := 1104748937734647} +lemma t27_contains : t27.Contains (sourcePower false 19 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 27 coarse_19_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -150128174659659, hi := 150128174659659} +lemma t28_contains : t28.Contains (sourcePower false 19 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (1/1) 2 28 coarse_19_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 19 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -88441022552632104701542875, hi := 88441022552632104701542875} +lemma t13_contains : t13.Contains (sourcePower true 19 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 13 coarse_19_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -17961769109023805605644033, hi := 17961769109023805605644033} +lemma t14_contains : t14.Contains (sourcePower true 19 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 14 coarse_19_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -3499152986883578905581056, hi := 3499152986883578905581056} +lemma t15_contains : t15.Contains (sourcePower true 19 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 15 coarse_19_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -657025204371517831247787, hi := 657025204371517831247787} +lemma t16_contains : t16.Contains (sourcePower true 19 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 16 coarse_19_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -119404930671123464551117, hi := 119404930671123464551117} +lemma t17_contains : t17.Contains (sourcePower true 19 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 17 coarse_19_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -21074327843674396260647, hi := 21074327843674396260647} +lemma t18_contains : t18.Contains (sourcePower true 19 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 18 coarse_19_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3621158106959460131472, hi := 3621158106959460131472} +lemma t19_contains : t19.Contains (sourcePower true 19 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 19 coarse_19_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -606685585115109330584, hi := 606685585115109330584} +lemma t20_contains : t20.Contains (sourcePower true 19 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 20 coarse_19_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -99171959366183814819, hi := 99171959366183814819} +lemma t21_contains : t21.Contains (sourcePower true 19 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 21 coarse_19_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -15816651699858251513, hi := 15816651699858251513} +lemma t22_contains : t22.Contains (sourcePower true 19 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 22 coarse_19_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -2460008358849052878, hi := 2460008358849052878} +lemma t23_contains : t23.Contains (sourcePower true 19 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 23 coarse_19_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -372867321116342342, hi := 372867321116342342} +lemma t24_contains : t24.Contains (sourcePower true 19 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 24 coarse_19_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -55036650600723914, hi := 55036650600723914} +lemma t25_contains : t25.Contains (sourcePower true 19 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 25 coarse_19_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -7905972890555824, hi := 7905972890555824} +lemma t26_contains : t26.Contains (sourcePower true 19 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 26 coarse_19_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1104748937734647, hi := 1104748937734647} +lemma t27_contains : t27.Contains (sourcePower true 19 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 27 coarse_19_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -150128174659659, hi := 150128174659659} +lemma t28_contains : t28.Contains (sourcePower true 19 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (1/1) 2 28 coarse_19_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 19 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -17212348193259286506845451795, hi := 17212348193259286506845451795} +lemma t13_contains : t13.Contains (sourcePower false 19 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 13 coarse_19_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -5243565968848784330677590020, hi := 5243565968848784330677590020} +lemma t14_contains : t14.Contains (sourcePower false 19 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 14 coarse_19_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1532257714464254563700694382, hi := 1532257714464254563700694382} +lemma t15_contains : t15.Contains (sourcePower false 19 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 15 coarse_19_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -431560984230784735538460829, hi := 431560984230784735538460829} +lemma t16_contains : t16.Contains (sourcePower false 19 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 16 coarse_19_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -117645051650028866617248316, hi := 117645051650028866617248316} +lemma t17_contains : t17.Contains (sourcePower false 19 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 17 coarse_19_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -31145577997370339035337953, hi := 31145577997370339035337953} +lemma t18_contains : t18.Contains (sourcePower false 19 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 18 coarse_19_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -8027520243899622043481178, hi := 8027520243899622043481178} +lemma t19_contains : t19.Contains (sourcePower false 19 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 19 coarse_19_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -2017385324946328166284412, hi := 2017385324946328166284412} +lemma t20_contains : t20.Contains (sourcePower false 19 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 20 coarse_19_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -494658337976382597555488, hi := 494658337976382597555488} +lemma t21_contains : t21.Contains (sourcePower false 19 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 21 coarse_19_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -118337461902628652472489, hi := 118337461902628652472489} +lemma t22_contains : t22.Contains (sourcePower false 19 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 22 coarse_19_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -27608037810688158630507, hi := 27608037810688158630507} +lemma t23_contains : t23.Contains (sourcePower false 19 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 23 coarse_19_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -6276890317904993958782, hi := 6276890317904993958782} +lemma t24_contains : t24.Contains (sourcePower false 19 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 24 coarse_19_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -1389739726659286490149, hi := 1389739726659286490149} +lemma t25_contains : t25.Contains (sourcePower false 19 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 25 coarse_19_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -299452577981342345968, hi := 299452577981342345968} +lemma t26_contains : t26.Contains (sourcePower false 19 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 26 coarse_19_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -62766453036154687587, hi := 62766453036154687587} +lemma t27_contains : t27.Contains (sourcePower false 19 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 27 coarse_19_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -12794327338528462519, hi := 12794327338528462519} +lemma t28_contains : t28.Contains (sourcePower false 19 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 19 (-3/2) 2 28 coarse_19_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 19 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -17212348193259286506845451795, hi := 17212348193259286506845451795} +lemma t13_contains : t13.Contains (sourcePower true 19 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 13 coarse_19_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -5243565968848784330677590020, hi := 5243565968848784330677590020} +lemma t14_contains : t14.Contains (sourcePower true 19 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 14 coarse_19_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1532257714464254563700694382, hi := 1532257714464254563700694382} +lemma t15_contains : t15.Contains (sourcePower true 19 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 15 coarse_19_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -431560984230784735538460829, hi := 431560984230784735538460829} +lemma t16_contains : t16.Contains (sourcePower true 19 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 16 coarse_19_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -117645051650028866617248316, hi := 117645051650028866617248316} +lemma t17_contains : t17.Contains (sourcePower true 19 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 17 coarse_19_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -31145577997370339035337953, hi := 31145577997370339035337953} +lemma t18_contains : t18.Contains (sourcePower true 19 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 18 coarse_19_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -8027520243899622043481178, hi := 8027520243899622043481178} +lemma t19_contains : t19.Contains (sourcePower true 19 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 19 coarse_19_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -2017385324946328166284412, hi := 2017385324946328166284412} +lemma t20_contains : t20.Contains (sourcePower true 19 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 20 coarse_19_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -494658337976382597555488, hi := 494658337976382597555488} +lemma t21_contains : t21.Contains (sourcePower true 19 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 21 coarse_19_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -118337461902628652472489, hi := 118337461902628652472489} +lemma t22_contains : t22.Contains (sourcePower true 19 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 22 coarse_19_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -27608037810688158630507, hi := 27608037810688158630507} +lemma t23_contains : t23.Contains (sourcePower true 19 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 23 coarse_19_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -6276890317904993958782, hi := 6276890317904993958782} +lemma t24_contains : t24.Contains (sourcePower true 19 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 24 coarse_19_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -1389739726659286490149, hi := 1389739726659286490149} +lemma t25_contains : t25.Contains (sourcePower true 19 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 25 coarse_19_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -299452577981342345968, hi := 299452577981342345968} +lemma t26_contains : t26.Contains (sourcePower true 19 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 26 coarse_19_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -62766453036154687587, hi := 62766453036154687587} +lemma t27_contains : t27.Contains (sourcePower true 19 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 27 coarse_19_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -12794327338528462519, hi := 12794327338528462519} +lemma t28_contains : t28.Contains (sourcePower true 19 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 19 (-3/2) 2 28 coarse_19_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 19 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -26063889024553967598026327108, hi := 16738984000761394528842340517} +lemma t10_checked : ((hm21_0_0_12.realAnswer).add tr10).scale (-59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 21 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm21_0_0_12.realContains tr10_contains) (-59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -118092620930630225462300918, hi := 118092620930630225462300918} +lemma tr11_contains : tr11.Contains (fullMoment true true 21 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 21 mixed_21_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -10334915409011369615460661094, hi := 10094531387862087184931194888} +lemma t11_checked : ((hm21_0_0_13.realAnswer).add tr11).scale (-177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 21 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm21_0_0_13.realContains tr11_contains) (-177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -51162317996940730898206516312, hi := 51162317996940730898206516312} +lemma t12_contains : t12.Contains (sourcePower false 21 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 12 coarse_21_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -16073196934339071663200440071, hi := 16073196934339071663200440071} +lemma t13_contains : t13.Contains (sourcePower false 21 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 13 coarse_21_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4801042232493527104590166183, hi := 4801042232493527104590166183} +lemma t14_contains : t14.Contains (sourcePower false 21 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 14 coarse_21_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1370423344206941770097461362, hi := 1370423344206941770097461362} +lemma t15_contains : t15.Contains (sourcePower false 21 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 15 coarse_21_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -375651332374229463579451301, hi := 375651332374229463579451301} +lemma t16_contains : t16.Contains (sourcePower false 21 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 16 coarse_21_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -99341861518469404294500801, hi := 99341861518469404294500801} +lemma t17_contains : t17.Contains (sourcePower false 21 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 17 coarse_21_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -25451841483023795969396598, hi := 25451841483023795969396598} +lemma t18_contains : t18.Contains (sourcePower false 21 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 18 coarse_21_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -6340229876241134019004759, hi := 6340229876241134019004759} +lemma t19_contains : t19.Contains (sourcePower false 21 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 19 coarse_21_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1539969542447927337362309, hi := 1539969542447927337362309} +lemma t20_contains : t20.Contains (sourcePower false 21 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 20 coarse_21_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -365409763453884912068065, hi := 365409763453884912068065} +lemma t21_contains : t21.Contains (sourcePower false 21 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 21 coarse_21_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -84793777425826568097104, hi := 84793777425826568097104} +lemma t22_contains : t22.Contains (sourcePower false 21 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 22 coarse_21_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -19247738723856548849879, hi := 19247738723856548849879} +lemma t23_contains : t23.Contains (sourcePower false 21 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 23 coarse_21_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -4272541658258472116877, hi := 4272541658258472116877} +lemma t24_contains : t24.Contains (sourcePower false 21 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 24 coarse_21_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -926793089502574754670, hi := 926793089502574754670} +lemma t25_contains : t25.Contains (sourcePower false 21 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 25 coarse_21_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -196290930856939223080, hi := 196290930856939223080} +lemma t26_contains : t26.Contains (sourcePower false 21 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 26 coarse_21_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -40557817829263615547, hi := 40557817829263615547} +lemma t27_contains : t27.Contains (sourcePower false 21 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 27 coarse_21_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -8169491131565603124, hi := 8169491131565603124} +lemma t28_contains : t28.Contains (sourcePower false 21 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (3/2) 2 28 coarse_21_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 21 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -25897090971808994131515506437, hi := 16905782053506325654008060165} +lemma t10_checked : ((hm21_1_0_12.realAnswer).add tr10).scale (59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 21 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm21_1_0_12.realContains tr10_contains) (59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -118092620930630225462300918, hi := 118092620930630225462300918} +lemma tr11_contains : tr11.Contains (fullMoment false true 21 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 21 mixed_21_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -10394135058019566630244128111, hi := 10035311738853878421022840857} +lemma t11_checked : ((hm21_1_0_13.realAnswer).add tr11).scale (177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 21 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm21_1_0_13.realContains tr11_contains) (177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -51162317996940730898206516312, hi := 51162317996940730898206516312} +lemma t12_contains : t12.Contains (sourcePower true 21 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 12 coarse_21_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -16073196934339071663200440071, hi := 16073196934339071663200440071} +lemma t13_contains : t13.Contains (sourcePower true 21 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 13 coarse_21_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4801042232493527104590166183, hi := 4801042232493527104590166183} +lemma t14_contains : t14.Contains (sourcePower true 21 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 14 coarse_21_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1370423344206941770097461362, hi := 1370423344206941770097461362} +lemma t15_contains : t15.Contains (sourcePower true 21 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 15 coarse_21_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -375651332374229463579451301, hi := 375651332374229463579451301} +lemma t16_contains : t16.Contains (sourcePower true 21 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 16 coarse_21_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -99341861518469404294500801, hi := 99341861518469404294500801} +lemma t17_contains : t17.Contains (sourcePower true 21 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 17 coarse_21_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -25451841483023795969396598, hi := 25451841483023795969396598} +lemma t18_contains : t18.Contains (sourcePower true 21 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 18 coarse_21_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -6340229876241134019004759, hi := 6340229876241134019004759} +lemma t19_contains : t19.Contains (sourcePower true 21 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 19 coarse_21_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1539969542447927337362309, hi := 1539969542447927337362309} +lemma t20_contains : t20.Contains (sourcePower true 21 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 20 coarse_21_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -365409763453884912068065, hi := 365409763453884912068065} +lemma t21_contains : t21.Contains (sourcePower true 21 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 21 coarse_21_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -84793777425826568097104, hi := 84793777425826568097104} +lemma t22_contains : t22.Contains (sourcePower true 21 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 22 coarse_21_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -19247738723856548849879, hi := 19247738723856548849879} +lemma t23_contains : t23.Contains (sourcePower true 21 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 23 coarse_21_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -4272541658258472116877, hi := 4272541658258472116877} +lemma t24_contains : t24.Contains (sourcePower true 21 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 24 coarse_21_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -926793089502574754670, hi := 926793089502574754670} +lemma t25_contains : t25.Contains (sourcePower true 21 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 25 coarse_21_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -196290930856939223080, hi := 196290930856939223080} +lemma t26_contains : t26.Contains (sourcePower true 21 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 26 coarse_21_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -40557817829263615547, hi := 40557817829263615547} +lemma t27_contains : t27.Contains (sourcePower true 21 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 27 coarse_21_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -8169491131565603124, hi := 8169491131565603124} +lemma t28_contains : t28.Contains (sourcePower true 21 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (3/2) 2 28 coarse_21_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 21 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -451987711242243946897982336, hi := 290279591809847211596039843} +lemma t10_checked : ((hm21_0_0_12.realAnswer).add tr10).scale (-1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 21 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm21_0_0_12.realContains tr10_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -118092620930630225462300918, hi := 118092620930630225462300918} +lemma tr11_contains : tr11.Contains (fullMoment true true 21 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 21 mixed_21_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -116703078699281131234167596, hi := 119482163161980078536263295} +lemma t11_checked : ((hm21_0_0_13.realAnswer).add tr11).scale (1) 1=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 21 (-1/1) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm21_0_0_13.realContains tr11_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -394325719158795113209281728, hi := 394325719158795113209281728} +lemma t12_contains : t12.Contains (sourcePower false 21 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 12 coarse_21_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -82587800142195574588673691, hi := 82587800142195574588673691} +lemma t13_contains : t13.Contains (sourcePower false 21 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 13 coarse_21_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -16445909630017244117953782, hi := 16445909630017244117953782} +lemma t14_contains : t14.Contains (sourcePower false 21 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 14 coarse_21_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -3129578590409225449893404, hi := 3129578590409225449893404} +lemma t15_contains : t15.Contains (sourcePower false 21 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 15 coarse_21_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -571906178834794457983058, hi := 571906178834794457983058} +lemma t16_contains : t16.Contains (sourcePower false 21 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 16 coarse_21_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -100827938965423342075918, hi := 100827938965423342075918} +lemma t17_contains : t17.Contains (sourcePower false 21 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 17 coarse_21_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -17221720903165216877834, hi := 17221720903165216877834} +lemma t18_contains : t18.Contains (sourcePower false 21 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 18 coarse_21_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -2860033250465415001628, hi := 2860033250465415001628} +lemma t19_contains : t19.Contains (sourcePower false 21 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 19 coarse_21_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -463112976666628679145, hi := 463112976666628679145} +lemma t20_contains : t20.Contains (sourcePower false 21 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 20 coarse_21_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -73259458966171742099, hi := 73259458966171742099} +lemma t21_contains : t21.Contains (sourcePower false 21 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 21 coarse_21_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -11333297353995478269, hi := 11333297353995478269} +lemma t22_contains : t22.Contains (sourcePower false 21 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 22 coarse_21_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -1715065680303394038, hi := 1715065680303394038} +lemma t23_contains : t23.Contains (sourcePower false 21 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 23 coarse_21_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -253802612725042730, hi := 253802612725042730} +lemma t24_contains : t24.Contains (sourcePower false 21 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 24 coarse_21_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -36702978599261021, hi := 36702978599261021} +lemma t25_contains : t25.Contains (sourcePower false 21 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 25 coarse_21_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -5182359051567824, hi := 5182359051567824} +lemma t26_contains : t26.Contains (sourcePower false 21 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 26 coarse_21_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -713855953241536, hi := 713855953241536} +lemma t27_contains : t27.Contains (sourcePower false 21 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 27 coarse_21_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -95860513728366, hi := 95860513728366} +lemma t28_contains : t28.Contains (sourcePower false 21 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 21 (-1/1) 2 28 coarse_21_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 21 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -449095177820664363336752165, hi := 293172125231426060893567268} +lemma t10_checked : ((hm21_1_0_12.realAnswer).add tr10).scale (1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 21 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm21_1_0_12.realContains tr10_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -118092620930630225462300918, hi := 118092620930630225462300918} +lemma tr11_contains : tr11.Contains (fullMoment false true 21 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 21 mixed_21_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -116018439156027158271123858, hi := 120166802705233915667439891} +lemma t11_checked : ((hm21_1_0_13.realAnswer).add tr11).scale (-1) 1=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 21 (-1/1) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm21_1_0_13.realContains tr11_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -394325719158795113209281728, hi := 394325719158795113209281728} +lemma t12_contains : t12.Contains (sourcePower true 21 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 12 coarse_21_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -82587800142195574588673691, hi := 82587800142195574588673691} +lemma t13_contains : t13.Contains (sourcePower true 21 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 13 coarse_21_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -16445909630017244117953782, hi := 16445909630017244117953782} +lemma t14_contains : t14.Contains (sourcePower true 21 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 14 coarse_21_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -3129578590409225449893404, hi := 3129578590409225449893404} +lemma t15_contains : t15.Contains (sourcePower true 21 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 15 coarse_21_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -571906178834794457983058, hi := 571906178834794457983058} +lemma t16_contains : t16.Contains (sourcePower true 21 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 16 coarse_21_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -100827938965423342075918, hi := 100827938965423342075918} +lemma t17_contains : t17.Contains (sourcePower true 21 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 17 coarse_21_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -17221720903165216877834, hi := 17221720903165216877834} +lemma t18_contains : t18.Contains (sourcePower true 21 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 18 coarse_21_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -2860033250465415001628, hi := 2860033250465415001628} +lemma t19_contains : t19.Contains (sourcePower true 21 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 19 coarse_21_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -463112976666628679145, hi := 463112976666628679145} +lemma t20_contains : t20.Contains (sourcePower true 21 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 20 coarse_21_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -73259458966171742099, hi := 73259458966171742099} +lemma t21_contains : t21.Contains (sourcePower true 21 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 21 coarse_21_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -11333297353995478269, hi := 11333297353995478269} +lemma t22_contains : t22.Contains (sourcePower true 21 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 22 coarse_21_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -1715065680303394038, hi := 1715065680303394038} +lemma t23_contains : t23.Contains (sourcePower true 21 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 23 coarse_21_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -253802612725042730, hi := 253802612725042730} +lemma t24_contains : t24.Contains (sourcePower true 21 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 24 coarse_21_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -36702978599261021, hi := 36702978599261021} +lemma t25_contains : t25.Contains (sourcePower true 21 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 25 coarse_21_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -5182359051567824, hi := 5182359051567824} +lemma t26_contains : t26.Contains (sourcePower true 21 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 26 coarse_21_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -713855953241536, hi := 713855953241536} +lemma t27_contains : t27.Contains (sourcePower true 21 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 27 coarse_21_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -95860513728366, hi := 95860513728366} +lemma t28_contains : t28.Contains (sourcePower true 21 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 21 (-1/1) 2 28 coarse_21_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 21 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -124086872703215010463964, hi := 238191225319190658504733} +lemma t10_checked : ((hm24_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 24 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm24_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -58997102609725292366925614, hi := 58997102609725292366925614} +lemma tr11_contains : tr11.Contains (fullMoment true true 24 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 24 mixed_24_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -27650510125182466740477, hi := 29963847892127760219069} +lemma t11_checked : ((hm24_0_0_13.realAnswer).add tr11).scale (-1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 24 (1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm24_0_0_13.realContains tr11_contains) (-1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -92005094558355516319346, hi := 92005094558355516319346} +lemma t12_contains : t12.Contains (sourcePower false 24 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 12 coarse_24_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9492764401100362812387, hi := 9492764401100362812387} +lemma t13_contains : t13.Contains (sourcePower false 24 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 13 coarse_24_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -927581682407947607361, hi := 927581682407947607361} +lemma t14_contains : t14.Contains (sourcePower false 24 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 14 coarse_24_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -86223802489917842930, hi := 86223802489917842930} +lemma t15_contains : t15.Contains (sourcePower false 24 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 15 coarse_24_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7658197989607200361, hi := 7658197989607200361} +lemma t16_contains : t16.Contains (sourcePower false 24 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 16 coarse_24_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -652747664927167744, hi := 652747664927167744} +lemma t17_contains : t17.Contains (sourcePower false 24 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 17 coarse_24_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -53623681422163501, hi := 53623681422163501} +lemma t18_contains : t18.Contains (sourcePower false 24 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 18 coarse_24_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4263623176223224, hi := 4263623176223224} +lemma t19_contains : t19.Contains (sourcePower false 24 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 19 coarse_24_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -329394523921959, hi := 329394523921959} +lemma t20_contains : t20.Contains (sourcePower false 24 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 20 coarse_24_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -24813157369210, hi := 24813157369210} +lemma t21_contains : t21.Contains (sourcePower false 24 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 21 coarse_24_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1827741453474, hi := 1827741453474} +lemma t22_contains : t22.Contains (sourcePower false 24 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 22 coarse_24_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -131921188015, hi := 131921188015} +lemma t23_contains : t23.Contains (sourcePower false 24 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 23 coarse_24_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -9341435340, hi := 9341435340} +lemma t24_contains : t24.Contains (sourcePower false 24 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 24 coarse_24_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -649223786, hi := 649223786} +lemma t25_contains : t25.Contains (sourcePower false 24 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 25 coarse_24_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -44274198, hi := 44274198} +lemma t26_contains : t26.Contains (sourcePower false 24 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 26 coarse_24_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -2960569, hi := 2960569} +lemma t27_contains : t27.Contains (sourcePower false 24 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 27 coarse_24_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -193934, hi := 193934} +lemma t28_contains : t28.Contains (sourcePower false 24 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (1/2) 2 28 coarse_24_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 24 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -125023940880328252207948, hi := 237254157142076695970327} +lemma t10_checked : ((hm24_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 24 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm24_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -58997102609725292366925614, hi := 58997102609725292366925614} +lemma tr11_contains : tr11.Contains (fullMoment false true 24 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 24 mixed_24_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -27442525004042190656057, hi := 30171833013267969621905} +lemma t11_checked : ((hm24_1_0_13.realAnswer).add tr11).scale (1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 24 (1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm24_1_0_13.realContains tr11_contains) (1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -92005094558355516319346, hi := 92005094558355516319346} +lemma t12_contains : t12.Contains (sourcePower true 24 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 12 coarse_24_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9492764401100362812387, hi := 9492764401100362812387} +lemma t13_contains : t13.Contains (sourcePower true 24 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 13 coarse_24_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -927581682407947607361, hi := 927581682407947607361} +lemma t14_contains : t14.Contains (sourcePower true 24 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 14 coarse_24_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -86223802489917842930, hi := 86223802489917842930} +lemma t15_contains : t15.Contains (sourcePower true 24 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 15 coarse_24_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7658197989607200361, hi := 7658197989607200361} +lemma t16_contains : t16.Contains (sourcePower true 24 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 16 coarse_24_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -652747664927167744, hi := 652747664927167744} +lemma t17_contains : t17.Contains (sourcePower true 24 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 17 coarse_24_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -53623681422163501, hi := 53623681422163501} +lemma t18_contains : t18.Contains (sourcePower true 24 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 18 coarse_24_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4263623176223224, hi := 4263623176223224} +lemma t19_contains : t19.Contains (sourcePower true 24 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 19 coarse_24_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -329394523921959, hi := 329394523921959} +lemma t20_contains : t20.Contains (sourcePower true 24 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 20 coarse_24_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -24813157369210, hi := 24813157369210} +lemma t21_contains : t21.Contains (sourcePower true 24 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 21 coarse_24_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1827741453474, hi := 1827741453474} +lemma t22_contains : t22.Contains (sourcePower true 24 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 22 coarse_24_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -131921188015, hi := 131921188015} +lemma t23_contains : t23.Contains (sourcePower true 24 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 23 coarse_24_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -9341435340, hi := 9341435340} +lemma t24_contains : t24.Contains (sourcePower true 24 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 24 coarse_24_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -649223786, hi := 649223786} +lemma t25_contains : t25.Contains (sourcePower true 24 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 25 coarse_24_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -44274198, hi := 44274198} +lemma t26_contains : t26.Contains (sourcePower true 24 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 26 coarse_24_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -2960569, hi := 2960569} +lemma t27_contains : t27.Contains (sourcePower true 24 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 27 coarse_24_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -193934, hi := 193934} +lemma t28_contains : t28.Contains (sourcePower true 24 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (1/2) 2 28 coarse_24_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 24 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -7327205746252143152886601356, hi := 14064953663872889194045939648} +lemma t10_checked : ((hm24_0_0_12.realAnswer).add tr10).scale (-59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 24 (-3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm24_0_0_12.realContains tr10_contains) (-59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -58997102609725292366925614, hi := 58997102609725292366925614} +lemma tr11_contains : tr11.Contains (fullMoment true true 24 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 24 mixed_24_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -5308005762546756339527350146, hi := 4898204917145698435675215457} +lemma t11_checked : ((hm24_0_0_13.realAnswer).add tr11).scale (177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 24 (-3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm24_0_0_13.realContains tr11_contains) (177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -48895279457187013948269047943, hi := 48895279457187013948269047943} +lemma t12_contains : t12.Contains (sourcePower false 24 (-3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 12 coarse_24_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -15134532618255533740132000351, hi := 15134532618255533740132000351} +lemma t13_contains : t13.Contains (sourcePower false 24 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 13 coarse_24_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4436594431925058759630009084, hi := 4436594431925058759630009084} +lemma t14_contains : t14.Contains (sourcePower false 24 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 14 coarse_24_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1237217323114199565829174978, hi := 1237217323114199565829174978} +lemma t15_contains : t15.Contains (sourcePower false 24 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 15 coarse_24_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -329660312221382053495992951, hi := 329660312221382053495992951} +lemma t16_contains : t16.Contains (sourcePower false 24 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 16 coarse_24_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -84295939846563825576348090, hi := 84295939846563825576348090} +lemma t17_contains : t17.Contains (sourcePower false 24 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 17 coarse_24_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -20774912878554798685150661, hi := 20774912878554798685150661} +lemma t18_contains : t18.Contains (sourcePower false 24 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 18 coarse_24_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4955444927532403499927245, hi := 4955444927532403499927245} +lemma t19_contains : t19.Contains (sourcePower false 24 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 19 coarse_24_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1148527687785906431688423, hi := 1148527687785906431688423} +lemma t20_contains : t20.Contains (sourcePower false 24 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 20 coarse_24_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -259554390163556698989919, hi := 259554390163556698989919} +lemma t21_contains : t21.Contains (sourcePower false 24 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 21 coarse_24_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -57356463501299681808300, hi := 57356463501299681808300} +lemma t22_contains : t22.Contains (sourcePower false 24 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 22 coarse_24_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -12419479994321041648233, hi := 12419479994321041648233} +lemma t23_contains : t23.Contains (sourcePower false 24 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 23 coarse_24_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -2638297253070937662254, hi := 2638297253070937662254} +lemma t24_contains : t24.Contains (sourcePower false 24 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 24 coarse_24_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -550079918257030980703, hi := 550079918257030980703} +lemma t25_contains : t25.Contains (sourcePower false 24 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 25 coarse_24_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -112539070762571183662, hi := 112539070762571183662} +lemma t26_contains : t26.Contains (sourcePower false 24 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 26 coarse_24_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -22576099940430149943, hi := 22576099940430149943} +lemma t27_contains : t27.Contains (sourcePower false 24 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 27 coarse_24_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -4436570569074936528, hi := 4436570569074936528} +lemma t28_contains : t28.Contains (sourcePower false 24 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 24 (-3/2) 2 28 coarse_24_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 24 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -7382538685042502964627119780, hi := 14009620725082486820351820167} +lemma t10_checked : ((hm24_1_0_12.realAnswer).add tr10).scale (59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 24 (-3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm24_1_0_12.realContains tr10_contains) (59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -58997102609725292366925614, hi := 58997102609725292366925614} +lemma tr11_contains : tr11.Contains (fullMoment false true 24 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 24 mixed_24_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -5344849702801381014611530388, hi := 4861360976891061948148389426} +lemma t11_checked : ((hm24_1_0_13.realAnswer).add tr11).scale (-177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 24 (-3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm24_1_0_13.realContains tr11_contains) (-177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -48895279457187013948269047943, hi := 48895279457187013948269047943} +lemma t12_contains : t12.Contains (sourcePower true 24 (-3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 12 coarse_24_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -15134532618255533740132000351, hi := 15134532618255533740132000351} +lemma t13_contains : t13.Contains (sourcePower true 24 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 13 coarse_24_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4436594431925058759630009084, hi := 4436594431925058759630009084} +lemma t14_contains : t14.Contains (sourcePower true 24 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 14 coarse_24_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1237217323114199565829174978, hi := 1237217323114199565829174978} +lemma t15_contains : t15.Contains (sourcePower true 24 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 15 coarse_24_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -329660312221382053495992951, hi := 329660312221382053495992951} +lemma t16_contains : t16.Contains (sourcePower true 24 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 16 coarse_24_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -84295939846563825576348090, hi := 84295939846563825576348090} +lemma t17_contains : t17.Contains (sourcePower true 24 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 17 coarse_24_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -20774912878554798685150661, hi := 20774912878554798685150661} +lemma t18_contains : t18.Contains (sourcePower true 24 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 18 coarse_24_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4955444927532403499927245, hi := 4955444927532403499927245} +lemma t19_contains : t19.Contains (sourcePower true 24 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 19 coarse_24_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1148527687785906431688423, hi := 1148527687785906431688423} +lemma t20_contains : t20.Contains (sourcePower true 24 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 20 coarse_24_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -259554390163556698989919, hi := 259554390163556698989919} +lemma t21_contains : t21.Contains (sourcePower true 24 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 21 coarse_24_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -57356463501299681808300, hi := 57356463501299681808300} +lemma t22_contains : t22.Contains (sourcePower true 24 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 22 coarse_24_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -12419479994321041648233, hi := 12419479994321041648233} +lemma t23_contains : t23.Contains (sourcePower true 24 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 23 coarse_24_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -2638297253070937662254, hi := 2638297253070937662254} +lemma t24_contains : t24.Contains (sourcePower true 24 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 24 coarse_24_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -550079918257030980703, hi := 550079918257030980703} +lemma t25_contains : t25.Contains (sourcePower true 24 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 25 coarse_24_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -112539070762571183662, hi := 112539070762571183662} +lemma t26_contains : t26.Contains (sourcePower true 24 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 26 coarse_24_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -22576099940430149943, hi := 22576099940430149943} +lemma t27_contains : t27.Contains (sourcePower true 24 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 27 coarse_24_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -4436570569074936528, hi := 4436570569074936528} +lemma t28_contains : t28.Contains (sourcePower true 24 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 24 (-3/2) 2 28 coarse_24_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 24 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -503864974496040793348982304, hi := 1781270020292729747064924144} +lemma t8_checked : ((hm25_0_0_10.realAnswer).add tr8).scale (-1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 25 (1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm25_0_0_10.realContains tr8_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -429035170759864269207836261, hi := 429035170759864269207836261} +lemma tr9_contains : tr9.Contains (fullMoment true true 25 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 25 mixed_25_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -398518728801133769593338404, hi := 459551612718615316606923582} +lemma t9_checked : ((hm25_0_0_11.realAnswer).add tr9).scale (-1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 25 (1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm25_0_0_11.realContains tr9_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -147751113260532258274768477, hi := 147751113260532258274768477} +lemma tr10_contains : tr10.Contains (fullMoment true true 25 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 25 mixed_25_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -200767112318810163341042426, hi := 94735114202258464323806212} +lemma t10_checked : ((hm25_0_0_12.realAnswer).add tr10).scale (-1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 25 (1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm25_0_0_12.realContains tr10_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1709635599354057588977945053, hi := 1709635599354057588977945053} +lemma t11_contains : t11.Contains (sourcePower false 25 (1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 11 coarse_25_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -373303454578363789549965966, hi := 373303454578363789549965966} +lemma t12_contains : t12.Contains (sourcePower false 25 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 12 coarse_25_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -76785249843842576607819054, hi := 76785249843842576607819054} +lemma t13_contains : t13.Contains (sourcePower false 25 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 13 coarse_25_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14944038864773772626460091, hi := 14944038864773772626460091} +lemma t14_contains : t14.Contains (sourcePower false 25 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 14 coarse_25_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2763638568673854239576766, hi := 2763638568673854239576766} +lemma t15_contains : t15.Contains (sourcePower false 25 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 15 coarse_25_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -487679883890270618281306, hi := 487679883890270618281306} +lemma t16_contains : t16.Contains (sourcePower false 25 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 16 coarse_25_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -82459113489707738598146, hi := 82459113489707738598146} +lemma t17_contains : t17.Contains (sourcePower false 25 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 17 coarse_25_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -13415358447817719868817, hi := 13415358447817719868817} +lemma t18_contains : t18.Contains (sourcePower false 25 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 18 coarse_25_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -2108727150330305406116, hi := 2108727150330305406116} +lemma t19_contains : t19.Contains (sourcePower false 25 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 19 coarse_25_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -321538539951788029867, hi := 321538539951788029867} +lemma t20_contains : t20.Contains (sourcePower false 25 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 20 coarse_25_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -47737694023601780598, hi := 47737694023601780598} +lemma t21_contains : t21.Contains (sourcePower false 25 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 21 coarse_25_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -6923525363928755660, hi := 6923525363928755660} +lemma t22_contains : t22.Contains (sourcePower false 25 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 22 coarse_25_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -983493777958713191, hi := 983493777958713191} +lemma t23_contains : t23.Contains (sourcePower false 25 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 23 coarse_25_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -137086330848278101, hi := 137086330848278101} +lemma t24_contains : t24.Contains (sourcePower false 25 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 24 coarse_25_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -18768592723534679, hi := 18768592723534679} +lemma t25_contains : t25.Contains (sourcePower false 25 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 25 coarse_25_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -2524547656204976, hi := 2524547656204976} +lemma t26_contains : t26.Contains (sourcePower false 25 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 26 coarse_25_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -333485942635723, hi := 333485942635723} +lemma t27_contains : t27.Contains (sourcePower false 25 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 27 coarse_25_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -43227396073138, hi := 43227396073138} +lemma t28_contains : t28.Contains (sourcePower false 25 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (1/1) 2 28 coarse_25_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 25 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -509332298757771549635289121, hi := 1775802696030982007558737419} +lemma t8_checked : ((hm25_1_0_10.realAnswer).add tr8).scale (1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 25 (1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm25_1_0_10.realContains tr8_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -429035170759864269207836261, hi := 429035170759864269207836261} +lemma tr9_contains : tr9.Contains (fullMoment false true 25 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 25 mixed_25_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -393965622491575124144032021, hi := 464104719028170261934683912} +lemma t9_checked : ((hm25_1_0_11.realAnswer).add tr9).scale (1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 25 (1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm25_1_0_11.realContains tr9_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -147751113260532258274768477, hi := 147751113260532258274768477} +lemma tr10_contains : tr10.Contains (fullMoment false true 25 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 25 mixed_25_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -200430389231047175666789199, hi := 95071837290020711647146340} +lemma t10_checked : ((hm25_1_0_12.realAnswer).add tr10).scale (1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 25 (1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm25_1_0_12.realContains tr10_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1709635599354057588977945053, hi := 1709635599354057588977945053} +lemma t11_contains : t11.Contains (sourcePower true 25 (1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 11 coarse_25_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -373303454578363789549965966, hi := 373303454578363789549965966} +lemma t12_contains : t12.Contains (sourcePower true 25 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 12 coarse_25_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -76785249843842576607819054, hi := 76785249843842576607819054} +lemma t13_contains : t13.Contains (sourcePower true 25 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 13 coarse_25_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14944038864773772626460091, hi := 14944038864773772626460091} +lemma t14_contains : t14.Contains (sourcePower true 25 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 14 coarse_25_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2763638568673854239576766, hi := 2763638568673854239576766} +lemma t15_contains : t15.Contains (sourcePower true 25 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 15 coarse_25_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -487679883890270618281306, hi := 487679883890270618281306} +lemma t16_contains : t16.Contains (sourcePower true 25 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 16 coarse_25_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -82459113489707738598146, hi := 82459113489707738598146} +lemma t17_contains : t17.Contains (sourcePower true 25 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 17 coarse_25_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -13415358447817719868817, hi := 13415358447817719868817} +lemma t18_contains : t18.Contains (sourcePower true 25 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 18 coarse_25_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -2108727150330305406116, hi := 2108727150330305406116} +lemma t19_contains : t19.Contains (sourcePower true 25 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 19 coarse_25_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -321538539951788029867, hi := 321538539951788029867} +lemma t20_contains : t20.Contains (sourcePower true 25 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 20 coarse_25_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -47737694023601780598, hi := 47737694023601780598} +lemma t21_contains : t21.Contains (sourcePower true 25 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 21 coarse_25_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -6923525363928755660, hi := 6923525363928755660} +lemma t22_contains : t22.Contains (sourcePower true 25 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 22 coarse_25_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -983493777958713191, hi := 983493777958713191} +lemma t23_contains : t23.Contains (sourcePower true 25 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 23 coarse_25_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -137086330848278101, hi := 137086330848278101} +lemma t24_contains : t24.Contains (sourcePower true 25 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 24 coarse_25_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -18768592723534679, hi := 18768592723534679} +lemma t25_contains : t25.Contains (sourcePower true 25 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 25 coarse_25_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -2524547656204976, hi := 2524547656204976} +lemma t26_contains : t26.Contains (sourcePower true 25 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 26 coarse_25_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -333485942635723, hi := 333485942635723} +lemma t27_contains : t27.Contains (sourcePower true 25 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 27 coarse_25_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -43227396073138, hi := 43227396073138} +lemma t28_contains : t28.Contains (sourcePower true 25 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (1/1) 2 28 coarse_25_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 25 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -1968222556625159349019463, hi := 6958086016768475574472360} +lemma t8_checked : ((hm25_0_0_10.realAnswer).add tr8).scale (-1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 25 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm25_0_0_10.realContains tr8_contains) (-1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -429035170759864269207836261, hi := 429035170759864269207836261} +lemma tr9_contains : tr9.Contains (fullMoment true true 25 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 25 mixed_25_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -897561743591045540247898, hi := 778356892189714393736990} +lemma t9_checked : ((hm25_0_0_11.realAnswer).add tr9).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 25 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm25_0_0_11.realContains tr9_contains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -147751113260532258274768477, hi := 147751113260532258274768477} +lemma tr10_contains : tr10.Contains (fullMoment true true 25 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 25 mixed_25_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -196061633123838050137737, hi := 92514759963143031566218} +lemma t10_checked : ((hm25_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 25 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm25_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -834783007497098432118138, hi := 834783007497098432118138} +lemma t11_contains : t11.Contains (sourcePower false 25 (-1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 11 coarse_25_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -91138538715420847058098, hi := 91138538715420847058098} +lemma t12_contains : t12.Contains (sourcePower false 25 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 12 coarse_25_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9373199443828439527322, hi := 9373199443828439527322} +lemma t13_contains : t13.Contains (sourcePower false 25 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 13 coarse_25_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -912111747117539833158, hi := 912111747117539833158} +lemma t14_contains : t14.Contains (sourcePower false 25 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 14 coarse_25_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -84339555928767524402, hi := 84339555928767524402} +lemma t15_contains : t15.Contains (sourcePower false 25 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 15 coarse_25_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7441404478306131261, hi := 7441404478306131261} +lemma t16_contains : t16.Contains (sourcePower false 25 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 16 coarse_25_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -629113109510099325, hi := 629113109510099325} +lemma t17_contains : t17.Contains (sourcePower false 25 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 17 coarse_25_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -51175531188269501, hi := 51175531188269501} +lemma t18_contains : t18.Contains (sourcePower false 25 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 18 coarse_25_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4022077847157108, hi := 4022077847157108} +lemma t19_contains : t19.Contains (sourcePower false 25 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 19 coarse_25_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -306643047286786, hi := 306643047286786} +lemma t20_contains : t20.Contains (sourcePower false 25 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 20 coarse_25_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -22763106357385, hi := 22763106357385} +lemma t21_contains : t21.Contains (sourcePower false 25 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 21 coarse_25_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1650697079642, hi := 1650697079642} +lemma t22_contains : t22.Contains (sourcePower false 25 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 22 coarse_25_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -117241594549, hi := 117241594549} +lemma t23_contains : t23.Contains (sourcePower false 25 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 23 coarse_25_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -8170982054, hi := 8170982054} +lemma t24_contains : t24.Contains (sourcePower false 25 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 24 coarse_25_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -559347652, hi := 559347652} +lemma t25_contains : t25.Contains (sourcePower false 25 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 25 coarse_25_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -37618692, hi := 37618692} +lemma t26_contains : t26.Contains (sourcePower false 25 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 26 coarse_25_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -2484664, hi := 2484664} +lemma t27_contains : t27.Contains (sourcePower false 25 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 27 coarse_25_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -161035, hi := 161035} +lemma t28_contains : t28.Contains (sourcePower false 25 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 25 (-1/2) 2 28 coarse_25_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 25 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -1989579292022545115762849, hi := 6936729281371023467026319} +lemma t8_checked : ((hm25_1_0_10.realAnswer).add tr8).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 25 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm25_1_0_10.realContains tr8_contains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -429035170759864269207836261, hi := 429035170759864269207836261} +lemma tr9_contains : tr9.Contains (fullMoment false true 25 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 25 mixed_25_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -906454529351895042841180, hi := 769464106428857664343813} +lemma t9_checked : ((hm25_1_0_11.realAnswer).add tr9).scale (-1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 25 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm25_1_0_11.realContains tr9_contains) (-1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -147751113260532258274768477, hi := 147751113260532258274768477} +lemma tr10_contains : tr10.Contains (fullMoment false true 25 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 25 mixed_25_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -195732801983444507487099, hi := 92843591103535851217917} +lemma t10_checked : ((hm25_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 25 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm25_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -834783007497098432118138, hi := 834783007497098432118138} +lemma t11_contains : t11.Contains (sourcePower true 25 (-1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 11 coarse_25_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -91138538715420847058098, hi := 91138538715420847058098} +lemma t12_contains : t12.Contains (sourcePower true 25 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 12 coarse_25_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9373199443828439527322, hi := 9373199443828439527322} +lemma t13_contains : t13.Contains (sourcePower true 25 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 13 coarse_25_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -912111747117539833158, hi := 912111747117539833158} +lemma t14_contains : t14.Contains (sourcePower true 25 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 14 coarse_25_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -84339555928767524402, hi := 84339555928767524402} +lemma t15_contains : t15.Contains (sourcePower true 25 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 15 coarse_25_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7441404478306131261, hi := 7441404478306131261} +lemma t16_contains : t16.Contains (sourcePower true 25 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 16 coarse_25_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -629113109510099325, hi := 629113109510099325} +lemma t17_contains : t17.Contains (sourcePower true 25 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 17 coarse_25_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -51175531188269501, hi := 51175531188269501} +lemma t18_contains : t18.Contains (sourcePower true 25 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 18 coarse_25_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4022077847157108, hi := 4022077847157108} +lemma t19_contains : t19.Contains (sourcePower true 25 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 19 coarse_25_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -306643047286786, hi := 306643047286786} +lemma t20_contains : t20.Contains (sourcePower true 25 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 20 coarse_25_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -22763106357385, hi := 22763106357385} +lemma t21_contains : t21.Contains (sourcePower true 25 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 21 coarse_25_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1650697079642, hi := 1650697079642} +lemma t22_contains : t22.Contains (sourcePower true 25 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 22 coarse_25_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -117241594549, hi := 117241594549} +lemma t23_contains : t23.Contains (sourcePower true 25 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 23 coarse_25_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -8170982054, hi := 8170982054} +lemma t24_contains : t24.Contains (sourcePower true 25 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 24 coarse_25_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -559347652, hi := 559347652} +lemma t25_contains : t25.Contains (sourcePower true 25 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 25 coarse_25_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -37618692, hi := 37618692} +lemma t26_contains : t26.Contains (sourcePower true 25 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 26 coarse_25_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -2484664, hi := 2484664} +lemma t27_contains : t27.Contains (sourcePower true 25 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 27 coarse_25_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -161035, hi := 161035} +lemma t28_contains : t28.Contains (sourcePower true 25 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 25 (-1/2) 2 28 coarse_25_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 25 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -406633684498555347771173, hi := 5287240760493054529717172} +lemma t8_checked : ((hm27_0_0_10.realAnswer).add tr8).scale (-1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 27 (1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm27_0_0_10.realContains tr8_contains) (-1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -273586055473683921267866222, hi := 273586055473683921267866222} +lemma tr9_contains : tr9.Contains (fullMoment true true 27 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 27 mixed_27_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -594319915571777109305213, hi := 474375613622340952710297} +lemma t9_checked : ((hm27_0_0_11.realAnswer).add tr9).scale (-1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 27 (1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm27_0_0_11.realContains tr9_contains) (-1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -94191747073031887938338274, hi := 94191747073031887938338274} +lemma tr10_contains : tr10.Contains (fullMoment true true 27 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 27 mixed_27_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -142678018040181174330846, hi := 41290237961838258068390} +lemma t10_checked : ((hm27_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 27 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm27_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -826462401871455103132452, hi := 826462401871455103132452} +lemma t11_contains : t11.Contains (sourcePower false 27 (1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 11 coarse_27_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -89909022963477775641683, hi := 89909022963477775641683} +lemma t12_contains : t12.Contains (sourcePower false 27 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 12 coarse_27_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9203579534301380843272, hi := 9203579534301380843272} +lemma t13_contains : t13.Contains (sourcePower false 27 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 13 coarse_27_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -890168433085651111959, hi := 890168433085651111959} +lemma t14_contains : t14.Contains (sourcePower false 27 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 14 coarse_27_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -81667185972791006988, hi := 81667185972791006988} +lemma t15_contains : t15.Contains (sourcePower false 27 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 15 coarse_27_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7133969330518964885, hi := 7133969330518964885} +lemma t16_contains : t16.Contains (sourcePower false 27 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 16 coarse_27_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -595600727454733885, hi := 595600727454733885} +lemma t17_contains : t17.Contains (sourcePower false 27 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 17 coarse_27_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -47704585830818839, hi := 47704585830818839} +lemma t18_contains : t18.Contains (sourcePower false 27 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 18 coarse_27_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3679656824384760, hi := 3679656824384760} +lemma t19_contains : t19.Contains (sourcePower false 27 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 19 coarse_27_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -274393575161513, hi := 274393575161513} +lemma t20_contains : t20.Contains (sourcePower false 27 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 20 coarse_27_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -19857565186914, hi := 19857565186914} +lemma t21_contains : t21.Contains (sourcePower false 27 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 21 coarse_27_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1399802782276, hi := 1399802782276} +lemma t22_contains : t22.Contains (sourcePower false 27 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 22 coarse_27_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -96441529722, hi := 96441529722} +lemma t23_contains : t23.Contains (sourcePower false 27 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 23 coarse_27_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -6512766124, hi := 6512766124} +lemma t24_contains : t24.Contains (sourcePower false 27 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 24 coarse_27_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -432038233, hi := 432038233} +lemma t25_contains : t25.Contains (sourcePower false 27 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 25 coarse_27_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -28192908, hi := 28192908} +lemma t26_contains : t26.Contains (sourcePower false 27 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 26 coarse_27_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1810811, hi := 1810811} +lemma t27_contains : t27.Contains (sourcePower false 27 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 27 coarse_27_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -114464, hi := 114464} +lemma t28_contains : t28.Contains (sourcePower false 27 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (1/2) 2 28 coarse_27_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 27 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -369036465002890643656529, hi := 5324837979988652257441112} +lemma t8_checked : ((hm27_1_0_10.realAnswer).add tr8).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 27 (1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm27_1_0_10.realContains tr8_contains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -273586055473683921267866222, hi := 273586055473683921267866222} +lemma tr9_contains : tr9.Contains (fullMoment false true 27 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 27 mixed_27_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -587212221373609432351700, hi := 481483307820501332090967} +lemma t9_checked : ((hm27_1_0_11.realAnswer).add tr9).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 27 (1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm27_1_0_11.realContains tr9_contains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -94191747073031887938338274, hi := 94191747073031887938338274} +lemma tr10_contains : tr10.Contains (fullMoment false true 27 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 27 mixed_27_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -143456314438875109710952, hi := 40511941563143592428876} +lemma t10_checked : ((hm27_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 27 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm27_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -826462401871455103132452, hi := 826462401871455103132452} +lemma t11_contains : t11.Contains (sourcePower true 27 (1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 11 coarse_27_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -89909022963477775641683, hi := 89909022963477775641683} +lemma t12_contains : t12.Contains (sourcePower true 27 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 12 coarse_27_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9203579534301380843272, hi := 9203579534301380843272} +lemma t13_contains : t13.Contains (sourcePower true 27 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 13 coarse_27_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -890168433085651111959, hi := 890168433085651111959} +lemma t14_contains : t14.Contains (sourcePower true 27 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 14 coarse_27_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -81667185972791006988, hi := 81667185972791006988} +lemma t15_contains : t15.Contains (sourcePower true 27 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 15 coarse_27_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7133969330518964885, hi := 7133969330518964885} +lemma t16_contains : t16.Contains (sourcePower true 27 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 16 coarse_27_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -595600727454733885, hi := 595600727454733885} +lemma t17_contains : t17.Contains (sourcePower true 27 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 17 coarse_27_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -47704585830818839, hi := 47704585830818839} +lemma t18_contains : t18.Contains (sourcePower true 27 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 18 coarse_27_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3679656824384760, hi := 3679656824384760} +lemma t19_contains : t19.Contains (sourcePower true 27 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 19 coarse_27_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -274393575161513, hi := 274393575161513} +lemma t20_contains : t20.Contains (sourcePower true 27 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 20 coarse_27_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -19857565186914, hi := 19857565186914} +lemma t21_contains : t21.Contains (sourcePower true 27 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 21 coarse_27_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1399802782276, hi := 1399802782276} +lemma t22_contains : t22.Contains (sourcePower true 27 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 22 coarse_27_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -96441529722, hi := 96441529722} +lemma t23_contains : t23.Contains (sourcePower true 27 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 23 coarse_27_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -6512766124, hi := 6512766124} +lemma t24_contains : t24.Contains (sourcePower true 27 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 24 coarse_27_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -432038233, hi := 432038233} +lemma t25_contains : t25.Contains (sourcePower true 27 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 25 coarse_27_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -28192908, hi := 28192908} +lemma t26_contains : t26.Contains (sourcePower true 27 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 26 coarse_27_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1810811, hi := 1810811} +lemma t27_contains : t27.Contains (sourcePower true 27 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 27 coarse_27_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -114464, hi := 114464} +lemma t28_contains : t28.Contains (sourcePower true 27 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (1/2) 2 28 coarse_27_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 27 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -104098223231630169029420271, hi := 1353533634686221959607595917} +lemma t8_checked : ((hm27_0_0_10.realAnswer).add tr8).scale (-1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 27 (-1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm27_0_0_10.realContains tr8_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -273586055473683921267866222, hi := 273586055473683921267866222} +lemma tr9_contains : tr9.Contains (fullMoment true true 27 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 27 mixed_27_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -242880314174638567787671928, hi := 304291796772749879964269046} +lemma t9_checked : ((hm27_0_0_11.realAnswer).add tr9).scale (1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 27 (-1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm27_0_0_11.realContains tr9_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -94191747073031887938338274, hi := 94191747073031887938338274} +lemma tr10_contains : tr10.Contains (fullMoment true true 27 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 27 mixed_27_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -146102290473145522514785846, hi := 42281203672922376262030869} +lemma t10_checked : ((hm27_0_0_12.realAnswer).add tr10).scale (-1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 27 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm27_0_0_12.realContains tr10_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1692594999032740051215259804, hi := 1692594999032740051215259804} +lemma t11_contains : t11.Contains (sourcePower false 27 (-1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 11 coarse_27_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -368267358058404969028329713, hi := 368267358058404969028329713} +lemma t12_contains : t12.Contains (sourcePower false 27 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 12 coarse_27_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -75395723544996911868080822, hi := 75395723544996911868080822} +lemma t13_contains : t13.Contains (sourcePower false 27 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 13 coarse_27_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14584519607675307818323276, hi := 14584519607675307818323276} +lemma t14_contains : t14.Contains (sourcePower false 27 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 14 coarse_27_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2676070349956415716955635, hi := 2676070349956415716955635} +lemma t15_contains : t15.Contains (sourcePower false 27 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 15 coarse_27_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -467531814044890882677192, hi := 467531814044890882677192} +lemma t16_contains : t16.Contains (sourcePower false 27 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 16 coarse_27_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -78066578548946879717983, hi := 78066578548946879717983} +lemma t17_contains : t17.Contains (sourcePower false 27 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 17 coarse_27_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -12505470948034173484841, hi := 12505470948034173484841} +lemma t18_contains : t18.Contains (sourcePower false 27 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 18 coarse_27_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1929199917143036737388, hi := 1929199917143036737388} +lemma t19_contains : t19.Contains (sourcePower false 27 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 19 coarse_27_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -287722517468558106377, hi := 287722517468558106377} +lemma t20_contains : t20.Contains (sourcePower false 27 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 20 coarse_27_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -41644332546865669400, hi := 41644332546865669400} +lemma t21_contains : t21.Contains (sourcePower false 27 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 21 coarse_27_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -5871198408907366325, hi := 5871198408907366325} +lemma t22_contains : t22.Contains (sourcePower false 27 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 22 coarse_27_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -809010187757680160, hi := 809010187757680160} +lemma t23_contains : t23.Contains (sourcePower false 27 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 23 coarse_27_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -109266084005681632, hi := 109266084005681632} +lemma t24_contains : t24.Contains (sourcePower false 27 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 24 coarse_27_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -14496797495949849, hi := 14496797495949849} +lemma t25_contains : t25.Contains (sourcePower false 27 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 25 coarse_27_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1891993966608611, hi := 1891993966608611} +lemma t26_contains : t26.Contains (sourcePower false 27 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 26 coarse_27_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -243042902681483, hi := 243042902681483} +lemma t27_contains : t27.Contains (sourcePower false 27 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 27 coarse_27_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -30725956372471, hi := 30725956372471} +lemma t28_contains : t28.Contains (sourcePower false 27 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 27 (-1/1) 2 28 coarse_27_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 27 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -94473335040740004776071389, hi := 1363158522877094977904924468} +lemma t8_checked : ((hm27_1_0_10.realAnswer).add tr8).scale (1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 27 (-1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm27_1_0_10.realContains tr8_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -273586055473683921267866222, hi := 273586055473683921267866222} +lemma tr9_contains : tr9.Contains (fullMoment false true 27 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 27 mixed_27_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -246519453604096682030574692, hi := 300652657343288029364070110} +lemma t9_checked : ((hm27_1_0_11.realAnswer).add tr9).scale (-1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 27 (-1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm27_1_0_11.realContains tr9_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -94191747073031887938338274, hi := 94191747073031887938338274} +lemma tr10_contains : tr10.Contains (fullMoment false true 27 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 27 mixed_27_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -146899265985408112344013964, hi := 41484228160659038647168137} +lemma t10_checked : ((hm27_1_0_12.realAnswer).add tr10).scale (1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 27 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm27_1_0_12.realContains tr10_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1692594999032740051215259804, hi := 1692594999032740051215259804} +lemma t11_contains : t11.Contains (sourcePower true 27 (-1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 11 coarse_27_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -368267358058404969028329713, hi := 368267358058404969028329713} +lemma t12_contains : t12.Contains (sourcePower true 27 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 12 coarse_27_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -75395723544996911868080822, hi := 75395723544996911868080822} +lemma t13_contains : t13.Contains (sourcePower true 27 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 13 coarse_27_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14584519607675307818323276, hi := 14584519607675307818323276} +lemma t14_contains : t14.Contains (sourcePower true 27 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 14 coarse_27_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2676070349956415716955635, hi := 2676070349956415716955635} +lemma t15_contains : t15.Contains (sourcePower true 27 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 15 coarse_27_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -467531814044890882677192, hi := 467531814044890882677192} +lemma t16_contains : t16.Contains (sourcePower true 27 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 16 coarse_27_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -78066578548946879717983, hi := 78066578548946879717983} +lemma t17_contains : t17.Contains (sourcePower true 27 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 17 coarse_27_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -12505470948034173484841, hi := 12505470948034173484841} +lemma t18_contains : t18.Contains (sourcePower true 27 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 18 coarse_27_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1929199917143036737388, hi := 1929199917143036737388} +lemma t19_contains : t19.Contains (sourcePower true 27 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 19 coarse_27_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -287722517468558106377, hi := 287722517468558106377} +lemma t20_contains : t20.Contains (sourcePower true 27 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 20 coarse_27_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -41644332546865669400, hi := 41644332546865669400} +lemma t21_contains : t21.Contains (sourcePower true 27 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 21 coarse_27_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -5871198408907366325, hi := 5871198408907366325} +lemma t22_contains : t22.Contains (sourcePower true 27 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 22 coarse_27_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -809010187757680160, hi := 809010187757680160} +lemma t23_contains : t23.Contains (sourcePower true 27 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 23 coarse_27_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -109266084005681632, hi := 109266084005681632} +lemma t24_contains : t24.Contains (sourcePower true 27 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 24 coarse_27_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -14496797495949849, hi := 14496797495949849} +lemma t25_contains : t25.Contains (sourcePower true 27 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 25 coarse_27_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1891993966608611, hi := 1891993966608611} +lemma t26_contains : t26.Contains (sourcePower true 27 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 26 coarse_27_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -243042902681483, hi := 243042902681483} +lemma t27_contains : t27.Contains (sourcePower true 27 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 27 coarse_27_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -30725956372471, hi := 30725956372471} +lemma t28_contains : t28.Contains (sourcePower true 27 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 27 (-1/1) 2 28 coarse_27_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 27 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -32959788579715799069888989955, hi := -3060232435846498396282852568} +lemma t8_checked : ((hm28_0_0_10.realAnswer).add tr8).scale (-6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 28 (3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_10.realContains tr8_contains) (-6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -218934359068331366565401467, hi := 218934359068331366565401467} +lemma tr9_contains : tr9.Contains (fullMoment true true 28 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 28 mixed_28_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -6292552990910282725827201296, hi := 10540591499488817082477624227} +lemma t9_checked : ((hm28_0_0_11.realAnswer).add tr9).scale (-19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 28 (3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_11.realContains tr9_contains) (-19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -75365738378018125404513893, hi := 75365738378018125404513893} +lemma tr10_contains : tr10.Contains (fullMoment true true 28 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 28 mixed_28_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -1108807378404120305639285454, hi := 7583129116681259198826308762} +lemma t10_checked : ((hm28_0_0_12.realAnswer).add tr10).scale (-59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 28 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_12.realContains tr10_contains) (-59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -23959747803008070727398235, hi := 23959747803008070727398235} +lemma tr11_contains : tr11.Contains (fullMoment true true 28 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 28 mixed_28_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -2293706629503702921410202363, hi := 1851212749460690100801475673} +lemma t11_checked : ((hm28_0_0_13.realAnswer).add tr11).scale (-177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 28 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_13.realContains tr11_contains) (-177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -47551748981776413753898836465, hi := 47551748981776413753898836465} +lemma t12_contains : t12.Contains (sourcePower false 28 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 12 coarse_28_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14578471500289312856490453923, hi := 14578471500289312856490453923} +lemma t13_contains : t13.Contains (sourcePower false 28 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 13 coarse_28_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4220780499850943816803078776, hi := 4220780499850943816803078776} +lemma t14_contains : t14.Contains (sourcePower false 28 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 14 coarse_28_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1158366745494303787974643957, hi := 1158366745494303787974643957} +lemma t15_contains : t15.Contains (sourcePower false 28 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 15 coarse_28_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -302446302716274629369327260, hi := 302446302716274629369327260} +lemma t16_contains : t16.Contains (sourcePower false 28 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 16 coarse_28_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -75396249374312909453520699, hi := 75396249374312909453520699} +lemma t17_contains : t17.Contains (sourcePower false 28 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 17 coarse_28_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -18009576036600048324944622, hi := 18009576036600048324944622} +lemma t18_contains : t18.Contains (sourcePower false 28 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 18 coarse_28_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4136995935440357267488668, hi := 4136995935440357267488668} +lemma t19_contains : t19.Contains (sourcePower false 28 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 19 coarse_28_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -917275826786287346187836, hi := 917275826786287346187836} +lemma t20_contains : t20.Contains (sourcePower false 28 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 20 coarse_28_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -197048374827896082858002, hi := 197048374827896082858002} +lemma t21_contains : t21.Contains (sourcePower false 28 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 21 coarse_28_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -41163784493358540938996, hi := 41163784493358540938996} +lemma t22_contains : t22.Contains (sourcePower false 28 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 22 coarse_28_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -8392059223461790609972, hi := 8392059223461790609972} +lemma t23_contains : t23.Contains (sourcePower false 28 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 23 coarse_28_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1675046444258822050151, hi := 1675046444258822050151} +lemma t24_contains : t24.Contains (sourcePower false 28 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 24 coarse_28_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -328210851349012800663, hi := 328210851349012800663} +lemma t25_contains : t25.Contains (sourcePower false 28 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 25 coarse_28_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -63256426471434251136, hi := 63256426471434251136} +lemma t26_contains : t26.Contains (sourcePower false 28 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 26 coarse_28_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -12005859662292129143, hi := 12005859662292129143} +lemma t27_contains : t27.Contains (sourcePower false 28 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 27 coarse_28_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -2244844860502577062, hi := 2244844860502577062} +lemma t28_contains : t28.Contains (sourcePower false 28 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (3/2) 2 28 coarse_28_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 28 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -33409359046836491817371859608, hi := -3509802902967633979947623916} +lemma t8_checked : ((hm28_1_0_10.realAnswer).add tr8).scale (6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 28 (3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_10.realContains tr8_contains) (6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -218934359068331366565401467, hi := 218934359068331366565401467} +lemma tr9_contains : tr9.Contains (fullMoment false true 28 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 28 mixed_28_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -6418338087775682420911137007, hi := 10414806402623272614693288274} +lemma t9_checked : ((hm28_1_0_11.realAnswer).add tr9).scale (19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 28 (3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_11.realContains tr9_contains) (19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -75365738378018125404513893, hi := 75365738378018125404513893} +lemma tr10_contains : tr10.Contains (fullMoment false true 28 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 28 mixed_28_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -1030332550963118175973099781, hi := 7661603944122217859009779201} +lemma t10_checked : ((hm28_1_0_12.realAnswer).add tr10).scale (59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 28 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_12.realContains tr10_contains) (59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -23959747803008070727398235, hi := 23959747803008070727398235} +lemma tr11_contains : tr11.Contains (fullMoment false true 28 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 28 mixed_28_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -2268041930336048725092328254, hi := 1876877448628332225540424362} +lemma t11_checked : ((hm28_1_0_13.realAnswer).add tr11).scale (177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 28 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_13.realContains tr11_contains) (177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -47551748981776413753898836465, hi := 47551748981776413753898836465} +lemma t12_contains : t12.Contains (sourcePower true 28 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 12 coarse_28_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14578471500289312856490453923, hi := 14578471500289312856490453923} +lemma t13_contains : t13.Contains (sourcePower true 28 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 13 coarse_28_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4220780499850943816803078776, hi := 4220780499850943816803078776} +lemma t14_contains : t14.Contains (sourcePower true 28 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 14 coarse_28_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1158366745494303787974643957, hi := 1158366745494303787974643957} +lemma t15_contains : t15.Contains (sourcePower true 28 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 15 coarse_28_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -302446302716274629369327260, hi := 302446302716274629369327260} +lemma t16_contains : t16.Contains (sourcePower true 28 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 16 coarse_28_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -75396249374312909453520699, hi := 75396249374312909453520699} +lemma t17_contains : t17.Contains (sourcePower true 28 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 17 coarse_28_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -18009576036600048324944622, hi := 18009576036600048324944622} +lemma t18_contains : t18.Contains (sourcePower true 28 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 18 coarse_28_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -4136995935440357267488668, hi := 4136995935440357267488668} +lemma t19_contains : t19.Contains (sourcePower true 28 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 19 coarse_28_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -917275826786287346187836, hi := 917275826786287346187836} +lemma t20_contains : t20.Contains (sourcePower true 28 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 20 coarse_28_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -197048374827896082858002, hi := 197048374827896082858002} +lemma t21_contains : t21.Contains (sourcePower true 28 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 21 coarse_28_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -41163784493358540938996, hi := 41163784493358540938996} +lemma t22_contains : t22.Contains (sourcePower true 28 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 22 coarse_28_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -8392059223461790609972, hi := 8392059223461790609972} +lemma t23_contains : t23.Contains (sourcePower true 28 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 23 coarse_28_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1675046444258822050151, hi := 1675046444258822050151} +lemma t24_contains : t24.Contains (sourcePower true 28 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 24 coarse_28_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -328210851349012800663, hi := 328210851349012800663} +lemma t25_contains : t25.Contains (sourcePower true 28 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 25 coarse_28_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -63256426471434251136, hi := 63256426471434251136} +lemma t26_contains : t26.Contains (sourcePower true 28 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 26 coarse_28_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -12005859662292129143, hi := 12005859662292129143} +lemma t27_contains : t27.Contains (sourcePower true 28 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 27 coarse_28_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -2244844860502577062, hi := 2244844860502577062} +lemma t28_contains : t28.Contains (sourcePower true 28 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (3/2) 2 28 coarse_28_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 28 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -5023592223703063415620941, hi := -466427745137402590501882} +lemma t8_checked : ((hm28_0_0_10.realAnswer).add tr8).scale (-1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 28 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_10.realContains tr8_contains) (-1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -218934359068331366565401467, hi := 218934359068331366565401467} +lemma tr9_contains : tr9.Contains (fullMoment true true 28 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 28 mixed_28_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -535517527789910942563513, hi := 319694812320798797227415} +lemma t9_checked : ((hm28_0_0_11.realAnswer).add tr9).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 28 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_11.realContains tr9_contains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -75365738378018125404513893, hi := 75365738378018125404513893} +lemma tr10_contains : tr10.Contains (fullMoment true true 28 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 28 mixed_28_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -18777750315909165365024, hi := 128420957453661521767114} +lemma t10_checked : ((hm28_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 28 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -23959747803008070727398235, hi := 23959747803008070727398235} +lemma tr11_contains : tr11.Contains (fullMoment true true 28 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 28 mixed_28_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -10450150154734147915582, hi := 12948041059141294638974} +lemma t11_checked : ((hm28_0_0_13.realAnswer).add tr11).scale (1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 28 (-1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm28_0_0_13.realContains tr11_contains) (1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -89477004938979893824336, hi := 89477004938979893824336} +lemma t12_contains : t12.Contains (sourcePower false 28 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 12 coarse_28_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9143988702596219747499, hi := 9143988702596219747499} +lemma t13_contains : t13.Contains (sourcePower false 28 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 13 coarse_28_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -882460350433160619859, hi := 882460350433160619859} +lemma t14_contains : t14.Contains (sourcePower false 28 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 14 coarse_28_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -80728570161776349096, hi := 80728570161776349096} +lemma t15_contains : t15.Contains (sourcePower false 28 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 15 coarse_28_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7026000951762960747, hi := 7026000951762960747} +lemma t16_contains : t16.Contains (sourcePower false 28 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 16 coarse_28_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -583832694824095193, hi := 583832694824095193} +lemma t17_contains : t17.Contains (sourcePower false 28 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 17 coarse_28_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -46485863675114117, hi := 46485863675114117} +lemma t18_contains : t18.Contains (sourcePower false 28 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 18 coarse_28_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3559436540659536, hi := 3559436540659536} +lemma t19_contains : t19.Contains (sourcePower false 28 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 19 coarse_28_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -263072137905406, hi := 263072137905406} +lemma t20_contains : t20.Contains (sourcePower false 28 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 20 coarse_28_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -18837640661253, hi := 18837640661253} +lemma t21_contains : t21.Contains (sourcePower false 28 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 21 coarse_28_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1311739788467, hi := 1311739788467} +lemma t22_contains : t22.Contains (sourcePower false 28 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 22 coarse_28_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -89141447400, hi := 89141447400} +lemma t23_contains : t23.Contains (sourcePower false 28 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 23 coarse_28_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -5930847266, hi := 5930847266} +lemma t24_contains : t24.Contains (sourcePower false 28 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 24 coarse_28_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -387366062, hi := 387366062} +lemma t25_contains : t25.Contains (sourcePower false 28 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 25 coarse_28_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -24885825, hi := 24885825} +lemma t26_contains : t26.Contains (sourcePower false 28 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 26 coarse_28_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1574416, hi := 1574416} +lemma t27_contains : t27.Contains (sourcePower false 28 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 27 coarse_28_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -98128, hi := 98128} +lemma t28_contains : t28.Contains (sourcePower false 28 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 28 (-1/2) 2 28 coarse_28_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 28 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -5092113861733956990911730, hi := -534949383168363661019299} +lemma t8_checked : ((hm28_1_0_10.realAnswer).add tr8).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 28 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_10.realContains tr8_contains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -218934359068331366565401467, hi := 218934359068331366565401467} +lemma tr9_contains : tr9.Contains (fullMoment false true 28 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 28 mixed_28_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -529126982808681228201661, hi := 326085357302021156374087} +lemma t9_checked : ((hm28_1_0_11.realAnswer).add tr9).scale (-1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 28 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_11.realContains tr9_contains) (-1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -75365738378018125404513893, hi := 75365738378018125404513893} +lemma tr10_contains : tr10.Contains (fullMoment false true 28 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 28 mixed_28_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -17448772222444379684214, hi := 129749935547125571288418} +lemma t10_checked : ((hm28_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 28 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -23959747803008070727398235, hi := 23959747803008070727398235} +lemma tr11_contains : tr11.Contains (fullMoment false true 28 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 28 mixed_28_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -10595028132727803606838, hi := 12803163081147570803301} +lemma t11_checked : ((hm28_1_0_13.realAnswer).add tr11).scale (-1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 28 (-1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm28_1_0_13.realContains tr11_contains) (-1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -89477004938979893824336, hi := 89477004938979893824336} +lemma t12_contains : t12.Contains (sourcePower true 28 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 12 coarse_28_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -9143988702596219747499, hi := 9143988702596219747499} +lemma t13_contains : t13.Contains (sourcePower true 28 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 13 coarse_28_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -882460350433160619859, hi := 882460350433160619859} +lemma t14_contains : t14.Contains (sourcePower true 28 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 14 coarse_28_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -80728570161776349096, hi := 80728570161776349096} +lemma t15_contains : t15.Contains (sourcePower true 28 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 15 coarse_28_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -7026000951762960747, hi := 7026000951762960747} +lemma t16_contains : t16.Contains (sourcePower true 28 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 16 coarse_28_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -583832694824095193, hi := 583832694824095193} +lemma t17_contains : t17.Contains (sourcePower true 28 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 17 coarse_28_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -46485863675114117, hi := 46485863675114117} +lemma t18_contains : t18.Contains (sourcePower true 28 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 18 coarse_28_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3559436540659536, hi := 3559436540659536} +lemma t19_contains : t19.Contains (sourcePower true 28 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 19 coarse_28_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -263072137905406, hi := 263072137905406} +lemma t20_contains : t20.Contains (sourcePower true 28 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 20 coarse_28_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -18837640661253, hi := 18837640661253} +lemma t21_contains : t21.Contains (sourcePower true 28 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 21 coarse_28_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1311739788467, hi := 1311739788467} +lemma t22_contains : t22.Contains (sourcePower true 28 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 22 coarse_28_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -89141447400, hi := 89141447400} +lemma t23_contains : t23.Contains (sourcePower true 28 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 23 coarse_28_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -5930847266, hi := 5930847266} +lemma t24_contains : t24.Contains (sourcePower true 28 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 24 coarse_28_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -387366062, hi := 387366062} +lemma t25_contains : t25.Contains (sourcePower true 28 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 25 coarse_28_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -24885825, hi := 24885825} +lemma t26_contains : t26.Contains (sourcePower true 28 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 26 coarse_28_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1574416, hi := 1574416} +lemma t27_contains : t27.Contains (sourcePower true 28 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 27 coarse_28_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -98128, hi := 98128} +lemma t28_contains : t28.Contains (sourcePower true 28 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 28 (-1/2) 2 28 coarse_28_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 28 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -4043086167462381503002572, hi := 4043086167462381503002572} +lemma t13_contains : t13.Contains (sourcePower false 3 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 13 coarse_3_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -715864126238454682678554, hi := 715864126238454682678554} +lemma t14_contains : t14.Contains (sourcePower false 3 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 14 coarse_3_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -122249712386770544494617, hi := 122249712386770544494617} +lemma t15_contains : t15.Contains (sourcePower false 3 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 15 coarse_3_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -20198686864620612491610, hi := 20198686864620612491610} +lemma t16_contains : t16.Contains (sourcePower false 3 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 16 coarse_3_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -3236965951437818359099, hi := 3236965951437818359099} +lemma t17_contains : t17.Contains (sourcePower false 3 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 17 coarse_3_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -504105662040223246579, hi := 504105662040223246579} +lemma t18_contains : t18.Contains (sourcePower false 3 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 18 coarse_3_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -76398703323662302251, hi := 76398703323662302251} +lemma t19_contains : t19.Contains (sourcePower false 3 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 19 coarse_3_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -11279056507469007889, hi := 11279056507469007889} +lemma t20_contains : t20.Contains (sourcePower false 3 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 20 coarse_3_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -1623305987221238879, hi := 1623305987221238879} +lemma t21_contains : t21.Contains (sourcePower false 3 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 21 coarse_3_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -227882158301826892, hi := 227882158301826892} +lemma t22_contains : t22.Contains (sourcePower false 3 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 22 coarse_3_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -31218112438688220, hi := 31218112438688220} +lemma t23_contains : t23.Contains (sourcePower false 3 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 23 coarse_3_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -4175288966584807, hi := 4175288966584807} +lemma t24_contains : t24.Contains (sourcePower false 3 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 24 coarse_3_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -545457456936434, hi := 545457456936434} +lemma t25_contains : t25.Contains (sourcePower false 3 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 25 coarse_3_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -69641010703742, hi := 69641010703742} +lemma t26_contains : t26.Contains (sourcePower false 3 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 26 coarse_3_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -8694835330545, hi := 8694835330545} +lemma t27_contains : t27.Contains (sourcePower false 3 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 27 coarse_3_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1062269013594, hi := 1062269013594} +lemma t28_contains : t28.Contains (sourcePower false 3 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (1/2) 2 28 coarse_3_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 3 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -4043086167462381503002572, hi := 4043086167462381503002572} +lemma t13_contains : t13.Contains (sourcePower true 3 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 13 coarse_3_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -715864126238454682678554, hi := 715864126238454682678554} +lemma t14_contains : t14.Contains (sourcePower true 3 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 14 coarse_3_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -122249712386770544494617, hi := 122249712386770544494617} +lemma t15_contains : t15.Contains (sourcePower true 3 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 15 coarse_3_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -20198686864620612491610, hi := 20198686864620612491610} +lemma t16_contains : t16.Contains (sourcePower true 3 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 16 coarse_3_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -3236965951437818359099, hi := 3236965951437818359099} +lemma t17_contains : t17.Contains (sourcePower true 3 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 17 coarse_3_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -504105662040223246579, hi := 504105662040223246579} +lemma t18_contains : t18.Contains (sourcePower true 3 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 18 coarse_3_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -76398703323662302251, hi := 76398703323662302251} +lemma t19_contains : t19.Contains (sourcePower true 3 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 19 coarse_3_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -11279056507469007889, hi := 11279056507469007889} +lemma t20_contains : t20.Contains (sourcePower true 3 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 20 coarse_3_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -1623305987221238879, hi := 1623305987221238879} +lemma t21_contains : t21.Contains (sourcePower true 3 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 21 coarse_3_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -227882158301826892, hi := 227882158301826892} +lemma t22_contains : t22.Contains (sourcePower true 3 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 22 coarse_3_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -31218112438688220, hi := 31218112438688220} +lemma t23_contains : t23.Contains (sourcePower true 3 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 23 coarse_3_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -4175288966584807, hi := 4175288966584807} +lemma t24_contains : t24.Contains (sourcePower true 3 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 24 coarse_3_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -545457456936434, hi := 545457456936434} +lemma t25_contains : t25.Contains (sourcePower true 3 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 25 coarse_3_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -69641010703742, hi := 69641010703742} +lemma t26_contains : t26.Contains (sourcePower true 3 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 26 coarse_3_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -8694835330545, hi := 8694835330545} +lemma t27_contains : t27.Contains (sourcePower true 3 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 27 coarse_3_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1062269013594, hi := 1062269013594} +lemma t28_contains : t28.Contains (sourcePower true 3 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (1/2) 2 28 coarse_3_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 3 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -33120961883851829272597065973, hi := 33120961883851829272597065973} +lemma t13_contains : t13.Contains (sourcePower false 3 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 13 coarse_3_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -11728717844290841521005417025, hi := 11728717844290841521005417025} +lemma t14_contains : t14.Contains (sourcePower false 3 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 14 coarse_3_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -4005878575489697201999608859, hi := 4005878575489697201999608859} +lemma t15_contains : t15.Contains (sourcePower false 3 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 15 coarse_3_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1323741142359776460250142926, hi := 1323741142359776460250142926} +lemma t16_contains : t16.Contains (sourcePower false 3 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 16 coarse_3_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -424275601186857727963730598, hi := 424275601186857727963730598} +lemma t17_contains : t17.Contains (sourcePower false 3 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 17 coarse_3_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -132148274669872282750965635, hi := 132148274669872282750965635} +lemma t18_contains : t18.Contains (sourcePower false 3 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 18 coarse_3_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -40054923368156261122308451, hi := 40054923368156261122308451} +lemma t19_contains : t19.Contains (sourcePower false 3 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 19 coarse_3_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -11826947956375822415775753, hi := 11826947956375822415775753} +lemma t20_contains : t20.Contains (sourcePower false 3 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 20 coarse_3_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -3404319397712995555990714, hi := 3404319397712995555990714} +lemma t21_contains : t21.Contains (sourcePower false 3 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 21 coarse_3_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -955807048093985739496594, hi := 955807048093985739496594} +lemma t22_contains : t22.Contains (sourcePower false 3 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 22 coarse_3_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -261876507748079506096636, hi := 261876507748079506096636} +lemma t23_contains : t23.Contains (sourcePower false 3 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 23 coarse_3_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -70049724854810084957006, hi := 70049724854810084957006} +lemma t24_contains : t24.Contains (sourcePower false 3 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 24 coarse_3_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -18302515147666469904221, hi := 18302515147666469904221} +lemma t25_contains : t25.Contains (sourcePower false 3 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 25 coarse_3_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -4673529116139955813959, hi := 4673529116139955813959} +lemma t26_contains : t26.Contains (sourcePower false 3 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 26 coarse_3_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1167001043399812052418, hi := 1167001043399812052418} +lemma t27_contains : t27.Contains (sourcePower false 3 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 27 coarse_3_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -285150667058617221983, hi := 285150667058617221983} +lemma t28_contains : t28.Contains (sourcePower false 3 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 3 (-1/1) 2 28 coarse_3_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 3 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -33120961883851829272597065973, hi := 33120961883851829272597065973} +lemma t13_contains : t13.Contains (sourcePower true 3 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 13 coarse_3_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -11728717844290841521005417025, hi := 11728717844290841521005417025} +lemma t14_contains : t14.Contains (sourcePower true 3 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 14 coarse_3_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -4005878575489697201999608859, hi := 4005878575489697201999608859} +lemma t15_contains : t15.Contains (sourcePower true 3 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 15 coarse_3_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -1323741142359776460250142926, hi := 1323741142359776460250142926} +lemma t16_contains : t16.Contains (sourcePower true 3 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 16 coarse_3_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -424275601186857727963730598, hi := 424275601186857727963730598} +lemma t17_contains : t17.Contains (sourcePower true 3 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 17 coarse_3_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -132148274669872282750965635, hi := 132148274669872282750965635} +lemma t18_contains : t18.Contains (sourcePower true 3 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 18 coarse_3_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -40054923368156261122308451, hi := 40054923368156261122308451} +lemma t19_contains : t19.Contains (sourcePower true 3 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 19 coarse_3_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -11826947956375822415775753, hi := 11826947956375822415775753} +lemma t20_contains : t20.Contains (sourcePower true 3 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 20 coarse_3_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -3404319397712995555990714, hi := 3404319397712995555990714} +lemma t21_contains : t21.Contains (sourcePower true 3 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 21 coarse_3_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -955807048093985739496594, hi := 955807048093985739496594} +lemma t22_contains : t22.Contains (sourcePower true 3 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 22 coarse_3_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -261876507748079506096636, hi := 261876507748079506096636} +lemma t23_contains : t23.Contains (sourcePower true 3 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 23 coarse_3_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -70049724854810084957006, hi := 70049724854810084957006} +lemma t24_contains : t24.Contains (sourcePower true 3 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 24 coarse_3_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -18302515147666469904221, hi := 18302515147666469904221} +lemma t25_contains : t25.Contains (sourcePower true 3 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 25 coarse_3_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -4673529116139955813959, hi := 4673529116139955813959} +lemma t26_contains : t26.Contains (sourcePower true 3 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 26 coarse_3_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -1167001043399812052418, hi := 1167001043399812052418} +lemma t27_contains : t27.Contains (sourcePower true 3 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 27 coarse_3_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -285150667058617221983, hi := 285150667058617221983} +lemma t28_contains : t28.Contains (sourcePower true 3 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 3 (-1/1) 2 28 coarse_3_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 3 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -12426989432135384731531185053, hi := -9235840349504847671181159701} +lemma t6_checked : ((hm31_0_0_8.realAnswer).add tr6).scale (-1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 31 (1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_8.realContains tr6_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -730532592140359898388862477, hi := 730532592140359898388862477} +lemma tr7_contains : tr7.Contains (fullMoment true true 31 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 31 mixed_31_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -133602055107308959007806168, hi := 1327463129173812219596153184} +lemma t7_checked : ((hm31_0_0_9.realAnswer).add tr7).scale (-1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 31 (1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_9.realContains tr7_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -301261453327846246821723796, hi := 301261453327846246821723796} +lemma tr8_contains : tr8.Contains (fullMoment true true 31 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 31 mixed_31_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 775423127211655802478209831, hi := 1377946033867444335569661335} +lemma t8_checked : ((hm31_0_0_10.realAnswer).add tr8).scale (-1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 31 (1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_10.realContains tr8_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -113019595441228187975959620, hi := 113019595441228187975959620} +lemma tr9_contains : tr9.Contains (fullMoment true true 31 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 31 mixed_31_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -150717377729198793039746676, hi := 75321813153278513163462827} +lemma t9_checked : ((hm31_0_0_11.realAnswer).add tr9).scale (-1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 31 (1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_11.realContains tr9_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -38890056305794465335597165, hi := 38890056305794465335597165} +lemma tr10_contains : tr10.Contains (fullMoment true true 31 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 31 mixed_31_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -113805918366965769537442860, hi := -36025805755372649558015392} +lemma t10_checked : ((hm31_0_0_12.realAnswer).add tr10).scale (-1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 31 (1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_12.realContains tr10_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -12359268881528133451052428, hi := 12359268881528133451052428} +lemma tr11_contains : tr11.Contains (fullMoment true true 31 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 31 mixed_31_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -10631773177397223151575126, hi := 14086764585659819349267152} +lemma t11_checked : ((hm31_0_0_13.realAnswer).add tr11).scale (-1) 1=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 31 (1/1) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_13.realContains tr11_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -363070699164326615018086872, hi := 363070699164326615018086872} +lemma t12_contains : t12.Contains (sourcePower false 31 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 12 coarse_31_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73962271777329974046821796, hi := 73962271777329974046821796} +lemma t13_contains : t13.Contains (sourcePower false 31 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 13 coarse_31_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14213721997609591849798918, hi := 14213721997609591849798918} +lemma t14_contains : t14.Contains (sourcePower false 31 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 14 coarse_31_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2585773992524154980080041, hi := 2585773992524154980080041} +lemma t15_contains : t15.Contains (sourcePower false 31 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 15 coarse_31_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -446759975292680258207762, hi := 446759975292680258207762} +lemma t16_contains : t16.Contains (sourcePower false 31 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 16 coarse_31_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -73538835195571904113332, hi := 73538835195571904113332} +lemma t17_contains : t17.Contains (sourcePower false 31 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 17 coarse_31_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11567724912324847730582, hi := 11567724912324847730582} +lemma t18_contains : t18.Contains (sourcePower false 31 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 18 coarse_31_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1744203475531886507303, hi := 1744203475531886507303} +lemma t19_contains : t19.Contains (sourcePower false 31 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 19 coarse_31_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -252881220492250857440, hi := 252881220492250857440} +lemma t20_contains : t20.Contains (sourcePower false 31 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 20 coarse_31_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -35367081633198004494, hi := 35367081633198004494} +lemma t21_contains : t21.Contains (sourcePower false 31 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 21 coarse_31_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4787259615656135378, hi := 4787259615656135378} +lemma t22_contains : t22.Contains (sourcePower false 31 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 22 coarse_31_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -629309525621986588, hi := 629309525621986588} +lemma t23_contains : t23.Contains (sourcePower false 31 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 23 coarse_31_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -80618018826638037, hi := 80618018826638037} +lemma t24_contains : t24.Contains (sourcePower false 31 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 24 coarse_31_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -10098538453300210, hi := 10098538453300210} +lemma t25_contains : t25.Contains (sourcePower false 31 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 25 coarse_31_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1240816760230138, hi := 1240816760230138} +lemma t26_contains : t26.Contains (sourcePower false 31 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 26 coarse_31_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -149953099101626, hi := 149953099101626} +lemma t27_contains : t27.Contains (sourcePower false 31 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 27 coarse_31_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -17861124354033, hi := 17861124354033} +lemma t28_contains : t28.Contains (sourcePower false 31 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (1/1) 2 28 coarse_31_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 31 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -12846268396986379028540237134, hi := -9655119314356126195443103514} +lemma t6_checked : ((hm31_1_0_8.realAnswer).add tr6).scale (1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 31 (1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_8.realContains tr6_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -730532592140359898388862477, hi := 730532592140359898388862477} +lemma tr7_contains : tr7.Contains (fullMoment false true 31 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 31 mixed_31_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -171140162084975839289290726, hi := 1289925022196069888874047314} +lemma t7_checked : ((hm31_1_0_9.realAnswer).add tr7).scale (1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 31 (1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_9.realContains tr7_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -301261453327846246821723796, hi := 301261453327846246821723796} +lemma tr8_contains : tr8.Contains (fullMoment false true 31 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 31 mixed_31_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 817306530861319695703099649, hi := 1419829437517090164562225539} +lemma t8_checked : ((hm31_1_0_10.realAnswer).add tr8).scale (1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 31 (1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_10.realContains tr8_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -113019595441228187975959620, hi := 113019595441228187975959620} +lemma tr9_contains : tr9.Contains (fullMoment false true 31 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 31 mixed_31_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -146209744677340089918116475, hi := 79829446205133276313086420} +lemma t9_checked : ((hm31_1_0_11.realAnswer).add tr9).scale (1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 31 (1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_11.realContains tr9_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -38890056305794465335597165, hi := 38890056305794465335597165} +lemma tr10_contains : tr10.Contains (fullMoment false true 31 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 31 mixed_31_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -116730932096266323117801739, hi := -38950819484673992514511785} +lemma t10_checked : ((hm31_1_0_12.realAnswer).add tr10).scale (1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 31 (1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_12.realContains tr10_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -12359268881528133451052428, hi := 12359268881528133451052428} +lemma tr11_contains : tr11.Contains (fullMoment false true 31 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 31 mixed_31_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -10977853565005649380164083, hi := 13740684198051246829061020} +lemma t11_checked : ((hm31_1_0_13.realAnswer).add tr11).scale (1) 1=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 31 (1/1) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_13.realContains tr11_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -363070699164326615018086872, hi := 363070699164326615018086872} +lemma t12_contains : t12.Contains (sourcePower true 31 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 12 coarse_31_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73962271777329974046821796, hi := 73962271777329974046821796} +lemma t13_contains : t13.Contains (sourcePower true 31 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 13 coarse_31_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14213721997609591849798918, hi := 14213721997609591849798918} +lemma t14_contains : t14.Contains (sourcePower true 31 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 14 coarse_31_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2585773992524154980080041, hi := 2585773992524154980080041} +lemma t15_contains : t15.Contains (sourcePower true 31 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 15 coarse_31_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -446759975292680258207762, hi := 446759975292680258207762} +lemma t16_contains : t16.Contains (sourcePower true 31 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 16 coarse_31_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -73538835195571904113332, hi := 73538835195571904113332} +lemma t17_contains : t17.Contains (sourcePower true 31 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 17 coarse_31_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11567724912324847730582, hi := 11567724912324847730582} +lemma t18_contains : t18.Contains (sourcePower true 31 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 18 coarse_31_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1744203475531886507303, hi := 1744203475531886507303} +lemma t19_contains : t19.Contains (sourcePower true 31 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 19 coarse_31_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -252881220492250857440, hi := 252881220492250857440} +lemma t20_contains : t20.Contains (sourcePower true 31 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 20 coarse_31_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -35367081633198004494, hi := 35367081633198004494} +lemma t21_contains : t21.Contains (sourcePower true 31 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 21 coarse_31_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4787259615656135378, hi := 4787259615656135378} +lemma t22_contains : t22.Contains (sourcePower true 31 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 22 coarse_31_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -629309525621986588, hi := 629309525621986588} +lemma t23_contains : t23.Contains (sourcePower true 31 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 23 coarse_31_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -80618018826638037, hi := 80618018826638037} +lemma t24_contains : t24.Contains (sourcePower true 31 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 24 coarse_31_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -10098538453300210, hi := 10098538453300210} +lemma t25_contains : t25.Contains (sourcePower true 31 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 25 coarse_31_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1240816760230138, hi := 1240816760230138} +lemma t26_contains : t26.Contains (sourcePower true 31 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 26 coarse_31_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -149953099101626, hi := 149953099101626} +lemma t27_contains : t27.Contains (sourcePower true 31 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 27 coarse_31_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -17861124354033, hi := 17861124354033} +lemma t28_contains : t28.Contains (sourcePower true 31 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (1/1) 2 28 coarse_31_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 31 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -141551176500417116707597404745, hi := -105201993981078655504547897219} +lemma t6_checked : ((hm31_0_0_8.realAnswer).add tr6).scale (-729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 31 (-3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_8.realContains tr6_contains) (-729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -730532592140359898388862477, hi := 730532592140359898388862477} +lemma tr7_contains : tr7.Contains (fullMoment true true 31 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 31 mixed_31_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -22680952058618182220756148543, hi := 2282716363435036666797438199} +lemma t7_checked : ((hm31_0_0_9.realAnswer).add tr7).scale (2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 31 (-3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_9.realContains tr7_contains) (2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -301261453327846246821723796, hi := 301261453327846246821723796} +lemma tr8_contains : tr8.Contains (fullMoment true true 31 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 31 mixed_31_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 19873246631389350468982557426, hi := 35315249719548055803408390699} +lemma t8_checked : ((hm31_0_0_10.realAnswer).add tr8).scale (-6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 31 (-3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_10.realContains tr8_contains) (-6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -113019595441228187975959620, hi := 113019595441228187975959620} +lemma tr9_contains : tr9.Contains (fullMoment true true 31 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 31 mixed_31_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -2895623531828087841008669578, hi := 5794082316101210631643230125} +lemma t9_checked : ((hm31_0_0_11.realAnswer).add tr9).scale (19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 31 (-3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_11.realContains tr9_contains) (19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -38890056305794465335597165, hi := 38890056305794465335597165} +lemma tr10_contains : tr10.Contains (fullMoment true true 31 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 31 mixed_31_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -6562622728174767309977015079, hi := -2077429496141601156007080939} +lemma t10_checked : ((hm31_0_0_12.realAnswer).add tr10).scale (-59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 31 (-3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_12.realContains tr10_contains) (-59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -12359268881528133451052428, hi := 12359268881528133451052428} +lemma tr11_contains : tr11.Contains (fullMoment true true 31 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 31 mixed_31_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -1218470745144472665168275477, hi := 919622423367375922671913499} +lemma t11_checked : ((hm31_0_0_13.realAnswer).add tr11).scale (177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 31 (-3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm31_0_0_13.realContains tr11_contains) (177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -47107093611960180813434351891, hi := 47107093611960180813434351891} +lemma t12_contains : t12.Contains (sourcePower false 31 (-3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 12 coarse_31_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14394500857769538111847053988, hi := 14394500857769538111847053988} +lemma t13_contains : t13.Contains (sourcePower false 31 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 13 coarse_31_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4149401348216842768569389712, hi := 4149401348216842768569389712} +lemma t14_contains : t14.Contains (sourcePower false 31 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 14 coarse_31_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1132294633232049409874126003, hi := 1132294633232049409874126003} +lemma t15_contains : t15.Contains (sourcePower false 31 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 15 coarse_31_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -293450195471052557636680464, hi := 293450195471052557636680464} +lemma t16_contains : t16.Contains (sourcePower false 31 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 16 coarse_31_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -72454964935198155024841805, hi := 72454964935198155024841805} +lemma t17_contains : t17.Contains (sourcePower false 31 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 17 coarse_31_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -17095846718408106363802409, hi := 17095846718408106363802409} +lemma t18_contains : t18.Contains (sourcePower false 31 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 18 coarse_31_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3866616230427148851881964, hi := 3866616230427148851881964} +lemma t19_contains : t19.Contains (sourcePower false 31 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 19 coarse_31_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -840894980352613288021724, hi := 840894980352613288021724} +lemma t20_contains : t20.Contains (sourcePower false 31 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 20 coarse_31_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -176406939336102112504016, hi := 176406939336102112504016} +lemma t21_contains : t21.Contains (sourcePower false 31 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 21 coarse_31_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -35817451325097945676707, hi := 35817451325097945676707} +lemma t22_contains : t22.Contains (sourcePower false 31 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 22 coarse_31_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -7062578106899883956562, hi := 7062578106899883956562} +lemma t23_contains : t23.Contains (sourcePower false 31 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 23 coarse_31_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1357132773949141042559, hi := 1357132773949141042559} +lemma t24_contains : t24.Contains (sourcePower false 31 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 24 coarse_31_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -254999894008141724024, hi := 254999894008141724024} +lemma t25_contains : t25.Contains (sourcePower false 31 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 25 coarse_31_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -46998109251959411980, hi := 46998109251959411980} +lemma t26_contains : t26.Contains (sourcePower false 31 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 26 coarse_31_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -8519604618663829526, hi := 8519604618663829526} +lemma t27_contains : t27.Contains (sourcePower false 31 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 27 coarse_31_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1522173117322706802, hi := 1522173117322706802} +lemma t28_contains : t28.Contains (sourcePower false 31 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 31 (-3/2) 2 28 coarse_31_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 31 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -146327025959422973621966138605, hi := -109977843440087749944969100964} +lemma t6_checked : ((hm31_1_0_8.realAnswer).add tr6).scale (729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 31 (-3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_8.realContains tr6_contains) (729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -730532592140359898388862477, hi := 730532592140359898388862477} +lemma tr7_contains : tr7.Contains (fullMoment false true 31 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 31 mixed_31_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -22039578308928162866933917780, hi := 2924090113123766879106865764} +lemma t7_checked : ((hm31_1_0_9.realAnswer).add tr7).scale (-2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 31 (-3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_9.realContains tr7_contains) (-2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -301261453327846246821723796, hi := 301261453327846246821723796} +lemma tr8_contains : tr8.Contains (fullMoment false true 31 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 31 mixed_31_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 20946672456957494232453268738, hi := 36388675545115736600362350631} +lemma t8_checked : ((hm31_1_0_10.realAnswer).add tr8).scale (6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 31 (-3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_10.realContains tr8_contains) (6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -113019595441228187975959620, hi := 113019595441228187975959620} +lemma tr9_contains : tr9.Contains (fullMoment false true 31 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 31 mixed_31_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -3068912089171168511075156260, hi := 5620793758757978495816965972} +lemma t9_checked : ((hm31_1_0_11.realAnswer).add tr9).scale (-19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 31 (-3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_11.realContains tr9_contains) (-19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -38890056305794465335597165, hi := 38890056305794465335597165} +lemma tr10_contains : tr10.Contains (fullMoment false true 31 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 31 mixed_31_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -6731293759133232532991284069, hi := -2246100527100111898427154680} +lemma t10_checked : ((hm31_1_0_12.realAnswer).add tr10).scale (59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 31 (-3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_12.realContains tr10_contains) (59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -12359268881528133451052428, hi := 12359268881528133451052428} +lemma tr11_contains : tr11.Contains (fullMoment false true 31 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 31 mixed_31_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -1188535636539152452161949468, hi := 949557531972683481810511139} +lemma t11_checked : ((hm31_1_0_13.realAnswer).add tr11).scale (-177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 31 (-3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm31_1_0_13.realContains tr11_contains) (-177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -47107093611960180813434351891, hi := 47107093611960180813434351891} +lemma t12_contains : t12.Contains (sourcePower true 31 (-3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 12 coarse_31_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14394500857769538111847053988, hi := 14394500857769538111847053988} +lemma t13_contains : t13.Contains (sourcePower true 31 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 13 coarse_31_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4149401348216842768569389712, hi := 4149401348216842768569389712} +lemma t14_contains : t14.Contains (sourcePower true 31 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 14 coarse_31_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1132294633232049409874126003, hi := 1132294633232049409874126003} +lemma t15_contains : t15.Contains (sourcePower true 31 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 15 coarse_31_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -293450195471052557636680464, hi := 293450195471052557636680464} +lemma t16_contains : t16.Contains (sourcePower true 31 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 16 coarse_31_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -72454964935198155024841805, hi := 72454964935198155024841805} +lemma t17_contains : t17.Contains (sourcePower true 31 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 17 coarse_31_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -17095846718408106363802409, hi := 17095846718408106363802409} +lemma t18_contains : t18.Contains (sourcePower true 31 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 18 coarse_31_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3866616230427148851881964, hi := 3866616230427148851881964} +lemma t19_contains : t19.Contains (sourcePower true 31 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 19 coarse_31_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -840894980352613288021724, hi := 840894980352613288021724} +lemma t20_contains : t20.Contains (sourcePower true 31 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 20 coarse_31_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -176406939336102112504016, hi := 176406939336102112504016} +lemma t21_contains : t21.Contains (sourcePower true 31 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 21 coarse_31_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -35817451325097945676707, hi := 35817451325097945676707} +lemma t22_contains : t22.Contains (sourcePower true 31 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 22 coarse_31_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -7062578106899883956562, hi := 7062578106899883956562} +lemma t23_contains : t23.Contains (sourcePower true 31 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 23 coarse_31_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1357132773949141042559, hi := 1357132773949141042559} +lemma t24_contains : t24.Contains (sourcePower true 31 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 24 coarse_31_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -254999894008141724024, hi := 254999894008141724024} +lemma t25_contains : t25.Contains (sourcePower true 31 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 25 coarse_31_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -46998109251959411980, hi := 46998109251959411980} +lemma t26_contains : t26.Contains (sourcePower true 31 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 26 coarse_31_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -8519604618663829526, hi := 8519604618663829526} +lemma t27_contains : t27.Contains (sourcePower true 31 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 27 coarse_31_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1522173117322706802, hi := 1522173117322706802} +lemma t28_contains : t28.Contains (sourcePower true 31 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 31 (-3/2) 2 28 coarse_31_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 31 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -134671973237440369753504968627, hi := -111131203668425585128689678836} +lemma t6_checked : ((hm33_0_0_8.realAnswer).add tr6).scale (-729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 33 (3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_8.realContains tr6_contains) (-729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -472929364761718766176575957, hi := 472929364761718766176575957} +lemma tr7_contains : tr7.Contains (fullMoment true true 33 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 33 mixed_33_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -17063905251812994917836487104, hi := -903022115339153669948582961} +lemma t7_checked : ((hm33_0_0_9.realAnswer).add tr7).scale (-2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 33 (3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_9.realContains tr7_contains) (-2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -194962356813489477136288679, hi := 194962356813489477136288679} +lemma tr8_contains : tr8.Contains (fullMoment true true 33 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 33 mixed_33_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 22469995638882034345608793806, hi := 32463339568988482202955725742} +lemma t8_checked : ((hm33_0_0_10.realAnswer).add tr8).scale (-6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 33 (3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_10.realContains tr8_contains) (-6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -73118819746921046531747332, hi := 73118819746921046531747332} +lemma tr9_contains : tr9.Contains (fullMoment true true 33 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 33 mixed_33_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -1640634051058389708043328694, hi := 3981232078155894678345955158} +lemma t9_checked : ((hm33_0_0_11.realAnswer).add tr9).scale (-19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 33 (3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_11.realContains tr9_contains) (-19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -25153474459011621003745446, hi := 25153474459011621003745446} +lemma tr10_contains : tr10.Contains (fullMoment true true 33 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 33 mixed_33_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -5746812960521941347213489100, hi := -2845860786048692798555899705} +lemma t10_checked : ((hm33_0_0_12.realAnswer).add tr10).scale (-59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 33 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_12.realContains tr10_contains) (-59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -7991902354459712621332914, hi := 7991902354459712621332914} +lemma tr11_contains : tr11.Contains (fullMoment true true 33 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 33 mixed_33_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -795651522963982569108555018, hi := 586908561396900974677950332} +lemma t11_checked : ((hm33_0_0_13.realAnswer).add tr11).scale (-177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 33 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_13.realContains tr11_contains) (-177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -46939733625600342871073523762, hi := 46939733625600342871073523762} +lemma t12_contains : t12.Contains (sourcePower false 33 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 12 coarse_33_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14325273944965435803399662012, hi := 14325273944965435803399662012} +lemma t13_contains : t13.Contains (sourcePower false 33 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 13 coarse_33_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4122547382498648728361320336, hi := 4122547382498648728361320336} +lemma t14_contains : t14.Contains (sourcePower false 33 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 14 coarse_33_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1122487668878055295737428716, hi := 1122487668878055295737428716} +lemma t15_contains : t15.Contains (sourcePower false 33 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 15 coarse_33_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -290066870738915377148187494, hi := 290066870738915377148187494} +lemma t16_contains : t16.Contains (sourcePower false 33 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 16 coarse_33_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -71348940079428091398830425, hi := 71348940079428091398830425} +lemma t17_contains : t17.Contains (sourcePower false 33 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 17 coarse_33_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -16752295692802850447624612, hi := 16752295692802850447624612} +lemma t18_contains : t18.Contains (sourcePower false 33 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 18 coarse_33_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3764968040736910512304789, hi := 3764968040736910512304789} +lemma t19_contains : t19.Contains (sourcePower false 33 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 19 coarse_33_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -812182741993809472235986, hi := 812182741993809472235986} +lemma t20_contains : t20.Contains (sourcePower false 33 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 20 coarse_33_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -168648330431872783378767, hi := 168648330431872783378767} +lemma t21_contains : t21.Contains (sourcePower false 33 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 21 coarse_33_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -33808057854417327530838, hi := 33808057854417327530838} +lemma t22_contains : t22.Contains (sourcePower false 33 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 22 coarse_33_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -6562935926769463852608, hi := 6562935926769463852608} +lemma t23_contains : t23.Contains (sourcePower false 33 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 23 coarse_33_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1237663451307691708881, hi := 1237663451307691708881} +lemma t24_contains : t24.Contains (sourcePower false 33 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 24 coarse_33_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -227489596311237854163, hi := 227489596311237854163} +lemma t25_contains : t25.Contains (sourcePower false 33 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 25 coarse_33_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -40889139706780378980, hi := 40889139706780378980} +lemma t26_contains : t26.Contains (sourcePower false 33 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 26 coarse_33_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -7209743405788544081, hi := 7209743405788544081} +lemma t27_contains : t27.Contains (sourcePower false 33 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 27 coarse_33_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1250666140180536284, hi := 1250666140180536284} +lemma t28_contains : t28.Contains (sourcePower false 33 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (3/2) 2 28 coarse_33_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 33 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -140006500497126807885815012512, hi := -116465730928115463084778248546} +lemma t6_checked : ((hm33_1_0_8.realAnswer).add tr6).scale (729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 33 (3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_8.realContains tr6_contains) (729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -472929364761718766176575957, hi := 472929364761718766176575957} +lemma tr7_contains : tr7.Contains (fullMoment false true 33 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 33 mixed_33_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -18417328550782952408091838523, hi := -2256445414310481566409059616} +lemma t7_checked : ((hm33_1_0_9.realAnswer).add tr7).scale (2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 33 (3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_9.realContains tr7_contains) (2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -194962356813489477136288679, hi := 194962356813489477136288679} +lemma tr8_contains : tr8.Contains (fullMoment false true 33 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 33 mixed_33_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 23678355810949965020139617069, hi := 33671699741055920388257081044} +lemma t8_checked : ((hm33_1_0_10.realAnswer).add tr8).scale (6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 33 (3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_10.realContains tr8_contains) (6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -73118819746921046531747332, hi := 73118819746921046531747332} +lemma tr9_contains : tr9.Contains (fullMoment false true 33 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 33 mixed_33_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -1376352370323839032551494007, hi := 4245513758890284091970065007} +lemma t9_checked : ((hm33_1_0_11.realAnswer).add tr9).scale (19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 33 (3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_11.realContains tr9_contains) (19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -25153474459011621003745446, hi := 25153474459011621003745446} +lemma tr10_contains : tr10.Contains (fullMoment false true 33 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 33 mixed_33_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -5939388614488620029288148716, hi := -3038436440015419993243968702} +lemma t10_checked : ((hm33_1_0_12.realAnswer).add tr10).scale (59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 33 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_12.realContains tr10_contains) (59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -7991902354459712621332914, hi := 7991902354459712621332914} +lemma tr11_contains : tr11.Contains (fullMoment false true 33 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 33 mixed_33_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -833374057530900407152623719, hi := 549186026829969634717089547} +lemma t11_checked : ((hm33_1_0_13.realAnswer).add tr11).scale (177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 33 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_13.realContains tr11_contains) (177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -46939733625600342871073523762, hi := 46939733625600342871073523762} +lemma t12_contains : t12.Contains (sourcePower true 33 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 12 coarse_33_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14325273944965435803399662012, hi := 14325273944965435803399662012} +lemma t13_contains : t13.Contains (sourcePower true 33 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 13 coarse_33_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4122547382498648728361320336, hi := 4122547382498648728361320336} +lemma t14_contains : t14.Contains (sourcePower true 33 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 14 coarse_33_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1122487668878055295737428716, hi := 1122487668878055295737428716} +lemma t15_contains : t15.Contains (sourcePower true 33 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 15 coarse_33_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -290066870738915377148187494, hi := 290066870738915377148187494} +lemma t16_contains : t16.Contains (sourcePower true 33 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 16 coarse_33_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -71348940079428091398830425, hi := 71348940079428091398830425} +lemma t17_contains : t17.Contains (sourcePower true 33 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 17 coarse_33_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -16752295692802850447624612, hi := 16752295692802850447624612} +lemma t18_contains : t18.Contains (sourcePower true 33 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 18 coarse_33_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3764968040736910512304789, hi := 3764968040736910512304789} +lemma t19_contains : t19.Contains (sourcePower true 33 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 19 coarse_33_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -812182741993809472235986, hi := 812182741993809472235986} +lemma t20_contains : t20.Contains (sourcePower true 33 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 20 coarse_33_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -168648330431872783378767, hi := 168648330431872783378767} +lemma t21_contains : t21.Contains (sourcePower true 33 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 21 coarse_33_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -33808057854417327530838, hi := 33808057854417327530838} +lemma t22_contains : t22.Contains (sourcePower true 33 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 22 coarse_33_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -6562935926769463852608, hi := 6562935926769463852608} +lemma t23_contains : t23.Contains (sourcePower true 33 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 23 coarse_33_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1237663451307691708881, hi := 1237663451307691708881} +lemma t24_contains : t24.Contains (sourcePower true 33 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 24 coarse_33_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -227489596311237854163, hi := 227489596311237854163} +lemma t25_contains : t25.Contains (sourcePower true 33 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 25 coarse_33_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -40889139706780378980, hi := 40889139706780378980} +lemma t26_contains : t26.Contains (sourcePower true 33 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 26 coarse_33_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -7209743405788544081, hi := 7209743405788544081} +lemma t27_contains : t27.Contains (sourcePower true 33 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 27 coarse_33_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1250666140180536284, hi := 1250666140180536284} +lemma t28_contains : t28.Contains (sourcePower true 33 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (3/2) 2 28 coarse_33_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 33 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -11823053891901486507852288055, hi := -9756374533304852466716240666} +lemma t6_checked : ((hm33_0_0_8.realAnswer).add tr6).scale (-1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 33 (-1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_8.realContains tr6_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -472929364761718766176575957, hi := 472929364761718766176575957} +lemma tr7_contains : tr7.Contains (fullMoment true true 33 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 33 mixed_33_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 52851774468866790010708102, hi := 998710503992713008451335322} +lemma t7_checked : ((hm33_0_0_9.realAnswer).add tr7).scale (1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 33 (-1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_9.realContains tr7_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -194962356813489477136288679, hi := 194962356813489477136288679} +lemma tr8_contains : tr8.Contains (fullMoment true true 33 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 33 mixed_33_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 876744228555677608973609391, hi := 1266668942182754373412081358} +lemma t8_checked : ((hm33_0_0_10.realAnswer).add tr8).scale (-1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 33 (-1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_10.realContains tr8_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -73118819746921046531747332, hi := 73118819746921046531747332} +lemma tr9_contains : tr9.Contains (fullMoment true true 33 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 33 mixed_33_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -103560982777819340309563026, hi := 42676656716044075116505832} +lemma t9_checked : ((hm33_0_0_11.realAnswer).add tr9).scale (1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 33 (-1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_11.realContains tr9_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -25153474459011621003745446, hi := 25153474459011621003745446} +lemma tr10_contains : tr10.Contains (fullMoment true true 33 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 33 mixed_33_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -99658528875585834468773609, hi := -49351579957558323184494933} +lemma t10_checked : ((hm33_0_0_12.realAnswer).add tr10).scale (-1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 33 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_12.realContains tr10_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -7991902354459712621332914, hi := 7991902354459712621332914} +lemma tr11_contains : tr11.Contains (fullMoment true true 33 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 33 mixed_33_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -6785261583548426990806744, hi := 9198543125371788974887075} +lemma t11_checked : ((hm33_0_0_13.realAnswer).add tr11).scale (1) 1=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 33 (-1/1) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm33_0_0_13.realContains tr11_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -361780797737583295981900443, hi := 361780797737583295981900443} +lemma t12_contains : t12.Contains (sourcePower false 33 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 12 coarse_33_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73606567901960173754910411, hi := 73606567901960173754910411} +lemma t13_contains : t13.Contains (sourcePower false 33 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 13 coarse_33_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14121734076649432761423265, hi := 14121734076649432761423265} +lemma t14_contains : t14.Contains (sourcePower false 33 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 14 coarse_33_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2563378237366519688971715, hi := 2563378237366519688971715} +lemma t15_contains : t15.Contains (sourcePower false 33 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 15 coarse_33_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -441609070310966499789464, hi := 441609070310966499789464} +lemma t16_contains : t16.Contains (sourcePower false 33 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 16 coarse_33_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -72416265063029220396969, hi := 72416265063029220396969} +lemma t17_contains : t17.Contains (sourcePower false 33 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 17 coarse_33_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11335264723425896113982, hi := 11335264723425896113982} +lemma t18_contains : t18.Contains (sourcePower false 33 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 18 coarse_33_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1698350689743612861834, hi := 1698350689743612861834} +lemma t19_contains : t19.Contains (sourcePower false 33 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 19 coarse_33_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -244246627530126076516, hi := 244246627530126076516} +lemma t20_contains : t20.Contains (sourcePower false 33 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 20 coarse_33_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -33811590927964850998, hi := 33811590927964850998} +lemma t21_contains : t21.Contains (sourcePower false 33 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 21 coarse_33_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4518689746548450098, hi := 4518689746548450098} +lemma t22_contains : t22.Contains (sourcePower false 33 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 22 coarse_33_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -584789015037979950, hi := 584789015037979950} +lemma t23_contains : t23.Contains (sourcePower false 33 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 23 coarse_33_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -73521159708065903, hi := 73521159708065903} +lemma t24_contains : t24.Contains (sourcePower false 33 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 24 coarse_33_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -9009072121423814, hi := 9009072121423814} +lemma t25_contains : t25.Contains (sourcePower false 33 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 25 coarse_33_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1079531297473408, hi := 1079531297473408} +lemma t26_contains : t26.Contains (sourcePower false 33 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 26 coarse_33_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -126898302892730, hi := 126898302892730} +lemma t27_contains : t27.Contains (sourcePower false 33 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 27 coarse_33_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -14675271295313, hi := 14675271295313} +lemma t28_contains : t28.Contains (sourcePower false 33 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 33 (-1/1) 2 28 coarse_33_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 33 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -12291380016208663518096242525, hi := -10224700657612331464232932657} +lemma t6_checked : ((hm33_1_0_8.realAnswer).add tr6).scale (1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 33 (-1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_8.realContains tr6_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -472929364761718766176575957, hi := 472929364761718766176575957} +lemma tr7_contains : tr7.Contains (fullMoment false true 33 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 33 mixed_33_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 132064477838016296525084422, hi := 1077923207361782308292526443} +lemma t7_checked : ((hm33_1_0_9.realAnswer).add tr7).scale (-1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 33 (-1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_9.realContains tr7_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -194962356813489477136288679, hi := 194962356813489477136288679} +lemma tr8_contains : tr8.Contains (fullMoment false true 33 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 33 mixed_33_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 923892560219965103666474923, hi := 1313817273847022651942358291} +lemma t8_checked : ((hm33_1_0_10.realAnswer).add tr8).scale (1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 33 (-1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_10.realContains tr8_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -73118819746921046531747332, hi := 73118819746921046531747332} +lemma tr9_contains : tr9.Contains (fullMoment false true 33 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 33 mixed_33_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -110435555786812246867280053, hi := 35802083707046973767533655} +lemma t9_checked : ((hm33_1_0_11.realAnswer).add tr9).scale (-1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 33 (-1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_11.realContains tr9_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -25153474459011621003745446, hi := 25153474459011621003745446} +lemma tr10_contains : tr10.Contains (fullMoment false true 33 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 33 mixed_33_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -102998085339910022354164580, hi := -52691136421883352352822638} +lemma t10_checked : ((hm33_1_0_12.realAnswer).add tr10).scale (1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 33 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_12.realContains tr10_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -7991902354459712621332914, hi := 7991902354459712621332914} +lemma tr11_contains : tr11.Contains (fullMoment false true 33 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 33 mixed_33_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -6349150609086113859679246, hi := 9634654099833946010085259} +lemma t11_checked : ((hm33_1_0_13.realAnswer).add tr11).scale (-1) 1=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 33 (-1/1) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm33_1_0_13.realContains tr11_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -361780797737583295981900443, hi := 361780797737583295981900443} +lemma t12_contains : t12.Contains (sourcePower true 33 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 12 coarse_33_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73606567901960173754910411, hi := 73606567901960173754910411} +lemma t13_contains : t13.Contains (sourcePower true 33 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 13 coarse_33_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14121734076649432761423265, hi := 14121734076649432761423265} +lemma t14_contains : t14.Contains (sourcePower true 33 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 14 coarse_33_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2563378237366519688971715, hi := 2563378237366519688971715} +lemma t15_contains : t15.Contains (sourcePower true 33 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 15 coarse_33_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -441609070310966499789464, hi := 441609070310966499789464} +lemma t16_contains : t16.Contains (sourcePower true 33 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 16 coarse_33_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -72416265063029220396969, hi := 72416265063029220396969} +lemma t17_contains : t17.Contains (sourcePower true 33 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 17 coarse_33_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11335264723425896113982, hi := 11335264723425896113982} +lemma t18_contains : t18.Contains (sourcePower true 33 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 18 coarse_33_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1698350689743612861834, hi := 1698350689743612861834} +lemma t19_contains : t19.Contains (sourcePower true 33 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 19 coarse_33_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -244246627530126076516, hi := 244246627530126076516} +lemma t20_contains : t20.Contains (sourcePower true 33 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 20 coarse_33_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -33811590927964850998, hi := 33811590927964850998} +lemma t21_contains : t21.Contains (sourcePower true 33 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 21 coarse_33_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4518689746548450098, hi := 4518689746548450098} +lemma t22_contains : t22.Contains (sourcePower true 33 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 22 coarse_33_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -584789015037979950, hi := 584789015037979950} +lemma t23_contains : t23.Contains (sourcePower true 33 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 23 coarse_33_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -73521159708065903, hi := 73521159708065903} +lemma t24_contains : t24.Contains (sourcePower true 33 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 24 coarse_33_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -9009072121423814, hi := 9009072121423814} +lemma t25_contains : t25.Contains (sourcePower true 33 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 25 coarse_33_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1079531297473408, hi := 1079531297473408} +lemma t26_contains : t26.Contains (sourcePower true 33 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 26 coarse_33_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -126898302892730, hi := 126898302892730} +lemma t27_contains : t27.Contains (sourcePower true 33 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 27 coarse_33_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -14675271295313, hi := 14675271295313} +lemma t28_contains : t28.Contains (sourcePower true 33 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 33 (-1/1) 2 28 coarse_33_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 33 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -1690572071041722764824134520, hi := -1465901236378428577093212980} +lemma t4_checked : ((hm36_0_0_6.realAnswer).add tr4).scale (-1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 36 (1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_6.realContains tr4_contains) (-1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -1054748594041481953701852891, hi := 1054748594041481953701852891} +lemma tr5_contains : tr5.Contains (fullMoment true true 36 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 36 mixed_36_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -288345560368785275787074630, hi := -222423773241020638464269611} +lemma t5_checked : ((hm36_0_0_7.realAnswer).add tr5).scale (-1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 36 (1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_7.realContains tr5_contains) (-1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -542205561747256519505331368, hi := 542205561747256519505331368} +lemma tr6_contains : tr6.Contains (fullMoment true true 36 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 36 mixed_36_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 78505306548487620666794207, hi := 95449230353115021161421130} +lemma t6_checked : ((hm36_0_0_8.realAnswer).add tr6).scale (-1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 36 (1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_8.realContains tr6_contains) (-1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -248007659112966961373842623, hi := 248007659112966961373842623} +lemma tr7_contains : tr7.Contains (fullMoment true true 36 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 36 mixed_36_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 4325629047989256110644267, hi := 8200748721632768003775457} +lemma t7_checked : ((hm36_0_0_9.realAnswer).add tr7).scale (-1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 36 (1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_9.realContains tr7_contains) (-1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -102187287443684063655955502, hi := 102187287443684063655955502} +lemma tr8_contains : tr8.Contains (fullMoment true true 36 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 36 mixed_36_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -3063469735856202019372389, hi := -2265131552702012794156543} +lemma t8_checked : ((hm36_0_0_10.realAnswer).add tr8).scale (-1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 36 (1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_10.realContains tr8_contains) (-1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -38307059161154352730149430, hi := 38307059161154352730149430} +lemma tr9_contains : tr9.Contains (fullMoment true true 36 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 36 mixed_36_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -172742991348237789749619, hi := -23106041499934151029172} +lemma t9_checked : ((hm36_0_0_11.realAnswer).add tr9).scale (-1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 36 (1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_11.realContains tr9_contains) (-1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -13172692487444001619504985, hi := 13172692487444001619504985} +lemma tr10_contains : tr10.Contains (fullMoment true true 36 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 36 mixed_36_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 40235275232920764615564, hi := 65963190247464284204049} +lemma t10_checked : ((hm36_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 36 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -4183834238406027061996438, hi := 4183834238406027061996438} +lemma tr11_contains : tr11.Contains (fullMoment true true 36 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 36 mixed_36_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -990636605535078486950, hi := 3095139017908720217424} +lemma t11_checked : ((hm36_0_0_13.realAnswer).add tr11).scale (-1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 36 (1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_13.realContains tr11_contains) (-1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -88050869421777572522194, hi := 88050869421777572522194} +lemma t12_contains : t12.Contains (sourcePower false 36 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 12 coarse_36_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8947333922685233817253, hi := 8947333922685233817253} +lemma t13_contains : t13.Contains (sourcePower false 36 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 13 coarse_36_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -857029939340576458208, hi := 857029939340576458208} +lemma t14_contains : t14.Contains (sourcePower false 36 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 14 coarse_36_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77632643843105102825, hi := 77632643843105102825} +lemma t15_contains : t15.Contains (sourcePower false 36 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 15 coarse_36_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6669954225551631815, hi := 6669954225551631815} +lemma t16_contains : t16.Contains (sourcePower false 36 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 16 coarse_36_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -545032650142071095, hi := 545032650142071095} +lemma t17_contains : t17.Contains (sourcePower false 36 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 17 coarse_36_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -42468327468036483, hi := 42468327468036483} +lemma t18_contains : t18.Contains (sourcePower false 36 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 18 coarse_36_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3163188611309559, hi := 3163188611309559} +lemma t19_contains : t19.Contains (sourcePower false 36 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 19 coarse_36_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -225761628138761, hi := 225761628138761} +lemma t20_contains : t20.Contains (sourcePower false 36 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 20 coarse_36_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15476837523320, hi := 15476837523320} +lemma t21_contains : t21.Contains (sourcePower false 36 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 21 coarse_36_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1021592911047, hi := 1021592911047} +lemma t22_contains : t22.Contains (sourcePower false 36 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 22 coarse_36_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -65092026637, hi := 65092026637} +lemma t23_contains : t23.Contains (sourcePower false 36 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 23 coarse_36_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -4013972563, hi := 4013972563} +lemma t24_contains : t24.Contains (sourcePower false 36 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 24 coarse_36_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -240228394, hi := 240228394} +lemma t25_contains : t25.Contains (sourcePower false 36 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 25 coarse_36_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -13994330, hi := 13994330} +lemma t26_contains : t26.Contains (sourcePower false 36 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 26 coarse_36_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -795957, hi := 795957} +lemma t27_contains : t27.Contains (sourcePower false 36 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 27 coarse_36_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -44340, hi := 44340} +lemma t28_contains : t28.Contains (sourcePower false 36 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (1/2) 2 28 coarse_36_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 36 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -1772573321117334816270061366, hi := -1547902486454265894915494309} +lemma t4_checked : ((hm36_1_0_6.realAnswer).add tr4).scale (1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 36 (1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_6.realContains tr4_contains) (1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -1054748594041481953701852891, hi := 1054748594041481953701852891} +lemma tr5_contains : tr5.Contains (fullMoment false true 36 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 36 mixed_36_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -307290205088959007857801753, hi := -241368417961232647976646243} +lemma t5_checked : ((hm36_1_0_7.realAnswer).add tr5).scale (1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 36 (1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_7.realContains tr5_contains) (1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -542205561747256519505331368, hi := 542205561747256519505331368} +lemma tr6_contains : tr6.Contains (fullMoment false true 36 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 36 mixed_36_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 83193150443962139632666557, hi := 100137074248583831225195686} +lemma t6_checked : ((hm36_1_0_8.realAnswer).add tr6).scale (1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 36 (1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_8.realContains tr6_contains) (1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -248007659112966961373842623, hi := 248007659112966961373842623} +lemma tr7_contains : tr7.Contains (fullMoment false true 36 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 36 mixed_36_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 4902354393540312354597746, hi := 8777474067183065274325582} +lemma t7_checked : ((hm36_1_0_9.realAnswer).add tr7).scale (1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 36 (1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_9.realContains tr7_contains) (1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -102187287443684063655955502, hi := 102187287443684063655955502} +lemma tr8_contains : tr8.Contains (fullMoment false true 36 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 36 mixed_36_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -3211433092753347532357987, hi := -2413094909599249362638948} +lemma t8_checked : ((hm36_1_0_10.realAnswer).add tr8).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 36 (1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_10.realContains tr8_contains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -38307059161154352730149430, hi := 38307059161154352730149430} +lemma tr9_contains : tr9.Contains (fullMoment false true 36 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 36 mixed_36_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -184774507636044784902388, hi := -35137557787751103377189} +lemma t9_checked : ((hm36_1_0_11.realAnswer).add tr9).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 36 (1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_11.realContains tr9_contains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -13172692487444001619504985, hi := 13172692487444001619504985} +lemma tr10_contains : tr10.Contains (fullMoment false true 36 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 36 mixed_36_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 43265304187579719615676, hi := 68993219202122238472647} +lemma t10_checked : ((hm36_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 36 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -4183834238406027061996438, hi := 4183834238406027061996438} +lemma tr11_contains : tr11.Contains (fullMoment false true 36 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 36 mixed_36_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -805051455784256284190, hi := 3280724167659449335755} +lemma t11_checked : ((hm36_1_0_13.realAnswer).add tr11).scale (1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 36 (1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_13.realContains tr11_contains) (1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -88050869421777572522194, hi := 88050869421777572522194} +lemma t12_contains : t12.Contains (sourcePower true 36 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 12 coarse_36_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8947333922685233817253, hi := 8947333922685233817253} +lemma t13_contains : t13.Contains (sourcePower true 36 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 13 coarse_36_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -857029939340576458208, hi := 857029939340576458208} +lemma t14_contains : t14.Contains (sourcePower true 36 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 14 coarse_36_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77632643843105102825, hi := 77632643843105102825} +lemma t15_contains : t15.Contains (sourcePower true 36 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 15 coarse_36_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6669954225551631815, hi := 6669954225551631815} +lemma t16_contains : t16.Contains (sourcePower true 36 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 16 coarse_36_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -545032650142071095, hi := 545032650142071095} +lemma t17_contains : t17.Contains (sourcePower true 36 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 17 coarse_36_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -42468327468036483, hi := 42468327468036483} +lemma t18_contains : t18.Contains (sourcePower true 36 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 18 coarse_36_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3163188611309559, hi := 3163188611309559} +lemma t19_contains : t19.Contains (sourcePower true 36 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 19 coarse_36_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -225761628138761, hi := 225761628138761} +lemma t20_contains : t20.Contains (sourcePower true 36 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 20 coarse_36_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15476837523320, hi := 15476837523320} +lemma t21_contains : t21.Contains (sourcePower true 36 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 21 coarse_36_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1021592911047, hi := 1021592911047} +lemma t22_contains : t22.Contains (sourcePower true 36 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 22 coarse_36_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -65092026637, hi := 65092026637} +lemma t23_contains : t23.Contains (sourcePower true 36 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 23 coarse_36_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -4013972563, hi := 4013972563} +lemma t24_contains : t24.Contains (sourcePower true 36 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 24 coarse_36_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -240228394, hi := 240228394} +lemma t25_contains : t25.Contains (sourcePower true 36 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 25 coarse_36_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -13994330, hi := 13994330} +lemma t26_contains : t26.Contains (sourcePower true 36 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 26 coarse_36_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -795957, hi := 795957} +lemma t27_contains : t27.Contains (sourcePower true 36 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 27 coarse_36_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -44340, hi := 44340} +lemma t28_contains : t28.Contains (sourcePower true 36 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (1/2) 2 28 coarse_36_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 36 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -136936337754379543950754896095, hi := -118738000146652714744550251425} +lemma t4_checked : ((hm36_0_0_6.realAnswer).add tr4).scale (-81) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 36 (-3/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_6.realContains tr4_contains) (-81) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -1054748594041481953701852891, hi := 1054748594041481953701852891} +lemma tr5_contains : tr5.Contains (fullMoment true true 36 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 36 mixed_36_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 54048976897568015146817515662, hi := 70067971169614822016259135007} +lemma t5_checked : ((hm36_0_0_7.realAnswer).add tr5).scale (243) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 36 (-3/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_7.realContains tr5_contains) (243) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -542205561747256519505331368, hi := 542205561747256519505331368} +lemma tr6_contains : tr6.Contains (fullMoment true true 36 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 36 mixed_36_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 57230368473847475466092977483, hi := 69582488927420850426676003087} +lemma t6_checked : ((hm36_0_0_8.realAnswer).add tr6).scale (-729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 36 (-3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_8.realContains tr6_contains) (-729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -248007659112966961373842623, hi := 248007659112966961373842623} +lemma tr7_contains : tr7.Contains (fullMoment true true 36 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 36 mixed_36_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -17935037454210863624256922768, hi := -9460150727952503113979012766} +lemma t7_checked : ((hm36_0_0_9.realAnswer).add tr7).scale (2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 36 (-3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_9.realContains tr7_contains) (2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -102187287443684063655955502, hi := 102187287443684063655955502} +lemma tr8_contains : tr8.Contains (fullMoment true true 36 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 36 mixed_36_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -20099424936952541449102238719, hi := -14861528117277905942461085107} +lemma t8_checked : ((hm36_0_0_10.realAnswer).add tr8).scale (-6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 36 (-3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_10.realContains tr8_contains) (-6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -38307059161154352730149430, hi := 38307059161154352730149430} +lemma tr9_contains : tr9.Contains (fullMoment true true 36 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 36 mixed_36_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := 454796214843203894707208968, hi := 3400100298707364415641750239} +lemma t9_checked : ((hm36_0_0_11.realAnswer).add tr9).scale (19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 36 (-3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_11.realContains tr9_contains) (19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -13172692487444001619504985, hi := 13172692487444001619504985} +lemma tr10_contains : tr10.Contains (fullMoment true true 36 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 36 mixed_36_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 2375852767228738229784497166, hi := 3895060420922518517964871756} +lemma t10_checked : ((hm36_0_0_12.realAnswer).add tr10).scale (-59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 36 (-3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_12.realContains tr10_contains) (-59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -4183834238406027061996438, hi := 4183834238406027061996438} +lemma tr11_contains : tr11.Contains (fullMoment true true 36 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 36 mixed_36_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -548294591605476060355929664, hi := 175488302760722548727584951} +lemma t11_checked : ((hm36_0_0_13.realAnswer).add tr11).scale (177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 36 (-3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm36_0_0_13.realContains tr11_contains) (177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -46793842096378894918766913353, hi := 46793842096378894918766913353} +lemma t12_contains : t12.Contains (sourcePower false 36 (-3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 12 coarse_36_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14264940261617290035222848399, hi := 14264940261617290035222848399} +lemma t13_contains : t13.Contains (sourcePower false 36 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 13 coarse_36_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4099147631937857641734979784, hi := 4099147631937857641734979784} +lemma t14_contains : t14.Contains (sourcePower false 36 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 14 coarse_36_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1113943586668837711657210604, hi := 1113943586668837711657210604} +lemma t15_contains : t15.Contains (sourcePower false 36 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 15 coarse_36_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -287119658630092165815552628, hi := 287119658630092165815552628} +lemma t16_contains : t16.Contains (sourcePower false 36 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 16 coarse_36_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -70385605279669034351869203, hi := 70385605279669034351869203} +lemma t17_contains : t17.Contains (sourcePower false 36 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 17 coarse_36_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -16453100194678825906419940, hi := 16453100194678825906419940} +lemma t18_contains : t18.Contains (sourcePower false 36 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 18 coarse_36_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3676452235778340063267296, hi := 3676452235778340063267296} +lemma t19_contains : t19.Contains (sourcePower false 36 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 19 coarse_36_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -787182123338594070900422, hi := 787182123338594070900422} +lemma t20_contains : t20.Contains (sourcePower false 36 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 20 coarse_36_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -161893186959370361506375, hi := 161893186959370361506375} +lemma t21_contains : t21.Contains (sourcePower false 36 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 21 coarse_36_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -32058668037672876068172, hi := 32058668037672876068172} +lemma t22_contains : t22.Contains (sourcePower false 36 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 22 coarse_36_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -6127970303894711358004, hi := 6127970303894711358004} +lemma t23_contains : t23.Contains (sourcePower false 36 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 23 coarse_36_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1133664410226523058330, hi := 1133664410226523058330} +lemma t24_contains : t24.Contains (sourcePower false 36 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 24 coarse_36_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -203542781882395719468, hi := 203542781882395719468} +lemma t25_contains : t25.Contains (sourcePower false 36 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 25 coarse_36_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -35571707206776473197, hi := 35571707206776473197} +lemma t26_contains : t26.Contains (sourcePower false 36 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 26 coarse_36_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -6069644414832718076, hi := 6069644414832718076} +lemma t27_contains : t27.Contains (sourcePower false 36 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 27 coarse_36_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1014355712285277065, hi := 1014355712285277065} +lemma t28_contains : t28.Contains (sourcePower false 36 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 36 (-3/2) 2 28 coarse_36_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 36 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -143578439010504120117874970606, hi := -125380101402795537488155039079} +lemma t4_checked : ((hm36_1_0_6.realAnswer).add tr4).scale (81) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 36 (-3/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_6.realContains tr4_contains) (81) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -1054748594041481953701852891, hi := 1054748594041481953701852891} +lemma tr5_contains : tr5.Contains (fullMoment false true 36 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 36 mixed_36_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 58652525564579533458325037124, hi := 74671519836617038909445825812} +lemma t5_checked : ((hm36_1_0_7.realAnswer).add tr5).scale (-243) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 36 (-3/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_7.realContains tr5_contains) (-243) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -542205561747256519505331368, hi := 542205561747256519505331368} +lemma tr6_contains : tr6.Contains (fullMoment false true 36 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 36 mixed_36_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 60647806673648399792213920702, hi := 72999927127217612963167654878} +lemma t6_checked : ((hm36_1_0_8.realAnswer).add tr6).scale (729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 36 (-3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_8.realContains tr6_contains) (729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -248007659112966961373842623, hi := 248007659112966961373842623} +lemma tr7_contains : tr7.Contains (fullMoment false true 36 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 36 mixed_36_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -19196335784929363754950046468, hi := -10721449058672663119505272620} +lemma t7_checked : ((hm36_1_0_9.realAnswer).add tr7).scale (-2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 36 (-3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_9.realContains tr7_contains) (-2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -102187287443684063655955502, hi := 102187287443684063655955502} +lemma tr8_contains : tr8.Contains (fullMoment false true 36 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 36 mixed_36_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -21070212521554713159800750401, hi := -15832315701880675068274141902} +lemma t8_checked : ((hm36_1_0_10.realAnswer).add tr8).scale (6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 36 (-3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_10.realContains tr8_contains) (6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -38307059161154352730149430, hi := 38307059161154352730149430} +lemma tr9_contains : tr9.Contains (fullMoment false true 36 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 36 mixed_36_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := 691612549936304967773212317, hi := 3636916633800269501233699314} +lemma t9_checked : ((hm36_1_0_11.realAnswer).add tr9).scale (-19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 36 (-3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_11.realContains tr9_contains) (-19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -13172692487444001619504985, hi := 13172692487444001619504985} +lemma tr10_contains : tr10.Contains (fullMoment false true 36 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 36 mixed_36_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 2554772946972394863586059966, hi := 4073980600666116059571302718} +lemma t10_checked : ((hm36_1_0_12.realAnswer).add tr10).scale (59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 36 (-3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_12.realContains tr10_contains) (59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -4183834238406027061996438, hi := 4183834238406027061996438} +lemma tr11_contains : tr11.Contains (fullMoment false true 36 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 36 mixed_36_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -581170444128368471480832089, hi := 142612450237813647975334830} +lemma t11_checked : ((hm36_1_0_13.realAnswer).add tr11).scale (-177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 36 (-3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm36_1_0_13.realContains tr11_contains) (-177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -46793842096378894918766913353, hi := 46793842096378894918766913353} +lemma t12_contains : t12.Contains (sourcePower true 36 (-3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 12 coarse_36_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14264940261617290035222848399, hi := 14264940261617290035222848399} +lemma t13_contains : t13.Contains (sourcePower true 36 (-3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 13 coarse_36_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4099147631937857641734979784, hi := 4099147631937857641734979784} +lemma t14_contains : t14.Contains (sourcePower true 36 (-3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 14 coarse_36_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1113943586668837711657210604, hi := 1113943586668837711657210604} +lemma t15_contains : t15.Contains (sourcePower true 36 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 15 coarse_36_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -287119658630092165815552628, hi := 287119658630092165815552628} +lemma t16_contains : t16.Contains (sourcePower true 36 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 16 coarse_36_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -70385605279669034351869203, hi := 70385605279669034351869203} +lemma t17_contains : t17.Contains (sourcePower true 36 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 17 coarse_36_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -16453100194678825906419940, hi := 16453100194678825906419940} +lemma t18_contains : t18.Contains (sourcePower true 36 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 18 coarse_36_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3676452235778340063267296, hi := 3676452235778340063267296} +lemma t19_contains : t19.Contains (sourcePower true 36 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 19 coarse_36_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -787182123338594070900422, hi := 787182123338594070900422} +lemma t20_contains : t20.Contains (sourcePower true 36 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 20 coarse_36_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -161893186959370361506375, hi := 161893186959370361506375} +lemma t21_contains : t21.Contains (sourcePower true 36 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 21 coarse_36_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -32058668037672876068172, hi := 32058668037672876068172} +lemma t22_contains : t22.Contains (sourcePower true 36 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 22 coarse_36_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -6127970303894711358004, hi := 6127970303894711358004} +lemma t23_contains : t23.Contains (sourcePower true 36 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 23 coarse_36_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1133664410226523058330, hi := 1133664410226523058330} +lemma t24_contains : t24.Contains (sourcePower true 36 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 24 coarse_36_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -203542781882395719468, hi := 203542781882395719468} +lemma t25_contains : t25.Contains (sourcePower true 36 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 25 coarse_36_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -35571707206776473197, hi := 35571707206776473197} +lemma t26_contains : t26.Contains (sourcePower true 36 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 26 coarse_36_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -6069644414832718076, hi := 6069644414832718076} +lemma t27_contains : t27.Contains (sourcePower true 36 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 27 coarse_36_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1014355712285277065, hi := 1014355712285277065} +lemma t28_contains : t28.Contains (sourcePower true 36 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 36 (-3/2) 2 28 coarse_36_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 36 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 18269376187487400116945154208, hi := 21174751337580962213617333480} +lemma t4_checked : ((hm37_0_0_6.realAnswer).add tr4).scale (-1) 1=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 37 (1/1) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_6.realContains tr4_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -852272187863596681075941712, hi := 852272187863596681075941712} +lemma tr5_contains : tr5.Contains (fullMoment true true 37 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 37 mixed_37_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 3160462380914480501602014604, hi := 4865006756647388104406072324} +lemma t5_checked : ((hm37_0_0_7.realAnswer).add tr5).scale (-1) 1=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 37 (1/1) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_7.realContains tr5_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -438025165280374769114116401, hi := 438025165280374769114116401} +lemma tr6_contains : tr6.Contains (fullMoment true true 37 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 37 mixed_37_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -5047888374880759082932230164, hi := -4171838044318306212602573575} +lemma t6_checked : ((hm37_0_0_8.realAnswer).add tr6).scale (-1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 37 (1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_8.realContains tr6_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -200316477263320258439541379, hi := 200316477263320258439541379} +lemma tr7_contains : tr7.Contains (fullMoment true true 37 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 37 mixed_37_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -623444570877380431393531089, hi := -222811616350287557294804039} +lemma t7_checked : ((hm37_0_0_9.realAnswer).add tr7).scale (-1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 37 (1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_9.realContains tr7_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -82522924134594386764164681, hi := 82522924134594386764164681} +lemma tr8_contains : tr8.Contains (fullMoment true true 37 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 37 mixed_37_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 514646549230832851099033854, hi := 679692397500129984820338539} +lemma t8_checked : ((hm37_0_0_10.realAnswer).add tr8).scale (-1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 37 (1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_10.realContains tr8_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -30930815277007553323999573, hi := 30930815277007553323999573} +lemma tr9_contains : tr9.Contains (fullMoment true true 37 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 37 mixed_37_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -3884823574057179209898359, hi := 57976806979981576738875190} +lemma t9_checked : ((hm37_0_0_11.realAnswer).add tr9).scale (-1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 37 (1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_11.realContains tr9_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -10634808089414144644373220, hi := 10634808089414144644373220} +lemma tr10_contains : tr10.Contains (fullMoment true true 37 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 37 mixed_37_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -60196468222685075591888461, hi := -38926852043852044570406526} +lemma t10_checked : ((hm37_0_0_12.realAnswer).add tr10).scale (-1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 37 (1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_12.realContains tr10_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1666024019441666465554773939, hi := 1666024019441666465554773939} +lemma t11_contains : t11.Contains (sourcePower false 37 (1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 11 coarse_37_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -360418283188298954644165192, hi := 360418283188298954644165192} +lemma t12_contains : t12.Contains (sourcePower false 37 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 12 coarse_37_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73230933690684009964846178, hi := 73230933690684009964846178} +lemma t13_contains : t13.Contains (sourcePower false 37 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 13 coarse_37_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14024613211358169787693858, hi := 14024613211358169787693858} +lemma t14_contains : t14.Contains (sourcePower false 37 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 14 coarse_37_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2539737320118086768090961, hi := 2539737320118086768090961} +lemma t15_contains : t15.Contains (sourcePower false 37 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 15 coarse_37_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -436172697025750189852343, hi := 436172697025750189852343} +lemma t16_contains : t16.Contains (sourcePower false 37 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 16 coarse_37_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -71231655286935315009798, hi := 71231655286935315009798} +lemma t17_contains : t17.Contains (sourcePower false 37 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 17 coarse_37_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11089989111095300851251, hi := 11089989111095300851251} +lemma t18_contains : t18.Contains (sourcePower false 37 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 18 coarse_37_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1649975540272999228512, hi := 1649975540272999228512} +lemma t19_contains : t19.Contains (sourcePower false 37 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 19 coarse_37_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -235137951616111849218, hi := 235137951616111849218} +lemma t20_contains : t20.Contains (sourcePower false 37 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 20 coarse_37_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -32170839535591669585, hi := 32170839535591669585} +lemma t21_contains : t21.Contains (sourcePower false 37 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 21 coarse_37_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4235420694999396572, hi := 4235420694999396572} +lemma t22_contains : t22.Contains (sourcePower false 37 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 22 coarse_37_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -537835042776084524, hi := 537835042776084524} +lemma t23_contains : t23.Contains (sourcePower false 37 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 23 coarse_37_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -66036844332233099, hi := 66036844332233099} +lemma t24_contains : t24.Contains (sourcePower false 37 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 24 coarse_37_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -7860187966536990, hi := 7860187966536990} +lemma t25_contains : t25.Contains (sourcePower false 37 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 25 coarse_37_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -909457826982059, hi := 909457826982059} +lemma t26_contains : t26.Contains (sourcePower false 37 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 26 coarse_37_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -102588381853087, hi := 102588381853087} +lemma t27_contains : t27.Contains (sourcePower false 37 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 27 coarse_37_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -11316112539702, hi := 11316112539702} +lemma t28_contains : t28.Contains (sourcePower false 37 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (1/1) 2 28 coarse_37_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 37 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 19469678309732272350419470641, hi := 22375053459821840507272858523} +lemma t4_checked : ((hm37_1_0_6.realAnswer).add tr4).scale (1) 1=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 37 (1/1) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_6.realContains tr4_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -852272187863596681075941712, hi := 852272187863596681075941712} +lemma tr5_contains : tr5.Contains (fullMoment false true 37 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 37 mixed_37_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 3503854590694609336441173826, hi := 5208398966426159624884366566} +lemma t5_checked : ((hm37_1_0_7.realAnswer).add tr5).scale (1) 1=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 37 (1/1) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_7.realContains tr5_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -438025165280374769114116401, hi := 438025165280374769114116401} +lemma tr6_contains : tr6.Contains (fullMoment false true 37 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 37 mixed_37_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -5330675210627286263616923280, hi := -4454624880065238364984264351} +lemma t6_checked : ((hm37_1_0_8.realAnswer).add tr6).scale (1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 37 (1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_8.realContains tr6_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -200316477263320258439541379, hi := 200316477263320258439541379} +lemma tr7_contains : tr7.Contains (fullMoment false true 37 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 37 mixed_37_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -670903149397222094402464126, hi := -270270194870236944429087941} +lemma t7_checked : ((hm37_1_0_9.realAnswer).add tr7).scale (1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 37 (1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_9.realContains tr7_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -82522924134594386764164681, hi := 82522924134594386764164681} +lemma tr8_contains : tr8.Contains (fullMoment false true 37 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 37 mixed_37_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 551856561295574271735811561, hi := 716902409564845542505892615} +lemma t8_checked : ((hm37_1_0_10.realAnswer).add tr8).scale (1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 37 (1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_10.realContains tr8_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -30930815277007553323999573, hi := 30930815277007553323999573} +lemma tr9_contains : tr9.Contains (fullMoment false true 37 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 37 mixed_37_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := 488579973260598836196892, hi := 62350210527293694204117638} +lemma t9_checked : ((hm37_1_0_11.realAnswer).add tr9).scale (1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 37 (1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_11.realContains tr9_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -10634808089414144644373220, hi := 10634808089414144644373220} +lemma tr10_contains : tr10.Contains (fullMoment false true 37 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 37 mixed_37_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -63337012714785769031102801, hi := -42067396535953876839131941} +lemma t10_checked : ((hm37_1_0_12.realAnswer).add tr10).scale (1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 37 (1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_12.realContains tr10_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1666024019441666465554773939, hi := 1666024019441666465554773939} +lemma t11_contains : t11.Contains (sourcePower true 37 (1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 11 coarse_37_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -360418283188298954644165192, hi := 360418283188298954644165192} +lemma t12_contains : t12.Contains (sourcePower true 37 (1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 12 coarse_37_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73230933690684009964846178, hi := 73230933690684009964846178} +lemma t13_contains : t13.Contains (sourcePower true 37 (1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 13 coarse_37_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -14024613211358169787693858, hi := 14024613211358169787693858} +lemma t14_contains : t14.Contains (sourcePower true 37 (1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 14 coarse_37_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2539737320118086768090961, hi := 2539737320118086768090961} +lemma t15_contains : t15.Contains (sourcePower true 37 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 15 coarse_37_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -436172697025750189852343, hi := 436172697025750189852343} +lemma t16_contains : t16.Contains (sourcePower true 37 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 16 coarse_37_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -71231655286935315009798, hi := 71231655286935315009798} +lemma t17_contains : t17.Contains (sourcePower true 37 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 17 coarse_37_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11089989111095300851251, hi := 11089989111095300851251} +lemma t18_contains : t18.Contains (sourcePower true 37 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 18 coarse_37_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1649975540272999228512, hi := 1649975540272999228512} +lemma t19_contains : t19.Contains (sourcePower true 37 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 19 coarse_37_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -235137951616111849218, hi := 235137951616111849218} +lemma t20_contains : t20.Contains (sourcePower true 37 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 20 coarse_37_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -32170839535591669585, hi := 32170839535591669585} +lemma t21_contains : t21.Contains (sourcePower true 37 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 21 coarse_37_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4235420694999396572, hi := 4235420694999396572} +lemma t22_contains : t22.Contains (sourcePower true 37 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 22 coarse_37_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -537835042776084524, hi := 537835042776084524} +lemma t23_contains : t23.Contains (sourcePower true 37 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 23 coarse_37_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -66036844332233099, hi := 66036844332233099} +lemma t24_contains : t24.Contains (sourcePower true 37 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 24 coarse_37_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -7860187966536990, hi := 7860187966536990} +lemma t25_contains : t25.Contains (sourcePower true 37 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 25 coarse_37_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -909457826982059, hi := 909457826982059} +lemma t26_contains : t26.Contains (sourcePower true 37 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 26 coarse_37_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -102588381853087, hi := 102588381853087} +lemma t27_contains : t27.Contains (sourcePower true 37 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 27 coarse_37_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -11316112539702, hi := 11316112539702} +lemma t28_contains : t28.Contains (sourcePower true 37 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (1/1) 2 28 coarse_37_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 37 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 1141836011717962507309072138, hi := 1323421958598810138351083343} +lemma t4_checked : ((hm37_0_0_6.realAnswer).add tr4).scale (-1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 37 (-1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_6.realContains tr4_contains) (-1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -852272187863596681075941712, hi := 852272187863596681075941712} +lemma tr5_contains : tr5.Contains (fullMoment true true 37 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 37 mixed_37_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -152031461145230878262689761, hi := -98764449403577515675062956} +lemma t5_checked : ((hm37_0_0_7.realAnswer).add tr5).scale (1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 37 (-1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_7.realContains tr5_contains) (1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -438025165280374769114116401, hi := 438025165280374769114116401} +lemma tr6_contains : tr6.Contains (fullMoment true true 37 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 37 mixed_37_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -78873255857511860670816097, hi := -65184969442473534571915212} +lemma t6_checked : ((hm37_0_0_8.realAnswer).add tr6).scale (-1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 37 (-1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_8.realContains tr6_contains) (-1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -200316477263320258439541379, hi := 200316477263320258439541379} +lemma tr7_contains : tr7.Contains (fullMoment true true 37 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 37 mixed_37_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 1740715752736621541365656, hi := 4870660709979534620261962} +lemma t7_checked : ((hm37_0_0_9.realAnswer).add tr7).scale (1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 37 (-1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_9.realContains tr7_contains) (1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -82522924134594386764164681, hi := 82522924134594386764164681} +lemma tr8_contains : tr8.Contains (fullMoment true true 37 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 37 mixed_37_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 2010338082932940824605600, hi := 2655048427734882753204448} +lemma t8_checked : ((hm37_0_0_10.realAnswer).add tr8).scale (-1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 37 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_10.realContains tr8_contains) (-1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -30930815277007553323999573, hi := 30930815277007553323999573} +lemma tr9_contains : tr9.Contains (fullMoment true true 37 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 37 mixed_37_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -113235951132776517068116, hi := 7587546043080428144333} +lemma t9_checked : ((hm37_0_0_11.realAnswer).add tr9).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 37 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_11.realContains tr9_contains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -10634808089414144644373220, hi := 10634808089414144644373220} +lemma tr10_contains : tr10.Contains (fullMoment true true 37 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 37 mixed_37_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -58785613498715894132704, hi := -38014503949074262275787} +lemma t10_checked : ((hm37_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 37 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm37_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -813488290743001203884167, hi := 813488290743001203884167} +lemma t11_contains : t11.Contains (sourcePower false 37 (-1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 11 coarse_37_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -87992744919018299473674, hi := 87992744919018299473674} +lemma t12_contains : t12.Contains (sourcePower false 37 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 12 coarse_37_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8939322960288575435162, hi := 8939322960288575435162} +lemma t13_contains : t13.Contains (sourcePower false 37 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 13 coarse_37_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -855994458701060167706, hi := 855994458701060167706} +lemma t14_contains : t14.Contains (sourcePower false 37 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 14 coarse_37_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77506632083681847171, hi := 77506632083681847171} +lemma t15_contains : t15.Contains (sourcePower false 37 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 15 coarse_37_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6655467178737643278, hi := 6655467178737643278} +lemma t16_contains : t16.Contains (sourcePower false 37 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 16 coarse_37_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -543454401298029442, hi := 543454401298029442} +lemma t17_contains : t17.Contains (sourcePower false 37 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 17 coarse_37_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -42304951137906269, hi := 42304951137906269} +lemma t18_contains : t18.Contains (sourcePower false 37 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 18 coarse_37_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3147078590913772, hi := 3147078590913772} +lemma t19_contains : t19.Contains (sourcePower false 37 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 19 coarse_37_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -224245025268662, hi := 224245025268662} +lemma t20_contains : t20.Contains (sourcePower false 37 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 20 coarse_37_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15340251701161, hi := 15340251701161} +lemma t21_contains : t21.Contains (sourcePower false 37 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 21 coarse_37_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1009802984000, hi := 1009802984000} +lemma t22_contains : t22.Contains (sourcePower false 37 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 22 coarse_37_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -64114933345, hi := 64114933345} +lemma t23_contains : t23.Contains (sourcePower false 37 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 23 coarse_37_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -3936102649, hi := 3936102649} +lemma t24_contains : t24.Contains (sourcePower false 37 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 24 coarse_37_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -234251856, hi := 234251856} +lemma t25_contains : t25.Contains (sourcePower false 37 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 25 coarse_37_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -13551978, hi := 13551978} +lemma t26_contains : t26.Contains (sourcePower false 37 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 26 coarse_37_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -764344, hi := 764344} +lemma t27_contains : t27.Contains (sourcePower false 37 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 27 coarse_37_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -42156, hi := 42156} +lemma t28_contains : t28.Contains (sourcePower false 37 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 37 (-1/2) 2 28 coarse_37_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 37 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 1216854894358267021901216915, hi := 1398440841238865031704553658} +lemma t4_checked : ((hm37_1_0_6.realAnswer).add tr4).scale (1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 37 (-1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_6.realContains tr4_contains) (1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -852272187863596681075941712, hi := 852272187863596681075941712} +lemma tr5_contains : tr5.Contains (fullMoment false true 37 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 37 mixed_37_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -162762467700817488277636456, hi := -109495455959206541763786682} +lemma t5_checked : ((hm37_1_0_7.realAnswer).add tr5).scale (-1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 37 (-1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_7.realContains tr5_contains) (-1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -438025165280374769114116401, hi := 438025165280374769114116401} +lemma tr6_contains : tr6.Contains (fullMoment false true 37 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 37 mixed_37_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -83291800166051347869014427, hi := -69603513751019349452879130} +lemma t6_checked : ((hm37_1_0_8.realAnswer).add tr6).scale (1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 37 (-1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_8.realContains tr6_contains) (1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -200316477263320258439541379, hi := 200316477263320258439541379} +lemma tr7_contains : tr7.Contains (fullMoment false true 37 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 37 mixed_37_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 2111485897423726128352249, hi := 5241430854665797612519251} +lemma t7_checked : ((hm37_1_0_9.realAnswer).add tr7).scale (-1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 37 (-1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_9.realContains tr7_contains) (-1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -82522924134594386764164681, hi := 82522924134594386764164681} +lemma tr8_contains : tr8.Contains (fullMoment false true 37 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 37 mixed_37_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 2155689692560836998968013, hi := 2800400037362677900413644} +lemma t8_checked : ((hm37_1_0_10.realAnswer).add tr8).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 37 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_10.realContains tr8_contains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -30930815277007553323999573, hi := 30930815277007553323999573} +lemma tr9_contains : tr9.Contains (fullMoment false true 37 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 37 mixed_37_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -121777754936120496492418, hi := -954257760274607101947} +lemma t9_checked : ((hm37_1_0_11.realAnswer).add tr9).scale (-1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 37 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_11.realContains tr9_contains) (-1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -10634808089414144644373220, hi := 10634808089414144644373220} +lemma tr10_contains : tr10.Contains (fullMoment false true 37 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 37 mixed_37_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -61852551479282977569437, hi := -41081441929642457850714} +lemma t10_checked : ((hm37_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 37 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm37_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -813488290743001203884167, hi := 813488290743001203884167} +lemma t11_contains : t11.Contains (sourcePower true 37 (-1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 11 coarse_37_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -87992744919018299473674, hi := 87992744919018299473674} +lemma t12_contains : t12.Contains (sourcePower true 37 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 12 coarse_37_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8939322960288575435162, hi := 8939322960288575435162} +lemma t13_contains : t13.Contains (sourcePower true 37 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 13 coarse_37_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -855994458701060167706, hi := 855994458701060167706} +lemma t14_contains : t14.Contains (sourcePower true 37 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 14 coarse_37_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77506632083681847171, hi := 77506632083681847171} +lemma t15_contains : t15.Contains (sourcePower true 37 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 15 coarse_37_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6655467178737643278, hi := 6655467178737643278} +lemma t16_contains : t16.Contains (sourcePower true 37 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 16 coarse_37_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -543454401298029442, hi := 543454401298029442} +lemma t17_contains : t17.Contains (sourcePower true 37 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 17 coarse_37_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -42304951137906269, hi := 42304951137906269} +lemma t18_contains : t18.Contains (sourcePower true 37 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 18 coarse_37_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3147078590913772, hi := 3147078590913772} +lemma t19_contains : t19.Contains (sourcePower true 37 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 19 coarse_37_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -224245025268662, hi := 224245025268662} +lemma t20_contains : t20.Contains (sourcePower true 37 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 20 coarse_37_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15340251701161, hi := 15340251701161} +lemma t21_contains : t21.Contains (sourcePower true 37 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 21 coarse_37_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1009802984000, hi := 1009802984000} +lemma t22_contains : t22.Contains (sourcePower true 37 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 22 coarse_37_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -64114933345, hi := 64114933345} +lemma t23_contains : t23.Contains (sourcePower true 37 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 23 coarse_37_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -3936102649, hi := 3936102649} +lemma t24_contains : t24.Contains (sourcePower true 37 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 24 coarse_37_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -234251856, hi := 234251856} +lemma t25_contains : t25.Contains (sourcePower true 37 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 25 coarse_37_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -13551978, hi := 13551978} +lemma t26_contains : t26.Contains (sourcePower true 37 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 26 coarse_37_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -764344, hi := 764344} +lemma t27_contains : t27.Contains (sourcePower true 37 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 27 coarse_37_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -42156, hi := 42156} +lemma t28_contains : t28.Contains (sourcePower true 37 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 37 (-1/2) 2 28 coarse_37_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 37 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 1157105663708280819829289628, hi := 1275978727779178242134228371} +lemma t4_checked : ((hm39_0_0_6.realAnswer).add tr4).scale (-1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 39 (1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_6.realContains tr4_contains) (-1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -557658605426100677627684034, hi := 557658605426100677627684034} +lemma tr5_contains : tr5.Contains (fullMoment true true 39 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 39 mixed_39_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -144524912224341302404564595, hi := -109671249385009582011183563} +lemma t5_checked : ((hm39_0_0_7.realAnswer).add tr5).scale (-1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 39 (1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_7.realContains tr5_contains) (-1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -286484792976969139723090417, hi := 286484792976969139723090417} +lemma tr6_contains : tr6.Contains (fullMoment true true 39 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 39 mixed_39_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -75558472592100375794679700, hi := -66605822811540209037193880} +lemma t6_checked : ((hm39_0_0_8.realAnswer).add tr6).scale (-1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 39 (1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_8.realContains tr6_contains) (-1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -130964293330677630666136863, hi := 130964293330677630666136863} +lemma tr7_contains : tr7.Contains (fullMoment true true 39 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 39 mixed_39_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 2451792599391428338645828, hi := 4498109682687236213344907} +lemma t7_checked : ((hm39_0_0_9.realAnswer).add tr7).scale (-1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 39 (1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_9.realContains tr7_contains) (-1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -53934136505805891769016377, hi := 53934136505805891769016377} +lemma tr8_contains : tr8.Contains (fullMoment true true 39 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 39 mixed_39_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 2093280535918847318897588, hi := 2514640977370931688540136} +lemma t8_checked : ((hm39_0_0_10.realAnswer).add tr8).scale (-1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 39 (1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_10.realContains tr8_contains) (-1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -20209267537129097201365382, hi := 20209267537129097201365382} +lemma tr9_contains : tr9.Contains (fullMoment true true 39 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 39 mixed_39_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -98791229698309799967807, hi := -19848778381347289012264} +lemma t9_checked : ((hm39_0_0_11.realAnswer).add tr9).scale (-1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 39 (1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_11.realContains tr9_contains) (-1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -6946632271962133634215599, hi := 6946632271962133634215599} +lemma tr10_contains : tr10.Contains (fullMoment true true 39 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 39 mixed_39_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -54633278150644329153893, hi := -41065636994463070298464} +lemma t10_checked : ((hm39_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 39 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -812916126211309011353084, hi := 812916126211309011353084} +lemma t11_contains : t11.Contains (sourcePower false 39 (1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 11 coarse_39_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -87908302074304336339431, hi := 87908302074304336339431} +lemma t12_contains : t12.Contains (sourcePower false 39 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 12 coarse_39_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8927686191517795332792, hi := 8927686191517795332792} +lemma t13_contains : t13.Contains (sourcePower false 39 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 13 coarse_39_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -854490483495713626741, hi := 854490483495713626741} +lemma t14_contains : t14.Contains (sourcePower false 39 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 14 coarse_39_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77323625460143770825, hi := 77323625460143770825} +lemma t15_contains : t15.Contains (sourcePower false 39 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 15 coarse_39_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6634429492819200158, hi := 6634429492819200158} +lemma t16_contains : t16.Contains (sourcePower false 39 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 16 coarse_39_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -541162686131840994, hi := 541162686131840994} +lemma t17_contains : t17.Contains (sourcePower false 39 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 17 coarse_39_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -42067734326804533, hi := 42067734326804533} +lemma t18_contains : t18.Contains (sourcePower false 39 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 18 coarse_39_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3123688754100502, hi := 3123688754100502} +lemma t19_contains : t19.Contains (sourcePower false 39 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 19 coarse_39_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -222043209846211, hi := 222043209846211} +lemma t20_contains : t20.Contains (sourcePower false 39 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 20 coarse_39_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15141964192164, hi := 15141964192164} +lemma t21_contains : t21.Contains (sourcePower false 39 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 21 coarse_39_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -992687705435, hi := 992687705435} +lemma t22_contains : t22.Contains (sourcePower false 39 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 22 coarse_39_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -62696548386, hi := 62696548386} +lemma t23_contains : t23.Contains (sourcePower false 39 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 23 coarse_39_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -3823067150, hi := 3823067150} +lemma t24_contains : t24.Contains (sourcePower false 39 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 24 coarse_39_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -225576575, hi := 225576575} +lemma t25_contains : t25.Contains (sourcePower false 39 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 25 coarse_39_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -12909895, hi := 12909895} +lemma t26_contains : t26.Contains (sourcePower false 39 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 26 coarse_39_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -718457, hi := 718457} +lemma t27_contains : t27.Contains (sourcePower false 39 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 27 coarse_39_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -38986, hi := 38986} +lemma t28_contains : t28.Contains (sourcePower false 39 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (1/2) 2 28 coarse_39_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 39 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 1251528494534060489025431933, hi := 1370401558604626812243373675} +lemma t4_checked : ((hm39_1_0_6.realAnswer).add tr4).scale (1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 39 (1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_6.realContains tr4_contains) (1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -557658605426100677627684034, hi := 557658605426100677627684034} +lemma tr5_contains : tr5.Contains (fullMoment false true 39 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 39 mixed_39_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -151558159737823685202371908, hi := -116704496898548220211523354} +lemma t5_checked : ((hm39_1_0_7.realAnswer).add tr5).scale (1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 39 (1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_7.realContains tr5_contains) (1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -286484792976969139723090417, hi := 286484792976969139723090417} +lemma tr6_contains : tr6.Contains (fullMoment false true 39 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 39 mixed_39_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -81070328091693104131223742, hi := -72117678311141332899686244} +lemma t6_checked : ((hm39_1_0_8.realAnswer).add tr6).scale (1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 39 (1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_8.realContains tr6_contains) (1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -130964293330677630666136863, hi := 130964293330677630666136863} +lemma tr7_contains : tr7.Contains (fullMoment false true 39 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 39 mixed_39_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 2567828230349949894627143, hi := 4614145313644640290828928} +lemma t7_checked : ((hm39_1_0_9.realAnswer).add tr7).scale (1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 39 (1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_9.realContains tr7_contains) (1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -53934136505805891769016377, hi := 53934136505805891769016377} +lemma tr8_contains : tr8.Contains (fullMoment false true 39 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 39 mixed_39_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 2271153018901614800119361, hi := 2692513460353564877989645} +lemma t8_checked : ((hm39_1_0_10.realAnswer).add tr8).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 39 (1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_10.realContains tr8_contains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -20209267537129097201365382, hi := 20209267537129097201365382} +lemma tr9_contains : tr9.Contains (fullMoment false true 39 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 39 mixed_39_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -98560922649690163797214, hi := -19618471332742369529931} +lemma t9_checked : ((hm39_1_0_11.realAnswer).add tr9).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 39 (1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_11.realContains tr9_contains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -6946632271962133634215599, hi := 6946632271962133634215599} +lemma tr10_contains : tr10.Contains (fullMoment false true 39 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 39 mixed_39_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -58314988478651022560092, hi := -44747347322471246604929} +lemma t10_checked : ((hm39_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 39 (1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -812916126211309011353084, hi := 812916126211309011353084} +lemma t11_contains : t11.Contains (sourcePower true 39 (1/2) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 11 coarse_39_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -87908302074304336339431, hi := 87908302074304336339431} +lemma t12_contains : t12.Contains (sourcePower true 39 (1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 12 coarse_39_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8927686191517795332792, hi := 8927686191517795332792} +lemma t13_contains : t13.Contains (sourcePower true 39 (1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 13 coarse_39_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -854490483495713626741, hi := 854490483495713626741} +lemma t14_contains : t14.Contains (sourcePower true 39 (1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 14 coarse_39_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77323625460143770825, hi := 77323625460143770825} +lemma t15_contains : t15.Contains (sourcePower true 39 (1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 15 coarse_39_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6634429492819200158, hi := 6634429492819200158} +lemma t16_contains : t16.Contains (sourcePower true 39 (1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 16 coarse_39_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -541162686131840994, hi := 541162686131840994} +lemma t17_contains : t17.Contains (sourcePower true 39 (1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 17 coarse_39_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -42067734326804533, hi := 42067734326804533} +lemma t18_contains : t18.Contains (sourcePower true 39 (1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 18 coarse_39_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3123688754100502, hi := 3123688754100502} +lemma t19_contains : t19.Contains (sourcePower true 39 (1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 19 coarse_39_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -222043209846211, hi := 222043209846211} +lemma t20_contains : t20.Contains (sourcePower true 39 (1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 20 coarse_39_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15141964192164, hi := 15141964192164} +lemma t21_contains : t21.Contains (sourcePower true 39 (1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 21 coarse_39_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -992687705435, hi := 992687705435} +lemma t22_contains : t22.Contains (sourcePower true 39 (1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 22 coarse_39_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -62696548386, hi := 62696548386} +lemma t23_contains : t23.Contains (sourcePower true 39 (1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 23 coarse_39_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -3823067150, hi := 3823067150} +lemma t24_contains : t24.Contains (sourcePower true 39 (1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 24 coarse_39_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -225576575, hi := 225576575} +lemma t25_contains : t25.Contains (sourcePower true 39 (1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 25 coarse_39_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -12909895, hi := 12909895} +lemma t26_contains : t26.Contains (sourcePower true 39 (1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 26 coarse_39_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -718457, hi := 718457} +lemma t27_contains : t27.Contains (sourcePower true 39 (1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 27 coarse_39_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -38986, hi := 38986} +lemma t28_contains : t28.Contains (sourcePower true 39 (1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (1/2) 2 28 coarse_39_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 39 (1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 18513690619332493117268634054, hi := 20415659644466851874147653927} +lemma t4_checked : ((hm39_0_0_6.realAnswer).add tr4).scale (-1) 1=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 39 (-1/1) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_6.realContains tr4_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -557658605426100677627684034, hi := 557658605426100677627684034} +lemma tr5_contains : tr5.Contains (fullMoment true true 39 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 39 mixed_39_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 3509479980320306624357874030, hi := 4624797191178921676946067036} +lemma t5_checked : ((hm39_0_0_7.realAnswer).add tr5).scale (1) 1=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 39 (-1/1) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_7.realContains tr5_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -286484792976969139723090417, hi := 286484792976969139723090417} +lemma tr6_contains : tr6.Contains (fullMoment true true 39 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 39 mixed_39_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -4835742245894424050859500763, hi := -4262772659938573378380408351} +lemma t6_checked : ((hm39_0_0_8.realAnswer).add tr6).scale (-1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 39 (-1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_8.realContains tr6_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -130964293330677630666136863, hi := 130964293330677630666136863} +lemma tr7_contains : tr7.Contains (fullMoment true true 39 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 39 mixed_39_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -575758039383966235308148074, hi := -313829452722102827346666063} +lemma t7_checked : ((hm39_0_0_9.realAnswer).add tr7).scale (1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 39 (-1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_9.realContains tr7_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -53934136505805891769016377, hi := 53934136505805891769016377} +lemma tr8_contains : tr8.Contains (fullMoment true true 39 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 39 mixed_39_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 535879817195224913637782713, hi := 643748090206958512266274783} +lemma t8_checked : ((hm39_0_0_10.realAnswer).add tr8).scale (-1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 39 (-1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_10.realContains tr8_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -20209267537129097201365382, hi := 20209267537129097201365382} +lemma tr9_contains : tr9.Contains (fullMoment true true 39 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 39 mixed_39_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := 10162574531249811974279223, hi := 50581109605534617583516986} +lemma t9_checked : ((hm39_0_0_11.realAnswer).add tr9).scale (1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 39 (-1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_11.realContains tr9_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -6946632271962133634215599, hi := 6946632271962133634215599} +lemma tr10_contains : tr10.Contains (fullMoment true true 39 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 39 mixed_39_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -55944476826259793053586291, hi := -42051212282330183985627719} +lemma t10_checked : ((hm39_0_0_12.realAnswer).add tr10).scale (-1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 39 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm39_0_0_12.realContains tr10_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1664852226480760855251115215, hi := 1664852226480760855251115215} +lemma t11_contains : t11.Contains (sourcePower false 39 (-1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 11 coarse_39_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -360072405296350561646305502, hi := 360072405296350561646305502} +lemma t12_contains : t12.Contains (sourcePower false 39 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 12 coarse_39_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73135605280913779366227181, hi := 73135605280913779366227181} +lemma t13_contains : t13.Contains (sourcePower false 39 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 13 coarse_39_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -13999972081593772060522585, hi := 13999972081593772060522585} +lemma t14_contains : t14.Contains (sourcePower false 39 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 14 coarse_39_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2533740559077991082380588, hi := 2533740559077991082380588} +lemma t15_contains : t15.Contains (sourcePower false 39 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 15 coarse_39_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -434793971241399101497012, hi := 434793971241399101497012} +lemma t16_contains : t16.Contains (sourcePower false 39 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 16 coarse_39_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -70931275596672662697091, hi := 70931275596672662697091} +lemma t17_contains : t17.Contains (sourcePower false 39 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 17 coarse_39_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11027804147365847283637, hi := 11027804147365847283637} +lemma t18_contains : t18.Contains (sourcePower false 39 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 18 coarse_39_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1637712529509843641519, hi := 1637712529509843641519} +lemma t19_contains : t19.Contains (sourcePower false 39 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 19 coarse_39_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -232829180807700478412, hi := 232829180807700478412} +lemma t20_contains : t20.Contains (sourcePower false 39 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 20 coarse_39_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -31755000489523633449, hi := 31755000489523633449} +lemma t21_contains : t21.Contains (sourcePower false 39 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 21 coarse_39_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4163634013653937202, hi := 4163634013653937202} +lemma t22_contains : t22.Contains (sourcePower false 39 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 22 coarse_39_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -525936767355968363, hi := 525936767355968363} +lemma t23_contains : t23.Contains (sourcePower false 39 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 23 coarse_39_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -64140423352441557, hi := 64140423352441557} +lemma t24_contains : t24.Contains (sourcePower false 39 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 24 coarse_39_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -7569093846066644, hi := 7569093846066644} +lemma t25_contains : t25.Contains (sourcePower false 39 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 25 coarse_39_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -866368337543320, hi := 866368337543320} +lemma t26_contains : t26.Contains (sourcePower false 39 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 26 coarse_39_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -96429547209064, hi := 96429547209064} +lemma t27_contains : t27.Contains (sourcePower false 39 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 27 coarse_39_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -10465115562657, hi := 10465115562657} +lemma t28_contains : t28.Contains (sourcePower false 39 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 39 (-1/1) 2 28 coarse_39_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 39 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := 20024455912544967824406910940, hi := 21926424937674028995893978800} +lemma t4_checked : ((hm39_1_0_6.realAnswer).add tr4).scale (1) 1=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 39 (-1/1) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_6.realContains tr4_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -557658605426100677627684034, hi := 557658605426100677627684034} +lemma tr5_contains : tr5.Contains (fullMoment false true 39 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 39 mixed_39_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 3734543900753543046768747349, hi := 4849861111610357926475901041} +lemma t5_checked : ((hm39_1_0_7.realAnswer).add tr5).scale (-1) 1=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 39 (-1/1) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_7.realContains tr5_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -286484792976969139723090417, hi := 286484792976969139723090417} +lemma tr6_contains : tr6.Contains (fullMoment false true 39 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 39 mixed_39_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := -5188500997868358664398319444, hi := -4615531411913045305579919655} +lemma t6_checked : ((hm39_1_0_8.realAnswer).add tr6).scale (1) 1=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 39 (-1/1) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_8.realContains tr6_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -130964293330677630666136863, hi := 130964293330677630666136863} +lemma tr7_contains : tr7.Contains (fullMoment false true 39 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 39 mixed_39_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -590610600146513957226102674, hi := -328682013484793586512274350} +lemma t7_checked : ((hm39_1_0_9.realAnswer).add tr7).scale (-1) 1=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 39 (-1/1) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_9.realContains tr7_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -53934136505805891769016377, hi := 53934136505805891769016377} +lemma tr8_contains : tr8.Contains (fullMoment false true 39 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 39 mixed_39_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := 581415172838813388830556472, hi := 689283445850512608765349102} +lemma t8_checked : ((hm39_1_0_10.realAnswer).add tr8).scale (1) 1=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 39 (-1/1) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_10.realContains tr8_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -20209267537129097201365382, hi := 20209267537129097201365382} +lemma tr9_contains : tr9.Contains (fullMoment false true 39 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 39 mixed_39_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := 10044657322364093199324825, hi := 50463192396641363864173144} +lemma t9_checked : ((hm39_1_0_11.realAnswer).add tr9).scale (-1) 1=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 39 (-1/1) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_11.realContains tr9_contains) (-1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -6946632271962133634215599, hi := 6946632271962133634215599} +lemma tr10_contains : tr10.Contains (fullMoment false true 39 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 39 mixed_39_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := -59714548202138647101533629, hi := -45821283658210556523447973} +lemma t10_checked : ((hm39_1_0_12.realAnswer).add tr10).scale (1) 1=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 39 (-1/1) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm39_1_0_12.realContains tr10_contains) (1) 1 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t11 : RBox := {lo := -1664852226480760855251115215, hi := 1664852226480760855251115215} +lemma t11_contains : t11.Contains (sourcePower true 39 (-1/1) 2 11) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 11 coarse_39_13) <;> norm_num [t11,precision] +noncomputable def t12 : RBox := {lo := -360072405296350561646305502, hi := 360072405296350561646305502} +lemma t12_contains : t12.Contains (sourcePower true 39 (-1/1) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 12 coarse_39_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -73135605280913779366227181, hi := 73135605280913779366227181} +lemma t13_contains : t13.Contains (sourcePower true 39 (-1/1) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 13 coarse_39_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -13999972081593772060522585, hi := 13999972081593772060522585} +lemma t14_contains : t14.Contains (sourcePower true 39 (-1/1) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 14 coarse_39_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -2533740559077991082380588, hi := 2533740559077991082380588} +lemma t15_contains : t15.Contains (sourcePower true 39 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 15 coarse_39_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -434793971241399101497012, hi := 434793971241399101497012} +lemma t16_contains : t16.Contains (sourcePower true 39 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 16 coarse_39_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -70931275596672662697091, hi := 70931275596672662697091} +lemma t17_contains : t17.Contains (sourcePower true 39 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 17 coarse_39_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -11027804147365847283637, hi := 11027804147365847283637} +lemma t18_contains : t18.Contains (sourcePower true 39 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 18 coarse_39_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -1637712529509843641519, hi := 1637712529509843641519} +lemma t19_contains : t19.Contains (sourcePower true 39 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 19 coarse_39_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -232829180807700478412, hi := 232829180807700478412} +lemma t20_contains : t20.Contains (sourcePower true 39 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 20 coarse_39_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -31755000489523633449, hi := 31755000489523633449} +lemma t21_contains : t21.Contains (sourcePower true 39 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 21 coarse_39_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -4163634013653937202, hi := 4163634013653937202} +lemma t22_contains : t22.Contains (sourcePower true 39 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 22 coarse_39_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -525936767355968363, hi := 525936767355968363} +lemma t23_contains : t23.Contains (sourcePower true 39 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 23 coarse_39_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -64140423352441557, hi := 64140423352441557} +lemma t24_contains : t24.Contains (sourcePower true 39 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 24 coarse_39_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -7569093846066644, hi := 7569093846066644} +lemma t25_contains : t25.Contains (sourcePower true 39 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 25 coarse_39_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -866368337543320, hi := 866368337543320} +lemma t26_contains : t26.Contains (sourcePower true 39 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 26 coarse_39_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -96429547209064, hi := 96429547209064} +lemma t27_contains : t27.Contains (sourcePower true 39 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 27 coarse_39_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -10465115562657, hi := 10465115562657} +lemma t28_contains : t28.Contains (sourcePower true 39 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 39 (-1/1) 2 28 coarse_39_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 39 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -10630176914062335878967891547, hi := 10630176914062335878967891547} +lemma t19_contains : t19.Contains (sourcePower false 4 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 19 coarse_4_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -4170725355037302657130575501, hi := 4170725355037302657130575501} +lemma t20_contains : t20.Contains (sourcePower false 4 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 20 coarse_4_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -1597009396858088585591364134, hi := 1597009396858088585591364134} +lemma t21_contains : t21.Contains (sourcePower false 4 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 21 coarse_4_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -597753179407336111151532935, hi := 597753179407336111151532935} +lemma t22_contains : t22.Contains (sourcePower false 4 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 22 coarse_4_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -218976203799358635786654501, hi := 218976203799358635786654501} +lemma t23_contains : t23.Contains (sourcePower false 4 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 23 coarse_4_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -78583460860525641873577874, hi := 78583460860525641873577874} +lemma t24_contains : t24.Contains (sourcePower false 4 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 24 coarse_4_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -27643541892856090644505557, hi := 27643541892856090644505557} +lemma t25_contains : t25.Contains (sourcePower false 4 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 25 coarse_4_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -9535506295045417796923251, hi := 9535506295045417796923251} +lemma t26_contains : t26.Contains (sourcePower false 4 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 26 coarse_4_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -3225929251695361699015075, hi := 3225929251695361699015075} +lemma t27_contains : t27.Contains (sourcePower false 4 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 27 coarse_4_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1070388235927703327726843, hi := 1070388235927703327726843} +lemma t28_contains : t28.Contains (sourcePower false 4 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (3/2) 2 28 coarse_4_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 4 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -10630176914062335878967891547, hi := 10630176914062335878967891547} +lemma t19_contains : t19.Contains (sourcePower true 4 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 19 coarse_4_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -4170725355037302657130575501, hi := 4170725355037302657130575501} +lemma t20_contains : t20.Contains (sourcePower true 4 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 20 coarse_4_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -1597009396858088585591364134, hi := 1597009396858088585591364134} +lemma t21_contains : t21.Contains (sourcePower true 4 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 21 coarse_4_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -597753179407336111151532935, hi := 597753179407336111151532935} +lemma t22_contains : t22.Contains (sourcePower true 4 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 22 coarse_4_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -218976203799358635786654501, hi := 218976203799358635786654501} +lemma t23_contains : t23.Contains (sourcePower true 4 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 23 coarse_4_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -78583460860525641873577874, hi := 78583460860525641873577874} +lemma t24_contains : t24.Contains (sourcePower true 4 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 24 coarse_4_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -27643541892856090644505557, hi := 27643541892856090644505557} +lemma t25_contains : t25.Contains (sourcePower true 4 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 25 coarse_4_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -9535506295045417796923251, hi := 9535506295045417796923251} +lemma t26_contains : t26.Contains (sourcePower true 4 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 26 coarse_4_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -3225929251695361699015075, hi := 3225929251695361699015075} +lemma t27_contains : t27.Contains (sourcePower true 4 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 27 coarse_4_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -1070388235927703327726843, hi := 1070388235927703327726843} +lemma t28_contains : t28.Contains (sourcePower true 4 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (3/2) 2 28 coarse_4_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 4 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -9146114894009762331, hi := 9146114894009762331} +lemma t19_contains : t19.Contains (sourcePower false 4 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 19 coarse_4_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1196152349953484451, hi := 1196152349953484451} +lemma t20_contains : t20.Contains (sourcePower false 4 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 20 coarse_4_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -152672607307377610, hi := 152672607307377610} +lemma t21_contains : t21.Contains (sourcePower false 4 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 21 coarse_4_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -19048215288304101, hi := 19048215288304101} +lemma t22_contains : t22.Contains (sourcePower false 4 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 22 coarse_4_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -2325991182024511, hi := 2325991182024511} +lemma t23_contains : t23.Contains (sourcePower false 4 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 23 coarse_4_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -278240944058669, hi := 278240944058669} +lemma t24_contains : t24.Contains (sourcePower false 4 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 24 coarse_4_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -32625886368317, hi := 32625886368317} +lemma t25_contains : t25.Contains (sourcePower false 4 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 25 coarse_4_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -3751380654625, hi := 3751380654625} +lemma t26_contains : t26.Contains (sourcePower false 4 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 26 coarse_4_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -423039539925, hi := 423039539925} +lemma t27_contains : t27.Contains (sourcePower false 4 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 27 coarse_4_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -46789262002, hi := 46789262002} +lemma t28_contains : t28.Contains (sourcePower false 4 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 4 (-1/2) 2 28 coarse_4_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 4 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -9146114894009762331, hi := 9146114894009762331} +lemma t19_contains : t19.Contains (sourcePower true 4 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 19 coarse_4_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -1196152349953484451, hi := 1196152349953484451} +lemma t20_contains : t20.Contains (sourcePower true 4 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 20 coarse_4_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -152672607307377610, hi := 152672607307377610} +lemma t21_contains : t21.Contains (sourcePower true 4 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 21 coarse_4_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -19048215288304101, hi := 19048215288304101} +lemma t22_contains : t22.Contains (sourcePower true 4 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 22 coarse_4_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -2325991182024511, hi := 2325991182024511} +lemma t23_contains : t23.Contains (sourcePower true 4 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 23 coarse_4_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -278240944058669, hi := 278240944058669} +lemma t24_contains : t24.Contains (sourcePower true 4 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 24 coarse_4_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -32625886368317, hi := 32625886368317} +lemma t25_contains : t25.Contains (sourcePower true 4 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 25 coarse_4_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -3751380654625, hi := 3751380654625} +lemma t26_contains : t26.Contains (sourcePower true 4 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 26 coarse_4_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -423039539925, hi := 423039539925} +lemma t27_contains : t27.Contains (sourcePower true 4 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 27 coarse_4_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -46789262002, hi := 46789262002} +lemma t28_contains : t28.Contains (sourcePower true 4 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 4 (-1/2) 2 28 coarse_4_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 4 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (1:ℝ)/50 norm_num [tr2,precision] +noncomputable def t2 : RBox := {lo := 83543377372653557933545260267, hi := 89744401017444835140922174437} +lemma t2_checked : ((hm40_0_0_4.realAnswer).add tr2).scale (-9) 4=t2 := by decide +kernel +lemma t2_contains : t2.Contains (sourcePower false 40 (3/2) 2 2) := by + rw [← t2_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_4.realContains tr2_contains) (-9) 4 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr3 : RBox := {lo := -1127662331737765183970897290, hi := 1127662331737765183970897290} +lemma tr3_contains : tr3.Contains (fullMoment true true 40 5) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 5 40 mixed_40_5) <;> norm_num [tr3,precision] +noncomputable def t3 : RBox := {lo := -158882124292789256973025315895, hi := -151270403553383759186317313350} +lemma t3_checked : ((hm40_0_0_5.realAnswer).add tr3).scale (-27) 8=t3 := by decide +kernel +lemma t3_contains : t3.Contains (sourcePower false 40 (3/2) 2 3) := by + rw [← t3_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_5.realContains tr3_contains) (-27) 8 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr4 : RBox := {lo := -770206922867263530745282246, hi := 770206922867263530745282246} +lemma tr4_contains : tr4.Contains (fullMoment true true 40 6) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 6 40 mixed_40_6) <;> norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -128354913863081125238050050180, hi := -120556568768946041507644431813} +lemma t4_checked : ((hm40_0_0_6.realAnswer).add tr4).scale (-81) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 40 (3/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_6.realContains tr4_contains) (-81) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -451541240469518315478157760, hi := 451541240469518315478157760} +lemma tr5_contains : tr5.Contains (fullMoment true true 40 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 40 mixed_40_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 58600097061403100437198366477, hi := 65457879651086942964199521971} +lemma t5_checked : ((hm40_0_0_7.realAnswer).add tr5).scale (-243) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 40 (3/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_7.realContains tr5_contains) (-243) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -231919502450331624380412515, hi := 231919502450331624380412515} +lemma tr6_contains : tr6.Contains (fullMoment true true 40 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 40 mixed_40_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 59211466313684077033197628956, hi := 64494882478904417476703817609} +lemma t6_checked : ((hm40_0_0_8.realAnswer).add tr6).scale (-729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 40 (3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_8.realContains tr6_contains) (-729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -105999991106160182956535889, hi := 105999991106160182956535889} +lemma tr7_contains : tr7.Contains (fullMoment true true 40 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 40 mixed_40_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -15834476240752524456905481979, hi := -12212257794662248874294000011} +lemma t7_checked : ((hm40_0_0_9.realAnswer).add tr7).scale (-2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 40 (3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_9.realContains tr7_contains) (-2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -43645893453395484376071552, hi := 43645893453395484376071552} +lemma tr8_contains : tr8.Contains (fullMoment true true 40 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 40 mixed_40_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -18200868006310246800158692147, hi := -15963674983277721121686340352} +lemma t8_checked : ((hm40_0_0_10.realAnswer).add tr8).scale (-6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 40 (3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_10.realContains tr8_contains) (-6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -16351797364128125134540904, hi := 16351797364128125134540904} +lemma tr9_contains : tr9.Contains (fullMoment true true 40 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 40 mixed_40_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := 1426806523037837882125503753, hi := 2684042568031663925593167247} +lemma t9_checked : ((hm40_0_0_11.realAnswer).add tr9).scale (-19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 40 (3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_11.realContains tr9_contains) (-19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -5619945822412676134103778, hi := 5619945822412676134103778} +lemma tr10_contains : tr10.Contains (fullMoment true true 40 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 40 mixed_40_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 2744767027786655953900195155, hi := 3392915818544113390712227322} +lemma t10_checked : ((hm40_0_0_12.realAnswer).add tr10).scale (-59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 40 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_12.realContains tr10_contains) (-59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -1784145647367326687478989, hi := 1784145647367326687478989} +lemma tr11_contains : tr11.Contains (fullMoment true true 40 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 40 mixed_40_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -367177817251386361556666683, hi := -58529331905413898135406720} +lemma t11_checked : ((hm40_0_0_13.realAnswer).add tr11).scale (-177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 40 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_13.realContains tr11_contains) (-177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -46701938752094289344693015302, hi := 46701938752094289344693015302} +lemma t12_contains : t12.Contains (sourcePower false 40 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 12 coarse_40_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14226944918381974251029064191, hi := 14226944918381974251029064191} +lemma t13_contains : t13.Contains (sourcePower false 40 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 13 coarse_40_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4084415447830513492880711507, hi := 4084415447830513492880711507} +lemma t14_contains : t14.Contains (sourcePower false 40 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 14 coarse_40_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1108565585779813984855987127, hi := 1108565585779813984855987127} +lemma t15_contains : t15.Contains (sourcePower false 40 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 15 coarse_40_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -285264936549415184266627703, hi := 285264936549415184266627703} +lemma t16_contains : t16.Contains (sourcePower false 40 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 16 coarse_40_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -69779472687187080016182321, hi := 69779472687187080016182321} +lemma t17_contains : t17.Contains (sourcePower false 40 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 17 coarse_40_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -16264874903222436903988511, hi := 16264874903222436903988511} +lemma t18_contains : t18.Contains (sourcePower false 40 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 18 coarse_40_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3620774099258225813167868, hi := 3620774099258225813167868} +lemma t19_contains : t19.Contains (sourcePower false 40 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 19 coarse_40_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -771458127210527778096725, hi := 771458127210527778096725} +lemma t20_contains : t20.Contains (sourcePower false 40 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 20 coarse_40_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -157645020874272310770310, hi := 157645020874272310770310} +lemma t21_contains : t21.Contains (sourcePower false 40 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 21 coarse_40_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -30958614408405690714176, hi := 30958614408405690714176} +lemma t22_contains : t22.Contains (sourcePower false 40 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 22 coarse_40_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -5854476527190135979518, hi := 5854476527190135979518} +lemma t23_contains : t23.Contains (sourcePower false 40 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 23 coarse_40_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1068277418013106576834, hi := 1068277418013106576834} +lemma t24_contains : t24.Contains (sourcePower false 40 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 24 coarse_40_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -188487704728201524407, hi := 188487704728201524407} +lemma t25_contains : t25.Contains (sourcePower false 40 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 25 coarse_40_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -32228882231906787482, hi := 32228882231906787482} +lemma t26_contains : t26.Contains (sourcePower false 40 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 26 coarse_40_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -5352951031644319619, hi := 5352951031644319619} +lemma t27_contains : t27.Contains (sourcePower false 40 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 27 coarse_40_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -865811656978999856, hi := 865811656978999856} +lemma t28_contains : t28.Contains (sourcePower false 40 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (3/2) 2 28 coarse_40_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 40 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr2,precision] +noncomputable def t2 : RBox := {lo := 91224876236734049914703070335, hi := 97425899881447900859689773634} +lemma t2_checked : ((hm40_1_0_4.realAnswer).add tr2).scale (9) 4=t2 := by decide +kernel +lemma t2_contains : t2.Contains (sourcePower true 40 (3/2) 2 2) := by + rw [← t2_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_4.realContains tr2_contains) (9) 4 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr3 : RBox := {lo := -1127662331737765183970897290, hi := 1127662331737765183970897290} +lemma tr3_contains : tr3.Contains (fullMoment false true 40 5) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 5 40 mixed_40_5) <;> norm_num [tr3,precision] +noncomputable def t3 : RBox := {lo := -170514417887930876063912793341, hi := -162902697148579824231517608900} +lemma t3_checked : ((hm40_1_0_5.realAnswer).add tr3).scale (27) 8=t3 := by decide +kernel +lemma t3_contains : t3.Contains (sourcePower true 40 (3/2) 2 3) := by + rw [← t3_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_5.realContains tr3_contains) (27) 8 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr4 : RBox := {lo := -770206922867263530745282246, hi := 770206922867263530745282246} +lemma tr4_contains : tr4.Contains (fullMoment false true 40 6) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 6 40 mixed_40_6) <;> norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -138962324581811896435280419470, hi := -131163979487709010165925685600} +lemma t4_checked : ((hm40_1_0_6.realAnswer).add tr4).scale (81) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 40 (3/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_6.realContains tr4_contains) (81) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -451541240469518315478157760, hi := 451541240469518315478157760} +lemma tr5_contains : tr5.Contains (fullMoment false true 40 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 40 mixed_40_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := 62733695221372301084137056469, hi := 69591477811039733933411734255} +lemma t5_checked : ((hm40_1_0_7.realAnswer).add tr5).scale (243) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 40 (3/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_7.realContains tr5_contains) (243) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -231919502450331624380412515, hi := 231919502450331624380412515} +lemma tr6_contains : tr6.Contains (fullMoment false true 40 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 40 mixed_40_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 64406523241659875117285998811, hi := 69689939406872867821585394830} +lemma t6_checked : ((hm40_1_0_8.realAnswer).add tr6).scale (729) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 40 (3/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_8.realContains tr6_contains) (729) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -105999991106160182956535889, hi := 105999991106160182956535889} +lemma tr7_contains : tr7.Contains (fullMoment false true 40 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 40 mixed_40_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := -16572847711492542502252919739, hi := -12950629265405201787764488114} +lemma t7_checked : ((hm40_1_0_9.realAnswer).add tr7).scale (2187) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 40 (3/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_9.realContains tr7_contains) (2187) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -43645893453395484376071552, hi := 43645893453395484376071552} +lemma tr8_contains : tr8.Contains (fullMoment false true 40 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 40 mixed_40_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -19621010918030115925218891941, hi := -17383817894998648781765411563} +lemma t8_checked : ((hm40_1_0_10.realAnswer).add tr8).scale (6561) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 40 (3/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_10.realContains tr8_contains) (6561) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -16351797364128125134540904, hi := 16351797364128125134540904} +lemma tr9_contains : tr9.Contains (fullMoment false true 40 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 40 mixed_40_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := 1488133253270539957355761609, hi := 2745369298264017799839076596} +lemma t9_checked : ((hm40_1_0_11.realAnswer).add tr9).scale (19683) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 40 (3/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_11.realContains tr9_contains) (19683) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -5619945822412676134103778, hi := 5619945822412676134103778} +lemma tr10_contains : tr10.Contains (fullMoment false true 40 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 40 mixed_40_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 2997976234318846561036298146, hi := 3646125025076198668351286782} +lemma t10_checked : ((hm40_1_0_12.realAnswer).add tr10).scale (59049) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 40 (3/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_12.realContains tr10_contains) (59049) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -1784145647367326687478989, hi := 1784145647367326687478989} +lemma tr11_contains : tr11.Contains (fullMoment false true 40 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 40 mixed_40_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := -365892306114699728667126851, hi := -57243820768756769616437610} +lemma t11_checked : ((hm40_1_0_13.realAnswer).add tr11).scale (177147) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 40 (3/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_13.realContains tr11_contains) (177147) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -46701938752094289344693015302, hi := 46701938752094289344693015302} +lemma t12_contains : t12.Contains (sourcePower true 40 (3/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 12 coarse_40_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -14226944918381974251029064191, hi := 14226944918381974251029064191} +lemma t13_contains : t13.Contains (sourcePower true 40 (3/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 13 coarse_40_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -4084415447830513492880711507, hi := 4084415447830513492880711507} +lemma t14_contains : t14.Contains (sourcePower true 40 (3/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 14 coarse_40_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -1108565585779813984855987127, hi := 1108565585779813984855987127} +lemma t15_contains : t15.Contains (sourcePower true 40 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 15 coarse_40_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -285264936549415184266627703, hi := 285264936549415184266627703} +lemma t16_contains : t16.Contains (sourcePower true 40 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 16 coarse_40_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -69779472687187080016182321, hi := 69779472687187080016182321} +lemma t17_contains : t17.Contains (sourcePower true 40 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 17 coarse_40_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -16264874903222436903988511, hi := 16264874903222436903988511} +lemma t18_contains : t18.Contains (sourcePower true 40 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 18 coarse_40_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3620774099258225813167868, hi := 3620774099258225813167868} +lemma t19_contains : t19.Contains (sourcePower true 40 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 19 coarse_40_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -771458127210527778096725, hi := 771458127210527778096725} +lemma t20_contains : t20.Contains (sourcePower true 40 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 20 coarse_40_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -157645020874272310770310, hi := 157645020874272310770310} +lemma t21_contains : t21.Contains (sourcePower true 40 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 21 coarse_40_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -30958614408405690714176, hi := 30958614408405690714176} +lemma t22_contains : t22.Contains (sourcePower true 40 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 22 coarse_40_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -5854476527190135979518, hi := 5854476527190135979518} +lemma t23_contains : t23.Contains (sourcePower true 40 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 23 coarse_40_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -1068277418013106576834, hi := 1068277418013106576834} +lemma t24_contains : t24.Contains (sourcePower true 40 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 24 coarse_40_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -188487704728201524407, hi := 188487704728201524407} +lemma t25_contains : t25.Contains (sourcePower true 40 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 25 coarse_40_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -32228882231906787482, hi := 32228882231906787482} +lemma t26_contains : t26.Contains (sourcePower true 40 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 26 coarse_40_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -5352951031644319619, hi := 5352951031644319619} +lemma t27_contains : t27.Contains (sourcePower true 40 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 27 coarse_40_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -865811656978999856, hi := 865811656978999856} +lemma t28_contains : t28.Contains (sourcePower true 40 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (3/2) 2 28 coarse_40_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 40 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr2,precision] +noncomputable def t2 : RBox := {lo := 9282597485850395325949473363, hi := 9971600113049426126769130493} +lemma t2_checked : ((hm40_0_0_4.realAnswer).add tr2).scale (-1) 4=t2 := by decide +kernel +lemma t2_contains : t2.Contains (sourcePower false 40 (-1/2) 2 2) := by + rw [← t2_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_4.realContains tr2_contains) (-1) 4 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr3 : RBox := {lo := -1127662331737765183970897290, hi := 1127662331737765183970897290} +lemma tr3_contains : tr3.Contains (fullMoment true true 40 5) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 5 40 mixed_40_5) <;> norm_num [tr3,precision] +noncomputable def t3 : RBox := {lo := 5602607539014213303196937531, hi := 5884523121955157665667604293} +lemma t3_checked : ((hm40_0_0_5.realAnswer).add tr3).scale (1) 8=t3 := by decide +kernel +lemma t3_contains : t3.Contains (sourcePower false 40 (-1/2) 2 3) := by + rw [← t3_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_5.realContains tr3_contains) (1) 8 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr4 : RBox := {lo := -770206922867263530745282246, hi := 770206922867263530745282246} +lemma tr4_contains : tr4.Contains (fullMoment true true 40 6) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 6 40 mixed_40_6) <;> norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -1584628566210878089358642595, hi := -1488352700851185697625239898} +lemma t4_checked : ((hm40_0_0_6.realAnswer).add tr4).scale (-1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower false 40 (-1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_6.realContains tr4_contains) (-1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -451541240469518315478157760, hi := 451541240469518315478157760} +lemma tr5_contains : tr5.Contains (fullMoment true true 40 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 7 40 mixed_40_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -269373990333691123309463054, hi := -241152662804127985338264882} +lemma t5_checked : ((hm40_0_0_7.realAnswer).add tr5).scale (1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower false 40 (-1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_7.realContains tr5_contains) (1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -231919502450331624380412515, hi := 231919502450331624380412515} +lemma tr6_contains : tr6.Contains (fullMoment true true 40 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 8 40 mixed_40_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 81222861884340297713576994, hi := 88470346335945702985876294} +lemma t6_checked : ((hm40_0_0_8.realAnswer).add tr6).scale (-1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower false 40 (-1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_8.realContains tr6_contains) (-1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -105999991106160182956535889, hi := 105999991106160182956535889} +lemma tr7_contains : tr7.Contains (fullMoment true true 40 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 9 40 mixed_40_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 5584022768478394547002286, hi := 7240272629516472088205525} +lemma t7_checked : ((hm40_0_0_9.realAnswer).add tr7).scale (1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower false 40 (-1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_9.realContains tr7_contains) (1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -43645893453395484376071552, hi := 43645893453395484376071552} +lemma tr8_contains : tr8.Contains (fullMoment true true 40 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 10 40 mixed_40_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -2774099680888621673549565, hi := -2433116138283450864454555} +lemma t8_checked : ((hm40_0_0_10.realAnswer).add tr8).scale (-1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower false 40 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_10.realContains tr8_contains) (-1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -16351797364128125134540904, hi := 16351797364128125134540904} +lemma tr9_contains : tr9.Contains (fullMoment true true 40 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 11 40 mixed_40_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -136363489713542850459441, hi := -72489281259860685979043} +lemma t9_checked : ((hm40_0_0_11.realAnswer).add tr9).scale (1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower false 40 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_11.realContains tr9_contains) (1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -5619945822412676134103778, hi := 5619945822412676134103778} +lemma tr10_contains : tr10.Contains (fullMoment true true 40 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 12 40 mixed_40_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 46482870629251231246933, hi := 57459327313656681581606} +lemma t10_checked : ((hm40_0_0_12.realAnswer).add tr10).scale (-1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower false 40 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_12.realContains tr10_contains) (-1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -1784145647367326687478989, hi := 1784145647367326687478989} +lemma tr11_contains : tr11.Contains (fullMoment true true 40 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap true 13 40 mixed_40_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := 330399791728981569743, hi := 2072729525486665659349} +lemma t11_checked : ((hm40_0_0_13.realAnswer).add tr11).scale (1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower false 40 (-1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm40_0_0_13.realContains tr11_contains) (1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -87877937065627773063601, hi := 87877937065627773063601} +lemma t12_contains : t12.Contains (sourcePower false 40 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 12 coarse_40_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8923502275499992317134, hi := 8923502275499992317134} +lemma t13_contains : t13.Contains (sourcePower false 40 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 13 coarse_40_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -853949805618751343127, hi := 853949805618751343127} +lemma t14_contains : t14.Contains (sourcePower false 40 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 14 coarse_40_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77257841714342004228, hi := 77257841714342004228} +lemma t15_contains : t15.Contains (sourcePower false 40 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 15 coarse_40_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6626867968629136335, hi := 6626867968629136335} +lemma t16_contains : t16.Contains (sourcePower false 40 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 16 coarse_40_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -540339047637620529, hi := 540339047637620529} +lemma t17_contains : t17.Contains (sourcePower false 40 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 17 coarse_40_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -41982485090566382, hi := 41982485090566382} +lemma t18_contains : t18.Contains (sourcePower false 40 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 18 coarse_40_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3115283610497797, hi := 3115283610497797} +lemma t19_contains : t19.Contains (sourcePower false 40 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 19 coarse_40_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -221252030090899, hi := 221252030090899} +lemma t20_contains : t20.Contains (sourcePower false 40 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 20 coarse_40_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15070716811844, hi := 15070716811844} +lemma t21_contains : t21.Contains (sourcePower false 40 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 21 coarse_40_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -986538211079, hi := 986538211079} +lemma t22_contains : t22.Contains (sourcePower false 40 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 22 coarse_40_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -62186943337, hi := 62186943337} +lemma t23_contains : t23.Contains (sourcePower false 40 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 23 coarse_40_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -3782456437, hi := 3782456437} +lemma t24_contains : t24.Contains (sourcePower false 40 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 24 coarse_40_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -222459860, hi := 222459860} +lemma t25_contains : t25.Contains (sourcePower false 40 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 25 coarse_40_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -12679223, hi := 12679223} +lemma t26_contains : t26.Contains (sourcePower false 40 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 26 coarse_40_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -701972, hi := 701972} +lemma t27_contains : t27.Contains (sourcePower false 40 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 27 coarse_40_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -37847, hi := 37847} +lemma t28_contains : t28.Contains (sourcePower false 40 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 40 (-1/2) 2 28 coarse_40_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 40 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [tr2,precision] +noncomputable def t2 : RBox := {lo := 10136097359637116657189230037, hi := 10825099986827544539965530404} +lemma t2_checked : ((hm40_1_0_4.realAnswer).add tr2).scale (1) 4=t2 := by decide +kernel +lemma t2_contains : t2.Contains (sourcePower true 40 (-1/2) 2 2) := by + rw [← t2_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_4.realContains tr2_contains) (1) 4 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr3 : RBox := {lo := -1127662331737765183970897290, hi := 1127662331737765183970897290} +lemma tr3_contains : tr3.Contains (fullMoment false true 40 5) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 5 40 mixed_40_5) <;> norm_num [tr3,precision] +noncomputable def t3 : RBox := {lo := 6033433227725178675241392922, hi := 6315348810664106520885659013} +lemma t3_checked : ((hm40_1_0_5.realAnswer).add tr3).scale (-1) 8=t3 := by decide +kernel +lemma t3_contains : t3.Contains (sourcePower true 40 (-1/2) 2 3) := by + rw [← t3_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_5.realContains tr3_contains) (-1) 8 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr4 : RBox := {lo := -770206922867263530745282246, hi := 770206922867263530745282246} +lemma tr4_contains : tr4.Contains (fullMoment false true 40 6) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 6 40 mixed_40_6) <;> norm_num [tr4,precision] +noncomputable def t4 : RBox := {lo := -1715584254096443165867659500, hi := -1619308388737148273653403525} +lemma t4_checked : ((hm40_1_0_6.realAnswer).add tr4).scale (1) 16=t4 := by decide +kernel +lemma t4_contains : t4.Contains (sourcePower true 40 (-1/2) 2 4) := by + rw [← t4_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_6.realContains tr4_contains) (1) 16 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr5 : RBox := {lo := -451541240469518315478157760, hi := 451541240469518315478157760} +lemma tr5_contains : tr5.Contains (fullMoment false true 40 7) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 7 40 mixed_40_7) <;> norm_num [tr5,precision] +noncomputable def t5 : RBox := {lo := -286384682349957752812393969, hi := -258163354820462144379164841} +lemma t5_checked : ((hm40_1_0_7.realAnswer).add tr5).scale (-1) 32=t5 := by decide +kernel +lemma t5_contains : t5.Contains (sourcePower true 40 (-1/2) 2 5) := by + rw [← t5_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_7.realContains tr5_contains) (-1) 32 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr6 : RBox := {lo := -231919502450331624380412515, hi := 231919502450331624380412515} +lemma tr6_contains : tr6.Contains (fullMoment false true 40 8) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 8 40 mixed_40_8) <;> norm_num [tr6,precision] +noncomputable def t6 : RBox := {lo := 88349140249190500846757200, hi := 95596624700785826915755000} +lemma t6_checked : ((hm40_1_0_8.realAnswer).add tr6).scale (1) 64=t6 := by decide +kernel +lemma t6_contains : t6.Contains (sourcePower true 40 (-1/2) 2 6) := by + rw [← t6_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_8.realContains tr6_contains) (1) 64 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr7 : RBox := {lo := -105999991106160182956535889, hi := 105999991106160182956535889} +lemma tr7_contains : tr7.Contains (fullMoment false true 40 9) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 9 40 mixed_40_9) <;> norm_num [tr7,precision] +noncomputable def t7 : RBox := {lo := 5921641182169731041501823, hi := 7577891043206466621972072} +lemma t7_checked : ((hm40_1_0_9.realAnswer).add tr7).scale (-1) 128=t7 := by decide +kernel +lemma t7_contains : t7.Contains (sourcePower true 40 (-1/2) 2 7) := by + rw [← t7_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_9.realContains tr7_contains) (-1) 128 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr8 : RBox := {lo := -43645893453395484376071552, hi := 43645893453395484376071552} +lemma tr8_contains : tr8.Contains (fullMoment false true 40 10) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 10 40 mixed_40_10) <;> norm_num [tr8,precision] +noncomputable def t8 : RBox := {lo := -2990551885083084274534201, hi := -2649568342478074802890628} +lemma t8_checked : ((hm40_1_0_10.realAnswer).add tr8).scale (1) 256=t8 := by decide +kernel +lemma t8_contains : t8.Contains (sourcePower true 40 (-1/2) 2 8) := by + rw [← t8_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_10.realContains tr8_contains) (1) 256 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr9 : RBox := {lo := -16351797364128125134540904, hi := 16351797364128125134540904} +lemma tr9_contains : tr9.Contains (fullMoment false true 40 11) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 11 40 mixed_40_11) <;> norm_num [tr9,precision] +noncomputable def t9 : RBox := {lo := -139479210398009337999242, hi := -75605001944344863961579} +lemma t9_checked : ((hm40_1_0_11.realAnswer).add tr9).scale (-1) 512=t9 := by decide +kernel +lemma t9_contains : t9.Contains (sourcePower true 40 (-1/2) 2 9) := by + rw [← t9_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_11.realContains tr9_contains) (-1) 512 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr10 : RBox := {lo := -5619945822412676134103778, hi := 5619945822412676134103778} +lemma tr10_contains : tr10.Contains (fullMoment false true 40 12) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 12 40 mixed_40_12) <;> norm_num [tr10,precision] +noncomputable def t10 : RBox := {lo := 50770990775776838914059, hi := 61747447460180505484450} +lemma t10_checked : ((hm40_1_0_12.realAnswer).add tr10).scale (1) 1024=t10 := by decide +kernel +lemma t10_contains : t10.Contains (sourcePower true 40 (-1/2) 2 10) := by + rw [← t10_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_12.realContains tr10_contains) (1) 1024 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def tr11 : RBox := {lo := -1784145647367326687478989, hi := 1784145647367326687478989} +lemma tr11_contains : tr11.Contains (fullMoment false true 40 13) := by + apply RBox.contains_of_abs (fullMoment_transformed_cap false 13 40 mixed_40_13) <;> norm_num [tr11,precision] +noncomputable def t11 : RBox := {lo := 323143043736313737271, hi := 2065472777493831273842} +lemma t11_checked : ((hm40_1_0_13.realAnswer).add tr11).scale (-1) 2048=t11 := by decide +kernel +lemma t11_contains : t11.Contains (sourcePower true 40 (-1/2) 2 11) := by + rw [← t11_checked] + convert RBox.contains_scale (RBox.contains_add hm40_1_0_13.realContains tr11_contains) (-1) 2048 (by norm_num) using 1 + norm_num [sourcePower,normalizedH] +noncomputable def t12 : RBox := {lo := -87877937065627773063601, hi := 87877937065627773063601} +lemma t12_contains : t12.Contains (sourcePower true 40 (-1/2) 2 12) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 12 coarse_40_14) <;> norm_num [t12,precision] +noncomputable def t13 : RBox := {lo := -8923502275499992317134, hi := 8923502275499992317134} +lemma t13_contains : t13.Contains (sourcePower true 40 (-1/2) 2 13) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 13 coarse_40_15) <;> norm_num [t13,precision] +noncomputable def t14 : RBox := {lo := -853949805618751343127, hi := 853949805618751343127} +lemma t14_contains : t14.Contains (sourcePower true 40 (-1/2) 2 14) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 14 coarse_40_16) <;> norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -77257841714342004228, hi := 77257841714342004228} +lemma t15_contains : t15.Contains (sourcePower true 40 (-1/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 15 coarse_40_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -6626867968629136335, hi := 6626867968629136335} +lemma t16_contains : t16.Contains (sourcePower true 40 (-1/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 16 coarse_40_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -540339047637620529, hi := 540339047637620529} +lemma t17_contains : t17.Contains (sourcePower true 40 (-1/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 17 coarse_40_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -41982485090566382, hi := 41982485090566382} +lemma t18_contains : t18.Contains (sourcePower true 40 (-1/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 18 coarse_40_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -3115283610497797, hi := 3115283610497797} +lemma t19_contains : t19.Contains (sourcePower true 40 (-1/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 19 coarse_40_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -221252030090899, hi := 221252030090899} +lemma t20_contains : t20.Contains (sourcePower true 40 (-1/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 20 coarse_40_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -15070716811844, hi := 15070716811844} +lemma t21_contains : t21.Contains (sourcePower true 40 (-1/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 21 coarse_40_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -986538211079, hi := 986538211079} +lemma t22_contains : t22.Contains (sourcePower true 40 (-1/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 22 coarse_40_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -62186943337, hi := 62186943337} +lemma t23_contains : t23.Contains (sourcePower true 40 (-1/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 23 coarse_40_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -3782456437, hi := 3782456437} +lemma t24_contains : t24.Contains (sourcePower true 40 (-1/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 24 coarse_40_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -222459860, hi := 222459860} +lemma t25_contains : t25.Contains (sourcePower true 40 (-1/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 25 coarse_40_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -12679223, hi := 12679223} +lemma t26_contains : t26.Contains (sourcePower true 40 (-1/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 26 coarse_40_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -701972, hi := 701972} +lemma t27_contains : t27.Contains (sourcePower true 40 (-1/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 27 coarse_40_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -37847, hi := 37847} +lemma t28_contains : t28.Contains (sourcePower true 40 (-1/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 40 (-1/2) 2 28 coarse_40_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 40 (-1/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -52937841163001576803968807, hi := 52937841163001576803968807} +lemma t15_contains : t15.Contains (sourcePower false 7 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 15 coarse_7_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -13154196706614470209797439, hi := 13154196706614470209797439} +lemma t16_contains : t16.Contains (sourcePower false 7 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 16 coarse_7_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -3139490217511196715330409, hi := 3139490217511196715330409} +lemma t17_contains : t17.Contains (sourcePower false 7 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 17 coarse_7_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -721027148307673611577041, hi := 721027148307673611577041} +lemma t18_contains : t18.Contains (sourcePower false 7 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 18 coarse_7_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -159653917264451567983550, hi := 159653917264451567983550} +lemma t19_contains : t19.Contains (sourcePower false 7 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 19 coarse_7_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -34150320816868495224516, hi := 34150320816868495224516} +lemma t20_contains : t20.Contains (sourcePower false 7 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 20 coarse_7_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -7070434194851407944553, hi := 7070434194851407944553} +lemma t21_contains : t21.Contains (sourcePower false 7 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 21 coarse_7_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1419603453451501127661, hi := 1419603453451501127661} +lemma t22_contains : t22.Contains (sourcePower false 7 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 22 coarse_7_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -276927823249205454678, hi := 276927823249205454678} +lemma t23_contains : t23.Contains (sourcePower false 7 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 23 coarse_7_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -52580065247005273152, hi := 52580065247005273152} +lemma t24_contains : t24.Contains (sourcePower false 7 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 24 coarse_7_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -9733461848536277803, hi := 9733461848536277803} +lemma t25_contains : t25.Contains (sourcePower false 7 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 25 coarse_7_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1759524875452051454, hi := 1759524875452051454} +lemma t26_contains : t26.Contains (sourcePower false 7 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 26 coarse_7_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -311059105492441427, hi := 311059105492441427} +lemma t27_contains : t27.Contains (sourcePower false 7 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 27 coarse_7_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -53850542623120176, hi := 53850542623120176} +lemma t28_contains : t28.Contains (sourcePower false 7 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (1/1) 2 28 coarse_7_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 7 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -52937841163001576803968807, hi := 52937841163001576803968807} +lemma t15_contains : t15.Contains (sourcePower true 7 (1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 15 coarse_7_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -13154196706614470209797439, hi := 13154196706614470209797439} +lemma t16_contains : t16.Contains (sourcePower true 7 (1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 16 coarse_7_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -3139490217511196715330409, hi := 3139490217511196715330409} +lemma t17_contains : t17.Contains (sourcePower true 7 (1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 17 coarse_7_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -721027148307673611577041, hi := 721027148307673611577041} +lemma t18_contains : t18.Contains (sourcePower true 7 (1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 18 coarse_7_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -159653917264451567983550, hi := 159653917264451567983550} +lemma t19_contains : t19.Contains (sourcePower true 7 (1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 19 coarse_7_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -34150320816868495224516, hi := 34150320816868495224516} +lemma t20_contains : t20.Contains (sourcePower true 7 (1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 20 coarse_7_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -7070434194851407944553, hi := 7070434194851407944553} +lemma t21_contains : t21.Contains (sourcePower true 7 (1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 21 coarse_7_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -1419603453451501127661, hi := 1419603453451501127661} +lemma t22_contains : t22.Contains (sourcePower true 7 (1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 22 coarse_7_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -276927823249205454678, hi := 276927823249205454678} +lemma t23_contains : t23.Contains (sourcePower true 7 (1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 23 coarse_7_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -52580065247005273152, hi := 52580065247005273152} +lemma t24_contains : t24.Contains (sourcePower true 7 (1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 24 coarse_7_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -9733461848536277803, hi := 9733461848536277803} +lemma t25_contains : t25.Contains (sourcePower true 7 (1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 25 coarse_7_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -1759524875452051454, hi := 1759524875452051454} +lemma t26_contains : t26.Contains (sourcePower true 7 (1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 26 coarse_7_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -311059105492441427, hi := 311059105492441427} +lemma t27_contains : t27.Contains (sourcePower true 7 (1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 27 coarse_7_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -53850542623120176, hi := 53850542623120176} +lemma t28_contains : t28.Contains (sourcePower true 7 (1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (1/1) 2 28 coarse_7_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 7 (1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -23181157215230757642013722002, hi := 23181157215230757642013722002} +lemma t15_contains : t15.Contains (sourcePower false 7 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 15 coarse_7_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -8640213556041747340148343249, hi := 8640213556041747340148343249} +lemma t16_contains : t16.Contains (sourcePower false 7 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 16 coarse_7_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -3093218066606913743155163705, hi := 3093218066606913743155163705} +lemma t17_contains : t17.Contains (sourcePower false 7 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 17 coarse_7_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -1065600167768991214941304342, hi := 1065600167768991214941304342} +lemma t18_contains : t18.Contains (sourcePower false 7 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 18 coarse_7_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -353926841911464894018194304, hi := 353926841911464894018194304} +lemma t19_contains : t19.Contains (sourcePower false 7 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 19 coarse_7_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -113558584130671164338288672, hi := 113558584130671164338288672} +lemma t20_contains : t20.Contains (sourcePower false 7 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 20 coarse_7_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -35266513336522412873203574, hi := 35266513336522412873203574} +lemma t21_contains : t21.Contains (sourcePower false 7 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 21 coarse_7_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -10621228359676316661276951, hi := 10621228359676316661276951} +lemma t22_contains : t22.Contains (sourcePower false 7 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 22 coarse_7_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -3107889364519333518196917, hi := 3107889364519333518196917} +lemma t23_contains : t23.Contains (sourcePower false 7 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 23 coarse_7_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -885138717642571691851745, hi := 885138717642571691851745} +lemma t24_contains : t24.Contains (sourcePower false 7 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 24 coarse_7_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -245781283221030089397521, hi := 245781283221030089397521} +lemma t25_contains : t25.Contains (sourcePower false 7 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 25 coarse_7_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -66645088121390481702150, hi := 66645088121390481702150} +lemma t26_contains : t26.Contains (sourcePower false 7 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 26 coarse_7_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -17672863099913800238592, hi := 17672863099913800238592} +lemma t27_contains : t27.Contains (sourcePower false 7 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 27 coarse_7_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -4589288261443940474514, hi := 4589288261443940474514} +lemma t28_contains : t28.Contains (sourcePower false 7 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 7 (-3/2) 2 28 coarse_7_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 7 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -23181157215230757642013722002, hi := 23181157215230757642013722002} +lemma t15_contains : t15.Contains (sourcePower true 7 (-3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 15 coarse_7_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -8640213556041747340148343249, hi := 8640213556041747340148343249} +lemma t16_contains : t16.Contains (sourcePower true 7 (-3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 16 coarse_7_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -3093218066606913743155163705, hi := 3093218066606913743155163705} +lemma t17_contains : t17.Contains (sourcePower true 7 (-3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 17 coarse_7_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -1065600167768991214941304342, hi := 1065600167768991214941304342} +lemma t18_contains : t18.Contains (sourcePower true 7 (-3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 18 coarse_7_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -353926841911464894018194304, hi := 353926841911464894018194304} +lemma t19_contains : t19.Contains (sourcePower true 7 (-3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 19 coarse_7_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -113558584130671164338288672, hi := 113558584130671164338288672} +lemma t20_contains : t20.Contains (sourcePower true 7 (-3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 20 coarse_7_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -35266513336522412873203574, hi := 35266513336522412873203574} +lemma t21_contains : t21.Contains (sourcePower true 7 (-3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 21 coarse_7_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -10621228359676316661276951, hi := 10621228359676316661276951} +lemma t22_contains : t22.Contains (sourcePower true 7 (-3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 22 coarse_7_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -3107889364519333518196917, hi := 3107889364519333518196917} +lemma t23_contains : t23.Contains (sourcePower true 7 (-3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 23 coarse_7_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -885138717642571691851745, hi := 885138717642571691851745} +lemma t24_contains : t24.Contains (sourcePower true 7 (-3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 24 coarse_7_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -245781283221030089397521, hi := 245781283221030089397521} +lemma t25_contains : t25.Contains (sourcePower true 7 (-3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 25 coarse_7_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -66645088121390481702150, hi := 66645088121390481702150} +lemma t26_contains : t26.Contains (sourcePower true 7 (-3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 26 coarse_7_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -17672863099913800238592, hi := 17672863099913800238592} +lemma t27_contains : t27.Contains (sourcePower true 7 (-3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 27 coarse_7_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -4589288261443940474514, hi := 4589288261443940474514} +lemma t28_contains : t28.Contains (sourcePower true 7 (-3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 7 (-3/2) 2 28 coarse_7_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 7 (-3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -8955548517723090074167299394, hi := 8955548517723090074167299394} +lemma t15_contains : t15.Contains (sourcePower false 9 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 15 coarse_9_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -3117343267724612720253941592, hi := 3117343267724612720253941592} +lemma t16_contains : t16.Contains (sourcePower false 9 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 16 coarse_9_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1043611529103946578452946112, hi := 1043611529103946578452946112} +lemma t17_contains : t17.Contains (sourcePower false 9 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 17 coarse_9_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -336330703192688062311941054, hi := 336330703192688062311941054} +lemma t18_contains : t18.Contains (sourcePower false 9 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 18 coarse_9_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -104464247929191556467561863, hi := 104464247929191556467561863} +lemma t19_contains : t19.Contains (sourcePower false 9 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 19 coarse_9_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -31311921055406004370038208, hi := 31311921055406004370038208} +lemma t20_contains : t20.Contains (sourcePower false 9 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 20 coarse_9_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -9069918620381098445985624, hi := 9069918620381098445985624} +lemma t21_contains : t21.Contains (sourcePower false 9 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 21 coarse_9_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -2542619576258117963444198, hi := 2542619576258117963444198} +lemma t22_contains : t22.Contains (sourcePower false 9 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 22 coarse_9_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -690845821005163497155363, hi := 690845821005163497155363} +lemma t23_contains : t23.Contains (sourcePower false 9 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 23 coarse_9_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -182193425404558644194995, hi := 182193425404558644194995} +lemma t24_contains : t24.Contains (sourcePower false 9 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 24 coarse_9_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -46703709063382411011594, hi := 46703709063382411011594} +lemma t25_contains : t25.Contains (sourcePower false 9 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 25 coarse_9_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -11652904893164252489548, hi := 11652904893164252489548} +lemma t26_contains : t26.Contains (sourcePower false 9 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 26 coarse_9_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -2833736695269006434692, hi := 2833736695269006434692} +lemma t27_contains : t27.Contains (sourcePower false 9 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 27 coarse_9_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -672493511073217294268, hi := 672493511073217294268} +lemma t28_contains : t28.Contains (sourcePower false 9 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (3/2) 2 28 coarse_9_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 9 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -8955548517723090074167299394, hi := 8955548517723090074167299394} +lemma t15_contains : t15.Contains (sourcePower true 9 (3/2) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 15 coarse_9_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -3117343267724612720253941592, hi := 3117343267724612720253941592} +lemma t16_contains : t16.Contains (sourcePower true 9 (3/2) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 16 coarse_9_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1043611529103946578452946112, hi := 1043611529103946578452946112} +lemma t17_contains : t17.Contains (sourcePower true 9 (3/2) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 17 coarse_9_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -336330703192688062311941054, hi := 336330703192688062311941054} +lemma t18_contains : t18.Contains (sourcePower true 9 (3/2) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 18 coarse_9_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -104464247929191556467561863, hi := 104464247929191556467561863} +lemma t19_contains : t19.Contains (sourcePower true 9 (3/2) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 19 coarse_9_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -31311921055406004370038208, hi := 31311921055406004370038208} +lemma t20_contains : t20.Contains (sourcePower true 9 (3/2) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 20 coarse_9_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -9069918620381098445985624, hi := 9069918620381098445985624} +lemma t21_contains : t21.Contains (sourcePower true 9 (3/2) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 21 coarse_9_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -2542619576258117963444198, hi := 2542619576258117963444198} +lemma t22_contains : t22.Contains (sourcePower true 9 (3/2) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 22 coarse_9_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -690845821005163497155363, hi := 690845821005163497155363} +lemma t23_contains : t23.Contains (sourcePower true 9 (3/2) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 23 coarse_9_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -182193425404558644194995, hi := 182193425404558644194995} +lemma t24_contains : t24.Contains (sourcePower true 9 (3/2) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 24 coarse_9_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -46703709063382411011594, hi := 46703709063382411011594} +lemma t25_contains : t25.Contains (sourcePower true 9 (3/2) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 25 coarse_9_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -11652904893164252489548, hi := 11652904893164252489548} +lemma t26_contains : t26.Contains (sourcePower true 9 (3/2) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 26 coarse_9_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -2833736695269006434692, hi := 2833736695269006434692} +lemma t27_contains : t27.Contains (sourcePower true 9 (3/2) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 27 coarse_9_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -672493511073217294268, hi := 672493511073217294268} +lemma t28_contains : t28.Contains (sourcePower true 9 (3/2) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (3/2) 2 28 coarse_9_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 9 (3/2) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -20451412349996429383110091, hi := 20451412349996429383110091} +lemma t15_contains : t15.Contains (sourcePower false 9 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 15 coarse_9_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -4745964469479573583190281, hi := 4745964469479573583190281} +lemma t16_contains : t16.Contains (sourcePower false 9 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 16 coarse_9_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1059223150761490721759307, hi := 1059223150761490721759307} +lemma t17_contains : t17.Contains (sourcePower false 9 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 17 coarse_9_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -227574633663074075069637, hi := 227574633663074075069637} +lemma t18_contains : t18.Contains (sourcePower false 9 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 18 coarse_9_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -47123089918544105667460, hi := 47123089918544105667460} +lemma t19_contains : t19.Contains (sourcePower false 9 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 19 coarse_9_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -9416392055435665704734, hi := 9416392055435665704734} +lemma t20_contains : t20.Contains (sourcePower false 9 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 20 coarse_9_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -1818389647599499070968, hi := 1818389647599499070968} +lemma t21_contains : t21.Contains (sourcePower false 9 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 21 coarse_9_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -339839367824252017804, hi := 339839367824252017804} +lemma t22_contains : t22.Contains (sourcePower false 9 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 22 coarse_9_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -61557670487205021490, hi := 61557670487205021490} +lemma t23_contains : t23.Contains (sourcePower false 9 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 23 coarse_9_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -10822871042022909343, hi := 10822871042022909343} +lemma t24_contains : t24.Contains (sourcePower false 9 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 24 coarse_9_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -1849566266381483885, hi := 1849566266381483885} +lemma t25_contains : t25.Contains (sourcePower false 9 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 25 coarse_9_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -307653221096403378, hi := 307653221096403378} +lemma t26_contains : t26.Contains (sourcePower false 9 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 26 coarse_9_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -49876445975286458, hi := 49876445975286458} +lemma t27_contains : t27.Contains (sourcePower false 9 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 27 coarse_9_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -7891014557979819, hi := 7891014557979819} +lemma t28_contains : t28.Contains (sourcePower false 9 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap false 9 (-1/1) 2 28 coarse_9_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower false 9 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 norm_num [t14,precision] +noncomputable def t15 : RBox := {lo := -20451412349996429383110091, hi := 20451412349996429383110091} +lemma t15_contains : t15.Contains (sourcePower true 9 (-1/1) 2 15) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 15 coarse_9_17) <;> norm_num [t15,precision] +noncomputable def t16 : RBox := {lo := -4745964469479573583190281, hi := 4745964469479573583190281} +lemma t16_contains : t16.Contains (sourcePower true 9 (-1/1) 2 16) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 16 coarse_9_18) <;> norm_num [t16,precision] +noncomputable def t17 : RBox := {lo := -1059223150761490721759307, hi := 1059223150761490721759307} +lemma t17_contains : t17.Contains (sourcePower true 9 (-1/1) 2 17) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 17 coarse_9_19) <;> norm_num [t17,precision] +noncomputable def t18 : RBox := {lo := -227574633663074075069637, hi := 227574633663074075069637} +lemma t18_contains : t18.Contains (sourcePower true 9 (-1/1) 2 18) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 18 coarse_9_20) <;> norm_num [t18,precision] +noncomputable def t19 : RBox := {lo := -47123089918544105667460, hi := 47123089918544105667460} +lemma t19_contains : t19.Contains (sourcePower true 9 (-1/1) 2 19) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 19 coarse_9_21) <;> norm_num [t19,precision] +noncomputable def t20 : RBox := {lo := -9416392055435665704734, hi := 9416392055435665704734} +lemma t20_contains : t20.Contains (sourcePower true 9 (-1/1) 2 20) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 20 coarse_9_22) <;> norm_num [t20,precision] +noncomputable def t21 : RBox := {lo := -1818389647599499070968, hi := 1818389647599499070968} +lemma t21_contains : t21.Contains (sourcePower true 9 (-1/1) 2 21) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 21 coarse_9_23) <;> norm_num [t21,precision] +noncomputable def t22 : RBox := {lo := -339839367824252017804, hi := 339839367824252017804} +lemma t22_contains : t22.Contains (sourcePower true 9 (-1/1) 2 22) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 22 coarse_9_24) <;> norm_num [t22,precision] +noncomputable def t23 : RBox := {lo := -61557670487205021490, hi := 61557670487205021490} +lemma t23_contains : t23.Contains (sourcePower true 9 (-1/1) 2 23) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 23 coarse_9_25) <;> norm_num [t23,precision] +noncomputable def t24 : RBox := {lo := -10822871042022909343, hi := 10822871042022909343} +lemma t24_contains : t24.Contains (sourcePower true 9 (-1/1) 2 24) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 24 coarse_9_26) <;> norm_num [t24,precision] +noncomputable def t25 : RBox := {lo := -1849566266381483885, hi := 1849566266381483885} +lemma t25_contains : t25.Contains (sourcePower true 9 (-1/1) 2 25) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 25 coarse_9_27) <;> norm_num [t25,precision] +noncomputable def t26 : RBox := {lo := -307653221096403378, hi := 307653221096403378} +lemma t26_contains : t26.Contains (sourcePower true 9 (-1/1) 2 26) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 26 coarse_9_28) <;> norm_num [t26,precision] +noncomputable def t27 : RBox := {lo := -49876445975286458, hi := 49876445975286458} +lemma t27_contains : t27.Contains (sourcePower true 9 (-1/1) 2 27) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 27 coarse_9_29) <;> norm_num [t27,precision] +noncomputable def t28 : RBox := {lo := -7891014557979819, hi := 7891014557979819} +lemma t28_contains : t28.Contains (sourcePower true 9 (-1/1) 2 28) := by + apply RBox.contains_of_abs (sourcePower_of_cap true 9 (-1/1) 2 28 coarse_9_30) <;> norm_num [t28,precision] +noncomputable def ts : Fin 29 → RBox := ![t0,t1,t2,t3,t4,t5,t6,t7,t8,t9,t10,t11,t12,t13,t14,t15,t16,t17,t18,t19,t20,t21,t22,t23,t24,t25,t26,t27,t28] +lemma ts_contains (r : Fin 29) : (ts r).Contains (sourcePower true 9 (-1/1) 2 r.val) := by + fin_cases r + · exact t0_contains + · exact t1_contains + · exact t2_contains + · exact t3_contains + · exact t4_contains + · exact t5_contains + · exact t6_contains + · exact t7_contains + · exact t8_contains + · exact t9_contains + · exact t10_contains + · exact t11_contains + · exact t12_contains + · exact t13_contains + · exact t14_contains + · exact t15_contains + · exact t16_contains + · exact t17_contains + · exact t18_contains + · exact t19_contains + · exact t20_contains + · exact t21_contains + · exact t22_contains + · exact t23_contains + · exact t24_contains + · exact t25_contains + · exact t26_contains + · exact t27_contains + · exact t28_contains +lemma bound0 : (9:ℝ)/1000 S (columnVector (jNode j) (jDeriv j)) (jNode i,jDeriv i) +noncomputable def dentry0_0 : RBox := ⟨(-245926663229645305249767762805),(-245926663229645304859284756738)⟩ +lemma dentry0_0_contains : dentry0_0.Contains (S (columnVector node1 false) (node1,false)) := by + have h0 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) false false cm1_1_0_0.contains + have h1 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) false true cm1_1_0_1.contains + have hh := S_column_value_contains (m:=node1) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry3_0 : RBox := ⟨424700589287547025857931921651,424700589287547027999275868645⟩ +lemma dentry3_0_contains : dentry3_0.Contains (S (columnVector node1 false) (node1,true)) := by + have h0 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) false false cm1_1_0_0.contains + have h1 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) false true cm1_1_0_1.contains + have hh := S_column_derivative_contains (m:=node1) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry0_3 : RBox := ⟨30452555066926640622749259400,30452555066926640828004301927⟩ +lemma dentry0_3_contains : dentry0_3.Contains (S (columnVector node1 true) (node1,false)) := by + have h0 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) true false cm1_1_1_0.contains + have h1 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) true true cm1_1_1_1.contains + have hh := S_column_value_contains (m:=node1) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry3_3 : RBox := ⟨931968827424315928087138852293,931968827424315929373850684394⟩ +lemma dentry3_3_contains : dentry3_3.Contains (S (columnVector node1 true) (node1,true)) := by + have h0 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) true false cm1_1_1_0.contains + have h1 := K_column_contains (n:=node1) (m:=1) (by decide) (by decide) true true cm1_1_1_1.contains + have hh := S_column_derivative_contains (m:=node1) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry1_0 : RBox := ⟨(-23655100336718873202242240942),(-23655100336718873120273669237)⟩ +lemma dentry1_0_contains : dentry1_0.Contains (S (columnVector node1 false) (node3,false)) := by + have h0 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) false false cm1_3_0_0.contains + have h1 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) false true cm1_3_0_1.contains + have hh := S_column_value_contains (m:=node3) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry4_0 : RBox := ⟨145671047970350036773325436387,145671047970350037199231909594⟩ +lemma dentry4_0_contains : dentry4_0.Contains (S (columnVector node1 false) (node3,true)) := by + have h0 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) false false cm1_3_0_0.contains + have h1 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) false true cm1_3_0_1.contains + have hh := S_column_derivative_contains (m:=node3) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry1_3 : RBox := ⟨80528838586735272363974753180,80528838586735272472281451816⟩ +lemma dentry1_3_contains : dentry1_3.Contains (S (columnVector node1 true) (node3,false)) := by + have h0 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) true false cm1_3_1_0.contains + have h1 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) true true cm1_3_1_1.contains + have hh := S_column_value_contains (m:=node3) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry4_3 : RBox := ⟨521756342810954494199096553637,521756342810954494790549200675⟩ +lemma dentry4_3_contains : dentry4_3.Contains (S (columnVector node1 true) (node3,true)) := by + have h0 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) true false cm1_3_1_0.contains + have h1 := K_column_contains (n:=node1) (m:=3) (by decide) (by decide) true true cm1_3_1_1.contains + have hh := S_column_derivative_contains (m:=node3) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry2_0 : RBox := ⟨(-1097737034296297013723665259),(-1097737034296296987012474958)⟩ +lemma dentry2_0_contains : dentry2_0.Contains (S (columnVector node1 false) (node4,false)) := by + have h0 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) false false cm1_4_0_0.contains + have h1 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) false true cm1_4_0_1.contains + have hh := S_column_value_contains (m:=node4) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry5_0 : RBox := ⟨(-49222269312866616533668297810),(-49222269312866616362895656546)⟩ +lemma dentry5_0_contains : dentry5_0.Contains (S (columnVector node1 false) (node4,true)) := by + have h0 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) false false cm1_4_0_0.contains + have h1 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) false true cm1_4_0_1.contains + have hh := S_column_derivative_contains (m:=node4) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry2_3 : RBox := ⟨(-56406703537031364478831607653),(-56406703537031364430188588560)⟩ +lemma dentry2_3_contains : dentry2_3.Contains (S (columnVector node1 true) (node4,false)) := by + have h0 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) true false cm1_4_1_0.contains + have h1 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) true true cm1_4_1_1.contains + have hh := S_column_value_contains (m:=node4) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry5_3 : RBox := ⟨27834593699646376815605650731,27834593699646377127655114131⟩ +lemma dentry5_3_contains : dentry5_3.Contains (S (columnVector node1 true) (node4,true)) := by + have h0 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) true false cm1_4_1_0.contains + have h1 := K_column_contains (n:=node1) (m:=4) (by decide) (by decide) true true cm1_4_1_1.contains + have hh := S_column_derivative_contains (m:=node4) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry0_1 : RBox := ⟨84919083920626310662179677360,84919083920626310963649378583⟩ +lemma dentry0_1_contains : dentry0_1.Contains (S (columnVector node3 false) (node1,false)) := by + have h0 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) false false cm3_1_0_0.contains + have h1 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) false true cm3_1_0_1.contains + have hh := S_column_value_contains (m:=node1) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry3_1 : RBox := ⟨(-401818617642335374122553965636),(-401818617642335372392607050014)⟩ +lemma dentry3_1_contains : dentry3_1.Contains (S (columnVector node3 false) (node1,true)) := by + have h0 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) false false cm3_1_0_0.contains + have h1 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) false true cm3_1_0_1.contains + have hh := S_column_derivative_contains (m:=node1) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry0_4 : RBox := ⟨(-106450383559834775553375548749),(-106450383559834775291307669099)⟩ +lemma dentry0_4_contains : dentry0_4.Contains (S (columnVector node3 true) (node1,false)) := by + have h0 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) true false cm3_1_1_0.contains + have h1 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) true true cm3_1_1_1.contains + have hh := S_column_value_contains (m:=node1) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry3_4 : RBox := ⟨51160635846592449630662157438,51160635846592451095925214287⟩ +lemma dentry3_4_contains : dentry3_4.Contains (S (columnVector node3 true) (node1,true)) := by + have h0 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) true false cm3_1_1_0.contains + have h1 := K_column_contains (n:=node3) (m:=1) (by decide) (by decide) true true cm3_1_1_1.contains + have hh := S_column_derivative_contains (m:=node1) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry1_1 : RBox := ⟨(-58681970988985215880538687120),(-58681970988985215799134371859)⟩ +lemma dentry1_1_contains : dentry1_1.Contains (S (columnVector node3 false) (node3,false)) := by + have h0 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) false false cm3_3_0_0.contains + have h1 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) false true cm3_3_0_1.contains + have hh := S_column_value_contains (m:=node3) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry4_1 : RBox := ⟨(-13628559633735631908901705881),(-13628559633735631522414018748)⟩ +lemma dentry4_1_contains : dentry4_1.Contains (S (columnVector node3 false) (node3,true)) := by + have h0 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) false false cm3_3_0_0.contains + have h1 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) false true cm3_3_0_1.contains + have hh := S_column_derivative_contains (m:=node3) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry1_4 : RBox := ⟨(-9335195132489238242468768282),(-9335195132489238117842659765)⟩ +lemma dentry1_4_contains : dentry1_4.Contains (S (columnVector node3 true) (node3,false)) := by + have h0 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) true false cm3_3_1_0.contains + have h1 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) true true cm3_3_1_1.contains + have hh := S_column_value_contains (m:=node3) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry4_4 : RBox := ⟨696603759878277757337123237275,696603759878277758050967540167⟩ +lemma dentry4_4_contains : dentry4_4.Contains (S (columnVector node3 true) (node3,true)) := by + have h0 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) true false cm3_3_1_0.contains + have h1 := K_column_contains (n:=node3) (m:=3) (by decide) (by decide) true true cm3_3_1_1.contains + have hh := S_column_derivative_contains (m:=node3) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry2_1 : RBox := ⟨11552892703545774298548951595,11552892703545774325348299103⟩ +lemma dentry2_1_contains : dentry2_1.Contains (S (columnVector node3 false) (node4,false)) := by + have h0 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) false false cm3_4_0_0.contains + have h1 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) false true cm3_4_0_1.contains + have hh := S_column_value_contains (m:=node4) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry5_1 : RBox := ⟨(-85515720483106714613961869326),(-85515720483106714442684097804)⟩ +lemma dentry5_1_contains : dentry5_1.Contains (S (columnVector node3 false) (node4,true)) := by + have h0 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) false false cm3_4_0_0.contains + have h1 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) false true cm3_4_0_1.contains + have hh := S_column_derivative_contains (m:=node4) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry2_4 : RBox := ⟨(-46599334773430376018515334202),(-46599334773430375961386819313)⟩ +lemma dentry2_4_contains : dentry2_4.Contains (S (columnVector node3 true) (node4,false)) := by + have h0 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) true false cm3_4_1_0.contains + have h1 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) true true cm3_4_1_1.contains + have hh := S_column_value_contains (m:=node4) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry5_4 : RBox := ⟨(-113965371204432533744771266896),(-113965371204432533377810928653)⟩ +lemma dentry5_4_contains : dentry5_4.Contains (S (columnVector node3 true) (node4,true)) := by + have h0 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) true false cm3_4_1_0.contains + have h1 := K_column_contains (n:=node3) (m:=4) (by decide) (by decide) true true cm3_4_1_1.contains + have hh := S_column_derivative_contains (m:=node4) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry0_2 : RBox := ⟨38513567412242708706244438853,38513567412242709174634148764⟩ +lemma dentry0_2_contains : dentry0_2.Contains (S (columnVector node4 false) (node1,false)) := by + have h0 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) false false cm4_1_0_0.contains + have h1 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) false true cm4_1_0_1.contains + have hh := S_column_value_contains (m:=node1) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry3_2 : RBox := ⟨227145133131591005392854971615,227145133131591008209757733306⟩ +lemma dentry3_2_contains : dentry3_2.Contains (S (columnVector node4 false) (node1,true)) := by + have h0 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) false false cm4_1_0_0.contains + have h1 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) false true cm4_1_0_1.contains + have hh := S_column_derivative_contains (m:=node1) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry0_5 : RBox := ⟨(-35236824314615944648195425884),(-35236824314615944265946143652)⟩ +lemma dentry0_5_contains : dentry0_5.Contains (S (columnVector node4 true) (node1,false)) := by + have h0 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) true false cm4_1_1_0.contains + have h1 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) true true cm4_1_1_1.contains + have hh := S_column_value_contains (m:=node1) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry3_5 : RBox := ⟨13947539579869521084614770631,13947539579869523328647289424⟩ +lemma dentry3_5_contains : dentry3_5.Contains (S (columnVector node4 true) (node1,true)) := by + have h0 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) true false cm4_1_1_0.contains + have h1 := K_column_contains (n:=node4) (m:=1) (by decide) (by decide) true true cm4_1_1_1.contains + have hh := S_column_derivative_contains (m:=node1) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry1_2 : RBox := ⟨(-50367220418701310824260347488),(-50367220418701310746671987499)⟩ +lemma dentry1_2_contains : dentry1_2.Contains (S (columnVector node4 false) (node3,false)) := by + have h0 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) false false cm4_3_0_0.contains + have h1 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) false true cm4_3_0_1.contains + have hh := S_column_value_contains (m:=node3) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry4_2 : RBox := ⟨(-140501438496878817810768594789),(-140501438496878817401660852855)⟩ +lemma dentry4_2_contains : dentry4_2.Contains (S (columnVector node4 false) (node3,true)) := by + have h0 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) false false cm4_3_0_0.contains + have h1 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) false true cm4_3_0_1.contains + have hh := S_column_derivative_contains (m:=node3) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry1_5 : RBox := ⟨(-65563767968601851989120599895),(-65563767968601851839857744056)⟩ +lemma dentry1_5_contains : dentry1_5.Contains (S (columnVector node4 true) (node3,false)) := by + have h0 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) true false cm4_3_1_0.contains + have h1 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) true true cm4_3_1_1.contains + have hh := S_column_value_contains (m:=node3) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry4_5 : RBox := ⟨617641971506705838665457646400,617641971506705839485675654971⟩ +lemma dentry4_5_contains : dentry4_5.Contains (S (columnVector node4 true) (node3,true)) := by + have h0 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) true false cm4_3_1_0.contains + have h1 := K_column_contains (n:=node4) (m:=3) (by decide) (by decide) true true cm4_3_1_1.contains + have hh := S_column_derivative_contains (m:=node3) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry2_2 : RBox := ⟨16906689819273463213216826620,16906689819273463235453873264⟩ +lemma dentry2_2_contains : dentry2_2.Contains (S (columnVector node4 false) (node4,false)) := by + have h0 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) false false cm4_4_0_0.contains + have h1 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) false true cm4_4_0_1.contains + have hh := S_column_value_contains (m:=node4) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry5_2 : RBox := ⟨(-78390776109438054485518877398),(-78390776109438054339396429593)⟩ +lemma dentry5_2_contains : dentry5_2.Contains (S (columnVector node4 false) (node4,true)) := by + have h0 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) false false cm4_4_0_0.contains + have h1 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) false true cm4_4_0_1.contains + have hh := S_column_derivative_contains (m:=node4) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dentry2_5 : RBox := ⟨(-32138315292585356201983505971),(-32138315292585356140057198794)⟩ +lemma dentry2_5_contains : dentry2_5.Contains (S (columnVector node4 true) (node4,false)) := by + have h0 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) true false cm4_4_1_0.contains + have h1 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) true true cm4_4_1_1.contains + have hh := S_column_value_contains (m:=node4) h0 + convert hh using 1 + decide +kernel +noncomputable def dentry5_5 : RBox := ⟨(-197772066238261852433723686168),(-197772066238261852031962127069)⟩ +lemma dentry5_5_contains : dentry5_5.Contains (S (columnVector node4 true) (node4,true)) := by + have h0 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) true false cm4_4_1_0.contains + have h1 := K_column_contains (n:=node4) (m:=4) (by decide) (by decide) true true cm4_4_1_1.contains + have hh := S_column_derivative_contains (m:=node4) h0 h1 + convert hh using 1 + decide +kernel +noncomputable def dEntries : Matrix (Fin 6) (Fin 6) RBox := ![![dentry0_0,dentry0_1,dentry0_2,dentry0_3,dentry0_4,dentry0_5], +![dentry1_0,dentry1_1,dentry1_2,dentry1_3,dentry1_4,dentry1_5], +![dentry2_0,dentry2_1,dentry2_2,dentry2_3,dentry2_4,dentry2_5], +![dentry3_0,dentry3_1,dentry3_2,dentry3_3,dentry3_4,dentry3_5], +![dentry4_0,dentry4_1,dentry4_2,dentry4_3,dentry4_4,dentry4_5], +![dentry5_0,dentry5_1,dentry5_2,dentry5_3,dentry5_4,dentry5_5]] +lemma dEntries_contains (i j : Fin 6) : (dEntries i j).Contains (Dmat i j) := by + fin_cases i <;> fin_cases j + · exact dentry0_0_contains + · exact dentry0_1_contains + · exact dentry0_2_contains + · exact dentry0_3_contains + · exact dentry0_4_contains + · exact dentry0_5_contains + · exact dentry1_0_contains + · exact dentry1_1_contains + · exact dentry1_2_contains + · exact dentry1_3_contains + · exact dentry1_4_contains + · exact dentry1_5_contains + · exact dentry2_0_contains + · exact dentry2_1_contains + · exact dentry2_2_contains + · exact dentry2_3_contains + · exact dentry2_4_contains + · exact dentry2_5_contains + · exact dentry3_0_contains + · exact dentry3_1_contains + · exact dentry3_2_contains + · exact dentry3_3_contains + · exact dentry3_4_contains + · exact dentry3_5_contains + · exact dentry4_0_contains + · exact dentry4_1_contains + · exact dentry4_2_contains + · exact dentry4_3_contains + · exact dentry4_4_contains + · exact dentry4_5_contains + · exact dentry5_0_contains + · exact dentry5_1_contains + · exact dentry5_2_contains + · exact dentry5_3_contains + · exact dentry5_4_contains + · exact dentry5_5_contains +end SharpPlanar.Numerical + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments1.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments1.lean new file mode 100644 index 0000000000000000000000000000000000000000..24a95d0528538e56fd6a3fca8fcd01313e8f2452 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments1.lean @@ -0,0 +1,3929 @@ +import OAI.Analysis.PlanarPacking.Certificate.Columns10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid +namespace cm1_1_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_0 j i k).mul (kernel1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-38944104734615713647870923),(-38944104734615713598060080)⟩,⟨(-11357678828776714398217709),(-11357678828776714348256197)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-111328335414597739528345324),(-111328335414597739391958276)⟩,⟨(-33406111052742331982621717),(-33406111052742331845892655)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-169223230097320626647768901),(-169223230097320626459291256)⟩,⟨(-54824377358855649778675651),(-54824377358855649590055032)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-208026203686911135866404729),(-208026203686911135638429408)⟩,⟨(-78678078878656371193190893),(-78678078878656370966251624)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-225679695534732718854243920),(-225679695534732718596840252)⟩,⟨(-109694199580034054194736489),(-109694199580034053940539415)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-219597639628801509247566626),(-219597639628801508982678409)⟩,⟨(-150148862758720325446992130),(-150148862758720325185857654)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-186483128258660081357146227),(-186483128258660081111268067)⟩,⟨(-195614778596026613202832886),(-195614778596026612959066499)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-126209997365695736029614471),(-126209997365695735825626808)⟩,⟨(-234276907132168381724650937),(-234276907132168381519467565)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-46397973369882123495336102),(-46397973369882123345970383)⟩,⟨(-251609392766917227525082876),(-251609392766917227370651013)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨37076690270045478806532162,37076690270045478930470824⟩,⟨(-238181482462652736306970402),(-238181482462652736176316097)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨105250021780871071614603097,105250021780871071728183800⟩,⟨(-195520155364971400983804706),(-195520155364971400866987929)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨143825861673704764525871145,143825861673704764618163570⟩,⟨(-135992053267984124772494707),(-135992053267984124680741221)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨148377923397049153274880724,148377923397049153342212715⟩,⟨(-76836488690895923653815480),(-76836488690895923589634537)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨124008084450509169644185206,124008084450509169688032312⟩,⟨(-32262897167858328430166981),(-32262897167858328390273249)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨80633657412929787091941495,80633657412929787115995701⟩,⟨(-8042713187741889967804934),(-8042713187741889946841692)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨27764513559133889089244873,27764513559133889096821525⟩,⟨(-556876682265800126543786),(-556876682265800120115417)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-329475021577272229139926517),(-329475021577272228409861728)⟩,⟨192936461440160920025271816,192936461440160920756801757⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-929637174261129450532350888),(-929637174261129448454107600)⟩,⟨550621088331345806730651767,550621088331345808813083820⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1373280657425224857900959180),(-1373280657425224854782031065)⟩,⟨829179452922237149983736798,829179452922237153108840485⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1614914349951587703797339166),(-1614914349951587700057737910)⟩,⟨994775906479688528753229253,994775906479688532499982763⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1666050370466036051629539611),(-1666050370466036047702758753)⟩,⟨1036999687527196385801938217,1036999687527196389735807259⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1576583604125131498198743688),(-1576583604125131494446992182)⟩,⟨969143213184632429713663686,969143213184632433471719597⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1406514336806344475326337487),(-1406514336806344471994236385)⟩,⟨821845907944050470353685535,821845907944050473690902336⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1204269585352756910228810462),(-1204269585352756907446464691)⟩,⟨633047658774144421558532118,633047658774144424345430152⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-999152847741727806073285248),(-999152847741727803865697775)⟩,⟨438430426576023042640161724,438430426576023044851682307⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-805053786046392048492454493),(-805053786046392046818637954)⟩,⟨265170220208276427825257467,265170220208276429502013354⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-627813747314422630421213778),(-627813747314422629207209602)⟩,⟨129481272173251489193319946,129481272173251490409295057⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-470430186074433874730350637),(-470430186074433873887194127)⟩,⟨37058885081286338807026745,37058885081286339651286226⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-334601251225011639035762212),(-334601251225011638477535681)⟩,⟨(-14661597726045037728562302),(-14661597726045037169883205)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-220076959379434806918263385),(-220076959379434806572784797)⟩,⟨(-33384036915107071908163271),(-33384036915107071562616129)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-123790633914884197943020824),(-123790633914884197757168569)⟩,⟨(-28919156054025170215557648),(-28919156054025170029774697)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-39803035520271289360538610),(-39803035520271289302221423)⟩,⟨(-11077583431563413457118189),(-11077583431563413398843736)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1903370420769056243176210247,1903370420769056247177760257⟩,⟨(-3240955150191565916676954217),(-3240955150191565912613729517)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨5282028476933377523481777927,5282028476933377535044453178⟩,⟨(-9059618534164797326541813403),(-9059618534164797314794286960)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨7511563770403094823849309576,7511563770403094841690886875⟩,⟨(-13077740287831707832904417745),(-13077740287831707814762360110)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨8235908990316304942447908311,8235908990316304964638761014⟩,⟨(-14686752243772364033034137952),(-14686752243772364010447255528)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨7530124441138603831014012731,7530124441138603855283770316⟩,⟨(-13933392455912984165618361806),(-13933392455912984140896274920)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨5807025139549402657518286090,5807025139549402681636211988⟩,⟨(-11423625873919555773327742094),(-11423625873919555748750753439)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨3624862959167997971445260632,3624862959167997993563700686⟩,⟨(-8053847693305631726626302206),(-8053847693305631704088445854)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1494920540365155099771991431,1494920540365155118713753941⟩,⟨(-4694474763493932188979315140),(-4694474763493932169690645327)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-236772605443318427576350030),(-236772605443318412076114166)⟩,⟨(-1954057311975408833574794895),(-1954057311975408817811810571)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1415077923483627020783956411),(-1415077923483627008420561267)⟩,⟨(-94175844598260101607666086),(-94175844598260089049447442)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2036556307188025347043854671),(-2036556307188025337074844070)⟩,⟨916177229605657644214035150,916177229605657654330632818⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2187208252717322526318591624),(-2187208252717322518546609781)⟩,⟨1274047283034635806397021810,1274047283034635814273954638⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1986917969559188962579822254),(-1986917969559188956806205634)⟩,⟨1217345790415145622531911159,1217345790415145628375809553⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1552282191328161839257581389),(-1552282191328161835291875952)⟩,⟨944071634668563423591054629,944071634668563427600392962⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-978016303513167507553407800),(-978016303513167505241548875)⟩,⟨582226574996750753046597241,582226574996750755381921355⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-332964155249479817656972323),(-332964155249479816898764483)⟩,⟨195222132934645611405926162,195222132934645612171473413⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨8054666190201432694778068873,8054666190201432711021460772⟩,⟨(-6946219719408129617627514536),(-6946219719408129601558582637)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨23366010758949521436314924814,23366010758949521483717131520⟩,⟨(-20446158982795312277283834769),(-20446158982795312230395606409)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨36388073296751481581063285193,36388073296751481655681681245⟩,⟨(-32759797502030536352308570706),(-32759797502030536278508565229)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨46005315990127598939869233285,46005315990127599035568929596⟩,⟨(-43151874485126289696411722239),(-43151874485126289601769019038)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨51625358442953122398125374996,51625358442953122507272135629⟩,⟨(-50992771713177007603925038396),(-50992771713177007495962131599)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨53237497005645451999349054981,53237497005645452113844797210⟩,⟨(-55841873709986632035512226384),(-55841873709986631922160354532)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨51351132715536976740993520742,51351132715536976853131687523⟩,⟨(-57528411018763669067648677201),(-57528411018763668956479951465)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨46833846053610762573095003434,46833846053610762676551253623⟩,⟨(-56197628871359343667164783493),(-56197628871359343564407226311)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨40695130305372016358224798008,40695130305372016448714445102⟩,⟨(-52293043710010871756197041106),(-52293043710010871666097565951)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨33877144272815255475351046161,33877144272815255550772574810⟩,⟨(-46468246036518109798439420869),(-46468246036518109723124601715)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨27106493994555583589656497839,27106493994555583649769078182⟩,⟨(-39451557643700013298300703264),(-39451557643700013238081839136)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨20832843251924332882548199672,20832843251924332928388428838⟩,⟨(-31906636473283138624975795925),(-31906636473283138578904801475)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨15245544452035065445094999789,15245544452035065478306451975⟩,⟨(-24330275448183457252335910611),(-24330275448183457218853554669)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨10336152990529105686901196746,10336152990529105709276523258⟩,⟨(-17008168492704095754322415438),(-17008168492704095731704743216)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨5971177598711926741858161700,5971177598711926754730029150⟩,⟨(-10024753650513281197267069483),(-10024753650513281184230950519)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1950646935893928904847635034,1950646935893928909039466939⟩,⟨(-3307362732847746895662695375),(-3307362732847746891413457242)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨14865319957564973824636975749,14865319957564973848300573485⟩,⟨12471355993690062556211275366,12471355993690062580204992362⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨43778762496951182660946416504,43778762496951182730004687836⟩,⟨35212762551169663768410372893,35212762551169663838408612471⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨70240182136148461328129489661,70240182136148461436858382190⟩,⟨51770858231706048135928410388,51770858231706048246069051407⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨92777286894023054663971805262,92777286894023054803495491757⟩,⟨59452973788616255813109754182,59452973788616255954289897454⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨110158325377711411964209573627,110158325377711412123463605190⟩,⟨57345678966580717734752044891,57345678966580717895610081020⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨121511303857789472250487911524,121511303857789472417714141910⟩,⟨46416938541975699755156662678,46416938541975699923588585678⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨126434406973310993434105374401,126434406973310993608721050008⟩,⟨29190000673698013660644499911,29190000673698013835674550323⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨125069638136959948426403298921,125069638136959948606020374143⟩,⟨9094029249953454191834189666,9094029249953454370922999656⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨118099103909521866551171707501,118099103909521866726911343775⟩,⟨(-10321764650909708614942815802),(-10321764650909708440571160052)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨106637305587136778132101721937,106637305587136778296497920640⟩,⟨(-26095336268837234918421580830),(-26095336268837234755933881427)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨92029283374749181497912029271,92029283374749181645614938590⟩,⟨(-36307585533391438982904386286),(-36307585533391438837232396052)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨75605375899098095377793857462,75605375899098095503536661523⟩,⟨(-40212936804620558865977492476),(-40212936804620558742138617034)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨58463369707060583788378035183,58463369707060583888557519649⟩,⟨(-38085739959480959955283909253),(-38085739959480959856704702183)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨41335234840701463802015217565,41335234840701463874499579698⟩,⟨(-30905552771614861493912670263),(-30905552771614861422616720654)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨24558760975810229115725227758,24558760975810229159468370013⟩,⟨(-20024284531763953977067613655),(-20024284531763953934049259781)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨8135916334909329180301498522,8135916334909329194899253632⟩,⟨(-6918385789049610450493727594),(-6918385789049610436138367472)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨100965451010996906062867763,100965451010996912376146058⟩,⟨88740929519946311366222811,88740929519946317685821873⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1476893784014058568832867005,1476893784014058587720610690⟩,⟨1299595137044323147708314658,1299595137044323166625141205⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨6087160107790874667279510912,6087160107790874698534320887⟩,⟨5366871642932317245331802691,5366871642932317276657830884⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨15198966974280735244802654897,15198966974280735287983658366⟩,⟨13432021135715840464508844870,13432021135715840507805578082⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨28971049759381673900036789559,28971049759381673954341259278⟩,⟨25658950165902773878481880119,25658950165902773932907938768⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨46396433908969973386492651060,46396433908969973450632366373⟩,⟨41149811632821220951583534711,41149811632821221015765600283⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨65503086333822323215947674336,65503086333822323288075199692⟩,⟨58100176621008169568418988604,58100176621008169640393203201⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨83749068841003287838989576878,83749068841003287916615205366⟩,⟨74162600311170054543413376791,74162600311170054620601473798⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨98507995359683046783427612507,98507995359683046863500428213⟩,⟨86927810607517075710307894779,86927810607517075789635829428⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨107530740574321929876879346132,107530740574321929955943222406⟩,⟨94395668455310525859096298895,94395668455310525937169556642⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨109289193002231047281593608429,109289193002231047356037556404⟩,⟨95313567939292088729030638584,95313567939292088802361590882⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨103148878862019301253637198798,103148878862019301320005077960⟩,⟨89310087268399207950327087332,89310087268399208015589570170⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨89366954493686623410706620278,89366954493686623465871285601⟩,⟨76825963096942733728269501506,76825963096942733782458317115⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨68956155978774719901235304411,68956155978774719942568443345⟩,⟨58909681941552963585090367282,58909681941552963625676389801⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨43480715627336673313446023922,43480715627336673339013368533⟩,⟨36974055464274045158594035609,36974055464274045183697726501⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨14845438957536307676372993940,14845438957536307685008659588⟩,⟨12592820085264039863908775235,12592820085264039872389485624⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨433577319443059304795947121443,433577319443059305449059444914⟩,⟨40641791528534792660630111745,40641791528534793311593287244⟩⟩ +lemma checked : cachedMomentRuleBox column1_0 kernel1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 1 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_0_contains kernel1_0_contains +end cm1_1_0_0 +namespace cm1_1_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_0 j i k).mul (kernel1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨256962003309640187494897462,256962003309640187967543762⟩,⟨231513775813231079247848975,231513775813231079721749680⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨738306635769277353834516906,738306635769277355188648238⟩,⟨665090164895495300013245796,665090164895495301369907985⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1129359559916791666974550400,1129359559916791669027169774⟩,⟨1030362401682663214646710518,1030362401682663216699459937⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1388908954956129587312739871,1388908954956129589794661680⟩,⟨1333741052817302074317195108,1333741052817302076791657626⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1484897349559687640896694996,1484897349559687643502061340⟩,⟨1612634503919905353588807799,1612634503919905356174388906⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1386650089725582303270160969,1386650089725582305783908040⟩,⟨1893751111039693671103359529,1893751111039693673593546528⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1074097547309876010468362295,1074097547309876012683279962⟩,⟨2155805185436430231413096844,2155805185436430233615055012⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨564059646970950907478604757,564059646970950909243664860⟩,⟨2326529152848088365897945145,2326529152848088367673992180⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-68155207219183462782120916),(-68155207219183461397834450)⟩,⟨2319391135182850903687795406,2319391135182850905111921131⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-696010070619667157946304001),(-696010070619667156671037763)⟩,⟨2087258819301277773155959077,2087258819301277774482356244⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1181586321980393026677539131),(-1181586321980393025574178027)⟩,⟨1658227490387971056954741868,1658227490387971058082540730⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1426439447127443035273061259),(-1426439447127443034403993928)⟩,⟨1130815589934104450807592843,1130815589934104451670090901⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1403109475451453728981481992),(-1403109475451453728356369466)⟩,⟨632144048804878411930440108,632144048804878412526480233⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1150886483764156451832883740),(-1150886483764156451427019657)⟩,⟨264163756335267150135186452,264163756335267150504838771⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-743906855699576316475088474),(-743906855699576316251787360)⟩,⟨65751357866080880109396260,65751357866080880304290811⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-255873353389455991950302968),(-255873353389455991879727015)⟩,⟨4551567892950286476940408,4551567892950286536932104⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2619394619831417886354458145,2619394619831417892329026224⟩,⟨743838205073793484432160603,743838205073793490401018628⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨7462512189693293648084002280,7462512189693293665131737235⟩,⟨2032951390805419792342234191,2032951390805419809373647292⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨11219315036220890852758927141,11219315036220890878437317824⟩,⟨2818546353434622050095852529,2818546353434622075750119439⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨13488471632746978760924046871,13488471632746978791810396832⟩,⟨3022958484676093470883602176,3022958484676093501741799161⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨14223189549559748337816369427,14223189549559748370266685761⟩,⟨2794809115339890383554916052,2794809115339890415977185512⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨13677184392950045226895421202,13677184392950045257777194535⟩,⟨2394523762963966203644596446,2394523762963966234502459840⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨12264275663970878271858679081,12264275663970878299022947001⟩,⟨2049814942312062275314860912,2049814942312062302464402803⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨10406813183729055876874988843,10406813183729055899215640553⟩,⟨1866872806168890963641814904,1866872806168890985977761969⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨8436703164075497056794603499,8436703164075497074187945301⟩,⟨1827217126242375464824342696,1827217126242375482220994886⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨6567493218418259786901782975,6567493218418259799816053350⟩,⟨1842237641118267184868697498,1842237641118267197790419466⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨4913953240178638105531414788,4913953240178638114691105529⟩,⟨1817116636396734788390711825,1817116636396734797558683936⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨3524025146480525314735641358,3524025146480525320974157293⟩,⟨1691238749804276030055179564,1691238749804276036300572152⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2402214853458785996658398362,2402214853458786001069966250⟩,⟨1447920377700274151875031049,1447920377700274156290739646⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1521828459399337034872091506,1521828459399337037865962827⟩,⟨1103190509172850022984285961,1103190509172850025979876965⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨831864169794355832520603641,831864169794355834243875793⟩,⟨687816592283409101621340071,687816592283409103345030259⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨263310297456976286437822905,263310297456976286998398767⟩,⟨233266554254884211666587697,233266554254884212227184776⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-21963091489952816717570516363),(-21963091489952816697886728267)⟩,⟨(-528733590072295916663671744),(-528733590072295898006200902)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-61514325866788669275453156792),(-61514325866788669217631513365)⟩,⟨(-1031699565168555544536553554),(-1031699565168555489616466453)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-89115025659177850993816543303),(-89115025659177850901781835979)⟩,⟨(-189074020612672010848562498),(-189074020612671923059032201)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-100523270432098835013904300178),(-100523270432098834894415165646)⟩,⟨2030056101394789769484093063,2030056101394789884099255747⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-95717860423086048223217756477),(-95717860423086048085714144320)⟩,⟨4923040739409924307985193252,4923040739409924440726805121⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-78426522844290393036211615793),(-78426522844290392891871344256)⟩,⟨7498755374163140622220787014,7498755374163140762457211230⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-54517545884127460136150257826),(-54517545884127459996333666095)⟩,⟨9027089966949290421334437794,9027089966949290557970221509⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-29977113159961633768739149251),(-29977113159961633642701598460)⟩,⟨9341865980871960042893063819,9341865980871960166688063000⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-9286076392860094027543828882),(-9286076392860093919215506037)⟩,⟨8761021812061528420826701165,8761021812061528527704945290⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨5293482547428108370142771897,5293482547428108460688951606⟩,⟨7766931268802186979179563717,7766931268802187068794409103⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨13517071574428584284004988044,13517071574428584360702818598⟩,⟨6709686992584327858189965080,6709686992584327934245567068⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨16424518330222768122100447882,16424518330222768184187234579⟩,⟨5699416781560011969997774233,5699416781560012031656222483⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨15538307163471984864120553626,15538307163471984911493159967⟩,⟨4674392158688153587177047431,4674392158688153634273016828⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨12291587353963459303165196648,12291587353963459336289720698⟩,⟨3530640855180144414083797587,3530640855180144447038894368⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨7761361253831184566291516845,7761361253831184585810285602⟩,⟨2215686728239541823635764660,2215686728239541843063444891⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2641180448530404456531918672,2641180448530404462964793067⟩,⟨756735677861227362604315010,756735677861227369008611780⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-44354606209979802706867158162),(-44354606209979802622541694986)⟩,⟨(-26673442947974651354805417362),(-26673442947974651270170506401)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-130702431939318864568980667522),(-130702431939318864322905479755)⟩,⟨(-76769753890432450724391621800),(-76769753890432450477467318285)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-209872501771213356109591703480),(-209872501771213355722261479248)⟩,⟨(-117601671567117274599107323867),(-117601671567117274210632433210)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-277316263521367444411359979202),(-277316263521367443914706775128)⟩,⟨(-144803390519386547950610984123),(-144803390519386547452926040490)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-329006303703468156052962161400),(-329006303703468155486677617537)⟩,⟨(-156344035240563316725607197430),(-156344035240563316158973916298)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-361958856645545408952835169571),(-361958856645545408358774614242)⟩,⟨(-152800008296756059034722316652),(-152800008296756058441696193157)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-374788525451974821564059772118),(-374788525451974820982264067933)⟩,⟨(-137059289004860785886542269320),(-137059289004860785307659968685)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-368082855884867644438429774908),(-368082855884867643901754818610)⟩,⟨(-113515879486318168413323280232),(-113515879486318167881592843946)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-344381739673687338318655065044),(-344381739673687337849289947658)⟩,⟨(-86972161117907181638803689968),(-86972161117907181176165736498)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-307682391381053962118973098129),(-307682391381053961727714806551)⟩,⟨(-61581571516167396506485178292),(-61581571516167396123121450182)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-262594254055581403857182227277),(-262594254055581403545166704387)⟩,⟨(-40146187861176354801783374575),(-40146187861176354498014737165)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-213422024538368387741661166136),(-213422024538368387503445004808)⟩,⟨(-23922691056131907877933333263),(-23922691056131907647538521720)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-163464958203100626912817256456),(-163464958203100626739900924625)⟩,⟨(-12871223803077036668612650651),(-12871223803077036502425317160)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-114691958126327096676753923628),(-114691958126327096559745068882)⟩,⟨(-6129157735461096325023513905),(-6129157735461096213128478706)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-67780862132679769263744440834),(-67780862132679769196141754935)⟩,⟨(-2473919818580243578089866255),(-2473919818580243513664694692)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-22393723932486727627576996345),(-22393723932486727605454286335)⟩,⟨(-627499859733819592358345203),(-627499859733819571301078193)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨40464428154479080504367254712,40464428154479080593417407755⟩,⟨(-69587338862636302178625744036),(-69587338862636302091244751548)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨112778988461580530710763463099,112778988461580530973857013230⟩,⟨(-204717355432811633769702106539),(-204717355432811633511277423806)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨160864777688910098575150373021,160864777688910099007183503244⟩,⟨(-327647774468422533796962305366),(-327647774468422533371534638655)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨174039268966765047139801682318,174039268966765047729033556398⟩,⟨(-430851459571074091935876426144),(-430851459571074091353690779737)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨148607676140940378004026265096,148607676140940378730510224985⟩,⟨(-507868044184914380625556482681),(-507868044184914379904957980007)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨88532862834045376424500145831,88532862834045377258923185531⟩,⟨(-554090378340133416625414241473),(-554090378340133415794317241416)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4443545747473532246510504312,4443545747473533150897303885⟩,⟨(-567588694485873139420586491748),(-567588694485873138516240195020)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-88796439767420148365320868077),(-88796439767420147435329846235)⟩,⟨(-549706323811816233163228018165),(-549706323811816232230007750168)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-175349194428360026116881683488),(-175349194428360025207225333733)⟩,⟨(-505099906022407914781447949421),(-505099906022407913865953076259)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-241623115902995713134890107127),(-241623115902995712283472036482)⟩,⟨(-441026876928488996330899705371),(-441026876928488995472414473290)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-278597265485346474192304407631),(-278597265485346473425157839903)⟩,⟨(-365963225895775658071289833362),(-365963225895775657297528809050)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-282731047828117147655063385537),(-282731047828117146999770444353)⟩,⟨(-287929345553904987295480855507),(-287929345553904986634744372549)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-255472108778361715157574313147),(-255472108778361714633692214301)⟩,⟨(-213035264990878494895160668641),(-213035264990878494367294765081)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-201853308387645572723200890281),(-201853308387645572342957706108)⟩,⟨(-144644658269325324213541365620),(-144644658269325323830726239571)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-128874642956770285158122123226),(-128874642956770284928109276644)⟩,⟨(-83279557981760913983242866489),(-83279557981760913751841941278)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-44233910499915724802212723513),(-44233910499915724725359610618)⟩,⟨(-27116479538748512306364635562),(-27116479538748512229080170690)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨301466325282980621228759795,301466325282980643991837567⟩,⟨(-381768711303253362570785311),(-381768711303253339844991932)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4414253308887834164330565552,4414253308887834232608130001⟩,⟨(-5608763085676762992960004031),(-5608763085676762924817756840)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨18223584636828555037253462919,18223584636828555150773237443⟩,⟨(-23303989968450485805065014518),(-23303989968450485691807612563)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨45584532325286632960280879239,45584532325286633118091182780⟩,⟨(-58870981776508369516830190770),(-58870981776508369359345929329)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨87003610467243687617896221628,87003610467243687817742465558⟩,⟨(-113899717882352840143611843448),(-113899717882352839943914776503)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨139345155909444943214135191728,139345155909444943451886654738⟩,⟨(-185640166197092024322740249032),(-185640166197092024084534735025)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨196365901164480024727862121702,196365901164480024997162733282⟩,⟨(-267263005870566668618732533009),(-267263005870566668347834706825)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨249985353467381688593132636196,249985353467381688885170525994⟩,⟨(-348873632409716181103943846886),(-348873632409716180808790865691)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨291985921841986536994430392776,291985921841986537298203001051⟩,⟨(-419108942450396794831302967226),(-419108942450396794522852989755)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨315687279893663027564394614027,315687279893663027867193944336⟩,⟨(-467025876050318734915735306140),(-467025876050318734607065756890)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨317135914768425247741622124148,317135914768425248029749990852⟩,⟨(-483914291156120910678249572513),(-483914291156120910383723734661)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨295521579382966537030918458700,295521579382966537290592695215⟩,⟨(-464671910522310638960198406468),(-464671910522310638694283569707)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨252817435487189496150972841252,252817435487189496369058833312⟩,⟨(-408490061436897707037605571317),(-408490061436897706814070529210)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨192911829078723737880694508873,192911829078723738045587013048⟩,⟨(-318794286266014600392925061991),(-318794286266014600223886100456)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨120632811671501537892744529957,120632811671501537995420714754⟩,⟨(-202587549973071427173479789010),(-202587549973071427068239148242)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨41004131770411722778427644578,41004131770411722813233107811⟩,⟨(-69442443074746104974243201808),(-69442443074746104938581570944)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-390671080300381900086165859141),(-390671080300381896913979704744)⟩,⟨(-1693225015211390271001754701697),(-1693225015211390267835520423850)⟩⟩ +lemma checked : cachedMomentRuleBox column1_0 kernel1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 1 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_0_contains kernel1_1_contains +end cm1_1_0_1 +namespace cm1_1_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_1 j i k).mul (kernel1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨168319125330261325935233619,168319125330261325992666778⟩,⟨102180337490303530570546546,102180337490303530628134619⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨459582421613168911260203920,459582421613168911420838530⟩,⟨313722884877695271936477063,313722884877695272097648482⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨627323023685270188764514466,627323023685270188995678071⟩,⟨535254115129275800909359533,535254115129275801141636816⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨629415745197108714803137231,629415745197108715074273226⟩,⟨744012541610621821706890443,744012541610621821979783508⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨471679005145388219850980498,471679005145388220131797446⟩,⟨895527185391482974774707856,895527185391482975057984512⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨205092931090041791801694844,205092931090041792092542499⟩,⟨944172476299340013055532901,944172476299340013348993430⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-92168021845216723488401569),(-92168021845216723204488385)⟩,⟨867527617412277828374704599,867527617412277828659747311⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-341731288589524129431471026),(-341731288589524129182169762)⟩,⟨680078020775163714228512699,680078020775163714475889398⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-490382181677581793751686610),(-490382181677581793555373379)⟩,⟨428966512166067702607106313,428966512166067702797760298⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-523552434660810340859305099),(-523552434660810340704400364)⟩,⟨175209318423321876922868809,175209318423321877070879437⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-462596204125494497733222035),(-462596204125494497608061102)⟩,⟨(-28838538316288476784228581),(-28838538316288476662319485)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-349437727626378983984096899),(-349437727626378983891886569)⟩,⟨(-154699521770329535695735578),(-154699521770329535602996321)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-227354588279744269383133005),(-227354588279744269321288893)⟩,⟨(-200341009072493486375169046),(-200341009072493486310263222)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-126447879606537973953692044),(-126447879606537973916253956)⟩,⟨(-182148013580112218770061799),(-182148013580112218728845661)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-57891945935611430747854979),(-57891945935611430728468907)⟩,⟨(-122973933986786797627331247),(-122973933986786797605029680)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-15936573522104696710418707),(-15936573522104696704516958)⟩,⟨(-43001379676583361748040723),(-43001379676583361741063470)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨613342166689720831559772648,613342166689720831919450675⟩,⟨(-432280395574247846635184136),(-432280395574247846272281091)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1755587245550754091572561933,1755587245550754092606838685⟩,⟨(-1199818102916501585572149589),(-1199818102916501584528949833)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨2662740064216992025074443873,2662740064216992026655941262⟩,⟨(-1705952580394826235112033840),(-1705952580394826233518272605)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3238280111786873981943672614,3238280111786873983889602594⟩,⟨(-1867518158536042007780337934),(-1867518158536042005821829645)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨3453885796556323747984807123,3453885796556323750091356912⟩,⟨(-1699660827212292831713799960),(-1699660827212292829597207967)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨3344763301473537226380703166,3344763301473537228459377327⟩,⟨(-1297800716728823067349859645),(-1297800716728823065265336514)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨2990473676882412755102082885,2990473676882412757004794963⟩,⟨(-795009181687796832016332151),(-795009181687796830112506115)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨2490303411777287222346528362,2490303411777287223977889538⟩,⟨(-315488264921351783567325124),(-315488264921351781939018007)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1940629348401817066247307699,1940629348401817067575762541⟩,⟨57468826448121080945755707,57468826448121082269181894⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1418594197977927913797474104,1418594197977927914829330442⟩,⟨291135088428218182576706794,291135088428218183604012864⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨973784313410300384377217796,973784313410300385139328818⟩,⟨394157856363339161677312485,394157856363339162436435915⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨627688753148212009543227899,627688753148212010079719721⟩,⟨398309473195074803781135271,398309473195074804316397004⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨379050538341645161537320020,379050538341645161895965954⟩,⟨340745377050557736974866569,340745377050557737333631658⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨212030530560681415243599949,212030530560681415467036618⟩,⟨252256920289355047975398884,252256920289355048199604409⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨104003848277531954737483774,104003848277531954858163762⟩,⟨152545975924837429919021319,152545975924837430040461010⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨30841882224036971199655427,30841882224036971237566806⟩,⟨50789291489904291013422078,50789291489904291051635365⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨9733305631771045191250445546,9733305631771045193866873353⟩,⟨7005096707268392338275274421,7005096707268392340861657500⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨28043845528535702361167044459,28043845528535702368875977893⟩,⟨20177145530587037299118032630,20177145530587037306727905551⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨43075854042786313517101756680,43075854042786313529442870373⟩,⟨30997273387226650080048806327,30997273387226650092210170001⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨53330787961283474085840318393,53330787961283474102047967953⟩,⟨38457861718636999405274600667,38457861718636999421214735904⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨58164334285207315991491085353,58164334285207316010512306041⟩,⟨42205492922240448127196703053,42205492922240448145875323491⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨57836634539437191952779706005,57836634539437191973387645261⟩,⟨42515911713507043128765229969,42515911713507043148979055679⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨53351414350703185957840561640,53351414350703185978754330264⟩,⟨40110893668102405740646482507,40110893668102405761149403191⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨46140971201739387942206419774,46140971201739387962227775702⟩,⟨35903335693630446860408859090,35903335693630446880047757014⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨37699784550342214193895040013,37699784550342214212075991320⟩,⟨30766028620396943091723984807,30766028620396943109583926509⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨29279166447728379061291229028,29279166447728379077018621337⟩,⟨25387020450397187388034031094,25387020450397187403514554392⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨21718080462820660250912774562,21718080462820660263902414013⟩,⟨20222143282216172156757882806,20222143282216172169571519294⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨15421438110723267609470038411,15421438110723267619710742385⟩,⟨15515625639820679820295168418,15515625639820679830414931670⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨10442662493050522185015520370,10442662493050522192650017760⟩,⟨11349291858490198327520516163,11349291858490198335075617841⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨6606600570688996321105459688,6606600570688996326341330900⟩,⟨7692582264593703460844576826,7692582264593703466031855065⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨3620815573893533524452856241,3620815573893533527493611348⟩,⟨4442253280000275226399629139,4442253280000275229414424856⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1149452310099931410292114810,1149452310099931411285026531⟩,⟨1450704433453613155299743453,1450704433453613156284629721⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-4735705191425263112215278990),(-4735705191425263108426098399)⟩,⟨2279689578067179847549844966,2279689578067179851293799133⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-13790027821500724694271778324),(-13790027821500724683164407748)⟩,⟨6680390196429582773287855979,6680390196429582784263492016⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-21638763196200166623477758325),(-21638763196200166605844131583)⟩,⟨10612957028023196328536969337,10612957028023196345964466364⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-27671068069155461470929220010),(-27671068069155461448024481221)⟩,⟨13815358016467619159583464854,13815358016467619182225711955⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-31525257872795729399676144704),(-31525257872795729373103896929)⟩,⟨16095118071565391355961470107,16095118071565391382242879685⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-33125088432186689116517844495),(-33125088432186689088015354331)⟩,⟨17350751132673475389210401824,17350751132673475417437090247⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-32662529175845827747131145976),(-32662529175845827718454933846)⟩,⟨17583172921161849765493621108,17583172921161849793926174439⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-30532967145075463571510081259),(-30532967145075463544228114455)⟩,⟨16893353174142281648054272562,16893353174142281675130091962⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-27239624647007863133184907020),(-27239624647007863108499644691)⟩,⟨15463383619395209230502777037,15463383619395209255017376549⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-23292102984550275285922664792),(-23292102984550275264593452178)⟩,⟨13522470570499951688304816172,13522470570499951709493316837⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-19123804374544721678408979360),(-19123804374544721660774700341)⟩,⟨11305019590266127787906004705,11305019590266127805424232272⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-15043961471959299912849945844),(-15043961471959299898914672653)⟩,⟨9011657624126113763811906765,9011657624126113777652809343⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-11226436086473882835664055068),(-11226436086473882825239190244)⟩,⟨6783005480860104639039350589,6783005480860104649390644867⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-7726008171076129824164267701),(-7726008171076129816984923963)⟩,⟨4690619461138495697349121048,4690619461138495704475476478⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4508163631822867005277773609),(-4508163631822867001091091230)⟩,⟨2743099918046863263961967017,2743099918046863268116620848⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1480062815957114801312263182),(-1480062815957114799940192846)⟩,⟨901270365766158798053428662,901270365766158799414726426⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-45972700186154003606223882332),(-45972700186154003596861164022)⟩,⟨(-3266886597487613638434904129),(-3266886597487613629352802227)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-134970114545964884751091799737),(-134970114545964884723530664932)⟩,⟨(-9418652779135450240997824821),(-9418652779135450214287455925)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-215273801702168305112090651681),(-215273801702168305068047794906)⟩,⟨(-14462206695791136161086177398),(-14462206695791136118477763413)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-282051325203321330591270420741),(-282051325203321330533508697600)⟩,⟨(-17819990196134792824995279564),(-17819990196134792769258687111)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-331756308108772612195875895193),(-331756308108772612128049492012)⟩,⟨(-19147308447868443409311083651),(-19147308447868443344075358135)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-362444248824469818366240036272),(-362444248824469818290650496599)⟩,⟨(-18400811831560195749774393163),(-18400811831560195677135499479)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-373875943889819229884535901822),(-373875943889819229801130245401)⟩,⟨(-15858355908850147814898506215),(-15858355908850147734511391583)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-367399000112169684485593222282),(-367399000112169684396147041030)⟩,⟨(-12071343797684130230021349552),(-12071343797684130143448857944)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-345619480932272225238260533850),(-345619480932272225146872370675)⟩,⟨(-7750359671840027507444830997),(-7750359671840027418639957537)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-311916880697709382369499712291),(-311916880697709382280579206715)⟩,⟨(-3612295806112405161087071173),(-3612295806112405074370455188)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-269892016501218627882531525731),(-269892016501218627800335140446)⟩,⟨(-235705456580274918387940946),(-235705456580274837981377080)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-222854237112486338756273991082),(-222854237112486338684413630361)⟩,⟨2031660695057499962704897855,2031660695057500033183346965⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-173441501535821806113671917740),(-173441501535821806055072643042)⟩,⟨3092926064705322882671128287,3092926064705322940263481962⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-123427123804989164192815815910),(-123427123804989164149649808398)⟩,⟨3060567339246192612961904179,3060567339246192655451013669⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-73716709058405193891620861900),(-73716709058405193865263821971)⟩,⟨2185023643489565436200021901,2185023643489565462169685970⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-24492147243135894933095535721),(-24492147243135894924262766229)⟩,⟨786746170384451865119064048,786746170384451873825941480⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨35351722743601743355929165679,35351722743601743361615744954⟩,⟨(-40225459715522488665242090690),(-40225459715522488659936144387)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨104249835599783838746856879899,104249835599783838763906482374⟩,⟨(-118491154633892829250733103369),(-118491154633892829234729506056)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨167730702272563616483163995255,167730702272563616511416974570⟩,⟨(-190269159210063885998732268501),(-190269159210063885971935151847)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨222563245431524833228370381428,222563245431524833267487233782⟩,⟨(-251868255845827680912326143439),(-251868255845827680874715220913)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨266059096664275587961620673122,266059096664275588010931045718⟩,⟨(-300422511406911761429619292232),(-300422511406911761381495800037)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨296298558362892937869242307237,296298558362892937927717589935⟩,⟨(-334084682873553906962346612318),(-334084682873553906904429714779)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨312300445483102015575323514582,312300445483102015641433000731⟩,⟨(-352087245566457634066747554455),(-352087245566457634000375814048)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨314100386494309230695103808260,314100386494309230766611181906⟩,⟨(-354685673852548548976002445772),(-354685673852548548903445106987)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨302700766702617593703680272714,302700766702617593777779419252⟩,⟨(-343003050063435455284135489057),(-343003050063435455208396782224)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨279882765926479547275342735272,279882765926479547348812492117⟩,⟨(-318805082487047814236893431361),(-318805082487047814161484724207)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨247908446255822395212774585126,247908446255822395282200090241⟩,⟨(-284239146231454683171844115542),(-284239146231454683100471246207)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨209173880213157375761035282809,209173880213157375823143380331⟩,⟨(-241572082547980694383872316271),(-241572082547980694319995110483)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨165888946154989244379204276855,165888946154989244430966739612⟩,⟨(-192960736949518415263168147773),(-192960736949518415209948905510)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨119849793255631017443200018454,119849793255631017482042868744⟩,⟨(-140285804453911922096102718611),(-140285804453911922056201822829)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨72341413412715038645540587422,72341413412715038669577134834⟩,⟨(-85071237863471373387443793945),(-85071237863471373362772715118)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨24166518865519704735392826100,24166518865519704743504412327⟩,⟨(-28489426169491470933196951294),(-28489426169491470924877416020)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-53688921008865141814048631650),(-53688921008865141456725993704)⟩,⟨(-524989866005610645161461548226),(-524989866005610644808437840300)⟩⟩ +lemma checked : cachedMomentRuleBox column1_1 kernel1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 1 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_1_contains kernel1_0_contains +end cm1_1_1_0 +namespace cm1_1_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_1 j i k).mul (kernel1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-913886307164062887793958699),(-913886307164062887177707927)⟩,⟨(-1408315414270304071032676042),(-1408315414270304070415136425)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-2405201341202319717205764769),(-2405201341202319715452368864)⟩,⟨(-4104764251831973210921041619),(-4104764251831973209163968388)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-3006389797783933833137803853),(-3006389797783933830525097920)⟩,⟨(-6418974075338380078689764440),(-6418974075338380076071848639)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-2480791552609520747130940144),(-2480791552609520744065214762)⟩,⟨(-8066542831161574288936530285),(-8066542831161574285864404675)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-973123150610918525444705677),(-973123150610918522362886285)⟩,⟨(-8791091394457402243187856421),(-8791091394457402240098074555)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1068159362842889566643254744,1068159362842889569745115969⟩,⟨(-8460045597992203535540623201),(-8460045597992203532432218663)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨3068674565700368862796591432,3068674565700368865749709315⟩,⟨(-7145872953178810209031030789),(-7145872953178810206082205403)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4528231631187687790509128637,4528231631187687793041074501⟩,⟨(-5137730399827235100006321619),(-5137730399827235097499442348)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨5167928555776487816347197157,5167928555776487818359846308⟩,⟨(-2867032182554259944834276478),(-2867032182554259942869383760)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨4979552616774489711030062561,4979552616774489712649630349⟩,⟨(-778660690582617174401818845),(-778660690582617172833961176)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨4175813573599567502902812278,4175813573599567504165869781⟩,⟨793773640499328791125721524,793773640499328792364727208⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨3077436195347655920418556253,3077436195347655921325570652⟩,⟨1697606073887703032325513788,1697606073887703033239049039⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1990112025823339865776134870,1990112025823339866373917772⟩,⟨1956896203388645108456655902,1956896203388645109082554821⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1116165324868978341577332300,1116165324868978341935511367⟩,⟨1711644606549528338505785998,1711644606549528338898464809⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨520714536679659478879079176,520714536679659479063702520⟩,⟨1139285870945569129626412030,1139285870945569129837796525⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨145962491297862693522833152,145962491297862693578968919⟩,⟨396609783102389199887600510,396609783102389199953647960⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-5252597429223113599969110043),(-5252597429223113596756495234)⟩,⟨(-1023849619247277859584891017),(-1023849619247277856384179152)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-14915114580937525726024561193),(-14915114580937525716752818105)⟩,⟨(-3042064772709073723146647518),(-3042064772709073713908107925)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-22257647704334479425194683160),(-22257647704334479410925754989)⟩,⟨(-4967342476142827880777754515),(-4967342476142827866555597140)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-26402525012677930098536509309),(-26402525012677930080840481559)⟩,⟨(-6728285339596056327989393327),(-6728285339596056310344526567)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-27220876488255625001555823143),(-27220876488255624982251071375)⟩,⟨(-8229174227012205779153902531),(-8229174227012205759896782981)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-25249123536138584421272746338),(-25249123536138584402109371870)⟩,⟨(-9346002290321665912325639018),(-9346002290321665893202500700)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-21426159360355231059198422458),(-21426159360355231041604271239)⟩,⟨(-9950538191981674461847861168),(-9950538191981674444285319433)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16778187333012043668387232717),(-16778187333012043653309767203)⟩,⟨(-9959159193215134254843783874),(-9959159193215134239790019156)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-12168156102568777621277767415),(-12168156102568777609028657869)⟩,⟨(-9378174848858903151053245179),(-9378174848858903138820252909)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-8168078360213198120872999784),(-8168078360213198111391528939)⟩,⟨(-8314937836575728665140563762),(-8314937836575728655667269779)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-5048042676258353416780455250),(-5048042676258353409815708092)⟩,⟨(-6946620902882685750920072901),(-6946620902882685743956356670)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-2839117247187169964904701174),(-2839117247187169960029319441)⟩,⟨(-5464928624767777177270431558),(-5464928624767777172390330925)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1422848123506124713611495740),(-1422848123506124710238279484)⟩,⟨(-4024582016509116811351748209),(-4024582016509116807971532780)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-613279872386845827832720305),(-613279872386845825627587548)⟩,⟨(-2714267390929687156724296839),(-2714267390929687154512601757)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-214072015851275239390840257),(-214072015851275238155495837)⟩,⟨(-1552976966152689924504215832),(-1552976966152689923264249515)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-46581587503144534842449321),(-46581587503144534446565333)⟩,⟨(-503773813838375003964018230),(-503773813838375003566493027)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨8173866463263128401129945970,8173866463263128417655366218⟩,⟨(-69617909540920053678906597613),(-69617909540920053661556871647)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨22770820028004574312188154545,22770820028004574361482279378⟩,⟨(-201402448956040775080812433738),(-201402448956040775029121882716)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨32695701697998978134459578235,32695701697998978215384074711⟩,⟨(-311895897033717968073659291451),(-311895897033717967989120430542)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨36605668364940399368155029353,36605668364940399478201514028⟩,⟨(-390952419479099123914408869649),(-390952419479099123800028944326)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨35035429029939861451700215412,35035429029939861586378315651⟩,⟨(-433584362142114794980679996152),(-433584362142114794841536161310)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨29960946260958166142052863778,29960946260958166294683795220⟩,⟨(-440477682379104555469436502624),(-440477682379104555312631075067)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨23848847285425343281183184256,23848847285425343443290914845⟩,⟨(-417243605040168860197274886424),(-417243605040168860031584054506)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨18668004307101348740680884835,18668004307101348902882881324⟩,⟨(-372635184265125643765507106501),(-372635184265125643600495787252)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨15313288068897694155543063610,15313288068897694308996081575⟩,⟨(-316291704006361076238585005390),(-316291704006361076083102864084)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨13618178480302323215374843943,13618178480302323353023284742⟩,⟨(-256720951139873157561555549878),(-256720951139873157422531860775)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨12796020916854553069513145741,12796020916854553186763771838⟩,⟨(-200056462997582103124262746131),(-200056462997582103006126395286)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨11974730319035219227466894141,11974730319035219322224756367⟩,⟨(-149733436683355708127013042990),(-149733436683355708031692148210)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨10554341081247356686746297007,10554341081247356758753074583⟩,⟨(-106857815424217601597198924659),(-106857815424217601524842051945)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨8309822804956825719806789655,8309822804956825769881861762⟩,⟨(-70885630228954843959306674687),(-70885630228954843909024036995)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨5317899632997460380468889916,5317899632997460409811790095⟩,⟨(-40289925566214327718981960322),(-40289925566214327689529913107)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1829196495128436995984180326,1829196495128437005608184068⟩,⟨(-13047357291180245716169776756),(-13047357291180245706512216191)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨17737508321434960335342584458,17737508321434960355157123875⟩,⟨18425540233342799181561952034,18425540233342799201573085334⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨52182582733453798139999699146,52182582733453798198122486310⟩,⟨53601617667040234468098722422,53601617667040234526797300719⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨83539815638335716994379703308,83539815638335717086779410773⟩,⟨83933876128441716689393980287,83933876128441716782708092808⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨109958882947176443749364706509,109958882947176443869623512214⟩,⟨106960385109032421654765213482,106960385109032421776216296671⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨129913929007496465863632579041,129913929007496466003553884302⟩,⟨121227283062954372440690678751,121227283062954372581990821523⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨142376255666610182833705616932,142376255666610182984491061032⟩,⟨126458051301345519130794462392,126458051301345519283005166368⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨146966373168088197602957716010,146966373168088197755507859542⟩,⟨123503669948075973951464953030,123503669948075974105419407528⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨144034932316838708266602905123,144034932316838708412686252420⟩,⟨114079924513979435734415827856,114079924513979435881851914655⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨134618865200869706452180300930,134618865200869706585375244536⟩,⟨100352587024891433676445712439,100352587024891433810926711784⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨120253426010652983001215348740,120253426010652983117327348406⟩,⟨84482057242211029665334931777,84482057242211029782654086429⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨102676792306883509140471626003,102676792306883509237430974744⟩,⟨68251205969236976443665565241,68251205969236976541732242545⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨83510911609937307634442533055,83510911609937307711880414091⟩,⟨52860885421567647908247491087,52860885421567647986653155099⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨64010629071095331931491363945,64010629071095331990029623568⟩,⟨38905939171372291577641110967,38905939171372291636968904471⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨44938301356556610231956988369,44938301356556610272640670456⟩,⟨26480267540085383493538668506,26480267540085383534807331244⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨26567698237813294039740508427,26567698237813294063623071093⟩,⟨15333467910933422716588056083,15333467910933422740829899780⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨8779075309232724542604415954,8779075309232724550472285286⟩,⟨5014510263886947452303479639,5014510263886947460292749908⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨19165268085129444596250627637,19165268085129444633536996697⟩,⟨190235598510150368981929243380,190235598510150369020735323824⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨58527284372272367271149624887,58527284372272367381957574324⟩,⟨559813823817932942419935648042,559813823817932942535305263263⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨100587149066769778656570016775,100587149066769778839019555385⟩,⟨896958761129408774540722123438,896958761129408774730680160134⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨146070642730741044487910466073,146070642730741044737703441556⟩,⟨1182881970976824080212263602338,1182881970976824080472379865920⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨194243840428520995417332215971,194243840428520995726940909622⟩,⟨1402719749474363866699015689802,1402719749474363867021561198222⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨242700937391366650518725872958,242700937391366650887240273821⟩,⟨1546857633237473415665371202865,1546857633237473416048450142934⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨287525890782010002112761007879,287525890782010002535232759421⟩,⟨1611760729898367373075949753732,1611760729898367373513164565084⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨323875938424907768186450659746,323875938424907768648134428138⟩,⟨1600147482279243706479401973029,1600147482279243706954930062043⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨346897491161712058892969803736,346897491161712059373930909337⟩,⟨1520344436427707676082579590787,1520344436427707676575842703086⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨352738599774205506980044067630,352738599774205507457143520912⟩,⟨1384814197152633480834561134959,1384814197152633481322071108321⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨339345637521093481827023986363,339345637521093482276275139393⟩,⟨1208074474632827365201119432035,1208074474632827365658798663969⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨306791112308258723465089670541,306791112308258723864527536140⟩,⟨1004432614648395047526348416871,1004432614648395047932314958561⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨257065370527006211751459954038,257065370527006212081942149539⟩,⟨786039069979394666711352081852,786039069979394667046639004821⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨193483525376240420884463559630,193483525376240421130725416482⟩,⟨561662209972088650124376353219,561662209972088650373910611371⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨119991363120316260867141461820,119991363120316261018706225206⟩,⟨336354123990978360382396765824,336354123990978360535857608982⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨40627368129540987442696908818,40627368129540987493694340030⟩,⟨111901135121327786407597503338,111901135121327786459214754256⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-152047816876045770933210734771),(-152047816876045770912877929139)⟩,⟨(-120096486229325884733397504582),(-120096486229325884711993487951)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-449718003233960866012031561857),(-449718003233960865950478114712)⟩,⟨(-354106525412082700123257597907),(-354106525412082700058866220894)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-727968272628119987611596521393),(-727968272628119987507780207185)⟩,⟨(-569555927163568705011872681650),(-569555927163568704904422831727)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-974987546340169745463205339698),(-974987546340169745315967736478)⟩,⟨(-755340640185469637138919742839),(-755340640185469636988619867458)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1180448580632073484322881298758),(-1180448580632073484131988928707)⟩,⟨(-902178168553842231925820156170),(-902178168553842231733810520058)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1336050955882866860754680771905),(-1336050955882866860521383528822)⟩,⟨(-1003395778045313322902428218326),(-1003395778045313322671097082646)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1435929393773523701706042877384),(-1435929393773523701434115844647)⟩,⟨(-1055559818596042978543514721750),(-1055559818596042978277295583703)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1476952196438099694093379752540),(-1476952196438099693790691513059)⟩,⟨(-1058820013816604794306149311413),(-1058820013816604794012567369160)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1458874468649048948507524812239),(-1458874468649048948185628548917)⟩,⟨(-1016815370600395989708010997628),(-1016815370600395989397562590485)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1384291130817653206922389920638),(-1384291130817653206595892791491)⟩,⟨(-936065681396387898602607847959),(-936065681396387898288458143432)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1258335953510138691876218543499),(-1258335953510138691561630673317)⟩,⟨(-824906978592109101977634984918),(-824906978592109101674884469494)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1088114890098704447637062804833),(-1088114890098704447350913089902)⟩,⟨(-692173605121957180136196141954),(-692173605121957179860500392035)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-881942504822288387035224356581),(-881942504822288386793485500370)⟩,⟨(-545921232449560240756588401484),(-545921232449560240523308474612)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-648535943611513275106778876890),(-648535943611513274923516768022)⟩,⟨(-392479806822255749178944942030),(-392479806822255749001766172438)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-396362533064948297347352990652),(-396362533064948297233169246164)⟩,⟨(-236025230872894497586694463428),(-236025230872894497476138258141)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-133264648507119468565328155503),(-133264648507119468526668633287)⟩,⟨(-78689914521421412923318727535),(-78689914521421412885846091100)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1687435288041089451849048261029),(-1687435288041089450009438706928)⟩,⟨428902569513448254445583799915,428902569513448256302539731382⟩⟩ +lemma checked : cachedMomentRuleBox column1_1 kernel1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 1 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_1_contains kernel1_1_contains +end cm1_1_1_1 +namespace cm1_3_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_0 j i k).mul (kernel3_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-5767017585863026499),(-5767017585863026466)⟩,⟨6484232286595602997,6484232286595603029⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16664332811964327457),(-16664332811964327399)⟩,⟨15132260013201034687,15132260013201034746⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-24697164852739260339),(-24697164852739260269)⟩,⟨14004430031011845267,14004430031011845340⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-26576552370267048762),(-26576552370267048702)⟩,⟨4408922485977145682,4408922485977145745⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-20415865287879563830),(-20415865287879563790)⟩,⟨(-7110398615374126219),(-7110398615374126174)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-8510330805928102412),(-8510330805928102371)⟩,⟨(-13127607438200077453),(-13127607438200077413)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨2601937862876523863,2601937862876523895⟩,⟨(-10389895342308280809),(-10389895342308280777)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨6754640956559251851,6754640956559251877⟩,⟨(-2576454578760839181),(-2576454578760839153)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3814862735814902131,3814862735814902157⟩,⟨3203399232543339667,3203399232543339688⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-847302198456209644),(-847302198456209622)⟩,⟨3487139014169254592,3487139014169254613⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2645701548382348297),(-2645701548382348276)⟩,⟨639504951152807519,639504951152807537⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1527189054722106483),(-1527189054722106460)⟩,⟨(-1506683296945880908),(-1506683296945880887)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨147104908486616071,147104908486616091⟩,⟨(-1691129386473996126),(-1691129386473996104)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨895779674305045728,895779674305045747⟩,⟨(-900145207212085242),(-900145207212085222)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨762693620751154236,762693620751154254⟩,⟨(-241801358435290725),(-241801358435290705)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨274287372003910970,274287372003910988⟩,⟨(-16988367224800927),(-16988367224800911)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨3335119701874477473477,3335119701874477527758⟩,⟨(-19432387355102269903481),(-19432387355102269849173)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨9238073503925068956222,9238073503925069096638⟩,⟨(-49870452723154195626919),(-49870452723154195486431)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨13197849708874567498251,13197849708874567672202⟩,⟨(-60927853912536947395025),(-60927853912536947220968)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨14763662409282348587991,14763662409282348744067⟩,⟨(-53809222275834025759690),(-53809222275834025603494)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨14058731203347001071978,14058731203347001182676⟩,⟨(-37695210704897433511418),(-37695210704897433400607)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨11641845554338514622863,11641845554338514686739⟩,⟨(-21654673553699799841195),(-21654673553699799777232)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨8407168133684614548815,8407168133684614581563⟩,⟨(-10208169391101873416884),(-10208169391101873384088)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨5283504339391163136165,5283504339391163153242⟩,⟨(-3753667050489819182938),(-3753667050489819165841)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨2875468146792039655046,2875468146792039663400⟩,⟨(-835199281440047485328),(-835199281440047476964)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1339349976217270215863,1339349976217270219805⟩,⟨155764930008627359479,155764930008627363423⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨517344065038056315987,517344065038056317770⟩,⟨323390936856935279035,323390936856935280818⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨149524872093027826695,149524872093027827628⟩,⟨241323655300976061464,241323655300976062399⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨16476812550596981332,16476812550596981787⟩,⟨136174233288665734278,136174233288665734732⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16798209754450325059),(-16798209754450324849)⟩,⟨65636500949385341704,65636500949385341919⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-15764534911261137175),(-15764534911261137071)⟩,⟨27443866715579211852,27443866715579211958⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-5731350538856328858),(-5731350538856328813)⟩,⟨7319687942673351806,7319687942673351848⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨3365640184256557913661201,3365640184256557930367771⟩,⟨12436419625157233008132851,12436419625157233025284785⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨9367063826752457040554541,9367063826752457086455002⟩,⟨32436090276122055940559243,32436090276122055987603373⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨13221820980686080269070086,13221820980686080332945986⟩,⟨40768321128533225960113697,40768321128533226025367318⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨13994098511541856315805060,13994098511541856383487069⟩,⟨37224835343270049340177244,37224835343270049409032193⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨11883266787770605944074398,11883266787770606003389462⟩,⟨26843269843519486740771577,26843269843519486800844545⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨8239540952794380530471401,8239540952794380574768530⟩,⟨15651037182197082549662461,15651037182197082594338760⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨4682485251076529627352182,4682485251076529655967023⟩,⟨7304358545437339421151802,7304358545437339449910952⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨2172703311137448085665371,2172703311137448101922010⟩,⟨2522554913997311492314840,2522554913997311508610533⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨811546560852742640052930,811546560852742648709572⟩,⟨378590316647319316651346,378590316647319325313008⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨236631623067926245473122,236631623067926250051438⟩,⟨(-325084395536844210434017),(-325084395536844205856507)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨53078586768502258005273,53078586768502260741646⟩,⟨(-421046505855790273070000),(-421046505855790270333778)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨14506096585221931324601,14506096585221932933929⟩,⟨(-330769260180136728734963),(-330769260180136727125052)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨12391520065962826663239,12391520065962827586962⟩,⟨(-218701918897531994612300),(-218701918897531993687806)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨12642397834760660717173,12642397834760661228405⟩,⟨(-130185974730490753553663),(-130185974730490753041801)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨9259416691256703810766,9259416691256704065591⟩,⟨(-67314424793951973789298),(-67314424793951973534085)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨3343854651697366503047,3343854651697366579963⟩,⟨(-20652894466218980827273),(-20652894466218980750232)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-438244733904912769980353601),(-438244733904912769164531871)⟩,⟨257968020791105182720568960,257968020791105183526710994⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1209973514911868689144121054),(-1209973514911868686828074396)⟩,⟨758043971733265967219253115,758043971733265969508032691⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1703456808387946954063472824),(-1703456808387946950624221914)⟩,⟨1200350902403768462948565437,1200350902403768466348413559⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1842285927616780810602773584),(-1842285927616780806589357226)⟩,⟨1527529533623010251125256208,1527529533623010255095376792⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1664074484207632895572285324),(-1664074484207632891553142428)⟩,⟨1684726488304057122951059505,1684726488304057126933132843⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1290144011460846636315914656),(-1290144011460846632690743762)⟩,⟨1650552529630461852352727062,1650552529630461855957049029⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-864783526898641829057209276),(-864783526898641826112724328)⟩,⟨1454329047656497994322400004,1454329047656497997263514037⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-498088505162407829148833230),(-498088505162407826970178358)⟩,⟨1164529878002280812980638481,1164529878002280815169176142⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-239826518065162164801828944),(-239826518065162163311689801)⟩,⟨857449489184953587458588967,857449489184953588965366114⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-87806736165531898694577622),(-87806736165531897736309625)⟩,⟨588682796267451983234132608,588682796267451984210020060⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-13543980860087583998188805),(-13543980860087583408409468)⟩,⟨382636338403165998342387627,382636338403165998947298686⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨14656668363250293657007121,14656668363250294022735850⟩,⟨238779053289755642769517553,238779053289755643145957981⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨20221271019768652974940390,20221271019768653209514096⟩,⟨144110040079962007155947839,144110040079962007396695605⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨16660223567693757996079028,16660223567693758139112734⟩,⟨83147236359755155482344146,83147236359755155628754817⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨10295244373766330440054348,10295244373766330516569785⟩,⟨42767227172208978914575220,42767227172208978992751432⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨3431084513098552755692266,3431084513098552779637380⟩,⟨13147433847749990341307855,13147433847749990365748570⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1733827399784662068805393892,1733827399784662075579942189⟩,⟨(-4384632448404347725813413452),(-4384632448404347719111025113)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4400826594841784234558493250,4400826594841784254340802526⟩,⟨(-12575166094872211539496937835),(-12575166094872211519897416489)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨5001352806073083729211059459,5001352806073083760301665872⟩,⟨(-19067799289496476359686473339),(-19067799289496476328806383124)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨3137922528687880185689530881,3137922528687880225204030242⟩,⟨(-22953971689789839532785460762),(-22953971689789839493413223165)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-596851118540631745448843068),(-596851118540631701388041882)⟩,⟨(-23757410224246379783597444403),(-23757410224246379739546225591)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-4943010213694430513075007596),(-4943010213694430468638653540)⟩,⟨(-21637672864432591221023926143),(-21637672864432591176491981518)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-8564210868389459925928248295),(-8564210868389459885000221321)⟩,⟨(-17398829458048711390169543977),(-17398829458048711349104037126)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-10590092066357958195024273129),(-10590092066357958160396088922)⟩,⟨(-12232088616955740769708088626),(-12232088616955740734966510733)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-10848343611528147505038929631),(-10848343611528147477938020209)⟩,⟨(-7302095820598853174967925218),(-7302095820598853147825950159)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-9736388058031928823111870200),(-9736388058031928803098726888)⟩,⟨(-3396660545149145528477618832),(-3396660545149145508509028782)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7892860529177392527125103274),(-7892860529177392512768203436)⟩,⟨(-801976398226535080377167198),(-801976398226535066127878521)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-5891173501800297157682081343),(-5891173501800297147853353744)⟩,⟨596658752443246852711064674,596658752443246862406208163⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-4085467933562620103059618250),(-4085467933562620096154716840)⟩,⟨1110857349500472946831324964,1110857349500472953620314258⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2605995341353187167531584613),(-2605995341353187162807709885)⟩,⟨1070760078921411725599258449,1070760078921411730244137479⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1429284897063917548309603839),(-1429284897063917545589299639)⟩,⟨731472081298192245514488675,731472081298192248190069347⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-453243142369727400753492580),(-453243142369727399869708685)⟩,⟨256299674668882115195103931,256299674668882116064557685⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨89564623919474406776520866,89564623919474410441012006⟩,⟨(-20346890352441095230676308),(-20346890352441091539211729)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1283602573384707402239854347,1283602573384707413354447277⟩,⟨(-314753721891975431198764831),(-314753721891975420043935082)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨5087566804143453210177039047,5087566804143453229001339097⟩,⟨(-1420449799260473450897344296),(-1420449799260473432122046933)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨11966321710051600988976556050,11966321710051601015666944942⟩,⟨(-3950390366987695591516940269),(-3950390366987695565074967515)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨21018179775015756326547662059,21018179775015756360881119783⟩,⟨(-8375166229338984547776700739),(-8375166229338984513893809396)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨30303010595565307655892812850,30303010595565307696989884808⟩,⟨(-14699803097346686368819725208),(-14699803097346686328268497845)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨37598156760078680741991456033,37598156760078680788190774596⟩,⟨(-22238194140719934790023886871),(-22238194140719934744297781178)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨41243197741057137192375902053,41243197741057137241310083428⟩,⟨(-29690142215701684201646517124),(-29690142215701684152958709170)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨40691442761621047062847261398,40691442761621047111761357178⟩,⟨(-35540836829631222835106694058),(-35540836829631222786145675234)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨36548777944968111179245383087,36548777944968111225426361870⟩,⟨(-38584793319980225528337520719),(-38584793319980225481857257395)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨30158930215453708924839757523,30158930215453708966442558794⟩,⟨(-38294990364541824843124289803),(-38294990364541824801077983489)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨23008415109938901457270660814,23008415109938901492901287877⟩,⟨(-34870654342311029117938555377),(-34870654342311029081832217196)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨16246755995268659654700928237,16246755995268659683175714093⟩,⟨(-29002084086368398783238097028),(-29002084086368398754340793482)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨10473194792082407849375240466,10473194792082407870448387510⟩,⟨(-21529863261026310996578557583),(-21529863261026310975204185321)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨5764884434999876436513132025,5764884434999876449617387547⟩,⟨(-13175353914579896915135807177),(-13175353914579896901862345926)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1828411323590711327903895244,1828411323590711332331244095⟩,⟨(-4425673998480295935380140427),(-4425673998480295930898963702)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨41704770277689954625904635516,41704770277689954766839710663⟩,⟨(-70942201267223581382147220538),(-70942201267223581241311690460)⟩⟩ +lemma checked : cachedMomentRuleBox column1_0 kernel3_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 3 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_0_contains kernel3_0_contains +end cm1_3_0_0 +namespace cm1_3_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_0 j i k).mul (kernel3_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨68311480758131380163,68311480758131380350⟩,⟨(-28421606539090142260),(-28421606539090142072)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨184129430395653593384,184129430395653593841⟩,⟨(-56011066370410179526),(-56011066370410179069)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨243104139651161974583,243104139651161975112⟩,⟨(-21701402943857646799),(-21701402943857646266)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨226684300714712781279,226684300714712781706⟩,⟨55494654015569950042,55494654015569950468⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨143283922915371558056,143283922915371558380⟩,⟨123326459171051149570,123326459171051149893⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨32107949172119211215,32107949172119211459⟩,⟨134457696274655662219,134457696274655662457⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-49711847228538801653),(-49711847228538801466)⟩,⟨81709143999685148981,81709143999685149172⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-64826466273438677273),(-64826466273438677132)⟩,⟨6911355317983795750,6911355317983795887⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-27735841638901088796),(-27735841638901088689)⟩,⟨(-35817919408373919100),(-35817919408373918994)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨13003901134965802953,13003901134965803037⟩,⟨(-30161628012088867471),(-30161628012088867393)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨24866386879058449571,24866386879058449643⟩,⟨(-2773088345301827670),(-2773088345301827595)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨12804128151155568599,12804128151155568664⟩,⟨15060028071608087278,15060028071608087339⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2207457123167734141),(-2207457123167734093)⟩,⟨15498668319326051466,15498668319326051515⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-8497833060129468119),(-8497833060129468078)⟩,⟨8058567275607524569,8058567275607524610⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7055603696749462144),(-7055603696749462115)⟩,⟨2149714387103132039,2149714387103132068⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-2528108732878371480),(-2528108732878371458)⟩,⟨150826577261911317,150826577261911336⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-116497506607267895860732),(-116497506607267895470235)⟩,⟨78740759905584365733486,78740759905584366124584⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-302316849951364320320368),(-302316849951364319293356)⟩,⟨201024087136179022734650,201024087136179023763179⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-378953072189299065461659),(-378953072189299064145056)⟩,⟨241735092583196507500668,241735092583196508819020⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-350821211012940472312049),(-350821211012940471064465)⟩,⟨205478009983649888215675,205478009983649889464627⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-265928277467082627693669),(-265928277467082626736102)⟩,⟨132448181632964104041496,132448181632964104999796⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-173123332545849313206403),(-173123332545849312589676)⟩,⟨63531690330783377895940,63531690330783378512908⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-99181843103656897879751),(-99181843103656897541667)⟩,⟨18641496286198480788096,18641496286198481126197⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-50307233319560545956813),(-50307233319560545799371)⟩,⟨(-2299044608105266630928),(-2299044608105266473494)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-22284760009306692581759),(-22284760009306692512257)⟩,⟨(-8036859765453625955558),(-8036859765453625886054)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-8234549947585456169350),(-8234549947585456133387)⟩,⟨(-7069390402513002864533),(-7069390402513002828567)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2182189241284069037400),(-2182189241284069018242)⟩,⟨(-4485245650795231128325),(-4485245650795231109169)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-64151522783772699721),(-64151522783772690518)⟩,⟨(-2351542522301046598958),(-2351542522301046589762)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨425327798846884862263,425327798846884866416⟩,⟨(-1067460974771622627896),(-1067460974771622623739)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨380650612676273877359,380650612676273879435⟩,⟨(-427256409248377367330),(-427256409248377365252)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨223648100162728835209,223648100162728836211⟩,⟨(-149033199499927605982),(-149033199499927604981)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨71172540387204387358,71172540387204387662⟩,⟨(-34639841120800807487),(-34639841120800807184)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨53999262514671766477492724,53999262514671766597136217⟩,⟨(-52491708680248216078612978),(-52491708680248215959017308)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨139093891627695425846644464,139093891627695426173311277⟩,⟨(-140991855679733222837962355),(-140991855679733222511031727)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨170372683683093742284484511,170372683683093742733611502⟩,⟨(-187322081085852790932193263),(-187322081085852790481718916)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨149302317194612965859729328,149302317194612966327442927⟩,⟨(-184571693547706480238183358),(-184571693547706479767744200)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨101367359753269610024977848,101367359753269610425729960⟩,⟨(-145803540584689427658551678),(-145803540584689427254249648)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨54104139824873100858593459,54104139824873101149311845⟩,⟨(-94259150924547664582573370),(-94259150924547664288428557)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨21842047401442567041013911,21842047401442567221615104⟩,⟨(-49661783519043128452367081),(-49661783519043128269143296)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨5248883740133376275709843,5248883740133376372915310⟩,⟨(-20544419095923037088562638),(-20544419095923036989698675)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1143663302162003367348614),(-1143663302162003318059248)⟩,⟨(-5691408867342417620314709),(-5691408867342417570125403)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2661235370440237924084977),(-2661235370440237898332824)⟩,⟨92103350763057437365922,92103350763057463576378⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2426795102783764773490838),(-2426795102783764756563383)⟩,⟨1525168405997738546584772,1525168405997738563749140⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1789000290457094265258743),(-1789000290457094254366281)⟩,⟨1402347923016825131533641,1402347923016825142542166⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1193607599818304315610423),(-1193607599818304308889368)⟩,⟨949133888403685387216222,949133888403685393992554⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-734192893924424123447788),(-734192893924424119522329)⟩,⟨555336228837841168101851,555336228837841172053119⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-392442231059102934136253),(-392442231059102932109023)⟩,⟨279540743972727507465602,279540743972727509504119⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-122834697281717135517020),(-122834697281717134894538)⟩,⟨84204102455034869488740,84204102455034870114390⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1858711241442412722752113430,1858711241442412727289750856⟩,⟨1633645804669639045876600391,1633645804669639050438916328⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨5374746766917181057869910194,5374746766917181070683304505⟩,⟨4438351381193428196108654694,4438351381193428208987217257⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨8273280487711940962155428626,8273280487711940980990827868⟩,⟨6031072426006634165038042419,6031072426006634183953731275⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨10164246171914499857727456489,10164246171914499879394613209⟩,⟨6126171306367496883000644094,6126171306367496904728068958⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨10795334297554351018633532862,10795334297554351039976548005⟩,⟨4968935471172767057336828826,4968935471172767078684186566⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨10183180319877819884391946283,10183180319877819903407404063⟩,⟨3166878708108197778114736613,3166878708108197797052830471⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨8642537954486209400879259850,8642537954486209416173067521⟩,⟨1381509072586577824054747786,1381509072586577839200034324⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨6665392069957454707447673224,6665392069957454718693499891⟩,⟨58481267225580309176235018,58481267225580320235473635⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨4722851347466622075072203477,4722851347466622083082110063⟩,⟨(-670156356312788303142415912),(-670156356312788295304375780)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨3115933283208806495238805096,3115933283208806501241585039⟩,⟨(-909772797853322069834451159),(-909772797853322063938955574)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1943904179389595500695799653,1943904179389595504907600732⟩,⟨(-855665706876750594443497919),(-855665706876750590290714989)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1164303138824223744887080982,1164303138824223747681640152⟩,⟨(-678894852629321523408296331),(-678894852629321520642975360)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨676003459972448959844165109,676003459972448961614834573⟩,⟨(-483037847892027995897252164),(-483037847892027994139263281)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨377265725852047376628010479,377265725852047377700032643⟩,⟨(-311587633297832854454105502),(-311587633297832853386835449)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨189345637866049649935766766,189345637866049650507526033⟩,⟨(-171823879574204096759796877),(-171823879574204096189500831)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨57454359959365530473222950,57454359959365530651951812⟩,⟨(-54622431648103117174773444),(-54622431648103116996334364)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-19149630981498835439087059421),(-19149630981498835407758206598)⟩,⟨(-3985888629186396363520807599),(-3985888629186396331985847656)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-54691036045363560537907912755),(-54691036045363560446442654056)⟩,⟨(-8983107667154001649789304234),(-8983107667154001557826218776)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-82206655206515847235695709582),(-82206655206515847092032622336)⟩,⟨(-6404500117563472276127623761),(-6404500117563472131967289061)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-97562808484818889000985510548),(-97562808484818888818631372676)⟩,⟨4893862976104399857830439388,4893862976104400040360065046⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-98793323781533104331598786708),(-98793323781533104128778350140)⟩,⟨22134731189794642794224211338,22134731189794642996718339749⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-86968801584513708393917183563),(-86968801584513708190390515563)⟩,⟨39992789014010739036095804067,39992789014010739238962774057⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-66130296099496361226174690015),(-66130296099496361040295024753)⟩,⟨53089175624077800408360003887,53089175624077800593551494224⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-41995113111968537880733401810),(-41995113111968537725517025435)⟩,⟨58263933517376908706666708855,58263933517376908861459764937⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-19969711035550042993649945933),(-19969711035550042874496941946)⟩,⟨55474031488426435200732593300,55474031488426435319909008264⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-3515257253625219376132516482),(-3515257253625219290149081222)⟩,⟨47088426344638869175222781041,47088426344638869261676312934⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨6368245435649902719794521632,6368245435649902786284217555⟩,⟨36318438967913059638926050756,36318438967913059706078742001⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨10563291289102442700789741191,10563291289102442754488712606⟩,⟨25819255693190034244179757011,25819255693190034298456645436⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨10784434131406340813798302982,10784434131406340853796397379⟩,⟨17057617722483092916054161807,17057617722483092956464074525⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨8699344215420514389348902045,8699344215420514416437015954⟩,⟨10394680877363521962607449649,10394680877363521989946375657⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨5501058281366287408913983271,5501058281366287424424821953⟩,⟨5493691479707140886148431865,5493691479707140901788094393⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1868036634026860678466723718,1868036634026860683492871684⟩,⟨1705652513710159045136239863,1705652513710159050201288538⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-90585301319494587468188330),(-90585301319494573694904781)⟩,⟨(-319794647279709278374602802),(-319794647279709264689713876)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1395531095592488599035186614),(-1395531095592488557319778336)⟩,⟨(-4587399639269551955388913323),(-4587399639269551913792543772)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-6261298538828461712771365410),(-6261298538828461642239637958)⟩,⟨(-18208473616409213331418014029),(-18208473616409213260672912408)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-17317432169750013913577686888),(-17317432169750013813581525889)⟩,⟨(-42889831013478333184990947321),(-42889831013478333084075435687)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-36574014831916967873498458621),(-36574014831916967744243529652)⟩,⟨(-75381162072290902922299092396),(-75381162072290902791449335213)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-64078721002080918288098685044),(-64078721002080918131743113822)⟩,⟨(-108541158470307068197652232125),(-108541158470307068039471538622)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-96934296808197524652537018227),(-96934296808197524473986900786)⟩,⟨(-134055747649609906935171305301),(-134055747649609906755238766367)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-129555357761469090385279610273),(-129555357761469090192403715858)⟩,⟨(-145653782685985281345633701159),(-145653782685985281152406102898)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-155325035141551437269990829861),(-155325035141551437072921996243)⟩,⟨(-141347969676790940785692291123),(-141347969676790940589516610595)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-168873686609884698246915621876),(-168873686609884698056639863936)⟩,⟨(-123715547952802930117045887833),(-123715547952802929928678100949)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-167768619021242428127533290666),(-167768619021242427952270303095)⟩,⟨(-98305706697589355560704226552),(-98305706697589355387866851317)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-152814571344678090783168489508),(-152814571344678090628866212180)⟩,⟨(-71213522703200789084800801026),(-71213522703200788932911562995)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-127057601372522267412950107460),(-127057601372522267280932105856)⟩,⟨(-47066695687352151503719182046),(-47066695687352151373535675909)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-94256168171267551754510156849),(-94256168171267551653491259408)⟩,⟨(-28121562077271069251049704406),(-28121562077271069151230386219)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-57637397825415417072617839829),(-57637397825415417009584206820)⟩,⟨(-14400141105338020879528795411),(-14400141105338020817153102498)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-19351487575999186281131145073),(-19351487575999186259796039385)⟩,⟨(-4361591459270766561614414690),(-4361591459270766540486093711)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-291267073153570047284150432819),(-291267073153570046671085420487)⟩,⟨(-112837224348112306591101954176),(-112837224348112305978730645995)⟩⟩ +lemma checked : cachedMomentRuleBox column1_0 kernel3_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 3 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_0_contains kernel3_1_contains +end cm1_3_0_1 +namespace cm1_3_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_1 j i k).mul (kernel3_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨35180064943192417736,35180064943192417793⟩,⟨(-23158228619791577360),(-23158228619791577306)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨97853674151941479494,97853674151941479612⟩,⟨(-44986130022537160107),(-44986130022537159988)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨130404093879632168833,130404093879632168972⟩,⟨(-16483823334226192541),(-16483823334226192404)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨111176345868104628949,111176345868104629068⟩,⟨38993366378713620080,38993366378713620197⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨49831541412657023954,49831541412657024033⟩,⟨71340574911589620710,71340574911589620788⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-9744382902795911735),(-9744382902795911662)⟩,⟨55872204427404559496,55872204427404559568⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-30805806929526947408),(-30805806929526947347)⟩,⟨15577775238573541671,15577775238573541732⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-17210445818407195013),(-17210445818407194966)⟩,⟨(-11409220000807568063),(-11409220000807568015)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1931917922652104098,1931917922652104136⟩,⟨(-12520765064281450709),(-12520765064281450673)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨7960352447579804161,7960352447579804192⟩,⟨(-2004067967390955574),(-2004067967390955545)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3544529436479204838,3544529436479204867⟩,⟨4431611692560583802,4431611692560583833⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1526532636137158605),(-1526532636137158583)⟩,⟨3845798234661723075,3845798234661723098⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2950898723074664994),(-2950898723074664971)⟩,⟨869311475918388252,869311475918388273⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1997288128146092553),(-1997288128146092530)⟩,⟨(-914346841089105009),(-914346841089104988)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-809989609404464046),(-809989609404464028)⟩,⟨(-1069756407857218774),(-1069756407857218755)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-175373826505430468),(-175373826505430452)⟩,⟨(-418561895656662458),(-418561895656662441)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3318600866476365129468),(-3318600866476365086162)⟩,⟨38606079512154231025628,38606079512154231068970⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-11753661729734176177587),(-11753661729734176063818)⟩,⟨99113849785991612208590,99113849785991612322479⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-22696604598890313130563),(-22696604598890312985368)⟩,⟨120750377659185866936455,120750377659185867081842⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-31963815660702111402656),(-31963815660702111266750)⟩,⟨105180857702006942111294,105180857702006942247430⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-34577691588014932130853),(-34577691588014932029136)⟩,⟨70898668351638134073285,70898668351638134175204⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-29613429690906148486944),(-29613429690906148424206)⟩,⟨37318846603200688686786,37318846603200688749664⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-20478855976684437576694),(-20478855976684437543585)⟩,⟨14531308665491817987584,14531308665491818020743⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-11539714820267754826869),(-11539714820267754811173)⟩,⟨3124094708026199423076,3124094708026199438767⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-5262890773865981891358),(-5262890773865981883699)⟩,⟨(-826540854796699412856),(-826540854796699405211)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1858624074713227002482),(-1858624074713226998444)⟩,⟨(-1361138299402302337105),(-1361138299402302333069)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-414763544766569449749),(-414763544766569447767)⟩,⟨(-909792507850475863496),(-909792507850475861514)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨38684247992893141344,38684247992893142321⟩,⟨(-445567504147494890882),(-445567504147494889899)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨111975667206962161349,111975667206962161812⟩,⟨(-176169295799657501761),(-176169295799657501299)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨82782434007198805679,82782434007198805898⟩,⟨(-56630872249850646459),(-56630872249850646239)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨43818107626133158417,43818107626133158525⟩,⟨(-13884956781005044360),(-13884956781005044251)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨13214263467992244929,13214263467992244972⟩,⟨(-2036710891422602975),(-2036710891422602935)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-40502397853622764500502716),(-40502397853622764477577804)⟩,⟨7015132890542857854180628,7015132890542857876659894⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-109275651412042806359434327),(-109275651412042806295145455)⟩,⟨20497503288878512802269550,20497503288878512865378580⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-147290823491085006920552062),(-147290823491085006827308110)⟩,⟨31634466550134084866001877,31634466550134084957759706⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-150255449465140445966888324),(-150255449465140445861497747)⟩,⟨37820553568711645019631800,37820553568711645123669827⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-127296335269861726846898726),(-127296335269861726745837523)⟩,⟨37391009424942757342439815,37391009424942757442544703⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-93339916684230210106392988),(-93339916684230210021419484)⟩,⟨31238266745570817583849368,31238266745570817668274197⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-60901004686439991675494770),(-60901004686439991611694725)⟩,⟨22356246016610778120453831,22356246016610778184002583⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-36228419199254183304707482),(-36228419199254183261270288)⟩,⟨13882655171668778043257581,13882655171668778086604961⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-20119108266483825855236143),(-20119108266483825827975675)⟩,⟨7577299608663583946130262,7577299608663583973367389⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-10669858436907187849832192),(-10669858436907187833769722)⟩,⟨3676913912131136880349671,3676913912131136896408616⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-5514744463093232579172069),(-5514744463093232570115709)⟩,⟨1595983410809259139441327,1595983410809259148497781⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2822902511161590867685759),(-2822902511161590862712389)⟩,⟨615194470977066316772683,615194470977066321746058⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1443240264763984813365562),(-1443240264763984810677798)⟩,⟨202258248095320741016571,202258248095320743703996⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-730174145772902377417690),(-730174145772902375999812)⟩,⟨49124343202482367328030,49124343202482368745512⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-342401192299292679653715),(-342401192299292678970283)⟩,⟨3591548503353486170332,3591548503353486853489⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-100315451701556567151876),(-100315451701556566949338)⟩,⟨(-2079551946275161536815),(-2079551946275161334372)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨242252774312622718745725851,242252774312622718952406385⟩,⟨(-66792754129265563131426951),(-66792754129265562926026502)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨674846052033042937017762010,674846052033042937607360513⟩,⟨(-202832591311016330106091955),(-202832591311016329520380986)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨968174466570704262946730277,968174466570704263830392985⟩,⟨(-339143296015212692466336755),(-339143296015212691589120654)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1080026876705651065221215563,1080026876705651066266542601⟩,⟨(-459263256639923189427076270),(-459263256639923188390378041)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1022320819518150820746512338,1022320819518150821816823918⟩,⟨(-538222744306691011204971718),(-538222744306691010144027102)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨849066196297670417087970558,849066196297670418097563568⟩,⟨(-557341641625357316451751311),(-557341641625357315449556782)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨629779817342513942172509268,629779817342513943041050354⟩,⟨(-516038831654789961448921553),(-516038831654789960585746540)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨422657054461700366152258738,422657054461700366840634893⟩,⟨(-432016718951294210673165705),(-432016718951294209988616808)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨259967933462703841974674400,259967933462703842483897128⟩,⟨(-331196169251923811646351505),(-331196169251923811139905927)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨148720454290078311040638179,148720454290078311397043443⟩,⟨(-235889293290455865031248963),(-235889293290455864676900851)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨80493345399332550778439778,80493345399332551017460857⟩,⟨(-158482771078473677503055570),(-158482771078473677265557244)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨41977866665786671695255363,41977866665786671853354802⟩,⟨(-101806836434974091651446099),(-101806836434974091494344958)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨21416086134665458130964295,21416086134665458234954160⟩,⟨(-62945721847119945218112229),(-62945721847119945114659670)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨10688937976475441678262095,10688937976475441742260915⟩,⟨(-37000967356543629315539133),(-37000967356543629251821836)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨4935365303580882307689843,4935365303580882342011249⟩,⟨(-19273270190545341815666437),(-19273270190545341781480010)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1431832750410788892356851,1431832750410788903105532⟩,⟨(-5962683423822751592583788),(-5962683423822751581875446)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨2776771810291478141215747195,2776771810291478145404215214⟩,⟨10849458343610955126478424125,10849458343610955130805120237⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨8595217624796328618569207268,8595217624796328630805203086⟩,⟨30911663287705937876144008736,30911663287705937888789814350⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨14960594470854923511163167877,14960594470854923530403810908⟩,⟨46392377371138923970352278723,46392377371138923990255967256⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨21580621431518876167467168454,21580621431518876191979360953⟩,⟨55367898275328167999555130751,55367898275328168024949093905⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨27584439098469376007778651677,27584439098469376035297239178⟩,⟨57313471174996695964101227373,57313471174996695992654598764⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨31869181276660554612511602009,31869181276660554642021391516⟩,⟨53130697081999315350978947499,53130697081999315381370233690⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨33595042758296980683373975297,33595042758296980713265773902⟩,⟨44769408859290242236729274609,44769408859290242267213279401⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨32551051767856678106708413030,32551051767856678134792795909⟩,⟨34574204817352843212852381104,34574204817352843241272177803⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨29205317804958922773619510628,29205317804958922798207845136⟩,⟨24610201075319062233165001723,24610201075319062257906147498⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨24455262453640902020823862198,24455262453640902040997814301⟩,⟨16222987632231452797597428590,16222987632231452817818883624⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨19257685923115380235729478371,19257685923115380251332663776⟩,⟨9947179880160346561891984803,9947179880160346577495016088⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨14339173517059821138107419329,14339173517059821149544183077⟩,⟨5694421475395890077948165434,5694421475395890089370487671⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨10083477085338873450250243747,10083477085338873458317388509⟩,⟨3048979445335999418836854371,3048979445335999426886957528⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6569604508946619712673414535,6569604508946619717999787746⟩,⟨1518506478954909916364291226,1518506478954909921675582349⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨3676186169878990770860682219,3676186169878990773860541720⟩,⟨673916292622057488881096679,673916292622057491871186433⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1179883566448389784434096115,1179883566448389785397112847⟩,⟨187901772385736795331070228,187901772385736796290740486⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-8068796311647433136368129932),(-8068796311647433129554133150)⟩,⟨(-35739900767424564813603661942),(-35739900767424564805883583818)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-25063300299373377990089049419),(-25063300299373377969623998723)⟩,⟨(-103280434984683906735770692206),(-103280434984683906712661073050)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-44109558755247650051791793070),(-44109558755247650017747995668)⟩,⟨(-159517731283152674212139691322),(-159517731283152674174000510977)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-65136392517697812596698753792),(-65136392517697812549419544647)⟩,⟨(-198929261021691479709314462006),(-198929261021691479656984711807)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-86544534494313843253627789929),(-86544534494313843193132948505)⟩,⟨(-218652185476084367674278936853),(-218652185476084367608933317487)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-105611459026387411323378926116),(-105611459026387411251153147412)⟩,⟨(-218897636431188097094448530125),(-218897636431188097018361713017)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-119382550802976064355923215831),(-119382550802976064275145619307)⟩,⟨(-202725305066408806848225518007),(-202725305066408806764938837240)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-125671196385683161810153406020),(-125671196385683161725345458254)⟩,⟨(-175190077370560632667288059850),(-175190077370560632581321408700)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-123742185806434965378787584907),(-123742185806434965295073627988)⟩,⟨(-142079040483096432536802412861),(-142079040483096432452991715021)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-114416989672197761686526157833),(-114416989672197761608717896749)⟩,⟨(-108626652247991817975976497089),(-108626652247991817898714137644)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-99627874954532035402522201421),(-99627874954532035333264098928)⟩,⟨(-78601039694094049515261193367),(-78601039694094049446804705069)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-81691323996317814450606224272),(-81691323996317814391911812310)⟩,⟨(-53973308569711536812171902842),(-53973308569711536754282760704)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-62636247689135168894951844548),(-62636247689135168848622247060)⟩,⟨(-35120051958438576708771482325),(-35120051958438576663113656444)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-43807151420302962112885424471),(-43807151420302962079590641535)⟩,⟨(-21320952045371876181874471977),(-21320952045371876149039112921)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-25779442091666991890661894818),(-25779442091666991870650282965)⟩,⟨(-11282098476263953745844060949),(-11282098476263953726085446202)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-8493232296522678988382416348),(-8493232296522678981736936676)⟩,⟨(-3508954461078174666827778581),(-3508954461078174660261938326)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-141975162488564935175557720009),(-141975162488564934996310229849)⟩,⟨(-229346587781830766019726579413),(-229346587781830765836050314953)⟩⟩ +lemma checked : cachedMomentRuleBox column1_1 kernel3_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 3 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_1_contains kernel3_0_contains +end cm1_3_1_0 +namespace cm1_3_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_1 j i k).mul (kernel3_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-355958222693648889252),(-355958222693648888794)⟩,⟨47466611994113714653,47466611994113715109⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-920836545610922936477),(-920836545610922935329)⟩,⟨(-10204471487854793310),(-10204471487854792160)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1079243952912257949979),(-1079243952912257948612)⟩,⟨(-335257961433223024129),(-335257961433223022762)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-752457648063468760902),(-752457648063468759770)⟩,⟨(-689905137872379690708),(-689905137872379689573)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-176353801068456944863),(-176353801068456944143)⟩,⟨(-740468220280545320220),(-740468220280545319500)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨246415334509816410837,246415334509816411440⟩,⟨(-436528512765145586302),(-436528512765145585696)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨304069424264824144382,304069424264824144897⟩,⟨(-51087464254367941184),(-51087464254367940666)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨123739523676639369962,123739523676639370331⟩,⟨139200088803926934068,139200088803926934434⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-41344009655715594533),(-41344009655715594281)⟩,⟨107557797291801113229,107557797291801113480⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-74916910841580976554),(-74916910841580976383)⟩,⟨5818883179196691076,5818883179196691249⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-27188750344469983463),(-27188750344469983312)⟩,⟨(-44524683108694482598),(-44524683108694482445)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨17119119587256499636,17119119587256499748⟩,⟨(-34069108888008397354),(-34069108888008397238)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨27614130445485807565,27614130445485807650⟩,⟨(-6513376503718891217),(-6513376503718891131)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨18167115383918905072,18167115383918905135⟩,⟨8963479609437084378,8963479609437084443⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨7355175670519711925,7355175670519711968⟩,⟨9945394287267771008,9945394287267771051⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1607435988178600936,1607435988178600958⟩,⟨3861020666001667713,3861020666001667737⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨215121815042109076487175,215121815042109076873439⟩,⟨(-173458898310633397733868),(-173458898310633397346365)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨567931656357188520321982,567931656357188521346791⟩,⟨(-433473012605397226237632),(-433473012605397225209753)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨733526770462036297305697,733526770462036298638959⟩,⟨(-496801240099314645295684),(-496801240099314643959028)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨702040561504533116114311,702040561504533117398326⟩,⟨(-385836420171505996814925),(-385836420171505995528413)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨544155695203917675645954,544155695203917676643913⟩,⟨(-208058362347162431673336),(-208058362347162430674117)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨352006816790318057407212,352006816790318058052909⟩,⟨(-61897798544983601606493),(-61897798544983600960400)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨191060675421676791616604,191060675421676791968409⟩,⟨15151067637823214866700,15151067637823215218514⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨85605242936950555610544,85605242936950555771879⟩,⟨36113740569003651349023,36113740569003651510281⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨29825689569257929321615,29825689569257929398146⟩,⟨29791010767512986558997,29791010767512986635485⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨6269123664726805597298,6269123664726805639470⟩,⟨17453203417754257811686,17453203417754257853853⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1074120642503648862395),(-1074120642503648840489)⟩,⟨8104562289331969771102,8104562289331969793017⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-2135903068102082951883),(-2135903068102082941379)⟩,⟨3028949303361436355632,3028949303361436366144⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1530550432621854807813),(-1530550432621854802995)⟩,⟨845955569679466695578,845955569679466700395⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-840774298623269830331),(-840774298623269828037)⟩,⟨103677489744351235905,103677489744351238198⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-385661172597165109739),(-385661172597165108678)⟩,⟨(-60159776310313364404),(-60159776310313363345)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-108734416353179646482),(-108734416353179646166)⟩,⟨(-33710268166649093521),(-33710268166649093205)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨150789729680570956761911462,150789729680570956938266009⟩,⟨187060740187498423582890086,187060740187498423759580376⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨418426618126926202916813104,418426618126926203413494810⟩,⟨500334847148493592905627457,500334847148493593402876419⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨594092658797378253865270112,594092658797378254592030535⟩,⟨662835159696544912089856670,662835159696544912816493556⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨649111839234637897790207439,649111839234637898622365633⟩,⟨659087548428494554587040137,659087548428494555417770943⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨593707582806281767288879161,593707582806281768100364445⟩,⟨540318886412896619263639239,540318886412896620072593103⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨469585438239618493240096839,469585438239618493936114213⟩,⟨381561721018608595620903540,381561721018608596313994571⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨327521609354669948660621756,327521609354669949195029301⟩,⟨239827438517545881573443102,239827438517545882105253249⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨204983526415326294019276213,204983526415326294391952459⟩,⟨138564674538833937431395486,138564674538833937802212894⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨117298667045372317572356445,117298667045372317812079982⟩,⟨76075698618278905619708274,76075698618278905858314304⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨62646810618632501247148804,62646810618632501391872685⟩,⟨40908547426527327558967787,40908547426527327703101029⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨31903371932712860696075679,31903371932712860779569551⟩,⟨22015728054301312852668677,22015728054301312935879465⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨15807734015407097542053981,15807734015407097588860534⟩,⟨11973827610114298695107367,11973827610114298741781946⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨7735471782676863897339257,7735471782676863923082101⟩,⟨6562247145928276642890740,6562247145928276668573246⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨3735179400011646950911748,3735179400011646964680149⟩,⟨3545859521911451276926560,3545859521911451290667696⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1683382693514761090273927,1683382693514761096973501⟩,⟨1749751821401408160667503,1749751821401408167355391⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨481961896942821894497592,481961896942821896492529⟩,⟨527080045464383245412686,527080045464383247404410⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-677035439852966012068789048),(-677035439852966010900267544)⟩,⟨(-1018290774177861109198036501),(-1018290774177861108022868276)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1978688963017573153405119139),(-1978688963017573150085465545)⟩,⟨(-2814097610702294287607794010),(-2814097610702294284268430027)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-3105916353866644952661814080),(-3105916353866644947724809276)⟩,⟨(-3969343494452225279286325810),(-3969343494452225274317671727)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3916442445605202883474049496),(-3916442445605202877695797833)⟩,⟨(-4305036835744344935918355220),(-4305036835744344930099039326)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-4288217927431909427139222662),(-4288217927431909421285428350)⟩,⟨(-3902698991633487139394714431),(-3902698991633487133496268344)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-4183700668631037361302914210),(-4183700668631037355789003335)⟩,⟨(-3037732378976118467365112503),(-3037732378976118461812457191)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-3683022641650578893772512594),(-3683022641650578889007658487)⟩,⟨(-2042911468641239956579121348),(-2042911468641239951782798845)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2954921139929792231549072706),(-2954921139929792227729807602)⟩,⟨(-1177144735390715453897255299),(-1177144735390715450053079737)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2184634608623521856262456389),(-2184634608623521853304169740)⟩,⟨(-562139495533059419629624249),(-562139495533059416653595429)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1507924991027103271961682365),(-1507924991027103269639028496)⟩,⟨(-197788416805780841084821199),(-197788416805780838753196116)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-985850308852019606990415684),(-985850308852019605282081552)⟩,⟨(-19667466470069790178579174),(-19667466470069788466422289)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-618649404380433696746555829),(-618649404380433695559099560)⟩,⟨46778353956830377675761132,46778353956830378864495402⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-375180856460559988195297529),(-375180856460559987411079931)⟩,⟨57874060312624328814706330,57874060312624329599188494⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-217284332485167937922980737),(-217284332485167937438073996)⟩,⟨46619762050949696679076839,46619762050949697163892055⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-112045752741352288481701155),(-112045752741352288220566106)⟩,⟨28609853850204594560298895,28609853850204594821295528⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-34488792825085011473445891),(-34488792825085011391474778)⟩,⟨9514944801963182599866631,9514944801963182681780462⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨42385536532476539496609771189,42385536532476539517171828397⟩,⟨(-19025210775437662061366822090),(-19025210775437662041355358183)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨120472325669062823162225065113,120472325669062823222443434283⟩,⟨(-57460276654292795705380032107),(-57460276654292795646776776633)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨179841993197709412581891858432,179841993197709412677051513272⟩,⟨(-96087964726933456920956700169),(-96087964726933456828358236074)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨212627687185161700517472302527,212627687185161700639587446321⟩,⟨(-132599350384609194806829725950),(-132599350384609194688024473872)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨216755607643208115839347611058,216755607643208115977686293562⟩,⟨(-162670274474659341837047935359),(-162670274474659341702459987662)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨196155934216023468067876135263,196155934216023468216944569414⟩,⟨(-181505257145697358539813263890),(-181505257145697358393829667178)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨159234488690210240079006677879,159234488690210240230940738449⟩,⟨(-185954389057881422214573929978),(-185954389057881422064595529039)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨116073636690784813896586891029,116073636690784814040825080054⟩,⟨(-176002940058888164398908896347),(-176002940058888164255655455049)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨75454908901891673902263988869,75454908901891674030326818289⟩,⟨(-154809074866137024212297854959),(-154809074866137024084562355872)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨42887406000834297729968278603,42887406000834297836796076678⟩,⟨(-127372913058453221053489104706),(-127372913058453220946642838137)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨20225423165352323897026953941,20225423165352323982748643937⟩,⟨(-98695176277382783568381306998),(-98695176277382783482494320603)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨6587954089722506353645765253,6587954089722506419924800335⟩,⟨(-72390671225811711911049282262),(-72390671225811711844557777856)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-229537927708928061188395215),(-229537927708928013171878398)⟩,⟨(-50213571741091367059057025812),(-50213571741091367010861725924)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2585490253380019367023114717),(-2585490253380019335070380485)⟩,⟨(-32337024344474765183991693242),(-32337024344474765151916876927)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2376876142008511945077013032),(-2376876142008511926981238889)⟩,⟨(-17940490352018978774364527119),(-17940490352018978756198472704)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-914555676204858768563576771),(-914555676204858762737988119)⟩,⟨(-5731766002407549623243099192),(-5731766002407549617394641863)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-127601047879321208994506061673),(-127601047879321208965019372653)⟩,⟨35935670881949403866622464821,35935670881949403892742464661⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-369062165065110462042000970432),(-369062165065110461953431044561)⟩,⟨111183214055024384267245724693,111183214055024384346045422325⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-570857782583355947506201087299),(-570857782583355947359014277269)⟩,⟨194509085026931120841025669940,194509085026931120973235894956⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-712963522553661012814995099935),(-712963522553661012610969337754)⟩,⟨285603926563380409617575315955,285603926563380409803421159506⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-784191465281695871774068954723),(-784191465281695871515740889142)⟩,⟨377974159251378788605495023076,377974159251378788846714889712⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-784116258016087886498598791413),(-784116258016087886192756749202)⟩,⟨460387850906459688143005971606,460387850906459688435771208108⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-722921070068412737917540093909),(-722921070068412737576422226427)⟩,⟨520370948373177319004864111547,520370948373177319338293548022⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-618839410070019474650137980214),(-618839410070019474290834600024)⟩,⟨548362493559151992171624099219,548362493559151992528515884358⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-493685364691041612910871361093),(-493685364691041612553129445168)⟩,⟨540780878440022634749636046992,540780878440022635108992566071⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-367835151471609004166174546337),(-367835151471609003829388479431)⟩,⟨500759972384364588208141170148,500759972384364588548815523208⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-256318879832768734752288381147),(-256318879832768734447765393977)⟩,⟨436462389223398089323079270586,436462389223398089632174816420⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-167129745137668424461742384085),(-167129745137668424198998439876)⟩,⟨357998072673166466911520549540,357998072673166467178469386123⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-101785593185443461919280800344),(-101785593185443461706154772728)⟩,⟨274409160104073651121026294721,274409160104073651337201419453⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-57266978879555591107868105823),(-57266978879555590951775353969)⟩,⟨191785131862743551198893667693,191785131862743551356915744272⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-28185951117237078182389754256),(-28185951117237078087679915158)⟩,⟨112775898262810416292266351479,112775898262810416388011216082⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-8370618339021284496807538458),(-8370618339021284465202410125)⟩,⟨37137103510738075912581783772,37137103510738075944508699895⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-802617606074687354075272562282),(-802617606074687353256311591341)⟩,⟨566042241323675210286671517475,566042241323675211091790010739⟩⟩ +lemma checked : cachedMomentRuleBox column1_1 kernel3_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 3 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_1_contains kernel3_1_contains +end cm1_3_1_1 +namespace cm1_4_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_0 j i k).mul (kernel4_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨651087439001798,651087439001814⟩,⟨(-3960389521263503),(-3960389521263487)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨3094744590814560,3094744590814576⟩,⟨(-9409646835081358),(-9409646835081340)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨6740907692729611,6740907692729629⟩,⟨(-9118477250686597),(-9118477250686580)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨8496421419725426,8496421419725443⟩,⟨(-3942402088511290),(-3942402088511273)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨6107029940578282,6107029940578299⟩,⟨1662378373249267,1662378373249288⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1439801524827711,1439801524827729⟩,⟨3489046614861689,3489046614861708⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-1413213962832315),(-1413213962832297)⟩,⟨1571962819660161,1571962819660178⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1049783750695024),(-1049783750695007)⟩,⟨(-531566170189875),(-531566170189855)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨226849968079273,226849968079290⟩,⟨(-645501748428465),(-645501748428443)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨414987267290317,414987267290336⟩,⟨114022578812547,114022578812564⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-51530316979288),(-51530316979272)⟩,⟨291955234469456,291955234469474⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-220290962761972),(-220290962761953)⟩,⟨6273163505770,6273163505789⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-68839393282114),(-68839393282097)⟩,⟨(-154920064194880),(-154920064194863)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨62036995640369,62036995640385⟩,⟨(-109414690560809),(-109414690560792)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨72746070572041,72746070572058⟩,⟨(-31694434686633),(-31694434686615)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨27238516420974,27238516420990⟩,⟨(-2259437752468),(-2259437752452)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨136726215536012462335,136726215536012462797⟩,⟨(-37192001122958707745),(-37192001122958707282)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨337453369237913416220,337453369237913417348⟩,⟨(-83847024793701776827),(-83847024793701775698)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨381933876448089320469,381933876448089321766⟩,⟨(-75265872097337522219),(-75265872097337520921)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨301764927492744288001,301764927492744289047⟩,⟨(-33104637749744752558),(-33104637749744751510)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨182948182552076804910,182948182552076805561⟩,⟨4691745352583507720,4691745352583508368⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨87871037181790663761,87871037181790664085⟩,⟨20177535161735567061,20177535161735567383⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨33189334553346831289,33189334553346831422⟩,⟨18399015206430722479,18399015206430722614⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨9100919077555655517,9100919077555655576⟩,⟨10967406826208640285,10967406826208640349⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1123375003086666949,1123375003086666983⟩,⟨4867284803523976991,4867284803523977026⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-542159696292123965),(-542159696292123941)⟩,⟨1622428206376660662,1622428206376660685⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-479059327085271468),(-479059327085271449)⟩,⟨357413927196302075,357413927196302097⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-220717539704363439),(-220717539704363419)⟩,⟨3476559393982131,3476559393982149⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-73664384081877413),(-73664384081877393)⟩,⟨(-47927097705360731),(-47927097705360713)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-17544013527414011),(-17544013527413994)⟩,⟨(-33021535593897900),(-33021535593897881)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1881383529862445),(-1881383529862429)⟩,⟨(-15680484085942569),(-15680484085942553)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨331140880431976,331140880431993⟩,⟨(-4397433581008042),(-4397433581008026)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-595026761014499072492005),(-595026761014499071243259)⟩,⟨463656279476157190446442,463656279476157191686769⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1483277977225518915153355),(-1483277977225518911852935)⟩,⟨1213036946664569669828190,1213036946664569673111515⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1702593961415864852788950),(-1702593961415864848537840)⟩,⟨1526098810171156640137757,1526098810171156644378824⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1356193005977802311498917),(-1356193005977802307485021)⟩,⟨1380779343099311706450950,1380779343099311710469480⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-814728163202876195226250),(-814728163202876192206022)⟩,⟨969918234248947419696089,969918234248947422730771⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-377413186339232341117873),(-377413186339232339250029)⟩,⟨540456730236968488826022,540456730236968490708993⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-132096389375707206653764),(-132096389375707205689271)⟩,⟨238953933445658236981232,238953933445658237956258⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-29857890303019495977074),(-29857890303019495553639)⟩,⟨81658381196897818163839,81658381196897818592870⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1362520018016720523170,1362520018016720696867⟩,⟨19149414801814123826456,19149414801814124002597⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨6756220101930394613158,6756220101930394686367⟩,⟨851776986047935896088,851776986047935970266⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨5445330096176950169752,5445330096176950208808⟩,⟨(-2215723082878098151538),(-2215723082878098112100)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3412099423540393841040,3412099423540393861629⟩,⟨(-1676426874826904912311),(-1676426874826904891583)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1939149318006320062015,1939149318006320072640⟩,⟨(-880827860593092804701),(-880827860593092794023)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1037366113945853507198,1037366113945853512563⟩,⟨(-399348974631456733501),(-399348974631456728118)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨499946853936129218370,499946853936129220877⟩,⟨(-161297961833358956434),(-161297961833358953924)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨148067978520007733265,148067978520007734006⟩,⟨(-42498182449172181095),(-42498182449172180357)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-47584455425224061143646292),(-47584455425224060962869024)⟩,⟨(-100500460601391304406322636),(-100500460601391304223307794)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-141395067665342294285667959),(-141395067665342293779109322)⟩,⟨(-271612282319097624710891822),(-271612282319097624198150877)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-226215305127300965536284204),(-226215305127300964805203403)⟩,⟨(-365695180937506061200660733),(-365695180937506060461019136)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-286347905850107226593733961),(-286347905850107225780536724)⟩,⟨(-368091888876712880220555276),(-368091888876712879398617166)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-306144840664144642243862647),(-306144840664144641481457959)⟩,⟨(-299193858111176976598957977),(-299193858111176975829979138)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-282129116883364687652039990),(-282129116883364687010785222)⟩,⟨(-199522961469104809246225615),(-199522961469104808602365270)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-226878296904706079192011512),(-226878296904706078715156167)⟩,⟨(-107281904279813611960060952),(-107281904279813611484022424)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-161298624001104226846175055),(-161298624001104226528595630)⟩,⟨(-42976747594348353842020227),(-42976747594348353527146100)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-103064665160465095692243555),(-103064665160465095499061657)⟩,⟨(-8261050593327052587634999),(-8261050593327052397556854)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-60413211644842786869305430),(-60413211644842786756583191)⟩,⟨5539032599404660554769624,5539032599404660665029070⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-33265526941016670147347956),(-33265526941016670077594848)⟩,⟨8377251604458622964412485,8377251604458623032878702⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-17627794984036951891136794),(-17627794984036951849862098)⟩,⟨7045584953865222224131485,7045584953865222264800878⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-9159004336869364185082646),(-9159004336869364161588091)⟩,⟨4866098240280869437062867,4866098240280869460287952⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-4665179932499412579545386),(-4665179932499412566534066)⟩,⟨2985797559437873800029909,2985797559437873812927024⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2194331766471768369466590),(-2194331766471768362956464)⟩,⟨1575938683054839325726968,1575938683054839332192113⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-643813970322906726135259),(-643813970322906724167085)⟩,⟨488759187323802234856412,488759187323802236812908⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1253383015920876749802698060,1253383015920876754034407038⟩,⟨1957303130580604057849341980,1957303130580604062106269161⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨3764757271759908243148001310,3764757271759908255043164768⟩,⟨5283941214336624905766745869,5283941214336624917736594184⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨6164538040983753811211423945,6164538040983753828533690834⟩,⟨7056585470949548343072632482,7056585470949548360512785206⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨8094106635259771351480556455,8094106635259771371104185695⟩,⟨6881219904804751845186234923,6881219904804751864951518680⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨9083116872471162132488960944,9083116872471162151212440796⟩,⟨5059911674542505288486024180,5059911674542505307341705663⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨8845981945591932498721768708,8845981945591932515918810519⟩,⟨2417479653980585080512952286,2417479653980585097777152895⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨7498477950032250788813175665,7498477950032250804861224171⟩,⟨(-99689832189770722807104494),(-99689832189770706777342808)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨5518282990268165480911115737,5518282990268165494391130859⟩,⟨(-1830293448769253129795958601),(-1830293448769253116377337601)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨3491785650657166783007687686,3491785650657166793300350966⟩,⟨(-2586167246682626260020016519),(-2586167246682626249774996300)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1848768186855986024806209390,1848768186855986032113922433⟩,⟨(-2565099932885112349196543865),(-2565099932885112341905559801)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨751025146639565477427828056,751025146639565482431973478⟩,⟨(-2118495316026642879913920120),(-2118495316026642874899833339)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨145795517061618027223605073,145795517061618030461981078⟩,⟨(-1550851612859879565165444763),(-1550851612859879561904042456)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-113515901543789052912698786),(-113515901543789050918655640)⟩,⟨(-1037033434461769959688323260),(-1037033434461769957669079061)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-171474134751956398092240108),(-171474134751956396894749071)⟩,⟨(-635659764395399793979409466),(-635659764395399792762322614)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-129827680407164032236406119),(-129827680407164031566308284)⟩,⟨(-337319125671756219134299210),(-337319125671756218453398832)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-46840506615661170728225121),(-46840506615661170513777628)⟩,⟨(-104997959081847344028726636),(-104997959081847343810879962)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-58282350494629024855473816),(-58282350494629021274815532)⟩,⟨48653538994819535020532230,48653538994819538604225748⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-813340723218291310084766934),(-813340723218291299415772353)⟩,⟨715488827294069300278979000,715488827294069310941624713⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-3060559361698496560573073788),(-3060559361698496543109466019)⟩,⟨2965370722312374368041767932,2965370722312374385465805317⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-6629662548059223666465267332),(-6629662548059223642863273610)⟩,⟨7396114189684644268638967302,7396114189684644292182885800⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-10329523792787137956562742354),(-10329523792787137927890084628)⟩,⟨13877221863737170878563968318,13877221863737170907238271992⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-12567815146857188017899113878),(-12567815146857187985651455867)⟩,⟨21403670902026982722077272473,21403670902026982754500630879⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-12222799785471105771979779092),(-12222799785471105737966979849)⟩,⟨28330554197783653347545635418,28330554197783653381998353384⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-9237170997719045912810833472),(-9237170997719045878680576433)⟩,⟨32983841698607777486985083760,32983841698607777521805516704⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-4593555538715226438539411000),(-4593555538715226402553596848)⟩,⟨34342311753759224156308652202,34342311753759224193006189947⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨245540563016307990605223555,245540563016308026604167700⟩,⟨32391915193339347993460752204,32391915193339348030052945106⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨4023141772518019002487394033,4023141772518019036069811541⟩,⟨27975455035574412243631428595,27975455035574412277593948636⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨6097817663824777113323029023,6097817663824777142541177291⟩,⟨22300404033324476621747725851,22300404033324476651149024522⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6453802866087941270424534822,6453802866087941293765928115⟩,⟨16434668892592895791151218990,16434668892592895814557894385⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨5456986980326774601541053795,5456986980326774618297067934⟩,⟨11025247778192362264984529982,11025247778192362281750495758⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨3580763864473607873204134094,3580763864473607883203601129⟩,⟨6268402488080637989711480328,6268402488080637999704289685⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1240252321540053501572380082,1240252321540053504879995225⟩,⟨2025344784494589199207927173,2025344784494589202511556017⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3611410088309837648866763584,3611410088309837736520066415⟩,⟨45758278403216285015449645559,45758278403216285103714533856⟩⟩ +lemma checked : cachedMomentRuleBox column1_0 kernel4_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 4 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_0_contains kernel4_0_contains +end cm1_4_0_0 +namespace cm1_4_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_0 j i k).mul (kernel4_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-19675320782125565),(-19675320782125549)⟩,⟨27998525067801034,27998525067801052⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-58337283981544911),(-58337283981544889)⟩,⟨61403435139217157,61403435139217179⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-85224784861681636),(-85224784861681608)⟩,⟨47351838058706170,47351838058706197⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-81129263727288772),(-81129263727288740)⟩,⟨2392584409866356,2392584409866389⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-44348513789724280),(-44348513789724243)⟩,⟨(-33158172937594185),(-33158172937594150)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1658541147557180),(-1658541147557141)⟩,⟨(-33333696462667241),(-33333696462667203)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨16241463526427941,16241463526427980⟩,⟨(-9654182493162176),(-9654182493162133)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨7931451081034665,7931451081034706⟩,⟨7068895361963889,7068895361963929⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3268859930513279),(-3268859930513234)⟩,⟨5304463870944177,5304463870944226⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3573006375952088),(-3573006375952041)⟩,⟨(-1671464457857175),(-1671464457857127)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨809696738161135,809696738161182⟩,⟨(-2605838995357633),(-2605838995357587)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨2029114116033503,2029114116033548⟩,⟨120498323839644,120498323839688⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨556023186629160,556023186629198⟩,⟨1462361031499634,1462361031499671⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-601336603997525),(-601336603997493)⟩,⟨992400046156855,992400046156885⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-673958626892064),(-673958626892038)⟩,⟨284641164377091,284641164377117⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-251073534091138),(-251073534091119)⟩,⟨20253267057806,20253267057823⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-866277284103280725703),(-866277284103280722205)⟩,⟨(-520299512557729189501),(-520299512557729186009)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2112253643621361128837),(-2112253643621361120186)⟩,⟨(-1316467994475300327765),(-1316467994475300319125)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-2323912934572108460811),(-2323912934572108450982)⟩,⟨(-1573690369720809622093),(-1573690369720809612277)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1741552517946639691060),(-1741552517946639683306)⟩,⟨(-1363401669777206905408),(-1363401669777206897665)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-962667402263691360521),(-962667402263691355578)⟩,⟨(-948203100072444817103),(-948203100072444812169)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-392123487170840143672),(-392123487170840140985)⟩,⟨(-550841480359186255047),(-550841480359186252362)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-104096154545191343744),(-104096154545191342545)⟩,⟨(-270190750913555869115),(-270190750913555867917)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-3139671275874979244),(-3139671275874978798)⟩,⟨(-110683634310470661922),(-110683634310470661478)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨15497282958075766569,15497282958075766743⟩,⟨(-36354023487846893454),(-36354023487846893283)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨10930536203209099730,10930536203209099828⟩,⟨(-8373434607916715499),(-8373434607916715402)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨4871145256710880984,4871145256710881040⟩,⟨(-394486606531967982),(-394486606531967927)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1594516746994603356,1594516746994603400⟩,⟨896872762981645735,896872762981645775⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨349088030163628578,349088030163628613⟩,⟨648309160121471694,648309160121471729⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨3436172925639400,3436172925639428⟩,⟨315827779467784257,315827779467784285⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-45013218764636626),(-45013218764636601)⟩,⟨126334004145557400,126334004145557423⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-18940241627273428),(-18940241627273410)⟩,⟨32420572264428721,32420572264428741⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨4057903721280204207912481,4057903721280204215936817⟩,⟨1724808370947007340777997,1724808370947007348691169⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨10462176148059943127718885,10462176148059943148848567⟩,⟨4109405218317230257635238,4109405218317230278448342⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨12817798151657216950546668,12817798151657216977546601⟩,⟨4260898124017941751524815,4260898124017941778068279⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨11205670599297821729383650,11205670599297821754533975⟩,⟨2807222977739755260752119,2807222977739755285414322⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨7572228904854950918325345,7572228904854950936837238⟩,⟨1162319093682758303200681,1162319093682758321302798⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨4045427329591897434773649,4045427329591897446396627⟩,⟨180974445622552038255399,180974445622552049629356⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1701159528093678125300949,1701159528093678131695639⟩,⟨(-138226414055709504469999),(-138226414055709498184877)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨535171534955649894664002,535171534955649897614206⟩,⟨(-141636849647861360964257),(-141636849647861358055302)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨94729501567534533354550,94729501567534534620216⟩,⟨(-80664840679511596554310),(-80664840679511595302532)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-23097916529381307362187),(-23097916529381306805867)⟩,⟨(-38713683250207759841455),(-38713683250207759289853)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-34868998120762139306913),(-34868998120762138990187)⟩,⟨(-18970584435348606515106),(-18970584435348606200245)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-23976575574100928832217),(-23976575574100928659074)⟩,⟨(-10301480049318326652811),(-10301480049318326480452)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-13559225400093716555572),(-13559225400093716464452)⟩,⟨(-5994736143991793512255),(-5994736143991793421488)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-7012846709557519537937),(-7012846709557519491454)⟩,⟨(-3466442365152032527295),(-3466442365152032480978)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3263381837292300270255),(-3263381837292300248486)⟩,⟨(-1796071808388508292006),(-1796071808388508270312)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-946170609916978364126),(-946170609916978357767)⟩,⟨(-554187768319583180169),(-554187768319583173834)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-392230487241505527104505386),(-392230487241505526047105013)⟩,⟨372746023617295884336933802,372746023617295885387919251⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1040592847857382757825825453),(-1040592847857382754888436977)⟩,⟨1073208065356795602595452603,1073208065356795605516188015⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1344373321807648365195947904),(-1344373321807648361026396010)⟩,⟨1629559243563336967620147503,1629559243563336971769947263⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1254801801351735816543025267),(-1254801801351735812013821182)⟩,⟨1942355206083904446988078990,1942355206083904451503464435⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-887825766419606391626198881),(-887825766419606387501002450)⟩,⟨1955924025591713666554835987,1955924025591713670679807353⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-441369444870226286706702890),(-441369444870226283323561777)⟩,⟨1702412708838415360964419166,1702412708838415364364237546⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-82803432586782765159874602),(-82803432586782762699566641)⟩,⟨1295220200590595819944193629,1295220200590595822432418612⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨118109055814206434821105310,118109055814206436476042568⟩,⟨870282156143629670481665044,870282156143629672165293116⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨181325447958422152690775860,181325447958422153877058399⟩,⟨523274879551431845855900793,523274879551431847058948436⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨165341533755625029077885743,165341533755625029866960424⟩,⟨286485560669901980459897380,286485560669901981256522735⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨122068077764309250982559132,122068077764309251469890817⟩,⟨145925487963255272883938023,145925487963255273373688161⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨80103576895551006584776186,80103576895551006871192639⟩,⟨70836750914815458706545162,70836750914815458993203860⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨48816073008494873478228037,48816073008494873641191805⟩,⟨33504098163119103323381350,33504098163119103485914146⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨27907318575479938764369336,27907318575479938855010554⟩,⟨15570953006611360675975492,15570953006611360766137647⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨14157819347080314870289294,14157819347080314915872579⟩,⟨6791890366713345743713815,6791890366713345788978425⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4312637926052899535827992,4312637926052899549648992⟩,⟨1908344772010726766997430,1908344772010726780710545⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨7114318151209509384964370137,7114318151209509402586445955⟩,⟨(-6508004379194620037229252287),(-6508004379194620019754947101)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨18940844226004139505209473103,18940844226004139554652522340⟩,⟨(-19227238133552100361830115143),(-19227238133552100312814233043)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨24460630766389481287447614931,24460630766389481359136985306⟩,⟨(-30621977532622681061859683765),(-30621977532622680990819907741)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨22202408301989241380475724865,22202408301989241461064443587⟩,⟨(-38903134921096455698171204097),(-38903134921096455618332189767)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨13636442251528111896892474304,13636442251528111982115236363⟩,⟨(-42139494006267156689940889891),(-42139494006267156605249852011)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨2385438287173363080590064461,2385438287173363167240734306⟩,⟨(-39473662499655647209442525739),(-39473662499655647122932533474)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-7548938749972048966823442410),(-7548938749972048887687258513)⟩,⟨(-31908655382941299685599377466),(-31908655382941299606317131490)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-13551742170426432327329488842),(-13551742170426432262194772357)⟩,⟨(-21959003882200077142623453565),(-21959003882200077077239981879)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-15151234766870406517553107033),(-15151234766870406468704706913)⟩,⟨(-12414227287785954277202929037),(-12414227287785954228212802803)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-13531111344419119248454305302),(-13531111344419119214275126781)⟩,⟨(-5145642312319541738152963102),(-5145642312319541703988237450)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-10422382652653427003930662390),(-10422382652653426980641067790)⟩,⟨(-687580371340145655659937471),(-687580371340145632499488310)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-7200605058205811570582310109),(-7200605058205811554919190285)⟩,⟨1412095503756142273461480358,1412095503756142288965165997⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-4565478894509877617419944243),(-4565478894509877606256437625)⟩,⟨1969701766868859887900844357,1969701766868859898948603906⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2665812871941795309449740068),(-2665812871941795302174578815)⟩,⟨1710441494471483831928468133,1710441494471483839133474153⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1360350667813799629893909833),(-1360350667813799625856368926)⟩,⟨1101065531241904886946563270,1101065531241904890948973436⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-414061265847796813125742981),(-414061265847796811840274916)⟩,⟨374874481392276078092826928,374874481392276079367842166⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨186922973714109180034887012,186922973714109193043727180⟩,⟨201356076132107637936173551,201356076132107650942333469⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2753695066325548281039880311,2753695066325548319821299407⟩,⟨2804099065495717120506812724,2804099065495717159329311646⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨11447810188419910052886398773,11447810188419910116511234383⟩,⟨10500366092482006664851666253,10500366092482006728625828395⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨28667350736566470840448712241,28667350736566470926945327655⟩,⟨22521889862298563856752454910,22521889862298563943414790722⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨54024087297438413526913513598,54024087297438413633175687756⟩,⟨34424806535223169428326338342,34424806535223169534436556802⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨83664644567469888128049319480,83664644567469888249630469238⟩,⟨40340702409335537526854175801,40340702409335537647503784893⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨111077926221797726463302052300,111077926221797726594502565717⟩,⟨36240551856920251961523658539,36240551856920252090664413432⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨129483878935715861527132567374,129483878935715861668928045521⟩,⟨22230350545776705495947858932,22230350545776705634871667576⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨134646098497799437329890800136,134646098497799437486514263381⟩,⟨2481270711839032435008613225,2481270711839032588955285535⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨126442906226989634634146093711,126442906226989634792092912191⟩,⟨(-16996666786045819684635710391),(-16996666786045819528777486564)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨108348110266632391838621945266,108348110266632391987198256369⟩,⟨(-31143846379190127295010747718),(-31143846379190127147651326478)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨85406755448514612495684797951,85406755448514612626130164578⟩,⟨(-37534727259749431553399626547),(-37534727259749431423421785572)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨62087849744888235150472113128,62087849744888235255683314902⟩,⟨(-36383581262371346240041943784),(-36383581262371346134881703230)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨41061429346181705190046443471,41061429346181705266230712748⟩,⟨(-29463491258839532129271345799),(-29463491258839532052979193724)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨23063498889276160128127425348,23063498889276160173886773001⟩,⟨(-18904767373401317178683733591),(-18904767373401317132811571622)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨7399415483439912887791834914,7399415483439912902980073998⟩,⟨(-6484019105911497825961706029),(-6484019105911497810729605095)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨169576877489817673863711355668,169576877489817674238281039546⟩,⟨(-39274390666654006416420173839),(-39274390666654006044267562829)⟩⟩ +lemma checked : cachedMomentRuleBox column1_0 kernel4_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 4 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_0_contains kernel4_1_contains +end cm1_4_0_1 +namespace cm1_4_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_1 j i k).mul (kernel4_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-8024312308673640),(-8024312308673621)⟩,⟨17749801921823042,17749801921823060⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-27665023920617294),(-27665023920617273)⟩,⟨38463939750559830,38463939750559848⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-44846721176376880),(-44846721176376862)⟩,⟨27224927614680175,27224927614680196⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-40840019979647849),(-40840019979647821)⟩,⟨(-2641645370384889),(-2641645370384866)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16063644949065090),(-16063644949065066)⟩,⟨(-19744034374928130),(-19744034374928108)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨4709804973436561,4709804973436587⟩,⟨(-12835940992179057),(-12835940992179029)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨6808371500267337,6808371500267365⟩,⟨91679802417754,91679802417782⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨526920069958012,526920069958035⟩,⟨3317810791789347,3317810791789370⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1700225540222365),(-1700225540222340)⟩,⟨366405634396921,366405634396949⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-215587654916385),(-215587654916361)⟩,⟨(-960005053945871),(-960005053945844)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨596035283624286,596035283624313⟩,⟨(-162330158891470),(-162330158891447)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨177653100338914,177653100338936⟩,⟨385906822385983,385906822386007⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-215555177677385),(-215555177677367)⟩,⟨218746923404394,218746923404413⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-214689426210126),(-214689426210108)⟩,⟨(-34967200370018),(-34967200369999)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-90915035485309),(-90915035485291)⟩,⟨(-97161705251449),(-97161705251432)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-18309409410589),(-18309409410573)⟩,⟨(-41254349067500),(-41254349067483)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-261600876509568480876),(-261600876509568480431)⟩,⟨95442111485385510151,95442111485385510596⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-651853190824979122456),(-651853190824979121359)⟩,⟨207973555285516212662,207973555285516213761⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-748207204946466277139),(-748207204946466275856)⟩,⟨169327069072297547733,169327069072297549017⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-595931940789047637345),(-595931940789047636285)⟩,⟨49506843264481923229,49506843264481924290⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-356115916322562023337),(-356115916322562022655)⟩,⟨(-43342889635784631926),(-43342889635784631245)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-160779370668117324201),(-160779370668117323851)⟩,⟨(-68255281736503269233),(-68255281736503268885)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-51780610778760294337),(-51780610778760294185)⟩,⟨(-50092788082900050967),(-50092788082900050815)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-8806263541236727763),(-8806263541236727700)⟩,⟨(-24768130626944360336),(-24768130626944360273)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1847070795629425737,1847070795629425772⟩,⟨(-8693531591448199155),(-8693531591448199117)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2170033617441614041,2170033617441614067⟩,⟨(-1958004480800999013),(-1958004480800998984)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨977940602393684646,977940602393684665⟩,⟨(-57158416127594160),(-57158416127594138)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨282197449929549693,282197449929549714⟩,⟨203256734106317059,203256734106317079⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨40582751543242096,40582751543242114⟩,⟨127438898250197817,127438898250197837⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-12695897326179157),(-12695897326179139)⟩,⟨53880316031824100,53880316031824118⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-13381442257906833),(-13381442257906816)⟩,⟨18628479522077817,18628479522077833⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-4674677341320534),(-4674677341320518)⟩,⟨4286245988056899,4286245988056915⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1296994811508862872426970),(-1296994811508862870497015)⟩,⟨(-2027274258045967956826599),(-2027274258045967954881867)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-3509246784442508565521442),(-3509246784442508560260665)⟩,⟨(-5242846069391424694647827),(-5242846069391424689353329)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-4725223824282613666440083),(-4725223824282613659231336)⟩,⟨(-6495695524457145342295872),(-6495695524457145335056660)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-4746237063277649184719195),(-4746237063277649177242450)⟩,⟨(-5848725438431445049613341),(-5848725438431445042123764)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-3859613519815109068848554),(-3859613519815109062457285)⟩,⟨(-4212943301976470208795093),(-4212943301976470202407326)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-2624360662947979851266284),(-2624360662947979846606915)⟩,⟨(-2546121244558394960661575),(-2546121244558394956012670)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1524758255219510088088934),(-1524758255219510085129426)⟩,⟨(-1341484789555313560830332),(-1341484789555313557880517)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-773388443241262018057778),(-773388443241262016386256)⟩,⟨(-640720921928202763508991),(-640720921928202761843531)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-350800626602010287138584),(-350800626602010286279508)⟩,⟨(-288652560879865744871734),(-288652560879865744015621)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-146115580029189041801360),(-146115580029189041388829)⟩,⟨(-127036857846231856481429),(-127036857846231856070129)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-57447696058713037651308),(-57447696058713037460961)⟩,⟨(-56021061004599902881001),(-56021061004599902691114)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-21900203877507029948773),(-21900203877507029862075)⟩,⟨(-25130752609695993228225),(-25130752609695993141689)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-8289463626199011223421),(-8289463626199011183659)⟩,⟨(-11536864014649994016772),(-11536864014649993977069)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-3157941441554686997450),(-3157941441554686979078)⟩,⟨(-5366852134254981035001),(-5366852134254981016646)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1174382991105071331356),(-1174382991105071323284)⟩,⟨(-2373846461378441503871),(-2373846461378441495806)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-300789879720263122663),(-300789879720263120373)⟩,⟨(-674807245393919859211),(-674807245393919856921)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨9794677275783016194576354,9794677275783016242848791⟩,⟨54067813805950220708337118,54067813805950220756788998⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨31841450423154634208117553,31841450423154634343753487⟩,⟨147733879133162843699249053,147733879133162843835476477⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨57913127744521846174047906,57913127744521846370837520⟩,⟨203615446601494836412884067,203615446601494836610754679⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨82922710682371745157805166,82922710682371745378454129⟩,⟨213153854425405339569581420,213153854425405339791777196⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨98306421664226407537604741,98306421664226407748275020⟩,⟨184294596675187368436993484,184294596675187368649345134⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨98565018949166199836442869,98565018949166200023138765⟩,⟨135491135006855163047496805,135491135006855163235401420⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨85064102373715765845394897,85064102373715765993970892⟩,⟨85748656428256495343442362,85748656428256495492804827⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨64351352670285580382092376,64351352670285580489397170⟩,⟨46966287352662958618231183,46966287352662958726041469⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨43544390442276981153656022,43544390442276981225217799⟩,⟨22258391443254342279022192,22258391443254342350916681⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨26959616712308394683343082,26959616712308394728953313⟩,⟨9018913767942655826106724,9018913767942655871923427⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨15648591265974870153605465,15648591265974870183075316⟩,⟨2972159462872506408543407,2972159462872506438099267⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨8716947464706098852393703,8716947464706098870537261⟩,⟨628914777660722971203773,628914777660722989376601⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4738052614444534031471909,4738052614444534042183667⟩,⟨(-100013410863675265505322),(-100013410863675254785845)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2505448630040947415708840,2505448630040947421743104⟩,⟨(-227112347812199325550751),(-227112347812199319515714)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1210622011500476167124428,1210622011500476170164406⟩,⟨(-165579342700048407364830),(-165579342700048404325573)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨360230921256155775232152,360230921256155776153892⟩,⟨(-57540821241871056652105),(-57540821241871055730722)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-5138733425307023125979145377),(-5138733425307023122925751384)⟩,⟨(-2017387422023494781702937563),(-2017387422023494778641945116)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-14709895463275267940921008886),(-14709895463275267932185172887)⟩,⟨(-5266739773360873418097598086),(-5266739773360873409354343186)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-22241298709662844470783659478),(-22241298709662844457608313873)⟩,⟨(-6494713093166295919132899318),(-6494713093166295905987601142)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-26726273550042581971358177478),(-26726273550042581955599052753)⟩,⟨(-5326020546421688509914146065),(-5326020546421688494261013289)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-27733154788042114415623769408),(-27733154788042114399366478998)⟩,⟨(-2341707467097458627755712830),(-2341707467097458611697431390)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-25573077705940166979002379019),(-25573077705940166962719164148)⟩,⟨1271958151453982278368076673,1271958151453982294393947368⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-21219897474539834710251362213),(-21219897474539834694459253136)⟩,⟨4313909959271860502384940150,4313909959271860517914835263⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-15961797944922856797531022901),(-15961797944922856783501401707)⟩,⟨6061540739875728430190419948,6061540739875728443999208064⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-10953462321298764102868879462),(-10953462321298764091310046314)⟩,⟨6427122078008256004888234394,6427122078008256016327348071⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-6905458086113029833798088811),(-6905458086113029824953201042)⟩,⟨5780930481978397987124013591,5780930481978397995916509473⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4032010762955552270541823244),(-4032010762955552264201776195)⟩,⟨4637729340447918316082835559,4637729340447918322404138992⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2199421574927687573078952973),(-2199421574927687568778681517)⟩,⟨3413949921005061148090372771,3413949921005061152385797744⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1129201661922006791014521875),(-1129201661922006788243620063)⟩,⟨2338400403613532824619820906,2338400403613532827390372481⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-545467587156191565019718102),(-545467587156191563334561323)⟩,⟨1478642420794622919191516251,1478642420794622920877535292⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-238095473941919752435117812),(-238095473941919751529135094)⟩,⟨807036162968087366459266831,807036162968087367366289570⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-66024700845967739860613990),(-66024700845967739576754290)⟩,⟨255416571745749742668127765,255416571745749742952405469⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨19374201084257546728397298639,19374201084257546736813210427⟩,⟨23304874443443856165474136106,23304874443443856174303079176⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨57365024724933285484542184850,57365024724933285509722967342⟩,⟨65690809007852448588052917779,65690809007852448614293187189⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨92664855376969474558396524623,92664855376969474599889795414⟩,⟨96364606112733318196683917131,96364606112733318239405389597⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨122598762793480007613875721881,122598762793480007670491641691⟩,⟨110708834305358524106630636265,110708834305358524164061799746⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨144026376672478374039577479345,144026376672478374109735267362⟩,⟨107984933747529466680796876338,107984933747529466750910659976⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨154329594250062628408702761822,154329594250062628489194789695⟩,⟨91284204974390058336746295054,91284204974390058416178221298⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨152544200585231198290623867526,152544200585231198376647946560⟩,⟨66332880201430496429661995557,66332880201430496513754090436⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨139962691846505109372133532741,139962691846505109458132611491⟩,⟨39574278788083485150317310405,39574278788083485233945747610⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨119819174928905300801217822041,119819174928905300882935952491⟩,⟨16282942699421620894801533830,16282942699421620974463647284⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨96217203235405095274116920055,96217203235405095347261071059⟩,⟨(-566967047673986194439016870),(-566967047673986122813430127)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨72878621566359631521167084670,72878621566359631583942772755⟩,⟨(-10385351863776555739010816710),(-10385351863776555677120805822)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨52294923851091460745197188304,52294923851091460796541386521⟩,⟨(-14248870531014434242158929827),(-14248870531014434191218941429)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨35517573546998729541585577471,35517573546998729580711324474⟩,⟨(-13924300860825718786162058473),(-13924300860825718747187706511)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨22441395423263534891125803506,22441395423263534918263165512⟩,⟨(-11099119785141279977871439334),(-11099119785141279950773624511)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨12266714755844267381824395767,12266714755844267397655608008⟩,⟨(-7005459702121841579178537873),(-7005459702121841563349297730)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3886864627281942586550816410,3886864627281942591726759951⟩,⟨(-2380118397208659005114347147),(-2380118397208658999936165364)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨185570616493342481993069052725,185570616493342482151716791926⟩,⟨95722461924153719933952794439,95722461924153720091235239260⟩⟩ +lemma checked : cachedMomentRuleBox column1_1 kernel4_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 4 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_1_contains kernel4_0_contains +end cm1_4_1_0 +namespace cm1_4_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column1_1 j i k).mul (kernel4_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨127392965226629846,127392965226629875⟩,⟨(-106562989447879632),(-106562989447879603)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨354537772212527756,354537772212527807⟩,⟨(-196074164098380143),(-196074164098380094)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨447977579080026955,447977579080027032⟩,⟨(-53293234862246165),(-53293234862246088)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨316281755600614377,316281755600614470⟩,⟨160579951401834241,160579951401834331⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨67176541196816854,67176541196816963⟩,⟨212373550635558698,212373550635558810⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-77332045776311231),(-77332045776311106)⟩,⟨92971711934811958,92971711934812082⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-57856272483325765),(-57856272483325637)⟩,⟨(-18931979012899331),(-18931979012899204)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨3098137347867937,3098137347868059⟩,⟨(-30179038201108948),(-30179038201108827)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨15841223704876931,15841223704877054⟩,⟨41069275484597,41069275484717⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨460233699449659,460233699449773⟩,⟨9007732163235115,9007732163235226⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-5631563870084319),(-5631563870084221)⟩,⟨787850675912178,787850675912276⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1319451065964402),(-1319451065964315)⟩,⟨(-3689972652289625),(-3689972652289539)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2097265226286961,2097265226287031⟩,⟨(-1906527031250356),(-1906527031250287)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1970467285989277,1970467285989330⟩,⟨380009468961754,380009468961811⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨828058413224446,828058413224484⟩,⟨905236442943649,905236442943687⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨167873590031092,167873590031114⟩,⟨380577850831660,380577850831681⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1782470626668122185067,1782470626668122189099⟩,⟨875659664741600617983,875659664741600622005⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨4316713069290353182738,4316713069290353192878⟩,⟨2313872187557590513893,2313872187557590524012⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨4664743962503965794702,4664743962503965806614⟩,⟨2972123462005226207408,2972123462005226219298⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3358630144830226891956,3358630144830226901832⟩,⟨2775700451289452222644,2775700451289452232503⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1701309567965058801853,1701309567965058808267⟩,⟨2030626529641495379216,2030626529641495385620⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨561292105893621027773,561292105893621031152⟩,⟨1183856688584532690301,1183856688584532693679⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨57572155040351490797,57572155040351492248⟩,⟨546796208136614350794,546796208136614352248⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-64822789715974888431),(-64822789715974887914)⟩,⟨193715766927564930602,193715766927564931120⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-52337507124274170657),(-52337507124274170440)⟩,⟨46971804063746757520,46971804063746757739⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-23301870729177622419),(-23301870729177622291)⟩,⟨3266202971061280294,3266202971061280421⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-7022374202972572375),(-7022374202972572299)⟩,⟨(-3854453343893406532),(-3854453343893406459)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1170966137694349722),(-1170966137694349668)⟩,⟨(-2633888515586596824),(-2633888515586596770)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨213676730369140745,213676730369140789⟩,⟨(-1100061357391618543),(-1100061357391618502)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨304417651440085847,304417651440085880⟩,⟨(-354922186856555805),(-354922186856555772)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨172210205386518841,172210205386518868⟩,⟨(-91007583390412446),(-91007583390412418)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨51768999475117007,51768999475117027⟩,⟨(-15364734977753346),(-15364734977753327)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-6678715685782643320606118),(-6678715685782643305790424)⟩,⟨12380866264033148646522172,12380866264033148661410900⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-16758056403493201514696563),(-16758056403493201474177735)⟩,⟨32998345878379685023698770,32998345878379685064440474⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-19469884080880229348764263),(-19469884080880229292845660)⟩,⟨43278873292810855755190373,43278873292810855811456935⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-15755635362284734062526953),(-15755635362284734003874721)⟩,⟨42113446916803684969206098,42113446916803685028263283⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-9637180980342960180557445),(-9637180980342960129631932)⟩,⟨33193592820841269587181251,33193592820841269638474478⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-4574786548863496381691348),(-4574786548863496343630148)⟩,⟨22000825378416968717608700,22000825378416968755915656⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1708865998467538892215398),(-1708865998467538867248529)⟩,⟨12588382098730991083636114,12588382098730991108723473⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-523138383753768772320526),(-523138383753768757773640)⟩,⟨6381300229729549349410525,6381300229729549364008358⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-158494668198700589079994),(-158494668198700581384476)⟩,⟨2949062062566967552068060,2949062062566967559782833⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-71366243496520010968731),(-71366243496520007176682)⟩,⟨1281252198292109220943972,1281252198292109224742994⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-47693589684890672026117),(-47693589684890670236960)⟩,⟨539524805208205933479563,539524805208205935271258⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-33360491967288001287260),(-33360491967288000457155)⟩,⟨226310681206589803244947,226310681206589804076054⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-21572209041117624730598),(-21572209041117624344349)⟩,⟨96488695847678119460949,96488695847678119847623⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-12734336794836684633833),(-12734336794836684453454)⟩,⟨41928437429572370249560,41928437429572370430126⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-6542654046839453222252),(-6542654046839453142498)⟩,⟨17602741456810576881454,17602741456810576961289⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1999651439525404193479),(-1999651439525404170871)⟩,⟨4863930526377521249667,4863930526377521272298⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨235041871708608869808687027,235041871708608870092690983⟩,⟨(-127471976572640431855786361),(-127471976572640431572915308)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨635378896698987896735728949,635378896698987897529420382⟩,⟨(-374959767965517169857171847),(-374959767965517169066936732)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨855921127838014301424293704,855921127838014302564290362⟩,⟨(-590760387046261695768719148),(-590760387046261694634461973)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨862206866939426190051386126,862206866939426191312090186⟩,⟨(-736728708436924316152112508),(-736728708436924314898984479)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨701292654170041448506033315,701292654170041449692123021⟩,⟨(-778942865625954354413472970),(-778942865625954353235421171)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨467364034379569907602004935,467364034379569908648521908⟩,⟨(-713286187454898283245081881),(-713286187454898282204935902)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨249900150729385085695534799,249900150729385086533028870⟩,⟨(-572480209459264844342059270),(-572480209459264843509216095)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨97698017528260611451004673,97698017528260612076005037⟩,⟨(-407625873096418148191810349),(-407625873096418147569898454)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨15453940693597080615980606,15453940693597081086544982⟩,⟨(-261483843681635962394095709),(-261483843681635961924776883)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-16882513590896925492082216),(-16882513590896925163962383)⟩,⟨(-154080702258959304588769964),(-154080702258959304260923974)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-22896050886949431997425305),(-22896050886949431784124802)⟩,⟨(-85320682887748241172848472),(-85320682887748240959494810)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-18917777450689086479834848),(-18917777450689086348008442)⟩,⟨(-45449393954044208543027573),(-45449393954044208411062423)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-13018553816984320343588283),(-13018553816984320265197321)⟩,⟨(-23716270930999321487775788),(-23716270930999321409256878)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-7990095833948001692699774),(-7990095833948001648195361)⟩,⟨(-12117840010928862588921793),(-12117840010928862544326617)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4221904823691647065400429),(-4221904823691647042839744)⟩,⟨(-5710950903028614683762490),(-5710950903028614661149921)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1310384559290894451332305),(-1310384559290894444468989)⟩,⟨(-1677123374448131292926197),(-1677123374448131286046119)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-4611595086102585774169846761),(-4611595086102585760172708859)⟩,⟨22432781894062144112255151965,22432781894062144126272166325⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-10995330737311482348379586086),(-10995330737311482308273550601)⟩,⟨64061056952289464792533817890,64061056952289464832754433977⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-10192632167296164756235629586),(-10192632167296164695551504185)⟩,⟨96381380068372417614847425652,96381380068372417675870675119⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1235708945828085383470364080),(-1235708945828085310511638759)⟩,⟨114903507500211280705329389446,114903507500211280778977928246⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨13133907512253559715218591479,13133907512253559793509072974⟩,⟨117843623068246584931408492167,117843623068246585010726948680⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨27965255183285699728811118785,27965255183285699810628838526⟩,⟨106834416702153474336466691874,106834416702153474419441384098⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨38565448826807323524403214039,38565448826807323604737622381⟩,⟨86489320829273920046693325794,86489320829273920128081869403⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨42509166020112455808623626517,42509166020112455881136695560⟩,⟨62751068531230268980151007427,62751068531230269053478326686⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨40158413937517659113744310272,40158413937517659174787331784⟩,⟨40814096326250760775586016162,40814096326250760837042852083⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨33731054391014732276085914387,33731054391014732323821094383⟩,⟨23721297487609461003656512393,23721297487609461051552598585⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨25827159652166816408278551227,25827159652166816443205415739⟩,⟨12191162850423548802538945273,12191162850423548837508042411⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨18359128796109176116864658497,18359128796109176141173788332⟩,⟨5380316016150079453236910320,5380316016150079477541976884⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨12234905095508751374275574913,12234905095508751390620146590⟩,⟨1870226223843291428314768082,1870226223843291444637216844⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨7573943436483771042783568954,7573943436483771053000623288⟩,⟨352329328163223300666418380,352329328163223310862441853⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4072841076592586334931318695,4072841076592586340461447475⟩,⟨(-106468569716788072622895313),(-106468569716788067105383916)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1279075538148366166743331055,1279075538148366168481561720⟩,⟨(-80935557944930528101015106),(-80935557944930526366946241)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨80526469779705563484048923740,80526469779705563517546465582⟩,⟨(-74423559424849755785166487414),(-74423559424849755753039470300)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨226547901369391287141403080641,226547901369391287241335579405⟩,⟨(-220726767230529113529993925591),(-220726767230529113433492625011)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨330755242289001537261824941580,330755242289001537425757142396⟩,⟨(-357650138273752361191483459910),(-357650138273752361031252964923)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨376320416334367030511006674403,376320416334367030733845547594⟩,⟨(-475099945589904352620025484501),(-475099945589904352398983586096)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨360198629024923152220924432633,360198629024923152496940194292⟩,⟨(-560610515118233528757131409679),(-560610515118233528479368777938)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨293423079862151659034598890272,293423079862151659352758188475⟩,⟨(-603196303977872722787629132487),(-603196303977872722463657846565)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨197183414092184059314750445895,197183414092184059658240119471⟩,⟨(-598061906774728108539400710781),(-598061906774728108186699004872)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨95862363636142395422454825136,95862363636142395774273092673⟩,⟨(-549446737540620510089185980505),(-549446737540620509727243398438)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨9725355596964340612191430577,9725355596964340956853541097⟩,⟨(-469794699410118588432318765145),(-469794699410118588079698430738)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-49792719645008694155006363258),(-49792719645008693838512657963)⟩,⟨(-375614831842448375499634196975),(-375614831842448375177626740324)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-80716769712177566786896336167),(-80716769712177566508044056557)⟩,⟨(-282283393518237799287969258521),(-282283393518237799006136779238)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-87795490405257361266799728087),(-87795490405257361033263486051)⟩,⟨(-200300319184387359578110323816),(-200300319184387359343407093875)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-78525942116004037646557792464),(-78525942116004037465189215668)⟩,⟨(-134191655380027214445185653762),(-134191655380027214263545132747)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-59934145692449125031789071778),(-59934145692449124904182812342)⟩,⟨(-83583392754961595825799120536),(-83583392754961595698257890944)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-36986939750572996295359451757),(-36986939750572996220201588258)⟩,⟨(-45134349814995417534689774126),(-45134349814995417459650227295)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-12443267189165460702117876046),(-12443267189165460677427374590)⟩,⟨(-14200353505334576721513097498),(-14200353505334576696871730385)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨301113701092017858944717572968,301113701092017859628614305855⟩,⟨(-715526899478834085397882000365),(-715526899478834084707321286995)⟩⟩ +lemma checked : cachedMomentRuleBox column1_1 kernel4_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 1 4 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column1_1_contains kernel4_1_contains +end cm1_4_1_1 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments3.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments3.lean new file mode 100644 index 0000000000000000000000000000000000000000..7d7a7a736fac7a6ea6e9f3e15d1b5f9315a26d2e --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments3.lean @@ -0,0 +1,3929 @@ +import OAI.Analysis.PlanarPacking.Certificate.Columns10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid +namespace cm3_1_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_0 j i k).mul (kernel1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨36830556380966713246116200,36830556380966713289652646⟩,⟨16989804861344620821042634,16989804861344620865969802⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨98881994061169073676961576,98881994061169073799613855⟩,⟨60800579246229283541701489,60800579246229283668529742⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨125540795422055934514109645,125540795422055934692113793⟩,⟨125169057665319045496439618,125169057665319045681421803⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨96723851564753288045622638,96723851564753288274098960⟩,⟨198830620563616166867425056,198830620563616167104250190⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨8720467614562153874817076,8720467614562154147881867⟩,⟨248769391865460996309550058,248769391865460996591041934⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-113694511738519241473726500),(-113694511738519241177762267)⟩,⟨237745180967265294269752556,237745180967265294572211658⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-221000562234765345435396353),(-221000562234765345137821035)⟩,⟨150897185494313505581583203,150897185494313505881080498⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-263291899879331870592985878),(-263291899879331870327653647)⟩,⟨12114097380375568067127697,12114097380375568331470077⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-220445632913933977305291929),(-220445632913933977102986527)⟩,⟨(-125432110239335288566410221),(-125432110239335288364360118)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-114542867666839777477275116),(-114542867666839777308457467)⟩,⟨(-210067538856031787033750925),(-210067538856031786862757764)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨5538758594146935394425506,5538758594146935544334038⟩,⟨(-220673391150597053075185356),(-220673391150597052923289395)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨94171956987198222971706070,94171956987198223088455098⟩,⟨(-173137397997381453570138391),(-173137397997381453453986377)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨130579509553399053150121307,130579509553399053231430642⟩,⟨(-103512151154625528709236218),(-103512151154625528631335255)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨119979943790662969009807579,119979943790662969060539356⟩,⟨(-44443697803914789679857159),(-44443697803914789633769564)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨80219250358326280563570716,80219250358326280590519857⟩,⟨(-11142253480114100534992752),(-11142253480114100511855794)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨27757670555086508269994367,27757670555086508278340275⟩,⟨(-771454949895271680914248),(-771454949895271674017335)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-381783469296547809117439597),(-381783469296547808479700208)⟩,⟨(-3299487610717366089464645),(-3299487610717365454955760)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1078083605212848102050140476),(-1078083605212848100199934659)⟩,⟨(-67179171706567861914355427),(-67179171706567860073478114)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1580173248844753925359973418),(-1580173248844753922491365263)⟩,⟨(-269565037471490559740809039),(-269565037471490556886260768)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1793260590018495377316970996),(-1793260590018495373721013201)⟩,⟨(-609508890513391432627433479),(-609508890513391429048058073)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1683565729817152745497385693),(-1683565729817152741482662487)⟩,⟨(-999661455488231098187578815),(-999661455488231094188043054)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1299290070837111275145798678),(-1299290070837111271097818290)⟩,⟨(-1309644926843012455947022886),(-1309644926843012451910087832)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-761958995843428375290230760),(-761958995843428371556191098)⟩,⟨(-1432537241060027909099856242),(-1432537241060027905370581649)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-223340262379156084518785658),(-223340262379156081352392106)⟩,⟨(-1335797178835821366424744756),(-1335797178835821363257280970)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨191798426088483865635208028,191798426088483868120914474⟩,⟨(-1068824681223203859061076273),(-1068824681223203856570404442)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨425346799822621428134026077,425346799822621429949162011⟩,⟨(-728626199582916317395094541),(-728626199582916315574145269)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨489058822686060299852123918,489058822686060301097005797⟩,⟨(-410379608883578410694130281),(-410379608883578409444594008)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨437496133050910425593673114,437496133050910426433793184⟩,⟨(-172775089164362905915952544),(-172775089164362905073348864)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨332751359015237208587798979,332751359015237209128256092⟩,⟨(-30916409111481317643426832),(-30916409111481317101553566)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨220251008642280533380016237,220251008642280533704523375⟩,⟨30257828801490622656330313,30257828801490622981851398⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨121472224329312227879053375,121472224329312228049286139⟩,⟨37278086260048462951560185,37278086260048463122494268⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨38350638679329151856228373,38350638679329151908881254⟩,⟨15363553724055427669258775,15363553724055427722172152⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1716218189136180369622120338,1716218189136180374054739990⟩,⟨(-3343808389796851476894061112),(-3343808389796851472570245581)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨4998054434768395719348131772,4998054434768395732343913550⟩,⟨(-9218753375116918342248195001),(-9218753375116918329563457456)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨7780347000955112871520507206,7780347000955112892219870006⟩,⟨(-12917280672011273132778967228),(-12917280672011273112546024051)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨9651246241332252587385241142,9651246241332252614124481507⟩,⟨(-13792494431476022096149489703),(-13792494431476022069957313971)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨10240024601263321449061517465,10240024601263321479349052037⟩,⟨(-12072807205657450581680251490),(-12072807205657450551930972068)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨9403442263624333529739086396,9403442263624333560587560296⟩,⟨(-8691669714351520393442840053),(-8691669714351520363034574172)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨7355392679734029777869957924,7355392679734029806391535895⟩,⟨(-4867462847540031545769806035),(-4867462847540031517524582195)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨4631073415667078672118002208,4631073415667078696200349860⟩,⟨(-1636728601684133218996413610),(-1636728601684133195002483709)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1891609725719911515404522075,1891609725719911534180194522⟩,⟨448756490786898014811687043,448756490786898033666234885⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-316300174155506265333441633),(-316300174155506251131703857)⟩,⟨1360387413414875714116969598,1360387413414875728506688627⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1713934767190009302380500692),(-1713934767190009291669106585)⟩,⟨1418269025204598786919482948,1418269025204598797854958934⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2299890258664533947539719075),(-2299890258664533939756503995)⟩,⟨1047143548115463036976664044,1047143548115463044968716042⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-2251560849679332870655943035),(-2251560849679332865271018162)⟩,⟨592424947512546126017576096,592424947512546131569286020⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1799226595721191340312649697),(-1799226595721191336843845256)⟩,⟨246715355272641779935329120,246715355272641783520805674⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1136265485612238073079001898),(-1136265485612238071153635196)⟩,⟨63355571785729711110838439,63355571785729713103924430⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-385924977392616295187666041),(-385924977392616294572940526)⟩,⟨5807171976871096195469180,5807171976871096832318678⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-6886310545811127127096624110),(-6886310545811127118964189998)⟩,⟨(-8105880145533367595357375074),(-8105880145533367587552870970)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-19572813950921406622417058465),(-19572813950921406598198087946)⟩,⟨(-24100667054495910653278500306),(-24100667054495910629914579380)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-29186072670777794441067397191),(-29186072670777794401520613093)⟩,⟨(-39305910555132058393108028661),(-39305910555132058354612648250)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-34339134288589875870742467260),(-34339134288589875817625699093)⟩,⟨(-52894745216471157444195693370),(-52894745216471157391918695722)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-34515688658610299602384577811),(-34515688658610299537701552670)⟩,⟨(-63805015140548259286731367485),(-63805015140548259222485929859)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-30172838481718112841213595935),(-30172838481718112767799064033)⟩,⟨(-70976651540395111510201524041),(-70976651540395111436886578453)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-22601519962484782886614360007),(-22601519962484782809364375206)⟩,⟨(-73690921822243347724927129462),(-73690921822243347647550068850)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-13564694087524530160736292683),(-13564694087524530085132477932)⟩,⟨(-71849752119481476181445028798),(-71849752119481476105679302799)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4827301724392074007739652058),(-4827301724392073938727846152)⟩,⟨(-66053111214383437538441033802),(-66053111214383437469408738829)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2255355325291902823638257611,2255355325291902882580026504⟩,⟨(-57434965519094617988650665466),(-57434965519094617929919403617)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨6955902982655844509100875582,6955902982655844556365728035⟩,⟨(-47338420164723748341961197702),(-47338420164723748295124695128)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨9163093776833558027896960583,9163093776833558063578593681⟩,⟨(-36974789607699211531609571668),(-36974789607699211496486493567)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨9204517375791504658238302609,9204517375791504683519838979⟩,⟨(-27189953273961518957260797157),(-27189953273961518932551337810)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨7616532648065348095494595799,7616532648065348111989027927⟩,⟨(-18384798242928877041276729394),(-18384798242928877025264546030)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨4958026945918332320698672470,4958026945918332329904966779⟩,⟨(-10561965934567492807787993405),(-10561965934567492798899283023)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1713404494901348430195290986,1713404494901348433139578011⟩,⟨(-3436240543199361301126351675),(-3436240543199361298292721144)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-3647034251040447837742635006),(-3647034251040447826713319047)⟩,⟨19057899977665241996312056328,19057899977665242010730590115⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-12646548549719134289078682150),(-12646548549719134255817228047)⟩,⟨54735553082992803467636180388,54735553082992803510669433198⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-26034853201786796631384112352),(-26034853201786796575793706419)⟩,⟨83259524089255930318729220139,83259524089255930389221151196⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-44604791727567631525355671404),(-44604791727567631448362598931)⟩,⟨100701795589405981024166322644,100701795589405981119103793102⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-66765849527312141234947674509),(-66765849527312141139587106759)⟩,⟨104605593632756664032094798583,104605593632756664145658057332⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-88966327532571781339759581822),(-88966327532571781231651370888)⟩,⟨94708187245259944858884041971,94708187245259944982399897101⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-106891075217356516801359871639),(-106891075217356516680979247089)⟩,⟨73279206783464366529543617122,73279206783464366659221653548⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-116957360741061958045110858597),(-116957360741061957916687593142)⟩,⟨44757091879122935660754819686,44757091879122935791421922469⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-117477954136874095213227041509),(-117477954136874095085387945692)⟩,⟨14678101800646496648028368118,14678101800646496772462022986⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-109026663274551386560082769993),(-109026663274551386436841554572)⟩,⟨(-11727062925628097754646160817),(-11727062925628097637853822009)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-93947376076155100328491903878),(-93947376076155100217906958661)⟩,⟨(-30715441871155219183545227459),(-30715441871155219080333401912)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-75344108478591246875809126385),(-75344108478591246783735968222)⟩,⟨(-40581634341855261586424920099),(-40581634341855261501147703315)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-56047492152710626644795351486),(-56047492152710626573991686478)⟩,⟨(-41510737515393755011989798688),(-41510737515393754946594387579)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-37931759875858504254981907418),(-37931759875858504205737295358)⟩,⟨(-34982646531822178526651744631),(-34982646531822178481175877364)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-21698664934508603706396413541),(-21698664934508603677671815050)⟩,⟨(-23089268332666257286512724788),(-23089268332666257259964725377)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-7031679265522700191165724471),(-7031679265522700181769301920)⟩,⟨(-8038076868015251483342102404),(-8038076868015251474653170701)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨100369550502307889485109373,100369550502307895834853183⟩,⟨89413772104425041860974199,89413772104425048217004947⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1440035876774563717678978878,1440035876774563737095226108⟩,⟨1340221958444390377189417480,1340221958444390396633946311⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨5713490048592608449680862016,5713490048592608483073285309⟩,⟨5761952571835026154596898810,5761952571835026188055317104⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨13424472494809068809570573417,13424472494809068857922859775⟩,⟨15200813478070493983476051840,15200813478070494031926896464⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨23425965490441431978270729564,23425965490441432041965007620⟩,⟨30791828829476370667639860607,30791828829476370731423910925⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨33195541336045394116196316346,33195541336045394194343020730⟩,⟨52358126264842355192687363936,52358126264842355270856507570⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨39714654686716076642381493891,39714654686716076732394161004⟩,⟨77993386673610120361671011822,77993386673610120451616986453⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨40639997888395888462212757563,40639997888395888559727684114⟩,⟨104172246470068506103596437420,104172246470068506201035516604⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨35267193092293080045915212666,35267193092293080145300595861⟩,⟨126499886128394998448311835709,126499886128394998547794890252⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨24847096325924347232011326496,24847096325924347327259811954⟩,⟨140856832806295905452790536369,140856832806295905548514765533⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨12125702783206305873953663843,12125702783206305959696015290⟩,⟨144459635272733513305636712865,144459635272733513392348081058⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨355825227793446321831335259,355825227793446394136955408⟩,⟨136407585998443518922867868983,136407585998443518996589150352⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-7761740641886698351740903126),(-7761740641886698295141487560)⟩,⟨117575767355455848716418798990,117575767355455848774671250600⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-10807711060230710309981784269),(-10807711060230710269886987406)⟩,⟨90039324760793631061117424252,90039324760793631102756425124⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-8878254970001439324980742013),(-8878254970001439301242872484)⟩,⟨56379242975029822053798056568,56379242975029822078627943892⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3386815061198967909125556086),(-3386815061198967901296435122)⟩,⟨19170103890715195807201093059,19170103890715195815419521995⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-149715318755347544294407479675),(-149715318755347543775233860023)⟩,⟨129429806850937959232550405719,129429806850937959760918877365⟩⟩ +lemma checked : cachedMomentRuleBox column3_0 kernel1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 1 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_0_contains kernel1_0_contains +end cm3_1_0_0 +namespace cm3_1_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_0 j i k).mul (kernel1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-219865998359052849322208784),(-219865998359052848904850949)⟩,⟨(-266937085261288819278127985),(-266937085261288818850700442)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-542028137971871373278572104),(-542028137971871372047395872)⟩,⟨(-831483047655284117501748327),(-831483047655284116243990566)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-537588277221498832110840128),(-537588277221498830147771962)⟩,⟨(-1426242118196151267963349614),(-1426242118196151265965838207)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-93809950973062482692510313),(-93809950973062480173132702)⟩,⟨(-1913376659494697864795031291),(-1913376659494697862241834879)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨724655459016402730019169908,724655459016402732816387649⟩,⟨(-2052460020118741356692594582),(-2052460020118741353865323949)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1645829854390157179996820712,1645829854390157182818793603⟩,⟨(-1645886699761467284755112455),(-1645886699761467281913807540)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨2281070892004879138578738870,2281070892004879141262751910⟩,⟨(-704541542620087656470464601),(-704541542620087653789236038)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨2321052455465449110789103259,2321052455465449113089064111⟩,⟨495937121777364136511320950,495937121777364138797903259⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1716863331502188016184666921,1716863331502188018057046054⟩,⟨1533928483736082815635678518,1533928483736082817506267621⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨711678408609766426764846713,711678408609766428493818543⟩,⟨2066454115311744244675818603,2066454115311744246420081860⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-303525611018719764678318218),(-303525611018719763223334384)⟩,⟨2002453058532920753924431172,2002453058532920755392018949⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1001710677925833962923696100),(-1001710677925833961824209658)⟩,⟨1511438751363498828303757681,1511438751363498829394211879⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1253157831479949848611597552),(-1253157831479949847856830267)⟩,⟨886618521850235630594219713,886618521850235631316232934⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1117183439283856760330267048),(-1117183439283856759860965574)⟩,⟨377489059335318652002750570,377489059335318652428966078⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-740448042928596082024603110),(-740448042928596081774653410)⟩,⟨94362480133616753313922759,94362480133616753528710210⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-255816269736248417893143056),(-255816269736248417815480371)⟩,⟨6529175576756764807562845,6529175576756764871863309⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1867371008318377736175063865,1867371008318377741366019658⟩,⟨1981693521150736415195282651,1981693521150736420396784210⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨5027735428139975112505776167,5027735428139975127579921311⟩,⟨5875294187862963080154600852,5875294187862963095258501916⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨6645701418570355964973250962,6645701418570355988362519920⟩,⟨9460356635385801989496209063,9460356635385802012927834872⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨6258164494199508560402895748,6258164494199508589735100116⟩,⟨12308037250273606218531272651,12308037250273606247909905056⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨4052925157088743339605458433,4052925157088743372427784346⟩,⟨13890052079354793712029123244,13890052079354793744893545375⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨783228147061032958002480349,783228147061032991024010413⟩,⟨13827941816128346535560343885,13827941816128346568614216237⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-2535044436124002446397979239),(-2535044436124002416195177418)⟩,⟨12132244095237227288401224540,12132244095237227318622139185⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-5015002790167401555637856933),(-5015002790167401530429557752)⟩,⟨9262735092244459761682104421,9262735092244459786902157083⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-6195942582135738676681171945),(-6195942582135738657337216679)⟩,⟨5960802947788420544548564616,5960802947788420563906340887⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-6116756729422466615634776745),(-6116756729422466601923205461)⟩,⟨2957712901937687997186666378,2957712901937688010917449398⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-5169681231528067323673534276),(-5169681231528067314582963563)⟩,⟨730110913803851728993827631,730110913803851738107822607⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-3854196503453609961020001198),(-3854196503453609954939139422)⟩,⟨(-583028284044597769411821883),(-583028284044597763308655564)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2571773993029611402234788790),(-2571773993029611397983460831)⟩,⟨(-1105910415578495506450177342),(-1105910415578495502181214264)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1535426875225815942266860355),(-1535426875225815939438228018)⟩,⟨(-1080672356199755587735794615),(-1080672356199755584895193271)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-782670166824219098292785300),(-782670166824219096698500511)⟩,⟨(-742666822923013327617976431),(-742666822923013326016870116)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-236206623696293232236535775),(-236206623696293231724778622)⟩,⟨(-260653676496731546476509716),(-260653676496731545962536172)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-21957603847969560055955992925),(-21957603847969560036011722571)⟩,⟨719472493265749154287339581,719472493265749175663044684⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-61515023905670202215649090721),(-61515023905670202156091555146)⟩,⟨876929254285681481820077245,876929254285681545310218861⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-89084848946291242121497597913),(-89084848946291242022773593805)⟩,⟨(-2042940022465989519768390839),(-2042940022465989415540602227)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-100211308764984245566080358772),(-100211308764984245431421368611)⟩,⟨(-7971830938210083783596904688),(-7971830938210083643076747001)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-94643126152008785778985466957),(-94643126152008785616512434700)⟩,⟨(-14956974403283241389200070683),(-14956974403283241221601346122)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-76113635232959963430346391738),(-76113635232959963253406593716)⟩,⟨(-20194064564624860061804862654),(-20194064564624859881191172286)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-50862771876836143605475671706),(-50862771876836143430676798363)⟩,⟨(-21480118753515149358642905606),(-21480118753515149181828628471)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-25476113493446831285894192797),(-25476113493446831128917628962)⟩,⟨(-18246662373578160782099153215),(-18246662373578160624541200229)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4925831204699239423674757729),(-4925831204699239294295707485)⟩,⟨(-11662429129887659914448478660),(-11662429129887659785475626773)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨8442776954336887941378311683,8442776954336888045000586679⟩,⟨(-3900359335403788476182854836),(-3900359335403788373473538949)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨14770444645127131937570296515,14770444645127132020216822379⟩,⟨2886707973440561891479050560,2886707973440561973142276964⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨15750827388104865151962977465,15750827388104865214717303618⟩,⟨7309993001997879966377565912,7309993001997880028283054981⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨13521400301455716192345705773,13521400301455716237165731990⟩,⟨8951383195931263374995198214,8951383195931263419167374294⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨9860695663754368366132792354,9860695663754368395637631117⟩,⟨8137095503495533276689301007,8137095503495533305749353495⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨5853293546650971694678671319,5853293546650971711275955557⟩,⟨5556264919379067471836625180,5556264919379067488176258967⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1925360739520557607305867466,1925360739520557612638826524⟩,⟨1959917458031297947445484958,1959917458031297952693999066⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-27001402643771779175272568556),(-27001402643771779132874039345)⟩,⟨44155559601886918841410936502,44155559601886918883619745603⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-81521745056447293428926934249),(-81521745056447293302259499034)⟩,⟨127788260053084999141619361702,127788260053084999267407240206⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-136835344465849514332404675377),(-136835344465849514124524164690)⟩,⟨197852375231169087819777768255,197852375231169088025355957225⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-191517165570248209686659022943),(-191517165570248209406056949802)⟩,⟨247329551036503222332036748014,247329551036503222608257022658⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-242090029710247654296192152042),(-242090029710247653952719254606)⟩,⟨272099508465063859186750588050,272099508465063859524174171309⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-283671929770240880005345272949),(-283671929770240879613602659015)⟩,⟨271713272980089933913250148731,271713272980089934298758754508⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-311343090826006683923079253084),(-311343090826006683509706528750)⟩,⟨249478723428765721997591657954,249478723428765722406131888849⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-321688718570602903418141485174),(-321688718570602903013303480429)⟩,⟨211680914786927782045784972211,211680914786927782448635311335⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-313869551561648451402860908129),(-313869551561648451033825728609)⟩,⟨166075821661195473446864207972,166075821661195473817513529293⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-289793720491395151295743596730),(-289793720491395150981573152027)⟩,⟨120125777487160216783448219156,120125777487160217102656905523⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-253389845144318834944349811969),(-253389845144318834693644919202)⟩,⟨79557475290683118497574542559,79557475290683118755749039009⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-209367601725340246771241155608),(-209367601725340246583153860748)⟩,⟨47643296155814412483188549043,47643296155814412679738259491⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-161993045736704344146343786771),(-161993045736704344014014922685)⟩,⟨25257066321291389588402434374,25257066321291389728740275448⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-114274957989032075330765658943),(-114274957989032075245054471555)⟩,⟨11451365786221182394581635521,11451365786221182486735897111⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-67694515571329204510364569423),(-67694515571329204462827764291)⟩,⟨4190234460788350715691735315,4190234460788350767360374967⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-22382389726974384823400815162),(-22382389726974384808221461810)⟩,⟨947621993413829985713417006,947621993413830002309581362⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨80483731027679953841361393263,80483731027679953897664608006⟩,⟨1427508157096835519667540003,1427508157096835558635365415⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨233379789616276816360098486198,233379789616276816529463618000⟩,⟨12439488893361416933174052430,12439488893361417053345852736⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨362121442542383840869135758347,362121442542383841154636956374⟩,⟨45274340805128781018312817816,45274340805128781232564818659⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨452162352868586542611971751637,452162352868586543014262132299⟩,⟨106415075039115029481092078195,106415075039115029803865932702⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨492512389781981057252817128368,492512389781981057765227076186⟩,⟨192747818358457214518688689522,192747818358457214958105292694⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨478597636080466651157513336118,478597636080466651761443313106⟩,⟨292156644546259567423771043240,292156644546259567973201096366⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨414488205897990876712715674797,414488205897990877375576734982⟩,⟨387085326072647555628586699981,387085326072647556261722191031⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨313074790152507341270488041884,313074790152507341947836314056⟩,⟨459880214460815451143798474790,459880214460815451815500789813⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨193549990418623355935146648848,193549990418623356588834933161⟩,⟨497917068110776996386082343475,497917068110776997051324487125⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨76877483004237060328389803825,76877483004237060951348468594⟩,⟨496592309371241582936182471973,496592309371241583577042131979⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-19055993991433370121299719490),(-19055993991433369562676888046)⟩,⟨459283050001012492533129388202,459283050001012493108695347414⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-82853289995905529628255296527),(-82853289995905529160523531360)⟩,⟨394772738774782896432845896636,394772738774782896912687186148⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-110690062542058212220122958524),(-110690062542058211857295965503)⟩,⟨313597005435508067622209364192,313597005435508067991617578898⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-105322067400041306969915999507),(-105322067400041306715270665878)⟩,⟨224851900056310090658653958442,224851900056310090915735600744⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-74019745181955021775407541786),(-74019745181955021625788732485)⟩,⟨134398894299242473185911492244,134398894299242473335881624890⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-26493858416406033964773394839),(-26493858416406033915639982807)⟩,⟨44609306261490919974348124046,44609306261490920023395041027⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨304011754142135881142996007,304011754142135904037242490⟩,⟨(-379743382209120360391056884),(-379743382209120337533900731)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4568835098904464585986875971,4568835098904464656168699756⟩,⟨(-5483320838924597463314789209),(-5483320838924597393264634556)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨19742425792626307550027337100,19742425792626307671274408121⟩,⟨(-22028979772153791024156071479),(-22028979772153790903152229974)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨52490120865482551983847260770,52490120865482552160449130262⟩,⟨(-52791636010320292613926522049),(-52791636010320292437601877221)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨107463640988485563218922474460,107463640988485563453154973132⟩,⟨(-94793238317643029530860637328),(-94793238317643029296734942659)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨185212073320782687392091587802,185212073320782687681717579560⟩,⟨(-139810695852396696418118243801),(-139810695852396696128207791863)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨280407321196340132028243955319,280407321196340132364895015879⟩,⟨(-176898692806432996455562065317),(-176898692806432996118247637796)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨381579060226721348777287637748,381579060226721349146051224867⟩,⟨(-196172224504679333753045296653),(-196172224504679333383767368507)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨473000281155400234211762738324,473000281155400234592696853598⟩,⟨(-192391624901002265519054390616),(-192391624901002265138761455512)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨538293781932001887962335290122,538293781932001888333245537025⟩,⟨(-166828750968471261688098364463),(-166828750968471261320042017033)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨564406860818008609660908650890,564406860818008610000744943404⟩,⟨(-126637432256733867967002827059),(-126637432256733867632777761637)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨544430403765379372200030060352,544430403765379372491935504386⟩,⟨(-82114522600682399812100681377),(-82114522600682399528236147367)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨478401361645429282224629490254,478401361645429282457267683709⟩,⟨(-43127719460783172157415900345),(-43127719460783171934057412370)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨372246141939945576168258880209,372246141939945576335621757320⟩,⟨(-16134805532623376451586791142),(-16134805532623376292838559567)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨235762914902949685536834551238,235762914902949685637048756812⟩,⟨(-2693489847956081420867939638),(-2693489847956081326724987319)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨80643719847391668644450258009,80643719847391668677682137206⟩,⟨384818001003350833290607907,384818001003350864360040285⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨584770611708785520541567136054,584770611708785523104070799724⟩,⟨807264028681765193632252897244,807264028681765196142201679816⟩⟩ +lemma checked : cachedMomentRuleBox column3_0 kernel1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 1 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_0_contains kernel1_1_contains +end cm3_1_0_1 +namespace cm3_1_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_1 j i k).mul (kernel1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨194051238031715107517278535,194051238031715107573727627⟩,⟨33379761846930751902087247,33379761846930751956039034⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨539908714798684374169551569,539908714798684374330472292⟩,⟨134126180870870440617955984,134126180870870440771266975⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨762318193040974035085245600,762318193040974035324646861⟩,⟨313094562667363731143421146,313094562667363731370484054⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨798705629679308846640391185,798705629679308846933915451⟩,⟨556319574748010188619330838,556319574748010188899173068⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨629832714768926169777111436,629832714768926170096700024⟩,⟨789878644150949194248294281,789878644150949194557598827⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨300925808780138196878821215,300925808780138197219474853⟩,⟨915511454704848707917175551,915511454704848708254307353⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-83733408258271422875260707),(-83733408258271422539351311)⟩,⟨865580887177442206318954604,865580887177442206655667289⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-400557653960661357378838689),(-400557653960661357085799287)⟩,⟨643928253557282447861796119,643928253557282448154471006⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-561488756500843856296275134),(-561488756500843856071967095)⟩,⟨325592018488657424311977565,325592018488657424530189158⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-549858432598008168288305715),(-549858432598008168112844860)⟩,⟨16082160215533883278863264,16082160215533883443612338⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-415904908749951995347987176),(-415904908749951995208212228)⟩,⟨(-201242518401230238186891152),(-201242518401230238052904656)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-239826057278163295292353712),(-239826057278163295190031238)⟩,⟨(-296318831466499188795167415),(-296318831466499188692049495)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-90111215845634203122844125),(-90111215845634203051804460)⟩,⟨(-288790714767478302204141082),(-288790714767478302128717905)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-877121462417520419855074),(-877121462417520375949334)⟩,⟨(-221529252380481429676511369),(-221529252380481429627913328)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨27260187115059751087128885,27260187115059751110151698⟩,⟨(-133108868210828441069523283),(-133108868210828441043259555)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨13858675339743850816944428,13858675339743850824000037⟩,⟨(-43713411790961753673190094),(-43713411790961753665008202)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-747131776120082295779748562),(-747131776120082295433290645)⟩,⟨(-69553005717283123610879442),(-69553005717283123264245175)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2109092240452696642476208669),(-2109092240452696641473446824)⟩,⟨(-269359545325149255158757385),(-269359545325149254156523249)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-3101292375629876623736206767),(-3101292375629876622189044742)⟩,⟨(-614360190977453945072729862),(-614360190977453943528629091)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-3571031017605476294397073082),(-3571031017605476292464003492)⟩,⟨(-1099279582678687435691833195),(-1099279582678687433766246704)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-3486252744619256482475071838),(-3486252744619256480262303268)⟩,⟨(-1625283356323676022401383632),(-1625283356323676020199308314)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2941681027151727011653833748),(-2941681027151727009344970911)⟩,⟨(-2047039616697911310318702688),(-2047039616697911308022472431)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-2125439945544286561302125662),(-2125439945544286559093725131)⟩,⟨(-2242925365916766723434089384),(-2242925365916766721237709758)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1255395463401375980160440549),(-1255395463401375978213794310)⟩,⟨(-2168905901163114671761854912),(-2168905901163114669823920719)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-511204627087455743634165798),(-511204627087455742034877332)⟩,⟨(-1869278786755253374733665632),(-1869278786755253373137725429)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨8973205542991584645425454,8973205542991585876398342⟩,⟨(-1445441470896137353171976098),(-1445441470896137351940231770)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨292934010415080518138371697,292934010415080519025428507⟩,⟨(-1006986371982040877242345298),(-1006986371982040876352969191)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨387555160461192474034102008,387555160461192474636171186⟩,⟨(-633150104403795039099653267),(-633150104403795038495468175)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨361239379562901094971674538,361239379562901095357374978⟩,⟨(-358840914142102557220597492),(-358840914142102556833743469)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨274513645625467122430725063,274513645625467122661219277⟩,⟨(-181949871134539810693440157),(-181949871134539810462640285)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨166579164723201980004529651,166579164723201980124954197⟩,⟨(-79516540921063153972792836),(-79516540921063153852463706)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨55341308919982473269362570,55341308919982473306499128⟩,⟨(-21631628820774509362896088),(-21631628820774509325835617)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨11130294734381942013580533254,11130294734381942016593675307⟩,⟨4463628614003863922690985340,4463628614003863925711209339⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨31805123496978762393965888615,31805123496978762402761553376⟩,⟨13487828023122202274667713175,13487828023122202283479072218⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨48008115899073960427961502811,48008115899073960441749281705⟩,⟨22605872377979865311594069799,22605872377979865325400292727⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨57766901978641518470615110915,57766901978641518488982513655⟩,⟨31377727793351198030543157902,31377727793351198048908300076⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨60387521392258202884417846271,60387521392258202906844102411⟩,⟨38919779258244631126528919071,38919779258244631148919806642⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨56537771322525277808816151182,56537771322525277833880261891⟩,⟨44181661507789509469589418742,44181661507789509494593104281⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨47976999310395636847460535258,47976999310395636873343486700⟩,⟨46356437384665114283293839138,46356437384665114309116319667⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨37010528924570059368562767486,37010528924570059393365442476⟩,⟨45212306016803345743790148429,45212306016803345768559832706⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨25858948935998148167978517743,25858948935998148190135137922⟩,⟨41182757083575012104575930147,41182757083575012126738900493⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨16164992429215583019901340615,16164992429215583038448444625⟩,⟨35191701044310890680366314465,35191701044310890698951444521⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨8781568448707365257705530728,8781568448707365272325405603⟩,⟨28326647676643796301732556611,28326647676643796316406354665⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3843468485732994019318196540,3843468485732994030211948996⟩,⟨21524077184054947782123864377,21524077184054947793075262522⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1010673995548325693765073344,1010673995548325701414065836⟩,⟨15383601777227566327686413288,15383601777227566335388238152⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-260483130067483152317856959),(-260483130067483147355471117)⟩,⟨10134589323676545371628909538,10134589323676545376632072105⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-519456634908915738375390683),(-519456634908915735615174683)⟩,⟨5706871600276563588570418592,5706871600276563591356071045⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-230136556078795133445489277),(-230136556078795132565051391)⟩,⟨1836505437977650284923268832,1836505437977650285812059251⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-4327200145984661865825137466),(-4327200145984661863522096917)⟩,⟨(-2983128150767123807884220898),(-2983128150767123805461337685)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-12462040902142671788549495290),(-12462040902142671781675571231)⟩,⟨(-8914989269784439832341584349),(-8914989269784439825129020771)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-19110727529007596680984750059),(-19110727529007596669715846619)⟩,⟨(-14682178714732157026162574778),(-14682178714732157014394536942)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-23559629124149244821283851772),(-23559629124149244806058799639)⟩,⟨(-20031065143477869535906342460),(-20031065143477869520097768601)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-25462707317359821186147348657),(-25462707317359821167784457043)⟩,⟨(-24577499011775694036319461955),(-24577499011775694017365104649)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-24896340656351035204075073988),(-24896340656351035183760537733)⟩,⟨(-27888600657727138395912853290),(-27888600657727138375069047160)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-22320547279506843934401449891),(-22320547279506843913318779667)⟩,⟨(-29613530016032042553363013567),(-29613530016032042531865704122)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-18450325951692851917012850545),(-18450325951692851895747347978)⟩,⟨(-29604302145940188237091890578),(-29604302145940188215572156261)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-14074040592821011306070424280),(-14074040592821011285986877353)⟩,⟨(-27970694491597451869384982108),(-27970694491597451849147356120)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-9877994882073567606472289391),(-9877994882073567588697907954)⟩,⟨(-25046536379190965049587333081),(-25046536379190965031696446430)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-6330840916964851866877334257),(-6330840916964851852089642022)⟩,⟨(-21287538608835525068947603718),(-21287538608835525054042942740)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-3651119883750672456624825004),(-3651119883750672445034071709)⟩,⟨(-17148141184212806827749757502),(-17148141184212806816032166165)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1845031411345357988700479092),(-1845031411345357980184319219)⟩,⟨(-12983940495378867150550638947),(-12983940495378867141908026311)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-779361466721067628730635168),(-779361466721067622993390631)⟩,⟨(-9003932031597520541258225915),(-9003932031597520535413361029)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-253612182337275214958287513),(-253612182337275211677729688)⟩,⟨(-5270848673360686000420353586),(-5270848673360685997067895154)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-49211770678954593285022445),(-49211770678954592222709198)⟩,⟨(-1732174351450011764160895274),(-1732174351450011763073439353)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-33577364247803184648305304332),(-33577364247803184636468957862)⟩,⟨31570663438742153995172261023,31570663438742154006549396321⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-100276240206800395975837403932),(-100276240206800395940648759008)⟩,⟨90824800013812776703306769860,90824800013812776737160702945⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-165072079964914654207317427167),(-165072079964914654150008968053)⟩,⟨138907725121309672155988196541,138907725121309672211193559374⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-225488266639773315759088838937),(-225488266639773315682132262423)⟩,⟨170298306683920686456022968173,170298306683920686530276318578⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-277874296562174778755879031193),(-277874296562174778663409588855)⟩,⟨182115575348491035845016584882,182115575348491035934389051782⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-318004129208264307326451320022),(-318004129208264307224212258532)⟩,⟨174652344736803914770311737710,174652344736803914869307353776⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-342141705581241514638048744526),(-342141705581241514529146485564)⟩,⟨151268813990150016520601598623,151268813990150016626448847048⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-348149953699866617276822891958),(-348149953699866617165894259278)⟩,⟨117581826012740229289970073621,117581826012740229398124318611⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-336169282336377984634355540998),(-336169282336377984527871523682)⟩,⟨80133886174863991836384997090,80133886174863991940294211817⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-308584114870817795248966868273),(-308584114870817795147113537541)⟩,⟨44949361750762371863491792581,44949361750762371963384433966⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-269321027175180607293715384709),(-269321027175180607197283537635)⟩,⟨16428006839837640344225346406,16428006839837640439644572139⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-222796973315464274616289239920),(-222796973315464274531061192404)⟩,⟨(-3144934553445552510216270054),(-3144934553445552425316214693)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-172922077573149408895603323966),(-172922077573149408826004865594)⟩,⟨(-13470880217881785238221695540),(-13470880217881785168549428868)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-122451576105248539727536224813),(-122451576105248539676462575067)⟩,⟨(-15716279185719970376385204585),(-15716279185719970325078239524)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-72781548595581259367787300402),(-72781548595581259336767328446)⟩,⟨(-11894217096734367574411242763),(-11894217096734367543179256293)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-24111028682575303873851856535),(-24111028682575303863493237349)⟩,⟨(-4374787749969792331734325881),(-4374787749969792321292554974)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨35553058587442820913521608297,35553058587442820921228682750⟩,⟨(-40047304267503764981344413763),(-40047304267503764974016025027)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨107166969666326371873611171648,107166969666326371897073833154⟩,⟨(-115851151758100524538119159345),(-115851151758100524515675106953)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨179535942655771753395400831039,179535942655771753435384003639⟩,⟨(-179135982573776538508162490687),(-179135982573776538469531308004)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨251223904630721667977932592768,251223904630721668035244110255⟩,⟨(-223197981312268177130057413793),(-223197981312268177074031289663)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨318625556589262828253468439683,318625556589262828328283684905⟩,⟨(-243788204043211811758927485876),(-243788204043211811684990115282)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨376418423172063010172685470423,376418423172063010263975236630⟩,⟨(-239953512235627047450277768890),(-239953512235627047359298236619)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨418767265102858643160402488256,418767265102858643265411314106⟩,⟨(-214370949261414222994547987905),(-214370949261414222889395555585)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨440875597531804038187284964273,440875597531804038301204842524⟩,⟨(-172916641244081367396992746676),(-172916641244081367282854583902)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨440300770634936733625700716852,440300770634936733742235804648⟩,⟨(-123453043061152822321313279343),(-123453043061152822204947501447)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨417537527130245664688992564934,417537527130245664801291696432⟩,⟨(-74149249813267276568933855417),(-74149249813267276457509168331)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨375694508875983619753417568189,375694508875983619855187645741⟩,⟨(-31856959449545446999032245159),(-31856959449545446898893050972)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨319470352950314877485397800516,319470352950314877571921923520⟩,⟨(-1019858007947286852112345676),(-1019858007947286767781367250)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨253879426060158968814169501905,253879426060158968882492421672⟩,⟨16667977469731778834928076876,16667977469731778900854273132⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨183183691458427578106705820042,183183691458427578155475349117⟩,⟨21953499336190207175493535208,21953499336190207222138326042⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨110309152244461578299748373990,110309152244461578328784706647⟩,⟨17363150030309868107343870225,17363150030309868134928798770⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨36788822366245837114502065870,36788822366245837124095729473⟩,⟨6499258640802627509456360867,6499258640802627518543137698⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨187675754029402721331971058141,187675754029402721778602817439⟩,⟨(-55383093302963651459357455234),(-55383093302963651018734474596)⟩⟩ +lemma checked : cachedMomentRuleBox column3_1 kernel1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 1 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_1_contains kernel1_0_contains +end cm3_1_1_0 +namespace cm3_1_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_1 j i k).mul (kernel1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1366415167305844796132120469),(-1366415167305844795536648501)⟩,⟨(-975355855162602776782077176),(-975355855162602776203393769)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-3682641013509168559755326196),(-3682641013509168558030342778)⟩,⟨(-3010452773653323752346589923),(-3010452773653323750667935223)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-4852875005969409623468262469),(-4852875005969409620812125807)⟩,⟨(-5160855772738194325214579003),(-5160855772738194322621481616)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-4467876223698762945796397501),(-4467876223698762942544737403)⟩,⟨(-7149092406733841750581667137),(-7149092406733841747390847014)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-2597135257814572655515344488),(-2597135257814572652093643316)⟩,⟨(-8439459110730360224581765008),(-8439459110730360221198584589)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨187119295292540197703939249,187119295292540201237972205⟩,⟨(-8505594524584828429312357837),(-8505594524584828425779502587)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨2993319919953982891423792557,2993319919953982894807034734⟩,⟨(-7153700896709271545539964709),(-7153700896709271542136814986)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4959811552909912182208335791,4959811552909912185070554790⟩,⟨(-4690073197075600765477844689),(-4690073197075600762611320776)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨5603242310917838467639193413,5603242310917838469871319848⟩,⟨(-1814856718361749073882526165),(-1814856718361749071695136979)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨4975425851349305949557911785,4975425851349305951370688256⟩,⟨694206532994052522796344136,694206532994052524526294413⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3553971339678024118636322173,3553971339678024120017796801⟩,⟨2309576617548583390034560228,2309576617548583391370432765⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1960017162084149041432241433,1960017162084149042417045115⟩,⟨2907913876718442662546178273,2907913876718442663539588292⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨683499186226391811416872450,683499186226391812092542943⟩,⟨2701720332429225522027145173,2701720332429225522742597043⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-51072376064395186901022386),(-51072376064395186485628516)⟩,⟨2041066106039542751718313868,2041066106039542752176484976⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-265067586485568509850080789),(-265067586485568509632464841)⟩,⟨1223869853776009296802892314,1223869853776009297050257505⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-128628975308119700916645389),(-128628975308119700849909865)⟩,⟨402549448167971454248202777,402549448167971454325318445⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨3329538188101558879198202067,3329538188101558882228202660⟩,⟨4189484414661630654188884633,4189484414661630657213577108⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨9127059120589323808439449973,9127059120589323817211016111⟩,⟨12181100698456591583407043801,12181100698456591592165751622⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨12606262076137692291974110746,12606262076137692305507989348⟩,⟨18998910792997394675852561293,18998910792997394689369977818⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨13044979007256275721598667908,13044979007256275738508122312⟩,⟨23908907268388572264805449568,23908907268388572281698680282⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨10635914694173937139232560609,10635914694173937158729477397⟩,⟨26355147442266579300950301423,26355147442266579320432094875⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨6343969814097996392651362160,6343969814097996413126023545⟩,⟨26141148356948786935329047528,26141148356948786955791999084⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1503396484605937262778508231,1503396484605937282433624464⟩,⟨23549131392538901476183689872,23549131392538901495831709269⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2664055877052254405038344115),(-2664055877052254387703268136)⟩,⟨19301482608220284623292542546,19301482608220284640626945969⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-5406787570483647262891036109),(-5406787570483647248661869658)⟩,⟨14354655498940645209617602207,14354655498940645223855103396⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-6553963703590922782339337368),(-6553963703590922771411362705)⟩,⟨9616320274586841405003584177,9616320274586841415948111819⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-6390479051412069501404631554),(-6390479051412069493565747259)⟩,⟨5716960160115764773488547069,5716960160115764781348168051⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-5411908624228380072350770688),(-5411908624228380067055900315)⟩,⟨2923114616341163382227713116,2923114616341163387541751726⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-4094965309907765721232859810),(-4094965309907765717699569288)⟩,⟨1192055529057789860395166700,1192055529057789863940622094⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-2764903365839805745339484227),(-2764903365839805743108682273)⟩,⟨301289340935095858484812107,301289340935095860721246018⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1567146764018393642823180534),(-1567146764018393641609505611)⟩,⟨(-25172260366789072176516582),(-25172260366789070961119713)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-504255866411411745024386052),(-504255866411411744641919513)⟩,⟨(-40891548934091211835109884),(-40891548934091211452326410)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-8777686544231255480863044051),(-8777686544231255462309680960)⟩,⟨(-69544191311489515893140079019),(-69544191311489515874292937333)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-22249733635784480286149953684),(-22249733635784480231661132549)⟩,⟨(-201456388836510334148921672958),(-201456388836510334093554114267)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-24808906507345013071011895499),(-24808906507345012984430069329)⟩,⟨(-312604026530861911725055455949),(-312604026530861911637155618697)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-13245821174492984963039645791),(-13245821174492984843638685419)⟩,⟨(-392395861315677337619605294647),(-392395861315677337498642893048)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨11093134186896518049591263402,11093134186896518202839764178⟩,⟨(-434780083264279866921558792622),(-434780083264279866766787443500)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨42955452267808108783829236528,42955452267808108964372513561⟩,⟨(-439290649857508944499671426525),(-439290649857508944317839151359)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨75125915715563656751358745310,75125915715563656947844630021⟩,⟨(-410979095531626202972978020413),(-410979095531626202775611781969)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨100837919950931891632969878861,100837919950931891830862450523⟩,⟨(-359064939392001370524705667607),(-359064939392001370326406695821)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨115692547525985679744862102304,115692547525985679929784820290⟩,⟨(-294620182737554883509331266949),(-294620182737554883324403361320)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨118439372305931879099885898389,118439372305931879260819492463⟩,⟨(-228039147240638006997502074655),(-228039147240638006836807749555)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨110554397204370004408651914444,110554397204370004539660524628⟩,⟨(-167118045244727175272371226682),(-167118045244727175141698327686)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨95063211539824941742524546753,95063211539824941842673878369⟩,⟨(-116229986580864503031463220100),(-116229986580864502931655442081)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨75245747888541022816339274358,75245747888541022888045546557⟩,⟨(-76561319634948509653748825568),(-76561319634948509582338100494)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨53706128050502911217197449734,53706128050502911264368167395⟩,⟨(-46987177482992259116625946716),(-46987177482992259069673395667)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨31980071082701471361980607930,31980071082701471388450810118⟩,⟨(-25072217882564832499816390705),(-25072217882564832473477630420)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨10592695826551212164536013143,10592695826551212173013659897⟩,⟨(-7834004829837883988780427043),(-7834004829837883980345331799)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-7211417153636143504668811441),(-7211417153636143491751048146)⟩,⟨24537987005324140955834810618,24537987005324140968653226717⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-22114978051340534333487418299),(-22114978051340534294997676378)⟩,⟨71462604264856131157869968727,71462604264856131196112156775⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-38155390860030186956492623680),(-38155390860030186893587586133)⟩,⟨112101683031462189034137765248,112101683031462189096768666080⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-55257118631504159550329429391),(-55257118631504159465671728130)⟩,⟨143089473286580779488761577205,143089473286580779573231706695⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-72426492377419125544159057849),(-72426492377419125442501868371)⟩,⟨162237853964618468352153869155,162237853964618468453740386853⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-87940089914943528067137468107),(-87940089914943527955250647037)⟩,⟨168875226754960452658680691598,168875226754960452770554598110⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-99825280466770603721471403793),(-99825280466770603605658829266)⟩,⟨163935442841519035676747331373,163935442841519035792464317515⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-106447391912549228455724810368),(-106447391912549228337852358524)⟩,⟨149722725935517912713544403755,149722725935517912831113499384⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-106972483263476067826531047524),(-106972483263476067713530493394)⟩,⟨129380228559665495161616167078,129380228559665495273782152326⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-101537678818836577394088075386),(-101537678818836577292073195977)⟩,⟨106209724381173685167301639130,106209724381173685267816040778⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-91098743937344329716084299001),(-91098743937344329629192512177)⟩,⟨83048005519042883306350628390,83048005519042883391187682142⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-77060646404765440307170350034),(-77060646404765440237324738783)⟩,⟨61866944365399725475727442974,61866944365399725543251882446⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-60861589588512099420414405820),(-60861589588512099367812187781)⟩,⟨43656527787539603808033236491,43656527787539603858398583236⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-43656671087512181229480171505),(-43656671087512181193265932901)⟩,⟨28538912164276963387056330068,28538912164276963421441784282⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-26170100453386707764470460829),(-26170100453386707743427756785)⟩,⟨16001427093831533854739205107,16001427093831533874595101337⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-8706456695177590772589294764),(-8706456695177590765708326518)⟩,⟨5139514747687832221201548388,5139514747687832227675364459⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨152804320781689478386815271469,152804320781689478433602065061⟩,⟨114924057770661421163445217405,114924057770661421212554926114⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨444308136031434601717276113560,444308136031434601858038866619⟩,⟨345532586666050900976432023130,345532586666050901123844039157⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨694614343429768355073662890588,694614343429768355310824594990⟩,⟨576252449456293703994518223893,576252449456293704241641105059⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨881638339201846660925278996404,881638339201846661259397270563⟩,⟨801848199415581654461635423687,801848199415581654807733630249⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨991054535140497223976827047871,991054535140497224402683441041⟩,⟨1011213235022023802585414267209,1011213235022023803024132434420⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1018645351138676961134459893154,1018645351138676961637815552248⟩,⟨1188734435701786806987359057650,1188734435701786807503743021945⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨971061244164929727347543765276,971061244164929727903817715269⟩,⟨1317691010622390823037833875161,1317691010622390823607030161715⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨864419134464558867620864744556,864419134464558868195233176979⟩,⟨1384532401283557555814417119175,1384532401283557556401640547091⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨720811954908930969817457801409,720811954908930970374553073356⟩,⟨1382441780123387315830123384281,1382441780123387316400192856426⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨563634091565608834019352353184,563634091565608834560883753100⟩,⟨1312878468010656362664906404697,1312878468010656363217357544197⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨413110507882856789946736334695,413110507882856790471212208814⟩,⟨1184664862571995357993862229653,1184664862571995358525531001504⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨283257932384889723028123231238,283257932384889723500930344039⟩,⟨1011189646222859986877674006176,1011189646222859987354924919108⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨180820495812987814315973238819,180820495812987814708489674308⟩,⟨806929513232584498155611035050,806929513232584498550738696975⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨105927914512377379658942209287,105927914512377379950702006899⟩,⟨584507571188668544232476906463,584507571188668544525697644310⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨53730272104793465759428433112,53730272104793465938188467377⟩,⟨353045247746208486619670071181,353045247746208486799165909138⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨16218808509091175851698496406,16218808509091175911660386767⟩,⟨117937887946664567459353237758,117937887946664567519539023534⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-151442336259725568006728097512),(-151442336259725567979109002185)⟩,⟨(-120858001509838279047644098596),(-120858001509838279018959358666)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-440734282475259913468366015729),(-440734282475259913383516198746)⟩,⟨(-365199387425931354870704004326),(-365199387425931354783091945206)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-689987408805002571988306975270),(-689987408805002571841382396697)⟩,⟨(-614906554747708341367988959336),(-614906554747708341217696433672)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-876784600912404689581319906192),(-876784600912404689366412381206)⟩,⟨(-867148673604571618725203893352),(-867148673604571618507702122982)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-985348819454574965150821882914),(-985348819454574964864193883654)⟩,⟨(-1111547054878965651364011836902),(-1111547054878965651076608815840)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1009329578988217151002017313946),(-1009329578988217150645056940624)⟩,⟨(-1331008529764066064963019767927),(-1331008529764066064607366257904)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-953468777147896878033002495389),(-953468777147896877615124080656)⟩,⟨(-1505002361468630495934987722378),(-1505002361468630495519595737457)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-833220677028434298737201881645),(-833220677028434298277696857725)⟩,⟨(-1614336715524584329157414489065),(-1614336715524584328699582408371)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-671935824518216292866573258832),(-671935824518216292392218773516)⟩,⟨(-1645823376445021247786843827246),(-1645823376445021247311138048168)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-496164303563561874289894569421),(-496164303563561873830497552752)⟩,⟨(-1595218219218481615041881205422),(-1595218219218481614576750513911)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-330423281341401423832644832775),(-330423281341401423415786183061)⟩,⟨(-1467530147206591310333585070981),(-1467530147206591309906649581377)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-192949200613091500566019024030),(-192949200613091500212409342908)⟩,⟨(-1274868131830366352186942400465),(-1274868131830366351820203898320)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-93442013197625053368525905141),(-93442013197625053090780501079)⟩,⟨(-1032896110433862446076083707338),(-1032896110433862445784266607263)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-32947084796143087655978323435),(-32947084796143087458959511992)⟩,⟨(-757286182847581935948756479136),(-757286182847581935739391278718)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-5296961136581689914615555314),(-5296961136581689797990225550)⟩,⟨(-461273475160629416688268420750),(-461273475160629416563257904710)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨737481698578820817403987152,737481698578820855832474327⟩,⟨(-154760782430635864325052211322),(-154760782430635864283699285806)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨64803162971034220607217379226,64803162971034222812834521269⟩,⟨(-730678046898273670707250866691),(-730678046898273668470149552398)⟩⟩ +lemma checked : cachedMomentRuleBox column3_1 kernel1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 1 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_1_contains kernel1_1_contains +end cm3_1_1_1 +namespace cm3_3_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_0 j i k).mul (kernel3_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨6658646625090308128,6658646625090308158⟩,⟨(-5559447742673827102),(-5559447742673827068)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨19902682873967829558,19902682873967829617⟩,⟨(-10349794820742897945),(-10349794820742897889)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨28105932645119706317,28105932645119706389⟩,⟨(-1415253240464875988),(-1415253240464875916)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨22135740873135628497,22135740873135628560⟩,⟨14623142495227553489,14623142495227553553⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨3429834163035653637,3429834163035653682⟩,⟨20885260962723102015,20885260962723102063⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-11267533977067006764),(-11267533977067006725)⟩,⟨10285594977920559060,10285594977920559102⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-9614410247326992706),(-9614410247326992673)⟩,⟨(-4037575096903963201),(-4037575096903963166)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨529809864013720324,529809864013720355⟩,⟨(-7021812542535399604),(-7021812542535399575)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨4785102857938928595,4785102857938928621⟩,⟨(-865484950539952386),(-865484950539952359)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1431565409060817943,1431565409060817966⟩,⟨3210365971896495485,3210365971896495510⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2033357139811965767),(-2033357139811965746)⟩,⟨1741835841779270389,1741835841779270416⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1897369049303637006),(-1897369049303636986)⟩,⟨(-945278613041467830),(-945278613041467811)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-178503575173028604),(-178503575173028584)⟩,⟨(-1675035069631882602),(-1675035069631882583)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨797817805594754780,797817805594754796⟩,⟨(-981346949771735645),(-981346949771735625)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨751653915075967196,751653915075967214⟩,⟨(-270658756313952355),(-270658756313952338)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨274101472810688312,274101472810688328⟩,⟨(-19105219003498816),(-19105219003498799)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨12824995401064955411536,12824995401064955458678⟩,⟨(-14973961167237117982954),(-14973961167237117935813)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨35619006142636978820997,35619006142636978943982⟩,⟨(-36072629672469328073908),(-36072629672469327950936)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨49631467569670161855144,49631467569670162009141⟩,⟨(-37585197159326081392544),(-37585197159326081238577)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨50617734897209848023271,50617734897209848164518⟩,⟨(-23122467649452520548743),(-23122467649452520407568)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨39721417807748528284127,39721417807748528391624⟩,⟨(-5155648439863192396944),(-5155648439863192289572)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨23652459751852932036873,23652459751852932102924⟩,⟨6109633216901441326126,6109633216901441392056⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨9885510189777090312532,9885510189777090347960⟩,⟨8617179850036504635480,8617179850036504670858⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨1970124789143595559160,1970124789143595578053⟩,⟨6106765768493885664634,6106765768493885683528⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-864308755676412509743),(-864308755676412500676)⟩,⟨2832949793991127470753,2832949793991127479831⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1086133612492350683579),(-1086133612492350679602)⟩,⟨774223676480229569889,774223676480229573866⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-603234737512523916832),(-603234737512523915215)⟩,⟨(-33309038277982984568),(-33309038277982982955)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-213186652715742056027),(-213186652715742055154)⟩,⟨(-184065317362289299599),(-184065317362289298726)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-35187130452761033041),(-35187130452761032606)⟩,⟨(-131792610086953487189),(-131792610086953486754)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨15686462491103882444,15686462491103882651⟩,⟨(-65692107423900318317),(-65692107423900318111)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨17557974722970007907,17557974722970008010⟩,⟨(-26286356419028081719),(-26286356419028081617)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨6496042122779506346,6496042122779506388⟩,⟨(-6648578318988579823),(-6648578318988579782)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨4066967962556064177639053,4066967962556064195880073⟩,⟨12225082162178122356256917,12225082162178122373979569⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨10379473006508327840820717,10379473006508327891216189⟩,⟨32127132458055758679700465,32127132458055758728811310⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨12408602737051632381596041,12408602737051632453902101⟩,⟨41025024816001211346629409,41025024816001211417465250⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨10293364379529974735106467,10293364379529974814740625⟩,⟨38415084847878960957617916,38415084847878961036100296⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨6166929038192269811102899,6166929038192269883567594⟩,⟨28700959375186582610654238,28700959375186582682457646⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2376096344689800970627742,2376096344689801026374158⟩,⟨17524414441281098323923903,17524414441281098379396460⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨126353035248630796050679,126353035248630832644598⟩,⟨8670628540847702337600079,8670628540847702374118231⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-644117339174434648243233),(-644117339174434627588730)⟩,⟨3259912157067476618637774,3259912157067476639281330⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-588608139816304683193276),(-588608139816304672932615)⟩,⟨662879118067720499940746,662879118067720510201027⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-299168655025659518645759),(-299168655025659513441353)⟩,⟨(-258201682699996952736734),(-258201682699996947532721)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-67958165789571411935293),(-67958165789571409021816)⟩,⟨(-416780565206759939827579),(-416780565206759936914264)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨44946273872097870551988,44946273872097872170019⟩,⟨(-327234248712774905141214),(-327234248712774903521969)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨74043309498922240700836,74043309498922241575828⟩,⟨(-205851394514325747398935),(-205851394514325746521987)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨63260068919355144583315,63260068919355145041566⟩,⟨(-114380633915348380495150),(-114380633915348380035073)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨39323575664453592683822,39323575664453592902620⟩,⟨(-55391922570840979897132),(-55391922570840979677130)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨13085013650694457644713,13085013650694457709200⟩,⟨(-16324229890095742137458),(-16324229890095742072558)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨254726161282930905297327562,254726161282930905760170396⟩,⟨440141751871346219464158190,440141751871346219900652608⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨713379714642425006852575638,713379714642425008177793711⟩,⟨1236951553110416323778192640,1236951553110416325038103980⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1035911612633326387387992018,1035911612633326389386405964⟩,⟨1808627467945267958217220412,1808627467945267960143723442⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1180658423012149452786277202,1180658423012149455162645149⟩,⟨2082615283822285196068683107,2082615283822285198398284910⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1156230427579748083780139256,1156230427579748086297617286⟩,⟨2067878777961373769768244701,2067878777961373772272652988⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1009113021552904835839559378,1009113021552904838344071193⟩,⟨1837387074458869965712769011,1837387074458869968223734248⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨800679325895966431079111819,800679325895966433322701107⟩,⟨1491947248267438778295091708,1491947248267438780549946490⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨585552283405282664577316254,585552283405282666395188864⟩,⟨1124139070713643039820447129,1124139070713643041643536071⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨399285296954502571833778040,399285296954502573178264769⟩,⟨796481257874008093080164584,796481257874008094420860923⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨256717512336921013222250337,256717512336921014141119100⟩,⟨537361937416274059750923102,537361937416274060659765268⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨157381935008553043593330322,157381935008553044182027195⟩,⟨349215291843911978865320477,349215291843911979442029213⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨92955341047773498746648110,92955341047773499113335942⟩,⟨220505168586088993107353094,220505168586088993464043466⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨53205145989328438657347066,53205145989328438883645769⟩,⟨135472666183313663462924849,135472666183313663683010298⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨29231707744190417599193426,29231707744190417729882152⟩,⟨79609400648733871267681711,79609400648733871394853461⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨14457509043584379193950463,14457509043584379260507403⟩,⟨41546457342222202335145504,41546457342222202399951630⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4346970010467364933584081,4346970010467364953834905⟩,⟨12873702143817350577462385,12873702143817350597184978⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨4673767168269156820055936967,4673767168269156824324432162⟩,⟨(-622612486975672977761045471),(-622612486975672974384843178)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨13238174674177709196654221554,13238174674177709209355231680⟩,⟨(-1514969620946800600187885541),(-1514969620946800589864560379)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨19661886186103530782753437495,19661886186103530803404635699⟩,⟨(-1503851712504867049977173571),(-1503851712504867032407324016)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨23178351553720126969500573283,23178351553720126996905807421⟩,⟨(-429403249119513114741685382),(-429403249119513090195297779)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨23745824413423506561436418759,23745824413423506593385862150⟩,⟨1441040324445619570293068580,1441040324445619600291400156⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨21939328156495770872751892274,21939328156495770906222621562⟩,⟨3568785845793109527336761998,3568785845793109559953114853⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨18665819857070314596750321153,18665819857070314628285445220⟩,⟨5390301555675229893454488222,5390301555675229924899966806⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨14843570951135237412229285279,14843570951135237438852288211⟩,⟨6523220374175628086611276551,6523220374175628113367514443⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨11172153113283162372590366634,11172153113283162393314384237⟩,⟨6850226959488944142239341928,6850226959488944162895247853⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨8047594253836858650799911865,8047594253836858667366001845⟩,⟨6479572806240638505434322458,6479572806240638521588490510⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨5598941343737183600476839707,5598941343737183612858259466⟩,⟨5638345395170496893912558727,5638345395170496905646409222⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨3782226609179371222164946332,3782226609179371230788678294⟩,⟨4564736602523178870536526389,4564736602523178878449252401⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨2473558318317902606322589029,2473558318317902612214325168⟩,⟨3439848230507280919330492196,3439848230507280924662590156⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1532176554621828762769414668,1532176554621828766583573389⟩,⟨2365631676378213806060342714,2365631676378213809529106864⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨830760479670599758646426882,830760479670599760744498948⟩,⟨1374212693282369994631374942,1374212693282369996548348839⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨262651732108666618267128173,262651732108666618931053151⟩,⟨449601306425470909530622226,449601306425470910138797059⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨89698732144105316795997445,89698732144105320481788496⟩,⟨(-19748005217601637933059604),(-19748005217601634220426585)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1291890815515848308658974165,1291890815515848320084934124⟩,⟨(-278915590218088120204796591),(-278915590218088108739523337)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨5171421654062623194375097855,5171421654062623214474796808⟩,⟨(-1077362315695161884414633742),(-1077362315695161864360104117)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨12362798712110030350497850577,12362798712110030380309886809⟩,⟨(-2448652219959600629148502191),(-2448652219959600599548772139)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨22247249629861754088920343951,22247249629861754128964135133⟩,⟨(-4141400878460025155936932611),(-4141400878460025116230823613)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨33191219769925647478742642273,33191219769925647528338104710⟩,⟨(-5767403321522996111940318270),(-5767403321522996062673692355)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨43133572333658490281593306147,43133572333658490338460561518⟩,⟨(-6988442426136843417257384721),(-6988442426136843360582937119)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨50260268147800814293610367593,50260268147800814353986249337⟩,⟨(-7632210055692156190237177587),(-7632210055692156129901214686)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨53496529464818186901066318316,53496529464818186960434160420⟩,⟨(-7698329717671300812272917378),(-7698329717671300752912378982)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨52664122322283558043191557773,52664122322283558097321257554⟩,⟨(-7291087124501035315357946686),(-7291087124501035261374886860)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨48319906440054485621026930544,48319906440054485667313485040⟩,⟨(-6542297065685799791464704956),(-6542297065685799745568395393)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨41416069658944604269838409394,41416069658944604306988412391⟩,⟨(-5564748199212476645858426246),(-5564748199212476609323122551)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨32950952312242309853910418198,32950952312242309881587423224⟩,⟨(-4439805210618187698839973536),(-4439805210618187671884976537)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨23726624647218066695327180736,23726624647218066714555217896⟩,⟨(-3222903832194774731430632258),(-3222903832194774712831130644)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨14248854530535517833329545904,14248854530535517844746428858⟩,⟨(-1951984037480357474600338687),(-1951984037480357463587441622)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨4743748374741161133689775601,4743748374741161137450001586⟩,⟨(-653250228617039822493706857),(-653250228617039818870939166)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨103458369852645269220866128625,103458369852645269355803912854⟩,⟨(-1209995894039405865717317930),(-1209995894039405734004154208)⟩⟩ +lemma checked : cachedMomentRuleBox column3_0 kernel3_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 3 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_0_contains kernel3_0_contains +end cm3_3_0_0 +namespace cm3_3_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_0 j i k).mul (kernel3_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-71732815096413950505),(-71732815096413950324)⟩,⟨18016248006304823225,18016248006304823403⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-191699738026914746639),(-191699738026914746197)⟩,⟨7197253229676379699,7197253229676380141⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-225058025099271712804),(-225058025099271712270)⟩,⟨(-89013745209982610395),(-89013745209982609857)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-126475276185190075164),(-126475276185190074717)⟩,⟨(-192086224642059896705),(-192086224642059896252)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨39173921294906368128,39173921294906368476⟩,⟨(-181064458354876159422),(-181064458354876159072)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨124357750532546137975,124357750532546138232⟩,⟨(-52400727425355177604),(-52400727425355177349)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨71352674797550223103,71352674797550223325⟩,⟨59987082362230038211,59987082362230038432⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-20824253228295535120),(-20824253228295534947)⟩,⟨60060818874254151881,60060818874254152055⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-44236198822559519960),(-44236198822559519823)⟩,⟨(-1533229218340282422),(-1533229218340282288)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-7985603998707909351),(-7985603998707909249)⟩,⟨(-31191705659911056538),(-31191705659911056437)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨20570060707868500435,20570060707868500529⟩,⟨(-13540384131638192172),(-13540384131638192082)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨16661127748048629346,16661127748048629418⟩,⟨10210106955899925465,10210106955899925538⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨799078914485588390,799078914485588447⟩,⟨15518909088327848199,15518909088327848256⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-7617596310702582953),(-7617596310702582910)⟩,⟨8834499334544734561,8834499334544734604⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-6957202067765323880),(-6957202067765323850)⟩,⟨2416991263139986157,2416991263139986184⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-2526454542602113107),(-2526454542602113083)⟩,⟨170339724657814900,170339724657814920⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-140384700682533564796138),(-140384700682533564456845)⟩,⟨7881980850230642778209,7881980850230643116418⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-362885662621511305998063),(-362885662621511305103785)⟩,⟨(-3315854214162888536069),(-3315854214162887644498)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-444466186117473366238023),(-444466186117473365092734)⟩,⟨(-63367364022190986845408),(-63367364022190985703117)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-381724829230748830114772),(-381724829230748829013952)⟩,⟨(-137125536139653598095464),(-137125536139653596996839)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-240334048997681911736002),(-240334048997681910820352)⟩,⟨(-172645012570560192206746),(-172645012570560191292183)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-102287957047361030320519),(-102287957047361029687019)⟩,⟨(-152161280046923105858192),(-152161280046923105225025)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-15693925619786857596749),(-15693925619786857232450)⟩,⟨(-98909679306549317152129),(-98909679306549316787843)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨17190904715474482831763,17190904715474483004234⟩,⟨(-46841903926346903333802),(-46841903926346903161294)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨18732903975150249502825,18732903975150249576582⟩,⟨(-14107092537033942533387),(-14107092537033942459593)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨10739681729992582119144,10739681729992582154371⟩,⟨(-271727977878849949258),(-271727977878849914018)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨4037281780925123751462,4037281780925123768682⟩,⟨2850403282730394672032,2850403282730394689243⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨758685215936157206302,758685215936157214791⟩,⟨2208179970387099225688,2208179970387099234163⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-270372035859638054801),(-270372035859638050830)⟩,⟨1110617336122785623771,1110617336122785627731⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-372611047345814034278),(-372611047345814032258)⟩,⟨432031933339552746119,432031933339552748138⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-232922611476131045390),(-232922611476131044409)⟩,⟨133452896634240298595,133452896634240299574⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-74522023909374085403),(-74522023909374085107)⟩,⟨26650657302420388658,26650657302420388955⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨50929257062668977560605388,50929257062668977687256512⟩,⟨(-55475791011481263375468947),(-55475791011481263249098690)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨134613646039281992846190319,134613646039281993194552804⟩,⟨(-145286248299537933508522796),(-145286248299537933161403769)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨174091862063716535794325460,174091862063716536291191370⟩,⟨(-183904717050567390843547987),(-183904717050567390349462240)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨166651069383135304025460742,166651069383135304567518420⟩,⟨(-169123755593588218047346805),(-169123755593588217509400507)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨128981287828878270137770067,128981287828878270624000431⟩,⟨(-122103892978339146315900694),(-122103892978339145833997169)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨83160652838128619888331687,83160652838128620254583349⟩,⟨(-69996861593861839937206784),(-69996861593861839574256367)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨44755928854613473877903910,44755928854613474110909284⟩,⟨(-30656277831853293864509259),(-30656277831853293633242813)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨19397516361803308370093487,19397516361803308495367419⟩,⟨(-8517579002803179530759899),(-8517579002803179405928297)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨5742451237585304249991140,5742451237585304307953288⟩,⟨542881073624287301894856,542881073624287360108415⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-136270759781430231613800),(-136270759781430202603200)⟩,⟨2626351291656826304220483,2626351291656826333665486⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1890212295698379910062573),(-1890212295698379892294981)⟩,⟨2140073521274546354886688,2140073521274546373010288⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1907837197902858031831502),(-1907837197902858020968275)⟩,⟨1227823516843154487649823,1227823516843154498742579⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1412954301989166302938084),(-1412954301989166296588597)⟩,⟨569203288216143657119550,569203288216143663600218⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-893850653942531601294534),(-893850653942531597771131)⟩,⟨217906807664871207216278,217906807664871210809208⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-477120885573800555717295),(-477120885573800553969823)⟩,⟨66391936052451631426520,66391936052451633207049⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-148374269283481258872768),(-148374269283481258348143)⟩,⟨12753963901808630621138,12753963901808631155494⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1647350237172172468280260528,1647350237172172470827156035⟩,⟨(-1846609673668611404037121211),(-1846609673668611401445468424)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4632273168618510900827827677,4632273168618510908131571644⟩,⟨(-5209372969952618638532432139),(-5209372969952618631139154212)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨6780592020824418904813159882,6780592020824418915837646641⟩,⟨(-7674223213272832425619332994),(-7674223213272832414559372724)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨7820015280834019475379896304,7820015280834019488449750751⟩,⟨(-8933539397642755164134347873),(-8933539397642755151159773097)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨7780335511890379743615301724,7780335511890379757398986951⟩,⟨(-8992839614406215482494913580),(-8992839614406215468916348652)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨6930812918112785891173752241,6930812918112785904880552526⟩,⟨(-8116077411736729798615429425),(-8116077411736729785125495011)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨5646810222969745512609300744,5646810222969745524885300152⟩,⟨(-6697398460105973861167311491),(-6697398460105973849040396470)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨4274673594695607268707417279,4274673594695607278670631840⟩,⟨(-5122736717072723619636814623),(-5122736717072723609720752711)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3048814173711071509144445025,3048814173711071516785758632⟩,⟨(-3674273702787978319198200252),(-3674273702787978311522873675)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2075784947358438422446471943,2075784947358438428311602621⟩,⟨(-2498871735227312768828054936),(-2498871735227312762909183766)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1365052553028647866390026607,1365052553028647870525287738⟩,⟨(-1628838640322060582105640862),(-1628838640322060577930905029)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨874183411538377741152520493,874183411538377743864156870⟩,⟨(-1026584532743896768847892022),(-1026584532743896766115792914)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨545264085828612759848476743,545264085828612761523216196⟩,⟨(-627183656025311836937315430),(-627183656025311835254837639)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨325011353054410157664104992,325011353054410158633808081⟩,⟨(-365852295187157898421723413),(-365852295187157897450488815)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨171514698113265876666876024,171514698113265877162192365⟩,⟨(-189641981459740510582138320),(-189641981459740510087268761)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨53472210095170034916234322,53472210095170035067195995⟩,⟨(-58526923173416480952702386),(-58526923173416480802087743)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-5851073821391463147193634940),(-5851073821391463130733816652)⟩,⟨(-18664754024523224742826229433),(-18664754024523224723510911520)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-15731625973007876177590214854),(-15731625973007876127477053135)⟩,⟨(-53152826354299624761090657685),(-53152826354299624703526854952)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-20808834996456656700201921502),(-20808834996456656615519543264)⟩,⟨(-79821475079204490046101801185),(-79821475079204489952237482644)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-19838268377003545478691667039),(-19838268377003545361355432871)⟩,⟨(-95728416988864248140152575785),(-95728416988864248015153025916)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-13585456667474069372514123956),(-13585456667474069230333898159)⟩,⟨(-100456583498347764613271523709),(-100456583498347764467062402149)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-4295494265025327181080659650),(-4295494265025327027863103789)⟩,⟨(-95799302056413148784723034805),(-95799302056413148631189199726)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨5313471428416796199759528434,5313471428416796345884611379⟩,⟨(-84830689304998754039837993941),(-84830689304998753895270663210)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨13024605601338078079707004203,13024605601338078202053040731⟩,⟨(-70819181319160273797127263426),(-70819181319160273675858400467)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨17674874826493612970168683678,17674874826493613062730432729⟩,⟨(-56409422476293722036787219009),(-56409422476293721943318999752)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨19178772944765437680872045684,19178772944765437753455624980⟩,⟨(-43272039461221277295685146986),(-43272039461221277220124317567)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨18178157068591878059535280915,18178157068591878116809893485⟩,⟨(-32161998716380158989844072540),(-32161998716380158929017818684)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨15582588993402890663484002550,15582588993402890708585026257⟩,⟨(-23185832997999689946050425613),(-23185832997999689898296181922)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨12211993621641596834626100706,12211993621641596866940111151⟩,⟨(-16089130828425509508680107409),(-16089130828425509474731053332)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨8623254582851248542994014858,8623254582851248563962488088⟩,⟨(-10466127590005494603137391897),(-10466127590005494581306701295)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨5092296152742939429948710483,5092296152742939441524414093⟩,⟨(-5876356734620321595374374274),(-5876356734620321583416295018)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1679255664440134420289954939,1679255664440134423961114779⟩,⟨(-1891865973841205763926389016),(-1891865973841205760150748301)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-88446420512523458820331439),(-88446420512523444967987017)⟩,⟨(-320393575372454520300851916),(-320393575372454506536473264)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1267323793652924236265685381),(-1267323793652924193388233649)⟩,⟨(-4624593916205139339884166023),(-4624593916205139297123107617)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-5030497750581412546218883391),(-5030497750581412470879570663)⟩,⟨(-18587755799966736837715852103),(-18587755799966736762179625840)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-11909793433459834140870171331),(-11909793433459834028940570484)⟩,⟨(-44701585395743515297749898978),(-44701585395743515185034740536)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-21262778058798422812649305291),(-21262778058798422661237297294)⟩,⟨(-81062757625304172301472075374),(-81062757625304172148865337121)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-31635029546745996607918924065),(-31635029546745996418149912907)⟩,⟨(-122052069256391139668061358689),(-122052069256391139477193729574)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-41337440998459169583328076126),(-41337440998459169362493856935)⟩,⟨(-160250491296234914790611621413),(-160250491296234914569214379782)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-48932502924488743764055827691),(-48932502924488743525945260898)⟩,⟨(-188784677377213836946501492878),(-188784677377213836708332310372)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-53477124314768278328441710970),(-53477124314768278090993629330)⟩,⟨(-203192628006503474317855805166),(-203192628006503474080277672048)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-54551078991566069236879794351),(-54551078991566069017947295402)⟩,⟨(-202208598417957768467813190268),(-202208598417957768247942631744)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-52177509738363051804158606472),(-52177509738363051615348191380)⟩,⟨(-187399417289135662022535012623),(-187399417289135661831584293225)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-46711966404672172076535839187),(-46711966404672171922857001612)⟩,⟨(-162049380977077655159483166482),(-162049380977077655002682529507)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-38722109011076107527990958495),(-38722109011076107405439245629)⟩,⟨(-129875757678270851416194221453),(-129875757678270851290496503034)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-28863380460600460417519451155),(-28863380460600460329405107566)⟩,⟨(-94044621327149674704386420732),(-94044621327149674613748873908)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-17770662712737506674042191623),(-17770662712737506621651556488)⟩,⟨(-56691967218976156356684539906),(-56691967218976156302709641167)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-5993664729491016574857115817),(-5993664729491016557585791950)⟩,⟨(-18909888770690425156647721447),(-18909888770690425138843574396)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-61418502127829317981031997477),(-61418502127829317414030319275)⟩,⟨(-421137249079348776676708275219),(-421137249079348776099816653388)⟩⟩ +lemma checked : cachedMomentRuleBox column3_0 kernel3_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 3 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_0_contains kernel3_1_contains +end cm3_3_0_1 +namespace cm3_3_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_1 j i k).mul (kernel3_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨24241418211894654175,24241418211894654227⟩,⟨(-34439089919361109790),(-34439089919361109740)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨76004392288505376780,76004392288505376889⟩,⟨(-76211554099080266154),(-76211554099080266044)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨118535195686088879105,118535195686088879236⟩,⟨(-56291802329742164106),(-56291802329742163969)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨117111175612962499968,117111175612962500085⟩,⟨8842724803876130062,8842724803876130178⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨62149438758001955631,62149438758001955713⟩,⟨60294623008298069197,60294623008298069280⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-3710767993132033619),(-3710767993132033546)⟩,⟨56205606475473831328,56205606475473831402⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-30341984387222276406),(-30341984387222276341)⟩,⟨15833182337434382329,15833182337434382391⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-15987737418081472150),(-15987737418081472102)⟩,⟨(-12743752980133274044),(-12743752980133273997)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨4222044957155533379,4222044957155533417⟩,⟨(-11804985172200466021),(-11804985172200465985)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨8118276694818187303,8118276694818187334⟩,⟨365195945313149893,365195945313149924⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1595516262070131353,1595516262070131380⟩,⟨5394036088306033606,5394036088306033634⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-3089345680154112501),(-3089345680154112476)⟩,⟨2709827838022007007,2709827838022007033⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2959722525694781010),(-2959722525694780989)⟩,⟨(-784921297267816339),(-784921297267816315)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1124034091044431190),(-1124034091044431172)⟩,⟨(-1880716414567346967),(-1880716414567346946)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-8172879312969925),(-8172879312969907)⟩,⟨(-1340490272549248611),(-1340490272549248594)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨118913005105321843,118913005105321860⟩,⟨(-437909336161003303),(-437909336161003287)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨27591930580411885098771,27591930580411885137128⟩,⟨(-27204314718413913868773),(-27204314718413913830292)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨74590072714044112896104,74590072714044112996035⟩,⟨(-66293402302210095537293),(-66293402302210095437029)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨99909043177764568752321,99909043177764568877286⟩,⟨(-71416306934780481230981),(-71416306934780481105586)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨98619342826130433550820,98619342826130433665396⟩,⟨(-48344671654661579149271),(-48344671654661579034330)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨76758300328787999597890,76758300328787999688740⟩,⟨(-17659750136364531733214),(-17659750136364531642182)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨47404223252292582427285,47404223252292582487023⟩,⟨3540316224225440081805,3540316224225440141566⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨22535592472150237410009,22535592472150237443497⟩,⟨10907647742039164148933,10907647742039164182374⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨7375481171473929377972,7375481171473929394887⟩,⟨9353478795441756508966,9353478795441756525844⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨769042080404272717439,769042080404272725903⟩,⟨5249246456680614457647,5249246456680614466103⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-959367561424495488420),(-959367561424495484009)⟩,⟨2083461365279902890788,2083461365279902895199⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-857648019212704985843),(-857648019212704983726)⟩,⟨505929536372317914957,505929536372317917072⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-444665371451493264940),(-444665371451493263914)⟩,⟨(-30111508752343644022),(-30111508752343643001)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-169360478840869915686),(-169360478840869915217)⟩,⟨(-121119962991545373293),(-121119962991545372823)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-46897452495154730128),(-46897452495154729912)⟩,⟨(-88491216375434396903),(-88491216375434396686)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-7056122191908707420),(-7056122191908707319)⟩,⟨(-45393294776846265986),(-45393294776846265885)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨269363446462098485,269363446462098528⟩,⟨(-13366679045083424236),(-13366679045083424196)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-37633561569348561216135643),(-37633561569348561192115523)⟩,⟨16534134794903557319595288,16534134794903557343376310⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-102045589564320694306664790),(-102045589564320694240766790)⟩,⟨44140440312529713866290001,44140440312529713931527002⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-139002624739310092839654464),(-139002624739310092748367468)⟩,⟨58094698007815546967894147,58094698007815547058293292⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-144183522912906972693555096),(-144183522912906972589518051)⟩,⟨56743078488829144187194533,56743078488829144290398200⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-124958673153933268878248232),(-124958673153933268773081809)⟩,⟨44584806894085042177743695,44584806894085042282336730⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-94141656804414056746645319),(-94141656804414056654225832)⟩,⟨28704751935588154513248209,28704751935588154605359530⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-63134373888034346228362110),(-63134373888034346156879227)⟩,⟨14865353130914070895719886,14865353130914070967081377⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-38371059172524405588736315),(-38371059172524405539494050)⟩,⟨5631861434254043333554507,5631861434254043382765332⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-21470865263512223839271452),(-21470865263512223808600145)⟩,⟨817382323248591476053067,817382323248591506721308⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-11231244199494634584807715),(-11231244199494634567202067)⟩,⟨(-1020922743078498521343368),(-1020922743078498503736752)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-5577876957777705580984010),(-5577876957777705571467674)⟩,⟨(-1339961216463886945124829),(-1339961216463886935608555)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2671658805377523585370481),(-2671658805377523580417747)⟩,⟨(-1094199322955087792175620),(-1094199322955087787223616)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1251235943386585912765426),(-1251235943386585910241586)⟩,⟨(-745525902598653479200508),(-745525902598653476677331)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-574685188447267362707703),(-574685188447267361448459)⟩,⟨(-452681484008655187440711),(-452681484008655186181860)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-247263195925785673188644),(-247263195925785672607735)⟩,⟨(-236807774329305596942297),(-236807774329305596361567)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-68787399675031472498438),(-68787399675031472330399)⟩,⟨(-73044223208920105376062),(-73044223208920105208078)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨178087473666947456483076170,178087473666947456637729750⟩,⟨177294190653083502655545940,177294190653083502818045749⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨500997566075709754399285452,500997566075709754842664881⟩,⟨495588615346057125505422539,495588615346057125969489543⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨733880676039995120731079723,733880676039995121400973040⟩,⟨716985789691608070183739064,716985789691608070880092337⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨846905056906918583093410005,846905056906918583891673652⟩,⟨812875640520250062481819272,812875640520250063304972818⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨842442389826044850197603418,842442389826044851020388124⟩,⟨791211092175607374999508490,791211092175607375840911033⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨748872368580757344779023435,748872368580757345560067400⟩,⟨686745758048601526065634010,686745758048601526857101071⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨606774008617985496495892122,606774008617985497173965080⟩,⟨543500413342094275689138221,543500413342094276371575011⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨454453044656162445702492780,454453044656162446282701456⟩,⟨398896202167314406644630306,398896202167314407226322252⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨318508504405891607139953617,318508504405891607596989827⟩,⟨275669649162090402575382877,275669649162090403034149354⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨211425130683444303052334816,211425130683444303386163572⟩,⟨181997330265003332644913579,181997330265003332981522159⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨134507711618507099873644844,134507711618507100102759051⟩,⟨116287596538579851463960611,116287596538579851696378361⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨82843731457520686441577255,82843731457520686593502480⟩,⟨72585321524187474717619278,72585321524187474872418103⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨49585690671434783741105691,49585690671434783839506722⟩,⟨44307039513800054238679505,44307039513800054338964258⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨28444883477487556887826998,28444883477487556947247220⟩,⟨25968803121144717229036122,25968803121144717289575551⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨14570831840778926899416260,14570831840778926930747638⟩,⟨13547037836037508359073997,13547037836037508390983997⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4469232438717826829229479,4469232438717826838942707⟩,⟨4198790940578437930034754,4198790940578437939925153⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨9856656896924926367387574176,9856656896924926372723040778⟩,⟨5316827541883690949542377057,5316827541883690954979015010⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨28251933418153705828903277473,28251933418153705844683285750⟩,⟨15209188139452134239730830575,15209188139452134255784805313⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨42968252976508776306525477776,42968252976508776331900322156⟩,⟨23028471384431591055438739211,23028471384431591081195437012⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨52478004359757696337675839828,52478004359757696370902488992⟩,⟨27906710855635151064058156198,27906710855635151097715715911⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨56325232887430958818428491565,56325232887430958856696114035⟩,⟨29591195733121790952381696517,29591195733121790991110518919⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨55073358748715048663949215421,55073358748715048703976763239⟩,⟨28434619091289989819171119932,28434619091289989859642565124⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨49997989828443743078550659199,49997989828443743116581033745⟩,⟨25222461365239408896685640289,25222461365239408935089128708⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨42663762988344653070061305657,42663762988344653102781158707⟩,⟨20908822511613433961292050151,20908822511613433994292568990⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨34533366419132032871027030208,34533366419132032896641368667⟩,⟨16360449561274765658179529315,16360449561274765683984463770⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨26711424099338496272659225021,26711424099338496292871520326⟩,⟨12191657590342090030415362547,12191657590342090050743293600⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨19854217094979224330238700821,19854217094979224346565060520⟩,⟨8719699125238703401420483072,8719699125238703417835372076⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨14213520725128636617923181185,14213520725128636630187110405⟩,⟨6014835637404927216107501555,6014835637404927228460760703⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨9751351748657609683450820443,9751351748657609692245622554⟩,⟨3991948001035286622232050142,3991948001035286631100259519⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6264556606385387112996141669,6264556606385387118861220631⟩,⟨2496519505898943833085067795,2496519505898943838998217678⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨3480911753991905902307399585,3480911753991905905620253263⟩,⟨1361295445586395480010047548,1361295445586395483349970014⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1114115914220767687898064489,1114115914220767688961846239⟩,⟨431501860465975326127582193,431501860465975327200127519⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-7889532205988720432909950699),(-7889532205988720424899655529)⟩,⟨(-35779995830969321228263913674),(-35779995830969321219351978090)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-22487626721226459674545147584),(-22487626721226459650021153064)⟩,⟨(-103874146070420249804616259712),(-103874146070420249777513992072)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-33846587989408053698707646517),(-33846587989408053656525912618)⟩,⟨(-162016519980341146724768412237),(-162016519980341146678771246568)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-40775704777362038009930309293),(-40775704777362037949015416177)⟩,⟨(-205336666918268632489121221338),(-205336666918268632423862046054)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-43139485625568501130864764892),(-43139485625568501050377368506)⟩,⟨(-231209418557130153807427083636),(-231209418557130153723278605982)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-41696938910364952124206813607),(-41696938910364952026171681270)⟩,⟨(-239501143292214255387844272329),(-239501143292214255287462874820)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-37694148669342558446383390464),(-37694148669342558336322578160)⟩,⟨(-232300089549068346139155069245),(-232300089549068346028061035733)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-32415211056215205057306580164),(-32415211056215204943493451906)⟩,⟨(-213230379315542097369244986219),(-213230379315542097255244409264)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-26864881649059898074975138961),(-26864881649059897966500753573)⟩,⟨(-186557206851173439788376284427),(-186557206851173439679922853268)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-21651722464709871942206658973),(-21651722464709871846683222603)⟩,⟨(-156334367522727120776262444841),(-156334367522727120680488557763)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-17034349736977487913523028352),(-17034349736977487834403209963)⟩,⟨(-125794080374607592917551874176),(-125794080374607592837748259765)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-13041909536941607086767337153),(-13041909536941607025121272230)⟩,⟨(-97064314485748049811309424004),(-97064314485748049748647001212)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-9590427514290991349674651908),(-9590427514290991305081871000)⟩,⟨(-71180075673293193458509436899),(-71180075673293193412791505185)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-6558098662582651798427499277),(-6558098662582651768565549423)⟩,⟨(-48281727758280975785794822010),(-48281727758280975754991215220)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3819389940715434631214109219),(-3819389940715434614075127424)⟩,⟨(-27880815345322800104177227320),(-27880815345322800086443879488)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1253642469647382775822808377),(-1253642469647382770272188568)⟩,⟨(-9103674871771525792908580256),(-9103674871771525787157724253)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨16458275930182539546761870447,16458275930182539764948824997⟩,⟨(-318772634339100228925992827087),(-318772634339100228703277131945)⟩⟩ +lemma checked : cachedMomentRuleBox column3_1 kernel3_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 3 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_1_contains kernel3_0_contains +end cm3_3_1_0 +namespace cm3_3_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_1 j i k).mul (kernel3_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-313765068998288723297),(-313765068998288722876)⟩,⟨174625263771671349081,174625263771671349504⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-866200381353168458916),(-866200381353168457847)⟩,⟨311047053701210161059,311047053701210162134⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1128167988324131333587),(-1128167988324131332277)⟩,⟨18510746475837165095,18510746475837166402⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-902705741748287431191),(-902705741748287430070)⟩,⟨(-470120339172608266200),(-470120339172608265087)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-312064342187287924032),(-312064342187287923291)⟩,⟨(-690321448974880339394),(-690321448974880338657)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨197247121948235884866,197247121948235885498⟩,⟨(-457264499077990237467),(-457264499077990236836)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨300902243005191535291,300902243005191535827⟩,⟨(-54484671226689658510),(-54484671226689657975)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨110026016666194069845,110026016666194070216⟩,⟨148084049587239571481,148084049587239571853⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-60350099905867122904),(-60350099905867122657)⟩,⟨96807935255017308399,96807935255017308645⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-72718056883726488574),(-72718056883726488419)⟩,⟨(-15813926910416988688),(-15813926910416988530)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-8298905247303616065),(-8298905247303615935)⟩,⟨(-51059510249345305770),(-51059510249345305641)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨30555265928518452144,30555265928518452237⟩,⟨(-22384120584174921119),(-22384120584174921020)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨26863324573524251037,26863324573524251115⟩,⟨8726432932549152359,8726432932549152439⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨9859248333263751460,9859248333263751521⟩,⟨17639743132135266105,17639743132135266167⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-64206757621410575),(-64206757621410534)⟩,⟨12357984511268830141,12357984511268830183⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-1105038824511082971),(-1105038824511082949)⟩,⟨4033177163912054117,4033177163912054142⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-276229285742302098432943),(-276229285742302098099037)⟩,⟨(-7773925519085628628972),(-7773925519085628294463)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-712385244749493888334639),(-712385244749493887459354)⟩,⟨(-53007671115564382062975),(-53007671115564381186356)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-872943934374627757969163),(-872943934374627756860511)⟩,⟨(-149061831578571346892731),(-149061831578571345782692)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-760432481424220866101133),(-760432481424220865059355)⟩,⟨(-249906142303897443305618),(-249906142303897442262887)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-503211239886869640134019),(-503211239886869639266911)⟩,⟨(-292005379422725421398662),(-292005379422725420531085)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-248352976541454943355280),(-248352976541454942748513)⟩,⟨(-256033827316632335757590),(-256033827316632335150722)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-78569892055962064727307),(-78569892055962064373876)⟩,⟨(-174248300809603080625409),(-174248300809603080271998)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-365579624167969535047),(-365579624167969364690)⟩,⟨(-92597466890416063917374),(-92597466890416063747027)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨19529844136885790111587,19529844136885790193762⟩,⟨(-37174534838264398735821),(-37174534838264398653614)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨15791152905971068897709,15791152905971068942930⟩,⟨(-9579294491255976011615),(-9579294491255975966369)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨8140795763652560229770,8140795763652560253081⟩,⟨217085045968424046126,217085045968424069435⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨3058661449584546525958,3058661449584546536851⟩,⟨2071419277375792700954,2071419277375792711839⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨759195701967573669434,759195701967573674252⟩,⟨1570710992000807447212,1570710992000807452023⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨8481729151383095438,8481729151383097655⟩,⟨845902505804712805809,845902505804712808027⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-118043854518142611845),(-118043854518142610843)⟩,⟨371819050009692680780,371819050009692681782⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-51928835814858608208),(-51928835814858607914)⟩,⟨101297956647718452129,101297956647718452423⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨191290864159559259565698986,191290864159559259749748066⟩,⟨145387355213360186123941186,145387355213360186308381317⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨518661648844587496847195476,518661648844587497352814990⟩,⟨395514322806078763745081360,395514322806078764251670866⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨705540229652810107195816572,705540229652810107898140108⟩,⟨542792248764900599685392623,542792248764900600388801453⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨728173357198442955589637044,728173357198442956397169785⟩,⟨570693774705224381909263754,570693774705224382717393804⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨623557554454003852329289221,623557554454003853158156811⟩,⟨505724732608221745028001301,505724732608221745856803900⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨459096353033068214124334264,459096353033068214866481355⟩,⟨394186359612668529099332147,394186359612668529841044604⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨296245453325397904999507133,296245453325397905586052438⟩,⟨277517513781756948463546333,277517513781756949049682367⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨169706280595351046907378616,169706280595351047321116392⟩,⟨179987642956129827910900808,179987642956129828324457721⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨87129998595096811067159942,87129998595096811331341899⟩,⟨109273676230141193547079009,109273676230141193811275112⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨40332571557330954898085583,40332571557330955053547837⟩,⟨62973305561288809476420327,62973305561288809631971908⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨16820991624816318555487853,16820991624816318641547819⟩,⟨34896378184313637310502846,34896378184313637396647841⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨6218212437678480766047863,6218212437678480811815537⟩,⟨18818205790163935959627280,18818205790163936005455005⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1921041365520657684109222,1921041365520657707868599⟩,⟨9955465358296210282810805,9955465358296210306606404⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨395966094484910041986330,395966094484910054017009⟩,⟨5133397594778933437431904,5133397594778933449481903⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-19996687118514099479915),(-19996687118514093872843)⟩,⟨2427658037037813705276550,2427658037037813710892706⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-38521618446104163251853),(-38521618446104161621451)⟩,⟨713163008537688507139623,713163008537688508772543⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨548823072272497356123671976,548823072272497357059068770⟩,⟨(-1092751948250749540993117213),(-1092751948250749540074433950)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1524633589358205830301491251,1524633589358205832968184763⟩,⟨(-3084035693183603309858147611),(-3084035693183603307231849055)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2177876314119343694561371072,2177876314119343698547475022⟩,⟨(-4546134343883242234286352119),(-4546134343883242230341723981)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨2420819010437899919214695429,2420819010437899923893704857⟩,⟨(-5294426076421978641021722688),(-5294426076421978636365699708)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2292551226331900826474134783,2292551226331900831212729973⟩,⟨(-5328465447385525395371686108),(-5328465447385525390632028529)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1920523802854349964667610922,1920523802854349969103101778⟩,⟨(-4803315290157950505155187135),(-4803315290157950500700759395)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1455659457662935297007301980,1455659457662935300834459023⟩,⟨(-3954926479949034552851629980),(-3954926479949034549004090256)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1016871901028132736608811058,1016871901028132739948488017⟩,⟨(-3016039529479468065481574424),(-3016039529479468062133572095)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨666923045553500284477094885,666923045553500287251876111⟩,⟨(-2156441436749011100105878491),(-2156441436749011097339242509)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨418738185655209527723858775,418738185655209529974228945⟩,⟨(-1462926052091478217700063453),(-1462926052091478215463207470)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨256459571404148539188039187,256459571404148540863968487⟩,⟨(-952553711381886920110906694),(-952553711381886918445860144)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨155360467901175041681082553,155360467901175042842954465⟩,⟨(-600844401039484331713465184),(-600844401039484330558133848)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨93313320989661624737994912,93313320989661625495509691⟩,⟨(-368044791734500402524231942),(-368044791734500401769846644)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨54421663316356316317825893,54421663316356316778124956⟩,⟨(-215484510222082752012103314),(-215484510222082751552971784)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨28423972424319704056612644,28423972424319704300546039⟩,⟨(-112097064770278967550692013),(-112097064770278967307066014)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨8828962697228064938854193,8828962697228065014685436⟩,⟨(-34670878493518335699540874),(-34670878493518335623751949)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨14761624308167234597928459687,14761624308167234623741922008⟩,⟨(-44052364226989354531656945141),(-44052364226989354506134055687)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨41991039998489904544391970338,41991039998489904620807955798⟩,⟨(-126703485120143572612032761234),(-126703485120143572536392224234)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨62843308601221720225357768277,62843308601221720348552345551⟩,⟨(-194004404797505040215038865807),(-194004404797505040092896894658)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨74751678777453228691872144646,74751678777453228853964546454⟩,⟨(-239240081341437598210284584068),(-239240081341437598049346564787)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨77151650383932637348194470597,77151650383932637536291264623⟩,⟨(-259896909322287367663272654067),(-259896909322287367476402651581)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨71414465048220348096332760615,71414465048220348294870057214⟩,⟨(-257665565087203328952627720105),(-257665565087203328755271432084)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨60234706218519611507492216915,60234706218519611697923200491⟩,⟨(-237439701717111016798715908952),(-237439701717111016609278209264)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨46720874408552727231388056601,46720874408552727396742161677⟩,⟨(-205732248695051544524810505600),(-205732248695051544360209309759)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨33539751904941236559168230327,33539751904941236689504230433⟩,⟨(-169039180721059535778768825239),(-169039180721059535648953183086)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨22403631876986497690260089656,22403631876986497794446746573⟩,⟨(-132605148356187599772135077265),(-132605148356187599668320047773)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨13993946052761426038737357293,13993946052761426127182911352⟩,⟨(-99825045468162133415685463792),(-99825045468162133327539391107)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨8210072673098897532130872875,8210072673098897603358308836⟩,⟨(-72255621928790826751535505698),(-72255621928790826680490486789)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨4535135415353926203368832753,4535135415353926256068380901⟩,⟨(-50023332184945105433841570384),(-50023332184945105381258749108)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2344412536803317341621674100,2344412536803317376995908351⟩,⟨(-32360561610897828594736428423),(-32360561610897828559434026919)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1081174101837703488394976685,1081174101837703508471323735⟩,⟨(-18066026204774168378886654276),(-18066026204774168358846568978)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨309581498478934255675971786,309581498478934262138957572⟩,⟨(-5796048185780276653810626972),(-5796048185780276647358478121)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-127780080351409519287143155802),(-127780080351409519253204639952)⟩,⟨35295479982066736188127140886,35295479982066736218715521481⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-371725207484352379480950690250),(-371725207484352379377398384671)⟩,⟨101970575809478992639885759328,101970575809478992733913479703⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-582153998067745054214021201261),(-582153998067745054037099959898)⟩,⟨157698566970205358832709765771,157698566970205358995680649986⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-742228982385938043597385688423),(-742228982385938043343887525018)⟩,⟨197898819743192122741370660850,197898819743192122979236204767⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-842216315802729760154202423383),(-842216315802729759822999814499)⟩,⟨221025238573500945200333843234,221025238573500945518631960457⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-880467813668164743659678288589),(-880467813668164743258391752669)⟩,⟨228267904876446705801574458722,228267904876446706194925370560⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-862840715967515040406525046159),(-862840715967515039954718364156)⟩,⟨222576664594612016467384202807,222576664594612016916035125267⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-800762034261570331858235946908),(-800762034261570331386143214628)⟩,⟨207518279459736492188773040609,207518279459736492660491062981⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-708472325069092011666883563730),(-708472325069092011209511770994)⟩,⟨186402729692291660993715401649,186402729692291661450905213345⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-600183098779577172242506275166),(-600183098779577171831481879608)⟩,⟨161858656200248693809519861000,161858656200248694218718985299⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-487822565215108401188570466215),(-487822565215108400840396616194)⟩,⟨135779021584634751443698947537,135779021584634751787940590962⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-379761376091671431269585651222),(-379761376091671430991232628338)⟩,⟨109439488253921570988324189753,109439488253921571261343415245⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-280544703347030853498083042062),(-280544703347030853286768081147)⟩,⟨83627985420734735449230840587,83627985420734735655391837280⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-191369373989543995538535938682),(-191369373989543995392751895374)⟩,⟨58727329819849910582886437737,58727329819849910724660390941⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-110928732808564504862506280619),(-110928732808564504778120820093)⟩,⟨34770335086455212980126672251,34770335086455213062046008193⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-36289730164463845183010674298),(-36289730164463845155570770515)⟩,⟨11502314775922713273449189396,11502314775922713300068158821⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1241729691407246716611615325490),(-1241729691407246715633236976400)⟩,⟨(-4019135626627360108194716563),(-4019135626627359146433620079)⟩⟩ +lemma checked : cachedMomentRuleBox column3_1 kernel3_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 3 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_1_contains kernel3_1_contains +end cm3_3_1_1 +namespace cm3_4_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_0 j i k).mul (kernel4_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1227645586948162),(-1227645586948146)⟩,⟨3819041273959126,3819041273959142⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5358270251825094),(-5358270251825078)⟩,⟨8278663372734328,8278663372734346⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-9987604443988512),(-9987604443988495)⟩,⟨5089255790580115,5089255790580134⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-8744629608965761),(-8744629608965744)⟩,⟨(-2796265133890321),(-2796265133890304)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1449299967100935),(-1449299967100916)⟩,⟨(-5983120815090101),(-5983120815090082)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨3090070769812463,3090070769812479⟩,⟨(-1946303544214385),(-1946303544214369)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1302095353500239,1302095353500257⟩,⟨1571080493581637,1571080493581657⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-892669512778033),(-892669512778012)⟩,⟨703220095464607,703220095464625⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-342443789068164),(-342443789068143)⟩,⟨(-567189194467327),(-567189194467310)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨386835895407279,386835895407299⟩,⟨(-159976448579637),(-159976448579615)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨85110762731980,85110762732000⟩,⟨277228336587286,277228336587303⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-204063865305479),(-204063865305462)⟩,⟨73465942863518,73465942863538⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-96311601526975),(-96311601526954)⟩,⟨(-137409566038733),(-137409566038716)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨50480541610358,50480541610376⟩,⟨(-114461675362087),(-114461675362068)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨71325504810493,71325504810509⟩,⟨(-34411436626232),(-34411436626215)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨27214165281046,27214165281064⟩,⟨(-2469414535364),(-2469414535348)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨136452595484497829327,136452595484497829730⟩,⟨38150286062416211396,38150286062416211799⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨326224256342169234525,326224256342169235508⟩,⟨119760601771923562850,119760601771923563833⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨338547528260001095574,338547528260001096706⟩,⟨190858639948547978942,190858639948547980071⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨218768033940456417867,218768033940456418792⟩,⟨209039353804474139426,209039353804474140349⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨81505685929576279499,81505685929576280121⟩,⟨162750504125920251584,162750504125920252202⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1774657005051313520,1774657005051313850⟩,⟨89429975112324147485,89429975112324147812⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-18929789536510053307),(-18929789536510053165)⟩,⟨32435416184731262553,32435416184731262696⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-13000337895512729168),(-13000337895512729104)⟩,⟨5394235165369789791,5394235165369789854⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-4635616837214652864),(-4635616837214652830)⟩,⟨(-1670370241071006062),(-1670370241071006028)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-684967320044670500),(-684967320044670478)⟩,⟨(-1542028940393646933),(-1542028940393646908)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨241699709951929724,241699709951929741⟩,⟨(-538525381603898952),(-538525381603898934)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨207222063296823168,207222063296823187⟩,⟨(-69326973929662698),(-69326973929662681)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨79156528612999485,79156528612999502⟩,⟨36711536781192520,36711536781192539⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨18036352225627680,18036352225627697⟩,⟨32580803104018280,32580803104018298⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨824548870861671,824548870861687⟩,⟨15746371275281710,15746371275281728⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-809390755511796),(-809390755511779)⟩,⟨4334154504239738,4334154504239754⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-567710697365258683420271),(-567710697365258682108640)⟩,⟨496735002565407775835736,496735002565407777149739⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1444403805523530945344305),(-1444403805523530941854131)⟩,⟨1259229629563448658431564,1259229629563448661922782⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1732203695177325401979462),(-1732203695177325397312953)⟩,⟨1492857623507128274983522,1492857623507128279640853⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1483779361854312178747880),(-1483779361854312174127170)⟩,⟨1243271653397612541469311,1243271653397612546070155⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-994315372778927898955888),(-994315372778927895311467)⟩,⟨785234725736538134152891,785234725736538137775292⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-539008686713075075456483),(-539008686713075073112943)⟩,⟨379647421255071326060380,379647421255071328388266⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-237700404226370517391200),(-237700404226370516150148)⟩,⟨134242395873792083934639,134242395873792085168502⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-82361241160642318605732),(-82361241160642318060525)⟩,⟨27491141696727872826814,27491141696727873370479⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-18688308779056156700703),(-18688308779056156496721)⟩,⟨(-3566496665620394388044),(-3566496665620394183402)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1116277441870876553791,1116277441870876636391⟩,⟨(-6592994779895316117496),(-6592994779895316033989)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨4535832688499068533839,4535832688499068574919⟩,⟨(-3689155030466272470455),(-3689155030466272428806)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3537889439514537656604,3537889439514537677194⟩,⟨(-1363162675707279357790),(-1363162675707279336916)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨2105853607785580273699,2105853607785580283772⟩,⟨(-295774995038713272035),(-295774995038713261847)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1109781215502941886191,1109781215502941891024⟩,⟨44453164428608850369,44453164428608855250⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨517744582817702716119,517744582817702718287⟩,⟨87946756827701630696,87946756827701632884⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨149783697445962133206,149783697445962133835⟩,⟨35963908232407886678,35963908232407887313⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-100850088766258483873144108),(-100850088766258483769427619)⟩,⟨46842752991096099020499857,46842752991096099131079669⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-276618548427315805907920078),(-276618548427315805614332108)⟩,⟨131423074787560315864989431,131423074787560316175250207⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-385329993653787762736837569),(-385329993653787762305449005)⟩,⟨191184636357339113578348483,191184636357339114027319889⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-412791626964029293275203727),(-412791626964029292784797175)⟩,⟨217606267181417866657946205,217606267181417867158933866⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-372670054601147131825055890),(-372670054601147131334534262)⟩,⟨211382113938055925015011181,211382113938055925507810156⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-294699354348804266875784386),(-294699354348804266414723755)⟩,⟨181182496716273721538682583,181182496716273721997936505⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-208993113729374923177888523),(-208993113729374922796219127)⟩,⟨139522871974678682257622081,139522871974678682637006113⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-135501347474571598345210894),(-135501347474571598065172718)⟩,⟨97865681811939664190894443,97865681811939664470091341⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-81846669992779528512187694),(-81846669992779528327376337)⟩,⟨63392108358248418208025087,63392108358248418393477667⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-46967319002135242557700541),(-46967319002135242443832487)⟩,⟨38503017689639648837593760,38503017689639648952699515⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-26107738910456905640551271),(-26107738910456905570032055)⟩,⟨22296897198809763933877618,22296897198809764005265305⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-14293669960014371804295287),(-14293669960014371763297191)⟩,⟨12509865786962527292205932,12509865786962527333640623⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-7773174621617486368184411),(-7773174621617486345535223)⟩,⟨6871794355115955906342494,6871794355115955929168768⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-4150623235888385329274333),(-4150623235888385317323560)⟩,⟨3669102134838376209274205,3669102134838376221282672⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2028297804684194615687196),(-2028297804684194609976438)⟩,⟨1784827330869260319770748,1784827330869260325495127⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-607851611336010406995426),(-607851611336010405314356)⟩,⟨532829614859855930219889,532829614859855931902768⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1098403553763468019357082764),(-1098403553763468016999398607)⟩,⟨2048361721581237048635266970,2048361721581237051194657352⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-3116982831663756000178804884),(-3116982831663755993339806700)⟩,⟨5691829573265009834237444124,5691829573265009841706241603⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-4654939511336662528646861109),(-4654939511336662518090901745)⟩,⟨8138687186200640174608505848,8138687186200640186236988439⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-5554773561172978257573764780),(-5554773561172978244661238736)⟩,⟨9070972406040888222074789525,9070972406040888236396605108⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-5820027668849101181918003812),(-5820027668849101168494284472)⟩,⟨8640064885980460917172723881,8640064885980460932070448853⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-5571518281696148005254866300),(-5571518281696147991931514371)⟩,⟨7315131280268773664409592436,7315131280268773678766156700⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-4978963613830495973432763008),(-4978963613830495960535284442)⟩,⟨5641997073059197756074487628,5641997073059197769350909589⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-4206291490795881316340364946),(-4206291490795881305562190845)⟩,⟨4045936652152734723281123023,4045936652152734734073121556⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-3384848288467301342910006907),(-3384848288467301334820322613)⟩,⟨2751467970887378850480820062,2751467970887378858518056671⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-2607007784760221603942432217),(-2607007784760221597729666456)⟩,⟨1808664539069170926778260828,1808664539069170933021356415⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1928037363788784514642070157),(-1928037363788784510291014886)⟩,⟨1167612404396267834879186540,1167612404396267839340651978⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1370694398675393875421744148),(-1370694398675393872628926482)⟩,⟨746663828384515070642684903,746663828384515073578732388⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-932269763348198209745368504),(-932269763348198208073914865)⟩,⟨471183774467210206925397323,471183774467210208730526705⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-593549873512959067832924315),(-593549873512959066872581102)⟩,⟨285925680716200907487448772,285925680716200908542591617⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-327351663688705187679725191),(-327351663688705187168062467)⟩,⟨153444082108832483904543390,153444082108832484464316992⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-104330709997104576281023837),(-104330709997104576121773218)⟩,⟨48316018440521361649164337,48316018440521361822916545⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-58606276758712321980929703),(-58606276758712318379616844)⟩,⟨48263336021332976883620075,48263336021332980487955283⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-832958747328517386278332555),(-832958747328517375312613887)⟩,⟨692631454719455054258747286,692631454719455065218333449⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-3252117834146201360495135114),(-3252117834146201341853589033)⟩,⟨2754844559929739183831166639,2754844559929739202436052990⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-7490149116210168591359654801),(-7490149116210168564998324622)⟩,⟨6527179766167713647517650114,6527179766167713673829307452⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-12826940557064268696471141788),(-12826940557064268663019633183)⟩,⟨11618384739334450053941147338,11618384739334450087393782241⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-17991324240698745894085747085),(-17991324240698745855163767934)⟩,⟨17118682733294060737310445486,17118682733294060776337948630⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-21723666264433876814963901510),(-21723666264433876773151962051)⟩,⟨21940020668269979760117239305,21940020668269979802107058155⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-23262052934762233212143260852),(-23262052934762233170247603252)⟩,⟨25177078427686335070038520277,25177078427686335112043702752⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-22537802704762870650437045292),(-22537802704762870607129864080)⟩,⟨26351409510131819502021385669,26351409510131819545228997462⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-20052064308554814708798235137),(-20052064308554814667082453983)⟩,⟨25470762161183602484500754237,25470762161183602525922474642⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-16568571162295203075405099923),(-16568571162295203038648586107)⟩,⟨22919978470426533640168901276,22919978470426533676587974579⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-12807080909149237149845422032),(-12807080909149237120047977189)⟩,⟨19261717266439539622426226558,19261717266439539651982107339⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-9259593400213232084402300118),(-9259593400213232062323220104)⟩,⟨15040873172379813766925351931,15040873172379813788887902157⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-6149162022343604438280173524),(-6149162022343604423506869845)⟩,⟨10657483602570644270995004523,10657483602570644285743198632⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3481199242123084772466815985),(-3481199242123084764122589106)⟩,⟨6324857463349523043016623248,6324857463349523051373754571⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1123365759294874349609503619),(-1123365759294874346931628002)⟩,⟨2092461092393892667638061097,2092461092393892670325020461⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-38007493557409504373816805765),(-38007493557409504286092449619)⟩,⟨45565877009002443833242478912,45565877009002443921966943196⟩⟩ +lemma checked : cachedMomentRuleBox column3_0 kernel4_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 4 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_0_contains kernel4_0_contains +end cm3_4_0_0 +namespace cm3_4_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_0 j i k).mul (kernel4_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨23579441357296375,23579441357296391⟩,⟨(-24776934469791582),(-24776934469791564)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨71708386036792268,71708386036792287⟩,⟨(-44385924353955439),(-44385924353955412)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨96323302272362716,96323302272362747⟩,⟨(-4246144431245638),(-4246144431245612)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨60128971953703065,60128971953703097⟩,⟨52175864815661662,52175864815661697⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-7464790612349622),(-7464790612349584)⟩,⟨53389957829128980,53389957829129016⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-31546546504820661),(-31546546504820625)⟩,⟨7056313020765042,7056313020765082⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-6932973298285299),(-6932973298285253)⟩,⟨(-16891836718894134),(-16891836718894088)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨9429582850535141,9429582850535192⟩,⟨(-4072541985621956),(-4072541985621903)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1949105526127477,1949105526127534⟩,⟨5716292262828448,5716292262828506⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3745305500800738),(-3745305500800679)⟩,⟨847614559126541,847614559126602⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-455088752844229),(-455088752844174)⟩,⟨(-2631839964955035),(-2631839964954979)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1935242959335124,1935242959335175⟩,⟨(-510150469879248),(-510150469879197)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨818239180813906,818239180813948⟩,⟨1315272819421330,1315272819421374⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-496191572601500),(-496191572601466)⟩,⟨1042181095871279,1042181095871313⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-661179299094687),(-661179299094658)⟩,⟨309853562901999,309853562902028⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-250854972893704),(-250854972893682)⟩,⟨22189018722933,22189018722953⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-477066916738787082967),(-477066916738787079941)⟩,⟨(-890752536605109150598),(-890752536605109147564)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1009899173254938706345),(-1009899173254938698895)⟩,⟨(-2273412358269148565056),(-2273412358269148557590)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-740836239554198878784),(-740836239554198870449)⟩,⟨(-2702782275128909232917),(-2702782275128909224564)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-75990445680841481234),(-75990445680841474707)⟩,⟨(-2203895524454013464916),(-2203895524454013458370)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨382140376404475918866,382140376404475923421⟩,⟨(-1289085090393866012018),(-1289085090393866007457)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨435982173941434812398,435982173941434815094⟩,⟨(-510354898474156017263),(-510354898474156014565)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨269831674338520789233,269831674338520790509⟩,⟨(-97037293917428999338),(-97037293917428998064)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨105429403768783880898,105429403768783881379⟩,⟨29341329867753126888,29341329867753127369⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨21857189967744927375,21857189967744927553⟩,⟨32312671372874150228,32312671372874150405⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-2392310396178687287),(-2392310396178687196)⟩,⟨13378458708376017254,13378458708376017345⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-4016856126473832363),(-4016856126473832314)⟩,⟨2680549599326882931,2680549599326882981⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1773596445767077528),(-1773596445767077490)⟩,⟨(-369646925547003563),(-369646925547003521)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-434575104528576825),(-434575104528576792)⟩,⟨(-588132239012654629),(-588132239012654592)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-8822133859215270),(-8822133859215243)⟩,⟨(-314482567663014327),(-314482567663014298)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨53303323392465072,53303323392465097⟩,⟨(-122843198177069179),(-122843198177069152)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨22364693940734196,22364693940734214⟩,⟨(-30152169014481155),(-30152169014481138)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨4149423930354688000875578,4149423930354688009111601⟩,⟨1491361179230423016452812,1491361179230423024862886⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨10587150812420925741598644,10587150812420925763296397⟩,⟨3778240094391332638408180,3778240094391332660578640⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨12734553552089627672392722,12734553552089627701068193⟩,⟨4511070418544941172736376,4511070418544941202045073⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨10884332928077299938504374,10884332928077299966434400⟩,⟨3880931429304123333482267,3880931429304123362024305⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨7183077103718467234774213,7183077103718467256296434⟩,⟨2672253927930812907925810,2672253927930812929900529⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨3743139201565697985924467,3743139201565698000065710⟩,⟨1549599591573106882956458,1549599591573106897325832⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1521368260734065658984991,1521368260734065667052667⟩,⟨774722881551348625830318,774722881551348633969616⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨443817770176058018609262,443817770176058022364226⟩,⟨330542016964545778770820,330542016964545782537468⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨53038398747812879907095,53038398747812881362956⟩,⟨111799272230355602123265,111799272230355603575712⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-39209867997956526604261),(-39209867997956525981709)⟩,⟨21012967089408457379954,21012967089408457998024⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-38713236429958206129638),(-38713236429958205797372)⟩,⟨(-7956660737820031962591),(-7956660737820031633140)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-22911535058412074589113),(-22911535058412074415243)⟩,⟨(-12369002392953519328716),(-12369002392953519156402)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-11292781731755163746999),(-11292781731755163659948)⟩,⟨(-9574864216398006307127),(-9574864216398006220910)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-5060688298918573298667),(-5060688298918573256356)⟩,⟨(-5958057390321764241910),(-5958057390321764200033)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2063506301094569530954),(-2063506301094569511888)⟩,⟨(-3099992063893055919757),(-3099992063893055900898)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-550327278089177904979),(-550327278089177899524)⟩,⟨(-948381875074644951266),(-948381875074644945879)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨369848889869886478393901516,369848889869886479031897092⟩,⟨394975740144626141615226351,394975740144626142237642895⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1034717447017759820914730119,1034717447017759822695380254⟩,⟨1079175003584907733880662040,1079175003584907735628285731⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1497565841192500493402186433,1497565841192500495949857986⟩,⟨1491143993128087758667835637,1491143993128087761194349155⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1693674173407405867451712102,1693674173407405870241180311⟩,⟨1576734452458165206263296818,1576734452458165209064248000⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1634581499078723009009842722,1634581499078723011703176824⟩,⟨1396900605550212407049920059,1396900605550212409780908178⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1393457476537919485694484635,1393457476537919488197334923⟩,⟨1076699161517610587055463495,1076699161517610589597841541⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1069455142420457557094034407,1069455142420457559173356663⟩,⟨738724185223807807006348993,738724185223807809110724785⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨749793804643283935784170347,749793804643283937366788153⟩,⟨459935749072653886677466678,459935749072653888266905608⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨487138603908095843231359552,487138603908095844432245768⟩,⟨265142494029076089657237348,265142494029076090855106527⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨297898669397538968400557396,297898669397538969221801329⟩,⟨144747394039657505069373742,144747394039657505887513313⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨174339115755840138623179018,174339115755840139133701766⟩,⟨76650884443533930225796026,76650884443533930735400457⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨99156930316610923653606113,99156930316610923949746799⟩,⟨40238810506010706878969520,40238810506010707175647403⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨55310904002820709015211349,55310904002820709178888133⟩,⟨21200432954512564831063419,21200432954512564995715455⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨29978385538375110373199500,29978385538375110459693306⟩,⟨11092880895041162035483586,11092880895041162122832308⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨14759906390075854636524093,14759906390075854677912697⟩,⟨5362886640411125889506265,5362886640411125931431608⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4436204326512153534808785,4436204326512153547000128⟩,⟨1600353539327064671395625,1600353539327064683766652⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨9150121958949487067809645317,9150121958949487078814675829⟩,⟨3041077662964284863887791688,3041077662964284873584023311⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨25564195308422309049615968472,25564195308422309081696910763⟩,⟨8676654146508137991595111047,8676654146508138019766973988⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨36963207691782258169115426499,36963207691782258218956881709⟩,⟨13111157539144308125176536750,13111157539144308168775628916⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨41920219102410771733765087568,41920219102410771794961061796⟩,⟨15953785959451863627080310577,15953785959451863680577206456⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨40921442213718508576947524220,40921442213718508645507503314⟩,⟨17193706916461452086300539103,17193706916461452148519777939⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨35805409942304086995549628168,35805409942304087067025032768⟩,⟨17069556109372450029493044125,17069556109372450097651263481⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨28814582585570548002758596138,28814582585570548068555112568⟩,⟨15909951249421810283543673848,15909951249421810348392441662⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨21780931749404084849077626073,21780931749404084902127824560⟩,⟨14043145949818556744750498699,14043145949818556797919853450⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨15757419759300948653253507037,15757419759300948692352685707⟩,⟨11778383904786752582563061362,11778383904786752621686495347⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨11081873915602689550507504244,11081873915602689581083949259⟩,⟨9402773469522950888631209206,9402773469522950918690478555⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨7653667854960109840565848888,7653667854960109862630185780⟩,⟨7156474707806128495562268258,7156474707806128516734599207⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨5203131661602296274790275104,5203131661602296289801293272⟩,⟨5197898844625755042112476955,5197898844625755056236697534⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3452356528918839283544497289,3452356528918839293659724793⟩,⟨3588427610287689578404891015,3588427610287689587976374024⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2174069897395229741633318349,2174069897395229747839583446⟩,⟨2306725524794042255919309745,2306725524794042261842823265⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1194992635461790459931799888,1194992635461790463210157861⟩,⟨1279301003542643972541035476,1279301003542643975693445390⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨380679408683510387270620112,380679408683510388285240380⟩,⟨408754592082797511470500184,408754592082797512450304435⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨185574511477289509511230376,185574511477289522595052401⟩,⟨202601228135024825267786965,202601228135024838348933959⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2674789220263873635935185912,2674789220263873675797115100⟩,⟨2879754001639594093730146811,2879754001639594133631918912⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨10722809373048576444116858692,10722809373048576512052056121⟩,⟨11243090962716944520030052643,11243090962716944588103658867⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨25689373330162037225995784281,25689373330162037322640133022⟩,⟨25882402006270224459192970975,25882402006270224555979054631⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨46351672102379702637521594764,46351672102379702761402447242⟩,⟨44260008814937188025860496659,44260008814937188149627957073⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨69338294490061568558175022267,69338294490061568704266714591⟩,⟨61886932276365254953749059727,61886932276365255099281246696⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨90283877399257255079314897795,90283877399257255238670463255⟩,⟨74303755872001747832376985875,74303755872001747990900089324⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨105233343562202900736443098626,105233343562202900907150647193⟩,⟨78837116644864120034537882732,78837116644864120204782038053⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨111764717627430506834179945092,111764717627430507018640989069⟩,⟨75339077590596077688519635344,75339077590596077873358134047⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨109452517412196552391979639617,109452517412196552570716887251⟩,⟨65756346876353992682526166572,65756346876353992862301797509⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨99598071681802972130570026425,99598071681802972289632941722⟩,⟨52989913909033051203816727138,52989913909033051363964436122⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨84465485536181214058585475748,84465485536181214189247569347⟩,⟨39732839691152607572417439771,39732839691152607703704578299⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨66419602838139585637685683518,66419602838139585735837378154⟩,⟨27769923712027755125680685934,27769923712027755223940070264⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨47299489739134589528143395273,47299489739134589594627964703⟩,⟨17833133453555463773225966352,17833133453555463839503044622⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨28160738902840099517027988484,28160738902840099554925994418⟩,⟨9820279173384842401011712546,9820279173384842438652996603⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨9330936992839797008799312929,9330936992839797021019822197⟩,⟨3119187385402187279718219644,3119187385402187291831440764⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨200907814821806075787086425506,200907814821806076161335298795⟩,⟨124462255925427935256406198622,124462255925427935625347582700⟩⟩ +lemma checked : cachedMomentRuleBox column3_0 kernel4_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 4 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_0_contains kernel4_1_contains +end cm3_4_0_1 +namespace cm3_4_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_1 j i k).mul (kernel4_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-959265131932568),(-959265131932551)⟩,⟨19453968592724111,19453968592724127⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-12513234139777933),(-12513234139777914)⟩,⟨45658008768663343,45658008768663361⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-34007247012254203),(-34007247012254182)⟩,⟨39799166624456430,39799166624456451⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-39958806696925575),(-39958806696925554)⟩,⟨8027532489739413,8027532489739436⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-19412384209122786),(-19412384209122761)⟩,⟨(-16208338903703966),(-16208338903703944)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨3263910424413558,3263910424413583⟩,⟨(-13151786703550117),(-13151786703550095)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨6732477215675830,6732477215675857⟩,⟨(-8121962403863),(-8121962403836)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨238018872762426,238018872762451⟩,⟨3307197056997875,3307197056997903⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1714798946447305),(-1714798946447278)⟩,⟨40392773387618,40392773387640⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨67333742691058,67333742691079⟩,⟨(-968432415964941),(-968432415964918)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨606105191551228,606105191551250⟩,⟨73296140568272,73296140568297⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-17274544725831),(-17274544725808)⟩,⟨420607904329428,420607904329450⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-295938496456560),(-295938496456540)⟩,⟨74680002819389,74680002819410⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-156503988962650),(-156503988962631)⟩,⟨(-150002894682254),(-150002894682235)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-14618550849156),(-14618550849138)⟩,⟨(-132087261203769),(-132087261203748)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨10912124088786,10912124088803⟩,⟨(-43789183573119),(-43789183573103)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨260917199018223128090,260917199018223128478⟩,⟨97278486944420526240,97278486944420526627⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨625425565493478986837,625425565493478987780⟩,⟨277173535219969618737,277173535219969619679⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨657070102305609776839,657070102305609777913⟩,⟨395087604130149609258,395087604130149610332⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨442623677810934502618,442623677810934503485⟩,⟨401102826419779851526,401102826419779852390⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨190239570751290944352,190239570751290944946⟩,⟨303372421884908177902,303372421884908178496⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨34009297386403042773,34009297386403043098⟩,⟨170841934742399157073,170841934742399157400⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-18721275501388506239),(-18721275501388506089)⟩,⟨69297599360837470927,69297599360837471077⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-19196104127158922159),(-19196104127158922094)⟩,⟨17783736971960207395,17783736971960207461⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-8802121969883720589),(-8802121969883720552)⟩,⟨831934423478308335,831934423478308371⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-2341991697157030475),(-2341991697157030448)⟩,⟨(-1721786818634822396),(-1721786818634822371)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-160516569194535913),(-160516569194535893)⟩,⟨(-961161035349444857),(-961161035349444837)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨196569651723727442,196569651723727463⟩,⟨(-285008004319709432),(-285008004319709412)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨129008207296516660,129008207296516676⟩,⟨(-33575207559262429),(-33575207559262411)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨52020644998486325,52020644998486341⟩,⟨18608914540341367,18608914540341385⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨16367490250916257,16367490250916274⟩,⟨16043194386192931,16043194386192949⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨3416979726645943,3416979726645960⟩,⟨5342436407496144,5342436407496162⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1745814565516990010091684),(-1745814565516990008084921)⟩,⟨(-1656569888329521242229446),(-1656569888329521240210102)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4581808048397999106697877),(-4581808048397999101365163)⟩,⟨(-4337337403130261075130606),(-4337337403130261069766539)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-5837968224714227207864223),(-5837968224714227200934153)⟩,⟨(-5518352510117925636002352),(-5518352510117925629037053)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-5459608151313461424937069),(-5459608151313461417725160)⟩,⟨(-5190667133245497312889095),(-5190667133245497305653625)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-4097587613096895931172750),(-4097587613096895924676204)⟩,⟨(-3983053287090231064686193),(-3983053287090231058180750)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-2558012995633835158983821),(-2558012995633835154033670)⟩,⟨(-2613171526824548489872764),(-2613171526824548484921692)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1354460074376634788771483),(-1354460074376634785530951)⟩,⟨(-1513057253303333137267429),(-1513057253303333134027879)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-615897018985943105633164),(-615897018985943103779537)⟩,⟨(-792940219586042366574572),(-792940219586042364721446)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-241902994816947374879431),(-241902994816947373932624)⟩,⟨(-384250143006575351846785),(-384250143006575350899933)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-81405305523070308919167),(-81405305523070308475526)⟩,⟨(-175517275886949792420301),(-175517275886949791976483)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-22307518420591727783202),(-22307518420591727586630)⟩,⟨(-77006676586007795625714),(-77006676586007795429009)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-3811435966925014199352),(-3811435966925014114373)⟩,⟨(-33087777296076207592299),(-33087777296076207507243)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨748210970330093410933,748210970330093447722⟩,⟨(-14176843460141135798335),(-14176843460141135761505)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1249145221418164707927,1249145221418164724023⟩,⟨(-6097728206634120605903),(-6097728206634120589789)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨819641707050631725875,819641707050631732646⟩,⟨(-2517941516641517369879),(-2517941516641517363096)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨270838966554797593608,270838966554797595486⟩,⟨(-687359219126738007627),(-687359219126738005747)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-42103923586109648978505338),(-42103923586109648936913660)⟩,⟨35306989052686412483026983,35306989052686412522691492⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-114498988153118673187201978),(-114498988153118673071025892)⟩,⟨98656613029138225480042035,98656613029138225591272703⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-156732436952640643533025291),(-156732436952640643366339287)⟩,⟨142367789773736990446154057,142367789773736990606867044⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-163433728983335618701860121),(-163433728983335618517911989)⟩,⟨160134707341798947218724163,160134707341798947397555481⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-142167334174603577761575724),(-142167334174603577588718693)⟩,⟨153198201053268770171435175,153198201053268770340981175⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-107166567530810433724384371),(-107166567530810433573185670)⟩,⟨128963104363088303683201427,128963104363088303833006795⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-71669606884208924094916311),(-71669606884208923975410151)⟩,⟨97354782391859631732120988,97354782391859631851340116⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-43390561874623394932153158),(-43390561874623394838649659)⟩,⟨66901830003421468046295672,66901830003421468139807065⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-24294239385922674542960054),(-24294239385922674475929779)⟩,⟨42491405739115571292015074,42491405739115571358880116⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-12884213512199142846209004),(-12884213512199142801303665)⟩,⟨25365003802389621315015167,25365003802389621359609008⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-6639446045640682026927978),(-6639446045640681997566051)⟩,⟨14489028016715488589200521,14489028016715488618323355⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-3402172529294111039764567),(-3402172529294111021772303)⟩,⟨8054179066551882141692546,8054179066551882159546950⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1756790807955341832541922),(-1756790807955341822071239)⟩,⟨4402763379596841727114809,4402763379596841737517115⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-905146888729942892564041),(-905146888729942886773471)⟩,⟨2347592954171171872889425,2347592954171171878649440⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-433059323252729126469263),(-433059323252729123600357)⟩,⟨1142636035748922146405816,1142636035748922149262483⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-128553807819798743874010),(-128553807819798743012786)⟩,⟨341397852425532155814317,341397852425532156672360⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-4967477760990203991823524278),(-4967477760990203987934777118)⟩,⟨2408551855854804364244770687,2408551855854804368098732676⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-13987610061778227858178174266),(-13987610061778227846932273824)⟩,⟨6964445018059867007872288661,6964445018059867019016445795⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-20525189499668521445402853012),(-20525189499668521428104471036)⟩,⟨10760616500663230190194318630,10760616500663230207330310907⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-23740379210848027260257987720),(-23740379210848027239059500056)⟩,⟨13401757525175551937091300756,13401757525175551958076788776⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-23673366153060518882048970546),(-23673366153060518859687141278)⟩,⟨14664675067301532448465862995,14664675067301532470578007065⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-21089212061752990851720325298),(-21089212061752990830004283480)⟩,⟨14554042246731335770323327211,14554042246731335791799132475⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-17108975382414259450603739170),(-17108975382414259430968381369)⟩,⟨13304600342134489692498473952,13304600342134489711922948471⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-12810231672425408500877506428),(-12810231672425408484949251179)⟩,⟨11313289876033023335088889999,11313289876033023350820989962⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-8955794620061561781690551659),(-8955794620061561769983142518)⟩,⟨9022233288538546207650893646,9022233288538546219224671336⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-5914024649578266189212048372),(-5914024649578266180567194561)⟩,⟨6802918388547229863451186787,6802918388547229872024786152⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-3732358671646774529083574172),(-3732358671646774522542002212)⟩,⟨4888284442575900009506443270,4888284442575900016011576148⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2274840942130132171837069313),(-2274840942130132167252106248)⟩,⟨3367181051533366781069453590,3367181051533366785628979340⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1345604365730785540743227666),(-1345604365730785537737891334)⟩,⟨2222198702572156302960699184,2222198702572156305945135005⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-763091296151780530553064698),(-763091296151780528709850169)⟩,⟨1379402381713377012062913880,1379402381713377013891066481⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-387314946274664792280606063),(-387314946274664791284599721)⟩,⟨747065746222688039145654212,747065746222688040133815624⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-118191735363121414474933540),(-118191735363121414162425848)⟩,⟨235857956181017285237850892,235857956181017285547926804⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨19257311968829241926314698172,19257311968829241935901044997⟩,⟨23401791724010464911416424397,23401791724010464921413751497⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨55718610519945492881510399703,55718610519945492910656573935⟩,⟨67099028015404365327332901263,67099028015404365357511845234⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨86349740483392181719989480058,86349740483392181769348441683⟩,⟨102087047486449581704870513473,102087047486449581755373526779⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨108460736991607056855384390897,108460736991607056924833455902⟩,⟨124650236782194245545113798761,124650236782194245615263862069⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨120795646772636377075668461802,120795646772636377163878178242⟩,⟨133562978727995744020539624552,133562978727995744108715629225⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨123569476803519850282272060425,123569476803519850384734501749⟩,⟨130061935997155564052675716307,130061935997155564154491604600⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨118198152810426695259526027579,118198152810426695368513577873⟩,⟨117199784944573850730327512982,117199784944573850838516218793⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨106845318499920779744617577783,106845318499920779851032356482⟩,⟨98849832465317457709594950357,98849832465317457815610848436⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨91918658766672328130460310684,91918658766672328228986392658⟩,⟨78710173629345755130793733361,78710173629345755229590576013⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨75627829130106795010398368113,75627829130106795095253354391⟩,⟨59599916337819937100607971146,59599916337819937186205800788⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨59680513514936308407316406349,59680513514936308476285284366⟩,⟨43178387230474305796835337692,43178387230474305866585688759⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨45149313802712380536799045742,45149313802712380589620822361⟩,⟨30038547085754580687016392043,30038547085754580740370617452⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨32494396264162398780876790651,32494396264162398818392041329⟩,⟨20012884666482345553897032531,20012884666482345591683046369⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨21688366075432284659170671874,21688366075432284683528670080⟩,⟨12516677275827570102597204080,12516677275827570127048899209⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨12376162678653751076444296907,12376162678653751089938577786⟩,⟨6812439499890768784184340987,6812439499890768797691093079⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨4015629187478489092472361095,4015629187478489096760539301⟩,⟨2155866112499179755286587846,2155866112499179759571872845⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨153305666522561609550667241781,153305666522561609737436548253⟩,⟨194488311605636246215978986926,194488311605636246403142742081⟩⟩ +lemma checked : cachedMomentRuleBox column3_1 kernel4_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 4 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_1_contains kernel4_0_contains +end cm3_4_1_0 +namespace cm3_4_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column3_1 j i k).mul (kernel4_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨79456859674728341,79456859674728370⟩,⟨(-145830332800028805),(-145830332800028778)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨263760667736219983,263760667736220034⟩,⟨(-307114311057499980),(-307114311057499930)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨407980218291016921,407980218291016993⟩,⟨(-190324076775623980),(-190324076775623905)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨345761108298645115,345761108298645208⟩,⟨72612935128506432,72612935128506522⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨105814770160301169,105814770160301277⟩,⟨194428786866799116,194428786866799224⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-66251829415706510),(-66251829415706385)⟩,⟨99915740722194299,99915740722194424⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-57492720984883110),(-57492720984882981)⟩,⟨(-17891381688798333),(-17891381688798206)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨5600901754831991,5600901754832113⟩,⟨(-29427217303753625),(-29427217303753506)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨15343886841362694,15343886841362811⟩,⟨2973399496620580,2973399496620695⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2110579331948299),(-2110579331948196)⟩,⟨8648710087419254,8648710087419352⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-5450778148187961),(-5450778148187879)⟩,⟨(-1376145357206165),(-1376145357206084)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨500010257002607,500010257002679⟩,⟨(-3851742224325811),(-3851742224325741)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2765456833865638,2765456833865701⟩,⟨(-538242538701857),(-538242538701795)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1403177883352514,1403177883352566⟩,⟨1425391572337812,1425391572337862⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨121020626514646,121020626514681⟩,⟨1219322477113251,1219322477113289⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-101481635273556),(-101481635273532)⟩,⟨403328436380331,403328436380356⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-786973479140852418816),(-786973479140852415385)⟩,⟨(-1823322240429854088030),(-1823322240429854084605)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1691668134798457580657),(-1691668134798457572172)⟩,⟨(-4595422327925878882730),(-4595422327925878874253)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1311678938465503207142),(-1311678938465503197520)⟩,⟨(-5370520512360423088894),(-5370520512360423079285)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-265200973210906784801),(-265200973210906777137)⟩,⟨(-4344733202860642407656),(-4344733202860642399999)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨505447358796518561777,505447358796518567106⟩,⟨(-2595934243169981859004),(-2595934243169981853680)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨660926976041549022369,660926976041549025437⟩,⟨(-1127447482177694631863),(-1127447482177694628798)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨449205374612771884418,449205374612771885838⟩,⟨(-313774946565845060772),(-313774946565845059351)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨202708737200594309022,202708737200594309556⟩,⟨(-16768888729234114673),(-16768888729234114139)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨60166086002272617898,60166086002272618125⟩,⟨35735045284645010142,35735045284645010371⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨7847390175073640371,7847390175073640506⟩,⟨22052314839476981217,22052314839476981350⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-3067219695506117568),(-3067219695506117492)⟩,⟨7356716881537354802,7356716881537354878⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-2598360727373721082),(-2598360727373721027)⟩,⟨1219013704511560933,1219013704511560985⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1083569271683193191),(-1083569271683193152)⟩,⟨(-271603634378058741),(-271603634378058699)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-318029031882774635),(-318029031882774603)⟩,⟨(-341592398453748925),(-341592398453748892)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-63747847410393961),(-63747847410393938)⟩,⟨(-183899723712483893),(-183899723712483866)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-6220444931107162),(-6220444931107142)⟩,⟨(-53636855607390738),(-53636855607390717)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-3510730404973989801824689),(-3510730404973989786606543)⟩,⟨13622351556774149024870569,13622351556774149040099914⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-9048100966641333218515156),(-9048100966641333178025985)⟩,⟨35888827675162725188358346,35888827675162725228891892⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-11196911428192242195224317),(-11196911428192242142481440)⟩,⟨46123531307928820932624981,46123531307928820985450151⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-10215211280003683294630644),(-10215211280003683239240393)⟩,⟨43798472769765914046330219,43798472769765914101834287⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-7704959842225009715150563),(-7704959842225009664411343)⟩,⟨33703710136126136289059866,33703710136126136339908725⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-5144686642984797025308712),(-5144686642984796985513778)⟩,⟨21879866522297830943514340,21879866522297830983379938⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-3194766627681603401125394),(-3194766627681603374068570)⟩,⟨12297053666262579257850680,12297053666262579284936094⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1895106889533091175997912),(-1895106889533091159969130)⟩,⟨6115273872626463865859170,6115273872626463881895434⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1079386564930987700632579),(-1079386564930987692185517)⟩,⟨2747996025637056584170065,2747996025637056592617329⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-588442505462080759955815),(-588442505462080755889927)⟩,⟨1139591413862413140245162,1139591413862413144309904⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-307539153241523371497522),(-307539153241523369655101)⟩,⟨445403210316831202099212,445403210316831203940717⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-155584154802102891224502),(-155584154802102890413508)⟩,⟨167482672918337416107514,167482672918337416917938⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-77144547137703360873936),(-77144547137703360517945)⟩,⟨61748271502155962254064,61748271502155962609739⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-37525802207613740676577),(-37525802207613740519334)⟩,⟨22595197120763248063982,22595197120763248221061⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16981512400763543801151),(-16981512400763543734625)⟩,⟨8011312822756333029958,8011312822756333096408⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-4871738091153573959075),(-4871738091153573940668)⟩,⟨1980294261788089112778,1980294261788089131160⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨227216570442241617736204522,227216570442241617976624694⟩,⟨140953953881627414572312912,140953953881627414817656668⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨633326836347350790890827239,633326836347350791562767439⟩,⟨378557166794119809803640911,378557166794119810487287261⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨909709127347348393798382839,909709127347348394762353211⟩,⟨504568164197495445212966462,504568164197495446188548345⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1016894068847253672898637098,1016894068847253673958737850⟩,⟨503288271941535065447896024,503288271941535066514047827⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨965898149406066553876432161,965898149406066554865993979⟩,⟨408799721648815138901144524,408799721648815139890247988⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨807011593501932127175557936,807011593501932128041128908⟩,⟨277893906547882721923655829,277893906547882722784549355⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨604761913825232876453980622,604761913825232877141097660⟩,⟨158880229614247629076419066,158880229614247629758881775⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨412818642568343276506448941,412818642568343277065451709⟩,⟨75240700043477968809337423,75240700043477969366399267⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨260737472335980976699647764,260737472335980977145085185⟩,⟨27749158754915886291095636,27749158754915886736883919⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨155030311166381517807011298,155030311166381518128666010⟩,⟨5919540295088620037834092,5919540295088620360112231⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨88385608749271078177136597,88385608749271078389870694⟩,⟨(-1773822217089107228540530),(-1773822217089107015555058)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨49145501176094516591852762,49145501176094516723633185⟩,⟨(-3281911523815552565590143),(-3281911523815552433891058)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨26924853194496016487902231,26924853194496016565604465⟩,⟨(-2733869033070235277885123),(-2733869033070235200394257)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨14405031515862731476252855,14405031515862731519758694⟩,⟨(-1802689475641670576374674),(-1802689475641670533070056)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨7034608417035308480926074,7034608417035308502684042⟩,⟨(-979708375142773832395192),(-979708375142773810768678)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨2106107970871723919027937,2106107970871723925592185⟩,⟨(-306952973404395562204895),(-306952973404395555685255)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨13359306330115013628385870200,13359306330115013646033296390⟩,⟨18602031142034518908036867363,18602031142034518925888776436⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨38600098691425875365336726169,38600098691425875416530863625⟩,⟨52301718573588045195994288727,52301718573588045247779359901⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨59557949855365812662353788876,59557949855365812741582305918⟩,⟨76487773731286786721575352321,76487773731286786801724249638⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨74041890614066024448434922088,74041890614066024546402273117⟩,⟨87938351995224415274587716554,87938351995224415373717254447⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨80854160337641728817605508489,80854160337641728925573406161⟩,⟨86832675107348836512965800631,86832675107348836622037243321⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨80074174457211746673077631489,80074174457211746782743531101⟩,⟨76184656969202012622472422771,76184656969202012733031750991⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨73042937512912883565500246866,73042937512912883665723923021⟩,⟨60418071332082213338343523958,60418071332082213439339477580⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨61973680945274536546408590172,61973680945274536628442702466⟩,⟨43779196338338555231926452160,43779196338338555314665933217⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨49307450367595145803098040160,49307450367595145863981481369⟩,⟨29233259551512274921116788998,29233259551512274982485444203⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨37083279634912918660403573616,37083279634912918706056460106⟩,⟨18134774655427592928570257704,18134774655427592974498224565⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨26571830077028453988529718011,26571830077028454023809270416⟩,⟨10538857328938074668978593807,10538857328938074704428287606⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨18249439462043179531131153258,18249439462043179556561001253⟩,⟨5785433365782904701123426492,5785433365782904726677935798⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨12008988211763250196914547665,12008988211763250214449423040⟩,⟨3019707463812298574488962004,3019707463812298592091008776⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨7435316891748107083216158506,7435316891748107094306698243⟩,⟨1494883565842253638272759190,1494883565842253649397674109⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4019100778684345374060132873,4019100778684345380087238457⟩,⟨670425657357725190057233898,670425657357725196100707875⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1267563803091867674246244936,1267563803091867676142258691⟩,⟨189482382421313444197407185,189482382421313446098195881⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨80898968823918479462089497962,80898968823918479499836278445⟩,⟨(-74019600433583885252516845727),(-74019600433583885216133758098)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨231976766473527486722793589483,231976766473527486837154371596⟩,⟨(-215042518123951157750214158605),(-215042518123951157639197765951)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨352934495802795447718306250386,352934495802795447911075460045⟩,⟨(-335898287789799733263347318886),(-335898287789799733074025269014)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨430747883403266016873855326652,430747883403266017144468914107⟩,⟨(-426633247240013213976316628791),(-426633247240013213707246357941)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨460899134887786359572792976831,460899134887786359917649687216⟩,⟨(-481673543888109967104246415729),(-481673543888109966758069496487)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨447440802703872198235113700655,447440802703872198639856225053⟩,⟨(-500297086708749647682633967076),(-500297086708749647274351870979)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨400934705450874328121638483448,400934705450874328559634035336⟩,⟨(-486218399021862552586359739574),(-486218399021862552144561662545)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨335078984388990649766415221916,335078984388990650210163747719⟩,⟨(-446461174281456725994106795536),(-446461174281456725548641408274)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨263175159175891370976922939890,263175159175891371402759012103⟩,⟨(-389775498186387727015144496165),(-389775498186387726590374218964)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨195497280035316171613532220655,195497280035316171988855624808⟩,⟨(-324938509054085683087001798475),(-324938509054085682714391454024)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨138131724149914370971531711241,138131724149914371282268526328⟩,⟨(-259314059715826781725607884097),(-259314059715826781417520103094)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨93215461908914309700044303485,93215461908914309941142858357⟩,⟨(-197974147675531991943911644805),(-197974147675531991704377326659)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨60031630137102296574207710823,60031630137102296746992519552⟩,⟨(-143488316784521138769244820878),(-143488316784521138596985504919)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨36304210006131354648129420995,36304210006131354760960716234⟩,⟨(-96254576985608758369552004504),(-96254576985608758256638954331)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨19218586675576271688177788552,19218586675576271750883172316⟩,⟨(-55103203128786722159662272357),(-55103203128786722096712051236)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨5986113460726815207215921792,5986113460726815227170752239⟩,⟨(-17906932745503911346381730175),(-17906932745503911326315139837)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨699341050287829403709131721248,699341050287829404513371755234⟩,⟨(-646116471161713259903912880118),(-646116471161713259099646960325)⟩⟩ +lemma checked : cachedMomentRuleBox column3_1 kernel4_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 3 4 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column3_1_contains kernel4_1_contains +end cm3_4_1_1 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments4.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments4.lean new file mode 100644 index 0000000000000000000000000000000000000000..bc2eb3db7c002f37cc0a2e36c2ec6d58fc0197f7 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/DMoments4.lean @@ -0,0 +1,3929 @@ +import OAI.Analysis.PlanarPacking.Certificate.Columns10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid +namespace cm4_1_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_0 j i k).mul (kernel1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨164568447233795299311364481,164568447233795299405981228⟩,⟨42360583132017054301861629,42360583132017054397296108⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨451763501436377302017067141,451763501436377302277766849⟩,⟨165133561993253345397802694,165133561993253345661606552⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨611448884782874778574245652,611448884782874778936823415⟩,⟨371732331227017880271136283,371732331227017880641299467⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨570791872861935432394475759,570791872861935432816149932⟩,⟨632260018885720182636108619,632260018885720183070993853⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨311265691246837032284468142,311265691246837032716818916⟩,⟨839424233650567827588257971,839424233650567828038844757⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-90706734647475963919427519),(-90706734647475963497603713)⟩,⟨865098907307281163081424358,865098907307281163520161745⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-474706070122964785785585749),(-474706070122964785363486588)⟩,⟨649340131799952187242397571,649340131799952187670280294⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-675621905533009603003467323),(-675621905533009602615597316)⟩,⟨256900192788166083916429638,256900192788166084297561035⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-621876112509278109912459504),(-621876112509278109589052089)⟩,⟨(-152000366791204679024376525),(-152000366791204678711281021)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-373972080217475251707707013),(-373972080217475251432440380)⟩,⟨(-420403287797987343998531140),(-420403287797987343727001893)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-72958419795850172560225600),(-72958419795850172320891273)⟩,⟨(-484560713098157077982425117),(-484560713098157077741794672)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨153175351882940469227042518,153175351882940469409569917⟩,⟨(-389131704792361363723141129),(-389131704792361363541462974)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨250509218824174240928313544,250509218824174241052707600⟩,⟨(-232475076231242654747897714),(-232475076231242654628769621)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨236327750687336708837446619,236327750687336708913498046⟩,⟨(-98864110584863746027232294),(-98864110584863745958733125)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨157786260174988897572234717,157786260174988897611997209⟩,⟨(-24525472726789767820466336),(-24525472726789767787019101)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨54314657085582067476191241,54314657085582067488395972⟩,⟨(-1686210151136463716929701),(-1686210151136463707139192)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1951534570768422663718236624),(-1951534570768422662297318893)⟩,⟨505554769626243031013385299,505554769626243032422552787⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-5596730504277762578491383306),(-5596730504277762574425033605)⟩,⟨1141582288519161352475837297,1141582288519161356512453099⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-8453679505029431462282873869),(-8453679505029431456152496550)⟩,⟨824436334421821249706948926,824436334421821255802601115⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-10027168973902031379502115856),(-10027168973902031372196843378)⟩,⟨(-575432664282156604876772312),(-575432664282156597598335887)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-10006047082139907665024859961),(-10006047082139907657572276968)⟩,⟨(-2666527022842437002625891272),(-2666527022842436995187166698)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-8449527626080388572773390445),(-8449527626080388565626217615)⟩,⟨(-4716074960173471719740882543),(-4716074960173471712586841394)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-5848265433824674220507675080),(-5848265433824674214102425708)⟩,⟨(-6005787090179074642926279666),(-6005787090179074636494406660)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2965355897477561794322078384),(-2965355897477561789113987293)⟩,⟨(-6168438474748047434246380612),(-6168438474748047429001734965)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-527087139179197900848436435),(-527087139179197896614362176)⟩,⟨(-5312072284419034246306327494),(-5312072284419034242041061166)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1047063502767598796430740669,1047063502767598799872622645⟩,⟨(-3883248028864884305163603254),(-3883248028864884301701897288)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1722671542086195065674039943,1722671542086195068212146615⟩,⟨(-2394932191768716740376429954),(-2394932191768716737826388066)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1734617347968077923767444521,1734617347968077925493305543⟩,⟨(-1203808808309922623329187319),(-1203808808309922621596884604)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1395796351396995267569742143,1395796351396995268754211659⟩,⟨(-438635517026955143181426876),(-438635517026955141994423126)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨952820016086058784243979668,952820016086058785010476068⟩,⟨(-56085689997660665994786106),(-56085689997660665226590736)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨534719517287417894956196498,534719517287417895378133253⟩,⟨61598756475244115758866339,61598756475244116182307793⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨170204817762646307445670272,170204817762646307579210606⟩,⟨35294558610204262044115176,35294558610204262178288188⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨8385600889549790644066062505,8385600889549790649428719046⟩,⟨2799687750319373528451107384,2799687750319373533905104635⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨23807324262193859541576412427,23807324262193859557362321854⟩,⟨9248301744357065103679435856,9248301744357065119722421618⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨35290066752877983554021086835,35290066752877983579246791236⟩,⟨17717191303678983025636232752,17717191303678983051235066385⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨40772425552969601637208937865,40772425552969601671267144454⟩,⟨28063233175431276674198518800,28063233175431276708638629099⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨39263639517905086445616384936,39263639517905086486403278098⟩,⟨38660381102972099148203062427,38660381102972099189283851240⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨31342799929572595854333142786,31342799929572595898548274862⟩,⟨47008170109956386076067716664,47008170109956386120443913623⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨19189844962412432697753577924,19189844962412432741213919998⟩,⟨50850507693384943297705292571,50850507693384943341171630453⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨5939031911470896433261340575,5939031911470896471935861738⟩,⟨49217433624892426289258625186,49217433624892426327790967609⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-5409189400637178085977040604),(-5409189400637178054811975998)⟩,⟨42814476746979769040142677392,42814476746979769071054765902⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-12953698705527349849066096694),(-12953698705527349824485476032)⟩,⟨33590722840896419355525936766,33590722840896419379797479070⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16256638801711315484303506178),(-16256638801711315464320443848)⟩,⟨23824943416964360790975683599,23824943416964360810649031343⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16041861256068718378656370241),(-16041861256068718362038520693)⟩,⟨15288729683979490296284201035,15288729683979490312689363952⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-13546956945856956203858260040),(-13546956945856956190912079235)⟩,⟨8860162617470041026011260259,8860162617470041038834867279⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-9930974308069817665541316693),(-9930974308069817656508144005)⟩,⟨4599211982156627634114644195,4599211982156627643082669911⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-5961033193401511025582994059),(-5961033193401511020317445055)⟩,⟨2055757271511875115264544315,2055757271511875120499469317⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1976528882284119274701540376),(-1976528882284119272982227303)⟩,⟨567967767587909788403228788,567967767587909790113621014⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1736778278819662686680629398,1736778278819662709707682032⟩,⟨(-20491769724299703541603827540),(-20491769724299703518343939936)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨7215301267386393151774376949,7215301267386393218749147043⟩,⟨(-59803672570238837941528733546),(-59803672570238837873876418445)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨18015214645694887058274960407,18015214645694887162600349721⟩,⟨(-93921424550289371077123918505),(-93921424550289370971767547764)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨35556247048386986583054879388,35556247048386986713595447938⟩,⟨(-119243276512656011332398793027),(-119243276512656011200694852971)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨58669997622759895510972899517,58669997622759895652780071798⟩,⟨(-132603696846611543112099002257),(-132603696846611542969343644535)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨83758419065975399300210980662,83758419065975399444541427852⟩,⟨(-132276513153552078299338257429),(-132276513153552078154696888968)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨105888271817966437192377747156,105888271817966437349414233534⟩,⟨(-118899405306751510273887846732),(-118899405306751510117507585368)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨120475173274907296186851599310,120475173274907296346517705737⟩,⟨(-95694956526830013534316674880),(-95694956526830013375718260390)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨124835563049104942791969804205,124835563049104942946022937888⟩,⟨(-67692546701961418253693218930),(-67692546701961418100370599638)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨118898459541718473244165794844,118898459541718473380979992991⟩,⟨(-40245322682310228350494376149),(-40245322682310228213952439148)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨104827516113543363659677871047,104827516113543363772035335037⟩,⟨(-17551112787786596956124026838),(-17551112787786596843636960266)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨85891245092197031089456203969,85891245092197031175229017115⟩,⟨(-1823300474206315784547833176),(-1823300474206315698394485173)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨65223196911053719712268554739,65223196911053719773123864792⟩,⟨6689737128753107783728371529,6689737128753107845044579469⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨44990697572459978195431400300,44990697572459978234936969157⟩,⟨9101032544420389262604445690,9101032544420389302519609093⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨26134585670392939310070334882,26134585670392939331962731712⟩,⟨7146905728275775608204574105,7146905728275775630370986217⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨8543470580331495311428634056,8543470580331495318393320114⟩,⟨2655595158377812476039873093,2655595158377812483100728170⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-12820370100750161925717454702),(-12820370100750161894961618346)⟩,⟨14656140904529939961840393047,14656140904529939993130918260⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-40231309927146120784736913749),(-40231309927146120693893882563)⟩,⟨40655671684493248304411010042,40655671684493248396587209964⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-71776233671241913853838966636),(-71776233671241913708030193984)⟩,⟨56917569474385197993320438318,56917569474385198140464595938⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-106856091829202466814551223695),(-106856091829202466624131579615)⟩,⟨58066728712712497527874434133,58066728712712497718440185577⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-141262385150169926244324831250),(-141262385150169926025941207737)⟩,⟨41094525212639656334560347492,41094525212639656550582474686⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-168240595397665804449925952517),(-168240595397665804224846551248)⟩,⟨6853440669408922257094644384,6853440669408922476311465200⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-181007856750336838120384872835),(-181007856750336837890927849700)⟩,⟨(-39267886608023970234345333149),(-39267886608023970013380690107)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-175669629281827629050283312970),(-175669629281827628826257999739)⟩,⟨(-88314405639938193504789483716),(-88314405639938193290089563986)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-153074866721886108991615448128),(-153074866721886108764788219985)⟩,⟨(-130328336843843857621108697680),(-130328336843843857401274444374)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-118627791126476375044883871929),(-118627791126476374808429028175)⟩,⟨(-157415495815226831814480635969),(-157415495815226831581093495571)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-80218671711511178549119953356),(-80218671711511178325535977883)⟩,⟨(-165845185963630375319466076946),(-165845185963630375096093463520)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-45439781709284936871303557063),(-45439781709284936675763900321)⟩,⟨(-156312895256533645285096420944),(-156312895256533645088329679197)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-19425459269498688455614847401),(-19425459269498688294269145925)⟩,⟨(-132578676045376220132150100672),(-132578676045376219969519596808)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-4018124669135538548021228901),(-4018124669135538429252117696)⟩,⟨(-99456657099142329450885237612),(-99456657099142329331147754718)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1879499798392554752583250849,1879499798392554824667763992⟩,⟨(-61168163238630303370795420867),(-61168163238630303298145055792)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1372657206805590023521104891,1372657206805590047590724129⟩,⟨(-20585585781496246954107973103),(-20585585781496246929855623406)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨100069709501902762849758905,100069709501902762869241811⟩,⟨89748508962548696443584115,89748508962548696463882194⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1421151500523071748718883812,1421151500523071749018493475⟩,⟨1360112506912048953384702081,1360112506912048953694658357⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨5516567253766315765533857982,5516567253766315766877485015⟩,⟨5949456017506509145610433516,5949456017506509146985620914⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨12457216439435201112289517152,12457216439435201116026496890⟩,⟨15997489481579806647632403071,15997489481579806651413403568⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨20301018520384454894154388995,20301018520384454902149071918⟩,⟨32921226762676623712154912950,32921226762676623720170526697⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨25547911196669130001657662056,25547911196669130015938607776⟩,⟨56456784367344645254489847659,56456784367344645268741545366⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨24500306785834551609481968830,24500306785834551631590221572⟩,⟨83978278780512207533457985766,83978278780512207555540919255⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨15033735660916613846667522610,15033735660916613876814711883⟩,⟨110743385769769412391704642405,110743385769769412422021184829⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-2106613446373680361156642760),(-2106613446373680324549728728)⟩,⟨131237380380430018789562154748,131237380380430018826820190326⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-23238214527899435013778901572),(-23238214527899434973904234171)⟩,⟨141060479930364549957463316210,141060479930364549998706124510⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-42987426231186806360000379203),(-42987426231186806320473086080)⟩,⟨138384973887983422358008425926,138384973887983422399612552495⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-56186077574957234371187342538),(-56186077574957234331394641135)⟩,⟨124252087505361827702771348049,124252087505361827744586031308⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-59477688828843421337910251483),(-59477688828843421300899270920)⟩,⟨101690016586629688975763798148,101690016586629689014343953591⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-52026282958602471613904811389),(-52026282958602471584020786079)⟩,⟨74264706061842361281564107815,74264706061842361312484105972⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-35321255662833302664876287432),(-35321255662833302645550360739)⟩,⟨44828182126346029068172439573,44828182126346029088056667836⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-12480612425515951414537719349),(-12480612425515951407879020209)⟩,⟨14939676953731355845623919923,14939676953731355852453216615⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-67900768064326003725841603689),(-67900768064326002905754594499)⟩,⟨(-47199341242866067770224593911),(-47199341242866066952722581101)⟩⟩ +lemma checked : cachedMomentRuleBox column4_0 kernel1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 1 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_0_contains kernel1_0_contains +end cm4_1_0_0 +namespace cm4_1_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_0 j i k).mul (kernel1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1106746007819939323118044068),(-1106746007819939322179677045)⟩,⟨(-935078707303975385323927228),(-935078707303975384378905714)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-2888090271682275130959007418),(-2888090271682275128274061784)⟩,⟨(-2928010753330029477340478503),(-2928010753330029474634703800)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-3463880110146191735402768120),(-3463880110146191731375541646)⟩,⟨(-5083938535512465457708207127),(-5083938535512465453645054462)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-2394432897729882902236781562),(-2394432897729882897524781203)⟩,⟨(-6979620317804241001526933859),(-6979620317804240996765506249)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨152967984799084506515905368,152967984799084511121877847⟩,⟨(-7825842086680998331958035472),(-7825842086680998327297018508)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨3300198851664623678278817974,3300198851664623682567045139⟩,⟨(-6936838404102426151526118809),(-6936838404102426147210612449)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨5757053746774900269125415309,5757053746774900273159112199⟩,⟨(-4283465649394721314041066750),(-4283465649394721310039339160)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨6472398910809759243463875674,6472398910809759246989031367⟩,⟨(-692101396253416360641255686),(-692101396253416357208871273)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨5228400221160380506562765396,5228400221160380509653562005⟩,⟨2537976236207865767645923756,2537976236207865770646675238⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨2727179468626434545388922567,2727179468626434548222181079⟩,⟨4357416605845165943328789571,4357416605845165946133810667⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨107518181973676638993523819,107518181973676641344340229⟩,⟨4495422771964529329450334048,4495422771964529331809297685⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1716086644186654106183827361),(-1716086644186654104443267237)⟩,⟨3444074118059405440198957367,3444074118059405441928102723⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2421520338281148563385181857),(-2421520338281148562218462210)⟩,⟨2012713312966049212190951993,2012713312966049213307999259⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-2203716651611806625818364654),(-2203716651611806625109492570)⟩,⟨847822009192274352614157600,847822009192274353253434204⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1456719655156660972829318413),(-1456719655156660972458582414)⟩,⟨209637744125694447985520390,209637744125694448298131039⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-500571898336610955765633665),(-500571898336610955651610565)⟩,⟨14403335416087297860911166,14403335416087297952677343⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨12234708570975693623643836288,12234708570975693635733765422⟩,⟨7551179031240592763966917592,7551179031240592776096939588⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨33759993217518566434412383689,33759993217518566469115735045⟩,⟨23073162262891431258525487016,23073162262891431293324748437⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨47159343058257273679562274477,47159343058257273732131867397⟩,⟨39098778199919038963391728420,39098778199919039016052608791⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨49409534608089678586579010508,49409534608089678649486806495⟩,⟨54035149396493946980586185002,54035149396493947043508348741⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨40601873054082842640826784515,40601873054082842705049521929⟩,⟨64862988448011423059149492086,64862988448011423123247877086⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨24010594499502269193999549757,24010594499502269256319407193⟩,⟨68563260030243140581364199768,68563260030243140643387426482⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨4940780871923452180453369562,4940780871923452237378307420⟩,⟨63840497512966750927474013656,63840497512966750983936340483⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-11296689416015430919512932566),(-11296689416015430872311990932)⟩,⟨52015788079958607977021826217,52015788079958608023633420748⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-21307118485578027096472502226),(-21307118485578027058070918301)⟩,⟨36500920667713105047755520619,36500920667713105085626710144⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-24450054311229338018351471729),(-24450054311229337987898135114)⟩,⟨21242268362765252706613750283,21242268362765252736738275344⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-22320982434172670038163549043),(-22320982434172670016409304461)⟩,⟨9156556570544550323953941504,9156556570544550345548932307⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-17441285229867633690973072726),(-17441285229867633676704724073)⟩,⟨1404332223925019069052349429,1404332223925019083275963216⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-12025904328078594890826638721),(-12025904328078594880501028159)⟩,⟨(-2366956777851801052152023320),(-2366956777851801041814840478)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-7367026952684445974200082995),(-7367026952684445966987927224)⟩,⟨(-3272289084878104716699086467),(-3272289084878104709462423686)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3832793344838000777612030551),(-3832793344838000773427903757)⟩,⟨(-2489936483380894086178643772),(-2489936483380894081975946218)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1171012398551609273291320396),(-1171012398551609271930755066)⟩,⟨(-905082445334871724343147994),(-905082445334871722976012557)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-9491184766327175000715543775),(-9491184766327174972366225063)⟩,⟨(-50796580327791284599600629034),(-50796580327791284572299411068)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-20991241600759635736149631524),(-20991241600759635652090423235)⟩,⟨(-148368625056059151699484405613),(-148368625056059151618194329824)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-12583952869475806246286028858),(-12583952869475806109500426869)⟩,⟨(-233032234140449384097320168777),(-233032234140449383964128354564)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨21139893030425759626832407928,21139893030425759820580994522⟩,⟨(-294895312103703468564671246437),(-294895312103703468374243755899)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨76311719380805988097146474187,76311719380805988343497492000⟩,⟨(-324794870890940139799927949932),(-324794870890940139555872464634)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨140798436065848125511132240238,140798436065848125795384162850⟩,⟨(-317846766045742216631501564078),(-317846766045742216348411336068)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨198556782678659574544045121607,198556782678659574840759458412⟩,⟨(-276576256464324644809162517647),(-276576256464324644512594429340)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨235662881718318112694120946802,235662881718318112972857561256⟩,⟨(-211329367255116448058103412661),(-211329367255116447778773756837)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨245206847798770685881505962830,245206847798770686116461809593⟩,⟨(-137209218986778726132425462845),(-137209218986778725896487947995)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨228766458008035059270107692809,228766458008035059464776139544⟩,⟨(-69024094520033100469267602284),(-69024094520033100273439880189)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨194190465968437643134406302686,194190465968437643301272606428⟩,⟨(-16920894219514433280639563479),(-16920894219514433112588850772)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨151441262210344649311492703651,151441262210344649454865092976⟩,⟨15336316670669248145115841720,15336316670669248289294502800⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨108845538734482729519349358642,108845538734482729633396334849⟩,⟨29322539286937374129062963663,29322539286937374243585196496⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨71177960820110429061102774107,71177960820110429141775962367⟩,⟨29477027530812454956116074242,29477027530812455037054637768⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨39600220002043237026361405037,39600220002043237073764636064⟩,⟨20768913747121940916955454395,20768913747121940964489787448⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨12633899492757244086948353978,12633899492757244102481243401⟩,⟨7394391514775042972687887195,7394391514775042988260032600⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-97365731783559385556515413385),(-97365731783559385434414711160)⟩,⟨23123950694618278152152728639,23123950694618278273942176701⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-288181979904399514015056530785),(-288181979904399513659771026990)⟩,⟨58650074180551295618600029419,58650074180551295973230704478⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-465494169175810229397317555279),(-465494169175810228843536852389)⟩,⟨64409562505315850856841977860,64409562505315851410510072153⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-616579004424804012891280980544),(-616579004424804012198034886379)⟩,⟨28550310683885037965848058905,28550310683885038661031159037⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-726331226616346201458404014976),(-726331226616346200705349235386)⟩,⟨(-50031207018166364460240284428),(-50031207018166363701386317009)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-781176409799187265143244182275),(-781176409799187264378852663053)⟩,⟨(-160488277959540276662271075163),(-160488277959540275887654326117)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-774312290460649060443652091358),(-774312290460649059621363549178)⟩,⟨(-282388597026977339070377340339),(-282388597026977338236593266711)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-709554026057186084300298655405),(-709554026057186083469239323057)⟩,⟨(-391502186830657801382587782754),(-391502186830657800542114149137)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-601449712468062902198471850582),(-601449712468062901388023222016)⟩,⟨(-467037815848006712031914652345),(-467037815848006711216873699463)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-471289681057779764547601461473),(-471289681057779763818647956264)⟩,⟨(-497316448201965715798706962012),(-497316448201965715069882111159)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-340886814200486545610907087834),(-340886814200486545003877700115)⟩,⟨(-481590304864240324470893220248),(-481590304864240323867470310740)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-227004732058794837555917216648),(-227004732058794837085778228033)⟩,⟨(-427788379486727482325634573056),(-427788379486727481860868534842)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-138507180068949917150019824038),(-138507180068949916811792033323)⟩,⟨(-347934530255154536634651908433),(-347934530255154536301933701048)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-76522059309623590293678298534),(-76522059309623590071408419293)⟩,⟨(-253624466075198719465715366511),(-253624466075198719247989927633)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-36483131392784644100253636264),(-36483131392784643975958534154)⟩,⟨(-153214662783631221432998070169),(-153214662783631221311631143070)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-10548979900567720869047247792),(-10548979900567720829226454437)⟩,⟨(-51121369363125790588719225281),(-51121369363125790549908249082)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨68979331424687693365747836251,68979331424687693481220090877⟩,⟨42039572119513974263004985557,42039572119513974375734631045⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨195536100353044963757448791617,195536100353044964102009776639⟩,⟨135602613691536750124005631014,135602613691536750461834627406⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨287698788997535403573746442152,287698788997535404148282803391⟩,⟨253184499963257343834123032336,253184499963257344402262319737⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨323976726097748950452513715719,323976726097748951245388904669⟩,⟨397705237944137622033352165624,397705237944137622825685976895⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨288546315551227730229935178069,288546315551227731204849821310⟩,⟨556753584400589286661029887425,556753584400589287645954682481⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨177564186622344852838984969129,177564186622344853928784211149⟩,⟨704682805785494672067148099682,704682805785494673179281437532⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4096690457060582422104313820,4096690457060583572835092674⟩,⟨810641031688672825517229731308,810641031688672826697450423266⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-202147738263972862415733565130),(-202147738263972861287939186536)⟩,⟨849883717381743538427501207703,849883717381743539584982178108⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-401759206862769511969402256847),(-401759206862769510808640109102)⟩,⟨813410732787373825533430491063,813410732787373826713854879519⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-556818696211650379152598709284),(-556818696211650377919558876992)⟩,⟨711286052059155518286036729143,711286052059155519525041881106⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-641264242124688089210284084883),(-641264242124688088030387199684)⟩,⟨568228359882478919929527984678,568228359882478921106367889498⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-645934386738571744664319791788),(-645934386738571743624543986886)⟩,⟨414125747831664438569936963620,414125747831664439603186603606⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-577053865134768793550291887189),(-577053865134768792686729461197)⟩,⟨274247960590799003892092238142,274247960590799004750558732825⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-450370264117771229645793297157),(-450370264117771229007095358213)⟩,⟨163021306009212851212250669400,163021306009212851847851115552⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-284614012387140701062006577731),(-284614012387140700673167605319)⟩,⟨82552291349018988655088142029,82552291349018989042430003328⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-97125161830591835692572411808),(-97125161830591835562542843838)⟩,⟨24755764867850312708749067218,24755764867850312838354092632⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨305278741457838791419756106,305278741457838791495047455⟩,⟨(-378723562181909636602335794),(-378723562181909636528879214)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4644684697392056608880653595,4644684697392056610034645949⟩,⟨(-5418864315433153829996380548),(-5418864315433153828863375909)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨20467485018090792909778081478,20467485018090792914933254031⟩,⟨(-21352566427773468760349881272),(-21352566427773468755241341108)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨55640596585578895505761980246,55640596585578895520074374156⟩,⟨(-49437634846434642838131612558),(-49437634846434642823816442385)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨116173567012654360896403754015,116173567012654360927113154867⟩,⟨(-83819260439157553140518856662),(-83819260439157553109615625511)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨202847471373239019943587033469,202847471373239019998930829263⟩,⟨(-112524738936224578258353151752),(-112524738936224578202603747998)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨308287326437145316032069928181,308287326437145316119034597582⟩,⟨(-121576602177106107464476338359),(-121576602177106107377325764423)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨416778093438826695062149903357,416778093438826695183171285441⟩,⟨(-101011680522064776128482481257),(-101011680522064776008596372800)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨507920312876137935086628548394,507920312876137935237154794799⟩,⟨(-50097074283842036546781811461),(-50097074283842036400230477060)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨562910571393095265781523335166,562910571393095265949691875762⟩,⟨21060231717477734793715051317,21060231717477734953899117513⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨570441713822700155470472769736,570441713822700155641152254906⟩,⟨94550966510653922009833034507,94550966510653922168684647375⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨529355960751533492908984237866,529355960751533493082514146307⟩,⟨150857384353830008762500331039,150857384353830008924684635729⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨447151429641096232680145600246,447151429641096232842089265131⟩,⟨175203101628938757540249398133,175203101628938757693473015434⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨335737833784559757054911206729,335737833784559757185821598672⟩,⟨161489248199561798210521361633,161489248199561798335707906217⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨206937913878457189737305261218,206937913878457189821972940264⟩,⟨112976739673292683224759949922,112976739673292683306354177410⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨69748553792870107932320943640,69748553792870107961483109211⟩,⟨40480106675412938488447563692,40480106675412938516671940937⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-456543978176627199722956656939),(-456543978176627195467188455395)⟩,⟨343314619828485452629683155253,343314619828485456891306898334⟩⟩ +lemma checked : cachedMomentRuleBox column4_0 kernel1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 1 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_0_contains kernel1_1_contains +end cm4_1_0_1 +namespace cm4_1_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_1 j i k).mul (kernel1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨266383871380957027695687955,266383871380957027777681024⟩,⟨32231491193542142571041650,32231491193542142651362345⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨742391580019651296691297688,742391580019651296922270401⟩,⟨153154125882430160662654150,153154125882430160888147653⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1047037588885017606490764018,1047037588885017606826699077⟩,⟨404981105022740264060666789,404981105022740264386630965⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1081891197355242657202246034,1081891197355242657602037816⟩,⟨765778100234302857650665905,765778100234302858037832273⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨809765055013420688467543828,809765055013420688880498228⟩,⟨1111469555208663060662329981,1111469555208663061065275803⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨301141179633621083879111145,301141179633621084297282621⟩,⟨1276223355263322951194483542,1276223355263322951610676706⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-268989756224313547676469607),(-268989756224313547257715057)⟩,⟨1151849248438787848662332623,1151849248438787849083953438⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-695033099171576382019848346),(-695033099171576381652334698)⟩,⟨761826625886759502774854942,761826625886759503141193405⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-845399332741424963542864495),(-845399332741424963265149626)⟩,⟨253384149441879408801241285,253384149441879409066912145⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-723820018658073419348284132),(-723820018658073419125165016)⟩,⟨(-188910468759094941916509573),(-188910468759094941711068865)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-445677686277201117687301240),(-445677686277201117489197634)⟩,⟨(-443140006888470897158331454),(-443140006888470896966798114)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-156239388303634677520582338),(-156239388303634677366958320)⟩,⟨(-494673466030078615953807570),(-494673466030078615799584736)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨44494036300100795558431409,44494036300100795664196577⟩,⟨(-409459684008884008597837137),(-409459684008884008489196045)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨127197897334017616210745855,127197897334017616275636406⟩,⟨(-273613076639837474807929980),(-273613076639837474740567883)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨113602993444428633880298765,113602993444428633914175428⟩,⟨(-146168734294158664224083337),(-146168734294158664188840292)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨43756134056422044403746531,43756134056422044414108437⟩,⟨(-44616735178982237302221173),(-44616735178982237291450792)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1613046503141096543783910737),(-1613046503141096543056425712)⟩,⟨421431094988040527888135599,421431094988040528620832105⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-4618612974757537872145038053),(-4618612974757537870053367324)⟩,⟨991481086485808616491031334,991481086485808618593860795⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-6969663522189161320942491939),(-6969663522189161317760589979)⟩,⟨865251855103168272470788364,865251855103168275658042619⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-8298441071882577981946323053),(-8298441071882577978102239726)⟩,⟨(-64207984988425438352201537),(-64207984988425434522058172)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-8401516588178732315443656956),(-8401516588178732311455230920)⟩,⟨(-1539741273978731787098121234),(-1539741273978731783151817901)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-7343070682608865698927988619),(-7343070682608865695170451149)⟩,⟨(-3063405158901188323189766363),(-3063405158901188319499054390)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-5474266284153587866928589767),(-5474266284153587863393413864)⟩,⟨(-4132161108820311420201654814),(-4132161108820311416735762429)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-3323152626888767738487567783),(-3323152626888767735432164133)⟩,⟨(-4459614120971712900964115239),(-4459614120971712897963206427)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1399997737377460189846655054),(-1399997737377460187270962994)⟩,⟨(-4066187540118732506037289947),(-4066187540118732503486242061)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-26494213533798503376035734),(-26494213533798501256270946)⟩,⟨(-3207579366427050104060342734),(-3207579366427050101941517493)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨723246636596701960400974656,723246636596701962000194351⟩,⟨(-2212318894333870808875159794),(-2212318894333870807268765474)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨963948063042980348113939274,963948063042980349231692686⟩,⟨(-1336555877068473119570041061),(-1336555877068473118446422613)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨886061805692060518911379886,886061805692060519639422003⟩,⟨(-702245544783637521641557361),(-702245544783637520911971676)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨660281916051573560241435598,660281916051573560679737713⟩,⟨(-314780477763663430779963851),(-314780477763663430343349320)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨393498819204902245750465158,393498819204902245979893216⟩,⟨(-115374308716631678592961184),(-115374308716631678365944881)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨129322919942191481763475897,129322919942191481834198109⟩,⟨(-26540847545935477693376022),(-26540847545935477623711183)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨16617599563208906411858585243,16617599563208906416134976436⟩,⟨2923575146184577178358840196,2923575146184577182588920208⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨47600289735686339245820626376,47600289735686339258348935862⟩,⟨9835475567045654280486363342,9835475567045654292882076591⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨72101406267846285060708674955,72101406267846285080443496850⟩,⟨19350953814319382347877555348,19350953814319382367422279227⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨86932224343479821919565742079,86932224343479821944575151866⟩,⟨31533290628269952696265690603,31533290628269952721072830178⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨90597012639559277876818362461,90597012639559277905793964716⟩,⟨44757369127584519967878740389,44757369127584519996680251715⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨83738799571897283073266712754,83738799571897283106581323011⟩,⟨56312179913811975943767714444,56312179913811975976961004347⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨69028161600899910913856913965,69028161600899910948972469338⟩,⟨63532558864489690619360162686,63532558864489690654474677833⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨50387886917867976734686742452,50387886917867976768611136922⟩,⟨64893466557035104392845547374,64893466557035104426922766807⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨31810901284517536801959669220,31810901284517536832099596895⟩,⟨60525561697105113949854148071,60525561697105113980279912234⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨16284127019325913799518509249,16284127019325913824262310681⟩,⟨51962828389581673481100780716,51962828389581673506201118237⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨5258585770410989384532400959,5258585770410989403449607441⟩,⟨41370871245305700744165419622,41370871245305700763435191293⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1232393605493085338066424910),(-1232393605493085324102778647)⟩,⟨30725044680430413747377395861,30725044680430413761586413283⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-4041481804502129823454734573),(-4041481804502129813742251961)⟩,⟨21304755586543728377879667975,21304755586543728387740925490⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4314099436270803803866249868),(-4314099436270803797169386876)⟩,⟨13593481507174357947191802100,13593481507174357953972330722⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3080564570492662406708438754),(-3080564570492662402652293860)⟩,⟨7450539781443691576243645997,7450539781443691580340932913⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1099761934855644426786009521),(-1099761934855644425436252564)⟩,⟨2360568484258077456519281618,2360568484258077457881191965⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-8374642430143464217957009278),(-8374642430143464209525238333)⟩,⟨(-17737261727457844770573699217),(-17737261727457844761957758765)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-22991600810893747137963461874),(-22991600810893747113098304659)⟩,⟨(-52356200854593834615509410952),(-52356200854593834590133593578)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-31694282850769015447741962218),(-31694282850769015407929017248)⟩,⟨(-84160641453490723957382268719),(-84160641453490723916852561837)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-32145643244315871672469105259),(-32145643244315871620449493281)⟩,⟨(-110819320319289309520538755246),(-110819320319289309467767770015)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-24054747339820577824163230845),(-24054747339820577763987929910)⟩,⟨(-129826170082969924095636464700),(-129826170082969924034872445302)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-9268805369546359167771356459),(-9268805369546359102489271448)⟩,⟨(-139159074341599838583950135076),(-139159074341599838518391261955)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨8777327148959477945320193827,8777327148959478016319641556⟩,⟨(-138055173841311752750998068658),(-138055173841311752680014312994)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨26117359160722966678992492737,26117359160722966750365548942⟩,⟨(-127473271025429140038838356286),(-127473271025429139967738024121)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨39422574590168434417294961858,39422574590168434483187837683⟩,⟨(-109945650872702006457884756781),(-109945650872702006392439269616)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨46816090424355385869223035416,46816090424355385925169104500⟩,⟨(-88856588146752278264770763633),(-88856588146752278209349332843)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨48054978722973887014180400854,48054978722973887058251276818⟩,⟨(-67491986743225370601556754769),(-67491986743225370557997142734)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨44134118527743733317222101710,44134118527743733352411524857⟩,⟨(-48279410528714887134547356589),(-48279410528714887099722876239)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨36614043106366972770507570876,36614043106366972797388010153⟩,⟨(-32463264921104870522162200176),(-32463264921104870495518740824)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨27008295754292011239827022611,27008295754292011258486499893⟩,⟨(-20196853184318509715843193499),(-20196853184318509697333083610)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨16426903407205257400291753377,16426903407205257411180054434⟩,⟨(-10861341260241152388459291226),(-10861341260241152377654163179)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨5498063283228215013066450108,5498063283228215016627826114⟩,⟨(-3405168084448427140007369798),(-3405168084448427136472993926)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-42004943822132436064100859544),(-42004943822132436044807850469)⟩,⟨48831762057719454727496676467,48831762057719454747037014007⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-127346851752210945875987588994),(-127346851752210945818646575991)⟩,⟨139760287568045188057004150627,139760287568045188115003195121⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-215200145717043241530528359397),(-215200145717043241437269158610)⟩,⟨211141109964418519171324730682,211141109964418519265337624699⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-303293000145577652791228750557),(-303293000145577652666565156664)⟩,⟨252802670728920857212330071685,252802670728920857337290028913⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-385170779510234957252500433269),(-385170779510234957104216776648)⟩,⟨259060022667396795638527573908,259060022667396795785889120277⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-451493582182356667944522591608),(-451493582182356667783573669578)⟩,⟨230340692057128113858306954822,230340692057128114016320683621⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-492900042247389525473098969189),(-492900042247389525306149452003)⟩,⟨173610985921840370977131296062,173610985921840371138632687087⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-503284885438863392791981750861),(-503284885438863392628780572426)⟩,⟨100979954019195345971322703408,100979954019195346126846766080⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-482014149971146506962246180414),(-482014149971146506798133506245)⟩,⟨26659740164826225946031396393,26659740164826226102713096638⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-434082676755618240194506748400),(-434082676755618240024603585381)⟩,⟨(-36640069457539000715970677759),(-36640069457539000551072191757)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-368263489678979106092182136970),(-368263489678979105930275061028)⟩,⟨(-80476477103422588092907492161),(-80476477103422587933732406638)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-294246367829036776504757266399),(-294246367829036776362478137259)⟩,⟨(-101674512046060367280524375850),(-101674512046060367139282562389)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-220041907751034491671850309055),(-220041907751034491557206688740)⟩,⟨(-101582344309297068604910793468),(-101582344309297068490245567385)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-150496961450856007811166863905),(-150496961450856007728374078037)⟩,⟨(-84347236723742419741001361797),(-84347236723742419657734680100)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-87059106449232074254359797559),(-87059106449232074204772167166)⟩,⟨(-55162038383607835777390222370),(-55162038383607835727335570756)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-28414380153418497628052203096),(-28414380153418497611621598162)⟩,⟨(-19118132026789840620329055011),(-19118132026789840603714245428)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨35653278322173878877851301276,35653278322173878885564386973⟩,⟨(-39957723033040657719546529550),(-39957723033040657712210282879)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨108597588342147675099982100221,108597588342147675123665080798⟩,⟨(-114500960697919578825593267637),(-114500960697919578802912153488)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨185151514802067161534085069618,185151514802067161575059451097⟩,⟨(-173279703970546368371466432202),(-173279703970546368331785021281)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨264168928288891756426557447773,264168928288891756486382556373⟩,⟨(-207593721789906286394781253389),(-207593721789906286336117564514)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨340506556379197256645819131017,340506556379197256725339236175⟩,⟨(-211905806247455705391229251210),(-211905806247455705312414306694)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨405838164400416755614769521116,405838164400416755713198939070⟩,⟨(-185455829643812656524540948344),(-185455829643812656426288489265)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨450968031956407718047503204476,450968031956407718161612386299⟩,⟨(-133146141651672658855530107476),(-133146141651672658741359415463)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨468841750043883296759943790198,468841750043883296883645088773⟩,⟨(-64950315321729304793013312518),(-64950315321729304669573181371)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨456993538170724756373909008927,456993538170724756499121660383⟩,⟨6316165041654381445359972547,6316165041654381569425947902⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨418345763408921525336796589040,418345763408921525454975598645⟩,⟨68168282715111728118792877290,68168282715111728234682341326⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨360066179858600498974748399905,360066179858600499079382094889⟩,⟨111339434078276420567965967706,111339434078276420669387167698⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨291119277252155952896444191362,291119277252155952991207063684⟩,⟨131330551181928271923181068721,131330551181928272015019077488⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨219642990344638775895163393656,219642990344638775975932318496⟩,⟨128305331691319208726717358697,128305331691319208805337083619⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨151117263628773675938693618962,151117263628773675999797833666⟩,⟨105801249935476443071974930417,105801249935476443131717393102⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨87715087460358728938466964222,87715087460358728976311448307⟩,⟨69098182522575408660004009781,69098182522575408697132586522⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨28670563948886819293877664779,28670563948886819306636580266⟩,⟨23950839438668668700799877798,23950839438668668713343129434⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨62123755234099068809858243781,62123755234099069478544642113⟩,⟨(-33333473322029269421512766322),(-33333473322029268760846302475)⟩⟩ +lemma checked : cachedMomentRuleBox column4_1 kernel1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 1 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_1_contains kernel1_0_contains +end cm4_1_1_0 +namespace cm4_1_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_1 j i k).mul (kernel1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1926107563680712407512115821),(-1926107563680712406655620918)⟩,⟨(-1234562322724135072204162314),(-1234562322724135071357979043)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5178133297921502211043954717),(-5178133297921502208577876961)⟩,⟨(-3897835587226323320531355177),(-3897835587226323318097115915)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-6754629083048833596147400528),(-6754629083048833592406014728)⟩,⟨(-6892685706793563458549906620),(-6892685706793563454860680433)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-6010630917784278819963506546),(-6010630917784278815512262592)⟩,⟨(-9781940438617568302824651701),(-9781940438617568298432632305)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-3032229759320052154644732559),(-3032229759320052150189101088)⟩,⟨(-11632195367352151786913588906),(-11632195367352151782495366642)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1246608622831453888048623912,1246608622831453892446894244⟩,⟨(-11510395666468180249027472822),(-11510395666468180244615353436)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨5326922707954403025980792688,5326922707954403030242677392⟩,⟨(-9105918874465399818730119540),(-9105918874465399814429199233)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨7794808598123811421291550545,7794808598123811424890016590⟩,⟨(-5043745541023883836469479550),(-5043745541023883832868135347)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨7985254062162733986142657847,7985254062162733988889719597⟩,⟨(-631436826295747398175670376),(-631436826295747395516334520)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨6230025591681544359455703821,6230025591681544361751556489⟩,⟨2806041794802856643597138775,2806041794802856645755884137⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3547397470510911170678835352,3547397470510911172645577780⟩,⟨4546125289048803898454423434,4546125289048803900369615564⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1034952863766157795194132859,1034952863766157796684362063⟩,⟨4659138684221295957663802641,4659138684221295959161703290⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-615431646960444272662762605),(-615431646960444271651634029)⟩,⟨3744203788297420167098495467,3744203788297420168136804256⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1244924580985272549094228764),(-1244924580985272548478437981)⟩,⟨2486796546640155203180748073,2486796546640155203819675335⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1062161841682788434628147478),(-1062161841682788434307394635)⟩,⟨1335269572734471408909817484,1335269572734471409243283331⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-404167671795738690665744021),(-404167671795738690567630304)⟩,⟨410249085761259687975468499,410249085761259688077355815⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨10130971422676088939635108047,10130971422676088946171020501⟩,⟨6223848351550690896977372196,6223848351550690903488197385⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨28113673418870674410722321885,28113673418870674429541057928⟩,⟨18794190110986972296184530373,18794190110986972314942576722⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨39830225349085342242782440166,39830225349085342271470103170⟩,⟨31291375918210568156974486835,31291375918210568185603375964⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨42987153609799240461694999895,42987153609799240496392634720⟩,⟨42565683589388873000464563225,42565683589388873035146879818⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨37616244289366307483784762098,37616244289366307519707567769⟩,⟨50680234151308524524533068754,50680234151308524560511970447⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨26018679687073396159254219869,26018679687073396193040392038⟩,⟨53761660879102935514424496032,53761660879102935548346031527⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨11910727412516888239154741138,11910727412516888271503348455⟩,⟨51011843412779458077071246423,51011843412779458109637381629⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-931095204595182185896344593),(-931095204595182157364332286)⟩,⟨43237975530174184645279169155,43237975530174184674103643305⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-9919469774782903544332325005),(-9919469774782903520003729799)⟩,⟨32567115072509599729792214616,32567115072509599754406723789⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-14237352613295032881169930632),(-14237352613295032861219507343)⟩,⟨21550167441007775358701989184,21550167441007775378856834674⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-14594868386051361886945788853),(-14594868386051361872031049999)⟩,⟨12215817271827787958139948528,12215817271827787973179644731⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-12470601650204824131000466629),(-12470601650204824120708305648)⟩,⟨5563631371122673358099879373,5563631371122673368449454378⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-9332001548952319733508923316),(-9332001548952319726641918064)⟩,⟨1614973218750755373286393571,1614973218750755380162378413⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-6174432958072339908739026346),(-6174432958072339904437529716)⟩,⟨(-197250504646687350460526749),(-197250504646687346170870246)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3428068504722959089812459984),(-3428068504722959087489383504)⟩,⟨(-610434598887997754624607388),(-610434598887997752315271287)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1088795365111468337919948337),(-1088795365111468337191206738)⟩,⟨(-279308153581305376617209852),(-279308153581305375894073709)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-32220105357250386486013263299),(-32220105357250386459089037072)⟩,⟨(-93214256643004124489206449842),(-93214256643004124461213930131)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-86264398195563136193079374147),(-86264398195563136113712992746)⟩,⟨(-271804296252909766253186624163),(-271804296252909766170838360641)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-112159834972520065440287114377),(-112159834972520065313592175107)⟩,⟨(-426681852685881052327527479567),(-426681852685881052196675155160)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-100688870990287414467454545915),(-100688870990287414303811866121)⟩,⟨(-543063238489052392155625460022),(-543063238489052391987618141144)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-53817077299447300765135099170),(-53817077299447300568380321465)⟩,⟨(-609396733704908180059782662283),(-609396733704908179859402773112)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨16276174728280128359863588628,16276174728280128600285275707⟩,⟨(-620588277316534568705852015489),(-620588277316534568463155292551)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨91649362604888033418593117270,91649362604888033687219258044⟩,⟨(-580372582500059326782647368237),(-580372582500059326513344795100)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨154801172152229125873095145320,154801172152229126146809193218⟩,⟨(-501115899598641938689633759139),(-501115899598641938416626779472)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨194028596932029507312103769649,194028596932029507566980727436⟩,⟨(-400591459104312440740544853439),(-400591459104312440487248136442)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨205829133094091587187534910170,205829133094091587405293153534⟩,⟨(-297008497655871858564268974670),(-297008497655871858348407898158)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨193869759624633015070423845881,193869759624633015242319883307⟩,⟨(-204511569379673486405065937660),(-204511569379673486234949761773)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨165743973602426811568031757334,165743973602426811697021889686⟩,⟨(-130880169901521217514464414938),(-130880169901521217386706382459)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨129439073314828988816268270469,129439073314828988906767976368⟩,⟨(-77757827608065362885876197136),(-77757827608065362796140771641)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨90948278599407408529238562594,90948278599407408592284640834⟩,⟨(-42499021394315055421542125935),(-42499021394315055358925302343)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨53435044272332192757470413233,53435044272332192796013642878⟩,⟨(-20333520838916786696035892002),(-20333520838916786657699789197)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨17563957084999351156352089020,17563957084999351169235345583⟩,⟨(-5927208919263985851108386470),(-5927208919263985838285651847)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-69260865080286921554402185053),(-69260865080286921508204813149)⟩,⟨65677530878652204664538451606,65677530878652204710003615082⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-207166445173144191142380526861),(-207166445173144191005931354108)⟩,⟨187132042097374791998939661695,187132042097374792133323199052⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-341604438187297152093795233280),(-341604438187297151874564283692)⟩,⟨280320676460660530953901982952,280320676460660531170098985586⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-466361814996945958780917336440),(-466361814996945958492802126865)⟩,⟨331809575160703400336783817703,331809575160703400621405869589⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-571626726249210559969728435020),(-571626726249210559633463259939)⟩,⟨335693018894877782720275431191,335693018894877783053148186783⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-646166484139944126672439346203),(-646166484139944126303862541244)⟩,⟨295074382536273698604218261828,295074382536273698970070517156⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-680947448746823847156753841217),(-680947448746823846754510890924)⟩,⟨221428116779475285025953444268,221428116779475285426683113182⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-672557055193608664044428475432),(-672557055193608663638919981603)⟩,⟨131621166531695263319167143248,131621166531695263724416650284⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-624753267065435795979794301295),(-624753267065435795604750702382)⟩,⟨43415395953640243940591840297,43415395953640244316399592903⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-547399202645315681086546888438),(-547399202645315680768321883172)⟩,⟨(-28906988027676073110554128354),(-28906988027676072790883930420)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-453376928506668931132369558111),(-453376928506668930882275029492)⟩,⟨(-77203492153489711387065741075),(-77203492153489711135209922155)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-354966339887536737956368230516),(-354966339887536737751306624986)⟩,⟨(-99745890012908238064085677800),(-99745890012908237857366081284)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-261134666078181571079735432079),(-261134666078181570917759789319)⟩,⟨(-99592334179560773379267590968),(-99592334179560773215856464001)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-176418905558486876273718431050),(-176418905558486876158122290552)⟩,⟨(-82212045281579903386398722929),(-82212045281579903269668502216)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-101224847640970606481178542848),(-101224847640970606412381778552)⟩,⟨(-53458995587532777201560286106),(-53458995587532777132033073610)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-32904070426222968636301321073),(-32904070426222968613540961709)⟩,⟨(-18466430367369240073151137958),(-18466430367369240050136454098)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨229324772061764752127186640446,229324772061764752206156284838⟩,⟨137164288465332909052187564575,137164288465332909129846510365⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨664301220058930596623854251821,664301220058930596860891346087⟩,⟨421249765771153891235601245091,421249765771153891469199020547⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1029264404818535961918536967232,1029264404818535962315932617170⟩,⟨728919247343569968854750811892,728919247343569969248356529821⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1284259820889568176876013011550,1284259820889568177430373440434⟩,⟨1060073006206465825008176527899,1060073006206465825561155787396⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1401419912875500852262480844470,1401419912875500852957084264813⟩,⟨1396302148054602912895900661426,1396302148054602913594793471938⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1371779235218821705736019122011,1371779235218821706535013924468⟩,⟨1703453293054160075538112587178,1703453293054160076349865706456⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1209625954607585786454681154323,1209625954607585787302357708587⟩,⟨1940569807568631393381081522340,1940569807568631394251355226271⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨951297616897776428204627624189,951297616897776429031450906365⟩,⟨2072252101296016719441097455200,2072252101296016720298739948607⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨647395610530997567972530952890,647395610530997568815765137781⟩,⟨2079556758419498943815333325957,2079556758419498944687429467868⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨350667052114484734824787728328,350667052114484735722524392214⟩,⟨1964967950317802593734003466104,1964967950317802594650460768226⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨104069952654497035689025585647,104069952654497036565232544936⟩,⟨1749772978078883484531413504462,1749772978078883485417408241162⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-66739390179017388622356196536),(-66739390179017387837043243556)⟩,⟨1465732858733754803236663315323,1465732858733754804025424537665⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-154767444067050029057312225273),(-154767444067050028414437414753)⟩,⟨1145113412456218601703681207694,1145113412456218602346308524383⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-168112081270518177519468879028),(-168112081270518177049655337062)⟩,⟨812928405913043790493546999256,812928405913043790961670539352⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-124321100765397173129246622754),(-124321100765397172845636195022)⟩,⟨483343410018835882216014827239,483343410018835882498043662070⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-45356971662786017108116022241),(-45356971662786017013779893787)⟩,⟨160077516857703995336795812140,160077516857703995430516646095⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-151137690692427993860665593382),(-151137690692427993833014643125)⟩,⟨(-121237235378497823965217727374),(-121237235378497823936509525707)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-436127441227048599436820620020),(-436127441227048599351078229431)⟩,⟨(-370650575343072301488506892849),(-370650575343072301400058090790)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-669880479939585247170108314578),(-669880479939585247019241217943)⟩,⟨(-636599431365019373191244817075),(-636599431365019373037176916938)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-822701522136604431490721382406),(-822701522136604431265903397330)⟩,⟨(-918279853976928100982190949412),(-918279853976928100755063496942)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-873439325822109595873546550950),(-873439325822109595568591637415)⟩,⟨(-1200925011483896238826807905951),(-1200925011483896238521289262556)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-814977739556756106384026515294),(-814977739556756105999870273765)⟩,⟨(-1457383180450556319473197903849),(-1457383180450556319089973802397)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-658252118100131300187167973457),(-658252118100131299736117733851)⟩,⟨(-1654675527961516011108240572015),(-1654675527961516010657836939413)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-432151550615239707887738661970),(-432151550615239707395461921981)⟩,⟨(-1763623608918462326723166944375),(-1763623608918462326228432211550)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-178045465328648861061996944705),(-178045465328648860563578289734)⟩,⟨(-1767903438731022544834605502486),(-1767903438731022544328052888831)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨59749268571394572185683636619,59749268571394572653174767499⟩,⟨(-1668791322340689906940171328557),(-1668791322340689906457976647867)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨244122929285790979893408089831,244122929285790980302953950397⟩,⟨(-1483760804740691373448225820913),(-1483760804740691373019023516680)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨352271092723868488185450667092,352271092723868488561508330363⟩,⟨(-1239952333563969931016746245945),(-1239952333563969930623307560321)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨377797822149199978748997608727,377797822149199979075967642292⟩,⟨(-965643487808994926948809535881),(-965643487808994926609310108015)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨328352917694665681032563749971,328352917694665681283954428012⟩,⟨(-683105272128549085949548923772),(-683105272128549085690311290990)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨221002354161381276340753539131,221002354161381276498206149568⟩,⟨(-404898177973737163084939634959),(-404898177973737162923392700005)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨77682664225658333154460857288,77682664225658333207862258199⟩,⟨(-133853032531253194125496513423),(-133853032531253194070865362952)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨26717926088925079141008433348,26717926088925082542311823346⟩,⟨(-35452899493121962013526289136),(-35452899493121958576083825110)⟩⟩ +lemma checked : cachedMomentRuleBox column4_1 kernel1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 1 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_1_contains kernel1_1_contains +end cm4_1_1_1 +namespace cm4_3_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_0 j i k).mul (kernel3_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨23271140269607863033,23271140269607863094⟩,⟨(-27917843948424335705),(-27917843948424335646)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨72309275870983328820,72309275870983328950⟩,⟨(-58502375813528011847),(-58502375813528011719)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨109094271750930147952,109094271750930148110⟩,⟨(-32307029679415152464),(-32307029679415152309)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨97868910459094028856,97868910459094028987⟩,⟨30444455918349702717,30444455918349702852⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨35616353792284734894,35616353792284734982⟩,⟨67595523147600208654,67595523147600208741⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-23574056274708854056),(-23574056274708853982)⟩,⟨44704122446066436870,44704122446066436941⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-31381615153683382588),(-31381615153683382529)⟩,⟨(-1615207159499849627),(-1615207159499849571)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-4755878126060657630),(-4755878126060657583)⟩,⟨(-18732990200676665438),(-18732990200676665393)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨10972420707953700692,10972420707953700731⟩,⟨(-5476020842292609118),(-5476020842292609078)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨5009737912564472159,5009737912564472191⟩,⟨6553491674046143647,6553491674046143679⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-3745627389235636185),(-3745627389235636152)⟩,⟨4595218760778915301,4595218760778915332⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-4235774957496876644),(-4235774957496876617)⟩,⟨(-1481186816821214974),(-1481186816821214947)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-636093275001674932),(-636093275001674911)⟩,⟨(-3389764620465328655),(-3389764620465328629)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1511555146003556564,1511555146003556586⟩,⟨(-2028417979172275923),(-2028417979172275901)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1472434981891180762,1472434981891180781⟩,⟨(-557706089920944060),(-557706089920944044)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨536248303673404484,536248303673404500⟩,⟨(-39143277288305056),(-39143277288305040)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨44916744509365758058515,44916744509365758199075⟩,⟨(-93911824327098466581134),(-93911824327098466440622)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨132185632734585679153382,132185632734585679518596⟩,⟨(-233211537978963970057628),(-233211537978963969692471)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨201348485658235506868066,201348485658235507321242⟩,⟨(-261294401010378808775914),(-261294401010378808322589)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨225962689496769782849943,225962689496769783251031⟩,⟨(-189819578952787107533710),(-189819578952787107132109)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨194798860837967751683626,194798860837967751955793⟩,⟨(-83357311035342496095439),(-83357311035342495822428)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨128152545183290500817917,128152545183290500984087⟩,⟨(-3523208383915047644478),(-3523208383915047477366)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨61538150872936892956447,61538150872936893049456⟩,⟨28479528274177922922266,28479528274177923016033⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨18199820460616454504053,18199820460616454550117⟩,⟨26880688352697744403391,26880688352697744449750⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-270814302953842873275),(-270814302953842850434)⟩,⟨14574834116992849608049,14574834116992849630919⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-4027425171593413616356),(-4027425171593413604385)⟩,⟨4929050970166497772792,4929050970166497784718⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2740761644331574548171),(-2740761644331574542679)⟩,⟨542652941569205969220,542652941569205974673⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1121791075516394908352),(-1121791075516394905834)⟩,⟨(-584398988653076813908),(-584398988653076811408)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-272544562195584053847),(-272544562195584052603)⟩,⟨(-531552011528144901414),(-531552011528144900176)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨11151176166678738184,11151176166678738807⟩,⟨(-289768730732295953488),(-289768730732295952865)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨52834318414854503684,52834318414854503983⟩,⟨(-123046320546483434170),(-123046320546483433870)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨21992633591160479478,21992633591160479576⟩,⟨(-32340228828856299431),(-32340228828856299330)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-26974175890195343448848699),(-26974175890195343420859279)⟩,⟨13809472537890558113676458,13809472537890558141992776⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-74400424222063287980130975),(-74400424222063287902986638)⟩,⟨34950624098833097961211672,34950624098833098039093978⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-104464732580891241664918301),(-104464732580891241556115166)⟩,⟨40710441117974603478942312,40710441117974603588424285⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-112398065360577391099437073),(-112398065360577390969778666)⟩,⟨31276918576002045708094553,31276918576002045838142876⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-100750241345940787133606926),(-100750241345940787002087759)⟩,⟨14209678395982124046174909,14209678395982124177830619⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-77451120167214713864261725),(-77451120167214713750442593)⟩,⟨(-1557939594215480972305711),(-1557939594215480858450814)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-51678532271395394035851907),(-51678532271395393951479387)⟩,⟨(-10829733869244325415040581),(-10829733869244325330644563)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-30064003233749368848210740),(-30064003233749368794419776)⟩,⟨(-13281357902281552420234940),(-13281357902281552366416486)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-15223579364132464876663199),(-15223579364132464846965094)⟩,⟨(-11435125965708623546864214),(-11435125965708623517144040)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-6623484569156429593430513),(-6623484569156429576957505)⟩,⟨(-8104790353463375645441247),(-8104790353463375628959493)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2365940105790382582912582),(-2365940105790382572811336)⟩,⟨(-5042913325752171348234691),(-5042913325752171338133005)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-575392287155942061103240),(-575392287155942055101655)⟩,⟨(-2864978879313269657942870),(-2864978879313269651943033)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨34017463817524687587558,34017463817524690986207⟩,⟨(-1527406187290703028033507),(-1527406187290703024636289)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨162215369608639178307872,162215369608639180129973⟩,⟨(-772447829243362204233326),(-772447829243362202411958)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨125832670185371182297545,125832670185371183176641⟩,⟨(-355002936190716632227123),(-355002936190716631348305)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨44528060559203815898293,44528060559203816158161⟩,⟨(-102201438801690430140064),(-102201438801690429880259)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-256705652986768520774143137),(-256705652986768519546988331)⟩,⟨949175642508993952217473218,949175642508993953458619832⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-762770310121358903636876151),(-762770310121358900155259098)⟩,⟨2663421250647250938360216207,2663421250647250941881756365⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1233482391651214180605731047),(-1233482391651214175463650641)⟩,⟨3880422884783963485361612382,3880422884783963490560595675⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1616899033144264057417991132),(-1616899033144264051523449769)⟩,⟨4438809033287958533499174224,4438809033287958539448222619⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1852192504590648897226820173),(-1852192504590648891535856184)⟩,⟨4359167635727492602843374826,4359167635727492608563034926⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1901445800177404065411854246),(-1901445800177404060348045086)⟩,⟨3807813375263009793398469541,3807813375263009798454685622⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-1772429600941279168711490128),(-1772429600941279164251118333)⟩,⟨3015762359866237658662252590,3015762359866237663092531622⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1515996537203799619181403980),(-1515996537203799615595872005)⟩,⟨2194703257111118761169355737,2194703257111118764729324225⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1202420385805142607825610807),(-1202420385805142604991983585)⟩,⟨1484700993120928465663411855,1484700993120928468487195375⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-894245063439821456918063671),(-894245063439821454873678209)⟩,⟨944391469897635138853162980,944391469897635140898806614⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-630429509734796339212573528),(-630429509734796337847672827)⟩,⟨571459974568278023653360856,571459974568278025024389512⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-425000947072747037660713380),(-425000947072747036783090706)⟩,⟨332589919717110666425850545,332589919717110667309661062⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-274538503209858034311244912),(-274538503209858033756816744)⟩,⟨187444695701244972659369684,187444695701244973217765196⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-167231128394071629166808098),(-167231128394071628842372428)⟩,⟨101479585661311485071209405,101479585661311485397837259⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-89302017400369383199172183),(-89302017400369383032932019)⟩,⟨49596104521904017738821889,49596104521904017906110820⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-27981549013633013344364953),(-27981549013633013293689770)⟩,⟨14811660936055436340149925,14811660936055436391135664⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨4363407442272011520603560666,4363407442272011529133307976⟩,⟨1830190303756201256881786532,1830190303756201265264831008⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨12280153909268600933589830986,12280153909268600958826707218⟩,⟨5766030463218213691540915486,5766030463218213716441329313⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨17964733624622134136759820965,17964733624622134177236739666⟩,⟨10298345861678128944912378489,10298345861678128985115563152⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨20579387571667412426855334425,20579387571667412479182941628⟩,⟨15219178988018406861072571693,15219178988018406913436101188⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨20060440812218839846182547420,20060440812218839904555276197⟩,⟨19811518376082138968239588089,19811518376082139027043596130⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨17071052199534817955268955018,17071052199534818012558474166⟩,⟨23177005100388545232212984543,23177005100388545290113929058⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨12717200527336865913751108010,12717200527336865967092286120⟩,⟨24654756760760499543519765417,24654756760760499597190281680⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨8150652145188366399229200782,8150652145188366444849398980⟩,⟨24088329454473024548475951006,24088329454473024593988463837⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨4234639387325952665951399572,4234639387325952704507901015⟩,⟨21825015773830046362649872148,21825015773830046400851208891⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1395752857843101373225865102,1395752857843101405043933210⟩,⟨18505852966691474635942205595,18505852966691474667456339794⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-330699991436168120590492942),(-330699991436168097381066253)⟩,⟨14800024767447194419024432322,14800024767447194442087398313⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1146874842625217427160065376),(-1146874842625217411358688321)⟩,⟨11215175194444836773026411961,11215175194444836788817053956⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1332132204168511049753438110),(-1332132204168511038013241304)⟩,⟨8029350796835732830881863102,8029350796835732842668137635⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1137056559387464097382509165),(-1137056559387464089115847617)⟩,⟨5316513281876443007579364517,5316513281876443015893607447⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-741225038607065826896528196),(-741225038607065822081074503)⟩,⟨3011599332468417378701070093,3011599332468417383546344332⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-255275892039417090131355668),(-255275892039417088562210379)⟩,⟨972971330148672398799443766,972971330148672400378362083⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨89764098667737743323088768,89764098667737743346443827⟩,⟨(-19448189207597132411724910),(-19448189207597132391290417)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1295628543752941456244003944,1295628543752941456599435290⟩,⟨(-260906851590140823505411215),(-260906851590140823190166205)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨5204339756695836618442670140,5204339756695836620005964626⟩,⟨(-903837379685404961483072637),(-903837379685404960064955489)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨12489296297677964853376094679,12489296297677964857601496297⟩,⟨(-1682035871709090219268455447),(-1682035871709090215329159550)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨22542531634698146660823373840,22542531634698146669593995198⟩,⟨(-1954255008130333394603999747),(-1954255008130333386170222133)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨33666707948426668061260496903,33666707948426668076334574563⟩,⟨(-1085851243326735845083357482),(-1085851243326735830242724020)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨43674825305860223290929895428,43674825305860223313084035857⟩,⟨1141382789264854357668062189,1141382789264854379779569610⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨50641531998293247456616397231,50641531998293247484874817058⟩,⟨4361773035968878837376273461,4361773035968878865696963431⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨53476372980274756732812398224,53476372980274756764381214241⟩,⟨7786200739722176832792729809,7786200739722176864293276850⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨52101723443071105708658399670,52101723443071105739756568441⟩,⟨10555535062736107422008798258,10555535062736107452682611793⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨47240787828930165782015687687,47240787828930165809886871156⟩,⟨12061709580297294053892560866,12061709580297294080938759850⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨39999462201512442693044297990,39999462201512442719697665241⟩,⟨12085944469337094267784844620,12085944469337094293574995975⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨31462197381048032230990347624,31462197381048032254716123704⟩,⟨10747798207953921530899303820,10747798207953921553950988698⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨22438400265865398471700448233,22438400265865398490301476782⟩,⟨8356613354962947222365319329,8356613354962947240552045881⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨13382635231762034355382792916,13382635231762034367244691381⟩,⟨5267055332926049408071217509,5267055332926049419731852338⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨4439354647316816021599004598,4439354647316816025648052519⟩,⟨1794985814752769929226677319,1794985814752769933217396636⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨88799173420841823023800405780,88799173420841823153198027892⟩,⟨50974760734298041962986389552,50974760734298042091625827648⟩⟩ +lemma checked : cachedMomentRuleBox column4_0 kernel3_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 3 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_0_contains kernel3_0_contains +end cm4_3_0_0 +namespace cm4_3_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_0 j i k).mul (kernel3_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-282150618485464574395),(-282150618485464573914)⟩,⟨128144963703833762240,128144963703833762725⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-772897863090790993575),(-772897863090790992352)⟩,⟨187686555728759470617,187686555728759471839⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-968971502600035476493),(-968971502600035475034)⟩,⟨(-135630166834910843391),(-135630166834910841928)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-675807675102973299024),(-675807675102973297831)⟩,⟨(-576658809404074612162),(-576658809404074610956)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-72678941221795651758),(-72678941221795650967)⟩,⟨(-664689004152094687900),(-664689004152094687102)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨328825897931553591647,328825897931553592256⟩,⟨(-302762972160129243863),(-302762972160129243266)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨263543154584342813024,263543154584342813495⟩,⟨97179260206854816808,97179260206854817266⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1778546362945624499),(-1778546362945624174)⟩,⟨174471362703124746448,174471362703124746774⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-108193814401024447570),(-108193814401024447306)⟩,⟨27507917712561112634,27507917712561112897⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-35136434640695759578),(-35136434640695759382)⟩,⟨(-66906918981258744752),(-66906918981258744554)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨39511434756392211781,39511434756392211959⟩,⟨(-37593072936830627897),(-37593072936830627717)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨37705343306113628393,37705343306113628530⟩,⟨17024257909878568042,17024257909878568175⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨4146710494262110573,4146710494262110673⟩,⟨31547770837470975981,31547770837470976076⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-14479088905266461688),(-14479088905266461617)⟩,⟨18297872592129822883,18297872592129822949⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-13631865559855067125),(-13631865559855067079)⟩,⟨4988190768830373557,4988190768830373605⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-4942769934708731650),(-4942769934708731625)⟩,⟨349519840626685535,349519840626685559⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-705148125176495557057620),(-705148125176495555882431)⟩,⟨232277430022670881486178,232277430022670882657235⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1857276650500994945370439),(-1857276650500994942287870)⟩,⟨482720838052593420117981,482720838052593423191780⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-2360430052408160404895344),(-2360430052408160400994936)⟩,⟨295389169563993687950099,295389169563993691844042⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-2144958773676744132851969),(-2144958773676744129291694)⟩,⟨(-160477943412828825599055),(-160477943412828822039389)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1471680853802181435113449),(-1471680853802181432583684)⟩,⟨(-533337264288752680096045),(-533337264288752677563131)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-736709276183305481498761),(-736709276183305479826638)⟩,⟨(-618888203366195245132177),(-618888203366195243457417)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-220943149771181880886695),(-220943149771181879901602)⟩,⟨(-468308775975378530440743),(-468308775975378529455625)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨17332828773071897364713,17332828773071897833417⟩,⟨(-251826558772871527533052),(-251826558772871527066249)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨69653078875737759807967,69653078875737760032671⟩,⟨(-92026238497881809579875),(-92026238497881809357017)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨49102224648694903037579,49102224648694903160081⟩,⟨(-14740085045723543679524),(-14740085045723543557652)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨21356017425806292873353,21356017425806292933753⟩,⟨8141845073717067585712,8141845073717067646025⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨5594935144780356757632,5594935144780356783965⟩,⟨8868585646866521745905,8868585646866521772212⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-130031336491449350701),(-130031336491449338134)⟩,⟨5003959198554213973112,5003959198554213985670⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1208179209514643846637),(-1208179209514643840033)⟩,⟨2130909555755417267163,2130909555755417273763⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-867133106828485999473),(-867133106828485996253)⟩,⟨735713714006612073103,735713714006612076322⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-288975308138301375111),(-288975308138301374153)⟩,⟨165470496101550010426,165470496101550011386⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨147117561807182349951144896,147117561807182350157326755⟩,⟨98650177449623214305527795,98650177449623214512093334⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨392320934304838612256651248,392320934304838612821791931⟩,⟨280436235824936726052020272,280436235824936726618592314⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨515119185567098252071696623,515119185567098252861164624⟩,⟨416621644143065904014356495,416621644143065904806559141⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨500964560276878273075099690,500964560276878274017164401⟩,⟨484164674082056455734370577,484164674082056456679611718⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨390405779921410940010088463,390405779921410940973488506⟩,⟨476256390068369691685903872,476256390068369692651763614⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨247027105926612829614638399,247027105926612830458338564⟩,⟨407344041519462293661386965,407344041519462294506308877⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨122635241434454473984099676,122635241434454474618887296⟩,⟨306957711459919118919652698,306957711459919119554504505⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨40464896726016341643664867,40464896726016342055091228⟩,⟨205772345457126542463417103,205772345457126542874216267⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1146364756145466106921672),(-1146364756145465876238097)⟩,⟨123879014112900910640516544,123879014112900910870383769⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-15517583312985299669046522),(-15517583312985299536426704)⟩,⟨67671070558110848203224350,67671070558110848335139185⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16272532465638867602438754),(-16272532465638867516406277)⟩,⟨33924750192675956740364958,33924750192675956825903350⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-12377016539235930121780039),(-12377016539235930069130411)⟩,⟨15791506759123049312623495,15791506759123049365035450⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-8096296544461908148929237),(-8096296544461908118513257)⟩,⟨6898452530830515156260852,6898452530830515186579689⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4772918716789754276041628),(-4772918716789754259467409)⟩,⟨2842752578727189406067799,2842752578727189422604361⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2444220801666486791862995),(-2444220801666486783774102)⟩,⟨1076675726900092183056488,1076675726900092191131808⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-745278179986473391461756),(-745278179986473389056568)⟩,⟨272512235146538366111159,272512235146538368512986⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨4777901696762721190093424210,4777901696762721197101635427⟩,⟨(-256318173256628145259944531),(-256318173256628138284447237)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨13513678797861562997796560599,13513678797861563017598767350⟩,⟨(-566726794851625746359625705),(-566726794851625726639289128)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨20002362032962689570050336540,20002362032962689599063696531⟩,⟨(-384163608007663074764234954),(-384163608007663045827422460)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨23427647671674831941397052222,23427647671674831974264010758⟩,⟨312126232117738039353676138,312126232117738072240151699⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨23739597231869263223591454623,23739597231869263254883795976⟩,⟨1285433726283377180847065689,1285433726283377212339809325⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨21560155819690175704615585277,21560155819690175732137509524⟩,⟨2193984460091068131654407012,2193984460091068159536221543⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨17886635160657052650829815706,17886635160657052674504851935⟩,⟨2770109382049530758541132338,2770109382049530782548717556⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨13735821370945755211865026408,13735821370945755230627610870⟩,⟨2918716303248032110469338373,2918716303248032129431005457⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨9875689361419225172197316567,9875689361419225187931336113⟩,⟨2704777445627090963372164657,2704777445627090979165637591⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨6721130219760975685519813033,6721130219760975698607728295⟩,⟨2273986080289690179902540636,2273986080289690192977883708⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4376460148628498367164486923,4376460148628498376918441360⟩,⟨1771415232117293290000801077,1771415232117293299733022386⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2750949421306165267633642145,2750949421306165274268109896⟩,⟨1296296268152727321695973650,1296296268152727328318449728⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1674140824481304283531316608,1674140824481304287722103571⟩,⟨894753160178540180796359170,894753160178540184983795692⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨972302165480615256070988047,972302165480615258527171673⟩,⟨573414680751327923252669622,573414680751327925709514753⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨502068704503461734915919603,502068704503461736177168590⟩,⟨316993375226800503462422343,316993375226800504725091997⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨154598659082292835650095467,154598659082292836035094464⟩,⟨101089190650604002268633161,101089190650604002654248630⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨4394909054439312158479817413,4394909054439312197603398680⟩,⟨(-19131112650015688942961105535),(-19131112650015688903358087648)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨14791705874240748094403706394,14791705874240748210367950443⟩,⟨(-54466586617959341502646739457),(-54466586617959341385608920789)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨29039783897087600727903557740,29039783897087600914397094452⟩,⟨(-81613464369868321580766950107),(-81613464369868321393462946076)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨47047315114783974394407484209,47047315114783974635962515839⟩,⟨(-97157542249082447579111498517),(-97157542249082447337754981157)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨66261187072097233696976390497,66261187072097233966195098227⟩,⟨(-100234582698502933272925867937),(-100234582698502933004980202878)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨82815701670521616595072319840,82815701670521616857493149251⟩,⟨(-92566995452578021840400270258),(-92566995452578021579314175783)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨93238693797892207425704055812,93238693797892207668602133823⟩,⟨(-77719214509923208937862943118),(-77719214509923208694625090060)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨95785477405966508302235555962,95785477405966508509542965885⟩,⟨(-59858427500598614519013359825),(-59858427500598614309338944653)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨90818336289921257857628792420,90818336289921258031807985527⟩,⟨(-42548027222492509338487018678),(-42548027222492509161341951042)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨80266671450240077144693213746,80266671450240077286446398078⟩,⟨(-28035400741307870725338418443),(-28035400741307870581582958371)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨66652120203754961255640433910,66652120203754961365750018335⟩,⟨(-17172937403155375111912896384),(-17172937403155375001104325230)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨52217728609788084555321963515,52217728609788084643030138774⟩,⟨(-9785639365579812314235621909),(-9785639365579812226647779357)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨38456045257837990401967779505,38456045257837990471290070337⟩,⟨(-5173282617083843191422370836),(-5173282617083843122361531573)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨26037812823486847992937633502,26037812823486848041427054799⟩,⟨(-2512566744896556047337003127),(-2512566744896555999039811646)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨14979682421170530884166238042,14979682421170530912305464505⟩,⟨(-1075650462899745693031215716),(-1075650462899745664992990776)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨4878160962244696197516206406,4878160962244696206669292500⟩,⟨(-290925386736833845371134041),(-290925386736833836248038722)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-87375308108474642124728797),(-87375308108474642046545694)⟩,⟨(-320687011177069756375263851),(-320687011177069756286505573)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1202813657492412864901933424),(-1202813657492412863690960947)⟩,⟨(-4641736128786376165993688844),(-4641736128786376164637925269)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-4405930585431642284450831273),(-4405930585431642278964413893)⟩,⟨(-18745021490182325674894281013),(-18745021490182325668889843482)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-9131030614585921837066291673),(-9131030614585921821676136821)⟩,⟨(-45348299568967964592121059556),(-45348299568967964575726600077)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-13261146538382838766167157478),(-13261146538382838732834472189)⟩,⟨(-82742650787086504090422647202),(-82742650787086504055938672525)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-14311978338488976012137089061),(-14311978338488975952707961963)⟩,⟨(-125258537154647162951661592813),(-125258537154647162891478212041)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-10855986540762117643014007095),(-10855986540762117553219813174)⟩,⟨(-165123184507601934106837273047),(-165123184507601934016921659710)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-3303118598848523835626568697),(-3303118598848523718984804405)⟩,⟨(-194976156620406501313372282857),(-194976156620406501196767961875)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨6347079190132947374802564232,6347079190132947506261239733⟩,⟨(-209997848198982561959887179702),(-209997848198982561827586403407)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨15485221344108939832941137561,15485221344108939962370732907⟩,⟨(-208849632754377215339612996175),(-208849632754377215207552346362)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨21944297117956838495838709173,21944297117956838611011498193⟩,⟨(-193275839810864740203354953784),(-193275839810864740083707015739)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨24597556727758845217512683704,24597556727758845329972328829⟩,⟨(-166838260137218021293960096557),(-166838260137218021177135067306)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨23379655528829900497424309417,23379655528829900603757506830⟩,⟨(-133490684519764265691533387946),(-133490684519764265582285272561)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨18940553702214840093656881648,18940553702214840179997902882⟩,⟨(-96532636815572998194613599261),(-96532636815572998106634402038)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨12230656220183286448915170439,12230656220183286504593027911⟩,⟨(-58139165872675487872737404340),(-58139165872675487816283127138)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨4215567780224758607129432156,4215567780224758626240773446⟩,⟨(-19383926571811324501161861358),(-19383926571811324481828449267)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨174369837132910846361468121345,174369837132910846954895267669⟩,⟨(-398645547049271334553884003021),(-398645547049271333955506887369)⟩⟩ +lemma checked : cachedMomentRuleBox column4_0 kernel3_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 3 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_0_contains kernel3_1_contains +end cm4_3_0_1 +namespace cm4_3_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_1 j i k).mul (kernel3_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨30649435229562659783,30649435229562659847⟩,⟨(-48521900362869329856),(-48521900362869329788)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨99281853966508481716,99281853966508481864⟩,⟨(-107904974136094372923),(-107904974136094372775)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨159734627783315216297,159734627783315216478⟩,⟨(-80035320691252498914),(-80035320691252498732)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨159238296673266704182,159238296673266704339⟩,⟨13097334803325414236,13097334803325414391⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨80931009553322997793,80931009553322997896⟩,⟨85444022299552325487,85444022299552325590⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-11446071573215039631),(-11446071573215039542)⟩,⟨75617892390349702504,75617892390349702595⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-43615986886740673957),(-43615986886740673876)⟩,⟨15905021204437959976,15905021204437960053⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-18199496298378296696),(-18199496298378296638)⟩,⟨(-20902354095506437226),(-20902354095506437168)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨9258999739423222088,9258999739423222131⟩,⟨(-14245987233813514162),(-14245987233813514119)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨10426610663999481886,10426610663999481922⟩,⟨3552963775633134112,3552963775633134142⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-332624638551377172),(-332624638551377140)⟩,⟨7622682846888353782,7622682846888353817⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-5249318326178530076),(-5249318326178530044)⟩,⟨1891919653730043229,1891919653730043258⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-3263307487762866208),(-3263307487762866185)⟩,⟨(-2584203846982141844),(-2584203846982141815)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-296561752995289608),(-296561752995289584)⟩,⟨(-2967024195288297389),(-2967024195288297366)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨798433486028594345,798433486028594364⟩,⟨(-1642053882143349176),(-1642053882143349155)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨414104509951647641,414104509951647657⟩,⟨(-459203582886511976),(-459203582886511959)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨36986701286058151378902,36986701286058151469134⟩,⟨(-77741197723620465879580),(-77741197723620465789127)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨107368021832115607506077,107368021832115607741588⟩,⟨(-193967606493737089868254),(-193967606493737089632149)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨160850183933038141938321,160850183933038142233534⟩,⟨(-220314076150875202063954),(-220314076150875201768011)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨178856646622038631734379,178856646622038632000447⟩,⟨(-165808227045197228436428),(-165808227045197228169842)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨154882232218426686104600,154882232218426686290259⟩,⟨(-81115790483168435364105),(-81115790483168435178440)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨104445606166955408223594,104445606166955408330625⟩,⟨(-14712167904795211052435),(-14712167904795210945923)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨53321183077076527901130,53321183077076527962913⟩,⟨15504068402805325100916,15504068402805325162073⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨18680518261734300934958,18680518261734300966095⟩,⟨18667773570548220875684,18667773570548220906517⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨2479757725710682413964,2479757725710682429905⟩,⟨11494949700948132079144,11494949700948132095048⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-2049090532930764149140),(-2049090532930764140296)⟩,⟨4652531619746670475388,4652531619746670484260⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1935031304594847249352),(-1935031304594847244984)⟩,⟨1062006476128097387354,1062006476128097391733⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-978415101911722845023),(-978415101911722842938)⟩,⟨(-139628438016247755587),(-139628438016247753506)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-343702046766945233143),(-343702046766945232207)⟩,⟨(-308689197637199312045),(-308689197637199311112)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-75691129045443340066),(-75691129045443339653)⟩,⟨(-209057982780376159328),(-209057982780376158914)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨587518636526027623,587518636526027809⟩,⟨(-102034566083273457937),(-102034566083273457748)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5619358600019003321,5619358600019003384⟩,⟨(-29167513268091365255),(-29167513268091365193)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-47030466100671349677979504),(-47030466100671349641192895)⟩,⟨33662097825428512144857156,33662097825428512181099472⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-128604260611209430296217622),(-128604260611209430195038167)⟩,⟨89063523328655195725685960,89063523328655195825438038⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-177983780091824912365407898),(-177983780091824912224838928)⟩,⟨115105230975351137930046827,115105230975351138068836995⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-188615570025145391411448780),(-188615570025145391264099089)⟩,⟨109284365469714675362051388,109284365469714675507791623⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-167464572784646547741149665),(-167464572784646547605466049)⟩,⟨82399226237814419933755504,82399226237814420068344635⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-129145910896271510490228112),(-129145910896271510366367684)⟩,⟨49866494214801162377914337,49866494214801162501262933⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-88227639967222511670879363),(-88227639967222511572310396)⟩,⟨23186260251616699620964606,23186260251616699719373113⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-54135954961370905915753434),(-54135954961370905846956600)⟩,⟨6619105838448226191376380,6619105838448226260149652⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-30192809197015175770889622),(-30192809197015175728174659)⟩,⟨(-1117194431405864695195040),(-1117194431405864652475408)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-15489280744337051234588580),(-15489280744337051210547063)⟩,⟨(-3396652797858916204647720),(-3396652797858916180603544)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-7402691921121280184830260),(-7402691921121280172280925)⟩,⟨(-3203892482395800130739906),(-3203892482395800118190887)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-3340776309950187189605718),(-3340776309950187183322236)⟩,⟨(-2306856780410420713860645),(-2306856780410420707578096)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1442372286751646191913968),(-1442372286751646188852174)⟩,⟨(-1454567448404440158414703),(-1454567448404440155353817)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-599965630219890294851184),(-599965630219890293239771)⟩,⟨(-836067088986654299847991),(-836067088986654298237083)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-233407002073364468485694),(-233407002073364467665639)⟩,⟨(-421340943477936740852612),(-421340943477936740032742)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-60652291494504870146580),(-60652291494504869897540)⟩,⟨(-127478404649850756296242),(-127478404649850756047250)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨242488392609262838544176515,242488392609262839067389051⟩,⟨905948221873784578281149019,905948221873784578810296686⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨663029733796499475255100253,663029733796499476763599072⟩,⟨2545031364992157585464388810,2545031364992157586989406279⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨916478095936587611065305030,916478095936587613363975760⟩,⟨3717704387765949450112458808,3717704387765949452434384899⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨966369560833579783799086732,966369560833579786559751601⟩,⟨4273027408991951947771423012,4273027408991951950556664433⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨845996323285865998173388135,845996323285866001036936427⟩,⟨4229365473257216316827322833,4229365473257216319710111595⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨630816714253708970054303514,630816714253708972876420727⟩,⟨3739094890790698079427178471,3739094890790698082258714780⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨399804180085978369789821556,399804180085978372420835747⟩,⟨3013545709411036251758613892,3013545709411036254392819290⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨207408525774757355084047494,207408525774757357271469277⟩,⟨2247009149068472854845907112,2247009149068472857033310227⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨75431369151899652932234535,75431369151899654553713861⟩,⟨1570134272250116722917911210,1570134272250116724538401341⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨574667198426219132010934,574667198426220212368205⟩,⟨1041023137753273318465691399,1041023137753273319545080776⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-32461166889746800437474345),(-32461166889746799775464157)⟩,⟨662720649965011698280477031,662720649965011698941721816⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-40337505410741205531033573),(-40337505410741205073580489)⟩,⟨409040855245901915804101409,409040855245901916260861493⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-35729649398340263301320994),(-35729649398340262981338324)⟩,⟨245566589440380978906072579,245566589440380979225545184⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-26281184617362978752638494),(-26281184617362978548888058)⟩,⟨141314536405615471962656526,141314536405615472166056040⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-15678732711027317827747977),(-15678732711027317716652782)⟩,⟨72575440739704536537373426,72575440739704536648265316⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-5174603485604849121883781),(-5174603485604849086881055)⟩,⟨22292952787467127073098631,22292952787467127108033738⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨14483285971148781863399473111,14483285971148781871657962557⟩,⟨5934282742228981255674251803,5934282742228981263832835376⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨41338241258280839806862838717,41338241258280839831314331466⟩,⟨17377490404871015066351527192,17377490404871015090551530276⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨62333773880618844090538562211,62333773880618844129882040313⟩,⟨27502528062085169544568219522,27502528062085169583653365325⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨75135245348547540360834104703,75135245348547540412217615985⟩,⟨35419645434961687137248255615,35419645434961687188560428598⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨79217845424195986557267354401,79217845424195986615905269188⟩,⟨40384690444261865080820398227,40384690444261865139736556277⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨75738409277522651661186727951,75738409277522651721295778321⟩,⟨42029910687371348844322533125,42029910687371348905001032638⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨66951837303596994400748005941,66951837303596994455923050931⟩,⟨40522890007112796775656307499,40522890007112796831441926264⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨55440277155060907853154395127,55440277155060907898166710614⟩,⟨36539296743618953627066731606,36539296743618953672482030618⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨43447842117227763727326055163,43447842117227763765213387106⟩,⟨31051282639951579353420024172,31051282639951579391379556904⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨32507856983038195023596992205,32507856983038195057028302229⟩,⟨25041442644793830029458712527,25041442644793830062784838443⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨23386027781661985551182578106,23386027781661985577871412038⟩,⟨19274341579852819266817449952,19274341579852819293395076793⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨16238268357393949920997380161,16238268357393949940566228801⟩,⟨14197424932712421983472647214,14197424932712422002984383197⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨10844857794564463803737959098,10844857794564463817384802948⟩,⟨9962004221311212674395521045,9962004221311212688038852411⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6816951396507176630369118524,6816951396507176639246149155⟩,⟨6508177135977637370712806940,6508177135977637379610230622⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨3730069662336756833742921595,3730069662336756838659063024⟩,⟨3656927249514855624481953070,3656927249514855629418476653⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1184395265527410299032085908,1184395265527410300593768828⟩,⟨1177019494478434356999814150,1177019494478434358569412223⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-7799800696758980049637923538),(-7799800696758980041614760307)⟩,⟨(-35799593948616078086430081395),(-35799593948616078077502782195)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-21193844399072644067417846669),(-21193844399072644042607735722)⟩,⟨(-104144061972849753521339070903),(-104144061972849753493971947329)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-28658203579927734836401171803),(-28658203579927734793015337619)⟩,⟨(-163007214836733190412145839008),(-163007214836733190365074760894)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-28345627728059619190021653550),(-28345627728059619126238557338)⟩,⟨(-207402671360326224156942851871),(-207402671360326224089179579441)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-20726564748041957095792256348),(-20726564748041957010385974157)⟩,⟨(-234259661948910125092179521331),(-234259661948910125003753274081)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-8212939006702629841664581560),(-8212939006702629737151296570)⟩,⟨(-242933310160648043034878714761),(-242933310160648042928849742927)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨5837375282977866242389788826,5837375282977866358905650455⟩,⟨(-235231998934755065710323215991),(-235231998934755065593577891656)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨18273330404662718140812096824,18273330404662718258778029657⟩,⟨(-214873006209446141260567743036),(-214873006209446141142923734638)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨26994045968071497988279156215,26994045968071498096569766435⟩,⟨(-186512610673170374951085781236),(-186512610673170374842859645777)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨31234909863331912046012811216,31234909863331912136185121723⟩,⟨(-154686095557824472166228291625),(-154686095557824472075401568106)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨31344347523576930857572017966,31344347523576930927576925274⟩,⟨(-122999522807482409280303905096),(-122999522807482409208966249695)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨28296276321988160974102007577,28296276321988161034200500039⟩,⟨(-93753021749826038653471659708),(-93753021749826038592033392825)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨23204622033956077610389636587,23204622033956077659928794209⟩,⟨(-67968340535200090142281279761),(-67968340535200090091744916590)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨17000724539788025492348629981,17000724539788025529141955904⟩,⟨(-45661861713896794151503532209),(-45661861713896794114115636105)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨10305193609255462339387043094,10305193609255462362050778538⟩,⟨(-26186216924752309264412937327),(-26186216924752309241463334842)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3444705599461907379577809112,3444705599461907387182186647⟩,⟨(-8519528677991396995574113784),(-8519528677991396987887365705)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨115591218923131258225918733152,115591218923131258479510652474⟩,⟨(-293004724905877638993912180082),(-293004724905877638736669141335)⟩⟩ +lemma checked : cachedMomentRuleBox column4_1 kernel3_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 3 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_1_contains kernel3_0_contains +end cm4_3_1_0 +namespace cm4_3_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_1 j i k).mul (kernel3_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-415157745183835092577),(-415157745183835092004)⟩,⟨259020383053914414006,259020383053914414580⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1162056959489169949295),(-1162056959489169947828)⟩,⟨470867977894964163623,470867977894964165094⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1535223905246277944634),(-1535223905246277942843)⟩,⟨57626525383612462989,57626525383612464781⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1223832976180375583416),(-1223832976180375581893)⟩,⟨(-647860774177257769560),(-647860774177257768042)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-384119513485865114046),(-384119513485865113061)⟩,⟨(-955435468174184305193),(-955435468174184304206)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨319211534849684891720,319211534849684892548⟩,⟨(-596166770456675084213),(-596166770456675083382)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨414408003378241066483,414408003378241067181⟩,⟨(-19823057301504058061),(-19823057301504057365)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨110486523233024007181,110486523233024007646⟩,⟨224407532196079932935,224407532196079933403⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-109880483518536484458),(-109880483518536484161)⟩,⟨108797218241534777331,108797218241534777624⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-88654812298797976022),(-88654812298797975836)⟩,⟨(-48160259150450089827),(-48160259150450089640)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨11879625684989266885,11879625684989267074⟩,⟨(-69165585556132456018),(-69165585556132455833)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨49732767862798767956,49732767862798768106⟩,⟨(-13129917660979680081),(-13129917660979679928)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨28751706410733367582,28751706410733367699⟩,⟨25454371400196751207,25454371400196751325⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1939792399112958140,1939792399112958230⟩,⟨27434396216496689988,27434396216496690081⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7531323885561333844),(-7531323885561333788)⟩,⟨15054191637587105205,15054191637587105262⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-3825904944596410078),(-3825904944596410048)⟩,⟨4223249368849243146,4223249368849243177⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-582761691102185416031116),(-582761691102185415217618)⟩,⟨193290143568540689156036,193290143568540689972205⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1531899517586259964076799),(-1531899517586259961937075)⟩,⟨414724225618790940487186,414724225618790942632737⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1944894841302182242327078),(-1944894841302182239603191)⟩,⟨294764071931847602953159,294764071931847605681644⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1776948542265390223948702),(-1776948542265390221435459)⟩,⟨(-45823470997975669131874),(-45823470997975666617519)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1244932955015656180980489),(-1244932955015656179168922)⟩,⟨(-343918851052052396568054),(-343918851052052394757720)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-659393682799348702697757),(-659393682799348701603648)⟩,⟨(-437885716688261132793368),(-437885716688261131700525)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-236369975815740087294394),(-236369975815740086641095)⟩,⟨(-351997073514308751707767),(-351997073514308751054571)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-24967608794206685777127),(-24967608794206685455327)⟩,⟨(-203805139922865748807139),(-203805139922865748484423)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨37687264955555158465285,37687264955555158627975⟩,⟨(-85121395440664558156900),(-85121395440664557993209)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨34646949089374715530957,34646949089374715624655⟩,⟨(-21812038684685750777230),(-21812038684685750683176)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨18024380025631900247136,18024380025631900295755⟩,⟨1041822485631027956579,1041822485631028005217⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨6424271194569023135059,6424271194569023157676⟩,⟨5084033428412241335125,5084033428412241357715⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1288211964482728886914,1288211964482728896753⟩,⟨3650373778108043162367,3650373778108043172198⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-243364440311235567277),(-243364440311235562877)⟩,⟨1862275904004025339950,1862275904004025344355⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-390404938237802800483),(-390404938237802798552)⟩,⟨773567487507199395690,773567487507199397623⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-151824166106371953936),(-151824166106371953387)⟩,⟨202271766568927385912,202271766568927386463⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨305483419699383017091632944,305483419699383017374995877⟩,⟨144798903319083108820592896,144798903319083109104278500⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨824739582109353617008880579,824739582109353617790130579⟩,⟨402526887319446884958103988,402526887319446885739923755⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1112304167368727052671630481,1112304167368727053761877960⟩,⟨575669204240408617328910779,575669204240408618419241859⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1133065209371922113609573080,1133065209371922114758412227⟩,⟨640607062570067487139616398,640607062570067488287808379⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨952772458431978066032242789,952772458431978067100744177⟩,⟨606588782693376442625383544,606588782693376443692847456⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨684270569264546000706809391,684270569264546001702866195⟩,⟨506290358643684974266325825,506290358643684975261495444⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨426574143463132121857222191,426574143463132122668291296⟩,⟨379526022780607557660872571,379526022780607558471870497⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨232498546959829126387423365,232498546959829126967329173⟩,⟨258831188564191079728220398,258831188564191080308806908⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨110653692297741674653354957,110653692297741675022339627⟩,⟨162435431898084615831979997,162435431898084616201923925⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨45205668228799971035115243,45205668228799971247823423⟩,⟨94949233282504304356180442,94949233282504304569726617⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨14866303847956133644118260,14866303847956133757643719⟩,⟨52408416929613623336128143,52408416929613623450216549⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2878975701232072309901034,2878975701232072367653665⟩,⟨27722850857402601247426587,27722850857402601305444564⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-878922422000089703451341),(-878922422000089674974599)⟩,⟨14233496785134362876549297,14233496785134362905133041⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1468614643443967146169204),(-1468614643443967130950484)⟩,⟨7092141652807733162346970,7092141652807733177607103⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1039855919421756772278048),(-1039855919421756764425262)⟩,⟨3253422303955284618775456,3253422303955284626643510⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-358945134942819324136456),(-358945134942819321735357)⟩,⟨938589585424999929724241,938589585424999932129157⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3819186318468180608559476874,3819186318468180611616947961⟩,⟨(-2498171221979726307321439275),(-2498171221979726304290890101)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨10769957832104935355174530527,10769957832104935363978757520⟩,⟨(-6989996542639193998130582850),(-6989996542639193989401402387)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨15852034391564028987182468189,15852034391564029000576621417⟩,⟨(-10131145218057369749671539482),(-10131145218057369736384914776)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨18426331190675138247676315486,18426331190675138263750016586⟩,⟨(-11512014726675755708028546170),(-11512014726675755692074888971)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨18511210879168402375141696797,18511210879168402391864576278⟩,⟨(-11225463462142867309104535581),(-11225463462142867292492898488)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨16668731497436665267773235696,16668731497436665284446830122⟩,⟨(-9741087770559574423185272130),(-9741087770559574406595631043)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨13729788621640875697722800104,13729788621640875713397959420⟩,⟨(-7672702887013255078885799020),(-7672702887013255063261039162)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨10496682289433225239949300493,10496682289433225253126377135⟩,⟨(-5560681214655366154629005274),(-5560681214655366141477931515)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨7543027730866747439774915213,7543027730866747449852144250⟩,⟨(-3750476646442681089677421353),(-3750476646442681079611834693)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨5156071792555075140780608582,5156071792555075148047193388⟩,⟨(-2379922926813271980625042919),(-2379922926813271973365014427)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3389568695623493699065603519,3389568695623493703849608394⟩,⟨(-1436585169857096615371161831),(-1436585169857096610594443063)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2160871311928207359226259501,2160871311928207362682320376⟩,⟨(-833453481420131921674673745),(-833453481420131918223692476)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1337539566524561641266028212,1337539566524561643703480071⟩,⟨(-467748059805142831003061205),(-467748059805142828568173095)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨790234505901280945977685640,790234505901280947543733616⟩,⟨(-251957511457876155898908694),(-251957511457876154334217472)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨413823622589291126158475134,413823622589291127018694386⟩,⟨(-122544873559245588883533677),(-122544873559245588024004838)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨128441063602553013717422511,128441063602553013989552008⟩,⟨(-36486038691424198784106123),(-36486038691424198512191257)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨14012980646422344143224532546,14012980646422344182028158067⟩,⟨(-63401612881378839848201218864),(-63401612881378839809019341197)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨41460918064816760539872393221,41460918064816760655168664337⟩,⟨(-181884455778487125689819189455),(-181884455778487125573585617929)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨66864172050098482965874881719,66864172050098483152717593047⟩,⟨(-277052357115259732077989839874),(-277052357115259731890213147055)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨88238384799479288959226923076,88238384799479289205733393718⟩,⟨(-339001383328630300281388251593),(-339001383328630300034648725409)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨103370272944751130815992388789,103370272944751131100798136654⟩,⟨(-364517624341022354890954329032),(-364517624341022354607105177830)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨110588229291638670622800712807,110588229291638670918359525351⟩,⟨(-356943919025320879296203666381),(-356943919025320879002424154835)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨109498100213314045131806892055,109498100213314045405721080311⟩,⟨(-324370292016768741757179859521),(-324370292016768741484798279055)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨101219813002620251271578576934,101219813002620251496099460576⟩,⟨(-276933106449819609314049078702),(-276933106449819609089874156965)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨87997350963373951218824391424,87997350963373951408949438976⟩,⟨(-224204906377479201399408963974),(-224204906377479201208384642218)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨72436667595489117414931837443,72436667595489117585274626355⟩,⟨(-173438030870458097496516821970),(-173438030870458097324993711786)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨56778456140888498590443622983,56778456140888498732995026642⟩,⟨(-128932848423347556726550127058),(-128932848423347556583240708506)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨42488768882123444259751731043,42488768882123444372262286785⟩,⟨(-92327604783335032594234320253),(-92327604783335032481443498597)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨30209928367216601267133288019,30209928367216601348365912439⟩,⟨(-63366719081237078593974475373),(-63366719081237078512738331036)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨19941543550835440114191939793,19941543550835440167398761703⟩,⟨(-40725385679745133086233805384),(-40725385679745133033118615509)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨11285654117683723045686985102,11285654117683723075291925643⟩,⟨(-22636831743763408803351098996),(-22636831743763408773829871413)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨3645764966197597312060777752,3645764966197597321486896833⟩,⟨(-7246626830315017260807428674),(-7246626830315017251412806681)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-127867991307492020832477921229),(-127867991307492020798481345507)⟩,⟨34974939353580903205694216741,34974939353580903236333323908⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-372960297716995305013938424834),(-372960297716995304909371500215)⟩,⟨97337329661284161080920259939,97337329661284161176046605566⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-586872667352973707371555187199),(-586872667352973707190484239108)⟩,⟨139030364811055100306061703303,139030364811055100473666338749⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-752752782300146223815841835884),(-752752782300146223552564609913)⟩,⟨152859266525319134601668001239,152859266525319134850632111450⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-859492079644190256024083743036),(-859492079644190255675994656491)⟩,⟨139056548980417556103077525780,139056548980417556440531065732⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-903478888616300995126226031494),(-903478888616300994702453743287)⟩,⟨104408886864833303870095176067,104408886864833304288749137892⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-889013507835341219506202155960),(-889013507835341219031916831944)⟩,⟨59412297641456007861617034723,59412297641456008335204434225⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-827002175468360084925730243812),(-827002175468360084439855232801)⟩,⟨14733545468041010959085083792,14733545468041011445622884147⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-732200645012473994431737851960),(-732200645012473993977793900564)⟩,⟨(-21631897752563435579453664007),(-21631897752563435126692002041)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-619903086039295836751534883604),(-619903086039295836365525949365)⟩,⟨(-45647562162368668993844230793),(-45647562162368668612503578878)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-503127874098464659695358402555),(-503127874098464659388890151719)⟩,⟨(-56942889222175044966757663607),(-56942889222175044667915451067)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-390989432226971256846379126909),(-390989432226971256576816159245)⟩,⟨(-57551514742194130809613328454),(-57551514742194130547074890834)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-288355900711147435921539917311),(-288355900711147435688583214634)⟩,⟨(-50461650238162471773628134628),(-50461650238162471545221943656)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-196433092734636573106724942526),(-196433092734636572929700039664)⟩,⟨(-38527728232205099065534393734),(-38527728232205098891014690951)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-113760640973237816441185044365),(-113760640973237816331855198600)⟩,⟨(-23928737756855302287316311240),(-23928737756855302179156778385)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-37199456750786078418008353833),(-37199456750786078381271508586)⟩,⟨(-8089939008403380907172077636),(-8089939008403380870767619873)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1184391059060060221416955375385),(-1184391059060060220269606814393)⟩,⟨(-428114264403568161572034907046),(-428114264403568160438899357430)⟩⟩ +lemma checked : cachedMomentRuleBox column4_1 kernel3_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 3 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_1_contains kernel3_1_contains +end cm4_3_1_1 +namespace cm4_4_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_0 j i k).mul (kernel4_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2191975087297400),(-2191975087297384)⟩,⟨16664871092557148,16664871092557165⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-14934796968104731),(-14934796968104714)⟩,⟨38075582621434096,38075582621434113⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-34432445992440254),(-34432445992440233)⟩,⟨29524799365632215,29524799365632234⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-35507787703254330),(-35507787703254309)⟩,⟨(-959080984447860),(-959080984447836)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-11843215344905316),(-11843215344905293)⟩,⟨(-18855623615302446),(-18855623615302421)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨7442309762530784,7442309762530808⟩,⟨(-9568158698319921),(-9568158698319895)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨5314359269647529,5314359269647554⟩,⟨3111410801394668,3111410801394692⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1700375273647756),(-1700375273647729)⟩,⟨2617140566859914,2617140566859936⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1233263025602514),(-1233263025602487)⟩,⟨(-1126542157417532),(-1126542157417503)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨793959325215407,793959325215431⟩,⟨(-576833510045240),(-576833510045219)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨295357567634118,295357567634144⟩,⟨569215576728399,569215576728426⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-408244589465907),(-408244589465884)⟩,⟨208817306440850,208817306440876⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-218879574359226),(-218879574359204)⟩,⟨(-264411674471341),(-264411674471320)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨91088508285324,91088508285341⟩,⟨(-232911707090805),(-232911707090786)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨139402382238557,139402382238574⟩,⟨(-70125091489334),(-70125091489316)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨53236482287476,53236482287493⟩,⟨(-5007333676604),(-5007333676586)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨748077654982309710676,748077654982309712008⟩,⟨7859047526853061699,7859047526853063030⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1830412609289056243551,1830412609289056246843⟩,⟨162295339977278791158,162295339977278794444⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1996579587802561826007,1996579587802561829758⟩,⟨504022953986121801382,504022953986121805122⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1413927561706256401660,1413927561706256404599⟩,⟨758781764439789841126,758781764439789844055⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨648949274149521852160,648949274149521853865⟩,⟨711451813716475481922,711451813716475483621⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨138797493442142052802,138797493442142053672⟩,⟨448548213587890424235,448548213587890425104⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-47057713970500131021),(-47057713970500130634)⟩,⟨188480368363819542991,188480368363819543377⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-55546084087324270299),(-55546084087324270147)⟩,⟨44615082663451722745,44615082663451722899⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-24209813564121382007),(-24209813564121381935)⟩,⟨(-1644016925775511778),(-1644016925775511702)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-5098020240845377498),(-5098020240845377454)⟩,⟨(-6238389711915811481),(-6238389711915811438)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨463371135731072737,463371135731072764⟩,⟨(-2691356704711451156),(-2691356704711451124)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨833992681338894988,833992681338895014⟩,⟨(-517642749886876092),(-517642749886876068)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨372867296817770542,372867296817770562⟩,⟨83717025076356327,83717025076356347⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨103234347607406119,103234347607406139⟩,⟨122108556063812714,122108556063812733⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨15601722166565938,15601722166565955⟩,⟨64948838112449250,64948838112449270⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-148704322782115),(-148704322782097)⟩,⟨18550531305540423,18550531305540439⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1357072691114854991552239),(-1357072691114854989360024)⟩,⟨(-1142930063332660835821441),(-1142930063332660833626167)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-3485560431058684313416042),(-3485560431058684307607058)⟩,⟨(-3099930315916928027306557),(-3099930315916928021484446)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-4245742707020280396169322),(-4245742707020280388583607)⟩,⟨(-4209175908740188229067998),(-4209175908740188221456599)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3688651390006025720505276),(-3688651390006025712281821)⟩,⟨(-4309198921083782033091743),(-4309198921083782024842497)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-2467967081823629139238993),(-2467967081823629131829572)⟩,⟨(-3621100728360460474276811),(-3621100728360460466850833)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1278368477914136360903023),(-1278368477914136355359422)⟩,⟨(-2578177500387204695414951),(-2578177500387204689864743)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-479293456615233011887112),(-479293456615233008418412)⟩,⟨(-1581514930037029940104411),(-1581514930037029936635503)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-85509416288062133180511),(-85509416288062131349823)⟩,⟨(-846109275968177542581617),(-846109275968177540753174)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨47499453723018337684391,47499453723018338509114⟩,⟨(-399253311366678224787391),(-399253311366678223964951)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨63024084149568585925977,63024084149568586302586⟩,⟨(-167996854709373674500726),(-167996854709373674125627)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨44747946218363592270631,44747946218363592466763⟩,⟨(-63630682748234361386035),(-63630682748234361190697)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨25708186500643329758297,25708186500643329856046⟩,⟨(-21773727230171741438308),(-21773727230171741340851)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨13316543469049606904349,13316543469049606951524⟩,⟨(-6648981457137670610361),(-6648981457137670563275)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨6490540821523297049271,6490540821523297071503⟩,⟨(-1716505812546309545992),(-1716505812546309523790)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨2895589518643384942659,2895589518643384952459⟩,⟨(-315733079135812954193),(-315733079135812944404)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨820498325439065583489,820498325439065586263⟩,⟨(-23950442981379453278),(-23950442981379450505)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-201678930154891895801867755),(-201678930154891895514219808)⟩,⟨(-74519140885824004811267124),(-74519140885824004526955179)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-556435969521113597823499069),(-556435969521113597017825316)⟩,⟨(-208466881003649056100755070),(-208466881003649055304503718)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-784326768137691910044136040),(-784326768137691908888385923)⟩,⟨(-301693156727526868488277433),(-301693156727526867345553999)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-855298999581440989010185763),(-855298999581440987751135096)⟩,⟨(-341273556859834703760751424),(-341273556859834702513331699)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-790545324236116431158152256),(-790545324236116430025569449)⟩,⟨(-329819192572889930627654584),(-329819192572889929500086739)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-643209721326415928091950098),(-643209721326415927155446747)⟩,⟨(-282314998829775102361390951),(-282314998829775101422338588)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-470909321012789588591716804),(-470909321012789587850030434)⟩,⟨(-218599866134206844233823326),(-218599866134206843486557985)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-315441219598551330351768201),(-315441219598551329821521124)⟩,⟨(-155698062778878855043846986),(-155698062778878854509849431)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-196328192660828950706596838),(-196328192660828950326594027)⟩,⟨(-103637325104381715176992636),(-103637325104381714795894775)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-115337762417063375449350695),(-115337762417063375196775103)⟩,⟨(-65495045125656015464553126),(-65495045125656015212269254)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-65003180358689556093940625),(-65003180358689555927784234)⟩,⟨(-39891518827042274535838947),(-39891518827042274370158045)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-35682441599690095267558521),(-35682441599690095167061453)⟩,⟨(-23702071648112984490063707),(-23702071648112984389824058)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-19262257555557575258527804),(-19262257555557575201655293)⟩,⟨(-13801684504088585437953334),(-13801684504088585381164129)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-10147467217714131915280199),(-10147467217714131884878898)⟩,⟨(-7765644602358605542490373),(-7765644602358605512096080)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4890102472354127186981770),(-4890102472354127172370762)⟩,⟨(-3930335170944461339155287),(-3930335170944461324532848)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1452740332661148670896956),(-1452740332661148666588170)⟩,⟨(-1198673776103733265255940),(-1198673776103733260941520)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1989712652643394670070962350),(-1989712652643394664831498172)⟩,⟨1217179735274704666623577123,1217179735274704671892621874⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-5743970540423523965725124008),(-5743970540423523950790013528)⟩,⟨3265409941463419894107117818,3265409941463419909124415610⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-8845587217137162293019838426),(-8845587217137162270781072672)⟩,⟨4323321111512261859272170289,4323321111512261881607295893⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-10963827846503047828173926974),(-10963827846503047802477162597)⟩,⟨4207382010265661563901105177,4207382010265661589614410616⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-11929575346479099889881861657),(-11929575346479099865314118259)⟩,⟨3173483171842201135649665811,3173483171842201160028375591⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-11778104429413315140583944872),(-11778104429413315118645973469)⟩,⟨1729463119242303485348600321,1729463119242303506878758374⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-10732943230235156134018769726),(-10732943230235156112674148599)⟩,⟨374365587823130826715163596,374365587823130847660380210⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-9130194623756320769188197260),(-9130194623756320750602967563)⟩,⟨(-585798896756223061351667189),(-585798896756223042994246921)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-7317401744267036467710579119),(-7317401744267036452386946656)⟩,⟨(-1078442987581811845265694017),(-1078442987581811829971863290)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-5570925144736475529875691210),(-5570925144736475517880803445)⟩,⟨(-1193237011998433725503571633),(-1193237011998433713459831797)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4057638176594950129322332671),(-4057638176594950121082120740)⟩,⟨(-1078028308068801953980353388),(-1078028308068801945700490918)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2839792464918172730975329832),(-2839792464918172725684716725)⟩,⟨(-863032486518810642231020354),(-863032486518810636930021076)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1904791242927378467899924592),(-1904791242927378464389573674)⟩,⟨(-630939733776924414021144929),(-630939733776924410517583049)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1199563142439843083783531987),(-1199563142439843081577252080)⟩,⟨(-419643135190196919907968513),(-419643135190196917711874370)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-656705165703063858877218554),(-656705165703063857626736595)⟩,⟨(-237294381168982660446496721),(-237294381168982659202740270)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-208524895874067943695631615),(-208524895874067943294283533)⟩,⟨(-76495371652370967445812781),(-76495371652370967046688371)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-58767139068630699806689669),(-58767139068630699780910245)⟩,⟨48067324979668534614564856,48067324979668534639238898⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-842507265478386751489259620),(-842507265478386751099355840)⟩,⟨680983395642990651213959811,680983395642990651590796041⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-3342294155154091706808884108),(-3342294155154091705114133379)⟩,⟨2644706343082318262864233271,2644706343082318264525861263⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-7877716523093038193603454060),(-7877716523093038189107388382)⟩,⟨6053775262808900279165250697,6053775262808900283636159892⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-13896710022804729782817765121),(-13896710022804729773708371212)⟩,⟨10315182724620382353473352588,10315182724620382362618171076⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-20199450910716249360157115144),(-20199450910716249345014003090)⟩,⟨14447885036959727874798161547,14447885036959727890039739414⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-25417098660220485220126113078),(-25417098660220485198836463030)⟩,⟨17530409653441511635584896774,17530409653441511656914750335⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-28513291174053008693472842170),(-28513291174053008667722191586)⟩,⟨19029289183536622463683239682,19029289183536622489199598422⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-29082689083546366855812314715),(-29082689083546366827753304649)⟩,⟨18886348025769332518610939917,18886348025769332546103897576⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-27352505109386355311285008815),(-27352505109386355284276804224)⟩,⟨17402001871403386466583961211,17402001871403386492830821499⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-23955783126572832039407382270),(-23955783126572832015847128170)⟩,⟨15035677673739949392048709618,15035677673739949414943198611⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-19633513869585057437589479433),(-19633513869585057415421264825)⟩,⟨12232032185064317328627429092,12232032185064317350474945628⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-15003239752335822491168895610),(-15003239752335822471760405891)⟩,⟨9321881357437977431872008652,9321881357437977451181283918⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-10451064247501391199075424861),(-10451064247501391184337113988)⟩,⟨6494384695622919974449830101,6494384695622919989176969159⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-6130021378839866186623429109),(-6130021378839866177550763624)⟩,⟨3813980105873512658349007254,3813980105873512667430948928⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-2015942799440172241558296033),(-2015942799440172238517301277)⟩,⟨1255520476982330452351174875,1255520476982330455396949196⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-55620780082718008607293290921),(-55620780082718008534690432666)⟩,⟨27520993974174440891771656692,27520993974174440963786258089⟩⟩ +lemma checked : cachedMomentRuleBox column4_0 kernel4_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 4 false false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_0_contains kernel4_0_contains +end cm4_4_0_0 +namespace cm4_4_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_0 j i k).mul (kernel4_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨78587609600620322,78587609600620345⟩,⟨(-119845496203366375),(-119845496203366350)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨254748217032504388,254748217032504431⟩,⟨(-239656139100668298),(-239656139100668252)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨374739419508554748,374739419508554815⟩,⟨(-108395530559473063),(-108395530559472995)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨279637188925353333,279637188925353417⟩,⟨129027815661264031,129027815661264114⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨35682816417629653,35682816417629751⟩,⟨191660923213307852,191660923213307950⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-90471838001352669),(-90471838001352566)⟩,⟨57659733609947961,57659733609948068⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-37079922455955128),(-37079922455955032)⟩,⟨(-40758150489462504),(-40758150489462404)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨20933346053326808,20933346053326906⟩,⟨(-18910803297045602),(-18910803297045505)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨8793757739312269,8793757739312385⟩,⟨12431764511379656,12431764511379770⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-8074258859931696),(-8074258859931578)⟩,⟨3984588921428131,3984588921428248⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2035378472401125),(-2035378472401017)⟩,⟨(-5545518301559374),(-5545518301559265)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨3922460342789666,3922460342789763⟩,⟨(-1588728527977246),(-1588728527977153)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1883742273768924,1883742273768998⟩,⟨2548316447876259,2548316447876330⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-902530494799697),(-902530494799642)⟩,⟨2123873290474999,2123873290475056⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1292578807455927),(-1292578807455888)⟩,⟨632047037699345,632047037699385⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-490728669824195),(-490728669824175)⟩,⟨45033681064984,45033681065007⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3651699536786727634821),(-3651699536786727623156)⟩,⟨(-3889906614792823878926),(-3889906614792823867231)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-8286020140841113515512),(-8286020140841113486541)⟩,⟨(-10216407831317894232705),(-10216407831317894203672)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-7552722908397273264058),(-7552722908397273231189)⟩,⟨(-12784615056211356809938),(-12784615056211356777023)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-3507300939866466143697),(-3507300939866466118252)⟩,⟨(-11156227017952101116435),(-11156227017952101090984)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨92438767500878186577,92438767500878201498⟩,⟨(-7112481159611349694996),(-7112481159611349680101)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1458318967871658108189,1458318967871658116372⟩,⟨(-3207358174532044614220),(-3207358174532044606059)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1199562679116251051886,1199562679116251055781⟩,⟨(-872404560683679900570),(-872404560683679896679)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨553887845421834744663,553887845421834746113⟩,⟨(-6579026586205523171),(-6579026586205521720)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨147166666265384486498,147166666265384487088⟩,⟨123482840636130940326,123482840636130940920⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨5836713090671511521,5836713090671511854⟩,⟨64628249003915598834,64628249003915599166⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-14917206563506941682),(-14917206563506941515)⟩,⟨16632943397572761391,16632943397572761559⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-8135527445963829352),(-8135527445963829250)⟩,⟨220328349238491613,220328349238491714⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2405545300928097352),(-2405545300928097270)⟩,⟨(-2114497779548966594),(-2114497779548966511)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-300400262920986949),(-300400262920986889)⟩,⟨(-1317033294076608246),(-1317033294076608187)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨127102279170784044,127102279170784087⟩,⟨(-552849394560257855),(-552849394560257810)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨70347054652048700,70347054652048726⟩,⟨(-141423436860987165),(-141423436860987141)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1989236735297128352348599),(-1989236735297128337101781)⟩,⟨10178234886861015392681731,10178234886861015407791378⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-5862249170969880215037691),(-5862249170969880174836253)⟩,⟨26729764742036089916828030,26729764742036089956669288⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-9150036030457264070873770),(-9150036030457264018831554)⟩,⟨34119947801281522444581719,34119947801281522496173675⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-11035289832539014899334340),(-11035289832539014842368586)⟩,⟨32019850971305481589414771,32019850971305481646008226⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-10962238636453175305919619),(-10962238636453175253670901)⟩,⟨24145492935502797044364936,24145492935502797096399213⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-9179120622356872653075558),(-9179120622356872612314313)⟩,⟨15124783635055953460479056,15124783635055953501164466⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-6584611158174860414446972),(-6584611158174860387367169)⟩,⟨7975078216014474016252967,7975078216014474043326531⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-4111844032291891474745556),(-4111844032291891459728011)⟩,⟨3537858586269040781170539,3537858586269040796198596⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-2274483082855960585022727),(-2274483082855960577992597)⟩,⟨1290680116522408606957476,1290680116522408613996721⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1136318846631327957982183),(-1136318846631327954652620)⟩,⟨352620108156947577931497,352620108156947581266807⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-523956297553336614984851),(-523956297553336613190605)⟩,⟨37566287373579927809848,37566287373579929607550⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-228295645995479448587233),(-228295645995479447675337)⟩,⟨(-36978082621665869477286),(-36978082621665868563875)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-96221415576652947734468),(-96221415576652947289148)⟩,⟨(-38431945649190932274179),(-38431945649190931828245)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-39825148792034453627556),(-39825148792034453416221)⟩,⟨(-25426927979993535727418),(-25426927979993535515833)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-15708070674213404191764),(-15708070674213404098316)⟩,⟨(-13411098308179739515303),(-13411098308179739421767)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-4153070472718293979463),(-4153070472718293953067)⟩,⟨(-4109965863691561819107),(-4109965863691561792684)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-37874063568262356232419292),(-37874063568262354566062680)⟩,⟨1045563114199811346134172925,1045563114199811347809552688⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-109137746602046811704701821),(-109137746602046807065347395)⟩,⟨2898804604708640882656905201,2898804604708640887319215184⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-166114512245597668137885154),(-166114512245597661550857687)⟩,⟨4125411991902836561187503746,4125411991902836567797670335⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-199404377939892011455848585),(-199404377939892004366624236)⟩,⟨4562377849748922412722922804,4562377849748922419813683508⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-204593359308566466553392173),(-204593359308566460233772587)⟩,⟨4294234849434999726787618855,4294234849434999733070162595⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-185681143617604747365643857),(-185681143617604742136022161)⟩,⟨3571186381044546690557989450,3571186381044546695721783494⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-153014142056359299199629579),(-153014142056359295132079709)⟩,⟨2681378801481428710319598093,2681378801481428714332472079⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-117485760252148884529684552),(-117485760252148881600576999)⟩,⟨1847713068288949254422894339,1847713068288949257325352439⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-86069527655623677551747594),(-86069527655623675111383832)⟩,⟨1186375547285659521882728932,1186375547285659524319063215⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-61194990279648333340378635),(-61194990279648331535522794)⟩,⟨720818189020165028119343471,720818189020165029925651537⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-42545847249984163578940453),(-42545847249984162387810233)⟩,⟨420950553130521173384664813,420950553130521174576503477⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-28895947214103621571597643),(-28895947214103620849343016)⟩,⟨239611301606509594360939437,239611301606509595082786201⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-19000399145480775221742982),(-19000399145480774809940253)⟩,⟨133955669210229146701040269,133955669210229147112049106⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-11799664491937811824116922),(-11799664491937811602081814)⟩,⟨72780446498663453422416920,72780446498663453643750892⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-6398188781399366272402083),(-6398188781399366164932567)⟩,⟨35900994677075085250150529,35900994677075085357182148⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2021430656247422833890335),(-2021430656247422802075764)⟩,⟨10800980453159527339047690,10800980453159527370715941⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨6382943509377815908995163166,6382943509377815930555731274⟩,⟨7272471739067322960071025340,7272471739067322981433270317⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨17512327560795040877841673277,17512327560795040939156447580⟩,⟨21186619062049009838073441448,21186619062049009898868288380⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨24373854907463137848100307241,24373854907463137938829865027⟩,⟨33200169825547381656238581610,33200169825547381746407100803⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨25980127460240470538414238870,25980127460240470641918365919⟩,⟨42163495898479847440480911964,42163495898479847543902851988⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨23119163593608694068296900775,23119163593608694177814421017⟩,⟨47251587182883996412204327842,47251587182883996522545798461⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨17702405710597779811590522039,17702405710597779919935872522⟩,⟨48213324441746481820861967502,48213324441746481930645942473⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨11783288549631244705112754111,11783288549631244809199836162⟩,⟨45482451736760636005490502045,45482451736760636110743042118⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨6800835781390058509979059335,6800835781390058600942536494⟩,⟨40056848715390317370078836870,40056848715390317461374410896⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨3334774925191938363126801202,3334774925191938438561581703⟩,⟨33193503366335886736131447679,33193503366335886811210430486⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1297008520072353142517484769,1297008520072353201054318216⟩,⟨26064560847491204741958208349,26064560847491204800056492644⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨288792247413410295725892518,288792247413410335131707230⟩,⟨19515241727497854861505059510,19515241727497854900674493541⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-110546512632682826933582003),(-110546512632682801223465818)⟩,⟨13984728084261246390787022963,13984728084261246416465838885⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-208045133495423026427950958),(-208045133495423006891612689)⟩,⟨9563102399943858563754313108,9563102399943858583340394209⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-181190781364164221406177770),(-181190781364164208208353386)⟩,⟨6111683434799676590201733715,6111683434799676603445971089⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-114043665018555166652941970),(-114043665018555159212578013)⟩,⟨3379208493244071658309655338,3379208493244071665775205666⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-38240863434267434729800874),(-38240863434267432349147887)⟩,⟨1078379316670244066546464017,1078379316670244068934677336⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨184896782699934635420813759,184896782699934635514508524⟩,⟨203219999051138543873053049,203219999051138543970237975⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2634488990525609563514218952,2634488990525609564950359089⟩,⟨2916681338991327405092408821,2916681338991327406568174201⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨10341343341258165848851589091,10341343341258165855226125127⟩,⟨11595109012959249976826000880,11595109012959249983288159540⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨24047428581049000926379176181,24047428581049000943693958632⟩,⟨27415597206025860550907369195,27415597206025860568234469075⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨41824832236801310412303065155,41824832236801310448147704150⟩,⟨48563308237303911477424481049,48563308237303911513010371513⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨60048829910428099961987412991,60048829910428100022580465720⟩,⟨70942744493147299926730082736,70942744493147299986826697058⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨74935964788551102348978112446,74935964788551102435116760610⟩,⟨89771482496108127119522949107,89771482496108127205475280313⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨83843576319679448253138369108,83843576319679448359817105111⟩,⟨101306188507219724121051456295,101306188507219724228675505681⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨85839905403896304846256622889,85839905403896304964798284355⟩,⟨103936825488861074811836780141,103936825488861074932482270431⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨81532499435852979280480067022,81532499435852979395566441398⟩,⟨98285074217040149233630582721,98285074217040149351369106175⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨72464260277391579145399545153,72464260277391579247233008804⟩,⟨86483424166836911540348153762,86483424166836911644284709605⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨60440295193674800862158280776,60440295193674800960700227012⟩,⟨71145278739622610510564954157,71145278739622610609908133730⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨47024744155162507871842134040,47024744155162507960052667085⟩,⟨54516714113646923474259130700,54516714113646923562530792477⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨33286296343265275221835570386,33286296343265275289811882362⟩,⟨38045692451323011604650403384,38045692451323011672468148890⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨19759215096371526303899402588,19759215096371526346123273654⟩,⟨22339747804167714766347003759,22339747804167714808430960952⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨6539760510916578546102582240,6539760510916578560315752611⟩,⟨7350344978464828535879844269,7350344978464828550043504266⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨140196224820554090775227340134,140196224820554091098317317963⟩,⟨210089669723436917490042973694,210089669723436917814608338053⟩⟩ +lemma checked : cachedMomentRuleBox column4_0 kernel4_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 4 false true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_0_contains kernel4_1_contains +end cm4_4_0_1 +namespace cm4_4_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_1 j i k).mul (kernel4_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨18553923216549,18553923216567⟩,⟨26542222323674457,26542222323674474⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-14524000703604505),(-14524000703604485)⟩,⟨62831390928578893,62831390928578918⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-45122006874310536),(-45122006874310513)⟩,⟨55150978250820891,55150978250820915⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-54402636097426093),(-54402636097426068)⟩,⟨10575579752038666,10575579752038690⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-25425585775798403),(-25425585775798375)⟩,⟨(-23090158863200489),(-23090158863200463)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨5898416596700098,5898416596700126⟩,⟨(-17406888015746807),(-17406888015746780)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨9044303712833366,9044303712833395⟩,⟨1174224986844489,1174224986844519⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-486507514624818),(-486507514624791)⟩,⟨4461112442878234,4461112442878265⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-2270274005805044),(-2270274005805020)⟩,⟨(-480215842496812),(-480215842496786)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨453197186205889,453197186205917⟩,⟨(-1232971572536464),(-1232971572536440)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨744153855387956,744153855387983⟩,⟨360514045399786,360514045399811⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-230176275998240),(-230176275998217)⟩,⟨522476207292711,522476207292735⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-409084226423956),(-409084226423932)⟩,⟨(-67393433323020),(-67393433322997)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-105966948365390),(-105966948365369)⟩,⟨(-275204590633827),(-275204590633805)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨61794789830932,61794789830951⟩,⟨(-170106472978681),(-170106472978663)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨40218219916842,40218219916858⟩,⟨(-46520107550042),(-46520107550025)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨618673567306264582323,618673567306264583244⟩,⟨5234943449897087629,5234943449897088548⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1515101156145309019122,1515101156145309021397⟩,⟨119040448646833757081,119040448646833759353⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1661289916877130770230,1661289916877130772835⟩,⟨374234659342425442555,374234659342425445160⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1197670101098810253331,1197670101098810255401⟩,⟨569734446260905291372,569734446260905293438⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨579476893138188627953,579476893138188629183⟩,⟨543890336913434226746,543890336913434227968⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨154686233456462360929,154686233456462361513⟩,⟨354103616006853160929,354103616006853161508⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-15096143708623489819),(-15096143708623489553)⟩,⟨158434567982780846417,158434567982780846686⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-37552973797229250079),(-37552973797229249968)⟩,⟨44189838626575630168,44189838626575630284⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-19329247125872133050),(-19329247125872132994)⟩,⟨3167222244468831144,3167222244468831202⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-5254749283316893042),(-5254749283316893003)⟩,⟨(-3721204226969349893),(-3721204226969349853)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-291430572178743016),(-291430572178742989)⟩,⟨(-2139161964725982239),(-2139161964725982216)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨480852576646655069,480852576646655092⟩,⟨(-598048753808055500),(-598048753808055480)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨292596316829060603,292596316829060624⟩,⟨(-42466753052417581),(-42466753052417558)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨108586429483833885,108586429483833902⟩,⟨56978949348472529,56978949348472549⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨30215626522834389,30215626522834407⟩,⟨40963714095084948,40963714095084965⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5471981815877623,5471981815877639⟩,⟨12983801882065692,12983801882065709⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-2883464491236313835617426),(-2883464491236313832516012)⟩,⟨(-1775441193100109289949441),(-1775441193100109286831908)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-7518797933292235389217837),(-7518797933292235380947502)⟩,⟨(-4719023063310498189897317),(-4719023063310498181588487)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-9461021411467755880812972),(-9461021411467755870017062)⟩,⟨(-6183891114721667396624134),(-6183891114721667385788547)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-8689397428850211897923813),(-8689397428850211887631821)⟩,⟨(-6068705815943930501922703),(-6068705815943930491604605)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-6369534769204143385544136),(-6369534769204143377175560)⟩,⟨(-4905120735369244907569802),(-4905120735369244899191277)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-3857390249168650381960687),(-3857390249168650375319383)⟩,⟨(-3403241950742534877460995),(-3403241950742534870819147)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1960804492506316179910188),(-1960804492506316175428754)⟩,⟨(-2077013372124366602154029),(-2077013372124366597671899)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-840030454580273381916971),(-840030454580273379317724)⟩,⟨(-1135000620099985357512601),(-1135000620099985354910944)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-299186927618491207765825),(-299186927618491206442446)⟩,⟨(-564058025962560914536038),(-564058025962560913210093)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-82958340420856386694138),(-82958340420856386086521)⟩,⟨(-259088259496020765318842),(-259088259496020764709483)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-12374830759192106136278),(-12374830759192105876643)⟩,⟨(-112047071466198984132364),(-112047071466198983871827)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨4691691682005217848918,4691691682005217956305⟩,⟨(-46598878042308098442768),(-46598878042308098335042)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨5987548700791058561736,5987548700791058605907⟩,⟨(-19046527201505226065668),(-19046527201505226021384)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨4066164548854793309089,4066164548854793329436⟩,⟨(-7753785519970599944945),(-7753785519970599924554)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨2151575982459509945161,2151575982459509954641⟩,⟨(-3041185688062509384461),(-3041185688062509374965)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨658973331567217734971,658973331567217737731⟩,⟨(-803912126351647402307),(-803912126351647399544)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-202054205029172342481440043),(-202054205029172342350491296)⟩,⟨35042919544450903326340285,35042919544450903456322878⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-555426713547274227720225429),(-555426713547274227348082771)⟩,⟨98362648729397544206094555,98362648729397544575480548⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-777180244369036923877935989),(-777180244369036923328608595)⟩,⟨143159589060668159281069890,143159589060668159826379618⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-838314808502858070513839188),(-838314808502858069888741869)⟩,⟨162876860109330689793991775,162876860109330690414698413⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-763958389949557426536798118),(-763958389949557425932056088)⟩,⟨157791121776854458280744908,157791121776854458882010056⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-611283085881249719673942468),(-611283085881249719110336684)⟩,⟨134326643339318192577976351,134326643339318193139880678⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-439534228031863542178472671),(-439534228031863541692728185)⟩,⟨102086430477412174915399224,102086430477412175400417440⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-289277327307749155108354905),(-289277327307749154741413176)⟩,⟨70049345017573555591624891,70049345017573555958260472⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-177341475656133227261500829),(-177341475656133227017767321)⟩,⟨43885638907321266984189153,43885638907321267227737971⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-103094719052041362947743004),(-103094719052041362802060508)⟩,⟨25428933702401868122953550,25428933702401868268488218⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-57852427506182114460481090),(-57852427506182114376886795)⟩,⟨13834012428324380883705879,13834012428324380967154087⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-31830731533242047533703483),(-31830731533242047480314492)⟩,⟨7181378733014252863988288,7181378733014252917285626⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-17319355853559185041055306),(-17319355853559185007352696)⟩,⟨3607440391623687143322580,3607440391623687176979740⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-9224133365137939676618027),(-9224133365137939656887405)⟩,⟨1756756077338769811096331,1756756077338769830805630⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4491470834602862638035454),(-4491470834602862627898424)⟩,⟨789611481259674707825334,789611481259674717953090⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1342732580281843236196648),(-1342732580281843233099451)⟩,⟨224971498269953762398490,224971498269953765493154⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-6548145863988425307402937370),(-6548145863988425301614852874)⟩,⟨4080584476212196585547266129,4080584476212196591336922805⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-18526990775624031277899680926),(-18526990775624031261148726759)⟩,⟨11561173056260419629524692828,11561173056260419646289813230⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-27452906228060523677309614340),(-27452906228060523651538491275)⟩,⟨17188376672317367599001112299,17188376672317367624805324843⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-32237154768278643221879761983),(-32237154768278643190387844515)⟩,⟨20312712297295495048437635239,20312712297295495079949348092⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-32830629005607821580445037545),(-32830629005607821547526716673)⟩,⟨20907376489699662947564438878,20907376489699662980409516629⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-30070252426914364409958179782),(-30070252426914364378437408533)⟩,⟨19456056750629088342746604395,19456056750629088374038674991⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-25270676499738011361264093505),(-25270676499738011333422813603)⟩,⟨16708128265055103806427260264,16708128265055103833909407913⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-19761439664689857600023930946),(-19761439664689857578490712012)⟩,⟨13424082522123682524137827630,13424082522123682545282413811⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-14551235911956008652974976282),(-14551235911956008635879793991)⟩,⟨10199531494267574664750189149,10199531494267574681641586523⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-10201227647390331277954319396),(-10201227647390331263774301108)⟩,⟨7395945023657623726040058490,7395945023657623740171122914⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-6877470701468136779336622275),(-6877470701468136768772541899)⟩,⟨5158018264235515191201462679,5158018264235515201768655485⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-4491393573903755585735025484),(-4491393573903755578523258932)⟩,⟨3476829556378430584088934421,3476829556378430591308941342⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-2841424732966144305078607056),(-2841424732966144300500378282)⟩,⟨2260634831378615782274085741,2260634831378615786853286195⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1709611017849379270962288784),(-1709611017849379268236685056)⟩,⟨1389816893505009767187894705,1389816893505009769909496366⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-907183325883061989715262077),(-907183325883061988270393096)⟩,⟨748465779922106998325853135,748465779922106999766585188⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-283539000478725632845124724),(-283539000478725632396514086)⟩,⟨235688829785886411036660256,235688829785886411483666235⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨19198625199590486674633252772,19198625199590486684237350106⟩,⟨23449957104837787982068281487,23449957104837787992082984559⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨54880862880349415555925148410,54880862880349415585397652022⟩,⟨67785847435231327549526760379,67785847435231327580019536568⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨83052215154523950111664005339,83052215154523950162332145823⟩,⟨104787084381004184018691639890,104787084381004184070459699726⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨100774319010860303911421131251,100774319010860303983821948351⟩,⟨130942748920094322733847984170,130942748920094322806886171458⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨107423092067882719541057828695,107423092067882719633975884300⟩,⟨144538571277545985462473175993,144538571277545985555360144825⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨104442730520664465578798169589,104442730520664465686790523211⟩,⟨145871152892877127878933178256,145871152892877127986507531935⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨94558789743828734328410909565,94558789743828734441759706961⟩,⟨136992797612550217777632489968,136992797612550217890811036439⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨80835967202473262197260323805,80835967202473262304605895986⟩,⟨121056993355267130306152433872,121056993355267130414168514135⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨65929010717218168527198813251,65929010717218168622432957827⟩,⟨101486408419761035070679946281,101486408419761035167387618226⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨51697988876986216312145780467,51697988876986216389609024002⟩,⟨81242270065594532082075759460,81242270065594532161369401063⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨39164918132692032940642571642,39164918132692032999853875268⟩,⟨62393740114014250306695978792,62393740114014250367398416802⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨28678057994399556927047400289,28678057994399556977804548144⟩,⟨46029191173777682766284984786,46029191173777682817736696634⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨20141453439318353140433073054,20141453439318353181787740305⟩,⟨32416784657395845084122386788,32416784657395845125710494744⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨13217036922460708033370518393,13217036922460708063093356454⟩,⟨21269554306921077508782176135,21269554306921077538558716510⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨7463140918255831513063212635,7463140918255831530694284411⟩,⟨11995175251899164226327653088,11995175251899164243961250073⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨2409466278099224716849182187,2409466278099224722649533694⟩,⟨3868792647133974651197475659,3868792647133974656995415304⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨105730819351765956365353086151,105730819351765956568209367464⟩,⟨231933269568358673751858639714,231933269568358673956005941686⟩⟩ +lemma checked : cachedMomentRuleBox column4_1 kernel4_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 4 true false) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_1_contains kernel4_0_contains +end cm4_4_1_0 +namespace cm4_4_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (column4_1 j i k).mul (kernel4_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨98215573699768976,98215573699769005⟩,⟨(-203884120963806016),(-203884120963805987)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨342139919268488783,342139919268488842⟩,⟨(-432497016682358592),(-432497016682358530)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨549699839393206154,549699839393206249⟩,⟨(-270877794633341165),(-270877794633341074)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨469564704948181598,469564704948181717⟩,⟨101697012228923226,101697012228923341⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨132603008991850958,132603008991851098⟩,⟨269837751333452450,269837751333452591⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-100863568508854759),(-100863568508854599)⟩,⟨127568374583143973,127568374583144134⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-74084137841888003),(-74084137841887838)⟩,⟨(-34162557955521555),(-34162557955521393)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨14611317932266047,14611317932266196⟩,⟨(-37826232041762209),(-37826232041762062)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨19280470089863778,19280470089863914⟩,⟨8690527897472941,8690527897473073⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-6010129786621102),(-6010129786620981)⟩,⟨10443116404927146,10443116404927266⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-6377850017872265),(-6377850017872145)⟩,⟨(-4161454021421489),(-4161454021421372)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨2539798860119610,2539798860119720⟩,⟨(-4615839980770133),(-4615839980770025)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨3736563604563096,3736563604563187⟩,⟨828673007254159,828673007254252⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨903561832964262,903561832964333⟩,⟨2566661264473484,2566661264473556⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-587454593330724),(-587454593330672)⟩,⟨1561914267086378,1561914267086427⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-371621621432261),(-371621621432233)⟩,⟨427883759051122,427883759051149⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3026530074036741336985),(-3026530074036741328463)⟩,⟨(-3210775369526460122933),(-3210775369526460114430)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-6937260119672193697817),(-6937260119672193676560)⟩,⟨(-8380169236701736345713),(-8380169236701736324496)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-6515613544546375549333),(-6515613544546375524955)⟩,⟨(-10408170352490865804050),(-10408170352490865779700)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-3342666831209576119471),(-3342666831209576100191)⟩,⟨(-9068879823625042492394),(-9068879823625042473121)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-379058922884454582754),(-379058922884454571224)⟩,⟨(-5857824161581632657503),(-5857824161581632645965)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨898084565682713094449,898084565682713100083⟩,⟨(-2756777089216849687973),(-2756777089216849682328)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨865046663484736277586,865046663484736280271⟩,⟨(-853214245560745004083),(-853214245560745001395)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨441689227989815821755,441689227989815822788⟩,⟨(-90290043246571812422),(-90290043246571811390)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨138388100091574335588,138388100091574336039⟩,⟨69923717810487139248,69923717810487139698⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨18246818419628481959,18246818419628482226⟩,⟨48539951546332715514,48539951546332715779⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-7284238564776090016),(-7284238564776089867)⟩,⟨16088385111299435611,16088385111299435757⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-5942506439479291119),(-5942506439479291021)⟩,⟨2272110612941985783,2272110612941985880⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2322335596760393398),(-2322335596760393327)⟩,⟨(-863815152005560031),(-863815152005559961)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-593440720241256923),(-593440720241256874)⟩,⟨(-849129293771071471),(-849129293771071425)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-74754589889889251),(-74754589889889219)⟩,⟨(-425769542693060983),(-425769542693060950)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨6560071714031892,6560071714031914⟩,⟨(-119787634164950244),(-119787634164950223)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-889664664263052947965420),(-889664664263052924229635)⟩,⟨19773157020777080687985160,19773157020777080711821755⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2575044588555644287104522),(-2575044588555644223705222)⟩,⟨52012570437227675843717514,52012570437227675907401075⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3992678944702671512159648),(-3992678944702671429129130)⟩,⟨66661672540910723748173006,66661672540910723831595662⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-4972969664883350733837781),(-4972969664883350654352312)⟩,⟨63081935520339111888899433,63081935520339111968771513⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-5330432578118258905008421),(-5330432578118258839721851)⟩,⟨48348986580487727852933613,48348986580487727918500514⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-4971157857106628320977047),(-4971157857106628267514615)⟩,⟨31227408159175819636595870,31227408159175819690186694⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-4035756903873928633493866),(-4035756903873928595976996)⟩,⟨17410686718302001267766547,17410686718302001305305825⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-2865369360258292031745404),(-2865369360258292009200402)⟩,⟨8536723726609495323363790,8536723726609495345896766⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1800527922168557419452445),(-1800527922168557407609170)⟩,⟨3741377215676564445652406,3741377215676564457481222⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1020035071448970369810244),(-1020035071448970364224479)⟩,⟨1487398307136090981575623,1487398307136090987151980⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-533292143513412558967308),(-533292143513412556526771)⟩,⟨543046485723026166739948,543046485723026169175435⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-264017433647445057260593),(-264017433647445056235206)⟩,⟨183401582775802008623403,183401582775802009646637⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-126718843275224146333561),(-126718843275224145907490)⟩,⟨57062642348918572679605,57062642348918573104814⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-59528687013062447598961),(-59528687013062447401001)⟩,⟨15901943387164809144120,15901943387164809341738⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-26158280744959197365246),(-26158280744959197272434)⟩,⟨3680261811970190442555,3680261811970190535237⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-7378497809289391270733),(-7378497809289391243724)⟩,⟨552863354669147556260,552863354669147583239⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨469155894231525117253716304,469155894231525118025630946⟩,⟨880738285391192646535151990,880738285391192647311991918⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1310787244350941167563083399,1310787244350941169751368407⟩,⟨2421734077345062164989613883,2421734077345062167191686276⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1892423393896155330592952919,1892423393896155333811271508⟩,⟨3390131013489294859712400420,3390131013489294862950539985⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨2133148781315156050159566337,2133148781315156053809551154⟩,⟨3658432058176954961478770763,3658432058176954965150872528⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2050728327141404780561552789,2050728327141404784099064984⟩,⟨3334841854975134860792823757,3334841854975134864350476555⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1740575016866974046884068624,1740575016866974050235426736⟩,⟨2668486430814771828373911616,2668486430814771831739870961⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1329126670871659866094317076,1329126670871659869024794849⟩,⟨1918692056925091462290653447,1918692056925091465229767703⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨926100882825170965522980439,926100882825170967798098870⟩,⟨1263277721906100589297780528,1263277721906100591577419897⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨596904586411677125605319676,596904586411677127244466208⟩,⟨775691009155945556918984121,775691009155945558560279537⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨361232809489561171989832547,361232809489561173037007654⟩,⟨452614208658826123276716586,452614208658826124325590609⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨208607218067246442763771752,208607218067246443370140188⟩,⟨255652421069100561934947419,255652421069100562542621596⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨116762642369073232696952254,116762642369073233088504893⟩,⟨141991108335227785607528352,141991108335227785999843623⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨63994722195418117272458019,63994722195418117523414130⟩,⟨78145042173460084752615961,78145042173460085003997300⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨34096650900753858053526285,34096650900753858202497375⟩,⟨42106054031980483228241984,42106054031980483377455751⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨16557308546040808758059222,16557308546040808835387441⟩,⟨20699639711442684910332948,20699639711442684987787969⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4937934237258882835586153,4937934237258882859340651⟩,⟨6221764244663445237033157,6221764244663445260827450⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨21312228667634273111055583654,21312228667634273137265856996⟩,⟨23880685613913126352376051697,23880685613913126378538693371⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨60700677672861477238333106422,60700677672861477314454582639⟩,⟨67594596472917804450311441728,67594596472917804526272061162⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨91168474150792021426435943794,91168474150792021544296314529⟩,⟨100227583369819547142333002514,100227583369819547259953071874⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨109303695460045941921622417134,109303695460045942066855181111⟩,⟨117769280369828478349320768829,117769280369828478494437437391⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨114512378607038631757548581383,114512378607038631916744055556⟩,⟨119958352460996238475509797999,119958352460996238635049892794⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨108702338450349913979779909809,108702338450349914139260530094⟩,⟨109783571390871898321430715883,109783571390871898481832792550⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨95320695313574593822208790336,95320695313574593963577121231⟩,⟨92044344469878487110063019430,92044344469878487252723785174⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨78199387952987563210225132791,78199387952987563320009065569⟩,⟨71662432827366873451368751454,71662432827366873562377870074⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨60613153448524898690234195954,60613153448524898778877862746⟩,⟨52412489112884888401455720574,52412489112884888490584571025⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨44769613284668815831628992066,44769613284668815906833953996⟩,⟨36408654870826297838135879075,36408654870826297913325144483⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨31741540201253538357762202601,31741540201253538414818828033⟩,⟨24272531989818894044835990791,24272531989818894101774537211⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨21702735119194263614381947673,21702735119194263654350724325⟩,⟨15655721942313561864216922447,15655721942313561904118698279⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨14278504922253412709494306261,14278504922253412736251334879⟩,⟨9781975907620107506888278367,9781975907620107533642139105⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨8858790979785747952882496560,8858790979785747969340054817⟩,⟨5820920791421834056586850023,5820920791421834073065191780⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4800682469427072877751186185,4800682469427072886500452866⟩,⟨3063336855675776410758302811,3063336855675776419526492580⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1516531869541351102391479918,1516531869541351105110743303⟩,⟨953207419869487159484735580,953207419869487162211022055⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨81084204664616255195638680096,81084204664616255233451759276⟩,⟨(-73816689607949876043815105795),(-73816689607949876007363267720)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨234631451985316814311067486663,234631451985316814426625930988⟩,⟨(-212144249822912981476215415469),(-212144249822912981363957193245)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨363467593332534364184445258594,363467593332534364382070629437⟩,⟨(-324478081710108134361220173988),(-324478081710108134166902491293)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨455624338155913448743239211158,455624338155913449025031012620⟩,⟨(-399975627629666026228373706527),(-399975627629666025947974193327)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨505022842747514308655775249418,505022842747514309019027944123⟩,⟨(-435224613545914849342053280155),(-435224613545914848977697894828)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨512240776703553472019832489914,512240776703553472447195894651⟩,⟨(-433773174518563022335489542854),(-433773174518563021905840188891)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨483786789351863534659411189889,483786789351863535116835899279⟩,⟨(-403940687382786376388852478470),(-403940687382786375930620008263)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨430062513939277706244611260609,430062513939277706695992087785⟩,⟨(-355966175583356651500961092648),(-355966175583356651052410314966)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨362665242779477698710339177568,362665242779477699126416060532⟩,⟨(-299514540199172978280116265122),(-299514540199172977869751789991)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨291907748716409336151616533927,291907748716409336497710755602⟩,⟨(-242130440511679292799964713474),(-242130440511679292460523502282)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨225239995916786775175015723696,225239995916786775443248652653⟩,⟨(-188705306221785299762356432652),(-188705306221785299499155718727)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨166790195738378021788689615477,166790195738378022019621597129⟩,⟨(-141677443999239007204027907750),(-141677443999239006975124637133)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨117790102613204010399204468393,117790102613204010588629032895⟩,⟨(-101593769024561280532022810717),(-101593769024561280343036378988)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨77428497592643694696724779925,77428497592643694833936739597⟩,⟨(-67738859135712832949351007365),(-67738859135712832812065219454)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨43714154028040316202495071303,43714154028040316284405712273⟩,⟨(-38663789677494601164927208324),(-38663789677494601082884117516)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨14106032823444786627646815668,14106032823444786654689540558⟩,⟨(-12550411344783103035420287507),(-12550411344783103008326324849)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨874380926859457143843680297955,874380926859457144728097805845⟩,⟨(-476496945705541963353532055628),(-476496945705541962473104283952)⟩⟩ +lemma checked : cachedMomentRuleBox column4_1 kernel4_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (momentRuleValue quadraturePoint fejerWeight 4 4 true true) := by + rw [← checked] + exact cachedMomentRuleBox_contains column4_1_contains kernel4_1_contains +end cm4_4_1_1 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders0.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders0.lean new file mode 100644 index 0000000000000000000000000000000000000000..0ca616452be366cfb1a1e2dfb800666d6e206d84 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders0.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk0_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_0 j i k) +lemma hk0_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_0 j i k).Contains (fullFactor false 0 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 0 (power0_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha0_0_0 : Fin 7 → CBox := ![⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩,⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩,⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩,⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩,⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩,⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩,⟨⟨1000000000000000000000000000000,1000000000000000000000000000000⟩,⟨0,0⟩⟩] +lemma ha0_0_0_eq (j : Fin 7) : ha0_0_0 j = ((atomPoints j).direct.powBin 7 0).conj := by fin_cases j <;> decide +kernel +lemma ha0_0_0_contains (j : Fin 7) : (ha0_0_0 j).Contains (fullFactor false 0 0 ((j.val:ℝ)/6)) := by + rw [ha0_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 0) ((j.val:ℝ)/6) 0 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 0 (by norm_num)) +noncomputable def hk0_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_1 j i k) +lemma hk0_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_1 j i k).Contains (fullFactor false 0 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 1 (power0_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha0_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨523598775598298873076666666664,523598775598298873078333333335⟩⟩,⟨⟨0,0⟩,⟨1047197551196597746153333333332,1047197551196597746156666666669⟩⟩,⟨⟨0,0⟩,⟨1570796326794896619230000000000,1570796326794896619235000000000⟩⟩,⟨⟨0,0⟩,⟨2094395102393195492306666666664,2094395102393195492313333333335⟩⟩,⟨⟨0,0⟩,⟨2617993877991494365383333333332,2617993877991494365391666666669⟩⟩,⟨⟨0,0⟩,⟨3141592653589793238460000000000,3141592653589793238470000000000⟩⟩] +lemma ha0_0_1_eq (j : Fin 7) : ha0_0_1 j = ((ha0_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha0_0_1_contains (j : Fin 7) : (ha0_0_1 j).Contains (fullFactor false 0 1 ((j.val:ℝ)/6)) := by + rw [ha0_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_0 j) false 0 0 j (ha0_0_0_contains j) +noncomputable def hk0_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_2 j i k) +lemma hk0_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_2 j i k).Contains (fullFactor false 0 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 2 (power0_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha0_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-137077838904018869706676583140),(-137077838904018869705803918511)⟩,⟨0,0⟩⟩,⟨⟨(-548311355616075478826706332557),(-548311355616075478823215674048)⟩,⟨0,0⟩⟩,⟨⟨(-1233700550136169827360089248246),(-1233700550136169827352235266611)⟩,⟨0,0⟩⟩,⟨⟨(-2193245422464301915306825330218),(-2193245422464301915292862696192)⟩,⟨0,0⟩⟩,⟨⟨(-3426945972600471742666914578467),(-3426945972600471742645097962806)⟩,⟨0,0⟩⟩,⟨⟨(-4934802200544679309440356992983),(-4934802200544679309408941066446)⟩,⟨0,0⟩⟩] +lemma ha0_0_2_eq (j : Fin 7) : ha0_0_2 j = ((ha0_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha0_0_2_contains (j : Fin 7) : (ha0_0_2 j).Contains (fullFactor false 0 2 ((j.val:ℝ)/6)) := by + rw [ha0_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_1 j) false 0 1 j (ha0_0_1_contains j) +noncomputable def hk0_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_3 j i k) +lemma hk0_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_3 j i k).Contains (fullFactor false 0 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 3 (power0_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha0_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨(-23924596203935046431862759073),(-23924596203935046431634296006)⟩⟩,⟨⟨0,0⟩,⟨(-191396769631480371454902072579),(-191396769631480371453074368056)⟩⟩,⟨⟨0,0⟩,⟨(-645964097506246253660294494946),(-645964097506246253654125992194)⟩⟩,⟨⟨0,0⟩,⟨(-1531174157051842971639216580616),(-1531174157051842971624594944455)⟩⟩,⟨⟨0,0⟩,⟨(-2990574525491880803982844884016),(-2990574525491880803954287000897)⟩⟩,⟨⟨0,0⟩,⟨(-5167712780049970029282355959565),(-5167712780049970029233007937558)⟩⟩] +lemma ha0_0_3_eq (j : Fin 7) : ha0_0_3 j = ((ha0_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha0_0_3_contains (j : Fin 7) : (ha0_0_3 j).Contains (fullFactor false 0 3 ((j.val:ℝ)/6)) := by + rw [ha0_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_2 j) false 0 2 j (ha0_0_2_contains j) +noncomputable def hk0_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_4 j i k) +lemma hk0_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_4 j i k).Contains (fullFactor false 0 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 4 (power0_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha0_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨3131722319766024859700118531,3131722319766024859739992859⟩,⟨0,0⟩⟩,⟨⟨50107557116256397755201896499,50107557116256397755839885733⟩,⟨0,0⟩⟩,⟨⟨253669507901048013635709601029,253669507901048013638939421518⟩,⟨0,0⟩⟩,⟨⟨801720913860102364083230343990,801720913860102364093438171712⟩,⟨0,0⟩⟩,⟨⟨1957326449853765537312574082013,1957326449853765537337495536405⟩,⟨0,0⟩⟩,⟨⟨4058712126416768218171353616472,4058712126416768218223030744275⟩,⟨0,0⟩⟩] +lemma ha0_0_4_eq (j : Fin 7) : ha0_0_4 j = ((ha0_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha0_0_4_contains (j : Fin 7) : (ha0_0_4 j).Contains (fullFactor false 0 4 ((j.val:ℝ)/6)) := by + rw [ha0_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_3 j) false 0 3 j (ha0_0_3_contains j) +noncomputable def hk0_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_5 j i k) +lemma hk0_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_5 j i k).Contains (fullFactor false 0 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 5 (power0_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha0_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨327953194428670967572717187,327953194428670967577936726⟩⟩,⟨⟨0,0⟩,⟨10494502221717470962326950007,10494502221717470962493975199⟩⟩,⟨⟨0,0⟩,⟨79692626246167045120170276622,79692626246167045121438624163⟩⟩,⟨⟨0,0⟩,⟨335824071094959070794462400250,335824071094959070799807206348⟩⟩,⟨⟨0,0⟩,⟨1024853732589596773664741211707,1024853732589596773681052265465⟩⟩,⟨⟨0,0⟩,⟨2550164039877345443845448851923,2550164039877345443886035973189⟩⟩] +lemma ha0_0_5_eq (j : Fin 7) : ha0_0_5 j = ((ha0_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha0_0_5_contains (j : Fin 7) : (ha0_0_5 j).Contains (fullFactor false 0 5 ((j.val:ℝ)/6)) := by + rw [ha0_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_4 j) false 0 4 j (ha0_0_4_contains j) +noncomputable def hk0_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_6 j i k) +lemma hk0_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_6 j i k).Contains (fullFactor false 0 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 6 (power0_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha0_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-28619315176067161691830963),(-28619315176067161691284373)⟩,⟨0,0⟩⟩,⟨⟨(-1831636171268298348277181568),(-1831636171268298348242199892)⟩,⟨0,0⟩⟩,⟨⟨(-20863480763352960873344771286),(-20863480763352960872946308154)⟩,⟨0,0⟩⟩,⟨⟨(-117224714961171094289739620283),(-117224714961171094287500793139)⟩,⟨0,0⟩⟩,⟨⟨(-447176799626049401434858780983),(-447176799626049401426318333206)⟩,⟨0,0⟩⟩,⟨⟨(-1335262768854589495894065362267),(-1335262768854589495868563721867)⟩,⟨0,0⟩⟩] +lemma ha0_0_6_eq (j : Fin 7) : ha0_0_6 j = ((ha0_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha0_0_6_contains (j : Fin 7) : (ha0_0_6 j).Contains (fullFactor false 0 6 ((j.val:ℝ)/6)) := by + rw [ha0_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_5 j) false 0 5 j (ha0_0_5_contains j) +noncomputable def hk0_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_7 j i k) +lemma hk0_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_7 j i k).Contains (fullFactor false 0 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 7 (power0_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha0_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨(-2140719769235797028240607),(-2140719769235797028192907)⟩⟩,⟨⟨0,0⟩,⟨(-274012130462182019614797623),(-274012130462182019608692168)⟩⟩,⟨⟨0,0⟩,⟨(-4681754135318688100762206250),(-4681754135318688100657888845)⟩⟩,⟨⟨0,0⟩,⟨(-35073552699159298510694095655),(-35073552699159298509912597553)⟩⟩,⟨⟨0,0⟩,⟨(-167243731971546642831297376890),(-167243731971546642827570903557)⟩⟩,⟨⟨0,0⟩,⟨(-599264529320792076897562399958),(-599264529320792076884209772268)⟩⟩] +lemma ha0_0_7_eq (j : Fin 7) : ha0_0_7 j = ((ha0_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha0_0_7_contains (j : Fin 7) : (ha0_0_7 j).Contains (fullFactor false 0 7 ((j.val:ℝ)/6)) := by + rw [ha0_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_6 j) false 0 6 j (ha0_0_6_contains j) +noncomputable def hk0_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_8 j i k) +lemma hk0_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_8 j i k).Contains (fullFactor false 0 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 8 (power0_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha0_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨140109781258867029452145,140109781258867029455714⟩,⟨0,0⟩⟩,⟨⟨35868104002269959539749316,35868104002269959540662691⟩,⟨0,0⟩⟩,⟨⟨919260274839426580235528386,919260274839426580258937158⟩,⟨0,0⟩⟩,⟨⟨9182234624581109642175825077,9182234624581109642409648763⟩,⟨0,0⟩⟩,⟨⟨54730383304244933379744440781,54730383304244933381138138549⟩,⟨0,0⟩⟩,⟨⟨235330630358893204540295266938,235330630358893204546287912233⟩,⟨0,0⟩⟩] +lemma ha0_0_8_eq (j : Fin 7) : ha0_0_8 j = ((ha0_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha0_0_8_contains (j : Fin 7) : (ha0_0_8 j).Contains (fullFactor false 0 8 ((j.val:ℝ)/6)) := by + rw [ha0_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_7 j) false 0 7 j (ha0_0_7_contains j) +noncomputable def hk0_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_9 j i k) +lemma hk0_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_9 j i k).Contains (fullFactor false 0 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 9 (power0_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha0_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨8151256657387584304803,8151256657387584305037⟩⟩,⟨⟨0,0⟩,⟨4173443408582443164059355,4173443408582443164178917⟩⟩,⟨⟨0,0⟩,⟨160441184787359821871445891,160441184787359821876042194⟩⟩,⟨⟨0,0⟩,⟨2136803025194210899998390072,2136803025194210900059604970⟩⟩,⟨⟨0,0⟩,⟨15920423158960125595319197120,15920423158960125595775283649⟩⟩,⟨⟨0,0⟩,⟨82145886611128228798180296470,82145886611128228800533602775⟩⟩] +lemma ha0_0_9_eq (j : Fin 7) : ha0_0_9 j = ((ha0_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha0_0_9_contains (j : Fin 7) : (ha0_0_9 j).Contains (fullFactor false 0 9 ((j.val:ℝ)/6)) := by + rw [ha0_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_8 j) false 0 8 j (ha0_0_8_contains j) +noncomputable def hk0_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_10 j i k) +lemma hk0_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_10 j i k).Contains (fullFactor false 0 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 10 (power0_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha0_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-426798800539562151462),(-426798800539562151447)⟩,⟨0,0⟩⟩,⟨⟨(-437041971752511643096456),(-437041971752511643082544)⟩,⟨0,0⟩⟩,⟨⟨(-25202042373060605481643175),(-25202042373060605480840967)⟩,⟨0,0⟩⟩,⟨⟨(-447530979074571922530770593),(-447530979074571922516525238)⟩,⟨0,0⟩⟩,⟨⟨(-4167957036519161635365063252),(-4167957036519161635232393058)⟩,⟨0,0⟩⟩,⟨⟨(-25806891390014060013202610057),(-25806891390014060012381151189)⟩,⟨0,0⟩⟩] +lemma ha0_0_10_eq (j : Fin 7) : ha0_0_10 j = ((ha0_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha0_0_10_contains (j : Fin 7) : (ha0_0_10 j).Contains (fullFactor false 0 10 ((j.val:ℝ)/6)) := by + rw [ha0_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_9 j) false 0 9 j (ha0_0_9_contains j) +noncomputable def hk0_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_11 j i k) +lemma hk0_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_11 j i k).Contains (fullFactor false 0 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 11 (power0_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha0_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨(-20315575399030665722),(-20315575399030665720)⟩⟩,⟨⟨0,0⟩,⟨(-41606298417214803397455),(-41606298417214803395998)⟩⟩,⟨⟨0,0⟩,⟨(-3598843235212085340551242),(-3598843235212085340425230)⟩⟩,⟨⟨0,0⟩,⟨(-85209699158455917357987615),(-85209699158455917355004074)⟩⟩,⟨⟨0,0⟩,⟨(-991971455030794224678394552),(-991971455030794224643661576)⟩⟩,⟨⟨0,0⟩,⟨(-7370430945714350777448941367),(-7370430945714350777190872451)⟩⟩] +lemma ha0_0_11_eq (j : Fin 7) : ha0_0_11 j = ((ha0_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha0_0_11_contains (j : Fin 7) : (ha0_0_11 j).Contains (fullFactor false 0 11 ((j.val:ℝ)/6)) := by + rw [ha0_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_10 j) false 0 10 j (ha0_0_10_contains j) +noncomputable def hk0_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_12 j i k) +lemma hk0_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_12 j i k).Contains (fullFactor false 0 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 12 (power0_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha0_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨886434200375614885,886434200375614886⟩,⟨0,0⟩⟩,⟨⟨3630834484738518570986,3630834484738518571126⟩,⟨0,0⟩⟩,⟨⟨471087477881817150362271,471087477881817150380266⟩,⟨0,0⟩⟩,⟨⟨14871898049488972066762446,14871898049488972067330512⟩,⟨0,0⟩⟩,⟨⟨216414599701077852904017301,216414599701077852912283730⟩,⟨0,0⟩⟩,⟨⟨1929574309403923047883862689,1929574309403923047957567000⟩,⟨0,0⟩⟩] +lemma ha0_0_12_eq (j : Fin 7) : ha0_0_12 j = ((ha0_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha0_0_12_contains (j : Fin 7) : (ha0_0_12 j).Contains (fullFactor false 0 12 ((j.val:ℝ)/6)) := by + rw [ha0_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_11 j) false 0 11 j (ha0_0_11_contains j) +noncomputable def hk0_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_13 j i k) +lemma hk0_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_13 j i k).Contains (fullFactor false 0 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 13 (power0_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha0_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨35702758612702236,35702758612702237⟩⟩,⟨⟨0,0⟩,⟨292476998555256723019,292476998555256723033⟩⟩,⟨⟨0,0⟩,⟨56921729219679268117129,56921729219679268119486⟩⟩,⟨⟨0,0⟩,⟨2395971572164663074980419,2395971572164663075079566⟩⟩,⟨⟨0,0⟩,⟨43582469009646285030256328,43582469009646285032059784⟩⟩,⟨⟨0,0⟩,⟨466302805767612564415528309,466302805767612564434824054⟩⟩] +lemma ha0_0_13_eq (j : Fin 7) : ha0_0_13 j = ((ha0_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha0_0_13_contains (j : Fin 7) : (ha0_0_13 j).Contains (fullFactor false 0 13 ((j.val:ℝ)/6)) := by + rw [ha0_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_12 j) false 0 12 j (ha0_0_12_contains j) +noncomputable def hk0_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_14 j i k) +lemma hk0_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_14 j i k).Contains (fullFactor false 0 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 14 (power0_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha0_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1335280049649466),(-1335280049649465)⟩,⟨0,0⟩⟩,⟨⟨(-21877228333456835519),(-21877228333456835517)⟩,⟨0,0⟩⟩,⟨⟨(-6386603083791852241300),(-6386603083791852241014)⟩,⟨0,0⟩⟩,⟨⟨(-358436509015356793129496),(-358436509015356793113522)⟩,⟨0,0⟩⟩,⟨⟨(-8149902646786285757332178),(-8149902646786285756968990)⟩,⟨0,0⟩⟩,⟨⟨(-104638104924845707121447140),(-104638104924845707116784111)⟩,⟨0,0⟩⟩] +lemma ha0_0_14_eq (j : Fin 7) : ha0_0_14 j = ((ha0_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha0_0_14_contains (j : Fin 7) : (ha0_0_14 j).Contains (fullFactor false 0 14 ((j.val:ℝ)/6)) := by + rw [ha0_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_13 j) false 0 13 j (ha0_0_13_contains j) +noncomputable def hk0_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_15 j i k) +lemma hk0_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_15 j i k).Contains (fullFactor false 0 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 15 (power0_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha0_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨(-46610066605154),(-46610066605153)⟩⟩,⟨⟨0,0⟩,⟨(-1527318662517654887),(-1527318662517654886)⟩⟩,⟨⟨0,0⟩,⟨(-668803510981146723272),(-668803510981146723239)⟩⟩,⟨⟨0,0⟩,⟨(-50047177933378515329214),(-50047177933378515326824)⟩⟩,⟨⟨0,0⟩,⟨(-1422426349034211492869813),(-1422426349034211492801896)⟩⟩,⟨⟨0,0⟩,⟨(-21915353447830215828154435),(-21915353447830215827108053)⟩⟩] +lemma ha0_0_15_eq (j : Fin 7) : ha0_0_15 j = ((ha0_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha0_0_15_contains (j : Fin 7) : (ha0_0_15 j).Contains (fullFactor false 0 15 ((j.val:ℝ)/6)) := by + rw [ha0_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_14 j) false 0 14 j (ha0_0_14_contains j) +noncomputable def hk0_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_16 j i k) +lemma hk0_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_16 j i k).Contains (fullFactor false 0 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 16 (power0_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha0_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1525310862813,1525310862814⟩,⟨0,0⟩⟩,⟨⟨99962772705334443,99962772705334444⟩,⟨0,0⟩⟩,⟨⟨65659631149794723621,65659631149794723625⟩,⟨0,0⟩⟩,⟨⟨6551160272016798098662,6551160272016798098997⟩,⟨0,0⟩⟩,⟨⟨232743967104084891369912,232743967104084891381767⟩,⟨0,0⟩⟩,⟨⟨4303069587032947007239892,4303069587032947007459047⟩,⟨0,0⟩⟩] +lemma ha0_0_16_eq (j : Fin 7) : ha0_0_16 j = ((ha0_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha0_0_16_contains (j : Fin 7) : (ha0_0_16 j).Contains (fullFactor false 0 16 ((j.val:ℝ)/6)) := by + rw [ha0_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_15 j) false 0 15 j (ha0_0_15_contains j) +noncomputable def hk0_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_17 j i k) +lemma hk0_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_17 j i k).Contains (fullFactor false 0 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 17 (power0_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha0_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨46979464716,46979464717⟩⟩,⟨⟨0,0⟩,⟨6157692399285195,6157692399285196⟩⟩,⟨⟨0,0⟩,⟨6066935731106195666,6066935731106195668⟩⟩,⟨⟨0,0⟩,⟨807101058159109193405,807101058159109193450⟩⟩,⟨⟨0,0⟩,⟨35842487118702823485606,35842487118702823487546⟩⟩,⟨⟨0,0⟩,⟨795205400147551278466945,795205400147551278509977⟩⟩] +lemma ha0_0_17_eq (j : Fin 7) : ha0_0_17 j = ((ha0_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha0_0_17_contains (j : Fin 7) : (ha0_0_17 j).Contains (fullFactor false 0 17 ((j.val:ℝ)/6)) := by + rw [ha0_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_16 j) false 0 16 j (ha0_0_16_contains j) +noncomputable def hk0_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_18 j i k) +lemma hk0_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_18 j i k).Contains (fullFactor false 0 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 18 (power0_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha0_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1366577234),(-1366577233)⟩,⟨0,0⟩⟩,⟨⟨(-358240022308520),(-358240022308519)⟩,⟨0,0⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨0,0⟩⟩,⟨⟨(-93910472408044662742),(-93910472408044662736)⟩,⟨0,0⟩⟩,⟨⟨(-5213078436041832671824),(-5213078436041832671524)⟩,⟨0,0⟩⟩,⟨⟨(-138789524622137721150531),(-138789524622137721142578)⟩,⟨0,0⟩⟩] +lemma ha0_0_18_eq (j : Fin 7) : ha0_0_18 j = ((ha0_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha0_0_18_contains (j : Fin 7) : (ha0_0_18 j).Contains (fullFactor false 0 18 ((j.val:ℝ)/6)) := by + rw [ha0_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_17 j) false 0 17 j (ha0_0_17_contains j) +noncomputable def hk0_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_19 j i k) +lemma hk0_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_19 j i k).Contains (fullFactor false 0 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 19 (power0_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha0_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨(-37659904),(-37659903)⟩⟩,⟨⟨0,0⟩,⟨(-19744635479058),(-19744635479057)⟩⟩,⟨⟨0,0⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨0,0⟩,⟨(-10351875446044213762),(-10351875446044213761)⟩⟩,⟨⟨0,0⟩,⟨(-718305654265631155073),(-718305654265631155028)⟩⟩,⟨⟨0,0⟩,⟨(-22948428997269873111225),(-22948428997269873109836)⟩⟩] +lemma ha0_0_19_eq (j : Fin 7) : ha0_0_19 j = ((ha0_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha0_0_19_contains (j : Fin 7) : (ha0_0_19 j).Contains (fullFactor false 0 19 ((j.val:ℝ)/6)) := by + rw [ha0_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_18 j) false 0 18 j (ha0_0_18_contains j) +noncomputable def hk0_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_20 j i k) +lemma hk0_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_20 j i k).Contains (fullFactor false 0 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 20 (power0_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha0_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨985933,985934⟩,⟨0,0⟩⟩,⟨⟨1033826696146,1033826696147⟩,⟨0,0⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨0,0⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨0,0⟩⟩,⟨⟨94025990269704865211,94025990269704865218⟩,⟨0,0⟩⟩,⟨⟨3604730797462500933798,3604730797462500934029⟩,⟨0,0⟩⟩] +lemma ha0_0_20_eq (j : Fin 7) : ha0_0_20 j = ((ha0_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha0_0_20_contains (j : Fin 7) : (ha0_0_20 j).Contains (fullFactor false 0 20 ((j.val:ℝ)/6)) := by + rw [ha0_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_19 j) false 0 19 j (ha0_0_19_contains j) +noncomputable def hk0_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_21 j i k) +lemma hk0_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_21 j i k).Contains (fullFactor false 0 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 21 (power0_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha0_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨24582,24583⟩⟩,⟨⟨0,0⟩,⟨51553370693,51553370694⟩⟩,⟨⟨0,0⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨0,0⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨0,0⟩,⟨11721879376103578822,11721879376103578824⟩⟩,⟨⟨0,0⟩,⟨539266466260812848925,539266466260812848962⟩⟩] +lemma ha0_0_21_eq (j : Fin 7) : ha0_0_21 j = ((ha0_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha0_0_21_contains (j : Fin 7) : (ha0_0_21 j).Contains (fullFactor false 0 21 ((j.val:ℝ)/6)) := by + rw [ha0_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_20 j) false 0 20 j (ha0_0_20_contains j) +noncomputable def hk0_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_22 j i k) +lemma hk0_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_22 j i k).Contains (fullFactor false 0 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 22 (power0_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha0_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-586),(-585)⟩,⟨0,0⟩⟩,⟨⟨(-2453934707),(-2453934706)⟩,⟨0,0⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨0,0⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨0,0⟩⟩,⟨⟨(-1394900383872451220),(-1394900383872451219)⟩,⟨0,0⟩⟩,⟨⟨(-77007071306013533802),(-77007071306013533796)⟩,⟨0,0⟩⟩] +lemma ha0_0_22_eq (j : Fin 7) : ha0_0_22 j = ((ha0_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha0_0_22_contains (j : Fin 7) : (ha0_0_22 j).Contains (fullFactor false 0 22 ((j.val:ℝ)/6)) := by + rw [ha0_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_21 j) false 0 21 j (ha0_0_21_contains j) +noncomputable def hk0_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_23 j i k) +lemma hk0_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_23 j i k).Contains (fullFactor false 0 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 23 (power0_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha0_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨(-14),(-13)⟩⟩,⟨⟨0,0⟩,⟨(-111728453),(-111728452)⟩⟩,⟨⟨0,0⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨0,0⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨0,0⟩,⟨(-158775681103741858),(-158775681103741857)⟩⟩,⟨⟨0,0⟩,⟨(-10518471716932064456),(-10518471716932064454)⟩⟩] +lemma ha0_0_23_eq (j : Fin 7) : ha0_0_23 j = ((ha0_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha0_0_23_contains (j : Fin 7) : (ha0_0_23 j).Contains (fullFactor false 0 23 ((j.val:ℝ)/6)) := by + rw [ha0_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_22 j) false 0 22 j (ha0_0_22_contains j) +noncomputable def hk0_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_24 j i k) +lemma hk0_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_24 j i k).Contains (fullFactor false 0 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 24 (power0_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha0_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,0⟩⟩,⟨⟨4875073,4875074⟩,⟨0,0⟩⟩,⟨⟨82067533018,82067533019⟩,⟨0,0⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨0,0⟩⟩,⟨⟨17319740045980249,17319740045980250⟩,⟨0,0⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨0,0⟩⟩] +lemma ha0_0_24_eq (j : Fin 7) : ha0_0_24 j = ((ha0_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha0_0_24_contains (j : Fin 7) : (ha0_0_24 j).Contains (fullFactor false 0 24 ((j.val:ℝ)/6)) := by + rw [ha0_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_23 j) false 0 23 j (ha0_0_23_contains j) +noncomputable def hk0_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_25 j i k) +lemma hk0_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_25 j i k).Contains (fullFactor false 0 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 25 (power0_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha0_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨0,1⟩⟩,⟨⟨0,0⟩,⟨204206,204207⟩⟩,⟨⟨0,0⟩,⟨5156455176,5156455177⟩⟩,⟨⟨0,0⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨0,0⟩,⟨1813718936351216,1813718936351217⟩⟩,⟨⟨0,0⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha0_0_25_eq (j : Fin 7) : ha0_0_25 j = ((ha0_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha0_0_25_contains (j : Fin 7) : (ha0_0_25 j).Contains (fullFactor false 0 25 ((j.val:ℝ)/6)) := by + rw [ha0_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_24 j) false 0 24 j (ha0_0_24_contains j) +noncomputable def hk0_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_26 j i k) +lemma hk0_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_26 j i k).Contains (fullFactor false 0 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 26 (power0_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha0_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,0⟩⟩,⟨⟨(-8225),(-8224)⟩,⟨0,0⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨0,0⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨0,0⟩⟩,⟨⟨(-182627118144798),(-182627118144797)⟩,⟨0,0⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨0,0⟩⟩] +lemma ha0_0_26_eq (j : Fin 7) : ha0_0_26 j = ((ha0_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha0_0_26_contains (j : Fin 7) : (ha0_0_26 j).Contains (fullFactor false 0 26 ((j.val:ℝ)/6)) := by + rw [ha0_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_25 j) false 0 25 j (ha0_0_25_contains j) +noncomputable def hk0_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_27 j i k) +lemma hk0_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_27 j i k).Contains (fullFactor false 0 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 27 (power0_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha0_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨(-1),0⟩⟩,⟨⟨0,0⟩,⟨(-320),(-318)⟩⟩,⟨⟨0,0⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨0,0⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨0,0⟩,⟨(-17708025083642),(-17708025083641)⟩⟩,⟨⟨0,0⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha0_0_27_eq (j : Fin 7) : ha0_0_27 j = ((ha0_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha0_0_27_contains (j : Fin 7) : (ha0_0_27 j).Contains (fullFactor false 0 27 ((j.val:ℝ)/6)) := by + rw [ha0_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_26 j) false 0 26 j (ha0_0_26_contains j) +noncomputable def hk0_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_28 j i k) +lemma hk0_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_28 j i k).Contains (fullFactor false 0 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 28 (power0_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha0_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,0⟩⟩,⟨⟨11,12⟩,⟨0,0⟩⟩,⟨⟨1016753,1016754⟩,⟨0,0⟩⟩,⟨⟨3202582746,3202582747⟩,⟨0,0⟩⟩,⟨⟨1655696473581,1655696473582⟩,⟨0,0⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨0,0⟩⟩] +lemma ha0_0_28_eq (j : Fin 7) : ha0_0_28 j = ((ha0_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha0_0_28_contains (j : Fin 7) : (ha0_0_28 j).Contains (fullFactor false 0 28 ((j.val:ℝ)/6)) := by + rw [ha0_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_27 j) false 0 27 j (ha0_0_27_contains j) +noncomputable def hk0_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_29 j i k) +lemma hk0_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_29 j i k).Contains (fullFactor false 0 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 29 (power0_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha0_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,0⟩,⟨0,1⟩⟩,⟨⟨0,0⟩,⟨0,1⟩⟩,⟨⟨0,0⟩,⟨55072,55073⟩⟩,⟨⟨0,0⟩,⟨231292193,231292194⟩⟩,⟨⟨0,0⟩,⟨149469076953,149469076954⟩⟩,⟨⟨0,0⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha0_0_29_eq (j : Fin 7) : ha0_0_29 j = ((ha0_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha0_0_29_contains (j : Fin 7) : (ha0_0_29 j).Contains (fullFactor false 0 29 ((j.val:ℝ)/6)) := by + rw [ha0_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_28 j) false 0 28 j (ha0_0_28_contains j) +noncomputable def hk0_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power0 j i k).conj.mul (mpower0_30 j i k) +lemma hk0_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk0_0_30 j i k).Contains (fullFactor false 0 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power0 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 30 (power0_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha0_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,0⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨0,0⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨0,0⟩⟩,⟨⟨(-13043637614),(-13043637613)⟩,⟨0,0⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨0,0⟩⟩] +lemma ha0_0_30_eq (j : Fin 7) : ha0_0_30 j = ((ha0_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha0_0_30_contains (j : Fin 7) : (ha0_0_30 j).Contains (fullFactor false 0 30 ((j.val:ℝ)/6)) := by + rw [ha0_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_0_29 j) false 0 29 j (ha0_0_29_contains j) +noncomputable def hk0_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_0 j i k) +lemma hk0_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_0 j i k).Contains (fullFactor true 0 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 0 (kernel0_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha0_1_0 : Fin 7 → CBox := ![⟨⟨2886751345948128822491487805010,2886751345948128822591487805032⟩,⟨0,0⟩⟩,⟨⟨2459717123174736984844818011358,2459717123174736984930025111996⟩,⟨1024882134656140410352007504727,1024882134656140410387510463337⟩⟩,⟨⟨1703656532034961272290058376722,1703656532034961272349074770188⟩,⟨1419713776695801060241715313933,1419713776695801060290895641830⟩⟩,⟨⟨1126537110613903930728385484882,1126537110613903930767409875134⟩,⟨1408171388267379913410481856103,1408171388267379913459262343918⟩⟩,⟨⟨764140062162739982424217360149,764140062162739982450687948391⟩,⟨1273566770271233304040362266913,1273566770271233304084479913987⟩⟩,⟨⟨540562020567660013574478860754,540562020567660013593204478445⟩,⟨1126170876182625028280164293239,1126170876182625028319175996763⟩⟩,⟨⟨398172599441121216895377628277,398172599441121216909170731728⟩,⟨995431498602803042238444070694,995431498602803042272926829319⟩⟩] +lemma ha0_1_0_eq (j : Fin 7) : ha0_1_0 j = atomKernel0_0 j := by fin_cases j <;> decide +kernel +lemma ha0_1_0_contains (j : Fin 7) : (ha0_1_0 j).Contains (fullFactor true 0 0 ((j.val:ℝ)/6)) := by + rw [ha0_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel0_0_contains j +noncomputable def hk0_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_1 j i k) +lemma hk0_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_1 j i k).Contains (fullFactor true 0 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 1 (kernel0_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha0_1_1 : Fin 7 → CBox := ![⟨⟨(-26602390675435195142530321043993),(-26602390675435195141524109159245)⟩,⟨0,0⟩⟩,⟨⟨(-15046386883137311960977771542034),(-15046386883137311960120407568771)⟩,⟨(-17001868484744399809876351294364),(-17001868484744399809233270664782)⟩⟩,⟨⟨(-1076288362329791189253868592463),(-1076288362329791188660038627375)⟩,⟨(-15764114872167322034205686079730),(-15764114872167322033609422385277)⟩⟩,⟨⟨4005248804305423355782453862022,4005248804305423356175121914620⟩,⟨(-9739775289205357801899857956194),(-9739775289205357801531459575359)⟩⟩,⟨⟨4725920142797114330304028335327,4725920142797114330570378540195⟩,⟨(-5460226459805430899811586813878),(-5460226459805430899605058580158)⟩⟩,⟨⟨4220020865203592699679309874866,4220020865203592699867729265570⟩,⟨(-3001523701832900019824858424479),(-3001523701832900019711328446699)⟩⟩,⟨⟨3519762856635247957323462123219,3519762856635247957462249969389⟩,⟨(-1624727135620028673173671104732),(-1624727135620028673112217238669)⟩⟩] +lemma ha0_1_1_eq (j : Fin 7) : ha0_1_1 j = ((ha0_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha0_1_1_contains (j : Fin 7) : (ha0_1_1 j).Contains (fullFactor true 0 1 ((j.val:ℝ)/6)) := by + rw [ha0_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_0 j) true 0 0 j (ha0_1_0_contains j) +noncomputable def hk0_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_2 j i k) +lemma hk0_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_2 j i k).Contains (fullFactor true 0 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 2 (kernel0_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha0_1_2 : Fin 7 → CBox := ![⟨⟨122575016833680145946165485035154,122575016833680145951191944967226⟩,⟨0,0⟩⟩,⟨⟨26069235626031647609706478198461,26069235626031647614472481490359⟩,⟨93140302574601179954538338970151,93140302574601179958893595750607⟩⟩,⟨⟨(-37944215806102898524592466427378),(-37944215806102898521457519868065)⟩,⟨41579190390315638283331423405430,41579190390315638286460796966097⟩⟩,⟨⟨(-30544155331490608593580758448756),(-30544155331490608591986969360482)⟩,⟨3551753641853769198810116530290,3551753641853769200410758846473⟩⟩,⟨⟨(-16193820427748643248264124005335),(-16193820427748643247533690618239)⟩,⟨(-6779755291778911362119083938956),(-6779755291778911361299416263861)⟩⟩,⟨⟨(-7617147420123301957985362582104),(-7617147420123301957662862301530)⟩,⟨(-7563023130467542967409370602406),(-7563023130467542966953713355555)⟩⟩,⟨⟨(-3263924834630237228947001158148),(-3263924834630237228812625677755)⟩,⟨(-6202437430717943902551971093760),(-6202437430717943902274904058483)⟩⟩] +lemma ha0_1_2_eq (j : Fin 7) : ha0_1_2 j = ((ha0_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha0_1_2_contains (j : Fin 7) : (ha0_1_2 j).Contains (fullFactor true 0 2 ((j.val:ℝ)/6)) := by + rw [ha0_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_1 j) true 0 1 j (ha0_1_1_contains j) +noncomputable def hk0_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_3 j i k) +lemma hk0_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_3 j i k).Contains (fullFactor true 0 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 3 (kernel0_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha0_1_3 : Fin 7 → CBox := ![⟨⟨(-376523421900594012592614772005042),(-376523421900594012575976084235160)⟩,⟨0,0⟩⟩,⟨⟨48809987803041999942073976988457,48809987803041999960229949915667⟩,⟨(-270318915570165811505208398992392),(-270318915570165811487312034815282)⟩⟩,⟨⟨133653069306944076432706769753192,133653069306944076443649467444468⟩,⟨(-3099516268066432372302167307032),(-3099516268066432361359922639148)⟩⟩,⟨⟨34860977790970562072704284207216,34860977790970562077044227997550⟩,⟨48658900604437533985790410931007,48658900604437533990190400092070⟩⟩,⟨⟨(-2260995287684620558357027388427),(-2260995287684620556666515253049)⟩,⟨28363007126667795566074427517862,28363007126667795567703604127357⟩⟩,⟨⟨(-8510797712665954827391102609601),(-8510797712665954826656416343930)⟩,⟨12148325821975021555980353941061,12148325821975021556565166867529⟩⟩,⟨⟨(-7261428317245967727087566777747),(-7261428317245967726721242894602)⟩,⟨4316923348433606886716098826636,4316923348433606886908926408839⟩⟩] +lemma ha0_1_3_eq (j : Fin 7) : ha0_1_3 j = ((ha0_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha0_1_3_contains (j : Fin 7) : (ha0_1_3 j).Contains (fullFactor true 0 3 ((j.val:ℝ)/6)) := by + rw [ha0_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_2 j) true 0 2 j (ha0_1_2_contains j) +noncomputable def hk0_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_4 j i k) +lemma hk0_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_4 j i k).Contains (fullFactor true 0 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 4 (kernel0_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha0_1_4 : Fin 7 → CBox := ![⟨⟨867447691841424037375730087701830,867447691841424037416824044255820⟩,⟨0,0⟩⟩,⟨⟨(-344799191015893237782636282188664),(-344799191015893237730107738612249)⟩,⟨472714532087218802170662546348818,472714532087218802223630815843831⟩⟩,⟨⟨(-168502477119929481021617292068649),(-168502477119929480993523159811359)⟩,⟨(-168268249794520808740366920378689),(-168268249794520808712249220012564)⟩⟩,⟨⟨37476798071125241954044574792413,37476798071125241963010474926808⟩,⟨(-78945935801875602754545117424259),(-78945935801875602745638433276186)⟩⟩,⟨⟨33615750077841320707998364320310,33615750077841320710627493279873⟩,⟨(-8133573042759238926567384524429),(-8133573042759238923955136817870)⟩⟩,⟨⟨13905926263215755875669178915598,13905926263215755876440087146115⟩,⟨6553250277975291833751138323388,6553250277975291834638939861295⟩⟩,⟨⟨4238006341972060242893386947745,4238006341972060243098149762052⟩,⟨6352650888734558808361745896356,6352650888734558808723010367829⟩⟩] +lemma ha0_1_4_eq (j : Fin 7) : ha0_1_4 j = ((ha0_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha0_1_4_contains (j : Fin 7) : (ha0_1_4 j).Contains (fullFactor true 0 4 ((j.val:ℝ)/6)) := by + rw [ha0_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_3 j) true 0 3 j (ha0_1_3_contains j) +noncomputable def hk0_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_5 j i k) +lemma hk0_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_5 j i k).Contains (fullFactor true 0 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 5 (kernel0_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha0_1_5 : Fin 7 → CBox := ![⟨⟨(-1598764813689965140490052670095148),(-1598764813689965140409224700052429)⟩,⟨0,0⟩⟩,⟨⟨880159352830126332701690401746935,880159352830126332824416945644927⟩,⟨(-468404530205674225270505881647072),(-468404530205674225147110568541910)⟩⟩,⟨⟨(-7395496229973392529015512495709),(-7395496229973392471309023135855)⟩,⟨339257937224101252378477233823803,339257937224101252436182688835634⟩⟩,⟨⟨(-101867374863453155668837116279098),(-101867374863453155654338616627522)⟩,⟨6394801612272420045432204455373,6394801612272420059897539275786⟩⟩,⟨⟨(-17703372700914776771292337060819),(-17703372700914776768025460729844)⟩,⟨(-28595827953225404735516853939339),(-28595827953225404732189130816710)⟩⟩,⟨⟨3395590697593533936409390239866,3395590697593533937266646197770⟩,⟨(-12285062530841304032610489393765),(-12285062530841304031816450538056)⟩⟩,⟨⟨4428760621654995248566013589851,4428760621654995248849720880012⟩,⟨(-3299281963373695137025726534974),(-3299281963373695136853776655157)⟩⟩] +lemma ha0_1_5_eq (j : Fin 7) : ha0_1_5 j = ((ha0_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha0_1_5_contains (j : Fin 7) : (ha0_1_5 j).Contains (fullFactor true 0 5 ((j.val:ℝ)/6)) := by + rw [ha0_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_4 j) true 0 4 j (ha0_1_4_contains j) +noncomputable def hk0_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_6 j i k) +lemma hk0_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_6 j i k).Contains (fullFactor true 0 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 6 (kernel0_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha0_1_6 : Fin 7 → CBox := ![⟨⟨2455526476825277280058497997797438,2455526476825277280190457031367505⟩,⟨0,0⟩⟩,⟨⟨(-1414827786667715020236885853709034),(-1414827786667715019999112899090889)⟩,⟨53097741910714307998261014478895,53097741910714308235611567960456⟩⟩,⟨⟨297273661166520986271217600146506,297273661166520986369049246171276⟩,⟨(-272043977029042819660125305689424),(-272043977029042819562333516631313)⟩⟩,⟨⟨53491640388523389895742478263826,53491640388523389915066674847407⟩,⟨83711656664765128452749033612300,83711656664765128472201218431782⟩⟩,⟨⟨(-17547582680759076158733007766277),(-17547582680759076155261266659985)⟩,⟨20853710522524487871235595170437,20853710522524487874657911271924⟩⟩,⟨⟨(-8763274820287268917616073715360),(-8763274820287268916946903765043)⟩,⟨(-869926967404599801785881395354),(-869926967404599801097033494485)⟩⟩,⟨⟨(-2124232719080088710657698913707),(-2124232719080088710538572577149)⟩,⟨(-2562142113913751173883818053394),(-2562142113913751173698878170568)⟩⟩] +lemma ha0_1_6_eq (j : Fin 7) : ha0_1_6 j = ((ha0_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha0_1_6_contains (j : Fin 7) : (ha0_1_6 j).Contains (fullFactor true 0 6 ((j.val:ℝ)/6)) := by + rw [ha0_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_5 j) true 0 5 j (ha0_1_5_contains j) +noncomputable def hk0_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_7 j i k) +lemma hk0_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_7 j i k).Contains (fullFactor true 0 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 7 (kernel0_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha0_1_7 : Fin 7 → CBox := ![⟨⟨(-3232643936883226917773237766128494),(-3232643936883226917589226918611983)⟩,⟨0,0⟩⟩,⟨⟨1577686393455906750370832667679233,1577686393455906750762320095248118⟩,⟨693296249765990635183047897382840,693296249765990635571852170235058⟩⟩,⟨⟨(-409244016092063194237369751191339),(-409244016092063194095306929978559)⟩,⟨(-27369098399286924816328417972231),(-27369098399286924674261706714316)⟩⟩,⟨⟨39463138294956164152879978741715,39463138294956164175151047477900⟩,⟨(-72879037225148672050585150013334),(-72879037225148672028387045744207)⟩⟩,⟨⟨17562108575747576133385804677433,17562108575747576136451990707720⟩,⟨7066976789719042660862309744334,7066976789719042663945749226886⟩⟩,⟨⟨374015629019298092985038314230,374015629019298093458810593804⟩,⟨5201895121772923680135740341424,5201895121772923680612143686970⟩⟩,⟨⟨(-1264726797943523122759333808060),(-1264726797943523122656346515208)⟩,⟨1164537382691026244145604000566,1164537382691026244215724421801⟩⟩] +lemma ha0_1_7_eq (j : Fin 7) : ha0_1_7 j = ((ha0_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha0_1_7_contains (j : Fin 7) : (ha0_1_7 j).Contains (fullFactor true 0 7 ((j.val:ℝ)/6)) := by + rw [ha0_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_6 j) true 0 6 j (ha0_1_6_contains j) +noncomputable def hk0_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_8 j i k) +lemma hk0_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_8 j i k).Contains (fullFactor true 0 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 8 (kernel0_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha0_1_8 : Fin 7 → CBox := ![⟨⟨3723738496054108744502617800747911,3723738496054108744726436108322157⟩,⟨0,0⟩⟩,⟨⟨(-1189665878201300779265569897725647),(-1189665878201300778703887799236207)⟩,⟨(-1397573397413262972223644018642461),(-1397573397413262971664675562753822)⟩⟩,⟨⟨234247050052601412598126672380769,234247050052601412777874205370450⟩,⟨280302729584929402694968535766483,280302729584929402874750389912882⟩⟩,⟨⟨(-60495846405266676032920492846514),(-60495846405266676010675304184064)⟩,⟨582247156042652058946927933532,582247156042652081182604253999⟩⟩,⟨⟨754562725148757516078660223484,754562725148757518463717644991⟩,⟨(-11480717599090984490110365048947),(-11480717599090984487719038756962)⟩⟩,⟨⟨2623482555263848135963066703520,2623482555263848136256618244621⟩,⟨(-648960687993370566361520301568),(-648960687993370566075575433927)⟩⟩,⟨⟨555332100573006390123999604184,555332100573006390159835398204⟩,⟨543536538610673671409349353332,543536538610673671459385563057⟩⟩] +lemma ha0_1_8_eq (j : Fin 7) : ha0_1_8 j = ((ha0_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha0_1_8_contains (j : Fin 7) : (ha0_1_8 j).Contains (fullFactor true 0 8 ((j.val:ℝ)/6)) := by + rw [ha0_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_7 j) true 0 7 j (ha0_1_7_contains j) +noncomputable def hk0_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_9 j i k) +lemma hk0_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_9 j i k).Contains (fullFactor true 0 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 9 (kernel0_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha0_1_9 : Fin 7 → CBox := ![⟨⟨(-3812834504711823004642566730148701),(-3812834504711823004401256605894691)⟩,⟨0,0⟩⟩,⟨⟨436029779665833495772881401000412,436029779665833496487294850257288⟩,⟨1681903459729391382822678914731646,1681903459729391383536192200713899⟩⟩,⟨⟨32252854678313675367562289219527,32252854678313675569691760113375⟩,⟨(-287387894315032030551503961936558),(-287387894315032030349379046364275)⟩⟩,⟨⟨19352974754520385713994106431730,19352974754520385733671229254843⟩,⟨34153557189255984149916607009275,34153557189255984169644415085074⟩⟩,⟨⟨(-6020469196966551652856073759826),(-6020469196966551651207786255929)⟩,⟨1545700877786890007968862817710,1545700877786890009603210078403⟩⟩,⟨⟨(-499880945114411518661863942528),(-499880945114411518507503964940)⟩,⟨(-1140070734293967039014126575594),(-1140070734293967038854547936297)⟩⟩,⟨⟨206494224749534439906533662372,206494224749534439928088165983⟩,⟨(-234153372680575324232183833792),(-234153372680575324216016339096)⟩⟩] +lemma ha0_1_9_eq (j : Fin 7) : ha0_1_9 j = ((ha0_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha0_1_9_contains (j : Fin 7) : (ha0_1_9 j).Contains (fullFactor true 0 9 ((j.val:ℝ)/6)) := by + rw [ha0_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_8 j) true 0 8 j (ha0_1_8_contains j) +noncomputable def hk0_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_10 j i k) +lemma hk0_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_10 j i k).Contains (fullFactor true 0 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 10 (kernel0_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha0_1_10 : Fin 7 → CBox := ![⟨⟨3513656041677860039312087919852527,3513656041677860039545647681055097⟩,⟨0,0⟩⟩,⟨⟨291037907098962430397909081541977,291037907098962431213923603265140⟩,⟨(-1451495633503554669863955680538988),(-1451495633503554669046730756510256)⟩⟩,⟨⟨(-163888969548784857950487938113228),(-163888969548784857746349502920945)⟩,⟨124886018935341366281753946749526,124886018935341366485874081985008⟩⟩,⟨⟨11969728111190136703970359994674,11969728111190136719689447063027⟩,⟨(-19551456905560631709121460841397),(-19551456905560631693424654790254)⟩⟩,⟨⟨1626427822473326756622937381668,1626427822473326757632955442113⟩,⟨2547221484270369346671637672226,2547221484270369347690405790208⟩⟩,⟨⟨(-430545778683493740604544317727),(-430545778683493740526885464801)⟩,⟨284511920552457943817955609450,284511920552457943893161063465⟩⟩,⟨⟨(-88430803894209769824217860403),(-88430803894209769817693515834)⟩,⟨(-70168825825250057564513242611),(-70168825825250057556174927703)⟩⟩] +lemma ha0_1_10_eq (j : Fin 7) : ha0_1_10 j = ((ha0_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha0_1_10_contains (j : Fin 7) : (ha0_1_10 j).Contains (fullFactor true 0 10 ((j.val:ℝ)/6)) := by + rw [ha0_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_9 j) true 0 9 j (ha0_1_9_contains j) +noncomputable def hk0_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_11 j i k) +lemma hk0_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_11 j i k).Contains (fullFactor true 0 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 11 (kernel0_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha0_1_11 : Fin 7 → CBox := ![⟨⟨(-2943593602073748658317270020841335),(-2943593602073748658112233703404174)⟩,⟨0,0⟩⟩,⟨⟨(-693420238709213552484898630347855),(-693420238709213551637774723613048)⟩,⟨913223666937108357981116331189836,913223666937108358830000583560964⟩⟩,⟨⟨131826974295335034158520428042053,131826974295335034345879547684918⟩,⟨20833738762883269547119948036078,20833738762883269734482002239739⟩⟩,⟨⟨(-12158955634272761580312817697288),(-12158955634272761568940613416110)⟩,⟨(-528577485031563430692678701287),(-528577485031563419320858079525)⟩⟩,⟨⟨845774348781293067805293494378,845774348781293068376433435271⟩,⟨(-1034002499164252522386354581687),(-1034002499164252521818511488346)⟩⟩,⟨⟨133231907503014887088853008216,133231907503014887122180013519⟩,⟨141683980481636900798579216895,141683980481636900832803180399⟩⟩,⟨⟨(-21525137137162247539767274487),(-21525137137162247536840514146)⟩,⟨30227433749918256434521159936,30227433749918256436901494254⟩⟩] +lemma ha0_1_11_eq (j : Fin 7) : ha0_1_11 j = ((ha0_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha0_1_11_contains (j : Fin 7) : (ha0_1_11 j).Contains (fullFactor true 0 11 ((j.val:ℝ)/6)) := by + rw [ha0_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_10 j) true 0 10 j (ha0_1_10_contains j) +noncomputable def hk0_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_12 j i k) +lemma hk0_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_12 j i k).Contains (fullFactor true 0 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 12 (kernel0_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha0_1_12 : Fin 7 → CBox := ![⟨⟨2260517608660374788210741455408337,2260517608660374788375393494756009⟩,⟨0,0⟩⟩,⟨⟨725929797062619660886299315683820,725929797062619661692800036415733⟩,⟨(-368578516548605769133937409647717),(-368578516548605768326627272817175)⟩⟩,⟨⟨(-45146595706461678253920992181173),(-45146595706461678096435852197792)⟩,⟨(-65125399634853769161008156587736),(-65125399634853769003516400295651)⟩⟩,⟨⟨2642464218391766458829705419506,2642464218391766466362353147120⟩,⟨5300602212145842245642156949330,5300602212145842253181906174376⟩⟩,⟨⟨(-504894166280150813408545989587),(-504894166280150813116196398746)⟩,⟨(-195048832577319844211081272438),(-195048832577319843918033734610)⟩⟩,⟨⟨40415425052457423855240828300,40415425052457423869026539440⟩,⟨(-53673377086763792320959630315),(-53673377086763792307434216596)⟩⟩,⟨⟨9432824795583496248224109195,9432824795583496249016219543⟩,⟨6004327005721240540302824779,6004327005721240541242912572⟩⟩] +lemma ha0_1_12_eq (j : Fin 7) : ha0_1_12 j = ((ha0_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha0_1_12_contains (j : Fin 7) : (ha0_1_12 j).Contains (fullFactor true 0 12 ((j.val:ℝ)/6)) := by + rw [ha0_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_11 j) true 0 11 j (ha0_1_11_contains j) +noncomputable def hk0_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_13 j i k) +lemma hk0_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_13 j i k).Contains (fullFactor true 0 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 13 (kernel0_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha0_1_13 : Fin 7 → CBox := ![⟨⟨(-1602418064399093470617130550010718),(-1602418064399093470495312643419349)⟩,⟨0,0⟩⟩,⟨⟨(-533497559334657600837614023742851),(-533497559334657600129432255036803)⟩,⟨9746259713948121886040683957501,9746259713948122594122811527524⟩⟩,⟨⟨(-8701876549661017563231409202711),(-8701876549661017441057036459112)⟩,⟨42550744195529186512203391653623,42550744195529186634376540532567⟩⟩,⟨⟨1507601799605413776025979318763,1507601799605413780636936793690⟩,⟨(-2192237478530848890137392497778),(-2192237478530848885529162422585)⟩⟩,⟨⟨(-10463758815251599700487063721),(-10463758815251599561856753267)⟩,⟨202167238564182152362426506653,202167238564182152501125673406⟩⟩,⟨⟨(-19056647863277587462456332078),(-19056647863277587457398390969)⟩,⟨(-9792811232569650169494635807),(-9792811232569650164379973100)⟩⟩,⟨⟨1531580616334536026493248868,1531580616334536026771562098⟩,⟨(-2706894505762408199249089964),(-2706894505762408199006869456)⟩⟩] +lemma ha0_1_13_eq (j : Fin 7) : ha0_1_13 j = ((ha0_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha0_1_13_contains (j : Fin 7) : (ha0_1_13 j).Contains (fullFactor true 0 13 ((j.val:ℝ)/6)) := by + rw [ha0_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_12 j) true 0 12 j (ha0_1_12_contains j) +noncomputable def hk0_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_14 j i k) +lemma hk0_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_14 j i k).Contains (fullFactor true 0 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 14 (kernel0_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha0_1_14 : Fin 7 → CBox := ![⟨⟨1054773200191494299232533696702989,1054773200191494299316076375403188⟩,⟨0,0⟩⟩,⟨⟨294725003293158601362261600038693,294725003293158601939030816619834⟩,⟨136339483774161985183159225905218,136339483774161985759430160268314⟩⟩,⟨⟨18713348448116571849730229258249,18713348448116571937699890067826⟩,⟨(-11763180479196340294889336842017),(-11763180479196340206921400192518)⟩⟩,⟨⟨(-1104647055334257746385521000076),(-1104647055334257743768498722415)⟩,⟨(-106946322060047951014622350064),(-106946322060047948397510871254)⟩⟩,⟨⟨67847627323076763073701641602,67847627323076763134693535020⟩,⟨(-18429498396970023871799948847),(-18429498396970023810958645070)⟩⟩,⟨⟨(-1898917132492807640001036894),(-1898917132492807638241943177)⟩,⟨6053512450024425851188025455,6053512450024425852940542205⟩⟩,⟨⟨(-718732612381274659639000910),(-718732612381274659570504228)⟩,⟨(-358735344680059668305668996),(-358735344680059668229261769)⟩⟩] +lemma ha0_1_14_eq (j : Fin 7) : ha0_1_14 j = ((ha0_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha0_1_14_contains (j : Fin 7) : (ha0_1_14 j).Contains (fullFactor true 0 14 ((j.val:ℝ)/6)) := by + rw [ha0_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_13 j) true 0 13 j (ha0_1_13_contains j) +noncomputable def hk0_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_15 j i k) +lemma hk0_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_15 j i k).Contains (fullFactor true 0 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 15 (kernel0_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha0_1_15 : Fin 7 → CBox := ![⟨⟨(-648006135220887869147836989149545),(-648006135220887869094449384272053)⟩,⟨0,0⟩⟩,⟨⟨(-116835886063254293265433551418553),(-116835886063254292827237148307118)⟩,⟨(-142730428393819731502210013429252),(-142730428393819731064277476886506)⟩⟩,⟨⟨(-10181212217768484333834206413574),(-10181212217768484274723742794050)⟩,⟨(-2564002401413315214098284423864),(-2564002401413315154987460541529)⟩⟩,⟨⟨171988370211309723097335334448,171988370211309724483120023251⟩,⟨396366935480575956887731784727,396366935480575958273985282316⟩⟩,⟨⟨(-12530494907205456367569140875),(-12530494907205456342628546694)⟩,⟨(-19035203056867144488154358570),(-19035203056867144463150038195)⟩⟩,⟨⟨1737853822152525982586462476,1737853822152525983151893458⟩,⟨232941288564883328970520952,232941288564883329534453586⟩⟩,⟨⟨(-77362922489835425084008726),(-77362922489835425064453837)⟩,⟨177514874465192841713786851,177514874465192841731797935⟩⟩] +lemma ha0_1_15_eq (j : Fin 7) : ha0_1_15 j = ((ha0_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha0_1_15_contains (j : Fin 7) : (ha0_1_15 j).Contains (fullFactor true 0 15 ((j.val:ℝ)/6)) := by + rw [ha0_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_14 j) true 0 14 j (ha0_1_14_contains j) +noncomputable def hk0_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_16 j i k) +lemma hk0_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_16 j i k).Contains (fullFactor true 0 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 16 (kernel0_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha0_1_16 : Fin 7 → CBox := ![⟨⟨373224740880026841431601079950799,373224740880026841463538144199432⟩,⟨0,0⟩⟩,⟨⟨22814926374318185286416785682787,22814926374318185598418460740269⟩,⟨95536490055561122485035519268995,95536490055561122796992419412787⟩⟩,⟨⟨2307666050569911074221630920023,2307666050569911111450653133517⟩,⟨4066173193370065816535442022896,4066173193370065853764802532825⟩⟩,⟨⟨96126789922046678212905225747,96126789922046678901100207633⟩,⟨(-125017397674459483743337763124),(-125017397674459483055311236521)⟩⟩,⟨⟨(-4309641632192142929707990518),(-4309641632192142920104618574)⟩,⟨5420991809334498599645476724,5420991809334498609232465653⟩⟩,⟨⟨(-17021567324879402485195716),(-17021567324879402315883663)⟩,⟨(-453981816122712493693562866),(-453981816122712493522921950)⟩⟩,⟨⟨40971095585372700713639361,40971095585372700718064176⟩,⟨15376685260568953183305910,15376685260568953187992820⟩⟩] +lemma ha0_1_16_eq (j : Fin 7) : ha0_1_16 j = ((ha0_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha0_1_16_contains (j : Fin 7) : (ha0_1_16 j).Contains (fullFactor true 0 16 ((j.val:ℝ)/6)) := by + rw [ha0_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_15 j) true 0 15 j (ha0_1_15_contains j) +noncomputable def hk0_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_17 j i k) +lemma hk0_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_17 j i k).Contains (fullFactor true 0 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 17 (kernel0_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha0_1_17 : Fin 7 → CBox := ![⟨⟨(-202317194430637044549638480430867),(-202317194430637044531682081495494)⟩,⟨0,0⟩⟩,⟨⟨10605113986302861128147140814412,10605113986302861337169274438422⟩,⟨(-48072200020569110415794831370721),(-48072200020569110206729334205808)⟩⟩,⟨⟨563500672749097368685831598465,563500672749097390752799832169⟩,⟨(-1876754012660895579111219849311),(-1876754012660895557044330738644)⟩⟩,⟨⟨(-53568328296592431519191222456),(-53568328296592431197713893361)⟩,⟨(-8073232532004175034274421651),(-8073232532004174712786841092)⟩⟩,⟨⟨1857386286204321649085359053,1857386286204321652552701708⟩,⟨687986049573731118720590298,687986049573731122190278864⟩⟩,⟨⟨(-108391867020127638470194368),(-108391867020127638421823327)⟩,⟨22898813022231402480639181,22898813022231402528469314⟩⟩,⟨⟨2813666519292644384423446,2813666519292644385479720⟩,⟨(-8872648514942035949700234),(-8872648514942035948680332)⟩⟩] +lemma ha0_1_17_eq (j : Fin 7) : ha0_1_17 j = ((ha0_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha0_1_17_contains (j : Fin 7) : (ha0_1_17 j).Contains (fullFactor true 0 17 ((j.val:ℝ)/6)) := by + rw [ha0_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_16 j) true 0 16 j (ha0_1_16_contains j) +noncomputable def hk0_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_18 j i k) +lemma hk0_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_18 j i k).Contains (fullFactor true 0 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 18 (kernel0_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha0_1_18 : Fin 7 → CBox := ![⟨⟨103578967835556427786774587618132,103578967835556427796297306020701⟩,⟨0,0⟩⟩,⟨⟨(-14445944614989657226049363438720),(-14445944614989657093798482630577)⟩,⟨18283565774466192717063898973019,18283565774466192849350452189535⟩⟩,⟨⟨(-691110514692608489597944766609),(-691110514692608477245992316558)⟩,⟨352120509448384041417954697653,352120509448384053769855517987⟩⟩,⟨⟨6130964598573962603574037473,6130964598573962745387341348⟩,⟨16471622608944049928192800166,16471622608944050070023136045⟩⟩,⟨⟨20215878635818402420621697,20215878635818403604136162⟩,⟨(-534647148781619432014133051),(-534647148781619430830381183)⟩⟩,⟨⟨9438298224518590756400101,9438298224518590769178380⟩,⟨23704728643718998620525493,23704728643718998633456487⟩⟩,⟨⟨(-1809316467681524803697637),(-1809316467681524803476253)⟩,⟨(-471898671919231725472976),(-471898671919231725248342)⟩⟩] +lemma ha0_1_18_eq (j : Fin 7) : ha0_1_18 j = ((ha0_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha0_1_18_contains (j : Fin 7) : (ha0_1_18 j).Contains (fullFactor true 0 18 ((j.val:ℝ)/6)) := by + rw [ha0_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_17 j) true 0 17 j (ha0_1_17_contains j) +noncomputable def hk0_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_19 j i k) +lemma hk0_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_19 j i k).Contains (fullFactor true 0 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 19 (kernel0_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha0_1_19 : Fin 7 → CBox := ![⟨⟨(-50237644471643132164178796923382),(-50237644471643132159400197479224)⟩,⟨0,0⟩⟩,⟨⟨9406404598397513344527218541887,9406404598397513423803931495603⟩,⟨(-4550420949692139690051069124353),(-4550420949692139610764404632815)⟩⟩,⟨⟨274536208968430725812906199879,274536208968430732362704373821⟩,⟨96086467227326991908819202017,96086467227326998458630861066⟩⟩,⟨⟨3515322059848394809442296185,3515322059848394868713986392⟩,⟨(-4101746048451185286730736623),(-4101746048451185227465035610)⟩⟩,⟨⟨(-131615700710536994218163657),(-131615700710536993835514861)⟩,⟨37725466733039574261904399,37725466733039574644246834⟩⟩,⟨⟨4747020686359656227694574,4747020686359656230965952⟩,⟨(-2908084322731030199882339),(-2908084322731030196646217)⟩⟩,⟨⟨(-71805103699340482398982),(-71805103699340482353758)⟩,⟨348531519645263477578158,348531519645263477623564⟩⟩] +lemma ha0_1_19_eq (j : Fin 7) : ha0_1_19 j = ((ha0_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha0_1_19_contains (j : Fin 7) : (ha0_1_19 j).Contains (fullFactor true 0 19 ((j.val:ℝ)/6)) := by + rw [ha0_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_18 j) true 0 18 j (ha0_1_18_contains j) +noncomputable def hk0_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_20 j i k) +lemma hk0_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_20 j i k).Contains (fullFactor true 0 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 20 (kernel0_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha0_1_20 : Fin 7 → CBox := ![⟨⟨23147844838179593232127123230037,23147844838179593234402625668477⟩,⟨0,0⟩⟩,⟨⟨(-4451474548549043889493135058891),(-4451474548549043844352450821112)⟩,⟨(-4356701230817925823237778276),(-4356701230817880683640435184)⟩⟩,⟨⟨(-42841576758221668944061702411),(-42841576758221665644730198908)⟩,⟨(-94349462053290777092958878388),(-94349462053290773793621091783)⟩⟩,⟨⟨(-1545059395899196461451191717),(-1545059395899196437922074491)⟩,⟨(-317468090099444859437903385),(-317468090099444835908316540)⟩⟩,⟨⟨18686797528906789383423315,18686797528906789500796160⟩,⟨27544779289029235210884119,27544779289029235328350913⟩⟩,⟨⟨(-761186797175995805270919),(-761186797175995804492267)⟩,⟨(-867240318397072782443455),(-867240318397072781657853)⟩⟩,⟨⟨63601973893574466150775,63601973893574466159601⟩,⟨9692258337107754598435,9692258337107754607079⟩⟩] +lemma ha0_1_20_eq (j : Fin 7) : ha0_1_20 j = ((ha0_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha0_1_20_contains (j : Fin 7) : (ha0_1_20 j).Contains (fullFactor true 0 20 ((j.val:ℝ)/6)) := by + rw [ha0_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_19 j) true 0 19 j (ha0_1_19_contains j) +noncomputable def hk0_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_21 j i k) +lemma hk0_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_21 j i k).Contains (fullFactor true 0 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 21 (kernel0_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha0_1_21 : Fin 7 → CBox := ![⟨⟨(-10157867837341913524759706938530),(-10157867837341913523728824625962)⟩,⟨0,0⟩⟩,⟨⟨1624277549844302967861670932692,1624277549844302992337398750840⟩,⟨789683983844511823026481640308,789683983844511847499343599008⟩⟩,⟨⟨(-13094362879676462635702127821),(-13094362879676461052906095159)⟩,⟨32627355682037620530946540777,32627355682037622113740736438⟩⟩,⟨⟨130989651995254227525864300,130989651995254236421194003⟩,⟨418620375530646612035249140,418620375530646620930951824⟩⟩,⟨⟨4711401116595262930944177,4711401116595262965279998⟩,⟨(-6098712468413171913985007),(-6098712468413171879667244)⟩⟩,⟨⟨(-143182178180077639067746),(-143182178180077638888182)⟩,⟨177165482457656683093313,177165482457656683271703⟩⟩,⟨⟨1097916250891256309739,1097916250891256311313⟩,⟨(-11023253890118668452387),(-11023253890118668450756)⟩⟩] +lemma ha0_1_21_eq (j : Fin 7) : ha0_1_21 j = ((ha0_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha0_1_21_contains (j : Fin 7) : (ha0_1_21 j).Contains (fullFactor true 0 21 ((j.val:ℝ)/6)) := by + rw [ha0_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_20 j) true 0 20 j (ha0_1_20_contains j) +noncomputable def hk0_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_22 j i k) +lemma hk0_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_22 j i k).Contains (fullFactor true 0 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 22 (kernel0_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha0_1_22 : Fin 7 → CBox := ![⟨⟨4254917729857252845698984040626,4254917729857252846144342837729⟩,⟨0,0⟩⟩,⟨⟨(-432552241827585182491346069135),(-432552241827585169824426341861)⟩,⟨(-549669869689692496523808604443),(-549669869689692483857879999018)⟩⟩,⟨⟨10568478417066088377047554111,10568478417066089101835664705⟩,⟨(-4236559225796058546834782373),(-4236559225796057822047293284)⟩⟩,⟨⟨80351423597483050358405489,80351423597483053568560290⟩,⟨(-84264652639745643586928473),(-84264652639745640376907111)⟩⟩,⟨⟨(-1605247173511678803210534),(-1605247173511678793633664)⟩,⟨(-569313588357886788739691),(-569313588357886779160896)⟩⟩,⟨⟨37482607861138001078429,37482607861138001117424⟩,⟨20916501982560748810970,20916501982560748850129⟩⟩,⟨⟨(-1818700738375698710149),(-1818700738375698709862)⟩,⟨(-86124127961573633107),(-86124127961573632833)⟩⟩] +lemma ha0_1_22_eq (j : Fin 7) : ha0_1_22 j = ((ha0_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha0_1_22_contains (j : Fin 7) : (ha0_1_22 j).Contains (fullFactor true 0 22 ((j.val:ℝ)/6)) := by + rw [ha0_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_21 j) true 0 21 j (ha0_1_21_contains j) +noncomputable def hk0_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_23 j i k) +lemma hk0_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_23 j i k).Contains (fullFactor true 0 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 23 (kernel0_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha0_1_23 : Fin 7 → CBox := ![⟨⟨(-1704804650425896415800460320443),(-1704804650425896415616593234907)⟩,⟨0,0⟩⟩,⟨⟨55323851223332981711798355407,55323851223332987982004417807⟩,⟨253133244217801512476029251239,253133244217801518746129166926⟩⟩,⟨⟨(-3211013251042785395164579833),(-3211013251042785077706850761)⟩,⟨(-1459581662251571579126951902),(-1459581662251571261669018129)⟩⟩,⟨⟨(-28601783853112188300778438),(-28601783853112187192757467)⟩,⟨(-7477813622827618162858473),(-7477813622827617054825518)⟩⟩,⟨⟨(-8595693871736428224586),(-8595693871736425668827)⟩,⟨359953809613934521811244,359953809613934524367187⟩⟩,⟨⟨2567431007409637150556,2567431007409637158723⟩,⟨(-7298223787407985654930),(-7298223787407985646780)⟩⟩,⟨⟨1326394302577871851,1326394302577871898⟩,⟨286241197351318080156,286241197351318080206⟩⟩] +lemma ha0_1_23_eq (j : Fin 7) : ha0_1_23 j = ((ha0_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha0_1_23_contains (j : Fin 7) : (ha0_1_23 j).Contains (fullFactor true 0 23 ((j.val:ℝ)/6)) := by + rw [ha0_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_22 j) true 0 22 j (ha0_1_22_contains j) +noncomputable def hk0_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_24 j i k) +lemma hk0_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_24 j i k).Contains (fullFactor true 0 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 24 (kernel0_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha0_1_24 : Fin 7 → CBox := ![⟨⟨654597993571342547950236620064,654597993571342548022920162823⟩,⟨0,0⟩⟩,⟨⟨21541204190706455928517760637,21541204190706458902873846025⟩,⟨(-89427665725107391351303364387),(-89427665725107388376861155187)⟩⟩,⟨⟨345520901943246880784648140,345520901943247014036661043⟩,⟨988480094418843916448719884,988480094418844049700783493⟩⟩,⟨⟨1780996679648801416413344,1780996679648801782922019⟩,⟨6969502533752295269303519,6969502533752295635817439⟩⟩,⟨⟨69833677160229208488925,69833677160229209142537⟩,⟨(-21072763191427638368252),(-21072763191427637714809)⟩⟩,⟨⟨(-1317652471557531306214),(-1317652471557531304582)⟩,⟨(-222855831198608193735),(-222855831198608192103)⟩⟩,⟨⟨43057306477136804562,43057306477136804571⟩,⟨(-2439088085245768535),(-2439088085245768527)⟩⟩] +lemma ha0_1_24_eq (j : Fin 7) : ha0_1_24 j = ((ha0_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha0_1_24_contains (j : Fin 7) : (ha0_1_24 j).Contains (fullFactor true 0 24 ((j.val:ℝ)/6)) := by + rw [ha0_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_23 j) true 0 23 j (ha0_1_23_contains j) +noncomputable def hk0_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_25 j i k) +lemma hk0_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_25 j i k).Contains (fullFactor true 0 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 25 (kernel0_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha0_1_25 : Fin 7 → CBox := ![⟨⟨(-241293682391912884886769410525),(-241293682391912884859209211026)⟩,⟨0,0⟩⟩,⟨⟨(-19904778416447496107110458232),(-19904778416447494752620704511)⟩,⟨24219432660822787875009130362,24219432660822789229546614036⟩⟩,⟨⟨135585393864685413549289519,135585393864685467243781384⟩,⟨(-265852462342779436907410846),(-265852462342779383212937991)⟩⟩,⟨⟨1222479086062008539439512,1222479086062008655823527⟩,⟨(-1152857451333707370889214),(-1152857451333707254507183)⟩⟩,⟨⟨(-8127154073815314563419),(-8127154073815314403018)⟩,⟨(-11627923450876749110235),(-11627923450876748949794)⟩⟩,⟨⟨703889137214255766,703889137214256080⟩,⟨221598356263623670782,221598356263623671096⟩⟩,⟨⟨(-675705017521252253),(-675705017521252251)⟩,⟨(-6200922363632815994),(-6200922363632815991)⟩⟩] +lemma ha0_1_25_eq (j : Fin 7) : ha0_1_25 j = ((ha0_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha0_1_25_contains (j : Fin 7) : (ha0_1_25 j).Contains (fullFactor true 0 25 ((j.val:ℝ)/6)) := by + rw [ha0_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_24 j) true 0 24 j (ha0_1_24_contains j) +noncomputable def hk0_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_26 j i k) +lemma hk0_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_26 j i k).Contains (fullFactor true 0 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 26 (kernel0_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha0_1_26 : Fin 7 → CBox := ![⟨⟨85523190354468574856651357295,85523190354468574866691915533⟩,⟨0,0⟩⟩,⟨⟨9332272679116857535420636632,9332272679116858128520025417⟩,⟨(-4294943490440916720219520164),(-4294943490440916127110797447)⟩⟩,⟨⟨(-78336206843192625623961059),(-78336206843192604819790590)⟩,⟨23486586321533778567369488,23486586321533799371536509⟩⟩,⟨⟨(-359566156896607253809319),(-359566156896607218274428)⟩,⟨(-114699775302073863356880),(-114699775302073827821795)⟩⟩,⟨⟨(-1592513281617125057105),(-1592513281617125019238)⟩,⟨2121838957507806662470,2121838957507806700331⟩⟩,⟨⟨34799966704316379910,34799966704316379969⟩,⟨(-6113401308409143732),(-6113401308409143673)⟩⟩,⟨⟨(-856338950808112631),(-856338950808112630)⟩,⟨138629092417247708,138629092417247710⟩⟩] +lemma ha0_1_26_eq (j : Fin 7) : ha0_1_26 j = ((ha0_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha0_1_26_contains (j : Fin 7) : (ha0_1_26 j).Contains (fullFactor true 0 26 ((j.val:ℝ)/6)) := by + rw [ha0_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_25 j) true 0 25 j (ha0_1_25_contains j) +noncomputable def hk0_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_27 j i k) +lemma hk0_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_27 j i k).Contains (fullFactor true 0 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 27 (kernel0_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha0_1_27 : Fin 7 → CBox := ![⟨⟨(-29189820166130956436190703278),(-29189820166130956432670857994)⟩,⟨0,0⟩⟩,⟨⟨(-3241161071801606097315338638),(-3241161071801605847233466772)⟩,⟨(-65558174658857429687752653),(-65558174658857179606860623)⟩⟩,⟨⟨18764864547021019260020391,18764864547021027022113231⟩,⟨10659484973469284924535687,10659484973469292686630021⟩⟩,⟨⟨15987003220282519797116,15987003220282530244953⟩,⟨80050511362438609819072,80050511362438620266959⟩⟩,⟨⟨452448086798722323219,452448086798722331825⟩,⟨153409325648267318099,153409325648267326705⟩⟩,⟨⟨(-1832772073530565542),(-1832772073530565530)⟩,⟨(-5106017288199958289),(-5106017288199958278)⟩⟩,⟨⟨24495959236594590,24495959236594591⟩,⟨113564125910997956,113564125910997957⟩⟩] +lemma ha0_1_27_eq (j : Fin 7) : ha0_1_27 j = ((ha0_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha0_1_27_contains (j : Fin 7) : (ha0_1_27 j).Contains (fullFactor true 0 27 ((j.val:ℝ)/6)) := by + rw [ha0_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_26 j) true 0 26 j (ha0_1_26_contains j) +noncomputable def hk0_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_28 j i k) +lemma hk0_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_28 j i k).Contains (fullFactor true 0 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 28 (kernel0_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha0_1_28 : Fin 7 → CBox := ![⟨⟨9606931147893012552728397476,9606931147893012553917426060⟩,⟨0,0⟩⟩,⟨⟨878705318217083792629038810,878705318217083894308715795⟩,⟨448313242223517886667138421,448313242223517988345251840⟩⟩,⟨⟨(-1338989007970705854770986),(-1338989007970703062147819)⟩,⟨(-5325869956917321966082246),(-5325869956917319173458882)⟩⟩,⟨⟨12988480910365772534811,12988480910365775496935⟩,⟨(-11007430336248213108404),(-11007430336248210146301)⟩⟩,⟨⟨826046342761578017,826046342761579904⟩,⟨(-82956253038068107040),(-82956253038068105153)⟩⟩,⟨⟨(-698884342741524279),(-698884342741524276)⟩,⟨395843220953149448,395843220953149451⟩⟩,⟨⟨14481547403249622,14481547403249623⟩,⟨(-3920709409332273),(-3920709409332272)⟩⟩] +lemma ha0_1_28_eq (j : Fin 7) : ha0_1_28 j = ((ha0_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha0_1_28_contains (j : Fin 7) : (ha0_1_28 j).Contains (fullFactor true 0 28 ((j.val:ℝ)/6)) := by + rw [ha0_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_27 j) true 0 27 j (ha0_1_27_contains j) +noncomputable def hk0_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_29 j i k) +lemma hk0_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_29 j i k).Contains (fullFactor true 0 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 29 (kernel0_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha0_1_29 : Fin 7 → CBox := ![⟨⟨(-3052797310302529882591970126),(-3052797310302529882204414810)⟩,⟨0,0⟩⟩,⟨⟨(-174813461545535431099307212),(-174813461545535391183734533)⟩,⟨(-231164710851134947758546994),(-231164710851134907843373719)⟩⟩,⟨⟨(-718498838513151174740022),(-718498838513150204665911)⟩,⟨1142005457792919088773196,1142005457792920058847207⟩⟩,⟨⟨(-3206423563734735854542),(-3206423563734735043702)⟩,⟨(-1213721250719765199532),(-1213721250719764388691)⟩⟩,⟨⟨(-13258922326659661568),(-13258922326659661168)⟩,⟨4203171326336672529,4203171326336672930⟩⟩,⟨⟨72736707079834220,72736707079834222⟩,⟨88839829736672856,88839829736672858⟩⟩,⟨⟨(-581966637725765),(-581966637725764)⟩,⟨(-1777828965400159),(-1777828965400158)⟩⟩] +lemma ha0_1_29_eq (j : Fin 7) : ha0_1_29 j = ((ha0_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha0_1_29_contains (j : Fin 7) : (ha0_1_29 j).Contains (fullFactor true 0 29 ((j.val:ℝ)/6)) := by + rw [ha0_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_28 j) true 0 28 j (ha0_1_28_contains j) +noncomputable def hk0_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel0_0 j i k).mul (mpower1_30 j i k) +lemma hk0_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk0_1_30 j i k).Contains (fullFactor true 0 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk0_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel0_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 0 30 (kernel0_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha0_1_30 : Fin 7 → CBox := ![⟨⟨937752014510188366842383715,937752014510188366964417120⟩,⟨0,0⟩⟩,⟨⟨16024061627868274676685549,16024061627868289823619528⟩,⟨80736464436127435910159778,80736464436127451057064798⟩⟩,⟨⟨313968769379739008895259,313968769379739334637334⟩,⟨(-64077911573074331505489),(-64077911573074005763423)⟩⟩,⟨⟨95803660365903055654,95803660365903270212⟩,⟨660470924325592463142,660470924325592677701⟩⟩,⟨⟨1317019989054446518,1317019989054446601⟩,⟨1829559169964478083,1829559169964478166⟩⟩,⟨⟨10390272510291510,10390272510291511⟩,⟨(-11990710695265079),(-11990710695265078)⟩⟩,⟨⟨(-210350295292229),(-210350295292228)⟩,⟨81177519670486,81177519670487⟩⟩] +lemma ha0_1_30_eq (j : Fin 7) : ha0_1_30 j = ((ha0_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha0_1_30_contains (j : Fin 7) : (ha0_1_30 j).Contains (fullFactor true 0 30 ((j.val:ℝ)/6)) := by + rw [ha0_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha0_1_29 j) true 0 29 j (ha0_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders1.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders1.lean new file mode 100644 index 0000000000000000000000000000000000000000..1765d9b2ac6598387848ad77cddaa37055b939fa --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders1.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk1_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_0 j i k) +lemma hk1_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_0 j i k).Contains (fullFactor false 1 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 0 (power1_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha1_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999989,1000000000000000000000000000015⟩,⟨(-15),15⟩⟩,⟨⟨866025403784438646763098939526,866025403784438646763954632529⟩,⟨499999999999999999999469888220,500000000000000000001210408427⟩⟩,⟨⟨499999999999999999997708137538,500000000000000000000931269165⟩,⟨866025403784438646762180554973,866025403784438646766051325440⟩⟩,⟨⟨(-4444983321),2088366603⟩,⟨999999999999999999996733325039,1000000000000000000003266674962⟩⟩,⟨⟨(-500000000000000000006328835244),(-499999999999999999996392351351)⟩,⟨866025403784438646758206118258,866025403784438646767669145432⟩⟩,⟨⟨(-866025403784438646770926677365),(-866025403784438646758483511404)⟩,⟨499999999999999999992312631744,500000000000000000004285885012⟩⟩,⟨⟨(-1000000000000000000006553197785),(-999999999999999999993446802219)⟩,⟨(-8909814505),4196581061⟩⟩] +lemma ha1_0_0_eq (j : Fin 7) : ha1_0_0 j = ((atomPoints j).direct.powBin 7 1).conj := by fin_cases j <;> decide +kernel +lemma ha1_0_0_contains (j : Fin 7) : (ha1_0_0 j).Contains (fullFactor false 1 0 ((j.val:ℝ)/6)) := by + rw [ha1_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 1) ((j.val:ℝ)/6) 1 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 1 (by norm_num)) +noncomputable def hk1_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_1 j i k) +lemma hk1_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_1 j i k).Contains (fullFactor false 1 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 1 (power1_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha1_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-261799387799149436539800435038),(-261799387799149436538055767453)⟩,⟨453449841058554462647811178190,453449841058554462649702593676⟩⟩,⟨⟨(-906899682117108925301600839033),(-906899682117108925294660626328)⟩,⟨523598775598298873074266633908,523598775598298873079308556124⟩⟩,⟨⟨(-1570796326794896619240131281032),(-1570796326794896619224868718970)⟩,⟨(-6982163474),3280398589⟩⟩,⟨⟨(-1813799364234217850606590032330),(-1813799364234217850580997211866)⟩,⟨(-1047197551196597746169921748207),(-1047197551196597746145777491670)⟩⟩,⟨⟨(-1308996938995747182707053754058),(-1308996938995747182671541183633)⟩,⟨(-2267249205292772313266765739071),(-2267249205292772313226972728393)⟩⟩,⟨⟨(-13183948232),27991007794⟩,⟨(-3141592653589793238490587478019),(-3141592653589793238439412521993)⟩⟩] +lemma ha1_0_1_eq (j : Fin 7) : ha1_0_1 j = ((ha1_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha1_0_1_contains (j : Fin 7) : (ha1_0_1 j).Contains (fullFactor false 1 1 ((j.val:ℝ)/6)) := by + rw [ha1_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_0 j) false 1 0 j (ha1_0_0_contains j) +noncomputable def hk1_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_2 j i k) +lemma hk1_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_2 j i k).Contains (fullFactor false 1 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 2 (power1_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha1_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-118712890786751174408525015863),(-118712890786751174407651969578)⟩,⟨(-68538919452009434853504211742),(-68538919452009434852829292678)⟩⟩,⟨⟨(-274155677808037739413863791737),(-274155677808037739410351182810)⟩,⟨(-474851563147004697635249703984),(-474851563147004697630104317636)⟩⟩,⟨⟨(-2576419028),5483778370⟩,⟨(-1233700550136169827364119346945),(-1233700550136169827348205167914)⟩⟩,⟨⟨1096622711232150957638518889210,1096622711232150957667293354039⟩,⟨(-1899406252588018790544547092218),(-1899406252588018790511700355414)⟩⟩,⟨⟨2967822269668779360175482416665,2967822269668779360237018217530⟩,⟨(-1713472986300235871348144785615),(-1713472986300235871296204785717)⟩⟩,⟨⟨4934802200544679309376602331615,4934802200544679309472695727833⟩,⟨(-20709297456),43968172227⟩⟩] +lemma ha1_0_2_eq (j : Fin 7) : ha1_0_2 j = ((ha1_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha1_0_2_contains (j : Fin 7) : (ha1_0_2 j).Contains (fullFactor false 1 2 ((j.val:ℝ)/6)) := by + rw [ha1_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_1 j) false 1 1 j (ha1_0_1_contains j) +noncomputable def hk1_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_3 j i k) +lemma hk1_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_3 j i k).Contains (fullFactor false 1 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 3 (power1_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha1_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11962298101967523215804465293,11962298101967523215960338070⟩,⟨(-20719308087892496642566511763),(-20719308087892496642348184834)⟩⟩,⟨⟨165754464703139973138609702841,165754464703139973140933394351⟩,⟨(-95698384815740185727629278199),(-95698384815740185726098528956)⟩⟩,⟨⟨645964097506246253652015837451,645964097506246253662404649691⟩,⟨(-1349009849),2871299641⟩⟩,⟨⟨1326035717625119785102792067944,1326035717625119785129944318962⟩,⟨765587078525921485806773533848,765587078525921485829298839279⟩⟩,⟨⟨1495287262745940401954153852773,1495287262745940402004239700545⟩,⟨2589913510986562080279720322587,2589913510986562080341664389988⟩⟩,⟨⟨(-46043362287),21686725583⟩,⟨5167712780049970029199142893634,5167712780049970029316221003509⟩⟩] +lemma ha1_0_3_eq (j : Fin 7) : ha1_0_3 j = ((ha1_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha1_0_3_contains (j : Fin 7) : (ha1_0_3 j).Contains (fullFactor false 1 3 ((j.val:ℝ)/6)) := by + rw [ha1_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_2 j) false 1 2 j (ha1_0_2_contains j) +noncomputable def hk1_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_4 j i k) +lemma hk1_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_4 j i k).Contains (fullFactor false 1 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 4 (power1_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha1_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2712151086516110563384867168,2712151086516110563422079143⟩,⟨1565861159883012429848399102,1565861159883012429873787093⟩⟩,⟨⟨25053778558128198877486108620,25053778558128198877966606490⟩,⟨43394417384257769014111856697,43394417384257769014858326433⟩⟩,⟨⟨(-1127556733),529754929⟩,⟨253669507901048013634880945199,253669507901048013639768077348⟩⟩,⟨⟨(-400860456930051182051793045432),(-400860456930051182038722844623)⟩,⟨694310678148124304222603318122,694310678148124304239030263042⟩⟩,⟨⟨(-1695094429072569102152446031543),(-1695094429072569102106508081083)⟩,⟨978663224926882768641240351789,978663224926882768677136644299⟩⟩,⟨⟨(-4058712126416768218249628287592),(-4058712126416768218144756073171)⟩,⟨(-36162372177),17032714443⟩⟩] +lemma ha1_0_4_eq (j : Fin 7) : ha1_0_4 j = ((ha1_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha1_0_4_contains (j : Fin 7) : (ha1_0_4 j).Contains (fullFactor false 1 4 ((j.val:ℝ)/6)) := by + rw [ha1_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_3 j) false 1 3 j (ha1_0_3_contains j) +noncomputable def hk1_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_5 j i k) +lemma hk1_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_5 j i k).Contains (fullFactor false 1 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 5 (power1_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha1_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-163976597214335483789365320),(-163976597214335483786184741)⟩,⟨284015797627486289485824466,284015797627486289490625346⟩⟩,⟨⟨(-9088505524079561263722014810),(-9088505524079561263536744941)⟩,⟨5247251110858735481139423048,5247251110858735481256760806⟩⟩,⟨⟨(-79692626246167045121698954070),(-79692626246167045119909946715)⟩,⟨(-354232395),166427420⟩⟩,⟨⟨(-290832176770545960439647776797),(-290832176770545960431841126627)⟩,⟨(-167912035547479535402028978391),(-167912035547479535396019664868)⟩⟩,⟨⟨(-512426866294798386844918537985),(-512426866294798386824492177802)⟩,⟨(-887549367585894654665349531347),(-887549367585894654638471319349)⟩⟩,⟨⟨(-10701970113),22721488554⟩,⟨(-2550164039877345443902747702527),(-2550164039877345443828737122595)⟩⟩] +lemma ha1_0_5_eq (j : Fin 7) : ha1_0_5 j = ((ha1_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha1_0_5_contains (j : Fin 7) : (ha1_0_5 j).Contains (fullFactor false 1 5 ((j.val:ℝ)/6)) := by + rw [ha1_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_4 j) false 1 4 j (ha1_0_4_contains j) +noncomputable def hk1_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_6 j i k) +lemma hk1_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_6 j i k).Contains (fullFactor false 1 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 6 (power1_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha1_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24785053981387676527259306),(-24785053981387676526761455)⟩,⟨(-14309657588033580845950123),(-14309657588033580845627015)⟩⟩,⟨⟨(-915818085634149174140296530),(-915818085634149174116902088)⟩,⟨(-1586243454808811297748435899),(-1586243454808811297711051036)⟩⟩,⟨⟨(-43570597),92737825⟩,⟨(-20863480763352960873412925496),(-20863480763352960872878153943)⟩⟩,⟨⟨58612357480585547143327490984,58612357480585547145611706049⟩,⟨(-101519581107763923056089545957),(-101519581107763923053041364113)⟩⟩,⟨⟨387266468459182445728583837304,387266468459182445741544377171⟩,⟨(-223588399813024700719345938835),(-223588399813024700709721553868)⟩⟩,⟨⟨1335262768854589495859813480852,1335262768854589495902815603287⟩,⟨(-5603538448),11896943587⟩⟩] +lemma ha1_0_6_eq (j : Fin 7) : ha1_0_6 j = ((ha1_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha1_0_6_contains (j : Fin 7) : (ha1_0_6 j).Contains (fullFactor false 1 6 ((j.val:ℝ)/6)) := by + rw [ha1_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_5 j) false 1 5 j (ha1_0_5_contains j) +noncomputable def hk1_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_7 j i k) +lemma hk1_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_7 j i k).Contains (fullFactor false 1 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 7 (power1_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha1_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1070359884617898514095318,1070359884617898514122895⟩,⟨(-1853917702541761442288448),(-1853917702541761442245307)⟩⟩,⟨⟨237301465925345464607147672,237301465925345464613495790⟩,⟨(-137006065231091009807653991),(-137006065231091009803718086)⟩⟩,⟨⟨4681754135318688100642595076,4681754135318688100777500019⟩,⟨(-9777220),20810320⟩⟩,⟨⟨30374587638444219469575504497,30374587638444219470584203689⟩,⟨17536776349579649254829765721,17536776349579649255569022564⟩⟩,⟨⟨83621865985773321412499787622,83621865985773321416365475850⟩,⟨144837320511075112674642723376,144837320511075112679950985462⟩⟩,⟨⟨(-5339335797),2514862175⟩,⟨599264529320792076880282673284,599264529320792076901489498945⟩⟩] +lemma ha1_0_7_eq (j : Fin 7) : ha1_0_7 j = ((ha1_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha1_0_7_contains (j : Fin 7) : (ha1_0_7 j).Contains (fullFactor false 1 7 ((j.val:ℝ)/6)) := by + rw [ha1_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_6 j) false 1 6 j (ha1_0_6_contains j) +noncomputable def hk1_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_8 j i k) +lemma hk1_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_8 j i k).Contains (fullFactor false 1 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 8 (power1_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha1_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨121338629888859693713686,121338629888859693716897⟩,⟨70054890629433514725998,70054890629433514728027⟩⟩,⟨⟨17934052001134979769792453,17934052001134979770364749⟩,⟨31062689251548081590670895,31062689251548081591600739⟩⟩,⟨⟨(-4086097),1919753⟩,⟨919260274839426580232525461,919260274839426580261940082⟩⟩,⟨⟨(-4591117312290554821262937232),(-4591117312290554821054786262)⟩,⟨7952048448396308887175255146,7952048448396308887464644134⟩⟩,⟨⟨(-47397902300335817858544323181),(-47397902300335817856656326266)⟩,⟨27365191652122466689451487779,27365191652122466690803637405⟩⟩,⟨⟨(-235330630358893204547830080398),(-235330630358893204538753098773)⟩,⟨(-2096752265),987584067⟩⟩] +lemma ha1_0_8_eq (j : Fin 7) : ha1_0_8 j = ((ha1_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha1_0_8_contains (j : Fin 7) : (ha1_0_8 j).Contains (fullFactor false 1 8 ((j.val:ℝ)/6)) := by + rw [ha1_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_7 j) false 1 7 j (ha1_0_7_contains j) +noncomputable def hk1_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_9 j i k) +lemma hk1_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_9 j i k).Contains (fullFactor false 1 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 9 (power1_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha1_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-4075628328693792152529),(-4075628328693792152397)⟩,⟨7059195338064676366503,7059195338064676366713⟩⟩,⟨⟨(-3614308013089114299765750),(-3614308013089114299646052)⟩,⟨2086721704291221582020112,2086721704291221582093345⟩⟩,⟨⟨(-160441184787359821876566303),(-160441184787359821870921782)⟩,⟨(-713159),335061⟩⟩,⟨⟨(-1850525702701626521483520556),(-1850525702701626521410286274)⟩,⟨(-1068401512597105450043325960),(-1068401512597105449991486201)⟩⟩,⟨⟨(-7960211579480062797955874928),(-7960211579480062797537212404)⟩,⟨(-13787490894657571028847107738),(-13787490894657571028254024750)⟩⟩,⟨⟨(-344731873),731904613⟩,⟨(-82145886611128228801071921017),(-82145886611128228797641978228)⟩⟩] +lemma ha1_0_9_eq (j : Fin 7) : ha1_0_9 j = ((ha1_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha1_0_9_contains (j : Fin 7) : (ha1_0_9 j).Contains (fullFactor false 1 9 ((j.val:ℝ)/6)) := by + rw [ha1_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_8 j) false 1 8 j (ha1_0_8_contains j) +noncomputable def hk1_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_10 j i k) +lemma hk1_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_10 j i k).Contains (fullFactor false 1 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 10 (power1_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha1_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-369618603571988403199),(-369618603571988403186)⟩,⟨(-213399400269781075732),(-213399400269781075723)⟩⟩,⟨⟨(-218520985876255821548635),(-218520985876255821540270)⟩,⟨(-378489450057716124876308),(-378489450057716124862567)⟩⟩,⟨⟨(-52632),112023⟩,⟨(-25202042373060605481725501),(-25202042373060605480758641)⟩⟩,⟨⟨223765489537285961256648084,223765489537285961268217647⟩,⟨(-387573196859101311874062639),(-387573196859101311857490802)⟩⟩,⟨⟨3609556675507699249848862591,3609556675507699250015620931⟩,⟨(-2083978518259580817700395011),(-2083978518259580817584155908)⟩⟩,⟨⟨25806891390014060012212033526,25806891390014060013371727720⟩,⟨(-108300712),229934616⟩⟩] +lemma ha1_0_10_eq (j : Fin 7) : ha1_0_10 j = ((ha1_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha1_0_10_contains (j : Fin 7) : (ha1_0_10 j).Contains (fullFactor false 1 10 ((j.val:ℝ)/6)) := by + rw [ha1_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_9 j) false 1 9 j (ha1_0_9_contains j) +noncomputable def hk1_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_11 j i k) +lemma hk1_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_11 j i k).Contains (fullFactor false 1 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 11 (power1_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha1_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨10157787699515332860,10157787699515332861⟩,⟨(-17593804388058740566),(-17593804388058740564)⟩⟩,⟨⟨36032111386744300675768,36032111386744300677192⟩,⟨(-20803149208607401698767),(-20803149208607401697903)⟩⟩,⟨⟨3598843235212085340413474,3598843235212085340562998⟩,⟨(-7516),15997⟩⟩,⟨⟨73793764120052327783635112,73793764120052327787025276⟩,⟨42604849579227958677194630,42604849579227958679533086⟩⟩,⟨⟨495985727515397112314205138,495985727515397112343448752⟩,⟨859072479885680691614499650,859072479885680691656922555⟩⟩,⟨⟨(-65669173),30930612⟩,⟨7370430945714350777142572560,7370430945714350777497241258⟩⟩] +lemma ha1_0_11_eq (j : Fin 7) : ha1_0_11 j = ((ha1_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha1_0_11_contains (j : Fin 7) : (ha1_0_11 j).Contains (fullFactor false 1 11 ((j.val:ℝ)/6)) := by + rw [ha1_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_10 j) false 1 10 j (ha1_0_10_contains j) +noncomputable def hk1_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_12 j i k) +lemma hk1_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_12 j i k).Contains (fullFactor false 1 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 12 (power1_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha1_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨767674536308627877,767674536308627878⟩,⟨443217100187807442,443217100187807443⟩⟩,⟨⟨1815417242369259285485,1815417242369259285567⟩,⟨3144394900720139784887,3144394900720139785022⟩⟩,⟨⟨(-2095),984⟩,⟨471087477881817150360732,471087477881817150381805⟩⟩,⟨⟨(-7435949024744486033759378),(-7435949024744486033327570)⟩,⟨12879441513349692558840825,12879441513349692559473518⟩⟩,⟨⟨(-187420541090973602833720545),(-187420541090973602823868724)⟩,⟨108207299850538926450344991,108207299850538926457069394⟩⟩,⟨⟨(-1929574309403923047970211882),(-1929574309403923047871217807)⟩,⟨(-17192150),8097616⟩⟩] +lemma ha1_0_12_eq (j : Fin 7) : ha1_0_12 j = ((ha1_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha1_0_12_contains (j : Fin 7) : (ha1_0_12 j).Contains (fullFactor false 1 12 ((j.val:ℝ)/6)) := by + rw [ha1_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_11 j) false 1 11 j (ha1_0_11_contains j) +noncomputable def hk1_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_13 j i k) +lemma hk1_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_13 j i k).Contains (fullFactor false 1 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 13 (power1_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha1_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-17851379306351119),(-17851379306351118)⟩,⟨30919495943783799,30919495943783800⟩⟩,⟨⟨(-253292510771476882290),(-253292510771476882277)⟩,⟨146238499277628361509,146238499277628361517⟩⟩,⟨⟨(-56921729219679268119672),(-56921729219679268116943)⟩,⟨(-254),119⟩⟩,⟨⟨(-2074972248239938619717654),(-2074972248239938619609117)⟩,⟨(-1197985786082331537554947),(-1197985786082331537481565)⟩⟩,⟨⟨(-21791234504823142516216682),(-21791234504823142514793129)⟩,⟨(-37743525322001707895205223),(-37743525322001707893101080)⟩⟩,⟨⟨(-1956878),4154672⟩,⟨(-466302805767612564437879828),(-466302805767612564412472535)⟩⟩] +lemma ha1_0_13_eq (j : Fin 7) : ha1_0_13 j = ((ha1_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha1_0_13_contains (j : Fin 7) : (ha1_0_13 j).Contains (fullFactor false 1 13 ((j.val:ℝ)/6)) := by + rw [ha1_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_12 j) false 1 12 j (ha1_0_12_contains j) +noncomputable def hk1_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_14 j i k) +lemma hk1_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_14 j i k).Contains (fullFactor false 1 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 14 (power1_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha1_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1156386444162984),(-1156386444162983)⟩,⟨(-667640024824733),(-667640024824732)⟩⟩,⟨⟨(-10938614166728417760),(-10938614166728417758)⟩,⟨(-18946235501166317752),(-18946235501166317750)⟩⟩,⟨⟨(-14),29⟩,⟨(-6386603083791852241321),(-6386603083791852240993)⟩⟩,⟨⟨179218254507678396555467,179218254507678396567017⟩,⟨(-310415122451108950042893),(-310415122451108950025667)⟩⟩,⟨⟨7058022730486958381010646,7058022730486958381426587⟩,⟨(-4074951323393142878701019),(-4074951323393142878421843)⟩⟩,⟨⟨104638104924845707116098397,104638104924845707122132854⟩,⟨(-439123),932307⟩⟩] +lemma ha1_0_14_eq (j : Fin 7) : ha1_0_14 j = ((ha1_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha1_0_14_contains (j : Fin 7) : (ha1_0_14 j).Contains (fullFactor false 1 14 ((j.val:ℝ)/6)) := by + rw [ha1_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_13 j) false 1 13 j (ha1_0_13_contains j) +noncomputable def hk1_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_15 j i k) +lemma hk1_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_15 j i k).Contains (fullFactor false 1 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 15 (power1_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha1_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23305033302576,23305033302577⟩,⟨(-40365501752148),(-40365501752147)⟩⟩,⟨⟨1322696761414360852,1322696761414360853⟩,⟨(-763659331258827444),(-763659331258827443)⟩⟩,⟨⟨668803510981146723237,668803510981146723274⟩,⟨(-2),4⟩⟩,⟨⟨43342127478025776419581,43342127478025776422125⟩,⟨25023588966689257663231,25023588966689257664924⟩⟩,⟨⟨711213174517105746390013,711213174517105746441003⟩,⟨1231857353275977869191000,1231857353275977869267518⟩⟩,⟨⟨(-195262),91970⟩,⟨21915353447830215826964437,21915353447830215828298051⟩⟩] +lemma ha1_0_15_eq (j : Fin 7) : ha1_0_15 j = ((ha1_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha1_0_15_contains (j : Fin 7) : (ha1_0_15 j).Contains (fullFactor false 1 15 ((j.val:ℝ)/6)) := by + rw [ha1_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_14 j) false 1 14 j (ha1_0_14_contains j) +noncomputable def hk1_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_16 j i k) +lemma hk1_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_16 j i k).Contains (fullFactor false 1 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 16 (power1_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha1_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1320957955864,1320957955865⟩,⟨762655431406,762655431407⟩⟩,⟨⟨49981386352667221,49981386352667222⟩,⟨86570300595549323,86570300595549324⟩⟩,⟨⟨(-1),1⟩,⟨65659631149794723620,65659631149794723625⟩⟩,⟨⟨(-3275580136008399049540),(-3275580136008399049307)⟩,⟨5673471219829920494641,5673471219829920494993⟩⟩,⟨⟨(-201562188089707223604331),(-201562188089707223591168)⟩,⟨116371983552042445683167,116371983552042445691881⟩⟩,⟨⟨(-4303069587032947007487246),(-4303069587032947007211694)⟩,⟨(-38340),18059⟩⟩] +lemma ha1_0_16_eq (j : Fin 7) : ha1_0_16 j = ((ha1_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha1_0_16_contains (j : Fin 7) : (ha1_0_16 j).Contains (fullFactor false 1 16 ((j.val:ℝ)/6)) := by + rw [ha1_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_15 j) false 1 15 j (ha1_0_15_contains j) +noncomputable def hk1_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_17 j i k) +lemma hk1_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_17 j i k).Contains (fullFactor false 1 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 17 (power1_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha1_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23489732359),(-23489732358)⟩,⟨40685409900,40685409901⟩⟩,⟨⟨(-5332718046471331),(-5332718046471330)⟩,⟨3078846199642597,3078846199642598⟩⟩,⟨⟨(-6066935731106195668),(-6066935731106195666)⟩,⟨(-1),1⟩⟩,⟨⟨(-698970019787090239246),(-698970019787090239199)⟩,⟨(-403550529079554596730),(-403550529079554596699)⟩⟩,⟨⟨(-17921243559351411743927),(-17921243559351411742527)⟩,⟨(-31040504379613153640340),(-31040504379613153638213)⟩⟩,⟨⟨(-3338),7086⟩,⟨(-795205400147551278515188),(-795205400147551278461734)⟩⟩] +lemma ha1_0_17_eq (j : Fin 7) : ha1_0_17 j = ((ha1_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha1_0_17_contains (j : Fin 7) : (ha1_0_17 j).Contains (fullFactor false 1 17 ((j.val:ℝ)/6)) := by + rw [ha1_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_16 j) false 1 16 j (ha1_0_16_contains j) +noncomputable def hk1_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_18 j i k) +lemma hk1_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_18 j i k).Contains (fullFactor false 1 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 18 (power1_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha1_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1183490601),(-1183490600)⟩,⟨(-683288617),(-683288616)⟩⟩,⟨⟨(-179120011154260),(-179120011154259)⟩,⟨(-310244959971483),(-310244959971482)⟩⟩,⟨⟨(-1),1⟩,⟨(-529440020073462377),(-529440020073462376)⟩⟩,⟨⟨46955236204022331367,46955236204022331372⟩,⟨(-81328854786764263387),(-81328854786764263380)⟩⟩,⟨⟨4514658357533078058030,4514658357533078058355⟩,⟨(-2606539218020916335935),(-2606539218020916335722)⟩⟩,⟨⟨138789524622137721141669,138789524622137721151441⟩,⟨(-583),1237⟩⟩] +lemma ha1_0_18_eq (j : Fin 7) : ha1_0_18 j = ((ha1_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha1_0_18_contains (j : Fin 7) : (ha1_0_18 j).Contains (fullFactor false 1 18 ((j.val:ℝ)/6)) := by + rw [ha1_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_17 j) false 1 17 j (ha1_0_17_contains j) +noncomputable def hk1_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_19 j i k) +lemma hk1_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_19 j i k).Contains (fullFactor false 1 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 19 (power1_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha1_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨18829951,18829952⟩,⟨(-32614434),(-32614433)⟩⟩,⟨⟨17099355913327,17099355913328⟩,⟨(-9872317739529),(-9872317739528)⟩⟩,⟨⟨43770654673137422,43770654673137423⟩,⟨(-1),1⟩⟩,⟨⟨8964987113086656144,8964987113086656146⟩,⟨5175937723022106880,5175937723022106882⟩⟩,⟨⟨359152827132815577508,359152827132815577540⟩,⟨622070944276038605474,622070944276038605521⟩⟩,⟨⟨(-205),97⟩,⟨22948428997269873109686,22948428997269873111376⟩⟩] +lemma ha1_0_19_eq (j : Fin 7) : ha1_0_19 j = ((ha1_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha1_0_19_contains (j : Fin 7) : (ha1_0_19 j).Contains (fullFactor false 1 19 ((j.val:ℝ)/6)) := by + rw [ha1_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_18 j) false 1 18 j (ha1_0_18_contains j) +noncomputable def hk1_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_20 j i k) +lemma hk1_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_20 j i k).Contains (fullFactor false 1 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 20 (power1_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha1_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨853843,853844⟩,⟨492966,492967⟩⟩,⟨⟨516913348073,516913348074⟩,⟨895320181973,895320181974⟩⟩,⟨⟨(-1),1⟩,⟨3437739179098606,3437739179098608⟩⟩,⟨⟨(-542022930869484434),(-542022930869484433)⟩,⟨938811255133340262,938811255133340263⟩⟩,⟨⟨(-81428896189552855160),(-81428896189552855153)⟩,⟨47012995134852432604,47012995134852432610⟩⟩,⟨⟨(-3604730797462500934052),(-3604730797462500933775)⟩,⟨(-33),16⟩⟩] +lemma ha1_0_20_eq (j : Fin 7) : ha1_0_20 j = ((ha1_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha1_0_20_contains (j : Fin 7) : (ha1_0_20 j).Contains (fullFactor false 1 20 ((j.val:ℝ)/6)) := by + rw [ha1_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_19 j) false 1 19 j (ha1_0_19_contains j) +noncomputable def hk1_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_21 j i k) +lemma hk1_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_21 j i k).Contains (fullFactor false 1 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 21 (power1_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha1_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-12292),(-12291)⟩,⟨21289,21290⟩⟩,⟨⟨(-44646528672),(-44646528671)⟩,⟨25776685346,25776685347⟩⟩,⟨⟨(-257142289286048),(-257142289286047)⟩,⟨(-1),1⟩⟩,⟨⟨(-93630556896327456),(-93630556896327455)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨(-5860939688051789412),(-5860939688051789411)⟩,⟨(-10151445319802585616),(-10151445319802585614)⟩⟩,⟨⟨(-3),5⟩,⟨(-539266466260812848966),(-539266466260812848922)⟩⟩] +lemma ha1_0_21_eq (j : Fin 7) : ha1_0_21 j = ((ha1_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha1_0_21_contains (j : Fin 7) : (ha1_0_21 j).Contains (fullFactor false 1 21 ((j.val:ℝ)/6)) := by + rw [ha1_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_20 j) false 1 20 j (ha1_0_20_contains j) +noncomputable def hk1_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_22 j i k) +lemma hk1_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_22 j i k).Contains (fullFactor false 1 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 22 (power1_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha1_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-507),(-506)⟩,⟨(-293),(-292)⟩⟩,⟨⟨(-1226967354),(-1226967353)⟩,⟨(-2125169796),(-2125169795)⟩⟩,⟨⟨(-1),1⟩,⟨(-18359916521553),(-18359916521552)⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨1208019168182208037,1208019168182208038⟩,⟨(-697450191936225610),(-697450191936225609)⟩⟩,⟨⟨77007071306013533795,77007071306013533803⟩,⟨(-1),1⟩⟩] +lemma ha1_0_22_eq (j : Fin 7) : ha1_0_22 j = ((ha1_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha1_0_22_contains (j : Fin 7) : (ha1_0_22 j).Contains (fullFactor false 1 22 ((j.val:ℝ)/6)) := by + rw [ha1_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_21 j) false 1 21 j (ha1_0_21_contains j) +noncomputable def hk1_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_23 j i k) +lemma hk1_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_23 j i k).Contains (fullFactor false 1 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 23 (power1_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha1_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨6,7⟩,⟨(-12),(-11)⟩⟩,⟨⟨96759678,96759679⟩,⟨(-55864227),(-55864226)⟩⟩,⟨⟨1253899540535,1253899540536⟩,⟨(-1),1⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨79387840551870928,79387840551870929⟩,⟨137503773339017306,137503773339017308⟩⟩,⟨⟨(-1),1⟩,⟨10518471716932064454,10518471716932064456⟩⟩] +lemma ha1_0_23_eq (j : Fin 7) : ha1_0_23 j = ((ha1_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha1_0_23_contains (j : Fin 7) : (ha1_0_23 j).Contains (fullFactor false 1 23 ((j.val:ℝ)/6)) := by + rw [ha1_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_22 j) false 1 22 j (ha1_0_22_contains j) +noncomputable def hk1_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_24 j i k) +lemma hk1_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_24 j i k).Contains (fullFactor false 1 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 24 (power1_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha1_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨2437536,2437537⟩,⟨4221937,4221938⟩⟩,⟨⟨(-1),1⟩,⟨82067533018,82067533019⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-14999334866761558),(-14999334866761557)⟩,⟨8659870022990124,8659870022990125⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha1_0_24_eq (j : Fin 7) : ha1_0_24 j = ((ha1_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha1_0_24_contains (j : Fin 7) : (ha1_0_24 j).Contains (fullFactor false 1 24 ((j.val:ℝ)/6)) := by + rw [ha1_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_23 j) false 1 23 j (ha1_0_23_contains j) +noncomputable def hk1_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_25 j i k) +lemma hk1_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_25 j i k).Contains (fullFactor false 1 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 25 (power1_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha1_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-176849),(-176848)⟩,⟨102103,102104⟩⟩,⟨⟨(-5156455177),(-5156455176)⟩,⟨(-1),1⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨(-906859468175609),(-906859468175608)⟩,⟨(-1570726674205046),(-1570726674205044)⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha1_0_25_eq (j : Fin 7) : ha1_0_25 j = ((ha1_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha1_0_25_contains (j : Fin 7) : (ha1_0_25 j).Contains (fullFactor false 1 25 ((j.val:ℝ)/6)) := by + rw [ha1_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_24 j) false 1 24 j (ha1_0_24_contains j) +noncomputable def hk1_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_26 j i k) +lemma hk1_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_26 j i k).Contains (fullFactor false 1 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 26 (power1_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha1_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-4113),(-4112)⟩,⟨(-7123),(-7122)⟩⟩,⟨⟨(-1),1⟩,⟨(-311528495),(-311528494)⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨158159723733336,158159723733337⟩,⟨(-91313559072399),(-91313559072398)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha1_0_26_eq (j : Fin 7) : ha1_0_26 j = ((ha1_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha1_0_26_contains (j : Fin 7) : (ha1_0_26 j).Contains (fullFactor false 1 26 ((j.val:ℝ)/6)) := by + rw [ha1_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_25 j) false 1 25 j (ha1_0_25_contains j) +noncomputable def hk1_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_27 j i k) +lemma hk1_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_27 j i k).Contains (fullFactor false 1 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 27 (power1_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha1_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨276,277⟩,⟨(-160),(-159)⟩⟩,⟨⟨18123993,18123994⟩,⟨(-1),1⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨8854012541820,8854012541821⟩,⟨15335599573285,15335599573286⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha1_0_27_eq (j : Fin 7) : ha1_0_27 j = ((ha1_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha1_0_27_contains (j : Fin 7) : (ha1_0_27 j).Contains (fullFactor false 1 27 ((j.val:ℝ)/6)) := by + rw [ha1_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_26 j) false 1 26 j (ha1_0_26_contains j) +noncomputable def hk1_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_28 j i k) +lemma hk1_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_28 j i k).Contains (fullFactor false 1 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 28 (power1_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha1_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨5,6⟩,⟨10,11⟩⟩,⟨⟨(-1),1⟩,⟨1016753,1016754⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-1433875207079),(-1433875207078)⟩,⟨827848236790,827848236791⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha1_0_28_eq (j : Fin 7) : ha1_0_28 j = ((ha1_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha1_0_28_contains (j : Fin 7) : (ha1_0_28 j).Contains (fullFactor false 1 28 ((j.val:ℝ)/6)) := by + rw [ha1_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_27 j) false 1 27 j (ha1_0_27_contains j) +noncomputable def hk1_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_29 j i k) +lemma hk1_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_29 j i k).Contains (fullFactor false 1 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 29 (power1_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha1_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-55073),(-55072)⟩,⟨(-1),1⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨(-74734538477),(-74734538476)⟩,⟨(-129444017722),(-129444017721)⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha1_0_29_eq (j : Fin 7) : ha1_0_29 j = ((ha1_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha1_0_29_contains (j : Fin 7) : (ha1_0_29 j).Contains (fullFactor false 1 29 ((j.val:ℝ)/6)) := by + rw [ha1_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_28 j) false 1 28 j (ha1_0_28_contains j) +noncomputable def hk1_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power1 j i k).conj.mul (mpower0_30 j i k) +lemma hk1_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk1_0_30 j i k).Contains (fullFactor false 1 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power1 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 30 (power1_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha1_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨(-2884),(-2883)⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨11296121531,11296121532⟩,⟨(-6521818807),(-6521818806)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha1_0_30_eq (j : Fin 7) : ha1_0_30 j = ((ha1_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha1_0_30_contains (j : Fin 7) : (ha1_0_30 j).Contains (fullFactor false 1 30 ((j.val:ℝ)/6)) := by + rw [ha1_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_0_29 j) false 1 29 j (ha1_0_29_contains j) +noncomputable def hk1_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_0 j i k) +lemma hk1_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_0 j i k).Contains (fullFactor true 1 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 0 (kernel1_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha1_1_0 : Fin 7 → CBox := ![⟨⟨287235913262267589131245569,287235913262267589152589145⟩,⟨(-3),3⟩⟩,⟨⟨(-1227594407139841125053370123),(-1227594407139841124878361402)⟩,⟨225258927663398569617556379,225258927663398569785347626⟩⟩,⟨⟨(-4099475087999640329578559768),(-4099475087999640327343491894)⟩,⟨15600083655785914278280280272,15600083655785914280549783452⟩⟩,⟨⟨(-51036477369635067913459257139),(-51036477369635067901487188489)⟩,⟨93385323635182926762172010361,93385323635182926773837146635⟩⟩,⟨⟨(-294139142057855203281176399137),(-294139142057855203251857742481)⟩,⟨141367692329865808421293419379,141367692329865808447103276276⟩⟩,⟨⟨(-607731118347857408150380104706),(-607731118347857408104316711950)⟩,⟨(-110320451301813891842385438936),(-110320451301813891798653618696)⟩⟩,⟨⟨(-667529588463563842466349351680),(-667529588463563842419653782517)⟩,⟨(-586481159748591935787351906668),(-586481159748591935733302259315)⟩⟩] +lemma ha1_1_0_eq (j : Fin 7) : ha1_1_0 j = atomKernel1_0 j := by fin_cases j <;> decide +kernel +lemma ha1_1_0_contains (j : Fin 7) : (ha1_1_0 j).Contains (fullFactor true 1 0 ((j.val:ℝ)/6)) := by + rw [ha1_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel1_0_contains j +noncomputable def hk1_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_1 j i k) +lemma hk1_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_1 j i k).Contains (fullFactor true 1 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 1 (kernel1_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha1_1_1 : Fin 7 → CBox := ![⟨⟨(-2646976155858891764422936308),(-2646976155858891764217822444)⟩,⟨(-28),28⟩⟩,⟨⟨10248502049497462764170562060,10248502049497462766168665657⟩,⟨2837138858378663619951611366,2837138858378663621908620316⟩⟩,⟨⟨100526751266157010641267391192,100526751266157010664280121597⟩,⟨(-55694797749507294492877899648),(-55694797749507294469881268035)⟩⟩,⟨⟨621471044354675043360749079671,621471044354675043456196879347⟩,⟨(-3570646982377401830921203437),(-3570646982377401735081237023)⟩⟩,⟨⟨1098842859300173353297675724200,1098842859300173353464842925351⟩,⟨1144697213258281395037408564524,1144697213258281395216979041672⟩⟩,⟨⟨(-22663614851943702239959505301),(-22663614851943702026062341800)⟩,⟨2560460779786166905954461002828,2560460779786166906181594339863⟩⟩,⟨⟨(-1992454469280585019061246880751),(-1992454469280585018850163867175)⟩,⟨2520592259912149515844324457216,2520592259912149516031115751282⟩⟩] +lemma ha1_1_1_eq (j : Fin 7) : ha1_1_1 j = ((ha1_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha1_1_1_contains (j : Fin 7) : (ha1_1_1 j).Contains (fullFactor true 1 1 ((j.val:ℝ)/6)) := by + rw [ha1_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_0 j) true 1 0 j (ha1_1_0_contains j) +noncomputable def hk1_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_2 j i k) +lemma hk1_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_2 j i k).Contains (fullFactor true 1 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 2 (kernel1_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha1_1_2 : Fin 7 → CBox := ![⟨⟨12196390573361347335076360578,12196390573361347336060279735⟩,⟨(-130),130⟩⟩,⟨⟨(-34009640985647258686134702127),(-34009640985647258674695966201)⟩,⟨(-29926332711991384080832120016),(-29926332711991384069521085676)⟩⟩,⟨⟨(-390892336210065946434368050320),(-390892336210065946317253619215)⟩,⟨(-121756091788458023867561267047),(-121756091788458023750428842993)⟩⟩,⟨⟨(-888497586055070015111484179785),(-888497586055070014728809235609)⟩,⟨(-1582271839194707634054197981546),(-1582271839194707633669729255890)⟩⟩,⟨⟨1811675068507691695296714654735,1811675068507691695849247477462⟩,⟨(-3405633225673014004949345343088),(-3405633225673014004416292903187)⟩⟩,⟨⟨5238101189218518216233101047695,5238101189218518216789052327499⟩,⟨(-855378924179136656114289373347),(-855378924179136655594369708218)⟩⟩,⟨⟨4738027070831674426430075107891,4738027070831674426802228712530⟩,⟨3360752453292758894601793870823,3360752453292758895012648382098⟩⟩] +lemma ha1_1_2_eq (j : Fin 7) : ha1_1_2 j = ((ha1_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha1_1_2_contains (j : Fin 7) : (ha1_1_2 j).Contains (fullFactor true 1 2 ((j.val:ℝ)/6)) := by + rw [ha1_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_1 j) true 1 1 j (ha1_1_1_contains j) +noncomputable def hk1_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_3 j i k) +lemma hk1_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_3 j i k).Contains (fullFactor true 1 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 3 (kernel1_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha1_1_3 : Fin 7 → CBox := ![⟨⟨(-37464622336126396887965735586),(-37464622336126396884824099308)⟩,⟨(-400),400⟩⟩,⟨⟨49821256299583075567372271902,49821256299583075611015240203⟩,⟨118621753759090402050217381969,118621753759090402093675172892⟩⟩,⟨⟨432504574126370630636910636051,432504574126370631032907332316⟩,⟨870875508940356452212502387702,870875508940356452608562435214⟩⟩,⟨⟨(-1856083889996852295561614781199),(-1856083889996852294534724379791)⟩,⟨3005501558658382000443723818508,3005501558658382001467574875380⟩⟩,⟨⟨(-6159774073909780147087354235313),(-6159774073909780145967753500819)⟩,⟨(-1069723649070674514368451779461),(-1069723649070674513233941919231)⟩⟩,⟨⟨(-2394565727468471308003710582934),(-2394565727468471307157560098460)⟩,⟨(-6932248784196985862276325625828),(-6932248784196985861373845292200)⟩⟩,⟨⟨3748696461229969194790660635331,3748696461229969195322310012555⟩,⟨(-5913399628183859166641986241106),(-5913399628183859166149495343359)⟩⟩] +lemma ha1_1_3_eq (j : Fin 7) : ha1_1_3 j = ((ha1_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha1_1_3_contains (j : Fin 7) : (ha1_1_3 j).Contains (fullFactor true 1 3 ((j.val:ℝ)/6)) := by + rw [ha1_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_2 j) true 1 2 j (ha1_1_2_contains j) +noncomputable def hk1_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_4 j i k) +lemma hk1_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_4 j i k).Contains (fullFactor true 1 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 4 (kernel1_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha1_1_4 : Fin 7 → CBox := ![⟨⟨86312293687173228303222231626,86312293687173228310734782588⟩,⟨(-922),922⟩⟩,⟨⟨14769503800638230741352708750,14769503800638230866044362099⟩,⟨(-273652529403738708553243509167),(-273652529403738708428518470973)⟩⟩,⟨⟨588921331491213552857984591529,588921331491213553860617580309⟩,⟨(-1628814797274688215164792342915),(-1628814797274688214162241993586)⟩⟩,⟨⟨5151409994869979770237062172670,5151409994869979772287511035262⟩,⟨243966413586880668556205949827,243966413586880670606302038345⟩⟩,⟨⟨1098035427798879984112440752731,1098035427798879985858305897955⟩,⟨7519775578073350750253021663420,7519775578073350751999890387386⟩⟩,⟨⟨(-6658445948115395215178764130656),(-6658445948115395214084173638250)⟩,⟨3666231904245789672956063938847,3666231904245789673990833084238⟩⟩,⟨⟨(-5514336335438565913976223418805),(-5514336335438565913489113980508)⟩,⟨(-3106565412642726723968033368582),(-3106565412642726723453308537794)⟩⟩] +lemma ha1_1_4_eq (j : Fin 7) : ha1_1_4 j = ((ha1_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha1_1_4_contains (j : Fin 7) : (ha1_1_4 j).Contains (fullFactor true 1 4 ((j.val:ℝ)/6)) := by + rw [ha1_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_3 j) true 1 3 j (ha1_1_3_contains j) +noncomputable def hk1_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_5 j i k) +lemma hk1_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_5 j i k).Contains (fullFactor true 1 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 5 (kernel1_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha1_1_5 : Fin 7 → CBox := ![⟨⟨(-159079399753770086279525542603),(-159079399753770086265173037197)⟩,⟨(-1700),1700⟩⟩,⟨⟨(-226125701939186556349820942897),(-226125701939186556065176118251)⟩,⟨408594433963913454764777754126,408594433963913455050099672730⟩⟩,⟨⟨(-2257644881598426108315853630384),(-2257644881598426106288708238550)⟩,⟨997301796121189057750877925182,997301796121189059777877044926⟩⟩,⟨⟨(-2666435421810330547830228225564),(-2666435421810330544565111710923)⟩,⟨(-5401054071167189622238074926813),(-5401054071167189618965679879530)⟩⟩,⟨⟨6615473371111462706601380531648,6615473371111462708767781330380⟩,⟨(-3293610457390052365309166813778),(-3293610457390052363156081544278)⟩⟩,⟨⟨3933443938926397284084516859589,3933443938926397285096690178097⟩,⟨4923915451432749411741058434824,4923915451432749412800123299162⟩⟩,⟨⟨(-2036488633372645452773995261431),(-2036488633372645452376164358762)⟩,⟨4099148459978458920646320388630,4099148459978458921030491678082⟩⟩] +lemma ha1_1_5_eq (j : Fin 7) : ha1_1_5 j = ((ha1_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha1_1_5_contains (j : Fin 7) : (ha1_1_5 j).Contains (fullFactor true 1 5 ((j.val:ℝ)/6)) := by + rw [ha1_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_4 j) true 1 4 j (ha1_1_4_contains j) +noncomputable def hk1_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_6 j i k) +lemma hk1_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_6 j i k).Contains (fullFactor true 1 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 6 (kernel1_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha1_1_6 : Fin 7 → CBox := ![⟨⟨244328418206359943580614262277,244328418206359943603435849610⟩,⟨(-2612),2612⟩⟩,⟨⟨542104820585143372412522600647,542104820585143372954738151199⟩,⟨(-381945800975115803165120644407),(-381945800975115802622077311833)⟩⟩,⟨⟨2708645394883852982987387389408,2708645394883852986399358497113⟩,⟨1119492262887064207479030672730,1119492262887064210891158821464⟩⟩,⟨⟨(-3340686914106598561045545560344),(-3340686914106598556700813357652)⟩,⟨4817636060972483549340646137688,4817636060972483553679309311237⟩⟩,⟨⟨(-4206874169296466836866172315851),(-4206874169296466834647764732475)⟩,⟨(-4262070272063111759726689541891),(-4262070272063111757495920683551)⟩⟩,⟨⟨2890884651410802741649829576483,2890884651410802742501883018401⟩,⟨(-3256203565940719660623354668845),(-3256203565940719659799501123137)⟩⟩,⟨⟨2530755021032148929044250002463,2530755021032148929295964741302⟩,⟨1097350437922380124861218908538,1097350437922380125116981052064⟩⟩] +lemma ha1_1_6_eq (j : Fin 7) : ha1_1_6 j = ((ha1_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha1_1_6_contains (j : Fin 7) : (ha1_1_6 j).Contains (fullFactor true 1 6 ((j.val:ℝ)/6)) := by + rw [ha1_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_5 j) true 1 5 j (ha1_1_5_contains j) +noncomputable def hk1_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_7 j i k) +lemma hk1_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_7 j i k).Contains (fullFactor true 1 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 7 (kernel1_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha1_1_7 : Fin 7 → CBox := ![⟨⟨(-321652723836322512112172550720),(-321652723836322512081104605264)⟩,⟨(-3439),3439⟩⟩,⟨⟨(-796560213426525364539448415581),(-796560213426525363654668796240)⟩,⟨130373397563733933558416608595,130373397563733934443375585412⟩⟩,⟨⟨(-1081511837017671519563840575844),(-1081511837017671514644872745393)⟩,⟨(-2780257995586590279692675111801),(-2780257995586590274773548611656)⟩⟩,⟨⟨4866277113520346705113761855105,4866277113520346710051915619809⟩,⟨490188091944792565916858522290,490188091944792570855457450514⟩⟩,⟨⟨(-1902257811086116291148644196151),(-1902257811086116289184247658248)⟩,⟨3699181273936940160055725789841,3699181273936940162014561943983⟩⟩,⟨⟨(-2191231449984051785903869019778),(-2191231449984051785330352519489)⟩,⟨(-1359537005858171990513425535763),(-1359537005858171989926850175086)⟩⟩,⟨⟨498193235192244269606603448315,498193235192244269747311296797⟩,⟨(-1334953635791130924319782322136),(-1334953635791130924178822491052)⟩⟩] +lemma ha1_1_7_eq (j : Fin 7) : ha1_1_7 j = ((ha1_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha1_1_7_contains (j : Fin 7) : (ha1_1_7 j).Contains (fullFactor true 1 7 ((j.val:ℝ)/6)) := by + rw [ha1_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_6 j) true 1 6 j (ha1_1_6_contains j) +noncomputable def hk1_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_8 j i k) +lemma hk1_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_8 j i k).Contains (fullFactor true 1 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 8 (kernel1_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha1_1_8 : Fin 7 → CBox := ![⟨⟨370517339210823706052582441046,370517339210823706089549538410⟩,⟨(-3962),3962⟩⟩,⟨⟨823915463846596816021602633372,823915463846596817283360028888⟩,⟨245253481054223121162495933631,245253481054223122423295266894⟩⟩,⟨⟨(-1124234818917947214011401503976),(-1124234818917947207809459412415)⟩,⟨2407334520456433060390453793746,2407334520456433066592238225216⟩⟩,⟨⟨(-1408435644264619567851741256486),(-1408435644264619562944932514072)⟩,⟨(-3280691978677604981015022891045),(-3280691978677604976104373982773)⟩⟩,⟨⟨2496597022144665665829461652895,2496597022144665667340728923865⟩,⟨397854038637289394317985958996,397854038637289395829191369664⟩⟩,⟨⟨(-501351974583334850041146718955),(-501351974583334849688289680977)⟩,⟨1238669740408552015657883416307,1238669740408552016006340308030⟩⟩,⟨⟨(-614262469236681305725290677289),(-614262469236681305656406568484)⟩,⟨(-193540002862600254328008895327),(-193540002862600254260372336910)⟩⟩] +lemma ha1_1_8_eq (j : Fin 7) : ha1_1_8 j = ((ha1_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha1_1_8_contains (j : Fin 7) : (ha1_1_8 j).Contains (fullFactor true 1 8 ((j.val:ℝ)/6)) := by + rw [ha1_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_7 j) true 1 7 j (ha1_1_7_contains j) +noncomputable def hk1_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_9 j i k) +lemma hk1_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_9 j i k).Contains (fullFactor true 1 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 9 (kernel1_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha1_1_9 : Fin 7 → CBox := ![⟨⟨(-379382520290843648588076847231),(-379382520290843648549017644746)⟩,⟨(-4057),4057⟩⟩,⟨⟨(-600500752411898582609787047422),(-600500752411898581011630749608)⟩,⟨(-549263642632947803742446898086),(-549263642632947802145518981831)⟩⟩,⟨⟨1992595487597180966959768292692,1992595487597180973907852485905⟩,⟨(-673626695925647692002221345814),(-673626695925647685054236017904)⟩⟩,⟨⟨(-1419204481376796484371063016621),(-1419204481376796480033594935534)⟩,⟨1831000228500242791227515810120,1831000228500242795562503148139⟩⟩,⟨⟨(-216128117373209165886749693970),(-216128117373209164854554750492)⟩,⟨(-1348571328486694070220927731456),(-1348571328486694069186406946596)⟩⟩,⟨⟨601493033833309103272705758317,601493033833309103460405764397⟩,⟨130641099806405113287852746192,130641099806405113476324065604⟩⟩,⟨⟨(-64837318417744383891357131091),(-64837318417744383862494495881)⟩,⟨250495491825117084238672215067,250495491825117084268518750758⟩⟩] +lemma ha1_1_9_eq (j : Fin 7) : ha1_1_9 j = ((ha1_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha1_1_9_contains (j : Fin 7) : (ha1_1_9 j).Contains (fullFactor true 1 9 ((j.val:ℝ)/6)) := by + rw [ha1_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_8 j) true 1 8 j (ha1_1_8_contains j) +noncomputable def hk1_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_10 j i k) +lemma hk1_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_10 j i k).Contains (fullFactor true 1 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 10 (kernel1_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha1_1_10 : Fin 7 → CBox := ![⟨⟨349613832669521221915156642034,349613832669521221952263874479⟩,⟨(-3739),3739⟩⟩,⟨⟨256149072492868162565622962831,256149072492868164386637284518⟩,⟨644335962619595055802001189934,644335962619595057622466106271⟩⟩,⟨⟨(-1327991376622188701502492091431),(-1327991376622188694499026322594)⟩,⟨(-694553792805492225667046301609),(-694553792805492218663483153684)⟩⟩,⟨⟨1336959418051612477372430781885,1336959418051612480818617745038⟩,⟨206798710333507061792735994575,206798710333507065239189508122⟩⟩,⟨⟨(-590287383017911433390815763387),(-590287383017911432754366508071)⟩,⟨304207583690322321215901766252,304207583690322321850509812886⟩⟩,⟨⟨11007299403209770664214298582,11007299403209770754734949482⟩,⟨(-254928829292876404316513992295),(-254928829292876404225747389540)⟩⟩,⟨⟨91672046427881796967513744065,91672046427881796979125170389⟩,⟨18709286641625305320617205800,18709286641625305331689514739⟩⟩] +lemma ha1_1_10_eq (j : Fin 7) : ha1_1_10 j = ((ha1_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha1_1_10_contains (j : Fin 7) : (ha1_1_10 j).Contains (fullFactor true 1 10 ((j.val:ℝ)/6)) := by + rw [ha1_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_9 j) true 1 9 j (ha1_1_9_contains j) +noncomputable def hk1_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_11 j i k) +lemma hk1_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_11 j i k).Contains (fullFactor true 1 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 11 (kernel1_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha1_1_11 : Fin 7 → CBox := ![⟨⟨(-292891799548783765999168029745),(-292891799548783765967148843831)⟩,⟨(-3133),3133⟩⟩,⟨⟨39259455957372622295812825565,39259455957372624181487884667⟩,⟨(-535632194452509245351707172780),(-535632194452509243465785795822)⟩⟩,⟨⟨269215277183579806287411651987,269215277183579812704092824609⟩,⟨932638572538822193791126540209,932638572538822200207847243653⟩⟩,⟨⟨(-247926600980377252169877607399),(-247926600980377249681375397574)⟩,⟨(-674072892116899856404029363771),(-674072892116899853914837273742)⟩⟩,⟨⟨209084686103535579934805450663,209084686103535580289682788590⟩,⟨206012582391311559129521325413,206012582391311559485175337731⟩⟩,⟨⟨(-95382930256173682262883287464),(-95382930256173682223073983889)⟩,⟨12234507446344396621811530569,12234507446344396661306593099⟩⟩,⟨⟨4576923054563444836563540049,4576923054563444840421044969⟩,⟨(-30413022924312660188944679285),(-30413022924312660184847121863)⟩⟩] +lemma ha1_1_11_eq (j : Fin 7) : ha1_1_11 j = ((ha1_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha1_1_11_contains (j : Fin 7) : (ha1_1_11 j).Contains (fullFactor true 1 11 ((j.val:ℝ)/6)) := by + rw [ha1_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_10 j) true 1 10 j (ha1_1_10_contains j) +noncomputable def hk1_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_12 j i k) +lemma hk1_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_12 j i k).Contains (fullFactor true 1 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 12 (kernel1_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha1_1_12 : Fin 7 → CBox := ![⟨⟨224924755185570830432122811187,224924755185570830457427738512⟩,⟨(-2406),2406⟩⟩,⟨⟨(-191031510009805371564735295276),(-191031510009805369775159571301)⟩,⟨330026516980086659906719279505,330026516980086661696895919293⟩⟩,⟨⟨289811393352166711620245415276,289811393352166717008529951782⟩,⟨(-498198978621180652190091696624),(-498198978621180646801847784518)⟩⟩,⟨⟨(-228477031809919704135298820085),(-228477031809919702487705810572)⟩,⟨264508046514232780040132344395,264508046514232781687336839230⟩⟩,⟨⟨52911506329382344544784603420,52911506329382344726861393655⟩,⟨(-106512623981388505866688356800),(-106512623981388505684809977326)⟩⟩,⟨⟨9763355252478050948759550238,9763355252478050964572870924⟩,⟨31754223491159149826804115845,31754223491159149842780544185⟩⟩,⟨⟨(-9223470157124546158166184612),(-9223470157124546156843431795)⟩,⟨(-901386083894002516930556987),(-901386083894002515699744567)⟩⟩] +lemma ha1_1_12_eq (j : Fin 7) : ha1_1_12 j = ((ha1_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha1_1_12_contains (j : Fin 7) : (ha1_1_12 j).Contains (fullFactor true 1 12 ((j.val:ℝ)/6)) := by + rw [ha1_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_11 j) true 1 11 j (ha1_1_11_contains j) +noncomputable def hk1_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_13 j i k) +lemma hk1_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_13 j i k).Contains (fullFactor true 1 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 13 (kernel1_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha1_1_13 : Fin 7 → CBox := ![⟨⟨(-159442903456742416324932655252),(-159442903456742416306487173513)⟩,⟨(-1706),1706⟩⟩,⟨⟨207037244954061604250711567196,207037244954061605818672634363⟩,⟨(-139986957182931470441399154411),(-139986957182931468873121200097)⟩⟩,⟨⟨(-307130762218868813231359735916),(-307130762218868809055017717375)⟩,⟨73871730633658541951744449537,73871730633658546128075613724⟩⟩,⟨⟨153674500732897821277018915973,153674500732897822283435051017⟩,⟨32197719055108401617717247516,32197719055108402624181371196⟩⟩,⟨⟨(-44020535755093054101581714217),(-44020535755093054015581024199)⟩,⟨(-6388153474434469595086100728),(-6388153474434469509078773220)⟩⟩,⟨⟨9449924857747458835832653629,9449924857747458841743473461⟩,⟨(-4788527391316955811108433174),(-4788527391316955805258238870)⟩⟩,⟨⟨(-117154360983701017496599997),(-117154360983701017134388683)⟩,⟨2575034399379846388717241539,2575034399379846389110638794⟩⟩] +lemma ha1_1_13_eq (j : Fin 7) : ha1_1_13 j = ((ha1_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha1_1_13_contains (j : Fin 7) : (ha1_1_13 j).Contains (fullFactor true 1 13 ((j.val:ℝ)/6)) := by + rw [ha1_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_12 j) true 1 12 j (ha1_1_12_contains j) +noncomputable def hk1_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_14 j i k) +lemma hk1_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_14 j i k).Contains (fullFactor true 1 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 14 (kernel1_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha1_1_14 : Fin 7 → CBox := ![⟨⟨104951451349219330902335088125,104951451349219330914810684479⟩,⟨(-1123),1123⟩⟩,⟨⟨(-150546223707535979131377220794),(-150546223707535977855827355601)⟩,⟨21674031155625376977087008885,21674031155625378252666052366⟩⟩,⟨⟨135187344696563867682505329922,135187344696563870688017685697⟩,⟨87004233607412107611386008003,87004233607412110616910557499⟩⟩,⟨⟨(-19315852321128066572196336370),(-19315852321128066001385317310)⟩,⟨(-62580831094351540442229059333),(-62580831094351539871362924460)⟩⟩,⟨⟨2656685931080540525193063473,2656685931080540562905985085⟩,⟨15218194944493848875734050718,15218194944493848913472064439⟩⟩,⟨⟨(-1872727261342353100947768032),(-1872727261342353098937321541)⟩,⟨(-2516654044542493522172506536),(-2516654044542493520143835726)⟩⟩,⟨⟨665751052412352704693120601,665751052412352704801566994⟩,⟨(-4319671271995090020646311),(-4319671271995089921738473)⟩⟩] +lemma ha1_1_14_eq (j : Fin 7) : ha1_1_14 j = ((ha1_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha1_1_14_contains (j : Fin 7) : (ha1_1_14 j).Contains (fullFactor true 1 14 ((j.val:ℝ)/6)) := by + rw [ha1_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_13 j) true 1 13 j (ha1_1_13_contains j) +noncomputable def hk1_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_15 j i k) +lemma hk1_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_15 j i k).Contains (fullFactor true 1 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 15 (kernel1_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha1_1_15 : Fin 7 → CBox := ![⟨⟨(-64477543003826390760359201576),(-64477543003826390752489506997)⟩,⟨(-690),690⟩⟩,⟨⟨82313530757326829579989120715,82313530757326830548323395146⟩,⟨26236790196739006436750319631,26236790196739007404984296383⟩⟩,⟨⟨(-14501065660182567137796166574),(-14501065660182565119114241788)⟩,⟨(-74973642426171908905723779610),(-74973642426171906887039722034)⟩⟩,⟨⟨(-17667788856382034339759006867),(-17667788856382034037577398879)⟩,⟨18384917857845495510330503996,18384917857845495812482823384⟩⟩,⟨⟨4418804670315139951886236070,4418804670315139967335192506⟩,⟨(-2355656684295322145931493840),(-2355656684295322130496006674)⟩⟩,⟨⟨(-597487037015741051501885196),(-597487037015741050852510985)⟩,⟨628209158796972077017257631,628209158796972077662062095⟩⟩,⟨⟨(-9373916899133741481151209),(-9373916899133741455953228)⟩,⟨(-160215551088624634111824925),(-160215551088624634083969598)⟩⟩] +lemma ha1_1_15_eq (j : Fin 7) : ha1_1_15 j = ((ha1_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha1_1_15_contains (j : Fin 7) : (ha1_1_15 j).Contains (fullFactor true 1 15 ((j.val:ℝ)/6)) := by + rw [ha1_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_14 j) true 1 14 j (ha1_1_14_contains j) +noncomputable def hk1_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_16 j i k) +lemma hk1_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_16 j i k).Contains (fullFactor true 1 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 16 (kernel1_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha1_1_16 : Fin 7 → CBox := ![⟨⟨37136398827429175811478124299,37136398827429175816128951819⟩,⟨(-398),398⟩⟩,⟨⟨(-33343105464407602900457886606),(-33343105464407602211360916115)⟩,⟨(-31697970950057856971018560835),(-31697970950057856281990389552)⟩⟩,⟨⟨(-19670562124073366963156965662),(-19670562124073365692090867378)⟩,⟨27738675538810406724655092391,27738675538810407995718434245⟩⟩,⟨⟨8994683992253732315266512632,8994683992253732465210709533⟩,⟨2388933577376688140618494985,2388933577376688290566537348⟩⟩,⟨⟨(-1098698288681292028236420925),(-1098698288681292022312769919)⟩,⟨(-1052823142025405981131791624),(-1052823142025405975204252750)⟩⟩,⟨⟨186702094843846215422183614,186702094843846215616001322⟩,⟨124903784406946674497212374,124903784406946674691975060⟩⟩,⟨⟨(-36048897184672988701502315),(-36048897184672988694804503)⟩,⟨3995854337414128684020325,3995854337414128690046861⟩⟩] +lemma ha1_1_16_eq (j : Fin 7) : ha1_1_16 j = ((ha1_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha1_1_16_contains (j : Fin 7) : (ha1_1_16 j).Contains (fullFactor true 1 16 ((j.val:ℝ)/6)) := by + rw [ha1_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_15 j) true 1 15 j (ha1_1_15_contains j) +noncomputable def hk1_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_17 j i k) +lemma hk1_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_17 j i k).Contains (fullFactor true 1 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 17 (kernel1_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha1_1_17 : Fin 7 → CBox := ![⟨⟨(-20130852001683972016701624161),(-20130852001683972014116430982)⟩,⟨(-216),216⟩⟩,⟨⟨8103955857998026332942995720,8103955857998026794453316539⟩,⟨21586409432734185162963960602,21586409432734185624457086082⟩⟩,⟨⟨14100429068633123910108060666,14100429068633124663348277313⟩,⟨(-2074484723546142233559511388),(-2074484723546141480319600330)⟩⟩,⟨⟨(-779500008540357537190986054),(-779500008540357467165293501)⟩,⟨(-3100471953444549428658545041),(-3100471953444549358630549898)⟩⟩,⟨⟨(-188183058617990689768062830),(-188183058617990687627922203)⟩,⟨392433915860396545317532542,392433915860396547456989814⟩⟩,⟨⟨22280806459140456098155534,22280806459140456153109230⟩,⟨(-50041393702561073095714125),(-50041393702561073040909245)⟩⟩,⟨⟨1246950375972618290063044,1246950375972618291421112⟩,⟨7613128907407587163650380,7613128907407587165164166⟩⟩] +lemma ha1_1_17_eq (j : Fin 7) : ha1_1_17 j = ((ha1_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha1_1_17_contains (j : Fin 7) : (ha1_1_17 j).Contains (fullFactor true 1 17 ((j.val:ℝ)/6)) := by + rw [ha1_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_16 j) true 1 16 j (ha1_1_16_contains j) +noncomputable def hk1_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_18 j i k) +lemma hk1_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_18 j i k).Contains (fullFactor true 1 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 18 (kernel1_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha1_1_18 : Fin 7 → CBox := ![⟨⟨10306256360724907489286185273,10306256360724907490642515002⟩,⟨(-111),111⟩⟩,⟨⟨1007138104310771300777464328,1007138104310771592681057235⟩,⟨(-10867541913154431564115649374),(-10867541913154431272206414546)⟩⟩,⟨⟨(-4450445077366248593194671481),(-4450445077366248171629826857)⟩,⟨(-3466974006336426536380375190),(-3466974006336426114815044805)⟩⟩,⟨⟨(-757339214131383486066507591),(-757339214131383455180289185)⟩,⟨708677879975736577257968164,708677879975736608142960030⟩⟩,⟨⟨116566936914816941000104172,116566936914816941729772184⟩,⟨15262579424833824412798828,15262579424833825142472566⟩⟩,⟨⟨(-12229243981741613510096767),(-12229243981741613495469044)⟩,⟨(-3098849150929427543655597),(-3098849150929427529016518)⟩⟩,⟨⟨1514281259197659095382418,1514281259197659095705174⟩,⟨(-329572945884832952584932),(-329572945884832952295645)⟩⟩] +lemma ha1_1_18_eq (j : Fin 7) : ha1_1_18 j = ((ha1_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha1_1_18_contains (j : Fin 7) : (ha1_1_18 j).Contains (fullFactor true 1 18 ((j.val:ℝ)/6)) := by + rw [ha1_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_17 j) true 1 17 j (ha1_1_17_contains j) +noncomputable def hk1_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_19 j i k) +lemma hk1_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_19 j i k).Contains (fullFactor true 1 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 19 (kernel1_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha1_1_19 : Fin 7 → CBox := ![⟨⟨(-4998717922210960306866145712),(-4998717922210960306192390218)⟩,⟨(-54),54⟩⟩,⟨⟨(-2532892822906867717759010249),(-2532892822906867542852106999)⟩,⟨4187824862916710257790470582,4187824862916710432705068696⟩⟩,⟨⟨213501305186712006350190677,213501305186712229868382135⟩,⟨2104751125602955054006051150,2104751125602955277524274151⟩⟩,⟨⟨303336110227108911472939372,303336110227108924377948181⟩,⟨98060618800453425863498120,98060618800453438768672577⟩⟩,⟨⟨(-5585658337274997360227159),(-5585658337274997124565125)⟩,⟨(-29561380920193906210722332),(-29561380920193905975008542)⟩⟩,⟨⟨(-212978843404191120029389),(-212978843404191116335963)⟩,⟨2744348266221071331157658,2744348266221071334854234⟩⟩,⟨⟨(-77602008429562564101521),(-77602008429562564043103)⟩,⟨(-284538107331648698016458),(-284538107331648697951330)⟩⟩] +lemma ha1_1_19_eq (j : Fin 7) : ha1_1_19 j = ((ha1_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha1_1_19_contains (j : Fin 7) : (ha1_1_19 j).Contains (fullFactor true 1 19 ((j.val:ℝ)/6)) := by + rw [ha1_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_18 j) true 1 18 j (ha1_1_18_contains j) +noncomputable def hk1_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_20 j i k) +lemma hk1_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_20 j i k).Contains (fullFactor true 1 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 20 (kernel1_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha1_1_20 : Fin 7 → CBox := ![⟨⟨2303243873595219638672964929,2303243873595219638990740628⟩,⟨(-25),25⟩⟩,⟨⟨1749374466122183260863873710,1749374466122183360428675758⟩,⟨(-1134394167575409556158974334),(-1134394167575409456591613216)⟩⟩,⟨⟨489430233092341487472737366,489430233092341600057365840⟩,⟨(-573120073449755735186389687),(-573120073449755622601829779)⟩⟩,⟨⟨(-17875811939329458591039091),(-17875811939329453468609337)⟩,⟨(-91351816856341021725632693),(-91351816856341016603147376)⟩⟩,⟨⟨(-6405449852938034163290558),(-6405449852938034090962116)⟩,⟨3530085530596229852995443,3530085530596229925304004⟩⟩,⟨⟨568073858619441900146990,568073858619441901033944⟩,⟨(-53138834101762526538662),(-53138834101762525653602)⟩⟩,⟨⟨(-50645146257527185861232),(-50645146257527185848758)⟩,⟨16682577392207956558510,16682577392207956569724⟩⟩] +lemma ha1_1_20_eq (j : Fin 7) : ha1_1_20 j = ((ha1_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha1_1_20_contains (j : Fin 7) : (ha1_1_20 j).Contains (fullFactor true 1 20 ((j.val:ℝ)/6)) := by + rw [ha1_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_19 j) true 1 19 j (ha1_1_19_contains j) +noncomputable def hk1_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_21 j i k) +lemma hk1_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_21 j i k).Contains (fullFactor true 1 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 21 (kernel1_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha1_1_21 : Fin 7 → CBox := ![⟨⟨(-1010722468061420243132112827),(-1010722468061420242989447471)⟩,⟨(-11),11⟩⟩,⟨⟨(-839458398852362150323854489),(-839458398852362096346693894)⟩,⟨104409279620573312388568883,104409279620573366365842576⟩⟩,⟨⟨(-255304157565512851574705762),(-255304157565512797567079192)⟩,⟨14340121459990032042875112,14340121459990086050499548⟩⟩,⟨⟨(-19812495311192135078510529),(-19812495311192133142074727)⟩,⟨16659008010285762172593022,16659008010285764108997421⟩⟩,⟨⟨1238833181188313052412662,1238833181188313073543660⟩,⟨1154465296116492549077555,1154465296116492570212846⟩⟩,⟨⟨(-29389768975147703289887),(-29389768975147703087868)⟩,⟨(-108729711221957448416771),(-108729711221957448214183)⟩⟩,⟨⟨3321477634826510347330,3321477634826510349381⟩,⟨8559447540698206135836,8559447540698206138111⟩⟩] +lemma ha1_1_21_eq (j : Fin 7) : ha1_1_21 j = ((ha1_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha1_1_21_contains (j : Fin 7) : (ha1_1_21 j).Contains (fullFactor true 1 21 ((j.val:ℝ)/6)) := by + rw [ha1_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_20 j) true 1 20 j (ha1_1_20_contains j) +noncomputable def hk1_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_22 j i k) +lemma hk1_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_22 j i k).Contains (fullFactor true 1 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 22 (kernel1_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha1_1_22 : Fin 7 → CBox := ![⟨⟨423370437397320302099113585,423370437397320302160220741⟩,⟨(-5),5⟩⟩,⟨⟨310166366674967495148700530,310166366674967523080656753⟩,⟨105480192511169377960087113,105480192511169405891643719⟩⟩,⟨⟨60493425690918870049816320,60493425690918894779847974⟩,⟨56556861527465619298696835,56556861527465644028736411⟩⟩,⟨⟨6416727471211444887855522,6416727471211445586593515⟩,⟨2457409238768263077566364,2457409238768263776308648⟩⟩,⟨⟨157106515280838876924007,157106515280838882818952⟩,⟨(-339673743341080839769214),(-339673743341080833874837)⟩⟩,⟨⟨(-19249713463340800775227),(-19249713463340800731072)⟩,⟨8938399547945541847444,8938399547945541891473⟩⟩,⟨⟨1376577406809809367429,1376577406809809367825⟩,⟨(-618235381781154214591),(-618235381781154214232)⟩⟩] +lemma ha1_1_22_eq (j : Fin 7) : ha1_1_22 j = ((ha1_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha1_1_22_contains (j : Fin 7) : (ha1_1_22 j).Contains (fullFactor true 1 22 ((j.val:ℝ)/6)) := by + rw [ha1_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_21 j) true 1 21 j (ha1_1_21_contains j) +noncomputable def hk1_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_23 j i k) +lemma hk1_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_23 j i k).Contains (fullFactor true 1 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 23 (kernel1_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha1_1_23 : Fin 7 → CBox := ![⟨⟨(-169630516111532848341941681),(-169630516111532848316918115)⟩,⟨(-3),3⟩⟩,⟨⟨(-86332429918969983143844405),(-86332429918969969318311511)⟩,⟨(-85295254653495969421963823),(-85295254653495955596611379)⟩⟩,⟨⟨(-285464731267465599057936),(-285464731267454767546450)⟩,⟨(-25652634577029348917593689),(-25652634577029338086082157)⟩⟩,⟨⟨(-243744453882053748005569),(-243744453882053506836467)⟩,⟨(-1727516645114820514365808),(-1727516645114820273195883)⟩⟩,⟨⟨(-78580930297157535361684),(-78580930297157533789046)⟩,⟨(-9178417532003549300934),(-9178417532003547728298)⟩⟩,⟨⟨2177116452923626296715,2177116452923626305895⟩,⟨3145452970825682444490,3145452970825682453694⟩⟩,⟨⟨(-108302113840389166381),(-108302113840389166320)⟩,⟨(-211076901258598283640),(-211076901258598283573)⟩⟩] +lemma ha1_1_23_eq (j : Fin 7) : ha1_1_23 j = ((ha1_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha1_1_23_contains (j : Fin 7) : (ha1_1_23 j).Contains (fullFactor true 1 23 ((j.val:ℝ)/6)) := by + rw [ha1_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_22 j) true 1 22 j (ha1_1_22_contains j) +noncomputable def hk1_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_24 j i k) +lemma hk1_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_24 j i k).Contains (fullFactor true 1 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 24 (kernel1_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha1_1_24 : Fin 7 → CBox := ![⟨⟨65133442396077813545291231,65133442396077813555106918⟩,⟨(-2),2⟩⟩,⟨⟨14363680084106971048784808,14363680084106977606850089⟩,⟨40619374804049278167288194,40619374804049284725323246⟩⟩,⟨⟨(-5446227748738038470139601),(-5446227748738033923731639)⟩,⟨5323837198661289014762850,5323837198661293561170050⟩⟩,⟨⟨(-338951926557324941945088),(-338951926557324862174273)⟩,⟨255581902490504445758957,255581902490504525529245⟩⟩,⟨⟨3194747093343434527650,3194747093343434929701⟩,⟨15706317636970696521616,15706317636970696923695⟩⟩,⟨⟨471531353205455306582,471531353205455308421⟩,⟨(-462896816314156866386),(-462896816314156864551)⟩⟩,⟨⟨(-30911163976323348768),(-30911163976323348757)⟩,⟨17946515450704531734,17946515450704531745⟩⟩] +lemma ha1_1_24_eq (j : Fin 7) : ha1_1_24 j = ((ha1_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha1_1_24_contains (j : Fin 7) : (ha1_1_24 j).Contains (fullFactor true 1 24 ((j.val:ℝ)/6)) := by + rw [ha1_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_23 j) true 1 23 j (ha1_1_23_contains j) +noncomputable def hk1_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_25 j i k) +lemma hk1_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_25 j i k).Contains (fullFactor true 1 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 25 (kernel1_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha1_1_25 : Fin 7 → CBox := ![⟨⟨(-24009068645118425909862464),(-24009068645118425906167845)⟩,⟨(-1),1⟩⟩,⟨⟨1636076981908468244512203,1636076981908471230845376⟩,⟨(-14591984928472993258459042),(-14591984928472990272117444)⟩⟩,⟨⟨2169332750012151823855577,2169332750012153655827794⟩,⟨73469880498864665227130,73469880498866497199358⟩⟩,⟨⟨90592553372368874884816,90592553372368900214683⟩,⟨40326720032098256487827,40326720032098281817766⟩⟩,⟨⟨2708873486572865580600,2708873486572865679285⟩,⟨(-1542414675787805987054),(-1542414675787805888378)⟩⟩,⟨⟨(-88926897483773123616),(-88926897483773123263)⟩,⟨(-64012984396465745721),(-64012984396465745367)⟩⟩,⟨⟨2824385101236288391,2824385101236288394⟩,⟨4330045624131425382,4330045624131425384⟩⟩] +lemma ha1_1_25_eq (j : Fin 7) : ha1_1_25 j = ((ha1_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha1_1_25_contains (j : Fin 7) : (ha1_1_25 j).Contains (fullFactor true 1 25 ((j.val:ℝ)/6)) := by + rw [ha1_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_24 j) true 1 24 j (ha1_1_24_contains j) +noncomputable def hk1_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_26 j i k) +lemma hk1_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_26 j i k).Contains (fullFactor true 1 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 26 (kernel1_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha1_1_26 : Fin 7 → CBox := ![⟨⟨8509680517183672537373340,8509680517183672538709935⟩,⟨(-1),1⟩⟩,⟨⟨(-2568981362184987329053891),(-2568981362184986021479588)⟩,⟨4068569248181913455580988,4068569248181914763162834⟩⟩,⟨⟨(-396247185450621400472223),(-396247185450620690673434)⟩,⟨(-443620209347069897788859),(-443620209347069187990013)⟩⟩,⟨⟨(-1937522656903222641460),(-1937522656903214907724)⟩,⟨(-22188319619892245593053),(-22188319619892237859309)⟩⟩,⟨⟨(-431955694851713849049),(-431955694851713825762)⟩,⟨(-391448392502796075550),(-391448392502796052261)⟩⟩,⟨⟨(-7649243451556011185),(-7649243451556011119)⟩,⟨15706821898100367399,15706821898100367465⟩⟩,⟨⟨580983201293651323,580983201293651324⟩,⟨(-423538282056646497),(-423538282056646496)⟩⟩] +lemma ha1_1_26_eq (j : Fin 7) : ha1_1_26 j = ((ha1_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha1_1_26_contains (j : Fin 7) : (ha1_1_26 j).Contains (fullFactor true 1 26 ((j.val:ℝ)/6)) := by + rw [ha1_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_25 j) true 1 25 j (ha1_1_25_contains j) +noncomputable def hk1_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_27 j i k) +lemma hk1_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_27 j i k).Contains (fullFactor true 1 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 27 (kernel1_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha1_1_27 : Fin 7 → CBox := ![⟨⟨(-2904429113767749108416612),(-2904429113767749107951174)⟩,⟨(-1),1⟩⟩,⟨⟨1289658390288705565261199,1289658390288706116582809⟩,⟨(-801461860921930737422728),(-801461860921930186099317)⟩⟩,⟨⟨(-12361871445742553441818),(-12361871445742288615455)⟩,⟨156478420273017451886139,156478420273017716712500⟩⟩,⟨⟨(-3994851879902161037345),(-3994851879902158763534)⟩,⟨2692225091544112662324,2692225091544114936129⟩⟩,⟨⟨(-42737796046087404040),(-42737796046087398746)⟩,⟨95882018240872054649,95882018240872059942⟩⟩,⟨⟨2576089554437808966,2576089554437808979⟩,⟨747667784865743001,747667784865743014⟩⟩,⟨⟨(-60685219599380569),(-60685219599380568)⟩,⟨(-74756157929383080),(-74756157929383079)⟩⟩] +lemma ha1_1_27_eq (j : Fin 7) : ha1_1_27 j = ((ha1_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha1_1_27_contains (j : Fin 7) : (ha1_1_27 j).Contains (fullFactor true 1 27 ((j.val:ℝ)/6)) := by + rw [ha1_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_26 j) true 1 26 j (ha1_1_26_contains j) +noncomputable def hk1_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_28 j i k) +lemma hk1_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_28 j i k).Contains (fullFactor true 1 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 28 (kernel1_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha1_1_28 : Fin 7 → CBox := ![⟨⟨955903474605103032252441,955903474605103032408669⟩,⟨(-1),1⟩⟩,⟨⟨(-459519331600635937794161),(-459519331600635713639056)⟩,⟨48193567172068358283137,48193567172068582438276⟩⟩,⟨⟨30955423750280815422529,30955423750280910700506⟩,⟨(-25241537881216690712536),(-25241537881216595434563)⟩⟩,⟨⟨894929377678363021798,894929377678363666448⟩,⟨456709338364086615692,456709338364087260343⟩⟩,⟨⟨18133460127840363494,18133460127840364655⟩,⟨1862597164846029741,1862597164846030902⟩⟩,⟨⟨44288978234625539,44288978234625542⟩,⟨(-394666951372099371),(-394666951372099368)⟩⟩,⟨⟨(-9233977343089228),(-9233977343089227)⟩,⟨8327611522828318,8327611522828319⟩⟩] +lemma ha1_1_28_eq (j : Fin 7) : ha1_1_28 j = ((ha1_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha1_1_28_contains (j : Fin 7) : (ha1_1_28 j).Contains (fullFactor true 1 28 ((j.val:ℝ)/6)) := by + rw [ha1_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_27 j) true 1 27 j (ha1_1_27_contains j) +noncomputable def hk1_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_29 j i k) +lemma hk1_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_29 j i k).Contains (fullFactor true 1 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 29 (kernel1_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha1_1_29 : Fin 7 → CBox := ![⟨⟨(-303757725673230720529902),(-303757725673230720479290)⟩,⟨(-1),1⟩⟩,⟨⟨127653714252159796058816,127653714252159884052402⟩,⟨46171245079579513772993,46171245079579601766406⟩⟩,⟨⟨(-9738213183408938343873),(-9738213183408905247239)⟩,⟨(-1211975216987692450646),(-1211975216987659354012)⟩⟩,⟨⟨(-6884119378801936284),(-6884119378801759820)⟩,⟨(-202208008042148252582),(-202208008042148076118)⟩⟩,⟨⟨(-650809555287453391),(-650809555287453145)⟩,⟨(-2986168569809377889),(-2986168569809377642)⟩⟩,⟨⟨(-56673251152222625),(-56673251152222623)⟩,⟨3345942567997232,3345942567997233⟩⟩,⟨⟨1096728170513645,1096728170513646⟩,⟨1095876864803655,1095876864803656⟩⟩] +lemma ha1_1_29_eq (j : Fin 7) : ha1_1_29 j = ((ha1_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha1_1_29_contains (j : Fin 7) : (ha1_1_29 j).Contains (fullFactor true 1 29 ((j.val:ℝ)/6)) := by + rw [ha1_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_28 j) true 1 28 j (ha1_1_28_contains j) +noncomputable def hk1_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel1_0 j i k).mul (mpower1_30 j i k) +lemma hk1_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk1_1_30 j i k).Contains (fullFactor true 1 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk1_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel1_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 1 30 (kernel1_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha1_1_30 : Fin 7 → CBox := ![⟨⟨93307674968069502156449,93307674968069502172294⟩,⟨(-1),1⟩⟩,⟨⟨(-26898813713713992561041),(-26898813713713959170040)⟩,⟨(-27618604999837585076998),(-27618604999837551686054)⟩⟩,⟨⟨1390155879903790051627,1390155879903801165149⟩,⟨1870683060482900456998,1870683060482911570520⟩⟩,⟨⟨(-33781776682384171208),(-33781776682384124513)⟩,⟨20247071845331095770,20247071845331142465⟩⟩,⟨⟨(-426995268993283891),(-426995268993283840)⟩,⟨251061431221641959,251061431221642010⟩⟩,⟨⟨1786147405653289,1786147405653290⟩,⟨7639014807186454,7639014807186455⟩⟩,⟨⟨125043452230103,125043452230104⟩,⟨(-138869681849478),(-138869681849477)⟩⟩] +lemma ha1_1_30_eq (j : Fin 7) : ha1_1_30 j = ((ha1_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha1_1_30_contains (j : Fin 7) : (ha1_1_30 j).Contains (fullFactor true 1 30 ((j.val:ℝ)/6)) := by + rw [ha1_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha1_1_29 j) true 1 29 j (ha1_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders12.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders12.lean new file mode 100644 index 0000000000000000000000000000000000000000..80c37a97d561c630e117aa4800fd8a96974835d5 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders12.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.KernelValues20 +import OAI.Analysis.PlanarPacking.Certificate.Powers20 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk12_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_0 j i k) +lemma hk12_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_0 j i k).Contains (fullFactor false 12 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 0 (power12_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha12_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999857,1000000000000000000000000000191⟩,⟨(-191),191⟩⟩,⟨⟨999999999999999999986851087693,1000000000000000000013148912323⟩,⟨(-8609239891),18035706735⟩⟩,⟨⟨999999999999999999963771228521,1000000000000000000036228771487⟩,⟨(-26675268679),45528202431⟩⟩,⟨⟨999999999999999999960799900457,1000000000000000000039200099555⟩,⟨(-25060399247),53339799863⟩⟩,⟨⟨999999999999999999901146248937,1000000000000000000098853751035⟩,⟨(-80093686963),117799554499⟩⟩,⟨⟨999999999999999999875477146681,1000000000000000000124522853283⟩,⟨(-100864511599),147996845975⟩⟩,⟨⟨999999999999999999921361626617,1000000000000000000078638373431⟩,⟨(-50358972743),106917774071⟩⟩] +lemma ha12_0_0_eq (j : Fin 7) : ha12_0_0 j = ((atomPoints j).direct.powBin 7 12).conj := by fin_cases j <;> decide +kernel +lemma ha12_0_0_contains (j : Fin 7) : (ha12_0_0 j).Contains (fullFactor false 12 0 ((j.val:ℝ)/6)) := by + rw [ha12_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 12) ((j.val:ℝ)/6) 12 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 12 (by norm_num)) +noncomputable def hk12_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_1 j i k) +lemma hk12_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_1 j i k).Contains (fullFactor false 12 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 1 (power12_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha12_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-9443473964),4507787466⟩,⟨523598775598298873069781912279,523598775598298873085218087728⟩⟩,⟨⟨(-47677022097),27934276039⟩,⟨1047197551196597746115394652556,1047197551196597746194605347454⟩⟩,⟨⟨(-83785961697),39364783086⟩,⟨1570796326794896619168424627627,1570796326794896619296575372391⟩⟩,⟨⟨(-246718810007),167747825708⟩,⟨2094395102393195492099627854584,2094395102393195492520372145356⟩⟩,⟨⟨(-387454836725),264062673873⟩,⟨2617993877991494365057333265672,2617993877991494365717666734234⟩⟩,⟨⟨(-335892093560),158207378812⟩,⟨3141592653589793238212950263889,3141592653589793238717049736262⟩⟩] +lemma ha12_0_1_eq (j : Fin 7) : ha12_0_1 j = ((ha12_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha12_0_1_contains (j : Fin 7) : (ha12_0_1 j).Contains (fullFactor false 12 1 ((j.val:ℝ)/6)) := by + rw [ha12_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_0 j) false 12 0 j (ha12_0_0_contains j) +noncomputable def hk12_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_2 j i k) +lemma hk12_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_2 j i k).Contains (fullFactor false 12 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 2 (power12_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha12_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-137077838904018869708479007625),(-137077838904018869704001494027)⟩,⟨(-2472295703),1180135999⟩⟩,⟨⟨(-548311355616075478846570979363),(-548311355616075478803351027246)⟩,⟨(-24963630395),14626352732⟩⟩,⟨⟨(-1233700550136169827408450432633),(-1233700550136169827303874082239)⟩,⟨(-65805340436),30917028339⟩⟩,⟨⟨(-2193245422464301915523635867169),(-2193245422464301915076052159180)⟩,⟨(-258363333674),175665112300⟩⟩,⟨⟨(-3426945972600471743093647669022),(-3426945972600471742218364872127)⟩,⟨(-507177195273),345657231803⟩⟩,⟨⟨(-4934802200544679309828421811239),(-4934802200544679309020876248427)⟩,⟨(-527618066764),248511569510⟩⟩] +lemma ha12_0_2_eq (j : Fin 7) : ha12_0_2 j = ((ha12_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha12_0_2_contains (j : Fin 7) : (ha12_0_2 j).Contains (fullFactor false 12 2 ((j.val:ℝ)/6)) := by + rw [ha12_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_1 j) false 12 1 j (ha12_0_1_contains j) +noncomputable def hk12_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_3 j i k) +lemma hk12_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_3 j i k).Contains (fullFactor false 12 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 3 (power12_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha12_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-205972589),431497002⟩,⟨(-23924596203935046432177341491),(-23924596203935046431319713589)⟩⟩,⟨⟨(-5105560255),8713950873⟩,⟨(-191396769631480371461836142409),(-191396769631480371446140298228)⟩⟩,⟨⟨(-16188118184),34455595681⟩,⟨(-645964097506246253685616351878),(-645964097506246253628804135270)⟩⟩,⟨⟨(-122637383621),180371633562⟩,⟨(-1531174157051842971790578889528),(-1531174157051842971473232635500)⟩⟩,⟨⟨(-301642838915),442595597428⟩,⟨(-2990574525491880804355239756886),(-2990574525491880803581892127919)⟩⟩,⟨⟨(-260240707035),552520347483⟩,⟨(-5167712780049970029688736486949),(-5167712780049970028826627410423)⟩⟩] +lemma ha12_0_3_eq (j : Fin 7) : ha12_0_3 j = ((ha12_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha12_0_3_contains (j : Fin 7) : (ha12_0_3 j).Contains (fullFactor false 12 3 ((j.val:ℝ)/6)) := by + rw [ha12_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_2 j) false 12 2 j (ha12_0_2_contains j) +noncomputable def hk12_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_4 j i k) +lemma hk12_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_4 j i k).Contains (fullFactor false 12 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 4 (power12_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha12_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨3131722319766024859658939788,3131722319766024859781171601⟩,⟨(-26961749),56482826⟩⟩,⟨⟨50107557116256397753386561263,50107557116256397757655220970⟩,⟨(-1336632550),2281307004⟩⟩,⟨⟨253669507901048013625765731068,253669507901048013648883291482⟩,⟨(-6357059146),13530680784⟩⟩,⟨⟨801720913860102364003977224349,801720913860102364172691291330⟩,⟨(-64212783907),94442366486⟩⟩,⟨⟨1957326449853765537068842207601,1957326449853765537581227410748⟩,⟨(-197424776405),289678141124⟩⟩,⟨⟨4058712126416768217852183096820,4058712126416768218542201264123⟩,⟨(-204392573347),433948466153⟩⟩] +lemma ha12_0_4_eq (j : Fin 7) : ha12_0_4 j = ((ha12_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha12_0_4_contains (j : Fin 7) : (ha12_0_4 j).Contains (fullFactor false 12 4 ((j.val:ℝ)/6)) := by + rw [ha12_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_3 j) false 12 3 j (ha12_0_3_contains j) +noncomputable def hk12_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_5 j i k) +lemma hk12_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_5 j i k).Contains (fullFactor false 12 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 5 (power12_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha12_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-5914868),2823428⟩,⟨327953194428670967568404959,327953194428670967582248953⟩⟩,⟨⟨(-477795822),279943667⟩,⟨10494502221717470961946747085,10494502221717470962874178122⟩⟩,⟨⟨(-4250788735),1997129032⟩,⟨79692626246167045117046317740,79692626246167045124562583046⟩⟩,⟨⟨(-39559925966),26897388026⟩,⟨335824071094959070761264931125,335824071094959070833004675464⟩⟩,⟨⟨(-151675120011),103371371199⟩,⟨1024853732589596773537123500690,1024853732589596773808669976445⟩⟩,⟨⟨(-272657862661),128423641376⟩,⟨2550164039877345443644908099966,2550164039877345444086576725269⟩⟩] +lemma ha12_0_5_eq (j : Fin 7) : ha12_0_5 j = ((ha12_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha12_0_5_contains (j : Fin 7) : (ha12_0_5 j).Contains (fullFactor false 12 5 ((j.val:ℝ)/6)) := by + rw [ha12_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_4 j) false 12 4 j (ha12_0_4_contains j) +noncomputable def hk12_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_6 j i k) +lemma hk12_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_6 j i k).Contains (fullFactor false 12 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 6 (power12_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha12_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-28619315176067161692207275),(-28619315176067161690908060)⟩,⟨(-516170),246391⟩⟩,⟨⟨(-1831636171268298348343539496),(-1831636171268298348175841964)⟩,⟨(-83391103),48859388⟩⟩,⟨⟨(-20863480763352960874162621809),(-20863480763352960872128457631)⟩,⟨(-1112853889),522847158⟩⟩,⟨⟨(-117224714961171094301327723071),(-117224714961171094275912690348)⟩,⟨(-13809019200),9388959625⟩⟩,⟨⟨(-447176799626049401490542511995),(-447176799626049401370634602179)⟩,⟨(-66180755939),45104269494⟩⟩,⟨⟨(-1335262768854589495999068254514),(-1335262768854589495763560829684)⟩,⟨(-142763323047),67242461383⟩⟩] +lemma ha12_0_6_eq (j : Fin 7) : ha12_0_6 j = ((ha12_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha12_0_6_contains (j : Fin 7) : (ha12_0_6 j).Contains (fullFactor false 12 6 ((j.val:ℝ)/6)) := by + rw [ha12_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_5 j) false 12 5 j (ha12_0_5_contains j) +noncomputable def hk12_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_7 j i k) +lemma hk12_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_7 j i k).Contains (fullFactor false 12 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 7 (power12_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha12_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-18431),38610⟩,⟨(-2140719769235797028268755),(-2140719769235797028164759)⟩⟩,⟨⟨(-7309348),12475280⟩,⟨(-274012130462182019624724746),(-274012130462182019598765045)⟩⟩,⟨⟨(-117326628),249723829⟩,⟨(-4681754135318688100945731479),(-4681754135318688100474363617)⟩⟩,⟨⟨(-2809170151),4131648884⟩,⟨(-35073552699159298514161247901),(-35073552699159298506445445306)⟩⟩,⟨⟨(-16868957344),24751544842⟩,⟨(-167243731971546642852123043589),(-167243731971546642806745236852)⟩⟩,⟨⟨(-30178346099),64072029556⟩,⟨(-599264529320792076944687587800),(-599264529320792076837084584456)⟩⟩] +lemma ha12_0_7_eq (j : Fin 7) : ha12_0_7 j = ((ha12_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha12_0_7_contains (j : Fin 7) : (ha12_0_7 j).Contains (fullFactor false 12 7 ((j.val:ℝ)/6)) := by + rw [ha12_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_6 j) false 12 6 j (ha12_0_6_contains j) +noncomputable def hk12_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_8 j i k) +lemma hk12_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_8 j i k).Contains (fullFactor false 12 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 8 (power12_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha12_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨140109781258867029450303,140109781258867029457556⟩,⟨(-1207),2528⟩⟩,⟨⟨35868104002269959538449859,35868104002269959541962148⟩,⟨(-956792),1633011⟩⟩,⟨⟨919260274839426580199493292,919260274839426580294972252⟩,⟨(-23037030),49033160⟩⟩,⟨⟨9182234624581109641268126742,9182234624581109643317347099⟩,⟨(-735439026),1081663149⟩⟩,⟨⟨54730383304244933372929257288,54730383304244933387953322039⟩,⟨(-5520353382),8099924109⟩⟩,⟨⟨235330630358893204521789248959,235330630358893204564793930223⟩,⟨(-11851008801),25161027170⟩⟩] +lemma ha12_0_8_eq (j : Fin 7) : ha12_0_8 j = ((ha12_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha12_0_8_contains (j : Fin 7) : (ha12_0_8 j).Contains (fullFactor false 12 8 ((j.val:ℝ)/6)) := by + rw [ha12_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_7 j) false 12 7 j (ha12_0_7_contains j) +noncomputable def hk12_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_9 j i k) +lemma hk12_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_9 j i k).Contains (fullFactor false 12 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 9 (power12_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha12_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-148),71⟩,⟨8151256657387584304696,8151256657387584305145⟩⟩,⟨⟨(-190010),111328⟩,⟨4173443408582443163908156,4173443408582443164330115⟩⟩,⟨⟨(-8557901),4020721⟩,⟨160441184787359821865156581,160441184787359821882331504⟩⟩,⟨⟨(-251714445),171144433⟩,⟨2136803025194210899787159077,2136803025194210900270835965⟩⟩,⟨⟨(-2356172415),1605805707⟩,⟨15920423158960125593336740602,15920423158960125597757740166⟩⟩,⟨⟨(-8782855347),4136782466⟩,⟨82145886611128228791720477566,82145886611128228806993421682⟩⟩] +lemma ha12_0_9_eq (j : Fin 7) : ha12_0_9 j = ((ha12_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha12_0_9_contains (j : Fin 7) : (ha12_0_9 j).Contains (fullFactor false 12 9 ((j.val:ℝ)/6)) := by + rw [ha12_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_8 j) false 12 8 j (ha12_0_8_contains j) +noncomputable def hk12_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_10 j i k) +lemma hk12_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_10 j i k).Contains (fullFactor false 12 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 10 (power12_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha12_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-426798800539562151468),(-426798800539562151442)⟩,⟨(-8),4⟩⟩,⟨⟨(-437041971752511643112290),(-437041971752511643066710)⟩,⟨(-19898),11659⟩⟩,⟨⟨(-25202042373060605482631097),(-25202042373060605479853045)⟩,⟨(-1344272),631574⟩⟩,⟨⟨(-447530979074571922575010709),(-447530979074571922472285122)⟩,⟨(-52718951),35844407⟩⟩,⟨⟨(-4167957036519161635884069155),(-4167957036519161634713387155)⟩,⟨(-616844496),420398952⟩⟩,⟨⟨(-25806891390014060015232022019),(-25806891390014060010351739228)⟩,⟨(-2759215384),1299608541⟩⟩] +lemma ha12_0_10_eq (j : Fin 7) : ha12_0_10 j = ((ha12_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha12_0_10_contains (j : Fin 7) : (ha12_0_10 j).Contains (fullFactor false 12 10 ((j.val:ℝ)/6)) := by + rw [ha12_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_9 j) false 12 9 j (ha12_0_9_contains j) +noncomputable def hk12_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_11 j i k) +lemma hk12_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_11 j i k).Contains (fullFactor false 12 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 11 (power12_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha12_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-20315575399030665722),(-20315575399030665720)⟩⟩,⟨⟨(-1110),1895⟩,⟨(-41606298417214803398963),(-41606298417214803394490)⟩⟩,⟨⟨(-90189),191962⟩,⟨(-3598843235212085340692316),(-3598843235212085340284155)⟩⟩,⟨⟨(-6824760),10037665⟩,⟨(-85209699158455917366410913),(-85209699158455917346580775)⟩⟩,⟨⟨(-100054717),146808647⟩,⟨(-991971455030794224801917668),(-991971455030794224520138460)⟩⟩,⟨⟨(-371167332),788030071⟩,⟨(-7370430945714350778028540068),(-7370430945714350776611273751)⟩⟩] +lemma ha12_0_11_eq (j : Fin 7) : ha12_0_11 j = ((ha12_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha12_0_11_contains (j : Fin 7) : (ha12_0_11 j).Contains (fullFactor false 12 11 ((j.val:ℝ)/6)) := by + rw [ha12_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_10 j) false 12 10 j (ha12_0_10_contains j) +noncomputable def hk12_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_12 j i k) +lemma hk12_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_12 j i k).Contains (fullFactor false 12 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 12 (power12_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha12_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨886434200375614885,886434200375614886⟩,⟨(-1),1⟩⟩,⟨⟨3630834484738518570855,3630834484738518571258⟩,⟨(-97),166⟩⟩,⟨⟨471087477881817150343804,471087477881817150398733⟩,⟨(-11806),25128⟩⟩,⟨⟨14871898049488972065292303,14871898049488972068800655⟩,⟨(-1191146),1751904⟩⟩,⟨⟨216414599701077852877068737,216414599701077852939232294⟩,⟨(-21828554),32028679⟩⟩,⟨⟨1929574309403923047732124104,1929574309403923048109305585⟩,⟨(-97171381),206305791⟩⟩] +lemma ha12_0_12_eq (j : Fin 7) : ha12_0_12 j = ((ha12_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha12_0_12_contains (j : Fin 7) : (ha12_0_12 j).Contains (fullFactor false 12 12 ((j.val:ℝ)/6)) := by + rw [ha12_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_11 j) false 12 11 j (ha12_0_11_contains j) +noncomputable def hk12_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_13 j i k) +lemma hk12_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_13 j i k).Contains (fullFactor false 12 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 13 (power12_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha12_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨35702758612702236,35702758612702237⟩⟩,⟨⟨(-14),8⟩,⟨292476998555256723009,292476998555256723043⟩⟩,⟨⟨(-3037),1427⟩,⟨56921729219679268114898,56921729219679268121717⟩⟩,⟨⟨(-282245),191903⟩,⟨2395971572164663074743568,2395971572164663075316417⟩⟩,⟨⟨(-6450069),4395925⟩,⟨43582469009646285024829314,43582469009646285037486797⟩⟩,⟨⟨(-49856059),23482531⟩,⟨466302805767612564378859015,466302805767612564471493348⟩⟩] +lemma ha12_0_13_eq (j : Fin 7) : ha12_0_13 j = ((ha12_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha12_0_13_contains (j : Fin 7) : (ha12_0_13 j).Contains (fullFactor false 12 13 ((j.val:ℝ)/6)) := by + rw [ha12_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_12 j) false 12 12 j (ha12_0_12_contains j) +noncomputable def hk12_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_14 j i k) +lemma hk12_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_14 j i k).Contains (fullFactor false 12 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 14 (power12_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha12_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1335280049649466),(-1335280049649465)⟩,⟨(-1),1⟩⟩,⟨⟨(-21877228333456835519),(-21877228333456835516)⟩,⟨(-2),1⟩⟩,⟨⟨(-6386603083791852241550),(-6386603083791852240764)⟩,⟨(-341),161⟩⟩,⟨⟨(-358436509015356793164929),(-358436509015356793078089)⟩,⟨(-42224),28709⟩⟩,⟨⟨(-8149902646786285758347027),(-8149902646786285755954140)⟩,⟨(-1206161),822037⟩⟩,⟨⟨(-104638104924845707129675710),(-104638104924845707108555540)⟩,⟨(-11187674),5269468⟩⟩] +lemma ha12_0_14_eq (j : Fin 7) : ha12_0_14 j = ((ha12_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha12_0_14_contains (j : Fin 7) : (ha12_0_14 j).Contains (fullFactor false 12 14 ((j.val:ℝ)/6)) := by + rw [ha12_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_13 j) false 12 13 j (ha12_0_13_contains j) +noncomputable def hk12_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_15 j i k) +lemma hk12_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_15 j i k).Contains (fullFactor false 12 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 15 (power12_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha12_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-46610066605154),(-46610066605153)⟩⟩,⟨⟨(-1),1⟩,⟨(-1527318662517654887),(-1527318662517654886)⟩⟩,⟨⟨(-17),36⟩,⟨(-668803510981146723298),(-668803510981146723213)⟩⟩,⟨⟨(-4009),5896⟩,⟨(-50047177933378515334162),(-50047177933378515321876)⟩⟩,⟨⟨(-143473),210515⟩,⟨(-1422426349034211493046937),(-1422426349034211492624771)⟩⟩,⟨⟨(-1103635),2343141⟩,⟨(-21915353447830215829877823),(-21915353447830215825384665)⟩⟩] +lemma ha12_0_15_eq (j : Fin 7) : ha12_0_15 j = ((ha12_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha12_0_15_contains (j : Fin 7) : (ha12_0_15 j).Contains (fullFactor false 12 15 ((j.val:ℝ)/6)) := by + rw [ha12_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_14 j) false 12 14 j (ha12_0_14_contains j) +noncomputable def hk12_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_16 j i k) +lemma hk12_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_16 j i k).Contains (fullFactor false 12 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 16 (power12_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha12_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1525310862813,1525310862814⟩,⟨(-1),1⟩⟩,⟨⟨99962772705334443,99962772705334444⟩,⟨(-1),1⟩⟩,⟨⟨65659631149794723618,65659631149794723628⟩,⟨(-2),4⟩⟩,⟨⟨6551160272016798098015,6551160272016798099645⟩,⟨(-525),772⟩⟩,⟨⟨232743967104084891340930,232743967104084891410749⟩,⟨(-23476),34446⟩⟩,⟨⟨4303069587032947006901506,4303069587032947007797434⟩,⟨(-216699),460075⟩⟩] +lemma ha12_0_16_eq (j : Fin 7) : ha12_0_16 j = ((ha12_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha12_0_16_contains (j : Fin 7) : (ha12_0_16 j).Contains (fullFactor false 12 16 ((j.val:ℝ)/6)) := by + rw [ha12_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_15 j) false 12 15 j (ha12_0_15_contains j) +noncomputable def hk12_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_17 j i k) +lemma hk12_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_17 j i k).Contains (fullFactor false 12 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 17 (power12_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha12_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨46979464716,46979464717⟩⟩,⟨⟨(-1),1⟩,⟨6157692399285195,6157692399285196⟩⟩,⟨⟨(-1),1⟩,⟨6066935731106195666,6066935731106195668⟩⟩,⟨⟨(-96),65⟩,⟨807101058159109193325,807101058159109193530⟩⟩,⟨⟨(-5305),3616⟩,⟨35842487118702823481142,35842487118702823492010⟩⟩,⟨⟨(-85022),40046⟩,⟨795205400147551278404412,795205400147551278572511⟩⟩] +lemma ha12_0_17_eq (j : Fin 7) : ha12_0_17 j = ((ha12_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha12_0_17_contains (j : Fin 7) : (ha12_0_17 j).Contains (fullFactor false 12 17 ((j.val:ℝ)/6)) := by + rw [ha12_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_16 j) false 12 16 j (ha12_0_16_contains j) +noncomputable def hk12_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_18 j i k) +lemma hk12_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_18 j i k).Contains (fullFactor false 12 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 18 (power12_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha12_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1366577234),(-1366577233)⟩,⟨(-1),1⟩⟩,⟨⟨(-358240022308520),(-358240022308519)⟩,⟨(-1),1⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨(-1),1⟩⟩,⟨⟨(-93910472408044662752),(-93910472408044662727)⟩,⟨(-12),8⟩⟩,⟨⟨(-5213078436041832672473),(-5213078436041832670875)⟩,⟨(-772),526⟩⟩,⟨⟨(-138789524622137721161446),(-138789524622137721131664)⟩,⟨(-14840),6990⟩⟩] +lemma ha12_0_18_eq (j : Fin 7) : ha12_0_18 j = ((ha12_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha12_0_18_contains (j : Fin 7) : (ha12_0_18 j).Contains (fullFactor false 12 18 ((j.val:ℝ)/6)) := by + rw [ha12_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_17 j) false 12 17 j (ha12_0_17_contains j) +noncomputable def hk12_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_19 j i k) +lemma hk12_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_19 j i k).Contains (fullFactor false 12 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 19 (power12_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha12_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-37659904),(-37659903)⟩⟩,⟨⟨(-1),1⟩,⟨(-19744635479058),(-19744635479057)⟩⟩,⟨⟨(-1),1⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨(-1),2⟩,⟨(-10351875446044213763),(-10351875446044213760)⟩⟩,⟨⟨(-73),107⟩,⟨(-718305654265631155162),(-718305654265631154939)⟩⟩,⟨⟨(-1156),2454⟩,⟨(-22948428997269873113030),(-22948428997269873108032)⟩⟩] +lemma ha12_0_19_eq (j : Fin 7) : ha12_0_19 j = ((ha12_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha12_0_19_contains (j : Fin 7) : (ha12_0_19 j).Contains (fullFactor false 12 19 ((j.val:ℝ)/6)) := by + rw [ha12_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_18 j) false 12 18 j (ha12_0_18_contains j) +noncomputable def hk12_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_20 j i k) +lemma hk12_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_20 j i k).Contains (fullFactor false 12 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 20 (power12_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha12_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨985933,985934⟩,⟨(-1),1⟩⟩,⟨⟨1033826696146,1033826696147⟩,⟨(-1),1⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨(-1),1⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨94025990269704865199,94025990269704865230⟩,⟨(-10),15⟩⟩,⟨⟨3604730797462500933515,3604730797462500934312⟩,⟨(-182),386⟩⟩] +lemma ha12_0_20_eq (j : Fin 7) : ha12_0_20 j = ((ha12_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha12_0_20_contains (j : Fin 7) : (ha12_0_20 j).Contains (fullFactor false 12 20 ((j.val:ℝ)/6)) := by + rw [ha12_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_19 j) false 12 19 j (ha12_0_19_contains j) +noncomputable def hk12_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_21 j i k) +lemma hk12_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_21 j i k).Contains (fullFactor false 12 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 21 (power12_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha12_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨24582,24583⟩⟩,⟨⟨(-1),1⟩,⟨51553370693,51553370694⟩⟩,⟨⟨(-1),1⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨(-2),2⟩,⟨11721879376103578820,11721879376103578825⟩⟩,⟨⟨(-58),28⟩,⟨539266466260812848883,539266466260812849005⟩⟩] +lemma ha12_0_21_eq (j : Fin 7) : ha12_0_21 j = ((ha12_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha12_0_21_contains (j : Fin 7) : (ha12_0_21 j).Contains (fullFactor false 12 21 ((j.val:ℝ)/6)) := by + rw [ha12_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_20 j) false 12 20 j (ha12_0_20_contains j) +noncomputable def hk12_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_22 j i k) +lemma hk12_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_22 j i k).Contains (fullFactor false 12 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 22 (power12_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha12_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-586),(-585)⟩,⟨(-1),1⟩⟩,⟨⟨(-2453934707),(-2453934706)⟩,⟨(-1),1⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨(-1),1⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-1394900383872451220),(-1394900383872451219)⟩,⟨(-1),1⟩⟩,⟨⟨(-77007071306013533809),(-77007071306013533790)⟩,⟨(-9),4⟩⟩] +lemma ha12_0_22_eq (j : Fin 7) : ha12_0_22 j = ((ha12_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha12_0_22_contains (j : Fin 7) : (ha12_0_22 j).Contains (fullFactor false 12 22 ((j.val:ℝ)/6)) := by + rw [ha12_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_21 j) false 12 21 j (ha12_0_21_contains j) +noncomputable def hk12_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_23 j i k) +lemma hk12_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_23 j i k).Contains (fullFactor false 12 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 23 (power12_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha12_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-14),(-13)⟩⟩,⟨⟨(-1),1⟩,⟨(-111728453),(-111728452)⟩⟩,⟨⟨(-1),1⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨(-1),1⟩,⟨(-158775681103741858),(-158775681103741857)⟩⟩,⟨⟨(-1),2⟩,⟨(-10518471716932064457),(-10518471716932064454)⟩⟩] +lemma ha12_0_23_eq (j : Fin 7) : ha12_0_23 j = ((ha12_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha12_0_23_contains (j : Fin 7) : (ha12_0_23 j).Contains (fullFactor false 12 23 ((j.val:ℝ)/6)) := by + rw [ha12_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_22 j) false 12 22 j (ha12_0_22_contains j) +noncomputable def hk12_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_24 j i k) +lemma hk12_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_24 j i k).Contains (fullFactor false 12 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 24 (power12_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha12_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨4875073,4875074⟩,⟨(-1),1⟩⟩,⟨⟨82067533018,82067533019⟩,⟨(-1),1⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨17319740045980249,17319740045980250⟩,⟨(-1),1⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨(-1),1⟩⟩] +lemma ha12_0_24_eq (j : Fin 7) : ha12_0_24 j = ((ha12_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha12_0_24_contains (j : Fin 7) : (ha12_0_24 j).Contains (fullFactor false 12 24 ((j.val:ℝ)/6)) := by + rw [ha12_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_23 j) false 12 23 j (ha12_0_23_contains j) +noncomputable def hk12_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_25 j i k) +lemma hk12_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_25 j i k).Contains (fullFactor false 12 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 25 (power12_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha12_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨204206,204207⟩⟩,⟨⟨(-1),1⟩,⟨5156455176,5156455177⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨(-1),1⟩,⟨1813718936351216,1813718936351217⟩⟩,⟨⟨(-1),1⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha12_0_25_eq (j : Fin 7) : ha12_0_25 j = ((ha12_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha12_0_25_contains (j : Fin 7) : (ha12_0_25 j).Contains (fullFactor false 12 25 ((j.val:ℝ)/6)) := by + rw [ha12_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_24 j) false 12 24 j (ha12_0_24_contains j) +noncomputable def hk12_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_26 j i k) +lemma hk12_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_26 j i k).Contains (fullFactor false 12 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 26 (power12_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha12_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-8225),(-8224)⟩,⟨(-1),1⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨(-1),1⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-182627118144798),(-182627118144797)⟩,⟨(-1),1⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨(-1),1⟩⟩] +lemma ha12_0_26_eq (j : Fin 7) : ha12_0_26 j = ((ha12_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha12_0_26_contains (j : Fin 7) : (ha12_0_26 j).Contains (fullFactor false 12 26 ((j.val:ℝ)/6)) := by + rw [ha12_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_25 j) false 12 25 j (ha12_0_25_contains j) +noncomputable def hk12_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_27 j i k) +lemma hk12_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_27 j i k).Contains (fullFactor false 12 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 27 (power12_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha12_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨(-320),(-318)⟩⟩,⟨⟨(-1),1⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨(-1),1⟩,⟨(-17708025083642),(-17708025083641)⟩⟩,⟨⟨(-1),1⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha12_0_27_eq (j : Fin 7) : ha12_0_27 j = ((ha12_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha12_0_27_contains (j : Fin 7) : (ha12_0_27 j).Contains (fullFactor false 12 27 ((j.val:ℝ)/6)) := by + rw [ha12_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_26 j) false 12 26 j (ha12_0_26_contains j) +noncomputable def hk12_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_28 j i k) +lemma hk12_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_28 j i k).Contains (fullFactor false 12 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 28 (power12_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha12_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨11,12⟩,⟨(-1),1⟩⟩,⟨⟨1016753,1016754⟩,⟨(-1),1⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨1655696473581,1655696473582⟩,⟨(-1),1⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨(-1),1⟩⟩] +lemma ha12_0_28_eq (j : Fin 7) : ha12_0_28 j = ((ha12_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha12_0_28_contains (j : Fin 7) : (ha12_0_28 j).Contains (fullFactor false 12 28 ((j.val:ℝ)/6)) := by + rw [ha12_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_27 j) false 12 27 j (ha12_0_27_contains j) +noncomputable def hk12_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_29 j i k) +lemma hk12_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_29 j i k).Contains (fullFactor false 12 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 29 (power12_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha12_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨55072,55073⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨(-1),1⟩,⟨149469076953,149469076954⟩⟩,⟨⟨(-1),1⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha12_0_29_eq (j : Fin 7) : ha12_0_29 j = ((ha12_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha12_0_29_contains (j : Fin 7) : (ha12_0_29 j).Contains (fullFactor false 12 29 ((j.val:ℝ)/6)) := by + rw [ha12_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_28 j) false 12 28 j (ha12_0_28_contains j) +noncomputable def hk12_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power12 j i k).conj.mul (mpower0_30 j i k) +lemma hk12_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk12_0_30 j i k).Contains (fullFactor false 12 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power12 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 30 (power12_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha12_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨(-1),1⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-13043637614),(-13043637613)⟩,⟨(-1),1⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨(-1),1⟩⟩] +lemma ha12_0_30_eq (j : Fin 7) : ha12_0_30 j = ((ha12_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha12_0_30_contains (j : Fin 7) : (ha12_0_30 j).Contains (fullFactor false 12 30 ((j.val:ℝ)/6)) := by + rw [ha12_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_0_29 j) false 12 29 j (ha12_0_29_contains j) +noncomputable def hk12_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_0 j i k) +lemma hk12_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_0 j i k).Contains (fullFactor true 12 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 0 (kernel12_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha12_1_0 : Fin 7 → CBox := ![⟨⟨0,3⟩,⟨(-3),3⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨(-7456),(-7452)⟩,⟨48027,48031⟩⟩,⟨⟨(-2433521169088633),(-2433521169088629)⟩,⟨2104633841203363,2104633841203366⟩⟩,⟨⟨(-10126433418478817995544),(-10126433418478817959972)⟩,⟨15855193807734678938298,15855193807734678973769⟩⟩,⟨⟨(-190318804329798986529500314),(-190318804329798986262853704)⟩,⟨186919098208693442779401710,186919098208693443043376098⟩⟩,⟨⟨(-29985267079005839469470031008),(-29985267079005839367492391446)⟩,⟨108564951811294072989478110531,108564951811294073091885636862⟩⟩] +lemma ha12_1_0_eq (j : Fin 7) : ha12_1_0 j = atomKernel12_0 j := by fin_cases j <;> decide +kernel +lemma ha12_1_0_contains (j : Fin 7) : (ha12_1_0 j).Contains (fullFactor true 12 0 ((j.val:ℝ)/6)) := by + rw [ha12_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel12_0_contains j +noncomputable def hk12_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_1 j i k) +lemma hk12_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_1 j i k).Contains (fullFactor true 12 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 1 (kernel12_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha12_1_1 : Fin 7 → CBox := ![⟨⟨(-28),0⟩,⟨(-28),28⟩⟩,⟨⟨(-42),8⟩,⟨(-31),23⟩⟩,⟨⟨284036,284077⟩,⟨(-198104),(-198063)⟩⟩,⟨⟨17637895069707079,17637895069707107⟩,⟨6475021789587754,6475021789587784⟩⟩,⟨⟨88595980360819229063312,88595980360819229281375⟩,⟨22757742687381368101870,22757742687381368320190⟩⟩,⟨⟨897662343959606823409130490,897662343959606824678201911⟩,⟨645860594990278562951585548,645860594990278564229728316⟩⟩,⟨⟨397661302041150198906510073424,397661302041150199296720796209⟩,⟨87891975067646749052475051597,87891975067646749440357915747⟩⟩] +lemma ha12_1_1_eq (j : Fin 7) : ha12_1_1 j = ((ha12_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha12_1_1_contains (j : Fin 7) : (ha12_1_1 j).Contains (fullFactor true 12 1 ((j.val:ℝ)/6)) := by + rw [ha12_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_0 j) true 12 0 j (ha12_1_0_contains j) +noncomputable def hk12_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_2 j i k) +lemma hk12_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_2 j i k).Contains (fullFactor true 12 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 2 (kernel12_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha12_1_2 : Fin 7 → CBox := ![⟨⟨0,130⟩,⟨(-130),130⟩⟩,⟨⟨(-89),204⟩,⟨(-104),197⟩⟩,⟨⟨(-1209466),(-1209259)⟩,⟨(-243934),(-243727)⟩⟩,⟨⟨(-8419396997543991),(-8419396997543874)⟩,⟨(-54211775273678897),(-54211775273678782)⟩⟩,⟨⟨(-14556982751376640076510),(-14556982751376639406589)⟩,⟨(-221899282215820242350707),(-221899282215820241680859)⟩⟩,⟨⟨1003151809858409199745334801,1003151809858409202808242868⟩,⟨(-2061049643971255242679803127),(-2061049643971255239630875182)⟩⟩,⟨⟨121355007055359754570274445483,121355007055359755307861562369⟩,⟨(-726234543583272508307474649490),(-726234543583272507564215399696)⟩⟩] +lemma ha12_1_2_eq (j : Fin 7) : ha12_1_2 j = ((ha12_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha12_1_2_contains (j : Fin 7) : (ha12_1_2 j).Contains (fullFactor true 12 2 ((j.val:ℝ)/6)) := by + rw [ha12_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_1 j) true 12 1 j (ha12_1_1_contains j) +noncomputable def hk12_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_3 j i k) +lemma hk12_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_3 j i k).Contains (fullFactor true 12 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 3 (kernel12_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha12_1_3 : Fin 7 → CBox := ![⟨⟨(-400),0⟩,⟨(-400),400⟩⟩,⟨⟨(-651),472⟩,⟨(-757),377⟩⟩,⟨⟨1565848,1566544⟩,⟨2475956,2476652⟩⟩,⟨⟨(-84367392959080205),(-84367392959079898)⟩,⟨65475763810682239,65475763810682548⟩⟩,⟨⟨(-334371089579930022060605),(-334371089579930020689539)⟩,⟨134503204342974931346563,134503204342974932717021⟩⟩,⟨⟨(-3042174272738510667139680138),(-3042174272738510662258998317)⟩,⟨(-882188156327165039792445665),(-882188156327165034899803331)⟩⟩,⟨⟨(-881746361238965949165084040176),(-881746361238965948221468117250)⟩,⟨(-100616198115873475850220498452),(-100616198115873474915273990647)⟩⟩] +lemma ha12_1_3_eq (j : Fin 7) : ha12_1_3 j = ((ha12_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha12_1_3_contains (j : Fin 7) : (ha12_1_3 j).Contains (fullFactor true 12 3 ((j.val:ℝ)/6)) := by + rw [ha12_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_2 j) true 12 2 j (ha12_1_2_contains j) +noncomputable def hk12_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_4 j i k) +lemma hk12_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_4 j i k).Contains (fullFactor true 12 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 4 (kernel12_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha12_1_4 : Fin 7 → CBox := ![⟨⟨0,922⟩,⟨(-922),922⟩⟩,⟨⟨(-1609),1599⟩,⟨(-1162),2056⟩⟩,⟨⟨1259649,1261403⟩,⟨(-5065462),(-5063709)⟩⟩,⟨⟨143306813236192521,143306813236193134⟩,⟨61419183329985352,61419183329985963⟩⟩,⟨⟨282023685098541581227140,282023685098541583330327⟩,⟨335242630588426771929975,335242630588426774034128⟩⟩,⟨⟨(-365345279102973091818743130),(-365345279102973085957824832)⟩,⟨3262378016722954847165573977,3262378016722954853022194137⟩⟩,⟨⟨(-49439809917090287570797620483),(-49439809917090286682051210487)⟩,⟨800725527717580900573211989170,800725527717580901471505705119⟩⟩] +lemma ha12_1_4_eq (j : Fin 7) : ha12_1_4 j = ((ha12_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha12_1_4_contains (j : Fin 7) : (ha12_1_4 j).Contains (fullFactor true 12 4 ((j.val:ℝ)/6)) := by + rw [ha12_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_3 j) true 12 3 j (ha12_1_3_contains j) +noncomputable def hk12_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_5 j i k) +lemma hk12_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_5 j i k).Contains (fullFactor true 12 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 5 (kernel12_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha12_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),0⟩,⟨(-1700),1700⟩⟩,⟨⟨(-3316),3996⟩,⟨(-4342),2979⟩⟩,⟨⟨(-6459695),(-6456161)⟩,⟨3686996,3690530⟩⟩,⟨⟨(-18362012620301129),(-18362012620300157)⟩,⟨(-181173391290789430),(-181173391290788457)⟩⟩,⟨⟨224290183885505711843934,224290183885505714426841⟩,⟨(-362191692607018569302627),(-362191692607018566720424)⟩⟩,⟨⟨2717018901613117668572573769,2717018901613117674192002593⟩,⟨(-161033129697945136053872206),(-161033129697945130437772579)⟩⟩,⟨⟨580144841859343371046372105467,580144841859343371730347742431⟩,⟨5634704595080413397679880952,5634704595080414073481665032⟩⟩] +lemma ha12_1_5_eq (j : Fin 7) : ha12_1_5 j = ((ha12_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha12_1_5_contains (j : Fin 7) : (ha12_1_5 j).Contains (fullFactor true 12 5 ((j.val:ℝ)/6)) := by + rw [ha12_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_4 j) true 12 4 j (ha12_1_4_contains j) +noncomputable def hk12_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_6 j i k) +lemma hk12_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_6 j i k).Contains (fullFactor true 12 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 6 (kernel12_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha12_1_6 : Fin 7 → CBox := ![⟨⟨0,2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-7797),6083⟩,⟨(-6283),7603⟩⟩,⟨⟨8462631,8468566⟩,⟨2513286,2519220⟩⟩,⟨⟨(-145586713028482100),(-145586713028480812)⟩,⟨101086125539641714,101086125539643002⟩⟩,⟨⟨(-335533547526137494846980),(-335533547526137492205282)⟩,⟨(-81228117760337498069450),(-81228117760337495427615)⟩⟩,⟨⟨(-428579684156756623710990271),(-428579684156756619226089127)⟩,⟨(-1831068351809184380019116382),(-1831068351809184375527754642)⟩⟩,⟨⟨(-14764779625578476764683221683),(-14764779625578476336486261911)⟩,⟨(-349329362916570933261791842100),(-349329362916570932827887991785)⟩⟩] +lemma ha12_1_6_eq (j : Fin 7) : ha12_1_6 j = ((ha12_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha12_1_6_contains (j : Fin 7) : (ha12_1_6 j).Contains (fullFactor true 12 6 ((j.val:ℝ)/6)) := by + rw [ha12_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_5 j) true 12 5 j (ha12_1_5_contains j) +noncomputable def hk12_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_7 j i k) +lemma hk12_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_7 j i k).Contains (fullFactor true 12 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 7 (kernel12_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha12_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),0⟩,⟨(-3439),3439⟩⟩,⟨⟨(-9999),12578⟩,⟨(-11558),11023⟩⟩,⟨⟨(-4107367),(-4098825)⟩,⟨(-8002557),(-7994016)⟩⟩,⟨⟨132626412875364609,132626412875366070⟩,⟨65375046744878292,65375046744879754⟩⟩,⟨⟨19025700156272412036256,19025700156272414352139⟩,⟨239035845330222402287450,239035845330222404603631⟩⟩,⟨⟨(-1025515064786729755508828481),(-1025515064786729752432820959)⟩,⟨434357935598569773825031536,434357935598569776895762366⟩⟩,⟨⟨(-179809284764419594904920963680),(-179809284764419594669025794248)⟩,⟨16987249972927504572110876586,16987249972927504804694370495⟩⟩] +lemma ha12_1_7_eq (j : Fin 7) : ha12_1_7 j = ((ha12_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha12_1_7_contains (j : Fin 7) : (ha12_1_7 j).Contains (fullFactor true 12 7 ((j.val:ℝ)/6)) := by + rw [ha12_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_6 j) true 12 6 j (ha12_1_6_contains j) +noncomputable def hk12_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_8 j i k) +lemma hk12_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_8 j i k).Contains (fullFactor true 12 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 8 (kernel12_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha12_1_8 : Fin 7 → CBox := ![⟨⟨0,3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-17425),14705⟩,⟨(-16409),15723⟩⟩,⟨⟨(-2629205),(-2618448)⟩,⟨7558558,7569315⟩⟩,⟨⟨(-5172125299657550),(-5172125299656099)⟩,⟨(-107812939643808127),(-107812939643806676)⟩⟩,⟨⟨134439038177650509380385,134439038177650511157102⟩,⟨(-56265380089764138489733),(-56265380089764136713404)⟩⟩,⟨⟨312094522408203376760596274,312094522408203378600501213⟩,⟨485451518706925730875613496,485451518706925732718543747⟩⟩,⟨⟨11888099307316885150631782042,11888099307316885261189608016⟩,⟨80763282045648610158473863463,80763282045648610270670552043⟩⟩] +lemma ha12_1_8_eq (j : Fin 7) : ha12_1_8 j = ((ha12_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha12_1_8_contains (j : Fin 7) : (ha12_1_8 j).Contains (fullFactor true 12 8 ((j.val:ℝ)/6)) := by + rw [ha12_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_7 j) true 12 7 j (ha12_1_7_contains j) +noncomputable def hk12_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_9 j i k) +lemma hk12_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_9 j i k).Contains (fullFactor true 12 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 9 (kernel12_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha12_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),0⟩,⟨(-4057),4057⟩⟩,⟨⟨(-19305),21338⟩,⟨(-19468),21176⟩⟩,⟨⟨5757752,5769793⟩,⟨(-2642496),(-2630455)⟩⟩,⟨⟨(-59566856971790963),(-59566856971789683)⟩,⟨36836660294892444,36836660294893724⟩⟩,⟨⟨(-51518723627657546463402),(-51518723627657545252239)⟩,⟨(-59538310774410478478294),(-59538310774410477266912)⟩⟩,⟨⟨195933713564883926082194220,195933713564883927063503378⟩,⟨(-179656051765103063237525125),(-179656051765103062257559770)⟩⟩,⟨⟨32156227350071706879117530623,32156227350071706926544241382⟩,⟨(-6454825388740991421378976578),(-6454825388740991374659015020)⟩⟩] +lemma ha12_1_9_eq (j : Fin 7) : ha12_1_9 j = ((ha12_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha12_1_9_contains (j : Fin 7) : (ha12_1_9 j).Contains (fullFactor true 12 9 ((j.val:ℝ)/6)) := by + rw [ha12_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_8 j) true 12 8 j (ha12_1_8_contains j) +noncomputable def hk12_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_10 j i k) +lemma hk12_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_10 j i k).Contains (fullFactor true 12 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 10 (kernel12_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha12_1_10 : Fin 7 → CBox := ![⟨⟨0,3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-23597),22673⟩,⟨(-24168),22102⟩⟩,⟨⟨(-4201710),(-4189579)⟩,⟨(-1676415),(-1664284)⟩⟩,⟨⟨35674546456790503,35674546456791520⟩,⟨20003693883524556,20003693883525573⟩⟩,⟨⟨(-19699712207640474563068),(-19699712207640473819763)⟩,⟨32823771021233969849599,32823771021233970592828⟩⟩,⟨⟨(-87194525795308043228230677),(-87194525795308042758494171)⟩,⟨(-67391456163921622735072291),(-67391456163921622264863928)⟩⟩,⟨⟨(-2934662521517390782245028598),(-2934662521517390764474440250)⟩,⟨(-11490493005176072737951515324),(-11490493005176072719910983201)⟩⟩] +lemma ha12_1_10_eq (j : Fin 7) : ha12_1_10 j = ((ha12_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha12_1_10_contains (j : Fin 7) : (ha12_1_10 j).Contains (fullFactor true 12 10 ((j.val:ℝ)/6)) := by + rw [ha12_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_9 j) true 12 9 j (ha12_1_9_contains j) +noncomputable def hk12_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_11 j i k) +lemma hk12_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_11 j i k).Contains (fullFactor true 12 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 11 (kernel12_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha12_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),0⟩,⟨(-3133),3133⟩⟩,⟨⟨(-23970),23916⟩,⟨(-23067),24819⟩⟩,⟨⟨1090344,1101454⟩,⟨2706467,2717578⟩⟩,⟨⟨111451143979659,111451143980394⟩,⟨(-21713254791105582),(-21713254791104847)⟩⟩,⟨⟨16499777598985442559887,16499777598985442974493⟩,⟨3752067657357486987944,3752067657357487402560⟩⟩,⟨⟨(-19445682288577721204839725),(-19445682288577721000035180)⟩,⟨36698144803440582446380892,36698144803440582651059781⟩⟩,⟨⟨(-3721947092145361633426796985),(-3721947092145361627189023992)⟩,⟨1159522835501150289178579955,1159522835501150295323869784⟩⟩] +lemma ha12_1_11_eq (j : Fin 7) : ha12_1_11 j = ((ha12_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha12_1_11_contains (j : Fin 7) : (ha12_1_11 j).Contains (fullFactor true 12 11 ((j.val:ℝ)/6)) := by + rw [ha12_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_10 j) true 12 10 j (ha12_1_10_contains j) +noncomputable def hk12_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_12 j i k) +lemma hk12_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_12 j i k).Contains (fullFactor true 12 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 12 (kernel12_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha12_1_12 : Fin 7 → CBox := ![⟨⟨0,2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-22426),23003⟩,⟨(-23266),22163⟩⟩,⟨⟨709638,718966⟩,⟨(-1587732),(-1578404)⟩⟩,⟨⟨(-9269400545525877),(-9269400545525390)⟩,⟨5073243044346633,5073243044347120⟩⟩,⟨⟨(-639044372753523510328),(-639044372753523298333)⟩,⟨(-6826209516733269815607),(-6826209516733269603603)⟩⟩,⟨⟨13634873130783275536921651,13634873130783275618666613⟩,⟨4466223382015006406271286,4466223382015006488036179⟩⟩,⟨⟨407162470023963183778106510,407162470023963185726243312⟩,⟨1101860031015938724259271972,1101860031015938726236118342⟩⟩] +lemma ha12_1_12_eq (j : Fin 7) : ha12_1_12 j = ((ha12_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha12_1_12_contains (j : Fin 7) : (ha12_1_12 j).Contains (fullFactor true 12 12 ((j.val:ℝ)/6)) := by + rw [ha12_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_11 j) true 12 11 j (ha12_1_11_contains j) +noncomputable def hk12_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_13 j i k) +lemma hk12_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_13 j i k).Contains (fullFactor true 12 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 13 (kernel12_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha12_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),0⟩,⟨(-1706),1706⟩⟩,⟨⟨(-20219),19564⟩,⟨(-19649),20134⟩⟩,⟨⟨(-901302),(-894073)⟩,⟨312966,320195⟩⟩,⟨⟨4011372127826766,4011372127827064⟩,⟨2537960439248751,2537960439249049⟩⟩,⟨⟨(-2351433400295992433173),(-2351433400295992333110)⟩,⟨1022809135565645839958,1022809135565645940014⟩⟩,⟨⟨664825758783034719549813,664825758783034749680262⟩,⟨(-4526775139293341501751547),(-4526775139293341471618691)⟩⟩,⟨⟨300183923098352559350460168,300183923098352559928703270⟩,⟨(-129013402682440290084988849),(-129013402682440289514888047)⟩⟩] +lemma ha12_1_13_eq (j : Fin 7) : ha12_1_13 j = ((ha12_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha12_1_13_contains (j : Fin 7) : (ha12_1_13 j).Contains (fullFactor true 12 13 ((j.val:ℝ)/6)) := by + rw [ha12_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_12 j) true 12 12 j (ha12_1_12_contains j) +noncomputable def hk12_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_14 j i k) +lemma hk12_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_14 j i k).Contains (fullFactor true 12 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 14 (kernel12_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha12_1_14 : Fin 7 → CBox := ![⟨⟨0,1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-15932),16419⟩,⟨(-16221),16129⟩⟩,⟨⟨429559,434762⟩,⟨216294,221496⟩⟩,⟨⟨115177237867249,115177237867419⟩,⟨(-1976686525918239),(-1976686525918069)⟩⟩,⟨⟨592044781526464558595,592044781526464602447⟩,⟨665262605590692995240,665262605590693039095⟩⟩,⟨⟨(-1354389762449831494643053),(-1354389762449831484329979)⟩,⟨33730035249169909361574,33730035249169919671098⟩⟩,⟨⟨(-37302664176799394749652024),(-37302664176799394594731321)⟩,⟨(-75696191667594046603359272),(-75696191667594046446314404)⟩⟩] +lemma ha12_1_14_eq (j : Fin 7) : ha12_1_14 j = ((ha12_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha12_1_14_contains (j : Fin 7) : (ha12_1_14 j).Contains (fullFactor true 12 14 ((j.val:ℝ)/6)) := by + rw [ha12_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_13 j) true 12 13 j (ha12_1_13_contains j) +noncomputable def hk12_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_15 j i k) +lemma hk12_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_15 j i k).Contains (fullFactor true 12 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 15 (kernel12_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha12_1_15 : Fin 7 → CBox := ![⟨⟨(-690),0⟩,⟨(-690),690⟩⟩,⟨⟨(-12412),12141⟩,⟨(-12313),12240⟩⟩,⟨⟨(-68442),(-64947)⟩,⟨(-221976),(-218481)⟩⟩,⟨⟨(-694894656750334),(-694894656750243)⟩,⟨333709370046484,333709370046575⟩⟩,⟨⟨145089811229911627220,145089811229911645159⟩,⟨(-249556698605227573365),(-249556698605227555426)⟩⟩,⟨⟨72780047412093170491536,72780047412093173783836⟩,⟨367288459824434332656522,367288459824434335950570⟩⟩,⟨⟨(-17755764851287819942344986),(-17755764851287819902539954)⟩,⟨9927641296462630329576723,9927641296462630368869094⟩⟩] +lemma ha12_1_15_eq (j : Fin 7) : ha12_1_15 j = ((ha12_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha12_1_15_contains (j : Fin 7) : (ha12_1_15 j).Contains (fullFactor true 12 15 ((j.val:ℝ)/6)) := by + rw [ha12_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_14 j) true 12 14 j (ha12_1_14_contains j) +noncomputable def hk12_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_16 j i k) +lemma hk12_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_16 j i k).Contains (fullFactor true 12 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 16 (kernel12_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha12_1_16 : Fin 7 → CBox := ![⟨⟨0,398⟩,⟨(-398),398⟩⟩,⟨⟨(-8679),8792⟩,⟨(-8686),8784⟩⟩,⟨⟨(-51466),(-49264)⟩,⟨88136,90338⟩⟩,⟨⟨229451522452512,229451522452558⟩,⟨162832727143196,162832727143242⟩⟩,⟨⟨(-85800752104362923376),(-85800752104362916495)⟩,⟨(-18259125369958110177),(-18259125369958103297)⟩⟩,⟨⟨90576420994478944542385,90576420994478945528691⟩,⟨(-34750696979472963738664),(-34750696979472962752925)⟩⟩,⟨⟨2448939421412117926768433,2448939421412117936111235⟩,⟨3890773919362264140698550,3890773919362264150156369⟩⟩] +lemma ha12_1_16_eq (j : Fin 7) : ha12_1_16 j = ((ha12_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha12_1_16_contains (j : Fin 7) : (ha12_1_16 j).Contains (fullFactor true 12 16 ((j.val:ℝ)/6)) := by + rw [ha12_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_15 j) true 12 15 j (ha12_1_15_contains j) +noncomputable def hk12_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_17 j i k) +lemma hk12_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_17 j i k).Contains (fullFactor true 12 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 17 (kernel12_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha12_1_17 : Fin 7 → CBox := ![⟨⟨(-216),0⟩,⟨(-216),216⟩⟩,⟨⟨(-5865),5835⟩,⟨(-5884),5816⟩⟩,⟨⟨40968,42274⟩,⟨(-11240),(-9934)⟩⟩,⟨⟨10732372738145,10732372738168⟩,⟨(-96053963494581),(-96053963494558)⟩⟩,⟨⟨2685985983682311391,2685985983682313875⟩,⟨24945154781658022493,24945154781658024978⟩⟩,⟨⟨(-12103547896911307343880),(-12103547896911307066094)⟩,⟨(-20326847232071309020638),(-20326847232071308742703)⟩⟩,⟨⟨799402374366918776037730,799402374366918778152610⟩,⟨(-563162805071724530034411),(-563162805071724527943616)⟩⟩] +lemma ha12_1_17_eq (j : Fin 7) : ha12_1_17 j = ((ha12_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha12_1_17_contains (j : Fin 7) : (ha12_1_17 j).Contains (fullFactor true 12 17 ((j.val:ℝ)/6)) := by + rw [ha12_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_16 j) true 12 16 j (ha12_1_16_contains j) +noncomputable def hk12_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_18 j i k) +lemma hk12_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_18 j i k).Contains (fullFactor true 12 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 18 (kernel12_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha12_1_18 : Fin 7 → CBox := ![⟨⟨0,111⟩,⟨(-111),111⟩⟩,⟨⟨(-3701),3700⟩,⟨(-3683),3718⟩⟩,⟨⟨(-14780),(-14048)⟩,⟨(-9379),(-8647)⟩⟩,⟨⟨(-28946838471415),(-28946838471404)⟩,⟨12055974768646,12055974768657⟩⟩,⟨⟨6176451077383268828,6176451077383269676⟩,⟨(-2789445976758883829),(-2789445976758882981)⟩⟩,⟨⟨(-4139811040120070668450),(-4139811040120070594484)⟩,⟨3542382064852513198377,3542382064852513272311⟩⟩,⟨⟨(-121316778784812561895302),(-121316778784812561453413)⟩,⟨(-154495323355782595617540),(-154495323355782595170928)⟩⟩] +lemma ha12_1_18_eq (j : Fin 7) : ha12_1_18 j = ((ha12_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha12_1_18_contains (j : Fin 7) : (ha12_1_18 j).Contains (fullFactor true 12 18 ((j.val:ℝ)/6)) := by + rw [ha12_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_17 j) true 12 17 j (ha12_1_17_contains j) +noncomputable def hk12_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_19 j i k) +lemma hk12_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_19 j i k).Contains (fullFactor true 12 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 19 (kernel12_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha12_1_19 : Fin 7 → CBox := ![⟨⟨(-54),0⟩,⟨(-54),54⟩⟩,⟨⟨(-2214),2221⟩,⟨(-2225),2211⟩⟩,⟨⟨1098,1487⟩,⟨6048,6437⟩⟩,⟨⟨7552868186813,7552868186819⟩,⟨5986858901887,5986858901893⟩⟩,⟨⟨(-1170880804984483039),(-1170880804984482764)⟩,⟨(-1279375383114849324),(-1279375383114849049)⟩⟩,⟨⟨915124693907503222479,915124693907503241122⟩,⟨758812426888307749312,758812426888307767961⟩⟩,⟨⟨(-28163504054274280263151),(-28163504054274280173806)⟩,⟨24583586955638690226656,24583586955638690315132⟩⟩] +lemma ha12_1_19_eq (j : Fin 7) : ha12_1_19 j = ((ha12_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha12_1_19_contains (j : Fin 7) : (ha12_1_19 j).Contains (fullFactor true 12 19 ((j.val:ℝ)/6)) := by + rw [ha12_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_18 j) true 12 18 j (ha12_1_18_contains j) +noncomputable def hk12_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_20 j i k) +lemma hk12_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_20 j i k).Contains (fullFactor true 12 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 20 (kernel12_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha12_1_20 : Fin 7 → CBox := ![⟨⟨0,25⟩,⟨(-25),25⟩⟩,⟨⟨(-1265),1260⟩,⟨(-1261),1265⟩⟩,⟨⟨1191,1388⟩,⟨(-1968),(-1771)⟩⟩,⟨⟨460401661652,460401661655⟩,⟨(-2776245354990),(-2776245354986)⟩⟩,⟨⟨(-206819933032496471),(-206819933032496385)⟩,⟨367408320818785892,367408320818785978⟩⟩,⟨⟨122772323504097661794,122772323504097666261⟩,⟨(-213649535057756680219),(-213649535057756675752)⟩⟩,⟨⟨4703016411804920125259,4703016411804920142088⟩,⟨4854150195112699790509,4854150195112699807489⟩⟩] +lemma ha12_1_20_eq (j : Fin 7) : ha12_1_20 j = ((ha12_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha12_1_20_contains (j : Fin 7) : (ha12_1_20 j).Contains (fullFactor true 12 20 ((j.val:ℝ)/6)) := by + rw [ha12_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_19 j) true 12 19 j (ha12_1_19_contains j) +noncomputable def hk12_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_21 j i k) +lemma hk12_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_21 j i k).Contains (fullFactor true 12 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 21 (kernel12_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha12_1_21 : Fin 7 → CBox := ![⟨⟨(-11),0⟩,⟨(-11),11⟩⟩,⟨⟨(-684),686⟩,⟨(-685),685⟩⟩,⟨⟨(-809),(-713)⟩,⟨74,170⟩⟩,⟨⟨(-737370077630),(-737370077628)⟩,⟨262137085294,262137085296⟩⟩,⟨⟨95753733033877437,95753733033877463⟩,⟨18988156434296078,18988156434296104⟩⟩,⟨⟨(-45680512621259045580),(-45680512621259044560)⟩,⟨(-16718421102142236901),(-16718421102142235881)⟩⟩,⟨⟨792636265917762104832,792636265917762107906⟩,⟨(-852104513620291070903),(-852104513620291067854)⟩⟩] +lemma ha12_1_21_eq (j : Fin 7) : ha12_1_21 j = ((ha12_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha12_1_21_contains (j : Fin 7) : (ha12_1_21 j).Contains (fullFactor true 12 21 ((j.val:ℝ)/6)) := by + rw [ha12_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_20 j) true 12 20 j (ha12_1_20_contains j) +noncomputable def hk12_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_22 j i k) +lemma hk12_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_22 j i k).Contains (fullFactor true 12 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 22 (kernel12_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha12_1_22 : Fin 7 → CBox := ![⟨⟨0,5⟩,⟨(-5),5⟩⟩,⟨⟨(-355),355⟩,⟨(-355),355⟩⟩,⟨⟨176,221⟩,⟨128,173⟩⟩,⟨⟨155718997593,155718997595⟩,⟨137493121900,137493121902⟩⟩,⟨⟨(-2607998181537085),(-2607998181537076)⟩,⟨(-21416138072061820),(-21416138072061812)⟩⟩,⟨⟨(-1642122016580049803),(-1642122016580049580)⟩,⟨9017876610944314623,9017876610944314846⟩⟩,⟨⟨(-146627616202662846276),(-146627616202662845747)⟩,⟨(-122828530585784551379),(-122828530585784550847)⟩⟩] +lemma ha12_1_22_eq (j : Fin 7) : ha12_1_22 j = ((ha12_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha12_1_22_contains (j : Fin 7) : (ha12_1_22 j).Contains (fullFactor true 12 22 ((j.val:ℝ)/6)) := by + rw [ha12_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_21 j) true 12 21 j (ha12_1_21_contains j) +noncomputable def hk12_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_23 j i k) +lemma hk12_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_23 j i k).Contains (fullFactor true 12 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 23 (kernel12_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha12_1_23 : Fin 7 → CBox := ![⟨⟨(-3),0⟩,⟨(-3),3⟩⟩,⟨⟨(-176),176⟩,⟨(-176),176⟩⟩,⟨⟨(-19),2⟩,⟨(-87),(-66)⟩⟩,⟨⟨11376984564,11376984566⟩,⟨(-51502616354),(-51502616353)⟩⟩,⟨⟨(-4130012158259014),(-4130012158259011)⟩,⟨1934869848805713,1934869848805716⟩⟩,⟨⟨1652054365299038671,1652054365299038719⟩,⟨15531245591146493,15531245591146540⟩⟩,⟨⟨(-18087141867166175134),(-18087141867166175045)⟩,⟨24023481097517485766,24023481097517485854⟩⟩] +lemma ha12_1_23_eq (j : Fin 7) : ha12_1_23 j = ((ha12_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha12_1_23_contains (j : Fin 7) : (ha12_1_23 j).Contains (fullFactor true 12 23 ((j.val:ℝ)/6)) := by + rw [ha12_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_22 j) true 12 22 j (ha12_1_22_contains j) +noncomputable def hk12_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_24 j i k) +lemma hk12_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_24 j i k).Contains (fullFactor true 12 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 24 (kernel12_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha12_1_24 : Fin 7 → CBox := ![⟨⟨0,2⟩,⟨(-2),2⟩⟩,⟨⟨(-84),84⟩,⟨(-84),84⟩⟩,⟨⟨(-20),(-10)⟩,⟨13,22⟩⟩,⟨⟨(-12303606146),(-12303606144)⟩,⟨3651455452,3651455454⟩⟩,⟨⟨633229932800537,633229932800539⟩,⟨672858084776373,672858084776375⟩⟩,⟨⟨(-45837519785308592),(-45837519785308582)⟩,⟨(-281669578683673109),(-281669578683673099)⟩⟩,⟨⟨3756070794749000448,3756070794749000463⟩,⟨2533423776072111742,2533423776072111758⟩⟩] +lemma ha12_1_24_eq (j : Fin 7) : ha12_1_24 j = ((ha12_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha12_1_24_contains (j : Fin 7) : (ha12_1_24 j).Contains (fullFactor true 12 24 ((j.val:ℝ)/6)) := by + rw [ha12_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_23 j) true 12 23 j (ha12_1_23_contains j) +noncomputable def hk12_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_25 j i k) +lemma hk12_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_25 j i k).Contains (fullFactor true 12 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 25 (kernel12_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha12_1_25 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨4,9⟩,⟨(-3),2⟩⟩,⟨⟨2138868459,2138868461⟩,⟨2100668034,2100668036⟩⟩,⟨⟨85961120613435,85961120613437⟩,⟨(-157805411657712),(-157805411657710)⟩⟩,⟨⟨(-44736800715453273),(-44736800715453270)⟩,⟨15425645641545957,15425645641545960⟩⟩,⟨⟨337718768448286647,337718768448286651⟩,⟨(-561559156890124354),(-561559156890124351)⟩⟩] +lemma ha12_1_25_eq (j : Fin 7) : ha12_1_25 j = ((ha12_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha12_1_25_contains (j : Fin 7) : (ha12_1_25 j).Contains (fullFactor true 12 25 ((j.val:ℝ)/6)) := by + rw [ha12_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_24 j) true 12 24 j (ha12_1_24_contains j) +noncomputable def hk12_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_26 j i k) +lemma hk12_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_26 j i k).Contains (fullFactor true 12 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 26 (kernel12_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha12_1_26 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-18),18⟩,⟨(-18),18⟩⟩,⟨⟨(-3),0⟩,⟨(-3),0⟩⟩,⟨⟨179916576,179916577⟩,⟨(-648877112),(-648877111)⟩⟩,⟨⟨(-33050809081732),(-33050809081731)⟩,⟨(-6077230735886),(-6077230735884)⟩⟩,⟨⟨3635641658270842,3635641658270843⟩,⟨6611489031238316,6611489031238318⟩⟩,⟨⟨(-80431512446630962),(-80431512446630960)⟩,⟨(-42848670008874491),(-42848670008874489)⟩⟩] +lemma ha12_1_26_eq (j : Fin 7) : ha12_1_26 j = ((ha12_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha12_1_26_contains (j : Fin 7) : (ha12_1_26 j).Contains (fullFactor true 12 26 ((j.val:ℝ)/6)) := by + rw [ha12_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_25 j) true 12 25 j (ha12_1_25_contains j) +noncomputable def hk12_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_27 j i k) +lemma hk12_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_27 j i k).Contains (fullFactor true 12 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 27 (kernel12_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha12_1_27 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-8),8⟩,⟨(-8),8⟩⟩,⟨⟨(-1),1⟩,⟨0,2⟩⟩,⟨⟨(-141622524),(-141622522)⟩,⟨33972212,33972214⟩⟩,⟨⟨815074688456,815074688457⟩,⟨5996427841651,5996427841652⟩⟩,⟨⟨905529230184848,905529230184850⟩,⟨(-722562129290903),(-722562129290902)⟩⟩,⟨⟨(-5171287713399826),(-5171287713399825)⟩,⟨11055041638956256,11055041638956257⟩⟩] +lemma ha12_1_27_eq (j : Fin 7) : ha12_1_27 j = ((ha12_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha12_1_27_contains (j : Fin 7) : (ha12_1_27 j).Contains (fullFactor true 12 27 ((j.val:ℝ)/6)) := by + rw [ha12_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_26 j) true 12 26 j (ha12_1_26_contains j) +noncomputable def hk12_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_28 j i k) +lemma hk12_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_28 j i k).Contains (fullFactor true 12 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 28 (kernel12_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha12_1_28 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨20511770,20511771⟩,⟨22403809,22403810⟩⟩,⟨⟨945296541218,945296541219⟩,⟨(-459012925014),(-459012925013)⟩⟩,⟨⟨(-128201750083820),(-128201750083819)⟩,⟨(-113944672484683),(-113944672484681)⟩⟩,⟨⟨1460395473380750,1460395473380751⟩,⟨592779012106575,592779012106577⟩⟩] +lemma ha12_1_28_eq (j : Fin 7) : ha12_1_28 j = ((ha12_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha12_1_28_contains (j : Fin 7) : (ha12_1_28 j).Contains (fullFactor true 12 28 ((j.val:ℝ)/6)) := by + rw [ha12_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_27 j) true 12 27 j (ha12_1_27_contains j) +noncomputable def hk12_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_29 j i k) +lemma hk12_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_29 j i k).Contains (fullFactor true 12 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 29 (kernel12_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha12_1_29 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨1944720,1944721⟩,⟨(-5799393),(-5799392)⟩⟩,⟨⟨(-122520550745),(-122520550744)⟩,⟨(-126610055462),(-126610055460)⟩⟩,⟨⟨(-12938088991960),(-12938088991958)⟩,⟨20827376155776,20827376155777⟩⟩,⟨⟨64355761780807,64355761780808⟩,⟨(-185683937390799),(-185683937390798)⟩⟩] +lemma ha12_1_29_eq (j : Fin 7) : ha12_1_29 j = ((ha12_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha12_1_29_contains (j : Fin 7) : (ha12_1_29 j).Contains (fullFactor true 12 29 ((j.val:ℝ)/6)) := by + rw [ha12_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_28 j) true 12 28 j (ha12_1_28_contains j) +noncomputable def hk12_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel12_0 j i k).mul (mpower1_30 j i k) +lemma hk12_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk12_1_30 j i k).Contains (fullFactor true 12 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk12_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel12_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 12 30 (kernel12_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha12_1_30 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1170949),(-1170948)⟩,⟨215934,215935⟩⟩,⟨⟨(-13309159360),(-13309159359)⟩,⟨25263432859,25263432860⟩⟩,⟨⟨3139945284923,3139945284924⟩,⟨1272903258987,1272903258988⟩⟩,⟨⟨(-22753127670298),(-22753127670296)⟩,⟨(-6584127860527),(-6584127860526)⟩⟩] +lemma ha12_1_30_eq (j : Fin 7) : ha12_1_30 j = ((ha12_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha12_1_30_contains (j : Fin 7) : (ha12_1_30 j).Contains (fullFactor true 12 30 ((j.val:ℝ)/6)) := by + rw [ha12_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha12_1_29 j) true 12 29 j (ha12_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders13.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders13.lean new file mode 100644 index 0000000000000000000000000000000000000000..cabbb3576fbf8399ab131d607ec0e1832ea25dee --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders13.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.KernelValues20 +import OAI.Analysis.PlanarPacking.Certificate.Powers20 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk13_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_0 j i k) +lemma hk13_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_0 j i k).Contains (fullFactor false 13 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 0 (power13_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha13_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999845,1000000000000000000000000000207⟩,⟨(-207),207⟩⟩,⟨⟨866025403784438646742693794068,866025403784438646779646544579⟩,⟨499999999999999999985439611613,500000000000000000023404244797⟩⟩,⟨⟨499999999999999999940165171904,500000000000000000042147115238⟩,⟨866025403784438646717467884184,866025403784438646820190463112⟩⟩,⟨⟨(-57784783185),27148765851⟩,⟨999999999999999999957533225495,1000000000000000000042466774518⟩⟩,⟨⟨(-500000000000000000157773117513),(-499999999999999999877602308226)⟩,⟨866025403784438646613696481328,866025403784438646893325848570⟩⟩,⟨⟨(-866025403784438646952765054648),(-866025403784438646600211301278)⟩,⟨499999999999999999801882176790,500000000000000000153898541039⟩⟩,⟨⟨(-1000000000000000000085191571217),(-999999999999999999914808428835)⟩,⟨(-115827588577),54555553805⟩⟩] +lemma ha13_0_0_eq (j : Fin 7) : ha13_0_0 j = ((atomPoints j).direct.powBin 7 13).conj := by fin_cases j <;> decide +kernel +lemma ha13_0_0_contains (j : Fin 7) : (ha13_0_0 j).Contains (fullFactor false 13 0 ((j.val:ℝ)/6)) := by + rw [ha13_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 13) ((j.val:ℝ)/6) 13 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 13 (by norm_num)) +noncomputable def hk13_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_1 j i k) +lemma hk13_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_1 j i k).Contains (fullFactor false 13 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 1 (power13_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha13_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-261799387799149436551421100588),(-261799387799149436530709531800)⟩,⟨453449841058554462637127069012,453449841058554462657918859612⟩⟩,⟨⟨(-906899682117108925358295211427),(-906899682117108925247837626971)⟩,⟨523598775598298873014007781207,523598775598298873122469689202⟩⟩,⟨⟨(-1570796326794896619301706653424),(-1570796326794896619163293346596)⟩,⟨(-90768125172),42645181676⟩⟩,⟨⟨(-1813799364234217850869764815965),(-1813799364234217850278336936032)⟩,⟨(-1047197551196597746487105911277),(-1047197551196597745896984207136)⟩⟩,⟨⟨(-1308996938995747183098738771607),(-1308996938995747182172995418381)⟩,⟨(-2267249205292772313742817497581),(-2267249205292772312812617051227)⟩⟩,⟨⟨(-171391327047),363883101357⟩,⟨(-3141592653589793238737637214284),(-3141592653589793238192362785880)⟩⟩] +lemma ha13_0_1_eq (j : Fin 7) : ha13_0_1 j = ((ha13_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha13_0_1_contains (j : Fin 7) : (ha13_0_1 j).Contains (fullFactor false 13 1 ((j.val:ℝ)/6)) := by + rw [ha13_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_0 j) false 13 0 j (ha13_0_0_contains j) +noncomputable def hk13_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_2 j i k) +lemma hk13_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_2 j i k).Contains (fullFactor false 13 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 2 (power13_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha13_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-118712890786751174410676029255),(-118712890786751174404854876336)⟩,⟨(-68538919452009434856546494868),(-68538919452009434850906052681)⟩⟩,⟨⟨(-274155677808037739436462908170),(-274155677808037739378799721317)⟩,⟨(-474851563147004697664934807952),(-474851563147004697605587852503)⟩⟩,⟨⟨(-33493447367),71289118806⟩,⟨(-1233700550136169827412480531332),(-1233700550136169827299843983541)⟩⟩,⟨⟨1096622711232150957377983170892,1096622711232150957999447832884⟩,⟨(-1899406252588018790820143081177),(-1899406252588018790194755255716)⟩⟩,⟨⟨2967822269668779359633092103599,2967822269668779360860168512223⟩,⟨(-1713472986300235871860859274637),(-1713472986300235870643609905053)⟩⟩,⟨⟨4934802200544679308988537513593,4934802200544679309860760546094⟩,⟨(-269220866970),571586238995⟩⟩] +lemma ha13_0_2_eq (j : Fin 7) : ha13_0_2 j = ((ha13_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha13_0_2_contains (j : Fin 7) : (ha13_0_2 j).Contains (fullFactor false 13 2 ((j.val:ℝ)/6)) := by + rw [ha13_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_1 j) false 13 1 j (ha13_0_1_contains j) +noncomputable def hk13_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_3 j i k) +lemma hk13_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_3 j i k).Contains (fullFactor false 13 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 3 (power13_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha13_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11962298101967523215468796590,11962298101967523216491316643⟩,⟨(-20719308087892496642941934423),(-20719308087892496641859999968)⟩⟩,⟨⟨165754464703139973130051842090,165754464703139973151295450412⟩,⟨(-95698384815740185735517857995),(-95698384815740185715084991219)⟩⟩,⟨⟨645964097506246253626693980527,645964097506246253687726506622⟩,⟨(-17537128032),37326895321⟩⟩,⟨⟨1326035717625119784881522646432,1326035717625119785322346615467⟩,⟨765587078525921485624885289700,765587078525921486061186410523⟩⟩,⟨⟨1495287262745940401384657385310,1495287262745940402451667498351⟩,⟨2589913510986562079806395482890,2589913510986562080885465608846⟩⟩,⟨⟨(-598563709774),281927432623⟩,⟨5167712780049970028792762366496,5167712780049970029722601530898⟩⟩] +lemma ha13_0_3_eq (j : Fin 7) : ha13_0_3 j = ((ha13_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha13_0_3_contains (j : Fin 7) : (ha13_0_3 j).Contains (fullFactor false 13 3 ((j.val:ℝ)/6)) := by + rw [ha13_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_2 j) false 13 2 j (ha13_0_2_contains j) +noncomputable def hk13_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_4 j i k) +lemma hk13_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_4 j i k).Contains (fullFactor false 13 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 4 (power13_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha13_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2712151086516110563320963919,2712151086516110563471221854⟩,⟨1565861159883012429804460172,1565861159883012429943292026⟩⟩,⟨⟨25053778558128198874602771183,25053778558128198880031831851⟩,⟨43394417384257769011871413991,43394417384257769017571106366⟩⟩,⟨⟨(-14658237516),6886814074⟩,⟨253669507901048013624937075238,253669507901048013649711947312⟩⟩,⟨⟨(-400860456930051182173209093812),(-400860456930051181943486382691)⟩,⟨694310678148124304106746919941,694310678148124304339771869914⟩⟩,⟨⟨(-1695094429072569102508363096996),(-1695094429072569101796717697926)⟩,⟨978663224926882768268505785450,978663224926882768969977453173⟩⟩,⟨⟨(-4058712126416768218568798807444),(-4058712126416768217825585553516)⟩,⟨(-470110838333),221425287794⟩⟩] +lemma ha13_0_4_eq (j : Fin 7) : ha13_0_4 j = ((ha13_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha13_0_4_contains (j : Fin 7) : (ha13_0_4 j).Contains (fullFactor false 13 4 ((j.val:ℝ)/6)) := by + rw [ha13_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_3 j) false 13 3 j (ha13_0_3_contains j) +noncomputable def hk13_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_5 j i k) +lemma hk13_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_5 j i k).Contains (fullFactor false 13 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 5 (power13_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha13_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-163976597214335483796643860),(-163976597214335483781583467)⟩,⟨284015797627486289479132533,284015797627486289495771559⟩⟩,⟨⟨(-9088505524079561264290178111),(-9088505524079561263067507718)⟩,⟨5247251110858735480535538267,5247251110858735481689300594⟩⟩,⟨⟨(-79692626246167045124822912952),(-79692626246167045116785987833)⟩,⟨(-4605021130),2163556451⟩⟩,⟨⟨(-290832176770545960481846322405),(-290832176770545960383311312041)⟩,⟨(-167912035547479535452887613807),(-167912035547479535356127108981)⟩⟩,⟨⟨(-512426866294798386998249626957),(-512426866294798386629328815244)⟩,⟨(-887549367585894654851707271033),(-887549367585894654476265454036)⟩⟩,⟨⟨(-139125611491),295379351216⟩,⟨(-2550164039877345444103288454609),(-2550164039877345443628196370637)⟩⟩] +lemma ha13_0_5_eq (j : Fin 7) : ha13_0_5 j = ((ha13_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha13_0_5_contains (j : Fin 7) : (ha13_0_5 j).Contains (fullFactor false 13 5 ((j.val:ℝ)/6)) := by + rw [ha13_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_4 j) false 13 4 j (ha13_0_4_contains j) +noncomputable def hk13_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_6 j i k) +lemma hk13_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_6 j i k).Contains (fullFactor false 13 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 6 (power13_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha13_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24785053981387676527708397),(-24785053981387676526177474)⟩,⟨(-14309657588033580846585295),(-14309657588033580845225478)⟩⟩,⟨⟨(-915818085634149174215788965),(-915818085634149174011504310)⟩,⟨(-1586243454808811297847599101),(-1586243454808811297629153690)⟩⟩,⟨⟨(-566417755),1205591713⟩,⟨(-20863480763352960874230776019),(-20863480763352960872060303420)⟩⟩,⟨⟨58612357480585547129402362039,58612357480585547163364718871⟩,⟨(-101519581107763923070819617166),(-101519581107763923036101263115)⟩⟩,⟨⟨387266468459182445657808176910,387266468459182445822858280773⟩,⟨(-223588399813024700786249247541),(-223588399813024700624565472471)⟩⟩,⟨⟨1335262768854589495754810588670,1335262768854589496007818495534⟩,⟨(-72845999832),154660266634⟩⟩] +lemma ha13_0_6_eq (j : Fin 7) : ha13_0_6 j = ((ha13_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha13_0_6_contains (j : Fin 7) : (ha13_0_6 j).Contains (fullFactor false 13 6 ((j.val:ℝ)/6)) := by + rw [ha13_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_5 j) false 13 5 j (ha13_0_5_contains j) +noncomputable def hk13_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_7 j i k) +lemma hk13_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_7 j i k).Contains (fullFactor false 13 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 7 (power13_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha13_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1070359884617898514065284,1070359884617898514170406⟩,⟨(-1853917702541761442322040),(-1853917702541761442201625)⟩⟩,⟨⟨237301465925345464594895858,237301465925345464628330570⟩,⟨(-137006065231091009818947633),(-137006065231091009787950615)⟩⟩,⟨⟨4681754135318688100459069848,4681754135318688100961025247⟩,⟨(-127103847),270534148⟩⟩,⟨⟨30374587638444219464507038131,30374587638444219474991430689⟩,⟨17536776349579649250663376883,17536776349579649260880711579⟩⟩,⟨⟨83621865985773321380651487654,83621865985773321441387254794⟩,⟨144837320511075112648172688287,144837320511075112710362314294⟩⟩,⟨⟨(-69411365352),32693208274⟩,⟨599264529320792076833157485472,599264529320792076948614686786⟩⟩] +lemma ha13_0_7_eq (j : Fin 7) : ha13_0_7 j = ((ha13_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha13_0_7_contains (j : Fin 7) : (ha13_0_7 j).Contains (fullFactor false 13 7 ((j.val:ℝ)/6)) := by + rw [ha13_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_6 j) false 13 6 j (ha13_0_6_contains j) +noncomputable def hk13_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_8 j i k) +lemma hk13_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_8 j i k).Contains (fullFactor false 13 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 8 (power13_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha13_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨121338629888859693710827,121338629888859693719096⟩,⟨70054890629433514724032,70054890629433514731137⟩⟩,⟨⟨17934052001134979767728496,17934052001134979771843083⟩,⟨31062689251548081589067137,31062689251548081593542607⟩⟩,⟨⟨(-53119256),24956782⟩,⟨919260274839426580196490367,919260274839426580297975176⟩⟩,⟨⟨(-4591117312290554822653534164),(-4591117312290554819964028215)⟩,⟨7952048448396308885848333754,7952048448396308888618453464⟩⟩,⟨⟨(-47397902300335817868496407269),(-47397902300335817847994027539)⟩,⟨27365191652122466679029155986,27365191652122466698991995416⟩⟩,⟨⟨(-235330630358893204566336098388),(-235330630358893204520247080794)⟩,⟨(-27257779434),12838592867⟩⟩] +lemma ha13_0_8_eq (j : Fin 7) : ha13_0_8 j = ((ha13_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha13_0_8_contains (j : Fin 7) : (ha13_0_8 j).Contains (fullFactor false 13 8 ((j.val:ℝ)/6)) := by + rw [ha13_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_7 j) false 13 7 j (ha13_0_7_contains j) +noncomputable def hk13_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_9 j i k) +lemma hk13_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_9 j i k).Contains (fullFactor false 13 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 9 (power13_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha13_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-4075628328693792152710),(-4075628328693792152282)⟩,⟨7059195338064676366337,7059195338064676366841⟩⟩,⟨⟨(-3614308013089114299991696),(-3614308013089114299459446)⟩,⟨2086721704291221581779960,2086721704291221582265357⟩⟩,⟨⟨(-160441184787359821882855613),(-160441184787359821864632471)⟩,⟨(-9271060),4355781⟩⟩,⟨⟨(-1850525702701626521752024180),(-1850525702701626521101497644)⟩,⟨(-1068401512597105450366932560),(-1068401512597105449737655277)⟩⟩,⟨⟨(-7960211579480062800337771722),(-7960211579480062794505478979)⟩,⟨(-13787490894657571031742051651),(-13787490894657571025734264190)⟩⟩,⟨⟨(-4481514338),9514759959⟩,⟨(-82145886611128228807531739924),(-82145886611128228791182159324)⟩⟩] +lemma ha13_0_9_eq (j : Fin 7) : ha13_0_9 j = ((ha13_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha13_0_9_contains (j : Fin 7) : (ha13_0_9 j).Contains (fullFactor false 13 9 ((j.val:ℝ)/6)) := by + rw [ha13_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_8 j) false 13 8 j (ha13_0_8_contains j) +noncomputable def hk13_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_10 j i k) +lemma hk13_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_10 j i k).Contains (fullFactor false 13 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 10 (power13_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha13_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-369618603571988403206),(-369618603571988403177)⟩,⟨(-213399400269781075741),(-213399400269781075717)⟩⟩,⟨⟨(-218520985876255821566648),(-218520985876255821515121)⟩,⟨(-378489450057716124899969),(-378489450057716124843026)⟩⟩,⟨⟨(-684205),1456295⟩,⟨(-25202042373060605482713424),(-25202042373060605479770718)⟩⟩,⟨⟨223765489537285961203485860,223765489537285961335993654⟩,⟨(-387573196859101311930297906),(-387573196859101311792818262)⟩⟩,⟨⟨3609556675507699249189190819,3609556675507699250773515475⟩,⟨(-2083978518259580818323974134),(-2083978518259580816790449953)⟩⟩,⟨⟨25806891390014060010182621565,25806891390014060015401139682⟩,⟨(-1407909253),2989149999⟩⟩] +lemma ha13_0_10_eq (j : Fin 7) : ha13_0_10 j = ((ha13_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha13_0_10_contains (j : Fin 7) : (ha13_0_10 j).Contains (fullFactor false 13 10 ((j.val:ℝ)/6)) := by + rw [ha13_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_9 j) false 13 9 j (ha13_0_9_contains j) +noncomputable def hk13_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_11 j i k) +lemma hk13_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_11 j i k).Contains (fullFactor false 13 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 11 (power13_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha13_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨10157787699515332860,10157787699515332862⟩,⟨(-17593804388058740566),(-17593804388058740563)⟩⟩,⟨⟨36032111386744300673908,36032111386744300679444⟩,⟨(-20803149208607401700482),(-20803149208607401695509)⟩⟩,⟨⟨3598843235212085340272399,3598843235212085340704073⟩,⟨(-97705),207959⟩⟩,⟨⟨73793764120052327771321489,73793764120052327797732446⟩,⟨42604849579227958667072566,42604849579227958692437608⟩⟩,⟨⟨495985727515397112125303562,495985727515397112491860236⟩,⟨859072479885680691457498135,859072479885680691837301035⟩⟩,⟨⟨(-853699244),402097943⟩,⟨7370430945714350776562973859,7370430945714350778076839959⟩⟩] +lemma ha13_0_11_eq (j : Fin 7) : ha13_0_11 j = ((ha13_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha13_0_11_contains (j : Fin 7) : (ha13_0_11 j).Contains (fullFactor false 13 11 ((j.val:ℝ)/6)) := by + rw [ha13_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_10 j) false 13 10 j (ha13_0_10_contains j) +noncomputable def hk13_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_12 j i k) +lemma hk13_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_12 j i k).Contains (fullFactor false 13 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 12 (power13_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha13_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨767674536308627877,767674536308627878⟩,⟨443217100187807442,443217100187807443⟩⟩,⟨⟨1815417242369259285276,1815417242369259285716⟩,⟨3144394900720139784725,3144394900720139785219⟩⟩,⟨⟨(-27222),12790⟩,⟨471087477881817150342265,471087477881817150400272⟩⟩,⟨⟨(-7435949024744486036011642),(-7435949024744486031560937)⟩,⟨12879441513349692556691692,12879441513349692561342271⟩⟩,⟨⟨(-187420541090973602873073025),(-187420541090973602789616307)⟩,⟨108207299850538926409133060,108207299850538926489447757⟩⟩,⟨⟨(-1929574309403923048121950467),(-1929574309403923047719479222)⟩,⟨(-223497940),105268996⟩⟩] +lemma ha13_0_12_eq (j : Fin 7) : ha13_0_12 j = ((ha13_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha13_0_12_contains (j : Fin 7) : (ha13_0_12 j).Contains (fullFactor false 13 12 ((j.val:ℝ)/6)) := by + rw [ha13_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_11 j) false 13 11 j (ha13_0_11_contains j) +noncomputable def hk13_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_13 j i k) +lemma hk13_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_13 j i k).Contains (fullFactor false 13 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 13 (power13_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha13_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-17851379306351119),(-17851379306351118)⟩,⟨30919495943783799,30919495943783800⟩⟩,⟨⟨(-253292510771476882306),(-253292510771476882264)⟩,⟨146238499277628361492,146238499277628361529⟩⟩,⟨⟨(-56921729219679268121903),(-56921729219679268114712)⟩,⟨(-3290),1546⟩⟩,⟨⟨(-2074972248239938620018724),(-2074972248239938619262876)⟩,⟨(-1197985786082331537917803),(-1197985786082331537196948)⟩⟩,⟨⟨(-21791234504823142522737171),(-21791234504823142506493700)⟩,⟨(-37743525322001707903130189),(-37743525322001707886203187)⟩⟩,⟨⟨(-25439409),54010730⟩,⟨(-466302805767612564474549122),(-466302805767612564375803241)⟩⟩] +lemma ha13_0_13_eq (j : Fin 7) : ha13_0_13 j = ((ha13_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha13_0_13_contains (j : Fin 7) : (ha13_0_13 j).Contains (fullFactor false 13 13 ((j.val:ℝ)/6)) := by + rw [ha13_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_12 j) false 13 12 j (ha13_0_12_contains j) +noncomputable def hk13_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_14 j i k) +lemma hk13_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_14 j i k).Contains (fullFactor false 13 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 14 (power13_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha13_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1156386444162984),(-1156386444162983)⟩,⟨(-667640024824733),(-667640024824732)⟩⟩,⟨⟨(-10938614166728417761),(-10938614166728417757)⟩,⟨(-18946235501166317753),(-18946235501166317749)⟩⟩,⟨⟨(-174),370⟩,⟨(-6386603083791852241571),(-6386603083791852240743)⟩⟩,⟨⟨179218254507678396512889,179218254507678396621300⟩,⟨(-310415122451108950087933),(-310415122451108949973870)⟩⟩,⟨⟨7058022730486958379720743,7058022730486958382908553⟩,⟨(-4074951323393142879920348),(-4074951323393142876869854)⟩⟩,⟨⟨104638104924845707107869826,104638104924845707130361424⟩,⟨(-5708591),12119980⟩⟩] +lemma ha13_0_14_eq (j : Fin 7) : ha13_0_14 j = ((ha13_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha13_0_14_contains (j : Fin 7) : (ha13_0_14 j).Contains (fullFactor false 13 14 ((j.val:ℝ)/6)) := by + rw [ha13_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_13 j) false 13 13 j (ha13_0_13_contains j) +noncomputable def hk13_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_15 j i k) +lemma hk13_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_15 j i k).Contains (fullFactor false 13 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 15 (power13_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha13_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23305033302576,23305033302577⟩,⟨(-40365501752148),(-40365501752147)⟩⟩,⟨⟨1322696761414360852,1322696761414360853⟩,⟨(-763659331258827444),(-763659331258827443)⟩⟩,⟨⟨668803510981146723210,668803510981146723300⟩,⟨(-19),39⟩⟩,⟨⟨43342127478025776412348,43342127478025776428414⟩,⟨25023588966689257657286,25023588966689257672504⟩⟩,⟨⟨711213174517105746119140,711213174517105746653816⟩,⟨1231857353275977868965870,1231857353275977869526170⟩⟩,⟨⟨(-2538403),1195605⟩,⟨21915353447830215825241049,21915353447830215830021438⟩⟩] +lemma ha13_0_15_eq (j : Fin 7) : ha13_0_15 j = ((ha13_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha13_0_15_contains (j : Fin 7) : (ha13_0_15 j).Contains (fullFactor false 13 15 ((j.val:ℝ)/6)) := by + rw [ha13_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_14 j) false 13 14 j (ha13_0_14_contains j) +noncomputable def hk13_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_16 j i k) +lemma hk13_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_16 j i k).Contains (fullFactor false 13 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 16 (power13_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha13_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1320957955864,1320957955865⟩,⟨762655431406,762655431407⟩⟩,⟨⟨49981386352667221,49981386352667222⟩,⟨86570300595549323,86570300595549324⟩⟩,⟨⟨(-4),2⟩,⟨65659631149794723618,65659631149794723628⟩⟩,⟨⟨(-3275580136008399050533),(-3275580136008399048529)⟩,⟨5673471219829920493694,5673471219829920495816⟩⟩,⟨⟨(-201562188089707223646653),(-201562188089707223554332)⟩,⟨116371983552042445638845,116371983552042445726703⟩⟩,⟨⟨(-4303069587032947007825632),(-4303069587032947006873307)⟩,⟨(-498415),234757⟩⟩] +lemma ha13_0_16_eq (j : Fin 7) : ha13_0_16 j = ((ha13_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha13_0_16_contains (j : Fin 7) : (ha13_0_16 j).Contains (fullFactor false 13 16 ((j.val:ℝ)/6)) := by + rw [ha13_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_15 j) false 13 15 j (ha13_0_15_contains j) +noncomputable def hk13_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_17 j i k) +lemma hk13_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_17 j i k).Contains (fullFactor false 13 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 17 (power13_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha13_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23489732359),(-23489732358)⟩,⟨40685409900,40685409901⟩⟩,⟨⟨(-5332718046471331),(-5332718046471330)⟩,⟨3078846199642597,3078846199642598⟩⟩,⟨⟨(-6066935731106195668),(-6066935731106195666)⟩,⟨(-1),1⟩⟩,⟨⟨(-698970019787090239347),(-698970019787090239082)⟩,⟨(-403550529079554596853),(-403550529079554596604)⟩⟩,⟨⟨(-17921243559351411749290),(-17921243559351411735701)⟩,⟨(-31040504379613153646857),(-31040504379613153632540)⟩⟩,⟨⟨(-43383),92107⟩,⟨(-795205400147551278577722),(-795205400147551278399201)⟩⟩] +lemma ha13_0_17_eq (j : Fin 7) : ha13_0_17 j = ((ha13_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha13_0_17_contains (j : Fin 7) : (ha13_0_17 j).Contains (fullFactor false 13 17 ((j.val:ℝ)/6)) := by + rw [ha13_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_16 j) false 13 16 j (ha13_0_16_contains j) +noncomputable def hk13_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_18 j i k) +lemma hk13_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_18 j i k).Contains (fullFactor false 13 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 18 (power13_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha13_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1183490601),(-1183490600)⟩,⟨(-683288617),(-683288616)⟩⟩,⟨⟨(-179120011154260),(-179120011154259)⟩,⟨(-310244959971483),(-310244959971482)⟩⟩,⟨⟨(-1),1⟩,⟨(-529440020073462377),(-529440020073462376)⟩⟩,⟨⟨46955236204022331356,46955236204022331386⟩,⟨(-81328854786764263398),(-81328854786764263366)⟩⟩,⟨⟨4514658357533078057205,4514658357533078059302⟩,⟨(-2606539218020916336715),(-2606539218020916334729)⟩⟩,⟨⟨138789524622137721130755,138789524622137721162355⟩,⟨(-7572),16076⟩⟩] +lemma ha13_0_18_eq (j : Fin 7) : ha13_0_18 j = ((ha13_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha13_0_18_contains (j : Fin 7) : (ha13_0_18 j).Contains (fullFactor false 13 18 ((j.val:ℝ)/6)) := by + rw [ha13_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_17 j) false 13 17 j (ha13_0_17_contains j) +noncomputable def hk13_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_19 j i k) +lemma hk13_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_19 j i k).Contains (fullFactor false 13 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 19 (power13_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha13_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨18829951,18829952⟩,⟨(-32614434),(-32614433)⟩⟩,⟨⟨17099355913327,17099355913328⟩,⟨(-9872317739529),(-9872317739528)⟩⟩,⟨⟨43770654673137422,43770654673137423⟩,⟨(-1),1⟩⟩,⟨⟨8964987113086656143,8964987113086656147⟩,⟨5175937723022106879,5175937723022106883⟩⟩,⟨⟨359152827132815577372,359152827132815577647⟩,⟨622070944276038605360,622070944276038605652⟩⟩,⟨⟨(-2659),1253⟩,⟨22948428997269873107881,22948428997269873113180⟩⟩] +lemma ha13_0_19_eq (j : Fin 7) : ha13_0_19 j = ((ha13_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha13_0_19_contains (j : Fin 7) : (ha13_0_19 j).Contains (fullFactor false 13 19 ((j.val:ℝ)/6)) := by + rw [ha13_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_18 j) false 13 18 j (ha13_0_18_contains j) +noncomputable def hk13_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_20 j i k) +lemma hk13_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_20 j i k).Contains (fullFactor false 13 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 20 (power13_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha13_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨853843,853844⟩,⟨492966,492967⟩⟩,⟨⟨516913348073,516913348074⟩,⟨895320181973,895320181974⟩⟩,⟨⟨(-1),1⟩,⟨3437739179098606,3437739179098608⟩⟩,⟨⟨(-542022930869484434),(-542022930869484433)⟩,⟨938811255133340262,938811255133340263⟩⟩,⟨⟨(-81428896189552855177),(-81428896189552855138)⟩,⟨47012995134852432587,47012995134852432624⟩⟩,⟨⟨(-3604730797462500934336),(-3604730797462500933491)⟩,⟨(-418),197⟩⟩] +lemma ha13_0_20_eq (j : Fin 7) : ha13_0_20 j = ((ha13_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha13_0_20_contains (j : Fin 7) : (ha13_0_20 j).Contains (fullFactor false 13 20 ((j.val:ℝ)/6)) := by + rw [ha13_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_19 j) false 13 19 j (ha13_0_19_contains j) +noncomputable def hk13_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_21 j i k) +lemma hk13_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_21 j i k).Contains (fullFactor false 13 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 21 (power13_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha13_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-12292),(-12291)⟩,⟨21289,21290⟩⟩,⟨⟨(-44646528672),(-44646528671)⟩,⟨25776685346,25776685347⟩⟩,⟨⟨(-257142289286048),(-257142289286047)⟩,⟨(-1),1⟩⟩,⟨⟨(-93630556896327456),(-93630556896327455)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨(-5860939688051789414),(-5860939688051789408)⟩,⟨(-10151445319802585618),(-10151445319802585612)⟩⟩,⟨⟨(-30),63⟩,⟨(-539266466260812849008),(-539266466260812848879)⟩⟩] +lemma ha13_0_21_eq (j : Fin 7) : ha13_0_21 j = ((ha13_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha13_0_21_contains (j : Fin 7) : (ha13_0_21 j).Contains (fullFactor false 13 21 ((j.val:ℝ)/6)) := by + rw [ha13_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_20 j) false 13 20 j (ha13_0_20_contains j) +noncomputable def hk13_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_22 j i k) +lemma hk13_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_22 j i k).Contains (fullFactor false 13 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 22 (power13_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha13_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-507),(-506)⟩,⟨(-293),(-292)⟩⟩,⟨⟨(-1226967354),(-1226967353)⟩,⟨(-2125169796),(-2125169795)⟩⟩,⟨⟨(-1),1⟩,⟨(-18359916521553),(-18359916521552)⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨1208019168182208037,1208019168182208038⟩,⟨(-697450191936225611),(-697450191936225609)⟩⟩,⟨⟨77007071306013533789,77007071306013533809⟩,⟨(-5),9⟩⟩] +lemma ha13_0_22_eq (j : Fin 7) : ha13_0_22 j = ((ha13_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha13_0_22_contains (j : Fin 7) : (ha13_0_22 j).Contains (fullFactor false 13 22 ((j.val:ℝ)/6)) := by + rw [ha13_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_21 j) false 13 21 j (ha13_0_21_contains j) +noncomputable def hk13_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_23 j i k) +lemma hk13_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_23 j i k).Contains (fullFactor false 13 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 23 (power13_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha13_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨6,7⟩,⟨(-12),(-11)⟩⟩,⟨⟨96759678,96759679⟩,⟨(-55864227),(-55864226)⟩⟩,⟨⟨1253899540535,1253899540536⟩,⟨(-1),1⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨79387840551870928,79387840551870929⟩,⟨137503773339017306,137503773339017308⟩⟩,⟨⟨(-2),1⟩,⟨10518471716932064453,10518471716932064457⟩⟩] +lemma ha13_0_23_eq (j : Fin 7) : ha13_0_23 j = ((ha13_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha13_0_23_contains (j : Fin 7) : (ha13_0_23 j).Contains (fullFactor false 13 23 ((j.val:ℝ)/6)) := by + rw [ha13_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_22 j) false 13 22 j (ha13_0_22_contains j) +noncomputable def hk13_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_24 j i k) +lemma hk13_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_24 j i k).Contains (fullFactor false 13 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 24 (power13_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha13_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨2437536,2437537⟩,⟨4221937,4221938⟩⟩,⟨⟨(-1),1⟩,⟨82067533018,82067533019⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-14999334866761558),(-14999334866761557)⟩,⟨8659870022990124,8659870022990125⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha13_0_24_eq (j : Fin 7) : ha13_0_24 j = ((ha13_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha13_0_24_contains (j : Fin 7) : (ha13_0_24 j).Contains (fullFactor false 13 24 ((j.val:ℝ)/6)) := by + rw [ha13_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_23 j) false 13 23 j (ha13_0_23_contains j) +noncomputable def hk13_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_25 j i k) +lemma hk13_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_25 j i k).Contains (fullFactor false 13 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 25 (power13_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha13_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-176849),(-176848)⟩,⟨102103,102104⟩⟩,⟨⟨(-5156455177),(-5156455176)⟩,⟨(-1),1⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨(-906859468175609),(-906859468175608)⟩,⟨(-1570726674205046),(-1570726674205044)⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha13_0_25_eq (j : Fin 7) : ha13_0_25 j = ((ha13_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha13_0_25_contains (j : Fin 7) : (ha13_0_25 j).Contains (fullFactor false 13 25 ((j.val:ℝ)/6)) := by + rw [ha13_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_24 j) false 13 24 j (ha13_0_24_contains j) +noncomputable def hk13_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_26 j i k) +lemma hk13_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_26 j i k).Contains (fullFactor false 13 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 26 (power13_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha13_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-4113),(-4112)⟩,⟨(-7123),(-7122)⟩⟩,⟨⟨(-1),1⟩,⟨(-311528495),(-311528494)⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨158159723733336,158159723733337⟩,⟨(-91313559072399),(-91313559072398)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha13_0_26_eq (j : Fin 7) : ha13_0_26 j = ((ha13_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha13_0_26_contains (j : Fin 7) : (ha13_0_26 j).Contains (fullFactor false 13 26 ((j.val:ℝ)/6)) := by + rw [ha13_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_25 j) false 13 25 j (ha13_0_25_contains j) +noncomputable def hk13_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_27 j i k) +lemma hk13_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_27 j i k).Contains (fullFactor false 13 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 27 (power13_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha13_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨276,277⟩,⟨(-160),(-159)⟩⟩,⟨⟨18123993,18123994⟩,⟨(-1),1⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨8854012541820,8854012541821⟩,⟨15335599573285,15335599573286⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha13_0_27_eq (j : Fin 7) : ha13_0_27 j = ((ha13_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha13_0_27_contains (j : Fin 7) : (ha13_0_27 j).Contains (fullFactor false 13 27 ((j.val:ℝ)/6)) := by + rw [ha13_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_26 j) false 13 26 j (ha13_0_26_contains j) +noncomputable def hk13_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_28 j i k) +lemma hk13_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_28 j i k).Contains (fullFactor false 13 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 28 (power13_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha13_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨5,6⟩,⟨10,11⟩⟩,⟨⟨(-1),1⟩,⟨1016753,1016754⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-1433875207079),(-1433875207078)⟩,⟨827848236790,827848236791⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha13_0_28_eq (j : Fin 7) : ha13_0_28 j = ((ha13_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha13_0_28_contains (j : Fin 7) : (ha13_0_28 j).Contains (fullFactor false 13 28 ((j.val:ℝ)/6)) := by + rw [ha13_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_27 j) false 13 27 j (ha13_0_27_contains j) +noncomputable def hk13_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_29 j i k) +lemma hk13_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_29 j i k).Contains (fullFactor false 13 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 29 (power13_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha13_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-55073),(-55072)⟩,⟨(-1),1⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨(-74734538477),(-74734538476)⟩,⟨(-129444017722),(-129444017721)⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha13_0_29_eq (j : Fin 7) : ha13_0_29 j = ((ha13_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha13_0_29_contains (j : Fin 7) : (ha13_0_29 j).Contains (fullFactor false 13 29 ((j.val:ℝ)/6)) := by + rw [ha13_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_28 j) false 13 28 j (ha13_0_28_contains j) +noncomputable def hk13_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power13 j i k).conj.mul (mpower0_30 j i k) +lemma hk13_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk13_0_30 j i k).Contains (fullFactor false 13 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power13 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 30 (power13_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha13_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨(-2884),(-2883)⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨11296121531,11296121532⟩,⟨(-6521818807),(-6521818806)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha13_0_30_eq (j : Fin 7) : ha13_0_30 j = ((ha13_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha13_0_30_contains (j : Fin 7) : (ha13_0_30 j).Contains (fullFactor false 13 30 ((j.val:ℝ)/6)) := by + rw [ha13_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_0_29 j) false 13 29 j (ha13_0_29_contains j) +noncomputable def hk13_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_0 j i k) +lemma hk13_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_0 j i k).Contains (fullFactor true 13 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 0 (kernel13_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha13_1_0 : Fin 7 → CBox := ![⟨⟨0,3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),0⟩,⟨(-2),3⟩⟩,⟨⟨(-341),(-337)⟩,⟨98,102⟩⟩,⟨⟨(-169976153021903),(-169976153021900)⟩,⟨(-84606803526621),(-84606803526617)⟩⟩,⟨⟨(-3263693326028840015143),(-3263693326028840004989)⟩,⟨(-2537037848528971869479),(-2537037848528971859297)⟩⟩,⟨⟨(-19618607417581830024810844),(-19618607417581829855857605)⟩,⟨(-130432011910631655003953346),(-130432011910631654833571214)⟩⟩,⟨⟨(-18541242464926204931798182214),(-18541242464926204806447611936)⟩,⟨(-91487929281433214680992385330),(-91487929281433214554185512444)⟩⟩] +lemma ha13_1_0_eq (j : Fin 7) : ha13_1_0 j = atomKernel13_0 j := by fin_cases j <;> decide +kernel +lemma ha13_1_0_contains (j : Fin 7) : (ha13_1_0 j).Contains (fullFactor true 13 0 ((j.val:ℝ)/6)) := by + rw [ha13_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel13_0_contains j +noncomputable def hk13_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_1 j i k) +lemma hk13_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_1 j i k).Contains (fullFactor true 13 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 1 (kernel13_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha13_1_1 : Fin 7 → CBox := ![⟨⟨(-28),0⟩,⟨(-28),28⟩⟩,⟨⟨(-8),42⟩,⟨(-23),31⟩⟩,⟨⟨2163,2205⟩,⟨1233,1274⟩⟩,⟨⟨48835088491071,48835088491101⟩,⟨1107722107138669,1107722107138696⟩⟩,⟨⟨(-6775428697773202029332),(-6775428697773201966850)⟩,⟨18922744590791917501633,18922744590791917564035⟩⟩,⟨⟨(-519035897525465939974967179),(-519035897525465939158171005)⟩,⟨172011742142599044405582776,172011742142599045216355299⟩⟩,⟨⟨(-326883743568561696968067370144),(-326883743568561696485564285752)⟩,⟨84131904661401513556648150900,84131904661401514033371076133⟩⟩] +lemma ha13_1_1_eq (j : Fin 7) : ha13_1_1 j = ((ha13_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha13_1_1_contains (j : Fin 7) : (ha13_1_1 j).Contains (fullFactor true 13 1 ((j.val:ℝ)/6)) := by + rw [ha13_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_0 j) true 13 0 j (ha13_1_0_contains j) +noncomputable def hk13_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_2 j i k) +lemma hk13_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_2 j i k).Contains (fullFactor true 13 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 2 (kernel13_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha13_1_2 : Fin 7 → CBox := ![⟨⟨0,130⟩,⟨(-130),130⟩⟩,⟨⟨(-204),89⟩,⟨(-197),104⟩⟩,⟨⟨(-2254),(-2044)⟩,⟨(-8815),(-8605)⟩⟩,⟨⟨2760176405530330,2760176405530442⟩,⟨(-1692151545105966),(-1692151545105850)⟩⟩,⟨⟨48845032599524479814526,48845032599524480006172⟩,⟨1313852097947150019291,1313852097947150211002⟩⟩,⟨⟨534139242887687895050152966,534139242887687896995612902⟩,⟨999633279784417540395057059,999633279784417542352567292⟩⟩,⟨⟨182591277655268899504498524374,182591277655268900411109789811⟩,⟨582293989853362588239181519142,582293989853362589157008836243⟩⟩] +lemma ha13_1_2_eq (j : Fin 7) : ha13_1_2 j = ((ha13_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha13_1_2_contains (j : Fin 7) : (ha13_1_2 j).Contains (fullFactor true 13 2 ((j.val:ℝ)/6)) := by + rw [ha13_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_1 j) true 13 1 j (ha13_1_1_contains j) +noncomputable def hk13_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_3 j i k) +lemma hk13_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_3 j i k).Contains (fullFactor true 13 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 3 (kernel13_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha13_1_3 : Fin 7 → CBox := ![⟨⟨(-400),0⟩,⟨(-400),400⟩⟩,⟨⟨(-472),651⟩,⟨(-377),757⟩⟩,⟨⟨(-11779),(-11073)⟩,⟨17631,18337⟩⟩,⟨⟨(-5485083315752250),(-5485083315751946)⟩,⟨(-3103662731815189),(-3103662731814887)⟩⟩,⟨⟨(-22649217672109940303763),(-22649217672109939911639)⟩,⟨(-75884825723250568401803),(-75884825723250568009590)⟩⟩,⟨⟨1235866972863728180200608917,1235866972863728183327743131⟩,⟨(-962054562367831363678094400),(-962054562367831360566210722)⟩⟩,⟨⟨689464327622705912420089806480,689464327622705913583869122641⟩,⟨(-256227051176441857486368010911),(-256227051176441856336838948166)⟩⟩] +lemma ha13_1_3_eq (j : Fin 7) : ha13_1_3 j = ((ha13_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha13_1_3_contains (j : Fin 7) : (ha13_1_3 j).Contains (fullFactor true 13 3 ((j.val:ℝ)/6)) := by + rw [ha13_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_2 j) true 13 2 j (ha13_1_2_contains j) +noncomputable def hk13_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_4 j i k) +lemma hk13_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_4 j i k).Contains (fullFactor true 13 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 4 (kernel13_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha13_1_4 : Fin 7 → CBox := ![⟨⟨0,922⟩,⟨(-922),922⟩⟩,⟨⟨(-1599),1609⟩,⟨(-2056),1162⟩⟩,⟨⟨36330,38109⟩,⟨(-8314),(-6535)⟩⟩,⟨⟨(-82915792964556),(-82915792963955)⟩,⟨9200668067424293,9200668067424895⟩⟩,⟨⟨(-79066359195910865669898),(-79066359195910865068034)⟩,⟨54907925389668894341541,54907925389668894943204⟩⟩,⟨⟨(-1200176256633177587039657055),(-1200176256633177583306981164)⟩,⟨(-1092825643537363590870776926),(-1092825643537363587124473860)⟩⟩,⟨⟨(-263676395715119290114324209685),(-263676395715119289021108370840)⟩,⟨(-610390256737678504310629280639),(-610390256737678503204037689130)⟩⟩] +lemma ha13_1_4_eq (j : Fin 7) : ha13_1_4 j = ((ha13_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha13_1_4_contains (j : Fin 7) : (ha13_1_4 j).Contains (fullFactor true 13 4 ((j.val:ℝ)/6)) := by + rw [ha13_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_3 j) true 13 3 j (ha13_1_3_contains j) +noncomputable def hk13_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_5 j i k) +lemma hk13_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_5 j i k).Contains (fullFactor true 13 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 5 (kernel13_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha13_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),0⟩,⟨(-1700),1700⟩⟩,⟨⟨(-3996),3316⟩,⟨(-2979),4342⟩⟩,⟨⟨(-46090),(-42505)⟩,⟨(-32819),(-29234)⟩⟩,⟨⟨9446849224275024,9446849224275980⟩,⟨(-5122843747512184),(-5122843747511229)⟩⟩,⟨⟨74697547998916742219019,74697547998916742957601⟩,⟨56416129207872985797256,56416129207872986536010⟩⟩,⟨⟨(-723845217883143919567514799),(-723845217883143915977394569)⟩,⟨1134551582408423153079996947,1134551582408423156661133567⟩⟩,⟨⟨(-430924741919376684124963183671),(-430924741919376683283286896587)⟩,⟨213351471291017857680766176774,213351471291017858512529150510⟩⟩] +lemma ha13_1_5_eq (j : Fin 7) : ha13_1_5 j = ((ha13_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha13_1_5_contains (j : Fin 7) : (ha13_1_5 j).Contains (fullFactor true 13 5 ((j.val:ℝ)/6)) := by + rw [ha13_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_4 j) true 13 4 j (ha13_1_4_contains j) +noncomputable def hk13_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_6 j i k) +lemma hk13_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_6 j i k).Contains (fullFactor true 13 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 6 (kernel13_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha13_1_6 : Fin 7 → CBox := ![⟨⟨0,2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-6083),7797⟩,⟨(-7603),6283⟩⟩,⟨⟨6708,12728⟩,⟨60473,66493⟩⟩,⟨⟨(-8817231587687975),(-8817231587686710)⟩,⟨(-5626595667738985),(-5626595667737719)⟩⟩,⟨⟨24574749301001984059298,24574749301001984814873⟩,⟨(-71765401733179323166362),(-71765401733179322410847)⟩⟩,⟨⟨857464486341701723623671140,857464486341701726486157703⟩,⟨359675267804115930754305571,359675267804115933621117712⟩⟩,⟨⟨141888983720414355336479928680,141888983720414355863858597932⟩,⟨252669790400821602609904231353,252669790400821603143333996427⟩⟩] +lemma ha13_1_6_eq (j : Fin 7) : ha13_1_6 j = ((ha13_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha13_1_6_contains (j : Fin 7) : (ha13_1_6 j).Contains (fullFactor true 13 6 ((j.val:ℝ)/6)) := by + rw [ha13_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_5 j) true 13 5 j (ha13_1_5_contains j) +noncomputable def hk13_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_7 j i k) +lemma hk13_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_7 j i k).Contains (fullFactor true 13 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 7 (kernel13_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha13_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),0⟩,⟨(-3439),3439⟩⟩,⟨⟨(-12578),9999⟩,⟨(-11023),11558⟩⟩,⟨⟨35539,44204⟩,⟨(-56134),(-47469)⟩⟩,⟨⟨(-541367833933428),(-541367833931992)⟩,⟨8709155692288295,8709155692289731⟩⟩,⟨⟨(-52684983672169639510038),(-52684983672169638847664)⟩,⟨(-683558773004893116034),(-683558773004892453700)⟩⟩,⟨⟨123637627127261647650643986,123637627127261649612706772⟩,⟨(-536616767428347176290016710),(-536616767428347174329277856)⟩⟩,⟨⟨126536317419616170666598825001,126536317419616170956348180815⟩,⟨(-79972781258022134335226993193),(-79972781258022134048609288638)⟩⟩] +lemma ha13_1_7_eq (j : Fin 7) : ha13_1_7 j = ((ha13_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha13_1_7_contains (j : Fin 7) : (ha13_1_7 j).Contains (fullFactor true 13 7 ((j.val:ℝ)/6)) := by + rw [ha13_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_6 j) true 13 6 j (ha13_1_6_contains j) +noncomputable def hk13_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_8 j i k) +lemma hk13_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_8 j i k).Contains (fullFactor true 13 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 8 (kernel13_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha13_1_8 : Fin 7 → CBox := ![⟨⟨0,3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-14705),17425⟩,⟨(-15723),16409⟩⟩,⟨⟨(-63343),(-52431)⟩,⟨757,11669⟩⟩,⟨⟨5752609560200473,5752609560201899⟩,⟨(-2735167889476390),(-2735167889474964)⟩⟩,⟨⟨9584812002312223512470,9584812002312224020468⟩,⟨30554986322611210427193,30554986322611210935270⟩⟩,⟨⟨(-284914619713582947122491795),(-284914619713582945947573711)⟩,⟨(-15894302006669254500263098),(-15894302006669253325341050)⟩⟩,⟨⟨(-39067993028544540536854133596),(-39067993028544540400555875981)⟩,⟨(-55238647458222753096063561489),(-55238647458222752958361826929)⟩⟩] +lemma ha13_1_8_eq (j : Fin 7) : ha13_1_8 j = ((ha13_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha13_1_8_contains (j : Fin 7) : (ha13_1_8 j).Contains (fullFactor true 13 8 ((j.val:ℝ)/6)) := by + rw [ha13_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_7 j) true 13 7 j (ha13_1_7_contains j) +noncomputable def hk13_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_9 j i k) +lemma hk13_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_9 j i k).Contains (fullFactor true 13 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 9 (kernel13_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha13_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),0⟩,⟨(-4057),4057⟩⟩,⟨⟨(-21338),19305⟩,⟨(-21176),19468⟩⟩,⟨⟨29116,41330⟩,⟨23619,35834⟩⟩,⟨⟨(-3361313195115143),(-3361313195113884)⟩,⟨(-2405050399016979),(-2405050399015720)⟩⟩,⟨⟨14071033328540994924106,14071033328540995270507⟩,⟨(-10064824855674054380362),(-10064824855674054034011)⟩⟩,⟨⟨15081541418509049339926184,15081541418509049965287356⟩,⟨130572778242652870485762055,130572778242652871111443428⟩⟩,⟨⟨(-21348029580429440803236481140),(-21348029580429440745070258028)⟩,⟨16827542911816119928619651535,16827542911816119986232467915⟩⟩] +lemma ha13_1_9_eq (j : Fin 7) : ha13_1_9 j = ((ha13_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha13_1_9_contains (j : Fin 7) : (ha13_1_9 j).Contains (fullFactor true 13 9 ((j.val:ℝ)/6)) := by + rw [ha13_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_8 j) true 13 8 j (ha13_1_8_contains j) +noncomputable def hk13_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_10 j i k) +lemma hk13_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_10 j i k).Contains (fullFactor true 13 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 10 (kernel13_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha13_1_10 : Fin 7 → CBox := ![⟨⟨0,3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-22673),23597⟩,⟨(-22102),24168⟩⟩,⟨⟨(-8185),4120⟩,⟨(-38929),(-26624)⟩⟩,⟨⟨(-277319820423234),(-277319820422234)⟩,⟨2397679408232195,2397679408233195⟩⟩,⟨⟨(-6782201330058256009673),(-6782201330058255797144)⟩,⟨(-4975622463286817479620),(-4975622463286817267072)⟩⟩,⟨⟨52280644810052441823982991,52280644810052442123810035⟩,⟨(-15357562682695983564426029),(-15357562682695983264831537)⟩⟩,⟨⟨6477328673614970815493547274,6477328673614970837410509943⟩,⟨7392852651566533800736117655,7392852651566533822847451204⟩⟩] +lemma ha13_1_10_eq (j : Fin 7) : ha13_1_10 j = ((ha13_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha13_1_10_contains (j : Fin 7) : (ha13_1_10 j).Contains (fullFactor true 13 10 ((j.val:ℝ)/6)) := by + rw [ha13_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_9 j) true 13 9 j (ha13_1_9_contains j) +noncomputable def hk13_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_11 j i k) +lemma hk13_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_11 j i k).Contains (fullFactor true 13 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 11 (kernel13_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha13_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),0⟩,⟨(-3133),3133⟩⟩,⟨⟨(-23916),23970⟩,⟨(-24819),23067⟩⟩,⟨⟨(-20071),(-8801)⟩,⟨9987,21257⟩⟩,⟨⟨1184802833555247,1184802833555970⟩,⟨(-488070484188893),(-488070484188170)⟩⟩,⟨⟨(-1155442677424044368538),(-1155442677424044249980)⟩,⟨3533958045235689272388,3533958045235689390943⟩⟩,⟨⟨(-9051064678853364685811396),(-9051064678853364555318777)⟩,⟨(-18433227488874013452298251),(-18433227488874013321698030)⟩⟩,⟨⟨2316319426759211056685814532,2316319426759211064326620861⟩,⟨(-2252543930829199664174145176),(-2252543930829199656594734910)⟩⟩] +lemma ha13_1_11_eq (j : Fin 7) : ha13_1_11 j = ((ha13_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha13_1_11_contains (j : Fin 7) : (ha13_1_11 j).Contains (fullFactor true 13 11 ((j.val:ℝ)/6)) := by + rw [ha13_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_10 j) true 13 10 j (ha13_1_10_contains j) +noncomputable def hk13_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_12 j i k) +lemma hk13_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_12 j i k).Contains (fullFactor true 13 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 12 (kernel13_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha13_1_12 : Fin 7 → CBox := ![⟨⟨0,2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-23003),22426⟩,⟨(-22163),23266⟩⟩,⟨⟨7897,17359⟩,⟨(-4945),4517⟩⟩,⟨⟨(-487181524646578),(-487181524646098)⟩,⟨(-389256009092657),(-389256009092178)⟩⟩,⟨⟨1506479625916169508828,1506479625916169569449⟩,⟨(-1422787817008995771),(-1422787817008935151)⟩⟩,⟨⟨(-5744206732736001736064142),(-5744206732736001683921877)⟩,⟨4163241137144289910132698,4163241137144289962236232⟩⟩,⟨⟨(-714078154587542154274049133),(-714078154587542151871427179)⟩,⟨(-661776836235156282263248585),(-661776836235156279843054201)⟩⟩] +lemma ha13_1_12_eq (j : Fin 7) : ha13_1_12 j = ((ha13_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha13_1_12_contains (j : Fin 7) : (ha13_1_12 j).Contains (fullFactor true 13 12 ((j.val:ℝ)/6)) := by + rw [ha13_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_11 j) true 13 11 j (ha13_1_11_contains j) +noncomputable def hk13_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_13 j i k) +lemma hk13_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_13 j i k).Contains (fullFactor true 13 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 13 (kernel13_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha13_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),0⟩,⟨(-1706),1706⟩⟩,⟨⟨(-19564),20219⟩,⟨(-20134),19649⟩⟩,⟨⟨(-8534),(-1201)⟩,⟨(-8588),(-1255)⟩⟩,⟨⟨(-46900871869911),(-46900871869617)⟩,⟨276173049938498,276173049938792⟩⟩,⟨⟨(-176109760920533965299),(-176109760920533936688)⟩,⟨(-535212581977576878551),(-535212581977576849938)⟩⟩,⟨⟨1619518943110304045264022,1619518943110304064467826⟩,⟨1579584100474629079635979,1579584100474629098851164⟩⟩,⟨⟨(-173508349021761392124750608),(-173508349021761391417168548)⟩,⟨207909143535531104764087803,207909143535531105467086404⟩⟩] +lemma ha13_1_13_eq (j : Fin 7) : ha13_1_13 j = ((ha13_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha13_1_13_contains (j : Fin 7) : (ha13_1_13 j).Contains (fullFactor true 13 13 ((j.val:ℝ)/6)) := by + rw [ha13_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_12 j) true 13 12 j (ha13_1_12_contains j) +noncomputable def hk13_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_14 j i k) +lemma hk13_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_14 j i k).Contains (fullFactor true 13 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 14 (kernel13_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha13_1_14 : Fin 7 → CBox := ![⟨⟨0,1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-16419),15932⟩,⟨(-16129),16221⟩⟩,⟨⟨(-2737),2540⟩,⟨883,6160⟩⟩,⟨⟨110249882407226,110249882407394⟩,⟨(-38713104765464),(-38713104765296)⟩⟩,⟨⟨(-157557663092208391915),(-157557663092208379374)⟩,⟨116047359607822127229,116047359607822139769⟩⟩,⟨⟨379459522779161671899565,379459522779161678474511⟩,⟨(-552051668636543077432771),(-552051668636543070860543)⟩⟩,⟨⟨55953255401131351213075368,55953255401131351404068567⟩,⟨41964526358793112980017863,41964526358793113172105026⟩⟩] +lemma ha13_1_14_eq (j : Fin 7) : ha13_1_14 j = ((ha13_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha13_1_14_contains (j : Fin 7) : (ha13_1_14 j).Contains (fullFactor true 13 14 ((j.val:ℝ)/6)) := by + rw [ha13_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_13 j) true 13 13 j (ha13_1_13_contains j) +noncomputable def hk13_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_15 j i k) +lemma hk13_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_15 j i k).Contains (fullFactor true 13 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 15 (kernel13_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha13_1_15 : Fin 7 → CBox := ![⟨⟨(-690),0⟩,⟨(-690),690⟩⟩,⟨⟨(-12141),12412⟩,⟨(-12240),12313⟩⟩,⟨⟨(-531),3014⟩,⟨(-2895),650⟩⟩,⟨⟨(-33984213307097),(-33984213307007)⟩,⟨(-30241983129272),(-30241983129182)⟩⟩,⟨⟨51659571312886998122,51659571312887003252⟩,⟨36804105711370736570,36804105711370741701⟩⟩,⟨⟨(-168169983210662732612274),(-168169983210662730513053)⟩,⟨(-77426114283267638611231),(-77426114283267636511522)⟩⟩,⟨⟨9401897796345060580999080,9401897796345060629666479⟩,⟨(-13995232137477086324510427),(-13995232137477086276082526)⟩⟩] +lemma ha13_1_15_eq (j : Fin 7) : ha13_1_15 j = ((ha13_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha13_1_15_contains (j : Fin 7) : (ha13_1_15 j).Contains (fullFactor true 13 15 ((j.val:ℝ)/6)) := by + rw [ha13_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_14 j) true 13 14 j (ha13_1_14_contains j) +noncomputable def hk13_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_16 j i k) +lemma hk13_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_16 j i k).Contains (fullFactor true 13 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 16 (kernel13_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha13_1_16 : Fin 7 → CBox := ![⟨⟨0,398⟩,⟨(-398),398⟩⟩,⟨⟨(-8792),8679⟩,⟨(-8784),8686⟩⟩,⟨⟨(-1860),373⟩,⟨(-1171),1062⟩⟩,⟨⟨(-3644352503520),(-3644352503474)⟩,⟨16199083582030,16199083582076⟩⟩,⟨⟨5734494115373043925,5734494115373045893⟩,⟨(-18402375035762237755),(-18402375035762235787)⟩⟩,⟨⟨(-12366601981441535326053),(-12366601981441534697439)⟩,⟨46347235530570450131219,46347235530570450759791⟩⟩,⟨⟨(-3268910846753978339022012),(-3268910846753978327510803)⟩,⟨(-1957660379773265460832635),(-1957660379773265449273312)⟩⟩] +lemma ha13_1_16_eq (j : Fin 7) : ha13_1_16 j = ((ha13_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha13_1_16_contains (j : Fin 7) : (ha13_1_16 j).Contains (fullFactor true 13 16 ((j.val:ℝ)/6)) := by + rw [ha13_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_15 j) true 13 15 j (ha13_1_15_contains j) +noncomputable def hk13_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_17 j i k) +lemma hk13_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_17 j i k).Contains (fullFactor true 13 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 17 (kernel13_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha13_1_17 : Fin 7 → CBox := ![⟨⟨(-216),0⟩,⟨(-216),216⟩⟩,⟨⟨(-5835),5865⟩,⟨(-5816),5884⟩⟩,⟨⟨(-463),861⟩,⟨(-421),903⟩⟩,⟨⟨5474290515447,5474290515469⟩,⟨(-1601578165748),(-1601578165725)⟩⟩,⟨⟨(-5512269208028139207),(-5512269208028138495)⟩,⟨81932762591983489,81932762591984201⟩⟩,⟨⟨11650119869057567266912,11650119869057567444047⟩,⟨1051684626320867785569,1051684626320867962690⟩⟩,⟨⟨(-379726367792195836307583),(-379726367792195833723642)⟩,⟨715983449472812879471836,715983449472812882046928⟩⟩] +lemma ha13_1_17_eq (j : Fin 7) : ha13_1_17 j = ((ha13_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha13_1_17_contains (j : Fin 7) : (ha13_1_17 j).Contains (fullFactor true 13 17 ((j.val:ℝ)/6)) := by + rw [ha13_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_16 j) true 13 16 j (ha13_1_16_contains j) +noncomputable def hk13_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_18 j i k) +lemma hk13_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_18 j i k).Contains (fullFactor true 13 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 18 (kernel13_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha13_1_18 : Fin 7 → CBox := ![⟨⟨0,111⟩,⟨(-111),111⟩⟩,⟨⟨(-3700),3701⟩,⟨(-3718),3683⟩⟩,⟨⟨(-356),386⟩,⟨(-494),248⟩⟩,⟨⟨(-1315193598916),(-1315193598905)⟩,⟨(-1301764808712),(-1301764808701)⟩⟩,⟨⟨485087845112077795,485087845112078039⟩,⟨1407914824903179340,1407914824903179584⟩⟩,⟨⟨(-217155281565886610801),(-217155281565886563668)⟩,⟨(-2685271962697031146368),(-2685271962697031099225)⟩⟩,⟨⟨147596520719159857896599,147596520719159858440620⟩,⟨68708843773474047054191,68708843773474047599693⟩⟩] +lemma ha13_1_18_eq (j : Fin 7) : ha13_1_18 j = ((ha13_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha13_1_18_contains (j : Fin 7) : (ha13_1_18 j).Contains (fullFactor true 13 18 ((j.val:ℝ)/6)) := by + rw [ha13_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_17 j) true 13 17 j (ha13_1_17_contains j) +noncomputable def hk13_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_19 j i k) +lemma hk13_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_19 j i k).Contains (fullFactor true 13 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 19 (kernel13_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha13_1_19 : Fin 7 → CBox := ![⟨⟨(-54),0⟩,⟨(-54),54⟩⟩,⟨⟨(-2221),2214⟩,⟨(-2211),2225⟩⟩,⟨⟨(-234),160⟩,⟨(-169),225⟩⟩,⟨⟨(-154094663925),(-154094663919)⟩,⟨547492436906,547492436912⟩⟩,⟨⟨303656330660654126,303656330660654206⟩,⟨(-230241759146353892),(-230241759146353812)⟩⟩,⟨⟨(-569325650148297228405),(-569325650148297216518)⟩,⟨146231272665711444020,146231272665711455903⟩⟩,⟨⟨11599722642812166090680,11599722642812166199778⟩,⟨(-28730345766858248704667),(-28730345766858248595791)⟩⟩] +lemma ha13_1_19_eq (j : Fin 7) : ha13_1_19 j = ((ha13_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha13_1_19_contains (j : Fin 7) : (ha13_1_19 j).Contains (fullFactor true 13 19 ((j.val:ℝ)/6)) := by + rw [ha13_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_18 j) true 13 18 j (ha13_1_18_contains j) +noncomputable def hk13_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_20 j i k) +lemma hk13_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_20 j i k).Contains (fullFactor true 13 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 20 (kernel13_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha13_1_20 : Fin 7 → CBox := ![⟨⟨0,25⟩,⟨(-25),25⟩⟩,⟨⟨(-1260),1265⟩,⟨(-1265),1261⟩⟩,⟨⟨(-83),116⟩,⟨(-97),102⟩⟩,⟨⟨161641552325,161641552329⟩,⟨(-38111898251),(-38111898248)⟩⟩,⟨⟨(-76193101051690185),(-76193101051690160)⟩,⟨(-52699531541181317),(-52699531541181291)⟩⟩,⟨⟨49918848101738665337,49918848101738668184⟩,⟨111143620062230221850,111143620062230224698⟩⟩,⟨⟨(-5296207274428164286732),(-5296207274428164266032)⟩,⟨(-1824605355869686504641),(-1824605355869686483913)⟩⟩] +lemma ha13_1_20_eq (j : Fin 7) : ha13_1_20 j = ((ha13_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha13_1_20_contains (j : Fin 7) : (ha13_1_20 j).Contains (fullFactor true 13 20 ((j.val:ℝ)/6)) := by + rw [ha13_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_19 j) true 13 19 j (ha13_1_19_contains j) +noncomputable def hk13_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_21 j i k) +lemma hk13_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_21 j i k).Contains (fullFactor true 13 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 21 (kernel13_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha13_1_21 : Fin 7 → CBox := ![⟨⟨(-11),0⟩,⟨(-11),11⟩⟩,⟨⟨(-686),684⟩,⟨(-685),685⟩⟩,⟨⟨(-51),45⟩,⟨(-53),44⟩⟩,⟨⟨(-31053802520),(-31053802517)⟩,⟨(-34183534830),(-34183534827)⟩⟩,⟨⟨(-6095788512564738),(-6095788512564729)⟩,⟨20565232336924463,20565232336924472⟩⟩,⟨⟨19947452122923390013,19947452122923390664⟩,⟨(-13438680182829295894),(-13438680182829295244)⟩⟩,⟨⟨(-266390992704363197630),(-266390992704363193879)⟩,⟨927016887678203849940,927016887678203853688⟩⟩] +lemma ha13_1_21_eq (j : Fin 7) : ha13_1_21 j = ((ha13_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha13_1_21_contains (j : Fin 7) : (ha13_1_21 j).Contains (fullFactor true 13 21 ((j.val:ℝ)/6)) := by + rw [ha13_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_20 j) true 13 20 j (ha13_1_20_contains j) +noncomputable def hk13_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_22 j i k) +lemma hk13_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_22 j i k).Contains (fullFactor true 13 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 22 (kernel13_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha13_1_22 : Fin 7 → CBox := ![⟨⟨0,5⟩,⟨(-5),5⟩⟩,⟨⟨(-355),355⟩,⟨(-355),355⟩⟩,⟨⟨(-23),22⟩,⟨(-21),24⟩⟩,⟨⟨(-3942600849),(-3942600847)⟩,⟨11607750839,11607750841⟩⟩,⟨⟨4738565622671909,4738565622671912⟩,⟨(-136417296725784),(-136417296725781)⟩⟩,⟨⟨(-3134094450884164939),(-3134094450884164797)⟩,⟨(-3273923499621043274),(-3273923499621043131)⟩⟩,⟨⟨154431965900625431326,154431965900625431975⟩,⟨35812533676602747667,35812533676602748316⟩⟩] +lemma ha13_1_22_eq (j : Fin 7) : ha13_1_22 j = ((ha13_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha13_1_22_contains (j : Fin 7) : (ha13_1_22 j).Contains (fullFactor true 13 22 ((j.val:ℝ)/6)) := by + rw [ha13_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_21 j) true 13 21 j (ha13_1_21_contains j) +noncomputable def hk13_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_23 j i k) +lemma hk13_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_23 j i k).Contains (fullFactor true 13 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 23 (kernel13_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha13_1_23 : Fin 7 → CBox := ![⟨⟨(-3),0⟩,⟨(-3),3⟩⟩,⟨⟨(-176),176⟩,⟨(-176),176⟩⟩,⟨⟨(-10),11⟩,⟨(-11),10⟩⟩,⟨⟨3063180923,3063180925⟩,⟨(-552603398),(-552603397)⟩⟩,⟨⟨(-339602715115267),(-339602715115265)⟩,⟨(-942843528351169),(-942843528351167)⟩⟩,⟨⟨(-485547312825471062),(-485547312825471031)⟩,⟨656936715480859687,656936715480859718⟩⟩,⟨⟨4361816670070208692,4361816670070208800⟩,⟨(-24538369114117272971),(-24538369114117272862)⟩⟩] +lemma ha13_1_23_eq (j : Fin 7) : ha13_1_23 j = ((ha13_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha13_1_23_contains (j : Fin 7) : (ha13_1_23 j).Contains (fullFactor true 13 23 ((j.val:ℝ)/6)) := by + rw [ha13_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_22 j) true 13 22 j (ha13_1_22_contains j) +noncomputable def hk13_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_24 j i k) +lemma hk13_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_24 j i k).Contains (fullFactor true 13 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 24 (kernel13_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha13_1_24 : Fin 7 → CBox := ![⟨⟨0,2⟩,⟨(-2),2⟩⟩,⟨⟨(-84),84⟩,⟨(-84),84⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-478817380),(-478817379)⟩,⟨(-586821975),(-586821974)⟩⟩,⟨⟨(-160054489498203),(-160054489498202)⟩,⟨124904370959028,124904370959030⟩⟩,⟨⟨126073099142750849,126073099142750856⟩,⟨63371694827256420,63371694827256427⟩⟩,⟨⟨(-3726155115074205307),(-3726155115074205289)⟩,⟨(-464290904201092748),(-464290904201092730)⟩⟩] +lemma ha13_1_24_eq (j : Fin 7) : ha13_1_24 j = ((ha13_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha13_1_24_contains (j : Fin 7) : (ha13_1_24 j).Contains (fullFactor true 13 24 ((j.val:ℝ)/6)) := by + rw [ha13_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_23 j) true 13 23 j (ha13_1_23_contains j) +noncomputable def hk13_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_25 j i k) +lemma hk13_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_25 j i k).Contains (fullFactor true 13 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 25 (kernel13_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha13_1_25 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-65704168),(-65704166)⟩,⟨164265298,164265299⟩⟩,⟨⟨32783857938547,32783857938548⟩,⟨22007014694235,22007014694236⟩⟩,⟨⟨6803928602750483,6803928602750485⟩,⟨(-22387157454350206),(-22387157454350204)⟩⟩,⟨⟨(-39075756041965584),(-39075756041965580)⟩,⟨541696984189840146,541696984189840149⟩⟩] +lemma ha13_1_25_eq (j : Fin 7) : ha13_1_25 j = ((ha13_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha13_1_25_contains (j : Fin 7) : (ha13_1_25 j).Contains (fullFactor true 13 25 ((j.val:ℝ)/6)) := by + rw [ha13_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_24 j) true 13 24 j (ha13_1_24_contains j) +noncomputable def hk13_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_26 j i k) +lemma hk13_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_26 j i k).Contains (fullFactor true 13 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 26 (kernel13_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha13_1_26 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-18),18⟩,⟨(-18),18⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨39425201,39425202⟩,⟨(-4970517),(-4970515)⟩⟩,⟨⟨1999728436134,1999728436135⟩,⟨(-7108059280695),(-7108059280693)⟩⟩,⟨⟨(-3701931032599262),(-3701931032599260)⟩,⟨(-462641338728508),(-462641338728507)⟩⟩,⟨⟨75516126950686264,75516126950686265⟩,⟨1514896652642508,1514896652642509⟩⟩] +lemma ha13_1_26_eq (j : Fin 7) : ha13_1_26 j = ((ha13_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha13_1_26_contains (j : Fin 7) : (ha13_1_26 j).Contains (fullFactor true 13 26 ((j.val:ℝ)/6)) := by + rw [ha13_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_25 j) true 13 25 j (ha13_1_25_contains j) +noncomputable def hk13_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_27 j i k) +lemma hk13_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_27 j i k).Contains (fullFactor true 13 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 27 (kernel13_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha13_1_27 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-8),8⟩,⟨(-8),8⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5072727),(-5072726)⟩,⟨(-6938093),(-6938092)⟩⟩,⟨⟨(-1328498462274),(-1328498462273)⟩,⟨56759990849,56759990851⟩⟩,⟨⟨26565253506185,26565253506186⟩,⟨572197215089038,572197215089039⟩⟩,⟨⟨(-322577228915015),(-322577228915014)⟩,⟨(-10110191036269239),(-10110191036269238)⟩⟩] +lemma ha13_1_27_eq (j : Fin 7) : ha13_1_27 j = ((ha13_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha13_1_27_contains (j : Fin 7) : (ha13_1_27 j).Contains (fullFactor true 13 27 ((j.val:ℝ)/6)) := by + rw [ha13_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_26 j) true 13 26 j (ha13_1_26_contains j) +noncomputable def hk13_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_28 j i k) +lemma hk13_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_28 j i k).Contains (fullFactor true 13 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 28 (kernel13_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha13_1_28 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-753071),(-753070)⟩,⟨1626700,1626702⟩⟩,⟨⟨81263545238,81263545240⟩,⟨216129890164,216129890165⟩⟩,⟨⟨82817320506323,82817320506324⟩,⟨(-18268868059780),(-18268868059779)⟩⟩,⟨⟨(-1301699702824259),(-1301699702824258)⟩,⟨109402116200462,109402116200463⟩⟩] +lemma ha13_1_28_eq (j : Fin 7) : ha13_1_28 j = ((ha13_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha13_1_28_contains (j : Fin 7) : (ha13_1_28 j).Contains (fullFactor true 13 28 ((j.val:ℝ)/6)) := by + rw [ha13_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_27 j) true 13 27 j (ha13_1_27_contains j) +noncomputable def hk13_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_29 j i k) +lemma hk13_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_29 j i k).Contains (fullFactor true 13 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 29 (kernel13_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha13_1_29 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨360028,360029⟩,⟨(-26092),(-26091)⟩⟩,⟨⟨30185328263,30185328264⟩,⟨(-24239673296),(-24239673294)⟩⟩,⟨⟨(-4584910010288),(-4584910010287)⟩,⟨(-11222979847810),(-11222979847808)⟩⟩,⟨⟨22050979634099,22050979634100⟩,⟨161376852381153,161376852381154⟩⟩] +lemma ha13_1_29_eq (j : Fin 7) : ha13_1_29 j = ((ha13_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha13_1_29_contains (j : Fin 7) : (ha13_1_29 j).Contains (fullFactor true 13 29 ((j.val:ℝ)/6)) := by + rw [ha13_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_28 j) true 13 28 j (ha13_1_28_contains j) +noncomputable def hk13_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel13_0 j i k).mul (mpower1_30 j i k) +lemma hk13_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk13_1_30 j i k).Contains (fullFactor true 13 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk13_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel13_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 13 30 (kernel13_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha13_1_30 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-38406),(-38405)⟩,⟨(-58844),(-58842)⟩⟩,⟨⟨(-5257618695),(-5257618693)⟩,⟨(-3424138169),(-3424138167)⟩⟩,⟨⟨(-1420667329920),(-1420667329919)⟩,⟨887837197971,887837197972⟩⟩,⟨⟨19286514319068,19286514319069⟩,⟨(-3664297815547),(-3664297815545)⟩⟩] +lemma ha13_1_30_eq (j : Fin 7) : ha13_1_30 j = ((ha13_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha13_1_30_contains (j : Fin 7) : (ha13_1_30 j).Contains (fullFactor true 13 30 ((j.val:ℝ)/6)) := by + rw [ha13_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha13_1_29 j) true 13 29 j (ha13_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders15.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders15.lean new file mode 100644 index 0000000000000000000000000000000000000000..8f80711dd075715c9f3121e267c382fffe9949cd --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders15.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.KernelValues20 +import OAI.Analysis.PlanarPacking.Certificate.Powers20 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk15_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_0 j i k) +lemma hk15_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_0 j i k).Contains (fullFactor false 15 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 0 (power15_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha15_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999821,1000000000000000000000000000239⟩,⟨(-239),239⟩⟩,⟨⟨(-42956189891),31173106335⟩,⟨999999999999999999962970231043,1000000000000000000037029768974⟩⟩,⟨⟨(-1000000000000000000101240687395),(-999999999999999999898759312614)⟩,⟨(-112998241606),89432074414⟩⟩,⟨⟨(-31325499059),66674749829⟩,⟨(-1000000000000000000049000124444),(-999999999999999999950999875571)⟩⟩,⟨⟨999999999999999999723183942652,1000000000000000000276816057312⟩,⟨(-253268553387),300400887807⟩⟩,⟨⟨(-377863658631),318948240660⟩,⟨999999999999999999651575526767,1000000000000000000348424473187⟩⟩,⟨⟨(-1000000000000000000098297966789),(-999999999999999999901702033271)⟩,⟨(-133647217589),62948715929⟩⟩] +lemma ha15_0_0_eq (j : Fin 7) : ha15_0_0 j = ((atomPoints j).direct.powBin 7 15).conj := by fin_cases j <;> decide +kernel +lemma ha15_0_0_contains (j : Fin 7) : (ha15_0_0 j).Contains (fullFactor false 15 0 ((j.val:ℝ)/6)) := by + rw [ha15_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 15) ((j.val:ℝ)/6) 15 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 15 (by norm_num)) +noncomputable def hk15_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_1 j i k) +lemma hk15_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_1 j i k).Contains (fullFactor false 15 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 1 (power15_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha15_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-523598775598298873097722075031),(-523598775598298873057277924977)⟩,⟨(-22491808432),16322200309⟩⟩,⟨⟨(-93653049325),118331481900⟩,⟨(-1047197551196597746262685666591),(-1047197551196597746047314333419)⟩⟩,⟨⟨1570796326794896619153030784534,1570796326794896619311969215490⟩,⟨(-49205978857),104732452122⟩⟩,⟨⟨(-629158148178),530444417804⟩,⟨2094395102393195491726904471890,2094395102393195492893095528034⟩⟩,⟨⟨(-2617993877991494366303839804415),(-2617993877991494364471160195465)⟩,⟨(-989244745012),835004541445⟩⟩,⟨⟨(-197759223516),419865116951⟩,⟨(-3141592653589793238778812170328),(-3141592653589793238151187829861)⟩⟩] +lemma ha15_0_1_eq (j : Fin 7) : ha15_0_1 j = ((ha15_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha15_0_1_contains (j : Fin 7) : (ha15_0_1 j).Contains (fullFactor false 15 1 ((j.val:ℝ)/6)) := by + rw [ha15_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_0 j) false 15 0 j (ha15_0_0_contains j) +noncomputable def hk15_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_2 j i k) +lemma hk15_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_2 j i k).Contains (fullFactor false 15 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 2 (power15_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha15_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-4273142049),5888341678⟩,⟨(-137077838904018869711752543846),(-137077838904018869700727957807)⟩⟩,⟨⟨548311355616075478767704255503,548311355616075478882217751106⟩,⟨(-49036621958),61958219038⟩⟩,⟨⟨(-82256675545),38646285423⟩,⟨1233700550136169827291783786146,1233700550136169827420540728730⟩⟩,⟨⟨(-2193245422464301915913950880784),(-2193245422464301914685737145549)⟩,⟨(-658852872088),555480095371⟩⟩,⟨⟨(-1093018388800),1294918343139⟩,⟨(-3426945972600471743860946423610),(-3426945972600471741451066117504)⟩⟩,⟨⟨4934802200544679308923860043922,4934802200544679309925438015804⟩,⟨(-310639461889),659522583456⟩⟩] +lemma ha15_0_2_eq (j : Fin 7) : ha15_0_2 j = ((ha15_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha15_0_2_contains (j : Fin 7) : (ha15_0_2 j).Contains (fullFactor false 15 2 ((j.val:ℝ)/6)) := by + rw [ha15_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_1 j) false 15 1 j (ha15_0_1_contains j) +noncomputable def hk15_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_3 j i k) +lemma hk15_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_3 j i k).Contains (fullFactor false 15 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 3 (power15_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha15_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23924596203935046430748373736,23924596203935046432748681343⟩,⟨(-745803982),1027709498⟩⟩,⟨⟨(-21627498418),17117010145⟩,⟨191396769631480371433697227535,191396769631480371474279213101⟩⟩,⟨⟨(-645964097506246253691946816111),(-645964097506246253622473671039)⟩,⟨(-43069494601),20235147729⟩⟩,⟨⟨(-387798263741),459966076167⟩,⟨(-1531174157051842972063070173830),(-1531174157051842971200741351187)⟩⟩,⟨⟨2990574525491880802912297647187,2990574525491880805024834237587⟩,⟨(-953838483471),1130029431613⟩⟩,⟨⟨(-690650434354),325300883796⟩,⟨5167712780049970028725032278639,5167712780049970029790331618796⟩⟩] +lemma ha15_0_3_eq (j : Fin 7) : ha15_0_3 j = ((ha15_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha15_0_3_contains (j : Fin 7) : (ha15_0_3 j).Contains (fullFactor false 15 3 ((j.val:ℝ)/6)) := by + rw [ha15_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_2 j) false 15 2 j (ha15_0_2_contains j) +noncomputable def hk15_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_4 j i k) +lemma hk15_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_4 j i k).Contains (fullFactor false 15 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 4 (power15_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha15_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-134526859),97625513⟩,⟨3131722319766024859584151577,3131722319766024859855959813⟩⟩,⟨⟨(-50107557116256397760912809259),(-50107557116256397750128972973)⟩,⟨(-5662065846),4481222777⟩⟩,⟨⟨(-7946323932),16913350980⟩,⟨(-253669507901048013651369258973),(-253669507901048013623279763578)⟩⟩,⟨⟨801720913860102363861301121522,801720913860102364315367394152⟩,⟨(-203050696074),240837674298⟩⟩,⟨⟨(-739602533479),624285827580⟩,⟨1957326449853765536630593644777,1957326449853765538019475973551⟩⟩,⟨⟨(-4058712126416768218621993894085),(-4058712126416768217772390466906)⟩,⟨(-542435582692),255490716685⟩⟩] +lemma ha15_0_4_eq (j : Fin 7) : ha15_0_4 j = ((ha15_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha15_0_4_contains (j : Fin 7) : (ha15_0_4 j).Contains (fullFactor false 15 4 ((j.val:ℝ)/6)) := by + rw [ha15_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_3 j) false 15 3 j (ha15_0_3_contains j) +noncomputable def hk15_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_5 j i k) +lemma hk15_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_5 j i k).Contains (fullFactor false 15 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 5 (power15_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha15_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-327953194428670967590080757),(-327953194428670967560573156)⟩,⟨(-14087620),10223320⟩⟩,⟨⟨(-938545104),1185860298⟩,⟨(-10494502221717470963556445818),(-10494502221717470961264479388)⟩⟩,⟨⟨79692626246167045116265328020,79692626246167045125343572766⟩,⟨(-2496411289),5313485919⟩⟩,⟨⟨(-100881849105),85053676679⟩,⟨335824071094959070701500904927,335824071094959070892768701659⟩⟩,⟨⟨(-1024853732589596774038136387336),(-1024853732589596773307657089788)⟩,⟨(-387254980960),326875294945⟩⟩,⟨⟨(-160529551720),340822328327⟩,⟨(-2550164039877345444136711913289),(-2550164039877345443594772911977)⟩⟩] +lemma ha15_0_5_eq (j : Fin 7) : ha15_0_5 j = ((ha15_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha15_0_5_contains (j : Fin 7) : (ha15_0_5 j).Contains (fullFactor false 15 5 ((j.val:ℝ)/6)) := by + rw [ha15_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_4 j) false 15 4 j (ha15_0_4_contains j) +noncomputable def hk15_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_6 j i k) +lemma hk15_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_6 j i k).Contains (fullFactor false 15 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 6 (power15_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha15_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-892153),1229377⟩,⟨(-28619315176067161692890729),(-28619315176067161690224606)⟩⟩,⟨⟨1831636171268298348056763787,1831636171268298348462617673⟩,⟨(-163807023),206971667⟩⟩,⟨⟨(-1391067361),653558948⟩,⟨20863480763352960871923995000,20863480763352960874367084440⟩⟩,⟨⟨(-117224714961171094322189303698),(-117224714961171094255051109720)⟩,⟨(-35214408448),29689333980⟩⟩,⟨⟨(-142626253506),168971861563⟩,⟨(-447176799626049401590666121815),(-447176799626049401270510992354)⟩⟩,⟨⟨1335262768854589495737310106639,1335262768854589496025318977576⟩,⟨(-84053076728),178454153809⟩⟩] +lemma ha15_0_6_eq (j : Fin 7) : ha15_0_6 j = ((ha15_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha15_0_6_contains (j : Fin 7) : (ha15_0_6 j).Contains (fullFactor false 15 6 ((j.val:ℝ)/6)) := by + rw [ha15_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_5 j) false 15 5 j (ha15_0_5_contains j) +noncomputable def hk15_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_7 j i k) +lemma hk15_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_7 j i k).Contains (fullFactor false 15 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 7 (power15_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha15_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2140719769235797028113637,2140719769235797028319877⟩,⟨(-66733),91958⟩⟩,⟨⟨(-30962889),24505474⟩,⟨274012130462182019580950991,274012130462182019642538799⟩⟩,⟨⟨(-4681754135318688100991612786),(-4681754135318688100428482310)⟩,⟨(-312154786),146658285⟩⟩,⟨⟨(-8883027955),10536126370⟩,⟨(-35073552699159298520403018229),(-35073552699159298500203674978)⟩⟩,⟨⟨167243731971546642769299094343,167243731971546642889569186097⟩,⟨(-53342094075),63195328447⟩⟩,⟨⟨(-80090036945),37722932623⟩,⟨599264529320792076825303287503,599264529320792076956468884760⟩⟩] +lemma ha15_0_7_eq (j : Fin 7) : ha15_0_7 j = ((ha15_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha15_0_7_contains (j : Fin 7) : (ha15_0_7 j).Contains (fullFactor false 15 7 ((j.val:ℝ)/6)) := by + rw [ha15_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_6 j) false 15 6 j (ha15_0_6_contains j) +noncomputable def hk15_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_8 j i k) +lemma hk15_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_8 j i k).Contains (fullFactor false 15 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 8 (power15_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha15_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-6019),4368⟩,⟨140109781258867029446957,140109781258867029460902⟩⟩,⟨⟨(-35868104002269959544294003),(-35868104002269959536118005)⟩,⟨(-4053033),3207760⟩⟩,⟨⟨(-28796287),61291449⟩,⟨(-919260274839426580303981026),(-919260274839426580190484518)⟩⟩,⟨⟨9182234624581109639634035091,9182234624581109644951438750⟩,⟨(-2325571281),2758351434⟩⟩,⟨⟨(-20680622874),17456159466⟩,⟨54730383304244933360675035808,54730383304244933400207543520⟩⟩,⟨⟨(-235330630358893204569420434720),(-235330630358893204517162744464)⟩,⟨(-31451283962),14813761001⟩⟩] +lemma ha15_0_8_eq (j : Fin 7) : ha15_0_8 j = ((ha15_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha15_0_8_contains (j : Fin 7) : (ha15_0_8 j).Contains (fullFactor false 15 8 ((j.val:ℝ)/6)) := by + rw [ha15_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_7 j) false 15 7 j (ha15_0_7_contains j) +noncomputable def hk15_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_9 j i k) +lemma hk15_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_9 j i k).Contains (fullFactor false 15 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 9 (power15_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha15_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-8151256657387584305339),(-8151256657387584304501)⟩,⟨(-351),255⟩⟩,⟨⟨(-373240),471592⟩,⟨(-4173443408582443164601439),(-4173443408582443163636833)⟩⟩,⟨⟨160441184787359821863584253,160441184787359821883903832⟩,⟨(-5025901),10697376⟩⟩,⟨⟨(-641897527),541185012⟩,⟨2136803025194210899406888683,2136803025194210900651106359⟩⟩,⟨⟨(-15920423158960125601322348701),(-15920423158960125589772132067)⟩,⟨(-6015749342),5077790958⟩⟩,⟨⟨(-5170978082),10978569183⟩,⟨(-82145886611128228808608376409),(-82145886611128228790105522840)⟩⟩] +lemma ha15_0_9_eq (j : Fin 7) : ha15_0_9 j = ((ha15_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha15_0_9_contains (j : Fin 7) : (ha15_0_9 j).Contains (fullFactor false 15 9 ((j.val:ℝ)/6)) := by + rw [ha15_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_8 j) false 15 8 j (ha15_0_8_contains j) +noncomputable def hk15_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_10 j i k) +lemma hk15_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_10 j i k).Contains (fullFactor false 15 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 10 (power15_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha15_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-14),19⟩,⟨(-426798800539562151478),(-426798800539562151431)⟩⟩,⟨⟨437041971752511643038297,437041971752511643140703⟩,⟨(-39086),49385⟩⟩,⟨⟨(-1680340),789467⟩,⟨25202042373060605479606064,25202042373060605482878078⟩⟩,⟨⟨(-447530979074571922654654354),(-447530979074571922392641477)⟩,⟨(-134438704),113345524⟩⟩,⟨⟨(-1329362565),1574919495⟩,⟨(-4167957036519161636817281487),(-4167957036519161633780174823)⟩⟩,⟨⟨25806891390014060009844386238,25806891390014060015739375010⟩,⟨(-1624510676),3449019230⟩⟩] +lemma ha15_0_10_eq (j : Fin 7) : ha15_0_10 j = ((ha15_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha15_0_10_contains (j : Fin 7) : (ha15_0_10 j).Contains (fullFactor false 15 10 ((j.val:ℝ)/6)) := by + rw [ha15_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_9 j) false 15 9 j (ha15_0_9_contains j) +noncomputable def hk15_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_11 j i k) +lemma hk15_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_11 j i k).Contains (fullFactor false 15 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 11 (power15_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha15_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20315575399030665719,20315575399030665723⟩,⟨(-1),1⟩⟩,⟨⟨(-4702),3721⟩,⟨41606298417214803391785,41606298417214803401668⟩⟩,⟨⟨(-3598843235212085340727585),(-3598843235212085340248886)⟩,⟨(-239952),112736⟩⟩,⟨⟨(-21580938),25597070⟩,⟨(-85209699158455917381575028),(-85209699158455917331416661)⟩⟩,⟨⟨991971455030794224298034444,991971455030794225024021684⟩,⟨(-316387551),374829964⟩⟩,⟨⟨(-985037589),463959165⟩,⟨7370430945714350776466374076,7370430945714350778173439743⟩⟩] +lemma ha15_0_11_eq (j : Fin 7) : ha15_0_11 j = ((ha15_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha15_0_11_contains (j : Fin 7) : (ha15_0_11 j).Contains (fullFactor false 15 11 ((j.val:ℝ)/6)) := by + rw [ha15_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_10 j) false 15 10 j (ha15_0_10_contains j) +noncomputable def hk15_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_12 j i k) +lemma hk15_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_12 j i k).Contains (fullFactor false 15 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 12 (power15_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha15_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨886434200375614885,886434200375614886⟩⟩,⟨⟨(-3630834484738518571494),(-3630834484738518570619)⟩,⟨(-411),325⟩⟩,⟨⟨(-14758),31410⟩,⟨(-471087477881817150403349),(-471087477881817150339187)⟩⟩,⟨⟨14871898049488972062645666,14871898049488972071447292⟩,⟨(-3766585),4467532⟩⟩,⟨⟨(-81775213),69025056⟩,⟨216414599701077852828613158,216414599701077852987687873⟩⟩,⟨⟨(-1929574309403923048147240231),(-1929574309403923047694189458)⟩,⟨(-257882238),121464226⟩⟩] +lemma ha15_0_12_eq (j : Fin 7) : ha15_0_12 j = ((ha15_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha15_0_12_contains (j : Fin 7) : (ha15_0_12 j).Contains (fullFactor false 15 12 ((j.val:ℝ)/6)) := by + rw [ha15_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_11 j) false 15 11 j (ha15_0_11_contains j) +noncomputable def hk15_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_13 j i k) +lemma hk15_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_13 j i k).Contains (fullFactor false 15 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 13 (power15_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha15_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-35702758612702237),(-35702758612702236)⟩,⟨(-1),1⟩⟩,⟨⟨(-27),34⟩,⟨(-292476998555256723062),(-292476998555256722990)⟩⟩,⟨⟨56921729219679268114340,56921729219679268122275⟩,⟨(-1784),3796⟩⟩,⟨⟨(-719753),606825⟩,⟨2395971572164663074317176,2395971572164663075742810⟩⟩,⟨⟨(-43582469009646285047244983),(-43582469009646285015071129)⟩,⟨(-16468232),13900552⟩⟩,⟨⟨(-29353164),62320073⟩,⟨(-466302805767612564480660671),(-466302805767612564369691692)⟩⟩] +lemma ha15_0_13_eq (j : Fin 7) : ha15_0_13 j = ((ha15_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha15_0_13_contains (j : Fin 7) : (ha15_0_13 j).Contains (fullFactor false 15 13 ((j.val:ℝ)/6)) := by + rw [ha15_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_12 j) false 15 12 j (ha15_0_12_contains j) +noncomputable def hk15_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_14 j i k) +lemma hk15_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_14 j i k).Contains (fullFactor false 15 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 14 (power15_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha15_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1335280049649466),(-1335280049649465)⟩⟩,⟨⟨21877228333456835514,21877228333456835521⟩,⟨(-3),3⟩⟩,⟨⟨(-426),201⟩,⟨6386603083791852240701,6386603083791852241613⟩⟩,⟨⟨(-358436509015356793228717),(-358436509015356793014301)⟩,⟨(-107675),90781⟩⟩,⟨⟨(-2599398),3079553⟩,⟨(-8149902646786285760171804),(-8149902646786285754129364)⟩⟩,⟨⟨104638104924845707106498398,104638104924845707131732853⟩,⟨(-6586835),13984592⟩⟩] +lemma ha15_0_14_eq (j : Fin 7) : ha15_0_14 j = ((ha15_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha15_0_14_contains (j : Fin 7) : (ha15_0_14 j).Contains (fullFactor false 15 14 ((j.val:ℝ)/6)) := by + rw [ha15_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_13 j) false 15 13 j (ha15_0_13_contains j) +noncomputable def hk15_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_15 j i k) +lemma hk15_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_15 j i k).Contains (fullFactor false 15 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 15 (power15_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha15_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨46610066605153,46610066605154⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1527318662517654886,1527318662517654887⟩⟩,⟨⟨(-668803510981146723305),(-668803510981146723206)⟩,⟨(-45),22⟩⟩,⟨⟨(-12676),15035⟩,⟨(-50047177933378515343068),(-50047177933378515312970)⟩⟩,⟨⟨1422426349034211492306287,1422426349034211493365421⟩,⟨(-453681),537484⟩⟩,⟨⟨(-2928927),1379544⟩,⟨21915353447830215824953818,21915353447830215830308670⟩⟩] +lemma ha15_0_15_eq (j : Fin 7) : ha15_0_15 j = ((ha15_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha15_0_15_contains (j : Fin 7) : (ha15_0_15 j).Contains (fullFactor false 15 15 ((j.val:ℝ)/6)) := by + rw [ha15_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_14 j) false 15 14 j (ha15_0_14_contains j) +noncomputable def hk15_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_16 j i k) +lemma hk15_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_16 j i k).Contains (fullFactor false 15 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 16 (power15_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha15_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1525310862813,1525310862814⟩⟩,⟨⟨(-99962772705334444),(-99962772705334443)⟩,⟨(-1),1⟩⟩,⟨⟨(-3),5⟩,⟨(-65659631149794723628),(-65659631149794723617)⟩⟩,⟨⟨6551160272016798096849,6551160272016798100811⟩,⟨(-1660),1969⟩⟩,⟨⟨(-87946),74234⟩,⟨232743967104084891288818,232743967104084891462860⟩⟩,⟨⟨(-4303069587032947007882030),(-4303069587032947006816909)⟩,⟨(-575094),270873⟩⟩] +lemma ha15_0_16_eq (j : Fin 7) : ha15_0_16 j = ((ha15_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha15_0_16_contains (j : Fin 7) : (ha15_0_16 j).Contains (fullFactor false 15 16 ((j.val:ℝ)/6)) := by + rw [ha15_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_15 j) false 15 15 j (ha15_0_15_contains j) +noncomputable def hk15_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_17 j i k) +lemma hk15_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_17 j i k).Contains (fullFactor false 15 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 17 (power15_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha15_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-46979464717),(-46979464716)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-6157692399285196),(-6157692399285195)⟩⟩,⟨⟨6066935731106195666,6066935731106195668⟩,⟨(-1),1⟩⟩,⟨⟨(-243),205⟩,⟨807101058159109193182,807101058159109193673⟩⟩,⟨⟨(-35842487118702823500035),(-35842487118702823473117)⟩,⟨(-13544),11433⟩⟩,⟨⟨(-50058),106278⟩,⟨(-795205400147551278588144),(-795205400147551278388778)⟩⟩] +lemma ha15_0_17_eq (j : Fin 7) : ha15_0_17 j = ((ha15_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha15_0_17_contains (j : Fin 7) : (ha15_0_17 j).Contains (fullFactor false 15 17 ((j.val:ℝ)/6)) := by + rw [ha15_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_16 j) false 15 16 j (ha15_0_16_contains j) +noncomputable def hk15_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_18 j i k) +lemma hk15_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_18 j i k).Contains (fullFactor false 15 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 18 (power15_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha15_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1366577234),(-1366577233)⟩⟩,⟨⟨358240022308519,358240022308520⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨529440020073462376,529440020073462377⟩⟩,⟨⟨(-93910472408044662768),(-93910472408044662710)⟩,⟨(-29),24⟩⟩,⟨⟨(-1663),1970⟩,⟨(-5213078436041832673641),(-5213078436041832669708)⟩⟩,⟨⟨138789524622137721128935,138789524622137721164174⟩,⟨(-8737),18550⟩⟩] +lemma ha15_0_18_eq (j : Fin 7) : ha15_0_18 j = ((ha15_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha15_0_18_contains (j : Fin 7) : (ha15_0_18 j).Contains (fullFactor false 15 18 ((j.val:ℝ)/6)) := by + rw [ha15_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_17 j) false 15 17 j (ha15_0_17_contains j) +noncomputable def hk15_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_19 j i k) +lemma hk15_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_19 j i k).Contains (fullFactor false 15 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 19 (power15_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha15_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨37659903,37659904⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨19744635479057,19744635479058⟩⟩,⟨⟨(-43770654673137423),(-43770654673137422)⟩,⟨(-1),1⟩⟩,⟨⟨(-3),4⟩,⟨(-10351875446044213765),(-10351875446044213758)⟩⟩,⟨⟨718305654265631154778,718305654265631155323⟩,⟨(-230),272⟩⟩,⟨⟨(-3068),1445⟩,⟨22948428997269873107581,22948428997269873113481⟩⟩] +lemma ha15_0_19_eq (j : Fin 7) : ha15_0_19 j = ((ha15_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha15_0_19_contains (j : Fin 7) : (ha15_0_19 j).Contains (fullFactor false 15 19 ((j.val:ℝ)/6)) := by + rw [ha15_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_18 j) false 15 18 j (ha15_0_18_contains j) +noncomputable def hk15_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_20 j i k) +lemma hk15_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_20 j i k).Contains (fullFactor false 15 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 20 (power15_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha15_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨985933,985934⟩⟩,⟨⟨(-1033826696147),(-1033826696146)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-3437739179098608),(-3437739179098606)⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨(-36),31⟩,⟨94025990269704865178,94025990269704865251⟩⟩,⟨⟨(-3604730797462500934383),(-3604730797462500933444)⟩,⟨(-482),227⟩⟩] +lemma ha15_0_20_eq (j : Fin 7) : ha15_0_20 j = ((ha15_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha15_0_20_contains (j : Fin 7) : (ha15_0_20 j).Contains (fullFactor false 15 20 ((j.val:ℝ)/6)) := by + rw [ha15_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_19 j) false 15 19 j (ha15_0_19_contains j) +noncomputable def hk15_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_21 j i k) +lemma hk15_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_21 j i k).Contains (fullFactor false 15 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 21 (power15_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha15_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24583),(-24582)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-51553370694),(-51553370693)⟩⟩,⟨⟨257142289286047,257142289286048⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨(-11721879376103578828),(-11721879376103578818)⟩,⟨(-5),4⟩⟩,⟨⟨(-34),73⟩,⟨(-539266466260812849015),(-539266466260812848872)⟩⟩] +lemma ha15_0_21_eq (j : Fin 7) : ha15_0_21 j = ((ha15_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha15_0_21_contains (j : Fin 7) : (ha15_0_21 j).Contains (fullFactor false 15 21 ((j.val:ℝ)/6)) := by + rw [ha15_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_20 j) false 15 20 j (ha15_0_20_contains j) +noncomputable def hk15_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_22 j i k) +lemma hk15_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_22 j i k).Contains (fullFactor false 15 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 22 (power15_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha15_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-586),(-585)⟩⟩,⟨⟨2453934706,2453934707⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨18359916521552,18359916521553⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1394900383872451221),(-1394900383872451218)⟩⟩,⟨⟨77007071306013533788,77007071306013533810⟩,⟨(-5),11⟩⟩] +lemma ha15_0_22_eq (j : Fin 7) : ha15_0_22 j = ((ha15_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha15_0_22_contains (j : Fin 7) : (ha15_0_22 j).Contains (fullFactor false 15 22 ((j.val:ℝ)/6)) := by + rw [ha15_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_21 j) false 15 21 j (ha15_0_21_contains j) +noncomputable def hk15_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_23 j i k) +lemma hk15_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_23 j i k).Contains (fullFactor false 15 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 23 (power15_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha15_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨13,14⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨111728452,111728453⟩⟩,⟨⟨(-1253899540536),(-1253899540535)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨158775681103741856,158775681103741858⟩,⟨(-1),1⟩⟩,⟨⟨(-2),1⟩,⟨10518471716932064453,10518471716932064457⟩⟩] +lemma ha15_0_23_eq (j : Fin 7) : ha15_0_23 j = ((ha15_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha15_0_23_contains (j : Fin 7) : (ha15_0_23 j).Contains (fullFactor false 15 23 ((j.val:ℝ)/6)) := by + rw [ha15_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_22 j) false 15 22 j (ha15_0_22_contains j) +noncomputable def hk15_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_24 j i k) +lemma hk15_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_24 j i k).Contains (fullFactor false 15 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 24 (power15_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha15_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-4875074),(-4875073)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-82067533019),(-82067533018)⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨17319740045980248,17319740045980250⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha15_0_24_eq (j : Fin 7) : ha15_0_24 j = ((ha15_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha15_0_24_contains (j : Fin 7) : (ha15_0_24 j).Contains (fullFactor false 15 24 ((j.val:ℝ)/6)) := by + rw [ha15_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_23 j) false 15 23 j (ha15_0_23_contains j) +noncomputable def hk15_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_25 j i k) +lemma hk15_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_25 j i k).Contains (fullFactor false 15 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 25 (power15_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha15_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-204207),(-204206)⟩⟩,⟨⟨5156455176,5156455177⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨(-1813718936351217),(-1813718936351216)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha15_0_25_eq (j : Fin 7) : ha15_0_25 j = ((ha15_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha15_0_25_contains (j : Fin 7) : (ha15_0_25 j).Contains (fullFactor false 15 25 ((j.val:ℝ)/6)) := by + rw [ha15_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_24 j) false 15 24 j (ha15_0_24_contains j) +noncomputable def hk15_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_26 j i k) +lemma hk15_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_26 j i k).Contains (fullFactor false 15 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 26 (power15_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha15_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨8224,8225⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨311528494,311528495⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-182627118144798),(-182627118144797)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha15_0_26_eq (j : Fin 7) : ha15_0_26 j = ((ha15_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha15_0_26_contains (j : Fin 7) : (ha15_0_26 j).Contains (fullFactor false 15 26 ((j.val:ℝ)/6)) := by + rw [ha15_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_25 j) false 15 25 j (ha15_0_25_contains j) +noncomputable def hk15_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_27 j i k) +lemma hk15_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_27 j i k).Contains (fullFactor false 15 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 27 (power15_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha15_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨318,320⟩⟩,⟨⟨(-18123994),(-18123993)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨17708025083641,17708025083642⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha15_0_27_eq (j : Fin 7) : ha15_0_27 j = ((ha15_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha15_0_27_contains (j : Fin 7) : (ha15_0_27 j).Contains (fullFactor false 15 27 ((j.val:ℝ)/6)) := by + rw [ha15_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_26 j) false 15 26 j (ha15_0_26_contains j) +noncomputable def hk15_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_28 j i k) +lemma hk15_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_28 j i k).Contains (fullFactor false 15 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 28 (power15_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha15_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-12),(-11)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1016754),(-1016753)⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1655696473581,1655696473582⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha15_0_28_eq (j : Fin 7) : ha15_0_28 j = ((ha15_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha15_0_28_contains (j : Fin 7) : (ha15_0_28 j).Contains (fullFactor false 15 28 ((j.val:ℝ)/6)) := by + rw [ha15_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_27 j) false 15 27 j (ha15_0_27_contains j) +noncomputable def hk15_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_29 j i k) +lemma hk15_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_29 j i k).Contains (fullFactor false 15 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 29 (power15_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha15_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨55072,55073⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨(-149469076954),(-149469076953)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha15_0_29_eq (j : Fin 7) : ha15_0_29 j = ((ha15_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha15_0_29_contains (j : Fin 7) : (ha15_0_29 j).Contains (fullFactor false 15 29 ((j.val:ℝ)/6)) := by + rw [ha15_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_28 j) false 15 28 j (ha15_0_28_contains j) +noncomputable def hk15_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power15 j i k).conj.mul (mpower0_30 j i k) +lemma hk15_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk15_0_30 j i k).Contains (fullFactor false 15 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power15 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 30 (power15_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha15_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2883,2884⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-13043637614),(-13043637613)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha15_0_30_eq (j : Fin 7) : ha15_0_30 j = ((ha15_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha15_0_30_contains (j : Fin 7) : (ha15_0_30 j).Contains (fullFactor false 15 30 ((j.val:ℝ)/6)) := by + rw [ha15_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_0_29 j) false 15 29 j (ha15_0_29_contains j) +noncomputable def hk15_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_0 j i k) +lemma hk15_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_0 j i k).Contains (fullFactor true 15 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 0 (kernel15_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha15_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨0,4⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨625573895434,625573895437⟩,⟨(-214227081645),(-214227081642)⟩⟩,⟨⟨132384326353275230385,132384326353275230804⟩,⟨149359938803361118801,149359938803361119222⟩⟩,⟨⟨(-28810067062832780021385073),(-28810067062832779936816669)⟩,⟨14486376964375100047519274,14486376964375100131573904⟩⟩,⟨⟨(-58231720871487424966415309699),(-58231720871487424854159620381)⟩,⟨(-26845578778470410410385226492),(-26845578778470410298096885403)⟩⟩] +lemma ha15_1_0_eq (j : Fin 7) : ha15_1_0 j = atomKernel15_0 j := by fin_cases j <;> decide +kernel +lemma ha15_1_0_contains (j : Fin 7) : (ha15_1_0 j).Contains (fullFactor true 15 0 ((j.val:ℝ)/6)) := by + rw [ha15_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel15_0_contains j +noncomputable def hk15_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_1 j i k) +lemma hk15_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_1 j i k).Contains (fullFactor true 15 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 1 (kernel15_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha15_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-23),31⟩,⟨(-42),8⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-2864698396932),(-2864698396907)⟩,⟨(-2589347110637),(-2589347110612)⟩⟩,⟨⟨489431859984239291916,489431859984239294500⟩,⟨(-837947705130953727508),(-837947705130953724930)⟩⟩,⟨⟨79472213774095043298203588,79472213774095043701406556⟩,⟨107494824575706493716140980,107494824575706494121235166⟩⟩,⟨⟨(-86005718452907319310299713598),(-86005718452907318883401587765)⟩,⟨215317144707460205231342483657,215317144707460205658470834949⟩⟩] +lemma ha15_1_1_eq (j : Fin 7) : ha15_1_1 j = ((ha15_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha15_1_1_contains (j : Fin 7) : (ha15_1_1 j).Contains (fullFactor true 15 1 ((j.val:ℝ)/6)) := by + rw [ha15_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_0 j) true 15 0 j (ha15_1_0_contains j) +noncomputable def hk15_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_2 j i k) +lemma hk15_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_2 j i k).Contains (fullFactor true 15 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 2 (kernel15_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha15_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-197),104⟩,⟨(-89),204⟩⟩,⟨⟨(-53),154⟩,⟨(-100),107⟩⟩,⟨⟨(-2560025615819),(-2560025615719)⟩,⟨10980751835020,10980751835121⟩⟩,⟨⟨(-2306486536956523932688),(-2306486536956523924766)⟩,⟨(-495690220200613276416),(-495690220200613268488)⟩⟩,⟨⟨191587750265370151223355066,191587750265370152193596853⟩,⟨(-200188333252064110004307444),(-200188333252064109037413542)⟩⟩,⟨⟨396832699157656569054233384096,396832699157656569866762387436⟩,⟨135069033182822761642779371455,135069033182822762454209790513⟩⟩] +lemma ha15_1_2_eq (j : Fin 7) : ha15_1_2 j = ((ha15_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha15_1_2_contains (j : Fin 7) : (ha15_1_2 j).Contains (fullFactor true 15 2 ((j.val:ℝ)/6)) := by + rw [ha15_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_1 j) true 15 1 j (ha15_1_1_contains j) +noncomputable def hk15_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_3 j i k) +lemma hk15_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_3 j i k).Contains (fullFactor true 15 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 3 (kernel15_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha15_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-377),757⟩,⟨(-651),472⟩⟩,⟨⟨(-425),271⟩,⟨(-440),256⟩⟩,⟨⟨21112534549322,21112534549589⟩,⟨(-5999353735881),(-5999353735615)⟩⟩,⟨⟨401688601115852264813,401688601115852281030⟩,⟨3802363419361090332217,3802363419361090348434⟩⟩,⟨⟨(-317588274110024087716860362),(-317588274110024086171384778)⟩,⟨(-213899675238427037127015273),(-213899675238427035577797486)⟩⟩,⟨⟨137741062977387383480494090471,137741062977387384508646548109⟩,⟨(-486111858337694741492911411797),(-486111858337694740462554603186)⟩⟩] +lemma ha15_1_3_eq (j : Fin 7) : ha15_1_3 j = ((ha15_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha15_1_3_contains (j : Fin 7) : (ha15_1_3 j).Contains (fullFactor true 15 3 ((j.val:ℝ)/6)) := by + rw [ha15_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_2 j) true 15 2 j (ha15_1_2_contains j) +noncomputable def hk15_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_4 j i k) +lemma hk15_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_4 j i k).Contains (fullFactor true 15 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 4 (kernel15_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha15_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2056),1162⟩,⟨(-1609),1599⟩⟩,⟨⟨(-901),853⟩,⟨(-665),1089⟩⟩,⟨⟨(-22598648149796),(-22598648149266)⟩,⟨(-22717664327240),(-22717664326710)⟩⟩,⟨⟨4239544125816975678769,4239544125816975703659⟩,⟨(-1904433238686230489227),(-1904433238686230464346)⟩⟩,⟨⟨(-162541118681205133191023302),(-162541118681205131335775039)⟩,⟨362023184194780211338230350,362023184194780213190594499⟩⟩,⟨⟨(-445306669878462460210889292884),(-445306669878462459231045612640)⟩,⟨(-101526927733513473539826172242),(-101526927733513472562818014691)⟩⟩] +lemma ha15_1_4_eq (j : Fin 7) : ha15_1_4 j = ((ha15_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha15_1_4_contains (j : Fin 7) : (ha15_1_4 j).Contains (fullFactor true 15 4 ((j.val:ℝ)/6)) := by + rw [ha15_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_3 j) true 15 3 j (ha15_1_3_contains j) +noncomputable def hk15_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_5 j i k) +lemma hk15_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_5 j i k).Contains (fullFactor true 15 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 5 (kernel15_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha15_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-2979),4342⟩,⟨(-3316),3996⟩⟩,⟨⟨(-1525),2009⟩,⟨(-1951),1583⟩⟩,⟨⟨(-10418862931842),(-10418862930999)⟩,⟨35946189151787,35946189152630⟩⟩,⟨⟨(-3044576310301885074431),(-3044576310301885043887)⟩,⟨(-3340150571014782556265),(-3340150571014782525711)⟩⟩,⟨⟨318690081768096833058830388,318690081768096834834668134⟩,⟨81810767217361637703150258,81810767217361639480508871⟩⟩,⟨⟨(-56599930540124757150322128673),(-56599930540124756407637415155)⟩,⟨325415606367997381944026281898,325415606367997382689401540299⟩⟩] +lemma ha15_1_5_eq (j : Fin 7) : ha15_1_5 j = ((ha15_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha15_1_5_contains (j : Fin 7) : (ha15_1_5 j).Contains (fullFactor true 15 5 ((j.val:ℝ)/6)) := by + rw [ha15_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_4 j) true 15 4 j (ha15_1_4_contains j) +noncomputable def hk15_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_6 j i k) +lemma hk15_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_6 j i k).Contains (fullFactor true 15 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 6 (kernel15_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha15_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-7603),6283⟩,⟨(-7797),6083⟩⟩,⟨⟨(-3324),2611⟩,⟨(-3024),2910⟩⟩,⟨⟨35518079631519,35518079632635⟩,⟨(-8084131697515),(-8084131696399)⟩⟩,⟨⟨(-1802973530615136234569),(-1802973530615136203317)⟩,⟨3187904732439952240391,3187904732439952271638⟩⟩,⟨⟨18294362229336327109471060,18294362229336328528395377⟩,⟨(-226593843997383169441327698),(-226593843997383168022835504)⟩⟩,⟨⟨197618697793113608511014677922,197618697793113608983481362151⟩,⟨23879907184948611096909296487,23879907184948611567352717564⟩⟩] +lemma ha15_1_6_eq (j : Fin 7) : ha15_1_6 j = ((ha15_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha15_1_6_contains (j : Fin 7) : (ha15_1_6 j).Contains (fullFactor true 15 6 ((j.val:ℝ)/6)) := by + rw [ha15_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_5 j) true 15 5 j (ha15_1_5_contains j) +noncomputable def hk15_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_7 j i k) +lemma hk15_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_7 j i k).Contains (fullFactor true 15 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 7 (kernel15_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha15_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-11023),11558⟩,⟨(-9999),12578⟩⟩,⟨⟨(-4062),4479⟩,⟨(-3968),4573⟩⟩,⟨⟨(-20258819518622),(-20258819517356)⟩,⟨(-22651190020228),(-22651190018961)⟩⟩,⟨⟨2494319000515089241861,2494319000515089269258⟩,⟨499843744875283091634,499843744875283119031⟩⟩,⟨⟨(-134083963527644779933418743),(-134083963527644778962375356)⟩,⟨12121900020882973530682592,12121900020882974501614447⟩⟩,⟨⟨7017634420739189197267071111,7017634420739189452680313366⟩,⟨(-102584324816062481936021609509),(-102584324816062481679348468007)⟩⟩] +lemma ha15_1_7_eq (j : Fin 7) : ha15_1_7 j = ((ha15_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha15_1_7_contains (j : Fin 7) : (ha15_1_7 j).Contains (fullFactor true 15 7 ((j.val:ℝ)/6)) := by + rw [ha15_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_6 j) true 15 6 j (ha15_1_6_contains j) +noncomputable def hk15_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_8 j i k) +lemma hk15_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_8 j i k).Contains (fullFactor true 15 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 8 (kernel15_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha15_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-15723),16409⟩,⟨(-17425),14705⟩⟩,⟨⟨(-5312),5444⟩,⟨(-5698),5058⟩⟩,⟨⟨(-7297053885566),(-7297053884308)⟩,⟨20948790345937,20948790347194⟩⟩,⟨⟨(-183813712575673850108),(-183813712575673829093)⟩,⟨(-1535146035112526515883),(-1535146035112526494866)⟩⟩,⟨⟨17994695129012496248721797,17994695129012496830085929⟩,⟨67404396222478305509399851,67404396222478306090975188⟩⟩,⟨⟨(-46469049102037817827503005770),(-46469049102037817705503440376)⟩,⟨(-759782235425478337082612924),(-759782235425478215752335137)⟩⟩] +lemma ha15_1_8_eq (j : Fin 7) : ha15_1_8 j = ((ha15_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha15_1_8_contains (j : Fin 7) : (ha15_1_8 j).Contains (fullFactor true 15 8 ((j.val:ℝ)/6)) := by + rw [ha15_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_7 j) true 15 7 j (ha15_1_7_contains j) +noncomputable def hk15_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_9 j i k) +lemma hk15_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_9 j i k).Contains (fullFactor true 15 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 9 (kernel15_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha15_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-21176),19468⟩,⟨(-19305),21338⟩⟩,⟨⟨(-6239),5801⟩,⟨(-5883),6157⟩⟩,⟨⟨14184763743012,14184763744122⟩,⟨(-2445490624864),(-2445490623754)⟩⟩,⟨⟨(-757090533452023006356),(-757090533452022992025)⟩,⟨352834535793565789884,352834535793565804213⟩⟩,⟨⟨29188128716051348340310780,29188128716051348649897667⟩,⟨(-13442990277986974236270631),(-13442990277986973926822170)⟩⟩,⟨⟨664672863515847585481122140,664672863515847636711296327⟩,⟨18660401461724227774186828652,18660401461724227825726915504⟩⟩] +lemma ha15_1_9_eq (j : Fin 7) : ha15_1_9 j = ((ha15_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha15_1_9_contains (j : Fin 7) : (ha15_1_9 j).Contains (fullFactor true 15 9 ((j.val:ℝ)/6)) := by + rw [ha15_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_8 j) true 15 8 j (ha15_1_8_contains j) +noncomputable def hk15_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_10 j i k) +lemma hk15_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_10 j i k).Contains (fullFactor true 15 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 10 (kernel15_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha15_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-22102),24168⟩,⟨(-23597),22673⟩⟩,⟨⟨(-5886),6243⟩,⟨(-6020),6110⟩⟩,⟨⟨(-5263495714484),(-5263495713602)⟩,⟨(-6553904743419),(-6553904742537)⟩⟩,⟨⟨277735377147687386750,277735377147687395543⟩,⟨296307999341825349684,296307999341825358478⟩⟩,⟨⟨(-7547594100426376764901197),(-7547594100426376616653954)⟩,⟨(-10977418084869787108871500),(-10977418084869786960560510)⟩⟩,⟨⟨6725838771628259267563751076,6725838771628259287158465271⟩,⟨(-590407718691001156908759945),(-590407718691001137439745825)⟩⟩] +lemma ha15_1_10_eq (j : Fin 7) : ha15_1_10 j = ((ha15_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha15_1_10_contains (j : Fin 7) : (ha15_1_10 j).Contains (fullFactor true 15 10 ((j.val:ℝ)/6)) := by + rw [ha15_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_9 j) true 15 9 j (ha15_1_9_contains j) +noncomputable def hk15_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_11 j i k) +lemma hk15_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_11 j i k).Contains (fullFactor true 15 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 11 (kernel15_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha15_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-24819),23067⟩,⟨(-23970),23916⟩⟩,⟨⟨(-5613),5496⟩,⟨(-5658),5451⟩⟩,⟨⟨(-1689414375471),(-1689414374834)⟩,⟨4130443859177,4130443859814⟩⟩,⟨⟨86188332621887914661,86188332621887919568⟩,⟨(-157467880162956726687),(-157467880162956721781)⟩⟩,⟨⟨(-3593654006583865313223255),(-3593654006583865248635504)⟩,⟨3505964284482908939751413,3505964284482909004316215⟩⟩,⟨⟨(-308628268204759549822896842),(-308628268204759543096234252)⟩,⟨(-2197846918024064348573568131),(-2197846918024064341801709344)⟩⟩] +lemma ha15_1_11_eq (j : Fin 7) : ha15_1_11 j = ((ha15_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha15_1_11_contains (j : Fin 7) : (ha15_1_11 j).Contains (fullFactor true 15 11 ((j.val:ℝ)/6)) := by + rw [ha15_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_10 j) true 15 10 j (ha15_1_10_contains j) +noncomputable def hk15_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_12 j i k) +lemma hk15_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_12 j i k).Contains (fullFactor true 15 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 12 (kernel15_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha15_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-22163),23266⟩,⟨(-22426),23003⟩⟩,⟨⟨(-4684),4643⟩,⟨(-4596),4731⟩⟩,⟨⟨2156707367896,2156707368319⟩,⟨(-254925141847),(-254925141425)⟩⟩,⟨⟨(-71508829287481362095),(-71508829287481359586)⟩,⟨(-13297433057265845842),(-13297433057265843332)⟩⟩,⟨⟨1404494218386461420922392,1404494218386461446698181⟩,⟨1017656014294769912723169,1017656014294769938505503⟩⟩,⟨⟨(-656544190399913219629145732),(-656544190399913217483987941)⟩,⟨127263483344247139595633642,127263483344247141726182768⟩⟩] +lemma ha15_1_12_eq (j : Fin 7) : ha15_1_12 j = ((ha15_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha15_1_12_contains (j : Fin 7) : (ha15_1_12 j).Contains (fullFactor true 15 12 ((j.val:ℝ)/6)) := by + rw [ha15_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_11 j) true 15 11 j (ha15_1_11_contains j) +noncomputable def hk15_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_13 j i k) +lemma hk15_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_13 j i k).Contains (fullFactor true 15 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 13 (kernel15_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha15_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-20134),19649⟩,⟨(-20219),19564⟩⟩,⟨⟨(-3580),3649⟩,⟨(-3632),3597⟩⟩,⟨⟨(-569668011292),(-569668011033)⟩,⟨(-791971671935),(-791971671676)⟩⟩,⟨⟨3609797622146720276,3609797622146721461⟩,⟨26963105368978648840,26963105368978650025⟩⟩,⟨⟨243710287018291043505728,243710287018291053005642⟩,⟨(-496501147944250074930468),(-496501147944250065431937)⟩⟩,⟨⟨44833327446599466684009381,44833327446599467306942232⟩,⟨180530882763175071693781929,180530882763175072321005279⟩⟩] +lemma ha15_1_13_eq (j : Fin 7) : ha15_1_13 j = ((ha15_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha15_1_13_contains (j : Fin 7) : (ha15_1_13 j).Contains (fullFactor true 15 13 ((j.val:ℝ)/6)) := by + rw [ha15_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_12 j) true 15 12 j (ha15_1_12_contains j) +noncomputable def hk15_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_14 j i k) +lemma hk15_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_14 j i k).Contains (fullFactor true 15 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 14 (kernel15_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha15_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-16129),16221⟩,⟨(-15932),16419⟩⟩,⟨⟨(-2620),2583⟩,⟨(-2608),2595⟩⟩,⟨⟨(-173818590698),(-173818590550)⟩,⟨367949577243,367949577390⟩⟩,⟨⟨8507080383887302937,8507080383887303457⟩,⟨(-4109710130156672208),(-4109710130156671687)⟩⟩,⟨⟨(-157142896822890047951179),(-157142896822890044701024)⟩,⟨(-46138600764435763749781),(-46138600764435760499487)⟩⟩,⟨⟨45963086726065309246952429,45963086726065309417237566⟩,⟨(-13985228726111315582829828),(-13985228726111315413699412)⟩⟩] +lemma ha15_1_14_eq (j : Fin 7) : ha15_1_14 j = ((ha15_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha15_1_14_contains (j : Fin 7) : (ha15_1_14 j).Contains (fullFactor true 15 14 ((j.val:ℝ)/6)) := by + rw [ha15_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_13 j) true 15 13 j (ha15_1_13_contains j) +noncomputable def hk15_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_15 j i k) +lemma hk15_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_15 j i k).Contains (fullFactor true 15 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 15 (kernel15_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha15_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-12240),12313⟩,⟨(-12412),12141⟩⟩,⟨⟨(-1744),1751⟩,⟨(-1739),1756⟩⟩,⟨⟨158099612087,158099612166⟩,⟨(-10225237149),(-10225237070)⟩⟩,⟨⟨(-2125205039136247149),(-2125205039136246935)⟩,⟨(-2204996245807952913),(-2204996245807952699)⟩⟩,⟨⟨(-5187553943830586139198),(-5187553943830585101299)⟩,⟨44964726852375325914609,44964726852375326952556⟩⟩,⟨⟨(-3942111202732563382593650),(-3942111202732563339733811)⟩,⟨(-10889856645213153745299472),(-10889856645213153702152876)⟩⟩] +lemma ha15_1_15_eq (j : Fin 7) : ha15_1_15 j = ((ha15_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha15_1_15_contains (j : Fin 7) : (ha15_1_15 j).Contains (fullFactor true 15 15 ((j.val:ℝ)/6)) := by + rw [ha15_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_14 j) true 15 14 j (ha15_1_14_contains j) +noncomputable def hk15_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_16 j i k) +lemma hk15_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_16 j i k).Contains (fullFactor true 15 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 16 (kernel15_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha15_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-8784),8686⟩,⟨(-8679),8792⟩⟩,⟨⟨(-1099),1102⟩,⟨(-1104),1097⟩⟩,⟨⟨(-31228332042),(-31228332002)⟩,⟨(-48667494379),(-48667494339)⟩⟩,⟨⟨(-435413478534336185),(-435413478534336102)⟩,⟨822486226160486884,822486226160486967⟩⟩,⟨⟨11709240053361893858973,11709240053361894169719⟩,⟨(-654761877177932907779),(-654761877177932597070)⟩⟩,⟨⟨(-2411458278760950122135610),(-2411458278760950111886925)⟩,⟨1017493194193356470556535,1017493194193356480739136⟩⟩] +lemma ha15_1_16_eq (j : Fin 7) : ha15_1_16 j = ((ha15_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha15_1_16_contains (j : Fin 7) : (ha15_1_16 j).Contains (fullFactor true 15 16 ((j.val:ℝ)/6)) := by + rw [ha15_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_15 j) true 15 15 j (ha15_1_15_contains j) +noncomputable def hk15_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_17 j i k) +lemma hk15_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_17 j i k).Contains (fullFactor true 15 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 17 (kernel15_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha15_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-5816),5884⟩,⟨(-5865),5835⟩⟩,⟨⟨(-654),651⟩,⟨(-652),653⟩⟩,⟨⟨(-9425378470),(-9425378450)⟩,⟨17485381697,17485381717⟩⟩,⟨⟨262334359118344426,262334359118344457⟩,⟨45014456098625043,45014456098625073⟩⟩,⟨⟨(-642457226611800476393),(-642457226611800388849)⟩,⟨(-2786738818555085824850),(-2786738818555085737292)⟩⟩,⟨⟨242764825140712194912229,242764825140712197189124⟩,⟨500987089757133509120961,500987089757133511412057⟩⟩] +lemma ha15_1_17_eq (j : Fin 7) : ha15_1_17 j = ((ha15_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha15_1_17_contains (j : Fin 7) : (ha15_1_17 j).Contains (fullFactor true 15 17 ((j.val:ℝ)/6)) := by + rw [ha15_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_16 j) true 15 16 j (ha15_1_16_contains j) +noncomputable def hk15_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_18 j i k) +lemma hk15_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_18 j i k).Contains (fullFactor true 15 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 18 (kernel15_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha15_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-3718),3683⟩,⟨(-3701),3700⟩⟩,⟨⟨(-365),366⟩,⟨(-365),366⟩⟩,⟨⟨6444107887,6444107897⟩,⟨(-74218501),(-74218491)⟩⟩,⟨⟨(-10531320220854831),(-10531320220854820)⟩,⟨(-71121936203773337),(-71121936203773325)⟩⟩,⟨⟨(-607342621940853143638),(-607342621940853120337)⟩,⟨254852341643027207340,254852341643027230637⟩⟩,⟨⟨97971814481565340434885,97971814481565340918589⟩,⟨(-53927896166649930642501),(-53927896166649930161654)⟩⟩] +lemma ha15_1_18_eq (j : Fin 7) : ha15_1_18 j = ((ha15_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha15_1_18_contains (j : Fin 7) : (ha15_1_18 j).Contains (fullFactor true 15 18 ((j.val:ℝ)/6)) := by + rw [ha15_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_17 j) true 15 17 j (ha15_1_17_contains j) +noncomputable def hk15_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_19 j i k) +lemma hk15_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_19 j i k).Contains (fullFactor true 15 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 19 (kernel15_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha15_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-2211),2225⟩,⟨(-2214),2221⟩⟩,⟨⟨(-194),194⟩,⟨(-195),194⟩⟩,⟨⟨(-979782838),(-979782833)⟩,⟨(-1721488150),(-1721488145)⟩⟩,⟨⟨(-16453888042155436),(-16453888042155431)⟩,⟨8233140571867490,8233140571867495⟩⟩,⟨⟨77310617344702121125,77310617344702126999⟩,⟨121141085236577360601,121141085236577366476⟩⟩,⟨⟨(-11217449129925969720171),(-11217449129925969623967)⟩,⟨(-18086976379205769019271),(-18086976379205768922527)⟩⟩] +lemma ha15_1_19_eq (j : Fin 7) : ha15_1_19 j = ((ha15_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha15_1_19_contains (j : Fin 7) : (ha15_1_19 j).Contains (fullFactor true 15 19 ((j.val:ℝ)/6)) := by + rw [ha15_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_18 j) true 15 18 j (ha15_1_18_contains j) +noncomputable def hk15_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_20 j i k) +lemma hk15_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_20 j i k).Contains (fullFactor true 15 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 20 (kernel15_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha15_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1265),1261⟩,⟨(-1265),1260⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨(-301053578),(-301053575)⟩,⟨493839787,493839790⟩⟩,⟨⟨3148526298655337,3148526298655340⟩,⟨3177032113605567,3177032113605570⟩⟩,⟨⟨22022346920094668566,22022346920094669974⟩,⟨(-20057851764723305843),(-20057851764723304435)⟩⟩,⟨⟨(-3160310230924031310217),(-3160310230924031291835)⟩,⟨2195137655675748406775,2195137655675748425061⟩⟩] +lemma ha15_1_20_eq (j : Fin 7) : ha15_1_20 j = ((ha15_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha15_1_20_contains (j : Fin 7) : (ha15_1_20 j).Contains (fullFactor true 15 20 ((j.val:ℝ)/6)) := by + rw [ha15_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_19 j) true 15 19 j (ha15_1_19_contains j) +noncomputable def hk15_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_21 j i k) +lemma hk15_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_21 j i k).Contains (fullFactor true 15 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 21 (kernel15_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha15_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-685),685⟩,⟨(-684),686⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨160697625,160697627⟩,⟨6681225,6681227⟩⟩,⟨⟨471748304129511,471748304129513⟩,⟨(-921928267152629),(-921928267152627)⟩⟩,⟨⟨(-4640605343711136063),(-4640605343711135741)⟩,⟨(-3611474314318475652),(-3611474314318475330)⟩⟩,⟨⟨405720061178166583300,405720061178166586611⟩,⟨523798770182581203669,523798770182581206996⟩⟩] +lemma ha15_1_21_eq (j : Fin 7) : ha15_1_21 j = ((ha15_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha15_1_21_contains (j : Fin 7) : (ha15_1_21 j).Contains (fullFactor true 15 21 ((j.val:ℝ)/6)) := by + rw [ha15_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_20 j) true 15 20 j (ha15_1_20_contains j) +noncomputable def hk15_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_22 j i k) +lemma hk15_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_22 j i k).Contains (fullFactor true 15 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 22 (kernel15_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha15_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-355),355⟩,⟨(-355),355⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-19120124),(-19120122)⟩,⟨(-38172563),(-38172562)⟩⟩,⟨⟨(-226098430574011),(-226098430574009)⟩,⟨(-35564641660123),(-35564641660121)⟩⟩,⟨⟨(-522069999585921152),(-522069999585921081)⟩,⟨977355735340744596,977355735340744667⟩⟩,⟨⟨82512162792955925322,82512162792955925898⟩,⟨(-71064598054666030852),(-71064598054666030279)⟩⟩] +lemma ha15_1_22_eq (j : Fin 7) : ha15_1_22 j = ((ha15_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha15_1_22_contains (j : Fin 7) : (ha15_1_22 j).Contains (fullFactor true 15 22 ((j.val:ℝ)/6)) := by + rw [ha15_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_21 j) true 15 21 j (ha15_1_21_contains j) +noncomputable def hk15_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_23 j i k) +lemma hk15_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_23 j i k).Contains (fullFactor true 15 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 23 (kernel15_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha15_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-176),176⟩,⟨(-176),176⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-6125499),(-6125497)⟩,⟨8943427,8943428⟩⟩,⟨⟨7752672013700,7752672013702⟩,⟨47759365910783,47759365910785⟩⟩,⟨⟨189586262789742919,189586262789742935⟩,⟨62802344945326088,62802344945326104⟩⟩,⟨⟨(-11830856502292973303),(-11830856502292973207)⟩,⟨(-12374327409537990826),(-12374327409537990729)⟩⟩] +lemma ha15_1_23_eq (j : Fin 7) : ha15_1_23 j = ((ha15_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha15_1_23_contains (j : Fin 7) : (ha15_1_23 j).Contains (fullFactor true 15 23 ((j.val:ℝ)/6)) := by + rw [ha15_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_22 j) true 15 22 j (ha15_1_22_contains j) +noncomputable def hk15_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_24 j i k) +lemma hk15_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_24 j i k).Contains (fullFactor true 15 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 24 (kernel15_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha15_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-84),84⟩,⟨(-84),84⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨2625858,2625860⟩,⟨249207,249208⟩⟩,⟨⟨8704153872782,8704153872784⟩,⟨(-4507905184802),(-4507905184800)⟩⟩,⟨⟨5126650465711862,5126650465711866⟩,⟨(-34114500675306509),(-34114500675306505)⟩⟩,⟨⟨(-1769270786662302653),(-1769270786662302637)⟩,⟨1876879160420998496,1876879160420998512⟩⟩] +lemma ha15_1_24_eq (j : Fin 7) : ha15_1_24 j = ((ha15_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha15_1_24_contains (j : Fin 7) : (ha15_1_24 j).Contains (fullFactor true 15 24 ((j.val:ℝ)/6)) := by + rw [ha15_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_23 j) true 15 23 j (ha15_1_23_contains j) +noncomputable def hk15_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_25 j i k) +lemma hk15_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_25 j i k).Contains (fullFactor true 15 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 25 (kernel15_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha15_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-246326),(-246324)⟩,⟨(-564756),(-564754)⟩⟩,⟨⟨(-1360654760856),(-1360654760854)⟩,⟨(-1335280545191),(-1335280545189)⟩⟩,⟨⟨(-5719142408384237),(-5719142408384235)⟩,⟨123325192930835,123325192930837⟩⟩,⟨⟨284387257174484265,284387257174484268⟩,⟨241458199398735454,241458199398735457⟩⟩] +lemma ha15_1_25_eq (j : Fin 7) : ha15_1_25 j = ((ha15_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha15_1_25_contains (j : Fin 7) : (ha15_1_25 j).Contains (fullFactor true 15 25 ((j.val:ℝ)/6)) := by + rw [ha15_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_24 j) true 15 24 j (ha15_1_24_contains j) +noncomputable def hk15_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_26 j i k) +lemma hk15_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_26 j i k).Contains (fullFactor true 15 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 26 (kernel15_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha15_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-18),18⟩,⟨(-18),18⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-84148),(-84147)⟩,⟨109866,109868⟩⟩,⟨⟨(-157965566007),(-157965566006)⟩,⟨319601395790,319601395792⟩⟩,⟨⟨174301566456258,174301566456259⟩,⟨895289664226572,895289664226573⟩⟩,⟨⟨31481211390298999,31481211390299000⟩,⟨(-41241123333053736),(-41241123333053735)⟩⟩] +lemma ha15_1_26_eq (j : Fin 7) : ha15_1_26 j = ((ha15_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha15_1_26_contains (j : Fin 7) : (ha15_1_26 j).Contains (fullFactor true 15 26 ((j.val:ℝ)/6)) := by + rw [ha15_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_25 j) true 15 25 j (ha15_1_25_contains j) +noncomputable def hk15_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_27 j i k) +lemma hk15_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_27 j i k).Contains (fullFactor true 15 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 27 (kernel15_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha15_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-8),8⟩,⟨(-8),8⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨29605,29607⟩,⟨4404,4405⟩⟩,⟨⟨63552930965,63552930966⟩,⟨9092191472,9092191473⟩⟩,⟨⟨130917105456939,130917105456940⟩,⟨(-49727056261603),(-49727056261601)⟩⟩,⟨⟨(-5734596402523010),(-5734596402523009)⟩,⟨(-3923536666890048),(-3923536666890047)⟩⟩] +lemma ha15_1_27_eq (j : Fin 7) : ha15_1_27 j = ((ha15_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha15_1_27_contains (j : Fin 7) : (ha15_1_27 j).Contains (fullFactor true 15 27 ((j.val:ℝ)/6)) := by + rw [ha15_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_26 j) true 15 26 j (ha15_1_26_contains j) +noncomputable def hk15_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_28 j i k) +lemma hk15_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_28 j i k).Contains (fullFactor true 15 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 28 (kernel15_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha15_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2189),(-2188)⟩,⟨(-5847),(-5846)⟩⟩,⟨⟨(-1939268497),(-1939268495)⟩,⟨(-10978277340),(-10978277339)⟩⟩,⟨⟨(-10548404384211),(-10548404384210)⟩,⟨(-17850432717514),(-17850432717513)⟩⟩,⟨⟨(-467542452399819),(-467542452399818)⟩,⟨765875448926351,765875448926352⟩⟩] +lemma ha15_1_28_eq (j : Fin 7) : ha15_1_28 j = ((ha15_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha15_1_28_contains (j : Fin 7) : (ha15_1_28 j).Contains (fullFactor true 15 28 ((j.val:ℝ)/6)) := by + rw [ha15_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_27 j) true 15 27 j (ha15_1_27_contains j) +noncomputable def hk15_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_29 j i k) +lemma hk15_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_29 j i k).Contains (fullFactor true 15 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 29 (kernel15_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha15_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-817),(-816)⟩,⟨955,957⟩⟩,⟨⟨(-1647615162),(-1647615160)⟩,⟨882600101,882600102⟩⟩,⟨⟨(-2258448542260),(-2258448542259)⟩,⟨1919500148939,1919500148940⟩⟩,⟨⟨98392696649395,98392696649396⟩,⟨53258516137027,53258516137028⟩⟩] +lemma ha15_1_29_eq (j : Fin 7) : ha15_1_29 j = ((ha15_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha15_1_29_contains (j : Fin 7) : (ha15_1_29 j).Contains (fullFactor true 15 29 ((j.val:ℝ)/6)) := by + rw [ha15_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_28 j) true 15 28 j (ha15_1_28_contains j) +noncomputable def hk15_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel15_0 j i k).mul (mpower1_30 j i k) +lemma hk15_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk15_1_30 j i k).Contains (fullFactor true 15 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk15_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel15_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 15 30 (kernel15_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha15_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨239,241⟩,⟨48,50⟩⟩,⟨⟨219144240,219144241⟩,⟨209150349,209150350⟩⟩,⟨⟨314412101283,314412101284⟩,⟨262483908643,262483908644⟩⟩,⟨⟨5794745396292,5794745396293⟩,⟨(-12176637327149),(-12176637327147)⟩⟩] +lemma ha15_1_30_eq (j : Fin 7) : ha15_1_30 j = ((ha15_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha15_1_30_contains (j : Fin 7) : (ha15_1_30 j).Contains (fullFactor true 15 30 ((j.val:ℝ)/6)) := by + rw [ha15_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha15_1_29 j) true 15 29 j (ha15_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders16.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders16.lean new file mode 100644 index 0000000000000000000000000000000000000000..1136d5aa4eb88831a2e4b5bf2a7c232329365078 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders16.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.KernelValues20 +import OAI.Analysis.PlanarPacking.Certificate.Powers20 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk16_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_0 j i k) +lemma hk16_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_0 j i k).Contains (fullFactor false 16 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 0 (power16_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha16_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999809,1000000000000000000000000000255⟩,⟨(-255),255⟩⟩,⟨⟨(-500000000000000000041666486146),(-499999999999999999969218260206)⟩,⟨866025403784438646724483957650,866025403784438646796678072649⟩⟩,⟨⟨(-500000000000000000087874065327),(-499999999999999999890356441924)⟩,⟨(-866025403784438646868859290461),(-866025403784438646671155673552)⟩⟩,⟨⟨999999999999999999947733200609,1000000000000000000052266799407⟩,⟨(-33413865663),71119733151⟩⟩,⟨⟨(-500000000000000000292003818150),(-499999999999999999751535167376)⟩,⟨866025403784438646480988208164,866025403784438647021320888286⟩⟩,⟨⟨(-500000000000000000312831245029),(-499999999999999999632745023075)⟩,⟨(-866025403784438647119544536264),(-866025403784438646439323361456)⟩⟩,⟨⟨999999999999999999895148835489,1000000000000000000104851164575⟩,⟨(-67145296991),142557032095⟩⟩] +lemma ha16_0_0_eq (j : Fin 7) : ha16_0_0 j = ((atomPoints j).direct.powBin 7 16).conj := by fin_cases j <;> decide +kernel +lemma ha16_0_0_contains (j : Fin 7) : (ha16_0_0 j).Contains (fullFactor false 16 0 ((j.val:ℝ)/6)) := by + rw [ha16_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 16) ((j.val:ℝ)/6) 16 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 16 (by norm_num)) +noncomputable def hk16_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_1 j i k) +lemma hk16_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_1 j i k).Contains (fullFactor false 16 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 1 (power16_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha16_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-453449841058554462666836546856),(-453449841058554462627592420960)⟩,⟨(-261799387799149436560983187798),(-261799387799149436522216052065)⟩⟩,⟨⟨906899682117108925199339593406,906899682117108925409261088246⟩,⟨(-523598775598298873170354839359),(-523598775598298872961848201144)⟩⟩,⟨⟨(-111714615597),52486377448⟩,⟨1570796326794896619147899503503,1570796326794896619317100496522⟩⟩,⟨⟨(-1813799364234217851137837000277),(-1813799364234217850000393378670)⟩,⟨(-1047197551196597746768238033281),(-1047197551196597745632949804767)⟩⟩,⟨⟨2267249205292772312391413409730,2267249205292772314179445159427⟩,⟨(-1308996938995747183514823617665),(-1308996938995747181730195385414)⟩⟩,⟨⟨(-447856124748),210943171751⟩,⟨3141592653589793238130600351851,3141592653589793238799399648350⟩⟩] +lemma ha16_0_1_eq (j : Fin 7) : ha16_0_1 j = ((ha16_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha16_0_1_contains (j : Fin 7) : (ha16_0_1 j).Contains (fullFactor false 16 1 ((j.val:ℝ)/6)) := by + rw [ha16_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_0 j) false 16 0 j (ha16_0_0_contains j) +noncomputable def hk16_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_2 j i k) +lemma hk16_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_2 j i k).Contains (fullFactor false 16 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 2 (power16_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha16_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨68538919452009434848682464886,68538919452009434859049843446⟩,⟨(-118712890786751174413010674317),(-118712890786751174402358711313)⟩⟩,⟨⟨274155677808037739351489029060,274155677808037739461535514162⟩,⟨474851563147004697580194341509,474851563147004697691620478652⟩⟩,⟨⟨(-1233700550136169827424570827429),(-1233700550136169827287753687448)⟩,⟨(-87740453915),41222704452⟩⟩,⟨⟨1096622711232150957101486991300,1096622711232150958293848702609⟩,⟨(-1899406252588018791100867616133),(-1899406252588018789903693443076)⟩⟩,⟨⟨1713472986300235870063986017312,1713472986300235872405513064489⟩,⟨2967822269668779359081737826186,2967822269668779361431712785060⟩⟩,⟨⟨(-4934802200544679309957776750659),(-4934802200544679308891521309086)⟩,⟨(-703490755687),331348759349⟩⟩] +lemma ha16_0_2_eq (j : Fin 7) : ha16_0_2 j = ((ha16_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha16_0_2_contains (j : Fin 7) : (ha16_0_2 j).Contains (fullFactor false 16 2 ((j.val:ℝ)/6)) := by + rw [ha16_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_1 j) false 16 1 j (ha16_0_1_contains j) +noncomputable def hk16_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_3 j i k) +lemma hk16_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_3 j i k).Contains (fullFactor false 16 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 3 (power16_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha16_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20719308087892496641424336985,20719308087892496643349406855⟩,⟨11962298101967523215080707308,11962298101967523216928233393⟩⟩,⟨⟨(-165754464703139973160610506749),(-165754464703139973121187834581)⟩,⟨95698384815740185705551761201,95698384815740185744269848528⟩⟩,⟨⟨(-21584157578),45940794241⟩,⟨(-645964097506246253694056970855),(-645964097506246253620363516296)⟩⟩,⟨⟨1326035717625119784678323168137,1326035717625119785518329312511⟩,⟨765587078525921485431854541577,765587078525921486266716990420⟩⟩,⟨⟨(-2589913510986562081384232077942),(-2589913510986562079325248108600)⟩,⟨1495287262745940400878840122096,1495287262745940402926967594170⟩⟩,⟨⟨(-346987609383),736693796645⟩,⟨(-5167712780049970029824196662745),(-5167712780049970028691167234710)⟩⟩] +lemma ha16_0_3_eq (j : Fin 7) : ha16_0_3 j = ((ha16_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha16_0_3_contains (j : Fin 7) : (ha16_0_3 j).Contains (fullFactor false 16 3 ((j.val:ℝ)/6)) := by + rw [ha16_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_2 j) false 16 2 j (ha16_0_2_contains j) +noncomputable def hk16_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_4 j i k) +lemma hk16_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_4 j i k).Contains (fullFactor false 16 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 4 (power16_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha16_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1565861159883012430000484294),(-1565861159883012429753659403)⟩,⟨2712151086516110563263935768,2712151086516110563524559871⟩⟩,⟨⟨(-25053778558128198882323097614),(-25053778558128198872106977400)⟩,⟨(-43394417384257769020009782413),(-43394417384257769009550822252)⟩⟩,⟨⟨253669507901048013622451107748,253669507901048013652197914803⟩,⟨(-8476078861),18040907711⟩⟩,⟨⟨(-400860456930051182280824653794),(-400860456930051181842415719321)⟩,⟨694310678148124304000351921904,694310678148124304442388170125⟩⟩,⟨⟨(-978663224926882769281060638439),(-978663224926882767937449160830)⟩,⟨(-1695094429072569102834804987656),(-1695094429072569101481807477850)⟩⟩,⟨⟨4058712126416768217745792923601,4058712126416768218648591437406⟩,⟨(-272523431132),578597954872⟩⟩] +lemma ha16_0_4_eq (j : Fin 7) : ha16_0_4 j = ((ha16_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha16_0_4_contains (j : Fin 7) : (ha16_0_4 j).Contains (fullFactor false 16 4 ((j.val:ℝ)/6)) := by + rw [ha16_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_3 j) false 16 3 j (ha16_0_3_contains j) +noncomputable def hk16_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_5 j i k) +lemma hk16_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_5 j i k).Contains (fullFactor false 16 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 5 (power16_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha16_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-284015797627486289501357103),(-284015797627486289473160559)⟩,⟨(-163976597214335483802633020),(-163976597214335483776263623)⟩⟩,⟨⟨9088505524079561262581484121,9088505524079561264800933227⟩,⟨(-5247251110858735482169182174),(-5247251110858735480012820439)⟩⟩,⟨⟨(-5667718313),2662838709⟩,⟨79692626246167045116004998113,79692626246167045125603902673⟩⟩,⟨⟨(-290832176770545960524830137722),(-290832176770545960338744679479)⟩,⟨(-167912035547479535497965514161),(-167912035547479535313790728509)⟩⟩,⟨⟨887549367585894654311378848381,887549367585894655022631845287⟩,⟨(-512426866294798387161132401872),(-512426866294798386455987971939)⟩⟩,⟨⟨(-363543816882),171231521836⟩,⟨2550164039877345443578061182647,2550164039877345444153423642629⟩⟩] +lemma ha16_0_5_eq (j : Fin 7) : ha16_0_5 j = ((ha16_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha16_0_5_contains (j : Fin 7) : (ha16_0_5 j).Contains (fullFactor false 16 5 ((j.val:ℝ)/6)) := by + rw [ha16_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_4 j) false 16 4 j (ha16_0_4_contains j) +noncomputable def hk16_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_6 j i k) +lemma hk16_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_6 j i k).Contains (fullFactor false 16 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 6 (power16_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha16_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨14309657588033580844761234,14309657588033580847107948⟩,⟨(-24785053981387676528195828),(-24785053981387676525656321)⟩⟩,⟨⟨915818085634149173920272839,915818085634149174299544101⟩,⟨1586243454808811297544326570,1586243454808811297936742686⟩⟩,⟨⟨(-20863480763352960874435238650),(-20863480763352960871855840790)⟩,⟨(-1483805185),697129544⟩⟩,⟨⟨58612357480585547114624177387,58612357480585547179099874492⟩,⟨(-101519581107763923085823799213),(-101519581107763923020544573620)⟩⟩,⟨⟨223588399813024700548931261374,223588399813024700857320265467⟩,⟨387266468459182445585862822882,387266468459182445897438195606⟩⟩,⟨⟨(-1335262768854589496034069218596),(-1335262768854589495728559865624)⟩,⟨(-190351097396),89656615178⟩⟩] +lemma ha16_0_6_eq (j : Fin 7) : ha16_0_6 j = ((ha16_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha16_0_6_contains (j : Fin 7) : (ha16_0_6 j).Contains (fullFactor false 16 6 ((j.val:ℝ)/6)) := by + rw [ha16_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_5 j) false 16 5 j (ha16_0_5_contains j) +noncomputable def hk16_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_7 j i k) +lemma hk16_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_7 j i k).Contains (fullFactor false 16 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 7 (power16_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha16_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1853917702541761442162643,1853917702541761442358500⟩,⟨1070359884617898514030558,1070359884617898514209500⟩⟩,⟨⟨(-237301465925345464641666419),(-237301465925345464582205750)⟩,⟨137006065231091009774302419,137006065231091009831477372⟩⟩,⟨⟨(-156435504),332965105⟩,⟨(-4681754135318688101006906555),(-4681754135318688100413188541)⟩⟩,⟨⟨30374587638444219459852487519,30374587638444219479480671459⟩,⟨17536776349579649246241754375,17536776349579649265588659132⟩⟩,⟨⟨(-144837320511075112738255137216),(-144837320511075112621265188802)⟩,⟨83621865985773321352364358852,83621865985773321467967753342⟩⟩,⟨⟨(-40237794799),85429372741⟩,⟨(-599264529320792076960395983747),(-599264529320792076821376188519)⟩⟩] +lemma ha16_0_7_eq (j : Fin 7) : ha16_0_7 j = ((ha16_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha16_0_7_contains (j : Fin 7) : (ha16_0_7 j).Contains (fullFactor false 16 7 ((j.val:ℝ)/6)) := by + rw [ha16_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_6 j) false 16 6 j (ha16_0_6_contains j) +noncomputable def hk16_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_8 j i k) +lemma hk16_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_8 j i k).Contains (fullFactor false 16 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 8 (power16_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha16_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-70054890629433514733695),(-70054890629433514721760)⟩,⟨121338629888859693708276,121338629888859693721482⟩⟩,⟨⟨(-17934052001134979773483222),(-17934052001134979765941951)⟩,⟨(-31062689251548081595288265),(-31062689251548081587406005)⟩⟩,⟨⟨919260274839426580187481593,919260274839426580306983950⟩,⟨(-30716040),65377546⟩⟩,⟨⟨(-4591117312290554823886071952),(-4591117312290554818806450149)⟩,⟨7952048448396308884629775253,7952048448396308889793733950⟩⟩,⟨⟨(-27365191652122466707690443225),(-27365191652122466669772214732)⟩,⟨(-47397902300335817877624312226),(-47397902300335817839188568924)⟩⟩,⟨⟨235330630358893204515620576300,235330630358893204570962602886⟩,⟨(-15801345068),33548036226⟩⟩] +lemma ha16_0_8_eq (j : Fin 7) : ha16_0_8 j = ((ha16_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha16_0_8_contains (j : Fin 7) : (ha16_0_8 j).Contains (fullFactor false 16 8 ((j.val:ℝ)/6)) := by + rw [ha16_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_7 j) false 16 7 j (ha16_0_7_contains j) +noncomputable def hk16_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_9 j i k) +lemma hk16_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_9 j i k).Contains (fullFactor false 16 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 9 (power16_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha16_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-7059195338064676366980),(-7059195338064676366188)⟩,⟨(-4075628328693792152859),(-4075628328693792152150)⟩⟩,⟨⟨3614308013089114299266165,3614308013089114300194813⟩,⟨(-2086721704291221582456196),(-2086721704291221581572086)⟩⟩,⟨⟨(-11410535),5360961⟩,⟨160441184787359821863060144,160441184787359821884427941⟩⟩,⟨⟨(-1850525702701626522025524368),(-1850525702701626520817926205)⟩,⟨(-1068401512597105450653757128),(-1068401512597105449468274629)⟩⟩,⟨⟨13787490894657571023172860107,13787490894657571034397251573⟩,⟨(-7960211579480062802868047623),(-7960211579480062791812743919)⟩⟩,⟨⟨(-11710473795),5515709954⟩,⟨82145886611128228789567204599,82145886611128228809146694651⟩⟩] +lemma ha16_0_9_eq (j : Fin 7) : ha16_0_9 j = ((ha16_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha16_0_9_contains (j : Fin 7) : (ha16_0_9 j).Contains (fullFactor false 16 9 ((j.val:ℝ)/6)) := by + rw [ha16_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_8 j) false 16 8 j (ha16_0_8_contains j) +noncomputable def hk16_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_10 j i k) +lemma hk16_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_10 j i k).Contains (fullFactor false 16 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 10 (power16_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha16_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨213399400269781075710,213399400269781075749⟩,⟨(-369618603571988403213),(-369618603571988403169)⟩⟩,⟨⟨218520985876255821493353,218520985876255821586633⟩,⟨378489450057716124822786,378489450057716124921239⟩⟩,⟨⟨(-25202042373060605482960405),(-25202042373060605479523737)⟩,⟨(-1792363),842098⟩⟩,⟨⟨223765489537285961147066909,223765489537285961396066051⟩,⟨(-387573196859101311987579652),(-387573196859101311733427199)⟩⟩,⟨⟨2083978518259580816085493563,2083978518259580818986398816⟩,⟨3609556675507699248518616798,3609556675507699251468645189⟩⟩,⟨⟨(-25806891390014060015908492673),(-25806891390014060009675268575)⟩,⟨(-3678953845),1732811388⟩⟩] +lemma ha16_0_10_eq (j : Fin 7) : ha16_0_10 j = ((ha16_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha16_0_10_contains (j : Fin 7) : (ha16_0_10 j).Contains (fullFactor false 16 10 ((j.val:ℝ)/6)) := by + rw [ha16_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_9 j) false 16 9 j (ha16_0_9_contains j) +noncomputable def hk16_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_11 j i k) +lemma hk16_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_11 j i k).Contains (fullFactor false 16 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 11 (power16_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha16_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨17593804388058740563,17593804388058740566⟩,⟨10157787699515332859,10157787699515332862⟩⟩,⟨⟨(-36032111386744300681469),(-36032111386744300671981)⟩,⟨20803149208607401693437,20803149208607401702384⟩⟩,⟨⟨(-120252),255949⟩,⟨(-3598843235212085340739342),(-3598843235212085340237130)⟩⟩,⟨⟨73793764120052327760013457,73793764120052327808638865⟩,⟨42604849579227958656330423,42604849579227958703875365⟩⟩,⟨⟨(-859072479885680692002741520),(-859072479885680691297901891)⟩,⟨495985727515397111957524334,495985727515397112649516942⟩⟩,⟨⟨(-494889776),1050706762⟩,⟨(-7370430945714350778221739635),(-7370430945714350776418074184)⟩⟩] +lemma ha16_0_11_eq (j : Fin 7) : ha16_0_11 j = ((ha16_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha16_0_11_contains (j : Fin 7) : (ha16_0_11 j).Contains (fullFactor false 16 11 ((j.val:ℝ)/6)) := by + rw [ha16_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_10 j) false 16 10 j (ha16_0_10_contains j) +noncomputable def hk16_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_12 j i k) +lemma hk16_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_12 j i k).Contains (fullFactor false 16 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 12 (power16_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha16_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-443217100187807443),(-443217100187807442)⟩,⟨767674536308627877,767674536308627878⟩⟩,⟨⟨(-1815417242369259285882),(-1815417242369259285095)⟩,⟨(-3144394900720139785396),(-3144394900720139784557)⟩⟩,⟨⟨471087477881817150337648,471087477881817150404888⟩,⟨(-15741),33504⟩⟩,⟨⟨(-7435949024744486038007907),(-7435949024744486029686079)⟩,⟨12879441513349692554718068,12879441513349692563245801⟩⟩,⟨⟨(-108207299850538926523843114),(-108207299850538926372529311)⟩,⟨(-187420541090973602909166540),(-187420541090973602754797808)⟩⟩,⟨⟨1929574309403923047681544576,1929574309403923048159885113⟩,⟨(-129561841),275074388⟩⟩] +lemma ha16_0_12_eq (j : Fin 7) : ha16_0_12 j = ((ha16_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha16_0_12_contains (j : Fin 7) : (ha16_0_12 j).Contains (fullFactor false 16 12 ((j.val:ℝ)/6)) := by + rw [ha16_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_11 j) false 16 11 j (ha16_0_11_contains j) +noncomputable def hk16_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_13 j i k) +lemma hk16_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_13 j i k).Contains (fullFactor false 16 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 13 (power16_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha16_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-30919495943783800),(-30919495943783799)⟩,⟨(-17851379306351119),(-17851379306351118)⟩⟩,⟨⟨253292510771476882251,253292510771476882320⟩,⟨(-146238499277628361542),(-146238499277628361477)⟩⟩,⟨⟨(-4049),1902⟩,⟨56921729219679268114154,56921729219679268122461⟩⟩,⟨⟨(-2074972248239938620325396),(-2074972248239938618944910)⟩,⟨(-1197985786082331538239416),(-1197985786082331536894895)⟩⟩,⟨⟨37743525322001707879191293,37743525322001707910398850⟩,⟨(-21791234504823142529663850),(-21791234504823142499122285)⟩⟩,⟨⟨(-66474745),31310041⟩,⟨466302805767612564366635917,466302805767612564483716446⟩⟩] +lemma ha16_0_13_eq (j : Fin 7) : ha16_0_13 j = ((ha16_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha16_0_13_contains (j : Fin 7) : (ha16_0_13 j).Contains (fullFactor false 16 13 ((j.val:ℝ)/6)) := by + rw [ha16_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_12 j) false 16 12 j (ha16_0_12_contains j) +noncomputable def hk16_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_14 j i k) +lemma hk16_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_14 j i k).Contains (fullFactor false 16 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 14 (power16_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha16_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨667640024824732,667640024824733⟩,⟨(-1156386444162984),(-1156386444162983)⟩⟩,⟨⟨10938614166728417756,10938614166728417762⟩,⟨18946235501166317748,18946235501166317754⟩⟩,⟨⟨(-6386603083791852241634),(-6386603083791852240680)⟩,⟨(-455),214⟩⟩,⟨⟨179218254507678396467702,179218254507678396669413⟩,⟨(-310415122451108950133811),(-310415122451108949926302)⟩⟩,⟨⟨4074951323393142875491402,4074951323393142881215633⟩,⟨7058022730486958378409522,7058022730486958384267789⟩⟩,⟨⟨(-104638104924845707132418567),(-104638104924845707105812683)⟩,⟨(-14916898),7025957⟩⟩] +lemma ha16_0_14_eq (j : Fin 7) : ha16_0_14 j = ((ha16_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha16_0_14_contains (j : Fin 7) : (ha16_0_14 j).Contains (fullFactor false 16 14 ((j.val:ℝ)/6)) := by + rw [ha16_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_13 j) false 16 13 j (ha16_0_13_contains j) +noncomputable def hk16_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_15 j i k) +lemma hk16_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_15 j i k).Contains (fullFactor false 16 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 15 (power16_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha16_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨40365501752147,40365501752148⟩,⟨23305033302576,23305033302577⟩⟩,⟨⟨(-1322696761414360853),(-1322696761414360852)⟩,⟨763659331258827443,763659331258827444⟩⟩,⟨⟨(-23),48⟩,⟨(-668803510981146723307),(-668803510981146723204)⟩⟩,⟨⟨43342127478025776405707,43342127478025776434819⟩,⟨25023588966689257650977,25023588966689257679221⟩⟩,⟨⟨(-1231857353275977869763401),(-1231857353275977868737019)⟩,⟨711213174517105745878554,711213174517105746879886⟩⟩,⟨⟨(-1471513),3124188⟩,⟨(-21915353447830215830452285),(-21915353447830215824810202)⟩⟩] +lemma ha16_0_15_eq (j : Fin 7) : ha16_0_15 j = ((ha16_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha16_0_15_contains (j : Fin 7) : (ha16_0_15 j).Contains (fullFactor false 16 15 ((j.val:ℝ)/6)) := by + rw [ha16_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_14 j) false 16 14 j (ha16_0_14_contains j) +noncomputable def hk16_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_16 j i k) +lemma hk16_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_16 j i k).Contains (fullFactor false 16 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 16 (power16_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha16_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-762655431407),(-762655431406)⟩,⟨1320957955864,1320957955865⟩⟩,⟨⟨(-49981386352667222),(-49981386352667221)⟩,⟨(-86570300595549324),(-86570300595549323)⟩⟩,⟨⟨65659631149794723617,65659631149794723629⟩,⟨(-3),5⟩⟩,⟨⟨(-3275580136008399051412),(-3275580136008399047703)⟩,⟨5673471219829920492825,5673471219829920496654⟩⟩,⟨⟨(-116371983552042445763693),(-116371983552042445599479)⟩,⟨(-201562188089707223685470),(-201562188089707223516886)⟩⟩,⟨⟨4303069587032947006788710,4303069587032947007910229⟩,⟨(-288931),613433⟩⟩] +lemma ha16_0_16_eq (j : Fin 7) : ha16_0_16 j = ((ha16_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha16_0_16_contains (j : Fin 7) : (ha16_0_16 j).Contains (fullFactor false 16 16 ((j.val:ℝ)/6)) := by + rw [ha16_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_15 j) false 16 15 j (ha16_0_15_contains j) +noncomputable def hk16_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_17 j i k) +lemma hk16_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_17 j i k).Contains (fullFactor false 16 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 17 (power16_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha16_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-40685409901),(-40685409900)⟩,⟨(-23489732359),(-23489732358)⟩⟩,⟨⟨5332718046471330,5332718046471331⟩,⟨(-3078846199642598),(-3078846199642597)⟩⟩,⟨⟨(-1),1⟩,⟨6066935731106195666,6066935731106195668⟩⟩,⟨⟨(-698970019787090239450),(-698970019787090238975)⟩,⟨(-403550529079554596961),(-403550529079554596502)⟩⟩,⟨⟨31040504379613153626774,31040504379613153652835⟩,⟨(-17921243559351411754986),(-17921243559351411729639)⟩⟩,⟨⟨(-113363),53395⟩,⟨795205400147551278383567,795205400147551278593356⟩⟩] +lemma ha16_0_17_eq (j : Fin 7) : ha16_0_17 j = ((ha16_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha16_0_17_contains (j : Fin 7) : (ha16_0_17 j).Contains (fullFactor false 16 17 ((j.val:ℝ)/6)) := by + rw [ha16_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_16 j) false 16 16 j (ha16_0_16_contains j) +noncomputable def hk16_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_18 j i k) +lemma hk16_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_18 j i k).Contains (fullFactor false 16 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 18 (power16_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha16_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨683288616,683288617⟩,⟨(-1183490601),(-1183490600)⟩⟩,⟨⟨179120011154259,179120011154260⟩,⟨310244959971482,310244959971483⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨(-1),1⟩⟩,⟨⟨46955236204022331344,46955236204022331399⟩,⟨(-81328854786764263410),(-81328854786764263354)⟩⟩,⟨⟨2606539218020916333847,2606539218020916337543⟩,⟨4514658357533078056366,4514658357533078060172⟩⟩,⟨⟨(-138789524622137721165084),(-138789524622137721128026)⟩,⟨(-19786),9320⟩⟩] +lemma ha16_0_18_eq (j : Fin 7) : ha16_0_18 j = ((ha16_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha16_0_18_contains (j : Fin 7) : (ha16_0_18 j).Contains (fullFactor false 16 18 ((j.val:ℝ)/6)) := by + rw [ha16_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_17 j) false 16 17 j (ha16_0_17_contains j) +noncomputable def hk16_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_19 j i k) +lemma hk16_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_19 j i k).Contains (fullFactor false 16 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 19 (power16_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha16_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨32614433,32614434⟩,⟨18829951,18829952⟩⟩,⟨⟨(-17099355913328),(-17099355913327)⟩,⟨9872317739528,9872317739529⟩⟩,⟨⟨(-1),1⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨8964987113086656141,8964987113086656148⟩,⟨5175937723022106877,5175937723022106885⟩⟩,⟨⟨(-622070944276038605772),(-622070944276038605244)⟩,⟨359152827132815577250,359152827132815577761⟩⟩,⟨⟨(-1542),3272⟩,⟨(-22948428997269873113632),(-22948428997269873107430)⟩⟩] +lemma ha16_0_19_eq (j : Fin 7) : ha16_0_19 j = ((ha16_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha16_0_19_contains (j : Fin 7) : (ha16_0_19 j).Contains (fullFactor false 16 19 ((j.val:ℝ)/6)) := by + rw [ha16_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_18 j) false 16 18 j (ha16_0_18_contains j) +noncomputable def hk16_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_20 j i k) +lemma hk16_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_20 j i k).Contains (fullFactor false 16 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 20 (power16_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha16_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-492967),(-492966)⟩,⟨853843,853844⟩⟩,⟨⟨(-516913348074),(-516913348073)⟩,⟨(-895320181974),(-895320181973)⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨(-1),1⟩⟩,⟨⟨(-542022930869484434),(-542022930869484433)⟩,⟨938811255133340262,938811255133340263⟩⟩,⟨⟨(-47012995134852432639),(-47012995134852432571)⟩,⟨(-81428896189552855193),(-81428896189552855123)⟩⟩,⟨⟨3604730797462500933420,3604730797462500934407⟩,⟨(-243),514⟩⟩] +lemma ha16_0_20_eq (j : Fin 7) : ha16_0_20 j = ((ha16_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha16_0_20_contains (j : Fin 7) : (ha16_0_20 j).Contains (fullFactor false 16 20 ((j.val:ℝ)/6)) := by + rw [ha16_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_19 j) false 16 19 j (ha16_0_19_contains j) +noncomputable def hk16_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_21 j i k) +lemma hk16_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_21 j i k).Contains (fullFactor false 16 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 21 (power16_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha16_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-21290),(-21289)⟩,⟨(-12292),(-12291)⟩⟩,⟨⟨44646528671,44646528672⟩,⟨(-25776685347),(-25776685346)⟩⟩,⟨⟨(-1),1⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨(-93630556896327456),(-93630556896327455)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨10151445319802585611,10151445319802585620⟩,⟨(-5860939688051789416),(-5860939688051789406)⟩⟩,⟨⟨(-77),37⟩,⟨539266466260812848869,539266466260812849019⟩⟩] +lemma ha16_0_21_eq (j : Fin 7) : ha16_0_21 j = ((ha16_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha16_0_21_contains (j : Fin 7) : (ha16_0_21 j).Contains (fullFactor false 16 21 ((j.val:ℝ)/6)) := by + rw [ha16_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_20 j) false 16 20 j (ha16_0_20_contains j) +noncomputable def hk16_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_22 j i k) +lemma hk16_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_22 j i k).Contains (fullFactor false 16 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 22 (power16_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha16_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨292,293⟩,⟨(-507),(-506)⟩⟩,⟨⟨1226967353,1226967354⟩,⟨2125169795,2125169796⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨(-1),1⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨697450191936225609,697450191936225611⟩,⟨1208019168182208036,1208019168182208039⟩⟩,⟨⟨(-77007071306013533811),(-77007071306013533788)⟩,⟨(-11),6⟩⟩] +lemma ha16_0_22_eq (j : Fin 7) : ha16_0_22 j = ((ha16_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha16_0_22_contains (j : Fin 7) : (ha16_0_22 j).Contains (fullFactor false 16 22 ((j.val:ℝ)/6)) := by + rw [ha16_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_21 j) false 16 21 j (ha16_0_21_contains j) +noncomputable def hk16_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_23 j i k) +lemma hk16_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_23 j i k).Contains (fullFactor false 16 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 23 (power16_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha16_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11,12⟩,⟨6,7⟩⟩,⟨⟨(-96759679),(-96759678)⟩,⟨55864226,55864227⟩⟩,⟨⟨(-1),1⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨(-137503773339017308),(-137503773339017306)⟩,⟨79387840551870928,79387840551870929⟩⟩,⟨⟨(-1),2⟩,⟨(-10518471716932064457),(-10518471716932064453)⟩⟩] +lemma ha16_0_23_eq (j : Fin 7) : ha16_0_23 j = ((ha16_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha16_0_23_contains (j : Fin 7) : (ha16_0_23 j).Contains (fullFactor false 16 23 ((j.val:ℝ)/6)) := by + rw [ha16_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_22 j) false 16 22 j (ha16_0_22_contains j) +noncomputable def hk16_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_24 j i k) +lemma hk16_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_24 j i k).Contains (fullFactor false 16 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 24 (power16_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha16_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-2437537),(-2437536)⟩,⟨(-4221938),(-4221937)⟩⟩,⟨⟨82067533018,82067533019⟩,⟨(-1),1⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-8659870022990125),(-8659870022990124)⟩,⟨(-14999334866761558),(-14999334866761557)⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨(-1),1⟩⟩] +lemma ha16_0_24_eq (j : Fin 7) : ha16_0_24 j = ((ha16_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha16_0_24_contains (j : Fin 7) : (ha16_0_24 j).Contains (fullFactor false 16 24 ((j.val:ℝ)/6)) := by + rw [ha16_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_23 j) false 16 23 j (ha16_0_23_contains j) +noncomputable def hk16_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_25 j i k) +lemma hk16_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_25 j i k).Contains (fullFactor false 16 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 25 (power16_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha16_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨176848,176849⟩,⟨(-102104),(-102103)⟩⟩,⟨⟨(-1),1⟩,⟨5156455176,5156455177⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨1570726674205044,1570726674205046⟩,⟨(-906859468175609),(-906859468175608)⟩⟩,⟨⟨(-1),1⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha16_0_25_eq (j : Fin 7) : ha16_0_25 j = ((ha16_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha16_0_25_contains (j : Fin 7) : (ha16_0_25 j).Contains (fullFactor false 16 25 ((j.val:ℝ)/6)) := by + rw [ha16_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_24 j) false 16 24 j (ha16_0_24_contains j) +noncomputable def hk16_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_26 j i k) +lemma hk16_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_26 j i k).Contains (fullFactor false 16 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 26 (power16_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha16_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨4112,4113⟩,⟨7122,7123⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨(-1),1⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨91313559072398,91313559072399⟩,⟨158159723733336,158159723733337⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨(-1),1⟩⟩] +lemma ha16_0_26_eq (j : Fin 7) : ha16_0_26 j = ((ha16_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha16_0_26_contains (j : Fin 7) : (ha16_0_26 j).Contains (fullFactor false 16 26 ((j.val:ℝ)/6)) := by + rw [ha16_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_25 j) false 16 25 j (ha16_0_25_contains j) +noncomputable def hk16_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_27 j i k) +lemma hk16_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_27 j i k).Contains (fullFactor false 16 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 27 (power16_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha16_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-277),(-276)⟩,⟨159,160⟩⟩,⟨⟨(-1),1⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨(-15335599573286),(-15335599573285)⟩,⟨8854012541820,8854012541821⟩⟩,⟨⟨(-1),1⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha16_0_27_eq (j : Fin 7) : ha16_0_27 j = ((ha16_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha16_0_27_contains (j : Fin 7) : (ha16_0_27 j).Contains (fullFactor false 16 27 ((j.val:ℝ)/6)) := by + rw [ha16_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_26 j) false 16 26 j (ha16_0_26_contains j) +noncomputable def hk16_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_28 j i k) +lemma hk16_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_28 j i k).Contains (fullFactor false 16 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 28 (power16_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha16_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-6),(-5)⟩,⟨(-11),(-10)⟩⟩,⟨⟨1016753,1016754⟩,⟨(-1),1⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-827848236791),(-827848236790)⟩,⟨(-1433875207079),(-1433875207078)⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨(-1),1⟩⟩] +lemma ha16_0_28_eq (j : Fin 7) : ha16_0_28 j = ((ha16_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha16_0_28_contains (j : Fin 7) : (ha16_0_28 j).Contains (fullFactor false 16 28 ((j.val:ℝ)/6)) := by + rw [ha16_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_27 j) false 16 27 j (ha16_0_27_contains j) +noncomputable def hk16_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_29 j i k) +lemma hk16_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_29 j i k).Contains (fullFactor false 16 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 29 (power16_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha16_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨55072,55073⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨129444017721,129444017722⟩,⟨(-74734538477),(-74734538476)⟩⟩,⟨⟨(-1),1⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha16_0_29_eq (j : Fin 7) : ha16_0_29 j = ((ha16_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha16_0_29_contains (j : Fin 7) : (ha16_0_29 j).Contains (fullFactor false 16 29 ((j.val:ℝ)/6)) := by + rw [ha16_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_28 j) false 16 28 j (ha16_0_28_contains j) +noncomputable def hk16_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power16 j i k).conj.mul (mpower0_30 j i k) +lemma hk16_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk16_0_30 j i k).Contains (fullFactor false 16 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power16 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 30 (power16_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha16_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨(-1),1⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨6521818806,6521818807⟩,⟨11296121531,11296121532⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨(-1),1⟩⟩] +lemma ha16_0_30_eq (j : Fin 7) : ha16_0_30 j = ((ha16_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha16_0_30_contains (j : Fin 7) : (ha16_0_30 j).Contains (fullFactor false 16 30 ((j.val:ℝ)/6)) := by + rw [ha16_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_0_29 j) false 16 29 j (ha16_0_29_contains j) +noncomputable def hk16_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_0 j i k) +lemma hk16_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_0 j i k).Contains (fullFactor true 16 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 0 (kernel16_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha16_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩,⟨⟨25900948433,25900948436⟩,⟨29186647703,29186647707⟩⟩,⟨⟨(-35362811819921003609),(-35362811819921003509)⟩,⟨25936559903539299125,25936559903539299225⟩⟩,⟨⟨2558988247663461789901146,2558988247663461822219051⟩,⟨(-15737954547823165151092270),(-15737954547823165118709214)⟩⟩,⟨⟨53107114358929705735138510744,53107114358929705810825491739⟩,⟨(-1990265249209479056273496423),(-1990265249209478981209968663)⟩⟩] +lemma ha16_1_0_eq (j : Fin 7) : ha16_1_0 j = atomKernel16_0 j := by fin_cases j <;> decide +kernel +lemma ha16_1_0_contains (j : Fin 7) : (ha16_1_0 j).Contains (fullFactor true 16 0 ((j.val:ℝ)/6)) := by + rw [ha16_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel16_0_contains j +noncomputable def hk16_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_1 j i k) +lemma hk16_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_1 j i k).Contains (fullFactor true 16 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 1 (kernel16_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha16_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-30),11⟩,⟨(-31),10⟩⟩,⟨⟨75794229201,75794229231⟩,⟨(-214907164993),(-214907164965)⟩⟩,⟨⟨173413891756673643302,173413891756673643917⟩,⟨124072675056722227766,124072675056722228381⟩⟩,⟨⟨(-66096511680512424745057204),(-66096511680512424589790778)⟩,⟨630096109946563809592209,630096109946563964496528⟩⟩,⟨⟨(-17159000623478874601575700458),(-17159000623478874316252730094)⟩,⟨(-191397454004269867419843465767),(-191397454004269867131829260053)⟩⟩] +lemma ha16_1_1_eq (j : Fin 7) : ha16_1_1 j = ((ha16_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha16_1_1_contains (j : Fin 7) : (ha16_1_1 j).Contains (fullFactor true 16 1 ((j.val:ℝ)/6)) := by + rw [ha16_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_0 j) true 16 0 j (ha16_1_0_contains j) +noncomputable def hk16_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_2 j i k) +lemma hk16_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_2 j i k).Contains (fullFactor true 16 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 2 (kernel16_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha16_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-104),197⟩,⟨(-204),89⟩⟩,⟨⟨(-107),100⟩,⟨(-53),154⟩⟩,⟨⟨(-656151427379),(-656151427264)⟩,⟨110503197729,110503197847⟩⟩,⟨⟨155215278913991613146,155215278913991615035⟩,⟨(-494592317822908282939),(-494592317822908281050)⟩⟩,⟨⟨24563117624381976371901844,24563117624381976743072495⟩,⟨134790018730789871186533032,134790018730789871558668099⟩⟩,⟨⟨(-343959593517194279799311401329),(-343959593517194279251404864260)⟩,⟨48950469967399627017259360017,48950469967399627559610208607⟩⟩] +lemma ha16_1_2_eq (j : Fin 7) : ha16_1_2 j = ((ha16_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha16_1_2_contains (j : Fin 7) : (ha16_1_2 j).Contains (fullFactor true 16 2 ((j.val:ℝ)/6)) := by + rw [ha16_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_1 j) true 16 1 j (ha16_1_1_contains j) +noncomputable def hk16_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_3 j i k) +lemma hk16_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_3 j i k).Contains (fullFactor true 16 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 3 (kernel16_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha16_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-757),377⟩,⟨(-472),651⟩⟩,⟨⟨(-256),440⟩,⟨(-425),271⟩⟩,⟨⟨807127237475,807127237785⟩,⟨1013027675009,1013027675317⟩⟩,⟨⟨(-840072546677271221374),(-840072546677271217507)⟩,⟨10796916803272233743,10796916803272237609⟩⟩,⟨⟨177785734026401981014338986,177785734026401981608841366⟩,⟨(-65093632085839843735282329),(-65093632085839843142262265)⟩⟩,⟨⟨80449289390754261673915759125,80449289390754262361280265325⟩,⟨410951818164637086090139401074,410951818164637086784914943166⟩⟩] +lemma ha16_1_3_eq (j : Fin 7) : ha16_1_3 j = ((ha16_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha16_1_3_contains (j : Fin 7) : (ha16_1_3 j).Contains (fullFactor true 16 3 ((j.val:ℝ)/6)) := by + rw [ha16_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_2 j) true 16 2 j (ha16_1_2_contains j) +noncomputable def hk16_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_4 j i k) +lemma hk16_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_4 j i k).Contains (fullFactor true 16 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 4 (kernel16_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha16_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-1162),2056⟩,⟨(-1599),1609⟩⟩,⟨⟨(-1089),665⟩,⟨(-901),853⟩⟩,⟨⟨722667435480,722667436094⟩,⟨(-1747472052200),(-1747472051585)⟩⟩,⟨⟨330722749117346092801,330722749117346098734⟩,⟨966191228075115295111,966191228075115301046⟩⟩,⟨⟨(-97785536319491083281806297),(-97785536319491082571151650)⟩,⟨(-170115395489784926217503086),(-170115395489784925505292316)⟩⟩,⟨⟨367212870777440732128401144570,367212870777440732789074389818⟩,⟨(-91917570002480830322462534998),(-91917570002480829669032086353)⟩⟩] +lemma ha16_1_4_eq (j : Fin 7) : ha16_1_4 j = ((ha16_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha16_1_4_contains (j : Fin 7) : (ha16_1_4 j).Contains (fullFactor true 16 4 ((j.val:ℝ)/6)) := by + rw [ha16_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_3 j) true 16 3 j (ha16_1_3_contains j) +noncomputable def hk16_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_5 j i k) +lemma hk16_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_5 j i k).Contains (fullFactor true 16 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 5 (kernel16_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha16_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-4342),2979⟩,⟨(-3996),3316⟩⟩,⟨⟨(-1583),1951⟩,⟨(-1525),2009⟩⟩,⟨⟨(-2194343531025),(-2194343530048)⟩,⟨250747193822,250747194798⟩⟩,⟨⟨792526036450294726125,792526036450294733411⟩,⟨(-598411928712212552263),(-598411928712212544979)⟩⟩,⟨⟨(-125220181099945675473526022),(-125220181099945674791017847)⟩,⟨103859198813383626491669797,103859198813383627172970042⟩⟩,⟨⟨(-80173906213056706889737199994),(-80173906213056706392759759395)⟩,⟨(-261751113535616935058496470323),(-261751113535616934555960291244)⟩⟩] +lemma ha16_1_5_eq (j : Fin 7) : ha16_1_5 j = ((ha16_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha16_1_5_contains (j : Fin 7) : (ha16_1_5 j).Contains (fullFactor true 16 5 ((j.val:ℝ)/6)) := by + rw [ha16_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_4 j) true 16 4 j (ha16_1_4_contains j) +noncomputable def hk16_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_6 j i k) +lemma hk16_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_6 j i k).Contains (fullFactor true 16 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 6 (kernel16_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha16_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-6283),7603⟩,⟨(-6083),7797⟩⟩,⟨⟨(-2910),3024⟩,⟨(-3324),2611⟩⟩,⟨⟨1248475313948,1248475315241⟩,⟨1749951891998,1749951893291⟩⟩,⟨⟨(-660936015318381254452),(-660936015318381247000)⟩,⟨(-459109057754482555487),(-459109057754482548034)⟩⟩,⟨⟨85414796293133637657809885,85414796293133638202082959⟩,⟨73068825486432390647110027,73068825486432391192102083⟩⟩,⟨⟨(-155022593889746777855529754917),(-155022593889746777537021937847)⟩,⟨56443324576027397697941537698,56443324576027398012948099458⟩⟩] +lemma ha16_1_6_eq (j : Fin 7) : ha16_1_6 j = ((ha16_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha16_1_6_contains (j : Fin 7) : (ha16_1_6 j).Contains (fullFactor true 16 6 ((j.val:ℝ)/6)) := by + rw [ha16_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_5 j) true 16 5 j (ha16_1_5_contains j) +noncomputable def hk16_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_7 j i k) +lemma hk16_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_7 j i k).Contains (fullFactor true 16 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 7 (kernel16_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha16_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-11558),11023⟩,⟨(-12578),9999⟩⟩,⟨⟨(-4573),3968⟩,⟨(-4062),4479⟩⟩,⟨⟨772296567089,772296568556⟩,⟨(-1618557776830),(-1618557775363)⟩⟩,⟨⟨(-159932175530838942804),(-159932175530838936269)⟩,⟨535604446456639983204,535604446456639989738⟩⟩,⟨⟨34049958861360727324490221,34049958861360727697480197⟩,⟨(-57201067251999297343347995),(-57201067251999296970686305)⟩⟩,⟨⟨33275346735905410659939090744,33275346735905410831088463454⟩,⟨78456010105941935464730751236,78456010105941935637745817625⟩⟩] +lemma ha16_1_7_eq (j : Fin 7) : ha16_1_7 j = ((ha16_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha16_1_7_contains (j : Fin 7) : (ha16_1_7 j).Contains (fullFactor true 16 7 ((j.val:ℝ)/6)) := by + rw [ha16_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_6 j) true 16 6 j (ha16_1_6_contains j) +noncomputable def hk16_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_8 j i k) +lemma hk16_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_8 j i k).Contains (fullFactor true 16 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 8 (kernel16_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha16_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-16409),15723⟩,⟨(-14705),17425⟩⟩,⟨⟨(-5058),5698⟩,⟨(-5312),5444⟩⟩,⟨⟨(-1306704646423),(-1306704644966)⟩,⟨79423829221,79423830677⟩⟩,⟨⟨339605126373248506647,339605126373248511661⟩,⟨(-9093341614568992035),(-9093341614568987022)⟩⟩,⟨⟨(-32208106372270897666660573),(-32208106372270897443416545)⟩,⟨(-12352145282172659499883396),(-12352145282172659276531770)⟩⟩,⟨⟨34632308989444358629963146809,34632308989444358712190757246⟩,⟨(-16861261458343508627933597675),(-16861261458343508546565869029)⟩⟩] +lemma ha16_1_8_eq (j : Fin 7) : ha16_1_8 j = ((ha16_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha16_1_8_contains (j : Fin 7) : (ha16_1_8 j).Contains (fullFactor true 16 8 ((j.val:ℝ)/6)) := by + rw [ha16_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_7 j) true 16 7 j (ha16_1_7_contains j) +noncomputable def hk16_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_9 j i k) +lemma hk16_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_9 j i k).Contains (fullFactor true 16 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 9 (kernel16_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha16_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-19468),21176⟩,⟨(-21338),19305⟩⟩,⟨⟨(-6157),5883⟩,⟨(-6239),5801⟩⟩,⟨⟨455964118414,455964119699⟩,⟨716693968583,716693969869⟩⟩,⟨⟨(-61848217878660003105),(-61848217878659999686)⟩,⟨(-172799151219901248337),(-172799151219901244918)⟩⟩,⟨⟨(-3086426515184659624845011),(-3086426515184659505964761)⟩,⟨15586591945547874307302054,15586591945547874426165626⟩⟩,⟨⟨(-7487719887316651116338819348),(-7487719887316651081952636189)⟩,⟨(-13543563769022368030278952905),(-13543563769022367995544187992)⟩⟩] +lemma ha16_1_9_eq (j : Fin 7) : ha16_1_9 j = ((ha16_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha16_1_9_contains (j : Fin 7) : (ha16_1_9 j).Contains (fullFactor true 16 9 ((j.val:ℝ)/6)) := by + rw [ha16_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_8 j) true 16 8 j (ha16_1_8_contains j) +noncomputable def hk16_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_10 j i k) +lemma hk16_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_10 j i k).Contains (fullFactor true 16 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 10 (kernel16_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha16_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-24168),22102⟩,⟨(-22673),23597⟩⟩,⟨⟨(-6110),6020⟩,⟨(-5886),6243⟩⟩,⟨⟨237070122218,237070123240⟩,⟨(-435742772623),(-435742771601)⟩⟩,⟨⟨(-70460811551106122837),(-70460811551106120738)⟩,⟨54759040788742504750,54759040788742506849⟩⟩,⟨⟨6584962806960290010752570,6584962806960290067705615⟩,⟨163125079810063848064158,163125079810063905009390⟩⟩,⟨⟨(-4750016714838929780131191631),(-4750016714838929766926681825)⟩,⟨2958147187703659165637835196,2958147187703659178716417879⟩⟩] +lemma ha16_1_10_eq (j : Fin 7) : ha16_1_10 j = ((ha16_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha16_1_10_contains (j : Fin 7) : (ha16_1_10 j).Contains (fullFactor true 16 10 ((j.val:ℝ)/6)) := by + rw [ha16_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_9 j) true 16 9 j (ha16_1_9_contains j) +noncomputable def hk16_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_11 j i k) +lemma hk16_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_11 j i k).Contains (fullFactor true 16 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 11 (kernel16_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha16_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-23067),24819⟩,⟨(-23916),23970⟩⟩,⟨⟨(-5451),5658⟩,⟨(-5613),5496⟩⟩,⟨⟨(-263345627645),(-263345626906)⟩,⟨2011442301,2011443039⟩⟩,⟨⟨32705402051095491351,32705402051095492523⟩,⟨22049883830187379661,22049883830187380833⟩⟩,⟨⟨(-361037111936081702838604),(-361037111936081678041572)⟩,⟨(-2456037480379854346536216),(-2456037480379854321730501)⟩⟩,⟨⟨1052170280997595765472152129,1052170280997595769994279265⟩,⟨1508815711093426874414982607,1508815711093426878978073886⟩⟩] +lemma ha16_1_11_eq (j : Fin 7) : ha16_1_11 j = ((ha16_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha16_1_11_contains (j : Fin 7) : (ha16_1_11 j).Contains (fullFactor true 16 11 ((j.val:ℝ)/6)) := by + rw [ha16_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_10 j) true 16 10 j (ha16_1_10_contains j) +noncomputable def hk16_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_12 j i k) +lemma hk16_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_12 j i k).Contains (fullFactor true 16 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 12 (kernel16_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha16_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-23266),22163⟩,⟨(-23003),22426⟩⟩,⟨⟨(-4731),4596⟩,⟨(-4684),4643⟩⟩,⟨⟨62961654318,62961654807⟩,⟨111629252877,111629253366⟩⟩,⟨⟨4359156910004727590,4359156910004728190⟩,⟨(-15376003163963917957),(-15376003163963917357)⟩⟩,⟨⟨(-814946661038109714623227),(-814946661038109704720217)⟩,⟨267061920975924068969387,267061920975924078868072⟩⟩,⟨⟨437566939797545679519660527,437566939797545680965039528⟩,⟨(-340227472365358019913991442),(-340227472365358018480712981)⟩⟩] +lemma ha16_1_12_eq (j : Fin 7) : ha16_1_12 j = ((ha16_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha16_1_12_contains (j : Fin 7) : (ha16_1_12 j).Contains (fullFactor true 16 12 ((j.val:ℝ)/6)) := by + rw [ha16_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_11 j) true 16 11 j (ha16_1_11_contains j) +noncomputable def hk16_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_13 j i k) +lemma hk16_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_13 j i k).Contains (fullFactor true 16 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 13 (kernel16_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha16_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-19649),20134⟩,⟨(-19564),20219⟩⟩,⟨⟨(-3597),3632⟩,⟨(-3580),3649⟩⟩,⟨⟨30157912641,30157912940⟩,⟨(-49041169486),(-49041169186)⟩⟩,⟨⟨(-5972511159259968556),(-5972511159259968271)⟩,⟨243143679910657157,243143679910657442⟩⟩,⟨⟨128076772774941510252505,128076772774941513900129⟩,⟨241631177674373828632827,241631177674373832282029⟩⟩,⟨⟨(-100825667203851765301751305),(-100825667203851764882429635)⟩,⟨(-116629227663983228794515690),(-116629227663983228371926029)⟩⟩] +lemma ha16_1_13_eq (j : Fin 7) : ha16_1_13 j = ((ha16_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha16_1_13_contains (j : Fin 7) : (ha16_1_13 j).Contains (fullFactor true 16 13 ((j.val:ℝ)/6)) := by + rw [ha16_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_12 j) true 16 12 j (ha16_1_12_contains j) +noncomputable def hk16_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_14 j i k) +lemma hk16_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_14 j i k).Contains (fullFactor true 16 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 14 (kernel16_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha16_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-16221),16129⟩,⟨(-16419),15932⟩⟩,⟨⟨(-2595),2608⟩,⟨(-2620),2583⟩⟩,⟨⟨(-23990184211),(-23990184040)⟩,⟨(-1090656327),(-1090656156)⟩⟩,⟨⟨726700322907348574,726700322907348700⟩,⟨1944606263306918905,1944606263306919031⟩⟩,⟨⟨64066412623825242196848,64066412623825243445459⟩,⟨(-49529541998499009832540),(-49529541998499008584398)⟩⟩,⟨⟨(-28729914589754833443284389),(-28729914589754833328561493)⟩,⟨27570283634787122878821998,27570283634787122992733512⟩⟩] +lemma ha16_1_14_eq (j : Fin 7) : ha16_1_14 j = ((ha16_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha16_1_14_contains (j : Fin 7) : (ha16_1_14 j).Contains (fullFactor true 16 14 ((j.val:ℝ)/6)) := by + rw [ha16_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_13 j) true 16 13 j (ha16_1_13_contains j) +noncomputable def hk16_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_15 j i k) +lemma hk16_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_15 j i k).Contains (fullFactor true 16 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 15 (kernel16_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha16_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-12313),12240⟩,⟨(-12141),12412⟩⟩,⟨⟨(-1756),1739⟩,⟨(-1744),1751⟩⟩,⟨⟨4154702862,4154702953⟩,⟨8375675889,8375675980⟩⟩,⟨⟨525523326775000076,525523326775000128⟩,⟨(-420274619814902357),(-420274619814902305)⟩⟩,⟨⟨(-16497675921983197678725),(-16497675921983197280109)⟩,⟨(-15123090385341000151049),(-15123090385340999752317)⟩⟩,⟨⟨6996781634661517200929028,6996781634661517229809924⟩,⟨6571167002771297178795268,6571167002771297207862177⟩⟩] +lemma ha16_1_15_eq (j : Fin 7) : ha16_1_15 j = ((ha16_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha16_1_15_contains (j : Fin 7) : (ha16_1_15 j).Contains (fullFactor true 16 15 ((j.val:ℝ)/6)) := by + rw [ha16_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_14 j) true 16 14 j (ha16_1_14_contains j) +noncomputable def hk16_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_16 j i k) +lemma hk16_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_16 j i k).Contains (fullFactor true 16 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 16 (kernel16_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha16_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-8686),8784⟩,⟨(-8792),8679⟩⟩,⟨⟨(-1097),1104⟩,⟨(-1099),1102⟩⟩,⟨⟨1939221641,1939221687⟩,⟨(-2807902978),(-2807902931)⟩⟩,⟨⟨(-171126210582893626),(-171126210582893605)⟩,⟨(-111940389598287301),(-111940389598287280)⟩⟩,⟨⟨(-3135181561848804109411),(-3135181561848803990040)⟩,⟨4878072426380454488944,4878072426380454608292⟩⟩,⟨⟨1400927874765968976318933,1400927874765968983222942⟩,⟨(-1656215671067409590268458),(-1656215671067409583403957)⟩⟩] +lemma ha16_1_16_eq (j : Fin 7) : ha16_1_16 j = ((ha16_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha16_1_16_contains (j : Fin 7) : (ha16_1_16 j).Contains (fullFactor true 16 16 ((j.val:ℝ)/6)) := by + rw [ha16_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_15 j) true 16 15 j (ha16_1_15_contains j) +noncomputable def hk16_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_17 j i k) +lemma hk16_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_17 j i k).Contains (fullFactor true 16 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 17 (kernel16_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha16_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-5884),5816⟩,⟨(-5835),5865⟩⟩,⟨⟨(-653),652⟩,⟨(-654),651⟩⟩,⟨⟨(-1166560582),(-1166560559)⟩,⟨(-115279913),(-115279890)⟩⟩,⟨⟨(-15167422501097453),(-15167422501097444)⟩,⟨56484166837484507,56484166837484516⟩⟩,⟨⟨1302146713231019342510,1302146713231019376141⟩,⟨551323166683312568665,551323166683312602300⟩⟩,⟨⟨(-367276167032015402492579),(-367276167032015400957039)⟩,⟨(-279281991910390503207727),(-279281991910390501664395)⟩⟩] +lemma ha16_1_17_eq (j : Fin 7) : ha16_1_17 j = ((ha16_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha16_1_17_contains (j : Fin 7) : (ha16_1_17 j).Contains (fullFactor true 16 17 ((j.val:ℝ)/6)) := by + rw [ha16_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_16 j) true 16 16 j (ha16_1_16_contains j) +noncomputable def hk16_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_18 j i k) +lemma hk16_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_18 j i k).Contains (fullFactor true 16 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 18 (kernel16_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha16_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-3683),3718⟩,⟨(-3700),3701⟩⟩,⟨⟨(-366),365⟩,⟨(-365),366⟩⟩,⟨⟨150692759,150692770⟩,⟨349186637,349186649⟩⟩,⟨⟨15774460676362512,15774460676362516⟩,⟨(-862239933917983),(-862239933917979)⟩⟩,⟨⟨74178325538178316302,74178325538178325253⟩,⟨(-317108582911588424521),(-317108582911588415570)⟩⟩,⟨⟨(-52196103731795287670827),(-52196103731795287345005)⟩,⟨76593639936003126204614,76593639936003126529008⟩⟩] +lemma ha16_1_18_eq (j : Fin 7) : ha16_1_18 j = ((ha16_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha16_1_18_contains (j : Fin 7) : (ha16_1_18 j).Contains (fullFactor true 16 18 ((j.val:ℝ)/6)) := by + rw [ha16_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_17 j) true 16 17 j (ha16_1_17_contains j) +noncomputable def hk16_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_19 j i k) +lemma hk16_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_19 j i k).Contains (fullFactor true 16 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 19 (kernel16_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha16_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-2225),2211⟩,⟨(-2221),2214⟩⟩,⟨⟨(-194),195⟩,⟨(-194),194⟩⟩,⟨⟨71436037,71436043⟩,⟨(-92524992),(-92524986)⟩⟩,⟨⟨(-1467761579589366),(-1467761579589363)⟩,⟨(-3766907213360389),(-3766907213360387)⟩⟩,⟨⟨(-70932979255338572311),(-70932979255338570053)⟩,⟨(-4194697222675565795),(-4194697222675563538)⟩⟩,⟨⟨15072771877084077644234,15072771877084077709156⟩,⟨9163118159105693082853,9163118159105693148017⟩⟩] +lemma ha16_1_19_eq (j : Fin 7) : ha16_1_19 j = ((ha16_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha16_1_19_contains (j : Fin 7) : (ha16_1_19 j).Contains (fullFactor true 16 19 ((j.val:ℝ)/6)) := by + rw [ha16_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_18 j) true 16 18 j (ha16_1_18_contains j) +noncomputable def hk16_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_20 j i k) +lemma hk16_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_20 j i k).Contains (fullFactor true 16 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 20 (kernel16_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha16_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1261),1265⟩,⟨(-1260),1265⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨(-33740338),(-33740334)⟩,⟨(-5153541),(-5153537)⟩⟩,⟨⟨(-758944432181703),(-758944432181701)⟩,⟨624462490362091,624462490362092⟩⟩,⟨⟨1641093731746318589,1641093731746319131⟩,⟨14636828276602889005,14636828276602889547⟩⟩,⟨⟨1512899666891436919156,1512899666891436931538⟩,⟨(-2807438057603362280053),(-2807438057603362267710)⟩⟩] +lemma ha16_1_20_eq (j : Fin 7) : ha16_1_20 j = ((ha16_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha16_1_20_contains (j : Fin 7) : (ha16_1_20 j).Contains (fullFactor true 16 20 ((j.val:ℝ)/6)) := by + rw [ha16_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_19 j) true 16 19 j (ha16_1_19_contains j) +noncomputable def hk16_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_21 j i k) +lemma hk16_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_21 j i k).Contains (fullFactor true 16 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 21 (kernel16_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha16_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-685),685⟩,⟨(-686),684⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨3293285,3293287⟩,⟨8901883,8901885⟩⟩,⟨⟨192146728783256,192146728783257⟩,⟨121906276705541,121906276705543⟩⟩,⟨⟨2792378380608537401,2792378380608537526⟩,⟨(-810149790594419348),(-810149790594419223)⟩⟩,⟨⟨(-496276865357941984591),(-496276865357941982355)⟩,⟨(-235045620509659402288),(-235045620509659400047)⟩⟩] +lemma ha16_1_21_eq (j : Fin 7) : ha16_1_21 j = ((ha16_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha16_1_21_contains (j : Fin 7) : (ha16_1_21 j).Contains (fullFactor true 16 21 ((j.val:ℝ)/6)) := by + rw [ha16_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_20 j) true 16 20 j (ha16_1_20_contains j) +noncomputable def hk16_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_22 j i k) +lemma hk16_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_22 j i k).Contains (fullFactor true 16 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 22 (kernel16_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha16_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-355),355⟩,⟨(-355),355⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨1643334,1643336⟩,⟨(-1909785),(-1909783)⟩⟩,⟨⟨12365222514303,12365222514305⟩,⟨(-48747603390860),(-48747603390859)⟩⟩,⟨⟨(-239835813129811706),(-239835813129811678)⟩,⟨(-492595443543864927),(-492595443543864899)⟩⟩,⟨⟨(-34344012927123102099),(-34344012927123101711)⟩,⟨83463817621576003531,83463817621576003918⟩⟩] +lemma ha16_1_22_eq (j : Fin 7) : ha16_1_22 j = ((ha16_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha16_1_22_contains (j : Fin 7) : (ha16_1_22 j).Contains (fullFactor true 16 22 ((j.val:ℝ)/6)) := by + rw [ha16_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_21 j) true 16 21 j (ha16_1_21_contains j) +noncomputable def hk16_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_23 j i k) +lemma hk16_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_23 j i k).Contains (fullFactor true 16 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 23 (kernel16_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha16_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-176),176⟩,⟨(-176),176⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-626363),(-626361)⟩,⟨(-129999),(-129997)⟩⟩,⟨⟨(-10606570469184),(-10606570469182)⟩,⟨727947874188,727947874189⟩⟩,⟨⟨(-80151332297122232),(-80151332297122225)⟩,⟨57684249972704638,57684249972704645⟩⟩,⟨⟨13384300400462115406,13384300400462115471⟩,⟨4710645390307683617,4710645390307683682⟩⟩] +lemma ha16_1_23_eq (j : Fin 7) : ha16_1_23 j = ((ha16_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha16_1_23_contains (j : Fin 7) : (ha16_1_23 j).Contains (fullFactor true 16 23 ((j.val:ℝ)/6)) := by + rw [ha16_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_22 j) true 16 22 j (ha16_1_22_contains j) +noncomputable def hk16_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_24 j i k) +lemma hk16_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_24 j i k).Contains (fullFactor true 16 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 24 (kernel16_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha16_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-84),84⟩,⟨(-84),84⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨46188,46190⟩,⟨148646,148648⟩⟩,⟨⟨809826931477,809826931479⟩,⟨1995797519498,1995797519499⟩⟩,⟨⟨12171176039912591,12171176039912594⟩,⟨11950608854121036,11950608854121039⟩⟩,⟨⟨604043674408891099,604043674408891110⟩,⟨(-2050649622462992639),(-2050649622462992628)⟩⟩] +lemma ha16_1_24_eq (j : Fin 7) : ha16_1_24 j = ((ha16_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha16_1_24_contains (j : Fin 7) : (ha16_1_24 j).Contains (fullFactor true 16 24 ((j.val:ℝ)/6)) := by + rw [ha16_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_23 j) true 16 23 j (ha16_1_23_contains j) +noncomputable def hk16_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_25 j i k) +lemma hk16_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_25 j i k).Contains (fullFactor true 16 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 25 (kernel16_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha16_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨25144,25145⟩,⟨(-26265),(-26264)⟩⟩,⟨⟨319735460367,319735460368⟩,⟨(-270629453254),(-270629453253)⟩⟩,⟨⟨1609982176704411,1609982176704413⟩,⟨(-2325589250842123),(-2325589250842121)⟩⟩,⟨⟨(-300734899579534681),(-300734899579534678)⟩,⟨(-71846403169724296),(-71846403169724293)⟩⟩] +lemma ha16_1_25_eq (j : Fin 7) : ha16_1_25 j = ((ha16_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha16_1_25_contains (j : Fin 7) : (ha16_1_25 j).Contains (fullFactor true 16 25 ((j.val:ℝ)/6)) := by + rw [ha16_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_24 j) true 16 24 j (ha16_1_24_contains j) +noncomputable def hk16_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_26 j i k) +lemma hk16_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_26 j i k).Contains (fullFactor true 16 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 26 (kernel16_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha16_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-18),18⟩,⟨(-18),18⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-7898),(-7896)⟩,⟨(-2082),(-2081)⟩⟩,⟨⟨(-66723782481),(-66723782480)⟩,⟨(-41041318590),(-41041318589)⟩⟩,⟨⟨(-409024581160782),(-409024581160780)⟩,⟨(-189974214810452),(-189974214810451)⟩⟩,⟨⟨(-7806508917887070),(-7806508917887068)⟩,⟨42286630507565997,42286630507565999⟩⟩] +lemma ha16_1_26_eq (j : Fin 7) : ha16_1_26 j = ((ha16_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha16_1_26_contains (j : Fin 7) : (ha16_1_26 j).Contains (fullFactor true 16 26 ((j.val:ℝ)/6)) := by + rw [ha16_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_25 j) true 16 25 j (ha16_1_25_contains j) +noncomputable def hk16_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_27 j i k) +lemma hk16_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_27 j i k).Contains (fullFactor true 16 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 27 (kernel16_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha16_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-8),8⟩,⟨(-8),8⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨433,435⟩,⟨1712,1713⟩⟩,⟨⟨(-3277782738),(-3277782737)⟩,⟨13720569678,13720569679⟩⟩,⟨⟨(-18074919792447),(-18074919792445)⟩,⟨66843936942736,66843936942737⟩⟩,⟨⟨5709776970757746,5709776970757747⟩,⟨749970538260544,749970538260545⟩⟩] +lemma ha16_1_27_eq (j : Fin 7) : ha16_1_27 j = ((ha16_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha16_1_27_contains (j : Fin 7) : (ha16_1_27 j).Contains (fullFactor true 16 27 ((j.val:ℝ)/6)) := by + rw [ha16_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_26 j) true 16 26 j (ha16_1_26_contains j) +noncomputable def hk16_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_28 j i k) +lemma hk16_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_28 j i k).Contains (fullFactor true 16 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 28 (kernel16_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha16_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨268,269⟩,⟨(-253),(-252)⟩⟩,⟨⟨2441281889,2441281891⟩,⟨(-201722608),(-201722607)⟩⟩,⟨⟨10207411708651,10207411708652⟩,⟨955817026427,955817026428⟩⟩,⟨⟨58429256050481,58429256050482⟩,⟨(-741392064265433),(-741392064265432)⟩⟩] +lemma ha16_1_28_eq (j : Fin 7) : ha16_1_28 j = ((ha16_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha16_1_28_contains (j : Fin 7) : (ha16_1_28 j).Contains (fullFactor true 16 28 ((j.val:ℝ)/6)) := by + rw [ha16_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_27 j) true 16 27 j (ha16_1_27_contains j) +noncomputable def hk16_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_29 j i k) +lemma hk16_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_29 j i k).Contains (fullFactor true 16 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 29 (kernel16_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha16_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-71),(-70)⟩,⟨(-23),(-22)⟩⟩,⟨⟨(-159702364),(-159702363)⟩,⟨(-378379804),(-378379803)⟩⟩,⟨⟨(-113252964480),(-113252964479)⟩,⟨(-1461154667679),(-1461154667678)⟩⟩,⟨⟨(-92695086422804),(-92695086422803)⟩,⟨(-2475030705968),(-2475030705967)⟩⟩] +lemma ha16_1_29_eq (j : Fin 7) : ha16_1_29 j = ((ha16_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha16_1_29_contains (j : Fin 7) : (ha16_1_29 j).Contains (fullFactor true 16 29 ((j.val:ℝ)/6)) := by + rw [ha16_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_28 j) true 16 28 j (ha16_1_28_contains j) +noncomputable def hk16_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel16_0 j i k).mul (mpower1_30 j i k) +lemma hk16_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk16_1_30 j i k).Contains (fullFactor true 16 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk16_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel16_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 16 30 (kernel16_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha16_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨2,3⟩,⟨13,15⟩⟩,⟨⟨(-50203487),(-50203486)⟩,⟨43706782,43706783⟩⟩,⟨⟨(-196316158072),(-196316158070)⟩,⟨49725682648,49725682649⟩⟩,⟨⟨282275565067,282275565068⟩,⟨11172970518026,11172970518027⟩⟩] +lemma ha16_1_30_eq (j : Fin 7) : ha16_1_30 j = ((ha16_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha16_1_30_contains (j : Fin 7) : (ha16_1_30 j).Contains (fullFactor true 16 30 ((j.val:ℝ)/6)) := by + rw [ha16_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha16_1_29 j) true 16 29 j (ha16_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders19.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders19.lean new file mode 100644 index 0000000000000000000000000000000000000000..5462b354bf126f1d694226fed02c35c8555c8ba9 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders19.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.KernelValues20 +import OAI.Analysis.PlanarPacking.Certificate.Powers20 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk19_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_0 j i k) +lemma hk19_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_0 j i k).Contains (fullFactor false 19 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 0 (power19_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha19_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999773,1000000000000000000000000000303⟩,⟨(-303),303⟩⟩,⟨⟨(-866025403784438646812202266006),(-866025403784438646707781455940)⟩,⟨(-500000000000000000059187675620),(-499999999999999999953737960674)⟩⟩,⟨⟨499999999999999999843899897497,500000000000000000130248829862⟩,⟨866025403784438646627634776787,866025403784438646914736803947⟩⟩,⟨⟨(-39678965475),84454683117⟩,⟨(-1000000000000000000062066824296),(-999999999999999999937933175723)⟩⟩,⟨⟨(-500000000000000000418039296860),(-499999999999999999633663248451)⟩,⟨866025403784438646356885182472,866025403784438647140710680530⟩⟩,⟨⟨866025403784438646288804563125,866025403784438647275954876385⟩,⟨(-500000000000000000460987851192),(-499999999999999999474383967179)⟩⟩,⟨⟨(-1000000000000000000124510757933),(-999999999999999999875489242143)⟩,⟨(-169286475613),79735040177⟩⟩] +lemma ha19_0_0_eq (j : Fin 7) : ha19_0_0 j = ((atomPoints j).direct.powBin 7 19).conj := by fin_cases j <;> decide +kernel +lemma ha19_0_0_contains (j : Fin 7) : (ha19_0_0 j).Contains (fullFactor false 19 0 ((j.val:ℝ)/6)) := by + rw [ha19_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 19) ((j.val:ℝ)/6) 19 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 19 (by norm_num)) +noncomputable def hk19_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_1 j i k) +lemma hk19_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_1 j i k).Contains (fullFactor false 19 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 1 (power19_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha19_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨261799387799149436514110586184,261799387799149436570157261153⟩,⟨(-453449841058554462674964995490),(-453449841058554462618847011515)⟩⟩,⟨⟨(-906899682117108925457303908024),(-906899682117108925153764616888)⟩,⟨523598775598298872913199021583,523598775598298873214729589013⟩⟩,⟨⟨1570796326794896619132505660409,1570796326794896619332494339620⟩,⟨(-62327573220),132661106021⟩⟩,⟨⟨(-1813799364234217851387886396428),(-1813799364234217849740472609468)⟩,⟨(-1047197551196597747032206122619),(-1047197551196597745386079435061)⟩⟩,⟨⟨1308996938995747181315607110566,1308996938995747183902696705584⟩,⟨2267249205292772311997356117177,2267249205292772314588926472318⟩⟩,⟨⟨(-250495016454),531829148138⟩,⟨(-3141592653589793238861162082416),(-3141592653589793238068837917823)⟩⟩] +lemma ha19_0_1_eq (j : Fin 7) : ha19_0_1 j = ((ha19_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha19_0_1_contains (j : Fin 7) : (ha19_0_1 j).Contains (fullFactor false 19 1 ((j.val:ℝ)/6)) := by + rw [ha19_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_0 j) false 19 0 j (ha19_0_0_contains j) +noncomputable def hk19_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_2 j i k) +lemma hk19_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_2 j i k).Contains (fullFactor false 19 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 2 (power19_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha19_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨118712890786751174400069168474,118712890786751174415138697193⟩,⟨68538919452009434846560458881,68538919452009434861451610234⟩⟩,⟨⟨(-274155677808037739484770078748),(-274155677808037739326016378208)⟩,⟨(-474851563147004697716775640264),(-474851563147004697556331339607)⟩⟩,⟨⟨(-104191789024),48951961537⟩,⟨1233700550136169827275663391355,1233700550136169827436661123525⟩⟩,⟨⟨1096622711232150956842964944681,1096622711232150958570275439358⟩,⟨(-1899406252588018791362718731460),(-1899406252588018789631505050062)⟩⟩,⟨⟨(-2967822269668779361967722570210),(-2967822269668779358565918036445)⟩,⟨1713472986300235869521291234592,1713472986300235872913237749294⟩⟩,⟨⟨4934802200544679308794505104581,4934802200544679310054792955223⟩,⟨(-393476651727),835395272378⟩⟩] +lemma ha19_0_2_eq (j : Fin 7) : ha19_0_2 j = ((ha19_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha19_0_2_contains (j : Fin 7) : (ha19_0_2 j).Contains (fullFactor false 19 2 ((j.val:ℝ)/6)) := by + rw [ha19_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_1 j) false 19 1 j (ha19_0_1_contains j) +noncomputable def hk19_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_3 j i k) +lemma hk19_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_3 j i k).Contains (fullFactor false 19 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 3 (power19_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha19_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-11962298101967523217347420776),(-11962298101967523214710347392)⟩,⟨20719308087892496641024736376,20719308087892496643720816912⟩⟩,⟨⟨165754464703139973112858075529,165754464703139973169391314629⟩,⟨(-95698384815740185752380241574),(-95698384815740185696660128669)⟩⟩,⟨⟨(-645964097506246253700387435088),(-645964097506246253614033052065)⟩,⟨(-54554693161),25631187124⟩⟩,⟨⟨1326035717625119784488299822384,1326035717625119785701135877010⟩,⟨765587078525921485251372105477,765587078525921486459699258293⟩⟩,⟨⟨(-1495287262745940403370040966345),(-1495287262745940400405249582503)⟩,⟨(-2589913510986562081851988856631),(-2589913510986562078875110424704)⟩⟩,⟨⟨(-874823883516),412047786142⟩,⟨5167712780049970028589572102926,5167712780049970029925791794590⟩⟩] +lemma ha19_0_3_eq (j : Fin 7) : ha19_0_3 j = ((ha19_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha19_0_3_contains (j : Fin 7) : (ha19_0_3 j).Contains (fullFactor false 19 3 ((j.val:ℝ)/6)) := by + rw [ha19_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_2 j) false 19 2 j (ha19_0_2_contains j) +noncomputable def hk19_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_4 j i k) +lemma hk19_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_4 j i k).Contains (fullFactor false 19 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 4 (power19_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha19_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2712151086516110563573177333),(-2712151086516110563211628170)⟩,⟨(-1565861159883012430055355794),(-1565861159883012429705179404)⟩⟩,⟨⟨25053778558128198869779153447,25053778558128198884446393549⟩,⟨43394417384257769007370096432,43394417384257769022308592540⟩⟩,⟨⟨(-10065343647),21423577907⟩,⟨(-253669507901048013654683882294),(-253669507901048013619965140257)⟩⟩,⟨⟨(-400860456930051182381869932965),(-400860456930051181747915336762)⟩,⟨694310678148124303900855930732,694310678148124304538105463468⟩⟩,⟨⟨1695094429072569101187193052677,1695094429072569103140951083406⟩,⟨(-978663224926882769571051482403),(-978663224926882767627484877498)⟩⟩,⟨⟨(-4058712126416768218728384067368),(-4058712126416768217666000293688)⟩,⟨(-687085071410),323621574468⟩⟩] +lemma ha19_0_4_eq (j : Fin 7) : ha19_0_4 j = ((ha19_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha19_0_4_contains (j : Fin 7) : (ha19_0_4 j).Contains (fullFactor false 19 4 ((j.val:ℝ)/6)) := by + rw [ha19_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_3 j) false 19 3 j (ha19_0_3_contains j) +noncomputable def hk19_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_5 j i k) +lemma hk19_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_5 j i k).Contains (fullFactor false 19 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 5 (power19_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha19_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨163976597214335483771186810,163976597214335483808379150⟩,⟨(-284015797627486289506448312),(-284015797627486289467682921)⟩⟩,⟨⟨(-9088505524079561265282394895),(-9088505524079561262124753973)⟩,⟨5247251110858735479525282131,5247251110858735482613884234⟩⟩,⟨⟨79692626246167045115224008392,79692626246167045126384892394⟩,⟨(-3162120966),6730415497⟩⟩,⟨⟨(-290832176770545960564924103801),(-290832176770545960297067896155)⟩,⟨(-167912035547479535540291261724),(-167912035547479535274206500828)⟩⟩,⟨⟨512426866294798386293691052707,512426866294798387312971252706⟩,⟨887549367585894654157119096086,887549367585894655182929566175⟩⟩,⟨⟨(-203337432179),431708282547⟩,⟨(-2550164039877345444203558830649),(-2550164039877345443527925994658)⟩⟩] +lemma ha19_0_5_eq (j : Fin 7) : ha19_0_5 j = ((ha19_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha19_0_5_contains (j : Fin 7) : (ha19_0_5 j).Contains (fullFactor false 19 5 ((j.val:ℝ)/6)) := by + rw [ha19_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_4 j) false 19 4 j (ha19_0_4_contains j) +noncomputable def hk19_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_6 j i k) +lemma hk19_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_6 j i k).Contains (fullFactor false 19 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 6 (power19_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha19_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨24785053981387676525178307,24785053981387676528640120⟩,⟨14309657588033580844318198,14309657588033580847609392⟩⟩,⟨⟨(-915818085634149174377159252),(-915818085634149173835181352)⟩,⟨(-1586243454808811298020773599),(-1586243454808811297464612122)⟩⟩,⟨⟨(-1762018657),827841334⟩,⟨20863480763352960871651378159,20863480763352960874639701281⟩⟩,⟨⟨58612357480585547100806675289,58612357480585547193874347559⟩,⟨(-101519581107763923099819233578),(-101519581107763923005996631807)⟩⟩,⟨⟨(-387266468459182445967381270929),(-387266468459182445518554308361)⟩,⟨223588399813024700478115871213,223588399813024700923572462455⟩⟩,⟨⟨1335262768854589495702309142578,1335262768854589496060319941658⟩,⟨(-106467230523),226041928158⟩⟩] +lemma ha19_0_6_eq (j : Fin 7) : ha19_0_6 j = ((ha19_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha19_0_6_contains (j : Fin 7) : (ha19_0_6 j).Contains (fullFactor false 19 6 ((j.val:ℝ)/6)) := by + rw [ha19_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_5 j) false 19 5 j (ha19_0_5_contains j) +noncomputable def hk19_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_7 j i k) +lemma hk19_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_7 j i k).Contains (fullFactor false 19 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 7 (power19_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha19_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1070359884617898514247008),(-1070359884617898513997419)⟩,⟨1853917702541761442126887,1853917702541761442391733⟩⟩,⟨⟨237301465925345464570280497,237301465925345464654237414⟩,⟨(-137006065231091009843088571),(-137006065231091009761572762)⟩⟩,⟨⟨(-4681754135318688101052787862),(-4681754135318688100367307234)⟩,⟨(-395396063),185767161⟩⟩,⟨⟨30374587638444219455499753507,30374587638444219483668095629⟩,⟨17536776349579649242107567415,17536776349579649270009171137⟩⟩,⟨⟨(-83621865985773321492746017073),(-83621865985773321325879464865)⟩,⟨(-144837320511075112764413786217),(-144837320511075112596091863237)⟩⟩,⟨⟨(-101447380130),47782381323⟩,⟨599264529320792076809594891565,599264529320792076972177280707⟩⟩] +lemma ha19_0_7_eq (j : Fin 7) : ha19_0_7 j = ((ha19_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha19_0_7_contains (j : Fin 7) : (ha19_0_7 j).Contains (fullFactor false 19 7 ((j.val:ℝ)/6)) := by + rw [ha19_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_6 j) false 19 6 j (ha19_0_6_contains j) +noncomputable def hk19_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_8 j i k) +lemma hk19_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_8 j i k).Contains (fullFactor false 19 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 8 (power19_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha19_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-121338629888859693723657),(-121338629888859693705936)⟩,⟨(-70054890629433514736150),(-70054890629433514719591)⟩⟩,⟨⟨17934052001134979764275643,17934052001134979775003124⟩,⟨31062689251548081585844993,31062689251548081596933805⟩⟩,⟨⟨(-36475297),77635836⟩,⟨(-919260274839426580315992724),(-919260274839426580178472820)⟩⟩,⟨⟨(-4591117312290554825043359288),(-4591117312290554817724122534)⟩,⟨7952048448396308883490232154,7952048448396308890889999034⟩⟩,⟨⟨47397902300335817830950617397,47397902300335817886184710093⟩,⟨(-27365191652122466715799111069),(-27365191652122466661105053443)⟩⟩,⟨⟨(-235330630358893204575589107384),(-235330630358893204510994071805)⟩,⟨(-39838293018),18764097267⟩⟩] +lemma ha19_0_8_eq (j : Fin 7) : ha19_0_8 j = ((ha19_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha19_0_8_contains (j : Fin 7) : (ha19_0_8 j).Contains (fullFactor false 19 8 ((j.val:ℝ)/6)) := by + rw [ha19_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_7 j) false 19 7 j (ha19_0_7_contains j) +noncomputable def hk19_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_9 j i k) +lemma hk19_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_9 j i k).Contains (fullFactor false 19 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 9 (power19_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha19_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨4075628328693792152024,4075628328693792153001⟩,⟨(-7059195338064676367107),(-7059195338064676366052)⟩⟩,⟨⟨(-3614308013089114300386280),(-3614308013089114299084533)⟩,⟨2086721704291221581378202,2086721704291221582633045⟩⟩,⟨⟨160441184787359821861487816,160441184787359821886000268⟩,⟨(-6366141),13550010⟩⟩,⟨⟨(-1850525702701626522280636837),(-1850525702701626520552742484)⟩,⟨(-1068401512597105450923070120),(-1068401512597105449216405557)⟩⟩,⟨⟨7960211579480062789291568898,7960211579480062805226763487⟩,⟨13787490894657571020776537144,13787490894657571036887370374⟩⟩,⟨⟨(-6549905570),13906187631⟩,⟨(-82145886611128228810761649378),(-82145886611128228787952249873)⟩⟩] +lemma ha19_0_9_eq (j : Fin 7) : ha19_0_9 j = ((ha19_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha19_0_9_contains (j : Fin 7) : (ha19_0_9 j).Contains (fullFactor false 19 9 ((j.val:ℝ)/6)) := by + rw [ha19_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_8 j) false 19 8 j (ha19_0_8_contains j) +noncomputable def hk19_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_10 j i k) +lemma hk19_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_10 j i k).Contains (fullFactor false 19 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 10 (power19_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha19_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨369618603571988403162,369618603571988403220⟩,⟨213399400269781075704,213399400269781075756⟩⟩,⟨⟨(-218520985876255821605153),(-218520985876255821473049)⟩,⟨(-378489450057716124941290),(-378489450057716124803765)⟩⟩,⟨⟨(-2128431),999992⟩,⟨25202042373060605479276757,25202042373060605483207385⟩⟩,⟨⟨223765489537285961094315574,223765489537285961452470833⟩,⟨(-387573196859101312041010282),(-387573196859101311677887250)⟩⟩,⟨⟨(-3609556675507699252120556767),(-3609556675507699247891260914)⟩,⟨2083978518259580815425451486,2083978518259580819603909185⟩⟩,⟨⟨25806891390014060009167915584,25806891390014060016415845664⟩,⟨(-2057713523),4368757691⟩⟩] +lemma ha19_0_10_eq (j : Fin 7) : ha19_0_10 j = ((ha19_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha19_0_10_contains (j : Fin 7) : (ha19_0_10 j).Contains (fullFactor false 19 10 ((j.val:ℝ)/6)) := by + rw [ha19_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_9 j) false 19 9 j (ha19_0_9_contains j) +noncomputable def hk19_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_11 j i k) +lemma hk19_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_11 j i k).Contains (fullFactor false 19 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 11 (power19_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha19_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-10157787699515332862),(-10157787699515332859)⟩,⟨17593804388058740563,17593804388058740567⟩⟩,⟨⟨36032111386744300670170,36032111386744300683378⟩,⟨(-20803149208607401704147),(-20803149208607401691504)⟩⟩,⟨⟨(-3598843235212085340774610),(-3598843235212085340201861)⟩,⟨(-303940),142799⟩⟩,⟨⟨73793764120052327749438675,73793764120052327818812033⟩,⟨42604849579227958646286592,42604849579227958714614811⟩⟩,⟨⟨(-495985727515397112796484066),(-495985727515397111800434687)⟩,⟨(-859072479885680692157896113),(-859072479885680691148591540)⟩⟩,⟨⟨(-1247714279),587681608⟩,⟨7370430945714350776273174509,7370430945714350778366639310⟩⟩] +lemma ha19_0_11_eq (j : Fin 7) : ha19_0_11 j = ((ha19_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha19_0_11_contains (j : Fin 7) : (ha19_0_11 j).Contains (fullFactor false 19 11 ((j.val:ℝ)/6)) := by + rw [ha19_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_10 j) false 19 10 j (ha19_0_10_contains j) +noncomputable def hk19_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_12 j i k) +lemma hk19_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_12 j i k).Contains (fullFactor false 19 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 12 (power19_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha19_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-767674536308627878),(-767674536308627877)⟩,⟨(-443217100187807443),(-443217100187807442)⟩⟩,⟨⟨1815417242369259284926,1815417242369259286036⟩,⟨3144394900720139784399,3144394900720139785562⟩⟩,⟨⟨(-18693),39786⟩,⟨(-471087477881817150409505),(-471087477881817150333032)⟩⟩,⟨⟨(-7435949024744486039882294),(-7435949024744486027933100)⟩,⟨12879441513349692552872421,12879441513349692565021353⟩⟩,⟨⟨187420541090973602722223342,187420541090973602943016021⟩,⟨(-108207299850538926555906367),(-108207299850538926338257667)⟩⟩,⟨⟨(-1929574309403923048197819760),(-1929574309403923047643609930)⟩,⟨(-326650835),153854686⟩⟩] +lemma ha19_0_12_eq (j : Fin 7) : ha19_0_12 j = ((ha19_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha19_0_12_contains (j : Fin 7) : (ha19_0_12 j).Contains (fullFactor false 19 12 ((j.val:ℝ)/6)) := by + rw [ha19_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_11 j) false 19 11 j (ha19_0_11_contains j) +noncomputable def hk19_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_13 j i k) +lemma hk19_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_13 j i k).Contains (fullFactor false 19 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 13 (power19_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha19_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨17851379306351118,17851379306351119⟩,⟨(-30919495943783800),(-30919495943783799)⟩⟩,⟨⟨(-253292510771476882333),(-253292510771476882238)⟩,⟨146238499277628361464,146238499277628361555⟩⟩,⟨⟨56921729219679268113596,56921729219679268123019⟩,⟨(-2259),4808⟩⟩,⟨⟨(-2074972248239938620611451),(-2074972248239938618647563)⟩,⟨(-1197985786082331538541394),(-1197985786082331536612477)⟩⟩,⟨⟨21791234504823142492220519,21791234504823142536120881⟩,⟨37743525322001707872631312,37743525322001707917215599⟩⟩,⟨⟨(-37180674),78938759⟩,⟨(-466302805767612564492883770),(-466302805767612564357468594)⟩⟩] +lemma ha19_0_13_eq (j : Fin 7) : ha19_0_13 j = ((ha19_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha19_0_13_contains (j : Fin 7) : (ha19_0_13 j).Contains (fullFactor false 19 13 ((j.val:ℝ)/6)) := by + rw [ha19_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_12 j) false 19 12 j (ha19_0_12_contains j) +noncomputable def hk19_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_14 j i k) +lemma hk19_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_14 j i k).Contains (fullFactor false 19 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 14 (power19_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha19_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1156386444162983,1156386444162984⟩,⟨667640024824732,667640024824733⟩⟩,⟨⟨(-10938614166728417762),(-10938614166728417755)⟩,⟨(-18946235501166317755),(-18946235501166317747)⟩⟩,⟨⟨(-540),254⟩,⟨6386603083791852240618,6386603083791852241696⟩⟩,⟨⟨179218254507678396425452,179218254507678396714589⟩,⟨(-310415122451108950176605),(-310415122451108949881819)⟩⟩,⟨⟨(-7058022730486958385542518),(-7058022730486958377182808)⟩,⟨4074951323393142874200775,4074951323393142882423095⟩⟩,⟨⟨104638104924845707103755541,104638104924845707134475710⟩,⟨(-8343324),17713817⟩⟩] +lemma ha19_0_14_eq (j : Fin 7) : ha19_0_14 j = ((ha19_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha19_0_14_contains (j : Fin 7) : (ha19_0_14 j).Contains (fullFactor false 19 14 ((j.val:ℝ)/6)) := by + rw [ha19_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_13 j) false 19 13 j (ha19_0_13_contains j) +noncomputable def hk19_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_15 j i k) +lemma hk19_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_15 j i k).Contains (fullFactor false 19 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 15 (power19_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha19_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23305033302577),(-23305033302576)⟩,⟨40365501752147,40365501752148⟩⟩,⟨⟨1322696761414360852,1322696761414360853⟩,⟨(-763659331258827444),(-763659331258827443)⟩⟩,⟨⟨(-668803510981146723313),(-668803510981146723197)⟩,⟨(-57),27⟩⟩,⟨⟨43342127478025776399496,43342127478025776440795⟩,⟨25023588966689257645077,25023588966689257685529⟩⟩,⟨⟨(-711213174517105747090628),(-711213174517105745653297)⟩,⟨(-1231857353275977869985883),(-1231857353275977868522917)⟩⟩,⟨⟨(-3709974),1747422⟩,⟨21915353447830215824379356,21915353447830215830883132⟩⟩] +lemma ha19_0_15_eq (j : Fin 7) : ha19_0_15 j = ((ha19_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha19_0_15_contains (j : Fin 7) : (ha19_0_15 j).Contains (fullFactor false 19 15 ((j.val:ℝ)/6)) := by + rw [ha19_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_14 j) false 19 14 j (ha19_0_14_contains j) +noncomputable def hk19_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_16 j i k) +lemma hk19_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_16 j i k).Contains (fullFactor false 19 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 16 (power19_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha19_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1320957955865),(-1320957955864)⟩,⟨(-762655431407),(-762655431406)⟩⟩,⟨⟨49981386352667221,49981386352667222⟩,⟨86570300595549323,86570300595549324⟩⟩,⟨⟨(-3),6⟩,⟨(-65659631149794723629),(-65659631149794723617)⟩⟩,⟨⟨(-3275580136008399052237),(-3275580136008399046931)⟩,⟨5673471219829920492012,5673471219829920497437⟩⟩,⟨⟨201562188089707223481854,201562188089707223721873⟩,⟨(-116371983552042445798176),(-116371983552042445562622)⟩⟩,⟨⟨(-4303069587032947007994826),(-4303069587032947006704114)⟩,⟨(-728452),343106⟩⟩] +lemma ha19_0_16_eq (j : Fin 7) : ha19_0_16 j = ((ha19_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha19_0_16_contains (j : Fin 7) : (ha19_0_16 j).Contains (fullFactor false 19 16 ((j.val:ℝ)/6)) := by + rw [ha19_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_15 j) false 19 15 j (ha19_0_15_contains j) +noncomputable def hk19_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_17 j i k) +lemma hk19_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_17 j i k).Contains (fullFactor false 19 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 17 (power19_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha19_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23489732358,23489732359⟩,⟨(-40685409901),(-40685409900)⟩⟩,⟨⟨(-5332718046471331),(-5332718046471330)⟩,⟨3078846199642597,3078846199642598⟩⟩,⟨⟨6066935731106195666,6066935731106195668⟩,⟨(-1),1⟩⟩,⟨⟨(-698970019787090239547),(-698970019787090238875)⟩,⟨(-403550529079554597063),(-403550529079554596407)⟩⟩,⟨⟨17921243559351411723963,17921243559351411760296⟩,⟨31040504379613153621379,31040504379613153658441⟩⟩,⟨⟨(-63406),134618⟩,⟨(-795205400147551278608989),(-795205400147551278367934)⟩⟩] +lemma ha19_0_17_eq (j : Fin 7) : ha19_0_17 j = ((ha19_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha19_0_17_contains (j : Fin 7) : (ha19_0_17 j).Contains (fullFactor false 19 17 ((j.val:ℝ)/6)) := by + rw [ha19_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_16 j) false 19 16 j (ha19_0_16_contains j) +noncomputable def hk19_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_18 j i k) +lemma hk19_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_18 j i k).Contains (fullFactor false 19 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 18 (power19_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha19_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1183490600,1183490601⟩,⟨683288616,683288617⟩⟩,⟨⟨(-179120011154260),(-179120011154259)⟩,⟨(-310244959971483),(-310244959971482)⟩⟩,⟨⟨(-1),1⟩,⟨529440020073462376,529440020073462377⟩⟩,⟨⟨46955236204022331333,46955236204022331411⟩,⟨(-81328854786764263422),(-81328854786764263342)⟩⟩,⟨⟨(-4514658357533078060987),(-4514658357533078055581)⟩,⟨2606539218020916333022,2606539218020916338315⟩⟩,⟨⟨138789524622137721125297,138789524622137721167812⟩,⟨(-11067),23496⟩⟩] +lemma ha19_0_18_eq (j : Fin 7) : ha19_0_18 j = ((ha19_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha19_0_18_contains (j : Fin 7) : (ha19_0_18 j).Contains (fullFactor false 19 18 ((j.val:ℝ)/6)) := by + rw [ha19_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_17 j) false 19 17 j (ha19_0_17_contains j) +noncomputable def hk19_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_19 j i k) +lemma hk19_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_19 j i k).Contains (fullFactor false 19 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 19 (power19_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha19_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-18829952),(-18829951)⟩,⟨32614433,32614434⟩⟩,⟨⟨17099355913327,17099355913328⟩,⟨(-9872317739529),(-9872317739528)⟩⟩,⟨⟨(-43770654673137423),(-43770654673137422)⟩,⟨(-1),1⟩⟩,⟨⟨8964987113086656140,8964987113086656150⟩,⟨5175937723022106876,5175937723022106886⟩⟩,⟨⟨(-359152827132815577868),(-359152827132815577136)⟩,⟨(-622070944276038605884),(-622070944276038605136)⟩⟩,⟨⟨(-3885),1830⟩,⟨22948428997269873106979,22948428997269873114083⟩⟩] +lemma ha19_0_19_eq (j : Fin 7) : ha19_0_19 j = ((ha19_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha19_0_19_contains (j : Fin 7) : (ha19_0_19 j).Contains (fullFactor false 19 19 ((j.val:ℝ)/6)) := by + rw [ha19_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_18 j) false 19 18 j (ha19_0_18_contains j) +noncomputable def hk19_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_20 j i k) +lemma hk19_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_20 j i k).Contains (fullFactor false 19 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 20 (power19_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha19_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-853844),(-853843)⟩,⟨(-492967),(-492966)⟩⟩,⟨⟨516913348073,516913348074⟩,⟨895320181973,895320181974⟩⟩,⟨⟨(-1),1⟩,⟨(-3437739179098608),(-3437739179098606)⟩⟩,⟨⟨(-542022930869484435),(-542022930869484432)⟩,⟨938811255133340262,938811255133340264⟩⟩,⟨⟨81428896189552855109,81428896189552855208⟩,⟨(-47012995134852432653),(-47012995134852432556)⟩⟩,⟨⟨(-3604730797462500934478),(-3604730797462500933349)⟩,⟨(-611),288⟩⟩] +lemma ha19_0_20_eq (j : Fin 7) : ha19_0_20 j = ((ha19_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha19_0_20_contains (j : Fin 7) : (ha19_0_20 j).Contains (fullFactor false 19 20 ((j.val:ℝ)/6)) := by + rw [ha19_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_19 j) false 19 19 j (ha19_0_19_contains j) +noncomputable def hk19_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_21 j i k) +lemma hk19_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_21 j i k).Contains (fullFactor false 19 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 21 (power19_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha19_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨12291,12292⟩,⟨(-21290),(-21289)⟩⟩,⟨⟨(-44646528672),(-44646528671)⟩,⟨25776685346,25776685347⟩⟩,⟨⟨257142289286047,257142289286048⟩,⟨(-1),1⟩⟩,⟨⟨(-93630556896327456),(-93630556896327455)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨5860939688051789405,5860939688051789418⟩,⟨10151445319802585609,10151445319802585622⟩⟩,⟨⟨(-44),92⟩,⟨(-539266466260812849030),(-539266466260812848858)⟩⟩] +lemma ha19_0_21_eq (j : Fin 7) : ha19_0_21 j = ((ha19_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha19_0_21_contains (j : Fin 7) : (ha19_0_21 j).Contains (fullFactor false 19 21 ((j.val:ℝ)/6)) := by + rw [ha19_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_20 j) false 19 20 j (ha19_0_20_contains j) +noncomputable def hk19_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_22 j i k) +lemma hk19_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_22 j i k).Contains (fullFactor false 19 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 22 (power19_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha19_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨506,507⟩,⟨292,293⟩⟩,⟨⟨(-1226967354),(-1226967353)⟩,⟨(-2125169796),(-2125169795)⟩⟩,⟨⟨(-1),1⟩,⟨18359916521552,18359916521553⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨(-1208019168182208039),(-1208019168182208036)⟩,⟨697450191936225608,697450191936225611⟩⟩,⟨⟨77007071306013533786,77007071306013533812⟩,⟨(-7),14⟩⟩] +lemma ha19_0_22_eq (j : Fin 7) : ha19_0_22 j = ((ha19_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha19_0_22_contains (j : Fin 7) : (ha19_0_22 j).Contains (fullFactor false 19 22 ((j.val:ℝ)/6)) := by + rw [ha19_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_21 j) false 19 21 j (ha19_0_21_contains j) +noncomputable def hk19_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_23 j i k) +lemma hk19_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_23 j i k).Contains (fullFactor false 19 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 23 (power19_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha19_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-7),(-6)⟩,⟨11,12⟩⟩,⟨⟨96759678,96759679⟩,⟨(-55864227),(-55864226)⟩⟩,⟨⟨(-1253899540536),(-1253899540535)⟩,⟨(-1),1⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨(-79387840551870929),(-79387840551870928)⟩,⟨(-137503773339017308),(-137503773339017306)⟩⟩,⟨⟨(-2),1⟩,⟨10518471716932064453,10518471716932064458⟩⟩] +lemma ha19_0_23_eq (j : Fin 7) : ha19_0_23 j = ((ha19_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha19_0_23_contains (j : Fin 7) : (ha19_0_23 j).Contains (fullFactor false 19 23 ((j.val:ℝ)/6)) := by + rw [ha19_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_22 j) false 19 22 j (ha19_0_22_contains j) +noncomputable def hk19_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_24 j i k) +lemma hk19_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_24 j i k).Contains (fullFactor false 19 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 24 (power19_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha19_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨2437536,2437537⟩,⟨4221937,4221938⟩⟩,⟨⟨(-1),1⟩,⟨(-82067533019),(-82067533018)⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨14999334866761557,14999334866761558⟩,⟨(-8659870022990125),(-8659870022990124)⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha19_0_24_eq (j : Fin 7) : ha19_0_24 j = ((ha19_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha19_0_24_contains (j : Fin 7) : (ha19_0_24 j).Contains (fullFactor false 19 24 ((j.val:ℝ)/6)) := by + rw [ha19_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_23 j) false 19 23 j (ha19_0_23_contains j) +noncomputable def hk19_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_25 j i k) +lemma hk19_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_25 j i k).Contains (fullFactor false 19 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 25 (power19_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha19_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-176849),(-176848)⟩,⟨102103,102104⟩⟩,⟨⟨5156455176,5156455177⟩,⟨(-1),1⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨906859468175608,906859468175609⟩,⟨1570726674205044,1570726674205046⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha19_0_25_eq (j : Fin 7) : ha19_0_25 j = ((ha19_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha19_0_25_contains (j : Fin 7) : (ha19_0_25 j).Contains (fullFactor false 19 25 ((j.val:ℝ)/6)) := by + rw [ha19_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_24 j) false 19 24 j (ha19_0_24_contains j) +noncomputable def hk19_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_26 j i k) +lemma hk19_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_26 j i k).Contains (fullFactor false 19 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 26 (power19_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha19_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-4113),(-4112)⟩,⟨(-7123),(-7122)⟩⟩,⟨⟨(-1),1⟩,⟨311528494,311528495⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨(-158159723733337),(-158159723733336)⟩,⟨91313559072398,91313559072399⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha19_0_26_eq (j : Fin 7) : ha19_0_26 j = ((ha19_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha19_0_26_contains (j : Fin 7) : (ha19_0_26 j).Contains (fullFactor false 19 26 ((j.val:ℝ)/6)) := by + rw [ha19_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_25 j) false 19 25 j (ha19_0_25_contains j) +noncomputable def hk19_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_27 j i k) +lemma hk19_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_27 j i k).Contains (fullFactor false 19 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 27 (power19_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha19_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨276,277⟩,⟨(-160),(-159)⟩⟩,⟨⟨(-18123994),(-18123993)⟩,⟨(-1),1⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨(-8854012541821),(-8854012541820)⟩,⟨(-15335599573286),(-15335599573285)⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha19_0_27_eq (j : Fin 7) : ha19_0_27 j = ((ha19_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha19_0_27_contains (j : Fin 7) : (ha19_0_27 j).Contains (fullFactor false 19 27 ((j.val:ℝ)/6)) := by + rw [ha19_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_26 j) false 19 26 j (ha19_0_26_contains j) +noncomputable def hk19_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_28 j i k) +lemma hk19_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_28 j i k).Contains (fullFactor false 19 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 28 (power19_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha19_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨5,6⟩,⟨10,11⟩⟩,⟨⟨(-1),1⟩,⟨(-1016754),(-1016753)⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨1433875207078,1433875207079⟩,⟨(-827848236791),(-827848236790)⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha19_0_28_eq (j : Fin 7) : ha19_0_28 j = ((ha19_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha19_0_28_contains (j : Fin 7) : (ha19_0_28 j).Contains (fullFactor false 19 28 ((j.val:ℝ)/6)) := by + rw [ha19_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_27 j) false 19 27 j (ha19_0_27_contains j) +noncomputable def hk19_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_29 j i k) +lemma hk19_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_29 j i k).Contains (fullFactor false 19 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 29 (power19_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha19_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨55072,55073⟩,⟨(-1),1⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨74734538476,74734538477⟩,⟨129444017721,129444017722⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha19_0_29_eq (j : Fin 7) : ha19_0_29 j = ((ha19_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha19_0_29_contains (j : Fin 7) : (ha19_0_29 j).Contains (fullFactor false 19 29 ((j.val:ℝ)/6)) := by + rw [ha19_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_28 j) false 19 28 j (ha19_0_28_contains j) +noncomputable def hk19_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power19 j i k).conj.mul (mpower0_30 j i k) +lemma hk19_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk19_0_30 j i k).Contains (fullFactor false 19 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power19 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 30 (power19_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha19_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨2883,2884⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨(-11296121532),(-11296121531)⟩,⟨6521818806,6521818807⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha19_0_30_eq (j : Fin 7) : ha19_0_30 j = ((ha19_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha19_0_30_contains (j : Fin 7) : (ha19_0_30 j).Contains (fullFactor false 19 30 ((j.val:ℝ)/6)) := by + rw [ha19_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_0_29 j) false 19 29 j (ha19_0_29_contains j) +noncomputable def hk19_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_0 j i k) +lemma hk19_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_0 j i k).Contains (fullFactor true 19 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 0 (kernel19_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha19_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-4),0⟩,⟨(-2),2⟩⟩,⟨⟨(-2694941),(-2694938)⟩,⟨(-7553494),(-7553491)⟩⟩,⟨⟨161985630457654811,161985630457654815⟩,⟨436136473825194671,436136473825194675⟩⟩,⟨⟨875795745701851962050983,875795745701851969854345⟩,⟨(-1717008702880404811713990),(-1717008702880404803916317)⟩⟩,⟨⟨(-3773270257214874982714516262),(-3773270257214874921032772599)⟩,⟨30019734216488397017839289471,30019734216488397079757731725⟩⟩] +lemma ha19_1_0_eq (j : Fin 7) : ha19_1_0 j = atomKernel19_0 j := by fin_cases j <;> decide +kernel +lemma ha19_1_0_contains (j : Fin 7) : (ha19_1_0 j).Contains (fullFactor true 19 0 ((j.val:ℝ)/6)) := by + rw [ha19_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel19_0_contains j +noncomputable def hk19_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_1 j i k) +lemma hk19_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_1 j i k).Contains (fullFactor true 19 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 1 (kernel19_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha19_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-11),30⟩,⟨(-10),31⟩⟩,⟨⟨(-30958727),(-30958703)⟩,⟨35142785,35142810⟩⟩,⟨⟨1769479826288535701,1769479826288535726⟩,⟨(-1409274084194273722),(-1409274084194273697)⟩⟩,⟨⟨(-7631316207020498734798912),(-7631316207020498697422870)⟩,⟨(-2368587012362611643398018),(-2368587012362611606011795)⟩⟩,⟨⟨109110561539634485129127268825,109110561539634485364645873668⟩,⟨7988470969262919066081260666,7988470969262919300503590470⟩⟩] +lemma ha19_1_1_eq (j : Fin 7) : ha19_1_1 j = ((ha19_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha19_1_1_contains (j : Fin 7) : (ha19_1_1 j).Contains (fullFactor true 19 1 ((j.val:ℝ)/6)) := by + rw [ha19_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_0 j) true 19 0 j (ha19_1_0_contains j) +noncomputable def hk19_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_2 j i k) +lemma hk19_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_2 j i k).Contains (fullFactor true 19 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 2 (kernel19_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha19_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-177),255⟩,⟨(-219),205⟩⟩,⟨⟨(-100),107⟩,⟨(-154),53⟩⟩,⟨⟨133565977,133566076⟩,⟨29346016,29346113⟩⟩,⟨⟨(-4596111861562243883),(-4596111861562243806)⟩,⟨(-3019712549212694957),(-3019712549212694879)⟩⟩,⟨⟨(-2150802347297484515006745),(-2150802347297484425453828)⟩,⟨16422196816187689448032916,16422196816187689537596942⟩⟩,⟨⟨4179260290361574195554509713,4179260290361574640997655879⟩,⟨(-197750550397078292256571304667),(-197750550397078291808700804220)⟩⟩] +lemma ha19_1_2_eq (j : Fin 7) : ha19_1_2 j = ((ha19_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha19_1_2_contains (j : Fin 7) : (ha19_1_2 j).Contains (fullFactor true 19 2 ((j.val:ℝ)/6)) := by + rw [ha19_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_1 j) true 19 1 j (ha19_1_1_contains j) +noncomputable def hk19_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_3 j i k) +lemma hk19_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_3 j i k).Contains (fullFactor true 19 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 3 (kernel19_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha19_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-924),707⟩,⟨(-840),779⟩⟩,⟨⟨(-440),256⟩,⟨(-271),425⟩⟩,⟨⟨(-76027548),(-76027288)⟩,⟨(-255114050),(-255113788)⟩⟩,⟨⟨(-2328763856612328119),(-2328763856612327959)⟩,⟨8603309351384496550,8603309351384496709⟩⟩,⟨⟨22868118841049176338572596,22868118841049176481634765⟩,⟨(-926523875944949058447102),(-926523875944948915448649)⟩⟩,⟨⟨(-238289046785031641968742893630),(-238289046785031641401012931830)⟩,⟨7346955458100419993732702775,7346955458100420557989762363⟩⟩] +lemma ha19_1_3_eq (j : Fin 7) : ha19_1_3 j = ((ha19_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha19_1_3_contains (j : Fin 7) : (ha19_1_3 j).Contains (fullFactor true 19 3 ((j.val:ℝ)/6)) := by + rw [ha19_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_2 j) true 19 2 j (ha19_1_2_contains j) +noncomputable def hk19_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_4 j i k) +lemma hk19_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_4 j i k).Contains (fullFactor true 19 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 4 (kernel19_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha19_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2136),2495⟩,⟨(-2151),2469⟩⟩,⟨⟨(-665),1089⟩,⟨(-853),901⟩⟩,⟨⟨(-272009478),(-272008959)⟩,⟨277584392,277584910⟩⟩,⟨⟨10819025900699310642,10819025900699310888⟩,⟨(-569554128425957473),(-569554128425957227)⟩⟩,⟨⟨(-4972813901797147646372603),(-4972813901797147475119169)⟩,⟨(-23192619969007155635514257),(-23192619969007155464147933)⟩⟩,⟨⟨17818595250453951295317019165,17818595250453951831411610951⟩,⟨214772097546986240919462570370,214772097546986241459158435722⟩⟩] +lemma ha19_1_4_eq (j : Fin 7) : ha19_1_4 j = ((ha19_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha19_1_4_contains (j : Fin 7) : (ha19_1_4 j).Contains (fullFactor true 19 4 ((j.val:ℝ)/6)) := by + rw [ha19_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_3 j) true 19 3 j (ha19_1_3_contains j) +noncomputable def hk19_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_5 j i k) +lemma hk19_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_5 j i k).Contains (fullFactor true 19 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 5 (kernel19_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha19_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5425),5111⟩,⟨(-5641),4887⟩⟩,⟨⟨(-1951),1583⟩,⟨(-2009),1525⟩⟩,⟨⟨437552192,437553016⟩,⟨120787258,120788082⟩⟩,⟨⟨(-3805202934222615043),(-3805202934222614740)⟩,⟨(-9824141050320606241),(-9824141050320605939)⟩⟩,⟨⟨(-18249268120410069345151169),(-18249268120410069180949255)⟩,⟨7330019199856127906313651,7330019199856128070400012⟩⟩,⟨⟨154440355842989514856201575260,154440355842989515266601454716⟩,⟨(-20934377704896460532232464219),(-20934377704896460124727421448)⟩⟩] +lemma ha19_1_5_eq (j : Fin 7) : ha19_1_5 j = ((ha19_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha19_1_5_contains (j : Fin 7) : (ha19_1_5 j).Contains (fullFactor true 19 5 ((j.val:ℝ)/6)) := by + rw [ha19_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_4 j) true 19 4 j (ha19_1_4_contains j) +noncomputable def hk19_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_6 j i k) +lemma hk19_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_6 j i k).Contains (fullFactor true 19 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 6 (kernel19_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha19_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-10026),9960⟩,⟨(-9412),10570⟩⟩,⟨⟨(-3024),2910⟩,⟨(-2611),3324⟩⟩,⟨⟨(-103542393),(-103541302)⟩,⟨(-429495402),(-429494311)⟩⟩,⟨⟨(-6603531113751344547),(-6603531113751344237)⟩,⟨5411178669330811427,5411178669330811737⟩⟩,⟨⟨7133058309754072907852901,7133058309754073038873873⟩,⟨11565182218904509405513681,11565182218904509536619353⟩⟩,⟨⟨(-17432394434205249749694734783),(-17432394434205249491543665387)⟩,⟨(-92292871340892753487656813024),(-92292871340892753227611658253)⟩⟩] +lemma ha19_1_6_eq (j : Fin 7) : ha19_1_6 j = ((ha19_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha19_1_6_contains (j : Fin 7) : (ha19_1_6 j).Contains (fullFactor true 19 6 ((j.val:ℝ)/6)) := by + rw [ha19_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_5 j) true 19 5 j (ha19_1_5_contains j) +noncomputable def hk19_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_7 j i k) +lemma hk19_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_7 j i k).Contains (fullFactor true 19 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 7 (kernel19_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha19_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-15907),16595⟩,⟨(-16866),15633⟩⟩,⟨⟨(-3968),4573⟩,⟨(-4479),4062⟩⟩,⟨⟨(-271566071),(-271564833)⟩,⟨249197368,249198607⟩⟩,⟨⟨5000898642986824463,5000898642986824736⟩,⟨3186911124354648273,3186911124354648545⟩⟩,⟨⟨6031906315165059307602774,6031906315165059397324289⟩,⟨(-5326581563722765197388740),(-5326581563722765107714949)⟩⟩,⟨⟨(-47142660345522125790848657697),(-47142660345522125649623661382)⟩,⟨11468424602842061990946668400,11468424602842062131128857014⟩⟩] +lemma ha19_1_7_eq (j : Fin 7) : ha19_1_7 j = ((ha19_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha19_1_7_contains (j : Fin 7) : (ha19_1_7 j).Contains (fullFactor true 19 7 ((j.val:ℝ)/6)) := by + rw [ha19_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_6 j) true 19 6 j (ha19_1_6_contains j) +noncomputable def hk19_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_8 j i k) +lemma hk19_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_8 j i k).Contains (fullFactor true 19 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 8 (kernel19_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha19_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-23741),22509⟩,⟨(-22694),23555⟩⟩,⟨⟨(-5698),5058⟩,⟨(-5444),5312⟩⟩,⟨⟨255186900,255188130⟩,⟨85250056,85251286⟩⟩,⟨⟨893168864742913692,893168864742913902⟩,⟨(-3491675506443947167),(-3491675506443946957)⟩⟩,⟨⟨(-3251120570199236038126050),(-3251120570199235984423788)⟩,⟨(-2611323093539420116235076),(-2611323093539420062511696)⟩⟩,⟨⟨6283114414076144423751820394,6283114414076144490361798227⟩,⟨21009988685514834245050623323,21009988685514834312155416209⟩⟩] +lemma ha19_1_8_eq (j : Fin 7) : ha19_1_8 j = ((ha19_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha19_1_8_contains (j : Fin 7) : (ha19_1_8 j).Contains (fullFactor true 19 8 ((j.val:ℝ)/6)) := by + rw [ha19_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_7 j) true 19 7 j (ha19_1_7_contains j) +noncomputable def hk19_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_9 j i k) +lemma hk19_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_9 j i k).Contains (fullFactor true 19 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 9 (kernel19_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha19_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-28549),29954⟩,⟨(-29363),29139⟩⟩,⟨⟨(-5883),6157⟩,⟨(-5801),6239⟩⟩,⟨⟨(-31855335),(-31854249)⟩,⟨(-171648077),(-171646991)⟩⟩,⟨⟨(-1942774702575184421),(-1942774702575184277)⟩,⟨129411390750167914,129411390750168058⟩⟩,⟨⟨(-930916366180930791912364),(-930916366180930763319038)⟩,⟨1680106443794698550931763,1680106443794698579517922⟩⟩,⟨⟨8298646083014296406207736817,8298646083014296434548846032⟩,⟨(-2959289532881161415734763283),(-2959289532881161387599692858)⟩⟩] +lemma ha19_1_9_eq (j : Fin 7) : ha19_1_9 j = ((ha19_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha19_1_9_contains (j : Fin 7) : (ha19_1_9 j).Contains (fullFactor true 19 9 ((j.val:ℝ)/6)) := by + rw [ha19_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_8 j) true 19 8 j (ha19_1_8_contains j) +noncomputable def hk19_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_10 j i k) +lemma hk19_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_10 j i k).Contains (fullFactor true 19 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 10 (kernel19_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha19_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-33881),32720⟩,⟨(-33476),33125⟩⟩,⟨⟨(-6020),6110⟩,⟨(-6243),5886⟩⟩,⟨⟨(-78667944),(-78667081)⟩,⟨64847929,64848792⟩⟩,⟨⟨354187541611467975,354187541611468064⟩,⟨877949375053473648,877949375053473737⟩⟩,⟨⟨751938128481459963597514,751938128481459977292043⟩,⟨261976151179624053574562,261976151179624067270708⟩⟩,⟨⟨(-1224433616774698596923872593),(-1224433616774698586228157395)⟩,⟨(-2941095136989598447269495618),(-2941095136989598436497430079)⟩⟩] +lemma ha19_1_10_eq (j : Fin 7) : ha19_1_10 j = ((ha19_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha19_1_10_contains (j : Fin 7) : (ha19_1_10 j).Contains (fullFactor true 19 10 ((j.val:ℝ)/6)) := by + rw [ha19_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_9 j) true 19 9 j (ha19_1_9_contains j) +noncomputable def hk19_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_11 j i k) +lemma hk19_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_11 j i k).Contains (fullFactor true 19 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 11 (kernel19_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha19_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34119),34809⟩,⟨(-34145),34782⟩⟩,⟨⟨(-5658),5451⟩,⟨(-5496),5613⟩⟩,⟨⟨50353480,50354104⟩,⟨19848387,19849011⟩⟩,⟨⟨319945113619212357,319945113619212408⟩,⟨(-269704442697875539),(-269704442697875489)⟩⟩,⟨⟨49150574651159287983172,49150574651159293947084⟩,⟨(-296036452756779617495888),(-296036452756779611531993)⟩⟩,⟨⟨(-944586828610372500846884240),(-944586828610372497124964511)⟩,⟨452156451913613702348161854,452156451913613706044620473⟩⟩] +lemma ha19_1_11_eq (j : Fin 7) : ha19_1_11 j = ((ha19_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha19_1_11_contains (j : Fin 7) : (ha19_1_11 j).Contains (fullFactor true 19 11 ((j.val:ℝ)/6)) := by + rw [ha19_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_10 j) true 19 10 j (ha19_1_10_contains j) +noncomputable def hk19_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_12 j i k) +lemma hk19_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_12 j i k).Contains (fullFactor true 19 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 12 (kernel19_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha19_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32817),32574⟩,⟨(-33006),32385⟩⟩,⟨⟨(-4596),4731⟩,⟨(-4643),4684⟩⟩,⟨⟨(-3425863),(-3425449)⟩,⟨(-26116280),(-26115866)⟩⟩,⟨⟨(-144238542094061510),(-144238542094061483)⟩,⟨(-89120383317285786),(-89120383317285759)⟩⟩,⟨⟨(-103667795416028570151103),(-103667795416028567770381)⟩,⟨642109742571968360268,642109742571970740773⟩⟩,⟨⟨150843079862060999887446983,150843079862061001058500938⟩,⟨277168725027257233618347763,277168725027257234797112186⟩⟩] +lemma ha19_1_12_eq (j : Fin 7) : ha19_1_12 j = ((ha19_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha19_1_12_contains (j : Fin 7) : (ha19_1_12 j).Contains (fullFactor true 19 12 ((j.val:ℝ)/6)) := by + rw [ha19_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_11 j) true 19 11 j (ha19_1_11_contains j) +noncomputable def hk19_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_13 j i k) +lemma hk19_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_13 j i k).Contains (fullFactor true 19 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 13 (kernel19_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha19_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28649),28615⟩,⟨(-28414),28850⟩⟩,⟨⟨(-3632),3597⟩,⟨(-3649),3580⟩⟩,⟨⟨(-9516563),(-9516309)⟩,⟨7031210,7031463⟩⟩,⟨⟨(-14858646313883249),(-14858646313883236)⟩,⟨61648434957468829,61648434957468843⟩⟩,⟨⟨5818227605944683973470,5818227605944684850553⟩,⟨32543184061911994640421,32543184061911995517645⟩⟩,⟨⟨74810705548225137490494895,74810705548225137835088570⟩,⟨(-45903322326943795243031332),(-45903322326943794900573918)⟩⟩] +lemma ha19_1_13_eq (j : Fin 7) : ha19_1_13 j = ((ha19_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha19_1_13_contains (j : Fin 7) : (ha19_1_13 j).Contains (fullFactor true 19 13 ((j.val:ℝ)/6)) := by + rw [ha19_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_12 j) true 19 12 j (ha19_1_12_contains j) +noncomputable def hk19_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_14 j i k) +lemma hk19_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_14 j i k).Contains (fullFactor true 19 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 14 (kernel19_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha19_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23215),23350⟩,⟨(-23397),23168⟩⟩,⟨⟨(-2608),2595⟩,⟨(-2583),2620⟩⟩,⟨⟨4489173,4489318⟩,⟨2050930,2051075⟩⟩,⟨⟨21952232079111683,21952232079111690⟩,⟨(-1769469178426308),(-1769469178426301)⟩⟩,⟨⟨9203623851294521228588,9203623851294521528724⟩,⟨(-3334965046103480144406),(-3334965046103479844324)⟩⟩,⟨⟨(-12843253519837436017546084),(-12843253519837435924553191)⟩,⟨(-18680284636280242088269868),(-18680284636280241994732121)⟩⟩] +lemma ha19_1_14_eq (j : Fin 7) : ha19_1_14 j = ((ha19_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha19_1_14_contains (j : Fin 7) : (ha19_1_14 j).Contains (fullFactor true 19 14 ((j.val:ℝ)/6)) := by + rw [ha19_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_13 j) true 19 13 j (ha19_1_13_contains j) +noncomputable def hk19_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_15 j i k) +lemma hk19_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_15 j i k).Contains (fullFactor true 19 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 15 (kernel19_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha19_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17733),17608⟩,⟨(-17629),17712⟩⟩,⟨⟨(-1739),1756⟩,⟨(-1751),1744⟩⟩,⟨⟨(-148533),(-148455)⟩,⟨(-1915815),(-1915737)⟩⟩,⟨⟨(-2762692340139029),(-2762692340139025)⟩,⟨(-6582513233305751),(-6582513233305747)⟩⟩,⟨⟨(-1340431875249325234671),(-1340431875249325138845)⟩,⟨(-2350046358602387699353),(-2350046358602387603511)⟩⟩,⟨⟨(-4336224896029612195603331),(-4336224896029612171906582)⟩,⟨3325665505370755990531695,3325665505370756014099858⟩⟩] +lemma ha19_1_15_eq (j : Fin 7) : ha19_1_15 j = ((ha19_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha19_1_15_contains (j : Fin 7) : (ha19_1_15 j).Contains (fullFactor true 19 15 ((j.val:ℝ)/6)) := by + rw [ha19_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_14 j) true 19 14 j (ha19_1_14_contains j) +noncomputable def hk19_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_16 j i k) +lemma hk19_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_16 j i k).Contains (fullFactor true 19 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 16 (kernel19_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha19_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12534),12613⟩,⟨(-12579),12568⟩⟩,⟨⟨(-1104),1097⟩,⟨(-1102),1099⟩⟩,⟨⟨(-585400),(-585360)⟩,⟨386241,386281⟩⟩,⟨⟨(-1639042271788660),(-1639042271788657)⟩,⟨1421153918265472,1421153918265475⟩⟩,⟨⟨(-541035134843753901112),(-541035134843753872419)⟩,⟨445700657339520783322,445700657339520812011⟩⟩,⟨⟨801455764253527543695125,801455764253527549294856⟩,⟨939609352661017771359396,939609352661017776987327⟩⟩] +lemma ha19_1_16_eq (j : Fin 7) : ha19_1_16 j = ((ha19_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha19_1_16_contains (j : Fin 7) : (ha19_1_16 j).Contains (fullFactor true 19 16 ((j.val:ℝ)/6)) := by + rw [ha19_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_15 j) true 19 15 j (ha19_1_15_contains j) +noncomputable def hk19_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_17 j i k) +lemma hk19_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_17 j i k).Contains (fullFactor true 19 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 17 (kernel19_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha19_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8439),8401⟩,⟨(-8427),8414⟩⟩,⟨⟨(-652),653⟩,⟨(-651),654⟩⟩,⟨⟨213505,213524⟩,⟨111588,111608⟩⟩,⟨⟨532320531636224,532320531636226⟩,⟨318753107209568,318753107209570⟩⟩,⟨⟨129521935321114445871,129521935321114453956⟩,⟨111551733828312439500,111551733828312447585⟩⟩,⟨⟨190733047155104716282367,190733047155104717540331⟩,⟨(-180618307830521253063094),(-180618307830521251810897)⟩⟩] +lemma ha19_1_17_eq (j : Fin 7) : ha19_1_17 j = ((ha19_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha19_1_17_contains (j : Fin 7) : (ha19_1_17 j).Contains (fullFactor true 19 17 ((j.val:ℝ)/6)) := by + rw [ha19_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_16 j) true 19 16 j (ha19_1_16_contains j) +noncomputable def hk19_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_18 j i k) +lemma hk19_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_18 j i k).Contains (fullFactor true 19 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 18 (kernel19_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha19_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5319),5333⟩,⟨(-5319),5333⟩⟩,⟨⟨(-365),366⟩,⟨(-366),365⟩⟩,⟨⟨(-1903),(-1893)⟩,⟨(-78144),(-78135)⟩⟩,⟨⟨36998919840871,36998919840873⟩,⟨(-163463315790577),(-163463315790575)⟩⟩,⟨⟨20249939157843312598,20249939157843314750⟩,⟨(-33761216516028120806),(-33761216516028118653)⟩⟩,⟨⟨(-38223999811662041465820),(-38223999811662041201368)⟩,⟨(-36379260791321516815237),(-36379260791321516549682)⟩⟩] +lemma ha19_1_18_eq (j : Fin 7) : ha19_1_18 j = ((ha19_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha19_1_18_contains (j : Fin 7) : (ha19_1_18 j).Contains (fullFactor true 19 18 ((j.val:ℝ)/6)) := by + rw [ha19_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_17 j) true 19 17 j (ha19_1_17_contains j) +noncomputable def hk19_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_19 j i k) +lemma hk19_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_19 j i k).Contains (fullFactor true 19 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 19 (kernel19_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha19_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3193),3190⟩,⟨(-3196),3187⟩⟩,⟨⟨(-195),194⟩,⟨(-194),194⟩⟩,⟨⟨(-20728),(-20723)⟩,⟨12146,12151⟩⟩,⟨⟨(-42698173949019),(-42698173949017)⟩,⟨4040556896239,4040556896241⟩⟩,⟨⟨(-8009826222927950960),(-8009826222927950417)⟩,⟨(-3102568493281103675),(-3102568493281103131)⟩⟩,⟨⟨(-6536263649188618255003),(-6536263649188618201895)⟩,⟨7624153391305344161621,7624153391305344214531⟩⟩] +lemma ha19_1_19_eq (j : Fin 7) : ha19_1_19 j = ((ha19_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha19_1_19_contains (j : Fin 7) : (ha19_1_19 j).Contains (fullFactor true 19 19 ((j.val:ℝ)/6)) := by + rw [ha19_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_18 j) true 19 18 j (ha19_1_18_contains j) +noncomputable def hk19_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_20 j i k) +lemma hk19_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_20 j i k).Contains (fullFactor true 19 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 20 (kernel19_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha19_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1815),1819⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨6034,6037⟩,⟨3573,3576⟩⟩,⟨⟨4168514139000,4168514139002⟩,⟨9557110918625,9557110918627⟩⟩,⟨⟨(-351677491006819747),(-351677491006819616)⟩,⟨1745383297749337746,1745383297749337877⟩⟩,⟨⟨1437917628321945988094,1437917628321945998151⟩,⟨1108550268933949104887,1108550268933949114978⟩⟩] +lemma ha19_1_20_eq (j : Fin 7) : ha19_1_20 j = ((ha19_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha19_1_20_contains (j : Fin 7) : (ha19_1_20 j).Contains (fullFactor true 19 20 ((j.val:ℝ)/6)) := by + rw [ha19_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_19 j) true 19 19 j (ha19_1_19_contains j) +noncomputable def hk19_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_21 j i k) +lemma hk19_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_21 j i k).Contains (fullFactor true 19 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 21 (kernel19_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha19_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-985),986⟩,⟨(-986),985⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨55,57⟩,⟨(-1951),(-1949)⟩⟩,⟨⟨1801760208527,1801760208529⟩,⟨(-1606710477281),(-1606710477279)⟩⟩,⟨⟨351337890488046537,351337890488046567⟩,⟨9877352984422367,9877352984422398⟩⟩,⟨⟨177761965255747286071,177761965255747287897⟩,⟨(-257167342825200565744),(-257167342825200563923)⟩⟩] +lemma ha19_1_21_eq (j : Fin 7) : ha19_1_21 j = ((ha19_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha19_1_21_contains (j : Fin 7) : (ha19_1_21 j).Contains (fullFactor true 19 21 ((j.val:ℝ)/6)) := by + rw [ha19_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_20 j) true 19 20 j (ha19_1_20_contains j) +noncomputable def hk19_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_22 j i k) +lemma hk19_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_22 j i k).Contains (fullFactor true 19 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 22 (kernel19_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha19_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-511),510⟩,⟨(-510),511⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-461),(-459)⟩,⟨237,239⟩⟩,⟨⟨(-461513364174),(-461513364172)⟩,⟨(-267698800120),(-267698800119)⟩⟩,⟨⟨(-9413506134254430),(-9413506134254422)⟩,⟨(-65557998256255393),(-65557998256255386)⟩⟩,⟨⟨(-43728042347851890679),(-43728042347851890364)⟩,⟨(-26982450486785325981),(-26982450486785325665)⟩⟩] +lemma ha19_1_22_eq (j : Fin 7) : ha19_1_22 j = ((ha19_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha19_1_22_contains (j : Fin 7) : (ha19_1_22 j).Contains (fullFactor true 19 22 ((j.val:ℝ)/6)) := by + rw [ha19_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_21 j) true 19 21 j (ha19_1_21_contains j) +noncomputable def hk19_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_23 j i k) +lemma hk19_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_23 j i k).Contains (fullFactor true 19 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 23 (kernel19_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha19_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨109,110⟩,⟨72,74⟩⟩,⟨⟨(-23365578623),(-23365578622)⟩,⟨110341124418,110341124420⟩⟩,⟨⟨(-11356254381754053),(-11356254381754050)⟩,⟨3679555987312379,3679555987312382⟩⟩,⟨⟨(-3879276961626668024),(-3879276961626667971)⟩,⟨7085638467945122390,7085638467945122443⟩⟩] +lemma ha19_1_23_eq (j : Fin 7) : ha19_1_23 j = ((ha19_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha19_1_23_contains (j : Fin 7) : (ha19_1_23 j).Contains (fullFactor true 19 23 ((j.val:ℝ)/6)) := by + rw [ha19_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_22 j) true 19 22 j (ha19_1_22_contains j) +noncomputable def hk19_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_24 j i k) +lemma hk19_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_24 j i k).Contains (fullFactor true 19 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 24 (kernel19_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha19_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨2,3⟩,⟨(-33),(-31)⟩⟩,⟨⟨22715915964,22715915966⟩,⟨(-2469058938),(-2469058937)⟩⟩,⟨⟨959597610884631,959597610884633⟩,⟨1825088800909163,1825088800909164⟩⟩,⟨⟨1096452077255351093,1096452077255351102⟩,⟨528236500791581099,528236500791581109⟩⟩] +lemma ha19_1_24_eq (j : Fin 7) : ha19_1_24 j = ((ha19_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha19_1_24_contains (j : Fin 7) : (ha19_1_24 j).Contains (fullFactor true 19 24 ((j.val:ℝ)/6)) := by + rw [ha19_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_23 j) true 19 23 j (ha19_1_23_contains j) +noncomputable def hk19_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_25 j i k) +lemma hk19_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_25 j i k).Contains (fullFactor true 19 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 25 (kernel19_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha19_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-8),(-6)⟩,⟨2,4⟩⟩,⟨⟨(-1833189422),(-1833189421)⟩,⟨(-4048231278),(-4048231277)⟩⟩,⟨⟨271207144694150,271207144694151⟩,⟨(-208226382151770),(-208226382151769)⟩⟩,⟨⟨68063650993886843,68063650993886846⟩,⟨(-162340229620754464),(-162340229620754462)⟩⟩] +lemma ha19_1_25_eq (j : Fin 7) : ha19_1_25 j = ((ha19_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha19_1_25_contains (j : Fin 7) : (ha19_1_25 j).Contains (fullFactor true 19 25 ((j.val:ℝ)/6)) := by + rw [ha19_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_24 j) true 19 24 j (ha19_1_24_contains j) +noncomputable def hk19_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_26 j i k) +lemma hk19_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_26 j i k).Contains (fullFactor true 19 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 26 (kernel19_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha19_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨1,2⟩,⟨0,2⟩⟩,⟨⟨(-612494206),(-612494205)⟩,⟨561685720,561685721⟩⟩,⟨⟨(-40064575853804),(-40064575853803)⟩,⟨(-36973330155125),(-36973330155124)⟩⟩,⟨⟨(-23038282165670420),(-23038282165670419)⟩,⟨(-8280632562132854),(-8280632562132852)⟩⟩] +lemma ha19_1_26_eq (j : Fin 7) : ha19_1_26 j = ((ha19_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha19_1_26_contains (j : Fin 7) : (ha19_1_26 j).Contains (fullFactor true 19 26 ((j.val:ℝ)/6)) := by + rw [ha19_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_25 j) true 19 25 j (ha19_1_25_contains j) +noncomputable def hk19_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_27 j i k) +lemma hk19_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_27 j i k).Contains (fullFactor true 19 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 27 (kernel19_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha19_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨130486259,130486260⟩,⟨73280093,73280094⟩⟩,⟨⟨(-4549233949320),(-4549233949319)⟩,⟨7026524284556,7026524284557⟩⟩,⟨⟨(-947244603155260),(-947244603155259)⟩,⟨3138767367946408,3138767367946409⟩⟩] +lemma ha19_1_27_eq (j : Fin 7) : ha19_1_27 j = ((ha19_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha19_1_27_contains (j : Fin 7) : (ha19_1_27 j).Contains (fullFactor true 19 27 ((j.val:ℝ)/6)) := by + rw [ha19_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_26 j) true 19 26 j (ha19_1_26_contains j) +noncomputable def hk19_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_28 j i k) +lemma hk19_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_28 j i k).Contains (fullFactor true 19 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 28 (kernel19_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha19_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨5029287,5029288⟩,⟨(-25496092),(-25496091)⟩⟩,⟨⟨1139624293182,1139624293183⟩,⟨487005392314,487005392315⟩⟩,⟨⟨411144213963953,411144213963954⟩,⟨101112430385583,101112430385584⟩⟩] +lemma ha19_1_28_eq (j : Fin 7) : ha19_1_28 j = ((ha19_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha19_1_28_contains (j : Fin 7) : (ha19_1_28 j).Contains (fullFactor true 19 28 ((j.val:ℝ)/6)) := by + rw [ha19_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_27 j) true 19 27 j (ha19_1_27_contains j) +noncomputable def hk19_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_29 j i k) +lemma hk19_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_29 j i k).Contains (fullFactor true 19 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 29 (kernel19_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha19_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-4324581),(-4324580)⟩,⟨531048,531049⟩⟩,⟨⟨40928209307,40928209308⟩,⟨(-172369067627),(-172369067626)⟩⟩,⟨⟨9928196238362,9928196238363⟩,⟨(-51849609739056),(-51849609739055)⟩⟩] +lemma ha19_1_29_eq (j : Fin 7) : ha19_1_29 j = ((ha19_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha19_1_29_contains (j : Fin 7) : (ha19_1_29 j).Contains (fullFactor true 19 29 ((j.val:ℝ)/6)) := by + rw [ha19_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_28 j) true 19 28 j (ha19_1_28_contains j) +noncomputable def hk19_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel19_0 j i k).mul (mpower1_30 j i k) +lemma hk19_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk19_1_30 j i k).Contains (fullFactor true 19 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk19_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel19_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 19 30 (kernel19_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha19_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨300223,300225⟩,⟨639159,639160⟩⟩,⟨⟨(-24433487104),(-24433487103)⟩,⟨(-1526781627),(-1526781626)⟩⟩,⟨⟨(-6303151385546),(-6303151385545)⟩,⟨(-870500000282),(-870500000281)⟩⟩] +lemma ha19_1_30_eq (j : Fin 7) : ha19_1_30 j = ((ha19_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha19_1_30_contains (j : Fin 7) : (ha19_1_30 j).Contains (fullFactor true 19 30 ((j.val:ℝ)/6)) := by + rw [ha19_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha19_1_29 j) true 19 29 j (ha19_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders21.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders21.lean new file mode 100644 index 0000000000000000000000000000000000000000..5c3b8757ebf0f39a631ddd69fe3fc10843bc7e0f --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders21.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers30 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues30 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk21_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_0 j i k) +lemma hk21_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_0 j i k).Contains (fullFactor false 21 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 0 (power21_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha21_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999749,1000000000000000000000000000335⟩,⟨(-335),335⟩⟩,⟨⟨(-69211756054),85708073036⟩,⟨(-1000000000000000000077346766017),(-999999999999999999922653234016)⟩⟩,⟨⟨(-1000000000000000000211538567651),(-999999999999999999788461432360)⟩,⟨(-227952066935),194959432869⟩⟩,⟨⟨(-93344649761),43855698683⟩,⟨999999999999999999931399825799,1000000000000000000068600174222⟩⟩,⟨⟨999999999999999999421654447563,1000000000000000000578345552390⟩,⟨(-545413462277),611398730460⟩⟩,⟨⟨(-686678776404),769160361558⟩,⟨(-1000000000000000000727979659711),(-999999999999999999272020340233)⟩⟩,⟨⟨(-1000000000000000000137617153505),(-999999999999999999862382846579)⟩,⟨(-187106104625),88128202301⟩⟩] +lemma ha21_0_0_eq (j : Fin 7) : ha21_0_0 j = ((atomPoints j).direct.powBin 7 21).conj := by fin_cases j <;> decide +kernel +lemma ha21_0_0_contains (j : Fin 7) : (ha21_0_0 j).Contains (fullFactor false 21 0 ((j.val:ℝ)/6)) := by + rw [ha21_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 21) ((j.val:ℝ)/6) 21 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 21 (by norm_num)) +noncomputable def hk21_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_1 j i k) +lemma hk21_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_1 j i k).Contains (fullFactor false 21 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 1 (power21_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha21_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨523598775598298873036167994698,523598775598298873118832005318⟩,⟨(-36239190727),44876642101⟩⟩,⟨⟨(-204161040684),238710846285⟩,⟨(-1047197551196597746378189336697),(-1047197551196597745931810663315)⟩⟩,⟨⟨(-1570796326794896619342756901686),(-1570796326794896619122243098347)⟩,⟨(-146625432971),68888370401⟩⟩,⟨⟨(-1280510506685),1142311284173⟩,⟨2094395102393195491095382574149,2094395102393195493524617425752⟩⟩,⟨⟨2617993877991494363477487040759,2617993877991494367297512959095⟩,⟨(-1797720832773),2013657117753⟩⟩,⟨⟨(-276862912923),587811163732⟩,⟨(-3141592653589793238902337038460),(-3141592653589793238027662961804)⟩⟩] +lemma ha21_0_1_eq (j : Fin 7) : ha21_0_1 j = ((ha21_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha21_0_1_contains (j : Fin 7) : (ha21_0_1 j).Contains (fullFactor false 21 1 ((j.val:ℝ)/6)) := by + rw [ha21_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_0 j) false 21 0 j (ha21_0_0_contains j) +noncomputable def hk21_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_2 j i k) +lemma hk21_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_2 j i k).Contains (fullFactor false 21 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 2 (power21_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha21_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-11748677429),9487397947⟩,⟨137077838904018869695201390983,137077838904018869717279110672⟩⟩,⟨⟨548311355616075478707226675260,548311355616075478942695331350⟩,⟨(-106898470928),124988706837⟩⟩,⟨⟨(-54104799593),115159345763⟩,⟨(-1233700550136169827444721320924),(-1233700550136169827267603193959)⟩⟩,⟨⟨(-2193245422464301916575279065601),(-2193245422464301914024408960707)⟩,⟨(-1340947466883),1196225579491⟩⟩,⟨⟨(-2635871003326),2353211067269⟩,⟨3426945972600471740150350999632,3426945972600471745161661541449⟩⟩,⟨⟨4934802200544679308729827634910,4934802200544679310119470424933⟩,⟨(-434895246646),923331616840⟩⟩] +lemma ha21_0_2_eq (j : Fin 7) : ha21_0_2 j = ((ha21_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha21_0_2_contains (j : Fin 7) : (ha21_0_2 j).Contains (fullFactor false 21 2 ((j.val:ℝ)/6)) := by + rw [ha21_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_1 j) false 21 1 j (ha21_0_1_contains j) +noncomputable def hk21_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_3 j i k) +lemma hk21_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_3 j i k).Contains (fullFactor false 21 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 3 (power21_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha21_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23924596203935046433713249218),(-23924596203935046429783805862)⟩,⟨(-2050531039),1655863317⟩⟩,⟨⟨(-43629289243),37314605661⟩,⟨191396769631480371412586569558,191396769631480371495389871079⟩⟩,⟨⟨645964097506246253609812742577,645964097506246253704607744577⟩,⟨(-28329206821),60297292441⟩⟩,⟨⟨(-835122998348),936157935736⟩,⟨(-1531174157051842972524764344282),(-1531174157051842970739047180718)⟩⟩,⟨⟨(-2990574525491880806159922309425),(-2990574525491880801777209575321)⟩,⟨(-2300231383295),2053564055911⟩⟩,⟨⟨(-966910608098),455421237315⟩,⟨5167712780049970028521842015069,5167712780049970029993521882488⟩⟩] +lemma ha21_0_3_eq (j : Fin 7) : ha21_0_3 j = ((ha21_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha21_0_3_contains (j : Fin 7) : (ha21_0_3 j).Contains (fullFactor false 21 3 ((j.val:ℝ)/6)) := by + rw [ha21_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_2 j) false 21 2 j (ha21_0_2_contains j) +noncomputable def hk21_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_4 j i k) +lemma hk21_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_4 j i k).Contains (fullFactor false 21 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 4 (power21_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha21_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-216752002),268413886⟩,⟨(-3131722319766024859982221452),(-3131722319766024859457889937)⟩⟩,⟨⟨(-50107557116256397766439566594),(-50107557116256397744602215639)⟩,⟨(-11422121214),9768940919⟩⟩,⟨⟨(-23678691371),11124853504⟩,⟨253669507901048013618307828597,253669507901048013656341193955⟩⟩,⟨⟨801720913860102363619558619163,801720913860102364557109896501⟩,⟨(-437269379409),490171148919⟩⟩,⟨⟨(-1344054531610),1505497919858⟩,⟨(-1957326449853765538762389379314),(-1957326449853765535887680238996)⟩⟩,⟨⟨(-4058712126416768218781579154009),(-4058712126416768217612805207078)⟩,⟨(-759409815770),357687003360⟩⟩] +lemma ha21_0_4_eq (j : Fin 7) : ha21_0_4 j = ((ha21_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha21_0_4_contains (j : Fin 7) : (ha21_0_4 j).Contains (fullFactor false 21 4 ((j.val:ℝ)/6)) := by + rw [ha21_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_3 j) false 21 3 j (ha21_0_3_contains j) +noncomputable def hk21_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_5 j i k) +lemma hk21_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_5 j i k).Contains (fullFactor false 21 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 5 (power21_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha21_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨327953194428670967547351068,327953194428670967603302844⟩,⟨(-22698217),28108237⟩⟩,⟨⟨(-2046002202),2392243473⟩,⟨(-10494502221717470964713967167),(-10494502221717470960106958039)⟩⟩,⟨⟨(-79692626246167045126905552208),(-79692626246167045114703348579)⟩,⟨(-7438880286),3494975805⟩⟩,⟨⟨(-205322410727),183162969333⟩,⟨335824071094959070600240042331,335824071094959070994029564251⟩⟩,⟨⟨1024853732589596772918668540146,1024853732589596774427124936970⟩,⟨(-703745307089),788276867504⟩⟩,⟨⟨(-224741372409),477151259658⟩,⟨(-2550164039877345444236982289328),(-2550164039877345443494502535997)⟩⟩] +lemma ha21_0_5_eq (j : Fin 7) : ha21_0_5 j = ((ha21_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha21_0_5_contains (j : Fin 7) : (ha21_0_5 j).Contains (fullFactor false 21 5 ((j.val:ℝ)/6)) := by + rw [ha21_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_4 j) false 21 4 j (ha21_0_4_contains j) +noncomputable def hk21_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_6 j i k) +lemma hk21_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_6 j i k).Contains (fullFactor false 21 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 6 (power21_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha21_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2452907),1980794⟩,⟨28619315176067161689070761,28619315176067161694044574⟩⟩,⟨⟨1831636171268298347854738200,1831636171268298348664643260⟩,⟨(-357094750),417525252⟩⟩,⟨⟨(-914982527),1947494305⟩,⟨(-20863480763352960874776009701),(-20863480763352960871515069739)⟩⟩,⟨⟨(-117224714961171094357536012811),(-117224714961171094219704400605)⟩,⟨(-71671041907),63935937652⟩⟩,⟨⟨(-343950668882),307066817605⟩,⟨447176799626049401100782718759,447176799626049401760394395406⟩⟩,⟨⟨1335262768854589495684808660547,1335262768854589496077820423698⟩,⟨(-117674307420),249835815333⟩⟩] +lemma ha21_0_6_eq (j : Fin 7) : ha21_0_6 j = ((ha21_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha21_0_6_contains (j : Fin 7) : (ha21_0_6 j).Contains (fullFactor false 21 6 ((j.val:ℝ)/6)) := by + rw [ha21_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_5 j) false 21 5 j (ha21_0_5_contains j) +noncomputable def hk21_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_7 j i k) +lemma hk21_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_7 j i k).Contains (fullFactor false 21 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 7 (power21_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha21_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2140719769235797028406185),(-2140719769235797028027329)⟩,⟨(-183478),148164⟩⟩,⟨⟨(-62461632),53421250⟩,⟨274012130462182019550728034,274012130462182019672761757⟩⟩,⟨⟨4681754135318688100336719696,4681754135318688101083375400⟩,⟨(-205321599),437016701⟩⟩,⟨⟨(-19129587813),21443925594⟩,⟨(-35073552699159298530978728865),(-35073552699159298489627964341)⟩⟩,⟨⟨(-167243731971546642953047411980),(-167243731971546642705820868458)⟩,⟨(-128637249353),114842721233⟩⟩,⟨⟨(-112126051722),52812105673⟩,⟨599264529320792076801740693597,599264529320792076980031478680⟩⟩] +lemma ha21_0_7_eq (j : Fin 7) : ha21_0_7 j = ((ha21_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha21_0_7_contains (j : Fin 7) : (ha21_0_7 j).Contains (fullFactor false 21 7 ((j.val:ℝ)/6)) := by + rw [ha21_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_6 j) false 21 6 j (ha21_0_6_contains j) +noncomputable def hk21_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_8 j i k) +lemma hk21_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_8 j i k).Contains (fullFactor false 21 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 8 (power21_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha21_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-9698),12009⟩,⟨(-140109781258867029466551),(-140109781258867029441308)⟩⟩,⟨⟨(-35868104002269959548250178),(-35868104002269959532161829)⟩,⟨(-8176209),6992826⟩⟩,⟨⟨(-85808029),40314802⟩,⟨919260274839426580172466971,919260274839426580321998573⟩⟩,⟨⟨9182234624581109636865320521,9182234624581109647720153320⟩,⟨(-5008114379),5614006593⟩⟩,⟨⟨(-37582192640),42096441411⟩,⟨(-54730383304244933420980744363),(-54730383304244933339901834964)⟩⟩,⟨⟨(-235330630358893204578673443715),(-235330630358893204507909735475)⟩,⟨(-44031797546),20739265401⟩⟩] +lemma ha21_0_8_eq (j : Fin 7) : ha21_0_8 j = ((ha21_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha21_0_8_contains (j : Fin 7) : (ha21_0_8 j).Contains (fullFactor false 21 8 ((j.val:ℝ)/6)) := by + rw [ha21_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_7 j) false 21 7 j (ha21_0_7_contains j) +noncomputable def hk21_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_9 j i k) +lemma hk21_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_9 j i k).Contains (fullFactor false 21 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 9 (power21_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha21_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨8151256657387584304172,8151256657387584305668⟩,⟨(-565),699⟩⟩,⟨⟨(-813653),951346⟩,⟨(-4173443408582443165061761),(-4173443408582443163176511)⟩⟩,⟨⟨(-160441184787359821887048487),(-160441184787359821860439598)⟩,⟨(-14976327),7036261⟩⟩,⟨⟨(-1306438658),1165441137⟩,⟨2136803025194210898762579546,2136803025194210901295415497⟩⟩,⟨⟨15920423158960125583729452885,15920423158960125607365027883⟩,⟨(-10932216695),12245358434⟩⟩,⟨⟨(-7239369314),15369996855⟩,⟨(-82145886611128228811838285862),(-82145886611128228786875613389)⟩⟩] +lemma ha21_0_9_eq (j : Fin 7) : ha21_0_9 j = ((ha21_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha21_0_9_contains (j : Fin 7) : (ha21_0_9 j).Contains (fullFactor false 21 9 ((j.val:ℝ)/6)) := by + rw [ha21_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_8 j) false 21 8 j (ha21_0_8_contains j) +noncomputable def hk21_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_10 j i k) +lemma hk21_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_10 j i k).Contains (fullFactor false 21 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 10 (power21_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha21_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-37),30⟩,⟨426798800539562151414,426798800539562151495⟩⟩,⟨⟨437041971752511642990092,437041971752511643188907⟩,⟨(-85206),99625⟩⟩,⟨⟨(-1105254),2352476⟩,⟨(-25202042373060605483372039),(-25202042373060605479112103)⟩⟩,⟨⟨(-447530979074571922789598144),(-447530979074571922257697687)⟩,⟨(-273619873),244089421⟩⟩,⟨⟨(-3205827342),2862047639⟩,⟨4167957036519161632198205113,4167957036519161638399251198⟩⟩,⟨⟨25806891390014060008829680257,25806891390014060016754080990⟩,⟨(-2274314946),4828626921⟩⟩] +lemma ha21_0_10_eq (j : Fin 7) : ha21_0_10 j = ((ha21_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha21_0_10_contains (j : Fin 7) : (ha21_0_10 j).Contains (fullFactor false 21 10 ((j.val:ℝ)/6)) := by + rw [ha21_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_9 j) false 21 9 j (ha21_0_9_contains j) +noncomputable def hk21_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_11 j i k) +lemma hk21_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_11 j i k).Contains (fullFactor false 21 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 11 (power21_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha21_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-20315575399030665724),(-20315575399030665719)⟩,⟨(-2),2⟩⟩,⟨⟨(-9485),8112⟩,⟨41606298417214803387196,41606298417214803406257⟩⟩,⟨⟨3598843235212085340178349,3598843235212085340798123⟩,⟨(-157830),335933⟩⟩,⟨⟨(-46474518),52097102⟩,⟨(-85209699158455917407268265),(-85209699158455917305723423)⟩⟩,⟨⟨(-991971455030794225400529595),(-991971455030794223921526533)⟩,⟨(-762985124),681165746⟩⟩,⟨⟨(-1379052624),649542830⟩,⟨7370430945714350776176574725,7370430945714350778463239093⟩⟩] +lemma ha21_0_11_eq (j : Fin 7) : ha21_0_11 j = ((ha21_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha21_0_11_contains (j : Fin 7) : (ha21_0_11 j).Contains (fullFactor false 21 11 ((j.val:ℝ)/6)) := by + rw [ha21_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_10 j) false 21 10 j (ha21_0_10_contains j) +noncomputable def hk21_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_12 j i k) +lemma hk21_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_12 j i k).Contains (fullFactor false 21 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 12 (power21_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha21_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-886434200375614886),(-886434200375614885)⟩⟩,⟨⟨(-3630834484738518571894),(-3630834484738518570218)⟩,⟨(-828),708⟩⟩,⟨⟨(-43974),20660⟩,⟨471087477881817150329954,471087477881817150412583⟩⟩,⟨⟨14871898049488972058161350,14871898049488972075931608⟩,⟨(-8111334),9092660⟩⟩,⟨⟨(-148607313),166457532⟩,⟨(-216414599701077853069829157),(-216414599701077852746471874)⟩⟩,⟨⟨(-1929574309403923048223109524),(-1929574309403923047618320165)⟩,⟨(-361035133),170049916⟩⟩] +lemma ha21_0_12_eq (j : Fin 7) : ha21_0_12 j = ((ha21_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha21_0_12_contains (j : Fin 7) : (ha21_0_12 j).Contains (fullFactor false 21 12 ((j.val:ℝ)/6)) := by + rw [ha21_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_11 j) false 21 11 j (ha21_0_11_contains j) +noncomputable def hk21_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_13 j i k) +lemma hk21_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_13 j i k).Contains (fullFactor false 21 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 13 (power21_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha21_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨35702758612702236,35702758612702237⟩,⟨(-1),1⟩⟩,⟨⟨(-58),67⟩,⟨(-292476998555256723095),(-292476998555256722958)⟩⟩,⟨⟨(-56921729219679268123391),(-56921729219679268113225)⟩,⟨(-5314),2497⟩⟩,⟨⟨(-1464895),1306796⟩,⟨2395971572164663073594720,2395971572164663076465266⟩⟩,⟨⟨43582469009646284998529177,43582469009646285063786935⟩,⟨(-29927157),33521908⟩⟩,⟨⟨(-41094429),87248102⟩,⟨(-466302805767612564498995319),(-466302805767612564351357045)⟩⟩] +lemma ha21_0_13_eq (j : Fin 7) : ha21_0_13 j = ((ha21_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha21_0_13_contains (j : Fin 7) : (ha21_0_13 j).Contains (fullFactor false 21 13 ((j.val:ℝ)/6)) := by + rw [ha21_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_12 j) false 21 12 j (ha21_0_12_contains j) +noncomputable def hk21_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_14 j i k) +lemma hk21_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_14 j i k).Contains (fullFactor false 21 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 14 (power21_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha21_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1335280049649465,1335280049649466⟩⟩,⟨⟨21877228333456835512,21877228333456835523⟩,⟨(-5),6⟩⟩,⟨⟨(-281),597⟩,⟨(-6386603083791852241738),(-6386603083791852240576)⟩⟩,⟨⟨(-358436509015356793336796),(-358436509015356792906222)⟩,⟨(-219148),195497⟩⟩,⟨⟨(-6268583),5596366⟩,⟨8149902646786285751036026,8149902646786285763265141⟩⟩,⟨⟨104638104924845707102384113,104638104924845707135847138⟩,⟨(-9221569),19578429⟩⟩] +lemma ha21_0_14_eq (j : Fin 7) : ha21_0_14 j = ((ha21_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha21_0_14_contains (j : Fin 7) : (ha21_0_14 j).Contains (fullFactor false 21 14 ((j.val:ℝ)/6)) := by + rw [ha21_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_13 j) false 21 13 j (ha21_0_13_contains j) +noncomputable def hk21_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_15 j i k) +lemma hk21_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_15 j i k).Contains (fullFactor false 21 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 15 (power21_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha21_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-46610066605154),(-46610066605153)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1527318662517654886,1527318662517654888⟩⟩,⟨⟨668803510981146723193,668803510981146723318⟩,⟨(-30),63⟩⟩,⟨⟨(-27297),30599⟩,⟨(-50047177933378515358159),(-50047177933378515297879)⟩⟩,⟨⟨(-1422426349034211493905310),(-1422426349034211491766398)⟩,⟨(-1094075),976751⟩⟩,⟨⟨(-4100497),1931361⟩,⟨21915353447830215824092124,21915353447830215831170364⟩⟩] +lemma ha21_0_15_eq (j : Fin 7) : ha21_0_15 j = ((ha21_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha21_0_15_contains (j : Fin 7) : (ha21_0_15 j).Contains (fullFactor false 21 15 ((j.val:ℝ)/6)) := by + rw [ha21_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_14 j) false 21 14 j (ha21_0_14_contains j) +noncomputable def hk21_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_16 j i k) +lemma hk21_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_16 j i k).Contains (fullFactor false 21 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 16 (power21_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha21_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1525310862814),(-1525310862813)⟩⟩,⟨⟨(-99962772705334444),(-99962772705334443)⟩,⟨(-1),1⟩⟩,⟨⟨(-7),3⟩,⟨65659631149794723616,65659631149794723630⟩⟩,⟨⟨6551160272016798094873,6551160272016798102786⟩,⟨(-3574),4006⟩⟩,⟨⟨(-159821),179018⟩,⟨(-232743967104084891551200),(-232743967104084891200479)⟩⟩,⟨⟨(-4303069587032947008051223),(-4303069587032947006647716)⟩,⟨(-805131),379222⟩⟩] +lemma ha21_0_16_eq (j : Fin 7) : ha21_0_16 j = ((ha21_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha21_0_16_contains (j : Fin 7) : (ha21_0_16 j).Contains (fullFactor false 21 16 ((j.val:ℝ)/6)) := by + rw [ha21_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_15 j) false 21 15 j (ha21_0_15_contains j) +noncomputable def hk21_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_17 j i k) +lemma hk21_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_17 j i k).Contains (fullFactor false 21 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 17 (power21_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha21_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨46979464716,46979464717⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-6157692399285196),(-6157692399285195)⟩⟩,⟨⟨(-6066935731106195668),(-6066935731106195666)⟩,⟨(-1),1⟩⟩,⟨⟨(-494),441⟩,⟨807101058159109192938,807101058159109193917⟩⟩,⟨⟨35842487118702823459513,35842487118702823513639⟩,⟨(-24613),27569⟩⟩,⟨⟨(-70081),148788⟩,⟨(-795205400147551278619411),(-795205400147551278357511)⟩⟩] +lemma ha21_0_17_eq (j : Fin 7) : ha21_0_17 j = ((ha21_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha21_0_17_contains (j : Fin 7) : (ha21_0_17 j).Contains (fullFactor false 21 17 ((j.val:ℝ)/6)) := by + rw [ha21_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_16 j) false 21 16 j (ha21_0_16_contains j) +noncomputable def hk21_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_18 j i k) +lemma hk21_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_18 j i k).Contains (fullFactor false 21 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 18 (power21_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha21_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1366577233,1366577234⟩⟩,⟨⟨358240022308519,358240022308520⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-529440020073462377),(-529440020073462376)⟩⟩,⟨⟨(-93910472408044662797),(-93910472408044662682)⟩,⟨(-58),52⟩⟩,⟨⟨(-4010),3580⟩,⟨5213078436041832667729,5213078436041832675619⟩⟩,⟨⟨138789524622137721123478,138789524622137721169631⟩,⟨(-12232),25969⟩⟩] +lemma ha21_0_18_eq (j : Fin 7) : ha21_0_18 j = ((ha21_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha21_0_18_contains (j : Fin 7) : (ha21_0_18 j).Contains (fullFactor false 21 18 ((j.val:ℝ)/6)) := by + rw [ha21_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_17 j) false 21 17 j (ha21_0_17_contains j) +noncomputable def hk21_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_19 j i k) +lemma hk21_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_19 j i k).Contains (fullFactor false 21 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 19 (power21_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha21_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-37659904),(-37659903)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨19744635479057,19744635479058⟩⟩,⟨⟨43770654673137422,43770654673137423⟩,⟨(-1),1⟩⟩,⟨⟨(-6),7⟩,⟨(-10351875446044213768),(-10351875446044213755)⟩⟩,⟨⟨(-718305654265631155596),(-718305654265631154505)⟩,⟨(-553),494⟩⟩,⟨⟨(-4294),2023⟩,⟨22948428997269873106678,22948428997269873114384⟩⟩] +lemma ha21_0_19_eq (j : Fin 7) : ha21_0_19 j = ((ha21_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha21_0_19_contains (j : Fin 7) : (ha21_0_19 j).Contains (fullFactor false 21 19 ((j.val:ℝ)/6)) := by + rw [ha21_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_18 j) false 21 18 j (ha21_0_18_contains j) +noncomputable def hk21_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_20 j i k) +lemma hk21_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_20 j i k).Contains (fullFactor false 21 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 20 (power21_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha21_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-985934),(-985933)⟩⟩,⟨⟨(-1033826696147),(-1033826696146)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨3437739179098606,3437739179098608⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨(-65),73⟩,⟨(-94025990269704865287),(-94025990269704865143)⟩⟩,⟨⟨(-3604730797462500934525),(-3604730797462500933302)⟩,⟨(-675),318⟩⟩] +lemma ha21_0_20_eq (j : Fin 7) : ha21_0_20 j = ((ha21_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha21_0_20_contains (j : Fin 7) : (ha21_0_20 j).Contains (fullFactor false 21 20 ((j.val:ℝ)/6)) := by + rw [ha21_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_19 j) false 21 19 j (ha21_0_19_contains j) +noncomputable def hk21_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_21 j i k) +lemma hk21_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_21 j i k).Contains (fullFactor false 21 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 21 (power21_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha21_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨24582,24583⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-51553370694),(-51553370693)⟩⟩,⟨⟨(-257142289286048),(-257142289286047)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨11721879376103578813,11721879376103578832⟩,⟨(-9),10⟩⟩,⟨⟨(-48),101⟩,⟨(-539266466260812849037),(-539266466260812848851)⟩⟩] +lemma ha21_0_21_eq (j : Fin 7) : ha21_0_21 j = ((ha21_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha21_0_21_contains (j : Fin 7) : (ha21_0_21 j).Contains (fullFactor false 21 21 ((j.val:ℝ)/6)) := by + rw [ha21_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_20 j) false 21 20 j (ha21_0_20_contains j) +noncomputable def hk21_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_22 j i k) +lemma hk21_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_22 j i k).Contains (fullFactor false 21 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 22 (power21_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha21_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨585,586⟩⟩,⟨⟨2453934706,2453934707⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-18359916521553),(-18359916521552)⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨1394900383872451218,1394900383872451221⟩⟩,⟨⟨77007071306013533785,77007071306013533813⟩,⟨(-7),15⟩⟩] +lemma ha21_0_22_eq (j : Fin 7) : ha21_0_22 j = ((ha21_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha21_0_22_contains (j : Fin 7) : (ha21_0_22 j).Contains (fullFactor false 21 22 ((j.val:ℝ)/6)) := by + rw [ha21_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_21 j) false 21 21 j (ha21_0_21_contains j) +noncomputable def hk21_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_23 j i k) +lemma hk21_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_23 j i k).Contains (fullFactor false 21 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 23 (power21_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha21_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-14),(-13)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨111728452,111728453⟩⟩,⟨⟨1253899540535,1253899540536⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨(-158775681103741858),(-158775681103741856)⟩,⟨(-1),1⟩⟩,⟨⟨(-3),1⟩,⟨10518471716932064453,10518471716932064458⟩⟩] +lemma ha21_0_23_eq (j : Fin 7) : ha21_0_23 j = ((ha21_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha21_0_23_contains (j : Fin 7) : (ha21_0_23 j).Contains (fullFactor false 21 23 ((j.val:ℝ)/6)) := by + rw [ha21_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_22 j) false 21 22 j (ha21_0_22_contains j) +noncomputable def hk21_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_24 j i k) +lemma hk21_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_24 j i k).Contains (fullFactor false 21 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 24 (power21_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha21_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-4875074),(-4875073)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨82067533018,82067533019⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-17319740045980250),(-17319740045980248)⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha21_0_24_eq (j : Fin 7) : ha21_0_24 j = ((ha21_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha21_0_24_contains (j : Fin 7) : (ha21_0_24 j).Contains (fullFactor false 21 24 ((j.val:ℝ)/6)) := by + rw [ha21_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_23 j) false 21 23 j (ha21_0_23_contains j) +noncomputable def hk21_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_25 j i k) +lemma hk21_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_25 j i k).Contains (fullFactor false 21 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 25 (power21_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha21_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-204207),(-204206)⟩⟩,⟨⟨(-5156455177),(-5156455176)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨1813718936351216,1813718936351217⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha21_0_25_eq (j : Fin 7) : ha21_0_25 j = ((ha21_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha21_0_25_contains (j : Fin 7) : (ha21_0_25 j).Contains (fullFactor false 21 25 ((j.val:ℝ)/6)) := by + rw [ha21_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_24 j) false 21 24 j (ha21_0_24_contains j) +noncomputable def hk21_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_26 j i k) +lemma hk21_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_26 j i k).Contains (fullFactor false 21 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 26 (power21_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha21_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨8224,8225⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-311528495),(-311528494)⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨182627118144797,182627118144798⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha21_0_26_eq (j : Fin 7) : ha21_0_26 j = ((ha21_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha21_0_26_contains (j : Fin 7) : (ha21_0_26 j).Contains (fullFactor false 21 26 ((j.val:ℝ)/6)) := by + rw [ha21_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_25 j) false 21 25 j (ha21_0_25_contains j) +noncomputable def hk21_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_27 j i k) +lemma hk21_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_27 j i k).Contains (fullFactor false 21 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 27 (power21_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha21_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨318,320⟩⟩,⟨⟨18123993,18123994⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨(-17708025083642),(-17708025083641)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha21_0_27_eq (j : Fin 7) : ha21_0_27 j = ((ha21_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha21_0_27_contains (j : Fin 7) : (ha21_0_27 j).Contains (fullFactor false 21 27 ((j.val:ℝ)/6)) := by + rw [ha21_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_26 j) false 21 26 j (ha21_0_26_contains j) +noncomputable def hk21_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_28 j i k) +lemma hk21_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_28 j i k).Contains (fullFactor false 21 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 28 (power21_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha21_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-12),(-11)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1016753,1016754⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1655696473582),(-1655696473581)⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha21_0_28_eq (j : Fin 7) : ha21_0_28 j = ((ha21_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha21_0_28_contains (j : Fin 7) : (ha21_0_28 j).Contains (fullFactor false 21 28 ((j.val:ℝ)/6)) := by + rw [ha21_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_27 j) false 21 27 j (ha21_0_27_contains j) +noncomputable def hk21_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_29 j i k) +lemma hk21_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_29 j i k).Contains (fullFactor false 21 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 29 (power21_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha21_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-55073),(-55072)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨149469076953,149469076954⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha21_0_29_eq (j : Fin 7) : ha21_0_29 j = ((ha21_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha21_0_29_contains (j : Fin 7) : (ha21_0_29 j).Contains (fullFactor false 21 29 ((j.val:ℝ)/6)) := by + rw [ha21_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_28 j) false 21 28 j (ha21_0_28_contains j) +noncomputable def hk21_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power21 j i k).conj.mul (mpower0_30 j i k) +lemma hk21_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk21_0_30 j i k).Contains (fullFactor false 21 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power21 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 30 (power21_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha21_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-2884),(-2883)⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨13043637613,13043637614⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha21_0_30_eq (j : Fin 7) : ha21_0_30 j = ((ha21_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha21_0_30_contains (j : Fin 7) : (ha21_0_30 j).Contains (fullFactor false 21 30 ((j.val:ℝ)/6)) := by + rw [ha21_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_0_29 j) false 21 29 j (ha21_0_29_contains j) +noncomputable def hk21_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_0 j i k) +lemma hk21_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_0 j i k).Contains (fullFactor true 21 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 0 (kernel21_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha21_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩,⟨⟨25312,25315⟩,⟨11801,11804⟩⟩,⟨⟨(-3818447111475508),(-3818447111475505)⟩,⟨(-22135735523014202),(-22135735523014199)⟩⟩,⟨⟨(-465579338219423601664417),(-465579338219423599382689)⟩,⟨(-72777510407062961050706),(-72777510407062958771017)⟩⟩,⟨⟨15107785144520704772910159032,15107785144520704814094127433⟩,⟨14272246381970123218210380229,14272246381970123259587922189⟩⟩] +lemma ha21_1_0_eq (j : Fin 7) : ha21_1_0 j = atomKernel21_0 j := by fin_cases j <;> decide +kernel +lemma ha21_1_0_contains (j : Fin 7) : (ha21_1_0 j).Contains (fullFactor true 21 0 ((j.val:ℝ)/6)) := by + rw [ha21_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel21_0_contains j +noncomputable def hk21_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_1 j i k) +lemma hk21_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_1 j i k).Contains (fullFactor true 21 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 1 (kernel21_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha21_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-30),11⟩,⟨(-31),10⟩⟩,⟨⟨(-11359),(-11334)⟩,⟨(-162722),(-162697)⟩⟩,⟨⟨(-96480550487984323),(-96480550487984304)⟩,⟨51184714145044773,51184714145044792⟩⟩,⟨⟨30592198090449795242469,30592198090449806164697⟩,⟨1953286993187611677087887,1953286993187611688021236⟩⟩,⟨⟨48700613826522762890528929747,48700613826522763047850641807⟩,⟨(-57234553114940164290854633226),(-57234553114940164134186467881)⟩⟩] +lemma ha21_1_1_eq (j : Fin 7) : ha21_1_1 j = ((ha21_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha21_1_1_contains (j : Fin 7) : (ha21_1_1 j).Contains (fullFactor true 21 1 ((j.val:ℝ)/6)) := by + rw [ha21_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_0 j) true 21 0 j (ha21_1_0_contains j) +noncomputable def hk21_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_2 j i k) +lemma hk21_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_2 j i k).Contains (fullFactor true 21 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 2 (kernel21_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha21_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-177),255⟩,⟨(-219),205⟩⟩,⟨⟨(-107),100⟩,⟨(-53),154⟩⟩,⟨⟨(-399578),(-399478)⟩,⟨259163,259264⟩⟩,⟨⟨191337625738189147,191337625738189206⟩,⟨184088006935988298,184088006935988358⟩⟩,⟨⟨3979104688035727781992774,3979104688035727808184783⟩,⟨(-750344026870806919582443),(-750344026870806893419580)⟩⟩,⟨⟨(-107910069603317323581483525279),(-107910069603317323283503211851)⟩,⟨(-82556030310145458717691266524),(-82556030310145458418638820578)⟩⟩] +lemma ha21_1_2_eq (j : Fin 7) : ha21_1_2 j = ((ha21_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha21_1_2_contains (j : Fin 7) : (ha21_1_2 j).Contains (fullFactor true 21 2 ((j.val:ℝ)/6)) := by + rw [ha21_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_1 j) true 21 1 j (ha21_1_1_contains j) +noncomputable def hk21_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_3 j i k) +lemma hk21_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_3 j i k).Contains (fullFactor true 21 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 3 (kernel21_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha21_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-924),707⟩,⟨(-840),779⟩⟩,⟨⟨(-256),440⟩,⟨(-425),271⟩⟩,⟨⟨818131,818399⟩,⟨435643,435910⟩⟩,⟨⟨186846632239843988,186846632239844111⟩,⟨(-387645571216347740),(-387645571216347618)⟩⟩,⟨⟨(-1955960318379645113927833),(-1955960318379645072144871)⟩,⟨(-5242449847029821582968734),(-5242449847029821541141342)⟩⟩,⟨⟨(-92616446464503346817578897168),(-92616446464503346438628113846)⟩,⟨135055964623526129813364557477,135055964623526130191184037826⟩⟩] +lemma ha21_1_3_eq (j : Fin 7) : ha21_1_3 j = ((ha21_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha21_1_3_contains (j : Fin 7) : (ha21_1_3 j).Contains (fullFactor true 21 3 ((j.val:ℝ)/6)) := by + rw [ha21_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_2 j) true 21 2 j (ha21_1_2_contains j) +noncomputable def hk21_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_4 j i k) +lemma hk21_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_4 j i k).Contains (fullFactor true 21 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 4 (kernel21_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha21_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2136),2495⟩,⟨(-2151),2469⟩⟩,⟨⟨(-1089),665⟩,⟨(-901),853⟩⟩,⟨⟨(-22669),(-22137)⟩,⟨(-1353558),(-1353026)⟩⟩,⟨⟨(-518514400400403956),(-518514400400403767)⟩,⟨(-68952050797530133),(-68952050797529944)⟩⟩,⟨⟨(-5009841721879808147076639),(-5009841721879808096982191)⟩,⟨2920740193439121010097645,2920740193439121060145696⟩⟩,⟨⟨126270376428478578139822751975,126270376428478578499092893323⟩,⟨77270122082663491997768083490,77270122082663492357890797722⟩⟩] +lemma ha21_1_4_eq (j : Fin 7) : ha21_1_4 j = ((ha21_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha21_1_4_contains (j : Fin 7) : (ha21_1_4 j).Contains (fullFactor true 21 4 ((j.val:ℝ)/6)) := by + rw [ha21_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_3 j) true 21 3 j (ha21_1_3_contains j) +noncomputable def hk21_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_5 j i k) +lemma hk21_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_5 j i k).Contains (fullFactor true 21 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 5 (kernel21_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha21_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5425),5111⟩,⟨(-5641),4887⟩⟩,⟨⟨(-1583),1951⟩,⟨(-1525),2009⟩⟩,⟨⟨(-1370342),(-1369496)⟩,⟨788425,789271⟩⟩,⟨⟨93435282928897793,93435282928898026⟩,⟨500003572683429201,500003572683429433⟩⟩,⟨⟨3092109020228483345861991,3092109020228483393820410⟩,⟨3681918901938586981315658,3681918901938587029309947⟩⟩,⟨⟨51062842150640993944172671928,51062842150640994217940170308⟩,⟨(-94094977435246888430107396874),(-94094977435246888156816826215)⟩⟩] +lemma ha21_1_5_eq (j : Fin 7) : ha21_1_5 j = ((ha21_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha21_1_5_contains (j : Fin 7) : (ha21_1_5 j).Contains (fullFactor true 21 5 ((j.val:ℝ)/6)) := by + rw [ha21_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_4 j) true 21 4 j (ha21_1_4_contains j) +noncomputable def hk21_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_6 j i k) +lemma hk21_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_6 j i k).Contains (fullFactor true 21 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 6 (kernel21_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha21_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-10026),9960⟩,⟨(-9412),10570⟩⟩,⟨⟨(-2910),3024⟩,⟨(-3324),2611⟩⟩,⟨⟨1317192,1318312⟩,⟨793690,794810⟩⟩,⟨⟨361403890790211805,361403890790212043⟩,⟨(-198225606634482607),(-198225606634482368)⟩⟩,⟨⟨2143990124347311540008031,2143990124347311578325206⟩,⟨(-2537562459911188635493223),(-2537562459911188597197319)⟩⟩,⟨⟨(-58227942459464784799907780503),(-58227942459464784626678167181)⟩,⟨(-27786787183841953699076873125),(-27786787183841953525653302766)⟩⟩] +lemma ha21_1_6_eq (j : Fin 7) : ha21_1_6 j = ((ha21_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha21_1_6_contains (j : Fin 7) : (ha21_1_6 j).Contains (fullFactor true 21 6 ((j.val:ℝ)/6)) := by + rw [ha21_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_5 j) true 21 5 j (ha21_1_5_contains j) +noncomputable def hk21_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_7 j i k) +lemma hk21_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_7 j i k).Contains (fullFactor true 21 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 7 (kernel21_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha21_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-15907),16595⟩,⟨(-16866),15633⟩⟩,⟨⟨(-4573),3968⟩,⟨(-4062),4479⟩⟩,⟨⟨46226,47497⟩,⟨(-1283373),(-1282102)⟩⟩,⟨⟨(-209065125771816914),(-209065125771816704)⟩,⟨(-195614231166143180),(-195614231166142970)⟩⟩,⟨⟨(-1696673844113512512752951),(-1696673844113512486542251)⟩,⟨(-995945191318522043159649),(-995945191318522016939281)⟩⟩,⟨⟨(-12772165142508555911782359212),(-12772165142508555817622484204)⟩,⟨30782890660336954233874125728,30782890660336954327986534975⟩⟩] +lemma ha21_1_7_eq (j : Fin 7) : ha21_1_7 j = ((ha21_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha21_1_7_contains (j : Fin 7) : (ha21_1_7 j).Contains (fullFactor true 21 7 ((j.val:ℝ)/6)) := by + rw [ha21_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_6 j) true 21 6 j (ha21_1_6_contains j) +noncomputable def hk21_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_8 j i k) +lemma hk21_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_8 j i k).Contains (fullFactor true 21 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 8 (kernel21_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha21_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-23741),22509⟩,⟨(-22694),23555⟩⟩,⟨⟨(-5058),5698⟩,⟨(-5312),5444⟩⟩,⟨⟨(-836281),(-835019)⟩,⟨423213,424475⟩⟩,⟨⟨(-73365930813289982),(-73365930813289820)⟩,⟨157787988823759811,157787988823759973⟩⟩,⟨⟨(-359219376252830628549745),(-359219376252830612850363)⟩,⟨954108018600215020818439,954108018600215036514678⟩⟩,⟨⟨14194511500609732960319473904,14194511500609733005055040925⟩,⟨5042551784208670541405379837,5042551784208670586136725919⟩⟩] +lemma ha21_1_8_eq (j : Fin 7) : ha21_1_8 j = ((ha21_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha21_1_8_contains (j : Fin 7) : (ha21_1_8 j).Contains (fullFactor true 21 8 ((j.val:ℝ)/6)) := by + rw [ha21_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_7 j) true 21 7 j (ha21_1_7_contains j) +noncomputable def hk21_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_9 j i k) +lemma hk21_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_9 j i k).Contains (fullFactor true 21 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 9 (kernel21_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha21_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-28549),29954⟩,⟨(-29363),29139⟩⟩,⟨⟨(-6157),5883⟩,⟨(-6239),5801⟩⟩,⟨⟨502776,503890⟩,⟨340472,341586⟩⟩,⟨⟨93350482292964928,93350482292965039⟩,⟨11093862236993857,11093862236993968⟩⟩,⟨⟨461201524973641178301879,461201524973641186656785⟩,⟨88392712375110500386156,88392712375110508741531⟩⟩,⟨⟨1727048306760188064322564848,1727048306760188083210636776⟩,⟨(-5800400832812695332967893443),(-5800400832812695314067135498)⟩⟩] +lemma ha21_1_9_eq (j : Fin 7) : ha21_1_9 j = ((ha21_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha21_1_9_contains (j : Fin 7) : (ha21_1_9 j).Contains (fullFactor true 21 9 ((j.val:ℝ)/6)) := by + rw [ha21_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_8 j) true 21 8 j (ha21_1_8_contains j) +noncomputable def hk21_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_10 j i k) +lemma hk21_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_10 j i k).Contains (fullFactor true 21 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 10 (kernel21_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha21_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-33881),32720⟩,⟨(-33476),33125⟩⟩,⟨⟨(-6110),6020⟩,⟨(-5886),6243⟩⟩,⟨⟨31322,32207⟩,⟨(-354070),(-353185)⟩⟩,⟨⟨(-9020573237231440),(-9020573237231371)⟩,⟨(-44808937544507244),(-44808937544507175)⟩⟩,⟨⟨3628384056985018137058,3628384056985022139136⟩,⟨(-194640019547781279409532),(-194640019547781275407212)⟩⟩,⟨⟨(-2126969209474934723941776402),(-2126969209474934716755225477)⟩,⟨(-514725568668045225166969124),(-514725568668045217989199493)⟩⟩] +lemma ha21_1_10_eq (j : Fin 7) : ha21_1_10 j = ((ha21_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha21_1_10_contains (j : Fin 7) : (ha21_1_10 j).Contains (fullFactor true 21 10 ((j.val:ℝ)/6)) := by + rw [ha21_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_9 j) true 21 9 j (ha21_1_9_contains j) +noncomputable def hk21_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_11 j i k) +lemma hk21_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_11 j i k).Contains (fullFactor true 21 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 11 (kernel21_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha21_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34119),34809⟩,⟨(-34145),34782⟩⟩,⟨⟨(-5451),5658⟩,⟨(-5613),5496⟩⟩,⟨⟨(-172713),(-172073)⟩,⟨75907,76547⟩⟩,⟨⟨(-17577038496770089),(-17577038496770049)⟩,⟨9961496701455977,9961496701456016⟩⟩,⟨⟨(-72519780905046542338913),(-72519780905046540596013)⟩,⟨11114811196522972421005,11114811196522974163643⟩⟩,⟨⟨(-132663571714906582844480992),(-132663571714906580364867946)⟩,⟨707017540468709262971556584,707017540468709265455499491⟩⟩] +lemma ha21_1_11_eq (j : Fin 7) : ha21_1_11 j = ((ha21_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha21_1_11_contains (j : Fin 7) : (ha21_1_11 j).Contains (fullFactor true 21 11 ((j.val:ℝ)/6)) := by + rw [ha21_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_10 j) true 21 10 j (ha21_1_10_contains j) +noncomputable def hk21_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_12 j i k) +lemma hk21_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_12 j i k).Contains (fullFactor true 21 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 12 (kernel21_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha21_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32817),32574⟩,⟨(-33006),32385⟩⟩,⟨⟨(-4731),4596⟩,⟨(-4684),4643⟩⟩,⟨⟨72893,73317⟩,⟨55197,55621⟩⟩,⟨⟨6054790492698686,6054790492698707⟩,⟨5509209134869157,5509209134869178⟩⟩,⟨⟨8040278427132549156070,8040278427132549851658⟩,⟨24036379677609155897654,24036379677609156593370⟩⟩,⟨⟨214830786016776349448255625,214830786016776350235205102⟩,⟨28857713076777863009964384,28857713076777863795157137⟩⟩] +lemma ha21_1_12_eq (j : Fin 7) : ha21_1_12 j = ((ha21_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha21_1_12_contains (j : Fin 7) : (ha21_1_12 j).Contains (fullFactor true 21 12 ((j.val:ℝ)/6)) := by + rw [ha21_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_11 j) true 21 11 j (ha21_1_11_contains j) +noncomputable def hk21_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_13 j i k) +lemma hk21_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_13 j i k).Contains (fullFactor true 21 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 13 (kernel21_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha21_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28649),28615⟩,⟨(-28414),28850⟩⟩,⟨⟨(-3597),3632⟩,⟨(-3580),3649⟩⟩,⟨⟨5728,5988⟩,⟨(-40918),(-40658)⟩⟩,⟨⟨1252101601432533,1252101601432544⟩,⟨(-2793960176573697),(-2793960176573686)⟩⟩,⟨⟨7117916775454916127883,7117916775454916384226⟩,⟨(-3828912375816956778218),(-3828912375816956521922)⟩⟩,⟨⟨4912804315421372182970529,4912804315421372412476662⟩,⟨(-60090636290371233318815600),(-60090636290371233088690992)⟩⟩] +lemma ha21_1_13_eq (j : Fin 7) : ha21_1_13 j = ((ha21_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha21_1_13_contains (j : Fin 7) : (ha21_1_13 j).Contains (fullFactor true 21 13 ((j.val:ℝ)/6)) := by + rw [ha21_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_12 j) true 21 12 j (ha21_1_12_contains j) +noncomputable def hk21_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_14 j i k) +lemma hk21_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_14 j i k).Contains (fullFactor true 21 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 14 (kernel21_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha21_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23215),23350⟩,⟨(-23397),23168⟩⟩,⟨⟨(-2595),2608⟩,⟨(-2620),2583⟩⟩,⟨⟨(-16141),(-15993)⟩,⟨6033,6182⟩⟩,⟨⟨(-1057531862638861),(-1057531862638855)⟩,⟨(-110775019920221),(-110775019920215)⟩⟩,⟨⟨(-1475387514196049881400),(-1475387514196049793709)⟩,⟨(-1884433923738260370747),(-1884433923738260283043)⟩⟩,⟨⟨(-15565096147500065443112018),(-15565096147500065380628108)⟩,⟨(-461203141777090261063187),(-461203141777090198773452)⟩⟩] +lemma ha21_1_14_eq (j : Fin 7) : ha21_1_14 j = ((ha21_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha21_1_14_contains (j : Fin 7) : (ha21_1_14 j).Contains (fullFactor true 21 14 ((j.val:ℝ)/6)) := by + rw [ha21_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_13 j) true 21 13 j (ha21_1_13_contains j) +noncomputable def hk21_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_15 j i k) +lemma hk21_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_15 j i k).Contains (fullFactor true 21 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 15 (kernel21_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha21_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17733),17608⟩,⟨(-17629),17712⟩⟩,⟨⟨(-1756),1739⟩,⟨(-1744),1751⟩⟩,⟨⟨5071,5151⟩,⟨4280,4359⟩⟩,⟨⟨72717222711301,72717222711304⟩,⟨336909961463142,336909961463145⟩⟩,⟨⟨(-443956505706476393902),(-443956505706476365895)⟩,⟨490307404760758790855,490307404760758818858⟩⟩,⟨⟨83819583668170213251705,83819583668170229030191⟩,⟨3752837942859004519445812,3752837942859004535279584⟩⟩] +lemma ha21_1_15_eq (j : Fin 7) : ha21_1_15 j = ((ha21_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha21_1_15_contains (j : Fin 7) : (ha21_1_15 j).Contains (fullFactor true 21 15 ((j.val:ℝ)/6)) := by + rw [ha21_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_14 j) true 21 14 j (ha21_1_14_contains j) +noncomputable def hk21_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_16 j i k) +lemma hk21_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_16 j i k).Contains (fullFactor true 21 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 16 (kernel21_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha21_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12534),12613⟩,⟨(-12579),12568⟩⟩,⟨⟨(-1097),1104⟩,⟨(-1099),1102⟩⟩,⟨⟨455,495⟩,⟨(-2416),(-2376)⟩⟩,⟨⟨90395491825513,90395491825515⟩,⟨(-52905716791484),(-52905716791482)⟩⟩,⟨⟨144733231343663972305,144733231343663980689⟩,⟨91772986196964009699,91772986196964018084⟩⟩,⟨⟨845991027874165170219117,845991027874165173980501⟩,⟨(-62959854171811811230017),(-62959854171811807482960)⟩⟩] +lemma ha21_1_16_eq (j : Fin 7) : ha21_1_16 j = ((ha21_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha21_1_16_contains (j : Fin 7) : (ha21_1_16 j).Contains (fullFactor true 21 16 ((j.val:ℝ)/6)) := by + rw [ha21_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_15 j) true 21 15 j (ha21_1_15_contains j) +noncomputable def hk21_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_17 j i k) +lemma hk21_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_17 j i k).Contains (fullFactor true 21 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 17 (kernel21_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha21_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8439),8401⟩,⟨(-8427),8414⟩⟩,⟨⟨(-653),652⟩,⟨(-654),651⟩⟩,⟨⟨(-809),(-789)⟩,⟨246,266⟩⟩,⟨⟨(-22435601892826),(-22435601892824)⟩,⟨(-19850304477633),(-19850304477631)⟩⟩,⟨⟨16057851358134041222,16057851358134043585⟩,⟨(-38583192534504231157),(-38583192534504228793)⟩⟩,⟨⟨(-22717896797985879520981),(-22717896797985878683437)⟩,⟨(-179004320417499552148258),(-179004320417499551307327)⟩⟩] +lemma ha21_1_17_eq (j : Fin 7) : ha21_1_17 j = ((ha21_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha21_1_17_contains (j : Fin 7) : (ha21_1_17 j).Contains (fullFactor true 21 17 ((j.val:ℝ)/6)) := by + rw [ha21_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_16 j) true 21 16 j (ha21_1_16_contains j) +noncomputable def hk21_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_18 j i k) +lemma hk21_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_18 j i k).Contains (fullFactor true 21 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 18 (kernel21_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha21_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5319),5333⟩,⟨(-5319),5333⟩⟩,⟨⟨(-366),365⟩,⟨(-365),366⟩⟩,⟨⟨193,203⟩,⟨182,191⟩⟩,⟨⟨(-3206125447260),(-3206125447258)⟩,⟨7429584745180,7429584745182⟩⟩,⟨⟨(-9385188289362566449),(-9385188289362565819)⟩,⟨(-2134818871831520354),(-2134818871831519724)⟩⟩,⟨⟨(-35673524798518564512904),(-35673524798518564335350)⟩,⟨6424842139256380886180,6424842139256381062996⟩⟩] +lemma ha21_1_18_eq (j : Fin 7) : ha21_1_18 j = ((ha21_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha21_1_18_contains (j : Fin 7) : (ha21_1_18 j).Contains (fullFactor true 21 18 ((j.val:ℝ)/6)) := by + rw [ha21_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_17 j) true 21 17 j (ha21_1_17_contains j) +noncomputable def hk21_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_19 j i k) +lemma hk21_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_19 j i k).Contains (fullFactor true 21 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 19 (kernel21_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha21_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3193),3190⟩,⟨(-3196),3187⟩⟩,⟨⟨(-194),195⟩,⟨(-194),194⟩⟩,⟨⟨18,23⟩,⟨(-84),(-78)⟩⟩,⟨⟨2062264429133,2062264429134⟩,⟨187041879818,187041879820⟩⟩,⟨⟨(-111122720750244567),(-111122720750244407)⟩,⟨2097096643341633098,2097096643341633258⟩⟩,⟨⟨1573621561026333788544,1573621561026333823910⟩,⟨6716400672576576397939,6716400672576576433454⟩⟩] +lemma ha21_1_19_eq (j : Fin 7) : ha21_1_19 j = ((ha21_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha21_1_19_contains (j : Fin 7) : (ha21_1_19 j).Contains (fullFactor true 21 19 ((j.val:ℝ)/6)) := by + rw [ha21_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_18 j) true 21 18 j (ha21_1_18_contains j) +noncomputable def hk21_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_20 j i k) +lemma hk21_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_20 j i k).Contains (fullFactor true 21 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 20 (kernel21_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha21_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1815),1819⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨(-25),(-22)⟩,⟨5,8⟩⟩,⟨⟨(-113046712677),(-113046712675)⟩,⟨(-490553725153),(-490553725151)⟩⟩,⟨⟨432276245065147118,432276245065147157⟩,⟨(-51151325909299032),(-51151325909298992)⟩⟩,⟨⟨1197880675797602033769,1197880675797602040518⟩,⟨(-347177475646580633062),(-347177475646580626341)⟩⟩] +lemma ha21_1_20_eq (j : Fin 7) : ha21_1_20 j = ((ha21_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha21_1_20_contains (j : Fin 7) : (ha21_1_20 j).Contains (fullFactor true 21 20 ((j.val:ℝ)/6)) := by + rw [ha21_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_19 j) true 21 19 j (ha21_1_19_contains j) +noncomputable def hk21_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_21 j i k) +lemma hk21_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_21 j i k).Contains (fullFactor true 21 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 21 (kernel21_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha21_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-985),986⟩,⟨(-986),985⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨4,6⟩,⟨4,6⟩⟩,⟨⟨(-99764135456),(-99764135454)⟩,⟨60268492661,60268492663⟩⟩,⟨⟨(-24448697423311813),(-24448697423311803)⟩,⟨(-82378585476382865),(-82378585476382855)⟩⟩,⟨⟨(-70409379846372144846),(-70409379846372143629)⟩,⟨(-202875601543502997378),(-202875601543502996156)⟩⟩] +lemma ha21_1_21_eq (j : Fin 7) : ha21_1_21 j = ((ha21_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha21_1_21_contains (j : Fin 7) : (ha21_1_21 j).Contains (fullFactor true 21 21 ((j.val:ℝ)/6)) := by + rw [ha21_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_20 j) true 21 20 j (ha21_1_20_contains j) +noncomputable def hk21_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_22 j i k) +lemma hk21_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_22 j i k).Contains (fullFactor true 21 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 22 (kernel21_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha21_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-511),510⟩,⟨(-510),511⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨0,1⟩,⟨(-3),(-1)⟩⟩,⟨⟨19528091443,19528091445⟩,⟨16799135387,16799135388⟩⟩,⟨⟨(-14514616734452756),(-14514616734452753)⟩,⟨7177264519278800,7177264519278803⟩⟩,⟨⟨(-32698548834758724346),(-32698548834758724134)⟩,⟨13288397097077496660,13288397097077496871⟩⟩] +lemma ha21_1_22_eq (j : Fin 7) : ha21_1_22 j = ((ha21_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha21_1_22_contains (j : Fin 7) : (ha21_1_22 j).Contains (fullFactor true 21 22 ((j.val:ℝ)/6)) := by + rw [ha21_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_21 j) true 21 21 j (ha21_1_21_contains j) +noncomputable def hk21_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_23 j i k) +lemma hk21_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_23 j i k).Contains (fullFactor true 21 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 23 (kernel21_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha21_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨2087817588,2087817590⟩,⟨(-5029402165),(-5029402163)⟩⟩,⟨⟨1719302955843843,1719302955843845⟩,⟨2358327073575622,2358327073575623⟩⟩,⟨⟨2353246265861244544,2353246265861244580⟩,⟨5025221929336364150,5025221929336364186⟩⟩] +lemma ha21_1_23_eq (j : Fin 7) : ha21_1_23 j = ((ha21_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha21_1_23_contains (j : Fin 7) : (ha21_1_23 j).Contains (fullFactor true 21 23 ((j.val:ℝ)/6)) := by + rw [ha21_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_22 j) true 21 22 j (ha21_1_22_contains j) +noncomputable def hk21_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_24 j i k) +lemma hk21_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_24 j i k).Contains (fullFactor true 21 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 24 (kernel21_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha21_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1099982148),(-1099982146)⟩,⟨(-84348237),(-84348235)⟩⟩,⟨⟨350981271630286,350981271630287⟩,⟨(-361868466306042),(-361868466306041)⟩⟩,⟨⟨737680428853148904,737680428853148911⟩,⟨(-393384846566192278),(-393384846566192272)⟩⟩] +lemma ha21_1_24_eq (j : Fin 7) : ha21_1_24 j = ((ha21_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha21_1_24_contains (j : Fin 7) : (ha21_1_24 j).Contains (fullFactor true 21 24 ((j.val:ℝ)/6)) := by + rw [ha21_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_23 j) true 21 23 j (ha21_1_23_contains j) +noncomputable def hk21_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_25 j i k) +lemma hk21_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_25 j i k).Contains (fullFactor true 21 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 25 (kernel21_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha21_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨51087084,51087085⟩,⟨208388930,208388932⟩⟩,⟨⟨(-69021507574559),(-69021507574558)⟩,⟨(-47159864600332),(-47159864600331)⟩⟩,⟨⟨(-62361586098251161),(-62361586098251159)⟩,⟨(-103596641788216740),(-103596641788216738)⟩⟩] +lemma ha21_1_25_eq (j : Fin 7) : ha21_1_25 j = ((ha21_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha21_1_25_contains (j : Fin 7) : (ha21_1_25 j).Contains (fullFactor true 21 25 ((j.val:ℝ)/6)) := by + rw [ha21_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_24 j) true 21 24 j (ha21_1_24_contains j) +noncomputable def hk21_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_26 j i k) +lemma hk21_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_26 j i k).Contains (fullFactor true 21 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 26 (kernel21_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha21_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨34051517,34051519⟩,⟨(-21223281),(-21223280)⟩⟩,⟨⟨(-5540377406866),(-5540377406864)⟩,⟨12122623909537,12122623909538⟩⟩,⟨⟨(-13937704877953426),(-13937704877953425)⟩,⟨9409307696240134,9409307696240135⟩⟩] +lemma ha21_1_26_eq (j : Fin 7) : ha21_1_26 j = ((ha21_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha21_1_26_contains (j : Fin 7) : (ha21_1_26 j).Contains (fullFactor true 21 26 ((j.val:ℝ)/6)) := by + rw [ha21_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_25 j) true 21 25 j (ha21_1_25_contains j) +noncomputable def hk21_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_27 j i k) +lemma hk21_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_27 j i k).Contains (fullFactor true 21 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 27 (kernel21_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha21_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5542649),(-5542648)⟩,⟨(-4635438),(-4635437)⟩⟩,⟨⟨1978763820307,1978763820309⟩,⟨522076177421,522076177422⟩⟩,⟨⟨1355347581055892,1355347581055894⟩,⟨1798614739545324,1798614739545325⟩⟩] +lemma ha21_1_27_eq (j : Fin 7) : ha21_1_27 j = ((ha21_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha21_1_27_contains (j : Fin 7) : (ha21_1_27 j).Contains (fullFactor true 21 27 ((j.val:ℝ)/6)) := by + rw [ha21_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_26 j) true 21 26 j (ha21_1_26_contains j) +noncomputable def hk21_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_28 j i k) +lemma hk21_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_28 j i k).Contains (fullFactor true 21 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 28 (kernel21_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha21_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-464879),(-464877)⟩,⟨1165404,1165405⟩⟩,⟨⟨26399371916,26399371917⟩,⟨(-301840602774),(-301840602773)⟩⟩,⟨⟨222869517742249,222869517742250⟩,⟨(-186854547456092),(-186854547456090)⟩⟩] +lemma ha21_1_28_eq (j : Fin 7) : ha21_1_28 j = ((ha21_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha21_1_28_contains (j : Fin 7) : (ha21_1_28 j).Contains (fullFactor true 21 28 ((j.val:ℝ)/6)) := by + rw [ha21_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_27 j) true 21 27 j (ha21_1_27_contains j) +noncomputable def hk21_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_29 j i k) +lemma hk21_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_29 j i k).Contains (fullFactor true 21 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 29 (kernel21_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha21_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨209952,209953⟩,⟨13162,13164⟩⟩,⟨⟨(-43162118255),(-43162118254)⟩,⟨3611676117,3611676118⟩⟩,⟨⟨(-24709848039620),(-24709848039619)⟩,⟨(-26541425058348),(-26541425058347)⟩⟩] +lemma ha21_1_29_eq (j : Fin 7) : ha21_1_29 j = ((ha21_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha21_1_29_contains (j : Fin 7) : (ha21_1_29 j).Contains (fullFactor true 21 29 ((j.val:ℝ)/6)) := by + rw [ha21_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_28 j) true 21 28 j (ha21_1_28_contains j) +noncomputable def hk21_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel21_0 j i k).mul (mpower1_30 j i k) +lemma hk21_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk21_1_30 j i k).Contains (fullFactor true 21 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk21_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel21_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 21 30 (kernel21_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha21_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-8579),(-8577)⟩,⟨(-32998),(-32997)⟩⟩,⟨⟨1505135447,1505135448⟩,⟨5792876967,5792876968⟩⟩,⟨⟨(-3040064198136),(-3040064198135)⟩,⟨3140389236149,3140389236150⟩⟩] +lemma ha21_1_30_eq (j : Fin 7) : ha21_1_30 j = ((ha21_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha21_1_30_contains (j : Fin 7) : (ha21_1_30 j).Contains (fullFactor true 21 30 ((j.val:ℝ)/6)) := by + rw [ha21_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha21_1_29 j) true 21 29 j (ha21_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders24.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders24.lean new file mode 100644 index 0000000000000000000000000000000000000000..b3143e30ab436f518af85ae03c1be431b50f5128 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders24.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers30 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues30 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk24_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_0 j i k) +lemma hk24_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_0 j i k).Contains (fullFactor false 24 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 0 (power24_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha24_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999713,1000000000000000000000000000383⟩,⟨(-383),383⟩⟩,⟨⟨999999999999999999973702175385,1000000000000000000026297824647⟩,⟨(-17218479783),36071413471⟩⟩,⟨⟨999999999999999999927542457041,1000000000000000000072457542975⟩,⟨(-53350537359),91056404863⟩⟩,⟨⟨999999999999999999921599800913,1000000000000000000078400199111⟩,⟨(-50120798495),106679599727⟩⟩,⟨⟨999999999999999999802292497873,1000000000000000000197707502071⟩,⟨(-160187373927),235599108999⟩⟩,⟨⟨999999999999999999750954293361,1000000000000000000249045706567⟩,⟨(-201729023199),295993691951⟩⟩,⟨⟨999999999999999999842723253233,1000000000000000000157276746863⟩,⟨(-100717945487),213835548143⟩⟩] +lemma ha24_0_0_eq (j : Fin 7) : ha24_0_0 j = ((atomPoints j).direct.powBin 7 24).conj := by fin_cases j <;> decide +kernel +lemma ha24_0_0_contains (j : Fin 7) : (ha24_0_0 j).Contains (fullFactor false 24 0 ((j.val:ℝ)/6)) := by + rw [ha24_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 24) ((j.val:ℝ)/6) 24 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 24 (by norm_num)) +noncomputable def hk24_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_1 j i k) +lemma hk24_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_1 j i k).Contains (fullFactor false 24 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 1 (power24_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha24_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-18886947928),9015574933⟩,⟨523598775598298873062897157894,523598775598298873092102842122⟩⟩,⟨⟨(-95354044194),55868552078⟩,⟨1047197551196597746077455971779,1047197551196597746232544028239⟩⟩,⟨⟨(-167571923396),78729566172⟩,⟨1570796326794896619106849255254,1570796326794896619358150744784⟩⟩,⟨⟨(-493437620016),335495651418⟩,⟨2094395102393195491892589042502,2094395102393195492727410957379⟩⟩,⟨⟨(-774909673452),528125347749⟩,⟨2617993877991494364731333198011,2617993877991494366043666801802⟩⟩,⟨⟨(-671784187123),316414757627⟩,⟨3141592653589793237965900527776,3141592653589793238964099472526⟩⟩] +lemma ha24_0_1_eq (j : Fin 7) : ha24_0_1 j = ((ha24_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha24_0_1_contains (j : Fin 7) : (ha24_0_1 j).Contains (fullFactor false 24 1 ((j.val:ℝ)/6)) := by + rw [ha24_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_0 j) false 24 0 j (ha24_0_0_contains j) +noncomputable def hk24_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_2 j i k) +lemma hk24_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_2 j i k).Contains (fullFactor false 24 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 2 (power24_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha24_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-137077838904018869710281432111),(-137077838904018869702199069544)⟩,⟨(-4944591405),2360271999⟩⟩,⟨⟨(-548311355616075478866435626170),(-548311355616075478783486380443)⟩,⟨(-49927260789),29252705463⟩⟩,⟨⟨(-1233700550136169827456811617020),(-1233700550136169827255512897867)⟩,⟨(-131610680873),61834056677⟩⟩,⟨⟨(-2193245422464301915740446404123),(-2193245422464301914859241622165)⟩,⟨(-516726667350),351330224603⟩⟩,⟨⟨(-3426945972600471743520380759581),(-3426945972600471741791631781446)⟩,⟨(-1014354390547),691314463610⟩⟩,⟨⟨(-4934802200544679310216486629498),(-4934802200544679308632811430405)⟩,⟨(-1055236133532),497023139025⟩⟩] +lemma ha24_0_2_eq (j : Fin 7) : ha24_0_2 j = ((ha24_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha24_0_2_contains (j : Fin 7) : (ha24_0_2 j).Contains (fullFactor false 24 2 ((j.val:ℝ)/6)) := by + rw [ha24_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_1 j) false 24 1 j (ha24_0_1_contains j) +noncomputable def hk24_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_3 j i k) +lemma hk24_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_3 j i k).Contains (fullFactor false 24 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 3 (power24_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha24_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-411945177),862994002⟩,⟨(-23924596203935046432491923909),(-23924596203935046431005131171)⟩⟩,⟨⟨(-10211120509),17427901746⟩,⟨(-191396769631480371468770212239),(-191396769631480371439206228398)⟩⟩,⟨⟨(-32376236367),68911191361⟩,⟨(-645964097506246253710938208809),(-645964097506246253603482278347)⟩⟩,⟨⟨(-245274767244),360743267125⟩,⟨(-1531174157051842971941941198443),(-1531174157051842971321870326543)⟩⟩,⟨⟨(-603285677833),885191194856⟩,⟨(-2990574525491880804727634629760),(-2990574525491880803209497254939)⟩⟩,⟨⟨(-520481414076),1105040694969⟩,⟨(-5167712780049970030095117014335),(-5167712780049970028420246883285)⟩⟩] +lemma ha24_0_3_eq (j : Fin 7) : ha24_0_3 j = ((ha24_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha24_0_3_contains (j : Fin 7) : (ha24_0_3 j).Contains (fullFactor false 24 3 ((j.val:ℝ)/6)) := by + rw [ha24_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_2 j) false 24 2 j (ha24_0_2_contains j) +noncomputable def hk24_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_4 j i k) +lemma hk24_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_4 j i k).Contains (fullFactor false 24 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 4 (power24_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha24_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨3131722319766024859617761046,3131722319766024859822350343⟩,⟨(-53923498),112965651⟩⟩,⟨⟨50107557116256397751571226026,50107557116256397759470556206⟩,⟨(-2673265098),4562614008⟩⟩,⟨⟨253669507901048013615821861107,253669507901048013658827161446⟩,⟨(-12714118291),27061361567⟩⟩,⟨⟨801720913860102363924724104707,801720913860102364251944410949⟩,⟨(-128425567815),188884732972⟩⟩,⟨⟨1957326449853765536825110333186,1957326449853765537824959285093⟩,⟨(-394849552812),579356282247⟩⟩,⟨⟨4058712126416768217533012577165,4058712126416768218861371783972⟩,⟨(-408785146698),867896932309⟩⟩] +lemma ha24_0_4_eq (j : Fin 7) : ha24_0_4 j = ((ha24_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha24_0_4_contains (j : Fin 7) : (ha24_0_4 j).Contains (fullFactor false 24 4 ((j.val:ℝ)/6)) := by + rw [ha24_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_3 j) false 24 3 j (ha24_0_3_contains j) +noncomputable def hk24_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_5 j i k) +lemma hk24_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_5 j i k).Contains (fullFactor false 24 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 5 (power24_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha24_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-11829736),5646856⟩,⟨327953194428670967564092732,327953194428670967586561181⟩⟩,⟨⟨(-955591644),559887333⟩,⟨10494502221717470961566544162,10494502221717470963254381045⟩⟩,⟨⟨(-8501577470),3994258062⟩,⟨79692626246167045113922358858,79692626246167045127686541928⟩⟩,⟨⟨(-79119851931),53794776051⟩,⟨335824071094959070728067462000,335824071094959070866202144579⟩⟩,⟨⟨(-303350240020),206742742398⟩,⟨1024853732589596773409505789673,1024853732589596773936287687426⟩⟩,⟨⟨(-545315725324),256847282753⟩,⟨2550164039877345443444367348008,2550164039877345444287117477349⟩⟩] +lemma ha24_0_5_eq (j : Fin 7) : ha24_0_5 j = ((ha24_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha24_0_5_contains (j : Fin 7) : (ha24_0_5 j).Contains (fullFactor false 24 5 ((j.val:ℝ)/6)) := by + rw [ha24_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_4 j) false 24 4 j (ha24_0_4_contains j) +noncomputable def hk24_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_6 j i k) +lemma hk24_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_6 j i k).Contains (fullFactor false 24 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 6 (power24_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha24_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-28619315176067161692583588),(-28619315176067161690531747)⟩,⟨(-1032340),492782⟩⟩,⟨⟨(-1831636171268298348409897424),(-1831636171268298348109484036)⟩,⟨(-166782205),97718775⟩⟩,⟨⟨(-20863480763352960874980472332),(-20863480763352960871310607108)⟩,⟨(-2225707777),1045694316⟩⟩,⟨⟨(-117224714961171094312915825858),(-117224714961171094264324587556)⟩,⟨(-27618038398),18777919250⟩⟩,⟨⟨(-447176799626049401546226243007),(-447176799626049401314950871151)⟩,⟨(-132361511877),90208538987⟩⟩,⟨⟨(-1335262768854589496104071146761),(-1335262768854589495658557937502)⟩,⟨(-285526646095),134484922766⟩⟩] +lemma ha24_0_6_eq (j : Fin 7) : ha24_0_6 j = ((ha24_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha24_0_6_contains (j : Fin 7) : (ha24_0_6 j).Contains (fullFactor false 24 6 ((j.val:ℝ)/6)) := by + rw [ha24_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_5 j) false 24 5 j (ha24_0_5_contains j) +noncomputable def hk24_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_7 j i k) +lemma hk24_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_7 j i k).Contains (fullFactor false 24 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 7 (power24_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha24_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-36861),77219⟩,⟨(-2140719769235797028296903),(-2140719769235797028136611)⟩⟩,⟨⟨(-14618695),24950560⟩,⟨(-274012130462182019634651869),(-274012130462182019588837922)⟩⟩,⟨⟨(-234653256),499447658⟩,⟨(-4681754135318688101129256707),(-4681754135318688100290838389)⟩⟩,⟨⟨(-5618340302),8263297766⟩,⟨(-35073552699159298517628400147),(-35073552699159298502978293058)⟩⟩,⟨⟨(-33737914688),49503089683⟩,⟨(-167243731971546642872948710288),(-167243731971546642785919570147)⟩⟩,⟨⟨(-60356692198),128144059111⟩,⟨(-599264529320792076991812775641),(-599264529320792076789959396644)⟩⟩] +lemma ha24_0_7_eq (j : Fin 7) : ha24_0_7 j = ((ha24_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha24_0_7_contains (j : Fin 7) : (ha24_0_7 j).Contains (fullFactor false 24 7 ((j.val:ℝ)/6)) := by + rw [ha24_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_6 j) false 24 6 j (ha24_0_6_contains j) +noncomputable def hk24_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_8 j i k) +lemma hk24_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_8 j i k).Contains (fullFactor false 24 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 8 (power24_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha24_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨140109781258867029448461,140109781258867029459399⟩,⟨(-2413),5054⟩⟩,⟨⟨35868104002269959537150401,35868104002269959543261606⟩,⟨(-1913583),3266021⟩⟩,⟨⟨919260274839426580163458197,919260274839426580331007346⟩,⟨(-46074060),98066319⟩⟩,⟨⟨9182234624581109640360428406,9182234624581109644225045434⟩,⟨(-1470878052),2163326297⟩⟩,⟨⟨54730383304244933366114073796,54730383304244933394768505530⟩,⟨(-11040706764),16199848217⟩⟩,⟨⟨235330630358893204503283230980,235330630358893204583299948213⟩,⟨(-23702017601),50322054339⟩⟩] +lemma ha24_0_8_eq (j : Fin 7) : ha24_0_8 j = ((ha24_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha24_0_8_contains (j : Fin 7) : (ha24_0_8 j).Contains (fullFactor false 24 8 ((j.val:ℝ)/6)) := by + rw [ha24_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_7 j) false 24 7 j (ha24_0_7_contains j) +noncomputable def hk24_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_9 j i k) +lemma hk24_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_9 j i k).Contains (fullFactor false 24 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 9 (power24_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha24_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-295),141⟩,⟨8151256657387584304589,8151256657387584305252⟩⟩,⟨⟨(-380019),222656⟩,⟨4173443408582443163756958,4173443408582443164481314⟩⟩,⟨⟨(-17115802),8041441⟩,⟨160441184787359821858867270,160441184787359821888620814⟩⟩,⟨⟨(-503428890),342288866⟩,⟨2136803025194210899575928083,2136803025194210900482066959⟩⟩,⟨⟨(-4712344829),3211611413⟩,⟨15920423158960125591354284084,15920423158960125599740196683⟩⟩,⟨⟨(-17565710692),8273564931⟩,⟨82145886611128228785260658663,82145886611128228813453240589⟩⟩] +lemma ha24_0_9_eq (j : Fin 7) : ha24_0_9 j = ((ha24_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha24_0_9_contains (j : Fin 7) : (ha24_0_9 j).Contains (fullFactor false 24 9 ((j.val:ℝ)/6)) := by + rw [ha24_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_8 j) false 24 8 j (ha24_0_8_contains j) +noncomputable def hk24_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_10 j i k) +lemma hk24_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_10 j i k).Contains (fullFactor false 24 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 10 (power24_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha24_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-426798800539562151473),(-426798800539562151436)⟩,⟨(-16),8⟩⟩,⟨⟨(-437041971752511643128123),(-437041971752511643050877)⟩,⟨(-39796),23317⟩⟩,⟨⟨(-25202042373060605483619020),(-25202042373060605478865122)⟩,⟨(-2688544),1263147⟩⟩,⟨⟨(-447530979074571922619250825),(-447530979074571922428045006)⟩,⟨(-105437901),71688813⟩⟩,⟨⟨(-4167957036519161636403075057),(-4167957036519161634194381253)⟩,⟨(-1233688992),840797902⟩⟩,⟨⟨(-25806891390014060017261433981),(-25806891390014060008322327267)⟩,⟨(-5518430767),2599217081⟩⟩] +lemma ha24_0_10_eq (j : Fin 7) : ha24_0_10 j = ((ha24_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha24_0_10_contains (j : Fin 7) : (ha24_0_10 j).Contains (fullFactor false 24 10 ((j.val:ℝ)/6)) := by + rw [ha24_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_9 j) false 24 9 j (ha24_0_9_contains j) +noncomputable def hk24_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_11 j i k) +lemma hk24_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_11 j i k).Contains (fullFactor false 24 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 11 (power24_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha24_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-20315575399030665722),(-20315575399030665720)⟩⟩,⟨⟨(-2220),3789⟩,⟨(-41606298417214803400470),(-41606298417214803392983)⟩⟩,⟨⟨(-180377),383924⟩,⟨(-3598843235212085340833392),(-3598843235212085340143080)⟩⟩,⟨⟨(-13649519),20075330⟩,⟨(-85209699158455917374834212),(-85209699158455917338157477)⟩⟩,⟨⟨(-200109433),293617294⟩,⟨(-991971455030794224925440784),(-991971455030794224396615344)⟩⟩,⟨⟨(-742334663),1576060142⟩,⟨(-7370430945714350778608138769),(-7370430945714350776031675050)⟩⟩] +lemma ha24_0_11_eq (j : Fin 7) : ha24_0_11 j = ((ha24_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha24_0_11_contains (j : Fin 7) : (ha24_0_11 j).Contains (fullFactor false 24 11 ((j.val:ℝ)/6)) := by + rw [ha24_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_10 j) false 24 10 j (ha24_0_10_contains j) +noncomputable def hk24_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_12 j i k) +lemma hk24_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_12 j i k).Contains (fullFactor false 24 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 12 (power24_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha24_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨886434200375614885,886434200375614886⟩,⟨(-1),1⟩⟩,⟨⟨3630834484738518570723,3630834484738518571389⟩,⟨(-194),331⟩⟩,⟨⟨471087477881817150325337,471087477881817150417199⟩,⟨(-23612),50256⟩⟩,⟨⟨14871898049488972063822161,14871898049488972070270798⟩,⟨(-2382291),3503807⟩⟩,⟨⟨216414599701077852850120174,216414599701077852966180857⟩,⟨(-43657106),64057357⟩⟩,⟨⟨1929574309403923047580385519,1929574309403923048261044170⟩,⟨(-194342761),412611581⟩⟩] +lemma ha24_0_12_eq (j : Fin 7) : ha24_0_12 j = ((ha24_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha24_0_12_contains (j : Fin 7) : (ha24_0_12 j).Contains (fullFactor false 24 12 ((j.val:ℝ)/6)) := by + rw [ha24_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_11 j) false 24 11 j (ha24_0_11_contains j) +noncomputable def hk24_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_13 j i k) +lemma hk24_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_13 j i k).Contains (fullFactor false 24 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 13 (power24_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha24_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨35702758612702236,35702758612702237⟩⟩,⟨⟨(-27),16⟩,⟨292476998555256722998,292476998555256723054⟩⟩,⟨⟨(-6073),2854⟩,⟨56921729219679268112667,56921729219679268123949⟩⟩,⟨⟨(-564489),383805⟩,⟨2395971572164663074506718,2395971572164663075553268⟩⟩,⟨⟨(-12900137),8791849⟩,⟨43582469009646285019402301,43582469009646285042913811⟩⟩,⟨⟨(-99712117),46965061⟩,⟨466302805767612564342189721,466302805767612564508162642⟩⟩] +lemma ha24_0_13_eq (j : Fin 7) : ha24_0_13 j = ((ha24_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha24_0_13_contains (j : Fin 7) : (ha24_0_13 j).Contains (fullFactor false 24 13 ((j.val:ℝ)/6)) := by + rw [ha24_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_12 j) false 24 12 j (ha24_0_12_contains j) +noncomputable def hk24_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_14 j i k) +lemma hk24_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_14 j i k).Contains (fullFactor false 24 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 14 (power24_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha24_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1335280049649466),(-1335280049649465)⟩,⟨(-1),1⟩⟩,⟨⟨(-21877228333456835520),(-21877228333456835515)⟩,⟨(-3),2⟩⟩,⟨⟨(-6386603083791852241801),(-6386603083791852240513)⟩,⟨(-682),321⟩⟩,⟨⟨(-358436509015356793200362),(-358436509015356793042656)⟩,⟨(-84448),57418⟩⟩,⟨⟨(-8149902646786285759361876),(-8149902646786285754939291)⟩,⟨(-2412320),1644072⟩⟩,⟨⟨(-104638104924845707137904281),(-104638104924845707100326970)⟩,⟨(-22375347),10538936⟩⟩] +lemma ha24_0_14_eq (j : Fin 7) : ha24_0_14 j = ((ha24_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha24_0_14_contains (j : Fin 7) : (ha24_0_14 j).Contains (fullFactor false 24 14 ((j.val:ℝ)/6)) := by + rw [ha24_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_13 j) false 24 13 j (ha24_0_13_contains j) +noncomputable def hk24_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_15 j i k) +lemma hk24_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_15 j i k).Contains (fullFactor false 24 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 15 (power24_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha24_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-46610066605154),(-46610066605153)⟩⟩,⟨⟨(-1),1⟩,⟨(-1527318662517654887),(-1527318662517654886)⟩⟩,⟨⟨(-34),72⟩,⟨(-668803510981146723324),(-668803510981146723186)⟩⟩,⟨⟨(-8018),11792⟩,⟨(-50047177933378515339109),(-50047177933378515316929)⟩⟩,⟨⟨(-286945),421030⟩,⟨(-1422426349034211493224062),(-1422426349034211492447646)⟩⟩,⟨⟨(-2207270),4686282⟩,⟨(-21915353447830215831601211),(-21915353447830215823661277)⟩⟩] +lemma ha24_0_15_eq (j : Fin 7) : ha24_0_15 j = ((ha24_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha24_0_15_contains (j : Fin 7) : (ha24_0_15 j).Contains (fullFactor false 24 15 ((j.val:ℝ)/6)) := by + rw [ha24_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_14 j) false 24 14 j (ha24_0_14_contains j) +noncomputable def hk24_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_16 j i k) +lemma hk24_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_16 j i k).Contains (fullFactor false 24 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 16 (power24_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha24_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1525310862813,1525310862814⟩,⟨(-1),1⟩⟩,⟨⟨99962772705334443,99962772705334444⟩,⟨(-1),1⟩⟩,⟨⟨65659631149794723615,65659631149794723630⟩,⟨(-4),8⟩⟩,⟨⟨6551160272016798097367,6551160272016798100292⟩,⟨(-1050),1544⟩⟩,⟨⟨232743967104084891311948,232743967104084891439731⟩,⟨(-46952),68891⟩⟩,⟨⟨4303069587032947006563120,4303069587032947008135820⟩,⟨(-433397),920150⟩⟩] +lemma ha24_0_16_eq (j : Fin 7) : ha24_0_16 j = ((ha24_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha24_0_16_contains (j : Fin 7) : (ha24_0_16 j).Contains (fullFactor false 24 16 ((j.val:ℝ)/6)) := by + rw [ha24_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_15 j) false 24 15 j (ha24_0_15_contains j) +noncomputable def hk24_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_17 j i k) +lemma hk24_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_17 j i k).Contains (fullFactor false 24 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 17 (power24_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha24_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨46979464716,46979464717⟩⟩,⟨⟨(-1),1⟩,⟨6157692399285195,6157692399285196⟩⟩,⟨⟨(-1),1⟩,⟨6066935731106195666,6066935731106195668⟩⟩,⟨⟨(-191),130⟩,⟨807101058159109193246,807101058159109193610⟩⟩,⟨⟨(-10610),7231⟩,⟨35842487118702823476679,35842487118702823496473⟩⟩,⟨⟨(-170044),80092⟩,⟨795205400147551278341878,795205400147551278635045⟩⟩] +lemma ha24_0_17_eq (j : Fin 7) : ha24_0_17 j = ((ha24_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha24_0_17_contains (j : Fin 7) : (ha24_0_17 j).Contains (fullFactor false 24 17 ((j.val:ℝ)/6)) := by + rw [ha24_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_16 j) false 24 16 j (ha24_0_16_contains j) +noncomputable def hk24_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_18 j i k) +lemma hk24_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_18 j i k).Contains (fullFactor false 24 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 18 (power24_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha24_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1366577234),(-1366577233)⟩,⟨(-1),1⟩⟩,⟨⟨(-358240022308520),(-358240022308519)⟩,⟨(-1),1⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨(-1),1⟩⟩,⟨⟨(-93910472408044662761),(-93910472408044662717)⟩,⟨(-23),16⟩⟩,⟨⟨(-5213078436041832673122),(-5213078436041832670226)⟩,⟨(-1544),1052⟩⟩,⟨⟨(-138789524622137721172360),(-138789524622137721120750)⟩,⟨(-29679),13979⟩⟩] +lemma ha24_0_18_eq (j : Fin 7) : ha24_0_18 j = ((ha24_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha24_0_18_contains (j : Fin 7) : (ha24_0_18 j).Contains (fullFactor false 24 18 ((j.val:ℝ)/6)) := by + rw [ha24_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_17 j) false 24 17 j (ha24_0_17_contains j) +noncomputable def hk24_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_19 j i k) +lemma hk24_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_19 j i k).Contains (fullFactor false 24 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 19 (power24_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha24_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-37659904),(-37659903)⟩⟩,⟨⟨(-1),1⟩,⟨(-19744635479058),(-19744635479057)⟩⟩,⟨⟨(-1),1⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨(-2),3⟩,⟨(-10351875446044213764),(-10351875446044213759)⟩⟩,⟨⟨(-145),213⟩,⟨(-718305654265631155252),(-718305654265631154849)⟩⟩,⟨⟨(-2312),4908⟩,⟨(-22948428997269873114835),(-22948428997269873106227)⟩⟩] +lemma ha24_0_19_eq (j : Fin 7) : ha24_0_19 j = ((ha24_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha24_0_19_contains (j : Fin 7) : (ha24_0_19 j).Contains (fullFactor false 24 19 ((j.val:ℝ)/6)) := by + rw [ha24_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_18 j) false 24 18 j (ha24_0_18_contains j) +noncomputable def hk24_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_20 j i k) +lemma hk24_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_20 j i k).Contains (fullFactor false 24 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 20 (power24_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha24_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨985933,985934⟩,⟨(-1),1⟩⟩,⟨⟨1033826696146,1033826696147⟩,⟨(-1),1⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨(-1),1⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨94025990269704865188,94025990269704865242⟩,⟨(-19),28⟩⟩,⟨⟨3604730797462500933231,3604730797462500934596⟩,⟨(-364),771⟩⟩] +lemma ha24_0_20_eq (j : Fin 7) : ha24_0_20 j = ((ha24_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha24_0_20_contains (j : Fin 7) : (ha24_0_20 j).Contains (fullFactor false 24 20 ((j.val:ℝ)/6)) := by + rw [ha24_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_19 j) false 24 19 j (ha24_0_19_contains j) +noncomputable def hk24_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_21 j i k) +lemma hk24_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_21 j i k).Contains (fullFactor false 24 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 21 (power24_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha24_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨24582,24583⟩⟩,⟨⟨(-1),1⟩,⟨51553370693,51553370694⟩⟩,⟨⟨(-1),1⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨(-4),3⟩,⟨11721879376103578819,11721879376103578827⟩⟩,⟨⟨(-116),55⟩,⟨539266466260812848840,539266466260812849047⟩⟩] +lemma ha24_0_21_eq (j : Fin 7) : ha24_0_21 j = ((ha24_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha24_0_21_contains (j : Fin 7) : (ha24_0_21 j).Contains (fullFactor false 24 21 ((j.val:ℝ)/6)) := by + rw [ha24_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_20 j) false 24 20 j (ha24_0_20_contains j) +noncomputable def hk24_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_22 j i k) +lemma hk24_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_22 j i k).Contains (fullFactor false 24 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 22 (power24_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha24_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-586),(-585)⟩,⟨(-1),1⟩⟩,⟨⟨(-2453934707),(-2453934706)⟩,⟨(-1),1⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨(-1),1⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-1394900383872451221),(-1394900383872451219)⟩,⟨(-1),1⟩⟩,⟨⟨(-77007071306013533815),(-77007071306013533784)⟩,⟨(-17),8⟩⟩] +lemma ha24_0_22_eq (j : Fin 7) : ha24_0_22 j = ((ha24_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha24_0_22_contains (j : Fin 7) : (ha24_0_22 j).Contains (fullFactor false 24 22 ((j.val:ℝ)/6)) := by + rw [ha24_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_21 j) false 24 21 j (ha24_0_21_contains j) +noncomputable def hk24_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_23 j i k) +lemma hk24_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_23 j i k).Contains (fullFactor false 24 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 23 (power24_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha24_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-14),(-13)⟩⟩,⟨⟨(-1),1⟩,⟨(-111728453),(-111728452)⟩⟩,⟨⟨(-1),1⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨(-1),1⟩,⟨(-158775681103741858),(-158775681103741857)⟩⟩,⟨⟨(-2),3⟩,⟨(-10518471716932064458),(-10518471716932064453)⟩⟩] +lemma ha24_0_23_eq (j : Fin 7) : ha24_0_23 j = ((ha24_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha24_0_23_contains (j : Fin 7) : (ha24_0_23 j).Contains (fullFactor false 24 23 ((j.val:ℝ)/6)) := by + rw [ha24_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_22 j) false 24 22 j (ha24_0_22_contains j) +noncomputable def hk24_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_24 j i k) +lemma hk24_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_24 j i k).Contains (fullFactor false 24 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 24 (power24_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha24_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨4875073,4875074⟩,⟨(-1),1⟩⟩,⟨⟨82067533018,82067533019⟩,⟨(-1),1⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨17319740045980249,17319740045980250⟩,⟨(-1),1⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨(-1),1⟩⟩] +lemma ha24_0_24_eq (j : Fin 7) : ha24_0_24 j = ((ha24_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha24_0_24_contains (j : Fin 7) : (ha24_0_24 j).Contains (fullFactor false 24 24 ((j.val:ℝ)/6)) := by + rw [ha24_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_23 j) false 24 23 j (ha24_0_23_contains j) +noncomputable def hk24_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_25 j i k) +lemma hk24_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_25 j i k).Contains (fullFactor false 24 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 25 (power24_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha24_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨204206,204207⟩⟩,⟨⟨(-1),1⟩,⟨5156455176,5156455177⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨(-1),1⟩,⟨1813718936351216,1813718936351217⟩⟩,⟨⟨(-1),1⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha24_0_25_eq (j : Fin 7) : ha24_0_25 j = ((ha24_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha24_0_25_contains (j : Fin 7) : (ha24_0_25 j).Contains (fullFactor false 24 25 ((j.val:ℝ)/6)) := by + rw [ha24_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_24 j) false 24 24 j (ha24_0_24_contains j) +noncomputable def hk24_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_26 j i k) +lemma hk24_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_26 j i k).Contains (fullFactor false 24 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 26 (power24_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha24_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-8225),(-8224)⟩,⟨(-1),1⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨(-1),1⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-182627118144798),(-182627118144797)⟩,⟨(-1),1⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨(-1),1⟩⟩] +lemma ha24_0_26_eq (j : Fin 7) : ha24_0_26 j = ((ha24_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha24_0_26_contains (j : Fin 7) : (ha24_0_26 j).Contains (fullFactor false 24 26 ((j.val:ℝ)/6)) := by + rw [ha24_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_25 j) false 24 25 j (ha24_0_25_contains j) +noncomputable def hk24_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_27 j i k) +lemma hk24_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_27 j i k).Contains (fullFactor false 24 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 27 (power24_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha24_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨(-320),(-318)⟩⟩,⟨⟨(-1),1⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨(-1),1⟩,⟨(-17708025083642),(-17708025083641)⟩⟩,⟨⟨(-1),1⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha24_0_27_eq (j : Fin 7) : ha24_0_27 j = ((ha24_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha24_0_27_contains (j : Fin 7) : (ha24_0_27 j).Contains (fullFactor false 24 27 ((j.val:ℝ)/6)) := by + rw [ha24_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_26 j) false 24 26 j (ha24_0_26_contains j) +noncomputable def hk24_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_28 j i k) +lemma hk24_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_28 j i k).Contains (fullFactor false 24 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 28 (power24_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha24_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨11,12⟩,⟨(-1),1⟩⟩,⟨⟨1016753,1016754⟩,⟨(-1),1⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨1655696473581,1655696473582⟩,⟨(-1),1⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨(-1),1⟩⟩] +lemma ha24_0_28_eq (j : Fin 7) : ha24_0_28 j = ((ha24_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha24_0_28_contains (j : Fin 7) : (ha24_0_28 j).Contains (fullFactor false 24 28 ((j.val:ℝ)/6)) := by + rw [ha24_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_27 j) false 24 27 j (ha24_0_27_contains j) +noncomputable def hk24_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_29 j i k) +lemma hk24_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_29 j i k).Contains (fullFactor false 24 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 29 (power24_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha24_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨55072,55073⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨(-1),1⟩,⟨149469076953,149469076954⟩⟩,⟨⟨(-1),1⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha24_0_29_eq (j : Fin 7) : ha24_0_29 j = ((ha24_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha24_0_29_contains (j : Fin 7) : (ha24_0_29 j).Contains (fullFactor false 24 29 ((j.val:ℝ)/6)) := by + rw [ha24_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_28 j) false 24 28 j (ha24_0_28_contains j) +noncomputable def hk24_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power24 j i k).conj.mul (mpower0_30 j i k) +lemma hk24_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk24_0_30 j i k).Contains (fullFactor false 24 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power24 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 30 (power24_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha24_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨(-1),1⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-13043637614),(-13043637613)⟩,⟨(-1),1⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨(-1),1⟩⟩] +lemma ha24_0_30_eq (j : Fin 7) : ha24_0_30 j = ((ha24_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha24_0_30_contains (j : Fin 7) : (ha24_0_30 j).Contains (fullFactor false 24 30 ((j.val:ℝ)/6)) := by + rw [ha24_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_0_29 j) false 24 29 j (ha24_0_29_contains j) +noncomputable def hk24_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_0 j i k) +lemma hk24_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_0 j i k).Contains (fullFactor true 24 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 0 (kernel24_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha24_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-4),0⟩,⟨(-2),2⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-236955311709037),(-236955311709034)⟩,⟨(-25302583633154),(-25302583633151)⟩⟩,⟨⟨(-50902692348634872196574),(-50902692348634872055211)⟩,⟨(-25572105302796923445599),(-25572105302796923304077)⟩⟩,⟨⟨(-9409877970793072962720468375),(-9409877970793072933272212257)⟩,⟨7173247941176577457230122546,7173247941176577486520048649⟩⟩] +lemma ha24_1_0_eq (j : Fin 7) : ha24_1_0 j = atomKernel24_0 j := by fin_cases j <;> decide +kernel +lemma ha24_1_0_contains (j : Fin 7) : (ha24_1_0 j).Contains (fullFactor true 24 0 ((j.val:ℝ)/6)) := by + rw [ha24_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel24_0_contains j +noncomputable def hk24_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_1 j i k) +lemma hk24_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_1 j i k).Contains (fullFactor true 24 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 1 (kernel24_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha24_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-11),30⟩,⟨(-10),31⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨242174098457843,242174098457862⟩,⟨1133073413611544,1133073413611563⟩⟩,⟨⟨(-68618597869347544447143),(-68618597869347543768973)⟩,⟨225963129972071328187395,225963129972071328865300⟩⟩,⟨⟨27669709444365382060075635835,27669709444365382171459994905⟩,⟨32632369547623298580507136818,32632369547623298692457871091⟩⟩] +lemma ha24_1_1_eq (j : Fin 7) : ha24_1_1 j = ((ha24_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha24_1_1_contains (j : Fin 7) : (ha24_1_1 j).Contains (fullFactor true 24 1 ((j.val:ℝ)/6)) := by + rw [ha24_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_0 j) true 24 0 j (ha24_1_0_contains j) +noncomputable def hk24_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_2 j i k) +lemma hk24_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_2 j i k).Contains (fullFactor true 24 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 2 (kernel24_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha24_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-177),255⟩,⟨(-219),205⟩⟩,⟨⟨(-100),107⟩,⟨(-154),53⟩⟩,⟨⟨55,156⟩,⟨(-74),27⟩⟩,⟨⟨2433903422998170,2433903422998229⟩,⟨(-1417925915735287),(-1417925915735227)⟩⟩,⟨⟨485727351915311382835550,485727351915311384460638⟩,⟨60590157709179552859568,60590157709179554484257⟩⟩,⟨⟨56320350995595835814092500472,56320350995595836026874327530⟩,⟨(-53021765381761217058863982855),(-53021765381761216847078616456)⟩⟩] +lemma ha24_1_2_eq (j : Fin 7) : ha24_1_2 j = ((ha24_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha24_1_2_contains (j : Fin 7) : (ha24_1_2 j).Contains (fullFactor true 24 2 ((j.val:ℝ)/6)) := by + rw [ha24_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_1 j) true 24 1 j (ha24_1_1_contains j) +noncomputable def hk24_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_3 j i k) +lemma hk24_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_3 j i k).Contains (fullFactor true 24 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 3 (kernel24_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha24_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-924),707⟩,⟨(-840),779⟩⟩,⟨⟨(-440),256⟩,⟨(-271),425⟩⟩,⟨⟨(-274),(-5)⟩,⟨(-292),(-23)⟩⟩,⟨⟨(-3413011226152312),(-3413011226152189)⟩,⟨(-3031981442769580),(-3031981442769458)⟩⟩,⟨⟨(-31523829772962407256156),(-31523829772962404661565)⟩,⟨(-675671326609801028861767),(-675671326609801026265202)⟩⟩,⟨⟨(-67346145537295596620561162910),(-67346145537295596352107716802)⟩,⟨(-64472726409183884222733638545),(-64472726409183883953131165826)⟩⟩] +lemma ha24_1_3_eq (j : Fin 7) : ha24_1_3 j = ((ha24_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha24_1_3_contains (j : Fin 7) : (ha24_1_3 j).Contains (fullFactor true 24 3 ((j.val:ℝ)/6)) := by + rw [ha24_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_2 j) true 24 2 j (ha24_1_2_contains j) +noncomputable def hk24_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_4 j i k) +lemma hk24_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_4 j i k).Contains (fullFactor true 24 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 4 (kernel24_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha24_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2136),2495⟩,⟨(-2151),2469⟩⟩,⟨⟨(-665),1089⟩,⟨(-853),901⟩⟩,⟨⟨(-370),165⟩,⟨22,557⟩⟩,⟨⟨(-2208948228001528),(-2208948228001339)⟩,⟨5090651911825972,5090651911826162⟩⟩,⟨⟨(-684528750454172925636989),(-684528750454172922525993)⟩,⟨151165723899910304199049,151165723899910307306643⟩⟩,⟨⟨(-55041720554162006471354930696),(-55041720554162006215172112765)⟩,⟨63823736303748481242903157957,63823736303748481498110451371⟩⟩] +lemma ha24_1_4_eq (j : Fin 7) : ha24_1_4 j = ((ha24_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha24_1_4_contains (j : Fin 7) : (ha24_1_4 j).Contains (fullFactor true 24 4 ((j.val:ℝ)/6)) := by + rw [ha24_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_3 j) true 24 3 j (ha24_1_3_contains j) +noncomputable def hk24_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_5 j i k) +lemma hk24_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_5 j i k).Contains (fullFactor true 24 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 5 (kernel24_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha24_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5425),5111⟩,⟨(-5641),4887⟩⟩,⟨⟨(-1951),1583⟩,⟨(-2009),1525⟩⟩,⟨⟨(-71),779⟩,⟨(-484),366⟩⟩,⟨⟨5373220158957954,5373220158958188⟩,⟨498232941366912,498232941367145⟩⟩,⟨⟨219934755988246350646921,219934755988246353624929⟩,⟨538007162337074117955404,538007162337074120936860⟩⟩,⟨⟨48160908430591055774094996718,48160908430591055968181195396⟩,⟨37354537819972240089067473050,37354537819972240283802426375⟩⟩] +lemma ha24_1_5_eq (j : Fin 7) : ha24_1_5 j = ((ha24_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha24_1_5_contains (j : Fin 7) : (ha24_1_5 j).Contains (fullFactor true 24 5 ((j.val:ℝ)/6)) := by + rw [ha24_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_4 j) true 24 4 j (ha24_1_4_contains j) +noncomputable def hk24_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_6 j i k) +lemma hk24_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_6 j i k).Contains (fullFactor true 24 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 6 (kernel24_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha24_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-10026),9960⟩,⟨(-9412),10570⟩⟩,⟨⟨(-3024),2910⟩,⟨(-2611),3324⟩⟩,⟨⟨(-780),346⟩,⟨(-836),289⟩⟩,⟨⟨(-973418842217271),(-973418842217032)⟩,⟨(-4263203264845779),(-4263203264845538)⟩⟩,⟨⟨340502895417882883040621,340502895417882885421463⟩,⟨(-212903290292775536453211),(-212903290292775534074882)⟩⟩,⟨⟨20974145570009116620368578716,20974145570009116743717804035⟩,⟨(-30154080206631394217974316862),(-30154080206631394094975608027)⟩⟩] +lemma ha24_1_6_eq (j : Fin 7) : ha24_1_6 j = ((ha24_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha24_1_6_contains (j : Fin 7) : (ha24_1_6 j).Contains (fullFactor true 24 6 ((j.val:ℝ)/6)) := by + rw [ha24_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_5 j) true 24 5 j (ha24_1_5_contains j) +noncomputable def hk24_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_7 j i k) +lemma hk24_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_7 j i k).Contains (fullFactor true 24 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 7 (kernel24_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha24_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-15907),16595⟩,⟨(-16866),15633⟩⟩,⟨⟨(-3968),4573⟩,⟨(-4479),4062⟩⟩,⟨⟨(-750),527⟩,⟨(-370),908⟩⟩,⟨⟨(-2602982356930032),(-2602982356929820)⟩,⟨1565351018165400,1565351018165610⟩⟩,⟨⟨(-158512981825632089278155),(-158512981825632087650075)⟩,⟨(-177300895712402720637467),(-177300895712402719007977)⟩⟩,⟨⟨(-16117936351082083258592113647),(-16117936351082083191781774651)⟩,⟨(-10010864716208899387733946680),(-10010864716208899320766482418)⟩⟩] +lemma ha24_1_7_eq (j : Fin 7) : ha24_1_7 j = ((ha24_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha24_1_7_contains (j : Fin 7) : (ha24_1_7 j).Contains (fullFactor true 24 7 ((j.val:ℝ)/6)) := by + rw [ha24_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_6 j) true 24 6 j (ha24_1_6_contains j) +noncomputable def hk24_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_8 j i k) +lemma hk24_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_8 j i k).Contains (fullFactor true 24 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 8 (kernel24_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha24_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-23741),22509⟩,⟨(-22694),23555⟩⟩,⟨⟨(-5698),5058⟩,⟨(-5444),5312⟩⟩,⟨⟨(-423),846⟩,⟨(-658),610⟩⟩,⟨⟨1397043864143901,1397043864144063⟩,⟨1206710699451510,1206710699451673⟩⟩,⟨⟨(-76585644417188966778107),(-76585644417188965802322)⟩,⟨96555796327557180451627,96555796327557181426791⟩⟩,⟨⟨(-4140371773862156091503066007),(-4140371773862156059691671038)⟩,⟨7510257687084849820677899839,7510257687084849852430378125⟩⟩] +lemma ha24_1_8_eq (j : Fin 7) : ha24_1_8 j = ((ha24_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha24_1_8_contains (j : Fin 7) : (ha24_1_8 j).Contains (fullFactor true 24 8 ((j.val:ℝ)/6)) := by + rw [ha24_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_7 j) true 24 7 j (ha24_1_7_contains j) +noncomputable def hk24_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_9 j i k) +lemma hk24_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_9 j i k).Contains (fullFactor true 24 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 9 (kernel24_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha24_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-28549),29954⟩,⟨(-29363),29139⟩⟩,⟨⟨(-5883),6157⟩,⟨(-5801),6239⟩⟩,⟨⟨(-640),480⟩,⟨(-672),447⟩⟩,⟨⟨384218995028481,384218995028592⟩,⟨(-920324934309594),(-920324934309483)⟩⟩,⟨⟨49822074150731007470512,49822074150731007989681⟩,⟨27207810670394856586986,27207810670394857106364⟩⟩,⟨⟨3099687506615916050702759782,3099687506615916064116221751⟩,⟨1504529334396891991248610780,1504529334396892004680402367⟩⟩] +lemma ha24_1_9_eq (j : Fin 7) : ha24_1_9 j = ((ha24_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha24_1_9_contains (j : Fin 7) : (ha24_1_9 j).Contains (fullFactor true 24 9 ((j.val:ℝ)/6)) := by + rw [ha24_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_8 j) true 24 8 j (ha24_1_8_contains j) +noncomputable def hk24_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_10 j i k) +lemma hk24_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_10 j i k).Contains (fullFactor true 24 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 10 (kernel24_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha24_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-33881),32720⟩,⟨(-33476),33125⟩⟩,⟨⟨(-6020),6110⟩,⟨(-6243),5886⟩⟩,⟨⟨(-480),410⟩,⟨(-372),518⟩⟩,⟨⟨(-483411998854150),(-483411998854081)⟩,⟨(-38046727487889),(-38046727487820)⟩⟩,⟨⟨7606202336760695279757,7606202336760695528551⟩,⟨(-22270052025856935038732),(-22270052025856934789984)⟩⟩,⟨⟨485085588286525145578695256,485085588286525150682733860⟩,⟨(-1147556281726357429213719919),(-1147556281726357424114217833)⟩⟩] +lemma ha24_1_10_eq (j : Fin 7) : ha24_1_10 j = ((ha24_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha24_1_10_contains (j : Fin 7) : (ha24_1_10 j).Contains (fullFactor true 24 10 ((j.val:ℝ)/6)) := by + rw [ha24_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_9 j) true 24 9 j (ha24_1_9_contains j) +noncomputable def hk24_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_11 j i k) +lemma hk24_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_11 j i k).Contains (fullFactor true 24 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 11 (kernel24_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha24_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34119),34809⟩,⟨(-34145),34782⟩⟩,⟨⟨(-5658),5451⟩,⟨(-5496),5613⟩⟩,⟨⟨(-279),365⟩,⟨(-324),319⟩⟩,⟨⟨50615093057119,50615093057159⟩,⟨208273869662530,208273869662569⟩⟩,⟨⟨(-8757894721492374913241),(-8757894721492374804900)⟩,⟨(-1398970768856371193763),(-1398970768856371085422)⟩⟩,⟨⟨(-384994705634226914979853921),(-384994705634226913217461420)⟩,⟨(-139652381665842069633805132),(-139652381665842067870657085)⟩⟩] +lemma ha24_1_11_eq (j : Fin 7) : ha24_1_11 j = ((ha24_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha24_1_11_contains (j : Fin 7) : (ha24_1_11 j).Contains (fullFactor true 24 11 ((j.val:ℝ)/6)) := by + rw [ha24_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_10 j) true 24 10 j (ha24_1_10_contains j) +noncomputable def hk24_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_12 j i k) +lemma hk24_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_12 j i k).Contains (fullFactor true 24 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 12 (kernel24_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha24_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32817),32574⟩,⟨(-33006),32385⟩⟩,⟨⟨(-4596),4731⟩,⟨(-4643),4684⟩⟩,⟨⟨(-225),202⟩,⟨(-231),196⟩⟩,⟨⟨73793593307294,73793593307315⟩,⟨(-45787528016838),(-45787528016817)⟩⟩,⟨⟨37751635516807954659,37751635516807997906⟩,⟨3063657897524248189013,3063657897524248232266⟩⟩,⟨⟨(-35999719949748262495798076),(-35999719949748261937503144)⟩,⟨118037408572694834623061435,118037408572694835181363613⟩⟩] +lemma ha24_1_12_eq (j : Fin 7) : ha24_1_12 j = ((ha24_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha24_1_12_contains (j : Fin 7) : (ha24_1_12 j).Contains (fullFactor true 24 12 ((j.val:ℝ)/6)) := by + rw [ha24_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_11 j) true 24 11 j (ha24_1_11_contains j) +noncomputable def hk24_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_13 j i k) +lemma hk24_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_13 j i k).Contains (fullFactor true 24 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 13 (kernel24_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha24_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28649),28615⟩,⟨(-28414),28850⟩⟩,⟨⟨(-3632),3597⟩,⟨(-3649),3580⟩⟩,⟨⟨(-135),126⟩,⟨(-123),139⟩⟩,⟨⟨(-24873960217859),(-24873960217848)⟩,⟨(-20887782895603),(-20887782895593)⟩⟩,⟨⟨960720061919826514494,960720061919826530433⟩,⟨(-177844330461319642847),(-177844330461319626911)⟩⟩,⟨⟨33307380311094320553560194,33307380311094320716810570⟩,⟨8294742001161786167909795,8294742001161786331089500⟩⟩] +lemma ha24_1_13_eq (j : Fin 7) : ha24_1_13 j = ((ha24_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha24_1_13_contains (j : Fin 7) : (ha24_1_13 j).Contains (fullFactor true 24 13 ((j.val:ℝ)/6)) := by + rw [ha24_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_12 j) true 24 12 j (ha24_1_12_contains j) +noncomputable def hk24_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_14 j i k) +lemma hk24_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_14 j i k).Contains (fullFactor true 24 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 14 (kernel24_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha24_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23215),23350⟩,⟨(-23397),23168⟩⟩,⟨⟨(-2608),2595⟩,⟨(-2583),2620⟩⟩,⟨⟨(-71),79⟩,⟨(-75),75⟩⟩,⟨⟨(-4200601078737),(-4200601078732)⟩,⟨10469276010787,10469276010793⟩⟩,⟨⟨(-100227622677776329660),(-100227622677776324207)⟩,⟨(-271397800378277490821),(-271397800378277485366)⟩⟩,⟨⟨1692735059679679405072507,1692735059679679449359329⟩,⟨(-8702239221957094712344069),(-8702239221957094668020499)⟩⟩] +lemma ha24_1_14_eq (j : Fin 7) : ha24_1_14 j = ((ha24_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha24_1_14_contains (j : Fin 7) : (ha24_1_14 j).Contains (fullFactor true 24 14 ((j.val:ℝ)/6)) := by + rw [ha24_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_13 j) true 24 13 j (ha24_1_13_contains j) +noncomputable def hk24_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_15 j i k) +lemma hk24_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_15 j i k).Contains (fullFactor true 24 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 15 (kernel24_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha24_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17733),17608⟩,⟨(-17629),17712⟩⟩,⟨⟨(-1739),1756⟩,⟨(-1751),1744⟩⟩,⟨⟨(-41),39⟩,⟨(-42),39⟩⟩,⟨⟨3648890002008,3648890002011⟩,⟨236136440345,236136440348⟩⟩,⟨⟨(-69209969282348548312),(-69209969282348546569)⟩,⟨40040423181192667626,40040423181192669369⟩⟩,⟨⟨(-2116124197619576403353531),(-2116124197619576392122164)⟩,⟨(-298564115392377786482324),(-298564115392377775264436)⟩⟩] +lemma ha24_1_15_eq (j : Fin 7) : ha24_1_15 j = ((ha24_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha24_1_15_contains (j : Fin 7) : (ha24_1_15 j).Contains (fullFactor true 24 15 ((j.val:ℝ)/6)) := by + rw [ha24_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_14 j) true 24 14 j (ha24_1_14_contains j) +noncomputable def hk24_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_16 j i k) +lemma hk24_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_16 j i k).Contains (fullFactor true 24 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 16 (kernel24_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha24_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12534),12613⟩,⟨(-12579),12568⟩⟩,⟨⟨(-1104),1097⟩,⟨(-1102),1099⟩⟩,⟨⟨(-21),20⟩,⟨(-20),21⟩⟩,⟨⟨(-277401326256),(-277401326254)⟩,⟨(-1075978954240),(-1075978954238)⟩⟩,⟨⟨13270119511226416852,13270119511226417375⟩,⟨15908908850056780874,15908908850056781397⟩⟩,⟨⟨(-42548191049519827397379),(-42548191049519824733520)⟩,⟨481090122741771045329714,481090122741771047997695⟩⟩] +lemma ha24_1_16_eq (j : Fin 7) : ha24_1_16 j = ((ha24_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha24_1_16_contains (j : Fin 7) : (ha24_1_16 j).Contains (fullFactor true 24 16 ((j.val:ℝ)/6)) := by + rw [ha24_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_15 j) true 24 15 j (ha24_1_15_contains j) +noncomputable def hk24_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_17 j i k) +lemma hk24_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_17 j i k).Contains (fullFactor true 24 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 17 (kernel24_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha24_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8439),8401⟩,⟨(-8427),8414⟩⟩,⟨⟨(-652),653⟩,⟨(-651),654⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-267685250203),(-267685250201)⟩,⟨171298987392,171298987394⟩⟩,⟨⟨3273317075756093392,3273317075756093540⟩,⟨(-3848064194479459877),(-3848064194479459729)⟩⟩,⟨⟨102659904510496590294007,102659904510496590890473⟩,⟨3723924696961336319265,3723924696961336914620⟩⟩] +lemma ha24_1_17_eq (j : Fin 7) : ha24_1_17 j = ((ha24_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha24_1_17_contains (j : Fin 7) : (ha24_1_17 j).Contains (fullFactor true 24 17 ((j.val:ℝ)/6)) := by + rw [ha24_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_16 j) true 24 16 j (ha24_1_16_contains j) +noncomputable def hk24_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_18 j i k) +lemma hk24_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_18 j i k).Contains (fullFactor true 24 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 18 (kernel24_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha24_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5319),5333⟩,⟨(-5319),5333⟩⟩,⟨⟨(-365),366⟩,⟨(-366),365⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨66502113516,66502113518⟩,⟨54284663191,54284663193⟩⟩,⟨⟨(-1001438617432239996),(-1001438617432239956)⟩,⟨(-592347682626051308),(-592347682626051268)⟩⟩,⟨⟨(-323866974749793663380),(-323866974749793537716)⟩,⟨(-20633713452162932706618),(-20633713452162932580682)⟩⟩] +lemma ha24_1_18_eq (j : Fin 7) : ha24_1_18 j = ((ha24_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha24_1_18_contains (j : Fin 7) : (ha24_1_18 j).Contains (fullFactor true 24 18 ((j.val:ℝ)/6)) := by + rw [ha24_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_17 j) true 24 17 j (ha24_1_17_contains j) +noncomputable def hk24_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_19 j i k) +lemma hk24_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_19 j i k).Contains (fullFactor true 24 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 19 (kernel24_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha24_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3193),3190⟩,⟨(-3196),3187⟩⟩,⟨⟨(-195),194⟩,⟨(-194),194⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨7895797388,7895797390⟩,⟨(-20499982150),(-20499982149)⟩⟩,⟨⟨(-90241967299813062),(-90241967299813051)⟩,⟨237282456480201624,237282456480201635⟩⟩,⟨⟨(-3918319103202904857932),(-3918319103202904832742)⟩,⟨265471245232249509747,265471245232249534877⟩⟩] +lemma ha24_1_19_eq (j : Fin 7) : ha24_1_19 j = ((ha24_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha24_1_19_contains (j : Fin 7) : (ha24_1_19 j).Contains (fullFactor true 24 19 ((j.val:ℝ)/6)) := by + rw [ha24_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_18 j) true 24 18 j (ha24_1_18_contains j) +noncomputable def hk24_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_20 j i k) +lemma hk24_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_20 j i k).Contains (fullFactor true 24 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 20 (kernel24_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha24_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1815),1819⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-5333732181),(-5333732180)⟩,⟨(-270685917),(-270685916)⟩⟩,⟨⟨51646347579002299,51646347579002303⟩,⟨10077296110784366,10077296110784369⟩⟩,⟨⟨84718974955815787616,84718974955815792392⟩,⟨704965194156736913030,704965194156736917817⟩⟩] +lemma ha24_1_20_eq (j : Fin 7) : ha24_1_20 j = ((ha24_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha24_1_20_contains (j : Fin 7) : (ha24_1_20 j).Contains (fullFactor true 24 20 ((j.val:ℝ)/6)) := by + rw [ha24_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_19 j) true 24 19 j (ha24_1_19_contains j) +noncomputable def hk24_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_21 j i k) +lemma hk24_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_21 j i k).Contains (fullFactor true 24 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 21 (kernel24_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha24_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-985),986⟩,⟨(-986),985⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨325330451,325330452⟩,⟨1192950985,1192950986⟩⟩,⟨⟨228283577889413,228283577889415⟩,⟨(-10385148075089297),(-10385148075089295)⟩⟩,⟨⟨120463795539878642340,120463795539878643208⟩,⟨(-20871243023580324702),(-20871243023580323836)⟩⟩] +lemma ha24_1_21_eq (j : Fin 7) : ha24_1_21 j = ((ha24_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha24_1_21_contains (j : Fin 7) : (ha24_1_21 j).Contains (fullFactor true 24 21 ((j.val:ℝ)/6)) := by + rw [ha24_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_20 j) true 24 20 j (ha24_1_20_contains j) +noncomputable def hk24_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_22 j i k) +lemma hk24_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_22 j i k).Contains (fullFactor true 24 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 22 (kernel24_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha24_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-511),510⟩,⟨(-510),511⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨228110411,228110413⟩,⟨(-150489507),(-150489506)⟩⟩,⟨⟨(-1935781161997826),(-1935781161997825)⟩,⟨290077550146567,290077550146568⟩⟩,⟨⟨(-4453931497331855040),(-4453931497331854889)⟩,⟨(-19594492686332756182),(-19594492686332756031)⟩⟩] +lemma ha24_1_22_eq (j : Fin 7) : ha24_1_22 j = ((ha24_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha24_1_22_contains (j : Fin 7) : (ha24_1_22 j).Contains (fullFactor true 24 22 ((j.val:ℝ)/6)) := by + rw [ha24_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_21 j) true 24 21 j (ha24_1_21_contains j) +noncomputable def hk24_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_23 j i k) +lemma hk24_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_23 j i k).Contains (fullFactor true 24 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 23 (kernel24_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha24_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-45257761),(-45257759)⟩,⟨(-35905322),(-35905321)⟩⟩,⟨⟨110801438671964,110801438671965⟩,⟨334953740555303,334953740555304⟩⟩,⟨⟨(-3039995375995912174),(-3039995375995912148)⟩,⟨859242879253795247,859242879253795273⟩⟩] +lemma ha24_1_23_eq (j : Fin 7) : ha24_1_23 j = ((ha24_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha24_1_23_contains (j : Fin 7) : (ha24_1_23 j).Contains (fullFactor true 24 23 ((j.val:ℝ)/6)) := by + rw [ha24_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_22 j) true 24 22 j (ha24_1_22_contains j) +noncomputable def hk24_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_24 j i k) +lemma hk24_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_24 j i k).Contains (fullFactor true 24 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 24 (kernel24_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha24_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-4054191),(-4054189)⟩,⟨10979154,10979156⟩⟩,⟨⟨53764465749867,53764465749868⟩,⟨(-28690261879610),(-28690261879609)⟩⟩,⟨⟨153065772433055615,153065772433055620⟩,⟨450673314276140780,450673314276140785⟩⟩] +lemma ha24_1_24_eq (j : Fin 7) : ha24_1_24 j = ((ha24_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha24_1_24_contains (j : Fin 7) : (ha24_1_24 j).Contains (fullFactor true 24 24 ((j.val:ℝ)/6)) := by + rw [ha24_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_23 j) true 24 23 j (ha24_1_23_contains j) +noncomputable def hk24_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_25 j i k) +lemma hk24_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_25 j i k).Contains (fullFactor true 24 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 25 (kernel24_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha24_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨2274684,2274686⟩,⟨83718,83720⟩⟩,⟨⟨(-6202991889630),(-6202991889629)⟩,⟨(-7977482519329),(-7977482519328)⟩⟩,⟨⟨63946055971352540,63946055971352542⟩,⟨(-25493957186357555),(-25493957186357553)⟩⟩] +lemma ha24_1_25_eq (j : Fin 7) : ha24_1_25 j = ((ha24_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha24_1_25_contains (j : Fin 7) : (ha24_1_25 j).Contains (fullFactor true 24 25 ((j.val:ℝ)/6)) := by + rw [ha24_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_24 j) true 24 24 j (ha24_1_24_contains j) +noncomputable def hk24_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_26 j i k) +lemma hk24_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_26 j i k).Contains (fullFactor true 24 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 26 (kernel24_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha24_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-117700),(-117698)⟩,⟨(-409073),(-409072)⟩⟩,⟨⟨(-1085445357720),(-1085445357719)⟩,⟨1190755358254,1190755358255⟩⟩,⟨⟨(-4002565716631611),(-4002565716631610)⟩,⟨(-8697068743503449),(-8697068743503448)⟩⟩] +lemma ha24_1_26_eq (j : Fin 7) : ha24_1_26 j = ((ha24_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha24_1_26_contains (j : Fin 7) : (ha24_1_26 j).Contains (fullFactor true 24 26 ((j.val:ℝ)/6)) := by + rw [ha24_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_25 j) true 24 25 j (ha24_1_25_contains j) +noncomputable def hk24_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_27 j i k) +lemma hk24_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_27 j i k).Contains (fullFactor true 24 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 27 (kernel24_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha24_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-63392),(-63390)⟩,⟨43098,43099⟩⟩,⟨⟨208484177064,208484177065⟩,⟨133174467525,133174467526⟩⟩,⟨⟨(-1135324685300557),(-1135324685300556)⟩,⟨595794325629746,595794325629747⟩⟩] +lemma ha24_1_27_eq (j : Fin 7) : ha24_1_27 j = ((ha24_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha24_1_27_contains (j : Fin 7) : (ha24_1_27 j).Contains (fullFactor true 24 27 ((j.val:ℝ)/6)) := by + rw [ha24_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_26 j) true 24 26 j (ha24_1_26_contains j) +noncomputable def hk24_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_28 j i k) +lemma hk24_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_28 j i k).Contains (fullFactor true 24 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 28 (kernel24_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha24_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨10541,10543⟩,⟨8126,8128⟩⟩,⟨⟨14186452448,14186452449⟩,⟨(-33768393962),(-33768393961)⟩⟩,⟨⟨84450448126823,84450448126824⟩,⟨142421882216914,142421882216915⟩⟩] +lemma ha24_1_28_eq (j : Fin 7) : ha24_1_28 j = ((ha24_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha24_1_28_contains (j : Fin 7) : (ha24_1_28 j).Contains (fullFactor true 24 28 ((j.val:ℝ)/6)) := by + rw [ha24_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_27 j) true 24 27 j (ha24_1_27_contains j) +noncomputable def hk24_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_29 j i k) +lemma hk24_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_29 j i k).Contains (fullFactor true 24 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 29 (kernel24_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha24_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨743,745⟩,⟨(-2105),(-2103)⟩⟩,⟨⟨(-5101568138),(-5101568137)⟩,⟨(-1178365795),(-1178365793)⟩⟩,⟨⟨17187295905543,17187295905544⟩,⟨(-11437786264349),(-11437786264348)⟩⟩] +lemma ha24_1_29_eq (j : Fin 7) : ha24_1_29 j = ((ha24_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha24_1_29_contains (j : Fin 7) : (ha24_1_29 j).Contains (fullFactor true 24 29 ((j.val:ℝ)/6)) := by + rw [ha24_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_28 j) true 24 28 j (ha24_1_28_contains j) +noncomputable def hk24_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel24_0 j i k).mul (mpower1_30 j i k) +lemma hk24_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk24_1_30 j i k).Contains (fullFactor true 24 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk24_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel24_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 24 30 (kernel24_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha24_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-362),(-361)⟩,⟨(-9),(-8)⟩⟩,⟨⟨(-40697100),(-40697098)⟩,⟨722378168,722378169⟩⟩,⟨⟨(-1484315340771),(-1484315340770)⟩,⟨(-1997202051964),(-1997202051963)⟩⟩] +lemma ha24_1_30_eq (j : Fin 7) : ha24_1_30 j = ((ha24_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha24_1_30_contains (j : Fin 7) : (ha24_1_30 j).Contains (fullFactor true 24 30 ((j.val:ℝ)/6)) := by + rw [ha24_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha24_1_29 j) true 24 29 j (ha24_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders25.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders25.lean new file mode 100644 index 0000000000000000000000000000000000000000..b793fbb6a1142acbcd0c9c4a78cba196c4965720 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders25.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers30 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues30 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk25_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_0 j i k) +lemma hk25_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_0 j i k).Contains (fullFactor false 25 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 0 (power25_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha25_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999701,1000000000000000000000000000399⟩,⟨(-399),399⟩⟩,⟨⟨866025403784438646722288648609,866025403784438646795338456630⟩,⟨499999999999999999971409335005,500000000000000000045598081167⟩⟩,⟨⟨499999999999999999882622206269,500000000000000000083362961311⟩,⟨866025403784438646672755213395,866025403784438646874329600784⟩⟩,⟨⟨(-111124583049),52209165099⟩,⟨999999999999999999918333125951,1000000000000000000081666874074⟩⟩,⟨⟨(-500000000000000000309217399782),(-499999999999999999758812265101)⟩,⟨866025403784438646469186844397,866025403784438647018982551708⟩⟩,⟨⟨(-866025403784438647134603431931),(-866025403784438646441939091151)⟩,⟨499999999999999999611451721834,500000000000000000303511197067⟩⟩,⟨⟨(-1000000000000000000163829944649),(-999999999999999999836170055451)⟩,⟨(-222745362649),104914526549⟩⟩] +lemma ha25_0_0_eq (j : Fin 7) : ha25_0_0 j = ((atomPoints j).direct.powBin 7 25).conj := by fin_cases j <;> decide +kernel +lemma ha25_0_0_contains (j : Fin 7) : (ha25_0_0 j).Contains (fullFactor false 25 0 ((j.val:ℝ)/6)) := by + rw [ha25_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 25) ((j.val:ℝ)/6) 25 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 25 (by norm_num)) +noncomputable def hk25_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_1 j i k) +lemma hk25_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_1 j i k).Contains (fullFactor false 25 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 1 (power25_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha25_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-261799387799149436563041766137),(-261799387799149436523363296147)⟩,⟨453449841058554462626442959834,453449841058554462666135125549⟩⟩,⟨⟨(-906899682117108925414989583821),(-906899682117108925201014627613)⟩,⟨523598775598298872953748928506,523598775598298873165630822280⟩⟩,⟨⟨(-1570796326794896619363282025817),(-1570796326794896619101717974223)⟩,⟨(-174554086870),82009964763⟩⟩,⟨⟨(-1813799364234217851132939599600),(-1813799364234217849975676660195)⟩,⟨(-1047197551196597746804290074346),(-1047197551196597745648190922602)⟩⟩,⟨⟨(-1308996938995747183490423789158),(-1308996938995747181674449653123)⟩,⟨(-2267249205292772314218869256092),(-2267249205292772312398261374058)⟩⟩,⟨⟨(-329598705862),699775194920⟩,⟨(-3141592653589793238984686950548),(-3141592653589793237945313049766)⟩⟩] +lemma ha25_0_1_eq (j : Fin 7) : ha25_0_1 j = ((ha25_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha25_0_1_contains (j : Fin 7) : (ha25_0_1 j).Contains (fullFactor false 25 1 ((j.val:ℝ)/6)) := by + rw [ha25_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_0 j) false 25 0 j (ha25_0_0_contains j) +noncomputable def hk25_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_2 j i k) +lemma hk25_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_2 j i k).Contains (fullFactor false 25 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 2 (power25_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha25_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-118712890786751174412827042648),(-118712890786751174402057783094)⟩,⟨(-68538919452009434859588777995),(-68538919452009434848982812685)⟩⟩,⟨⟨(-274155677808037739459062024603),(-274155677808037739347248259824)⟩,⟨(-474851563147004697694619911921),(-474851563147004697581071387369)⟩⟩,⟨⟨(-64410475706),137094459242⟩,⟨(-1233700550136169827460841715720),(-1233700550136169827251482799169)⟩⟩,⟨⟨1096622711232150957117447452574,1096622711232150958331602311728⟩,⟨(-1899406252588018791095739070136),(-1899406252588018789877810156015)⟩⟩,⟨⟨2967822269668779359090701790529,2967822269668779361483318806917⟩,⟨(-1713472986300235872373573763662),(-1713472986300235869991015024381)⟩⟩,⟨⟨4934802200544679308600472695569,4934802200544679310248825364353⟩,⟨(-517732436485),1099204305763⟩⟩] +lemma ha25_0_2_eq (j : Fin 7) : ha25_0_2 j = ((ha25_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha25_0_2_contains (j : Fin 7) : (ha25_0_2 j).Contains (fullFactor false 25 2 ((j.val:ℝ)/6)) := by + rw [ha25_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_1 j) false 25 1 j (ha25_0_1_contains j) +noncomputable def hk25_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_3 j i k) +lemma hk25_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_3 j i k).Contains (fullFactor false 25 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 3 (power25_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha25_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11962298101967523215133127888,11962298101967523217022295216⟩,⟨(-20719308087892496643317357082),(-20719308087892496641371815103)⟩⟩,⟨⟨165754464703139973121493981340,165754464703139973161657506473⟩,⟨(-95698384815740185743406437791),(-95698384815740185704071453481)⟩⟩,⟨⟨645964097506246253601372123603,645964097506246253713048363554⟩,⟨(-33725246216),71782491001⟩⟩,⟨⟨1326035717625119784660253224918,1326035717625119785514748911972⟩,⟨765587078525921485442997045552,765587078525921486293073981766⟩⟩,⟨⟨1495287262745940400815160917841,1495287262745940402899095296159⟩,⟨2589913510986562079333070643191,2589913510986562081429266827705⟩⟩,⟨⟨(-1151084057260),542168139663⟩,⟨5167712780049970028386381839356,5167712780049970030128982058284⟩⟩] +lemma ha25_0_3_eq (j : Fin 7) : ha25_0_3 j = ((ha25_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha25_0_3_contains (j : Fin 7) : (ha25_0_3 j).Contains (fullFactor false 25 3 ((j.val:ℝ)/6)) := by + rw [ha25_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_2 j) false 25 2 j (ha25_0_2_contains j) +noncomputable def hk25_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_4 j i k) +lemma hk25_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_4 j i k).Contains (fullFactor false 25 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 4 (power25_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha25_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2712151086516110563257060669,2712151086516110563520364565⟩,⟨1565861159883012429760521241,1565861159883012430012796958⟩⟩,⟨⟨25053778558128198871719433745,25053778558128198882097057212⟩,⟨43394417384257769009630971286,43394417384257769020283886299⟩⟩,⟨⟨(-28188918299),13243873220⟩,⟨253669507901048013614993205277,253669507901048013659655817276⟩⟩,⟨⟨(-400860456930051182294625142191),(-400860456930051181848249920759)⟩,⟨694310678148124303990890521759,694310678148124304440513476786⟩⟩,⟨⟨(-1695094429072569102864280162450),(-1695094429072569101486927314767)⟩,⟨978663224926882767895771219107,978663224926882769262818262050⟩⟩,⟨⟨(-4058712126416768218887969327293),(-4058712126416768217506415033860)⟩,⟨(-904059304489),425817861144⟩⟩] +lemma ha25_0_4_eq (j : Fin 7) : ha25_0_4 j = ((ha25_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha25_0_4_contains (j : Fin 7) : (ha25_0_4 j).Contains (fullFactor false 25 4 ((j.val:ℝ)/6)) := by + rw [ha25_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_3 j) false 25 3 j (ha25_0_3_contains j) +noncomputable def hk25_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_5 j i k) +lemma hk25_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_5 j i k).Contains (fullFactor false 25 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 5 (power25_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha25_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-163976597214335483803922399),(-163976597214335483776982193)⟩,⟨284015797627486289472440601,284015797627486289500917772⟩⟩,⟨⟨(-9088505524079561264858341411),(-9088505524079561262598270496)⟩,⟨5247251110858735479931653486,5247251110858735482121840383⟩⟩,⟨⟨(-79692626246167045127946871835),(-79692626246167045113662028952)⟩,⟨(-8855809865),4160685482⟩⟩,⟨⟨(-290832176770545960524044868013),(-290832176770545960334781497454)⟩,⟨(-167912035547479535503746249223),(-167912035547479535316234553093)⟩⟩,⟨⟨(-512426866294798387151580715930),(-512426866294798386434165452683)⟩,⟨(-887549367585894655038065010719),(-887549367585894654314059588722)⟩⟩,⟨⟨(-267549252868),568037213879⟩,⟨(-2550164039877345444303829206689),(-2550164039877345443427655618678)⟩⟩] +lemma ha25_0_5_eq (j : Fin 7) : ha25_0_5 j = ((ha25_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha25_0_5_contains (j : Fin 7) : (ha25_0_5 j).Contains (fullFactor false 25 5 ((j.val:ℝ)/6)) := by + rw [ha25_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_4 j) false 25 4 j (ha25_0_4_contains j) +noncomputable def hk25_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_6 j i k) +lemma hk25_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_6 j i k).Contains (fullFactor false 25 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 6 (power25_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha25_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24785053981387676528157489),(-24785053981387676525593493)⟩,⟨(-14309657588033580847220467),(-14309657588033580844823941)⟩⟩,⟨⟨(-915818085634149174291281399),(-915818085634149173906106533)⟩,⟨(-1586243454808811297946762304),(-1586243454808811297547256346)⟩⟩,⟨⟨(-1089264913),2318445602⟩,⟨(-20863480763352960875048626542),(-20863480763352960871242452898)⟩⟩,⟨⟨58612357480585547115477233093,58612357480585547181117731692⟩,⟨(-101519581107763923085549688374),(-101519581107763923019161162116)⟩⟩,⟨⟨387266468459182445587032516516,387266468459182445904172184376⟩,⟨(-223588399813024700853152556247),(-223588399813024700539409391072)⟩⟩,⟨⟨1335262768854589495649807696486,1335262768854589496112821387781⟩,⟨(-140088461214),297423589682⟩⟩] +lemma ha25_0_6_eq (j : Fin 7) : ha25_0_6 j = ((ha25_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha25_0_6_contains (j : Fin 7) : (ha25_0_6 j).Contains (fullFactor false 25 6 ((j.val:ℝ)/6)) := by + rw [ha25_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_5 j) false 25 5 j (ha25_0_5_contains j) +noncomputable def hk25_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_7 j i k) +lemma hk25_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_7 j i k).Contains (fullFactor false 25 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 7 (power25_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha25_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1070359884617898514035249,1070359884617898514217916⟩,⟨(-1853917702541761442355632),(-1853917702541761442157943)⟩⟩,⟨⟨237301465925345464582644044,237301465925345464643165350⟩,⟨(-137006065231091009830241274),(-137006065231091009772183144)⟩⟩,⟨⟨4681754135318688100275544620,4681754135318688101144550476⟩,⟨(-244430475),520257977⟩⟩,⟨⟨30374587638444219459438571765,30374587638444219479398657688⟩,⟨17536776349579649246496988046,17536776349579649266192400594⟩⟩,⟨⟨83621865985773321348803187686,83621865985773321466409033738⟩,⟨144837320511075112621702653198,144837320511075112740773643127⟩⟩,⟨⟨(-133483394908),62871554372⟩,⟨599264529320792076786032297659,599264529320792076995739874627⟩⟩] +lemma ha25_0_7_eq (j : Fin 7) : ha25_0_7 j = ((ha25_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha25_0_7_contains (j : Fin 7) : (ha25_0_7 j).Contains (fullFactor false 25 7 ((j.val:ℝ)/6)) := by + rw [ha25_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_6 j) false 25 6 j (ha25_0_6_contains j) +noncomputable def hk25_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_8 j i k) +lemma hk25_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_8 j i k).Contains (fullFactor false 25 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 8 (power25_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha25_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨121338629888859693707968,121338629888859693721294⟩,⟨70054890629433514722067,70054890629433514734246⟩⟩,⟨⟨17934052001134979765664539,17934052001134979773321417⟩,⟨31062689251548081587463378,31062689251548081595484475⟩⟩,⟨⟨(-102152415),47993812⟩,⟨919260274839426580160455273,919260274839426580334010271⟩⟩,⟨⟨(-4591117312290554824044131097),(-4591117312290554818873270168)⟩,⟨7952048448396308884521412362,7952048448396308889772262795⟩⟩,⟨⟨(-47397902300335817878448491358),(-47397902300335817839331728813)⟩,⟨27365191652122466668606824194,27365191652122466707180353428⟩⟩,⟨⟨(-235330630358893204584842116379),(-235330630358893204501741062815)⟩,⟨(-52418806603),24689601667⟩⟩] +lemma ha25_0_8_eq (j : Fin 7) : ha25_0_8 j = ((ha25_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha25_0_8_contains (j : Fin 7) : (ha25_0_8 j).Contains (fullFactor false 25 8 ((j.val:ℝ)/6)) := by + rw [ha25_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_7 j) false 25 7 j (ha25_0_7_contains j) +noncomputable def hk25_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_9 j i k) +lemma hk25_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_9 j i k).Contains (fullFactor false 25 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 9 (power25_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha25_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-4075628328693792152891),(-4075628328693792152168)⟩,⟨7059195338064676366170,7059195338064676366969⟩⟩,⟨⟨(-3614308013089114300217643),(-3614308013089114299272840)⟩,⟨2086721704291221581539808,2086721704291221582437369⟩⟩,⟨⟨(-160441184787359821889144924),(-160441184787359821858343161)⟩,⟨(-17828960),8376501⟩⟩,⟨⟨(-1850525702701626522020527803),(-1850525702701626520792709015)⟩,⟨(-1068401512597105450690539161),(-1068401512597105449483824354)⟩⟩,⟨⟨(-7960211579480062802719668516),(-7960211579480062791473745553)⟩,⟨(-13787490894657571034636995564),(-13787490894657571023214503631)⟩⟩,⟨⟨(-8618296802),18297615304⟩,⟨(-82145886611128228813991558831),(-82145886611128228784722340421)⟩⟩] +lemma ha25_0_9_eq (j : Fin 7) : ha25_0_9 j = ((ha25_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha25_0_9_contains (j : Fin 7) : (ha25_0_9 j).Contains (fullFactor false 25 9 ((j.val:ℝ)/6)) := by + rw [ha25_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_8 j) false 25 8 j (ha25_0_8_contains j) +noncomputable def hk25_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_10 j i k) +lemma hk25_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_10 j i k).Contains (fullFactor false 25 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 10 (power25_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha25_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-369618603571988403213),(-369618603571988403169)⟩,⟨(-213399400269781075751),(-213399400269781075711)⟩⟩,⟨⟨(-218520985876255821584661),(-218520985876255821489973)⟩,⟨(-378489450057716124923630),(-378489450057716124823485)⟩⟩,⟨⟨(-1315778),2800567⟩,⟨(-25202042373060605483701347),(-25202042373060605478782795)⟩⟩,⟨⟨223765489537285961150323636,223765489537285961403769662⟩,⟨(-387573196859101311986533174),(-387573196859101311728145723)⟩⟩,⟨⟨3609556675507699248529519048,3609556675507699251531410020⟩,⟨(-2083978518259580818947553256),(-2083978518259580815996743999)⟩⟩,⟨⟨25806891390014060008153209604,25806891390014060017430551645⟩,⟨(-2707517792),5748365382⟩⟩] +lemma ha25_0_10_eq (j : Fin 7) : ha25_0_10 j = ((ha25_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha25_0_10_contains (j : Fin 7) : (ha25_0_10 j).Contains (fullFactor false 25 10 ((j.val:ℝ)/6)) := by + rw [ha25_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_9 j) false 25 9 j (ha25_0_9_contains j) +noncomputable def hk25_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_11 j i k) +lemma hk25_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_11 j i k).Contains (fullFactor false 25 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 11 (power25_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha25_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨10157787699515332859,10157787699515332862⟩,⟨(-17593804388058740566),(-17593804388058740563)⟩⟩,⟨⟨36032111386744300672047,36032111386744300681697⟩,⟨(-20803149208607401702196),(-20803149208607401693115)⟩⟩,⟨⟨3598843235212085340131324,3598843235212085340845148⟩,⟨(-187893),399921⟩⟩,⟨⟨73793764120052327759007866,73793764120052327808439616⟩,⟨42604849579227958656950502,42604849579227958705342129⟩⟩,⟨⟨495985727515397111936401987,495985727515397112640271720⟩,⟨859072479885680691300496621,859072479885680692017679515⟩⟩,⟨⟨(-1641729315),773265274⟩,⟨7370430945714350775983375158,7370430945714350778656438661⟩⟩] +lemma ha25_0_11_eq (j : Fin 7) : ha25_0_11 j = ((ha25_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha25_0_11_contains (j : Fin 7) : (ha25_0_11 j).Contains (fullFactor false 25 11 ((j.val:ℝ)/6)) := by + rw [ha25_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_10 j) false 25 10 j (ha25_0_10_contains j) +noncomputable def hk25_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_12 j i k) +lemma hk25_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_12 j i k).Contains (fullFactor false 25 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 12 (power25_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha25_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨767674536308627877,767674536308627878⟩,⟨443217100187807442,443217100187807443⟩⟩,⟨⟨1815417242369259285067,1815417242369259285866⟩,⟨3144394900720139784562,3144394900720139785416⟩⟩,⟨⟨(-52350),24596⟩,⟨471087477881817150323798,471087477881817150418738⟩⟩,⟨⟨(-7435949024744486038263906),(-7435949024744486029794303)⟩,⟨12879441513349692554542560,12879441513349692563211025⟩⟩,⟨⟨(-187420541090973602912425505),(-187420541090973602755363890)⟩,⟨108207299850538926367921130,108207299850538926521826120⟩⟩,⟨⟨(-1929574309403923048273689052),(-1929574309403923047567740637)⟩,⟨(-429803730),202440376⟩⟩] +lemma ha25_0_12_eq (j : Fin 7) : ha25_0_12 j = ((ha25_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha25_0_12_contains (j : Fin 7) : (ha25_0_12 j).Contains (fullFactor false 25 12 ((j.val:ℝ)/6)) := by + rw [ha25_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_11 j) false 25 11 j (ha25_0_11_contains j) +noncomputable def hk25_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_13 j i k) +lemma hk25_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_13 j i k).Contains (fullFactor false 25 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 13 (power25_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha25_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-17851379306351119),(-17851379306351118)⟩,⟨30919495943783799,30919495943783800⟩⟩,⟨⟨(-253292510771476882322),(-253292510771476882251)⟩,⟨146238499277628361475,146238499277628361541⟩⟩,⟨⟨(-56921729219679268124135),(-56921729219679268112481)⟩,⟨(-6326),2972⟩⟩,⟨⟨(-2074972248239938620319794),(-2074972248239938618916635)⟩,⟨(-1197985786082331538280660),(-1197985786082331536912330)⟩⟩,⟨⟨(-21791234504823142529257660),(-21791234504823142498194270)⟩,⟨(-37743525322001707911055154),(-37743525322001707879305293)⟩⟩,⟨⟨(-48921939),103866788⟩,⟨(-466302805767612564511218417),(-466302805767612564339133947)⟩⟩] +lemma ha25_0_13_eq (j : Fin 7) : ha25_0_13 j = ((ha25_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha25_0_13_contains (j : Fin 7) : (ha25_0_13 j).Contains (fullFactor false 25 13 ((j.val:ℝ)/6)) := by + rw [ha25_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_12 j) false 25 12 j (ha25_0_12_contains j) +noncomputable def hk25_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_14 j i k) +lemma hk25_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_14 j i k).Contains (fullFactor false 25 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 14 (power25_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha25_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1156386444162984),(-1156386444162983)⟩,⟨(-667640024824733),(-667640024824732)⟩⟩,⟨⟨(-10938614166728417761),(-10938614166728417755)⟩,⟨(-18946235501166317755),(-18946235501166317748)⟩⟩,⟨⟨(-334),710⟩,⟨(-6386603083791852241821),(-6386603083791852240493)⟩⟩,⟨⟨179218254507678396470310,179218254507678396675583⟩,⟨(-310415122451108950132973),(-310415122451108949922072)⟩⟩,⟨⟨7058022730486958378430840,7058022730486958384390518⟩,⟨(-4074951323393142881139676),(-4074951323393142875317864)⟩⟩,⟨⟨104638104924845707099641256,104638104924845707138589995⟩,⟨(-10978058),23307653⟩⟩] +lemma ha25_0_14_eq (j : Fin 7) : ha25_0_14 j = ((ha25_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha25_0_14_contains (j : Fin 7) : (ha25_0_14 j).Contains (fullFactor false 25 14 ((j.val:ℝ)/6)) := by + rw [ha25_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_13 j) false 25 13 j (ha25_0_13_contains j) +noncomputable def hk25_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_15 j i k) +lemma hk25_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_15 j i k).Contains (fullFactor false 25 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 15 (power25_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha25_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23305033302576,23305033302577⟩,⟨(-40365501752148),(-40365501752147)⟩⟩,⟨⟨1322696761414360852,1322696761414360853⟩,⟨(-763659331258827444),(-763659331258827443)⟩⟩,⟨⟨668803510981146723184,668803510981146723326⟩,⟨(-35),75⟩⟩,⟨⟨43342127478025776405116,43342127478025776434702⟩,⟨25023588966689257651341,25023588966689257680083⟩⟩,⟨⟨711213174517105745848266,711213174517105746866629⟩,⟨1231857353275977868740739,1231857353275977869784821⟩⟩,⟨⟨(-4881544),2299240⟩,⟨21915353447830215823517662,21915353447830215831744826⟩⟩] +lemma ha25_0_15_eq (j : Fin 7) : ha25_0_15 j = ((ha25_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha25_0_15_contains (j : Fin 7) : (ha25_0_15 j).Contains (fullFactor false 25 15 ((j.val:ℝ)/6)) := by + rw [ha25_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_14 j) false 25 14 j (ha25_0_14_contains j) +noncomputable def hk25_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_16 j i k) +lemma hk25_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_16 j i k).Contains (fullFactor false 25 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 16 (power25_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha25_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1320957955864,1320957955865⟩,⟨762655431406,762655431407⟩⟩,⟨⟨49981386352667221,49981386352667222⟩,⟨86570300595549323,86570300595549324⟩⟩,⟨⟨(-8),4⟩,⟨65659631149794723615,65659631149794723630⟩⟩,⟨⟨(-3275580136008399051525),(-3275580136008399047751)⟩,⟨5673471219829920492747,5673471219829920496639⟩⟩,⟨⟨(-201562188089707223688975),(-201562188089707223517495)⟩,⟨116371983552042445594523,116371983552042445761524⟩⟩,⟨⟨(-4303069587032947008164019),(-4303069587032947006534921)⟩,⟨(-958489),451455⟩⟩] +lemma ha25_0_16_eq (j : Fin 7) : ha25_0_16 j = ((ha25_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha25_0_16_contains (j : Fin 7) : (ha25_0_16 j).Contains (fullFactor false 25 16 ((j.val:ℝ)/6)) := by + rw [ha25_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_15 j) false 25 15 j (ha25_0_15_contains j) +noncomputable def hk25_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_17 j i k) +lemma hk25_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_17 j i k).Contains (fullFactor false 25 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 17 (power25_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha25_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23489732359),(-23489732358)⟩,⟨40685409900,40685409901⟩⟩,⟨⟨(-5332718046471331),(-5332718046471330)⟩,⟨3078846199642597,3078846199642598⟩⟩,⟨⟨(-6066935731106195668),(-6066935731106195666)⟩,⟨(-1),1⟩⟩,⟨⟨(-698970019787090239449),(-698970019787090238966)⟩,⟨(-403550529079554596975),(-403550529079554596508)⟩⟩,⟨⟨(-17921243559351411754652),(-17921243559351411728876)⟩,⟨(-31040504379613153653375),(-31040504379613153626867)⟩⟩,⟨⟨(-83429),177129⟩,⟨(-795205400147551278640256),(-795205400147551278336667)⟩⟩] +lemma ha25_0_17_eq (j : Fin 7) : ha25_0_17 j = ((ha25_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha25_0_17_contains (j : Fin 7) : (ha25_0_17 j).Contains (fullFactor false 25 17 ((j.val:ℝ)/6)) := by + rw [ha25_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_16 j) false 25 16 j (ha25_0_16_contains j) +noncomputable def hk25_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_18 j i k) +lemma hk25_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_18 j i k).Contains (fullFactor false 25 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 18 (power25_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha25_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1183490601),(-1183490600)⟩,⟨(-683288617),(-683288616)⟩⟩,⟨⟨(-179120011154260),(-179120011154259)⟩,⟨(-310244959971483),(-310244959971482)⟩⟩,⟨⟨(-1),1⟩,⟨(-529440020073462377),(-529440020073462376)⟩⟩,⟨⟨46955236204022331345,46955236204022331401⟩,⟨(-81328854786764263410),(-81328854786764263353)⟩⟩,⟨⟨4514658357533078056380,4514658357533078060250⟩,⟨(-2606539218020916337495),(-2606539218020916333736)⟩⟩,⟨⟨138789524622137721119840,138789524622137721173269⟩,⟨(-14562),30915⟩⟩] +lemma ha25_0_18_eq (j : Fin 7) : ha25_0_18 j = ((ha25_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha25_0_18_contains (j : Fin 7) : (ha25_0_18 j).Contains (fullFactor false 25 18 ((j.val:ℝ)/6)) := by + rw [ha25_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_17 j) false 25 17 j (ha25_0_17_contains j) +noncomputable def hk25_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_19 j i k) +lemma hk25_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_19 j i k).Contains (fullFactor false 25 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 19 (power25_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha25_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨18829951,18829952⟩,⟨(-32614434),(-32614433)⟩⟩,⟨⟨17099355913327,17099355913328⟩,⟨(-9872317739529),(-9872317739528)⟩⟩,⟨⟨43770654673137422,43770654673137423⟩,⟨(-1),1⟩⟩,⟨⟨8964987113086656141,8964987113086656148⟩,⟨5175937723022106878,5175937723022106885⟩⟩,⟨⟨359152827132815577235,359152827132815577755⟩,⟨622070944276038605246,622070944276038605783⟩⟩,⟨⟨(-5112),2408⟩,⟨22948428997269873106077,22948428997269873114985⟩⟩] +lemma ha25_0_19_eq (j : Fin 7) : ha25_0_19 j = ((ha25_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha25_0_19_contains (j : Fin 7) : (ha25_0_19 j).Contains (fullFactor false 25 19 ((j.val:ℝ)/6)) := by + rw [ha25_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_18 j) false 25 18 j (ha25_0_18_contains j) +noncomputable def hk25_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_20 j i k) +lemma hk25_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_20 j i k).Contains (fullFactor false 25 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 20 (power25_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha25_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨853843,853844⟩,⟨492966,492967⟩⟩,⟨⟨516913348073,516913348074⟩,⟨895320181973,895320181974⟩⟩,⟨⟨(-1),1⟩,⟨3437739179098606,3437739179098608⟩⟩,⟨⟨(-542022930869484434),(-542022930869484433)⟩,⟨938811255133340262,938811255133340263⟩⟩,⟨⟨(-81428896189552855194),(-81428896189552855123)⟩,⟨47012995134852432569,47012995134852432638⟩⟩,⟨⟨(-3604730797462500934619),(-3604730797462500933208)⟩,⟨(-803),379⟩⟩] +lemma ha25_0_20_eq (j : Fin 7) : ha25_0_20 j = ((ha25_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha25_0_20_contains (j : Fin 7) : (ha25_0_20 j).Contains (fullFactor false 25 20 ((j.val:ℝ)/6)) := by + rw [ha25_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_19 j) false 25 19 j (ha25_0_19_contains j) +noncomputable def hk25_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_21 j i k) +lemma hk25_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_21 j i k).Contains (fullFactor false 25 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 21 (power25_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha25_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-12292),(-12291)⟩,⟨21289,21290⟩⟩,⟨⟨(-44646528672),(-44646528671)⟩,⟨25776685346,25776685347⟩⟩,⟨⟨(-257142289286048),(-257142289286047)⟩,⟨(-1),1⟩⟩,⟨⟨(-93630556896327456),(-93630556896327455)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨(-5860939688051789416),(-5860939688051789406)⟩,⟨(-10151445319802585620),(-10151445319802585611)⟩⟩,⟨⟨(-57),121⟩,⟨(-539266466260812849051),(-539266466260812848837)⟩⟩] +lemma ha25_0_21_eq (j : Fin 7) : ha25_0_21 j = ((ha25_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha25_0_21_contains (j : Fin 7) : (ha25_0_21 j).Contains (fullFactor false 25 21 ((j.val:ℝ)/6)) := by + rw [ha25_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_20 j) false 25 20 j (ha25_0_20_contains j) +noncomputable def hk25_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_22 j i k) +lemma hk25_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_22 j i k).Contains (fullFactor false 25 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 22 (power25_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha25_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-507),(-506)⟩,⟨(-293),(-292)⟩⟩,⟨⟨(-1226967354),(-1226967353)⟩,⟨(-2125169796),(-2125169795)⟩⟩,⟨⟨(-1),1⟩,⟨(-18359916521553),(-18359916521552)⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨1208019168182208036,1208019168182208039⟩,⟨(-697450191936225611),(-697450191936225609)⟩⟩,⟨⟨77007071306013533783,77007071306013533815⟩,⟨(-9),18⟩⟩] +lemma ha25_0_22_eq (j : Fin 7) : ha25_0_22 j = ((ha25_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha25_0_22_contains (j : Fin 7) : (ha25_0_22 j).Contains (fullFactor false 25 22 ((j.val:ℝ)/6)) := by + rw [ha25_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_21 j) false 25 21 j (ha25_0_21_contains j) +noncomputable def hk25_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_23 j i k) +lemma hk25_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_23 j i k).Contains (fullFactor false 25 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 23 (power25_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha25_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨6,7⟩,⟨(-12),(-11)⟩⟩,⟨⟨96759678,96759679⟩,⟨(-55864227),(-55864226)⟩⟩,⟨⟨1253899540535,1253899540536⟩,⟨(-1),1⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨79387840551870928,79387840551870929⟩,⟨137503773339017306,137503773339017308⟩⟩,⟨⟨(-3),2⟩,⟨10518471716932064453,10518471716932064458⟩⟩] +lemma ha25_0_23_eq (j : Fin 7) : ha25_0_23 j = ((ha25_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha25_0_23_contains (j : Fin 7) : (ha25_0_23 j).Contains (fullFactor false 25 23 ((j.val:ℝ)/6)) := by + rw [ha25_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_22 j) false 25 22 j (ha25_0_22_contains j) +noncomputable def hk25_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_24 j i k) +lemma hk25_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_24 j i k).Contains (fullFactor false 25 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 24 (power25_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha25_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨2437536,2437537⟩,⟨4221937,4221938⟩⟩,⟨⟨(-1),1⟩,⟨82067533018,82067533019⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-14999334866761558),(-14999334866761557)⟩,⟨8659870022990124,8659870022990125⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha25_0_24_eq (j : Fin 7) : ha25_0_24 j = ((ha25_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha25_0_24_contains (j : Fin 7) : (ha25_0_24 j).Contains (fullFactor false 25 24 ((j.val:ℝ)/6)) := by + rw [ha25_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_23 j) false 25 23 j (ha25_0_23_contains j) +noncomputable def hk25_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_25 j i k) +lemma hk25_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_25 j i k).Contains (fullFactor false 25 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 25 (power25_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha25_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-176849),(-176848)⟩,⟨102103,102104⟩⟩,⟨⟨(-5156455177),(-5156455176)⟩,⟨(-1),1⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨(-906859468175609),(-906859468175608)⟩,⟨(-1570726674205046),(-1570726674205044)⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha25_0_25_eq (j : Fin 7) : ha25_0_25 j = ((ha25_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha25_0_25_contains (j : Fin 7) : (ha25_0_25 j).Contains (fullFactor false 25 25 ((j.val:ℝ)/6)) := by + rw [ha25_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_24 j) false 25 24 j (ha25_0_24_contains j) +noncomputable def hk25_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_26 j i k) +lemma hk25_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_26 j i k).Contains (fullFactor false 25 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 26 (power25_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha25_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-4113),(-4112)⟩,⟨(-7123),(-7122)⟩⟩,⟨⟨(-1),1⟩,⟨(-311528495),(-311528494)⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨158159723733336,158159723733337⟩,⟨(-91313559072399),(-91313559072398)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha25_0_26_eq (j : Fin 7) : ha25_0_26 j = ((ha25_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha25_0_26_contains (j : Fin 7) : (ha25_0_26 j).Contains (fullFactor false 25 26 ((j.val:ℝ)/6)) := by + rw [ha25_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_25 j) false 25 25 j (ha25_0_25_contains j) +noncomputable def hk25_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_27 j i k) +lemma hk25_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_27 j i k).Contains (fullFactor false 25 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 27 (power25_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha25_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨276,277⟩,⟨(-160),(-159)⟩⟩,⟨⟨18123993,18123994⟩,⟨(-1),1⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨8854012541820,8854012541821⟩,⟨15335599573285,15335599573286⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha25_0_27_eq (j : Fin 7) : ha25_0_27 j = ((ha25_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha25_0_27_contains (j : Fin 7) : (ha25_0_27 j).Contains (fullFactor false 25 27 ((j.val:ℝ)/6)) := by + rw [ha25_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_26 j) false 25 26 j (ha25_0_26_contains j) +noncomputable def hk25_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_28 j i k) +lemma hk25_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_28 j i k).Contains (fullFactor false 25 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 28 (power25_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha25_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨5,6⟩,⟨10,11⟩⟩,⟨⟨(-1),1⟩,⟨1016753,1016754⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-1433875207079),(-1433875207078)⟩,⟨827848236790,827848236791⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha25_0_28_eq (j : Fin 7) : ha25_0_28 j = ((ha25_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha25_0_28_contains (j : Fin 7) : (ha25_0_28 j).Contains (fullFactor false 25 28 ((j.val:ℝ)/6)) := by + rw [ha25_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_27 j) false 25 27 j (ha25_0_27_contains j) +noncomputable def hk25_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_29 j i k) +lemma hk25_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_29 j i k).Contains (fullFactor false 25 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 29 (power25_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha25_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-55073),(-55072)⟩,⟨(-1),1⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨(-74734538477),(-74734538476)⟩,⟨(-129444017722),(-129444017721)⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha25_0_29_eq (j : Fin 7) : ha25_0_29 j = ((ha25_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha25_0_29_contains (j : Fin 7) : (ha25_0_29 j).Contains (fullFactor false 25 29 ((j.val:ℝ)/6)) := by + rw [ha25_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_28 j) false 25 28 j (ha25_0_28_contains j) +noncomputable def hk25_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power25 j i k).conj.mul (mpower0_30 j i k) +lemma hk25_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk25_0_30 j i k).Contains (fullFactor false 25 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power25 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 30 (power25_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha25_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨(-2884),(-2883)⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨11296121531,11296121532⟩,⟨(-6521818807),(-6521818806)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha25_0_30_eq (j : Fin 7) : ha25_0_30 j = ((ha25_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha25_0_30_contains (j : Fin 7) : (ha25_0_30 j).Contains (fullFactor false 25 30 ((j.val:ℝ)/6)) := by + rw [ha25_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_0_29 j) false 25 29 j (ha25_0_29_contains j) +noncomputable def hk25_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_0 j i k) +lemma hk25_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_0 j i k).Contains (fullFactor true 25 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 0 (kernel25_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha25_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨10340074628317,10340074628320⟩,⟨(-51331061870575),(-51331061870572)⟩⟩,⟨⟨25007424357324989033834,25007424357324989135643⟩,⟨(-12960697545205626522481),(-12960697545205626421114)⟩⟩,⟨⟨4265780981286296484845899622,4265780981286296520258313301⟩,⟨(-8830170284357607012539510376),(-8830170284357606977137540426)⟩⟩] +lemma ha25_1_0_eq (j : Fin 7) : ha25_1_0 j = atomKernel25_0 j := by fin_cases j <;> decide +kernel +lemma ha25_1_0_contains (j : Fin 7) : (ha25_1_0 j).Contains (fullFactor true 25 0 ((j.val:ℝ)/6)) := by + rw [ha25_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel25_0_contains j +noncomputable def hk25_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_1 j i k) +lemma hk25_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_1 j i k).Contains (fullFactor true 25 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 1 (kernel25_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha25_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-252817850132719),(-252817850132700)⟩,⟨30013822947977,30013822947997⟩⟩,⟨⟨(-70561141275445737041550),(-70561141275445736555506)⟩,⟨(-93034447094966848163873),(-93034447094966847676205)⟩⟩,⟨⟨(-32686974824484623380691466343),(-32686974824484623246100477472)⟩,⟨(-13745775507675035894603552736),(-13745775507675035760026548446)⟩⟩] +lemma ha25_1_1_eq (j : Fin 7) : ha25_1_1 j = ((ha25_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha25_1_1_contains (j : Fin 7) : (ha25_1_1 j).Contains (fullFactor true 25 1 ((j.val:ℝ)/6)) := by + rw [ha25_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_0 j) true 25 0 j (ha25_1_0_contains j) +noncomputable def hk25_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_2 j i k) +lemma hk25_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_2 j i k).Contains (fullFactor true 25 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 2 (kernel25_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha25_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-255),177⟩,⟨(-205),219⟩⟩,⟨⟨(-53),154⟩,⟨(-100),107⟩⟩,⟨⟨(-37),79⟩,⟨(-43),70⟩⟩,⟨⟨260886349632600,260886349632662⟩,⟨561267047948791,561267047948851⟩⟩,⟨⟨(-165188345469972477744359),(-165188345469972476576378)⟩,⟨176893890314855271819936,176893890314855272985051⟩⟩,⟨⟨(-21749305191965104494679921231),(-21749305191965104238974319955)⟩,⟨60307303792541003787230446104,60307303792541004043063180637⟩⟩] +lemma ha25_1_2_eq (j : Fin 7) : ha25_1_2 j = ((ha25_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha25_1_2_contains (j : Fin 7) : (ha25_1_2 j).Contains (fullFactor true 25 2 ((j.val:ℝ)/6)) := by + rw [ha25_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_1 j) true 25 1 j (ha25_1_1_contains j) +noncomputable def hk25_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_3 j i k) +lemma hk25_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_3 j i k).Contains (fullFactor true 25 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 3 (kernel25_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha25_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-707),924⟩,⟨(-779),840⟩⟩,⟨⟨(-425),271⟩,⟨(-440),256⟩⟩,⟨⟨(-148),155⟩,⟨(-201),104⟩⟩,⟨⟨732570627845894,732570627846018⟩,⟨(-685270587233500),(-685270587233373)⟩⟩,⟨⟨279668964369348591191938,279668964369348593053648⟩,⟨183418678460675947148676,183418678460675949013573⟩⟩,⟨⟨73951728098799313987339584899,73951728098799314311519435334⟩,⟨22404400888518113079861395758,22404400888518113403756126697⟩⟩] +lemma ha25_1_3_eq (j : Fin 7) : ha25_1_3 j = ((ha25_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha25_1_3_contains (j : Fin 7) : (ha25_1_3 j).Contains (fullFactor true 25 3 ((j.val:ℝ)/6)) := by + rw [ha25_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_2 j) true 25 2 j (ha25_1_2_contains j) +noncomputable def hk25_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_4 j i k) +lemma hk25_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_4 j i k).Contains (fullFactor true 25 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 4 (kernel25_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha25_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2495),2136⟩,⟨(-2469),2151⟩⟩,⟨⟨(-901),853⟩,⟨(-665),1089⟩⟩,⟨⟨(-367),238⟩,⟨(-272),332⟩⟩,⟨⟨(-1069012085092607),(-1069012085092412)⟩,⟨(-586509794379631),(-586509794379439)⟩⟩,⟨⟨138086835047750505029783,138086835047750507263004⟩,⟨(-317928302837332978858734),(-317928302837332976627948)⟩⟩,⟨⟨16754177742024521258665722084,16754177742024521566357314057⟩,⟨(-67812141316065853021566187166),(-67812141316065852713490164143)⟩⟩] +lemma ha25_1_4_eq (j : Fin 7) : ha25_1_4 j = ((ha25_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha25_1_4_contains (j : Fin 7) : (ha25_1_4 j).Contains (fullFactor true 25 4 ((j.val:ℝ)/6)) := by + rw [ha25_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_3 j) true 25 3 j (ha25_1_3_contains j) +noncomputable def hk25_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_5 j i k) +lemma hk25_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_5 j i k).Contains (fullFactor true 25 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 5 (kernel25_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha25_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5111),5425⟩,⟨(-4887),5641⟩⟩,⟨⟨(-1525),2009⟩,⟨(-1951),1583⟩⟩,⟨⟨(-413),547⟩,⟨(-432),529⟩⟩,⟨⟨(-217946909698971),(-217946909698733)⟩,⟨1165519137536813,1165519137537052⟩⟩,⟨⟨(-279217297914728741462206),(-279217297914728739324059)⟩,⟨(-68041419016536676685572),(-68041419016536674546165)⟩⟩,⟨⟨(-49603479234880927410934724214),(-49603479234880927176727466788)⟩,⟨(-9553291772914737353007843843),(-9553291772914737119175058491)⟩⟩] +lemma ha25_1_5_eq (j : Fin 7) : ha25_1_5 j = ((ha25_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha25_1_5_contains (j : Fin 7) : (ha25_1_5 j).Contains (fullFactor true 25 5 ((j.val:ℝ)/6)) := by + rw [ha25_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_4 j) true 25 4 j (ha25_1_4_contains j) +noncomputable def hk25_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_6 j i k) +lemma hk25_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_6 j i k).Contains (fullFactor true 25 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 6 (kernel25_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha25_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-9960),10026⟩,⟨(-10570),9412⟩⟩,⟨⟨(-3324),2611⟩,⟨(-3024),2910⟩⟩,⟨⟨(-626),646⟩,⟨(-716),556⟩⟩,⟨⟨952492180075809,952492180076055⟩,⟨(-126544096993189),(-126544096992944)⟩⟩,⟨⟨(-13552531702071274740440),(-13552531702071273032518)⟩,⟨198101205864318969645098,198101205864318971352690⟩⟩,⟨⟨(-4197162280006775796660391078),(-4197162280006775648578121935)⟩,⟨30152218126794634822794761002,30152218126794634971163417058⟩⟩] +lemma ha25_1_6_eq (j : Fin 7) : ha25_1_6 j = ((ha25_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha25_1_6_contains (j : Fin 7) : (ha25_1_6 j).Contains (fullFactor true 25 6 ((j.val:ℝ)/6)) := by + rw [ha25_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_5 j) true 25 5 j (ha25_1_5_contains j) +noncomputable def hk25_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_7 j i k) +lemma hk25_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_7 j i k).Contains (fullFactor true 25 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 7 (kernel25_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha25_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-16595),15907⟩,⟨(-15633),16866⟩⟩,⟨⟨(-4062),4479⟩,⟨(-3968),4573⟩⟩,⟨⟨(-784),659⟩,⟨(-697),747⟩⟩,⟨⟨(-289713933681168),(-289713933680952)⟩,⟨(-601249166751071),(-601249166750855)⟩⟩,⟨⟨116978169696799790134198,116978169696799791302988⟩,⟨(-12022510436979685339007),(-12022510436979684170342)⟩⟩,⟨⟨15666937145186253230891626372,15666937145186253311451350737⟩,⟨1356325593276120189673749810,1356325593276120270053017692⟩⟩] +lemma ha25_1_7_eq (j : Fin 7) : ha25_1_7 j = ((ha25_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha25_1_7_contains (j : Fin 7) : (ha25_1_7 j).Contains (fullFactor true 25 7 ((j.val:ℝ)/6)) := by + rw [ha25_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_6 j) true 25 6 j (ha25_1_6_contains j) +noncomputable def hk25_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_8 j i k) +lemma hk25_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_8 j i k).Contains (fullFactor true 25 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 8 (kernel25_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha25_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-22509),23741⟩,⟨(-23555),22694⟩⟩,⟨⟨(-5312),5444⟩,⟨(-5698),5058⟩⟩,⟨⟨(-679),755⟩,⟨(-686),748⟩⟩,⟨⟨(-292343096855569),(-292343096855403)⟩,⟨281197756304022,281197756304189⟩⟩,⟨⟨(-16437978550148815494398),(-16437978550148814794654)⟩,⟨(-58677867324027633991312),(-58677867324027633291374)⟩⟩,⟨⟨244486712421613164350056881,244486712421613202525501010⟩,⟨(-7103549972786668007969613984),(-7103549972786667969697459298)⟩⟩] +lemma ha25_1_8_eq (j : Fin 7) : ha25_1_8 j = ((ha25_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha25_1_8_contains (j : Fin 7) : (ha25_1_8 j).Contains (fullFactor true 25 8 ((j.val:ℝ)/6)) := by + rw [ha25_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_7 j) true 25 7 j (ha25_1_7_contains j) +noncomputable def hk25_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_9 j i k) +lemma hk25_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_9 j i k).Contains (fullFactor true 25 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 9 (kernel25_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha25_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-29954),28549⟩,⟨(-29139),29363⟩⟩,⟨⟨(-6239),5801⟩,⟨(-5883),6157⟩⟩,⟨⟨(-627),639⟩,⟨(-664),602⟩⟩,⟨⟨193570510611875,193570510611989⟩,⟨102723012619895,102723012620009⟩⟩,⟨⟨(-25348789759298101560929),(-25348789759298101188362)⟩,⟨12053458463357661934324,12053458463357662306767⟩⟩,⟨⟨(-2855223556477147259068799363),(-2855223556477147242907479980)⟩,⟨50112168789207822075376704,50112168789207838191606664⟩⟩] +lemma ha25_1_9_eq (j : Fin 7) : ha25_1_9 j = ((ha25_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha25_1_9_contains (j : Fin 7) : (ha25_1_9 j).Contains (fullFactor true 25 9 ((j.val:ℝ)/6)) := by + rw [ha25_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_8 j) true 25 8 j (ha25_1_8_contains j) +noncomputable def hk25_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_10 j i k) +lemma hk25_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_10 j i k).Contains (fullFactor true 25 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 10 (kernel25_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha25_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-32720),33881⟩,⟨(-33125),33476⟩⟩,⟨⟨(-5886),6243⟩,⟨(-6020),6110⟩⟩,⟨⟨(-521),485⟩,⟨(-497),509⟩⟩,⟨⟨18125088549951,18125088550022⟩,⟨(-104995564817822),(-104995564817751)⟩⟩,⟨⟨6709522642049826115681,6709522642049826294098⟩,⟨9506799887446045577094,9506799887446045755567⟩⟩,⟨⟨71709124999040651499629688,71709124999040657622937064⟩,⟨1030087687847850492075730587,1030087687847850498217529816⟩⟩] +lemma ha25_1_10_eq (j : Fin 7) : ha25_1_10 j = ((ha25_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha25_1_10_contains (j : Fin 7) : (ha25_1_10 j).Contains (fullFactor true 25 10 ((j.val:ℝ)/6)) := by + rw [ha25_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_9 j) true 25 9 j (ha25_1_9_contains j) +noncomputable def hk25_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_11 j i k) +lemma hk25_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_11 j i k).Contains (fullFactor true 25 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 11 (kernel25_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha25_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34809),34119⟩,⟨(-34782),34145⟩⟩,⟨⟨(-5613),5496⟩,⟨(-5658),5451⟩⟩,⟨⟨(-356),371⟩,⟨(-357),370⟩⟩,⟨⟨(-46594940462897),(-46594940462857)⟩,⟨6851635796179,6851635796219⟩⟩,⟨⟨3101140120536544640988,3101140120536544718708⟩,⟨(-3100552119676879333236),(-3100552119676879255536)⟩⟩,⟨⟨336928036359550851459564795,336928036359550853581371510⟩,⟨(-41124230695144795050846040),(-41124230695144792935743444)⟩⟩] +lemma ha25_1_11_eq (j : Fin 7) : ha25_1_11 j = ((ha25_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha25_1_11_contains (j : Fin 7) : (ha25_1_11 j).Contains (fullFactor true 25 11 ((j.val:ℝ)/6)) := by + rw [ha25_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_10 j) true 25 10 j (ha25_1_10_contains j) +noncomputable def hk25_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_12 j i k) +lemma hk25_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_12 j i k).Contains (fullFactor true 25 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 12 (kernel25_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha25_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32574),32817⟩,⟨(-32385),33006⟩⟩,⟨⟨(-4684),4643⟩,⟨(-4596),4731⟩⟩,⟨⟨(-240),242⟩,⟨(-246),236⟩⟩,⟨⟨8521868935341,8521868935363⟩,⟨17073787583910,17073787583932⟩⟩,⟨⟨(-1237568491587701306373),(-1237568491587701275354)⟩,⟨(-873778414476682069232),(-873778414476682038208)⟩⟩,⟨⟨(-17647231275364937624514087),(-17647231275364936954782137)⟩,⟨(-100744489808592621676157539),(-100744489808592621004244494)⟩⟩] +lemma ha25_1_12_eq (j : Fin 7) : ha25_1_12 j = ((ha25_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha25_1_12_contains (j : Fin 7) : (ha25_1_12 j).Contains (fullFactor true 25 12 ((j.val:ℝ)/6)) := by + rw [ha25_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_11 j) true 25 11 j (ha25_1_11_contains j) +noncomputable def hk25_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_13 j i k) +lemma hk25_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_13 j i k).Contains (fullFactor true 25 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 13 (kernel25_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha25_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28615),28649⟩,⟨(-28850),28414⟩⟩,⟨⟨(-3580),3649⟩,⟨(-3632),3597⟩⟩,⟨⟨(-150),145⟩,⟨(-147),148⟩⟩,⟨⟨5074388082163,5074388082174⟩,⟨(-5018755128165),(-5018755128154)⟩⟩,⟨⟨(-207539828682312096036),(-207539828682312084604)⟩,⟨436249245738152118720,436249245738152130151⟩⟩,⟨⟨(-27729022779975267569166961),(-27729022779975267372765280)⟩,⟨6357057107219053486051818,6357057107219053681809506⟩⟩] +lemma ha25_1_13_eq (j : Fin 7) : ha25_1_13 j = ((ha25_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha25_1_13_contains (j : Fin 7) : (ha25_1_13 j).Contains (fullFactor true 25 13 ((j.val:ℝ)/6)) := by + rw [ha25_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_12 j) true 25 12 j (ha25_1_12_contains j) +noncomputable def hk25_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_14 j i k) +lemma hk25_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_14 j i k).Contains (fullFactor true 25 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 14 (kernel25_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha25_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23350),23215⟩,⟨(-23168),23397⟩⟩,⟨⟨(-2620),2583⟩,⟨(-2608),2595⟩⟩,⟨⟨(-83),85⟩,⟨(-83),85⟩⟩,⟨⟨(-2205435801041),(-2205435801035)⟩,⟨(-1131315366539),(-1131315366533)⟩⟩,⟨⟨137741333009233024631,137741333009233028544⟩,⟨38614935626199733157,38614935626199737069⟩⟩,⟨⟨2011590739560218877279301,2011590739560218930411785⟩,⟨7066895524930774814545945,7066895524930774867852531⟩⟩] +lemma ha25_1_14_eq (j : Fin 7) : ha25_1_14 j = ((ha25_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha25_1_14_contains (j : Fin 7) : (ha25_1_14 j).Contains (fullFactor true 25 14 ((j.val:ℝ)/6)) := by + rw [ha25_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_13 j) true 25 13 j (ha25_1_13_contains j) +noncomputable def hk25_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_15 j i k) +lemma hk25_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_15 j i k).Contains (fullFactor true 25 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 15 (kernel25_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha25_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17608),17733⟩,⟨(-17712),17629⟩⟩,⟨⟨(-1744),1751⟩,⟨(-1739),1756⟩⟩,⟨⟨(-45),45⟩,⟨(-45),44⟩⟩,⟨⟨(-125642892723),(-125642892720)⟩,⟨793562374613,793562374616⟩⟩,⟨⟨4049435259578303484,4049435259578304735⟩,⟨(-39327387716239953010),(-39327387716239951760)⟩⟩,⟨⟨1676068040839744234466085,1676068040839744247969471⟩,⟨(-572725414314307775335459),(-572725414314307761875479)⟩⟩] +lemma ha25_1_15_eq (j : Fin 7) : ha25_1_15 j = ((ha25_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha25_1_15_contains (j : Fin 7) : (ha25_1_15 j).Contains (fullFactor true 25 15 ((j.val:ℝ)/6)) := by + rw [ha25_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_14 j) true 25 14 j (ha25_1_14_contains j) +noncomputable def hk25_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_16 j i k) +lemma hk25_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_16 j i k).Contains (fullFactor true 25 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 16 (kernel25_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha25_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12613),12534⟩,⟨(-12568),12579⟩⟩,⟨⟨(-1099),1102⟩,⟨(-1104),1097⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨241040210382,241040210384⟩,⟨(-38878816312),(-38878816310)⟩⟩,⟨⟨(-10219753680707307939),(-10219753680707307564)⟩,⟨697208464868361140,697208464868361515⟩⟩,⟨⟨(-148927956352225314415830),(-148927956352225311219110)⟩,⟨(-371548922873836931325925),(-371548922873836928119167)⟩⟩] +lemma ha25_1_16_eq (j : Fin 7) : ha25_1_16 j = ((ha25_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha25_1_16_contains (j : Fin 7) : (ha25_1_16 j).Contains (fullFactor true 25 16 ((j.val:ℝ)/6)) := by + rw [ha25_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_15 j) true 25 15 j (ha25_1_15_contains j) +noncomputable def hk25_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_17 j i k) +lemma hk25_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_17 j i k).Contains (fullFactor true 25 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 17 (kernel25_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha25_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8401),8439⟩,⟨(-8414),8427⟩⟩,⟨⟨(-654),651⟩,⟨(-652),653⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-32051855906),(-32051855905)⟩,⟨(-62040464858),(-62040464856)⟩⟩,⟨⟨590948645534448402,590948645534448509⟩,⟨2427039517196943610,2427039517196943717⟩⟩,⟨⟨(-77276949014398349291829),(-77276949014398348575105)⟩,⟨35738218570038813539736,35738218570038814254297⟩⟩] +lemma ha25_1_17_eq (j : Fin 7) : ha25_1_17 j = ((ha25_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha25_1_17_contains (j : Fin 7) : (ha25_1_17 j).Contains (fullFactor true 25 17 ((j.val:ℝ)/6)) := by + rw [ha25_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_16 j) true 25 16 j (ha25_1_16_contains j) +noncomputable def hk25_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_18 j i k) +lemma hk25_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_18 j i k).Contains (fullFactor true 25 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 18 (kernel25_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha25_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5333),5319⟩,⟨(-5333),5319⟩⟩,⟨⟨(-365),366⟩,⟨(-365),366⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-13225349478),(-13225349477)⟩,⟨13449591499,13449591500⟩⟩,⟨⟨527720378730931689,527720378730931719⟩,⟨(-229087573199306733),(-229087573199306704)⟩⟩,⟨⟨7975677207434517189944,7975677207434517340798⟩,⟨15129910550449668669527,15129910550449668820817⟩⟩] +lemma ha25_1_18_eq (j : Fin 7) : ha25_1_18 j = ((ha25_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha25_1_18_contains (j : Fin 7) : (ha25_1_18 j).Contains (fullFactor true 25 18 ((j.val:ℝ)/6)) := by + rw [ha25_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_17 j) true 25 17 j (ha25_1_17_contains j) +noncomputable def hk25_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_19 j i k) +lemma hk25_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_19 j i k).Contains (fullFactor true 25 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 19 (kernel25_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha25_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3190),3193⟩,⟨(-3187),3196⟩⟩,⟨⟨(-194),194⟩,⟨(-195),194⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨4325162428,4325162429⟩,⟨2143160336,2143160337⟩⟩,⟨⟨(-68819298744275403),(-68819298744275394)⟩,⟨(-104976128469875914),(-104976128469875906)⟩⟩,⟨⟨2796677963146087861346,2796677963146087891601⟩,⟨(-1665335374814732796860),(-1665335374814732766688)⟩⟩] +lemma ha25_1_19_eq (j : Fin 7) : ha25_1_19 j = ((ha25_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha25_1_19_contains (j : Fin 7) : (ha25_1_19 j).Contains (fullFactor true 25 19 ((j.val:ℝ)/6)) := by + rw [ha25_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_18 j) true 25 18 j (ha25_1_18_contains j) +noncomputable def hk25_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_20 j i k) +lemma hk25_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_20 j i k).Contains (fullFactor true 25 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 20 (kernel25_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha25_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1819),1815⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨167360739,167360740⟩,⟨(-1161492778),(-1161492777)⟩⟩,⟨⟨(-19019439151102675),(-19019439151102672)⟩,⟨17754121229023339,17754121229023343⟩⟩,⟨⟨(-326935550134593826382),(-326935550134593820648)⟩,⟨(-489308566882390542433),(-489308566882390536684)⟩⟩] +lemma ha25_1_20_eq (j : Fin 7) : ha25_1_20 j = ((ha25_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha25_1_20_contains (j : Fin 7) : (ha25_1_20 j).Contains (fullFactor true 25 20 ((j.val:ℝ)/6)) := by + rw [ha25_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_19 j) true 25 19 j (ha25_1_19_contains j) +noncomputable def hk25_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_21 j i k) +lemma hk25_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_21 j i k).Contains (fullFactor true 25 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 21 (kernel25_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha25_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-986),985⟩,⟨(-985),986⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-267604537),(-267604536)⟩,⟨46993846,46993847⟩⟩,⟨⟨4091729900917561,4091729900917563⟩,⟨3104558209922431,3104558209922433⟩⟩,⟨⟨(-81215056720649091311),(-81215056720649090270)⟩,⟨60592947391959683998,60592947391959685037⟩⟩] +lemma ha25_1_21_eq (j : Fin 7) : ha25_1_21 j = ((ha25_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha25_1_21_contains (j : Fin 7) : (ha25_1_21 j).Contains (fullFactor true 25 21 ((j.val:ℝ)/6)) := by + rw [ha25_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_20 j) true 25 20 j (ha25_1_20_contains j) +noncomputable def hk25_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_22 j i k) +lemma hk25_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_22 j i k).Contains (fullFactor true 25 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 22 (kernel25_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha25_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-510),511⟩,⟨(-511),510⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨28301241,28301243⟩,⟨52959892,52959893⟩⟩,⟨⟨445509698946538,445509698946540⟩,⟨(-859203815443372),(-859203815443371)⟩⟩,⟨⟨10638760653854011578,10638760653854011759⟩,⟨12813270162925862671,12813270162925862852⟩⟩] +lemma ha25_1_22_eq (j : Fin 7) : ha25_1_22 j = ((ha25_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha25_1_22_contains (j : Fin 7) : (ha25_1_22 j).Contains (fullFactor true 25 22 ((j.val:ℝ)/6)) := by + rw [ha25_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_21 j) true 25 21 j (ha25_1_21_contains j) +noncomputable def hk25_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_23 j i k) +lemma hk25_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_23 j i k).Contains (fullFactor true 25 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 23 (kernel25_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha25_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨8773376,8773377⟩,⟨(-9174111),(-9174110)⟩⟩,⟨⟨(-166255507325723),(-166255507325722)⟩,⟨(-52821627528463),(-52821627528462)⟩⟩,⟨⟨1924842453373807696,1924842453373807727⟩,⟨(-1774905758864966824),(-1774905758864966793)⟩⟩] +lemma ha25_1_23_eq (j : Fin 7) : ha25_1_23 j = ((ha25_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha25_1_23_contains (j : Fin 7) : (ha25_1_23 j).Contains (fullFactor true 25 23 ((j.val:ℝ)/6)) := by + rw [ha25_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_22 j) true 25 22 j (ha25_1_22_contains j) +noncomputable def hk25_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_24 j i k) +lemma hk25_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_24 j i k).Contains (fullFactor true 25 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 24 (kernel25_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha25_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2319962),(-2319961)⟩,⟨(-1109620),(-1109618)⟩⟩,⟨⟨(-4112391435164),(-4112391435162)⟩,⟨29850229324399,29850229324400⟩⟩,⟨⟨(-282111043114363796),(-282111043114363790)⟩,⟨(-275724008831798844),(-275724008831798838)⟩⟩] +lemma ha25_1_24_eq (j : Fin 7) : ha25_1_24 j = ((ha25_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha25_1_24_contains (j : Fin 7) : (ha25_1_24 j).Contains (fullFactor true 25 24 ((j.val:ℝ)/6)) := by + rw [ha25_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_23 j) true 25 23 j (ha25_1_23_contains j) +noncomputable def hk25_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_25 j i k) +lemma hk25_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_25 j i k).Contains (fullFactor true 25 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 25 (kernel25_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha25_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-64435),(-64434)⟩,⟨495986,495987⟩⟩,⟨⟨4993736064346,4993736064348⟩,⟨(-168933217242),(-168933217241)⟩⟩,⟨⟨(-37706945543723463),(-37706945543723461)⟩,⟨42819357775355523,42819357775355525⟩⟩] +lemma ha25_1_25_eq (j : Fin 7) : ha25_1_25 j = ((ha25_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha25_1_25_contains (j : Fin 7) : (ha25_1_25 j).Contains (fullFactor true 25 25 ((j.val:ℝ)/6)) := by + rw [ha25_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_24 j) true 25 24 j (ha25_1_24_contains j) +noncomputable def hk25_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_26 j i k) +lemma hk25_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_26 j i k).Contains (fullFactor true 25 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 26 (kernel25_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha25_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨91888,91889⟩,⟨(-17459),(-17457)⟩⟩,⟨⟨(-161817525651),(-161817525649)⟩,⟨(-780073447887),(-780073447886)⟩⟩,⟨⟨6219314442978888,6219314442978889⟩,⟨4927708760340872,4927708760340874⟩⟩] +lemma ha25_1_26_eq (j : Fin 7) : ha25_1_26 j = ((ha25_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha25_1_26_contains (j : Fin 7) : (ha25_1_26 j).Contains (fullFactor true 25 26 ((j.val:ℝ)/6)) := by + rw [ha25_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_25 j) true 25 25 j (ha25_1_25_contains j) +noncomputable def hk25_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_27 j i k) +lemma hk25_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_27 j i k).Contains (fullFactor true 25 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 27 (kernel25_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha25_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-8145),(-8144)⟩,⟨(-14744),(-14743)⟩⟩,⟨⟨(-113809706222),(-113809706221)⟩,⟨44832672410,44832672412⟩⟩,⟨⟨615787522655033,615787522655034⟩,⟨(-866051807310952),(-866051807310951)⟩⟩] +lemma ha25_1_27_eq (j : Fin 7) : ha25_1_27 j = ((ha25_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha25_1_27_contains (j : Fin 7) : (ha25_1_27 j).Contains (fullFactor true 25 27 ((j.val:ℝ)/6)) := by + rw [ha25_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_26 j) true 25 26 j (ha25_1_26_contains j) +noncomputable def hk25_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_28 j i k) +lemma hk25_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_28 j i k).Contains (fullFactor true 25 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 28 (kernel25_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha25_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1993),(-1991)⟩,⟨2141,2142⟩⟩,⟨⟨9403981726,9403981727⟩,⟨15477516605,15477516606⟩⟩,⟨⟨(-115820146981043),(-115820146981042)⟩,⟨(-73607261641238),(-73607261641237)⟩⟩] +lemma ha25_1_28_eq (j : Fin 7) : ha25_1_28 j = ((ha25_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha25_1_28_contains (j : Fin 7) : (ha25_1_28 j).Contains (fullFactor true 25 28 ((j.val:ℝ)/6)) := by + rw [ha25_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_27 j) true 25 27 j (ha25_1_27_contains j) +noncomputable def hk25_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_29 j i k) +lemma hk25_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_29 j i k).Contains (fullFactor true 25 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 29 (kernel25_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha25_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨445,446⟩,⟨205,206⟩⟩,⟨⟨1951964330,1951964331⟩,⟨(-1700653180),(-1700653179)⟩⟩,⟨⟨(-8415510377825),(-8415510377824)⟩,⟨14898312032474,14898312032475⟩⟩] +lemma ha25_1_29_eq (j : Fin 7) : ha25_1_29 j = ((ha25_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha25_1_29_contains (j : Fin 7) : (ha25_1_29 j).Contains (fullFactor true 25 29 ((j.val:ℝ)/6)) := by + rw [ha25_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_28 j) true 25 28 j (ha25_1_28_contains j) +noncomputable def hk25_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel25_0 j i k).mul (mpower1_30 j i k) +lemma hk25_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk25_1_30 j i k).Contains (fullFactor true 25 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk25_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel25_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 25 30 (kernel25_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha25_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨9,10⟩,⟨(-80),(-78)⟩⟩,⟨⟨(-277415001),(-277415000)⟩,⟨(-225885785),(-225885784)⟩⟩,⟨⟨1845946709663,1845946709664⟩,⟨919704036103,919704036104⟩⟩] +lemma ha25_1_30_eq (j : Fin 7) : ha25_1_30 j = ((ha25_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha25_1_30_contains (j : Fin 7) : (ha25_1_30 j).Contains (fullFactor true 25 30 ((j.val:ℝ)/6)) := by + rw [ha25_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha25_1_29 j) true 25 29 j (ha25_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders27.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders27.lean new file mode 100644 index 0000000000000000000000000000000000000000..b0f8a3c029227743a289cefceaaa8163b875c674 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders27.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers30 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues30 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk27_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_0 j i k) +lemma hk27_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_0 j i k).Contains (fullFactor false 27 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 0 (power27_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha27_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999677,1000000000000000000000000000431⟩,⟨(-431),431⟩⟩,⟨⟨(-81403453103),60193902703⟩,⟨999999999999999999929227690160,1000000000000000000070772309877⟩⟩,⟨⟨(-1000000000000000000193424181923),(-999999999999999999806575818095)⟩,⟨(-214614432606),172195331664⟩⟩,⟨⟨(-56385898307),120014549693⟩,⟨(-1000000000000000000088200224000),(-999999999999999999911799776027)⟩⟩,⟨⟨999999999999999999471081323067,1000000000000000000528918676871⟩,⟨(-486513685039),571351886994⟩⟩,⟨⟨(-718728105770),612680353424⟩,⟨999999999999999999334281766862,1000000000000000000665718233058⟩⟩,⟨⟨(-1000000000000000000176936340221),(-999999999999999999823063659887)⟩,⟨(-240564991661),113307688673⟩⟩] +lemma ha27_0_0_eq (j : Fin 7) : ha27_0_0 j = ((atomPoints j).direct.powBin 7 27).conj := by fin_cases j <;> decide +kernel +lemma ha27_0_0_contains (j : Fin 7) : (ha27_0_0 j).Contains (fullFactor false 27 0 ((j.val:ℝ)/6)) := by + rw [ha27_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 27) ((j.val:ℝ)/6) 27 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 27 (by norm_num)) +noncomputable def hk27_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_1 j i k) +lemma hk27_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_1 j i k).Contains (fullFactor false 27 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 1 (power27_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha27_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-523598775598298873115389628133),(-523598775598298873039610371885)⟩,⟨(-42622748375),31517453754⟩⟩,⟨⟨(-180322529647),224743708277⟩,⟨(-1047197551196597746359219996321),(-1047197551196597745950780003698)⟩⟩,⟨⟨1570796326794896619091455412160,1570796326794896619373544587882⟩,⟨(-88570761944),188518413820⟩⟩,⟨⟨(-1196636593864),1018951879193⟩,⟨2094395102393195491198901980131,2094395102393195493421098019738⟩⟩,⟨⟨(-2617993877991494367134512925283),(-2617993877991494363640487074509)⟩,⟨(-1881625780847),1603993414430⟩⟩,⟨⟨(-355966602331),755757210514⟩,⟨(-3141592653589793239025861906592),(-3141592653589793237904138093747)⟩⟩] +lemma ha27_0_1_eq (j : Fin 7) : ha27_0_1 j = ((ha27_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha27_0_1_contains (j : Fin 7) : (ha27_0_1 j).Contains (fullFactor false 27 1 ((j.val:ℝ)/6)) := by + rw [ha27_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_0 j) false 27 0 j (ha27_0_0_contains j) +noncomputable def hk27_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_2 j i k) +lemma hk27_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_2 j i k).Contains (fullFactor false 27 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 2 (power27_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha27_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-8251250098),11158609431⟩,⟨(-137077838904018869716377898432),(-137077838904018869696102603223)⟩⟩,⟨⟨548311355616075478717158998658,548311355616075478932763007956⟩,⟨(-94416655736),117675530478⟩⟩,⟨⟨(-148062015981),69563313762⟩,⟨1233700550136169827243422601773,1233700550136169827468901913117⟩⟩,⟨⟨(-2193245422464301916466873797122),(-2193245422464301914132814229153)⟩,⟨(-1253114910767),1067043912679⟩⟩,⟨⟨(-2099622469659),2463042387465⟩,⟨(-3426945972600471744948294996133),(-3426945972600471740363717544867)⟩⟩,⟨⟨4934802200544679308535795225899,4934802200544679310313502834063⟩,⟨(-559151031404),1187140650225⟩⟩] +lemma ha27_0_2_eq (j : Fin 7) : ha27_0_2 j = ((ha27_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha27_0_2_contains (j : Fin 7) : (ha27_0_2 j).Contains (fullFactor false 27 2 ((j.val:ℝ)/6)) := by + rw [ha27_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_1 j) false 27 1 j (ha27_0_1_contains j) +noncomputable def hk27_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_3 j i k) +lemma hk27_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_3 j i k).Contains (fullFactor false 27 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 3 (power27_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha27_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23924596203935046429941097071,23924596203935046433555958009⟩,⟨(-1440114817),1947544746⟩⟩,⟨⟨(-41076509118),32957630227⟩,⟨191396769631480371416053604471,191396769631480371491922836167⟩⟩,⟨⟨(-645964097506246253717268673042),(-645964097506246253597151814115)⟩,⟨(-77525090281),36423265913⟩⟩,⟨⟨(-744937181585),874839243949⟩,⟨(-1531174157051842972449083189823),(-1531174157051842970814728335153)⟩⟩,⟨⟨2990574525491880801963407011719,2990574525491880805973724872956⟩,⟨(-1832266257221),2149409963873⟩⟩,⟨⟨(-1243170781842),585541590836⟩,⟨5167712780049970028318651751500,5167712780049970030196712146182⟩⟩] +lemma ha27_0_3_eq (j : Fin 7) : ha27_0_3 j = ((ha27_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha27_0_3_contains (j : Fin 7) : (ha27_0_3 j).Contains (fullFactor false 27 3 ((j.val:ℝ)/6)) := by + rw [ha27_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_2 j) false 27 2 j (ha27_0_2_contains j) +noncomputable def hk27_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_4 j i k) +lemma hk27_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_4 j i k).Contains (fullFactor false 27 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 4 (power27_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha27_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-254933012),188510589⟩,⟨3131722319766024859478479308,3131722319766024859961632081⟩⟩,⟨⟨(-50107557116256397765531898976),(-50107557116256397745509883256)⟩,⟨(-10753804941),8628287417⟩⟩,⟨⟨(-14303383077),30444031762⟩,⟨(-253669507901048013661313128937),(-253669507901048013613335893617)⟩⟩,⟨⟨801720913860102363659185178961,801720913860102364517483336691⟩,⟨(-390048196176),458064756978⟩⟩,⟨⟨(-1406785531679),1199215461064⟩,⟨1957326449853765536009546176143,1957326449853765538640523442121⟩⟩,⟨⟨(-4058712126416768218941164413935),(-4058712126416768217453219947251)⟩,⟨(-976384048849),459883290036⟩⟩] +lemma ha27_0_4_eq (j : Fin 7) : ha27_0_4 j = ((ha27_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha27_0_4_contains (j : Fin 7) : (ha27_0_4 j).Contains (fullFactor false 27 4 ((j.val:ℝ)/6)) := by + rw [ha27_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_3 j) false 27 3 j (ha27_0_3_contains j) +noncomputable def hk27_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_5 j i k) +lemma hk27_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_5 j i k).Contains (fullFactor false 27 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 5 (power27_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha27_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-327953194428670967601146731),(-327953194428670967549507182)⟩,⟨(-26696523),19740783⟩⟩,⟨⟨(-1807104291),2252271641⟩,⟨(-10494502221717470964523865706),(-10494502221717470960297059500)⟩⟩,⟨⟨79692626246167045113141369138,79692626246167045128467531649⟩,⟨(-4493540320),9564274653⟩⟩,⟨⟨(-191873716719),163383006354⟩,⟨335824071094959070616838776884,335824071094959070977430829693⟩⟩,⟨⟨(-1024853732589596774363316081468),(-1024853732589596772982477395623)⟩,⟨(-736591181917),627907747092⟩⟩,⟨⟨(-288953193098),613480190990⟩,⟨(-2550164039877345444337252665369),(-2550164039877345443394232160019)⟩⟩] +lemma ha27_0_5_eq (j : Fin 7) : ha27_0_5 j = ((ha27_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha27_0_5_contains (j : Fin 7) : (ha27_0_5 j).Contains (fullFactor false 27 5 ((j.val:ℝ)/6)) := by + rw [ha27_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_4 j) false 27 4 j (ha27_0_4_contains j) +noncomputable def hk27_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_6 j i k) +lemma hk27_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_6 j i k).Contains (fullFactor false 27 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 6 (power27_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha27_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1722709),2329712⟩,⟨(-28619315176067161693856418),(-28619315176067161689258918)⟩⟩,⟨⟨1831636171268298347887917164,1831636171268298348631464296⟩,⟨(-315399199),393095558⟩⟩,⟨⟨(-2503921249),1176406105⟩,⟨20863480763352960871106144477,20863480763352960875184934963⟩⟩,⟨⟨(-117224714961171094351741961416),(-117224714961171094225498451998)⟩,⟨(-66976562096),57031428054⟩⟩,⟨⟨(-273976439639),321398534141⟩,⟨(-447176799626049401732552529895),(-447176799626049401128624584259)⟩⟩,⟨⟨1335262768854589495632307214456,1335262768854589496130321869822⟩,⟨(-151295538112),321217476857⟩⟩] +lemma ha27_0_6_eq (j : Fin 7) : ha27_0_6 j = ((ha27_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha27_0_6_contains (j : Fin 7) : (ha27_0_6 j).Contains (fullFactor false 27 6 ((j.val:ℝ)/6)) := by + rw [ha27_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_5 j) false 27 5 j (ha27_0_5_contains j) +noncomputable def hk27_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_7 j i k) +lemma hk27_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_7 j i k).Contains (fullFactor false 27 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 7 (power27_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha27_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2140719769235797028041403,2140719769235797028392111⟩,⟨(-128859),174263⟩⟩,⟨⟨(-58806958),47183610⟩,⟨274012130462182019555691596,274012130462182019667798195⟩⟩,⟨⟨(-4681754135318688101175138014),(-4681754135318688100244957082)⟩,⟨(-561878615),263984913⟩⟩,⟨⟨(-17063763372),20039340519⟩,⟨(-35073552699159298529245152741),(-35073552699159298491361540464)⟩⟩,⟨⟨167243731971546642716233701805,167243731971546642942634578629⟩,⟨(-102466948813),120202770683⟩⟩,⟨⟨(-144162066500),67901278722⟩,⟨599264529320792076778178099690,599264529320792077003594072601⟩⟩] +lemma ha27_0_7_eq (j : Fin 7) : ha27_0_7 j = ((ha27_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha27_0_7_contains (j : Fin 7) : (ha27_0_7 j).Contains (fullFactor false 27 7 ((j.val:ℝ)/6)) := by + rw [ha27_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_6 j) false 27 6 j (ha27_0_6_contains j) +noncomputable def hk27_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_8 j i k) +lemma hk27_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_8 j i k).Contains (fullFactor false 27 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 8 (power27_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha27_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-11406),8434⟩,⟨140109781258867029442229,140109781258867029465630⟩⟩,⟨⟨(-35868104002269959547600450),(-35868104002269959532811558)⟩,⟨(-7697813),6176321⟩⟩,⟨⟨(-51833317),110324609⟩,⟨(-919260274839426580340016120),(-919260274839426580154449424)⟩⟩,⟨⟨9182234624581109637319169688,9182234624581109647266304152⟩,⟨(-4467282805),5246287080⟩⟩,⟨⟨(-39336264721),33532230587⟩,⟨54730383304244933343309426708,54730383304244933417573152617⟩⟩,⟨⟨(-235330630358893204587926452710),(-235330630358893204498656726485)⟩,⟨(-56612311131),26664769801⟩⟩] +lemma ha27_0_8_eq (j : Fin 7) : ha27_0_8 j = ((ha27_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha27_0_8_contains (j : Fin 7) : (ha27_0_8 j).Contains (fullFactor false 27 8 ((j.val:ℝ)/6)) := by + rw [ha27_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_7 j) false 27 7 j (ha27_0_7_contains j) +noncomputable def hk27_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_9 j i k) +lemma hk27_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_9 j i k).Contains (fullFactor false 27 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 9 (power27_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha27_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-8151256657387584305614),(-8151256657387584304226)⟩,⟨(-664),491⟩⟩,⟨⟨(-718648),895682⟩,⟨(-4173443408582443164986161),(-4173443408582443163252110)⟩⟩,⟨⟨160441184787359821857294943,160441184787359821890193142⟩,⟨(-9046621),19255277⟩⟩,⟨⟨(-1220866441),1039583915⟩,⟨2136803025194210898868195043,2136803025194210901189799999⟩⟩,⟨⟨(-15920423158960125606373799624),(-15920423158960125584720681143)⟩,⟨(-11442455581),9754130489⟩⟩,⟨⟨(-9307760547),19761424528⟩,⟨(-82145886611128228815068195316),(-82145886611128228783645703937)⟩⟩] +lemma ha27_0_9_eq (j : Fin 7) : ha27_0_9 j = ((ha27_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha27_0_9_contains (j : Fin 7) : (ha27_0_9 j).Contains (fullFactor false 27 9 ((j.val:ℝ)/6)) := by + rw [ha27_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_8 j) false 27 8 j (ha27_0_8_contains j) +noncomputable def hk27_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_10 j i k) +lemma hk27_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_10 j i k).Contains (fullFactor false 27 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 10 (power27_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha27_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-26),35⟩,⟨(-426798800539562151492),(-426798800539562151417)⟩⟩,⟨⟨437041971752511642998009,437041971752511643180991⟩,⟨(-75257),93796⟩⟩,⟨⟨(-3024612),1421040⟩,⟨25202042373060605478618142,25202042373060605483866000⟩⟩,⟨⟨(-447530979074571922767478086),(-447530979074571922279817745)⟩,⟨(-255697670),217729947⟩⟩,⟨⟨(-2553625391),2995627867⟩,⟨(-4167957036519161638139748246),(-4167957036519161632457708064)⟩⟩,⟨⟨25806891390014060007814974277,25806891390014060017768786972⟩,⟨(-2924119216),6208234613⟩⟩] +lemma ha27_0_10_eq (j : Fin 7) : ha27_0_10 j = ((ha27_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha27_0_10_contains (j : Fin 7) : (ha27_0_10 j).Contains (fullFactor false 27 10 ((j.val:ℝ)/6)) := by + rw [ha27_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_9 j) false 27 9 j (ha27_0_9_contains j) +noncomputable def hk27_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_11 j i k) +lemma hk27_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_11 j i k).Contains (fullFactor false 27 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 11 (power27_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha27_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20315575399030665719,20315575399030665723⟩,⟨(-2),2⟩⟩,⟨⟨(-8930),7165⟩,⟨41606298417214803387950,41606298417214803405503⟩⟩,⟨⟨(-3598843235212085340868660),(-3598843235212085340107811)⟩,⟨(-431914),202925⟩⟩,⟨⟨(-41455685),48684723⟩,⟨(-85209699158455917403056616),(-85209699158455917309935073)⟩⟩,⟨⟨991971455030794223983288091,991971455030794225338768037⟩,⟨(-607761422),712957766⟩⟩,⟨⟨(-1773067660),835126496⟩,⟨7370430945714350775886775375,7370430945714350778753038444⟩⟩] +lemma ha27_0_11_eq (j : Fin 7) : ha27_0_11 j = ((ha27_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha27_0_11_contains (j : Fin 7) : (ha27_0_11 j).Contains (fullFactor false 27 11 ((j.val:ℝ)/6)) := by + rw [ha27_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_10 j) false 27 10 j (ha27_0_10_contains j) +noncomputable def hk27_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_12 j i k) +lemma hk27_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_12 j i k).Contains (fullFactor false 27 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 12 (power27_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha27_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨886434200375614885,886434200375614886⟩⟩,⟨⟨(-3630834484738518571828),(-3630834484738518570284)⟩,⟨(-780),626⟩⟩,⟨⟨(-26563),56538⟩,⟨(-471087477881817150421816),(-471087477881817150320721)⟩⟩,⟨⟨14871898049488972058896422,14871898049488972075196537⟩,⟨(-7235382),8497088⟩⟩,⟨⟨(-155543256),132592974⟩,⟨216414599701077852759946155,216414599701077853056354876⟩⟩,⟨⟨(-1929574309403923048298978816),(-1929574309403923047542450873)⟩,⟨(-464188028),218635606⟩⟩] +lemma ha27_0_12_eq (j : Fin 7) : ha27_0_12 j = ((ha27_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha27_0_12_contains (j : Fin 7) : (ha27_0_12 j).Contains (fullFactor false 27 12 ((j.val:ℝ)/6)) := by + rw [ha27_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_11 j) false 27 11 j (ha27_0_11_contains j) +noncomputable def hk27_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_13 j i k) +lemma hk27_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_13 j i k).Contains (fullFactor false 27 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 13 (power27_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha27_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-35702758612702237),(-35702758612702236)⟩,⟨(-1),1⟩⟩,⟨⟨(-51),63⟩,⟨(-292476998555256723089),(-292476998555256722963)⟩⟩,⟨⟨56921729219679268112109,56921729219679268124506⟩,⟨(-3210),6832⟩⟩,⟨⟨(-1368944),1165673⟩,⟨2395971572164663073713145,2395971572164663076346841⟩⟩,⟨⟨(-43582469009646285061073428),(-43582469009646285001242683)⟩,⟨(-31323946),26702123⟩⟩,⟨⟨(-52835694),112176131⟩,⟨(-466302805767612564517329966),(-466302805767612564333022398)⟩⟩] +lemma ha27_0_13_eq (j : Fin 7) : ha27_0_13 j = ((ha27_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha27_0_13_contains (j : Fin 7) : (ha27_0_13 j).Contains (fullFactor false 27 13 ((j.val:ℝ)/6)) := by + rw [ha27_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_12 j) false 27 12 j (ha27_0_12_contains j) +noncomputable def hk27_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_14 j i k) +lemma hk27_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_14 j i k).Contains (fullFactor false 27 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 14 (power27_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha27_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1335280049649466),(-1335280049649465)⟩⟩,⟨⟨21877228333456835512,21877228333456835523⟩,⟨(-4),5⟩⟩,⟨⟨(-767),361⟩,⟨6386603083791852240451,6386603083791852241863⟩⟩,⟨⟨(-358436509015356793319080),(-358436509015356792923938)⟩,⟨(-204794),174385⟩⟩,⟨⟨(-4993286),5857565⟩,⟨(-8149902646786285762757717),(-8149902646786285751543451)⟩⟩,⟨⟨104638104924845707098269827,104638104924845707139961423⟩,⟨(-11856303),25172265⟩⟩] +lemma ha27_0_14_eq (j : Fin 7) : ha27_0_14 j = ((ha27_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha27_0_14_contains (j : Fin 7) : (ha27_0_14 j).Contains (fullFactor false 27 14 ((j.val:ℝ)/6)) := by + rw [ha27_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_13 j) false 27 13 j (ha27_0_13_contains j) +noncomputable def hk27_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_15 j i k) +lemma hk27_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_15 j i k).Contains (fullFactor false 27 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 15 (power27_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha27_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨46610066605153,46610066605154⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1527318662517654886,1527318662517654888⟩⟩,⟨⟨(-668803510981146723331),(-668803510981146723180)⟩,⟨(-81),38⟩⟩,⟨⟨(-24349),28595⟩,⟨(-50047177933378515355685),(-50047177933378515300353)⟩⟩,⟨⟨1422426349034211491854961,1422426349034211493816748⟩,⟨(-871493),1022338⟩⟩,⟨⟨(-5272067),2483179⟩,⟨21915353447830215823230430,21915353447830215832032057⟩⟩] +lemma ha27_0_15_eq (j : Fin 7) : ha27_0_15 j = ((ha27_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha27_0_15_contains (j : Fin 7) : (ha27_0_15 j).Contains (fullFactor false 27 15 ((j.val:ℝ)/6)) := by + rw [ha27_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_14 j) false 27 14 j (ha27_0_14_contains j) +noncomputable def hk27_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_16 j i k) +lemma hk27_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_16 j i k).Contains (fullFactor false 27 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 16 (power27_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha27_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1525310862813,1525310862814⟩⟩,⟨⟨(-99962772705334444),(-99962772705334443)⟩,⟨(-1),1⟩⟩,⟨⟨(-4),8⟩,⟨(-65659631149794723631),(-65659631149794723615)⟩⟩,⟨⟨6551160272016798095197,6551160272016798102462⟩,⟨(-3188),3744⟩⟩,⟨⟨(-167280),142598⟩,⟨232743967104084891214970,232743967104084891536709⟩⟩,⟨⟨(-4303069587032947008220416),(-4303069587032947006478523)⟩,⟨(-1035168),487572⟩⟩] +lemma ha27_0_16_eq (j : Fin 7) : ha27_0_16 j = ((ha27_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha27_0_16_contains (j : Fin 7) : (ha27_0_16 j).Contains (fullFactor false 27 16 ((j.val:ℝ)/6)) := by + rw [ha27_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_15 j) false 27 15 j (ha27_0_15_contains j) +noncomputable def hk27_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_17 j i k) +lemma hk27_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_17 j i k).Contains (fullFactor false 27 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 17 (power27_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha27_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-46979464717),(-46979464716)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-6157692399285196),(-6157692399285195)⟩⟩,⟨⟨6066935731106195666,6066935731106195668⟩,⟨(-1),1⟩⟩,⟨⟨(-462),393⟩,⟨807101058159109192978,807101058159109193877⟩⟩,⟨⟨(-35842487118702823511407),(-35842487118702823461745)⟩,⟨(-25762),21961⟩⟩,⟨⟨(-90104),191299⟩,⟨(-795205400147551278650678),(-795205400147551278326245)⟩⟩] +lemma ha27_0_17_eq (j : Fin 7) : ha27_0_17 j = ((ha27_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha27_0_17_contains (j : Fin 7) : (ha27_0_17 j).Contains (fullFactor false 27 17 ((j.val:ℝ)/6)) := by + rw [ha27_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_16 j) false 27 16 j (ha27_0_16_contains j) +noncomputable def hk27_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_18 j i k) +lemma hk27_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_18 j i k).Contains (fullFactor false 27 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 18 (power27_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha27_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1366577234),(-1366577233)⟩⟩,⟨⟨358240022308519,358240022308520⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨529440020073462376,529440020073462377⟩⟩,⟨⟨(-93910472408044662792),(-93910472408044662686)⟩,⟨(-54),46⟩⟩,⟨⟨(-3195),3747⟩,⟨(-5213078436041832675295),(-5213078436041832668054)⟩⟩,⟨⟨138789524622137721118021,138789524622137721175088⟩,⟨(-15727),33388⟩⟩] +lemma ha27_0_18_eq (j : Fin 7) : ha27_0_18 j = ((ha27_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha27_0_18_contains (j : Fin 7) : (ha27_0_18 j).Contains (fullFactor false 27 18 ((j.val:ℝ)/6)) := by + rw [ha27_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_17 j) false 27 17 j (ha27_0_17_contains j) +noncomputable def hk27_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_19 j i k) +lemma hk27_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_19 j i k).Contains (fullFactor false 27 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 19 (power27_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha27_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨37659903,37659904⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨19744635479057,19744635479058⟩⟩,⟨⟨(-43770654673137423),(-43770654673137422)⟩,⟨(-1),1⟩⟩,⟨⟨(-6),6⟩,⟨(-10351875446044213768),(-10351875446044213755)⟩⟩,⟨⟨718305654265631154550,718305654265631155551⟩,⟨(-441),517⟩⟩,⟨⟨(-5521),2601⟩,⟨22948428997269873105776,22948428997269873115286⟩⟩] +lemma ha27_0_19_eq (j : Fin 7) : ha27_0_19 j = ((ha27_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha27_0_19_contains (j : Fin 7) : (ha27_0_19 j).Contains (fullFactor false 27 19 ((j.val:ℝ)/6)) := by + rw [ha27_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_18 j) false 27 18 j (ha27_0_18_contains j) +noncomputable def hk27_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_20 j i k) +lemma hk27_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_20 j i k).Contains (fullFactor false 27 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 20 (power27_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha27_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨985933,985934⟩⟩,⟨⟨(-1033826696147),(-1033826696146)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-3437739179098608),(-3437739179098606)⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨(-68),58⟩,⟨94025990269704865148,94025990269704865281⟩⟩,⟨⟨(-3604730797462500934667),(-3604730797462500933160)⟩,⟨(-868),409⟩⟩] +lemma ha27_0_20_eq (j : Fin 7) : ha27_0_20 j = ((ha27_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha27_0_20_contains (j : Fin 7) : (ha27_0_20 j).Contains (fullFactor false 27 20 ((j.val:ℝ)/6)) := by + rw [ha27_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_19 j) false 27 19 j (ha27_0_19_contains j) +noncomputable def hk27_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_21 j i k) +lemma hk27_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_21 j i k).Contains (fullFactor false 27 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 21 (power27_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha27_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24583),(-24582)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-51553370694),(-51553370693)⟩⟩,⟨⟨257142289286047,257142289286048⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨(-11721879376103578832),(-11721879376103578814)⟩,⟨(-9),8⟩⟩,⟨⟨(-62),130⟩,⟨(-539266466260812849058),(-539266466260812848830)⟩⟩] +lemma ha27_0_21_eq (j : Fin 7) : ha27_0_21 j = ((ha27_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha27_0_21_contains (j : Fin 7) : (ha27_0_21 j).Contains (fullFactor false 27 21 ((j.val:ℝ)/6)) := by + rw [ha27_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_20 j) false 27 20 j (ha27_0_20_contains j) +noncomputable def hk27_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_22 j i k) +lemma hk27_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_22 j i k).Contains (fullFactor false 27 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 22 (power27_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha27_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-586),(-585)⟩⟩,⟨⟨2453934706,2453934707⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨18359916521552,18359916521553⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),2⟩,⟨(-1394900383872451221),(-1394900383872451218)⟩⟩,⟨⟨77007071306013533782,77007071306013533816⟩,⟨(-9),19⟩⟩] +lemma ha27_0_22_eq (j : Fin 7) : ha27_0_22 j = ((ha27_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha27_0_22_contains (j : Fin 7) : (ha27_0_22 j).Contains (fullFactor false 27 22 ((j.val:ℝ)/6)) := by + rw [ha27_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_21 j) false 27 21 j (ha27_0_21_contains j) +noncomputable def hk27_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_23 j i k) +lemma hk27_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_23 j i k).Contains (fullFactor false 27 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 23 (power27_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha27_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨13,14⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨111728452,111728453⟩⟩,⟨⟨(-1253899540536),(-1253899540535)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨158775681103741856,158775681103741858⟩,⟨(-1),1⟩⟩,⟨⟨(-3),2⟩,⟨10518471716932064452,10518471716932064458⟩⟩] +lemma ha27_0_23_eq (j : Fin 7) : ha27_0_23 j = ((ha27_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha27_0_23_contains (j : Fin 7) : (ha27_0_23 j).Contains (fullFactor false 27 23 ((j.val:ℝ)/6)) := by + rw [ha27_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_22 j) false 27 22 j (ha27_0_22_contains j) +noncomputable def hk27_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_24 j i k) +lemma hk27_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_24 j i k).Contains (fullFactor false 27 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 24 (power27_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha27_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-4875074),(-4875073)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-82067533019),(-82067533018)⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨17319740045980248,17319740045980250⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha27_0_24_eq (j : Fin 7) : ha27_0_24 j = ((ha27_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha27_0_24_contains (j : Fin 7) : (ha27_0_24 j).Contains (fullFactor false 27 24 ((j.val:ℝ)/6)) := by + rw [ha27_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_23 j) false 27 23 j (ha27_0_23_contains j) +noncomputable def hk27_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_25 j i k) +lemma hk27_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_25 j i k).Contains (fullFactor false 27 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 25 (power27_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha27_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-204207),(-204206)⟩⟩,⟨⟨5156455176,5156455177⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨(-1813718936351217),(-1813718936351216)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha27_0_25_eq (j : Fin 7) : ha27_0_25 j = ((ha27_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha27_0_25_contains (j : Fin 7) : (ha27_0_25 j).Contains (fullFactor false 27 25 ((j.val:ℝ)/6)) := by + rw [ha27_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_24 j) false 27 24 j (ha27_0_24_contains j) +noncomputable def hk27_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_26 j i k) +lemma hk27_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_26 j i k).Contains (fullFactor false 27 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 26 (power27_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha27_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨8224,8225⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨311528494,311528495⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-182627118144798),(-182627118144797)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha27_0_26_eq (j : Fin 7) : ha27_0_26 j = ((ha27_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha27_0_26_contains (j : Fin 7) : (ha27_0_26 j).Contains (fullFactor false 27 26 ((j.val:ℝ)/6)) := by + rw [ha27_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_25 j) false 27 25 j (ha27_0_25_contains j) +noncomputable def hk27_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_27 j i k) +lemma hk27_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_27 j i k).Contains (fullFactor false 27 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 27 (power27_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha27_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨318,320⟩⟩,⟨⟨(-18123994),(-18123993)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨17708025083641,17708025083642⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha27_0_27_eq (j : Fin 7) : ha27_0_27 j = ((ha27_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha27_0_27_contains (j : Fin 7) : (ha27_0_27 j).Contains (fullFactor false 27 27 ((j.val:ℝ)/6)) := by + rw [ha27_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_26 j) false 27 26 j (ha27_0_26_contains j) +noncomputable def hk27_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_28 j i k) +lemma hk27_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_28 j i k).Contains (fullFactor false 27 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 28 (power27_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha27_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-12),(-11)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1016754),(-1016753)⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1655696473581,1655696473582⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha27_0_28_eq (j : Fin 7) : ha27_0_28 j = ((ha27_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha27_0_28_contains (j : Fin 7) : (ha27_0_28 j).Contains (fullFactor false 27 28 ((j.val:ℝ)/6)) := by + rw [ha27_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_27 j) false 27 27 j (ha27_0_27_contains j) +noncomputable def hk27_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_29 j i k) +lemma hk27_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_29 j i k).Contains (fullFactor false 27 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 29 (power27_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha27_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨55072,55073⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨(-149469076954),(-149469076953)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha27_0_29_eq (j : Fin 7) : ha27_0_29 j = ((ha27_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha27_0_29_contains (j : Fin 7) : (ha27_0_29 j).Contains (fullFactor false 27 29 ((j.val:ℝ)/6)) := by + rw [ha27_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_28 j) false 27 28 j (ha27_0_28_contains j) +noncomputable def hk27_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power27 j i k).conj.mul (mpower0_30 j i k) +lemma hk27_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk27_0_30 j i k).Contains (fullFactor false 27 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power27 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 30 (power27_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha27_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2883,2884⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-13043637614),(-13043637613)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha27_0_30_eq (j : Fin 7) : ha27_0_30 j = ((ha27_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha27_0_30_contains (j : Fin 7) : (ha27_0_30 j).Contains (fullFactor false 27 30 ((j.val:ℝ)/6)) := by + rw [ha27_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_0_29 j) false 27 29 j (ha27_0_29_contains j) +noncomputable def hk27_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_0 j i k) +lemma hk27_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_0 j i k).Contains (fullFactor true 27 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 0 (kernel27_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha27_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-946122032372),(-946122032369)⟩,⟨2344393842845,2344393842848⟩⟩,⟨⟨(-4914715484280113312030),(-4914715484280113277429)⟩,⟨(-4823446996496663396948),(-4823446996496663362281)⟩⟩,⟨⟨(-3163347492825092488356998232),(-3163347492825092453738357979)⟩,⟨(-5947311263201831421663297862),(-5947311263201831386929852948)⟩⟩] +lemma ha27_1_0_eq (j : Fin 7) : ha27_1_0 j = atomKernel27_0 j := by fin_cases j <;> decide +kernel +lemma ha27_1_0_contains (j : Fin 7) : (ha27_1_0 j).Contains (fullFactor true 27 0 ((j.val:ℝ)/6)) := by + rw [ha27_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel27_0_contains j +noncomputable def hk27_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_1 j i k) +lemma hk27_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_1 j i k).Contains (fullFactor true 27 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 1 (kernel27_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha27_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-30),11⟩,⟨(-31),10⟩⟩,⟨⟨(-6),21⟩,⟨(-19),11⟩⟩,⟨⟨12264786356508,12264786356528⟩,⟨818481221881,818481221900⟩⟩,⟨⟨(-16243750035431970811935),(-16243750035431970645865)⟩,⟨23475245713674834422464,23475245713674834588311⟩⟩,⟨⟨(-20881903462514637627417506508),(-20881903462514637495423423685)⟩,⟨12539676748978747560769434746,12539676748978747692340176601⟩⟩] +lemma ha27_1_1_eq (j : Fin 7) : ha27_1_1 j = ((ha27_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha27_1_1_contains (j : Fin 7) : (ha27_1_1 j).Contains (fullFactor true 27 1 ((j.val:ℝ)/6)) := by + rw [ha27_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_0 j) true 27 0 j (ha27_1_0_contains j) +noncomputable def hk27_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_2 j i k) +lemma hk27_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_2 j i k).Contains (fullFactor true 27 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 2 (kernel27_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha27_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-255),177⟩,⟨(-205),219⟩⟩,⟨⟨(-107),100⟩,⟨(-53),154⟩⟩,⟨⟨(-79),37⟩,⟨(-70),43⟩⟩,⟨⟨(-7402074394800),(-7402074394740)⟩,⟨(-28951735634038),(-28951735633976)⟩⟩,⟨⟨53671941643325120508479,53671941643325120905900⟩,⟨24913396934018834537390,24913396934018834935149⟩⟩,⟨⟨24601082153761121970449348705,24601082153761122220472829581⟩,⟨36525239988765613792927511352,36525239988765614043721044534⟩⟩] +lemma ha27_1_2_eq (j : Fin 7) : ha27_1_2 j = ((ha27_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha27_1_2_contains (j : Fin 7) : (ha27_1_2 j).Contains (fullFactor true 27 2 ((j.val:ℝ)/6)) := by + rw [ha27_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_1 j) true 27 1 j (ha27_1_1_contains j) +noncomputable def hk27_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_3 j i k) +lemma hk27_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_3 j i k).Contains (fullFactor true 27 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 3 (kernel27_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha27_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-707),924⟩,⟨(-779),840⟩⟩,⟨⟨(-256),440⟩,⟨(-425),271⟩⟩,⟨⟨(-155),148⟩,⟨(-104),201⟩⟩,⟨⟨(-40846641540932),(-40846641540805)⟩,⟨26023234417691,26023234417816⟩⟩,⟨⟨21325727650937897969276,21325727650937898604382⟩,⟨(-78937467174387176132642),(-78937467174387175497815)⟩⟩,⟨⟨42424721652547976666625516367,42424721652547976984293603254⟩,⟨(-31897871684604996148844397440),(-31897871684604995832098315828)⟩⟩] +lemma ha27_1_3_eq (j : Fin 7) : ha27_1_3 j = ((ha27_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha27_1_3_contains (j : Fin 7) : (ha27_1_3 j).Contains (fullFactor true 27 3 ((j.val:ℝ)/6)) := by + rw [ha27_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_2 j) true 27 2 j (ha27_1_2_contains j) +noncomputable def hk27_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_4 j i k) +lemma hk27_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_4 j i k).Contains (fullFactor true 27 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 4 (kernel27_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha27_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2495),2136⟩,⟨(-2469),2151⟩⟩,⟨⟨(-1089),665⟩,⟨(-901),853⟩⟩,⟨⟨(-238),367⟩,⟨(-332),272⟩⟩,⟨⟨45531070962301,45531070962495⟩,⟨37319141584397,37319141584592⟩⟩,⟨⟨(-84375684834499056560829),(-84375684834499055800368)⟩,⟨(-7881463737110887351982),(-7881463737110886591440)⟩⟩,⟨⟨(-30787569376714149173502672879),(-30787569376714148872547685384)⟩,⟨(-36801801054040890938650385258),(-36801801054040890636877656915)⟩⟩] +lemma ha27_1_4_eq (j : Fin 7) : ha27_1_4 j = ((ha27_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha27_1_4_contains (j : Fin 7) : (ha27_1_4 j).Contains (fullFactor true 27 4 ((j.val:ℝ)/6)) := by + rw [ha27_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_3 j) true 27 3 j (ha27_1_3_contains j) +noncomputable def hk27_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_5 j i k) +lemma hk27_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_5 j i k).Contains (fullFactor true 27 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 5 (kernel27_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha27_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5111),5425⟩,⟨(-4887),5641⟩⟩,⟨⟨(-1583),1951⟩,⟨(-1525),2009⟩⟩,⟨⟨(-547),413⟩,⟨(-529),432⟩⟩,⟨⟨20683645717876,20683645718116⟩,⟨(-53380971619739),(-53380971619500)⟩⟩,⟨⟨5445621449894507270751,5445621449894507999338⟩,⟨70050121121503144302193,70050121121503145030889⟩⟩,⟨⟨(-25422235342047785484843690583),(-25422235342047785255511306948)⟩,⟨23617022460446931986099165676,23617022460446932214858575723⟩⟩] +lemma ha27_1_5_eq (j : Fin 7) : ha27_1_5 j = ((ha27_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha27_1_5_contains (j : Fin 7) : (ha27_1_5 j).Contains (fullFactor true 27 5 ((j.val:ℝ)/6)) := by + rw [ha27_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_4 j) true 27 4 j (ha27_1_4_contains j) +noncomputable def hk27_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_6 j i k) +lemma hk27_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_6 j i k).Contains (fullFactor true 27 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 6 (kernel27_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha27_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-9960),10026⟩,⟨(-10570),9412⟩⟩,⟨⟨(-2910),3024⟩,⟨(-3324),2611⟩⟩,⟨⟨(-646),626⟩,⟨(-556),716⟩⟩,⟨⟨(-46327101376852),(-46327101376606)⟩,⟨(-2444503294417),(-2444503294171)⟩⟩,⟨⟨47056683949276816179125,47056683949276816760961⟩,⟨(-11930604814499768636747),(-11930604814499768055088)⟩⟩,⟨⟨15009216909272499496012443215,15009216909272499640913335223⟩,⟨14560951043451159946126790752,14560951043451160091357866755⟩⟩] +lemma ha27_1_6_eq (j : Fin 7) : ha27_1_6 j = ((ha27_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha27_1_6_contains (j : Fin 7) : (ha27_1_6 j).Contains (fullFactor true 27 6 ((j.val:ℝ)/6)) := by + rw [ha27_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_5 j) true 27 5 j (ha27_1_5_contains j) +noncomputable def hk27_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_7 j i k) +lemma hk27_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_7 j i k).Contains (fullFactor true 27 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 7 (kernel27_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha27_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-16595),15907⟩,⟨(-15633),16866⟩⟩,⟨⟨(-4573),3968⟩,⟨(-4062),4479⟩⟩,⟨⟨(-659),784⟩,⟨(-747),697⟩⟩,⟨⟨8415499052594,8415499052811⟩,⟨31105000244660,31105000244877⟩⟩,⟨⟨(-11697473159557446073521),(-11697473159557445675477)⟩,⟨(-26262528493742091003563),(-26262528493742090605379)⟩⟩,⟨⟨7108806052104249030070971144,7108806052104249108902122835⟩,⟨(-8133261670497586310531484572),(-8133261670497586231861106979)⟩⟩] +lemma ha27_1_7_eq (j : Fin 7) : ha27_1_7 j = ((ha27_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha27_1_7_contains (j : Fin 7) : (ha27_1_7 j).Contains (fullFactor true 27 7 ((j.val:ℝ)/6)) := by + rw [ha27_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_6 j) true 27 6 j (ha27_1_6_contains j) +noncomputable def hk27_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_8 j i k) +lemma hk27_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_8 j i k).Contains (fullFactor true 27 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 8 (kernel27_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha27_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-22509),23741⟩,⟨(-23555),22694⟩⟩,⟨⟨(-5058),5698⟩,⟨(-5312),5444⟩⟩,⟨⟨(-755),679⟩,⟨(-748),686⟩⟩,⟨⟨16369035532782,16369035532949⟩,⟨(-10751834706917),(-10751834706749)⟩⟩,⟨⟨(-12381451793633135993903),(-12381451793633135755475)⟩,⟨8285558982791051397800,8285558982791051636149⟩⟩,⟨⟨(-3838033003297572698839076306),(-3838033003297572661466463003)⟩,⟨(-3017859241834758516627504289),(-3017859241834758479187490069)⟩⟩] +lemma ha27_1_8_eq (j : Fin 7) : ha27_1_8 j = ((ha27_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha27_1_8_contains (j : Fin 7) : (ha27_1_8 j).Contains (fullFactor true 27 8 ((j.val:ℝ)/6)) := by + rw [ha27_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_7 j) true 27 7 j (ha27_1_7_contains j) +noncomputable def hk27_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_9 j i k) +lemma hk27_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_9 j i k).Contains (fullFactor true 27 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 9 (kernel27_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha27_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-29954),28549⟩,⟨(-29139),29363⟩⟩,⟨⟨(-6157),5883⟩,⟨(-6239),5801⟩⟩,⟨⟨(-639),627⟩,⟨(-602),664⟩⟩,⟨⟨(-8275364874283),(-8275364874167)⟩,⟨(-6592433908578),(-6592433908463)⟩⟩,⟨⟨4729920017002173327627,4729920017002173454493⟩,⟨4971815004102221930309,4971815004102222057210⟩⟩,⟨⟨(-1130765330366744530449225351),(-1130765330366744514643510993)⟩,⟨1602878962634490966017942454,1602878962634490981799013112⟩⟩] +lemma ha27_1_9_eq (j : Fin 7) : ha27_1_9 j = ((ha27_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha27_1_9_contains (j : Fin 7) : (ha27_1_9 j).Contains (fullFactor true 27 9 ((j.val:ℝ)/6)) := by + rw [ha27_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_8 j) true 27 8 j (ha27_1_8_contains j) +noncomputable def hk27_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_10 j i k) +lemma hk27_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_10 j i k).Contains (fullFactor true 27 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 10 (kernel27_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha27_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-32720),33881⟩,⟨(-33125),33476⟩⟩,⟨⟨(-6110),6020⟩,⟨(-5886),6243⟩⟩,⟨⟨(-485),521⟩,⟨(-509),497⟩⟩,⟨⟨(-1791684584454),(-1791684584382)⟩,⟨4822198360220,4822198360292⟩⟩,⟨⟨1698002964756471452403,1698002964756471513190⟩,⟨(-2282479785836676778143),(-2282479785836676717369)⟩⟩,⟨⟨600036526949021140589603125,600036526949021146586888008⟩,⟨378224509262836843606915678,378224509262836849612122280⟩⟩] +lemma ha27_1_10_eq (j : Fin 7) : ha27_1_10 j = ((ha27_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha27_1_10_contains (j : Fin 7) : (ha27_1_10 j).Contains (fullFactor true 27 10 ((j.val:ℝ)/6)) := by + rw [ha27_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_9 j) true 27 9 j (ha27_1_9_contains j) +noncomputable def hk27_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_11 j i k) +lemma hk27_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_11 j i k).Contains (fullFactor true 27 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 11 (kernel27_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha27_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34809),34119⟩,⟨(-34782),34145⟩⟩,⟨⟨(-5451),5658⟩,⟨(-5613),5496⟩⟩,⟨⟨(-371),356⟩,⟨(-370),357⟩⟩,⟨⟨2272140466384,2272140466425⟩,⟨88201273073,88201273114⟩⟩,⟨⟨(-956410697087398034270),(-956410697087398007803)⟩,⟨(-484480252286519094184),(-484480252286519067714)⟩⟩,⟨⟨113918880017806356639463334,113918880017806358713626403⟩,⟨(-203433455236507935165474206),(-203433455236507933093556687)⟩⟩] +lemma ha27_1_11_eq (j : Fin 7) : ha27_1_11 j = ((ha27_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha27_1_11_contains (j : Fin 7) : (ha27_1_11 j).Contains (fullFactor true 27 11 ((j.val:ℝ)/6)) := by + rw [ha27_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_10 j) true 27 10 j (ha27_1_10_contains j) +noncomputable def hk27_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_12 j i k) +lemma hk27_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_12 j i k).Contains (fullFactor true 27 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 12 (kernel27_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha27_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32574),32817⟩,⟨(-32385),33006⟩⟩,⟨⟨(-4731),4596⟩,⟨(-4684),4643⟩⟩,⟨⟨(-242),240⟩,⟨(-236),246⟩⟩,⟨⟨(-252967816419),(-252967816397)⟩,⟨(-885910064700),(-885910064678)⟩⟩,⟨⟨(-108803365329629026293),(-108803365329629015727)⟩,⟨354036892833176947317,354036892833176957883⟩⟩,⟨⟨(-62999536180746694972691122),(-62999536180746694316555532)⟩,⟨(-31097054985528417558369122),(-31097054985528416901674224)⟩⟩] +lemma ha27_1_12_eq (j : Fin 7) : ha27_1_12 j = ((ha27_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha27_1_12_contains (j : Fin 7) : (ha27_1_12 j).Contains (fullFactor true 27 12 ((j.val:ℝ)/6)) := by + rw [ha27_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_11 j) true 27 11 j (ha27_1_11_contains j) +noncomputable def hk27_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_13 j i k) +lemma hk27_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_13 j i k).Contains (fullFactor true 27 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 13 (kernel27_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha27_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28615),28649⟩,⟨(-28850),28414⟩⟩,⟨⟨(-3597),3632⟩,⟨(-3580),3649⟩⟩,⟨⟨(-145),150⟩,⟨(-148),147⟩⟩,⟨⟨(-285350654931),(-285350654920)⟩,⟨193167547318,193167547329⟩⟩,⟨⟨117152021078031221078,117152021078031224972⟩,⟨15011076187391322393,15011076187391326287⟩⟩,⟨⟨(-7727895466708578649946224),(-7727895466708578458027588)⟩,⟨17948627991027455320342923,17948627991027455512141019⟩⟩] +lemma ha27_1_13_eq (j : Fin 7) : ha27_1_13 j = ((ha27_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha27_1_13_contains (j : Fin 7) : (ha27_1_13 j).Contains (fullFactor true 27 13 ((j.val:ℝ)/6)) := by + rw [ha27_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_12 j) true 27 12 j (ha27_1_12_contains j) +noncomputable def hk27_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_14 j i k) +lemma hk27_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_14 j i k).Contains (fullFactor true 27 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 14 (kernel27_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha27_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23350),23215⟩,⟨(-23168),23397⟩⟩,⟨⟨(-2595),2608⟩,⟨(-2620),2583⟩⟩,⟨⟨(-85),83⟩,⟨(-85),83⟩⟩,⟨⟨94631424214,94631424219⟩,⟨73257089493,73257089499⟩⟩,⟨⟨(-1513290604448923457),(-1513290604448922123)⟩,⟨(-34940933155705711228),(-34940933155705709894)⟩⟩,⟨⟨4733146848865016657736977,4733146848865016709796695⟩,⟨1752525548301550207148789,1752525548301550259230027⟩⟩] +lemma ha27_1_14_eq (j : Fin 7) : ha27_1_14 j = ((ha27_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha27_1_14_contains (j : Fin 7) : (ha27_1_14 j).Contains (fullFactor true 27 14 ((j.val:ℝ)/6)) := by + rw [ha27_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_13 j) true 27 13 j (ha27_1_13_contains j) +noncomputable def hk27_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_15 j i k) +lemma hk27_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_15 j i k).Contains (fullFactor true 27 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 15 (kernel27_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha27_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17608),17733⟩,⟨(-17712),17629⟩⟩,⟨⟨(-1756),1739⟩,⟨(-1744),1751⟩⟩,⟨⟨(-45),45⟩,⟨(-44),45⟩⟩,⟨⟨13003108156,13003108159⟩,⟨(-36547117406),(-36547117403)⟩⟩,⟨⟨(-9445215840435310910),(-9445215840435310483)⟩,⟨2052754355442755580,2052754355442756007⟩⟩,⟨⟨362643768628142655287578,362643768628142668478587⟩,⟨(-1161372941066681208714626),(-1161372941066681195526364)⟩⟩] +lemma ha27_1_15_eq (j : Fin 7) : ha27_1_15 j = ((ha27_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha27_1_15_contains (j : Fin 7) : (ha27_1_15 j).Contains (fullFactor true 27 15 ((j.val:ℝ)/6)) := by + rw [ha27_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_14 j) true 27 14 j (ha27_1_14_contains j) +noncomputable def hk27_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_16 j i k) +lemma hk27_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_16 j i k).Contains (fullFactor true 27 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 16 (kernel27_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha27_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12613),12534⟩,⟨(-12568),12579⟩⟩,⟨⟨(-1097),1104⟩,⟨(-1099),1102⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-11784476968),(-11784476966)⟩,⟨(-293269306),(-293269304)⟩⟩,⟨⟨939901395534247847,939901395534247976⟩,⟨2321296101448219740,2321296101448219869⟩⟩,⟨⟨(-266365172967058666868116),(-266365172967058663736012)⟩,⟨(-68215074928604220346403),(-68215074928604217214255)⟩⟩] +lemma ha27_1_16_eq (j : Fin 7) : ha27_1_16 j = ((ha27_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha27_1_16_contains (j : Fin 7) : (ha27_1_16 j).Contains (fullFactor true 27 16 ((j.val:ℝ)/6)) := by + rw [ha27_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_15 j) true 27 15 j (ha27_1_15_contains j) +noncomputable def hk27_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_17 j i k) +lemma hk27_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_17 j i k).Contains (fullFactor true 27 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 17 (kernel27_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha27_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8401),8439⟩,⟨(-8414),8427⟩⟩,⟨⟨(-653),652⟩,⟨(-654),651⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨970751895,970751897⟩,⟨3228739047,3228739048⟩⟩,⟨⟨518894381187749601,518894381187749638⟩,⟨(-322039763790166568),(-322039763790166530)⟩⟩,⟨⟨(-11547654698470252306706),(-11547654698470251606744)⟩,⟨57332973457403290230006,57332973457403290930087⟩⟩] +lemma ha27_1_17_eq (j : Fin 7) : ha27_1_17 j = ((ha27_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha27_1_17_contains (j : Fin 7) : (ha27_1_17 j).Contains (fullFactor true 27 17 ((j.val:ℝ)/6)) := by + rw [ha27_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_16 j) true 27 16 j (ha27_1_16_contains j) +noncomputable def hk27_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_18 j i k) +lemma hk27_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_18 j i k).Contains (fullFactor true 27 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 18 (kernel27_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha27_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5333),5319⟩,⟨(-5333),5319⟩⟩,⟨⟨(-366),365⟩,⟨(-365),366⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨746983575,746983577⟩,⟨(-520975214),(-520975212)⟩⟩,⟨⟨(-93393760977968894),(-93393760977968883)⟩,⟨(-105167940671800377),(-105167940671800366)⟩⟩,⟨⟨11622177882178536833071,11622177882178536980856⟩,⟨1718515393317336430833,1718515393317336578567⟩⟩] +lemma ha27_1_18_eq (j : Fin 7) : ha27_1_18 j = ((ha27_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha27_1_18_contains (j : Fin 7) : (ha27_1_18 j).Contains (fullFactor true 27 18 ((j.val:ℝ)/6)) := by + rw [ha27_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_17 j) true 27 17 j (ha27_1_17_contains j) +noncomputable def hk27_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_19 j i k) +lemma hk27_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_19 j i k).Contains (fullFactor true 27 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 19 (kernel27_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha27_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3190),3193⟩,⟨(-3187),3196⟩⟩,⟨⟨(-194),195⟩,⟨(-194),194⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-186255066),(-186255064)⟩,⟨(-140083838),(-140083836)⟩⟩,⟨⟨(-19150761848269666),(-19150761848269662)⟩,⟨23979551162709931,23979551162709935⟩⟩,⟨⟨211750974274149593096,211750974274149622636⟩,⟨(-2225825176695200406198),(-2225825176695200376643)⟩⟩] +lemma ha27_1_19_eq (j : Fin 7) : ha27_1_19 j = ((ha27_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha27_1_19_contains (j : Fin 7) : (ha27_1_19 j).Contains (fullFactor true 27 19 ((j.val:ℝ)/6)) := by + rw [ha27_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_18 j) true 27 18 j (ha27_1_18_contains j) +noncomputable def hk27_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_20 j i k) +lemma hk27_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_20 j i k).Contains (fullFactor true 27 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 20 (kernel27_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha27_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1819),1815⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-18247151),(-18247149)⟩,⟨53638666,53638668⟩⟩,⟨⟨5572577170113712,5572577170113714⟩,⟨3067380642143704,3067380642143706⟩⟩,⟨⟨(-403863693054580048447),(-403863693054580042831)⟩,⟨(-17334381147100334316),(-17334381147100328704)⟩⟩] +lemma ha27_1_20_eq (j : Fin 7) : ha27_1_20 j = ((ha27_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha27_1_20_contains (j : Fin 7) : (ha27_1_20 j).Contains (fullFactor true 27 20 ((j.val:ℝ)/6)) := by + rw [ha27_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_19 j) true 27 19 j (ha27_1_19_contains j) +noncomputable def hk27_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_21 j i k) +lemma hk27_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_21 j i k).Contains (fullFactor true 27 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 21 (kernel27_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha27_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-986),985⟩,⟨(-985),986⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨13117190,13117191⟩,⟨143806,143807⟩⟩,⟨⟨409826848365942,409826848365943⟩,⟨(-1186952336854351),(-1186952336854350)⟩⟩,⟨⟨630473262925210382,630473262925211399⟩,⟨69600821264595356753,69600821264595357770⟩⟩] +lemma ha27_1_21_eq (j : Fin 7) : ha27_1_21 j = ((ha27_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha27_1_21_contains (j : Fin 7) : (ha27_1_21 j).Contains (fullFactor true 27 21 ((j.val:ℝ)/6)) := by + rw [ha27_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_20 j) true 27 20 j (ha27_1_20_contains j) +noncomputable def hk27_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_22 j i k) +lemma hk27_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_22 j i k).Contains (fullFactor true 27 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 22 (kernel27_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha27_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-510),511⟩,⟨(-511),510⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-873311),(-873310)⟩,⟨(-2764510),(-2764508)⟩⟩,⟨⟨(-233531581510427),(-233531581510425)⟩,⟨(-38103976842093),(-38103976842092)⟩⟩,⟨⟨11418726900719557094,11418726900719557271⟩,⟨(-697537955436855816),(-697537955436855639)⟩⟩] +lemma ha27_1_22_eq (j : Fin 7) : ha27_1_22 j = ((ha27_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha27_1_22_contains (j : Fin 7) : (ha27_1_22 j).Contains (fullFactor true 27 22 ((j.val:ℝ)/6)) := by + rw [ha27_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_21 j) true 27 21 j (ha27_1_21_contains j) +noncomputable def hk27_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_23 j i k) +lemma hk27_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_23 j i k).Contains (fullFactor true 27 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 23 (kernel27_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha27_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-497767),(-497766)⟩,⟨357560,357562⟩⟩,⟨⟨383106240041,383106240042⟩,⟨42647063809782,42647063809784⟩⟩,⟨⟨(-202737407332443963),(-202737407332443933)⟩,⟨(-1787058309774906797),(-1787058309774906767)⟩⟩] +lemma ha27_1_23_eq (j : Fin 7) : ha27_1_23 j = ((ha27_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha27_1_23_contains (j : Fin 7) : (ha27_1_23 j).Contains (fullFactor true 27 23 ((j.val:ℝ)/6)) := by + rw [ha27_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_22 j) true 27 22 j (ha27_1_22_contains j) +noncomputable def hk27_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_24 j i k) +lemma hk27_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_24 j i k).Contains (fullFactor true 27 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 24 (kernel27_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha27_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨100259,100260⟩,⟨73243,73244⟩⟩,⟨⟨7248169049177,7248169049178⟩,⟨(-1316735177529),(-1316735177528)⟩⟩,⟨⟨(-267293558589669585),(-267293558589669579)⟩,⟨44485499562967922,44485499562967928⟩⟩] +lemma ha27_1_24_eq (j : Fin 7) : ha27_1_24 j = ((ha27_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha27_1_24_contains (j : Fin 7) : (ha27_1_24 j).Contains (fullFactor true 27 24 ((j.val:ℝ)/6)) := by + rw [ha27_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_23 j) true 27 23 j (ha27_1_23_contains j) +noncomputable def hk27_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_25 j i k) +lemma hk27_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_25 j i k).Contains (fullFactor true 27 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 25 (kernel27_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha27_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨7458,7459⟩,⟨(-22968),(-22967)⟩⟩,⟨⟨(-419366999004),(-419366999003)⟩,⟨(-1147341323395),(-1147341323394)⟩⟩,⟨⟨8433156210537254,8433156210537256⟩,⟨38274032342484034,38274032342484035⟩⟩] +lemma ha27_1_25_eq (j : Fin 7) : ha27_1_25 j = ((ha27_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha27_1_25_contains (j : Fin 7) : (ha27_1_25 j).Contains (fullFactor true 27 25 ((j.val:ℝ)/6)) := by + rw [ha27_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_24 j) true 27 24 j (ha27_1_24_contains j) +noncomputable def hk27_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_26 j i k) +lemma hk27_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_26 j i k).Contains (fullFactor true 27 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 26 (kernel27_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha27_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-4516),(-4515)⟩,⟨13,14⟩⟩,⟨⟨(-168917948981),(-168917948979)⟩,⟨96973715883,96973715884⟩⟩,⟨⟨5254807898644157,5254807898644158⟩,⟨(-1447661157240500),(-1447661157240499)⟩⟩] +lemma ha27_1_26_eq (j : Fin 7) : ha27_1_26 j = ((ha27_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha27_1_26_contains (j : Fin 7) : (ha27_1_26 j).Contains (fullFactor true 27 26 ((j.val:ℝ)/6)) := by + rw [ha27_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_25 j) true 27 25 j (ha27_1_25_contains j) +noncomputable def hk27_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_27 j i k) +lemma hk27_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_27 j i k).Contains (fullFactor true 27 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 27 (kernel27_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha27_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨255,256⟩,⟨771,773⟩⟩,⟨⟨19079114801,19079114802⟩,⟨23028916712,23028916713⟩⟩,⟨⟨(-230157593987875),(-230157593987874)⟩,⟨(-692719109590016),(-692719109590014)⟩⟩] +lemma ha27_1_27_eq (j : Fin 7) : ha27_1_27 j = ((ha27_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha27_1_27_contains (j : Fin 7) : (ha27_1_27 j).Contains (fullFactor true 27 27 ((j.val:ℝ)/6)) := by + rw [ha27_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_26 j) true 27 26 j (ha27_1_26_contains j) +noncomputable def hk27_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_28 j i k) +lemma hk27_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_28 j i k).Contains (fullFactor true 27 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 28 (kernel27_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha27_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨113,114⟩,⟨(-85),(-83)⟩⟩,⟨⟨2880086627,2880086628⟩,⟨(-3362971935),(-3362971933)⟩⟩,⟨⟨(-87793188528505),(-87793188528504)⟩,⟨34327830552382,34327830552384⟩⟩] +lemma ha27_1_28_eq (j : Fin 7) : ha27_1_28 j = ((ha27_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha27_1_28_contains (j : Fin 7) : (ha27_1_28 j).Contains (fullFactor true 27 28 ((j.val:ℝ)/6)) := by + rw [ha27_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_27 j) true 27 27 j (ha27_1_27_contains j) +noncomputable def hk27_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_29 j i k) +lemma hk27_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_29 j i k).Contains (fullFactor true 27 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 29 (kernel27_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha27_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-20),(-19)⟩,⟨(-14),(-13)⟩⟩,⟨⟨(-543696395),(-543696394)⟩,⟨(-324049946),(-324049945)⟩⟩,⟨⟨4842893498021,4842893498023⟩,⟨10709573721045,10709573721046⟩⟩] +lemma ha27_1_29_eq (j : Fin 7) : ha27_1_29 j = ((ha27_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha27_1_29_contains (j : Fin 7) : (ha27_1_29 j).Contains (fullFactor true 27 29 ((j.val:ℝ)/6)) := by + rw [ha27_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_28 j) true 27 28 j (ha27_1_28_contains j) +noncomputable def hk27_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel27_0 j i k).mul (mpower1_30 j i k) +lemma hk27_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk27_1_30 j i k).Contains (fullFactor true 27 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk27_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel27_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 27 30 (kernel27_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha27_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),0⟩,⟨3,4⟩⟩,⟨⟨(-31363729),(-31363728)⟩,⟨81646357,81646358⟩⟩,⟨⟨1258772773795,1258772773796⟩,⟨(-649959570039),(-649959570038)⟩⟩] +lemma ha27_1_30_eq (j : Fin 7) : ha27_1_30 j = ((ha27_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha27_1_30_contains (j : Fin 7) : (ha27_1_30 j).Contains (fullFactor true 27 30 ((j.val:ℝ)/6)) := by + rw [ha27_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha27_1_29 j) true 27 29 j (ha27_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders28.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders28.lean new file mode 100644 index 0000000000000000000000000000000000000000..5a9f4576dca5b6fe5bc95003ce8d335c1d9de57a --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders28.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers30 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues30 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk28_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_0 j i k) +lemma hk28_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_0 j i k).Contains (fullFactor false 28 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 0 (power28_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha28_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999665,1000000000000000000000000000447⟩,⟨(-447),447⟩⟩,⟨⟨(-500000000000000000081972379005),(-499999999999999999937075927107)⟩,⟨866025403784438646686030283432,866025403784438646830418513450⟩⟩,⟨⟨(-500000000000000000178469317254),(-499999999999999999783434070433)⟩,⟨(-866025403784438646972424332367),(-866025403784438646577017098533)⟩⟩,⟨⟨999999999999999999908533101065,1000000000000000000091466898963⟩,⟨(-58474264911),124459533015⟩⟩,⟨⟨(-500000000000000000578565263118),(-499999999999999999497627961551)⟩,⟨866025403784438646201395401196,866025403784438647282060761459⟩⟩,⟨⟨(-500000000000000000632465456545),(-499999999999999999272293012623)⟩,⟨(-866025403784438647471438207249),(-866025403784438646110995857621)⟩⟩,⟨⟨999999999999999999816510462105,1000000000000000000183489538007⟩,⟨(-117504269735),249474806167⟩⟩] +lemma ha28_0_0_eq (j : Fin 7) : ha28_0_0 j = ((atomPoints j).direct.powBin 7 28).conj := by fin_cases j <;> decide +kernel +lemma ha28_0_0_contains (j : Fin 7) : (ha28_0_0 j).Contains (fullFactor false 28 0 ((j.val:ℝ)/6)) := by + rw [ha28_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 28) ((j.val:ℝ)/6) 28 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 28 (by norm_num)) +noncomputable def hk28_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_1 j i k) +lemma hk28_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_1 j i k).Contains (fullFactor false 28 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 1 (power28_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha28_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-453449841058554462684503000348),(-453449841058554462607458124222)⟩,⟨(-261799387799149436582087303948),(-261799387799149436505386365809)⟩⟩,⟨⟨906899682117108925100757908173,906899682117108925517714146520⟩,⟨(-523598775598298873265225965327),(-523598775598298872849879355550)⟩⟩,⟨⟨(-195500577295),91851160535⟩,⟨1570796326794896619086324131129,1570796326794896619378675868915⟩⟩,⟨⟨(-1813799364234217851683929313649),(-1813799364234217849414815573092)⟩,⟨(-1047197551196597747368410920157),(-1047197551196597745101167796425)⟩⟩,⟨⟨2267249205292772311531854014714,2267249205292772315100700635769⟩,⟨(-1308996938995747184351624026611),(-1308996938995747180786534228741)⟩⟩,⟨⟨(-783748218310),369150550565⟩,⟨3141592653589793237883550615738,3141592653589793239046449384614⟩⟩] +lemma ha28_0_1_eq (j : Fin 7) : ha28_0_1 j = ((ha28_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha28_0_1_contains (j : Fin 7) : (ha28_0_1 j).Contains (fullFactor false 28 1 ((j.val:ℝ)/6)) := by + rw [ha28_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_0 j) false 28 0 j (ha28_0_0_contains j) +noncomputable def hk28_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_2 j i k) +lemma hk28_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_2 j i k).Contains (fullFactor false 28 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 2 (power28_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha28_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨68538919452009434844276463328,68538919452009434864574888134⟩,⟨(-118712890786751174417635741025),(-118712890786751174397087564753)⟩⟩,⟨⟨274155677808037739292862278602,274155677808037739511209919558⟩,⟨474851563147004697528577091825,474851563147004697748406367174⟩⟩,⟨⟨(-1233700550136169827472932011816),(-1233700550136169827239392503075)⟩,⟨(-153545794351),72139732791⟩⟩,⟨⟨1096622711232150956544606174393,1096622711232150958922348280040⟩,⟨(-1899406252588018791672734149423),(-1899406252588018789290477799040)⟩⟩,⟨⟨1713472986300235868828736451777,1713472986300235873500882238350⟩,⟨2967822269668779357956577209225,2967822269668779362637633383625⟩⟩,⟨⟨(-4934802200544679310345841568918),(-4934802200544679308503456491064)⟩,⟨(-1231108822454),579860328862⟩⟩] +lemma ha28_0_2_eq (j : Fin 7) : ha28_0_2 j = ((ha28_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha28_0_2_contains (j : Fin 7) : (ha28_0_2 j).Contains (fullFactor false 28 2 ((j.val:ℝ)/6)) := by + rw [ha28_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_1 j) false 28 1 j (ha28_0_1_contains j) +noncomputable def hk28_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_3 j i k) +lemma hk28_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_3 j i k).Contains (fullFactor false 28 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 3 (power28_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha28_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20719308087892496640504348357,20719308087892496644156633276⟩,⟨11962298101967523214311714967,11962298101967523217892535604⟩⟩,⟨⟨(-165754464703139973180432521216),(-165754464703139973103170015424)⟩,⟨95698384815740185685087164696,95698384815740185761609487090⟩⟩,⟨⟨(-37772275762),80396389921⟩,⟨(-645964097506246253719378827787),(-645964097506246253595041659371)⟩⟩,⟨⟨1326035717625119784250217887610,1326035717625119785917567468026⟩,⟨765587078525921485043078389728,765587078525921486705492469363⟩⟩,⟨⟨(-2589913510986562082436596326071),(-2589913510986562078343360239613)⟩,⟨1495287262745940399800881521975,1495287262745940403882857524606⟩⟩,⟨⟨(-607228316421),1289214144131⟩,⟨(-5167712780049970030230577190131),(-5167712780049970028284786707572)⟩⟩] +lemma ha28_0_3_eq (j : Fin 7) : ha28_0_3 j = ((ha28_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha28_0_3_contains (j : Fin 7) : (ha28_0_3 j).Contains (fullFactor false 28 3 ((j.val:ℝ)/6)) := by + rw [ha28_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_2 j) false 28 2 j (ha28_0_2_contains j) +noncomputable def hk28_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_4 j i k) +lemma hk28_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_4 j i k).Contains (fullFactor false 28 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 4 (power28_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha28_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1565861159883012430126711159),(-1565861159883012429652998541)⟩,⟨2712151086516110563143509538,2712151086516110563630225562⟩⟩,⟨⟨(-25053778558128198886862604375),(-25053778558128198866749358564)⟩,⟨(-43394417384257769025199173665),(-43394417384257769004833768227)⟩⟩,⟨⟨253669507901048013612507237786,253669507901048013662141784767⟩,⟨(-14833138006),31571588494⟩⟩,⟨⟨(-400860456930051182510566957331),(-400860456930051181638853002231)⟩,⟨694310678148124303776196521192,694310678148124304651428779524⟩⟩,⟨⟨(-978663224926882769906689134918),(-978663224926882767231926906869)⟩,⟨(-1695094429072569103523575777411),(-1695094429072569100839163370380)⟩⟩,⟨⟨4058712126416768217426622403947,4058712126416768218967761957256⟩,⟨(-476916004480),1012546421027⟩⟩] +lemma ha28_0_4_eq (j : Fin 7) : ha28_0_4 j = ((ha28_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha28_0_4_contains (j : Fin 7) : (ha28_0_4 j).Contains (fullFactor false 28 4 ((j.val:ℝ)/6)) := by + rw [ha28_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_3 j) false 28 3 j (ha28_0_3_contains j) +noncomputable def hk28_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_5 j i k) +lemma hk28_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_5 j i k).Contains (fullFactor false 28 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 5 (power28_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha28_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-284015797627486289512422388),(-284015797627486289460549554)⟩,⟨(-163976597214335483815851467),(-163976597214335483765722443)⟩⟩,⟨⟨9088505524079561261593546636,9088505524079561265887796790⟩,⟨(-5247251110858735483119934246),(-5247251110858735478890723374)⟩⟩,⟨⟨(-9918507048),4659967739⟩,⟨79692626246167045112881039231,79692626246167045128727861556⟩⟩,⟨⟨(-290832176770545960612392863428),(-290832176770545960244850684794)⟩,⟨(-167912035547479535594199745229),(-167912035547479535228522576968)⟩⟩,⟨⟨887549367585894653974891180564,887549367585894655383271387470⟩,⟨(-512426866294798387488710716607),(-512426866294798386086577383608)⟩⟩,⟨⟨(-636201679544),299655163211⟩,⟨2550164039877345443377520430689,2550164039877345444353964394709⟩⟩] +lemma ha28_0_5_eq (j : Fin 7) : ha28_0_5 j = ((ha28_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha28_0_5_contains (j : Fin 7) : (ha28_0_5 j).Contains (fullFactor false 28 5 ((j.val:ℝ)/6)) := by + rw [ha28_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_4 j) false 28 4 j (ha28_0_4_contains j) +noncomputable def hk28_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_6 j i k) +lemma hk28_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_6 j i k).Contains (fullFactor false 28 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 6 (power28_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha28_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨14309657588033580843841342,14309657588033580848261475⟩,⟨(-24785053981387676529161456),(-24785053981387676524555803)⟩⟩,⟨⟨915818085634149173724429956,915818085634149174465481641⟩,⟨1586243454808811297371898951,1586243454808811298126436163⟩⟩,⟨⟨(-20863480763352960875253089173),(-20863480763352960871037990267)⟩,⟨(-2596659074),1219976702⟩⟩,⟨⟨58612357480585547084859977557,58612357480585547212691958197⟩,⟨(-101519581107763923116388956524),(-101519581107763922987769386518)⟩⟩,⟨⟨223588399813024700387745484922,223588399813024701000253269224⟩,⟨387266468459182445439042380488,387266468459182446054796881205⟩⟩,⟨⟨(-1335262768854589496139072110843),(-1335262768854589495623556973441)⟩,⟨(-333114420443),156899076559⟩⟩] +lemma ha28_0_6_eq (j : Fin 7) : ha28_0_6 j = ((ha28_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha28_0_6_contains (j : Fin 7) : (ha28_0_6 j).Contains (fullFactor false 28 6 ((j.val:ℝ)/6)) := by + rw [ha28_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_5 j) false 28 5 j (ha28_0_5_contains j) +noncomputable def hk28_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_7 j i k) +lemma hk28_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_7 j i k).Contains (fullFactor false 28 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 7 (power28_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha28_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1853917702541761442080324,1853917702541761442430728⟩,⟨1070359884617898513961750,1070359884617898514295784⟩⟩,⟨⟨(-237301465925345464670044497),(-237301465925345464556410639)⟩,⟨137006065231091009745004392,137006065231091009856301570⟩⟩,⟨⟨(-273762132),582688934⟩,⟨(-4681754135318688101190431783),(-4681754135318688100229663313)⟩⟩,⟨⟨30374587638444219450046174469,30374587638444219488625745142⟩,⟨17536776349579649237336326611,17536776349579649275639387073⟩⟩,⟨⟨(-144837320511075112797107148009),(-144837320511075112566354471751)⟩,⟨83621865985773321292081019427,83621865985773321521424571741⟩⟩,⟨⟨(-70416140897),149501402296⟩,⟨(-599264529320792077007521171588),(-599264529320792076774251000706)⟩⟩] +lemma ha28_0_7_eq (j : Fin 7) : ha28_0_7 j = ((ha28_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha28_0_7_contains (j : Fin 7) : (ha28_0_7 j).Contains (fullFactor false 28 7 ((j.val:ℝ)/6)) := by + rw [ha28_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_6 j) false 28 6 j (ha28_0_6_contains j) +noncomputable def hk28_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_8 j i k) +lemma hk28_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_8 j i k).Contains (fullFactor false 28 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 8 (power28_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha28_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-70054890629433514739343),(-70054890629433514717256)⟩,⟨121338629888859693702888,121338629888859693726209⟩⟩,⟨⟨(-17934052001134979776732702),(-17934052001134979762106849)⟩,⟨(-31062689251548081599002947),(-31062689251548081584029433)⟩⟩,⟨⟨919260274839426580151446499,919260274839426580343019045⟩,⟨(-53753069),114410705⟩⟩,⟨⟨(-4591117312290554826517346373),(-4591117312290554816475014612)⟩,⟨7952048448396308882062488500,7952048448396308892187908641⟩⟩,⟨⟨(-27365191652122466725184146138),(-27365191652122466650044538038)⟩,⟨(-47397902300335817896883587721),(-47397902300335817821219078789)⟩⟩,⟨⟨235330630358893204497114558321,235330630358893204589468620876⟩,⟨(-27652353868),58709063395⟩⟩] +lemma ha28_0_8_eq (j : Fin 7) : ha28_0_8 j = ((ha28_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha28_0_8_contains (j : Fin 7) : (ha28_0_8 j).Contains (fullFactor false 28 8 ((j.val:ℝ)/6)) := by + rw [ha28_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_7 j) false 28 7 j (ha28_0_7_contains j) +noncomputable def hk28_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_9 j i k) +lemma hk28_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_9 j i k).Contains (fullFactor false 28 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 9 (power28_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha28_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-7059195338064676367255),(-7059195338064676365875)⟩,⟨(-4075628328693792153187),(-4075628328693792151888)⟩⟩,⟨⟨3614308013089114298873283,3614308013089114300627036⟩,⟨(-2086721704291221582834290),(-2086721704291221581125852)⟩⟩,⟨⟨(-19968436),9381681⟩,⟨160441184787359821856770833,160441184787359821890717251⟩⟩,⟨⟨(-1850525702701626522582674118),(-1850525702701626520220491449)⟩,⟨(-1068401512597105451266082490),(-1068401512597105448925724944)⟩⟩,⟨⟨13787490894657571017945747311,13787490894657571039999547721⟩,⟨(-7960211579480062807956759526),(-7960211579480062786074195385)⟩⟩,⟨⟨(-20493329141),9652492419⟩,⟨82145886611128228783107385695,82145886611128228815606513558⟩⟩] +lemma ha28_0_9_eq (j : Fin 7) : ha28_0_9 j = ((ha28_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha28_0_9_contains (j : Fin 7) : (ha28_0_9 j).Contains (fullFactor false 28 9 ((j.val:ℝ)/6)) := by + rw [ha28_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_8 j) false 28 8 j (ha28_0_8_contains j) +noncomputable def hk28_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_10 j i k) +lemma hk28_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_10 j i k).Contains (fullFactor false 28 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 10 (power28_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha28_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨213399400269781075697,213399400269781075766⟩,⟨(-369618603571988403228),(-369618603571988403153)⟩⟩,⟨⟨218520985876255821446623,218520985876255821626227⟩,⟨378489450057716124781643,378489450057716124966501⟩⟩,⟨⟨(-25202042373060605483948327),(-25202042373060605478535815)⟩,⟨(-3136635),1473672⟩⟩,⟨⟨223765489537285961033435568,223765489537285961524311175⟩,⟨(-387573196859101312104268822),(-387573196859101311608300756)⟩⟩,⟨⟨2083978518259580814583145070,2083978518259580820318620476⟩,⟨3609556675507699247150161869,3609556675507699252935322891⟩⟩,⟨⟨(-25806891390014060017937904635),(-25806891390014060007645856613)⟩,⟨(-6438169228),3032419928⟩⟩] +lemma ha28_0_10_eq (j : Fin 7) : ha28_0_10 j = ((ha28_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha28_0_10_contains (j : Fin 7) : (ha28_0_10 j).Contains (fullFactor false 28 10 ((j.val:ℝ)/6)) := by + rw [ha28_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_9 j) false 28 9 j (ha28_0_9_contains j) +noncomputable def hk28_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_11 j i k) +lemma hk28_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_11 j i k).Contains (fullFactor false 28 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 11 (power28_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha28_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨17593804388058740562,17593804388058740567⟩,⟨10157787699515332859,10157787699515332863⟩⟩,⟨⟨(-36032111386744300685778),(-36032111386744300668064)⟩,⟨20803149208607401688988,20803149208607401706153⟩⟩,⟨⟨(-210440),447911⟩,⟨(-3598843235212085340880416),(-3598843235212085340096055)⟩⟩,⟨⟨73793764120052327736189438,73793764120052327830856431⟩,⟨42604849579227958634695066,42604849579227958728293180⟩⟩,⟨⟨(-859072479885680692351809997),(-859072479885680690972210380)⟩,⟨495985727515397111599966228,495985727515397112966584956⟩⟩,⟨⟨(-866057107),1838736832⟩,⟨(-7370430945714350778801338336),(-7370430945714350775838475483)⟩⟩] +lemma ha28_0_11_eq (j : Fin 7) : ha28_0_11 j = ((ha28_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha28_0_11_contains (j : Fin 7) : (ha28_0_11 j).Contains (fullFactor false 28 11 ((j.val:ℝ)/6)) := by + rw [ha28_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_10 j) false 28 10 j (ha28_0_10_contains j) +noncomputable def hk28_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_12 j i k) +lemma hk28_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_12 j i k).Contains (fullFactor false 28 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 12 (power28_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha28_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-443217100187807443),(-443217100187807442)⟩,⟨767674536308627877,767674536308627878⟩⟩,⟨⟨(-1815417242369259286211),(-1815417242369259284707)⟩,⟨(-3144394900720139785772),(-3144394900720139784215)⟩⟩,⟨⟨471087477881817150319182,471087477881817150423355⟩,⟨(-27547),58632⟩⟩,⟨⟨(-7435949024744486042269620),(-7435949024744486025909997)⟩,⟨12879441513349692550559993,12879441513349692567123497⟩⟩,⟨⟨(-108207299850538926593016624),(-108207299850538926294522233)⟩,⟨(-187420541090973602985321468),(-187420541090973602683742943)⟩⟩,⟨⟨1929574309403923047529805991,1929574309403923048311623699⟩,⟨(-226733221),481380177⟩⟩] +lemma ha28_0_12_eq (j : Fin 7) : ha28_0_12 j = ((ha28_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha28_0_12_contains (j : Fin 7) : (ha28_0_12 j).Contains (fullFactor false 28 12 ((j.val:ℝ)/6)) := by + rw [ha28_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_11 j) false 28 11 j (ha28_0_11_contains j) +noncomputable def hk28_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_13 j i k) +lemma hk28_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_13 j i k).Contains (fullFactor false 28 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 13 (power28_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha28_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-30919495943783800),(-30919495943783799)⟩,⟨(-17851379306351119),(-17851379306351118)⟩⟩,⟨⟨253292510771476882223,253292510771476882350⟩,⟨(-146238499277628361569),(-146238499277628361446)⟩⟩,⟨⟨(-7085),3329⟩,⟨56921729219679268111923,56921729219679268124692⟩⟩,⟨⟨(-2074972248239938620950122),(-2074972248239938618275014)⟩,⟨(-1197985786082331538926009),(-1197985786082331536286540)⟩⟩,⟨⟨37743525322001707864881970,37743525322001707925735245⟩,⟨(-21791234504823142543594298),(-21791234504823142483412896)⟩⟩,⟨⟨(-116330803),54792571⟩,⟨466302805767612564329966623,466302805767612564520385740⟩⟩] +lemma ha28_0_13_eq (j : Fin 7) : ha28_0_13 j = ((ha28_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha28_0_13_contains (j : Fin 7) : (ha28_0_13 j).Contains (fullFactor false 28 13 ((j.val:ℝ)/6)) := by + rw [ha28_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_12 j) false 28 12 j (ha28_0_12_contains j) +noncomputable def hk28_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_14 j i k) +lemma hk28_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_14 j i k).Contains (fullFactor false 28 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 14 (power28_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha28_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨667640024824732,667640024824733⟩,⟨(-1156386444162984),(-1156386444162983)⟩⟩,⟨⟨10938614166728417753,10938614166728417764⟩,⟨18946235501166317746,18946235501166317757⟩⟩,⟨⟨(-6386603083791852241884),(-6386603083791852240430)⟩,⟨(-795),374⟩⟩,⟨⟨179218254507678396376692,179218254507678396772127⟩,⟨(-310415122451108950227270),(-310415122451108949826086)⟩⟩,⟨⟨4074951323393142872553753,4074951323393142883820621⟩,⟨7058022730486958375733685,7058022730486958387135688⟩⟩,⟨⟨(-104638104924845707140647138),(-104638104924845707097584113)⟩,⟨(-26104572),12295425⟩⟩] +lemma ha28_0_14_eq (j : Fin 7) : ha28_0_14 j = ((ha28_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha28_0_14_contains (j : Fin 7) : (ha28_0_14 j).Contains (fullFactor false 28 14 ((j.val:ℝ)/6)) := by + rw [ha28_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_13 j) false 28 13 j (ha28_0_13_contains j) +noncomputable def hk28_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_15 j i k) +lemma hk28_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_15 j i k).Contains (fullFactor false 28 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 15 (power28_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha28_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨40365501752147,40365501752148⟩,⟨23305033302576,23305033302577⟩⟩,⟨⟨(-1322696761414360854),(-1322696761414360852)⟩,⟨763659331258827442,763659331258827444⟩⟩,⟨⟨(-40),84⟩,⟨(-668803510981146723333),(-668803510981146723178)⟩⟩,⟨⟨43342127478025776391714,43342127478025776447869⟩,⟨25023588966689257638269,25023588966689257693563⟩⟩,⟨⟨(-1231857353275977870263944),(-1231857353275977868269997)⟩,⟨711213174517105745365838,711213174517105747334542⟩⟩,⟨⟨(-2575148),5467329⟩,⟨(-21915353447830215832175673),(-21915353447830215823086815)⟩⟩] +lemma ha28_0_15_eq (j : Fin 7) : ha28_0_15 j = ((ha28_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha28_0_15_contains (j : Fin 7) : (ha28_0_15 j).Contains (fullFactor false 28 15 ((j.val:ℝ)/6)) := by + rw [ha28_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_14 j) false 28 14 j (ha28_0_14_contains j) +noncomputable def hk28_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_16 j i k) +lemma hk28_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_16 j i k).Contains (fullFactor false 28 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 16 (power28_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha28_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-762655431407),(-762655431406)⟩,⟨1320957955864,1320957955865⟩⟩,⟨⟨(-49981386352667222),(-49981386352667221)⟩,⟨(-86570300595549325),(-86570300595549323)⟩⟩,⟨⟨65659631149794723615,65659631149794723631⟩,⟨(-4),9⟩⟩,⟨⟨(-3275580136008399053289),(-3275580136008399046040)⟩,⟨5673471219829920490993,5673471219829920498363⟩⟩,⟨⟨(-116371983552042445838086),(-116371983552042445515586)⟩,⟨(-201562188089707223767371),(-201562188089707223440470)⟩⟩,⟨⟨4303069587032947006450324,4303069587032947008248615⟩,⟨(-505630),1073508⟩⟩] +lemma ha28_0_16_eq (j : Fin 7) : ha28_0_16 j = ((ha28_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha28_0_16_contains (j : Fin 7) : (ha28_0_16 j).Contains (fullFactor false 28 16 ((j.val:ℝ)/6)) := by + rw [ha28_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_15 j) false 28 15 j (ha28_0_15_contains j) +noncomputable def hk28_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_17 j i k) +lemma hk28_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_17 j i k).Contains (fullFactor false 28 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 17 (power28_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha28_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-40685409901),(-40685409900)⟩,⟨(-23489732359),(-23489732358)⟩⟩,⟨⟨5332718046471330,5332718046471331⟩,⟨(-3078846199642598),(-3078846199642597)⟩⟩,⟨⟨(-1),1⟩,⟨6066935731106195666,6066935731106195668⟩⟩,⟨⟨(-698970019787090239661),(-698970019787090238750)⟩,⟨(-403550529079554597192),(-403550529079554596297)⟩⟩,⟨⟨31040504379613153615005,31040504379613153665448⟩,⟨(-17921243559351411766443),(-17921243559351411716720)⟩⟩,⟨⟨(-198384),93441⟩,⟨795205400147551278321034,795205400147551278655889⟩⟩] +lemma ha28_0_17_eq (j : Fin 7) : ha28_0_17 j = ((ha28_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha28_0_17_contains (j : Fin 7) : (ha28_0_17 j).Contains (fullFactor false 28 17 ((j.val:ℝ)/6)) := by + rw [ha28_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_16 j) false 28 16 j (ha28_0_16_contains j) +noncomputable def hk28_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_18 j i k) +lemma hk28_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_18 j i k).Contains (fullFactor false 28 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 18 (power28_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha28_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨683288616,683288617⟩,⟨(-1183490601),(-1183490600)⟩⟩,⟨⟨179120011154259,179120011154260⟩,⟨310244959971482,310244959971483⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨(-1),1⟩⟩,⟨⟨46955236204022331321,46955236204022331426⟩,⟨(-81328854786764263435),(-81328854786764263328)⟩⟩,⟨⟨2606539218020916331968,2606539218020916339210⟩,⟨4514658357533078054654,4514658357533078062006⟩⟩,⟨⟨(-138789524622137721175998),(-138789524622137721117112)⟩,⟨(-34625),16309⟩⟩] +lemma ha28_0_18_eq (j : Fin 7) : ha28_0_18 j = ((ha28_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha28_0_18_contains (j : Fin 7) : (ha28_0_18 j).Contains (fullFactor false 28 18 ((j.val:ℝ)/6)) := by + rw [ha28_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_17 j) false 28 17 j (ha28_0_17_contains j) +noncomputable def hk28_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_19 j i k) +lemma hk28_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_19 j i k).Contains (fullFactor false 28 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 19 (power28_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha28_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨32614433,32614434⟩,⟨18829951,18829952⟩⟩,⟨⟨(-17099355913328),(-17099355913327)⟩,⟨9872317739528,9872317739529⟩⟩,⟨⟨(-1),1⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨8964987113086656138,8964987113086656151⟩,⟨5175937723022106875,5175937723022106888⟩⟩,⟨⟨(-622070944276038606025),(-622070944276038605009)⟩,⟨359152827132815576991,359152827132815577991⟩⟩,⟨⟨(-2697),5726⟩,⟨(-22948428997269873115436),(-22948428997269873105626)⟩⟩] +lemma ha28_0_19_eq (j : Fin 7) : ha28_0_19 j = ((ha28_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha28_0_19_contains (j : Fin 7) : (ha28_0_19 j).Contains (fullFactor false 28 19 ((j.val:ℝ)/6)) := by + rw [ha28_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_18 j) false 28 18 j (ha28_0_18_contains j) +noncomputable def hk28_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_20 j i k) +lemma hk28_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_20 j i k).Contains (fullFactor false 28 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 20 (power28_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha28_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-492967),(-492966)⟩,⟨853843,853844⟩⟩,⟨⟨(-516913348074),(-516913348073)⟩,⟨(-895320181974),(-895320181973)⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨(-1),1⟩⟩,⟨⟨(-542022930869484435),(-542022930869484432)⟩,⟨938811255133340261,938811255133340264⟩⟩,⟨⟨(-47012995134852432669),(-47012995134852432537)⟩,⟨(-81428896189552855226),(-81428896189552855092)⟩⟩,⟨⟨3604730797462500933137,3604730797462500934690⟩,⟨(-424),900⟩⟩] +lemma ha28_0_20_eq (j : Fin 7) : ha28_0_20 j = ((ha28_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha28_0_20_contains (j : Fin 7) : (ha28_0_20 j).Contains (fullFactor false 28 20 ((j.val:ℝ)/6)) := by + rw [ha28_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_19 j) false 28 19 j (ha28_0_19_contains j) +noncomputable def hk28_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_21 j i k) +lemma hk28_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_21 j i k).Contains (fullFactor false 28 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 21 (power28_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha28_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-21290),(-21289)⟩,⟨(-12292),(-12291)⟩⟩,⟨⟨44646528671,44646528672⟩,⟨(-25776685347),(-25776685346)⟩⟩,⟨⟨(-1),1⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨(-93630556896327456),(-93630556896327454)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨10151445319802585607,10151445319802585624⟩,⟨(-5860939688051789420),(-5860939688051789402)⟩⟩,⟨⟨(-135),64⟩,⟨539266466260812848826,539266466260812849061⟩⟩] +lemma ha28_0_21_eq (j : Fin 7) : ha28_0_21 j = ((ha28_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha28_0_21_contains (j : Fin 7) : (ha28_0_21 j).Contains (fullFactor false 28 21 ((j.val:ℝ)/6)) := by + rw [ha28_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_20 j) false 28 20 j (ha28_0_20_contains j) +noncomputable def hk28_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_22 j i k) +lemma hk28_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_22 j i k).Contains (fullFactor false 28 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 22 (power28_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha28_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨292,293⟩,⟨(-507),(-506)⟩⟩,⟨⟨1226967353,1226967354⟩,⟨2125169795,2125169796⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨(-1),1⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨697450191936225608,697450191936225611⟩,⟨1208019168182208036,1208019168182208039⟩⟩,⟨⟨(-77007071306013533817),(-77007071306013533782)⟩,⟨(-20),10⟩⟩] +lemma ha28_0_22_eq (j : Fin 7) : ha28_0_22 j = ((ha28_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha28_0_22_contains (j : Fin 7) : (ha28_0_22 j).Contains (fullFactor false 28 22 ((j.val:ℝ)/6)) := by + rw [ha28_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_21 j) false 28 21 j (ha28_0_21_contains j) +noncomputable def hk28_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_23 j i k) +lemma hk28_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_23 j i k).Contains (fullFactor false 28 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 23 (power28_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha28_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11,12⟩,⟨6,7⟩⟩,⟨⟨(-96759679),(-96759678)⟩,⟨55864226,55864227⟩⟩,⟨⟨(-1),1⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨(-137503773339017308),(-137503773339017306)⟩,⟨79387840551870928,79387840551870929⟩⟩,⟨⟨(-2),3⟩,⟨(-10518471716932064458),(-10518471716932064452)⟩⟩] +lemma ha28_0_23_eq (j : Fin 7) : ha28_0_23 j = ((ha28_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha28_0_23_contains (j : Fin 7) : (ha28_0_23 j).Contains (fullFactor false 28 23 ((j.val:ℝ)/6)) := by + rw [ha28_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_22 j) false 28 22 j (ha28_0_22_contains j) +noncomputable def hk28_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_24 j i k) +lemma hk28_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_24 j i k).Contains (fullFactor false 28 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 24 (power28_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha28_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-2437537),(-2437536)⟩,⟨(-4221938),(-4221937)⟩⟩,⟨⟨82067533018,82067533019⟩,⟨(-1),1⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-8659870022990125),(-8659870022990124)⟩,⟨(-14999334866761558),(-14999334866761557)⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨(-1),1⟩⟩] +lemma ha28_0_24_eq (j : Fin 7) : ha28_0_24 j = ((ha28_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha28_0_24_contains (j : Fin 7) : (ha28_0_24 j).Contains (fullFactor false 28 24 ((j.val:ℝ)/6)) := by + rw [ha28_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_23 j) false 28 23 j (ha28_0_23_contains j) +noncomputable def hk28_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_25 j i k) +lemma hk28_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_25 j i k).Contains (fullFactor false 28 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 25 (power28_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha28_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨176848,176849⟩,⟨(-102104),(-102103)⟩⟩,⟨⟨(-1),1⟩,⟨5156455176,5156455177⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨1570726674205044,1570726674205046⟩,⟨(-906859468175609),(-906859468175608)⟩⟩,⟨⟨(-1),1⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha28_0_25_eq (j : Fin 7) : ha28_0_25 j = ((ha28_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha28_0_25_contains (j : Fin 7) : (ha28_0_25 j).Contains (fullFactor false 28 25 ((j.val:ℝ)/6)) := by + rw [ha28_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_24 j) false 28 24 j (ha28_0_24_contains j) +noncomputable def hk28_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_26 j i k) +lemma hk28_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_26 j i k).Contains (fullFactor false 28 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 26 (power28_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha28_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨4112,4113⟩,⟨7122,7123⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨(-1),1⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨91313559072398,91313559072399⟩,⟨158159723733336,158159723733337⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨(-1),1⟩⟩] +lemma ha28_0_26_eq (j : Fin 7) : ha28_0_26 j = ((ha28_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha28_0_26_contains (j : Fin 7) : (ha28_0_26 j).Contains (fullFactor false 28 26 ((j.val:ℝ)/6)) := by + rw [ha28_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_25 j) false 28 25 j (ha28_0_25_contains j) +noncomputable def hk28_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_27 j i k) +lemma hk28_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_27 j i k).Contains (fullFactor false 28 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 27 (power28_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha28_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-277),(-276)⟩,⟨159,160⟩⟩,⟨⟨(-1),1⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨(-15335599573286),(-15335599573285)⟩,⟨8854012541820,8854012541821⟩⟩,⟨⟨(-1),1⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha28_0_27_eq (j : Fin 7) : ha28_0_27 j = ((ha28_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha28_0_27_contains (j : Fin 7) : (ha28_0_27 j).Contains (fullFactor false 28 27 ((j.val:ℝ)/6)) := by + rw [ha28_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_26 j) false 28 26 j (ha28_0_26_contains j) +noncomputable def hk28_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_28 j i k) +lemma hk28_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_28 j i k).Contains (fullFactor false 28 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 28 (power28_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha28_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-6),(-5)⟩,⟨(-11),(-10)⟩⟩,⟨⟨1016753,1016754⟩,⟨(-1),1⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-827848236791),(-827848236790)⟩,⟨(-1433875207079),(-1433875207078)⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨(-1),1⟩⟩] +lemma ha28_0_28_eq (j : Fin 7) : ha28_0_28 j = ((ha28_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha28_0_28_contains (j : Fin 7) : (ha28_0_28 j).Contains (fullFactor false 28 28 ((j.val:ℝ)/6)) := by + rw [ha28_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_27 j) false 28 27 j (ha28_0_27_contains j) +noncomputable def hk28_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_29 j i k) +lemma hk28_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_29 j i k).Contains (fullFactor false 28 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 29 (power28_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha28_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨55072,55073⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨129444017721,129444017722⟩,⟨(-74734538477),(-74734538476)⟩⟩,⟨⟨(-1),1⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha28_0_29_eq (j : Fin 7) : ha28_0_29 j = ((ha28_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha28_0_29_contains (j : Fin 7) : (ha28_0_29 j).Contains (fullFactor false 28 29 ((j.val:ℝ)/6)) := by + rw [ha28_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_28 j) false 28 28 j (ha28_0_28_contains j) +noncomputable def hk28_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power28 j i k).conj.mul (mpower0_30 j i k) +lemma hk28_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk28_0_30 j i k).Contains (fullFactor false 28 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power28 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 30 (power28_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha28_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨(-1),1⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨6521818806,6521818807⟩,⟨11296121531,11296121532⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨(-1),1⟩⟩] +lemma ha28_0_30_eq (j : Fin 7) : ha28_0_30 j = ((ha28_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha28_0_30_contains (j : Fin 7) : (ha28_0_30 j).Contains (fullFactor false 28 30 ((j.val:ℝ)/6)) := by + rw [ha28_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_0_29 j) false 28 29 j (ha28_0_29_contains j) +noncomputable def hk28_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_0 j i k) +lemma hk28_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_0 j i k).Contains (fullFactor true 28 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 0 (kernel28_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha28_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),2⟩,⟨0,4⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-493754047503),(-493754047500)⟩,⟨(-254534926262),(-254534926259)⟩⟩,⟨⟨3357153827198104502458,3357153827198104516477⟩,⟨(-568253757477525623876),(-568253757477525609895)⟩⟩,⟨⟨4568030054686774396541880045,4568030054686774407918970971⟩,⟨3209886730187197181988549093,3209886730187197193397127950⟩⟩] +lemma ha28_1_0_eq (j : Fin 7) : ha28_1_0 j = atomKernel28_0 j := by fin_cases j <;> decide +kernel +lemma ha28_1_0_contains (j : Fin 7) : (ha28_1_0 j).Contains (fullFactor true 28 0 ((j.val:ℝ)/6)) := by + rw [ha28_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel28_0_contains j +noncomputable def hk28_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_1 j i k) +lemma hk28_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_1 j i k).Contains (fullFactor true 28 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 1 (kernel28_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha28_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-10),31⟩,⟨(-30),11⟩⟩,⟨⟨(-6),21⟩,⟨(-19),11⟩⟩,⟨⟨(-427735225680),(-427735225661)⟩,⟨2666849509051,2666849509071⟩⟩,⟨⟨(-4685945174865765828890),(-4685945174865765761884)⟩,⟨(-13314743247109872706579),(-13314743247109872639414)⟩⟩,⟨⟨10733230239114978357051547456,10733230239114978400424162862⟩,⟨(-17098006669934193027518235080),(-17098006669934192984238611740)⟩⟩] +lemma ha28_1_1_eq (j : Fin 7) : ha28_1_1 j = ((ha28_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha28_1_1_contains (j : Fin 7) : (ha28_1_1 j).Contains (fullFactor true 28 1 ((j.val:ℝ)/6)) := by + rw [ha28_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_0 j) true 28 0 j (ha28_1_0_contains j) +noncomputable def hk28_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_2 j i k) +lemma hk28_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_2 j i k).Contains (fullFactor true 28 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 2 (kernel28_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha28_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-255),177⟩,⟨(-205),219⟩⟩,⟨⟨(-154),53⟩,⟨(-107),100⟩⟩,⟨⟨(-79),37⟩,⟨(-70),43⟩⟩,⟨⟨6484493628119,6484493628181⟩,⟨(-1032547750211),(-1032547750151)⟩⟩,⟨⟨(-25547166525425907308106),(-25547166525425907147222)⟩,⟨14260556997577409906764,14260556997577410067332⟩⟩,⟨⟨(-31878380967388563336379975931),(-31878380967388563254064469747)⟩,⟨(-17773711906285126222017443831),(-17773711906285126139577447036)⟩⟩] +lemma ha28_1_2_eq (j : Fin 7) : ha28_1_2 j = ((ha28_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha28_1_2_contains (j : Fin 7) : (ha28_1_2 j).Contains (fullFactor true 28 2 ((j.val:ℝ)/6)) := by + rw [ha28_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_1 j) true 28 1 j (ha28_1_1_contains j) +noncomputable def hk28_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_3 j i k) +lemma hk28_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_3 j i k).Contains (fullFactor true 28 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 3 (kernel28_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha28_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-707),924⟩,⟨(-779),840⟩⟩,⟨⟨(-271),425⟩,⟨(-256),440⟩⟩,⟨⟨(-155),148⟩,⟨(-104),201⟩⟩,⟨⟨(-4865559578997),(-4865559578873)⟩,⟨(-9464537535637),(-9464537535510)⟩⟩,⟨⟨25417198358163888449103,25417198358163888705611⟩,⟨31441318692122649502369,31441318692122649759274⟩⟩,⟨⟨(-19398475327249652548291993600),(-19398475327249652443834332594)⟩,⟨39483697746581819786216551954,39483697746581819890583389440⟩⟩] +lemma ha28_1_3_eq (j : Fin 7) : ha28_1_3 j = ((ha28_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha28_1_3_contains (j : Fin 7) : (ha28_1_3 j).Contains (fullFactor true 28 3 ((j.val:ℝ)/6)) := by + rw [ha28_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_2 j) true 28 2 j (ha28_1_2_contains j) +noncomputable def hk28_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_4 j i k) +lemma hk28_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_4 j i k).Contains (fullFactor true 28 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 4 (kernel28_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha28_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2495),2136⟩,⟨(-2469),2151⟩⟩,⟨⟨(-853),901⟩,⟨(-1089),665⟩⟩,⟨⟨(-238),367⟩,⟨(-332),272⟩⟩,⟨⟨(-9088251010517),(-9088251010322)⟩,⟨9205245187683,9205245187875⟩⟩,⟨⟨27636408466630806852822,27636408466630807160487⟩,⟨(-31495264721916455077269),(-31495264721916454769955)⟩⟩,⟨⟨36554794359576350005982116024,36554794359576350105219906821⟩,⟨15658603290377833276090819030,15658603290377833375351622876⟩⟩] +lemma ha28_1_4_eq (j : Fin 7) : ha28_1_4 j = ((ha28_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha28_1_4_contains (j : Fin 7) : (ha28_1_4 j).Contains (fullFactor true 28 4 ((j.val:ℝ)/6)) := by + rw [ha28_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_3 j) true 28 3 j (ha28_1_3_contains j) +noncomputable def hk28_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_5 j i k) +lemma hk28_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_5 j i k).Contains (fullFactor true 28 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 5 (kernel28_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha28_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5111),5425⟩,⟨(-4887),5641⟩⟩,⟨⟨(-2009),1525⟩,⟨(-1583),1951⟩⟩,⟨⟨(-547),413⟩,⟨(-529),432⟩⟩,⟨⟨11260014632807,11260014633044⟩,⟨5607678750765,5607678751005⟩⟩,⟨⟨(-29626388377567493745494),(-29626388377567493450967)⟩,⟨(-18144127288028032778373),(-18144127288028032483617)⟩⟩,⟨⟨9935921573568820690265604707,9935921573568820765719483290⟩,⟨(-26988116545467155499799051604),(-26988116545467155424315389632)⟩⟩] +lemma ha28_1_5_eq (j : Fin 7) : ha28_1_5 j = ((ha28_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha28_1_5_contains (j : Fin 7) : (ha28_1_5 j).Contains (fullFactor true 28 5 ((j.val:ℝ)/6)) := by + rw [ha28_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_4 j) true 28 4 j (ha28_1_4_contains j) +noncomputable def hk28_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_6 j i k) +lemma hk28_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_6 j i k).Contains (fullFactor true 28 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 6 (kernel28_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha28_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-9960),10026⟩,⟨(-10570),9412⟩⟩,⟨⟨(-2611),3324⟩,⟨(-2910),3024⟩⟩,⟨⟨(-646),626⟩,⟨(-556),716⟩⟩,⟨⟨1474079895327,1474079895573⟩,⟨(-10086463026260),(-10086463026016)⟩⟩,⟨⟨(-8876352794665062936640),(-8876352794665062701322)⟩,⟨22301927885805534417018,22301927885805534652228⟩⟩,⟨⟨(-16553415482953545671139655835),(-16553415482953545623296681888)⟩,⟨(-5135203726273558986739222252),(-5135203726273558938944209337)⟩⟩] +lemma ha28_1_6_eq (j : Fin 7) : ha28_1_6 j = ((ha28_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha28_1_6_contains (j : Fin 7) : (ha28_1_6 j).Contains (fullFactor true 28 6 ((j.val:ℝ)/6)) := by + rw [ha28_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_5 j) true 28 5 j (ha28_1_5_contains j) +noncomputable def hk28_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_7 j i k) +lemma hk28_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_7 j i k).Contains (fullFactor true 28 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 7 (kernel28_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha28_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-16595),15907⟩,⟨(-15633),16866⟩⟩,⟨⟨(-4479),4062⟩,⟨(-4573),3968⟩⟩,⟨⟨(-659),784⟩,⟨(-747),697⟩⟩,⟨⟨(-6976158099833),(-6976158099618)⟩,⟨1210621953833,1210621954049⟩⟩,⟨⟨13908805375154267714462,13908805375154267875455⟩,⟨2936452680378083247514,2936452680378083408539⟩⟩,⟨⟨(-2205009146231279427035635215),(-2205009146231279401086836476)⟩,⟨8677009823436139786137684074,8677009823436139812127711651⟩⟩] +lemma ha28_1_7_eq (j : Fin 7) : ha28_1_7 j = ((ha28_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha28_1_7_contains (j : Fin 7) : (ha28_1_7 j).Contains (fullFactor true 28 7 ((j.val:ℝ)/6)) := by + rw [ha28_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_6 j) true 28 6 j (ha28_1_6_contains j) +noncomputable def hk28_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_8 j i k) +lemma hk28_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_8 j i k).Contains (fullFactor true 28 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 8 (kernel28_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha28_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-22509),23741⟩,⟨(-23555),22694⟩⟩,⟨⟨(-5444),5312⟩,⟨(-5058),5698⟩⟩,⟨⟨(-755),679⟩,⟨(-748),686⟩⟩,⟨⟨2020553320635,2020553320802⟩,⟨3799406407328,3799406407494⟩⟩,⟨⟨275029602185696829490,275029602185696925902⟩,⟨(-7361218239110540503272),(-7361218239110540406858)⟩⟩,⟨⟨3968368796587380336814275492,3968368796587380349167302116⟩,⟨791629275638498607796883228,791629275638498620123452449⟩⟩] +lemma ha28_1_8_eq (j : Fin 7) : ha28_1_8 j = ((ha28_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha28_1_8_contains (j : Fin 7) : (ha28_1_8 j).Contains (fullFactor true 28 8 ((j.val:ℝ)/6)) := by + rw [ha28_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_7 j) true 28 7 j (ha28_1_7_contains j) +noncomputable def hk28_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_9 j i k) +lemma hk28_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_9 j i k).Contains (fullFactor true 28 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 9 (kernel28_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha28_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-29954),28549⟩,⟨(-29139),29363⟩⟩,⟨⟨(-5801),6239⟩,⟨(-6157),5883⟩⟩,⟨⟨(-639),627⟩,⟨(-602),664⟩⟩,⟨⟨1610150892727,1610150892841⟩,⟨(-1676932171466),(-1676932171352)⟩⟩,⟨⟨(-3362940049418340078320),(-3362940049418340026999)⟩,⟨451218415581786561877,451218415581786613189⟩⟩,⟨⟨234826667597909936902803030,234826667597909942107536670⟩,⟨(-1608725548833069416613427969),(-1608725548833069411394784787)⟩⟩] +lemma ha28_1_9_eq (j : Fin 7) : ha28_1_9 j = ((ha28_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha28_1_9_contains (j : Fin 7) : (ha28_1_9 j).Contains (fullFactor true 28 9 ((j.val:ℝ)/6)) := by + rw [ha28_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_8 j) true 28 8 j (ha28_1_8_contains j) +noncomputable def hk28_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_10 j i k) +lemma hk28_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_10 j i k).Contains (fullFactor true 28 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 10 (kernel28_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha28_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-32720),33881⟩,⟨(-33125),33476⟩⟩,⟨⟨(-6243),5886⟩,⟨(-6110),6020⟩⟩,⟨⟨(-485),521⟩,⟨(-509),497⟩⟩,⟨⟨(-1018736106667),(-1018736106596)⟩,⟨(-489772973673),(-489772973602)⟩⟩,⟨⟨421189642171226051379,421189642171226075958⟩,⟨1342081025863208068154,1342081025863208092740⟩⟩,⟨⟨(-585324403679700287012141317),(-585324403679700285028081500)⟩,⟨(-54588941927361483113968359),(-54588941927361481136167206)⟩⟩] +lemma ha28_1_10_eq (j : Fin 7) : ha28_1_10 j = ((ha28_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha28_1_10_contains (j : Fin 7) : (ha28_1_10 j).Contains (fullFactor true 28 10 ((j.val:ℝ)/6)) := by + rw [ha28_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_9 j) true 28 9 j (ha28_1_9_contains j) +noncomputable def hk28_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_11 j i k) +lemma hk28_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_11 j i k).Contains (fullFactor true 28 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 11 (kernel28_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha28_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34809),34119⟩,⟨(-34782),34145⟩⟩,⟨⟨(-5496),5613⟩,⟨(-5451),5658⟩⟩,⟨⟨(-371),356⟩,⟨(-370),357⟩⟩,⟨⟨(-65363410050),(-65363410010)⟩,⟨495339131295,495339131335⟩⟩,⟨⟨471468391977111431641,471468391977111442348⟩,⟨(-242356254839358529757),(-242356254839358519052)⟩⟩,⟨⟨(-7928524023485484863463353),(-7928524023485484180243140)⟩,⟨193079273767098993471291408,193079273767098994156985092⟩⟩] +lemma ha28_1_11_eq (j : Fin 7) : ha28_1_11 j = ((ha28_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha28_1_11_contains (j : Fin 7) : (ha28_1_11 j).Contains (fullFactor true 28 11 ((j.val:ℝ)/6)) := by + rw [ha28_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_10 j) true 28 10 j (ha28_1_10_contains j) +noncomputable def hk28_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_12 j i k) +lemma hk28_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_12 j i k).Contains (fullFactor true 28 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 12 (kernel28_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha28_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32574),32817⟩,⟨(-32385),33006⟩⟩,⟨⟨(-4643),4684⟩,⟨(-4731),4596⟩⟩,⟨⟨(-242),240⟩,⟨(-236),246⟩⟩,⟨⟨198959191711,198959191732⟩,⟨(-37386425226),(-37386425204)⟩⟩,⟨⟨(-110179550922274969061),(-110179550922274964787)⟩,⟨(-146282935247653628256),(-146282935247653623981)⟩⟩,⟨⟨58225254219743512917736865,58225254219743513134951228⟩,⟨(-635419677339146467434770),(-635419677339146251094142)⟩⟩] +lemma ha28_1_12_eq (j : Fin 7) : ha28_1_12 j = ((ha28_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha28_1_12_contains (j : Fin 7) : (ha28_1_12 j).Contains (fullFactor true 28 12 ((j.val:ℝ)/6)) := by + rw [ha28_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_11 j) true 28 11 j (ha28_1_11_contains j) +noncomputable def hk28_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_13 j i k) +lemma hk28_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_13 j i k).Contains (fullFactor true 28 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 13 (kernel28_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha28_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28615),28649⟩,⟨(-28850),28414⟩⟩,⟨⟨(-3649),3580⟩,⟨(-3597),3632⟩⟩,⟨⟨(-145),150⟩,⟨(-148),147⟩⟩,⟨⟨(-36478382800),(-36478382789)⟩,⟨(-66348888887),(-66348888876)⟩⟩,⟨⟨(-40000698705503772693),(-40000698705503771117)⟩,⟨42549530079313509815,42549530079313511391⟩⟩,⟨⟨(-1017512944085107383093759),(-1017512944085107319859849)⟩,⟨(-16164122631392575296618999),(-16164122631392575233106739)⟩⟩] +lemma ha28_1_13_eq (j : Fin 7) : ha28_1_13 j = ((ha28_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha28_1_13_contains (j : Fin 7) : (ha28_1_13 j).Contains (fullFactor true 28 13 ((j.val:ℝ)/6)) := by + rw [ha28_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_12 j) true 28 12 j (ha28_1_12_contains j) +noncomputable def hk28_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_14 j i k) +lemma hk28_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_14 j i k).Contains (fullFactor true 28 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 14 (kernel28_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha28_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23350),23215⟩,⟨(-23168),23397⟩⟩,⟨⟨(-2583),2620⟩,⟨(-2595),2608⟩⟩,⟨⟨(-85),83⟩,⟨(-85),83⟩⟩,⟨⟨(-17946671213),(-17946671207)⟩,⟨19219425108,19219425114⟩⟩,⟨⟨14428580018234540159,14428580018234540699⟩,⟨9531917685691578974,9531917685691579515⟩⟩,⟨⟨(-4155571849640704153785347),(-4155571849640704136542170)⟩,⟨479246946914341680458139,479246946914341697621466⟩⟩] +lemma ha28_1_14_eq (j : Fin 7) : ha28_1_14 j = ((ha28_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha28_1_14_contains (j : Fin 7) : (ha28_1_14 j).Contains (fullFactor true 28 14 ((j.val:ℝ)/6)) := by + rw [ha28_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_13 j) true 28 13 j (ha28_1_13_contains j) +noncomputable def hk28_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_15 j i k) +lemma hk28_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_15 j i k).Contains (fullFactor true 28 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 15 (kernel28_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha28_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17608),17733⟩,⟨(-17712),17629⟩⟩,⟨⟨(-1751),1744⟩,⟨(-1756),1739⟩⟩,⟨⟨(-45),45⟩,⟨(-44),45⟩⟩,⟨⟨7732609363,7732609366⟩,⟨3585943143,3585943146⟩⟩,⟨⟨1918572265091405702,1918572265091405876⟩,⟨(-4377226561865541087),(-4377226561865540913)⟩⟩,⟨⟨167391924550560480587554,167391924550560484935756⟩,⟨994392556516195436139939,994392556516195440509035⟩⟩] +lemma ha28_1_15_eq (j : Fin 7) : ha28_1_15 j = ((ha28_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha28_1_15_contains (j : Fin 7) : (ha28_1_15 j).Contains (fullFactor true 28 15 ((j.val:ℝ)/6)) := by + rw [ha28_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_14 j) true 28 14 j (ha28_1_14_contains j) +noncomputable def hk28_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_16 j i k) +lemma hk28_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_16 j i k).Contains (fullFactor true 28 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 16 (kernel28_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha28_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12613),12534⟩,⟨(-12568),12579⟩⟩,⟨⟨(-1102),1099⟩,⟨(-1097),1104⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨303084940,303084942⟩,⟨(-2572409615),(-2572409613)⟩⟩,⟨⟨(-1202095402683007419),(-1202095402683007366)⟩,⟨(-297189559897050281),(-297189559897050228)⟩⟩,⟨⟨222459104442015903718748,222459104442015904756556⟩,⟨(-49448563983890209871957),(-49448563983890208839181)⟩⟩] +lemma ha28_1_16_eq (j : Fin 7) : ha28_1_16 j = ((ha28_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha28_1_16_contains (j : Fin 7) : (ha28_1_16 j).Contains (fullFactor true 28 16 ((j.val:ℝ)/6)) := by + rw [ha28_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_15 j) true 28 15 j (ha28_1_15_contains j) +noncomputable def hk28_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_17 j i k) +lemma hk28_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_17 j i k).Contains (fullFactor true 28 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 17 (kernel28_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha28_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8401),8439⟩,⟨(-8414),8427⟩⟩,⟨⟨(-651),654⟩,⟨(-653),652⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-726105080),(-726105078)⟩,⟨146933432,146933434⟩⟩,⟨⟨(-21615616742345886),(-21615616742345870)⟩,⟨301189864143714343,301189864143714358⟩⟩,⟨⟨(-12960702605192211705314),(-12960702605192211474434)⟩,⟨(-46707087997390079914349),(-46707087997390079682344)⟩⟩] +lemma ha28_1_17_eq (j : Fin 7) : ha28_1_17 j = ((ha28_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha28_1_17_contains (j : Fin 7) : (ha28_1_17 j).Contains (fullFactor true 28 17 ((j.val:ℝ)/6)) := by + rw [ha28_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_16 j) true 28 16 j (ha28_1_16_contains j) +noncomputable def hk28_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_18 j i k) +lemma hk28_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_18 j i k).Contains (fullFactor true 28 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 18 (kernel28_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha28_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5333),5319⟩,⟨(-5333),5319⟩⟩,⟨⟨(-366),365⟩,⟨(-366),365⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨98841049,98841050⟩,⟨173996727,173996728⟩⟩,⟨⟨69204097031463841,69204097031463846⟩,⟨(-6879074720729438),(-6879074720729433)⟩⟩,⟨⟨(-9234824241539036892233),(-9234824241539036843250)⟩,⟨3087321175289841983220,3087321175289842031969⟩⟩] +lemma ha28_1_18_eq (j : Fin 7) : ha28_1_18 j = ((ha28_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha28_1_18_contains (j : Fin 7) : (ha28_1_18 j).Contains (fullFactor true 28 18 ((j.val:ℝ)/6)) := by + rw [ha28_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_17 j) true 28 17 j (ha28_1_17_contains j) +noncomputable def hk28_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_19 j i k) +lemma hk28_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_19 j i k).Contains (fullFactor true 28 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 19 (kernel28_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha28_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3190),3193⟩,⟨(-3187),3196⟩⟩,⟨⟨(-194),194⟩,⟨(-194),195⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨34425451,34425452⟩,⟨(-37911140),(-37911139)⟩⟩,⟨⟨(-4044413201453568),(-4044413201453566)⟩,⟨(-14624960867008672),(-14624960867008670)⟩⟩,⟨⟨678023740790816481660,678023740790816491412⟩,⟨1724603902431137822507,1724603902431137832305⟩⟩] +lemma ha28_1_19_eq (j : Fin 7) : ha28_1_19 j = ((ha28_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha28_1_19_contains (j : Fin 7) : (ha28_1_19 j).Contains (fullFactor true 28 19 ((j.val:ℝ)/6)) := by + rw [ha28_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_18 j) true 28 18 j (ha28_1_18_contains j) +noncomputable def hk28_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_20 j i k) +lemma hk28_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_20 j i k).Contains (fullFactor true 28 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 20 (kernel28_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha28_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1819),1815⟩⟩,⟨⟨(-98),98⟩,⟨(-98),98⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-11365795),(-11365794)⟩,⟨(-5079817),(-5079816)⟩⟩,⟨⟨(-2844939705163059),(-2844939705163057)⟩,⟨1341152941746088,1341152941746090⟩⟩,⟨⟨305013740303017263092,305013740303017264954⟩,⟨(-138609802094244642422),(-138609802094244640568)⟩⟩] +lemma ha28_1_20_eq (j : Fin 7) : ha28_1_20 j = ((ha28_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha28_1_20_contains (j : Fin 7) : (ha28_1_20 j).Contains (fullFactor true 28 20 ((j.val:ℝ)/6)) := by + rw [ha28_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_19 j) true 28 19 j (ha28_1_19_contains j) +noncomputable def hk28_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_21 j i k) +lemma hk28_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_21 j i k).Contains (fullFactor true 28 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 21 (kernel28_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha28_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-986),985⟩,⟨(-985),986⟩⟩,⟨⟨(-48),48⟩,⟨(-48),48⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-297404),(-297403)⟩,⟨2867027,2867028⟩⟩,⟨⟨356319626872007,356319626872009⟩,⟨508468577852757,508468577852759⟩⟩,⟨⟨(-26561764647803454745),(-26561764647803454408)⟩,⟨(-51208825282387177984),(-51208825282387177646)⟩⟩] +lemma ha28_1_21_eq (j : Fin 7) : ha28_1_21 j = ((ha28_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha28_1_21_contains (j : Fin 7) : (ha28_1_21 j).Contains (fullFactor true 28 21 ((j.val:ℝ)/6)) := by + rw [ha28_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_20 j) true 28 20 j (ha28_1_20_contains j) +noncomputable def hk28_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_22 j i k) +lemma hk28_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_22 j i k).Contains (fullFactor true 28 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 22 (kernel28_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha28_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-510),511⟩,⟨(-511),510⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨622559,622560⟩,⟨(-135026),(-135025)⟩⟩,⟨⟨83013043581483,83013043581485⟩,⟨(-82444915483969),(-82444915483968)⟩⟩,⟨⟨(-8178582266590750576),(-8178582266590750517)⟩,⟨4796858029667616359,4796858029667616418⟩⟩] +lemma ha28_1_22_eq (j : Fin 7) : ha28_1_22 j = ((ha28_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha28_1_22_contains (j : Fin 7) : (ha28_1_22 j).Contains (fullFactor true 28 22 ((j.val:ℝ)/6)) := by + rw [ha28_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_21 j) true 28 21 j (ha28_1_21_contains j) +noncomputable def hk28_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_23 j i k) +lemma hk28_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_23 j i k).Contains (fullFactor true 28 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 23 (kernel28_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha28_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-68140),(-68139)⟩,⟨(-116157),(-116156)⟩⟩,⟨⟨(-17186017015360),(-17186017015359)⟩,⟨(-12220282123144),(-12220282123142)⟩⟩,⟨⟨819882568341981990,819882568341982001⟩,⟨1244884843592842478,1244884843592842489⟩⟩] +lemma ha28_1_23_eq (j : Fin 7) : ha28_1_23 j = ((ha28_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha28_1_23_contains (j : Fin 7) : (ha28_1_23 j).Contains (fullFactor true 28 23 ((j.val:ℝ)/6)) := by + rw [ha28_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_22 j) true 28 22 j (ha28_1_22_contains j) +noncomputable def hk28_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_24 j i k) +lemma hk28_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_24 j i k).Contains (fullFactor true 28 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 24 (kernel28_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha28_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-18058),(-18057)⟩,⟨20450,20452⟩⟩,⟨⟨(-1575802991513),(-1575802991512)⟩,⟨3284032228473,3284032228474⟩⟩,⟨⟨180889978563891695,180889978563891698⟩,⟨(-133098896054967576),(-133098896054967574)⟩⟩] +lemma ha28_1_24_eq (j : Fin 7) : ha28_1_24 j = ((ha28_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha28_1_24_contains (j : Fin 7) : (ha28_1_24 j).Contains (fullFactor true 28 24 ((j.val:ℝ)/6)) := by + rw [ha28_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_23 j) true 28 23 j (ha28_1_23_contains j) +noncomputable def hk28_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_25 j i k) +lemma hk28_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_25 j i k).Contains (fullFactor true 28 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 25 (kernel28_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha28_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨4873,4875⟩,⟨2097,2098⟩⟩,⟨⟨581043593500,581043593501⟩,⟨164986451134,164986451135⟩⟩,⟨⟨(-20583595893836469),(-20583595893836468)⟩,⟨(-25128239863626808),(-25128239863626806)⟩⟩] +lemma ha28_1_25_eq (j : Fin 7) : ha28_1_25 j = ((ha28_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha28_1_25_contains (j : Fin 7) : (ha28_1_25 j).Contains (fullFactor true 28 25 ((j.val:ℝ)/6)) := by + rw [ha28_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_24 j) true 28 24 j (ha28_1_24_contains j) +noncomputable def hk28_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_26 j i k) +lemma hk28_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_26 j i k).Contains (fullFactor true 28 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 26 (kernel28_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha28_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨88,89⟩,⟨(-989),(-988)⟩⟩,⟨⟨10184098676,10184098677⟩,⟨(-95766764589),(-95766764587)⟩⟩,⟨⟨(-3341295292824767),(-3341295292824765)⟩,⟨3040242870013470,3040242870013472⟩⟩] +lemma ha28_1_26_eq (j : Fin 7) : ha28_1_26 j = ((ha28_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha28_1_26_contains (j : Fin 7) : (ha28_1_26 j).Contains (fullFactor true 28 26 ((j.val:ℝ)/6)) := by + rw [ha28_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_25 j) true 28 25 j (ha28_1_25_contains j) +noncomputable def hk28_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_27 j i k) +lemma hk28_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_27 j i k).Contains (fullFactor true 28 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 27 (kernel28_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha28_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-175),(-173)⟩,⟨40,41⟩⟩,⟨⟨(-14755862815),(-14755862814)⟩,⟨957183581,957183582⟩⟩,⟨⟨429844533006577,429844533006579⟩,⟨425726952013757,425726952013758⟩⟩] +lemma ha28_1_27_eq (j : Fin 7) : ha28_1_27 j = ((ha28_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha28_1_27_contains (j : Fin 7) : (ha28_1_27 j).Contains (fullFactor true 28 27 ((j.val:ℝ)/6)) := by + rw [ha28_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_26 j) true 28 26 j (ha28_1_26_contains j) +noncomputable def hk28_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_28 j i k) +lemma hk28_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_28 j i k).Contains (fullFactor true 28 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 28 (kernel28_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha28_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨15,17⟩,⟨26,27⟩⟩,⟨⟨510821671,510821672⟩,⟨2128854238,2128854239⟩⟩,⟨⟨52021348549814,52021348549815⟩,⟨(-58289999246842),(-58289999246840)⟩⟩] +lemma ha28_1_28_eq (j : Fin 7) : ha28_1_28 j = ((ha28_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha28_1_28_contains (j : Fin 7) : (ha28_1_28 j).Contains (fullFactor true 28 28 ((j.val:ℝ)/6)) := by + rw [ha28_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_27 j) true 28 27 j (ha28_1_27_contains j) +noncomputable def hk28_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_29 j i k) +lemma hk28_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_29 j i k).Contains (fullFactor true 28 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 29 (kernel28_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha28_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨3,4⟩,⟨(-5),(-3)⟩⟩,⟨⟨287490534,287490535⟩,⟨(-123662777),(-123662776)⟩⟩,⟨⟨(-7594997523036),(-7594997523035)⟩,⟨(-6100177086664),(-6100177086663)⟩⟩] +lemma ha28_1_29_eq (j : Fin 7) : ha28_1_29 j = ((ha28_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha28_1_29_contains (j : Fin 7) : (ha28_1_29 j).Contains (fullFactor true 28 29 ((j.val:ℝ)/6)) := by + rw [ha28_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_28 j) true 28 28 j (ha28_1_28_contains j) +noncomputable def hk28_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel28_0 j i k).mul (mpower1_30 j i k) +lemma hk28_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk28_1_30 j i k).Contains (fullFactor true 28 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk28_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel28_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 28 30 (kernel28_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha28_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-23589337),(-23589336)⟩,⟨(-36246255),(-36246254)⟩⟩,⟨⟨(-686725338050),(-686725338049)⟩,⟨952372817681,952372817682⟩⟩] +lemma ha28_1_30_eq (j : Fin 7) : ha28_1_30 j = ((ha28_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha28_1_30_contains (j : Fin 7) : (ha28_1_30 j).Contains (fullFactor true 28 30 ((j.val:ℝ)/6)) := by + rw [ha28_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha28_1_29 j) true 28 29 j (ha28_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders3.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders3.lean new file mode 100644 index 0000000000000000000000000000000000000000..33255934d85fafa1f234828baf914503b997c28d --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders3.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk3_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_0 j i k) +lemma hk3_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_0 j i k).Contains (fullFactor false 3 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 0 (power3_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha3_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999965,1000000000000000000000000000047⟩,⟨(-47),47⟩⟩,⟨⟨(-4508926683),2152309972⟩,⟨999999999999999999996712771924,1000000000000000000003287228080⟩⟩,⟨⟨(-1000000000000000000009057192871),(-999999999999999999990942807131)⟩,⟨(-11382050607),6668817169⟩⟩,⟨⟨(-6265099811),13334949965⟩,⟨(-1000000000000000000009800024888),(-999999999999999999990199975115)⟩⟩,⟨⟨999999999999999999975286562235,1000000000000000000024713437758⟩,⟨(-20023421740),29449888624⟩⟩,⟨⟨(-36999211493),25216127899⟩,⟨999999999999999999968869286671,1000000000000000000031130713320⟩⟩,⟨⟨(-1000000000000000000019659593357),(-999999999999999999980340406655)⟩,⟨(-26729443517),12589743185⟩⟩] +lemma ha3_0_0_eq (j : Fin 7) : ha3_0_0 j = ((atomPoints j).direct.powBin 7 3).conj := by fin_cases j <;> decide +kernel +lemma ha3_0_0_contains (j : Fin 7) : (ha3_0_0 j).Contains (fullFactor false 3 0 ((j.val:ℝ)/6)) := by + rw [ha3_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 3) ((j.val:ℝ)/6) 3 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 3 (by norm_num)) +noncomputable def hk3_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_1 j i k) +lemma hk3_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_1 j i k).Contains (fullFactor false 3 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 1 (power3_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha3_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-523598775598298873080054521933),(-523598775598298873074945478068)⟩,⟨(-2360868491),1126946867⟩⟩,⟨⟨(-6983569009),11919255524⟩,⟨(-1047197551196597746166151336865),(-1047197551196597746143848663138)⟩⟩,⟨⟨1570796326794896619214606156908,1570796326794896619250393843097⟩,⟨(-9841195771),20946490424⟩⟩,⟨⟨(-61679702501),41936956426⟩,⟨2094395102393195492254906963645,2094395102393195492365093036339⟩⟩,⟨⟨(-2617993877991494365473166683559),(-2617993877991494365301833316419)⟩,⟨(-96863709180),66015668467⟩⟩,⟨⟨(-39551844701),83973023388⟩,⟨(-3141592653589793238531762434063),(-3141592653589793238398237565974)⟩⟩] +lemma ha3_0_1_eq (j : Fin 7) : ha3_0_1 j = ((ha3_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha3_0_1_contains (j : Fin 7) : (ha3_0_1 j).Contains (fullFactor false 3 1 ((j.val:ℝ)/6)) := by + rw [ha3_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_0 j) false 3 0 j (ha3_0_0_contains j) +noncomputable def hk3_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_2 j i k) +lemma hk3_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_2 j i k).Contains (fullFactor false 3 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 2 (power3_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha3_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-295034000),618073926⟩,⟨(-137077838904018869707127189261),(-137077838904018869705353312390)⟩⟩,⟨⟨548311355616075478818249512347,548311355616075478831672494258⟩,⟨(-3656588183),6240907599⟩⟩,⟨⟨(-16451335109),7729257085⟩,⟨1233700550136169827340144970519,1233700550136169827372179544342⟩⟩,⟨⟨(-2193245422464301915361027964455),(-2193245422464301915238660061940)⟩,⟨(-64590833418),43916278074⟩⟩,⟨⟨(-86414307950),126794298817⟩,⟨(-3426945972600471742773597851104),(-3426945972600471742538414690139)⟩⟩,⟨⟨4934802200544679309311924861944,4934802200544679309537373197543⟩,⟨(-62127892375),131904516688⟩⟩] +lemma ha3_0_2_eq (j : Fin 7) : ha3_0_2 j = ((ha3_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha3_0_2_contains (j : Fin 7) : (ha3_0_2 j).Contains (fullFactor false 3 2 ((j.val:ℝ)/6)) := by + rw [ha3_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_1 j) false 3 1 j (ha3_0_1_contains j) +noncomputable def hk3_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_3 j i k) +lemma hk3_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_3 j i k).Contains (fullFactor false 3 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 3 (power3_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha3_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23924596203935046431555650402,23924596203935046431941404677⟩,⟨(-51493148),107874251⟩⟩,⟨⟨(-2178487719),1276390064⟩,⟨191396769631480371451340850599,191396769631480371456635590036⟩⟩,⟨⟨(-645964097506246253666624959179),(-645964097506246253647795527964)⟩,⟨(-8613898921),4047029546⟩⟩,⟨⟨(-30659345905),45092908391⟩,⟨(-1531174157051842971677057157843),(-1531174157051842971586754367217)⟩⟩,⟨⟨2990574525491880803861188282654,2990574525491880804075943602232⟩,⟨(-75410709728),110648899356⟩⟩,⟨⟨(-138130086868),65060176757⟩,⟨5167712780049970029131412805777,5167712780049970029383951091407⟩⟩] +lemma ha3_0_3_eq (j : Fin 7) : ha3_0_3 j = ((ha3_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha3_0_3_contains (j : Fin 7) : (ha3_0_3 j).Contains (fullFactor false 3 3 ((j.val:ℝ)/6)) := by + rw [ha3_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_2 j) false 3 2 j (ha3_0_2_contains j) +noncomputable def hk3_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_4 j i k) +lemma hk3_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_4 j i k).Contains (fullFactor false 3 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 4 (power3_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha3_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-14120707),6740438⟩,⟨3131722319766024859689823845,3131722319766024859750287544⟩⟩,⟨⟨(-50107557116256397756293719542),(-50107557116256397754748062690)⟩,⟨(-570326752),334158138⟩⟩,⟨⟨(-1589264787),3382670197⟩,⟨(-253669507901048013641425389009),(-253669507901048013633223633539)⟩⟩,⟨⟨801720913860102364063417064080,801720913860102364113251451616⟩,⟨(-16053195977),23610591622⟩⟩,⟨⟨(-72419535281),49356194101⟩,⟨1957326449853765537251641113411,1957326449853765537398428504990⟩⟩,⟨⟨(-4058712126416768218302823374234),(-4058712126416768218091560986561)⟩,⟨(-108487116537),51098143336⟩⟩] +lemma ha3_0_4_eq (j : Fin 7) : ha3_0_4 j = ((ha3_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha3_0_4_contains (j : Fin 7) : (ha3_0_4 j).Contains (fullFactor false 3 4 ((j.val:ℝ)/6)) := by + rw [ha3_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_3 j) false 3 3 j (ha3_0_3_contains j) +noncomputable def hk3_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_5 j i k) +lemma hk3_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_5 j i k).Contains (fullFactor false 3 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 5 (power3_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha3_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-327953194428670967579014782),(-327953194428670967571639130)⟩,⟨(-1478717),705858⟩⟩,⟨⟨(-69985917),119448956⟩,⟨(-10494502221717470962589025930),(-10494502221717470962231899277)⟩⟩,⟨⟨79692626246167045119389286902,79692626246167045122219613884⟩,⟨(-499282258),1062697185⟩⟩,⟨⟨(-9889981492),6724347007⟩,⟨335824071094959070786163032969,335824071094959070808106573627⟩⟩,⟨⟨(-1024853732589596773712956693210),(-1024853732589596773632836783953)⟩,⟨(-37918780003),25842842800⟩⟩,⟨⟨(-32105910344),68164465665⟩,⟨(-2550164039877345443936171161207),(-2550164039877345443795313663935)⟩⟩] +lemma ha3_0_5_eq (j : Fin 7) : ha3_0_5 j = ((ha3_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha3_0_5_contains (j : Fin 7) : (ha3_0_5 j).Contains (fullFactor false 3 5 ((j.val:ℝ)/6)) := by + rw [ha3_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_4 j) false 3 4 j (ha3_0_4_contains j) +noncomputable def hk3_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_6 j i k) +lemma hk3_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_6 j i k).Contains (fullFactor false 3 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 6 (power3_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha3_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-61598),129043⟩,⟨(-28619315176067161691925041),(-28619315176067161691190295)⟩⟩,⟨⟨1831636171268298348225610410,1831636171268298348293771050⟩,⟨(-12214847),20847776⟩⟩,⟨⟨(-278213473),130711790⟩,⟨20863480763352960872741845523,20863480763352960873549233917⟩⟩,⟨⟨(-117224714961171094292636645980),(-117224714961171094284603767441)⟩,⟨(-3452254800),2347239907⟩⟩,⟨⟨(-11276067374),16545188985⟩,⟨(-447176799626049401448779713736),(-447176799626049401412397400449)⟩⟩,⟨⟨1335262768854589495842312998822,1335262768854589495920316085328⟩,⟨(-16810615346),35690830762⟩⟩] +lemma ha3_0_6_eq (j : Fin 7) : ha3_0_6 j = ((ha3_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha3_0_6_contains (j : Fin 7) : (ha3_0_6 j).Contains (fullFactor false 3 6 ((j.val:ℝ)/6)) := by + rw [ha3_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_5 j) false 3 5 j (ha3_0_5_contains j) +noncomputable def hk3_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_7 j i k) +lemma hk3_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_7 j i k).Contains (fullFactor false 3 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 7 (power3_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha3_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2140719769235797028185870,2140719769235797028247644⟩,⟨(-4608),9653⟩⟩,⟨⟨(-3118820),1827337⟩,⟨274012130462182019606210387,274012130462182019617279404⟩⟩,⟨⟨(-4681754135318688100808087557),(-4681754135318688100612007538)⟩,⟨(-62430958),29331658⟩⟩,⟨⟨(-702292538),1032912221⟩,⟨(-35073552699159298511560883716),(-35073552699159298509045809491)⟩⟩,⟨⟨167243731971546642822364486881,167243731971546642836503793565⟩,⟨(-4217239337),6187886211⟩⟩,⟨⟨(-16018007389),7544586525⟩,⟨599264529320792076872428475316,599264529320792076909343696918⟩⟩] +lemma ha3_0_7_eq (j : Fin 7) : ha3_0_7 j = ((ha3_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha3_0_7_contains (j : Fin 7) : (ha3_0_7 j).Contains (fullFactor false 3 7 ((j.val:ℝ)/6)) := by + rw [ha3_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_6 j) false 3 6 j (ha3_0_6_contains j) +noncomputable def hk3_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_8 j i k) +lemma hk3_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_8 j i k).Contains (fullFactor false 3 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 8 (power3_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha3_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-632),302⟩,⟨140109781258867029451685,140109781258867029456175⟩⟩,⟨⟨(-35868104002269959540987555),(-35868104002269959539424452)⟩,⟨(-408253),239198⟩⟩,⟨⟨(-5759258),12258290⟩,⟨(-919260274839426580267945931),(-919260274839426580226519612)⟩⟩,⟨⟨9182234624581109641948900493,9182234624581109642636573347⟩,⟨(-183859757),270415788⟩⟩,⟨⟨(-2024981028),1380088346⟩,⟨54730383304244933378040644908,54730383304244933382841934422⟩⟩,⟨⟨(-235330630358893204550914416730),(-235330630358893204535668762443)⟩,⟨(-6290256793),2962752201⟩⟩] +lemma ha3_0_8_eq (j : Fin 7) : ha3_0_8 j = ((ha3_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha3_0_8_contains (j : Fin 7) : (ha3_0_8 j).Contains (fullFactor false 3 8 ((j.val:ℝ)/6)) := by + rw [ha3_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_7 j) false 3 7 j (ha3_0_7_contains j) +noncomputable def hk3_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_9 j i k) +lemma hk3_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_9 j i k).Contains (fullFactor false 3 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 9 (power3_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha3_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-8151256657387584305064),(-8151256657387584304776)⟩,⟨(-37),18⟩⟩,⟨⟨(-27832),47503⟩,⟨(-4173443408582443164216716),(-4173443408582443164021555)⟩⟩,⟨⟨160441184787359821869873563,160441184787359821877614521⟩,⟨(-1005181),2139476⟩⟩,⟨⟨(-62928612),42786109⟩,⟨2136803025194210899945582323,2136803025194210900112412719⟩⟩,⟨⟨(-15920423158960125596270897778),(-15920423158960125594823582990)⟩,⟨(-589043104),401451427⟩⟩,⟨⟨(-1034195617),2195713837⟩,⟨(-82145886611128228802148557501),(-82145886611128228796565341744)⟩⟩] +lemma ha3_0_9_eq (j : Fin 7) : ha3_0_9 j = ((ha3_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha3_0_9_contains (j : Fin 7) : (ha3_0_9 j).Contains (fullFactor false 3 9 ((j.val:ℝ)/6)) := by + rw [ha3_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_8 j) false 3 8 j (ha3_0_8_contains j) +noncomputable def hk3_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_10 j i k) +lemma hk3_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_10 j i k).Contains (fullFactor false 3 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 10 (power3_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha3_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),2⟩,⟨(-426798800539562151463),(-426798800539562151446)⟩⟩,⟨⟨437041971752511643078585,437041971752511643100415⟩,⟨(-2915),4975⟩⟩,⟨⟨(-336069),157894⟩,⟨25202042373060605480593987,25202042373060605481890155⟩⟩,⟨⟨(-447530979074571922541830622),(-447530979074571922505465209)⟩,⟨(-13179738),8961102⟩⟩,⟨⟨(-105099738),154211125⟩,⟨(-4167957036519161635494814728),(-4167957036519161635102641582)⟩⟩,⟨⟨25806891390014060011873798199,25806891390014060013709963047⟩,⟨(-324902136),689803846⟩⟩] +lemma ha3_0_10_eq (j : Fin 7) : ha3_0_10 j = ((ha3_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha3_0_10_contains (j : Fin 7) : (ha3_0_10 j).Contains (fullFactor false 3 10 ((j.val:ℝ)/6)) := by + rw [ha3_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_9 j) false 3 9 j (ha3_0_9_contains j) +noncomputable def hk3_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_11 j i k) +lemma hk3_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_11 j i k).Contains (fullFactor false 3 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 11 (power3_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha3_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20315575399030665720,20315575399030665722⟩,⟨(-1),1⟩⟩,⟨⟨(-474),278⟩,⟨41606298417214803395621,41606298417214803397832⟩⟩,⟨⟨(-3598843235212085340586510),(-3598843235212085340389961)⟩,⟨(-47991),22548⟩⟩,⟨⟨(-1706190),2509417⟩,⟨(-85209699158455917360093440),(-85209699158455917352898249)⟩⟩,⟨⟨991971455030794224612780797,991971455030794224709275331⟩,⟨(-25013680),36702162⟩⟩,⟨⟨(-197007518),92791834⟩,⟨7370430945714350777045972776,7370430945714350777593841042⟩⟩] +lemma ha3_0_11_eq (j : Fin 7) : ha3_0_11 j = ((ha3_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha3_0_11_contains (j : Fin 7) : (ha3_0_11 j).Contains (fullFactor false 3 11 ((j.val:ℝ)/6)) := by + rw [ha3_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_10 j) false 3 10 j (ha3_0_10_contains j) +noncomputable def hk3_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_12 j i k) +lemma hk3_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_12 j i k).Contains (fullFactor false 3 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 12 (power3_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha3_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨886434200375614885,886434200375614886⟩⟩,⟨⟨(-3630834484738518571159),(-3630834484738518570954)⟩,⟨(-42),25⟩⟩,⟨⟨(-2952),6283⟩,⟨(-471087477881817150384883),(-471087477881817150357654)⟩⟩,⟨⟨14871898049488972066394911,14871898049488972067698048⟩,⟨(-297787),437976⟩⟩,⟨⟨(-8007170),5457139⟩,⟨216414599701077852897280160,216414599701077852919020871⟩⟩,⟨⟨(-1929574309403923047995501646),(-1929574309403923047845928043)⟩,⟨(-51576448),24292846⟩⟩] +lemma ha3_0_12_eq (j : Fin 7) : ha3_0_12 j = ((ha3_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha3_0_12_contains (j : Fin 7) : (ha3_0_12 j).Contains (fullFactor false 3 12 ((j.val:ℝ)/6)) := by + rw [ha3_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_11 j) false 3 11 j (ha3_0_11_contains j) +noncomputable def hk3_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_13 j i k) +lemma hk3_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_13 j i k).Contains (fullFactor false 3 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 13 (power3_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha3_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-35702758612702237),(-35702758612702236)⟩,⟨(-1),1⟩⟩,⟨⟨(-3),4⟩,⟨(-292476998555256723035),(-292476998555256723017)⟩⟩,⟨⟨56921729219679268116572,56921729219679268120044⟩,⟨(-357),760⟩⟩,⟨⟨(-70562),47976⟩,⟨2395971572164663074921207,2395971572164663075138779⟩⟩,⟨⟨(-43582469009646285033416537),(-43582469009646285028899574)⟩,⟨(-1612518),1098982⟩⟩,⟨⟨(-5870633),12464015⟩,⟨(-466302805767612564443991377),(-466302805767612564406360986)⟩⟩] +lemma ha3_0_13_eq (j : Fin 7) : ha3_0_13 j = ((ha3_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha3_0_13_contains (j : Fin 7) : (ha3_0_13 j).Contains (fullFactor false 3 13 ((j.val:ℝ)/6)) := by + rw [ha3_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_12 j) false 3 12 j (ha3_0_12_contains j) +noncomputable def hk3_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_14 j i k) +lemma hk3_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_14 j i k).Contains (fullFactor false 3 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 14 (power3_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha3_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1335280049649466),(-1335280049649465)⟩⟩,⟨⟨21877228333456835516,21877228333456835519⟩,⟨(-1),1⟩⟩,⟨⟨(-86),41⟩,⟨6386603083791852240952,6386603083791852241362⟩⟩,⟨⟨(-358436509015356793138354),(-358436509015356793104664)⟩,⟨(-10557),7178⟩⟩,⟨⟨(-205510),301541⟩,⟨(-8149902646786285757585890),(-8149902646786285756715277)⟩⟩,⟨⟨104638104924845707114726968,104638104924845707123504283⟩,⟨(-1317367),2796919⟩⟩] +lemma ha3_0_14_eq (j : Fin 7) : ha3_0_14 j = ((ha3_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha3_0_14_contains (j : Fin 7) : (ha3_0_14 j).Contains (fullFactor false 3 14 ((j.val:ℝ)/6)) := by + rw [ha3_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_13 j) false 3 13 j (ha3_0_13_contains j) +noncomputable def hk3_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_15 j i k) +lemma hk3_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_15 j i k).Contains (fullFactor false 3 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 15 (power3_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha3_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨46610066605153,46610066605154⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1527318662517654886,1527318662517654887⟩⟩,⟨⟨(-668803510981146723278),(-668803510981146723232)⟩,⟨(-10),5⟩⟩,⟨⟨(-1003),1475⟩,⟨(-50047177933378515330451),(-50047177933378515325587)⟩⟩,⟨⟨1422426349034211492757614,1422426349034211492914094⟩,⟨(-35869),52629⟩⟩,⟨⟨(-585786),275909⟩,⟨21915353447830215826677206,21915353447830215828585282⟩⟩] +lemma ha3_0_15_eq (j : Fin 7) : ha3_0_15 j = ((ha3_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha3_0_15_contains (j : Fin 7) : (ha3_0_15 j).Contains (fullFactor false 3 15 ((j.val:ℝ)/6)) := by + rw [ha3_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_14 j) false 3 14 j (ha3_0_14_contains j) +noncomputable def hk3_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_16 j i k) +lemma hk3_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_16 j i k).Contains (fullFactor false 3 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 16 (power3_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha3_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1525310862813,1525310862814⟩⟩,⟨⟨(-99962772705334444),(-99962772705334443)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-65659631149794723626),(-65659631149794723620)⟩⟩,⟨⟨6551160272016798098500,6551160272016798099159⟩,⟨(-132),194⟩⟩,⟨⟨(-8612),5870⟩,⟨232743967104084891362666,232743967104084891389012⟩⟩,⟨⟨(-4303069587032947007543644),(-4303069587032947007155296)⟩,⟨(-115019),54175⟩⟩] +lemma ha3_0_16_eq (j : Fin 7) : ha3_0_16 j = ((ha3_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha3_0_16_contains (j : Fin 7) : (ha3_0_16 j).Contains (fullFactor false 3 16 ((j.val:ℝ)/6)) := by + rw [ha3_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_15 j) false 3 15 j (ha3_0_15_contains j) +noncomputable def hk3_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_17 j i k) +lemma hk3_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_17 j i k).Contains (fullFactor false 3 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 17 (power3_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha3_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-46979464717),(-46979464716)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-6157692399285196),(-6157692399285195)⟩⟩,⟨⟨6066935731106195666,6066935731106195668⟩,⟨(-1),1⟩⟩,⟨⟨(-24),17⟩,⟨807101058159109193385,807101058159109193470⟩⟩,⟨⟨(-35842487118702823488662),(-35842487118702823484490)⟩,⟨(-1327),904⟩⟩,⟨⟨(-10012),21256⟩,⟨(-795205400147551278525611),(-795205400147551278451312)⟩⟩] +lemma ha3_0_17_eq (j : Fin 7) : ha3_0_17 j = ((ha3_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha3_0_17_contains (j : Fin 7) : (ha3_0_17 j).Contains (fullFactor false 3 17 ((j.val:ℝ)/6)) := by + rw [ha3_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_16 j) false 3 16 j (ha3_0_16_contains j) +noncomputable def hk3_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_18 j i k) +lemma hk3_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_18 j i k).Contains (fullFactor false 3 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 18 (power3_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha3_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1366577234),(-1366577233)⟩⟩,⟨⟨358240022308519,358240022308520⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨529440020073462376,529440020073462377⟩⟩,⟨⟨(-93910472408044662745),(-93910472408044662734)⟩,⟨(-3),2⟩⟩,⟨⟨(-132),194⟩,⟨(-5213078436041832671986),(-5213078436041832671362)⟩⟩,⟨⟨138789524622137721139850,138789524622137721153260⟩,⟨(-1748),3710⟩⟩] +lemma ha3_0_18_eq (j : Fin 7) : ha3_0_18 j = ((ha3_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha3_0_18_contains (j : Fin 7) : (ha3_0_18 j).Contains (fullFactor false 3 18 ((j.val:ℝ)/6)) := by + rw [ha3_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_17 j) false 3 17 j (ha3_0_17_contains j) +noncomputable def hk3_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_19 j i k) +lemma hk3_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_19 j i k).Contains (fullFactor false 3 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 19 (power3_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha3_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨37659903,37659904⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨19744635479057,19744635479058⟩⟩,⟨⟨(-43770654673137423),(-43770654673137422)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-10351875446044213763),(-10351875446044213760)⟩⟩,⟨⟨718305654265631155006,718305654265631155095⟩,⟨(-19),27⟩⟩,⟨⟨(-614),290⟩,⟨22948428997269873109385,22948428997269873111677⟩⟩] +lemma ha3_0_19_eq (j : Fin 7) : ha3_0_19 j = ((ha3_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha3_0_19_contains (j : Fin 7) : (ha3_0_19 j).Contains (fullFactor false 3 19 ((j.val:ℝ)/6)) := by + rw [ha3_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_18 j) false 3 18 j (ha3_0_18_contains j) +noncomputable def hk3_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_20 j i k) +lemma hk3_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_20 j i k).Contains (fullFactor false 3 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 20 (power3_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha3_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨985933,985934⟩⟩,⟨⟨(-1033826696147),(-1033826696146)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-3437739179098608),(-3437739179098606)⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨(-4),3⟩,⟨94025990269704865208,94025990269704865221⟩⟩,⟨⟨(-3604730797462500934100),(-3604730797462500933727)⟩,⟨(-97),46⟩⟩] +lemma ha3_0_20_eq (j : Fin 7) : ha3_0_20 j = ((ha3_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha3_0_20_contains (j : Fin 7) : (ha3_0_20 j).Contains (fullFactor false 3 20 ((j.val:ℝ)/6)) := by + rw [ha3_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_19 j) false 3 19 j (ha3_0_19_contains j) +noncomputable def hk3_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_21 j i k) +lemma hk3_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_21 j i k).Contains (fullFactor false 3 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 21 (power3_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha3_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24583),(-24582)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-51553370694),(-51553370693)⟩⟩,⟨⟨257142289286047,257142289286048⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨(-11721879376103578824),(-11721879376103578822)⟩,⟨(-1),1⟩⟩,⟨⟨(-7),15⟩,⟨(-539266466260812848973),(-539266466260812848914)⟩⟩] +lemma ha3_0_21_eq (j : Fin 7) : ha3_0_21 j = ((ha3_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha3_0_21_contains (j : Fin 7) : (ha3_0_21 j).Contains (fullFactor false 3 21 ((j.val:ℝ)/6)) := by + rw [ha3_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_20 j) false 3 20 j (ha3_0_20_contains j) +noncomputable def hk3_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_22 j i k) +lemma hk3_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_22 j i k).Contains (fullFactor false 3 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 22 (power3_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha3_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-586),(-585)⟩⟩,⟨⟨2453934706,2453934707⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨18359916521552,18359916521553⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1394900383872451220),(-1394900383872451219)⟩⟩,⟨⟨77007071306013533794,77007071306013533804⟩,⟨(-1),3⟩⟩] +lemma ha3_0_22_eq (j : Fin 7) : ha3_0_22 j = ((ha3_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha3_0_22_contains (j : Fin 7) : (ha3_0_22 j).Contains (fullFactor false 3 22 ((j.val:ℝ)/6)) := by + rw [ha3_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_21 j) false 3 21 j (ha3_0_21_contains j) +noncomputable def hk3_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_23 j i k) +lemma hk3_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_23 j i k).Contains (fullFactor false 3 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 23 (power3_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha3_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨13,14⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨111728452,111728453⟩⟩,⟨⟨(-1253899540536),(-1253899540535)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨158775681103741857,158775681103741858⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨10518471716932064454,10518471716932064456⟩⟩] +lemma ha3_0_23_eq (j : Fin 7) : ha3_0_23 j = ((ha3_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha3_0_23_contains (j : Fin 7) : (ha3_0_23 j).Contains (fullFactor false 3 23 ((j.val:ℝ)/6)) := by + rw [ha3_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_22 j) false 3 22 j (ha3_0_22_contains j) +noncomputable def hk3_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_24 j i k) +lemma hk3_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_24 j i k).Contains (fullFactor false 3 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 24 (power3_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha3_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-4875074),(-4875073)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-82067533019),(-82067533018)⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨17319740045980249,17319740045980250⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha3_0_24_eq (j : Fin 7) : ha3_0_24 j = ((ha3_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha3_0_24_contains (j : Fin 7) : (ha3_0_24 j).Contains (fullFactor false 3 24 ((j.val:ℝ)/6)) := by + rw [ha3_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_23 j) false 3 23 j (ha3_0_23_contains j) +noncomputable def hk3_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_25 j i k) +lemma hk3_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_25 j i k).Contains (fullFactor false 3 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 25 (power3_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha3_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-204207),(-204206)⟩⟩,⟨⟨5156455176,5156455177⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨(-1813718936351217),(-1813718936351216)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha3_0_25_eq (j : Fin 7) : ha3_0_25 j = ((ha3_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha3_0_25_contains (j : Fin 7) : (ha3_0_25 j).Contains (fullFactor false 3 25 ((j.val:ℝ)/6)) := by + rw [ha3_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_24 j) false 3 24 j (ha3_0_24_contains j) +noncomputable def hk3_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_26 j i k) +lemma hk3_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_26 j i k).Contains (fullFactor false 3 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 26 (power3_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha3_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨8224,8225⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨311528494,311528495⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-182627118144798),(-182627118144797)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha3_0_26_eq (j : Fin 7) : ha3_0_26 j = ((ha3_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha3_0_26_contains (j : Fin 7) : (ha3_0_26 j).Contains (fullFactor false 3 26 ((j.val:ℝ)/6)) := by + rw [ha3_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_25 j) false 3 25 j (ha3_0_25_contains j) +noncomputable def hk3_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_27 j i k) +lemma hk3_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_27 j i k).Contains (fullFactor false 3 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 27 (power3_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha3_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨318,320⟩⟩,⟨⟨(-18123994),(-18123993)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨17708025083641,17708025083642⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha3_0_27_eq (j : Fin 7) : ha3_0_27 j = ((ha3_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha3_0_27_contains (j : Fin 7) : (ha3_0_27 j).Contains (fullFactor false 3 27 ((j.val:ℝ)/6)) := by + rw [ha3_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_26 j) false 3 26 j (ha3_0_26_contains j) +noncomputable def hk3_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_28 j i k) +lemma hk3_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_28 j i k).Contains (fullFactor false 3 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 28 (power3_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha3_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-12),(-11)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1016754),(-1016753)⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1655696473581,1655696473582⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha3_0_28_eq (j : Fin 7) : ha3_0_28 j = ((ha3_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha3_0_28_contains (j : Fin 7) : (ha3_0_28 j).Contains (fullFactor false 3 28 ((j.val:ℝ)/6)) := by + rw [ha3_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_27 j) false 3 27 j (ha3_0_27_contains j) +noncomputable def hk3_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_29 j i k) +lemma hk3_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_29 j i k).Contains (fullFactor false 3 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 29 (power3_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha3_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨55072,55073⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨(-149469076954),(-149469076953)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha3_0_29_eq (j : Fin 7) : ha3_0_29 j = ((ha3_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha3_0_29_contains (j : Fin 7) : (ha3_0_29 j).Contains (fullFactor false 3 29 ((j.val:ℝ)/6)) := by + rw [ha3_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_28 j) false 3 28 j (ha3_0_28_contains j) +noncomputable def hk3_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power3 j i k).conj.mul (mpower0_30 j i k) +lemma hk3_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk3_0_30 j i k).Contains (fullFactor false 3 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power3 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 30 (power3_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha3_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2883,2884⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-13043637614),(-13043637613)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha3_0_30_eq (j : Fin 7) : ha3_0_30 j = ((ha3_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha3_0_30_contains (j : Fin 7) : (ha3_0_30 j).Contains (fullFactor false 3 30 ((j.val:ℝ)/6)) := by + rw [ha3_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_0_29 j) false 3 29 j (ha3_0_29_contains j) +noncomputable def hk3_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_0 j i k) +lemma hk3_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_0 j i k).Contains (fullFactor true 3 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 0 (kernel3_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha3_1_0 : Fin 7 → CBox := ![⟨⟨2843789610077025929,2843789610077025936⟩,⟨(-3),3⟩⟩,⟨⟨(-64228312723007910724),(-64228312723007910558)⟩,⟨266166603357464236131,266166603357464236302⟩⟩,⟨⟨(-494776904616736031147973),(-494776904616736030744849)⟩,⟨(-695181898442626142129027),(-695181898442626141728600)⟩⟩,⟨⟨(-106555917680778035558591732),(-106555917680778035421458844)⟩,⟨(-354976034124043666142003790),(-354976034124043666003755425)⟩⟩,⟨⟨15213751127784570539427089845,15213751127784570544253007311⟩,⟨(-4099688160756901354180537737),(-4099688160756901349483904669)⟩⟩,⟨⟨20629052952773211972690043554,20629052952773211997040008897⟩,⟨149592350264871972775750070482,149592350264871972801712808839⟩⟩,⟨⟨(-595922937275834702091915645087),(-595922937275834701979420127280)⟩,⟨132015435447815391188745737182,132015435447815391291484111950⟩⟩] +lemma ha3_1_0_eq (j : Fin 7) : ha3_1_0 j = atomKernel3_0 j := by fin_cases j <;> decide +kernel +lemma ha3_1_0_contains (j : Fin 7) : (ha3_1_0 j).Contains (fullFactor true 3 0 ((j.val:ℝ)/6)) := by + rw [ha3_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel3_0_contains j +noncomputable def hk3_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_1 j i k) +lemma hk3_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_1 j i k).Contains (fullFactor true 3 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 1 (kernel3_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha3_1_1 : Fin 7 → CBox := ![⟨⟨(-26206483738960704163),(-26206483738960704098)⟩,⟨(-28),28⟩⟩,⟨⟨1481959463502825266027,1481959463502825267941⟩,⟨(-1801702358473668140785),(-1801702358473668138848)⟩⟩,⟨⟨(-1144235911228454129864486),(-1144235911228454125798275)⟩,⟨5970935715710382851586040,5970935715710382855652717⟩⟩,⟨⟨(-1511765319270662542217988349),(-1511765319270662541116960688)⟩,⟨1548895291282867661132607122,1548895291282867662229291849⟩⟩,⟨⟨(-41994771009654300602998834631),(-41994771009654300573853781897)⟩,⟨(-64074876924145524496005170041),(-64074876924145524466348903640)⟩⟩,⟨⟨596599890019863798301114245875,596599890019863798426321053128⟩,⟨(-189634434098775036919004515716),(-189634434098775036800638386208)⟩⟩,⟨⟨588609623562744722558957134694,588609623562744722952945344464⟩,⟨2127104262412552993036337815244,2127104262412552993468782183206⟩⟩] +lemma ha3_1_1_eq (j : Fin 7) : ha3_1_1 j = ((ha3_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha3_1_1_contains (j : Fin 7) : (ha3_1_1 j).Contains (fullFactor true 3 1 ((j.val:ℝ)/6)) := by + rw [ha3_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_0 j) true 3 0 j (ha3_1_0_contains j) +noncomputable def hk3_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_2 j i k) +lemma hk3_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_2 j i k).Contains (fullFactor true 3 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 2 (kernel3_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha3_1_2 : Fin 7 → CBox := ![⟨⟨120750808626417676319,120750808626417676620⟩,⟨(-130),130⟩⟩,⟨⟨(-9029760369223308801402),(-9029760369223308790435)⟩,⟨4151272276095303051415,4151272276095303062429⟩⟩,⟨⟨18192461552773175521159842,18192461552773175541699841⟩,⟨(-11752591593888755694446934),(-11752591593888755673908729)⟩⟩,⟨⟨6095234490319404936856610149,6095234490319404941235045892⟩,⟨1669583651340407660105761894,1669583651340407664489010242⟩⟩,⟨⟨(-116194095883841057874140715987),(-116194095883841057782979908570)⟩,⟨145555833407333191032293738274,145555833407333191122551878647⟩⟩,⟨⟨(-597450555008754758946733123985),(-597450555008754758658959147301)⟩,⟨(-1151863340061965034546216729911),(-1151863340061965034244688731333)⟩⟩,⟨⟨3785251837595132000167293885354,3785251837595132000997468709104⟩,⟨(-1262449089469047539803437474687),(-1262449089469047539047467367527)⟩⟩] +lemma ha3_1_2_eq (j : Fin 7) : ha3_1_2 j = ((ha3_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha3_1_2_contains (j : Fin 7) : (ha3_1_2 j).Contains (fullFactor true 3 2 ((j.val:ℝ)/6)) := by + rw [ha3_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_1 j) true 3 1 j (ha3_1_1_contains j) +noncomputable def hk3_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_3 j i k) +lemma hk3_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_3 j i k).Contains (fullFactor true 3 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 3 (kernel3_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha3_1_3 : Fin 7 → CBox := ![⟨⟨(-370919856555874564935),(-370919856555874564008)⟩,⟨(-400),400⟩⟩,⟨⟨28219356825619465215280,28219356825619465257046⟩,⟨582262826925070975078,582262826925071016885⟩⟩,⟨⟨(-50033012907132862185474099),(-50033012907132862116346675)⟩,⟨(-11943174749198354387362816),(-11943174749198354318233708)⟩⟩,⟨⟨(-2906911861877585082538948334),(-2906911861877585070917669660)⟩,⟨(-11953689949653953915471739766),(-11953689949653953903843417613)⟩⟩,⟨⟨282847283740151868944126237442,282847283740151869130070818815⟩,⟨105415498583111998387838487021,105415498583111998574620497262⟩⟩,⟨⟨(-1428305101584093675146921370367),(-1428305101584093674663311395541)⟩,⟨1084008512647987889141524443258,1084008512647987889607644807910⟩⟩,⟨⟨(-1756501989266606212111809624477),(-1756501989266606211144314354171)⟩,⟨(-4477196216151633520338424332317),(-4477196216151633519277091946707)⟩⟩] +lemma ha3_1_3_eq (j : Fin 7) : ha3_1_3 j = ((ha3_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha3_1_3_contains (j : Fin 7) : (ha3_1_3 j).Contains (fullFactor true 3 3 ((j.val:ℝ)/6)) := by + rw [ha3_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_2 j) true 3 2 j (ha3_1_2_contains j) +noncomputable def hk3_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_4 j i k) +lemma hk3_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_4 j i k).Contains (fullFactor true 3 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 4 (kernel3_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha3_1_4 : Fin 7 → CBox := ![⟨⟨854538004046111320968,854538004046111323107⟩,⟨(-922),922⟩⟩,⟨⟨(-53542824396151617786868),(-53542824396151617667788)⟩,⟨(-27344852589898870700217),(-27344852589898870581184)⟩⟩,⟨⟨46207659229019142777133640,46207659229019142951472970⟩,⟨79120094211605436628852890,79120094211605436803198994⟩⟩,⟨⟨(-13209069949135841248572051687),(-13209069949135841225444711046)⟩,⟨12169528837008859704904165572,12169528837008859728011092553⟩⟩,⟨⟨14601001747881748835674117471,14601001747881749122578552835⟩,⟨(-366623362878199169140262737704),(-366623362878199168853569918729)⟩⟩,⟨⟨1358614539966023619922958117441,1358614539966023620488494876950⟩,⟨1267894129398617422807690583816,1267894129398617423388936729416⟩⟩,⟨⟨(-3959361961659830116318546932967),(-3959361961659830115301876782785)⟩,⟨1795868142541842386257516117400,1795868142541842387186467682020⟩⟩] +lemma ha3_1_4_eq (j : Fin 7) : ha3_1_4 j = ((ha3_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha3_1_4_contains (j : Fin 7) : (ha3_1_4 j).Contains (fullFactor true 3 4 ((j.val:ℝ)/6)) := by + rw [ha3_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_3 j) true 3 3 j (ha3_1_3_contains j) +noncomputable def hk3_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_5 j i k) +lemma hk3_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_5 j i k).Contains (fullFactor true 3 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 5 (kernel3_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha3_1_5 : Fin 7 → CBox := ![⟨⟨(-1574971385225068361048),(-1574971385225068357100)⟩,⟨(-1700),1700⟩⟩,⟨⟨61761444652058965354257,61761444652058965625672⟩,⟨81739341030025490402813,81739341030025490674126⟩⟩,⟨⟨35995000732812252235811489,35995000732812252587471033⟩,⟨(-125505564853774618569211161),(-125505564853774618217556672)⟩⟩,⟨⟨19909374592707441908303938160,19909374592707441945064662786⟩,⟨6607204548875766574484640343,6607204548875766611256174386⟩⟩,⟨⟨(-343184339586920015031767115579),(-343184339586920014678818682920)⟩,⟨97621721937127819222573225451,97621721937127819574957294500⟩⟩,⟨⟨844568760031360187920906616874,844568760031360188479387891880⟩,⟨(-1288665363940605269991255001902),(-1288665363940605269443201118368)⟩⟩,⟨⟨1445677859979626714395123163559,1445677859979626715108799269612⟩,⟨2792028591070177955378015769649,2792028591070177956156463376867⟩⟩] +lemma ha3_1_5_eq (j : Fin 7) : ha3_1_5 j = ((ha3_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha3_1_5_contains (j : Fin 7) : (ha3_1_5 j).Contains (fullFactor true 3 5 ((j.val:ℝ)/6)) := by + rw [ha3_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_4 j) true 3 4 j (ha3_1_4_contains j) +noncomputable def hk3_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_6 j i k) +lemma hk3_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_6 j i k).Contains (fullFactor true 3 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 6 (kernel3_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha3_1_6 : Fin 7 → CBox := ![⟨⟨2418982394124860654865,2418982394124860660938⟩,⟨(-2612),2612⟩⟩,⟨⟨(-28263649891130446354299),(-28263649891130445838980)⟩,⟨(-142708838973634928534757),(-142708838973634928019463)⟩⟩,⟨⟨(-137265955924376708935678431),(-137265955924376708344827217)⟩,⟨72092100217979848669426233,72092100217979849260266877⟩⟩,⟨⟨(-3765304345590307725836956954),(-3765304345590307677143874998)⟩,⟨(-20066830200117961788487451699),(-20066830200117961739782396285)⟩⟩,⟨⟨161842984238362614426573738464,161842984238362614787564447057⟩,⟨239596039109724466649996021379,239596039109724467011683209672⟩⟩,⟨⟨(-976568923007012275590989366915),(-976568923007012275149163595753)⟩,⟨(-423783317117408079278614062021),(-423783317117408078831709034797)⟩⟩,⟨⟨1635104693718682526110046500828,1635104693718682526606373217741⟩,⟨(-957441494809575308766832453610),(-957441494809575308309905702636)⟩⟩] +lemma ha3_1_6_eq (j : Fin 7) : ha3_1_6 j = ((ha3_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha3_1_6_contains (j : Fin 7) : (ha3_1_6 j).Contains (fullFactor true 3 6 ((j.val:ℝ)/6)) := by + rw [ha3_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_5 j) true 3 5 j (ha3_1_5_contains j) +noncomputable def hk3_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_7 j i k) +lemma hk3_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_7 j i k).Contains (fullFactor true 3 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 7 (kernel3_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha3_1_7 : Fin 7 → CBox := ![⟨⟨(-3184534495390584108493),(-3184534495390584100487)⟩,⟨(-3439),3439⟩⟩,⟨⟨(-44842287769613143438356),(-44842287769613142599966)⟩,⟨171302722500924379018174,171302722500924379856755⟩⟩,⟨⟨149588629396484016330390763,149588629396484017181152880⟩,⟨50284543990658276481062411,50284543990658277331831586⟩⟩,⟨⟨(-13121605405062001229866909567),(-13121605405062001174586892519)⟩,⟨10860444409204354507347261159,10860444409204354562606492744⟩⟩,⟨⟨123097328729395898963207508004,123097328729395899280682454999⟩,⟨(-158683749072160228782744283511),(-158683749072160228465688007489)⟩⟩,⟨⟨(-149068270729794245227005959192),(-149068270729794244920631725921)⟩,⟨612577982474023366463322154728,612577982474023366768092984496⟩⟩,⟨⟨(-537767894385041978033484919263),(-537767894385041977782748675484)⟩,⟨(-817803374874768601964218239493),(-817803374874768601693159105532)⟩⟩] +lemma ha3_1_7_eq (j : Fin 7) : ha3_1_7 j = ((ha3_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha3_1_7_contains (j : Fin 7) : (ha3_1_7 j).Contains (fullFactor true 3 7 ((j.val:ℝ)/6)) := by + rw [ha3_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_6 j) true 3 6 j (ha3_1_6_contains j) +noncomputable def hk3_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_8 j i k) +lemma hk3_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_8 j i k).Contains (fullFactor true 3 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 8 (kernel3_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha3_1_8 : Fin 7 → CBox := ![⟨⟨3668320397801524039113,3668320397801524048348⟩,⟨(-3962),3962⟩⟩,⟨⟨122581376141489953640518,122581376141489954834037⟩,⟨(-143316076404219185886973),(-143316076404219184693162)⟩⟩,⟨⟨(-59691667512049772956055205),(-59691667512049771884364588)⟩,⟨(-127247798521958596487309881),(-127247798521958595415610510)⟩⟩,⟨⟨11576522328530066732551375888,11576522328530066787428403492⟩,⟨4536740237904876153081145432,4536740237904876207966142210⟩⟩,⟨⟨(-114956692278342366342945074639),(-114956692278342366099343621049)⟩,⟨(-41030735644269367429114276114),(-41030735644269367185394304768)⟩⟩,⟨⟨325943992374629027794416535870,325943992374629027978061545226⟩,⟨22193282155358369897270882663,22193282155358370080969990522⟩⟩,⟨⟨(-356516349991094073503536843378),(-356516349991094073374086263441)⟩,⟨261931943996415281708389802370,261931943996415281828762656123⟩⟩] +lemma ha3_1_8_eq (j : Fin 7) : ha3_1_8 j = ((ha3_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha3_1_8_contains (j : Fin 7) : (ha3_1_8 j).Contains (fullFactor true 3 8 ((j.val:ℝ)/6)) := by + rw [ha3_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_7 j) true 3 7 j (ha3_1_7_contains j) +noncomputable def hk3_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_9 j i k) +lemma hk3_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_9 j i k).Contains (fullFactor true 3 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 9 (kernel3_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha3_1_9 : Fin 7 → CBox := ![⟨⟨(-3756090445636012283445),(-3756090445636012273976)⟩,⟨(-4057),4057⟩⟩,⟨⟨(-163618472166411634981019),(-163618472166411633470696)⟩,⟨71439268931558071404523,71439268931558072915004⟩⟩,⟨⟨(-40161207407591968489125034),(-40161207407591967289241337)⟩,⟨103770160328136386133931848,103770160328136387333809911⟩⟩,⟨⟨(-1065163449529194018662091281),(-1065163449529193970234610558)⟩,⟨(-7997227145816584795249382252),(-7997227145816584746818246350)⟩⟩,⟨⟨(-1706798838274707418035230471),(-1706798838274707251781390444)⟩,⟨65919429617459010688062748569,65919429617459010854356878406⟩⟩,⟨⟨(-15433096438910464651661251811),(-15433096438910464553791622158)⟩,⟨(-149689837913799218231569500343),(-149689837913799218133356974324)⟩⟩,⟨⟨112531926767879715029905856548,112531926767879715081261487777⟩,⟨137578442595745575518857433449,137578442595745575573780397389⟩⟩] +lemma ha3_1_9_eq (j : Fin 7) : ha3_1_9 j = ((ha3_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha3_1_9_contains (j : Fin 7) : (ha3_1_9 j).Contains (fullFactor true 3 9 ((j.val:ℝ)/6)) := by + rw [ha3_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_8 j) true 3 8 j (ha3_1_8_contains j) +noncomputable def hk3_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_10 j i k) +lemma hk3_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_10 j i k).Contains (fullFactor true 3 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 10 (kernel3_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha3_1_10 : Fin 7 → CBox := ![⟨⟨3461364470733813253872,3461364470733813262610⟩,⟨(-3739),3739⟩⟩,⟨⟨151993806312621580441974,151993806312621582161883⟩,⟨6064091613144275728809,6064091613144277448664⟩⟩,⟨⟨73216760773287174458314254,73216760773287175667270901⟩,⟨(-30408075732848886668724391),(-30408075732848885459772204)⟩⟩,⟨⟨(-3783768210465414114604028347),(-3783768210465414076145164700)⟩,⟨2807320701760530463468918831,2807320701760530501921922566⟩⟩,⟨⟨30713346130859398550142375383,30713346130859398652261230318⟩,⟨(-9200604108213715811667310682),(-9200604108213715709624421441)⟩⟩,⟨⟨(-60065769427074819595477572685),(-60065769427074819548263725933)⟩,⟨16847607457877419564652890205,16847607457877419611606316515⟩⟩,⟨⟨47566884124235523831054904958,47566884124235523852016914349⟩,⟨(-43218928333900428367791674571),(-43218928333900428348078145374)⟩⟩] +lemma ha3_1_10_eq (j : Fin 7) : ha3_1_10 j = ((ha3_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha3_1_10_contains (j : Fin 7) : (ha3_1_10 j).Contains (fullFactor true 3 10 ((j.val:ℝ)/6)) := by + rw [ha3_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_9 j) true 3 9 j (ha3_1_9_contains j) +noncomputable def hk3_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_11 j i k) +lemma hk3_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_11 j i k).Contains (fullFactor true 3 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 11 (kernel3_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha3_1_11 : Fin 7 → CBox := ![⟨⟨(-2899785918041085500056),(-2899785918041085492726)⟩,⟨(-3133),3133⟩⟩,⟨⟨(-103879452147605481309944),(-103879452147605479529654)⟩,⟨(-55598234833680371752263),(-55598234833680369972159)⟩⟩,⟨⟨(-47008385489636431563930734),(-47008385489636430456632001)⟩,⟨(-20669263945677123543828760),(-20669263945677122436527128)⟩⟩,⟨⟨2277145373785598421977450076,2277145373785598449736229616⟩,⟨1034897062735591089332585875,1034897062735591117093222854⟩⟩,⟨⟨(-8095305358091592468200683278),(-8095305358091592411249141300)⟩,⟨(-11632102952096796699968609677),(-11632102952096796642976300236)⟩⟩,⟨⟨10102917087844958614064747119,10102917087844958634557959939⟩,⟨21229145008548126990987942878,21229145008548127011603482450⟩⟩,⟨⟨(-14999678995108236494734330411),(-14999678995108236487857296399)⟩,⟨(-14877263092566918442879253088),(-14877263092566918435609378994)⟩⟩] +lemma ha3_1_11_eq (j : Fin 7) : ha3_1_11 j = ((ha3_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha3_1_11_contains (j : Fin 7) : (ha3_1_11 j).Contains (fullFactor true 3 11 ((j.val:ℝ)/6)) := by + rw [ha3_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_10 j) true 3 10 j (ha3_1_10_contains j) +noncomputable def hk3_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_12 j i k) +lemma hk3_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_12 j i k).Contains (fullFactor true 3 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 12 (kernel3_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha3_1_12 : Fin 7 → CBox := ![⟨⟨2226875722402468735530,2226875722402468741167⟩,⟨(-2406),2406⟩⟩,⟨⟨49138101638723075304389,49138101638723076993514⟩,⟨67703184449361513725729,67703184449361515414742⟩⟩,⟨⟨10416505192624511164025872,10416505192624512093666084⟩,⟨28655531739954259670075278,28655531739954260599717018⟩⟩,⟨⟨(-96479023142334125828825891),(-96479023142334107461870268)⟩,⟨(-1213420302535277861642897746),(-1213420302535277843275544037)⟩⟩,⟨⟨(-3456076394127468888667737295),(-3456076394127468859516416542)⟩,⟨4585583800566406675351941947,4585583800566406704489802710⟩⟩,⟨⟨6634317217499993090625137840,6634317217499993098871201700⟩,⟨(-4685433409790482367676713463),(-4685433409790482359475093471)⟩⟩,⟨⟨(-4242137031378780300482073434),(-4242137031378780298171823705)⟩,⟨4746482084288119683033101867,4746482084288119685231396851⟩⟩] +lemma ha3_1_12_eq (j : Fin 7) : ha3_1_12 j = ((ha3_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha3_1_12_contains (j : Fin 7) : (ha3_1_12 j).Contains (fullFactor true 3 12 ((j.val:ℝ)/6)) := by + rw [ha3_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_11 j) true 3 11 j (ha3_1_11_contains j) +noncomputable def hk3_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_13 j i k) +lemma hk3_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_13 j i k).Contains (fullFactor true 3 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 13 (kernel3_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha3_1_13 : Fin 7 → CBox := ![⟨⟨(-1578570266862105744683),(-1578570266862105740681)⟩,⟨(-1706),1706⟩⟩,⟨⟨(-9614841064523069425147),(-9614841064523067945859)⟩,⟨(-53978215217868471956531),(-53978215217868470477259)⟩⟩,⟨⟨7407246673650242969197333,7407246673650243689624626⟩,⟨(-14979491530419265575087743),(-14979491530419264854661489)⟩⟩,⟨⟨(-455804394286304355592051046),(-455804394286304344374785352)⟩,⟨302062019893804364389607721,302062019893804375606180565⟩⟩,⟨⟨2032502715064658520698756797,2032502715064658534458399075⟩,⟨693710891097758926792548923,693710891097758940554547057⟩⟩,⟨⟨(-1831843506241165918728304431),(-1831843506241165915698335800)⟩,⟨(-1831013499650748005568733992),(-1831013499650748002525593188)⟩⟩,⟨⟨1379710053592110315745319225,1379710053592110316393703577⟩,⟨1109784955304000336030279833,1109784955304000336707722167⟩⟩] +lemma ha3_1_13_eq (j : Fin 7) : ha3_1_13 j = ((ha3_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha3_1_13_contains (j : Fin 7) : (ha3_1_13 j).Contains (fullFactor true 3 13 ((j.val:ℝ)/6)) := by + rw [ha3_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_12 j) true 3 12 j (ha3_1_12_contains j) +noncomputable def hk3_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_14 j i k) +lemma hk3_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_14 j i k).Contains (fullFactor true 3 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 14 (kernel3_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha3_1_14 : Fin 7 → CBox := ![⟨⟨1039075662648418649856,1039075662648418652495⟩,⟨(-1123),1123⟩⟩,⟨⟨(-9069566323206616292811),(-9069566323206615089869)⟩,⟨32111145546080576779888,32111145546080577982864⟩⟩,⟨⟨(-8115469321250466293627589),(-8115469321250465775218828)⟩,⟨2543125591236969860587000,2543125591236970378995387⟩⟩,⟨⟨202352739219885546629763914,202352739219885552990559811⟩,⟨105253218446981810156844506,105253218446981816517832793⟩⟩,⟨⟨8926479309670190361917610,8926479309670196394135534⟩,⟨(-745811418792236046885247409),(-745811418792236040852606888)⟩⟩,⟨⟨(-442146827715742761173214737),(-442146827715742760130781141)⟩,⟨626658217845702091751473681,626658217845702092790726842⟩⟩,⟨⟨267742113324152619713965192,267742113324152619898364623⟩,⟨(-370754069466882180912570487),(-370754069466882180735066168)⟩⟩] +lemma ha3_1_14_eq (j : Fin 7) : ha3_1_14 j = ((ha3_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha3_1_14_contains (j : Fin 7) : (ha3_1_14 j).Contains (fullFactor true 3 14 ((j.val:ℝ)/6)) := by + rw [ha3_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_13 j) true 3 13 j (ha3_1_13_contains j) +noncomputable def hk3_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_15 j i k) +lemma hk3_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_15 j i k).Contains (fullFactor true 3 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 15 (kernel3_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha3_1_15 : Fin 7 → CBox := ![⟨⟨(-638362260467598257230),(-638362260467598255606)⟩,⟨(-690),690⟩⟩,⟨⟨12594277203327832603170,12594277203327833516179⟩,⟨(-14163468526568395436742),(-14163468526568394523704)⟩⟩,⟨⟨3536957543984352498775239,3536957543984352846939226⟩,⟨1951647056958397712400542,1951647056958398060564802⟩⟩,⟨⟨(-2332849334198170030744114),(-2332849334198166664196029)⟩,⟨(-88769326366413923146835002),(-88769326366413919780269194)⟩⟩,⟨⟨(-230611166364566750656170371),(-230611166364566748187990018)⟩,⟨72595327385234273425405295,72595327385234275893012704⟩⟩,⟨⟨191432704847570100193564335,191432704847570100526163556⟩,⟨90996142957706596584289817,90996142957706596917473525⟩⟩,⟨⟨(-92605162226208172070618105),(-92605162226208172025283465)⟩,⟨(-59813733847327859456059288),(-59813733847327859409225899)⟩⟩] +lemma ha3_1_15_eq (j : Fin 7) : ha3_1_15 j = ((ha3_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha3_1_15_contains (j : Fin 7) : (ha3_1_15 j).Contains (fullFactor true 3 15 ((j.val:ℝ)/6)) := by + rw [ha3_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_14 j) true 3 14 j (ha3_1_14_contains j) +noncomputable def hk3_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_16 j i k) +lemma hk3_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_16 j i k).Contains (fullFactor true 3 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 16 (kernel3_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha3_1_16 : Fin 7 → CBox := ![⟨⟨367670267765896474367,367670267765896475305⟩,⟨(-398),398⟩⟩,⟨⟨(-9325526897392541809657),(-9325526897392541160009)⟩,⟨3859789291662485272653,3859789291662485922310⟩⟩,⟨⟨(-460193224068138040751323),(-460193224068137821539611)⟩,⟨(-1739055693677571379710674),(-1739055693677571160498895)⟩⟩,⟨⟨(-27928544090028747941581625),(-27928544090028746271199325)⟩,⟨16445808491038470657308358,16445808491038472327648957⟩⟩,⟨⟨42802984256878160534690507,42802984256878161481107542⟩,⟨59713331195369669078048927,59713331195369670024674733⟩⟩,⟨⟨14807447754050061937031786,14807447754050062036845403⟩,⟨(-52884269536544138293203223),(-52884269536544138193445559)⟩⟩,⟨⟨(-12412510529967984103305619),(-12412510529967984092157362)⟩,⟨21601942345542436398384093,21601942345542436409234019⟩⟩] +lemma ha3_1_16_eq (j : Fin 7) : ha3_1_16 j = ((ha3_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha3_1_16_contains (j : Fin 7) : (ha3_1_16 j).Contains (fullFactor true 3 16 ((j.val:ℝ)/6)) := by + rw [ha3_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_15 j) true 3 15 j (ha3_1_15_contains j) +noncomputable def hk3_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_17 j i k) +lemma hk3_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_17 j i k).Contains (fullFactor true 3 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 17 (kernel3_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha3_1_17 : Fin 7 → CBox := ![⟨⟨(-199306232685867573579),(-199306232685867573069)⟩,⟨(-216),216⟩⟩,⟨⟨5049517138014745256212,5049517138014745691269⟩,⟨298881344460001522814,298881344460001957870⟩⟩,⟨⟨(-393565813323348531640146),(-393565813323348401739647)⟩,⟨643081431184360712450030,643081431184360842350473⟩⟩,⟨⟨9591014011461214219169395,9591014011461214999184030⟩,⟨5654435933845688442694937,5654435933845689222720059⟩⟩,⟨⟨12412539203443044334860277,12412539203443044676545264⟩,⟨(-16955076870889724429687271),(-16955076870889724088050242)⟩⟩,⟨⟨(-13322168051426541533206045),(-13322168051426541505055472)⟩,⟨(-1367420602068309155788921),(-1367420602068309127651326)⟩⟩,⟨⟨4725642060479456406920388,4725642060479456409363238⟩,⟨2397978209465855166268376,2397978209465855168765409⟩⟩] +lemma ha3_1_17_eq (j : Fin 7) : ha3_1_17 j = ((ha3_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha3_1_17_contains (j : Fin 7) : (ha3_1_17 j).Contains (fullFactor true 3 17 ((j.val:ℝ)/6)) := by + rw [ha3_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_16 j) true 3 16 j (ha3_1_16_contains j) +noncomputable def hk3_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_18 j i k) +lemma hk3_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_18 j i k).Contains (fullFactor true 3 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 18 (kernel3_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha3_1_18 : Fin 7 → CBox := ![⟨⟨102037466083353695140,102037466083353695402⟩,⟨(-111),111⟩⟩,⟨⟨(-2088864369655679407735),(-2088864369655679132576)⟩,⟨(-1170260917166284316542),(-1170260917166284041387)⟩⟩,⟨⟨291650340175275889338141,291650340175275962037847⟩,⟨(-63295376724394149588670),(-63295376724394076888973)⟩⟩,⟨⟨96777562415753775675586,96777562415754119686550⟩,⟨(-3610865294573012533501906),(-3610865294573012189490683)⟩⟩,⟨⟨(-5396760743961361497734813),(-5396760743961361381265749)⟩,⟨(-1758489545266251117152814),(-1758489545266251000677972)⟩⟩,⟨⟨210919560792516622988659,210919560792516630478918⟩,⟨3077115643456388264269568,3077115643456388271769412⟩⟩,⟨⟨431767338603453570175169,431767338603453570703277⟩,⟨(-973038496709205821908517),(-973038496709205821389304)⟩⟩] +lemma ha3_1_18_eq (j : Fin 7) : ha3_1_18 j = ((ha3_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha3_1_18_contains (j : Fin 7) : (ha3_1_18 j).Contains (fullFactor true 3 18 ((j.val:ℝ)/6)) := by + rw [ha3_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_17 j) true 3 17 j (ha3_1_17_contains j) +noncomputable def hk3_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_19 j i k) +lemma hk3_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_19 j i k).Contains (fullFactor true 3 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 19 (kernel3_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha3_1_19 : Fin 7 → CBox := ![⟨⟨(-49489988662767695286),(-49489988662767695157)⟩,⟨(-54),54⟩⟩,⟨⟨613834020265220558210,613834020265220723079⟩,⟨880926135818806326797,880926135818806491664⟩⟩,⟨⟨(-92733391520815811609945),(-92733391520815773064661)⟩,⟨(-62652942223562785365287),(-62652942223562746819994)⟩⟩,⟨⟨(-985220680253667520803636),(-985220680253667377071413)⟩,⟨511807199641042083412144,511807199641042227142995⟩⟩,⟨⟨2832291368408028393688,2832291368408066007191⟩,⟨1452511306260736425029294,1452511306260736462643745⟩⟩,⟨⟨653809296793516555818585,653809296793516557710954⟩,⟨(-159415625966559743788309),(-159415625966559741899269)⟩⟩,⟨⟨(-189196934184546992764988),(-189196934184546992660487)⟩,⟨(-72442757905910358138011),(-72442757905910358032218)⟩⟩] +lemma ha3_1_19_eq (j : Fin 7) : ha3_1_19 j = ((ha3_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha3_1_19_contains (j : Fin 7) : (ha3_1_19 j).Contains (fullFactor true 3 19 ((j.val:ℝ)/6)) := by + rw [ha3_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_18 j) true 3 18 j (ha3_1_18_contains j) +noncomputable def hk3_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_20 j i k) +lemma hk3_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_20 j i k).Contains (fullFactor true 3 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 20 (kernel3_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha3_1_20 : Fin 7 → CBox := ![⟨⟨22803349772014994810,22803349772014994871⟩,⟨(-25),25⟩⟩,⟨⟨(-71531576351852352561),(-71531576351852258715)⟩,⟨(-451776585125906692363),(-451776585125906598517)⟩⟩,⟨⟨6695243827949407143958,6695243827949426558761⟩,⟨39303282257944000452977,39303282257944019867781⟩⟩,⟨⟨270130854864957249570289,270130854864957306620046⟩,⟨179218791556927548287043,179218791556927605337128⟩⟩,⟨⟨335314730582127644843484,335314730582127656383365⟩,⟨(-110707877075691571231179),(-110707877075691559692162)⟩⟩,⟨⟨(-55587060311191311201586),(-55587060311191310748903)⟩,⟨(-127936365088034932779060),(-127936365088034932325548)⟩⟩,⟨⟨(-11303327110354362284522),(-11303327110354362264391)⟩,⟨34839893769547128122270,34839893769547128142243⟩⟩] +lemma ha3_1_20_eq (j : Fin 7) : ha3_1_20 j = ((ha3_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha3_1_20_contains (j : Fin 7) : (ha3_1_20 j).Contains (fullFactor true 3 20 ((j.val:ℝ)/6)) := by + rw [ha3_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_19 j) true 3 19 j (ha3_1_19_contains j) +noncomputable def hk3_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_21 j i k) +lemma hk3_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_21 j i k).Contains (fullFactor true 3 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 21 (kernel3_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha3_1_21 : Fin 7 → CBox := ![⟨⟨(-10006694569282650647),(-10006694569282650619)⟩,⟨(-11),11⟩⟩,⟨⟨(-53869767299326317425),(-53869767299326266550)⟩,⟨177588929423108327679,177588929423108378555⟩⟩,⟨⟨8069216084925468775995,8069216084925478089310⟩,⟨(-10856809984703068397434),(-10856809984703059084119)⟩⟩,⟨⟨7192045255164772198842,7192045255164793764714⟩,⟨(-89861485119992938091688),(-89861485119992916525820)⟩⟩,⟨⟨(-48551930379925316017886),(-48551930379925312646436)⟩,⟨(-65780406495081531358278),(-65780406495081527986595)⟩⟩,⟨⟨(-23024175185733036772876),(-23024175185733036669382)⟩,⟨15104563030059161237662,15104563030059161340985⟩⟩,⟨⟨6091915582245794765859,6091915582245794769494⟩,⟨1632124038667881289029,1632124038667881292678⟩⟩] +lemma ha3_1_21_eq (j : Fin 7) : ha3_1_21 j = ((ha3_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha3_1_21_contains (j : Fin 7) : (ha3_1_21 j).Contains (fullFactor true 3 21 ((j.val:ℝ)/6)) := by + rw [ha3_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_20 j) true 3 20 j (ha3_1_20_contains j) +noncomputable def hk3_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_22 j i k) +lemma hk3_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_22 j i k).Contains (fullFactor true 3 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 22 (kernel3_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha3_1_22 : Fin 7 → CBox := ![⟨⟨4191594419410034061,4191594419410034074⟩,⟨(-5),5⟩⟩,⟨⟨48783135668268379012,48783135668268405339⟩,⟨(-52779872812534259601),(-52779872812534233273)⟩⟩,⟨⟨(-4347425939135485050984),(-4347425939135480786446)⟩,⟨540741195171458956800,540741195171463221338⟩⟩,⟨⟨(-21790504175583226427153),(-21790504175583218645462)⟩,⟨9889449815932339502411,9889449815932347284075⟩⟩,⟨⟨(-10469603916909664389588),(-10469603916909663449255)⟩,⟨14726825341441761502201,14726825341441762442493⟩⟩,⟨⟨3541938821204688782999,3541938821204688805511⟩,⟨3791925084147362819022,3791925084147362841564⟩⟩,⟨⟨215897408211794435643,215897408211794436275⟩,⟨(-1013842508972473632271),(-1013842508972473631639)⟩⟩] +lemma ha3_1_22_eq (j : Fin 7) : ha3_1_22 j = ((ha3_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha3_1_22_contains (j : Fin 7) : (ha3_1_22 j).Contains (fullFactor true 3 22 ((j.val:ℝ)/6)) := by + rw [ha3_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_21 j) true 3 21 j (ha3_1_21_contains j) +noncomputable def hk3_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_23 j i k) +lemma hk3_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_23 j i k).Contains (fullFactor true 3 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 23 (kernel3_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha3_1_23 : Fin 7 → CBox := ![⟨⟨(-1679433096618109155),(-1679433096618109149)⟩,⟨(-3),3⟩⟩,⟨⟨(-24791780801317887149),(-24791780801317874117)⟩,⟨9706682690944295090,9706682690944308122⟩⟩,⟨⟨1051723801667252300148,1051723801667254167964⟩,⟨857719139207729014458,857719139207730882274⟩⟩,⟨⟨4877606132975508315015,4877606132975511000814⟩,⟨3622825786857048028827,3622825786857050714633⟩⟩,⟨⟨3647954602929601421813,3647954602929601672655⟩,⟨1132742048839631371937,1132742048839631622783⟩⟩,⟨⟨565066572688439679145,565066572688439683842⟩,⟨(-745240894418225100993),(-745240894418225096300)⟩⟩,⟨⟨(-160937020843901259584),(-160937020843901259478)⟩,⟨(-25619067581550814906),(-25619067581550814801)⟩⟩] +lemma ha3_1_23_eq (j : Fin 7) : ha3_1_23 j = ((ha3_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha3_1_23_contains (j : Fin 7) : (ha3_1_23 j).Contains (fullFactor true 3 23 ((j.val:ℝ)/6)) := by + rw [ha3_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_22 j) true 3 22 j (ha3_1_22_contains j) +noncomputable def hk3_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_24 j i k) +lemma hk3_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_24 j i k).Contains (fullFactor true 3 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 24 (kernel3_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha3_1_24 : Fin 7 → CBox := ![⟨⟨644856016264901116,644856016264901119⟩,⟨(-2),2⟩⟩,⟨⟨9422815968501706332,9422815968501712515⟩,⟨739947480355619167,739947480355625350⟩⟩,⟨⟨(-31701076537731099405),(-31701076537730315411)⟩,⟨(-401648178487178602855),(-401648178487177818861)⟩⟩,⟨⟨195951944030806953346,195951944030807841710⟩,⟨(-1465363885395898614401),(-1465363885395897726037)⟩⟩,⟨⟨(-12278980513748252464),(-12278980513748188335)⟩,⟨(-773750784661769028457),(-773750784661768964328)⟩⟩,⟨⟨(-143437871128441372742),(-143437871128441371804)⟩,⟨(-74316138130764867417),(-74316138130764866478)⟩⟩,⟨⟨(-2595476497250068721),(-2595476497250068703)⟩,⟨24414931295409036773,24414931295409036791⟩⟩] +lemma ha3_1_24_eq (j : Fin 7) : ha3_1_24 j = ((ha3_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha3_1_24_contains (j : Fin 7) : (ha3_1_24 j).Contains (fullFactor true 3 24 ((j.val:ℝ)/6)) := by + rw [ha3_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_23 j) true 3 23 j (ha3_1_23_contains j) +noncomputable def hk3_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_25 j i k) +lemma hk3_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_25 j i k).Contains (fullFactor true 3 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 25 (kernel3_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha3_1_25 : Fin 7 → CBox := ![⟨⟨(-237702657669663247),(-237702657669663245)⟩,⟨(-1),1⟩⟩,⟨⟨(-2779457966458301334),(-2779457966458298518)⟩,⟨(-1628213140859876883),(-1628213140859874067)⟩⟩,⟨⟨(-76498697701268272427),(-76498697701267956517)⟩,⟨85631932949697536579,85631932949697852489⟩⟩,⟨⟨(-321601266682923540222),(-321601266682923258137)⟩,⟨125839359174146949031,125839359174147231116⟩⟩,⟨⟨(-142244529339456871283),(-142244529339456855543)⟩,⟨49169480181109765237,49169480181109780976⟩⟩,⟨⟨(-8103176382538899870),(-8103176382538899690)⟩,⟨25533095884286614634,25533095884286614815⟩⟩,⟨⟨3546012558628299070,3546012558628299073⟩,⟨191514387078475572,191514387078475576⟩⟩] +lemma ha3_1_25_eq (j : Fin 7) : ha3_1_25 j = ((ha3_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha3_1_25_contains (j : Fin 7) : (ha3_1_25 j).Contains (fullFactor true 3 25 ((j.val:ℝ)/6)) := by + rw [ha3_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_24 j) true 3 24 j (ha3_1_24_contains j) +noncomputable def hk3_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_26 j i k) +lemma hk3_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_26 j i k).Contains (fullFactor true 3 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 26 (kernel3_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha3_1_26 : Fin 7 → CBox := ![⟨⟨84250401577555069,84250401577555071⟩,⟨(-1),1⟩⟩,⟨⟨586711258449261527,586711258449262760⟩,⟨877534407072659800,877534407072661034⟩⟩,⟨⟨31448548380821172653,31448548380821295053⟩,⟨(-1062799249395099129),(-1062799249394976729)⟩⟩,⟨⟨59728859553412531760,59728859553412617887⟩,⟨49488682257555740283,49488682257555826410⟩⟩,⟨⟨17027447429212043344,17027447429212047060⟩,⟨22409957675041625500,22409957675041629215⟩⟩,⟨⟨4231437054167551596,4231437054167551630⟩,⟨581568705088867172,581568705088867206⟩⟩,⟨⟨989106423910377,989106423910379⟩,⟨(-493873268509369580),(-493873268509369578)⟩⟩] +lemma ha3_1_26_eq (j : Fin 7) : ha3_1_26 j = ((ha3_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha3_1_26_contains (j : Fin 7) : (ha3_1_26 j).Contains (fullFactor true 3 26 ((j.val:ℝ)/6)) := by + rw [ha3_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_25 j) true 3 25 j (ha3_1_25_contains j) +noncomputable def hk3_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_27 j i k) +lemma hk3_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_27 j i k).Contains (fullFactor true 3 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 27 (kernel3_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha3_1_27 : Fin 7 → CBox := ![⟨⟨(-28755406115934878),(-28755406115934876)⟩,⟨(-1),1⟩⟩,⟨⟨(-45752303065155052),(-45752303065154531)⟩,⟨(-329951528488761285),(-329951528488760764)⟩⟩,⟨⟨(-5937478786690024140),(-5937478786689978472)⟩,⟨(-5804891139461658937),(-5804891139461613268)⟩⟩,⟨⟨3102598321077493327,3102598321077518650⟩,⟨(-16487560604737105519),(-16487560604737080196)⟩⟩,⟨⟨2878929998267173685,2878929998267174531⟩,⟨(-4171322119168104857),(-4171322119168104012)⟩⟩,⟨⟨(-22383040894020982),(-22383040894020975)⟩,⟨(-655417585290226240),(-655417585290226233)⟩⟩,⟨⟨(-66058331858923524),(-66058331858923523)⟩,⟨3302390778927298,3302390778927300⟩⟩] +lemma ha3_1_27_eq (j : Fin 7) : ha3_1_27 j = ((ha3_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha3_1_27_contains (j : Fin 7) : (ha3_1_27 j).Contains (fullFactor true 3 27 ((j.val:ℝ)/6)) := by + rw [ha3_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_26 j) true 3 26 j (ha3_1_26_contains j) +noncomputable def hk3_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_28 j i k) +lemma hk3_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_28 j i k).Contains (fullFactor true 3 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 28 (kernel3_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha3_1_28 : Fin 7 → CBox := ![⟨⟨9463957130027925,9463957130027927⟩,⟨(-1),1⟩⟩,⟨⟨(-31284510710159025),(-31284510710158812)⟩,⟨96413746388363250,96413746388363463⟩⟩,⟨⟨(-23665209013092340),(-23665209013075908)⟩,⟨2112841484072144946,2112841484072161377⟩⟩,⟨⟨(-3321550100042053753),(-3321550100042046573)⟩,⟨1100380273162070255,1100380273162077435⟩⟩,⟨⟨(-844073867357085498),(-844073867357085311)⟩,⟨(-249270913720877686),(-249270913720877500)⟩⟩,⟨⟨(-95064656296048884),(-95064656296048882)⟩,⟨19751973391920797,19751973391920800⟩⟩,⟨⟨868893343773932,868893343773933⟩,⟨8497080550601476,8497080550601477⟩⟩] +lemma ha3_1_28_eq (j : Fin 7) : ha3_1_28 j = ((ha3_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha3_1_28_contains (j : Fin 7) : (ha3_1_28 j).Contains (fullFactor true 3 28 ((j.val:ℝ)/6)) := by + rw [ha3_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_27 j) true 3 27 j (ha3_1_27_contains j) +noncomputable def hk3_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_29 j i k) +lemma hk3_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_29 j i k).Contains (fullFactor true 3 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 29 (kernel3_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha3_1_29 : Fin 7 → CBox := ![⟨⟨(-3007364414983258),(-3007364414983257)⟩,⟨(-1),1⟩⟩,⟨⟨20630591843062691,20630591843062775⟩,⟨(-21476498436056345),(-21476498436056261)⟩⟩,⟨⟨379240389354640051,379240389354645759⟩,⟨(-354510039415434389),(-354510039415428680)⟩⟩,⟨⟨517965403865700865,517965403865702832⟩,⟨477701653278196805,477701653278198772⟩⟩,⟨⟨4394615732020839,4394615732020880⟩,⟨147494704714110418,147494704714110459⟩⟩,⟨⟨5091281893907678,5091281893907679⟩,⟨12912270669457335,12912270669457336⟩⟩,⟨⟨1052414624239458,1052414624239459⟩,⟨(-163211096669015),(-163211096669014)⟩⟩] +lemma ha3_1_29_eq (j : Fin 7) : ha3_1_29 j = ((ha3_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha3_1_29_contains (j : Fin 7) : (ha3_1_29 j).Contains (fullFactor true 3 29 ((j.val:ℝ)/6)) := by + rw [ha3_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_28 j) true 3 28 j (ha3_1_28_contains j) +noncomputable def hk3_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel3_0 j i k).mul (mpower1_30 j i k) +lemma hk3_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk3_1_30 j i k).Contains (fullFactor true 3 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk3_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel3_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 3 30 (kernel3_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha3_1_30 : Fin 7 → CBox := ![⟨⟨923796030938368,923796030938369⟩,⟨(-1),1⟩⟩,⟨⟨(-7933516451134029),(-7933516451133997)⟩,⟨2931403118415560,2931403118415593⟩⟩,⟨⟨(-123099591719247913),(-123099591719245995)⟩,⟨(-6923313423475851),(-6923313423473934)⟩⟩,⟨⟨32479950684937654,32479950684938176⟩,⟨(-133260080548342362),(-133260080548341840)⟩⟩,⟨⟨22492151099683881,22492151099683890⟩,⟨(-8127004342778989),(-8127004342778980)⟩⟩,⟨⟨1638821091028528,1638821091028529⟩,⟨(-996452367466598),(-996452367466597)⟩⟩,⟨⟨(-26232498122064),(-26232498122063)⟩,⟨(-125654997216958),(-125654997216957)⟩⟩] +lemma ha3_1_30_eq (j : Fin 7) : ha3_1_30 j = ((ha3_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha3_1_30_contains (j : Fin 7) : (ha3_1_30 j).Contains (fullFactor true 3 30 ((j.val:ℝ)/6)) := by + rw [ha3_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha3_1_29 j) true 3 29 j (ha3_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders31.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders31.lean new file mode 100644 index 0000000000000000000000000000000000000000..592494fd6f73cc38f009954f28a1a06984d281b2 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders31.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers40 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues40 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk31_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_0 j i k) +lemma hk31_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_0 j i k).Contains (fullFactor false 31 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 0 (power31_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha31_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999629,1000000000000000000000000000495⟩,⟨(-495),495⟩⟩,⟨⟨(-866025403784438646859265180121),(-866025403784438646656005308407)⟩,⟨(-500000000000000000112642480794),(-499999999999999999908446715259)⟩⟩,⟨⟨499999999999999999700748754523,500000000000000000257072853273⟩,⟨866025403784438646497394466211,866025403784438647054403581409⟩⟩,⟨⟨(-64739364723),137794482981⟩,⟨(-1000000000000000000101266923852),(-999999999999999999898733076179)⟩⟩,⟨⟨(-500000000000000000803454492878),(-499999999999999999280902291575)⟩,⟨866025403784438645978345754771,866025403784438647500397174436⟩⟩,⟨⟨866025403784438645836046380502,866025403784438647752279226158⟩,⟨(-500000000000000000905144916009),(-499999999999999998989409103426)⟩⟩,⟨⟨(-1000000000000000000203149131365),(-999999999999999999796850868759)⟩,⟨(-276204249685),130094012921⟩⟩] +lemma ha31_0_0_eq (j : Fin 7) : ha31_0_0 j = ((atomPoints j).direct.powBin 7 31).conj := by fin_cases j <;> decide +kernel +lemma ha31_0_0_contains (j : Fin 7) : (ha31_0_0 j).Contains (fullFactor false 31 0 ((j.val:ℝ)/6)) := by + rw [ha31_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 31) ((j.val:ℝ)/6) 31 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 31 (by norm_num)) +noncomputable def hk31_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_1 j i k) +lemma hk31_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_1 j i k).Contains (fullFactor false 31 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 1 (power31_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha31_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨261799387799149436490396145539,261799387799149436598146131692⟩,⟨(-453449841058554462699607079697),(-453449841058554462591737084061)⟩⟩,⟨⟨(-906899682117108925603562615365),(-906899682117108925017377282586)⟩,⟨523598775598298872763291495209,523598775598298873347539395762⟩⟩,⟨⟨1570796326794896619070930288036,1570796326794896619394069712013⟩,⟨(-101692356306),216447067720⟩⟩,⟨⟨(-1813799364234217852141212027662),(-1813799364234217848947661486029)⟩,⟨(-1047197551196597747839417821547),(-1047197551196597744647258614664)⟩⟩,⟨⟨1308996938995747180045945886281,1308996938995747185065497182142⟩,⟨2267249205292772310812037966859,2267249205292772315835940703962⟩⟩,⟨⟨(-408702395269),867721241701⟩,⟨(-3141592653589793239108211818680),(-3141592653589793237821788181710)⟩⟩] +lemma ha31_0_1_eq (j : Fin 7) : ha31_0_1 j = ((ha31_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha31_0_1_contains (j : Fin 7) : (ha31_0_1 j).Contains (fullFactor false 31 1 ((j.val:ℝ)/6)) := by + rw [ha31_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_0 j) false 31 0 j (ha31_0_0_contains j) +noncomputable def hk31_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_2 j i k) +lemma hk31_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_2 j i k).Contains (fullFactor false 31 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 2 (power31_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha31_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨118712890786751174392971806063,118712890786751174421589979752⟩,⟨68538919452009434840352032838,68538919452009434868779079406⟩⟩,⟨⟨(-274155677808037739554309130949),(-274155677808037739247524980946)⟩,⟨(-474851563147004697793356520348),(-474851563147004697484919098359)⟩⟩,⟨⟨(-169997129461),79868989875⟩,⟨1233700550136169827227302206982,1233700550136169827485022307913⟩⟩,⟨⟨1096622711232150956069273590788,1096622711232150959415585553773⟩,⟨(-1899406252588018792151599487742),(-1899406252588018788801275183036)⟩⟩,⟨⟨(-2967822269668779363600060382316),(-2967822269668779357014340205942)⟩,⟨1713472986300235867859308578441,1713472986300235874435340013771⟩⟩,⟨⟨4934802200544679308406440286559,4934802200544679310442857773483⟩,⟨(-641988221241),1363013339146⟩⟩] +lemma ha31_0_2_eq (j : Fin 7) : ha31_0_2 j = ((ha31_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha31_0_2_contains (j : Fin 7) : (ha31_0_2 j).Contains (fullFactor false 31 2 ((j.val:ℝ)/6)) := by + rw [ha31_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_1 j) false 31 1 j (ha31_0_1_contains j) +noncomputable def hk31_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_3 j i k) +lemma hk31_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_3 j i k).Contains (fullFactor false 31 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 3 (power31_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha31_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-11962298101967523218626305405),(-11962298101967523213626772634)⟩,⟨20719308087892496639786012953,20719308087892496644846778128⟩⟩,⟨⟨165754464703139973087930500808,165754464703139973196123084659⟩,⟨(-95698384815740185776653949966),(-95698384815740185669261462335)⟩⟩,⟨⟨(-645964097506246253725709292020),(-645964097506246253588711195141)⟩,⟨(-89010288842),41819305307⟩⟩,⟨⟨1326035717625119783908690033264,1326035717625119786251878541120⟩,⟨765587078525921484711233644691,765587078525921487049837046171⟩⟩,⟨⟨(-1495287262745940404698325769704),(-1495287262745940398954896109459)⟩,⟨(-2589913510986562083276472322933),(-2589913510986562077521103337542)⟩⟩,⟨⟨(-1427344231002),672288493181⟩,⟨5167712780049970028183191575788,5167712780049970030332172321978⟩⟩] +lemma ha31_0_3_eq (j : Fin 7) : ha31_0_3 j = ((ha31_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha31_0_3_contains (j : Fin 7) : (ha31_0_3 j).Contains (fullFactor false 31 3 ((j.val:ℝ)/6)) := by + rw [ha31_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_2 j) false 31 2 j (ha31_0_2_contains j) +noncomputable def hk31_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_4 j i k) +lemma hk31_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_4 j i k).Contains (fullFactor false 31 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 4 (power31_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha31_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2712151086516110563720565312),(-2712151086516110563049479653)⟩,⟨(-1565861159883012430222761401),(-1565861159883012429563339800)⟩⟩,⟨⟨25053778558128198862606199374,25053778558128198890801235545⟩,⟨43394417384257769000844072630,43394417384257769029306953569⟩⟩,⟨⟨(-16422402792),34954258690⟩,⟨(-253669507901048013664627752258),(-253669507901048013610021270297)⟩⟩,⟨⟨(-400860456930051182690865356132),(-400860456930051181465099500041)⟩,⟨694310678148124303597372954824,694310678148124304826473648065⟩⟩,⟨⟨1695094429072569100300997486440,1695094429072569104073273331925⟩,⟨(-978663224926882770440411853259),(-978663224926882766678230749160)⟩⟩,⟨⟨(-4058712126416768219047554587219),(-4058712126416768217346829774033)⟩,⟨(-1121033537565),528014147818⟩⟩] +lemma ha31_0_4_eq (j : Fin 7) : ha31_0_4 j = ((ha31_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha31_0_4_contains (j : Fin 7) : (ha31_0_4 j).Contains (fullFactor false 31 4 ((j.val:ℝ)/6)) := by + rw [ha31_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_3 j) false 31 3 j (ha31_0_3_contains j) +noncomputable def hk31_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_5 j i k) +lemma hk31_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_5 j i k).Contains (fullFactor false 31 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 5 (power31_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha31_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨163976597214335483756333401,163976597214335483825909824⟩,⟨(-284015797627486289521882745),(-284015797627486289450702768)⟩⟩,⟨⟨(-9088505524079561266748128201),(-9088505524079561260757946745)⟩,⟨5247251110858735478022982143,5247251110858735483944839230⟩⟩,⟨⟨79692626246167045112100049511,79692626246167045129508851276⟩,⟨(-5159249997),10981204232⟩⟩,⟨⟨(-290832176770545960685715486502),(-290832176770545960169945244475)⟩,⟨(-167912035547479535669722961912),(-167912035547479535155740880166)⟩⟩,⟨⟨512426866294798385796662753378,512426866294798387768167278440⟩,⟨887549367585894653693108182664,887549367585894655671092353963⟩⟩,⟨⟨(-331761073556),704366145209⟩,⟨(-2550164039877345444404099582730),(-2550164039877345443327385242699)⟩⟩] +lemma ha31_0_5_eq (j : Fin 7) : ha31_0_5 j = ((ha31_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha31_0_5_contains (j : Fin 7) : (ha31_0_5 j).Contains (fullFactor false 31 5 ((j.val:ℝ)/6)) := by + rw [ha31_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_4 j) false 31 4 j (ha31_0_4_contains j) +noncomputable def hk31_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_6 j i k) +lemma hk31_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_6 j i k).Contains (fullFactor false 31 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 6 (power31_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha31_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨24785053981387676523696509,24785053981387676529987028⟩,⟨14309657588033580843021994,14309657588033580849139232⟩⟩,⟨⟨(-915818085634149174609454721),(-915818085634149173572980540)⟩,⟨(-1586243454808811298276592321),(-1586243454808811297226059258)⟩⟩,⟨⟨(-2874872546),1350688491⟩,⟨20863480763352960870833527636,20863480763352960875457551804⟩⟩,⟨⟨58612357480585547059454372670,58612357480585547239054534054⟩,⟨(-101519581107763923141983380301),(-101519581107763922961622455293)⟩⟩,⟨⟨(-387266468459182446180382469245),(-387266468459182445316091353251)⟩,⟨223588399813024700261246363741,223588399813024701122189197231⟩⟩,⟨⟨1335262768854589495597306250395,1335262768854589496165322833905⟩,⟨(-173709691906),368805251205⟩⟩] +lemma ha31_0_6_eq (j : Fin 7) : ha31_0_6 j = ((ha31_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha31_0_6_contains (j : Fin 7) : (ha31_0_6 j).Contains (fullFactor false 31 6 ((j.val:ℝ)/6)) := by + rw [ha31_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_5 j) false 31 5 j (ha31_0_5_contains j) +noncomputable def hk31_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_7 j i k) +lemma hk31_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_7 j i k).Contains (fullFactor false 31 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 7 (power31_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha31_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1070359884617898514361440),(-1070359884617898513900463)⟩,⟨1853917702541761442016049,1853917702541761442492481⟩⟩,⟨⟨237301465925345464534593072,237301465925345464692507806⟩,⟨(-137006065231091009877839892),(-137006065231091009722347612)⟩⟩,⟨⟨(-4681754135318688101236313090),(-4681754135318688100183782006)⟩,⟨(-645119891),303093789⟩⟩,⟨⟨30374587638444219442223030941,30374587638444219496283578828⟩,⟨17536776349579649229734987404,17536776349579649283527051325⟩⟩,⟨⟨(-83621865985773321567028502174),(-83621865985773321244770458738)⟩,⟨(-144837320511075112844076048102),(-144837320511075112520370895094)⟩⟩,⟨⟨(-165519409685),77960727422⟩,⟨599264529320792076762469703753,599264529320792077019302468548⟩⟩] +lemma ha31_0_7_eq (j : Fin 7) : ha31_0_7 j = ((ha31_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha31_0_7_contains (j : Fin 7) : (ha31_0_7 j).Contains (fullFactor false 31 7 ((j.val:ℝ)/6)) := by + rw [ha31_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_6 j) false 31 6 j (ha31_0_6_contains j) +noncomputable def hk31_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_8 j i k) +lemma hk31_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_8 j i k).Contains (fullFactor false 31 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 8 (power31_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha31_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-121338629888859693730251),(-121338629888859693698681)⟩,⟨(-70054890629433514743640),(-70054890629433514713245)⟩⟩,⟨⟨17934052001134979759141083,17934052001134979779552062⟩,⟨31062689251548081581173520,31062689251548081601943387⟩⟩,⟨⟨(-59512327),126668995⟩,⟨(-919260274839426580352027818),(-919260274839426580142437726)⟩⟩,⟨⟨(-4591117312290554828582332046),(-4591117312290554814484988662)⟩,⟨7952048448396308880014394314,7952048448396308894192724812⟩⟩,⟨⟨47397902300335817806170988517,47397902300335817912254124333⟩,⟨(-27365191652122466740107997474),(-27365191652122466634562193256)⟩⟩,⟨⟨(-235330630358893204594095125374),(-235330630358893204492488053826)⟩,⟨(-64999320187),30615106068⟩⟩] +lemma ha31_0_8_eq (j : Fin 7) : ha31_0_8 j = ((ha31_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha31_0_8_contains (j : Fin 7) : (ha31_0_8 j).Contains (fullFactor false 31 8 ((j.val:ℝ)/6)) := by + rw [ha31_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_7 j) false 31 7 j (ha31_0_7_contains j) +noncomputable def hk31_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_9 j i k) +lemma hk31_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_9 j i k).Contains (fullFactor false 31 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 9 (power31_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha31_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨4075628328693792151655,4075628328693792153437⟩,⟨(-7059195338064676367490),(-7059195338064676365630)⟩⟩,⟨⟨(-3614308013089114300969172),(-3614308013089114298540982)⟩,⟨2086721704291221580780769,2086721704291221583162338⟩⟩,⟨⟨160441184787359821855198506,160441184787359821892289579⟩,⟨(-10386861),22107911⟩⟩,⟨⟨(-1850525702701626523049216025),(-1850525702701626519743878290)⟩,⟨(-1068401512597105451746626477),(-1068401512597105448462624877)⟩⟩,⟨⟨7960211579480062781570563845,7960211579480062812297931908⟩,⟨13787490894657571013568435288,13787490894657571044470655583⟩⟩,⟨⟨(-10686688035),22689042977⟩,⟨(-82145886611128228817221468285),(-82145886611128228781492430969)⟩⟩] +lemma ha31_0_9_eq (j : Fin 7) : ha31_0_9 j = ((ha31_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha31_0_9_contains (j : Fin 7) : (ha31_0_9 j).Contains (fullFactor false 31 9 ((j.val:ℝ)/6)) := by + rw [ha31_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_8 j) false 31 8 j (ha31_0_8_contains j) +noncomputable def hk31_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_10 j i k) +lemma hk31_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_10 j i k).Contains (fullFactor false 31 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 10 (power31_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha31_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨369618603571988403140,369618603571988403240⟩,⟨213399400269781075684,213399400269781075779⟩⟩,⟨⟨(-218520985876255821660580),(-218520985876255821410486)⟩,⟨(-378489450057716125002330),(-378489450057716124746845)⟩⟩,⟨⟨(-3472703),1631565⟩,⟨25202042373060605478288834,25202042373060605484195308⟩⟩,⟨⟨223765489537285960936444117,223765489537285961624956073⟩,⟨(-387573196859101312201981131),(-387573196859101311508479130)⟩⟩,⟨⟨(-3609556675507699254105856192),(-3609556675507699246004184261)⟩,⟨2083978518259580813404097090,2083978518259580821455136748⟩⟩,⟨⟨25806891390014060007138503623,25806891390014060018445257626⟩,⟨(-3357322063),7127973074⟩⟩] +lemma ha31_0_10_eq (j : Fin 7) : ha31_0_10 j = ((ha31_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha31_0_10_contains (j : Fin 7) : (ha31_0_10 j).Contains (fullFactor false 31 10 ((j.val:ℝ)/6)) := by + rw [ha31_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_9 j) false 31 9 j (ha31_0_9_contains j) +noncomputable def hk31_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_11 j i k) +lemma hk31_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_11 j i k).Contains (fullFactor false 31 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 11 (power31_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha31_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-10157787699515332864),(-10157787699515332858)⟩,⟨17593804388058740562,17593804388058740567⟩⟩,⟨⟨36032111386744300664751,36032111386744300689189⟩,⟨(-20803149208607401709424),(-20803149208607401685548)⟩⟩,⟨⟨(-3598843235212085340915685),(-3598843235212085340060786)⟩,⟨(-495901),232987⟩⟩,⟨⟨73793764120052327717183445,73793764120052327849460811⟩,⟨42604849579227958616227937,42604849579227958747455924⟩⟩,⟨⟨(-495985727515397113237075196),(-495985727515397111319353465)⟩,⟨(-859072479885680692630396271),(-859072479885680690699468347)⟩⟩,⟨⟨(-2035744350),958848939⟩,⟨7370430945714350775693575808,7370430945714350778946238011⟩⟩] +lemma ha31_0_11_eq (j : Fin 7) : ha31_0_11 j = ((ha31_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha31_0_11_contains (j : Fin 7) : (ha31_0_11 j).Contains (fullFactor false 31 11 ((j.val:ℝ)/6)) := by + rw [ha31_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_10 j) false 31 10 j (ha31_0_10_contains j) +noncomputable def hk31_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_12 j i k) +lemma hk31_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_12 j i k).Contains (fullFactor false 31 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 12 (power31_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha31_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-767674536308627878),(-767674536308627877)⟩,⟨(-443217100187807443),(-443217100187807442)⟩⟩,⟨⟨1815417242369259284406,1815417242369259286497⟩,⟨3144394900720139783926,3144394900720139786069⟩⟩,⟨⟨(-30498),64914⟩,⟨(-471087477881817150427972),(-471087477881817150314565)⟩⟩,⟨⟨(-7435949024744486045614150),(-7435949024744486022686875)⟩,⟨12879441513349692547242821,12879441513349692570370574⟩⟩,⟨⟨187420541090973602624239862,187420541090973603046099564⟩,⟨(-108207299850538926652028440),(-108207299850538926233302025)⟩⟩,⟨⟨(-1929574309403923048349558345),(-1929574309403923047491871344)⟩,⟨(-532956625),251026066⟩⟩] +lemma ha31_0_12_eq (j : Fin 7) : ha31_0_12 j = ((ha31_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha31_0_12_contains (j : Fin 7) : (ha31_0_12 j).Contains (fullFactor false 31 12 ((j.val:ℝ)/6)) := by + rw [ha31_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_11 j) false 31 11 j (ha31_0_11_contains j) +noncomputable def hk31_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_13 j i k) +lemma hk31_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_13 j i k).Contains (fullFactor false 31 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 13 (power31_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha31_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨17851379306351118,17851379306351119⟩,⟨(-30919495943783800),(-30919495943783799)⟩⟩,⟨⟨(-253292510771476882374),(-253292510771476882200)⟩,⟨146238499277628361422,146238499277628361592⟩⟩,⟨⟨56921729219679268111365,56921729219679268125250⟩,⟨(-3686),7844⟩⟩,⟨⟨(-2074972248239938621473249),(-2074972248239938617740593)⟩,⟨(-1197985786082331539464838),(-1197985786082331535767272)⟩⟩,⟨⟨21791234504823142471084117,21791234504823142555478342⟩,⟨37743525322001707852898993,37743525322001707937974990⟩⟩,⟨⟨(-60663204),128794817⟩,⟨(-466302805767612564529553064),(-466302805767612564320799299)⟩⟩] +lemma ha31_0_13_eq (j : Fin 7) : ha31_0_13 j = ((ha31_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha31_0_13_contains (j : Fin 7) : (ha31_0_13 j).Contains (fullFactor false 31 13 ((j.val:ℝ)/6)) := by + rw [ha31_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_12 j) false 31 12 j (ha31_0_12_contains j) +noncomputable def hk31_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_14 j i k) +lemma hk31_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_14 j i k).Contains (fullFactor false 31 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 14 (power31_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha31_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1156386444162983,1156386444162984⟩,⟨667640024824732,667640024824733⟩⟩,⟨⟨(-10938614166728417765),(-10938614166728417752)⟩,⟨(-18946235501166317758),(-18946235501166317744)⟩⟩,⟨⟨(-881),414⟩,⟨6386603083791852240367,6386603083791852241947⟩⟩,⟨⟨179218254507678396299010,179218254507678396852736⟩,⟨(-310415122451108950305530),(-310415122451108949746137)⟩⟩,⟨⟨(-7058022730486958389424515),(-7058022730486958373492873)⟩,⟨4074951323393142870248277,4074951323393142886042932⟩⟩,⟨⟨104638104924845707095526970,104638104924845707142704280⟩,⟨(-13612792),28901490⟩⟩] +lemma ha31_0_14_eq (j : Fin 7) : ha31_0_14 j = ((ha31_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha31_0_14_contains (j : Fin 7) : (ha31_0_14 j).Contains (fullFactor false 31 14 ((j.val:ℝ)/6)) := by + rw [ha31_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_13 j) false 31 13 j (ha31_0_13_contains j) +noncomputable def hk31_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_15 j i k) +lemma hk31_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_15 j i k).Contains (fullFactor false 31 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 15 (power31_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha31_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23305033302577),(-23305033302576)⟩,⟨40365501752147,40365501752148⟩⟩,⟨⟨1322696761414360852,1322696761414360854⟩,⟨(-763659331258827444),(-763659331258827442)⟩⟩,⟨⟨(-668803510981146723340),(-668803510981146723171)⟩,⟨(-93),44⟩⟩,⟨⟨43342127478025776380551,43342127478025776458796⟩,⟨25023588966689257627423,25023588966689257704818⟩⟩,⟨⟨(-711213174517105747722409),(-711213174517105744963456)⟩,⟨(-1231857353275977870663420),(-1231857353275977867878901)⟩⟩,⟨⟨(-6053114),2851057⟩,⟨21915353447830215822655968,21915353447830215832606520⟩⟩] +lemma ha31_0_15_eq (j : Fin 7) : ha31_0_15 j = ((ha31_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha31_0_15_contains (j : Fin 7) : (ha31_0_15 j).Contains (fullFactor false 31 15 ((j.val:ℝ)/6)) := by + rw [ha31_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_14 j) false 31 14 j (ha31_0_14_contains j) +noncomputable def hk31_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_16 j i k) +lemma hk31_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_16 j i k).Contains (fullFactor false 31 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 16 (power31_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha31_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1320957955865),(-1320957955864)⟩,⟨(-762655431407),(-762655431406)⟩⟩,⟨⟨49981386352667221,49981386352667222⟩,⟨86570300595549323,86570300595549325⟩⟩,⟨⟨(-5),10⟩,⟨(-65659631149794723632),(-65659631149794723614)⟩⟩,⟨⟨(-3275580136008399054762),(-3275580136008399044620)⟩,⟨5673471219829920489532,5673471219829920499793⟩⟩,⟨⟨201562188089707223376477,201562188089707223832735⟩,⟨(-116371983552042445901551),(-116371983552042445449747)⟩⟩,⟨⟨(-4303069587032947008333212),(-4303069587032947006365728)⟩,⟨(-1188527),559804⟩⟩] +lemma ha31_0_16_eq (j : Fin 7) : ha31_0_16 j = ((ha31_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha31_0_16_contains (j : Fin 7) : (ha31_0_16 j).Contains (fullFactor false 31 16 ((j.val:ℝ)/6)) := by + rw [ha31_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_15 j) false 31 15 j (ha31_0_15_contains j) +noncomputable def hk31_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_17 j i k) +lemma hk31_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_17 j i k).Contains (fullFactor false 31 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 17 (power31_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha31_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23489732358,23489732359⟩,⟨(-40685409901),(-40685409900)⟩⟩,⟨⟨(-5332718046471331),(-5332718046471330)⟩,⟨3078846199642597,3078846199642598⟩⟩,⟨⟨6066935731106195666,6066935731106195669⟩,⟨(-1),1⟩⟩,⟨⟨(-698970019787090239837),(-698970019787090238570)⟩,⟨(-403550529079554597374),(-403550529079554596122)⟩⟩,⟨⟨17921243559351411706580,17921243559351411776216⟩,⟨31040504379613153605151,31040504379613153675514⟩⟩,⟨⟨(-103452),219640⟩,⟨(-795205400147551278671523),(-795205400147551278305400)⟩⟩] +lemma ha31_0_17_eq (j : Fin 7) : ha31_0_17 j = ((ha31_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha31_0_17_contains (j : Fin 7) : (ha31_0_17 j).Contains (fullFactor false 31 17 ((j.val:ℝ)/6)) := by + rw [ha31_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_16 j) false 31 16 j (ha31_0_16_contains j) +noncomputable def hk31_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_18 j i k) +lemma hk31_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_18 j i k).Contains (fullFactor false 31 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 18 (power31_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha31_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1183490600,1183490601⟩,⟨683288616,683288617⟩⟩,⟨⟨(-179120011154260),(-179120011154259)⟩,⟨(-310244959971483),(-310244959971482)⟩⟩,⟨⟨(-1),1⟩,⟨529440020073462376,529440020073462377⟩⟩,⟨⟨46955236204022331300,46955236204022331447⟩,⟨(-81328854786764263455),(-81328854786764263307)⟩⟩,⟨⟨(-4514658357533078063470),(-4514658357533078053221)⟩,⟨2606539218020916330493,2606539218020916340631⟩⟩,⟨⟨138789524622137721114383,138789524622137721178727⟩,⟨(-18056),38335⟩⟩] +lemma ha31_0_18_eq (j : Fin 7) : ha31_0_18 j = ((ha31_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha31_0_18_contains (j : Fin 7) : (ha31_0_18 j).Contains (fullFactor false 31 18 ((j.val:ℝ)/6)) := by + rw [ha31_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_17 j) false 31 17 j (ha31_0_17_contains j) +noncomputable def hk31_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_19 j i k) +lemma hk31_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_19 j i k).Contains (fullFactor false 31 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 19 (power31_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha31_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-18829952),(-18829951)⟩,⟨32614433,32614434⟩⟩,⟨⟨17099355913327,17099355913328⟩,⟨(-9872317739529),(-9872317739528)⟩⟩,⟨⟨(-43770654673137423),(-43770654673137422)⟩,⟨(-1),1⟩⟩,⟨⟨8964987113086656136,8964987113086656153⟩,⟨5175937723022106873,5175937723022106890⟩⟩,⟨⟨(-359152827132815578187),(-359152827132815576788)⟩,⟨(-622070944276038606226),(-622070944276038604811)⟩⟩,⟨⟨(-6339),2986⟩,⟨22948428997269873105174,22948428997269873115888⟩⟩] +lemma ha31_0_19_eq (j : Fin 7) : ha31_0_19 j = ((ha31_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha31_0_19_contains (j : Fin 7) : (ha31_0_19 j).Contains (fullFactor false 31 19 ((j.val:ℝ)/6)) := by + rw [ha31_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_18 j) false 31 18 j (ha31_0_18_contains j) +noncomputable def hk31_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_20 j i k) +lemma hk31_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_20 j i k).Contains (fullFactor false 31 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 20 (power31_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha31_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-853844),(-853843)⟩,⟨(-492967),(-492966)⟩⟩,⟨⟨516913348073,516913348074⟩,⟨895320181973,895320181974⟩⟩,⟨⟨(-1),1⟩,⟨(-3437739179098608),(-3437739179098606)⟩⟩,⟨⟨(-542022930869484435),(-542022930869484432)⟩,⟨938811255133340261,938811255133340264⟩⟩,⟨⟨81428896189552855066,81428896189552855252⟩,⟨(-47012995134852432695),(-47012995134852432510)⟩⟩,⟨⟨(-3604730797462500934761),(-3604730797462500933066)⟩,⟨(-996),470⟩⟩] +lemma ha31_0_20_eq (j : Fin 7) : ha31_0_20 j = ((ha31_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha31_0_20_contains (j : Fin 7) : (ha31_0_20 j).Contains (fullFactor false 31 20 ((j.val:ℝ)/6)) := by + rw [ha31_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_19 j) false 31 19 j (ha31_0_19_contains j) +noncomputable def hk31_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_21 j i k) +lemma hk31_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_21 j i k).Contains (fullFactor false 31 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 21 (power31_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha31_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨12291,12292⟩,⟨(-21290),(-21289)⟩⟩,⟨⟨(-44646528672),(-44646528671)⟩,⟨25776685346,25776685347⟩⟩,⟨⟨257142289286047,257142289286048⟩,⟨(-1),1⟩⟩,⟨⟨(-93630556896327456),(-93630556896327454)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨5860939688051789399,5860939688051789423⟩,⟨10151445319802585603,10151445319802585628⟩⟩,⟨⟨(-71),150⟩,⟨(-539266466260812849072),(-539266466260812848816)⟩⟩] +lemma ha31_0_21_eq (j : Fin 7) : ha31_0_21 j = ((ha31_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha31_0_21_contains (j : Fin 7) : (ha31_0_21 j).Contains (fullFactor false 31 21 ((j.val:ℝ)/6)) := by + rw [ha31_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_20 j) false 31 20 j (ha31_0_20_contains j) +noncomputable def hk31_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_22 j i k) +lemma hk31_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_22 j i k).Contains (fullFactor false 31 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 22 (power31_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha31_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨506,507⟩,⟨292,293⟩⟩,⟨⟨(-1226967354),(-1226967353)⟩,⟨(-2125169796),(-2125169795)⟩⟩,⟨⟨(-1),1⟩,⟨18359916521552,18359916521553⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨(-1208019168182208040),(-1208019168182208036)⟩,⟨697450191936225608,697450191936225612⟩⟩,⟨⟨77007071306013533780,77007071306013533818⟩,⟨(-11),22⟩⟩] +lemma ha31_0_22_eq (j : Fin 7) : ha31_0_22 j = ((ha31_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha31_0_22_contains (j : Fin 7) : (ha31_0_22 j).Contains (fullFactor false 31 22 ((j.val:ℝ)/6)) := by + rw [ha31_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_21 j) false 31 21 j (ha31_0_21_contains j) +noncomputable def hk31_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_23 j i k) +lemma hk31_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_23 j i k).Contains (fullFactor false 31 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 23 (power31_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha31_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-7),(-6)⟩,⟨11,12⟩⟩,⟨⟨96759678,96759679⟩,⟨(-55864227),(-55864226)⟩⟩,⟨⟨(-1253899540536),(-1253899540535)⟩,⟨(-1),1⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨(-79387840551870929),(-79387840551870928)⟩,⟨(-137503773339017308),(-137503773339017306)⟩⟩,⟨⟨(-4),2⟩,⟨10518471716932064452,10518471716932064458⟩⟩] +lemma ha31_0_23_eq (j : Fin 7) : ha31_0_23 j = ((ha31_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha31_0_23_contains (j : Fin 7) : (ha31_0_23 j).Contains (fullFactor false 31 23 ((j.val:ℝ)/6)) := by + rw [ha31_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_22 j) false 31 22 j (ha31_0_22_contains j) +noncomputable def hk31_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_24 j i k) +lemma hk31_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_24 j i k).Contains (fullFactor false 31 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 24 (power31_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha31_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨2437536,2437537⟩,⟨4221937,4221938⟩⟩,⟨⟨(-1),1⟩,⟨(-82067533019),(-82067533018)⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨14999334866761557,14999334866761558⟩,⟨(-8659870022990125),(-8659870022990124)⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha31_0_24_eq (j : Fin 7) : ha31_0_24 j = ((ha31_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha31_0_24_contains (j : Fin 7) : (ha31_0_24 j).Contains (fullFactor false 31 24 ((j.val:ℝ)/6)) := by + rw [ha31_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_23 j) false 31 23 j (ha31_0_23_contains j) +noncomputable def hk31_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_25 j i k) +lemma hk31_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_25 j i k).Contains (fullFactor false 31 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 25 (power31_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha31_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-176849),(-176848)⟩,⟨102103,102104⟩⟩,⟨⟨5156455176,5156455177⟩,⟨(-1),1⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨906859468175608,906859468175609⟩,⟨1570726674205044,1570726674205046⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha31_0_25_eq (j : Fin 7) : ha31_0_25 j = ((ha31_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha31_0_25_contains (j : Fin 7) : (ha31_0_25 j).Contains (fullFactor false 31 25 ((j.val:ℝ)/6)) := by + rw [ha31_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_24 j) false 31 24 j (ha31_0_24_contains j) +noncomputable def hk31_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_26 j i k) +lemma hk31_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_26 j i k).Contains (fullFactor false 31 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 26 (power31_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha31_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-4113),(-4112)⟩,⟨(-7123),(-7122)⟩⟩,⟨⟨(-1),1⟩,⟨311528494,311528495⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨(-158159723733337),(-158159723733336)⟩,⟨91313559072398,91313559072399⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha31_0_26_eq (j : Fin 7) : ha31_0_26 j = ((ha31_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha31_0_26_contains (j : Fin 7) : (ha31_0_26 j).Contains (fullFactor false 31 26 ((j.val:ℝ)/6)) := by + rw [ha31_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_25 j) false 31 25 j (ha31_0_25_contains j) +noncomputable def hk31_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_27 j i k) +lemma hk31_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_27 j i k).Contains (fullFactor false 31 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 27 (power31_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha31_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨276,277⟩,⟨(-160),(-159)⟩⟩,⟨⟨(-18123994),(-18123993)⟩,⟨(-1),1⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨(-8854012541821),(-8854012541820)⟩,⟨(-15335599573286),(-15335599573285)⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha31_0_27_eq (j : Fin 7) : ha31_0_27 j = ((ha31_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha31_0_27_contains (j : Fin 7) : (ha31_0_27 j).Contains (fullFactor false 31 27 ((j.val:ℝ)/6)) := by + rw [ha31_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_26 j) false 31 26 j (ha31_0_26_contains j) +noncomputable def hk31_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_28 j i k) +lemma hk31_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_28 j i k).Contains (fullFactor false 31 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 28 (power31_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha31_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨5,6⟩,⟨10,11⟩⟩,⟨⟨(-1),1⟩,⟨(-1016754),(-1016753)⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨1433875207078,1433875207079⟩,⟨(-827848236791),(-827848236790)⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha31_0_28_eq (j : Fin 7) : ha31_0_28 j = ((ha31_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha31_0_28_contains (j : Fin 7) : (ha31_0_28 j).Contains (fullFactor false 31 28 ((j.val:ℝ)/6)) := by + rw [ha31_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_27 j) false 31 27 j (ha31_0_27_contains j) +noncomputable def hk31_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_29 j i k) +lemma hk31_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_29 j i k).Contains (fullFactor false 31 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 29 (power31_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha31_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨55072,55073⟩,⟨(-1),1⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨74734538476,74734538477⟩,⟨129444017721,129444017722⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha31_0_29_eq (j : Fin 7) : ha31_0_29 j = ((ha31_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha31_0_29_contains (j : Fin 7) : (ha31_0_29 j).Contains (fullFactor false 31 29 ((j.val:ℝ)/6)) := by + rw [ha31_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_28 j) false 31 28 j (ha31_0_28_contains j) +noncomputable def hk31_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power31 j i k).conj.mul (mpower0_30 j i k) +lemma hk31_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk31_0_30 j i k).Contains (fullFactor false 31 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power31 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 30 (power31_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha31_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨2883,2884⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨(-11296121532),(-11296121531)⟩,⟨6521818806,6521818807⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha31_0_30_eq (j : Fin 7) : ha31_0_30 j = ((ha31_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha31_0_30_contains (j : Fin 7) : (ha31_0_30 j).Contains (fullFactor false 31 30 ((j.val:ℝ)/6)) := by + rw [ha31_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_0_29 j) false 31 29 j (ha31_0_29_contains j) +noncomputable def hk31_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_0 j i k) +lemma hk31_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_0 j i k).Contains (fullFactor true 31 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 0 (kernel31_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha31_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨0,3⟩,⟨(-2),2⟩⟩,⟨⟨(-4030720336),(-4030720333)⟩,⟨4299209323,4299209326⟩⟩,⟨⟨407412577843147764126,407412577843147767566⟩,⟨58579429178108479865,58579429178108483303⟩⟩,⟨⟨(-2224103963996790476325329693),(-2224103963996790455774833313)⟩,⟨2270745127693704504337839885,2270745127693704524857452908⟩⟩] +lemma ha31_1_0_eq (j : Fin 7) : ha31_1_0 j = atomKernel31_0 j := by fin_cases j <;> decide +kernel +lemma ha31_1_0_contains (j : Fin 7) : (ha31_1_0 j).Contains (fullFactor true 31 0 ((j.val:ℝ)/6)) := by + rw [ha31_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel31_0_contains j +noncomputable def hk31_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_1 j i k) +lemma hk31_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_1 j i k).Contains (fullFactor true 31 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 1 (kernel31_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha31_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),31⟩,⟨(-31),42⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-19),11⟩,⟨(-21),6⟩⟩,⟨⟨25970278706,25970278725⟩,⟨12107049782,12107049802⟩⟩,⟨⟨(-47628420768149630847),(-47628420768149614376)⟩,⟨(-1705658777325531325301),(-1705658777325531308820)⟩⟩,⟨⟨8617347244127811818499525611,8617347244127811896482648040⟩,⟨7604911897842197952003746458,7604911897842198030092082194⟩⟩] +lemma ha31_1_1_eq (j : Fin 7) : ha31_1_1 j = ((ha31_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha31_1_1_contains (j : Fin 7) : (ha31_1_1 j).Contains (fullFactor true 31 1 ((j.val:ℝ)/6)) := by + rw [ha31_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_0 j) true 31 0 j (ha31_1_0_contains j) +noncomputable def hk31_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_2 j i k) +lemma hk31_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_2 j i k).Contains (fullFactor true 31 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 2 (kernel31_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha31_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-177),255⟩,⟨(-219),205⟩⟩,⟨⟨(-132),179⟩,⟨(-128),182⟩⟩,⟨⟨(-70),43⟩,⟨(-37),79⟩⟩,⟨⟨8290104826,8290104887⟩,⟨(-69164451613),(-69164451553)⟩⟩,⟨⟨(-3467288054675362345310),(-3467288054675362305833)⟩,⟨697940133507067142245,697940133507067181697⟩⟩,⟨⟨12921713344878323947007610477,12921713344878324095364975222⟩,⟨(-16272732548135652174226306945),(-16272732548135652026043512041)⟩⟩] +lemma ha31_1_2_eq (j : Fin 7) : ha31_1_2 j = ((ha31_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha31_1_2_contains (j : Fin 7) : (ha31_1_2 j).Contains (fullFactor true 31 2 ((j.val:ℝ)/6)) := by + rw [ha31_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_1 j) true 31 1 j (ha31_1_1_contains j) +noncomputable def hk31_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_3 j i k) +lemma hk31_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_3 j i k).Contains (fullFactor true 31 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 3 (kernel31_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha31_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-924),707⟩,⟨(-840),779⟩⟩,⟨⟨(-514),530⟩,⟨(-606),437⟩⟩,⟨⟨(-104),201⟩,⟨(-148),155⟩⟩,⟨⟨(-110700494399),(-110700494275)⟩,⟨22169534400,22169534525⟩⟩,⟨⟨1764440168088632886350,1764440168088632949349⟩,⟨4557778467483777458304,4557778467483777521341⟩⟩,⟨⟨(-20395871468310250607942058962),(-20395871468310250420227306605)⟩,⟨(-14535019260787779429662887352),(-14535019260787779241761107621)⟩⟩] +lemma ha31_1_3_eq (j : Fin 7) : ha31_1_3 j = ((ha31_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha31_1_3_contains (j : Fin 7) : (ha31_1_3 j).Contains (fullFactor true 31 3 ((j.val:ℝ)/6)) := by + rw [ha31_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_2 j) true 31 2 j (ha31_1_2_contains j) +noncomputable def hk31_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_4 j i k) +lemma hk31_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_4 j i k).Contains (fullFactor true 31 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 4 (kernel31_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha31_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2136),2495⟩,⟨(-2151),2469⟩⟩,⟨⟨(-1433),1196⟩,⟨(-1221),1408⟩⟩,⟨⟨(-332),272⟩,⟨(-367),238⟩⟩,⟨⟨67543429537,67543429729⟩,⟨119460085078,119460085270⟩⟩,⟨⟨4344292554885931418359,4344292554885931493850⟩,⟨(-2604581690289197134667),(-2604581690289197059216)⟩⟩,⟨⟨(-12164132957218381327222555451),(-12164132957218381148736228505)⟩,⟨19094828067338493653710616205,19094828067338493832052848431⟩⟩] +lemma ha31_1_4_eq (j : Fin 7) : ha31_1_4 j = ((ha31_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha31_1_4_contains (j : Fin 7) : (ha31_1_4 j).Contains (fullFactor true 31 4 ((j.val:ℝ)/6)) := by + rw [ha31_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_3 j) true 31 3 j (ha31_1_3_contains j) +noncomputable def hk31_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_5 j i k) +lemma hk31_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_5 j i k).Contains (fullFactor true 31 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 5 (kernel31_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha31_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5425),5111⟩,⟨(-5641),4887⟩⟩,⟨⟨(-2436),2862⟩,⟨(-2619),2679⟩⟩,⟨⟨(-529),432⟩,⟨(-413),547⟩⟩,⟨⟨89910386027,89910386264⟩,⟨(-98614905428),(-98614905192)⟩⟩,⟨⟨(-2740038877997094277622),(-2740038877997094205331)⟩,⟨(-3182660232125969428172),(-3182660232125969355850)⟩⟩,⟨⟨14247204279578508634765396278,14247204279578508770313430661⟩,⟨8067900187042618666860116120,8067900187042618802491700894⟩⟩] +lemma ha31_1_5_eq (j : Fin 7) : ha31_1_5 j = ((ha31_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha31_1_5_contains (j : Fin 7) : (ha31_1_5 j).Contains (fullFactor true 31 5 ((j.val:ℝ)/6)) := by + rw [ha31_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_4 j) true 31 4 j (ha31_1_4_contains j) +noncomputable def hk31_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_6 j i k) +lemma hk31_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_6 j i k).Contains (fullFactor true 31 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 6 (kernel31_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha31_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-10026),9960⟩,⟨(-9412),10570⟩⟩,⟨⟨(-4597),4299⟩,⟨(-4655),4241⟩⟩,⟨⟨(-556),716⟩,⟨(-626),646⟩⟩,⟨⟨(-98641013669),(-98641013427)⟩,⟨(-44324713318),(-44324713075)⟩⟩,⟨⟨(-1845381009114195391786),(-1845381009114195334049)⟩,⟨2239238934368501006673,2239238934368501064392⟩⟩,⟨⟨4409692053250024995566941318,4409692053250025081454065215⟩,⟨(-8826993718143173172616917838),(-8826993718143173086766240773)⟩⟩] +lemma ha31_1_6_eq (j : Fin 7) : ha31_1_6 j = ((ha31_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha31_1_6_contains (j : Fin 7) : (ha31_1_6 j).Contains (fullFactor true 31 6 ((j.val:ℝ)/6)) := by + rw [ha31_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_5 j) true 31 5 j (ha31_1_5_contains j) +noncomputable def hk31_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_7 j i k) +lemma hk31_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_7 j i k).Contains (fullFactor true 31 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 7 (kernel31_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha31_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-15907),16595⟩,⟨(-16866),15633⟩⟩,⟨⟨(-6449),6354⟩,⟨(-6146),6657⟩⟩,⟨⟨(-747),697⟩,⟨(-784),659⟩⟩,⟨⟨(-7900485729),(-7900485515)⟩,⟨74698308071,74698308284⟩⟩,⟨⟨1492523583963903809913,1492523583963903849414⟩,⟨851688637917093544881,851688637917093584390⟩⟩,⟨⟨(-4671789546547486452982365223),(-4671789546547486406376588220)⟩,⟨(-2038005515753214138328360498),(-2038005515753214091711635873)⟩⟩] +lemma ha31_1_7_eq (j : Fin 7) : ha31_1_7 j = ((ha31_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha31_1_7_contains (j : Fin 7) : (ha31_1_7 j).Contains (fullFactor true 31 7 ((j.val:ℝ)/6)) := by + rw [ha31_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_6 j) true 31 6 j (ha31_1_6_contains j) +noncomputable def hk31_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_8 j i k) +lemma hk31_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_8 j i k).Contains (fullFactor true 31 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 8 (kernel31_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha31_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-23741),22509⟩,⟨(-22694),23555⟩⟩,⟨⟨(-7868),8255⟩,⟨(-8188),7935⟩⟩,⟨⟨(-748),686⟩,⟨(-679),755⟩⟩,⟨⟨44634678501,44634678666⟩,⟨(-9586800753),(-9586800588)⟩⟩,⟨⟨303526042552794978173,303526042552795001829⟩,⟨(-837156160321559299094),(-837156160321559275440)⟩⟩,⟨⟨(-810256673980045127453220706),(-810256673980045105314252305)⟩,⟨2156579603832901580063376879,2156579603832901602201248116⟩⟩] +lemma ha31_1_8_eq (j : Fin 7) : ha31_1_8 j = ((ha31_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha31_1_8_contains (j : Fin 7) : (ha31_1_8 j).Contains (fullFactor true 31 8 ((j.val:ℝ)/6)) := by + rw [ha31_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_7 j) true 31 7 j (ha31_1_7_contains j) +noncomputable def hk31_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_9 j i k) +lemma hk31_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_9 j i k).Contains (fullFactor true 31 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 9 (kernel31_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha31_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-28549),29954⟩,⟨(-29363),29139⟩⟩,⟨⟨(-9202),8845⟩,⟨(-9065),8982⟩⟩,⟨⟨(-602),664⟩,⟨(-627),639⟩⟩,⟨⟨(-12436484934),(-12436484821)⟩,⟨(-21298257007),(-21298256893)⟩⟩,⟨⟨(-403756185110019389819),(-403756185110019377228)⟩,⟨(-72264493190854866041),(-72264493190854853450)⟩⟩,⟨⟨882178857450436325141595782,882178857450436334488574715⟩,⟨280101084700267215752930848,280101084700267225098697070⟩⟩] +lemma ha31_1_9_eq (j : Fin 7) : ha31_1_9 j = ((ha31_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha31_1_9_contains (j : Fin 7) : (ha31_1_9 j).Contains (fullFactor true 31 9 ((j.val:ℝ)/6)) := by + rw [ha31_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_8 j) true 31 8 j (ha31_1_8_contains j) +noncomputable def hk31_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_10 j i k) +lemma hk31_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_10 j i k).Contains (fullFactor true 31 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 10 (kernel31_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha31_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-33881),32720⟩,⟨(-33476),33125⟩⟩,⟨⟨(-9024),9157⟩,⟨(-8978),9203⟩⟩,⟨⟨(-509),497⟩,⟨(-521),485⟩⟩,⟨⟨(-7955200971),(-7955200900)⟩,⟨8973087660,8973087731⟩⟩,⟨⟨(-1085433284876035825),(-1085433284876029793)⟩,⟨170035979009406642625,170035979009406648657⟩⟩,⟨⟨84580262739715913824265981,84580262739715917374932541⟩,⟨(-323816634509918000756467940),(-323816634509917997204730181)⟩⟩] +lemma ha31_1_10_eq (j : Fin 7) : ha31_1_10 j = ((ha31_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha31_1_10_contains (j : Fin 7) : (ha31_1_10 j).Contains (fullFactor true 31 10 ((j.val:ℝ)/6)) := by + rw [ha31_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_9 j) true 31 9 j (ha31_1_9_contains j) +noncomputable def hk31_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_11 j i k) +lemma hk31_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_11 j i k).Contains (fullFactor true 31 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 11 (kernel31_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha31_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34119),34809⟩,⟨(-34145),34782⟩⟩,⟨⟨(-8303),8348⟩,⟨(-8407),8244⟩⟩,⟨⟨(-370),357⟩,⟨(-356),371⟩⟩,⟨⟨4864593917,4864593958⟩,⟨2105046889,2105046930⟩⟩,⟨⟨63219253415982381898,63219253415982384526⟩,⟨(-10483898199503395770),(-10483898199503393143)⟩⟩,⟨⟨(-107744747142501816369492633),(-107744747142501815142591661)⟩,⟨(-22237945050918130674032227),(-22237945050918129447701604)⟩⟩] +lemma ha31_1_11_eq (j : Fin 7) : ha31_1_11 j = ((ha31_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha31_1_11_contains (j : Fin 7) : (ha31_1_11 j).Contains (fullFactor true 31 11 ((j.val:ℝ)/6)) := by + rw [ha31_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_10 j) true 31 10 j (ha31_1_10_contains j) +noncomputable def hk31_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_12 j i k) +lemma hk31_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_12 j i k).Contains (fullFactor true 31 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 12 (kernel31_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha31_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32817),32574⟩,⟨(-33006),32385⟩⟩,⟨⟨(-7034),6945⟩,⟨(-6966),7013⟩⟩,⟨⟨(-236),246⟩,⟨(-240),242⟩⟩,⟨⟨196141668,196141690⟩,⟨(-2138688999),(-2138688978)⟩⟩,⟨⟨(-7279622200052017099),(-7279622200052016050)⟩,⟨(-20907125268850722394),(-20907125268850721344)⟩⟩,⟨⟨(-5005850506363761899146913),(-5005850506363761510895985)⟩,⟨32770398415280101573530209,32770398415280101962021486⟩⟩] +lemma ha31_1_12_eq (j : Fin 7) : ha31_1_12 j = ((ha31_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha31_1_12_contains (j : Fin 7) : (ha31_1_12 j).Contains (fullFactor true 31 12 ((j.val:ℝ)/6)) := by + rw [ha31_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_11 j) true 31 11 j (ha31_1_11_contains j) +noncomputable def hk31_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_13 j i k) +lemma hk31_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_13 j i k).Contains (fullFactor true 31 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 13 (kernel31_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha31_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28649),28615⟩,⟨(-28414),28850⟩⟩,⟨⟨(-5390),5443⟩,⟨(-5408),5425⟩⟩,⟨⟨(-148),147⟩,⟨(-150),145⟩⟩,⟨⟨(-782918819),(-782918808)⟩,⟨179592589,179592600⟩⟩,⟨⟨(-6175747804123556992),(-6175747804123556604)⟩,⟨3420338874787397377,3420338874787397765⟩⟩,⟨⟨9174979024031312883405940,9174979024031312996954784⟩,⟨917142223173749072919493,917142223173749186381775⟩⟩] +lemma ha31_1_13_eq (j : Fin 7) : ha31_1_13 j = ((ha31_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha31_1_13_contains (j : Fin 7) : (ha31_1_13 j).Contains (fullFactor true 31 13 ((j.val:ℝ)/6)) := by + rw [ha31_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_12 j) true 31 12 j (ha31_1_12_contains j) +noncomputable def hk31_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_14 j i k) +lemma hk31_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_14 j i k).Contains (fullFactor true 31 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 14 (kernel31_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha31_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23215),23350⟩,⟨(-23397),23168⟩⟩,⟨⟨(-3904),3892⟩,⟨(-3911),3885⟩⟩,⟨⟨(-85),83⟩,⟨(-83),85⟩⟩,⟨⟨144008349,144008355⟩,⟨238923544,238923550⟩⟩,⟨⟨1308764795808281890,1308764795808282023⟩,⟨1630056867210863085,1630056867210863219⟩⟩,⟨⟨113500561763983995629020,113500561763984026418501⟩,⟨(-2378807359343961110033518),(-2378807359343961079216443)⟩⟩] +lemma ha31_1_14_eq (j : Fin 7) : ha31_1_14 j = ((ha31_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha31_1_14_contains (j : Fin 7) : (ha31_1_14 j).Contains (fullFactor true 31 14 ((j.val:ℝ)/6)) := by + rw [ha31_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_13 j) true 31 13 j (ha31_1_13_contains j) +noncomputable def hk31_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_15 j i k) +lemma hk31_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_15 j i k).Contains (fullFactor true 31 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 15 (kernel31_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha31_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17733),17608⟩,⟨(-17629),17712⟩⟩,⟨⟨(-2621),2616⟩,⟨(-2612),2625⟩⟩,⟨⟨(-44),45⟩,⟨(-45),45⟩⟩,⟨⟨59040013,59040016⟩,⟨(-68491426),(-68491423)⟩⟩,⟨⟨382499681608716706,382499681608716750⟩,⟨(-432983259856220839),(-432983259856220796)⟩⟩,⟨⟨(-574083179772655789504230),(-574083179772655781698221)⟩,⟨2454876831709580220275,2454876831709588018341⟩⟩] +lemma ha31_1_15_eq (j : Fin 7) : ha31_1_15 j = ((ha31_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha31_1_15_contains (j : Fin 7) : (ha31_1_15 j).Contains (fullFactor true 31 15 ((j.val:ℝ)/6)) := by + rw [ha31_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_14 j) true 31 14 j (ha31_1_14_contains j) +noncomputable def hk31_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_16 j i k) +lemma hk31_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_16 j i k).Contains (fullFactor true 31 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 16 (kernel31_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha31_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12534),12613⟩,⟨(-12579),12568⟩⟩,⟨⟨(-1646),1652⟩,⟨(-1650),1648⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-25368520),(-25368518)⟩,⟨(-10560958),(-10560956)⟩⟩,⟨⟨(-127391328039926045),(-127391328039926031)⟩,⟨(-78604508945456492),(-78604508945456478)⟩⟩,⟨⟨7291384269136156033132,7291384269136157884705⟩,⟨129535521876882595339194,129535521876882597192856⟩⟩] +lemma ha31_1_16_eq (j : Fin 7) : ha31_1_16 j = ((ha31_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha31_1_16_contains (j : Fin 7) : (ha31_1_16 j).Contains (fullFactor true 31 16 ((j.val:ℝ)/6)) := by + rw [ha31_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_15 j) true 31 15 j (ha31_1_15_contains j) +noncomputable def hk31_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_17 j i k) +lemma hk31_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_17 j i k).Contains (fullFactor true 31 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 17 (kernel31_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha31_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8439),8401⟩,⟨(-8427),8414⟩⟩,⟨⟨(-979),976⟩,⟨(-978),977⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-608775),(-608773)⟩,⟨7835640,7835642⟩⟩,⟨⟨(-13611784411086881),(-13611784411086876)⟩,⟨33870167021284595,33870167021284600⟩⟩,⟨⟨27434530278979347766012,27434530278979348180295⟩,⟨(-2979570462312354406720),(-2979570462312353992936)⟩⟩] +lemma ha31_1_17_eq (j : Fin 7) : ha31_1_17 j = ((ha31_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha31_1_17_contains (j : Fin 7) : (ha31_1_17 j).Contains (fullFactor true 31 17 ((j.val:ℝ)/6)) := by + rw [ha31_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_16 j) true 31 16 j (ha31_1_16_contains j) +noncomputable def hk31_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_18 j i k) +lemma hk31_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_18 j i k).Contains (fullFactor true 31 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 18 (kernel31_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha31_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5319),5333⟩,⟨(-5319),5333⟩⟩,⟨⟨(-547),548⟩,⟨(-547),548⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨2062393,2062395⟩,⟨(-503404),(-503402)⟩⟩,⟨⟨8219805971022006,8219805971022009⟩,⟨1764068871831757,1764068871831759⟩⟩,⟨⟨(-883932238299380975839),(-883932238299380888504)⟩,⟨(-5472628847510540996826),(-5472628847510540909381)⟩⟩] +lemma ha31_1_18_eq (j : Fin 7) : ha31_1_18 j = ((ha31_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha31_1_18_contains (j : Fin 7) : (ha31_1_18 j).Contains (fullFactor true 31 18 ((j.val:ℝ)/6)) := by + rw [ha31_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_17 j) true 31 17 j (ha31_1_17_contains j) +noncomputable def hk31_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_19 j i k) +lemma hk31_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_19 j i k).Contains (fullFactor true 31 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 19 (kernel31_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha31_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3193),3190⟩,⟨(-3196),3187⟩⟩,⟨⟨(-291),291⟩,⟨(-291),291⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-286894),(-286893)⟩,⟨(-461338),(-461336)⟩⟩,⟨⟨74604885519316,74604885519317⟩,⟨(-1832778071714825),(-1832778071714823)⟩⟩,⟨⟨(-1031359281415900878288),(-1031359281415900860802)⟩,⟨222079800147427553724,222079800147427571189⟩⟩] +lemma ha31_1_19_eq (j : Fin 7) : ha31_1_19 j = ((ha31_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha31_1_19_contains (j : Fin 7) : (ha31_1_19 j).Contains (fullFactor true 31 19 ((j.val:ℝ)/6)) := by + rw [ha31_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_18 j) true 31 18 j (ha31_1_18_contains j) +noncomputable def hk31_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_20 j i k) +lemma hk31_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_20 j i k).Contains (fullFactor true 31 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 20 (kernel31_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha31_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1815),1819⟩⟩,⟨⟨(-147),147⟩,⟨(-147),147⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-84832),(-84831)⟩,⟨101226,101227⟩⟩,⟨⟨(-376999279622250),(-376999279622249)⟩,⟨49302589220519,49302589220520⟩⟩,⟨⟨49779886621991705999,49779886621991709318⟩,⟨184128227571140357439,184128227571140360762⟩⟩] +lemma ha31_1_20_eq (j : Fin 7) : ha31_1_20 j = ((ha31_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha31_1_20_contains (j : Fin 7) : (ha31_1_20 j).Contains (fullFactor true 31 20 ((j.val:ℝ)/6)) := by + rw [ha31_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_19 j) true 31 19 j (ha31_1_19_contains j) +noncomputable def hk31_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_21 j i k) +lemma hk31_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_21 j i k).Contains (fullFactor true 31 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 21 (kernel31_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha31_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-985),986⟩,⟨(-986),985⟩⟩,⟨⟨(-71),71⟩,⟨(-71),71⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨28391,28392⟩,⟨11358,11359⟩⟩,⟨⟨22235150667872,22235150667873⟩,⟨71687123886815,71687123886816⟩⟩,⟨⟨31216404187103377246,31216404187103377848⟩,⟨(-10206230554739693482),(-10206230554739692880)⟩⟩] +lemma ha31_1_21_eq (j : Fin 7) : ha31_1_21 j = ((ha31_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha31_1_21_contains (j : Fin 7) : (ha31_1_21 j).Contains (fullFactor true 31 21 ((j.val:ℝ)/6)) := by + rw [ha31_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_20 j) true 31 20 j (ha31_1_20_contains j) +noncomputable def hk31_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_22 j i k) +lemma hk31_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_22 j i k).Contains (fullFactor true 31 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 22 (kernel31_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha31_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-511),510⟩,⟨(-510),511⟩⟩,⟨⟨(-33),33⟩,⟨(-33),33⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨429,430⟩,⟨(-6745),(-6744)⟩⟩,⟨⟨12600127027732,12600127027734⟩,⟨(-6423944335563),(-6423944335562)⟩⟩,⟨⟨(-1941662418340123829),(-1941662418340123724)⟩,⟨(-5036672282196954575),(-5036672282196954470)⟩⟩] +lemma ha31_1_22_eq (j : Fin 7) : ha31_1_22 j = ((ha31_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha31_1_22_contains (j : Fin 7) : (ha31_1_22 j).Contains (fullFactor true 31 22 ((j.val:ℝ)/6)) := by + rw [ha31_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_21 j) true 31 21 j (ha31_1_21_contains j) +noncomputable def hk31_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_23 j i k) +lemma hk31_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_23 j i k).Contains (fullFactor true 31 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 23 (kernel31_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha31_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-15),15⟩,⟨(-15),15⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1384),(-1382)⟩,⟨357,359⟩⟩,⟨⟨(-1526871620800),(-1526871620798)⟩,⟨(-2041340551199),(-2041340551198)⟩⟩,⟨⟨(-774911404100471603),(-774911404100471585)⟩,⟨345962886881747506,345962886881747524⟩⟩] +lemma ha31_1_23_eq (j : Fin 7) : ha31_1_23 j = ((ha31_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha31_1_23_contains (j : Fin 7) : (ha31_1_23 j).Contains (fullFactor true 31 23 ((j.val:ℝ)/6)) := by + rw [ha31_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_22 j) true 31 22 j (ha31_1_22_contains j) +noncomputable def hk31_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_24 j i k) +lemma hk31_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_24 j i k).Contains (fullFactor true 31 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 24 (kernel31_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha31_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-7),7⟩,⟨(-7),7⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨155,157⟩,⟨243,244⟩⟩,⟨⟨(-302670712232),(-302670712231)⟩,⟨319810375675,319810375677⟩⟩,⟨⟨58116196097043786,58116196097043790⟩,⟨113885943591244614,113885943591244618⟩⟩] +lemma ha31_1_24_eq (j : Fin 7) : ha31_1_24 j = ((ha31_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha31_1_24_contains (j : Fin 7) : (ha31_1_24 j).Contains (fullFactor true 31 24 ((j.val:ℝ)/6)) := by + rw [ha31_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_23 j) true 31 23 j (ha31_1_23_contains j) +noncomputable def hk31_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_25 j i k) +lemma hk31_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_25 j i k).Contains (fullFactor true 31 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 25 (kernel31_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha31_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨35,36⟩,⟨(-44),(-43)⟩⟩,⟨⟨60787702719,60787702721⟩,⟨40450216126,40450216127⟩⟩,⟨⟨16013297387049045,16013297387049046⟩,⟨(-9249753718951410),(-9249753718951409)⟩⟩] +lemma ha31_1_25_eq (j : Fin 7) : ha31_1_25 j = ((ha31_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha31_1_25_contains (j : Fin 7) : (ha31_1_25 j).Contains (fullFactor true 31 25 ((j.val:ℝ)/6)) := by + rw [ha31_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_24 j) true 31 24 j (ha31_1_24_contains j) +noncomputable def hk31_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_26 j i k) +lemma hk31_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_26 j i k).Contains (fullFactor true 31 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 26 (kernel31_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha31_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-10),(-9)⟩,⟨(-4),(-3)⟩⟩,⟨⟨4709154710,4709154711⟩,⟨(-10647117388),(-10647117387)⟩⟩,⟨⟨(-1400306618805461),(-1400306618805460)⟩,⟨(-2157214482656558),(-2157214482656557)⟩⟩] +lemma ha31_1_26_eq (j : Fin 7) : ha31_1_26 j = ((ha31_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha31_1_26_contains (j : Fin 7) : (ha31_1_26 j).Contains (fullFactor true 31 26 ((j.val:ℝ)/6)) := by + rw [ha31_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_25 j) true 31 25 j (ha31_1_25_contains j) +noncomputable def hk31_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_27 j i k) +lemma hk31_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_27 j i k).Contains (fullFactor true 31 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 27 (kernel31_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha31_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1,2⟩⟩,⟨⟨(-1733826218),(-1733826217)⟩,⟨(-434795285),(-434795284)⟩⟩,⟨⟨(-278771014714258),(-278771014714257)⟩,⟨202281891157974,202281891157975⟩⟩] +lemma ha31_1_27_eq (j : Fin 7) : ha31_1_27 j = ((ha31_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha31_1_27_contains (j : Fin 7) : (ha31_1_27 j).Contains (fullFactor true 31 27 ((j.val:ℝ)/6)) := by + rw [ha31_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_26 j) true 31 26 j (ha31_1_26_contains j) +noncomputable def hk31_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_28 j i k) +lemma hk31_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_28 j i k).Contains (fullFactor true 31 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 28 (kernel31_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha31_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-19825890),(-19825889)⟩,⟨263907924,263907925⟩⟩,⟨⟨27956819447982,27956819447984⟩,⟨34595222992317,34595222992318⟩⟩] +lemma ha31_1_28_eq (j : Fin 7) : ha31_1_28 j = ((ha31_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha31_1_28_contains (j : Fin 7) : (ha31_1_28 j).Contains (fullFactor true 31 28 ((j.val:ℝ)/6)) := by + rw [ha31_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_27 j) true 31 27 j (ha31_1_27_contains j) +noncomputable def hk31_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_29 j i k) +lemma hk31_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_29 j i k).Contains (fullFactor true 31 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 29 (kernel31_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha31_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨37658809,37658810⟩,⟨(-3616451),(-3616450)⟩⟩,⟨⟨4126713975227,4126713975228⟩,⟨(-3705133242665),(-3705133242664)⟩⟩] +lemma ha31_1_29_eq (j : Fin 7) : ha31_1_29 j = ((ha31_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha31_1_29_contains (j : Fin 7) : (ha31_1_29 j).Contains (fullFactor true 31 29 ((j.val:ℝ)/6)) := by + rw [ha31_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_28 j) true 31 28 j (ha31_1_28_contains j) +noncomputable def hk31_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel31_0 j i k).mul (mpower1_30 j i k) +lemma hk31_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk31_1_30 j i k).Contains (fullFactor true 31 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk31_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel31_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 31 30 (kernel31_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha31_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1376586),(-1376585)⟩,⟨(-5043344),(-5043343)⟩⟩,⟨⟨(-471807317998),(-471807317997)⟩,⟨(-473531544081),(-473531544080)⟩⟩] +lemma ha31_1_30_eq (j : Fin 7) : ha31_1_30 j = ((ha31_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha31_1_30_contains (j : Fin 7) : (ha31_1_30 j).Contains (fullFactor true 31 30 ((j.val:ℝ)/6)) := by + rw [ha31_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha31_1_29 j) true 31 29 j (ha31_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders33.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders33.lean new file mode 100644 index 0000000000000000000000000000000000000000..b6a09ad3f740b0204ce600c3ac2245244feae59a --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders33.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers40 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues40 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk33_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_0 j i k) +lemma hk33_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_0 j i k).Contains (fullFactor false 33 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 0 (power33_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha33_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999605,1000000000000000000000000000527⟩,⟨(-527),527⟩⟩,⟨⟨(-122942317822),148865101642⟩,⟨(-1000000000000000000135775819551),(-999999999999999999864224180501)⟩⟩,⟨⟨(-1000000000000000000371215853760),(-999999999999999999628784146255)⟩,⟨(-397045029932),345199462115⟩⟩,⟨⟨(-146684449625),68916097931⟩,⟨999999999999999999892199726255,1000000000000000000107800273778⟩⟩,⟨⟨999999999999999998985007789769,1000000000000000001014992210156⟩,⟨(-963215074312),1066906210036⟩⟩,⟨⟨(-1212681522260),1342295441787⟩,⟨(-1000000000000000001277556401719),(-999999999999999998722443598198)⟩⟩,⟨⟨(-1000000000000000000216255526937),(-999999999999999999783744473195)⟩,⟨(-294023878697),138487175045⟩⟩] +lemma ha33_0_0_eq (j : Fin 7) : ha33_0_0 j = ((atomPoints j).direct.powBin 7 33).conj := by fin_cases j <;> decide +kernel +lemma ha33_0_0_contains (j : Fin 7) : (ha33_0_0 j).Contains (fullFactor false 33 0 ((j.val:ℝ)/6)) := by + rw [ha33_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 33) ((j.val:ℝ)/6) 33 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 33 (by norm_num)) +noncomputable def hk33_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_1 j i k) +lemma hk33_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_1 j i k).Contains (fullFactor false 33 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 1 (power33_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha33_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨523598775598298873005574613818,523598775598298873149425386208⟩,⟨(-64372447081),77945584950⟩⟩,⟨⟨(-361492031402),415784583060⟩,⟨(-1047197551196597746545402999692),(-1047197551196597745764597000324)⟩⟩,⟨⟨(-1570796326794896619404332274078),(-1570796326794896619060667725973)⟩,⟨(-230411394669),108253153488⟩⟩,⟨⟨(-2234523141013),2017352934191⟩,⟨2094395102393195490180871952588,2094395102393195494439128047253⟩⟩,⟨⟨2617993877991494362038698494625,2617993877991494368736301505159⟩,⟨(-3174792801231),3514121249055⟩⟩,⟨⟨(-435070291738),923703257295⟩,⟨(-3141592653589793239149386774724),(-3141592653589793237780613225691)⟩⟩] +lemma ha33_0_1_eq (j : Fin 7) : ha33_0_1 j = ((ha33_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha33_0_1_contains (j : Fin 7) : (ha33_0_1 j).Contains (fullFactor false 33 1 ((j.val:ℝ)/6)) := by + rw [ha33_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_0 j) false 33 0 j (ha33_0_0_contains j) +noncomputable def hk33_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_2 j i k) +lemma hk33_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_2 j i k).Contains (fullFactor false 33 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 2 (power33_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha33_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-20406106422),16852667237⟩,⟨137077838904018869687192062598,137077838904018869725288439059⟩⟩,⟨⟨548311355616075478619673806054,548311355616075479030248200558⟩,⟨(-189276785031),217704298603⟩⟩,⟨⟨(-85021827932),180964686199⟩,⟨(-1233700550136169827493082505311),(-1233700550136169827219242009586)⟩⟩,⟨⟨(-2193245422464301917532952348980),(-2193245422464301913066735677265)⟩,⟨(-2339987161361),2112567052585⟩⟩,⟨⟨(-4599973958273),4155794058758⟩,⟨3426945972600471738266981196880,3426945972600471747045031344109⟩⟩,⟨⟨4934802200544679308341762816888,4934802200544679310507535243192⟩,⟨(-683406816160),1450949683608⟩⟩] +lemma ha33_0_2_eq (j : Fin 7) : ha33_0_2 j = ((ha33_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha33_0_2_contains (j : Fin 7) : (ha33_0_2 j).Contains (fullFactor false 33 2 ((j.val:ℝ)/6)) := by + rw [ha33_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_1 j) false 33 1 j (ha33_0_1_contains j) +noncomputable def hk33_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_3 j i k) +lemma hk33_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_3 j i k).Contains (fullFactor false 33 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 3 (power33_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha33_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23924596203935046435111140730),(-23924596203935046428385914350)⟩,⟨(-3561537446),2941345311⟩⟩,⟨⟨(-75993136128),66070061928⟩,⟨191396769631480371382024852813,191396769631480371525951587824⟩⟩,⟨⟨645964097506246253584490885653,645964097506246253729929601508⟩,⟨(-44517325005),94752888121⟩⟩,⟨⟨(-1474850029471),1633619216806⟩,⟨(-1531174157051842973193346422416),(-1531174157051842970070465102540)⟩⟩,⟨⟨(-2990574525491880807803472513877),(-2990574525491880800133659370788)⟩,⟨(-4014234553894),3626614468008⟩⟩,⟨⟨(-1519430955584),715661944354⟩,⟨5167712780049970028115461487930,5167712780049970030399902409875⟩⟩] +lemma ha33_0_3_eq (j : Fin 7) : ha33_0_3 j = ((ha33_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha33_0_3_contains (j : Fin 7) : (ha33_0_3 j).Contains (fullFactor false 33 3 ((j.val:ℝ)/6)) := by + rw [ha33_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_2 j) false 33 2 j (ha33_0_2_contains j) +noncomputable def hk33_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_4 j i k) +lemma hk33_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_4 j i k).Contains (fullFactor false 33 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 4 (power33_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha33_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-385021201),466204162⟩,⟨(-3131722319766024860165205023),(-3131722319766024859274906366)⟩⟩,⟨⟨(-50107557116256397774440605328),(-50107557116256397736601176905)⟩,⟨(-19894956516),17297101765⟩⟩,⟨⟨(-37209372154),17481912650⟩,⟨253669507901048013608363958636,253669507901048013666285063919⟩⟩,⟨⟨801720913860102363269489861642,801720913860102364907178653999⟩,⟨(-772229669623),855361021714⟩⟩,⟨⟨(-2373613618771),2627310371730⟩,⟨(-1957326449853765539838090472671),(-1957326449853765534811979145586)⟩⟩,⟨⟨(-4058712126416768219100749673860),(-4058712126416768217293634687423)⟩,⟨(-1193358281925),562079576710⟩⟩] +lemma ha33_0_4_eq (j : Fin 7) : ha33_0_4 j = ((ha33_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha33_0_4_contains (j : Fin 7) : (ha33_0_4 j).Contains (fullFactor false 33 4 ((j.val:ℝ)/6)) := by + rw [ha33_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_3 j) false 33 3 j (ha33_0_3_contains j) +noncomputable def hk33_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_5 j i k) +lemma hk33_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_5 j i k).Contains (fullFactor false 33 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 5 (power33_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha33_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨327953194428670967528189073,327953194428670967622464839⟩,⟨(-40319326),48820786⟩⟩,⟨⟨(-3622696523),4166789949⟩,⟨(-10494502221717470966389700801),(-10494502221717470958431224405)⟩⟩,⟨⟨(-79692626246167045130029511090),(-79692626246167045111579389697)⟩,⟨(-11689669021),5492104836⟩⟩,⟨⟨(-358292786932),323470807597⟩,⟨335824071094959070453603584081,335824071094959071140666022492⟩⟩,⟨⟨1024853732589596772355432764726,1024853732589596774990360712361⟩,⟨(-1242821184532),1375656493755⟩⟩,⟨⟨(-353165013785),749809122320⟩,⟨(-2550164039877345444437523041410),(-2550164039877345443293961784039)⟩⟩] +lemma ha33_0_5_eq (j : Fin 7) : ha33_0_5 j = ((ha33_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha33_0_5_contains (j : Fin 7) : (ha33_0_5 j).Contains (fullFactor false 33 5 ((j.val:ℝ)/6)) := by + rw [ha33_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_4 j) false 33 4 j (ha33_0_4_contains j) +noncomputable def hk33_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_6 j i k) +lemma hk33_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_6 j i k).Contains (fullFactor false 33 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 6 (power33_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha33_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-4260418),3518525⟩,⟨28619315176067161687398562,28619315176067161695716773⟩⟩,⟨⟨1831636171268298347562267507,1831636171268298348957113953⟩,⟨(-632279822),727242039⟩⟩,⟨⟨(-1437829684),3060348194⟩,⟨(-20863480763352960875593860224),(-20863480763352960870697219216)⟩⟩,⟨⟨(-117224714961171094408721792806),(-117224714961171094168518620607)⟩,⟨(-125067776363),112912612534⟩⟩,⟨⟨(-600243379812),542283042091⟩,⟨447176799626049400855024750106,447176799626049402006152364046⟩⟩,⟨⟨1335262768854589495579805768364,1335262768854589496182823315946⟩,⟨(-184916768802),392599138380⟩⟩] +lemma ha33_0_6_eq (j : Fin 7) : ha33_0_6 j = ((ha33_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha33_0_6_contains (j : Fin 7) : (ha33_0_6 j).Contains (fullFactor false 33 6 ((j.val:ℝ)/6)) := by + rw [ha33_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_5 j) false 33 5 j (ha33_0_5_contains j) +noncomputable def hk33_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_7 j i k) +lemma hk33_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_7 j i k).Contains (fullFactor false 33 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 7 (power33_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha33_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2140719769235797028531265),(-2140719769235797027902249)⟩,⟨(-318679),263186⟩⟩,⟨⟨(-108795155),94588841⟩,⟨274012130462182019506974521,274012130462182019716515270⟩⟩,⟨⟨4681754135318688100153194468,4681754135318688101266900628⟩,⟨(-322648227),686740529⟩⟩,⟨⟨(-33783374670),37420191184⟩,⟨(-35073552699159298546293478427),(-35073552699159298474313214778)⟩⟩,⟨⟨(-167243731971546643044960677318),(-167243731971546642613907603115)⟩,⟨(-224490499094),202813383477⟩⟩,⟨⟨(-176198081278),82990451771⟩,⟨599264529320792076754615505784,599264529320792077027156666522⟩⟩] +lemma ha33_0_7_eq (j : Fin 7) : ha33_0_7 j = ((ha33_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha33_0_7_contains (j : Fin 7) : (ha33_0_7 j).Contains (fullFactor false 33 7 ((j.val:ℝ)/6)) := by + rw [ha33_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_6 j) false 33 6 j (ha33_0_6_contains j) +noncomputable def hk33_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_8 j i k) +lemma hk33_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_8 j i k).Contains (fullFactor false 33 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 8 (power33_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha33_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-17226),20858⟩,⟨(-140109781258867029474738),(-140109781258867029433122)⟩⟩,⟨⟨(-35868104002269959553977500),(-35868104002269959526434507)⟩,⟨(-14241253),12381651⟩⟩,⟨⟨(-134841188),63351832⟩,⟨919260274839426580136431877,919260274839426580358033667⟩⟩,⟨⟨9182234624581109632855928461,9182234624581109651729545379⟩,⟨(-8844466807),9796583144⟩⟩,⟨⟨(-66370524540),73464344037⟩,⟨(-54730383304244933451059290108),(-54730383304244933309823289217)⟩⟩,⟨⟨(-235330630358893204597179461706),(-235330630358893204489403717496)⟩,⟨(-69192824715),32590274201⟩⟩] +lemma ha33_0_8_eq (j : Fin 7) : ha33_0_8 j = ((ha33_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha33_0_8_contains (j : Fin 7) : (ha33_0_8 j).Contains (fullFactor false 33 8 ((j.val:ℝ)/6)) := by + rw [ha33_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_7 j) false 33 7 j (ha33_0_7_contains j) +noncomputable def hk33_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_9 j i k) +lemma hk33_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_9 j i k).Contains (fullFactor false 33 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 9 (power33_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha33_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨8151256657387584303696,8151256657387584306144⟩,⟨(-1003),1214⟩⟩,⟨⟨(-1440671),1657046⟩,⟨(-4173443408582443165728165),(-4173443408582443162510107)⟩⟩,⟨⟨(-160441184787359821893337797),(-160441184787359821854150287)⟩,⟨(-23534227),11056981⟩⟩,⟨⟨(-2279768418),2058200885⟩,⟨2136803025194210897829551646,2136803025194210902228443396⟩⟩,⟨⟨15920423158960125574979958593,15920423158960125616114522174⟩,⟨(-19306402992),21369911438⟩⟩,⟨⟨(-11376151779),24152852201⟩,⟨(-82145886611128228818298104770),(-82145886611128228780415794485)⟩⟩] +lemma ha33_0_9_eq (j : Fin 7) : ha33_0_9 j = ((ha33_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha33_0_9_contains (j : Fin 7) : (ha33_0_9 j).Contains (fullFactor false 33 9 ((j.val:ℝ)/6)) := by + rw [ha33_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_8 j) false 33 8 j (ha33_0_8_contains j) +noncomputable def hk33_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_10 j i k) +lemma hk33_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_10 j i k).Contains (fullFactor false 33 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 10 (power33_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha33_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-64),53⟩,⟨426798800539562151389,426798800539562151520⟩⟩,⟨⟨437041971752511642920307,437041971752511643258693⟩,⟨(-150867),173526⟩⟩,⟨⟨(-1736827),3696748⟩,⟨(-25202042373060605484359962),(-25202042373060605478124180)⟩⟩,⟨⟨(-447530979074571922985011050),(-447530979074571922062284780)⟩,⟨(-477473581),431068586⟩⟩,⟨⟨(-5594629732),5054404484⟩,⟨4167957036519161629907592863,4167957036519161640689863447⟩⟩,⟨⟨25806891390014060006800268296,25806891390014060018783492953⟩,⟨(-3573923486),7587842304⟩⟩] +lemma ha33_0_10_eq (j : Fin 7) : ha33_0_10 j = ((ha33_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha33_0_10_contains (j : Fin 7) : (ha33_0_10 j).Contains (fullFactor false 33 10 ((j.val:ℝ)/6)) := by + rw [ha33_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_9 j) false 33 9 j (ha33_0_9_contains j) +noncomputable def hk33_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_11 j i k) +lemma hk33_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_11 j i k).Contains (fullFactor false 33 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 11 (power33_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha33_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-20315575399030665725),(-20315575399030665717)⟩,⟨(-4),3⟩⟩,⟨⟨(-16520),14363⟩,⟨41606298417214803380553,41606298417214803412900⟩⟩,⟨⟨3598843235212085340037274,3598843235212085340939198⟩,⟨(-248019),527895⟩⟩,⟨⟨(-82075267),90910758⟩,⟨(-85209699158455917444474796),(-85209699158455917268516893)⟩⟩,⟨⟨(-991971455030794225945694035),(-991971455030794223376362093)⟩,⟨(-1331518763),1202945455⟩⟩,⟨⟨(-2167082695),1020710161⟩,⟨7370430945714350775596976024,7370430945714350779042837795⟩⟩] +lemma ha33_0_11_eq (j : Fin 7) : ha33_0_11 j = ((ha33_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha33_0_11_contains (j : Fin 7) : (ha33_0_11 j).Contains (fullFactor false 33 11 ((j.val:ℝ)/6)) := by + rw [ha33_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_10 j) false 33 10 j (ha33_0_10_contains j) +noncomputable def hk33_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_12 j i k) +lemma hk33_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_12 j i k).Contains (fullFactor false 33 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 12 (power33_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha33_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-886434200375614886),(-886434200375614885)⟩⟩,⟨⟨(-3630834484738518572474),(-3630834484738518569639)⟩,⟨(-1442),1254⟩⟩,⟨⟨(-69102),32466⟩,⟨471087477881817150311487,471087477881817150431049⟩⟩,⟨⟨14871898049488972051667586,14871898049488972082425373⟩,⟨(-14324837),15866921⟩⟩,⟨⟨(-262441987),290492331⟩,⟨(-216414599701077853188765588),(-216414599701077852627535443)⟩⟩,⟨⟨(-1929574309403923048374848109),(-1929574309403923047466581580)⟩,⟨(-567340923),267221296⟩⟩] +lemma ha33_0_12_eq (j : Fin 7) : ha33_0_12 j = ((ha33_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha33_0_12_contains (j : Fin 7) : (ha33_0_12 j).Contains (fullFactor false 33 12 ((j.val:ℝ)/6)) := by + rw [ha33_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_11 j) false 33 11 j (ha33_0_11_contains j) +noncomputable def hk33_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_13 j i k) +lemma hk33_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_13 j i k).Contains (fullFactor false 33 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 13 (power33_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha33_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨35702758612702236,35702758612702237⟩,⟨(-1),1⟩⟩,⟨⟨(-102),117⟩,⟨(-292476998555256723141),(-292476998555256722911)⟩⟩,⟨⟨(-56921729219679268125622),(-56921729219679268110993)⟩,⟨(-8350),3923⟩⟩,⟨⟨(-2556278),2307837⟩,⟨2395971572164663072548527,2395971572164663077511459⟩⟩,⟨⟨43582469009646284974577265,43582469009646285087738846⟩,⟨(-52851656),58500550⟩⟩,⟨⟨(-64576959),137104160⟩,⟨(-466302805767612564535664613),(-466302805767612564314687750)⟩⟩] +lemma ha33_0_13_eq (j : Fin 7) : ha33_0_13 j = ((ha33_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha33_0_13_contains (j : Fin 7) : (ha33_0_13 j).Contains (fullFactor false 33 13 ((j.val:ℝ)/6)) := by + rw [ha33_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_12 j) false 33 12 j (ha33_0_12_contains j) +noncomputable def hk33_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_14 j i k) +lemma hk33_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_14 j i k).Contains (fullFactor false 33 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 14 (power33_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha33_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1335280049649465,1335280049649466⟩⟩,⟨⟨21877228333456835509,21877228333456835527⟩,⟨(-8),9⟩⟩,⟨⟨(-441),937⟩,⟨(-6386603083791852241988),(-6386603083791852240326)⟩⟩,⟨⟨(-358436509015356793493306),(-358436509015356792749712)⟩,⟨(-382419),345252⟩⟩,⟨⟨(-10939578),9883237⟩,⟨8149902646786285746557029,8149902646786285767744138⟩⟩,⟨⟨104638104924845707094155542,104638104924845707144075709⟩,⟨(-14491036),30766102⟩⟩] +lemma ha33_0_14_eq (j : Fin 7) : ha33_0_14 j = ((ha33_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha33_0_14_contains (j : Fin 7) : (ha33_0_14 j).Contains (fullFactor false 33 14 ((j.val:ℝ)/6)) := by + rw [ha33_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_13 j) false 33 13 j (ha33_0_13_contains j) +noncomputable def hk33_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_15 j i k) +lemma hk33_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_15 j i k).Contains (fullFactor false 33 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 15 (power33_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha33_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-46610066605154),(-46610066605153)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1527318662517654886,1527318662517654888⟩⟩,⟨⟨668803510981146723167,668803510981146723344⟩,⟨(-47),99⟩⟩,⟨⟨(-48207),53396⟩,⟨(-50047177933378515380012),(-50047177933378515276026)⟩⟩,⟨⟨(-1422426349034211494687043),(-1422426349034211490984666)⟩,⟨(-1909317),1724951⟩⟩,⟨⟨(-6443638),3034996⟩,⟨21915353447830215822368736,21915353447830215832893752⟩⟩] +lemma ha33_0_15_eq (j : Fin 7) : ha33_0_15 j = ((ha33_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha33_0_15_contains (j : Fin 7) : (ha33_0_15 j).Contains (fullFactor false 33 15 ((j.val:ℝ)/6)) := by + rw [ha33_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_14 j) false 33 14 j (ha33_0_14_contains j) +noncomputable def hk33_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_16 j i k) +lemma hk33_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_16 j i k).Contains (fullFactor false 33 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 16 (power33_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha33_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1525310862814),(-1525310862813)⟩⟩,⟨⟨(-99962772705334444),(-99962772705334443)⟩,⟨(-1),1⟩⟩,⟨⟨(-10),5⟩,⟨65659631149794723614,65659631149794723632⟩⟩,⟨⟨6551160272016798092013,6551160272016798105647⟩,⟨(-6311),6990⟩⟩,⟨⟨(-282245),312412⟩,⟨(-232743967104084891679110),(-232743967104084891072568)⟩⟩,⟨⟨(-4303069587032947008389610),(-4303069587032947006309330)⟩,⟨(-1265206),595921⟩⟩] +lemma ha33_0_16_eq (j : Fin 7) : ha33_0_16 j = ((ha33_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha33_0_16_contains (j : Fin 7) : (ha33_0_16 j).Contains (fullFactor false 33 16 ((j.val:ℝ)/6)) := by + rw [ha33_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_15 j) false 33 15 j (ha33_0_15_contains j) +noncomputable def hk33_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_17 j i k) +lemma hk33_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_17 j i k).Contains (fullFactor false 33 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 17 (power33_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha33_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨46979464716,46979464717⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-6157692399285196),(-6157692399285195)⟩⟩,⟨⟨(-6066935731106195669),(-6066935731106195666)⟩,⟨(-1),1⟩⟩,⟨⟨(-862),778⟩,⟨807101058159109192586,807101058159109194269⟩⟩,⟨⟨35842487118702823439815,35842487118702823533337⟩,⟨(-43466),48112⟩⟩,⟨⟨(-110126),233810⟩,⟨(-795205400147551278681945),(-795205400147551278294978)⟩⟩] +lemma ha33_0_17_eq (j : Fin 7) : ha33_0_17 j = ((ha33_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha33_0_17_contains (j : Fin 7) : (ha33_0_17 j).Contains (fullFactor false 33 17 ((j.val:ℝ)/6)) := by + rw [ha33_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_16 j) false 33 16 j (ha33_0_16_contains j) +noncomputable def hk33_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_18 j i k) +lemma hk33_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_18 j i k).Contains (fullFactor false 33 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 18 (power33_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha33_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1366577233,1366577234⟩⟩,⟨⟨358240022308519,358240022308520⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-529440020073462377),(-529440020073462376)⟩⟩,⟨⟨(-93910472408044662838),(-93910472408044662641)⟩,⟨(-101),91⟩⟩,⟨⟨(-6998),6322⟩,⟨5213078436041832664864,5213078436041832678484⟩⟩,⟨⟨138789524622137721112564,138789524622137721180546⟩,⟨(-19221),40808⟩⟩] +lemma ha33_0_18_eq (j : Fin 7) : ha33_0_18 j = ((ha33_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha33_0_18_contains (j : Fin 7) : (ha33_0_18 j).Contains (fullFactor false 33 18 ((j.val:ℝ)/6)) := by + rw [ha33_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_17 j) false 33 17 j (ha33_0_17_contains j) +noncomputable def hk33_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_19 j i k) +lemma hk33_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_19 j i k).Contains (fullFactor false 33 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 19 (power33_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha33_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-37659904),(-37659903)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨19744635479057,19744635479058⟩⟩,⟨⟨43770654673137422,43770654673137423⟩,⟨(-1),1⟩⟩,⟨⟨(-11),12⟩,⟨(-10351875446044213773),(-10351875446044213750)⟩⟩,⟨⟨(-718305654265631155990),(-718305654265631154111)⟩,⟨(-965),872⟩⟩,⟨⟨(-6748),3179⟩,⟨22948428997269873104874,22948428997269873116188⟩⟩] +lemma ha33_0_19_eq (j : Fin 7) : ha33_0_19 j = ((ha33_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha33_0_19_contains (j : Fin 7) : (ha33_0_19 j).Contains (fullFactor false 33 19 ((j.val:ℝ)/6)) := by + rw [ha33_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_18 j) false 33 18 j (ha33_0_18_contains j) +noncomputable def hk33_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_20 j i k) +lemma hk33_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_20 j i k).Contains (fullFactor false 33 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 20 (power33_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha33_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-985934),(-985933)⟩⟩,⟨⟨(-1033826696147),(-1033826696146)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨3437739179098606,3437739179098608⟩⟩,⟨⟨1084045861738968865,1084045861738968869⟩,⟨(-2),2⟩⟩,⟨⟨(-115),127⟩,⟨(-94025990269704865338),(-94025990269704865091)⟩⟩,⟨⟨(-3604730797462500934808),(-3604730797462500933019)⟩,⟨(-1060),500⟩⟩] +lemma ha33_0_20_eq (j : Fin 7) : ha33_0_20 j = ((ha33_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha33_0_20_contains (j : Fin 7) : (ha33_0_20 j).Contains (fullFactor false 33 20 ((j.val:ℝ)/6)) := by + rw [ha33_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_19 j) false 33 19 j (ha33_0_19_contains j) +noncomputable def hk33_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_21 j i k) +lemma hk33_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_21 j i k).Contains (fullFactor false 33 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 21 (power33_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha33_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨24582,24583⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-51553370694),(-51553370693)⟩⟩,⟨⟨(-257142289286048),(-257142289286047)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨11721879376103578807,11721879376103578839⟩,⟨(-15),16⟩⟩,⟨⟨(-75),159⟩,⟨(-539266466260812849079),(-539266466260812848809)⟩⟩] +lemma ha33_0_21_eq (j : Fin 7) : ha33_0_21 j = ((ha33_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha33_0_21_contains (j : Fin 7) : (ha33_0_21 j).Contains (fullFactor false 33 21 ((j.val:ℝ)/6)) := by + rw [ha33_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_20 j) false 33 20 j (ha33_0_20_contains j) +noncomputable def hk33_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_22 j i k) +lemma hk33_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_22 j i k).Contains (fullFactor false 33 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 22 (power33_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha33_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨585,586⟩⟩,⟨⟨2453934706,2453934707⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-18359916521553),(-18359916521552)⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨1394900383872451217,1394900383872451222⟩⟩,⟨⟨77007071306013533779,77007071306013533819⟩,⟨(-11),23⟩⟩] +lemma ha33_0_22_eq (j : Fin 7) : ha33_0_22 j = ((ha33_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha33_0_22_contains (j : Fin 7) : (ha33_0_22 j).Contains (fullFactor false 33 22 ((j.val:ℝ)/6)) := by + rw [ha33_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_21 j) false 33 21 j (ha33_0_21_contains j) +noncomputable def hk33_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_23 j i k) +lemma hk33_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_23 j i k).Contains (fullFactor false 33 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 23 (power33_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha33_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-14),(-13)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨111728452,111728453⟩⟩,⟨⟨1253899540535,1253899540536⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨(-158775681103741858),(-158775681103741856)⟩,⟨(-1),1⟩⟩,⟨⟨(-4),2⟩,⟨10518471716932064452,10518471716932064459⟩⟩] +lemma ha33_0_23_eq (j : Fin 7) : ha33_0_23 j = ((ha33_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha33_0_23_contains (j : Fin 7) : (ha33_0_23 j).Contains (fullFactor false 33 23 ((j.val:ℝ)/6)) := by + rw [ha33_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_22 j) false 33 22 j (ha33_0_22_contains j) +noncomputable def hk33_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_24 j i k) +lemma hk33_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_24 j i k).Contains (fullFactor false 33 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 24 (power33_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha33_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-4875074),(-4875073)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨82067533018,82067533019⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-17319740045980250),(-17319740045980248)⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha33_0_24_eq (j : Fin 7) : ha33_0_24 j = ((ha33_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha33_0_24_contains (j : Fin 7) : (ha33_0_24 j).Contains (fullFactor false 33 24 ((j.val:ℝ)/6)) := by + rw [ha33_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_23 j) false 33 23 j (ha33_0_23_contains j) +noncomputable def hk33_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_25 j i k) +lemma hk33_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_25 j i k).Contains (fullFactor false 33 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 25 (power33_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha33_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-204207),(-204206)⟩⟩,⟨⟨(-5156455177),(-5156455176)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨1813718936351216,1813718936351217⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha33_0_25_eq (j : Fin 7) : ha33_0_25 j = ((ha33_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha33_0_25_contains (j : Fin 7) : (ha33_0_25 j).Contains (fullFactor false 33 25 ((j.val:ℝ)/6)) := by + rw [ha33_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_24 j) false 33 24 j (ha33_0_24_contains j) +noncomputable def hk33_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_26 j i k) +lemma hk33_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_26 j i k).Contains (fullFactor false 33 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 26 (power33_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha33_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨8224,8225⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-311528495),(-311528494)⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨182627118144797,182627118144798⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha33_0_26_eq (j : Fin 7) : ha33_0_26 j = ((ha33_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha33_0_26_contains (j : Fin 7) : (ha33_0_26 j).Contains (fullFactor false 33 26 ((j.val:ℝ)/6)) := by + rw [ha33_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_25 j) false 33 25 j (ha33_0_25_contains j) +noncomputable def hk33_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_27 j i k) +lemma hk33_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_27 j i k).Contains (fullFactor false 33 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 27 (power33_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha33_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨318,320⟩⟩,⟨⟨18123993,18123994⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨(-17708025083642),(-17708025083641)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha33_0_27_eq (j : Fin 7) : ha33_0_27 j = ((ha33_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha33_0_27_contains (j : Fin 7) : (ha33_0_27 j).Contains (fullFactor false 33 27 ((j.val:ℝ)/6)) := by + rw [ha33_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_26 j) false 33 26 j (ha33_0_26_contains j) +noncomputable def hk33_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_28 j i k) +lemma hk33_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_28 j i k).Contains (fullFactor false 33 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 28 (power33_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha33_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-12),(-11)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1016753,1016754⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1655696473582),(-1655696473581)⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha33_0_28_eq (j : Fin 7) : ha33_0_28 j = ((ha33_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha33_0_28_contains (j : Fin 7) : (ha33_0_28 j).Contains (fullFactor false 33 28 ((j.val:ℝ)/6)) := by + rw [ha33_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_27 j) false 33 27 j (ha33_0_27_contains j) +noncomputable def hk33_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_29 j i k) +lemma hk33_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_29 j i k).Contains (fullFactor false 33 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 29 (power33_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha33_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-55073),(-55072)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨149469076953,149469076954⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha33_0_29_eq (j : Fin 7) : ha33_0_29 j = ((ha33_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha33_0_29_contains (j : Fin 7) : (ha33_0_29 j).Contains (fullFactor false 33 29 ((j.val:ℝ)/6)) := by + rw [ha33_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_28 j) false 33 28 j (ha33_0_28_contains j) +noncomputable def hk33_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power33 j i k).conj.mul (mpower0_30 j i k) +lemma hk33_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk33_0_30 j i k).Contains (fullFactor false 33 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power33 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 30 (power33_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha33_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-2884),(-2883)⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨13043637613,13043637614⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha33_0_30_eq (j : Fin 7) : ha33_0_30 j = ((ha33_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha33_0_30_contains (j : Fin 7) : (ha33_0_30 j).Contains (fullFactor false 33 30 ((j.val:ℝ)/6)) := by + rw [ha33_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_0_29 j) false 33 29 j (ha33_0_29_contains j) +noncomputable def hk33_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_0 j i k) +lemma hk33_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_0 j i k).Contains (fullFactor true 33 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 0 (kernel33_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha33_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨229435537,229435540⟩,⟨(-168277587),(-168277584)⟩⟩,⟨⟨(-17402041971918504781),(-17402041971918504071)⟩,⟨(-99113638007083976860),(-99113638007083976149)⟩⟩,⟨⟨356134034453168626612634853,356134034453168633806136668⟩,⟨2154120630586429646770321740,2154120630586429653996527604⟩⟩] +lemma ha33_1_0_eq (j : Fin 7) : ha33_1_0 j = atomKernel33_0 j := by fin_cases j <;> decide +kernel +lemma ha33_1_0_contains (j : Fin 7) : (ha33_1_0 j).Contains (fullFactor true 33 0 ((j.val:ℝ)/6)) := by + rw [ha33_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel33_0_contains j +noncomputable def hk33_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_1 j i k) +lemma hk33_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_1 j i k).Contains (fullFactor true 33 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 1 (kernel33_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha33_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-31),46⟩,⟨(-42),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-6),21⟩,⟨(-19),11⟩⟩,⟨⟨(-1125117261),(-1125117242)⟩,⟨(-804989193),(-804989174)⟩⟩,⟨⟨(-392652206894016658349),(-392652206894016654942)⟩,⟨140898727616430839872,140898727616430843274⟩⟩,⟨⟨7711713205226792022808918861,7711713205226792050278657229⟩,⟨(-1690495727387573553837620386),(-1690495727387573526499428095)⟩⟩] +lemma ha33_1_1_eq (j : Fin 7) : ha33_1_1 j = ((ha33_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha33_1_1_contains (j : Fin 7) : (ha33_1_1 j).Contains (fullFactor true 33 1 ((j.val:ℝ)/6)) := by + rw [ha33_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_0 j) true 33 0 j (ha33_1_0_contains j) +noncomputable def hk33_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_2 j i k) +lemma hk33_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_2 j i k).Contains (fullFactor true 33 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 2 (kernel33_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha33_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-255),177⟩,⟨(-205),219⟩⟩,⟨⟨(-132),179⟩,⟨(-128),182⟩⟩,⟨⟨(-79),37⟩,⟨(-70),43⟩⟩,⟨⟨(-1007043850),(-1007043790)⟩,⟨3208937522,3208937581⟩⟩,⟨⟨426079970437935490372,426079970437935498523⟩,⟨752432410875996504339,752432410875996512500⟩⟩,⟨⟨(-3776239171722179916779642263),(-3776239171722179864829117560)⟩,⟨(-13764883566845648964671531965),(-13764883566845648912463044277)⟩⟩] +lemma ha33_1_2_eq (j : Fin 7) : ha33_1_2 j = ((ha33_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha33_1_2_contains (j : Fin 7) : (ha33_1_2 j).Contains (fullFactor true 33 2 ((j.val:ℝ)/6)) := by + rw [ha33_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_1 j) true 33 1 j (ha33_1_1_contains j) +noncomputable def hk33_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_3 j i k) +lemma hk33_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_3 j i k).Contains (fullFactor true 33 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 3 (kernel33_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha33_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-707),924⟩,⟨(-779),840⟩⟩,⟨⟨(-514),530⟩,⟨(-606),437⟩⟩,⟨⟨(-155),148⟩,⟨(-104),201⟩⟩,⟨⟨5450428997,5450429119⟩,⟨(-70050951),(-70050828)⟩⟩,⟨⟨924606292671925802738,924606292671925815769⟩,⟨(-756868250770792996471),(-756868250770792983452)⟩⟩,⟨⟨(-16332091961163593608827930229),(-16332091961163593542680727941)⟩,⟨5406925443991841488324205765,5406925443991841554140769965⟩⟩] +lemma ha33_1_3_eq (j : Fin 7) : ha33_1_3 j = ((ha33_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha33_1_3_contains (j : Fin 7) : (ha33_1_3 j).Contains (fullFactor true 33 3 ((j.val:ℝ)/6)) := by + rw [ha33_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_2 j) true 33 2 j (ha33_1_2_contains j) +noncomputable def hk33_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_4 j i k) +lemma hk33_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_4 j i k).Contains (fullFactor true 33 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 4 (kernel33_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha33_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2495),2136⟩,⟨(-2469),2151⟩⟩,⟨⟨(-1433),1196⟩,⟨(-1221),1408⟩⟩,⟨⟨(-238),367⟩,⟨(-332),272⟩⟩,⟨⟨(-2145744399),(-2145744209)⟩,⟨(-6268692918),(-6268692730)⟩⟩,⟨⟨(-935808933931438190033),(-935808933931438174438)⟩,⟨(-811056075803995515709),(-811056075803995500103)⟩⟩,⟨⟨5647820063145290924850179127,5647820063145290987389658981⟩,⟨14490083202807509824161633725,14490083202807509887013839669⟩⟩] +lemma ha33_1_4_eq (j : Fin 7) : ha33_1_4 j = ((ha33_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha33_1_4_contains (j : Fin 7) : (ha33_1_4 j).Contains (fullFactor true 33 4 ((j.val:ℝ)/6)) := by + rw [ha33_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_3 j) true 33 3 j (ha33_1_3_contains j) +noncomputable def hk33_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_5 j i k) +lemma hk33_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_5 j i k).Contains (fullFactor true 33 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 5 (kernel33_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha33_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-5111),5425⟩,⟨(-4887),5641⟩⟩,⟨⟨(-2436),2862⟩,⟨(-2619),2679⟩⟩,⟨⟨(-547),413⟩,⟨(-529),432⟩⟩,⟨⟨(-5141945244),(-5141945011)⟩,⟨3882523813,3882524046⟩⟩,⟨⟨(-530861845519358357219),(-530861845519358342268)⟩,⟨878857482013637091211,878857482013637106155⟩⟩,⟨⟨10252711526171924584312879211,10252711526171924632087704918⟩,⟨(-4623055366447408034423132902),(-4623055366447407986881685317)⟩⟩] +lemma ha33_1_5_eq (j : Fin 7) : ha33_1_5 j = ((ha33_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha33_1_5_contains (j : Fin 7) : (ha33_1_5 j).Contains (fullFactor true 33 5 ((j.val:ℝ)/6)) := by + rw [ha33_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_4 j) true 33 4 j (ha33_1_4_contains j) +noncomputable def hk33_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_6 j i k) +lemma hk33_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_6 j i k).Contains (fullFactor true 33 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 6 (kernel33_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha33_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-9960),10026⟩,⟨(-10570),9412⟩⟩,⟨⟨(-4597),4299⟩,⟨(-4655),4241⟩⟩,⟨⟨(-646),626⟩,⟨(-556),716⟩⟩,⟨⟨4288182940,4288183179⟩,⟨2978720419,2978720659⟩⟩,⟨⟨660713610237594840710,660713610237594852643⟩,⟨258290673843763566348,258290673843763578285⟩⟩,⟨⟨(-3103193222852470612613818362),(-3103193222852470582496566523)⟩,⟨(-6025786945905339685507073848),(-6025786945905339655246445988)⟩⟩] +lemma ha33_1_6_eq (j : Fin 7) : ha33_1_6 j = ((ha33_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha33_1_6_contains (j : Fin 7) : (ha33_1_6 j).Contains (fullFactor true 33 6 ((j.val:ℝ)/6)) := by + rw [ha33_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_5 j) true 33 5 j (ha33_1_5_contains j) +noncomputable def hk33_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_7 j i k) +lemma hk33_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_7 j i k).Contains (fullFactor true 33 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 7 (kernel33_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha33_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-16595),15907⟩,⟨(-15633),16866⟩⟩,⟨⟨(-6449),6354⟩,⟨(-6146),6657⟩⟩,⟨⟨(-659),784⟩,⟨(-747),697⟩⟩,⟨⟨1037647155,1037647366⟩,⟨(-3475026221),(-3475026010)⟩⟩,⟨⟨84264277557540367981,84264277557540376150⟩,⟨(-411589445297043512327),(-411589445297043504160)⟩⟩,⟨⟨(-3025225223597894629230914973),(-3025225223597894612802593652)⟩,⟨1762456250846196591740634812,1762456250846196608094290627⟩⟩] +lemma ha33_1_7_eq (j : Fin 7) : ha33_1_7 j = ((ha33_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha33_1_7_contains (j : Fin 7) : (ha33_1_7 j).Contains (fullFactor true 33 7 ((j.val:ℝ)/6)) := by + rw [ha33_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_6 j) true 33 6 j (ha33_1_6_contains j) +noncomputable def hk33_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_8 j i k) +lemma hk33_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_8 j i k).Contains (fullFactor true 33 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 8 (kernel33_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha33_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-22509),23741⟩,⟨(-23555),22694⟩⟩,⟨⟨(-7868),8255⟩,⟨(-8188),7935⟩⟩,⟨⟨(-755),679⟩,⟨(-748),686⟩⟩,⟨⟨(-2203373655),(-2203373492)⟩,⟨58997934,58998097⟩⟩,⟨⟨(-217601560684657503820),(-217601560684657498929)⟩,⟨(-6794999972307240690),(-6794999972307235798)⟩⟩,⟨⟨866541512572288026186930715,866541512572288033956973749⟩,⟨1324153091694429687866434678,1324153091694429695670147553⟩⟩] +lemma ha33_1_8_eq (j : Fin 7) : ha33_1_8 j = ((ha33_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha33_1_8_contains (j : Fin 7) : (ha33_1_8 j).Contains (fullFactor true 33 8 ((j.val:ℝ)/6)) := by + rw [ha33_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_7 j) true 33 7 j (ha33_1_7_contains j) +noncomputable def hk33_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_9 j i k) +lemma hk33_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_9 j i k).Contains (fullFactor true 33 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 9 (kernel33_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha33_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-29954),28549⟩,⟨(-29139),29363⟩⟩,⟨⟨(-9202),8845⟩,⟨(-9065),8982⟩⟩,⟨⟨(-639),627⟩,⟨(-602),664⟩⟩,⟨⟨401274007,401274119⟩,⟨1121128731,1121128843⟩⟩,⟨⟨13944254309806885845,13944254309806888449⟩,⟨99305838504317855184,99305838504317857789⟩⟩,⟨⟨513204209667840666195845554,513204209667840669490751723⟩,⟨(-375304959186800768568344201),(-375304959186800765286798783)⟩⟩] +lemma ha33_1_9_eq (j : Fin 7) : ha33_1_9 j = ((ha33_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha33_1_9_contains (j : Fin 7) : (ha33_1_9 j).Contains (fullFactor true 33 9 ((j.val:ℝ)/6)) := by + rw [ha33_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_8 j) true 33 8 j (ha33_1_8_contains j) +noncomputable def hk33_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_10 j i k) +lemma hk33_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_10 j i k).Contains (fullFactor true 33 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 10 (kernel33_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha33_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-32720),33881⟩,⟨(-33125),33476⟩⟩,⟨⟨(-9024),9157⟩,⟨(-8978),9203⟩⟩,⟨⟨(-485),521⟩,⟨(-509),497⟩⟩,⟨⟨457152929,457152999⟩,⟨(-355279193),(-355279123)⟩⟩,⟨⟨39587274009137781130,39587274009137782379⟩,⟨(-12690800915682939736),(-12690800915682938488)⟩⟩,⟨⟨(-145160205578279353368480829),(-145160205578279352121174615)⟩,⟨(-178272149327208796117996423),(-178272149327208794865966224)⟩⟩] +lemma ha33_1_10_eq (j : Fin 7) : ha33_1_10 j = ((ha33_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha33_1_10_contains (j : Fin 7) : (ha33_1_10 j).Contains (fullFactor true 33 10 ((j.val:ℝ)/6)) := by + rw [ha33_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_9 j) true 33 9 j (ha33_1_9_contains j) +noncomputable def hk33_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_11 j i k) +lemma hk33_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_11 j i k).Contains (fullFactor true 33 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 11 (kernel33_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha33_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-34809),34119⟩,⟨(-34782),34145⟩⟩,⟨⟨(-8303),8348⟩,⟨(-8407),8244⟩⟩,⟨⟨(-371),356⟩,⟨(-370),357⟩⟩,⟨⟨(-212194162),(-212194122)⟩,⟨(-143060674),(-143060634)⟩⟩,⟨⟨(-7247926835729381000),(-7247926835729380456)⟩,⟨(-13889776243161612755),(-13889776243161612210)⟩⟩,⟨⟨(-56044377682678141614527233),(-56044377682678141182030833)⟩,⟨50695640138029223386918459,50695640138029223817911932⟩⟩] +lemma ha33_1_11_eq (j : Fin 7) : ha33_1_11 j = ((ha33_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha33_1_11_contains (j : Fin 7) : (ha33_1_11 j).Contains (fullFactor true 33 11 ((j.val:ℝ)/6)) := by + rw [ha33_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_10 j) true 33 10 j (ha33_1_10_contains j) +noncomputable def hk33_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_12 j i k) +lemma hk33_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_12 j i k).Contains (fullFactor true 33 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 12 (kernel33_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha33_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-32574),32817⟩,⟨(-32385),33006⟩⟩,⟨⟨(-7034),6945⟩,⟨(-6966),7013⟩⟩,⟨⟨(-242),240⟩,⟨(-236),246⟩⟩,⟨⟨(-28282420),(-28282399)⟩,⟨99760200,99760221⟩⟩,⟨⟨(-4303258040256849138),(-4303258040256848920)⟩,⟨3282713846709560778,3282713846709560996⟩⟩,⟨⟨16132243112760149149183848,16132243112760149285696863⟩,⟨16071534728958511180911956,16071534728958511317858569⟩⟩] +lemma ha33_1_12_eq (j : Fin 7) : ha33_1_12 j = ((ha33_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha33_1_12_contains (j : Fin 7) : (ha33_1_12 j).Contains (fullFactor true 33 12 ((j.val:ℝ)/6)) := by + rw [ha33_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_11 j) true 33 11 j (ha33_1_11_contains j) +noncomputable def hk33_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_13 j i k) +lemma hk33_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_13 j i k).Contains (fullFactor true 33 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 13 (kernel33_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha33_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-28615),28649⟩,⟨(-28850),28414⟩⟩,⟨⟨(-5390),5443⟩,⟨(-5408),5425⟩⟩,⟨⟨(-145),150⟩,⟨(-148),147⟩⟩,⟨⟨38749920,38749931⟩,⟨(-1577533),(-1577522)⟩⟩,⟨⟨1264743398986832203,1264743398986832285⟩,⟨1174465471310263141,1174465471310263223⟩⟩,⟨⟨4231194229979023232789915,4231194229979023272816506⟩,⟨(-4713211993958011178873868),(-4713211993958011138961405)⟩⟩] +lemma ha33_1_13_eq (j : Fin 7) : ha33_1_13 j = ((ha33_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha33_1_13_contains (j : Fin 7) : (ha33_1_13 j).Contains (fullFactor true 33 13 ((j.val:ℝ)/6)) := by + rw [ha33_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_12 j) true 33 12 j (ha33_1_12_contains j) +noncomputable def hk33_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_14 j i k) +lemma hk33_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_14 j i k).Contains (fullFactor true 33 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 14 (kernel33_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha33_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-23350),23215⟩,⟨(-23168),23397⟩⟩,⟨⟨(-3904),3892⟩,⟨(-3911),3885⟩⟩,⟨⟨(-85),83⟩,⟨(-85),83⟩⟩,⟨⟨(-4714868),(-4714862)⟩,⟨(-12616697),(-12616691)⟩⟩,⟨⟨279090999343703338,279090999343703367⟩,⟨(-428145224631312672),(-428145224631312643)⟩⟩,⟨⟨(-1272431197691962003205230),(-1272431197691961992369688)⟩,⟨(-1028138351043684120729484),(-1028138351043684109866410)⟩⟩] +lemma ha33_1_14_eq (j : Fin 7) : ha33_1_14 j = ((ha33_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha33_1_14_contains (j : Fin 7) : (ha33_1_14 j).Contains (fullFactor true 33 14 ((j.val:ℝ)/6)) := by + rw [ha33_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_13 j) true 33 13 j (ha33_1_13_contains j) +noncomputable def hk33_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_15 j i k) +lemma hk33_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_15 j i k).Contains (fullFactor true 33 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 15 (kernel33_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha33_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-17608),17733⟩,⟨(-17712),17629⟩⟩,⟨⟨(-2621),2616⟩,⟨(-2612),2625⟩⟩,⟨⟨(-45),45⟩,⟨(-44),45⟩⟩,⟨⟨(-3409621),(-3409618)⟩,⟨2726759,2726763⟩⟩,⟨⟨(-129711012447214624),(-129711012447214614)⟩,⟨(-55908301046935676),(-55908301046935665)⟩⟩,⟨⟨(-231580378878440645256398),(-231580378878440642504794)⟩,⟨319189278250896037510302,319189278250896040255801⟩⟩] +lemma ha33_1_15_eq (j : Fin 7) : ha33_1_15 j = ((ha33_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha33_1_15_contains (j : Fin 7) : (ha33_1_15 j).Contains (fullFactor true 33 15 ((j.val:ℝ)/6)) := by + rw [ha33_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_14 j) true 33 14 j (ha33_1_14_contains j) +noncomputable def hk33_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_16 j i k) +lemma hk33_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_16 j i k).Contains (fullFactor true 33 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 16 (kernel33_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha33_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-12613),12534⟩,⟨(-12568),12579⟩⟩,⟨⟨(-1646),1652⟩,⟨(-1650),1648⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨1110273,1110276⟩,⟨726273,726276⟩⟩,⟨⟨(-8565365084986799),(-8565365084986795)⟩,⟨35580273958560173,35580273958560177⟩⟩,⟨⟨74755338717072267421660,74755338717072268073821⟩,⟨48519221051282513579924,48519221051282514233331⟩⟩] +lemma ha33_1_16_eq (j : Fin 7) : ha33_1_16 j = ((ha33_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha33_1_16_contains (j : Fin 7) : (ha33_1_16 j).Contains (fullFactor true 33 16 ((j.val:ℝ)/6)) := by + rw [ha33_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_15 j) true 33 15 j (ha33_1_15_contains j) +noncomputable def hk33_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_17 j i k) +lemma hk33_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_17 j i k).Contains (fullFactor true 33 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 17 (kernel33_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha33_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-8401),8439⟩,⟨(-8414),8427⟩⟩,⟨⟨(-979),976⟩,⟨(-978),977⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨98406,98408⟩,⟨(-366473),(-366471)⟩⟩,⟨⟨8905210707309764,8905210707309766⟩,⟨584275640103846,584275640103848⟩⟩,⟨⟨9480418229901251104154,9480418229901251250186⟩,⟨(-16414946559001116478788),(-16414946559001116332990)⟩⟩] +lemma ha33_1_17_eq (j : Fin 7) : ha33_1_17 j = ((ha33_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha33_1_17_contains (j : Fin 7) : (ha33_1_17 j).Contains (fullFactor true 33 17 ((j.val:ℝ)/6)) := by + rw [ha33_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_16 j) true 33 16 j (ha33_1_16_contains j) +noncomputable def hk33_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_18 j i k) +lemma hk33_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_18 j i k).Contains (fullFactor true 33 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 18 (kernel33_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha33_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-5333),5319⟩,⟨(-5333),5319⟩⟩,⟨⟨(-547),548⟩,⟨(-547),548⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-102346),(-102345)⟩,⟨5593,5595⟩⟩,⟨⟨(-215835877728262),(-215835877728260)⟩,⟨(-2043996127818229),(-2043996127818227)⟩⟩,⟨⟨(-3391942743075084431953),(-3391942743075084401169)⟩,⟨(-1730652639657568349857),(-1730652639657568319033)⟩⟩] +lemma ha33_1_18_eq (j : Fin 7) : ha33_1_18 j = ((ha33_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha33_1_18_contains (j : Fin 7) : (ha33_1_18 j).Contains (fullFactor true 33 18 ((j.val:ℝ)/6)) := by + rw [ha33_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_17 j) true 33 17 j (ha33_1_17_contains j) +noncomputable def hk33_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_19 j i k) +lemma hk33_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_19 j i k).Contains (fullFactor true 33 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 19 (kernel33_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha33_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3190),3193⟩,⟨(-3187),3196⟩⟩,⟨⟨(-291),291⟩,⟨(-291),291⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨9522,9524⟩,⟨24439,24441⟩⟩,⟨⟨(-431490262514956),(-431490262514954)⟩,⟨122176327618126,122176327618128⟩⟩,⟨⟨(-295395541059033379405),(-295395541059033373240)⟩,⟨661756000920291874915,661756000920291881074⟩⟩] +lemma ha33_1_19_eq (j : Fin 7) : ha33_1_19 j = ((ha33_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha33_1_19_contains (j : Fin 7) : (ha33_1_19 j).Contains (fullFactor true 33 19 ((j.val:ℝ)/6)) := by + rw [ha33_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_18 j) true 33 18 j (ha33_1_18_contains j) +noncomputable def hk33_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_20 j i k) +lemma hk33_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_20 j i k).Contains (fullFactor true 33 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 20 (kernel33_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha33_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-1817),1817⟩,⟨(-1819),1815⟩⟩,⟨⟨(-147),147⟩,⟨(-147),147⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨4923,4925⟩,⟨(-4052),(-4051)⟩⟩,⟨⟨40151361626720,40151361626721⟩,⟨83835802857328,83835802857330⟩⟩,⟨⟨122254278101623560880,122254278101623562052⟩,⟨47121042331282391220,47121042331282392392⟩⟩] +lemma ha33_1_20_eq (j : Fin 7) : ha33_1_20 j = ((ha33_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha33_1_20_contains (j : Fin 7) : (ha33_1_20 j).Contains (fullFactor true 33 20 ((j.val:ℝ)/6)) := by + rw [ha33_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_19 j) true 33 19 j (ha33_1_19_contains j) +noncomputable def hk33_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_21 j i k) +lemma hk33_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_21 j i k).Contains (fullFactor true 33 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 21 (kernel33_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha33_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-986),985⟩,⟨(-985),986⟩⟩,⟨⟨(-71),71⟩,⟨(-71),71⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1247),(-1246)⟩,⟨(-792),(-790)⟩⟩,⟨⟨14962631764677,14962631764678⟩,⟨(-10622675087111),(-10622675087110)⟩⟩,⟨⟨7009486427796565430,7009486427796565643⟩,⟨(-21443402748532651275),(-21443402748532651061)⟩⟩] +lemma ha33_1_21_eq (j : Fin 7) : ha33_1_21 j = ((ha33_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha33_1_21_contains (j : Fin 7) : (ha33_1_21 j).Contains (fullFactor true 33 21 ((j.val:ℝ)/6)) := by + rw [ha33_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_20 j) true 33 20 j (ha33_1_20_contains j) +noncomputable def hk33_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_22 j i k) +lemma hk33_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_22 j i k).Contains (fullFactor true 33 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 22 (kernel33_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha33_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-510),511⟩,⟨(-511),510⟩⟩,⟨⟨(-33),33⟩,⟨(-33),33⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-81),(-80)⟩,⟨316,317⟩⟩,⟨⟨(-2451592244117),(-2451592244116)⟩,⟨(-2438417122856),(-2438417122855)⟩⟩,⟨⟨(-3579494566261312252),(-3579494566261312214)⟩,⟨(-967497197846377782),(-967497197846377744)⟩⟩] +lemma ha33_1_22_eq (j : Fin 7) : ha33_1_22 j = ((ha33_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha33_1_22_contains (j : Fin 7) : (ha33_1_22 j).Contains (fullFactor true 33 22 ((j.val:ℝ)/6)) := by + rw [ha33_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_21 j) true 33 21 j (ha33_1_21_contains j) +noncomputable def hk33_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_23 j i k) +lemma hk33_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_23 j i k).Contains (fullFactor true 33 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 23 (kernel33_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha33_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-253),253⟩,⟨(-253),253⟩⟩,⟨⟨(-15),15⟩,⟨(-15),15⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨68,70⟩,⟨(-5),(-4)⟩⟩,⟨⟨(-358042915039),(-358042915037)⟩,⟨510124762820,510124762821⟩⟩,⟨⟨(-122674951015016134),(-122674951015016127)⟩,⟨569883403376587314,569883403376587321⟩⟩] +lemma ha33_1_23_eq (j : Fin 7) : ha33_1_23 j = ((ha33_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha33_1_23_contains (j : Fin 7) : (ha33_1_23 j).Contains (fullFactor true 33 23 ((j.val:ℝ)/6)) := by + rw [ha33_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_22 j) true 33 22 j (ha33_1_22_contains j) +noncomputable def hk33_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_24 j i k) +lemma hk33_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_24 j i k).Contains (fullFactor true 33 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 24 (kernel33_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha33_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-121),121⟩,⟨(-121),121⟩⟩,⟨⟨(-7),7⟩,⟨(-7),7⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-6),(-5)⟩,⟨(-14),(-12)⟩⟩,⟨⟨97340920883,97340920885⟩,⟨45976160934,45976160936⟩⟩,⟨⟨86704120648698521,86704120648698523⟩,⟨13998896848124011,13998896848124013⟩⟩] +lemma ha33_1_24_eq (j : Fin 7) : ha33_1_24 j = ((ha33_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha33_1_24_contains (j : Fin 7) : (ha33_1_24 j).Contains (fullFactor true 33 24 ((j.val:ℝ)/6)) := by + rw [ha33_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_23 j) true 33 23 j (ha33_1_23_contains j) +noncomputable def hk33_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_25 j i k) +lemma hk33_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_25 j i k).Contains (fullFactor true 33 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 25 (kernel33_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha33_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-56),56⟩,⟨(-56),56⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3),(-1)⟩,⟨1,2⟩⟩,⟨⟨4770741089,4770741090⟩,⟨(-17201908809),(-17201908807)⟩⟩,⟨⟨1370786299595409,1370786299595410⟩,⟨(-12628778285228903),(-12628778285228901)⟩⟩] +lemma ha33_1_25_eq (j : Fin 7) : ha33_1_25 j = ((ha33_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha33_1_25_contains (j : Fin 7) : (ha33_1_25 j).Contains (fullFactor true 33 25 ((j.val:ℝ)/6)) := by + rw [ha33_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_24 j) true 33 24 j (ha33_1_24_contains j) +noncomputable def hk33_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_26 j i k) +lemma hk33_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_26 j i k).Contains (fullFactor true 33 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 26 (kernel33_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha33_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-2832113342),(-2832113341)⟩,⟨(-283634564),(-283634563)⟩⟩,⟨⟨(-1763855552495529),(-1763855552495528)⟩,⟨(-99176806368110),(-99176806368108)⟩⟩] +lemma ha33_1_26_eq (j : Fin 7) : ha33_1_26 j = ((ha33_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha33_1_26_contains (j : Fin 7) : (ha33_1_26 j).Contains (fullFactor true 33 26 ((j.val:ℝ)/6)) := by + rw [ha33_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_25 j) true 33 25 j (ha33_1_25_contains j) +noncomputable def hk33_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_27 j i k) +lemma hk33_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_27 j i k).Contains (fullFactor true 33 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 27 (kernel33_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha33_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨30960760,30960761⟩,⟨435918024,435918025⟩⟩,⟨⟨(-997220634971),(-997220634969)⟩,⟨236590781110290,236590781110291⟩⟩] +lemma ha33_1_27_eq (j : Fin 7) : ha33_1_27 j = ((ha33_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha33_1_27_contains (j : Fin 7) : (ha33_1_27 j).Contains (fullFactor true 33 27 ((j.val:ℝ)/6)) := by + rw [ha33_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_26 j) true 33 26 j (ha33_1_26_contains j) +noncomputable def hk33_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_28 j i k) +lemma hk33_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_28 j i k).Contains (fullFactor true 33 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 28 (kernel33_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha33_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨62823155,62823156⟩,⟨(-15482255),(-15482254)⟩⟩,⟨⟨30518668662407,30518668662408⟩,⟨(-1458016243474),(-1458016243473)⟩⟩] +lemma ha33_1_28_eq (j : Fin 7) : ha33_1_28 j = ((ha33_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha33_1_28_contains (j : Fin 7) : (ha33_1_28 j).Contains (fullFactor true 33 28 ((j.val:ℝ)/6)) := by + rw [ha33_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_27 j) true 33 27 j (ha33_1_27_contains j) +noncomputable def hk33_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_29 j i k) +lemma hk33_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_29 j i k).Contains (fullFactor true 33 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 29 (kernel33_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha33_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3706768),(-3706767)⟩,⟨(-8474034),(-8474032)⟩⟩,⟨⟨(-379156117052),(-379156117051)⟩,⟨(-3790687262187),(-3790687262186)⟩⟩] +lemma ha33_1_29_eq (j : Fin 7) : ha33_1_29 j = ((ha33_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha33_1_29_contains (j : Fin 7) : (ha33_1_29 j).Contains (fullFactor true 33 29 ((j.val:ℝ)/6)) := by + rw [ha33_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_28 j) true 33 28 j (ha33_1_28_contains j) +noncomputable def hk33_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel33_0 j i k).mul (mpower1_30 j i k) +lemma hk33_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk33_1_30 j i k).Contains (fullFactor true 33 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk33_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel33_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 33 30 (kernel33_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha33_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1066942),(-1066941)⟩,⟨703718,703719⟩⟩,⟨⟨(-453902499740),(-453902499739)⟩,⟨69364422419,69364422420⟩⟩] +lemma ha33_1_30_eq (j : Fin 7) : ha33_1_30 j = ((ha33_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha33_1_30_contains (j : Fin 7) : (ha33_1_30 j).Contains (fullFactor true 33 30 ((j.val:ℝ)/6)) := by + rw [ha33_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha33_1_29 j) true 33 29 j (ha33_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders36.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders36.lean new file mode 100644 index 0000000000000000000000000000000000000000..0b8f026c35bc8d7869060ccae6be1f3342c39a67 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders36.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers40 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues40 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk36_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_0 j i k) +lemma hk36_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_0 j i k).Contains (fullFactor false 36 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 0 (power36_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha36_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999569,1000000000000000000000000000575⟩,⟨(-575),575⟩⟩,⟨⟨999999999999999999924329150121,1000000000000000000075670849935⟩,⟨(-61924777171),90204177703⟩⟩,⟨⟨999999999999999999792554873861,1000000000000000000207445126155⟩,⟨(-178877614491),235436415747⟩⟩,⟨⟨999999999999999999882399701369,1000000000000000000117600298667⟩,⟨(-75181197743),160019399591⟩⟩,⟨⟨999999999999999999433204421429,1000000000000000000566795578487⟩,⟨(-510447400947),623565003555⟩⟩,⟨⟨999999999999999999286388329077,1000000000000000000713611670831⟩,⟨(-642704122203),784101125327⟩⟩,⟨⟨999999999999999999764084879849,1000000000000000000235915120295⟩,⟨(-151076918231),320753322215⟩⟩] +lemma ha36_0_0_eq (j : Fin 7) : ha36_0_0 j = ((atomPoints j).direct.powBin 7 36).conj := by fin_cases j <;> decide +kernel +lemma ha36_0_0_contains (j : Fin 7) : (ha36_0_0 j).Contains (fullFactor false 36 0 ((j.val:ℝ)/6)) := by + rw [ha36_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 36) ((j.val:ℝ)/6) 36 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 36 (by norm_num)) +noncomputable def hk36_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_1 j i k) +lemma hk36_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_1 j i k).Contains (fullFactor false 36 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 1 (power36_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha36_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-47230797000),32423737506⟩,⟨523598775598298873037045502318,523598775598298873117954497710⟩⟩,⟨⟨(-246548438033),187320199859⟩,⟨1047197551196597745936097305231,1047197551196597746373902694787⟩⟩,⟨⟨(-251357885094),118094349259⟩,⟨1570796326794896619045273882880,1570796326794896619419726117177⟩⟩,⟨⟨(-1305991489470),1069078536573⟩,⟨2094395102393195491119572782846,2094395102393195493500427216977⟩⟩,⟨⟨(-2052771945833),1682595457288⟩,⟨2617993877991494363515102347592,2617993877991494367259897652168⟩⟩,⟨⟨(-1007676280686),474622136442⟩,⟨3141592653589793237718850791662,3141592653589793239211149208790⟩⟩] +lemma ha36_0_1_eq (j : Fin 7) : ha36_0_1 j = ((ha36_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha36_0_1_contains (j : Fin 7) : (ha36_0_1 j).Contains (fullFactor false 36 1 ((j.val:ℝ)/6)) := by + rw [ha36_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_0 j) false 36 0 j (ha36_0_0_contains j) +noncomputable def hk36_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_2 j i k) +lemma hk36_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_2 j i k).Contains (fullFactor false 36 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 2 (power36_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha36_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-137077838904018869717049379717),(-137077838904018869695431121941)⟩,⟨(-12364993740),8488514630⟩⟩,⟨⟨(-548311355616075478940450850895),(-548311355616075478709471155718)⟩,⟨(-129092460280),98080627292⟩⟩,⟨⟨(-1233700550136169827505172801408),(-1233700550136169827207151713494)⟩,⟨(-197416021309),92751085016⟩⟩,⟨⟨(-2193245422464301916549947138209),(-2193245422464301914049740888018)⟩,⟨(-1367631089657),1119536425537⟩⟩,⟨⟨(-3426945972600471745112423219822),(-3426945972600471740199589321135)⟩,⟨(-2687072193552),2202512303159⟩⟩,⟨⟨(-4934802200544679310604551447757),(-4934802200544679308244746612382)⟩,⟨(-1582854200300),745534708539⟩⟩] +lemma ha36_0_2_eq (j : Fin 7) : ha36_0_2 j = ((ha36_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha36_0_2_contains (j : Fin 7) : (ha36_0_2 j).Contains (fullFactor false 36 2 ((j.val:ℝ)/6)) := by + rw [ha36_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_1 j) false 36 1 j (ha36_0_1_contains j) +noncomputable def hk36_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_3 j i k) +lemma hk36_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_3 j i k).Contains (fullFactor false 36 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 3 (power36_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha36_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1481525289),2158098528⟩,⟨(-23924596203935046433673153602),(-23924596203935046429823901478)⟩⟩,⟨⟨(-34236597574),45061769428⟩,⟨(-191396769631480371494606399600),(-191396769631480371413370041037)⟩⟩,⟨⟨(-48564354550),103366787041⟩,⟨(-645964097506246253736260065741),(-645964097506246253578160421423)⟩⟩,⟨⟨(-781583868866),954786618687⟩,⟨(-1531174157051842972507079322727),(-1531174157051842970756732202216)⟩⟩,⟨⟨(-1922054575291),2344912850814⟩,⟨(-2990574525491880806116953767897),(-2990574525491880801820178116740)⟩⟩,⟨⟨(-780722121115),1657561042456⟩,⟨(-5167712780049970030501497541721),(-5167712780049970028013866356145)⟩⟩] +lemma ha36_0_3_eq (j : Fin 7) : ha36_0_3 j = ((ha36_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha36_0_3_contains (j : Fin 7) : (ha36_0_3 j).Contains (fullFactor false 36 3 ((j.val:ℝ)/6)) := by + rw [ha36_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_2 j) false 36 2 j (ha36_0_2_contains j) +noncomputable def hk36_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_4 j i k) +lemma hk36_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_4 j i k).Contains (fullFactor false 36 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 4 (power36_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha36_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨3131722319766024859463138441,3131722319766024859976972949⟩,⟨(-193931207),282494437⟩⟩,⟨⟨50107557116256397744807327992,50107557116256397766234454240⟩,⟨(-8963120286),11797143650⟩⟩,⟨⟨253669507901048013605877991146,253669507901048013668771031410⟩,⟨(-19071177436),40592042350⟩⟩,⟨⟨801720913860102363628818474766,801720913860102364547850040869⟩,⟨(-409236356766),499925104503⟩⟩,⟨⟨1957326449853765535915803083591,1957326449853765538734266534647⟩,⟨(-1257981777820),1534741871964⟩⟩,⟨⟨4058712126416768217213842057509,4058712126416768219180542303822⟩,⟨(-613177720048),1301845398465⟩⟩] +lemma ha36_0_4_eq (j : Fin 7) : ha36_0_4 j = ((ha36_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha36_0_4_contains (j : Fin 7) : (ha36_0_4 j).Contains (fullFactor false 36 4 ((j.val:ℝ)/6)) := by + rw [ha36_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_3 j) false 36 3 j (ha36_0_3_contains j) +noncomputable def hk36_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_5 j i k) +lemma hk36_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_5 j i k).Contains (fullFactor false 36 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 5 (power36_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha36_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-29582749),20308429⟩,⟨327953194428670967547900690,327953194428670967602753223⟩⟩,⟨⟨(-2470787989),1877231523⟩,⟨10494502221717470960149916670,10494502221717470964671008536⟩⟩,⟨⟨(-12752366205),5991387093⟩,⟨79692626246167045110798399977,79692626246167045130810500811⟩⟩,⟨⟨(-209408138087),171420524267⟩,⟨335824071094959070604118801576,335824071094959070990150804994⟩⟩,⟨⟨(-803588965020),658677718592⟩,⟨1024853732589596772933393627142,1024853732589596774412399849936⟩⟩,⟨⟨(-817973587986),385270924130⟩,⟨2550164039877345443243826596050,2550164039877345444487658229429⟩⟩] +lemma ha36_0_5_eq (j : Fin 7) : ha36_0_5 j = ((ha36_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha36_0_5_contains (j : Fin 7) : (ha36_0_5 j).Contains (fullFactor false 36 5 ((j.val:ℝ)/6)) := by + rw [ha36_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_4 j) false 36 4 j (ha36_0_4_contains j) +noncomputable def hk36_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_6 j i k) +lemma hk36_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_6 j i k).Contains (fullFactor false 36 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 6 (power36_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha36_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-28619315176067161693996610),(-28619315176067161689118725)⟩,⟨(-2581582),1772245⟩⟩,⟨⟨(-1831636171268298348657145564),(-1831636171268298347862235896)⟩,⟨(-431233856),327638709⟩⟩,⟨⟨(-20863480763352960875798322855),(-20863480763352960870492756585)⟩,⟨(-3338561666),1568541474⟩⟩,⟨⟨(-117224714961171094356182070412),(-117224714961171094221058343000)⟩,⟨(-73097229802),59837051080⟩⟩,⟨⟨(-447176799626049401753969364122),(-447176799626049401107207750027)⟩,⟨(-350631831808),287402372474⟩⟩,⟨⟨(-1335262768854589496209074039007),(-1335262768854589495553555045319)⟩,⟨(-428289969142),201727384149⟩⟩] +lemma ha36_0_6_eq (j : Fin 7) : ha36_0_6 j = ((ha36_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha36_0_6_contains (j : Fin 7) : (ha36_0_6 j).Contains (fullFactor false 36 6 ((j.val:ℝ)/6)) := by + rw [ha36_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_5 j) false 36 5 j (ha36_0_5_contains j) +noncomputable def hk36_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_7 j i k) +lemma hk36_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_7 j i k).Contains (fullFactor false 36 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 7 (power36_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha36_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-132564),193102⟩,⟨(-2140719769235797028402597),(-2140719769235797028030917)⟩⟩,⟨⟨(-49014637),64512434⟩,⟨(-274012130462182019671640104),(-274012130462182019551849687)⟩⟩,⟨⟨(-351979884),749171486⟩,⟨(-4681754135318688101312781935),(-4681754135318688100107313161)⟩⟩,⟨⟨(-17903203818),21870640014⟩,⟨(-35073552699159298530573630246),(-35073552699159298490033062958)⟩⟩,⟨⟨(-107488235952),131135998444⟩,⟨(-167243731971546642950644455899),(-167243731971546642708223824533)⟩⟩,⟨⟨(-90535038296),192216088667⟩,⟨(-599264529320792077038937963482),(-599264529320792076742834208831)⟩⟩] +lemma ha36_0_7_eq (j : Fin 7) : ha36_0_7 j = ((ha36_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha36_0_7_contains (j : Fin 7) : (ha36_0_7 j).Contains (fullFactor false 36 7 ((j.val:ℝ)/6)) := by + rw [ha36_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_6 j) false 36 6 j (ha36_0_6_contains j) +noncomputable def hk36_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_8 j i k) +lemma hk36_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_8 j i k).Contains (fullFactor false 36 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 8 (power36_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha36_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨140109781258867029441543,140109781258867029466316⟩,⟨(-8677),12639⟩⟩,⟨⟨35868104002269959532308653,35868104002269959548103354⟩,⟨(-6416001),8444658⟩⟩,⟨⟨919260274839426580127423103,919260274839426580367042441⟩,⟨(-69111089),147099478⟩⟩,⟨⟨9182234624581109636971375090,9182234624581109647614098749⟩,⟨(-4687047800),5725720167⟩⟩,⟨⟨54730383304244933340688200501,54730383304244933420194378824⟩,⟨(-35175442960),42914155139⟩⟩,⟨⟨235330630358893204484777213001,235330630358893204601805966203⟩,⟨(-35553026401),75483081508⟩⟩] +lemma ha36_0_8_eq (j : Fin 7) : ha36_0_8 j = ((ha36_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha36_0_8_contains (j : Fin 7) : (ha36_0_8 j).Contains (fullFactor false 36 8 ((j.val:ℝ)/6)) := by + rw [ha36_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_7 j) false 36 7 j (ha36_0_7_contains j) +noncomputable def hk36_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_9 j i k) +lemma hk36_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_9 j i k).Contains (fullFactor false 36 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 9 (power36_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha36_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-736),505⟩,⟨8151256657387584304186,8151256657387584305654⟩⟩,⟨⟨(-982581),746536⟩,⟨4173443408582443163193595,4173443408582443165044677⟩⟩,⟨⟨(-25673703),12062161⟩,⟨160441184787359821852577960,160441184787359821894910125⟩⟩,⟨⟨(-1332435587),1090725551⟩,⟨2136803025194210898787259565,2136803025194210901270735477⟩⟩,⟨⟨(-12483221715),10232121592⟩,⟨15920423158960125583958197347,15920423158960125607136283420⟩⟩,⟨⟨(-26348566038),12410347395⟩,⟨82145886611128228778800839760,82145886611128228819913059496⟩⟩] +lemma ha36_0_9_eq (j : Fin 7) : ha36_0_9 j = ((ha36_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha36_0_9_contains (j : Fin 7) : (ha36_0_9 j).Contains (fullFactor false 36 9 ((j.val:ℝ)/6)) := by + rw [ha36_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_8 j) false 36 8 j (ha36_0_8_contains j) +noncomputable def hk36_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_10 j i k) +lemma hk36_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_10 j i k).Contains (fullFactor false 36 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 10 (power36_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha36_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-426798800539562151494),(-426798800539562151415)⟩,⟨(-39),27⟩⟩,⟨⟨(-437041971752511643187118),(-437041971752511642991881)⟩,⟨(-102896),78178⟩⟩,⟨⟨(-25202042373060605484606942),(-25202042373060605477877200)⟩,⟨(-4032816),1894720⟩⟩,⟨⟨(-447530979074571922784429173),(-447530979074571922262866658)⟩,⟨(-279064657),228441026⟩⟩,⟨⟨(-4167957036519161638339366037),(-4167957036519161632258090273)⟩,⟨(-3268099803),2678763169⟩⟩,⟨⟨(-25806891390014060019290845943),(-25806891390014060006292915306)⟩,⟨(-8277646150),3898825621⟩⟩] +lemma ha36_0_10_eq (j : Fin 7) : ha36_0_10 j = ((ha36_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha36_0_10_contains (j : Fin 7) : (ha36_0_10 j).Contains (fullFactor false 36 10 ((j.val:ℝ)/6)) := by + rw [ha36_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_9 j) false 36 9 j (ha36_0_9_contains j) +noncomputable def hk36_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_11 j i k) +lemma hk36_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_11 j i k).Contains (fullFactor false 36 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 11 (power36_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha36_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2),2⟩,⟨(-20315575399030665723),(-20315575399030665719)⟩⟩,⟨⟨(-7443),9796⟩,⟨(-41606298417214803406086),(-41606298417214803387366)⟩⟩,⟨⟨(-270566),575885⟩,⟨(-3598843235212085340974466),(-3598843235212085340002005)⟩⟩,⟨⟨(-43495070),53133787⟩,⟨(-85209699158455917406284096),(-85209699158455917306707593)⟩⟩,⟨⟨(-637544144),777805935⟩,⟨(-991971455030794225386276960),(-991971455030794223935779168)⟩⟩,⟨⟨(-1113501994),2364090213⟩,⟨(-7370430945714350779187737470),(-7370430945714350775452076349)⟩⟩] +lemma ha36_0_11_eq (j : Fin 7) : ha36_0_11 j = ((ha36_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha36_0_11_contains (j : Fin 7) : (ha36_0_11 j).Contains (fullFactor false 36 11 ((j.val:ℝ)/6)) := by + rw [ha36_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_10 j) false 36 10 j (ha36_0_10_contains j) +noncomputable def hk36_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_12 j i k) +lemma hk36_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_12 j i k).Contains (fullFactor false 36 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 12 (power36_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha36_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨886434200375614885,886434200375614886⟩,⟨(-1),1⟩⟩,⟨⟨3630834484738518570233,3630834484738518571879⟩,⟨(-650),855⟩⟩,⟨⟨471087477881817150306871,471087477881817150435666⟩,⟨(-35418),75384⟩⟩,⟨⟨14871898049488972058333120,14871898049488972075759838⟩,⟨(-7591322),9273596⟩⟩,⟨⟨216414599701077852749581316,216414599701077853066719715⟩,⟨(-139090556),169690932⟩⟩,⟨⟨1929574309403923047428646934,1929574309403923048412782755⟩,⟨(-291514141),618917371⟩⟩] +lemma ha36_0_12_eq (j : Fin 7) : ha36_0_12 j = ((ha36_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha36_0_12_contains (j : Fin 7) : (ha36_0_12 j).Contains (fullFactor false 36 12 ((j.val:ℝ)/6)) := by + rw [ha36_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_11 j) false 36 11 j (ha36_0_11_contains j) +noncomputable def hk36_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_13 j i k) +lemma hk36_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_13 j i k).Contains (fullFactor false 36 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 13 (power36_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha36_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨35702758612702236,35702758612702237⟩⟩,⟨⟨(-69),53⟩,⟨292476998555256722959,292476998555256723093⟩⟩,⟨⟨(-9109),4280⟩,⟨56921729219679268110435,56921729219679268126180⟩⟩,⟨⟨(-1494045),1223018⟩,⟨2395971572164663073622393,2395971572164663076437592⟩⟩,⟨⟨(-34173064),28010633⟩,⟨43582469009646284999155369,43582469009646285063160743⟩⟩,⟨⟨(-149568175),70447592⟩,⟨466302805767612564305520427,466302805767612564544831936⟩⟩] +lemma ha36_0_13_eq (j : Fin 7) : ha36_0_13 j = ((ha36_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha36_0_13_contains (j : Fin 7) : (ha36_0_13 j).Contains (fullFactor false 36 13 ((j.val:ℝ)/6)) := by + rw [ha36_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_12 j) false 36 12 j (ha36_0_12_contains j) +noncomputable def hk36_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_14 j i k) +lemma hk36_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_14 j i k).Contains (fullFactor false 36 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 14 (power36_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha36_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1335280049649466),(-1335280049649465)⟩,⟨(-1),1⟩⟩,⟨⟨(-21877228333456835523),(-21877228333456835512)⟩,⟨(-6),4⟩⟩,⟨⟨(-6386603083791852242051),(-6386603083791852240263)⟩,⟨(-1023),481⟩⟩,⟨⟨(-358436509015356793332656),(-358436509015356792910362)⟩,⟨(-223509),182964⟩⟩,⟨⟨(-8149902646786285763148044),(-8149902646786285751153124)⟩,⟨(-6390349),5237977⟩⟩,⟨⟨(-104638104924845707146132851),(-104638104924845707092098400)⟩,⟨(-33563020),15808403⟩⟩] +lemma ha36_0_14_eq (j : Fin 7) : ha36_0_14 j = ((ha36_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha36_0_14_contains (j : Fin 7) : (ha36_0_14 j).Contains (fullFactor false 36 14 ((j.val:ℝ)/6)) := by + rw [ha36_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_13 j) false 36 13 j (ha36_0_13_contains j) +noncomputable def hk36_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_15 j i k) +lemma hk36_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_15 j i k).Contains (fullFactor false 36 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 15 (power36_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha36_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-46610066605154),(-46610066605153)⟩⟩,⟨⟨(-1),1⟩,⟨(-1527318662517654888),(-1527318662517654886)⟩⟩,⟨⟨(-51),108⟩,⟨(-668803510981146723351),(-668803510981146723160)⟩⟩,⟨⟨(-25547),31208⟩,⟨(-50047177933378515357581),(-50047177933378515298457)⟩⟩,⟨⟨(-914200),1115327⟩,⟨(-1422426349034211493884873),(-1422426349034211491786836)⟩⟩,⟨⟨(-3310905),7029423⟩,⟨(-21915353447830215833324598),(-21915353447830215821937890)⟩⟩] +lemma ha36_0_15_eq (j : Fin 7) : ha36_0_15 j = ((ha36_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha36_0_15_contains (j : Fin 7) : (ha36_0_15 j).Contains (fullFactor false 36 15 ((j.val:ℝ)/6)) := by + rw [ha36_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_14 j) false 36 14 j (ha36_0_14_contains j) +noncomputable def hk36_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_16 j i k) +lemma hk36_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_16 j i k).Contains (fullFactor false 36 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 16 (power36_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha36_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1525310862813,1525310862814⟩,⟨(-1),1⟩⟩,⟨⟨99962772705334443,99962772705334444⟩,⟨(-1),1⟩⟩,⟨⟨65659631149794723613,65659631149794723633⟩,⟨(-6),11⟩⟩,⟨⟨6551160272016798094949,6551160272016798102710⟩,⟨(-3345),4086⟩⟩,⟨⟨232743967104084891203823,232743967104084891547856⟩,⟨(-149586),182495⟩⟩,⟨⟨4303069587032947006224733,4303069587032947008474206⟩,⟨(-650095),1380224⟩⟩] +lemma ha36_0_16_eq (j : Fin 7) : ha36_0_16 j = ((ha36_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha36_0_16_contains (j : Fin 7) : (ha36_0_16 j).Contains (fullFactor false 36 16 ((j.val:ℝ)/6)) := by + rw [ha36_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_15 j) false 36 15 j (ha36_0_15_contains j) +noncomputable def hk36_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_17 j i k) +lemma hk36_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_17 j i k).Contains (fullFactor false 36 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 17 (power36_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha36_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨46979464716,46979464717⟩⟩,⟨⟨(-1),1⟩,⟨6157692399285195,6157692399285196⟩⟩,⟨⟨(-2),1⟩,⟨6066935731106195666,6066935731106195669⟩⟩,⟨⟨(-504),413⟩,⟨807101058159109192948,807101058159109193907⟩⟩,⟨⟨(-28105),23037⟩,⟨35842487118702823460028,35842487118702823513124⟩⟩,⟨⟨(-255065),120138⟩,⟨795205400147551278279344,795205400147551278697578⟩⟩] +lemma ha36_0_17_eq (j : Fin 7) : ha36_0_17 j = ((ha36_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha36_0_17_contains (j : Fin 7) : (ha36_0_17 j).Contains (fullFactor false 36 17 ((j.val:ℝ)/6)) := by + rw [ha36_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_16 j) false 36 16 j (ha36_0_16_contains j) +noncomputable def hk36_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_18 j i k) +lemma hk36_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_18 j i k).Contains (fullFactor false 36 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 18 (power36_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha36_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1366577234),(-1366577233)⟩,⟨(-1),1⟩⟩,⟨⟨(-358240022308520),(-358240022308519)⟩,⟨(-1),1⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨(-1),1⟩⟩,⟨⟨(-93910472408044662796),(-93910472408044662683)⟩,⟨(-59),49⟩⟩,⟨⟨(-5213078436041832675544),(-5213078436041832667804)⟩,⟨(-4088),3351⟩⟩,⟨⟨(-138789524622137721183274),(-138789524622137721109836)⟩,⟨(-44518),20969⟩⟩] +lemma ha36_0_18_eq (j : Fin 7) : ha36_0_18 j = ((ha36_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha36_0_18_contains (j : Fin 7) : (ha36_0_18 j).Contains (fullFactor false 36 18 ((j.val:ℝ)/6)) := by + rw [ha36_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_17 j) false 36 17 j (ha36_0_17_contains j) +noncomputable def hk36_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_19 j i k) +lemma hk36_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_19 j i k).Contains (fullFactor false 36 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 19 (power36_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha36_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-37659904),(-37659903)⟩⟩,⟨⟨(-1),1⟩,⟨(-19744635479058),(-19744635479057)⟩⟩,⟨⟨(-1),1⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨(-6),7⟩,⟨(-10351875446044213768),(-10351875446044213755)⟩⟩,⟨⟨(-462),564⟩,⟨(-718305654265631155585),(-718305654265631154516)⟩⟩,⟨⟨(-3468),7361⟩,⟨(-22948428997269873116639),(-22948428997269873104423)⟩⟩] +lemma ha36_0_19_eq (j : Fin 7) : ha36_0_19 j = ((ha36_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha36_0_19_contains (j : Fin 7) : (ha36_0_19 j).Contains (fullFactor false 36 19 ((j.val:ℝ)/6)) := by + rw [ha36_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_18 j) false 36 18 j (ha36_0_18_contains j) +noncomputable def hk36_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_20 j i k) +lemma hk36_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_20 j i k).Contains (fullFactor false 36 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 20 (power36_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha36_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨985933,985934⟩,⟨(-1),1⟩⟩,⟨⟨1033826696146,1033826696147⟩,⟨(-1),1⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨(-1),1⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨94025990269704865144,94025990269704865285⟩,⟨(-61),74⟩⟩,⟨⟨3604730797462500932948,3604730797462500934879⟩,⟨(-545),1157⟩⟩] +lemma ha36_0_20_eq (j : Fin 7) : ha36_0_20 j = ((ha36_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha36_0_20_contains (j : Fin 7) : (ha36_0_20 j).Contains (fullFactor false 36 20 ((j.val:ℝ)/6)) := by + rw [ha36_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_19 j) false 36 19 j (ha36_0_19_contains j) +noncomputable def hk36_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_21 j i k) +lemma hk36_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_21 j i k).Contains (fullFactor false 36 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 21 (power36_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha36_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨24582,24583⟩⟩,⟨⟨(-1),1⟩,⟨51553370693,51553370694⟩⟩,⟨⟨(-1),1⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨(-10),8⟩,⟨11721879376103578814,11721879376103578832⟩⟩,⟨⟨(-174),82⟩,⟨539266466260812848798,539266466260812849090⟩⟩] +lemma ha36_0_21_eq (j : Fin 7) : ha36_0_21 j = ((ha36_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha36_0_21_contains (j : Fin 7) : (ha36_0_21 j).Contains (fullFactor false 36 21 ((j.val:ℝ)/6)) := by + rw [ha36_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_20 j) false 36 20 j (ha36_0_20_contains j) +noncomputable def hk36_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_22 j i k) +lemma hk36_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_22 j i k).Contains (fullFactor false 36 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 22 (power36_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha36_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-586),(-585)⟩,⟨(-1),1⟩⟩,⟨⟨(-2453934707),(-2453934706)⟩,⟨(-1),1⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨(-1),1⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-1394900383872451221),(-1394900383872451218)⟩,⟨(-2),1⟩⟩,⟨⟨(-77007071306013533821),(-77007071306013533778)⟩,⟨(-25),12⟩⟩] +lemma ha36_0_22_eq (j : Fin 7) : ha36_0_22 j = ((ha36_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha36_0_22_contains (j : Fin 7) : (ha36_0_22 j).Contains (fullFactor false 36 22 ((j.val:ℝ)/6)) := by + rw [ha36_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_21 j) false 36 21 j (ha36_0_21_contains j) +noncomputable def hk36_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_23 j i k) +lemma hk36_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_23 j i k).Contains (fullFactor false 36 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 23 (power36_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha36_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-14),(-13)⟩⟩,⟨⟨(-1),1⟩,⟨(-111728453),(-111728452)⟩⟩,⟨⟨(-1),1⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨(-1),1⟩,⟨(-158775681103741858),(-158775681103741856)⟩⟩,⟨⟨(-2),4⟩,⟨(-10518471716932064459),(-10518471716932064452)⟩⟩] +lemma ha36_0_23_eq (j : Fin 7) : ha36_0_23 j = ((ha36_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha36_0_23_contains (j : Fin 7) : (ha36_0_23 j).Contains (fullFactor false 36 23 ((j.val:ℝ)/6)) := by + rw [ha36_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_22 j) false 36 22 j (ha36_0_22_contains j) +noncomputable def hk36_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_24 j i k) +lemma hk36_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_24 j i k).Contains (fullFactor false 36 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 24 (power36_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha36_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨4875073,4875074⟩,⟨(-1),1⟩⟩,⟨⟨82067533018,82067533019⟩,⟨(-1),1⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨17319740045980248,17319740045980250⟩,⟨(-1),1⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨(-1),1⟩⟩] +lemma ha36_0_24_eq (j : Fin 7) : ha36_0_24 j = ((ha36_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha36_0_24_contains (j : Fin 7) : (ha36_0_24 j).Contains (fullFactor false 36 24 ((j.val:ℝ)/6)) := by + rw [ha36_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_23 j) false 36 23 j (ha36_0_23_contains j) +noncomputable def hk36_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_25 j i k) +lemma hk36_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_25 j i k).Contains (fullFactor false 36 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 25 (power36_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha36_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨204206,204207⟩⟩,⟨⟨(-1),1⟩,⟨5156455176,5156455177⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨(-1),1⟩,⟨1813718936351216,1813718936351217⟩⟩,⟨⟨(-1),1⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha36_0_25_eq (j : Fin 7) : ha36_0_25 j = ((ha36_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha36_0_25_contains (j : Fin 7) : (ha36_0_25 j).Contains (fullFactor false 36 25 ((j.val:ℝ)/6)) := by + rw [ha36_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_24 j) false 36 24 j (ha36_0_24_contains j) +noncomputable def hk36_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_26 j i k) +lemma hk36_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_26 j i k).Contains (fullFactor false 36 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 26 (power36_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha36_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-8225),(-8224)⟩,⟨(-1),1⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨(-1),1⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-182627118144798),(-182627118144797)⟩,⟨(-1),1⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨(-1),1⟩⟩] +lemma ha36_0_26_eq (j : Fin 7) : ha36_0_26 j = ((ha36_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha36_0_26_contains (j : Fin 7) : (ha36_0_26 j).Contains (fullFactor false 36 26 ((j.val:ℝ)/6)) := by + rw [ha36_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_25 j) false 36 25 j (ha36_0_25_contains j) +noncomputable def hk36_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_27 j i k) +lemma hk36_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_27 j i k).Contains (fullFactor false 36 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 27 (power36_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha36_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨(-320),(-318)⟩⟩,⟨⟨(-1),1⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨(-1),1⟩,⟨(-17708025083642),(-17708025083641)⟩⟩,⟨⟨(-1),1⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha36_0_27_eq (j : Fin 7) : ha36_0_27 j = ((ha36_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha36_0_27_contains (j : Fin 7) : (ha36_0_27 j).Contains (fullFactor false 36 27 ((j.val:ℝ)/6)) := by + rw [ha36_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_26 j) false 36 26 j (ha36_0_26_contains j) +noncomputable def hk36_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_28 j i k) +lemma hk36_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_28 j i k).Contains (fullFactor false 36 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 28 (power36_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha36_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨11,12⟩,⟨(-1),1⟩⟩,⟨⟨1016753,1016754⟩,⟨(-1),1⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨1655696473581,1655696473582⟩,⟨(-1),1⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨(-1),1⟩⟩] +lemma ha36_0_28_eq (j : Fin 7) : ha36_0_28 j = ((ha36_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha36_0_28_contains (j : Fin 7) : (ha36_0_28 j).Contains (fullFactor false 36 28 ((j.val:ℝ)/6)) := by + rw [ha36_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_27 j) false 36 27 j (ha36_0_27_contains j) +noncomputable def hk36_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_29 j i k) +lemma hk36_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_29 j i k).Contains (fullFactor false 36 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 29 (power36_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha36_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-1),1⟩,⟨55072,55073⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨(-1),1⟩,⟨149469076953,149469076954⟩⟩,⟨⟨(-1),1⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha36_0_29_eq (j : Fin 7) : ha36_0_29 j = ((ha36_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha36_0_29_contains (j : Fin 7) : (ha36_0_29 j).Contains (fullFactor false 36 29 ((j.val:ℝ)/6)) := by + rw [ha36_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_28 j) false 36 28 j (ha36_0_28_contains j) +noncomputable def hk36_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power36 j i k).conj.mul (mpower0_30 j i k) +lemma hk36_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk36_0_30 j i k).Contains (fullFactor false 36 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power36 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 30 (power36_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha36_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨(-1),1⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-13043637614),(-13043637613)⟩,⟨(-1),1⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨(-1),1⟩⟩] +lemma ha36_0_30_eq (j : Fin 7) : ha36_0_30 j = ((ha36_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha36_0_30_contains (j : Fin 7) : (ha36_0_30 j).Contains (fullFactor false 36 30 ((j.val:ℝ)/6)) := by + rw [ha36_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_0_29 j) false 36 29 j (ha36_0_29_contains j) +noncomputable def hk36_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_0 j i k) +lemma hk36_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_0 j i k).Contains (fullFactor true 36 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 0 (kernel36_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha36_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-1050972),(-1050969)⟩,⟨(-2829675),(-2829672)⟩⟩,⟨⟨1657458069911691374,1657458069911691465⟩,⟨(-12051186734807603617),(-12051186734807603525)⟩⟩,⟨⟨(-1243020940282687197299659347),(-1243020940282687190617026701)⟩,⟨1676392578950671605784059,1676392578950678274948786⟩⟩] +lemma ha36_1_0_eq (j : Fin 7) : ha36_1_0 j = atomKernel36_0 j := by fin_cases j <;> decide +kernel +lemma ha36_1_0_contains (j : Fin 7) : (ha36_1_0 j).Contains (fullFactor true 36 0 ((j.val:ℝ)/6)) := by + rw [ha36_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel36_0_contains j +noncomputable def hk36_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_1 j i k) +lemma hk36_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_1 j i k).Contains (fullFactor true 36 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 1 (kernel36_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha36_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-11480476),(-11480456)⟩,⟨9143427,9143446⟩⟩,⟨⟨(-50400021493982320839),(-50400021493982320398)⟩,⟨1716504632604075338,1716504632604075776⟩⟩,⟨⟨239459708312164333399207818,239459708312164358737317874⟩,⟨4488266200039790625597273898,4488266200039790650995014418⟩⟩] +lemma ha36_1_1_eq (j : Fin 7) : ha36_1_1 j = ((ha36_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha36_1_1_contains (j : Fin 7) : (ha36_1_1 j).Contains (fullFactor true 36 1 ((j.val:ℝ)/6)) := by + rw [ha36_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_0 j) true 36 0 j (ha36_1_0_contains j) +noncomputable def hk36_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_2 j i k) +lemma hk36_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_2 j i k).Contains (fullFactor true 36 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 2 (kernel36_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha36_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-262),262⟩,⟨(-262),262⟩⟩,⟨⟨(-179),132⟩,⟨(-182),128⟩⟩,⟨⟨(-37),79⟩,⟨(-43),70⟩⟩,⟨⟨29819758,29819818⟩,⟨19592001,19592062⟩⟩,⟨⟨21254709290211619583,21254709290211620634⟩,⟨102345032644875607971,102345032644875609027⟩⟩,⟨⟨8081140981986346309651619020,8081140981986346357912347341⟩,⟨(-853736019986821981515687197),(-853736019986821933380172618)⟩⟩] +lemma ha36_1_2_eq (j : Fin 7) : ha36_1_2 j = ((ha36_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha36_1_2_contains (j : Fin 7) : (ha36_1_2 j).Contains (fullFactor true 36 2 ((j.val:ℝ)/6)) := by + rw [ha36_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_1 j) true 36 1 j (ha36_1_1_contains j) +noncomputable def hk36_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_3 j i k) +lemma hk36_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_3 j i k).Contains (fullFactor true 36 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 3 (kernel36_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha36_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-995),995⟩,⟨(-995),995⟩⟩,⟨⟨(-530),514⟩,⟨(-437),606⟩⟩,⟨⟨(-148),155⟩,⟨(-201),104⟩⟩,⟨⟨15109059,15109184⟩,⟨(-55818732),(-55818608)⟩⟩,⟨⟨134379985869419321407,134379985869419323093⟩,⟨(-52971300556489538639),(-52971300556489536958)⟩⟩,⟨⟨(-1533428648222390008220618540),(-1533428648222389947255512367)⟩,⟨(-9673633877237525963043062824),(-9673633877237525901908825961)⟩⟩] +lemma ha36_1_3_eq (j : Fin 7) : ha36_1_3 j = ((ha36_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha36_1_3_contains (j : Fin 7) : (ha36_1_3 j).Contains (fullFactor true 36 3 ((j.val:ℝ)/6)) := by + rw [ha36_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_2 j) true 36 2 j (ha36_1_2_contains j) +noncomputable def hk36_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_4 j i k) +lemma hk36_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_4 j i k).Contains (fullFactor true 36 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 4 (kernel36_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha36_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2832),2832⟩,⟨(-2832),2832⟩⟩,⟨⟨(-1196),1433⟩,⟨(-1408),1221⟩⟩,⟨⟨(-367),238⟩,⟨(-272),332⟩⟩,⟨⟨(-70194435),(-70194244)⟩,⟨3695205,3695397⟩⟩,⟨⟨(-77761986310203023071),(-77761986310203021056)⟩,⟨(-127918517530736520708),(-127918517530736518689)⟩⟩,⟨⟨(-8660951694566569194698053396),(-8660951694566569136618790557)⟩,⟨1838425363912764107234955115,1838425363912764165147298640⟩⟩] +lemma ha36_1_4_eq (j : Fin 7) : ha36_1_4 j = ((ha36_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha36_1_4_contains (j : Fin 7) : (ha36_1_4 j).Contains (fullFactor true 36 4 ((j.val:ℝ)/6)) := by + rw [ha36_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_3 j) true 36 3 j (ha36_1_3_contains j) +noncomputable def hk36_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_5 j i k) +lemma hk36_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_5 j i k).Contains (fullFactor true 36 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 5 (kernel36_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha36_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-6448),6448⟩,⟨(-6448),6448⟩⟩,⟨⟨(-2862),2436⟩,⟨(-2679),2619⟩⟩,⟨⟨(-413),547⟩,⟨(-432),529⟩⟩,⟨⟨24688221,24688457⟩,⟨63739361,63739596⟩⟩,⟨⟨(-93563370853662712696),(-93563370853662710761)⟩,⟨81554878168809960889,81554878168809962821⟩⟩,⟨⟨1652979561543056305367785294,1652979561543056349378790574⟩,⟨6185942958307918919258611250,6185942958307918963398766330⟩⟩] +lemma ha36_1_5_eq (j : Fin 7) : ha36_1_5 j = ((ha36_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha36_1_5_contains (j : Fin 7) : (ha36_1_5 j).Contains (fullFactor true 36 5 ((j.val:ℝ)/6)) := by + rw [ha36_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_4 j) true 36 4 j (ha36_1_4_contains j) +noncomputable def hk36_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_6 j i k) +lemma hk36_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_6 j i k).Contains (fullFactor true 36 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 6 (kernel36_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha36_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-12235),12235⟩,⟨(-12235),12235⟩⟩,⟨⟨(-4299),4597⟩,⟨(-4241),4655⟩⟩,⟨⟨(-626),646⟩,⟨(-716),556⟩⟩,⟨⟨42843891,42844132⟩,⟨(-35108103),(-35107861)⟩⟩,⟨⟨66512162345950022257,66512162345950023801⟩,⟨54132426134363842678,54132426134363844224⟩⟩,⟨⟨3671202596570426832402027179,3671202596570426860356599547⟩,⟨(-1188417915833662494959927313),(-1188417915833662467087272624)⟩⟩] +lemma ha36_1_6_eq (j : Fin 7) : ha36_1_6 j = ((ha36_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha36_1_6_contains (j : Fin 7) : (ha36_1_6 j).Contains (fullFactor true 36 6 ((j.val:ℝ)/6)) := by + rw [ha36_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_5 j) true 36 5 j (ha36_1_5_contains j) +noncomputable def hk36_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_7 j i k) +lemma hk36_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_7 j i k).Contains (fullFactor true 36 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 7 (kernel36_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha36_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-19898),19898⟩,⟨(-19898),19898⟩⟩,⟨⟨(-6354),6449⟩,⟨(-6657),6146⟩⟩,⟨⟨(-784),659⟩,⟨(-697),747⟩⟩,⟨⟨(-32446170),(-32445957)⟩,⟨(-20676930),(-20676717)⟩⟩,⟨⟨24900305010811665133,24900305010811666191⟩,⟨(-44263944819402599810),(-44263944819402598752)⟩⟩,⟨⟨(-711537437660632100651439641),(-711537437660632085520888223)⟩,⟨(-1861950707315105923518842250),(-1861950707315105908344365302)⟩⟩] +lemma ha36_1_7_eq (j : Fin 7) : ha36_1_7 j = ((ha36_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha36_1_7_contains (j : Fin 7) : (ha36_1_7 j).Contains (fullFactor true 36 7 ((j.val:ℝ)/6)) := by + rw [ha36_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_6 j) true 36 6 j (ha36_1_6_contains j) +noncomputable def hk36_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_8 j i k) +lemma hk36_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_8 j i k).Contains (fullFactor true 36 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 8 (kernel36_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha36_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-28316),28316⟩,⟨(-28316),28316⟩⟩,⟨⟨(-8255),7868⟩,⟨(-7935),8188⟩⟩,⟨⟨(-679),755⟩,⟨(-686),748⟩⟩,⟨⟨(-5795001),(-5794836)⟩,⟨22654070,22654235⟩⟩,⟨⟨(-24796091082614424477),(-24796091082614423843)⟩,⟨(-8818724765285580462),(-8818724765285579827)⟩⟩,⟨⟨(-823743089443707069894563242),(-823743089443707062687266642)⟩,⟨364875618018392952534002726,364875618018392959720936360⟩⟩] +lemma ha36_1_8_eq (j : Fin 7) : ha36_1_8 j = ((ha36_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha36_1_8_contains (j : Fin 7) : (ha36_1_8 j).Contains (fullFactor true 36 8 ((j.val:ℝ)/6)) := by + rw [ha36_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_7 j) true 36 7 j (ha36_1_7_contains j) +noncomputable def hk36_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_9 j i k) +lemma hk36_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_9 j i k).Contains (fullFactor true 36 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 9 (kernel36_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha36_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-35817),35817⟩,⟨(-35817),35817⟩⟩,⟨⟨(-8845),9202⟩,⟨(-8982),9065⟩⟩,⟨⟨(-627),639⟩,⟨(-664),602⟩⟩,⟨⟨12604755,12604869⟩,⟨(-839685),(-839572)⟩⟩,⟨⟨(-2062565499980090153),(-2062565499980089814)⟩,⟨11945604993550582903,11945604993550583242⟩⟩,⟨⟨163583595584826029955734431,163583595584826032990204328⟩,⟨322893758501608925428064268,322893758501608928470835016⟩⟩] +lemma ha36_1_9_eq (j : Fin 7) : ha36_1_9 j = ((ha36_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha36_1_9_contains (j : Fin 7) : (ha36_1_9 j).Contains (fullFactor true 36 9 ((j.val:ℝ)/6)) := by + rw [ha36_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_8 j) true 36 8 j (ha36_1_8_contains j) +noncomputable def hk36_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_10 j i k) +lemma hk36_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_10 j i k).Contains (fullFactor true 36 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 10 (kernel36_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha36_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-40775),40775⟩,⟨(-40775),40775⟩⟩,⟨⟨(-9157),9024⟩,⟨(-9203),8978⟩⟩,⟨⟨(-521),485⟩,⟨(-497),509⟩⟩,⟨⟨(-2298021),(-2297951)⟩,⟨(-5696211),(-5696140)⟩⟩,⟨⟨5025400802822630782,5025400802822630945⟩,⟨1284089879857054,1284089879857217⟩⟩,⟨⟨113526112925002597448124151,113526112925002598604236771⟩,⟨(-65133546716807250313451225),(-65133546716807249160353789)⟩⟩] +lemma ha36_1_10_eq (j : Fin 7) : ha36_1_10 j = ((ha36_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha36_1_10_contains (j : Fin 7) : (ha36_1_10 j).Contains (fullFactor true 36 10 ((j.val:ℝ)/6)) := by + rw [ha36_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_9 j) true 36 9 j (ha36_1_9_contains j) +noncomputable def hk36_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_11 j i k) +lemma hk36_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_11 j i k).Contains (fullFactor true 36 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 11 (kernel36_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha36_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-42199),42199⟩,⟨(-42199),42199⟩⟩,⟨⟨(-8348),8303⟩,⟨(-8244),8407⟩⟩,⟨⟨(-356),371⟩,⟨(-357),370⟩⟩,⟨⟨(-2075839),(-2075798)⟩,⟨1749835,1749875⟩⟩,⟨⟨(-321288110112883670),(-321288110112883598)⟩,⟨(-1866468580227929348),(-1866468580227929276)⟩⟩,⟨⟨(-23319646561156793459441722),(-23319646561156793061099128)⟩,⟨(-36155945937165040388754121),(-36155945937165039989425250)⟩⟩] +lemma ha36_1_11_eq (j : Fin 7) : ha36_1_11 j = ((ha36_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha36_1_11_contains (j : Fin 7) : (ha36_1_11 j).Contains (fullFactor true 36 11 ((j.val:ℝ)/6)) := by + rw [ha36_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_10 j) true 36 10 j (ha36_1_10_contains j) +noncomputable def hk36_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_12 j i k) +lemma hk36_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_12 j i k).Contains (fullFactor true 36 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 12 (kernel36_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha36_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-40034),40034⟩,⟨(-40034),40034⟩⟩,⟨⟨(-6945),7034⟩,⟨(-7013),6966⟩⟩,⟨⟨(-240),242⟩,⟨(-246),236⟩⟩,⟨⟨935816,935837⟩,⟨578206,578228⟩⟩,⟨⟨(-616565988538150186),(-616565988538150156)⟩,⟨218926688831159953,218926688831159982⟩⟩,⟨⟨(-10515104498381581258562209),(-10515104498381581132127658)⟩,⟨7583081181619694641421321,7583081181619694767562860⟩⟩] +lemma ha36_1_12_eq (j : Fin 7) : ha36_1_12 j = ((ha36_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha36_1_12_contains (j : Fin 7) : (ha36_1_12 j).Contains (fullFactor true 36 12 ((j.val:ℝ)/6)) := by + rw [ha36_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_11 j) true 36 11 j (ha36_1_11_contains j) +noncomputable def hk36_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_13 j i k) +lemma hk36_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_13 j i k).Contains (fullFactor true 36 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 13 (kernel36_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha36_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-35058),35058⟩,⟨(-35058),35058⟩⟩,⟨⟨(-5443),5390⟩,⟨(-5425),5408⟩⟩,⟨⟨(-150),145⟩,⟨(-147),148⟩⟩,⟨⟨96398,96409⟩,⟨(-399983),(-399972)⟩⟩,⟨⟨102202374306935182,102202374306935194⟩,⟨181897186211573896,181897186211573908⟩⟩,⟨⟨2258243079932038781620552,2258243079932038818492466⟩,⟨2811262735012686847048983,2811262735012686884000513⟩⟩] +lemma ha36_1_13_eq (j : Fin 7) : ha36_1_13 j = ((ha36_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha36_1_13_contains (j : Fin 7) : (ha36_1_13 j).Contains (fullFactor true 36 13 ((j.val:ℝ)/6)) := by + rw [ha36_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_12 j) true 36 12 j (ha36_1_12_contains j) +noncomputable def hk36_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_14 j i k) +lemma hk36_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_14 j i k).Contains (fullFactor true 36 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 14 (kernel36_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha36_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-28508),28508⟩,⟨(-28508),28508⟩⟩,⟨⟨(-3892),3904⟩,⟨(-3885),3911⟩⟩,⟨⟨(-83),85⟩,⟨(-83),85⟩⟩,⟨⟨(-142430),(-142424)⟩,⟨11477,11483⟩⟩,⟨⟨47937300515665319,47937300515665324⟩,⟨(-38974147096446877),(-38974147096446872)⟩⟩,⟨⟨694821790015600458193723,694821790015600468221593⟩,⟨(-620175342563798435203016),(-620175342563798425195044)⟩⟩] +lemma ha36_1_14_eq (j : Fin 7) : ha36_1_14 j = ((ha36_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha36_1_14_contains (j : Fin 7) : (ha36_1_14 j).Contains (fullFactor true 36 14 ((j.val:ℝ)/6)) := by + rw [ha36_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_13 j) true 36 13 j (ha36_1_13_contains j) +noncomputable def hk36_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_15 j i k) +lemma hk36_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_15 j i k).Contains (fullFactor true 36 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 15 (kernel36_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha36_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-21636),21636⟩,⟨(-21636),21636⟩⟩,⟨⟨(-2616),2621⟩,⟨(-2625),2612⟩⟩,⟨⟨(-45),45⟩,⟨(-45),44⟩⟩,⟨⟨17923,17926⟩,⟨42706,42709⟩⟩,⟨⟨(-12865560730077539),(-12865560730077536)⟩,⟨(-11225891718524800),(-11225891718524797)⟩⟩,⟨⟨(-157995888563329718871937),(-157995888563329716336632)⟩,⟨(-159504478119544086433528),(-159504478119544083893627)⟩⟩] +lemma ha36_1_15_eq (j : Fin 7) : ha36_1_15 j = ((ha36_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha36_1_15_contains (j : Fin 7) : (ha36_1_15 j).Contains (fullFactor true 36 15 ((j.val:ℝ)/6)) := by + rw [ha36_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_14 j) true 36 14 j (ha36_1_14_contains j) +noncomputable def hk36_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_16 j i k) +lemma hk36_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_16 j i k).Contains (fullFactor true 36 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 16 (kernel36_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha36_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-15395),15395⟩,⟨(-15395),15395⟩⟩,⟨⟨(-1652),1646⟩,⟨(-1648),1650⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨10633,10635⟩,⟨(-9222),(-9219)⟩⟩,⟨⟨(-2299988233726216),(-2299988233726214)⟩,⟨3779129772871176,3779129772871178⟩⟩,⟨⟨(-34144212865590539538085),(-34144212865590538934982)⟩,⟨37529872401943248324859,37529872401943248926978⟩⟩] +lemma ha36_1_16_eq (j : Fin 7) : ha36_1_16 j = ((ha36_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha36_1_16_contains (j : Fin 7) : (ha36_1_16 j).Contains (fullFactor true 36 16 ((j.val:ℝ)/6)) := by + rw [ha36_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_15 j) true 36 15 j (ha36_1_15_contains j) +noncomputable def hk36_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_17 j i k) +lemma hk36_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_17 j i k).Contains (fullFactor true 36 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 17 (kernel36_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha36_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-10310),10310⟩,⟨(-10310),10310⟩⟩,⟨⟨(-976),979⟩,⟨(-977),978⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-3455),(-3453)⟩,⟨(-2069),(-2067)⟩⟩,⟨⟨1003456305184554,1003456305184556⟩,⟨396145452067724,396145452067726⟩⟩,⟨⟨8348983519930141615789,8348983519930141750376⟩,⟨6838148924062458626834,6838148924062458761617⟩⟩] +lemma ha36_1_17_eq (j : Fin 7) : ha36_1_17 j = ((ha36_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha36_1_17_contains (j : Fin 7) : (ha36_1_17 j).Contains (fullFactor true 36 17 ((j.val:ℝ)/6)) := by + rw [ha36_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_16 j) true 36 16 j (ha36_1_16_contains j) +noncomputable def hk36_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_18 j i k) +lemma hk36_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_18 j i k).Contains (fullFactor true 36 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 18 (kernel36_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha36_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-6521),6521⟩,⟨(-6521),6521⟩⟩,⟨⟨(-548),547⟩,⟨(-548),547⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-241),(-239)⟩,⟨1060,1061⟩⟩,⟨⟨50646228656044,50646228656045⟩,⟨(-243245739202544),(-243245739202543)⟩⟩,⟨⟨1284723176810186464885,1284723176810186493334⟩,⟨(-1746245502503329503895),(-1746245502503329475482)⟩⟩] +lemma ha36_1_18_eq (j : Fin 7) : ha36_1_18 j = ((ha36_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha36_1_18_contains (j : Fin 7) : (ha36_1_18 j).Contains (fullFactor true 36 18 ((j.val:ℝ)/6)) := by + rw [ha36_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_17 j) true 36 17 j (ha36_1_17_contains j) +noncomputable def hk36_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_19 j i k) +lemma hk36_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_19 j i k).Contains (fullFactor true 36 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 19 (kernel36_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha36_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3908),3908⟩,⟨(-3908),3908⟩⟩,⟨⟨(-291),291⟩,⟨(-291),291⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨276,278⟩,⟨(-27),(-25)⟩⟩,⟨⟨(-54179013088952),(-54179013088951)⟩,⟨(-1872928312373),(-1872928312372)⟩⟩,⟨⟨(-344577618906544153580),(-344577618906544147897)⟩,⟨(-226908972049481652362),(-226908972049481646673)⟩⟩] +lemma ha36_1_19_eq (j : Fin 7) : ha36_1_19 j = ((ha36_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha36_1_19_contains (j : Fin 7) : (ha36_1_19 j).Contains (fullFactor true 36 19 ((j.val:ℝ)/6)) := by + rw [ha36_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_18 j) true 36 18 j (ha36_1_18_contains j) +noncomputable def hk36_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_20 j i k) +lemma hk36_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_20 j i k).Contains (fullFactor true 36 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 20 (kernel36_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha36_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2225),2225⟩,⟨(-2225),2225⟩⟩,⟨⟨(-147),147⟩,⟨(-147),147⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-28),(-26)⟩,⟨(-63),(-61)⟩⟩,⟨⟨1525354260258,1525354260259⟩,⟨11132821019268,11132821019269⟩⟩,⟨⟨(-37733585562330668793),(-37733585562330667711)⟩,⟨64344310646478403937,64344310646478405017⟩⟩] +lemma ha36_1_20_eq (j : Fin 7) : ha36_1_20 j = ((ha36_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha36_1_20_contains (j : Fin 7) : (ha36_1_20 j).Contains (fullFactor true 36 20 ((j.val:ℝ)/6)) := by + rw [ha36_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_19 j) true 36 19 j (ha36_1_19_contains j) +noncomputable def hk36_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_21 j i k) +lemma hk36_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_21 j i k).Contains (fullFactor true 36 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 21 (kernel36_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha36_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1207),1207⟩,⟨(-1207),1207⟩⟩,⟨⟨(-71),71⟩,⟨(-71),71⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-12),(-11)⟩,⟨10,11⟩⟩,⟨⟨2114597853254,2114597853255⟩,⟨(-670115506523),(-670115506522)⟩⟩,⟨⟨11401635385740531415,11401635385740531611⟩,⟨5913086332107364907,5913086332107365104⟩⟩] +lemma ha36_1_21_eq (j : Fin 7) : ha36_1_21 j = ((ha36_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha36_1_21_contains (j : Fin 7) : (ha36_1_21 j).Contains (fullFactor true 36 21 ((j.val:ℝ)/6)) := by + rw [ha36_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_20 j) true 36 20 j (ha36_1_20_contains j) +noncomputable def hk36_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_22 j i k) +lemma hk36_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_22 j i k).Contains (fullFactor true 36 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 22 (kernel36_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha36_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-625),625⟩,⟨(-625),625⟩⟩,⟨⟨(-33),33⟩,⟨(-33),33⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨2,4⟩,⟨1,2⟩⟩,⟨⟨(-192133733795),(-192133733793)⟩,⟨(-371217841193),(-371217841192)⟩⟩,⟨⟨873244790737701987,873244790737702022⟩,⟨(-1921905559715956097),(-1921905559715956062)⟩⟩] +lemma ha36_1_22_eq (j : Fin 7) : ha36_1_22 j = ((ha36_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha36_1_22_contains (j : Fin 7) : (ha36_1_22 j).Contains (fullFactor true 36 22 ((j.val:ℝ)/6)) := by + rw [ha36_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_21 j) true 36 21 j (ha36_1_21_contains j) +noncomputable def hk36_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_23 j i k) +lemma hk36_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_23 j i k).Contains (fullFactor true 36 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 23 (kernel36_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha36_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-310),310⟩,⟨(-310),310⟩⟩,⟨⟨(-15),15⟩,⟨(-15),15⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-60052783459),(-60052783458)⟩,⟨45494512039,45494512040⟩⟩,⟨⟨(-308870570569920922),(-308870570569920915)⟩,⟨(-121409870626070744),(-121409870626070737)⟩⟩] +lemma ha36_1_23_eq (j : Fin 7) : ha36_1_23 j = ((ha36_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha36_1_23_contains (j : Fin 7) : (ha36_1_23 j).Contains (fullFactor true 36 23 ((j.val:ℝ)/6)) := by + rw [ha36_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_22 j) true 36 22 j (ha36_1_22_contains j) +noncomputable def hk36_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_24 j i k) +lemma hk36_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_24 j i k).Contains (fullFactor true 36 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 24 (kernel36_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha36_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-148),148⟩,⟨(-148),148⟩⟩,⟨⟨(-7),7⟩,⟨(-7),7⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨9506417820,9506417821⟩,⟨8887141015,8887141016⟩⟩,⟨⟨(-15850689216029618),(-15850689216029616)⟩,⟨47422383812711839,47422383812711841⟩⟩] +lemma ha36_1_24_eq (j : Fin 7) : ha36_1_24 j = ((ha36_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha36_1_24_contains (j : Fin 7) : (ha36_1_24 j).Contains (fullFactor true 36 24 ((j.val:ℝ)/6)) := by + rw [ha36_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_23 j) true 36 23 j (ha36_1_23_contains j) +noncomputable def hk36_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_25 j i k) +lemma hk36_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_25 j i k).Contains (fullFactor true 36 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 25 (kernel36_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha36_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-68),68⟩,⟨(-68),68⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨1184447361,1184447362⟩,⟨(-1803831570),(-1803831569)⟩⟩,⟨⟨6968791993521496,6968791993521497⟩,⟨1933303657017176,1933303657017177⟩⟩] +lemma ha36_1_25_eq (j : Fin 7) : ha36_1_25 j = ((ha36_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha36_1_25_contains (j : Fin 7) : (ha36_1_25 j).Contains (fullFactor true 36 25 ((j.val:ℝ)/6)) := by + rw [ha36_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_24 j) true 36 24 j (ha36_1_24_contains j) +noncomputable def hk36_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_26 j i k) +lemma hk36_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_26 j i k).Contains (fullFactor true 36 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 26 (kernel36_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha36_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-30),30⟩,⟨(-30),30⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-315515316),(-315515315)⟩,⟨(-137245018),(-137245017)⟩⟩,⟨⟨218179092308524,218179092308525⟩,⟨(-981827394548045),(-981827394548044)⟩⟩] +lemma ha36_1_26_eq (j : Fin 7) : ha36_1_26 j = ((ha36_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha36_1_26_contains (j : Fin 7) : (ha36_1_26 j).Contains (fullFactor true 36 26 ((j.val:ℝ)/6)) := by + rw [ha36_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_25 j) true 36 25 j (ha36_1_25_contains j) +noncomputable def hk36_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_27 j i k) +lemma hk36_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_27 j i k).Contains (fullFactor true 36 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 27 (kernel36_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha36_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-13),13⟩,⟨(-13),13⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-12535834),(-12535833)⟩,⟨51319845,51319846⟩⟩,⟨⟨(-132828611372952),(-132828611372951)⟩,⟨(-22351457795380),(-22351457795379)⟩⟩] +lemma ha36_1_27_eq (j : Fin 7) : ha36_1_27 j = ((ha36_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha36_1_27_contains (j : Fin 7) : (ha36_1_27 j).Contains (fullFactor true 36 27 ((j.val:ℝ)/6)) := by + rw [ha36_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_26 j) true 36 26 j (ha36_1_26_contains j) +noncomputable def hk36_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_28 j i k) +lemma hk36_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_28 j i k).Contains (fullFactor true 36 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 28 (kernel36_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha36_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-6),6⟩,⟨(-6),6⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨7803064,7803065⟩,⟨538134,538135⟩⟩,⟨⟨(-1991786508369),(-1991786508367)⟩,⟨17280163662042,17280163662043⟩⟩] +lemma ha36_1_28_eq (j : Fin 7) : ha36_1_28 j = ((ha36_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha36_1_28_contains (j : Fin 7) : (ha36_1_28 j).Contains (fullFactor true 36 28 ((j.val:ℝ)/6)) := by + rw [ha36_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_27 j) true 36 27 j (ha36_1_27_contains j) +noncomputable def hk36_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_29 j i k) +lemma hk36_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_29 j i k).Contains (fullFactor true 36 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 29 (kernel36_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha36_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-113701),(-113699)⟩,⟨(-1112305),(-1112304)⟩⟩,⟨⟨2164590529937,2164590529939⟩,⟨136125470911,136125470912⟩⟩] +lemma ha36_1_29_eq (j : Fin 7) : ha36_1_29 j = ((ha36_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha36_1_29_contains (j : Fin 7) : (ha36_1_29 j).Contains (fullFactor true 36 29 ((j.val:ℝ)/6)) := by + rw [ha36_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_28 j) true 36 28 j (ha36_1_28_contains j) +noncomputable def hk36_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel36_0 j i k).mul (mpower1_30 j i k) +lemma hk36_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk36_1_30 j i k).Contains (fullFactor true 36 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk36_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel36_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 36 30 (kernel36_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha36_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-148801),(-148800)⟩,⟨41596,41597⟩⟩,⟨⟨2836673203,2836673205⟩,⟨(-261398450093),(-261398450092)⟩⟩] +lemma ha36_1_30_eq (j : Fin 7) : ha36_1_30 j = ((ha36_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha36_1_30_contains (j : Fin 7) : (ha36_1_30 j).Contains (fullFactor true 36 30 ((j.val:ℝ)/6)) := by + rw [ha36_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha36_1_29 j) true 36 29 j (ha36_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders37.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders37.lean new file mode 100644 index 0000000000000000000000000000000000000000..f39c3884e376b49dbcea3bcb31920b0ec36751d7 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders37.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers40 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues40 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk37_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_0 j i k) +lemma hk37_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_0 j i k).Contains (fullFactor false 37 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 0 (power37_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha37_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999557,1000000000000000000000000000591⟩,⟨(-591),591⟩⟩,⟨⟨866025403784438646652463972353,866025403784438646860449899485⟩,⟨499999999999999999908006033126,500000000000000000117164942813⟩⟩,⟨⟨499999999999999999690091657455,500000000000000000259566390561⟩,⟨866025403784438646493088998599,866025403784438647063422282455⟩⟩,⟨⟨(-164464382913),77269564347⟩,⟨999999999999999999879133026407,1000000000000000000120866973630⟩⟩,⟨⟨(-500000000000000000829749758478),(-499999999999999999270934145549)⟩,⟨866025403784438645955564246685,866025403784438647513752215628⟩⟩,⟨⟨(-866025403784438647780983075406),(-866025403784438645819125614846)⟩,⟨499999999999999998956455302613,500000000000000000917689817373⟩⟩,⟨⟨(-1000000000000000000242468318081),(-999999999999999999757531682067)⟩,⟨(-329663136721),155273499293⟩⟩] +lemma ha37_0_0_eq (j : Fin 7) : ha37_0_0 j = ((atomPoints j).direct.powBin 7 37).conj := by fin_cases j <;> decide +kernel +lemma ha37_0_0_contains (j : Fin 7) : (ha37_0_0 j).Contains (fullFactor false 37 0 ((j.val:ℝ)/6)) := by + rw [ha37_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 37) ((j.val:ℝ)/6) 37 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 37 (by norm_num)) +noncomputable def hk37_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_1 j i k) +lemma hk37_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_1 j i k).Contains (fullFactor false 37 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 1 (power37_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha37_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-261799387799149436600514087268),(-261799387799149436490165404914)⟩,⟨453449841058554462589882844839,453449841058554462700227397305⟩⟩,⟨⟨(-906899682117108925613006977016),(-906899682117108925012868607446)⟩,⟨523598775598298872752131409257,523598775598298873350150621903⟩⟩,⟨⟨(-1570796326794896619424857398209),(-1570796326794896619040142601849)⟩,⟨(-258340048569),121374747850⟩⟩,⟨⟨(-1813799364234217852169182760527),(-1813799364234217848899948007068)⟩,⟨(-1047197551196597747894490497036),(-1047197551196597744626381378447)⟩⟩,⟨⟨(-1308996938995747185098339657113),(-1308996938995747179959673037496)⟩,⟨(-2267249205292772315911087205568),(-2267249205292772310767739505961)⟩⟩,⟨⟨(-487806084677),1035667288483⟩,⟨(-3141592653589793239231736686812),(-3141592653589793237698263313653)⟩⟩] +lemma ha37_0_1_eq (j : Fin 7) : ha37_0_1 j = ((ha37_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha37_0_1_contains (j : Fin 7) : (ha37_0_1 j).Contains (fullFactor false 37 1 ((j.val:ℝ)/6)) := by + rw [ha37_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_0 j) false 37 0 j (ha37_0_0_contains j) +noncomputable def hk37_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_2 j i k) +lemma hk37_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_2 j i k).Contains (fullFactor false 37 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 2 (power37_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha37_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-118712890786751174421752378522),(-118712890786751174392486367370)⟩,⟨(-68538919452009434869399008726),(-68538919452009434840291625084)⟩⟩,⟨⟨(-274155677808037739555676365759),(-274155677808037739241681573606)⟩,⟨(-474851563147004697798301576545),(-474851563147004697482558361576)⟩⟩,⟨⟨(-95327504045),202899799679⟩,⟨(-1233700550136169827509202900107),(-1233700550136169827203121614796)⟩⟩,⟨⟨1096622711232150956047411000146,1096622711232150959473257524682⟩,⟨(-1899406252588018792180890370703),(-1899406252588018788751309744709)⟩⟩,⟨⟨2967822269668779356956353656225,2967822269668779363698426922895⟩,⟨(-1713472986300235874478330712978),(-1713472986300235867746377683463)⟩⟩,⟨⟨4934802200544679308212407877547,4934802200544679310636890182612⟩,⟨(-766244005999),1626822372531⟩⟩] +lemma ha37_0_2_eq (j : Fin 7) : ha37_0_2 j = ((ha37_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha37_0_2_contains (j : Fin 7) : (ha37_0_2 j).Contains (fullFactor false 37 2 ((j.val:ℝ)/6)) := by + rw [ha37_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_1 j) false 37 1 j (ha37_0_1_contains j) +noncomputable def hk37_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_3 j i k) +lemma hk37_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_3 j i k).Contains (fullFactor false 37 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 3 (power37_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha37_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11962298101967523213616229492,11962298101967523218734503483⟩,⟨(-20719308087892496644875122061),(-20719308087892496639701287918)⟩⟩,⟨⟨165754464703139973087106448216,165754464703139973197849234906⟩,⟨(-95698384815740185777131204948),(-95698384815740185667221728383)⟩⟩,⟨⟨645964097506246253576050266679,645964097506246253738370220486⟩,⟨(-49913364399),106238086682⟩⟩,⟨⟨1326035717625119783873807576824,1326035717625119786272327435059⟩,⟨765587078525921484695970677103,765587078525921487090099677310⟩⟩,⟨⟨1495287262745940398856345312229,1495287262745940404735842232149⟩,⟨2589913510986562077470500526821,2589913510986562083362313323278⟩⟩,⟨⟨(-1703604404747),802408846702⟩,⟨5167712780049970027980001312217,5167712780049970030535362585670⟩⟩] +lemma ha37_0_3_eq (j : Fin 7) : ha37_0_3 j = ((ha37_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha37_0_3_contains (j : Fin 7) : (ha37_0_3 j).Contains (fullFactor false 37 3 ((j.val:ℝ)/6)) := by + rw [ha37_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_2 j) false 37 2 j (ha37_0_2_contains j) +noncomputable def hk37_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_4 j i k) +lemma hk37_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_4 j i k).Contains (fullFactor false 37 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 4 (power37_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha37_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2712151086516110563038389172,2712151086516110563724275524⟩,⟨1565861159883012429561959706,1565861159883012430236924496⟩⟩,⟨⟨25053778558128198862072198274,25053778558128198890926180607⟩,⟨43394417384257769000628336166,43394417384257769029758858647⟩⟩,⟨⟨(-41719599082),19600932364⟩,⟨253669507901048013605049335316,253669507901048013669599687240⟩⟩,⟨⟨(-400860456930051182711946820499),(-400860456930051181457107828900)⟩,⟨694310678148124303579108543342,694310678148124304837180663894⟩⟩,⟨⟨(-1695094429072569104129456135271),(-1695094429072569100267878024271)⟩,⟨978663224926882766613729403205,978663224926882770464966320510⟩⟩,⟨⟨(-4058712126416768219207139847142),(-4058712126416768217187244514204)⟩,⟨(-1338007770645),630210434494⟩⟩] +lemma ha37_0_4_eq (j : Fin 7) : ha37_0_4 j = ((ha37_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha37_0_4_contains (j : Fin 7) : (ha37_0_4 j).Contains (fullFactor false 37 4 ((j.val:ℝ)/6)) := by + rw [ha37_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_3 j) false 37 3 j (ha37_0_3_contains j) +noncomputable def hk37_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_5 j i k) +lemma hk37_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_5 j i k).Contains (fullFactor false 37 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 5 (power37_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha37_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-163976597214335483827392980),(-163976597214335483756188878)⟩,⟨284015797627486289449541375,284015797627486289522271277⟩⟩,⟨⟨(-9088505524079561266842774979),(-9088505524079561260712763005)⟩,⟨5247251110858735477911141214,5247251110858735483971007662⟩⟩,⟨⟨(-79692626246167045131070830718),(-79692626246167045110538070070)⟩,⟨(-13106598599),6157814512⟩⟩,⟨⟨(-290832176770545960690200430805),(-290832176770545960162294665684)⟩,⟨(-167912035547479535678553545057),(-167912035547479535152393336787)⟩⟩,⟨⟨(-512426866294798387781023967428),(-512426866294798385762889927611)⟩,⟨(-887549367585894655700509601005),(-887549367585894653675766872824)⟩⟩,⟨⟨(-395972894245),840695076541⟩,⟨(-2550164039877345444504369958769),(-2550164039877345443227114866719)⟩⟩] +lemma ha37_0_5_eq (j : Fin 7) : ha37_0_5 j = ((ha37_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha37_0_5_contains (j : Fin 7) : (ha37_0_5 j).Contains (fullFactor false 37 5 ((j.val:ℝ)/6)) := by + rw [ha37_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_4 j) false 37 4 j (ha37_0_4_contains j) +noncomputable def hk37_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_6 j i k) +lemma hk37_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_6 j i k).Contains (fullFactor false 37 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 6 (power37_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha37_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24785053981387676530020934),(-24785053981387676523595158)⟩,⟨(-14309657588033580849268662),(-14309657588033580843009382)⟩⟩,⟨⟨(-915818085634149174614021974),(-915818085634149173553460616)⟩,⟨(-1586243454808811298293111300),(-1586243454808811297218173208)⟩⟩,⟨⟨(-1612112070),3431299490⟩,⟨(-20863480763352960875866477065),(-20863480763352960870424602375)⟩⟩,⟨⟨58612357480585547058285859593,58612357480585547242136989069⟩,⟨(-101519581107763923143548921198),(-101519581107763922958951899502)⟩⟩,⟨⟨387266468459182445308524779418,387266468459182446193218164689⟩,⟨(-223588399813024701127798986075),(-223588399813024700246510188558)⟩⟩,⟨⟨1335262768854589495544804804303,1335262768854589496217824280028⟩,⟨(-207330922597),440186912729⟩⟩] +lemma ha37_0_6_eq (j : Fin 7) : ha37_0_6 j = ((ha37_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha37_0_6_contains (j : Fin 7) : (ha37_0_6 j).Contains (fullFactor false 37 6 ((j.val:ℝ)/6)) := by + rw [ha37_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_5 j) false 37 5 j (ha37_0_5_contains j) +noncomputable def hk37_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_7 j i k) +lemma hk37_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_7 j i k).Contains (fullFactor false 37 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 7 (power37_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha37_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1070359884617898513899520,1070359884617898514371121⟩,⟨(-1853917702541761442495017),(-1853917702541761442008468)⟩⟩,⟨⟨237301465925345464533413322,237301465925345464694979039⟩,⟨(-137006065231091009878523151),(-137006065231091009719427438)⟩⟩,⟨⟨4681754135318688100092019392,4681754135318688101328075704⟩,⟨(-361757103),769981806⟩⟩,⟨⟨30374587638444219441424002516,30374587638444219496751987569⟩,⟨17536776349579649229385369109,17536776349579649284449319709⟩⟩,⟨⟨83621865985773321239259142108,83621865985773321569126558296⟩,⟨144837320511075112517541003098,144837320511075112848876586972⟩⟩,⟨⟨(-197555424463),93049900471⟩,⟨599264529320792076738907109846,599264529320792077042865062469⟩⟩] +lemma ha37_0_7_eq (j : Fin 7) : ha37_0_7 j = ((ha37_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha37_0_7_contains (j : Fin 7) : (ha37_0_7 j).Contains (fullFactor false 37 7 ((j.val:ℝ)/6)) := by + rw [ha37_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_6 j) false 37 6 j (ha37_0_6_contains j) +noncomputable def hk37_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_8 j i k) +lemma hk37_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_8 j i k).Contains (fullFactor false 37 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 8 (power37_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha37_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨121338629888859693698185,121338629888859693730417⟩,⟨70054890629433514713183,70054890629433514744273⟩⟩,⟨⟨17934052001134979758758833,17934052001134979779641500⟩,⟨31062689251548081581019091,31062689251548081602266871⟩⟩,⟨⟨(-151185575),71030842⟩,⟨919260274839426580124420179,919260274839426580370045365⟩⟩,⟨⟨(-4591117312290554828823781344),(-4591117312290554814393458806)⟩,⟨7952048448396308879805209161,7952048448396308894315353934⟩⟩,⟨⟨(-47397902300335817913825097005),(-47397902300335817805244908527)⟩,⟨27365191652122466632758619107,27365191652122466740794584734⟩⟩,⟨⟨(-235330630358893204603348134369),(-235330630358893204483235044836)⟩,⟨(-77579833772),36540610468⟩⟩] +lemma ha37_0_8_eq (j : Fin 7) : ha37_0_8 j = ((ha37_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha37_0_8_contains (j : Fin 7) : (ha37_0_8 j).Contains (fullFactor false 37 8 ((j.val:ℝ)/6)) := by + rw [ha37_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_7 j) false 37 7 j (ha37_0_7_contains j) +noncomputable def hk37_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_9 j i k) +lemma hk37_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_9 j i k).Contains (fullFactor false 37 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 9 (power37_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha37_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-4075628328693792153474),(-4075628328693792151651)⟩,⟨7059195338064676365601,7059195338064676367500⟩⟩,⟨⟨(-3614308013089114301006811),(-3614308013089114298523013)⟩,⟨2086721704291221580736292,2086721704291221583172744⟩⟩,⟨⟨(-160441184787359821895434234),(-160441184787359821852053851)⟩,⟨(-26386861),12397221⟩⟩,⟨⟨(-1850525702701626523077753118),(-1850525702701626519695198694)⟩,⟨(-1068401512597105451802814280),(-1068401512597105448441324912)⟩⟩,⟨⟨(-7960211579480062812497652046),(-7960211579480062781045925392)⟩,⟨(-13787490894657571044927633009),(-13787490894657571013299049539)⟩⟩,⟨⟨(-12755079268),27080470650⟩,⟨(-82145886611128228820451377739),(-82145886611128228778262521518)⟩⟩] +lemma ha37_0_9_eq (j : Fin 7) : ha37_0_9 j = ((ha37_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha37_0_9_contains (j : Fin 7) : (ha37_0_9 j).Contains (fullFactor false 37 9 ((j.val:ℝ)/6)) := by + rw [ha37_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_8 j) false 37 8 j (ha37_0_8_contains j) +noncomputable def hk37_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_10 j i k) +lemma hk37_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_10 j i k).Contains (fullFactor false 37 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 10 (power37_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha37_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-369618603571988403240),(-369618603571988403139)⟩,⟨(-213399400269781075781),(-213399400269781075684)⟩⟩,⟨⟨(-218520985876255821661670),(-218520985876255821405829)⟩,⟨(-378489450057716125006271),(-378489450057716124744963)⟩⟩,⟨⟨(-1947351),4144839⟩,⟨(-25202042373060605484689269),(-25202042373060605477794873)⟩⟩,⟨⟨223765489537285960931983063,223765489537285961636724019⟩,⟨(-387573196859101312207957926),(-387573196859101311498283699)⟩⟩,⟨⟨3609556675507699245933659237,3609556675507699254225492603⟩,⟨(-2083978518259580821507423358),(-2083978518259580813266747064)⟩⟩,⟨⟨25806891390014060006123797643,25806891390014060019459963607⟩,⟨(-4007126333),8507580765⟩⟩] +lemma ha37_0_10_eq (j : Fin 7) : ha37_0_10 j = ((ha37_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha37_0_10_contains (j : Fin 7) : (ha37_0_10 j).Contains (fullFactor false 37 10 ((j.val:ℝ)/6)) := by + rw [ha37_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_9 j) false 37 9 j (ha37_0_9_contains j) +noncomputable def hk37_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_11 j i k) +lemma hk37_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_11 j i k).Contains (fullFactor false 37 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 11 (power37_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha37_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨10157787699515332858,10157787699515332864⟩,⟨(-17593804388058740567),(-17593804388058740562)⟩⟩,⟨⟨36032111386744300664572,36032111386744300689564⟩,⟨(-20803149208607401709528),(-20803149208607401685104)⟩⟩,⟨⟨3598843235212085339990249,3598843235212085340986223⟩,⟨(-278082),591882⟩⟩,⟨⟨73793764120052327715242239,73793764120052327850598790⟩,⟨42604849579227958615378554,42604849579227958749696535⟩⟩,⟨⟨495985727515397111286664236,495985727515397113249519380⟩,⟨859072479885680690682683430,859072479885680692658869670⟩⟩,⟨⟨(-2429759385),1144432605⟩,⟨7370430945714350775403776458,7370430945714350779236037362⟩⟩] +lemma ha37_0_11_eq (j : Fin 7) : ha37_0_11 j = ((ha37_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha37_0_11_contains (j : Fin 7) : (ha37_0_11 j).Contains (fullFactor false 37 11 ((j.val:ℝ)/6)) := by + rw [ha37_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_10 j) false 37 10 j (ha37_0_10_contains j) +noncomputable def hk37_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_12 j i k) +lemma hk37_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_12 j i k).Contains (fullFactor false 37 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 12 (power37_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha37_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨767674536308627877,767674536308627878⟩,⟨443217100187807442,443217100187807443⟩⟩,⟨⟨1815417242369259284368,1815417242369259286506⟩,⟨3144394900720139783910,3144394900720139786102⟩⟩,⟨⟨(-77478),36401⟩,⟨471087477881817150305332,471087477881817150437205⟩⟩,⟨⟨(-7435949024744486046005210),(-7435949024744486022538630)⟩,⟨12879441513349692546904017,12879441513349692570569189⟩⟩,⟨⟨(-187420541090973603052311496),(-187420541090973602620577961)⟩,⟨108207299850538926226170342,108207299850538926654743340⟩⟩,⟨⟨(-1929574309403923048425427637),(-1929574309403923047416002052)⟩,⟨(-636109520),299611756⟩⟩] +lemma ha37_0_12_eq (j : Fin 7) : ha37_0_12 j = ((ha37_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha37_0_12_contains (j : Fin 7) : (ha37_0_12 j).Contains (fullFactor false 37 12 ((j.val:ℝ)/6)) := by + rw [ha37_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_11 j) false 37 11 j (ha37_0_11_contains j) +noncomputable def hk37_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_13 j i k) +lemma hk37_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_13 j i k).Contains (fullFactor false 37 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 13 (power37_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha37_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-17851379306351119),(-17851379306351118)⟩,⟨30919495943783799,30919495943783800⟩⟩,⟨⟨(-253292510771476882377),(-253292510771476882198)⟩,⟨146238499277628361419,146238499277628361593⟩⟩,⟨⟨(-56921729219679268126366),(-56921729219679268110249)⟩,⟨(-9362),4399⟩⟩,⟨⟨(-2074972248239938621505248),(-2074972248239938617686010)⟩,⟨(-1197985786082331539527840),(-1197985786082331535743388)⟩⟩,⟨⟨(-21791234504823142556025080),(-21791234504823142469647909)⟩,⟨(-37743525322001707939225975),(-37743525322001707852161544)⟩⟩,⟨⟨(-72404469),153722846⟩,⟨(-466302805767612564547887711),(-466302805767612564302464652)⟩⟩] +lemma ha37_0_13_eq (j : Fin 7) : ha37_0_13 j = ((ha37_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha37_0_13_contains (j : Fin 7) : (ha37_0_13 j).Contains (fullFactor false 37 13 ((j.val:ℝ)/6)) := by + rw [ha37_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_12 j) false 37 12 j (ha37_0_12_contains j) +noncomputable def hk37_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_14 j i k) +lemma hk37_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_14 j i k).Contains (fullFactor false 37 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 14 (power37_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha37_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1156386444162984),(-1156386444162983)⟩,⟨(-667640024824733),(-667640024824732)⟩⟩,⟨⟨(-10938614166728417765),(-10938614166728417751)⟩,⟨(-18946235501166317759),(-18946235501166317744)⟩⟩,⟨⟨(-494),1051⟩,⟨(-6386603083791852242072),(-6386603083791852240242)⟩⟩,⟨⟨179218254507678396295437,179218254507678396862161⟩,⟨(-310415122451108950310317),(-310415122451108949737971)⟩⟩,⟨⟨7058022730486958373354971,7058022730486958389658449⟩,⟨(-4074951323393142886145172),(-4074951323393142869979707)⟩⟩,⟨⟨104638104924845707091412685,104638104924845707146818565⟩,⟨(-16247525),34495326⟩⟩] +lemma ha37_0_14_eq (j : Fin 7) : ha37_0_14 j = ((ha37_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha37_0_14_contains (j : Fin 7) : (ha37_0_14 j).Contains (fullFactor false 37 14 ((j.val:ℝ)/6)) := by + rw [ha37_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_13 j) false 37 13 j (ha37_0_13_contains j) +noncomputable def hk37_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_15 j i k) +lemma hk37_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_15 j i k).Contains (fullFactor false 37 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 15 (power37_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha37_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23305033302576,23305033302577⟩,⟨(-40365501752148),(-40365501752147)⟩⟩,⟨⟨1322696761414360852,1322696761414360854⟩,⟨(-763659331258827444),(-763659331258827442)⟩⟩,⟨⟨668803510981146723158,668803510981146723353⟩,⟨(-52),111⟩⟩,⟨⟨43342127478025776379411,43342127478025776459464⟩,⟨25023588966689257626924,25023588966689257706134⟩⟩,⟨⟨711213174517105744916582,711213174517105747740253⟩,⟨1231857353275977867854833,1231857353275977870704249⟩⟩,⟨⟨(-7224685),3402874⟩,⟨21915353447830215821794274,21915353447830215833468214⟩⟩] +lemma ha37_0_15_eq (j : Fin 7) : ha37_0_15 j = ((ha37_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha37_0_15_contains (j : Fin 7) : (ha37_0_15 j).Contains (fullFactor false 37 15 ((j.val:ℝ)/6)) := by + rw [ha37_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_14 j) false 37 14 j (ha37_0_14_contains j) +noncomputable def hk37_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_16 j i k) +lemma hk37_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_16 j i k).Contains (fullFactor false 37 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 16 (power37_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha37_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1320957955864,1320957955865⟩,⟨762655431406,762655431407⟩⟩,⟨⟨49981386352667221,49981386352667222⟩,⟨86570300595549323,86570300595549325⟩⟩,⟨⟨(-11),6⟩,⟨65659631149794723613,65659631149794723633⟩⟩,⟨⟨(-3275580136008399054935),(-3275580136008399044555)⟩,⟨5673471219829920489382,5673471219829920499880⟩⟩,⟨⟨(-201562188089707223839416),(-201562188089707223372539)⟩,⟨116371983552042445442077,116371983552042445904470⟩⟩,⟨⟨(-4303069587032947008502405),(-4303069587032947006196534)⟩,⟨(-1418564),668153⟩⟩] +lemma ha37_0_16_eq (j : Fin 7) : ha37_0_16 j = ((ha37_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha37_0_16_contains (j : Fin 7) : (ha37_0_16 j).Contains (fullFactor false 37 16 ((j.val:ℝ)/6)) := by + rw [ha37_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_15 j) false 37 15 j (ha37_0_15_contains j) +noncomputable def hk37_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_17 j i k) +lemma hk37_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_17 j i k).Contains (fullFactor false 37 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 17 (power37_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha37_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23489732359),(-23489732358)⟩,⟨40685409900,40685409901⟩⟩,⟨⟨(-5332718046471331),(-5332718046471330)⟩,⟨3078846199642597,3078846199642598⟩⟩,⟨⟨(-6066935731106195669),(-6066935731106195666)⟩,⟨(-2),1⟩⟩,⟨⟨(-698970019787090239848),(-698970019787090238551)⟩,⟨(-403550529079554597395),(-403550529079554596114)⟩⟩,⟨⟨(-17921243559351411776666),(-17921243559351411705399)⟩,⟨(-31040504379613153676543),(-31040504379613153604544)⟩⟩,⟨⟨(-123475),262151⟩,⟨(-795205400147551278702789),(-795205400147551278274133)⟩⟩] +lemma ha37_0_17_eq (j : Fin 7) : ha37_0_17 j = ((ha37_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha37_0_17_contains (j : Fin 7) : (ha37_0_17 j).Contains (fullFactor false 37 17 ((j.val:ℝ)/6)) := by + rw [ha37_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_16 j) false 37 16 j (ha37_0_16_contains j) +noncomputable def hk37_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_18 j i k) +lemma hk37_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_18 j i k).Contains (fullFactor false 37 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 18 (power37_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha37_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1183490601),(-1183490600)⟩,⟨(-683288617),(-683288616)⟩⟩,⟨⟨(-179120011154260),(-179120011154259)⟩,⟨(-310244959971483),(-310244959971482)⟩⟩,⟨⟨(-1),1⟩,⟨(-529440020073462377),(-529440020073462376)⟩⟩,⟨⟨46955236204022331299,46955236204022331449⟩,⟨(-81328854786764263457),(-81328854786764263305)⟩⟩,⟨⟨4514658357533078053133,4514658357533078063620⟩,⟨(-2606539218020916340696),(-2606539218020916330322)⟩⟩,⟨⟨138789524622137721108926,138789524622137721184183⟩,⟨(-21551),45754⟩⟩] +lemma ha37_0_18_eq (j : Fin 7) : ha37_0_18 j = ((ha37_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha37_0_18_contains (j : Fin 7) : (ha37_0_18 j).Contains (fullFactor false 37 18 ((j.val:ℝ)/6)) := by + rw [ha37_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_17 j) false 37 17 j (ha37_0_17_contains j) +noncomputable def hk37_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_19 j i k) +lemma hk37_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_19 j i k).Contains (fullFactor false 37 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 19 (power37_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha37_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨18829951,18829952⟩,⟨(-32614434),(-32614433)⟩⟩,⟨⟨17099355913327,17099355913328⟩,⟨(-9872317739529),(-9872317739528)⟩⟩,⟨⟨43770654673137422,43770654673137423⟩,⟨(-1),1⟩⟩,⟨⟨8964987113086656136,8964987113086656154⟩,⟨5175937723022106872,5175937723022106890⟩⟩,⟨⟨359152827132815576764,359152827132815578196⟩,⟨622070944276038604799,622070944276038606247⟩⟩,⟨⟨(-7566),3564⟩,⟨22948428997269873104272,22948428997269873116790⟩⟩] +lemma ha37_0_19_eq (j : Fin 7) : ha37_0_19 j = ((ha37_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha37_0_19_contains (j : Fin 7) : (ha37_0_19 j).Contains (fullFactor false 37 19 ((j.val:ℝ)/6)) := by + rw [ha37_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_18 j) false 37 18 j (ha37_0_18_contains j) +noncomputable def hk37_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_20 j i k) +lemma hk37_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_20 j i k).Contains (fullFactor false 37 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 20 (power37_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha37_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨853843,853844⟩,⟨492966,492967⟩⟩,⟨⟨516913348073,516913348074⟩,⟨895320181973,895320181974⟩⟩,⟨⟨(-1),1⟩,⟨3437739179098606,3437739179098608⟩⟩,⟨⟨(-542022930869484435),(-542022930869484432)⟩,⟨938811255133340261,938811255133340264⟩⟩,⟨⟨(-81428896189552855255),(-81428896189552855064)⟩,⟨47012995134852432507,47012995134852432696⟩⟩,⟨⟨(-3604730797462500934903),(-3604730797462500932924)⟩,⟨(-1189),560⟩⟩] +lemma ha37_0_20_eq (j : Fin 7) : ha37_0_20 j = ((ha37_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha37_0_20_contains (j : Fin 7) : (ha37_0_20 j).Contains (fullFactor false 37 20 ((j.val:ℝ)/6)) := by + rw [ha37_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_19 j) false 37 19 j (ha37_0_19_contains j) +noncomputable def hk37_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_21 j i k) +lemma hk37_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_21 j i k).Contains (fullFactor false 37 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 21 (power37_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha37_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-12292),(-12291)⟩,⟨21289,21290⟩⟩,⟨⟨(-44646528672),(-44646528671)⟩,⟨25776685346,25776685347⟩⟩,⟨⟨(-257142289286048),(-257142289286047)⟩,⟨(-1),1⟩⟩,⟨⟨(-93630556896327456),(-93630556896327454)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨(-5860939688051789423),(-5860939688051789398)⟩,⟨(-10151445319802585628),(-10151445319802585603)⟩⟩,⟨⟨(-84),178⟩,⟨(-539266466260812849093),(-539266466260812848794)⟩⟩] +lemma ha37_0_21_eq (j : Fin 7) : ha37_0_21 j = ((ha37_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha37_0_21_contains (j : Fin 7) : (ha37_0_21 j).Contains (fullFactor false 37 21 ((j.val:ℝ)/6)) := by + rw [ha37_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_20 j) false 37 20 j (ha37_0_20_contains j) +noncomputable def hk37_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_22 j i k) +lemma hk37_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_22 j i k).Contains (fullFactor false 37 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 22 (power37_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha37_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-507),(-506)⟩,⟨(-293),(-292)⟩⟩,⟨⟨(-1226967354),(-1226967353)⟩,⟨(-2125169796),(-2125169795)⟩⟩,⟨⟨(-1),1⟩,⟨(-18359916521553),(-18359916521552)⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨1208019168182208036,1208019168182208040⟩,⟨(-697450191936225612),(-697450191936225608)⟩⟩,⟨⟨77007071306013533777,77007071306013533821⟩,⟨(-12),26⟩⟩] +lemma ha37_0_22_eq (j : Fin 7) : ha37_0_22 j = ((ha37_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha37_0_22_contains (j : Fin 7) : (ha37_0_22 j).Contains (fullFactor false 37 22 ((j.val:ℝ)/6)) := by + rw [ha37_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_21 j) false 37 21 j (ha37_0_21_contains j) +noncomputable def hk37_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_23 j i k) +lemma hk37_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_23 j i k).Contains (fullFactor false 37 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 23 (power37_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha37_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨6,7⟩,⟨(-12),(-11)⟩⟩,⟨⟨96759678,96759679⟩,⟨(-55864227),(-55864226)⟩⟩,⟨⟨1253899540535,1253899540536⟩,⟨(-1),1⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨79387840551870928,79387840551870929⟩,⟨137503773339017306,137503773339017308⟩⟩,⟨⟨(-4),2⟩,⟨10518471716932064452,10518471716932064459⟩⟩] +lemma ha37_0_23_eq (j : Fin 7) : ha37_0_23 j = ((ha37_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha37_0_23_contains (j : Fin 7) : (ha37_0_23 j).Contains (fullFactor false 37 23 ((j.val:ℝ)/6)) := by + rw [ha37_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_22 j) false 37 22 j (ha37_0_22_contains j) +noncomputable def hk37_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_24 j i k) +lemma hk37_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_24 j i k).Contains (fullFactor false 37 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 24 (power37_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha37_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨2437536,2437537⟩,⟨4221937,4221938⟩⟩,⟨⟨(-1),1⟩,⟨82067533018,82067533019⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-14999334866761558),(-14999334866761557)⟩,⟨8659870022990124,8659870022990125⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha37_0_24_eq (j : Fin 7) : ha37_0_24 j = ((ha37_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha37_0_24_contains (j : Fin 7) : (ha37_0_24 j).Contains (fullFactor false 37 24 ((j.val:ℝ)/6)) := by + rw [ha37_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_23 j) false 37 23 j (ha37_0_23_contains j) +noncomputable def hk37_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_25 j i k) +lemma hk37_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_25 j i k).Contains (fullFactor false 37 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 25 (power37_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha37_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-176849),(-176848)⟩,⟨102103,102104⟩⟩,⟨⟨(-5156455177),(-5156455176)⟩,⟨(-1),1⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨(-906859468175609),(-906859468175608)⟩,⟨(-1570726674205046),(-1570726674205044)⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha37_0_25_eq (j : Fin 7) : ha37_0_25 j = ((ha37_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha37_0_25_contains (j : Fin 7) : (ha37_0_25 j).Contains (fullFactor false 37 25 ((j.val:ℝ)/6)) := by + rw [ha37_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_24 j) false 37 24 j (ha37_0_24_contains j) +noncomputable def hk37_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_26 j i k) +lemma hk37_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_26 j i k).Contains (fullFactor false 37 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 26 (power37_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha37_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-4113),(-4112)⟩,⟨(-7123),(-7122)⟩⟩,⟨⟨(-1),1⟩,⟨(-311528495),(-311528494)⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨158159723733336,158159723733337⟩,⟨(-91313559072399),(-91313559072398)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha37_0_26_eq (j : Fin 7) : ha37_0_26 j = ((ha37_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha37_0_26_contains (j : Fin 7) : (ha37_0_26 j).Contains (fullFactor false 37 26 ((j.val:ℝ)/6)) := by + rw [ha37_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_25 j) false 37 25 j (ha37_0_25_contains j) +noncomputable def hk37_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_27 j i k) +lemma hk37_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_27 j i k).Contains (fullFactor false 37 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 27 (power37_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha37_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨276,277⟩,⟨(-160),(-159)⟩⟩,⟨⟨18123993,18123994⟩,⟨(-1),1⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨8854012541820,8854012541821⟩,⟨15335599573285,15335599573286⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha37_0_27_eq (j : Fin 7) : ha37_0_27 j = ((ha37_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha37_0_27_contains (j : Fin 7) : (ha37_0_27 j).Contains (fullFactor false 37 27 ((j.val:ℝ)/6)) := by + rw [ha37_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_26 j) false 37 26 j (ha37_0_26_contains j) +noncomputable def hk37_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_28 j i k) +lemma hk37_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_28 j i k).Contains (fullFactor false 37 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 28 (power37_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha37_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨5,6⟩,⟨10,11⟩⟩,⟨⟨(-1),1⟩,⟨1016753,1016754⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-1433875207079),(-1433875207078)⟩,⟨827848236790,827848236791⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha37_0_28_eq (j : Fin 7) : ha37_0_28 j = ((ha37_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha37_0_28_contains (j : Fin 7) : (ha37_0_28 j).Contains (fullFactor false 37 28 ((j.val:ℝ)/6)) := by + rw [ha37_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_27 j) false 37 27 j (ha37_0_27_contains j) +noncomputable def hk37_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_29 j i k) +lemma hk37_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_29 j i k).Contains (fullFactor false 37 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 29 (power37_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha37_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-55073),(-55072)⟩,⟨(-1),1⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨(-74734538477),(-74734538476)⟩,⟨(-129444017722),(-129444017721)⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha37_0_29_eq (j : Fin 7) : ha37_0_29 j = ((ha37_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha37_0_29_contains (j : Fin 7) : (ha37_0_29 j).Contains (fullFactor false 37 29 ((j.val:ℝ)/6)) := by + rw [ha37_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_28 j) false 37 28 j (ha37_0_28_contains j) +noncomputable def hk37_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power37 j i k).conj.mul (mpower0_30 j i k) +lemma hk37_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk37_0_30 j i k).Contains (fullFactor false 37 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power37 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 30 (power37_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha37_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨(-2884),(-2883)⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨11296121531,11296121532⟩,⟨(-6521818807),(-6521818806)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha37_0_30_eq (j : Fin 7) : ha37_0_30 j = ((ha37_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha37_0_30_contains (j : Fin 7) : (ha37_0_30 j).Contains (fullFactor false 37 30 ((j.val:ℝ)/6)) := by + rw [ha37_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_0_29 j) false 37 29 j (ha37_0_29_contains j) +noncomputable def hk37_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_0 j i k) +lemma hk37_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_0 j i k).Contains (fullFactor true 37 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 0 (kernel37_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha37_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨0,3⟩,⟨(-2),2⟩⟩,⟨⟨640417,640420⟩,⟨(-172576),(-172573)⟩⟩,⟨⟨4344109497548861007,4344109497548861053⟩,⟨4160151813898398136,4160151813898398182⟩⟩,⟨⟨918146183807522803526732868,918146183807522811268423752⟩,⟨(-467290594442411598540061168),(-467290594442411590816352397)⟩⟩] +lemma ha37_1_0_eq (j : Fin 7) : ha37_1_0 j = atomKernel37_0 j := by fin_cases j <;> decide +kernel +lemma ha37_1_0_contains (j : Fin 7) : (ha37_1_0 j).Contains (fullFactor true 37 0 ((j.val:ℝ)/6)) := by + rw [ha37_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel37_0_contains j +noncomputable def hk37_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_1 j i k) +lemma hk37_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_1 j i k).Contains (fullFactor true 37 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 1 (kernel37_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha37_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-19),11⟩,⟨(-21),6⟩⟩,⟨⟨(-1767764),(-1767745)⟩,⟨(-2697224),(-2697205)⟩⟩,⟨⟨13935873524237933494,13935873524237933716⟩,⟨(-20676989198405546918),(-20676989198405546696)⟩⟩,⟨⟨(-1859801892531483976917095203),(-1859801892531483947566978519)⟩,⟨(-3227705054763723539994758263),(-3227705054763723510578171492)⟩⟩] +lemma ha37_1_1_eq (j : Fin 7) : ha37_1_1 j = ((ha37_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha37_1_1_contains (j : Fin 7) : (ha37_1_1 j).Contains (fullFactor true 37 1 ((j.val:ℝ)/6)) := by + rw [ha37_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_0 j) true 37 0 j (ha37_1_0_contains j) +noncomputable def hk37_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_2 j i k) +lemma hk37_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_2 j i k).Contains (fullFactor true 37 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 2 (kernel37_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha37_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-262),262⟩,⟨(-262),262⟩⟩,⟨⟨(-132),179⟩,⟨(-128),182⟩⟩,⟨⟨(-70),43⟩,⟨(-37),79⟩⟩,⟨⟨(-4891191),(-4891132)⟩,⟨6127094,6127154⟩⟩,⟨⟨(-47143363989244490672),(-47143363989244490139)⟩,⟨(-21184630629088004693),(-21184630629088004160)⟩⟩,⟨⟨(-5653052879275558233852965209),(-5653052879275558177966244052)⟩,⟨3660935032232944014075610826,3660935032232944069841107317⟩⟩] +lemma ha37_1_2_eq (j : Fin 7) : ha37_1_2 j = ((ha37_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha37_1_2_contains (j : Fin 7) : (ha37_1_2 j).Contains (fullFactor true 37 2 ((j.val:ℝ)/6)) := by + rw [ha37_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_1 j) true 37 1 j (ha37_1_1_contains j) +noncomputable def hk37_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_3 j i k) +lemma hk37_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_3 j i k).Contains (fullFactor true 37 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 3 (kernel37_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha37_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-995),995⟩,⟨(-995),995⟩⟩,⟨⟨(-514),530⟩,⟨(-606),437⟩⟩,⟨⟨(-104),201⟩,⟨(-148),155⟩⟩,⟨⟨11906305,11906428⟩,⟨4437384,4437507⟩⟩,⟨⟨(-17780726288434282856),(-17780726288434282003)⟩,⟨69171680068521329164,69171680068521330016⟩⟩,⟨⟨4760408142191049565667575376,4760408142191049636304293880⟩,⟨6575298364963613156734701198,6575298364963613227516982995⟩⟩] +lemma ha37_1_3_eq (j : Fin 7) : ha37_1_3 j = ((ha37_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha37_1_3_contains (j : Fin 7) : (ha37_1_3 j).Contains (fullFactor true 37 3 ((j.val:ℝ)/6)) := by + rw [ha37_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_2 j) true 37 2 j (ha37_1_2_contains j) +noncomputable def hk37_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_4 j i k) +lemma hk37_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_4 j i k).Contains (fullFactor true 37 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 4 (kernel37_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha37_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2832),2832⟩,⟨(-2832),2832⟩⟩,⟨⟨(-1433),1196⟩,⟨(-1221),1408⟩⟩,⟨⟨(-332),272⟩,⟨(-367),238⟩⟩,⟨⟨614545,614735⟩,⟨(-15432994),(-15432804)⟩⟩,⟨⟨73777461411469450171,73777461411469451192⟩,⟨5980391993766767191,5980391993766768213⟩⟩,⟨⟨5712423951050474562510354708,5712423951050474629745049618⟩,⟨(-4606155895862078175145584391),(-4606155895862078108040408476)⟩⟩] +lemma ha37_1_4_eq (j : Fin 7) : ha37_1_4 j = ((ha37_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha37_1_4_contains (j : Fin 7) : (ha37_1_4 j).Contains (fullFactor true 37 4 ((j.val:ℝ)/6)) := by + rw [ha37_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_3 j) true 37 3 j (ha37_1_3_contains j) +noncomputable def hk37_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_5 j i k) +lemma hk37_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_5 j i k).Contains (fullFactor true 37 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 5 (kernel37_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha37_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-6448),6448⟩,⟨(-6448),6448⟩⟩,⟨⟨(-2436),2862⟩,⟨(-2619),2679⟩⟩,⟨⟨(-529),432⟩,⟨(-413),547⟩⟩,⟨⟨(-14446362),(-14446128)⟩,⟨4109226,4109460⟩⟩,⟨⟨(-5506033194194289397),(-5506033194194288417)⟩,⟨(-61122958207581120856),(-61122958207581119876)⟩⟩,⟨⟨(-3541117976530520963240694540),(-3541117976530520912240738465)⟩,⟨(-3952559657833703827951031511),(-3952559657833703776859989286)⟩⟩] +lemma ha37_1_5_eq (j : Fin 7) : ha37_1_5 j = ((ha37_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha37_1_5_contains (j : Fin 7) : (ha37_1_5 j).Contains (fullFactor true 37 5 ((j.val:ℝ)/6)) := by + rw [ha37_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_4 j) true 37 4 j (ha37_1_4_contains j) +noncomputable def hk37_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_6 j i k) +lemma hk37_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_6 j i k).Contains (fullFactor true 37 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 6 (kernel37_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha37_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-12235),12235⟩,⟨(-12235),12235⟩⟩,⟨⟨(-4597),4299⟩,⟨(-4655),4241⟩⟩,⟨⟨(-556),716⟩,⟨(-626),646⟩⟩,⟨⟨6812602,6812842⟩,⟨10085609,10085850⟩⟩,⟨⟨(-40971242018793126507),(-40971242018793125723)⟩,⟨10923830489994791299,10923830489994792083⟩⟩,⟨⟨(-2267978040700473717894383236),(-2267978040700473685541872423)⟩,⟨2254875767150800268330887484,2254875767150800300630682597⟩⟩] +lemma ha37_1_6_eq (j : Fin 7) : ha37_1_6 j = ((ha37_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha37_1_6_contains (j : Fin 7) : (ha37_1_6 j).Contains (fullFactor true 37 6 ((j.val:ℝ)/6)) := by + rw [ha37_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_5 j) true 37 5 j (ha37_1_5_contains j) +noncomputable def hk37_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_7 j i k) +lemma hk37_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_7 j i k).Contains (fullFactor true 37 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 7 (kernel37_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha37_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-19898),19898⟩,⟨(-19898),19898⟩⟩,⟨⟨(-6449),6354⟩,⟨(-6146),6657⟩⟩,⟨⟨(-747),697⟩,⟨(-784),659⟩⟩,⟨⟨5181645,5181857⟩,⟨(-6679845),(-6679634)⟩⟩,⟨⟨10497619079020689615,10497619079020690152⟩,⟨22812277696157862769,22812277696157863307⟩⟩,⟨⟨1224040136075421604335228910,1224040136075421621869173817⟩,⟨1109474596327746114642455815,1109474596327746132202200999⟩⟩] +lemma ha37_1_7_eq (j : Fin 7) : ha37_1_7 j = ((ha37_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha37_1_7_contains (j : Fin 7) : (ha37_1_7 j).Contains (fullFactor true 37 7 ((j.val:ℝ)/6)) := by + rw [ha37_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_6 j) true 37 6 j (ha37_1_6_contains j) +noncomputable def hk37_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_8 j i k) +lemma hk37_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_8 j i k).Contains (fullFactor true 37 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 8 (kernel37_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha37_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-28316),28316⟩,⟨(-28316),28316⟩⟩,⟨⟨(-7868),8255⟩,⟨(-8188),7935⟩⟩,⟨⟨(-748),686⟩,⟨(-679),755⟩⟩,⟨⟨(-4839147),(-4838984)⟩,⟨(-1727263),(-1727099)⟩⟩,⟨⟨10725172713320644233,10725172713320644556⟩,⟨(-7369085465573956964),(-7369085465573956641)⟩⟩,⟨⟨472062441840471498172774701,472062441840471506512098317⟩,⟨(-578546321226195164728478133),(-578546321226195156400038578)⟩⟩] +lemma ha37_1_8_eq (j : Fin 7) : ha37_1_8 j = ((ha37_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha37_1_8_contains (j : Fin 7) : (ha37_1_8 j).Contains (fullFactor true 37 8 ((j.val:ℝ)/6)) := by + rw [ha37_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_7 j) true 37 7 j (ha37_1_7_contains j) +noncomputable def hk37_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_9 j i k) +lemma hk37_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_9 j i k).Contains (fullFactor true 37 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 9 (kernel37_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha37_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-35817),35817⟩,⟨(-35817),35817⟩⟩,⟨⟨(-9202),8845⟩,⟨(-9065),8982⟩⟩,⟨⟨(-602),664⟩,⟨(-627),639⟩⟩,⟨⟨(-71906),(-71794)⟩,⟨2774802,2774914⟩⟩,⟨⟨(-4184298758307195196),(-4184298758307195023)⟩,⟨(-4291713509554320739),(-4291713509554320566)⟩⟩,⟨⟨(-241976286499405232906370225),(-241976286499405229390031672)⟩,⟨(-177332687349981139256365634),(-177332687349981135736016127)⟩⟩] +lemma ha37_1_9_eq (j : Fin 7) : ha37_1_9 j = ((ha37_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha37_1_9_contains (j : Fin 7) : (ha37_1_9 j).Contains (fullFactor true 37 9 ((j.val:ℝ)/6)) := by + rw [ha37_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_8 j) true 37 8 j (ha37_1_8_contains j) +noncomputable def hk37_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_10 j i k) +lemma hk37_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_10 j i k).Contains (fullFactor true 37 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 10 (kernel37_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha37_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-40775),40775⟩,⟨(-40775),40775⟩⟩,⟨⟨(-9024),9157⟩,⟨(-8978),9203⟩⟩,⟨⟨(-509),497⟩,⟨(-521),485⟩⟩,⟨⟨1292834,1292904⟩,⟨(-387330),(-387260)⟩⟩,⟨⟨(-1458589750693653586),(-1458589750693653502)⟩,⟨2011677458340643893,2011677458340643977⟩⟩,⟨⟨(-59491625261097004472004932),(-59491625261097003134551796)⟩,⟨90708102475415221579488621,90708102475415222915639146⟩⟩] +lemma ha37_1_10_eq (j : Fin 7) : ha37_1_10 j = ((ha37_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha37_1_10_contains (j : Fin 7) : (ha37_1_10 j).Contains (fullFactor true 37 10 ((j.val:ℝ)/6)) := by + rw [ha37_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_9 j) true 37 9 j (ha37_1_9_contains j) +noncomputable def hk37_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_11 j i k) +lemma hk37_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_11 j i k).Contains (fullFactor true 37 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 11 (kernel37_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha37_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-42199),42199⟩,⟨(-42199),42199⟩⟩,⟨⟨(-8303),8348⟩,⟨(-8407),8244⟩⟩,⟨⟨(-370),357⟩,⟨(-356),371⟩⟩,⟨⟨(-340789),(-340749)⟩,⟨(-489670),(-489630)⟩⟩,⟨⟨840508187239479960,840508187239479998⟩,⟨412903305770674694,412903305770674732⟩⟩,⟨⟨30792751087470671147001011,30792751087470671608554701⟩,⟨17981203932682540307041509,17981203932682540768969655⟩⟩] +lemma ha37_1_11_eq (j : Fin 7) : ha37_1_11 j = ((ha37_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha37_1_11_contains (j : Fin 7) : (ha37_1_11 j).Contains (fullFactor true 37 11 ((j.val:ℝ)/6)) := by + rw [ha37_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_10 j) true 37 10 j (ha37_1_10_contains j) +noncomputable def hk37_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_12 j i k) +lemma hk37_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_12 j i k).Contains (fullFactor true 37 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 12 (kernel37_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha37_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-40034),40034⟩,⟨(-40034),40034⟩⟩,⟨⟨(-7034),6945⟩,⟨(-6966),7013⟩⟩,⟨⟨(-236),246⟩,⟨(-240),242⟩⟩,⟨⟨(-145493),(-145472)⟩,⟨193018,193039⟩⟩,⟨⟨91238174116560770,91238174116560786⟩,⟨(-310377887141678088),(-310377887141678072)⟩⟩,⟨⟨4929044787969739925127639,4929044787969740071371568⟩,⟨(-9547484745733043856323969),(-9547484745733043710175228)⟩⟩] +lemma ha37_1_12_eq (j : Fin 7) : ha37_1_12 j = ((ha37_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha37_1_12_contains (j : Fin 7) : (ha37_1_12 j).Contains (fullFactor true 37 12 ((j.val:ℝ)/6)) := by + rw [ha37_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_11 j) true 37 11 j (ha37_1_11_contains j) +noncomputable def hk37_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_13 j i k) +lemma hk37_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_13 j i k).Contains (fullFactor true 37 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 13 (kernel37_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha37_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-35058),35058⟩,⟨(-35058),35058⟩⟩,⟨⟨(-5390),5443⟩,⟨(-5408),5425⟩⟩,⟨⟨(-148),147⟩,⟨(-150),145⟩⟩,⟨⟨85552,85563⟩,⟨29196,29207⟩⟩,⟨⟨(-102480389105477069),(-102480389105477062)⟩,⟨(-11856480152202294),(-11856480152202287)⟩⟩,⟨⟨(-2723212253227302121209394),(-2723212253227302078492446)⟩,⟨(-1231241987829629277978823),(-1231241987829629235240681)⟩⟩] +lemma ha37_1_13_eq (j : Fin 7) : ha37_1_13 j = ((ha37_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha37_1_13_contains (j : Fin 7) : (ha37_1_13 j).Contains (fullFactor true 37 13 ((j.val:ℝ)/6)) := by + rw [ha37_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_12 j) true 37 12 j (ha37_1_12_contains j) +noncomputable def hk37_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_14 j i k) +lemma hk37_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_14 j i k).Contains (fullFactor true 37 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 14 (kernel37_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha37_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-28508),28508⟩,⟨(-28508),28508⟩⟩,⟨⟨(-3904),3892⟩,⟨(-3911),3885⟩⟩,⟨⟨(-85),83⟩,⟨(-83),85⟩⟩,⟨⟨373,379⟩,⟨(-31398),(-31392)⟩⟩,⟨⟨1695730203433430,1695730203433433⟩,⟨30500950451928800,30500950451928803⟩⟩,⟨⟨(-281050012815584380851932),(-281050012815584369254400)⟩,⟨718913199479470975148861,718913199479470986742372⟩⟩] +lemma ha37_1_14_eq (j : Fin 7) : ha37_1_14 j = ((ha37_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha37_1_14_contains (j : Fin 7) : (ha37_1_14 j).Contains (fullFactor true 37 14 ((j.val:ℝ)/6)) := by + rw [ha37_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_13 j) true 37 13 j (ha37_1_13_contains j) +noncomputable def hk37_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_15 j i k) +lemma hk37_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_15 j i k).Contains (fullFactor true 37 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 15 (kernel37_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha37_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-21636),21636⟩,⟨(-21636),21636⟩⟩,⟨⟨(-2621),2616⟩,⟨(-2612),2625⟩⟩,⟨⟨(-44),45⟩,⟨(-45),45⟩⟩,⟨⟨(-9709),(-9706)⟩,⟨3054,3058⟩⟩,⟨⟨8227406715157239,8227406715157241⟩,⟨(-1893968861334797),(-1893968861334795)⟩⟩,⟨⟨176585865758021682215873,176585865758021685152581⟩,⟨58659078114787604239036,58659078114787607176343⟩⟩] +lemma ha37_1_15_eq (j : Fin 7) : ha37_1_15 j = ((ha37_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha37_1_15_contains (j : Fin 7) : (ha37_1_15 j).Contains (fullFactor true 37 15 ((j.val:ℝ)/6)) := by + rw [ha37_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_14 j) true 37 14 j (ha37_1_14_contains j) +noncomputable def hk37_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_16 j i k) +lemma hk37_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_16 j i k).Contains (fullFactor true 37 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 16 (kernel37_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha37_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-15395),15395⟩,⟨(-15395),15395⟩⟩,⟨⟨(-1646),1652⟩,⟨(-1650),1648⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨1801,1803⟩,⟨2512,2515⟩⟩,⟨⟨(-845751717338876),(-845751717338875)⟩,⟨(-2017341265709903),(-2017341265709901)⟩⟩,⟨⟨11166333636847733441092,11166333636847734138525⟩,⟨(-40541923196445848628153),(-40541923196445847930768)⟩⟩] +lemma ha37_1_16_eq (j : Fin 7) : ha37_1_16 j = ((ha37_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha37_1_16_contains (j : Fin 7) : (ha37_1_16 j).Contains (fullFactor true 37 16 ((j.val:ℝ)/6)) := by + rw [ha37_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_15 j) true 37 15 j (ha37_1_15_contains j) +noncomputable def hk37_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_17 j i k) +lemma hk37_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_17 j i k).Contains (fullFactor true 37 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 17 (kernel37_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha37_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-10310),10310⟩,⟨(-10310),10310⟩⟩,⟨⟨(-979),976⟩,⟨(-978),977⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨521,523⟩,⟨(-715),(-713)⟩⟩,⟨⟨(-449751122733046),(-449751122733045)⟩,⟨286821750308002,286821750308003⟩⟩,⟨⟨(-8734981190388822501974),(-8734981190388822346108)⟩,⟨(-1924072271878494437590),(-1924072271878494281733)⟩⟩] +lemma ha37_1_17_eq (j : Fin 7) : ha37_1_17 j = ((ha37_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha37_1_17_contains (j : Fin 7) : (ha37_1_17 j).Contains (fullFactor true 37 17 ((j.val:ℝ)/6)) := by + rw [ha37_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_16 j) true 37 16 j (ha37_1_16_contains j) +noncomputable def hk37_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_18 j i k) +lemma hk37_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_18 j i k).Contains (fullFactor true 37 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 18 (kernel37_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha37_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-6521),6521⟩,⟨(-6521),6521⟩⟩,⟨⟨(-547),548⟩,⟨(-547),548⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-228),(-226)⟩,⟨(-75),(-73)⟩⟩,⟨⟨82695207857506,82695207857507⟩,⟨90853137584984,90853137584986⟩⟩,⟨⟨(-294871019922530828892),(-294871019922530795996)⟩,⟨1772418557172071199870,1772418557172071232771⟩⟩] +lemma ha37_1_18_eq (j : Fin 7) : ha37_1_18 j = ((ha37_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha37_1_18_contains (j : Fin 7) : (ha37_1_18 j).Contains (fullFactor true 37 18 ((j.val:ℝ)/6)) := by + rw [ha37_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_17 j) true 37 17 j (ha37_1_17_contains j) +noncomputable def hk37_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_19 j i k) +lemma hk37_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_19 j i k).Contains (fullFactor true 37 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 19 (kernel37_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha37_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3908),3908⟩,⟨(-3908),3908⟩⟩,⟨⟨(-291),291⟩,⟨(-291),291⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨60,62⟩⟩,⟨⟨16469437454035,16469437454036⟩,⟨(-21148564604886),(-21148564604885)⟩⟩,⟨⟨339769393772241242543,339769393772241249124⟩,⟨38524944936095360899,38524944936095367477⟩⟩] +lemma ha37_1_19_eq (j : Fin 7) : ha37_1_19 j = ((ha37_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha37_1_19_contains (j : Fin 7) : (ha37_1_19 j).Contains (fullFactor true 37 19 ((j.val:ℝ)/6)) := by + rw [ha37_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_18 j) true 37 18 j (ha37_1_18_contains j) +noncomputable def hk37_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_20 j i k) +lemma hk37_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_20 j i k).Contains (fullFactor true 37 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 20 (kernel37_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha37_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2225),2225⟩,⟨(-2225),2225⟩⟩,⟨⟨(-147),147⟩,⟨(-147),147⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨13,15⟩,⟨(-5),(-4)⟩⟩,⟨⟨(-4899882747792),(-4899882747791)⟩,⟨(-2619374350485),(-2619374350484)⟩⟩,⟨⟨3765747032122580063,3765747032122581313⟩,⟨(-61707504307877733182),(-61707504307877731931)⟩⟩] +lemma ha37_1_20_eq (j : Fin 7) : ha37_1_20 j = ((ha37_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha37_1_20_contains (j : Fin 7) : (ha37_1_20 j).Contains (fullFactor true 37 20 ((j.val:ℝ)/6)) := by + rw [ha37_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_19 j) true 37 19 j (ha37_1_19_contains j) +noncomputable def hk37_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_21 j i k) +lemma hk37_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_21 j i k).Contains (fullFactor true 37 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 21 (kernel37_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha37_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1207),1207⟩,⟨(-1207),1207⟩⟩,⟨⟨(-71),71⟩,⟨(-71),71⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3),(-1)⟩,⟨(-4),(-2)⟩⟩,⟨⟨(-345233693200),(-345233693199)⟩,⟨1041062387022,1041062387024⟩⟩,⟨⟨(-10644500561137476003),(-10644500561137475775)⟩,⟨(-95770739832207450),(-95770739832207223)⟩⟩] +lemma ha37_1_21_eq (j : Fin 7) : ha37_1_21 j = ((ha37_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha37_1_21_contains (j : Fin 7) : (ha37_1_21 j).Contains (fullFactor true 37 21 ((j.val:ℝ)/6)) := by + rw [ha37_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_20 j) true 37 20 j (ha37_1_20_contains j) +noncomputable def hk37_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_22 j i k) +lemma hk37_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_22 j i k).Contains (fullFactor true 37 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 22 (kernel37_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha37_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-625),625⟩,⟨(-625),625⟩⟩,⟨⟨(-33),33⟩,⟨(-33),33⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨204372630662,204372630664⟩,⟨30779834369,30779834370⟩⟩,⟨⟨75132860765014515,75132860765014555⟩,⟨1747979631240417095,1747979631240417135⟩⟩] +lemma ha37_1_22_eq (j : Fin 7) : ha37_1_22 j = ((ha37_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha37_1_22_contains (j : Fin 7) : (ha37_1_22 j).Contains (fullFactor true 37 22 ((j.val:ℝ)/6)) := by + rw [ha37_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_21 j) true 37 21 j (ha37_1_21_contains j) +noncomputable def hk37_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_23 j i k) +lemma hk37_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_23 j i k).Contains (fullFactor true 37 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 23 (kernel37_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha37_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-310),310⟩,⟨(-310),310⟩⟩,⟨⟨(-15),15⟩,⟨(-15),15⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-791127731),(-791127730)⟩,⟨(-37243525688),(-37243525687)⟩⟩,⟨⟨273821391917617059,273821391917617066⟩,⟨(-26066552811858473),(-26066552811858465)⟩⟩] +lemma ha37_1_23_eq (j : Fin 7) : ha37_1_23 j = ((ha37_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha37_1_23_contains (j : Fin 7) : (ha37_1_23 j).Contains (fullFactor true 37 23 ((j.val:ℝ)/6)) := by + rw [ha37_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_22 j) true 37 22 j (ha37_1_22_contains j) +noncomputable def hk37_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_24 j i k) +lemma hk37_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_24 j i k).Contains (fullFactor true 37 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 24 (kernel37_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha37_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-148),148⟩,⟨(-148),148⟩⟩,⟨⟨(-7),7⟩,⟨(-7),7⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-6316401363),(-6316401362)⟩,⟨1227616404,1227616406⟩⟩,⟨⟨(-6064306754158959),(-6064306754158957)⟩,⟨(-40995065503906793),(-40995065503906791)⟩⟩] +lemma ha37_1_24_eq (j : Fin 7) : ha37_1_24 j = ((ha37_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha37_1_24_contains (j : Fin 7) : (ha37_1_24 j).Contains (fullFactor true 37 24 ((j.val:ℝ)/6)) := by + rw [ha37_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_23 j) true 37 23 j (ha37_1_23_contains j) +noncomputable def hk37_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_25 j i k) +lemma hk37_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_25 j i k).Contains (fullFactor true 37 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 25 (kernel37_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha37_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-68),68⟩,⟨(-68),68⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨378553989,378553990⟩,⟨997590121,997590122⟩⟩,⟨⟨(-5875821350805101),(-5875821350805100)⟩,⟨1183846021712508,1183846021712509⟩⟩] +lemma ha37_1_25_eq (j : Fin 7) : ha37_1_25 j = ((ha37_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha37_1_25_contains (j : Fin 7) : (ha37_1_25 j).Contains (fullFactor true 37 25 ((j.val:ℝ)/6)) := by + rw [ha37_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_24 j) true 37 24 j (ha37_1_24_contains j) +noncomputable def hk37_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_26 j i k) +lemma hk37_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_26 j i k).Contains (fullFactor true 37 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 26 (kernel37_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha37_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-30),30⟩,⟨(-30),30⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨146493595,146493596⟩,⟨(-86504341),(-86504340)⟩⟩,⟨⟨206854672796077,206854672796078⟩,⟨807517275301772,807517275301773⟩⟩] +lemma ha37_1_26_eq (j : Fin 7) : ha37_1_26 j = ((ha37_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha37_1_26_contains (j : Fin 7) : (ha37_1_26 j).Contains (fullFactor true 37 26 ((j.val:ℝ)/6)) := by + rw [ha37_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_25 j) true 37 25 j (ha37_1_25_contains j) +noncomputable def hk37_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_27 j i k) +lemma hk37_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_27 j i k).Contains (fullFactor true 37 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 27 (kernel37_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha37_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-13),13⟩,⟨(-13),13⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-16910075),(-16910074)⟩,⟨(-19909047),(-19909046)⟩⟩,⟨⟨106560152297710,106560152297711⟩,⟨(-33281030995449),(-33281030995448)⟩⟩] +lemma ha37_1_27_eq (j : Fin 7) : ha37_1_27 j = ((ha37_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha37_1_27_contains (j : Fin 7) : (ha37_1_27 j).Contains (fullFactor true 37 27 ((j.val:ℝ)/6)) := by + rw [ha37_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_26 j) true 37 26 j (ha37_1_26_contains j) +noncomputable def hk37_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_28 j i k) +lemma hk37_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_28 j i k).Contains (fullFactor true 37 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 28 (kernel37_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha37_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-6),6⟩,⟨(-6),6⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2479447),(-2479446)⟩,⟨2968024,2968026⟩⟩,⟨⟨(-5006708097030),(-5006708097029)⟩,⟨(-13519364064655),(-13519364064654)⟩⟩] +lemma ha37_1_28_eq (j : Fin 7) : ha37_1_28 j = ((ha37_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha37_1_28_contains (j : Fin 7) : (ha37_1_28 j).Contains (fullFactor true 37 28 ((j.val:ℝ)/6)) := by + rw [ha37_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_27 j) true 37 27 j (ha37_1_27_contains j) +noncomputable def hk37_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_29 j i k) +lemma hk37_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_29 j i k).Contains (fullFactor true 37 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 29 (kernel37_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha37_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨478329,478330⟩,⟨277202,277203⟩⟩,⟨⟨(-1650987906586),(-1650987906585)⟩,⟨710963091053,710963091054⟩⟩] +lemma ha37_1_29_eq (j : Fin 7) : ha37_1_29 j = ((ha37_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha37_1_29_contains (j : Fin 7) : (ha37_1_29 j).Contains (fullFactor true 37 29 ((j.val:ℝ)/6)) := by + rw [ha37_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_28 j) true 37 28 j (ha37_1_28_contains j) +noncomputable def hk37_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel37_0 j i k).mul (mpower1_30 j i k) +lemma hk37_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk37_1_30 j i k).Contains (fullFactor true 37 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk37_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel37_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 37 30 (kernel37_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha37_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨26518,26519⟩,⟨(-71646),(-71645)⟩⟩,⟨⟨95910592364,95910592365⟩,⟨194275346530,194275346531⟩⟩] +lemma ha37_1_30_eq (j : Fin 7) : ha37_1_30 j = ((ha37_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha37_1_30_contains (j : Fin 7) : (ha37_1_30 j).Contains (fullFactor true 37 30 ((j.val:ℝ)/6)) := by + rw [ha37_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha37_1_29 j) true 37 29 j (ha37_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders39.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders39.lean new file mode 100644 index 0000000000000000000000000000000000000000..cb4665ef4f8a473985a63eb80ca51e72dc2e3788 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders39.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers40 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues40 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk39_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_0 j i k) +lemma hk39_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_0 j i k).Contains (fullFactor false 39 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 0 (power39_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha39_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999533,1000000000000000000000000000623⟩,⟨(-623),623⟩⟩,⟨⟨(-212028541263),181392524018⟩,⟨999999999999999999803313554891,1000000000000000000196686445169⟩⟩,⟨⟨(-1000000000000000000537468457059),(-999999999999999999462531542959)⟩,⟨(-568086843834),506814809139⟩⟩,⟨⟨(-81446297555),173354349557⟩,⟨(-1000000000000000000127400323556),(-999999999999999999872599676483)⟩⟩,⟨⟨999999999999999998530229426155,1000000000000000001469770573755⟩,⟨(-1408511427887),1531055497378⟩⟩,⟨⟨(-1926459745886),1773279659168⟩,⟨999999999999999998150117505069,1000000000000000001849882494830⟩⟩,⟨⟨(-1000000000000000000255574713653),(-999999999999999999744425286503)⟩,⟨(-347482765733),163666661417⟩⟩] +lemma ha39_0_0_eq (j : Fin 7) : ha39_0_0 j = ((atomPoints j).direct.powBin 7 39).conj := by fin_cases j <;> decide +kernel +lemma ha39_0_0_contains (j : Fin 7) : (ha39_0_0 j).Contains (fullFactor false 39 0 ((j.val:ℝ)/6)) := by + rw [ha39_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 39) ((j.val:ℝ)/6) 39 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 39 (by norm_num)) +noncomputable def hk39_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_1 j i k) +lemma hk39_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_1 j i k).Contains (fullFactor false 39 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 1 (power39_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha39_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-523598775598298873181318115203),(-523598775598298872973681884828)⟩,⟨(-111017884598),94976903479⟩⟩,⟨⟨(-530735227041),594899151730⟩,⟨(-1047197551196597746719502318747),(-1047197551196597745590497681273)⟩⟩,⟨⟨1570796326794896619029880039787,1570796326794896619435119960275⟩,⟨(-127935545031),272304375519⟩⟩,⟨⟨(-3206635135201),2949979436232⟩,⟨2094395102393195489228386375161,2094395102393195495391613624650⟩⟩,⟨⟨(-2617993877991494370234647713138),(-2617993877991494360540352286599)⟩,⟨(-5043459820927),4642435291669⟩⟩,⟨⟨(-514173981146),1091649304076⟩,⟨(-3141592653589793239272911642856),(-3141592653589793237657088357634)⟩⟩] +lemma ha39_0_1_eq (j : Fin 7) : ha39_0_1 j = ((ha39_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha39_0_1_contains (j : Fin 7) : (ha39_0_1 j).Contains (fullFactor false 39 1 ((j.val:ℝ)/6)) := by + rw [ha39_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_0 j) false 39 0 j (ha39_0_0_contains j) +noncomputable def hk39_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_2 j i k) +lemma hk39_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_2 j i k).Contains (fullFactor false 39 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 2 (power39_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha39_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24864895186),29064414223⟩,⟨(-137077838904018869733637935985),(-137077838904018869678842565673)⟩⟩,⟨⟨548311355616075478528515615767,548311355616075479121406390848⟩,⟨(-277892315046),311488467451⟩⟩,⟨⟨(-213867356418),100480342101⟩,⟨1233700550136169827195061417401,1233700550136169827517263097505⟩⟩,⟨⟨(-2193245422464301918530392913180),(-2193245422464301912069295113034)⟩,⟨(-3357980461164),3089211241703⟩⟩,⟨⟨(-6076933586281),6601873467542⟩,⟨(-3426945972600471749006361943909),(-3426945972600471736305650597018)⟩⟩,⟨⟨4934802200544679308147730407877,4934802200544679310701567652322⟩,⟨(-807662600918),1714758716991⟩⟩] +lemma ha39_0_2_eq (j : Fin 7) : ha39_0_2 j = ((ha39_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha39_0_2_contains (j : Fin 7) : (ha39_0_2 j).Contains (fullFactor false 39 2 ((j.val:ℝ)/6)) := by + rw [ha39_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_1 j) false 39 1 j (ha39_0_1_contains j) +noncomputable def hk39_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_3 j i k) +lemma hk39_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_3 j i k).Contains (fullFactor false 39 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 3 (power39_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha39_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23924596203935046426928652228,23924596203935046436568402852⟩,⟨(-4339742892),5072697234⟩⟩,⟨⟨(-108729986781),97002717271⟩,⟨191396769631480371350204641600,191396769631480371557771799039⟩⟩,⟨⟨(-645964097506246253742590529974),(-645964097506246253571829957192)⟩,⟨(-111980685961),52611384096⟩⟩,⟨⟨(-2156676298294),2344312610598⟩,⟨(-1531174157051842973889691299946),(-1531174157051842969374120224988)⟩⟩,⟨⟨2990574525491880798422075536402,2990574525491880809515056348209⟩,⟨(-5303124975282),5761221440434⟩⟩,⟨⟨(-1795691129326),845782297875⟩,⟨5167712780049970027912271224361,5167712780049970030603092673568⟩⟩] +lemma ha39_0_3_eq (j : Fin 7) : ha39_0_3 j = ((ha39_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha39_0_3_contains (j : Fin 7) : (ha39_0_3 j).Contains (fullFactor false 39 3 ((j.val:ℝ)/6)) := by + rw [ha39_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_2 j) false 39 2 j (ha39_0_2_contains j) +noncomputable def hk39_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_4 j i k) +lemma hk39_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_4 j i k).Contains (fullFactor false 39 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 4 (power39_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha39_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-664014516),568071017⟩,⟨3131722319766024859084151200,3131722319766024860355960189⟩⟩,⟨⟨(-50107557116256397782771117143),(-50107557116256397728270665089)⟩,⟨(-28465443975),25395251997⟩⟩,⟨⟨(-20660442222),43974712545⟩,⟨(-253669507901048013671256998901),(-253669507901048013603392023656)⟩⟩,⟨⟨801720913860102362904884536362,801720913860102365271783979268⟩,⟨(-1129233069149),1227479212529⟩⟩,⟨⟨(-3770710615203),3470887179879⟩,⟨1957326449853765533691750145563,1957326449853765540958319472658⟩⟩,⟨⟨(-4058712126416768219260334933784),(-4058712126416768217134049427596)⟩,⟨(-1410332515002),664275863386⟩⟩] +lemma ha39_0_4_eq (j : Fin 7) : ha39_0_4 j = ((ha39_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha39_0_4_contains (j : Fin 7) : (ha39_0_4 j).Contains (fullFactor false 39 4 ((j.val:ℝ)/6)) := by + rw [ha39_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_3 j) false 39 3 j (ha39_0_3_contains j) +noncomputable def hk39_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_5 j i k) +lemma hk39_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_5 j i k).Contains (fullFactor false 39 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 5 (power39_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha39_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-327953194428670967642440673),(-327953194428670967508213239)⟩,⟨(-69535438),59488258⟩⟩,⟨⟨(-5318769141),5961788645⟩,⟨(-10494502221717470968134439116),(-10494502221717470956686486091)⟩⟩,⟨⟨79692626246167045110017410256,79692626246167045131591490532⟩,⟨(-6490669351),13815063388⟩⟩,⟨⟨(-514165290203),473012041898⟩,⟨335824071094959070300878062566,335824071094959071293391544002⟩⟩,⟨⟨(-1024853732589596775576911245144),(-1024853732589596771768882231925)⟩,⟨(-1974339461256),1817352277625⟩⟩,⟨⟨(-417376834475),886138053650⟩,⟨(-2550164039877345444537793417449),(-2550164039877345443193691408061)⟩⟩] +lemma ha39_0_5_eq (j : Fin 7) : ha39_0_5 j = ((ha39_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha39_0_5_contains (j : Fin 7) : (ha39_0_5 j).Contains (fullFactor false 39 5 ((j.val:ℝ)/6)) := by + rw [ha39_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_4 j) false 39 4 j (ha39_0_4_contains j) +noncomputable def hk39_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_6 j i k) +lemma hk39_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_6 j i k).Contains (fullFactor false 39 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 6 (power39_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha39_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-5191330),6068112⟩,⟨(-28619315176067161697459994),(-28619315176067161685655341)⟩⟩,⟨⟨1831636171268298347257753225,1831636171268298349261628234⟩,⟨(-928300337),1040528412⟩⟩,⟨⟨(-3616775138),1699253263⟩,⟨20863480763352960870288293954,20863480763352960876002785486⟩⟩,⟨⟨(-117224714961171094462033056849),(-117224714961171094115207356562)⟩,⟨(-179477544271),165112350655⟩⟩,⟨⟨(-792969522830),861468103775⟩,⟨(-447176799626049402262083314706),(-447176799626049400599093799439)⟩⟩,⟨⟨1335262768854589495527304322273,1335262768854589496235324762069⟩,⟨(-218537999495),463980799903⟩⟩] +lemma ha39_0_6_eq (j : Fin 7) : ha39_0_6 j = ((ha39_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha39_0_6_contains (j : Fin 7) : (ha39_0_6 j).Contains (fullFactor false 39 6 ((j.val:ℝ)/6)) := by + rw [ha39_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_5 j) false 39 5 j (ha39_0_5_contains j) +noncomputable def hk39_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_7 j i k) +lemma hk39_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_7 j i k).Contains (fullFactor false 39 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 7 (power39_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha39_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨2140719769235797027771856,2140719769235797028661658⟩,⟨(-388311),453894⟩⟩,⟨⟨(-155662687),138873406⟩,⟨274012130462182019461419291,274012130462182019762070500⟩⟩,⟨⟨(-4681754135318688101358663242),(-4681754135318688100061431854)⟩,⟨(-811602444),381311541⟩⟩,⟨⟨(-49401499794),53699555673⟩,⟨(-35073552699159298562244171329),(-35073552699159298458362521876)⟩⟩,⟨⟨167243731971546642518189651396,167243731971546643140678629035⟩,⟨(-296569908029),322188317396⟩⟩,⟨⟨(-208234096055),98079624821⟩,⟨599264529320792076731052911878,599264529320792077050719260442⟩⟩] +lemma ha39_0_7_eq (j : Fin 7) : ha39_0_7 j = ((ha39_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha39_0_7_contains (j : Fin 7) : (ha39_0_7 j).Contains (fullFactor false 39 7 ((j.val:ℝ)/6)) := by + rw [ha39_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_6 j) false 39 6 j (ha39_0_6_contains j) +noncomputable def hk39_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_8 j i k) +lemma hk39_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_8 j i k).Contains (fullFactor false 39 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 8 (power39_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha39_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-29708),25415⟩,⟨140109781258867029424588,140109781258867029483272⟩⟩,⟨⟨(-35868104002269959559940666),(-35868104002269959520471342)⟩,⟨(-20376199),18178487⟩⟩,⟨⟨(-74870346),159357768⟩,⟨(-919260274839426580376051214),(-919260274839426580118414329)⟩⟩,⟨⟨9182234624581109628680046824,9182234624581109655905427016⟩,⟨(-12933282403),14058510801⟩⟩,⟨⟨(-105435880313),97052275453⟩,⟨54730383304244933278499662765,54730383304244933482382916559⟩⟩,⟨⟨(-235330630358893204606432470700),(-235330630358893204480150708507)⟩,⟨(-81773338300),38515778601⟩⟩] +lemma ha39_0_8_eq (j : Fin 7) : ha39_0_8 j = ((ha39_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha39_0_8_contains (j : Fin 7) : (ha39_0_8 j).Contains (fullFactor false 39 8 ((j.val:ℝ)/6)) := by + rw [ha39_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_7 j) false 39 7 j (ha39_0_7_contains j) +noncomputable def hk39_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_9 j i k) +lemma hk39_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_9 j i k).Contains (fullFactor false 39 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 9 (power39_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha39_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-8151256657387584306641),(-8151256657387584303200)⟩,⟨(-1729),1479⟩⟩,⟨⟨(-2115164),2370879⟩,⟨(-4173443408582443166422011),(-4173443408582443161816261)⟩⟩,⟨⟨160441184787359821851005632,160441184787359821896482452⟩,⟨(-13067341),27813178⟩⟩,⟨⟨(-3271564019),3009711481⟩,⟨2136803025194210896857779863,2136803025194210903200215179⟩⟩,⟨⟨(-15920423158960125625226195761),(-15920423158960125565868285006)⟩,⟨(-30670054354),28231362554⟩⟩,⟨⟨(-13444543012),28544279874⟩,⟨(-82145886611128228821528014223),(-82145886611128228777185885034)⟩⟩] +lemma ha39_0_9_eq (j : Fin 7) : ha39_0_9 j = ((ha39_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha39_0_9_contains (j : Fin 7) : (ha39_0_9 j).Contains (fullFactor false 39 9 ((j.val:ℝ)/6)) := by + rw [ha39_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_8 j) false 39 8 j (ha39_0_8_contains j) +noncomputable def hk39_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_10 j i k) +lemma hk39_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_10 j i k).Contains (fullFactor false 39 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 10 (power39_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha39_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-78),91⟩,⟨(-426798800539562151546),(-426798800539562151363)⟩⟩,⟨⟨437041971752511642847647,437041971752511643331353⟩,⟨(-221500),248278⟩⟩,⟨⟨(-4368884),2052614⟩,⟨25202042373060605477630219,25202042373060605484853923⟩⟩,⟨⟨(-447530979074571923188538457),(-447530979074571921858757374)⟩,⟨(-685194766),630352499⟩⟩,⟨⟨(-7390953434),8029401454⟩,⟨(-4167957036519161643075294014),(-4167957036519161627522162297)⟩⟩,⟨⟨25806891390014060005785562316,25806891390014060019798198934⟩,⟨(-4223727756),8967449996⟩⟩] +lemma ha39_0_10_eq (j : Fin 7) : ha39_0_10 j = ((ha39_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha39_0_10_contains (j : Fin 7) : (ha39_0_10 j).Contains (fullFactor false 39 10 ((j.val:ℝ)/6)) := by + rw [ha39_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_9 j) false 39 9 j (ha39_0_9_contains j) +noncomputable def hk39_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_11 j i k) +lemma hk39_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_11 j i k).Contains (fullFactor false 39 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 11 (power39_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha39_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20315575399030665716,20315575399030665726⟩,⟨(-4),5⟩⟩,⟨⟨(-23637),21087⟩,⟨41606298417214803373635,41606298417214803419818⟩⟩,⟨⟨(-3598843235212085341009735),(-3598843235212085339966736)⟩,⟨(-623876),293113⟩⟩,⟨⟨(-120018836),130460779⟩,⟨(-85209699158455917483226323),(-85209699158455917229765365)⟩⟩,⟨⟨991971455030794222808630946,991971455030794226513425182⟩,⟨(-1759042804),1910993078⟩⟩,⟨⟨(-2561097730),1206293827⟩,⟨7370430945714350775307176674,7370430945714350779332637145⟩⟩] +lemma ha39_0_11_eq (j : Fin 7) : ha39_0_11 j = ((ha39_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha39_0_11_contains (j : Fin 7) : (ha39_0_11 j).Contains (fullFactor false 39 11 ((j.val:ℝ)/6)) := by + rw [ha39_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_10 j) false 39 10 j (ha39_0_10_contains j) +noncomputable def hk39_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_12 j i k) +lemma hk39_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_12 j i k).Contains (fullFactor false 39 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 12 (power39_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha39_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨886434200375614885,886434200375614886⟩⟩,⟨⟨(-3630834484738518573078),(-3630834484738518569035)⟩,⟨(-2063),1841⟩⟩,⟨⟨(-38369),81666⟩,⟨(-471087477881817150440283),(-471087477881817150302254)⟩⟩,⟨⟨14871898049488972044904168,14871898049488972089188790⟩,⟨(-20947239),22769702⟩⟩,⟨⟨(-416914015),383763608⟩,⟨216414599701077852503675721,216414599701077853312625310⟩⟩,⟨⟨(-1929574309403923048450717401),(-1929574309403923047390712288)⟩,⟨(-670493818),315806986⟩⟩] +lemma ha39_0_12_eq (j : Fin 7) : ha39_0_12 j = ((ha39_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha39_0_12_contains (j : Fin 7) : (ha39_0_12 j).Contains (fullFactor false 39 12 ((j.val:ℝ)/6)) := by + rw [ha39_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_11 j) false 39 11 j (ha39_0_11_contains j) +noncomputable def hk39_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_13 j i k) +lemma hk39_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_13 j i k).Contains (fullFactor false 39 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 13 (power39_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha39_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-35702758612702237),(-35702758612702236)⟩,⟨(-1),1⟩⟩,⟨⟨(-149),167⟩,⟨(-292476998555256723190),(-292476998555256722862)⟩⟩,⟨⟨56921729219679268109878,56921729219679268126738⟩,⟨(-4637),9868⟩⟩,⟨⟨(-3668366),3374754⟩,⟨2395971572164663071458891,2395971572164663078601095⟩⟩,⟨⟨(-43582469009646285112682230),(-43582469009646284949633881)⟩,⟨(-83959873),77283906⟩⟩,⟨⟨(-76318224),162032189⟩,⟨(-466302805767612564553999260),(-466302805767612564296353103)⟩⟩] +lemma ha39_0_13_eq (j : Fin 7) : ha39_0_13 j = ((ha39_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha39_0_13_contains (j : Fin 7) : (ha39_0_13 j).Contains (fullFactor false 39 13 ((j.val:ℝ)/6)) := by + rw [ha39_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_12 j) false 39 12 j (ha39_0_12_contains j) +noncomputable def hk39_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_14 j i k) +lemma hk39_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_14 j i k).Contains (fullFactor false 39 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 14 (power39_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha39_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1335280049649466),(-1335280049649465)⟩⟩,⟨⟨21877228333456835505,21877228333456835530⟩,⟨(-12),13⟩⟩,⟨⟨(-1108),521⟩,⟨6386603083791852240200,6386603083791852242114⟩⟩,⟨⟨(-358436509015356793656316),(-358436509015356792586702)⟩,⟨(-548787),504863⟩⟩,⟨⟨(-14452057),15700460⟩,⟨(-8149902646786285772408540),(-8149902646786285741892627)⟩⟩,⟨⟨104638104924845707090041257,104638104924845707148189994⟩,⟨(-17125770),36359939⟩⟩] +lemma ha39_0_14_eq (j : Fin 7) : ha39_0_14 j = ((ha39_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha39_0_14_contains (j : Fin 7) : (ha39_0_14 j).Contains (fullFactor false 39 14 ((j.val:ℝ)/6)) := by + rw [ha39_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_13 j) false 39 13 j (ha39_0_13_contains j) +noncomputable def hk39_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_15 j i k) +lemma hk39_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_15 j i k).Contains (fullFactor false 39 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 15 (power39_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha39_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨46610066605153,46610066605154⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1527318662517654885,1527318662517654888⟩⟩,⟨⟨(-668803510981146723357),(-668803510981146723154)⟩,⟨(-117),55⟩⟩,⟨⟨(-70493),76626⟩,⟨(-50047177933378515402772),(-50047177933378515253266)⟩⟩,⟨⟨1422426349034211490170574,1422426349034211495501134⟩,⟨(-2522360),2740248⟩⟩,⟨⟨(-7615208),3586813⟩,⟨21915353447830215821507043,21915353447830215833755445⟩⟩] +lemma ha39_0_15_eq (j : Fin 7) : ha39_0_15 j = ((ha39_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha39_0_15_contains (j : Fin 7) : (ha39_0_15 j).Contains (fullFactor false 39 15 ((j.val:ℝ)/6)) := by + rw [ha39_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_14 j) false 39 14 j (ha39_0_14_contains j) +noncomputable def hk39_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_16 j i k) +lemma hk39_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_16 j i k).Contains (fullFactor false 39 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 16 (power39_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha39_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1525310862813,1525310862814⟩⟩,⟨⟨(-99962772705334444),(-99962772705334443)⟩,⟨(-1),1⟩⟩,⟨⟨(-6),12⟩,⟨(-65659631149794723633),(-65659631149794723612)⟩⟩,⟨⟨6551160272016798089034,6551160272016798108626⟩,⟨(-9228),10031⟩⟩,⟨⟨(-448373),412721⟩,⟨232743967104084890939363,232743967104084891812316⟩⟩,⟨⟨(-4303069587032947008558803),(-4303069587032947006140137)⟩,⟨(-1495243),704270⟩⟩] +lemma ha39_0_16_eq (j : Fin 7) : ha39_0_16 j = ((ha39_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha39_0_16_contains (j : Fin 7) : (ha39_0_16 j).Contains (fullFactor false 39 16 ((j.val:ℝ)/6)) := by + rw [ha39_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_15 j) false 39 15 j (ha39_0_15_contains j) +noncomputable def hk39_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_17 j i k) +lemma hk39_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_17 j i k).Contains (fullFactor false 39 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 17 (power39_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha39_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-46979464717),(-46979464716)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-6157692399285196),(-6157692399285195)⟩⟩,⟨⟨6066935731106195666,6066935731106195669⟩,⟨(-1),2⟩⟩,⟨⟨(-1236),1137⟩,⟨807101058159109192219,807101058159109194636⟩⟩,⟨⟨(-35842487118702823553851),(-35842487118702823419301)⟩,⟨(-69050),63559⟩⟩,⟨⟨(-130149),276321⟩,⟨(-795205400147551278713212),(-795205400147551278263711)⟩⟩] +lemma ha39_0_17_eq (j : Fin 7) : ha39_0_17 j = ((ha39_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha39_0_17_contains (j : Fin 7) : (ha39_0_17 j).Contains (fullFactor false 39 17 ((j.val:ℝ)/6)) := by + rw [ha39_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_16 j) false 39 16 j (ha39_0_16_contains j) +noncomputable def hk39_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_18 j i k) +lemma hk39_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_18 j i k).Contains (fullFactor false 39 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 18 (power39_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha39_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1366577234),(-1366577233)⟩⟩,⟨⟨358240022308519,358240022308520⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨529440020073462376,529440020073462377⟩⟩,⟨⟨(-93910472408044662880),(-93910472408044662598)⟩,⟨(-144),133⟩⟩,⟨⟨(-9245),10043⟩,⟨(-5213078436041832681468),(-5213078436041832661881)⟩⟩,⟨⟨138789524622137721107107,138789524622137721186003⟩,⟨(-22716),48228⟩⟩] +lemma ha39_0_18_eq (j : Fin 7) : ha39_0_18 j = ((ha39_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha39_0_18_contains (j : Fin 7) : (ha39_0_18 j).Contains (fullFactor false 39 18 ((j.val:ℝ)/6)) := by + rw [ha39_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_17 j) false 39 17 j (ha39_0_17_contains j) +noncomputable def hk39_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_19 j i k) +lemma hk39_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_19 j i k).Contains (fullFactor false 39 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 19 (power39_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha39_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨37659903,37659904⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨19744635479057,19744635479058⟩⟩,⟨⟨(-43770654673137423),(-43770654673137422)⟩,⟨(-1),1⟩⟩,⟨⟨(-15),16⟩,⟨(-10351875446044213778),(-10351875446044213745)⟩⟩,⟨⟨718305654265631153699,718305654265631156402⟩,⟨(-1274),1384⟩⟩,⟨⟨(-7975),3757⟩,⟨22948428997269873103971,22948428997269873117091⟩⟩] +lemma ha39_0_19_eq (j : Fin 7) : ha39_0_19 j = ((ha39_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha39_0_19_contains (j : Fin 7) : (ha39_0_19 j).Contains (fullFactor false 39 19 ((j.val:ℝ)/6)) := by + rw [ha39_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_18 j) false 39 18 j (ha39_0_18_contains j) +noncomputable def hk39_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_20 j i k) +lemma hk39_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_20 j i k).Contains (fullFactor false 39 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 20 (power39_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha39_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨985933,985934⟩⟩,⟨⟨(-1033826696147),(-1033826696146)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-3437739179098608),(-3437739179098606)⟩⟩,⟨⟨1084045861738968865,1084045861738968869⟩,⟨(-2),2⟩⟩,⟨⟨(-182),167⟩,⟨94025990269704865037,94025990269704865392⟩⟩,⟨⟨(-3604730797462500934950),(-3604730797462500932877)⟩,⟨(-1253),591⟩⟩] +lemma ha39_0_20_eq (j : Fin 7) : ha39_0_20 j = ((ha39_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha39_0_20_contains (j : Fin 7) : (ha39_0_20 j).Contains (fullFactor false 39 20 ((j.val:ℝ)/6)) := by + rw [ha39_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_19 j) false 39 19 j (ha39_0_19_contains j) +noncomputable def hk39_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_21 j i k) +lemma hk39_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_21 j i k).Contains (fullFactor false 39 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 21 (power39_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha39_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-24583),(-24582)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-51553370694),(-51553370693)⟩⟩,⟨⟨257142289286047,257142289286048⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨(-11721879376103578846),(-11721879376103578800)⟩,⟨(-23),21⟩⟩,⟨⟨(-89),188⟩,⟨(-539266466260812849100),(-539266466260812848787)⟩⟩] +lemma ha39_0_21_eq (j : Fin 7) : ha39_0_21 j = ((ha39_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha39_0_21_contains (j : Fin 7) : (ha39_0_21 j).Contains (fullFactor false 39 21 ((j.val:ℝ)/6)) := by + rw [ha39_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_20 j) false 39 20 j (ha39_0_20_contains j) +noncomputable def hk39_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_22 j i k) +lemma hk39_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_22 j i k).Contains (fullFactor false 39 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 22 (power39_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha39_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-586),(-585)⟩⟩,⟨⟨2453934706,2453934707⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨18359916521552,18359916521553⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-3),3⟩,⟨(-1394900383872451223),(-1394900383872451216)⟩⟩,⟨⟨77007071306013533776,77007071306013533822⟩,⟨(-13),27⟩⟩] +lemma ha39_0_22_eq (j : Fin 7) : ha39_0_22 j = ((ha39_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha39_0_22_contains (j : Fin 7) : (ha39_0_22 j).Contains (fullFactor false 39 22 ((j.val:ℝ)/6)) := by + rw [ha39_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_21 j) false 39 21 j (ha39_0_21_contains j) +noncomputable def hk39_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_23 j i k) +lemma hk39_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_23 j i k).Contains (fullFactor false 39 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 23 (power39_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha39_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨13,14⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨111728452,111728453⟩⟩,⟨⟨(-1253899540536),(-1253899540535)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨158775681103741856,158775681103741858⟩,⟨(-1),1⟩⟩,⟨⟨(-4),2⟩,⟨10518471716932064452,10518471716932064459⟩⟩] +lemma ha39_0_23_eq (j : Fin 7) : ha39_0_23 j = ((ha39_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha39_0_23_contains (j : Fin 7) : (ha39_0_23 j).Contains (fullFactor false 39 23 ((j.val:ℝ)/6)) := by + rw [ha39_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_22 j) false 39 22 j (ha39_0_22_contains j) +noncomputable def hk39_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_24 j i k) +lemma hk39_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_24 j i k).Contains (fullFactor false 39 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 24 (power39_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha39_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-4875074),(-4875073)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-82067533019),(-82067533018)⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨17319740045980248,17319740045980250⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha39_0_24_eq (j : Fin 7) : ha39_0_24 j = ((ha39_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha39_0_24_contains (j : Fin 7) : (ha39_0_24 j).Contains (fullFactor false 39 24 ((j.val:ℝ)/6)) := by + rw [ha39_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_23 j) false 39 23 j (ha39_0_23_contains j) +noncomputable def hk39_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_25 j i k) +lemma hk39_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_25 j i k).Contains (fullFactor false 39 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 25 (power39_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha39_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-204207),(-204206)⟩⟩,⟨⟨5156455176,5156455177⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨(-1813718936351217),(-1813718936351216)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha39_0_25_eq (j : Fin 7) : ha39_0_25 j = ((ha39_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha39_0_25_contains (j : Fin 7) : (ha39_0_25 j).Contains (fullFactor false 39 25 ((j.val:ℝ)/6)) := by + rw [ha39_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_24 j) false 39 24 j (ha39_0_24_contains j) +noncomputable def hk39_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_26 j i k) +lemma hk39_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_26 j i k).Contains (fullFactor false 39 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 26 (power39_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha39_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨8224,8225⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨311528494,311528495⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-182627118144798),(-182627118144797)⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha39_0_26_eq (j : Fin 7) : ha39_0_26 j = ((ha39_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha39_0_26_contains (j : Fin 7) : (ha39_0_26 j).Contains (fullFactor false 39 26 ((j.val:ℝ)/6)) := by + rw [ha39_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_25 j) false 39 25 j (ha39_0_25_contains j) +noncomputable def hk39_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_27 j i k) +lemma hk39_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_27 j i k).Contains (fullFactor false 39 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 27 (power39_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha39_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨318,320⟩⟩,⟨⟨(-18123994),(-18123993)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨17708025083641,17708025083642⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha39_0_27_eq (j : Fin 7) : ha39_0_27 j = ((ha39_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha39_0_27_contains (j : Fin 7) : (ha39_0_27 j).Contains (fullFactor false 39 27 ((j.val:ℝ)/6)) := by + rw [ha39_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_26 j) false 39 26 j (ha39_0_26_contains j) +noncomputable def hk39_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_28 j i k) +lemma hk39_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_28 j i k).Contains (fullFactor false 39 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 28 (power39_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha39_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨(-12),(-11)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1016754),(-1016753)⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1655696473581,1655696473582⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha39_0_28_eq (j : Fin 7) : ha39_0_28 j = ((ha39_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha39_0_28_contains (j : Fin 7) : (ha39_0_28 j).Contains (fullFactor false 39 28 ((j.val:ℝ)/6)) := by + rw [ha39_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_27 j) false 39 27 j (ha39_0_27_contains j) +noncomputable def hk39_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_29 j i k) +lemma hk39_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_29 j i k).Contains (fullFactor false 39 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 29 (power39_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha39_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨55072,55073⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨(-149469076954),(-149469076953)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha39_0_29_eq (j : Fin 7) : ha39_0_29 j = ((ha39_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha39_0_29_contains (j : Fin 7) : (ha39_0_29 j).Contains (fullFactor false 39 29 ((j.val:ℝ)/6)) := by + rw [ha39_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_28 j) false 39 28 j (ha39_0_28_contains j) +noncomputable def hk39_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power39 j i k).conj.mul (mpower0_30 j i k) +lemma hk39_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk39_0_30 j i k).Contains (fullFactor false 39 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power39 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 30 (power39_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha39_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2883,2884⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-13043637614),(-13043637613)⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha39_0_30_eq (j : Fin 7) : ha39_0_30 j = ((ha39_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha39_0_30_contains (j : Fin 7) : (ha39_0_30 j).Contains (fullFactor false 39 30 ((j.val:ℝ)/6)) := by + rw [ha39_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_0_29 j) false 39 29 j (ha39_0_29_contains j) +noncomputable def hk39_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_0 j i k) +lemma hk39_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_0 j i k).Contains (fullFactor true 39 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 0 (kernel39_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha39_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-31926),(-31923)⟩,⟨2507,2510⟩⟩,⟨⟨635863206902312638,635863206902312662⟩,⟨(-1325938779881954263),(-1325938779881954239)⟩⟩,⟨⟨113546669637062691669758862,113546669637062697375502405⟩,⟨(-698503320922647562276889979),(-698503320922647556566360541)⟩⟩] +lemma ha39_1_0_eq (j : Fin 7) : ha39_1_0 j = atomKernel39_0 j := by fin_cases j <;> decide +kernel +lemma ha39_1_0_contains (j : Fin 7) : (ha39_1_0 j).Contains (fullFactor true 39 0 ((j.val:ℝ)/6)) := by + rw [ha39_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel39_0_contains j +noncomputable def hk39_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_1 j i k) +lemma hk39_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_1 j i k).Contains (fullFactor true 39 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 1 (kernel39_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha39_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-11),19⟩,⟨(-6),21⟩⟩,⟨⟨59957,59976⟩,⟨143680,143699⟩⟩,⟨⟨(-5864694104202136490),(-5864694104202136374)⟩,⟨(-1663824078702990933),(-1663824078702990817)⟩⟩,⟨⟨(-2543634718900661190487942318),(-2543634718900661168787588579)⟩,⟨(-278859669301624039056922852),(-278859669301624017379326452)⟩⟩] +lemma ha39_1_1_eq (j : Fin 7) : ha39_1_1 j = ((ha39_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha39_1_1_contains (j : Fin 7) : (ha39_1_1 j).Contains (fullFactor true 39 1 ((j.val:ℝ)/6)) := by + rw [ha39_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_0 j) true 39 0 j (ha39_1_0_contains j) +noncomputable def hk39_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_2 j i k) +lemma hk39_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_2 j i k).Contains (fullFactor true 39 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 2 (kernel39_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha39_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-262),262⟩,⟨(-262),262⟩⟩,⟨⟨(-179),132⟩,⟨(-182),128⟩⟩,⟨⟨(-43),70⟩,⟨(-79),37⟩⟩,⟨⟨286457,286516⟩,⟨(-247422),(-247363)⟩⟩,⟨⟨(-1333340159599476396),(-1333340159599476117)⟩,⟨12565425635076138885,12565425635076139163⟩⟩,⟨⟨(-264671352213862046843782691),(-264671352213862005664863252)⟩,⟨4618746809031149370975874286,4618746809031149412206084906⟩⟩] +lemma ha39_1_2_eq (j : Fin 7) : ha39_1_2 j = ((ha39_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha39_1_2_contains (j : Fin 7) : (ha39_1_2 j).Contains (fullFactor true 39 2 ((j.val:ℝ)/6)) := by + rw [ha39_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_1 j) true 39 1 j (ha39_1_1_contains j) +noncomputable def hk39_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_3 j i k) +lemma hk39_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_3 j i k).Contains (fullFactor true 39 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 3 (kernel39_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha39_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-995),995⟩,⟨(-995),995⟩⟩,⟨⟨(-530),514⟩,⟨(-437),606⟩⟩,⟨⟨(-201),104⟩,⟨(-155),148⟩⟩,⟨⟨(-525754),(-525632)⟩,⟨(-316286),(-316165)⟩⟩,⟨⟨17424187253085025666,17424187253085026111⟩,⟨(-1134267765100067408),(-1134267765100066961)⟩⟩,⟨⟨5576037740222818895779760385,5576037740222818948002732113⟩,⟨29485854958038499753948179,29485854958038551902577547⟩⟩] +lemma ha39_1_3_eq (j : Fin 7) : ha39_1_3 j = ((ha39_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha39_1_3_contains (j : Fin 7) : (ha39_1_3 j).Contains (fullFactor true 39 3 ((j.val:ℝ)/6)) := by + rw [ha39_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_2 j) true 39 2 j (ha39_1_2_contains j) +noncomputable def hk39_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_4 j i k) +lemma hk39_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_4 j i k).Contains (fullFactor true 39 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 4 (kernel39_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha39_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2832),2832⟩,⟨(-2832),2832⟩⟩,⟨⟨(-1196),1433⟩,⟨(-1408),1221⟩⟩,⟨⟨(-272),332⟩,⟨(-238),367⟩⟩,⟨⟨(-166180),(-165993)⟩,⟨726879,727066⟩⟩,⟨⟨(-4226440613975573151),(-4226440613975572616)⟩,⟨(-17596023164606756250),(-17596023164606755716)⟩⟩,⟨⟨(-235139279632710041730525931),(-235139279632709992200572728)⟩,⟨(-5035188532523026243567479098),(-5035188532523026193958793153)⟩⟩] +lemma ha39_1_4_eq (j : Fin 7) : ha39_1_4 j = ((ha39_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha39_1_4_contains (j : Fin 7) : (ha39_1_4 j).Contains (fullFactor true 39 4 ((j.val:ℝ)/6)) := by + rw [ha39_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_3 j) true 39 3 j (ha39_1_3_contains j) +noncomputable def hk39_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_5 j i k) +lemma hk39_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_5 j i k).Contains (fullFactor true 39 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 5 (kernel39_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha39_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-6448),6448⟩,⟨(-6448),6448⟩⟩,⟨⟨(-2862),2436⟩,⟨(-2679),2619⟩⟩,⟨⟨(-432),529⟩,⟨(-547),413⟩⟩,⟨⟨721942,722172⟩,⟨(-66976),(-66746)⟩⟩,⟨⟨(-13781652062838665666),(-13781652062838665153)⟩,⟨5931845768746299672,5931845768746300185⟩⟩,⟨⟨(-3627608801810058856332667871),(-3627608801810058818633332190)⟩,⟨358913660053250843344142840,358913660053250880979113310⟩⟩] +lemma ha39_1_5_eq (j : Fin 7) : ha39_1_5 j = ((ha39_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha39_1_5_contains (j : Fin 7) : (ha39_1_5 j).Contains (fullFactor true 39 5 ((j.val:ℝ)/6)) := by + rw [ha39_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_4 j) true 39 4 j (ha39_1_4_contains j) +noncomputable def hk39_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_6 j i k) +lemma hk39_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_6 j i k).Contains (fullFactor true 39 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 6 (kernel39_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha39_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-12235),12235⟩,⟨(-12235),12235⟩⟩,⟨⟨(-4299),4597⟩,⟨(-4241),4655⟩⟩,⟨⟨(-716),556⟩,⟨(-646),626⟩⟩,⟨⟨(-233963),(-233727)⟩,⟨(-539214),(-538978)⟩⟩,⟨⟨5656638831070983627,5656638831070984038⟩,⟨8687383287027658524,8687383287027658935⟩⟩,⟨⟨329535807301389510656101488,329535807301389534487115273⟩,⟨2171999236579299717255176066,2171999236579299741128849166⟩⟩] +lemma ha39_1_6_eq (j : Fin 7) : ha39_1_6 j = ((ha39_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha39_1_6_contains (j : Fin 7) : (ha39_1_6 j).Contains (fullFactor true 39 6 ((j.val:ℝ)/6)) := by + rw [ha39_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_5 j) true 39 5 j (ha39_1_5_contains j) +noncomputable def hk39_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_7 j i k) +lemma hk39_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_7 j i k).Contains (fullFactor true 39 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 7 (kernel39_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha39_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-19898),19898⟩,⟨(-19898),19898⟩⟩,⟨⟨(-6354),6449⟩,⟨(-6657),6146⟩⟩,⟨⟨(-697),747⟩,⟨(-659),784⟩⟩,⟨⟨(-305284),(-305076)⟩,⟨270937,271144⟩⟩,⟨⟨4500933329404715413,4500933329404715696⟩,⟨(-4175373145053176653),(-4175373145053176371)⟩⟩,⟨⟨1111609679332003332940782148,1111609679332003345899131730⟩,⟨(-228257994624846603135653625),(-228257994624846590201034060)⟩⟩] +lemma ha39_1_7_eq (j : Fin 7) : ha39_1_7 j = ((ha39_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha39_1_7_contains (j : Fin 7) : (ha39_1_7 j).Contains (fullFactor true 39 7 ((j.val:ℝ)/6)) := by + rw [ha39_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_6 j) true 39 6 j (ha39_1_6_contains j) +noncomputable def hk39_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_8 j i k) +lemma hk39_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_8 j i k).Contains (fullFactor true 39 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 8 (kernel39_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha39_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-28316),28316⟩,⟨(-28316),28316⟩⟩,⟨⟨(-8255),7868⟩,⟨(-7935),8188⟩⟩,⟨⟨(-686),748⟩,⟨(-755),679⟩⟩,⟨⟨214253,214413⟩,⟨124821,124981⟩⟩,⟨⟨(-2528458172988339448),(-2528458172988339278)⟩,⟨(-1930863595314489044),(-1930863595314488874)⟩⟩,⟨⟨(-129122029993317590974152550),(-129122029993317584831181439)⟩,⟨(-496398840950980832007197489),(-496398840950980825852868961)⟩⟩] +lemma ha39_1_8_eq (j : Fin 7) : ha39_1_8 j = ((ha39_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha39_1_8_contains (j : Fin 7) : (ha39_1_8 j).Contains (fullFactor true 39 8 ((j.val:ℝ)/6)) := by + rw [ha39_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_7 j) true 39 7 j (ha39_1_7_contains j) +noncomputable def hk39_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_9 j i k) +lemma hk39_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_9 j i k).Contains (fullFactor true 39 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 9 (kernel39_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha39_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-35817),35817⟩,⟨(-35817),35817⟩⟩,⟨⟨(-8845),9202⟩,⟨(-8982),9065⟩⟩,⟨⟨(-664),602⟩,⟨(-639),627⟩⟩,⟨⟨27973,28083⟩,⟨(-131109),(-130999)⟩⟩,⟨⟨(-678593729957289091),(-678593729957288999)⟩,⟨1298824123730242788,1298824123730242880⟩⟩,⟨⟨(-196473718173463857833440033),(-196473718173463855235361170)⟩,⟨62163720861644459994845295,62163720861644462588159564⟩⟩] +lemma ha39_1_9_eq (j : Fin 7) : ha39_1_9 j = ((ha39_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha39_1_9_contains (j : Fin 7) : (ha39_1_9 j).Contains (fullFactor true 39 9 ((j.val:ℝ)/6)) := by + rw [ha39_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_8 j) true 39 8 j (ha39_1_8_contains j) +noncomputable def hk39_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_10 j i k) +lemma hk39_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_10 j i k).Contains (fullFactor true 39 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 10 (kernel39_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha39_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-40775),40775⟩,⟨(-40775),40775⟩⟩,⟨⟨(-9157),9024⟩,⟨(-9203),8978⟩⟩,⟨⟨(-497),509⟩,⟨(-485),521⟩⟩,⟨⟨(-64828),(-64760)⟩,⟨6876,6945⟩⟩,⟨⟨578401802946355155,578401802946355200⟩,⟨185748790416667622,185748790416667667⟩⟩,⟨⟨26136734372400521050476922,26136734372400522035797652⟩,⟨69779902186290868882883274,69779902186290869869981397⟩⟩] +lemma ha39_1_10_eq (j : Fin 7) : ha39_1_10 j = ((ha39_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha39_1_10_contains (j : Fin 7) : (ha39_1_10 j).Contains (fullFactor true 39 10 ((j.val:ℝ)/6)) := by + rw [ha39_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_9 j) true 39 9 j (ha39_1_9_contains j) +noncomputable def hk39_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_11 j i k) +lemma hk39_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_11 j i k).Contains (fullFactor true 39 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 11 (kernel39_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha39_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-42199),42199⟩,⟨(-42199),42199⟩⟩,⟨⟨(-8348),8303⟩,⟨(-8244),8407⟩⟩,⟨⟨(-357),370⟩,⟨(-371),356⟩⟩,⟨⟨11809,11848⟩,⟨26242,26281⟩⟩,⟨⟨31951590399716207,31951590399716228⟩,⟨(-226706036630800385),(-226706036630800364)⟩⟩,⟨⟨22460841953669943270891336,22460841953669943611825127⟩,⟨(-9771203150799157172047983),(-9771203150799156831710557)⟩⟩] +lemma ha39_1_11_eq (j : Fin 7) : ha39_1_11 j = ((ha39_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha39_1_11_contains (j : Fin 7) : (ha39_1_11 j).Contains (fullFactor true 39 11 ((j.val:ℝ)/6)) := by + rw [ha39_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_10 j) true 39 10 j (ha39_1_10_contains j) +noncomputable def hk39_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_12 j i k) +lemma hk39_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_12 j i k).Contains (fullFactor true 39 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 12 (kernel39_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha39_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-40034),40034⟩,⟨(-40034),40034⟩⟩,⟨⟨(-6945),7034⟩,⟨(-7013),6966⟩⟩,⟨⟨(-246),236⟩,⟨(-242),240⟩⟩,⟨⟨8606,8627⟩,⟨(-7881),(-7860)⟩⟩,⟨⟨(-79055411617222979),(-79055411617222970)⟩,⟨2428208153497309,2428208153497319⟩⟩,⟨⟨(-3291801386129195433513775),(-3291801386129195325754497)⟩,⟨(-6605992796288902511727680),(-6605992796288902403786753)⟩⟩] +lemma ha39_1_12_eq (j : Fin 7) : ha39_1_12 j = ((ha39_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha39_1_12_contains (j : Fin 7) : (ha39_1_12 j).Contains (fullFactor true 39 12 ((j.val:ℝ)/6)) := by + rw [ha39_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_11 j) true 39 11 j (ha39_1_11_contains j) +noncomputable def hk39_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_13 j i k) +lemma hk39_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_13 j i k).Contains (fullFactor true 39 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 13 (kernel39_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha39_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-35058),35058⟩,⟨(-35058),35058⟩⟩,⟨⟨(-5443),5390⟩,⟨(-5425),5408⟩⟩,⟨⟨(-147),148⟩,⟨(-145),150⟩⟩,⟨⟨(-3807),(-3796)⟩,⟨(-2150),(-2139)⟩⟩,⟨⟨5046082596681710,5046082596681714⟩,⟨24711889282048924,24711889282048929⟩⟩,⟨⟨(-1787407647020143448896309),(-1787407647020143417350945)⟩,⟨1009785380242402346052595,1009785380242402377547348⟩⟩] +lemma ha39_1_13_eq (j : Fin 7) : ha39_1_13 j = ((ha39_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha39_1_13_contains (j : Fin 7) : (ha39_1_13 j).Contains (fullFactor true 39 13 ((j.val:ℝ)/6)) := by + rw [ha39_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_12 j) true 39 12 j (ha39_1_12_contains j) +noncomputable def hk39_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_14 j i k) +lemma hk39_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_14 j i k).Contains (fullFactor true 39 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 14 (kernel39_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha39_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-28508),28508⟩,⟨(-28508),28508⟩⟩,⟨⟨(-3892),3904⟩,⟨(-3885),3911⟩⟩,⟨⟨(-83),85⟩,⟨(-85),83⟩⟩,⟨⟨(-299),(-293)⟩,⟨1484,1490⟩⟩,⟨⟨6957242999795529,6957242999795531⟩,⟨(-2715674952715930),(-2715674952715928)⟩⟩,⟨⟨284427773594420328658753,284427773594420337206213⟩,⟨447483197665891762736212,447483197665891771296652⟩⟩] +lemma ha39_1_14_eq (j : Fin 7) : ha39_1_14 j = ((ha39_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha39_1_14_contains (j : Fin 7) : (ha39_1_14 j).Contains (fullFactor true 39 14 ((j.val:ℝ)/6)) := by + rw [ha39_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_13 j) true 39 13 j (ha39_1_13_contains j) +noncomputable def hk39_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_15 j i k) +lemma hk39_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_15 j i k).Contains (fullFactor true 39 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 15 (kernel39_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha39_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-21636),21636⟩,⟨(-21636),21636⟩⟩,⟨⟨(-2616),2621⟩,⟨(-2625),2612⟩⟩,⟨⟨(-45),44⟩,⟨(-45),45⟩⟩,⟨⟨486,490⟩,⟨(-61),(-57)⟩⟩,⟨⟨(-1066290494316547),(-1066290494316545)⟩,⟨(-1767315581176763),(-1767315581176761)⟩⟩,⟨⟨104164368106051801950068,104164368106051804118220⟩,⟨(-74073434496054998141675),(-74073434496054995976604)⟩⟩] +lemma ha39_1_15_eq (j : Fin 7) : ha39_1_15 j = ((ha39_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha39_1_15_contains (j : Fin 7) : (ha39_1_15 j).Contains (fullFactor true 39 15 ((j.val:ℝ)/6)) := by + rw [ha39_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_14 j) true 39 14 j (ha39_1_14_contains j) +noncomputable def hk39_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_16 j i k) +lemma hk39_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_16 j i k).Contains (fullFactor true 39 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 16 (kernel39_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha39_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-15395),15395⟩,⟨(-15395),15395⟩⟩,⟨⟨(-1652),1646⟩,⟨(-1648),1650⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-65),(-62)⟩,⟨(-137),(-134)⟩⟩,⟨⟨(-404313348527132),(-404313348527131)⟩,⟨350052599884329,350052599884331⟩⟩,⟨⟨(-17940024593863254793092),(-17940024593863254278955)⟩,⟨(-22639451768000633130989),(-22639451768000632616173)⟩⟩] +lemma ha39_1_16_eq (j : Fin 7) : ha39_1_16 j = ((ha39_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha39_1_16_contains (j : Fin 7) : (ha39_1_16 j).Contains (fullFactor true 39 16 ((j.val:ℝ)/6)) := by + rw [ha39_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_15 j) true 39 15 j (ha39_1_15_contains j) +noncomputable def hk39_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_17 j i k) +lemma hk39_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_17 j i k).Contains (fullFactor true 39 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 17 (kernel39_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha39_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-10310),10310⟩,⟨(-10310),10310⟩⟩,⟨⟨(-976),979⟩,⟨(-977),978⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-32),(-30)⟩,⟨28,30⟩⟩,⟨⟨100872260439651,100872260439652⟩,⟨82658583042147,82658583042149⟩⟩,⟨⟨(-4610764190888951481069),(-4610764190888951366019)⟩,⟨4060763631358680080783,4060763631358680195692⟩⟩] +lemma ha39_1_17_eq (j : Fin 7) : ha39_1_17 j = ((ha39_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha39_1_17_contains (j : Fin 7) : (ha39_1_17 j).Contains (fullFactor true 39 17 ((j.val:ℝ)/6)) := by + rw [ha39_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_16 j) true 39 16 j (ha39_1_16_contains j) +noncomputable def hk39_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_18 j i k) +lemma hk39_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_18 j i k).Contains (fullFactor true 39 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 18 (kernel39_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha39_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-6521),6521⟩,⟨(-6521),6521⟩⟩,⟨⟨(-548),547⟩,⟨(-548),547⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨9,11⟩,⟨5,6⟩⟩,⟨⟨14813330040205,14813330040206⟩,⟨(-26128327908729),(-26128327908727)⟩⟩,⟨⟨862738992563006689043,862738992563006713300⟩,⟨882615908016288796936,882615908016288821219⟩⟩] +lemma ha39_1_18_eq (j : Fin 7) : ha39_1_18 j = ((ha39_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha39_1_18_contains (j : Fin 7) : (ha39_1_18 j).Contains (fullFactor true 39 18 ((j.val:ℝ)/6)) := by + rw [ha39_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_17 j) true 39 17 j (ha39_1_17_contains j) +noncomputable def hk39_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_19 j i k) +lemma hk39_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_19 j i k).Contains (fullFactor true 39 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 19 (kernel39_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha39_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3908),3908⟩,⟨(-3908),3908⟩⟩,⟨⟨(-291),291⟩,⟨(-291),291⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨0,1⟩,⟨(-4),(-2)⟩⟩,⟨⟨(-6167108287377),(-6167108287375)⟩,⟨(-2216553977608),(-2216553977607)⟩⟩,⟨⟨159218401666871429126,159218401666871433982⟩,⟨(-172689721895632483532),(-172689721895632478681)⟩⟩] +lemma ha39_1_19_eq (j : Fin 7) : ha39_1_19 j = ((ha39_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha39_1_19_contains (j : Fin 7) : (ha39_1_19 j).Contains (fullFactor true 39 19 ((j.val:ℝ)/6)) := by + rw [ha39_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_18 j) true 39 18 j (ha39_1_18_contains j) +noncomputable def hk39_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_20 j i k) +lemma hk39_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_20 j i k).Contains (fullFactor true 39 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 20 (kernel39_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha39_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2225),2225⟩,⟨(-2225),2225⟩⟩,⟨⟨(-147),147⟩,⟨(-147),147⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-235587687654),(-235587687652)⟩,⟨1337779659328,1337779659329⟩⟩,⟨⟨(-32674202783299826846),(-32674202783299825924)⟩,⟨(-27125763298088933760),(-27125763298088932836)⟩⟩] +lemma ha39_1_20_eq (j : Fin 7) : ha39_1_20 j = ((ha39_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha39_1_20_contains (j : Fin 7) : (ha39_1_20 j).Contains (fullFactor true 39 20 ((j.val:ℝ)/6)) := by + rw [ha39_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_19 j) true 39 19 j (ha39_1_19_contains j) +noncomputable def hk39_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_21 j i k) +lemma hk39_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_21 j i k).Contains (fullFactor true 39 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 21 (kernel39_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha39_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1207),1207⟩,⟨(-1207),1207⟩⟩,⟨⟨(-71),71⟩,⟨(-71),71⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨268150073223,268150073224⟩,⟨963833074,963833076⟩⟩,⟨⟨(-4372213949542643887),(-4372213949542643719)⟩,⟨5860994885513578728,5860994885513578895⟩⟩] +lemma ha39_1_21_eq (j : Fin 7) : ha39_1_21 j = ((ha39_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha39_1_21_contains (j : Fin 7) : (ha39_1_21 j).Contains (fullFactor true 39 21 ((j.val:ℝ)/6)) := by + rw [ha39_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_20 j) true 39 20 j (ha39_1_20_contains j) +noncomputable def hk39_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_22 j i k) +lemma hk39_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_22 j i k).Contains (fullFactor true 39 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 22 (kernel39_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha39_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-625),625⟩,⟨(-625),625⟩⟩,⟨⟨(-33),33⟩,⟨(-33),33⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-8405541083),(-8405541082)⟩,⟨(-49825057471),(-49825057470)⟩⟩,⟨⟨999326837340372069,999326837340372099⟩,⟨667619988667869920,667619988667869950⟩⟩] +lemma ha39_1_22_eq (j : Fin 7) : ha39_1_22 j = ((ha39_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha39_1_22_contains (j : Fin 7) : (ha39_1_22 j).Contains (fullFactor true 39 22 ((j.val:ℝ)/6)) := by + rw [ha39_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_21 j) true 39 21 j (ha39_1_21_contains j) +noncomputable def hk39_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_23 j i k) +lemma hk39_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_23 j i k).Contains (fullFactor true 39 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 23 (kernel39_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha39_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-310),310⟩,⟨(-310),310⟩⟩,⟨⟨(-15),15⟩,⟨(-15),15⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-8592610652),(-8592610651)⟩,⟨3018746201,3018746202⟩⟩,⟨⟨96658530912096557,96658530912096563⟩,⟨(-162345933703980344),(-162345933703980339)⟩⟩] +lemma ha39_1_23_eq (j : Fin 7) : ha39_1_23 j = ((ha39_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha39_1_23_contains (j : Fin 7) : (ha39_1_23 j).Contains (fullFactor true 39 23 ((j.val:ℝ)/6)) := by + rw [ha39_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_22 j) true 39 22 j (ha39_1_22_contains j) +noncomputable def hk39_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_24 j i k) +lemma hk39_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_24 j i k).Contains (fullFactor true 39 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 24 (kernel39_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha39_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-148),148⟩,⟨(-148),148⟩⟩,⟨⟨(-7),7⟩,⟨(-7),7⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨766012119,766012120⟩,⟨1374051670,1374051671⟩⟩,⟨⟨(-25182720433757277),(-25182720433757275)⟩,⟨(-13273009645673625),(-13273009645673623)⟩⟩] +lemma ha39_1_24_eq (j : Fin 7) : ha39_1_24 j = ((ha39_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha39_1_24_contains (j : Fin 7) : (ha39_1_24 j).Contains (fullFactor true 39 24 ((j.val:ℝ)/6)) := by + rw [ha39_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_23 j) true 39 23 j (ha39_1_23_contains j) +noncomputable def hk39_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_25 j i k) +lemma hk39_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_25 j i k).Contains (fullFactor true 39 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 25 (kernel39_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha39_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-68),68⟩,⟨(-68),68⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨202956065,202956067⟩,⟨(-163885512),(-163885511)⟩⟩,⟨⟨(-1728021582494054),(-1728021582494052)⟩,⟨3737111069930064,3737111069930066⟩⟩] +lemma ha39_1_25_eq (j : Fin 7) : ha39_1_25 j = ((ha39_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha39_1_25_contains (j : Fin 7) : (ha39_1_25 j).Contains (fullFactor true 39 25 ((j.val:ℝ)/6)) := by + rw [ha39_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_24 j) true 39 24 j (ha39_1_24_contains j) +noncomputable def hk39_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_26 j i k) +lemma hk39_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_26 j i k).Contains (fullFactor true 39 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 26 (kernel39_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha39_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-30),30⟩,⟨(-30),30⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-31248609),(-31248607)⟩,⟨(-27450394),(-27450392)⟩⟩,⟨⟨531510838116684,531510838116685⟩,⟨213007732683243,213007732683244⟩⟩] +lemma ha39_1_26_eq (j : Fin 7) : ha39_1_26 j = ((ha39_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha39_1_26_contains (j : Fin 7) : (ha39_1_26 j).Contains (fullFactor true 39 26 ((j.val:ℝ)/6)) := by + rw [ha39_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_25 j) true 39 25 j (ha39_1_25_contains j) +noncomputable def hk39_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_27 j i k) +lemma hk39_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_27 j i k).Contains (fullFactor true 39 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 27 (kernel39_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha39_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-13),13⟩,⟨(-13),13⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3338313),(-3338312)⟩,⟨5444194,5444196⟩⟩,⟨⟨24791588754801,24791588754803⟩,⟨(-72566542690286),(-72566542690285)⟩⟩] +lemma ha39_1_27_eq (j : Fin 7) : ha39_1_27 j = ((ha39_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha39_1_27_contains (j : Fin 7) : (ha39_1_27 j).Contains (fullFactor true 39 27 ((j.val:ℝ)/6)) := by + rw [ha39_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_26 j) true 39 26 j (ha39_1_26_contains j) +noncomputable def hk39_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_28 j i k) +lemma hk39_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_28 j i k).Contains (fullFactor true 39 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 28 (kernel39_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha39_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-6),6⟩,⟨(-6),6⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨878297,878298⟩,⟨350129,350130⟩⟩,⟨⟨(-9524816962790),(-9524816962789)⟩,⟨(-2710607479371),(-2710607479370)⟩⟩] +lemma ha39_1_28_eq (j : Fin 7) : ha39_1_28 j = ((ha39_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha39_1_28_contains (j : Fin 7) : (ha39_1_28 j).Contains (fullFactor true 39 28 ((j.val:ℝ)/6)) := by + rw [ha39_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_27 j) true 39 27 j (ha39_1_27_contains j) +noncomputable def hk39_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_29 j i k) +lemma hk39_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_29 j i k).Contains (fullFactor true 39 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 29 (kernel39_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha39_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨27992,27993⟩,⟨(-132232),(-132231)⟩⟩,⟨⟨(-275847150381),(-275847150380)⟩,⟨1203563514600,1203563514601⟩⟩] +lemma ha39_1_29_eq (j : Fin 7) : ha39_1_29 j = ((ha39_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha39_1_29_contains (j : Fin 7) : (ha39_1_29 j).Contains (fullFactor true 39 29 ((j.val:ℝ)/6)) := by + rw [ha39_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_28 j) true 39 28 j (ha39_1_28_contains j) +noncomputable def hk39_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel39_0 j i k).mul (mpower1_30 j i k) +lemma hk39_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk39_1_30 j i k).Contains (fullFactor true 39 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk39_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel39_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 39 30 (kernel39_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha39_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-18665),(-18663)⟩,⟨(-708),(-707)⟩⟩,⟨⟨146596531165,146596531166⟩,⟨25669802826,25669802827⟩⟩] +lemma ha39_1_30_eq (j : Fin 7) : ha39_1_30 j = ((ha39_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha39_1_30_contains (j : Fin 7) : (ha39_1_30 j).Contains (fullFactor true 39 30 ((j.val:ℝ)/6)) := by + rw [ha39_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha39_1_29 j) true 39 29 j (ha39_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders4.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders4.lean new file mode 100644 index 0000000000000000000000000000000000000000..b99b37d052b1d72b95711eeae846a3eefccce9a5 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders4.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk4_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_0 j i k) +lemma hk4_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_0 j i k).Contains (fullFactor false 4 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 0 (power4_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha4_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999953,1000000000000000000000000000063⟩,⟨(-63),63⟩⟩,⟨⟨(-500000000000000000006323737467),(-499999999999999999996397449121)⟩,⟨866025403784438646758211576414,866025403784438646767663687290⟩⟩,⟨⟨(-500000000000000000010429447776),(-499999999999999999984128179037)⟩,⟨(-866025403784438646778618417240),(-866025403784438646751970079893)⟩⟩,⟨⟨999999999999999999986933300153,1000000000000000000013066699851⟩,⟨(-8353466415),17779933287⟩⟩,⟨⟨(-500000000000000000041705784837),(-499999999999999999969178961544)⟩,⟨866025403784438646724444465820,866025403784438646796717564422⟩⟩,⟨⟨(-500000000000000000038695735702),(-499999999999999999947698331324)⟩,⟨(-866025403784438646813275480195),(-866025403784438646722026250364)⟩⟩,⟨⟨999999999999999999973787208873,1000000000000000000026212791143⟩,⟨(-16786324247),35639258023⟩⟩] +lemma ha4_0_0_eq (j : Fin 7) : ha4_0_0 j = ((atomPoints j).direct.powBin 7 4).conj := by fin_cases j <;> decide +kernel +lemma ha4_0_0_contains (j : Fin 7) : (ha4_0_0 j).Contains (fullFactor false 4 0 ((j.val:ℝ)/6)) := by + rw [ha4_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 4) ((j.val:ℝ)/6) 4 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 4 (by norm_num)) +noncomputable def hk4_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_1 j i k) +lemma hk4_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_1 j i k).Contains (fullFactor false 4 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 1 (power4_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha4_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-453449841058554462651644650207),(-453449841058554462645252160848)⟩,⟨(-261799387799149436542477767863),(-261799387799149436536447042102)⟩⟩,⟨⟨906899682117108925283968241828,906899682117108925314761066791⟩,⟨(-523598775598298873089255025506),(-523598775598298873060045734620)⟩⟩,⟨⟨(-27928653898),13121594361⟩,⟨1570796326794896619209474875877,1570796326794896619255525124130⟩⟩,⟨⟨(-1813799364234217850667428898795),(-1813799364234217850510286972351)⟩,⟨(-1047197551196597746244015058172),(-1047197551196597746088781901339)⟩⟩,⟨⟨2267249205292772313131527842182,2267249205292772313377634645620⟩,⟨(-1308996938995747182797138532507),(-1308996938995747182554741218263)⟩⟩,⟨⟨(-111964031185),52735792936⟩,⟨3141592653589793238377650087965,3141592653589793238552349912085⟩⟩] +lemma ha4_0_1_eq (j : Fin 7) : ha4_0_1 j = ((ha4_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha4_0_1_contains (j : Fin 7) : (ha4_0_1 j).Contains (fullFactor false 4 1 ((j.val:ℝ)/6)) := by + rw [ha4_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_0 j) false 4 0 j (ha4_0_0_contains j) +noncomputable def hk4_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_2 j i k) +lemma hk4_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_2 j i k).Contains (fullFactor false 4 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 2 (power4_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha4_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨68538919452009434852408129366,68538919452009434854205135836⟩,⟨(-118712890786751174409033445074),(-118712890786751174406982020404)⟩⟩,⟨⟨274155677808037739402905137355,274155677808037739419071750927⟩,⟨474851563147004697624505798204,474851563147004697642140383124⟩⟩,⟨⟨(-1233700550136169827376209643041),(-1233700550136169827336114871821)⟩,⟨(-21935113478),10305676112⟩⟩,⟨⟨1096622711232150957578833246587,1096622711232150957744883686794⟩,⟨(-1899406252588018790608257404198),(-1899406252588018790437652765749)⟩⟩,⟨⟨1713472986300235871143313988573,1713472986300235871466065484855⟩,⟨2967822269668779360050545352772,2967822269668779360382145276832⟩⟩,⟨⟨(-4934802200544679309569711932398),(-4934802200544679309279586127110)⟩,⟨(-175872688919),82837189835⟩⟩] +lemma ha4_0_2_eq (j : Fin 7) : ha4_0_2 j = ((ha4_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha4_0_2_contains (j : Fin 7) : (ha4_0_2 j).Contains (fullFactor false 4 2 ((j.val:ℝ)/6)) := by + rw [ha4_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_1 j) false 4 1 j (ha4_0_1_contains j) +noncomputable def hk4_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_3 j i k) +lemma hk4_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_3 j i k).Contains (fullFactor false 4 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 3 (power4_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha4_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20719308087892496642231256645,20719308087892496642655249401⟩,⟨11962298101967523215730958428,11962298101967523216082672402⟩⟩,⟨⟨(-165754464703139973143338695125),(-165754464703139973136655450894)⟩,⟨95698384815740185723499368767,95698384815740185729447198903⟩⟩,⟨⟨(-5396039394),11485198560⟩,⟨(-645964097506246253668735113923),(-645964097506246253645685373220)⟩⟩,⟨⟨1326035717625119785051097098231,1326035717625119785174422507423⟩,⟨765587078525921485765105094650,765587078525921485883467110251⟩⟩,⟨⟨(-2589913510986562080468311640916),(-2589913510986562080170692166451)⟩,⟨1495287262745940401820731462464,1495287262745940402107144923445⟩⟩,⟨⟨(-86746902344),184173449159⟩,⟨(-5167712780049970029417816135356),(-5167712780049970029097547761850)⟩⟩] +lemma ha4_0_3_eq (j : Fin 7) : ha4_0_3 j = ((ha4_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha4_0_3_contains (j : Fin 7) : (ha4_0_3 j).Contains (fullFactor false 4 3 ((j.val:ℝ)/6)) := by + rw [ha4_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_2 j) false 4 2 j (ha4_0_2_contains j) +noncomputable def hk4_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_4 j i k) +lemma hk4_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_4 j i k).Contains (fullFactor false 4 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 4 (power4_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha4_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1565861159883012429889800619),(-1565861159883012429838777076)⟩,⟨2712151086516110563369561304,2712151086516110563433694872⟩⟩,⟨⟨(-25053778558128198878442537017),(-25053778558128198876805650073)⟩,⟨(-43394417384257769015488032703),(-43394417384257769013600234733)⟩⟩,⟨⟨253669507901048013632394977709,253669507901048013642254044839⟩,⟨(-2119019715),4510226928⟩⟩,⟨⟨(-400860456930051182080155485789),(-400860456930051182016905300877)⟩,⟨694310678148124304195535895276,694310678148124304262318988061⟩⟩,⟨⟨(-978663224926882768744487955190),(-978663224926882768553915601535)⟩,⟨(-1695094429072569102235336463441),(-1695094429072569102035149319760)⟩⟩,⟨⟨4058712126416768218064963443257,4058712126416768218329420917555⟩,⟨(-68130857782),144649488717⟩⟩] +lemma ha4_0_4_eq (j : Fin 7) : ha4_0_4 j = ((ha4_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha4_0_4_contains (j : Fin 7) : (ha4_0_4 j).Contains (fullFactor false 4 4 ((j.val:ℝ)/6)) := by + rw [ha4_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_3 j) false 4 3 j (ha4_0_3_contains j) +noncomputable def hk4_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_5 j i k) +lemma hk4_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_5 j i k).Contains (fullFactor false 4 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 5 (power4_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha4_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-284015797627486289491841743),(-284015797627486289484221640)⟩,⟨(-163976597214335483791042253),(-163976597214335483785177125)⟩⟩,⟨⟨9088505524079561263429591088,9088505524079561263853900183⟩,⟨(-5247251110858735481356439463),(-5247251110858735480996908143)⟩⟩,⟨⟨(-1416929579),665709677⟩,⟨79692626246167045119128956995,79692626246167045122479943790⟩⟩,⟨⟨(-290832176770545960449402935121),(-290832176770545960420503151058)⟩,⟨(-167912035547479535413909409627),(-167912035547479535386880753515)⟩⟩,⟨⟨887549367585894654601107959292,887549367585894654708750859998⟩,⟨(-512426866294798386880183601903),(-512426866294798386778769045490)⟩⟩,⟨⟨(-90885954220),42807880459⟩,⟨2550164039877345443778601934605,2550164039877345443952882890548⟩⟩] +lemma ha4_0_5_eq (j : Fin 7) : ha4_0_5 j = ((ha4_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha4_0_5_contains (j : Fin 7) : (ha4_0_5 j).Contains (fullFactor false 4 5 ((j.val:ℝ)/6)) := by + rw [ha4_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_4 j) false 4 4 j (ha4_0_4_contains j) +noncomputable def hk4_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_6 j i k) +lemma hk4_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_6 j i k).Contains (fullFactor false 4 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 6 (power4_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha4_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨14309657588033580845539084,14309657588033580846096463⟩,⟨(-24785053981387676527365456),(-24785053981387676526621582)⟩⟩,⟨⟨915818085634149174092028544,915818085634149174157693738⟩,⟨1586243454808811297692349160,1586243454808811297771454239⟩⟩,⟨⟨(-20863480763352960873617388127),(-20863480763352960872673691313)⟩,⟨(-370951297),174282386⟩⟩,⟨⟨58612357480585547140137409121,58612357480585547149758758882⟩,⟨(-101519581107763923059494738593),(-101519581107763923049083664029)⟩⟩,⟨⟨223588399813024700689771073789,223588399813024700734733225743⟩,⟨387266468459182445712280995989,387266468459182445760481779288⟩⟩,⟨⟨(-1335262768854589495929066326349),(-1335262768854589495833562757806)⟩,⟨(-47587774349),22414153795⟩⟩] +lemma ha4_0_6_eq (j : Fin 7) : ha4_0_6 j = ((ha4_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha4_0_6_contains (j : Fin 7) : (ha4_0_6 j).Contains (fullFactor false 4 6 ((j.val:ℝ)/6)) := by + rw [ha4_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_5 j) false 4 5 j (ha4_0_5_contains j) +noncomputable def hk4_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_7 j i k) +lemma hk4_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_7 j i k).Contains (fullFactor false 4 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 7 (power4_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha4_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1853917702541761442234844,1853917702541761442296388⟩,⟨1070359884617898514088741,1070359884617898514133841⟩⟩,⟨⟨(-237301465925345464616939325),(-237301465925345464604349878)⟩,⟨137006065231091009799997012,137006065231091009810256607⟩⟩,⟨⟨(-39108876),83241277⟩,⟨(-4681754135318688100823381326),(-4681754135318688100596713769)⟩⟩,⟨⟨30374587638444219468391363401,30374587638444219471603034943⟩,⟨17536776349579649253875295459,17536776349579649256809817870⟩⟩,⟨⟨(-144837320511075112687033557292),(-144837320511075112668545474982)⟩,⟨83621865985773321405038325520,83621865985773321422120307696⟩⟩,⟨⟨(-10059448700),21357343186⟩,⟨(-599264529320792076913270795905),(-599264529320792076868501376331)⟩⟩] +lemma ha4_0_7_eq (j : Fin 7) : ha4_0_7 j = ((ha4_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha4_0_7_contains (j : Fin 7) : (ha4_0_7 j).Contains (fullFactor false 4 7 ((j.val:ℝ)/6)) := by + rw [ha4_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_6 j) false 4 6 j (ha4_0_6_contains j) +noncomputable def hk4_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_8 j i k) +lemma hk4_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_8 j i k).Contains (fullFactor false 4 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 8 (power4_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha4_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-70054890629433514728743),(-70054890629433514725568)⟩,⟨121338629888859693713002,121338629888859693717417⟩⟩,⟨⟨(-17934052001134979770705430),(-17934052001134979769305366)⟩,⟨(-31062689251548081592051496),(-31062689251548081590304665)⟩⟩,⟨⟨919260274839426580223516688,919260274839426580270948856⟩,⟨(-7679010),16344387⟩⟩,⟨⟨(-4591117312290554821587776684),(-4591117312290554820804906532)⟩,⟨7952048448396308886865247732,7952048448396308887731373533⟩⟩,⟨⟨(-27365191652122466692686901722),(-27365191652122466687009730016)⟩,⟨(-47397902300335817860862089393),(-47397902300335817854661006395)⟩⟩,⟨⟨235330630358893204534126594278,235330630358893204552456584896⟩,⟨(-3950336267),8387009057⟩⟩] +lemma ha4_0_8_eq (j : Fin 7) : ha4_0_8 j = ((ha4_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha4_0_8_contains (j : Fin 7) : (ha4_0_8 j).Contains (fullFactor false 4 8 ((j.val:ℝ)/6)) := by + rw [ha4_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_7 j) false 4 7 j (ha4_0_7_contains j) +noncomputable def hk4_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_9 j i k) +lemma hk4_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_9 j i k).Contains (fullFactor false 4 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 9 (power4_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha4_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-7059195338064676366744),(-7059195338064676366463)⟩,⟨(-4075628328693792152571),(-4075628328693792152372)⟩⟩,⟨⟨3614308013089114299603439,3614308013089114299818198⟩,⟨(-2086721704291221582132985),(-2086721704291221581963437)⟩⟩,⟨⟨(-2852634),1340241⟩,⟨160441184787359821869349454,160441184787359821878138630⟩⟩,⟨⟨(-1850525702701626521545591306),(-1850525702701626521338144273)⟩,⟨(-1068401512597105450118919533),(-1068401512597105449933336547)⟩⟩,⟨⟨13787490894657571027673609727,13787490894657571029521318599⟩,⟨(-7960211579480062798503694312),(-7960211579480062796826933862)⟩⟩,⟨⟨(-2927618449),1378927489⟩,⟨82145886611128228796027023502,82145886611128228802686875744⟩⟩] +lemma ha4_0_9_eq (j : Fin 7) : ha4_0_9 j = ((ha4_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha4_0_9_contains (j : Fin 7) : (ha4_0_9 j).Contains (fullFactor false 4 9 ((j.val:ℝ)/6)) := by + rw [ha4_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_8 j) false 4 8 j (ha4_0_8_contains j) +noncomputable def hk4_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_10 j i k) +lemma hk4_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_10 j i k).Contains (fullFactor false 4 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 10 (power4_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha4_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨213399400269781075722,213399400269781075734⟩,⟨(-369618603571988403201),(-369618603571988403184)⟩⟩,⟨⟨218520985876255821534335,218520985876255821552786⟩,⟨378489450057716124858105,378489450057716124881800⟩⟩,⟨⟨(-25202042373060605481972482),(-25202042373060605480511660)⟩,⟨(-448091),210525⟩⟩,⟨⟨223765489537285961244469249,223765489537285961284049927⟩,⟨(-387573196859101311887062706),(-387573196859101311842381416)⟩⟩,⟨⟨2083978518259580817398205421,2083978518259580817843813791⟩,⟨3609556675507699249696910294,3609556675507699250192128922⟩⟩,⟨⟨(-25806891390014060013879080711),(-25806891390014060011704680535)⟩,⟨(-919738462),433202847⟩⟩] +lemma ha4_0_10_eq (j : Fin 7) : ha4_0_10 j = ((ha4_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha4_0_10_contains (j : Fin 7) : (ha4_0_10 j).Contains (fullFactor false 4 10 ((j.val:ℝ)/6)) := by + rw [ha4_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_9 j) false 4 9 j (ha4_0_9_contains j) +noncomputable def hk4_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_11 j i k) +lemma hk4_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_11 j i k).Contains (fullFactor false 4 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 11 (power4_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha4_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨17593804388058740564,17593804388058740566⟩,⟨10157787699515332860,10157787699515332861⟩⟩,⟨⟨(-36032111386744300677715),(-36032111386744300675343)⟩,⟨20803149208607401697338,20803149208607401699162⟩⟩,⟨⟨(-30063),63988⟩,⟨(-3598843235212085340598266),(-3598843235212085340378205)⟩⟩,⟨⟨73793764120052327780758291,73793764120052327789500483⟩,⟨42604849579227958674875785,42604849579227958682547545⟩⟩,⟨⟨(-859072479885680691698931359),(-859072479885680691578335087)⟩,⟨495985727515397112269949025,495985727515397112377582342⟩⟩,⟨⟨(-123722444),262676691⟩,⟨(-7370430945714350777642140934),(-7370430945714350776997672884)⟩⟩] +lemma ha4_0_11_eq (j : Fin 7) : ha4_0_11 j = ((ha4_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha4_0_11_contains (j : Fin 7) : (ha4_0_11 j).Contains (fullFactor false 4 11 ((j.val:ℝ)/6)) := by + rw [ha4_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_10 j) false 4 10 j (ha4_0_10_contains j) +noncomputable def hk4_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_12 j i k) +lemma hk4_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_12 j i k).Contains (fullFactor false 4 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 12 (power4_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha4_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-443217100187807443),(-443217100187807442)⟩,⟨767674536308627877,767674536308627878⟩⟩,⟨⟨(-1815417242369259285601),(-1815417242369259285435)⟩,⟨(-3144394900720139785068),(-3144394900720139784850)⟩⟩,⟨⟨471087477881817150356115,471087477881817150386421⟩,⟨(-3936),8377⟩⟩,⟨⟨(-7435949024744486034285501),(-7435949024744486032922855)⟩,⟨12879441513349692558338725,12879441513349692559905523⟩⟩,⟨⟨(-108207299850538926464516188),(-108207299850538926440689805)⟩,⟨(-187420541090973602842885445),(-187420541090973602815978840)⟩⟩,⟨⟨1929574309403923047833283161,1929574309403923048008146528⟩,⟨(-32390461),68768597⟩⟩] +lemma ha4_0_12_eq (j : Fin 7) : ha4_0_12 j = ((ha4_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha4_0_12_contains (j : Fin 7) : (ha4_0_12 j).Contains (fullFactor false 4 12 ((j.val:ℝ)/6)) := by + rw [ha4_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_11 j) false 4 11 j (ha4_0_11_contains j) +noncomputable def hk4_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_13 j i k) +lemma hk4_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_13 j i k).Contains (fullFactor false 4 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 13 (power4_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha4_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-30919495943783800),(-30919495943783799)⟩,⟨(-17851379306351119),(-17851379306351118)⟩⟩,⟨⟨253292510771476882274,253292510771476882293⟩,⟨(-146238499277628361520),(-146238499277628361505)⟩⟩,⟨⟨(-1013),476⟩,⟨56921729219679268116386,56921729219679268120230⟩⟩,⟨⟨(-2074972248239938619787253),(-2074972248239938619528225)⟩,⟨(-1197985786082331537639709),(-1197985786082331537416363)⟩⟩,⟨⟨37743525322001707891512183,37743525322001707897050889⟩,⟨(-21791234504823142517716348),(-21791234504823142512848728)⟩⟩,⟨⟨(-16618687),7827511⟩,⟨466302805767612564403305211,466302805767612564447047152⟩⟩] +lemma ha4_0_13_eq (j : Fin 7) : ha4_0_13 j = ((ha4_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha4_0_13_contains (j : Fin 7) : (ha4_0_13 j).Contains (fullFactor false 4 13 ((j.val:ℝ)/6)) := by + rw [ha4_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_12 j) false 4 12 j (ha4_0_12_contains j) +noncomputable def hk4_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_14 j i k) +lemma hk4_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_14 j i k).Contains (fullFactor false 4 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 14 (power4_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha4_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨667640024824732,667640024824733⟩,⟨(-1156386444162984),(-1156386444162983)⟩⟩,⟨⟨10938614166728417758,10938614166728417760⟩,⟨18946235501166317750,18946235501166317752⟩⟩,⟨⟨(-6386603083791852241383),(-6386603083791852240931)⟩,⟨(-114),54⟩⟩,⟨⟨179218254507678396545713,179218254507678396579697⟩,⟨(-310415122451108950053305),(-310415122451108950013566)⟩⟩,⟨⟨4074951323393142878058241,4074951323393142878981456⟩,⟨7058022730486958380713523,7058022730486958381771726⟩⟩,⟨⟨(-104638104924845707124189997),(-104638104924845707114041254)⟩,⟨(-3729225),1756490⟩⟩] +lemma ha4_0_14_eq (j : Fin 7) : ha4_0_14 j = ((ha4_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha4_0_14_contains (j : Fin 7) : (ha4_0_14 j).Contains (fullFactor false 4 14 ((j.val:ℝ)/6)) := by + rw [ha4_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_13 j) false 4 13 j (ha4_0_13_contains j) +noncomputable def hk4_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_15 j i k) +lemma hk4_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_15 j i k).Contains (fullFactor false 4 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 15 (power4_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha4_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨40365501752147,40365501752148⟩,⟨23305033302576,23305033302577⟩⟩,⟨⟨(-1322696761414360853),(-1322696761414360852)⟩,⟨763659331258827443,763659331258827444⟩⟩,⟨⟨(-6),12⟩,⟨(-668803510981146723281),(-668803510981146723230)⟩⟩,⟨⟨43342127478025776417891,43342127478025776423579⟩,⟨25023588966689257661869,25023588966689257666695⟩⟩,⟨⟨(-1231857353275977869327756),(-1231857353275977869139143)⟩,⟨711213174517105746326552,711213174517105746489949⟩⟩,⟨⟨(-367879),781048⟩,⟨(-21915353447830215828728898),(-21915353447830215826533590)⟩⟩] +lemma ha4_0_15_eq (j : Fin 7) : ha4_0_15 j = ((ha4_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha4_0_15_contains (j : Fin 7) : (ha4_0_15 j).Contains (fullFactor false 4 15 ((j.val:ℝ)/6)) := by + rw [ha4_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_14 j) false 4 14 j (ha4_0_14_contains j) +noncomputable def hk4_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_16 j i k) +lemma hk4_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_16 j i k).Contains (fullFactor false 4 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 16 (power4_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha4_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-762655431407),(-762655431406)⟩,⟨1320957955864,1320957955865⟩⟩,⟨⟨(-49981386352667222),(-49981386352667221)⟩,⟨(-86570300595549324),(-86570300595549323)⟩⟩,⟨⟨65659631149794723620,65659631149794723626⟩,⟨(-1),2⟩⟩,⟨⟨(-3275580136008399049772),(-3275580136008399049129)⟩,⟨5673471219829920494419,5673471219829920495183⟩⟩,⟨⟨(-116371983552042445699890),(-116371983552042445672783)⟩,⟨(-201562188089707223614188),(-201562188089707223582683)⟩⟩,⟨⟨4303069587032947007127097,4303069587032947007571843⟩,⟨(-72233),153359⟩⟩] +lemma ha4_0_16_eq (j : Fin 7) : ha4_0_16 j = ((ha4_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha4_0_16_contains (j : Fin 7) : (ha4_0_16 j).Contains (fullFactor false 4 16 ((j.val:ℝ)/6)) := by + rw [ha4_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_15 j) false 4 15 j (ha4_0_15_contains j) +noncomputable def hk4_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_17 j i k) +lemma hk4_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_17 j i k).Contains (fullFactor false 4 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 17 (power4_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha4_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-40685409901),(-40685409900)⟩,⟨(-23489732359),(-23489732358)⟩⟩,⟨⟨5332718046471330,5332718046471331⟩,⟨(-3078846199642598),(-3078846199642597)⟩⟩,⟨⟨(-1),1⟩,⟨6066935731106195666,6066935731106195668⟩⟩,⟨⟨(-698970019787090239269),(-698970019787090239172)⟩,⟨(-403550529079554596759),(-403550529079554596677)⟩⟩,⟨⟨31040504379613153636906,31040504379613153641858⟩,⟨(-17921243559351411745160),(-17921243559351411740928)⟩⟩,⟨⟨(-28341),13349⟩,⟨795205400147551278446101,795205400147551278530822⟩⟩] +lemma ha4_0_17_eq (j : Fin 7) : ha4_0_17 j = ((ha4_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha4_0_17_contains (j : Fin 7) : (ha4_0_17 j).Contains (fullFactor false 4 17 ((j.val:ℝ)/6)) := by + rw [ha4_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_16 j) false 4 16 j (ha4_0_16_contains j) +noncomputable def hk4_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_18 j i k) +lemma hk4_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_18 j i k).Contains (fullFactor false 4 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 18 (power4_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha4_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨683288616,683288617⟩,⟨(-1183490601),(-1183490600)⟩⟩,⟨⟨179120011154259,179120011154260⟩,⟨310244959971482,310244959971483⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨(-1),1⟩⟩,⟨⟨46955236204022331365,46955236204022331375⟩,⟨(-81328854786764263389),(-81328854786764263377)⟩⟩,⟨⟨2606539218020916335489,2606539218020916336114⟩,⟨4514658357533078057840,4514658357533078058575⟩⟩,⟨⟨(-138789524622137721154170),(-138789524622137721138940)⟩,⟨(-4947),2330⟩⟩] +lemma ha4_0_18_eq (j : Fin 7) : ha4_0_18 j = ((ha4_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha4_0_18_contains (j : Fin 7) : (ha4_0_18 j).Contains (fullFactor false 4 18 ((j.val:ℝ)/6)) := by + rw [ha4_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_17 j) false 4 17 j (ha4_0_17_contains j) +noncomputable def hk4_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_19 j i k) +lemma hk4_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_19 j i k).Contains (fullFactor false 4 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 19 (power4_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha4_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨32614433,32614434⟩,⟨18829951,18829952⟩⟩,⟨⟨(-17099355913328),(-17099355913327)⟩,⟨9872317739528,9872317739529⟩⟩,⟨⟨(-1),1⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨8964987113086656144,8964987113086656146⟩,⟨5175937723022106880,5175937723022106882⟩⟩,⟨⟨(-622070944276038605552),(-622070944276038605448)⟩,⟨359152827132815577476,359152827132815577564⟩⟩,⟨⟨(-386),818⟩,⟨(-22948428997269873111827),(-22948428997269873109235)⟩⟩] +lemma ha4_0_19_eq (j : Fin 7) : ha4_0_19 j = ((ha4_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha4_0_19_contains (j : Fin 7) : (ha4_0_19 j).Contains (fullFactor false 4 19 ((j.val:ℝ)/6)) := by + rw [ha4_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_18 j) false 4 18 j (ha4_0_18_contains j) +noncomputable def hk4_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_20 j i k) +lemma hk4_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_20 j i k).Contains (fullFactor false 4 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 20 (power4_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha4_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-492967),(-492966)⟩,⟨853843,853844⟩⟩,⟨⟨(-516913348074),(-516913348073)⟩,⟨(-895320181974),(-895320181973)⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨(-1),1⟩⟩,⟨⟨(-542022930869484434),(-542022930869484433)⟩,⟨938811255133340262,938811255133340263⟩⟩,⟨⟨(-47012995134852432613),(-47012995134852432600)⟩,⟨(-81428896189552855164),(-81428896189552855149)⟩⟩,⟨⟨3604730797462500933704,3604730797462500934123⟩,⟨(-61),129⟩⟩] +lemma ha4_0_20_eq (j : Fin 7) : ha4_0_20 j = ((ha4_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha4_0_20_contains (j : Fin 7) : (ha4_0_20 j).Contains (fullFactor false 4 20 ((j.val:ℝ)/6)) := by + rw [ha4_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_19 j) false 4 19 j (ha4_0_19_contains j) +noncomputable def hk4_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_21 j i k) +lemma hk4_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_21 j i k).Contains (fullFactor false 4 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 21 (power4_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha4_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-21290),(-21289)⟩,⟨(-12292),(-12291)⟩⟩,⟨⟨44646528671,44646528672⟩,⟨(-25776685347),(-25776685346)⟩⟩,⟨⟨(-1),1⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨(-93630556896327456),(-93630556896327455)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨10151445319802585614,10151445319802585617⟩,⟨(-5860939688051789413),(-5860939688051789410)⟩⟩,⟨⟨(-20),10⟩,⟨539266466260812848911,539266466260812848976⟩⟩] +lemma ha4_0_21_eq (j : Fin 7) : ha4_0_21 j = ((ha4_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha4_0_21_contains (j : Fin 7) : (ha4_0_21 j).Contains (fullFactor false 4 21 ((j.val:ℝ)/6)) := by + rw [ha4_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_20 j) false 4 20 j (ha4_0_20_contains j) +noncomputable def hk4_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_22 j i k) +lemma hk4_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_22 j i k).Contains (fullFactor false 4 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 22 (power4_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha4_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨292,293⟩,⟨(-507),(-506)⟩⟩,⟨⟨1226967353,1226967354⟩,⟨2125169795,2125169796⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨(-1),1⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨697450191936225609,697450191936225610⟩,⟨1208019168182208037,1208019168182208038⟩⟩,⟨⟨(-77007071306013533804),(-77007071306013533794)⟩,⟨(-3),2⟩⟩] +lemma ha4_0_22_eq (j : Fin 7) : ha4_0_22 j = ((ha4_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha4_0_22_contains (j : Fin 7) : (ha4_0_22 j).Contains (fullFactor false 4 22 ((j.val:ℝ)/6)) := by + rw [ha4_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_21 j) false 4 21 j (ha4_0_21_contains j) +noncomputable def hk4_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_23 j i k) +lemma hk4_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_23 j i k).Contains (fullFactor false 4 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 23 (power4_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha4_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11,12⟩,⟨6,7⟩⟩,⟨⟨(-96759679),(-96759678)⟩,⟨55864226,55864227⟩⟩,⟨⟨(-1),1⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨(-137503773339017308),(-137503773339017306)⟩,⟨79387840551870928,79387840551870929⟩⟩,⟨⟨(-1),1⟩,⟨(-10518471716932064456),(-10518471716932064454)⟩⟩] +lemma ha4_0_23_eq (j : Fin 7) : ha4_0_23 j = ((ha4_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha4_0_23_contains (j : Fin 7) : (ha4_0_23 j).Contains (fullFactor false 4 23 ((j.val:ℝ)/6)) := by + rw [ha4_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_22 j) false 4 22 j (ha4_0_22_contains j) +noncomputable def hk4_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_24 j i k) +lemma hk4_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_24 j i k).Contains (fullFactor false 4 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 24 (power4_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha4_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-2437537),(-2437536)⟩,⟨(-4221938),(-4221937)⟩⟩,⟨⟨82067533018,82067533019⟩,⟨(-1),1⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-8659870022990125),(-8659870022990124)⟩,⟨(-14999334866761558),(-14999334866761557)⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨(-1),1⟩⟩] +lemma ha4_0_24_eq (j : Fin 7) : ha4_0_24 j = ((ha4_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha4_0_24_contains (j : Fin 7) : (ha4_0_24 j).Contains (fullFactor false 4 24 ((j.val:ℝ)/6)) := by + rw [ha4_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_23 j) false 4 23 j (ha4_0_23_contains j) +noncomputable def hk4_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_25 j i k) +lemma hk4_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_25 j i k).Contains (fullFactor false 4 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 25 (power4_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha4_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨176848,176849⟩,⟨(-102104),(-102103)⟩⟩,⟨⟨(-1),1⟩,⟨5156455176,5156455177⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨1570726674205044,1570726674205046⟩,⟨(-906859468175609),(-906859468175608)⟩⟩,⟨⟨(-1),1⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha4_0_25_eq (j : Fin 7) : ha4_0_25 j = ((ha4_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha4_0_25_contains (j : Fin 7) : (ha4_0_25 j).Contains (fullFactor false 4 25 ((j.val:ℝ)/6)) := by + rw [ha4_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_24 j) false 4 24 j (ha4_0_24_contains j) +noncomputable def hk4_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_26 j i k) +lemma hk4_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_26 j i k).Contains (fullFactor false 4 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 26 (power4_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha4_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨4112,4113⟩,⟨7122,7123⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨(-1),1⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨91313559072398,91313559072399⟩,⟨158159723733336,158159723733337⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨(-1),1⟩⟩] +lemma ha4_0_26_eq (j : Fin 7) : ha4_0_26 j = ((ha4_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha4_0_26_contains (j : Fin 7) : (ha4_0_26 j).Contains (fullFactor false 4 26 ((j.val:ℝ)/6)) := by + rw [ha4_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_25 j) false 4 25 j (ha4_0_25_contains j) +noncomputable def hk4_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_27 j i k) +lemma hk4_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_27 j i k).Contains (fullFactor false 4 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 27 (power4_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha4_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-277),(-276)⟩,⟨159,160⟩⟩,⟨⟨(-1),1⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨(-15335599573286),(-15335599573285)⟩,⟨8854012541820,8854012541821⟩⟩,⟨⟨(-1),1⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha4_0_27_eq (j : Fin 7) : ha4_0_27 j = ((ha4_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha4_0_27_contains (j : Fin 7) : (ha4_0_27 j).Contains (fullFactor false 4 27 ((j.val:ℝ)/6)) := by + rw [ha4_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_26 j) false 4 26 j (ha4_0_26_contains j) +noncomputable def hk4_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_28 j i k) +lemma hk4_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_28 j i k).Contains (fullFactor false 4 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 28 (power4_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha4_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-6),(-5)⟩,⟨(-11),(-10)⟩⟩,⟨⟨1016753,1016754⟩,⟨(-1),1⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-827848236791),(-827848236790)⟩,⟨(-1433875207079),(-1433875207078)⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨(-1),1⟩⟩] +lemma ha4_0_28_eq (j : Fin 7) : ha4_0_28 j = ((ha4_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha4_0_28_contains (j : Fin 7) : (ha4_0_28 j).Contains (fullFactor false 4 28 ((j.val:ℝ)/6)) := by + rw [ha4_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_27 j) false 4 27 j (ha4_0_27_contains j) +noncomputable def hk4_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_29 j i k) +lemma hk4_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_29 j i k).Contains (fullFactor false 4 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 29 (power4_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha4_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨55072,55073⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨129444017721,129444017722⟩,⟨(-74734538477),(-74734538476)⟩⟩,⟨⟨(-1),1⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha4_0_29_eq (j : Fin 7) : ha4_0_29 j = ((ha4_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha4_0_29_contains (j : Fin 7) : (ha4_0_29 j).Contains (fullFactor false 4 29 ((j.val:ℝ)/6)) := by + rw [ha4_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_28 j) false 4 28 j (ha4_0_28_contains j) +noncomputable def hk4_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power4 j i k).conj.mul (mpower0_30 j i k) +lemma hk4_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk4_0_30 j i k).Contains (fullFactor false 4 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power4 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 30 (power4_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha4_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨(-1),1⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨6521818806,6521818807⟩,⟨11296121531,11296121532⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨(-1),1⟩⟩] +lemma ha4_0_30_eq (j : Fin 7) : ha4_0_30 j = ((ha4_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha4_0_30_contains (j : Fin 7) : (ha4_0_30 j).Contains (fullFactor false 4 30 ((j.val:ℝ)/6)) := by + rw [ha4_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_0_29 j) false 4 29 j (ha4_0_29_contains j) +noncomputable def hk4_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_0 j i k) +lemma hk4_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_0 j i k).Contains (fullFactor true 4 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 0 (kernel4_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha4_1_0 : Fin 7 → CBox := ![⟨⟨282961158716610,282961158716614⟩,⟨(-3),3⟩⟩,⟨⟨(-42706143494991529),(-42706143494991525)⟩,⟨(-120926048035417579),(-120926048035417575)⟩⟩,⟨⟨3053947772385296866737,3053947772385296871889⟩,⟨(-5402739214956985245174),(-5402739214956985240000)⟩⟩,⟨⟨16903170382964137658517564,16903170382964137671935629⟩,⟨(-13880229317351426973322715),(-13880229317351426960021447)⟩⟩,⟨⟨588535793916102761833935025,588535793916102762958836647⟩,⟨3411772456086199165686422228,3411772456086199166834991902⟩⟩,⟨⟨(-65878528817845185855981007311),(-65878528817845185832427874592)⟩,⟨(-35143520097970271640063878406),(-35143520097970271616257367065)⟩⟩,⟨⟨390977274694468298190061327583,390977274694468298307974382443⟩,⟨(-321010859534684108975007802739),(-321010859534684108863412052127)⟩⟩] +lemma ha4_1_0_eq (j : Fin 7) : ha4_1_0 j = atomKernel4_0 j := by fin_cases j <;> decide +kernel +lemma ha4_1_0_contains (j : Fin 7) : (ha4_1_0 j).Contains (fullFactor true 4 0 ((j.val:ℝ)/6)) := by + rw [ha4_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel4_0_contains j +noncomputable def hk4_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_1 j i k) +lemma hk4_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_1 j i k).Contains (fullFactor true 4 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 1 (kernel4_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha4_1_1 : Fin 7 → CBox := ![⟨⟨(-2607582845927753),(-2607582845927715)⟩,⟨(-28),28⟩⟩,⟨⟨(-122191150045355554),(-122191150045355508)⟩,⟨1085822365390366632,1085822365390366679⟩⟩,⟨⟨(-42861177505166100888659),(-42861177505166100836508)⟩,⟨10872335876083759744346,10872335876083759796489⟩⟩,⟨⟨(-118739869432107462448785546),(-118739869432107462342488016)⟩,⟨(-47065263808519467727174204),(-47065263808519467620588654)⟩⟩,⟨⟨14870510372727659189857152835,14870510372727659196921171202⟩,⟨(-7889080428845410359742320073),(-7889080428845410352779682537)⟩⟩,⟨⟨(-97173103755644446269075637291),(-97173103755644446154625706676)⟩,⟨293885051024413729859965615305,293885051024413729973889646122⟩⟩,⟨⟨(-1232593686666143723165478075673),(-1232593686666143722736438517056)⟩,⟨(-1351551833658380839059320879344),(-1351551833658380838607893199339)⟩⟩] +lemma ha4_1_1_eq (j : Fin 7) : ha4_1_1 j = ((ha4_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha4_1_1_contains (j : Fin 7) : (ha4_1_1 j).Contains (fullFactor true 4 1 ((j.val:ℝ)/6)) := by + rw [ha4_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_0 j) true 4 0 j (ha4_1_0_contains j) +noncomputable def hk4_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_2 j i k) +lemma hk4_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_2 j i k).Contains (fullFactor true 4 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 2 (kernel4_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha4_1_2 : Fin 7 → CBox := ![⟨⟨12014879231510136,12014879231510312⟩,⟨(-130),130⟩⟩,⟨⟨2486841090913505882,2486841090913506146⟩,⟨(-3934936940956697680),(-3934936940956697414)⟩⟩,⟨⟨133511563142318150939238,133511563142318151202320⟩,⟨83605568591362063713747,83605568591362063976841⟩⟩,⟨⟨47804884559951365221832273,47804884559951365645394529⟩,⟨369875348703464375946013737,369875348703464376369507789⟩⟩,⟨⟨(-29490795127533781843000266021),(-29490795127533781821470485885)⟩,⟨(-28373414152288670562781444012),(-28373414152288670541059792276)⟩⟩,⟨⟨634523470578658676307603943434,634523470578658676582634221580⟩,⟨94998087037092720567628901702,94998087037092720842489701286⟩⟩,⟨⟨(-2324520306598060129494091392307),(-2324520306598060128630615839706)⟩,⟨2352356659248850429136836689285,2352356659248850429961344026763⟩⟩] +lemma ha4_1_2_eq (j : Fin 7) : ha4_1_2 j = ((ha4_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha4_1_2_contains (j : Fin 7) : (ha4_1_2 j).Contains (fullFactor true 4 2 ((j.val:ℝ)/6)) := by + rw [ha4_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_1 j) true 4 1 j (ha4_1_1_contains j) +noncomputable def hk4_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_3 j i k) +lemma hk4_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_3 j i k).Contains (fullFactor true 4 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 3 (kernel4_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha4_1_3 : Fin 7 → CBox := ![⟨⟨(-36907059520204013),(-36907059520203472)⟩,⟨(-400),400⟩⟩,⟨⟨(-11231414664805568267),(-11231414664805567262)⟩,⟨6973466803697525733,6973466803697526741⟩⟩,⟨⟨(-75589613240513251416411),(-75589613240513250531833)⟩,⟨(-366413541999585259943478),(-366413541999585259058888)⟩⟩,⟨⟨584713297321204061332221952,584713297321204062455037712⟩,⟨(-430314464975119848289644011),(-430314464975119847167555010)⟩⟩,⟨⟨(-28798600016050553172797180124),(-28798600016050553128284315625)⟩,⟨59747663736978219251757518487,59747663736978219296075500153⟩⟩,⟨⟨(-19600922602991995227272665644),(-19600922602991994787522394838)⟩,⟨(-886374617295088768059581451890),(-886374617295088767617704716712)⟩⟩,⟨⟨2976968041023874541031972729021,2976968041023874542087933767707⟩,⟨2650731151557149500556206935305,2650731151557149501656532882917⟩⟩] +lemma ha4_1_3_eq (j : Fin 7) : ha4_1_3 j = ((ha4_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha4_1_3_contains (j : Fin 7) : (ha4_1_3 j).Contains (fullFactor true 4 3 ((j.val:ℝ)/6)) := by + rw [ha4_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_2 j) true 4 2 j (ha4_1_2_contains j) +noncomputable def hk4_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_4 j i k) +lemma hk4_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_4 j i k).Contains (fullFactor true 4 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 4 (kernel4_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha4_1_4 : Fin 7 → CBox := ![⟨⟨85027761173133142,85027761173134389⟩,⟨(-922),922⟩⟩,⟨⟨28007246310331154485,28007246310331157350⟩,⟨(-2925839488081969562),(-2925839488081966695)⟩⟩,⟨⟨(-378729129556541797995253),(-378729129556541795765696)⟩,⟨548337907102478304874139,548337907102478307103643⟩⟩,⟨⟨(-963224607936117361382280585),(-963224607936117359151839488)⟩,⟨(-442273776109093407109570037),(-442273776109093404878435071)⟩⟩,⟨⟨79918426362245342226220254877,79918426362245342294525006410⟩,⟨10627553236579141772659348121,10627553236579141841038897168⟩⟩,⟨⟨(-901824421030882223725182978333),(-901824421030882223193561509030)⟩,⟨176088419780057836982612322956,176088419780057837510104342203⟩⟩,⟨⟨2253215983947022747624847398950,2253215983947022748675806025234⟩,⟨(-2811911447786099791049895883254),(-2811911447786099790036016616080)⟩⟩] +lemma ha4_1_4_eq (j : Fin 7) : ha4_1_4 j = ((ha4_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha4_1_4_contains (j : Fin 7) : (ha4_1_4 j).Contains (fullFactor true 4 4 ((j.val:ℝ)/6)) := by + rw [ha4_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_3 j) true 4 3 j (ha4_1_3_contains j) +noncomputable def hk4_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_5 j i k) +lemma hk4_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_5 j i k).Contains (fullFactor true 4 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 5 (kernel4_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha4_1_5 : Fin 7 → CBox := ![⟨⟨(-156711919380254455),(-156711919380252155)⟩,⟨(-1700),1700⟩⟩,⟨⟨(-45117569379132367963),(-45117569379132361438)⟩,⟨(-16339378989578838897),(-16339378989578832370)⟩⟩,⟨⟨937742700034152255703841,937742700034152260198748⟩,⟨(-149850786404783572613355),(-149850786404783568118469)⟩⟩,⟨⟨93331003296068141784047768,93331003296068145329098279⟩,⟨1234410196252837007027900162,1234410196252837010573390097⟩⟩,⟨⟨(-14401144447719123242314468059),(-14401144447719123158322347952)⟩,⟨(-77065359560897373805053062246),(-77065359560897373720970434529)⟩⟩,⟨⟨270906561200275866269322119105,270906561200275866776061388513⟩,⟨712039954725207094952867269487,712039954725207095463960943915⟩⟩,⟨⟨(-2115395875765526876901022454895),(-2115395875765526876122591648692)⟩,⟨(-1521683908983851018554166802495),(-1521683908983851017751567163973)⟩⟩] +lemma ha4_1_5_eq (j : Fin 7) : ha4_1_5 j = ((ha4_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha4_1_5_contains (j : Fin 7) : (ha4_1_5 j).Contains (fullFactor true 4 5 ((j.val:ℝ)/6)) := by + rw [ha4_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_4 j) true 4 4 j (ha4_1_4_contains j) +noncomputable def hk4_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_6 j i k) +lemma hk4_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_6 j i k).Contains (fullFactor true 4 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 6 (kernel4_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha4_1_6 : Fin 7 → CBox := ![⟨⟨240692229386867433,240692229386870966⟩,⟨(-2612),2612⟩⟩,⟨⟨47522350994145363755,47522350994145376138⟩,⟨48833714838449540435,48833714838449552819⟩⟩,⟨⟨(-898128814667689135160379),(-898128814667689127610815)⟩,⟨(-681953369778087734850317),(-681953369778087727300658)⟩⟩,⟨⟨1006931375397864074242747258,1006931375397864078936867112⟩,⟨(-661687737820782025218663830),(-661687737820782020526090022)⟩⟩,⟨⟨(-55703043562228543359822715543),(-55703043562228543273665780273)⟩,⟨30552436990556070099101274918,30552436990556070185108166391⟩⟩,⟨⟨453015525109719719168171480263,453015525109719719577293916689⟩,⟨(-268037804658572995451047844263),(-268037804658572995045170356903)⟩⟩,⟨⟨(-849604206537745474207117197996),(-849604206537745473696595239522)⟩,⟨1320746880114118466942723094543,1320746880114118467440533951857⟩⟩] +lemma ha4_1_6_eq (j : Fin 7) : ha4_1_6 j = ((ha4_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha4_1_6_contains (j : Fin 7) : (ha4_1_6 j).Contains (fullFactor true 4 6 ((j.val:ℝ)/6)) := by + rw [ha4_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_5 j) true 4 5 j (ha4_1_5_contains j) +noncomputable def hk4_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_7 j i k) +lemma hk4_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_7 j i k).Contains (fullFactor true 4 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 7 (kernel4_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha4_1_7 : Fin 7 → CBox := ![⟨⟨(-316865765173233329),(-316865765173228677)⟩,⟨(-3439),3439⟩⟩,⟨⟨(-26108612275312577803),(-26108612275312557663)⟩,⟨(-78721710566199994627),(-78721710566199974486)⟩⟩,⟨⟨129973483503895742112276,129973483503895752980529⟩,⟨1140446865590912620867492,1140446865590912631735764⟩⟩,⟨⟨(-889955708558685670528337767),(-889955708558685665203321372)⟩,⟨(-467302871873413077374509263),(-467302871873413072048632002)⟩⟩,⟨⟨32223127932428178606954408683,32223127932428178682472603451⟩,⟨30149946687664775190203232695,30149946687664775265823481471⟩⟩,⟨⟨(-202010699674757644655085161409),(-202010699674757644376402615098)⟩,⟨(-237417450594773946771809038900),(-237417450594773946491274795573)⟩⟩,⟨⟨704112057992034190187424051998,704112057992034190460161080078⟩,⟨402848834406473326418740928286,402848834406473326696960739316⟩⟩] +lemma ha4_1_7_eq (j : Fin 7) : ha4_1_7 j = ((ha4_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha4_1_7_contains (j : Fin 7) : (ha4_1_7 j).Contains (fullFactor true 4 7 ((j.val:ℝ)/6)) := by + rw [ha4_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_6 j) true 4 6 j (ha4_1_6_contains j) +noncomputable def hk4_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_8 j i k) +lemma hk4_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_8 j i k).Contains (fullFactor true 4 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 8 (kernel4_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha4_1_8 : Fin 7 → CBox := ![⟨⟨365003158682185382,365003158682190741⟩,⟨(-3962),3962⟩⟩,⟨⟨(-11565221277143725581),(-11565221277143696920)⟩,⟨87570863262705806927,87570863262705835589⟩⟩,⟨⟨654193032461853717743986,654193032461853731432027⟩,⟨(-785553110229146349336997),(-785553110229146335649048)⟩⟩,⟨⟨16431162154620406567612414,16431162154620411854040099⟩,⟨733575612847315341933857479,733575612847315347220423137⟩⟩,⟨⟨11307862876463573025707578769,11307862876463573083757644666⟩,⟨(-24319802412277659428432972345),(-24319802412277659370419950486)⟩⟩,⟨⟨(-103455427133102106890136036073),(-103455427133102106721900637404)⟩,⟨124060977180637501742225554227,124060977180637501909630750468⟩⟩,⟨⟨165310518492329878248483281534,165310518492329878381098659482⟩,⟨(-327276406537794775653843130974),(-327276406537794775523163530670)⟩⟩] +lemma ha4_1_8_eq (j : Fin 7) : ha4_1_8 j = ((ha4_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha4_1_8_contains (j : Fin 7) : (ha4_1_8 j).Contains (fullFactor true 4 8 ((j.val:ℝ)/6)) := by + rw [ha4_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_7 j) true 4 7 j (ha4_1_7_contains j) +noncomputable def hk4_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_9 j i k) +lemma hk4_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_9 j i k).Contains (fullFactor true 4 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 9 (kernel4_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha4_1_9 : Fin 7 → CBox := ![⟨⟨(-373736404752101923),(-373736404752096435)⟩,⟨(-4057),4057⟩⟩,⟨⟨46026438971459646812,46026438971459683067⟩,⟨(-69815606836412645563),(-69815606836412609308)⟩⟩,⟨⟨(-807407422918136490944112),(-807407422918136475620573)⟩,⟨55390307570908635797442,55390307570908651120972⟩⟩,⟨⟨411201132073586750592642394,411201132073586755256849285⟩,⟨(-239993869419179599326551127),(-239993869419179594662957025)⟩⟩,⟨⟨(-14388074158112811012320385145),(-14388074158112810972720577993)⟩,⟨(-1709892746615031001852185635),(-1709892746615030962253887421)⟩⟩,⟨⟨64409999671568227960920542608,64409999671568228050279879752⟩,⟨37252141722033286571057820694,37252141722033286660704396663⟩⟩,⟨⟨(-134760504037822101221170491461),(-134760504037822101165542749483)⟩,⟨(-59498533132063636178054899765),(-59498533132063636121886959305)⟩⟩] +lemma ha4_1_9_eq (j : Fin 7) : ha4_1_9 j = ((ha4_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha4_1_9_contains (j : Fin 7) : (ha4_1_9 j).Contains (fullFactor true 4 9 ((j.val:ℝ)/6)) := by + rw [ha4_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_8 j) true 4 8 j (ha4_1_8_contains j) +noncomputable def hk4_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_10 j i k) +lemma hk4_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_10 j i k).Contains (fullFactor true 4 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 10 (kernel4_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha4_1_10 : Fin 7 → CBox := ![⟨⟨344410746107485977,344410746107491036⟩,⟨(-3739),3739⟩⟩,⟨⟨(-61241398180848069516),(-61241398180848028242)⟩,⟨36410256661587610071,36410256661587651345⟩⟩,⟨⟨426057544523511009005628,426057544523511024443450⟩,⟨388555418264887262139144,388555418264887277577020⟩⟩,⟨⟨(-238965013579701798855809224),(-238965013579701795152789048)⟩,⟨(-142135116483130960597255694),(-142135116483130956893971748)⟩⟩,⟨⟨1390337505473758473816047355,1390337505473758498120655373⟩,⟨6906384418168149384297776169,6906384418168149408615381683⟩⟩,⟨⟨10682173979783230084786718401,10682173979783230127766503913⟩,⟨(-28937078755176425808484739001),(-28937078755176425765572841313)⟩⟩,⟨⟨(-18954632056797412926593369349),(-18954632056797412905189995256)⟩,⟨49779592818138701473805312280,49779592818138701495105772379⟩⟩] +lemma ha4_1_10_eq (j : Fin 7) : ha4_1_10 j = ((ha4_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha4_1_10_contains (j : Fin 7) : (ha4_1_10 j).Contains (fullFactor true 4 10 ((j.val:ℝ)/6)) := by + rw [ha4_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_9 j) true 4 9 j (ha4_1_9_contains j) +noncomputable def hk4_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_11 j i k) +lemma hk4_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_11 j i k).Contains (fullFactor true 4 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 11 (kernel4_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha4_1_11 : Fin 7 → CBox := ![⟨⟨(-288532871943646218),(-288532871943641979)⟩,⟨(-3133),3133⟩⟩,⟨⟨54987172752541545098,54987172752541587814⟩,⟨(-4676579574663171544),(-4676579574663128828)⟩⟩,⟨⟨(-8781287222846539040959),(-8781287222846524901933)⟩,⟨(-373393748751650466502921),(-373393748751650452363895)⟩⟩,⟨⟨(-4527097223383423975371289),(-4527097223383421302518676)⟩,⟨147540089349048341846152415,147540089349048344519014234⟩⟩,⟨⟨2709142225723565901311545603,2709142225723565914882953808⟩,⟨(-1535361679402339012069200583),(-1535361679402338998506416375)⟩⟩,⟨⟨(-11430912922189751433404198707),(-11430912922189751414678841612)⟩,⟨(-2114482974330347687133479671),(-2114482974330347668405116365)⟩⟩,⟨⟨16664961881176035410467977874,16664961881176035417878796768⟩,⟨5372580800431791485102728033,5372580800431791492515039184⟩⟩] +lemma ha4_1_11_eq (j : Fin 7) : ha4_1_11 j = ((ha4_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha4_1_11_contains (j : Fin 7) : (ha4_1_11 j).Contains (fullFactor true 4 11 ((j.val:ℝ)/6)) := by + rw [ha4_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_10 j) true 4 10 j (ha4_1_10_contains j) +noncomputable def hk4_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_12 j i k) +lemma hk4_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_12 j i k).Contains (fullFactor true 4 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 12 (kernel4_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha4_1_12 : Fin 7 → CBox := ![⟨⟨221577339088675828,221577339088679084⟩,⟨(-2406),2406⟩⟩,⟨⟨(-36577597281202215869),(-36577597281202175344)⟩,⟨(-14048578263458107062),(-14048578263458066538)⟩⟩,⟨⟨(-156649954720359189061737),(-156649954720359177191859)⟩,⟨156970497110931007550277,156970497110931019420133⟩⟩,⟨⟨63873985426687764490455294,63873985426687766258814288⟩,⟨(-32867577440256272188100181),(-32867577440256270419829363)⟩⟩,⟨⟨(-933222544554014460066491758),(-933222544554014453128068087)⟩,⟨(-849132298387962067200019948),(-849132298387962060258398439)⟩⟩,⟨⟨(-48953280789182958523140572),(-48953280789182951043774327)⟩,⟨4015658690562889804409288571,4015658690562889811896163125⟩⟩,⟨⟨1355941114837619286755074774,1355941114837619289107517888⟩,⟨(-5098869900160554237572824837),(-5098869900160554235210553419)⟩⟩] +lemma ha4_1_12_eq (j : Fin 7) : ha4_1_12 j = ((ha4_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha4_1_12_contains (j : Fin 7) : (ha4_1_12 j).Contains (fullFactor true 4 12 ((j.val:ℝ)/6)) := by + rw [ha4_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_11 j) true 4 11 j (ha4_1_11_contains j) +noncomputable def hk4_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_13 j i k) +lemma hk4_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_13 j i k).Contains (fullFactor true 4 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 13 (kernel4_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha4_1_13 : Fin 7 → CBox := ![⟨⟨(-157070013282310896),(-157070013282308587)⟩,⟨(-1706),1706⟩⟩,⟨⟨17552430588930803793,17552430588930839282⟩,⟨18745388791333306437,18745388791333341925⟩⟩,⟨⟨121515002802467601445596,121515002802467610643941⟩,⟨2609209362546418089024,2609209362546427287370⟩⟩,⟨⟨(-26819953452868261665428530),(-26819953452868260585554108)⟩,⟨(-17943955010317935478491415),(-17943955010317934398584243)⟩⟩,⟨⟨(-192985941286998963688248889),(-192985941286998960411218876)⟩,⟨430632014189237208820928326,430632014189237212097258561⟩⟩,⟨⟨1264587121744351847794697697,1264587121744351850556711794⟩,⟨(-202173846053296087347084457),(-202173846053296084590306923)⟩⟩,⟨⟨(-1435904737533013182087880812),(-1435904737533013181393160205)⟩,⟨(-302992828438247915450070469),(-302992828438247914761075230)⟩⟩] +lemma ha4_1_13_eq (j : Fin 7) : ha4_1_13 j = ((ha4_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha4_1_13_contains (j : Fin 7) : (ha4_1_13 j).Contains (fullFactor true 4 13 ((j.val:ℝ)/6)) := by + rw [ha4_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_12 j) true 4 12 j (ha4_1_12_contains j) +noncomputable def hk4_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_14 j i k) +lemma hk4_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_14 j i k).Contains (fullFactor true 4 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 14 (kernel4_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha4_1_14 : Fin 7 → CBox := ![⟨⟨103389523773266113,103389523773267634⟩,⟨(-1123),1123⟩⟩,⟨⟨(-4633443673673209603),(-4633443673673180744)⟩,⟨(-14925996763843429024),(-14925996763843400166)⟩⟩,⟨⟨(-41774770371837720324116),(-41774770371837713705308)⟩,⟨(-45619091552665876988714),(-45619091552665870369900)⟩⟩,⟨⟨(-1125901853237962722994658),(-1125901853237962110635120)⟩,⟨13413215749862543630209335,13413215749862544242568141⟩⟩,⟨⟨162996981809506414549212219,162996981809506415985622404⟩,⟨17073711483102164194986172,17073711483102165631383790⟩⟩,⟨⟨(-122613935141277530749972356),(-122613935141277529806185436)⟩,⟨(-358844335760074371899781242),(-358844335760074370953913000)⟩⟩,⟨⟨(-58892167457158499583102199),(-58892167457158499395761435)⟩,⟨374427383987842205015766639,374427383987842205205389133⟩⟩] +lemma ha4_1_14_eq (j : Fin 7) : ha4_1_14 j = ((ha4_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha4_1_14_contains (j : Fin 7) : (ha4_1_14 j).Contains (fullFactor true 4 14 ((j.val:ℝ)/6)) := by + rw [ha4_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_13 j) true 4 13 j (ha4_1_13_contains j) +noncomputable def hk4_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_15 j i k) +lemma hk4_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_15 j i k).Contains (fullFactor true 4 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 15 (kernel4_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha4_1_15 : Fin 7 → CBox := ![⟨⟨(-63517963587318999),(-63517963587318064)⟩,⟨(-690),690⟩⟩,⟨⟨(-1331449327586107711),(-1331449327586085808)⟩,⟨8776841268483944298,8776841268483966201⟩⟩,⟨⟨(-1951018677024513354744),(-1951018677024508909589)⟩,⟨29316938149061007253744,29316938149061011698898⟩⟩,⟨⟨4780317323109354176191061,4780317323109354500277648⟩,⟨(-2147187369417703010993958),(-2147187369417702686913200)⟩⟩,⟨⟨(-11207877744634551981961976),(-11207877744634551394371826)⟩,⟨(-51927803596403653882774188),(-51927803596403653295085299)⟩⟩,⟨⟨(-91975182078698675059755517),(-91975182078698674757501721)⟩,⟨50243339778780636999260026,50243339778780637300875205⟩⟩,⟨⟨90875027530436312785404506,90875027530436312833687729⟩,⟨9490244295613674650501421,9490244295613674698034699⟩⟩] +lemma ha4_1_15_eq (j : Fin 7) : ha4_1_15 j = ((ha4_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha4_1_15_contains (j : Fin 7) : (ha4_1_15 j).Contains (fullFactor true 4 15 ((j.val:ℝ)/6)) := by + rw [ha4_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_14 j) true 4 14 j (ha4_1_14_contains j) +noncomputable def hk4_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_16 j i k) +lemma hk4_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_16 j i k).Contains (fullFactor true 4 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 16 (kernel4_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha4_1_16 : Fin 7 → CBox := ![⟨⟨36583720759098776,36583720759099316⟩,⟨(-398),398⟩⟩,⟨⟨2677392080736579140,2677392080736594725⟩,⟨(-3895946064982510822),(-3895946064982495237)⟩⟩,⟨⟨10037038319273749196460,10037038319273751995190⟩,⟨(-8393451737851121688081),(-8393451737851118889353)⟩⟩,⟨⟨(-1531042142890191918961909),(-1531042142890191758166003)⟩,⟨(-1146418088998160947433510),(-1146418088998160786635582)⟩⟩,⟨⟨(-13932622606734916266739991),(-13932622606734916041343581)⟩,⟨8154337908989474819208504,8154337908989475044560605⟩⟩,⟨⟨16877343811142840107776326,16877343811142840198146684⟩,⟨21272450606302319761884223,21272450606302319852417599⟩⟩,⟨⟨1075350659330757033750342,1075350659330757045054943⟩,⟨(-20620881604590682034097105),(-20620881604590682022576625)⟩⟩] +lemma ha4_1_16_eq (j : Fin 7) : ha4_1_16 j = ((ha4_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha4_1_16_contains (j : Fin 7) : (ha4_1_16 j).Contains (fullFactor true 4 16 ((j.val:ℝ)/6)) := by + rw [ha4_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_15 j) true 4 15 j (ha4_1_15_contains j) +noncomputable def hk4_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_17 j i k) +lemma hk4_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_17 j i k).Contains (fullFactor true 4 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 17 (kernel4_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha4_1_17 : Fin 7 → CBox := ![⟨⟨(-19831256974987217),(-19831256974986924)⟩,⟨(-216),216⟩⟩,⟨⟨(-2059416998806460849),(-2059416998806450412)⟩,⟨1171355604922066850,1171355604922077288⟩⟩,⟨⟨(-5449727250552316936235),(-5449727250552315277773)⟩,⟨(-609807811738035030507),(-609807811738033372044)⟩⟩,⟨⟨(-89611486533065604243206),(-89611486533065529155923)⟩,⟨650902469489435354949834,650902469489435430037010⟩⟩,⟨⟨3457990745058905354513310,3457990745058905435858446⟩,⟨3059519842532257558258589,3059519842532257639615177⟩⟩,⟨⟨4412791760747938877470250,4412791760747938902988981⟩,⟨(-4937131760221530261847230),(-4937131760221530236363703)⟩⟩,⟨⟨(-4392027212546253517558359),(-4392027212546253514972409)⟩,⟨(-651007646453216783336),(-651007646453214253386)⟩⟩] +lemma ha4_1_17_eq (j : Fin 7) : ha4_1_17 j = ((ha4_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha4_1_17_contains (j : Fin 7) : (ha4_1_17 j).Contains (fullFactor true 4 17 ((j.val:ℝ)/6)) := by + rw [ha4_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_16 j) true 4 16 j (ha4_1_16_contains j) +noncomputable def hk4_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_18 j i k) +lemma hk4_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_18 j i k).Contains (fullFactor true 4 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 18 (kernel4_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha4_1_18 : Fin 7 → CBox := ![⟨⟨10152874717996636,10152874717996787⟩,⟨(-111),111⟩⟩,⟨⟨1119050062386385031,1119050062386391633⟩,⟨(-73514147686835132),(-73514147686828529)⟩⟩,⟨⟨1316187535226924803759,1316187535226925731923⟩,⟨1726074413045262573102,1726074413045263501266⟩⟩,⟨⟨198810663123377547543181,198810663123377580658395⟩,⟨(-76904735581677704486588),(-76904735581677671371586)⟩⟩,⟨⟨494158889834145099319115,494158889834145127052178⟩,⟨(-1145119057255289100082241),(-1145119057255289072350935)⟩⟩,⟨⟨(-1293199793664092864640983),(-1293199793664092857854603)⟩,⟨(-808350773977237131983964),(-808350773977237125191285)⟩⟩,⟨⟨45686381946115178703335,45686381946115179237998⟩,⟨881102603815161103752823,881102603815161104300795⟩⟩] +lemma ha4_1_18_eq (j : Fin 7) : ha4_1_18 j = ((ha4_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha4_1_18_contains (j : Fin 7) : (ha4_1_18 j).Contains (fullFactor true 4 18 ((j.val:ℝ)/6)) := by + rw [ha4_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_17 j) true 4 17 j (ha4_1_17_contains j) +noncomputable def hk4_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_19 j i k) +lemma hk4_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_19 j i k).Contains (fullFactor true 4 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 19 (kernel4_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha4_1_19 : Fin 7 → CBox := ![⟨⟨(-4924325093272123),(-4924325093272049)⟩,⟨(-54),54⟩⟩,⟨⟨(-465905797726687868),(-465905797726683911)⟩,⟨(-189310336280628435),(-189310336280624478)⟩⟩,⟨⟨126801924778189848949,126801924778190341061⟩,⟨(-804051112026100038102),(-804051112026099545991)⟩⟩,⟨⟨(-50288561925768433668250),(-50288561925768419832490)⟩,⟨(-41996907277114615954997),(-41996907277114602119166)⟩⟩,⟨⟨(-317856028283734568040137),(-317856028283734559084187)⟩,⟨(-28828693450783567548442),(-28828693450783558592543)⟩⟩,⟨⟨(-125870794003239511753570),(-125870794003239510040769)⟩,⟨308022606095740110862217,308022606095740112574171⟩⟩,⟨⟨167005566310115885399711,167005566310115885509675⟩,⟨(-17390647682132445089246),(-17390647682132444982160)⟩⟩] +lemma ha4_1_19_eq (j : Fin 7) : ha4_1_19 j = ((ha4_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha4_1_19_contains (j : Fin 7) : (ha4_1_19 j).Contains (fullFactor true 4 19 ((j.val:ℝ)/6)) := by + rw [ha4_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_18 j) true 4 18 j (ha4_1_18_contains j) +noncomputable def hk4_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_20 j i k) +lemma hk4_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_20 j i k).Contains (fullFactor true 4 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 20 (kernel4_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha4_1_20 : Fin 7 → CBox := ![⟨⟨2268966118746996,2268966118747031⟩,⟨(-25),25⟩⟩,⟨⟨143395564937588033,143395564937590286⟩,⟨159173478369501403,159173478369503657⟩⟩,⟨⟨(-238265018213193681465),(-238265018213193433594)⟩,⟨165286641342213632702,165286641342213880573⟩⟩,⟨⟨(-3610799469949467280787),(-3610799469949461789112)⟩,⟨18786940801909900920126,18786940801909906411796⟩⟩,⟨⟨17423846619338282891150,17423846619338285638629⟩,⟨75608858172521635091822,75608858172521637839452⟩⟩,⟨⟨67350748333829412390720,67350748333829412800944⟩,⟨14863879155404315747231,14863879155404316157500⟩⟩,⟨⟨(-4707863846622743593336),(-4707863846622743572953)⟩,⟨(-29989797414741186507773),(-29989797414741186486816)⟩⟩] +lemma ha4_1_20_eq (j : Fin 7) : ha4_1_20 j = ((ha4_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha4_1_20_contains (j : Fin 7) : (ha4_1_20 j).Contains (fullFactor true 4 20 ((j.val:ℝ)/6)) := by + rw [ha4_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_19 j) true 4 19 j (ha4_1_19_contains j) +noncomputable def hk4_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_21 j i k) +lemma hk4_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_21 j i k).Contains (fullFactor true 4 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 21 (kernel4_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha4_1_21 : Fin 7 → CBox := ![⟨⟨(-995680510335213),(-995680510335197)⟩,⟨(-11),11⟩⟩,⟨⟨(-24167544916724271),(-24167544916723049)⟩,⟨(-83494535036761162),(-83494535036759939)⟩⟩,⟨⟨96398090339335817951,96398090339335936856⟩,⟨19681180153674845558,19681180153674964463⟩⟩,⟨⟨5056546918286374916924,5056546918286376992863⟩,⟨(-1653420513831688192605),(-1653420513831686116670)⟩⟩,⟨⟨15376608068704869496132,15376608068704870298925⟩,⟨(-9289159739887357853110),(-9289159739887357050367)⟩⟩,⟨⟨632755968118618195706,632755968118618289295⟩,⟨(-13600783348369112516012),(-13600783348369112422404)⟩⟩,⟨⟨(-5114758474883154535204),(-5114758474883154531400)⟩,⟨1077690656331277764701,1077690656331277768398⟩⟩] +lemma ha4_1_21_eq (j : Fin 7) : ha4_1_21 j = ((ha4_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha4_1_21_contains (j : Fin 7) : (ha4_1_21 j).Contains (fullFactor true 4 21 ((j.val:ℝ)/6)) := by + rw [ha4_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_20 j) true 4 20 j (ha4_1_20_contains j) +noncomputable def hk4_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_22 j i k) +lemma hk4_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_22 j i k).Contains (fullFactor true 4 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 22 (kernel4_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha4_1_22 : Fin 7 → CBox := ![⟨⟨417069676878878,417069676878886⟩,⟨(-5),5⟩⟩,⟨⟨(-5688506223666242),(-5688506223665609)⟩,⟨33179084348972314,33179084348972948⟩⟩,⟨⟨(-16966331297947434677),(-16966331297947380230)⟩,⟨(-26971181249744854994),(-26971181249744800547)⟩⟩,⟨⟨(-1034368221745284543763),(-1034368221745283794697)⟩,⟨(-961413717613513667859),(-961413717613512918792)⟩⟩,⟨⟨(-3009857270793159298842),(-3009857270793159074960)⟩,⟨(-2589244316765056088331),(-2589244316765055864438)⟩⟩,⟨⟨(-2545858161311484954193),(-2545858161311484933806)⟩,⟨317913853180970144320,317913853180970164698⟩⟩,⟨⟨220544744333898411295,220544744333898411936⟩,⟨830325656585312049258,830325656585312049918⟩⟩] +lemma ha4_1_22_eq (j : Fin 7) : ha4_1_22 j = ((ha4_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha4_1_22_contains (j : Fin 7) : (ha4_1_22 j).Contains (fullFactor true 4 22 ((j.val:ℝ)/6)) := by + rw [ha4_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_21 j) true 4 21 j (ha4_1_21_contains j) +noncomputable def hk4_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_23 j i k) +lemma hk4_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_23 j i k).Contains (fullFactor true 4 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 23 (kernel4_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha4_1_23 : Fin 7 → CBox := ![⟨⟨(-167106009995311),(-167106009995307)⟩,⟨(-3),3⟩⟩,⟨⟨7259331436498960,7259331436499274⟩,⟨(-10139539301202605),(-10139539301202290)⟩⟩,⟨⟨(-2407442650495455086),(-2407442650495431238)⟩,⟨9572739713644638996,9572739713644662844⟩⟩,⟨⟨(-86257478564224296273),(-86257478564224037737)⟩,⟨348027482319142265882,348027482319142524418⟩⟩,⟨⟨(-321794527051609111071),(-321794527051609051344)⟩,⟨775179833332239811424,775179833332239871150⟩⟩,⟨⟨134427518763586881360,134427518763586885605⟩,⟨442464170991098208850,442464170991098213097⟩⟩,⟨⟨128561527830534868032,128561527830534868143⟩,⟨(-41404602083639300230),(-41404602083639300122)⟩⟩] +lemma ha4_1_23_eq (j : Fin 7) : ha4_1_23 j = ((ha4_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha4_1_23_contains (j : Fin 7) : (ha4_1_23 j).Contains (fullFactor true 4 23 ((j.val:ℝ)/6)) := by + rw [ha4_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_22 j) true 4 22 j (ha4_1_22_contains j) +noncomputable def hk4_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_24 j i k) +lemma hk4_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_24 j i k).Contains (fullFactor true 4 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 24 (kernel4_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha4_1_24 : Fin 7 → CBox := ![⟨⟨64164101634350,64164101634353⟩,⟨(-2),2⟩⟩,⟨⟨(-3889545871029426),(-3889545871029276)⟩,⟨2114285442955130,2114285442955280⟩⟩,⟨⟨2548092344363394647,2548092344363404658⟩,⟨(-1447213392689696731),(-1447213392689686720)⟩⟩,⟨⟨84247069693839234255,84247069693839319770⟩,⟨(-22678584098096393804),(-22678584098096308289)⟩⟩,⟨⟨169539827896627858735,169539827896627874005⟩,⟨13000561379869408527,13000561379869423797⟩⟩,⟨⟨71371631097390712785,71371631097390713634⟩,⟨(-35866914758470672164),(-35866914758470671315)⟩⟩,⟨⟨(-7235563563306400966),(-7235563563306400948)⟩,⟨(-19019347648117244127),(-19019347648117244108)⟩⟩] +lemma ha4_1_24_eq (j : Fin 7) : ha4_1_24 j = ((ha4_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha4_1_24_contains (j : Fin 7) : (ha4_1_24 j).Contains (fullFactor true 4 24 ((j.val:ℝ)/6)) := by + rw [ha4_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_23 j) true 4 23 j (ha4_1_23_contains j) +noncomputable def hk4_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_25 j i k) +lemma hk4_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_25 j i k).Contains (fullFactor true 4 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 25 (kernel4_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha4_1_25 : Fin 7 → CBox := ![⟨⟨(-23651756517391),(-23651756517389)⟩,⟨(-1),1⟩⟩,⟨⟨1507150861309058,1507150861309128⟩,⟨(-69912253740847),(-69912253740778)⟩⟩,⟨⟨(-799960665706457510),(-799960665706453475)⟩,⟨(-239905681667305917),(-239905681667301882)⟩⟩,⟨⟨(-14170669234308460126),(-14170669234308432971)⟩,⟨(-14647102925907551858),(-14647102925907524703)⟩⟩,⟨⟨(-7874032788143656372),(-7874032788143652624)⟩,⟨(-32118906315026203165),(-32118906315026199417)⟩⟩,⟨⟨(-7871774562336731974),(-7871774562336731811)⟩,⟨(-10652519722186220085),(-10652519722186219921)⟩⟩,⟨⟨(-2692828542251588346),(-2692828542251588342)⟩,⟨1187965405201376517,1187965405201376521⟩⟩] +lemma ha4_1_25_eq (j : Fin 7) : ha4_1_25 j = ((ha4_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha4_1_25_contains (j : Fin 7) : (ha4_1_25 j).Contains (fullFactor true 4 25 ((j.val:ℝ)/6)) := by + rw [ha4_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_24 j) true 4 24 j (ha4_1_24_contains j) +noncomputable def hk4_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_26 j i k) +lemma hk4_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_26 j i k).Contains (fullFactor true 4 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 26 (kernel4_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha4_1_26 : Fin 7 → CBox := ![⟨⟨8383036202202,8383036202204⟩,⟨(-1),1⟩⟩,⟨⟨(-454388025616779),(-454388025616747)⟩,⟨(-194900546528633),(-194900546528601)⟩⟩,⟨⟨103965069308940120,103965069308941684⟩,⟨203888669409401143,203888669409402708⟩⟩,⟨⟨(-1335334482009259728),(-1335334482009251436)⟩,⟨4378418280698589550,4378418280698597842⟩⟩,⟨⟨(-5248347452064477218),(-5248347452064476333)⟩,⟨3271136095074790554,3271136095074791440⟩⟩,⟨⟨(-1460560236392765555),(-1460560236392765524)⟩,⟨1525428951259400239,1525428951259400270⟩⟩,⟨⟨184439056088267927,184439056088267929⟩,⟨365415605192313431,365415605192313433⟩⟩] +lemma ha4_1_26_eq (j : Fin 7) : ha4_1_26 j = ((ha4_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha4_1_26_contains (j : Fin 7) : (ha4_1_26 j).Contains (fullFactor true 4 26 ((j.val:ℝ)/6)) := by + rw [ha4_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_25 j) true 4 25 j (ha4_1_25_contains j) +noncomputable def hk4_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_27 j i k) +lemma hk4_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_27 j i k).Contains (fullFactor true 4 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 27 (kernel4_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha4_1_27 : Fin 7 → CBox := ![⟨⟨(-2861204290606),(-2861204290605)⟩,⟨(-1),1⟩⟩,⟨⟨102178881013114,102178881013129⟩,⟨117907552804125,117907552804139⟩⟩,⟨⟨19932625835250058,19932625835250642⟩,⟨(-57010777019742819),(-57010777019742234)⟩⟩,⟨⟨968339618325924218,968339618325926657⟩,⟨(-206281693212696787),(-206281693212694348)⟩⟩,⟨⟨854286319129416942,854286319129417144⟩,⟨714458197267627210,714458197267627413⟩⟩,⟨⟨268907732701577294,268907732701577300⟩,⟨181201987173529506,181201987173529512⟩⟩,⟨⟨47588612040436755,47588612040436756⟩,⟨(-27208501772773898),(-27208501772773896)⟩⟩] +lemma ha4_1_27_eq (j : Fin 7) : ha4_1_27 j = ((ha4_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha4_1_27_contains (j : Fin 7) : (ha4_1_27 j).Contains (fullFactor true 4 27 ((j.val:ℝ)/6)) := by + rw [ha4_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_26 j) true 4 26 j (ha4_1_26_contains j) +noncomputable def hk4_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_28 j i k) +lemma hk4_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_28 j i k).Contains (fullFactor true 4 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 28 (kernel4_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha4_1_28 : Fin 7 → CBox := ![⟨⟨941677354072,941677354073⟩,⟨(-1),1⟩⟩,⟨⟨(-12320102128234),(-12320102128227)⟩,⟨(-45849759527991),(-45849759527984)⟩⟩,⟨⟨(-13991190910553465),(-13991190910553253)⟩,⟨6358538834099595,6358538834099806⟩⟩,⟨⟨(-135504780116346921),(-135504780116346228)⟩,⟨(-155813428590181302),(-155813428590180609)⟩⟩,⟨⟨71651459405594189,71651459405594235⟩,⟨(-179623300255066272),(-179623300255066227)⟩⟩,⟨⟨19673953204478241,19673953204478243⟩,⟨(-43792470264598324),(-43792470264598321)⟩⟩,⟨⟨(-3828088631015248),(-3828088631015247)⟩,⟨(-5954810199424272),(-5954810199424271)⟩⟩] +lemma ha4_1_28_eq (j : Fin 7) : ha4_1_28 j = ((ha4_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha4_1_28_contains (j : Fin 7) : (ha4_1_28 j).Contains (fullFactor true 4 28 ((j.val:ℝ)/6)) := by + rw [ha4_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_27 j) true 4 27 j (ha4_1_27_contains j) +noncomputable def hk4_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_29 j i k) +lemma hk4_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_29 j i k).Contains (fullFactor true 4 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 29 (kernel4_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha4_1_29 : Fin 7 → CBox := ![⟨⟨(-299237087207),(-299237087205)⟩,⟨(-1),1⟩⟩,⟨⟨(-2621182983148),(-2621182983145)⟩,⟨13699972917322,13699972917326⟩⟩,⟨⟨3504610405587233,3504610405587308⟩,⟨1405179480039517,1405179480039591⟩⟩,⟨⟨(-14222824073209684),(-14222824073209493)⟩,⟨39074017855588667,39074017855588858⟩⟩,⟨⟨(-32359834766673598),(-32359834766673587)⟩,⟨(-2028815192965765),(-2028815192965755)⟩⟩,⟨⟨(-6646954125083435),(-6646954125083434)⟩,⟨(-1707953989515821),(-1707953989515819)⟩⟩,⟨⟨(-716695229083135),(-716695229083134)⟩,⟨515223531321514,515223531321515⟩⟩] +lemma ha4_1_29_eq (j : Fin 7) : ha4_1_29 j = ((ha4_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha4_1_29_contains (j : Fin 7) : (ha4_1_29 j).Contains (fullFactor true 4 29 ((j.val:ℝ)/6)) := by + rw [ha4_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_28 j) true 4 28 j (ha4_1_28_contains j) +noncomputable def hk4_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel4_0 j i k).mul (mpower1_30 j i k) +lemma hk4_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk4_1_30 j i k).Contains (fullFactor true 4 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk4_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel4_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 4 30 (kernel4_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha4_1_30 : Fin 7 → CBox := ![⟨⟨91919034518,91919034519⟩,⟨(-1),1⟩⟩,⟨⟨2367639582216,2367639582218⟩,⟨(-3176064807266),(-3176064807263)⟩⟩,⟨⟨(-333940667051865),(-333940667051839)⟩,⟨(-832258020107671),(-832258020107645)⟩⟩,⟨⟨7995048916627251,7995048916627303⟩,⟨(-1264160165897850),(-1264160165897798)⟩⟩,⟨⟨1322119342327348,1322119342327351⟩,⟨5085882174089953,5085882174089956⟩⟩,⟨⟨(-76533813201476),(-76533813201474)⟩,⟨945256531766263,945256531766264⟩⟩,⟨⟨66502061809075,66502061809077⟩,⟨83041996114203,83041996114204⟩⟩] +lemma ha4_1_30_eq (j : Fin 7) : ha4_1_30 j = ((ha4_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha4_1_30_contains (j : Fin 7) : (ha4_1_30 j).Contains (fullFactor true 4 30 ((j.val:ℝ)/6)) := by + rw [ha4_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha4_1_29 j) true 4 29 j (ha4_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders40.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders40.lean new file mode 100644 index 0000000000000000000000000000000000000000..e34b2436d934196bf915aa3ef1e085afe6191725 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders40.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers40 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues40 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk40_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_0 j i k) +lemma hk40_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_0 j i k).Contains (fullFactor false 40 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 0 (power40_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha40_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999521,1000000000000000000000000000639⟩,⟨(-639),639⟩⟩,⟨⟨(-500000000000000000166688152963),(-499999999999999999860523712926)⟩,⟨866025403784438646602883133868,866025403784438646908852429614⟩⟩,⟨⟨(-500000000000000000390901517984),(-499999999999999999554674750144)⟩,⟨(-866025403784438647197618749590),(-866025403784438646361249148188)⟩⟩,⟨⟨999999999999999999869333001521,1000000000000000000130666998519⟩,⟨(-83534664159),177799332879⟩⟩,⟨⟨(-500000000000000001197951372854),(-499999999999999998910896090953)⟩,⟨866025403784438645588826182762,866025403784438647875777046111⟩⟩,⟨⟨(-500000000000000001371166930146),(-499999999999999998492773740111)⟩,⟨(-866025403784438648242248529504),(-866025403784438645363751702534)⟩⟩,⟨⟨999999999999999999737872088721,1000000000000000000262127911439⟩,⟨(-167863242479),356392580239⟩⟩] +lemma ha40_0_0_eq (j : Fin 7) : ha40_0_0 j = ((atomPoints j).direct.powBin 7 40).conj := by fin_cases j <;> decide +kernel +lemma ha40_0_0_contains (j : Fin 7) : (ha40_0_0 j).Contains (fullFactor false 40 0 ((j.val:ℝ)/6)) := by + rw [ha40_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 40) ((j.val:ℝ)/6) 40 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 40 (by norm_num)) +noncomputable def hk40_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_1 j i k) +lemma hk40_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_1 j i k).Contains (fullFactor false 40 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 1 (power40_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha40_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-453449841058554462725570902817),(-453449841058554462563922378516)⟩,⟨(-261799387799149436626444379466),(-261799387799149436465303720195)⟩⟩,⟨⟨906899682117108924874806238945,906899682117108925753537188779⟩,⟨(-523598775598298873487684445727),(-523598775598298872610323155530)⟩⟩,⟨⟨(-279286538993),131215943622⟩,⟨1570796326794896619024748758755,1570796326794896619440251241307⟩⟩,⟨⟨(-1813799364234217852927405792435),(-1813799364234217848131853602127)⟩,⟨(-1047197551196597748665650154879),(-1047197551196597743872319440226)⟩⟩,⟨⟨2267249205292772309575573391331,2267249205292772317118677340526⟩,⟨(-1308996938995747186285539962162),(-1308996938995747178745757545528)⟩⟩,⟨⟨(-1119640311873),527357929380⟩,⟨3141592653589793237636500879625,3141592653589793239293499120878⟩⟩] +lemma ha40_0_1_eq (j : Fin 7) : ha40_0_1 j = ((ha40_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha40_0_1_contains (j : Fin 7) : (ha40_0_1 j).Contains (fullFactor false 40 1 ((j.val:ℝ)/6)) := by + rw [ha40_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_0 j) false 40 0 j (ha40_0_0_contains j) +noncomputable def hk40_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_2 j i k) +lemma hk40_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_2 j i k).Contains (fullFactor false 40 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 2 (power40_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha40_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨68538919452009434833782851245,68538919452009434876187543349⟩,⟨(-118712890786751174428387292750),(-118712890786751174385689933180)⟩⟩,⟨⟨274155677808037739167430945585,274155677808037739627688907517⟩,⟨474851563147004697410269074473,474851563147004697871883023359⟩⟩,⟨⟨(-1233700550136169827521293196204),(-1233700550136169827191031318702)⟩,⟨(-219351134787),103056761130⟩⟩,⟨⟨1096622711232150955257759184990,1096622711232150960280814029957⟩,⟨(-1899406252588018792974899672978),(-1899406252588018787946963164767)⟩⟩,⟨⟨1713472986300235866157366020278,1713472986300235876032372278262⟩,⟨2967822269668779355395811861400,2967822269668779365279158713116⟩⟩,⟨⟨(-4934802200544679310733906387177),(-4934802200544679308115391673042)⟩,⟨(-1758726889222),828371898377⟩⟩] +lemma ha40_0_2_eq (j : Fin 7) : ha40_0_2 j = ((ha40_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha40_0_2_contains (j : Fin 7) : (ha40_0_2 j).Contains (fullFactor false 40 2 ((j.val:ℝ)/6)) := by + rw [ha40_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_1 j) false 40 1 j (ha40_0_1_contains j) +noncomputable def hk40_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_3 j i k) +lemma hk40_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_3 j i k).Contains (fullFactor false 40 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 3 (power40_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha40_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨20719308087892496638515086378,20719308087892496646033133049⟩,⟨11962298101967523212480234155,11962298101967523219919326288⟩⟩,⟨⟨(-165754464703139973223534005212),(-165754464703139973061872726738)⟩,⟨95698384815740185641303369770,95698384815740185802268324076⟩⟩,⟨⟨(-53960393945),114851985601⟩,⟨(-645964097506246253744700684719),(-645964097506246253569719802447)⟩⟩,⟨⟨1326035717625119783312267730938,1326035717625119786826650499706⟩,⟨765587078525921484144689712350,765587078525921487653880473828⟩⟩,⟨⟨(-2589913510986562084741762039793),(-2589913510986562076108670905087)⟩,⟨1495287262745940397469671043471,1495287262745940406091999333501⟩⟩,⟨⟨(-867469023461),1841734491617⟩,⟨(-5167712780049970030636957717517),(-5167712780049970027878406180433)⟩⟩] +lemma ha40_0_3_eq (j : Fin 7) : ha40_0_3 j = ((ha40_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha40_0_3_contains (j : Fin 7) : (ha40_0_3 j).Contains (fullFactor false 40 3 ((j.val:ℝ)/6)) := by + rw [ha40_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_2 j) false 40 2 j (ha40_0_2_contains j) +noncomputable def hk40_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_4 j i k) +lemma hk40_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_4 j i k).Contains (fullFactor false 40 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 4 (power40_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha40_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1565861159883012430392017439),(-1565861159883012429413258264)⟩,⟨2712151086516110562883115754,2712151086516110563875858808⟩⟩,⟨⟨(-25053778558128198897507063006),(-25053778558128198855286787857)⟩,⟨(-43394417384257769036483115789),(-43394417384257768994022163331)⟩⟩,⟨⟨253669507901048013602563367825,253669507901048013672085654731⟩,⟨(-21190197151),45102269277⟩⟩,⟨⟨(-400860456930051183007141755261),(-400860456930051181168457790744)⟩,⟨694310678148124303285086967587,694310678148124305127423541829⟩⟩,⟨⟨(-978663224926882771352569067744),(-978663224926882765706153216611)⟩,⟨(-1695094429072569105032303208981),(-1695094429072569099376562621129)⟩⟩,⟨⟨4058712126416768217107451884291,4058712126416768219286932477105⟩,⟨(-681308577831),1446494887182⟩⟩] +lemma ha40_0_4_eq (j : Fin 7) : ha40_0_4 j = ((ha40_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha40_0_4_contains (j : Fin 7) : (ha40_0_4 j).Contains (fullFactor false 40 4 ((j.val:ℝ)/6)) := by + rw [ha40_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_3 j) false 40 3 j (ha40_0_3_contains j) +noncomputable def hk40_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_5 j i k) +lemma hk40_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_5 j i k).Contains (fullFactor false 40 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 5 (power40_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha40_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-284015797627486289538145042),(-284015797627486289433281181)⟩,⟨(-163976597214335483843634275),(-163976597214335483740616899)⟩⟩,⟨⟨9088505524079561259329169402,9088505524079561268251100102⟩,⟨(-5247251110858735485349304449),(-5247251110858735476490008179)⟩⟩,⟨⟨(-14169295783),6657096770⟩,⟨79692626246167045109757080349,79692626246167045131851820439⟩⟩,⟨⟨(-290832176770545960811777083215),(-290832176770545960039135196032)⟩,⟨(-167912035547479535802204510180),(-167912035547479535031483891543)⟩⟩,⟨⟨887549367585894653209075219067,887549367585894656173239223352⟩,⟨(-512426866294798388245771679097),(-512426866294798385287684147549)⟩⟩,⟨⟨(-908859542206),428078804589⟩,⟨2550164039877345443176979678730,2550164039877345444554505146789⟩⟩] +lemma ha40_0_5_eq (j : Fin 7) : ha40_0_5 j = ((ha40_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha40_0_5_contains (j : Fin 7) : (ha40_0_5 j).Contains (fullFactor false 40 5 ((j.val:ℝ)/6)) := by + rw [ha40_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_4 j) false 40 4 j (ha40_0_4_contains j) +noncomputable def hk40_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_6 j i k) +lemma hk40_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_6 j i k).Contains (fullFactor false 40 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 6 (power40_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha40_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨14309657588033580841650470,14309657588033580850685982⟩,⟨(-24785053981387676531406181),(-24785053981387676522176189)⟩⟩,⟨⟨915818085634149173305426110,915818085634149174854580144⟩,⟨1586243454808811296976690569,1586243454808811298538910403⟩⟩,⟨⟨(-20863480763352960876070939696),(-20863480763352960870220139744)⟩,⟨(-3709512962),1742823859⟩⟩,⟨⟨58612357480585547016080501268,58612357480585547285299318362⟩,⟨(-101519581107763923185987178760),(-101519581107763922915961134493)⟩⟩,⟨⟨223588399813024700039162551393,223588399813024701330583430068⟩,⟨387266468459182445104892130677,387266468459182446399485374230⟩⟩,⟨⟨(-1335262768854589496244075003089),(-1335262768854589495518554081257)⟩,⟨(-475877743490),224141537943⟩⟩] +lemma ha40_0_6_eq (j : Fin 7) : ha40_0_6 j = ((ha40_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha40_0_6_contains (j : Fin 7) : (ha40_0_6 j).Contains (fullFactor false 40 6 ((j.val:ℝ)/6)) := by + rw [ha40_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_5 j) false 40 5 j (ha40_0_5_contains j) +noncomputable def hk40_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_7 j i k) +lemma hk40_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_7 j i k).Contains (fullFactor false 40 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 7 (power40_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha40_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1853917702541761441902330,1853917702541761442598634⟩,⟨1070359884617898513797874,1070359884617898514477136⟩⟩,⟨⟨(-237301465925345464731750499),(-237301465925345464497287603)⟩,⟨137006065231091009682321563,137006065231091009914510570⟩⟩,⟨⟨(-391088760),832412763⟩,⟨(-4681754135318688101373957011),(-4681754135318688100046138085)⟩⟩,⟨⟨30374587638444219428561195704,30374587638444219509449484540⟩,⟨17536776349579649216757555427,17536776349579649297363458435⟩⟩,⟨⟨(-144837320511075112926020342945),(-144837320511075112441382570561)⟩,⟨83621865985773321161711307149,83621865985773321644967762999⟩⟩,⟨⟨(-100594486996),213573431851⟩,⟨(-599264529320792077054646359429),(-599264529320792076727125812893)⟩⟩] +lemma ha40_0_7_eq (j : Fin 7) : ha40_0_7 j = ((ha40_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha40_0_7_contains (j : Fin 7) : (ha40_0_7 j).Contains (fullFactor false 40 7 ((j.val:ℝ)/6)) := by + rw [ha40_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_6 j) false 40 6 j (ha40_0_6_contains j) +noncomputable def hk40_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_8 j i k) +lemma hk40_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_8 j i k).Contains (fullFactor false 40 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 8 (power40_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha40_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-70054890629433514751212),(-70054890629433514706530)⟩,⟨121338629888859693691239,121338629888859693737199⟩⟩,⟨⟨(-17934052001134979784352242),(-17934052001134979753901685)⟩,⟨(-31062689251548081607080244),(-31062689251548081576290246)⟩⟩,⟨⟨919260274839426580115411405,919260274839426580379054139⟩,⟨(-76790099),163443864⟩⟩,⟨⟨(-4591117312290554832204694957),(-4591117312290554811087504915)⟩,⟨7952048448396308876437734213,7952048448396308897639550867⟩⟩,⟨⟨(-27365191652122466765613560936),(-27365191652122466607381149460)⟩,⟨(-47397902300335817939070332113),(-47397902300335817780322119760)⟩⟩,⟨⟨235330630358893204478608540342,235330630358893204607974638866⟩,⟨(-39503362668),83870090564⟩⟩] +lemma ha40_0_8_eq (j : Fin 7) : ha40_0_8 j = ((ha40_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha40_0_8_contains (j : Fin 7) : (ha40_0_8 j).Contains (fullFactor false 40 8 ((j.val:ℝ)/6)) := by + rw [ha40_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_7 j) false 40 7 j (ha40_0_7_contains j) +noncomputable def hk40_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_9 j i k) +lemma hk40_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_9 j i k).Contains (fullFactor false 40 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 9 (power40_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha40_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-7059195338064676367895),(-7059195338064676365197)⟩,⟨(-4075628328693792153878),(-4075628328693792151264)⟩⟩,⟨⟨3614308013089114297972787,3614308013089114301566872⟩,⟨(-2086721704291221583720864),(-2086721704291221580171137)⟩⟩,⟨⟨(-28526336),13402401⟩,⟨160441184787359821850481523,160441184787359821897006562⟩⟩,⟨⟨(-1850525702701626523851328871),(-1850525702701626518911551690)⟩,⟨(-1068401512597105452589588603),(-1068401512597105447671994508)⟩⟩,⟨⟨13787490894657571006049304159,13787490894657571052271174227⟩,⟨(-7960211579480062819717199574),(-7960211579480062773663918706)⟩⟩,⟨⟨(-29276184486),13789274884⟩,⟨82145886611128228776647566792,82145886611128228822066332465⟩⟩] +lemma ha40_0_9_eq (j : Fin 7) : ha40_0_9 j = ((ha40_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha40_0_9_contains (j : Fin 7) : (ha40_0_9 j).Contains (fullFactor false 40 9 ((j.val:ℝ)/6)) := by + rw [ha40_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_8 j) false 40 8 j (ha40_0_8_contains j) +noncomputable def hk40_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_10 j i k) +lemma hk40_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_10 j i k).Contains (fullFactor false 40 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 10 (power40_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha40_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨213399400269781075664,213399400269781075802⟩,⟨(-369618603571988403261),(-369618603571988403118)⟩⟩,⟨⟨218520985876255821346646,218520985876255821719069⟩,⟨378489450057716124687343,378489450057716125064921⟩⟩,⟨⟨(-25202042373060605484936250),(-25202042373060605477547892)⟩,⟨(-4480907),2105245⟩⟩,⟨⟨223765489537285960770854880,223765489537285961801505647⟩,⟨(-387573196859101312369975253),(-387573196859101311334157054)⟩⟩,⟨⟨2083978518259580811334142233,2083978518259580823397496481⟩,⟨3609556675507699244035680334,3609556675507699256148027198⟩⟩,⟨⟨(-25806891390014060019967316597),(-25806891390014060005616444652)⟩,⟨(-9197384611),4332028468⟩⟩] +lemma ha40_0_10_eq (j : Fin 7) : ha40_0_10 j = ((ha40_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha40_0_10_contains (j : Fin 7) : (ha40_0_10 j).Contains (fullFactor false 40 10 ((j.val:ℝ)/6)) := by + rw [ha40_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_9 j) false 40 9 j (ha40_0_9_contains j) +noncomputable def hk40_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_11 j i k) +lemma hk40_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_11 j i k).Contains (fullFactor false 40 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 11 (power40_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha40_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨17593804388058740561,17593804388058740568⟩,⟨10157787699515332857,10157787699515332865⟩⟩,⟨⟨(-36032111386744300695148),(-36032111386744300659087)⟩,⟨20803149208607401679470,20803149208607401714992⟩⟩,⟨⟨(-300629),639873⟩,⟨(-3598843235212085341021492),(-3598843235212085339954980)⟩⟩,⟨⟨73793764120052327683992599,73793764120052327881446817⟩,⟨42604849579227958584699820,42604849579227958781070884⟩⟩,⟨⟨(-859072479885680693116431834),(-859072479885680690230965508)⟩,⟨495985727515397110826705361,495985727515397113699355731⟩⟩,⟨⟨(-1237224438),2626766903⟩,⟨(-7370430945714350779380937037),(-7370430945714350775258876782)⟩⟩] +lemma ha40_0_11_eq (j : Fin 7) : ha40_0_11 j = ((ha40_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha40_0_11_contains (j : Fin 7) : (ha40_0_11 j).Contains (fullFactor false 40 11 ((j.val:ℝ)/6)) := by + rw [ha40_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_10 j) false 40 10 j (ha40_0_10_contains j) +noncomputable def hk40_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_12 j i k) +lemma hk40_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_12 j i k).Contains (fullFactor false 40 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 12 (power40_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha40_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-443217100187807443),(-443217100187807442)⟩,⟨767674536308627877,767674536308627878⟩⟩,⟨⟨(-1815417242369259286983),(-1815417242369259283876)⟩,⟨(-3144394900720139786589),(-3144394900720139783431)⟩⟩,⟨⟨471087477881817150300715,471087477881817150441822⟩,⟨(-39353),83760⟩⟩,⟨⟨(-7435949024744486051481067),(-7435949024744486017184181)⟩,⟨12879441513349692541449926,12879441513349692575953185⟩⟩,⟨⟨(-108207299850538926752882408),(-108207299850538926125822882)⟩,⟨(-187420541090973603152136075),(-187420541090973602522028398)⟩⟩,⟨⟨1929574309403923047378067406,1929574309403923048463362284⟩,⟨(-323904601),687685968⟩⟩] +lemma ha40_0_12_eq (j : Fin 7) : ha40_0_12 j = ((ha40_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha40_0_12_contains (j : Fin 7) : (ha40_0_12 j).Contains (fullFactor false 40 12 ((j.val:ℝ)/6)) := by + rw [ha40_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_11 j) false 40 11 j (ha40_0_11_contains j) +noncomputable def hk40_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_13 j i k) +lemma hk40_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_13 j i k).Contains (fullFactor false 40 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 13 (power40_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha40_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-30919495943783800),(-30919495943783799)⟩,⟨(-17851379306351119),(-17851379306351118)⟩⟩,⟨⟨253292510771476882160,253292510771476882416⟩,⟨(-146238499277628361631),(-146238499277628361379)⟩⟩,⟨⟨(-10121),4756⟩,⟨56921729219679268109692,56921729219679268126924⟩⟩,⟨⟨(-2074972248239938622372649),(-2074972248239938616807316)⟩,⟨(-1197985786082331540410041),(-1197985786082331534880747)⟩⟩,⟨⟨37743525322001707832315224,37743525322001707959329062⟩,⟨(-21791234504823142575788733),(-21791234504823142449439522)⟩⟩,⟨⟨(-166186861),78275102⟩,⟨466302805767612564293297329,466302805767612564557055034⟩⟩] +lemma ha40_0_13_eq (j : Fin 7) : ha40_0_13 j = ((ha40_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha40_0_13_contains (j : Fin 7) : (ha40_0_13 j).Contains (fullFactor false 40 13 ((j.val:ℝ)/6)) := by + rw [ha40_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_12 j) false 40 12 j (ha40_0_12_contains j) +noncomputable def hk40_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_14 j i k) +lemma hk40_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_14 j i k).Contains (fullFactor false 40 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 14 (power40_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha40_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨667640024824732,667640024824733⟩,⟨(-1156386444162984),(-1156386444162983)⟩⟩,⟨⟨10938614166728417748,10938614166728417768⟩,⟨18946235501166317741,18946235501166317762⟩⟩,⟨⟨(-6386603083791852242134),(-6386603083791852240180)⟩,⟨(-1136),534⟩⟩,⟨⟨179218254507678396166386,179218254507678396994138⟩,⟨(-310415122451108950440080),(-310415122451108949606519)⟩⟩,⟨⟨4074951323393142866200747,4074951323393142889840966⟩,⟨7058022730486958369643718,7058022730486958393417717⟩⟩,⟨⟨(-104638104924845707148875708),(-104638104924845707089355543)⟩,⟨(-37292245),17564892⟩⟩] +lemma ha40_0_14_eq (j : Fin 7) : ha40_0_14 j = ((ha40_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha40_0_14_contains (j : Fin 7) : (ha40_0_14 j).Contains (fullFactor false 40 14 ((j.val:ℝ)/6)) := by + rw [ha40_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_13 j) false 40 13 j (ha40_0_13_contains j) +noncomputable def hk40_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_15 j i k) +lemma hk40_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_15 j i k).Contains (fullFactor false 40 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 15 (power40_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha40_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨40365501752147,40365501752148⟩,⟨23305033302576,23305033302577⟩⟩,⟨⟨(-1322696761414360854),(-1322696761414360851)⟩,⟨763659331258827442,763659331258827445⟩⟩,⟨⟨(-56),119⟩,⟨(-668803510981146723359),(-668803510981146723151)⟩⟩,⟨⟨43342127478025776361057,43342127478025776477583⟩,⟨25023588966689257608905,25023588966689257724562⟩⟩,⟨⟨(-1231857353275977871360365),(-1231857353275977867207097)⟩,⟨711213174517105744257029,711213174517105748385291⟩⟩,⟨⟨(-3678783),7810470⟩,⟨(-21915353447830215833899061),(-21915353447830215821363427)⟩⟩] +lemma ha40_0_15_eq (j : Fin 7) : ha40_0_15 j = ((ha40_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha40_0_15_contains (j : Fin 7) : (ha40_0_15 j).Contains (fullFactor false 40 15 ((j.val:ℝ)/6)) := by + rw [ha40_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_14 j) false 40 14 j (ha40_0_14_contains j) +noncomputable def hk40_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_16 j i k) +lemma hk40_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_16 j i k).Contains (fullFactor false 40 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 16 (power40_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha40_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-762655431407),(-762655431406)⟩,⟨1320957955864,1320957955865⟩⟩,⟨⟨(-49981386352667222),(-49981386352667221)⟩,⟨(-86570300595549325),(-86570300595549323)⟩⟩,⟨⟨65659631149794723612,65659631149794723634⟩,⟨(-6),12⟩⟩,⟨⟨(-3275580136008399057347),(-3275580136008399042196)⟩,⟨5673471219829920486980,5673471219829920502252⟩⟩,⟨⟨(-116371983552042446010015),(-116371983552042445334158)⟩,⟨(-201562188089707223946773),(-201562188089707223266553)⟩⟩,⟨⟨4303069587032947006111938,4303069587032947008587002⟩,⟨(-722328),1533583⟩⟩] +lemma ha40_0_16_eq (j : Fin 7) : ha40_0_16 j = ((ha40_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha40_0_16_contains (j : Fin 7) : (ha40_0_16 j).Contains (fullFactor false 40 16 ((j.val:ℝ)/6)) := by + rw [ha40_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_15 j) false 40 15 j (ha40_0_15_contains j) +noncomputable def hk40_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_17 j i k) +lemma hk40_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_17 j i k).Contains (fullFactor false 40 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 17 (power40_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha40_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-40685409901),(-40685409900)⟩,⟨(-23489732359),(-23489732358)⟩⟩,⟨⟨5332718046471330,5332718046471331⟩,⟨(-3078846199642598),(-3078846199642597)⟩⟩,⟨⟨(-2),1⟩,⟨6066935731106195666,6066935731106195669⟩⟩,⟨⟨(-698970019787090240140),(-698970019787090238255)⟩,⟨(-403550529079554597692),(-403550529079554595823)⟩⟩,⟨⟨31040504379613153588222,31040504379613153693076⟩,⟨(-17921243559351411792920),(-17921243559351411688780)⟩⟩,⟨⟨(-283406),133486⟩,⟨795205400147551278258500,795205400147551278718423⟩⟩] +lemma ha40_0_17_eq (j : Fin 7) : ha40_0_17 j = ((ha40_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha40_0_17_contains (j : Fin 7) : (ha40_0_17 j).Contains (fullFactor false 40 17 ((j.val:ℝ)/6)) := by + rw [ha40_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_16 j) false 40 16 j (ha40_0_16_contains j) +noncomputable def hk40_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_18 j i k) +lemma hk40_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_18 j i k).Contains (fullFactor false 40 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 18 (power40_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha40_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨683288616,683288617⟩,⟨(-1183490601),(-1183490600)⟩⟩,⟨⟨179120011154259,179120011154260⟩,⟨310244959971482,310244959971483⟩⟩,⟨⟨(-529440020073462377),(-529440020073462376)⟩,⟨(-1),1⟩⟩,⟨⟨46955236204022331265,46955236204022331484⟩,⟨(-81328854786764263491),(-81328854786764263270)⟩⟩,⟨⟨2606539218020916327905,2606539218020916343060⟩,⟨4514658357533078050759,4514658357533078066025⟩⟩,⟨⟨(-138789524622137721186912),(-138789524622137721106198)⟩,⟨(-49464),23298⟩⟩] +lemma ha40_0_18_eq (j : Fin 7) : ha40_0_18 j = ((ha40_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha40_0_18_contains (j : Fin 7) : (ha40_0_18 j).Contains (fullFactor false 40 18 ((j.val:ℝ)/6)) := by + rw [ha40_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_17 j) false 40 17 j (ha40_0_17_contains j) +noncomputable def hk40_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_19 j i k) +lemma hk40_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_19 j i k).Contains (fullFactor false 40 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 19 (power40_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha40_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨32614433,32614434⟩,⟨18829951,18829952⟩⟩,⟨⟨(-17099355913328),(-17099355913327)⟩,⟨9872317739528,9872317739529⟩⟩,⟨⟨(-1),1⟩,⟨(-43770654673137423),(-43770654673137422)⟩⟩,⟨⟨8964987113086656132,8964987113086656157⟩,⟨5175937723022106869,5175937723022106894⟩⟩,⟨⟨(-622070944276038606578),(-622070944276038604472)⟩,⟨359152827132815576431,359152827132815578522⟩⟩,⟨⟨(-3853),8179⟩,⟨(-22948428997269873117241),(-22948428997269873103821)⟩⟩] +lemma ha40_0_19_eq (j : Fin 7) : ha40_0_19 j = ((ha40_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha40_0_19_contains (j : Fin 7) : (ha40_0_19 j).Contains (fullFactor false 40 19 ((j.val:ℝ)/6)) := by + rw [ha40_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_18 j) false 40 18 j (ha40_0_18_contains j) +noncomputable def hk40_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_20 j i k) +lemma hk40_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_20 j i k).Contains (fullFactor false 40 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 20 (power40_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha40_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-492967),(-492966)⟩,⟨853843,853844⟩⟩,⟨⟨(-516913348074),(-516913348073)⟩,⟨(-895320181974),(-895320181973)⟩⟩,⟨⟨3437739179098606,3437739179098608⟩,⟨(-1),1⟩⟩,⟨⟨(-542022930869484435),(-542022930869484432)⟩,⟨938811255133340261,938811255133340264⟩⟩,⟨⟨(-47012995134852432738),(-47012995134852432464)⟩,⟨(-81428896189552855299),(-81428896189552855022)⟩⟩,⟨⟨3604730797462500932853,3604730797462500934974⟩,⟨(-606),1285⟩⟩] +lemma ha40_0_20_eq (j : Fin 7) : ha40_0_20 j = ((ha40_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha40_0_20_contains (j : Fin 7) : (ha40_0_20 j).Contains (fullFactor false 40 20 ((j.val:ℝ)/6)) := by + rw [ha40_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_19 j) false 40 19 j (ha40_0_19_contains j) +noncomputable def hk40_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_21 j i k) +lemma hk40_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_21 j i k).Contains (fullFactor false 40 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 21 (power40_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha40_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-21290),(-21289)⟩,⟨(-12292),(-12291)⟩⟩,⟨⟨44646528671,44646528672⟩,⟨(-25776685347),(-25776685346)⟩⟩,⟨⟨(-1),1⟩,⟨257142289286047,257142289286048⟩⟩,⟨⟨(-93630556896327456),(-93630556896327454)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨10151445319802585598,10151445319802585633⟩,⟨(-5860939688051789428),(-5860939688051789393)⟩⟩,⟨⟨(-193),91⟩,⟨539266466260812848784,539266466260812849104⟩⟩] +lemma ha40_0_21_eq (j : Fin 7) : ha40_0_21 j = ((ha40_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha40_0_21_contains (j : Fin 7) : (ha40_0_21 j).Contains (fullFactor false 40 21 ((j.val:ℝ)/6)) := by + rw [ha40_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_20 j) false 40 20 j (ha40_0_20_contains j) +noncomputable def hk40_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_22 j i k) +lemma hk40_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_22 j i k).Contains (fullFactor false 40 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 22 (power40_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha40_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨292,293⟩,⟨(-507),(-506)⟩⟩,⟨⟨1226967353,1226967354⟩,⟨2125169795,2125169796⟩⟩,⟨⟨(-18359916521553),(-18359916521552)⟩,⟨(-1),1⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨697450191936225607,697450191936225612⟩,⟨1208019168182208035,1208019168182208040⟩⟩,⟨⟨(-77007071306013533823),(-77007071306013533776)⟩,⟨(-28),13⟩⟩] +lemma ha40_0_22_eq (j : Fin 7) : ha40_0_22 j = ((ha40_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha40_0_22_contains (j : Fin 7) : (ha40_0_22 j).Contains (fullFactor false 40 22 ((j.val:ℝ)/6)) := by + rw [ha40_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_21 j) false 40 21 j (ha40_0_21_contains j) +noncomputable def hk40_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_23 j i k) +lemma hk40_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_23 j i k).Contains (fullFactor false 40 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 23 (power40_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha40_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨11,12⟩,⟨6,7⟩⟩,⟨⟨(-96759679),(-96759678)⟩,⟨55864226,55864227⟩⟩,⟨⟨(-1),1⟩,⟨(-1253899540536),(-1253899540535)⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨(-137503773339017308),(-137503773339017306)⟩,⟨79387840551870928,79387840551870929⟩⟩,⟨⟨(-2),4⟩,⟨(-10518471716932064459),(-10518471716932064452)⟩⟩] +lemma ha40_0_23_eq (j : Fin 7) : ha40_0_23 j = ((ha40_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha40_0_23_contains (j : Fin 7) : (ha40_0_23 j).Contains (fullFactor false 40 23 ((j.val:ℝ)/6)) := by + rw [ha40_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_22 j) false 40 22 j (ha40_0_22_contains j) +noncomputable def hk40_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_24 j i k) +lemma hk40_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_24 j i k).Contains (fullFactor false 40 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 24 (power40_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha40_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-2437537),(-2437536)⟩,⟨(-4221938),(-4221937)⟩⟩,⟨⟨82067533018,82067533019⟩,⟨(-1),1⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨(-8659870022990125),(-8659870022990124)⟩,⟨(-14999334866761558),(-14999334866761557)⟩⟩,⟨⟨1376864728037741370,1376864728037741371⟩,⟨(-1),1⟩⟩] +lemma ha40_0_24_eq (j : Fin 7) : ha40_0_24 j = ((ha40_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha40_0_24_contains (j : Fin 7) : (ha40_0_24 j).Contains (fullFactor false 40 24 ((j.val:ℝ)/6)) := by + rw [ha40_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_23 j) false 40 23 j (ha40_0_23_contains j) +noncomputable def hk40_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_25 j i k) +lemma hk40_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_25 j i k).Contains (fullFactor false 40 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 25 (power40_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha40_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨176848,176849⟩,⟨(-102104),(-102103)⟩⟩,⟨⟨(-1),1⟩,⟨5156455176,5156455177⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨1570726674205044,1570726674205046⟩,⟨(-906859468175609),(-906859468175608)⟩⟩,⟨⟨(-1),1⟩,⟨173021924583611076,173021924583611077⟩⟩] +lemma ha40_0_25_eq (j : Fin 7) : ha40_0_25 j = ((ha40_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha40_0_25_contains (j : Fin 7) : (ha40_0_25 j).Contains (fullFactor false 40 25 ((j.val:ℝ)/6)) := by + rw [ha40_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_24 j) false 40 24 j (ha40_0_24_contains j) +noncomputable def hk40_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_26 j i k) +lemma hk40_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_26 j i k).Contains (fullFactor false 40 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 26 (power40_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha40_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨4112,4113⟩,⟨7122,7123⟩⟩,⟨⟨(-311528495),(-311528494)⟩,⟨(-1),1⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨91313559072398,91313559072399⟩,⟨158159723733336,158159723733337⟩⟩,⟨⟨(-20906323353147685),(-20906323353147684)⟩,⟨(-1),1⟩⟩] +lemma ha40_0_26_eq (j : Fin 7) : ha40_0_26 j = ((ha40_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha40_0_26_contains (j : Fin 7) : (ha40_0_26 j).Contains (fullFactor false 40 26 ((j.val:ℝ)/6)) := by + rw [ha40_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_25 j) false 40 25 j (ha40_0_25_contains j) +noncomputable def hk40_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_27 j i k) +lemma hk40_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_27 j i k).Contains (fullFactor false 40 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 27 (power40_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha40_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-277),(-276)⟩,⟨159,160⟩⟩,⟨⟨(-1),1⟩,⟨(-18123994),(-18123993)⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨(-15335599573286),(-15335599573285)⟩,⟨8854012541820,8854012541821⟩⟩,⟨⟨(-1),1⟩,⟨(-2432561179993389),(-2432561179993388)⟩⟩] +lemma ha40_0_27_eq (j : Fin 7) : ha40_0_27 j = ((ha40_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha40_0_27_contains (j : Fin 7) : (ha40_0_27 j).Contains (fullFactor false 40 27 ((j.val:ℝ)/6)) := by + rw [ha40_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_26 j) false 40 26 j (ha40_0_26_contains j) +noncomputable def hk40_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_28 j i k) +lemma hk40_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_28 j i k).Contains (fullFactor false 40 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 28 (power40_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha40_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨(-6),(-5)⟩,⟨(-11),(-10)⟩⟩,⟨⟨1016753,1016754⟩,⟨(-1),1⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨(-827848236791),(-827848236790)⟩,⟨(-1433875207079),(-1433875207078)⟩⟩,⟨⟨272932726159819,272932726159820⟩,⟨(-1),1⟩⟩] +lemma ha40_0_28_eq (j : Fin 7) : ha40_0_28 j = ((ha40_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha40_0_28_contains (j : Fin 7) : (ha40_0_28 j).Contains (fullFactor false 40 28 ((j.val:ℝ)/6)) := by + rw [ha40_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_27 j) false 40 27 j (ha40_0_27_contains j) +noncomputable def hk40_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_29 j i k) +lemma hk40_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_29 j i k).Contains (fullFactor false 40 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 29 (power40_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha40_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨55072,55073⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨129444017721,129444017722⟩,⟨(-74734538477),(-74734538476)⟩⟩,⟨⟨(-1),1⟩,⟨29567015428549,29567015428550⟩⟩] +lemma ha40_0_29_eq (j : Fin 7) : ha40_0_29 j = ((ha40_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha40_0_29_contains (j : Fin 7) : (ha40_0_29 j).Contains (fullFactor false 40 29 ((j.val:ℝ)/6)) := by + rw [ha40_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_28 j) false 40 28 j (ha40_0_28_contains j) +noncomputable def hk40_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power40 j i k).conj.mul (mpower0_30 j i k) +lemma hk40_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk40_0_30 j i k).Contains (fullFactor false 40 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power40 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 30 (power40_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha40_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-2884),(-2883)⟩,⟨(-1),1⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨6521818806,6521818807⟩,⟨11296121531,11296121532⟩⟩,⟨⟨(-3096250615297),(-3096250615296)⟩,⟨(-1),1⟩⟩] +lemma ha40_0_30_eq (j : Fin 7) : ha40_0_30 j = ((ha40_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha40_0_30_contains (j : Fin 7) : (ha40_0_30 j).Contains (fullFactor false 40 30 ((j.val:ℝ)/6)) := by + rw [ha40_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_0_29 j) false 40 29 j (ha40_0_29_contains j) +noncomputable def hk40_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_0 j i k) +lemma hk40_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_0 j i k).Contains (fullFactor true 40 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 0 (kernel40_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha40_1_0 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨97,100⟩,⟨(-7038),(-7035)⟩⟩,⟨⟨346384015365736346,346384015365736351⟩,⟨639293806035028343,639293806035028348⟩⟩,⟨⟨177965390395636590606821606,177965390395636592442449226⟩,⟨558868935012030951364803856,558868935012030953210918094⟩⟩] +lemma ha40_1_0_eq (j : Fin 7) : ha40_1_0 j = atomKernel40_0 j := by fin_cases j <;> decide +kernel +lemma ha40_1_0_contains (j : Fin 7) : (ha40_1_0 j).Contains (fullFactor true 40 0 ((j.val:ℝ)/6)) := by + rw [ha40_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel40_0_contains j +noncomputable def hk40_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_1 j i k) +lemma hk40_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_1 j i k).Contains (fullFactor true 40 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 1 (kernel40_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha40_1_1 : Fin 7 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-21),41⟩,⟨(-30),31⟩⟩,⟨⟨(-11),19⟩,⟨(-6),21⟩⟩,⟨⟨(-32668),(-32648)⟩,⟨10198,10217⟩⟩,⟨⟨2367744446448568917,2367744446448568942⟩,⟨(-1865339093500727158),(-1865339093500727133)⟩⟩,⟨⟨1984673118246228857746059855,1984673118246228864763638546⟩,⟨(-747578353067753521244344664),(-747578353067753514266814852)⟩⟩] +lemma ha40_1_1_eq (j : Fin 7) : ha40_1_1 j = ((ha40_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha40_1_1_contains (j : Fin 7) : (ha40_1_1 j).Contains (fullFactor true 40 1 ((j.val:ℝ)/6)) := by + rw [ha40_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_0 j) true 40 0 j (ha40_1_0_contains j) +noncomputable def hk40_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_2 j i k) +lemma hk40_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_2 j i k).Contains (fullFactor true 40 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 2 (kernel40_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha40_1_2 : Fin 7 → CBox := ![⟨⟨(-130),130⟩,⟨(-130),130⟩⟩,⟨⟨(-262),262⟩,⟨(-262),262⟩⟩,⟨⟨(-179),132⟩,⟨(-182),128⟩⟩,⟨⟨(-43),70⟩,⟨(-79),37⟩⟩,⟨⟨48294,48354⟩,⟨67675,67737⟩⟩,⟨⟨(-4644038374569682974),(-4644038374569682913)⟩,⟨(-4179584643938460437),(-4179584643938460376)⟩⟩,⟨⟨(-1536096813425002938101767972),(-1536096813425002924840000361)⟩,⟨(-3513165506687654169263843136),(-3513165506687654155926786775)⟩⟩] +lemma ha40_1_2_eq (j : Fin 7) : ha40_1_2 j = ((ha40_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha40_1_2_contains (j : Fin 7) : (ha40_1_2 j).Contains (fullFactor true 40 2 ((j.val:ℝ)/6)) := by + rw [ha40_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_1 j) true 40 1 j (ha40_1_1_contains j) +noncomputable def hk40_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_3 j i k) +lemma hk40_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_3 j i k).Contains (fullFactor true 40 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 3 (kernel40_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha40_1_3 : Fin 7 → CBox := ![⟨⟨(-400),400⟩,⟨(-400),400⟩⟩,⟨⟨(-995),995⟩,⟨(-995),995⟩⟩,⟨⟨(-530),514⟩,⟨(-437),606⟩⟩,⟨⟨(-201),104⟩,⟨(-155),148⟩⟩,⟨⟨79794,79921⟩,⟨(-108681),(-108556)⟩⟩,⟨⟨(-4601340322993136421),(-4601340322993136323)⟩,⟨7305324697201660938,7305324697201661036⟩⟩,⟨⟨(-4132564690618217080853584866),(-4132564690618217063956263624)⟩,⟨2068854820492237686352821530,2068854820492237703157050889⟩⟩] +lemma ha40_1_3_eq (j : Fin 7) : ha40_1_3 j = ((ha40_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha40_1_3_contains (j : Fin 7) : (ha40_1_3 j).Contains (fullFactor true 40 3 ((j.val:ℝ)/6)) := by + rw [ha40_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_2 j) true 40 2 j (ha40_1_2_contains j) +noncomputable def hk40_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_4 j i k) +lemma hk40_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_4 j i k).Contains (fullFactor true 40 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 4 (kernel40_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha40_1_4 : Fin 7 → CBox := ![⟨⟨(-922),922⟩,⟨(-922),922⟩⟩,⟨⟨(-2832),2832⟩,⟨(-2832),2832⟩⟩,⟨⟨(-1196),1433⟩,⟨(-1408),1221⟩⟩,⟨⟨(-272),332⟩,⟨(-238),367⟩⟩,⟨⟨(-155804),(-155610)⟩,⟨(-51184),(-50989)⟩⟩,⟨⟨8271290302966393984,8271290302966394102⟩,⟨3413165102952179402,3413165102952179520⟩⟩,⟨⟨2061668539877541451666416628,2061668539877541467636323238⟩,⟨3633580723864899643535444287,3633580723864899659590641987⟩⟩] +lemma ha40_1_4_eq (j : Fin 7) : ha40_1_4 j = ((ha40_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha40_1_4_contains (j : Fin 7) : (ha40_1_4 j).Contains (fullFactor true 40 4 ((j.val:ℝ)/6)) := by + rw [ha40_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_3 j) true 40 3 j (ha40_1_3_contains j) +noncomputable def hk40_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_5 j i k) +lemma hk40_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_5 j i k).Contains (fullFactor true 40 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 5 (kernel40_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha40_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),1700⟩,⟨(-1700),1700⟩⟩,⟨⟨(-6448),6448⟩,⟨(-6448),6448⟩⟩,⟨⟨(-2862),2436⟩,⟨(-2679),2619⟩⟩,⟨⟨(-432),529⟩,⟨(-547),413⟩⟩,⟨⟨(-133),106⟩,⟨159236,159475⟩⟩,⟨⟨1623655690123195417,1623655690123195531⟩,⟨(-7238915776409818093),(-7238915776409817979)⟩⟩,⟨⟨2546765638135768935440963307,2546765638135768947644454795⟩,⟨(-1625405684011285392378477584),(-1625405684011285380236806371)⟩⟩] +lemma ha40_1_5_eq (j : Fin 7) : ha40_1_5 j = ((ha40_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha40_1_5_contains (j : Fin 7) : (ha40_1_5 j).Contains (fullFactor true 40 5 ((j.val:ℝ)/6)) := by + rw [ha40_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_4 j) true 40 4 j (ha40_1_4_contains j) +noncomputable def hk40_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_6 j i k) +lemma hk40_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_6 j i k).Contains (fullFactor true 40 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 6 (kernel40_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha40_1_6 : Fin 7 → CBox := ![⟨⟨(-2612),2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-12235),12235⟩,⟨(-12235),12235⟩⟩,⟨⟨(-4299),4597⟩,⟨(-4241),4655⟩⟩,⟨⟨(-716),556⟩,⟨(-646),626⟩⟩,⟨⟨122584,122830⟩,⟨(-40359),(-40114)⟩⟩,⟨⟨(-5119443804201172519),(-5119443804201172427)⟩,⟨(-255784885787529464),(-255784885787529372)⟩⟩,⟨⟨(-1057932829001996977349198973),(-1057932829001996969656601229)⟩,⟨(-1481871526105482806833486306),(-1481871526105482799103944217)⟩⟩] +lemma ha40_1_6_eq (j : Fin 7) : ha40_1_6 j = ((ha40_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha40_1_6_contains (j : Fin 7) : (ha40_1_6 j).Contains (fullFactor true 40 6 ((j.val:ℝ)/6)) := by + rw [ha40_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_5 j) true 40 5 j (ha40_1_5_contains j) +noncomputable def hk40_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_7 j i k) +lemma hk40_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_7 j i k).Contains (fullFactor true 40 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 7 (kernel40_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha40_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),3439⟩,⟨(-3439),3439⟩⟩,⟨⟨(-19898),19898⟩,⟨(-19898),19898⟩⟩,⟨⟨(-6354),6449⟩,⟨(-6657),6146⟩⟩,⟨⟨(-697),747⟩,⟨(-659),784⟩⟩,⟨⟨(-53228),(-53012)⟩,⟨(-72384),(-72168)⟩⟩,⟨⟨365813296785601149,365813296785601213⟩,⟨3013513439424633265,3013513439424633329⟩⟩,⟨⟨(-736060724431938420772835023),(-736060724431938416576591027)⟩,⟨585496997041533399932033514,585496997041533404109550467⟩⟩] +lemma ha40_1_7_eq (j : Fin 7) : ha40_1_7 j = ((ha40_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha40_1_7_contains (j : Fin 7) : (ha40_1_7 j).Contains (fullFactor true 40 7 ((j.val:ℝ)/6)) := by + rw [ha40_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_6 j) true 40 6 j (ha40_1_6_contains j) +noncomputable def hk40_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_8 j i k) +lemma hk40_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_8 j i k).Contains (fullFactor true 40 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 8 (kernel40_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha40_1_8 : Fin 7 → CBox := ![⟨⟨(-3962),3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-28316),28316⟩,⟨(-28316),28316⟩⟩,⟨⟨(-8255),7868⟩,⟨(-7935),8188⟩⟩,⟨⟨(-686),748⟩,⟨(-755),679⟩⟩,⟨⟨(-31761),(-31594)⟩,⟨44284,44451⟩⟩,⟨⟨1506681296055313545,1506681296055313584⟩,⟨(-452111038342034514),(-452111038342034475)⟩⟩,⟨⟨281557186603028290420797546,281557186603028292405826935⟩,⟨318499213378149643897238281,318499213378149645890486172⟩⟩] +lemma ha40_1_8_eq (j : Fin 7) : ha40_1_8 j = ((ha40_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha40_1_8_contains (j : Fin 7) : (ha40_1_8 j).Contains (fullFactor true 40 8 ((j.val:ℝ)/6)) := by + rw [ha40_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_7 j) true 40 7 j (ha40_1_7_contains j) +noncomputable def hk40_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_9 j i k) +lemma hk40_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_9 j i k).Contains (fullFactor true 40 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 9 (kernel40_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha40_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),4057⟩,⟨(-4057),4057⟩⟩,⟨⟨(-35817),35817⟩,⟨(-35817),35817⟩⟩,⟨⟨(-8845),9202⟩,⟨(-8982),9065⟩⟩,⟨⟨(-664),602⟩,⟨(-639),627⟩⟩,⟨⟨28051,28166⟩,⟨8733,8848⟩⟩,⟨⟨(-323130073323018360),(-323130073323018338)⟩,⟨(-648535005380141616),(-648535005380141594)⟩⟩,⟨⟨121915557279061779596669674,121915557279061780438251326⟩,⟨(-119612888636203860505051893),(-119612888636203859666640969)⟩⟩] +lemma ha40_1_9_eq (j : Fin 7) : ha40_1_9 j = ((ha40_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha40_1_9_contains (j : Fin 7) : (ha40_1_9 j).Contains (fullFactor true 40 9 ((j.val:ℝ)/6)) := by + rw [ha40_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_8 j) true 40 8 j (ha40_1_8_contains j) +noncomputable def hk40_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_10 j i k) +lemma hk40_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_10 j i k).Contains (fullFactor true 40 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 10 (kernel40_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha40_1_10 : Fin 7 → CBox := ![⟨⟨(-3739),3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-40775),40775⟩,⟨(-40775),40775⟩⟩,⟨⟨(-9157),9024⟩,⟨(-9203),8978⟩⟩,⟨⟨(-497),509⟩,⟨(-485),521⟩⟩,⟨⟨(-234),(-162)⟩,⟨(-14354),(-14282)⟩⟩,⟨⟨(-242187535003552317),(-242187535003552305)⟩,⟨177684847944160322,177684847944160334⟩⟩,⟨⟨(-45481774851456876984216890),(-45481774851456876665517088)⟩,⟨(-41778013856444853089006940),(-41778013856444852769219208)⟩⟩] +lemma ha40_1_10_eq (j : Fin 7) : ha40_1_10 j = ((ha40_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha40_1_10_contains (j : Fin 7) : (ha40_1_10 j).Contains (fullFactor true 40 10 ((j.val:ℝ)/6)) := by + rw [ha40_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_9 j) true 40 9 j (ha40_1_9_contains j) +noncomputable def hk40_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_11 j i k) +lemma hk40_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_11 j i k).Contains (fullFactor true 40 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 11 (kernel40_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha40_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),3133⟩,⟨(-3133),3133⟩⟩,⟨⟨(-42199),42199⟩,⟨(-42199),42199⟩⟩,⟨⟨(-8348),8303⟩,⟨(-8244),8407⟩⟩,⟨⟨(-357),370⟩,⟨(-371),356⟩⟩,⟨⟨(-6007),(-5966)⟩,⟨2035,2076⟩⟩,⟨⟨81497191473969017,81497191473969023⟩,⟨78569403991563599,78569403991563605⟩⟩,⟨⟨(-12938293678809876355135207),(-12938293678809876244670428)⟩,⟨15643697368760384497823902,15643697368760384607953780⟩⟩] +lemma ha40_1_11_eq (j : Fin 7) : ha40_1_11 j = ((ha40_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha40_1_11_contains (j : Fin 7) : (ha40_1_11 j).Contains (fullFactor true 40 11 ((j.val:ℝ)/6)) := by + rw [ha40_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_10 j) true 40 10 j (ha40_1_10_contains j) +noncomputable def hk40_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_12 j i k) +lemma hk40_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_12 j i k).Contains (fullFactor true 40 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 12 (kernel40_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha40_1_12 : Fin 7 → CBox := ![⟨⟨(-2406),2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-40034),40034⟩,⟨(-40034),40034⟩⟩,⟨⟨(-6945),7034⟩,⟨(-7013),6966⟩⟩,⟨⟨(-246),236⟩,⟨(-242),240⟩⟩,⟨⟨1536,1558⟩,⟨2034,2056⟩⟩,⟨⟨21965032701093443,21965032701093447⟩,⟨(-32356415038641788),(-32356415038641784)⟩⟩,⟨⟨4909938778159874873450914,4909938778159874908335228⟩,⟨3648587153778259364987562,3648587153778259399964956⟩⟩] +lemma ha40_1_12_eq (j : Fin 7) : ha40_1_12 j = ((ha40_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha40_1_12_contains (j : Fin 7) : (ha40_1_12 j).Contains (fullFactor true 40 12 ((j.val:ℝ)/6)) := by + rw [ha40_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_11 j) true 40 11 j (ha40_1_11_contains j) +noncomputable def hk40_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_13 j i k) +lemma hk40_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_13 j i k).Contains (fullFactor true 40 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 13 (kernel40_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha40_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),1706⟩,⟨(-1706),1706⟩⟩,⟨⟨(-35058),35058⟩,⟨(-35058),35058⟩⟩,⟨⟨(-5443),5390⟩,⟨(-5425),5408⟩⟩,⟨⟨(-147),148⟩,⟨(-145),150⟩⟩,⟨⟨541,552⟩,⟨(-794),(-782)⟩⟩,⟨⟨(-11358124411285479),(-11358124411285477)⟩,⟨(-5149605768211994),(-5149605768211992)⟩⟩,⟨⟨942552888006158443861305,942552888006158454084344⟩,⟨(-1416540324858875858334417),(-1416540324858875848134831)⟩⟩] +lemma ha40_1_13_eq (j : Fin 7) : ha40_1_13 j = ((ha40_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha40_1_13_contains (j : Fin 7) : (ha40_1_13 j).Contains (fullFactor true 40 13 ((j.val:ℝ)/6)) := by + rw [ha40_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_12 j) true 40 12 j (ha40_1_12_contains j) +noncomputable def hk40_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_14 j i k) +lemma hk40_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_14 j i k).Contains (fullFactor true 40 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 14 (kernel40_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha40_1_14 : Fin 7 → CBox := ![⟨⟨(-1123),1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-28508),28508⟩,⟨(-28508),28508⟩⟩,⟨⟨(-3892),3904⟩,⟨(-3885),3911⟩⟩,⟨⟨(-83),85⟩,⟨(-85),83⟩⟩,⟨⟨(-322),(-316)⟩,⟨(-98),(-92)⟩⟩,⟨⟨(-931291415034147),(-931291415034146)⟩,⟨3573442424518372,3573442424518374⟩⟩,⟨⟨(-378010736779680055172301),(-378010736779680052403198)⟩,⟨(-224113892390746525015629),(-224113892390746522241161)⟩⟩] +lemma ha40_1_14_eq (j : Fin 7) : ha40_1_14 j = ((ha40_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha40_1_14_contains (j : Fin 7) : (ha40_1_14 j).Contains (fullFactor true 40 14 ((j.val:ℝ)/6)) := by + rw [ha40_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_13 j) true 40 13 j (ha40_1_13_contains j) +noncomputable def hk40_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_15 j i k) +lemma hk40_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_15 j i k).Contains (fullFactor true 40 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 15 (kernel40_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha40_1_15 : Fin 7 → CBox := ![⟨⟨(-690),690⟩,⟨(-690),690⟩⟩,⟨⟨(-21636),21636⟩,⟨(-21636),21636⟩⟩,⟨⟨(-2616),2621⟩,⟨(-2625),2612⟩⟩,⟨⟨(-45),44⟩,⟨(-45),45⟩⟩,⟨⟨1,5⟩,⟨106,110⟩⟩,⟨⟨1016965561011323,1016965561011325⟩,⟨85853841957985,85853841957986⟩⟩,⟨⟨(-49220050476064148297996),(-49220050476064147595232)⟩,⟨93805948709273671364437,93805948709273672066088⟩⟩] +lemma ha40_1_15_eq (j : Fin 7) : ha40_1_15 j = ((ha40_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha40_1_15_contains (j : Fin 7) : (ha40_1_15 j).Contains (fullFactor true 40 15 ((j.val:ℝ)/6)) := by + rw [ha40_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_14 j) true 40 14 j (ha40_1_14_contains j) +noncomputable def hk40_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_16 j i k) +lemma hk40_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_16 j i k).Contains (fullFactor true 40 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 16 (kernel40_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha40_1_16 : Fin 7 → CBox := ![⟨⟨(-398),398⟩,⟨(-398),398⟩⟩,⟨⟨(-15395),15395⟩,⟨(-15395),15395⟩⟩,⟨⟨(-1652),1646⟩,⟨(-1648),1650⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨30,32⟩,⟨(-12),(-10)⟩⟩,⟨⟨(-22844725416934),(-22844725416933)⟩,⟨(-263442041938007),(-263442041938005)⟩⟩,⟨⟨21748621082995046956479,21748621082995047123152⟩,⟨10007539142231467342543,10007539142231467509424⟩⟩] +lemma ha40_1_16_eq (j : Fin 7) : ha40_1_16 j = ((ha40_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha40_1_16_contains (j : Fin 7) : (ha40_1_16 j).Contains (fullFactor true 40 16 ((j.val:ℝ)/6)) := by + rw [ha40_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_15 j) true 40 15 j (ha40_1_15_contains j) +noncomputable def hk40_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_17 j i k) +lemma hk40_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_17 j i k).Contains (fullFactor true 40 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 17 (kernel40_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha40_1_17 : Fin 7 → CBox := ![⟨⟨(-216),216⟩,⟨(-216),216⟩⟩,⟨⟨(-10310),10310⟩,⟨(-10310),10310⟩⟩,⟨⟨(-976),979⟩,⟨(-977),978⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-7),(-5)⟩,⟨(-8),(-7)⟩⟩,⟨⟨(-62361710301011),(-62361710301009)⟩,⟨16404177844075,16404177844077⟩⟩,⟨⟨1885510170541198203898,1885510170541198241196⟩,⟨(-4730234483802039233298),(-4730234483802039196035)⟩⟩] +lemma ha40_1_17_eq (j : Fin 7) : ha40_1_17 j = ((ha40_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha40_1_17_contains (j : Fin 7) : (ha40_1_17 j).Contains (fullFactor true 40 17 ((j.val:ℝ)/6)) := by + rw [ha40_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_16 j) true 40 16 j (ha40_1_16_contains j) +noncomputable def hk40_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_18 j i k) +lemma hk40_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_18 j i k).Contains (fullFactor true 40 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 18 (kernel40_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha40_1_18 : Fin 7 → CBox := ![⟨⟨(-111),111⟩,⟨(-111),111⟩⟩,⟨⟨(-6521),6521⟩,⟨(-6521),6521⟩⟩,⟨⟨(-548),547⟩,⟨(-548),547⟩⟩,⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-2),(-1)⟩,⟨1,3⟩⟩,⟨⟨6163199413551,6163199413553⟩,⟨13511805720081,13511805720082⟩⟩,⟨⟨(-968613803248514031848),(-968613803248514023979)⟩,⟨(-328911907090003044810),(-328911907090003036936)⟩⟩] +lemma ha40_1_18_eq (j : Fin 7) : ha40_1_18 j = ((ha40_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha40_1_18_contains (j : Fin 7) : (ha40_1_18 j).Contains (fullFactor true 40 18 ((j.val:ℝ)/6)) := by + rw [ha40_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_17 j) true 40 17 j (ha40_1_17_contains j) +noncomputable def hk40_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_19 j i k) +lemma hk40_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_19 j i k).Contains (fullFactor true 40 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 19 (kernel40_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha40_1_19 : Fin 7 → CBox := ![⟨⟨(-54),54⟩,⟨(-54),54⟩⟩,⟨⟨(-3908),3908⟩,⟨(-3908),3908⟩⟩,⟨⟨(-291),291⟩,⟨(-291),291⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨2676787052090,2676787052092⟩,⟨(-1826048788243),(-1826048788242)⟩⟩,⟨⟨(-52938399912444025343),(-52938399912444023768)⟩,⟨187339502992304506687,187339502992304508262⟩⟩] +lemma ha40_1_19_eq (j : Fin 7) : ha40_1_19 j = ((ha40_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha40_1_19_contains (j : Fin 7) : (ha40_1_19 j).Contains (fullFactor true 40 19 ((j.val:ℝ)/6)) := by + rw [ha40_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_18 j) true 40 18 j (ha40_1_18_contains j) +noncomputable def hk40_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_20 j i k) +lemma hk40_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_20 j i k).Contains (fullFactor true 40 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 20 (kernel40_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha40_1_20 : Fin 7 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-2225),2225⟩,⟨(-2225),2225⟩⟩,⟨⟨(-147),147⟩,⟨(-147),147⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-467261224227),(-467261224226)⟩,⟨(-482468609017),(-482468609016)⟩⟩,⟨⟨34321412213631553232,34321412213631553532⟩,⟨7799228685556768865,7799228685556769165⟩⟩] +lemma ha40_1_20_eq (j : Fin 7) : ha40_1_20 j = ((ha40_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha40_1_20_contains (j : Fin 7) : (ha40_1_20 j).Contains (fullFactor true 40 20 ((j.val:ℝ)/6)) := by + rw [ha40_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_19 j) true 40 19 j (ha40_1_19_contains j) +noncomputable def hk40_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_21 j i k) +lemma hk40_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_21 j i k).Contains (fullFactor true 40 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 21 (kernel40_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha40_1_21 : Fin 7 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-1207),1207⟩,⟨(-1207),1207⟩⟩,⟨⟨(-71),71⟩,⟨(-71),71⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-78187269680),(-78187269679)⟩,⟨107081214276,107081214277⟩⟩,⟨⟨1034217675189435481,1034217675189435536⟩,⟨(-5971428595914992448),(-5971428595914992393)⟩⟩] +lemma ha40_1_21_eq (j : Fin 7) : ha40_1_21 j = ((ha40_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha40_1_21_contains (j : Fin 7) : (ha40_1_21 j).Contains (fullFactor true 40 21 ((j.val:ℝ)/6)) := by + rw [ha40_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_20 j) true 40 20 j (ha40_1_20_contains j) +noncomputable def hk40_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_22 j i k) +lemma hk40_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_22 j i k).Contains (fullFactor true 40 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 22 (kernel40_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha40_1_22 : Fin 7 → CBox := ![⟨⟨(-5),5⟩,⟨(-5),5⟩⟩,⟨⟨(-625),625⟩,⟨(-625),625⟩⟩,⟨⟨(-33),33⟩,⟨(-33),33⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨22387552197,22387552198⟩,⟨11090922931,11090922932⟩⟩,⟨⟨(-988962848599431676),(-988962848599431666)⟩,⟨(-118786899046655844),(-118786899046655833)⟩⟩] +lemma ha40_1_22_eq (j : Fin 7) : ha40_1_22 j = ((ha40_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha40_1_22_contains (j : Fin 7) : (ha40_1_22 j).Contains (fullFactor true 40 22 ((j.val:ℝ)/6)) := by + rw [ha40_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_21 j) true 40 21 j (ha40_1_21_contains j) +noncomputable def hk40_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_23 j i k) +lemma hk40_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_23 j i k).Contains (fullFactor true 40 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 23 (kernel40_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha40_1_23 : Fin 7 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-310),310⟩,⟨(-310),310⟩⟩,⟨⟨(-15),15⟩,⟨(-15),15⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨1284436423,1284436424⟩,⟨(-4316137878),(-4316137877)⟩⟩,⟨⟨(-10575726714460746),(-10575726714460743)⟩,⟨156238070085025944,156238070085025947⟩⟩] +lemma ha40_1_23_eq (j : Fin 7) : ha40_1_23 j = ((ha40_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha40_1_23_contains (j : Fin 7) : (ha40_1_23 j).Contains (fullFactor true 40 23 ((j.val:ℝ)/6)) := by + rw [ha40_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_22 j) true 40 22 j (ha40_1_22_contains j) +noncomputable def hk40_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_24 j i k) +lemma hk40_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_24 j i k).Contains (fullFactor true 40 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 24 (kernel40_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha40_1_24 : Fin 7 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-148),148⟩,⟨(-148),148⟩⟩,⟨⟨(-7),7⟩,⟨(-7),7⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-772389001),(-772389000)⟩,⟨(-91976058),(-91976057)⟩⟩,⟨⟨23590232457303446,23590232457303447⟩,⟨368828254149167,368828254149169⟩⟩] +lemma ha40_1_24_eq (j : Fin 7) : ha40_1_24 j = ((ha40_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha40_1_24_contains (j : Fin 7) : (ha40_1_24 j).Contains (fullFactor true 40 24 ((j.val:ℝ)/6)) := by + rw [ha40_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_23 j) true 40 23 j (ha40_1_23_contains j) +noncomputable def hk40_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_25 j i k) +lemma hk40_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_25 j i k).Contains (fullFactor true 40 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 25 (kernel40_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha40_1_25 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-68),68⟩,⟨(-68),68⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨6729921,6729922⟩,⟨128808676,128808678⟩⟩,⟨⟨(-123910745632842),(-123910745632841)⟩,⟨(-3410167991139813),(-3410167991139812)⟩⟩] +lemma ha40_1_25_eq (j : Fin 7) : ha40_1_25 j = ((ha40_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha40_1_25_contains (j : Fin 7) : (ha40_1_25 j).Contains (fullFactor true 40 25 ((j.val:ℝ)/6)) := by + rw [ha40_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_24 j) true 40 24 j (ha40_1_24_contains j) +noncomputable def hk40_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_26 j i k) +lemma hk40_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_26 j i k).Contains (fullFactor true 40 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 26 (kernel40_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha40_1_26 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-30),30⟩,⟨(-30),30⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨20056986,20056988⟩,⟨(-4546705),(-4546704)⟩⟩,⟨⟨(-472728395220447),(-472728395220445)⟩,⟨41837831168059,41837831168060⟩⟩] +lemma ha40_1_26_eq (j : Fin 7) : ha40_1_26 j = ((ha40_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha40_1_26_contains (j : Fin 7) : (ha40_1_26 j).Contains (fullFactor true 40 26 ((j.val:ℝ)/6)) := by + rw [ha40_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_25 j) true 40 25 j (ha40_1_25_contains j) +noncomputable def hk40_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_27 j i k) +lemma hk40_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_27 j i k).Contains (fullFactor true 40 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 27 (kernel40_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha40_1_27 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-13),13⟩,⟨(-13),13⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1211144),(-1211143)⟩,⟨(-2916166),(-2916165)⟩⟩,⟨⟨8883084964888,8883084964889⟩,⟨62932537572148,62932537572150⟩⟩] +lemma ha40_1_27_eq (j : Fin 7) : ha40_1_27 j = ((ha40_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha40_1_27_contains (j : Fin 7) : (ha40_1_27 j).Contains (fullFactor true 40 27 ((j.val:ℝ)/6)) := by + rw [ha40_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_26 j) true 40 26 j (ha40_1_26_contains j) +noncomputable def hk40_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_28 j i k) +lemma hk40_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_28 j i k).Contains (fullFactor true 40 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 28 (kernel40_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha40_1_28 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-6),6⟩,⟨(-6),6⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-395014),(-395013)⟩,⟨250062,250063⟩⟩,⟨⟨8056536613963,8056536613964⟩,⟨(-1567646598841),(-1567646598840)⟩⟩] +lemma ha40_1_28_eq (j : Fin 7) : ha40_1_28 j = ((ha40_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha40_1_28_contains (j : Fin 7) : (ha40_1_28 j).Contains (fullFactor true 40 28 ((j.val:ℝ)/6)) := by + rw [ha40_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_27 j) true 40 27 j (ha40_1_27_contains j) +noncomputable def hk40_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_29 j i k) +lemma hk40_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_29 j i k).Contains (fullFactor true 40 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 29 (kernel40_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha40_1_29 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨44820,44821⟩,⟨49573,49574⟩⟩,⟨⟨(-247366054809),(-247366054808)⟩,⟨(-993034525320),(-993034525319)⟩⟩] +lemma ha40_1_29_eq (j : Fin 7) : ha40_1_29 j = ((ha40_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha40_1_29_contains (j : Fin 7) : (ha40_1_29 j).Contains (fullFactor true 40 29 ((j.val:ℝ)/6)) := by + rw [ha40_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_28 j) true 40 28 j (ha40_1_28_contains j) +noncomputable def hk40_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel40_0 j i k).mul (mpower1_30 j i k) +lemma hk40_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk40_1_30 j i k).Contains (fullFactor true 40 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk40_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel40_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 40 30 (kernel40_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha40_1_30 : Fin 7 → CBox := ![⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨5698,5699⟩,⟨(-7268),(-7267)⟩⟩,⟨⟨(-117980825813),(-117980825812)⟩,⟨35990356281,35990356282⟩⟩] +lemma ha40_1_30_eq (j : Fin 7) : ha40_1_30 j = ((ha40_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha40_1_30_contains (j : Fin 7) : (ha40_1_30 j).Contains (fullFactor true 40 30 ((j.val:ℝ)/6)) := by + rw [ha40_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha40_1_29 j) true 40 29 j (ha40_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders7.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders7.lean new file mode 100644 index 0000000000000000000000000000000000000000..15b94dfed0eb5a824a844b7165172b655bb1e13d --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders7.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk7_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_0 j i k) +lemma hk7_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_0 j i k).Contains (fullFactor false 7 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 0 (power7_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha7_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999917,1000000000000000000000000000111⟩,⟨(-111),111⟩⟩,⟨⟨(-866025403784438646771800588553),(-866025403784438646752896366797)⟩,⟨(-500000000000000000012307326611),(-499999999999999999992454749917)⟩⟩,⟨⟨499999999999999999968936654721,500000000000000000021539192201⟩,⟨866025403784438646739824219579,866025403784438646793120894275⟩⟩,⟨⟨(-14618566227),31114883253⟩,⟨(-1000000000000000000022866724740),(-999999999999999999977133275267)⟩⟩,⟨⟨(-500000000000000000082050976378),(-499999999999999999936997329789)⟩,⟨866025403784438646685951299793,866025403784438646830497497000⟩⟩,⟨⟨866025403784438646679347406341,866025403784438646861845866006⟩,⟨(-500000000000000000079092213025),(-499999999999999999897097404267)⟩⟩,⟨⟨(-1000000000000000000045872384501),(-999999999999999999954127615527)⟩,⟨(-62368701541),29376067433⟩⟩] +lemma ha7_0_0_eq (j : Fin 7) : ha7_0_0 j = ((atomPoints j).direct.powBin 7 7).conj := by fin_cases j <;> decide +kernel +lemma ha7_0_0_contains (j : Fin 7) : (ha7_0_0 j).Contains (fullFactor false 7 0 ((j.val:ℝ)/6)) := by + rw [ha7_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 7) ((j.val:ℝ)/6) 7 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 7 (by norm_num)) +noncomputable def hk7_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_1 j i k) +lemma hk7_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_1 j i k).Contains (fullFactor false 7 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 1 (power7_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha7_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨261799387799149436534382649626,261799387799149436545610767812⟩,⟨(-453449841058554462653810726644),(-453449841058554462642469123601)⟩⟩,⟨⟨(-906899682117108925329948025229),(-906899682117108925271249126650)⟩,⟨523598775598298873044137207557,523598775598298873100889122663⟩⟩,⟨⟨1570796326794896619194081032783,1570796326794896619270918967228⟩,⟨(-22962790133),48875144323⟩⟩,⟨⟨(-1813799364234217850738177424145),(-1813799364234217850429667073949)⟩,⟨(-1047197551196597746328513829741),(-1047197551196597746021380849404)⟩⟩,⟨⟨1308996938995747182422268301007,1308996938995747182902896262831⟩,⟨2267249205292772313019794889810,2267249205292772313504791618325⟩⟩,⟨⟨(-92287637639),195937054576⟩,⟨(-3141592653589793238614112346151),(-3141592653589793238315887653936)⟩⟩] +lemma ha7_0_1_eq (j : Fin 7) : ha7_0_1 j = ((ha7_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha7_0_1_contains (j : Fin 7) : (ha7_0_1 j).Contains (fullFactor false 7 1 ((j.val:ℝ)/6)) := by + rw [ha7_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_0 j) false 7 0 j (ha7_0_0_contains j) +noncomputable def hk7_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_2 j i k) +lemma hk7_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_2 j i k).Contains (fullFactor false 7 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 2 (power7_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha7_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨118712890786751174406253422957,118712890786751174409600522559⟩,⟨68538919452009434851867672679,68538919452009434855025353305⟩⟩,⟨⟨(-274155677808037739425163349954),(-274155677808037739394575452063)⟩,⟨(-474851563147004697650092255967),(-474851563147004697617846085070)⟩⟩,⟨⟨(-38386448588),18034933197⟩,⟨1233700550136169827324024575728,1233700550136169827388299939138⟩⟩,⟨⟨1096622711232150957508251030052,1096622711232150957833370593460⟩,⟨(-1899406252588018790682345086695),(-1899406252588018790353227805565)⟩⟩,⟨⟨(-2967822269668779360548593364875),(-2967822269668779359904287260132)⟩,⟨1713472986300235870969907345385,1713472986300235871604502030124⟩⟩,⟨⟨4934802200544679309182569922603,4934802200544679309666728136963⟩,⟨(-144965082212),307777205611⟩⟩] +lemma ha7_0_2_eq (j : Fin 7) : ha7_0_2 j = ((ha7_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha7_0_2_contains (j : Fin 7) : (ha7_0_2 j).Contains (fullFactor false 7 2 ((j.val:ℝ)/6)) := by + rw [ha7_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_1 j) false 7 1 j (ha7_0_1_contains j) +noncomputable def hk7_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_3 j i k) +lemma hk7_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_3 j i k).Contains (fullFactor false 7 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 3 (power7_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha7_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-11962298101967523216225827356),(-11962298101967523215636630941)⟩,⟨20719308087892496642104092401,20719308087892496642754223093⟩⟩,⟨⟨165754464703139973134330772466,165754464703139973146114422381⟩,⟨(-95698384815740185731573568098),(-95698384815740185720591760087)⟩⟩,⟨⟨(-645964097506246253675065578156),(-645964097506246253639354908989)⟩,⟨(-20099097481),9443068940⟩⟩,⟨⟨1326035717625119784992157357188,1326035717625119785226145467213⟩,⟨765587078525921485715829411774,765587078525921485945242624900⟩⟩,⟨⟨(-1495287262745940402227953599446),(-1495287262745940401669405619041)⟩,⟨(-2589913510986562080613564999416),(-2589913510986562080043057902739)⟩⟩,⟨⟨(-322303536030),151807079102⟩,⟨5167712780049970028995952630064,5167712780049970029519411267203⟩⟩] +lemma ha7_0_3_eq (j : Fin 7) : ha7_0_3 j = ((ha7_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha7_0_3_contains (j : Fin 7) : (ha7_0_3 j).Contains (fullFactor false 7 3 ((j.val:ℝ)/6)) := by + rw [ha7_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_2 j) false 7 2 j (ha7_0_2_contains j) +noncomputable def hk7_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_4 j i k) +lemma hk7_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_4 j i k).Contains (fullFactor false 7 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 4 (power7_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha7_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2712151086516110563446650498),(-2712151086516110563352915544)⟩,⟨(-1565861159883012429908539559),(-1565861159883012429826429637)⟩⟩,⟨⟨25053778558128198876044439901,25053778558128198878999219170⟩,⟨43394417384257769012991635344,43394417384257769016214716400⟩⟩,⟨⟨(-3708284502),7892897124⟩,⟨(-253669507901048013644740012330),(-253669507901048013629909010218)⟩⟩,⟨⟨(-400860456930051182112501069622),(-400860456930051181991104613657)⟩,⟨694310678148124304164675119032,694310678148124304289401066477⟩⟩,⟨⟨1695094429072569101951612889505,1695094429072569102330404564269⟩,⟨(-978663224926882768823557048735),(-978663224926882768454873068619)⟩⟩,⟨⟨(-4058712126416768218409213547517),(-4058712126416768217985170813343)⟩,⟨(-253136605255),119229001118⟩⟩] +lemma ha7_0_4_eq (j : Fin 7) : ha7_0_4 j = ((ha7_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha7_0_4_contains (j : Fin 7) : (ha7_0_4 j).Contains (fullFactor false 7 4 ((j.val:ℝ)/6)) := by + rw [ha7_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_3 j) false 7 3 j (ha7_0_3_contains j) +noncomputable def hk7_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_5 j i k) +lemma hk7_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_5 j i k).Contains (fullFactor false 7 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 5 (power7_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha7_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨163976597214335483783884104,163976597214335483793004590⟩,⟨(-284015797627486289493198453),(-284015797627486289482478500)⟩⟩,⟨⟨(-9088505524079561264006096460),(-9088505524079561263302126330)⟩,⟨5247251110858735480837480657,5247251110858735481473030700⟩⟩,⟨⟨79692626246167045118347967274,79692626246167045123260933511⟩,⟨(-1164991935),2479626763⟩⟩,⟨⟨(-290832176770545960460747049600),(-290832176770545960407576219334)⟩,⟨(-167912035547479535427458296099),(-167912035547479535376073386925)⟩⟩,⟨⟨512426866294798386726910496523,512426866294798386921584082471⟩,⟨887549367585894654557368386693,887549367585894654758528401190⟩⟩,⟨⟨(-74913790802),159050419885⟩,⟨(-2550164039877345444003018078567),(-2550164039877345443728466746616)⟩⟩] +lemma ha7_0_5_eq (j : Fin 7) : ha7_0_5 j = ((ha7_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha7_0_5_contains (j : Fin 7) : (ha7_0_5 j).Contains (fullFactor false 7 5 ((j.val:ℝ)/6)) := by + rw [ha7_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_4 j) false 7 4 j (ha7_0_4_contains j) +noncomputable def hk7_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_6 j i k) +lemma hk7_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_6 j i k).Contains (fullFactor false 7 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 6 (power7_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha7_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨24785053981387676526469465,24785053981387676527483851⟩,⟨14309657588033580845426246,14309657588033580846267709⟩⟩,⟨⟨(-915818085634149174178042748),(-915818085634149174064203199)⟩,⟨(-1586243454808811297798017500),(-1586243454808811297670102363)⟩⟩,⟨⟨(-649164769),304994176⟩,⟨20863480763352960872469228682,20863480763352960873821850758⟩⟩,⟨⟨58612357480585547136364926512,58612357480585547154488212460⟩,⟨(-101519581107763923063454581561),(-101519581107763923044571313614)⟩⟩,⟨⟨(-387266468459182445782201328972),(-387266468459182445693196007107)⟩,⟨223588399813024700667143513170,223588399813024700752797593188⟩⟩,⟨⟨1335262768854589495807312034761,1335262768854589495955317049410⟩,⟨(-39224769140),83278605111⟩⟩] +lemma ha7_0_6_eq (j : Fin 7) : ha7_0_6 j = ((ha7_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha7_0_6_contains (j : Fin 7) : (ha7_0_6 j).Contains (fullFactor false 7 6 ((j.val:ℝ)/6)) := by + rw [ha7_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_5 j) false 7 5 j (ha7_0_5_contains j) +noncomputable def hk7_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_7 j i k) +lemma hk7_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_7 j i k).Contains (fullFactor false 7 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 7 (power7_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha7_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1070359884617898514146650),(-1070359884617898514080301)⟩,⟨1853917702541761442223466,1853917702541761442305244⟩⟩,⟨⟨237301465925345464601021765,237301465925345464620913180⟩,⟨(-137006065231091009813300812),(-137006065231091009795834350)⟩⟩,⟨⟨(-4681754135318688100869262633),(-4681754135318688100550832462)⟩,⟨(-145672234),68440534⟩⟩,⟨⟨30374587638444219467041271314,30374587638444219472787817189⟩,⟨17536776349579649252746571302,17536776349579649258224867072⟩⟩,⟨⟨(-83621865985773321428876365322),(-83621865985773321396575637638)⟩,⟨(-144837320511075112695156649878),(-144837320511075112661407705831)⟩⟩,⟨⟨(-37375350574),17604035225⟩,⟨599264529320792076856720079378,599264529320792076925052092865⟩⟩] +lemma ha7_0_7_eq (j : Fin 7) : ha7_0_7 j = ((ha7_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha7_0_7_contains (j : Fin 7) : (ha7_0_7 j).Contains (fullFactor false 7 7 ((j.val:ℝ)/6)) := by + rw [ha7_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_6 j) false 7 6 j (ha7_0_6_contains j) +noncomputable def hk7_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_8 j i k) +lemma hk7_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_8 j i k).Contains (fullFactor false 7 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 8 (power7_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha7_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-121338629888859693717996),(-121338629888859693712257)⟩,⟨(-70054890629433514729582),(-70054890629433514725015)⟩⟩,⟨⟨17934052001134979768760474,17934052001134979771103916⟩,⟨31062689251548081589869016,31062689251548081592571673⟩⟩,⟨⟨(-13438268),28602677⟩,⟨(-919260274839426580279957629),(-919260274839426580214507914)⟩⟩,⟨⟨(-4591117312290554821958235698),(-4591117312290554820509407238)⟩,⟨7952048448396308886511794450,7952048448396308888041548799⟩⟩,⟨⟨47397902300335817852325176903,47397902300335817863520365225⟩,⟨(-27365191652122466694897816410),(-27365191652122466684240321882)⟩⟩,⟨⟨(-235330630358893204557083089393),(-235330630358893204529500089784)⟩,⟨(-14677265849),6913088468⟩⟩] +lemma ha7_0_8_eq (j : Fin 7) : ha7_0_8 j = ((ha7_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha7_0_8_contains (j : Fin 7) : (ha7_0_8 j).Contains (fullFactor false 7 8 ((j.val:ℝ)/6)) := by + rw [ha7_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_7 j) false 7 7 j (ha7_0_7_contains j) +noncomputable def hk7_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_9 j i k) +lemma hk7_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_9 j i k).Contains (fullFactor false 7 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 9 (power7_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha7_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨4075628328693792152340,4075628328693792152619⟩,⟨(-7059195338064676366777),(-7059195338064676366420)⟩⟩,⟨⟨(-3614308013089114299878723),(-3614308013089114299552749)⟩,⟨2086721704291221581900036,2086721704291221582179351⟩⟩,⟨⟨160441184787359821867777126,160441184787359821879710958⟩,⟨(-2345421),4992109⟩⟩,⟨⟨(-1850525702701626521617772368),(-1850525702701626521255891959)⟩,⟨(-1068401512597105450205129260),(-1068401512597105449864570739)⟩⟩,⟨⟨7960211579480062796021345691,7960211579480062799146823325⟩,⟨13787490894657571026994144470,13787490894657571030294579694⟩⟩,⟨⟨(-2413123105),5123332286⟩,⟨(-82145886611128228804301830470),(-82145886611128228794412068776)⟩⟩] +lemma ha7_0_9_eq (j : Fin 7) : ha7_0_9 j = ((ha7_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha7_0_9_contains (j : Fin 7) : (ha7_0_9 j).Contains (fullFactor false 7 9 ((j.val:ℝ)/6)) := by + rw [ha7_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_8 j) false 7 8 j (ha7_0_8_contains j) +noncomputable def hk7_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_10 j i k) +lemma hk7_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_10 j i k).Contains (fullFactor false 7 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 10 (power7_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha7_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨369618603571988403182,369618603571988403202⟩,⟨213399400269781075720,213399400269781075736⟩⟩,⟨⟨(-218520985876255821557642),(-218520985876255821527696)⟩,⟨(-378489450057716124888138),(-378489450057716124852797)⟩⟩,⟨⟨(-784159),368418⟩,⟨25202042373060605480264679,25202042373060605482219463⟩⟩,⟨⟨223765489537285961230066972,223765489537285961302105650⟩,⟨(-387573196859101311902180272),(-387573196859101311825154532)⟩⟩,⟨⟨(-3609556675507699250394568203),(-3609556675507699249519026705)⟩,⟨2083978518259580817187302931,2083978518259580818012184572⟩⟩,⟨⟨25806891390014060011197327545,25806891390014060014386433701⟩,⟨(-758104982),1609542308⟩⟩] +lemma ha7_0_10_eq (j : Fin 7) : ha7_0_10 j = ((ha7_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha7_0_10_contains (j : Fin 7) : (ha7_0_10 j).Contains (fullFactor false 7 10 ((j.val:ℝ)/6)) := by + rw [ha7_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_9 j) false 7 9 j (ha7_0_9_contains j) +noncomputable def hk7_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_11 j i k) +lemma hk7_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_11 j i k).Contains (fullFactor false 7 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 11 (power7_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha7_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-10157787699515332861),(-10157787699515332860)⟩,⟨17593804388058740564,17593804388058740566⟩⟩,⟨⟨36032111386744300674838,36032111386744300678318⟩,⟨(-20803149208607401699624),(-20803149208607401696706)⟩⟩,⟨⟨(-3598843235212085340633535),(-3598843235212085340342936)⟩,⟨(-111978),52610⟩⟩,⟨⟨73793764120052327777478300,73793764120052327792378861⟩,⟨42604849579227958672133598,42604849579227958685985347⟩⟩,⟨⟨(-495985727515397112417654494),(-495985727515397112219754350)⟩,⟨(-859072479885680691747111795),(-859072479885680691535998892)⟩⟩,⟨⟨(-459684209),216514277⟩,⟨7370430945714350776852773209,7370430945714350777787040609⟩⟩] +lemma ha7_0_11_eq (j : Fin 7) : ha7_0_11 j = ((ha7_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha7_0_11_contains (j : Fin 7) : (ha7_0_11 j).Contains (fullFactor false 7 11 ((j.val:ℝ)/6)) := by + rw [ha7_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_10 j) false 7 10 j (ha7_0_10_contains j) +noncomputable def hk7_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_12 j i k) +lemma hk7_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_12 j i k).Contains (fullFactor false 7 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 12 (power7_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha7_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-767674536308627878),(-767674536308627877)⟩,⟨(-443217100187807443),(-443217100187807442)⟩⟩,⟨⟨1815417242369259285380,1815417242369259285642⟩,⟨3144394900720139784806,3144394900720139785121⟩⟩,⟨⟨(-6887),14658⟩,⟨(-471087477881817150391038),(-471087477881817150351498)⟩⟩,⟨⟨(-7435949024744486034885510),(-7435949024744486032444254)⟩,⟨12879441513349692557766258,12879441513349692560407894⟩⟩,⟨⟨187420541090973602806742515,187420541090973602853396785⟩,⟨(-108207299850538926473258575),(-108207299850538926429739026)⟩⟩,⟨⟨(-1929574309403923048046081175),(-1929574309403923047795348514)⟩,⟨(-120345045),56683306⟩⟩] +lemma ha7_0_12_eq (j : Fin 7) : ha7_0_12 j = ((ha7_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha7_0_12_contains (j : Fin 7) : (ha7_0_12 j).Contains (fullFactor false 7 12 ((j.val:ℝ)/6)) := by + rw [ha7_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_11 j) false 7 11 j (ha7_0_11_contains j) +noncomputable def hk7_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_13 j i k) +lemma hk7_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_13 j i k).Contains (fullFactor false 7 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 13 (power7_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha7_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨17851379306351118,17851379306351119⟩,⟨(-30919495943783800),(-30919495943783799)⟩⟩,⟨⟨(-253292510771476882298),(-253292510771476882271)⟩,⟨146238499277628361500,146238499277628361523⟩⟩,⟨⟨56921729219679268115828,56921729219679268120788⟩,⟨(-833),1772⟩⟩,⟨⟨(-2074972248239938619868189),(-2074972248239938619435996)⟩,⟨(-1197985786082331537736375),(-1197985786082331537339257)⟩⟩,⟨⟨21791234504823142510643414,21791234504823142519476926⟩,⟨37743525322001707889652133,37743525322001707899167706⟩⟩,⟨⟨(-13698143),29082701⟩,⟨(-466302805767612564456214475),(-466302805767612564394137888)⟩⟩] +lemma ha7_0_13_eq (j : Fin 7) : ha7_0_13 j = ((ha7_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha7_0_13_contains (j : Fin 7) : (ha7_0_13 j).Contains (fullFactor false 7 13 ((j.val:ℝ)/6)) := by + rw [ha7_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_12 j) false 7 12 j (ha7_0_12_contains j) +noncomputable def hk7_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_14 j i k) +lemma hk7_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_14 j i k).Contains (fullFactor false 7 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 14 (power7_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha7_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1156386444162983,1156386444162984⟩,⟨667640024824732,667640024824733⟩⟩,⟨⟨(-10938614166728417760),(-10938614166728417757)⟩,⟨(-18946235501166317753),(-18946235501166317750)⟩⟩,⟨⟨(-199),94⟩,⟨6386603083791852240868,6386603083791852241446⟩⟩,⟨⟨179218254507678396534178,179218254507678396594158⟩,⟨(-310415122451108950065413),(-310415122451108949999768)⟩⟩,⟨⟨(-7058022730486958382167570),(-7058022730486958380365695)⟩,⟨4074951323393142877645848,4074951323393142879310683⟩⟩,⟨⟨104638104924845707111984111,104638104924845707126247139⟩,⟨(-3073857),6526143⟩⟩] +lemma ha7_0_14_eq (j : Fin 7) : ha7_0_14 j = ((ha7_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha7_0_14_contains (j : Fin 7) : (ha7_0_14 j).Contains (fullFactor false 7 14 ((j.val:ℝ)/6)) := by + rw [ha7_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_13 j) false 7 13 j (ha7_0_13_contains j) +noncomputable def hk7_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_15 j i k) +lemma hk7_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_15 j i k).Contains (fullFactor false 7 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 15 (power7_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha7_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23305033302577),(-23305033302576)⟩,⟨40365501752147,40365501752148⟩⟩,⟨⟨1322696761414360852,1322696761414360853⟩,⟨(-763659331258827444),(-763659331258827443)⟩⟩,⟨⟨(-668803510981146723287),(-668803510981146723224)⟩,⟨(-21),10⟩⟩,⟨⟨43342127478025776415965,43342127478025776425269⟩,⟨25023588966689257660258,25023588966689257668714⟩⟩,⟨⟨(-711213174517105746547409),(-711213174517105746254576)⟩,⟨(-1231857353275977869396844),(-1231857353275977869078435)⟩⟩,⟨⟨(-1366833),643788⟩,⟨21915353447830215826102743,21915353447830215829159745⟩⟩] +lemma ha7_0_15_eq (j : Fin 7) : ha7_0_15 j = ((ha7_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha7_0_15_contains (j : Fin 7) : (ha7_0_15 j).Contains (fullFactor false 7 15 ((j.val:ℝ)/6)) := by + rw [ha7_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_14 j) false 7 14 j (ha7_0_14_contains j) +noncomputable def hk7_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_16 j i k) +lemma hk7_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_16 j i k).Contains (fullFactor false 7 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 16 (power7_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha7_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1320957955865),(-1320957955864)⟩,⟨(-762655431407),(-762655431406)⟩⟩,⟨⟨49981386352667221,49981386352667222⟩,⟨86570300595549323,86570300595549324⟩⟩,⟨⟨(-1),3⟩,⟨(-65659631149794723627),(-65659631149794723619)⟩⟩,⟨⟨(-3275580136008399050036),(-3275580136008399048918)⟩,⟨5673471219829920494167,5673471219829920495404⟩⟩,⟨⟨201562188089707223572750,201562188089707223625492⟩,⟨(-116371983552042445709292),(-116371983552042445661006)⟩⟩,⟨⟨(-4303069587032947007656439),(-4303069587032947007042500)⟩,⟨(-268378),126408⟩⟩] +lemma ha7_0_16_eq (j : Fin 7) : ha7_0_16 j = ((ha7_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha7_0_16_contains (j : Fin 7) : (ha7_0_16 j).Contains (fullFactor false 7 16 ((j.val:ℝ)/6)) := by + rw [ha7_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_15 j) false 7 15 j (ha7_0_15_contains j) +noncomputable def hk7_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_17 j i k) +lemma hk7_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_17 j i k).Contains (fullFactor false 7 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 17 (power7_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha7_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨23489732358,23489732359⟩,⟨(-40685409901),(-40685409900)⟩⟩,⟨⟨(-5332718046471331),(-5332718046471330)⟩,⟨3078846199642597,3078846199642598⟩⟩,⟨⟨6066935731106195666,6066935731106195668⟩,⟨(-1),1⟩⟩,⟨⟨(-698970019787090239296),(-698970019787090239141)⟩,⟨(-403550529079554596791),(-403550529079554596651)⟩⟩,⟨⟨17921243559351411739114,17921243559351411746608⟩,⟨31040504379613153635377,31040504379613153643599⟩⟩,⟨⟨(-23361),49597⟩,⟨(-795205400147551278546455),(-795205400147551278430467)⟩⟩] +lemma ha7_0_17_eq (j : Fin 7) : ha7_0_17 j = ((ha7_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha7_0_17_contains (j : Fin 7) : (ha7_0_17 j).Contains (fullFactor false 7 17 ((j.val:ℝ)/6)) := by + rw [ha7_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_16 j) false 7 16 j (ha7_0_16_contains j) +noncomputable def hk7_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_18 j i k) +lemma hk7_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_18 j i k).Contains (fullFactor false 7 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 18 (power7_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha7_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨1183490600,1183490601⟩,⟨683288616,683288617⟩⟩,⟨⟨(-179120011154260),(-179120011154259)⟩,⟨(-310244959971483),(-310244959971482)⟩⟩,⟨⟨(-1),1⟩,⟨529440020073462376,529440020073462377⟩⟩,⟨⟨46955236204022331362,46955236204022331379⟩,⟨(-81328854786764263392),(-81328854786764263373)⟩⟩,⟨⟨(-4514658357533078058829),(-4514658357533078057617)⟩,⟨2606539218020916335225,2606539218020916336325⟩⟩,⟨⟨138789524622137721136212,138789524622137721156898⟩,⟨(-4078),8657⟩⟩] +lemma ha7_0_18_eq (j : Fin 7) : ha7_0_18 j = ((ha7_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha7_0_18_contains (j : Fin 7) : (ha7_0_18 j).Contains (fullFactor false 7 18 ((j.val:ℝ)/6)) := by + rw [ha7_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_17 j) false 7 17 j (ha7_0_17_contains j) +noncomputable def hk7_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_19 j i k) +lemma hk7_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_19 j i k).Contains (fullFactor false 7 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 19 (power7_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha7_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-18829952),(-18829951)⟩,⟨32614433,32614434⟩⟩,⟨⟨17099355913327,17099355913328⟩,⟨(-9872317739529),(-9872317739528)⟩⟩,⟨⟨(-43770654673137423),(-43770654673137422)⟩,⟨(-1),1⟩⟩,⟨⟨8964987113086656143,8964987113086656147⟩,⟨5175937723022106879,5175937723022106882⟩⟩,⟨⟨(-359152827132815577594),(-359152827132815577440)⟩,⟨(-622070944276038605587),(-622070944276038605417)⟩⟩,⟨⟨(-1432),675⟩,⟨22948428997269873108784,22948428997269873112278⟩⟩] +lemma ha7_0_19_eq (j : Fin 7) : ha7_0_19 j = ((ha7_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha7_0_19_contains (j : Fin 7) : (ha7_0_19 j).Contains (fullFactor false 7 19 ((j.val:ℝ)/6)) := by + rw [ha7_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_18 j) false 7 18 j (ha7_0_18_contains j) +noncomputable def hk7_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_20 j i k) +lemma hk7_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_20 j i k).Contains (fullFactor false 7 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 20 (power7_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha7_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-853844),(-853843)⟩,⟨(-492967),(-492966)⟩⟩,⟨⟨516913348073,516913348074⟩,⟨895320181973,895320181974⟩⟩,⟨⟨(-1),1⟩,⟨(-3437739179098608),(-3437739179098606)⟩⟩,⟨⟨(-542022930869484434),(-542022930869484433)⟩,⟨938811255133340262,938811255133340263⟩⟩,⟨⟨81428896189552855145,81428896189552855169⟩,⟨(-47012995134852432617),(-47012995134852432596)⟩⟩,⟨⟨(-3604730797462500934194),(-3604730797462500933633)⟩,⟨(-225),107⟩⟩] +lemma ha7_0_20_eq (j : Fin 7) : ha7_0_20 j = ((ha7_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha7_0_20_contains (j : Fin 7) : (ha7_0_20 j).Contains (fullFactor false 7 20 ((j.val:ℝ)/6)) := by + rw [ha7_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_19 j) false 7 19 j (ha7_0_19_contains j) +noncomputable def hk7_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_21 j i k) +lemma hk7_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_21 j i k).Contains (fullFactor false 7 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 21 (power7_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha7_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨12291,12292⟩,⟨(-21290),(-21289)⟩⟩,⟨⟨(-44646528672),(-44646528671)⟩,⟨25776685346,25776685347⟩⟩,⟨⟨257142289286047,257142289286048⟩,⟨(-1),1⟩⟩,⟨⟨(-93630556896327456),(-93630556896327455)⟩,⟨(-54057627228469228),(-54057627228469227)⟩⟩,⟨⟨5860939688051789410,5860939688051789413⟩,⟨10151445319802585613,10151445319802585617⟩⟩,⟨⟨(-17),34⟩,⟨(-539266466260812848987),(-539266466260812848900)⟩⟩] +lemma ha7_0_21_eq (j : Fin 7) : ha7_0_21 j = ((ha7_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha7_0_21_contains (j : Fin 7) : (ha7_0_21 j).Contains (fullFactor false 7 21 ((j.val:ℝ)/6)) := by + rw [ha7_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_20 j) false 7 20 j (ha7_0_20_contains j) +noncomputable def hk7_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_22 j i k) +lemma hk7_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_22 j i k).Contains (fullFactor false 7 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 22 (power7_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha7_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨506,507⟩,⟨292,293⟩⟩,⟨⟨(-1226967354),(-1226967353)⟩,⟨(-2125169796),(-2125169795)⟩⟩,⟨⟨(-1),1⟩,⟨18359916521552,18359916521553⟩⟩,⟨⟨5146274077922863,5146274077922864⟩,⟨(-8913608172637076),(-8913608172637075)⟩⟩,⟨⟨(-1208019168182208038),(-1208019168182208037)⟩,⟨697450191936225609,697450191936225610⟩⟩,⟨⟨77007071306013533792,77007071306013533806⟩,⟨(-3),5⟩⟩] +lemma ha7_0_22_eq (j : Fin 7) : ha7_0_22 j = ((ha7_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha7_0_22_contains (j : Fin 7) : (ha7_0_22 j).Contains (fullFactor false 7 22 ((j.val:ℝ)/6)) := by + rw [ha7_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_21 j) false 7 21 j (ha7_0_21_contains j) +noncomputable def hk7_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_23 j i k) +lemma hk7_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_23 j i k).Contains (fullFactor false 7 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 23 (power7_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha7_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-7),(-6)⟩,⟨11,12⟩⟩,⟨⟨96759678,96759679⟩,⟨(-55864227),(-55864226)⟩⟩,⟨⟨(-1253899540536),(-1253899540535)⟩,⟨(-1),1⟩⟩,⟨⟨811679013105350,811679013105351⟩,⟨468623096711943,468623096711944⟩⟩,⟨⟨(-79387840551870929),(-79387840551870928)⟩,⟨(-137503773339017308),(-137503773339017306)⟩⟩,⟨⟨(-1),1⟩,⟨10518471716932064454,10518471716932064457⟩⟩] +lemma ha7_0_23_eq (j : Fin 7) : ha7_0_23 j = ((ha7_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha7_0_23_contains (j : Fin 7) : (ha7_0_23 j).Contains (fullFactor false 7 23 ((j.val:ℝ)/6)) := by + rw [ha7_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_22 j) false 7 22 j (ha7_0_22_contains j) +noncomputable def hk7_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_24 j i k) +lemma hk7_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_24 j i k).Contains (fullFactor false 7 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 24 (power7_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha7_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨2437536,2437537⟩,⟨4221937,4221938⟩⟩,⟨⟨(-1),1⟩,⟨(-82067533019),(-82067533018)⟩⟩,⟨⟨(-40895079942577),(-40895079942576)⟩,⟨70832356240132,70832356240133⟩⟩,⟨⟨14999334866761557,14999334866761558⟩,⟨(-8659870022990125),(-8659870022990124)⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha7_0_24_eq (j : Fin 7) : ha7_0_24 j = ((ha7_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha7_0_24_contains (j : Fin 7) : (ha7_0_24 j).Contains (fullFactor false 7 24 ((j.val:ℝ)/6)) := by + rw [ha7_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_23 j) false 7 23 j (ha7_0_23_contains j) +noncomputable def hk7_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_25 j i k) +lemma hk7_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_25 j i k).Contains (fullFactor false 7 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 25 (power7_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha7_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-176849),(-176848)⟩,⟨102103,102104⟩⟩,⟨⟨5156455176,5156455177⟩,⟨(-1),1⟩⟩,⟨⟨(-5934037600013),(-5934037600012)⟩,⟨(-3426018205749),(-3426018205748)⟩⟩,⟨⟨906859468175608,906859468175609⟩,⟨1570726674205044,1570726674205046⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha7_0_25_eq (j : Fin 7) : ha7_0_25 j = ((ha7_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha7_0_25_contains (j : Fin 7) : (ha7_0_25 j).Contains (fullFactor false 7 25 ((j.val:ℝ)/6)) := by + rw [ha7_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_24 j) false 7 24 j (ha7_0_24_contains j) +noncomputable def hk7_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_26 j i k) +lemma hk7_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_26 j i k).Contains (fullFactor false 7 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 26 (power7_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha7_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-4113),(-4112)⟩,⟨(-7123),(-7122)⟩⟩,⟨⟨(-1),1⟩,⟨311528494,311528495⟩⟩,⟨⟨275978298108,275978298109⟩,⟨(-478008434111),(-478008434110)⟩⟩,⟨⟨(-158159723733337),(-158159723733336)⟩,⟨91313559072398,91313559072399⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha7_0_26_eq (j : Fin 7) : ha7_0_26 j = ((ha7_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha7_0_26_contains (j : Fin 7) : (ha7_0_26 j).Contains (fullFactor false 7 26 ((j.val:ℝ)/6)) := by + rw [ha7_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_25 j) false 7 25 j (ha7_0_25_contains j) +noncomputable def hk7_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_27 j i k) +lemma hk7_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_27 j i k).Contains (fullFactor false 7 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 27 (power7_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha7_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨276,277⟩,⟨(-160),(-159)⟩⟩,⟨⟨(-18123994),(-18123993)⟩,⟨(-1),1⟩⟩,⟨⟨37079204566,37079204567⟩,⟨21407688737,21407688739⟩⟩,⟨⟨(-8854012541821),(-8854012541820)⟩,⟨(-15335599573286),(-15335599573285)⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha7_0_27_eq (j : Fin 7) : ha7_0_27 j = ((ha7_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha7_0_27_contains (j : Fin 7) : (ha7_0_27 j).Contains (fullFactor false 7 27 ((j.val:ℝ)/6)) := by + rw [ha7_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_26 j) false 7 26 j (ha7_0_26_contains j) +noncomputable def hk7_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_28 j i k) +lemma hk7_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_28 j i k).Contains (fullFactor false 7 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 28 (power7_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha7_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨5,6⟩,⟨10,11⟩⟩,⟨⟨(-1),1⟩,⟨(-1016754),(-1016753)⟩⟩,⟨⟨(-1601291374),(-1601291373)⟩,⟨2773518015,2773518016⟩⟩,⟨⟨1433875207078,1433875207079⟩,⟨(-827848236791),(-827848236790)⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha7_0_28_eq (j : Fin 7) : ha7_0_28 j = ((ha7_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha7_0_28_contains (j : Fin 7) : (ha7_0_28 j).Contains (fullFactor false 7 28 ((j.val:ℝ)/6)) := by + rw [ha7_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_27 j) false 7 27 j (ha7_0_27_contains j) +noncomputable def hk7_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_29 j i k) +lemma hk7_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_29 j i k).Contains (fullFactor false 7 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 29 (power7_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha7_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),0⟩⟩,⟨⟨(-1),0⟩,⟨0,1⟩⟩,⟨⟨55072,55073⟩,⟨(-1),1⟩⟩,⟨⟨(-200304916),(-200304915)⟩,⟨(-115646097),(-115646096)⟩⟩,⟨⟨74734538476,74734538477⟩,⟨129444017721,129444017722⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha7_0_29_eq (j : Fin 7) : ha7_0_29 j = ((ha7_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha7_0_29_contains (j : Fin 7) : (ha7_0_29 j).Contains (fullFactor false 7 29 ((j.val:ℝ)/6)) := by + rw [ha7_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_28 j) false 7 28 j (ha7_0_28_contains j) +noncomputable def hk7_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power7 j i k).conj.mul (mpower0_30 j i k) +lemma hk7_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk7_0_30 j i k).Contains (fullFactor false 7 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power7 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 30 (power7_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha7_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨0,1⟩⟩,⟨⟨(-1),0⟩,⟨(-1),0⟩⟩,⟨⟨(-1),1⟩,⟨2883,2884⟩⟩,⟨⟨8073620,8073621⟩,⟨(-13983922),(-13983921)⟩⟩,⟨⟨(-11296121532),(-11296121531)⟩,⟨6521818806,6521818807⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha7_0_30_eq (j : Fin 7) : ha7_0_30 j = ((ha7_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha7_0_30_contains (j : Fin 7) : (ha7_0_30 j).Contains (fullFactor false 7 30 ((j.val:ℝ)/6)) := by + rw [ha7_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_0_29 j) false 7 29 j (ha7_0_29_contains j) +noncomputable def hk7_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_0 j i k) +lemma hk7_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_0 j i k).Contains (fullFactor true 7 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 0 (kernel7_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha7_1_0 : Fin 7 → CBox := ![⟨⟨277,281⟩,⟨(-3),3⟩⟩,⟨⟨11580277,11580282⟩,⟨(-6288733),(-6288728)⟩⟩,⟨⟨(-1665710323167166),(-1665710323167162)⟩,⟨1710986465904294,1710986465904298⟩⟩,⟨⟨(-4288482058811659370282),(-4288482058811659363575)⟩,⟨1347241831520230599839,1347241831520230606532⟩⟩,⟨⟨36521831631557482951131335,36521831631557482985427878⟩,⟨3899877544961305718935797,3899877544961305753146455⟩⟩,⟨⟨(-6285013554969111273878743515),(-6285013554969111268462701209)⟩,⟨(-6478261771340776764017300108),(-6478261771340776758509615976)⟩⟩,⟨⟨144338024383918188411416917775,144338024383918188519066263138⟩,⟨249223963933666164018182252952,249223963933666164130533379093⟩⟩] +lemma ha7_1_0_eq (j : Fin 7) : ha7_1_0 j = atomKernel7_0 j := by fin_cases j <;> decide +kernel +lemma ha7_1_0_contains (j : Fin 7) : (ha7_1_0 j).Contains (fullFactor true 7 0 ((j.val:ℝ)/6)) := by + rw [ha7_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel7_0_contains j +noncomputable def hk7_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_1 j i k) +lemma hk7_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_1 j i k).Contains (fullFactor true 7 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 1 (kernel7_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha7_1_1 : Fin 7 → CBox := ![⟨⟨(-2590),(-2552)⟩,⟨(-28),28⟩⟩,⟨⟨(-112157738),(-112157680)⟩,⟨5156952,5157010⟩⟩,⟨⟨17013040262490527,17013040262490568⟩,⟨154541955914585,154541955914626⟩⟩,⟨⟨19018440239828876646774,19018440239828876700006⟩,⟨18094092713122343905337,18094092713122343958622⟩⟩,⟨⟨(-37326201238580442081012481),(-37326201238580441870754607)⟩,⟨(-174640172189637644844922541),(-174640172189637644634075644)⟩⟩,⟨⟨(-22039050446094185125438974516),(-22039050446094185099025575597)⟩,⟨30238813374675442746566322808,30238813374675442772667801795⟩⟩,⟨⟨872851388260399717489646974695,872851388260399717918514409563⟩,⟨(-568005984018613276009284490086),(-568005984018613275597655333954)⟩⟩] +lemma ha7_1_1_eq (j : Fin 7) : ha7_1_1 j = ((ha7_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha7_1_1_contains (j : Fin 7) : (ha7_1_1 j).Contains (fullFactor true 7 1 ((j.val:ℝ)/6)) := by + rw [ha7_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_0 j) true 7 0 j (ha7_1_0_contains j) +noncomputable def hk7_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_2 j i k) +lemma hk7_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_2 j i k).Contains (fullFactor true 7 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 2 (kernel7_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha7_1_2 : Fin 7 → CBox := ![⟨⟨11758,11934⟩,⟨(-130),130⟩⟩,⟨⟨439499681,439500012⟩,⟨188725927,188726259⟩⟩,⟨⟨(-41484279155020408),(-41484279155020201)⟩,⟨(-44190317894108296),(-44190317894108088)⟩⟩,⟨⟨19303878288826371350227,19303878288826371561881⟩,⟨(-74178794327358818574522),(-74178794327358818362925)⟩⟩,⟨⟨(-375136604371051098279313533),(-375136604371051097631576384)⟩,⟨218544379473940161253409543,218544379473940161899553849⟩⟩,⟨⟨69528359364234200487201722872,69528359364234200550040717819⟩,⟨34369348452773435290199474044,34369348452773435353521645191⟩⟩,⟨⟨(-1107491315550409323350028402780),(-1107491315550409322563036409571)⟩,⟨(-1522616351064340442050391577779),(-1522616351064340441232233210732)⟩⟩] +lemma ha7_1_2_eq (j : Fin 7) : ha7_1_2 j = ((ha7_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha7_1_2_contains (j : Fin 7) : (ha7_1_2 j).Contains (fullFactor true 7 2 ((j.val:ℝ)/6)) := by + rw [ha7_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_1 j) true 7 1 j (ha7_1_1_contains j) +noncomputable def hk7_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_3 j i k) +lemma hk7_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_3 j i k).Contains (fullFactor true 7 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 3 (kernel7_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha7_1_3 : Fin 7 → CBox := ![⟨⟨(-36659),(-36117)⟩,⟨(-400),400⟩⟩,⟨⟨(-889217078),(-889215820)⟩,⟨(-1026939618),(-1026938358)⟩⟩,⟨⟨(-7779041811418171),(-7779041811417473)⟩,⟨143741122215489835,143741122215490532⟩⟩,⟨⟨(-144518613669232090619019),(-144518613669232090058600)⟩,⟨37105144403422090830809,37105144403422091391139⟩⟩,⟨⟨526046115865125922880711395,526046115865125924204629981⟩,⟨467318140978446544546627701,467318140978446545872710517⟩⟩,⟨⟨30479929787426174545204233849,30479929787426174646387715494⟩,⟨(-102750145435817668478464673229),(-102750145435817668377699602285)⟩⟩,⟨⟨(-1763416643883276281730794609174),(-1763416643883276280690684416015)⟩,⟨1428362252364027510308178570036,1428362252364027511311217495084⟩⟩] +lemma ha7_1_3_eq (j : Fin 7) : ha7_1_3 j = ((ha7_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha7_1_3_contains (j : Fin 7) : (ha7_1_3 j).Contains (fullFactor true 7 3 ((j.val:ℝ)/6)) := by + rw [ha7_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_2 j) true 7 2 j (ha7_1_2_contains j) +noncomputable def hk7_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_4 j i k) +lemma hk7_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_4 j i k).Contains (fullFactor true 7 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 4 (kernel7_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha7_1_4 : Fin 7 → CBox := ![⟨⟨83207,84457⟩,⟨(-922),922⟩⟩,⟨⟨749728448,749732031⟩,⟨2794681554,2794685139⟩⟩,⟨⟨194647269111047915,194647269111049673⟩,⟨(-166913166642253874),(-166913166642252116)⟩⟩,⟨⟨149632342188558044724599,149632342188558045837152⟩,⟨158308638628646215385936,158308638628646216498734⟩⟩,⟨⟨340464346142019281650974645,340464346142019283686501293⟩,⟨(-784620233569081777198723064),(-784620233569081775164731109)⟩⟩,⟨⟨(-110307982544932220283105104068),(-110307982544932220162024187620)⟩,⟨(-13038022856820289467269434243),(-13038022856820289346029300623)⟩⟩,⟨⟨1372243985896886756732468287720,1372243985896886757691162439894⟩,⟨1524883761778648221965611354551,1524883761778648222956944320623⟩⟩] +lemma ha7_1_4_eq (j : Fin 7) : ha7_1_4 j = ((ha7_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha7_1_4_contains (j : Fin 7) : (ha7_1_4 j).Contains (fullFactor true 7 4 ((j.val:ℝ)/6)) := by + rw [ha7_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_3 j) true 7 3 j (ha7_1_3_contains j) +noncomputable def hk7_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_5 j i k) +lemma hk7_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_5 j i k).Contains (fullFactor true 7 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 5 (kernel7_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha7_1_5 : Fin 7 → CBox := ![⟨⟨(-155660),(-153356)⟩,⟨(-1700),1700⟩⟩,⟨⟨928523998,928532158⟩,⟨(-4842419529),(-4842411367)⟩⟩,⟨⟨(-363596557980772762),(-363596557980769219)⟩,⟨(-36131695871066267),(-36131695871062724)⟩⟩,⟨⟨77045461404964505837792,77045461404964507605177⟩,⟨(-242475096860821541124888),(-242475096860821539357627)⟩⟩,⟨⟨(-828172369504533420075376004),(-828172369504533417576425987)⟩,⟨(-76792452832817874009329675),(-76792452832817871510304588)⟩⟩,⟨⟨4885256920971816311270025270,4885256920971816427469340976⟩,⟨91964701854872144180252186875,91964701854872144296553204634⟩⟩,⟨⟨1049744822777194244616056091486,1049744822777194245371674883732⟩,⟨(-1048308260563840941893130561981),(-1048308260563840941160190600637)⟩⟩] +lemma ha7_1_5_eq (j : Fin 7) : ha7_1_5 j = ((ha7_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha7_1_5_contains (j : Fin 7) : (ha7_1_5 j).Contains (fullFactor true 7 5 ((j.val:ℝ)/6)) := by + rw [ha7_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_4 j) true 7 4 j (ha7_1_4_contains j) +noncomputable def hk7_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_6 j i k) +lemma hk7_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_6 j i k).Contains (fullFactor true 7 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 6 (kernel7_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha7_1_6 : Fin 7 → CBox := ![⟨⟨235537,239077⟩,⟨(-2612),2612⟩⟩,⟨⟨(-4186964016),(-4186948531)⟩,⟨5611813994,5611829480⟩⟩,⟨⟨267350061473778404,267350061473784354⟩,⟨341745589792223843,341745589792229792⟩⟩,⟨⟨(-242778093589932093607397),(-242778093589932091268400)⟩,⟨48771942283650417681477,48771942283650420020322⟩⟩,⟨⟨150032674119139377215873122,150032674119139379772105283⟩,⟨657085889853306493999368376,657085889853306496556799260⟩⟩,⟨⟨62043720185150139784281893939,62043720185150139877310344356⟩,⟨(-14121487248646576838199996656),(-14121487248646576745385047107)⟩⟩,⟨⟨(-663763755268325022031952601049),(-663763755268325021565081382038)⟩,⟨(-598968588470563277351838747229),(-598968588470563276872025691161)⟩⟩] +lemma ha7_1_6_eq (j : Fin 7) : ha7_1_6 j = ((ha7_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha7_1_6_contains (j : Fin 7) : (ha7_1_6 j).Contains (fullFactor true 7 6 ((j.val:ℝ)/6)) := by + rw [ha7_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_5 j) true 7 5 j (ha7_1_5_contains j) +noncomputable def hk7_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_7 j i k) +lemma hk7_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_7 j i k).Contains (fullFactor true 7 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 7 (kernel7_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha7_1_7 : Fin 7 → CBox := ![⟨⟨(-314740),(-310079)⟩,⟨(-3439),3439⟩⟩,⟨⟨7566007723,7566032908⟩,⟨(-3922154335),(-3922129150)⟩⟩,⟨⟨63390225935340755,63390225935349318⟩,⟨(-437070469377547907),(-437070469377539344)⟩⟩,⟨⟨133742821482412655429906,133742821482412658082734⟩,⟨157450667224983875645000,157450667224983878298079⟩⟩,⟨⟨401196675837523625366129355,401196675837523627608885453⟩,⟨(-241266954166986591946317479),(-241266954166986589704808877)⟩⟩,⟨⟨(-14484022936717885888904846818),(-14484022936717885825330606751)⟩,⟨(-34788732812174303747469273787),(-34788732812174303683718235869)⟩⟩,⟨⟨(-291179146097228615848248274597),(-291179146097228615587167582797)⟩,⟨358476934937305768743017939854,358476934937305768997870469575⟩⟩] +lemma ha7_1_7_eq (j : Fin 7) : ha7_1_7 j = ((ha7_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha7_1_7_contains (j : Fin 7) : (ha7_1_7 j).Contains (fullFactor true 7 7 ((j.val:ℝ)/6)) := by + rw [ha7_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_6 j) true 7 6 j (ha7_1_6_contains j) +noncomputable def hk7_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_8 j i k) +lemma hk7_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_8 j i k).Contains (fullFactor true 7 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 8 (kernel7_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha7_1_8 : Fin 7 → CBox := ![⟨⟨357185,362555⟩,⟨(-3962),3962⟩⟩,⟨⟨(-9073121367),(-9073085527)⟩,⟨242310390,242346229⟩⟩,⟨⟨(-320385493444403813),(-320385493444393030)⟩,⟨228183365380930082,228183365380940866⟩⟩,⟨⟨53226461707993327765929,53226461707993330398919⟩,⟨(-141097412922479145014608),(-141097412922479142381712)⟩⟩,⟨⟨(-215325836843105898887925551),(-215325836843105897167950089)⟩,⟨(-185989858912664168745506467),(-185989858912664167024849318)⟩⟩,⟨⟨(-16490137753801682392558006351),(-16490137753801682354345208757)⟩,⟨10459175159529297712199182093,10459175159529297750309945710⟩⟩,⟨⟨168643153897388135464408527846,168643153897388135586108225428⟩,⟨123017882756181088672612154228,123017882756181088796885259150⟩⟩] +lemma ha7_1_8_eq (j : Fin 7) : ha7_1_8 j = ((ha7_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha7_1_8_contains (j : Fin 7) : (ha7_1_8 j).Contains (fullFactor true 7 8 ((j.val:ℝ)/6)) := by + rw [ha7_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_7 j) true 7 7 j (ha7_1_7_contains j) +noncomputable def hk7_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_9 j i k) +lemma hk7_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_9 j i k).Contains (fullFactor true 7 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 9 (kernel7_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha7_1_9 : Fin 7 → CBox := ![⟨⟨(-371230),(-365731)⟩,⟨(-4057),4057⟩⟩,⟨⟨7828581515,7828626849⟩,⟨3541621127,3541666462⟩⟩,⟨⟨305845716852972509,305845716852984580⟩,⟨58506982200543103,58506982200555174⟩⟩,⟨⟨(-96821713263816682697368),(-96821713263816680374736)⟩,⟨14156467757521802447882,14156467757521804770467⟩⟩,⟨⟨(-59219526858756957466242106),(-59219526858756956292956868)⟩,⟨141849330385344226557594473,141849330385344227730676769⟩⟩,⟨⟨6038101547372975081393483072,6038101547372975101702393775⟩,⟨6666738299054809562328396232,6666738299054809582682849307⟩⟩,⟨⟨45839343023263364660937449513,45839343023263364713506357850⟩,⟨(-70230477822739578962511054968),(-70230477822739578910865731681)⟩⟩] +lemma ha7_1_9_eq (j : Fin 7) : ha7_1_9 j = ((ha7_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha7_1_9_contains (j : Fin 7) : (ha7_1_9 j).Contains (fullFactor true 7 9 ((j.val:ℝ)/6)) := by + rw [ha7_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_8 j) true 7 8 j (ha7_1_8_contains j) +noncomputable def hk7_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_10 j i k) +lemma hk7_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_10 j i k).Contains (fullFactor true 7 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 10 (kernel7_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha7_1_10 : Fin 7 → CBox := ![⟨⟨337033,342102⟩,⟨(-3739),3739⟩⟩,⟨⟨(-4684879573),(-4684827963)⟩,⟨(-5625697589),(-5625645978)⟩⟩,⟨⟨(-120452536855020786),(-120452536855008625)⟩,⟨(-186321366888812213),(-186321366888800052)⟩⟩,⟨⟨34631945259166303059628,34631945259166304903483⟩,⟨45452986563879102202105,45452986563879104046030⟩⟩,⟨⟨74508106627733545159539919,74508106627733545879534376⟩,⟨5864127566591063651919831,5864127566591064371895636⟩⟩,⟨⟨2298293422876451474481525882,2298293422876451484237312371⟩,⟨(-2936284969602183650368921914),(-2936284969602183640629209801)⟩⟩,⟨⟨(-26221149130684761893762896237),(-26221149130684761874043066986)⟩,⟨(-15233964887539507149728298387),(-15233964887539507129718880562)⟩⟩] +lemma ha7_1_10_eq (j : Fin 7) : ha7_1_10 j = ((ha7_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha7_1_10_contains (j : Fin 7) : (ha7_1_10 j).Contains (fullFactor true 7 10 ((j.val:ℝ)/6)) := by + rw [ha7_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_9 j) true 7 9 j (ha7_1_9_contains j) +noncomputable def hk7_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_11 j i k) +lemma hk7_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_11 j i k).Contains (fullFactor true 7 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 11 (kernel7_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha7_1_11 : Fin 7 → CBox := ![⟨⟨(-286599),(-282352)⟩,⟨(-3133),3133⟩⟩,⟨⟨1363582239,1363635652⟩,⟨5504093977,5504147391⟩⟩,⟨⟨(-33320893584189246),(-33320893584178108)⟩,⟨139791866686725267,139791866686736405⟩⟩,⟨⟨12198058413958445163197,12198058413958446493964⟩,⟨(-27776462180406639934431),(-27776462180406638603685)⟩⟩,⟨⟨(-7801284948270583706723856),(-7801284948270583305108008)⟩,⟨(-32101171930717794057200283),(-32101171930717793655517501)⟩⟩,⟨⟨(-1237662998952027813606004586),(-1237662998952027809360187084)⟩,⟨(-665560792861892017989286652),(-665560792861892013739152674)⟩⟩,⟨⟨(-4553328251086897706469672325),(-4553328251086897699547112077)⟩,⟨8867798632265419853053210884,8867798632265419859896533638⟩⟩] +lemma ha7_1_11_eq (j : Fin 7) : ha7_1_11 j = ((ha7_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha7_1_11_contains (j : Fin 7) : (ha7_1_11 j).Contains (fullFactor true 7 11 ((j.val:ℝ)/6)) := by + rw [ha7_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_10 j) true 7 10 j (ha7_1_10_contains j) +noncomputable def hk7_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_12 j i k) +lemma hk7_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_12 j i k).Contains (fullFactor true 7 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 12 (kernel7_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha7_1_12 : Fin 7 → CBox := ![⟨⟨216830,220093⟩,⟨(-2406),2406⟩⟩,⟨⟨834126081,834176754⟩,⟨(-3938822158),(-3938771485)⟩⟩,⟨⟨73667189375947624,73667189375956975⟩,⟨(-43055326018758034),(-43055326018748683)⟩⟩,⟨⟨(-14700859991494403187726),(-14700859991494402307355)⟩,⟨1357994560641981661355,1357994560641982541720⟩⟩,⟨⟨(-11373778333217441510141343),(-11373778333217441304735427)⟩,⟨7057214193658567375976018,7057214193658567581344606⟩⟩,⟨⟨(-153943382177754593196847554),(-153943382177754591499777909)⟩,⟨460414797121216966334844993,460414797121216968031211556⟩⟩,⟨⟨2739737123654648210043501434,2739737123654648212219829707⟩,⟨1231420882096958716568538643,1231420882096958718763553342⟩⟩] +lemma ha7_1_12_eq (j : Fin 7) : ha7_1_12 j = ((ha7_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha7_1_12_contains (j : Fin 7) : (ha7_1_12 j).Contains (fullFactor true 7 12 ((j.val:ℝ)/6)) := by + rw [ha7_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_11 j) true 7 11 j (ha7_1_11_contains j) +noncomputable def hk7_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_13 j i k) +lemma hk7_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_13 j i k).Contains (fullFactor true 7 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 13 (kernel7_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha7_1_13 : Fin 7 → CBox := ![⟨⟨(-156018),(-153704)⟩,⟨(-1706),1706⟩⟩,⟨⟨(-1618383412),(-1618339037)⟩,⟨2084167184,2084211560⟩⟩,⟨⟨(-44957323534751221),(-44957323534743974)⟩,⟨(-12877874660291348),(-12877874660284101)⟩⟩,⟨⟨3733866760879634870529,3733866760879635408126⟩,⟨5481000942258830565008,5481000942258831102614⟩⟩,⟨⟨3833813981777287978766181,3833813981777288075706373⟩,⟨3219425994578671820227985,3219425994578671917180373⟩⟩,⟨⟨153027218940144285249788926,153027218940144285875307897⟩,⟨23433217586417430921087699,23433217586417431546535813⟩⟩,⟨⟨302480249302383148706622916,302480249302383149348984725⟩,⟨(-778806932437459144399584224),(-778806932437459143760878793)⟩⟩] +lemma ha7_1_13_eq (j : Fin 7) : ha7_1_13 j = ((ha7_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha7_1_13_contains (j : Fin 7) : (ha7_1_13 j).Contains (fullFactor true 7 13 ((j.val:ℝ)/6)) := by + rw [ha7_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_12 j) true 7 12 j (ha7_1_12_contains j) +noncomputable def hk7_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_14 j i k) +lemma hk7_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_14 j i k).Contains (fullFactor true 7 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 14 (kernel7_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha7_1_14 : Fin 7 → CBox := ![⟨⟨101173,102698⟩,⟨(-1123),1123⟩⟩,⟨⟨1439657347,1439693432⟩,⟨(-711520333),(-711484248)⟩⟩,⟨⟨11073314593928576,11073314593933791⟩,⟨21067274492463644,21067274492468860⟩⟩,⟨⟨1245121083504391105990,1245121083504391410831⟩,⟨(-2470343140142409891908),(-2470343140142409587069)⟩⟩,⟨⟨647437038833958222495958,647437038833958264987657⟩,⟨(-1613625510281335584602570),(-1613625510281335542113142)⟩⟩,⟨⟨(-860443580586065515550567),(-860443580586065301525948)⟩,⟨(-45833258892538462191726829),(-45833258892538461977585477)⟩⟩,⟨⟨(-204934988786672549194147568),(-204934988786672549020138069)⟩,⟨(-67573204754830807099436572),(-67573204754830806924903760)⟩⟩] +lemma ha7_1_14_eq (j : Fin 7) : ha7_1_14 j = ((ha7_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha7_1_14_contains (j : Fin 7) : (ha7_1_14 j).Contains (fullFactor true 7 14 ((j.val:ℝ)/6)) := by + rw [ha7_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_13 j) true 7 13 j (ha7_1_13_contains j) +noncomputable def hk7_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_15 j i k) +lemma hk7_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_15 j i k).Contains (fullFactor true 7 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 15 (kernel7_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha7_1_15 : Fin 7 → CBox := ![⟨⟨(-63094),(-62156)⟩,⟨(-690),690⟩⟩,⟨⟨(-912156951),(-912129564)⟩,⟨6788092,6815479⟩⟩,⟨⟨3598646570904566,3598646570908070⟩,⟨(-10716995364559133),(-10716995364555629)⟩⟩,⟨⟨(-1076192227721879930534),(-1076192227721879769203)⟩,⟨42040815412579300994,42040815412579462325⟩⟩,⟨⟨(-562402021437243974695334),(-562402021437243957314159)⟩,⟨(-36395619301407600146359),(-36395619301407582765350)⟩⟩,⟨⟨(-12442427749089766406831498),(-12442427749089766338420339)⟩,⟨2386384123518979546184723,2386384123518979614537304⟩⟩,⟨⟨(-13701818112263452726919974),(-13701818112263452682665569)⟩,⟨50180935201904712119062198,50180935201904712163296960⟩⟩] +lemma ha7_1_15_eq (j : Fin 7) : ha7_1_15 j = ((ha7_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha7_1_15_contains (j : Fin 7) : (ha7_1_15 j).Contains (fullFactor true 7 15 ((j.val:ℝ)/6)) := by + rw [ha7_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_14 j) true 7 14 j (ha7_1_14_contains j) +noncomputable def hk7_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_16 j i k) +lemma hk7_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_16 j i k).Contains (fullFactor true 7 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 16 (kernel7_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha7_1_16 : Fin 7 → CBox := ![⟨⟨35799,36340⟩,⟨(-398),398⟩⟩,⟨⟨438614493,438633980⟩,⟨208682626,208702113⟩⟩,⟨⟨(-4557015813951268),(-4557015813949061)⟩,⟨2139502170487275,2139502170489482⟩⟩,⟨⟨203772929399466450193,203772929399466530237⟩,⟨336157315216055962143,336157315216056042189⟩⟩,⟨⟨42755760395473508208579,42755760395473514873705⟩,⟨165840224987454521349628,165840224987454528015111⟩⟩,⟨⟨1157021883919423492581753,1157021883919423513049365⟩,⟨3071891152119813664069209,3071891152119813684555964⟩⟩,⟨⟨11486093749923091518386099,11486093749923091528925328⟩,⟨2503436216847760679686219,2503436216847760690204808⟩⟩] +lemma ha7_1_16_eq (j : Fin 7) : ha7_1_16 j = ((ha7_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha7_1_16_contains (j : Fin 7) : (ha7_1_16 j).Contains (fullFactor true 7 16 ((j.val:ℝ)/6)) := by + rw [ha7_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_15 j) true 7 15 j (ha7_1_15_contains j) +noncomputable def hk7_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_17 j i k) +lemma hk7_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_17 j i k).Contains (fullFactor true 7 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 17 (kernel7_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha7_1_17 : Fin 7 → CBox := ![⟨⟨(-19700),(-19405)⟩,⟨(-216),216⟩⟩,⟨⟨(-152165636),(-152152585)⟩,⟨(-190043445),(-190030394)⟩⟩,⟨⟨1967966736623697,1967966736625006⟩,⟨760905173721916,760905173723225⟩⟩,⟨⟨67088887602124617893,67088887602124655273⟩,⟨(-117191196458426122863),(-117191196458426085484)⟩⟩,⟨⟨41258225306742928710560,41258225306742931116275⟩,⟨(-26402247457947417461548),(-26402247457947415055969)⟩⟩,⟨⟨690275789034642324571523,690275789034642330345197⟩,⟨(-405313254733281895063885),(-405313254733281889295230)⟩⟩,⟨⟨404893589244965806058790,404893589244965808411587⟩,⟨(-2467450719285744467170038),(-2467450719285744464807328)⟩⟩] +lemma ha7_1_17_eq (j : Fin 7) : ha7_1_17 j = ((ha7_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha7_1_17_contains (j : Fin 7) : (ha7_1_17 j).Contains (fullFactor true 7 17 ((j.val:ℝ)/6)) := by + rw [ha7_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_16 j) true 7 16 j (ha7_1_16_contains j) +noncomputable def hk7_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_18 j i k) +lemma hk7_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_18 j i k).Contains (fullFactor true 7 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 18 (kernel7_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha7_1_18 : Fin 7 → CBox := ![⟨⟨9934,10086⟩,⟨(-111),111⟩⟩,⟨⟨25548973,25557228⟩,⟨112361045,112369300⟩⟩,⟨⟨(-320588665335719),(-320588665334986)⟩,⟨(-771204368448841),(-771204368448107)⟩⟩,⟨⟨(-43805902594443855879),(-43805902594443839393)⟩,⟨(-614402655677971652),(-614402655677955166)⟩⟩,⟨⟨(-10249945339865937616028),(-10249945339865936796035)⟩,⟨(-8366874390679063830784),(-8366874390679063010760)⟩⟩,⟨⟨(-118999408281338401750395),(-118999408281338400214843)⟩,⟨(-140806487750863024077613),(-140806487750863022540949)⟩⟩,⟨⟨(-499225390199664147324569),(-499225390199664146824446)⟩,⟨(-55486655345583314930012),(-55486655345583314433023)⟩⟩] +lemma ha7_1_18_eq (j : Fin 7) : ha7_1_18 j = ((ha7_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha7_1_18_contains (j : Fin 7) : (ha7_1_18 j).Contains (fullFactor true 7 18 ((j.val:ℝ)/6)) := by + rw [ha7_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_17 j) true 7 17 j (ha7_1_17_contains j) +noncomputable def hk7_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_19 j i k) +lemma hk7_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_19 j i k).Contains (fullFactor true 7 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 19 (kernel7_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha7_1_19 : Fin 7 → CBox := ![⟨⟨(-4892),(-4818)⟩,⟨(-54),54⟩⟩,⟨⟨11674483,11679430⟩,⟨(-50340373),(-50335426)⟩⟩,⟨⟨(-125967728931120),(-125967728930730)⟩,⟨286744204928975,286744204929365⟩⟩,⟨⟨6359558777380443354,6359558777380450243⟩,⟨11869031593002625851,11869031593002632740⟩⟩,⟨⟨(-1216976233902185923116),(-1216976233902185658312)⟩,⟨3159654413818806958844,3159654413818807223644⟩⟩,⟨⟨(-25864437049687863275066),(-25864437049687862887627)⟩,⟨30806238410682156261245,30806238410682156648474⟩⟩,⟨⟨(-5611712174981349323778),(-5611712174981349224331)⟩,⟨95428147290663788361678,95428147290663788461944⟩⟩] +lemma ha7_1_19_eq (j : Fin 7) : ha7_1_19 j = ((ha7_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha7_1_19_contains (j : Fin 7) : (ha7_1_19 j).Contains (fullFactor true 7 19 ((j.val:ℝ)/6)) := by + rw [ha7_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_18 j) true 7 18 j (ha7_1_18_contains j) +noncomputable def hk7_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_20 j i k) +lemma hk7_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_20 j i k).Contains (fullFactor true 7 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 20 (kernel7_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha7_1_20 : Fin 7 → CBox := ![⟨⟨2219,2255⟩,⟨(-25),25⟩⟩,⟨⟨(-13834786),(-13831969)⟩,⟨17123021,17125838⟩⟩,⟨⟨104849200870767,104849200870965⟩,⟨(-38152255935253),(-38152255935056)⟩⟩,⟨⟨2131643671622914318,2131643671622917053⟩,⟨(-3303781149326288314),(-3303781149326285579)⟩⟩,⟨⟨822086102487532792311,822086102487532873547⟩,⟨41720716843997142859,41720716843997224094⟩⟩,⟨⟨7203452851685605566556,7203452851685605659321⟩,⟨4198344666592872661321,4198344666592872754119⟩⟩,⟨⟨17282362734980985230268,17282362734980985249361⟩,⟨117258775076553700322,117258775076553719226⟩⟩] +lemma ha7_1_20_eq (j : Fin 7) : ha7_1_20 j = ((ha7_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha7_1_20_contains (j : Fin 7) : (ha7_1_20 j).Contains (fullFactor true 7 20 ((j.val:ℝ)/6)) := by + rw [ha7_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_19 j) true 7 19 j (ha7_1_19_contains j) +noncomputable def hk7_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_21 j i k) +lemma hk7_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_21 j i k).Contains (fullFactor true 7 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 21 (kernel7_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha7_1_21 : Fin 7 → CBox := ![⟨⟨(-990),(-973)⟩,⟨(-11),11⟩⟩,⟨⟨8080955,8082483⟩,⟨(-3803108),(-3801580)⟩⟩,⟨⟨(-33939033026593),(-33939033026497)⟩,⟨(-16768807298512),(-16768807298416)⟩⟩,⟨⟨(-1090912695822704559),(-1090912695822703524)⟩,⟨(-73303564630663250),(-73303564630662215)⟩⟩,⟨⟨(-50143058193538875695),(-50143058193538851960)⟩,⟨(-183869079508829723858),(-183869079508829700123)⟩⟩,⟨⟨575145367005792410747,575145367005792431916⟩,⟨(-1542150128297189283688),(-1542150128297189262524)⟩⟩,⟨⟨(-134368701231792829333),(-134368701231792825910)⟩,⟨(-2972813329437353085587),(-2972813329437353082125)⟩⟩] +lemma ha7_1_21_eq (j : Fin 7) : ha7_1_21 j = ((ha7_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha7_1_21_contains (j : Fin 7) : (ha7_1_21 j).Contains (fullFactor true 7 21 ((j.val:ℝ)/6)) := by + rw [ha7_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_20 j) true 7 20 j (ha7_1_20_contains j) +noncomputable def hk7_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_22 j i k) +lemma hk7_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_22 j i k).Contains (fullFactor true 7 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 22 (kernel7_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha7_1_22 : Fin 7 → CBox := ![⟨⟨407,415⟩,⟨(-5),5⟩⟩,⟨⟨(-3459164),(-3458372)⟩,⟨(-41172),(-40380)⟩⟩,⟨⟨3669929945392,3669929945437⟩,⟨11697870724601,11697870724646⟩⟩,⟨⟨123309733489684010,123309733489684384⟩,⟨262733476550927036,262733476550927411⟩⟩,⟨⟨(-35158570632451282424),(-35158570632451275803)⟩,⟨23194890177468411341,23194890177468417961⟩⟩,⟨⟨(-304782617676364542090),(-304782617676364537480)⟩,⟨(-57431590279822282217),(-57431590279822277607)⟩⟩,⟨⟨(-486803430855369266820),(-486803430855369266220)⟩,⟨47428364028600870493,47428364028600871086⟩⟩] +lemma ha7_1_22_eq (j : Fin 7) : ha7_1_22 j = ((ha7_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha7_1_22_contains (j : Fin 7) : (ha7_1_22 j).Contains (fullFactor true 7 22 ((j.val:ℝ)/6)) := by + rw [ha7_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_21 j) true 7 21 j (ha7_1_21_contains j) +noncomputable def hk7_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_23 j i k) +lemma hk7_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_23 j i k).Contains (fullFactor true 7 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 23 (kernel7_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha7_1_23 : Fin 7 → CBox := ![⟨⟨(-167),(-163)⟩,⟨(-3),3⟩⟩,⟨⟨1146069,1146462⟩,⟨572491,572884⟩⟩,⟨⟨1833771523401,1833771523422⟩,⟨(-3325899652088),(-3325899652068)⟩⟩,⟨⟨43180493454018387,43180493454018517⟩,⟨(-59714486883557486),(-59714486883557355)⟩⟩,⟨⟨6975561262603222506,6975561262603224273⟩,⟨5534073473824407673,5534073473824409440⟩⟩,⟨⟨(-868048496691271892),(-868048496691270931)⟩,⟨55894633865618370793,55894633865618371754⟩⟩,⟨⟨11420598714350161078,11420598714350161177⟩,⟨76041481804963775571,76041481804963775671⟩⟩] +lemma ha7_1_23_eq (j : Fin 7) : ha7_1_23 j = ((ha7_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha7_1_23_contains (j : Fin 7) : (ha7_1_23 j).Contains (fullFactor true 7 23 ((j.val:ℝ)/6)) := by + rw [ha7_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_22 j) true 7 22 j (ha7_1_22_contains j) +noncomputable def hk7_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_24 j i k) +lemma hk7_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_24 j i k).Contains (fullFactor true 7 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 24 (kernel7_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha7_1_24 : Fin 7 → CBox := ![⟨⟨62,65⟩,⟨(-2),2⟩⟩,⟨⟨(-277525),(-277338)⟩,⟨(-360594),(-360407)⟩⟩,⟨⟨(-1089897724145),(-1089897724136)⟩,⟨288792308946,288792308955⟩⟩,⟨⟨(-17801609210552986),(-17801609210552942)⟩,⟨(-2149451241318045),(-2149451241318001)⟩⟩,⟨⟨624870744370813799,624870744370814252⟩,⟨(-1692212985058327630),(-1692212985058327177)⟩⟩,⟨⟨9539895718000562382,9539895718000562575⟩,⟨(-1492526545415293276),(-1492526545415293083)⟩⟩,⟨⟨11351803611948513116,11351803611948513133⟩,⟨(-2313276809010556638),(-2313276809010556622)⟩⟩] +lemma ha7_1_24_eq (j : Fin 7) : ha7_1_24 j = ((ha7_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha7_1_24_contains (j : Fin 7) : (ha7_1_24 j).Contains (fullFactor true 7 24 ((j.val:ℝ)/6)) := by + rw [ha7_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_23 j) true 7 23 j (ha7_1_23_contains j) +noncomputable def hk7_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_25 j i k) +lemma hk7_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_25 j i k).Contains (fullFactor true 7 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 25 (kernel7_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha7_1_25 : Fin 7 → CBox := ![⟨⟨(-24),(-22)⟩,⟨(-1),1⟩⟩,⟨⟨31419,31506⟩,⟨151762,151848⟩⟩,⟨⟨274139398914,274139398918⟩,⟨167650273450,167650273454⟩⟩,⟨⟨1575933267302100,1575933267302115⟩,⟨3880741505352921,3880741505352936⟩⟩,⟨⟨(-350596305039699786),(-350596305039699673)⟩,⟨(-12903608623957017),(-12903608623956904)⟩⟩,⟨⟨(-512656375610894045),(-512656375610894007)⟩,⟨(-1516884168816044951),(-1516884168816044913)⟩⟩,⟨⟨(-419394761203970734),(-419394761203970731)⟩,⟨(-1622291467309809393),(-1622291467309809389)⟩⟩] +lemma ha7_1_25_eq (j : Fin 7) : ha7_1_25 j = ((ha7_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha7_1_25_contains (j : Fin 7) : (ha7_1_25 j).Contains (fullFactor true 7 25 ((j.val:ℝ)/6)) := by + rw [ha7_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_24 j) true 7 24 j (ha7_1_24_contains j) +noncomputable def hk7_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_26 j i k) +lemma hk7_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_26 j i k).Contains (fullFactor true 7 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 26 (kernel7_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha7_1_26 : Fin 7 → CBox := ![⟨⟨7,9⟩,⟨(-1),1⟩⟩,⟨⟨12411,12450⟩,⟨(-49279),(-49240)⟩⟩,⟨⟨(-18704359654),(-18704359651)⟩,⟨(-86049740164),(-86049740161)⟩⟩,⟨⟨590924830262043,590924830262048⟩,⟨(-732029215957015),(-732029215957009)⟩⟩,⟨⟨18140917000270885,18140917000270912⟩,⟨63050181086165834,63050181086165862⟩⟩,⟨⟨(-224455939157093426),(-224455939157093418)⟩,⟨121642393118367865,121642393118367873⟩⟩,⟨⟨(-222284060373243878),(-222284060373243877)⟩,⟨69964173583019409,69964173583019411⟩⟩] +lemma ha7_1_26_eq (j : Fin 7) : ha7_1_26 j = ((ha7_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha7_1_26_contains (j : Fin 7) : (ha7_1_26 j).Contains (fullFactor true 7 26 ((j.val:ℝ)/6)) := by + rw [ha7_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_25 j) true 7 25 j (ha7_1_25_contains j) +noncomputable def hk7_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_27 j i k) +lemma hk7_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_27 j i k).Contains (fullFactor true 7 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 27 (kernel7_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha7_1_27 : Fin 7 → CBox := ![⟨⟨(-4),(-2)⟩,⟨(-1),1⟩⟩,⟨⟨(-10321),(-10304)⟩,⟨12266,12284⟩⟩,⟨⟨(-13002869323),(-13002869321)⟩,⟨19259262186,19259262188⟩⟩,⟨⟨(-200434097895347),(-200434097895344)⟩,⟨(-35073199112424),(-35073199112421)⟩⟩,⟨⟨9770414805577701,9770414805577708⟩,⟨(-6642753316426649),(-6642753316426642)⟩⟩,⟨⟨24260393898442428,24260393898442431⟩,⟨30788726254122220,30788726254122222⟩⟩,⟨⟨10903017634695057,10903017634695058⟩,⟨29242078608942635,29242078608942636⟩⟩] +lemma ha7_1_27_eq (j : Fin 7) : ha7_1_27 j = ((ha7_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha7_1_27_contains (j : Fin 7) : (ha7_1_27 j).Contains (fullFactor true 7 27 ((j.val:ℝ)/6)) := by + rw [ha7_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_26 j) true 7 26 j (ha7_1_26_contains j) +noncomputable def hk7_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_28 j i k) +lemma hk7_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_28 j i k).Contains (fullFactor true 7 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 28 (kernel7_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha7_1_28 : Fin 7 → CBox := ![⟨⟨0,2⟩,⟨(-1),1⟩⟩,⟨⟨4449,4457⟩,⟨(-1996),(-1987)⟩⟩,⟨⟨5828869303,5828869305⟩,⟨(-994896287),(-994896286)⟩⟩,⟨⟨13859366068567,13859366068568⟩,⟨40111798482218,40111798482220⟩⟩,⟨⟨(-1624825346939808),(-1624825346939806)⟩,⟨(-1252609704288943),(-1252609704288940)⟩⟩,⟨⟨3881940849023714,3881940849023716⟩,⟨(-4314126645352071),(-4314126645352070)⟩⟩,⟨⟨3698093253209658,3698093253209659⟩,⟨(-1602212991316196),(-1602212991316195)⟩⟩] +lemma ha7_1_28_eq (j : Fin 7) : ha7_1_28 j = ((ha7_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha7_1_28_contains (j : Fin 7) : (ha7_1_28 j).Contains (fullFactor true 7 28 ((j.val:ℝ)/6)) := by + rw [ha7_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_27 j) true 7 27 j (ha7_1_27_contains j) +noncomputable def hk7_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_29 j i k) +lemma hk7_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_29 j i k).Contains (fullFactor true 7 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 29 (kernel7_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha7_1_29 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1435),(-1430)⟩,⟨(-47),(-42)⟩⟩,⟨⟨(-1166295467),(-1166295465)⟩,⟨(-866246395),(-866246393)⟩⟩,⟨⟨5713120496780,5713120496781⟩,⟨(-6355635247484),(-6355635247483)⟩⟩,⟨⟨(-114650128314549),(-114650128314548)⟩,⟨324304336268259,324304336268260⟩⟩,⟨⟨(-702019137489121),(-702019137489120)⟩,⟨(-442083325703484),(-442083325703482)⟩⟩,⟨⟨(-223449524297539),(-223449524297538)⟩,⟨(-450105452528624),(-450105452528623)⟩⟩] +lemma ha7_1_29_eq (j : Fin 7) : ha7_1_29 j = ((ha7_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha7_1_29_contains (j : Fin 7) : (ha7_1_29 j).Contains (fullFactor true 7 29 ((j.val:ℝ)/6)) := by + rw [ha7_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_28 j) true 7 28 j (ha7_1_28_contains j) +noncomputable def hk7_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel7_0 j i k).mul (mpower1_30 j i k) +lemma hk7_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk7_1_30 j i k).Contains (fullFactor true 7 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk7_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel7_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 7 30 (kernel7_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha7_1_30 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨359,362⟩,⟨187,190⟩⟩,⟨⟨42700264,42700266⟩,⟨342386735,342386737⟩⟩,⟨⟨(-1621147628829),(-1621147628828)⟩,⟨(-373261829943),(-373261829942)⟩⟩,⟨⟨55733944736529,55733944736530⟩,⟨1274856145689,1274856145691⟩⟩,⟨⟨(-43720188151538),(-43720188151537)⟩,⟨105977250480059,105977250480060⟩⟩,⟨⟨(-52779488085733),(-52779488085731)⟩,⟨29713328701054,29713328701055⟩⟩] +lemma ha7_1_30_eq (j : Fin 7) : ha7_1_30 j = ((ha7_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha7_1_30_contains (j : Fin 7) : (ha7_1_30 j).Contains (fullFactor true 7 30 ((j.val:ℝ)/6)) := by + rw [ha7_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha7_1_29 j) true 7 29 j (ha7_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders9.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders9.lean new file mode 100644 index 0000000000000000000000000000000000000000..587384205e20e580e6778a75996c4746aba0fd5b --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighHeaders9.lean @@ -0,0 +1,577 @@ +import OAI.Analysis.PlanarPacking.Certificate.Powers10 +import OAI.Analysis.PlanarPacking.Certificate.KernelValues10 +import OAI.Analysis.PlanarPacking.HighRuleBridge +import OAI.Analysis.PlanarPacking.Certificate.MomentPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +noncomputable def hk9_0_0 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_0 j i k) +lemma hk9_0_0_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_0 j i k).Contains (fullFactor false 9 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 0 (power9_contains j i k) (mpower0_0_contains j i k) +noncomputable def ha9_0_0 : Fin 7 → CBox := ![⟨⟨999999999999999999999999999893,1000000000000000000000000000143⟩,⟨(-143),143⟩⟩,⟨⟨(-15481194292),22551044425⟩,⟨(-1000000000000000000018917712483),(-999999999999999999981082287531)⟩⟩,⟨⟨(-1000000000000000000051861281538),(-999999999999999999948138718466)⟩,⟨(-58859103936),44719403622⟩⟩,⟨⟨(-40004849897),18795299435⟩,⟨999999999999999999970599925343,1000000000000000000029400074666⟩⟩,⟨⟨999999999999999999858301105358,1000000000000000000141698894621⟩,⟨(-127611850236),155891250888⟩⟩,⟨⟨(-160676030550),196025281331⟩,⟨(-1000000000000000000178402917707),(-999999999999999999821597082270)⟩⟩,⟨⟨(-1000000000000000000058978780073),(-999999999999999999941021219963)⟩,⟨(-80188330553),37769229557⟩⟩] +lemma ha9_0_0_eq (j : Fin 7) : ha9_0_0 j = ((atomPoints j).direct.powBin 7 9).conj := by fin_cases j <;> decide +kernel +lemma ha9_0_0_contains (j : Fin 7) : (ha9_0_0 j).Contains (fullFactor false 9 0 ((j.val:ℝ)/6)) := by + rw [ha9_0_0_eq] + simpa only [Complex.ofReal_div,Complex.ofReal_natCast,Complex.ofReal_ofNat,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @direct_factor_zero_full ((atomPoints j).direct.powBin 7 9) ((j.val:ℝ)/6) 9 (@direct_power_bin_contains (atomPoints j) ((j.val:ℝ)/6) (atomPoints_contains j) 9 (by norm_num)) +noncomputable def hk9_0_1 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_1 j i k) +lemma hk9_0_1_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_1 j i k).Contains (fullFactor false 9 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 1 (power9_contains j i k) (mpower0_1_contains j i k) +noncomputable def ha9_0_1 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨523598775598298873066761375578,523598775598298873088238624429⟩,⟨(-8105934377),11807699250⟩⟩,⟨⟨(-46830049964),61637109508⟩,⟨(-1047197551196597746210975673698),(-1047197551196597746099024326307)⟩⟩,⟨⟨(-1570796326794896619281181529293),(-1570796326794896619183818470721)⟩,⟨(-62839471273),29523587314⟩⟩,⟨⟨(-326497872366),267269634142⟩,⟨2094395102393195492009893195711,2094395102393195492610106804244⟩⟩,⟨⟨2617993877991494364916275586899,2617993877991494365858724413042⟩,⟨(-420648864320),513192986457⟩⟩,⟨⟨(-118655534109),251919070169⟩,⟨(-3141592653589793238655287302196),(-3141592653589793238274712697918)⟩⟩] +lemma ha9_0_1_eq (j : Fin 7) : ha9_0_1 j = ((ha9_0_0 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha9_0_1_contains (j : Fin 7) : (ha9_0_1 j).Contains (fullFactor false 9 1 ((j.val:ℝ)/6)) := by + rw [ha9_0_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_0 j) false 9 0 j (ha9_0_0_contains j) +noncomputable def hk9_0_2 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_2 j i k) +lemma hk9_0_2_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_2 j i k).Contains (fullFactor false 9 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 2 (power9_contains j i k) (mpower0_2_contains j i k) +noncomputable def ha9_0_2 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-3091248435),2122128658⟩,⟨137077838904018869703210719368,137077838904018869709269782284⟩⟩,⟨⟨548311355616075478794779544465,548311355616075478855142462141⟩,⟨(-24520156823),32273115070⟩⟩,⟨⟨(-23187771254),49354005327⟩,⟨(-1233700550136169827396360136536),(-1233700550136169827315964378333)⟩⟩,⟨⟨(-2193245422464301915617605782214),(-2193245422464301914982082244150)⟩,⟨(-341907772413),279884106383⟩⟩,⟨⟨(-671768048387),550628075787⟩,⟨3426945972600471742033720802391,3426945972600471743278291738803⟩⟩,⟨⟨4934802200544679309117892452934,4934802200544679309731405606674⟩,⟨(-186383677133),395713550072⟩⟩] +lemma ha9_0_2_eq (j : Fin 7) : ha9_0_2 j = ((ha9_0_1 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha9_0_2_contains (j : Fin 7) : (ha9_0_2 j).Contains (fullFactor false 9 2 ((j.val:ℝ)/6)) := by + rw [ha9_0_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_1 j) false 9 1 j (ha9_0_1_contains j) +noncomputable def hk9_0_3 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_3 j i k) +lemma hk9_0_3_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_3 j i k).Contains (fullFactor false 9 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 3 (power9_contains j i k) (mpower0_3_contains j i k) +noncomputable def ha9_0_3 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-23924596203935046432315357705),(-23924596203935046431181697374)⟩,⟨(-539524632),370381323⟩⟩,⟨⟨(-11265442357),8559149394⟩,⟨191396769631480371443148286301,191396769631480371464828154334⟩⟩,⟨⟨645964097506246253635134599502,645964097506246253679285887645⟩,⟨(-12141088638),25841696761⟩⟩,⟨⟨(-195395967216),238696654671⟩,⟨(-1531174157051842971856182266143),(-1531174157051842971407629258896)⟩⟩,⟨⟨(-2990574525491880804516372104984),(-2990574525491880803420759779860)⟩,⟨(-586228212703),480513643821⟩⟩,⟨⟨(-414390260611),195180530277⟩,⟨5167712780049970028928222542209,5167712780049970029587141355102⟩⟩] +lemma ha9_0_3_eq (j : Fin 7) : ha9_0_3 j = ((ha9_0_2 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha9_0_3_contains (j : Fin 7) : (ha9_0_3 j).Contains (fullFactor false 9 3 ((j.val:ℝ)/6)) := by + rw [ha9_0_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_2 j) false 9 2 j (ha9_0_2_contains j) +noncomputable def hk9_0_4 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_4 j i k) +lemma hk9_0_4_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_4 j i k).Contains (fullFactor false 9 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 4 (power9_contains j i k) (mpower0_4_contains j i k) +noncomputable def ha9_0_4 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-48482802),70623610⟩,⟨(-3131722319766024859799237881),(-3131722319766024859640873508)⟩⟩,⟨⟨(-50107557116256397758438527860),(-50107557116256397752603254372)⟩,⟨(-2949285913),2240780072⟩⟩,⟨⟨(-10148010588),4767794359⟩,⟨253669507901048013628251698558,253669507901048013646397323991⟩⟩,⟨⟨801720913860102363969627376684,801720913860102364207041139001⟩,⟨(-102309089192),124981276126⟩⟩,⟨⟨(-314495444454),383685467991⟩,⟨(-1957326449853765537686688285964),(-1957326449853765536963381332409)⟩⟩,⟨⟨(-4058712126416768218462408634160),(-4058712126416768217931975726735)⟩,⟨(-325461349614),153294430011⟩⟩] +lemma ha9_0_4_eq (j : Fin 7) : ha9_0_4 j = ((ha9_0_3 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha9_0_4_contains (j : Fin 7) : (ha9_0_4 j).Contains (fullFactor false 9 4 ((j.val:ℝ)/6)) := by + rw [ha9_0_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_3 j) false 9 3 j (ha9_0_3_contains j) +noncomputable def hk9_0_5 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_5 j i k) +lemma hk9_0_5_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_5 j i k).Contains (fullFactor false 9 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 5 (power9_contains j i k) (mpower0_5_contains j i k) +noncomputable def ha9_0_5 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨327953194428670967566513063,327953194428670967584140850⟩,⟨(-5077108),7395688⟩⟩,⟨⟨(-469307881),617696998⟩,⟨(-10494502221717470963038233533),(-10494502221717470961782691673)⟩⟩,⟨⟨(-79692626246167045123781593325),(-79692626246167045117827307461)⟩,⟨(-3188091552),1497846774⟩⟩,⟨⟨(-52352034522),42855131067⟩,⟨335824071094959070746876500582,335824071094959070847393106010⟩⟩,⟨⟨1024853732589596773481904315566,1024853732589596773863889161582⟩,⟨(-164669429648),200897241255⟩⟩,⟨⟨(-96317731032),204493396995⟩,⟨(-2550164039877345444036441537248),(-2550164039877345443695043287957)⟩⟩] +lemma ha9_0_5_eq (j : Fin 7) : ha9_0_5 j = ((ha9_0_4 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha9_0_5_contains (j : Fin 7) : (ha9_0_5 j).Contains (fullFactor false 9 5 ((j.val:ℝ)/6)) := by + rw [ha9_0_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_4 j) false 9 4 j (ha9_0_4_contains j) +noncomputable def hk9_0_6 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_6 j i k) +lemma hk9_0_6_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_6 j i k).Contains (fullFactor false 9 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 6 (power9_contains j i k) (mpower0_6_contains j i k) +noncomputable def ha9_0_6 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-645396),443062⟩,⟨28619315176067161690742961,28619315176067161692372375⟩⟩,⟨⟨1831636171268298348147208893,1831636171268298348372172567⟩,⟨(-81909678),107808464⟩⟩,⟨⟨(-392135369),834640417⟩,⟨(-20863480763352960873958159178),(-20863480763352960872332920262)⟩⟩,⟨⟨(-117224714961171094306350232815),(-117224714961171094270890180604)⟩,⟨(-18274307451),14959262770⟩⟩,⟨⟨(-87657957952),71850593119⟩,⟨447176799626049401346540687412,447176799626049401514636426768⟩⟩,⟨⟨1335262768854589495789811552731,1335262768854589495972817531452⟩,⟨(-50431846037),107072492285⟩⟩] +lemma ha9_0_6_eq (j : Fin 7) : ha9_0_6 j = ((ha9_0_5 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha9_0_6_contains (j : Fin 7) : (ha9_0_6 j).Contains (fullFactor false 9 6 ((j.val:ℝ)/6)) := by + rw [ha9_0_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_5 j) false 9 5 j (ha9_0_5_contains j) +noncomputable def hk9_0_7 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_7 j i k) +lemma hk9_0_7_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_7 j i k).Contains (fullFactor false 9 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 7 (power9_contains j i k) (mpower0_7_contains j i k) +noncomputable def ha9_0_7 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2140719769235797028281105),(-2140719769235797028152410)⟩,⟨(-48276),33141⟩⟩,⟨⟨(-16128109),12253660⟩,⟨274012130462182019594481548,274012130462182019629008243⟩⟩,⟨⟨4681754135318688100520244924,4681754135318688100899850171⟩,⟨(-87994972),187292872⟩⟩,⟨⟨(-4475800955),5467660004⟩,⟨(-35073552699159298515663979303),(-35073552699159298504942713904)⟩⟩,⟨⟨(-167243731971546642861134146643),(-167243731971546642797734133801)⟩,⟨(-32783999611),26872058988⟩⟩,⟨⟨(-48054022167),22633759574⟩,⟨599264529320792076848865881410,599264529320792076932906290839⟩⟩] +lemma ha9_0_7_eq (j : Fin 7) : ha9_0_7 j = ((ha9_0_6 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha9_0_7_contains (j : Fin 7) : (ha9_0_7 j).Contains (fullFactor false 9 7 ((j.val:ℝ)/6)) := by + rw [ha9_0_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_6 j) false 9 6 j (ha9_0_6_contains j) +noncomputable def hk9_0_8 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_8 j i k) +lemma hk9_0_8_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_8 j i k).Contains (fullFactor false 9 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 8 (power9_contains j i k) (mpower0_8_contains j i k) +noncomputable def ha9_0_8 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-2170),3160⟩,⟨(-140109781258867029458365),(-140109781258867029449495)⟩⟩,⟨⟨(-35868104002269959542522857),(-35868104002269959537889150)⟩,⟨(-2111165),1604001⟩⟩,⟨⟨(-36774870),17277773⟩,⟨919260274839426580208502065,919260274839426580285963478⟩⟩,⟨⟨9182234624581109640874712580,9182234624581109643710761260⟩,⟨(-1171761950),1431430042⟩⟩,⟨⟨(-8793860740),10728538785⟩,⟨(-54730383304244933390902198618),(-54730383304244933369980380711)⟩⟩,⟨⟨(-235330630358893204560167425725),(-235330630358893204526415753454)⟩,⟨(-18870770377),8888256601⟩⟩] +lemma ha9_0_8_eq (j : Fin 7) : ha9_0_8 j = ((ha9_0_7 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha9_0_8_contains (j : Fin 7) : (ha9_0_8 j).Contains (fullFactor false 9 8 ((j.val:ℝ)/6)) := by + rw [ha9_0_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_7 j) false 9 7 j (ha9_0_7_contains j) +noncomputable def hk9_0_9 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_9 j i k) +lemma hk9_0_9_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_9 j i k).Contains (fullFactor false 9 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 9 (power9_contains j i k) (mpower0_9_contains j i k) +noncomputable def ha9_0_9 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨8151256657387584304649,8151256657387584305192⟩,⟨(-127),184⟩⟩,⟨⟨(-186634),245646⟩,⟨(-4173443408582443164395357),(-4173443408582443163842915)⟩⟩,⟨⟨(-160441184787359821880759176),(-160441184787359821866728908)⟩,⟨(-6418426),3015541⟩⟩,⟨⟨(-333108897),272681388⟩,⟨2136803025194210899695607445,2136803025194210900362387597⟩⟩,⟨⟨15920423158960125592478947177,15920423158960125598615533591⟩,⟨(-2558030398),3120805429⟩⟩,⟨⟨(-3102586849),6587141510⟩,⟨(-82145886611128228805378466955),(-82145886611128228793335432292)⟩⟩] +lemma ha9_0_9_eq (j : Fin 7) : ha9_0_9 j = ((ha9_0_8 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha9_0_9_contains (j : Fin 7) : (ha9_0_9 j).Contains (fullFactor false 9 9 ((j.val:ℝ)/6)) := by + rw [ha9_0_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_8 j) false 9 8 j (ha9_0_8_contains j) +noncomputable def hk9_0_10 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_10 j i k) +lemma hk9_0_10_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_10 j i k).Contains (fullFactor false 9 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 10 (power9_contains j i k) (mpower0_10_contains j i k) +noncomputable def ha9_0_10 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-10),7⟩,⟨426798800539562151439,426798800539562151470⟩⟩,⟨⟨437041971752511643059878,437041971752511643119122⟩,⟨(-19545),25724⟩⟩,⟨⟨(-473681),1008204⟩,⟨(-25202042373060605482384116),(-25202042373060605480100025)⟩⟩,⟨⟨(-447530979074571922594185238),(-447530979074571922453110593)⟩,⟨(-69766165),57110257⟩⟩,⟨⟨(-817024951),669690793⟩,⟨4167957036519161634488817362,4167957036519161636108638948⟩⟩,⟨⟨25806891390014060010859092218,25806891390014060014724669028⟩,⟨(-974706406),2069411538⟩⟩] +lemma ha9_0_10_eq (j : Fin 7) : ha9_0_10 j = ((ha9_0_9 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha9_0_10_contains (j : Fin 7) : (ha9_0_10 j).Contains (fullFactor false 9 10 ((j.val:ℝ)/6)) := by + rw [ha9_0_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_9 j) false 9 9 j (ha9_0_9_contains j) +noncomputable def hk9_0_11 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_11 j i k) +lemma hk9_0_11_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_11 j i k).Contains (fullFactor false 9 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 11 (power9_contains j i k) (mpower0_11_contains j i k) +noncomputable def ha9_0_11 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-20315575399030665722),(-20315575399030665720)⟩,⟨(-1),1⟩⟩,⟨⟨(-2449),1861⟩,⟨41606298417214803393840,41606298417214803399613⟩⟩,⟨⟨3598843235212085340319424,3598843235212085340657048⟩,⟨(-67642),143972⟩⟩,⟨⟨(-10873768),13283447⟩,⟨(-85209699158455917370061735),(-85209699158455917342929954)⟩⟩,⟨⟨(-991971455030794224855365154),(-991971455030794224466690974)⟩,⟨(-194451484),159386037⟩⟩,⟨⟨(-591022554),278375499⟩,⟨7370430945714350776756173426,7370430945714350777883640392⟩⟩] +lemma ha9_0_11_eq (j : Fin 7) : ha9_0_11 j = ((ha9_0_10 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha9_0_11_contains (j : Fin 7) : (ha9_0_11 j).Contains (fullFactor false 9 11 ((j.val:ℝ)/6)) := by + rw [ha9_0_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_10 j) false 9 10 j (ha9_0_10_contains j) +noncomputable def hk9_0_12 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_12 j i k) +lemma hk9_0_12_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_12 j i k).Contains (fullFactor false 9 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 12 (power9_contains j i k) (mpower0_12_contains j i k) +noncomputable def ha9_0_12 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-886434200375614886),(-886434200375614885)⟩⟩,⟨⟨(-3630834484738518571314),(-3630834484738518570798)⟩,⟨(-214),163⟩⟩,⟨⟨(-18846),8855⟩,⟨471087477881817150348421,471087477881817150394116⟩⟩,⟨⟨14871898049488972064655115,14871898049488972069437844⟩,⟨(-1897831),2318399⟩⟩,⟨⟨(-34772640),42422733⟩,⟨(-216414599701077852950892727),(-216414599701077852865408304)⟩⟩,⟨⟨(-1929574309403923048071370939),(-1929574309403923047770058750)⟩,⟨(-154729343),72878536⟩⟩] +lemma ha9_0_12_eq (j : Fin 7) : ha9_0_12 j = ((ha9_0_11 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha9_0_12_contains (j : Fin 7) : (ha9_0_12 j).Contains (fullFactor false 9 12 ((j.val:ℝ)/6)) := by + rw [ha9_0_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_11 j) false 9 11 j (ha9_0_11_contains j) +noncomputable def hk9_0_13 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_13 j i k) +lemma hk9_0_13_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_13 j i k).Contains (fullFactor false 9 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 13 (power9_contains j i k) (mpower0_13_contains j i k) +noncomputable def ha9_0_13 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨35702758612702236,35702758612702237⟩,⟨(-1),1⟩⟩,⟨⟨(-14),18⟩,⟨(-292476998555256723048),(-292476998555256723004)⟩⟩,⟨⟨(-56921729219679268121159),(-56921729219679268115456)⟩,⟨(-2278),1070⟩⟩,⟨⟨(-373512),305755⟩,⟨2395971572164663074640913,2395971572164663075419073⟩⟩,⟨⟨43582469009646285022481088,43582469009646285039835024⟩,⟨(-7002659),8543266⟩⟩,⟨⟨(-17611898),37392044⟩,⟨(-466302805767612564462326024),(-466302805767612564388026339)⟩⟩] +lemma ha9_0_13_eq (j : Fin 7) : ha9_0_13 j = ((ha9_0_12 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha9_0_13_contains (j : Fin 7) : (ha9_0_13 j).Contains (fullFactor false 9 13 ((j.val:ℝ)/6)) := by + rw [ha9_0_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_12 j) false 9 12 j (ha9_0_12_contains j) +noncomputable def hk9_0_14 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_14 j i k) +lemma hk9_0_14_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_14 j i k).Contains (fullFactor false 9 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 14 (power9_contains j i k) (mpower0_14_contains j i k) +noncomputable def ha9_0_14 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1335280049649465,1335280049649466⟩⟩,⟨⟨21877228333456835515,21877228333456835520⟩,⟨(-2),2⟩⟩,⟨⟨(-121),256⟩,⟨(-6386603083791852241488),(-6386603083791852240826)⟩⟩,⟨⟨(-358436509015356793180286),(-358436509015356793062732)⟩,⟨(-55878),45741⟩⟩,⟨⟨(-1597588),1309495⟩,⟨8149902646786285755515023,8149902646786285758786145⟩⟩,⟨⟨104638104924845707110612683,104638104924845707127618568⟩,⟨(-3952101),8390756⟩⟩] +lemma ha9_0_14_eq (j : Fin 7) : ha9_0_14 j = ((ha9_0_13 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha9_0_14_contains (j : Fin 7) : (ha9_0_14 j).Contains (fullFactor false 9 14 ((j.val:ℝ)/6)) := by + rw [ha9_0_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_13 j) false 9 13 j (ha9_0_13_contains j) +noncomputable def hk9_0_15 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_15 j i k) +lemma hk9_0_15_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_15 j i k).Contains (fullFactor false 9 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 15 (power9_contains j i k) (mpower0_15_contains j i k) +noncomputable def ha9_0_15 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-46610066605154),(-46610066605153)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1527318662517654886,1527318662517654887⟩⟩,⟨⟨668803510981146723219,668803510981146723292⟩,⟨(-13),27⟩⟩,⟨⟨(-6387),7803⟩,⟨(-50047177933378515336306),(-50047177933378515319732)⟩⟩,⟨⟨(-1422426349034211493123578),(-1422426349034211492548131)⟩,⟨(-278832),228550⟩⟩,⟨⟨(-1757356),827727⟩,⟨21915353447830215825815512,21915353447830215829446976⟩⟩] +lemma ha9_0_15_eq (j : Fin 7) : ha9_0_15 j = ((ha9_0_14 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha9_0_15_contains (j : Fin 7) : (ha9_0_15 j).Contains (fullFactor false 9 15 ((j.val:ℝ)/6)) := by + rw [ha9_0_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_14 j) false 9 14 j (ha9_0_14_contains j) +noncomputable def hk9_0_16 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_16 j i k) +lemma hk9_0_16_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_16 j i k).Contains (fullFactor false 9 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 16 (power9_contains j i k) (mpower0_16_contains j i k) +noncomputable def ha9_0_16 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1525310862814),(-1525310862813)⟩⟩,⟨⟨(-99962772705334444),(-99962772705334443)⟩,⟨(-1),1⟩⟩,⟨⟨(-3),2⟩,⟨65659631149794723619,65659631149794723627⟩⟩,⟨⟨6551160272016798097734,6551160272016798099925⟩,⟨(-837),1022⟩⟩,⟨⟨(-37397),45624⟩,⟨(-232743967104084891423289),(-232743967104084891328390)⟩⟩,⟨⟨(-4303069587032947007712837),(-4303069587032947006986103)⟩,⟨(-345057),162524⟩⟩] +lemma ha9_0_16_eq (j : Fin 7) : ha9_0_16 j = ((ha9_0_15 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha9_0_16_contains (j : Fin 7) : (ha9_0_16 j).Contains (fullFactor false 9 16 ((j.val:ℝ)/6)) := by + rw [ha9_0_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_15 j) false 9 15 j (ha9_0_15_contains j) +noncomputable def hk9_0_17 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_17 j i k) +lemma hk9_0_17_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_17 j i k).Contains (fullFactor false 9 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 17 (power9_contains j i k) (mpower0_17_contains j i k) +noncomputable def ha9_0_17 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨46979464716,46979464717⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-6157692399285196),(-6157692399285195)⟩⟩,⟨⟨(-6066935731106195668),(-6066935731106195666)⟩,⟨(-1),1⟩⟩,⟨⟨(-126),104⟩,⟨807101058159109193291,807101058159109193564⟩⟩,⟨⟨35842487118702823479211,35842487118702823493941⟩,⟨(-5760),7027⟩⟩,⟨⟨(-30035),63767⟩,⟨(-795205400147551278556878),(-795205400147551278420045)⟩⟩] +lemma ha9_0_17_eq (j : Fin 7) : ha9_0_17 j = ((ha9_0_16 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha9_0_17_contains (j : Fin 7) : (ha9_0_17 j).Contains (fullFactor false 9 17 ((j.val:ℝ)/6)) := by + rw [ha9_0_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_16 j) false 9 16 j (ha9_0_16_contains j) +noncomputable def hk9_0_18 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_18 j i k) +lemma hk9_0_18_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_18 j i k).Contains (fullFactor false 9 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 18 (power9_contains j i k) (mpower0_18_contains j i k) +noncomputable def ha9_0_18 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨1366577233,1366577234⟩⟩,⟨⟨358240022308519,358240022308520⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-529440020073462377),(-529440020073462376)⟩⟩,⟨⟨(-93910472408044662756),(-93910472408044662723)⟩,⟨(-15),13⟩⟩,⟨⟨(-1023),838⟩,⟨5213078436041832670594,5213078436041832672754⟩⟩,⟨⟨138789524622137721134393,138789524622137721158717⟩,⟨(-5243),11130⟩⟩] +lemma ha9_0_18_eq (j : Fin 7) : ha9_0_18 j = ((ha9_0_17 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha9_0_18_contains (j : Fin 7) : (ha9_0_18 j).Contains (fullFactor false 9 18 ((j.val:ℝ)/6)) := by + rw [ha9_0_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_17 j) false 9 17 j (ha9_0_17_contains j) +noncomputable def hk9_0_19 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_19 j i k) +lemma hk9_0_19_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_19 j i k).Contains (fullFactor false 9 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 19 (power9_contains j i k) (mpower0_19_contains j i k) +noncomputable def ha9_0_19 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-37659904),(-37659903)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨19744635479057,19744635479058⟩⟩,⟨⟨43770654673137422,43770654673137423⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-10351875446044213764),(-10351875446044213759)⟩⟩,⟨⟨(-718305654265631155201),(-718305654265631154900)⟩,⟨(-141),116⟩⟩,⟨⟨(-1841),867⟩,⟨22948428997269873108483,22948428997269873112579⟩⟩] +lemma ha9_0_19_eq (j : Fin 7) : ha9_0_19 j = ((ha9_0_18 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha9_0_19_contains (j : Fin 7) : (ha9_0_19 j).Contains (fullFactor false 9 19 ((j.val:ℝ)/6)) := by + rw [ha9_0_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_18 j) false 9 18 j (ha9_0_18_contains j) +noncomputable def hk9_0_20 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_20 j i k) +lemma hk9_0_20_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_20 j i k).Contains (fullFactor false 9 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 20 (power9_contains j i k) (mpower0_20_contains j i k) +noncomputable def ha9_0_20 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-985934),(-985933)⟩⟩,⟨⟨(-1033826696147),(-1033826696146)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨3437739179098606,3437739179098608⟩⟩,⟨⟨1084045861738968866,1084045861738968868⟩,⟨(-1),1⟩⟩,⟨⟨(-16),19⟩,⟨(-94025990269704865235),(-94025990269704865194)⟩⟩,⟨⟨(-3604730797462500934241),(-3604730797462500933586)⟩,⟨(-290),137⟩⟩] +lemma ha9_0_20_eq (j : Fin 7) : ha9_0_20 j = ((ha9_0_19 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha9_0_20_contains (j : Fin 7) : (ha9_0_20 j).Contains (fullFactor false 9 20 ((j.val:ℝ)/6)) := by + rw [ha9_0_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_19 j) false 9 19 j (ha9_0_19_contains j) +noncomputable def hk9_0_21 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_21 j i k) +lemma hk9_0_21_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_21 j i k).Contains (fullFactor false 9 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 21 (power9_contains j i k) (mpower0_21_contains j i k) +noncomputable def ha9_0_21 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨24582,24583⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-51553370694),(-51553370693)⟩⟩,⟨⟨(-257142289286048),(-257142289286047)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨108115254456938454,108115254456938455⟩⟩,⟨⟨11721879376103578820,11721879376103578826⟩,⟨(-2),3⟩⟩,⟨⟨(-21),44⟩,⟨(-539266466260812848994),(-539266466260812848893)⟩⟩] +lemma ha9_0_21_eq (j : Fin 7) : ha9_0_21 j = ((ha9_0_20 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha9_0_21_contains (j : Fin 7) : (ha9_0_21 j).Contains (fullFactor false 9 21 ((j.val:ℝ)/6)) := by + rw [ha9_0_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_20 j) false 9 20 j (ha9_0_20_contains j) +noncomputable def hk9_0_22 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_22 j i k) +lemma hk9_0_22_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_22 j i k).Contains (fullFactor false 9 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 22 (power9_contains j i k) (mpower0_22_contains j i k) +noncomputable def ha9_0_22 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨585,586⟩⟩,⟨⟨2453934706,2453934707⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-18359916521553),(-18359916521552)⟩⟩,⟨⟨(-10292548155845728),(-10292548155845727)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1394900383872451219,1394900383872451220⟩⟩,⟨⟨77007071306013533791,77007071306013533807⟩,⟨(-3),7⟩⟩] +lemma ha9_0_22_eq (j : Fin 7) : ha9_0_22 j = ((ha9_0_21 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha9_0_22_contains (j : Fin 7) : (ha9_0_22 j).Contains (fullFactor false 9 22 ((j.val:ℝ)/6)) := by + rw [ha9_0_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_21 j) false 9 21 j (ha9_0_21_contains j) +noncomputable def hk9_0_23 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_23 j i k) +lemma hk9_0_23_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_23 j i k).Contains (fullFactor false 9 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 23 (power9_contains j i k) (mpower0_23_contains j i k) +noncomputable def ha9_0_23 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-14),(-13)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨111728452,111728453⟩⟩,⟨⟨1253899540535,1253899540536⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-937246193423888),(-937246193423887)⟩⟩,⟨⟨(-158775681103741858),(-158775681103741857)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨10518471716932064454,10518471716932064457⟩⟩] +lemma ha9_0_23_eq (j : Fin 7) : ha9_0_23 j = ((ha9_0_22 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha9_0_23_contains (j : Fin 7) : (ha9_0_23 j).Contains (fullFactor false 9 23 ((j.val:ℝ)/6)) := by + rw [ha9_0_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_22 j) false 9 22 j (ha9_0_22_contains j) +noncomputable def hk9_0_24 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_24 j i k) +lemma hk9_0_24_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_24 j i k).Contains (fullFactor false 9 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 24 (power9_contains j i k) (mpower0_24_contains j i k) +noncomputable def ha9_0_24 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-4875074),(-4875073)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨82067533018,82067533019⟩⟩,⟨⟨81790159885152,81790159885153⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-17319740045980250),(-17319740045980249)⟩⟩,⟨⟨(-1376864728037741371),(-1376864728037741370)⟩,⟨(-1),1⟩⟩] +lemma ha9_0_24_eq (j : Fin 7) : ha9_0_24 j = ((ha9_0_23 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha9_0_24_contains (j : Fin 7) : (ha9_0_24 j).Contains (fullFactor false 9 24 ((j.val:ℝ)/6)) := by + rw [ha9_0_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_23 j) false 9 23 j (ha9_0_23_contains j) +noncomputable def hk9_0_25 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_25 j i k) +lemma hk9_0_25_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_25 j i k).Contains (fullFactor false 9 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 25 (power9_contains j i k) (mpower0_25_contains j i k) +noncomputable def ha9_0_25 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-204207),(-204206)⟩⟩,⟨⟨(-5156455177),(-5156455176)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨6852036411496,6852036411497⟩⟩,⟨⟨1813718936351216,1813718936351217⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-173021924583611077),(-173021924583611076)⟩⟩] +lemma ha9_0_25_eq (j : Fin 7) : ha9_0_25 j = ((ha9_0_24 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha9_0_25_contains (j : Fin 7) : (ha9_0_25 j).Contains (fullFactor false 9 25 ((j.val:ℝ)/6)) := by + rw [ha9_0_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_24 j) false 9 24 j (ha9_0_24_contains j) +noncomputable def hk9_0_26 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_26 j i k) +lemma hk9_0_26_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_26 j i k).Contains (fullFactor false 9 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 26 (power9_contains j i k) (mpower0_26_contains j i k) +noncomputable def ha9_0_26 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨8224,8225⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-311528495),(-311528494)⟩⟩,⟨⟨(-551956596218),(-551956596217)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨182627118144797,182627118144798⟩⟩,⟨⟨20906323353147684,20906323353147685⟩,⟨(-1),1⟩⟩] +lemma ha9_0_26_eq (j : Fin 7) : ha9_0_26 j = ((ha9_0_25 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha9_0_26_contains (j : Fin 7) : (ha9_0_26 j).Contains (fullFactor false 9 26 ((j.val:ℝ)/6)) := by + rw [ha9_0_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_25 j) false 9 25 j (ha9_0_25_contains j) +noncomputable def hk9_0_27 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_27 j i k) +lemma hk9_0_27_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_27 j i k).Contains (fullFactor false 9 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 27 (power9_contains j i k) (mpower0_27_contains j i k) +noncomputable def ha9_0_27 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨318,320⟩⟩,⟨⟨18123993,18123994⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-42815377477),(-42815377475)⟩⟩,⟨⟨(-17708025083642),(-17708025083641)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨2432561179993388,2432561179993389⟩⟩] +lemma ha9_0_27_eq (j : Fin 7) : ha9_0_27 j = ((ha9_0_26 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha9_0_27_contains (j : Fin 7) : (ha9_0_27 j).Contains (fullFactor false 9 27 ((j.val:ℝ)/6)) := by + rw [ha9_0_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_26 j) false 9 26 j (ha9_0_26_contains j) +noncomputable def hk9_0_28 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_28 j i k) +lemma hk9_0_28_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_28 j i k).Contains (fullFactor false 9 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 28 (power9_contains j i k) (mpower0_28_contains j i k) +noncomputable def ha9_0_28 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-12),(-11)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨1016753,1016754⟩⟩,⟨⟨3202582746,3202582747⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1655696473582),(-1655696473581)⟩⟩,⟨⟨(-272932726159820),(-272932726159819)⟩,⟨(-1),1⟩⟩] +lemma ha9_0_28_eq (j : Fin 7) : ha9_0_28 j = ((ha9_0_27 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha9_0_28_contains (j : Fin 7) : (ha9_0_28 j).Contains (fullFactor false 9 28 ((j.val:ℝ)/6)) := by + rw [ha9_0_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_27 j) false 9 27 j (ha9_0_27_contains j) +noncomputable def hk9_0_29 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_29 j i k) +lemma hk9_0_29_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_29 j i k).Contains (fullFactor false 9 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 29 (power9_contains j i k) (mpower0_29_contains j i k) +noncomputable def ha9_0_29 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),0⟩⟩,⟨⟨(-55073),(-55072)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨231292193,231292194⟩⟩,⟨⟨149469076953,149469076954⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-29567015428550),(-29567015428549)⟩⟩] +lemma ha9_0_29_eq (j : Fin 7) : ha9_0_29 j = ((ha9_0_28 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha9_0_29_contains (j : Fin 7) : (ha9_0_29 j).Contains (fullFactor false 9 29 ((j.val:ℝ)/6)) := by + rw [ha9_0_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_28 j) false 9 28 j (ha9_0_28_contains j) +noncomputable def hk9_0_30 (j : Fin 6) (i k : Fin 16) : CBox := (power9 j i k).conj.mul (mpower0_30 j i k) +lemma hk9_0_30_contains (j : Fin 6) (i k : Fin 16) : + (hk9_0_30 j i k).Contains (fullFactor false 9 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_0_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_direct_full (power9 j i k) (mpower0_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 30 (power9_contains j i k) (mpower0_30_contains j i k) +noncomputable def ha9_0_30 : Fin 7 → CBox := ![⟨⟨0,0⟩,⟨0,0⟩⟩,⟨⟨(-1),1⟩,⟨0,1⟩⟩,⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-2884),(-2883)⟩⟩,⟨⟨(-16147242),(-16147241)⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨13043637613,13043637614⟩⟩,⟨⟨3096250615296,3096250615297⟩,⟨(-1),1⟩⟩] +lemma ha9_0_30_eq (j : Fin 7) : ha9_0_30 j = ((ha9_0_29 j).mul (piI.mul (rcast (atomPoints j).t))).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha9_0_30_contains (j : Fin 7) : (ha9_0_30 j).Contains (fullFactor false 9 30 ((j.val:ℝ)/6)) := by + rw [ha9_0_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_0_29 j) false 9 29 j (ha9_0_29_contains j) +noncomputable def hk9_1_0 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_0 j i k) +lemma hk9_1_0_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_0 j i k).Contains (fullFactor true 9 0 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_0,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_0 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 0 (kernel9_0_contains j i k) (mpower1_0_contains j i k) +noncomputable def ha9_1_0 : Fin 7 → CBox := ![⟨⟨0,3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-13055430470),(-13055430466)⟩,⟨(-125645570149),(-125645570145)⟩⟩,⟨⟨7154252614161620552,7154252614161620589⟩,⟨(-13924345974453591569),(-13924345974453591532)⟩⟩,⟨⟨(-1698695877854235861304740),(-1698695877854235858983332)⟩,⟨(-509093624274864032090577),(-509093624274864029767916)⟩⟩,⟨⟨(-1026692507277594175516071066),(-1026692507277594173128666505)⟩,⟨1953323598494588998753708432,1953323598494589001134169251⟩⟩,⟨⟨196702530130659703536642999895,196702530130659703684165160486⟩,⟨21124309294066164671702566946,21124309294066164817617441453⟩⟩] +lemma ha9_1_0_eq (j : Fin 7) : ha9_1_0 j = atomKernel9_0 j := by fin_cases j <;> decide +kernel +lemma ha9_1_0_contains (j : Fin 7) : (ha9_1_0 j).Contains (fullFactor true 9 0 ((j.val:ℝ)/6)) := by + rw [ha9_1_0_eq] + simpa only [fullFactor,ite_true] using atomKernel9_0_contains j +noncomputable def hk9_1_1 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_1 j i k) +lemma hk9_1_1_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_1 j i k).Contains (fullFactor true 9 1 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_1,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_1 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 1 (kernel9_0_contains j i k) (mpower1_1_contains j i k) +noncomputable def ha9_1_1 : Fin 7 → CBox := ![⟨⟨(-28),0⟩,⟨(-28),28⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-582814768607),(-582814768566)⟩,⟨685859094687,685859094729⟩⟩,⟨⟨(-91375913998733273822),(-91375913998733273527)⟩,⟨2859794631161188478,2859794631161188773⟩⟩,⟨⟨222122721895776563286434,222122721895776577550545⟩,⟨8619414914226240484798227,8619414914226240499070203⟩⟩,⟨⟨8703009863156394059139731164,8703009863156394070573781917⟩,⟨2818607183340039793692065116,2818607183340039805139620169⟩⟩,⟨⟨39344937084074217692613206192,39344937084074218247576725826⟩,⟨(-714264540569317372231588285146),(-714264540569317371669209421945)⟩⟩] +lemma ha9_1_1_eq (j : Fin 7) : ha9_1_1 j = ((ha9_1_0 j).mul (piI.mul (atomPoints j).z)).scale 1 1 := by fin_cases j <;> decide +kernel +lemma ha9_1_1_contains (j : Fin 7) : (ha9_1_1 j).Contains (fullFactor true 9 1 ((j.val:ℝ)/6)) := by + rw [ha9_1_1_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_0 j) true 9 0 j (ha9_1_0_contains j) +noncomputable def hk9_1_2 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_2 j i k) +lemma hk9_1_2_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_2 j i k).Contains (fullFactor true 9 2 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_2,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_2 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 2 (kernel9_0_contains j i k) (mpower1_2_contains j i k) +noncomputable def ha9_1_2 : Fin 7 → CBox := ![⟨⟨0,130⟩,⟨(-130),130⟩⟩,⟨⟨(-104),197⟩,⟨(-204),89⟩⟩,⟨⟨3200896687215,3200896687425⟩,⟨(-187636838327),(-187636838117)⟩⟩,⟨⟨136600665429248516037,136600665429248517209⟩,⟨229340319107349378769,229340319107349379942⟩⟩,⟨⟨19742504341373547697917781,19742504341373547741757490⟩,⟨(-7043845308215801203413309),(-7043845308215801159627302)⟩⟩,⟨⟨2692635538075423827809461096,2692635538075423855247398484⟩,⟨(-18769765476717899865438273884),(-18769765476717899837991501398)⟩⟩,⟨⟨(-1293307892625183252853903107632),(-1293307892625183251782300340739)⟩,⟨(-3977871933288998970321567459),(-3977871933288997915088246138)⟩⟩] +lemma ha9_1_2_eq (j : Fin 7) : ha9_1_2 j = ((ha9_1_1 j).mul (piI.mul (atomPoints j).z)).scale 1 2 := by fin_cases j <;> decide +kernel +lemma ha9_1_2_contains (j : Fin 7) : (ha9_1_2 j).Contains (fullFactor true 9 2 ((j.val:ℝ)/6)) := by + rw [ha9_1_2_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_1 j) true 9 1 j (ha9_1_1_contains j) +noncomputable def hk9_1_3 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_3 j i k) +lemma hk9_1_3_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_3 j i k).Contains (fullFactor true 9 3 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_3,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_3 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 3 (kernel9_0_contains j i k) (mpower1_3_contains j i k) +noncomputable def ha9_1_3 : Fin 7 → CBox := ![⟨⟨(-400),0⟩,⟨(-400),400⟩⟩,⟨⟨(-757),377⟩,⟨(-472),651⟩⟩,⟨⟨(-5575372588060),(-5575372587353)⟩,⟨(-5187088557639),(-5187088556933)⟩⟩,⟨⟨261652184958392015520,261652184958392018625⟩,⟨(-448941596942274237145),(-448941596942274234040)⟩⟩,⟨⟨(-20819806881801901813070960),(-20819806881801901723430132)⟩,⟨(-26845406767390610548821365),(-26845406767390610459083132)⟩⟩,⟨⟨(-26192161772521422379129645263),(-26192161772521422335228650217)⟩,⟨739809024142488190247004911,739809024142488234080368651⟩⟩,⟨⟨76161520544486145692686058175,76161520544486147030190118206⟩,⟨1556971804854247129341139471991,1556971804854247130702005531942⟩⟩] +lemma ha9_1_3_eq (j : Fin 7) : ha9_1_3 j = ((ha9_1_2 j).mul (piI.mul (atomPoints j).z)).scale 1 3 := by fin_cases j <;> decide +kernel +lemma ha9_1_3_contains (j : Fin 7) : (ha9_1_3 j).Contains (fullFactor true 9 3 ((j.val:ℝ)/6)) := by + rw [ha9_1_3_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_2 j) true 9 2 j (ha9_1_2_contains j) +noncomputable def hk9_1_4 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_4 j i k) +lemma hk9_1_4_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_4 j i k).Contains (fullFactor true 9 4 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_4,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_4 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 4 (kernel9_0_contains j i k) (mpower1_4_contains j i k) +noncomputable def ha9_1_4 : Fin 7 → CBox := ![⟨⟨0,922⟩,⟨(-922),922⟩⟩,⟨⟨(-1162),2056⟩,⟨(-1599),1609⟩⟩,⟨⟨184076260062,184076261842⟩,⟨13563220170516,13563220172296⟩⟩,⟨⟨(-758448033051428425526),(-758448033051428419361)⟩,⟨(-16523423985783738474),(-16523423985783732309)⟩⟩,⟨⟨(-23119015114920287065250108),(-23119015114920286927519436)⟩,⟨34216910834217679136948599,34216910834217679274588783⟩⟩,⟨⟨5367402585686739206551193708,5367402585686739259066268478⟩,⟨26620420876579341259374931442,26620420876579341312015651158⟩⟩,⟨⟨1401991156137427327394072183985,1401991156137427328689875221580⟩,⟨(-141844762929760366431298371768),(-141844762929760365159522772874)⟩⟩] +lemma ha9_1_4_eq (j : Fin 7) : ha9_1_4 j = ((ha9_1_3 j).mul (piI.mul (atomPoints j).z)).scale 1 4 := by fin_cases j <;> decide +kernel +lemma ha9_1_4_contains (j : Fin 7) : (ha9_1_4 j).Contains (fullFactor true 9 4 ((j.val:ℝ)/6)) := by + rw [ha9_1_4_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_3 j) true 9 3 j (ha9_1_3_contains j) +noncomputable def hk9_1_5 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_5 j i k) +lemma hk9_1_5_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_5 j i k).Contains (fullFactor true 9 5 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_5,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_5 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 5 (kernel9_0_contains j i k) (mpower1_5_contains j i k) +noncomputable def ha9_1_5 : Fin 7 → CBox := ![⟨⟨(-1700),0⟩,⟨(-1700),1700⟩⟩,⟨⟨(-4342),2979⟩,⟨(-3996),3316⟩⟩,⟨⟨13789267242824,13789267246411⟩,⟨(-13545429678265),(-13545429674678)⟩⟩,⟨⟨412398437232314253707,412398437232314263497⟩,⟨784225312294913144630,784225312294913154421⟩⟩,⟨⟨38623061442207697722712866,38623061442207697891757253⟩,⟨10991756662329869415200333,10991756662329869584278972⟩⟩,⟨⟨20994402254565462265129639042,20994402254565462315609190594⟩,⟨(-8135265006310953622437971642),(-8135265006310953572089126095)⟩⟩,⟨⟨(-155092342811337823484425252151),(-155092342811337822516785160812)⟩,⟨(-1007198380765596727908354253728),(-1007198380765596726921517513511)⟩⟩] +lemma ha9_1_5_eq (j : Fin 7) : ha9_1_5 j = ((ha9_1_4 j).mul (piI.mul (atomPoints j).z)).scale 1 5 := by fin_cases j <;> decide +kernel +lemma ha9_1_5_contains (j : Fin 7) : (ha9_1_5 j).Contains (fullFactor true 9 5 ((j.val:ℝ)/6)) := by + rw [ha9_1_5_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_4 j) true 9 4 j (ha9_1_4_contains j) +noncomputable def hk9_1_6 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_6 j i k) +lemma hk9_1_6_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_6 j i k).Contains (fullFactor true 9 6 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_6,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_6 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 6 (kernel9_0_contains j i k) (mpower1_6_contains j i k) +noncomputable def ha9_1_6 : Fin 7 → CBox := ![⟨⟨0,2612⟩,⟨(-2612),2612⟩⟩,⟨⟨(-6283),7603⟩,⟨(-6083),7797⟩⟩,⟨⟨(-22942183490918),(-22942183484895)⟩,⟨(-720880903737),(-720880897714)⟩⟩,⟨⟨473160103751570248353,473160103751570261310⟩,⟨(-720999141085659263772),(-720999141085659250816)⟩⟩,⟨⟨(-1290984748966059446520855),(-1290984748966059273578866)⟩,⟨(-32515759337148378579861221),(-32515759337148378406891445)⟩⟩,⟨⟨(-8003571526609040643382188445),(-8003571526609040603149555338)⟩,⟨(-13339773373207868626948550359),(-13339773373207868586619199547)⟩⟩,⟨⟨(-601316228266459635783903018074),(-601316228266459635157759704412)⟩,⟨124861251064675641912314993814,124861251064675642525958307922⟩⟩] +lemma ha9_1_6_eq (j : Fin 7) : ha9_1_6 j = ((ha9_1_5 j).mul (piI.mul (atomPoints j).z)).scale 1 6 := by fin_cases j <;> decide +kernel +lemma ha9_1_6_contains (j : Fin 7) : (ha9_1_6 j).Contains (fullFactor true 9 6 ((j.val:ℝ)/6)) := by + rw [ha9_1_6_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_5 j) true 9 5 j (ha9_1_5_contains j) +noncomputable def hk9_1_7 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_7 j i k) +lemma hk9_1_7_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_7 j i k).Contains (fullFactor true 9 7 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_7,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_7 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 7 (kernel9_0_contains j i k) (mpower1_7_contains j i k) +noncomputable def ha9_1_7 : Fin 7 → CBox := ![⟨⟨(-3439),0⟩,⟨(-3439),3439⟩⟩,⟨⟨(-11558),11023⟩,⟨(-12578),9999⟩⟩,⟨⟨15606318772377,15606318781045⟩,⟨17386431335831,17386431344500⟩⟩,⟨⟨(-717443316691677932663),(-717443316691677917966)⟩,⟨(-53802295195031030846),(-53802295195031016149)⟩⟩,⟨⟨(-21180879253952447470729166),(-21180879253952447319061786)⟩,⟨7891043062932220669019994,7891043062932220820630968⟩⟩,⟨⟨(-6979995367902027654093779187),(-6979995367902027626481665566)⟩,⟨6013175518710165388231369096,6013175518710165415788564138⟩⟩,⟨⟨80541199115523784843004293450,80541199115523785176611380588⟩,⟨306846134544329448742833908633,306846134544329449083295620533⟩⟩] +lemma ha9_1_7_eq (j : Fin 7) : ha9_1_7 j = ((ha9_1_6 j).mul (piI.mul (atomPoints j).z)).scale 1 7 := by fin_cases j <;> decide +kernel +lemma ha9_1_7_contains (j : Fin 7) : (ha9_1_7 j).Contains (fullFactor true 9 7 ((j.val:ℝ)/6)) := by + rw [ha9_1_7_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_6 j) true 9 6 j (ha9_1_6_contains j) +noncomputable def hk9_1_8 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_8 j i k) +lemma hk9_1_8_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_8 j i k).Contains (fullFactor true 9 8 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_8,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_8 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 8 (kernel9_0_contains j i k) (mpower1_8_contains j i k) +noncomputable def ha9_1_8 : Fin 7 → CBox := ![⟨⟨0,3962⟩,⟨(-3962),3962⟩⟩,⟨⟨(-16409),15723⟩,⟨(-14705),17425⟩⟩,⟨⟨1588043272067,1588043282984⟩,⟨(-20747224114107),(-20747224103190)⟩⟩,⟨⟨219439801316764780804,219439801316764795389⟩,⟨477145212418502667840,477145212418502682426⟩⟩,⟨⟨8569139478751380660132246,8569139478751380776443424⟩,⟨10737211283906283018943551,10737211283906283135293036⟩⟩,⟨⟨3685206002668269754258482632,3685206002668269770773544313⟩,⟨3035029702336479121085337762,3035029702336479137624909964⟩⟩,⟨⟨136613236324045010921023264668,136613236324045011082977481560⟩,⟨(-43556736879327671197978959789),(-43556736879327671039266124903)⟩⟩] +lemma ha9_1_8_eq (j : Fin 7) : ha9_1_8 j = ((ha9_1_7 j).mul (piI.mul (atomPoints j).z)).scale 1 8 := by fin_cases j <;> decide +kernel +lemma ha9_1_8_contains (j : Fin 7) : (ha9_1_8 j).Contains (fullFactor true 9 8 ((j.val:ℝ)/6)) := by + rw [ha9_1_8_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_7 j) true 9 7 j (ha9_1_7_contains j) +noncomputable def hk9_1_9 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_9 j i k) +lemma hk9_1_9_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_9 j i k).Contains (fullFactor true 9 9 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_9,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_9 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 9 (kernel9_0_contains j i k) (mpower1_9_contains j i k) +noncomputable def ha9_1_9 : Fin 7 → CBox := ![⟨⟨(-4057),0⟩,⟨(-4057),4057⟩⟩,⟨⟨(-19468),21176⟩,⟨(-21338),19305⟩⟩,⟨⟨(-12741128711433),(-12741128699212)⟩,⟨10441247965985,10441247978205⟩⟩,⟨⟨201819977400460323257,201819977400460336124⟩,⟨(-274586123399150917843),(-274586123399150904976)⟩⟩,⟨⟨4068944366274353442639076,4068944366274353521970798⟩,⟨(-6206670473105841624991819),(-6206670473105841545675692)⟩⟩,⟨⟨1089276185492577064284691213,1089276185492577073090071093⟩,⟨(-1910304910064375132865419100),(-1910304910064375124068469512)⟩⟩,⟨⟨(-20326315179388789957487019056),(-20326315179388789890363777725)⟩,⟨(-53903906556811653497127513785),(-53903906556811653428658709719)⟩⟩] +lemma ha9_1_9_eq (j : Fin 7) : ha9_1_9 j = ((ha9_1_8 j).mul (piI.mul (atomPoints j).z)).scale 1 9 := by fin_cases j <;> decide +kernel +lemma ha9_1_9_contains (j : Fin 7) : (ha9_1_9 j).Contains (fullFactor true 9 9 ((j.val:ℝ)/6)) := by + rw [ha9_1_9_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_8 j) true 9 8 j (ha9_1_8_contains j) +noncomputable def hk9_1_10 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_10 j i k) +lemma hk9_1_10_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_10 j i k).Contains (fullFactor true 9 10 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_10,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_10 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 10 (kernel9_0_contains j i k) (mpower1_10_contains j i k) +noncomputable def ha9_1_10 : Fin 7 → CBox := ![⟨⟨0,3739⟩,⟨(-3739),3739⟩⟩,⟨⟨(-24168),22102⟩,⟨(-22673),23597⟩⟩,⟨⟨11650553610829,11650553623140⟩,⟨1421079161758,1421079174069⟩⟩,⟨⟨(-197381102402241965027),(-197381102402241954811)⟩,⟨(-25387779826030942692),(-25387779826030932476)⟩⟩,⟨⟨(-3484065164802736851200611),(-3484065164802736802523971)⟩,⟨(-939316083876580953270226),(-939316083876580904590857)⟩⟩,⟨⟨(-857134378553481601465987409),(-857134378553481597249277394)⟩,⟨(-310457831497308956811382772),(-310457831497308952592706077)⟩⟩,⟨⟨(-19083166978354024617262689172),(-19083166978354024591214856705)⟩,⟨8352057071003376070862087225,8352057071003376096412711572⟩⟩] +lemma ha9_1_10_eq (j : Fin 7) : ha9_1_10 j = ((ha9_1_9 j).mul (piI.mul (atomPoints j).z)).scale 1 10 := by fin_cases j <;> decide +kernel +lemma ha9_1_10_contains (j : Fin 7) : (ha9_1_10 j).Contains (fullFactor true 9 10 ((j.val:ℝ)/6)) := by + rw [ha9_1_10_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_9 j) true 9 9 j (ha9_1_9_contains j) +noncomputable def hk9_1_11 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_11 j i k) +lemma hk9_1_11_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_11 j i k).Contains (fullFactor true 9 11 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_11,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_11 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 11 (kernel9_0_contains j i k) (mpower1_11_contains j i k) +noncomputable def ha9_1_11 : Fin 7 → CBox := ![⟨⟨(-3133),0⟩,⟨(-3133),3133⟩⟩,⟨⟨(-23067),24819⟩,⟨(-23916),23970⟩⟩,⟨⟨(-4549386720770),(-4549386709495)⟩,⟨(-6090806212046),(-6090806200771)⟩⟩,⟨⟨38990741047750080122,38990741047750087495⟩,⟨98193198513013353492,98193198513013360866⟩⟩,⟨⟨85451862051436260983608,85451862051436288137358⟩,⟨1592703828497615188189894,1592703828497615215345160⟩⟩,⟨⟨(-60420735354598515653430023),(-60420735354598513816125291)⟩,⟨338209517787106953603163469,338209517787106955440398566⟩⟩,⟨⟨3067527802541374910162699502,3067527802541374919004741810⟩,⟨6121956280806660201934519275,6121956280806660210941925321⟩⟩] +lemma ha9_1_11_eq (j : Fin 7) : ha9_1_11 j = ((ha9_1_10 j).mul (piI.mul (atomPoints j).z)).scale 1 11 := by fin_cases j <;> decide +kernel +lemma ha9_1_11_contains (j : Fin 7) : (ha9_1_11 j).Contains (fullFactor true 9 11 ((j.val:ℝ)/6)) := by + rw [ha9_1_11_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_10 j) true 9 10 j (ha9_1_10_contains j) +noncomputable def hk9_1_12 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_12 j i k) +lemma hk9_1_12_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_12 j i k).Contains (fullFactor true 9 12 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_12,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_12 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 12 (kernel9_0_contains j i k) (mpower1_12_contains j i k) +noncomputable def ha9_1_12 : Fin 7 → CBox := ![⟨⟨0,2406⟩,⟨(-2406),2406⟩⟩,⟨⟨(-23266),22163⟩,⟨(-23003),22426⟩⟩,⟨⟨(-747455499914),(-747455490448)⟩,⟨4451532687297,4451532696763⟩⟩,⟨⟨32604592802159065881,32604592802159070760⟩,⟨(-39755098218494496150),(-39755098218494491272)⟩⟩,⟨⟨602398704161514650572172,602398704161514664457879⟩,⟨(-234025059100093498634412),(-234025059100093484750338)⟩⟩,⟨⟨118686719286903063799932204,118686719286903064533616017⟩,⟨719493652991894027564389,719493652991894761018691⟩⟩,⟨⟨1794211962768628630960705577,1794211962768628633815578786⟩,⟨(-1018871919422432028502543557),(-1018871919422432025697617398)⟩⟩] +lemma ha9_1_12_eq (j : Fin 7) : ha9_1_12 j = ((ha9_1_11 j).mul (piI.mul (atomPoints j).z)).scale 1 12 := by fin_cases j <;> decide +kernel +lemma ha9_1_12_contains (j : Fin 7) : (ha9_1_12 j).Contains (fullFactor true 9 12 ((j.val:ℝ)/6)) := by + rw [ha9_1_12_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_11 j) true 9 11 j (ha9_1_11_contains j) +noncomputable def hk9_1_13 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_13 j i k) +lemma hk9_1_13_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_13 j i k).Contains (fullFactor true 9 13 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_13,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_13 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 13 (kernel9_0_contains j i k) (mpower1_13_contains j i k) +noncomputable def ha9_1_13 : Fin 7 → CBox := ![⟨⟨(-1706),0⟩,⟨(-1706),1706⟩⟩,⟨⟨(-19649),20134⟩,⟨(-19564),20219⟩⟩,⟨⟨2046630798926,2046630806262⟩,⟨(-1389831782261),(-1389831774925)⟩⟩,⟨⟨(-22719291804146023451),(-22719291804146020471)⟩,⟨(-4157460093088943326),(-4157460093088940346)⟩⟩,⟨⟨(-153387846957154043747500),(-153387846957154037194236)⟩,⟨(-186803393916120003268136),(-186803393916119996714203)⟩⟩,⟨⟨(-6204023819422090639649442),(-6204023819422090369388626)⟩,⟨(-37336702086668004986989748),(-37336702086668004716571583)⟩⟩,⟨⟨(-308929094545510194049580369),(-308929094545510193228233130)⟩,⟨(-483663778363617350949786048),(-483663778363617350114636509)⟩⟩] +lemma ha9_1_13_eq (j : Fin 7) : ha9_1_13 j = ((ha9_1_12 j).mul (piI.mul (atomPoints j).z)).scale 1 13 := by fin_cases j <;> decide +kernel +lemma ha9_1_13_contains (j : Fin 7) : (ha9_1_13 j).Contains (fullFactor true 9 13 ((j.val:ℝ)/6)) := by + rw [ha9_1_13_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_12 j) true 9 12 j (ha9_1_12_contains j) +noncomputable def hk9_1_14 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_14 j i k) +lemma hk9_1_14_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_14 j i k).Contains (fullFactor true 9 14 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_14,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_14 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 14 (kernel9_0_contains j i k) (mpower1_14_contains j i k) +noncomputable def ha9_1_14 : Fin 7 → CBox := ![⟨⟨0,1123⟩,⟨(-1123),1123⟩⟩,⟨⟨(-16221),16129⟩,⟨(-16419),15932⟩⟩,⟨⟨(-1231037434309),(-1231037429029)⟩,⟨(-264111424434),(-264111419154)⟩⟩,⟨⟨3075559939550879804,3075559939550881495⟩,⟨9130148636275798543,9130148636275800233⟩⟩,⟨⟨(-45042314109153599574023),(-45042314109153596701656)⟩,⟨70837423204632157736946,70837423204632160609140⟩⟩,⟨⟨(-10582996849900898767988285),(-10582996849900898675446588)⟩,⟨3688692948426796946839275,3688692948426797039319040⟩⟩,⟨⟨(-120608131812118024714845629),(-120608131812118024488008638)⟩,⟨86169298168791612940068772,86169298168791613163394851⟩⟩] +lemma ha9_1_14_eq (j : Fin 7) : ha9_1_14 j = ((ha9_1_13 j).mul (piI.mul (atomPoints j).z)).scale 1 14 := by fin_cases j <;> decide +kernel +lemma ha9_1_14_contains (j : Fin 7) : (ha9_1_14 j).Contains (fullFactor true 9 14 ((j.val:ℝ)/6)) := by + rw [ha9_1_14_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_13 j) true 9 13 j (ha9_1_13_contains j) +noncomputable def hk9_1_15 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_15 j i k) +lemma hk9_1_15_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_15 j i k).Contains (fullFactor true 9 15 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_15,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_15 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 15 (kernel9_0_contains j i k) (mpower1_15_contains j i k) +noncomputable def ha9_1_15 : Fin 7 → CBox := ![⟨⟨(-690),0⟩,⟨(-690),690⟩⟩,⟨⟨(-12313),12240⟩,⟨(-12141),12412⟩⟩,⟨⟨313390298829,313390302376⟩,⟨509359617019,509359620566⟩⟩,⟨⟨2529037742481016868,2529037742481017763⟩,⟨(-2769935358086130445),(-2769935358086129549)⟩⟩,⟨⟨26368219427222726310275,26368219427222727485171⟩,⟨6716737197141222463958,6716737197141223638872⟩⟩,⟨⟨1501537378511149489572723,1501537378511149519109823⟩,⟨2709114005498712393800046,2709114005498712423356052⟩⟩,⟨⟨22253771523141716820394925,22253771523141716877067778⟩,⟨27955920420793263346723384,27955920420793263404222503⟩⟩] +lemma ha9_1_15_eq (j : Fin 7) : ha9_1_15 j = ((ha9_1_14 j).mul (piI.mul (atomPoints j).z)).scale 1 15 := by fin_cases j <;> decide +kernel +lemma ha9_1_15_contains (j : Fin 7) : (ha9_1_15 j).Contains (fullFactor true 9 15 ((j.val:ℝ)/6)) := by + rw [ha9_1_15_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_14 j) true 9 14 j (ha9_1_14_contains j) +noncomputable def hk9_1_16 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_16 j i k) +lemma hk9_1_16_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_16 j i k).Contains (fullFactor true 9 16 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_16,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_16 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 16 (kernel9_0_contains j i k) (mpower1_16_contains j i k) +noncomputable def ha9_1_16 : Fin 7 → CBox := ![⟨⟨0,398⟩,⟨(-398),398⟩⟩,⟨⟨(-8686),8784⟩,⟨(-8792),8679⟩⟩,⟨⟨67518004586,67518006820⟩,⟨(-257616423587),(-257616421353)⟩⟩,⟨⟨(-1331672044033337788),(-1331672044033337343)⟩,⟨(-317509516626733124),(-317509516626732678)⟩⟩,⟨⟨(-557874891723565905934),(-557874891723565455389)⟩,⟨(-8249946247588780988706),(-8249946247588780538152)⟩⟩,⟨⟨625624523466886805121462,625624523466886813970635⟩,⟨(-502641709001863480346008),(-502641709001863471501642)⟩⟩,⟨⟨6048180703408985188146730,6048180703408985201809675⟩,⟨(-5350520335568938295105665),(-5350520335568938281623386)⟩⟩] +lemma ha9_1_16_eq (j : Fin 7) : ha9_1_16 j = ((ha9_1_15 j).mul (piI.mul (atomPoints j).z)).scale 1 16 := by fin_cases j <;> decide +kernel +lemma ha9_1_16_contains (j : Fin 7) : (ha9_1_16 j).Contains (fullFactor true 9 16 ((j.val:ℝ)/6)) := by + rw [ha9_1_16_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_15 j) true 9 15 j (ha9_1_15_contains j) +noncomputable def hk9_1_17 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_17 j i k) +lemma hk9_1_17_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_17 j i k).Contains (fullFactor true 9 17 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_17,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_17 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 17 (kernel9_0_contains j i k) (mpower1_17_contains j i k) +noncomputable def ha9_1_17 : Fin 7 → CBox := ![⟨⟨(-216),0⟩,⟨(-216),216⟩⟩,⟨⟨(-5884),5816⟩,⟨(-5835),5865⟩⟩,⟨⟨(-97599510003),(-97599508679)⟩,⟨54156359195,54156360520⟩⟩,⟨⟨126275737001629171,126275737001629380⟩,⟨453006036678069645,453006036678069854⟩⟩,⟨⟨(-2192310777420104042514),(-2192310777420103879900)⟩,⟨886999134369535428190,886999134369535590798⟩⟩,⟨⟨(-146710040336986518917721),(-146710040336986516425231)⟩,⟨(-129520488224759660731943),(-129520488224759658238420)⟩⟩,⟨⟨(-1203326789892336651361098),(-1203326789892336648342537)⟩,⟨(-1225614873948593314041712),(-1225614873948593310986324)⟩⟩] +lemma ha9_1_17_eq (j : Fin 7) : ha9_1_17 j = ((ha9_1_16 j).mul (piI.mul (atomPoints j).z)).scale 1 17 := by fin_cases j <;> decide +kernel +lemma ha9_1_17_contains (j : Fin 7) : (ha9_1_17 j).Contains (fullFactor true 9 17 ((j.val:ℝ)/6)) := by + rw [ha9_1_17_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_16 j) true 9 16 j (ha9_1_16_contains j) +noncomputable def hk9_1_18 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_18 j i k) +lemma hk9_1_18_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_18 j i k).Contains (fullFactor true 9 18 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_18,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_18 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 18 (kernel9_0_contains j i k) (mpower1_18_contains j i k) +noncomputable def ha9_1_18 : Fin 7 → CBox := ![⟨⟨0,111⟩,⟨(-111),111⟩⟩,⟨⟨(-3683),3718⟩,⟨(-3700),3701⟩⟩,⟨⟨42191614943,42191615685⟩,⟨13111722493,13111723235⟩⟩,⟨⟨108706847237476293,108706847237476386⟩,⟨(-107058519395772653),(-107058519395772560)⟩⟩,⟨⟨412225483840756596673,412225483840756652101⟩,⟨488018457879595715723,488018457879595771153⟩⟩,⟨⟨(-23655606502979579157110),(-23655606502979578493539)⟩,⟨38365326602746403882665,38365326602746404546053⟩⟩,⟨⟨(-233320806434969121312476),(-233320806434969120667214)⟩,⟨254187899269998218566318,254187899269998219204562⟩⟩] +lemma ha9_1_18_eq (j : Fin 7) : ha9_1_18 j = ((ha9_1_17 j).mul (piI.mul (atomPoints j).z)).scale 1 18 := by fin_cases j <;> decide +kernel +lemma ha9_1_18_contains (j : Fin 7) : (ha9_1_18 j).Contains (fullFactor true 9 18 ((j.val:ℝ)/6)) := by + rw [ha9_1_18_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_17 j) true 9 17 j (ha9_1_17_contains j) +noncomputable def hk9_1_19 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_19 j i k) +lemma hk9_1_19_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_19 j i k).Contains (fullFactor true 9 19 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_19,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_19 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 19 (kernel9_0_contains j i k) (mpower1_19_contains j i k) +noncomputable def ha9_1_19 : Fin 7 → CBox := ![⟨⟨(-54),0⟩,⟨(-54),54⟩⟩,⟨⟨(-2225),2211⟩,⟨(-2221),2214⟩⟩,⟨⟨(-7379208676),(-7379208281)⟩,⟨(-14834178496),(-14834178101)⟩⟩,⟨⟨(-44974947072362385),(-44974947072362345)⟩,⟨(-13280569424316148),(-13280569424316108)⟩⟩,⟨⟨85787971296237366361,85787971296237384261⟩,⟨(-139157852781918556800),(-139157852781918538900)⟩⟩,⟨⟨9126025242066296846233,9126025242066297013500⟩,⟨3664171724245675069109,3664171724245675236400⟩⟩,⟨⟨50615292281439051339400,50615292281439051467240⟩,⟨41831462789043352062789,41831462789043352191882⟩⟩] +lemma ha9_1_19_eq (j : Fin 7) : ha9_1_19 j = ((ha9_1_18 j).mul (piI.mul (atomPoints j).z)).scale 1 19 := by fin_cases j <;> decide +kernel +lemma ha9_1_19_contains (j : Fin 7) : (ha9_1_19 j).Contains (fullFactor true 9 19 ((j.val:ℝ)/6)) := by + rw [ha9_1_19_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_18 j) true 9 18 j (ha9_1_18_contains j) +noncomputable def hk9_1_20 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_20 j i k) +lemma hk9_1_20_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_20 j i k).Contains (fullFactor true 9 20 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_20,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_20 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 20 (kernel9_0_contains j i k) (mpower1_20_contains j i k) +noncomputable def ha9_1_20 : Fin 7 → CBox := ![⟨⟨0,25⟩,⟨(-25),25⟩⟩,⟨⟨(-1261),1265⟩,⟨(-1260),1265⟩⟩,⟨⟨(-2003320344),(-2003320144)⟩,⟨5552039499,5552039699⟩⟩,⟨⟨2971883117017843,2971883117017860⟩,⟨13366425082267105,13366425082267122⟩⟩,⟨⟨(-38645356632142089350),(-38645356632142083858)⟩,⟨(-9273287494870418761),(-9273287494870413268)⟩⟩,⟨⟨427086034164069794590,427086034164069834656⟩,⟨(-1993160468520435060438),(-1993160468520435020373)⟩⟩,⟨⟨7077514908428655459334,7077514908428655483869⟩,⟨(-9531398622551247483121),(-9531398622551247458796)⟩⟩] +lemma ha9_1_20_eq (j : Fin 7) : ha9_1_20 j = ((ha9_1_19 j).mul (piI.mul (atomPoints j).z)).scale 1 20 := by fin_cases j <;> decide +kernel +lemma ha9_1_20_contains (j : Fin 7) : (ha9_1_20 j).Contains (fullFactor true 9 20 ((j.val:ℝ)/6)) := by + rw [ha9_1_20_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_19 j) true 9 19 j (ha9_1_19_contains j) +noncomputable def hk9_1_21 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_21 j i k) +lemma hk9_1_21_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_21 j i k).Contains (fullFactor true 9 21 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_21,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_21 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 21 (kernel9_0_contains j i k) (mpower1_21_contains j i k) +noncomputable def ha9_1_21 : Fin 7 → CBox := ![⟨⟨(-11),0⟩,⟨(-11),11⟩⟩,⟨⟨(-685),685⟩,⟨(-686),684⟩⟩,⟨⟨1831299239,1831299336⟩,⟨(-810395973),(-810395876)⟩⟩,⟨⟨2850907600950423,2850907600950430⟩,⟨(-2524191884079635),(-2524191884079628)⟩⟩,⟨⟨748523935329314346,748523935329315952⟩,⟨9171117438639129434,9171117438639131040⟩⟩,⟨⟨(-402069019581262721177),(-402069019581262712037)⟩,⟨(-16237139326884301157),(-16237139326884292017)⟩⟩,⟨⟨(-1702242729656619714741),(-1702242729656619710332)⟩,⟨(-1131778473106594025951),(-1131778473106594021509)⟩⟩] +lemma ha9_1_21_eq (j : Fin 7) : ha9_1_21 j = ((ha9_1_20 j).mul (piI.mul (atomPoints j).z)).scale 1 21 := by fin_cases j <;> decide +kernel +lemma ha9_1_21_contains (j : Fin 7) : (ha9_1_21 j).Contains (fullFactor true 9 21 ((j.val:ℝ)/6)) := by + rw [ha9_1_21_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_20 j) true 9 20 j (ha9_1_20_contains j) +noncomputable def hk9_1_22 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_22 j i k) +lemma hk9_1_22_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_22 j i k).Contains (fullFactor true 9 22 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_22,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_22 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 22 (kernel9_0_contains j i k) (mpower1_22_contains j i k) +noncomputable def ha9_1_22 : Fin 7 → CBox := ![⟨⟨0,5⟩,⟨(-5),5⟩⟩,⟨⟨(-355),355⟩,⟨(-355),355⟩⟩,⟨⟨(-599552156),(-599552111)⟩,⟨(-247338592),(-247338546)⟩⟩,⟨⟨(-952832442508607),(-952832442508603)⟩,⟨(-337263855941651),(-337263855941647)⟩⟩,⟨⟨1874371950351768224,1874371950351768673⟩,⟨(-788894750813525623),(-788894750813525174)⟩⟩,⟨⟨9856623398087553564,9856623398087555555⟩,⟨75182130541141739241,75182130541141741232⟩⟩,⟨⟨(-171238441347373238006),(-171238441347373237238)⟩,⟨289061848214170109875,289061848214170110638⟩⟩] +lemma ha9_1_22_eq (j : Fin 7) : ha9_1_22 j = ((ha9_1_21 j).mul (piI.mul (atomPoints j).z)).scale 1 22 := by fin_cases j <;> decide +kernel +lemma ha9_1_22_contains (j : Fin 7) : (ha9_1_22 j).Contains (fullFactor true 9 22 ((j.val:ℝ)/6)) := by + rw [ha9_1_22_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_21 j) true 9 21 j (ha9_1_21_contains j) +noncomputable def hk9_1_23 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_23 j i k) +lemma hk9_1_23_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_23 j i k).Contains (fullFactor true 9 23 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_23,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_23 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 23 (kernel9_0_contains j i k) (mpower1_23_contains j i k) +noncomputable def ha9_1_23 : Fin 7 → CBox := ![⟨⟨(-3),0⟩,⟨(-3),3⟩⟩,⟨⟨(-176),176⟩,⟨(-176),176⟩⟩,⟨⟨72960461,72960482⟩,⟨187198563,187198584⟩⟩,⟨⟨42333281320336,42333281320339⟩,⟨253121222536362,253121222536364⟩⟩,⟨⟨(-281957689679555390),(-281957689679555269)⟩,⟨(-324527017681290011),(-324527017681289890)⟩⟩,⟨⟨13052138719855043992,13052138719855044408⟩,⟨(-4052972945914228104),(-4052972945914227689)⟩⟩,⟨⟨46781038136375641332,46781038136375641459⟩,⟨24524711207015131070,24524711207015131198⟩⟩] +lemma ha9_1_23_eq (j : Fin 7) : ha9_1_23 j = ((ha9_1_22 j).mul (piI.mul (atomPoints j).z)).scale 1 23 := by fin_cases j <;> decide +kernel +lemma ha9_1_23_contains (j : Fin 7) : (ha9_1_23 j).Contains (fullFactor true 9 23 ((j.val:ℝ)/6)) := by + rw [ha9_1_23_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_22 j) true 9 22 j (ha9_1_22_contains j) +noncomputable def hk9_1_24 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_24 j i k) +lemma hk9_1_24_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_24 j i k).Contains (fullFactor true 9 24 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_24,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_24 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 24 (kernel9_0_contains j i k) (mpower1_24_contains j i k) +noncomputable def ha9_1_24 : Fin 7 → CBox := ![⟨⟨0,2⟩,⟨(-2),2⟩⟩,⟨⟨(-84),84⟩,⟨(-84),84⟩⟩,⟨⟨25203200,25203209⟩,⟨(-54059928),(-54059918)⟩⟩,⟨⟨48883816965205,48883816965206⟩,⟨(-38857507855314),(-38857507855312)⟩⟩,⟨⟨(-44668537922808875),(-44668537922808843)⟩,⟨74767316321201932,74767316321201964⟩⟩,⟨⟨(-1072928390185788433),(-1072928390185788349)⟩,⟨(-2102805056046841348),(-2102805056046841264)⟩⟩,⟨⟨3323964096794532566,3323964096794532587⟩,⟨(-7230526420959238870),(-7230526420959238849)⟩⟩] +lemma ha9_1_24_eq (j : Fin 7) : ha9_1_24 j = ((ha9_1_23 j).mul (piI.mul (atomPoints j).z)).scale 1 24 := by fin_cases j <;> decide +kernel +lemma ha9_1_24_contains (j : Fin 7) : (ha9_1_24 j).Contains (fullFactor true 9 24 ((j.val:ℝ)/6)) := by + rw [ha9_1_24_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_23 j) true 9 23 j (ha9_1_23_contains j) +noncomputable def hk9_1_25 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_25 j i k) +lemma hk9_1_25_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_25 j i k).Contains (fullFactor true 9 25 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_25,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_25 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 25 (kernel9_0_contains j i k) (mpower1_25_contains j i k) +noncomputable def ha9_1_25 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-16100240),(-16100235)⟩,⟨5454643,5454648⟩⟩,⟨⟨(-13473426049927),(-13473426049925)⟩,⟨(-5589839918321),(-5589839918320)⟩⟩,⟨⟨16524518039715132,16524518039715141⟩,⟨3722761084280405,3722761084280414⟩⟩,⟨⟨(-313396491823039453),(-313396491823039436)⟩,⟨234569851794820012,234569851794820029⟩⟩,⟨⟨(-1069350842639600658),(-1069350842639600654)⟩,⟨(-425808828304872129),(-425808828304872125)⟩⟩] +lemma ha9_1_25_eq (j : Fin 7) : ha9_1_25 j = ((ha9_1_24 j).mul (piI.mul (atomPoints j).z)).scale 1 25 := by fin_cases j <;> decide +kernel +lemma ha9_1_25_contains (j : Fin 7) : (ha9_1_25 j).Contains (fullFactor true 9 25 ((j.val:ℝ)/6)) := by + rw [ha9_1_25_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_24 j) true 9 24 j (ha9_1_24_contains j) +noncomputable def hk9_1_26 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_26 j i k) +lemma hk9_1_26_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_26 j i k).Contains (fullFactor true 9 26 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_26,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_26 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 26 (kernel9_0_contains j i k) (mpower1_26_contains j i k) +noncomputable def ha9_1_26 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-18),18⟩,⟨(-18),18⟩⟩,⟨⟨4129325,4129328⟩,⟨2156248,2156251⟩⟩,⟨⟨368275234926,368275234927⟩,⟨3255585385202,3255585385204⟩⟩,⟨⟨(-301593042716862),(-301593042716859)⟩,⟨(-3153246340959908),(-3153246340959905)⟩⟩,⟨⟨45346692848594515,45346692848594520⟩,⟨42888796860089324,42888796860089328⟩⟩,⟨⟨(-51415814313273184),(-51415814313273183)⟩,⟨151592664962958008,151592664962958010⟩⟩] +lemma ha9_1_26_eq (j : Fin 7) : ha9_1_26 j = ((ha9_1_25 j).mul (piI.mul (atomPoints j).z)).scale 1 26 := by fin_cases j <;> decide +kernel +lemma ha9_1_26_contains (j : Fin 7) : (ha9_1_26 j).Contains (fullFactor true 9 26 ((j.val:ℝ)/6)) := by + rw [ha9_1_26_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_25 j) true 9 25 j (ha9_1_25_contains j) +noncomputable def hk9_1_27 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_27 j i k) +lemma hk9_1_27_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_27 j i k).Contains (fullFactor true 9 27 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_27,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_27 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 27 (kernel9_0_contains j i k) (mpower1_27_contains j i k) +noncomputable def ha9_1_27 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-8),8⟩,⟨(-8),8⟩⟩,⟨⟨(-341702),(-341699)⟩,⟨(-1180855),(-1180853)⟩⟩,⟨⟨577341844100,577341844102⟩,⟨(-410908123227),(-410908123225)⟩⟩,⟨⟨(-522627520907417),(-522627520907416)⟩,⟨228579585207012,228579585207014⟩⟩,⟨⟨5306501026723676,5306501026723678⟩,⟨(-7980054085678830),(-7980054085678828)⟩⟩,⟨⟨20631836309111253,20631836309111255⟩,⟨5822177079202134,5822177079202135⟩⟩] +lemma ha9_1_27_eq (j : Fin 7) : ha9_1_27 j = ((ha9_1_26 j).mul (piI.mul (atomPoints j).z)).scale 1 27 := by fin_cases j <;> decide +kernel +lemma ha9_1_27_contains (j : Fin 7) : (ha9_1_27 j).Contains (fullFactor true 9 27 ((j.val:ℝ)/6)) := by + rw [ha9_1_27_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_26 j) true 9 26 j (ha9_1_26_contains j) +noncomputable def hk9_1_28 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_28 j i k) +lemma hk9_1_28_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_28 j i k).Contains (fullFactor true 9 28 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_28,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_28 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 28 (kernel9_0_contains j i k) (mpower1_28_contains j i k) +noncomputable def ha9_1_28 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-157115),(-157113)⟩,⟨270492,270494⟩⟩,⟨⟨(-133318009619),(-133318009618)⟩,⟨(-63798548468),(-63798548466)⟩⟩,⟨⟨66000078653772,66000078653774⟩,⟨73862641075335,73862641075336⟩⟩,⟨⟨(-1297795669471852),(-1297795669471851)⟩,⟨(-573508404796806),(-573508404796804)⟩⟩,⟨⟨612497283260435,612497283260436⟩,⟨(-2699833851939530),(-2699833851939528)⟩⟩] +lemma ha9_1_28_eq (j : Fin 7) : ha9_1_28 j = ((ha9_1_27 j).mul (piI.mul (atomPoints j).z)).scale 1 28 := by fin_cases j <;> decide +kernel +lemma ha9_1_28_contains (j : Fin 7) : (ha9_1_28 j).Contains (fullFactor true 9 28 ((j.val:ℝ)/6)) := by + rw [ha9_1_28_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_27 j) true 9 27 j (ha9_1_27_contains j) +noncomputable def hk9_1_29 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_29 j i k) +lemma hk9_1_29_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_29 j i k).Contains (fullFactor true 9 29 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_29,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_29 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 29 (kernel9_0_contains j i k) (mpower1_29_contains j i k) +noncomputable def ha9_1_29 : Fin 7 → CBox := ![⟨⟨(-1),0⟩,⟨(-1),1⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨74711,74712⟩,⟨(-18022),(-18021)⟩⟩,⟨⟨1771979597,1771979599⟩,⟨29709479896,29709479897⟩⟩,⟨⟨8318308912977,8318308912978⟩,⟨(-14374064840990),(-14374064840988)⟩⟩,⟨⟨(-49272675417273),(-49272675417272)⟩,⟨196751874673349,196751874673350⟩⟩,⟨⟨(-340144172705861),(-340144172705860)⟩,⟨(-58785751061675),(-58785751061674)⟩⟩] +lemma ha9_1_29_eq (j : Fin 7) : ha9_1_29 j = ((ha9_1_28 j).mul (piI.mul (atomPoints j).z)).scale 1 29 := by fin_cases j <;> decide +kernel +lemma ha9_1_29_contains (j : Fin 7) : (ha9_1_29 j).Contains (fullFactor true 9 29 ((j.val:ℝ)/6)) := by + rw [ha9_1_29_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_28 j) true 9 28 j (ha9_1_28_contains j) +noncomputable def hk9_1_30 (j : Fin 6) (i k : Fin 16) : CBox := (kernel9_0 j i k).mul (mpower1_30 j i k) +lemma hk9_1_30_contains (j : Fin 6) (i k : Fin 16) : + (hk9_1_30 j i k).Contains (fullFactor true 9 30 (quadraturePoint j.val (16*i.val+k.val))) := by + simpa only [hk9_1_30,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one] using @momentPower_trans_full (kernel9_0 j i k) (mpower1_30 j i k) (quadraturePoint j.val (16*i.val+k.val)) 9 30 (kernel9_0_contains j i k) (mpower1_30_contains j i k) +noncomputable def ha9_1_30 : Fin 7 → CBox := ![⟨⟨0,1⟩,⟨(-1),1⟩⟩,⟨⟨(-1),1⟩,⟨(-1),1⟩⟩,⟨⟨(-15356),(-15355)⟩,⟨(-9869),(-9868)⟩⟩,⟨⟨4891656123,4891656124⟩,⟨(-3104307562),(-3104307560)⟩⟩,⟨⟨(-2633774246415),(-2633774246414)⟩,⟨(-554955511624),(-554955511622)⟩⟩,⟨⟨27949754921690,27949754921691⟩,⟨2090670976971,2090670976972⟩⟩,⟨⟨(-4946895520926),(-4946895520924)⟩,⟨41310262072222,41310262072223⟩⟩] +lemma ha9_1_30_eq (j : Fin 7) : ha9_1_30 j = ((ha9_1_29 j).mul (piI.mul (atomPoints j).z)).scale 1 30 := by fin_cases j <;> decide +kernel +lemma ha9_1_30_contains (j : Fin 7) : (ha9_1_30 j).Contains (fullFactor true 9 30 ((j.val:ℝ)/6)) := by + rw [ha9_1_30_eq] + simpa only [Bool.false_eq_true,ite_false,ite_true,Nat.cast_ofNat,Nat.cast_zero,Nat.cast_one,Int.reduceAdd,Nat.reduceAdd] using @fullFactor_step_atom_contains (ha9_1_29 j) true 9 29 j (ha9_1_29_contains j) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_0.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_0.lean new file mode 100644 index 0000000000000000000000000000000000000000..256ce29e278f8ee2f2197cf14256c9267d3946fc --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_0.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨105466140671000245737117697591,105466140671000290715029182668⟩,⟨77030111962162894051158626191,77030111962162939035361872822⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨315464212253938598992810248572,315464212253938705025457578241⟩,⟨224542897740951515204561485455,224542897740951621255612294350⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨522273350412706462475997789982,522273350412706569187029165090⟩,⟨353308058265669366464427175682,353308058265669473204616584932⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨722978351279413599062202896502,722978351279413666153876764221⟩,⟨454614883350588224043510266422,454614883350588291172958008956⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨911812228592108100783965440501,911812228592108128804947609532⟩,⟨524238666673334690076130112117,524238666673334718140834489689⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1078909994154965012004466145624,1078909994154965019965590856619⟩,⟨560911894682440306901066874551,560911894682440314908845394311⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1212640118704842352142173684917,1212640118704842353852744781842⟩,⟨564210665553999924090196559093,564210665553999925847173886181⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1303199131043577247462142406913,1303199131043577247878143696604⟩,⟨535433855791633272809785639955,535433855791633273269493999228⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1343659925132348488547437055964,1343659925132348488762843609642⟩,⟨479438459452804091281829577632,479438459452804091536523138190⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1329602490952811654185831564938,1329602490952811654362821316988⟩,⟨404517203484456463863533482501,404517203484456464074299146926⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1258971139629643364611891669153,1258971139629643364766291266139⟩,⟨320965146065459913350257039628,320965146065459913532470047909⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1131842459070545457493921743358,1131842459070545457624845244326⟩,⟨239196404745951037548714651126,239196404745951037701238447636⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨950225762794141849560339410627,950225762794141849665398277771⟩,⟨167150723702073428809354822398,167150723702073428930084812715⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨719181664336637892620369382364,719181664336637892696683389788⟩,⟨107918693714419077417435523310,107918693714419077504248599882⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨448495903170739647184229979036,448495903170739647230345818177⟩,⟨59927265906069749341933193200,59927265906069749394036448352⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨152352030397082362948759562809,152352030397082362964083051393⟩,⟨19152266596419097558451000279,19152266596419097575746226130⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨63655282271256169595338014895,63655282271256224712346637725⟩,⟨91380472828907845886877187655,91380472828907901012085276355⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨190198324516163920576297202093,190198324516164130009238988600⟩,⟨270081094446508963915043298370,270081094446509173372192477851⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨313935973686494277444437630357,313935973686494812841749932946⟩,⟨436411296010182293391394505516,436411296010182828827623615835⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨432175137279029840648761189740,432175137279031132820085124009⟩,⟨582504214492777371584849796860,582504214492778663807757208176⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨541460601119087523067787405061,541460601119090464737040687907⟩,⟨701148012262770804035192821571,701148012262773745765987736870⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨637961884771045032510799774096,637961884771051010278629401592⟩,⟨786663379476423699524667938322,786663379476429677360944529638⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨717440704163382721558052625746,717440704163392806026209934867⟩,⟨836055815678236785166233004269,836055815678246869706471884476⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨774741325520577227319848992247,774741325520590428894051400750⟩,⟨849240484548921921982844747461,849240484548935123629503313263⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨804070323450354686938725613317,804070323450368102795901615517⟩,⟨828126922223957643315827379563,828126922223971059242862655971⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨800280972279224719652840131446,800280972279235295733621048367⟩,⟨775750698756279870261350118456,775750698756290446406805715322⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨760302819903523024118985203921,760302819903529483404826755803⟩,⟨695963397937315799802503414058,695963397937322259145753218870⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨683995899389976543319395403416,683995899389979802213315467345⟩,⟨593609523047008421628872622300,593609523047011680571391106830⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨573829270623829841436724663469,573829270623831302665834938715⟩,⟨474592121188860374830694704706,474592121188861836098495094923⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨434041441718251476901572158134,434041441718252091784339618268⟩,⟨344838650482343908118099903947,344838650482344523028939992530⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨270685341476916140577503701360,270685341476916383225614742520⟩,⟨208941963705425959184302774361,208941963705426201849420139210⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨91975106353941016229979817909,91975106353941080155434412003⟩,⟨69938612848381778618247789940,69938612848381842549396884772⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1272885490275879118422433706),(-1272885490275879109239651514)⟩,⟨79603624112657434018258435582,79603624112657434036276439857⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-576184306657926812854302618),(-576184306657926785158122637)⟩,⟨236888949630030989647526126279,236888949630030989701556976357⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨9244495931524614537994272227,9244495931524614584338842090⟩,⟨388372492170140452444415543197,388372492170140452533625314030⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨32023459714678429526618497363,32023459714678429591433604735⟩,⟨530631108825221695710640784146,530631108825221695833301577458⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨68193423858176437634948178469,68193423858176437717702692376⟩,⟨659796421134737927024387566053,659796421134737927177634771009⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨114893544330046233934299870477,114893544330046234037126154601⟩,⟨770364891418085718449636805324,770364891418085718631883442401⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨167580607283827474769813256429,167580607283827474901148000214⟩,⟨855452604105434791820322870641,855452604105434792036408666536⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨221031780516571284875482647928,221031780516571285094843089571⟩,⟨908677124891374510750547419628,908677124891374511055921927991⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨269315060398134972692193888504,269315060398134973479949876128⟩,⟨925619955480904117487516267149,925619955480904118358355506393⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨305974707828229600613287992821,305974707828229605277866359619⟩,⟨904307021366307850092976135483,904307021366307854834301294400⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨324604757187071675494387667362,324604757187071699884006403427⟩,⟨845238477160564236159007472919,845238477160564260616473008069⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨319515667919785271169525523259,319515667919785362348262943001⟩,⟨750837469541132464337642002716,750837469541132555573834289053⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨287031214959208748994738790261,287031214959208977537867245458⟩,⟨624308874529306855501905994020,624308874529307084090873677409⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨227488458206142846833080318850,227488458206143223525842718964⟩,⟨469383334557001502119034149630,469383334557001878845042361757⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨145865685320271250986605221583,145865685320271634289909359513⟩,⟨291576252123462853242272311057,291576252123463236565696111446⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨50194827554182965513866512750,50194827554183129726743292082⟩,⟨98872720776659023906039114192,98872720776659188125622771180⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-15683207364194899856616735533),(-15683207364194827989231952531)⟩,⟨42793961675638117291566258279,42793961675638189166616884578⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-45828036051571592499227546911),(-45828036051571424098304595863)⟩,⟨128198606322596817041365847662,128198606322596985465001944065⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-72438807890540643611439892036),(-72438807890540475946600541747)⟩,⟨212588032993839270768342080750,212588032993839438470049256664⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-93596774803499814272508740062),(-93596774803499710236782269427)⟩,⟨294277596299685922264404380527,294277596299686026349712186435⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-107610414454714881929147688180),(-107610414454714839046042093711)⟩,⟨370509148977838960374637805120,370509148977839003318103809518⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-113055112590663052490195153559),(-113055112590663040482089171790)⟩,⟨438091702821963697948847433193,438091702821963710025734134312⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-109621851281967016376321961699),(-109621851281967013914692769270)⟩,⟨494026315231090068337477029806,494026315231090070873624006293⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-98805705960489886368705394392),(-98805705960489885898059712469)⟩,⟨535135971471965282934063873363,535135971471965283482054071357⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-83327102520722501619260995574),(-83327102520722501462924648414)⟩,⟨557635755896231605305535389911,557635755896231605539011471226⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-66037913605855164890296355690),(-66037913605855164787256262644)⟩,⟨557620569843407115351853047576,557620569843407115528790986840⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-49156229007634317410783131838),(-49156229007634317327012636501)⟩,⟨532107165496725847951300265086,532107165496725848102850617803⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-34050125449210378852759178753),(-34050125449210378784061829062)⟩,⟨480084674296688714301226729473,480084674296688714429074109698⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-21534262887938780041806596533),(-21534262887938779987941170844)⟩,⟨403008655882137397011146421379,403008655882137397113399443735⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-12100082129879463945927745979),(-12100082129879463907418777053)⟩,⟨304461085874235412044927234592,304461085874235412119274849185⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-5719758262714109363869573079),(-5719758262714109340854414697)⟩,⟨189530257783927016725344420964,189530257783927016770374677910⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1622725640126171298382600126),(-1622725640126171290754321767)⟩,⟨64321457365189354203972991482,64321457365189354219010750243⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-28225650791030115246789596160),(-28225650791029901617216274036)⟩,⟨1583362461712867474545673297,1583362461713081108805047745⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-83264954198231121629213565733),(-83264954198230308404720321042)⟩,⟨6703052758373070607473487002,6703052758373883845807743830⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-134211313992223266756534943305),(-134211313992221180632139920943)⟩,⟨17414696321964236467376944162,17414696321966322614302913452⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-179056209282422541382175174506),(-179056209282417482137368639670)⟩,⟨36371690582318304860652797294,36371690582323364135912635533⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-216403003825945360002051117028),(-216403003825933772563420402773)⟩,⟨64272157274594693175750167902,64272157274606280651807121853⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-244869733992494173866443253944),(-244869733992470475700360475231)⟩,⟨99432964424687965494130851394,99432964424711663703290311198⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-262763658195876631014206753818),(-262763658195836457943528252518)⟩,⟨138489652313985406557655120189,138489652314025579675420430869⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-268692995634454779978374743883),(-268692995634401904925974534543)⟩,⟨177331032648991074556028008852,177331032649043949657951180302⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-262301592763804889108537270753),(-262301592763750826971144976361)⟩,⟨211522849806277276119531813231,211522849806331338307328426589⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-244524500556683894628611390195),(-244524500556640997297669501497)⟩,⟨236618503295198121872239453806,236618503295241019252727935042⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-217549797651987850076869847300),(-217549797651961474407880577305)⟩,⟨248516738650178485022364870234,248516738650204860737980924329⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-184370405724601014850921469956),(-184370405724587620060916819316)⟩,⟨243590061387662015835583423968,243590061387675410667045660214⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-147531599957446368298239638217),(-147531599957440325680559937315)⟩,⟨219027299441294934509417615902,219027299441300977161478479954⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-108071521726297985674429189693),(-108071521726295429169863245694)⟩,⟨174245951911835835526455265370,174245951911838392056799904535⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-66150029722680305006769648918),(-66150029722679291336669610923)⟩,⟨112166257495297109136791155292,112166257495298122822861676882⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-22287775262655307200635386314),(-22287775262655039043640493300)⟩,⟨38688135389279983853870253119,38688135389280252016275534572⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-95668050146986675223862110),(-95668050146986673374115925)⟩,⟨(-7555117831446078627729308878),(-7555117831446078625061272450)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1404559483889578931832039841),(-1404559483889578926130398270)⟩,⟨(-22413461604849090670300505099),(-22413461604849090662170781663)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-5789243529263902476934879902),(-5789243529263902466954987212)⟩,⟨(-36663355527621957841391126083),(-36663355527621957827622333132)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-14267221272770611468876171342),(-14267221272770611453972466132)⟩,⟨(-50257118561737377726419853552),(-50257118561737377706744643162)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-26367365650689858985469703853),(-26367365650689858964675272619)⟩,⟨(-62952702064632318242169653455),(-62952702064632318216142534199)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-40553749935226088704808410188),(-40553749935226088675925527143)⟩,⟨(-73563601591070796042991005560),(-73563601591070796008805585456)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-55413601188968210625014057849),(-55413601188968210579678715590)⟩,⟨(-80290706271587447410650675624),(-80290706271587447360275666400)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-69958536180108608370892331727),(-69958536180108608256757138931)⟩,⟨(-81999132711627519661824129527),(-81999132711627519543411308082)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-83033504516672774615884743160),(-83033504516672774010951664692)⟩,⟨(-78769844975146436604413136677),(-78769844975146435996439294193)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-93062243066417882136861446302),(-93062243066417878069316695956)⟩,⟨(-71606008748863369012220241672),(-71606008748863364942983030169)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-98205894822799662748059506315),(-98205894822799640725461989108)⟩,⟨(-62015969917912863289009356574),(-62015969917912841265887964242)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-96579750811849083662059146011),(-96579750811848999875634835666)⟩,⟨(-51488614712843973316386109161),(-51488614712843889530210993480)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-86763396300160997936727418252),(-86763396300160785286410122089)⟩,⟨(-40791965202174080794796871123),(-40791965202173868145156575347)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-68695276131914734811513143609),(-68695276131914380931909203753)⟩,⟨(-29809652831435584756191837161),(-29809652831435230877372146916)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-43964937485906178357331277677),(-43964937485905815671730267180)⟩,⟨(-18240909529976174661567462804),(-18240909529975811976569993443)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-15107328544592277517242896455),(-15107328544592121400412898158)⟩,⟨(-6143660499504593176261703823),(-6143660499504437059656335430)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3289868133696423130297248132289,3289868133696482615615769612490⟩,⟨4972256453543356872643838694717,4972256453543416358519991842244⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 0) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_0 (tableDensity false) (fullFactor false 0 0) density0_contains hk0_0_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨0,0⟩,⟨(-67549981495186214448580000000),(-67549981495186214446760000000)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_0 0 0 ha0_0_0_contains + def realAnswer : RBox := ⟨3289868133696423130297148132289,3289868133696482615615869612490⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_0 +namespace hm0_1_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨16140075137133244697945404803,16140075137133281546641784309⟩,⟨15438062186870151364906584259,15438062186870188212140430403⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨48263943131508723536689546227,48263943131508810373719483899⟩,⟨45768928312980419331805103748,45768928312980506164535488931⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨79338363620088471501773095647,79338363620088558830291027441⟩,⟨74004296025610363732397973906,74004296025610451054010516223⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨107725757654480280155440343467,107725757654480334998677918324⟩,⟨97307528686445607745519730645,97307528686445662579578230590⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨132564910465887421931660619678,132564910465887444797414566702⟩,⟨111485947582733262042575685134,111485947582733284897276747740⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨155338323067275255851750785127,155338323067275262322067438545⟩,⟨113446658677915440100823439102,113446658677915446558662551386⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨178207607946389156900196048438,178207607946389158264568756674⟩,⟨104182284201259843899573326998,104182284201259845250557288097⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨200777512646492228525239032717,200777512646492228829268279436⟩,⟨88170277338355927688575325255,88170277338355927978899735572⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨219480382976156808073431692676,219480382976156808211403973807⟩,⟨70342284342630321886973251441,70342284342630322011509893652⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨229277534808732849335118167624,229277534808732849442074364776⟩,⟨54027036107064390576833914535,54027036107064390670975969806⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨225735323057846592837374627128,225735323057846592928418276212⟩,⟨40333291557771003306513069080,40333291557771003385708288405⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨206904949189207036058632000850,206904949189207036134408440315⟩,⟨28595063063304716503244026836,28595063063304716568528665952⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨174238838419081576533305158306,174238838419081576593194068307⟩,⟨18001902787810210512645926312,18001902787810210563840077411⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨131305200513352039666843259664,131305200513352039709732978009⟩,⟨9151942734794840693382579466,9151942734794840729729369308⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨81539333313410546633414958246,81539333313410546659021702428⟩,⟨3358632549765096342962572191,3358632549765096364498406399⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨27647641087516402647864302437,27647641087516402656332586572⟩,⟨682986434987683182662750927,682986434987683189741645497⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1955440343145086422638728921,1955440343145131810707496026⟩,⟨17258948447620858313467446653,17258948447620903700463400042⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨6605789045699892561955264233,6605789045700065088892515472⟩,⟨50412408865134332094448651787,50412408865134504618236133150⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨13410369380330324316133319074,13410369380330765657373109638⟩,⟨79727452721372308957039520234,79727452721372750293237358827⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨23526546025042914836807602685,23526546025043980904615106904⟩,⟨103618515826710729380115485547,103618515826711795441277837677⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨37414849085948466273476697190,37414849085950895307223935316⟩,⟨121672156426718100870183107662,121672156426720529896026308902⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨54272004585682964446246606806,54272004585687904494167100411⟩,⟨134363101904510633993926580177,134363101904515574033054963750⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨72084161064064456250531033419,72084161064072797326530936137⟩,⟨142131035999416165930410427833,142131035999424506997097731842⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨88600364406641437755750533591,88600364406652362175709058178⟩,⟨144919453998329229766198630800,144919453998340154176736205567⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨102042652983661548004591802663,102042652983672649312357043897⟩,⟨142690819867919656208608865650,142690819867930757507176465782⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨110933404395272920065559942099,110933404395281666747543371900⟩,⟨135924844865255249053481157888,135924844865263995726705885736⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨113653096035952127376499253686,113653096035957464158974680899⟩,⟨125413832500817698254707246985,125413832500823035029126595704⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨108507171400492321272178643660,108507171400495010448519999579⟩,⟨111495154493826966938576935353,111495154493829656107858377419⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨94688172974331930232132038083,94688172974333134393480154921⟩,⟨93623953650896326243280657173,93623953650897530398857996672⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨73129540483379676966528006780,73129540483380183058478585976⟩,⟨71189284252991727846981953613,71189284252992233934667310148⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨46000738911787225787570119343,46000738911787425321271181105⟩,⟨44578509955461830519837321878,44578509955462030050922481513⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨15671680031807520501932987969,15671680031807573043242465866⟩,⟨15174543897563740257834609115,15174543897563792798258318078⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-9663163124830068768616921342),(-9663163124830068762454651692)⟩,⟨15155590633865469705970878246,15155590633865469712537643941⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-28376323942135313424474381762),(-28376323942135313405756543994)⟩,⟨45410691625340987015501186077,45410691625340987035464117718⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-45281610528291507299719012525),(-45281610528291507267996628257)⟩,⟨74983343239447945021920331701,74983343239447945055619979345⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-59032554947995523722637964292),(-59032554947995523677585915208)⟩,⟨102261399977276443941413496104,102261399977276443989006612652⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-67619168422496114782415201445),(-67619168422496114723970954370)⟩,⟨125254208253489845479459139875,125254208253489845540734842603⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-68922888101414675073357341948),(-68922888101414675000085668648)⟩,⟨143094412537058755679088599907,143094412537058755755420443768⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-62464543802502949772248327192),(-62464543802502949677010999963)⟩,⟨156377004470461220791007712315,156377004470461220889571764431⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-50186230445102977851661677686),(-50186230445102977684256579449)⟩,⟨165776423958162190500540043901,165776423958162190671176900443⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-35475039543218041347365054992),(-35475039543218040712705693224)⟩,⟨170878272386268177960196756713,170878272386268178597343043728⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-21716415266183103170405322144),(-21716415266183099369267709186)⟩,⟨170136018308123979113374407962,170136018308123982916048320195⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-11108450009926501883005426477),(-11108450009926482000024660453)⟩,⟨161538983161778030587722596076,161538983161778050471437686210⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-3996861493211402530432772790),(-3996861493211328177892489736)⟩,⟨143844380767325916394613645228,143844380767325990747490940437⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨540224931781698235786311329,540224931781884722273748289⟩,⟨117912080738888992713234446004,117912080738889179199843421874⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨3071375424310221201818406536,3071375424310528774595687922⟩,⟨86530901973319917648705150197,86530901973320225221455289546⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨3333422183525053794743540168,3333422183525366914526445808⟩,⟨52541437101871190471803257957,52541437101871503591506532840⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1418212930774296758078350000,1418212930774430936258286863⟩,⟨17585978549142496152723618099,17585978549142630330853707433⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-12753548324238141341083163986),(-12753548324238080953202456305)⟩,⟨8334296287300809041388541848,8334296287300869428477163570⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-37392105435138391937871318669),(-37392105435138250529024541326)⟩,⟨24725228652142204413438338633,24725228652142345819938940959⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-59422143795118825784332778472),(-59422143795118685181375744112)⟩,⟨40413729745877059005389040972,40413729745877199604556116924⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-77383381129230446222604965249),(-77383381129230359155748291602)⟩,⟨55415863004215148156883113528,55415863004215235218672365674⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-90593841303739394853561013846),(-90593841303739359062476535441)⟩,⟨70121390082217498279963917342,70121390082217534064947063592⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-99462306180971997584054865028),(-99462306180971987596881074411)⟩,⟨84565898288620521558467522550,84565898288620531538751155262⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-104781593402311576207407250481),(-104781593402311574172579996690)⟩,⟨97710717206968258349280318968,97710717206968260376659593944⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-106739242017643067773449920577),(-106739242017643067393774768817)⟩,⟨107903019981767255348689185216,107903019981767255720695684885⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-104958047597896103784012841822),(-104958047597896103666227464530)⟩,⟨113868869206844692269528633883,113868869206844692379736292164⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-99185149582144724557128291667),(-99185149582144724483631662355)⟩,⟨115042928420838976559014064299,115042928420838976625325365628⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-89738831948056009798239224538),(-89738831948056009739907283758)⟩,⟨111247113847667199236805917554,111247113847667199288646493365⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-77390030497056406776895358071),(-77390030497056406729723148799)⟩,⟨102238332603228679838675153156,102238332603228679880235458136⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-62852545910539619641108495759),(-62852545910539619604489834944)⟩,⟨87671736539281126549913612996,87671736539281126581969916310⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-46514792927829581821133809121),(-46514792927829581795210805082)⟩,⟨67567506802281757062672987002,67567506802281757085239164619⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-28647175184069759292943699941),(-28647175184069759277585245079)⟩,⟨42699585390228684237028270628,42699585390228684250334096662⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-9681205973211195798212398697),(-9681205973211195793146794816)⟩,⟨14607535575894659070327749798,14607535575894659074705933613⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-9235090994055585897117965730),(-9235090994055410323983501735)⟩,⟨993976113031903266899794765,993976113032078839192309004⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-27801026906867196586340109211),(-27801026906866528185787716708)⟩,⟨3422512764969988235261676978,3422512764970656633269520849⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-46378050484314133996875107154),(-46378050484312419162689661993)⟩,⟨6953127081049271322614208769,6953127081050986152595716328⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-64244022684292887063197092235),(-64244022684288727619026752905)⟩,⟨11895028385694420928464993459,11895028385698580366843675983⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-80116587180445334349317399632),(-80116587180435806631190972028)⟩,⟨18567378577391303238788471609,18567378577400830949699532985⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-92977210846607544005644409024),(-92977210846588058383535647171)⟩,⟨27458853078539537873536162741,27458853078559023487155890099⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-102716931671483507805654997177),(-102716931671450482957650476259)⟩,⟨38536944762434858937404965972,38536944762467883775773962715⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-109732031280892690410428335999),(-109732031280849245040179507678)⟩,⟨50538021240911231661798551472,50538021240954677021687717543⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-114115953933358168801096203733),(-114115953933313783448519274015)⟩,⟨61143924759949649481260435297,61143924759994034823456457627⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-115215790680174012412798187063),(-115215790680138830996969854725)⟩,⟨67744532678506562165112483912,67744532678541743571216500580⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-111618948455595379832339611878),(-111618948455573775725918215982)⟩,⟨68390914918390846562909991323,68390914918412450660638530575⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-101749055018027420587067049783),(-101749055018016463741361532376)⟩,⟨62762322044054822770116071808,62762322044065779608292139234⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-85184840893949808420798415504),(-85184840893944871866938658751)⟩,⟨52341358272237800738315589757,52341358272242737286029806552⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-63411924013196442546216324380),(-63411924013194356191922767444)⟩,⟨39102458847209407375145660558,39102458847211493724936762218⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-38770513764635317673524178676),(-38770513764634491030246627988)⟩,⟨24206829769347239663715063846,24206829769348066304252417975⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-13005011226896890075166348164),(-13005011226896671476133803972)⟩,⟨8208534595553778431528072263,8208534595553997029649875146⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-13539691606597287997677429),(-13539691606597286753923796)⟩,⟨(-224307419731718046239356572),(-224307419731718044405275166)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-202835616224258111762053868),(-202835616224258107910684536)⟩,⟨(-624445543885633020117878511),(-624445543885633014487856486)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-915530915882364718042986388),(-915530915882364711243773010)⟩,⟨(-673161411406591395169754916),(-673161411406591385506992446)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2787923404776267172436459727),(-2787923404776267162163900549)⟩,⟨307848452389435578422845026,307848452389435592483678693⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-6999724006565458677847129821),(-6999724006565458663271367445)⟩,⟨2842360883808416180447960672,2842360883808416199493173019⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-14715543946526255635054762086),(-14715543946526255614199457087)⟩,⟨6358610777566070103214618227,6358610777566070129090827629⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-25764669228856705550722295871),(-25764669228856705516232952498)⟩,⟨9268661133556623856331808814,9268661133556623896309576842⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-38260622843291181375420618480),(-38260622843291181283206693069)⟩,⟨10259472326351613163068416700,10259472326351613260901731304⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-49547581070620949128395296296),(-49547581070620948631027458949)⟩,⟨9141655088093953120309753752,9141655088093953622962753726⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-57252302117411810198091144323),(-57252302117411806866307258099)⟩,⟨6723044444254553452030768925,6723044444254556788500166066⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-59940098243176307526531448200),(-59940098243176289531347791555)⟩,⟨4280785046065254935862371694,4280785046065272935031876456⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-57407601770625924955236666645),(-57407601770625856522838370908)⟩,⟨2845366807107156441742059221,2845366807107224877503213408⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-50344031895148189584206922680),(-50344031895148015850929983320)⟩,⟨2495188758004352412852773145,2495188758004526148829894583⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-39485298217908734492380714717),(-39485298217908445245478799988)⟩,⟨2425694814134613127388536761,2425694814134902376235278077⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-25342459553658357338729498311),(-25342459553658060785370955425)⟩,⟨1871078914763342425755114667,1871078914763638980276707802⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-8752970264762306688008288165),(-8752970264762179012529246554)⟩,⟨706648025570213520293814916,706648025570341196151900758⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-24448959531044601),24448954519137686⟩,⟨983696206427992533367383589992,983696206428041431224726699724⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 0) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_0 (tableDensity true) (fullFactor false 0 0) density1_contains hk0_0_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨0,0⟩,⟨88334591186012741968840000000,88334591186012741971220000000⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_0 0 0 ha0_0_0_contains + def realAnswer : RBox := ⟨(-24448959631044601),24448954619137686⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_0 +namespace hm0_0_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-40139697099728580410585441398),(-40139697099728556967607793789)⟩,⟨54956887313648880504352843494,54956887313648903944099536118⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-114775994976544664669140081532),(-114775994976544610417020580342)⟩,⟨161235695447665986849851022174,161235695447666041092718854660⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-173706189840232144325454312029),(-173706189840232091719855969388)⟩,⟨256713009936100813773635970623,256713009936100866365198235969⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-210640975558633237573225615477),(-210640975558633206310596039384)⟩,⟨334822548744581730166199035954,334822548744581761411827143302⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-223998393619813844457903870643),(-223998393619813832357255398115)⟩,⟨389313610600664063959497901181,389313610600664076042232413798⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-215883620450594651905626680740),(-215883620450594648779531214608)⟩,⟨414821757405588260655814364752,414821757405588263765054468775⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-190573622932926744210998701753),(-190573622932926743605729620598)⟩,⟨409013757532657660139942688862,409013757532657660731017830649⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-154079107559932142736370053841),(-154079107559932142601104922406)⟩,⟨374282205236691782337765631541,374282205236691782462343669500⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-113518755698243522443002201942),(-113518755698243522381285956599)⟩,⟨317286472528448112831422844503,317286472528448112886122628678⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-75540969811636455757795272215),(-75540969811636455717346923578)⟩,⟨247377631081037770071089137946,247377631081037770107848465809⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-44798614183386778534182741676),(-44798614183386778507865606246)⟩,⟨174847080317017650382199679958,174847080317017650407450994344⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-23215409121828262820445158829),(-23215409121828262804944006469)⟩,⟨109145760755302090285426277654,109145760755302090301657799607⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-10164998490939370848656846653),(-10164998490939370840802969329)⟩,⟨57336454579222582769599947028,57336454579222582779082357993⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-3482598403293167616956208899),(-3482598403293167613804918764)⟩,⟨23005784989277024282370813440,23005784989277024287259429450⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-753544214244626556652705164),(-753544214244626555794336201)⟩,⟨5589575435678944319899838297,5589575435678944322025503773⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-48316727205497958118885254),(-48316727205497958008933452)⟩,⟨382383390703701568290144744,382383390703701568857015700⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-95463977926439043179825291037),(-95463977926438985593865793101)⟩,⟨66499690101520828792846501014,66499690101520886370147498008⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-279460271486469004263721726351),(-279460271486468787625176607479)⟩,⟨196799571623653153615483427999,196799571623653370228710930742⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-443040433207751675274809323048),(-443040433207751132277121302417)⟩,⟨318688144259962184962683551410,318688144259962727920442298227⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-574831710890301932287343462239),(-574831710890300659269963189534)⟩,⟨426441133215198315016175462055,426441133215199587982120373629⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-666604585256494767961010956623),(-666604585256491977236290977405)⟩,⟨514704823318968506613553700301,514704823318971297279181345257⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-714517570377047133333497291645),(-714517570377041715959831475190)⟩,⟨579326050112459049326777337733,579326050112464466637706924468⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-719945639021237155278220214358),(-719945639021228486680743910840)⟩,⟨617629143380715715134974347115,617629143380724383669908706934⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-688768158546196590519698702124),(-688768158546185890748903589116)⟩,⟨628140899081810172599713103896,628140899081820872311432938427⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-629351457933725867988231805413),(-629351457933715669587736780810)⟩,⟨610857622559397847994144061514,610857622559408046341442156623⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-550685898165731021043207606398),(-550685898165723500595986628110)⟩,⟨567905914913599593876580244426,567905914913607114277997942820⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-461201936174369796075099132041),(-461201936174365504169464591854)⟩,⟨503679783995825934085860265598,503679783995830225953750567414⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-368156976883925528863137072059),(-368156976883923501615075937171)⟩,⟨424099236959929584572641769349,424099236959931611790997524037⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-277191423576612874321323931926),(-277191423576612018583092294924)⟩,⟨335082420263311840593328925346,335082420263312696309455331628⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-191612634382321698636681087879),(-191612634382321356343178970332)⟩,⟨241148278950788619185279297411,241148278950788961463634201397⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-112011478656487025126350631271),(-112011478656486894933301133359)⟩,⟨145103955230756581663385797759,145103955230756711847634619839⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-36795524587186946372833060244),(-36795524587186912734231919067)⟩,⟨48388890893515915370309791893,48388890893515949006028125790⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-124841108568671773844768565974),(-124841108568671773816112648790)⟩,⟨(-1996473142179006044200909927),(-1996473142179006029793365374)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-369147153269875033266808350085),(-369147153269875033181417924198)⟩,⟨(-903793713490957232258463937),(-903793713490957189093379116)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-597608649380861118964930274541),(-597608649380861118825677926668)⟩,⟨14199975166081391700956742863,14199975166081391772314653587⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-801439398657227644390743381924),(-801439398657227644202727827861)⟩,⟨48308368335815942750967518487,48308368335815942849023363659⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-972678951325140764770682590016),(-972678951325140764541268139240)⟩,⟨100433596782363456886211214725,100433596782363457008560789138⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1102952526124317451554843956391),(-1102952526124317451289727911404)⟩,⟨164361531272799947384041140078,164361531272799947531854992977⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1184405986281611282826001501954),(-1184405986281611282522116564770)⟩,⟨231857005330392256503407709993,231857005330392256686073264777⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1212584382665928696107290640523),(-1212584382665928695695190311902)⟩,⟨294772023344456593833088031740,294772023344456594126403407960⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1187928172315599766246946688296),(-1187928172315599765128992685760)⟩,⟨345447498074267594347454352185,345447498074267595354841683505⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1115286052012901182309224365936),(-1115286052012901176489518852669)⟩,⟨377186698963119943514257575588,377186698963119949235608791425⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1002559736281416110795388485944),(-1002559736281416081923189840236)⟩,⟨384881679175498014792213704927,384881679175498043580631202178⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-858707210507710884424418212798),(-858707210507710780456144724082)⟩,⟨365323955505065810629521886620,365323955505065914529273895672⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-691459214576690685442409154865),(-691459214576690432849627113892)⟩,⟨317853867592099028460518774797,317853867592099281000290979888⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-506556979236126172364333615908),(-506556979236125766287617296469)⟩,⟨245485837777782479180954006641,245485837777782885220161919423⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-308972818513428013383796313521),(-308972818513427607361211535678)⟩,⟨154564515790747856878079941771,154564515790748262878355037073⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-103787463255247569915224296818),(-103787463255247397539837008077)⟩,⟨52689751367881389412447076003,52689751367881561780463008768⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-89519898618140139812661241916),(-89519898618139989454597241581)⟩,⟨(-32807494671314234247239637725),(-32807494671314083905392645726)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-266896683422599367326453620800),(-266896683422599016605260073131)⟩,⟨(-95411484981194853223085014205),(-95411484981194502549730880095)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-438425430162537894970414397214),(-438425430162537548890702373816)⟩,⟨(-149400860985387333673204887654),(-149400860985386987670477006781)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-598535590685827707315975610783),(-598535590685827495341442912498)⟩,⟨(-190387977660523973686025052536),(-190387977660523761813718019566)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-740191848686836797604131887300),(-740191848686836711630043109921)⟩,⟨(-215017485009475992685623894212),(-215017485009475906833963346099)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-856589881194335705214910595600),(-856589881194335681527832256736)⟩,⟨(-221110964107125382182812941698),(-221110964107125358632546312459)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-942634172113876133055786693376),(-942634172113876128195690214147)⟩,⟨(-209240916274605610726923974826),(-209240916274605606011825741323)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-994259917057628147860431180744),(-994259917057628146835343904942)⟩,⟨(-183660406008484452408985016512),(-183660406008484451530870852852)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1007583799975644931090640439059),(-1007583799975644930664059313051)⟩,⟨(-150641628427993801997807756581),(-150641628427993801714248433270)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-979634047422680787043008440104),(-979634047422680786727692571181)⟩,⟨(-116081209090836782650145177837),(-116081209090836782468513457521)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-909719987012066859767111097330),(-909719987012066859503711845498)⟩,⟨(-84087589938424502478119309171),(-84087589938424502334472248966)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-800408460686119138503379050590),(-800408460686119138286285473325)⟩,⟨(-56799916033701083618958735286),(-56799916033701083504127954923)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-657363495291394206024663885166),(-657363495291394205854520205080)⟩,⟨(-35142462583463420031015631016),(-35142462583463419942965940774)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-487986968761137322192626214231),(-487986968761137322070901696386)⟩,⟨(-19401070430531796789768599006),(-19401070430531796727941521751)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-300075870427040466576568138146),(-300075870427040466503669852366)⟩,⟨(-9057597325250325499267723926),(-9057597325250325462779436211)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-101197359941817505186596859197),(-101197359941817505162393147115)⟩,⟨(-2553112002943605009221872108),(-2553112002943604997206458886)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-4141115903659295329207574360),(-4141115903658736583802247472)⟩,⟨(-73823727229605859571378930054),(-73823727229605300838007684055)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-17461189140532450864694329802),(-17461189140530332318190264882)⟩,⟨(-216949068378070063603499374395),(-216949068378067945092417256027)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-45017575578452499126162486553),(-45017575578447106629304947627)⟩,⟨(-347069195547137515655554506297),(-347069195547132123215975943134)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-92983957671913669436832587003),(-92983957671900738343610312465)⟩,⟨(-457957889516063300590204223008),(-457957889516050369573652130743)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-161989558239793078609517989679),(-161989558239763884637116338642)⟩,⟨(-545661795915753226962377830284),(-545661795915724033083031485782)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-246392726762278626196572044173),(-246392726762219925269267652752)⟩,⟨(-607043819909378007262636866715),(-607043819909319306440838967410)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-336654312111031495758476027232),(-336654312110933860285613613583)⟩,⟨(-639010151520998415693669920802),(-639010151520900780334200955105)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-422211157485551170233040934048),(-422211157485425260913420341163)⟩,⟨(-639978026373350652534433508486),(-639978026373224743331926600135)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-492840659840108115188942007793),(-492840659839982099461049497356)⟩,⟨(-611365943648808669443253380389),(-611365943648682653832360064575)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-539487434758729518792468274035),(-539487434758631633604751764000)⟩,⟨(-557687338886625553007436615467),(-557687338886527667932635117936)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-554917481654016587596430985098),(-554917481653957632055129317249)⟩,⟨(-485899631585343200487873257597),(-485899631585284245051004373878)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-533601060733300772661184581529),(-533601060733271400039453815100)⟩,⟨(-403957034194693235530668587090),(-403957034194663863000347231167)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-471910532210147768474474572802),(-471910532210134738136313420158)⟩,⟨(-317907675655028116933960108577),(-317907675655015086670594504052)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-370499559697163422262914327789),(-370499559697157983397518468397)⟩,⟨(-229806980886018582467122452149),(-229806980886013143657208329070)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-236315155144702011750700224994),(-236315155144699875608941942757)⟩,⟨(-139369768315640944275091600847),(-139369768315638808167446713034)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-81125222257516401231741325271),(-81125222257515838905923243196)⟩,⟨(-46735382568117356684204038793),(-46735382568116794369897225595)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨23716129734598063849863837807,23716129734598063858314598023⟩,⟨(-300230148383059918434480991),(-300230148383059912627034838)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨70134277829134288323837993794,70134277829134288349501544838⟩,⟨(-4392965904525881655190306498),(-4392965904525881637335501983)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨114006460339176595250682272132,114006460339176595293866350240⟩,⟨(-17993489527068139344954974319),(-17993489527068139313865072110)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨154848719963459031520041841194,154848719963459031581173590915⟩,⟨(-43940862112461609236170057309),(-43940862112461609190108061218)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨191690035276090312348518438584,191690035276090312428411649717⟩,⟨(-80260395092348022522347808250),(-80260395092348022458766042708)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨220878281217266368050966953645,220878281217266368154359139894⟩,⟨(-121727839651693776047824454756),(-121727839651693775960702693561)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨237295108988699703920376926574,237295108988699704070016376784⟩,⟨(-163723527285353963510883126107),(-163723527285353963376405139105)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨238245076526792025259563015568,238245076526792025603892188805⟩,⟨(-203198785796037178079967268428),(-203198785796037177748200957180)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨224845884185753209106632736980,224845884185753210838199100748⟩,⟨(-236941652656762974237482782244),(-236941652656762972514553607889)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨200812797560891857327124942438,200812797560891868708502255621⟩,⟨(-260906545068623198876869007004),(-260906545068623187500002944880)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨170990621070730530233880420635,170990621070730590819971017368⟩,⟨(-270704423452275749237319965260),(-270704423452275688652266232665)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨139773936813737710169559065616,139773936813737937251274157612⟩,⟨(-262133263785461084908751216502),(-262133263785460857825843962988)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨109259525736840805179382393268,109259525736841374178650411522⟩,⟨(-232368130330932852479859202991),(-232368130330932283478244519994)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨78996595450314711555867991706,78996595450315648868254584950⟩,⟨(-182036508648965674654436962705),(-182036508648964737339516491593)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨47982220430310796905314646834,47982220430311750767176942998⟩,⟨(-115646893424365344201875600255),(-115646893424364390338122583095)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨16099496026018837736212968954,16099496026019246832795814210⟩,⟨(-39588776693897927993330830284),(-39588776693897518896053569763)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-5514145538705500175046468274367),(-5514145538705379040507015375831)⟩,⟨387033719422892725463581260060,387033719423013859227569804075⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 1) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_1 (tableDensity false) (fullFactor false 0 1) density0_contains hk0_0_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1736634492),1736634492⟩,⟨81681408993334624199613333333,81681408993334624200566666667⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_1 0 1 ha0_0_1_contains + def realAnswer : RBox := ⟨(-5514145538705500175048304908859),(-5514145538705379040505178741339)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_1 +namespace hm0_1_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-8044577239671468100461491263),(-8044577239671448898044410101)⟩,⟨8410356274423136678822575547,8410356274423155882002946202⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-23393598901598099774655992358),(-23393598901598055354143999256)⟩,⟨24668119585208954278757807206,24668119585208998701471714900⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-36380440825675548188820399409),(-36380440825675505153607608918)⟩,⟨38999235780861404134194298508,38999235780861447172811257945⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-45083256677303629275231217312),(-45083256677303603738857677741)⟩,⟨49896705434813632148068186626,49896705434813657688713269881⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-47646011371307927070157469859),(-47646011371307917216176740806)⟩,⟨56610201928544352632657458241,56610201928544362491401661512⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-43694569576217381163870861978),(-43694569576217378643124933044)⟩,⟨59722490520801610451516436373,59722490520801612977150558819⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-35235229675355510262505563201),(-35235229675355509797334014586)⟩,⟨60081775306585842238105041926,60081775306585842707964786883⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-25417013104311013861552744117),(-25417013104311013776405200826)⟩,⟨57616072825376502971253459617,57616072825376503060617198617⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16687581491358707912827506507),(-16687581491358707883000877868)⟩,⟨51772315668694549351329794002,51772315668694549384726645566⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-10106179462118728635868305830),(-10106179462118728618143925977)⟩,⟨42612865817855438936518963232,42612865817855438957124336800⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-5636607589426462167731811973),(-5636607589426462156585774433)⟩,⟨31325404428967789316817186874,31325404428967789330166811243⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2781237673035051523170627729),(-2781237673035051516765235426)⟩,⟨19945544937204174987449106344,19945544937204174995429193402⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1102591080819619648613597656),(-1102591080819619645455643481)⟩,⟨10514701449711833307177171223,10514701449711833311374560890⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-301426895610643554478124325),(-301426895610643553280079528)⟩,⟨4201671757137128419697072288,4201671757137128421519239920⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-44272655188246247961674338),(-44272655188246247680537490)⟩,⟨1016524049520344354596955858,1016524049520344355198921870⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-1814722300750830950217086),(-1814722300750830929995411)⟩,⟨69400861156345379006115038,69400861156345379123307734⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-18030240238134815655526048448),(-18030240238134768242683259582)⟩,⟨2042765188921106461173184049,2042765188921153875085596268⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-52164172929688385020637693191),(-52164172929688206582440916683)⟩,⟨6833641982855713411833282355,6833641982855891853141475235⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-80942570380134045332233714719),(-80942570380133597765129618611)⟩,⟨13607100032605765847988564955,13607100032606213419983459394⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-102261347010661267513098276662),(-102261347010660217300055984623)⟩,⟨23198709791113279272136064896,23198709791114329491453711706⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-115686333511575481117782246217),(-115686333511573176787864826260)⟩,⟨35537997844659901159126742967,35537997844662205496252176833⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-122045631492566534057023066001),(-122045631492562057199173210148)⟩,⟨49245389094501159035378134293,49245389094505635900910253747⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-122391952701190609225380566312),(-122391952701183439331782512499)⟩,⟨62012587706101338895568949091,62012587706108508796909755084⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-117531240133249269558246942903),(-117531240133240415472058474651)⟩,⟨71791755081577961747247840425,71791755081586815840844975348⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-108433061506076973246820930624),(-108433061506068534347921776220)⟩,⟨77481274081135624161734960494,77481274081144063067448950074⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-96477638111450411516877480251),(-96477638111444191937973029771)⟩,⟨78684814826415413602024297995,78684814826421633187033384560⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-83092863690304148776421311476),(-83092863690300602739726935438)⟩,⟨75262739141601655662721501986,75262739141605201704699486114⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-69131990589138145058499084630),(-69131990589136472231956772603)⟩,⟨67260052968993972032211587433,67260052968995644863116927125⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-54669696185731847247504367185),(-54669696185731142074930923047)⟩,⟨55284814912192531067653028778,55284814912193236243601925538⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-39551176201044701244008230724),(-39551176201044419527489425017)⟩,⟨40627943745325942935463333061,40627943745326224654361853487⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-23896657829554782615159392283),(-23896657829554675564563311614)⟩,⟨24658953995355337910239646584,24658953995355444962245331958⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-7983452321984170885536683080),(-7983452321984143240595985003)⟩,⟨8244998509061611147270383787,8244998509061638792679640019⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-23768247806901485930386209585),(-23768247806901485920011815894)⟩,⟨(-15154613558889562626696269853),(-15154613558889562616983721787)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-70763581262446573910553768402),(-70763581262446573879217037379)⟩,⟨(-44219894068072941785176525974),(-44219894068072941755865910313)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-115380050004791500407307227353),(-115380050004791500355071369991)⟩,⟨(-69680317673690328668147833784),(-69680317673690328619106281076)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-154452989973304351658953682033),(-154452989973304351586544627539)⟩,⟨(-89169636373565932438385217325),(-89169636373565932370039072118)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-184659583579566664947769980831),(-184659583579566664856782675305)⟩,⟨(-99708526977325479191455982500),(-99708526977325479104947945212)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-204883594279299636810435907947),(-204883594279299636700392165515)⟩,⟨(-98722403135244775666981651342),(-98722403135244775561726536992)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-216516027446345447427921228078),(-216516027446345447290670778243)⟩,⟨(-86545849213628747517698957577),(-86545849213628747385582589321)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-221216405732504779315605927265),(-221216405732504779087509862524)⟩,⟨(-67039486545305018664749798368),(-67039486545305018441639427527)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-219290481845380748312535695487),(-219290481845380747498084203573)⟩,⟨(-45590583314060044427475342944),(-45590583314060043617028188519)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-209816054566208851343368311959),(-209816054566208846679694462928)⟩,⟨(-26829694002790742471150839611),(-26829694002790737810289546432)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-191599258800845442292172802724),(-191599258800845418822968175383)⟩,⟨(-13205139921182985266637046697),(-13205139921182961799256691305)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-164512930496536567964855627612),(-164512930496536483239337018291)⟩,⟨(-4587692118445228973395450774),(-4587692118445144249172704246)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-130601472957529566534013209701),(-130601472957529360467739626547)⟩,⟨588428141896361479923470986,588428141896567545287070101⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-93388331218505769235373733649),(-93388331218505437702043846890)⟩,⟨3309437235342915809172844357,3309437235343247341970264869⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-55677496732681585809039487258),(-55677496732681254148825567108)⟩,⟨3530806506316687908947303754,3530806506317019568911514753⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-18460187875121386301628125459),(-18460187875121245460110856886)⟩,⟨1488644827768640648007828186,1488644827768781489467452129⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-17434379135692652289114507633),(-17434379135692525963316508816)⟩,⟨(-26678969652342407395117353152),(-26678969652342281067632907610)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-51475869787574104829827247322),(-51475869787573810368811582761)⟩,⟨(-77848119548140106543981090221),(-77848119548139812077995916025)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-83347360133025089611115118902),(-83347360133024799462298474022)⟩,⟨(-122554014727040243797546994522),(-122554014727039953640785316705)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-112711693968657846140226313394),(-112711693968657668835504572466)⟩,⟨(-157405608696167062314791923083),(-157405608696166884999612259453)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-140083258403980094612403358439),(-140083258403980022970894689175)⟩,⟨(-181008166863063714196016655658),(-181008166863063642542175406977)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-165341866801792330698718244270),(-165341866801792311125297710103)⟩,⟨(-194503119616867774529940581946),(-194503119616867754942940540724)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-186429219125419859164885964486),(-186429219125419855281381556986)⟩,⟨(-199957585920306328035041789143),(-199957585920306324137273404984)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-200472096698781598133365606054),(-200472096698781597438949785098)⟩,⟨(-198343787917226322843298982996),(-198343787917226322134642070168)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-205742946558459795114961161412),(-205742946558459794914592044092)⟩,⟨(-189672679442792721416842625313),(-189672679442792721202848086561)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-202103543653557865361017134773),(-202103543653557865243545687358)⟩,⟨(-174272125551145457638184511854),(-174272125551145457508212327040)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-190187573718093436455427970723),(-190187573718093436365880632479)⟩,⟨(-153439459757116385427475790932),(-153439459757116385327001701217)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-170447185144691524944805113325),(-170447185144691524874667068622)⟩,⟨(-129036576823831209540815848064),(-129036576823831209461523260770)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-142999774904395092319964527607),(-142999774904395092266942305344)⟩,⟨(-102525808542443543603624037522),(-102525808542443543543365453879)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-108294019177718925945721441256),(-108294019177718925908982469166)⟩,⟨(-74554815693705473431372385387),(-74554815693705473389429736913)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-67603963166575155811162205029),(-67603963166575155789733873823)⟩,⟨(-45356198935900679213742641264),(-45356198935900679189183236439)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-22982104169730807522018134059),(-22982104169730807515006188802)⟩,⟨(-15231510713195048474914351360),(-15231510713195048466862590962)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2599692024252602916228676927),(-2599692024252143719230428515)⟩,⟨(-24154187939879389363659104359),(-24154187939878930164390023085)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-8916564709790916045456234244),(-8916564709789174818907162570)⟩,⟨(-72435318669843029326884244300),(-72435318669841288093501224235)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-17977281635318273387542311920),(-17977281635313840711229881901)⟩,⟨(-119929626119877241040323396063),(-119929626119872808352807255880)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-30414895901484275026906044184),(-30414895901473643844939356078)⟩,⟨(-164305637585766751058691710485),(-164305637585756119861466302903)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-46801766907936126433514250495),(-46801766907912121922472722789)⟩,⟨(-202007371987499545793855619869),(-202007371987475541264090347085)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-68043756928415414902023632524),(-68043756928367148650326796958)⟩,⟨(-230486246114920611670377876984),(-230486246114872345397060870557)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-93676007451171363441059769254),(-93676007451091100874845634588)⟩,⟨(-249780821018986986861605361622),(-249780821018906724271386702972)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-120322169344718129898174960563),(-120322169344614675119522746386)⟩,⟨(-261336959593817004525754087275),(-261336959593713549721888359106)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-142462042344963988441884267141),(-142462042344860528683946170030)⟩,⟨(-265943283751435393842806988918),(-265943283751331934060181193861)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-154463404461239702469761392795),(-154463404461159423771472647750)⟩,⟨(-262732633283384382421737888751),(-262732633283304103700820332416)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-152725388571834157664205137702),(-152725388571785867634883513892)⟩,⟨(-249267303451634490707334735259),(-249267303451586200658181156887)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-137500788127026662890816141422),(-137500788127002636334069195229)⟩,⟨(-222912557895564209620066590866),(-222912557895540183046438971579)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-112783649641619256829103782111),(-112783649641608611673542903157)⟩,⟨(-183553372997662358616920648938),(-183553372997651713447789977177)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-83147709686845154827195001569),(-83147709686840716240155421648)⟩,⟨(-134840717904080924590289537431),(-134840717904076485993431159049)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-51000465135556125699749183313),(-51000465135554383719371013647)⟩,⟨(-81684823953532913348005188347),(-81684823953531171361706338063)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-17212518116296309424927272901),(-17212518116295851033645300245)⟩,⟨(-27270309665478974754744539371),(-27270309665478516361504207281)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨704120125717129529763482231,704120125717129535523030066⟩,⟨(-42490910062489172520297682),(-42490910062489168615929804)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1954074387483127127151638392,1954074387483127144774598634⟩,⟨(-634389465563060450523401006),(-634389465563060438470285535)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2094395210597787176823362334,2094395210597787206875930875⟩,⟨(-2845303965321372913503823498),(-2845303965321372892353296932)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-944037665686898088689956248),(-944037665686898045364531376)⟩,⟨(-8584397038650352182469343722),(-8584397038650352150792780808)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-8645973032739577384187647102),(-8645973032739577326173668484)⟩,⟨(-21299212324958576657638890526),(-21299212324958576613190865565)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-19081674219690164980080786065),(-19081674219690164902339238502)⟩,⟨(-44154805499847175394809391313),(-44154805499847175332057405138)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-27386537448536676512615186303),(-27386537448536676394447094756)⟩,⟨(-76101887699823209571034994945),(-76101887699823209468912063621)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-29808588349263652145630291593),(-29808588349263651861772888264)⟩,⟨(-111110375917407647411557917837),(-111110375917407647143725681466)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-26100278669534418302201943215),(-26100278669534416871195870287)⟩,⟨(-141375541978450149024065800497),(-141375541978450147607702553123)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-18861773196327371812586874742),(-18861773196327362481221244927)⟩,⟨(-160508945991790598964156698570),(-160508945991790589645367768512)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-11808076139162825994725931146),(-11808076139162776479040552799)⟩,⟨(-165229581429397161572766129480),(-165229581429397112067438722868)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-7724902606283467366030934894),(-7724902606283281888262528098)⟩,⟨(-155819108999265938674801134748),(-155819108999265753205535460905)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-6681548817658419198955035498),(-6681548817657954323838641161)⟩,⟨(-134832865026729662222432101670),(-134832865026729197353991768505)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-6426781151923982534154458276),(-6426781151923216406512439532)⟩,⟨(-104632733494304314375955765040),(-104632733494303548253033026837)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-4921415331287298100725015129),(-4921415331286518162335887964)⟩,⟨(-66661493704541817948597081687),(-66661493704541038012990681344)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1851758409400343908783070930),(-1851758409400009339963078609)⟩,⟨(-22937159161774749889538843517),(-22937159161774415321617198313)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1210671473200344404373407553490),(-1210671473200244910124091309388)⟩,⟨(-909016267934022131714716172403),(-909016267933922637413893521025)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 1) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_1 (tableDensity true) (fullFactor false 0 1) density1_contains hk0_0_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-2270983567),2270983567⟩,⟨(-106814150222052970108433333334),(-106814150222052970107186666666)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_1 0 1 ha0_0_1_contains + def realAnswer : RBox := ⟨(-1210671473200344404375778537057),(-1210671473200244910121720325821)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_1 +namespace hm0_0_0_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-14318731600952115089357721167),(-14318731600952108981626892419)⟩,⟨(-10458297739003870857711598150),(-10458297739003864749151359463)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-41207181677396980722307801807),(-41207181677396966846891135798)⟩,⟨(-29336170734700820660380164267),(-29336170734700806782638486112)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-63103755839561751785873598305),(-63103755839561738823700705721)⟩,⟨(-42710466898127129790069734857),(-42710466898127116824519191084)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-77562575544095251970597457335),(-77562575544095244691997656910)⟩,⟨(-48819128736168018058148890417),(-48819128736168010775724311865)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-83171556319456727266293625426),(-83171556319456724659559707359)⟩,⟨(-47889619721775435356235103986),(-47889619721775432745834458266)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-79837518806412670094422078828),(-79837518806412669486674378780)⟩,⟨(-41592290932789793925109533276),(-41592290932789793314324850936)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-69099896036596194331557661921),(-69099896036596194229307184263)⟩,⟨(-32241500999071449505010530134),(-32241500999071449400606559937)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-53888493522031903883485803172),(-53888493522031903864816412780)⟩,⟨(-22227194770668957989753775231),(-22227194770668957969811552951)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-37606845685822591846926892246),(-37606845685822591839993183381)⟩,⟨(-13490999846300700483198861548),(-13490999846300700475697895073)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-23145878659582834582358244453),(-23145878659582834578565585299)⟩,⟨(-7093811051920604355079048225),(-7093811051920604351179771376)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-12248511092491464577797190237),(-12248511092491464575766898337)⟩,⟨(-3153605475596640788781806964),(-3153605475596640786868110548)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-5336505663866242876648026257),(-5336505663866242875683540889)⟩,⟨(-1142185326311689861995787977),(-1142185326311689861199836710)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1771640899478439667149630561),(-1771640899478439666764401074)⟩,⟨(-316424404665955388588283181),(-316424404665955388328642601)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-385432766551544268177509531),(-385432766551544268058441414)⟩,⟨(-58811085751125627958662958),(-58811085751125627900080541)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-38961100198502645343292652),(-38961100198502645319978130)⟩,⟨(-5289184455624255717488311),(-5289184455624255710336853)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-639160499563254678880413),(-639160499563254677489356)⟩,⟨(-80967596728582977619515),(-80967596728582977379029)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-34735666066063220112594047935),(-34735666066063190038828999997)⟩,⟨(-49865076537250711146070257364),(-49865076537250681067734106544)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-101816716013671933671005587459),(-101816716013671821649249042352)⟩,⟨(-144585067780582062038151429977),(-144585067780581950003156775974)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-161763750071341194527583285792),(-161763750071340919202305144762)⟩,⟨(-224895733904721075999606717648),(-224895733904720800653845834158)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-210410615206506067240745343643),(-210410615206505440162165504769)⟩,⟨(-283655758796925713487082840666),(-283655758796925086382859529162)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-244670946166135652758429837610),(-244670946166134328864041262383)⟩,⟨(-316927301223890001224364104049),(-316927301223888677301603789902)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-263093993518360051039582887245),(-263093993518357595841137066456)⟩,⟨(-324561051170663791036122998140),(-324561051170661335808922317725)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-265923584305721479751700770312),(-265923584305717753051658268017)⟩,⟨(-310064025834562606728017888924),(-310064025834558880000836683480)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-254724341796704635772355483704),(-254724341796700298365314724594)⟩,⟨(-279401269323597647764053903313),(-279401269323593310332922415298)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-232123364537599610381371551970),(-232123364537595732697987790900)⟩,⟨(-239233708472809182325240586855),(-239233708472805304621594066716)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-201582540037612940967868355372),(-201582540037610266132768729312)⟩,⟨(-195536681083095807898442864705),(-195536681083093133047116788194)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-166901669026749807011000389104),(-166901669026748380607841867928)⟩,⟨(-152874118778233559349582785284),(-152874118778232132934011515746)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-131522194972877268024046416581),(-131522194972876637292991589574)⟩,⟨(-114204357529040188035742015424),(-114204357529039557295606779469)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-97859422235373104770060595053),(-97859422235372854147513759005)⟩,⟨(-80969424153284703218332739467),(-80969424153284452589472146857)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-67000105258393394193896552638),(-67000105258393298913500142076)⟩,⟨(-53243999762013713714497925519),(-53243999762013618430017786436)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-38894805141347579916507702468),(-38894805141347544991417505587)⟩,⟨(-30025982104481830275629235793),(-30025982104481795348264631423)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-12729001055837137398637822756),(-12729001055837128549501898287)⟩,⟨(-9679351668795320477890092481),(-9679351668795311628025582463)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1565697928251748215465233436,1565697928251748226767771831⟩,⟨(-97893254315734443876349799412),(-97893254315734443853566937869)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨708813372164746340933002783,708813372164746374570118553⟩,⟨(-287625603577529628669950029859),(-287625603577529628602487156634)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-10906100489129307426323072429),(-10906100489129307371386304724)⟩,⟨(-459794955323208534251718622872),(-459794955323208534143055251877)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-36438676647227703641726339257),(-36438676647227703567551875145)⟩,⟨(-605250874243099604042990015418),(-605250874243099603898919742908)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-73962437586354452013403221073),(-73962437586354451922954384992)⟩,⟨(-717009962017895678961310799552),(-717009962017895678789621703792)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-117573775379783248630149513328),(-117573775379783248523901293160)⟩,⟨(-789629173230290492733052832817),(-789629173230290492540252343632)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-160410149494971111180592737958),(-160410149494971111053553888779)⟩,⟨(-820012723588172505168954664727),(-820012723588172504955305615704)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-196580520367764995587692976902),(-196580520367764995391568528286)⟩,⟨(-809165115167981231974124939589),(-809165115167981231696063134881)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-221579958981374629737240568632),(-221579958981374629093029883668)⟩,⟨(-762385709858859147092049067881),(-762385709858859146374351431938)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-232516797366139768893760285103),(-232516797366139765384583858459)⟩,⟨(-687834261364232445724533322762),(-687834261364232442152415257991)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-228203378427225996457539193865),(-228203378427225979465430664745)⟩,⟨(-594653193764540197931751707496),(-594653193764540180887988482780)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-208870695238622721232154615739),(-208870695238622662028914507877)⟩,⟨(-491086127497478966998412137363),(-491086127497478907754376865174)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-176005816170765264105621783278),(-176005816170765124568045166145)⟩,⟨(-382943573029094443568706183677),(-382943573029094304000530994203)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-132459049531190704595337266360),(-132459049531190485750444922032)⟩,⟨(-273348729763421583012677813565),(-273348729763421364146665751372)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-81892397454042788646680359999),(-81892397454042573622563003880)⟩,⟨(-163706350574105789820082484684),(-163706350574105574783620216694)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-27654394917040369354488940273),(-27654394917040278890239562245)⟩,⟨(-54473356689812119485901849685),(-54473356689812029017609802472)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨34314799134014393478031582325,34314799134014550730739617992⟩,⟨(-93632556606404534462089235780),(-93632556606404377192229876399)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨99321189921805388168640045255,99321189921805753286353552066⟩,⟨(-277827288139583002467143081380),(-277827288139582637299055388610)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨154067086489621387965243092905,154067086489621744984710765374⟩,⟨(-452092834997426935182857763985),(-452092834997426578083025785565)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨193641034751768828845510208957,193641034751769044592464612772⟩,⟨(-608698175442843628907612668093),(-608698175442843413055292251692)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨214821358017174650754662293915,214821358017174736694430071530⟩,⟨(-739390520045020418015275749324),(-739390520045020331951372719400)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨216231837836793207947011862725,216231837836793231041271090138⟩,⟨(-837471759934055944515067345119),(-837471759934055921284776137685)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨199705454386579695922346335828,199705454386579700438292603655⟩,⟨(-899352946098271136270949561784),(-899352946098271131613979467533)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨170704991604359007770651339342,170704991604359008589870834036⟩,⟨(-923704292762631229712191377003),(-923704292762631228753391539371)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨136176581364787856335376998411,136176581364787856592548173783⟩,⟨(-910354501662100214875844340863),(-910354501662100214486166029451)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨102030157828071389203599305486,102030157828071389363692080094⟩,⟨(-860571835276213355141956910959),(-860571835276213354861038424228)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨71925086303913679772110830305,71925086303913679895278002450⟩,⟨(-777699165994546701422967440216),(-777699165994546701194117806561)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨47376934444060571696539210878,47376934444060571792515758008⟩,⟨(-667261263192302822195567560110),(-667261263192302822011300407531)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨28676003678064714886913297449,28676003678064714958879522395⟩,⟨(-536143639446574996851594396862),(-536143639446574996710089966658)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨15553968593158301966226469231,15553968593158302015859749772⟩,⟨(-391077539579164995546518405679),(-391077539579164995446914936713)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨7171690210598973401487998282,7171690210598973430412481538⟩,⟨(-237550960500380628956969085207),(-237550960500380628897990685592)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨2008468418259853833407945157,2008468418259853842870768087⟩,⟨(-79607293819595528112709212785),(-79607293819595528093240771442)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨96542404077840207348141617840,96542404077840938012605797468⟩,⟨(-5415325473711161273781374777),(-5415325473710430593870316713)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨282634071012059966544974263638,282634071012062725992905158654⟩,⟨(-22742916581000133849024352120),(-22742916580997374355782249188)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨448762097680963853522880536769,448762097680970823052744958291⟩,⟨(-58186388592386214536992308014),(-58186388592379244934340702967)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨585649195609130611553628786661,585649195609147137082270238119⟩,⟨(-118857977222757798780516700447),(-118857977222741273155384953855)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨687959290655789833924310737342,687959290655826610805906237464⟩,⟨(-204140894327133409927136052280),(-204140894327096632929877035115)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨752466197747035357127521621400,752466197747108060644176554547⟩,⟨(-305286311807418348050287452507),(-305286311807345644404441789371)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨777024871234906995236165106851,777024871235025644144886852383⟩,⟨(-409200062980270601460725788228),(-409200062980151952415477850096)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨762184929427838401366661182586,762184929427988318255827035407⟩,⟨(-502644821514264740455824020023),(-502644821514114823428183996812)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨712506560369837734988106401506,712506560369984608214848190801⟩,⟨(-574173392857316760879132767516),(-574173392857169887516599312094)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨635983583240039606113851171129,635983583240151289654969587220⟩,⟨(-615036192665202864865303321591),(-615036192665091181195516863018)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨542649319174362742094344965041,542649319174428633497035985947⟩,⟨(-619563708911862508441450598409),(-619563708911796616921805810247)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨442548591673583314914374536944,442548591673615520289405342037⟩,⟨(-584461117996589697185708481538),(-584461117996557491709906197873)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨342527315481019098523196562351,342527315481033147973071608709⟩,⟨(-508392721550305576652309280812),(-508392721550291527121082530284)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨244337338306681967884019916820,244337338306687753315870299077⟩,⟨(-393901255189076399685646487371),(-393901255189070614194099511618)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨146817869872139173791266910109,146817869872141424511028987953⟩,⟨(-248938876469540985389349359598),(-248938876469538734633160397720)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨48999888880867693548712607607,48999888880868283124102751256⟩,⟨(-85055854335286073119912905161),(-85055854335285483532279487732)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨471098525073870270235595998,471098525073870279352099183⟩,⟨37223438568316223269342097799,37223438568316223282724533286⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨6869834153705196463947412673,6869834153705196491903766423⟩,⟨109729283814425229113521254827,109729283814425229154025003455⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨27962825824511263177676625802,27962825824511263226103093065⟩,⟨177255165650838674521567225942,177255165650838674589283300698⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨67666184904692874069817598728,67666184904692874140997926962⟩,⟨238556736127766784786134650948,238556736127766784881098423533⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨122155183165395245506808187474,122155183165395245604012477255⟩,⟨291850754705833965942093844844,291850754705833966064708284535⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨182695124682294569419003195484,182695124682294569550398681061⟩,⟨331605125883492873264840541904,331605125883492873421187620215⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨241872079168662037606348252014,241872079168662037805800347612⟩,⟨350664859273931159255685115630,350664859273931159477937209381⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨295109117217828662931024660411,295109117217828663413223640183⟩,⟨346114461828310145942692047328,346114461828310146443337824460⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨338073391993657517134809742973,338073391993657519588435729653⟩,⟨320916045305699023782314301738,320916045305699026248207965256⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨365744230536944000164935900390,365744230536944016075750841034⟩,⟨281588140633400223261856486230,281588140633400239178668520267⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨373106540359961976581728936301,373106540359962059919330952870⟩,⟨235733202870634884222506659750,235733202870634967560977082907⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨355742612049950061552093060349,355742612049950369283835773916⟩,⟨189722523932179977322056320760,189722523932180285051481480385⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨311165838896733558479886739668,311165838896734319745192806085⟩,⟨146325267454047954514202882892,146325267454048715775652217034⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨241192127924320871302083332140,241192127924322112635563955237⟩,⟨104672558665053718748564361730,104672558665054960078083974366⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨152101200608862141636726162343,152101200608863395971694268686⟩,⟨63108136180202077146299064095,63108136180203331478381763162⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨51871239602716390643850606352,51871239602716926654712483301⟩,⟨21094415230204699212537676089,21094415230205235222351106759⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1230977053417655379004036178034,1230977053417790787229616211650⟩,⟨(-3734891004308535167733718733168),(-3734891004308399758833829858705)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 2) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_2 (tableDensity false) (fullFactor false 0 2) density0_contains hk0_0_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-42768285738053887349390665151),(-42768285738053887347303251364)⟩,⟨(-74076843850932732832874242918),(-74076843850932732828672223342)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_2 0 2 ha0_0_2_contains + def realAnswer : RBox := ⟨1188208767679601491654545512883,1188208767679736899882412960286⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_2 +namespace hm0_1_0_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2191273484716173190859605314),(-2191273484716168187087274607)⟩,⟨(-2095979422743120960972657136),(-2095979422743115957399506078)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-6304489183833610692207642822),(-6304489183833599328878854341)⟩,⟨(-5978936618319476042046707225),(-5978936618319464679281784122)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-9587077525952848358721566578),(-9587077525952837751160533692)⟩,⟨(-8944091576575532049432639469),(-8944091576575521442710842201)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-11560383865299808083192750842),(-11560383865299802133716211015)⟩,⟨(-10447970162296159486301459558),(-10447970162296153537819171679)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-12096006164273217657212289698),(-12096006164273215530502053121)⟩,⟨(-10188564106389082350588574125),(-10188564106389080224905351641)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-11493888071207831001374495897),(-11493888071207830507959043636)⟩,⟨(-8424219244923862125049019941),(-8424219244923861632591601365)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-10145978530514038805812042161),(-10145978530514038724790987127)⟩,⟨(-5968810548803776389860496992),(-5968810548803776309660152952)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-8288626737825353202872910317),(-8288626737825353189711112698)⟩,⟨(-3673023517714134185117073818),(-3673023517714134172602004504)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-6129928488697753360367261855),(-6129928488697753356312778580)⟩,⟨(-1987026181082489032507049621),(-1987026181082489028922029271)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3982889173488871924335432100),(-3982889173488871922342470563)⟩,⟨(-950616241154381613932192037),(-950616241154381612254335853)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2192701715528412882723543499),(-2192701715528412881740008865)⟩,⟨(-397279983514705014080728952),(-397279983514705013289668934)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-974879562695743450464286343),(-974879562695743450042252410)⟩,⟨(-137112929154487905346712898),(-137112929154487905028249738)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-324926340689040507785940400),(-324926340689040507639111760)⟩,⟨(-34548878369746000139287680),(-34548878369746000039630603)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-70414477337246135069736698),(-70414477337246135032367684)⟩,⟨(-5181433977276057342650863),(-5181433977276057322012820)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7087184312013810953096189),(-7087184312013810947349506)⟩,⟨(-321779215431320181531762),(-321779215431320179493956)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-116012323927406500287623),(-116012323927406500011170)⟩,⟨(-3116406505413210547368),(-3116406505413210511164)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1066996910050945343430005811),(-1066996910050920578294000125)⟩,⟨(-9418018337940943340479155872),(-9418018337940918575875153839)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-3534737768895149789750377246),(-3534737768895057508959495225)⟩,⟨(-26988868454618006699492235029),(-26988868454617914420234675976)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-6903682446903541306813367932),(-6903682446903314350910818655)⟩,⟨(-41090040448311433766065319941),(-41090040448311206812529810297)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-11438749793941129624077652327),(-11438749793940612275014970799)⟩,⟨(-50465536443413561516631409491),(-50465536443413044170526025924)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16880077959084318441781076819),(-16880077959083225265860734727)⟩,⟨(-55005445915294024764540835353),(-55005445915292931591901586801)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-22346760056624091456586159383),(-22346760056622062489259066765)⟩,⟨(-55440098616268647785933895032),(-55440098616266618821958406843)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-26681298253482850457825817414),(-26681298253479768048523430880)⟩,⟨(-52711343040410466897542305711),(-52711343040407384491455324189)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-29095548229965933306338107538),(-29095548229962344073971449828)⟩,⟨(-47675244222563072379691636061),(-47675244222559483150236025574)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-29426908084066345405768786131),(-29426908084063136704399179409)⟩,⟨(-41215470473878306417195726224),(-41215470473875097718349889118)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-27916576121495210279619713025),(-27916576121492998106048867158)⟩,⟨(-34252881021964121825499108713),(-34252881021961909654055599538)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-24929698283728038958183445446),(-24929698283726860423585574140)⟩,⟨(-27537233728518687435037015560),(-27537233728517508902172112306)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-20853238659866051968009589981),(-20853238659865531495047725322)⟩,⟨(-21439751698464463643827249534),(-21439751698463943172213916358)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16143511813014597856644220956),(-16143511813014391323708324430)⟩,⟨(-15965716872400277052177946162),(-15965716872400070520229456323)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-11287432807248740582250687347),(-11287432807248662159956402920)⟩,⟨(-10988604224668807021185615957),(-10988604224668728599555279356)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-6609708823320067578688050812),(-6609708823320038859580972743)⟩,⟨(-6405405359022239882154202232),(-6405405359022211163426927107)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-2168896820958266756039667939),(-2168896820958259482958526061)⟩,⟨(-2100095822607327159549070942),(-2100095822607319886591856355)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨11883402174758546997784444575,11883402174758547005438388406⟩,⟨(-18637679578114797017729603618),(-18637679578114797009535129755)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨34455024280708517366536909353,34455024280708517389485565434⟩,⟨(-55135940723657992440107643623),(-55135940723657992415513416396)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨53613886595080839868147101192,53613886595080839906055207642⟩,⟨(-88771908566317397247693077361),(-88771908566317397207210544989)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨67348689808308138410518555919,67348689808308138462361771343⟩,⟨(-116645410166634850703456535033),(-116645410166634850648375128806)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨73517517239348414989234202012,73517517239348415053260832109⟩,⟨(-136128005626466318104187620103),(-136128005626466318036634325444)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨70708865580128145112030085234,70708865580128145187635436738⟩,⟨(-146689060765357561969872240379),(-146689060765357561890547258104)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨59961709793076573915426243788,59961709793076574007073924327⟩,⟨(-149907233230927527297793875846),(-149907233230927527202226481154)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨44781547992605144359805047335,44781547992605144508500130745⟩,⟨(-147616440252282444957741998199),(-147616440252282444805271406647)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨29299060100426676288651559537,29299060100426676806176712809⟩,⟨(-140727777915106774374566563487),(-140727777915106773853950667822)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨16575598280580267998343973356,16575598280580270856183661623⟩,⟨(-129392270602698779820722084287),(-129392270602698776960582370385)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨7849699641907390918460878967,7849699641907404768920346144⟩,⟨(-113640407228539737306673558748),(-113640407228539723454567080492)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2633158448170179473388459442,2633158448170227749173804984⟩,⟨(-94085030860312453882547225479),(-94085030860312405605500384267)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-320400071840937727563649633),(-320400071840823869867779207)⟩,⟨(-72333417408183590770827005563),(-72333417408183476912197776340)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1783046306863531512809822875),(-1783046306863352825856041034)⟩,⟨(-50396701428444895411965960744),(-50396701428444716724421687187)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1869969767679882208931698242),(-1869969767679706557104490778)⟩,⟨(-29500853513679963946478442545),(-29500853513679788294341903558)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-781288754124494348546462491),(-781288754124420430587593250)⟩,⟨(-9688945716917534073023698429),(-9688945716917460154976855246)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨27904695373643920365271660516,27904695373644052499739387730⟩,⟨(-18235356088877698585297178506),(-18235356088877566452624227566)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨81037900850564204868143084903,81037900850564511463465973414⟩,⟨(-53584467656019381483771688905),(-53584467656019074893710328484)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨126380984322265737461467581754,126380984322266036857324277539⟩,⟨(-85946803822556255165663474947),(-85946803822555955778132447010)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨160092853112985404811377029992,160092853112985585369799565114⟩,⟨(-114625989584871133332612152208),(-114625989584870952784978974226)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨180834748045747217158671613259,180834748045747288886403229130⟩,⟨(-139928499755007426584817359744),(-139928499755007354869548502058)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨190188363677517950921127344805,190188363677517970129037350304⟩,⟨(-161644051530180957283692558198),(-161644051530180938089164167279)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨190802763338507527472146813915,190802763338507531205458479395⟩,⟨(-177860553288465448181223581709),(-177860553288465444461571545658)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨184293634121117749380604297933,184293634121117750041983693232⟩,⟨(-186239373591094242888712355009),(-186239373591094242240557270506)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨171392815923164985844122542448,171392815923164986038524686045⟩,⟨(-185884725935880605377914833495),(-185884725935880605195763325094)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨153111344568406996347773861042,153111344568406996462698516848⟩,⟨(-177535867047284624536583627290),(-177535867047284624432533008423)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨131186448243236057813815604997,131186448243236057900346885654⟩,⟨(-162581376943820370568334757041),(-162581376943820370490998337827)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨107579882132906701515679146748,107579882132906701582319995842⟩,⟨(-142087648751856087191565926190),(-142087648751856087132388742843)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨83623415067473212385894068683,83623415067473212435471754830⟩,⟨(-116626023107801071587742478245),(-116626023107801071543899254830)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨59750085014598781296943194499,59750085014598781330871818958⟩,⟨(-86785919207993167550101406466),(-86785919207993167520201564326)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨35905807172781508198128113733,35905807172781508217762566108⟩,⟨(-53517257512907400032088162062),(-53517257512907400014838365193)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨11981932583693236845700265348,11981932583693236852098729911⟩,⟨(-18078941363450473972204056927),(-18078941363450473966590758109)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨31587397121844303386245220129,31587397121844903888234718232⟩,⟨(-3399679628212877424665022677),(-3399679628212276925735065686)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨94365032628904343455559521110,94365032628906611483201972725⟩,⟨(-11615053978270566894523386960),(-11615053978268298876049814452)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨155064944769976408968410824291,155064944769982138052681626918⟩,⟨(-23240262026230789270475178348),(-23240262026225060201120564060)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨210110640619285078382628063449,210110640619298664794344805977⟩,⟨(-38885080933108590272421495508),(-38885080933095003880788185822)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨254677701848006121255961223904,254677701848036360869474482098⟩,⟨(-58986523812282204854531772011),(-58986523812251965265293447287)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨285690327723474030805350272339,285690327723533810687432167975⟩,⟨(-84309430065872157191416525472),(-84309430065812377336847492978)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨303711231008778644185360905874,303711231008876181328862337626⟩,⟨(-113858148780908172264698989779),(-113858148780810635151082400462)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨311210928954828673076681792788,311210928954951854224581842262⟩,⟨(-143238447289824170240935875182),(-143238447289700989123705655863)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨309898171136390974295895522929,309898171136511558549266227379⟩,⟨(-165971032950460181408672987259),(-165971032950339597184647772459)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨299573062408056152229702236443,299573062408147747714876009516⟩,⟨(-176101740436277875554566167752),(-176101740436186280095711913928)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨278341211223059254469904448246,278341211223113225846926461202⟩,⟨(-170533166123759317497051323625),(-170533166123705346142642369744)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨244185856410285037488356203827,244185856410311381365040331164⟩,⟨(-150623656763192687907943165490),(-150623656763166344050172493120)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨197761001363821694950080895510,197761001363833172767192277042⟩,⟨(-121513780332278561250668159225),(-121513780332267083448529841433)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨143365894972419827145165042216,143365894972424548622797090288⟩,⟨(-88403851264981792600239246022),(-88403851264977071133306910931)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨86050422023064993739394056265,86050422023066829191782318803⟩,⟨(-53725710089854917739354439411),(-53725710089853082293358580690)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨28591676313753845490780145227,28591676313754326106956937425⟩,⟨(-18046517155915837986516263251),(-18046517155915357372443696489)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨66673516043862762917888003,66673516043862769046148042⟩,⟨1105146805186070002675129694,1105146805186070011718456009⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨992061124752092240489572675,992061124752092259350116305⟩,⟨3057443423084247429877156816,3057443423084247457458690818⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨4421365235368204853959744127,4421365235368204886856691900⟩,⟨3258142488307733852397064081,3258142488307733899131194491⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨13216383632065676019671182549,13216383632065676068510623532⟩,⟨(-1447458303302539038777316066),(-1447458303302538972027747869)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨32405753024384038407983943882,32405753024384038475755559447⟩,⟨(-13149951889782874493349413649),(-13149951889782874404989541870)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨66245695347510114551633810939,66245695347510114646042773841⟩,⟨(-28631804671166226295769801647),(-28631804671166226178985788279)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨112394775150861245836743103271,112394775150861245987938604079⟩,⟨(-40461047317069119059972090643),(-40461047317069118885324788283)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨161338592332780995840278319673,161338592332780996229243329407⟩,⟨(-43305082861083386876775375634),(-43305082861083386464967262692)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨201700794823130167190830487698,201700794823130169207580960241⟩,⟨(-37260348690768913111464761147),(-37260348690768911074447247375)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨225002098487941328144597995880,225002098487941341176912767668⟩,⟨(-26459400047534600891915380937),(-26459400047534587842754342775)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨227739238554430646614084155103,227739238554430714710794513884⟩,⟨(-16286003441769595907070059580),(-16286003441769527796950350986)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨211470469894369540878638917585,211470469894369792217246418670⟩,⟨(-10486379203250503162022881601),(-10486379203250251812723922800)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨180558884619020240396695629573,180558884619020862341994668456⟩,⟨(-8945945586454293693064281837),(-8945945586453671739569182854)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨138634949722743497597823630185,138634949722744512212496318498⟩,⟨(-8513808261932656509532187337),(-8513808261931641889182101097)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨87674334889409252805179730514,87674334889410278423571746734⟩,⟨(-6472306711871505857156420558),(-6472306711870480235468293951)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨30053422707756191785204882220,30053422707756630145527098030⟩,⟨(-2426250500184676602760268691),(-2426250500184238241385386265)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1158234605470062748709548634335,1158234605470173935762039128919⟩,⟨(-932878419265619509625697612396),(-932878419265508322608964241663)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 2) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_2 (tableDensity true) (fullFactor false 0 2) density1_contains hk0_0_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨55927758272839698838781174861,55927758272839698841510869813⟩,⟨96869718881988958314417522832,96869718881988958319912471508⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_2 0 2 ha0_0_2_contains + def realAnswer : RBox := ⟨1214162363742902447548229809196,1214162363743013634603649998732⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_2 +namespace hm0_0_0_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1816602878482637166742032822,1816602878482638227892651292⟩,⟨(-2487133261938961198301536744),(-2487133261938960137292831594)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨4999138014208683411833133942,4999138014208685778624327189⟩,⟨(-7021404322592886134438238421),(-7021404322592883768036493875)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨7002438242748442038634690098,7002438242748444169438147349⟩,⟨(-10343286459826307835781499764),(-10343286459826305705519789823)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨7546118323529468843830585439,7546118323529469975193720492⟩,⟨(-11983299898220684447919024606),(-11983299898220683317129307174)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨6830561587752131746790731119,6830561587752132122447440938⟩,⟨(-11854119983216427346681766785),(-11854119983216426971524911253)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨5348238049054245867756675901,5348238049054245947390978922⟩,⟨(-10255550406037544394098578829),(-10255550406037544314827955249)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨3642776439429934366804319385,3642776439429934378826835578⟩,⟨(-7796245019970332148383193542),(-7796245019970332136576279231)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨2143169027805967513261028062,2143169027805967515225145130⟩,⟨(-5185991990886420142552924917),(-5185991990886420140685971581)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1072945404801867317362588626,1072945404801867317972264740⟩,⟨(-2983017289224013103122736901),(-2983017289224013102537360775)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨446596783740874801432164875,446596783740874801683917902⟩,⟨(-1451974941526105253605573181),(-1451974941526105253345802062)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨149248220321439719882680174,149248220321439719976089382⟩,⟨(-576943487272401365883934093),(-576943487272401365776232336)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨37957161187407598765119789,37957161187407598792647996⟩,⟨(-176291878426563694008198051),(-176291878426563693970858036)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨6710608447760301134405170,6710608447760301140219622⟩,⟨(-37315918785052376502427258),(-37315918785052376492459943)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨688674040406636685174765,688674040406636685919078⟩,⟨(-4482504208421044659545811),(-4482504208421044657762432)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨26767117338003930919724,26767117338003930960930⟩,⟨(-196163631430758580931241),(-196163631430758580776590)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨101536229627659758603,101536229627659758990⟩,⟨(-800323058234436347279),(-800323058234436344964)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨17364529717221785255025006855,17364529717221795728735905249⟩,⟨(-12095984277512945356046669766),(-12095984277512934883944416359)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨49870419342021629634065585596,49870419342021668260785500844⟩,⟨(-35118037057302510391790060979),(-35118037057302471769684354079)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨76111149257825005526471155722,76111149257825098613197086797⟩,⟨(-54742637295899626088908963287),(-54742637295899533009187368879)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨93323379566553556959603921709,93323379566553762924125898522⟩,⟨(-69218818294113619219523394920),(-69218818294113413263524474863)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨100466779493888190300596284435,100466779493888609073662723266⟩,⟨(-77549333453087681511823218790),(-77549333453087262747838600173)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨98305557987160173274251800335,98305557987160915253251684728⟩,⟨(-79670410872940352904495351810),(-79670410872939610934283099538)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨89048975684328844476068147562,89048975684329912869653686791⟩,⟨(-76350503721881217119493017911),(-76350503721880148733760127641)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨75584927789638708796947900385,75584927789639881373350572100⟩,⟨(-68886716263808024816769699495),(-68886716263806852246918610669)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨60648884639585798496290324744,60648884639586781798062708343⟩,⟨(-58825984509732137452724868246),(-58825984509731154156100009674)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨46305601065065642321706813074,46305601065066276824469538377⟩,⟨(-47721119506581576427056536828),(-47721119506580941928127825598)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨33795077124354462380569296983,33795077124354778545778735722⟩,⟨(-36884478836074248562771993953),(-36884478836073932400285036313)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨23625898663118848590311326399,23625898663118979461930440147⟩,⟨(-27201119320917067017611501384),(-27201119320916936147843233220)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨15771860998263576048618086579,15771860998263624997022382745⟩,⟨(-19057870353783651671989759022),(-19057870353783602724787475870)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨9864934958953081672711940453,9864934958953099358370858127⟩,⟨(-12412059788571591081283827963),(-12412059788571573396358362962)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨5366220011893429335705950725,5366220011893435582829713793⟩,⟨(-6950891628274533124893937725),(-6950891628274526878161523843)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1697499130281514038147806306,1697499130281515590346557247⟩,⟨(-2232312540240616647310292479),(-2232312540240615095234097235)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨51174902765701504143253078643,51174902765701504155326478540⟩,⟨818580861838383972515768886,818580861838383978426906639⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨149405848067196376440831483139,149405848067196376476357770954⟩,⟨370585254857886029039163593,370585254857886046514158753⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨235846361627536056051499357306,235846361627536056108018500656⟩,⟨(-5584286822193181860707727812),(-5584286822193181832510882148)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨304737326909019023139939296157,304737326909019023213524248798⟩,⟨(-18324312517699692403890240159),(-18324312517699692366482817669)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨352383613518022099138942961140,352383613518022099224587603195⟩,⟨(-36314315185155879822193986465),(-36314315185155879777614810950)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨376907091738726663415127525276,376907091738726663508585862988⟩,⟨(-56074479191386082180556488896),(-56074479191386082129639517955)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨378525089591419624590603090941,378525089591419624690728336682⟩,⟨(-73994150549529736362016371503),(-73994150549529736303110553231)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨360017704636231517626712237701,360017704636231517751792255761⟩,⟨(-87408997019427881986815825391),(-87408997019427881899380303325)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨326230921559679002285800308135,326230921559679002593006351198⟩,⟨(-94764281413081222257827836237),(-94764281413081221983149056062)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨282844163049420833586234365025,282844163049420835048119417660⟩,⟨(-95569247539428164792225491518),(-95569247539428163357161559104)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨235168131805132934752091003715,235168131805132941460311907133⟩,⟨(-90214867634424076899917245730),(-90214867634424070212899909009)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨187250217929944336497669924256,187250217929944359005698174832⟩,⟨(-79621248128944469308249152761),(-79621248128944446816389335568)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨141397877014412261067830947531,141397877014412312482905777765⟩,⟨(-64978012544214388773893588589),(-64978012544214337370575088753)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨98340558544111471134530135714,98340558544111549780246478521⟩,⟨(-47650084955834064232910474513),(-47650084955833985595108588336)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨57826464838840741741091836708,57826464838840817666973384862⟩,⟨(-28926323362388146111613624042),(-28926323362388070190277918563)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨19060440938440125184412835161,19060440938440156838303107233⟩,⟨(-9676353746616850768493472010),(-9676353746616819116078551166)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨65289468087513252535966855922,65289468087513362202274145153⟩,⟨23927581468951630735229029008,23927581468951740389444807266⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨192804518960312807991279763039,192804518960313061465733371062⟩,⟨68927695528544739117044899596,68927695528544992556140814368⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨310794419661051961280908300443,310794419661052206930887651080⟩,⟨105920577404612602343717529492,105920577404612847937776044515⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨412697650705675491673283762188,412697650705675638210271409578⟩,⟨131302574387036375854603545411,131302574387036522319200806257⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨492409487896977611988366245087,492409487896977669425950594940⟩,⟨143088284611766817884735927337,143088284611766875238425567712⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨545877832159634414327700967192,545877832159634429516489815158⟩,⟨140979842359946526284007849495,140979842359946541382647267069⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨572070778296948998567804390158,572070778296949001542816708951⟩,⟨127076661629208541356830613547,127076661629208544240432815693⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨572139551210387365711753187481,572139551210387366309631765560⟩,⟨105782246701442647644127237107,105782246701442648153669984019⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨548374751914368171367112996398,548374751914368171604412077110⟩,⟨82072426416015982135206600819,82072426416015982290707800379⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨504019446399417606783427530625,504019446399417606950254261782⟩,⟨59790469692310354013748914549,59790469692310354107826266426⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨443250803666609579020898165657,443250803666609579153425813802⟩,⟨41016890700112350337689196474,41016890700112350408097601550⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨370859411597200514175475666350,370859411597200514279716662206⟩,⟨26346032594615423929718104035,26346032594615423983199056965⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨291527705481109625156790843913,291527705481109625235221176261⟩,⟨15600123869785632717328697171,15600123869785632756543632419⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨208946199703416064968641345407,208946199703416065022954228440⟩,⟨8313303329263811965633291243,8313303329263811992196676537⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨125370234596424825459471887005,125370234596424825491268373443⟩,⟨3785662966812799373832340492,3785662966812799389118172465⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨41748958580481147310973118833,41748958580481147321407796711⟩,⟨1053341643697742517992760061,1053341643697742522961099717⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨4721071903153711275992716204,4721071903154348290382835240⟩,⟨84168410203284362664773821616,84168410203284999665950264759⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨19748240146999477290646481319,19748240147001873532109486775⟩,⟨245471545927652477049438425826,245471545927654873252273546594⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨50138639523526465383127464624,50138639523532470728445759592⟩,⟨386837141629288020875591082619,386837141629294026159265121601⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨101289202297858767719291276254,101289202297872847471532735151⟩,⟨499302959091891132691525461462,499302959091905212362831069426⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨171510452959118535689000016038,171510452959149422766454317814⟩,⟨578255266315734478251325921451,578255266315765365232955385258⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨252178161493560855740898475803,252178161493620888452326043758⟩,⟨621834344289038649686714111984,621834344289098682292694300945⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨331597003761333539799112813387,331597003761429666519445683389⟩,⟨629920180227497590712630588820,629920180227593717323386028142⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨398949573081087426850462151595,398949573081206432947956676532⟩,⟨605174977690075207412623254167,605174977690194213400966628610⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨445969983526293567576164887710,445969983526407694261819851457⟩,⟨553608227658002311975772050108,553608227658116438556357408262⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨467461082464421123262205906430,467461082464506077997328721482⟩,⟨483533396518750024738119789589,483533396518834979375494231463⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨461176402383484855393286437023,461176402383533952697829560775⟩,⟨404031751040499770572308426285,404031751040548867789533034678⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨426790872987170798928897486802,426790872987194340584356712349⟩,⟨323226761104485587582527449298,323226761104509129163926758794⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨365137088289253208231099013616,365137088289263307379616541629⟩,⟨246040374455808347129132027009,246040374455818446218665741663⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨279190373437866972366171213264,279190373437871075215264724381⟩,⟨173192813445694151425252036901,173192813445698254231530176226⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨174825354953891077520054890444,174825354953892658540056278482⟩,⟨103109766235711783951391031274,103109766235713364945465539311⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨59451315682362609909879625077,59451315682363022024151368236⟩,⟨34249429022831877924937751953,34249429022832290030530032549⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-38949150877494961294573387730),(-38949150877494961280446410530)⟩,⟨492808273163850786979639089,492808273163850796520337522⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-114452245498043088618398074420),(-114452245498043088575784251687)⟩,⟨7162161903812768905586859527,7162161903812768934768851493⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-183729656179126879637007173821),(-183729656179126879566222454581)⟩,⟨28970603548299560297255516142,28970603548299560347542422030⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-245012654479912451706929032943),(-245012654479912451608588621349)⟩,⟨69468430751453273651063286486,69468430751453273724393799219⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-296235404913486118861988956319),(-296235404913486118736541889795)⟩,⟨123947365096996769078190147463,123947365096996769177260659245⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-331899335646055917094123411213),(-331899335646055916936512549617)⟩,⟨182801977321191552367751910833,182801977321191552499863457396⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-345473224474376019712409166975),(-345473224474376019492343006919)⟩,⟨238220455142721244682342143197,238220455142721244879556219366⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-335224250654106857296255480019),(-335224250654106856810958377868)⟩,⟨285735373385279271751424872406,285735373385279272218665226948⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-305364251737401935240583382013),(-305364251737401932899433178750)⟩,⟨321588744656563897221255132336,321588744656563899550788404774⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-263243176578179147503454354224),(-263243176578179132663397258926)⟩,⟨341813951589111977014711915416,341813951589111991849469123762⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-216664459037335971554377202752),(-216664459037335895129382673979)⟩,⟨342837898235217099426701043750,342837898235217175851412308695⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-171683291611883133628468672964),(-171683291611882855611250134994)⟩,⟨321859314444487104520022634270,321859314444487382539970703494⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-130645185952549554244264270137),(-130645185952548875244249022102)⟩,⟨277793018398311496091006223181,277793018398312175095102106919⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-92463228131072149154056751489),(-92463228131071053176932325010)⟩,⟨213049002600273616786838055646,213049002600274712767994524098⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-55335044476207497054240757024),(-55335044476206397416935450190)⟩,⟨133364797572890940948133282320,133364797572892040588318130188⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-18426021480626482280678929118),(-18426021480626014083811997579)⟩,⟨45309580845334989690284737272,45309580845335457888188544081⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1826471180388207986540084103502,1826471180388312619870324036588⟩,⟨1407728202897507264906975170066,1407728202897611897802860153434⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 3) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_3 (tableDensity false) (fullFactor false 0 3) density0_contains hk0_0_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨90501937727914425332521125145,90501937727914425336294179080⟩,⟨7464474015627734485410611940,7464474015627734488000469245⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_3 0 3 ha0_0_3_contains + def realAnswer : RBox := ⟨1916973118116122411872505228647,1916973118116227045206718215668⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_3 +namespace hm0_1_0_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨364068319315031760408806368,364068319315032629602750581⟩,⟨(-380619346442928667039385534),(-380619346442927797810790653)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨1018802976931472338571868101,1018802976931474276436976092⟩,⟨(-1074244427543370945479367373),(-1074244427543369007517990292)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1466224440737479848190580585,1466224440737481591328884752⟩,⟨(-1571492664819988566795654151),(-1571492664819986823519392477)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1614859890531756402501645259,1614859890531757326622381473⟩,⟨(-1786319923190965434081631305),(-1786319923190964509806557212)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1453507439090046354398599192,1453507439090046660292726818⟩,⟨(-1724283171442268947031420126),(-1724283171442268640989594930)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1084013053085998187339228006,1084013053085998251539414823⟩,⟨(-1476396603347484607593600064),(-1476396603347484543268164002)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨675240750802591852921814104,675240750802591862153080698⟩,⟨(-1144235172252303887001072642),(-1144235172252303877674021755)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨354768798780849741785461380,354768798780849743014535052⟩,⟨(-797009391204367421964003877),(-797009391204367420668933754)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨158328321868530748721844884,158328321868530749010159365⟩,⟨(-485726273517255275234871532),(-485726273517255274905710698)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨59944401251540119460642183,59944401251540119567111842⟩,⟨(-249594237237962330347705002),(-249594237237962330218668583)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨18824279205311995864685985,18824279205311995902426146⟩,⟨(-103203472651241694173944629),(-103203472651241694125387546)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨4565200995543736098881193,4565200995543736109572900⟩,⟨(-32194700235428028457599913),(-32194700235428028442637470)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨737050759483653417064910,737050759483653419206699⟩,⟨(-6844487937483359664459038),(-6844487937483359661022154)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨61581856758771761454149,61581856758771761700496⟩,⟨(-819115253482439043179744),(-819115253482439042671745)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1668818710517781778445,1668818710517781789086⟩,⟨(-35689322578409881449680),(-35689322578409881413935)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨3963810664693145480,3963810664693145546⟩,⟨(-145270217696967122086),(-145270217696967121623)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨3279647163118635140236500641,3279647163118643763593226092⟩,⟨(-371550155787561366589204829),(-371550155787552743056520222)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨9309218796918039532689217447,9309218796918071348025774724⟩,⟨(-1218928898269159173212625552),(-1218928898269127357373559515)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨13906740565615376963777959330,13906740565615453690154817240⟩,⟨(-2335205872619559302111878513),(-2335205872619482574973082220)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨16604516890889198735255754045,16604516890889368650465916951⟩,⟨(-3760461265360112773562161419),(-3760461265359942857424894989)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨17438165862087774661222958587,17438165862088120443944662436⟩,⟨(-5345979014651432963825170068),(-5345979014651087180109609534)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨16792832506027756537434069224,16792832506028369695431331911⟩,⟨(-6761789124159153796254969100),(-6761789124158540637284368379)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨15138442766668856342393426606,15138442766669740016032361458⟩,⟨(-7655259620777476667509360796),(-7655259620776592992981252057)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨12896863176563634104034189880,12896863176564604410977047669⟩,⟨(-7863758443641631570644498346),(-7863758443640661262939683345)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨10447928634346593239341767625,10447928634347406897124726805⟩,⟨(-7453565567562410282462604549),(-7453565567561596624056799894)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨8110519988467615581252828363,8110519988468140333687122850⟩,⟨(-6605636695334343615097711847),(-6605636695333818862169220575)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨6086305385679836420238779882,6086305385680097643747247216⟩,⟨(-5507201009568131926320443980),(-5507201009567870702432975997)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨4434214149379805627462535548,4434214149379913620214357254⟩,⟨(-4311675039630038907946472971),(-4311675039629930914916707410)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨3109216248509487682660984295,3109216248509528018990870568⟩,⟨(-3143481309221845363194532826),(-3143481309221805026672042605)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨2035648173805421031864961891,2035648173805435587628244482⟩,⟨(-2090944772558621897916189268),(-2090944772558607342029395090)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1144702524216179847134865440,1144702524216184983756379279⟩,⟨(-1181208523318069558604444140),(-1181208523318064421914705343)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨368298125083243209758288274,368298125083244485369762089⟩,⟨(-380363841357658185634222627),(-380363841357656910000897894)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨9743065572277235139221065991,9743065572277235143535915402⟩,⟨6212205797479971749671940712,6212205797479971753692956810⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨28639920484057319763878275398,28639920484057319776746003204⟩,⟨17897792025575024211935907823,17897792025575024223914105189⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨45534234469144884701010892573,45534234469144884721926056317⟩,⟨27501862669219526954739789633,27501862669219526974274558834⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨58730604771087887490196496844,58730604771087887518129629784⟩,⟨33913044577497978112678526906,33913044577497978138895773065⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨66904903440258729195626693791,66904903440258729229063482378⟩,⟨36139667032231273307295586927,36139667032231273338888750283⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨70021761937787072763763396425,70021761937787072801885659887⟩,⟨33765768018328346196661006553,33765768018328346232868866796⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨69200499543673911039834349030,69200499543673911084199850166⟩,⟨27698455545419844212033537080,27698455545419844254421301529⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨65677056273236936978536649706,65677056273236937046490894641⟩,⟨19944745633566533074406683515,19944745633566533140481828476⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨60215141549172113464761003691,60215141549172113686649529614⟩,⟨12554433869982207048478328528,12554433869982207268821722558⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨53203945501789983709476024704,53203945501789984878989918408⟩,⟨6827901055779186405624555334,6827901055779187573960404983⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨44939986417549980362356425873,44939986417549985813515735786⟩,⟨3111158594473736255083894411,3111158594473741705368605668⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨35875098694316028607368898809,35875098694316046948075333412⟩,⟨1007641077868267964328728929,1007641077868286304355828739⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨26709746028239299687222942645,26709746028239341630616523713⟩,⟨(-116280632505763308799106621),(-116280632505721365908697721)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨18131697083734299039608123095,18131697083734363247420008018⟩,⟨(-640467491656762475894962137),(-640467491656698268404589201)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨10420902277810869327958169413,10420902277810931347609039268⟩,⟨(-660254032268636345342249207),(-660254032268574325863180332)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨3390209167401963671448694113,3390209167401989534504412714⟩,⟨(-273364187363232377658801399),(-273364187363206514654061499)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨12715427298577425895161653235,12715427298577518032855758721⟩,⟨19457832796097871346656868796,19457832796097963485623975024⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨37186451137352704682257000949,37186451137352917495627892088⟩,⟨56239159993105733415319429769,56239159993105946232403094165⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨59085554441664034338680043531,59085554441664240287921200552⟩,⟨86885964111791973252214472336,86885964111792179207270591180⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨77716852002596077306262950323,77716852002596199875309071856⟩,⟨108552957750441424088182495410,108552957750441546664648184957⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨93185659228773601271407971853,93185659228773649132240096753⟩,⟨120444938624628887024962281857,120444938624628934894189882292⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨105357310329451157924800029128,105357310329451170473932915079⟩,⟨123985063586026587092223503458,123985063586026599650147458521⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨113130032826971272141217517288,113130032826971274516466786410⟩,⟨121384729678018393805209424844,121384729678018396189179808965⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨115351977621906012850424613366,115351977621906013253760792708⟩,⟨114166329299461750004485693728,114166329299461750416009292804⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨111969565594819649188148881188,111969565594819649298545709765⟩,⟨103256637239507401556764673821,103256637239507401674505004856⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨103976499954877014505822700568,103976499954877014567264484169⟩,⟨89685804578505462175032651340,89685804578505462242780381682⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨92660249648889415905060161015,92660249648889415949585130775⟩,⟨74778178710718146057088840999,74778178710718146106771251082⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨78968152298015001940820284568,78968152298015001974103165769⟩,⟨59796868814043444555707660438,59796868814043444593045502192⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨63413056038583724613276871638,63413056038583724637441945420⟩,⟨45472171977105408298429308886,45472171977105408325621473152⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨46367215614815192542286285864,46367215614815192558505343839⟩,⟨31924073926055455721292719340,31924073926055455739588712120⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨28244082742199584989841673545,28244082742199584999096570181⟩,⟨18949801656532684788201507528,18949801656532684798665320234⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨9481243740290436902620846393,9481243740290436905615704948⟩,⟨6283764074245082685683147810,6283764074245082689072569828⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨2963895978501885587372658670,2963895978502409108615666011⟩,⟨27538743023412038218309732320,27538743023412561742298491809⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨10086832602690135826030920924,10086832602692105288937334825⟩,⟨81956184727204477639576366068,81956184727206447110676956399⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨20029490331546632363477004185,20029490331551568804905666284⟩,⟨133663451900498514465840231479,133663451900503450920497214890⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨33143184881239695336752565150,33143184881251270874295554258⟩,⟨179125827232274640688924322341,179125827232286216244075794004⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨49563388897629014475900703389,49563388897654411123134736897⟩,⟨214058406329646588956910804189,214058406329671985625110664628⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨69644165954654342361840531106,69644165954703703671770261518⟩,⟨236084142834610252597753879995,236084142834659613931009739083⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨92262084108332871291048461218,92262084108411893655702855971⟩,⟨246198874674494340029340381793,246198874674573362418786054074⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨113683864807276456310388765560,113683864807374239204369829959⟩,⟨247078053762522534620313352114,247078053762620317539155863696⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨128911435757231753552889587863,128911435757325452650766124565⟩,⟨240754858598745021249746157972,240754858598838720370869484290⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨133852697086464550966723374430,133852697086534225293157835551⟩,⟨227728278067890876441091147187,227728278067960550787926687207⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨126949209293252489945485703322,126949209293292705345880729690⟩,⟨207211213859644627976041481294,207211213859684843393619175688⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨110002292884220820359283280079,110002292884240077308305364531⟩,⟨178331076300984074454109725229,178331076301003331417252481762⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨87281437171863546085134078031,87281437171871796622443898316⟩,⟨142048254518524951051736961683,142048254518533201600055151608⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨62662178105205262700041662884,62662178105208610985613675660⟩,⟨101621136869723392731059249623,101621136869726741024399856963⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨37731210146843124110229981027,37731210146844413399864244509⟩,⟨60433141983218007725054377602,60433141983219297019287086922⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨12613956662057098921038270740,12613956662057434864013189093⟩,⟨19984722168991211158281357844,19984722168991547102762696543⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1156383856905888964344072271),(-1156383856905888954877848142)⟩,⟨69746028952710685401058751,69746028952710691813633861⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3189226162795739860432244492),(-3189226162795739831653788015)⟩,⟨1034261502429886042146060443,1034261502429886061821234067⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-3379031649644693322754274698),(-3379031649644693274303831914)⟩,⟨4580310513823240795603265113,4580310513823240829714753719⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1479537107675077053951393576,1479537107675077122510744800⟩,⟨13565259262462826644264413896,13565259262462826694465751379⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨13333643001393633129705024139,13333643001393633219425555484⟩,⟨32869672925868358409613750348,32869672925868358478503742762⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨28641629364514026756951145726,28641629364514026873909174420⟩,⟨66260410741672388506261714521,66260410741672388600953554315⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨39852514018320218356530535027,39852514018320218528615238706⟩,⟨110666300983595453081846676732,110666300983595453231081601521⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨41942677641968806918609059666,41942677641968807316908361857⟩,⟨156185861270570936308851951667,156185861270570936685450231694⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨35462461287625754594126005602,35462461287625756527282020651⟩,⟨191849723390477103394339064332,191849723390477105308811085633⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨24745551321513261262006510130,24745551321513273427733393819⟩,⟨210277918889294763799339260868,210277918889294775950054596088⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨14975050062973555398221893140,14975050062973617857616567375⟩,⟨209269710136553699027345718120,209269710136553761475215293856⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨9490184001704894095823513532,9490184001705121176040224501⟩,⟨191335335559357170071981334415,191335335559357397143291812917⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨7985267369617988942048738388,7985267369618543686978134228⟩,⟨161196657417957058780747045459,161196657417957613519023538117⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨7519101698029669130311630923,7519101698030564943979035801⟩,⟨122458696710180936906406806189,122458696710181832715567608645⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨5674636623957196429762451010,5674636623958095562857869772⟩,⟨76874059595802742860705046147,76874059595803641991229357577⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨2119316520047619958388027618,2119316520048002860682946587⟩,⟨26251681391303154318512363756,26251681391303537219996435372⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨547067260980949708893929509905,547067260981035619958581840120⟩,⟨907981755261185775238085024881,907981755261271686320763085740⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 3) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_3 (tableDensity true) (fullFactor false 0 3) density1_contains hk0_0_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-118348687798041940824384695720),(-118348687798041940819450702112)⟩,⟨(-9761235251205498945846767474),(-9761235251205498942460030999)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_3 0 3 ha0_0_3_contains + def realAnswer : RBox := ⟨428718573182907768069444814185,428718573182993679139231138008⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_3 +namespace hm0_0_0_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨324009818436842156762706935,324009818436842294999168924⟩,⟨236659314581880536371321837,236659314581880674625990984⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨897360441581749515427862200,897360441581749818134856732⟩,⟨638967376721196446699381348,638967376721196749455291050⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1271775263200027804721005597,1271775263200028067344589662⟩,⟨861217079800352363471276187,861217079800352626160013542⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1389119408102279254855156630,1389119408102279386663374547⟩,⟨875176757349884241257802479,875176757349884373130468917⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1268045279745234856442624000,1268045279745234896961981651⟩,⟨731208789420366270325949276,731208789420366310896354106⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨989162636806346403145588058,989162636806346410907439231⟩,⟨516372497125657617967285687,516372497125657625761679444⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨660860055985724366696825061,660860055985724367720581026⟩,⟨309215095378642369558734188,309215095378642370598464008⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨375273074066184257284278622,375273074066184257424440848⟩,⟨155380828944396059160010435,155380828944396059305389150⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨178133249176228097216556010,178133249176228097253605277⟩,⟨64237723844582652930762088,64237723844582652968042454⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨68693025213928418754086104,68693025213928418767395633⟩,⟨21202020446222194078955659,21202020446222194091201687⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨20550925440088702164016344,20550925440088702168274538⟩,⟨5340431301353839337720249,5340431301353839341162743⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨4423521676357767220852331,4423521676357767221922995⟩,⟨957755366228642074598451,957755366228642075319628⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨601543496537953362755220,601543496537953362944601⟩,⟨108848979849508277254495,108848979849508277353656⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨40445902372475907286343,40445902372475907305840⟩,⟨6249892558248680733268,6249892558248680740542⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨782845371479238814217,782845371479238814989⟩,⟨107219440618738120481,107219440618738120680⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨800704607050705553,800704607050705572⟩,⟨101685367693428401,101685367693428417⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨3159140140916276139608351279,3159140140916278874512062597⟩,⟨4535150013702857166743295142,4535150013702859902071541834⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨9084690025952211081468308520,9084690025952221068540950939⟩,⟨12901236304546578695223848183,12901236304546588683502609390⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨13894789018126641072836842585,13894789018126664674660145833⟩,⟨19319552774285934799689703255,19319552774285958403309317864⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨17079737979472713873608565968,17079737979472764610845506161⟩,⟨23029779671150544242448108359,23029779671150594981809617430⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨18437317512448406699704438229,18437317512448506058974728923⟩,⟨23889621203746443536969475115,23889621203746542898420211111⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨18098137763305197186891634112,18098137763305365390787303605⟩,⟨22336255263944467670901307732,22336255263944635876811411868⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨16445434326815572520482488465,16445434326815802298910603239⟩,⟨19186012388956483940080733864,19186012388956713720213380734⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨13976696475637168611941813696,13976696475637406432902759221⟩,⟨15340723698966515136919511874,15340723698966752959217197113⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨11185189464274024675255800907,11185189464274211751481240472⟩,⟨11535776095319305257518641665,11535776095319492334725237700⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨8476211691688244080453189567,8476211691688357006606024375⟩,⟨8227578154796069472264905450,8227578154796182399097474804⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨6115834356640844222647497754,6115834356640896800422052508⟩,⟨5605337455453363660754656214,5605337455453416238977227258⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨4220685620628973056441974713,4220685620628993428630016908⟩,⟨3666927339217718449300616436,3666927339217738821771654604⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2784320448176883272434468306,2784320448176890443851306812⟩,⟨2304718257800145945184424012,2304718257800153116772856914⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1724812012673965175492739055,1724812012673967637735102960⟩,⟨1371030989458323548757033143,1371030989458326011098117429⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨931705195910660925852704279,931705195910661763877807108⟩,⟨719331042689129777009514756,719331042689130615085050103⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨293616339117089141254916014,293616339117089345423889361⟩,⟨223273610802235301275624478,223273610802235505460031313⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-320979151085304010264110272),(-320979151085304007945499965)⟩,⟨20064249457371015742977746841,20064249457371015747775445627⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-145308409542789228169688895),(-145308409542789221360740153)⟩,⟨58206596823283409160426127491,58206596823283409174454875900⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨2144543135038868953940495423,2144543135038868964794922920⟩,⟨90732804059925601591589219623,90732804059925601613633432981⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨6911466286410443830112899266,6911466286410443844262237376⟩,⟨115078420883929306641485550139,115078420883929306669668912775⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨13373081533128107704119679769,13373081533128107720599109398⟩,⟨129895342839345809800922364414,129895342839345809832959131387⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨20059360386099980246565836396,20059360386099980264867494809⟩,⟨134940620895828906526864665984,134940620895828906560836701567⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨25601735309035047161678263293,25601735309035047182165069323⟩,⟨131061561988256682131690966084,131061561988256682166878813710⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨29153169085162204202021928652,29153169085162204231260490141⟩,⟨120150226146086055984107787711,120150226146086056026306239268⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨30400251193156001572682249474,30400251193156001660532075025⟩,⟨104711360798631005017674059554,104711360798631005116311421444⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨29464589685668290941042272552,29464589685668291381241828619⟩,⟨87242683146588819184268400720,87242683146588819633030480349⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨26751485287496133583038403012,26751485287496135556942718719⟩,⟨69760068305739137891985323674,69760068305739139872409541432⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨22765913292294680028029785768,22765913292294686437274740681⟩,⟨53553962804832910341350518772,53553962804832916755395097755⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨17992778453062609813923236968,17992778453062624016996406981⟩,⟨39160064065835403617336790961,39160064065835417823792753836⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨12856569391000136217326854793,12856569391000157410957842559⟩,⟨26535523159127680724322650617,26535523159127701920174590379⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨7663219644252572987213920337,7663219644252593092434997985⟩,⟨15319907537056453958330147378,15319907537056474064804619487⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2539343198414260635472732329,2539343198414268941604251351⟩,⟨5002001716177022838414679466,5002001716177031144949329731⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-12513465975362205144284420710),(-12513465975362147796848574318)⟩,⟨34144507273654273950691945569,34144507273654331304520328260⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-35876388009741352245528163631),(-35876388009741220305244895182)⟩,⟨100351212950311664965769094620,100351212950311796924663259747⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-54615640542676053918105670907),(-54615640542675927208390359445)⟩,⟨160245197933032923902005929370,160245197933033050640901337661⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-66775874018672394126343887418),(-66775874018672319551789242302)⟩,⟨209861364427316861831440617017,209861364427316936443290688559⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-71483557049383155610158896731),(-71483557049383126902171453391)⟩,⟨245954301830779153580025304240,245954301830779182330529027458⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-68940580499069551875234873142),(-68940580499069544471521063062)⟩,⟨266870961963713375959771518291,266870961963713383408282002366⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-60649431465640546903602233691),(-60649431465640545522572811903)⟩,⟨272932031064638753381516270332,272932031064638754806970603991⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-49166324375982040462801187840),(-49166324375982040225092825482)⟩,⟨265802754366447989588798569481,265802754366447989868418821722⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-37100694485582615894203765038),(-37100694485582615823680764119)⟩,⟨247761838163170892192432968873,247761838163170892300806871306⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-26279956478851113533953179070),(-26279956478851113492487930400)⟩,⟨221409821633569560343756540575,221409821633569560418051041322⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-17544113881434345487965325325),(-17544113881434345457777079752)⟩,⟨189484613499451085891986032941,189484613499451085949535252464⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-10988666840985126985682963338),(-10988666840985126963331143669)⟩,⟨154598175796449069601740667871,154598175796449069645956340941⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-6365213304106285781270503758),(-6365213304106285765243634445)⟩,⟨118892410724830372079814382775,118892410724830372112406798491⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-3332540518181822309905016221),(-3332540518181822299242429870)⟩,⟨83728932438922782222759168996,83728932438922782244962757331⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-1498741753157841551484972212),(-1498741753157841545426314390)⟩,⟨49624545269134299435846107943,49624545269134299448697101037⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-414319268475629404085427044),(-414319268475629402129003276)⟩,⟨16421017453508531974559785568,16421017453508531978752420629⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-55035324965002465361963188986),(-55035324965002048853453572829)⟩,⟨3086868020145226747823861430,3086868020145643264807863914⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-159896973253311945997310883188),(-159896973253310385412466067383)⟩,⟨12860950406446855778162672502,12860950406448416387696584639⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-250094752860784967511847467054),(-250094752860781086652144097265)⟩,⟨32403211353529861923358173307,32403211353533742822204717213⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-319269795192743707105700925096),(-319269795192734710127685423708)⟩,⟨64738852900328156976014778962,64738852900337154004933718671⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-364541217453631492956609963312),(-364541217453612037293219146660)⟩,⟨108074016003601880926310221957,108074016003621336649231063291⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-385421281509135487836835735708),(-385421281509098309321047753781)⟩,⟨156235901224515973280064031881,156235901224553151860394139604⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-383011736850449375976900705478),(-383011736850390964349454570096)⟩,⟨201540079810475433576280884467,201540079810533845269683111915⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-360395532291152103736281093543),(-360395532291081249673487152443)⟩,⟨237493981709229075480428819208,237493981709299929607749300580⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-322622584868068288325652860617),(-322622584868001774891201205303)⟩,⟨259804550124080156579075860090,259804550124146670074501872140⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-275730629923127706184434601133),(-275730629923079237332771030344)⟩,⟨266482209350710520207804069296,266482209350758989115163220099⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-225625295826775274879598827231),(-225625295826747836355843114210)⟩,⟨257468586672277143838292948799,257468586672304582410943816579⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-177062559359864263310192998367),(-177062559359851356596197543876)⟩,⟨233747892627310628409547299311,233747892627323535164363457109⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-132552230671321530453738520425),(-132552230671316085747937141285)⟩,⟨196689902060456728762021954147,196689902060462173499895451898⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-92073748664488610990714439079),(-92073748664486428803093539968)⟩,⟨148415562836339041352194197704,148415562836341223562843008638⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-54310493733900475056788071952),(-54310493733899642139051411604)⟩,⟨92082940107745190372945824102,92082940107746023304520195753⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-17954488872824687580877404704),(-17954488872824471538405162793)⟩,⟨31165937767477826168557168929,31165937767478042215643266393⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-386638911905987634203404132),(-386638911905987626714929623)⟩,⟨(-30566158065379546851053038349),(-30566158065379546839869192928)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-5600205962629402756317006895),(-5600205962629402733470971664)⟩,⟨(-89534037897767145977586336631),(-89534037897767145943963398570)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-22511134114345079603008602588),(-22511134114345079563844492053)⟩,⟨(-142831195089364201422759018820),(-142831195089364201367268355752)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-53489494047506132406193640409),(-53489494047506132349534560407)⟩,⟨(-188734213589054567769894410753),(-188734213589054567693521028412)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-94325695692498462617896504841),(-94325695692498462542167524607)⟩,⟨(-225517622827843325135403719253),(-225517622827843325039149557954)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-137184243388379050237503768959),(-137184243388379050137880619163)⟩,⟨(-249150050749738997971810256398),(-249150050749738997852650478497)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-175971993554092054717610952659),(-175971993554092054571358990998)⟩,⟨(-255274684864553034012983423579),(-255274684864553033849557496770)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-207499845431184865069898532124),(-207499845431184864730330341006)⟩,⟨(-243513758132619839984556793866),(-243513758132619839631733066695)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-229437016093084126662671948302),(-229437016093084125003842838932)⟩,⟨(-217930366331367181052284526265),(-217930366331367179385204304669)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-239593152005762116149747737372),(-239593152005762105775914753557)⟩,⟨(-184574709954013851608283007665),(-184574709954013841230948288509)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-236273906440404962868889399539),(-236273906440404910303914491635)⟩,⟨(-149356995970259922493860079273),(-149356995970259869929044317606)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-218406336892088224136960071947),(-218406336892088035751246080814)⟩,⟨(-116521517477856227891840990081),(-116521517477856039508408334676)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-186001878163467240406646924988),(-186001878163466786177398093241)⟩,⟨(-87485098943228413181789421825),(-87485098943227958955699642239)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-141143261463422992307067330530),(-141143261463422266565649478369)⟩,⟨(-61258947519471846002485629815),(-61258947519471120264092190953)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-87702545227371860395945731149),(-87702545227371137376319756206)⟩,⟨(-36389625990998398366277771911),(-36389625990997675348775298061)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-29683482946399864920280392714),(-29683482946399558197003716182)⟩,⟨(-12071383608607143109788429832),(-12071383608606836387270344191)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-960631233155762465483256418263),(-960631233155700977193513708023)⟩,⟨671614752086800547196758758310,671614752086862035711281248561⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 4) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_4 (tableDensity false) (fullFactor false 0 4) density0_contains hk0_0_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-32244213004310991956832613441),(-32244213004310991954522773425)⟩,⟨67695291119442119661347542785,67695291119442119663984152897⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_4 0 4 ha0_0_4_contains + def realAnswer : RBox := ⟨(-992875446160073457440189031704),(-992875446160011969147936481448)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_4 +namespace hm0_1_0_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨49584934366180443762684859,49584934366180557011866880⟩,⟨47428934817753460912581181,47428934817753574157242128⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨137292931234586981963293672,137292931234587229863109715⟩,⟨130211193938194443226809027,130211193938194691114297218⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨193235497718686958279528606,193235497718687173192453758⟩,⟨180307194750928130424134806,180307194750928345320048254⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨207102366971621902532974382,207102366971622010266410695⟩,⟨187273457034358317803186066,187273457034358425518647516⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨184478651186771287428897185,184478651186771320480133912⟩,⟨155629075207452539005809939,155629075207452572041107407⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨142395577015432743838415156,142395577015432750133828225⟩,⟨104734885901489445634590383,104734885901489451917715121⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨96951498890197939266824827,96951498890197940073211479⟩,⟨57389793347309339362159833,57389793347309340160161073⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨57627279342267414750030728,57627279342267414845799510⟩,⟨25764745918959566570832581,25764745918959566661558066⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨28975768841949183838924497,28975768841949183859027328⟩,⟨9496797043383350690844733,9496797043383350708296665⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨11796370847508511539264899,11796370847508511545556595⟩,⟨2850360812401794035304314,2850360812401794040398517⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3673390187096210080511408,3673390187096210082318827⟩,⟨674349520781684718955280,674349520781684720316496⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨807576052604754715234888,807576052604754715635219⟩,⟨115393784002940728614510,115393784002940728887012⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨110343249893619271595143,110343249893619271655887⟩,⟨12017882119998846571660,12017882119998846606875⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨7392508754591288809704,7392508754591288814930⟩,⟨565666891709500390062,565666891709500392358⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨142446743936656566446,142446743936656566629⟩,⟨6800436239704572126,6800436239704572185⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨145343264235087898,145343264235087915⟩,⟨4006189377682697,4006189377682713⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨97036210703345330343562782,97036210703347582465000867⟩,⟨856558068156686319890989168,856558068156688571968900520⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨315259560127496912984174775,315259560127505140034314890⟩,⟨2408299699171907251150501493,2408299699171915478077466223⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨592449327857481705574952841,592449327857501160878555100⟩,⟨3530171959047182022860576778,3530171959047201477980708945⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨927265395276260292132446869,927265395276302150806722663⟩,⟨4097868924996903586537252085,4097868924996945444994061913⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1270000564946171526505822746,1270000564946253569613046178⟩,⟨4146864795243341194276284470,4146864795243423237158187677⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1534826498468701609409478280,1534826498468840611338569721⟩,⟨3815702953147429095666644653,3815702953147568097384091146⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1647749797154806285398452125,1647749797154996337158532804⟩,⟨3261644347806088668723358752,3261644347806278720299255491⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨1594549085544449997354584082,1594549085544646795157269159⟩,⟨2617454408515315597909800545,2617454408515512395563033202⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1416470367689604158396974339,1416470367689758960470826715⟩,⟨1987118554110091483124306192,1987118554110246285082924686⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1172737716414989402059534295,1172737716415082796342638192⟩,⟨1440899427286058390594497953,1440899427286151784791503487⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨912796772091961231314743929,912796772092004673057469182⟩,⟨1009290693285145980799333169,1009290693285189422479881556⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨668847499948953728167233908,668847499948970539281074283⟩,⟨688053369950501794705630959,688053369950518605776495140⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨459194723167097830379917570,459194723167103740236518180⟩,⟨454241269979380208165529311,454241269979386117993946622⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨290549062425665341411635164,290549062425667368000659312⟩,⟨282873620670738199311571295,282873620670740225883360942⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨158328791806232482242567657,158328791806233171346139521⟩,⟨153436168514159066294712957,153436168514159755389092928⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨50029262563813773630521694,50029262563813941432785582⟩,⟨48442265874659747136742433,48442265874659914936116803⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-2435636683518109314363703908),(-2435636683518109312779403871)⟩,⟨3819979589800464443700972122,3819979589800464445404892454⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-6972859443993115304525849205),(-6972859443993115299836849743)⟩,⟨11157666681276106424732935127,11157666681276106429782019100⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-10580765676621622253236630477),(-10580765676621622245686657457)⟩,⟨17517442149502413840724739321,17517442149502413848828794187⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-12808031939208032918952262168),(-12808031939208032909008469848)⟩,⟨22178863872554985537046124127,22178863872554985547670162159⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-13324924444832218000921923962),(-13324924444832217989229449328)⟩,⟨24663560189316458444267745861,24663560189316458456680487619⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-12094182018821897452952766210),(-12094182018821897439946677201)⟩,⟨25070651216250478212053702184,25070651216250478225794888902⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-9597173547453868994611175451),(-9597173547453868979906133474)⟩,⟨23960864191795118111847836130,23960864191795118127295877325⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-6663023036346158865858368920),(-6663023036346158843834329546)⟩,⟨21918290804617475875725278560,21918290804617475898442852900⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4035133303550199563089284896),(-4035133303550199492719980190)⟩,⟨19326353745841030713736318862,19326353745841030784672916017⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2109706871016082687560456393),(-2109706871016082329292030144)⟩,⟨16409590079807547311015520650,16409590079807547669718869717⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-924916886775434097951562249),(-924916886775432489224333229)⟩,⟨13330510808971523294396678615,13330510808971524903449521175⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-289223274455509657012655304),(-289223274455504430979609873)⟩,⟨10260541041731498621755051609,10260541041731503848039081995⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨31643655085654381910328646,31643655085665970897755962⟩,⟨7397635192578347099077880451,7397635192578358688248565808⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨172548070359113447836352466,172548070359130752278127190⟩,⟨4892762807805831218815405742,4892762807805848523373369593⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨174846069772058320434343274,174846069772074744168310371⟩,⟨2760860412176928001512571465,2760860412176944425308621922⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨71735437428974358712138985,71735437428981145590725176⟩,⟨889689679198679474408744410,889689679198686261306008989⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-10175906768864561681133363989),(-10175906768864513493895807959)⟩,⟨6649808531064474757401187976,6649808531064522943961750560⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-29272012117386415251807576912),(-29272012117386304459261332688)⟩,⟨19355021399116176458871671311,19355021399116287249453516681⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-44800590450575052373747174342),(-44800590450574946114867877093)⟩,⟨30464855621192638229961406484,30464855621192744485795369450⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-55205439830411480779734858869),(-55205439830411418367971293820)⟩,⟨39520079287605929559450471381,39520079287605991967387997065⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-60168709567038051695172295884),(-60168709567038027734448272411)⟩,⟨46544403531927019457265180029,46544403531927043413747884349⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-60622713295912786392135700696),(-60622713295912780234222019840)⟩,⟨51505096060687214252946988182,51505096060687220406529189191⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-57920004421060098054859281256),(-57920004421060096913063869770)⟩,⟨53971106738461206153104830679,53971106738461207290723935544⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-53046193852525907807038649876),(-53046193852525907614985808172)⟩,⟨53587942064023873487444678682,53587942064023873675695470276⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-46658780299493132791896423476),(-46658780299493132738411930996)⟩,⟨50587863422725965627563016853,50587863422725965677745818585⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-39403015199943870433713121837),(-39403015199943870403759608759)⟩,⟨45674490657411978240065995458,45674490657411978267276885824⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-31970343560996100682120052106),(-31970343560996100660725879048)⟩,⟨39609801238034209126175292150,39609801238034209145400225270⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-24929151012103200876972745404),(-24929151012103200861283154332)⟩,⟨32917686168024390526257079064,32917686168024390540295153475⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-18545524506294956609283506991),(-18545524506294956598098286028)⟩,⟨25860536222064636831635329080,25860536222064636841623123619⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-12792857533861338914721156349),(-12792857533861338907322067447)⟩,⟨18579851650352780131736963533,18579851650352780138334059113⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-7500826103793877004660415745),(-7500826103793877000478409656)⟩,⟨11179581705226433598563011823,11179581705226433602286136043⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2471579022516575021818850198),(-2471579022516575020472388897)⟩,⟨3729230752414049109585332700,3729230752414049110783368831⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-18006768558760871624079476221),(-18006768558760529313660101512)⟩,⟨1937980121985691902271151839,1937980121986034210843921952⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-53384454868396075259681034399),(-53384454868394792594472665014)⟩,⟨6569780072285386894917666696,6569780072286669554638066146⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-86412413269263306816735279089),(-86412413269260116678768116286)⟩,⟨12946822077528228632680555317,12946822077531418761855975346⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-114534275714407285334742479200),(-114534275714399888500716973853)⟩,⟨21187150670419839159747251318,21187150670427235982202535581⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-134940972993465175917418973076),(-134940972993449178596412702015)⟩,⟨31234844346855505701581281026,31234844346871503009016157379⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-146322589136088066836822949758),(-146322589136057497094160483040)⟩,⟨43148586782650140444603257601,43148586782680710172442361173⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-149688089042036122312093727016),(-149688089041988104089896738137)⟩,⟨56073585532428897421525923687,56073585532476915628305912118⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-147126651411645532170249824390),(-147126651411587313881530882970)⟩,⟨67673066374614034430046339534,67673066374672252703656180695⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-140284500178753802559193135832),(-140284500178699194236839625449)⟩,⟨75098132531451153325865413439,75098132531505761634411767252⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-129840192281876003052587284380),(-129840192281836251923492817336)⟩,⟨76307734781847934436033139679,76307734781887685553271389603⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-115697790041351195911937138448),(-115697790041328721030732499355)⟩,⟨70880569105111921251482127040,70880569105134396122898193715⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-97680220898209044060095733562),(-97680220898198486375254207045)⟩,⟨60253650107920275181796147211,60253650107930832858734433710⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-76524524291972855683449016796),(-76524524291968407572457599256)⟩,⟨47020553351316205147928269220,47020553351320653252852689893⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-54024178958844491493827182259),(-54024178958842710612794145406)⟩,⟨33312384267362797952378119734,33312384267364578829183167021⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-31831742191448918975201508136),(-31831742191448239734023274109)⟩,⟨19873866586848049382799089824,19873866586848728621497751489⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-10476544966764265672281172631),(-10476544966764089556567267941)⟩,⟨6612576971279938791502950519,6612576971280114906408469621⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-54720106937949551705761152),(-54720106937949546673199640)⟩,⟨(-907497471277829154293720459),(-907497471277829146862046376)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-808694090379435317402523472),(-808694090379435302008755350)⟩,⟨(-2495021436554782408886939189),(-2495021436554782386366408279)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-3558744264082276491798290877),(-3558744264082276465270022198)⟩,⟨(-2628316829550045438960283751),(-2628316829550045401287746463)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-10442601560621974582723551139),(-10442601560621974544022355041)⟩,⟨1134230120194592414317043281,1134230120194592467131165892⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-25005518525726436895802024234),(-25005518525726436843281398253)⟩,⟨10140056688338261749044885438,10140056688338261817372373380⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-49707267123126655261734852934),(-49707267123126655190502383164)⟩,⟨21488989701588678125225904957,21488989701588678213076688230⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-81725158413776937683563288805),(-81725158413776937573086606092)⟩,⟨29440518897875887425177148344,29440518897875887552349853832⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-113401161870807898406121059390),(-113401161870807898132645333013)⟩,⟨30468127631157811103834341780,30468127631157811392767052789⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-136863458979944859644124078621),(-136863458979944858281055287121)⟩,⟨25314161186199055467467390141,25314161186199056843442115793⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-147391714888423869864059562850),(-147391714888423861367308740626)⟩,⟨17357471385231429184142410595,17357471385231437690902250519⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-144226761335233214137808017823),(-144226761335233171186245829698)⟩,⟨10327446229605107526797620248,10327446229605150485753788030⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-129840325489680406093260767320),(-129840325489680252230446134011)⟩,⟨6441585216394619999120820451,6441585216394773867458629083⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-107934377607993401147768843722),(-107934377607993030048224373542)⟩,⟨5345881148752901122489813476,5345881148753272226044188993⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-81128006623589994691093185405),(-81128006623589401500762105649)⟩,⟨4980492782599885369965250529,4980492782600478562945148909⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-50553307107736570320854250204),(-50553307107735979137640011015)⟩,⟨3731465594266841059918376267,3731465594267432244613649314⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-17198148920609105860251234269),(-17198148920608855015939432595)⟩,⟨1388408950219815748563973689,1388408950220066593335797845⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-538210366131914197208778434962),(-538210366131863710237421246331)⟩,⟨263108785048115358213603238582,263108785048165845179371540803⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 4) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_4 (tableDensity true) (fullFactor false 0 4) density1_contains hk0_0_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨42165509313329758709760549863,42165509313329758712781109884⟩,⟨(-88524611463885848791363892249),(-88524611463885848787916017488)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_4 0 4 ha0_0_4_contains + def realAnswer : RBox := ⟨(-496044856818584438499117885099),(-496044856818533951524540136447)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_4 +namespace hm0_0_0_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-24664966974965230874804703),(-24664966974965216464408825)⟩,⟨33768410419400322384246662,33768410419400336792774214⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-65340553789890673959596857),(-65340553789890642975022456)⟩,⟨91755148324001028326042937,91755148324001059305703398⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-84752589253470058790487148),(-84752589253470032877735999)⟩,⟨125123623502551224383681760,125123623502551250290165992⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-81233430156418166180187779),(-81233430156418153878587019)⟩,⟨128875407105597392181442914,128875407105597404477251547⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-62664811270494936816364310),(-62664811270494933308954104)⟩,⟨108592241707920345415376071,108592241707920348918621267⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-39929627887160626640439324),(-39929627887160626029561194)⟩,⟨76411567293804465407879322,76411567293804466016438248⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-21033937840053651273700451),(-21033937840053651201671808)⟩,⟨44892260633347439300338769,44892260633347439371437492⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-9034812676403363931106567),(-9034812676403363922481107)⟩,⟨21779931261250396498397839,21779931261250396506824838⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3087974161724710394379786),(-3087974161724710392550555)⟩,⟨8541435493945304369045714,8541435493945304370921634⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-809496716114345069176973),(-809496716114345068698294)⟩,⟨2613921664699665962656027,2613921664699665963200791⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-154052006185196264214440),(-154052006185196264112272)⟩,⟨590268014509029028707535,590268014509029028841762⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-19555039250039354002962),(-19555039250039353987689)⟩,⟨89850947622350337737241,89850947622350337761654⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1437214244688102680458),(-1437214244688102679072)⟩,⟨7899005028748373631276,7899005028748373634144⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-46603788342768411680),(-46603788342768411606)⟩,⟨300162656472584009067,300162656472584009252⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-356666522870148154),(-356666522870148136)⟩,⟨2597022063212894093,2597022063212894113⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-84730688396422),(-84730688396406)⟩,⟨666733088191932,666733088191948⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-947569575059734716365691593),(-947569575059734144875031681)⟩,⟨660066040027039037015158297,660066040027039608416196813⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2670035870029062065639799512),(-2670035870029059999351594434)⟩,⟨1880128145100779259090368125,1880128145100781325126379472⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-3923343222890029863118211572),(-3923343222890025074836496410)⟩,⟨2821555825967457983506671311,2821555825967462771419866042⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-4546930171574630741449378662),(-4546930171574620740844966740)⟩,⟨3371843614733175110082692538,3371843614733185110263429589⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-4545154723759084371882362808),(-4545154723759065508957789870)⟩,⟨3507277111944301784915292612,3507277111944320647421040909⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-4060896234915680899984290405),(-4060896234915650388069876094)⟩,⟨3289652861762992241707322084,3289652861763022753252262059⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3307861346937886469934430942),(-3307861346937846924167513313)⟩,⟨2834560672902422050704613451,2834560672902461596175467640⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2491659880229598482728884492),(-2491659880229559882007341987)⟩,⟨2269374159503612589566425566,2269374159503651190069705087⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1755992827622234172831913854),(-1755992827622205688561340024)⟩,⟨1702039804244799083587416134,1702039804244827567708316035⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1169962744918066163460817894),(-1169962744918050078554556440)⟩,⟨1204910581106429279788927129,1204910581106445364598737129⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-744058822520011617205222263),(-744058822520004619600881607)⟩,⟨811568665673181258916909455,811568665673188256462245871⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-455462895783999929742080382),(-455462895783997391850246885)⟩,⟨524102472829887656942546139,524102472829890194799756815⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-269497229107862510356381958),(-269497229107861669562086153)⟩,⟨325511075846524776183206735,325511075846525616957910067⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-152460895199804909497991481),(-152460895199804635194342146)⟩,⟨191777600666913294386830651,191777600666913568679859037⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-77144846251308385272966090),(-77144846251308295322449102)⟩,⟨99915833082130285678737111,99915833082130375624062706⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-23494082991483652124242960),(-23494082991483630636486434)⟩,⟨30895747520352219112899630,30895747520352240599104379⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-6293310616150544165772425252),(-6293310616150544164247497438)⟩,⟨(-100689089228637858598741327),(-100689089228637857871171360)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-18141370776124721476535347262),(-18141370776124721472104334570)⟩,⟨(-45579407481728380420023885),(-45579407481728378297578733)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-27925334296646640548365030219),(-27925334296646640541487836275)⟩,⟨658869555639658328111220097,658869555639658331454024876⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-34767132024134441775620630080),(-34767132024134441766986532153)⟩,⟨2085541575862305082859458385,2085541575862305087141177491⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-38307828459028830700839208227),(-38307828459028830691253599634)⟩,⟨3940042116478155015362942336,3940042116478155020236680349⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-38652454781855472206031354925),(-38652454781855472196153775493)⟩,⟨5741094647895243244267078948,5741094647895243249530088263⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-36307078048604328431163015659),(-36307078048604328421271109682)⟩,⟨7087231633277802825768871787,7087231633277802831469380324⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-32082488397953506750658630456),(-32082488397953506739269331625)⟩,⟨7779615210861656215038027230,7779615210861656222860874783⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-26891156245254443356915814349),(-26891156245254443331575874312)⟩,⟨7802911785524776480185050383,7802911785524776502665467119⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-21530686111793875334577925131),(-21530686111793875224357099548)⟩,⟨7268248096053580924761059744,7268248096053581032797261148⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16556850658320827418318490286),(-16556850658320826950532631268)⟩,⟨6346877775161549374914548708,6346877775161549841098360919⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-12254460891798311502505686369),(-12254460891798310040136324970)⟩,⟨5208042460139661484811652769,5208042460139662946042600644⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-8676908377242462293304686790),(-8676908377242459152788557439)⟩,⟨3986127300969527532867490431,3986127300969530672605960628⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-5728365637972291132389840647),(-5728365637972286562197437449)⟩,⟨2775202080885401449845121695,2775202080885406019539646343⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3247003475503428964657721205),(-3247003475503424704957030306)⟩,⟨1624151056377974913856331265,1624151056377979173280969309⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1050135984923586558791344283),(-1050135984923584814964011749)⟩,⟨533116195212583201837473379,533116195212584945576821170⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-14285280223318360704819238532),(-14285280223318336708656461820)⟩,⟨(-5235360899294291437109992622),(-5235360899294267443650585135)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-41784948948746213141872665986),(-41784948948746158183361901043)⟩,⟨(-14938792601060624070732644781),(-14938792601060569120057766131)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-66098527107305278638143449273),(-66098527107305226326553167640)⟩,⟨(-22529350354661397977384931619),(-22529350354661345677974239810)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-85375293456695926002474758610),(-85375293456695895609928981174)⟩,⟨(-27168467171336976060041535913),(-27168467171336945682865101036)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-98284861862769953659992622780),(-98284861862769942146751419906)⟩,⟨(-28570142746120920412414705508),(-28570142746120908916407602989)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-104379804894556213998626744667),(-104379804894556211076344321133)⟩,⟨(-26971313703556052022730032924),(-26971313703556049118251789107)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-104177302754357223507707388002),(-104177302754357222961288465800)⟩,⟨(-23158021141395991101733561551),(-23158021141395990572581914918)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-98794825266688137548659314905),(-98794825266688137444037151541)⟩,⟨(-18282677111038624603852195941),(-18282677111038624515132421658)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-89559188782167497377866030690),(-89559188782167497338272705176)⟩,⟨(-13417926966400694525448476159),(-13417926966400694499860136761)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-77815231212553794165793137501),(-77815231212553794139327376325)⟩,⟨(-9241347174337465056307941226),(-9241347174337465041686236131)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-64805759751008128473628716414),(-64805759751008128453640171110)⟩,⟨(-6003647697819409176606933314),(-6003647697819409166251606838)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-51559632513823220753202822310),(-51559632513823220738202716381)⟩,⟨(-3666781296138510792390379324),(-3666781296138510784916689168)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-38791160782678099048512797687),(-38791160782678099037680962142)⟩,⟨(-2077792076154004441607115195),(-2077792076154004436366901161)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-26841997330221543499082782556),(-26841997330221543491823877996)⟩,⟨(-1068748138291792447823123635),(-1068748138291792444399081306)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-15714183459489714320678805624),(-15714183459489714316525419849)⟩,⟨(-474684251593777077548158193),(-474684251593777075627029907)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-5167075801030940256854627630),(-5167075801030940255507550820)⟩,⟨(-130374111437340510821315640),(-130374111437340510204998288)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1614676881751311034143528746),(-1614676881751093159692190477)⟩,⟨(-28788833364911902922409467362),(-28788833364911685052304401788)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-6700525642501684847330630037),(-6700525642500871737728146392)⟩,⟨(-83324073482436446743734025870),(-83324073482435633646751015561)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-16753156750090470973406892667),(-16753156750088464563062646278)⟩,⟨(-129352294350241246219981086288),(-129352294350239239829514662845)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-33102638275321633480029858203),(-33102638275317034103804877375)⟩,⟨(-163323002603606700619615247896),(-163323002603602101268995392116)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-54481722374605962442046515862),(-54481722374596158140392247910)⟩,⟨(-183853791914354661957043686707),(-183853791914344857684969284610)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-77438360255533922529390646395),(-77438360255515502112608645087)⟩,⟨(-191116716819171764130059645554),(-191116716819153343744877178648)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-97997930644709893521177603595),(-97997930644681497336333338299)⟩,⟨(-186313070410600865856063812246),(-186313070410572469702976959329)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-113108111629345564123400340238),(-113108111629311814610755406587)⟩,⟨(-171705570082928339539761463754),(-171705570082894590057632504934)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-121086342442306904965154166528),(-121086342442275892273983215509)⟩,⟨(-150416083990453273601299984915),(-150416083990422260938437223246)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-121533968183532349652386437716),(-121533968183510226586999570528)⟩,⟨(-125791193480314948958244598931),(-125791193480292825918245994469)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-114996920695757050320086263971),(-114996920695744782431368274758)⟩,⟨(-100801004765014851503609031840),(-100801004765002583636794942667)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-102419367808275378563227239981),(-102419367808269717492098588266)⟩,⟨(-77597542128507206069431040694),(-77597542128501545016301806420)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-84763015009440094059874737099),(-84763015009437745686209253966)⟩,⟨(-57130222761350362153225561034),(-57130222761348013793510282172)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-63117981190119004971153545026),(-63117981190118076427415227202)⟩,⟨(-39159436699998270374480626502),(-39159436699997341840649355532)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-38801250718588618861385555533),(-38801250718588267808085632208)⟩,⟨(-22885451685039449679558770566),(-22885451685039098632166225669)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-13070407310131521906230632561),(-13070407310131431297642154122)⟩,⟨(-7529791489913666986958169018),(-7529791489913576380331433600)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨19189947839248051293817933507,19189947839248051300900492469⟩,⟨(-242673960358934676523647623),(-242673960358934671821496611)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨56032864969505478023176134983,56032864969505478044397825994⟩,⟨(-3503116440158028783316502041),(-3503116440158028769007907484)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨88829874205740958890985281889,88829874205740958925783917208⟩,⟨(-13993594319475560205939075120),(-13993594319475560181537852894)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨116307245064810908131393361632,116307245064810908178841280508⟩,⟨(-32949089719534364249514856113),(-32949089719534364214492679319)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨137347295335975067587980912062,137347295335975067647061904405⟩,⟨(-57427350453495589239642883260),(-57427350453495589193333676880)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨149628302431756508106091451742,149628302431756508178160607781⟩,⟨(-82361778084663243054028691625),(-82361778084663242993929622514)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨150904098308225539349258697280,150904098308225539446349428640⟩,⟨(-103993926417458777080485551206),(-103993926417458776993717716815)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨141518328705273801199301611533,141518328705273801404516826015⟩,⟨(-120551511519454528591276267386),(-120551511519454528393845423819)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨124428199718814410306485522664,124428199718814411256181867668⟩,⟨(-130956678926310520455323052095),(-130956678926310519510315430553)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨103535264274834420932253520386,103535264274834426737699648905⟩,⟨(-134356925328612312252881727579),(-134356925328612306449279975418)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨82368879453921597750050034461,82368879453921626673724202840⟩,⟨(-130269396081420322100505161965),(-130269396081420293176548062157)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨63267681224231569331957833795,63267681224231671451955930565⟩,⟨(-118566519836298442843898511562),(-118566519836298340722429089410)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨46867315409055137088662698281,46867315409055380179976732363⟩,⟨(-99634247381980197654348961945),(-99634247381979954561114183703)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨32468558043247830000500577087,32468558043248214460921416638⟩,⟨(-74805543488928016317869861653),(-74805543488927631855658904625)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨19144589713983269909409417627,19144589713983650220763692921⟩,⟨(-46139653340851747275771053868),(-46139653340851366963178688584)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨6326633093374750341342254022,6326633093374911092066371799⟩,⟨(-15557141102634872565032716214),(-15557141102634711813869455488)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-177700531602077903326282195068),(-177700531602048821573270551310)⟩,⟨(-499745604732740292608146654320),(-499745604732711210953071559166)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 5) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_5 (tableDensity false) (fullFactor false 0 5) density0_contains hk0_0_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-38103559409703560598549327536),(-38103559409703560597060816802)⟩,⟨(-31412668775155819959044750920),(-31412668775155819957425483454)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_5 0 5 ha0_0_5_contains + def realAnswer : RBox := ⟨(-215804091011781463924931522604),(-215804091011752382170231368112)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_5 +namespace hm0_1_0_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-4943074829614396798577398),(-4943074829614384995041940)⟩,⟨5167755498697049420775391,5167755498697061224782763⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-13314565850942927995396328),(-13314565850942902626247563)⟩,⟨14038277458402468660419876,14038277458402494030831645⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-17742003922178278894216604),(-17742003922178257696040778)⟩,⟨19012469556020812405826573,19012469556020833605680893⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-17381383929112525067988145),(-17381383929112515019944746)⟩,⟨19216666872295762622814322,19216666872295772672533065⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-13340150168257027254621618),(-13340150168257024398711138)⟩,⟨15800911964994468171923777,15800911964994471029211119⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-8104479530342051658075036),(-8104479530342051165687960)⟩,⟨10999507805538149345625639,10999507805538149838977813⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-3908729694737202690090238),(-3908729694737202634829801)⟩,⟨6583154019599062326452488,6583154019599062382300352⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1500633106485456050969747),(-1500633106485456045600831)⟩,⟨3341884189453283478783228,3341884189453283484460126⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-457349454652567781305458),(-457349454652567780457420)⟩,⟨1387981395047826715934288,1387981395047826716919416⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-108994807442251042425191),(-108994807442251042229178)⟩,⟨448436176179462456648066,448436176179462456894497⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-19473859827657540997381),(-19473859827657540957786)⟩,⟨105431886459744701218355,105431886459744701272474⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2359836342052265616632),(-2359836342052265610999)⟩,⟨16398637426155147736498,16398637426155147745137⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-159402127533242754452),(-159402127533242753965)⟩,⟨1449030656575968588444,1449030656575968589326⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-4259134610896314258),(-4259134610896314225)⟩,⟨54871956157119376656,54871956157119376717⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-22902067081306790),(-22902067081306774)⟩,⟨472600691867564747,472600691867564765⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-3359560628881),(-3359560628865)⟩,⟨121027093782991,121027093783007⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-178968795967138163912268457),(-178968795967137693388801695)⟩,⟨20274074063819343620297323,20274074063819814152350982⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-498431269528131477949793601),(-498431269528129776041405359)⟩,⟨65231235015920926610845622,65231235015922628543314427⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-716930093028757867325660772),(-716930093028753920632386031)⟩,⟨120250709798146174585412542,120250709798150121313927795⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-809131390391597810932419942),(-809131390391589560763573514)⟩,⟨182934703112273759899510577,182934703112282010109057352⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-789026465964909373976473107),(-789026465964893798890778813)⟩,⟨241397731525925950055152031,241397731525941525181620068⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-693752261063684087515434590),(-693752261063658873239430728)⟩,⟨278763743689565100748399357,278763743689590315061151598⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-562339798811314124582231033),(-562339798811281416327592703)⟩,⟨283811286727946693019602767,283811286727979401304720347⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-425115050635611376312550234),(-425115050635579434311388225)⟩,⟨258748795695637126941172246,258748795695669068965763476⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-302461000593484049625872751),(-302461000593460479533395902)⟩,⟨215428631228218911422879500,215428631228242481532403694⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-204870940908016224068529936),(-204870940908002921268276495)⟩,⟨166628493204047076320956427,166628493204060379133208749⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-133948013224273496143593605),(-133948013224267714482616749)⟩,⟨121080722944039011161426796,121080722944044792830565402⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-85440662829167118562821534),(-85440662829165024318722199)⟩,⟨83031960575818451172412654,83031960575820545421829421⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-53103602682256095958660826),(-53103602682255403089972769)⟩,⟨53676554437837296487405496,53676554437837989359393487⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-31451429492301844488373595),(-31451429492301618729198097)⟩,⟨32303873336223213471664927,32303873336223439232764561⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16454346804123155618265351),(-16454346804123081658197592)⟩,⟨16978957412586265621888432,16978957412586339582946960⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-5097328905541917281920698),(-5097328905541899623351284)⟩,⟨5264319572682784726408999,5264319572682802385284089⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1198165514923986083385598117),(-1198165514923986082847327037)⟩,⟨(-763958090437393079912923867),(-763958090437393079413557873)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-3477508810080891981679893573),(-3477508810080891980095020777)⟩,⟨(-2173279808062583751255473313),(-2173279808062583749787046746)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-5391408479228636709726303719),(-5391408479228636707214301431)⟩,⟨(-3256649173039248641417456358),(-3256649173039248639083072637)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-6700710306465735010588619269),(-6700710306465735007356078794)⟩,⟨(-3869944472470590201426181926),(-3869944472470590198408901721)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-7273938994260741974447040453),(-7273938994260741970760618415)⟩,⟨(-3930622775120070925381392152),(-3930622775120070921919373646)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-7181649027418758665097395798),(-7181649027418758661134837464)⟩,⟨(-3465789370189244734342619893),(-3465789370189244730604847403)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-6637905006566480271486473435),(-6637905006566480267182964303)⟩,⟨(-2660517107161281621405442996),(-2660517107161281617323870812)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-5852513708078174669947484506),(-5852513708078174663871019178)⟩,⟨(-1780968222112125999582581024),(-1780968222112125993709012744)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4962964396994545506891368227),(-4962964396994545488746534064)⟩,⟨(-1037682623021733127231354618),(-1037682623021733109250506363)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-4049474808140447693913462953),(-4049474808140447605888382153)⟩,⟨(-521557842057427430059321813),(-521557842057427342159216034)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-3163756414748362600383123498),(-3163756414748362220378315908)⟩,⟨(-220000302603992404751503051),(-220000302603992024839669737)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2347905994066213465209622260),(-2347905994066212273692130647)⟩,⟨(-66418288261528832535822282),(-66418288261527641088728530)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1639219647098566797298030427),(-1639219647098564235404200972)⟩,⟨6887399209194005105617754,6887399209196566949114085⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1056277315674464638952029613),(-1056277315674460907817178664)⟩,⟨37190363345105896741741590,37190363345109627845155435⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-585168153109085842378147174),(-585168153109082362894161533)⟩,⟨37042283306302348463454213,37042283306305827930769689⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-186784752959964732080564102),(-186784752959963307281813135)⟩,⟨15059712968098548845805271,15059712968099973639522098⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-2782130625620692202777336720),(-2782130625620672042118875075)⟩,⟨(-4257375593159969886902359875),(-4257375593159949725955952558)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-8059245961345045364097029796),(-8059245961344999221865667653)⟩,⟨(-12188721649243847914795006512),(-12188721649243801771732381919)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-12566428990235122673489479381),(-12566428990235078816361006560)⟩,⟨(-18480460830001395068353585786),(-18480460830001351209949510507)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-16077541542958840235811492420),(-16077541542958814814521730614)⟩,⟨(-22460597534625225658250531461),(-22460597534625200235382653493)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-18599020032052042182660990205),(-18599020032052032589344961646)⟩,⟨(-24046785717857606119761489585),(-24046785717857596524731460582)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-20143968269100786449853082764),(-20143968269100784035788002129)⟩,⟨(-23714319282406767586842815530),(-23714319282406765171070389911)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-20599590711519722785812389504),(-20599590711519722349905226601)⟩,⟨(-22110927866774908448153626223),(-22110927866774908010646431286)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-19917110126786377412595087784),(-19917110126786377342301374421)⟩,⟨(-19719124000695430133281565414),(-19719124000695430061575268609)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-18285694306562080130016931602),(-18285694306562080111767197814)⟩,⟨(-16868153310375391254292895116),(-16868153310375391234855515933)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-16052045399278759600597785851),(-16052045399278759590957039383)⟩,⟨(-13850113275718761049422452122),(-13850113275718761038827446684)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-13546500195084083141733701021),(-13546500195084083135093254527)⟩,⟨(-10935406922591024036366134627),(-10935406922591024028995910005)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-10977843116217791153974512410),(-10977843116217791149238156542)⟩,⟨(-8314706371454876979313655709),(-8314706371454876974039451735)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-8437246076880639092076993380),(-8437246076880639088774988276)⟩,⟨(-6051135608484303501832745723),(-6051135608484303498152151805)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-5956232830559974409568668972),(-5956232830559974407422410638)⟩,⟨(-4101238419150315872749865557),(-4101238419150315870356205661)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-3540110441855141311778637251),(-3540110441855141310580727011)⟩,⟨(-2375235649517024155374652954),(-2375235649517024154037649867)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1173447208761946774206128110),(-1173447208761946773822834227)⟩,⟨(-777713224465979162001056464),(-777713224465979161573188235)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1013738168262545251740300289),(-1013738168262366194716226951)⟩,⟨(-9419277060465226253052431957),(-9419277060465047195035603505)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-3423245218223443870948135622),(-3423245218222775578943989449)⟩,⟨(-27818842581085999543209277222),(-27818842581085331248266920752)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-6694984692697090706196994773),(-6694984692695441421435457998)⟩,⟨(-44692303177005999350693801206),(-44692303177004350061261202358)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-10835443178381354104924427904),(-10835443178377572771819333824)⟩,⟨(-58587985387785686129336259127),(-58587985387781904790153406723)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-15747680201040167709880292443),(-15747680201032106204791179962)⟩,⟨(-68054099825931013663800327144),(-68054099825922952151687929879)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-21387025354070672746638721039),(-21387025354055526735381791737)⟩,⟨(-72553428262452437654693261729),(-72553428262437291635904681803)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-27264531939453077210487468180),(-27264531939429733688606275876)⟩,⟨(-72810349442739909382780517888),(-72810349442716565853232909363)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-32228449367649933036733625846),(-32228449367622202251209251715)⟩,⟨(-70089844720605935184172115753),(-70089844720578204391304567349)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-35000487988903535512646160460),(-35000487988878073709508046944)⟩,⟨(-65396065705465550803997421153),(-65396065705440088994300879185)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-34802999696592714533301653792),(-34802999696574570562722788017)⟩,⟨(-59225405646362133320739964060),(-59225405646343989344650589786)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-31661330782985537455682302282),(-31661330782975488834379301998)⟩,⟨(-51682279563131829511875637857),(-51682279563121780886113187100)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-26403821000909783160558914084),(-26403821000905152416839833318)⟩,⟨(-42804362651000200144191666179),(-42804362650995569396935400181)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-20265242076656514426168166545),(-20265242076654595908421078412)⟩,⟨(-32980982291665169878040945263),(-32980982291663251357620222875)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-14167740749258756672540816302),(-14167740749257998898312171523)⟩,⟨(-22976662862517162636986431183),(-22976662862516404860917919419)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-8374440371169027621637719527),(-8374440371168741344857063347)⟩,⟨(-13413355394287920848870101663),(-13413355394287634571020387536)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-2773194560129751935940882320),(-2773194560129678074656114787)⟩,⟨(-4393678159039953613266917037),(-4393678159039879751635293463)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨569742879150954062621645464,569742879150954067289169288⟩,⟨(-34345072468621242029411015),(-34345072468621238869784205)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1561543339659819350189711555,1561543339659819364288458753⟩,⟨(-505858305927995976313211558),(-505858305927995966677982775)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1635517384114208429772893168,1635517384114208453206775933⟩,⟨(-2212028376554336356814661207),(-2212028376554336340309907984)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-695601737095676592713248681),(-695601737095676560165024744)⟩,⟨(-6431069316592113429160354458),(-6431069316592113405291767518)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-6169181872424102460818627428),(-6169181872424102419189754413)⟩,⟨(-15218515552070939303236334425),(-15218515552070939271203317666)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-12898294317843372756410955357),(-12898294317843372703620073480)⟩,⟨(-29832090025435502635951596455),(-29832090025435502593083093851)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-17399431414806912056009357166),(-17399431414806911980821875456)⟩,⟨(-48283193106413800969192551670),(-48283193106413800903763884344)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-17706651357127240979742469015),(-17706651357127240812060970946)⟩,⟨(-65871014726452879243124275296),(-65871014726452879084247418777)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-14456382542783844580830140089),(-14456382542783843797302769189)⟩,⟨(-78111565039576020879886221099),(-78111565039576020103483272044)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-9740397478828070717232610795),(-9740397478828065958517881627)⟩,⟨(-82652025052760089041751506756),(-82652025052760084288361811120)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-5697931412459885846644820847),(-5697931412459862208780493793)⟩,⟨(-79521584357120424691517133043),(-79521584357120401057426940517)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-3497910157550283475439338113),(-3497910157550200065788906229)⟩,⟨(-70489055834590676222426883159),(-70489055834590592815492325825)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2863152550046790621037810827),(-2863152550046592015222861675)⟩,⟨(-57817440950614938636856158315),(-57817440950614740032950965766)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-2639196084903337315961751353),(-2639196084903023071776965262)⟩,⟨(-42997674645521273081139835537),(-42997674645520958838180429134)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1962962342107783536838179241),(-1962962342107472570401988205)⟩,⟨(-26595641502758042759285983894),(-26595641502757731793518599837)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-727661010269214310315868548),(-727661010269082844676642250)⟩,⟨(-9013561057918555722347714948),(-9013561057918424256912278915)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-108123193166640658513004844530),(-108123193166616779125476916476)⟩,⟨(-260691147175728924684201982560),(-260691147175705045296578077958)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 5) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_5 (tableDensity true) (fullFactor false 0 5) density1_contains hk0_0_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨49827731535766194626925683511,49827731535766194628872197547⟩,⟨41078105321357610713556401440,41078105321357610715673905049⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_5 0 5 ha0_0_5_contains + def realAnswer : RBox := ⟨(-58295461630874463886179161019),(-58295461630850584496504718929)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_5 +namespace hm0_0_0_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2932818336418796183496457),(-2932818336418794931973872)⟩,⟨(-2142197818442544027516426),(-2142197818442542775834112)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-7818857542102705890912645),(-7818857542102703248626826)⟩,⟨(-5568474760512347158380314),(-5568474760512344515683221)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-10260630192584176883078217),(-10260630192584174753048630)⟩,⟨(-6951826866952210637596107),(-6951826866952208507064328)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-9967727905879507015607889),(-9967727905879506059398496)⟩,⟨(-6285920631199746354544687),(-6285920631199745397901735)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-7755125943688931304383770),(-7755125943688931051825485)⟩,⟨(-4478479318483083389929671),(-4478479318483083137088625)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-4924458342302515300026112),(-4924458342302515260229649)⟩,⟨(-2575917351005619510849145),(-2575917351005619470915692)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-2545610773419671443977080),(-2545610773419671439857529)⟩,⟨(-1194350223714604843866277),(-1194350223714604839702729)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1056014577961004244550532),(-1056014577961004244127846)⟩,⟨(-438864273528467930962008),(-438864273528467930534709)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-342533978017953915942129),(-342533978017953915862935)⟩,⟨(-124140816660299377006750),(-124140816660299376931716)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-83319295190178566484530),(-83319295190178566465945)⟩,⟨(-25886264622492161759684),(-25886264622492161744008)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-14234342492492741872802),(-14234342492492741869269)⟩,⟨(-3730124987030901218771),(-3730124987030901216216)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1537525278488339176458),(-1537525278488339175980)⟩,⟨(-336219786331339935941),(-336219786331339935653)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-87818044175378658390),(-87818044175378658339)⟩,⟨(-16055854231090064883),(-16055854231090064851)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1898335053018099734),(-1898335053018099717)⟩,⟨(-295889506927610990),(-295889506927610973)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7378619774432932),(-7378619774432915)⟩,⟨(-1015455861303536),(-1015455861303520)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-475266196650),(-475266196634)⟩,⟨(-60429420734),(-60429420718)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-114927900363676436264250216),(-114927900363676336778794061)⟩,⟨(-164987159066559545522214775),(-164987159066559446020994004)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-324258232267429951415473874),(-324258232267429595240211329)⟩,⟨(-460499415926181867277637605),(-460499415926181511058435116)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-477490296434093755898334006),(-477490296434092946455836303)⟩,⟨(-663979609445072712421937109),(-663979609445071902916439988)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-554768237701376111875684203),(-554768237701374469220610419)⟩,⟨(-748177606799989454130218956),(-748177606799987811404739018)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-556062776520350194769483517),(-556062776520347210272348061)⟩,⟨(-720724706251766567936572641),(-720724706251763583372392650)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-498395674192629784710156691),(-498395674192625171536580661)⟩,⟨(-615377049429181736915949192),(-615377049429177123685893221)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-407250587243053659493964092),(-407250587243047986407983051)⟩,⟨(-475384703010220141548313010),(-475384703010214468419468866)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-307162850205978289489298770),(-307162850205973066780722953)⟩,⟨(-337359056241589600164434867),(-337359056241584377426150994)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-215911965496666546022591016),(-215911965496662930546352456)⟩,⟨(-222832696470953101412213344),(-222832696470949485916939899)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-142790083611984695482035688),(-142790083611982785527398061)⟩,⟨(-138695336841675739998875046),(-138695336841673830032827295)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-89780224994615464372138580),(-89780224994614688002171601)⟩,⟨(-82337612593642424559780058),(-82337612593641648183334772)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-54251886500022405775144862),(-54251886500022142229532724)⟩,⟨(-47159462037155165753832521),(-47159462037154902204689827)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-31720689223500389547668035),(-31720689223500307383943858)⟩,⟨(-26267629699157592201309752),(-26267629699157510035721828)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-17772187858286076574603220),(-17772187858286051107256900)⟩,⟨(-14130466405204776447776841),(-14130466405204750979479169)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-8929695738625893100026995),(-8929695738625885054651065)⟩,⟨(-6894957177772958161925297),(-6894957177772950116104782)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-2709188537410794042286849),(-2709188537410792157979672)⟩,⟨(-2060163246525681053687441),(-2060163246525679169250524)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨26321286894353561972693044,26321286894353562162950143⟩,⟨(-1644956961465123503292600862),(-1644956961465123502888760887)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨11913815864868962922171025,11913815864868963473505401⟩,⟨(-4711834617069586452554055034),(-4711834617069586451387962905)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-168690436079541760136225360),(-168690436079541759278315665)⟩,⟨(-7162425058416562925710666936),(-7162425058416562923923041538)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-524448021248020630453885642),(-524448021248020629374112029)⟩,⟨(-8753451624922371068957582186),(-8753451624922371066753678304)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-967419333889599122894936653),(-967419333889599121693721364)⟩,⟨(-9415130056173502974747263565),(-9415130056173502972357556462)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1369389241366295261650438695),(-1369389241366295260389126783)⟩,⟨(-9227120433681567816130994009),(-9227120433681567813738027171)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1635113254126505364590736332),(-1635113254126505363268816471)⟩,⟨(-8382456108477198697275005648),(-8382456108477198694957946997)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1730222443644751472776368750),(-1730222443644751471031979561)⟩,⟨(-7139749048228128922262401376),(-7139749048228128919700754497)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1669213956457654130833763029),(-1669213956457654126039249332)⟩,⟨(-5755735944098168093607912303),(-5755735944098168088182269794)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1494290224443222987075624062),(-1494290224443222964977294038)⟩,⟨(-4428559748409622099619004604),(-4428559748409622077056627025)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1254999556302098416272240456),(-1254999556302098324511958627)⟩,⟨(-3275063307841581225547111012),(-3275063307841581133459129340)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-992946961735731146905862731),(-992946961735730869260603843)⟩,⟨(-2337000817546138566111025891),(-2337000817546138288241008928)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-735959605114809127911633401),(-735959605114808549478124237)⟩,⟨(-1602272930878385511836413205),(-1602272930878384933254109996)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-499230357047659581982549264),(-499230357047658760864580162)⟩,⟨(-1030553784397521627633554217),(-1030553784397520806422699330)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-286858312537229713010965939),(-286858312537228961009188585)⟩,⟨(-573502396666382353281774353),(-573502396666381601229402203)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-93269989758861941543297772),(-93269989758861636484250495)⟩,⟨(-183724393756919831579094204),(-183724393756919526504067626)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1825301432482564368581567542,1825301432482572734058314609⟩,⟨(-4980530907973847757645001662),(-4980530907973839391215662649)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨5183736083299136094939255466,5183736083299155166631607146⟩,⟨(-14498989146431116183922130608),(-14498989146431097109480768614)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨7744689627752223503543798651,7744689627752241492553641910⟩,⟨(-22720728585070768842316427402),(-22720728585070750849070723346)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨9211676380940146926438830494,9211676380940157238170900677⟩,⟨(-28944090995449645943957416174),(-28944090995449635626948059117)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨9515938026490911724870549251,9515938026490915561262074137⟩,⟨(-32730436970625534065915993885),(-32730436970625530223703892254)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨8793611421181039952587753990,8793611421181040902146929549⟩,⟨(-34022772420364177476185688140),(-34022772420364176520730966450)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7369171835433869835243715021,7369171835433870004208302626⟩,⟨(-33138613264773779574131389841),(-33138613264773779399575407871)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨5665753455034979547246352820,5665753455034979574841785781⟩,⟨(-30602357983244707027019694782),(-30602357983244706994397956088)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨4044232977689044169533555151,4044232977689044177270979758⟩,⟨(-26979470296842955970906255542),(-26979470296842955958852631395)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2708274226465278289935347097,2708274226465278294232245478⟩,⟨(-22791832321696389650771525676),(-22791832321696389642915918903)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1712153754533574552557527025,1712153754533574555517795059⟩,⟨(-18471291395040405204413678959),(-18471291395040405198629206536)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1019680176268538227833937572,1019680176268538229916483147⟩,⟨(-14330271258873931936710334568),(-14330271258873931932470724131)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨565228659644483731226996038,565228659644483732654841677⟩,⟨(-10547378373709962883972822820),(-10547378373709962880973834082)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨285628926593142743447504123,285628926593142744363812980⟩,⟨(-7171022207473576314883339829),(-7171022207473576312906452355)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨125286640531049747015678546,125286640531049747523320699⟩,⟨(-4146761351722617278666344754),(-4146761351722617277548163874)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨34187450284924064508231844,34187450284924064670026609⟩,⟨(-1354904619588941874650212801),(-1354904619588941874289690935)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨12549472852192559698757241689,12549472852192654669600330194⟩,⟨(-703836976773652736284540657),(-703836976773557763584623332)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨36184341677213609599465158567,36184341677213962634038313364⟩,⟨(-2909139834225688441180978461),(-2909139834225335401234642135)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨55752661075203523307304131870,55752661075204387727357926409⟩,⟨(-7218170046050998441307987200),(-7218170046050134012844999321)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨69624401040179492047419501779,69624401040181451437314359213⟩,⟨(-14105378540873023550394054248),(-14105378540871064149769070204)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨77272723220181308215921475191,77272723220185425512741138949⟩,⟨(-22888007165261002506083774771),(-22888007165256885197018391187)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨78975507311091688167126983652,78975507311099293810365547081⟩,⟨(-31986165434807266344987124001),(-31986165434799660688857907565)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨75528003799920539928059791948,75528003799932044037675621556⟩,⟨(-39710541097289680814003671160),(-39710541097278176691646374806)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨68174926858166474801470696730,68174926858179871711727730931⟩,⟨(-44892129126969711211505017612),(-44892129126956314289221926827)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨58442640742833836907161181815,58442640742845887394729094119⟩,⟨(-47030502826250202813137263923),(-47030502826238152314617177594)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨47824552009104609485779664108,47824552009113024639710107664⟩,⟨(-46191557027583387240381335546),(-46191557027574972076806495617)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨37529733065255387883835594493,37529733065259958876862859782⟩,⟨(-42803741345418461800298785522),(-42803741345413890799094368738)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨28339994277926657684123066988,28339994277928726915326455662⟩,⟨(-37397885728640685556157457230),(-37397885728638616318340343041)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨20519736293091263499148275862,20519736293092107575226187730⟩,⟨(-30440915602984337309504992923),(-30440915602983493228370917384)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨13879073184891708867132304418,13879073184892038117832983141⟩,⟨(-22369185719999345153587080319),(-22369185719999015899335007706)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨8036293350850089323201227759,8036293350850212619469566516⟩,⟨(-13624884456707201390321005303),(-13624884456707078091951441599)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2631551142359239793581754898,2631551142359271460058490446⟩,⟨(-4567904383638041776159971809),(-4567904383638010108988278791)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨126928635243452701305101430,126928635243452703765574337⟩,⟨10039811988490516289272162162,10039811988490516293009614872⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1826100274837813064979558919,1826100274837813072447521084⟩,⟨29222479111773065674978070822,29222479111773065686139319237⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨7249065486037401189930903377,7249065486037401202600232810⟩,⟨46037948258085161267643140232,46037948258085161285827402040⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨16913794518309912156143174723,16913794518309912174183085140⟩,⟨59729060178324379014537697553,59729060178324379039100996039⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨29136162838773219773437501012,29136162838773219797036247687⟩,⟨69708318856281562430248622066,69708318856281562460467232914⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨41207294634166554780954929987,41207294634166554811167806280⟩,⟨74884762325914877016234711773,74884762325914877052557106526⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨51215460757781213727254931735,51215460757781213770153017177⟩,⟨74340078723929611737035953746,74340078723929611785103570838⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨58365663196549951896488432154,58365663196549951992149039210⟩,⟨68538052000400873091195012164,68538052000400873190664939386⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨62290541953525566513268449559,62290541953525566961909190631⟩,⟨59203879217732314054681333255,59203879217732314505542554187⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨62787836712438966436595047337,62787836712438969142324024475⟩,⟨48398755207506512188993248978,48398755207506514895528514515⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨59854596245602341800083972984,59854596245602355063223432426⟩,⟨37855519015493619146081189441,37855519015493632409001057229⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨53639579206934773200430888850,53639579206934819333463711000⟩,⟨28627548188025711097292693615,28627548188025757229554595050⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨44475827664119216472195471977,44475827664119324888474261013⟩,⟨20923298377475989693848475383,20923298377476098109167858712⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨33039173463666542800052134215,33039173463666712525556036766⟩,⟨14340960199464666965204525953,14340960199464836689835125467⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨20228159385523127321391479899,20228159385523294027389962786⟩,⟨8393332824658601424392258309,8393332824658768129794931753⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨6794595539430490475435189668,6794595539430560682432615757⟩,⟨2763166992290933969267460665,2763166992291004176054937270⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨214830873576944314611950353209,214830873576955814522269740717⟩,⟨(-23940770158366785796341974301),(-23940770158355285848950854360)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 6) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_6 (tableDensity false) (fullFactor false 0 6) density0_contains hk0_0_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨20528291344010862274946094884,20528291344010862275881937748⟩,⟨(-17414573768618534832494062519),(-17414573768618534831793469230)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_6 0 6 ha0_0_6_contains + def realAnswer : RBox := ⟨235359164920955176886796448093,235359164920966676798251678465⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_6 +namespace hm0_1_0_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-448824206016442579793200),(-448824206016441554504973)⟩,⟨(-429312068566857353509163),(-429312068566856328261983)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1196268859057806485498808),(-1196268859057804321645692)⟩,⟨(-1134631994469233918334335),(-1134631994469231754589057)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1559178659281798315100668),(-1559178659281796572067507)⟩,⟨(-1455117110354942855081433),(-1455117110354941112186307)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1486505572848772138029402),(-1486505572848771356511818)⟩,⟨(-1344892187301427314023765),(-1344892187301426532636352)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1128610458571087374065464),(-1128610458571087168095382)⟩,⟨(-953573775605356866194705),(-953573775605356660323789)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-708856930314708028703617),(-708856930314707996455746)⟩,⟨(-523190866055629332744120),(-523190866055629300559453)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-373142486541754627852688),(-373142486541754624625326)⟩,⟨(-222218434250548755179583),(-222218434250548751986530)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-161906760786506230955377),(-161906760786506230674395)⟩,⟨(-73012669097578360198639),(-73012669097578359933320)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-55607007125714710165534),(-55607007125714710125174)⟩,⟨(-18418549078768212189818),(-18418549078768212155345)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-14280389235123446085805),(-14280389235123446077716)⟩,⟨(-3490630463856537273685),(-3490630463856537267353)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2540747935931060096002),(-2540747935931060094628)⟩,⟨(-472017574897415481312),(-472017574897415480334)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-280533609533280022499),(-280533609533280022325)⟩,⟨(-40632638585634137925),(-40632638585634137811)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16110552375145439080),(-16110552375145439052)⟩,⟨(-1787706288337508388),(-1787706288337508367)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-347079512945487501),(-347079512945487485)⟩,⟨(-27251801277076502),(-27251801277076486)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1342845267999057),(-1342845267999041)⟩,⟨(-65801632108721),(-65801632108705)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-86272712238),(-86272712222)⟩,⟨(-2407203861),(-2407203845)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3529943988694859033210445),(-3529943988694777110142417)⟩,⟨(-31161432106629486137882258),(-31161432106629404216220975)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-11247840494784490437322466),(-11247840494784197032876882)⟩,⟨(-85965907184151989059744364),(-85965907184151695659208441)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-20340576596278469659616602),(-20340576596277802429695980)⟩,⟨(-121338035712470152743782299),(-121338035712469485519484159)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-30077798180806232176478737),(-30077798180804876980889276)⟩,⟨(-133149011018345210328133310),(-133149011018343855138872967)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-38242285240619554032511022),(-38242285240617089685571541)⟩,⟨(-125125143201524553569701960),(-125125143201522089228895612)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-42200866385856941421250427),(-42200866385853129175484934)⟩,⟨(-105133748621015860916003130),(-105133748621012048675543987)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-40747765034002760110543100),(-40747765033998067886188576)⟩,⟨(-80815823166871422704006125),(-80815823166866730483848328)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-35000970919788109182195210),(-35000970919783787382633329)⟩,⟨(-57556529572649741443181510),(-57556529572645419646677240)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-27313689572770021303191345),(-27313689572767029556004628)⟩,⟨(-38379151325919765588165269),(-38379151325916773843079021)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-19737323425933854152672101),(-19737323425932274533686924)⟩,⟨(-24283824640658835498325747),(-24283824640657255880733908)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-13389430460510031746156131),(-13389430460509390272686247)⟩,⟨(-14819791992107151730368063),(-14819791992106510257791132)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-8592688720250611618829724),(-8592688720250394138791030)⟩,⟨(-8844485292150985375082606),(-8844485292150767895592326)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-5230012310044128769135975),(-5230012310044061058815745)⟩,⟨(-5174777801149384154000537),(-5174777801149316444002358)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-2993481824794738621249419),(-2993481824794717659984081)⟩,⟨(-2914575029592647441489941),(-2914575029592626480403642)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1517430088521978562982795),(-1517430088521971947402968)⟩,⟨(-1470551031382548851827759),(-1470551031382542236336925)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-461617668938190699817552),(-461617668938189151178231)⟩,⟨(-446974657133813265841143),(-446974657133811717228769)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨199685111812796750695878575,199685111812796750827040960⟩,⟨(-313178335986365235724061705),(-313178335986365235582368170)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨564472028585892375308723834,564472028585892375691933529⟩,⟨(-903202521662000546433932562),(-903202521662000546019383051)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨835319295198282937286699381,835319295198282937888174518⟩,⟨(-1382806593895427151157181792),(-1382806593895427150508333256)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨974456680316959485781341995,974456680316959486544310667⟩,⟨(-1687088547212720883759487276),(-1687088547212720882939868688)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨966279422681408480856046353,966279422681408481710307737⟩,⟨(-1787838833860665095236429051),(-1787838833860665094324070319)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨827717921019465494632879887,827717921019465495528100488⟩,⟨(-1714499916474065044011078679),(-1714499916474065043058804529)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨614684663734361978131013362,614684663734361979075189293⟩,⟨(-1532581693458728789354146599),(-1532581693458728788355016003)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨396745248731585055391232457,396745248731585056696748354⟩,⟨(-1302415851572762193744920169),(-1302415851572762192390315198)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨222405609816830151467067721,222405609816830155296283671⟩,⟨(-1062204512699218313551927021),(-1062204512699218309683700504)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨107462493635379246736986003,107462493635379264710763557⟩,⟨(-832866650584517480730880567),(-832866650584517462727773125)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨43612648321629732603468257,43612648321629807377263452⟩,⟨(-625792578533440423274448468),(-625792578533440348479160530)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨12711528790602637208066302,12711528790602863587372231⟩,⟨(-447768121919270323350473738),(-447768121919270096955270996)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1248929593282987458050176),(-1248929593282515494452453)⟩,⟨(-302713109776459024120923787),(-302713109776458552146235384)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-6680159453048254492213399),(-6680159453047584062026252)⟩,⟨(-190037184668054126973219184),(-190037184668053456536233050)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-6539814880502252476469557),(-6539814880501638177958494)⟩,⟨(-103357688385347732720093354),(-103357688385347118418017610)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2634627471997482775870069),(-2634627471997233515359443)⟩,⟨(-32678632181517223319685890),(-32678632181516974058099852)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1484327639018332844474324576,1484327639018339873720635160⟩,⟨(-969984634491309014114035634),(-969984634491301984969757795)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4229454344673595316704914117,4229454344673611331554809565⟩,⟨(-2796506055328126459401790246),(-2796506055328110444844954635)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨6352805622084251861540152245,6352805622084266947189240305⟩,⟨(-4319647951704137042652637732),(-4319647951704121957448713476)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨7615329886013873004619415973,7615329886013881634605699886⟩,⟨(-5450664693569562186849950864),(-5450664693569553557406015061)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨8008963707132072194862109132,8008963707132075396884445108⟩,⟨(-6193635257919641792886432350),(-6193635257919638591441268087)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨7730792320420747278668555170,7730792320420748068462544207⟩,⟨(-6565652915353682901603028349),(-6565652915353682112369862094)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7034414520287243637382566416,7034414520287243777090238717⟩,⟨(-6552370984252055561858977251),(-6552370984252055422662174042)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨6108955505659693097922011967,6108955505659693120233735224⟩,⟨(-6169238229083942689820228515),(-6169238229083942667945891019)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨5082170179215100064729872324,5082170179215100070616730250⟩,⟨(-5508382691468491555346768224),(-5508382691468491549815937525)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨4057178070673607479032094235,4057178070673607482155180421⟩,⟨(-4701473059991315183604215272),(-4701473059991315180757809876)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3117213686859266188301114108,3117213686859266190416976376⟩,⟨(-3860962288083063624296668456),(-3860962288083063622385360840)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2311135927277797039507512934,2311135927277797040984968047⟩,⟨(-3051011874832335874209863479),(-3051011874832335872878301376)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1645385848505827953070348061,1645385848505827954079584879⟩,⟨(-2294019039746933595005789518),(-2294019039746933594096204394)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1095694381033674002291677616,1095694381033674002936942452⟩,⟨(-1591212036365658608328409951),(-1591212036365658607746648620)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨626796052851246555497331033,626796052851246555853505466⟩,⟨(-934178810430052843678287343),(-934178810430052843357177120)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨203931159303153861491393281,203931159303153861604686458⟩,⟨(-307699631729292508079891773),(-307699631729292507977728450)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨4105993401551247808631617154,4105993401551325861040008005⟩,⟨(-441897114073158269476973234),(-441897114073080217513021813)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨12080453376763641832946421950,12080453376763931996564746090⟩,⟨(-1486432240729861680050978496),(-1486432240729571517742634538)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨19262437663190916780152108303,19262437663191627348981205023⟩,⟨(-2885080211099414696064301608),(-2885080211098704129301880917)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨24975043195760904387651825263,24975043195762515292478557150⟩,⟨(-4617909097033843800995489906),(-4617909097032232898827475685)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨28601737948926718323642689731,28601737948930103749237452499⟩,⟨(-6616395915455849614267817532),(-6616395915452464191699989080)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨29980251106088950129624970606,29980251106095203811472840967⟩,⟨(-8834153410847748491979063609),(-8834153410841494813318428668)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨29514296896791722134170610500,29514296896801179283951735010⟩,⟨(-11047682620293013458819597879),(-11047682620283556312213989611)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨27826217629985232894015563620,27826217629996240688630271684⟩,⟨(-12790816390941513095729075115),(-12790816390930505304087385465)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨25405609675853917350915288592,25405609675863810978920617612⟩,⟨(-13594245231015861055005312515),(-13594245231005967429595261829)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨22513468490654354438596015995,22513468490661256052273687639⟩,⟨(-13228184445267330974437624198),(-13228184445260429362893607311)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨19239412763745776226868928537,19239412763749520341477079302⟩,⟨(-11785952146407673164155837638),(-11785952146403929051240121680)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨15631476482040919959847273954,15631476482042612596360347203⟩,⟨(-9642302655311200466560123071),(-9642302655309507831365762797)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨11845503106323209787211261853,11845503106323899366172764889⟩,⟨(-7278515904266847911542196306),(-7278515904266158333562093326)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨8143463334704799447022069731,8143463334705068148586007109⟩,⟨(-5021331622532675042217431454),(-5021331622532406341320361113)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4710152947559833500031986379,4710152947559934047705422323⟩,⟨(-2940693590241046336341824402),(-2940693590240945789052293354)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1535526661895149509770074410,1535526661895175323968662262⟩,⟨(-969189944045279220610247158),(-969189944045253406535618116)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨17963905080545430255950330,17963905080545431909058709⟩,⟨298078899633894531218540548,298078899633894533661437872⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨263689583545484605967291087,263689583545484610993014838⟩,⟨814429259741905109856747679,814429259741905117212074257⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1145791063694366987101909521,1145791063694366995659072880⟩,⟨848112319011667082802737878,848112319011667094950175057⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨3300504406926535377783737220,3300504406926535390051094697⟩,⟨(-355494596280670826616837493),(-355494596280670809901038316)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨7718509401085399417884417417,7718509401085399434165705239⟩,⟨(-3127801394494576296707090145),(-3127801394494576275571313844)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨14920187453248785822907657763,14920187453248785844406856572⟩,⟨(-6451717554095294841241488795),(-6451717554095294814805312084)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨23771949748080501085370204686,23771949748080501117661956524⟩,⟨(-8569456527167942740170986084),(-8569456527167942703126299308)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨31886073015375581128597080277,31886073015375581205515912699⟩,⟨(-8575450154712750886644510902),(-8575450154712750805547726708)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨37151249899282730527826616088,37151249899282730896367802769⟩,⟨(-6879959918644499677593061626),(-6879959918644499305778110432)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨38624575433603075013760450897,38624575433603077229824233589⟩,⟨(-4555085757505386879528775849),(-4555085757505384661110914053)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨36538663545493567743197315929,36538663545493578580624382611⟩,⟨(-2619810429072846300997276294),(-2619810429072835461975099464)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨31890420295310120669881384183,31890420295310158348633170581⟩,⟨(-1582891255109285115514808434),(-1582891255109247435662158267)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨25809644388536828170582916108,25809644388536916745140803636⟩,⟨(-1277890956770655673116715432),(-1277890956770567097812660726)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨18990696449388917512416648253,18990696449389056238698323708⟩,⟨(-1165447611083643953675382123),(-1165447611083505226931328253)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨11659804772200232239568241209,11659804772200368548078967042⟩,⟨(-860526805455894571090827866),(-860526805455758262335269534)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3936678886230656776607537651,3936678886230714193250590648⟩,⟨(-317804243377572419203714118),(-317804243377515002487949812)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨107523780860198928963394181551,107523780860208372157153565765⟩,⟨(-38981651387878377815115498329),(-38981651387868934620225868068)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 6) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_6 (tableDensity true) (fullFactor false 0 6) density1_contains hk0_0_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-26844688680629589129999457055),(-26844688680629589128775662541)⟩,⟨22772904158962699395422228994,22772904158962699396338389447⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_6 0 6 ha0_0_6_contains + def realAnswer : RBox := ⟨80679092179569339833294724496,80679092179578783028477903224⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_6 +namespace hm0_0_0_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨159475936762193925598857,159475936762194018788776⟩,⟨(-218331431944299526134411),(-218331431944299432956195)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨406792987194422433643983,406792987194422626855329⟩,⟨(-571136530614354609461455),(-571136530614354416279608)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨488860399436232838612776,488860399436232988788262⟩,⟨(-721354713723481305578180),(-721354713723481155437180)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨417092053663526900784809,417092053663526964574805⟩,⟨(-661076757758479258909699),(-661076757758479195147503)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨274532977038863075057237,274532977038863090689547⟩,⟨(-475048328462652844308099),(-475048328462652828692217)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨142594537673416093408663,142594537673416095648194⟩,⟨(-272330404450314969877250),(-272330404450314967644606)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨58226123629885343558748,58226123629885343765310⟩,⟨(-123935577017806222332187),(-123935577017806222127349)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨18316496390344311241540,18316496390344311259731⟩,⟨(-43994794887663335544580),(-43994794887663335526372)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨4292401286984154781139,4292401286984154783799⟩,⟨(-11815551274607459994259),(-11815551274607459991372)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨712981264999235010211,712981264999235010669⟩,⟨(-2287781996663995949197),(-2287781996663995948637)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨77943594944587595372,77943594944587595441⟩,⟨(-296304078918890550816),(-296304078918890550719)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨5002274511325816244,5002274511325816265⟩,⟨(-22776513755149239026),(-22776513755149239005)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨155779167259073538,155779167259073554⟩,⟨(-848457882823762903),(-848457882823762885)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1638318890615744,1638318890615760⟩,⟨(-10477450958627001),(-10477450958626984)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨2527491697715,2527491697731⟩,⟨(-18336015966275),(-18336015966259)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨37658598,37658614⟩,⟨(-296062275),(-296062259)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨24623128051657361031312595,24623128051657375880467015⟩,⟨(-17152111788720928330636517),(-17152111788720913483858745)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨68077210047013632612552760,68077210047013685251161853⟩,⟨(-47935277873104757019115267),(-47935277873104704387067642)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨96322298359547497646200186,96322298359547614955760530⟩,⟨(-69265044154936359310878930),(-69265044154936242010549438)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨105531831036582863196120785,105531831036583094506830693⟩,⟨(-78243474866174040301557361),(-78243474866173809000876040)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨97972876744490083783302002,97972876744490488609074218⟩,⟨(-75577645404529304272594950),(-75577645404528899456022433)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨79947130012055494456535466,79947130012056092431174324⟩,⟨(-64735244990586208452621719),(-64735244990585610485384330)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨58575045423670730260506342,58575045423671428034626519⟩,⟨(-50165768425918536787694319),(-50165768425917839018894441)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨39164335271054485070640429,39164335271055090962733354⟩,⟨(-35647280993713658204470856),(-35647280993713052315845009)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨24246514064625116519095713,24246514064625510017415738⟩,⟨(-23485421707482137742432839),(-23485421707481744246188612)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨14098580618399089111012587,14098580618399283580769553⟩,⟨(-14509934318912580093501831),(-14509934318912385624902354)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨7812835553321436126993037,7812835553321509986814705⟩,⟨(-8516398059939154137583845),(-8516398059939080278372082)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨4186815885040068121419253,4186815885040091587620169⟩,⟨(-4815185243077343273881598),(-4815185243077319807989319)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2195087312237859196632656,2195087312237866080775679⟩,⟨(-2650232600870178738940842),(-2650232600870171854949739)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1122731041283877026770289,1122731041283879053927533⟩,⟨(-1411904057830583005059281),(-1411904057830580977975009)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨528247206995070357185289,528247206995070974089333⟩,⟨(-684100649241083873450316),(-684100649241083256578848)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨154846452969154539469842,154846452969154681123780⟩,⟨(-203627412023344830527927),(-203627412023344688883266)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨368539032376214245443569936,368539032376214245535223532⟩,⟨5897736967513997600604035,5897736967513997643248298⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1048978244527817939942928022,1048978244527817940205921507⟩,⟨2669144159903460265524855,2669144159903460388283009⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1574649567996747401691286435,1574649567996747402089509944⟩,⟨(-37020503144955410555028466),(-37020503144955410366301880)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1889120903948853152063331216,1889120903948853152545452820⟩,⟨(-113046069436068693063399629),(-113046069436068692829992444)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1983555675771165250053157188,1983555675771165250563733501⟩,⟨(-203614013129945377097270709),(-203614013129945376843493453)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1888184660617909993866272758,1888184660617909994363113642⟩,⟨(-279993640179706445875425421),(-279993640179706445616311897)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1659012776433858734628470679,1659012776433858735093629233⟩,⟨(-323383234535883324973468442),(-323383234535883324710693811)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1362083421558982206987963444,1362083421558982207481817809⟩,⟨(-329876740571780937371827395),(-329876740571780937038380918)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1056093480863430716757144905,1056093480863430717753038458⟩,⟨(-306110017046709419549074938),(-306110017046709418672485369)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨780867470118744611725905268,780867470118744615685170174⟩,⟨(-263360395925690133632194620),(-263360395925690129757345261)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨555350554955835186247763284,555350554955835201788103653⟩,⟨(-212731912221672266211682848),(-212731912221672250728742398)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨382049819791898905606646170,382049819791898950867256293⟩,⟨(-162283408245592447683845656),(-162283408245592402461230279)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨253625131733431214268148546,253625131733431305640042548⟩,⟨(-116477252706900276933913163),(-116477252706900185586393765)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨158921223361929983686266533,158921223361930110173282070⟩,⟨(-76980135441632614906315870),(-76980135441632488434135514)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨86825651471033603395408317,86825651471033717204613230⟩,⟨(-43427896126024540398847141),(-43427896126024426597580154)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨27551302793889908036943789,27551302793889953784075502⟩,⟨(-13986724377063023243210340),(-13986724377062977498562778)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1488387222456396704198710693,1488387222456399204497516038⟩,⟨545476420664613448126990509,545476420664615948138113436⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4312316510124526775280651368,4312316510124532449730187004⟩,⟨1541790347152983747923765060,1541790347152989421546753524⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨6694388232668166606807072632,6694388232668171911730663016⟩,⟨2282009954557073820073142631,2282009954557079123734179949⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨8411047076482834590965390902,8411047076482837592908696091⟩,⟨2677161941897124677968982140,2677161941897127678359335083⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨9342957907568110872883840170,9342957907568111971968326784⟩,⟨2716803262596972791240433468,2716803262596973888640212972⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨9505947923995754440656374702,9505947923995754708429881438⟩,⟨2457564317881830434185900295,2457564317881830700286430073⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨9035925075054832509372746038,9035925075054832557171295712⟩,⟨2010077883048751713819740573,2010077883048751760066778683⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨8125610569233207325176307446,8125610569233207333895041429⟩,⟨1505066961876670270191357687,1505066961876670277548839295⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨6966885320358073557945687661,6966885320358073561090879553⟩,⟨1044885478640597059268580274,1044885478640597061274105776⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨5722360495856027171367928119,5722360495856027173366313508⟩,⟨680348012570740772257529176,680348012570740773339934479⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4512937891415369099602671057,4512937891415369101037250786⟩,⟨418551167271689781514495792,418551167271689782239889946⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3414071475051464556717538093,3414071475051464557744394549⟩,⟨243061598590121632511396717,243061598590121633008819438⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2458237489759782147942378447,2458237489759782148653877858⟩,⟨131799472736909307781084121,131799472736909308114571852⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1642134498604611207661202684,1642134498604611208122516448⟩,⟨65432021787889886054635845,65432021787889886264822581⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨937956431409731155794449373,937956431409731156052382729⟩,⟨28343996361823750791700183,28343996361823750906678210⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨304527271673468593951621112,304527271673468594034290882⟩,⟨7684146557763012540818857,7684146557763012577225253⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨262973431628404792387339148,262973431628440277370658909⟩,⟨4689000121746605470323039368,4689000121746640954626685686⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1082616622090883043601599132,1082616622091014430780542190⟩,⟨13468686569815598242259064033,13468686569815729627477791529⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨2665716021465704531655934878,2665716021466023755028636504⟩,⟨20597448738622517346121647352,20597448738622836566446163656⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨5151881565361253808408193551,5151881565361969303231127120⟩,⟨25441027001909828057337810046,25441027001910543548307637384⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨8241897432682958634364912110,8241897432684440716412772106⟩,⟨27838252747338550790739056486,27838252747340032868442496684⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨11324874275131253978857564639,11324874275133945755178311861⟩,⟨27973795101532603768736073968,27973795101535295540550123175⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨13793122227325593026257233559,13793122227329588007578364980⟩,⟨26244637896510975179318199527,26244637896514970156257947591⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨15272721134135231772141580290,15272721134139790169763567546⟩,⟨23202497789141338393420830098,23202497789145896786980626120⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨15657938868017468199448855625,15657938868021481862385988416⟩,⟨19464169461881264801524714035,19464169461885278460829843092⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨15048646734801703994398295917,15048646734804447775420280804⟩,⟨15585526637793273314835564808,15585526637796017092717175675⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨13656684122954955615649326904,13656684122956415506805554517⟩,⟨11977166393864177460104864520,11977166393865637348644463273⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨11705151485360757664195593104,11705151485361405980416551701⟩,⟨8871898594490182525011256193,8871898594490830839149267063⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨9370666138342113011219927196,9370666138342373064538500577⟩,⟨6317410076726546888367448930,6317410076726806940115353886⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6795245107098455206444419597,6795245107098555279740420796⟩,⟨4216405496661481601133115296,4216405496661581673338042447⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4100860001440831798077497320,4100860001440868917106176165⟩,⟨2418839692328137227126794811,2418839692328174345514951939⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1368353490845585271798730663,1368353490845594758224332037⟩,⟨788304663909603721676435518,788304663909613207891053171⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-4502261005163963631939449665),(-4502261005163963630249076115)⟩,⟨56904854150827799230552555,56904854150827800334107238⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-13063071756497214578440956036),(-13063071756497214573409785949)⟩,⟨815921923674925685268573855,815921923674925688609452441⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-20451645984913600261950977511),(-20451645984913600253806649699)⟩,⟨3218770882513571678819496303,3218770882513571684457805390⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-26291891381999788602650327277),(-26291891381999788591751356541)⟩,⟨7442105733008700317436220906,7442105733008700325401073297⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-30325532335995167655232517185),(-30325532335995167641984999063)⟩,⟨12670834077534727631557811789,12670834077534727641865503946⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-32124365332371926091959613324),(-32124365332371926076269013065)⟩,⟨17671924919970042482800025873,17671924919970042495818731436⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-31391216724295629763062244164),(-31391216724295629742664601243)⟩,⟨21620082023254925428205529213,21620082023254925446384683229⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-28452154199839563760317760665),(-28452154199839563718990274367)⟩,⟨24221806427075864983959638573,24221806427075865023689392234⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-24146058077230116323655341133),(-24146058077230116140185223706)⟩,⟨25396935334042833793605248317,25396935334042833976173952564⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-19392970388836478123475478063),(-19392970388836477041905603330)⟩,⟨25150999483080603255048673476,25150999483080604336317806428⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-14912764680653774346266860669),(-14912764680653769133279411977)⟩,⟨23573036889363357017386954315,23573036889363362230496137419⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-11103177854430032523118602654),(-11103177854430014659928192373)⟩,⟨20800298151037790005465473670,20800298151037807868995640947⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-8006611490424192015208068445),(-8006611490424150570396022809)⟩,⟨17017586565150087891174403796,17017586565150129336392562489⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-5429372935695908010890420306),(-5429372935695843787347139018)⟩,⟨12507795717921655656922428821,12507795717921719880827613011⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3154112591642710782476366276),(-3154112591642648147860646038)⟩,⟨7601385757874153078273628385,7601385757874215713133165372⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1034415354827332382370732834),(-1034415354827306100358886863)⟩,⟨2543611449543175011205211150,2543611449543201293302449254⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-6617440438836928329403838533),(-6617440438833021324030101898)⟩,⟨79464883135223756381829952923,79464883135227663374731329094⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 7) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_7 (tableDensity false) (fullFactor false 0 7) density0_contains hk0_0_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨6729365308027706017102337474,6729365308027706017384256234⟩,⟨10540201987632755225284156051,10540201987632755225743956641⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_7 0 7 ha0_0_7_contains + def realAnswer : RBox := ⟨111924869190777687598498941,111924869194684693454154336⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_7 +namespace hm0_1_0_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨31959911232823378635934,31959911232823454967061⟩,⟨(-33412359044546019759954),(-33412359044545943425763)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨82883257021004422594285,82883257021004580788197⟩,⟨(-87383119846625718627904),(-87383119846625560426102)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨102313562088416002450286,102313562088416125301816⟩,⟨(-109620881120521088951266),(-109620881120520966090001)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨89231755100883939290892,89231755100883991394265⟩,⟨(-98601701612244069279252),(-98601701612244017167205)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨58466085753959340931459,58466085753959353659460⟩,⟨(-69145618804244822932475),(-69145618804244810198348)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨28981835374061257798232,28981835374061259603041⟩,⟨(-39199711342195743310885),(-39199711342195741502525)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨10846533406845156932522,10846533406845157090878⟩,⟨(-18159413504811295497458),(-18159413504811295337385)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨3052158524772794140491,3052158524772794151765⟩,⟨(-6740054397408637407339),(-6740054397408637395382)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨637946135003198364448,637946135003198365668⟩,⟨(-1916305071739901692402),(-1916305071739901690964)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨96278594619836183752,96278594619836183945⟩,⟨(-391752068845634517997),(-391752068845634517753)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨9872748337742832812,9872748337742832850⟩,⟨(-52854145154003743816),(-52854145154003743772)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨605317075944758126,605317075944758144⟩,⟨(-4154662398893010550),(-4154662398893010530)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨17402537901470123,17402537901470139⟩,⟨(-155658962585647451),(-155658962585647435)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨151831589023418,151831589023434⟩,⟨(-1915854574811358),(-1915854574811342)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨164928803801,164928803817⟩,⟨(-3337190000519),(-3337190000503)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1505423,1505439⟩,⟨(-53743284),(-53743268)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨4650627372500775672329991,4650627372500787897932048⟩,⟨(-526803488326377648931159),(-526803488326365423132343)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨12708898096078759482964551,12708898096078802838671615⟩,⟨(-1662429996823526038011202),(-1662429996823482681762161)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨17603164934211267980365019,17603164934211364670869330⟩,⟨(-2949256235347981113922688),(-2949256235347884422652289)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨18782317268160928134320129,18782317268161118956593467⟩,⟨(-4239243279265408892650564),(-4239243279265218069536407)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨17010352095374573218652176,17010352095374907480203814⟩,⟨(-5193621832153674561981111),(-5193621832153340299640962)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨13659099657157155218703177,13659099657157649365592544⟩,⟨(-5477078152497954306477117),(-5477078152497460158932489)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨9957803212275108009395189,9957803212275685133156739⟩,⟨(-5015889861628847389199919),(-5015889861628270264943906)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨6681555179419397129304518,6681555179419898502007994⟩,⟨(-4059545229099057990880905),(-4059545229098556617835793)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨4175761593759250997837759,4175761593759576609738893⟩,⟨(-2969425676668281468731310),(-2969425676667955856608477)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2468185325449614580822126,2468185325449775415670004⟩,⟨(-2004711693045764936397382),(-2004711693045604101410839)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1405943027321182117556311,1405943027321243143778511⟩,⟨(-1269607416543270847812308),(-1269607416543209821506354)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨785018832297848167345185,785018832297867531652789⟩,⟨(-762452164295962760309741),(-762452164295943395953645)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨432338583863734529143272,432338583863740202163960⟩,⟨(-436903366333857605960632),(-436903366333851932912999)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨231542851536745790592984,231542851536747458997476⟩,⟨(-237804428547893247227877),(-237804428547891578809099)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨112657613769898589330145,112657613769899096563084⟩,⟨(-116248499829146988400663),(-116248499829146481160871)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨33595385792846554163543,33595385792846670572519⟩,⟨(-34695974658904411665860),(-34695974658904295254848)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨70164944873664765305110695,70164944873664765337079847⟩,⟨44737881696593386877871772,44737881696593386907400387⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨201075217519352708572632041,201075217519352708665570052⟩,⟨125668291428147939468301803,125668291428147939554018914⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨304006423882783542124807177,304006423882783542268457654⟩,⟨183652211781036288558166912,183652211781036288691003054⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨364103498410870130988921234,364103498410870131167047468⟩,⟨210324692521976014269342957,210324692521976014434714113⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨376674610546281295340860746,376674610546281295534406759⟩,⟨203621338746241827124680500,203621338746241827305366756⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨350864898544989426926712531,350864898544989427122875919⟩,⟨169453871798669203191165299,169453871798669203374959930⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨303329536196343441093095736,303329536196343441291937057⟩,⟨121740953688306716002404091,121740953688306716189634794⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨248463613705761756907907089,248463613705761757166776922⟩,⟨75765650296449851056840622,75765650296449851305595724⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨194888080160786886340252681,194888080160786887047191483⟩,⟨40863520444269538430978781,40863520444269539130043001⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨146846111366178116883327697,146846111366178120039737080⟩,⟨18981027103842755658406273,18981027103842758809005710⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨106111709629536745195252302,106111709629536757815283993⟩,⟨7411473098666142315577508,7411473098666154931439142⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨73201854882884350829739436,73201854882884387704397915⟩,⟨2085440710430444791014444,2085440710430481662670300⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨47919202882045804891951919,47919202882045879426843842⟩,⟨(-194072923616980547053201),(-194072923616906014201136)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨29306942781561890645450023,29306942781561993908760783⟩,⟨(-1028522538315696249584236),(-1028522538315592987498269)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨15648230004100614439539828,15648230004100707402388841⟩,⟨(-989676942321129565466409),(-989676942321036603250988)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨4900499534815533927441853,4900499534815571305025046⟩,⟨(-395071564289287186656714),(-395071564289249809263981)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨289871561676190444180942859,289871561676192544830566449⟩,⟨443579023466810437095706473,443579023466812537776312079⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨831748781921375672918702823,831748781921380437078248634⟩,⟨1257956369881663972890390882,1257956369881668737138473128⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1272749680081774333209423833,1272749680081778780753020086⟩,⟨1871873542441246495488939385,1871873542441250943165668687⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1583950994206610942014430592,1583950994206613452917596018⟩,⟨2213189363770379378730374295,2213189363770381889793275952⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1767944452160000727484739380,1767944452160001643261093511⟩,⟨2286456934392772773061883018,2286456934392773689004815573⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1834354755019083962179547175,1834354755019084183352217843⟩,⟨2160279029354092004052939963,2160279029354092225383511335⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1786551067188267470492895675,1786551067188267508593951970⟩,⟨1918341833367740317254788222,1918341833367740355495664618⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1638012364942022750658889151,1638012364942022756493695809⟩,⟨1622283315715264937640517099,1622283315715264943591416180⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1422390138177809661837992194,1422390138177809663274774480⟩,⟨1312540804939426108215428040,1312540804939426109743697477⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1180371938909134498829989176,1180371938909134499550326502⟩,⟨1018769956111001085349269653,1018769956111001086138367341⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨943283998684523466153075999,943283998684523466624595930⟩,⟨761687143131368978225627004,761687143131368978746282289⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨726849314682706079562306710,726849314682706079883151245⟩,⟨550652546628569323001648796,550652546628569323356395705⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨534639308851037776984052773,534639308851037777198787778⟩,⟨383500724638495509794874297,383500724638495510032069062⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨364372728800031333316083036,364372728800031333451221347⟩,⟨250914217787937703692830018,250914217787937703841917107⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨211300056838189411342005549,211300056838189411415767934⟩,⟨141775831582142522958080741,141775831582142523039403273⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨69158246603997699951056335,69158246603997699974390791⟩,⟨45835425733260814241733799,45835425733260814267444293⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨165108668528199765695326615,165108668528228928524326634⟩,⟨1534165689506573150597705165,1534165689506602313597131300⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨553231127044669232162567041,553231127044777218823136229⟩,⟨4496574554650738811822388935,4496574554650846798983231736⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1065669527209884438501501235,1065669527210146842503742869⟩,⟨7116166821712984043366467892,7116166821713246448151950368⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1686953511211485415159486633,1686953511212073652165087635⟩,⟨9125632604998111848753314334,9125632604998700086755186334⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2382804980550983168360866373,2382804980552201797650476124⟩,⟨10303687560839530763925254839,10303687560840749394332398838⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨3127841181371441292124947997,3127841181373654579958963382⟩,⟨10618858032067387043746560347,10618858032069600332736061834⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨3837180385548990158097215503,3837180385552274297828099999⟩,⟨10255094725511331094108012569,10255094725514615234965857668⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨4351378660323981271601122138,4351378660327726754893478562⟩,⟨9469412645109587340807284916,9469412645113332825131026069⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨4525917118196773266425906046,4525917118200068544699250148⟩,⟨8460151527362152470725803648,8460151527365447749879175675⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨4309766185834577423215990197,4309766185836827712308915959⟩,⟨7335786745883232580616855309,7335786745885482870417699721⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨3760695542279146351591858799,3760695542280342152913023244⟩,⟨6139174399885437250852689722,6139174399886633052724220512⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨3018281580006213370291347021,3018281580006743693546505683⟩,⟨4893019962368792986776778171,4893019962369323310453172174⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨2240759823751757508919478972,2240759823751969961574651812⟩,⟨3646740561766504899488391415,3646740561766717352452202314⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1525439833358149631269890689,1525439833358231300072168685⟩,⟨2473940280009473191960271481,2473940280009554860969628745⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨885113097811075079539506620,885113097811105349343331033⟩,⟨1417710642059734154605612515,1417710642059764424527547344⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨290329306091410089256229087,290329306091417822285987253⟩,⟨459981006203887449324202088,459981006203895182391913341⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-133670897878370155879180899),(-133670897878370154783265260)⟩,⟨8053605227797999481210407,8053605227798000222555063⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-364088293106153345966763665),(-364088293106153342677661284)⟩,⟨117817822913123667783968433,117817822913123670030896362⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-376970001661167030258341794),(-376970001661167024860992127)⟩,⟨508716059999078787051195712,508716059999078790854015352⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨155722941225097418618574175,155722941225097425976985749⟩,⟨1451892781702397996465547127,1451892781702398001869751733⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1359282204351253253167559973,1359282204351253262365711552⟩,⟨3355473093821661035138626412,3355473093821661042231742978⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2766174986559797490771739561,2766174986559797502119215860⟩,⟨6396260518835450843476558727,6396260518835450852718524677⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨3617716978642256117085273208,3617716978642256132730055978⟩,⟨10032211803963731753537806051,10032211803963731767198592326⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨3559931915668175874936863646,3559931915668175908556007857⟩,⟨13230370676551170631889680532,13230370676551170663810159370⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2806576081358840865883710002,2806576081358841017122423724⟩,⟨15145940304594278290069622278,15145940304594278440020435296⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1825914931929657906802387789,1825914931929658793263530099⟩,⟨15471705457726915483764080675,15471705457726916369336075105⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1032488776793162189744832558,1032488776793166449982273002⟩,⟨14390742765804230159916223383,14390742765804234419580177611⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨613980386494142257340474438,613980386494156847579776550⟩,⟨12366867289619220508743561969,12366867289619235098605529363⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨488879338162495689371007596,488879338162529549737261148⟩,⟨9875605061290893141571211885,9875605061290927001692648034⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨441133525939321987525671375,441133525939374481480366676⟩,⟨7189406335216905756516261424,7189406335216958250325755728⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨323348762630876228815941207,323348762630927442774803280⟩,⟨4381536700582556619990173284,4381536700582607833875211996⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨118971687294850587747963504,118971687294872081774443946⟩,⟨1473726590381289898939515262,1473726590381311392944875532⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨12561337659672584910509771992,12561337659675793307153888952⟩,⟨38757723225846026038543727439,38757723225849234434328490051⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 7) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_7 (tableDensity true) (fullFactor false 0 7) density1_contains hk0_0_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-8799939248959307868887104305),(-8799939248959307868518441313)⟩,⟨(-13783341060750526064434404839),(-13783341060750526063833127144)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_7 0 7 ha0_0_7_contains + def realAnswer : RBox := ⟨3761398410713277041522667687,3761398410716485438735447639⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_7 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_1.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_1.lean new file mode 100644 index 0000000000000000000000000000000000000000..d5cc6ca3b63c41b5496ee037de131ab3a381850a --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_1.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_0_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨14221937339082765728763,14221937339082771798957⟩,⟨10388244156059177458263,10388244156059183529206⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨36506919070700590816843,36506919070700603176073⟩,⟨26004543767403559503610,26004543767403571864695⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨44383191435990358215773,44383191435990367477768⟩,⟨30086064297763118857003,30086064297763128121069⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨38378803549578154340304,38378803549578158062017⟩,⟨24225792970596757238051,24225792970596760961320⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨25479952732023178287837,25479952732023179133199⟩,⟨14735617105529747960904,14735617105529748807099⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨13192351999494547011492,13192351999494547121202⟩,⟨6914452095980202209435,6914452095980202319440⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨5288438646144213312384,5288438646144213321323⟩,⟨2487838451304117441022,2487838451304117450015⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1607615521191315560273,1607615521191315560975⟩,⟨670479518390553997579,670479518390553998273⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨357839559695127650640,357839559695127650748⟩,⟨130297060620380882609,130297060620380882706⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨55227566538573717421,55227566538573717455⟩,⟨17262113759623794542,17262113759623794570⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨5432552758580125669,5432552758580125688⟩,⟨1434135329251956511,1434135329251956529⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨297894808019447675,297894808019447694⟩,⟨65681349055807512,65681349055807529⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨7258458365264894,7258458365264914⟩,⟨1337548103870991,1337548103871007⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨51339662998702,51339662998719⟩,⟨8048920480567,8048920480584⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨40489753085,40489753102⟩,⟨5588387543,5588387559⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨163727,163743⟩,⟨20828,20844⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2239848321394599969130259,2239848321394601907844083⟩,⟨3215475375153309754251535,3215475375153311693278840⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨6200618446710739602131247,6200618446710746407509562⟩,⟨8806228165514726362859181,8806228165514733169094761⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨8792091073527847348629049,8792091073527862223075685⟩,⟨12227211361150397468908987,12227211361150412344539024⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨9656769437936002458430766,9656769437936030959052758⟩,⟨13025949754951754200325389,13025949754951782702197279⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨8989456841129911222567959,8989456841129959275031585⟩,⟨11655013515311169109386463,11655013515311217162954721⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨7358755273828694490875967,7358755273828762325573490⟩,⟨9089946151881679993580427,9089946151881747829126761⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨5408509434538234946962560,5408509434538310062207811⟩,⟨6316901969582726392255234,6316901969582801508078443⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨3621043351878250069678468,3621043351878311592821071⟩,⟨3979589921340334567234895,3979589921340396090731662⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨2236088592246854627102114,2236088592246892114241295⟩,⟨2309341658937501500010788,2309341658937538987348125⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1290658316745425225247247,1290658316745442557265370⟩,⟨1254488929334807953860487,1254488929334825285981402⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨707139915953884872059257,707139915953891022515349⟩,⟨648922364816692693237549,648922364816698843743902⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨374080516385837046099522,374080516385838874894214⟩,⟨325351216905987568911869,325351216905989397730170⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨193795859970155702784860,193795859970156207579169⟩,⟨160546785181768917904030,160546785181769422709177⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨98162475679826292138321,98162475679826433338010⟩,⟨78067613569405724928392,78067613569405866132974⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨45860539942410945701518,45860539942410987089915⟩,⟨35414299117181887527908,35414299117181928918383⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨13391973660266839192309,13391973660266848508979⟩,⟨10183855307958689980587,10183855307958699297834⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1156304184384097877301276),(-1156304184384097868937750)⟩,⟨72247174192025158088681202,72247174192025158106879333⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-523223395831702663171510),(-523223395831702639255027)⟩,⟨204340414473405807187521633,204340414473405807239413127⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨7109022106139969865506317,7109022106139969901834231⟩,⟨302917737528677040536193219,302917737528677040613803511⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨21322236680395931008524617,21322236680395931052673288⟩,⟨356750801512594551543619462,356750801512594551635890599⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨37500272919842175402051450,37500272919842175448966554⟩,⟨365676101977305223472506537,365676101977305223567945339⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨50097185422500791964906042,50097185422500792011485228⟩,⟨338116782437755336662462917,338116782437755336752713513⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨55968085956513330307981340,55968085956513330353690537⟩,⟨287330302608726703178114074,287330302608726703259815458⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨55037944520875408440773863,55037944520875408496552529⟩,⟨227397200724346194113184429,227397200724346194196493412⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨49125628114153424967063308,49125628114153425107317142⟩,⟨169577705871388453486084060,169577705871388453646056778⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨40619173850369356807618407,40619173850369357402198785⟩,⟨120491695549143347384752628,120491695549143347992758728⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨31556015508074478533898686,31556015508074480820067957⟩,⟨82409077315555163069958150,82409077315555165364916934⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨23209914547550357314792208,23209914547550363760492240⟩,⟨54655317293741915254125512,54655317293741921705440059⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨16131227496768261705662735,16131227496768274329120337⟩,⟨35130732450283097399772991,35130732450283110026720672⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨10386817595560121422318668,10386817595560138467843597⟩,⟨21444665591012244459167260,21444665591012261506763033⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨5752879983505881340112655,5752879983505896409322294⟩,⟨11502070768459514194032987,11502070768459529264331031⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1835265841689190035721123,1835265841689196037853093⟩,⟨3615150098579774196938339,3615150098579780199407801⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-142634843538147232565544591),(-142634843538146578830982872)⟩,⟨389192521960823376003233471,389192521960824029813806895⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-401252415752737207189716141),(-401252415752735730322002941)⟩,⟨1122259865176328191629956050,1122259865176329668715098474⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-588361248454381520775982088),(-588361248454380152552197363)⟩,⟨1725887758829249761067447282,1725887758829251129620472125⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-680813074863335012536685138),(-680813074863334248629398658)⟩,⟨2138737564733461073906324136,2138737564733461838213421014⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-678714304193789569916951874),(-678714304193789295236553204)⟩,⟨2333668894597286203571488208,2333668894597286478678487040⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-600993530449104112124376107),(-600993530449104046872346826)⟩,⟨2324066278693377358217897848,2324066278693377423885242415⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-479776391328898277305034300),(-479776391328898266228609563)⟩,⟨2155970496533403812981668642,2155970496533403824434700172⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-349855781896825305845779299),(-349855781896825304129250454)⟩,⟨1887958168171581811587818265,1887958168171581813626820148⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-236231504905442393746334196),(-236231504905442393291459069)⟩,⟨1574275400537461241629988432,1574275400537461242348057611⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-149556587613350904525042320),(-149556587613350904286449513)⟩,⟨1257208647205198569231248481,1257208647205198569676022865⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-89533878641937017655625678),(-89533878641937017500083672)⟩,⟨964838731426624673697671122,964838731426624674008930042⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-50698714835478198622021507),(-50698714835478198518057437)⟩,⟨711736505406707366484837497,711736505406707366702410247⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-26892142979469814805155016),(-26892142979469814736999702)⟩,⟨501332141672499182228875369,501332141672499182376534725⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-13115796358411827835509031),(-13115796358411827793321479)⟩,⟨329042989964902075464253572,329042989964902075558415468⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-5610849550424961502378749),(-5610849550424961479591973)⟩,⟨185638278262498711603210841,185638278262498711655252378⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1511238420232024070957188),(-1511238420232024063789164)⟩,⟨59889691986542243015745592,59889691986542243032326173⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1533003655352247739495888008),(-1533003655352236138628398742)⟩,⟨85972558902864387152269913,85972558902875988237354507⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-4386711251215509284590770731),(-4386711251215466500234487275)⟩,⟨352528308912426464310655137,352528308912469249292407826⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-6658439645959557507795850843),(-6658439645959454358230306504)⟩,⟨861413781060351169557830946,861413781060454320089823827⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-8134328328236796804688665128),(-8134328328236568191519742219)⟩,⟨1646496562372575824821140587,1646496562372804439200370333⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-8775557166042832947029903134),(-8775557166042366130103214918)⟩,⟨2596948570912975056468039953,2596948570913441874743039548⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-8670225860556492901048477991),(-8670225860555659295814829684)⟩,⟨3508525397501638759783611165,3508525397502472366395687500⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-7979871475320570417301015174),(-7979871475319356474694585892)⟩,⟨4192200927653767592996212767,4192200927654981536920820888⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-6909862380269144079965100293),(-6909862380267786881172281504)⟩,⟨4546605272715078997470133402,4546605272716436197463537398⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-5672405248694102115019573212),(-5672405248692932342134352686)⟩,⟨4561576021052655176045800684,4561576021053824949984933949⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-4444437332400093983958866881),(-4444437332399311166885089688)⟩,⟨4289997675332836660540678057,4289997675333619478509215718⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-3344687298280240090458083454),(-3344687298279832098786425773)⟩,⟨3812691383553911920035037146,3812691383554319912439344912⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2430262789438932525807868787),(-2430262789438754787320551027)⟩,⟨3205729676930298671804513568,3205729676930476410865829063⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1701855330302628383390188545),(-1701855330302558277580227071)⟩,⟨2524058986818274973526009174,2524058986818345079762870783⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1120822893391471478523270675),(-1120822893391444864357692565)⟩,⟨1806228937864339158096201815,1806228937864365772555049154⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-637042264119081475344509446),(-637042264119071697612650956)⟩,⟨1080007852460826222626456184,1080007852460836000529133355⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-206625842291626559190591803),(-206625842291624072656572494)⟩,⟨358664062984212268446082760,358664062984214755036138595⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-22322721072550127636495229),(-22322721072550127203406153)⟩,⟨(-1766623087486843757611754684),(-1766623087486843756942846476)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-318993151099726621231903184),(-318993151099726619924144610)⟩,⟨(-5109547466759641723217923315),(-5109547466759641721233638479)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1250570690220774378242947329),(-1250570690220774376047352566)⟩,⟨(-7949701244518954347215387117),(-7949701244518954344023876878)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2865250669264663387930885665),(-2865250669264663384853881535)⟩,⟨(-10126749232774242938174699582),(-10126749232774242933943447915)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-4821610996916652825159540271),(-4821610996916652821220052475)⟩,⟨(-11543737069306081448523342624),(-11543737069306081443441945916)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-6631470208302197621308472255),(-6631470208302197616399959972)⟩,⟨(-12058461242134628647370474088),(-12058461242134628641439857760)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-7986041802558248457880231551),(-7986041802558248451139284195)⟩,⟨(-11598752278779129401303725248),(-11598752278779129393729906636)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-8795789288752835924124932273),(-8795789288752835909686565064)⟩,⟨(-10335172310964704834310826069),(-10335172310964704819286119926)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-9060665702941485129699696255),(-9060665702941485064690759994)⟩,⟨(-8617114968100072897911326251),(-8617114968100072832582175527)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-8815644815326499537419837190),(-8815644815326499159324769668)⟩,⟨(-6799446522945243348957854845),(-6799446522945242970765150888)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-8123652417966789921462687985),(-8123652417966788128529831737)⟩,⟨(-5140494246263018869568847479),(-5140494246263017076690078937)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-7057802626810754880916101872),(-7057802626810748828374907126)⟩,⟨(-3768132669187757440531428352),(-3768132669187751388119358104)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-5697512362956019585041717507),(-5697512362956005721713015837)⟩,⟨(-2680900778264254814506882568),(-2680900778264240951327209066)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-4143271966726201569299478665),(-4143271966726180304694860361)⟩,⟨(-1798589997161437451121610376),(-1798589997161416186647239079)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-2499415089912381926618582482),(-2499415089912361335013973037)⟩,⟨(-1037120332100439307295357842),(-1037120332100418715777468279)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-833193969603539190645953838),(-833193969603530581742824985)⟩,⟨(-338837110900563850566692209),(-338837110900555241693760762)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-25927253609122364182512265894),(-25927253609121200396649590872)⟩,⟨(-6475195570006046584502274751),(-6475195570004882794844843372)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 8) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_8 (tableDensity false) (fullFactor false 0 8) density0_contains hk0_0_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4529364766859396731214888530),(-4529364766859396731018562805)⟩,⟨2256316090509323776528963724,2256316090509323776627898690⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_8 0 8 ha0_0_8_contains + def realAnswer : RBox := ⟨(-30456618375981760913827154424),(-30456618375980597127568153677)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_8 +namespace hm0_1_0_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2176453562588920703236,2176453562588925676080⟩,⟨2081849971702117386619,2081849971702122359264⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨5585536494351455557772,5585536494351465679018⟩,⟨5298063804029235075761,5298063804029245196498⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨6745054216741725616579,6745054216741733195652⟩,⟨6295976929332720036587,6295976929332727615060⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨5725136891976796716962,5725136891976799758596⟩,⟨5182441437130102806476,5182441437130105847605⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨3709342088940829876558,3709342088940830565858⟩,⟨3138792238182839220230,3138792238182839909199⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1898874364139524355783,1898874364139524444604⟩,⟨1406279378201426839348,1406279378201426927996⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨774568221583283608506,774568221583283615475⟩,⟨463991985604697419363,463991985604697426258⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨246104155203910263641,246104155203910264103⟩,⟨111899853240215653506,111899853240215653942⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨57982472516109648593,57982472516109648653⟩,⟨19397060711589863310,19397060711589863363⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨9448696752995983455,9448696752995983477⟩,⟨2334180651625019369,2334180651625019390⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨968454689263348028,968454689263348044⟩,⟨181820468735215804,181820468735215820⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨54325762012183619,54325762012183635⟩,⟨7957192139139201,7957192139139217⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1331685818622449,1331685818622465⟩,⟨149842853375080,149842853375096⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨9388614844510,9388614844526⟩,⟨749690674581,749690674597⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨7369553520,7369553537⟩,⟨366671216,366671232⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨29717,29733⟩,⟨832,848⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨68792066331844265838903,68792066331845862295692⟩,⟨607315776945056637112438,607315776945058233545263⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨214997345420041475335692,214997345420047081324250⟩,⟨1644012299107409857640912,1644012299107415463564020⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨374188326520735018885970,374188326520747279927781⟩,⟨2234668139856465035139837,2234668139856477296090694⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨522850881682563346353003,522850881682586859289401⟩,⟨2318502339418090086312282,2318502339418113599151306⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨617259063882882943365773,617259063882922620774767⟩,⟨2023729536239333929364811,2023729536239373606685383⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨622119447424923991372584,622119447424980048301541⟩,⟨1553097958175594056664667,1553097958175650113523003⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨540401990615145919189562,540401990615208046742343⟩,⟨1073877598842123640828684,1073877598842185768330587⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨412121026935765059373943,412121026935815969719609⟩,⟨678906189470278684470687,678906189470329594782997⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨282575257485554935799241,282575257485585955875555⟩,⟨397689986833738966336688,397689986833769986392543⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨178235672534221465836256,178235672534235800315185⟩,⟨219592054636673447759453,219592054636687782226313⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨105378354974446987458859,105378354974452069312560⟩,⟨116752822642801280955612,116752822642806362802439⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨59217534407623975800047,59217534407625484953144⟩,⟨60987601591507609287167,60987601591509118436510⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨31943851743884611481333,31943851743885027480018⟩,⟨31613708894718111462449,31613708894718527459159⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨16532528823592117852946,16532528823592234069094⟩,⟨16097689727312974315921,16097689727313090531073⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨7792949163688893431843,7792949163688927464379⟩,⟨7552257987353037808852,7552257987353071840924⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2281850003492823763933,2281850003492831420779⟩,⟨2209467908374451940867,2209467908374459597579⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-8770282243470220542008074),(-8770282243470220536191383)⟩,⟨13754888894110728647261817,13754888894110728653572844⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-24480503204749334783103973),(-24480503204749334766327506)⟩,⟨39169073480568175690004894,39169073480568175708235483⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-35331068025969269025766431),(-35331068025969269000096597)⟩,⟨58481840943462818642161545,58481840943462818669988554⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-39723064498603028425866793),(-39723064498603028394502903)⟩,⟨68760116424512267130667528,68760116424512267164540047⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-37547226380658515727707038),(-37547226380658515694265408)⟩,⟨69444591523811068783161249,69444591523811068819087846⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-30357386472691365349314780),(-30357386472691365316294857)⟩,⟨62832791625332239311994919,62832791625332239347353817⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-21099578901362708000286586),(-21099578901362707967796197)⟩,⟨52536246070559590576918421,52536246070559590611546705⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-12661721574815197080794202),(-12661721574815197039315363)⟩,⟨41479795047147547309929979,41479795047147547353222451⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-6570362927630363349244467),(-6570362927630363237561486)⟩,⟨31291569606755632608829011,31291569606755632721891350⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2933901528956566055767680),(-2933901528956565572479656)⟩,⟨22657626731230721022323213,22657626731230721506606131⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1102184182145404364471292),(-1102184182145402501782169)⟩,⟨15745502994773982246435882,15745502994773984109821732⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-299393616529905269117352),(-299393616529900013817475)⟩,⟨10472304271216625610842004,10472304271216630866629175⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨26380717291207429529962,26380717291217729245146⟩,⟨6637843953878715575749155,6637843953878725875786268⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨138569050667654018139590,138569050667667935412635⟩,⟨3954836863702382911344967,3954836863702396828807078⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨131049867175872430234866,131049867175884739967323⟩,⟨2073016808040963978657457,2073016808040976288486288⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨51837160618106445273611,51837160618111349532692⟩,⟨643021821769168979186277,643021821769173883474183⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-115989983648049029589647154),(-115989983648048480277060219)⟩,⟨75797455450240929447565314,75797455450241478751922640⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-327383444548959127200175292),(-327383444548957887045814990)⟩,⟨216460412285971538722322776,216460412285972778853284285⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-482614598089046732962230865),(-482614598089045585561027591)⟩,⟨328133561799858150463790168,328133561799859297830162030⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-562815055006832957739256877),(-562815055006832318414050006)⟩,⟨402764611521654063329950196,402764611521654702613997412⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-571178657401209546164697682),(-571178657401209316902039509)⟩,⟨441584550072347640914550389,441584550072347870135144824⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-528229955320463380851786076),(-528229955320463326577571882)⟩,⟨448452133121244614706600240,448452133121244668941914258⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-457779056837547772224193622),(-457779056837547763064884913)⟩,⟨426249904749230355110965901,426249904749230364236788597⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-376982910609691790671746369),(-376982910609691789282879935)⟩,⟨380573075860910265126693245,380573075860910266488595538⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-296628717841322497535683979),(-296628717841322497188514350)⟩,⟨321403178524441424536636488,321403178524441424863234314⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-223853726602536264515405485),(-223853726602536264340945176)⟩,⟨259322370475482965412424569,259322370475482965571932926⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-162862061633270861352824864),(-162862061633270861240719975)⟩,⟨201661346737092407081424851,201661346737092407183204598⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-114804322450779105584297923),(-114804322450779105509768940)⟩,⟨151521171028343852215257490,151521171028343852282896955⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-78214453880891803472960689),(-78214453880891803424184329)⟩,⟨109030288403030866512670700,109030288403030866557022685⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-50277927485465195117971847),(-50277927485465195087833178)⟩,⟨73009594629327376087587972,73009594629327376115050497⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-28060111764435337668626435),(-28060111764435337652380953)⟩,⟨41819656250590695178144123,41819656250590695192966744⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-9014203762354600341044099),(-9014203762354600335939209)⟩,⟨13600954609198034696782350,13600954609198034701444640⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-501573369861689190310624215),(-501573369861679656066759770)⟩,⟨53979240632655551879797685,53979240632665086066516522⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1464500736953825974829771843),(-1464500736953790809838688155)⟩,⟨180167862056179837534232067,180167862056215002358252472⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-2300340901700395297073410783),(-2300340901700310506315554207)⟩,⟨344427958659100598631242634,344427958659185389129529685⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-2917652757375629292517062239),(-2917652757375441339168972960)⟩,⟨539230846028260474697221179,539230846028448427718851981⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-3247954289341037794533780637),(-3247954289340653956883676235)⟩,⟨750883349721405165879206169,750883349721789003168498193⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-3291095039648812942933481790),(-3291095039648127517265430332)⟩,⟨969046236635074239430464343,969046236635759664732156214⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-3117953671344375854942699434),(-3117953671343377911574694540)⟩,⟨1166207880260915629188390971,1166207880261913572206580840⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2819788466113145857327185161),(-2819788466112030689771826183)⟩,⟨1295329014147609902213511166,1295329014148725069455892042⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2465199211905585982755470950),(-2465199211904625578660040409)⟩,⟨1318510011949915653732615100,1318510011950876057567011589⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-2091586111397733502805874806),(-2091586111397091479624890261)⟩,⟨1228660570836664866586624278,1228660570837306889562147920⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1714158500225748957128260680),(-1714158500225414768413355232)⟩,⟨1050012600508316030784518969,1050012600508650219342871256⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1340213021794673418482166304),(-1340213021794528027376044319)⟩,⟨826720301776119061052408321,826720301776264452040839237⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-982364133075729120580315994),(-982364133075671846564728819)⟩,⟨603620608141636345406072781,603620608141693619336766246⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-657630569880075747704595076),(-657630569880054027845399706)⟩,⟨405493576514960974512136629,405493576514982694315092360⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-373379133271369760697319650),(-373379133271361786987741429)⟩,⟨233108234253973219285532749,233108234253981192963330603⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-120567622132635785591874193),(-120567622132633758594256699)⟩,⟨76099378925980028762824655,76099378925982055750279140⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-3159279412481426181694371),(-3159279412481425890792081)⟩,⟨(-52450621823175786816336454),(-52450621823175786386149613)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-46061469116946455801094355),(-46061469116946454922095185)⟩,⟨(-142419325744755709044958121),(-142419325744755707758008153)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-197631237813264348009355504),(-197631237813264346530616273)⟩,⟨(-146612252477240144194112400),(-146612252477240142095719658)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-558857036473649597665452082),(-558857036473649595582286266)⟩,⟨59686238594862473117718064,59686238594862475952064488⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1276403861529669689014390590),(-1276403861529669686310446411)⟩,⟨516884857545292312273968705,516884857545292315776617335⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-2399352864640388481783519580),(-2399352864640388478307202027)⟩,⟨1037767437767272215102488956,1037767437767272219364510853⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-3704644150101778999904736639),(-3704644150101778994847943260)⟩,⟨1336391868178176498308160167,1336391868178176504089536212⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-4803547914600164638583510053),(-4803547914600164626992383546)⟩,⟨1293140075733932796993784373,1293140075733932809188988463⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-5403045409180231135195808447),(-5403045409180231081809432960)⟩,⟨1001814244510557315879117291,1001814244510557369708254932⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-5422901956274526607104227177),(-5422901956274526297445628410)⟩,⟨640447390850826673467925589,640447390850826983419317105⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-4959427229959457043827018252),(-4959427229959455578814941198)⟩,⟨356056132794023870770008337,356056132794025335960860057⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-4196380958493991760674235688),(-4196380958493986817327854243)⟩,⟨208388498213009990439808630,208388498213014933897409509⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-3306425840346525833582957306),(-3306425840346514507462240421)⟩,⟨163652630169219389332511974,163652630169230715521572520⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-2381530927674443092532899137),(-2381530927674425711786009805)⟩,⟨146102763008239577186606316,146102763008256957971708320⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1440690982216946346557998262),(-1440690982216929509675787897)⟩,⟨106313205109671623452251736,106313205109688460352758116⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-482738607572886125817433746),(-482738607572879085291644038)⟩,⟨38970478242997813027238021,38970478243004853557947822⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-12431981944566877394438498673),(-12431981944565921656564095343)⟩,⟨3668326871824426694933935761,3668326871825382433236792116⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 8) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_8 (tableDensity true) (fullFactor false 0 8) density1_contains hk0_0_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨5923015464354595725178120591,5923015464354595725434854232⟩,⟨(-2950567195281423400205713672),(-2950567195281423400076337178)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_8 0 8 ha0_0_8_contains + def realAnswer : RBox := ⟨(-6508966480212281669360378082),(-6508966480211325931029241111)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_8 +namespace hm0_0_0_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-601505989903586866594),(-601505989903586515024)⟩,⟨823478150430045138463,823478150430045489990⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1477756917797647827241),(-1477756917797647124220)⟩,⟨2074380576788204787419,2074380576788205490333⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1646189185966193158689),(-1646189185966192650590)⟩,⟨2427852261511057878373,2427852261511058386359⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1251254902848058090250),(-1251254902848057896994)⟩,⟨1981315065990120560337,1981315065990120753514⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-703540497704710334099),(-703540497704710293344)⟩,⟨1215650326079776445914,1215650326079776486632⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-298352874492633785963),(-298352874492633781143)⟩,⟨568683872708963978866,568683872708963983679⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-94639210068454136295),(-94639210068454135932)⟩,⟨200915684711628759629,200915684711628759991⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-21866133019419628213),(-21866133019419628178)⟩,⟨52339128924165146141,52339128924165146182⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3526978463281577633),(-3526978463281577615)⟩,⟨9664828374414725914,9664828374414725937⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-373121888887201134),(-373121888887201118)⟩,⟨1190433909236645558,1190433909236645578⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-23593324736997206),(-23593324736997190)⟩,⟨89078437986622252,89078437986622269⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-772509361491761),(-772509361491744)⟩,⟨3491373682921790,3491373682921806⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-10308098436892),(-10308098436876)⟩,⟨55762325242965,55762325242982⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-35551957578),(-35551957562)⟩,⟨226271643628,226271643646⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-11114576),(-11114560)⟩,⟨80444890,80444908⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-25),(-9)⟩,⟨79,96⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-373246257760114310152107),(-373246257760114085083737)⟩,⟨259996756743082259443884,259996756743082484475501⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1012588662886011963925110),(-1012588662886011181641064)⟩,⟨712967462365946591956115,712967462365947374140615⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1379735712345438252600621),(-1379735712345436575785694)⟩,⟨992060491515402447465738,992060491515404124145812⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1429294981065989049675671),(-1429294981065985927643383)⟩,⟨1059502971329705182673994,1059502971329708304567810⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1232620830756673175807425),(-1232620830756668104815908)⟩,⟨950568563048033782319908,950568563048038853193521⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-918873705111323316101621),(-918873705111316474334749)⟩,⟨743711008599492480886996,743711008599499322567330⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-605701716290534694048063),(-605701716290527504332508)⟩,⟨518455178695013482257335,518455178695020671917068⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-359562169532362081280503),(-359562169532356526402874)⟩,⟨327061645743490058911088,327061645743495613756551⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-195584460463210217411226),(-195584460463207041768116)⟩,⟨189316074391802536881762,189316074391805712508055⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-99260141783970877836494),(-99260141783969504227951)⟩,⟨102087915262796711993051,102087915262798085593481⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-47927987012717935949017),(-47927987012717480522292)⟩,⟨52211682831641421244288,52211682831641876667330⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-22480887585661502818873),(-22480887585661376087704)⟩,⟨25841043885150620753717,25841043885150747483274⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-10440215016104563415202),(-10440215016104530503477)⟩,⟨12599788826926968937904,12599788826927001848943⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-4825933409667801331556),(-4825933409667792587281)⟩,⟨6067379534998784923199,6067379534998793667184⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-2110548334474274191654),(-2110548334474271722996)⟩,⟨2732961732285812093483,2732961732285814562020⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-595352162341818330295),(-595352162341817785530)⟩,⟨782895303775505744160,782895303775506288894⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-12589430536899722691224476),(-12589430536899722688013156)⟩,⟨(-201514655449594722084677),(-201514655449594720626640)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-35382851459886281885875216),(-35382851459886281876775494)⟩,⟨(-91166624358679551410193),(-91166624358679547268327)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-51799059216268525921579115),(-51799059216268525908136138)⟩,⟨1213479774017163603096431,1213479774017163609312329⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-59887249347467202818947348),(-59887249347467202803252314)⟩,⟨3574981284934563442525624,3574981284934563449948684⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-59926965237683759720343257),(-59926965237683759704487764)⟩,⟨6139521116554405114124309,6139521116554405121834066⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-53823554258422897029489723),(-53823554258422897014919130)⟩,⟨7968229317675253174649894,7968229317675253182093235⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-44239047422496879222398404),(-44239047422496879209643871)⟩,⟨8611050183832167461650200,8611050183832167468718351⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-33749436969990487540305613),(-33749436969990487527813416)⟩,⟨8163433851823418982410807,8163433851823418990705673⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-24206912205848460815436773),(-24206912205848460792591836)⟩,⟨7008791174266222725475189,7008791174266222745425047⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-16528795769640245173424350),(-16528795769640245090419246)⟩,⟨5569499851692498344696469,5569499851692498425804992⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-10871327672731111443376852),(-10871327672731111142086155)⟩,⟨4161323778371933005563881,4161323778371933305659207⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-6950811457900477485535576),(-6950811457900476668078986)⟩,⟨2950962637786189969160842,2950962637786190785880631⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-4325742416965504426048972),(-4325742416965502874870036)⟩,⟨1985968146431468713948737,1985968146431470264683910⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-2572303539852096877758555),(-2572303539852094835335488)⟩,⟨1245810270430523619517894,1245810270430525661684284⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1354436393435182941721450),(-1354436393435181167855199)⟩,⟨677417533613944203202528,677417533613945976936275⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-421656528645049768233321),(-421656528645049068158661)⟩,⟨214057400902926774076639,214057400902927474110586⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-90460862901641232806902428),(-90460862901641080836276923)⟩,⟨(-33153009887496921743173199),(-33153009887496769790398132)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-259612474671446851548021838),(-259612474671446509775906457)⟩,⟨(-92823795030962980295720798),(-92823795030962638574440987)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-395518350527735072264855601),(-395518350527734758433437798)⟩,⟨(-134841327820022101085615997),(-134841327820021787330506489)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-483416688530981124694699781),(-483416688530980951717264576)⟩,⟨(-153899719957802716986623946),(-153899719957802544100671615)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-518150307444507479611822837),(-518150307444507418400409163)⟩,⟨(-150722281437161177239110578),(-150722281437161116123702721)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-505089514914333207865881105),(-505089514914333193550760144)⟩,⟨(-130647587609662705366815954),(-130647587609662691143323480)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-457282226058381871624273858),(-457282226058381869184827303)⟩,⟨(-101797251545567956169785657),(-101797251545567953811577901)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-389945030773611019506795325),(-389945030773611019082918914)⟩,⟨(-72293086540023634115882675),(-72293086540023633759888967)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-316227015533970602695535451),(-316227015533970602549816704)⟩,⟨(-47476962509031269947326136),(-47476962509031269855613778)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-245535949150907170926070838),(-245535949150907170838087046)⟩,⟨(-29225053024515600137196488),(-29225053024515600090444841)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-183367679102372046824280729),(-183367679102372046764260532)⟩,⟨(-17025453196776614247228187),(-17025453196776614217580453)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-131896637778641526091165946),(-131896637778641526050197122)⟩,⟨(-9400375046670590392623449),(-9400375046670590373307897)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-90884344831736890117537101),(-90884344831736890090305174)⟩,⟨(-4877517122368833840569983),(-4877517122368833828188273)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-58607371508379146750952249),(-58607371508379146733873206)⟩,⟨(-2336977778405213272138977),(-2336977778405213264612030)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-32659013708664563618549176),(-32659013708664563609219087)⟩,⟨(-987294705190560967614400),(-987294705190560963600171)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-10469496880751419915039303),(-10469496880751419912084435)⟩,⟨(-264191096063855726887881),(-264191096063855725633378)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-24983624436890912447766070),(-24983624436887541125811636)⟩,⟨(-445506194588386449016614505),(-445506194588383077756554428)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-102038001143790267491853456),(-102038001143777882995120661)⟩,⟨(-1269993523322467000165720926),(-1269993523322454615846313048)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-247434546017198671994589741),(-247434546017169044232027473)⟩,⟨(-1913295878124305719003878431),(-1913295878124276091513585968)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-467744883332295686466891130),(-467744883332230755209647914)⟩,⟨(-2311862885973205815242309457),(-2311862885973140884322892081)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-727370760138383395031983200),(-727370760138252693792010650)⟩,⟨(-2459029952450569858703834211),(-2459029952450439157835735474)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-966218419297038479500319688),(-966218419296809000649784376)⟩,⟨(-2388740154036800427815045601),(-2388740154036570949339214981)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-1132618748008463981848189601),(-1132618748008136079489325163)⟩,⟨(-2156817308738222933462711608),(-2156817308737895031456337298)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1203156484485632081593173185),(-1203156484485272879060033296)⟩,⟨(-1829228973981088268306690439),(-1829228973980729066088949364)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1181299492129295574243437954),(-1181299492128992514982676486)⟩,⟨(-1469478943129100480794348778),(-1469478943128797421805428165)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1087128430020518032838226812),(-1087128430020319498339807194)⟩,⟨(-1126616850913535145373250447),(-1126616850913336611101446897)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-946194283158865064260886044),(-946194283158763709176067173)⟩,⟨(-830269734814453949262683966),(-830269734814352594360214752)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-780433765475165481640389529),(-780433765475122166692186047)⟩,⟨(-591764874502523918199200531),(-591764874502480603391595746)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-604344035560955175612571855),(-604344035560938375724968450)⟩,⟨(-407532181341916735852126796),(-407532181341899936067653763)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-426768746867547831054976553),(-426768746867541539338813161)⟩,⟨(-264840108090723584555045551),(-264840108090717292908943160)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-252829742421226512220325497),(-252829742421224222702237413)⟩,⟨(-149134693113594486229646625),(-149134693113592196752045787)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-83565132751240857936802977),(-83565132751240278570191238)⟩,⟨(-48141859596513374339589214),(-48141859596512794986204631)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨616175895622772461416199461,616175895622772461651469806⟩,⟨(-7783814712786789056355974),(-7783814712786788905275568)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1776510824529678898608563605,1776510824529678899304160665⟩,⟨(-110856794040809352672351075),(-110856794040809352217318817)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2746774512510399666766671579,2746774512510399667878297222⟩,⟨(-431892830048529707908449239),(-431892830048529707148467804)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨3467127274774133266145260303,3467127274774133267605340322⟩,⟨(-980575045007864244338228062),(-980575045007864243281593338)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨3906051924264082532838866849,3906051924264082534571314220⟩,⟨(-1630920070305245561644454414),(-1630920070305245560306123851)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨4023508152641208341472661154,4023508152641208343465145887⟩,⟨(-2212032097919792626926125109),(-2212032097919792625281079950)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨3809533614788784359098365963,3809533614788784361598117652⟩,⟨(-2622184437404220895830591644),(-2622184437404220893608718853)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨3337174232626793231280156358,3337174232626793236135637038⟩,⟨(-2839237440463984336030885971),(-2839237440463984331366664010)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2733609804555581114145702542,2733609804555581134823646901⟩,⟨(-2873412100708348834688875590),(-2873412100708348814112051372)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2119148039383847511872311182,2119148039383847629423989693⟩,⟨(-2746701418444905033250449926),(-2746701418444904915726774609)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1575102293128396660214477641,1575102293128397208329021043⟩,⟨(-2488538259275162032238850367),(-2488538259275161484104024145)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1136737645117747218164465527,1136737645117749041021333822⟩,⟨(-2128749863377967363474799828),(-2128749863377965540574812909)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨797931349038435059758600829,797931349038439181759820680⟩,⟨(-1695607724576402093430013286),(-1695607724576397971380555810)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨529620948628077013644402797,529620948628083272075383743⟩,⟨(-1219990881171137239198857151),(-1219990881171130980726473196)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨303130571247941455501009701,303130571247947472929423584⟩,⟨(-730520883132792634284935027),(-730520883132786616829260468)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨98658518894391802982386026,98658518894394309562548364⟩,⟨(-242599038115866056005562018),(-242599038115863549415959020)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3024535502193977091439359342,3024535502194285817220968913⟩,⟨(-7590078589217609416894460446),(-7590078589217300692171121794)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 9) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_9 (tableDensity false) (fullFactor false 0 9) density0_contains hk0_0_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-668647547157113190635763158),(-668647547157113190605003953)⟩,⟨(-1685848966415853282343357017),(-1685848966415853282269274886)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_9 0 9 ha0_0_9_contains + def realAnswer : RBox := ⟨2355887955036863900703596184,2355887955037172626715964960⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_9 +namespace hm0_1_0_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-120543588282572363663),(-120543588282572075693)⟩,⟨126020875632432072562,126020875632432360545⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-301054799196337453776),(-301054799196336878176)⟩,⟨317380503226758677250,317380503226759252880⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-344450612953669164104),(-344450612953668748456)⟩,⟨368987458722075919945,368987458722076335629⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-267652332499558842808),(-267652332499558684958)⟩,⟨295603551599493816605,295603551599493974482⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-149888045278557168952),(-149888045278557135768)⟩,⟨177001935830518822424,177001935830518855624⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-60719846892175974355),(-60719846892175970468)⟩,⟨81852665583934600776,81852665583934604671⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-17671134030590307713),(-17671134030590307431)⟩,⟨29415480573482673767,29415480573482674053⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-3654910346844051338),(-3654910346844051305)⟩,⟨8006564058804307581,8006564058804307611⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-525890162631097662),(-525890162631097644)⟩,⟨1564639004236844896,1564639004236844913⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-50518539659551895),(-50518539659551879)⟩,⟨203497320992901641,203497320992901657⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2993705281731379),(-2993705281731363)⟩,⟨15870804090515292,15870804090515309⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-93684425302278),(-93684425302262)⟩,⟨636564032925614,636564032925630⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1157560855678),(-1157560855662)⟩,⟨10230781848909,10230781848925⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-3324987803),(-3324987787)⟩,⟨41382146545,41382146561⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-732497),(-732481)⟩,⟨14642349,14642365⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨13,29⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-70496230123732537340537),(-70496230123732352038846)⟩,⟨7985026775760827686066,7985026775761012990340⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-189041505895423342243477),(-189041505895422697921527)⟩,⟨24715976147899055479148,24715976147899699808090⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-252175685875007213637722),(-252175685875005831560604)⟩,⟨42202275920298835196408,42202275920300217283079⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-254420690863395473899525),(-254420690863392898364636)⟩,⟨57326308739347718704518,57326308739350294249388⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-214043188963714085655862),(-214043188963709898607300)⟩,⟨65219083739145265124759,65219083739149452182103⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-157004355695344615223061),(-157004355695338961457112)⟩,⟨62825394288834095624810,62825394288839749397506⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-102969646932054719058940),(-102969646932048772543779)⟩,⟨51766626563166697749460,51766626563172644269264⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-61338077946823595630613),(-61338077946818999010697)⟩,⟨37201576412193986471640,37201576412198583094446⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-33679144271943147385261),(-33679144271940519597663)⟩,⟨23911363213763813932431,23911363213766441721707⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-17372902752659297654337),(-17372902752658161611888)⟩,⟨14091435664127423610005,14091435664128559653388⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-8621441513534923433909),(-8621441513534547136126)⟩,⟨7777622711289800237418,7777622711290176535702⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-4213043445343828138601),(-4213043445343723558862)⟩,⟨4089603683843510778179,4089603683843615358179⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2055347286214205496960),(-2055347286214178375169)⟩,⟨2076574625672828909479,2076574625672856031402⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-994972514409584272165),(-994972514409577075388)⟩,⟨1021819058643657295649,1021819058643664492486⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-450057821477291318542),(-450057821477289288770)⟩,⟨464399299530684399622,464399299530686429422⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-129165497197847809088),(-129165497197847361417)⟩,⟨133396934797224923502,133396934797225371186⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-2396855386865491983409888),(-2396855386865491982302499)⟩,⟨(-1528268177284139062515856),(-1528268177284139061497381)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-6782328492117304880055508),(-6782328492117304876876882)⟩,⟨(-4239022685653536639347618),(-4239022685653536636429008)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-10000361249848252064455955),(-10000361249848252059664554)⟩,⟨(-6041902943329512683972476),(-6041902943329512679563089)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-11542836668146853600441611),(-11542836668146853594716140)⟩,⟨(-6668979801781325886358430),(-6668979801781325881070846)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-11381094113085132802789621),(-11381094113085132796861711)⟩,⟨(-6154685307263650702342313),(-6154685307263650696840351)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-10002675095483950004315941),(-10002675095483949998650356)⟩,⟨(-4834598202775105926270865),(-4834598202775105920997351)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-8089022086643629410077909),(-8089022086643629404717035)⟩,⟨(-3250895321423605636298623),(-3250895321423605631286443)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-6156167828916376973572042),(-6156167828916376967135604)⟩,⟨(-1881101584024878852990498),(-1881101584024878846841756)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4466565533142166865006169),(-4466565533142166848930822)⟩,⟨(-939173312960764087326895),(-939173312960764071464835)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-3107926432389402983521279),(-3107926432389402917466422)⟩,⟨(-403156464951506876003690),(-403156464951506810098795)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2077061969988963925157854),(-2077061969988963680566582)⟩,⟨(-145713775845574902142105),(-145713775845574657653018)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1331843057019919127310806),(-1331843057019918461369304)⟩,⟨(-38209477980671700916335),(-38209477980671035044142)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-817378086814758415032485),(-817378086814757149726124)⟩,⟨3186673862517062440319,3186673862518327702189⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-474408187310052759108772),(-474408187310051091710225)⟩,⟨16595241039428785428452,16595241039430452801468⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-244115310278872759953568),(-244115310278871311017641)⟩,⟨15425323507748129800447,15425323507749578723558⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-74999673411392776423827),(-74999673411392204433074)⟩,⟨6045816195931083009124,6045816195931654996073⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-17617785891394274585595274),(-17617785891394146906395376)⟩,⟨(-26959861639055494998925630),(-26959861639055367317783097)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-50074210634943591605271011),(-50074210634943304660636048)⟩,⟨(-75735094446235016207935342),(-75735094446234729257804805)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-75198771560569038032186596),(-75198771560568774922816259)⟩,⟨(-110605528768578636027372564),(-110605528768578372909903485)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-91036925271481449986009353),(-91036925271481305304200330)⟩,⟨(-127224144198292893496999193),(-127224144198292748805764237)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-98043952530701144634468314),(-98043952530701093633539663)⟩,⟨(-126836012668109966791522352),(-126836012668109915781152813)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-97457582020731889748322081),(-97457582020731877926163485)⟩,⟨(-114816141835585022960120005),(-114816141835585011129442816)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-90403339643802310981289902),(-90403339643802309038286172)⟩,⟨(-97108474931689374221155718),(-97108474931689372271022960)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-78602001686970998993349693),(-78602001686970998710775356)⟩,⟨(-77873779340227341050332559),(-77873779340227340762190822)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-64559152223592310361832254),(-64559152223592310295839397)⟩,⟨(-59592245347009305164939560),(-59592245347009305094834646)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-50645012274760465439002121),(-50645012274760465407605762)⟩,⟨(-43724824289567424801345775),(-43724824289567424767059422)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-38324417231857897163577053),(-38324417231857897144049184)⟩,⟨(-30955362346721945670312908),(-30955362346721945648856843)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-28078254957550080183493779),(-28078254957550080170819629)⟩,⟨(-21276817378507468007100642),(-21276817378507467993182730)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-19764929125745968183772166),(-19764929125745968175630458)⟩,⟨(-14179785529761045434225925),(-14179785529761045425310412)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-13003782431143639349418965),(-13003782431143639344459062)⟩,⟨(-8955403254793392561233410),(-8955403254793392555818004)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-7357189983160275400725160),(-7357189983160275398078070)⟩,⟨(-4936592246346099492508358),(-4936592246346099489623866)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2377621137061137552936356),(-2377621137061137552108516)⟩,⟨(-1575800799996262586637852),(-1575800799996262585736952)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-15686688639287767751225456),(-15686688639284997078275241)⟩,⟨(-145761988771103966707201932),(-145761988771101196017229890)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-52155089441473342648656599),(-52155089441463163875537151)⟩,⟨(-423980659548966930115170790),(-423980659548956751292490578)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-98952066445363703971895150),(-98952066445339349735724648)⟩,⟨(-660980905558258018097262146),(-660980905558233663784672819)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-153214420930514667808538297),(-153214420930461285235387603)⟩,⟨(-829196654738683348687907053),(-829196654738629966019723038)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-210335625042125178019689901),(-210335625042017710068197119)⟩,⟨(-910088294392864876412194187),(-910088294392757408357207198)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-266872473986072362852441602),(-266872473985883675974062139)⟩,⟨(-906697703418602342487809996),(-906697703418413655506227576)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-315066249899093500401969896),(-315066249898823942601856331)⟩,⟨(-842678292519648777526197847),(-842678292519379219629601359)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-342765685581074027064279682),(-342765685580778881649025506)⟩,⟨(-746404174868180856024222064),(-746404174867885710524571766)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-341448358999300790945122258),(-341448358999051973830595700)⟩,⟨(-638543776361423042821870109),(-638543776361174225638536927)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-311368231663883798350220454),(-311368231663720971252027362)⟩,⟨(-530113645515973034918928253),(-530113645515810207767743705)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-260605214394209519145492591),(-260605214394126498522715651)⟩,⟨(-425455605621839321155918405),(-425455605621756300493569570)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-201287464403203762597597394),(-201287464403168330796597288)⟩,⟨(-326309682420359530611045637),(-326309682420324098780827385)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-144540151856036766478956625),(-144540151856023041639272549)⟩,⟨(-235231687440116471280475576),(-235231687440102746420043731)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-95813127511609789816000704),(-95813127511604655204121059)⟩,⟨(-155391376404694913814916576),(-155391376404689779189466149)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-54571481126259456510081217),(-54571481126257589455472887)⟩,⟨(-87410129898640755203077465),(-87410129898638888140871410)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-17730420381681922024279870),(-17730420381681449743660892)⟩,⟨(-28091127866482993093001200),(-28091127866482520809964255)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨18294139524235844260589177,18294139524235844410690545⟩,⟨(-1101623713234128378425853),(-1101623713234128276959580)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨49519861803165350707274022,49519861803165351154878274⟩,⟨(-16007104333537075183001536),(-16007104333537074877343365)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨50685439705204108998199754,50685439705204109723374635⟩,⟨(-68247270012022094400297604),(-68247270012022093889172924)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-20334672992163874526995496),(-20334672992163873556545555)⟩,⟨(-191213379063188360346010910),(-191213379063188359632227217)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-174715378920777707053266346),(-174715378920777705867645946)⟩,⟨(-431594510678049306127459720),(-431594510678049305211217997)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-346079555409464385466198675),(-346079555409464384043256503)⟩,⟨(-800050949980104629684790049),(-800050949980104628522466729)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-438824042186373624351174571),(-438824042186373622452063339)⟩,⟨(-1216056208191078580636009398),(-1216056208191078578972100338)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-417549516466104981499999368),(-417549516466104977567665938)⟩,⟨(-1550282372694975446972497126),(-1550282372694975443231039128)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-317875073817636221196970685),(-317875073817636204166382550)⟩,⟨(-1713325922048440189719954970),(-1713325922048440172824483197)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-199684674418674023328050971),(-199684674418673926992970015)⟩,⟨(-1689599741273989896310124927),(-1689599741273989800060394985)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-109146214068335045145671551),(-109146214068334597215073146)⟩,⟨(-1519277192361872625857828967),(-1519277192361872177976219012)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-62870692255565980406524388),(-62870692255564491546641239)⟩,⟨(-1265742285255104180963873590),(-1265742285255102692132464492)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-48696432099771566713082631),(-48696432099768199050684625)⟩,⟨(-984026203531944560018487539),(-984026203531941192372375072)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-43012756236158776110836872),(-43012756236153660707139883)⟩,⟨(-701245203741412948813197527),(-701245203741407833417841387)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-31070758244530127209305617),(-31070758244525206988768801)⟩,⟨(-421079264159503399046839870),(-421079264159498478829903367)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-11346853815944632975593416),(-11346853815942583038073064)⟩,⟨(-140557737236144661122170968),(-140557737236142611185501407)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-981330128274863333472287195),(-981330128274609787324610853)⟩,⟨(-3596629797017353181907967616),(-3596629797017099635930241767)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 9) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_9 (tableDensity true) (fullFactor false 0 9) density1_contains hk0_0_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨874385253974686480021928246,874385253974686480062151822⟩,⟨2204571725313038907582897929,2204571725313038907679774561⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_9 0 9 ha0_0_9_contains + def realAnswer : RBox := ⟨(-106944874300176853550358949),(-106944874299923307162459031)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_9 +namespace hm0_0_0_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-42913234867821174572),(-42913234867821156236)⟩,⟨(-31346107449792378725),(-31346107449792360387)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-106090064017213983923),(-106090064017213947927)⟩,⟨(-75583978941522022669),(-75583978941521986665)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-119551465810456637865),(-119551465810456612771)⟩,⟨(-81081686711340271836),(-81081686711340246735)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-92094243315782920353),(-92094243315782911309)⟩,⟨(-58187467844735226446),(-58187467844735217404)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-52234888703807808853),(-52234888703807807072)⟩,⟨(-30251668171639056138),(-30251668171639054355)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-22086728386708021143),(-22086728386708020936)⟩,⟨(-11598691719509491461),(-11598691719509491254)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-6880770021241950187),(-6880770021241950159)⟩,⟨(-3245232391604164430),(-3245232391604164403)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1537098834199474782),(-1537098834199474763)⟩,⟨(-643232788463364192),(-643232788463364175)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-235673938152809302),(-235673938152809286)⟩,⟨(-86187352461153590),(-86187352461153574)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-23192711563215733),(-23192711563215714)⟩,⟨(-7288468059896766),(-7288468059896748)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1322019185318129),(-1322019185318112)⟩,⟨(-351216108584978),(-351216108584961)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-37095023036930),(-37095023036912)⟩,⟨(-8233669939643),(-8233669939626)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-388946574154),(-388946574138)⟩,⟨(-72096916368),(-72096916352)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-906298642),(-906298624)⟩,⟨(-142659616),(-142659600)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-145263),(-145247)⟩,⟨(-20096),(-20080)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-27161927956539390953438),(-27161927956539367445370)⟩,⟨(-38993218002339652364957),(-38993218002339628853009)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-73782673428146194369685),(-73782673428146113457080)⟩,⟨(-104791525008662483263494),(-104791525008662402340488)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-100750466630985307837291),(-100750466630985137730180)⟩,⟨(-140128771802524907333368),(-140128771802524737212428)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-104629481873377157389337),(-104629481873376849593055)⟩,⟨(-141161373208296767136164),(-141161373208296459326074)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-90477018745162236817826),(-90477018745161755142093)⟩,⟨(-117341314928948336338021),(-117341314928947854650958)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-67660497266702409609224),(-67660497266701788446888)⟩,⟨(-83614430131444753579442),(-83614430131444132409167)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-44740727927254012015089),(-44740727927253392506676)⟩,⟨(-52284300078429765610619),(-52284300078429146097352)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-26595528714208786437341),(-26595528714208334906071)⟩,⟨(-29247736126702659551799),(-29247736126702208017900)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-14430726818369383716539),(-14430726818369141515397)⟩,⟨(-14913586739710434854689),(-14913586739710192652261)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-7270242624543639087212),(-7270242624543541075643)⟩,⟨(-7071211174223296146139),(-7071211174223198133990)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-3470861658207656443546),(-3470861658207626082152)⟩,⟨(-3187075128544163565079),(-3187075128544133203438)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1607098088008982035445),(-1607098088008974129189)⟩,⟨(-1398496441103917695296),(-1398496441103909788943)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-737454147408820282988),(-737454147408818351380)⟩,⟨(-611181187538308093353),(-611181187538306161704)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-337572513541963474470),(-337572513541962987046)⟩,⟨(-268535617253803845169),(-268535617253803357732)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-146587917437508969964),(-146587917437508837432)⟩,⟨(-113209317813093358014),(-113209317813093225476)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-41191592039830328473),(-41191592039830299793)⟩,⟨(-31324304589884140646),(-31324304589884111967)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨31607056201498611599864,31607056201498611828641⟩,⟨(-1974395649362762176277793),(-1974395649362762175767847)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨14295962799831858202946,14295962799831858848526⟩,⟨(-5514132411858765907301700),(-5514132411858765905865746)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-186425533202556101735609),(-186425533202556100778361)⟩,⟨(-7972058029793037656761634),(-7972058029793037654666294)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-539477770560702205103241),(-539477770560702203979905)⟩,⟨(-9048216946164089710908516),(-9048216946164089708506120)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-904696514081682196185488),(-904696514081682195045146)⟩,⟨(-8839272643805926378271388),(-8839272643805926375900975)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1140745318061483378697588),(-1140745318061483377627012)⟩,⟨(-7711811452169422853599671),(-7711811452169422851482779)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1192503101924860833147455),(-1192503101924860832163694)⟩,⟨(-6130808100261858797680863),(-6130808100261858795888993)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1089880074829913725848243),(-1089880074829913724737920)⟩,⟨(-4508612633231848971271854),(-4508612633231848969585925)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-900072600961429030231572),(-900072600961429027677291)⟩,⟨(-3110349776419920060518532),(-3110349776419920057581952)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-687386152779055165636136),(-687386152779055155677077)⟩,⟨(-2040913385153343421330489),(-2040913385153343411130469)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-493941675543331412429994),(-493941675543331376973045)⟩,⟨(-1290876740032036349968954),(-1290876740032036314365805)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-337706660299787582087750),(-337706660299787488942684)⟩,⟨(-795653996756849541600121),(-795653996756849448368106)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-220064869598379675581329),(-220064869598379504118568)⟩,⟨(-479410613324567904933494),(-479410613324567733420000)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-134487494143845740096048),(-134487494143845519888443)⟩,⟨(-277706301425829735687742),(-277706301425829515451531)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-71792186335881715508592),(-71792186335881527604595)⟩,⟨(-143545908756271110083365),(-143545908756270922164863)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-22470091853848850375099),(-22470091853848776893924)⟩,⟨(-44262369353240085400718),(-44262369353240011915133)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨6935264247750277881423888,6935264247750309669082694⟩,⟨(-18923422340236822576325144),(-18923422340236790784893971)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨19326149489843494258341299,19326149489843565420119054⟩,⟨(-54050788849795274561698968),(-54050788849795203389225415)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨27813103031713016317821327,27813103031713081072596765⟩,⟨(-81577087311448639011973142),(-81577087311448574241282104)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨31311184493569897255723366,31311184493569932470905568⟩,⟨(-98341656351500648283858876),(-98341656351500613049839668)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨30124828696194111811913419,30124828696194124050436239⟩,⟨(-103544965503978351523133954),(-103544965503978339265168673)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨25561992590551020601408130,25561992590551023391878300⟩,⟨(-98798417007987898166480969),(-98798417007987895357820243)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨19440141923870645143422317,19440141923870645595305588⟩,⟨(-87295561756141816527027878),(-87295561756141816059376467)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨13445407158268746344926441,13445407158268746411376879⟩,⟨(-72490999671771396699094240),(-72490999671771396619786882)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨8588138046457162773296756,8588138046457162789939710⟩,⟨(-57172667475279372847694539),(-57172667475279372821081734)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨5140145315430107944296189,5140145315430107952541444⟩,⟨(-43161189897567488135607493),(-43161189897567488119944848)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2913918530035329096903209,2913918530035329101989501⟩,⟨(-31365957609726080597385665),(-31365957609726080586970896)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1568758349969117882516607,1568758349969117885746541⟩,⟨(-21999412395786110920138179),(-21999412395786110913196641)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨796212267544378940713571,796212267544378942738080⟩,⟨(-14828917852207129057643647),(-14828917852207129053124803)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨374770259915473219908634,374770259915473221117305⟩,⟨(-9395124915621998226550764),(-9395124915621998223763597)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨156354601577227553577996,156354601577227554214460⟩,⟨(-5171116200337541069690888),(-5171116200337541068185950)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨41566766603302758249727,41566766603302758447339⟩,⟨(-1647185158209996144235089),(-1647185158209996143761315)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨116521735912352642249845552,116521735912353523982016568⟩,⟨(-6534218815688754155646768),(-6534218815687872407638085)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨330908292949990777210920672,330908292949994003497693220⟩,⟨(-26581137219031333798562345),(-26581137219028107466564409)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨494808859939314583890436472,494808859939322242817824473⟩,⟨(-63966777418225099776511224),(-63966777418217440780116422)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨591358433679799110086083260,591358433679815707870485241⟩,⟨(-119592943753797612466466476),(-119592943753781014597225999)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨620160870273654726417421872,620160870273687661718906489⟩,⟨(-183357934885064600794853624),(-183357934885031665401082235)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨592327524694470214888218620,592327524694527071091235376⟩,⟨(-239486196433627438850481384),(-239486196433570582555807479)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨524672137149966923763412063,524672137150046640052358034⟩,⟨(-275411827441813125074327738),(-275411827441733408700556944)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨435838695031978168494699951,435838695032063732967952165⟩,⟨(-286560316324830611471792605),(-286560316324745046923971770)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨342625159800953034905443381,342625159801023701210777343⟩,⟨(-275337220581894487488590508),(-275337220581823821120150437)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨257036543523343504119397461,257036543523388821996605254⟩,⟨(-247949859380434456045095191),(-247949859380389138116230522)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨185498399547391695540458352,185498399547414357376752773⟩,⟨(-211342234308657295220395261),(-211342234308634633343253645)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨129687892866229386165880320,129687892866238886639118021⟩,⟨(-171001345866222052864368458),(-171001345866212552360136090)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨87831825290795488848074179,87831825290799112144760753⟩,⟨(-130232601684368374152048061),(-130232601684364750832940172)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨56321951238157296394144202,56321951238158635031044271⟩,⟨(-90752708090470525936173992),(-90752708090469187284212015)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨31421971780118439481857192,31421971780118921961470961⟩,⟨(-53268899208962083896959306),(-53268899208961601408710204)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨10094941415017984820342048,10094941415018106308908404⟩,⟨(-17522863057524887766710427),(-17522863057524766275334554)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨2442757843898654150870371,2442757843898654198303491⟩,⟨193422997723996169362259321,193422997723996169436729127⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨34672607475133716734398597,34672607475133716876893581⟩,⟨555899910898987868479432819,555899910898987868698877824⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨134241977862139183466727897,134241977862139183703481352⟩,⟨854161321114219155227490147,854161321114219155575937909⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨302026820784552804356144268,302026820784552804682704432⟩,⟨1068356132338725735191971493,1068356132338725735645395326⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨496502869050140281533651839,496502869050140281942844144⟩,⟨1189537731092593171673799532,1189537731092593172205369921⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨664085038645595649174098598,664085038645595649670287175⟩,⟨1208282729821613283654854491,1208282729821613284257303647⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨774902994484588232806918437,774902994484588233466036973⟩,⟨1126120305739772490790320041,1126120305739772491532862062⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨824863811455985697792695018,824863811455985699148803099⟩,⟨969825639490814702770610250,969825639490814704182864113⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨820143358435001837704059111,820143358435001843565943688⟩,⟨780486106983068272567763363,780486106983068278458389439⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨770233463554976169809810961,770233463554976202687548490⟩,⟨594432525407118558849027514,594432525407118591733941303⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨686103340344863339565852852,686103340344863490386911158⟩,⟨434375030513226374739580340,434375030513226525554023599⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨577869753921558102861171179,577869753921558596987044556⟩,⟨308634519854631170701628859,308634519854631664814665140⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨454164652891224657551277012,454164652891225760629981318⟩,⟨213746074650754901956181381,213746074650756005020924704⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨323307098670053321516792187,323307098670054979288896455⟩,⟨140360093428161220136515192,140360093428162877896838705⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨192163344416399469415604987,192163344416401052045146381⟩,⟨79739588946475923179663948,79739588946477505801530843⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨63573287885888129044402615,63573287885888785886967904⟩,⟨25853589825172938474603417,25853589825173595314524920⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2018918386308838177185592556,2018918386308912020438487313⟩,⟨1080658877797025562602426539,1080658877797099406128693779⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 10) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_10 (tableDensity false) (fullFactor false 0 10) density0_contains hk0_0_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨555495236253995522598577031,555495236253995522623611654⟩,⟨(-177600343336493339910406043),(-177600343336493339901826154)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_10 0 10 ha0_0_10_contains + def realAnswer : RBox := ⟨2574413622562833699684169587,2574413622562907543162098967⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_10 +namespace hm0_1_0_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-6567218014526646775),(-6567218014526631751)⟩,⟨(-6281807951630610267),(-6281807951630595245)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16231871945618309954),(-16231871945618280472)⟩,⟨(-15397383589309071730),(-15397383589309042251)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-18170488866733676114),(-18170488866733655578)⟩,⟨(-16963659239470739843),(-16963659239470719307)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-13742000582081579556),(-13742000582081572161)⟩,⟨(-12445819815381685045),(-12445819815381677654)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-7606777583415540044),(-7606777583415538591)⟩,⟨(-6446288380961774649),(-6446288380961773196)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-3178936648085720868),(-3178936648085720699)⟩,⟨(-2362063298540480853),(-2362063298540480684)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-1007007739700764071),(-1007007739700764048)⟩,⟨(-606643090449544044),(-606643090449544020)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-234970464292455211),(-234970464292455195)⟩,⟨(-107674801389964925),(-107674801389964909)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-38120435466735548),(-38120435466735532)⟩,⟨(-12870606669954332),(-12870606669954316)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3961511714903910),(-3961511714903894)⟩,⟨(-988020865510192),(-988020865510176)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-235413893323915),(-235413893323899)⟩,⟨(-44599962748368),(-44599962748352)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-6761957414532),(-6761957414516)⟩,⟨(-999428623095),(-999428623079)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-71361844477),(-71361844461)⟩,⟨(-8112701975),(-8112701959)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-165761211),(-165761195)⟩,⟨(-13387571),(-13387555)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-26449),(-26433)⟩,⟨(-1340),(-1324)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-834176095148778270992),(-834176095148758913134)⟩,⟨(-7364793334159859898322),(-7364793334159840540712)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2557245413851131742072),(-2557245413851065090081)⟩,⟨(-19564071692812787957987),(-19564071692812721306667)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-4283950591447612261810),(-4283950591447472043069)⟩,⟨(-25612755180772655056411),(-25612755180772514838569)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-5657333334383194155226),(-5657333334382940225921)⟩,⟨(-25129209503210885176327),(-25129209503210631247939)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-6202788490906239360662),(-6202788490905841638892)⟩,⟨(-20377694703238031783367),(-20377694703237634062375)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-5711210876809297855242),(-5711210876808784546291)⟩,⟨(-14287473654063658198913),(-14287473654063144890539)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-4464178602626455347691),(-4464178602625942958313)⟩,⟨(-8888357711126392191291),(-8888357711125879802293)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-3023303400191489930556),(-3023303400191116289950)⟩,⟨(-4989226681736004506926),(-4989226681735630866547)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1821702943881937986625),(-1821702943881737568076)⟩,⟨(-2567906523076229158362),(-2567906523076028739937)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1003062880925994935504),(-1003062880925913874201)⟩,⟨(-1237483247257234283814),(-1237483247257153222579)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-516832995548381816980),(-516832995548356730404)⟩,⟨(-573191217738916200434),(-573191217738891113892)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-254272764188228630697),(-254272764188222106246)⟩,⟨(-262021972589437144263),(-262021972589430619829)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-121523679083188180865),(-121523679083186589023)⟩,⟨(-120295119183957185401),(-120295119183955593567)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-56848496753863227457),(-56848496753862826275)⟩,⟨(-55356533426338004201),(-55356533426337603027)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-24908725533906560902),(-24908725533906451923)⟩,⟨(-24139598864861576630),(-24139598864861467652)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-7018598451732384089),(-7018598451732360517)⟩,⟨(-6795964948768098307),(-6795964948768074735)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨239678152705464797335047,239678152705464797495554⟩,⟨(-375897515921705535428242),(-375897515921705535253359)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨660627947718206269484327,660627947718206269941310⟩,⟨(-1056963874115302165621125),(-1056963874115302165122343)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨929912591479671954211114,929912591479671954892798⟩,⟨(-1539081970811209027927586),(-1539081970811209027185088)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1007709274704206379835803,1007709274704206380638112⟩,⟨(-1744004968789963041851020),(-1744004968789963040980019)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨908034333543092851577285,908034333543092852392023⟩,⟨(-1678796762542541436430728),(-1678796762542541435550408)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨693002017109513474253137,693002017109513475011202⟩,⟨(-1433257889617916389440098),(-1433257889617916388623031)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨450836674179944555316409,450836674179944556012385⟩,⟨(-1121038770276757027258267),(-1121038770276757026511265)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨251550813851802267454921,251550813851802268275369⟩,⟨(-822392817994840383902406),(-822392817994840383041054)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨120836961210353234308601,120836961210353236336436⟩,⟨(-573877658901823881552290),(-573877658901823879494948)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨49865345945821661866126,49865345945821669955670⟩,⟨(-383730519125812272139654),(-383730519125812264029933)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨17339584756321077671503,17339584756321106556322⟩,⟨(-246624956528360105697853),(-246624956528360076799683)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨4389129632931260764723,4389129632931336704270⟩,⟨(-152457735947875280186664),(-152457735947875204238343)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-346344311676324225870),(-346344311676184328845)⟩,⟨(-90592542027120877128146),(-90592542027120737225652)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1788796096590692115361),(-1788796096590512322753)⟩,⟨(-51219619070748313220345),(-51219619070748133424670)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1634111077541424068460),(-1634111077541270574355)⟩,⟨(-25872407052074609482195),(-25872407052074455986573)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-634617447352188003801),(-634617447352127963583)⟩,⟨(-7872929570438830174743),(-7872929570438770134079)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨5639720066103449804793517,5639720066103476514965655⟩,⟨(-3685451887289798388674327),(-3685451887289771678914798)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨15768195034224336886015134,15768195034224396642005075⟩,⟨(-10425432889071425849514467),(-10425432889071366094685917)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨22813960387324679565656664,22813960387324733869602541⟩,⟨(-15510232500148673851401578),(-15510232500148619549150131)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨25883625041868488082049149,25883625041868517554333312⟩,⟨(-18519770492671043037639373),(-18519770492671013567297703)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨25349528132008484305161381,25349528132008494520172698⟩,⟨(-19592256879361781094281198),(-19592256879361770881176789)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨22461804357944911265075929,22461804357944913586126254⟩,⟨(-19062373232552043128199024),(-19062373232552040808827613)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨18540637121414347814736830,18540637121414348188440387⟩,⟨(-17257226275076325203479250),(-17257226275076324831141740)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨14478730347291356610699703,14478730347291356664503716⟩,⟨(-14611635488580046702724764),(-14611635488580046649955406)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨10775501379586417487814784,10775501379586417500556137⟩,⟨(-11671769454166147372314992),(-11671769454166147360313444)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨7687097175894978084168471,7687097175894978090233051⟩,⟨(-8902336061613691491588765),(-8902336061613691486026910)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨5295653126304527505611406,5295653126304527509307331⟩,⟨(-6555354386317865661433739),(-6555354386317865658061816)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3549097666451008963919684,3549097666451008966258860⟩,⟨(-4683060772055554216083870),(-4683060772055554213946652)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2313711204482192759713321,2313711204482192761179929⟩,⟨(-3224780920725979734941174),(-3224780920725979733596212)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1435633681413646882117201,1435633681413646882992912⟩,⟨(-2084539687165818978345685),(-2084539687165818977539600)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨781647270440249375168498,781647270440249375629420⟩,⟨(-1164901439991575150662288),(-1164901439991575150236911)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨247923753642509944922132,247923753642509945065223⟩,⟨(-374075091648555818287559),(-374075091648555818155283)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨38123849127133439806136061,38123849127134164462735687⟩,⟨(-4102781837339730585071802),(-4102781837339005933032696)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨110470465766893204303680479,110470465766895856027359162⟩,⟨(-13588131704283935377413912),(-13588131704281283666959941)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨170935115135076235658484505,170935115135082531428589814⟩,⟨(-25585681594780260734434077),(-25585681594773964984565606)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨212094704533691327042642381,212094704533704972834580971⟩,⟨(-39180763727636359754801444),(-39180763727622713987747326)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨229513677201533383818784210,229513677201560464681770279⟩,⟨(-53027923241543832952531951),(-53027923241516752116249539)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨224822161179677252431614710,224822161179724002029820571⟩,⟨(-66148130486468803878054864),(-66148130486422054306002089)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨204979839774194142113363237,204979839774259674396688514⟩,⟨(-76609915914993635672201824),(-76609915914928103412817801)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨177824115902186782751400982,177824115902257088547818472⟩,⟨(-81634482438469838494760545),(-81634482438399532718819121)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨148863811935863943904673278,148863811935921962382566495⟩,⟨(-79584120423504694771517577),(-79584120423446676309943424)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨120926484163055078922083103,120926484163092246290451020⟩,⟨(-71019216098195611462637321),(-71019216098158444106566792)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨95041836316977370587040493,95041836316995933130431706⟩,⟨(-58214205486604325836997375),(-58214205486585763302605846)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨71505656476541819753148580,71505656476549591224848790⟩,⟨(-44109197980820428773655200),(-44109197980812657308481092)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨50695554411038992282336600,50695554411041952398316277⟩,⟨(-31150404000269975657315933),(-31150404000267015545898092)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨33046008040493187724335533,33046008040494280189524297⟩,⟨(-20375732344612249231101979),(-20375732344611156768859176)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨18416953788295013018942972,18416953788295406479728927⟩,⟨(-11497890771175628405329163),(-11497890771175234946177256)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨5890475763519736558122723,5890475763519835594369164⟩,⟨(-3717916818234966399449002),(-3717916818234867363720089)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨345717277846478630442175,345717277846478662294341⟩,⟨5742697421966345564779009,5742697421966345611915233⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨5006462828594492926459108,5006462828594493022118331⟩,⟨15496486513335216663641856,15496486513335216803752158⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨21210922653287663059512691,21210922653287663218516142⟩,⟨15770326292692773182748288,15770326292692773408298650⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨58881957470911521570619277,58881957470911521790737080⟩,⟨(-6235000625291993435837400),(-6235000625291993136790202)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨131344595044457485235245632,131344595044457485514673146⟩,⟨(-53151636932617102128310447),(-53151636932617101767114493)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨240099772247576505930809875,240099772247576506280579394⟩,⟨(-103872934049937313412003535),(-103872934049937312984431743)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨359263570729196189684452906,359263570729196190177211134⟩,⟨(-129687879096862581963323515),(-129687879096862581401859239)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨450311556231372711581371034,450311556231372712668322463⟩,⟨(-121345580041541305696704527),(-121345580041541304555494713)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨488984821086663417353140082,488984821086663422165560369⟩,⟨(-90777801105028408473323620),(-90777801105028403623848799)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨473793900760276964229747768,473793900760276991155513298⟩,⟨(-56035000996542833185060608),(-56035000996542806237007730)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨418884923224919445039075111,418884923224919568274755805⟩,⟨(-30112788883917320582544260),(-30112788883917197334949450)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨343610064029969714374335679,343610064029970117945070814⟩,⟨(-17071552541742922177615892),(-17071552541742518600527897)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨263573883817242894387915876,263573883817243795584076557⟩,⟨(-13041248606584486126057297),(-13041248606583584926620399)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨185835677736409046703723109,185835677736410401691674771⟩,⟨(-11396765929218030617806279),(-11396765929216675628415639)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨110764486454047699575796580,110764486454048993624101821⟩,⟨(-8172598369198822735539021),(-8172598369197528686746314)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨36833256927912827613208405,36833256927913364791478691⟩,⟨(-2973430732175091564010846),(-2973430732174554385670066)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨948368585933611658769764071,948368585933672306531972999⟩,⟨(-242528534057701929622412450),(-242528534057641281802883128)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 10) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_10 (tableDensity true) (fullFactor false 0 10) density1_contains hk0_0_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-726416847409071068046261394),(-726416847409071068013523810)⟩,⟨232246602824645136794695740,232246602824645136805915595⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_10 0 10 ha0_0_10_contains + def realAnswer : RBox := ⟨221951738524540590623502677,221951738524601238618449189⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_10 +namespace hm0_0_0_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1485039269237469844,1485039269237470727⟩,⟨(-2033017352751963229),(-2033017352751962343)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨3514748583158208795,3514748583158210485⟩,⟨(-4932859957653111196),(-4932859957653109506)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨3631274202819892602,3631274202819893747⟩,⟨(-5352800735362670356),(-5352800735362669214)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨2460893768243894021,2460893768243894420⟩,⟨(-3893070028932723789),(-3893070028932723389)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1183344116689151615,1183344116689151705⟩,⟨(-2041817389007765092),(-2041817389007765009)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨410347851877773323,410347851877773347⟩,⟨(-780660399184612512),(-780660399184612490)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨101320258063250316,101320258063250334⟩,⟨(-214559530054232049),(-214559530054232031)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨17238872501551217,17238872501551233⟩,⟨(-41128595329067697),(-41128595329067681)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1920276555805999,1920276555806015⟩,⟨(-5240208129821632),(-5240208129821615)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨129929708345668,129929708345684⟩,⟨(-412431942775261),(-412431942775245)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨4776619741398,4776619741415⟩,⟨(-17929559718990),(-17929559718971)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨80270084770,80270084787⟩,⟨(-360619579205),(-360619579188)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨461726520,461726536⟩,⟨(-2484994145),(-2484994128)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨524483,524499⟩,⟨(-3326858),(-3326840)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨29,45⟩,⟨(-253),(-237)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨3703316588031464365575,3703316588031466598494⟩,⟨(-2579653661181785869788),(-2579653661181783637240)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨9859026577924479178395,9859026577924486788576⟩,⟨(-6941508226213060878168),(-6941508226213053268974)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨12938574860750560221280,12938574860750575912565⟩,⟨(-9302157926699614449940),(-9302157926699598759947)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨12675239560998306227080,12675239560998333818548⟩,⟨(-9394038033956056546422),(-9394038033956028956203)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨10156447174719583643744,10156447174719625245044⟩,⟨(-7830016119077613184157),(-7830016119077571583847)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨6918343339366263092129,6918343339366314372296⟩,⟨(-5597084677574668297313),(-5597084677574617017809)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨4103987429364674726255,4103987429364723267725⟩,⟨(-3510892377816152415733),(-3510892377816103874648)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨2163502103209549810835,2163502103209583188280⟩,⟨(-1966685954194286848192),(-1966685954194253470942)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1034178486173359856502,1034178486173376655733⟩,⟨(-1000357531194803699877),(-1000357531194786900738)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨458128723712724169593,458128723712730529740⟩,⟨(-470867803944125152122),(-470867803944118792014)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨192737428548917713555,192737428548919554316⟩,⟨(-209835144817921027056),(-209835144817919186309)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨79115273896466495809,79115273896466944374⟩,⟨(-90892132041118332938),(-90892132041117884380)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨32534763174038800927,32534763174038904031⟩,⟨(-39248604558478495353),(-39248604558478392252)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨13586177426342040254,13586177426342064973⟩,⟨(-17076856213409532976),(-17076856213409508257)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨5520825809028305361,5520825809028311845⟩,⟨(-7148218500578146268),(-7148218500578139781)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1498302603077975179,1498302603077976566⟩,⟨(-1970262359034882079),(-1970262359034880692)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨281494535747079097107825,281494535747079097181440⟩,⟨4506808862048578609552,4506808862048578642196⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨781217852790857163618651,781217852790857163824630⟩,⟨2037908831133508553664,2037908831133508645152⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1115411828146772818126057,1115411828146772818422932⟩,⟨(-26037137634882768500291),(-26037137634882768366265)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1242841286951481857007929,1242841286951481857342195⟩,⟨(-74011111397561174902625),(-74011111397561174748067)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1185343165679884443439123,1185343165679884443761261⟩,⟨(-121200526058413093602639),(-121200526058413093449288)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1004577824947436712197207,1004577824947436712476783⟩,⟨(-148476850124489992693336),(-148476850124489992553332)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨772470755519955237237343,772470755519955237466188⟩,⟨(-150146576597985885910602),(-150146576597985885786105)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨547619643115654012008393,547619643115654012215256⟩,⟨(-132295319350697461628854),(-132295319350697461493712)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨363364903469803700399659,363364903469803700742886⟩,⟨(-105093566737706925392876),(-105093566737706925095515)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨229124701079390890960782,229124701079390892100418⟩,⟨(-77134661626121419862692),(-77134661626121418750866)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨139362634659914218373375,139362634659914222198533⟩,⟨(-53306405583667544947764),(-53306405583667541138849)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨82806302619883642181380,82806302619883651848895⟩,⟨(-35137111154448207119067),(-35137111154448197460873)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨48305096075061367238966,48305096075061384480376⟩,⟨(-22170093313910498001595),(-22170093313910480765451)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨27256785179672165156616,27256785179672186746846⟩,⟨(-13198886275288634073630),(-13198886275288612486296)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨13830486350294581111050,13830486350294599209146⟩,⟨(-6916913685152839428301),(-6916913685152821331644)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨4223948607519083072231,4223948607519090084670⟩,⟨(-2144310076553497833390),(-2144310076553490821391)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3598704282492375233390946,3598704282492381279389380⟩,⟨1318896105028305728358490,1318896105028311773632252⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨10230283671216868698150723,10230283671216882172153561⟩,⟨3657973106780971607240873,3657973106780985079198116⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨15296146142950070130944309,15296146142950082283643981⟩,⟨5215406185468136700338116,5215406185468148850020393⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨18187371587098660815670602,18187371587098667340225405⟩,⟨5791321735782196381420657,5791321735782202902449833⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨18811512733165389863975748,18811512733165392095616808⟩,⟨5473853627233986074862596,5473853627233988302924764⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨17569451549643819195485039,17569451549643819696472650⟩,⟨4546890718857868039805755,4546890718857868537510964⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨15150645381059127190141498,15150645381059127271645336⟩,⟨3375155534176714588003764,3375155534176714666725918⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨12251781695407780814236708,12251781695407780827726510⟩,⟨2273449967349129809662440,2273449967349129820939159⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨9397535001425891775001002,9397535001425891779419335⟩,⟨1412377714461664709976625,1412377714461664712722408⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨6897744638026526099450824,6897744638026526101985343⟩,⟨821921955778727505416504,821921955778727506738550⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4877831647005109796045897,4877831647005109797688561⟩,⟨453407127897211120821329,453407127897211121614648⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3335923664098027265970081,3335923664098027267039097⟩,⟨238009526538925522399293,238009526538925522890331⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2199639371668317627446087,2199639371668317628127614⟩,⟨118162695468706792769614,118162695468706793070563⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1369204729092532528351246,1369204729092532528764630⟩,⟨54637532295905228040084,54637532295905228216543⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨744348011573278192940198,744348011573278193160815⟩,⟨22510492968873000975179,22510492968873001066931⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨235595348007259560073938,235595348007259560142983⟩,⟨5945412477919142525944,5945412477919142554253⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1553600498937573314270219,1553600498937782964910847⟩,⟨27705602088250834157803987,27705602088251043804762259⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨6294969758711232078593163,6294969758711996175134967⟩,⟨78383073573043947741632689,78383073573044711827693565⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨15033463059445968961289234,15033463059447768890012563⟩,⟨116333090898491999469065075,116333090898493799381895124⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨27798103505970223222538944,27798103505974080349481775⟩,⟨137515821658364481808434775,137515821658368338916015389⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨42020359899194198582137085,42020359899201743632071910⟩,⟨142187404916262522941880141,142187404916270067970999660⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨53964102001487340461938355,53964102001500147055478910⟩,⟨133528578229204887841706343,133528578229217694414868115⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨60884033741831652592846573,60884033741849271234292381⟩,⟨116033827838692372163627529,116033827838709990786518125⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨62048866323115505464283039,62048866323134035320825908⟩,⟨94407682326564047737137852,94407682326582577577653972⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨58343763530672394539020459,58343763530687374903416877⟩,⟨72627266277980521309266934,72627266277995501660345342⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨51412757552214287582143762,51412757552223691910481279⟩,⟨53313534060379095198810025,53313534060388499516442613⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨42915520056310002961577848,42915520056314609427693993⟩,⟨37677597122587949726351628,37677597122592556184149489⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨34062940353632052303486296,34062940353633946714634911⟩,⟨25838588808452051349041126,25838588808453945753978306⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨25513540728500960043003015,25513540728501670474285653⟩,⟨17209071527445963350710052,17209071527446673777561553⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨17544401524026916415200376,17544401524027175342661078⟩,⟨10888889863130147551590835,10888889863130406476108171⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨10203012028520276062936685,10203012028520368498374003⟩,⟨6018625206721337842318379,6018625206721430276081582⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨3340354410776590531674485,3340354410776613692015958⟩,⟨1924386338929267169991179,1924386338929290329790235⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-55197438166861217905341660),(-55197438166861217883914177)⟩,⟨696908432641810280684330,696908432641810294222592⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-158136995252031387348630695),(-158136995252031387285698453)⟩,⟨9858679073042836010400800,9858679073042836050967029⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-241471728434241134017859495),(-241471728434241133918571012)⟩,⟨37932380310955161742206252,37932380310955161809255987⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-299277211700441591486904810),(-299277211700441591358902692)⟩,⟨84570997602445169673900021,84570997602445169765650411⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-329330429392309463311339315),(-329330429392309463163070268)⟩,⟨137411864231072624014458459,137411864231072624128194170⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-329873738812463317229514992),(-329873738812463317063922320)⟩,⟨181247257530800092533132149,181247257530800092669189375⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-302632115660241286569979891),(-302632115660241286369462371)⟩,⟨208184645846949806360797344,208184645846949806538551110⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-256228162739744776310913940),(-256228162739744775937481161)⟩,⟨217861873503381899867828695,217861873503381900226278376⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-202587501267080591841050715),(-202587501267080590315473712)⟩,⟨212814139776584443532484955,212814139776584445050634821⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-151587072816962297744461835),(-151587072816962289381086296)⟩,⟨196359393693327285742748711,196359393693327294104466837⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-108902523912378475466462387),(-108902523912378437741346837)⟩,⟨171969636336453969147150407,171969636336454006874180149⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-76180489197851005247366455),(-76180489197850883484591952)⟩,⟨142610107080864223820143628,142610107080864345586365403⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-52052717193918677669194048),(-52052717193918409316273775)⟩,⟨110589504906129555798492352,110589504906129824155065477⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-33816796197023098646473407),(-33816796197022699448543141)⟩,⟨77890450193999814431426594,77890450194000213632389849⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-19068947263106258893314208),(-19068947263105880492679682)⟩,⟨45953324109655874018574763,45953324109656252421164965⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-6159061835989495357442136),(-6159061835989338882453070)⟩,⟨15144945618396167336941986,15144945618396323812601338⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-326918636853424584851459327),(-326918636853408498877805886)⟩,⟨492743227489788073673750356,492743227489804159581457468⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 11) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_11 (tableDensity false) (fullFactor false 0 11) density0_contains hk0_0_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨42751256502264096558874653,42751256502264096561044041⟩,⟨164546162056035402212052908,164546162056035402219711135⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_11 0 11 ha0_0_11_contains + def realAnswer : RBox := ⟨(-284167380351160488392584674),(-284167380351144402216761845)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_11 +namespace hm0_1_0_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨297602005405379832,297602005405380562⟩,⟨(-311122223401544151),(-311122223401543423)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨715955594567639219,715955594567640607⟩,⟨(-754735476397555464),(-754735476397554078)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨759635842732053909,759635842732054849⟩,⟨(-813607717225583696),(-813607717225582759)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨526327080143687970,526327080143688301⟩,⟨(-580992800640312611),(-580992800640312283)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨252204464670004889,252204464670004964⟩,⟨(-297390581266677483),(-297390581266677408)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨83620352476026931,83620352476026951⟩,⟨(-112357444648612073),(-112357444648612051)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨18961226853185994,18961226853186010⟩,⟨(-31389268911327824),(-31389268911327808)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨2889851688180471,2889851688180487⟩,⟨(-6282846794719807),(-6282846794719791)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨287179984553936,287179984553952⟩,⟨(-846908161709037),(-846908161709021)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨17633493737784,17633493737800⟩,⟨(-70394144768761),(-70394144768745)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨607008674971,607008674987⟩,⟨(-3191160012179),(-3191160012163)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨9751266554,9751266570⟩,⟨(-65724123189),(-65724123173)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨52046083,52046099⟩,⟨(-455940062),(-455940045)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨49352,49368⟩,⟨(-608520),(-608503)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1,17⟩,⟨(-58),(-42)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨699460804035195300249,699460804035197138630⟩,⟨(-79222264166715269711),(-79222264166713431311)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1840670695645246999266,1840670695645253267283⟩,⟨(-240536964823318401841),(-240536964823312133766)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨2365032385346015355609,2365032385346028288705⟩,⟨(-395349125760741756081),(-395349125760728822911)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2256583943539034585849,2256583943539057347388⟩,⟨(-507593452850088016878),(-507593452850065255264)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1763916691356332967616,1763916691356367316995⟩,⟨(-536375673939855081078),(-536375673939820731637)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1182210026110684780104,1182210026110727155646⟩,⟨(-472081923345942332636),(-472081923345899957048)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨697679700573420655728,697679700573460803411⟩,⟨(-350071345747472859515),(-350071345747432711808)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨369048293453704558873,369048293453732178381⟩,⟨(-223434533754830725436),(-223434533754803105912)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨178058696315356801512,178058696315370702612⟩,⟨(-126217041197066571772),(-126217041197052670664)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨80164373718249909349,80164373718255169548⟩,⟨(-64934795100797130591),(-64934795100791870385)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨34656949125851116188,34656949125852637146⟩,⟨(-31233856132475635982),(-31233856132474115023)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨14819415762528817163,14819415762529187332⟩,⟨(-14377071650206207922),(-14377071650205837751)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨6402186014291598169,6402186014291683139⟩,⟨(-6466836115340176230),(-6466836115340091262)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨2800281124744548992,2800281124744569342⟩,⟨(-2875669194890472450),(-2875669194890452103)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1177136445748360793,1177136445748366128⟩,⟨(-1214636926083567778),(-1214636926083562444)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨325062097741745060,325062097741746202⟩,⟨(-335710971815168096),(-335710971815166952)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨53592592189515317438749,53592592189515317463864⟩,⟨34171576203998754087331,34171576203998754110342⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨149744911782719492803844,149744911782719492875008⟩,⟨93596315107723580440434,93596315107723580505492⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨215339661101034826418836,215339661101034826523447⟩,⟨130114806505791594779143,130114806505791594874961⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨239555917744589848721953,239555917744589848842422⟩,⟨138431556562106925269738,138431556562106925380423⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨225136307483645088973916,225136307483645089092776⟩,⟨121795682841100856481334,121795682841100856591030⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨186713474238225720027392,186713474238225720134526⟩,⟨90313249631720870134163,90313249631720870233246⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨141252980256050100022199,141252980256050100116846⟩,⟨56844343698245761164187,56844343698245761252062⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨99886755268764487355682,99886755268764487460498⟩,⟨30584251841284778661960,30584251841284778761510⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨67039210347333397451072,67039210347333397690479⟩,⟨14135661755906519141846,14135661755906519377563⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨43077051533009299809408,43077051533009300714668⟩,⟨5607712828442051397545,5607712828442052300355⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨26624653968247559195930,26624653968247562300186⟩,⟨1876000830523364721456,1876000830523367824138⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨15867052137858823880184,15867052137858831755171⟩,⟨458383603954814393980,458383603954822267964⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨9128516011321590183973,9128516011321604247470⟩,⟨(-34210346542412098508),(-34210346542398035616)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5027428177433685722525,5027428177433703348151⟩,⟨(-175292321177003232158),(-175292321176985606860)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨2492832390151729289676,2492832390151744072506⟩,⟨(-157377728138055055044),(-157377728138040272376)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨751314030504922197672,751314030504927927100⟩,⟨(-60558793604126161659),(-60558793604120432280)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨700870348152212017369914,700870348152217096944322⟩,⟨1072518912129183077102695,1072518912129188156756755⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1973255136677431214135622,1973255136677442526595247⟩,⟨2984530037294235665043446,2984530037294246977726150⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2908292901388036971810952,2908292901388047160339861⟩,⟨4277960786069528791056172,4277960786069538979907300⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3425075628983834182897358,3425075628983839640128897⟩,⟨4787372200491627539359793,4787372200491632996955196⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨3559341325160178973711683,3559341325160180833045932⟩,⟨4605944137580400174482224,4605944137580402034166602⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3389728392387120562210739,3389728392387120975893542⟩,⟨3994964202720125660942645,3994964202720126074926259⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2994943580881737548010913,2994943580881737612878282⟩,⟨3218275864775456623884349,3218275864775456688989694⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2469440229845382252790327,2469440229845382261749306⟩,⟨2447395339821414616862311,2447395339821414625996107⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1918454920014600007002006,1918454920014600008986278⟩,⟨1771418545757412328319085,1771418545757412330424363⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1422678214239754946814839,1422678214239754947710561⟩,⟨1228660805577205142661477,1228660805577205143636698⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1019410960868565901229712,1019410960868565901759015⟩,⟨823636584245591914572545,823636584245591915151329⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨710096144777895376536443,710096144777895376864064⟩,⟨538216349742601008558745,538216349742601008916157⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨478329123650788203499579,478329123650788203701549⟩,⟨343218176030935276036727,343218176030935276256057⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨303784884654120871762631,303784884654120871881717⟩,⟨209226961086481270284642,209226961086481270413384⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨167678313617771175654919,167678313617771175717061⟩,⟨112513563103764409791971,112513563103764409858934⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨53503551477657023956079,53503551477657023975298⟩,⟨35460319337558294683603,35460319337558294704274⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨975512906237418218248715,975512906237590516638966⟩,⟨9064767027024800974716859,9064767027024973274217266⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨3218335308998179700201257,3218335308998807708313261⟩,⟨26167053170262110206907073,26167053170262738218225366⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨6014223620015415593974043,6014223620016895148074009⟩,⟨40186865377511297621640832,40186865377512777180609993⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨9108760705661384450056261,9108760705664555546635252⟩,⟨49319113341648159993830675,49319113341651331096330209⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨12153815203024221778861613,12153815203030425628715214⟩,⟨52619878375828522583893652,52619878375834726440007923⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨14905641942322297794183163,14905641942332827900715071⟩,⟨50679816453681247367609546,50679816453691777480163911⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨16935190410674412655236537,16935190410688896380171619⟩,⟨45329662527843613971104962,45329662527858097701438870⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨17675585777137189662803610,17675585777152415097415185⟩,⟨38515108285659579128183472,38515108285674804567310031⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨16863682139594561528304940,16863682139606860719646864⟩,⟨31550932295000741503863781,31550932295013040698723430⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨14726564544433395099437883,14726564544441108045812801⟩,⟨25078287511032489895892420,25078287511040202844861039⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨11822162698360854805989455,11822162698364628009372480⟩,⟨19301785411429070968602459,19301785411432844173845655⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨8787406173941211655332307,8787406173942761297086939⟩,⟨14245245821012624050024829,14245245821014173693104162⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨6103154900760598053079432,6103154900761178448690272⟩,⟨9932520264923522367897905,9932520264924102764420238⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨3939248835597458269722193,3939248835597669578300124⟩,⟨6388855561978782319498623,6388855561978993628657697⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨2202316498500973872508278,2202316498501049251683358⟩,⟨3527629345470467250654144,3527629345470542630148581⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨708741440009442562505406,708741440009461442036437⟩,⟨1122894854087270580887352,1122894854087289460519042⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1638805030791433396939722),(-1638805030791433383483208)⟩,⟨98631643421857561557676,98631643421857570647678⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-4408544069778229298310332),(-4408544069778229258439610)⟩,⟨1423499281846927328461252,1423499281846927355677350⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-4460745562967787003055854),(-4460745562967786939280346)⟩,⟨5992985505076265645053095,5992985505076265690020263⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1737948352270390370947000,1737948352270390454722602⟩,⟨16483803184387931084383996,16483803184387931146093828⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨14699926057107828304541379,14699926057107828404576623⟩,⟨36338065166756027947287582,36338065166756028024758711⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨28342895357045563718309653,28342895357045563835110474⟩,⟨65506024250181816066062435,65506024250181816161748634⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨34843803236630757748407826,34843803236630757899315467⟩,⟨96491688457157321833185898,96491688457157321965849858⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨32059615024821635183557414,32059615024821635484649538⟩,⟨118914218166543798664112680,118914218166543798951189596⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨23567936212618501562002233,23567936212618502817388716⟩,⟨126873114427201875728292714,126873114427201876974456008⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨14295264805436961387978045,14295264805436968241080040⟩,⟨120785124527323231049989707,120785124527323237897829595⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨7552838133664861055240693,7552838133664891884436126⟩,⟨104995203506415822342670086,104995203506415853169278321⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨4214178016571639593302518,4214178016571739045332791⟩,⟨84801097203003937585766475,84801097203004037036568697⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨3175074282779068524603525,3175074282779287767589902⟩,⟨64181628049628482642353237,64181628049628701884806253⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨2745214616524473093351648,2745214616524799382133167⟩,⟨44771186823186516653031940,44771186823186842941652632⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨1954235648831866157370136,1954235648832175560853443⟩,⟨26487788014043465460501751,26487788014043774863978395⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨708349577042719896249184,708349577042847864964328⟩,⟨8774713287490426653203420,8774713287490554621938090⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨55752856290442973115245928,55752856290456185089507233⟩,⟨229852491129390711421003627,229852491129403923378264503⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 11) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_11 (tableDensity true) (fullFactor false 0 11) density1_contains hk0_0_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-55905489272191510887519131),(-55905489272191510884682238)⟩,⟨(-215175750380969372133468407),(-215175750380969372123453804)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_11 0 11 ha0_0_11_contains + def realAnswer : RBox := ⟨(-152632981748537872273203),(-152632981735325695175005)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_11 +namespace hm0_0_0_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨88288817559798633,88288817559798689⟩,⟨64492177480813781,64492177480813833⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨210263920708589640,210263920708589728⟩,⟨149830640625779540,149830640625779627⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨219737747546012022,219737747546012083⟩,⟨149105075714983174,149105075714983238⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨150916226585961350,150916226585961381⟩,⟨95441911137292626,95441911137292657⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨73211401725900783,73211401725900804⟩,⟨42459556198763365,42459556198763384⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨25319814782050606,25319814782050624⟩,⟨13321607769850535,13321607769850552⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨6142361050927016,6142361050927032⟩,⟨2904097159475410,2904097159475429⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1010942753833519,1010942753833536⟩,⟨424391898554610,424391898554626⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨107115201470308,107115201470327⟩,⟨39328653286588,39328653286604⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨6748471166415,6748471166432⟩,⟨2130915947957,2130915947973⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨223968385136,223968385152⟩,⟨59820790109,59820790126⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨3232195159,3232195177⟩,⟨721272383,721272400⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨14648854,14648872⟩,⟨2727486,2727502⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨11260,11277⟩,⟨1772,1788⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨224581761113105355857,224581761113105550226⟩,⟨322407305794174731164,322407305794174925569⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨598648914331311127414,598648914331311783393⟩,⟨850277747936425557541,850277747936426213602⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨787321648408017082289,787321648408018408950⟩,⟨1095159560165606888891,1095159560165608215662⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨773216257585570163340,773216257585572430592⟩,⟨1043390429297974955435,1043390429297977222795⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨621241670119028132780,621241670119031426711⟩,⟨805946271998432771108,805946271998436065117⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨424510244940666630344,424510244940670511709⟩,⟨524834435031338614625,524834435031342496040⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨252614544940490384205,252614544940493871598⟩,⟨295370188432426299366,295370188432429786785⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨133355922501326285186,133355922501328547570⟩,⟨146748160760685819994,146748160760688082394⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨63590459249884206185,63590459249885274674⟩,⟨65762424939419862691,65762424939420931190⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨27965839438899929578,27965839438900308055⟩,⟨27218188912401942352,27218188912402320835⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨11633054265338566858,11633054265338669209⟩,⟨10688424626648803554,10688424626648905905⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨4713735901860602045,4713735901860625397⟩,⟨4104060900145038161,4104060900145061513⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1915290280063819178,1915290280063824238⟩,⟨1587984200189581127,1587984200189586190⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨792004547408453379,792004547408454549⟩,⟨630189918465092685,630189918465093846⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨319548352591127065,319548352591127369⟩,⟨246811285566873516,246811285566873820⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨86388167209536619,86388167209536694⟩,⟨65695004449017901,65695004449017978⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-589068816904496592100),(-589068816904496587816)⟩,⟨36788964241813332681086,36788964241813332690839⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-266289600929407231308),(-266289600929407219410)⟩,⟨101456963337877678505114,101456963337877678532206⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨3333498115331309947186,3333498115331309964401⟩,⟨143060710228167621895951,143060710228167621934515⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨9307821112007884368461,9307821112007884387965⟩,⟨156493564742310420782702,156493564742310420825345⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨14884813453677028033546,14884813453677028052463⟩,⟨145716623860586512055812,145716623860586512095951⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨17716425305601171230331,17716425305601171247127⟩,⟨119965954169783597389359,119965954169783597423215⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨17331173630944761687115,17331173630944761701569⟩,⟨89228337760461824525910,89228337760461824552714⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨14722252288943238070972,14722252288943238086063⟩,⟨60978797425483124689889,60978797425483124713172⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨11249752107348064214288,11249752107348064246040⟩,⟨38917475547503161189689,38917475547503161226481⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨7935360306033838610138,7935360306033838723945⟩,⟨23582359205608448162581,23582359205608448279328⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨5274080526001200422282,5274080526001200797411⟩,⟨13793400414843715260906,13793400414843715637685⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3351560553631252845973,3351560553631253764078⟩,⟨7900544231990372519889,7900544231990373438908⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨2047513553785694578132,2047513553785696166517⟩,⟨4461908572365998601326,4461908572366000190211⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1187468719973301891636,1187468719973303831619⟩,⟨2452409671317884396725,2452409671317886336977⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨610894319281609856075,610894319281611453732⟩,⟨1221525780425933612513,1221525780425935210302⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨187578296808172957134,187578296808173570516⟩,⟨369500351780398081260,369500351780398694679⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-229916322760499291821211),(-229916322760498237956035)⟩,⟨627341886850494317862476,627341886850495371855246⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-634671454445979118485091),(-634671454445976780574653)⟩,⟨1774951946480639769501793,1774951946480642107770817⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-896485404280647867473064),(-896485404280645777819518)⟩,⟨2629131144419801304098526,2629131144419803394276394⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-981920975113294119004802),(-981920975113293012069013)⟩,⟨3083351414563508462420030,3083351414563509569960634⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-911774322631493231360922),(-911774322631492859526388)⟩,⟨3132882295133803527973194,3132882295133803900411530⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-741421095031924596154654),(-741421095031924514778951)⟩,⟨2864158995270433002186870,2864158995270433084105418⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-537184199412889985055215),(-537184199412889972483384)⟩,⟨2410490016820418388029055,2410490016820418401050618⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-352399419966775902063667),(-352399419966775900309368)⟩,⟨1898248114649029890483481,1898248114649029892586878⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-212932782015954173246306),(-212932782015954172831019)⟩,⟨1416053169158769699496735,1416053169158769700169138⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-120482770591819634108434),(-120482770591819633914100)⟩,⟨1010555797666421059978641,1010555797666421060354574⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-64674873044467372924158),(-64674873044467372810716)⟩,⟨695395156880308531481808,695395156880308531719280⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-33102755804308274499131),(-33102755804308274430685)⟩,⟨463716881439653615260118,463716881439653615411013⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-16075240783922104117820),(-16075240783922104076798)⟩,⟨299101970852135307698074,299101970852135307792283⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-7301911590545394884216),(-7301911590545394860588)⟩,⟨182916912165388649138408,182916912165388649194605⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2970803639460753946172),(-2970803639460753934036)⟩,⟨98216034600998600970392,98216034600998601000039⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-779524093673576294147),(-779524093673576290416)⟩,⟨30888925909470633586968,30888925909470633596201⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-6038649336474448935688773),(-6038649336474403242442204)⟩,⟨338607521998760741571514,338607521998806435602505⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-17019607646865172383168947),(-17019607646865006503103819)⟩,⟨1366552556833613178442395,1366552556833779060732972⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-25071692878269079473561840),(-25071692878268691725574951)⟩,⟨3238755385270458408129645,3238755385270846159470516⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-29313779429551970775409168),(-29313779429551149118370731)⟩,⟨5923003734742996487771443,5923003734743818148859158⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-29883966624398562485463178),(-29883966624396978028550953)⟩,⟨8827549095281593315208166,8827549095283177776422940⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-27593701456721267567184463),(-27593701456718623263481614)⟩,⟨11146867584805236583780931,11146867584807880891636443⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-23523792014934294366078468),(-23523792014930724738862591)⟩,⟨12338159024799887905540319,12338159024803457536476501⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-18746355038412340982461774),(-18746355038408662423428790)⟩,⟨12316282669510730055264137,12316282669514408617454532⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-14112658089654724479041601),(-14112658089651813359091683)⟩,⟨11333203497720256011515365,11333203497723167134041737⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-10136969873873014938759469),(-10136969873871225928693161)⟩,⟨9772508775977690258972247,9772508775979479271072143⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7015399646986562442893001),(-7015399646985704092006696)⟩,⟨7988563586750721370284525,7988563586751579722723650⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-4719123817314772650098618),(-4719123817314426373429153)⟩,⟨6219965695259422100794520,6219965695259768378605031⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-3090883422924648327179904),(-3090883422924520637958704)⟩,⟨4581855767563567353141726,4581855767563695043165624⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1929770301719011927200626),(-1929770301718966018018466)⟩,⟨3109092375081554083191990,3109092375081599992901340⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1056755228588514725298291),(-1056755228588498492420345)⟩,⟨1791415450381215040233579,1791415450381231273408994⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-336273290187240939001634),(-336273290187236891884137)⟩,⟨583702662484560994103814,583702662484565041317292⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-182256288821471788528661),(-182256288821471784986594)⟩,⟨(-14439137920947122988352351),(-14439137920947122982701096)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-2569585769168063625327972),(-2569585769168063614741735)⟩,⟨(-41236577838036363464148858),(-41236577838036363447606208)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-9825290082126247051442072),(-9825290082126247034035651)⟩,⟨(-62575784222411604954310292),(-62575784222411604928377646)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-21707648946027680620539791),(-21707648946027680596909816)⟩,⟨(-76850502881291409148635683),(-76850502881291409115513444)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-34861350772821857863400302),(-34861350772821857834421806)⟩,⟨(-83580131601836761815988092),(-83580131601836761778079840)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-45345980162562772511310947),(-45345980162562772477112477)⟩,⟨(-82555598875205356262561169),(-82555598875205356220839506)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-51270957810575682206309245),(-51270957810575682162366283)⟩,⟨(-74553254099171246810079580),(-74553254099171246760443779)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-52747610126728760823675107),(-52747610126728760736822056)⟩,⟨(-62055832260956044542133061),(-62055832260956044451614966)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-50621401242279658426759282),(-50621401242279658066334482)⟩,⟨(-48203997530744546015757644),(-48203997530744545653573392)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-45888458937608514936290131),(-45888458937608512986848142)⟩,⟨(-35435961588991778035107946),(-35435961588991776085318747)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-39512559489544762763981119),(-39512559489544754113038481)⟩,⟨(-25028346670089003076902517),(-25028346670088994426458484)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-32261888293920177257713899),(-32261888293920149751254939)⟩,⟨(-17237018156060817661679676),(-17237018156060790156063715)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-24684893616861218858250266),(-24684893616861159012331480)⟩,⟨(-11619981119986449069635300),(-11619981119986389224588409)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-17201551888356314192645807),(-17201551888356226073003520)⟩,⟨(-7468540035304552663628089),(-7468540035304464544698633)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-10073396085080245830616506),(-10073396085080162894915101)⟩,⟨(-4180151648130236245779022),(-4180151648130153310532717)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3307290435695439796367833),(-3307290435695405626455595)⟩,⟨(-1344992447759116865047176),(-1344992447759082695290147)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-111213896630683525058307473),(-111213896630680307153012252)⟩,⟨(-87320123142359394749315571),(-87320123142356176829072187)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 12) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_12 (tableDensity false) (fullFactor false 0 12) density0_contains hk0_0_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-44324415607430077934422405),(-44324415607430077932282841)⟩,⟨9410839108929622004993555,9410839108929622005495022⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_12 0 12 ha0_0_12_contains + def realAnswer : RBox := ⟨(-155538312238113603092729878),(-155538312238110384985295093)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_12 +namespace hm0_1_0_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨13511246470700535,13511246470700582⟩,⟨12924145378352921,12924145378352966⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨32170870399899584,32170870399899659⟩,⟨30518776848325817,30518776848325891⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨33401105535091163,33401105535091217⟩,⟨31188075204548294,31188075204548347⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨22525538665068625,22525538665068653⟩,⟨20411305238836476,20411305238836501⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨10664949819653952,10664949819653970⟩,⟨9051013952396642,9051013952396660⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨3644098446281517,3644098446281533⟩,⟨2716368955337957,2716368955337973⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨898277456809495,898277456809511⟩,⟨544066580020610,544066580020626⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨154329858043994,154329858044010⟩,⟨71241591670961,71241591670977⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨17298000656576,17298000656592⟩,⟨5889870616669,5889870616685⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1151020858630,1151020858646⟩,⟨289512240002,289512240019⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨39844308375,39844308391⟩,⟨7607043378,7607043394⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨588977787,588977803⟩,⟨87682955,87682971⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2687756,2687772⟩,⟨307894,307910⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2056,2072⟩,⟨163,179⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨6896822224607902732,6896822224608062787⟩,⟨60894556571813485247,60894556571813645300⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨20740066596576693115,20740066596577233477⟩,⟨158749310725609056414,158749310725609596768⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨33446369601424989611,33446369601426083168⟩,⟨200193375223431345931,200193375223432439482⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨41751378527681400723,41751378527683271178⟩,⟨185769537010765480722,185769537010767351168⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨42523114241830158790,42523114241832878586⟩,⟨139982730407271990311,139982730407274710101⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨35777230500177186135,35777230500180393548⟩,⟨89687754513382056069,89687754513385263479⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨25170896732398530776,25170896732401415143⟩,⟨50213049499568998660,50213049499571883029⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨15141561443020691624,15141561443022563737⟩,⟨25031307814283921286,25031307814285793398⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨8019163805349228072,8019163805350112239⟩,⟨11321821029347925616,11321821029348809785⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨3854841495531173859,3854841495531486891⟩,⟨4762136343575575236,4762136343575888264⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1730917428782434576,1730917428782519149⟩,⟨1921567105893565957,1921567105893650531⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨745412238679725070,745412238679744342⟩,⟨768563082322270014,768563082322289286⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨315532531627009110,315532531627013287⟩,⟨312413509249194649,312413509249198819⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨133363751241995435,133363751241996394⟩,⟨129871335831545005,129871335831545966⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨54297592514251548,54297592514251804⟩,⟨52621434735652209,52621434735652461⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨14719579082657224,14719579082657290⟩,⟨14252670798175106,14252670798175172⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4465945129358924320492),(-4465945129358924317459)⟩,⟨7004092613389310783125,7004092613389310786443⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-12155568915366419645173),(-12155568915366419636673)⟩,⟨19447274117264230962396,19447274117264230971717⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-16689050997384495603677),(-16689050997384495591317)⟩,⟨27618916308201490536154,27618916308201490549674⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-17432635744905348838141),(-17432635744905348824128)⟩,⟨30164367519211957683579,30164367519211957698863⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-14976103178752179191111),(-14976103178752179177560)⟩,⟨27677723413182850734873,27677723413182850749598⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-10789848969681820194079),(-10789848969681820182194)⟩,⟨22298425733869754191225,22298425733869754204116⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-6570691396510698031291),(-6570691396510698021105)⟩,⟨16316651727495225885097,16316651727495225896103⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-3409044209646246016660),(-3409044209646246005572)⟩,⟨11122445405093387567118,11122445405093387578827⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1515998365565585720302),(-1515998365565585695169)⟩,⟨7179702611952609878749,7179702611952609904306⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-578147078041042070910),(-578147078041041978524)⟩,⟨4433366595044359482324,4433366595044359574979⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-186074789183151910811),(-186074789183151605260)⟩,⟨2635083290682416567873,2635083290682416873591⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-43886106192867075166),(-43886106192866326686)⟩,⟨1513900961403938956260,1513900961403939704850⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨3096595164141195222,3096595164142491167⟩,⟨843238232707066490105,843238232707067786112⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨15746856575408608600,15746856575410192524⟩,⟨452360713591813027929,452360713591814611884⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨13893878608377730456,13893878608379035533⟩,⟨220174932142953610409,220174932142954915507⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨5297301419956250778,5297301419956751963⟩,⟨65723229412514642391,65723229412515143579⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-186966594147616147450183),(-186966594147615261920266)⟩,⟨122178917755725825292727,122178917755726710808552⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-517825232485599489251567),(-517825232485597526058399)⟩,⟨342362091745721004887623,342362091745722968041525⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-735341891973014473517782),(-735341891973012721109519)⟩,⟨499889915331561644733236,499889915331563397085340⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-811689523165000622242037),(-811689523164999695819826)⟩,⟨580664665032589823183807,580664665032590749543547⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-767172554987025774547622),(-767172554987025464189050)⟩,⟨592762119383111566878658,592762119383111877178308⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-651346098101926590239271),(-651346098101926522551609)⟩,⟨552565218635414540905383,552565218635414608543636⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-512102718678605894476693),(-512102718678605884079004)⟩,⟨476476559526719803847958,476476559526719814207644⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-379241886549859682577533),(-379241886549859681156110)⟩,⟨382592788275990674375180,382592788275990675769524⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-266959233654395806753741),(-266959233654395806434848)⟩,⟨289072391009109703095585,289072391009109703396335⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-180028420122049160339124),(-180028420122049160195355)⟩,⟨208424549982204381623482,208424549982204381755727⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-117432495525024154416807),(-117432495525024154333707)⟩,⟨145324567345638997511160,145324567345638997587331⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-74821702070216476723638),(-74821702070216476673569)⟩,⟨98704353837279186030341,98704353837279186076386⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-46672081201823844585694),(-46672081201823844555616)⟩,⟨65039801296106057223723,65039801296106057251535⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-27951897421929308777486),(-27951897421929308760127)⟩,⟨40582780212934962866114,40582780212934962882252⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-14846140573745998394048),(-14846140573745998385118)⟩,⟨22124794269860148189360,22124794269860148197688⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-4649207737728606415576),(-4649207737728606412830)⟩,⟨7014847537469308908319,7014847537469308910889⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1975732406346578518933053),(-1975732406346540965697928)⟩,⟨212617587792160578398318,212617587792198131385852⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-5681670785871056391584403),(-5681670785870920052841343)⟩,⟨698739743157088032120262,698739743157224370151121⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-8660671526495294136533810),(-8660671526494975401166961)⟩,⟨1295915653630911429920664,1295915653631230164214124⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-10512789517537795242878568),(-10512789517537119721638121)⟩,⟨1941167253918671209227436,1941167253919346729177291⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-11058887926624513064093594),(-11058887926623210253835027)⟩,⟨2553530155125921111114931,2553530155127223920028630⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-10472596741089972746918141),(-10472596741087798486996978)⟩,⟨3078982620848324651744670,3078982620850498910395097⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-9189247188969032046904127),(-9189247188966097564045097)⟩,⟨3431794734619407716750366,3431794734622342198493768⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-7647149343463796091330002),(-7647149343460773521311804)⟩,⟨3508342434720623523831348,3508342434723646092937196⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-6130049418460630576468799),(-6130049418458240479419722)⟩,⟨3275722559877062046762691,3275722559879452143116846⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-4767629000828527757418661),(-4767629000827060498131734)⟩,⟨2799336664672895780269063,2799336664674363039054646⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-3593406602639694470516922),(-3593406602638991383400930)⟩,⟨2200853285949878512280310,2200853285950581599043953⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2601493412142729659618609),(-2601493412142446401133677)⟩,⟨1604779871968997248940927,1604779871969280507179448⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1783892562799289534765387),(-1783892562799185216519846)⟩,⟨1096136794664612514254341,1096136794664716832333000⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1132252358136450084575546),(-1132252358136412617910834)⟩,⟨698119396737672097079434,698119396737709563639097⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-619385928827124225898951),(-619385928827110988026039)⟩,⟨386682507738969682927904,386682507738982920743627⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-196218275887739541446502),(-196218275887736242277903)⟩,⟨123847609972338624898671,123847609972341924049331⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-25794252949309536416331),(-25794252949309534038380)⟩,⟨(-428696733050560877327220),(-428696733050560873805759)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-371018588966237366670449),(-371018588966237359572422)⟩,⟨(-1149659890691480107205949),(-1149659890691480096805533)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1552174020597807833676968),(-1552174020597807822019661)⟩,⟨(-1156611911321489602002340),(-1156611911321489585472134)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-4230073823247018577495560),(-4230073823247018561636830)⟩,⟨444060695134440367716293,444060695134440389229787⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-9215710457075564504315720),(-9215710457075564484626592)⟩,⟨3726754483398666029487630,3726754483398666054884513⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-16382880171897826911945900),(-16382880171897826887950212)⟩,⟨7089335253688893253178931,7089335253688893282427324⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-23756800407130608679295902),(-23756800407130608646554969)⟩,⟨8581694136155484934536424,8581694136155484971717497⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-28785714444894286000791138),(-28785714444894285931287191)⟩,⟨7764529206561087249021328,7764529206561087321842259⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-30176354883321047625774412),(-30176354883321047329967235)⟩,⟨5609010800369827599028721,5609010800369827896936629⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-28226687479243485099071211),(-28226687479243483502602955)⟩,⟨3343084165513932927252413,3343084165513934524852345⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-24124889475100323937203934),(-24124889475100316868574740)⟩,⟨1736562367154552116839997,1736562367154559185971964⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-19184752473288173472162067),(-19184752473288151006690825)⟩,⟨953612505747027371428548,953612505747049837100746⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-14326359565850008795990278),(-14326359565849959903007106)⟩,⟨708606964172152793133986,708606964172201686177192⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-9887410416204400941509830),(-9887410416204328916584925)⟩,⟨606157410895409953635313,606157410895481978554695⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-5806353071689545131594523),(-5806353071689477318669220)⟩,⟨428357425999545599568452,428357425999613412471124⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1916184481539320340148658),(-1916184481539292395356330)⟩,⟨154685292685302288047885,154685292685330232828015⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-51562636202513729189070181),(-51562636202511086102382578)⟩,⟨11987292461448311479172195,11987292461450954570385702⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 12) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_12 (tableDensity true) (fullFactor false 0 12) density1_contains hk0_0_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨57962697332793178834523715,57962697332793178837321606⟩,⟨(-12306481911677198007185798),(-12306481911677198006530033)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_12 0 12 ha0_0_12_contains + def realAnswer : RBox := ⟨6400061130279449545453534,6400061130282092834939028⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_12 +namespace hm0_0_0_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2585338299211884),(-2585338299211868)⟩,⟨3539252540771752,3539252540771771⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5896241831952950),(-5896241831952930)⟩,⟨8273686340613409,8273686340613427⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-5652611128098595),(-5652611128098578)⟩,⟨8328214277864731,8328214277864748⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-3418169604382013),(-3418169604381997)⟩,⟨5402429452658072,5402429452658090⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1407232366586063),(-1407232366586047)⟩,⟨2424764979878492,2424764979878509⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-399614571033537),(-399614571033521)⟩,⟨758832201202463,758832201202482⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-76948583436711),(-76948583436695)⟩,⟨162558777902034,162558777902051⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-9663567544161),(-9663567544145)⟩,⟨22985027881354,22985027881371⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-745499283668),(-745499283652)⟩,⟨2026688995236,2026688995254⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-32369356675),(-32369356658)⟩,⟨102289998016,102289998035⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-694427946),(-694427930)⟩,⟨2593826022,2593826038⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-6011738),(-6011722)⟩,⟨26879142,26879158⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-14963),(-14947)⟩,⟨80157,80174⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-19),(-3)⟩,⟨30,47⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-25909416606720157484),(-25909416606720141846)⟩,⟨18047883949712761224,18047883949712776859⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-67691313602140560100),(-67691313602140507879)⟩,⟨47658010650418647825,47658010650418700042⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-85571003089696304854),(-85571003089696201282)⟩,⟨61514707269037556372,61514707269037659932⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-79289246967793730857),(-79289246967793558839)⟩,⟨58752515858087000365,58752515858087172378⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-59043228734093332064),(-59043228734093091259)⟩,⟨45504922403710465265,45504922403710706068⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-36759368671217079823),(-36759368671216808566)⟩,⟨29726260530927567249,29726260530927838501⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-19628142193419052009),(-19628142193418820654)⟩,⟨16782303496668125395,16782303496668356746⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-9191027156173069056),(-9191027156172927441)⟩,⟨8349612321494059902,8349612321494201515⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-3861487399291536315),(-3861487399291473544)⟩,⟨3732707562409199500,3732707562409262274⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1493256324121491666),(-1493256324121470850)⟩,⟨1533772704943907913,1533772704943928724⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-547344443056819395),(-547344443056814124)⟩,⟨595537932901566609,595537932901571882⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-196583678493253921),(-196583678493252785)⟩,⟨225727776194220157,225727776194221293⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-71563500809702481),(-71563500809702235)⟩,⟨86296308403936951,86296308403937196⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-26986756658415684),(-26986756658415619)⟩,⟨33911940072864106,33911940072864174⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-10185714708720000),(-10185714708719971)⟩,⟨13186844768806996,13186844768807024⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-2658926481780799),(-2658926481780780)⟩,⟨3496436386078368,3496436386078385⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4438164709749239256036),(-4438164709749239254831)⟩,⟨(-71072433305989184800),(-71072433305989184273)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-12162777027545820604528),(-12162777027545820601225)⟩,⟨(-32117993790783516045),(-32117993790783514605)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-16937616568053027170307),(-16937616568053027165671)⟩,⟨393960596764088507775,393960596764088509829⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-18189965898594076444245),(-18189965898594076439213)⟩,⟨1080571054298697564989,1080571054298697567273⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-16536285576282949333336),(-16536285576282949328710)⟩,⟨1687508831285606429828,1687508831285606431995⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-13225317034168942093469),(-13225317034168942089672)⟩,⟨1951493904742132370649,1951493904742132372521⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-9514947096612315891914),(-9514947096612315889002)⟩,⟨1846815707299661765417,1846815707299661766982⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-6268574609170535629470),(-6268574609170535627036)⟩,⟨1512496733796910556352,1512496733796910557919⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-3848049311651140759370),(-3848049311651140755715)⟩,⟨1111742960384292177631,1111742960384292180774⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2240768221589628354121),(-2240768221589628343065)⟩,⟨753665043094756226764,753665043094756237530⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1260335371627109137650),(-1260335371627109103373)⟩,⟨481730481395111699168,481730481395111733285⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-695875404347327731671),(-695875404347327651005)⟩,⟨295127095892042139346,295127095892042219928⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-380467195159783801806),(-380467195159783666620)⟩,⟨174564102287048397463,174564102287048532604⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-203688891268944616885),(-203688891268944455914)⟩,⟨98619551044186924227,98619551044187085176⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-99589333627330376438),(-99589333627330246215)⟩,⟨49804068714650891154,49804068714651021368⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-29836632458823313800),(-29836632458823264255)⟩,⟨15146640147928958231,15146640147929007777⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-100948649251887657282605),(-100948649251887487674984)⟩,⟨(-36997052446805616278664),(-36997052446805446691778)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-284266224875346183088108),(-284266224875345808518920)⟩,⟨(-101647607473681342864368),(-101647607473680968353197)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-417143350785929864733738),(-417143350785929532887855)⟩,⟨(-142246357615050765463402),(-142246357615050433701615)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-482528784265686266383468),(-482528784265686092837324)⟩,⟨(-153681815236158863536967),(-153681815236158690086585)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-481633303053282698141322),(-481633303053282640764700)⟩,⟨(-140195335418345023553132),(-140195335418344966270526)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-431015793553492275473225),(-431015793553492263108289)⟩,⟨(-111602110744227389635673),(-111602110744227377353596)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-354030936261704658929712),(-354030936261704657009249)⟩,⟨(-78924924671133799841767),(-78924924671133797988408)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-271501168476307378342303),(-271501168476307378039539)⟩,⟨(-50425443642484733489468),(-50425443642484733237522)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-196975272401192176727451),(-196975272401192176632985)⟩,⟨(-29634693812541669594427),(-29634693812541669536432)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-136671951748182489022609),(-136671951748182488971130)⟩,⟨(-16303652166950542150394),(-16303652166950542124012)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-91516531048105874152233),(-91516531048105874120534)⟩,⟨(-8516194041164891701814),(-8516194041164891686829)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-59504242302687529480894),(-59504242302687529461225)⟩,⟨(-4250029149040649512060),(-4250029149040649503241)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-37543890766113121175877),(-37543890766113121163846)⟩,⟨(-2018768858890457105374),(-2018768858890457100200)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-22557212142099482632451),(-22557212142099482625385)⟩,⟨(-900799323035800778606),(-900799323035800775675)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-11962717336886338193399),(-11962717336886338189710)⟩,⟨(-361912801209486160328),(-361912801209486158834)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-3738325935509737832135),(-3738325935509737830982)⟩,⟨(-94344232471088717475),(-94344232471088717008)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-68122703818963779457477),(-68122703818954586383038)⟩,⟨(-1214926642143258083402700),(-1214926642143248890482422)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-273840756094011230736711),(-273840756093977988450917)⟩,⟨(-3411268238532243454538532),(-3411268238532210212688707)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-644077707273254533650386),(-644077707273177426913678)⟩,⟨(-4987754827382087585958037),(-4987754827382010479874384)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1164964064656141060571981),(-1164964064655979488921846)⟩,⟨(-5768125369449615596740318),(-5768125369449454025871599)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1711856227856056375176838),(-1711856227855749227097491)⟩,⟨(-5797785671771383901994691),(-5797785671771076754736057)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-2125448591270928612326099),(-2125448591270424601132080)⟩,⟨(-5263753861549414553256086),(-5263753861548910542843041)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2308074790161467610252631),(-2308074790160799994322765)⟩,⟨(-4402329884187542743809190),(-4402329884186875128567792)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2256731495617874246722074),(-2256731495617200124807118)⟩,⟨(-3436218215392738121119593),(-3436218215392063999778805)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2032198443564403832978878),(-2032198443563881612934874)⟩,⟨(-2531471613255101604485975),(-2531471613254579384902061)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1714730328406112026650896),(-1714730328405797865144156)⟩,⟨(-1779235221928607661330182),(-1779235221928293500180050)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1372700194159584247983698),(-1372700194159436604049879)⟩,⟨(-1205797193071827699759934),(-1205797193071680056093700)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1048439915112229284915104),(-1048439915112170856465856)⟩,⟨(-795616218758553709940024),(-795616218758495281684256)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-759553223295257207550690),(-759553223295236022100135)⟩,⟨(-512452855128500693206927),(-512452855128479507890585)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-508594020848644984894961),(-508594020848637470856319)⟩,⟨(-315696804731783857584887),(-315696804731776343633404)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-290338031180369873146872),(-290338031180367241617993)⟩,⟨(-171273907355306599654436),(-171273907355303968174341)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-94151859347953253659775),(-94151859347952600821852)⟩,⟨(-54241361403228864571134),(-54241361403228211748884)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨3486595728480872180474263,3486595728480872181849986⟩,⟨(-43997427137813921032412),(-43997427137813920176967)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨9925912932791021917590431,9925912932791021921604167⟩,⟨(-618224376322021822627001),(-618224376322021820076893)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨14968779354981686677401496,14968779354981686683653350⟩,⟨(-2349203577309925029552886),(-2349203577309925025381686)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨18216363990697710464896390,18216363990697710472807533⟩,⟨(-5143348777414815019495798),(-5143348777414815013878123)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨19580250619819265206811079,19580250619819265215757262⟩,⟨(-8164096995861769942603747),(-8164096995861769935788346)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨19071787046794738728446950,19071787046794738738150014⟩,⟨(-10472544170981558084909066),(-10472544170981558076974396)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨16953759248601745333275696,16953759248601745344617341⟩,⟨(-11655797614129340493246045),(-11655797614129340483218334)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨13873541487499264327244800,13873541487499264347498683⟩,⟨(-11788902204331085375023037),(-11788902204331085355596673)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨10587729784315577313294017,10587729784315577392667286⟩,⟨(-11115199800242157314986939),(-11115199800242157235998441)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨7646719868089414982084468,7646719868089415401690175⟩,⟨(-9899293673395428707226892),(-9899293673395428287687452)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨5309748527063539574487596,5309748527063541405506706⟩,⟨(-8380427178226661983249824),(-8380427178226660152112504)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨3600195599196641357355268,3600195599196647092881860⟩,⟨(-6737128780158678882180585),(-6737128780158673146464776)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2394476911058711176195563,2394476911058723495696679⟩,⟨(-5086181138617012375232979),(-5086181138617000055540569)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1522579094800204975134306,1522579094800222930365090⟩,⟨(-3506646134239124368451198),(-3506646134239106413066328)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨845855945899233474466409,845855945899250253442893⟩,⟨(-2038327381421263786473177),(-2038327381421247007399259)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨271120997146628333393978,271120997146635221136088⟩,⟨(-666676240412617340045877),(-666676240412610452270694)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨21065272476537719956570599,21065272476538315231426431⟩,⟨(-23363350291960461603475131),(-23363350291959866331817785)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 13) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_13 (tableDensity false) (fullFactor false 0 13) density0_contains hk0_0_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1908700865471476500563987),(-1908700865471476500457252)⟩,⟨(-10956628798823250035346466),(-10956628798823250034796474)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_13 0 13 ha0_0_13_contains + def realAnswer : RBox := ⟨19156571611066243356006612,19156571611066838830969179⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_13 +namespace hm0_1_0_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-518094584605190),(-518094584605173)⟩,⟨541627911034247,541627911034263⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1200926595341841),(-1200926595341824)⟩,⟨1265899336571990,1265899336572010⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1182211309417682),(-1182211309417666)⟩,⟨1265989675120800,1265989675120819⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-730960784039234),(-730960784039217)⟩,⟨806470886990035,806470886990052⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-300031174593784),(-300031174593768)⟩,⟨353279951906087,353279951906103⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-81534326875739),(-81534326875723)⟩,⟨109210865061980,109210865061996⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-14431117484511),(-14431117484495)⟩,⟨23764662162506,23764662162522⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1624360763868),(-1624360763852)⟩,⟨3506623924083,3506623924100⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-111794799996),(-111794799980)⟩,⟨327042807643,327042807661⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-4402271258),(-4402271242)⟩,⟨17435038819,17435038835⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-88360346),(-88360330)⟩,⟨461249816,461249832⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-731297),(-731281)⟩,⟨4897211,4897227⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1700),(-1684)⟩,⟨14701,14717⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨3,19⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4893643046621311357),(-4893643046621298478)⟩,⟨554229372676829171,554229372676842046⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-12638424796196048805),(-12638424796196005792)⟩,⟨1650759568138634502,1650759568138677516⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-15643018766645293836),(-15643018766645208464)⟩,⟨2612014068488258593,2612014068488343964⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-14118034537423858308),(-14118034537423716400)⟩,⟨3170316556199015457,3170316556199157364⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-10255823429120417788),(-10255823429120218959)⟩,⟨3112299117293684381,3112299117293883211⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-6281988737643667186),(-6281988737643443031)⟩,⟨2503355454557123418,2503355454557347573⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3336791246187610585),(-3336791246187419233)⟩,⟨1671067692911919793,1671067692912111143⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1567689385322933604),(-1567689385322816418)⟩,⟨947477117029473043,947477117029590229⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-664758757247400159),(-664758757247348218)⟩,⟨470474984551935436,470474984551987381⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-261231811700950046),(-261231811700932832)⟩,⟨211320148221244956,211320148221262171⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-98383153086175694),(-98383153086171336)⟩,⟨88578452239016014,88578452239020371⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-36805165087875235),(-36805165087874292)⟩,⟨35686494042317325,35686494042318264⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-14075978752822330),(-14075978752822123)⟩,⟨14214900683619781,14214900683619983⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-5560709520053763),(-5560709520053707)⟩,⟨5710076413610641,5710076413610700⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-2171521398569948),(-2171521398569921)⟩,⟨2240681958684618,2240681958684644⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-576855909028814),(-576855909028795)⟩,⟨595753247380901,595753247380917⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-844962158043851238651),(-844962158043851238236)⟩,⟨(-538765796846184604909),(-538765796846184604529)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2331345193522172802896),(-2331345193522172801759)⟩,⟨(-1457246475923442923190),(-1457246475923442922152)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3269911731423095109978),(-3269911731423095108350)⟩,⟨(-1975983640091322949697),(-1975983640091322948211)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3506195458890226977464),(-3506195458890226975662)⟩,⟨(-2026495107394654005119),(-2026495107394654003470)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-3141080257530979920859),(-3141080257530979919165)⟩,⟨(-1699923909482264009597),(-1699923909482264008038)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-2458365091577803452719),(-2458365091577803451272)⟩,⟨(-1190015403499772157522),(-1190015403499772156195)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1739992159448929298247),(-1739992159448929297053)⟩,⟨(-701159835265601049036),(-701159835265601047933)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1143359499064046225500),(-1143359499064046224278)⟩,⟨(-350797385559690631599),(-350797385559690630445)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-709869253383359102781),(-709869253383359100252)⟩,⟨(-150097626440876809815),(-150097626440876807330)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-421226529666071696615),(-421226529666071687848)⟩,⟨(-55027880932521894882),(-55027880932521886141)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-240765641860443991180),(-240765641860443963371)⟩,⟨(-17038386637782162789),(-17038386637782134995)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-133345850227986081339),(-133345850227986015636)⟩,⟨(-3878810879610501400),(-3878810879610435703)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-71906672053715114022),(-71906672053715003757)⟩,⟨258648229793044839,258648229793155101⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-37573340078239933965),(-37573340078239802551)⟩,⟨1305810796693977792,1305810796694109202⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-17950959399704998716),(-17950959399704892347)⟩,⟨1132266650321064622,1132266650321170991⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-5307072351188680289),(-5307072351188639805)⟩,⟨427731144136871659,427731144136912144⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-19660427748696336313517),(-19660427748696193817256)⟩,⟨(-30085773108925902837688),(-30085773108925760339128)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-54831211138156154697597),(-54831211138155840218790)⟩,⟨(-82933539633256609033047),(-82933539633256294547859)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-79314658474173820363526),(-79314658474173542152728)⟩,⟨(-116676841328604411814597),(-116676841328604133594767)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-90871511607716606803754),(-90871511607716461648248)⟩,⟨(-127036871924181422983334),(-127036871924181277817926)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-91126214826793034254956),(-91126214826792986451894)⟩,⟨(-117955854379514526466883),(-117955854379514478654668)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-83149442944148857933727),(-83149442944148847724991)⟩,⟨(-98031997442496367365142),(-98031997442496357148916)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-69977128365961102523165),(-69977128365961100995859)⟩,⟨(-75223325152888626749507),(-75223325152888625216595)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-54719238422703073197092),(-54719238422703072996753)⟩,⟨(-54249209776121679278077),(-54249209776121679073867)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-40209454285167926603809),(-40209454285167926561718)⟩,⟨(-37139426302713891728338),(-37139426302713891683735)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-28187527945485988052072),(-28187527945485988034037)⟩,⟨(-24350954794517606746943),(-24350954794517606727367)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-19124576636105285493242),(-19124576636105285483111)⟩,⟨(-15456243295246584284843),(-15456243295246584273816)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-12665248078452617302352),(-12665248078452617296369)⟩,⟨(-9601884578106118066045),(-9601884578106118059560)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-8163639320903612674143),(-8163639320903612670594)⟩,⟨(-5858632574850528280093),(-5858632574850528276272)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-5004532635222069511057),(-5004532635222069509026)⟩,⟨(-3447077367286600976684),(-3447077367286600974513)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2694775976330357435360),(-2694775976330357434318)⟩,⟨(-1808270263515965671699),(-1808270263515965670588)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-848969567502589779727),(-848969567502589779397)⟩,⟨(-562669691268742516508),(-562669691268742516158)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-42776316074842113516952),(-42776316074834558319947)⟩,⟨(-397500451494698449037065),(-397500451494690893789117)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-140035668869136779718684),(-140035668869109458010621)⟩,⟨(-1138770966844353211461534),(-1138770966844325889607515)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-257759652516092584398164),(-257759652516029202133839)⟩,⟨(-1722899914174974124093045),(-1722899914174910741610407)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-381865429303306889375016),(-381865429303174054980004)⟩,⟨(-2068542299026716477085749),(-2068542299026583642431171)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-495240508773151974663556),(-495240508772899424961271)⟩,⟨(-2145457293428114403514275),(-2145457293427861853545437)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-587102174454732660765958),(-587102174454318241987680)⟩,⟨(-1997669371054269891198228),(-1997669371053855472172548)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-641955758571264104860456),(-641955758570715278414839)⟩,⟨(-1719609920998088830710172),(-1719609920997540004051820)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-642812893853577344285831),(-642812893853023437001195)⟩,⟨(-1401594711067605814902844),(-1401594711067051907448071)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-587377063106842796321968),(-587377063106414041314666)⟩,⟨(-1099438443419270478363602),(-1099438443418841723229606)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-491205685701070788080384),(-491205685700813127890268)⟩,⟨(-836684262936278441603911),(-836684262936020781324367)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-378214265181530186793151),(-378214265181409249616633)⟩,⟨(-617543994263150806286867),(-617543994263029869048757)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-270532791850914391735927),(-270532791850866596670080)⟩,⟨(-438556140239837692002527),(-438556140239789896894385)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-181727740334273918188123),(-181727740334256610427345)⟩,⟨(-295749510511592321775102),(-295749510511575013986128)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-114205902262025759558130),(-114205902262019627405522)⟩,⟨(-185227706880093404636088),(-185227706880087272465958)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-62671345040952924836822),(-62671345040950778880099)⟩,⟨(-100387448757739881524081),(-100387448757737735557906)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-19976782144967315094295),(-19976782144966782923295)⟩,⟨(-31650306452276344568281),(-31650306452275812394334)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨103516849329865917434795,103516849329865918285454⟩,⟨(-6226838387234895749627),(-6226838387234895175395)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨276746589440273139254109,276746589440273141758419⟩,⟨(-89263251439836346700194),(-89263251439836344991398)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨276826560994495498519191,276826560994495502474167⟩,⟨(-371088558990308369568859),(-371088558990308366779260)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-104731972538024044978083),(-104731972538024039878359)⟩,⟨(-1002028964652773301801734),(-1002028964652773298039682)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-872147624033178243353713),(-872147624033178237401865)⟩,⟨(-2157444987969986213615011),(-2157444987969986208995926)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1636864615504936812218546),(-1636864615504936805457645)⟩,⟨(-3782206585006659166162830),(-3782206585006659160608131)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1951049458911679013968239),(-1951049458911679005511926)⟩,⟨(-5399254130234835776526697),(-5399254130234835769067794)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1735884744599957322553559),(-1735884744599957306295727)⟩,⟨(-6432343561612888093385672),(-6432343561612888077852131)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1232254098745213850838854),(-1232254098745213785580672)⟩,⟨(-6625419255854868618536423),(-6625419255854868553719061)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-721690761418321388803606),(-721690761418321045011106)⟩,⟨(-6089130886831540061596818),(-6089130886831539718027305)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-368568358588243713638089),(-368568358588242217345155)⟩,⟨(-5116922041366573158861297),(-5116922041366571662655558)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-199194183011702677550670),(-199194183011697992974964)⟩,⟨(-4006420368082548393227521),(-4006420368082543708677733)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-145982301696921685381118),(-145982301696911620435029)⟩,⟨(-2951917277415871767285709),(-2951917277415861702339830)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-123547918721381320854490),(-123547918721366644970589)⟩,⟨(-2015614221618522689067827),(-2015614221618508013174436)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-86671181716497182137614),(-86671181716483462630352)⟩,⟨(-1174898202032866044084870),(-1174898202032852324568155)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-31180884738828259222916),(-31180884738822626276612)⟩,⟨(-386259993134203971913651),(-386259993134198338963294)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-2421471603391467190558851),(-2421471603390978234549986)⟩,⟨(-10769047781480945382476708),(-10769047781480456427564729)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 13) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_13 (tableDensity true) (fullFactor false 0 13) density1_contains hk0_0_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨2495993439462700039059483,2495993439462700039199060⟩,⟨14327899198461173122426158,14327899198461173123145378⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_13 0 13 ha0_0_13_contains + def realAnswer : RBox := ⟨74521836071232748500632,74521836071721904649074⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_13 +namespace hm0_0_0_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-131745583244679),(-131745583244663)⟩,⟨(-96237953398019),(-96237953398003)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-302328479224971),(-302328479224955)⟩,⟨(-215474362883416),(-215474362883400)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-293156752397788),(-293156752397772)⟩,⟨(-199024354057331),(-199024354057314)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-179650349018877),(-179650349018861)⟩,⟨(-113718880224407),(-113718880224391)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-74621498670778),(-74621498670762)⟩,⟨(-43336740380826),(-43336740380810)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-21139156106796),(-21139156106779)⟩,⟨(-11142321137947),(-11142321137930)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-4000683502619),(-4000683502602)⟩,⟨(-1895943745701),(-1895943745685)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-486233375591),(-486233375575)⟩,⟨(-204722319856),(-204722319839)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-35700594392),(-35700594373)⟩,⟨(-13155202027),(-13155202010)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1444482303),(-1444482286)⟩,⟨(-458026718),(-458026702)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-28005737),(-28005721)⟩,⟨(-7513946),(-7513930)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-208526),(-208507)⟩,⟨(-46737),(-46721)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-417),(-401)⟩,⟨(-88),(-72)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1346772516261236925),(-1346772516261235742)⟩,⟨(-1933421495980929760),(-1933421495980928577)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-3523079115802810695),(-3523079115802806820)⟩,⟨(-5004121473459952004),(-5004121473459948129)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-4463149379886079144),(-4463149379886071622)⟩,⟨(-6208855078877380216),(-6208855078877372690)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-4145779105554886394),(-4145779105554874261)⟩,⟨(-5595461024853407196),(-5595461024853395063)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-3095518055623880461),(-3095518055623864097)⟩,⟨(-4017085849421832004),(-4017085849421815639)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1933282574062594409),(-1933282574062576788)⟩,⟨(-2391202757118117823),(-2391202757118100199)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1035557274053155496),(-1035557274053141223)⟩,⟨(-1211491985551136349),(-1211491985551122081)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-485594492560951232),(-485594492560942982)⟩,⟨(-534697492749384885),(-534697492749376638)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-203529695369346311),(-203529695369342870)⟩,⟨(-210621340433181569),(-210621340433178128)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-78140257668964076),(-78140257668962998)⟩,⟨(-76100811571183799),(-76100811571182721)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-28320551556742515),(-28320551556742247)⟩,⟨(-26036553990047172),(-26036553990046903)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-10040659238697165),(-10040659238697098)⟩,⟨(-8746573408951861),(-8746573408951799)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-3611387080168964),(-3611387080168937)⟩,⟨(-2995441256753137),(-2995441256753112)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1348528281356696),(-1348528281356679)⟩,⟨(-1073278060990965),(-1073278060990946)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-505345201081852),(-505345201081836)⟩,⟨(-390356052995125),(-390356052995109)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-131406121014387),(-131406121014370)⟩,⟨(-99930694466411),(-99930694466394)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨7962547133155023277,7962547133155023350⟩,⟨(-497170047905553096653),(-497170047905553096502)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨3597037448204005339,3597037448204005512⟩,⟨(-1353948791611407981849),(-1353948791611407981466)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-43234296091067098383),(-43234296091067098144)⟩,⟨(-1862123267900482865496),(-1862123267900482864967)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-116490435354564585490),(-116490435354564585232)⟩,⟨(-1963357065691374860016),(-1963357065691374859450)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-177660102858726217161),(-177660102858726216919)⟩,⟨(-1742641649297265601362),(-1742641649297265600852)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-199622487701906440605),(-199622487701906440399)⟩,⟨(-1353958029466758407683),(-1353958029466758407274)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-182759340628859528921),(-182759340628859528750)⟩,⟨(-942258629463221651920),(-942258629463221651614)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-144305342844762976199),(-144305342844762976032)⟩,⟨(-598447661078321336893),(-598447661078321336643)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-102032324518667526566),(-102032324518667526263)⟩,⟨(-353352515224864059742),(-353352515224864059391)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-66475571382306313895),(-66475571382306312934)⟩,⟨(-197732599889051142655),(-197732599889051141668)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-40862869175455452921),(-40862869175455450025)⟩,⟨(-106946854500510303641),(-106946854500510300730)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-24134008567091605423),(-24134008567091598842)⟩,⟨(-56919906986486956434),(-56919906986486949842)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-13820678888773268457),(-13820678888773257766)⟩,⟨(-30127284385728079798),(-30127284385728069104)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-7605665614782767360),(-7605665614782754946)⟩,⟨(-15709957651858236796),(-15709957651858224380)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3770387512864169591),(-3770387512864159722)⟩,⟨(-7539550264276077459),(-7539550264276067588)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1135706646905377726),(-1135706646905373994)⟩,⟨(-2237179820164424839),(-2237179820164421107)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨5528151924639287813487,5528151924639313153988⟩,⟨(-15083852009051703963657),(-15083852009051678620028)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨15116892235407155632064,15116892235407211340239⟩,⟨(-42274753656636040435789),(-42274753656635984718903)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨20958459307753861739730,20958459307753910649842⟩,⟨(-61458035384767842372126),(-61458035384767793449491)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨22335359393052599175888,22335359393052624413731⟩,⟨(-70120977565709105855227),(-70120977565709080603307)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨20017471243326790485851,20017471243326798680388⟩,⟨(-68757239042709346654820),(-68757239042709338446694)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨15599631213202939206183,15599631213202940927591⟩,⟨(-60231516686048383178219),(-60231516686048381445070)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨10768222564939034800609,10768222564939035054339⟩,⟨(-48285437037705255911739),(-48285437037705255648712)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨6700487692176782946717,6700487692176782980329⟩,⟨(-36060589803461970366649),(-36060589803461970326169)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3830028297934594568368,3830028297934594575901⟩,⟨(-25444141117050789775809),(-25444141117050789763474)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2048744619180240577118,2048744619180240580457⟩,⟨(-17164920793040000616004),(-17164920793040000609446)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1041347355081805994417,1041347355081805996269⟩,⟨(-11184275909985710432061),(-11184275909985710428122)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨506704791902871488074,506704791902871489144⟩,⟨(-7090528083504542127749),(-7090528083504542125357)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨235420960359848446508,235420960359848447128⟩,⟨(-4376116840376979551499),(-4376116840376979550059)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨103191264784629992858,103191264784629993209⟩,⟨(-2583095712183454957490),(-2583095712183454956653)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨40940431930572170096,40940431930572170280⟩,⟨(-1352993750846623447135),(-1352993750846623446692)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨10602709223978496262,10602709223978496330⟩,⟨(-420114048034301271357),(-420114048034301271211)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨226973811196269564274355,226973811196271281670264⟩,⟨(-12726313026173872540941),(-12726313026172155116917)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨634890299802664007450767,634890299802670193204965⟩,⟨(-50954941786783203629425),(-50954941786777017795962)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨921393204895364713345021,921393204895378951252856⟩,⟨(-118936955479527799586822),(-118936955479513561560965)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1053946864176139431642286,1053946864176168933992846⟩,⟨(-212766946009643256296207),(-212766946009613753805673)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1044504437958121061102600,1044504437958176349879040⟩,⟨(-308261032793137466703717),(-308261032793082177781947)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨932413338243626597447117,932413338243715803616842⟩,⟨(-376335915361742428529638),(-376335915361653222223554)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨765046424221600772641712,765046424221716719643205⟩,⟨(-400939995754072641267418),(-400939995753956694147631)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨584893023675557029874698,584893023675671747496769⟩,⟨(-383983000016599420701037),(-383983000016484702982014)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨421667213184232326515451,421667213184319318364662⟩,⟨(-338385808142919638027471),(-338385808142832646101968)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨289995005250058671597373,289995005250109901528610⟩,⟨(-279394334983510962915505),(-279394334983459732926194)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨192453656816473207498738,192453656816496790245147⟩,⟨(-219034635373039598350003),(-219034635373016015560778)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨124558386560671227781425,124558386560680382590538⟩,⟨(-164106667083586690913045),(-164106667083577536073467)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨78894864597800037507611,78894864597803301423271⟩,⟨(-116922622122943936093006),(-116922622122940672156506)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨47957300669747254236760,47957300669748396213058⟩,⟨(-77255401519865722075042),(-77255401519864580085372)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨25776569797051392158967,25776569797051788274405⟩,⟨(-43694689475037748982626),(-43694689475037352859760)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨8124269335205316492479,8124269335205414274646⟩,⟨(-14102030543112469857988),(-14102030543112372073444)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨9862509089251526314467,9862509089251526506318⟩,⟨781766995589159095278293,781766995589159095589263⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨138116375444774326741955,138116375444774327312381⟩,⟨2218576658869261342387429,2218576658869261343291674⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨521570880411003490694472,521570880411003491622651⟩,⟨3324941209848824623867227,3324941209848824625266702⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1131614322141865221476709,1131614322141865222716839⟩,⟨4009553539169203382514303,4009553539169203384268812⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1775388863198782000914771,1775388863198782002403183⟩,⟨4259463187299079190626566,4259463187299079192586953⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2245893141209759398690765,2245893141209759400400258⟩,⟨4091284996329063241215575,4091284996329063243310954⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨2460581873446368873046341,2460581873446368875171223⟩,⟨3580062885130461256432104,3580062885130461258838538⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨2446641783163431312212268,2446641783163431316247104⟩,⟨2880172359979391243266757,2880172359979391247475084⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2266351326789738066934401,2266351326789738083008988⟩,⟨2159481285903660123982821,2159481285903660140135553⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1983039244333488168272733,1983039244333488252114505⟩,⟨1532259978677203679447251,1532259978677203763300571⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1650525262598228567910733,1650525262598228927827858⟩,⟨1046021803935329600591686,1046021803935329960483080⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1306420315552922684293112,1306420315552923794906969⟩,⟨698253385646939679674624,698253385646940790249236⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨973134849133867247272052,973134849133869602243493⟩,⟨458180414069223782486537,458180414069226137419149⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨663795912434152925297714,663795912434156322606207⟩,⟨288232089591240110995224,288232089591243508272892⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨382990885391923194693763,382990885391926346873123⟩,⟨158934158798647489376280,158934158798650641536326⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨124788070380627409345627,124788070380628698572992⟩,⟨50748348001263779429455,50748348001265068650296⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨4592985539350824735518856,4592985539350927169531577⟩,⟨4656188620975252168242387,4656188620975354602903340⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 14) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_14 (tableDensity false) (fullFactor false 0 14) density0_contains hk0_0_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨2503702050025207529305356,2503702050025207529436261⟩,⟨(-358945403537214847388108),(-358945403537214847367061)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_14 0 14 ha0_0_14_contains + def realAnswer : RBox := ⟨7096687589376032164824212,7096687589376134798967838⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_14 +namespace hm0_1_0_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-20161614928962),(-20161614928946)⟩,⟨(-19285678862783),(-19285678862767)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-46257402085031),(-46257402085015)⟩,⟨(-43884534222923),(-43884534222907)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-44565643245546),(-44565643245530)⟩,⟨(-41620012318436),(-41620012318420)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-26821780381318),(-26821780381302)⟩,⟨(-24316546605913),(-24316546605897)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-10873815799349),(-10873815799333)⟩,⟨(-9241325469622),(-9241325469606)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-3042278013010),(-3042278012994)⟩,⟨(-2274764765678),(-2274764765662)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-584663366351),(-584663366335)⟩,⟨(-355934882122),(-355934882106)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-74134409262),(-74134409246)⟩,⟨(-34456177718),(-34456177702)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-5756801869),(-5756801853)⟩,⟨(-1975246414),(-1975246398)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-246054782),(-246054766)⟩,⟨(-62351677),(-62351661)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-4978208),(-4978192)⟩,⟨(-956635),(-956619)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-37992),(-37976)⟩,⟨(-5696),(-5680)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-86),(-70)⟩,⟨(-22),(-6)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-41356730138793307),(-41356730138792332)⟩,⟨(-365176020769014191),(-365176020769013217)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-122005744504767310),(-122005744504764118)⟩,⟨(-934322526186656016),(-934322526186652821)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-189425212869487417),(-189425212869481212)⟩,⟨(-1135081621374066286),(-1135081621374060084)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-223557292385375688),(-223557292385365674)⟩,⟨(-996387061344459393),(-996387061344449385)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-211551065517172014),(-211551065517158501)⟩,⟨(-697820244703170811),(-697820244703157297)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-162682935802083140),(-162682935802068574)⟩,⟨(-408661539972386468),(-408661539972371906)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-103043279494805004),(-103043279494793197)⟩,⟨(-205954044239755119),(-205954044239743316)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-55070791314279949),(-55070791314273119)⟩,⟨(-91198840263594392),(-91198840263587562)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-25639937492037762),(-25639937492034912)⟩,⟨(-36256260630897001),(-36256260630894152)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-10761110973777419),(-10761110973776523)⟩,⟨(-13311606921198159),(-13311606921197265)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-4210729424089572),(-4210729424089348)⟩,⟨(-4679099764580057),(-4679099764579835)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1586971910705467),(-1586971910705408)⟩,⟨(-1637176485084674),(-1637176485084617)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-594795830105430),(-594795830105406)⟩,⟨(-589049325600246),(-589049325600224)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-227053674867250),(-227053674867233)⟩,⟨(-221120798044553),(-221120798044536)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-85866310866584),(-85866310866566)⟩,⟨(-83216315929560),(-83216315929544)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-22390100292754),(-22390100292738)⟩,⟨(-21679887825779),(-21679887825763)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨60353482844855413646,60353482844855413702⟩,⟨(-94653858972074145229),(-94653858972074145168)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨162221848160338365060,162221848160338365188⟩,⟨(-259521317552299253119),(-259521317552299252980)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨217249731513764160584,217249731513764160766⟩,⟨(-359492332240619541067),(-359492332240619540870)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨218756025884332823765,218756025884332823958⟩,⟨(-378451311654277250453),(-378451311654277250242)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨179184839983109482049,179184839983109482226⟩,⟨(-331031209692945939293),(-331031209692945939099)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨121882254966114912705,121882254966114912856⟩,⟨(-251692090277693976626),(-251692090277693976463)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨69483622468107915755,69483622468107915882⟩,⟨(-172315248746214021755),(-172315248746214021619)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨33523262005465493193,33523262005465493319⟩,⟨(-109152275940965226176),(-109152275940965226043)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨13801257037046067163,13801257037046067406⟩,⟨(-65181136846968302992),(-65181136846968302747)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨4864030967833461093,4864030967833461875⟩,⟨(-37168025836755951673),(-37168025836755950887)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1448882069890735346,1448882069890737708⟩,⟨(-20429690693113308176),(-20429690693113305813)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨318361820920259121,318361820920264491⟩,⟨(-10907361901064124335),(-10907361901064118967)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-20054133860534557),(-20054133860525831)⟩,⟨(-5694220330325601915),(-5694220330325593185)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-100554031083673253),(-100554031083663114)⟩,⟨(-2898064541703444591),(-2898064541703434453)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-85683331353258990),(-85683331353250925)⟩,⟨(-1359032617569187499),(-1359032617569179434)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-32070313276672764),(-32070313276669712)⟩,⟨(-397930531686728879),(-397930531686725829)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨4495457117528991665965,4495457117529012958801⟩,⟨(-2937684658394233855556),(-2937684658394212563071)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨12333727679551033272379,12333727679551080051777⟩,⟨(-8154309064487924512936),(-8154309064487877734501)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨17190966216793426669330,17190966216793467686063⟩,⟨(-11685648384100356743199),(-11685648384100315727813)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨18462655491482472774624,18462655491482493896935⟩,⟨(-13205493820842803163843),(-13205493820842782042987)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨16841292118940883230404,16841292118940890070192⟩,⟨(-13008754577598724111145),(-13008754577598717272678)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨13701193729148335062096,13701193729148336493974⟩,⟨(-11619025663075444915496),(-11619025663075443484669)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨10260936620618642368216,10260936620618642578088⟩,⟨(-9543546192805583215686),(-9543546192805583006580)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨7206308945089872537342,7206308945089872564595⟩,⟨(-7267511253494904892600),(-7267511253494904865859)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨4798100161063733795990,4798100161063733801796⟩,⟨(-5193901243132340782354),(-5193901243132340776873)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨3058680884936954456619,3058680884936954459110⟩,⟨(-3540042126304144030170),(-3540042126304144027874)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1889121942570766287819,1889121942570766289192⟩,⟨(-2337141863611292410390),(-2337141863611292409126)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1144250171026875914442,1144250171026875915233⟩,⟨(-1509130295522123735426),(-1509130295522123734690)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨682912367355927376833,682912367355927377296⟩,⟨(-951520281483331176776),(-951520281483331176341)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨394742855804808360200,394742855804808360464⟩,⟨(-573071447223796953256),(-573071447223796953006)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨204518037596650946804,204518037596650946946⟩,⟨(-304778689914468499000),(-304778689914468498866)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨63232998386644691116,63232998386644691172⟩,⟨(-95407319047474993154),(-95407319047474993103)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨74261305309343596902955,74261305309345008353089⟩,⟨(-7991402825652460766241),(-7991402825651049325838)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨211940132360277325393539,211940132360282409533956⟩,⟨(-26060238474762772843815),(-26060238474757688731157)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨318263621673847167695655,318263621673858871489832⟩,⟨(-47607086122469230665060),(-47607086122457526912096)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨377947948743246131931146,377947948743270387130657⟩,⟨(-69755567451456769752182),(-69755567451432514601125)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨386502681956448308928026,386502681956493769782488⟩,⟨(-89189876548509479665399),(-89189876548464018859975)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨353850767035885959095158,353850767035959308250525⟩,⟨(-103955497663058302562870),(-103955497662984953452212)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨298820181396076408297067,298820181396171724935987⟩,⟨(-111511303504849150699113),(-111511303504753834097850)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨238548764639930659754026,238548764640024920259441⟩,⟨(-109370209688333555055499),(-109370209688239294579537)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨183109315391276777582491,183109315391348200154393⟩,⟨(-97804635969198858600399),(-97804635969127436049944)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨136349243960164511657726,136349243960206528139067⟩,⟨(-80039362319604813162426),(-80039362319562796695891)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨98550656596471560904723,98550656596490877943448⟩,⟨(-60355212983634147139040),(-60355212983614830110309)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨68652248013560611442270,68652248013568100214982⟩,⟨(-42349809064247581510447),(-42349809064240092744474)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨45530550267190352716788,45530550267193019244906⟩,⟨(-27977005214633919021434),(-27977005214631252497737)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨28137702971490521079706,28137702971491453052492⟩,⟨(-17348717325442427502984),(-17348717325441495532910)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨15108265793876012260548,15108265793876335291884⟩,⟨(-9431931160131242546089),(-9431931160130919516203)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨4740584656790880493767,4740584656790960204776⟩,⟨(-2992119676853613042775),(-2992119676853533332218)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1395814197652119022265,1395814197652119151037⟩,⟨23210651200651229634842,23210651200651229825662⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨19941865082985811973159,19941865082985812355161⟩,⟨61860197435427928218879,61860197435427928778827⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨82381959065884758518970,82381959065884759138852⟩,⟨61524085160122651603395,61524085160122652482078⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨220410272723170512379825,220410272723170513208538⟩,⟨(-22936389562818886697379),(-22936389562818885574829)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨468999039856832175968171,468999039856832176974431⟩,⟨(-189526628524355980598918),(-189526628524355979303687)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨810818489978921812234308,810818489978921813428331⟩,⟨(-350948489258344696965312),(-350948489258344695514096)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨1139474977463510309430412,1139474977463510311008328⟩,⟨(-411897083014007921949114),(-411897083014007920163170)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1334712932765636390837958,1334712932765636394061693⟩,⟨(-360373623387089229550953),(-360373623387089226180431)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1350786726794230599211275,1350786726794230612399931⟩,⟨(-251385922345751603579142),(-251385922345751590304768)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1219767496092087502130230,1219767496092087570788697⟩,⟨(-144670879774786188205127),(-144670879774786119506225)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1007806800635506698739359,1007806800635506992823458⟩,⟨(-72639121075134206943233),(-72639121075133912845789)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨776926325885963045133600,776926325885963952207579⟩,⟨(-38637092551060043144964),(-38637092551059136069073)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨564798012036676861506042,564798012036678785469439⟩,⟨(-27926447017031548809701),(-27926447017029624848588)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨381549234603583296072269,381549234603586072871982⟩,⟨(-23383190580165162749602),(-23383190580162385953269)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨220756505169133251219377,220756505169135828618139⟩,⟨(-16283944276590217794237),(-16283944276587640398166)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨72299881767780606095687,72299881767781660449601⟩,⟨(-5836376407382424040917),(-5836376407381369688063)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2104491683247824279560116,2104491683247908421422025⟩,⟨(-461270405583782354038406),(-461270405583698211931973)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 14) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_14 (tableDensity true) (fullFactor false 0 14) density1_contains hk0_0_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-3274071911571425230801265),(-3274071911571425230630081)⟩,⟨469390143087127108095387,469390143087127108122910⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_14 0 14 ha0_0_14_contains + def realAnswer : RBox := ⟨(-1169580228323601051241149),(-1169580228323516709208056)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_14 +namespace hm0_0_0_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨3343609084988,3343609085004⟩,⟨(-4577208501843),(-4577208501827)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨7349926752310,7349926752327⟩,⟨(-10311603471616),(-10311603471600)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨6541614114155,6541614114171⟩,⟨(-9633184510457),(-9633184510441)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨3532451937994,3532451938011⟩,⟨(-5577930984292),(-5577930984275)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1246420808875,1246420808891⟩,⟨(-2144765466835),(-2144765466818)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨290250462672,290250462689⟩,⟨(-550173548687),(-550173548671)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨43660621261,43660621279⟩,⟨(-92026161708),(-92026161692)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4055451093,4055451111⟩,⟨(-9618666565),(-9618666547)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨217182209,217182226⟩,⟨(-588409584),(-588409565)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨6066856,6066872⟩,⟨(-19097104),(-19097086)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨76139,76155⟩,⟨(-283262),(-283246)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨333,349⟩,⟨(-1525),(-1509)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨134658279142457400,134658279142457499⟩,⟨(-93799345758745175),(-93799345758745081)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨345276464463668828,345276464463669109⟩,⟨(-243082175952129089),(-243082175952128807)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨420487938075040457,420487938075040980⟩,⟨(-302246319353932023),(-302246319353931502)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨368581041045645631,368581041045646441⟩,⟨(-273062114947250024),(-273062114947249212)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨255123484259035578,255123484259036629⟩,⟨(-196565267785801081),(-196565267785800031)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨145207330500680129,145207330500681211⟩,⟨(-117374703887742678),(-117374703887741597)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨69809034545005642,69809034545006477⟩,⟨(-59655016091299701),(-59655016091298865)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨29041940468825790,29041940468826251⟩,⟨(-26366673840854722),(-26366673840854257)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨10726091890797970,10726091890798161⟩,⟨(-10361530434440055),(-10361530434439864)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨3621131723400343,3621131723400412⟩,⟨(-3716975861967500),(-3716975861967432)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1156384989166763,1156384989166792⟩,⟨(-1257450836121562),(-1257450836121531)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨363333862896999,363333862897017⟩,⟨(-416982257672373),(-416982257672354)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨117050919140341,117050919140358⟩,⟨(-141091567409061),(-141091567409043)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨39845327263799,39845327263815⟩,⟨(-50057738262375),(-50057738262359)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨13963512302349,13963512302366⟩,⟨(-18075893249678),(-18075893249662)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨3505351182427,3505351182443⟩,⟨(-4609412899342),(-4609412899326)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨51980881890098002737,51980881890098002768⟩,⟨832606865671949654,832606865671949677⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨140673340504681445086,140673340504681445141⟩,⟨375980644505940848,375980644505940879⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨191077795840575361150,191077795840575361218⟩,⟨(-4428416946606514363),(-4428416946606514322)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨197797203618040000998,197797203618040001070⟩,⟨(-11721422413534878401),(-11721422413534878361)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨171411877595456648512,171411877595456648578⟩,⟨(-17458077857894932651),(-17458077857894932608)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨129382862510610083609,129382862510610083667⟩,⟨(-19060063232617738897),(-19060063232617738864)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨87099451820068480852,87099451820068480898⟩,⟨(-16881749911225049899),(-16881749911225049870)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨53330092080874980828,53330092080874980865⟩,⟨(-12851669387310885696),(-12851669387310885667)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨30287865745022824979,30287865745022825022⟩,⟨(-8741068071516954446),(-8741068071516954403)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨16287431594395012262,16287431594395012359⟩,⟨(-5473172498392578957),(-5473172498392578864)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨8471071930308426653,8471071930308426899⟩,⟨(-3235506842592423190),(-3235506842592422947)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨4345867499763907757,4345867499763908273⟩,⟨(-1842169574826717304),(-1842169574826716789)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨2226744559243598172,2226744559243598975⟩,⟨(-1021342784472288409),(-1021342784472287605)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1130934564612169086,1130934564612169996⟩,⟨(-547477463573249856),(-547477463573248946)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨532748135569342953,532748135569343664⟩,⟨(-266410316855682700),(-266410316855681988)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨156563161471144754,156563161471145030⟩,⟨(-79479225792214025),(-79479225792213751)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨2103589515304218976750,2103589515304222511272⟩,⟨770956365430238247895,770956365430241781975⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨5867803075054172574706,5867803075054180310073⟩,⟨2098294749870893891110,2098294749870901625255⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨8451109956925512892475,8451109956925519624186⟩,⟨2882167917220392717820,2882167917220399447792⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨9510835972850643607819,9510835972850647037239⟩,⟨3029768062522487851701,3029768062522491279191⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨9161599271748888885845,9161599271748889981837⟩,⟨2667692423338852940679,2667692423338854034835⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨7856161722128114474597,7856161722128114701350⟩,⟨2035223685121366436605,2035223685121366661807⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨6146836138217588747076,6146836138217588780712⟩,⟨1371305447914225251697,1371305447914225284132⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨4470517288949071272213,4470517288949071277276⟩,⟨831049059068771359015,831049059068771363213⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3067815574790371582016,3067815574790371583531⟩,⟨462028277119415559461,462028277119415560389⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2012189836757226021542,2012189836757226022334⟩,⟨240300753883498163178,240300753883498163587⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1275786687222015426289,1275786687222015426759⟩,⟨118852197332617680983,118852197332617681209⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨788617312574521515112,788617312574521515395⟩,⟨56386467839774211270,56386467839774211404⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨476090615392134457244,476090615392134457417⟩,⟨25624448175161923061,25624448175161923145⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨276083557512566793416,276083557512566793524⟩,⟨11033230144123021705,11033230144123021757⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨142824168498707686013,142824168498707686076⟩,⟨4322558031431411772,4322558031431411804⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨44065062214448913733,44065062214448913763⟩,⟨1112129829400842075,1112129829400842097⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨2218963887863204103861,2218963887863503558617⟩,⟨39576588359759109210678,39576588359759408660651⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨8849372427894489340346,8849372427895563684742⟩,⟨110285766831002989519102,110285766831004063850053⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨20499121902781649952578,20499121902784103797613⟩,⟨158863761419416443053114,158863761419418896878251⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨36269232113925243300834,36269232113930271294730⟩,⟨179740253102095594086810,179740253102100622057314⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨51810242983882731052275,51810242983892020160622⟩,⟨175632182542754992976536,175632182542764282060871⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨62194143013588274561493,62194143013603011239803⟩,⟨154159441665227031747114,154159441665241768403208⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨65007031323489606395972,65007031323508401494270⟩,⟨124092176595016419858367,124092176595035214937698⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨60981404893123224220136,60981404893141445367824⟩,⟨92923466581356901143765,92923466581375122276172⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨52591095729386280016570,52591095729399805666758⟩,⟨65557228130279287864994,65557228130292813503376⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨42490596049424518875618,42490596049432316253810⟩,⟨44116500485822091774647,44116500485829889144012⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨32621313818911346959762,32621313818914862772774⟩,⟨28670123494944599882141,28670123494948115688756⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨23974937408284822716666,23974937408286161546080⟩,⟨18200816241568681565843,18200816241570020390779⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨16799017321418012066609,16799017321418481409687⟩,⟨11336749131781834162589,11336749131782303502646⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨10952869079339607750082,10952869079339769741605⟩,⟨6799558425189970687426,6799558425190132677035⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨6137506496539757322249,6137506496539812975474⟩,⟨3620742321878152485799,3620742321878208137968⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1971384710716161252414,1971384710716174922536⟩,⟨1135729815408879177117,1135729815408892846904⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-163602500885924678920691),(-163602500885924678855080)⟩,⟨2063404578636488562866,2063404578636488603037⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-462824148936774937081395),(-462824148936774936891263)⟩,⟨28799286060106034682029,28799286060106034801127⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-689319417977082901745504),(-689319417977082901453123)⟩,⟨108079889339602688307425,108079889339602688500204⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-823703928591155971486934),(-823703928591155971123774)⟩,⟨232376192271294399097812,232376192271294399353336⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-864837231753323824604066),(-864837231753323824203129)⟩,⟨360347636864210454569607,360347636864210454873003⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-819168083640093156282658),(-819168083640093155860326)⟩,⟨449542667569355132353503,449542667569355132697264⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-705605554611653910204333),(-705605554611653909727770)⟩,⟨484819810411556857871581,484819810411556858291844⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-558081314954739333389567),(-558081314954739332573424)⟩,⟨473931217000276326960884,473931217000276327743078⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-411096989964275012074425),(-411096989964275009006339)⟩,⟨431306003157265944214304,431306003157265947267576⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-286574477907321215010887),(-286574477907321199370554)⟩,⟨370771405376259949885483,370771405376259965523981⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-192333072585749792672045),(-192333072585749726648980)⟩,⟨303406359029746110750669,303406359029746176778915⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-126399238209650774080158),(-126399238209650573371457)⟩,⟨236447905261095697986295,236447905261095898702558⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-81828479459812690959201),(-81828479459812270807840)⟩,⟨173778612950048642391908,173778612950049062550601⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-50926587513904576198836),(-50926587513903976254666)⟩,⟨117278116970765537525989,117278116970766137475900⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-27872506203232579039120),(-27872506203232026339723)⟩,⟨67164667748917940180676,67164667748918492883636⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-8865792740838973797721),(-8865792740838748573712)⟩,⟨21800581081279144812615,21800581081279370037823⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-952488531672767018888921),(-952488531672750538006987)⟩,⟨848854538499409534626905,848854538499426015384093⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 15) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_15 (tableDensity false) (fullFactor false 0 15) density0_contains hk0_0_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨62929618273591579373189,62929618273591579377056⟩,⟨532130753182064536088597,532130753182064536117602⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_15 0 15 ha0_0_15_contains + def realAnswer : RBox := ⟨(-889558913399175539515732),(-889558913399158858629931)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_15 +namespace hm0_1_0_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨670040305694,670040305710⟩,⟨(-700470282236),(-700470282220)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨1496833999184,1496833999200⟩,⟨(-1577721827102),(-1577721827086)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1367826523340,1367826523356⟩,⟨(-1464509051559),(-1464509051543)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨755291305250,755291305266⟩,⟨(-832898730584),(-832898730568)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨265839070334,265839070351⟩,⟨(-312583353704),(-312583353687)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨59291142288,59291142304⟩,⟨(-79177675387),(-79177675371)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨8204797993,8204798009⟩,⟨(-13444292836),(-13444292820)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨683402151,683402167⟩,⟨(-1465652752),(-1465652736)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨32648973,32648989⟩,⟨(-94817702),(-94817686)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨826620,826636⟩,⟨(-3251134),(-3251118)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨9692,9708⟩,⟨(-50341),(-50325)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨36,52⟩,⟨(-284),(-268)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨25433716425904604,25433716425904689⟩,⟨(-2880318130888279),(-2880318130888196)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨64468107182113987,64468107182114223⟩,⟨(-8416295495429109),(-8416295495428875)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨76875989800780794,76875989800781228⟩,⟨(-12822043831562203),(-12822043831561767)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨65638313176892500,65638313176893173⟩,⟨(-14714682325149284),(-14714682325148609)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨44321540474636974,44321540474637845⟩,⟨(-13422953849784871),(-13422953849783998)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨24817277150599971,24817277150600869⟩,⟨(-9869301250792937),(-9869301250792038)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨11867558462763271,11867558462763965⟩,⟨(-5931938241606315),(-5931938241605620)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨4953271212299002,4953271212299388⟩,⟨(-2988472269030298),(-2988472269029911)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1846263005327353,1846263005327513⟩,⟨(-1304640771087925),(-1304640771087764)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨633337836499391,633337836499448⟩,⟨(-511653082542385),(-511653082542326)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨207778527835961,207778527835988⟩,⟨(-186889363641572),(-186889363641547)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨67992397371062,67992397371079⟩,⟨(-65889055600711),(-65889055600694)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨23012827167721,23012827167738⟩,⟨(-23234717776427),(-23234717776410)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨8207912931642,8207912931659⟩,⟨(-8427891421263),(-8427891421247)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2976577741661,2976577741677⟩,⟨(-3071353213993),(-3071353213977)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨760478199712,760478199728⟩,⟨(-785390624301),(-785390624285)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨9896383935384492682,9896383935384492707⟩,⟨6310180804456425988,6310180804456426011⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨26963704544970392924,26963704544970392952⟩,⟨16854883032315725680,16854883032315725706⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨36888321787152619547,36888321787152619581⟩,⟨22293631067704198961,22293631067704198993⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨38127413842818529242,38127413842818529280⟩,⟨22040827692978305306,22040827692978305339⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨32562783517227598207,32562783517227598242⟩,⟨17629321327685552733,17629321327685552766⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨24052774155455022313,24052774155455022343⟩,⟨11651999364075890004,11651999364075890031⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨15928749573722746492,15928749573722746516⟩,⟨6427301641856341969,6427301641856341997⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨9726836412377148525,9726836412377148551⟩,⟨2990361553279673900,2990361553279673928⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨5586740377770167864,5586740377770167900⟩,⟨1184552864313913987,1184552864313914023⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨3061373496761656470,3061373496761656551⟩,⟨401328680426780734,401328680426780813⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1618145397874743093,1618145397874743295⟩,⟨115006526171952088,115006526171952287⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨832797678208769277,832797678208769698⟩,⟨24390204887799770,24390204887800192⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨420888388070969257,420888388070969914⟩,⟨(-1450716292312482),(-1450716292311823)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨208636878384708800,208636878384709544⟩,⟨(-7227249432380925),(-7227249432380181)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨96032000370200291,96032000370200876⟩,⟨(-6051845671092413),(-6051845671091829)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨27848199167318973,27848199167319202⟩,⟨(-2244259808522801),(-2244259808522571)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨409689064801728963383,409689064801731932918⟩,⟨626936459127818225997,626936459127821195578⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1131840209408604177485,1131840209408610671889⟩,⟨1711973861686122167773,1711973861686128662315⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1606918691225717988524,1606918691225723632198⟩,⟨2364055333005867681947,2364055333005873325813⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1791131771984891770977,1791131771984894639356⟩,⟨2504404756851772156743,2504404756851775025325⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1733321258435147659813,1733321258435148572910⟩,⟨2244306842751669714553,2244306842751670627828⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1515430742601040336000,1515430742601040523188⟩,⟨1787330744326829541645,1787330744326829728973⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1214853674590099368026,1214853674590099394757⟩,⟨1306417386746359611512,1306417386746359638344⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨900938653445993183367,900938653445993186711⟩,⟨893503194199958070708,893503194199958074118⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨626216594093220721390,626216594093220722070⟩,⟨578587076785472168243,578587076785472168960⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨414977572179739939078,414977572179739939362⟩,⟨358605561659359799508,358605561659359799815⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨266587763152988018623,266587763152988018783⟩,⟨215515179650164407492,215515179650164407659⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨167840538896306628586,167840538896306628684⟩,⟨127274834411942080754,127274834411942080859⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨103515022515337572591,103515022515337572652⟩,⟨74299307500988638339,74299307500988638404⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨61248998035037425126,61248998035037425166⟩,⟨42191259905666153504,42191259905666153547⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨32172624739000256453,32172624739000256482⟩,⟨21589364423574355577,21589364423574355608⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨10007103819444027217,10007103819444027238⟩,⟨6632407056995357047,6632407056995357066⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1393412091625560850257,1393412091625806952870⟩,⟨12948648458763706890484,12948648458763952994829⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4526432542067094618724,4526432542067977618187⟩,⟨36815268374285310133986,36815268374286193138372⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨8206692951516325745396,8206692951518342822241⟩,⟨54872390504896624744792,54872390504898641828896⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨11892961580120800033898,11892961580124933743543⟩,⟨64452859169399952357433,64452859169404086075517⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨14992037381937943464906,14992037381945581347568⟩,⟨64987649167884553646378,64987649167892191537457⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨17180271252655590254255,17180271252667707361511⟩,⟨58501287852289983736873,58501287852302100851668⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨18079405387258127603744,18079405387273578491183⟩,⟨48466463928409042598016,48466463928424493491677⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨17368680603888537897118,17368680603903509742979⟩,⟨37895285851375093557733,37895285851390065408354⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨15200432269128310361630,15200432269139415278299⟩,⟨28464527964449285615542,28464527964460390535599⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨12172990687398971396900,12172990687405366459042⟩,⟨20739453323421529519978,20739453323427924584405⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨8989658426398704924609,8989658426401584787841⟩,⟨14679209642900553701677,14679209642903433566421⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨6187732779881922239223,6187732779883017419416⟩,⟨10030737974460187853860,10030737974461283035054⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨4020001411266893573008,4020001411267277010637⟩,⟨6542244126065585147172,6542244126065968585450⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2459731079756792256972,2459731079756924457241⟩,⟨3989447596458747456478,3989447596458879657141⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1324862497218996139824,1324862497219041523858⟩,⟨2122210176712245090124,2122210176712290474368⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨418282186919015962511,418282186919027105916⟩,⟨662709012529622551275,662709012529633694747⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-4857362034460486243024),(-4857362034460486203063)⟩,⟨292027981466867225207,292027981466867252167⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-12905591458900300699229),(-12905591458900300582364)⟩,⟨4158113547145551496282,4158113547145551575997⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-12762076407900052712557),(-12762076407900052530343)⟩,⟨17069685636672381994079,17069685636672382122651⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨4688144979778356994439,4688144979778357225073⟩,⟨45250572564011499994491,45250572564011500164884⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨38440847459718124901243,38440847459718125164329⟩,⟨95158361260720180889822,95158361260720181094430⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨70229378872740034508783,70229378872740034799530⟩,⟨162235880809574319170995,162235880809574319410559⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨81162572335514300192895,81162572335514300544955⟩,⟨224451484580928477513875,224451484580928477825444⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨69828532026952339873605,69828532026952340525814⟩,⟨258496329973616990153161,258496329973616990777620⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨47866290617520790665173,47866290617520793185414⟩,⟨257044605769702813376399,257044605769702815881121⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨27068157170109325009164,27068157170109337822135⟩,⟨228058683782721558150776,228058683782721570956982⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨13361937373634391438666,13361937373634445391160⟩,⟨185264514661405001274672,185264514661405055225419⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨6994823385687499595986,6994823385687663526949⟩,⟨140620172446435261012771,140620172446435424943955⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨4986241538665398392016,4986241538665741651903⟩,⟨100861224327102457328142,100861224327102800588853⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨4130588070220096730114,4130588070220587099706⟩,⟨67411429945208042352560,67411429945208532723025⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2855501739111081675564,2855501739111533595755⟩,⟨38713702946861724170785,38713702946862176091611⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1019612289553605011873,1019612289553789204942⟩,⟨12630843513950400285720,12630843513950584479022⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨83119032328636933479238,83119032328650471646296⟩,⟨386476580682837611706301,386476580682851149822819⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 15) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_15 (tableDensity true) (fullFactor false 0 15) density1_contains hk0_0_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-82292577742388988416149),(-82292577742388988411094)⟩,⟨(-695863292622699777999942),(-695863292622699777962011)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_15 0 15 ha0_0_15_contains + def realAnswer : RBox := ⟨826454586247845063089,826454586261583235202⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_15 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_2.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_2.lean new file mode 100644 index 0000000000000000000000000000000000000000..715bb101013a37f26b4559d013bed1557e5031fb --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_2.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_0_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨149087058571,149087058587⟩,⟨108907862135,108907862151⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨329742516935,329742516952⟩,⟨235056336932,235056336949⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨296821953132,296821953148⟩,⟨201613393259,201613393275⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨162426768887,162426768903⟩,⟨102910071009,102910071026⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨57829333139,57829333158⟩,⟨33629623389,33629623405⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨13437180865,13437180882⟩,⟨7095108459,7095108475⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1987280003,1987280019⟩,⟨943867559,943867576⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨178713490,178713506⟩,⟨75450372,75450390⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨9113334,9113351⟩,⟨3369032,3369048⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨237370,237387⟩,⟨75536,75552⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨2687,2704⟩,⟨719,735⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨7,23⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨6124596500321996,6124596500322019⟩,⟨8792486009322056,8792486009322078⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨15723982995823449,15723982995823483⟩,⟨22334942402686521,22334942402686555⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨19189879128235036,19189879128235085⟩,⟨26698518476599123,26698518476599171⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨16862687066790889,16862687066790952⟩,⟨22763554595356280,22763554595356346⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨11703426822014325,11703426822014405⟩,⟨15192260695529193,15192260695529272⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨6682084812432542,6682084812432618⟩,⟨8268345641248888,8268345641248964⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨3222582650468017,3222582650468077⟩,⟨3772127678621963,3772127678622023⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨1342594313556408,1342594313556446⟩,⟨1479279239642161,1479279239642197⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨494704451848879,494704451848903⟩,⟨512277723234320,512277723234346⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨165820821968576,165820821968596⟩,⟨161596803783154,161596803783173⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨52361340155389,52361340155409⟩,⟨48167143774328,48167143774345⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨16239950200855,16239950200873⟩,⟨14154184648791,14154184648808⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨5169008770941,5169008770957⟩,⟨4289114249979,4289114249995⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1742289969808,1742289969824⟩,⟨1387012674884,1387012674901⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨606192036098,606192036114⟩,⟨468303317730,468303317746⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨151582889807,151582889823⟩,⟨115275951161,115275951177⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-81620565486128729),(-81620565486128712)⟩,⟨5095114823244180889,5095114823244180907⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-36842124509172079),(-36842124509172063)⟩,⟨13702377536293646727,13702377536293646746⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨425253242219363559,425253242219363582⟩,⟨18381975460261418716,18381975460261418737⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1105752650102959609,1105752650102959627⟩,⟨18682239987333936493,18682239987333936515⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1608422381275254008,1608422381275254027⟩,⟨15807780762099393414,15807780762099393433⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1706264294696895797,1706264294696895814⟩,⟨11591915298497819097,11591915298497819119⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1462081740653776838,1462081740653776855⟩,⟨7548778619870001460,7548778619870001480⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1073149608224819360,1073149608224819377⟩,⟨4455963909473912468,4455963909473912486⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨702132304049443389,702132304049443408⟩,⟨2434201071137394992,2434201071137395012⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨422516758377108496,422516758377108515⟩,⟨1257923662620969377,1257923662620969399⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨240203278881044428,240203278881044460⟩,⟨629117219851074606,629117219851074641⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨131839014276713662,131839014276713711⟩,⟨311102002511669966,311102002511670018⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨70764566362531433,70764566362531505⟩,⟨154306035977815171,154306035977815243⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨36947458109840716,36947458109840792⟩,⟨76328937975579954,76328937975580032⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨17647958481016098,17647958481016161⟩,⟨35292044392606212,35292044392606272⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨5214506205506086,5214506205506117⟩,⟨10271890278894892,10271890278894924⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-100797813437231679030),(-100797813437231216944)⟩,⟨275030726626140567576,275030726626141029718⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-273050886680257853211),(-273050886680256846549)⟩,⟨763559871427789220008,763559871427790226833⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-371582652431859795865),(-371582652431858927683)⟩,⟨1089494549248037180874,1089494549248038049282⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-385306461378558944476),(-385306461378558508069)⟩,⟨1209399852272060896323,1209399852272061332980⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-333309490295963022206),(-333309490295962885226)⟩,⟨1144483640274365733461,1144483640274365870677⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-248943240490235907679),(-248943240490235880047)⟩,⟨960699394411417263808,960699394411417291637⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-163726575588394152582),(-163726575588394148683)⟩,⟨733638474936034719607,733638474936034723653⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-96637331705528442646),(-96637331705528442143)⟩,⟨519614226946720028171,519614226946720028781⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-52255813756065492258),(-52255813756065492141)⟩,⟨346793169239546985656,346793169239546985842⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-26425382011651012208),(-26425382011651012150)⟩,⟨221154258985174912525,221154258985174912630⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-12717882198045909199),(-12717882198045909162)⟩,⟨136440909365843931615,136440909365843931684⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-5882826175170325039),(-5882826175170325012)⟩,⟨82232896730708270317,82232896730708270362⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-2614864951305898175),(-2614864951305898156)⟩,⟨48559689893688629899,48559689893688629932⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1105965984779990898),(-1105965984779990878)⟩,⟨27664323393124408866,27664323393124408888⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-427861963782778928),(-427861963782778911)⟩,⟨14134553086661248571,14134553086661248593⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-109361830379905537),(-109361830379905521)⟩,⟨4333045150817440983,4333045150817441002⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-6469524570790559622288),(-6469524570790510672631)⟩,⟨362718140420641427154,362718140420690377573⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-17960263204485806128158),(-17960263204485631201504)⟩,⟨1440824466491875383525,1440824466492050312314⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-25679058999027663467498),(-25679058999027266992815)⟩,⟨3312287995770461350982,3312287995770857828806⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-28737506869287714053715),(-28737506869286910701723)⟩,⟨5796283691423565171458,5796283691424368527110⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-27687138865934966865121),(-27687138865933503714853)⟩,⟨8163808111624463234312,8163808111625926388303⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-23895439354980831473385),(-23895439354978549102675)⟩,⟨9636216922726758602721,9636216922729040976823⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-18870652220344679726127),(-18870652220341823354767)⟩,⟨9881599115871482263329,9881599115874338637541⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-13840829169230514466462),(-13840829169227801101245)⟩,⟨9079682641889741888593,9079682641892455256065⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-9555640323513585620778),(-9555640323511613991454)⟩,⟨7663035617953003434889,7663035617954975065928⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-6292155766394217650594),(-6292155766393104997032)⟩,⟨6058372937011686848053,6058372937012799502873⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4004229364416095059393),(-4004229364415603652661)⟩,⟨4554871730379619077035,4554871730380110484661⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2493399072164610821210),(-2493399072164427259994)⟩,⟨3283763057447896733548,3283763057448080295383⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1527241853665775260617),(-1527241853665711988029)⟩,⟨2262813200180057664586,2262813200180120937584⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-903821406954426549052),(-903821406954405006692)⟩,⟨1455803894435253449337,1455803894435274991953⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-476807623232619130340),(-476807623232611800138)⟩,⟨808217686025901811143,808217686025909141490⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-148846019296700011648),(-148846019296698220057)⟩,⟨258364357116296136397,258364357116297928030⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-404718168288345455431),(-404718168288345447533)⟩,⟨(-32097699979178100185597),(-32097699979178100172609)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-5629765067960911051273),(-5629765067960911027950)⟩,⟨(-90516900858415674060845),(-90516900858415674023358)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-20996640810770345960086),(-20996640810770345922537)⟩,⟨(-133977081237414383409162),(-133977081237414383351887)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-44736300146582111746568),(-44736300146582111697200)⟩,⟨(-158643234498574838396812),(-158643234498574838326336)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-68568905607376545435989),(-68568905607376545378002)⟩,⟨(-164623287848070648479266),(-164623287848070648402382)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-84359148884277569183599),(-84359148884277569118782)⟩,⟨(-153767925502678380319982),(-153767925502678380240170)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-89557942618166260520827),(-89557942618166260442889)⟩,⟨(-130381062011606027336523),(-130381062011606027248036)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-86068185223224973741483),(-86068185223224973599307)⟩,⟨(-101381530407361227394825),(-101381530407361227246427)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-76953180919624143312882),(-76953180919624142769152)⟩,⟨(-73370570885237444749419),(-73370570885237444203056)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-64992535189405605670722),(-64992535189405602936007)⟩,⟨(-50248699758429532496566),(-50248699758429529761581)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-52288738342989031583986),(-52288738342989020227667)⟩,⟨(-33154932252830909158213),(-33154932252830897802865)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-40120559796276892581211),(-40120559796276858573246)⟩,⟨(-21451359068298823660252),(-21451359068298789653648)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-29093517041902146044467),(-29093517041902075766763)⟩,⟨(-13700898041596101169919),(-13700898041596030893512)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-19425565625545545139399),(-19425565625545445811946)⟩,⟨(-8435699468189535567720),(-8435699468189436241271)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-11042457458364207905459),(-11042457458364117051229)⟩,⟨(-4582550141738868163763),(-4582550141738777310150)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3570544734928965427999),(-3570544734928928540770)⟩,⟨(-1452060287756146588243),(-1452060287756109701222)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-148069530568928368193935),(-148069530568925877936844)⟩,⟨(-181681551727449574851405),(-181681551727447084571473)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 16) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_16 (tableDensity false) (fullFactor false 0 16) density0_contains hk0_0_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-105739889332786839573670),(-105739889332786839567658)⟩,⟨10333719027224876911619,10333719027224876912284⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_16 0 16 ha0_0_16_contains + def realAnswer : RBox := ⟨(-253809419901715307767605),(-253809419901712617504502)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_16 +namespace hm0_1_0_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨22815433910,22815433926⟩,⟨21824361365,21824361381⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨50452329251,50452329267⟩,⟨47867126976,47867126992⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨45127367438,45127367454⟩,⟨42151762998,42151763014⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨24256925354,24256925370⟩,⟨22002147153,22002147169⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨8429495462,8429495479⟩,⟨7173825747,7173825763⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1933764613,1933764629⟩,⟨1450194665,1450194681⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨290231959,290231975⟩,⟨177545161,177545177⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨27216036,27216052⟩,⟨12729523,12729539⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1467587,1467603⟩,⟨507036,507052⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨40383,40399⟩,⟨10295,10311⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨470,486⟩,⟨84,100⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨188064503067088,188064503067107⟩,⟨1660693577754896,1660693577754914⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨544302601207084,544302601207115⟩,⟨4170342699048320,4170342699048349⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨813707700275459,813707700275504⟩,⟨4881417265389306,4881417265389348⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨908078194423486,908078194423542⟩,⟨4054120637647175,4054120637647228⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨798572535496228,798572535496293⟩,⟨2639482021785038,2639482021785103⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨561422734908638,561422734908707⟩,⟨1413196011804698,1413196011804765⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨320227732040778,320227732040832⟩,⟨641262927400879,641262927400932⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨152084959632645,152084959632678⟩,⟨252291177175249,252291177175282⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨62257553988258,62257553988282⟩,⟨88171692108036,88171692108062⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨22815489614838,22815489614857⟩,⟨28260134722737,28260134722755⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨7779349890746,7779349890762⟩,⟨8653049754154,8653049754171⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨2565486283398,2565486283414⟩,⟨2648115846554,2648115846570⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨851111193225,851111193241⟩,⟨843077579306,843077579322⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨293323879853,293323879869⟩,⟨285676134828,285676134844⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨102999606179,102999606195⟩,⟨99821666037,99821666053⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨25827950067,25827950083⟩,⟨25008696664,25008696680⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-618518814547636808),(-618518814547636790)⟩,⟨970032739534032890,970032739534032906⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1641786602152806300),(-1641786602152806283)⟩,⟨2626398665145061967,2626398665145061983⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-2144778882642536635),(-2144778882642536617)⟩,⟨3548692139083852641,3548692139083852657⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2082014114109288029),(-2082014114109288009)⟩,⟨3601244533037245077,3601244533037245094⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1626173723495681266),(-1626173723495681247)⟩,⟨3003110047251307635,3003110047251307651⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1044400155798567158),(-1044400155798567141)⟩,⟨2155101074716017165,2155101074716017185⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-557429699404587111),(-557429699404587093)⟩,⟨1380561080646322880,1380561080646322896⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-250105340543964597),(-250105340543964578)⟩,⟨812706326642732794,812706326642732810⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-95326911164926306),(-95326911164926290)⟩,⟨448975262188832082,448975262188832099⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-31047644314711146),(-31047644314711127)⟩,⟨236423453694570405,236423453694570427⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-8559158914340568),(-8559158914340542)⟩,⟨120170025389663055,120170025389663087⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1751928277583596),(-1751928277583553)⟩,⟨59617433224622600,59617433224622645⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨98349632284740,98349632284801⟩,⟨29167665887239181,29167665887239241⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨487007274826350,487007274826414⟩,⟨14081968129939026,14081968129939092⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨400735410615820,400735410615872⟩,⟨6361806386038309,6361806386038360⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨147236390460869,147236390460899⟩,⟨1827086339438841,1827086339438872⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-81968064093929074383),(-81968064093928686105)⟩,⟨53564253043262432329,53564253043262820600⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-222778371159058920390),(-222778371159058075070)⟩,⟨147284210075606060716,147284210075606906019⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-304783332743175340782),(-304783332743174612708)⟩,⟨207162537091302669194,207162537091303397242⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-318489668837949937152),(-318489668837949571902)⟩,⟨227761819230714195609,227761819230714560832⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-280397711471479211167),(-280397711471479096830)⟩,⟨216524903081126134643,216524903081126248962⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-218595838700377928403),(-218595838700377905416)⟩,⟨185307491749035707667,185307491749035730637⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-155945138639105710027),(-155945138639105706798)⟩,⟨144988371186135007879,144988371186135011095⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-103866998203471649539),(-103866998203471649127)⟩,⟨104713587339470894150,104713587339470894556⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-65413579120801550379),(-65413579120801550284)⟩,⟨70787292212526781797,70787292212526781890⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-39418402023054913459),(-39418402023054913412)⟩,⟨45607896834152779627,45607896834152779673⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-23051120103164118116),(-23051120103164118082)⟩,⟨28509638685133334362,28509638685133334392⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-13272588392407097341),(-13272588392407097318)⟩,⟨17500826850698771391,17500826850698771415⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-7578619750720062458),(-7578619750720062434)⟩,⟨10557821002489684468,10557821002489684487⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-4227758531970640698),(-4227758531970640681)⟩,⟨6137177391105445488,6137177391105445505⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2136596736209925937),(-2136596736209925920)⟩,⟨3183925174257361598,3183925174257361614⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-652184109407439371),(-652184109407439355)⟩,⟨984026426429727577,984026426429727593⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2116692209339728993383),(-2116692209339688763891)⟩,⟨227775776575433464036,227775776575473693239⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-5995359011514740566665),(-5995359011514596792562)⟩,⟨737065647514031260844,737065647514175034129⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-8869419349004652103382),(-8869419349004326194832)⟩,⟨1326292124273420398849,1326292124273746306201⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-10304560890553451476374),(-10304560890552791005134)⟩,⟨1900983130496580602537,1900983130497241072400⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-10244465802940220205840),(-10244465802939017139912)⟩,⟨2362576838116721518177,2362576838117924582751⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-9067633560343151679011),(-9067633560341275015077)⟩,⟨2661925227452896866459,2661925227454773529201⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-7369850250880401117759),(-7369850250878052975777)⟩,⟨2748117818616499897913,2748117818618848038929⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-5643921775326297044266),(-5643921775324067537123)⟩,⟨2585963719605158132592,2585963719607387639013⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-4148451805757381143771),(-4148451805755762379256)⟩,⟨2214832917678802997434,2214832917680421761447⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-2957534375484926185743),(-2957534375484013633599)⟩,⟨1735716878482092526553,1735716878483005078365⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-2049896088244764765821),(-2049896088244362244252)⟩,⟨1255329134981942091838,1255329134982344613193⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1374023180306704038815),(-1374023180306553882381)⟩,⟨847607302044172030189,847607302044322186485⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-881312788331408882059),(-881312788331357189972)⟩,⟨541540159600575507549,541540159600627199548⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-530289247079595924166),(-530289247079578343307)⟩,⟨326951866921403959098,326951866921421539908⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-279470032494421959241),(-279470032494415981466)⟩,⟨174467311315368154855,174467311315374132604⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-86853101179354395871),(-86853101179352935386)⟩,⟨54819019410478594902,54819019410480055378⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-57278634912907667672),(-57278634912907662370)⟩,⟨(-952982644185032300832),(-952982644185032292978)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-812828485327559739219),(-812828485327559723611)⟩,⟨(-2524158432253511678985),(-2524158432253511656109)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-3315830245942940256904),(-3315830245942940231893)⟩,⟨(-2481822876616237398291),(-2481822876616237362855)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-8709465802369696109086),(-8709465802369696076230)⟩,⟨898341853905838522163,898341853905838566596⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-18100861123397394858394),(-18100861123397394819379)⟩,⟨7309583923456421493903,7309583923456421544014⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-30433335350757615961648),(-30433335350757615916577)⟩,⟨13175697446127061407864,13175697446127061462485⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-41449695124966961471594),(-41449695124966961413906)⟩,⟨14993534969910466921496,14993534969910466986569⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-46935697040277254852132),(-46935697040277254738716)⟩,⟨12685135997429728009338,12685135997429728127666⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-45857776553993653816391),(-45857776553993653370415)⟩,⟨8544786600806265935903,8544786600806266384505⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-39975921038719781881676),(-39975921038719779642284)⟩,⟨4748083361543568930451,4748083361543571170892⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-31929209979832983490254),(-31929209979832974211193)⟩,⟨2304353443297972439927,2304353443297981719166⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-23861315264673562139203),(-23861315264673534363882)⟩,⟨1187211494569030826995,1187211494569058602185⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-16886199289952712003516),(-16886199289952654588183)⟩,⟨834656130371590922950,834656130371648338077⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-11165823848052355260564),(-11165823848052274075087)⟩,⟨684060140256665094158,684060140256746279445⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-6364852575011948220126),(-6364852575011873932650)⟩,⟨469437394946505862331,469437394946580149673⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-2068704841104325297286),(-2068704841104295130236)⟩,⟨166992989050362550913,166992989050392717915⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-66949533502838726289792),(-66949533502836680612009)⟩,⟨14205747792719762362336,14205747792721808049867⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 16) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_16 (tableDensity true) (fullFactor false 0 16) density1_contains hk0_0_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨138275239896721251742322,138275239896721251750183⟩,⟨(-13513324881755608269909),(-13513324881755608269040)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_16 0 16 ha0_0_16_contains + def realAnswer : RBox := ⟨71325706393882425452530,71325706393884671138174⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_16 +namespace hm0_0_0_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-3338699817),(-3338699801)⟩,⟨4570393564,4570393580⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-7075582615),(-7075582599)⟩,⟨9924874818,9924874834⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-5849369233),(-5849369217)⟩,⟨8609497119,8609497135⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-2822772356),(-2822772340)⟩,⟨4453279739,4453279755⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-854523812),(-854523795)⟩,⟨1468470510,1468470526⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-163389850),(-163389833)⟩,⟨309174914,309174932⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-19229642),(-19229626)⟩,⟨40444519,40444536⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1323433),(-1323416)⟩,⟨3130678,3130695⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-49300),(-49284)⟩,⟨133134,133152⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-895),(-878)⟩,⟨2777,2794⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-18),(-2)⟩,⟨17,34⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-540333886957147),(-540333886957131)⟩,⟨376380441945224,376380441945240⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1359819324199667),(-1359819324199651)⟩,⟨957305445243998,957305445244015⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1595556361963527),(-1595556361963509)⟩,⟨1146766096997046,1146766096997065⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1323295547465821),(-1323295547465804)⟩,⟨980171048815915,980171048815938⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-851582290272045),(-851582290272023)⟩,⟨655921316089457,655921316089474⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-443206455427721),(-443206455427702)⟩,⟨358102380574426,358102380574445⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-191886308028917),(-191886308028896)⟩,⟨163887047942853,163887047942872⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-70938278812675),(-70938278812657)⟩,⟨64363710164690,64363710164709⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-23035248463873),(-23035248463855)⟩,⟨22237820725408,22237820725424⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-6789739982290),(-6789739982274)⟩,⟨6965004213714,6965004213731⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1888980315148),(-1888980315129)⟩,⟨2052861052809,2052861052828⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-519127139334),(-519127139317)⟩,⟨595473530732,595473530749⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-147957981070),(-147957981054)⟩,⟨178275607826,178275607842⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-45448642793),(-45448642777)⟩,⟨57083064444,57083064462⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-14782856263),(-14782856247)⟩,⟨19134594857,19134594874⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-3567962092),(-3567962076)⟩,⟨4691687609,4691687625⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-470040996808374791),(-470040996808374775)⟩,⟨(-7530618305962334),(-7530618305962318)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1256187332426893103),(-1256187332426893087)⟩,⟨(-3397679773915028),(-3397679773915012)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1664386121093014282),(-1664386121093014266)⟩,⟨38434884281706495,38434884281706511⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1660831067781077175),(-1660831067781077158)⟩,⟨98180011872305421,98180011872305437⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1372138092889117768),(-1372138092889117751)⟩,⟨139476403636023476,139476403636023492⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-977552886953582248),(-977552886953582232)⟩,⟨143772268416564469,143772268416564485⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-615819763359850272),(-615819763359850256)⟩,⟨119190568159023895,119190568159023911⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-350456268071181892),(-350456268071181874)⟩,⟨84349845875320350,84349845875320367⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-184149762757321064),(-184149762757321047)⟩,⟨53088544290071822,53088544290071838⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-91449843205380873),(-91449843205380856)⟩,⟨30702671116397646,30702671116397664⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-43979196396323226),(-43979196396323207)⟩,⟨16785657974577024,16785657974577041⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-20962489612623207),(-20962489612623186)⟩,⟨8881211317160015,8881211317160032⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-10064617473267805),(-10064617473267785)⟩,⟨4614897910657455,4614897910657475⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4848752438332562),(-4848752438332540)⟩,⟨2346885793444753,2346885793444776⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2200441658510839),(-2200441658510819)⟩,⟨1100312569136748,1100312569136768⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-634282962666902),(-634282962666884)⟩,⟨321991668340464,321991668340480⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-33843300001526015943),(-33843300001525959059)⟩,⟨(-12403484057261719800),(-12403484057261662927)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-93515492976742796994),(-93515492976742673644)⟩,⟨(-33442104016141278831),(-33442104016141155501)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-132194195305064699256),(-132194195305064593810)⟩,⟨(-45088687160955321726),(-45088687160955216303)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-144744277215472180433),(-144744277215472128091)⟩,⟨(-46119379053489381554),(-46119379053489329244)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-134565304253781852295),(-134565304253781836117)⟩,⟨(-39196271714614498207),(-39196271714614482053)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-110574472125325587313),(-110574472125325584082)⟩,⟨(-28660163674009279608),(-28660163674009276402)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-82415200334545837426),(-82415200334545836953)⟩,⟨(-18399190086437529276),(-18399190086437528825)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-56846318522860113876),(-56846318522860113794)⟩,⟨(-10576962331514791848),(-10576962331514791777)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-36898728941002387853),(-36898728941002387816)⟩,⟨(-5562882586902586406),(-5562882586902586379)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-22878135320648308654),(-22878135320648308625)⟩,⟨(-2735180446393904966),(-2735180446393904944)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-13734322726678166946),(-13734322726678166923)⟩,⟨(-1280908501329138748),(-1280908501329138731)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-8070792738641363375),(-8070792738641363357)⟩,⟨(-577681079162379561),(-577681079162379545)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-4661734508434115538),(-4661734508434115521)⟩,⟨(-251147651947223118),(-251147651947223102)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-2609028429169979698),(-2609028429169979680)⟩,⟨(-104342200604053969),(-104342200604053952)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-1316548025217955685),(-1316548025217955668)⟩,⟨(-39860316875605997),(-39860316875605981)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-401017633084353759),(-401017633084353743)⟩,⟨(-10121560576543936),(-10121560576543920)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-55803252371947981065),(-55803252371940450051)⟩,⟨(-995354017036017891637),(-995354017036010360738)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-220791271253980011717),(-220791271253953204516)⟩,⟨(-2752822222346672918174),(-2752822222346646111287)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-503726850371575228698),(-503726850371514935970)⟩,⟨(-3906677681252005483829),(-3906677681251945191566)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-871841953248890564631),(-871841953248769756035)⟩,⟨(-4324438417162385532634),(-4324438417162264724576)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1210737216985913128175),(-1210737216985696214988)⟩,⟨(-4108014925358721175053),(-4108014925358504262409)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1405227664744254554340),(-1405227664743921851091)⟩,⟨(-3486124795499913941940),(-3486124795499581239182)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-1413773561906606206918),(-1413773561906197632410)⟩,⟨(-2700940954085657587606),(-2700940954085249013503)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1272422990445670920772),(-1272422990445290618471)⟩,⟨(-1940377941446414954132),(-1940377941446034652145)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1050939685723665011451),(-1050939685723394502766)⟩,⟨(-1310953355393555823548),(-1310953355393285315097)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-813030643527763774888),(-813030643527614337379)⟩,⟨(-844666985604334674546),(-844666985604185237204)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-598599957851981576184),(-598599957851916929927)⟩,⟨(-526373587257546114103),(-526373587257481467964)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-423320205188774914295),(-423320205188751226636)⟩,⟨(-321495973092668791289),(-321495973092645103711)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-286875068124584784554),(-286875068124576756208)⟩,⟨(-193645031945291670083),(-193645031945283641791)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-182118296375489784512),(-182118296375487088123)⟩,⟨(-113073348880389513886),(-113073348880386817532)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-100169982259983214704),(-100169982259982305969)⟩,⟨(-59096481407941858461),(-59096481407940949742)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-31868753992775933109),(-31868753992775712095)⟩,⟨(-18359915987072414704),(-18359915987072193692)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨5926919681547839062057,5926919681547839064489⟩,⟨(-74712304801146818884),(-74712304801146817413)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨16661543025554120591624,16661543025554120598588⟩,⟨(-1035787364879743381356),(-1035787364879743377049)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨24508331959433336347889,24508331959433336358459⟩,⟨(-3839086564561748782116),(-3839086564561748775224)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨28757230399217837147340,28757230399217837160226⟩,⟨(-8105942506628377000596),(-8105942506628376991606)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨29493433356331505166275,29493433356331505180162⟩,⟨(-12280326005847442866172),(-12280326005847442855728)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨27166751621363806695333,27166751621363806709538⟩,⟨(-14899534051862173155996),(-14899534051862173144484)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨22675037052342327846489,22675037052342327861962⟩,⟨(-15570725782513647244058),(-15570725782513647230444)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨17334141557320784934524,17334141557320784959933⟩,⟨(-14711337566998080822733),(-14711337566998080798401)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨12324860905951920644592,12324860905951920736179⟩,⟨(-12922609984197466618989),(-12922609984197466527845)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨8292666346317380141267,8292666346317380591416⟩,⟨(-10722667168021549211353),(-10722667168021548761237)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨5379266274174728246612,5379266274174730084794⟩,⟨(-8481495012311643252830),(-8481495012311641414481)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨3426446061543542372251,3426446061543547795250⟩,⟨(-6407332299331289605086),(-6407332299331284181856)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2159086110369005404572,2159086110369016468005⟩,⟨(-4584294459707356825793),(-4584294459707345762141)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1315139082381107157341,1315139082381122634576⟩,⟨(-3028338551725784130221),(-3028338551725768652823)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨709105162309956837503,709105162309970893704⟩,⟨(-1708688181625577515073),(-1708688181625563458772)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨223832381417518735064,223832381417524421035⟩,⟨(-550391960043140074272),(-550391960043134388269)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨32504090440524224182703,32504090440524578951699⟩,⟨(-24461566452059493397210),(-24461566452059138632198)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 17) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_17 (tableDensity false) (fullFactor false 0 17) density0_contains hk0_0_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1595932729921965585253),(-1595932729921965585145)⟩,⟨(-19732628104434754804278),(-19732628104434754803107)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_17 0 17 ha0_0_17_contains + def realAnswer : RBox := ⟨30908157710602158597450,30908157710602713366554⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_17 +namespace hm0_1_0_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-669046908),(-669046892)⟩,⟨699426608,699426624⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1440795709),(-1440795693)⟩,⟨1518564851,1518564868⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1222801121),(-1222801105)⟩,⟨1309011473,1309011489⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-603465003),(-603464987)⟩,⟨665145619,665145635⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-182316631),(-182316615)⟩,⟨214084516,214084532⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-33414655),(-33414639)⟩,⟨44493097,44493113⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-3620566),(-3620550)⟩,⟨5904859,5904875⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-223542),(-223526)⟩,⟨476498,476514⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-7435),(-7419)⟩,⟨21419,21435⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-130),(-114)⟩,⟨466,482⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨1,17⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-102056596494409),(-102056596494393)⟩,⟨11556999556852,11556999556868⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-253908405489456),(-253908405489440)⟩,⟨33131291681300,33131291681317⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-291737659071125),(-291737659071107)⟩,⟨48603894373657,48603894373675⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-235692389481630),(-235692389481610)⟩,⟨52747959180309,52747959180327⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-147963553310567),(-147963553310549)⟩,⟨44721227010109,44721227010129⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-75754425596523),(-75754425596505)⟩,⟨30064383150331,30064383150351⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-32620736969930),(-32620736969912)⟩,⟨16274435392608,16274435392628⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-12098125629908),(-12098125629891)⟩,⟨7286709591351,7286709591368⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-3964500707817),(-3964500707800)⟩,⟨2797171368001,2797171368018⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1187258828205),(-1187258828189)⟩,⟨957895992233,957895992249⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-339286456057),(-339286456041)⟩,⟨304882281335,304882281351⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-97101123470),(-97101123454)⟩,⟨94045366602,94045366619⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-29076599237),(-29076599221)⟩,⟨29350390593,29350390610⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-9359504062),(-9359504046)⟩,⟨9609783130,9609783146⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3150873654),(-3150873638)⟩,⟨3251172051,3251172067⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-774051202),(-774051186)⟩,⟨799408011,799408027⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-89488592953578354),(-89488592953578338)⟩,⟨(-57060484778210416),(-57060484778210400)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-240777604709624518),(-240777604709624502)⟩,⟨(-150515776044391935),(-150515776044391919)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-321312553486829901),(-321312553486829885)⟩,⟨(-194206684882919199),(-194206684882919183)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-320151527530292395),(-320151527530292378)⟩,⟨(-185108817041145888),(-185108817041145872)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-260686097381766387),(-260686097381766371)⟩,⟨(-141187110030689705),(-141187110030689689)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-181750956288700319),(-181750956288700303)⟩,⟨(-88112925238081198),(-88112925238081182)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-112627704025366733),(-112627704025366717)⟩,⟨(-45505760686538569),(-45505760686538553)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-63917318557953364),(-63917318557953348)⟩,⟨(-19689907480014572),(-19689907480014556)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-33963571054267772),(-33963571054267756)⟩,⟨(-7221067948045000),(-7221067948044984)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-17186674770150862),(-17186674770150846)⟩,⟨(-2260899458913585),(-2260899458913568)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-8400348224310964),(-8400348224310948)⟩,⟨(-599595561017611),(-599595561017595)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-4017174794604100),(-4017174794604084)⟩,⟨(-118446763166188),(-118446763166169)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1902559312716526),(-1902559312716506)⟩,⟨6272880350390,6272880350411⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-894591289144525),(-894591289144504)⟩,⟨30887766403863,30887766403883⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-396664267077835),(-396664267077818)⟩,⟨24975014935129,24975014935146⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-112821770212018),(-112821770212000)⟩,⟨9091364652431,9091364652447⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-6591238137521400241),(-6591238137521352447)⟩,⟨(-10086421162757440307),(-10086421162757392517)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-18038489456219645439),(-18038489456219541875)⟩,⟨(-27284865922277544753),(-27284865922277441186)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-25136485417385122510),(-25136485417385034100)⟩,⟨(-36982886039598144346),(-36982886039598055935)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-27259292757195649395),(-27259292757195605616)⟩,⟨(-38121188681775420418),(-38121188681775376638)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-25457858347849624284),(-25457858347849610798)⟩,⟨(-32972499998281901188),(-32972499998281887703)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-21327509046068991767),(-21327509046068989099)⟩,⟨(-25163385259520459043),(-25163385259520456374)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-16286851659299195615),(-16286851659299195239)⟩,⟨(-17520900777342688351),(-17520900777342687972)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-11455364765674315520),(-11455364765674315460)⟩,⟨(-11364675521690993906),(-11364675521690993846)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-7531571844112648447),(-7531571844112648417)⟩,⟨(-6960919405768777095),(-6960919405768777067)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-4717962047993863269),(-4717962047993863251)⟩,⟨(-4078306839520394832),(-4078306839520394815)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-2869718792571535242),(-2869718792571535222)⟩,⟨(-2320610502713506329),(-2320610502713506312)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1717558799762932311),(-1717558799762932293)⟩,⟨(-1302746779201127420),(-1302746779201127403)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1013515902713875533),(-1013515902713875516)⟩,⟨(-727580091277292569),(-727580091277292553)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-578785465537559694),(-578785465537559678)⟩,⟨(-398728336884198455),(-398728336884198439)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-296560606047278581),(-296560606047278565)⟩,⟨(-199012113385968461),(-199012113385968445)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-91070253638424337),(-91070253638424321)⟩,⟨(-60358811709230961),(-60358811709230945)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-35043436724368658025),(-35043436724362468765)⟩,⟨(-325658318648676410588),(-325658318648670221284)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-112960999047165881200),(-112960999047143848465)⟩,⟨(-918913553592044589372),(-918913553592022556512)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-201736463502592934044),(-201736463502543373032)⟩,⟨(-1349306803763290849042),(-1349306803763241287847)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-285985097001196043790),(-285985097001096722370)⟩,⟨(-1550578231709140270288),(-1550578231709040948657)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-350421871125387735997),(-350421871125209381194)⟩,⟨(-1519944613910096601980),(-1519944613909918246972)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-388190365976167397515),(-388190365975893835056)⟩,⟨(-1322834531274207424810),(-1322834531273933862174)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-393162683369799617558),(-393162683369463740308)⟩,⟨(-1054779512560355931242),(-1054779512560020053854)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-362381168156323428250),(-362381168156010942971)⟩,⟨(-791160034377243636114),(-791160034376931150737)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-303748618547844953966),(-303748618547622858415)⟩,⟨(-569057826190880841716),(-569057826190658746098)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-232942207550572160209),(-232942207550449597706)⟩,⟨(-396962971583362375817),(-396962971583239813273)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-164990074160014653795),(-164990074159961700704)⟩,⟨(-269430538783986131938),(-269430538783933178815)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-109279991702946521071),(-109279991702927144177)⟩,⟨(-177148738060926785551),(-177148738060907408636)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-68661675158452307651),(-68661675158445748741)⟩,⟨(-111741027147919133878),(-111741027147912574958)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-40903053797738479095),(-40903053797736278586)⟩,⟨(-66342005016137541233),(-66342005016135340715)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-21623709175211666231),(-21623709175210925175)⟩,⟨(-34638171582792577938),(-34638171582791836879)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-6761832729500232456),(-6761832729500052291)⟩,⟨(-10713196010549852389),(-10713196010549672222)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨175970821692632622375,175970821692632623842⟩,⟨(-10573821486290197578),(-10573821486290196583)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨464651324446290336702,464651324446290340932⟩,⟨(-149545472728080233268),(-149545472728080230381)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨454248264805498427176,454248264805498433672⟩,⟨(-606222705715702669517),(-606222705715702664928)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-162011767424934259342),(-162011767424934251273)⟩,⟨(-1577734555852064875361),(-1577734555852064869388)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1308184916115478176567),(-1308184916115478167574)⟩,⟨(-3240623581589837805795),(-3240623581589837798783)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-2326523925126832208055),(-2326523925126832198387)⟩,⟨(-5373179562847325475408),(-5373179562847325467414)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-2606952999821659829301),(-2606952999821659817969)⟩,⟨(-7204455358247532670489),(-7204455358247532660426)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-2168899464736851790181),(-2168899464736851769967)⟩,⟨(-8021107281309986876227),(-8021107281309986856829)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1435671475433755040515),(-1435671475433754965348)⟩,⟨(-7700165616808454640929),(-7700165616808454566180)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-783898498650856435102),(-783898498650856066369)⟩,⟨(-6595267786134674912351),(-6595267786134674543770)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-374032496801346149853),(-374032496801344647761)⟩,⟨(-5179225933092908941275),(-5179225933092907439190)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-189652353826136158373),(-189652353826131729099)⟩,⟨(-3810832659420631666379),(-3810832659420627237070)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-131497742180637697822),(-131497742180628659113)⟩,⟨(-2660822889686592842165),(-2660822889686583803415)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-106622963846556938571),(-106622963846544288134)⟩,⟨(-1740692543448814977508),(-1740692543448802327034)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-72634868043441642877),(-72634868043430149689)⟩,⟨(-984882002382943756343),(-984882002382932263127)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-25741426406166485599),(-25741426406161835490)⟩,⟨(-318886328615205513942),(-318886328615200863821)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-2308046052120346439097),(-2308046052120055000398)⟩,⟨(-10976644087913814676841),(-10976644087913523239912)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 17) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_17 (tableDensity true) (fullFactor false 0 17) density1_contains hk0_0_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨2086988954513339611343,2086988954513339611485⟩,⟨25804205982722371665601,25804205982722371667132⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_17 0 17 ha0_0_17_contains + def realAnswer : RBox := ⟨(-221057097607106827754),(-221057097606615388913)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_17 +namespace hm0_0_0_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-132326567),(-132326551)⟩,⟨(-96666348),(-96666332)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-282151131),(-282151115)⟩,⟨(-201168075),(-201168059)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-235895801),(-235895785)⟩,⟨(-160309371),(-160309355)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-115357092),(-115357076)⟩,⟨(-73153342),(-73153326)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-35239734),(-35239718)⟩,⟨(-20519783),(-20519766)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-6724889),(-6724872)⟩,⟨(-3556875),(-3556857)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-778407),(-778390)⟩,⟨(-370480),(-370464)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-51894),(-51875)⟩,⟨(-21969),(-21953)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1850),(-1834)⟩,⟨(-690),(-672)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-40),(-23)⟩,⟨(-21),(-5)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-21845091203613),(-21845091203597)⟩,⟨(-31361005065206),(-31361005065190)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-55045568202540),(-55045568202524)⟩,⟨(-78191841896071),(-78191841896053)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-64725315228318),(-64725315228302)⟩,⟨(-90060393282309),(-90060393282293)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-53813594954357),(-53813594954339)⟩,⟨(-72658861609901),(-72658861609885)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-34723865362326),(-34723865362309)⟩,⟨(-45088756367451),(-45088756367434)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-18128638293911),(-18128638293893)⟩,⟨(-22441706857117),(-22441706857101)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-7873601424883),(-7873601424867)⟩,⟨(-9221236565738),(-9221236565722)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2915067550230),(-2915067550213)⟩,⟨(-3213819762549),(-3213819762532)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-944424724857),(-944424724840)⟩,⟨(-978606234466),(-978606234449)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-276401749015),(-276401748999)⟩,⟨(-269531475525),(-269531475506)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-76039904327),(-76039904311)⟩,⟨(-69990026352),(-69990026334)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-20627912907),(-20627912888)⟩,⟨(-17987751499),(-17987751483)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-5808444230),(-5808444212)⟩,⟨(-4821608534),(-4821608518)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1766594587),(-1766594571)⟩,⟨(-1406708132),(-1406708116)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-570469233),(-570469217)⟩,⟨(-440751049),(-440751031)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-137147439),(-137147423)⟩,⟨(-104299319),(-104299303)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨656203362878729,656203362878745⟩,⟨(-40953807730690421),(-40953807730690405)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨295926831377904,295926831377920⟩,⟨(-108765859475513506),(-108765859475513490)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3280860043140320),(-3280860043140304)⟩,⟨(-142331584883311936),(-142331584883311920)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-8233433036381525),(-8233433036381509)⟩,⟨(-139448880001820731),(-139448880001820715)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-11423618194646457),(-11423618194646441)⟩,⟨(-112493385669459756),(-112493385669459739)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-11442373890799954),(-11442373890799937)⟩,⟨(-77864095322631766),(-77864095322631750)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-9177691826006140),(-9177691826006124)⟩,⟨(-47451667986821325),(-47451667986821308)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-6262343357922756),(-6262343357922740)⟩,⟨(-26034789048235272),(-26034789048235255)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-3791537271232679),(-3791537271232663)⟩,⟨(-13158852555615135),(-13158852555615117)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2107371168458408),(-2107371168458392)⟩,⟨(-6279771550914324),(-6279771550914307)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1107964604153418),(-1107964604153402)⟩,⟨(-2903960787173551),(-2903960787173535)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-565092644890217),(-565092644890201)⟩,⟨(-1334141550067615),(-1334141550067597)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-284259891203240),(-284259891203223)⟩,⟨(-620038682963399),(-620038682963382)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-140797116094935),(-140797116094919)⟩,⟨(-290914381060681),(-290914381060664)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-64791971330522),(-64791971330506)⟩,⟨(-129576550892781),(-129576550892765)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-18778172315005),(-18778172314989)⟩,⟨(-36990734961938),(-36990734961922)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1441494196030071168,1441494196030077791⟩,⟨(-3933152766611887571),(-3933152766611880947)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨3868315209808809132,3868315209808823416⟩,⟨(-10816887170940605126),(-10816887170940590841)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨5167269494321820715,5167269494321832819⟩,⟨(-15148899258790095315),(-15148899258790083210)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨5213702086611546822,5213702086611552759⟩,⟨(-16361326650177760372),(-16361326650177754432)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4353437753392852320,4353437753392854132⟩,⟨(-14943322315595394032),(-14943322315595392216)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3116394753967386901,3116394753967387261⟩,⟨(-12020369758822546763),(-12020369758822546397)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1952891454510842356,1952891454510842417⟩,⟨(-8744452514916858541),(-8744452514916858477)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1093402478199980753,1093402478199980772⟩,⟨(-5873906557464466754),(-5873906557464466732)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨559332034082169280,559332034082169297⟩,⟨(-3708149039249359305),(-3708149039249359288)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨267395787926689048,267395787926689064⟩,⟨(-2235374137673127432),(-2235374137673127416)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨121849136623596379,121849136623596395⟩,⟨(-1305783934410895302),(-1305783934410895285)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨53578012056550733,53578012056550749⟩,⟨(-748141007005026154),(-748141007005026137)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨22782397958467915,22782397958467931⟩,⟨(-422678211625933010),(-422678211625932994)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨9297425163394978,9297425163394994⟩,⟨(-232392533212627733),(-232392533212627717)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨3507174593999452,3507174593999468⟩,⟨(-115816632419152002),(-115816632419151986)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨884720253199141,884720253199157⟩,⟨(-35051814708823777),(-35051814708823761)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨144630314118775148798,144630314118776243072⟩,⟨(-8108234405371250196),(-8108234405370155910)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨398493487324623426521,398493487324627306377⟩,⟨(-31954373300805981450),(-31954373300802101551)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨561326602144273393707,561326602144282053110⟩,⟨(-72350517962929937033),(-72350517962921277567)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨614600046110442090558,614600046110459248630⟩,⟨(-123853449846920797814),(-123853449846903639668)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨575666889531823205254,575666889531853576755⟩,⟨(-169586898573308789581),(-169586898573278418008)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨480351560304113392756,480351560304159197985⟩,⟨(-193541994298530843871),(-193541994298485038574)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨365118874707084759317,365118874707139956652⟩,⟨(-191039670023007858570),(-191039670022952661181)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨256923249117600945022,256923249117651288338⟩,⟨(-168416752587898668919),(-168416752587848325564)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨169866702894407092004,169866702894442145385⟩,⟨(-136128296629755137598),(-136128296629720084181)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨107093856692778560155,107093856692797516351⟩,⟨(-103050689613441558887),(-103050689613422602669)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨65352218488793863239,65352218488801895453⟩,⟨(-74299927154757505009),(-74299927154749472779)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨39151413346817244024,39151413346820131047⟩,⟨(-51541183670077171917),(-51541183670074284887)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨23189400125105229606,23189400125106191706⟩,⟨(-34349588442862568711),(-34349588442861606601)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨13360384533609985101,13360384533610303857⟩,⟨(-21517180221381985395),(-21517180221381666634)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨6917645042971138472,6917645042971244879⟩,⟨(-11725329636740200476),(-11725329636740094066)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2138852213249526101,2138852213249551864⟩,⟨(-3712566061590448826),(-3712566061590423064)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨13025909152642946554,13025909152642946823⟩,⟨1033619464292891034758,1033619464292891035196⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨179981591560705061436,179981591560705062200⟩,⟨2896529759433128065196,2896529759433128066429⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨662955694288899089433,662955694288899090639⟩,⟨4234241195294275698727,4234241195294275700581⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1387162545652370252390,1387162545652370253947⟩,⟨4923262528881075933074,4923262528881075935309⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨2077184479479380105841,2077184479479380107628⟩,⟨4990475344156562776906,4990475344156562779286⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2485408425837080165308,2485408425837080167249⟩,⟨4533088996623461083002,4533088996623461085400⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨2556818828353579283193,2556818828353579285451⟩,⟨3724498593107272639918,3724498593107272642482⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨2374921251747007378929,2374921251747007382872⟩,⟨2799196063354076267110,2799196063354076271229⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2049565664452328988522,2049565664452329002966⟩,⟨1955374871216700771231,1955374871216700785742⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1670819856991574873486,1670819856991574943469⟩,⟨1292560704237494430668,1292560704237494500653⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1299339901042546152691,1299339901042546433766⟩,⟨824297555452016437769,824297555452016718816⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨966432700273557018411,966432700273557835227⟩,⟨516912541825932740082,516912541825933556862⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨682229542645291485734,682229542645293130727⟩,⟨321345795498295617180,321345795498297262136⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨445876511977514759689,445876511977517037449⟩,⟨193642947821857366531,193642947821859644269⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨249710881665112065156,249710881665114119047⟩,⟨103631465539633998527,103631465539636052400⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨80128355986634279891,80128355986635107684⟩,⟨32586501056527101259,32586501056527929044⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3838821993789645378527,3838821993789693194102⟩,⟨5480453586526703089346,5480453586526750905583⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 18) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_18 (tableDensity false) (fullFactor false 0 18) density0_contains hk0_0_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨3471739243130349748593,3471739243130349748809⟩,⟨(-232647668234464728159),(-232647668234464728141)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_18 0 18 ha0_0_18_contains + def realAnswer : RBox := ⟨7310561236919895127120,7310561236920142942911⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_18 +namespace hm0_1_0_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-20250489),(-20250473)⟩,⟨(-19370975),(-19370959)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-43171009),(-43170993)⟩,⟨(-40961342),(-40961326)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-35868032),(-35868016)⟩,⟨(-33508607),(-33508591)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-17232145),(-17232129)⟩,⟨(-15637948),(-15637932)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-5138296),(-5138280)⟩,⟨(-4378722),(-4378706)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-967764),(-967748)⟩,⟨(-727818),(-727802)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-113618),(-113602)⟩,⟨(-69823),(-69807)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-7901),(-7884)⟩,⟨(-3724),(-3708)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-302),(-286)⟩,⟨(-112),(-96)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-17),(-1)⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-670749891045),(-670749891029)⟩,⟨(-5923384217836),(-5923384217820)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1904672028738),(-1904672028722)⟩,⟨(-14600451026260),(-14600451026244)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-2742019457367),(-2742019457351)⟩,⟨(-16467805803735),(-16467805803719)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-2894032807501),(-2894032807485)⟩,⟨(-12942237479043),(-12942237479027)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-2365654704372),(-2365654704356)⟩,⟨(-7834804099604),(-7834804099588)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1520822007735),(-1520822007719)⟩,⟨(-3835976401115),(-3835976401099)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-781344273370),(-781344273354)⟩,⟨(-1567613550905),(-1567613550889)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-329829405431),(-329829405414)⟩,⟨(-548080846638),(-548080846622)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-118734331076),(-118734331060)⟩,⟨(-168413043156),(-168413043140)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-37996661832),(-37996661816)⟩,⟨(-47125180463),(-47125180447)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-11288998826),(-11288998810)⟩,⟨(-12568885114),(-12568885098)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-3257023173),(-3257023157)⟩,⟨(-3363772245),(-3363772229)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-956147657),(-956147641)⟩,⟨(-947333703),(-947333687)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-297387414),(-297387398)⟩,⟨(-289650659),(-289650643)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-96927785),(-96927769)⟩,⟨(-93937956),(-93937940)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-23368289),(-23368273)⟩,⟨(-22627061),(-22627045)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨4971584035592467,4971584035592483⟩,⟨(-7796968011274060),(-7796968011274043)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨13032479246757793,13032479246757809⟩,⟨(-20847368180059305),(-20847368180059289)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨16608526758925087,16608526758925103⟩,⟨(-27477192495126714),(-27477192495126698)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨15544027214588643,15544027214588659⟩,⟨(-26881381801381597),(-26881381801381581)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨11577778570333397,11577778570333413⟩,⟨(-21373060507216143),(-21373060507216127)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨7021401468357166,7021401468357183⟩,⟨(-14477635908799708),(-14477635908799692)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨3508833284693746,3508833284693762⟩,⟨(-8678721633809879),(-8678721633809862)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1464168312494097,1464168312494113⟩,⟨(-4748227954287813),(-4748227954287797)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨516674833588623,516674833588639⟩,⟨(-2426814059921730),(-2426814059921714)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨155511708998250,155511708998266⟩,⟨(-1180117990727719),(-1180117990727702)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨39674326832491,39674326832507⟩,⟨(-554659149888841),(-554659149888825)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨7563820880178,7563820880194⟩,⟨(-255674336645690),(-255674336645673)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-377713675282),(-377713675265)⟩,⟨(-117214634260902),(-117214634260886)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1850254985409),(-1850254985392)⟩,⟨(-53676023992008),(-53676023991992)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1470067613684),(-1470067613668)⟩,⟨(-23358729789734),(-23358729789718)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-530176206597),(-530176206581)⟩,⟨(-6579668126319),(-6579668126303)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1172211944479460459,1172211944479466026⟩,⟨(-766012005461772446),(-766012005461766878)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨3156086398479301932,3156086398479313927⟩,⟨(-2086519291496404479),(-2086519291496392484)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨4238300524007493508,4238300524007503662⟩,⟨(-2880575460090092782),(-2880575460090082633)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨4309462691242041671,4309462691242046639⟩,⟨(-3081299202090147353),(-3081299202090142386)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨3662012432286470115,3662012432286471630⟩,⟨(-2827004166102384244),(-2827004166102382727)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨2735846906194915875,2735846906194916181⟩,⟨(-2318370834387857964),(-2318370834387857660)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1859263938772955835,1859263938772955886⟩,⟨(-1727989951668511526),(-1727989951668511473)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1174464266075882500,1174464266075882522⟩,⟨(-1183636086452132651),(-1183636086452132629)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨699632737050163807,699632737050163824⟩,⟨(-756869250311993437),(-756869250311993420)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨398533640150513860,398533640150513877⟩,⟨(-460970505296926933),(-460970505296926916)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨220655037995615664,220655037995615680⟩,⟨(-272827675760593493),(-272827675760593477)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨120770543370101721,120770543370101737⟩,⟨(-159206699738714680),(-159206699738714664)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨65972384220741738,65972384220741755⟩,⟨(-91891966429046745),(-91891966429046729)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨35516374426247756,35516374426247772⟩,⟨(-51552669745534266),(-51552669745534250)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨17507174669089851,17507174669089867⟩,⟨(-26088173324699053),(-26088173324699037)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨5275795249314201,5275795249314217⟩,⟨(-7960184127784041),(-7960184127784025)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨47319831590055206613,47319831590056105949⟩,⟨(-5091929652122519623),(-5091929652121620294)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨133018398279270189132,133018398279273378029⟩,⟨(-16350403327456670956),(-16350403327453482078)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨193867852263739918172,193867852263747036336⟩,⟨(-28980720450749069686),(-28980720450741951549)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨220363732472207802089,220363732472221908497⟩,⟨(-40634113450702149481),(-40634113450688043106)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨212986224828749012018,212986224828773984787⟩,⟨(-49088730189387361800),(-49088730189362389062)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨182265915487857234882,182265915487894897934⟩,⟨(-53466539066276534236),(-53466539066238871209)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨142579059990980345136,142579059991025721353⟩,⟨(-53125168698885422971),(-53125168698840046771)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨104746759152917928123,104746759152959294115⟩,⟨(-47962493956714850803),(-47962493956673484825)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨73725950904959091536,73725950904987871477⟩,⟨(-39344253635765779992),(-39344253635737000060)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨50322619325527600558,50322619325543147708⟩,⟨(-29526402528013402885),(-29526402527997855743)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨33446674012486726081,33446674012493305467⟩,⟨(-20480906012258288432),(-20480906012251709048)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨21570998316694863429,21570998316697225075⟩,⟨(-13306835579271575482),(-13306835579269213835)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨13380731593037170166,13380731593037956185⟩,⟨(-8222099648030784354),(-8222099648029998340)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨7838725106984716063,7838725106984976207⟩,⟨(-4832910115950756577),(-4832910115950496436)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4054645493802193641,4054645493802280419⟩,⟨(-2531188752223890401),(-2531188752223803625)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1248042556967613435,1248042556967634439⟩,⟨(-787724233902249070),(-787724233902228068)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1843519630333553644,1843519630333553829⟩,⟨30688300705571705808,30688300705571706076⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨25985122287781425521,25985122287781426035⟩,⟨80782069430289182482,80782069430289183233⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨104676841241383134929,104676841241383135734⟩,⟨78522510231819921141,78522510231819922276⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨269933443136416588280,269933443136416589318⟩,⟨(-27594408093225664835),(-27594408093225663437)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨547949289162569722431,547949289162569723630⟩,⟨(-221119862432080877579),(-221119862432080876047)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨895978683531252655018,895978683531252656368⟩,⟨(-387994807129264043508),(-387994807129264041880)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨1182680079184507360795,1182680079184507362464⟩,⟨(-428103372907781891682),(-428103372907781889809)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1294651550321768150603,1294651550321768153750⟩,⟨(-350244353421081770795),(-350244353421081767518)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1221167013329274944760,1221167013329274956606⟩,⟨(-227822529788655885123),(-227822529788655873220)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1027670360681961782351,1027670360681961839656⟩,⟨(-122233015190100418553),(-122233015190100361225)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨793464765117147040860,793464765117147270522⟩,⟨(-57339712203030998867),(-57339712203030769205)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨574816833841627729454,574816833841628396573⟩,⟨(-28613602340127056032),(-28613602340126388920)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨395987759811157431271,395987759811158775195⟩,⟨(-19566393931573140661),(-19566393931571796749)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨256290663065260268888,256290663065262130620⟩,⟨(-15695915005150817719),(-15695915005148955997)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨143932087996011871479,143932087996013550854⟩,⟨(-10614271527345412456),(-10614271527343733082)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨46424776181011823460,46424776181012500445⟩,⟨(-3747516275494774357),(-3747516275494097372)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1708355815549640799164,1708355815549680080208⟩,⟨(-357210839316967611406),(-357210839316928330061)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 18) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_18 (tableDensity true) (fullFactor false 0 18) density1_contains hk0_0_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4539966702555072748442),(-4539966702555072748161)⟩,⟨304231566152761567569,304231566152761567592⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_18 0 18 ha0_0_18_contains + def realAnswer : RBox := ⟨(-2831610887005531949278),(-2831610887005292667953)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_18 +namespace hm0_0_0_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2651513,2651530⟩,⟨(-3629640),(-3629624)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨5418814,5418830⟩,⟨(-7599553),(-7599537)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨4163039,4163055⟩,⟨(-6124434),(-6124418)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1796683,1796699⟩,⟨(-2831996),(-2831980)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨467087,467103⟩,⟨(-801665),(-801649)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨73413,73429⟩,⟨(-138709),(-138693)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨6762,6778⟩,⟨(-14219),(-14202)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨337,353⟩,⟨(-824),(-808)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨4,20⟩,⟨(-35),(-18)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1724397864333,1724397864350⟩,⟨(-1201158759705),(-1201158759689)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨4259592236775,4259592236792⟩,⟨(-2998613833786),(-2998613833770)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨4816091139086,4816091139103⟩,⟨(-3461088424815),(-3461088424799)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3779877312140,3779877312156⟩,⟨(-2799236547327),(-2799236547310)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨2261984386632,2261984386648⟩,⟨(-1741743916706),(-1741743916690)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1076738251970,1076738251987⟩,⟨(-869617010182),(-869617010166)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨419917275875,419917275892⟩,⟨(-358453070144),(-358453070127)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨137979414339,137979414357⟩,⟨(-125114898074),(-125114898056)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨39399613236,39399613252⟩,⟨(-38011279851),(-38011279832)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨10140115875,10140115893⟩,⟨(-10395333713),(-10395333696)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2457639872,2457639889⟩,⟨(-2669303738),(-2669303721)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨590657534,590657551⟩,⟨(-677180864),(-677180848)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨148891573,148891590⟩,⟨(-179329971),(-179329955)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨41254548,41254564⟩,⟨(-51802605),(-51802589)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨12450146,12450162⟩,⟨(-16113570),(-16113553)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2888444,2888460⟩,⟨(-3798124),(-3798108)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨3380431258155301,3380431258155318⟩,⟨54170835663333,54170835663349⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨8921810117531516,8921810117531532⟩,⟨24417039874535,24417039874551⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨11531246739420111,11531246739420128⟩,⟨(-265323985886653),(-265323985886637)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨11092773157446682,11092773157446698⟩,⟨(-654145140614761),(-654145140614745)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨8737775029187303,8737775029187319⟩,⟨(-886444214234550),(-886444214234534)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨5876091677274106,5876091677274122⟩,⟨(-862803289158003),(-862803289157987)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨3464277393372181,3464277393372198⟩,⟨(-669558952581080),(-669558952581063)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1832503073201334,1832503073201351⟩,⟨(-440514704094799),(-440514704094782)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨890921317695667,890921317695684⟩,⟨(-256569399197413),(-256569399197396)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨408582024074866,408582024074882⟩,⟨(-137050592714801),(-137050592714785)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨181678820086025,181678820086041⟩,⟨(-69292121170147),(-69292121170131)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨80449314997351,80449314997369⟩,⟨(-34066593508200),(-34066593508184)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨36190108896267,36190108896283⟩,⟨(-16588944613466),(-16588944613450)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨16536257640947,16536257640964⟩,⟨(-8002624667108),(-8002624667092)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨7228846014369,7228846014386⟩,⟨(-3614534031487),(-3614534031471)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2043725681515,2043725681531⟩,⟨(-1037484778076),(-1037484778060)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨433040023932062508,433040023932063249⟩,⟨158708875713205366,158708875713206110⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1185336833614945567,1185336833614947149⟩,⟨423907270109099837,423907270109101417⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1644650511802016894,1644650511802018224⟩,⟨561020180301828418,561020180301829749⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1752119549594595472,1752119549594596124⟩,⟨558389259315976300,558389259315976950⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1572151036917355092,1572151036917355299⟩,⟨458092196797914752,458092196797914959⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1237994869709560153,1237994869709560207⟩,⟨321043734341394270,321043734341394323⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨879023480561604542,879023480561604562⟩,⟨196381162536827461,196381162536827483⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨575039337007238544,575039337007238564⟩,⟨107088949473494017,107088949473494033⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨353061456695302048,353061456695302064⟩,⟨53282727242560931,53282727242560947⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨206931473733880407,206931473733880423⟩,⟨24766774159140716,24766774159140732⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨117619487134439022,117619487134439038⟩,⟨10981717930188852,10981717930188868⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨65703703906995841,65703703906995859⟩,⟨4707863134707039,4707863134707055⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨36308253358362586,36308253358362602⟩,⟨1957954831393935,1957954831393951⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨19610678200258942,19610678200258958⟩,⟨784860277121653,784860277121669⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨9652220827265470,9652220827265486⟩,⟨292345279384903,292345279384919⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨2902530660731385,2902530660731401⟩,⟨73262836691853,73262836691869⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1116123149016531698,1116123149016682347⟩,⟨19909489402399754984,19909489402399905631⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4381257471747371820,4381257471747903833⟩,⟨54649270902389869818,54649270902390401819⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨9844875099203624239,9844875099204802505⟩,⟨76409212196977601407,76409212196978779665⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨16668754719344077761,16668754719346386473⟩,⟨82752322072989293894,82752322072991602597⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨22504143728370508783,22504143728374537602⟩,⟨76425497968932055874,76425497968936084683⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨25254258201067622617,25254258201073597174⟩,⟨62705600064803041946,62705600064809016498⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨24456867171940108724,24456867171947173528⟩,⟨46761342365124376056,46761342365131440851⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨21119055644967533043,21119055644973846853⟩,⟨32229666513264486375,32229666513270800180⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨16705334527949567400,16705334527953870847⟩,⟨20852845202865215350,20852845202869518794⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨12374579372221543479,12374579372223821625⟩,⟨12864089551047741538,12864089551050019679⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨8737229626052181719,8737229626053127233⟩,⟨7687058042939236034,7687058042940181547⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨5945254715560863938,5945254715561197310⟩,⟨4516999000677717765,4516999000678051132⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3896524261759288857,3896524261759398103⟩,⟨2630872284455096242,2630872284455205486⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2408466993105452844,2408466993105488555⟩,⟨1495550972807717237,1495550972807752951⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1300269063714446304,1300269063714458122⟩,⟨767141765835319865,767141765835331682⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨409734381096436343,409734381096439200⟩,⟨236053245533755380,236053245533758239⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-170769895395537222228),(-170769895395537222141)⟩,⟨2151507780555675200,2151507780555675255⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-477046255940294134486),(-477046255940294134267)⟩,⟨29628195191732182201,29628195191732182339⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-693040343940933608688),(-693040343940933608369)⟩,⟨108458129189612342655,108458129189612342868⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-798512752927666053492),(-798512752927666053115)⟩,⟨224892026337837118304,224892026337837118568⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-799988057728859305018),(-799988057728859304621)⟩,⟨332862771572612415981,332862771572612416280⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-716601709871904831144),(-716601709871904830751)⟩,⟨392780496496383512263,392780496496383512584⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-579584048912833461467),(-579584048912833461054)⟩,⟨397758887834078777245,397758887834078777612⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-428246934997609284107),(-428246934997609283463)⟩,⟨363225465770259447767,363225465770259448387⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-293905956196841728689),(-293905956196841726500)⟩,⟨307966771440966035140,307966771440966037319⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-190869958310384613923),(-190869958310384603603)⟩,⟨246652981458097240269,246652981458097250586⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-119666760746880352639),(-119666760746880311914)⟩,⟨188582652840449867892,188582652840449908617⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-73878285228055906734),(-73878285228055790178)⟩,⟨138099648980120033276,138099648980120149838⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-45310566901828196808),(-45310566901827965086)⟩,⟨96186198474275384668,96186198474275616393⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-27011804027350959552),(-27011804027350641974)⟩,⟨62193739471317483969,62193739471317801551⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-14348043742425501867),(-14348043742425217541)⟩,⟨34572611024647225994,34572611024647510323⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-4494398564104513356),(-4494398564104399174)⟩,⟨11051453985137756503,11051453985137870688⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-874334236798414875766),(-874334236798408759476)⟩,⟨573805631417274708723,573805631417280824904⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 19) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_19 (tableDensity false) (fullFactor false 0 19) density0_contains hk0_0_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨32114598548245550981,32114598548245550984⟩,⟨577846356976628256196,577846356976628256235⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_19 0 19 ha0_0_19_contains + def realAnswer : RBox := ⟨(-842219638250269324785),(-842219638250063208492)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_19 +namespace hm0_1_0_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨531327,531343⟩,⟨(-555464),(-555448)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨1103294,1103310⟩,⟨(-1162794),(-1162778)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨870072,870088⟩,⟨(-931274),(-931258)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨384044,384060⟩,⟨(-423109),(-423093)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨99683,99699⟩,⟨(-116915),(-116899)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨15026,15042⟩,⟨(-19968),(-19952)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1271,1287⟩,⟨(-2084),(-2067)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨52,68⟩,⟨(-132),(-116)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨325700528335,325700528351⟩,⟨(-36880420256),(-36880420240)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨795393084616,795393084632⟩,⟨(-103735738976),(-103735738960)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨880679987874,880679987890⟩,⟨(-146557921269),(-146557921253)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨673333915352,673333915368⟩,⟨(-150438522166),(-150438522150)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨393080195917,393080195933⟩,⟨(-118568590858),(-118568590842)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨184055265443,184055265459⟩,⟨(-72897134674),(-72897134658)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨71386104309,71386104325⟩,⟨(-35547608515),(-35547608499)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨23530068838,23530068854⟩,⟨(-14148214821),(-14148214805)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨6780037739,6780037756⟩,⟨(-4776448966),(-4776448950)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1772712111,1772712127⟩,⟨(-1428408054),(-1428408038)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨441266639,441266655⟩,⟨(-396145125),(-396145109)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨110429580,110429597⟩,⟨(-106896033),(-106896017)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨29247411,29247427⟩,⟨(-29516277),(-29516261)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨8493385,8493401⟩,⟨(-8720012),(-8719996)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2653360,2653376⟩,⟨(-2737815),(-2737799)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨626617,626633⟩,⟨(-647159),(-647143)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨643580828693680,643580828693696⟩,⟨410367903841454,410367903841470⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1710049085207422,1710049085207438⟩,⟨1069040735702869,1069040735702885⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨2226100652200098,2226100652200114⟩,⟨1345630479129323,1345630479129339⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨2138371310432046,2138371310432062⟩,⟨1236617730936954,1236617730936970⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1660199333152588,1660199333152604⟩,⟨899497496958009,899497496958025⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1092629456712451,1092629456712467⟩,⟨530104993380142,530104993380159⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨633621050489818,633621050489835⟩,⟨256343037465834,256343037465850⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨334206609662107,334206609662123⟩,⟨103159029984181,103159029984197⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨164298732076959,164298732076975⟩,⟨35027198744834,35027198744850⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨76777436591722,76777436591738⟩,⟨10134828970841,10134828970857⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨34699657259548,34699657259564⟩,⟨2487292239088,2487292239104⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨15417533293670,15417533293687⟩,⟨457628151789,457628151805⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨6841873027739,6841873027755⟩,⟨(-21537431036),(-21537431020)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨3051215257552,3051215257568⟩,⟨(-105005776382),(-105005776366)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1303170868198,1303170868214⟩,⟨(-81977537619),(-81977537603)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨363525428756,363525428772⟩,⟨(-29290792191),(-29290792175)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨84337992924338139,84337992924338769⟩,⟨129060783751699525,129060783751700152⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨228646938267486452,228646938267487778⟩,⟨345857096135198900,345857096135200230⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨312735954490962313,312735954490963428⟩,⟨460157543554700069,460157543554701187⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨329975176516511364,329975176516511913⟩,⟨461538469219609046,461538469219609594⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨297415830130944272,297415830130944446⟩,⟨385319292013352717,385319292013352889⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨238761203198693973,238761203198694022⟩,⟨281807489518770317,281807489518770362⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨173695212952022709,173695212952022728⟩,⟨186925325720951393,186925325720951412⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨115870616253267176,115870616253267192⟩,⟨114992186283908283,114992186283908299⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨72061527571630201,72061527571630217⟩,⟨66622497426670187,66622497426670203⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨42671566184494685,42671566184494701⟩,⟨36897481689823485,36897481689823501⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨24574314747114300,24574314747114316⟩,⟨19877843664354000,19877843664354016⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨13981385634806529,13981385634806545⟩,⟨10607209064728003,10607209064728019⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨7893283591397063,7893283591397079⟩,⟨5667306649613024,5667306649613041⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨4350225744077257,4350225744077274⟩,⟨2997141399777685,2997141399777701⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2174182381254436,2174182381254452⟩,⟨1459065226378363,1459065226378379⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨659157126633588,659157126633604⟩,⟨436872245312685,436872245312701⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨700934014694372920,700934014694496732⟩,⟨6513932309761393889,6513932309761517699⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨2242066526841930544,2242066526842367804⟩,⟨18241848841494501490,18241848841494938751⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨3944173420571562997,3944173420572531544⟩,⟨26389000591045815584,26389000591046784132⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨5469692492411348983,5469692492413247065⟩,⟨29669572407823085107,29669572407824983198⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨6514786845262729216,6514786845266041876⟩,⟨28275029080570148667,28275029080573461334⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨6976704003947822546,6976704003952735087⟩,⟨23792290635552315859,23792290635557228402⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨6800830130681462606,6800830130687270383⟩,⟨18259266410375811481,18259266410381619261⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨6014137035961423374,6014137035966611296⟩,⟨13138694767458134490,13138694767463322413⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨4828191059254855637,4828191059258388908⟩,⟨9049414267040446696,9049414267043979970⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨3545752453940643583,3545752453942512035⟩,⟨6043826626461989325,6043826626463857776⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨2408652386127334908,2408652386128109403⟩,⟨3933622487810499018,3933622487811273514⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1535110289921615626,1535110289921888333⟩,⟨2488473881485955726,2488473881486228436⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨932777746261839552,932777746261928808⟩,⟨1518008336245843669,1518008336245932919⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨540985048373406446,540985048373435596⟩,⟨877456979765867863,877456979765897008⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨280698166979246388,280698166979256028⟩,⟨449646815810334793,449646815810344431⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨86936689890316792,86936689890319124⟩,⟨137739609975914036,137739609975916368⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-5070187454928231353),(-5070187454928231296)⟩,⟨304496653580810947,304496653580810992⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-13305232978221025424),(-13305232978221025287)⟩,⟨4277557816897290245,4277557816897290343⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-12859259583298941761),(-12859259583298941561)⟩,⟨17123400255878021169,17123400255878021315⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨4452537706467998901,4452537706467999139⟩,⟨43752440078896622102,43752440078896622285⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨35408783365682641525,35408783365682641784⟩,⟨87776258980807164608,87776258980807164814⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨61301524319274232440,61301524319274232711⟩,⟨141543852609172180168,141543852609172180395⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨66602858184624264234,66602858184624264540⟩,⟨183934082982445426847,183934082982445427123⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨53583708935670001705,53583708935670002217⟩,⟨197970952031523368649,197970952031523369146⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨34250624407400379240,34250624407400381042⟩,⟨183476511527342992974,183476511527342994763⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨18057053606537473940,18057053606537482395⟩,⟨151706837499513163036,151706837499513171490⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨8327796170947598785,8327796170947632064⟩,⟨115164605967656729989,115164605967656763271⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨4089907408291963064,4089907408292058267⟩,⟨82142073884364139188,82142073884364234393⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2758211508083961853,2758211508084151170⟩,⟨55830533664770389492,55830533664770578810⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨2188993319876204204,2188993319876463781⟩,⟨35749124211532118105,35749124211532377684⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨1469451627538113743,1469451627538346228⟩,⟨19927421629752616379,19927421629752848867⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨516860666174044866,516860666174138251⟩,⟨6402989257726069644,6402989257726163026⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨52759434826122700528,52759434826127725227⟩,⟨253062847441519849025,253062847441524873674⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 19) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_19 (tableDensity true) (fullFactor false 0 19) density1_contains hk0_0_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-41996013486167258979),(-41996013486167258975)⟩,⟨(-755645236046360027384),(-755645236046360027334)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_19 0 19 ha0_0_19_contains + def realAnswer : RBox := ⟨10763421339855441549,10763421340060466252⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_19 +namespace hm0_0_0_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨94573,94589⟩,⟨69085,69101⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨194458,194474⟩,⟨138668,138684⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨151075,151092⟩,⟨102713,102731⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨66063,66080⟩,⟨41929,41945⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨17327,17344⟩,⟨10100,10117⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2710,2727⟩,⟨1432,1450⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨238,255⟩,⟨110,127⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨6,22⟩,⟨1,17⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨62743884229,62743884245⟩,⟨90076067413,90076067429⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨155185010935,155185010952⟩,⟨220447742974,220447742990⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨175830854635,175830854651⟩,⟨244680524018,244680524035⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨138340479623,138340479640⟩,⟨186822342891,186822342907⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨83008958841,83008958857⟩,⟨107818964108,107818964124⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨39636933216,39636933232⟩,⟨49087751453,49087751469⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨15506911529,15506911546⟩,⟨18170703222,18170703239⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨5103005282,5103005298⟩,⟨5629407477,5629407496⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1453888566,1453888582⟩,⟨1507468556,1507468572⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨371550320,371550336⟩,⟨362540640,362540656⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨89049644,89049660⟩,⟨82011923,82011942⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨21125845,21125861⟩,⟨18431208,18431226⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨5261074,5261091⟩,⟨4368942,4368959⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1443290,1443308⟩,⟨1149547,1149563⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨432410,432426⟩,⟨334115,334131⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨99918,99934⟩,⟨75983,75999⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4248313791883),(-4248313791867)⟩,⟨265078134323394,265078134323410⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1913873856258),(-1913873856242)⟩,⟨695248803214195,695248803214211⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨20384342912159,20384342912175⟩,⟨887531389865892,887531389865908⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨49375019125835,49375019125851⟩,⟨838311553054871,838311553054887⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨65350456924452,65350456924468⟩,⟨644798622379430,644798622379446⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨61811141956967,61811141956983⟩,⟨421307180268102,421307180268119⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨46410107663157,46410107663173⟩,⟨240293348758399,240293348758416⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨29441470033579,29441470033596⟩,⟨122549159682260,122549159682277⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨16495822311548,16495822311565⟩,⟨57311224758113,57311224758129⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨8468380744864,8468380744880⟩,⟨25257695985179,25257695985195⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨4117341219797,4117341219813⟩,⟨10799222980959,10799222980978⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨1951209858340,1951209858356⟩,⟨4609022055800,4609022055817⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨919763708115,919763708131⟩,⟨2006851503658,2006851503676⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨432128299448,432128299464⟩,⟨892998672080,892998672096⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨191564109632,191564109648⟩,⟨383126534279,383126534296⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨54454600449,54454600465⟩,⟨107269602958,107269602975⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-16600200937251840),(-16600200937251749)⟩,⟨45293832941771652,45293832941771745⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-44131157939771055),(-44131157939770874)⟩,⟨123397599053844806,123397599053844984⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-57866125289120138),(-57866125289119986)⟩,⟨169626900514607025,169626900514607177⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-56814695054068104),(-56814695054068024)⟩,⟨178255015859077259,178255015859077339⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-45794267072047443),(-45794267072047407)⟩,⟨157137231252360285,157137231252360323⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-31420894530825470),(-31420894530825451)⟩,⟨121133038416855108,121133038416855130⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-18761542203823016),(-18761542203822999)⟩,⟨83949004229351927,83949004229351945⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-9964589717275294),(-9964589717275278)⟩,⟨53483346385581055,53483346385581073⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4822306341337573),(-4822306341337557)⟩,⟨31937097874812741,31937097874812758⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2179391605851997),(-2179391605851981)⟩,⟨18199282749843180,18199282749843196⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-940299588883837),(-940299588883821)⟩,⟨10065510319608860,10065510319608876⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-393010822887176),(-393010822887160)⟩,⟨5482012897191394,5482012897191410⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-159861362360534),(-159861362360518)⟩,⟨2963048191191240,2963048191191256⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-62943901721442),(-62943901721426)⟩,⟨1572153107864730,1572153107864746⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-23150562295527),(-23150562295511)⟩,⟨764205846433788,764205846433804⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-5763488919502),(-5763488919486)⟩,⟨228332166243414,228332166243430⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2603662290745647234),(-2603662290745627519)⟩,⟨145955906161320141,145955906161339855⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-7119873855776887665),(-7119873855776818349)⟩,⟨570679163409734446,570679163409803760⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-9881038107210378293),(-9881038107210225975)⟩,⟨1272639799867138075,1272639799867290394⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-10585154907507886715),(-10585154907507591586)⟩,⟨2131216695911506538,2131216695911801670⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-9639128904178443364),(-9639128904177935636)⟩,⟨2837038172634161083,2837038172634668812⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-7776586202668186141),(-7776586202667445790)⟩,⟨3130614586593654964,3130614586594395317⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-5689548921609627235),(-5689548921608768170)⟩,⟨2974516270585679282,2974516270586538349⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-3841034723684080448),(-3841034723683328152)⟩,⟨2515960490866256258,2515960490867008553⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2431997420090831169),(-2431997420090329228)⟩,⟨1947613532196539632,1947613532197041573⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1468025814468482699),(-1468025814468222581)⟩,⟨1411725421916495481,1411725421916755601⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-859010066148037692),(-859010066147931941)⟩,⟨976107073638576995,976107073638682746⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-495094247630887461),(-495094247630850879)⟩,⟨651511262219197091,651511262219233673⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-283557939139631399),(-283557939139619603)⟩,⟨419918535119889661,419918535119901457⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-159041967457909852),(-159041967457906036)⟩,⟨256108683532531096,256108683532534909⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-80819914562395578),(-80819914562394321)⟩,⟨136983041381342939,136983041381344201⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-24749303776265064),(-24749303776264754)⟩,⟨42959027014601561,42959027014601874⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-337599242485120782),(-337599242485120760)⟩,⟨(-26803138051722589909),(-26803138051722589881)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-4633473015185331570),(-4633473015185331536)⟩,⟨(-74639274684755965234),(-74639274684755965185)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-16856422884516326178),(-16856422884516326131)⟩,⟨(-107762392884328966017),(-107762392884328965955)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-34637643024579794413),(-34637643024579794356)⟩,⟨(-123037739283625602804),(-123037739283625602733)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-50673985908564651169),(-50673985908564651107)⟩,⟨(-121830155989632556208),(-121830155989632556133)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-58970367350707880875),(-58970367350707880813)⟩,⟨(-107620051038177794974),(-107620051038177794900)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-58785926351143602013),(-58785926351143601948)⟩,⟨(-85683762922860265707),(-85683762922860265635)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-52776196213468153562),(-52776196213468153457)⟩,⟨(-62242906849540766512),(-62242906849540766403)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-43962360591711988113),(-43962360591711987787)⟩,⟨(-41968340114340218784),(-41968340114340218460)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-34592165271366287264),(-34592165271366285808)⟩,⟨(-26776806211991657735),(-26776806211991656275)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-26002434170069068319),(-26002434170069062702)⟩,⟨(-16504269539378862252),(-16504269539378856635)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-18747563023974587999),(-18747563023974572186)⟩,⟨(-10031082634102126884),(-10031082634102111070)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-12883205143644452287),(-12883205143644421263)⟩,⟨(-6069533107731174119),(-6069533107731143094)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-8241482695733584103),(-8241482695733542024)⟩,⟨(-3579580218887726025),(-3579580218887683948)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-4547279535369997772),(-4547279535369960367)⟩,⟨(-1887202505392817687),(-1887202505392780283)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1448025949420589406),(-1448025949420574434)⟩,⟨(-588883210853611159),(-588883210853596186)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-81887349206783366297),(-81887349206782621604)⟩,⟨(-132432644427025591707),(-132432644427024846993)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 20) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_20 (tableDensity false) (fullFactor false 0 20) density0_contains hk0_0_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-91264053655252246533),(-91264053655252246525)⟩,⟨4209893462666587758,4209893462666587760⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_20 0 20 ha0_0_20_contains + def realAnswer : RBox := ⟨(-173151402862135612830),(-173151402861934868129)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_20 +namespace hm0_1_0_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨14467,14483⟩,⟨13837,13853⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨29746,29762⟩,⟨28225,28241⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨22969,22985⟩,⟨21458,21474⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨9866,9882⟩,⟨8957,8973⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2519,2535⟩,⟨2151,2167⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨383,399⟩,⟨288,304⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨28,44⟩,⟨14,30⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1926440264,1926440280⟩,⟨17013413577,17013413593⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨5367445837,5367445853⟩,⟨41165025883,41165025899⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨7442040890,7442040906⟩,⟨44744982632,44744982648⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨7429800298,7429800314⟩,⟨33282316984,33282317000⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨5646420043,5646420059⟩,⟨18737787461,18737787477⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨3320113178,3320113194⟩,⟨8391300129,8391300146⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1536787841,1536787857⟩,⟨3089027677,3089027693⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨576729401,576729417⟩,⟨959969658,959969674⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨182603496,182603512⟩,⟨259394690,259394706⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨51031954,51031970⟩,⟨63372991,63373008⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨13210888,13210904⟩,⟨14722536,14722552⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨3333975,3333991⟩,⟨3445114,3445130⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨865812,865828⟩,⟨858019,858036⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨242934,242950⟩,⟨236626,236642⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨73460,73476⟩,⟨71196,71212⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨17016,17032⟩,⟨16478,16494⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-32179253242683),(-32179253242667)⟩,⟨50466643302008,50466643302024⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-83308316718922),(-83308316718905)⟩,⟨133257852665282,133257852665298⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-103574533637920),(-103574533637904)⟩,⟨171336429593608,171336429593624⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-93464686599297),(-93464686599281)⟩,⟨161605022584184,161605022584200⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-66393240837147),(-66393240837131)⟩,⟨122518901779261,122518901779277⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-38024061720038),(-38024061720022)⟩,⟨78344245100013,78344245100030⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-17792923798369),(-17792923798353)⟩,⟨43951261173707,43951261173723⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-6905528485168),(-6905528485152)⟩,⟨22349794322837,22349794322854⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-2256161525216),(-2256161525200)⟩,⟨10568443134934,10568443134950⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-627546172122),(-627546172106)⟩,⟨4745925624538,4745925624554⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-148154420455),(-148154420439)⟩,⟨2062523292808,2062523292825⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-26305235568),(-26305235552)⟩,⟨883300759243,883300759259⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1166154963,1166154979⟩,⟨379421882093,379421882109⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5661559066,5661559082⟩,⟨164780901645,164780901661⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨4342933060,4342933076⟩,⟨69069163756,69069163772⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1537327615,1537327631⟩,⟨19080512279,19080512295⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-13499145136636494),(-13499145136636415)⟩,⟨8821344024692849,8821344024692928⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-36005591212552669),(-36005591212552516)⟩,⟨23803116670420418,23803116670420571⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-47462421661039506),(-47462421661039374)⟩,⟨32255585266912608,32255585266912734⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-46959716954068254),(-46959716954068184)⟩,⟨33570783403545720,33570783403545791⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-38517614653275747),(-38517614653275712)⟩,⟨29726203940023738,29726203940023770⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-27577568116775259),(-27577568116775239)⟩,⟨23360782245765689,23360782245765708⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-17854282400826284),(-17854282400826267)⟩,⟨16587530162971025,16587530162971042⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-10696637334101078),(-10696637334101062)⟩,⟨10776530110594270,10776530110594286⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-6027311257351716),(-6027311257351700)⟩,⟨6518356255236687,6518356255236703⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-3245486261510179),(-3245486261510163)⟩,⟨3752800172229199,3752800172229215⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1701269782233935),(-1701269782233919)⟩,⟨2102921161821929,2102921161821945⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-885085063267748),(-885085063267732)⟩,⟨1166495101089845,1166495101089861⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-462518485391666),(-462518485391650)⟩,⟨644133286160760,644133286160776⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-240279997734607),(-240279997734591)⟩,⟨348741968127016,348741968127032⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-115520787135065),(-115520787135049)⟩,⟨172137330563667,172137330563684⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-34367263195534),(-34367263195518)⟩,⟨51853581985242,51853581985258⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-851857654549793358),(-851857654549777153)⟩,⟨91663326632222641,91663326632238844⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-2376570895492746241),(-2376570895492689270)⟩,⟨292074270055037644,292074270055094613⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-3412454287221273001),(-3412454287221147788)⟩,⟨509952326927249302,509952326927374513⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-3795000916922618018),(-3795000916922375377)⟩,⟨699462554179814171,699462554180056814⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-3566047251131578683),(-3566047251131161206)⟩,⟨821393275027370799,821393275027788278⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-2950547442217713081),(-2950547442217104327)⟩,⟨864876560776069411,864876560776678163⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2221514284545338326),(-2221514284544632110)⟩,⟨827107202688411327,827107202689117543⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1565683280571494077),(-1565683280570875928)⟩,⟨716448538021483978,716448538022102126⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1055264550027448211),(-1055264550027036099)⟩,⟨562896323246122084,562896323246534201⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-689605892631360991),(-689605892631147648)⟩,⟨404526060617364958,404526060617578303⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-439511995259149324),(-439511995259062698)⟩,⟨269114685851844001,269114685851930630⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-272728976620885020),(-272728976620855091)⟩,⟨168244053692655309,168244053692685237⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-163606385019634301),(-163606385019624661)⟩,⟨100532252571174606,100532252571184248⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-93311353210777248),(-93311353210774132)⟩,⟨57529429349129723,57529429349132839⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-47371328042018368),(-47371328042017338)⟩,⟨29571954318389361,29571954318390391⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-14441493694796624),(-14441493694796364)⟩,⟨9114981806409756,9114981806410013⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-47779428215346413),(-47779428215346393)⟩,⟨(-795790754293872160),(-795790754293872134)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-668946431681915683),(-668946431681915653)⟩,⟨(-2081873838245384498),(-2081873838245384461)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-2661062651394756933),(-2661062651394756899)⟩,⟨(-2000614177628944072),(-2000614177628944028)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-6737137235940816267),(-6737137235940816226)⟩,⟨682512712215214923,682512712215214975⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-13358060027241540732),(-13358060027241540688)⟩,⟨5386709952624013920,5386709952624013974⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-21243010473069679420),(-21243010473069679374)⟩,⟨9201281302261568192,9201281302261568244⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-27176319930734598804),(-27176319930734598745)⟩,⟨9843976129116747066,9843976129116747124⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-28759726589742879391),(-28759726589742879305)⟩,⟨7788054854074569181,7788054854074569267⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-26189125327335180943),(-26189125327335180675)⟩,⟨4891873654868929354,4891873654868929624⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-21276054946567084214),(-21276054946567083019)⟩,⟨2534192542575775973,2534192542575777172⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-15879751213872348639),(-15879751213872344045)⟩,⟨1149046914809822354,1149046914809826947⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-11151496006496897877),(-11151496006496884958)⟩,⟨555374263423679397,555374263423692312⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-7478090551724961506),(-7478090551724936156)⟩,⟨369379948704222792,369379948704248138⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-4737231803044018873),(-4737231803043984477)⟩,⟨290020599443256724,290020599443291119⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-2621014085074032992),(-2621014085074002404)⟩,⟨193261415413577827,193261415413608414⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-838956542730658453),(-838956542730646206)⟩,⟨67721594638047993,67721594638060242⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-35765168450483269785),(-35765168450482657941)⟩,⟨7449016185810987244,7449016185811599093⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 20) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_20 (tableDensity true) (fullFactor false 0 20) density1_contains hk0_0_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨119345300933791399302,119345300933791399312⟩,⟨(-5505245297333230147),(-5505245297333230145)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_20 0 20 ha0_0_20_contains + def realAnswer : RBox := ⟨83580132483208129517,83580132483408741371⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_20 +namespace hm0_0_0_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1723),(-1707)⟩,⟨2338,2354⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-3390),(-3374)⟩,⟨4733,4749⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2423),(-2407)⟩,⟨3542,3558⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-940),(-924)⟩,⟨1459,1475⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-217),(-199)⟩,⟨351,367⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-36),(-19)⟩,⟨42,58⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4481185189),(-4481185173)⟩,⟨3121432303,3121432320⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-10865792973),(-10865792956)⟩,⟨7648867612,7648867628⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-11839545392),(-11839545376)⟩,⟨8507626663,8507626679⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-8794860018),(-8794860000)⟩,⟨6511904931,6511904947⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-4895215269),(-4895215252)⟩,⟨3768226040,3768226056⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2131726805),(-2131726788)⟩,⟨1720948703,1720948720⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-749030545),(-749030528)⟩,⟨639055891,639055907⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-218802740),(-218802723)⟩,⟨198283085,198283105⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-54949371),(-54949355)⟩,⟨52979638,52979654⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-12349141),(-12349124)⟩,⟨12652136,12652153⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2607352),(-2607335)⟩,⟨2830276,2830292⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-547930),(-547914)⟩,⟨627860,627877⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-122130),(-122114)⟩,⟨147025,147041⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-30519),(-30503)⟩,⟨38295,38312⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-8549),(-8533)⟩,⟨11045,11061⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1911),(-1895)⟩,⟨2497,2513⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-19796425134058),(-19796425134042)⟩,⟨(-317306306454),(-317306306438)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-51599027109503),(-51599027109487)⟩,⟨(-142867185154),(-142867185138)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-65059503925459),(-65059503925443)⟩,⟨1491541778528,1491541778544⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-60338994600280),(-60338994600264)⟩,⟨3549502892434,3549502892450⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-45319360569920),(-45319360569903)⟩,⟨4588623503892,4588623503908⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-28771013604562),(-28771013604546)⟩,⟨4217626538553,4217626538569⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-15875438857919),(-15875438857903)⟩,⟨3064021139545,3064021139561⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-7806167911537),(-7806167911520)⟩,⟨1874222313169,1874222313185⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-3511607433363),(-3511607433346)⟩,⟨1010205255285,1010205255301⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1487216497702),(-1487216497682)⟩,⟨498409552363,498409552380⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-611423770628),(-611423770612)⟩,⟨233030016948,233030016964⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-251505919531),(-251505919514)⟩,⟨106446768151,106446768167⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-105994144156),(-105994144140)⟩,⟨48570790286,48570790302⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-45929637416),(-45929637400)⟩,⟨22223968795,22223968813⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-19338967366),(-19338967350)⟩,⟨9669271805,9669271821⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-5362190874),(-5362190857)⟩,⟨2722067820,2722067836⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-4511916131317569),(-4511916131317549)⟩,⟨(-1653622539756079),(-1653622539756053)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-12234442500021743),(-12234442500021712)⟩,⟨(-4375546713693448),(-4375546713693416)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-16662166812746378),(-16662166812746350)⟩,⟨(-5684417466614320),(-5684417466614290)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-17271882626992827),(-17271882626992805)⟩,⟨(-5505593898328486),(-5505593898328466)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-14958523901195855),(-14958523901195839)⟩,⟨(-4360076180903869),(-4360076180903853)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-11288499067777279),(-11288499067777263)⟩,⟨(-2928886720457272),(-2928886720457256)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-7635982224179287),(-7635982224179271)⟩,⟨(-1707148440574983),(-1707148440574967)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-4737804594159768),(-4737804594159751)⟩,⟨(-883103056976079),(-883103056976063)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2751564231684232),(-2751564231684213)⟩,⟨(-415682536352575),(-415682536352558)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1524475471930601),(-1524475471930585)⟩,⟨(-182658164260724),(-182658164260708)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-820404311632041),(-820404311632025)⟩,⟨(-76682698592948),(-76682698592932)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-435633364230491),(-435633364230474)⟩,⟨(-31247530580535),(-31247530580519)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-230301633628385),(-230301633628369)⟩,⟨(-12431084930239),(-12431084930223)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-120037222518274),(-120037222518258)⟩,⟨(-4807659617976),(-4807659617960)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-57624523550515),(-57624523550498)⟩,⟨(-1745986397746),(-1745986397730)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-17106786902691),(-17106786902675)⟩,⟨(-431815534357),(-431815534341)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-18177831131982811),(-18177831131980342)⟩,⟨(-324279890555088519),(-324279890555086048)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-70794109003244198),(-70794109003235586)⟩,⟨(-883429921431287736),(-883429921431279123)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-156680378534221705),(-156680378534202938)⟩,⟨(-1216951516657968957),(-1216951516657950192)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-259518645669374727),(-259518645669338781)⟩,⟨(-1289527977144904409),(-1289527977144868464)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-340633575341252522),(-340633575341191569)⟩,⟨(-1157862197222624486),(-1157862197222563534)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-369613026938864750),(-369613026938777359)⟩,⟨(-918531976585125664),(-918531976585038276)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-344553940809562248),(-344553940809462747)⟩,⟨(-659316532675068093),(-659316532674968590)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-285469913382449815),(-285469913382364433)⟩,⟨(-435981187100581631),(-435981187100496246)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-216261053645406243),(-216261053645350472)⟩,⟨(-270139882544228492),(-270139882544172719)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-153390109204959158),(-153390109204930859)⟩,⟨(-159556885692436241),(-159556885692407941)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-103859590459576911),(-103859590459565631)⟩,⟨(-91424310868231373),(-91424310868220093)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-67997956635993747),(-67997956635989910)⟩,⟨(-51683056465933155),(-51683056465929316)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-43099438352987578),(-43099438352986352)⟩,⟨(-29107354971727972),(-29107354971726748)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-25937210498902098),(-25937210498901697)⟩,⟨(-16107851315457006),(-16107851315456604)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-13743991575703702),(-13743991575703561)⟩,⟨(-8109118494891467),(-8109118494891326)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-4289605690806143),(-4289605690806098)⟩,⟨(-2471308164636841),(-2471308164636796)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨4006551847489869802,4006551847489869818⟩,⟨(-50451114910507393),(-50451114910507377)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨11122075703778258650,11122075703778258675⟩,⟨(-690111884888829069),(-690111884888829049)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨15958380541925202788,15958380541925202809⟩,⟨(-2495063075782110263),(-2495063075782110244)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨18055501184317927756,18055501184317927783⟩,⟨(-5080860538235648932),(-5080860538235648911)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨17670258271026534930,17670258271026534954⟩,⟨(-7347197076077048027),(-7347197076077048003)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨15393146345616572165,15393146345616572192⟩,⟨(-8432116857066575114),(-8432116857066575092)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨12064274877388963641,12064274877388963666⟩,⟨(-8274608786384601053),(-8274608786384601030)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨8616030287286301576,8616030287286301608⟩,⟨(-7303342955542195681),(-7303342955542195655)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨5707649989612041042,5707649989612041101⟩,⟨(-5976960150602906404),(-5976960150602906345)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨3577681101150223694,3577681101150223900⟩,⟨(-4620519983075799657),(-4620519983075799449)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨2167900863911385201,2167900863911385954⟩,⟨(-3414653668266339607),(-3414653668266338857)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1297170805496564424,1297170805496566480⟩,⟨(-2423904206698500802),(-2423904206698498746)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨774331777284665421,774331777284669390⟩,⟨(-1643429586035139392),(-1643429586035135423)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨451777198580321249,451777198580326568⟩,⟨(-1040106315477633695),(-1040106315477628373)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨236404735995629120,236404735995633822⟩,⟨(-569617051010412043),(-569617051010407344)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨73484813353779752,73484813353781633⟩,⟨(-180694154332446422),(-180694154332444540)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨19100506825596237651,19100506825596324365⟩,⟨(-11180987027657074136),(-11180987027656987427)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 21) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_21 (tableDensity false) (fullFactor false 0 21) density0_contains hk0_0_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-525440759828809341),(-525440759828809340)⟩,⟨(-13714740390635844949),(-13714740390635844947)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_21 0 21 ha0_0_21_contains + def realAnswer : RBox := ⟨18575066065667428310,18575066065867515025⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_21 +namespace hm0_1_0_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-351),(-335)⟩,⟨351,367⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-697),(-681)⟩,⟨718,734⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-513),(-496)⟩,⟨533,549⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-207),(-191)⟩,⟨210,226⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-53),(-37)⟩,⟨44,60⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨1,17⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-846400662),(-846400646)⟩,⟨95835571,95835587⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2029051699),(-2029051683)⟩,⟨264499637,264499653⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-2165217150),(-2165217133)⟩,⟨359919913,359919929⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1566915446),(-1566915430)⟩,⟨349498030,349498046⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-850797993),(-850797976)⟩,⟨256123165,256123181⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-364422872),(-364422855)⟩,⟨144043086,144043102⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-127335580),(-127335563)⟩,⟨63290635,63290651⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-37310728),(-37310710)⟩,⟨22396838,22396854⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-9454724),(-9454708)⟩,⟨6650796,6650812⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-2158432),(-2158416)⟩,⟨1736996,1737013⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-467988),(-467972)⟩,⟨419729,419745⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-102403),(-102387)⟩,⟨99055,99071⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-23986),(-23970)⟩,⟨24185,24201⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-6288),(-6272)⟩,⟨6441,6457⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1827),(-1811)⟩,⟨1871,1887⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-422),(-406)⟩,⟨419,435⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-3768919055684),(-3768919055668)⟩,⟨(-2403198296128),(-2403198296112)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-9889880272317),(-9889880272301)⟩,⟨(-6182960223072),(-6182960223056)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-12559553343794),(-12559553343778)⟩,⟨(-7592760732759),(-7592760732743)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-11631986119356),(-11631986119340)⟩,⟨(-6728013915427),(-6728013915411)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-8611570350994),(-8611570350978)⟩,⟨(-4667496695846),(-4667496695830)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-5350412444220),(-5350412444204)⟩,⟨(-2597769712431),(-2597769712415)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-2903808531963),(-2903808531947)⟩,⟨(-1176324294158),(-1176324294142)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1423619726603),(-1423619726587)⟩,⟨(-440298203424),(-440298203407)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-647520969424),(-647520969408)⟩,⟨(-138419891878),(-138419891862)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-279430827069),(-279430827053)⟩,⟨(-37011587163),(-37011587147)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-116770774793),(-116770774777)⟩,⟨(-8405427671),(-8405427655)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-48200912215),(-48200912199)⟩,⟨(-1440179165),(-1440179149)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-20040611500),(-20040611484)⟩,⟨60107302,60107318⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-8475581369),(-8475581353)⟩,⟨290728254,290728270⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3486461078),(-3486461062)⟩,⟨219123619,219123635⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-953798849),(-953798833)⟩,⟨76844576,76844592⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-878733464982290),(-878733464982265)⟩,⟨(-1344711576652141),(-1344711576652117)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2360015226648604),(-2360015226648573)⟩,⟨(-3569897494978682),(-3569897494978651)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-3168456058598386),(-3168456058598360)⟩,⟨(-4662393063777622),(-4662393063777596)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3252831606675437),(-3252831606675416)⟩,⟨(-4550539739098709),(-4550539739098686)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2829695160227325),(-2829695160227307)⟩,⟨(-3667100299740776),(-3667100299740759)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-2176911879937650),(-2176911879937634)⟩,⟨(-2570331681837283),(-2570331681837267)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-1508724381608500),(-1508724381608484)⟩,⟨(-1624242497476007),(-1624242497475991)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-954601573070159),(-954601573070143)⟩,⟨(-947684291367876),(-947684291367860)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-561580217456829),(-561580217456813)⟩,⟨(-519356179459066),(-519356179459050)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-314348044869720),(-314348044869704)⟩,⟨(-271894976438125),(-271894976438109)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-171395814049675),(-171395814049659)⟩,⟨(-138679625173524),(-138679625173508)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-92692912434243),(-92692912434227)⟩,⟨(-70339575091958),(-70339575091942)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-50063215185867),(-50063215185851)⟩,⟨(-35950622167968),(-35950622167952)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-26626587671613),(-26626587671597)⟩,⟨(-18346231828703),(-18346231828687)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-12979801221094),(-12979801221078)⟩,⟨(-8710828365431),(-8710828365415)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-3884898176572),(-3884898176556)⟩,⟨(-2574817847240),(-2574817847224)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-11416288280277304),(-11416288280275271)⟩,⟨(-106096645502284830),(-106096645502282798)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-36236811865031448),(-36236811865024367)⟩,⟨(-294879495163380966),(-294879495163373885)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-62793834013931595),(-62793834013916165)⟩,⟨(-420266325334259302),(-420266325334243875)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-85188811654158464),(-85188811654128911)⟩,⟨(-462305443339264409),(-462305443339234857)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-98632874244415901),(-98632874244365782)⟩,⟨(-428342045849072174),(-428342045849022056)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-102112910403441168),(-102112910403369309)⟩,⟨(-348491015890339903),(-348491015890268047)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-95804749468199409),(-95804749468117607)⟩,⟨(-257418755306066928),(-257418755305985127)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-81287522815538284),(-81287522815468123)⟩,⟨(-177698085044525995),(-177698085044455834)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-62502917458432465),(-62502917458386672)⟩,⟨(-117200671542241625),(-117200671542195833)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-43955365879502548),(-43955365879479335)⟩,⟨(-74940609099179196),(-74940609099155982)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-28636903873883249),(-28636903873874009)⟩,⟨(-46770733941920693),(-46770733941911452)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-17561528055672263),(-17561528055669123)⟩,⟨(-28467669903504504),(-28467669903501364)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-10319330921250400),(-10319330921249392)⟩,⟨(-16793655027733151),(-16793655027732147)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-5826533179517840),(-5826533179517508)⟩,⟨(-9450580659930215),(-9450580659929884)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2967105424337114),(-2967105424336996)⟩,⟨(-4753046883654134),(-4753046883654017)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-910163508617772),(-910163508617731)⟩,⟨(-1442036617210304),(-1442036617210264)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨118955507692781038,118955507692781057⟩,⟨(-7140196014888345),(-7140196014888329)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨310240036190598621,310240036190598643⟩,⟨(-99631855929242387),(-99631855929242371)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨296430854317892745,296430854317892764⟩,⟨(-393851931205588184),(-393851931205588166)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-99636280759141472),(-99636280759141450)⟩,⟨(-988014090702016548),(-988014090702016528)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-780463535189694611),(-780463535189694592)⟩,⟨(-1936093990907651514),(-1936093990907651493)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1315358433682001675),(-1315358433682001656)⟩,⟨(-3036406614678806982),(-3036406614678806958)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1385698662064608485),(-1385698662064608465)⟩,⟨(-3824191959426444413),(-3824191959426444392)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1078069904430063749),(-1078069904430063724)⟩,⟨(-3979145636783495403),(-3979145636783495382)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-665432441011039003),(-665432441011038953)⟩,⟨(-3560276406543911310),(-3560276406543911257)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-338730085108473651),(-338730085108473477)⟩,⟨(-2841834401256668225),(-2841834401256668050)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-150996060106822777),(-150996060106822162)⟩,⟨(-2085396989778373719),(-2085396989778373102)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-71825134917314355),(-71825134917312676)⟩,⟨(-1441846343222849601),(-1441846343222847918)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-47112390379369779),(-47112390379366533)⟩,⟨(-953950144014076801),(-953950144014073561)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-36595439141129185),(-36595439141124833)⟩,⟨(-597857343474595771),(-597857343474591420)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-24207329073161023),(-24207329073157178)⟩,⟨(-328321600515183594),(-328321600515179750)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-8450680880310023),(-8450680880308481)⟩,⟨(-104690431678636550),(-104690431678635008)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1006920740510055001),(-1006920740509983720)⟩,⟨(-4833000246104350993),(-4833000246104279714)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 21) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_21 (tableDensity true) (fullFactor false 0 21) density1_contains hk0_0_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨687114839776135290,687114839776135292⟩,⟨17934660510831489546,17934660510831489548⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_21 0 21 ha0_0_21_contains + def realAnswer : RBox := ⟨(-319805900833919711),(-319805900633848428)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_21 +namespace hm0_0_0_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-64),(-48)⟩,⟨(-49),(-33)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-119),(-103)⟩,⟨(-87),(-70)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-88),(-72)⟩,⟨(-63),(-46)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-41),(-23)⟩,⟨(-27),(-11)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-148229252),(-148229236)⟩,⟨(-212801079),(-212801063)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-359872433),(-359872417)⟩,⟨(-511235791),(-511235775)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-392951185),(-392951169)⟩,⟨(-546874236),(-546874220)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-292618490),(-292618474)⟩,⟨(-395242727),(-395242711)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-163307439),(-163307422)⟩,⟨(-212180382),(-212180365)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-71337391),(-71337372)⟩,⟨(-88383434),(-88383418)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-25145385),(-25145369)⟩,⟨(-29480335),(-29480317)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-7356535),(-7356519)⟩,⟨(-8120256),(-8120239)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1843455),(-1843438)⟩,⟨(-1912589),(-1912571)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-411407),(-411388)⟩,⟨(-401677),(-401661)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-85904),(-85887)⟩,⟨(-79161),(-79144)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-17826),(-17809)⟩,⟨(-15561),(-15545)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-3933),(-3917)⟩,⟨(-3265),(-3249)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-978),(-962)⟩,⟨(-784),(-768)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-280),(-264)⟩,⟨(-216),(-199)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-67),(-51)⟩,⟨(-55),(-39)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨22622354160,22622354176⟩,⟨(-1411226170272),(-1411226170256)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨10179738284,10179738300⟩,⟨(-3655465403457),(-3655465403441)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-104178609299),(-104178609283)⟩,⟨(-4552429722723),(-4552429722706)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-243579544263),(-243579544247)⟩,⟨(-4145757389428),(-4145757389409)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-307566269804),(-307566269788)⟩,⟨(-3040645232192),(-3040645232175)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-274727243845),(-274727243829)⟩,⟨(-1875613320656),(-1875613320640)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-193113306679),(-193113306661)⟩,⟨(-1001268211090),(-1001268211074)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-113901919540),(-113901919523)⟩,⟨(-474693323385),(-474693323369)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-59060563092),(-59060563075)⟩,⟨(-205411092841),(-205411092825)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-28004293518),(-28004293501)⟩,⟨(-83600018824),(-83600018806)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-12590838555),(-12590838539)⟩,⟨(-33047566928),(-33047566910)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-5543703880),(-5543703864)⟩,⟨(-13101663226),(-13101663208)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-2448506852),(-2448506835)⟩,⟨(-5344113221),(-5344113205)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1091051064),(-1091051048)⟩,⟨(-2255016567),(-2255016549)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-465883262),(-465883245)⟩,⟨(-931811435),(-931811419)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-129885529),(-129885513)⟩,⟨(-255861721),(-255861705)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨157237540903982,157237540903999⟩,⟨(-429022218248238),(-429022218248221)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨414111969292256,414111969292274⟩,⟨(-1157870838708940),(-1157870838708922)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨533026844241563,533026844241580⟩,⟨(-1562319274602265),(-1562319274602248)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨509276275533296,509276275533312⟩,⟨(-1597509319591155),(-1597509319591138)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨396266800113209,396266800113225⟩,⟨(-1359280534897645),(-1359280534897629)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨260616660558621,260616660558637⟩,⟨(-1004212237348692),(-1004212237348675)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨148283883787400,148283883787416⟩,⟨(-663031920378671),(-663031920378654)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨74711321219815,74711321219831⟩,⟨(-400644461574901),(-400644461574883)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨34205287709376,34205287709392⟩,⟨(-226302209785684),(-226302209785668)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨14613920514449,14613920514465⟩,⟨(-121902026838197),(-121902026838181)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨5969659663138,5969659663154⟩,⟨(-63832457701590),(-63832457701572)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2371610042376,2371610042392⟩,⟨(-33046006626126),(-33046006626110)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨922752294462,922752294478⟩,⟨(-17087013775827),(-17087013775811)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨350524526023,350524526039⟩,⟨(-8748665672696),(-8748665672680)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨125695558890,125695558906⟩,⟨(-4147669440505),(-4147669440489)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨30882186465,30882186481⟩,⟨(-1223395206763),(-1223395206747)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨38552463000854985,38552463000855293⟩,⟨(-2161022067904125),(-2161022067903819)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨104633246637531069,104633246637532102⟩,⟨(-8383010343827180),(-8383010343826147)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨143068406711553159,143068406711555377⟩,⟨(-18412953558334195),(-18412953558331976)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨149957003143586077,149957003143590272⟩,⟨(-30165597996074591),(-30165597996070398)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨132764341545148785,132764341545155782⟩,⟨(-39040487039215549),(-39040487039208552)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨103563829418663077,103563829418672939⟩,⟨(-41655612235765793),(-41655612235755936)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨72932526691566027,72932526691577044⟩,⟨(-38098629180242713),(-38098629180231699)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨47238952279072949,47238952279082213⟩,⟨(-30919323056668813),(-30919323056659548)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨28643626633616134,28643626633622062⟩,⟨(-22922800348475065),(-22922800348469138)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨16554288721736904,16554288721739855⟩,⟨(-15909543217455535),(-15909543217452585)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨9288303257270295,9288303257271456⟩,⟨(-10548897936374390),(-10548897936373230)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨5150113796439205,5150113796439601⟩,⟨(-6774514506051445),(-6774514506051049)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨2852124421504984,2852124421505116⟩,⟨(-4222629647363097),(-4222629647362966)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1557272982390874,1557272982390929⟩,⟨(-2507399295685191),(-2507399295685138)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨776653528160991,776653528161019⟩,⟨(-1316307543511978),(-1316307543511948)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨235552458861975,235552458861993⟩,⟨(-408862358575325),(-408862358575304)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨7196755490256328,7196755490256344⟩,⟨571679471281638732,571679471281638748⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨98113714148601458,98113714148601474⟩,⟨1581982641158384094,1581982641158384110⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨352530223347462297,352530223347462313⟩,⟨2255844717584197219,2255844717584197235⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨711421193110914535,711421193110914554⟩,⟨2529189584915031046,2529189584915031065⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1016859633152678530,1016859633152678547⟩,⟨2446435137911323262,2446435137911323282⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨1150917456481038706,1150917456481038722⟩,⟨2101678895902556913,2101678895902556930⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨1111803698897512405,1111803698897512422⟩,⟨1621475571638942098,1621475571638942115⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨964746088544033312,964746088544033328⟩,⟨1138497861054586937,1138497861054586955⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨775689364923903655,775689364923903677⟩,⟨740970490120779915,740970490120779935⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨589130618767548819,589130618767548859⟩,⟨456301647832899121,456301647832899160⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨428041245493017103,428041245493017212⟩,⟨271824610198281378,271824610198281481⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨299150942701817728,299150942701817995⟩,⟨160121919831727708,160121919831727974⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨200115260718444565,200115260718445060⟩,⟨94297634815949315,94297634815949813⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨125299612971233763,125299612971234419⟩,⟨54427217018608936,54427217018609592⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨68110187949619262,68110187949619840⟩,⟨28267773949957934,28267773949958508⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨21523287512325544,21523287512325784⟩,⟨8753117619312659,8753117619312898⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1463494799333966934,1463494799333976797⟩,⟨2629938336533267407,2629938336533277270⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 22) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_22 (tableDensity false) (fullFactor false 0 22) density0_contains hk0_0_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨1965781686197785318,1965781686197785320⟩,⟨(-62585242822477399),(-62585242822477398)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_22 0 22 ha0_0_22_contains + def realAnswer : RBox := ⟨3429276485431752252,3429276485631762117⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_22 +namespace hm0_1_0_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-31),(-14)⟩,⟨(-25),(-9)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4550889),(-4550873)⟩,⟨(-40193708),(-40193692)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-12441904),(-12441888)⟩,⟨(-95468899),(-95468883)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16616398),(-16616382)⟩,⟨(-100017360),(-100017344)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-15694517),(-15694501)⟩,⟨(-70422651),(-70422635)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-11091309),(-11091293)⟩,⟨(-36880038),(-36880022)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-5966439),(-5966423)⟩,⟨(-15109950),(-15109934)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-2488706),(-2488690)⟩,⟨(-5011681),(-5011665)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-830492),(-830476)⟩,⟨(-1384644),(-1384628)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-231312),(-231296)⟩,⟨(-329072),(-329056)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-56466),(-56450)⟩,⟨(-70206),(-70190)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-12739),(-12723)⟩,⟨(-14214),(-14197)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-2820),(-2804)⟩,⟨(-2914),(-2898)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-653),(-637)⟩,⟨(-647),(-631)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-171),(-155)⟩,⟨(-167),(-151)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-54),(-38)⟩,⟨(-52),(-36)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-20),(-4)⟩,⟨(-19),(-3)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨171316911517,171316911533⟩,⟨(-268674336084),(-268674336068)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨438030595317,438030595333⟩,⟨(-700630693151),(-700630693135)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨531314792272,531314792289⟩,⟨(-878828540064),(-878828540048)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨462316448609,462316448625⟩,⟨(-799219513731),(-799219513715)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨313232112963,313232112979⟩,⟨(-577808444188),(-577808444172)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨169423694459,169423694475⟩,⟨(-348818272727),(-348818272711)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨74241465443,74241465459⟩,⟨(-183149315767),(-183149315750)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨26800502320,26800502336⟩,⟨(-86568958610),(-86568958594)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨8107295790,8107295806⟩,⟨(-37874631329),(-37874631313)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨2083906075,2083906091⟩,⟨(-15706503227),(-15706503211)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨455248029,455248045⟩,⟨(-6311271250),(-6311271234)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨75269907,75269923⟩,⟨(-2510965023),(-2510965006)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-2955859),(-2955843)⟩,⟨(-1010477514),(-1010477498)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-14251251),(-14251235)⟩,⟨(-416146854),(-416146838)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-10553568),(-10553552)⟩,⟨(-167992218),(-167992202)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3666556),(-3666540)⟩,⟨(-45511489),(-45511473)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨127864163633696,127864163633712⟩,⟨(-83555760045660),(-83555760045643)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨337862508698111,337862508698129⟩,⟨(-223354261082068),(-223354261082051)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨437189204504132,437189204504150⟩,⟨(-297092721301043),(-297092721301025)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨420926370946956,420926370946974⟩,⟨(-300862107836672),(-300862107836654)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨333270495791624,333270495791640⟩,⟨(-257128715247624),(-257128715247607)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨228685185237177,228685185237193⟩,⟨(-193646680726951),(-193646680726935)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨141052060073243,141052060073260⟩,⟨(-130996074750660),(-130996074750644)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨80149982343981,80149982343997⟩,⟨(-80721418960906),(-80721418960890)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨42720057027014,42720057027030⟩,⟨(-46186011195125),(-46186011195109)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨21744369378098,21744369378114⟩,⟨(-25135667596789),(-25135667596773)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨10791294829340,10791294829357⟩,⟨(-13335182208432),(-13335182208416)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨5336188998122,5336188998138⟩,⟨(-7031159201897),(-7031159201881)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2667439393826,2667439393842⟩,⟨(-3714262506939),(-3714262506923)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1337152421833,1337152421849⟩,⟨(-1940580218462),(-1940580218446)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨626987050438,626987050454⟩,⟨(-934245076048),(-934245076032)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨184138691727,184138691743⟩,⟨(-277828950986),(-277828950970)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨12613424796562229,12613424796562485⟩,⟨(-1357222297148894),(-1357222297148637)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨34924979984676531,34924979984677386⟩,⟨(-4291453900304305),(-4291453900303452)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨49406274439129523,49406274439131351⟩,⟨(-7380812685985984),(-7380812685984157)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨53758675995504171,53758675995507620⟩,⟨(-9903828141844388),(-9903828141840940)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨49113378309823528,49113378309829284⟩,⟨(-11305707913318073),(-11305707913312317)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨39290641011719293,39290641011727400⟩,⟨(-11508422293562824),(-11508422293554714)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨28473604854350530,28473604854359587⟩,⟨(-10593111535467271),(-10593111535458214)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨19251945458899878,19251945458907495⟩,⟨(-8803915959217507),(-8803915959209892)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨12425464145226798,12425464145231671⟩,⟨(-6625001510646802),(-6625001510641930)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨7774038019065870,7774038019068296⟩,⟨(-4559219435714780),(-4559219435712352)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨4751042739930435,4751042739931388⟩,⟨(-2908881434946280),(-2908881434945325)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨2836487718977020,2836487718977348⟩,⟨(-1749819380485068),(-1749819380484741)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1645489072418725,1645489072418839⟩,⟨(-1011119447172527),(-1011119447172411)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨913658209775116,913658209775161⟩,⟨(-563289488886553),(-563289488886507)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨455225989786898,455225989786922⟩,⟨(-284174001063416),(-284174001063392)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨137447638400063,137447638400082⟩,⟨(-86752071286373),(-86752071286355)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1018535089781193,1018535089781209⟩,⟨16973324985419922,16973324985419938⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨14164538801983921,14164538801983937⟩,⟨44130485017023229,44130485017023246⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨55642875035670663,55642875035670679⟩,⟨41925868255383318,41925868255383334⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨138309313886153751,138309313886153769⟩,⟨(-13883971692090752),(-13883971692090735)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨267862626119592213,267862626119592229⟩,⟨(-107940393875643758),(-107940393875643742)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨414293886714354906,414293886714354922⟩,⟨(-179491796731626403),(-179491796731626387)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨513683052662105447,513683052662105464⟩,⟨(-186197357820400765),(-186197357820400748)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨525536189708053439,525536189708053455⟩,⟨(-142453275010721372),(-142453275010721354)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨462013377608978066,462013377608978090⟩,⟨(-86405344977843222),(-86405344977843202)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨362338144223292837,362338144223292874⟩,⟨(-43219055839692248),(-43219055839692212)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨261420764059633897,261420764059633989⟩,⟨(-18940853814232978),(-18940853814232888)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨177954557581485600,177954557581485821⟩,⟨(-8866893344708146),(-8866893344707927)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨116161594674156525,116161594674156933⟩,⟨(-5735865364429909),(-5735865364429501)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨72022818844870114,72022818844870656⟩,⟨(-4407828624543191),(-4407828624542648)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨39257923731720530,39257923731721004⟩,⟨(-2894318772870548),(-2894318772870074)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12470138068242639,12470138068242836⟩,⟨(-1006590840343602),(-1006590840343404)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨625686120015028658,625686120015036810⟩,⟨(-130502736788626245),(-130502736788618094)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 22) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_22 (tableDensity true) (fullFactor false 0 22) density1_contains hk0_0_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-2570637589643257726),(-2570637589643257724)⟩,⟨81842240614008905,81842240614008906⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_22 0 22 ha0_0_22_contains + def realAnswer : RBox := ⟨(-1944951469728229068),(-1944951469528220914)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_22 +namespace hm0_0_0_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨9666072,9666088⟩,⟨(-6733024),(-6733007)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨23008229,23008245⟩,⟨(-16195802),(-16195786)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨24163217,24163233⟩,⟨(-17361371),(-17361355)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨16991495,16991511⟩,⟨(-12578501),(-12578485)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨8798182,8798198⟩,⟨(-6770651),(-6770635)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨3505804,3505820⟩,⟨(-2829091),(-2829073)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1110105,1110121⟩,⟨(-946641),(-946625)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨288335,288351⟩,⟨(-261155),(-261139)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨63688,63705⟩,⟨(-61385),(-61368)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨12492,12508⟩,⟨(-12810),(-12793)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2290,2307⟩,⟨(-2502),(-2486)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨414,430⟩,⟨(-492),(-476)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨75,91⟩,⟨(-107),(-91)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨10,26⟩,⟨(-31),(-15)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨96228050028,96228050044⟩,⟨1542737713,1542737729⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨247709107523,247709107539⟩,⟨693783651,693783667⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨304704912643,304704912659⟩,⟨(-6960242298),(-6960242282)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨272471515859,272471515876⟩,⟨(-15989149126),(-15989149110)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨195149852056,195149852072⟩,⟨(-19720398667),(-19720398651)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨116966489159,116966489175⟩,⟨(-17118502891),(-17118502874)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨60410708162,60410708180⟩,⟨(-11643191826),(-11643191809)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨27614304593,27614304609⟩,⟨(-6621973123),(-6621973107)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨11494538309,11494538327⟩,⟨(-3303208024),(-3303208008)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨4495606747,4495606763⟩,⟨(-1505265950),(-1505265934)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1708764023,1708764039⟩,⟨(-650793670),(-650793654)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨652892322,652892338⟩,⟨(-276187972),(-276187955)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨257747660,257747677⟩,⟨(-118073635),(-118073619)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨105905655,105905671⟩,⟨(-51236724),(-51236708)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨42946188,42946205⟩,⟨(-21471506),(-21471490)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨11677871,11677887⟩,⟨(-5928144),(-5928127)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨39020569375514,39020569375530⟩,⟨14301156368488,14301156368504⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨104817244046653,104817244046669⟩,⟨37488661035713,37488661035729⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨140122505475061,140122505475077⟩,⟨47809255513464,47809255513480⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨141335465125732,141335465125749⟩,⟨45061611465748,45061611465764⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨118151268947356,118151268947373⟩,⟨34450074122856,34450074122872⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨85453281429226,85453281429243⟩,⟨22182758494172,22182758494188⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨55070920142678,55070920142694⟩,⟨12320681298449,12320681298466⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨32408785603082,32408785603098⟩,⟨6046202419765,6046202419781⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨17804142073336,17804142073354⟩,⟨2692448274179,2692448274195⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨9324464804596,9324464804612⟩,⟨1118449550266,1118449550282⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4750889050804,4750889050820⟩,⟨444550371558,444550371574⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2397904120964,2397904120981⟩,⟨172181085536,172181085552⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1212674893759,1212674893776⟩,⟨65519416516,65519416532⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨609916963963,609916963979⟩,⟨24445897101,24445897117⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨285561039273,285561039290⟩,⟨8655596551,8655596567⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨83687446213,83687446229⟩,⟨2112579344,2112579360⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨245737432358545,245737432358592⟩,⟨4384087544756513,4384087544756564⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨949508577891335,949508577891469⟩,⟨11853956242870874,11853956242871008⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨2069808993391670,2069808993391933⟩,⟨16088375628108444,16088375628108709⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨3353945185566130,3353945185566608⟩,⟨16680282353735571,16680282353736047⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨4280029200105491,4280029200106271⟩,⟨14561621114700778,14561621114701560⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨4490622932717278,4490622932718352⟩,⟨11169369924474665,11169369924475742⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4029683691506295,4029683691507474⟩,⟨7717167632315941,7717167632317117⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨3203398284627594,3203398284628567⟩,⟨4896028849806406,4896028849807380⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨2324176328399130,2324176328399747⟩,⟨2905221260093132,2905221260093746⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1578445226881365,1578445226881672⟩,⟨1642921558204122,1642921558204428⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1024889715038790,1024889715038917⟩,⟨902652402268304,902652402268432⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨645605313931298,645605313931350⟩,⟨490898844457103,490898844457156⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨395728581158494,395728581158521⟩,⟨267323545734351,267323545734379⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨231858612277613,231858612277630⟩,⟨144009578549793,144009578549810⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨120586448567249,120586448567266⟩,⟨71150447560786,71150447560802⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨37276226132969,37276226132986⟩,⟨21475507289353,21475507289369⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-78024207143099222),(-78024207143099206)⟩,⟨981968674033440,981968674033457⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-215235172174475474),(-215235172174475458)⟩,⟨13342447374000727,13342447374000743⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-305018801507166900),(-305018801507166884)⟩,⟨47643990656206137,47643990656206153⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-338884794447773213),(-338884794447773197)⟩,⟨95282937310795120,95282937310795136⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-323985411283854662),(-323985411283854646)⟩,⟨134617416568728075,134617416568728091⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-274478489772848737),(-274478489772848720)⟩,⟨150263930645558538,150263930645558554⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-208460759058561820),(-208460759058561804)⟩,⟨142893846872875667,142893846872875683⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-143900762667185360),(-143900762667185344)⟩,⟨121901852841369448,121901852841369464⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-92013330750747415),(-92013330750747398)⟩,⟨96294539449432728,96294539449432744⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-55668334552980256),(-55668334552980236)⟩,⟨71851890473085177,71851890473085195⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-32601876521417235),(-32601876521417209)⟩,⟨51325017268707135,51325017268707161⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-18906315598514586),(-18906315598514541)⟩,⟨35315700139006696,35315700139006743⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-10984357677898993),(-10984357677898923)⟩,⟨23308239692348029,23308239692348100⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-6271996262974985),(-6271996262974896)⟩,⟨14438416644659461,14438416644659547⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3233129098427587),(-3233129098427505)⟩,⟨7789994951670861,7789994951670940⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-997293320232821),(-997293320232781)⟩,⟨2452268888796087,2452268888796128⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-346488256949073436),(-346488256949072154)⟩,⟨183954184639472185,183954184639473466⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 23) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_23 (tableDensity false) (fullFactor false 0 23) density0_contains hk0_0_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨7129092554256656,7129092554256658⟩,⟨269339847531150708,269339847531150709⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_23 0 23 ha0_0_23_contains + def realAnswer : RBox := ⟨(-339359164494816780),(-339359164294815496)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_23 +namespace hm0_1_0_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1825716,1825732⟩,⟨(-206719),(-206703)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨4296672,4296688⟩,⟨(-559832),(-559816)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨4419401,4419417⟩,⟨(-733816),(-733800)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3027686,3027703⟩,⟨(-674199),(-674183)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1529354,1529370⟩,⟨(-459496),(-459480)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨599366,599382⟩,⟨(-236448),(-236432)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨188712,188728⟩,⟨(-93637),(-93620)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨49158,49174⟩,⟨(-29475),(-29459)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨10949,10965⟩,⟨(-7704),(-7688)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2176,2192⟩,⟨(-1763),(-1747)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨402,418⟩,⟨(-376),(-359)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨71,87⟩,⟨(-86),(-70)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨7,23⟩,⟨(-23),(-7)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨18320223698,18320223714⟩,⟨11681700814,11681700831⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨47477234697,47477234714⟩,⟨29683189841,29683189857⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨58821732397,58821732413⟩,⟨35563769825,35563769841⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨52527856597,52527856613⟩,⟨30388072876,30388072893⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨37085648406,37085648422⟩,⟨20107998091,20107998107⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨21754101492,21754101508⟩,⟨10570052424,10570052440⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨11050487103,11050487119⟩,⟨4482329787,4482329803⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨5035889457,5035889474⟩,⟨1560569091,1560569107⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2119301715,2119301731⟩,⟨454256023,454256039⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨844567847,844567863⟩,⟨112244461,112244477⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨326320962,326320978⟩,⟨23587245,23587261⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨125130422,125130438⟩,⟨3763173,3763189⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨48737980,48737997⟩,⟨(-138974),(-138958)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨19545025,19545041⟩,⟨(-668246),(-668230)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨7742745,7742761⟩,⟨(-486202),(-486186)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2077204,2077220⟩,⟨(-167348),(-167332)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨7599598954997,7599598955013⟩,⟨11629568285116,11629568285132⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨20219497938373,20219497938389⟩,⟨30585877602545,30585877602561⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨26646251690862,26646251690878⟩,⟨39212971955274,39212971955290⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨26618123760350,26618123760366⟩,⟨37243746919592,37243746919608⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨22349636105172,22349636105188⟩,⟨28972090841253,28972090841269⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨16477571897063,16477571897079⟩,⟨19462595527988,19462595528006⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨10879903571512,10879903571528⟩,⟨11717265930013,11717265930029⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨6529456938479,6529456938495⟩,⟨6484323947053,6484323947069⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3633559235438,3633559235454⟩,⟨3361409011846,3361409011862⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1922616250608,1922616250624⟩,⟨1663469553810,1663469553826⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨992470062931,992470062947⟩,⟨803256180243,803256180259⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨510178716685,510178716701⟩,⟨387237675116,387237675132⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨263594006827,263594006843⟩,⟨189317936649,189317936665⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨135285329004,135285329020⟩,⟨93221902151,93221902167⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨64320827371,64320827387⟩,⟨43167382254,43167382270⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨19005117947,19005117963⟩,⟨12596178516,12596178532⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨154337699406947,154337699406989⟩,⟨1434363975041720,1434363975041763⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨486132819749160,486132819749273⟩,⟨3956614877695798,3956614877695909⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨829830433007669,829830433007888⟩,⟨5555685001206492,5555685001206713⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1101347338196713,1101347338197111⟩,⟨5979553905996125,5979553905996523⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1239588643330294,1239588643330939⟩,⟨5386573935883115,5386573935883761⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1240674226407562,1240674226408447⟩,⟨4237340926795115,4237340926796006⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1120390826253674,1120390826254643⟩,⟨3012687819315898,3012687819316870⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨912093204595580,912093204596384⟩,⟨1995160113308693,1995160113309495⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨671712928326654,671712928327164⟩,⟨1260106129583649,1260106129584157⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨452356162113083,452356162113339⟩,⟨771413978212390,771413978212646⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨282641215544540,282641215544650⟩,⟨461650391169125,461650391169233⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨166774907328718,166774907328766⟩,⟨270343831350418,270343831350464⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨94766842667030,94766842667058⟩,⟨154222521638509,154222521638532⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨52089785105260,52089785105281⟩,⟨84490624601641,84490624601661⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨26033487489780,26033487489797⟩,⟨41704089407462,41704089407479⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨7909250626226,7909250626242⟩,⟨12531219214827,12531219214843⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2316563639253635),(-2316563639253619)⟩,⟨138975025630086,138975025630102⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-6004477379864356),(-6004477379864340)⟩,⟨1926203762746665,1926203762746681⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-5672017349025489),(-5672017349025473)⟩,⟨7519398104846791,7519398104846807⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1850535928461737,1850535928461753⟩,⟨18519893833838845,18519893833838861⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨14279597715784301,14279597715784317⟩,⟨35448566750020048,35448566750020064⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨23428690439170753,23428690439170769⟩,⟨54070462574230675,54070462574230691⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨23932216799755904,23932216799755920⟩,⟨66001763488375195,66001763488375211⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨18005441371782239,18005441371782255⟩,⟨66392857725271434,66392857725271451⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨10732066797602783,10732066797602799⟩,⟨57349775805920986,57349775805921002⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨5274755546224534,5274755546224552⟩,⟨44191138948577664,44191138948577680⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨2272677384808006,2272677384808032⟩,⟨31346996309570553,31346996309570580⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1047053995442414,1047053995442455⟩,⟨21008825108979330,21008825108979371⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨667979252828811,667979252828874⟩,⟨13530056548283223,13530056548283285⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨507832265425851,507832265425930⟩,⟨8299281722935696,8299281722935775⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨331010560252768,331010560252835⟩,⟨4490050213360691,4490050213360761⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨114685687772816,114685687772852⟩,⟨1420792024001614,1420792024001653⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨16239213633378225,16239213633379327⟩,⟨77743581338484812,77743581338485916⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 23) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_23 (tableDensity true) (fullFactor false 0 23) density1_contains hk0_0_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-9322659494027937),(-9322659494027935)⟩,⟨(-352213646771504773),(-352213646771504772)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_23 0 23 ha0_0_23_contains + def realAnswer : RBox := ⟨6916554039350288,6916554239351392⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_23 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_3.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_3.lean new file mode 100644 index 0000000000000000000000000000000000000000..260f20e4e07ac5969c2f04ebc3f6df50c4bdbe75 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_3.lean @@ -0,0 +1,4721 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_0_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨293084,293100⟩,⟨420763,420779⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨698514,698530⟩,⟨992352,992368⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨735126,735142⟩,⟨1023187,1023203⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨518205,518221⟩,⟨700083,700099⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨269040,269058⟩,⟨349661,349677⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨107532,107549⟩,⟨133285,133303⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨34154,34170⟩,⟨40063,40079⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨8877,8894⟩,⟨9806,9822⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1950,1967⟩,⟨2025,2042⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨373,390⟩,⟨366,382⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨61,77⟩,⟨56,73⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨4,21⟩,⟨3,20⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-100823877),(-100823861)⟩,⟨6288161862,6288161878⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-45312374),(-45312358)⟩,⟨16086484757,16086484773⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨445650689,445650705⟩,⟨19545244616,19545244632⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1005872432,1005872448⟩,⟨17162141357,17162141374⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1211811627,1211811643⟩,⟨12003638429,12003638445⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1022308507,1022308523⟩,⟨6990870715,6990870732⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨672810823,672810839⟩,⟨3493315897,3493315915⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨368987642,368987658⟩,⟨1539651510,1539651526⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨177070499,177070516⟩,⟨616496231,616496247⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨77548558,77548574⟩,⟨231708278,231708294⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨32240319,32240335⟩,⟨84682110,84682128⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨13187668,13187685⟩,⟨31182799,31182816⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨5456963,5456979⟩,⟨11914082,11914098⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨2305952,2305968⟩,⟨4766748,4766764⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨948347,948364⟩,⟨1896896,1896912⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨259288,259304⟩,⟨510777,510794⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1246530385088),(-1246530385072)⟩,⟨3401137753558,3401137753574⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3252374233087),(-3252374233071)⟩,⟨9093347642732,9093347642748⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-4109570273867),(-4109570273851)⟩,⟨12043910966400,12043910966416⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3821076544953),(-3821076544937)⟩,⟨11983527550206,11983527550222⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2870273163432),(-2870273163415)⟩,⟨9842339804508,9842339804524⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1809524314175),(-1809524314159)⟩,⟨6968954576582,6968954576598⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-981104586791),(-981104586775)⟩,⟨4383795751749,4383795751767⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-468944966411),(-468944966395)⟩,⟨2512520957304,2512520957320⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-203116790802),(-203116790786)⟩,⟨1342450017092,1342450017109⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-82036995982),(-82036995966)⟩,⟨683567026708,683567026725⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-31727313508),(-31727313492)⟩,⟨338882866147,338882866163⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-11980195271),(-11980195255)⟩,⟨166755951710,166755951728⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-4458465658),(-4458465642)⟩,⟨82480902759,82480902775⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1633872497),(-1633872481)⟩,⟨40749694782,40749694798⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-571207403),(-571207387)⟩,⟨18841416384,18841416401⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-138495289),(-138495273)⟩,⟨5486189646,5486189662⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-477774573846078),(-477774573846058)⟩,⟨26779357746211,26779357746229⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1286988629296186),(-1286988629296158)⟩,⟨103066028481234,103066028481263⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-1733805577865671),(-1733805577865629)⟩,⟨222975321079117,222975321079157⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1778125671016720),(-1778125671016655)⟩,⟨357373529039345,357373529039410⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1530606177743920),(-1530606177743823)⟩,⟨449680149963249,449680149963343⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1154456949004256),(-1154456949004132)⟩,⟨463946838418956,463946838419081⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-782574558195109),(-782574558194978)⟩,⟨408473407038607,408473407038740⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-486318303295263),(-486318303295149)⟩,⟨318071653752261,318071653752373⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-282399591745735),(-282399591745662)⟩,⟨225841763411172,225841763411247⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-156263011699551),(-156263011699507)⟩,⟨150084039264008,150084039264052⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-84069003083411),(-84069003083384)⟩,⟨95428583662173,95428583662200⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-44843085027629),(-44843085027610)⟩,⟨58963650421674,58963650421691⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-24012132093984),(-24012132093968)⟩,⟨35541572012079,35541572012096⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-12762602749184),(-12762602749168)⟩,⟨20546800917328,20546800917345⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-6246638107739),(-6246638107723)⟩,⟨10586637279517,10586637279533⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1876359375324),(-1876359375308)⟩,⟨3256893418487,3256893418503⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-128403001198166),(-128403001198150)⟩,⟨(-10205230484416113),(-10205230484416097)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1738835918586886),(-1738835918586870)⟩,⟨(-28063522434508116),(-28063522434508100)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-6170759259386429),(-6170759259386413)⟩,⟨(-39524173116969427),(-39524173116969411)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-12229931920825079),(-12229931920825063)⟩,⟨(-43515441150021301),(-43515441150021284)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-17079068199247629),(-17079068199247613)⟩,⟨(-41118748846212232),(-41118748846212215)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-18801394771040939),(-18801394771040923)⟩,⟨(-34353817199259003),(-34353817199258986)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-17600518302489232),(-17600518302489216)⟩,⟨(-25684119428890109),(-25684119428890093)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-14761662809101160),(-14761662809101144)⟩,⟨(-17430971301449000),(-17430971301448984)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-11456278808446235),(-11456278808446219)⟩,⟨(-10950364915214562),(-10950364915214545)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-8398319842691304),(-8398319842691288)⟩,⟨(-6508665338404879),(-6508665338404862)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-5897919796883037),(-5897919796883021)⟩,⟨(-3747335986672236),(-3747335986672218)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-3995485268987425),(-3995485268987406)⟩,⟨(-2139376666194071),(-2139376666194051)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2601720558935394),(-2601720558935370)⟩,⟨(-1226225741386695),(-1226225741386673)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1594443020142441),(-1594443020142417)⟩,⟨(-692651922989872),(-692651922989847)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-853846933463733),(-853846933463713)⟩,⟨(-354382470818802),(-354382470818780)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-267759134918347),(-267759134918328)⟩,⟨(-108892954822462),(-108892954822443)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-22239726763217240),(-22239726763216875)⟩,⟨(-43768385147819416),(-43768385147819047)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 24) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_24 (tableDensity false) (fullFactor false 0 24) density0_contains hk0_0_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-35347102148322318),(-35347102148322317)⟩,⟨778123771589816,778123771589817⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_24 0 24 ha0_0_24_contains + def realAnswer : RBox := ⟨(-57586829011539558),(-57586828811539192)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_24 +namespace hm0_1_0_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨8991,9007⟩,⟨79467,79483⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨24133,24149⟩,⟨185316,185332⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨31052,31068⟩,⟨187141,187157⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨27749,27765⟩,⟨124749,124765⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨18237,18253⟩,⟨60779,60795⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨8973,8989⟩,⟨22782,22798⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨3369,3385⟩,⟨6806,6822⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨993,1009⟩,⟨1665,1682⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨239,255⟩,⟨342,358⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨45,61⟩,⟨57,73⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨3,19⟩,⟨4,20⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-763359106),(-763359090)⟩,⟨1197160340,1197160356⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1927687248),(-1927687232)⟩,⟨3083198969,3083198985⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-2281335250),(-2281335234)⟩,⟨3773087834,3773087850⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1914256168),(-1914256152)⟩,⟨3308616327,3308616343⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1237124447),(-1237124431)⟩,⟨2281235051,2281235067⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-632020684),(-632020668)⟩,⟨1300273457,1300273473⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-259370445),(-259370429)⟩,⟨639025164,639025180⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-87094091),(-87094075)⟩,⟨280774429,280774446⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-24394627),(-24394611)⟩,⟨113660220,113660236⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-5794556),(-5794540)⟩,⟨43527218,43527234⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1171309),(-1171293)⟩,⟨16171115,16171131⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-180326),(-180310)⟩,⟨5976448,5976466⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨6251,6267⟩,⟨2252962,2252978⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨30021,30037⟩,⟨879745,879761⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨21458,21474⟩,⟨341991,342007⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨7311,7327⟩,⟨90848,90864⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1013666620757),(-1013666620741)⟩,⟨662402185291,662402185307⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2653507544308),(-2653507544292)⟩,⟨1754142740550,1754142740566⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-3370634175885),(-3370634175869)⟩,⟨2290349600279,2290349600295⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3158103436448),(-3158103436432)⟩,⟨2256904404195,2256904404211⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2413756387966),(-2413756387950)⟩,⟨1861748529330,1861748529347⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1587446408424),(-1587446408408)⟩,⟨1343730119864,1343730119880⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-932852845927),(-932852845911)⟩,⟨866027967390,866027967406⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-502769820300),(-502769820284)⟩,⟨506184305846,506184305863⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-253486951311),(-253486951295)⟩,⟨273967385909,273967385925⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-121962691571),(-121962691555)⟩,⟨140941542187,140941542203⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-57302810074),(-57302810057)⟩,⟨70790879314,70790879330⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-26931507612),(-26931507596)⟩,⟨35477619326,35477619342⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-12877149933),(-12877149917)⟩,⟨17927894455,17927894471⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-6228446780),(-6228446764)⟩,⟨9038462585,9038462601⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2848214103),(-2848214087)⟩,⟨4243871286,4243871302⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-825751796),(-825751780)⟩,⟨1245892577,1245892593⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-156315643602120),(-156315643602100)⟩,⟨16819372370088,16819372370105⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-429565273413958),(-429565273413933)⟩,⟨52774387585338,52774387585366⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-598704971104345),(-598704971104306)⟩,⟨89411683694181,89411683694219⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-637399059832334),(-637399059832278)⟩,⟨117372928903095,117372928903153⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-566175277651961),(-566175277651880)⟩,⟨130251555887909,130251555887993⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-437951691066329),(-437951691066221)⟩,⟨128182374566406,128182374566513⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-305489969837423),(-305489969837311)⟩,⟨113565594802956,113565594803069⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-198159033116453),(-198159033116358)⟩,⟨90559835286506,90559835286600⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-122471586266249),(-122471586266185)⟩,⟨65270238929228,65270238929291⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-73360365024778),(-73360365024740)⟩,⟨43013390942247,43013390942286⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-42990127535372),(-42990127535350)⟩,⟨26319414021849,26319414021873⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-24693368239969),(-24693368239951)⟩,⟨15233387859019,15233387859036⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-13852410883376),(-13852410883358)⟩,⟨8512068879718,8512068879736⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-7487804903571),(-7487804903555)⟩,⟨4616307470960,4616307470976⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-3661412246399),(-3661412246383)⟩,⟨2285592241781,2285592241797⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1094879119129),(-1094879119113)⟩,⟨691047059193,691047059209⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-18172479413474),(-18172479413458)⟩,⟨(-302996931615422),(-302996931615406)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-251026364021201),(-251026364021185)⟩,⟨(-782941167771786),(-782941167771770)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-973812356205778),(-973812356205762)⟩,⟨(-735379653200945),(-735379653200929)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2376545248578153),(-2376545248578137)⟩,⟨236369029489198,236369029489214⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-4495809121795810),(-4495809121795794)⟩,⟨1810382295834913,1810382295834929⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-6762952870964586),(-6762952870964570)⟩,⟨2930731903822666,2930731903822682⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-8127226047225236),(-8127226047225220)⟩,⟨2947940997423148,2947940997423164⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-8038366155344479),(-8038366155344463)⟩,⟨2181035147675254,2181035147675270⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-6822396923676402),(-6822396923676386)⟩,⟨1277479626855703,1277479626855719⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-5165161786501454),(-5165161786501438)⟩,⟨616959554092529,616959554092545⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-3602284809490772),(-3602284809490755)⟩,⟨261337701857511,261337701857529⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-2376942513864306),(-2376942513864286)⟩,⟨118492530930588,118492530930606⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1510283802865217),(-1510283802865197)⟩,⟨74550225894732,74550225894754⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-916495831337086),(-916495831337061)⟩,⟨56070635928598,56070635928621⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-492144706650779),(-492144706650758)⟩,⟨36278981571798,36278981571817⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-155133819548348),(-155133819548328)⟩,⟨12522245076002,12522245076020⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-9286708674281581),(-9286708674281235)⟩,⟨1942637245784428,1942637245784773⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 24) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_24 (tableDensity true) (fullFactor false 0 24) density1_contains hk0_0_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨46223133578575337,46223133578575338⟩,⟨(-1017546470540530),(-1017546470540529)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_24 0 24 ha0_0_24_contains + def realAnswer : RBox := ⟨36936424804293756,36936425004294103⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_24 +namespace hm0_0_0_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-17592),(-17576)⟩,⟨12242,12258⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-41099),(-41083)⟩,⟨28914,28930⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-41604),(-41588)⟩,⟨29875,29891⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-27704),(-27687)⟩,⟨20489,20506⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-13352),(-13335)⟩,⟨10258,10274⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-4873),(-4857)⟩,⟨3915,3933⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1397),(-1380)⟩,⟨1177,1193⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-330),(-314)⟩,⟨282,299⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-70),(-54)⟩,⟨51,67⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-19),(-3)⟩,⟨3,20⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-394473063),(-394473047)⟩,⟨(-6325675),(-6325659)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1002893581),(-1002893564)⟩,⟨(-2840996),(-2840980)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1203601858),(-1203601842)⟩,⟨27393262,27393278⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1037790305),(-1037790289)⟩,⟨60750250,60750266⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-708850075),(-708850059)⟩,⟨71491031,71491047⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-401150488),(-401150470)⟩,⟨58614472,58614488⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-193944185),(-193944168)⟩,⟨37327542,37327560⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-82419998),(-82419980)⟩,⟨19740521,19740537⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-31746449),(-31746430)⟩,⟨9113444,9113460⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-11466237),(-11466219)⟩,⟨3835832,3835848⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-4029248),(-4029230)⟩,⟨1533471,1533487⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1429895),(-1429879)⟩,⟨604561,604577⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-528732),(-528715)⟩,⟨242123,242139⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-205987),(-205971)⟩,⟨99629,99645⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-80442),(-80426)⟩,⟨40206,40222⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-21456),(-21440)⟩,⟨10883,10899⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-284594355821),(-284594355805)⟩,⟨(-104305215287),(-104305215271)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-757334827066),(-757334827050)⟩,⟨(-270878271382),(-270878271366)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-993809982168),(-993809982152)⟩,⟨(-339122815786),(-339122815770)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-975435624063),(-975435624047)⟩,⟨(-311060692650),(-311060692634)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-787124839321),(-787124839305)⟩,⟨(-229583948445),(-229583948429)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-545628181278),(-545628181262)⟩,⟨(-141710947446),(-141710947430)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-335021729514),(-335021729498)⟩,⟨(-75005013509),(-75005013493)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-187005569800),(-187005569784)⟩,⟨(-34918741571),(-34918741555)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-97179487129),(-97179487112)⟩,⟨(-14711033756),(-14711033740)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-48110191999),(-48110191983)⟩,⟨(-5776986646),(-5776986630)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-23207071190),(-23207071174)⟩,⟨(-2173907818),(-2173907802)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-11133255756),(-11133255740)⟩,⟨(-800263946),(-800263930)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-5385770629),(-5385770613)⟩,⟨(-291263440),(-291263424)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-2613709994),(-2613709978)⟩,⟨(-104835800),(-104835784)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-1193445411),(-1193445395)⟩,⟨(-36188044),(-36188028)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-345265297),(-345265281)⟩,⟨(-8716235),(-8716219)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2801562807728),(-2801562807711)⟩,⟨(-49984829552586),(-49984829552570)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-10740007572314),(-10740007572297)⟩,⟨(-134140064271922),(-134140064271904)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-23059913942908),(-23059913942889)⟩,⟨(-179375437570909),(-179375437570890)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-36556603589077),(-36556603589056)⟩,⟨(-181969478870719),(-181969478870696)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-45356634343441),(-45356634343417)⟩,⟨(-154453333000570),(-154453333000544)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-46016443069213),(-46016443069188)⟩,⟨(-114553913839516),(-114553913839490)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-39750488567312),(-39750488567285)⟩,⟨(-76186716267311),(-76186716267283)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-30319824884723),(-30319824884693)⟩,⟨(-46375095543475),(-46375095543454)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-21068219978973),(-21068219978954)⟩,⟨(-26353431596746),(-26353431596724)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-13700212884490),(-13700212884471)⟩,⟨(-14268661333485),(-14268661333465)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-8530328334252),(-8530328334235)⟩,⟨(-7516870613156),(-7516870613139)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-5169929341119),(-5169929341103)⟩,⟨(-3932618995549),(-3932618995533)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-3064469281900),(-3064469281884)⟩,⟨(-2070635397042),(-2070635397025)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1747998595674),(-1747998595658)⟩,⟨(-1085832915357),(-1085832915341)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-892258296393),(-892258296377)⟩,⟨(-526487528456),(-526487528440)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-273178549652),(-273178549636)⟩,⟨(-157383808750),(-157383808734)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1281408487830212,1281408487830228⟩,⟨(-16118477236679),(-16118477236663)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3512717060141090,3512717060141106⟩,⟨(-217547285235228),(-217547285235212)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨4916685028636545,4916685028636561⟩,⟨(-767259746609080),(-767259746609064)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨5364261565682735,5364261565682751⟩,⟨(-1506982282951835),(-1506982282951819)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5009929938060442,5009929938060458⟩,⟨(-2080196728774198),(-2080196728774182)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨4127822865263800,4127822865263816⟩,⟨(-2258420381789020),(-2258420381789004)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨3037988599697563,3037988599697580⟩,⟨(-2081222619032954),(-2081222619032938)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨2027040030874633,2027040030874649⟩,⟨(-1716099965690553),(-1716099965690537)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1251091465849018,1251091465849034⟩,⟨(-1308483384404137),(-1308483384404121)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨730563222779694,730563222779710⟩,⟨(-942386077702180),(-942386077702164)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨413507615155365,413507615155381⟩,⟨(-650653137539049),(-650653137539032)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨232405540512213,232405540512230⟩,⟨(-433960450250583),(-433960450250566)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨131414329715696,131414329715713⟩,⟨(-278797173211911),(-278797173211894)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨73434226827021,73434226827040⟩,⟨(-169033455207714),(-169033455207696)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨37290122057896,37290122057912⟩,⟨(-89845278191272),(-89845278191255)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨11414266815992,11414266816008⟩,⟨(-28066733394347),(-28066733394331)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨5310811015628984,5310811015629259⟩,⟨(-2589925695905050),(-2589925695904777)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 25) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_25 (tableDensity false) (fullFactor false 0 25) density0_contains hk0_0_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-81523502071867),(-81523502071865)⟩,⟨(-4451324002225048),(-4451324002225046)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_25 0 25 ha0_0_25_contains + def realAnswer : RBox := ⟨5229287413557117,5229287613557394⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_25 +namespace hm0_1_0_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3331),(-3315)⟩,⟨368,384⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-7683),(-7667)⟩,⟨991,1007⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-7616),(-7600)⟩,⟨1253,1269⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-4940),(-4924)⟩,⟨1090,1106⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-2329),(-2313)⟩,⟨688,704⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-840),(-824)⟩,⟨320,336⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-246),(-230)⟩,⟨108,124⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-61),(-45)⟩,⟨25,41⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-19),(-3)⟩,⟨0,16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-75100965),(-75100949)⟩,⟨(-47887632),(-47887616)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-192217191),(-192217175)⟩,⟨(-120181362),(-120181346)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-232346489),(-232346473)⟩,⟨(-140491651),(-140491635)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-200074117),(-200074101)⟩,⟨(-115766972),(-115766956)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-134719662),(-134719646)⟩,⟨(-73072603),(-73072587)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-74616433),(-74616415)⟩,⟨(-36282000),(-36281984)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-35478850),(-35478834)⟩,⟨(-14409577),(-14409561)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-15030069),(-15030053)⟩,⟨(-4666756),(-4666740)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-5852624),(-5852608)⟩,⟨(-1257804),(-1257788)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2153847),(-2153831)⟩,⟨(-287216),(-287200)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-769418),(-769402)⟩,⟨(-55852),(-55836)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-274065),(-274049)⟩,⟨(-8302),(-8286)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-99996),(-99978)⟩,⟨263,279⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-38024),(-38008)⟩,⟨1287,1303⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-14512),(-14496)⟩,⟨901,917⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3824),(-3808)⟩,⟨300,316⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-55427370937),(-55427370921)⟩,⟨(-84819974791),(-84819974775)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-146094063689),(-146094063673)⟩,⟨(-221000258873),(-221000258857)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-188992080878),(-188992080862)⟩,⟨(-278143970418),(-278143970402)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-183708520464),(-183708520448)⟩,⟨(-257086763976),(-257086763960)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-148887039936),(-148887039920)⟩,⟨(-193059992706),(-193059992690)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-105201318785),(-105201318769)⟩,⟨(-124304711400),(-124304711384)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-66181026705),(-66181026689)⟩,⟨(-71300831706),(-71300831690)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-37673695457),(-37673695441)⟩,⟨(-37425836068),(-37425836052)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-19831926698),(-19831926682)⟩,⟨(-18352243008),(-18352242992)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-9919373566),(-9919373550)⟩,⟨(-8584951254),(-8584951238)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-4847672016),(-4847672000)⟩,⟨(-3924584521),(-3924584505)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-2368524837),(-2368524821)⟩,⟨(-1798187605),(-1798187589)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1170599915),(-1170599899)⟩,⟨(-840878325),(-840878309)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-579719392),(-579719376)⟩,⟨(-399503831),(-399503815)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-268811109),(-268811093)⟩,⟨(-180411402),(-180411386)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-78408342),(-78408326)⟩,⟨(-51967508),(-51967492)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1759620102287),(-1759620102271)⟩,⟨(-16353732243974),(-16353732243958)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-5500014961846),(-5500014961828)⟩,⟨(-44772048040444),(-44772048040427)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-9248548273252),(-9248548273234)⟩,⟨(-61938758376833),(-61938758376813)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-12008496625884),(-12008496625865)⟩,⟨(-65227555067226),(-65227555067207)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-13139183898617),(-13139183898595)⟩,⟨(-57130663967855),(-57130663967835)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-12713996312024),(-12713996312002)⟩,⟨(-43455239041501),(-43455239041475)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-11051211324060),(-11051211324032)⟩,⟨(-29738944530322),(-29738944530301)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-8632164888835),(-8632164888810)⟩,⟨(-18894595806420),(-18894595806398)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-6088847437808),(-6088847437785)⟩,⟨(-11427517556816),(-11427517556793)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-3926581636144),(-3926581636127)⟩,⟨(-6697661901063),(-6697661901046)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-2352896463404),(-2352896463387)⟩,⟨(-3843351802127),(-3843351802110)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1335811653064),(-1335811653047)⟩,⟨(-2165345206957),(-2165345206941)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-733995252357),(-733995252341)⟩,⟨(-1194489487395),(-1194489487379)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-392746903466),(-392746903450)⟩,⟨(-637054219930),(-637054219914)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-192636326440),(-192636326424)⟩,⟨(-308596963054),(-308596963038)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-57963065809),(-57963065793)⟩,⟨(-91835471194),(-91835471178)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨38045522318243,38045522318259⟩,⟨(-2281197581796),(-2281197581780)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨98006546896323,98006546896339⟩,⟨(-31405694639138),(-31405694639122)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨91529034092396,91529034092412⟩,⟨(-121071189156166),(-121071189156150)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-28983272353776),(-28983272353760)⟩,⟨(-292771536608544),(-292771536608528)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-220344191098137),(-220344191098121)⟩,⟨(-547386792812240),(-547386792812224)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-351952033268007),(-351952033267991)⟩,⟨(-812067245766202),(-812067245766186)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-348606695716819),(-348606695716803)⟩,⟨(-960749740352515),(-960749740352499)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-253631824439390),(-253631824439374)⟩,⟨(-934321907524090),(-934321907524074)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-145984612557255),(-145984612557239)⟩,⟨(-779156970076822),(-779156970076806)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-69277621603464),(-69277621603448)⟩,⟨(-579582004308855),(-579582004308839)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-28850079282425),(-28850079282409)⟩,⟨(-397412072124399),(-397412072124382)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-12873356914772),(-12873356914756)⟩,⟨(-258175180269975),(-258175180269959)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-7987512618175),(-7987512618159)⟩,⟨(-161843052808519),(-161843052808503)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-5943262509506),(-5943262509490)⟩,⟨(-97161612415521),(-97161612415504)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3817163067807),(-3817163067790)⟩,⟨(-51785339412937),(-51785339412919)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1312582290234),(-1312582290218)⟩,⟨(-16261246215404),(-16261246215388)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-223681669751394),(-223681669751124)⟩,⟨(-1068102000197295),(-1068102000197028)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 25) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_25 (tableDensity true) (fullFactor false 0 25) density1_contains hk0_0_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨106607656555516,106607656555518⟩,⟨5820962156755830,5820962156755831⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_25 0 25 ha0_0_25_contains + def realAnswer : RBox := ⟨(-117074113195878),(-117073913195606)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_25 +namespace hm0_0_0_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-502),(-486)⟩,⟨(-714),(-698)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1159),(-1143)⟩,⟨(-1646),(-1630)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1176),(-1160)⟩,⟨(-1634),(-1618)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-788),(-770)⟩,⟨(-1061),(-1044)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-383),(-367)⟩,⟨(-497),(-480)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-145),(-129)⟩,⟨(-181),(-165)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-49),(-31)⟩,⟨(-55),(-38)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-17),(-1)⟩,⟨(-19),(-2)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨381601,381617⟩,⟨(-23794584),(-23794568)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨171260,171276⟩,⟨(-60119940),(-60119924)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1619088),(-1619072)⟩,⟨(-71268915),(-71268899)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3528071),(-3528055)⟩,⟨(-60343564),(-60343548)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-4055659),(-4055643)⟩,⟨(-40252061),(-40252045)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-3231700),(-3231684)⟩,⟨(-22135285),(-22135268)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1991492),(-1991476)⟩,⟨(-10354430),(-10354411)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1015611),(-1015595)⟩,⟨(-4242880),(-4242864)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-451076),(-451060)⟩,⟨(-1572111),(-1572095)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-182469),(-182452)⟩,⟨(-545666),(-545650)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-70148),(-70132)⟩,⟨(-184370),(-184354)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-26663),(-26646)⟩,⟨(-63061),(-63045)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-10339),(-10322)⟩,⟨(-22571),(-22554)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4148),(-4132)⟩,⟨(-8567),(-8550)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1646),(-1630)⟩,⟨(-3288),(-3272)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-448),(-432)⟩,⟨(-873),(-857)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨8392204267,8392204283⟩,⟨(-22897876661),(-22897876645)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨21692835814,21692835830⟩,⟨(-60648570208),(-60648570192)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨26908482183,26908482199⟩,⟨(-78851648109),(-78851648092)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨24348955199,24348955215⟩,⟨(-76346367098),(-76346367082)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨17657956524,17657956540⟩,⟨(-60529849394),(-60529849377)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨10671559363,10671559379⟩,⟨(-41078220917),(-41078220901)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨5513851519,5513851535⟩,⟨(-24619867898),(-24619867880)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2500277219,2500277235⟩,⟨(-13384208222),(-13384208205)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1024553922,1024553938⟩,⟨(-6764658227),(-6764658210)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨391188961,391188977⟩,⟨(-3256021359),(-3256021343)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨143231914,143231930⟩,⟨(-1528207917),(-1528207900)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨51403041,51403057⟩,⟨(-714742729),(-714742712)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨18296452,18296468⟩,⟨(-338160716),(-338160699)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨6468075,6468091⟩,⟨(-161200085),(-161200068)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2204471,2204487⟩,⟨(-72687788),(-72687772)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨527451,527467⟩,⟨(-20893068),(-20893052)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨5028288536455,5028288536471⟩,⟨(-281817113618),(-281817113602)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨13443431790475,13443431790491⟩,⟨(-1076121873242),(-1076121873226)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨17844129139212,17844129139228⟩,⟨(-2293128282385),(-2293128282369)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨17906352150885,17906352150902⟩,⟨(-3595686045422),(-3595686045406)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨14986720806504,14986720806520⟩,⟨(-4398995008229),(-4398995008213)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨10930012562777,10930012562793⟩,⟨(-4388706044538),(-4388706044521)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨7132042762364,7132042762382⟩,⟨(-3719652991511),(-3719652991493)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨4252379176255,4252379176274⟩,⟨(-2779147001011),(-2779147000995)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨2364797457785,2364797457801⟩,⟨(-1889884445956),(-1889884445938)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1252833491968,1252833491984⟩,⟨(-1202550567421),(-1202550567405)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨646278169002,646278169018⟩,⟨(-733220095310),(-733220095293)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨331624491314,331624491330⟩,⟨(-435876295023),(-435876295007)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨171692516363,171692516379⟩,⟨(-254067293001),(-254067292984)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨88829671957,88829671973⟩,⟨(-142991182558),(-142991182541)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨42667607239,42667607255⟩,⟨(-72308876915),(-72308876899)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨12693194874,12693194890⟩,⟨(-22032131280),(-22032131264)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1945537327494,1945537327510⟩,⟨154710264249170,154710264249186⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨26170747226651,26170747226667⟩,⟨422777275646657,422777275646673⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨91730759808253,91730759808269⟩,⟨588099515589135,588099515589151⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨178551246504317,178551246504333⟩,⟨635839020089458,635839020089474⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨243622496167567,243622496167583⟩,⟨586943318072107,586943318072123⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨260852089481822,260852089481839⟩,⟨476916002151369,476916002151385⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨236640019502791,236640019502807⟩,⟨345528689383000,345528689383016⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨191834906463263,191834906463279⟩,⟨226663049174412,226663049174428⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨143704707599629,143704707599645⟩,⟨137444567150331,137444567150347⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨101681741180107,101681741180123⟩,⟨78849916653499,78849916653515⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨69020249482336,69020249482352⟩,⟨43875355954032,43875355954048⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨45321585780794,45321585780810⟩,⟨24276160160230,24276160160246⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨28726853091813,28726853091829⟩,⟨13542129986659,13542129986676⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨17230821876092,17230821876108⟩,⟨7486031754264,7486031754280⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨9090301922471,9090301922487⟩,⟨3772968619735,3772968619751⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨2828826001973,2828826001989⟩,⟨1150437556030,1150437556046⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨290917828549811,290917828550072⟩,⟨620032834807317,620032834807582⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 26) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_26 (tableDensity false) (fullFactor false 0 26) density0_contains hk0_0_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨538808910475056,538808910475057⟩,⟨(-8211877414477),(-8211877414476)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_26 0 26 ha0_0_26_contains + def realAnswer : RBox := ⟨829726639024867,829726839025129⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_26 +namespace hm0_1_0_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-24),(-8)⟩,⟨(-142),(-126)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-46),(-30)⟩,⟨(-314),(-298)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-63),(-47)⟩,⟨(-306),(-290)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-48),(-32)⟩,⟨(-195),(-179)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-34),(-18)⟩,⟨(-94),(-78)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-18),(-2)⟩,⟨(-37),(-21)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨2888574,2888590⟩,⟨(-4530086),(-4530070)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨7204553,7204569⟩,⟨(-11522670),(-11522654)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨8319303,8319319⟩,⟨(-13757866),(-13757850)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨6732118,6732134⟩,⟨(-11633727),(-11633711)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨4150369,4150385⟩,⟨(-7650403),(-7650387)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2002859,2002875⟩,⟨(-4117527),(-4117511)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨769814,769830⟩,⟨(-1894231),(-1894215)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨240458,240474⟩,⟨(-773723),(-773707)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨62357,62373⟩,⟨(-289817),(-289801)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨13683,13699⟩,⟨(-102500),(-102484)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2551,2567⟩,⟨(-35211),(-35195)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨360,376⟩,⟨(-12092),(-12076)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-20),(-4)⟩,⟨(-4274),(-4258)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-64),(-48)⟩,⟨(-1587),(-1571)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-43),(-27)⟩,⟨(-599),(-583)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-22),(-6)⟩,⟨(-162),(-146)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨6824455401,6824455417⟩,⟨(-4459577043),(-4459577027)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨17698389165,17698389181⟩,⟨(-11699537992),(-11699537976)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨22069844540,22069844556⟩,⟨(-14995364861),(-14995364845)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨20123748932,20123748948⟩,⟨(-14378754498),(-14378754482)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨14848131271,14848131287⟩,⟨(-11449156721),(-11449156705)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨9359695246,9359695262⟩,⟨(-7919832861),(-7919832845)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨5240419307,5240419323⟩,⟨(-4863234239),(-4863234223)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2678964814,2678964830⟩,⟨(-2696255753),(-2696255737)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1277666054,1277666070⟩,⟨(-1380466109),(-1380466093)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨581089090,581089107⟩,⟨(-671310856),(-671310840)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨258465598,258465614⟩,⟨(-319213006),(-319212990)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨115450541,115450557⟩,⟨(-152050613),(-152050597)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨52799197,52799213⟩,⟨(-73496828),(-73496812)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨24639779,24639795⟩,⟨(-35753288),(-35753272)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨10988154,10988170⟩,⟨(-16372019),(-16372003)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨3144706,3144722⟩,⟨(-4744732),(-4744716)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1645122022516,1645122022532⟩,⟨(-177008791631),(-177008791615)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4486964101473,4486964101489⟩,⟨(-551153253869),(-551153253853)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨6161435894443,6161435894460⟩,⟨(-919861981675),(-919861981659)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨6418347925391,6418347925407⟩,⟨(-1181358821587),(-1181358821571)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨5543233293517,5543233293534⟩,⟨(-1274469447039),(-1274469447022)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨4146070022990,4146070023007⟩,⟨(-1212591415209),(-1212591415190)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2783782693314,2783782693331⟩,⟨(-1034080325922),(-1034080325906)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1732384773151,1732384773168⟩,⟨(-791201217359),(-791201217342)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1025302922922,1025302922939⟩,⟨(-546183769288),(-546183769272)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨587987542312,587987542328⟩,⟨(-344674197052),(-344674197036)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨330394523252,330394523268⟩,⟨(-202260329198),(-202260329181)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨182579625995,182579626011⟩,⟨(-112634726845),(-112634726829)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨99040796382,99040796398⟩,⟨(-60859194382),(-60859194366)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨52115820138,52115820154⟩,⟨(-32129363234),(-32129363218)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨25009391450,25009391466⟩,⟨(-15611552067),(-15611552051)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨7406646386,7406646402⟩,⟨(-4674788223),(-4674788207)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨275345727153,275345727169⟩,⟨4593414361532,4593414361548⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3778025275796,3778025275812⟩,⟨11796373537243,11796373537259⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨14473550779845,14473550779861⟩,⟨10954051696091,10954051696107⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨34680249740174,34680249740190⟩,⟨(-3417144885409),(-3417144885393)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨64084568219939,64084568219955⟩,⟨(-25787268413540),(-25787268413524)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨93761039450309,93761039450325⟩,⟨(-40641113839916),(-40641113839900)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨109208081262713,109208081262729⟩,⟨(-39639590953808),(-39639590953792)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨104424650140529,104424650140545⟩,⟨(-28361058416117),(-28361058416101)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨85563999983550,85563999983566⟩,⟨(-16041245234705),(-16041245234689)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨62535050683572,62535050683588⟩,⟨(-7480085752552),(-7480085752536)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨42158037100932,42158037100948⟩,⟨(-3062443151558),(-3062443151542)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨26964018807667,26964018807683⟩,⟨(-1344828807588),(-1344828807572)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨16676370251484,16676370251500⟩,⟨(-822898330515),(-822898330498)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨9904409606297,9904409606313⟩,⟨(-605736874968),(-605736874952)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨5239485606054,5239485606070⟩,⟨(-386183892603),(-386183892587)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1638958506875,1638958506891⟩,⟨(-132293246543),(-132293246527)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨118449036569417,118449036569678⟩,⟨(-24818996138158),(-24818996137897)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 26) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_26 (tableDensity true) (fullFactor false 0 26) density1_contains hk0_0_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-704596267544305),(-704596267544304)⟩,⟨10738608926622,10738608926623⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_26 0 26 ha0_0_26_contains + def realAnswer : RBox := ⟨(-586147330974888),(-586147130974626)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_26 +namespace hm0_0_0_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨20,36⟩,⟨(-28),(-12)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨56,73⟩,⟨(-51),(-32)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨54,70⟩,⟨(-48),(-32)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨30,46⟩,⟨(-37),(-21)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨9,25⟩,⟨(-21),(-4)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1382121,1382138⟩,⟨22160,22176⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨3470515,3470531⟩,⟨9933,9949⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨4063823,4063840⟩,⟨(-92161),(-92145)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨3378914,3378930⟩,⟨(-197320),(-197304)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨2201179,2201195⟩,⟨(-221576),(-221560)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1176261,1176279⟩,⟨(-171602),(-171585)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨532378,532394⟩,⟨(-102333),(-102317)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨210345,210362⟩,⟨(-50332),(-50316)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨74969,74987⟩,⟨(-21510),(-21493)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨24997,25016⟩,⟨(-8365),(-8349)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨8116,8133⟩,⟨(-3096),(-3079)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2669,2686⟩,⟨(-1139),(-1123)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨919,938⟩,⟨(-432),(-416)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨332,349⟩,⟨(-173),(-157)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨122,138⟩,⟨(-73),(-57)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨26,42⟩,⟨(-26),(-10)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1774082983,1774082999⟩,⟨650213311,650213327⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4676970498,4676970514⟩,⟨1672899736,1672899752⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨6024662441,6024662457⟩,⟨2056060581,2056060597⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨5754358117,5754358133⟩,⟨1835414846,1835414862⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4482488566,4482488582⟩,⟨1307864955,1307864971⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨2978208024,2978208041⟩,⟨773892721,773892737⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1742334034,1742334051⟩,⟨390348483,390348499⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨922501306,922501322⟩,⟨172406434,172406450⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨453476465,453476482⟩,⟨68716894,68716910⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨212214192,212214208⟩,⟨25509865,25509881⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨96912274,96912292⟩,⟨9088075,9088091⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨44188254,44188270⟩,⟨3179600,3179616⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨20446641,20446657⟩,⟨1106797,1106813⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨9573936,9573953⟩,⟨384282,384298⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨4263165,4263181⟩,⟨129310,129326⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1217469,1217485⟩,⟨30729,30745⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨27298832748,27298832764⟩,⟨487092993338,487092993354⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨103831488219,103831488235⟩,⟨1297395975964,1297395975980⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨219589579626,219589579642⟩,⟨1709387289947,1709387289963⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨340575246951,340575246968⟩,⟨1696801666686,1696801666702⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨410851223813,410851223829⟩,⟨1400342841933,1400342841949⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨403070931080,403070931097⟩,⟨1004275441376,1004275441393⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨335186537997,335186538014⟩,⟨642943309026,642943309042⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨245314019260,245314019276⟩,⟨375495739778,375495739794⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨163256087008,163256087024⟩,⟨204351246306,204351246322⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨101649562354,101649562370⟩,⟨105932559682,105932559700⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨60691409467,60691409483⟩,⟨53508901675,53508901691⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨35388585764,35388585780⟩,⟨26929765239,26929765255⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨20284299564,20284299580⟩,⟨13709349147,13709349163⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨11263974790,11263974806⟩,⟨6997893681,6997893698⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨5642921645,5642921661⟩,⟨3329813198,3329813214⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1711103244,1711103260⟩,⟨985806398,985806414⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-17987066299543),(-17987066299527)⟩,⟨226133430006,226133430022⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-48999370654034),(-48999370654018)⟩,⟨3031718613586,3031718613602⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-67739348922975),(-67739348922959)⟩,⟨10560859327824,10560859327840⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-72576831191780),(-72576831191764)⟩,⟨20371883474163,20371883474179⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-66218043277447),(-66218043277431)⟩,⟨27475527218531,27475527218547⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-53061612759684),(-53061612759668)⟩,⟨29013598419371,29013598419387⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-37844390546759),(-37844390546743)⟩,⟨25910592380778,25910592380794⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-24407298106929),(-24407298106913)⟩,⟨20650632332311,20650632332327⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-14540758228688),(-14540758228672)⟩,⟨15198293973670,15198293973686⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-8195305613416),(-8195305613400)⟩,⟨10565198622851,10565198622867⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-4483084985252),(-4483084985236)⟩,⟨7050546316596,7050546316613⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-2441916014599),(-2441916014583)⟩,⟨4558031182649,4558031182665⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1343835505006),(-1343835504989)⟩,⟨2850379149283,2850379149299⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-734881613635),(-734881613619)⟩,⟨1691421700429,1691421700445⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-367606616445),(-367606616429)⟩,⟨885670331462,885670331478⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-111657473677),(-111657473661)⟩,⟨274555606980,274555606996⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-69756364596688),(-69756364596425)⟩,⟨31558914846968,31558914847230⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 27) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_27 (tableDensity false) (fullFactor false 0 27) density0_contains hk0_0_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨796487118477,796487118478⟩,⟨62785624485306,62785624485307⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_27 0 27 ha0_0_27_contains + def realAnswer : RBox := ⟨(-68959977478211),(-68959777477947)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_27 +namespace hm0_1_0_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨263125,263141⟩,⟨167778,167794⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨665153,665169⟩,⟨415895,415911⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨784474,784490⟩,⟨474391,474407⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨651430,651446⟩,⟨376996,377012⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨418372,418388⟩,⟨227007,227023⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨218811,218827⟩,⟨106469,106485⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨97388,97404⟩,⟨39600,39616⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨38351,38367⟩,⟨11924,11940⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨13813,13829⟩,⟨2968,2984⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨4690,4707⟩,⟨621,637⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1543,1560⟩,⟨105,121⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨505,521⟩,⟨8,24⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨169,185⟩,⟨(-11),5⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨56,72⟩,⟨(-16),0⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨15,31⟩,⟨(-16),0⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨345519724,345519740⟩,⟨528746674,528746690⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨902227948,902227964⟩,⟨1364853763,1364853779⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1145737130,1145737146⟩,⟨1686333285,1686333301⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1083757174,1083757190⟩,⟨1516899412,1516899428⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨847839680,847839696⟩,⟨1099701660,1099701676⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨574168602,574168618⟩,⟨678678857,678678873⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨344151652,344151669⟩,⟨370911535,370911551⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨185831835,185831851⟩,⟨184670934,184670950⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨92538875,92538891⟩,⟨85660982,85660998⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨43752216,43752233⟩,⟨37877776,37877792⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨20242400,20242416⟩,⟨16392522,16392538⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨9399994,9400010⟩,⟨7138157,7138173⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4443772,4443788⟩,⟨3192597,3192613⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2123390,2123406⟩,⟨1463418,1463434⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨960208,960224⟩,⟨644456,644472⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨276475,276491⟩,⟨183242,183258⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨17146697104,17146697120⟩,⟨159363575808,159363575824⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨53185303242,53185303258⟩,⟨433021031015,433021031031⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨88101743265,88101743281⟩,⟨590220247370,590220247386⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨111915548949,111915548965⟩,⟨608178139741,608178139758⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨119044395162,119044395178⟩,⟨517935256999,517935257015⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨111370060411,111370060427⟩,⟨380936501311,380936501327⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨93180035140,93180035156⟩,⟨250939600788,250939600804⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨69836134455,69836134471⟩,⟨152959704061,152959704077⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨47181223989,47181224005⟩,⟨88588865668,88588865684⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨29135938543,29135938559⟩,⟨49709466377,49709466393⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨16743367251,16743367267⟩,⟨27351411431,27351411447⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨9145778102,9145778118⟩,⟨14825138409,14825138425⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨4859335574,4859335590⟩,⟨7907945336,7907945352⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2531078960,2531078976⟩,⟨4105603266,4105603282⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1218331169,1218331185⟩,⟨1951758057,1951758073⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨363063268,363063284⟩,⟨575231351,575231367⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-534044409270),(-534044409254)⟩,⟨32003938362,32003938378⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1367263869553),(-1367263869537)⟩,⟨437654728864,437654728880⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1262415307156),(-1262415307140)⟩,⟨1666176666827,1666176666843⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨387954975268,387954975284⟩,⟨3955934617698,3955934617714⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨2906192828476,2906192828492⟩,⟨7224839995960,7224839995976⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨4519239799146,4519239799162⟩,⟨10424867517379,10424867517395⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨4340522635647,4340522635663⟩,⟨11954151763802,11954151763818⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨3053948042840,3053948042856⟩,⟨11239065319704,11239065319720⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1697422218646,1697422218662⟩,⟨9048534724963,9048534724979⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨777750724734,777750724750⟩,⟨6497595744600,6497595744616⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨313045923104,313045923120⟩,⟨4306643703686,4306643703703⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨135288061181,135288061197⟩,⟨2711889536513,2711889536529⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨81638639408,81638639424⟩,⟨1654717603781,1654717603797⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨59450526262,59450526278⟩,⟨972243513675,972243513691⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨37623425791,37623425807⟩,⟨510482919016,510482919032⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12839807842,12839807858⟩,⟨159071291805,159071291821⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2656626364318,2656626364579⟩,⟨12682004706012,12682004706273⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 27) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_27 (tableDensity true) (fullFactor false 0 27) density1_contains hk0_0_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1041560078010),(-1041560078009)⟩,⟨(-82104278173094),(-82104278173093)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_27 0 27 ha0_0_27_contains + def realAnswer : RBox := ⟨1614966286308,1615166286570⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_27 +namespace hm0_0_0_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1252),(-1236)⟩,⟨77405,77421⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-566),(-550)⟩,⟨193181,193197⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨5050,5066⟩,⟨223445,223461⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨10633,10649⟩,⟨182445,182461⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨11667,11683⟩,⟨116072,116091⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨8779,8795⟩,⟨60271,60288⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨5063,5080⟩,⟨26392,26408⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨2395,2411⟩,⟨10049,10067⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨980,996⟩,⟨3440,3456⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨360,376⟩,⟨1096,1112⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨123,139⟩,⟨336,353⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨38,54⟩,⟨102,118⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨8,24⟩,⟨28,44⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨0,16⟩,⟨4,21⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-48578229),(-48578213)⟩,⟨132543538,132543554⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-124403073),(-124403057)⟩,⟨347789336,347789352⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-151493257),(-151493241)⟩,⟨443879744,443879760⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-133414501),(-133414485)⟩,⟨418234909,418234926⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-93412518),(-93412502)⟩,⟨320102109,320102125⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-54120056),(-54120040)⟩,⟨208220322,208220338⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-26648871),(-26648855)⟩,⟨118906656,118906672⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-11464388),(-11464372)⟩,⟨61315958,61315974⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4444535),(-4444519)⟩,⟨29315500,29315516⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1604222),(-1604206)⟩,⟨13338117,13338133⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-556085),(-556069)⟩,⟨5926592,5926609⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-189671),(-189655)⟩,⟨2634439,2634456⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-64575),(-64559)⟩,⟨1192170,1192186⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-22027),(-22011)⟩,⟨548307,548324⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-7321),(-7305)⟩,⟨241101,241117⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1736),(-1720)⟩,⟨68403,68419⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-45499794991),(-45499794975)⟩,⟨2549920598,2549920614⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-120737409849),(-120737409833)⟩,⟨9660588783,9660588799⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-157904483110),(-157904483094)⟩,⟨20277012151,20277012167⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-155048147065),(-155048147049)⟩,⟨31106842873,31106842889⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-126175985238),(-126175985222)⟩,⟨37002435958,37002435974⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-88982092465),(-88982092448)⟩,⟨35698021551,35698021567⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-55892252947),(-55892252931)⟩,⟨29126683404,29126683420⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-31974225922),(-31974225905)⟩,⟨20881196032,20881196048⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-17028771715),(-17028771698)⟩,⟨13599607467,13599607483⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-8637492679),(-8637492662)⟩,⟨8285714123,8285714139⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4272212635),(-4272212619)⟩,⟨4844405359,4844405375⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2108802582),(-2108802566)⟩,⟨2770643297,2770643313⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1055592257),(-1055592241)⟩,⟨1561655307,1561655323⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-531602486),(-531602470)⟩,⟨855626959,855626975⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-250581495),(-250581478)⟩,⟨424642979,424642996⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-73827526),(-73827510)⟩,⟨128145050,128145066⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-25345202586),(-25345202570)⟩,⟨(-2016542446541),(-2016542446525)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-338663287273),(-338663287257)⟩,⟨(-5476157335434),(-5476157335418)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1172441992656),(-1172441992640)⟩,⟨(-7523832621495),(-7523832621479)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2241347459483),(-2241347459467)⟩,⟨(-7988377372532),(-7988377372516)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-2988040613546),(-2988040613530)⟩,⟨(-7203911026747),(-7203911026731)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-3111879409469),(-3111879409453)⟩,⟨(-5692890754834),(-5692890754818)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-2735786053722),(-2735786053706)⟩,⟨(-3997003142880),(-3997003142864)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-2143659906501),(-2143659906485)⟩,⟨(-2534401406522),(-2534401406506)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1550014961519),(-1550014961503)⟩,⟨(-1483418279060),(-1483418279043)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1058593149125),(-1058593149109)⟩,⟨(-821382960704),(-821382960688)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-694519441938),(-694519441922)⟩,⟨(-441721572680),(-441721572664)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-442041334185),(-442041334168)⟩,⟨(-236861681693),(-236861681677)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-272727072343),(-272727072326)⟩,⟨(-128592686730),(-128592686714)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-160105603922),(-160105603906)⟩,⟨(-69565165885),(-69565165869)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-83209473298),(-83209473282)⟩,⟨(-34537455075),(-34537455059)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-25695688837),(-25695688821)⟩,⟨(-10450050986),(-10450050970)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-3310149051194),(-3310149050932)⟩,⟨(-7573127944408),(-7573127944146)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 28) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_28 (tableDensity false) (fullFactor false 0 28) density0_contains hk0_0_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-7053161085396),(-7053161085395)⟩,⟨74489399298,74489399300⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_28 0 28 ha0_0_28_contains + def realAnswer : RBox := ⟨(-10363410136590),(-10363210136327)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_28 +namespace hm0_1_0_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-9406),(-9390)⟩,⟨14730,14747⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-23162),(-23146)⟩,⟨37019,37035⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-26094),(-26078)⟩,⟨43127,43143⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-20367),(-20351)⟩,⟨35168,35184⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-11983),(-11967)⟩,⟨22057,22073⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-5469),(-5453)⟩,⟨11206,11222⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1973),(-1957)⟩,⟨4820,4836⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-577),(-561)⟩,⟨1826,1843⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-146),(-130)⟩,⟨627,644⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-36),(-20)⟩,⟨198,214⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16),0⟩,⟨59,75⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16),0⟩,⟨12,28⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-5),11⟩,⟨0,16⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-39503294),(-39503278)⟩,⟨25814152,25814168⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-101495341),(-101495325)⟩,⟨67092099,67092115⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-124250528),(-124250512)⟩,⟨84415767,84415783⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-110260401),(-110260385)⟩,⟨78769404,78769420⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-78541233),(-78541217)⟩,⟨60544361,60544377⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-47456054),(-47456038)⟩,⟨40140936,40140952⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-25316505),(-25316489)⟩,⟨23485700,23485717⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-12276162),(-12276146)⟩,⟨12351259,12351275⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-5538384),(-5538368)⟩,⟨5982131,5982147⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2381010),(-2380994)⟩,⟨2749846,2749862⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1002588),(-1002572)⟩,⟨1237860,1237876⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-425608),(-425592)⟩,⟨560387,560403⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-186168),(-186152)⟩,⟨259084,259101⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-83823),(-83807)⟩,⟨121601,121617⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-36458),(-36442)⟩,⟨54299,54315⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-10304),(-10288)⟩,⟨15527,15543⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-14886269650),(-14886269634)⟩,⟨1601666084,1601666100⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-40296960957),(-40296960941)⟩,⟨4949004076,4949004092⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-54519912749),(-54519912733)⟩,⟨8136829449,8136829465⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-55571215692),(-55571215676)⟩,⟨10223758689,10223758705⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-46666192775),(-46666192759)⟩,⟨10722674193,10722674209⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-33750961553),(-33750961537)⟩,⟨9863706083,9863706099⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-21813396885),(-21813396869)⟩,⟨8096770074,8096770090⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-13023621512),(-13023621495)⟩,⟨5944229926,5944229943⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-7381232107),(-7381232091)⟩,⟨3930270703,3930270719⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-4052586379),(-4052586363)⟩,⟨2375043029,2375043045⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-2183468766),(-2183468750)⟩,⟨1336580838,1336580854⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1160813946),(-1160813930)⟩,⟨716121005,716121021⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-608873519),(-608873503)⟩,⟨374146308,374146324⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-311885200),(-311885184)⟩,⟨192273586,192273602⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-146877878),(-146877862)⟩,⟨91683698,91683714⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-43079389),(-43079373)⟩,⟨27189957,27189973⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-3587024181),(-3587024165)⟩,⟨(-59872162831),(-59872162815)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-48888290566),(-48888290550)⟩,⟨(-152813844103),(-152813844087)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-184958730371),(-184958730355)⟩,⟨(-140293459222),(-140293459206)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-435136655795),(-435136655779)⟩,⟨42471467633,42471467649⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-785443190860),(-785443190844)⟩,⟨315831190523,315831190539⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1117718754292),(-1117718754276)⟩,⟨484595058398,484595058414⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1261822854106),(-1261822854090)⟩,⟨458321733661,458321733677⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1166471619514),(-1166471619498)⟩,⟨317115532089,317115532105⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-922746993365),(-922746993349)⟩,⟨173204284212,173204284228⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-651026369416),(-651026369400)⟩,⟨77981331559,77981331575⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-424241240226),(-424241240210)⟩,⟨30857674744,30857674760⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-263010299829),(-263010299813)⟩,⟨13123973995,13123974011⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-158327838978),(-158327838962)⟩,⟨7810097146,7810097162⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-92030174826),(-92030174810)⟩,⟨5626471638,5626471654⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-47960164739),(-47960164722)⟩,⟨3534511564,3534511580⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-14887491362),(-14887491346)⟩,⟨1201670048,1201670064⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1312537317417),(-1312537317157)⟩,⟨274613540667,274613540928⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 28) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_28 (tableDensity true) (fullFactor false 0 28) density1_contains hk0_0_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨9223364496286,9223364496287⟩,⟨(-97409214469),(-97409214467)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_28 0 28 ha0_0_28_contains + def realAnswer : RBox := ⟨7910727178869,7910927179130⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_28 +namespace hm0_0_0_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4194),(-4178)⟩,⟨(-76),(-60)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-10390),(-10374)⟩,⟨(-39),(-23)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-11871),(-11855)⟩,⟨260,276⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-9519),(-9503)⟩,⟨547,563⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-5919),(-5903)⟩,⟨585,601⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-2989),(-2973)⟩,⟨425,441⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1272),(-1256)⟩,⟨235,251⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-471),(-455)⟩,⟨103,119⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-162),(-146)⟩,⟨35,52⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-55),(-38)⟩,⟨7,23⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-22),(-5)⟩,⟨0,16⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-9561011),(-9560995)⟩,⟨(-3504197),(-3504181)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-24970654),(-24970638)⟩,⟨(-8932121),(-8932105)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-31576427),(-31576411)⟩,⟨(-10777448),(-10777432)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-29350330),(-29350314)⟩,⟨(-9363569),(-9363553)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-22071514),(-22071498)⟩,⟨(-6442015),(-6441999)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-14056280),(-14056264)⟩,⟨(-3654393),(-3654377)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-7835465),(-7835448)⟩,⟨(-1756671),(-1756655)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3935207),(-3935191)⟩,⟨(-736104),(-736088)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1829911),(-1829895)⟩,⟨(-277580),(-277564)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-809481),(-809464)⟩,⟨(-97419),(-97403)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-349964),(-349948)⟩,⟨(-32860),(-32844)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-151661),(-151643)⟩,⟨(-10932),(-10916)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-67125),(-67109)⟩,⟨(-3643),(-3627)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-30330),(-30314)⟩,⟨(-1227),(-1211)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-13174),(-13158)⟩,⟨(-407),(-391)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-3720),(-3704)⟩,⟨(-103),(-87)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-229969066),(-229969050)⟩,⟨(-4103620250),(-4103620234)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-867839308),(-867839292)⟩,⟨(-10848566948),(-10848566932)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-1807837357),(-1807837341)⟩,⟨(-14083533377),(-14083533360)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-2743245234),(-2743245218)⟩,⟨(-13679427260),(-13679427244)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-3217695639),(-3217695623)⟩,⟨(-10977107005),(-10977106989)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-3052662530),(-3052662514)⟩,⟨(-7612446716),(-7612446700)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2443825095),(-2443825079)⟩,⟨(-4691427690),(-4691427673)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1716187818),(-1716187802)⟩,⟨(-2628883485),(-2628883469)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1093856897),(-1093856881)⟩,⟨(-1370144356),(-1370144340)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-652125125),(-652125109)⟩,⟨(-680020983),(-680020967)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-373360540),(-373360523)⟩,⟨(-329347406),(-329347390)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-209444899),(-209444883)⟩,⟨(-159445024),(-159445008)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-116085664),(-116085647)⟩,⟨(-78477248),(-78477231)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-62754085),(-62754069)⟩,⟨(-38991629),(-38991613)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-30853599),(-30853583)⟩,⟨(-18207073),(-18207057)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-9265911),(-9265895)⟩,⟨(-5338334),(-5338318)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨218280292010,218280292026⟩,⟨(-2742754015),(-2742753999)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨590911146797,590911146813⟩,⟨(-36526504406),(-36526504390)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨806862337529,806862337545⟩,⟨(-125674050769),(-125674050753)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨848952100155,848952100171⟩,⟨(-238095506640),(-238095506624)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨756704735487,756704735503⟩,⟨(-313756746878),(-313756746862)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨589730246164,589730246180⟩,⟨(-322264233903),(-322264233887)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨407602958826,407602958842⟩,⟨(-278905357178),(-278905357162)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨254098501135,254098501151⟩,⟨(-214857006920),(-214857006904)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨146120646656,146120646672⟩,⟨(-152632999058),(-152632999042)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨79487188436,79487188452⟩,⟨(-102412155535),(-102412155519)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨42023271476,42023271492⟩,⟨(-66056526495),(-66056526478)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨22183320062,22183320078⟩,⟨(-41391976194),(-41391976178)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨11880966000,11880966016⟩,⟨(-25195281003),(-25195280987)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨6358128404,6358128420⟩,⟨(-14632690875),(-14632690859)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨3132986566,3132986582⟩,⟨(-7548047728),(-7548047712)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨944298246,944298262⟩,⟨(-2321936715),(-2321936699)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨794416575910,794416576170⟩,⟨(-336060724619),(-336060724358)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 29) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_29 (tableDensity false) (fullFactor false 0 29) density0_contains hk0_0_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-6725880994),(-6725880993)⟩,⟨(-764853195480),(-764853195479)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_29 0 29 ha0_0_29_contains + def realAnswer : RBox := ⟨787590694916,787790695177⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_29 +namespace hm0_1_0_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-805),(-789)⟩,⟨(-515),(-499)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2000),(-1984)⟩,⟨(-1251),(-1235)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-2299),(-2282)⟩,⟨(-1392),(-1376)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1842),(-1826)⟩,⟨(-1069),(-1053)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1133),(-1117)⟩,⟨(-618),(-602)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-562),(-546)⟩,⟨(-279),(-263)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-241),(-224)⟩,⟨(-102),(-86)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-93),(-76)⟩,⟨(-34),(-18)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-37),(-20)⟩,⟨(-16),0⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-16),0⟩,⟨(-5),11⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1862107),(-1862091)⟩,⟨(-2849575),(-2849559)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-4817138),(-4817122)⟩,⟨(-7287331),(-7287315)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-6005205),(-6005189)⟩,⟨(-8839310),(-8839294)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-5527811),(-5527795)⟩,⟨(-7738413),(-7738397)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-4174541),(-4174525)⟩,⟨(-5416207),(-5416191)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-2709668),(-2709652)⟩,⟨(-3204048),(-3204032)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-1547542),(-1547526)⟩,⟨(-1668484),(-1668467)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-792674),(-792657)⟩,⟨(-787984),(-787968)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-373411),(-373395)⟩,⟨(-345763),(-345747)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-166889),(-166873)⟩,⟨(-144524),(-144508)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-73100),(-73084)⟩,⟨(-59218),(-59202)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-32265),(-32249)⟩,⟨(-24510),(-24494)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-14594),(-14578)⟩,⟨(-10489),(-10473)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-6732),(-6716)⟩,⟨(-4643),(-4627)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2973),(-2957)⟩,⟨(-1998),(-1982)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-849),(-833)⟩,⟨(-567),(-551)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-144452038),(-144452022)⟩,⟨(-1342588322),(-1342588306)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-444636593),(-444636577)⟩,⟨(-3620735587),(-3620735571)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-725586359),(-725586343)⟩,⟨(-4862497376),(-4862497360)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-901771728),(-901771712)⟩,⟨(-4902694473),(-4902694457)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-932537280),(-932537264)⟩,⟨(-4059739226),(-4059739210)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-843497484),(-843497468)⟩,⟨(-2887297984),(-2887297968)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-679321537),(-679321521)⟩,⟨(-1830846406),(-1830846390)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-488525756),(-488525740)⟩,⟨(-1070687754),(-1070687738)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-316120651),(-316120635)⟩,⟨(-593821124),(-593821108)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-186934943),(-186934927)⟩,⟨(-319008279),(-319008263)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-103020182),(-103020166)⟩,⟨(-168301839),(-168301823)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-54140707),(-54140691)⟩,⟨(-87760323),(-87760307)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-27814697),(-27814681)⟩,⟨(-45264605),(-45264589)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-14102578),(-14102562)⟩,⟨(-22875855),(-22875839)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-6661644),(-6661628)⟩,⟨(-10672075),(-10672059)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1966060),(-1966044)⟩,⟨(-3114999),(-3114983)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨6480860090,6480860106⟩,⟨(-388172965),(-388172949)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨16490503119,16490503135⟩,⟨(-5272770152),(-5272770136)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨15053399963,15053399979⟩,⟨(-19823975524),(-19823975508)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-4489163525),(-4489163509)⟩,⟨(-46213218155),(-46213218139)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-33139917126),(-33139917110)⟩,⟨(-82445584711),(-82445584695)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-50171916098),(-50171916082)⟩,⟨(-115707815954),(-115707815938)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-46727090480),(-46727090464)⟩,⟨(-128602066843),(-128602066827)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-31793938859),(-31793938843)⟩,⟨(-116893206063),(-116893206047)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-17064698032),(-17064698016)⟩,⟨(-90857026162),(-90857026146)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-7549384225),(-7549384209)⟩,⟨(-62981859141),(-62981859125)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-2936890531),(-2936890515)⟩,⟨(-40351204018),(-40351204002)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1229246460),(-1229246444)⟩,⟨(-24628683690),(-24628683674)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-721410603),(-721410587)⟩,⟨(-14627025499),(-14627025483)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-514137891),(-514137875)⟩,⟨(-8411016227),(-8411016211)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-320598644),(-320598628)⟩,⟨(-4350521370),(-4350521354)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-108585579),(-108585563)⟩,⟨(-1345276031),(-1345276015)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-27440237045),(-27440236783)⟩,⟨(-131460952856),(-131460952596)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 29) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_29 (tableDensity true) (fullFactor false 0 29) density1_contains hk0_0_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨8795382837,8795382839⟩,⟨1000192640241,1000192640243⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_29 0 29 ha0_0_29_contains + def realAnswer : RBox := ⟨(-18744854208),(-18544853944)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_29 +namespace hm0_0_0_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_0_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨0,16⟩,⟨(-227),(-210)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-5),11⟩,⟨(-549),(-533)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-22),(-6)⟩,⟨(-618),(-600)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-32),(-16)⟩,⟨(-487),(-471)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-32),(-16)⟩,⟨(-300),(-284)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-31),(-15)⟩,⟨(-150),(-133)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-16),0⟩,⟨(-67),(-50)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-16),0⟩,⟨(-28),(-12)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨244344,244360⟩,⟨(-666701),(-666685)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨619940,619956⟩,⟨(-1733100),(-1733084)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨741167,741183⟩,⟨(-2171421),(-2171405)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨635272,635288⟩,⟨(-1991099),(-1991083)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨429456,429472⟩,⟨(-1471189),(-1471173)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨238535,238551⟩,⟨(-917311),(-917294)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨111937,111955⟩,⟨(-499147),(-499131)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨45681,45697⟩,⟨(-244163),(-244147)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨16751,16767⟩,⟨(-110434),(-110418)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨5710,5726⟩,⟨(-47500),(-47484)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1868,1884⟩,⟨(-19985),(-19969)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨603,619⟩,⟨(-8448),(-8431)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨191,207⟩,⟨(-3662),(-3646)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨58,74⟩,⟨(-1628),(-1611)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨12,28⟩,⟨(-703),(-687)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨0,16⟩,⟨(-203),(-187)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨357768214,357768230⟩,⟨(-20048836),(-20048820)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨942281808,942281825⟩,⟨(-75362097),(-75362081)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1214251578,1214251594⟩,⟨(-155809755),(-155809739)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1166680092,1166680109⟩,⟨(-233859972),(-233859956)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨923176314,923176330⟩,⟨(-270486281),(-270486264)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨629556175,629556191⟩,⟨(-252349319),(-252349303)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨380670825,380670842⟩,⟨(-198216833),(-198216817)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨208946729,208946746⟩,⟨(-136353852),(-136353836)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨106571957,106571974⟩,⟨(-85052779),(-85052763)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨51754718,51754734⟩,⟨(-49616397),(-49616381)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨24544079,24544095⟩,⟨(-27816843),(-27816827)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨11653974,11653990⟩,⟨(-15305503),(-15305487)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨5639952,5639968⟩,⟨(-8341752),(-8341736)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2764621,2764637⟩,⟨(-4449199),(-4449182)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1278813,1278829⟩,⟨(-2167044),(-2167028)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨373129,373145⟩,⟨(-647675),(-647659)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨286915983,286915999⟩,⟨22840127262,22840127278⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3808251105,3808251121⟩,⟨61637640718,61637640734⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨13022030680,13022030696⟩,⟨83644749186,83644749202⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨24449722279,24449722295⟩,⟨87214471509,87214471525⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨31848022841,31848022857⟩,⟨76836466502,76836466518⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨32261633382,32261633398⟩,⟨59055290228,59055290245⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨27486422755,27486422771⟩,⟨40181554276,40181554292⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨20817614693,20817614709⟩,⟨24627283607,24627283624⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨14529450340,14529450356⟩,⟨13913860001,13913860017⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨9577709323,9577709340⟩,⟨7435945383,7435945399⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨6073421880,6073421896⟩,⟨3864714526,3864714542⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨3746742430,3746742446⟩,⟨2008364965,2008364981⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2250050192,2250050209⟩,⟨1061131641,1061131657⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1292770994,1292771010⟩,⟨561754414,561754430⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨661872587,661872603⟩,⟨274729071,274729087⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨202823068,202823084⟩,⟨82485344,82485360⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨33057743039,33057743300⟩,⟨80615799120,80615799382⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_0_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 0 30) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_0_30 (tableDensity false) (fullFactor false 0 30) density0_contains hk0_0_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨80163171355,80163171356⟩,⟨(-587034738),(-587034737)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_0_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 0 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha0_0_30 0 30 ha0_0_30_contains + def realAnswer : RBox := ⟨113120914394,113320914656⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 0 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_0_30 +namespace hm0_1_0_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_0_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨19,35⟩,⟨(-50),(-34)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨57,73⟩,⟨(-112),(-96)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨64,80⟩,⟨(-126),(-110)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨45,61⟩,⟨(-100),(-84)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨22,38⟩,⟨(-63),(-47)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨4,20⟩,⟨(-36),(-20)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨0,16⟩,⟨(-17),(-1)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-11),5⟩,⟨(-16),0⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨198696,198712⟩,⟨(-129853),(-129837)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨505780,505796⟩,⟨(-334346),(-334330)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨607873,607889⟩,⟨(-412974),(-412958)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨525005,525021⟩,⟨(-375010),(-374994)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨361054,361070⟩,⟨(-278259),(-278243)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨209115,209131⟩,⟨(-176830),(-176814)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨106293,106309⟩,⟨(-98586),(-98569)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨48889,48905⟩,⟨(-49187),(-49171)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨20858,20874⟩,⟨(-22541),(-22525)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨8471,8487⟩,⟨(-9799),(-9783)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3372,3388⟩,⟨(-4180),(-4163)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1355,1371⟩,⟨(-1803),(-1787)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨561,577⟩,⟨(-801),(-785)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨240,256⟩,⟨(-368),(-352)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨96,112⟩,⟨(-163),(-147)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨21,37⟩,⟨(-52),(-36)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨117051421,117051437⟩,⟨(-12593674),(-12593658)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨314484490,314484506⟩,⟨(-38616293),(-38616277)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨419221441,419221457⟩,⟨(-62546490),(-62546474)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨418121309,418121325⟩,⟨(-76889184),(-76889168)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨341412539,341412555⟩,⟨(-78399805),(-78399789)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨238773236,238773252⟩,⟨(-69729444),(-69729428)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨148549674,148549690⟩,⟨(-55097302),(-55097286)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨85091638,85091654⟩,⟨(-38812582),(-38812566)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨46182355,46182371⟩,⟨(-24579736),(-24579720)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨24275300,24275319⟩,⟨(-14223384),(-14223367)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨12540699,12540715⟩,⟨(-7676109),(-7676092)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨6413890,6413906⟩,⟨(-3956860),(-3956844)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3252925,3252941⟩,⟨(-1998913),(-1998897)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1621955,1621971⟩,⟨(-999914),(-999898)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨749573,749589⟩,⟨(-467903),(-467887)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨217722,217738⟩,⟨(-137429),(-137413)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨40606259,40606275⟩,⟨678136588,678136604⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨549731081,549731097⟩,⟨1720214730,1720214746⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2053929387,2053929403⟩,⟨1561386749,1561386765⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨4744467157,4744467173⟩,⟨(-458672193),(-458672177)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨8365710184,8365710200⟩,⟨(-3361478545),(-3361478529)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨11579177980,11579177996⟩,⟨(-5021427717),(-5021427701)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨12670219874,12670219890⟩,⟨(-4605254064),(-4605254048)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨11323799759,11323799775⟩,⟨(-3081476121),(-3081476105)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨8648137729,8648137745⟩,⟨(-1625273716),(-1625273700)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨5890064889,5890064905⟩,⟨(-706512368),(-706512352)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨3710107457,3710107473⟩,⟨(-270208150),(-270208134)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨2229430989,2229431006⟩,⟨(-111300473),(-111300457)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1306281558,1306281574⟩,⟨(-64415557),(-64415541)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨743098577,743098593⟩,⟨(-45415374),(-45415358)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨381487079,381487095⟩,⟨(-28110718),(-28110702)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨117510892,117510908⟩,⟨(-9484975),(-9484959)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨12755719721,12755719981⟩,⟨(-2652985474),(-2652985216)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_0_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 0 30) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_0_30 (tableDensity true) (fullFactor false 0 30) density1_contains hk0_0_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-104828762543),(-104828762541)⟩,⟨767660810,767660811⟩⟩ +lemma atomChecked : tableAtomBox true ha0_0_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 0 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha0_0_30 0 30 ha0_0_30_contains + def realAnswer : RBox := ⟨(-92173042822),(-91973042560)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 0 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_0_30 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_4.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_4.lean new file mode 100644 index 0000000000000000000000000000000000000000..efd26a69cc8fb6c8a43777ebae6b8fbf1b782102 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_4.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨181105098684666324931513920545,181105098684666481680261905656⟩,⟨297464283134938735949749882490,297464283134938892706149468538⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨555172662030313261388280917122,555172662030313630905186073583⟩,⟨873982685987612256392037902156,873982685987612625931364743820⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨961555266060437438954422568801,961555266060437810721266627174⟩,⟨1395939988698436967864701995975,1395939988698437339667099923329⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1411524622333719895469141586284,1411524622333720128969772679916⟩,⟨1832366068018008057088712656591,1832366068018008290635141534347⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1898499437566707693446638028731,1898499437566707790777575197189⟩,⟨2158074796343310006736983409320,2158074796343310104119928629899⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2394479339389789551117547234345,2394479339389789578738936892557⟩,⟨2351384138923050416140327652585,2351384138923050443814840159478⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨2856905836023885295245505722745,2856905836023885301260026822979⟩,⟨2395024298004332645732517503490,2395024298004332651795181275042⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨3238694320229854199327247861517,3238694320229854200897876227958⟩,⟨2285318904051645837196820883196,2285318904051645838805291203672⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3494352081667425047492660761159,3494352081667425048369683670469⟩,⟨2040162189192616597369319321543,2040162189192616598269977566546⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨3585750971753892947461013113335,3585750971753892948189203637966⟩,⟨1698266406566200697181598208276,1698266406566200697917377601486⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3488492583831588771503746599455,3488492583831588772132923675804⟩,⟨1311851065681506638337507504397,1311851065681506638959140842419⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨3194957597088787952924543803238,3194957597088787953450944459244⟩,⟨935552199279551225152736786346,935552199279551225659409644722⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2713312187915515938084605997397,2713312187915515938501347026352⟩,⟨612757391395992799453954105815,612757391395992799844330734071⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2066696342137499006771975989436,2066696342137499007071757056656⟩,⟨364129471322505586556231742828,364129471322505586830385561828⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1292822916692468392075320058216,1292822916692468392255370708155⟩,⟨185814462285841265800409060399,185814462285841265962090170801⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨439689099505985848549526816316,439689099505985848609257711208⟩,⟨56165940917648688697590982536,56165940917648688750763416470⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-21017201849461295332514696330),(-21017201849461123008052569410)⟩,⟨246319982046945932322746046767,246319982046946104649844946551⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-55366249769712619947064810282),(-55366249769711962818179744403)⟩,⟨734057836155272730470855699189,734057836155273387607928569606⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-67422454260014638373551460261),(-67422454260012946954322298017)⟩,⟨1205298384573085852657231299298,1205298384573087544090917912285⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-44993865964465677036833906521),(-44993865964461555471446034208)⟩,⟨1646096862092760038194719967826,1646096862092764159781816925362⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨20397879341340428954358398872,20397879341349921540574808142⟩,⟨2039247872171961057690911695156,2039247872171970550306998368115⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨131868574450658454988857820167,131868574450677993639551512560⟩,⟨2365848612935132882132532801189,2365848612935152420821764129660⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨284353582503681939550498689856,284353582503715335782954922524⟩,⟨2607826431920244313649327601239,2607826431920277709928732799384⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨462386186237954853889833390859,462386186237999124059947796026⟩,⟨2749344323560116611962688057821,2749344323560160882186897535541⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨641505047832091319396368166084,641505047832136820834400951649⟩,⟨2777882409272592276948438976503,2777882409272637778445475411004⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨792801801097780548484575234367,792801801097816757743058024928⟩,⟨2686615340519978814043964092197,2686615340520015023363271818397⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨888665677913775725988953936933,888665677913798002018056005563⟩,⟨2477173267913652321195912615356,2477173267913674597284096139968⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨907942890420666024452265321487,907942890420677320395790055564⟩,⟨2161322352278217321676936379612,2161322352278228617674193543828⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨838721736817143731255257329743,838721736817148811757863282311⟩,⟨1759622147401210965325908204713,1759622147401216045873644840208⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨679923638334561255671233653686,679923638334563396853072334115⟩,⟨1296011526761882066407820589613,1296011526761884207623639071234⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨443406760701877943524736213911,443406760701878788987808783331⟩,⟨792299300312872251750835355203,792299300312873097234967886519⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨153991210513877080820822728811,153991210513877303589709790068⟩,⟨266365390020229266684986888923,266365390020229489461002313326⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-113571321240514163225906408434),(-113571321240514163186223294431)⟩,⟨88058577478735315264748989501,88058577478735315301197957991⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-334804169317781008778521218933),(-334804169317781008659136744049)⟩,⟨268655488854974571722368092716,268655488854974571832311492384⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-538559707936022635277096062639),(-538559707936022635077839594119)⟩,⟨461648272320344114868631336239,461648272320344115053281214058⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-715246502858547439371737622614),(-715246502858547439093265692049)⟩,⟨672095216504052147528721814269,672095216504052147789067835282⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-857356959594501612241346670574),(-857356959594501611886054974189)⟩,⟨898777915718823550298499814477,898777915718823550634243292505⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-958027889601746568731784826483),(-958027889601746568296980681615)⟩,⟨1132203068242281811350776129221,1132203068242281811767029311010⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1010210266168079595831069062314),(-1010210266168079595296647542226)⟩,⟨1356265076273465459491137002204,1356265076273465460010196097817⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1009017409330155100265702941157),(-1009017409330155099468081131180)⟩,⟨1551397939230774969716875761055,1551397939230774970504045627441⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-954861101525778461628833071353),(-954861101525778459189085463285)⟩,⟨1696588254209009629088063467528,1696588254209009631523198840804⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-854794784023681482192934605553),(-854794784023681468387154054472)⟩,⟨1771322955956867478108253984591,1771322955956867491915152816227⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-722140270401680290959271478244),(-722140270401680218254488566236)⟩,⟨1758140579098226101692714287058,1758140579098226174403324053362⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-574257688673065111180581915434),(-574257688673064835618597524690)⟩,⟨1644678505954331099434317612511,1644678505954331375005160249055⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-427529616761234972412462328129),(-427529616761234273069463060271)⟩,⟨1425315752500939419220220957365,1425315752500940118573109702780⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-291726201702706388982137438228),(-291726201702705225047674043945)⟩,⟨1104419038979902701897980329639,1104419038979903865841300799638⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-168711266349908443448071406364),(-168711266349907251229288063818)⟩,⟨699432461376053105334411234799,699432461376054297559284618127⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-55083948179887743973949215922),(-55083948179887231498672523224)⟩,⟨239407283014551161565145070697,239407283014551674042580747852⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-66537049827543888645786903013),(-66537049827543742043330745695)⟩,⟨12773516647086121309221546652,12773516647086267907299103289⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-199054703458277211144744285092),(-199054703458276866284637931902)⟩,⟨40298528509496815464502444486,40298528509497160311659180132⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-329307491281423928933522812667),(-329307491281423582943170570213)⟩,⟨73245884167214907186790478763,73245884167215253156206450875⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-454493155029243082949214667243),(-454493155029242865837212073269)⟩,⟨113888591007130349511918905326,113888591007130566595957405829⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-570096437117910784126736772729),(-570096437117910693295680064553)⟩,⟨163236599860855998689382242740,163236599860856089486747263918⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-670566384691301181957434818253),(-670566384691301156006172322818)⟩,⟨221275792241043391987649384171,221275792241043417901067311059⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-750783157834713811077805580954),(-750783157834713805553631460367)⟩,⟨286130161413028834316929682130,286130161413028839800863665451⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-806357916691041669363313289719),(-806357916691041668176045284684)⟩,⟨352567564483179921846127768165,352567564483179922992607696462⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-832926695240112439537564187734),(-832926695240112439044111059995)⟩,⟨412088367165034037536458450927,412088367165034037990408795879⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-826167317396477961964286345340),(-826167317396477961591029245276)⟩,⟨454688083905352243649131607963,454688083905352243985854583077⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-782748688731271032564441890410),(-782748688731271032241149770301)⟩,⟨471115212899673614039943077959,471115212899673614331051998356⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-701721126392892265364336447927),(-701721126392892265088136438255)⟩,⟨454876259095398687920619755331,454876259095398688169937619785⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-585584793947924208833478421401),(-585584793947924208610112507163)⟩,⟨403277875798376837777943821666,403277875798376837980267622884⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-440046752763867080686220682755),(-440046752763867080522452559926)⟩,⟨317638339369376553747151957099,317638339369376553895938488091⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-272799928735946222619181023135),(-272799928735946222519458854270)⟩,⟨203419987069271718895306483840,203419987069271718986099742071⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-92368204564113883982529776809),(-92368204564113883949137935328)⟩,⟨70035260694830124205689026975,70035260694830124236124385172⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-17065774660018009315157590570),(-17065774660017652914280495203)⟩,⟨(-30948688418291118690629407375),(-30948688418290762291955067520)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-52932710063517406548794012456),(-52932710063516044723318221583)⟩,⟨(-90397436351185026007739695175),(-90397436351183664188801812093)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-93779182907870405389830496197),(-93779182907866886184357819432)⟩,⟨(-142696064625497688190193683401),(-142696064625494168995485118635)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-142085004043020732786035184200),(-142085004043012106834608028309)⟩,⟨(-184145719738097556857816777247),(-184145719738088930921170431427)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-198382047621341597932277754750),(-198382047621321573455599976437)⟩,⟨(-212448989161545730825973500481),(-212448989161525706367806828118)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-260296457355807014263740484140),(-260296457355765408411452183587)⟩,⟨(-226350335096661542838488150120),(-226350335096619937007925057334)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-322950541236897659377400794669),(-322950541236825880235186941335)⟩,⟨(-225048124909232699861898628044),(-225048124909160920743895952023)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-380223687502180395104688794263),(-380223687502084140557437190351)⟩,⟨(-208583311027909877133624225579),(-208583311027813622612338869977)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-425662627111660270532708529948),(-425662627111559934524005839024)⟩,⟨(-178698655372626792567403078418),(-178698655372526456585645572253)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-453157078153242987623610127175),(-453157078153161841856309382715)⟩,⟨(-139194865253425428591832639249),(-139194865253344282851506886813)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-457633354141058885078325984519),(-457633354141008072695788029900)⟩,⟨(-95810114374562184834429123564),(-95810114374511372477697799621)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-435254788499862612284435755210),(-435254788499836371677952174078)⟩,⟨(-55581529501792777849512654807),(-55581529501766537266300533784)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-383250836684428125387861497308),(-383250836684416114896069268519)⟩,⟨(-24841123802157766906795160197),(-24841123802145756434511396298)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-301073470829347976562418930142),(-301073470829342835926888442926)⟩,⟨(-6433280688188404419498998640),(-6433280688183263798694034343)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-192559725760313070380917833960),(-192559725760311015508620950798)⟩,⟨957085653825957801453004294,957085653828012664596889201⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-66245163148915949627924969630),(-66245163148915403758124569568)⟩,⟨1142250113666275041373663014,1142250113666820908069960682⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨7486795624458438550044279938,7486795624458438553701311349⟩,⟨(-3107696740555840117945169454),(-3107696740555840114931308935)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨21811828828721452115174390334,21811828828721452126372543655⟩,⟨(-10388526760483702642373510975),(-10388526760483702633061699025)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨34418883249506887074536901120,34418883249506887093751596003⟩,⟨(-20666034857415959186202676635),(-20666034857415959169895261735)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨44853925021630293372224719420,44853925021630293400203045712⟩,⟨(-35097719668074218094487359181),(-35097719668074218070115513138)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨52999904340630628252619161076,52999904340630628290497431118⟩,⟨(-53295157640921988948684616106),(-53295157640921988914707544156)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨58171444535524996084487135120,58171444535524996135367231533⟩,⟨(-73356224882526827593254686590),(-73356224882526827546248126728)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨58957053942814042436231317624,58957053942814042512531845724⟩,⟨(-93103673332408356991476279447),(-93103673332408356918722566198)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨54403773285920267068272313899,54403773285920267249293827214⟩,⟨(-110902230951982435204080798756),(-110902230951982435025874375461)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨44918023904356484169023250135,44918023904356485106698724619⟩,⟨(-125328723104616560106901990514),(-125328723104616559170944352872)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨32191144744095061552308242863,32191144744095067920796474048⟩,⟨(-134836927407564513432071286993),(-134836927407564507064111862454)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨18777439754476056124240163193,18777439754476091131584466238⟩,⟨(-137795742445877834111604379704),(-137795742445877799103757714400)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨7446313673601414260344078016,7446313673601549365551880659⟩,⟨(-132527867672608062487593311598),(-132527867672607927381216697496)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨86555401258228186554616491,86555401258575320385883636⟩,⟨(-117560687685530474726909328106),(-117560687685530127591630265224)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-3093712188193470738425927212),(-3093712188192887418796800793)⟩,⟨(-92573103319843498749802848743),(-92573103319842915428820948600)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3102052609639882208177862186),(-3102052609639280329913338915)⟩,⟨(-59149521926399089200576920069),(-59149521926398487321366518996)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1239090109977252356643187186),(-1239090109976992383369657202)⟩,⟨(-20319102784193269794383921534),(-20319102784193009820772331131)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3018375408590773585754361277660,3018375408590901432405452194440⟩,⟨11064243482674058487552215041200,11064243482674186334206499176539⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 0) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_0 (tableDensity false) (fullFactor true 0 0) density0_contains hk0_1_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-7715858200445238173369943992),(-7715858200445238151149556090)⟩,⟨(-97438240279210529403819607740),(-97438240279210529386017979622)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_0 0 0 ha0_1_0_contains + def realAnswer : RBox := ⟨3010659550390328347580891333668,3010659550390456194254402638350⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_0 +namespace hm0_1_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨23987746498795111253519818150,23987746498795239657377308606⟩,⟨54512665381533665073700658711,54512665381533793475414442875⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨73438571112954239718949722462,73438571112954542297959515360⟩,⟨161990507866890673886387542222,161990507866890976458952429559⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨126157756810674372986789847620,126157756810674677159760745117⟩,⟨262970020436026294782646893848,262970020436026598944811880238⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨182613983882647165297380728096,182613983882647356080066167421⟩,⟨348182771210624733525112990397,348182771210624924292494222301⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨244962740012336082958065373253,244962740012336162275842519280⟩,⟨405014534720374199319608671288,405014534720374278617271533704⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨318282814693352839730653479664,318282814693352862061933196011⟩,⟨424769096046521624831738526890,424769096046521647137545902451⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨404405183872296206399204944323,404405183872296211075874358347⟩,⟨409121798412753284175199381064,409121798412753288820560158010⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨495361676571571787961804751581,495361676571571789000959365174⟩,⟨367525880113423271374273144705,367525880113423272376415670532⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨574948728107322179898764300366,574948728107322180372072148813⟩,⟨310890351920334079081953550592,310890351920334079513581968437⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨624921202345280120765214819124,624921202345280121130591302300⟩,⟨248324792259936759049530794903,248324792259936759370121476384⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨630939461260942682818876893723,630939461260942683126764090987⟩,⟨186069716760715103876605050316,186069716760715104139015447174⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨587391678267169209662631358819,587391678267169209915673196183⟩,⟨127588496106861839570098065304,127588496106861839779972496455⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨499272830317995971393729148058,499272830317995971591021869753⟩,⟨75935865637419025179112856991,75935865637419025338737940538⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨378096324256505942916384896686,378096324256505943056056309503⟩,⟨36045407390318522528889809265,36045407390318522639148029368⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨235256183853140911124454271374,235256183853140911207181031741⟩,⟨12029212144485240499616397769,12029212144485240563570736992⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨79807272219274607987997254928,79807272219274608015255166016⟩,⟨2131027265866109552078310204,2131027265866109572855762012⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-21154050055309797188055469844),(-21154050055309655298263036834)⟩,⟨32236043250729691897387308480,32236043250729833787023217665⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-60045002035859377311561124242),(-60045002035858836031116905207)⟩,⟨96082786566868229013315131326,96082786566868770293259409902⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-89070002950787184444542446424),(-89070002950785790246280327757)⟩,⟨158181158762834963841493050204,158181158762836358038818160530⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-103256471232665966673606466907),(-103256471232662566403600974866)⟩,⟨217995524895371583957307092057,217995524895374984225792464488⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-100251404994264149693737662326),(-100251404994256311475059595989)⟩,⟨275321130332147886846241640226,275321130332155725062631123175⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-81147861541565499340619762882),(-81147861541549352662945750159)⟩,⟨329120665714296041426593423222,329120665714312188101019662099⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-49601775374704427502073644908),(-49601775374676804909553038302)⟩,⟨376182742785488598286491783214,376182742785516220874655973855⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-9911488516249337914413787254),(-9911488516212704105759699746)⟩,⟨411806528346823004423636940301,411806528346859638226791508246⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨33431178894544488461473226663,33431178894582139670964807199⟩,⟨431978789800558531861269410724,431978789800596183064162816325⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨74871008382008753828128720968,74871008382038699624031769623⟩,⟨434530342559748685150862675961,434530342559778630939181375924⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨107442653137449026772490932335,107442653137467431502737515382⟩,⟨418578170056030847111680943996,418578170056049251833724179119⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨124231620568134734228748441288,124231620568144055308856362994⟩,⟨383091519294575942341903080961,383091519294585263413817699083⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨121532666537745974028866133250,121532666537750160651451349208⟩,⟨326712856837243229960937079042,326712856837247416576145023222⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨100592898696781434301372781176,100592898696783196581164413650⟩,⟨249969483906246146564657572728,249969483906247908838620287839⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨65905273434782570584753689323,65905273434783265784742662735⟩,⟨156799006678135175240970915966,156799006678135870437233005370⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨22888737778993094524483872894,22888737778993277608651596278⟩,⟨53387743528338589348935982697,53387743528338772431816287505⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-32256292749679947346968845961),(-32256292749679947329644837570)⟩,⟨3494561798666728256984420833,3494561798666728274141860266⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-96334278237355037901146960366),(-96334278237355037848348285735)⟩,⟨11628916105256131488743862419,11628916105256131541039899925⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-158343364658321302037672922731),(-158343364658321301947846358255)⟩,⟨22566851090610442005173403901,22566851090610442094213673935⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-214841772376335825653711707748),(-214841772376335825525410175047)⟩,⟨36978273293587479900319792653,36978273293587480027639640103⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-260629724936242994780119380193),(-260629724936242994612547264326)⟩,⟨55798932428340363068305697929,55798932428340363234823458917⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-291325586138961062849577457480),(-291325586138961062637834152231)⟩,⟨81116451083447325703099012545,81116451083447325913780414678⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-306033993623805213889360672730),(-306033993623805213612380615365)⟩,⟨114181443436575627654382405441,114181443436575627930361345893⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-306855043898042688938078714067),(-306855043898042688453159550983)⟩,⟨152641090559231374811085487606,152641090559231375295191983877⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-296630100904422307017981739286),(-296630100904422305185785833951)⟩,⟨190290395589438987283833076048,190290395589438989115519214068⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-277389973500672499637330687289),(-277389973500672488518539924644)⟩,⟨218865062564666231573320431318,218865062564666242691911985362⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-249682067894225529194539530714),(-249682067894225470046278068478)⟩,⟨230622879953817562466424246603,230622879953817621614755560828⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-212983194855942566311996306129),(-212983194855942341710614681196)⟩,⟨221381293244304435482447982415,221381293244304660084106734205⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-167947461831498635237304012541),(-167947461831498064677232101950)⟩,⟨192337390326978985061213269290,192337390326979555621674745520⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-118351816794535349535641840695),(-118351816794534399240177740311)⟩,⟨148140213303585296315478736156,148140213303586246611301417925⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-69121869250368422799572252555),(-69121869250367448919516601630)⟩,⟨93383140164925024585480622024,93383140164925998465775031641⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-22566263052466532110576942300),(-22566263052466113381542760708)⟩,⟨31915897171285639586174902466,31915897171286058315288492234⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-20382964208567168387120544312),(-20382964208567045212189038106)⟩,⟨(-9871833779348368234780444970),(-9871833779348245059367970493)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-60401767733199942681756122459),(-60401767733199653128628900588)⟩,⟨(-28694372987837743377853536343),(-28694372987837453823315418781)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-98281483565912000901387334188),(-98281483565911710806614346954)⟩,⟨(-44633188784063340001570605815),(-44633188784063049904564574585)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-133239666873947282803186038081),(-133239666873947101172747723515)⟩,⟨(-55687171614636988784472779759),(-55687171614636807151150885032)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-165362168701657086568139703461),(-165362168701657010843524300977)⟩,⟨(-60469408918641904090220401780),(-60469408918641828362305069031)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-194951452530114693779970499049),(-194951452530114672293485857341)⟩,⟨(-59214250022686325868702806561),(-59214250022686304378729905904)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-221065281824124320162613688949),(-221065281824124315702313380119)⟩,⟨(-53591229039491418261554739671),(-53591229039491413797762761500)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-241254318433243804535431689058),(-241254318433243803686575597607)⟩,⟨(-45203519851115133437048836981),(-45203519851115132584886872373)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-252845423982267507116827912882),(-252845423982267506847923893452)⟩,⟨(-34844537958186175411795863536),(-34844537958186175139913987790)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-254046944543648715684899630019),(-254046944543648715513151611560)⟩,⟨(-23059575124412958675191512196),(-23059575124412958500900193198)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-244108817291628364271752161774),(-244108817291628364132139813993)⟩,⟨(-10960849345087974066797358291),(-10960849345087973925146804573)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-222793846152658978098605565157),(-222793846152658977983170395808)⟩,⟨(-443434453637705882948257038),(-443434453637705765966608024)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-189934344007629855343518018408),(-189934344007629855252148003530)⟩,⟨6554722770941624553647760035,6554722770941624646119537702⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-145825828892209827350002601898),(-145825828892209827284269090618)⟩,⟨9059282820678726256743990034,9059282820678726323196128419⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-91983878116333625753650946693),(-91983878116333625714253104093)⟩,⟨7371815293159559766007936123,7371815293159559805806487654⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-31447689918558536935894478371),(-31447689918558536922816947635)⟩,⟨2795935608007611259023516358,2795935608007611272228472405⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-6120013587424862683675609396),(-6120013587424569778390322185)⟩,⟨(-9868385208818301767599743242),(-9868385208818008861654308133)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-19011621918775987440141734264),(-19011621918774868153315653663)⟩,⟨(-29537607581192146507283680403),(-29537607581191027218474277313)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-33468332990091906623693894873),(-33468332990089013796428113601)⟩,⟨(-48796026360814099903616640548),(-48796026360811207073095278686)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-49659942272025916756522316854),(-49659942272018824990854892409)⟩,⟨(-66722457803902305210858032342),(-66722457803895213440754378504)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-67420190530890054404998341080),(-67420190530873589416728161071)⟩,⟨(-81661154714622793795213294328),(-81661154714606328801508152737)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-86848397535748563561960006531),(-86848397535714353552045802915)⟩,⟨(-92028597215001184478990104651),(-92028597214966974462850853423)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-107880668829087847558140909516),(-107880668829028840580005057698)⟩,⟨(-97473389636136655959548388544),(-97473389636077648974599716647)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-129215359023469149172945719241),(-129215359023390060712500583655)⟩,⟨(-98952610954510668677510630749),(-98952610954431580210001845359)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-147957866424796608773677162634),(-147957866424714232482183242200)⟩,⟨(-97842348515520350312724435227),(-97842348515437974014353689382)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-160150665199464465613144029240),(-160150665199397915678508864967)⟩,⟨(-95026418106470663152785735898),(-95026418106404113211826804722)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-161872466643812482473343818521),(-161872466643770862591271604070)⟩,⟨(-90224934067966140063577384607),(-90224934067924520175905863914)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-150913678009701368598687880765),(-150913678009679904059882906495)⟩,⟨(-81915596415686004008253028715),(-81915596415664539464626475758)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-128165396395821753537194076409),(-128165396395811941553878466210)⟩,⟨(-68665961027295777808160834473),(-68665961027285965820935261434)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-96823521971947189929007081328),(-96823521971942994715563815926)⟩,⟨(-50958914672486291032753688483),(-50958914672482095816469888159)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-60110663021831166036363476490),(-60110663021829490321707339283)⟩,⟨(-30901723930833309346568494034),(-30901723930831633630201594817)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-20368364346010529771037965593),(-20368364346010084791249238375)⟩,⟨(-10291965231591073257876625898),(-10291965231590628277522609991)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨218010744485883340021748761,218010744485883342352359028⟩,⟨(-102924361227761034915241852),(-102924361227761032941589280)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨541971551993844328098097394,541971551993844335287217747⟩,⟨(-452885892961216820426993763),(-452885892961216814309162333)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨303403087673570450099822380,303403087673570462582308053⟩,⟨(-1191034398381227217335829293),(-1191034398381227206559418130)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1460898391046904561248636245),(-1460898391046904542767747007)⟩,⟨(-2687800852939289015237082404),(-2687800852939288998971913245)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-5839753841813585647633080857),(-5839753841813585621913615032)⟩,⟨(-5932774266753902232882472556),(-5932774266753902209747214939)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-12878967214635957342450988074),(-12878967214635957306409117918)⟩,⟨(-12397446954855746720365375911),(-12397446954855746687146738162)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-21035810690822832143708372761),(-21035810690822832086118311811)⟩,⟨(-22694839936120031499325127004),(-22694839936120031444658903077)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-28211256184526755284395048905),(-28211256184526755138275908865)⟩,⟨(-35588700280474504084126494372),(-35588700280474503940751557662)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-32967251195141614837674590070),(-32967251195141614066234306650)⟩,⟨(-48476914749288053394506119967),(-48476914749288052625325630134)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-34891975722702201599145069196),(-34891975722702196381482821921)⟩,⟨(-58444339712458632267813744678),(-58444339712458627051813137167)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-34435227290265821225383180118),(-34435227290265792618466089847)⟩,⟨(-63184239985404529816467285277),(-63184239985404501210663070677)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-32383926115352241749352847012),(-32383926115352131400521352615)⟩,⟨(-61733120771665272709674003921),(-61733120771665162361594076809)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-28992880691529519894019196934),(-28992880691529236286948165336)⟩,⟨(-54586410212619504511108312572),(-54586410212619220904536600836)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-23638508687085804581887137244),(-23638508687085327798181679892)⟩,⟨(-42843496711028349133665161190),(-42843496711027872350252482640)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-15695039270101660093755772494),(-15695039270101167961063005272)⟩,⟨(-27451529040170666606133969953),(-27451529040170174473583125223)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-5519504830739196998265906208),(-5519504830738984386521464778)⟩,⟨(-9470042497861163489527026556),(-9470042497860950877819273443)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-289298551684965751142573674424),(-289298551684860581191266214380)⟩,⟨1281903536941803846454726516900,1281903536941909016337428738821⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 0) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_0 (tableDensity true) (fullFactor true 0 0) density1_contains hk0_1_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨10089968415966849889964804118,10089968415966849919022234451⟩,⟨127419237288198384581715819506,127419237288198384604994871660⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_0 0 0 ha0_1_0_contains + def realAnswer : RBox := ⟨(-279208583268998901252708870306),(-279208583268893731272143979929)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_0 +namespace hm0_0_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-288503251032881271602369367028),(-288503251032879827604171598224)⟩,⟨(-2955223976238342372604806882280),(-2955223976238340928624344840237)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1096807339212110398502367687516),(-1096807339212106973787682494326)⟩,⟨(-8783530613446715857143600487014),(-8783530613446712432474792927433)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2565807272415409431660378531930),(-2565807272415405946705953926181)⟩,⟨(-14338730763908264237826702049246),(-14338730763908260752926613934641)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-5013997279658746190618423314643),(-5013997279658743967915407356500)⟩,⟨(-19383638211949992286279663148838),(-19383638211949990063613810697555)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-8553073403069846812979465654832),(-8553073403069845869962643355048)⟩,⟨(-23597426407124395409220154911674),(-23597426407124394466200723525693)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-13028248908067406809756820197585),(-13028248908067406537093654097314)⟩,⟨(-26566051858436162552110895583109),(-26566051858436162279395310345993)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-18032492851599257796662903179734),(-18032492851599257736020167122095)⟩,⟨(-27862936817011740122029384536950),(-27862936817011740061296424044169)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-22955810509798142217960920534894),(-22955810509798142201669635981000)⟩,⟨(-27224223025385417188195682511249),(-27224223025385417171807287286427)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-27064817307734382286738782288943),(-27064817307734382277508975228170)⟩,⟨(-24700335966572260927618074681468),(-24700335966572260918325667884182)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-29649504044756066500273189020480),(-29649504044756066492662191670803)⟩,⟨(-20698232650282863248611163780584),(-20698232650282863241009773109700)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-30195544795673754621948498344378),(-30195544795673754615474246731314)⟩,⟨(-15905080705414950883565482227704),(-15905080705414950877191881513083)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-28490898478346382717535929762205),(-28490898478346382712225919591925)⟩,⟨(-11112886046357338815862937470371),(-11112886046357338810740616930645)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-24626426587102041427923054519151),(-24626426587102041423807043113321)⟩,⟨(-6991777109624374621038528562014),(-6991777109624374617163077374328)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-18932249628735948433545645102916),(-18932249628735948430640762507785)⟩,⟨(-3903285981121092136886842962021),(-3903285981121092134215733427581)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-11892698139828693887865066951805),(-11892698139828693886145393192083)⟩,⟨(-1846348784633012062857426189316),(-1846348784633012061306383347380)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-4050672631189637192638117222244),(-4050672631189637192071991154255)⟩,⟨(-526780450378095700286777921949),(-526780450378095699781165578859)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1371763406289119458318894349078,1371763406289120390744806356339⟩,⟨(-1107569380158791022724303825347),(-1107569380158790090418757080748)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨4047933723363285159823561833255,4047933723363288764559071646342⟩,⟨(-3374171061089776365625679597593),(-3374171061089772761243865977354)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨6511966748621921838807398342642,6511966748621931365333497507272⟩,⟨(-5777887648094378382644185617980),(-5777887648094368856680886470710)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨8606798363068380708244027476770,8606798363068404801235273876663⟩,⟨(-8365682041712785852149711392416),(-8365682041712761759891353468040)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨10162281720160325474866224909817,10162281720160383546384743481908⟩,⟨(-11122316815972957660012667292130),(-11122316815972899589344527811384)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨11016645738314530319358025398653,11016645738314656106954148784020⟩,⟨(-13957193715988776885681054254459),(-13957193715988651098992441182020)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨11059015000284879476648466963968,11059015000285106348775268638766⟩,⟨(-16695366407414589865766904766725),(-16695366407414362994541061942815)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨10272905809104290989425364100291,10272905809104608352017908625304⟩,⟨(-19076374429130501953523107541514),(-19076374429130184591765727521492)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨8760414696621622017492129168227,8760414696621965628527639638331⟩,⟨(-20783020033170904299357905766288),(-20783020033170560689045471461199)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨6743005908882877091542279946747,6743005908883163863936593296689⟩,⟨(-21505751259888874151504318383950),(-21505751259888587379693013563888)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨4532491472069595328092002646208,4532491472069779348656024515805⟩,⟨(-21021253644662244358489821474309),(-21021253644662060338361705529075)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨2473418484419528435583427087025,2473418484419625132639645000276⟩,⟨(-19255498032843028523975469309181),(-19255498032842931827220035486425)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨871657930746950644556151735632,871657930746995388786776014854⟩,⟨(-16297655271762872545572462830794),(-16297655271762827801531937398484)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-82589793992104165429290754390),(-82589793992084906582542880099)⟩,⟨(-12356353452053567164980020231126),(-12356353452053547906241858911652)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-376904570066673731614928051802),(-376904570066666021226295963847)⟩,⟨(-7699516816781026140319283685956),(-7699516816781018429983893072524)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-184940160527249608235052681143),(-184940160527247562716629641930)⟩,⟨(-2613080850628160250371175079301),(-2613080850628158204868416240344)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨772296942257175253211634649762,772296942257175253454213230751⟩,⟨330447951288172766219591828142,330447951288172766413073809669⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨2335554528795667614341236119008,2335554528795667615073334401347⟩,⟨942171750098670292298045894744,942171750098670292879900799776⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨3948096905868973058429650551549,3948096905868973059661254323942⟩,⟨1408698421831530794180325934241,1408698421831530795154352365075⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨5625467874198196160660049266412,5625467874198196162401656301661⟩,⟨1647436617904726238049131310902,1647436617904726239416595394622⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨7347331598419907745605808986967,7347331598419907747858883496529⟩,⟨1599949962492474135023017290053,1599949962492474136777027513353⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨9039397465207963020428324933424,9039397465207963023215232135969⟩,⟨1235620251197818047863098830838,1235620251197818050027850116407⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨10576332296454058091248485457157,10576332296454058094677386832992⟩,⟨551485037223613467187341402298,551485037223613469876271282355⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨11805545296081787575425147135331,11805545296081787580349461796644⟩,⟨(-415217614229672670035023535648),(-415217614229672665949023051184)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨12574263098196481897504666846326,12574263098196481911121865450193⟩,⟨(-1568691359276397200448388049083),(-1568691359276397187732929295379)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨12756620315989982954178055064071,12756620315989983026574322814874⟩,⟨(-2750424919150830010736695048713),(-2750424919150829939262009325348)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨12280266657768924628385359420167,12280266657768924999309276388458⟩,⟨(-3754731748239278228729089589508),(-3754731748239277858698110991885)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨11139608513284980609241061934284,11139608513284981985344009210059⟩,⟨(-4361625451919443151941739359450),(-4361625451919441776657233160466)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨9385419393592324584067074589216,9385419393592328076220693624708⟩,⟨(-4389321257351436426299771232735),(-4389321257351432934832381527508)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨7107595686074227219871684917978,7107595686074233241277517955115⟩,⟨(-3758785214798977829271987596359),(-3758785214798971808361607097688)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨4430061967652932690929921383081,4430061967652939016768403767833⟩,⟨(-2531060617048595180054288324184),(-2531060617048588854513626589371)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1504049159982951763383189376524,1504049159982954517563789328576⟩,⟨(-892018163489123566317535381593),(-892018163489120812235822080104)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨160200316450494113053847843265,160200316450494846316650724310⟩,⟨288154714244239014878678997772,288154714244239748137360699275⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨493215361514640463853087373717,493215361514642192633352218793⟩,⟨860149869151984308691412048580,860149869151986037458232657812⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨860740109982798327745383108267,860740109982800069759051949899⟩,⟨1416670378122520155207432544821,1416670378122521897195225190679⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1277109885537550685244604021071,1277109885537551785141827723765⟩,⟨1941722228236546820950817023180,1941722228236547920804905045123⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1746629806050075719494417358582,1746629806050076183164295391735⟩,⟨2410992627796776683537770795433,2410992627796777147141323187996⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨2264110294239874456888349855069,2264110294239874590513858813875⟩,⟨2794243111743942937168655906881,2794243111743943070698610205678⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2811676823713876227345247642717,2811676823713876256070787978227⟩,⟨3064116237459658972106773110581,3064116237459659000702573254969⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨3350740027179150720055337292135,3350740027179150726327767771877⟩,⟨3202243113242618560986343983721,3202243113242618567092435385353⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3819926591124435725498171837176,3819926591124435728183441965703⟩,⟨3198959509766390448249146998374,3198959509766390450733022278304⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨4143449016139430228126544245117,4143449016139430230218572281865⟩,⟨3052958743750981027030017265829,3052958743750981028892399615913⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4246017566296532881675636098181,4246017566296532883533349129239⟩,⟨2772632923188589020291241094942,2772632923188589021903523605340⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨4070179368332766132276666929761,4070179368332766133898832397154⟩,⟨2377558111199347310817688065249,2377558111199347312195983929379⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨3589912124085605408255330407105,3589912124085605409591845464588⟩,⟨1898276118997192935911847134500,1898276118997192937026626967116⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2816442459989206705015036282945,2816442459989206706009794440112⟩,⟨1370275741785815766421003953686,1370275741785815767237832099648⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1798592768317252381476563257424,1798592768317252382088801681247⟩,⟨823377750403112080931057946131,823377750403112081427945832268⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨618300270517097145534807509615,618300270517097145740964176833⟩,⟨274033935161360666548828430035,274033935161360666715097256951⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-114438387572961569909826236843),(-114438387572960024542409294031)⟩,⟨91652716084351531957553518780,91652716084353077328658844656⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-332305494853503115911409612836),(-332305494853497192819379231525)⟩,⟨281941457308111831478111233986,281941457308117754580882481933⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-517640525886880762591364949832),(-517640525886865364687581215185)⟩,⟨492211376987401466618115783458,492211376987416864538946506190⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-652335549251250453907010919321),(-652335549251212388762004365072)⟩,⟨732520735660118861310997278720,732520735660156926478088976835⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-723952829759895428832043099756),(-723952829759806117434291442200)⟩,⟨1005072092284633865542582821397,1005072092284723176965758622556⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-725505399194272787697225808505),(-725505399194084931209618949929)⟩,⟨1299474599878497756473706348959,1299474599878685612987763839635⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-653872554616985449645754034064),(-653872554616657011286679570491)⟩,⟨1593240685244379357196875032124,1593240685244707795580856295402⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-511797714034186772618690197706),(-511797714033740219932028045937)⟩,⟨1856921543839420736126744850669,1856921543839867288834482544937⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-312130853961732269202827405212),(-312130853961260270424219092119)⟩,⟨2059017903125298632379956817282,2059017903125770631174001433094⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-79821354780608372081498225107),(-79821354780221547466582726236)⟩,⟨2170383823176627084323590295360,2170383823177013908947110900995⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨148954408639157257200391516882,148954408639402483647455396076⟩,⟨2168885693141803877501110449886,2168885693142049103949731659408⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨330476617156701916748274977935,330476617156829948539452333515⟩,⟨2041353671080942614606321752018,2041353671081070646393045800207⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨423942659711127596458599660573,423942659711186737171637488545⟩,⟨1781319754371877708156898073195,1781319754371936848861685075409⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨408325367020104242037143140027,408325367020129735932446312969⟩,⟨1390281797614875689959283241924,1390281797614901183845429972485⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨291578410578102414252630646427,291578410578112654651344646952⟩,⟨885699993794846646602907271197,885699993794856886994573666979⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨105336641479022016501217606154,105336641479024743549710782185⟩,⟨304153828823482921211628457361,304153828823485648257482216344⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-12649264136039031644929160660),(-12649264136039031633585047991)⟩,⟨(-26460845543362253845725301350),(-26460845543362253832254517094)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-41935226649148119141192767766),(-41935226649148119106021462114)⟩,⟨(-76933814476523201660495546199),(-76933814476523201619111732582)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-82533787398346573322152468140),(-82533787398346573260164397857)⟩,⟨(-120788475170417706361419148482),(-120788475170417706289920976548)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-139160002623296133987432129925),(-139160002623296133893944004478)⟩,⟨(-155913517880336383999562279523),(-155913517880336383894397491035)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-210995754294834851058244370904),(-210995754294834850926461380014)⟩,⟨(-181431443201965306703890692801),(-181431443201965306559648449864)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-291310098772033973557841749846),(-291310098772033973373312226690)⟩,⟨(-194578831712526809715664425584),(-194578831712526809518993679738)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-371562955626853105363556399314),(-371562955626853105074733804465)⟩,⟨(-189963571429858236033927013424),(-189963571429858235734295278210)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-444606734333624898910488526957),(-444606734333624898196832863224)⟩,⟨(-163821839594835745088756057800),(-163821839594835744366888924770)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-503953777732294774995186717970),(-503953777732294771205191565051)⟩,⟨(-117755649957411683301436998071),(-117755649957411679506869761642)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-542881196123381539275561108500),(-542881196123381513124063117515)⟩,⟨(-58986413884954661325722610782),(-58986413884954635173437060912)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-554818022695472128451346667062),(-554818022695471982696633727531)⟩,⟨956377455267207677945470831,956377455267353430284728031⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-533498196188870038634589856852),(-533498196188869469171400904373)⟩,⟨48741395348884202686443586615,48741395348884772145312747897⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-473454086150958568563161945141),(-473454086150957090185598357749)⟩,⟨74068879786161912351869991815,74068879786163390724438815798⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-373250046956576423637666431702),(-373250046956573919210057772561)⟩,⟨74199866317181824555214760473,74199866317184328978333785899⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-238787023920107685629427449996),(-238787023920105087112847944316)⟩,⟨53404787708312822073589806306,53404787708315420587104890813⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-82090876247149337043833247425),(-82090876247148211463578523532)⟩,⟨19307951594314798602663598304,19307951594315924181836417557⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1294868511789859182449811909209),(-1294868511789152409652098187784)⟩,⟨(-67204450823446554049460655819095),(-67204450823445847279827190360208)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 1) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_1 (tableDensity false) (fullFactor true 0 1) density0_contains hk0_1_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨190510908882325231377026939955,190510908882325231598143945793⟩,⟨164257660829422547355831871282,164257660829422547506087478199⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_1 0 1 ha0_1_1_contains + def realAnswer : RBox := ⟨(-1104357602907533951072884969254),(-1104357602906827178053854241991)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_1 +namespace hm0_1_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨17783860931487304265226862738,17783860931488487074797418832⟩,⟨(-507476208906956821972826451395),(-507476208906955639160716550193)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨24403818196895479940760524917,24403818196898284064291274881⟩,⟨(-1520361569281386390901588822336),(-1520361569281383586772700479392)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-53080515177880945608278653646),(-53080515177878094601521494702)⟩,⟨(-2505933737002688065024143142646),(-2505933737002685214015612275172)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-271018536328517311910040520098),(-271018536328515496245533713721)⟩,⟨(-3392540243796447333265876021575),(-3392540243796445517613018962767)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-699626209070624046513648229142),(-699626209070623278473035833896)⟩,⟨(-4073484541448367948790901864402),(-4073484541448367180788129366332)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1402592224336627305787857087204),(-1402592224336627085803042081688)⟩,⟨(-4463828445153204394772334445102),(-4463828445153204174866794230684)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-2368422186457030641803232492503),(-2368422186457030595065337920007)⟩,⟨(-4539343126114855026316049353224),(-4539343126114854979713717432507)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-3470064839642778263102419035243),(-3470064839642778252638103327119)⟩,⟨(-4318812552469994477191252902320),(-4318812552469994466928481040596)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-4500379439039272793144500641224),(-4500379439039272788378986895885)⟩,⟨(-3843174528199897239845665351914),(-3843174528199897235347231847979)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-5239855553490468610761052780311),(-5239855553490468607097513509142)⟩,⟨(-3177989061594435128630901605178),(-3177989061594435125290066085410)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-5520065610269250833996212113328),(-5520065610269250830937203893660)⟩,⟨(-2410915636260700270975367220274),(-2410915636260700268273025832738)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-5273625945789773085695760928550),(-5273625945789773083215545644361)⟩,⟨(-1636486129508197911641895431818),(-1636486129508197909521628858600)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-4549892227481336618923419114019),(-4549892227481336617020244865139)⟩,⟨(-948219044114804506799172519448),(-948219044114804505223893964633)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-3471667964169489274562016851322),(-3471667964169489273235469348750)⟩,⟨(-432626747948108702078029547191),(-432626747948108701015054999397)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-2166358255224231530063703627665),(-2166358255224231529287550526787)⟩,⟨(-135272613856642273512163035712),(-135272613856642272907255177423)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-735398486671755760239910860494),(-735398486671755759985875122650)⟩,⟨(-21307384283885573161077051584),(-21307384283885572966668024805)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨270357240308145168035493808658,270357240308145935686693673743⟩,⟨(-50208634579254324103035504881),(-50208634579253556436131106732)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨792981979592428440775998212439,792981979592431409731021601208⟩,⟨(-170342521583966493589761456293),(-170342521583963524588817162883)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1262075586960380215261345034947,1262075586960388067309100136427⟩,⟨(-347628257747629846032247809803),(-347628257747621993911640261738)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1647639246207805429909387566348,1647639246207825305934423617904⟩,⟨(-612987496256817672797665041112),(-612987496256797796678086417035)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1928319673969002989270558888321,1928319673969050939482923945127⟩,⟨(-982715210355868171025531318605),(-982715210355820220703441200556)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨2091521115134655525307756386543,2091521115134759475333120119284⟩,⟨(-1447155042704756698886618071487),(-1447155042704652748743664901710)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨2126711634113726500252278056923,2126711634113914149746352551544⟩,⟨(-1966072109108192571723389631282),(-1966072109108004922111327536546)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨2024014271333217589581299661132,2024014271333480208198886240660⟩,⟨(-2479861533646478246914284053997),(-2479861533646215628186114308734)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1787007821469420726429522925107,1787007821469705053979889390757⟩,⟨(-2924595733105483179059636373030),(-2924595733105198851412087104578)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1446603829174423478644895298431,1446603829174660643693841342662⟩,⟨(-3239309274743236942570261053688),(-3239309274742999777441012896203)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1061732508956155479418354562004,1061732508956307518151143803540⟩,⟨(-3367759074716572637937321679745),(-3367759074716420599143169221301)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨701001144316153123473178367120,701001144316232914123490763880⟩,⟨(-3260773357639573963573683429096),(-3260773357639494172880873813244)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨413173264090228570785648134374,413173264090265441978316322407⟩,⟨(-2889372697254596144595621757216),(-2889372697254559273376746768207)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨213203327237514987323814168830,213203327237530837759424132378⟩,⟨(-2265033320590280216141691297699),(-2265033320590264365691968208670)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨91496206609335934356899434822,91496206609342274172031205683⟩,⟨(-1441220712303085096660373914379),(-1441220712303078756838888603015)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨23975078154067608576397501564,23975078154069289629436539043⟩,⟨(-493989299392315862515605142461),(-493989299392314181460820040904)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨109399996755867954792946186714,109399996755867954891103720107⟩,⟨154914120033529465564082772476,154914120033529465660038188086⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨335973828030327062302224805231,335973828030327062601590903348⟩,⟨459569069290427410915607657423,459569069290427411208008829513⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨580239369453176859989967078216,580239369453176860499577333273⟩,⟨746139084656624514911784401638,746139084656624515409787380426⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨840755523040624136573538943373,840755523040624137301608874640⟩,⟨994124098380536858522166509180,994124098380536859234240609352⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1109497719879105389119169201350,1109497719879105390068962179812⟩,⟨1171465778191362437410709308929,1171465778191362438341044806154⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1382464629155249836102652073507,1382464629155249837298044516482⟩,⟨1244435485312575703228262088640,1244435485312575704400448936051⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1657880375755687997425526884582,1657880375755687998974918500304⟩,⟨1197738307756117101980702875157,1197738307756117103501827667659⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1922267406229389733383255485580,1922267406229389736035524150936⟩,⟨1043623826246569909060251035053,1043623826246569911681807830446⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2143630242357403106323269472638,2143630242357403116039303931695⟩,⟨815777519896095620791823447459,815777519896095630481472203645⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨2276637737542255814336162507444,2276637737542255872034019313012⟩,⟨559033256393429195670991827116,559033256393429253350682087398⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2274328389399953538924994736047,2274328389399953840049180386728⟩,⟨317259852732324217929398026718,317259852732324519043754379203⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2106119707182805526825365473536,2106119707182806647820674105838⟩,⟨120137408530570945852429290597,120137408530572066842555562601⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1777727804782810601534067839906,1777727804782813450074265232057⟩,⟨(-19595143524401132955041853731),(-19595143524398284417188903081)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1331242753338917276948739434623,1331242753338922192726863391810⟩,⟨(-94132517750850509738517002073),(-94132517750845593960429279053)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨818078719259552236383017072700,818078719259557403475822128925⟩,⟨(-97450183070618293849794328920),(-97450183070613126756086522383)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨275273366929502346543785622134,275273366929504596819665149405⟩,⟨(-40482879671909230546464837833),(-40482879671906980269942869590)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-14646219652189129405082350361),(-14646219652188513313144461612)⟩,⟨109229800289326949648869820302,109229800289327565741136823526⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-39931518399270550505380122794),(-39931518399269098959524288297)⟩,⟨324018595419465280439323405491,324018595419466731986320016752⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-52525998465664479723525308084),(-52525998465663019108896253848)⟩,⟨527771608779360007640337024877,527771608779361468257353073167⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-42702539470781439916193712221),(-42702539470780519738379417459)⟩,⟨714988624891171197498895569277,714988624891172117681032138214⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2227443259019303954119532989),(-2227443259018917369201346361)⟩,⟨883914308302442802209783203501,883914308302443188801757817117⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨69832721164542538679087416101,69832721164542649336007389463⟩,⟨1035291052459886710435863106274,1035291052459886821103354240186⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨164870821609744152558748549602,164870821609744175758226525484⟩,⟨1165719921205484296491704781516,1165719921205484319705880753484⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨270255703128542880330915739795,270255703128542884805782496998⟩,⟨1264071357630827293014173227820,1264071357630827297507902929832⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨374533155928671363236941369052,374533155928671364683122786082⟩,⟨1316181008391368961105727408940,1316181008391368962574539313317⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨467068264096613880355755492744,467068264096613881294641460164⟩,⟨1311479409234646127047534213557,1311479409234646128011860482196⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨535228178578813931281718307204,535228178578813932052939570799⟩,⟨1246250028049503373299906081322,1246250028049503374097776370959⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨563145233630986064746552621375,563145233630986065389195776628⟩,⟨1122460650945457498506865890047,1122460650945457499175589647131⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨535385846012722045012240568714,535385846012722045524035697113⟩,⟨944211981747721115374148637779,944211981747721115909374634003⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨444191600420624509347229655118,444191600420624509717294654400⟩,⟨716731791917044392455088509496,716731791917044392843734871403⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨294294528257908694569871405425,294294528257908694792506439486⟩,⟨448473213229878482735870214434,448473213229878482970448024879⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨103024113824503410405103292221,103024113824503410479158555232⟩,⟨152696704871573779729092925335,152696704871573779807248988847⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-36010321038366953878787708731),(-36010321038365683823286538847)⟩,⟨31997733051359600386912157918,31997733051360870440774556087⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-107348239114000125963964526617),(-107348239113995257742013900866)⟩,⟨99157030099230141605728240040,99157030099235009822817940102⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-175975880780092934930190431735),(-175975880780080277640174952286)⟩,⟨174084123154027541090427336250,174084123154040198372651197561⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-237801597984182269480501957180),(-237801597984150974436161436933)⟩,⟨257874302858479555727386008450,257874302858510850761511160703⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-285606636436407555473181256096),(-285606636436334119726929589603)⟩,⟨349409073767836475911333138734,349409073767909911645771054284⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-311794981105000636267682821165),(-311794981104846173035618531053)⟩,⟨448185003910671829851550233143,448185003910826293071188510622⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-313665402484007692612445716041),(-313665402483737695621221355404)⟩,⟨553442988341271530017928880163,553442988341541526997159901908⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-295252861147557760424083245500),(-295252861147190846390294722422)⟩,⟨659854145159666042629141383925,659854145160032956652461097563⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-264814068897991481307832772802),(-264814068897603968657276439320)⟩,⟨755167705672651950080318051082,755167705673039462722766172958⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-231133111182885279955423508328),(-231133111182568034521393596220)⟩,⟨821337974213508887810234240253,821337974213826133238753629153⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-199500903210071288819721638971),(-199500903209870426653291144899)⟩,⟨838334133668072607145100122620,838334133668273469308328225409⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-168607103077868659287804821623),(-168607103077763930707178312399)⟩,⟨791520157591206775707544291352,791520157591311504286780757058⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-133336849185609529363017311624),(-133336849185561214302837612746)⟩,⟨680291203018131168946135392898,680291203018179484006235709255⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-92947974040169633938320807785),(-92947974040148828650959359896)⟩,⟨518195084767907801931233938177,518195084767928607219211239771⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-52724765410840572222160036901),(-52724765410832221333922132950)⟩,⟨323012564550306452767317732982,323012564550314803656252799028⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-16755935542759093006676220816),(-16755935542756869979135986350)⟩,⟨109594241046054268548485563107,109594241046056491576314300208⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-413253947792046456525474419),(-413253947792046449139010481)⟩,⟨(-768153688353753089225362103),(-768153688353753080704875359)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1747289341369665023287608410),(-1747289341369665000315091564)⟩,⟨(-1872764947371631971244333015),(-1872764947371631944883226843)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-4397062161166487381120682280),(-4397062161166487340411818763)⟩,⟨(-846987977048408422732191013),(-846987977048408376678323295)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-9493872100649038700103648662),(-9493872100649038638122512106)⟩,⟨5995346243970091520246966780,5995346243970091589061737201⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-20343471989756725818858091606),(-20343471989756725729684483413)⟩,⟨23174480590458387862223792188,23174480590458387959213644925⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-42318772007625438132807613535),(-42318772007625438003085017325)⟩,⟨51849150643453454993793027614,51849150643453455131806140817⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-78298210534941273269373267409),(-78298210534941273053140648947)⟩,⟨87259689248610950515680027950,87259689248610950740102951561⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-124709618221129519153731758691),(-124709618221129518580439677205)⟩,⟨121731632751877393216246865372,121731632751877393796667566100⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-172619283496392306977254343238),(-172619283496392303863407298998)⟩,⟨148897401311036136346144812528,148897401311036139465136981820⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-211170790220490606702141127659),(-211170790220490585282125338600)⟩,⟨165332814558400735108209857516,165332814558400756531154486856⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-230970585378352715995466090007),(-230970585378352596896147107142)⟩,⟨170557120355510261738875784903,170557120355510380839241285167⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-227305887634448985855931923151),(-227305887634448520747307017785)⟩,⟨165833762534661864398491706392,165833762534662329507043054378⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-201466089733206573302310226358),(-201466089733205365480052409513)⟩,⟨151302600284041864488852583426,151302600284043072310475458444⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-157953692347007555256982930321),(-157953692347005508236696817002)⟩,⟨124371953782170592151120253485,124371953782172639170587105783⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-100996454891333073693917834257),(-100996454891330948990560692410)⟩,⟨82850350973149960259957854454,82850350973152084962652432444⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-34794146336193103909482781472),(-34794146336192183387011517023)⟩,⟨29176276135462012575504014244,29176276135462933097714806909⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-288167913479046844755963585742),(-288167913478465023796705460894)⟩,⟨(-5879074427871787518129245781882),(-5879074427871205697433980695108)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 1) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_1 (tableDensity true) (fullFactor true 0 1) density1_contains hk0_1_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-249129650076886841320649775267),(-249129650076886841031496767633)⟩,⟨(-214798479546167946738729779184),(-214798479546167946542241677831)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_1 0 1 ha0_1_1_contains + def realAnswer : RBox := ⟨(-537297563555933686076713361009),(-537297563555351864828102228527)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_1 +namespace hm0_0_1_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-4367205808142281791849945243774),(-4367205808142276401076678430508)⟩,⟨11880849508277687953578356026216,11880849508277693343939233103874⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-11810620869770959577129200479818),(-11810620869770946616485845474811)⟩,⟨35946153540168713079702699323867,35946153540168726039178300227367⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-15425232315303501859707920625976),(-15425232315303488329591012189903)⟩,⟨60656049441573415513303003907964,60656049441573429041693625600715⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-12957649869505507114079489855506),(-12957649869505498181076080620387)⟩,⟨85676103388919560052201655651178,85676103388919568983212283202740⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-2847269716476717112352753038251),(-2847269716476713167415202478051)⟩,⟨109545021147921334853574152954441,109545021147921338796577422658248⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨15286323512867244458325637910082,15286323512867245648622199954322⟩,⟨129524368219621584505827081419675,129524368219621585694530851145188⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨40216278037153778020876348523678,40216278037153778297944925068784⟩,⟨142134648572985928299221955303394,142134648572985928575192930811182⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨68823882193207938293953572946592,68823882193207938372379519229736⟩,⟨144372713241548807620631546652083,144372713241548807698419326365717⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨96354105555876317496166507598302,96354105555876317542206443641614⟩,⟨135023689138996988999945867448876,135023689138996989045612735816890⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨117522472030014749559843798307756,117522472030014749598220996420056⟩,⟨115458001582411930764394665636505,115458001582411930802403796860738⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨128068047695068934316838906708637,128068047695068934349433879041753⟩,⟨89489374715228918403641068510755,89489374715228918435660096662515⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨125914737109248641152725316296584,125914737109248641179200243050822⟩,⟨62216203671297579334423085231168,62216203671297579360024606299446⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨111390128955479762663228294896785,111390128955479762683450190566540⟩,⟨38297613315226150479157208098223,38297613315226150498289589814029⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨86636703934803515579483372037801,86636703934803515593530222100345⟩,⟨20490565251355862080417432364562,20490565251355862093400197708379⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨54692620525746240361312693582299,54692620525746240369518191003092⟩,⟨9123477249297078394971283962776,9123477249297078402403028964974⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨18658450681131940662829312844147,18658450681131940665510391409108⟩,⟨2469567746862047760450471133192,2469567746862047762852382129532⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-6236134173590410409044265890886),(-6236134173590406013250673513223)⟩,⟨(-797518908600918317893300973665),(-797518908600913922138988212303)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-18756893245368806443800679237217),(-18756893245368789558416846791622)⟩,⟨(-1991328157039179633304010574492),(-1991328157039162748069877464025)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-31327732958310930360197442564141),(-31327732958310886311677783689672)⟩,⟨(-1989394040826442644406021898783),(-1989394040826398596237706546041)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-43741343791043575203689479323760),(-43741343791043465997923677252747)⟩,⟨(-45677984421375736637840470461),(-45677984421266531561533816214)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-55468948363485376771436894640173),(-55468948363485120646802226242170)⟩,⟨4458482444259980313830389167743,4458482444260236437277227034298⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-65649332792178446206320051151088),(-65649332792177910750107171912144)⟩,⟨11865411558449622765062365341729,11865411558450158219435409499168⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-73193837497561401949467299981440),(-73193837497560478119381360911690)⟩,⟨22017018422116729847844861349888,22017018422117653675330753729373⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-76994404781154945109314068162770),(-76994404781153720804345079293538)⟩,⟨34043606716977469674621051573677,34043606716978693976209123345605⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-76229323302045615773015417139050),(-76229323302044373607233402164439)⟩,⟨46329511250194243459406502735660,46329511250195485621117240961307⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-70709793813739834150108428919544),(-70709793813738872457513511210873)⟩,⟨56745368949930779413741912870538,56745368949931741101786791240690⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-61098524204769780029775115570221),(-61098524204769211467952315586422)⟩,⟨63124690076037382618337691232389,63124690076037951175459474819957⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-48846277614821998487929404546436),(-48846277614821693631476367132714)⟩,⟨63836096684906357931991055098205,63836096684906662784446489909285⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-35805688906348716888899409192537),(-35805688906348566093632508274585)⟩,⟨58189027111735687823779658494624,58189027111735838616065802279410⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-23612617250984937616372760808136),(-23612617250984869499755838631776)⟩,⟨46511633155042709150387095313401,46511633155042777264977424801180⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-13115950832347818041864348263137),(-13115950832347789903505829189380)⟩,⟨29981393103562030602053605743138,29981393103562058739247647960961⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-4166124533662474759998597978914),(-4166124533662467179282144754599)⟩,⟨10344600324580030912743332718026,10344600324580038493081303586070⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-251577188780357167895612899696),(-251577188780357167446108311724)⟩,⟨(-2442142013229069921864297442504),(-2442142013229069921172700869098)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-940901761738579964720272662653),(-940901761738579963338069189471)⟩,⟨(-7327439529351917076088954122273),(-7327439529351917073987192099534)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-2177368225571700090329974567012),(-2177368225571700087905637636467)⟩,⟨(-12193152682011186251069710567931),(-12193152682011186247482682853941)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-4275387183063962734975200414880),(-4275387183063962731339530090724)⟩,⟨(-16974037516478072830272022373488),(-16974037516478072825089406771954)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-7440726975956492707970847861253),(-7440726975956492702917925229512)⟩,⟨(-21509978511337973692651026740755),(-21509978511337973685758724847425)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-11713567845936475023250279364427),(-11713567845936475016435660820705)⟩,⟨(-25499207268604952345774525888234),(-25499207268604952336968158183951)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-16937617387512043138684138148643),(-16937617387512043129423005541102)⟩,⟨(-28509461811453608093489926636878),(-28509461811453608082231688056777)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-22726848272016294531032187462063),(-22726848272016294515822359286363)⟩,⟨(-30079835094179251744636816175626),(-30079835094179251727581129513331)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-28438059857053669636666053196727),(-28438059857053669586661037394020)⟩,⟨(-29864616889477324183077815167941),(-29864616889477324131519104808403)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-33211870977663760183515746315814),(-33211870977663759885059477775496)⟩,⟨(-27769856419604984411576618646291),(-27769856419604984111945114782222)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-36104784739418499226186524375681),(-36104784739418497578781550540991)⟩,⟨(-24045888057607651893190137529450),(-24045888057607650245010583015445)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-36272808577503206416977153638192),(-36272808577503199921311725458256)⟩,⟨(-19274262469496936389518742884812),(-19274262469496929893434592740134)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-33160800341286188926153266484737),(-33160800341286171921601206317307)⟩,⟨(-14193856457643334323206210842529),(-14193856457643317318505241730591)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-26680105021510699366000374950098),(-26680105021510670419131423308089)⟩,⟨(-9426428267620357342644880709423),(-9426428267620328395785128514975)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-17303846019370313155967325915944),(-17303846019370283070264660561061)⟩,⟨(-5275884338506706063966126732881),(-5275884338506675978321774069949)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-5991499885339101062523796086321),(-5991499885339088037725050936318)⟩,⟨(-1684145728762212584204150789341),(-1684145728762199559434271018175)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨544237908034760929120353440725,544237908034762582957652780049⟩,⟨(-589305623490356893596446255362),(-589305623490355239688046329431)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1612754197384472744917827966071,1612754197384476644701281515505⟩,⟨(-1804772839729561484629641028395),(-1804772839729557584628921230695)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2616472075725500846500749290819,2616472075725504776636560667995⟩,⟨(-3120931542016969185240738407159),(-3120931542016965254730598990058)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3500789354801509718652613843420,3500789354801512199456751963565⟩,⟨(-4578978404517022558659971000117),(-4578978404517020077308025158378)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4193577065142620699967323502600,4193577065142621744451698456315⟩,⟨(-6185986431284069821796099700172),(-6185986431284068776571471977391)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨4610380421969373724308017400430,4610380421969374024243560025092⟩,⟨(-7913256386684879143659658755635),(-7913256386684878842774604932123)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨4680709672359715663552215012396,4680709672359715727288094034081⟩,⟨(-9691275994361548871123584186220),(-9691275994361548806219943949607)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨4377182927802695466180455490751,4377182927802695479464099989072⟩,⟨(-11392703006770029397647732572186),(-11392703006770029382984313002186)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3728484188022375389553593726062,3728484188022375394716653334706⟩,⟨(-12826078455908918568098914775960),(-12826078455908918561372668837842)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2821703806031260687007149265601,2821703806031260690746330555862⟩,⟨(-13758160041602587086235085100749),(-13758160041602587080806312844821)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1795315931744616402178986355216,1795315931744616405332046891601⟩,⟨(-13959229930405882506355615685346),(-13959229930405882501472466847471)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨818482898062284476483919912321,818482898062284479187733372515⟩,⟨(-13259608097281751536288777750224),(-13259608097281751531958024990403)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨58855655782197776278225815304,58855655782197778635389834185⟩,⟨(-11596566204556215520863172700769),(-11596566204556215517167680018733)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-361077447697503498775917992251),(-361077447697503496938650849478)⟩,⟨(-9030733088711742431927390410077),(-9030733088711742429099994714551)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-410428248429213745660070846297),(-410428248429213744494367387007)⟩,⟨(-5734614632626571236453953102186),(-5734614632626571234681444384686)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-172761049536571610752123012393),(-172761049536571610353644620841)⟩,⟨(-1965335483941748973203028777881),(-1965335483941748972600669130930)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨227801639473742909141392421931,227801639473746159378772518073⟩,⟨201480930286853348564268365335,201480930286856598805406807966⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨697189419965409201116592283734,697189419965421685869383321490⟩,⟨579351206625148869214969719599,579351206625161353979973700779⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1205672162781924242156556058145,1205672162781956834165480551777⟩,⟨882329993350201540638864150844,882329993350234132671228981069⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1772414352438721560715924545853,1772414352438802604943706307329⟩,⟨1066029483376667073407561068734,1066029483376748117674499913837⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2400265228650185421267436279925,2400265228650376927648388489175⟩,⟨1097315529845275905008725161557,1097315529845467411450585066534⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨3064743053616561294739073653851,3064743053616967276075086914137⟩,⟨956822787911620049960067316571,956822787912026031385654261139⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨3713010527153526830647022703473,3713010527154242370611645323934⟩,⟨638301520438405467871152289089,638301520439121007960232469281⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨4274700399490014990445986474403,4274700399490995466778482266373⟩,⟨154337915759136077889148165927,154337915760116554385939421703⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨4675357588354102460934860571285,4675357588355146270271517155110⟩,⟨(-453110925552298124139727540187),(-453110925551254314596857445411)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨4850242368363669596828230921508,4850242368364530302078278680677⟩,⟨(-1107716705879807244564575910788),(-1107716705878946539069521493283)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨4758883696607819468981053418453,4758883696608367807163777748378⟩,⟨(-1702430085698140745074204848508),(-1702430085697592406619022587953)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨4391942321273053635303568572310,4391942321273340967816558346089⟩,⟨(-2110906814630552523547144513908),(-2110906814630265190754712998875)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3761682570127343126267043898635,3761682570127476176293394304075⟩,⟨(-2214342109977887854222360621075),(-2214342109977754803935576730282)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2891466752345931652192167792952,2891466752345989089194271073266⟩,⟨(-1947357995073962981376331092841),(-1947357995073905544160692515384)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1822796917976196495731916228307,1822796917976219583809952464749⟩,⟨(-1332094647608208359341581633968),(-1332094647608185271122994393163)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨622642123265183681451347158281,622642123265189831594979553350⟩,⟨(-472900154019380114845976245024),(-472900154019373964653247438478)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-46602697817661029903915483382),(-46602697817661029879172683625)⟩,⟨25362417946124476353187655995,25362417946124476374465549785⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-135155311069966623196001866103),(-135155311069966623119755277735)⟩,⟨83540778427274519269949730657,83540778427274519336132000976⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-210875170101211092022961959690),(-210875170101211091890382092169)⟩,⟨163026892756758769271763158801,163026892756758769389095178288⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-268942029371675418240759699758),(-268942029371675418043906967920)⟩,⟨273281027668779210741722435870,273281027668779210920158239180⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-306712257885493596878645838942),(-306712257885493596605385536435)⟩,⟨413868425439324140478407041748,413868425439324140732469917725⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-318412409260141346079037633366),(-318412409260141345701377488940)⟩,⟨572875054802504440078304716037,572875054802504440437879671409⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-293586196592961844617346103075),(-293586196592961844033952849066)⟩,⟨733560421775353351117407139391,733560421775353351685541415630⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-224802515757177672951918661003),(-224802515757177671528627159211)⟩,⟨880514515275490230818260540578,880514515275490232230969111054⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-115346310065105997527963905517),(-115346310065105989959146292691)⟩,⟨999249179892897881083096967675,999249179892897888647213815172⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨19272651270076855755341605471,19272651270076908533484705498⟩,⟨1075381883663182402163394920201,1075381883663182454942450159418⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨153236957369140198480445816066,153236957369140495840128813128⟩,⟨1096072387840045319785921382682,1096072387840045617150773993752⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨255254532269192925777407373075,255254532269194098640711123210⟩,⟨1050507131511688526552928329515,1050507131511689699423658464013⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨298994901239285295033395816792,298994901239288363791504003316⟩,⟨929818974511808313833606266678,929818974511811382599462070514⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨274715533294515046484334991702,274715533294520276280203634452⟩,⟨731905363434731818623257450877,731905363434737048425602815652⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨191057917627891305054564957578,191057917627896753326778272353⟩,⟨467902908011074264034083768005,467902908011079712310493952089⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨68199207110686094797578188069,68199207110688459605549907054⟩,⟨160812321857120858095974242791,160812321857123222905386132105⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-15589856564732240181036659258755),(-15589856564730239499677877160710)⟩,⟨205890396805551755136955371244424,205890396805553755815406159465217⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 2) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_2 (tableDensity false) (fullFactor true 0 2) density0_contains hk0_1_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1960229115587461528719659034850),(-1960229115587461527631479663462)⟩,⟨1958143165354188843785193230616,1958143165354188844520968025834⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_2 0 2 ha0_1_2_contains + def realAnswer : RBox := ⟨(-17550085680319701709756418293605),(-17550085680317701027309256824172)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_2 +namespace hm0_1_1_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1008438538512546871520270385802),(-1008438538512542456128138277054)⟩,⟨1915474351696146812107149208968,1915474351696151227596744558525⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-2872295595038071992080887863505),(-2872295595038061380925199873420)⟩,⟨5830607974333294266711310207500,5830607974333304878144092389660⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-4242819550083193724563083591056),(-4242819550083182657120944099559)⟩,⟨9898806495197808370002297154174,9898806495197819437857681161817⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-4683212583815781385671255018008),(-4683212583815774090345720048439)⟩,⟨13965047669024179562382900653316,13965047669024186858189774775145⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-3650585861444255372667553233036),(-3650585861444252161733689375386)⟩,⟨17670589834921874109288124414972,17670589834921877320682750796877⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-703180072301888363214036386623),(-703180072301887404960389978449)⟩,⟨20608973628586801476217361175202,20608973628586802434804670371405⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨4129450521974974496398418730190,4129450521974974708029862901819⟩,⟨22404890472609017647299116278666,22404890472609017859022700494305⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨10173330747765741038570103034603,10173330747765741087526859969248⟩,⟨22701537407846396021580367001721,22701537407846396070285656200581⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨16274534327540838757115200090726,16274534327540838779933921565237⟩,⟨21277014495756221926595027895509,21277014495756221948765267016714⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨21135329579878865854878294883741,21135329579878865872659545703246⟩,⟨18243653143067958576708184758980,18243653143067958593455890914036⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨23697617396812472754944247042651,23697617396812472769851771657359⟩,⟨14101017089505756493862264258127,14101017089505756507440602178114⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨23475115732148757669925309740937,23475115732148757681960631333670⟩,⟨9591515809218552516278540041202,9591515809218552526843703865258⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨20665970244528727220707666170036,20665970244528727229849129161340⟩,⟨5497272474200579305503187082752,5497272474200579313227664925865⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨15924199438947779247106021622214,15924199438947779253397620123176⟩,⟨2454063237081203454601457135421,2454063237081203459714320834261⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨9973040207484844337445386299811,9973040207484844341085443002624⟩,⟨735692102632561925033276553993,735692102632561927892488468639⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨3388207649428544598427686056464,3388207649428544599611348418335⟩,⟨105867882590296792250511875195,105867882590296793159865006218⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-796434367424148950127539144925),(-796434367424145330793310104219)⟩,⟨(-571975478759299614618995308013),(-571975478759295995284213762814)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2413777170514887679584376901554),(-2413777170514873771340652450075)⟩,⟨(-1612822671289501128579020927298),(-1612822671289487220329857832913)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-4095152192774322835910519303560),(-4095152192774286528312695809696)⟩,⟨(-2346819907372218193242183215848),(-2346819907372181885622964718790)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-5859476221366616229365444001320),(-5859476221366526136103930541424)⟩,⟨(-2588995065569339731155342909392),(-2588995065569249637838040186761)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-7684167342136723017872319171611),(-7684167342136511532008709042923)⟩,⟨(-2200482298106242466336623615365),(-2200482298106030980359730195836)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-9474282975845180528013423010341),(-9474282975844738030645758319332)⟩,⟨(-1127228416131257864263493976533),(-1127228416130815366701181883072)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-11037607726717485082140634877667),(-11037607726716720969505515139564)⟩,⟨582604010399745246236549533465,582604010400509359167627816156⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-12120277225286061880396949752795),(-12120277225285048765506697221510)⟩,⟨2785561198965016710147514176386,2785561198966029825443813601432⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-12502176188347110160356401624215),(-12502176188346082306063917160508)⟩,⟨5237058938993697550596703904651,5237058938994725405401837858252⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-12088931901407986658639165340866),(-12088931901407191322714208571243)⟩,⟨7583434350688717292472731814270,7583434350689512629002445617625⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-10951129699224561770545814647584),(-10951129699224092021827977660583)⟩,⟨9390253520750623440371081529680,9390253520751093189747259359657⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-9281636697779313496304665200047),(-9281636697779061945741058344031)⟩,⟨10225697367078571953152907114580,10225697367078823504301949224849⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-7298736257537817968368030683021),(-7298736257537693709624804644284)⟩,⟨9799787825144011077177378163870,9799787825144135336371912762871⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-5184926673017870072058935171890),(-5184926673017814012533633075844)⟩,⟨8084347150379891406410363898362,8084347150379947466249278392170⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3071093811856120155953758768659),(-3071093811856097020417840819075)⟩,⟨5305916609247449445439327347698,5305916609247472581157864318226⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1013122685436080416462238852584),(-1013122685436074186795035796687)⟩,⟨1845668671638703814324672765189,1845668671638710044051898545202⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨240572641549805200404267572839,240572641549805200648852189042⟩,⟨(-499341662836523711339999246784),(-499341662836523711084238815865)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨693695194970676737014672914267,693695194970676737770851754691⟩,⟨(-1519048386320454091436667704797),(-1519048386320454090646173840431)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1062877380870748276308372347540,1062877380870748277634535178648⟩,⟨(-2582705622129475610012251957768),(-2582705622129475608631812791969)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1286317342828239425906281813939,1286317342828239427884010754399⟩,⟨(-3668979841978976344508238212264),(-3668979841978976342461357655283)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1279937319122473508918347895504,1279937319122473511642502106028⟩,⟨(-4712868155938267002063495150880),(-4712868155938266999263481278783)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨948110537674414886752027233363,948110537674414890399564165603⟩,⟨(-5641289752130103444977602239602),(-5641289752130103441250281823235)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨240118297847947974246297037871,240118297847947979309888933592⟩,⟨(-6398682469925437860384567048455),(-6398682469925437855238547681733)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-797486870552668545842050864649),(-797486870552668536454406697760)⟩,⟨(-6933934544922495229738201411859),(-6933934544922495220276128044710)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-2013930638722238123266594695724),(-2013930638722238085800235370555)⟩,⟨(-7186585698804877006935020733312),(-7186585698804876969416892307710)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-3180128941972914892171593125831),(-3180128941972914652173234151471)⟩,⟨(-7096559575581639481838248805588),(-7096559575581639241812631527596)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-4040740064419664347553489753553),(-4040740064419663007936328927128)⟩,⟨(-6621419043262533661523365017614),(-6621419043262532321897801494324)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-4395805284713389157912164100070),(-4395805284713383864271655320244)⟩,⟨(-5756548548995612940515960546632),(-5756548548995607646877092944709)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-4172675966421512600119883844252),(-4172675966421498727710591048512)⟩,⟨(-4570884103167334806812640837795),(-4570884103167320934410505652800)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-3418742205770235594865123678808),(-3418742205770211961841785520623)⟩,⟨(-3220251389353376816084750814228),(-3220251389353353183069568195609)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2240778667173022906685966390976),(-2240778667172998331238699640821)⟩,⟨(-1873888208254681167272765373406),(-1873888208254656591831409746572)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-780280036726086280776428838017),(-780280036726075638749489181693)⟩,⟨(-609735396017690987675268824784),(-609735396017680345650395948961)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨263595353210234503466845132796,263595353210235893064064949001⟩,⟨(-49176770792182395112845168893),(-49176770792181005522875239380)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨781314860989332390870977337769,781314860989335665370119967435⟩,⟨(-156965293385602888172399548737),(-156965293385599613695456525025)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1269335926270407683718996165028,1269335926270410979170493046874⟩,⟨(-294401139574790760994224986583),(-294401139574787465580951183236)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1708806012520470464894993292667,1708806012520472540607173565646⟩,⟨(-485077419387582904337156473224),(-485077419387580828680885057130)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2087568302343097356683971473930,2087568302343098227884334786352⟩,⟨(-751541036074385487181285027075),(-751541036074384616056014556082)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨2402151339275707665222248562046,2402151339275707914072186854966⟩,⟨(-1100579501942014392927625097410),(-1100579501942014144173437559549)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2645729091376633537287060074208,2645729091376633589338629853527⟩,⟨(-1510923332466283138271955299981),(-1510923332466283086337943585202)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2796620064854057164068229617406,2796620064854057174174212281807⟩,⟨(-1940193197938583470536002511014),(-1940193197938583460567515593807)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨2825801309825969673532557731489,2825801309825969676902285811847⟩,⟨(-2339217862267317427473052327568),(-2339217862267317424257083615596)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2714429386611228598503887049465,2714429386611228600749978450378⟩,⟨(-2657707815775443724121192723659),(-2657707815775443722038793167871)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2466669900523183194459957393956,2466669900523183196324117928413⟩,⟨(-2843374303940073498859801697061),(-2843374303940073497159863596965)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2110056781738461552453793486968,2110056781738461554038847818022⟩,⟨(-2841459940839058344382393717846),(-2841459940839058342949452486680)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1682163860342122277967209205368,1682163860342122279302225373312⟩,⟨(-2603521926424362261842786168764),(-2603521926424362260631315969010)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1215753928600196087628876393028,1215753928600196088639253393326⟩,⟨(-2107680190574068047523571543791),(-2107680190574068046603445278032)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨732772545410040185578291357317,732772545410040186205653032211⟩,⟨(-1376127973221727801622055342144),(-1376127973221727801049499419561)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨244501668544970517812241871625,244501668544970518024273919414⟩,⟨(-478503659006162137750789864906),(-478503659006162137557034495795)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨78135776019433424853599931144,78135776019436096046566927008⟩,⟨62283323343520200958290548604,62283323343522872152238931053⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨241775310093022016410401025955,241775310093032277684313925121⟩,⟨184249084772653604865816832334,184249084772663866142371523381⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨423792298043985457650437639917,423792298044012248714576430882⟩,⟨297452959688137618869829424328,297452959688164409937362088493⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨627162056573949758730376358250,627162056574016388767898829131⟩,⟨392210596687538377728979576677,392210596687605007769105251754⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨848505264256731787669629163048,848505264256889252597870679020⟩,⟨452437955071929697063940215744,452437955072087161991842125560⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1084291021322504004641552159138,1084291021322837818948933735718⟩,⟨460055497610574640097561313095,460055497610908454399025198377⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1330992763435782103623534749292,1330992763436370322351602314719⟩,⟨406530398067934010861983455988,406530398068522229575553907856⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1577202404447236364825065993143,1577202404448041981716981716111⟩,⟨299886407163287555479750735048,299886407164093172346703400279⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1797810556625768603678439816946,1797810556626625574383745867241⟩,⟨162670254320828888384264700848,162670254321685859054522128134⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1954555258390058678745457056643,1954555258390764566308907069033⟩,⟨25559909534506114262235192905,25559909535212001783160027510⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨2001880430403775341977422344037,2001880430404224479363105941956⟩,⟨(-82664930708084782994815360202),(-82664930707635645655890099623)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1901333354922378947799653510190,1901333354922613982622037850360⟩,⟨(-147767863516169650635100561506),(-147767863515934615860526878324)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1643526835149189799752956589817,1643526835149298495172891790499⟩,⟨(-172825292726061594316924619651),(-172825292725952898941566283913)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1255972925947026563637461801445,1255972925947073437420296195437⟩,⟨(-163587081883974007876370219487),(-163587081883927134129634032716)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨783373694925967440635398816681,783373694925986268662594391147⟩,⟨(-119396845477152278455479504950),(-119396845477133450451796217436)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨265673785044621218357671085367,265673785044626231832834593142⟩,⟨(-44085709953497362661447856299),(-44085709953492349194368617664)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1348479527300929417783290851),(-1348479527300929402252100290)⟩,⟨819460549017245012743766062,819460549017245026514266818⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3217568899342129339517975676),(-3217568899342129291334232741)⟩,⟨3349017134990345831539708993,3349017134990345874498281644⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1066760762440110801242391163),(-1066760762440110716582887977)⟩,⟨8087146655332390534848980268,8087146655332390611391812681⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨12117975390442047009882575094,12117975390442047137456655129⟩,⟨16666933232466708055048496683,16666933232466708172512785724⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨45551880804673557573204504633,45551880804673557755116466517⟩,⟨34453612011545394091628418275,34453612011545394262381615320⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨103209333230016025125695855874,103209333230016025388176681528⟩,⟨71019515160944415466746207129,71019515160944415718052746226⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨178229500029497915842178856720,178229500029497916275705508593⟩,⟨132507041947508255158010712622,132507041947508255581569699950⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨256947609100623027326056243689,256947609100623028465894340968⟩,⟨213983275177131857968034268829,213983275177131859100763195579⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨325964502163705353157625126584,325964502163705359373079949115⟩,⟨300328373665147245330409544208,300328373665147251542898576646⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨375433930310919095212517594159,375433930310919138439234434322⟩,⟨371770438058500443547929659510,371770438058500486775840909850⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨400046189524858684657595718735,400046189524858927634535505130⟩,⟨409970915917867468113490483104,409970915917867711094830390673⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨398328198370230215757735104324,398328198370231173691646807801⟩,⟨404683492710957301623445449620,404683492710958259563412746175⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨368406406623620479146748835556,368406406623622986296424599890⟩,⟨357760634925585110860515845849,357760634925587618016548062008⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨304721330532372873657186730137,304721330532377148285931472178⟩,⟨278770978832634275432290710737,278770978832638550066535564734⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨203539711280900421370551689255,203539711280904876205180498020⟩,⟨177133828106899968168855485611,177133828106904423007198932820⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨71761076254133918510037049946,71761076254135852497979982879⟩,⟨60799524466745495444775158834,60799524466747429434027882493⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨7719378908250091622664278112871,7719378908251740029394881612679⟩,⟨24969994826941224050433215222796,24969994826942872456655160952756⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 2) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_2 (tableDensity true) (fullFactor true 0 2) density1_contains hk0_1_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨2563376535768218920748858021451,2563376535768218922171861814804⟩,⟨(-2560648754693939258219727418398),(-2560648754693939257257560378498)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_2 0 2 ha0_1_2_contains + def realAnswer : RBox := ⟨10282755444018310543413036134322,10282755444019958951566843427483⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_2 +namespace hm0_0_1_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨25852085051385504767120119556318,25852085051385519088464283448093⟩,⟨(-25016589556937662135330882437265),(-25016589556937647815290555866083)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨74211543673445419809075683085726,74211543673445453210134287623163⟩,⟨(-78217336140639009469569029757510),(-78217336140638976072523142186292)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨112039380332644385435112873285743,112039380332644418201000150717451⟩,⟨(-139945200655938949436861250104665),(-139945200655938916677958046240537)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨131369170213310546483549477770347,131369170213310566587874408634417⟩,⟨(-212693967328159088880101434161479),(-212693967328159068785655099078991)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨124091332210087427858124444832218,124091332210087437228638602397818⟩,⟨(-293789765572339708031281653530674),(-293789765572339698671235691672116)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨83978220249643530568760859939813,83978220249643533626255774212044⟩,⟨(-373902709319904493176714413033365),(-373902709319904490128661076583416)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨10013841353576571712178869697953,10013841353576572481555983037451⟩,⟨(-438114483786280183616132720451518),(-438114483786280182854085926006711)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-90055192714208168617704996807658),(-90055192714208168381510332501602)⟩,⟨(-470265424890534958602781442903338),(-470265424890534958371491858605849)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-198883783778286479439120394303388),(-198883783778286479292471741396349)⟩,⟨(-459334034980714340977576113407500),(-459334034980714340833886491153917)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-293641319374585748614876599323684),(-293641319374585748489522225500042)⟩,⟨(-405106396788132672281453965932208),(-405106396788132672158087686838495)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-353687494408262286266810763268279),(-353687494408262286159336029580230)⟩,⟨(-319694067243823792864813873974604),(-319694067243823792759361890386115)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-367461935703499451710544707343364),(-367461935703499451623398903958969)⟩,⟨(-223245828243942493603065192745362),(-223245828243942493518575289317602)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-334754355163629422724448457693991),(-334754355163629422658514946414445)⟩,⟨(-135910491561816894112141879689414),(-135910491561816894049473948869124)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-264064299482120184023784219821141),(-264064299482120183978581800839923)⟩,⟨(-70575839425545271219669668699360),(-70575839425545271177689614322836)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-167657345922372609965077279344506),(-167657345922372609938995981057950)⟩,⟨(-29913429227047477915386653720939),(-29913429227047477891671444388747)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-57296716446094431304857612655163),(-57296716446094431296398182425385)⟩,⟨(-7715964825180199534252800520584),(-7715964825180199526651936846743)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨8891415004729033145516800974070,8891415004729040754288560681063⟩,⟨12013062529522948566053141801859,12013062529522956175894770441500⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨27752083729657395006856342663890,27752083729657425006454273473086⟩,⟨35435295056318124277074868107595,35435295056318154279802893891568⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨49656152363158309197018206119234,49656152363158391411224671292542⟩,⟨56816996377805394662466468825246,56816996377805476881597108654091⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨76052193863662321040235728716268,76052193863662539149619374638713⟩,⟨74225273725833967677323452747507,74225273725834185792966259204747⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨107403101183369565024242421133191,107403101183370119512356437846195⟩,⟨85090828737568656980326199106347,85090828737569211475367529004137⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨142693844662943228058470026669747,142693844662944494309390241946242⟩,⟨86489543214138128872243097919556,86489543214139395129930236534922⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨179025094495469217043747191660279,179025094495471611105019294658416⟩,⟨75958816771808258045638164061280,75958816771810652112600613382425⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨211587049145863578004429393801737,211587049145867054039090380825478⟩,⟨52696221827826202296468302688726,52696221827829678334901534974854⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨234447110982948544703031290435871,234447110982952401849834234782243⟩,⟨18691365749864016257470957121710,18691365749867873405558549527050⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨242230371553890522092112805800664,242230371553893772863996694888561⟩,⟨(-20803869841896436342686094568536),(-20803869841893185572133973544279)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨232096376657757035927675350973498,232096376657759111441685202437463⟩,⟨(-58044599185990536534734591307869),(-58044599185988461024294292845187)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨205002200571258792021747765724279,205002200571259862838032807904914⟩,⟨(-84822403445990156375177114645032),(-84822403445989085563892848609398)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨165366879606662808983129247141127,165366879606663290899931709069069⟩,⟨(-94909583799981099260507934329891),(-94909583799980617349137027957664)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨119078681884519216150153213527999,119078681884519417201197247487918⟩,⟨(-85841484170395812239225656184886),(-85841484170395611192991085912513)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨71006279590902302580650224416822,71006279590902380917254999510944⟩,⟨(-59459239367443309773170474186064),(-59459239367443231439851216117335)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨23491462034876969667128516151028,23491462034876990122640778983844⟩,⟨(-21210561314072729352305531193700),(-21210561314072708897957744990341)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-3921834632953172102462043418874),(-3921834632953172101049707107600)⟩,⟨2738775130804106325789123636161,2738775130804106327057955604791⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-11597893027958904187968272438176),(-11597893027958904183680585185334)⟩,⟨8614629402334368273496118661589,8614629402334368277384577529266⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-18721227209743315059265119005996),(-18721227209743315051966005113913)⟩,⟨15646173284599328444825206336974,15646173284599328451575451947465⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-24812208877984296272322548840729),(-24812208877984296261789056395355)⟩,⟨24467659495398276773664579624513,24467659495398276783685278652486⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-29244770000815454941298850510373),(-29244770000815454927282397997900)⟩,⟨35414257728656345542009296881790,35414257728656345555806391302634⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-31225601342602231660658068278948),(-31225601342602231642689171474399)⟩,⟨48327076123601147096214559287119,48327076123601147114548166576443⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-29889494496037835398563138321577),(-29889494496037835375454128283712)⟩,⟨62435851671463399037935377809075,62435851671463399062282529000034⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-24605389506702539862957783944799),(-24605389506702539827404320993268)⟩,⟨76343816877294393294582390734694,76343816877294393332456207798205⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-15397180731292736596892098939389),(-15397180731292736488048854748875)⟩,⟨88133662473221938765685080107226,88133662473221938877985984785154⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-3280459132651558029755449744968),(-3280459132651557413049075638886)⟩,⟨95687585467932982692973359795916,95687585467932983314134270763971⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨9660630079042900885476334835761,9660630079042904138821687301308⟩,⟨97210928583026410421391310481474,97210928583026413679858489158213⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨20591964904584298661997090706375,20591964904584310912273696554084⟩,⟨91739119302621136537006344641101,91739119302621148792610438256685⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨26692307488502607353978280532336,26692307488502638001515060948532⟩,⟨79346767895070118679664114077308,79346767895070149332178671260148⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨26165626856131363358516753330152,26165626856131413450641376919980⟩,⟨61015041437445173349315901294800,61015041437445223445487854420390⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨18977491843941097704720565373584,18977491843941148433669194755440⟩,⟨38318976978532064808763928730844,38318976978532115540338786022815⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨6916508904477922274337505122120,6916508904477944532233010360869⟩,⟨13047249560053266290623433645955,13047249560053288549399565668228⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1183834871882598400269930513255),(-1183834871882596197221264003015)⟩,⟨(-539963604038644681416338989726),(-539963604038642478570736177212)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3614936932591223381306028810392),(-3614936932591218202484705048576)⟩,⟨(-1564194375643564019080001384430),(-1564194375643558840876996040784)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-6217738946499285434495103920999),(-6217738946499280249166726367827)⟩,⟨(-2415678453452510894639547950160),(-2415678453452505710369456264288)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-9056819208419115943898366338809),(-9056819208419112698836291579391)⟩,⟨(-2965649264067873908520094372028),(-2965649264067870664988545337048)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-12125340700248343515724513428699),(-12125340700248342090028087622620)⟩,⟨(-3065368063767083322605457911162),(-3065368063767081898825878436382)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-15336344032584362162611722958748),(-15336344032584361718481238389292)⟩,⟨(-2557135552056220321809973433048),(-2557135552056219879873912090263)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-18521080448535141493692663901448),(-18521080448535141388883652392009)⟩,⟨(-1326505115863419212392486883188),(-1326505115863419109955150471794)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-21416016912926396227057268013784),(-21416016912926396200951464894300)⟩,⟨624546835307607969887133890215,624546835307607993563850857426⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-23665721180218178995245123804749),(-23665721180218178982350199893567)⟩,⟨3128052693829202478412976410256,3128052693829202488952292963822⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-24874390820864399057593216734989),(-24874390820864399046679877610995)⟩,⟨5836958264141386932523963568973,5836958264141386941282529799940⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-24696460995074736343352493680903),(-24696460995074736333138431163049)⟩,⟨8258411804478132869916233292590,8258411804478132878280966382146⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-22937354735869197111813710524785),(-22937354735869197102532852882040)⟩,⟨9844516696327510627478758293685,9844516696327510635278882176514⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-19620645920186449529526667777013),(-19620645920186449521646345809171)⟩,⟨10122168119854691208187924768358,10122168119854691214973453387500⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-14977006779411386643221750036876),(-14977006779411386637228732978001)⟩,⟨8830693619611514532400558612360,8830693619611514537663128851503⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-9365477299440652808609086796784),(-9365477299440652804870182779325)⟩,⟨6032295650524293585839186811521,6032295650524293589167814637338⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-3182798178438103395796358916517),(-3182798178438103394529313246117)⟩,⟨2142822200815988953013178683776,2142822200815988954149214178069⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨220820288311167546544381516562,220820288311171971325761777096⟩,⟨(-357905565244756660124763921032),(-357905565244752235364070962456)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨624039022821235585721203416182,624039022821252603765197377366⟩,⟨(-1091207193692247899327358753287),(-1091207193692230881347311563226)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨911679503684508296677304621835,911679503684552827750375765961⟩,⟨(-1873230392175395939147534018752),(-1873230392175351408187874382627)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1011724584554314425276967392994,1011724584554425499117927923970⟩,⟨(-2725803586270616973691067936212),(-2725803586270505900022926187163)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨866890836888432476245108570092,866890836888695818622284606104⟩,⟨(-3647279102842983893750860276626),(-3647279102842720551619395190775)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨442617230320609119048809885008,442617230321169095365683482432⟩,⟨(-4596216994866073322072528550295),(-4596216994865513346088866111006)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-269037893284554701995646781392),(-269037893283565543427271032561)⟩,⟨(-5487908991871326495274471936845),(-5487908991870337337138923094359)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1238241113868213016131331407164),(-1238241113866856365228452841821)⟩,⟨(-6210551407877764969820285250997),(-6210551407876408319459282901113)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2380199599762682184817182962912),(-2380199599761239030709067362365)⟩,⟨(-6650151374354798482686525327442),(-6650151374353355329231684872541)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-3547956874129078333867254809612),(-3547956874127891528254996382464)⟩,⟨(-6718531793405089660865430884953),(-6718531793403902856006255124030)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4542431836918334279237464553870),(-4542431836917581638821829191277)⟩,⟨(-6382128982245102256276976140687),(-6382128982244349616680339364283)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-5136734005140657923899468551607),(-5136734005140265943868824257082)⟩,⟨(-5675693167033618791539761712686),(-5675693167033226812335535489344)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-5121211020714494227355652463826),(-5121211020714313981912534253079)⟩,⟨(-4679420201160763724475071109709),(-4679420201160583479793090653833)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-4378999486957415429533059723634),(-4378999486957338147015907888821)⟩,⟨(-3476683223755700385790722569282),(-3476683223755623103892310904995)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2951808562059217440649800419479),(-2951808562059186544777878949048)⟩,⟨(-2137006506691310072786230890970),(-2137006506691279177319248754414)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1041351657633704502658460756199),(-1041351657633696297842476303633)⟩,⟨(-720221384653419896821870835831),(-720221384653411692146923146934)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨33493783455164205842803724107,33493783455164205869327378662⟩,⟨54522478549560295117125970343,54522478549560295147345229593⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨109756223470507596026364456124,109756223470507596109109181650⟩,⟨157640573490274498671395163469,157640573490274498764786892947⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨212708460331768402241977101562,212708460331768402389472144887⟩,⟨244083412791388505715986534124,244083412791388505879361707719⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨354835230558977442398006063026,354835230558977442624035091199⟩,⟨306641176857936074124081635002,306641176857936074368797056854⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨536817156485908499431525113608,536817156485908499756293921268⟩,⟨340554217657296265026697891207,340554217657296265370179216724⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨744535787390058917380840143479,744535787390058917844847607347⟩,⟨337581882579892872287370301526,337581882579892872767922124885⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨956063676772757130342400707132,956063676772757131081252147367⟩,⟨284010727655471575381091003834,284010727655471576132388038583⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1149436534471403095391897882666,1149436534471403097236328337658⟩,⟨170057073233069808063285217098,170057073233069809914455216541⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1303383687542906549672779315813,1303383687542906559600647924552⟩,⟨361768283945745863728926125,361768283945755792211991579⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1397646774963914109109699341375,1397646774963914178959163730472⟩,⟨(-202798251108528413168301405014),(-202798251108528343323120980955)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1416037736983286072587236523281,1416037736983286469289005094635⟩,⟨(-401228049958760039012898704192),(-401228049958759642318210630558)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1347584209788839348961528560983,1347584209788840924200373745281⟩,⟨(-547065638073320372600097559163),(-547065638073318797368949405210)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1184980862807106076013960969788,1184980862807110219422986188782⟩,⟨(-597561655106585025631014951448),(-597561655106580882228574499861)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨928102761162151522078366755328,928102761162158610651936787187⟩,⟨(-533757124159328302179911564709),(-533757124159321213610868185110)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨591382353734320935070059809447,591382353734328338344427142028⟩,⟨(-366909000216718454910552072837),(-366909000216711051638623595021)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨202915585081215892531046828640,202915585081219109866079487034⟩,⟨(-130406097891366138937516404445),(-130406097891362921603223251712)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨33548235136427369916659986680620,33548235136431838025375815407453⟩,⟨(-465926089364587141583230095014351),(-465926089364582673483647412889610)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 3) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_3 (tableDensity false) (fullFactor true 0 3) density0_contains hk0_1_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨11797617345006669805968502924063,11797617345006669809600450173816⟩,⟨(-12394382836406823055039345754041),(-12394382836406823052537890450466)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_3 0 3 ha0_1_3_contains + def realAnswer : RBox := ⟨45345852481434039722628389604683,45345852481438507834976365581269⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_3 +namespace hm0_1_1_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨4946971754640406591736691159018,4946971754640418321587886574635⟩,⟨(-3657391265297086014909424507742),(-3657391265297074284727113359160)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨14501874146362082446781850617102,14501874146362109791868768757298⟩,⟨(-11522155044465854820718791210033),(-11522155044465827474604780389250)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨22785795348508788668623701873655,22785795348508815467834600462392⟩,⟨(-20796013001967002358725205141076),(-20796013001966975557695741806952)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨28238372019268947431217961452303,28238372019268963844022524306639⟩,⟨(-31757148101309359590696002341608),(-31757148101309343175239234264261)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨28666815733583031591135872331990,28666815733583039211075467852696⟩,⟨(-43995299937330839213142398924061),(-43995299937330831590222706012472)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨22053040142792572224000036730178,22053040142792574678241470537504⟩,⟨(-56422852014163076685489147402159),(-56422852014163074228366006064500)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨7841130736807669148591883113401,7841130736807669729733317850223⟩,⟨(-67115583369166630474943520084002),(-67115583369166629891479904293507)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-12289201413562285292108869053238),(-12289201413562285149327149659210)⟩,⟨(-73436212410123087344426012614126),(-73436212410123087200376796940573)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-34569115485602357560848057321649),(-34569115485602357491162469953225)⟩,⟨(-73054881287982334267073392959859),(-73054881287982334197549062692811)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-54090666966130490035489473702248),(-54090666966130489979557595957919)⟩,⟨(-65294132812452319244377182522044),(-65294132812452319190154354722479)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-66387891824990614552293812017616),(-66387891824990614504667830995205)⟩,⟨(-51706873936239975163390536664750),(-51706873936239975118818930590915)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-69044646304975611501693908573883),(-69044646304975611463101160389684)⟩,⟨(-35495391685146171968535088001608),(-35495391685146171933842392318809)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-62374320099869526929359186046876),(-62374320099869526900197386971404)⟩,⟨(-20290231389341288279564219606568),(-20290231389341288254451742156958)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-48651534819543998660353954398846),(-48651534819543998640484225432834)⟩,⟨(-8945271994246016299058589809906),(-8945271994246016282696207599267)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-30603533790257057905631994951975),(-30603533790257057894253879310753)⟩,⟨(-2604739245449440738589473639088),(-2604739245449440729584344508379)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-10406940312022815672330969034076),(-10406940312022815668654498529951)⟩,⟨(-348823519157533585413880697164),(-348823519157533582578695324896)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨328834842489246410712767460192,328834842489252675663854054746⟩,⟨2307679363944345861434687362767,2307679363944352126246841311548⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1247755604035959402259747910623,1247755604035984113022521474675⟩,⟨6813735133019526437355219585356,6813735133019551147713061419229⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨2930574121179678701429998925984,2930574121179746468653481793811⟩,⟨10960178668769599266153238285789,10960178668769667032739914870942⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨5809066197057357440918054490024,5809066197057537380253481325507⟩,⟨14436800398360445144164939765720,14436800398360625082689807328815⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨10146974759717573263596001520134,10146974759718031116732689166285⟩,⟨16861256577872232749391203131874,16861256577872690601623163372440⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨15889603800707853166029616188890,15889603800708899596677564472381⟩,⟨17799967089999647884286752780130,17799967090000694314035272793426⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨22544150474518756716024125359296,22544150474520736891316909212984⟩,⟨16806339076476353623894722362354,16806339076478333798404618034701⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨29217821212913862747806883488367,29217821212916739182987464597142⟩,⟨13554296881922409682972164689004,13554296881925286117601327747118⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨34804004644747392525858625883350,34804004644750584195560869389655⟩,⟨8106327582483538118209634307615,8106327582486729787681103556068⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨38249194138413947404654950250890,38249194138416635839865605082083⟩,⟨1155030264743858090102594555108,1155030264746546525451146193764⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨38831412073974278505828428850631,38831412073975993305005345881360⟩,⟨(-5960682339044823007165263809796),(-5960682339043108207493568471155)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨36318308587443459004558121387491,36318308587444342598307458320274⟩,⟨(-11575007271188499721796769047867),(-11575007271187616127283800489173)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨30960500006834291979637467615298,30960500006834689095835627798728⟩,⟨(-14295195692032635616294984271178),(-14295195692032238499228241224190)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨23400583369495500384860667061369,23400583369495665849318218808250⟩,⟨(-13526711313615237897383926815834),(-13526711313615072432138772787469)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨14466854302911454625263048618049,14466854302911519033405696486928⟩,⟨(-9578318950926736983924157441873),(-9578318950926672575236415418321)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨4879647733876326735641959889158,4879647733876343545120811649609⟩,⟨(-3448874831612206484276111802082),(-3448874831612189674601954060508)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1078134864417506654755312287546),(-1078134864417506654156548796085)⟩,⟨62594315048714285384269302123,62594315048714285975880124065⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-3254593202045490619657048337024),(-3254593202045490617809858193423)⟩,⟨269989977747577227182413829170,269989977747577229008903105325⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-5455802931953784806937412908211),(-5455802931953784803720172977991)⟩,⟨707844456838308375699758652464,707844456838308378887829226362⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-7594175544245671356695722545764),(-7594175544245671351935435087247)⟩,⟨1495288230247612801580426484025,1495288230247612806311695680871⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-9464290552982455122724732120544),(-9464290552982455116229918713415)⟩,⟨2744341557597167932942333548243,2744341557597167939419202422692⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-10802650129926442337286800240698),(-10802650129926442328698092028842)⟩,⟨4566521061694048922689940090608,4566521061694048931280645167787⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-11388497492461192248818400068444),(-11388497492461192237111406460071)⟩,⟨6993155680015078157883851434476,6993155680015078169626406541171⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-11098892997016216327856019474073),(-11098892997016216306791151968969)⟩,⟨9862525931026874224845123062785,9862525931026874245983530653864⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-9934622435052303552512682474505),(-9934622435052303471870832205305)⟩,⟨12784087015205687275096596527795,12784087015205687355830591025135⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-8053245540380436821310006472598),(-8053245540380436326236661263611)⟩,⟨15195253060150302660996577985407,15195253060150303156152741453860⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-5764050526168227447939607659570),(-5764050526168224803213629417409)⟩,⟨16489738869887873781549246323858,16489738869887876426331583066156⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-3446925685961146582124684005913),(-3446925685961136599602052567306)⟩,⟨16216319878662169994792318681027,16216319878662179977350863474958⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1462642358809076055363191324365),(-1462642358809051053837462174039)⟩,⟨14288738384212517281291478607075,14288738384212542282837311726960⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-118935043027954036843694196852),(-118935043027913141089386225467)⟩,⟨11017981018849328022376877353731,11017981018849368918133612386642⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨409254726325440042199125665411,409254726325481479500103176137⟩,⟨6892344015222225495861672082009,6892344015222266933155739289863⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨230240282966760801468667421256,230240282966778987291724777148⟩,⟨2338304208986971152240822024452,2338304208986989338058474366377⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-209352162059071132558892828371),(-209352162059069281650606079216)⟩,⟨(-381244060482514131137056002372),(-381244060482512280207690816199)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-643432354028422365969761890386),(-643432354028418017969036268654)⟩,⟨(-1126013799941714810793209924783),(-1126013799941710462728346750329)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1124619187361097573282365123143),(-1124619187361093226123565061890)⟩,⟨(-1813823667402454017806700250495),(-1813823667402449670538771163339)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1689293140644720674378501975549),(-1689293140644717960346257136564)⟩,⟨(-2402352715534283806893325384106),(-2402352715534281092704536522993)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2373862500108282525627529334854),(-2373862500108281337968887361326)⟩,⟨(-2854807289487826133294893767884),(-2854807289487824945443195699347)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-3192426276785400256476462894577),(-3192426276785399889802700612960)⟩,⟨(-3150969405726241913245051183305),(-3150969405726241546353940648233)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-4108715341527082073381486947033),(-4108715341527081989865692283282)⟩,⟨(-3278502669402901062345648871519),(-3278502669402900978598194464535)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-5035854693975206021528939732350),(-5035854693975206003855998285319)⟩,⟨(-3215854227548665280034097398436),(-3215854227548665262129538129471)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-5859742077007368828851684668631),(-5859742077007368822498515285148)⟩,⟨(-2940059348750964414260044250066),(-2940059348750964407689158408555)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-6459988360307415889038412185873),(-6459988360307415884488299226028)⟩,⟨(-2455155005907765610544073140998),(-2455155005907765605802649498098)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-6723303966658115381502354460923),(-6723303966658115377444483436708)⟩,⟨(-1817067849351071954634766835853),(-1817067849351071950421749850058)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-6552003502018360794192086653571),(-6552003502018360790566268887211)⟩,⟨(-1135957785352525792653755481737),(-1135957785352525788911488658056)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-5876040775139144215575769517195),(-5876040775139144212517515874847)⟩,⟨(-543702196221540908331287867126),(-543702196221540905193283885401)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-4678626357253765587349534832854),(-4678626357253765585037586025010)⟩,⟨(-142295233919644921739445964263),(-142295233919644919378804846448)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-3020717637846397157878988605472),(-3020717637846397156445102644527)⟩,⟨34653972760828811992703586786,34653972760828813451721679774⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1044487424493003149388723073871),(-1044487424493003148904414406994)⟩,⟨33939770256191831254352722740,33939770256191831746232705970⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨66442318118888956872263770075,66442318118892593346580232790⟩,⟨(-121152413611771911548138035641),(-121152413611768275071753862864)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨193652605365774816595639852556,193652605365788803762879958775⟩,⟨(-374424385580573804476891166704),(-374424385580559817302718841774)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨303058689976364283289857804101,303058689976400888352448998037⟩,⟨(-655315419013154840047585747601),(-655315419013118234971363642489)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨378750784837829469856453751323,378750784837920788453141524116⟩,⟨(-968459202297553387262325413162),(-968459202297462068642229206524)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨396429333394960146890571756337,396429333395176678351053530608⟩,⟨(-1307181432280836061856233597846),(-1307181432280619530358625821152)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨327733538275872811292856539771,327733538276333246258867056763⟩,⟨(-1662027218165161185499197412046),(-1662027218164700750477469168636)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨156585748050894765177358621403,156585748051707915184152764740⟩,⟨(-2023681005294273018431088219732),(-2023681005293459868344186939400)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-106877525661409956581190369573),(-106877525660295253030110617101)⟩,⟨(-2374609656257269742843598684014),(-2374609656256155039185582360678)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-424006484143160512033278174413),(-424006484141975678398685550461)⟩,⟨(-2681319861694112017287402062008),(-2681319861692927183522500573857)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-733400558626399143463176986035),(-733400558625425812460983425977)⟩,⟨(-2893959058125287964655933871129),(-2893959058124314633508383381107)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-965710251895619193329554369628),(-965710251895002714674608219474)⟩,⟨(-2951647443761885019006553518516),(-2951647443761268540199960131279)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1069504132223286874123091779841),(-1069504132222966239236719987666)⟩,⟨(-2798611227290607124871188982902),(-2798611227290286489835034544272)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1030264832652582496614998049855),(-1030264832652435245365906824598)⟩,⟨(-2415873483896532673874747829107),(-2415873483896385422489400149385)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-858886292514335784637228131156),(-858886292514272715613866958396)⟩,⟨(-1840949392141272096283692590454),(-1840949392141209027151917848745)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-572764045785269583434115324999),(-572764045785244388590594192740)⟩,⟨(-1143649764287700329434297911008),(-1143649764287675134521034428526)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-201618617684286646820542271210),(-201618617684279958536556163405)⟩,⟨(-386708510812971726297129081891),(-386708510812965037989308261716)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1072243068625249426949708414,1072243068625249444004392471⟩,⟨1572206246182021543404834606,1572206246182021562226087228⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4254801599768752672304360290,4254801599768752725657971721⟩,⟨3662444850967821848714156917,3662444850967821907253325881⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨9880769793853798852222116067,9880769793853798947760930964⟩,⟨712664458004298292343009258,712664458004298395737092679⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨19378907761316324473296337804,19378907761316324620963189877⟩,⟨(-16127316972556991553677796505),(-16127316972556991396662555045)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨38332882186271219799525927309,38332882186271220016194521772⟩,⟨(-59194483939693197813155861525),(-59194483939693197586865353389)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨77802408202968530651649496419,77802408202968530973845620248⟩,⟨(-135616868645350020831983018376),(-135616868645350020501328237952)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨145947029850501298919448890102,145947029850501299467621005327⟩,⟨(-239513569881833430126056418795),(-239513569881833429572347912971)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨238441167691743928530326497620,238441167691743930005876280556⟩,⟨(-355097545305548232165462771085),(-355097545305548230689198863782)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨338422905544485792089881759257,338422905544485800240109648282⟩,⟨(-464249539602103274740856039450),(-464249539602103266595756941392)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨422397737398037237017477393292,422397737398037294222987618525⟩,⟨(-550571864165232972223554531904),(-550571864165232915028444134456)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨467431670543934416852879422855,467431670543934741000299637245⟩,⟨(-601606290652797550662808932604),(-601606290652797226529394178548)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨459967915486992186951472122907,459967915486993473521766458608⟩,⟨(-609977428346008433839109224022),(-609977428346007147284325162044)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨402489802918427423720389656897,402489802918430808848874283742⟩,⟨(-570009238134424602146694330064),(-570009238134421217033121095418)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨309076728856934477933803343414,309076728856940271853141363599⟩,⟨(-473701088101447348456025763129),(-473701088101441554548918324486)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨193731909541373281377683995658,193731909541379334739040207481⟩,⟨(-317050062901580283896087222389),(-317050062901574230542713301065)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨65970633948856604010829626814,65970633948859235212513392981⟩,⟨(-111875377075428959912407433164),(-111875377075426328713466573373)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-16195795920969092027477135230524),(-16195795920965405969444753616089)⟩,⟨(-75398096176327774914056822996482),(-75398096176324088856411948233617)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 3) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_3 (tableDensity true) (fullFactor true 0 3) density1_contains hk0_1_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-15427653451162568212554434842682),(-15427653451162568207804965362236)⟩,⟨16208039093762768607164933665994,16208039093762768610436067524514⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_3 0 3 ha0_1_3_contains + def realAnswer : RBox := ⟨(-31623449372131660240031670073206),(-31623449372127974177249618978325)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_3 +namespace hm0_0_1_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-72801432016089576401073637979140),(-72801432016089539553812280128655)⟩,⟨24077768283902081646513091020795,24077768283902118493159738357675⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-214839912651018352935578809190348),(-214839912651018265523519190026785)⟩,⟨83330359543712012972377009187264,83330359543712100382147384676341⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-343410538589387914661449264926466),(-343410538589387826018988801042198)⟩,⟨174284374139138115106178640638266,174284374139138203743487290490700⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-442002827223001793799875454501276),(-442002827223001738096660948459694)⟩,⟨311795067237401357003102173052373,311795067237401412696828612760148⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-486189905617774542429999095854993),(-486189905617774519661655881274358)⟩,⟨498134291551570646129548584651510,498134291551570668882169282972639⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-448017920549787296373361743484498),(-448017920549787290248178166937897)⟩,⟨715745784060977507017464874691610,715745784060977513119095837741562⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-307958386983786776357616360021918),(-307958386983786774915260655037380)⟩,⟨925029578829797149923928899325651,925029578829797151342487777569791⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-71281151337510390939342447541360),(-71281151337510390437512015659526)⟩,⟨1072536001089620297825935791476160,1072536001089620298310908651074802⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨222216562300371200053884622881726,222216562300371200391352311225785⟩,⟨1110604674273926947878482696181251,1110604674273926948205576622480881⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨506062909288259119527362149537315,506062909288259119827114113774331⟩,⟨1020907813702388207578090314499533,1020907813702388207871615942966773⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨711802026273708109631069946991376,711802026273708109892904939561686⟩,⟨826791863247155132277605962688318,826791863247155132534394645652760⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨795892156488223685458363370354582,795892156488223685671707995107050⟩,⟨583889259028640777605470761679515,583889259028640777812873517395382⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨751852520023140451990268030518662,751852520023140452150852503423923⟩,⟨354120086973059055121164852346918,354120086973059055274463621538135⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨603076613097455954933217128434543,603076613097455955042132537989195⟩,⟨180019135981685881937620315201489,180019135981685882039232307099777⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨385402265789138783062960501817002,385402265789138783125088760348467⟩,⟨73254523977187536001395419577931,73254523977187536058098970176105⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨131959947002568094370925712914941,131959947002568094390932325251138⟩,⟨18075669942709220673410697229396,18075669942709220691436998209865⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨4489050630599998575810201031891,4489050630600017231312966488867⟩,⟨(-26266235779778986541223960759900),(-26266235779778967885672722706795)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨10938973293362037054155019665394,10938973293362109301145052782357⟩,⟨(-79804562491686881589936873641968),(-79804562491686809342564523833541)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨9632833845823621247135940124955,9632833845823812417051743780056⟩,⟨(-135697785595233822203515248979250),(-135697785595233631032182306944297)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-4917129815715746771987235825271),(-4917129815715264961401286213018)⟩,⟨(-193571937864557843373635969127721),(-193571937864557361559497317895829)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-37976677331101649709793113982392),(-37976677331100504500462542250779)⟩,⟨(-250180122570344733065462387613453),(-250180122570343587849056140428391)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-93168235704824516944316529180722),(-93168235704822113657881527546718)⟩,⟨(-298802444809282012600038646087964),(-298802444809279609301552000032823)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-170091306957471689514162910263078),(-170091306957467598656866474600837)⟩,⟨(-329804613785175654323516114847122),(-329804613785171563448026100719343)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-261829523160209605193523668996579),(-261829523160204395258710403976146)⟩,⟨(-332933007295763209046025031486691),(-332933007295757999086460116481453)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-354139309746894190472782438425946),(-354139309746888304198618626885059)⟩,⟨(-301400849489257854297193899858289),(-301400849489251967997628653716093)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-427935673701535414551299591746046),(-427935673701529747703146858754460)⟩,⟨(-236471224657192150437576151958732),(-236471224657186483569441102493126)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-465100630381930110443410237099385),(-465100630381926072206731039799370)⟩,⟨(-149756203271322508963064281761824),(-149756203271318470712881004394271)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-455179698676790589361443677285420),(-455179698676788310250513652658439)⟩,⟨(-60879404975350150175906912208859),(-60879404975347871057673297812776)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-398946790870845176558227997808187),(-398946790870844074841939220715223)⟩,⟨9148106738557309308168936359919,9148106738558411026974821428076⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-306425844401993315547723547063386),(-306425844401992830387335867317267)⟩,⟨45746555862658624976135016638717,45746555862659110136266008388528⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-191134384763408629283337281341440),(-191134384763408433202452653878647)⟩,⟨45931938983467695769587072787972,45931938983467891849395128882430⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-64728693315243726755626021018601),(-64728693315243674594935979661567)⟩,⟨18676207892046856151412848052147,18676207892046908311580760380711⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨6281346073607929587149089581766,6281346073607929589319088201060⟩,⟨3067043502537876990823046370352,3067043502537876992637934149110⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨19341488412021657453952277726647,19341488412021657460582855804232⟩,⟨8655412656310148064513983214188,8655412656310148070001280925602⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨33796054102420476172054513295537,33796054102420476183504501287302⟩,⟨12534966904957755619370895059338,12534966904957755628673706064840⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨50271177303064094028022209215854,50271177303064094044826393332327⟩,⟨13410914093708132358773392818637,13410914093708132372076121503547⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨68801874129177473590175131508140,68801874129177473612892955654011⟩,⟨9887779852461221575437749120677,9887779852461221592861323008627⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨88479542809885748343095177373741,88479542809885748372443519818090⟩,⟨625078071140055303508634361378,625078071140055325392671633422⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨107280975568208106457629196435665,107280975568208106494883138916334⟩,⟨(-15318498389775941706287961222041),(-15318498389775941678992761742968)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨122263996369878728970402243638459,122263996369878729026751503390637⟩,⟨(-37855651775133992911201189105030),(-37855651775133992865909662911052)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨130182019569359854820881672583903,130182019569359854990211944701057⟩,⟨(-65153169612808702430400302629034),(-65153169612808702271207552128688)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨128512262613023337808328855168328,128512262613023338832314382415063⟩,⟨(-93294014032444424140922372020556),(-93294014032444423125381595107617)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨116631007793785396478858637737162,116631007793785402478515789991773⟩,⟨(-116705479761032156935550970028863),(-116705479761032150942171901678595)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨96483951595298937917477958743621,96483951595298962883268743561323⟩,⟨(-129396126393086447273981302088981),(-129396126393086422312259651319036)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨72064171541721001125772192933878,72064171541721069204020621648763⟩,⟨(-126652611530624031217323406177297),(-126652611530623963141236552625124)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨47732251150048891378757907886024,47732251150049010597639699504907⟩,⟨(-106623164769022464804486949407614),(-106623164769022345586434251305452)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨26361281392430952227901990827019,26361281392431078327325463402809⟩,⟨(-71075479782670046794443032076802),(-71075479782669920695173112192756)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨8313433245452848365863454629979,8313433245452903411961140433186⟩,⟨(-24929181893266377171141458703876),(-24929181893266322125031225662935)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-174072256188220270695338522155),(-174072256188217251179072401435)⟩,⟨1573318401491205226940338291683,1573318401491208246658677323140⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-420019859590160596852292057539),(-420019859590153347033012869570)⟩,⟨4789090900678070482231766363247,4789090900678077732646477681106⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-355697038884149703594778094567),(-355697038884142137085513754097)⟩,⟨8186495655452496468234924406636,8186495655452504035698105550823⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨234760081973224171066417719400,234760081973229192006775526221⟩,⟨11815326013381184872847865150238,11815326013381189895039214760419⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1575607560365497625874801064630,1575607560365499876163891134576⟩,⟨15618333402805071279359959134842,15618333402805073531105687772083⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3877588745521905329170616567699,3877588745521906024149335327857⟩,⟨19413446617736915575612953322605,19413446617736916272131425915046⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7260827545819964861798089787059,7260827545819965022475462695475⟩,⟨22904002519899798200911271608953,22904002519899798363062240828793⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨11635692758171776730479631359788,11635692758171776768194873028056⟩,⟨25697051766729222906709001748595,25697051766729222945661215221061⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨16609390882384131432867120981327,16609390882384131450409718378450⟩,⟨27348694825678073423281002756280,27348694825678073441640805668701⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨21464901185386670610317562729365,21464901185386670625284378094889⟩,⟨27468687756050952923561280142237,27468687756050952938808644775643⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨25242862047907849364493391963036,25242862047907849378944113014632⟩,⟨25857504375061611205598445185878,25857504375061611219766584434276⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨26941237443860648679207108583073,26941237443860648692768572689088⟩,⟨22613131205974684713517840632499,22613131205974684726322181494966⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨25781563462451939637727804510068,25781563462451939649576359590595⟩,⟨18139678993670882666882108495662,18139678993670882677696513367390⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨21447846481501433345278924059300,21447846481501433354499703901662⟩,⟨13009847192190961883984196624444,13009847192190961892167256335741⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨14224221356787606298617544359761,14224221356787606304464422450596⟩,⟨7730284500098062354428569186790,7730284500098062359512783828355⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4981068211917292927530754543080,4981068211917292929528928312037⟩,⟨2551429856166243005522961856858,2551429856166243007241855684661⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-404807082017574094708412722967),(-404807082017569712477132885832)⟩,⟨(-162370624394369288649446340555),(-162370624394364906381387920050)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1230062414261415259185899262339),(-1230062414261398400938782167563)⟩,⟨(-442913228169290976048053349154),(-442913228169274117687875404910)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-2097393474181214516953813473030),(-2097393474181170394069463008139)⟩,⟨(-589773564696169473105473241192),(-589773564696125350022408125678)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-3021585251512528400153900403905),(-3021585251512418367889768285123)⟩,⟨(-516520861229142054899862572094),(-516520861229032022336341966872)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-3991008248374977330849775986767),(-3991008248374716782652669619107)⟩,⟨(-151283010883098103154929791346),(-151283010882837554537230746511)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-4950154451839747489504963442951),(-4950154451839195101909386340536)⟩,⟨549892317112228176362040591448,549892317112780564521377035800⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-5794985279907125839491389313285),(-5794985279906155386020910243074)⟩,⟨1592875136790320498411556185847,1592875136791290952606926240758⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-6392453398478748536888363438755),(-6392453398477428956491018357037)⟩,⟨2929533520720555178856977221626,2929533520721874760154539881733⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-6615374186536221883733738612009),(-6615374186534835594247767079289)⟩,⟨4437455647899313488765742302334,4437455647900699779330471606944⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-6383806376782378416125158598417),(-6383806376781255704001352932945)⟩,⟨5914162188672671406183155518365,5914162188673794119543155039813⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-5705891848235232779142370717278),(-5705891848234480247955518077165)⟩,⟨7096679039603123396427959870473,7096679039603875928851079683305⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-4695907817639043439269105536789),(-4695907817638612886793087127352)⟩,⟨7700316091554109083191307556523,7700316091554539636774497603981⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-3536332870523663235160314138377),(-3536332870523448746766084593519)⟩,⟨7474255210494895176863512364734,7474255210495109666176846949286⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2394396182771222564936147738647),(-2394396182771124576758967932767)⟩,⟨6285323482188122848774367408974,6285323482188220837638374641240⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1360737326028447626676177351888),(-1360737326028406684677756129106)⟩,⟨4196523557487564087732088036265,4196523557487605030153943671112⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-438145373992795341610863489253),(-438145373992784219177024738707)⟩,⟨1474051287153393612367036175192,1474051287153404734943829990713⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨47659824644302102078255586461,47659824644302102105867213612⟩,⟨(-32840976882086497521089911888),(-32840976882086497496365758193)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨137290665560753394619552524437,137290665560753394705116867913⟩,⟨(-107163433306581624030819444229),(-107163433306581623953474854569)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨210606925217795068005371003833,210606925217795068155902982090⟩,⟨(-206489130587526211277566280667),(-206489130587526211139001549793)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨259649749619221865508699174126,259649749619221865736028688555⟩,⟨(-343022995852281617644810966403),(-343022995852281617430970200936)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨278413458932016200453920753356,278413458932016200776268606148⟩,⟨(-518385784894103396333370056569),(-518385784894103396023571376488)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨257956146442457745903347215789,257956146442457746359325130146⟩,⟨(-719918509185315260816618504205),(-719918509185315260370313913400)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨184622242555261213339107569373,184622242555261214059314657247⟩,⟨(-925977621261803167150958342866),(-925977621261803166435913242037)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨48757968146248318724125169908,48757968146248320511567800110⟩,⟨(-1113196345712428731786671969710),(-1113196345712428729999073630365)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-144583763298718415050602141162),(-144583763298718405412214381482)⟩,⟨(-1258379048705881799232801279125),(-1258379048705881789589703778578)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-371371173588446508632320103190),(-371371173588446440431298113947)⟩,⟨(-1340332013799032302451878480783),(-1340332013799032234243776054559)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-589618315123904329847066790757),(-589618315123903940520510870560)⟩,⟨(-1344319124399529159702423010168),(-1344319124399528770368940382517)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-745555862949610507121704845421),(-745555862949608955279857859353)⟩,⟨(-1263977032769299015428079171022),(-1263977032769297463581239012616)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-789142608210869078039461076282),(-789142608210864985773993415381)⟩,⟨(-1098346052556668890120036098578),(-1098346052556664797852362937676)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-695547586904760537359967283204),(-695547586904753525625477571189)⟩,⟨(-851792742489035823105081030279),(-851792742489028811370820698835)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-475528562575191596625736066182),(-475528562575184267830391906598)⟩,⟨(-538970508008005195532215877741),(-538970508007997866738077602552)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-168681283561045820938296657088),(-168681283561042634963832033003)⟩,⟨(-184256135839982798804503867510),(-184256135839979612830661909286)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-40532269540512321928423623436283),(-40532269540505421066268836605367)⟩,⟨874727608102171218928325129165428,874727608102178119778811434219292⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 4) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_4 (tableDensity false) (fullFactor true 0 4) density0_contains hk0_1_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-45098678731741256247689741685615),(-45098678731741256238307468286109)⟩,⟨35444837200408217755538398724223,35444837200408217762183727099283⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_4 0 4 ha0_1_4_contains + def realAnswer : RBox := ⟨(-85630948272253578176113465121898),(-85630948272246677304576204891476)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_4 +namespace hm0_1_1_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-12884621102425834416531636566647),(-12884621102425804235431510988892)⟩,⟨2438752854731682871228109082013,2438752854731713052533464036688⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-38545769666991427384268358763916),(-38545769666991355816297010907048)⟩,⟨9014359613730371000742485893414,9014359613730442569466764023367⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-63037414183308657223787250309764),(-63037414183308584714313572757899)⟩,⟨20450343935608669710856280162505,20450343935608742222027810265417⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-83161959732723994727276357755957),(-83161959732723949238041710989151)⟩,⟨39229253218962737755608401883711,39229253218962783248100424829282⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-93299963958505287258845900067953),(-93299963958505268736929386399913)⟩,⟨66550034104187592945766468793482,66550034104187611473218326980380⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-87098106899753669237856608269025),(-87098106899753664329920728193981)⟩,⟨101122847282160455882976756598257,101122847282160460799344216653233⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-60569693080828446941305675217926),(-60569693080828445870096286083704)⟩,⟨137547554177539871748215673136580,137547554177539872828706977508541⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-14956642837890671234453143439575),(-14956642837890670943330685968575)⟩,⟨166443803744327681040728658777695,166443803744327681339070603947588⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨41871969617131471993159743274666,41871969617131472146099281189146⟩,⟨177996299331507051439144092763236,177996299331507051595827674690260⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨96777582188170214469881019030548,96777582188170214598448671525377⟩,⟨167082652990272910725142373244234,167082652990272910853212464323860⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨135991593611764104401079704708497,135991593611764104513478455833486⟩,⟨136330875698178172364550934031562,136330875698178172472385156106387⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨150837246493342363986526739184370,150837246493342364078603904139356⟩,⟨94950252947945415328585086095821,94950252947945415413169034722627⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨140720964918897804107891389323412,140720964918897804177419053001367⟩,⟨54420441396549506410923600797492,54420441396549506471853156013724⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨111379156344294510263247205943287,111379156344294510310257897327505⟩,⟨23827976004589816647470714768408,23827976004589816686670766433047⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨70423033228333173232439396196766,70423033228333173259107350158916⟩,⟨6794286240570107245664893628778,6794286240570107266925799650692⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨23973662621836873126525896902819,23973662621836873135089524667520⟩,⟨858042936668030446640307964050,858042936668030453268843186512⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2564146476093834098087369223980,2564146476093849457928115762580⟩,⟨(-3270702792846355827693954242557),(-3270702792846340467841016831798)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨7197952483940917083791094480888,7197952483940976591521863693888⟩,⟨(-10092920997278775518232229611971),(-10092920997278716010493218430722)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨10301373791263069918874832818689,10301373791263227492145020947359⟩,⟨(-17668750015087024207959832239533),(-17668750015086866634769635673142)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨10768366867281548332649144828631,10768366867281945819127188606635⟩,⟨(-26227345784592011807793432446887),(-26227345784591614321630818950975)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨7516470253567594052165746005483,7516470253568539668466402113302⟩,⟨(-35550515667320026021252754811250),(-35550515667319080405696639240856)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-233215798531267451880723115071),(-233215798529281392213322481297)⟩,⟨(-44749944762274256395918019724794),(-44749944762272270337635495624616)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-12593298987171809275142058485558),(-12593298987168425673790558443365)⟩,⟨(-52150326232552926756282712825583),(-52150326232549543157142171017765)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-28681736780815358741156133482975),(-28681736780811047511619197721008)⟩,⟨(-55596261895201869212343422843365),(-55596261895197557985930743928252)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-46404510489574881292926320578512),(-46404510489570010606474503762749)⟩,⟨(-53278788817258836298059471744610),(-53278788817253965614909666184398)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-62606235415888755171524896262381),(-62606235415884068649067203528392)⟩,⟨(-44745841762677403920316285278432),(-44745841762672717400559594083179)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-73773357522392491185455230965065),(-73773357522389154811385305278127)⟩,⟨(-31548820215011961243337159399379),(-31548820215008624871162663425647)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-77061697965880920649039294233278),(-77061697965879040038644049802931)⟩,⟨(-16960058849972092130142851237892),(-16960058849970211520777930098517)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-71222032522701305949689407426133),(-71222032522700398102890370250824)⟩,⟨(-4670314693276195482451263722331),(-4670314693275287635960389337458)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-56983700046033541098885625711358),(-56983700046033141813007267143689)⟩,⟨2722779771434529861977334865688,2722779771434929147981338008917⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-36546498519040758394462622063593),(-36546498519040597175677785842375)⟩,⟨4538520190482393200823315434907,4538520190482554419846378119255⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-12553000928507196030720739265492),(-12553000928507153166489974514176)⟩,⟨2048360490433706538762524197115,2048360490433749403102888780590⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨844897707188448865466347013649,844897707188448866341507193525⟩,⟨1332921320373112055156389292885,1332921320373112056015726260066⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨2680527305032538825960257792286,2680527305032538828652696365615⟩,⟨3969675903669809201175885211730,3969675903669809203815574346563⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨4908976512161541515530303307751,4908976512161541520189132183203⟩,⟨6478006455325763570615653713305,6478006455325763575177929311571⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨7672561138888891609973254134213,7672561138888891616771351721378⟩,⟨8641833079631858912501055896319,8641833079631858919148990729430⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨11001432101295925808155133544246,11001432101295925817213789810253⟩,⟨10067708598475044117605322284419,10067708598475044126454938957514⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨14839663650711153464222336682278,14839663650711153475778449802703⟩,⟨10247372856421396663186643009823,10247372856421396674459331474828⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨18998792278875876003937234644349,18998792278875876018838262454097⟩,⟨8755540371260421239261135242657,8755540371260421253772086059641⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨23052549409428171779989199060183,23052549409428171807402975504684⟩,⟨5452559037655269823717003527148,5452559037655269850712181267029⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨26333468513070599062555158228366,26333468513070599179771618607083⟩,⟨621574316157424387955577932560,621574316157424504861164417532⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨28087629771734093160003880679057,28087629771734093973051700733335⟩,⟨(-4962972488195404328187737101542),(-4962972488195403515317238904405)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨27709493096093613502552440075841,27709493096093618371435808578335⟩,⟨(-10126890112631943996752454766375),(-10126890112631939127937664172114)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨24978415537718825087016737646650,24978415537718845424203724879797⟩,⟨(-13639505980316153477479819562756),(-13639505980316133140305492327245)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨20246100434374953167656471236094,20246100434375008699212452035538⟩,⟨(-14666776011120600449407982663231),(-14666776011120544917832602485151)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨14396296322520565152260207299450,14396296322520662480666800275569⟩,⟨(-12986055748249247867849472885126),(-12986055748249150539412401899655)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨8394239054943604584976811135352,8394239054943707585857545286532⟩,⟨(-8908163206321903152653953254999),(-8908163206321800151748911498447)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2729218673114945544050122789299,2729218673114990518873008935182⟩,⟨(-3167660633431787262177513799529),(-3167660633431742287345686471105)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-361016446860580991245217969454),(-361016446860578454147324714364)⟩,⟨386834643311077487908915791284,386834643311080024985505859999⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1056474047441984208433397810189),(-1056474047441978120997116348388)⟩,⟨1178709721365240304591246638361,1178709721365246391964891995231⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1666045464429555402920932146802),(-1666045464429549058331168251417)⟩,⟨2024146867497234915087826582530,2024146867497241259578187655048⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-2120828384731221436337819648555),(-2120828384731217235336758965496)⟩,⟨2960368712055301184883908500253,2960368712055305385756655774976⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2351598168092518217223972011497),(-2351598168092516340470127992508)⟩,⟨4022919015804794399906585724889,4022919015804796276515456857042⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-2310541352516388049002767620007),(-2310541352516387472835851745197)⟩,⟨5222785248214729161126198583954,5222785248214729737146294364228⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-1977502210184595012349302252886),(-1977502210184594881924521576537)⟩,⟨6507687163508609838528763301608,6507687163508609968821365583781⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1348773653034384483097648083938),(-1348773653034384455603460434565)⟩,⟨7750197807707557970530337674144,7750197807707557997925482329431⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-445249298546283099401393636610),(-445249298546283089486660378942)⟩,⟨8776035893243655294528268153719,8776035893243655304391908860208⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨655895231280964580469801729387,655895231280964587566059821145⟩,⟨9406063966011268636482625010950,9406063966011268643583915728728⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1793913357657653681413906865961,1793913357657653687702792985045⟩,⟨9496318274585971383699393483871,9496318274585971390048088686659⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2728348606448967853037022224873,2728348606448967858615037054431⟩,⟨8964447125269241446273356045084,8964447125269241451953561383452⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨3196646559605490130602417847457,3196646559605490135275414416727⟩,⟨7795963424450906067441791632102,7795963424450906072237865765172⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨3012730215531300727044425213623,3012730215531300730559661005049⟩,⟨6044191961951017398278965978928,6044191961951017401910350800733⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2151754508006972583937197054673,2151754508006972586110961764706⟩,⟨3826605454633237680602568724836,3826605454633237682858932724223⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨780227596053105288566098218228,780227596053105289299348834986⟩,⟨1309466496225428696600293919574,1309466496225428697363273451693⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-135560117296004654548233470616),(-135560117296001053017726684695)⟩,⟨(-46474669411418854125005837154),(-46474669411415252600167817731)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-418392782967547996910512309814),(-418392782967534141001011721525)⟩,⟨(-131004827427692359066629128669),(-131004827427678503175248481923)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-730807501408622963812163196071),(-730807501408586694143985839623)⟩,⟨(-189989710574241768111083738566),(-189989710574205498476097838132)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1077362607076085783742195588086),(-1077362607075995321255747911078)⟩,⟨(-203531346047876045126203090750),(-203531346047785582692392464849)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1448177497060071974284277654107),(-1448177497059857740015958033741)⟩,⟨(-143871808521043461779977902246),(-143871808520829227589101682233)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1827189704367795439803851703842),(-1827189704367341244161919141922)⟩,⟨21770685546405655956999067973,21770685546859851490041774706⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2197866021696610526991515129455),(-2197866021695812753048105339445)⟩,⟨314258978997761184888057067962,314258978998558958683063146802⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2538271300383264209309054530417),(-2538271300382179963762441142869)⟩,⟨724088995974124609192779567371,724088995975208854548859109583⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2815348968909827503002862808437),(-2815348968908689353257548127901)⟩,⟨1203419880810576185888373266676,1203419880811714335407626510373⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-2985390787046721093383706339564),(-2985390787045800325201150662968)⟩,⟨1667986938961022318413145677265,1667986938961943086348274857198⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-2997647063288395007792746206356),(-2997647063287778624566708086758)⟩,⟨2012131803082217951678014218847,2012131803082834334668213963225⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2804828430149276767136650438461),(-2804828430148924582901278788438)⟩,⟨2143421178449007223831892741551,2143421178449359407860950041801⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-2391400031404797671150152038450),(-2391400031404622445522050376841)⟩,⟨2020201444733279965409183006548,2020201444733455190868488414643⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1798706424662879930527934128708),(-1798706424662799963564311565410)⟩,⟨1654115827419971539573800568832,1654115827420051506414172872242⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1103656981725961539208871829059),(-1103656981725928151582399656914)⟩,⟨1086061438244041505149276677714,1086061438244074892701214450510⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-370259330970991112978474232726),(-370259330970982046194619527867)⟩,⟨378766557053236297334208620470,378766557053245364093399063059⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1369244818920352396859418869,1369244818920352413918690518⟩,⟨(-1043129706098478635500886066),(-1043129706098478619712051105)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3104686243496765041182335112,3104686243496765094364693458⟩,⟨(-4033112363108473574242549521),(-4033112363108473524721589408)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨115918937660950212491275548,115918937660950306874546043⟩,⟨(-9022350389623382374378920010),(-9022350389623382285301911548)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-15929475647873063070992623772),(-15929475647873062926649943431)⟩,⟨(-16776800956018457613716258869),(-16776800956018457475149033217)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-57258503832027176987477247550),(-57258503832027176777423041681)⟩,⟨(-31411829836384011476791973815),(-31411829836384011271763479364)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-132464273365447564335415806723),(-132464273365447564024985056134)⟩,⟨(-62196952736657273391912492161),(-62196952736657273084236008649)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-238609538244979444591149207577),(-238609538244979444065005492801)⟩,⟨(-116796414165774601624302073230),(-116796414165774601096730981355)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-362405489648001863441498933162),(-362405489648001862022539859437)⟩,⟨(-192472131593966978212180807616),(-192472131593966976785962917453)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-485981467216916496256116386356),(-485981467216916488357587149603)⟩,⟨(-275225949143648233552652969587),(-275225949143648225640651170820)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-590358058608341780542803762284),(-590358058608341724704785277773)⟩,⟨(-344565716599818294228946075805),(-344565716599818238372395642736)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-658222455332907663382649027467),(-658222455332907345282312522484)⟩,⟨(-379860085397081520477080165440),(-379860085397081202355214225271)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-676929006510298901975561391315),(-676929006510297634537635339677)⟩,⟨(-368821373483489126388359602676),(-368821373483487858928038847668)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-637551392361596147758158116743),(-637551392361592804436527346851)⟩,⟨(-314985405433802040984874571470),(-314985405433798697642357259341)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-531595696649332575119766947961),(-531595696649326844025661293510)⟩,⟨(-234381558224043587354670484270),(-234381558224037856243788848255)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-356234999451617272396625750601),(-356234999451611279947539006651)⟩,⟨(-142639044980393273212834210280),(-142639044980387280752959816398)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-125758290472008377486798150653),(-125758290472005771937289096332)⟩,⟨(-47723485290451403125042739040),(-47723485290448797571872670427)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨13860039444182628674366321876394,13860039444188324505650277107586⟩,⟨150101358334343052076673457302949,150101358334348747905110367967663⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 4) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_4 (tableDensity true) (fullFactor true 0 4) density1_contains hk0_1_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨58975195264584719696248227758758,58975195264584719708517354511959⟩,⟨(-46350940954379977073624873899062),(-46350940954379977064934829100907)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_4 0 4 ha0_1_4_contains + def realAnswer : RBox := ⟨72835234708767348370614449635152,72835234708773044214167731619545⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_4 +namespace hm0_0_1_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨129648626041407256698808768898491,129648626041407317824312834593750⟩,⟨16970879140608287071827272226237,16970879140608348199939115373362⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨392973574060288712242339684074485,392973574060288860377264456824021⟩,⟨28204363150252951361714486571343,28204363150253099503346125635679⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨661176431325252188110292489097981,661176431325252344458383143832918⟩,⟨(-28847651170826523719985003122058),(-28847651170826367364265707806523)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨915431811599135768994654295602738,915431811599135872743406646602961⟩,⟨(-196297433737925139378835237811793),(-196297433737925035626143203351174)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1107694629861355042984745591953126,1107694629861355088234647834928975⟩,⟨(-499949584526180490830928094575111),(-499949584526180445585545923999743)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1163575424245410786154061522319261,1163575424245410799232608094590296⟩,⟨(-927987075925595696968727350363707),(-927987075925595683906118736931799)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1007836958009477347649075064802672,1007836958009477350463369452886821⟩,⟨(-1412215823401652571565509840584365),(-1412215823401652568780677050843006)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨610592770162677877831965449119719,610592770162677878643704325211914⟩,⟨(-1831050703140513032711144490222764),(-1831050703140513031937047089373583)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨27882592660719093756895244659906,27882592660719094357130075812012⟩,⟨(-2049770337639953999435744614206753),(-2049770337639953998859861659273365)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-599961178247875630541745465463742),(-599961178247875629980286526439814)⟩,⟨(-1987045290451597608347542906970683),(-1987045290451597607799966563013478)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1104033299675269540078576304630043),(-1104033299675269539574780148694484)⟩,⟨(-1664019638275421725977284484056789),(-1664019638275421725483158176993643)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1362926874468425095133416590413759),(-1362926874468425094718608823097582)⟩,⟨(-1195201831793833687349506401586010),(-1195201831793833686945128300651570)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1345926851359347308960848654327102),(-1345926851359347308649081690111249)⟩,⟨(-726011579879381834992228023738498),(-726011579879381834693362462339826)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1100810800365012990747618484735774),(-1100810800365012990537992947206021)⟩,⟨(-363572530281327885107783998722431),(-363572530281327884911372565667488)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-708650752729618222354006577299149),(-708650752729618222235694271949037)⟩,⟨(-142988374150217311281463020335144),(-142988374150217311173097116421256)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-243131649183538774624933219019402),(-243131649183538774587102218261266)⟩,⟨(-33866186044104099570118268408234),(-33866186044104099535941299076754)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-31474349195337530070862776840055),(-31474349195337511004671345711448)⟩,⟨21306749359154587187046283403036,21306749359154606250470482541258⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-92916440200124951927203231190418),(-92916440200124877101582550265980)⟩,⟨68311953006479293346749927811302,68311953006479368164082473247124⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-148687030839985406797455427650491),(-148687030839985193922067300150537)⟩,⟨128017184109890407240784896988937,128017184109890620103251646401272⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-191715213395301693102579117194382),(-191715213395301101413058475961864)⟩,⟨207149582785180989783999008005466,207149582785181581457521050578392⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-210908380508648516703785860411788),(-210908380508646939692266904775391)⟩,⟨308654309783428457202852243986169,308654309783430034197774956973476⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-192068900228084600535151121565488),(-192068900228080849868369136541886)⟩,⟨428590891438067416982971168676154,428590891438071167635931668835888⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-122020282452696922931157932867918),(-122020282452689631738205268879724)⟩,⟨553131000879136127624732351528592,553131000879143418810597805472128⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨4093434776161945947020941094263,4093434776172635382822881309598⟩,⟨658134322675361687188097141430318,658134322675372376627227634104304⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨174993215853323387991429726867441,174993215853335090849905762056947⟩,⟨714419753661669098509997460913288,714419753661680801384449299119442⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨360105064213752345984721834731838,360105064213761810491268277643444⟩,⟨699252806737252599787024682212324,699252806737262064322007844249005⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨515973005493568243087196390525793,515973005493573855739082014293583⟩,⟨609107416266820387023431618599773,609107416266825999713378311990805⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨601579772451962381692144524594319,601579772451965255496688233313790⟩,⟨465129800097710484255163126999278,465129800097713358097531257279635⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨594109819962523805739771607338504,594109819962525355815777662511736⟩,⟨305638679495114176782114784704706,305638679495115726884349072094398⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨495192260092528349615506650694668,495192260092529088451872669330319⟩,⟨168613956328170104070106876617620,168613956328170842922458270635043⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨325342712199867576569995115203623,325342712199867890443433191627635⟩,⟨74611266377492492738685837766031,74611266377492806620317463355235⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨113014098573616354119200565585468,113014098573616439662601464243075⟩,⟨19703899181436102531971593372537,19703899181436188077839733051937⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-430727636355559370827918387403),(-430727636355559369175107127192)⟩,⟨(-8160442735904863329753474722696),(-8160442735904863327248611903649)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2244253437129398006728993911726),(-2244253437129398001521184063405)⟩,⟨(-24761873122418337703188379429284),(-24761873122418337695451626269312)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-6968499132523950626607020367994),(-6968499132523950616998555752360)⟩,⟨(-42028696652334808015788847055903),(-42028696652334808002118135199291)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-16637438044324032859824823908120),(-16637438044324032844374702884910)⟩,⟨(-59878321312838113098437737465208),(-59878321312838113077677705295650)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-33146625062156325925187258625948),(-33146625062156325901924321470748)⟩,⟨(-77353027158527331756476806868280),(-77353027158527331727166679109737)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-57782779530927747164691790918149),(-57782779530927747130755399187309)⟩,⟨(-92251164761684708629609554816325),(-92251164761684708589711817653353)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-90531081558357336401690998559699),(-90531081558357336352440984636526)⟩,⟨(-101118133729673445193816838867125),(-101118133729673445139703996335023)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-129229228066848394577512578350442),(-129229228066848394494989538624106)⟩,⟨(-99966523522395774565680837888691),(-99966523522395774480507593474925)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-168970025640185084512572531442795),(-168970025640185084254430238287687)⟩,⟨(-85766791730873935169516081909265),(-85766791730873934911901618022763)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-202477142068771721074085022068394),(-202477142068771719578237093291713)⟩,⟨(-58350639492773507633224048675459),(-58350639492773506141515603656047)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-221851801436128017247491054204829),(-221851801436128009072134797891037)⟩,⟨(-21888761224756765889592144319885),(-21888761224756757721660268225208)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-221146072872060675019911318681961),(-221146072872060643336235244493905)⟩,⟨15200730135308175953530226339004,15200730135308207627538715582961⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-198382152952004941497708276554822),(-198382152952004860819721995132951)⟩,⟨42638853881918476691655803469656,42638853881918557359314584477200⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-155897171028684276786598220286085),(-155897171028684143875334319695124)⟩,⟨52332452062944609586020139796705,52332452062944742488166841298232⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-98998331594863215987675581510318),(-98998331594863081857702869930444)⟩,⟨41930074432240987000774635259543,41930074432241121124511673696187⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-33854786699212530276531287761036),(-33854786699212473218107838695878)⟩,⟨15920899257575965645765766074824,15920899257576022701984652440603⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1507488970403015054689231062779,1507488970403018402192458484252⟩,⟨(-317439777212138844600625846046),(-317439777212135497190648302089)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4566831887698831510495118428178,4566831887698839536085377605538⟩,⟨(-1085789509466978871126370965912),(-1085789509466970845798839117156)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨7730810312177970090941254862254,7730810312177978441956705870425⟩,⟨(-2254298286806445805361734505275),(-2254298286806437454725439421858)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨10987674508781192090324288844395,10987674508781197605664000755703⟩,⟨(-4088160790962342896016693026825),(-4088160790962337381080470653931)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨14201509875852197265107121668974,14201509875852199720500104858076⟩,⟨(-6837898395534845292457899037310),(-6837898395534842837359041983762)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨17090211196360157911147041073316,17090211196360158663003511055663⟩,⟨(-10703794636598628252440469512987),(-10703794636598627500596502092412)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨19253659115329496900755432161209,19253659115329497073141696255323⟩,⟨(-15746447012823338113488320296174),(-15746447012823337940634625313783)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨20242648149099013565946750195553,20242648149099013606334395539080⟩,⟨(-21749345739963983234847982831094),(-21749345739963983193317397517383)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨19672178565509198723720416484771,19672178565509198742191486469638⟩,⟨(-28111393524492648820428147577238),(-28111393524492648799990219456852)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨17388761691976814371554089592396,17388761691976814386560409224313⟩,⟨(-33845773452317054580225133198387),(-33845773452317054562390516881812)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨13631823986757456717822574263145,13631823986757456731495166559151⟩,⟨(-37728836573738961935795320141936),(-37728836573738961918557075748110)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨9083761867023712004559925254587,9083761867023712016671438122603⟩,⟨(-38597592354126425347451431694139),(-38597592354126425331343804665650)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4729461573429815899388079904019,4729461573429815909415712527145⟩,⟨(-35696567752229378710277424790736),(-35696567752229378696285386634564)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1517284655724109954601180643003,1517284655724109962085338683534⟩,⟨(-28914347644009076879643777987067),(-28914347644009076868794098781531)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-55915097460076073879818868094),(-55915097460076069015520010709)⟩,⟨(-18821057814977379905957237083864),(-18821057814977379898961155064068)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-205606991892431021003555924362),(-205606991892431019297540605136)⟩,⟨(-6527188020498598652791152199817),(-6527188020498598650368563576581)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-75475576053927550282145528049),(-75475576053924192399557669281)⟩,⟨353920779410495456537540125752,353920779410498814377869594341⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-185911742729401416883336477637),(-185911742729388513693202013321)⟩,⟨1071770726666590244864310270667,1071770726666603147924702202440⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-173419919863124978951371438489),(-173419919863091293874928418222)⟩,⟨1814566519946791447064330051459,1814566519946825131913157332917⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨43443454060003561377158218988,43443454060087175935783110207⟩,⟨2585159514099205741301337915665,2585159514099289355517787657125⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨534222987732185409441744919637,534222987732381897854114698230⟩,⟨3361723167956023481567025364551,3361723167956219969499748799462⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1340917214454289211608930730174,1340917214454700891329955194681⟩,⟨4083302796669896319871310468670,4083302796670307998950759348021⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2463585921998176971513407769396,2463585921998903700086464356255⟩,⟨4646230172768650235850743685931,4646230172769376963617130732747⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨3842917420262962634310484851540,3842917420264067587876367133870⟩,⟨4924281564538631581659600654573,4924281564539736534354704875357⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨5342197069377357432496393510320,5342197069378677074244368689087⟩,⟨4807640060223869511788533863456,4807640060225189152653319784206⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨6746761982787340902943557833159,6746761982788551067642584939389⟩,⟨4250274471899699938941008243158,4250274471900910102787902425602⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨7792708246511633354984330237257,7792708246512482036540977025649⟩,⟨3314137056766647917792684308277,3314137056767496598575323717488⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨8215490166831556559846529366071,8215490166832039980260444074249⟩,⟨2185572711727293730082978933263,2185572711727777149843353134335⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨7803530138264793725284744573507,7803530138265033553392745027746⟩,⟨1127423189964552175425442734532,1127423189964792003025048936258⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6462179476786760935427600716720,6462179476786870103484595897403⟩,⟨368139956403850193220682671392,368139956403959360921717007874⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4272560361525315504910939384635,4272560361525360993651187489573⟩,⟨2049920244311943693021467388,2049920244357432225567326689⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1493613984179061119436926623342,1493613984179073458776388488348⟩,⟨(-40692678975251959343945325388),(-40692678975239620072245350175)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-25540580120304480084933042509),(-25540580120304480066546714835)⟩,⟨(-33193528851768447513303571256),(-33193528851768447493169208345)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-83047904492342423286131944339),(-83047904492342423228465940040)⟩,⟨(-95196067776997094047024452998),(-95196067776997093984472415771)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-159235868204775193891002486341),(-159235868204775193787210191520)⟩,⟨(-144395249835059083595620247136),(-144395249835059083484987994695)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-263538818374336420240745975951),(-263538818374336420079531547892)⟩,⟨(-173864688579402998341227193850),(-173864688579402998172876497906)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-397768766881101334332641074667),(-397768766881101334097338947723)⟩,⟨(-177821195874651037600268816810),(-177821195874651037359304789851)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-552718799793989350654035024621),(-552718799793989350312603022715)⟩,⟨(-148465845168313858801301901805),(-148465845168313858457073661710)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-711183970329550098515998076927),(-711183970329550097966478434933)⟩,⟨(-74819214455968710479911311450),(-74819214455968709931576373653)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-853326073356127320782218903576),(-853326073356127319410034828813)⟩,⟨50716304850624722457252807983,50716304850624723824215715307⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-959047510840178370103055354786),(-959047510840178362709639741401)⟩,⟨223638223914188822198015789502,223638223914188829583707890124⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1010746407150608522132576646501),(-1010746407150608469729551743984)⟩,⟨423193624090938542652477462787,423193624090938595047834112948⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-998195115195002682247481133745),(-998195115195002382619498056295)⟩,⟨612795528760149919577333827045,612795528760150219200143751149⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-920900817255373953878181644710),(-920900817255372759117561956281)⟩,⟨745043884229170125253489072060,745043884229171320012601864453⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-784635593731281768776022425230),(-784635593731278620438078495558)⟩,⟨774647276723988038918007226315,774647276723991187258089802745⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-598000445680872818682057790143),(-598000445680867431518057974300)⟩,⟨677462603430945633957248024043,677462603430951021125640134106⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-373504832048896921975494752562),(-373504832048891298865284433891)⟩,⟨461683325817075972380329001388,461683325817081595494723319064⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-126799943714576028951940927433),(-126799943714573586528457771245)⟩,⟨163582386226705519374517246171,163582386226707961799701017568⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨52646632663159035663323422624616,52646632663169772103340985336546⟩,⟨(-1389377002601240779128512042711517),(-1389377002601230042699862262245984)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 5) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_5 (tableDensity false) (fullFactor true 0 5) density0_contains hk0_1_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨115535483846715928172655862319086,115535483846715928192127059727885⟩,⟨(-60023989877512369555118273397448),(-60023989877512369540883519869360)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_5 0 5 ha0_1_5_contains + def realAnswer : RBox := ⟨168182116509874963835979184943702,168182116509885700295468145064431⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_5 +namespace hm0_1_1_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨21595028196811073851361272481154,21595028196811123918411698374813⟩,⟨5802652523464682007719487502515,5802652523464732074190786017726⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨66168331996641048607125332530687,66168331996641169891247324863158⟩,⟨14236356123769388451793807976029,14236356123769509734466099255280⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨113173483719694585236430676564509,113173483719694713128590241946295⟩,⟨12768345698425384052245102169915,12768345698425511942940458555144⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨159043763369890575278995326183394,159043763369890660003808164305050⟩,⟨(-5981850803055200762726758769725),(-5981850803055116037979848784023)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨194057102158837528700341148089668,194057102158837565516351825397742⟩,⟨(-48709791241598652623608020046003),(-48709791241598615804353408635085)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨203941309091977950223299442933976,203941309091977960722620811127124⟩,⟨(-117150538911835838561642453708177),(-117150538911835828053511659457163)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨174947782130796721315904810109630,174947782130796723416313862810441⟩,⟨(-202211057775379686578911756091105),(-202211057775379684462509506989430)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨101459210548321513222295236515589,101459210548321513668610952573777⟩,⟨(-282338070714502201650767038686368),(-282338070714502201184729590598348)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-6671014633608955780090036159898),(-6671014633608955523275078661255)⟩,⟨(-330841721784795928841957432502141),(-330841721784795928571188016497004)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-123310868584112821856869917177505),(-123310868584112821626291699927264)⟩,⟨(-329389154790454497170812123546305),(-329389154790454496934886064146436)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-215897316754998272574419750131904),(-215897316754998272365166078427554)⟩,⟨(-278610834256912056192887769366911),(-278610834256912055987382500435756)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-260818053905644278530960552438392),(-260818053905644278356492944137685)⟩,⟨(-197768369752025260721158843357963),(-197768369752025260557642867098679)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-253097207441464230725315291734567),(-253097207441464230593128758178874)⟩,⟨(-114094981238491881218597849761182),(-114094981238491881100857298661967)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-203800000868454418539302449026377),(-203800000868454418450417138601510)⟩,⟨(-49804643564463913103431521211892),(-49804643564463913028429944743008)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-129624063364184337720464770552112),(-129624063364184337670473060240258)⟩,⟨(-13982351715159357910519157217145),(-13982351715159357870380837241720)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-44180712813786309066718900264708),(-44180712813786309050762411637645)⟩,⟨(-1681700852895319189514576309545),(-1681700852895319177118864145910)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-5898594721683203271592778463651),(-5898594721683187576352736186141)⟩,⟨588672421507694374512287927477,588672421507710070110001156890⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-17547004249838506529202345511134),(-17547004249838444905823324493984)⟩,⟨2663979863011306014074444059251,2663979863011367638522083836671⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-28550778916141997412746141969787),(-28550778916141821961712211098114)⟩,⟨7407508524557196612009238055928,7407508524557372064712637987249⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-37912850037359203740991406686277),(-37912850037358715621553555155613)⟩,⟨16437409036865466410668504972778,16437409036865954532186841946743⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-43919403822669444274994958357715),(-43919403822668142125983120179111)⟩,⟨30852972330882470623594253158246,30852972330883772774806957895536⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-44183651992976138711972986833207),(-44183651992973039180684448357410)⟩,⟨50554536381988343232502618407849,50554536381991442765708458316998⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-36072898063200233448538188573356),(-36072898063194202782263305052454)⟩,⟨73508053121782153206102098007094,73508053121788183873521119379792⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-17762261410035339726425068803307),(-17762261410026494194991871941560)⟩,⟨95562179597601560829346660559177,95562179597610406360643024292156⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨10180716647809005163051935849452,10180716647818688900412268103457⟩,⟨111280960878311418731319693717469,111280960878321102466862597841916⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨43608756314787998291584410316684,43608756314795825582724077080646⟩,⟨115853954370927457422769020682983,115853954370935284710200065114907⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨75132269714659218696031726538615,75132269714663855913306313252033⟩,⟨107418767301966008092423917618728,107418767301970645304373056849050⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨96337174020493958510092039454538,96337174020496329785302515867381⟩,⟨88271099534256952626610861814688,88271099534259323896283324513140⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨101030820831692480352982388410729,101030820831693757633919932231286⟩,⟨63832230034267756610663029376218,63832230034269033887647798600430⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨87612635350432462811114166746311,87612635350433070858590069310002⟩,⟨40033806643272035445225265863066,40033806643272643490263130453861⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨59001730294786141393897710680542,59001730294786399456343383621541⟩,⟨20719379773229895433905260913286,20719379773230153495102216551948⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨20743173815579934368725613555735,20743173815580004664198508538035⟩,⟨6229882285003979666127394488625,6229882285004049961224417092935⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨882697385132756162121071351301,882697385132756162979199379817⟩,⟨(-1620057099530100758565430005202),(-1620057099530100757668061023502)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨2523883513990421316160159407783,2523883513990421318868565654529⟩,⟨(-5021802286281093526101565312768),(-5021802286281093523272772085495)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨3766241465664574287019715269877,3766241465664574291959616305075⟩,⟨(-8837345404334314380198960498056),(-8837345404334314375069570763583)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨4251205826959939968799409029225,4251205826959939976571177015213⟩,⟨(-13132582874362126172645604808454),(-13132582874362126164635907520061)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨3473691406009625044771401305345,3473691406009625056155666044380⟩,⟨(-17717106014564391941009379752898),(-17717106014564391929373249241987)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨837950890833642089411901082369,837950890833642105621641956872⟩,⟨(-22168048422067441657797793047890),(-22168048422067441641341794354994)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-4082983906841915132184085239586),(-4082983906841915108442689282287)⟩,⟨(-25875621805156383769804244724714),(-25875621805156383745847447212346)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-11211043527281112271121800123592),(-11211043527281112225685122781761)⟩,⟨(-28079033342261580763026903325890),(-28079033342261580717455605526427)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-19738191115454178572765507546703),(-19738191115454178389220958938532)⟩,⟨(-28031020306518841189750236258910),(-28031020306518841006184936024845)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-28109765105284507872817391112824),(-28109765105284506684699706391018)⟩,⟨(-25338221448702926168538406751953),(-25338221448702924980481235624526)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-34317183977635982526548439127747),(-34317183977635975897320863282278)⟩,⟨(-20276910058754572179690160163610),(-20276910058754565550544309158195)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-36555038934453619992333289344197),(-36555038934453594193059973640975)⟩,⟨(-13829851292890544357824717406140),(-13829851292890518558622817959780)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-34010590767184126507554177376492),(-34010590767184060711702107147735)⟩,⟨(-7423114584287270591610046334418),(-7423114584287204795808576615177)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-27175432226712616047833575849998),(-27175432226712507554285428540175)⟩,⟨(-2509891454789008781079931008733),(-2509891454788900287543776462663)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-17358936141084872247972544280620),(-17358936141084762696986709732824)⟩,⟨1509667607038798693352607030,1509667607148349692206593968⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-5945017028668810534684114219774),(-5945017028668763919105378626443)⟩,⟨299183004998358259443479361730,299183004998404875034852629980⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨467403335557333674660266623856,467403335557336487197080868267⟩,⟨216148335819344548439539094472,216148335819347360986640774573⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1417529305831014209359714134295,1417529305831020947758706723178⟩,⟨615890508126253949169038914249,615890508126260687596849261439⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2409768714812695680228623595773,2409768714812702681966318728966⟩,⟨911249584703571580082322670535,911249584703578581860856528706⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3466436315524356256870901329519,3466436315524360870687792497669⟩,⟨1016894336696804414168461139108,1016894336696809028027185610338⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4602395585238199684494767650883,4602395585238201731371533167187⟩,⟨841359830090740126478363462045,841359830090742173382437080197⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨5808574114660724981898555741996,5808574114660725604313819531361⟩,⟨314689792827814786645093943236,314689792827815409054801557108⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7016046498654757025083651804627,7016046498654757164284103236287⟩,⟨(-587347623291878403584811552245),(-587347623291878264442619118271)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨8079154848669728870111819638850,8079154848669728899201362572488⟩,⟨(-1838549178094507761825382164217),(-1838549178094507732864074050845)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨8806119310095360694430163793032,8806119310095360705025684153320⟩,⟨(-3352007795944642562318072926522),(-3352007795944642551931738071369)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨9019430767342731249416775437744,9019430767342731257100105708826⟩,⟨(-4956489882083946220718729529764),(-4956489882083946213324675959525)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨8621742137055916876167587951642,8621742137055916883005631184354⟩,⟨(-6384718042829888731126098430852),(-6384718042829888724639879785274)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨7637814822368199655525169343085,7637814822368199661594805565377⟩,⟨(-7297206078071956336206965926451),(-7297206078071956330521402551520)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨6202155818394735299249141583120,6202155818394735304333495296884⟩,⟨(-7359816341024677444032474428461),(-7359816341024677439321928366726)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨4501002394180943668107539757431,4501002394180943671944989660221⟩,⟨(-6364256776115143194220163459679),(-6364256776115143190694882506779)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2701435331170184470914300575795,2701435331170184473373542282958⟩,⟨(-4330324018380265232439568838363),(-4330324018380265230175677935322)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨896981163977068545945866961617,896981163977068546797364123814⟩,⟨(-1535919063381158890340019966153),(-1535919063381158889553568561830)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-18816815420283558045720980566),(-18816815420280798411323735156)⟩,⟨117402173456513563698907607063,117402173456516323340818342166⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-47134436244107707416033944928),(-47134436244097102308417955035)⟩,⟨361729058444008641154006029840,361729058444019246285394218252⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-47658814328868227449104056561),(-47658814328840538015701210528)⟩,⟨629974668843650994294177465302,629974668843678683770433100224⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-573729224893804885773707254),(-573729224825061895363323314)⟩,⟨924820909371946016872360872270,924820909372014759929399330560⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨119425811665325812028496222213,119425811665487373063775269686⟩,⟨1234627019193375786714176202153,1234627019193537347845482194119⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨341884291717713982860158588078,341884291718052482193330487928⟩,⟨1539371657956565103370953051290,1539371657956903602836481663466⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨686782772733567499076676422793,686782772734164913952801200144⟩,⟨1817441423399272719278127543112,1817441423399870134327917519515⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1146402425088798232024859814237,1146402425089706120167480221827⟩,⟨2045493361727891622128907630494,2045493361728799510464275124992⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1674304907242506854969312926104,1674304907243590274426198076666⟩,⟨2197465264681528230346973245374,2197465264682611649997329514061⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨2183485664566129718989908420037,2183485664567122196607149016988⟩,⟨2247924231141351055483295539910,2247924231142343533279368832704⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨2558028376702076608805974113511,2558028376702771746147682008388⟩,⟨2174985422877605902990408437981,2174985422878301040487392908204⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨2687183842722067992263829576468,2687183842722463420770879466352⟩,⟨1962389312984991642903084347889,1962389312985387071538780068108⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨2511587626249946698394625792248,2511587626250142624528827944298⟩,⟨1613301487100185810885049489781,1613301487100381737118249333675⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2040507372294716730771610934854,2040507372294805820958048532571⟩,⟨1168915402611868152735215287217,1168915402611957242989556541183⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1329875591611699367585604374424,1329875591611736462678548053158⟩,⟨692975409120344159697976537728,692975409120381254829765347974⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨461635875533898402092323939925,461635875533908460758806484515⟩,⟨227501030304074026312204396224,227501030304084084991088924762⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-805761368478645291119502208),(-805761368478645279463125086)⟩,⟨(-949837860197936839728622138),(-949837860197936827392604303)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3043842657451880986268951777),(-3043842657451880949623058286)⟩,⟨(-2088597369674266008080198552),(-2088597369674265969541405673)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-6567771590006383633023719542),(-6567771590006383566837105585)⟩,⟨304386703592356565023467021,304386703592356633715884070⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-11524756593670164287449735149),(-11524756593670164183897544651)⟩,⟨12473905599746476765487654484,12473905599746476871207831295⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-20119498133802423840063751400),(-20119498133802423685693988718)⟩,⟨44003210679799123633976117652,44003210679799123789179271825⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-38302917524925634711306121873),(-38302917524925634477808133712)⟩,⟨102664115128569894020381726141,102664115128569894252079900566⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-71501070710947191840104868859),(-71501070710947191437235057070)⟩,⟨188177049574449298408663028771,188177049574449298805441287236⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-118299965107202691690760573918),(-118299965107202690599514916563)⟩,⟨291875868587836579323405586657,291875868587836580403112748786⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-169411303991007381186607911018),(-169411303991007375124702746812)⟩,⟨399960745290820811388989680593,399960745290820817434071437759⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-210850781902941354890413039331),(-210850781902941311981580796941)⟩,⟨495683258309438978070940298197,495683258309439020959039616165⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-228472598404409150958780911140),(-228472598404408906139795685078)⟩,⟨561787982150209245577481218296,561787982150209490373788900746⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-214337599039421026479017042033),(-214337599039420050671665438294)⟩,⟨584216379421617671300265362855,584216379421618647084722172832⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-172954974334585844208269162999),(-172954974334583272052103401979)⟩,⟨553362224380778960804321872792,553362224380781532939460617324⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-119222777729374953824492848725),(-119222777729370550576571191233)⟩,⟨462270181021764825893559387418,462270181021769229124788042995⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-67086364603096998430133571610),(-67086364603092400642058661859)⟩,⟨309865851176668441279786580568,309865851176673039057222740752⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-21331566695208845239576845864),(-21331566695206847777671985611)⟩,⟨109383796217510770914181482990,109383796217512768372505144508⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-7695804657149760641978227782821),(-7695804657140893306090005313269)⟩,⟨(-223853888122849879095715648400954),(-223853888122841011760925812278339)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 5) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_5 (tableDensity true) (fullFactor true 0 5) density1_contains hk0_1_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-151084863491859290712781539644158),(-151084863491859290687319204571113)⟩,⟨78492909839823867861155372136856,78492909839823867879770049827431⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_5 0 5 ha0_1_5_contains + def realAnswer : RBox := ⟨(-158780668149009051354759867426979),(-158780668149000183993409109884382)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_5 +namespace hm0_0_1_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-155444931791051319124053222837187),(-155444931791051251950975438239431)⟩,⟨(-101781454830887665743253790309736),(-101781454830887598562031307060247)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-488998614988524221850960018094603),(-488998614988524053223777516066367)⟩,⟨(-275646379637569369021991607744578),(-275646379637569200372022328410175)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-879280748022929262759066859212715),(-879280748022929073304138969664274)⟩,⟨(-353656385809334353270916213033336),(-353656385809334163783554975083932)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1325579561156194571533236042625933),(-1325579561156194435527633448166372)⟩,⟨(-257477618547095557095880357240139),(-257477618547095421056404410840357)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1765783011969168015744187828208286),(-1765783011969167951134230466842940)⟩,⟨89174414044359921192057539486483,89174414044359985827224779343805⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-2064277496466329171206818407086215),(-2064277496466329150832717498680614)⟩,⟨718646141360886739115233529868587,718646141360886759496914754008890⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-2043924478790832483529580874062248),(-2043924478790832478750368581193693)⟩,⟨1562118159856380763180961851184416,1562118159856380767946909296644305⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1576114712069466102208935534809547),(-1576114712069466100866873831831822)⟩,⟨2419823699063416525192508919791115,2419823699063416526501056936183338⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-688590432092354800849206842570630),(-688590432092354799986117253983900)⟩,⟨3013736759186687425630820403126224,3013736759186687426451108319175886⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨396847659064052237567489713326265,396847659064052238427539591700067⟩,⟨3125271426257139000382838809870254,3125271426257139001218850514935648⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1354305350258204581498248847172599,1354305350258204582297040173884682⟩,⟨2727976828642080689591667695577092,2727976828642080690375530955961717⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1918813027626737390442859875892423,1918813027626737391110685093383561⟩,⟨2003146607652317742167332799134177,2003146607652317742820216123281705⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2000011488420172483301860640840281,2000011488420172483804637657950467⟩,⟨1223950322907393819648479368200983,1223950322907393820132378836195160⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1672830158705927169139327923616400,1672830158705927169475067899492835⟩,⟨606674913427429088771367106441897,606674913427429089087227330945516⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1085688085240346252439258492190532,1085688085240346252626885484877727⟩,⟨231828305235274026318292951768245,231828305235274026490727490196880⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨373298796872714452815985107918769,373298796872714452875565600203886⟩,⟨52861392271941349058728653369274,52861392271941349112690661079569⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨44172131942319887301881098684945,44172131942319918916448163650998⟩,⟨9476885264477246373358070143217,9476885264477277988043163626168⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨135687625261108229817739894211571,135687625261108353358246817090733⟩,⟨22823307063426010958541135350214,22823307063426134498834085079020⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨235092090485350957823425952836139,235092090485351289676287982157760⟩,⟨18429627971465552384586311048519,18429627971465884235172744306783⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨342382708692541578915621203305939,342382708692542428431027581314061⟩,⟨(-17818549038798785490383200442079),(-17818549038797935982154201403602)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨448984932395723773369062242833525,448984932395725809442267523125791⟩,⟨(-101027819369803821599879583922812),(-101027819369801785542534358302201)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨534777599446811024920330321441933,534777599446815257198198407011936⟩,⟨(-242682612322856912215621509141551),(-242682612322852679966455325825673)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨568947930467596868725265617917654,568947930467603889567899091778210⟩,⟨(-442011695612405518428951864239216),(-442011695612398497630536655502192)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨518341697026731106463259779994474,518341697026742498512804229440517⟩,⟨(-676393753224500530315490309951156),(-676393753224489138309452944346135)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨364202528159579523848684958704177,364202528159594364721987465284563⟩,⟨(-898404405979163306052547183428883),(-898404405979148465209335642494584)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨120714893014636010116259009289345,120714893014649991306565247364694⟩,⟨(-1047388618515041402842484479251521),(-1047388618515027421663686300662328)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-158529900515439537948521040656523),(-158529900515429983207879495751889)⟩,⟨(-1075106492327028750767518880046122),(-1075106492327019196018948961766665)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-396449400995805830944723713344110),(-396449400995800759560025868606850)⟩,⟨(-971447614325001611341427632257889),(-971447614324996539933439317498749)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-524496976710473125990047434613226),(-524496976710470856033325172543153)⟩,⟨(-770565444118965391418411263735637),(-770565444118963121430293689540270)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-510376305836685091065303406450016),(-510376305836684171208165403681511)⟩,⟨(-530311341596496476851455406904145),(-530311341596495556963649741607444)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-365257448738907248909049188093933),(-365257448738906903085941649267311)⟩,⟨(-299438344247131999524537856022607),(-299438344247131653679488991687943)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-131908948408155878987607449710417),(-131908948408155786790267864188783)⟩,⟨(-95396786914329122275617476468329),(-95396786914329030070719675357682)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-6746306650499498719607267006797),(-6746306650499498716917985785890)⟩,⟨4226715837350952480472280615972,4226715837350952482863822711189⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-20043714465519116395023183104946),(-20043714465519116386763970362739)⟩,⟨13758471772837116717893351296558,13758471772837116725345246967595⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-32526173881719404215862540041230),(-32526173881719404201424656742693)⟩,⟨26507938506138669808450566033005,26507938506138669821866430644216⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-42975080182733084620247013502477),(-42975080182733084598531192664258)⟩,⟨44494212845277313649890741231669,44494212845277313670932437550634⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-49218867859932143965726593306998),(-49218867859932143935298601051622)⟩,⟨69186081424595928335051494079026,69186081424595928366013114288523⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-47988318629065348203049785471221),(-47988318629065348161932355468693)⟩,⟨100750629995442015559937849109697,100750629995442015603863326251076⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-35336906445401216809923014387820),(-35336906445401216754799851283427)⟩,⟨137170791510392794823931702930577,137170791510392794885327085389714⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-8027265142568643949492266146059),(-8027265142568643865586322216848)⟩,⟨173610228742502480602945392715461,173610228742502480697552759036634⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨34257840192531423123080009994174,34257840192531423349407798942994⟩,⟨202665456469061087027883803507243,202665456469061087269694846919931⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨86806871491723916245983453757553,86806871491723917546807915228993⟩,⟨216218762104536150766298265669030,216218762104536152084708560807589⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨139324845217681571426260940120386,139324845217681579804205807892598⟩,⟨208781782673063201406031833379973,208781782673063209798217401796398⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨178052632172675255370358866498898,178052632172675292868738584015391⟩,⟨180699374833907323051363489945333,180699374833907360559793631717252⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨190252690650964086471105963573692,190252690650964194148851329543463⟩,⟨138724330743838933796594606183310,138724330743839041480305420653135⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨169094495710298589311740625918331,169094495710298784460981080293550⟩,⟨92844158861841229080952777186650,92844158861841424232983555828247⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨116311631870410258296066381360113,116311631870410468982541649781974⟩,⟨51155669972363180596002588590251,51155669972363391283400919398424⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨41384162198318600816740353011250,41384162198318693662302982478820⟩,⟨16039330004797223532809956346414,16039330004797316378536085564118⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-626530481046182680256718288719),(-626530481046179905660696665160)⟩,⟨(-1080985217833525913863786197894),(-1080985217833523139288754639288)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2010503146388363200635315452926),(-2010503146388356566549207961328)⟩,⟨(-3247595882641638011988824092383),(-3247595882641631377985468147908)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-3782801714068177553008299511714),(-3782801714068170688859682695663)⟩,⟨(-5402046202278598957565168561406),(-5402046202278592093621250518678)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-6188253003175614009866130670912),(-6188253003175609517643696383699)⟩,⟨(-7459068817705616622870525802527),(-7459068817705612131077379670673)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-9433018233307222352812690873671),(-9433018233307220379267469192740)⟩,⟨(-9217575005051278740885514906072),(-9217575005051276768139193960107)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-13639159472125148087122484646784),(-13639159472125147493284373798540)⟩,⟨(-10343106254572117011199410143674),(-10343106254572116418709451642324)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-18760731887060125219206365175889),(-18760731887060125084905211735781)⟩,⟨(-10412522038095777429517976935545),(-10412522038095777297309184415824)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-24467762531247552145063948937979),(-24467762531247552112164067341962)⟩,⟨(-9025776993895667341765381477001),(-9025776993895667311873025288807)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-30072347422036791409091168473814),(-30072347422036791391849116004942)⟩,⟨(-5974186070952027239562018568608),(-5974186070952027226328476258491)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-34581538157021664366488460980603),(-34581538157021664350186041859790)⟩,⟨(-1441611847478229157119234071774),(-1441611847478229145093351759010)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-36911100719903640674518186373954),(-36911100719903640657457135033326)⟩,⟨3854234405720335122811012649482,3854234405720335136039215845541⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-36217673218443799404528171585085),(-36217673218443799387616520228864)⟩,⟨8711117696804850068921913999610,8711117696804850082679466811816⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-32201494407352126777497304101838),(-32201494407352126762132661538798)⟩,⟨11743916488582099988210606442856,11743916488582100001221061442956⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-25192342267031922005821561154899),(-25192342267031921993534042961140)⟩,⟨11872518412293930132362539524237,11872518412293930143091128606817⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-15969148341494246230786119450801),(-15969148341494246222861784801233)⟩,⟨8802006320760996689123300492970,8802006320760996696187395548620⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-5458439553468745517607343045119),(-5458439553468745514877811471029)⟩,⟨3245001557232879497806674667732,3245001557232879500265589391358⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨250021060580830274420526704051,250021060580832335789512203650⟩,⟨9694793441514081650228605497,9694793441516143055652692791⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨754217852998015177016537761469,754217852998023074120527999765⟩,⟨(-1596757707861134675096821931),(-1596757707853237459253761166)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1266458800799868484032663839071,1266458800799888964105351227809⟩,⟨(-106070948603509282535587483600),(-106070948603488802266684993881)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1780013863024968872041969703679,1780013863025020097861492291281⟩,⟨(-366253745251316897082424945986),(-366253745251265670972750369110)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2268426898019559950882182263644,2268426898019692696768149723819⟩,⟨(-836015489991029453403590263794),(-836015489990896707155114704064)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨2675914150938526530781716573459,2675914150938841223327492030763⟩,⟨(-1546316810885289819816358065339),(-1546316810884975126855686716201)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2916047199734384732804471182110,2916047199735007527816335373544⟩,⟨(-2490582981929394364714545082052),(-2490582981928771569259559620809)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨2889899037860231135002071276741,2889899037861188296412117662217⟩,⟨(-3609519268894086833939232130836),(-3609519268893129672085921764264)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨2521921421475140365753432492156,2521921421476278326657413190075⟩,⟨(-4778967732673689684192929610889),(-4778967732672551722876238338315)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1803603554235797217235331190822,1803603554236835392237682455022⟩,⟨(-5815521701859400063128428936120),(-5815521701858361887775102492183)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨831241191949392491046402903569,831241191950116247693874348723⟩,⟨(-6509630002506327507698762642559),(-6509630002505603750789176011974)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-184450960484285097384067002786),(-184450960483875531958924475751)⟩,⟨(-6674958781408680599545242485503),(-6674958781408271033961029025797)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-967088278181243747225756625913),(-967088278181041926599716014169)⟩,⟨(-6190184998460038993686805824604),(-6190184998459837172995407534253)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1285084000997853790501180519727),(-1285084000997762495072338143038)⟩,⟨(-5029163475653855723501620038260),(-5029163475653764428071240205085)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1060450988730623043881926425600),(-1060450988730585187212044528330)⟩,⟨(-3281123953269630340810654776361),(-3281123953269592484163029394407)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-407332092560708628123875249395),(-407332092560698386604300838735)⟩,⟨(-1139185838953144729054402087200),(-1139185838953134487546734212021)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-19180795981370400210696448394),(-19180795981370400198490236861)⟩,⟨16430065031749727677245266354,16430065031749727688609684309⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-54718402758671183870357232144),(-54718402758671183832345608835)⟩,⟨53263527299080766385394659986,53263527299080766421122699660⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-81869700273389636335544038092),(-81869700273389636267980278806)⟩,⟨101688548070951965140887076019,101688548070951965205471047144⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-95677634779221070025124515395),(-95677634779221069921582032351)⟩,⟨167714411518728190026715669099,167714411518728190127624891986⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-91661991574896321795237529069),(-91661991574896321645758170688)⟩,⟨252748962610877222547376699482,252748962610877222695648841098⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-64163437629346997581239442610),(-64163437629346997365832554930)⟩,⟨351106203353460546070403839341,351106203353460546286878978894⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-5783098482200289704972264734),(-5783098482200289359522785374)⟩,⟨451297823888632064988131223541,451297823888632065337564298363⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨88430047879055696696816042553,88430047879055697559286496407⟩,⟨539302688740838215803467743387,539302688740838216672516809679⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨215068161881834532181006727009,215068161881834536832409466257⟩,⟨600683218151028874899778314498,600683218151028879558741869212⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨359190270687529280384676736880,359190270687529313342739591205⟩,⟨623333520136087300092072743365,623333520136087333056419005529⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨494455873294507950015171050180,494455873294508138066275903937⟩,⟨601728802118156828834115471730,601728802118157016888279493381⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨586668173096789907982092272754,586668173096790654982736853208⟩,⟨539182841460152712390207001372,539182841460153459390033483942⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨602709870898664293190988692357,602709870898666251912996675829⟩,⟨444842386950394606125401714414,444842386950396564843192701521⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨524157494463093816754168971116,524157494463097151050706938256⟩,⟨328850762339529663423406356752,328850762339532997714024806577⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨356328333510369883102386314449,356328333510373348435759691126⟩,⟨200515945941670575141257283900,200515945941674040469557964750⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨126133692608846292847598685378,126133692608847794326061325192⟩,⟨67165053567562497883985650961,67165053567563999360462323490⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-87301854702044269153185047594484),(-87301854702030902649381945048096)⟩,⟨1881302697950612450405184971697630,1881302697950625816896696500482282⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 6) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_6 (tableDensity false) (fullFactor true 0 6) density0_contains hk0_1_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-211094171473399322633979433646845),(-211094171473399322600230289337660)⟩,⟨63449433928411725495075345681469,63449433928411725520988877486842⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_6 0 6 ha0_1_6_contains + def realAnswer : RBox := ⟨(-298396026175443591787164581241329),(-298396026175430225249612134385756)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_6 +namespace hm0_1_1_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-24054159706547428479689382925283),(-24054159706547373461001026546085)⟩,⟨(-20761882880835392520495443609726),(-20761882880835337503787201416809)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-76560272912486011421644315759843),(-76560272912485873365442017937244)⟩,⟨(-58633971354151621315689018266162),(-58633971354151483265057329576329)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-140030770725152134231226600654724),(-140030770725151979267455270633430)⟩,⟨(-83629570595118904459649333122268),(-83629570595118749503879760449138)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-214389847008363009588851826602225),(-214389847008362898534355834243106)⟩,⟨(-82057365207208678638466796366828),(-82057365207208567592288416324515)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-288690731841358736682022928551054),(-288690731841358684127560536847171)⟩,⟨(-37063452666334099936137922253552),(-37063452666334047387089467447362)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-339583763309299900144904057939361),(-339583763309299883799693740851532)⟩,⟨62883839047371985179538445671265,62883839047372001526547016621172⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-335997287882389812427545494368925),(-335997287882389808855429045567500)⟩,⟨210275282810672771901483514459632,210275282810672775487208624234782⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-253498012048661261726149981663494),(-253498012048661260975736521474110)⟩,⟨370312267824365453254175115110510,370312267824365454032446729085395⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-94556364937448751913887806706442),(-94556364937448751570649886716725)⟩,⟨489909871081281910654757732826913,489909871081281911028847559067462⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨101580055208537217239584011101641,101580055208537217575612327241210⟩,⟨524045190764130952950423917801615,524045190764130953303893085582576⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨273788712427307553141429571592251,273788712427307553461780858767016⟩,⟨462627823450476288698806817882517,462627823450476289020606162002540⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨371326916175655302727716179577107,371326916175655303001340973091372⟩,⟨336138987435692216481572460579321,336138987435692216742896499085926⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨377964769724924537363821751170865,377964769724924537572621574760638⟩,⟨195818900056386364979336254512997,195818900056386365168175047817297⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨310471025994222733805827909407875,310471025994222733945736678910155⟩,⟨85459014707149501905746677245168,85459014707149502025139328930980⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨198798421712372831561622525056561,198798421712372831639700212985706⟩,⟨23713922076240322455669942678604,23713922076240322518788798061243⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨67849526009811065180922280429609,67849526009811065205696452504186⟩,⟨2736887180499732521935829428779,2736887180499732541249897908217⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨5357354570433454658977405124611,5357354570433480686946614920980⟩,⟨4576593918153436777106164263680,4576593918153462805030105973565⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨16857483953163053962461136935129,16857483953163155713789216126809⟩,⟨12813559306316138880839934446834,12813559306316240632100253862564⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨30491176755370257856792229000061,30491176755370531378216017432601⟩,⟨18079844256195217440527880245803,18079844256195490962068515778403⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨46918826154081147147917186625802,46918826154081847965443351849694⟩,⟨17819725586594424819575095627134,17819725586595125637781314500715⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨65441854969055265892726340514884,65441854969056947073457267884778⟩,⟨9060946383483288382806366191543,9060946383484969565303302281454⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨83243066729159258122673018805599,83243066729162755586483783980354⟩,⟨(-10811855800543648474999696185333),(-10811855800540151007742721663291)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨95021845405007197908328176464417,95021845405013004860271230510028⟩,⟨(-42608795617503618558357180942429),(-42608795617497811600857675253509)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨94019319850494179339613993263455,94019319850503606249952946863348⟩,⟨(-83644713998410948506815240368519),(-83644713998401521590849497927275)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨74953793848652589428589638178983,74953793848664869651958842881815⟩,⟨(-126766925030361725547317464511063),(-126766925030349445319899016731016)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨37852844706286994468437430481828,37852844706298556956814643626849⟩,⟨(-161556061563033334252836648087416),(-161556061563021771762785159270169)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-9646905664338873344576042954992),(-9646905664330979283260635975004)⟩,⟨(-178195577939748751903462613534428),(-178195577939740857843240461385370)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-53972988823185882674557454082481),(-53972988823181698036700589371446)⟩,⟨(-172026597014815174671598598744807),(-172026597014810990037303345010187)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-81304046929150543557649938045515),(-81304046929148673075059585144039)⟩,⟨(-145572723971459232049989682257910),(-145572723971457361572342936588156)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-83723154569243543637945856003635),(-83723154569242786628715063332211)⟩,⟨(-106582803138367957993972767994229),(-106582803138367200989631113329088)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-61714548099226940220214497524443),(-61714548099226655905563146071842)⟩,⟨(-63412850118696329928055627568566),(-63412850118696045616923847370749)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-22586530581392819728421774753637),(-22586530581392743971313100835706)⟩,⟨(-20843146322998076179293551422395),(-20843146322998000423408583129254)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1797276474577889224119896399039),(-1797276474577889223029985609925)⟩,⟨14513428664163060946787873159,14513428664163062022158774639⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-5489947025318564850195284784734),(-5489947025318564846787003863799)⟩,⟨249705257966271794540337171808,249705257966271797907507822072⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-9397301890178024437085033720447),(-9397301890178024430994534987036)⟩,⟨1100857076366249763989334719236,1100857076366249770026126189424⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-13412600546499559545354722801260),(-13412600546499559536006675876806)⟩,⟨2980051444140570138053214507312,2980051444140570147360337694319⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-17085803247804254436850464031086),(-17085803247804254423553238806612)⟩,⟨6313137729833952803105793410869,6313137729833952816409268659130⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-19633854089962608929658675529925),(-19633854089962608911426636807117)⟩,⟨11473305685524125387108004265849,11473305685524125405427980213930⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-20095716855864495533808839084180),(-20095716855864495508492975245749)⟩,⟨18531066056150868280631809191867,18531066056150868306174964669228⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-17587994664028331639877268234265),(-17587994664028331595495870555373)⟩,⟨26920786408015933696689619334973,26920786408015933741455277602471⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-11699835028365996611932627345365),(-11699835028365996455151816575517)⟩,⟨35294095502811389530060570248681,35294095502811389687294568219917⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2976449461420894720612199960806),(-2976449461420893692540414566900)⟩,⟨41736412133685691846903380894183,41736412133685692875329576265522⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨6845061883670633710957472199846,6845061883670640500589840257879⟩,⟨44352797376780253337822811105902,44352797376780260127611027172679⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨15238916070164785940315392276222,15238916070164816473389839343431⟩,⟨42051022973309125327120589577920,42051022973309155860244154340529⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨19864135929761801203815505163143,19864135929761889021613213387517⟩,⟨35171058515193209902136498183564,35171058515193297719918563647245⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨19442049761733650034000839864497,19442049761733809336569438386393⟩,⟨25432985484442151498616589189274,25432985484442310801140440373392⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨14072228541674951936529954452957,14072228541675124019869488332712⟩,⟨14928335997414427170652996734637,14928335997414599253952701385145⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨5123322321621763477014876593506,5123322321621839331785883788859⟩,⟨4860184877927424743457125362023,4860184877927500598212703023037⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨48098236783224673689464929393,48098236783227004891080163624⟩,⟨(-414869277249713785041254343644),(-414869277249711453837831967917)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨111750770422497369448418620441,111750770422502939550066546994⟩,⟨(-1252605042375767792683220411975),(-1252605042375762222573941297062)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨72533391449839174569395572539,72533391449844929662104647335⟩,⟨(-2108571042343735620198939227988),(-2108571042343729865086171285385)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-152159292105371682482866639011),(-152159292105367924699954171572)⟩,⟨(-2982455616743514260311429242190),(-2982455616743510502484948705029)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-652203556683356791554545174086),(-652203556683355146793215739730)⟩,⟨(-3859952345853309173730360171617),(-3859952345853307528887227751563)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1498277042609625925696613794744),(-1498277042609625434979778299268)⟩,⟨(-4704779513957043427578258884369),(-4704779513957042936723945858630)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2707655512192021458730583397315),(-2707655512192021351767160033761)⟩,⟨(-5436425065492840569472846409804),(-5436425065492840462297440876358)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-4224840501383245515188662328444),(-4224840501383245493502002077119)⟩,⟨(-5919506971537307645841842613550),(-5919506971537307623855936052472)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-5910400567966516139792666954814),(-5910400567966516132084241769835)⟩,⟨(-5996487397313917732350202709039),(-5996487397313917724251378700031)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-7534104788532656759346437638913),(-7534104788532656753252970028255)⟩,⟨(-5555664359838413386758441812521),(-5555664359838413380259386202987)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-8791169894347352501684543456972),(-8791169894347352495451005766543)⟩,⟨(-4606105036351981729065505280689),(-4606105036351981722483277182679)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-9352073383927588055370700106123),(-9352073383927588049177096218788)⟩,⟨(-3318821247898708447227844101919),(-3318821247898708440760642496042)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-8943170754520123993435993526806),(-8943170754520123987760598216906)⟩,⟨(-1988561360254984320634114893690),(-1988561360254984314766179818640)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-7441368955332080554173316322238),(-7441368955332080549603771971088)⟩,⟨(-917831081651952319301096806195),(-917831081651952314613037070846)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4936710638026308078280205261392),(-4936710638026308075321916438232)⟩,⟨(-281587627983866278589287242443),(-281587627983866275570318662116)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1729075667766847213903910815937),(-1729075667766847212882901667787)⟩,⟨(-40992041301421928643490609486),(-40992041301421927604411060572)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨82203524731423195199064353217,82203524731424889339696691323⟩,⟨(-1021635931482996125576361598),(-1021635931481301991943168317)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨252684110023418634133817342069,252684110023425124840627194661⟩,⟨(-11201476822792953001063665964),(-11201476822786462316309885381)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨438143781230237706172555576807,438143781230254541134753311430⟩,⟨(-45436480959240003944695600965),(-45436480959223169022009419523)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨638916115782943968059456323335,638916115782986083194603705233⟩,⟨(-119889366813720798688153157599),(-119889366813678683613025143430)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨843742975631739793980274381117,843742975631848943650502364939⟩,⟨(-253532450803310907135813349254),(-253532450803201757542742319651)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1032997728815402964875166721285,1032997728815661717734445884874⟩,⟨(-467771859490352264180587713908),(-467771859490093511413020137344)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1184645357476739946792114807335,1184645357477251921728327048590⟩,⟨(-777167324969688922523123016357),(-777167324969176947689991403735)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1277420964456462612593737225371,1277420964457249067724200429670⟩,⟨(-1175365879419441224200695063299),(-1175365879418654769176976885094)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1294065947717856057116988052724,1294065947718790318468109488121⟩,⟨(-1624957895669893819592838144530),(-1624957895668959558341121559752)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1227439600244459219443223613742,1227439600245310646287143440018⟩,⟨(-2054403116556245541572375572782),(-2054403116555394114810946537366)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1083912444300063316419010454941,1083912444300656131240602804613⟩,⟨(-2365785319605387803112537650481),(-2365785319604794988350762553828)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨879567369954406057997746779254,879567369954741075117828623772⟩,⟨(-2461289654319709361063062042626),(-2461289654319374343980358873123)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨638614925540316391030645615634,638614925540481267463565597106⟩,⟨(-2284464760459054088352965045573),(-2284464760458889211937753907953)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨398991708223825648588040340437,398991708223900153334610766455⟩,⟨(-1843158773453372275260966327538),(-1843158773453297770518473160638)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨201539953310034397983945246149,201539953310065269310535782298⟩,⟨(-1193362873475259107776481191691),(-1193362873475228236448044986456)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨58860385817564870913829118079,58860385817573219500341327719⟩,⟨(-412530666878176619193048799542),(-412530666878168270605128801069)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-546482374634822374991092874),(-546482374634822367577649635)⟩,⟨515261527250148527249064696,515261527250148534398430325⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1159951134607868840114553630),(-1159951134607868816910434137)⟩,⟨1905952670540930817193699345,1905952670540930839718428797⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨420324273590981217378812180,420324273590981258899276315⟩,⟨3970189010719568069925971658,3970189010719568110756590352⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨8075528106541566368081302291,8075528106541566432343180861⟩,⟨6536100747269798618995780872,6536100747269798683202305860⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨27999790235059865768947929947,27999790235059865864029600748⟩,⟨10408922116305692972215421201,10408922116305693068564986261⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨65801824660211648717371671619,65801824660211648860581067327⟩,⟨18579352651692484460788493408,18579352651692484607513335864⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨122474451887857535905344351005,122474451887857536152700025535⟩,⟨34029252454469928705894009051,34029252454469928960206564172⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨193478154303607702841886486959,193478154303607703519253109623⟩,⟨56035991108433217987155454997,56035991108433218675599850536⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨270075202951920931105923816551,270075202951920934907647862636⟩,⟨79417980737801521593218082619,79417980737801525409747958412⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨340348437847440859612953234711,340348437847440886583717553959⟩,⟨96409366137741006703068589108,96409366137741033691160077849⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨390867016509754807007648530912,390867016509754960639592006462⟩,⟨99423854551894681782417692764,99423854551894835432693400321⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨409909299802657586212248223676,409909299802658196293061062098⟩,⟨84960396549578424299222159168,84960396549579034398209644457⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨389644962266108664046444508466,389644962266110264275056759883⟩,⟨57683636403140251906030270617,57683636403141852151169676968⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨325596308814876056201076574540,325596308814878781496680641705⟩,⟨29233534699493417182868611526,29233534699496142491485171647⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨218063386319934523257168107216,218063386319937356703842057573⟩,⟨9942176230465238327746818248,9942176230468071782657511343⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨76926110755182937859290715106,76926110755184165792586946278⟩,⟨1731057113174448151614472371,1731057113175676087665384888⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨13961239580440136784260727021571,13961239580451177753786263313247⟩,⟨279604817845763780714325585439125,279604817845774821683432188260305⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 6) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_6 (tableDensity true) (fullFactor true 0 6) density1_contains hk0_1_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨276046224234445268015685762980018,276046224234445268059819259384335⟩,⟨(-82972336675615333373600839790486),(-82972336675615333339713913583460)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_6 0 6 ha0_1_6_contains + def realAnswer : RBox := ⟨290007463814885404799946390001589,290007463814896445813605622697582⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_6 +namespace hm0_0_1_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨116645204928524174505316426162701,116645204928524276614450612822947⟩,⟨193930370888634436095011465279549,193930370888634538209041162834357⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨395996102854410183073299727720403,395996102854410422450592424483080⟩,⟨559573233364414918823020732307810,559573233364415158217398472319194⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨803429081158872226505143737969836,803429081158872461472159358508095⟩,⟨841274374937808371542804356417791,841274374937808606545949913188970⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1382538695928319010746056615413193,1382538695928319149928768856983094⟩,⟨935519018272881510288640865937371,935519018272881649534373799747167⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2090536372710215537351387766512755,2090536372710215605129675200348278⟩,⟨699752432248035257061485465223382,699752432248035324906162658224639⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2751234875763423896774439320784471,2751234875763423920938267802463875⟩,⟨8658548495877965575501425359187,8658548495877989786193748387178⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨3066052311644140728817187161947441,3066052311644140735156788760546967⟩,⟨(-1133991670633148624749319347409930),(-1133991670633148618393228198714098)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨2739181344948640064395430900432245,2739181344948640066360921065051109⟩,⟨(-2491613709070685894185497374885689),(-2491613709070685892232503049846249)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1685828209806026001040937999952633,1685828209806026002199231474716104⟩,⟨(-3622196083566984283488701488799043),(-3622196083566984282369324905051627)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨166257472493074270784505702143631,166257472493074271894719210175364⟩,⟨(-4094462913119614454569348170413501),(-4094462913119614453493061280879568)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1311987970007081194138680407989239),(-1311987970007081193063721670394199)⟩,⟨(-3758533824271311501367926797609733),(-3758533824271311500312124146619491)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2278795451224795222403149475952986),(-2278795451224795221486729331162338)⟩,⟨(-2835680860960991906115569988813051),(-2835680860960991905217072587095413)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2536837770331097848771282398035292),(-2536837770331097848078313655759708)⟩,⟨(-1749231710450016152537959962551381),(-1749231710450016151868449229496431)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-2176789138008849713658162907689883),(-2176789138008849713197860064357450)⟩,⟨(-861431904287661606224208061860254),(-861431904287661605789482045128805)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1425498979484150967845724755911075),(-1425498979484150967590845862219261)⟩,⟨(-321226748984193515559591437470046),(-321226748984193515324596178835242)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-491271839302639905626765448507253),(-491271839302639905546378155462960)⟩,⟨(-70704901702731083865052782439913),(-70704901702731083792070211000764)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-24176556542912889415147565125371),(-24176556542912865401259600161530)⟩,⟨(-39166702532067320519374498113606),(-39166702532067296502279766313901)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-79862846776564856921393895137201),(-79862846776564766005367896445679)⟩,⟨(-115849389222355984725855325490946),(-115849389222355893799682813936827)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-157150283782705340755860247872820),(-157150283782705078313558177892849)⟩,⟨(-185249939944865699037621263047158),(-185249939944865436579177729533509)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-268346990633700893206491252560720),(-268346990633700129763225161909929)⟩,⟨(-235379065295166125930963088781893),(-235379065295165362468274489537278)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-419311651323907263698403124976020),(-419311651323905142183446166051900)⟩,⟨(-244916878948383736084642114899488),(-244916878948381614551236119274228)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-601763701056720568361174692744631),(-601763701056715370815534548274316)⟩,⟨(-184428019069058723231839493070726),(-184428019069053525674980648542070)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-785022337963267946475182577541771),(-785022337963257742854878979019185)⟩,⟨(-25598432038940427787585675880955),(-25598432038930224170969752644339)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-914644439609734599855671673737743),(-914644439609719919148289165213887)⟩,⟨240317265668977442966309743817012,240317265668992123648122355601049⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-927560915438582956565698410945540),(-927560915438567833637669161077829)⟩,⟨582049737405962053133209817880441,582049737405977176010184897214013⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-784925739401310207153363595757286),(-784925739401297856751107330604354)⟩,⟨922565444068590639605330973206046,922565444068602989943372678528293⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-505345146818761992483724283698942),(-505345146818751991007132468823240)⟩,⟨1162933821131421553982270791012891,1162933821131431555414886894714928⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-170226285614053068904465689437796),(-170226285614046932761598936552653)⟩,⟨1229098157208413485811348573139206,1229098157208419621934020703142631⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨110885203002314466437152845840448,110885203002317549202365248620866⟩,⟨1109112218113805181918396276744513,1109112218113808264682598871581145⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨253729450605570103603362973753971,253729450605571473262436469828645⟩,⟨850562883873773034562973791722264,850562883873774404231314950543822⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨235065138632588984177858852841328,235065138632589534361153050101482⟩,⟨522385626746834459184257762801202,522385626746835009377675849261544⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨93386975412547833653092675382459,93386975412547978923020245832821⟩,⟨174596989250772952195545392396029,174596989250773097469658409773842⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨5820668246965924263790910258697,5820668246965924266212043350569⟩,⟨3211219068241387555264755750933,3211219068241387557399779765355⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨18275235206169832744640181368997,18275235206169832752145134667281⟩,⟨9010451732222641644619784998926,9010451732222641651142809410145⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨33057870478788865038962760453036,33057870478788865052350252361974⟩,⟨12726237945325722679061734868700,12726237945325722690405053057851⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨51310965943401180109655041075211,51310965943401180130253789269092⟩,⟨12353309612875211835476305968778,12353309612875211852339948946186⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨73243446733198274761745939071387,73243446733198274791215125105700⟩,⟨5184830825778054235062770683405,5184830825778054258244290996194⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨97329882701225058608297759132570,97329882701225058648804348202899⟩,⟨(-11957753188460781900581389365719),(-11957753188460781869630736054504)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨119611142289294290020651480439262,119611142289294290079453682721150⟩,⟨(-41826202557646292409888262210716),(-41826202557646292361615650049397)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨133742081411701976802543778225899,133742081411701976899101377340573⟩,⟨(-84986731286940267036597233541892),(-84986731286940266949309330987075)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨132493456312244945803946269616749,132493456312244946083885169786512⟩,⟨(-137705990458495275122912766507641),(-137705990458495274849227812094543)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨110977319663256841154051566775628,110977319663256842785868196552118⟩,⟨(-190902583500458113673006971751380),(-190902583500458112043021794210902)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨70534167326951400919574868760381,70534167326951410301599141646738⟩,⟨(-231732218402920830921996472207315),(-231732218402920821536844875764279)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨20711778324918281994277788223791,20711778324918319945483956308499⟩,⟨(-247978995017637873347585496884185),(-247978995017637835389020028244222)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-23161869012564266712245328726301),(-23161869012564167330087182174409)⟩,⟨(-233040114443908367869179552098406),(-233040114443908268477256560263942)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-46613798708588329291097090309140),(-46613798708588163098219734743394)⟩,⟨(-188278900989096086854461773949817),(-188278900989095920651971735653842)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-43103550532774271724259338745270),(-43103550532774103021047417800885)⟩,⟨(-121287143756686458388069843671234),(-121287143756686289677893973426230)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-17230878855701052181050579369306),(-17230878855700980319762401220738)⟩,⟨(-41714284014782930562096214798732),(-41714284014782858698282864068497)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-577779426275812656175702227349),(-577779426275810878972823076975)⟩,⟨648512037956275874110681629693,648512037956277651394055218914⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1707091025597861036395840897641),(-1707091025597856809111481248966)⟩,⟨2045087371283381502862954460273,2045087371283385730406570356617⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-2737504344541925956513892537400),(-2737504344541921630424471018957)⟩,⟨3733140011229766249619609971259,3733140011229770576200254535464⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3541971824161447681475432359308),(-3541971824161444901049849641313)⟩,⟨5883794052165591069780308553970,5883794052165593851018291593600⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-3905411199311805911992793737897),(-3905411199311804723757277333143)⟩,⟨8615391483624476473139738512090,8615391483624477662631448887764⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-3517655107397221701856783242135),(-3517655107397221358286864523510)⟩,⟨11947288870602276277789139333943,11947288870602276623195378548480⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2026103479560398833538224690274),(-2026103479560398750101320605859)⟩,⟨15735498299692197018726066068371,15735498299692197104326300954023⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨839313841451895682988199935466,839313841451895706418454787291⟩,⟨19602889450239314217350435521574,19602889450239314242964111243832⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨5088792996174960583271968037919,5088792996174960596602224359942⟩,⟨22925573885782511059784677516956,22925573885782511075103579287336⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨10292515531087432356706926426184,10292515531087432369834634457325⟩,⟨24945182511109703547130566706486,24945182511109703561827306268408⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨15502968822921371447238031407250,15502968822921371461335275575522⟩,⟨25013096540963549214235682595964,25013096540963549229300074274086⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨19397913788441204531778290461475,19397913788441204546324759264971⟩,⟨22878601192663401661349208604051,22878601192663401676171967370451⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨20659140322492701776737891171042,20659140322492701790438685141403⟩,⟨18849445158422790952595436187722,18849445158422790966001147491197⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨18450313363742545247244614251143,18450313363742545258519179980056⟩,⟨13666803573554755906578785268361,13666803573554755917265047955278⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨12778634744828295876823541869622,12778634744828295884240786163202⟩,⟨8123285521452548235386475679877,8123285521452548242262881699754⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4567788663921163926429481204603,4567788663921163929010586193984⟩,⟨2673678222728507420520429121940,2673678222728507422886155659840⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-19604280737351728112558657581),(-19604280737350524857742572017)⟩,⟨(-146982756308356478206700555515),(-146982756308355274973346462854)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-78479002141757051547241944287),(-78479002141752282637961138489)⟩,⟨(-441315333820880642311546784996),(-441315333820875873465512620838)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-197016811888729244339087488593),(-197016811888716030987802142271)⟩,⟨(-733495241705617458662211720613),(-733495241705604245413201866588)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-415305602668057577520608543138),(-415305602668021895929450850620)⟩,⟨(-1013038788682944621927135918093),(-1013038788682908940471946158628)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-767540870089439546872493570220),(-767540870089346468717329749388)⟩,⟨(-1255772232262037370616732512342),(-1255772232261944292622841314387)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1271339658655839130289952969562),(-1271339658655619180087966716446)⟩,⟨(-1418621452787457996613266808694),(-1418621452787238046584380479942)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-1916019661360047248222687187764),(-1916019661359613696493020556708)⟩,⟨(-1440220336075373752612628272815),(-1440220336074940201049320706886)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2651797752638842699945523504434),(-2651797752638179814637016025460)⟩,⟨(-1255214152180672575322004824103),(-1255214152180009690153061672028)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-3383913186780117639090968465266),(-3383913186779334828779305599131)⟩,⟨(-822093674425050994972852752598),(-822093674424268184751309290262)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-3982062514509143286243686098306),(-3982062514508435135850215763744)⟩,⟨(-156403677481373221617556220384),(-156403677480665071242580388598)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4311412173273020958904374931252),(-4311412173272532324040288553149)⟩,⟨643369575914670750117576091375,643369575915159385047377071758⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-4274128302812993519128501259156),(-4274128302812720234345251716536)⟩,⟨1394074846903605764630821356109,1394074846903879049557994662656⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-3836075356846423744339632885036),(-3836075356846290732350171243942)⟩,⟨1869402568498346196619575507707,1869402568498479208802386757247⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-3028230106436328381003713446618),(-3028230106436268906971474625768)⟩,⟨1887021008687575495380630027359,1887021008687634969609091891088⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1933504928557449459691233313618),(-1933504928557425023489025267217)⟩,⟨1397008520810075021237711311831,1397008520810099457586032432463⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-663539573734649322202575900661),(-663539573734642745037322001223)⟩,⟨514506432533159735610278953981,514506432533166312829582835856⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨9000539654384655118177733706,9000539654384655124183511548⟩,⟨9454887823276105334287095701,9454887823276105340615316128⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨29101868668170220832651446766,29101868668170220851574626196⟩,⟨26802549803601968746196206917,26802549803601968765946813622⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨55346015553954440994919791851,55346015553954441029262681640⟩,⟨39438877743026498360776716602,39438877743026498396045713250⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨90977672815501434657773932843,90977672815501434711723732521⟩,⟨44359319511013985859880689867,44359319511013985914286325998⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨136841782588353193756851807193,136841782588353193836598850377⟩,⟨38670017464573815253444634374,38670017464573815332603731992⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨189859049103325942247535935179,189859049103325942364563437895⟩,⟨18871028071857156660660532536,18871028071857156775603023128⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨243397650953452538741993677650,243397650953452538931141356287⟩,⟨(-19320762149290522355593803322),(-19320762149290522170346778460)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨288966013539167135860551894724,288966013539167136327584061244⟩,⟨(-78640934532857573952094867247),(-78640934532857573490412364282)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨317710531887186312565553435972,317710531887186315045399518025⟩,⟨(-156843615418248559845355357617),(-156843615418248557371068422044)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨322533859933487479817064968774,322533859933487497251625443985⟩,⟨(-244703488388281509096300403910),(-244703488388281491665901457857)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨301154414075824248824688994798,301154414075824347556776491467⟩,⟨(-326094788194631659794601980596),(-326094788194631561063969005533)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨257851264420268496171637434250,257851264420268884658061749121⟩,⟨(-380231207154674628902116417002),(-380231207154674240414119968919)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨201372961310711796733131542883,201372961310712804332474976667⟩,⟨(-386962678819712725063934164670),(-386962678819711717460524582072)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨140575834300363827837398543552,140575834300365576794805666751⟩,⟨(-334874589002018199975289174976),(-334874589002016451012842697285)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨81586389327492533888563241940,81586389327494462632673357101⟩,⟨(-227085821766802600359464369207),(-227085821766800671611410865382)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨26538778142127650815290873283,26538778142128512948876276384⟩,⟨(-80297874364230269423583795173),(-80297874364229407288519354178)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨137962170767946279493499254941682,137962170767960853147515901693871⟩,⟨(-2203667577740474786926449833142653),(-2203667577740460213281577624094258)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 7) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_7 (tableDensity false) (fullFactor true 0 7) density0_contains hk0_1_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨294018821723869414124813912965594,294018821723869414176236930864618⟩,⟨(-37853006400564008112702457619583),(-37853006400564008072535336399876)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_7 0 7 ha0_1_7_contains + def realAnswer : RBox := ⟨431980992491815693618313067907276,431980992491830267323752932558489⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_7 +namespace hm0_1_1_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨15397371103194228826340273668459,15397371103194312457298877747411⟩,⟨35507438723547809431381863834742,35507438723547893060965354343561⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨53921316168252211817158202561031,53921316168252407790115570627822⟩,⟨104698833593490296769528065502136,104698833593490492737733265410312⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨114101006622498021461081184248979,114101006622498213638450796712293⟩,⟨164507191492899997158580642126626,164507191492900189326045749922062⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨203998093162493392335725627626953,203998093162493505958349894205420⟩,⟨197277002041193281084386915476886,197277002041193394689847222400230⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨318256999084781179319883300484123,318256999084781234411371425467984⟩,⟨174380616766105164447066327471572,174380616766105219520081292587831⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨429405698886228527386295683271100,429405698886228546733597087214459⟩,⟨67155616015835093359495874006748,67155616015835112694733232660934⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨486524603097206309029122974930256,486524603097206313740867755414266⟩,⟨(-129891104053450886911399486319061),(-129891104053450882197551041448671)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨434291567042071810271972571527297,434291567042071811373094283906361⟩,⟨(-377290373286887650966914044145482),(-377290373286887649842557449348097)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨251927444030900394200193239985440,251927444030900394653035562675558⟩,⟨(-593492639593569341486894138550025),(-593492639593569340990819253343322)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-17187527234629312648778580477124),(-17187527234629312240001736203135)⟩,⟨(-694095205151769686724086159227671),(-694095205151769686281063319766853)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-279784051322484739515487254822873),(-279784051322484739100490370549372)⟩,⟨(-644557482405045182378767006522625),(-644557482405045181952484703289564)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-446880394343701890339364295727572),(-446880394343701889973856171061855)⟩,⟨(-481450907142060505049527123962975),(-481450907142060504694144813332169)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-481949293872787858785904096250824),(-481949293872787858503996134032726)⟩,⟨(-284006280427770135863502096238306),(-284006280427770135604853707721106)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-405026368957477854225202637440972),(-405026368957477854036621477913269)⟩,⟨(-124191534036600954948435659891958),(-124191534036600954785772749762152)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-261294907507391615767932569745763),(-261294907507391615663433163351992)⟩,⟨(-34160269239481034178962070750565),(-34160269239481034093921992288021)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-89312273332266592894792642507613),(-89312273332266592861825724428157)⟩,⟨(-3805727662021461396403625713505),(-3805727662021461370613075609386)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-411822336883202979834369418566),(-411822336883183210654969410349)⟩,⟨(-7166793587278471927472007227043),(-7166793587278452158704789673212)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2597649817934934185215978515876),(-2597649817934859308309715236280)⟩,⟨(-21497181262065188718651991550857),(-21497181262065113843049338530382)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-8910971221856490366519564423663),(-8910971221856274059976644572109)⟩,⟨(-35411701258882349285732235815589),(-35411701258882132981272940348882)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-22055569629612239914270985696881),(-22055569629611610104155811366750)⟩,⟨(-47364569383014336000620952609301),(-47364569383013706193042988663494)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-44005870556325215978687394752393),(-44005870556323464234957567123760)⟩,⟨(-54053022610982504657005586203155),(-54053022610980752915771904801081)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-74535748737015707811605160896459),(-74535748737011412606449793200055)⟩,⟨(-50354578182142801127486474190309),(-50354578182138505924035760071474)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-109359338894246381332795668105699),(-109359338894237941802974373856340)⟩,⟨(-30434744059732558209612657562384),(-30434744059724118679745380470453)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-139324329308813445506271082944405),(-139324329308801297288505129447670)⟩,⟨9379583145774069471598707389311,9379583145786217692220350781675⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-152443663226883890565736409507919),(-152443663226871376944541879353085)⟩,⟨66567306701273074791717603865601,66567306701285588419355229184133⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-139405999927735396186806176021442),(-139405999927725182579684161612152)⟩,⟨130022299848515417231897081198741,130022299848525630847623339382326⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-100210502911208016978974995406551),(-100210502911199754068728274749259)⟩,⟨182522978832659486686508864737879,182522978832667749602917993527070⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-46732305145266393509355853659117),(-46732305145261330446088128828507)⟩,⟨208043416061756498222021608500986,208043416061761561288133637783848⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2279778823477840974442498651227,2279778823480381143059336648942⟩,⟨199382576967280039594930845597864,199382576967282579763469776661331⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨30795472963880893086717430384457,30795472963882020231556984759772⟩,⟨160526820526462166044694859327554,160526820526463293187805854543016⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨32798445790016739445558737252730,32798445790017191761342691546215⟩,⟨102187199165004240666884586646019,102187199165004692980831656768776⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨13587944635848412474275853045375,13587944635848531837288630370902⟩,⟨34825408295950792787427169103936,34825408295950912149677884703090⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨739260643716785689799082828170,739260643716785690751865712123⟩,⟨1306139746365375161336456000318,1306139746365375162276603435719⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨2433449613346592626679425560474,2433449613346592629644040830650⟩,⟨3910678232098298212852261813571,3910678232098298215771833874687⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨4745194433244101792677574004846,4745194433244101797917601874026⟩,⟨6425339304225115328335275129644,6425339304225115333483579516065⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨7993482145783021315450756290182,7993482145783021323311653003599⟩,⟨8574219791096486747118750287301,8574219791096486754818998392119⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨12353355755387720234944392135542,12353355755387720245708205263675⟩,⟨9772356200730754431355017718190,9772356200730754441868111486661⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨17766051107939866246239471610091,17766051107939866260320770477047⟩,⟨9142669688002413400019175976120,9142669688002413413733157418546⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨23764018413962902417733441091348,23764018413962902439284490962278⟩,⟨5750026248254644379670938731098,5750026248254644400801570887110⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨29298622005476404189267480985573,29298622005476404233031649182975⟩,⟨(-984352309439362680178089031979),(-984352309439362636780271541779)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨32841664570888253039253000075102,32841664570888253224312219200021⟩,⟨(-10780630188162364132004352231792),(-10780630188162363947159974056626)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨32921145654989615476518181184210,32921145654989616757039727939569⟩,⟨(-22103558780285646787427572613641),(-22103558780285645506968647300436)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨28906845557986380981181140015440,28906845557986388573318585469157⟩,⟨(-32249048897334527900213085722261),(-32249048897334520308041050540161)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨21559529652478829986116703694960,21559529652478860873471284202474⟩,⟨(-38209517119804627436866147988188),(-38209517119804596549447995411211)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨12927424490881764471458802655448,12927424490881845506799774402810⟩,⟨(-38036528898905722147909768657316),(-38036528898905641112508955888198)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5550675891261186199838275656049,5550675891261321848552640390037⟩,⟨(-31704776729277880523613347791026),(-31704776729277744874877880139558)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1227561600330831611894207892026,1227561600330969392430830742214⟩,⟨(-20745833455022202792316568638299),(-20745833455022065011790086816268)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-17382151478043262760450326920),(-17382151477984556454231747533)⟩,⟨(-7181039035682491420870384093300),(-7181039035682432714577352454132)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-284413140272235575235187962242),(-284413140272234082005894969499)⟩,⟨58338924230635872833609342503,58338924230637366054683280266⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-853604960362896823091294299650),(-853604960362893273674016956219)⟩,⟨201595313534233157521925527484,201595313534236706912652268095⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1417951656348774775129766576880),(-1417951656348771147789728644242)⟩,⟨427410633701062460213012211657,427410633701066087502755160033⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1959283538117967428171019283812),(-1959283538117965101926319524756)⟩,⟨799231781868008827661808229391,799231781868011153823529337432⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2442502718868251272411250055817),(-2442502718868250281504790164732)⟩,⟨1384291335321090165563059859385,1384291335321091156342641164314⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-2814032803671433273340202814229),(-2814032803671432988516473835404)⟩,⟨2232961936585796026149375046899,2232961936585796310790233168209⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2994942507168322016045351740498),(-2994942507168321948414798943113)⟩,⟨3346052580947386959396198961101,3346052580947387026814276149075⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2881964355637786158808046371870),(-2881964355637786141892439414034)⟩,⟨4650813927023044449167199322614,4650813927023044465875079064456⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2380677681369373773951100154605),(-2380677681369373766463313725818)⟩,⟨5993218748563811062887811477557,5993218748563811070196456784596⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1467190547931984788114290634995),(-1467190547931984781854620868456)⟩,⟨7149154757893571341972891484927,7149154757893571348105356312749⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-250336657874939128951275316268),(-250336657874939122772076607434)⟩,⟨7865680066536018085723682231831,7865680066536018091843319932958⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1005850425320774134888151853660,1005850425320774140898841764786⟩,⟨7927012514281422955803859772938,7927012514281422961820509497042⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1941008180203145853515944178693,1941008180203145858942967661810⟩,⟨7218560485651461751801483843122,7218560485651461757283824166230⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2236110282890234783675364823800,2236110282890234788003964049830⟩,⟨5762919301533670209436798131307,5762919301533670213840900200964⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1763153827890453157326669451498,1763153827890453160114775521878⟩,⟨3708386372459399380175783129422,3708386372459399383026603999476⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨667176152031280831590006425894,667176152031280832550216054224⟩,⟨1277878163660379860181683965853,1277878163660379861165933575122⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-8903657538445306853931837671),(-8903657538444317978585208230)⟩,⟨(-47900654008398819282449496430),(-47900654008397830402676429145)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-32537313072029615556759483501),(-32537313072025696010372956442)⟩,⟨(-146758364845792324510551318379),(-146758364845788404950726901812)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-73302479602287896060737962213),(-73302479602277034572997838227)⟩,⟨(-252839581003897945681893927683),(-252839581003887084171769617057)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-142218801272098918041371738745),(-142218801272069582698523207147)⟩,⟨(-364929745213388368248771051610),(-364929745213359032874919730737)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-251192050653055008668258394464),(-251192050652978475816035998324)⟩,⟨(-473907259859794597805497338705),(-473907259859718064914916208842)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-412863350334398253176784113274),(-412863350334217401518250172122)⟩,⟨(-564011658372491442262151192049),(-564011658372310590560028646389)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-635257415924333839274071970049),(-635257415923977433899411335432)⟩,⟨(-617038676101470221534875794715),(-617038676101113816114838233233)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-912839224909235267584913564665),(-912839224908690605551540114502)⟩,⟨(-616452099040239346731449035850),(-616452099039694684657683972610)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1219548247985076866486751387286),(-1219548247984434182186500672073)⟩,⟨(-552390925588563798337609318467),(-552390925587921114009407957308)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1506699247363438264985272253636),(-1506699247362857497160811034112)⟩,⟨(-428590838208575547802746367504),(-428590838207994779967265398422)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1708086305193831336968785946162),(-1708086305193431105400387236020)⟩,⟨(-266133809684518535425019563314),(-266133809684118303863453767720)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1757077539528780251849748425481),(-1757077539528556709600614848192)⟩,⟨(-97882571190660639201282439018),(-97882571190437096974358844462)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1615090640031736015095633146998),(-1615090640031627351455445678379)⟩,⟨41701528277316937187986079907,41701528277425600796134574041⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1290587870487918556516940804553),(-1290587870487870020661154866310)⟩,⟨121499235708142103098446792918,121499235708190638921401194465⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-828338324292544674528069021195),(-828338324292524747292922796321)⟩,⟨121604683030928705210825051074,121604683030948632421583001815⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-284816713572623793623271714200),(-284816713572618432104250599490)⟩,⟨50191854177705437169443052402,50191854177710798679560658136⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨280772764200026107870096737,280772764200026111617590642⟩,⟨268097109268638072706410458,268097109268638076514635092⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1018767613768237672021043097,1018767613768237683850733155⟩,⟨546074681719766492295799605,546074681719766504235507208⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2049837172128209798798924289,2049837172128209820311745332⟩,⟨(-340583068944899856680155156),(-340583068944899835242559549)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨3142944644932231209717461886,3142944644932231243696197937⟩,⟨(-4449503293354652824328610380),(-4449503293354652790986370409)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨4413775241897537561074694944,4413775241897537612356927987⟩,⟨(-15179190724324320744996988761),(-15179190724324320695323179868)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨7023822074321651828436142407,7023822074321651906967398347⟩,⟨(-35889140282722208599160433543),(-35889140282722208523771449178)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨12241710393816665312745712154,12241710393816665449248478358⟩,⟨(-67702542774691744002960903008),(-67702542774691743871864966788)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨19630819652646273846355318232,19630819652646274214601729652⟩,⟨(-108667934155876453969525604495),(-108667934155876453609295193928)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨26659292564372041039002389249,26659292564372043068160048742⟩,⟨(-154094835617114218940328396985),(-154094835617114216921422877227)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨29727492886749557623002143616,29727492886749571894040508598⟩,⟨(-196883255333108333868770664628),(-196883255333108319609372703936)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨25669319685986774684452268096,25669319685986855350650914502⟩,⟨(-228458662059299779421021825405),(-228458662059299698766870975780)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨13774034656499654999384166051,13774034656499972285207297804⟩,⟨(-240986935816117144896603081701),(-240986935816116827622566832684)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2063690821851952126393517230),(-2063690821851128935777414725)⟩,⟨(-229372064360897592460194836107),(-229372064360896769280212556624)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-14056562299427326190166575867),(-14056562299425896665532915266)⟩,⟨(-191360076024721121452826473812),(-191360076024719691936260959219)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-15689227723473348677564118578),(-15689227723471771623633946467)⟩,⟨(-127866017440785615569683624792),(-127866017440784038520413611900)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-6696882631316970687938678607),(-6696882631316265619209818371)⟩,⟨(-45041662864327447517937308883),(-45041662864326742450683489538)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-37306297023774944450333301017117),(-37306297023762904550466029796759)⟩,⟨(-313181581939717893868548528805469),(-313181581939705853973076646124694)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 7) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_7 (tableDensity true) (fullFactor true 0 7) density1_contains hk0_1_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-384486151485060003153540601899885),(-384486151485060003086295116955008)⟩,⟨49500085293045241325623132215223,49500085293045241378149367656378⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_7 0 7 ha0_1_7_contains + def realAnswer : RBox := ⟨(-421792448508834947603874002917002),(-421792448508822907636761046751767)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_7 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_5.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_5.lean new file mode 100644 index 0000000000000000000000000000000000000000..4d198fa1049fe523744cfa48240bb8a2820bfc19 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_5.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_1_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-22144230599315082867842143571854),(-22144230599314965594025790961298)⟩,⟨(-240168240609928720447489179183136),(-240168240609928603175198186110098)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-126978568727908871569348658569079),(-126978568727908588009594526167819)⟩,⟨(-721426162280262566153606940368520),(-721426162280262282595414424817304)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-412420187058624794045045608931494),(-412420187058624498337762002805377)⟩,⟨(-1179311587893247071809589318840371),(-1179311587893246776095312565757629)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-978735512628128656424124948637009),(-978735512628128467283184450839983)⟩,⟨(-1517284792461411208060413487647791),(-1517284792461411018891775289455270)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1845009289556405799709990978261923),(-1845009289556405724092903889362766)⟩,⟨(-1542741831408033925544660979446236),(-1542741831408033849862406125564475)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-2855075290785754611865943569964630),(-2855075290785754589818476926997565)⟩,⟨(-1013941954105752514746747039168314),(-1013941954105752492613183460126376)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-3628682300669352666620132162984783),(-3628682300669352659869552082930013)⟩,⟨203405231658700947603577130524379,203405231658700954407227042606913⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-3679007200269542063440890025167254),(-3679007200269542061051084482403813)⟩,⟨1928396148277798564241381447031908,1928396148277798566645027734700967⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-2721258742864847592900632013461430),(-2721258742864847591410230737468285)⟩,⟨3605640091966610698537391796892532,3605640091966610700013537246580033⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-960375216838053289864244301902739),(-960375216838053288611301562245564)⟩,⟨4563285094101024956494338982439301,4563285094101024957710513751173149⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨953056340004594778183994092365474,953056340004594779438888853380829⟩,⟨4451517660949499810930401757363204,4451517660949499812164429536254678⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨2322309547376903106988654638535626,2322309547376903108083577973739400⟩,⟨3468447704046646504349696242689071,3468447704046646505426329371321302⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2803024620285754523749689652049015,2803024620285754524583221802792727⟩,⟨2167146143396911235736561442715695,2167146143396911236544849693725830⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2476007859044140111455335830454748,2476007859044140112006854229677145⟩,⟨1063619024117642118509886822354676,1063619024117642119032680280300497⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1637466144643391024629693856189248,1637466144643391024932464290915000⟩,⟨388432186626503654968492106242253,388432186626503655248499863987583⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨565707813365556353489338350289889,565707813365556353584193855706504⟩,⟨82728942458962139665338340909689,82728942458962139751655066740719⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-10286905359827591348464848877670),(-10286905359827562695618390995554)⟩,⟨39721671659328523094962591990645,39721671659328551747520217148761⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-24648036045378756805805560202264),(-24648036045378643732161044939905)⟩,⟨123472204018011338082958942567733,123472204018011451156397708166942⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-18701829871011364470360861577460),(-18701829871011055882102317696239)⟩,⟨218171889730293992674389543315426,218171889730294301264595009570346⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨25582147605107829120639560550291,25582147605108630771619936482873⟩,⟨324166047610014672913008698724193,324166047610015474571638018459467⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨129164595038547337245847011369900,129164595038549264288821020041754⟩,⟨429316104873421207153348482953806,429316104873423134214620138366687⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨308529316825567137337808069987719,308529316825571042784491611314238⟩,⟨503128853522121293939376012050027,503128853522125199420598904729533⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨560475538371645827809140305186350,560475538371653639502399948809954⟩,⟨497147034013695720590990491583651,497147034013703532326302015182682⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨844684499677061334495206591418354,844684499677075348677142916725499⟩,⟨360066709946034217395989219787522,360066709946048231606497582327655⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1080004296983759233985295931967109,1080004296983776996136873148620626⟩,⟨70030405773591436001267043498022,70030405773609198157470359038497⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1171600953578040493951106690530155,1171600953578056269911285734268694⟩,⟨(-331467560515588130918531015423130),(-331467560515572354983600423427951)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1064958638795950755511312573167947,1064958638795960502205158842803930⟩,⟨(-735829780154994962591732819032115),(-735829780154985215951234324646618)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨789877531564038111903310673477130,789877531564043025224092678613170⟩,⟨(-1012189571662162899397177371738122),(-1012189571662157986139286316437640)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨452323380711753018487644377456128,452323380711755842122763921663624⟩,⟨(-1074935262170510394414991779200300),(-1074935262170507570820265768008522)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨173585406954577491984375415109711,173585406954578889128595010840944⟩,⟨(-920359794189655164509933598193090),(-920359794189653767385983483689700)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨23343227802391532800225174878280,23343227802392133753422842820174⟩,⟨(-607461753548532504959564338262983),(-607461753548531904014057292210617)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-7930281306829998607301456360384),(-7930281306829834459365890845160)⟩,⟨(-210579800753865712089902742343598),(-210579800753865547943679979576108)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-13696434941687516521408393276),(-13696434941687515231229396623)⟩,⟨(-4857160866711125707111924964550),(-4857160866711125705289067536067)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-793307565142135512803041571078),(-793307565142135508659189153604)⟩,⟨(-14921508224002559335291942761691),(-14921508224002559329565939088891)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3963132264654267068862670982427),(-3963132264654267060878544583302)⟩,⟨(-25864387954538298457447043137975),(-25864387954538298446929880069722)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-11475569702760512164769556399830),(-11475569702760512151119131409524)⟩,⟨(-37691280578654223153065787379729),(-37691280578654223136167773995029)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-25510707770504407086630384691799),(-25510707770504407064578626827238)⟩,⟨(-49358105045950202510818584117513),(-49358105045950202485295503530500)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-47938682768981504348477274740642),(-47938682768981504314083963926426)⟩,⟨(-58194712922682542516942366351751),(-58194712922682542479715764226616)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-79207970351477814334698329397849),(-79207970351477814282065453923900)⟩,⟨(-59691844368720441097762166651603),(-59691844368720441044145304085119)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-116810071862350395579082033181976),(-116810071862350395490897376186296)⟩,⟨(-48336771315669832060570718897249),(-48336771315669831974705483658366)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-154166507894993501459941672229017),(-154166507894993501226157733498133)⟩,⟨(-19966080607304794901387408470518),(-19966080607304794674387057798548)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-181422292926091236535145191144480),(-181422292926091235399540241482760)⟩,⟨24815567940802032838334477039721,24815567940802033962330228452912⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-189065325643334952025395556001760),(-189065325643334945933132693197121)⟩,⟨78041721290248955121966455171482,78041721290248961199749696232201⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-173057666090064960156132175065883),(-173057666090064930706823135479147)⟩,⟨125167128677459806238954040314547,125167128677459835676924923477691⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-137815474520855313871688082347446),(-137815474520855223778884000615282)⟩,⟨150146943530624759181319300097065,150146943530624849266888134433722⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-93981956429310474608877714205780),(-93981956429310304573559715363243)⟩,⟨142434239590808690187312463146317,142434239590808860218922538702246⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-52028665199973251810286732634076),(-52028665199973063871289675414370)⟩,⟨101541494057748340251188303383825,101541494057748528188762016379681⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16287005573118884431289989277893),(-16287005573118800724683767361117)⟩,⟨36706975363272955426245191581004,36706975363273039132536725739594⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨484523458878856810542389416238,484523458878857691241241716436⟩,⟨210615260906749021178685157678,210615260906749901793313136711⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1512941795235832831716926127909,1512941795235834904872778380972⟩,⟨594918831835688426756835269718,594918831835690499647391482296⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2711672322091085714218564477636,2711672322091087874588258795670⟩,⟨855311046269003865688263633498,855311046269006025596338384531⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨4168525825263651410041031997493,4168525825263652963521992767879⟩,⟨868862595015908328962247288102,868862595015909881819508323739⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨5918538904067667067099733411132,5918538904067667833472117691466⟩,⟨458559578006084566350906569966,458559578006085331977682608849⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨7905924401586786773043477988797,7905924401586787035681054850156⟩,⟨(-603405582609565823864920661081),(-603405582609565562024575148917)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨9944081262385534910443272374636,9944081262385534978874733904861⟩,⟨(-2545744316240327498170338871595),(-2545744316240327430478799931342)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨11691565626245301867859548915877,11691565626245301887145149969127⟩,⟨(-5490329419504514279102115880518),(-5490329419504514260346524962198)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨12689065516853471746956788262264,12689065516853471758045599221301⟩,⟨(-9310611041952130662236456363769),(-9310611041952130651274802423223)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨12500243660477316314004206269108,12500243660477316324541068751993⟩,⟨(-13514544458354652915582926067169),(-13514544458354652904620482436970)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨10933758597000807653227816689590,10933758597000807663986265672977⟩,⟨(-17243669651789111359617791631876),(-17243669651789111347824190428597)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨8235564595896887055222835802168,8235564595896887065724577064824⟩,⟨(-19463055241498372195680308440041),(-19463055241498372183622488668959)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨5096796629391221502052489050282,5096796629391221511485980743975⟩,⟨(-19303878725716217471767722731504),(-19303878725716217460507065335181)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2388159130934059627917039183975,2388159130934059635402895923743⟩,⟨(-16390628504595350784138894940231),(-16390628504595350774926532224680)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨719661469630641634521936517959,719661469630641639325496093200⟩,⟨(-10978845689484145199873051174639),(-10978845689484145193834474977833)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨95307405447433651333558253597,95307405447433652988351448986⟩,⟨(-3858815819202888959438013833072),(-3858815819202888957338112497194)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-73369971602345326984026131671),(-73369971602344620935275344985)⟩,⟨23013749280914164670158883223,23013749280914870727221900899⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-218972153861729861200112709641),(-218972153861727064788537213259)⟩,⟨79897713975866413065041937612,79897713975869209500767861713⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-359103052540982708607948535305),(-359103052540974971079763262180)⟩,⟨169612251122050690541374343448,169612251122058428107412595018⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-484287250086450813155496632251),(-484287250086429962704423874758)⟩,⟨313986288925674032161675477183,313986288925694882660285514005⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-576736541170844015299559639609),(-576736541170789790757056992527)⟩,⟨531032767782093891535524348634,531032767782148116129050378017⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-608058912930623500551679969747),(-608058912930495916499932691814)⟩,⟨828120208618224137843794401814,828120208618351721941700910916⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-540733617885995947643821808345),(-540733617885745983895752342827)⟩,⟨1194197985560055641230215399141,1194197985560305605007386393219⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-338009934293051612386117928186),(-338009934292672613279582520374)⟩,⟨1593411987592614952092943489973,1593411987592993951196628777114⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨17592856328431006923707023808,17592856328873521540452830910⟩,⟨1963603428580642009825235976480,1963603428581084524391470349543⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨503070415048446147373004519711,503070415048840652576078049404⟩,⟨2226120964805665576760992073679,2226120964806060081853017474466⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1040749621627650874528313348138,1040749621627918205624177540202⟩,⟨2310012456385685688097199331367,2310012456385953019018154733541⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1501927399641061587090997190253,1501927399641207973054790127101⟩,⟨2181426442461935750904372897905,2181426442462082136642105105661⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1737170071894039871510233113710,1737170071894109513474012424072⟩,⟨1857456072169219679942795119145,1857456072169289321659330036896⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1632466024786735166439375653268,1632466024786765627715352846141⟩,⟨1393059512230557678626205164588,1393059512230588139676134980246⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1164965795523760475343557714994,1164965795523772770111429158915⟩,⟨853009256713280009429210299297,853009256713292304037829298383⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨422243427953439500950203315121,422243427953442777008085068961⟩,⟨285831287634228770758696995792,285831287634232046759102152501⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨4056676746685356106716740823,4056676746685356109581031227⟩,⟨(-4289287890725436890021456207),(-4289287890725436887250903944)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨11413024805995871536720082779,11413024805995871545678107466⟩,⟨(-13836473336631565316172639168),(-13836473336631565307425139578)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨16453812185556601715299207606,16453812185556601731365023080⟩,⟨(-26221000062794840157052555884),(-26221000062794840141118797464)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨17602848031999497412103271604,17602848031999497437036646211⟩,⟨(-42958803485804459047728558464),(-42958803485804459022574476262)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨13261007019092764140697979262,13261007019092764177233054328⟩,⟨(-64460032107149079786653870917),(-64460032107149079749274625415)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨1549929533800510113347529811,1549929533800510166743823707⟩,⟨(-89228566293583472633428307292),(-89228566293583472578348881397)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-19697413120106787414264918278),(-19697413120106787327944653193)⟩,⟨(-113886125682482120345329583543),(-113886125682482120256346507826)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-51781834452524491644483430499),(-51781834452524491430521348050)⟩,⟨(-133933435305355696647943408032),(-133933435305355696430603828498)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-93392299481567065279795956700),(-93392299481567064146470428576)⟩,⟨(-144637384592705639514181310380),(-144637384592705638377530785480)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-139540435776744849009648683639),(-139540435776744841118741208903)⟩,⟨(-142376475088512965278521315097),(-142376475088512957385298183307)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-181650238272539880604942672579),(-181650238272539836539437957408)⟩,⟨(-126511968688450555057968308164),(-126511968688450510991912725972)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-208848544345679358923725441731),(-208848544345679171024619393292)⟩,⟨(-100511825956677280192791557073),(-100511825956677092294973279347)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-210722202362538117554756960933),(-210722202362537565247388370333)⟩,⟨(-70726558628001489403099192073),(-70726558628000937098225008981)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-181413115363291942175468674979),(-181413115363290915650390446337)⟩,⟨(-43352273613633730934221762506),(-43352273613632704411913563497)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-122649453049041789421780161414),(-122649453049040656584698087991)⟩,⟨(-21971827856191921870040143667),(-21971827856190789035068174391)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-43306838057955734228246499699),(-43306838057955228169701524471)⟩,⟨(-6505443724312131914919020370),(-6505443724311625857156689452)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-182076864541149532987135023512964),(-182076864541135219121848435698719)⟩,⟨2270176066552035105084316422543552,2270176066552049418942737191962583⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 8) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_8 (tableDensity false) (fullFactor true 0 8) density0_contains hk0_1_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-332690632354035662325189189410696),(-332690632354035662255956589762543)⟩,⟨(-647920032786819176557660130284),(-647920032786819121956117311031)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_8 0 8 ha0_1_8_contains + def realAnswer : RBox := ⟨(-514767496895185195312324312923660),(-514767496895170881377804925461262)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_8 +namespace hm0_1_1_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1665882917589999038361933864377,1665882917590095080255238642949⟩,⟨(-41213192311559024876965202356004),(-41213192311558928834844951695753)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-4272139690307952644579889210730),(-4272139690307720526678953513365)⟩,⟨(-125771312693109321590146837095261),(-125771312693109089472382264596655)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-38584955979186336403509732003041),(-38584955979186094581924142538828)⟩,⟨(-211530410353351396999965776380520),(-211530410353351155181337687883840)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-119272211157200980938634098543506),(-119272211157200826557557602657039)⟩,⟨(-282832052522593169941408470021463),(-282832052522593015570122473872498)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-253830887849815872344663251803216),(-253830887849815810915486752350024)⟩,⟨(-303793396010504995873781402912660),(-303793396010504934465927546505023)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-421485996353447882972420632710211),(-421485996353447865398137798880361)⟩,⟨(-226612563028133651322339105155685),(-226612563028133633775560953064742)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-559312844905960214110488702003319),(-559312844905960209152784563527345)⟩,⟨(-20894049954158698135376233945792),(-20894049954158693192509425822219)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-578096417800594880647629306294504),(-578096417800594879330583095198877)⟩,⟨286495338428379575178113392539425,286495338428379576504411846009520⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-418836827367046075301428692736303),(-418836827367046074710160056465003)⟩,⟨596532549779017404563054945043452,596532549779017405193700788390272⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-111741517497460183575033771112641),(-111741517497460183141364334171353)⟩,⟨782129944961796376304520479288631,782129944961796376788032470446407⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨225694108817887721109672894885024,225694108817887721574150188608328⟩,⟨771186903508916076216478968852508,771186903508916076704458474358708⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨462877924026766313250349118575696,462877924026766313675017229342656⟩,⟨594849180500821693202265398194144,594849180500821693622334691495041⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨535538681585903301695946849034036,535538681585903302028109322933110⟩,⟨356243591983880803135604353050215,356243591983880803444539322271868⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨461890595344369714582181056327017,461890595344369714804392145190305⟩,⟨156375434880826910891766738202204,156375434880826911085408662938464⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨300465324667409137178868022670288,300465324667409137301221463667259⟩,⟨42731078870331335273365985113799,42731078870331335373576862026582⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨102868057356106009710656695369749,102868057356106009749038942092061⟩,⟨4617313132637723332663638959044,4617313132637723362792901910578⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4357605502896718341702279952726),(-4357605502896694755272389497490)⟩,⟨4686652606451079870100931004454,4686652606451103456594203801121⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-12188235260671982577189778498433),(-12188235260671889455980518671031)⟩,⟨15061637743664990898084384416366,15061637743665084019404661744595⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16992494436262250135311873374517),(-16992494436261995803892433841107)⟩,⟨28187023545448628290929707115679,28187023545448882622260663400004⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-15700272526899233072933827823186),(-15700272526898571761752600692335)⟩,⟨44927431645735293037635311612306,44927431645735954348056012765037⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-4279770026406160278755866945147),(-4279770026404569151563750329279)⟩,⟨64199572647721580765026258796838,64199572647723171890103919582474⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨21145080114307167657392553601429,21145080114310394987564092009646⟩,⟨81643369560047625410154288780407,81643369560050852736061230476752⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨61709585848493425245381325277677,61709585848499886423504690555043⟩,⟨88955194690468339085893429273983,88955194690474800258623637508596⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨112461894160756706024228393072533,112461894160768302699476929312506⟩,⟨75711579055360540068518347317762,75711579055372136739908351538574⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨160666150659899329739249887054096,160666150659914027129120963002443⟩,⟨34797954951765960551203943846000,34797954951780657940180783406056⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨189148166855607036406966241249464,189148166855620083102149616333403⟩,⟨(-30644427368732544080387081944526),(-30644427368719497382032258442437)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨185248720081485998494930548312476,185248720081494051044597402894148⟩,⟨(-104253048570143481168442441566691),(-104253048570135428611319439497983)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨149730716163343372968413570564766,149730716163347426865101171019231⟩,⟨(-162058221743202576376332333473853),(-162058221743198522470435025247412)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨97533709565441867414377713939441,97533709565444193910914669011725⟩,⟨(-184431961345656620002092978537225),(-184431961345654293499504674242739)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨48784492211970763703411555609239,48784492211971913379567005664291⟩,⟨(-165437695698890988520606535675209),(-165437695698889838841441276896953)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨17094859729042992127929679116321,17094859729043486137561223779930⟩,⟨(-112604080493691148223087132973750),(-112604080493690654212379350914941)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨3239108296833705255685338434082,3239108296833840116232518968220⟩,⟨(-39652973668815918691463732834082),(-39652973668815783830700294743636)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨572051611790590725768976544142,572051611790590726370561479075⟩,⟨(-935559504454405997021064507242),(-935559504454405996394998670838)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1628276183762657976039716948853,1628276183762657977975429897216⟩,⟨(-2959448135057162933682971855401),(-2959448135057162931672065730406)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨2379924133615684084772500318070,2379924133615684088432651667772⟩,⟨(-5399080235682940445590419293837),(-5399080235682940441812195598805)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨2491291235342763254932029045928,2491291235342763260975807116633⟩,⟨(-8388891966962992286449325741103),(-8388891966962992280259648350361)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1446166333857091213683865263842,1446166333857091223018323120097⟩,⟨(-11830229550773453949394241167854),(-11830229550773453939913387592167)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1403115238344410963818641883179),(-1403115238344410949898275399541)⟩,⟨(-15296771048630959252722674882977),(-15296771048630959238678452249323)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-6581961873755013582077289009082),(-6581961873755013561111282660884)⟩,⟨(-17967052145151177880298770484831),(-17967052145151177859271965365443)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-14076030634330450419395262087873),(-14076030634330450380042957113367)⟩,⟨(-18672316945795425427245056941438),(-18672316945795425387954526425130)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-22943789908780378871666557556777),(-22943789908780378725847485604371)⟩,⟨(-16250628671449558526163312758252),(-16250628671449558380527179124728)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-31242407188040520934324116390456),(-31242407188040520065881475767974)⟩,⟨(-10248280681487822828684283986613),(-10248280681487821960463580165139)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-36533381712641227294726194123621),(-36533381712641222397475917758609)⟩,⟨(-1603477117929701247799114154072),(-1603477117929696350706407754153)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-36934799888246605843086444670607),(-36934799888246581905082784351928)⟩,⟨7323839774416514277095239601884,7323839774416538215034222976390⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-32180338653184492875898391088577),(-32180338653184419437672590712030)⟩,⟨13661328509219123260956734026575,13661328509219196699182375561726⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-23816695627846816657909565071749),(-23816695627846677886920640415246)⟩,⟨15316284812907420982800992211556,15316284812907559753824322249783⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-14127846134880953487192663411892),(-14127846134880800003578472585353)⟩,⟨11820552030202867626166565269925,11820552030203021109815577912594⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-4614176908711855276520261919352),(-4614176908711786895284261883332)⟩,⟨4419833633281679518765177892271,4419833633281747900015404267478⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨87757555242885425009506365978,87757555242886164915006304447⟩,⟨153254259335950957871222955868,153254259335951697785469583929⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨281056117015935113612189804677,281056117015936854108950941868⟩,⟨455523766821778720049086738563,455523766821780460573388212072⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨528462193475662205366315722063,528462193475664016372346779548⟩,⟨740348423712755445339258486791,740348423712757256392949239171⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨868688515763700426283851138761,868688515763701725381393988090⟩,⟨983131694743408221730852020789,983131694743409520892224091607⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1339598577445050081020372566269,1339598577445050719291257074671⟩,⟨1144284678922044955417105975499,1144284678922045593762748261187⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1964407685467482546545523427032,1964407685467482763221824101778⟩,⟨1170911184803460319847463432908,1170911184803460536601181290907⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2727746461120540177619206569285,2727746461120540231991050468015⟩,⟨1000082843144790530842865281704,1000082843144790585282669627858⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨3556572660332074678796914712270,3556572660332074691780603202739⟩,⟨568611562776394674084809273765,568611562776394687110462490177⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨4318911980382005190929501075545,4318911980382005196541156500331⟩,⟨(-157510381163344407381452695917),(-157510381163344401770373965608)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨4846845001758554870372760330441,4846845001758554875087472774228⟩,⟨(-1137988738725068392635539544562),(-1137988738725068387975916605883)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4987680994978247602565556362924,4987680994978247607259766380704⟩,⟨(-2221600786093014403537064199445),(-2221600786093014398954317568603)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨4667160150423258863096837953007,4667160150423258867675382582763⟩,⟨(-3148487144671844434026581777562),(-3148487144671844429604410020541)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨3925754089094592721095698637061,3925754089094592725242739316461⟩,⟨(-3614756920756623513452365725388),(-3614756920756623509482134882231)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2899266932732693452747128474355,2899266932732693456071229245798⟩,⟨(-3388190994235186787748278213832),(-3388190994235186784586932256004)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1748567153582673743175200854434,1748567153582673745327542962720⟩,⟨(-2417544447021482236373543825677),(-2417544447021482234335738672129)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨580327974824615545139929276509,580327974824615545884828374119⟩,⟨(-876645612812464722144836070775),(-876645612812464721440781433335)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-23688434101863054240856916421),(-23688434101862473975246201552)⟩,⟨8785011693307827715534994904,8785011693308407979203902860⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-72240313872890591483095436235),(-72240313872888293091955657551)⟩,⟨29868582832325023741510703013,29868582832327322126803866642⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-123287621564632777859591010406),(-123287621564626417493525449543)⟩,⟨61241822512664825057104306222,61241822512671185413593036091⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-175187342461248641849735700443),(-175187342461231499746045669816)⟩,⟨109283652580046563531724034155,109283652580063705622547803197⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-221647820376232964393758734982),(-221647820376188378571845077784)⟩,⟨180305341339392872332157951602,180305341339437458139025328450⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-252019176650077080284735373717),(-252019176649972175607227607506)⟩,⟨280370075013959976242724146442,280370075014064880905320567625⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-253780861523501801952671959680),(-253780861523296316745575198628)⟩,⟨412556926359950838758370623978,412556926360156323953818622478⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-215965351894821969330686861068),(-215965351894510563197243431828)⟩,⟨572179260957868540602764786161,572179260958179946731809303009⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-133717314651160812560462346579),(-133717314650797509381149919662)⟩,⟨743082899576084738635857453175,743082899576448041821691285480⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-14069247065354215671463358915),(-14069247065030673878603580807)⟩,⟨897078498895811375235918799883,897078498896134917047834534021⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨120810540708706684787463798223,120810540708925650953193854814⟩,⟨997543103595845868611345587427,997543103596064834808043297422⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨238316035038899897879818414718,238316035039019639149076587891⟩,⟨1008991241392457507433227992046,1008991241392577248742626084899⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨306754421152751365556324538137,306754421152808259162605231666⟩,⟨912701156570058828382119379024,912701156570115722032285971319⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨304279547444616422852905502808,304279547444641281632546736583⟩,⟨717838931096312056731714799600,717838931096336915550837630510⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨224448535698893623561583282397,224448535698903649530912394692⟩,⟨454347289832952903049793766361,454347289832962929046529412341⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨82745999775558537911918657268,82745999775561208398076685048⟩,⟨154911392163817824091406275391,154911392163820494587278610979⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨114420135132885096304205079,114420135132885098011166279⟩,⟨(-133167791054226024060577215),(-133167791054226022346720245)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨221932637547309080754340025,221932637547309086113807902⟩,⟨(-474650651762895522949582638),(-474650651762895517530089704)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-210045641346712642012401236),(-210045641346712632361202358)⟩,⟨(-922724450697466986671113181),(-922724450697466976787931083)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2131424378086531061121072648),(-2131424378086531046048044721)⟩,⟨(-1305390510212423839853064965),(-1305390510212423824184315585)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-7158858921612818396565869102),(-7158858921612818373976827455)⟩,⟨(-1525993808605945054172597058),(-1525993808605945030409591462)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-17008583428190858073697142303),(-17008583428190858039197497950)⟩,⟨(-1901335533870983319816149106),(-1901335533870983283267279280)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-32461020784394692600950039566),(-32461020784394692540669682307)⟩,⟨(-2822513124696361027401581617),(-2822513124696360963809263316)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-52819797189835081487045484967),(-52819797189835081321377821170)⟩,⟨(-3995935478436506445522369189),(-3995935478436506275126808989)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-75893450360877864946714353667),(-75893450360877864023873994845)⟩,⟨(-4299933158832602922113321849),(-4299933158832601993383640183)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-98041871928743882464166763520),(-98041871928743876011406564439)⟩,⟨(-2319801130986934672072084821),(-2319801130986928212760449515)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-114627934464119861611060736684),(-114627934464119825616860150294)⟩,⟨2903896837154725051148585409,2903896837154761052017306543⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-121289141494366578613603732191),(-121289141494366425160923842000)⟩,⟨10970100965964019699726793606,10970100965964173158295937033⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-115295087832433487254996696924),(-115295087832433036035723320975)⟩,⟨19195821865847947809140895386,19195821865848399032754985698⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-95806753906617916878330896087),(-95806753906617077845504053868)⟩,⟨23059998704791663125607890989,23059998704792502161234186231⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-63750513464631921719405125731),(-63750513464630995449592625094)⟩,⟨19006237487998852026269304872,19006237487999778297577252734⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-22400249222239390345960193183),(-22400249222238976483322219754)⟩,⟨7366086897389918107157813875,7366086897390331970242597846⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨66862674172952782861780708776150,66862674172964609971617713590539⟩,⟨326241629793282468073626567719614,326241629793294295178750268235322⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 8) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_8 (tableDensity true) (fullFactor true 0 8) density1_contains hk0_1_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨435056980770662019873174001997172,435056980770662019963708939998602⟩,⟨847280042875071159481076483656,847280042875071230883094016525⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_8 0 8 ha0_1_8_contains + def realAnswer : RBox := ⟨501919654943614802734954610773322,501919654943626629935326753589141⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_8 +namespace hm0_0_1_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-79979823442203955807024301316334),(-79979823442203858776525608001366)⟩,⟨214028347533587750419939293930850,214028347533587847442926670292845⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-183835522652012790349699449929678),(-183835522652012546375935768527809)⟩,⟨671031465869562595546078874538299,671031465869562839500227749359384⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-106639834103521953410048846675918),(-106639834103521680378131776020727)⟩,⟨1187874571929265282213661732087596,1187874571929265555222821472534743⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨293539153129961387320645262152093,293539153129961579022797328499961⟩,⟨1710860557888444414789088816747372,1710860557888444606479975850475035⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1120131831511774056255267769058676,1120131831511774142126565426925170⟩,⟨2045382667419815360469223683065114,2045382667419815446357792406968695⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2307196789387980008017393940916184,2307196789387980031965227193987676⟩,⟨1862984566707163039582230050233617,1862984566707163063593464693916085⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨3486295795874061898298396118011420,3486295795874061904133404407929547⟩,⟨861256964287741346282990328765114,861256964287741352199577694347474⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4034453648542974857258792309014850,4034453648542974859720045367017861⟩,⟨(-934176663838356382930018281700798),(-934176663838356380428877031032425)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3432262894854816541622601603022565,3432262894854816543310626681570405⟩,⟨(-2970581526890443098573678662949902),(-2970581526890443096881141682141794)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1724099337907212086186828503055295,1724099337907212087522398487077613⟩,⟨(-4389879998770998973349550743815855),(-4389879998770998972034607596190496)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-397448087201345401147201888115602),(-397448087201345399854768729055228)⟩,⟨(-4609724371521414550723588121277693),(-4609724371521414549450715421702228)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2052284252813677225702269822487868),(-2052284252813677224544493660636617)⟩,⟨(-3729429158653431241626308845465672),(-3729429158653431240484538658241797)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2739788058930040951658050185442080),(-2739788058930040950768951360546406)⟩,⟨(-2367478378453813408807334985786114),(-2367478378453813407942099453805321)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-2500853046689185222750101709616191),(-2500853046689185222163386807646491)⟩,⟨(-1161031604528965859702765319250766),(-1161031604528965859144655248433940)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1671708122822284791004488468016157),(-1671708122822284790684977588835155)⟩,⟨(-416507413990146520318546238282031),(-416507413990146520022190575979042)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-579037824323200486642234352726651),(-579037824323200486542790440243803)⟩,⟨(-86021155057631276804100486439912),(-86021155057631276713408827225825)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨28361575175391425178633897573650,28361575175391442772605185008184⟩,⟨(-15900015217835636788715794692122),(-15900015217835619196903846779115)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨84140265953415941722702941722879,84140265953416007730339157145282⟩,⟨(-54309709843273164285184857809936),(-54309709843273098284606836396956)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨134608117326317279503493341805725,134608117326317468272649338191985⟩,⟨(-112525482640450099386225833061361),(-112525482640449910628828956783393)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨168255159218389231316444836287648,168255159218389805332039965532026⟩,⟨(-202536303934225331860306356182120),(-202536303934224757858426960722933)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨162542550729656676673208518102364,162542550729658331092030950674925⟩,⟨(-330058517689288755910734712242740),(-330058517689287101503456172116789)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨84755504981453940756458083215509,84755504981458072723779138977519⟩,⟨(-484566564582751277424466918944186),(-484566564582747145460056636253940)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-96367085173754219476796059793410),(-96367085173746178701452189322372)⟩,⟨(-627824875533431795692286395678449),(-627824875533423754903173426785575)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-385514279599542932933359862947296),(-385514279599531975765938355053934)⟩,⟨(-692348524828565818865178351527121),(-692348524828554861660380285164355)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-733355731186648474732188780134029),(-733355731186636163118465036651842)⟩,⟨(-605018128986939530942868533284475),(-605018128986927219278849068277912)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1034542632973532016714972966396318),(-1034542632973518300435188811834271)⟩,⟨(-336318295514247732599976343931141),(-336318295514234016291032268336482)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1173158846378912124189158844106926),(-1173158846378901769362708978468699)⟩,⟨56893720819405740185969503395267,56893720819416095012825911559406⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1095182833505386988360468142830039),(-1095182833505381274078957185971424)⟩,⟨441462880961961265507728157314500,441462880961966979763386938855126⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-847011107553411140538688398474662),(-847011107553408613467148169227973)⟩,⟨677399374087527097273000985794223,677399374087529624302564289181624⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-540470786548683491286753472456802),(-540470786548682474719195722106760)⟩,⟨692500028375536904063266236295011,692500028375537920589553943841827⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-274747227411541562382723246081599),(-274747227411541097973850434021060)⟩,⟨503340484838804337254651288358976,503340484838804801640387335083155⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-80536066862176131272928529939312),(-80536066862175998341496920954163)⟩,⟨182361616965143255429907243644762,182361616965143388354208220537768⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-2753490489474506757856273900099),(-2753490489474506756467288122553)⟩,⟨1539401040266266136482375791421,1539401040266266137730330271428⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-8230409484405039216605595830086),(-8230409484405039212275634976455)⟩,⟨5209508470599134509081499895248,5209508470599134513034222290990⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-13449823584748449404971390466687),(-13449823584748449397121147516110)⟩,⟨10690450182606990987669880324812,10690450182606990995070069044968⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-17694903893362676410498749044519),(-17694903893362676398008491908579)⟩,⟨19246575567815018722431610931430,19246575567815018734737991574637⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-19405829760393255041409932684247),(-19405829760393255022636180133152)⟩,⟨31937008090839095932229402920537,31937008090839095951652501280473⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-15957562843885112429462304268953),(-15957562843885112402164084596394)⟩,⟨48996195690601073795807394807834,48996195690601073825354466693643⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-3940855938467600156309472796413),(-3940855938467600117395590144018)⟩,⟨68892713974805842173719531175282,68892713974805842217401299020735⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨19571172670848491347091458526093,19571172670848491406862040124983⟩,⟨87482086524123734665839439012479,87482086524123734733342240259228⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨54737531645060313803224310635080,54737531645060313972735418917261⟩,⟨98178709136943185651384486956043,98178709136943185828231411714831⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨96684139689555438931985619196722,96684139689555439929424840302509⟩,⟨94176375258154755447303435811773,94176375258154756449539770000139⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨135287813925761362428591038130498,135287813925761368503207883245093⟩,⟨72563758799377450360585800016267,72563758799377456436421692088422⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨158459607652865509146956048256043,158459607652865535059731667308935⟩,⟨37950490958962412176891847988482,37950490958962438087243752495579⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨157642831177173100607185936123725,157642831177173170975598925325008⟩,⟨2117787330007319362855307431956,2117787330007389726226351705745⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨131710590704098642285493197049745,131710590704098762429059879769310⟩,⟨(-21473560052138369760343460574136),(-21473560052138249622562677481606)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨86336510858084162004096336512891,86336510858084285113216362038701⟩,⟨(-25043713798412643866611810994324),(-25043713798412520761988088854603)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨29901972085353054102824251978709,29901972085353106696899309857439⟩,⟨(-10707640284739806727763490126756),(-10707640284739754135366826011477)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨26330999518747082624393389238,26330999518747633296842812729⟩,⟨(-284438457225194697310648134145),(-284438457225194146602733600040)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨47361599653877204398886043703,47361599653878558374644602017⟩,⟨(-880605038450878614629345793878),(-880605038450877260550197321153)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-33611933039457496318512822008),(-33611933039456019140242779385)⟩,⟨(-1552019736286679280627918628256),(-1552019736286677803288848822674)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-306352992579261904098533812812),(-306352992579260863973789526214)⟩,⟨(-2326707599721861265145473023132),(-2326707599721860224824097037244)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-886401151759350640181173738374),(-886401151759350141336363610942)⟩,⟨(-3190623009131784987542131300964),(-3190623009131784488503493585814)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1906021342070225667679437182614),(-1906021342070225502235747474791)⟩,⟨(-4062019495997318825924588606208),(-4062019495997318660357150892173)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-3474797034989916113752248269379),(-3474797034989916072119652719244)⟩,⟨(-4772292487463728566913960984088),(-4772292487463728525320164664127)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-5604544679820388609178612631939),(-5604544679820388597482724826630)⟩,⟨(-5071090372146655221684674912995),(-5071090372146655210300884716434)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-8121886267660841397415658121993),(-8121886267660841390198793382332)⟩,⟨(-4684087989533939746394229113561),(-4684087989533939739871501847739)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-10619761595191940159169173561681),(-10619761595191940151824075223309)⟩,⟨(-3440869667672125091650520869102),(-3440869667672125085447753693653)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-12510443138657744515409789918313),(-12510443138657744507466869098568)⟩,⟨(-1434922394493144302487374818813),(-1434922394493144296080229761727)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-13206036287136370709507633617601),(-13206036287136370700933130133867)⟩,⟨886081063183234685353239505115,886081063183234692504192115116⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-12355056309543516993602107581848),(-12355056309543516985164349920632)⟩,⟨2806624254307822057693258952794,2806624254307822065033186051533⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-9983879994998924438062154145379),(-9983879994998924430898469088372)⟩,⟨3623945302180564480621289807848,3623945302180564487047349532435⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-6443380571472818083009974628534),(-6443380571472818078202411289172)⟩,⟨2996854835316574220813331711758,2996854835316574225213706338887⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2219317183440527510555134349338),(-2219317183440527508866177125286)⟩,⟨1155904751878270527976453093424,1155904751878270529537906059396⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨16219426985932593784767837698,16219426985932947546085587599⟩,⟨31515326398518801534860709472,31515326398519155293761067563⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨53886041130663562942711345676,53886041130664962880987290824⟩,⟨93302132258073899600355357432,93302132258075299531848794701⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨107274484123257856470139463626,107274484123261723086728530738⟩,⟨150224597485213937411674113366,150224597485217804018314888306⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨186589751116245125464793162914,186589751116255513929402546348⟩,⟨195777318811557337000578370512,195777318811567725454319671611⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨299712680007764374325193038215,299712680007791267658739295716⟩,⟨219016539523415558669829771949,219016539523442451995298407627⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨448392427215386817523147078228,448392427215449666059271884430⟩,⟨203791915564567115190210443471,203791915564629963726665132911⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨623851507454692930561241533951,623851507454814861369727987731⟩,⟨130205040902984898725039351811,130205040903106829549708125748⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨803626649956564010565096126655,803626649956746351742651872530⟩,⟨(-19347658412410333961087481612),(-19347658412227992742664752641)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨952135732216848409463505330444,952135732217057294903130720090⟩,⟨(-249500215894098415090508525926),(-249500215893889529576373113627)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1028474561350494233215151700822,1028474561350675842657762048085⟩,⟨(-540407989633538972380106209223),(-540407989633357362822877818137)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1002429735520114325413993391891,1002429735520233498323338662835⟩,⟨(-841773174887774878160269585612),(-841773174887655705096646851795)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨872184735734148719888927333498,872184735734211685647046559791⟩,⟨(-1078298491103829721464258242067),(-1078298491103766755524278353963)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨669825616898756279166587881080,669825616898788926950008612056⟩,⟨(-1168961541689518437413507972012),(-1168961541689485789465737856346)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨446087767445347854730895097686,446087767445364110300383506576⟩,⟨(-1057087062426264063874432577021),(-1057087062426247808182167742612)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨243588409238841086457509993467,243588409238848262933135925723⟩,⟨(-737690492061003393668969392223),(-737690492060996217118217741988)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨75776767909647476732263568696,75776767909649479390527907088⟩,⟨(-264600665805912036201707775676),(-264600665805910033518247007113)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1807506090946506278724654239),(-1807506090946506277591151185)⟩,⟨(-1538132103101466376559132205),(-1538132103101466375409271118)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-5818362846981556468085592941),(-5818362846981556464499955160)⟩,⟨(-4288130093293091961349020398),(-4288130093293091957745962029)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-10989325090858120397408510118),(-10989325090858120390855165660)⟩,⟨(-6027324379694120470696692996),(-6027324379694120464208768277)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-17942735308351960491120330763),(-17942735308351960480728554877)⟩,⟨(-6027991676184582205935259653),(-6027991676184582195810174779)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-26842863498093244947136799177),(-26842863498093244931622946261)⟩,⟨(-3519345300655641687404938473),(-3519345300655641672474121653)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-37027268252375184574890953524),(-37027268252375184551959780865)⟩,⟨2386032389357607776896779747,2386032389357607798836115829⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-46954348732704095934460466277),(-46954348732704095897498715067)⟩,⟨12658678260524540807746698940,12658678260524540843251809124⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-54505854023059062239302470174),(-54505854023059062150375863974)⟩,⟨27835284594288571420469842327,27835284594288571507624764557⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-57441043745458728802169268556),(-57441043745458728347329125634)⟩,⟨47229675828101023451989934423,47229675828101023905144066169⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-54126767315357129030536413986),(-54126767315357125857799163832)⟩,⟨68441601772105008702581292227,68441601772105011874220766718⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-44529558085635698428913879694),(-44529558085635677636823112950)⟩,⟨87443256908035837153309874057,87443256908035857945312691117⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-30832871673423391874550308517),(-30832871673423297143122349297)⟩,⟨99261169007807060674131906748,99261169007807155406312303203⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-16814716670094118759459601405),(-16814716670093840887444026298)⟩,⟨99260328597487832835613300442,99260328597488110708878347205⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-6098931932657988985793303493),(-6098931932657473424413541726)⟩,⟨84929871787445929097220467672,84929871787446444659920946231⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-549579929891341661944915749),(-549579929890773444577754182)⟩,⟨57190668191774669526009336741,57190668191775237744357738444⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨423218201005133358314882356,423218201005387012007351022⟩,⟨20153028290765404639307323471,20153028290765658293359476458⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨199483524788754677950386191703315,199483524788767052471190996867043⟩,⟨(-2086947001282098784459181432971308),(-2086947001282086409946738951598661)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 9) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_9 (tableDensity false) (fullFactor true 0 9) density0_contains hk0_1_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨322127977974761826092368870428120,322127977974761826175236597998550⟩,⟨31998827811250431947897511433068,31998827811250432014320135640275⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_9 0 9 ha0_1_9_contains + def realAnswer : RBox := ⟨521611502763516504042754962131435,521611502763528878646427694865593⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_9 +namespace hm0_1_1_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-18388139119487648010735525968689),(-18388139119487568561247231840984)⟩,⟨34477410896727630830811347320852,34477410896727710282076084460954⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-47390365268685288829126055815245),(-47390365268685089156524460140766)⟩,⟨109734709791807159084049625198015,109734709791807358761251571154322⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-49897317760879014609431766316799),(-49897317760878791393595914176249)⟩,⟨199112060455678776339965683216094,199112060455678999560882203547037⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1166792976034982749888012085456),(-1166792976034826352249950367347)⟩,⟨295104403228780818754464554835341,295104403228780975153344167681017⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨121682768216802260213013823848987,121682768216802329913630141880306⟩,⟨364043168248134786279705580723707,364043168248134855971400295389406⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨315552151289021593125606889943712,315552151289021612180175398419170⟩,⟨346026201644843001310649140406615,346026201644843020339408068082851⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨522073216179946495502327561214090,522073216179946499689099946908938⟩,⟨182039380810067210201394894043424,182039380810067214357791020909690⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨629626687134141642991842050389319,629626687134141644306739969774457⟩,⟨(-130914881347275952251036515269779),(-130914881347275950944390253675149)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨536838072071184695027040348411355,536838072071184695691742612805785⟩,⟨(-498105578481575468494516412789312),(-498105578481575467804839372879247)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨242632261235040289398811780784835,242632261235040289851086223483683⟩,⟨(-761295835411850397358931774419318),(-761295835411850396853524996200015)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-130041216507970425484133339890872),(-130041216507970425027872701498379)⟩,⟨(-806258310962672615408870680391945),(-806258310962672614918275043802129)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-417628222467046536015917845447712),(-417628222467046535579821645659875)⟩,⟨(-645318965539495306957473160411370),(-645318965539495306518835167163558)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-526667631723361131661730847580156),(-526667631723361131314699902385354)⟩,⟨(-393332428941055050512358391656893),(-393332428941055050185382416773543)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-467757266639092725128724969327286),(-467757266639092724896180489105889)⟩,⟨(-173591299363338232849131761167486),(-173591299363338232644493405715497)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-307073562407463004099299327130725),(-307073562407463003971985354288819)⟩,⟨(-47207878081310250389512219590395),(-47207878081310250284587218964546)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-105316016866547489442910129156573),(-105316016866547489403191402678330)⟩,⟨(-4966760871773639766848648717554),(-4966760871773639735566361212826)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨5070442906196540672311712798500,5070442906196555151091987171275⟩,⟨(-77751963683757245711370710113),(-77751963683742766655242486202)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨15348348605263048406232589359382,15348348605263102751944061503398⟩,⟨(-1383094405520057088352970935577),(-1383094405520002741738235238243)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨25617762239073256250483799006530,25617762239073411805369557944933⟩,⟨(-6249411487057239568674199800826),(-6249411487057084012271847241853)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨34482038831057423252451077739713,34482038831057896750131053816544⟩,⟨(-17198253542067106994585408439126),(-17198253542066633495104835842469)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨38468880780004326685200489221173,38468880780005692690657720239767⟩,⟨(-36157264078939379549090906196791),(-36157264078938013542027693703740)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨31813537682830652556901909874707,31813537682834067107722642737102⟩,⟨(-62672420310828954803823204386866),(-62672420310825540252368256558724)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨7908599244983996032955067187916,7908599244990646550137737224224⟩,⟨(-91436067970857560322454969580081),(-91436067970850909806671382853237)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-36648985382873008531105658035022),(-36648985382863941655265090307113)⟩,⟨(-111102260049899912450049610464265),(-111102260049890845578802349777006)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-96575533223926386038609306619900),(-96575533223916198905727151350317)⟩,⟨(-107351331447731449039962307698292),(-107351331447721261913619790334291)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-155659047751322697391736250491701),(-155659047751311354304450588697777)⟩,⟨(-71248012918729887762130635343564),(-71248012918718544678839555957635)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-192698991151754664927700724228615),(-192698991151746110140069646905591)⟩,⟨(-8373012192300293620748642302608),(-8373012192291738833186174273003)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-193863762276795615893928194877861),(-193863762276790901032191398728160)⟩,⟨59980882808472652439580682855580,59980882808477367305276287491632⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-161608035245769594667609975073788),(-161608035245767512557763794419745)⟩,⟨107390276375377921113104578020288,107390276375380003229484220145074⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-111806941569310603534055880195711),(-111806941569309767149418728455851)⟩,⟨116925492617418035570882872857862,116925492617418871961990627970815⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-61714821996515057504292309559267),(-61714821996514675816906193057316)⟩,⟨87944788221464239927416857762896,87944788221464621618459842410896⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-19189640158290237422108682258607),(-19189640158290128232485200456696)⟩,⟨32377987913242032650563822328488,32377987913242141841322293702942⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-711581284711374660088382341238),(-711581284711374659561715713441)⟩,⟨(-29787763469185549673364942729),(-29787763469185549153490303050)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2201817456793492367112923463736),(-2201817456793492365440982167750)⟩,⟨18033257744171383031763730665,18033257744171384684745084289⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3853155875028112758303154613309),(-3853155875028112755228462873680)⟩,⟨403528071884893206755313885580,403528071884893209806582147689⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-5636187670262827434250276513119),(-5636187670262827429337594251912)⟩,⟨1397838199389184737281508590274,1397838199389184742181426399653⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-7299424048744128577211806125152),(-7299424048744128569906387408384)⟩,⟨3312704334390457726787661951488,3312704334390457734113280331895⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-8303851335939897279623793910243),(-8303851335939897269250403857466)⟩,⟨6421667594271933436383523094662,6421667594271933446835784374027⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-7853059446534844478673084436610),(-7853059446534844464176368166030)⟩,⟨10747644037700212463086192921108,10747644037700212477765028520351⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-5095347054370489520682751090934),(-5095347054370489496439548162128)⟩,⟨15776976689914395873235236935277,15776976689914395897767657137009⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨430467743972600564827923184401,430467743972600666712542926453⟩,⟨20323381421626142664428524761160,20323381421626142766540202592840⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨8211187754572390203470468297855,8211187754572390966385377035079⟩,⟨22800939434092963852352235839653,22800939434092964615374680599306⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨16459929020378224506523569775187,16459929020378229394349713486242⟩,⟨21962827293152344159943075167700,21962827293152349047781833035800⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨22595357629200819333977954383943,22595357629200840389333579133501⟩,⟨17737242802054723983447235365672,17737242802054745038772930254951⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨24464470109890898646972841683637,24464470109890955987397437917885⟩,⟨11523472042707281870326012631741,11523472042707339210709840672597⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨21430299023208381790250936911898,21430299023208479818808445748896⟩,⟨5573828328793543687049745993637,5573828328793641715588045081232⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨14411975644161861154063168398523,14411975644161961673651769443119⟩,⟨1712351241126136320602687514943,1712351241126236840194544127602⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨5048267970542365267596506572480,5048267970542408225084172558879⟩,⟨229540255221717786635937065052,229540255221760744131413026158⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨63890688963044192829537453844,63890688963044655509345309159⟩,⟨(-70961613444416006598665649282),(-70961613444415543922601323780)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨186396124122287184725905356473,186396124122288321567447691323⟩,⟨(-222619090526497879369093893928),(-222619090526496742538452232668)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨290036240581914147901605159332,290036240581915386431848420003⟩,⟨(-403107428717318480095524446950),(-403107428717317241582095779771)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨353428804142045168950082241911,353428804142046039051824062770⟩,⟨(-630749815085352537732630668980),(-630749815085351667651090459860)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨344943084506798290017176878779,344943084506798705791740346979⟩,⟨(-920208326126241106974002450824),(-920208326126240691218437751190)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨225280837798037236000323034281,225280837798037372735713681107⟩,⟨(-1274335705984403513406840669447),(-1274335705984403376682102805988)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-45606711022555961488167895817),(-45606711022555928340477981285)⟩,⟨(-1670168731395405025995889821558),(-1670168731395404992841350860927)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-496342045563613210771490482476),(-496342045563613203065600245051)⟩,⟨(-2048263174951773753409737173070),(-2048263174951773745669248119452)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1122329439833571601969968839052),(-1122329439833571598645549506767)⟩,⟨(-2317017692018043890304730196267),(-2317017692018043886908867262162)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1859766333045120085490636216266),(-1859766333045120082710918267460)⟩,⟨(-2378094298979156693331166833802),(-2378094298979156690438953037479)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-2573623301675996176173131683509),(-2573623301675996173410782287962)⟩,⟨(-2171520278272132324080994075918),(-2171520278272132321173173064445)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-3077136455497123101824195739549),(-3077136455497123098831663134603)⟩,⟨(-1721294239812601899580022624738),(-1721294239812601896457675451715)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-3186815030752226696258089189980),(-3186815030752226693250727772464)⟩,⟨(-1145587058603082132032790829462),(-1145587058603082128930045775473)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-2793710614116479671746702295586),(-2793710614116479669150480292564)⟩,⟨(-609807276260588573862689827326),(-609807276260588571206226196018)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-1911935343560014378019147369853),(-1911935343560014376256798351020)⟩,⟨(-240975923052934657290564715678),(-240975923052934655497070115976)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-679364592324192219381069446524),(-679364592324192218758160263294)⟩,⟨(-54385461070364088258216456196),(-54385461070364087626027095896)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨5851974940621377773949770182,5851974940621668508864928443⟩,⟨10068660541255718775812420283,10068660541256009511434469556⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨19375663205000390555530369403,19375663205001541164739124168⟩,⟨30500668944320535889912695855,30500668944321686501216277122⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨38207875564291061280172901128,38207875564294239681659769012⟩,⟨51328125745497589615515163562,51328125745500768020260929338⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨65520214174507313827398715137,65520214174515854635557548676⟩,⟨71198373856756030603172294321,71198373856764571415272784556⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨104141830855928337612094480433,104141830855950450479875464761⟩,⟨86366184394246718248939025758,86366184394268831120470070539⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨156354019815005001851543553728,156354019815056678399480082653⟩,⟨90659223982120249566163709819,90659223982171926116321196272⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨222615117902776560365052510757,222615117902876794832691986933⟩,⟨76767487023757678383011360714,76767487023857912849415456093⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨299375323959161998340382188344,299375323959311819837375990517⟩,⟨38476481630037610447565615960,38476481630187431937634222335⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨377572229216213399858223608846,377572229216384894512415442011⟩,⟨(-26189351355573145696035950287),(-26189351355401651056166964838)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨443036270613850042841431564014,443036270613998984948864078576⟩,⟨(-111149644911448809477746399477),(-111149644911299867392350296508)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨479072590573264141789414776434,479072590573361754673471791078⟩,⟨(-200090559591416427882974550357),(-200090559591318815027743916947)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨471275066615111798012938449448,471275066615163303155835592040⟩,⟨(-269557779048359887832920864130),(-269557779048308382723405592039)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨414354437637717031846563288206,414354437637743702978228523694⟩,⟨(-297485567435528564562996946470),(-297485567435501893461249588238)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨316654492791879688662794199073,316654492791892954460551198163⟩,⟨(-271069789526805327325643279364),(-271069789526792061549828058237)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨195380651316979846226299364667,195380651316985698451506068325⟩,⟨(-190181749627108701106664773296),(-190181749627102848894670885206)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨65588504223153199980639887391,65588504223154832477651047986⟩,⟨(-68451332984923644811753225376),(-68451332984922012319092522177)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-55873798421680682270657467),(-55873798421680681575895885)⟩,⟨(-43125737170640955456266029),(-43125737170640954778091044)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-195856342986266381582636579),(-195856342986266379382330587)⟩,⟨(-78839882146245978934055023),(-78839882146245976802172703)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-367850435026394884398235528),(-367850435026394880376161603)⟩,⟨106973900881822293677889875,106973900881822297526307063⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-474372335709985754224024376),(-474372335709985747827844833)⟩,⟨902227408378863810838029135,902227408378863816868584535⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-411598972612866445733074224),(-411598972612866435994311122)⟩,⟨2984483531689867813094864379,2984483531689867822176694295⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-209037492490220002796095116),(-209037492490219987770737762)⟩,⟨7116496721520977899536515180,7116496721520977913475198203⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨74619485699829878841337536,74619485699829904957330065⟩,⟨13716617382316199167814232399,13716617382316199192233167914⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨626242857717454446586191334,626242857717454515818971584⟩,⟨22577679993104041868845742632,22577679993104041935710861277⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1908540621410753973719721352,1908540621410754344652932357⟩,⟨32788603835654118450312482594,32788603835654118818348377673⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨4396097618280475167747776090,4396097618280477763194434920⟩,⟨42709351855331367100309801180,42709351855331369692630938781⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨8227988179370505609603624769,8227988179370522595299940666⟩,⟨50166321862337470925117460342,50166321862337487908240886113⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨12850638658265229894186249269,12850638658265307262004337975⟩,⟨53083815489007142763235293571,53083815489007220129191459395⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨16702203521280343685465660808,16702203521280570701472493897⟩,⟨50236560945770193964152328787,50236560945770420978971632985⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨17480380177221027479764589797,17480380177221448877040376786⟩,⟨41451008403462918540224190622,41451008403463339936883564445⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨13484774119554953284366032784,13484774119555417891248468828⟩,⟨27396018593122222353920390617,27396018593122686960559256111⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨5087028282944750990509228063,5087028282944958432871946720⟩,⟨9587912912120320909280940693,9587912912120528351591754541⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-85734857875627387536290376214083),(-85734857875617163159949175160630)⟩,⟨(-319612512281799239104760849065348),(-319612512281789014730311914325918)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 9) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_9 (tableDensity true) (fullFactor true 0 9) density1_contains hk0_1_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-421244278890073157306078628151950),(-421244278890073157197713138252157)⟩,⟨(-41844620983942872634110946606514),(-41844620983942872547250591874012)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_9 0 9 ha0_1_9_contains + def realAnswer : RBox := ⟨(-506979136765700544842369104366033),(-506979136765690320357662213412787)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_9 +namespace hm0_0_1_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨140715498489721946546168568912665,140715498489722024441408988664558⟩,⟨(-134714633145828108617813681175271),(-134714633145828030729570371616003)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨387236292721262061299099331064506,387236292721262238766456804862089⟩,⟨(-451419997161706594011007146170489),(-451419997161706416567527996909718)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨505090188281334460811936610267313,505090188281334646114872843437554⟩,⟨(-891509163902515545072661254416451),(-891509163902515359810787471471561)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨346805744840832120020523441577133,346805744840832267647797464384559⟩,⟨(-1461290504024095850901029436642842),(-1461290504024095703314430265086266)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-259202654623041144916627134187156),(-259202654623041069463564701540680)⟩,⟨(-2018361381073166152327506649111417),(-2018361381073166076896253375494938)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1373122389144301339629536382683145),(-1373122389144301315466489950969280)⟩,⟨(-2221888040059049287405557737546669),(-2221888040059049263227835295150325)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-2738210144971934484784090596381269),(-2738210144971934479322296794195310)⟩,⟨(-1642524167478887917115621204950905),(-1642524167478887911589355749577871)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-3713790914171000193500883310412730),(-3713790914171000191311116929480500)⟩,⟨(-102696396433633038262782209582016),(-102696396433633036016668343490704)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3596902163441910526623702431576173),(-3596902163441910524950668053884728)⟩,⟨1977201932634439525071764689428375,1977201932634439526764291468490728⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2210509534299255046873233942949992),(-2210509534299255045521444658736582)⟩,⟨3679335782592820230773506081012228,3679335782592820232123052374381102⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-164454703174094349230450689515947),(-164454703174094348040096463050683)⟩,⟨4228452651006793208879527636914777,4228452651006793210053990427278831⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1579240909067389696757463548835014,1579240909067389697855067295194395⟩,⟨3573200627078023110560359219866929,3573200627078023111645970010953596⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2397539999106504947729467773483282,2397539999106504948581173705099777⟩,⟨2311371579021847366372589646630434,2311371579021847367204273803942722⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2270955724763231818934938162347508,2270955724763231819496079819540662⟩,⟨1135205484711726086028721599297616,1135205484711726086564293598779797⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1535769346165845499291950252146429,1535769346165845499595239334748902⟩,⟨401070978541128302611287293912361,401070978541128302893384663498472⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨533410021861697842915227517521511,533410021861697843009013537833423⟩,⟨80480596855167363433599206989708,80480596855167363519311463473463⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-22183579304967017670626387187428),(-22183579304967001539010920426237)⟩,⟨(-6752240870325674798202238909475),(-6752240870325658666321194832092)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-69843111641538826023454595973975),(-69843111641538761678495470937745)⟩,⟨(-16161210263557010854392164745684),(-16161210263556946509087611259905)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-125970306945850239871253554838118),(-125970306945850061320234628977687)⟩,⟨(-11711463304306147399100790064965),(-11711463304305968849111786531761)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-190816173494519472851165562946377),(-190816173494519002581970501604163)⟩,⟨20238905404877653409143576633570,20238905404878123673328647000417⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-253974560846833836957832015965558),(-253974560846832709708214017712866)⟩,⟨96585346987337832641761832461735,96585346987338959878614294799507⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-288199552942466650791379897914019),(-288199552942464286200876317539082)⟩,⟨230433765621438119767539724113569,230433765621440484334939969145664⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-249376447247352932548142569439386),(-249376447247347258995606857359610)⟩,⟨415550965503387685306241260753948,415550965503393358838708086953119⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-92955269755836414845826517040716),(-92955269755826444989751796624319)⟩,⟨608399615144906704805209708835461,608399615144916674655625704289703⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨190346684791690671925587432129673,190346684791702583407208790240167⟩,⟨727071501034629966137311761871687,727071501034641877636184617210262⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨540781200415271386377639609161131,540781200415280812519867920731782⟩,⟨687438599860906349522917695297880,687438599860915775708081707784021⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨838153434772287274656092087901379,838153434772294403090371566489476⟩,⟨466221049390917218481092134037168,466221049390924346955020921243576⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨967529153030988250284043626304284,967529153030993066550984729892988⟩,⟨138062198193116656030038691518516,138062198193121472313209951804134⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨893595324530320541346705175828724,893595324530323043096120180666546⟩,⟨(-159584912958140720463195715019780),(-159584912958138218717890286101128)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨673440994827572620398758023593451,673440994827573725691457499783624⟩,⟨(-310327301302686993562772408865193),(-310327301302685888284817744813178)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨399056195747437564469903651282606,399056195747437998029830157983253⟩,⟨(-278856651303196028421786044506826),(-278856651303195594876400961916749)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨129663794939780263355505669012506,129663794939780375564833437060261⟩,⟨(-109528347795608567215299380757601),(-109528347795608455011869142253098)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1568081009568063762874562496519,1568081009568063763796016921298⟩,⟨970161551276680277254953365771,970161551276680278111558741679⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨5027838107633050553756027216797,5027838107633050556659593939771⟩,⟨2716129597034303358979114448089,2716129597034303361640565263406⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨9429988158823547985219557319197,9429988158823547990609924055387⟩,⟨3762665011478237975270670051465,3762665011478237980093904804695⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨15265877170791285408597160459427,15265877170791285417409516807283⟩,⟨3278702347671689779584067082579,3278702347671689787237249776257⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨22621867217643185661148149288631,22621867217643185674748930205519⟩,⟨(-40362777646281603576410141958),(-40362777646281592118033390039)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨30693364187295261431745871261705,30693364187295261452801905044931⟩,⟨(-7905320134199594394292596588845),(-7905320134199594376139946993375)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨37245738135624957486784120261587,37245738135624957519990207399595⟩,⟨(-21902881517967746447361089642334),(-21902881517967746416786930142804)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨38499796388759259906246938641220,38499796388759259961308946149389⟩,⟨(-42318697957550646284309013706205),(-42318697957550646230759022493495)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨30141979760573375429649886970824,30141979760573375566616922034387⟩,⟨(-66651409702185054934300779924571),(-66651409702185054796734886477355)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨9791999350330725689842603011624,9791999350330726348644804729610⟩,⟨(-88998170778802149849099819000081),(-88998170778802149186862026419754)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-20069757069429195357169321220625),(-20069757069429192034774645672469)⟩,⟨(-101740839963733660820095635507576),(-101740839963733657491386114247082)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-51119450203334056178253103392927),(-51119450203334042131288128324838)⟩,⟨(-99513798543081861609051938652036),(-99513798543081847554854502312390)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-72024592522804137761832787083009),(-72024592522804091489156892545533)⟩,⟨(-82823541332477514572534227688847),(-82823541332477468294897031333490)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-73951249708695567386450296927304),(-73951249708695475803676754431559)⟩,⟨(-57904555702649559072167452191869),(-57904555702649467486684959296514)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-54914998820415148195290879439198),(-54914998820415044234360687077988)⟩,⟨(-32370205174262319995384190095223),(-32370205174262216033329589255413)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-20203070443835124674563559310309),(-20203070443835077820344784402579)⟩,⟨(-10147352380499793662008901460980),(-10147352380499746807519497427223)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-135487244979608837088203488041),(-135487244979608533857828796449)⟩,⟨31070785206253552885872052516,31070785206253856108427122677⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-415266632729354694098779825700),(-415266632729353953728783605741)⟩,⟨113672736922470997808398513554,113672736922471738157757050217⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-716847501790017206240044709012),(-716847501790016409521703561700)⟩,⟨260742894022399371002331228214,260742894022400167696495181359⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1039233420445424756028276419276),(-1039233420445424206285644348127)⟩,⟨524423138403227320669394240256,524423138403227870402165173581⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1353755248925563721832622201619),(-1353755248925563465207802615216)⟩,⟨965058242907515501501510534008,965058242907515758160159902342⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1589984954318430134523179214401),(-1589984954318430052317435212886)⟩,⟨1641450589587256997808642072194,1641450589587257080135187141601⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-1629957407206145273850951680880),(-1629957407206145254025925055500)⟩,⟨2584446948384007413529854797649,2584446948384007433618899486808⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1324149405522973222354153794797),(-1324149405522973217015536155293)⟩,⟨3753795852417733741670538398445,3753795852417733747477905289997⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-543976283825339887857930570993),(-543976283825339884498234746447)⟩,⟨4997332160946157568592779427841,4997332160946157572609990341819⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨728226091968895194412721413327,728226091968895198422207710785⟩,⟨6048748026329905834826725784618,6048748026329905839453291066509⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2309488167121669806837339436654,2309488167121669811734190689100⟩,⟨6597012563140189949615898272410,6597012563140189954994261061708⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3799256823031540561028267843151,3799256823031540566555958161768⟩,⟨6420501214932318226568113839936,6420501214932318232385990445912⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4688753080946580681318481432598,4688753080946580686936643098440⟩,⟨5511519583047660052097543469843,5511519583047660057801321155418⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨4568819108226656218150354756295,4568819108226656223057828115627⟩,⟨4086375142911163641696980021287,4086375142911163646545123179804⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨3326437394085719317309330537774,3326437394085719320668016309911⟩,⟨2449099944870643955361564797459,2449099944870643958620429243418⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1216564212566479549277349973706,1216564212566479550469159443644⟩,⟨807080987191183526794835507130,807080987191183527940869147348⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨11735314321523814726266464564,11735314321523968928727381767⟩,⟨(-8859422934510975184433937527),(-8859422934510820981523316870)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨34351546176468246229780745905,34351546176468855696958520118⟩,⟨(-28794689038745103014323256464),(-28794689038744493546016875185)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨53856064887989527105523390001,53856064887991205937450711686⟩,⟨(-55340450529140374278183277769),(-55340450529138695445122902453)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨66572383463138701754059716414,66572383463143191802102107063⟩,⟨(-92613215982363616615137774864),(-92613215982359126567227627544)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨66732527069239983579642179549,66732527069251524848110827842⟩,⟨(-143424290367160562156539827465),(-143424290367149020891520627986)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨46332384112534691092096728035,46332384112561375324089637528⟩,⟨(-207397112501509974843314771052),(-207397112501483290621100094566)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-3819058006822263597953537589),(-3819058006771299689030045599)⟩,⟨(-278810010061444002849970673324),(-278810010061393038961013567549)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-90824847272241791788700148786),(-90824847272167271834313076883)⟩,⟨(-345295927294416345587199833249),(-345295927294341825667475416950)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-214296114922076794628089609792),(-214296114921994115556115501147)⟩,⟨(-388896026772198576820813668918),(-388896026772115897802582358017)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-361025775959072297279955275291),(-361025775959002582306987042602)⟩,⟨(-391144417104331536890290661157),(-391144417104261821991620913461)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-503351314952015650216087304662),(-503351314951962142948829742290)⟩,⟨(-342193135273871794412814200362),(-342193135273818287220978491868)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-603945204529189779025419648145),(-603945204529155196549945404420)⟩,⟨(-249937226340743688799204902531),(-249937226340709106388517196841)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-626611807514262424344968136779),(-626611807514243558520410076831)⟩,⟨(-141312538932221277847020496293),(-141312538932202412072252110975)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-549730231875150153358088490869),(-549730231875140966655682513974)⟩,⟨(-50832253767647903358354673781),(-50832253767638716689501394035)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-376183396920941648260263246673),(-376183396920937652263950846174)⟩,⟨(-2195459561346301468172434445),(-2195459561342305490466162351)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-133622201735565356832707512583),(-133622201735564250054263272403)⟩,⟨4979071689649551073574239936,4979071689650657846185175044⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-521440676452447362638858802),(-521440676452447362224308488)⟩,⟨682263006443221572256644498,682263006443221572673104682⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1437767386261533288975824223),(-1437767386261533287674548836)⟩,⟨2191896681337320128023105125,2191896681337320129342818828⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1957500997078566899168658062),(-1957500997078566896816769721)⟩,⟨4126538526574551199062459806,4126538526574551201481898758⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1780997040262738271413921665),(-1780997040262738267724861905)⟩,⟨6713346285128131195648642421,6713346285128131199500628743⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-579260672443395999275994287),(-579260672443395993805270510)⟩,⟨10006564733011656919026634094,10006564733011656924800149850⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2021103943804885692472747090,2021103943804885700545731342⟩,⟨13736193758293950036757291448,13736193758293950045309041933⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨6408631872675893732818713792,6408631872675893745869427749⟩,⟨17264943426139161423743234301,17264943426139161437468974850⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨12775711050873213914138400300,12775711050873213945703693692⟩,⟨19696090445877517183410399766,19696090445877517215775902024⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨20797488310527906144586288544,20797488310527906309900934888⟩,⟨20078834542414943539106597483,20078834542414943705151385371⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨29433285895016212212804833967,29433285895016213582797310721⟩,⟨17754836659883660843443998352,17754836659883662213802350789⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨36990514890223498462639959808,36990514890223507622298824966⟩,⟨12821478608622977075026724582,12821478608622986234635551211⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨41455359408016820376934388151,41455359408016862006865087881⟩,⟨6425869624397351945051266818,6425869624397393574611446292⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨41035662250942275039421363535,41035662250942396852484929722⟩,⟨483352106213408160033074379,483352106213529972551483460⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨34838619410528690604193301572,34838619410528916100111229341⟩,⟨(-3186147835899677188796638148),(-3186147835899451693393949256)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨23332505915954942045710416725,23332505915955190121965120453⟩,⟨(-3718645403155739503640153106),(-3718645403155491427736877691)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨8198494094454110174218284147,8198494094454220803818715874⟩,⟨(-1586063170214744394696182882),(-1586063170214633765218947986)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-183870253246397544344782812141009),(-183870253246387751483423662541746)⟩,⟨1733599907684601270735050447894129,1733599907684611063586920524398617⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 10) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_10 (tableDensity false) (fullFactor true 0 10) density0_contains hk0_1_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-275621963687639354950701095146011),(-275621963687639354861321607669991)⟩,⟨(-47742212692256213150108997029056),(-47742212692256213076518051674689)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_10 0 10 ha0_1_10_contains + def realAnswer : RBox := ⟨(-459492216934036899295484007287020),(-459492216934027106344745170211737)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_10 +namespace hm0_1_1_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨26894300447510429598977899152515,26894300447510493370849761845666⟩,⟨(-19661527213773923156920441785344),(-19661527213773859383269038894721)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨76717264534905774399638683814099,76717264534905919602533369452377⟩,⟨(-67491635330871325316709479704487),(-67491635330871180107787535887597)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨109722037059085129352270218907148,109722037059085280759290301305443⟩,⟨(-138070494970266019336654161459678),(-138070494970265867919291197504048)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨101063292718479338881784125227180,101063292718479459218378703090455⟩,⟨(-234480581175397008335735992377970),(-234480581175396887989009300439351)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨17016664677075988679664797248209,17016664677076049821137325140554⟩,⟨(-334492462800855065077220132649180),(-334492462800855003931901450021250)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-161098446043781669167137789718078),(-161098446043781650013411322527552)⟩,⟨(-379640173326411164515861554599086),(-379640173326411145373031183494100)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-396095976500420566354890607084360),(-396095976500420562484842182610794)⟩,⟨(-290988771826592230383703924773739),(-290988771826592226544484566603563)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-576086258304567423300995585133266),(-576086258304567422189548889903997)⟩,⟨(-28849080707372675460802963421297),(-28849080707372674372034525950457)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-568775152591768355669765405266971),(-568775152591768355025107489966218)⟩,⟨338924210646409800002303615040456,338924210646409800655091705963355⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-332631740128708289002756840161533),(-332631740128708288544202842644354)⟩,⟨646619103855924877994298045513139,646619103855924878495491103418487⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨26244958201655143833049657694078,26244958201655144231237728136816⟩,⟨746470762407613477158970110988205,746470762407613477597668304129335⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨330443895950104617440870001590038,330443895950104617841736974575453⟩,⟨623260692738783201933567106881358,623260692738783202343417530875952⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨463965042198980696076699163621936,463965042198980696402249258951368⟩,⟨387586947833534467920673029181009,387586947833534468231236647014892⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨425906502138395509897896118182759,425906502138395510116738992516593⟩,⟨172227022949608481861790699121187,172227022949608482056183686401138⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨282403448811794927238837208534693,282403448811794927358041259601322⟩,⟨46679282726276117644671671205727,46679282726276117743508197483427⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨97039340540362464122487581154820,97039340540362464159476253303581⟩,⟨4797216697746408808616937680122,4797216697746408837844135003552⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-2542652559995710303698358924192),(-2542652559995697027610018364128)⟩,⟨(-2571798187782143376283894247014),(-2571798187782130100243892588443)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-8360622335252936847343834311319),(-8360622335252883866635140285696)⟩,⟨(-7196473266236948823924023962280),(-7196473266236895843306358022726)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16212279288061479411389865377689),(-16212279288061332273857564702452)⟩,⟨(-9933447983361022081935542112816),(-9933447983360874944363548536561)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-26746112504669011851339195599557),(-26746112504668623945332359595070)⟩,⟨(-8545533021066036255793940994895),(-8545533021065648349270058240457)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-38985021503143512560154525082984),(-38985021503142581872474551122320)⟩,⟨182954479112277490286595809802,182954479113208179481288902636⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-48992439814787935684077253563597),(-48992439814785981727915783016798)⟩,⟨19455068532800778018080725237862,19455068532802731977147065962365⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-49189799596323358553023840766138),(-49189799596318665978937613317561)⟩,⟨49827515077798288932727093131799,49827515077802981509462050199730⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-30376718852043490619594678284841),(-30376718852035240748796900533767)⟩,⟨85625417944786607065138006137542,85625417944794856936880411022517⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨12282260908529266915679186831402,12282260908539122993819695102237⟩,⟨113483056925965568074349807000908,113483056925975424150494786684587⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨72148574532677967845756815391928,72148574532685763115610755502088⟩,⟨117212036278268231739912155660951,117212036278276027004060368798839⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨130049046606654530320995791694782,130049046606660419287249288112821⟩,⟨88850059512583642415452807075624,88850059512589531376155712990069⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨163743900079535580041097045359310,163743900079539553775737770651025⟩,⟨37432786292858399575700760624973,37432786292862373308059351589074⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨161767571429964235452054614494144,161767571429966296635761980231926⟩,⟨(-14387832410210348423079212365195),(-14387832410208287238540577215313)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨129127153572301666647612017680208,129127153572302576044243053854634⟩,⟨(-44449286610052034362648690572707),(-44449286610051124963458006431636)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨80148076212535761891771609266180,80148076212536118200219082720173⟩,⟨(-43543488245254555517214165051227),(-43543488245254199206295334175853)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨26764629213981362875340805535698,26764629213981455027816150180996⟩,⟨(-17622297299363198116957255080551),(-17622297299363105963484687342599)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨186725346180172909940754248206,186725346180172910284572024673⟩,⟨372074684356385445347555651456,372074684356385445688546616599⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨641178446906287274868080115556,641178446906287275953987802570⟩,⟨1121455160412748996108556443315,1121455160412748997183439877366⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1337492432406482114780245297217,1337492432406482116756167520642⟩,⟨1858164296337905269464936924447,1858164296337905271415469656428⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨2426409331338395016485916433465,2426409331338395019573640448114⟩,⟨2477799383216130168299310348071,2477799383216130171337045248930⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨4012756966341758901582023599538,4012756966341758906010316763305⟩,⟨2727889817856747273988228993631,2727889817856747278330416777241⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨6074183918061801919184075451262,6074183918061801925752550207687⟩,⟨2187484168022636666471584504199,2187484168022636672926574429187⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨8326181570136506086021863981025,8326181570136506096691121788559⟩,⟨352607043234799590488993230946,352607043234799601049792994392⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨10106418181160701370758772198504,10106418181160701391455667864270⟩,⟨(-3127896372420469156780913034866),(-3127896372420469136152245631887)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨10459949049599847976963139074363,10459949049599848054779225916647⟩,⟨(-8096245538414079774505931600421),(-8096245538414079696686170436650)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨8571955843893620576928639684617,8571955843893621068870677041453⟩,⟨(-13599252852339323705521910103254),(-13599252852339323213519983374944)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨4417130379726472446013056645090,4417130379726475097688049619934⟩,⟨(-18005270577694781516527278473579),(-18005270577694778864783247221212)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-868499446504655093960717260807),(-868499446504643705964848551787)⟩,⟨(-19703374981931335990469874457217),(-19703374981931324602429654110373)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-5364591307104833591164239021228),(-5364591307104795904720063134367)⟩,⟨(-18045575380741401040130802441811),(-18045575380741363353679200943810)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-7339927013736181247628626533240),(-7339927013736106533453686830704)⟩,⟨(-13747431120173767081724891714174),(-13747431120173692367565925689610)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-6125854402525328811998747473240),(-6125854402525243931223921923977)⟩,⟨(-8269513237337155238526490929350),(-8269513237337070357770528522550)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2361154641463617705490646500496),(-2361154641463579437021047665623)⟩,⟨(-2713743861136577339054221798906),(-2713743861136539070592763857699)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-42515732075974219303130073859),(-42515732075973964539829114681)⟩,⟨(-18745944063612274863074392586),(-18745944063612020098907638330)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-131840301601330525548992185101),(-131840301601329903949196117869)⟩,⟨(-52072070416315065711526438360),(-52072070416314444109449437446)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-233363283941509477455245637040),(-233363283941508809510692205735)⟩,⟨(-71296662259075022898372378017),(-71296662259074354951168063562)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-353180987952796482142334637555),(-353180987952796022333706615405)⟩,⟨(-62205756301785745068319343329),(-62205756301785285258630156980)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-493330824204872027216889672941),(-493330824204871813397449905237)⟩,⟨(-5095261461940240508764715397),(-5095261461940026692944137537)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-647499131813104739817954006908),(-647499131813104671923755073884)⟩,⟨122921883163829172487871905449,122921883163829240369489679707⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-794441204112829909382711280424),(-794441204112829893594584348802)⟩,⟨341576425466903697111163204668,341576425466903712872342340193⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-894159213948228837538910191974),(-894159213948228833939123246405)⟩,⟨657534258370322870162278064024,657534258370322873715514474698⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-894522716270191753066950531951),(-894522716270191751339143507423)⟩,⟨1051219518283237902673915532795,1051219518283237904338325530936⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-751981597622609112462629880390),(-751981597622609110668501102720)⟩,⟨1465943249090561750545768224961,1465943249090561752283229641908⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-462251415905020584588895344402),(-462251415905020582543881357630)⟩,⟨1810975404350719087404773453186,1810975404350719089409718420088⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-84792561443918186795496816780),(-84792561443918184587947413915)⟩,⟨1985526164984534170471399461454,1985526164984534172659955207674⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨263107887456077380817565441626,263107887456077382993512109741⟩,⟨1916126863290052606280748947292,1916126863290052608456869526497⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨452869750018148731476777735875,452869750018148733339560991434⟩,⟨1586894934919586121828626431710,1586894934919586123703182513715⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨410744812791512271300145470619,410744812791512272560294323534⟩,⟨1042161758424906801676579603077,1042161758424906802949793378043⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨163949766092039739084531950911,163949766092039739529462935145⟩,⟨362262692557143603069228138275,362262692557143603519645440928⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨3701852999402269731962213275,3701852999402396462384162799⟩,⟨(-3104383680976914323529567802),(-3104383680976787593294772575)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨11103032646808071928036636672,11103032646808572851221870924⟩,⟨(-10134466393832565412380139172),(-10134466393832064489718894218)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨18286243485718240143025429821,18286243485719620164123626778⟩,⟨(-19549221556065538959712881908),(-19549221556064158939333435959)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨24394534173432962784821215201,24394534173436654250266221229⟩,⟨(-32713418495930569203504562737),(-32713418495926877738691101960)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨27481162868639625421446075794,27481162868649115152650334960⟩,⟨(-50687503304409402916488432842),(-50687503304399913185345385815)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨24434581120042209135916161543,24434581120064149959871936638⟩,⟨(-74057241129371000641899492334),(-74057241129349059816711457693)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨11580959128344850685031744603,11580959128386746091446736012⟩,⟨(-102380938347474859059862502993),(-102380938347432963649888153782)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-14092166444571342940403579716),(-14092166444510113210286898264)⟩,⟨(-133329262695603381703325329712),(-133329262695542151966231278508)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-53159588504760898044506411715),(-53159588504693018491766489945)⟩,⟨(-162268340084527489042467886686),(-162268340084459609478645017923)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-101683217903849600383470203608),(-101683217903792425698326822913)⟩,⟨(-182928155547645245702582599425),(-182928155547588071002592833250)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-150071407087774924211253182614),(-150071407087731098303745644379)⟩,⟨(-189116695555090433434106405710),(-189116695555046607512063707159)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-184836809521135036598054795556),(-184836809521106749223502476805)⟩,⟨(-176948015175461748417971928134),(-176948015175433461031066231342)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-193654734177150201100770202361),(-193654734177134788974954166769)⟩,⟨(-147116531647541322348852317430),(-147116531647525910213556493908)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-170383850402035907879768524942),(-170383850402028410868080537036)⟩,⟨(-105810560471037351701403696588),(-105810560471029854683392374898)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-116755270564911216342144698583),(-116755270564907957746346067965)⟩,⟨(-61647445547678000872426678022),(-61647445547674742273156673360)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-41513656809412349178014971423),(-41513656809411446982677905326)⟩,⟨(-19945116544671097703167812301),(-19945116544670195506760608470)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-14521093207082988976115835),(-14521093207082988734322890)⟩,⟨21006230549946960385439935,21006230549946960638218548⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-24666566414450257964903274),(-24666566414450257204087721)⟩,⟨72482695123653842073440586,72482695123653842875047866⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨46833510600545979614455052,46833510600545980990481083⟩,⟨131480625537116136316145348,131480625537116137784287309⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨341844215605856231037325850,341844215605856233198995086⟩,⟨152077556548460512951862838,152077556548460515292139976⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1113729738095977401422942014,1113729738095977404690684774⟩,⟨71449233098322600368626571,71449233098322603942668100⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2661856061165620660312799743,2661856061165620665345163178⟩,⟨(-140175560316426827775559557),(-140175560316426822251663218)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨5172253965033645284122216721,5172253965033645292940094661⟩,⟨(-506602988313332107282056378),(-506602988313332097712494240)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨8593378144807726713041101698,8593378144807726736987315123⟩,⟨(-1132160027646376080396456735),(-1132160027646376055417432770)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨12581548015620744754336797661,12581548015620744888232120452⟩,⟨(-2197372481669965533707938123),(-2197372481669965398592518137)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨16476450858936944833081342636,16476450858936945952844162267⟩,⟨(-3837354735772595407117992058),(-3837354735772594286308689124)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨19379675395525040210218500266,19379675395525047692044877804⟩,⟨(-5991171819892834194418137735),(-5991171819892826711865303011)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨20432578609207788824097071841,20432578609207822822540155026⟩,⟨(-8275975975723498431663083382),(-8275975975723464432802726623)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨19172073039642377398984217913,19172073039642476916923018304⟩,⟨(-9907732292965764076372044646),(-9907732292965664558277866996)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨15640505442697080934206574656,15640505442697265243868546549⟩,⟨(-9848809376440011106386568846),(-9848809376439826796715674716)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨10229243083357113579311999623,10229243083357316420039755740⟩,⟨(-7381187978500710023716708767),(-7381187978500507183030526486)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3557861121958499573486767204,3557861121958590048093510720⟩,⟨(-2749330032215491285318664190),(-2749330032215400810735639663)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨84432013336573149129873369731048,84432013336581240415911258879412⟩,⟨292184815323624423945036199407657,292184815323632515231025998504872⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 10) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_10 (tableDensity true) (fullFactor true 0 10) density1_contains hk0_1_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨360428721745374540972497486953065,360428721745374541089378355190937⟩,⟨62432124289873509407754375266902,62432124289873509503988688422611⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_10 0 10 ha0_1_10_contains + def realAnswer : RBox := ⟨444860735081947690102370756684113,444860735081955781505289714070349⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_10 +namespace hm0_0_1_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-143605627123625234944383137512891),(-143605627123625162282231949201840)⟩,⟨46643460765587397273670117136922,46643460765587469934661697985089⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-421986840821800122677557631489098),(-421986840821799949244256558182822)⟩,⟨188534827186376562110340979403433,188534827186376735537650006263547⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-646906349029148721980289895374569),(-646906349029148547893296692130896)⟩,⟨471094061329163511151464430212288,471094061329163685220239023283532⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-701561743691592546069287253821706),(-701561743691592443490654115283568)⟩,⟨950344802599276798603707825044940,950344802599276901140293686919137⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-392352688325923302950563542517418),(-392352688325923250994568485074817)⟩,⟨1565735978853351852226946378643376,1565735978853351904139057252994046⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨447462161361558139076363497178521,447462161361558158718553884790002⟩,⟨2042772080602877911674186531887274,2042772080602877931298573974712307⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1725655837194905315816189130302902,1725655837194905320968908916361456⟩,⟨1918870783984668917374238997586325,1918870783984668922547517222977131⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨2909252130104477015866492369227392,2909252130104477017644674002267628⟩,⟨845287677979826556611209246292137,845287677979826558444156345665186⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3230799592075009922625015564844569,3230799592075009924099693137489637⟩,⟨(-970650580261781372161435692564403),(-970650580261781370659281889292049)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨2308351956478813906001784374755897,2308351956478813907257677518217550⟩,⟨(-2697999731798472602743132147790083),(-2697999731798472601479890914206668)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨573402543260839088923758803147768,573402543260839089937091175353483⟩,⟨(-3470861120808214461850445339201519),(-3470861120808214460844419436832531)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1053747867016263887283869123829461),(-1053747867016263886341045965623520)⟩,⟨(-3083913083830689975458367697928907),(-3083913083830689974523104687139719)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1896280761735125081677569559636801),(-1896280761735125080937291382384415)⟩,⟨(-2038667334776136604527910223050005),(-2038667334776136603802647907991381)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1872690064120035153355629354728449),(-1872690064120035152868223507019198)⟩,⟨(-1004789256841058311573801462620264),(-1004789256841058311107116702912494)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1282429283653872919913634606272904),(-1282429283653872919652056001486006)⟩,⟨(-350393083195249252212266263244253),(-350393083195249251968313031837344)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-446703846725946892260716924722342),(-446703846725946892180342992858217)⟩,⟨(-68435765639568399186407764662674),(-68435765639568399112804463965302)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨6793902948698668470927044537754,6793902948698676883247925899623⟩,⟨13411317230886311804597528595360,13411317230886320217866085794073⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨24099226161113693191415051202942,24099226161113724798394777691805⟩,⟨39945819662246207603186350634856,39945819662246239213346940099257⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨52735065076393654630283666222436,52735065076393743646619453602760⟩,⟨64008477162535684984361828634493,64008477162535774006289683133645⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨99940344084593673886472487368144,99940344084593956075538245171414⟩,⟨78563584624750114239636651560719,78563584624750396435022542252208⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨168984196550771981465557411704709,168984196550772820870174990410619⟩,⟨68736761971496923120017126506606,68736761971497762529118817046595⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨251317666482413198396331402872794,251317666482415313730173303356293⟩,⟨12226108960311117206106471392362,12226108960313232538412309407158⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨317164832797567267747309016393187,317164832797571262586281250358465⟩,⟨(-111331752369702078184009465823567),(-111331752369698083357730741740616)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨315072022441882581696613170238550,315072022441888097151865327435789⟩,⟨(-299224827396817457838442671475054),(-299224827396811942407863202332086)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨194695197665652516209167729873101,194695197665660831549945265412931⟩,⟨(-503779495654150739518666579469615),(-503779495654142424193987886676390)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-48996485624290974735566858503938),(-48996485624282442233076919549886)⟩,⟨(-637383095926046711046163091489038),(-637383095926038178540719237361256)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-345780087301511412581893048909449),(-345780087301505756013363630622845)⟩,⟨(-622308361628945629821158529547317),(-622308361628939973228141731524922)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-577922876828286791929428901561615),(-577922876828283930364049092966775)⟩,⟨(-454661381320860285955658979649551),(-454661381320857424354991625297653)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-655332377993302268587966589533071),(-655332377993300535253514406054515)⟩,⟨(-217971399176558239949398627490562),(-217971399176556506594373308606666)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-568431312541584758620910677622333),(-568431312541583881008303471269321)⟩,⟨(-25282748959956938777666067803549),(-25282748959956061158072352260671)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-371581990084306081684731121177635),(-371581990084305704856464957130397)⟩,⟨55660891646693397828015872754034,55660891646693774656399616777792⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-127358916223013201895201145032446),(-127358916223013099654669671554952)⟩,⟨32236026796661840781146309315056,32236026796661943020941882744583⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨46121543469384084316547760515,46121543469384084762166759650⟩,⟨(-978752110909780719408727371908),(-978752110909780718857386234702)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-48445889887242932828885598155),(-48445889887242931422548874274)⟩,⟨(-3047458607526858306185833187174),(-3047458607526858304446141001370)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-760682762454362005658221254456),(-760682762454362002869346758436)⟩,⟨(-5401066510927282810127600285182),(-5401066510927282806802954518922)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2669285325539096232792308337897),(-2669285325539096227784614236077)⟩,⟨(-8045967494263380790193440478972),(-8045967494263380784513245788920)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-6502894864053193986236098947698),(-6502894864053193977637487153210)⟩,⟨(-10615505818167427066002794403338),(-10615505818167427056747902908554)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-12946709115443529791878047986266),(-12946709115443529777591609012751)⟩,⟨(-12102861313090328198663004468344),(-12102861313090328184028340582434)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-22142906457279714063859076008258),(-22142906457279714040577603727374)⟩,⟨(-10706923475256382550521559738931),(-10706923475256382527662099781016)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-32930808829192098237457591849499),(-32930808829192098198883165646104)⟩,⟨(-4157235817847823365469094105128),(-4157235817847823328620965050537)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-42298361190429253248927845866252),(-42298361190429253167730080784120)⟩,⟨9141867314662263962649787296756,9141867314662264040474981440116⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-45941637941545813006713398062294),(-45941637941545812612336394795869)⟩,⟨28367871848483474046153194363301,28367871848483474437257385033816⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-40479994099884906374439627248944),(-40479994099884903873083833688790)⟩,⟨49158118967958083949240131110438,49158118967958086448782984068548⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-26328196893665763536002126015107),(-26328196893665752194438994627227)⟩,⟨64676471414099371234551744738950,64676471414099382576102169009203⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-8714628853053744043831920201866),(-8714628853053711862578217133957)⟩,⟨68917925143708608910058204405406,68917925143708641092831367845285⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨4839239075375237050181706645961,4839239075375293440284711156311⟩,⟨59900058026863063204684440739589,59900058026863119597003464921932⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨9096554342471237874354537432568,9096554342471296384789506228726⟩,⟨40073475669786515314929188495325,40073475669786573827244543811433⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨4267665914673755163177343773720,4267665914673780269262834186433⟩,⟨13993640875849915144509269209089,13993640875849940251320660491259⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨31782350849434270884257029133,31782350849434407195062346192⟩,⟨52642317013595819442372003786,52642317013595955751873863789⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨106014173753038030320489928302,106014173753038360596708980688⟩,⟨158983097316197712050006734453,158983097316198042320518163076⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨213213894868354874958655904551,213213894868355224830666008484⟩,⟨265790324127023372626085122833,265790324127023722482252450357⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨377925712924415564189502181467,377925712924415799691156413785⟩,⟨364277068310941074841373459476,364277068310941310306449935201⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨624921111770661737471870397089,624921111770661843533565999740⟩,⟨430398927456926516921270423138,430398927456926622909079574254⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨971730055582386294239750813836,971730055582386326621958241140⟩,⟨418699269305732477184720140138,418699269305732509432820679238⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1413505172725884753815816697274,1413505172725884761688626868673⟩,⟨262843466264212426613081529841,262843466264212434282880060209⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1902604511276748045672118185896,1902604511276748048670370447426⟩,⟨(-109099678959490025253084967042),(-109099678959490022462656194512)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨2336073237583696465382464684074,2336073237583696467761905039141⟩,⟨(-738871023935060578578554311411),(-738871023935060576370419993843)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2572144443267485470526646778598,2572144443267485473235146395970⟩,⟨(-1587698160221190253245914677835),(-1587698160221190250626279859605)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2488077264150258766921399797525,2488077264150258770077144859994⟩,⟨(-2499756965938395414638960377144),(-2499756965938395411446487368420)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2060030070040197483872909172387,2060030070040197487312571143100⟩,⟨(-3220238117604851210092964411779),(-3220238117604851206483221537742)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1408626362526831933448425381757,1408626362526831936838163556997⟩,⟨(-3482973811604784542207802743222),(-3482973811604784538549393929362)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨754460865730010373793173672947,754460865730010376688368568648⟩,⟨(-3126145096932902736849264510500),(-3126145096932902733661848588861)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨291270187977263927039150526331,291270187977263928994120846168⟩,⟨(-2163366449481940595499155807387),(-2163366449481940593319277386096)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨62553986713955054992930204310,62553986713955055682227856789⟩,⟨(-771815571669993402099902691124),(-771815571669993401326474168587)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-4046945877812000220922644486),(-4046945877811940961125913811)⟩,⟨(-3791264323430628312290896203),(-3791264323430569052456515061)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-12973502004108387502266331563),(-12973502004108153722571168549)⟩,⟨(-10911660200363550412256267972),(-10911660200363316632344016702)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-24354060284730405972712015766),(-24354060284729764612502096697)⟩,⟨(-16409942101671028375702184658),(-16409942101670387014766754195)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-39618002945623356030607148025),(-39618002945621652538932575481)⟩,⟨(-18509217596819717342753337679),(-18509217596818013849233872369)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-59528510082377071006663003982),(-59528510082372739858441947330)⟩,⟨(-14560478370670499946673685713),(-14560478370666168794511166075)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-83347914790290388307539383545),(-83347914790280539617335722726)⟩,⟨(-1081011951151993272804942370),(-1081011951142144575163896577)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-107907358129868486163913297807),(-107907358129850139530466561696)⟩,⟨25628442791343601897359521234,25628442791361948543479827211⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-127177195272650254040830046417),(-127177195272624405614529806225)⟩,⟨67897292725871008160980706524,67897292725896856607177625209⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-133113291344117514310559918778),(-133113291344086324915335873956)⟩,⟨124265463978107028316071412583,124265463978138217736371551144⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-118479086134924416396027453286),(-118479086134890943409740335333)⟩,⟨187389917706167133495186883687,187389917706200606505280546008⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-81371332742503416537229892253),(-81371332742476793572663814966)⟩,⟨244077337824352846606033792055,244077337824379469590454949442⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-29244655449764438934488693859),(-29244655449747739052845195170)⟩,⟨278508354375954536582867563091,278508354375971236478272784841⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨21344223735413525132562688044,21344223735422410891041787887⟩,⟨277596783311968443528676076868,277596783311977329294145652877⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨51503987550940129163345427775,51503987550944369296886315232⟩,⟨235937627833125431733528975568,235937627833129671868696010442⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨50087562041165164318275976233,50087562041166981799049247700⟩,⟨157849316857063654649044045190,157849316857065472128905305445⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨20438862530020674177212323877,20438862530021173653434305672⟩,⟨55405726616317739270197852100,55405726616318238745733343220⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨233095678893871571609099449,233095678893871571747909111⟩,⟨159503653696962871646656054,159503653696962871782234420⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨747471170384753091708337454,747471170384753092148920115⟩,⟨433907260183367707214291541,433907260183367707640561223⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1402723749440224328181774778,1402723749440224328991768046⟩,⟨567097066898494593836515506,567097066898494594609580910⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2273238717484986024553627084,2273238717484986025847846668⟩,⟨447848042814873068430446468,447848042814873069648640605⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨3373294337321500109400457485,3373294337321500111346772754⟩,⟨(-49700188545353798150707483),(-49700188545353796335271482)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨4600975568247989485983806998,4600975568247989488869777457⟩,⟨(-1066836423618188812543489905),(-1066836423618188809856168167)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨5715566297758591294100510350,5715566297758591298703105955⟩,⟨(-2743655186147660591110513702),(-2743655186147660586781061920)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨6372519827469037460787041909,6372519827469037471496193418⟩,⟨(-5139592315415097331154405227),(-5139592315415097320760761079)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨6206790016783562105265177967,6206790016783562169060439098⟩,⟨(-8114595401692324953538047872),(-8114595401692324889979653783)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨4979163601981135461614738050,4979163601981135997647829490⟩,⟨(-11258020242050758124548439854),(-11258020242050757588610717831)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨2769166860432098697042972322,2769166860432102269968023088⟩,⟨(-13926671985233896950901074277),(-13926671985233893377926723378)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨98115715288345235122328582,98115715288361422887554819⟩,⟨(-15391863314005583099990673419),(-15391863314005566912079146982)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2186339272827600834032965944),(-2186339272827553628110615777)⟩,⟨(-15050012305842001622104697630),(-15050012305841954416007742811)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-3284617370455270040765309935),(-3284617370455182944256639296)⟩,⟨(-12647241704382635303279749903),(-12647241704382548206621286210)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-2839213911967769377448661329),(-2839213911967673816500786710)⟩,⟨(-8406661065990888365061694686),(-8406661065990792804018535708)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1111364906185324465660604236),(-1111364906185281914757683889)⟩,⟨(-2941903394847591994909139846),(-2941903394847549443974259140)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨144251513544540268350155166022203,144251513544547320409031911991708⟩,⟨(-1316443144371442986314468241030671),(-1316443144371435934262277154067448)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 11) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_11 (tableDensity false) (fullFactor true 0 11) density0_contains hk0_1_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨211293953850304095512064447518369,211293953850304095600054080949253⟩,⟨48441473548407746998958880555813,48441473548407747073530937786203⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_11 0 11 ha0_1_11_contains + def realAnswer : RBox := ⟨355545467394844363862219513540572,355545467394851416009086092940961⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_11 +namespace hm0_1_1_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-25396817040837613773749760946547),(-25396817040837554286193667248873)⟩,⟨4666397209653300941894393590947,4666397209653360429841819073181⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-76315442418427328889654964119409),(-76315442418427186981566568488728)⟩,⟨21936840771590291268532923819698,21936840771590433178488641371430⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-122594624469697597566910174166237),(-122594624469697455319436331346581)⟩,⟨62796171698449879439296702604692,62796171698450021692158355430374⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-145442928612746837176908392531953),(-145442928612746753646594653742062)⟩,⟨138482301147257498956384233329296,138482301147257582498343671230481⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-109337344894439354587007805150916),(-109337344894439312618064747737397)⟩,⟨242109737376994282410819857953530,242109737376994324391635237666497⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨20891989646072298335704621505836,20891989646072313796917471335913⟩,⟨329467396413116886669660341794652,329467396413116902133028673565357⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨236901738167390620175774032792139,236901738167390623778004973914082⟩,⟨318736221501549468317311246032168,318736221501549471902904839095610⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨448544225435451499249151605308506,448544225435451500095452001655227⟩,⟨141216944095571124371685590538327,141216944095571125189598292111503⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨515292835718607999802436462338422,515292835718608000350791247730650⟩,⟨(-174683575248166876120254134760936),(-174683575248166875577478912528862)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨360012564606489491817227846143431,360012564606489492242251036425554⟩,⟨(-481867286732621571503123826501853),(-481867286732621571051481403219025)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨55561397071489610817196554801633,55561397071489611141818263733012⟩,⟨(-618463238962513796765352838961911),(-618463238962513796401632400782440)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-229519032516634933014185726337933),(-229519032516634932680939937531438)⟩,⟨(-541894402963316004686991644340328),(-541894402963316004340735980460251)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-369675755563740171121865367283190),(-369675755563740170844838707835779)⟩,⟨(-344673697279224982484217062080041),(-344673697279224982216778361417287)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-352189010946392827124962249106133),(-352189010946392826937882532041866)⟩,⟨(-154408898894502369443192295385083),(-154408898894502369275514323700746)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-236070473006496317627687966798161),(-236070473006496317526243527880924)⟩,⟨(-41759430717612980688708408951837),(-41759430717612980604102395076032)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-81284095337356170957287589493047),(-81284095337356170925975211301346)⟩,⟨(-4203326067939548221318903564956),(-4203326067939548196497815720121)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-62665864056939865817263220696),(-62665864056932944958011723085)⟩,⟨2343889521991084138997600500707,2343889521991091059736610445492⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨427020923954091863874403267365,427020923954117880443882989054⟩,⟨7165892821284475795442187316132,7165892821284501811606350185610⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨2867005757184413079626179593754,2867005757184486420818901731862⟩,⟨12129003847385185022196782593721,12129003847385258362668920516225⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨8748048791975408542397003039804,8748048791975641294048854466876⟩,⟨16413855829575554686982458083986,16413855829575787437800098465000⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨19237981565834833731452900051473,19237981565835526764010551493342⟩,⟨17742706508987599203558075255914,17742706508988292235465305034334⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨33822505461378601096547350603681,33822505461380349083744366785652⟩,⟨12154155438785693475524362941745,12154155438787441462761102979672⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨48318537545220973580481071513129,48318537545224277580717157313746⟩,⟨(-4811626431862335733872164234616),(-4811626431859031732160196360937)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨53982080010528924163041508201166,53982080010533487964081898586721⟩,⟨(-34635031436380478128056381981751),(-34635031436375914323876190542903)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨40532727557752177517956043676707,40532727557759057820756623108532⟩,⟨(-71306727083924276787325291647205),(-71306727083917396482354425649385)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨3812819582542425602220351634326,3812819582549481673003020549148⟩,⟨(-100520803880654684891059399445661),(-100520803880647628820577527778595)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-47199278863888848851854889388815),(-47199278863884175745471727053999)⟩,⟨(-106961894591216003766190355424256),(-106961894591211330663224923272703)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-92517252990321352296519612538501),(-92517252990318991501869866229763)⟩,⟨(-86099285131871888329503002839432),(-86099285131869527540022053510510)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-113374946817615289753854277880041),(-113374946817613861811973029776856)⟩,⟨(-49148622434835378577230297898972),(-49148622434833950638406469880055)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-103700496097348883497563853448129),(-103700496097348161501971050800603)⟩,⟨(-15111304191538149762308408801818),(-15111304191537427767682779031940)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-70350171826940561465307579887261),(-70350171826940251808035111126739)⟩,⟨2566023711604021108111364995263,2566023711604330765482652664870⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-24598063674838547982832778539567),(-24598063674838464023207279478067)⟩,⟨3184882390026038389758998891477,3184882390026122349551279958861⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨124671642668859505164986457477,124671642668859505343322553605⟩,⟨(-182738547073834758595806177054),(-182738547073834758412617184107)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨354361735781970990842150264234,354361735781970991409575512037⟩,⟨(-590867361267817641633739410045),(-590867361267817641050495178107)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨509774206272713002689363837912,509774206272713003791471427980⟩,⟨(-1119341739944535956348574320746),(-1119341739944535955221510121577)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨491378858670390967828810379893,491378858670390969724365305318⟩,⟨(-1817591447985041266456937902701),(-1817591447985041264531084722939)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨131530862768205656717977615679,131530862768205659782931942298⟩,⟨(-2666822867460510093043947372945),(-2666822867460510089950852379837)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-792123496931787832013039293050),(-792123496931787827261520050201)⟩,⟨(-3521656647130850588586981633327),(-3521656647130850583817942464455)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-2464750152835205339890645146819),(-2464750152835205332588443818152)⟩,⟨(-4052388487017396228601969479592),(-4052388487017396221311715860801)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-4855513395621442753479967763954),(-4855513395621442740762786309949)⟩,⟨(-3753148188387971238787222499538),(-3753148188387971226130355907313)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-7531337524074700821007985784461),(-7531337524074700782890401183254)⟩,⟨(-2120826460117258957770151913722),(-2120826460117258919751543984695)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-9644880605151879544767285301146),(-9644880605151879262598365194561)⟩,⟨971317793307453149434697690091,971317793307453431535662280831⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-10267618521531236228823303825468),(-10267618521531234240690852164941)⟩,⟨4916502646854056289456179372562,4916502646854058277569042344981⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-8976077725854061171095166719427),(-8976077725854051982795997892822)⟩,⟨8423979828749019227647474629235,8423979828749028415953378120930⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-6254278814858349253860156923910),(-6254278814858323058271669334327)⟩,⟨10140892787458363053977261295234,10140892787458389249583711311986⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-3282844348371349426317219347909),(-3282844348371303440406016551515)⟩,⟨9414844065865730847292690324586,9414844065865776833214599652905⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1170623855994360817380320024487),(-1170623855994313060071989939515)⟩,⟨6529957344529827089757495827139,6529957344529874847066091561326⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-216844813265472018126267771808),(-216844813265451518187334521154)⟩,⟨2317606135560328531689952843563,2317606135560349031625973941890⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-2001751176922950171846477683),(-2001751176922835648752302540)⟩,⟨20457415816291012191031744813,20457415816291126714243412016⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3473698995842541291841573799),(-3473698995842264001392863212)⟩,⟨62816845068081341840071370249,62816845068081619131066729159⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨3343729466861389135423994976,3343729466861682446072841108⟩,⟨108946334431600648345330206701,108946334431600941657563385886⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨26093649602663968234253479561,26093649602664165176941961989⟩,⟨159584502927177400396986523671,159584502927177597343399979998⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨74666912687763842905325475632,74666912687763931201775485962⟩,⟨212420505845219726491883187463,212420505845219814795828488307⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨159551716205490942701749726962,159551716205490969302468953914⟩,⟨260100589281487363239900357633,260100589281487389854039839891⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨287563653617280316013471198122,287563653617280322049227602003⟩,⟨287865820453369557556432966715,287865820453369563612214771958⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨455665535082585105180169591909,455665535082585106971037186089⟩,⟨273353056982468836394261408578,273353056982468838204847843044⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨644605469789428325613105603970,644605469789428326657738780763⟩,⟨192571208997662955014037076743,192571208997662956073525248769⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨816720515007579803441690655646,816720515007579804517700816310⟩,⟨33324162819580002157840892246,33324162819580003239403139276⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨924091870752148159852870832020,924091870752148161087233429310⟩,⟨(-188361928777321839803117159501),(-188361928777321838575404767695)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨927857439714180487370795809912,927857439714180488719795361186⟩,⟨(-419593066579923923072801884505),(-419593066579923921742546961204)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨818440795665865505521154245963,818440795665865506863158461516⟩,⟨(-581869577014100274670981098934),(-581869577014100273355998768079)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨621021327311121967096799680758,621021327311121968255583024038⟩,⟨(-603276745964051778753654343758),(-603276745964051777622984900537)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨378874506998675446471418183921,378874506998675447261512558626⟩,⟨(-454826758425341508706898180532),(-454826758425341507937927326290)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨126109129661065543249376314190,126109129661065543529601225643⟩,⟨(-169048576707292041375716158889),(-169048576707292041103286005091)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1391689467834279479900954794),(-1391689467834230777715578961)⟩,⟨(-1176021377874387301124964349),(-1176021377874338598913045384)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-4501588399846395254182818267),(-4501588399846203110192840713)⟩,⟨(-3472732492724919116846007050),(-3472732492724726972798201182)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-8553491177301495255246301213),(-8553491177300968049352947765)⟩,⟨(-5520655775138603924769803244),(-5520655775138076718860088539)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-14057130149045956536815944355),(-14057130149044556021477940442)⟩,⟨(-6869833070494966104579926613),(-6869833070493565589407949350)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-21332177936377588358174334196),(-21332177936374027099128209354)⟩,⟨(-6627823188534035876279681717),(-6627823188530474617812191032)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-30398363194835065055165118436),(-30398363194826967070127185305)⟩,⟨(-3415999551996902814804566768),(-3415999551988804831095848848)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-40750412730926288854930538788),(-40750412730911206795698855614)⟩,⟨4370048394045266094629279360,4370048394060348151304206387⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-51067544557176775174314423206),(-51067544557155536608782374145)⟩,⟨17976314847581311184518230823,17976314847602549745801503159⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-59189059949739832982489100760),(-59189059949714226989270719092)⟩,⟨37435431112014115307504544436,37435431112039721295343882468⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-62653470581704062914458000725),(-62653470581676611518787274968)⟩,⟨60619051832218323062229553605,60619051832245774452912128050⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-59701241484376982973594621341),(-59701241484355176937633419566)⟩,⟨82778013391574094982372873801,82778013391595901014252925849⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-50230992190488881514323445715),(-50230992190475221477795761061)⟩,⟨97451053854582784679342909252,97451053854596444712982753989⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-36263876921204528024327378000),(-36263876921197268925952572642)⟩,⟨98976811676341380175597998827,98976811676348639272435259154⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-21589645205233607165760318630),(-21589645205230146907013119634)⟩,⟨85034277213338683066109547647,85034277213342143324388756411⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-9988739008515222215041275622),(-9988739008513740125820067915)⟩,⟨57257230599539187347356818702,57257230599540669436639303879⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-2671613257957653160885788346),(-2671613257957246012577283271)⟩,⟨20164646063801105065992448638,20164646063801512214387897906⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨7150316678065304160909440,7150316678065304244290397⟩,⟨4407137922095898932903747,4407137922095899011040915⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨24304627909078987184942523,24304627909078987449653166⟩,⟨6813896547637814546117086,6813896547637814792148913⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨42554286737664569924854175,42554286737664570410390243⟩,⟨(-18060874613365486355145849),(-18060874613365485909572668)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨43172536138918043222062544,43172536138918043997292945⟩,⟨(-117143242889292653918954035),(-117143242889292653217871304)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-3356500674030559579569408),(-3356500674030558393247195)⟩,⟨(-375814755204810742388646546),(-375814755204810741326087874)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-121754311323426633732414813),(-121754311323426631898318146)⟩,⟨(-899042791065916780199548886),(-899042791065916778560368792)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-337803413877730497661362715),(-337803413877730494502674751)⟩,⟨(-1757872003016762432596456914),(-1757872003016762429731745621)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-701975957744628995903255361),(-701975957744628987721452292)⟩,⟨(-2941268028447488557608493436),(-2941268028447488549822129012)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1281138921065677418624860977),(-1281138921065677366756922558)⟩,⟨(-4329543636596560952630589333),(-4329543636596560901142543219)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-2106906103361644880114120155),(-2106906103361644441759112584)⟩,⟨(-5681835952616165714744149278),(-5681835952616165276668703017)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-3114853555253760552245066974),(-3114853555253757633595119178)⟩,⟨(-6666288990230132686767061981),(-6666288990230129768265803742)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-4104571125592814639363407346),(-4104571125592801418970842388)⟩,⟨(-6970357218258997810040874538),(-6970357218258984589688521509)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-4731077849533105376363689496),(-4731077849533066810401175232)⟩,⟨(-6448083590101547512726434124),(-6448083590101508946735355886)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-4577361026684092997713705058),(-4577361026684021809211643666)⟩,⟨(-5167981359294610055112667716),(-5167981359294538866548670687)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3374245668105237693118260577),(-3374245668105159557316081264)⟩,⟨(-3325172654381222731635529605),(-3325172654381144595776405722)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1247284622848866629820878901),(-1247284622848831831056465996)⟩,⟨(-1145288965447973082177958863),(-1145288965447938283390873159)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-66460149071724188642660971192643),(-66460149071718362399251420800019)⟩,⟨(-245810566973127315905588407105317),(-245810566973121489662109567297720)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 11) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_11 (tableDensity true) (fullFactor true 0 11) density1_contains hk0_1_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-276307478111936125015455336625946),(-276307478111936124900391969831713)⟩,⟨(-63346542332533207711540457105034),(-63346542332533207614023151496063)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_11 0 11 ha0_1_11_contains + def realAnswer : RBox := ⟨(-342767627183660313658116407818589),(-342767627183654487299643290631732)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_11 +namespace hm0_0_1_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨106294851661426243703831486223469,106294851661426293810036741934114⟩,⟨14492511198965685336663425838937,14492511198965735445042601726590⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨329161139311364204892533643208613,329161139311364330032250017419265⟩,⟨7054617571072296391013757040571,7054617571072421535358108848659⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨561086421468852320508614006774483,561086421468852457409118156263069⟩,⟨(-115800687484528650912822550203070),(-115800687484528514011022806300128)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨733896565859880078210319295002848,733896565859880168880341646272311⟩,⟨(-431990435511514705801025470279200),(-431990435511514615142190487704937)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨680678353995281069736764209219930,680678353995281105769155327686050⟩,⟨(-956011396018089299550263342934796),(-956011396018089263553438877784959)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨187066170727409274682597383318389,187066170727409287716880437459439⟩,⟨(-1523146355803704125876614157968423),(-1523146355803704112875315287595055)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-804644469693479260106937459711725),(-804644469693479255972862288676018)⟩,⟨(-1734085798441811635378361921605580),(-1734085798441811631249011225149569)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1944578773271249831972784127080740),(-1944578773271249830481060596670928)⟩,⟨(-1159886513928578420879691447450721),(-1159886513928578419358194858162113)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-2532779750457134735478813970325890),(-2532779750457134734306258367693013)⟩,⟨206014201257550954785556794336467,206014201257550955986222781912298⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2065265947747815796438296006465151),(-2065265947747815795383750802962397)⟩,⟨1726843196226902368761083378075664,1726843196226902369825984905795475⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-762767360046842328947524081020472),(-762767360046842328131585284694535)⟩,⟨2569651926052823148798389093851033,2569651926052823149614649726637501⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨598053151326591961191979893930917,598053151326591961932254572799614⟩,⟨2419033104753907951259835846340775,2419033104753907951996326842909364⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1365963539240475756151626742669786,1365963539240475756740404533462928⟩,⟨1639055292216888505219034073182724,1639055292216888505797705754513293⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1414002861598302187794606423261304,1414002861598302188182322014582360⟩,⟨812161483848429222535142976729761,812161483848429222907511474358280⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨981491444710370599708118894207639,981491444710370599914816756503741⟩,⟨280091406557613917177962168371924,280091406557613917371227180596983⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨342915108759594625396898214633356,342915108759594625460011575101714⟩,⟨53332037781947242531460831214731,53332037781947242589369639142178⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2958842545487383506017997678608,2958842545487389689355016299062⟩,⟨(-8430712268763965604087278982267),(-8430712268763959420891843779365)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨7092993352998886033782082578665,7092993352998910982575844624917⟩,⟨(-26910533190055348400265413663106),(-26910533190055323451694148847119)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨4965759318787980916001107240175,4965759318788051359554214656530⟩,⟨(-49587254729863916780734844066451),(-49587254729863846336813011122418)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-10217623851251769319129474641814),(-10217623851251581400228560955471)⟩,⟨(-76519249455850856247014833291892),(-76519249455850668325898936792092)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-47291793227180886456415442825134),(-47291793227180440130102634535482)⟩,⟨(-101823881605803548159524340063436),(-101823881605803101827268982922061)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-112727916793949593269103903763975),(-112727916793948529862634478179996)⟩,⟨(-109662403299094558685418196715675),(-109662403299093495269750001102483)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-200372874849496622772446447059608),(-200372874849493933638568260681073)⟩,⟨(-74286395941298268478475324732251),(-74286395941295579339202572770985)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-279779589603728859694065371873254),(-279779589603724328615508952718713)⟩,⟨28109610771784482717025043475034,28109610771789013791835591170003⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-298100211522320687965179542525699),(-298100211522315818799396133053962)⟩,⟨194145889811877997370378575604744,194145889811882866519195878435975⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-210190859050109134395041000044462),(-210190859050104231121985945745472)⟩,⟨373124008266703729428410067756595,373124008266708632683663373169709⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-23609059709522958576589455143402),(-23609059709518720686644037147805)⟩,⟨483799195158021373154678675351937,483799195158025611040782933449869⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨187827100004834796039434601168511,187827100004837252719524591129550⟩,⟨471052528604121057187898741905083,471052528604123513878956919332840⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨328980420255128317745158857208083,328980420255129385098599324009552⟩,⟨351786772045877097376326459773576,351786772045878164750666551702109⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨347185747131364251600462131960977,347185747131364751915430083116689⟩,⟨199099691720738711157378539607660,199099691720739211489034806328476⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨252935063987353605164082102749281,252935063987353845891179884268478⟩,⟨81727642974883182587689543368098,81727642974883423322717310959848⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨91248947727991118588410132981273,91248947727991187402012470624204⟩,⟨19030053905438813249970901462843,19030053905438882065767083238800⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-427695747786520041703865739171),(-427695747786520041372377244703)⟩,⟨211835368670849741989245970873,211835368670849742295962799713⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1287836965390225765898243956437),(-1287836965390225764846200259473)⟩,⟨749556395142260613145051949525,749556395142260614131250543379⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-2122739906886932951351147560898),(-2122739906886932949356864861116)⟩,⟨1645791371242433239824429064490,1645791371242433241743480496799⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2777277019397070884025426154909),(-2777277019397070880629736344535)⟩,⟨3175819971142125634157829995764,3175819971142125637540343838821⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-2862461799886829836063642438603),(-2862461799886829830506657495819)⟩,⟨5589467724270874383214086651773,5589467724270874388949661283333⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1668049375078311996631885337235),(-1668049375078311987765812040825)⟩,⟨8929571085284981994493601199337,8929571085284982003918019259349⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1771646297439609647880926301443,1771646297439609661807449818859⟩,⟨12710841725892974892501581372681,12710841725892974907568600301729⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨8262399022445408584480972469242,8262399022445408608906403995473⟩,⟨15598964037049165768159583342726,15598964037049165793775198980321⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨17638186321121700504212358359610,17638186321121700561811023058682⟩,⟨15479118381868656738232848169703,15479118381868656796476307707306⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨27988140647739032464993048206002,27988140647739032720378626627396⟩,⟨10368725449105654070334298033847,10368725449105654325389092272646⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨35844573120567188427531581843520,35844573120567189750863646758108⟩,⟨59846396844969967136197688743,59846396844971288935803262565⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨37885388327463272268130254318821,37885388327463277211222564902653⟩,⟨(-12686464766148519464949869792708),(-12686464766148514524405559955865)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨33181933142827906076167923022681,33181933142827922056981869383067⟩,⟨(-22871794950813221058675315177988),(-22871794950813205080050392996663)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨23902418503549621797116247143307,23902418503549655212671195395467⟩,⟨(-25902908806554012496800409734066),(-25902908806553979082505789525925)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨13544702017935957071828672414672,13544702017935996153559659210303⟩,⟨(-20154051670127412383862062983336),(-20154051670127373302683223257365)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨4261552203981812079025778193203,4261552203981829923365986526760⟩,⟨(-7559770799884429424048202653864),(-7559770799884411579847511296654)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨16252135213465794388400233408,16252135213465845010238890179⟩,⟨(-18912318248282134373467591378),(-18912318248282083749216298777)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨47773236909318468677824755039,47773236909318590023295315935⟩,⟨(-61332608660896107242022236609),(-61332608660895985888400357995)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨74998077593140285901946843281,74998077593140411537677417554⟩,⟨(-117654603774489340621818973261),(-117654603774489214969348378348)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨90556411068793562314305206351,90556411068793643674252561114⟩,⟨(-197168884579966630965870186584),(-197168884579966549575493614219)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨79994603828265293213413565395,79994603828265329358561070567⟩,⟨(-307218486245507518659235818777),(-307218486245507482466017131684)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨19829344377764424694426667747,19829344377764438442249052442⟩,⟨(-448645122212043918945177499389),(-448645122212043905142679183566)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-120171800773544167715072019618),(-120171800773544163572410733276)⟩,⟨(-608379806068116974363558753579),(-608379806068116970169748533162)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-366600621869121957535098307817),(-366600621869121956026563310102)⟩,⟨(-751739917688683352517701614198),(-751739917688683350977344509830)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-722770971940376643790120927565),(-722770971940376642565550333174)⟩,⟨(-822174582173385889746608631244),(-822174582173385888532560644935)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1146472622038962199272663241820),(-1146472622038962197797858852478)⟩,⟨(-758564004877710913856231371697),(-758564004877710912455538983209)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1542285607803408733723189592412),(-1542285607803408731924481473206)⟩,⟨(-531748568347545033193955486197),(-531748568347545031544077102362)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1786316044386179586634350919956),(-1786316044386179584589238294124)⟩,⟨(-182313259601574936784165518296),(-182313259601574934948751254192)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1779667540760864611574070406949),(-1779667540760864609425574283579)⟩,⟨173653481826851791597496767441,173653481826851793561456375607⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1496160267307184662601825911299),(-1496160267307184660666932826911)⟩,⟨391783054729208170462931315164,391783054729208172270522433009⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-986997806242685079898473253349),(-986997806242685078547076426039)⟩,⟨379400814021112090705893518069,379400814021112091986287641852⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-343147724157370914263320363782),(-343147724157370913778954714010)⟩,⟨154890934252986981021274696058,154890934252986981483377917550⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1052912907668567714780041921),(-1052912907668547446462104383)⟩,⟨1602062685424409311794346674,1602062685424429580028541415⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-2947668407655223453706503959),(-2947668407655143716320051929)⟩,⟨5084310286888467176314104102,5084310286888546913405914449⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-4118691709155851881915631734),(-4118691709155634442009923686)⟩,⟨9372344742223971139786182302,9372344742224188579046458623⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-3814867506645054163024720319),(-3814867506644482585204548688)⟩,⟨14886961138362106669846249198,14886961138362678246413230117⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-963044145759329374506629783),(-963044145757900027306062731)⟩,⟨21741813981827899008998720580,21741813981829328353931604128⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨5774342552167166029332275005,5774342552170333065032883683⟩,⟨29409192221677097601566019539,29409192221680264633415161495⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨17687810262330194961149478374,17687810262335946520609242841⟩,⟨36365282752488056432214076121,36365282752493807985641880180⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨35329432647737744103290536258,35329432647747667623938606842⟩,⟨39990592446505297565976155602,39990592446515221079740466759⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨57549284248158751749278899508,57549284248172600563276222901⟩,⟨37076579929910950120423153891,37076579929924798928007942603⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨80811602443572482211685504803,80811602443586863485059365567⟩,⟨25188499693262809076421499790,25188499693277190344873483489⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨99586012505611169033866560099,99586012505622262817198417910⟩,⟨4634046613254695678031982718,4634046613265789458957445925⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨108143341844314161845322307119,108143341844320922877858764877⟩,⟨(-20032442467113106441498341377),(-20032442467106345408270236488)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨102919653847586920971310316018,102919653847590421701198774811⟩,⟨(-40547789213950362951424892374),(-40547789213946862218126148064)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨83934460623699720263500892562,83934460623701350564665151440⟩,⟨(-48287742597728867838455524495),(-48287742597727237532566296543)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨54375066788038210095752746699,54375066788038895826975136914⟩,⟨(-38848918579121861740295877790),(-38848918579121176005040077448)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨18746328817854205708080314904,18746328817854392196509445779⟩,⟨(-14838727865187271301439383085),(-14838727865187084811431423413)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨44338861503424423565233733,44338861503424423605793879⟩,⟨(-72705978324221042799215088),(-72705978324221042756889961)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨118619361992820476237594544,118619361992820476365306677⟩,⟨(-232728162402870829588922150),(-232728162402870829454383029)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨146903076200363604507297886,146903076200363604739636570⟩,⟨(-435337404006609972238031878),(-435337404006609971990057706)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨91638736208632872531043438,91638736208632872898682213⟩,⟨(-702534552132560166884364158),(-702534552132560166486890436)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-90756257270514900226773470),(-90756257270514899676581460)⟩,⟨(-1036923050183147887508336780),(-1036923050183147886908970383)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-448752769284176650385656266),(-448752769284176649569658921)⟩,⟨(-1402751157021523241163853745),(-1402751157021523240275092791)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1028119263418905562708747045),(-1028119263418905561402014529)⟩,⟨(-1716386752079666509289391022),(-1716386752079666507884260571)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1844257243436481538215435377),(-1844257243436481534698024315)⟩,⟨(-1856766343917820139679683677),(-1856766343917820136063517556)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-2841883306597163191024539227),(-2841883306597163168646634147)⟩,⟨(-1696113995319951823881885851),(-1696113995319951801439264375)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-3872342621139208044624459607),(-3872342621139207856611917029)⟩,⟨(-1155620100930687287376853017),(-1155620100930687099345275953)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-4712671770029262387466365772),(-4712671770029261138668578190)⟩,⟨(-277803390401852368677312933),(-277803390401851119901737730)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-5125561075195481012209501786),(-5125561075195475379293880740)⟩,⟨727800800621636854398065617,727800800621642487270024375⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-4934898071475270785620126832),(-4934898071475254440136608112)⟩,⟨1528246132529381982136918303,1528246132529398327574658016⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-4090476524848502672072687646),(-4090476524848472660245567510)⟩,⟨1811990758259847098253408134,1811990758259877110046605044⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-2690357177046036237015461879),(-2690357177046003438474675447)⟩,⟨1446661738708927910797127937,1446661738708960709319638933⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-935997703764058608479788321),(-935997703764044036731967630)⟩,⟨550050496080396985359343667,550050496080411557101779369⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-97454718278345758370506660853854),(-97454718278341089544813708729435)⟩,⟨923860041871122991389673427088175,923860041871127660211659495099446⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 12) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_12 (tableDensity false) (fullFactor true 0 12) density0_contains hk0_1_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-146287110721106249507521706158001),(-146287110721106249427678768415140)⟩,⟨(-38262976844411253275802376876951),(-38262976844411253206501474707486)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_12 0 12 ha0_1_12_contains + def realAnswer : RBox := ⟨(-243741828999452007878028467011855),(-243741828999447338972492377144575)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_12 +namespace hm0_1_1_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨17692247190858023551017228834225,17692247190858064564740829312858⟩,⟨4855489572602683947564273449292,4855489572602724960803886367194⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨55827021224857091095777319369321,55827021224857193468396918373916⟩,⟨9106553061222684661438441724653,9106553061222787033102575307001⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨98501863528480064156027201822439,98501863528480175995166161890449⟩,⟨(-4679880333176081774179941524856),(-4679880333175969934875943014594)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨135606519037975773093513093848791,135606519037975846928204730077484⟩,⟨(-50727730213357684081292963948884),(-50727730213357610242495151534450)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨138208015401300908889515760638692,138208015401300937916067104095221⟩,⟨(-134905260163249151082255261602463),(-134905260163249122044634160935002)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨65679882141427815642622946425574,65679882141427825774803894838539⟩,⟨(-233142103695256538313316159848604),(-233142103695256528171724565780074)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-98416511057075719919792180076334),(-98416511057075717104488587964227)⟩,⟨(-277152412459924873369091966809874),(-277152412459924870557465699510559)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-297717176575719403574433025673254),(-297717176575719402889014301909292)⟩,⟨(-186619441407076962168824945184042),(-186619441407076961505172127121569)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-407026726644620108194427104008830),(-407026726644620107780162682232104)⟩,⟨47572321061197266883278494416245,47572321061197267284238039806510⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-329712057861010792245341778403916),(-329712057861010791893403673186594)⟩,⟨315037699653351557546083122817248,315037699653351557910688124657611⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-100625211931921003223513213685213),(-100625211931921002968603564355193)⟩,⟨462316328880074082057493730483186,462316328880074082343481154581081⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨138894804146296435828880110281507,138894804146296436081557738688388⟩,⟨428006923839639733579386273119528,428006923839639733846170771550173⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨268489163385916609784904220776947,268489163385916610000547873152666⟩,⟨279156719523756280831959136980289,279156719523756281042540527667239⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨266685191748275777468219545829262,266685191748275777614709925322085⟩,⟨126234721989306757943943926699783,126234721989306758076379906243429⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨180867842073779882592841271720386,180867842073779882671962717479983⟩,⟨34101009648256020863861155983870,34101009648256020930226317222217⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨62412527343006790413172755593600,62412527343006790437469156270631⟩,⟨3369516559664085229699905313031,3369516559664085249019810374516⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1031266615738197520465344717476,1031266615738202606570517651467⟩,⟨(-937183063548379095723491814275),(-937183063548374009594902555049)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨2890705303161500030252444268409,2890705303161520564375797043417⟩,⟨(-3159240714089192641973602857272),(-3159240714089172107804157966678)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨3957777421499746559923285079996,3957777421499804595075341203299⟩,⟨(-6357446139931950495583123404634),(-6357446139931892460442254874581)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3144512436532967268258990256595,3144512436533122251159573267657⟩,⟨(-10847198961337786920713826033647),(-10847198961337631938048730428489)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1225769065828457110315950656672),(-1225769065828088649369117598878)⟩,⟨(-16056951186610726458865610313690),(-16056951186610357998638145175349)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-10825493457730159976070423146471),(-10825493457729281271772515510200)⟩,⟨(-19679742871363545376012201254878),(-19679742871362666672887911707310)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-25592942302682159062754786435269),(-25592942302679934967351283738504)⟩,⟨(-17256072195577384044084645741117),(-17256072195575159949438145793217)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-41337728747311044518844559750149),(-41337728747307295261884593779681)⟩,⟨(-3683907287853856403316327695161),(-3683907287850107146003867474280)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-49119763027815342723251048295826),(-49119763027811313938232784926149)⟩,⟨22487434952280598579972980240882,22487434952284627367137576793068⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-39564268819917091890536196891349),(-39564268819913037302210964275522)⟩,⟨54549885686948837658648158244108,54549885686952892249373214797323⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-11116357066401162791151553293570),(-11116357066397661889426902796889)⟩,⟨78765076763495563300652617513739,78765076763499064202917253229165⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨25478231340659522200165183941016,25478231340661548966315180092029⟩,⟨83356129698732364192533992752250,83356129698734390957002185369228⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨53112833332791847878528374805089,53112833332792727084581416744337⟩,⟨67869549854040427501849875125129,67869549854041306704679447480863⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨59955844545259014877573460389136,59955844545259426359091354748993⟩,⟨42885150708981674099446070230715,42885150708982085578373107025998⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨45378050433382560874821074121104,45378050433382758631949434164702⟩,⟨20523654763238404870760019472157,20523654763238602626660578089652⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨16678468367218959445713206722778,16678468367219015937471505712808⟩,⟨5615086339150547423451552533184,5615086339150603914872553105184⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-107301654577670659392401665653),(-107301654577670659276192035502)⟩,⟨(-9871901485051279003113015537),(-9871901485051278888084356592)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-336702079611177409975720714076),(-336702079611177409600802137463)⟩,⟨(-9774260573050936313428244377),(-9774260573050935941786296810)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-603124833793358834805639751791),(-603124833793358834093939435743)⟩,⟨55775934388492485654284477112,55775934388492486362101971521⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-903633277607030625976477948807),(-903633277607030624786658717586)⟩,⟨247983931463270977689812028430,247983931463270978878311773465⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1182914019094458470644686350798),(-1182914019094458468779328576537)⟩,⟨643963257007271167034004132020,643963257007271168905689372270⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1304436530884178543302233142182),(-1304436530884178540523081466147)⟩,⟨1311823046737659847235880299880,1311823046737659850035473807534⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1043947424386825662893632171688),(-1043947424386825658869582868130)⟩,⟨2243535418545547563487814991799,2243535418545547567556532967598⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-147923948875450498713420428591),(-147923948875450491150385639050)⟩,⟨3259878550365448276211259133830,3259878550365448283820632303089⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1507194604203694514799145099622,1507194604203694542075695723294⟩,⟨3965722084142422302418308602434,3965722084142422329717981948459⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨3703915071091415756416816557128,3703915071091415935550362998614⟩,⟨3871820123110688853700562602870,3871820123110689032831435546318⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨5805532830629503677538360924855,5805532830629504716648777231409⟩,⟨2711937455693955619658622415119,2711937455693956658752302800686⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨7002261028056735727442350961602,7002261028056739709456216023603⟩,⟨755187285308497895559399711637,755187285308501877557851685061⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨6804309005522750054773014856592,6804309005522763042119647130142⟩,⟨(-1214300017321027598626614719936),(-1214300017321014611285356010408)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5364410872834075931087419176417,5364410872834103167349105011533⟩,⟨(-2327700497734717330572693999221),(-2327700497734690094306160608318)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨3282323062154062480989913756732,3282323062154094373146978183145⟩,⟨(-2143266298663262334930609570084),(-2143266298663230442766609241457)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1083827859298792825613833968557,1083827859298807394097808288411⟩,⟨(-855460455943487594612533062646),(-855460455943473026125390274555)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨8134113993827444565154059466,8134113993827487096081572992⟩,⟨(-1820634420633198220634525156),(-1820634420633155689953766788)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨24697480904567440362086803627,24697480904567542242003787920⟩,⟨(-6720379561526009310045657977),(-6720379561525907430965340758)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨41803043452286917165835008277,41803043452287022495243040540⟩,⟨(-15633944557300205083084961375),(-15633944557300099755394712172)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨58703071001420361297218545972,58703071001420429344213318534⟩,⟨(-31956320098951563915838946820),(-31956320098951495871953903163)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨72865350366182842604148820066,72865350366182872705925126142⟩,⟨(-59697142044434785918195930678),(-59697142044434755821260342158)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨79185198560175162892760048526,79185198560175174215260081609⟩,⟨(-102471740621334692903763568088),(-102471740621334681586633492664)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨69482128787668129129607492975,69482128787668132371396275584⟩,⟨(-161156595688555865518395572446),(-161156595688555862281384744795)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨33443328251057779490453302874,33443328251057780429201702795⟩,⟨(-230785253571871077203773936178),(-230785253571871076267509077706)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-37321294636154912154961699730),(-37321294636154911612093307510)⟩,⟨(-298247784865080596205986738414),(-298247784865080595661272478548)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-142176685242347499828127173848),(-142176685242347499266805242711)⟩,⟨(-343475389105967410206725660945),(-343475389105967409637465480415)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-264727852522005076398878998829),(-264727852522005075756781018991)⟩,⟨(-346703853260462067384499169977),(-346703853260462066727768821889)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-372314420340305400321547286489),(-372314420340305399613968091993)⟩,⟨(-300268707305594998962996307088),(-300268707305594998235706241574)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-425862655706607638250287900263),(-425862655706607637495909098192)⟩,⟨(-216943645650849138414030317707),(-216943645650849137642993456114)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-396922731857985288283896807877),(-396922731857985287590160902006)⟩,⟨(-125817091211020982481140402809),(-125817091211020981776519660801)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-281385317933052856149125789499),(-281385317933052855657257243555)⟩,⟨(-55203640581785846289025906480),(-55203640581785845791429735498)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-101594040432912755533487345812),(-101594040432912755355763422314)⟩,⟨(-13908540299327072268748414413),(-13908540299327072089307760016)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-318567636170956383430221038),(-318567636170939726132934978)⟩,⟨543398353482414917497404985,543398353482431574801175712⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-915776728591039266397076549),(-915776728590973730300056299)⟩,⟨1745400336448233596121850416,1745400336448299132248591608⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-1363316906003051099448841048),(-1363316906002872361743951639)⟩,⟨3276759925269647877801537379,3276759925269826615591375015⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1458189715017395557253542292),(-1458189715016925639216814577)⟩,⟨5302063702484702610606074919,5302063702485172528843875441⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-836584740048959584774749290),(-836584740047784315485928574)⟩,⟨7888904873277602903298639864,7888904873278778173000727013⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1042373565638006961161308617,1042373565640611020602762170⟩,⟨10949588490034580687246838689,10949588490037184747452035685⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4790564993398997067798883357,4790564993403725193083993364⟩,⟨14155198999601089670991207989,14155198999605817797563603072⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨10842241439237438299179004307,10842241439245591905760917798⟩,⟨16853677273304876468775816296,16853677273313030076904165707⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨19095559026375464933202726306,19095559026386834606436502400⟩,⟨18128856015298361907033840201,18128856015309731581744007167⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨28546096371070800238150556917,28546096371082594435834411034⟩,⟨17123113265150625163584711018,17123113265162419362419128516⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨37157504431620384741222619342,37157504431629471333537672870⟩,⟨13547309793914037116055680115,13547309793923123708974588004⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨42299263307130770251424780766,42299263307136300597031655926⟩,⟨8057738799912959625796380575,8057738799918489971397914046⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨41823417368967131989717431198,41823417368969991864090442679⟩,⟨2206545771501473800560411287,2206545771504333674401553101⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨35118103146004453333744726179,35118103146005783775983574075⟩,⟨(-2055252764479913118280546467),(-2055252764478582676823745355)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨23223271328828276096961924711,23223271328828835282917765079⟩,⟨(-3281498934995700313274902697),(-3281498934995141127991654163)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨8095263068990534152039926720,8095263068990686167046857428⟩,⟨(-1510238877664145963170947378),(-1510238877663993948424466902)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1213840109214971226916017,1213840109214971249991073⟩,⟨(-2222600030772524476139671),(-2222600030772524450996094)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1654680666106293489536059,1654680666106293562221707⟩,⟨(-7446530598713648504459454),(-7446530598713648424564152)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-6238273669879277009883733),(-6238273669879276878152853)⟩,⟨(-12572983281959650724613518),(-12572983281959650577920125)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-36618649902277604712718740),(-36618649902277604505329947)⟩,⟨(-10832113811551308348966848),(-10832113811551308114548077)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-115628118316327062863635295),(-115628118316327062548917504)⟩,⟨9495898884248963328012515,9495898884248963687086457⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-276445903905319174555209667),(-276445903905319174069783668)⟩,⟨60838613367256402671338259,60838613367256403225763095⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-542836580601304406566932637),(-542836580601304405723638048)⟩,⟨157324502866584536889193432,157324502866584537835541376⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-912445888088933519697227217),(-912445888088933517065135940)⟩,⟨320298581146201965984076940,320298581146201968735152541⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1346224216837890177574024427),(-1346224216837890159440509257)⟩,⟨573166451094646160279461263,573166451094646178511094015⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1763656509581861099586280756),(-1763656509581860945904451899)⟩,⟨921311123081510127011984121,921311123081510280752667614⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-2054017779434932369039909180),(-2054017779434931349007155542)⟩,⟨1329387855993565451059746835,1329387855993566471109017292⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-2116409908288348124152429575),(-2116409908288343523902100186)⟩,⟨1709893220604008057958639869,1709893220604012658193949663⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1914083649435455069926132645),(-1914083649435441716203190621)⟩,⟨1928035613657124107490674403,1928035613657137461177811531⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1491840026167176177445116691),(-1491840026167151647298483513)⟩,⟨1833446977289465866171346589,1833446977289490396276320434⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-934814834933677522112674999),(-934814834933650704300504140)⟩,⟨1336351960619117770181606336,1336351960619144587961382902⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-316779437117009526706788028),(-316779437116997609729759626)⟩,⟨491303012404274694778504885,491303012404286611743499666⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨42622645965509944106938443379919,42622645965513800948198181019889⟩,⟨188487449033398207867502687205968,188487449033402064708643069716812⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 12) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_12 (tableDensity true) (fullFactor true 0 12) density1_contains hk0_1_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨191298529404523556943887620235184,191298529404523557048297615745078⟩,⟨50036200488845484962348082309789,50036200488845485052972338992936⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_12 0 12 ha0_1_12_contains + def realAnswer : RBox := ⟨233921175370033501050825963615103,233921175370037357996495896764967⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_12 +namespace hm0_0_1_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-58655374123127969297958219393694),(-58655374123127943955479186550227)⟩,⟨(-38855294671842122163707814655518),(-38855294671842096818127699013894)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-193691970460960974961746102119157),(-193691970460960907411851428707432)⟩,⟨(-96694508346191403603536145216038),(-96694508346191336045360493844501)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-369271010981271790884513867974101),(-369271010981271708503910309542215)⟩,⟨(-83484413783753911338580092816267),(-83484413783753828948027871882394)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-561966213636129817643669538183175),(-561966213636129755285968242494060)⟩,⟨73004903301351209969315227246458,73004903301351272331964961734915⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-659230989345317524582572757565524),(-659230989345317495833643590386994)⟩,⟨430883722314284934476758293870085,430883722314284963216886848813642⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-461420008435085968006793065631773),(-461420008435085959856635741658810)⟩,⟨931353694610001639379552439537639,931353694610001647501198056716909⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨177893191320602449317530326113286,177893191320602452163629466437176⟩,⟨1294822434111806649468960290161948,1294822434111806652299014418481221⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1096152191099804453287111691145620,1096152191099804454492563353368800⟩,⟨1112524561169632760800208129765313,1112524561169632762012832331923309⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1751857777690767729260491393604437,1751857777690767730118112509743741⟩,⟨228107822632531483526311449268045,228107822632531484406754513059745⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1625571590367877973669052389329581,1625571590367877974475668587942584⟩,⟨(-951902856197349429031427978839919),(-951902856197349428214658637487211)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨757177964767695958343337348648714,757177964767695958964146100337413⟩,⟨(-1726264689201475593864542113427722),(-1726264689201475593239791999081341)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-272350982805882881420003857414595),(-272350982805882880884742087551702)⟩,⟨(-1737352881656177266287651700058662),(-1737352881656177265753576067867348)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-901643211666480902942115370415618),(-901643211666480902510535828001823)⟩,⟨(-1210206403853558379449664237070364),(-1210206403853558379024190001825026)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-984403362007874571867430484024700),(-984403362007874571582989756148505)⟩,⟨(-603899221526261665551910212953873),(-603899221526261665277928654572197)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-693284281714378211304648373333603),(-693284281714378211153955125602213)⟩,⟨(-206320401203541171842260902615795),(-206320401203541171701014358596344)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-242990004120237496301499636977487),(-242990004120237496255770812735162)⟩,⟨(-38356203587629955262925583163675),(-38356203587629955220889639562107)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4461831769746908902909204753529),(-4461831769746906072601961487366)⟩,⟨2029249973970904677333136065793,2029249973970907507348496723348⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-13355103321208655050648903891132),(-13355103321208644389504855749373)⟩,⟨7514762616157643925245526542184,7514762616157654585380862360939⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-21457883885598284500501349571529),(-21457883885598254801108666730160)⟩,⟨17425703821959405949012053228258,17425703821959435646538062500846⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-25809937729003844113928549838446),(-25809937729003746382522706392528)⟩,⟨34733825408940742454739605083937,34733825408940840184098934727592⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-19747236032001180612092942540604),(-19747236032000882029338278443151)⟩,⟨60642172083813753165803964697382,60642172083814051747433947326698⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨6912267857794234111452800764318,6912267857794985288266468264097⟩,⟨90469607216922144161496896297775,90469607216922895339940201407870⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨62662636941199012528003874028399,62662636941200355399194599723239⟩,⟨108623891186647869248368726426728,108623891186649212126136413262198⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨142369376270708762895510209676429,142369376270711151910571254765745⟩,⟨89106506002151756060081915169477,89106506002154145082523261515426⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨216039350348175101978476957633971,216039350348178654144370057223691⟩,⟨10239097326025554561939862279568,10239097326029106728452350830623⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨236315247421828201447477879485176,236315247421831402962960817010296⟩,⟨(-119486757907491770251493506406735),(-119486757907488568745417590025028)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨172909757388870444553919690737780,172909757388872591634418155530497⟩,⟨(-250261086138091620298430088452380),(-250261086138089473232053369855936)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨46742355588960159069281280210181,46742355588961744633289179400810⟩,⟨(-319408779556570684180266793304604),(-319408779556569098621713909320984)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-77957150312627950069376697298079),(-77957150312627102999499546140801)⟩,⟨(-300085925724467314913698506334259),(-300085925724466467840733329701719)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-141076829201344510297856264111490),(-141076829201344143989532392469010)⟩,⟨(-218219796117355653672685687959181),(-218219796117355287356723272957706)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-124164563895570098467118227276617),(-124164563895569961258518589395490)⟩,⟨(-121301913420431544407037868279562),(-121301913420431407191224858667979)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-48260427297200375762154245038927),(-48260427297200341385139661186369)⟩,⟨(-37386540678299783281234930301774),(-37386540678299748901367108765146)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨176637757549982693548140651378,176637757549982693728792595734⟩,⟨121872859771456860960520122438,121872859771456861135332274338⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨579358022474002364935881446930,579358022474002365515106493947⟩,⟨341394350327958426746083229392,341394350327958427300767317659⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1128509167319414087232446610749,1128509167319414088355355220348⟩,⟨466106002618485540322044058197,466106002618485541378992534967⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1904481702837769445947730263503,1904481702837769447911247185913⟩,⟨359570330077246627782920617347,359570330077246629595847411009⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨2915965876718313812367454996999,2915965876718313815683278600806⟩,⟨(-218022867946804975633222967465),(-218022867946804972609072393169)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨3987436598500363679019517643170,3987436598500363684691177344887⟩,⟨(-1603914402508011514545664840656),(-1603914402508011509204807956826)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨4616669403980729310746977171637,4616669403980729320298840574365⟩,⟨(-4110295980090797337332172526974),(-4110295980090797328004978208631)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨3931573424444531901299388760498,3931573424444531917516061168184⟩,⟨(-7722083186057107760211974185728),(-7722083186057107743926574774868)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨968780046185790703012748052967,968780046185790736214400705614⟩,⟨(-11706626747908059364874196720403),(-11706626747908059331099571006509)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-4618610831769176262228958624267),(-4618610831769176148213519436060)⟩,⟨(-14512220461569187488927316909016),(-14512220461569187373796056354868)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-11791784088425129756449343852282),(-11791784088425129047280562014564)⟩,⟨(-14415518699045672475718684390019),(-14415518699045671765658354207205)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-18120704211082526423410186033224),(-18120704211082522985664116180170)⟩,⟨(-10810310706167922130590104506818),(-10810310706167918692521542141711)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-20973346190169830871181122116603),(-20973346190169820611988654344210)⟩,⟨(-5087664743589878145587970533405),(-5087664743589867886643541701530)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-19081653086933398217327136676130),(-19081653086933379684233890674127)⟩,⟨(-5787631660506258459761547261),(-5787631660487725941995720840)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-13067209496389523380758459341843),(-13067209496389503855395311953977)⟩,⟨2164293815778369321792867622811,2164293815778388846608402690242⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-4606181966843206876438094324817),(-4606181966843198451070068278357)⟩,⟨1167139020454065725993376207896,1167139020454074151141502151429⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-8625514174463687105878994248),(-8625514174463671793813301462)⟩,⟨(-3567294965620477946222059780),(-3567294965620462635675647990)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-27516866215128682116296165465),(-27516866215128645484923554986)⟩,⟨(-9759218228376329624225104458),(-9759218228376292997704236787)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-51222637506683516423369451372),(-51222637506683474175558961402)⟩,⟨(-12549215254016720276460195804),(-12549215254016678036670149045)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-82420040079255861644198338551),(-82420040079255829063321716326)⟩,⟨(-7775754249657683634345434940),(-7775754249657651064002945951)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-122064457777876138168038531812),(-122064457777876120896800914622)⟩,⟨11470217940391718608383115003,11470217940391735868070203443⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-167089734116746316914226460899),(-167089734116746310555162511814)⟩,⟨55101252009925141810743238032,55101252009925148160373848058⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-207344524403373525204312249726),(-207344524403373523378839639251)⟩,⟨134054874339413786705849194410,134054874339413788529960521328⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-223553864376367959861625006522),(-223553864376367959196808021588)⟩,⟨254603491271963401738986732305,254603491271963402418806343457⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-190168443775068141757089845656),(-190168443775068141208230489806)⟩,⟨409474361254580955850982815805,409474361254580956440629750540⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-86934692235159301422234401752),(-86934692235159300760996274020)⟩,⟨570529326719197477565917858782,570529326719197478298485401855⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨82742067980737903822206396937,82742067980737904700031247996⟩,⟨691612623911114356985923700759,691612623911114357934289640618⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨278425561969713558254444036821,278425561969713559337489278431⟩,⟨727038525262873989924721573258,727038525262873991058781531142⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨429777193896509608796384843492,429777193896509609971752735587⟩,⟨657579345778098923134019451533,657579345778098924335652191514⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨467521757539081890505872614741,467521757539081891588043870978⟩,⟨502814567006584123398585137134,502814567006584124485097533289⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨360716923787324663581176186333,360716923787324664349452303202⟩,⟨305674606526155533429554214291,305674606526155534191916051303⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨135333249903506787123047492599,135333249903506787400714888298⟩,⟨101165634757138059060731385360,101165634757138059334695292703⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨561048759203476214392504542,561048759203482423137296656⟩,⟨243904384412307084236853813,243904384412313293030016370⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1765709908537191999119212179,1765709908537216326164424349⟩,⟨647565446315800040211073633,647565446315824367417525044⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨3203624844579911513570980473,3203624844579977265708673202⟩,⟨767558401353040561999007880,767558401353106314463416508⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨4975079632310496913185143961,4975079632310667096676781529⟩,⟨322056407607002655035601776,322056407607172839115088748⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨7052517076091036776541315641,7052517076091451664612740312⟩,⟨(-1075806003782489951165363005),(-1075806003782075062095353834)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨9159085763765043460392997163,9159085763765982498939287665⟩,⟨(-3880526593242997592842252419),(-3880526593242058552771801117)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨10648976716972433569594007687,10648976716974604222920199144⟩,⟨(-8475830771640870776955598935),(-8475830771638700121958636596)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨10503364052076398396129292505,10503364052080288395095838461⟩,⟨(-14902044848889953990896054524),(-14902044848886063990401758714)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨7582446602052616894908047918,7582446602057872140371456917⟩,⟨(-22513947613646455903414624661),(-22513947613641200656906088348)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1206745394366462788449918635,1206745394371751673710231895⟩,⟨(-29807565299089946558305705831),(-29807565299084657672894175798)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-8088624817393144028521550633),(-8088624817389195306867141473)⟩,⟨(-34728922621792061578154564211),(-34728922621788112857607551865)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-18092200645815394993107064959),(-18092200645813071178874871972)⟩,⟨(-35531272007163339894653760044),(-35531272007161016082869401576)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-25316611893047902955520495423),(-25316611893046743053609697486)⟩,⟨(-31701510482208761860028601240),(-31701510482207601961535183422)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-26429216573876711416784837508),(-26429216573876190165606505141)⟩,⟨(-24209221458129731913957725078),(-24209221458129210666362175890)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-20006000111238360804574963195),(-20006000111238147936309847021)⟩,⟨(-14812275703766070431678251509),(-14812275703765857566139844127)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-7448653684228416406114787031),(-7448653684228359495614500325)⟩,⟨(-4934212632725493198279513205),(-4934212632725436288798709976)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-20854584090723332660694269),(-20854584090723332648804712)⟩,⟨(-11261744182806572267979350),(-11261744182806572256801977)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-66636170869759135440037270),(-66636170869759135402192866)⟩,⟨(-29500900745182189588412956),(-29500900745182189553172002)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-124236135037009263932572393),(-124236135037009263862660368)⟩,⟨(-33942072579406995306000097),(-33942072579406995241706225)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-199559553334172584487383408),(-199559553334172584375012593)⟩,⟨(-12967385530813634980709583),(-12967385530813634878599188)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-292664426785357290555255667),(-292664426785357290385450658)⟩,⟨47195707232072511467735255,47195707232072511621086213⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-391869148699139150221001068),(-391869148699139149969465166)⟩,⟨161727827395061176648617368,161727827395061176876214689⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-470303873366903298370722377),(-470303873366903297956613507)⟩,⟨344237908266748349902625116,344237908266748350286664933⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-488827270332867760089591028),(-488827270332867758934661313)⟩,⟨597807124662085969975527196,597807124662085971104500586⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-406413875670777704645388836),(-406413875670777697488186376)⟩,⟨902363138466729974619029112,902363138466729981760728565⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-199437275437496451728221963),(-199437275437496391999678418)⟩,⟨1208216307735919596052030472,1208216307735919655777973851⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨113674006941496335037238454,113674006941496729679772824⟩,⟨1444348209566683319362583992,1444348209566683714012484321⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨457285485353381968072064429,457285485353383737058335140⟩,⟨1540854577620100773851056606,1540854577620102542848507871⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨713902778961275857646444218,713902778961280954749116657⟩,⟨1454132694074246608805466195,1454132694074251705917500382⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨774764569382530923332729820,774764569382540216844422678⟩,⟨1182779447397759538860705981,1182779447397768832376983041⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨595936968493092807173719704,595936968493102905589344422⟩,⟨766223728726981751382625558,766223728726991849799024963⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨223243203270326550879643937,223243203270331022829819893⟩,⟨264292291397306646112977282,264292291397311118062929699⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨57649054621295425666713783578654,57649054621298286314512855129102⟩,⟨(-604900847840377383800660118243856),(-604900847840374523154810991118912)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 13) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_13 (tableDensity false) (fullFactor true 0 13) density0_contains hk0_1_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨92950311302417838362421545795349,92950311302417838429590437970503⟩,⟨23451949660083573842933320314044,23451949660083573902440528097533⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_13 0 13 ha0_1_13_contains + def realAnswer : RBox := ⟨150599365923713264029135229374003,150599365923716124744103393099605⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_13 +namespace hm0_1_1_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-9066556862863194855399691979755),(-9066556862863174122580467376107)⟩,⟨(-7910467515603617058424389608377),(-7910467515603596326359457252635)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-30628468486117764574149390608033),(-30628468486117709344242026254777)⟩,⟨(-21102274743407206276793765690763),(-21102274743407151048897799063036)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-60556716075584880746287932618560),(-60556716075584813489047934997041)⟩,⟨(-24075566578668859419712383462562),(-24075566578668792164830196066735)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-96249632740314566037115786525628),(-96249632740314515298775836234272)⟩,⟨(-4326714128125554137219725373451),(-4326714128125503399644865904100)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-119367156042485818580493609562936),(-119367156042485795431557893696822)⟩,⟨50475027911452513124560293864569,50475027911452536277407808023273⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-94296274062710198891052563724786),(-94296274062710192648243146347687)⟩,⟨134212468381745029693719480803949,134212468381745035946279035220892⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨8705679330803616760517095739337,8705679330803618619160582898789⟩,⟨200837745644156408442431695109940,200837745644156410304760534365316⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨166236951135113801007515693119115,166236951135113801539720413450096⟩,⟨176296883511737158877272186052447,176296883511737159398797489602681⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨283598310505149384918987433846417,283598310505149385202817071446942⟩,⟨26761224523212396484291639015638,26761224523212396753202136815285⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨264039414379362159322657195813141,264039414379362159585721295549792⟩,⟨(-179164420644031302648690821941248),(-179164420644031302382313866424934)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨110649126195821736139109503266257,110649126195821736330566226347452⟩,⟨(-313798844403126056373030790953483),(-313798844403126056160702615568208)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-71457504657428863439150507345772),(-71457504657428863263149206160208)⟩,⟨(-309421534264715865903060008824300),(-309421534264715865714231924212347)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-178877548109815889735276329172952),(-178877548109815889580630051387183)⟩,⟨(-207495159010131183592221915433660),(-207495159010131183439523070470013)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-186208082676707541188435929873257),(-186208082676707541082627261581206)⟩,⟨(-94823776069820809827179810603242),(-94823776069820809730725134095807)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-127895504328983572544402324344833),(-127895504328983572487449190354440)⟩,⟨(-25609474705389213076923654631897),(-25609474705389213028887730040272)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-44235696416882043894838333105236),(-44235696416882043877437365194461)⟩,⟨(-2488906293131132025243346860755),(-2488906293131132011364047401276)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-762652549132786653447589998727),(-762652549132784327140043959485)⟩,⟨(-52544583296895355272579235554),(-52544583296893028928281760963)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2356887627911292141677771149717),(-2356887627911283373353756325705)⟩,⟨68846227932589197758027853482,68846227932597966209982729297⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-4048814125524880537751451809726),(-4048814125524856081941554012274)⟩,⟨926855896298776858897429007715,926855896298801314947647724549⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-5503216684215103808993265524072),(-5503216684215023221146938545378)⟩,⟨3127946804791366920414840053835,3127946804791447508532909612528⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-5704020090728523945575291700586),(-5704020090728277461634309985365)⟩,⟨7150130624552878923259190320790,7150130624553125407375224937487⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2826498211850243966676545500780),(-2826498211849623289528709628394)⟩,⟨12644427270920825375632677121809,12644427270921446052629658714212⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨5094978167988140152727293883653,5094978167989250714829734686081⟩,⟨17379672159127562769857008112144,17379672159128673331151972707654⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨18168223413616661874284639834852,18168223413618638612332767607380⟩,⟨16861424674661931184578325126648,16861424674663907921661416228894⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨32218322880739916293721940946248,32218322880742855326669044085947⟩,⟨6368588724480776621821144086266,6368588724483715654629152021409⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨39085783745320640956830911179755,39085783745323288346305246489398⟩,⟨(-14436598409619656974113245317568),(-14436598409617009583411102460978)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨32025003277480033773882011130013,32025003277481807272201478337657⟩,⟨(-38338957453606826460135483850722),(-38338957453605052959839858368743)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨12540526028103471166165073805101,12540526028104779125888212928124⟩,⟨(-54050983478608582440857948642157),(-54050983478607274480369103809411)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-9186215843531307308551648458360),(-9186215843530609605116627522024)⟩,⟨(-54714029470319520322676203259143),(-54714029470318822619786965564313)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-21834031568539922446063052556129),(-21834031568539621212232383117413)⟩,⟨(-42591545252660006668394951838808),(-42591545252659705435832117608867)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-20572968197634425465830280744604),(-20572968197634312803724829097125)⟩,⟨(-25190101828638579513309662083513),(-25190101828638466852377212901857)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-8207925883695575508082817363787),(-8207925883695547310001624239259)⟩,⟨(-8091494769110692987238384965360),(-8091494769110664789620577535886)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨19544439070181131910835028731,19544439070181131973691951138⟩,⟨44333203875209443069167212502,44333203875209443131774868035⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨70491934748530103081285446000,70491934748530103283462010686⟩,⟨134682990657083922471029787306,134682990657083922672099907596⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨158136252821606993277065452525,158136252821606993658677202852⟩,⟨225392307453397777268286860882,225392307453397777646952838307⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨308719598388273311540721686517,308719598388273312170807650269⟩,⟨299992031680152937953400287232,299992031680152938576976198359⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨542834935072434638484169495137,542834935072434639462315502174⟩,⟨314003602136301924427869282022,314003602136301925394230925581⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨854942458531181725632334308380,854942458531181727225545254299⟩,⟨187183849053703805771221633714,187183849053703807351266595726⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1177674699208187003369228254018,1177674699208187005972698353023⟩,⟨(-182078410577702044261725031296),(-182078410577702041668176130098)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1350670290847157539700021835199,1350670290847157544380376533739⟩,⟨(-860840691696392226736595986699),(-860840691696392222055619479790)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1145531762148099101791038295612,1145531762148099115442691670441⟩,⟨(-1787856185782413396393899942329),(-1787856185782413382726641820147)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨393964960168618774341068025591,393964960168618847405726066933⟩,⟨(-2705303709024534097280328642964),(-2705303709024534024193759466800)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-824550469567552619052669067915),(-824550469567552068785998405170)⟩,⟨(-3225468490881886230549171933986),(-3225468490881885680272811422338)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2107205537557657547606805608227),(-2107205537557654779464119716500)⟩,⟨(-3064916769979608029600040588564),(-3064916769979605261457016212759)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-2912716899519688339892891465495),(-2912716899519680007563594992828)⟩,⟨(-2283624278802111151028293254238),(-2283624278802102818704430087716)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-2895094593865510674512703469724),(-2895094593865495578274173699825)⟩,⟨(-1280645777766384071382461910217),(-1280645777766368975147962662563)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2078714014099615920564487781662),(-2078714014099599996116201765116)⟩,⟨(-500945073344307975181149369953),(-500945073344292050733513808954)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-748515551195891410143410443641),(-748515551195884535109118562569)⟩,⟨(-106355369221368802763629962216),(-106355369221361927728616948668)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1598625908428667249574156689),(-1598625908428654386476870024)⟩,⟨(-2679443632718595381568427316),(-2679443632718582518313271197)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-5320680263983348097959163485),(-5320680263983317348232351176)⟩,⟨(-8005372069641677164345993878),(-8005372069641646414115038149)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-10673914727425685540253279879),(-10673914727425650131129280696)⟩,⟨(-13062688024473969839235880280),(-13062688024473934429282396279)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-18903329698390715924721845776),(-18903329698390688689849407656)⟩,⟨(-17116387540803050652341596632),(-17116387540803023416390306911)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-31274794313384470382139743935),(-31274794313384456015279143739)⟩,⟨(-18577743669861278409554519051),(-18577743669861264041544465158)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-48538909865232165240406029425),(-48538909865232160022098419054)⟩,⟨(-14760119749031554046767195373),(-14760119749031548827588096100)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-69843858892910395575273920518),(-69843858892910394167949042406)⟩,⟨(-1967320231874625933480625413),(-1967320231874624526153385083)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-91470257128474127711292628636),(-91470257128474127313556001398)⟩,⟨23607709788043611081633268090,23607709788043611477724959457⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-106364134098998925242905527263),(-106364134098998924999726094605)⟩,⟨63661670570225242180234256643,63661670570225242419305266713⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-105805364702959324355235844037),(-105805364702959324088593289425)⟩,⟨114709901190113667751173903074,114709901190113668010954179989⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-83947069628590035992952284572),(-83947069628590035651866429224)⟩,⟨166253253202113273379778529668,166253253202113273714471670463⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-43481407244575063687370437928),(-43481407244575063276412474789)⟩,⟨202771299218676923199399272214,202771299218676923606216851910⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2198936111969685671470018284,2198936111969686111821152207⟩,⟨209958636602388482102352832098,209958636602388482541163440838⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨34180172920940994113900536054,34180172920940994517005708789⟩,⟨181659392510492172395715786182,181659392510492172799190788862⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨38760299672763739527996981893,38760299672763739813817821941⟩,⟨122219962980246056735243511223,122219962980246057022090284988⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨16591014215667061419523998947,16591014215667061522868886918⟩,⟨42925855790813446367316407837,42925855790813446471161776153⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨188202075181033915710550332,188202075181039018327715602⟩,⟨70602229595718907079861205,70602229595724009689976619⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨600840159981321808865369359,600840159981341803340222863⟩,⟨192004507040336048371741938,192004507040356042821311793⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1115701765807274639494424182,1115701765807328688584708800⟩,⟨244087193798478910689124837,244087193798532959723544724⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1777961907757077898110083728,1777961907757217813427132995⟩,⟨146458921518703559045384940,146458921518843474252820209⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2590141563274236948449141748,2590141563274578087427431859⟩,⟨(-233635679009624253197476112),(-233635679009283114418047303)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨3485761291834387551912097418,3485761291835159665846221155⟩,⟨(-1084976267522493477854283595),(-1084976267521721364240539649)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4298859477584706761244274111,4298859477586491158823991779⟩,⟨(-2611255537417220080600880253),(-2611255537415435683402679991)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨4746494840625188026290421142,4746494840628384230760757324⟩,⟨(-4935286884457065451599527919),(-4935286884453869247509254810)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨4476803227954132492210797227,4476803227958446984100822006⟩,⟨(-7966212772184523844102527871),(-7966212772180209352495901183)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨3227403362006241881075732539,3227403362010579352401401149⟩,⟨(-11280137323760574561402450513),(-11280137323756237090162017470)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1051173452486435989441094238,1051173452489670281830703778⟩,⟨(-14108217457375925814844144119),(-14108217457372691522286564963)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1550408633166771449908977555),(-1550408633164870627947442022)⟩,⟨(-15533970002514963824655646678),(-15533970002513063002274318707)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-3737597293670347051132026386),(-3737597293669399487425415598)⟩,⟨(-14898590350361629838716633027),(-14898590350360682274409545268)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-4654502103607822639720852842),(-4654502103607397267020567615)⟩,⟨(-12160089947869853998917853345),(-12160089947869428625593595855)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-3827247750938519138862083732),(-3827247750938345558428835668)⟩,⟨(-7853408466933883659949797984),(-7853408466933710079047457800)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1477018997343041984789530959),(-1477018997342995596481199069)⟩,⟨(-2699817112086391400420997399),(-2699817112086345011940279086)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-635448884008647941342787),(-635448884008647934362897)⟩,⟨(-304908470225911590571354),(-304908470225911584301316)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-2099392688362666882230833),(-2099392688362666860036853)⟩,⟨(-347361654678176520858219),(-347361654678176501106205)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-3414066487637923939007127),(-3414066487637923898236456)⟩,⟨1953748620478805627011331,1953748620478805662809855⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2375115181076089945529453),(-2375115181076089880375567)⟩,⟨10517183056875597723851606,10517183056875597780178823⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5102504727165385657520240,5102504727165385757302214⟩,⟨32663176637806832250887684,32663176637806832336347321⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨23986335996121653966097367,23986335996121654119691094⟩,⟨77913032054992052522507183,77913032054992052654011410⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨60232626528242022696473446,60232626528242022971515287⟩,⟨153311259983457118780611090,153311259983457119025098242⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨121832527850341213451269195,121832527850341214327085306⟩,⟨258163361599989516351971047,258163361599989517198086019⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨216468069360164571721697862,216468069360164577530095646⟩,⟨380399323129562196134765536,380399323129562201921711441⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨344371691343709192736806800,344371691343709241560479447⟩,⟨495119449628067719891057798,495119449628067768705810098⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨490504541681718229892007067,490504541681718552230561635⟩,⟨568662802877487215576990763,568662802877487537918917055⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨621636970468912472552648454,621636970468913917213010086⟩,⟨572029125279692076785848864,572029125279693521459204946⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨690514181565808083174501730,690514181565812247303812815⟩,⟨498956591167498226704242504,498956591167502390852279355⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨648257346007516277350388023,648257346007523873354623512⟩,⟨371269183205353729793141035,371269183205361325816311405⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨468280749361240638134877549,468280749361248895098420382⟩,⟨222027842711153027925535057,222027842711161284902916717⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨171389656333456428492764853,171389656333460085703619206⟩,⟨72986448333975736244193963,72986448333979393460031909⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-22255610536664790448212700830557),(-22255610536662427654820964585925)⟩,⟨(-131400666089486479350578796499512),(-131400666089484116557451166082380)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 13) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_13 (tableDensity true) (fullFactor true 0 13) density1_contains hk0_1_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-121550407087777173331002880422966),(-121550407087777173243166636809302)⟩,⟨(-30667934170878519718576075204466),(-30667934170878519640758957333750)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_13 0 13 ha0_1_13_contains + def realAnswer : RBox := ⟨(-143806017624441963779215681253523),(-143806017624439600897987501395227)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_13 +namespace hm0_0_1_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨21888540268220238671899489817303,21888540268220258077179373997643⟩,⟨36834668700194348058280188087985,36834668700194367464473742065857⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨81686274213613212879294276107981,81686274213613257987404803970709⟩,⟨103917214606688955839737086276760,103917214606689000951573469140083⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨185186790974732764721272365665993,185186790974732807486260497860241⟩,⟨140251817891678583554130663091985,140251817891678626328224741354884⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨337119537200196990095623528898856,337119537200197023692607266346515⟩,⟨94610325209468475506979474877959,94610325209468509114120236922436⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨480362362803206818148899358844983,480362362803206836668342994239024⟩,⟨(-100285547611567919194447936891444),(-100285547611567900671533517894132)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨467835286994229941853009514828435,467835286994229947789470121674447⟩,⟨(-456462769602353085894769328703465),(-456462769602353079968574400538549)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨133249947361518832688935551746752,133249947361518834397854994846122⟩,⟨(-818854762584015122010475918095632),(-818854762584015120318761293534322)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-499632686086260428370360490895192),(-499632686086260427489591287340736)⟩,⟨(-866463047475528961025408720334487),(-866463047475528960147078053468434)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1074984099114211980261020801100992),(-1074984099114211979651476587824990)⟩,⟨(-380341005697292067273732219373457),(-380341005697292066652001340988725)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1144000331681663202521409564450301),(-1144000331681663201954114819887753)⟩,⟨434724720395057990575221253658430,434724720395057991150686653408991⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-630803364207689755941852582560534),(-630803364207689755496789908970120)⟩,⟨1056828543338443077717035548067187,1056828543338443078166700367754605⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨79030745533654107115790166669314,79030745533654107474492014254346⟩,⟨1149582875717265884943677155500910,1149582875717265885302613139978671⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨548023239682929817123488172170301,548023239682929817416827916103236⟩,⟨825852060496943864684589513643540,825852060496943864974635682595817⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨635616183801203213363639890178916,635616183801203213557249561780495⟩,⟨415676035349624020085950119395463,415676035349624020272963640239255⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨454658134123248441735165376893686,454658134123248441837132873344250⟩,⟨140901213670399501198632285451418,140901213670399501294433118813473⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨159883069501944242069358720069980,159883069501944242100113003331212⟩,⟨25609763679485191341118636724460,25609763679485191369439863169499⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2319189104080324094149146039167,2319189104080325810973765644126⟩,⟨925199086748560029882756792071,925199086748561746757841700234⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨7512670354724125437377818300048,7512670354724132450157944485345⟩,⟨2225584526082016017779249460193,2225584526082023030646824733575⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨14155955538206525274286013017320,14155955538206545435999556385374⟩,⟨1518033815314811454614481053427,1518033815314831616233127080281⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨22236186908059863558011970089838,22236186908059917975919133867873⟩,⟨(-3587979476292479060891615153107),(-3587979476292424643688753050256)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨29417448482468117722716909121658,29417448482468245117826959148159⟩,⟨(-16317708167952110558510167850849),(-16317708167951983165368787954727)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨29283389289760952564238617445741,29283389289761307970504820180087⟩,⟨(-38794304397897731689492175546214),(-38794304397897376285626496919833)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨11504765749244636269590843210785,11504765749245526142777218806672⟩,⟨(-67352193016170234535120599280681),(-67352193016169344662492896942709)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-32141459658192195421074265844345),(-32141459658190797539638338633258)⟩,⟨(-87427533374072679362685789523404),(-87427533374071281478001302752843)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-95553569929898928441008191498968),(-95553569929897292508201078672520)⟩,⟨(-75996531099897146911776898853982),(-75996531099895510972827086240809)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-150912385444036229495382499501376),(-150912385444034223019430836827520)⟩,⟨(-18412580820437448988996078786350),(-18412580820435442511283250778569)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-162638120902018457108271777954349),(-162638120902016989049283154458699)⟩,⟨70770650931677881283434694429096,70770650931679349337574433442495⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-118479631922548656771237276839414),(-118479631922547900671457731867140)⟩,⟨149555038441404625369205591744045,149555038441405381460035894638374⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-44688146853064253443804481451868),(-44688146853063774231374035780426)⟩,⟨179851622552667486081520196726244,179851622552667965289365626948122⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨15283293034572447009592442598095,15283293034572691991353871765626⟩,⟨155910130037963216243946915039012,155910130037963461225291899844733⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨34690676979126164157673589794438,34690676979126267666329046673838⟩,⟨99376112119326852805717103747140,99376112119326956315639618646326⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨16421442732828732108324039316203,16421442732828759728754802246984⟩,⟨33297036794794962855818117028137,33297036794794990476957402248102⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨8676658079174337928578772976,8676658079174338012256406003⟩,⟨(-89178641809919601523736877743),(-89178641809919601430948607045)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨5994035715803494407163931909,5994035715803494673404116734⟩,⟨(-281735330005151434293044058281),(-281735330005151433996182323866)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-65752838463747864113864573477),(-65752838463747863578198299782)⟩,⟨(-511162350353102109191568269882),(-511162350353102108604560419950)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-279893840274974905560674463359),(-279893840274974904559200956358)⟩,⟨(-777940938713243815154247826455),(-777940938713243814089814481519)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-737277395328902941315294489167),(-737277395328902939498073784327)⟩,⟨(-1027081631682755791966887254564),(-1027081631682755790095777929659)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1535467917400550015470749080579),(-1535467917400550012245393264699)⟩,⟨(-1098946383151088691032341824464),(-1098946383151088687805300278945)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-2675546976452429760077199727091),(-2675546976452429754480705226726)⟩,⟨(-695548902762642195781821406391),(-695548902762642190306433760234)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-3910155627256133054260625795849),(-3910155627256133044731883076471)⟩,⟨558663760903328568192453232136,558663760903328577403091256722⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4639540988139241467976251620749),(-4639540988139241448531552628899)⟩,⟨2878117236628500548647003683420,2878117236628500567761135236694⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-4072351774989554391281570328511),(-4072351774989554319077809167131)⟩,⟨5956581470891427498413332712837,5956581470891427570496805057888⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1765930331804721422057080843456),(-1765930331804721051662754629697)⟩,⟨8809954857752481819459828010681,8809954857752482190060738785662⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨1770312429943041964105230763173,1770312429943043395260176943704⟩,⟨10194905589546453743908882187656,10194905589546455175606145696674⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨5063547909666021549293015620670,5063547909666025541887006561563⟩,⟨9461845788022767703267082424650,9461845788022771696518968961851⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨6501117891053330325398541135647,6501117891053339111392351573958⟩,⟨7053507053951343960491911354360,7053507053951352746892752289398⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨5337483434468006523248800627644,5337483434468017146036669449137⟩,⟨4064207515911620204583590570067,4064207515911630827557661981164⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2045461605707493060589255036872,2045461605707497980170264351498⟩,⟨1285706740117784925596751515188,1285706740117789845226432988100⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-241206393965988735741778320),(-241206393965982417154185694)⟩,⟨3235392220309462725799437494,3235392220309469044778409586⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-202467548375400466518724447),(-202467548375384571158518774)⟩,⟨10179397536070862212199516808,10179397536070878108684708532⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1608039642891115938965432625,1608039642891134007577558798⟩,⟨18439792235896351504112189460,18439792235896369574395483371⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨7041510300756996432602072275,7041510300757009827914680400⟩,⟨28473423087623482986437071486,28473423087623496383520058791⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨18812180038157472141213458510,18812180038157478919596408779⟩,⟨39738359912314833146233871454,39738359912314839925508272796⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨40310738402968460896505370375,40310738402968463266831707419⟩,⟨49717468384485605027649816234,49717468384485607396289687021⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨74404846512777647209698216469,74404846512777647866855982761⟩,⟨52882659593150649019254365482,52882659593150649669550012299⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨120824014480068130230839742523,120824014480068130493544626196⟩,⟨40575713560546709792462353581,40575713560546710039831428830⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨172865750857996334384640998194,172865750857996334649646419491⟩,⟨3432952848424221579870272981,3432952848424221823891631499⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨216076398137809090874066398701,216076398137809091234958169831⟩,⟨(-62637094284411228006862873434),(-62637094284411227663130389459)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨232466693186902817932886340147,232466693186902818406696943343⟩,⟨(-149070968546558314029571372704),(-149070968546558313564039861092)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨210790366871967020258655059682,210790366871967020831107913170⟩,⟨(-231973898833321276776379724268),(-231973898833321276199447188828)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨156521626991310658887055406312,156521626991310659501260141708⟩,⟨(-279645599198314827113721491289),(-279645599198314826483349077575)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨91392129117941422789340264680,91392129117941423350084588244⟩,⟨(-267862368731886011677692214318),(-267862368731886011095225754244)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨39417097512675694650538277493,39417097512675695046848432636⟩,⟨(-192317645756116619649509274042),(-192317645756116619234874881522)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨9619715033811543864342232970,9619715033811544007332775157⟩,⟨(-69754993185512437346321594155),(-69754993185512437196215154602)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨42867048907892517240664490,42867048907894226352603806⟩,⟨(-176139783086458480809973024),(-176139783086456771718327598)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨98745482060953401808222544,98745482060960058790963114⟩,⟨(-550069414478285983657121749),(-550069414478279326740644701)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨55351723794145537024157009,55351723794163294165285421⟩,⟨(-982793309504170695372599604),(-982793309504152938361387172)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-182145267214186469075857500),(-182145267214141579976438269)⟩,⟨(-1490724711226896221368016764),(-1490724711226851332493970805)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-738575147234120566385796503),(-738575147234000784879931186)⟩,⟨(-2042108303700851856934001281),(-2042108303700732075756284687)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1750313135888623303306794057),(-1750313135888290272730197885)⟩,⟨(-2516875235554968966356357710),(-2516875235554635936140539774)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-3310251174699348356109630609),(-3310251174698585761036989521)⟩,⟨(-2671179566941086824999243997),(-2671179566940324230255393868)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-5370106747647600559630478468),(-5370106747646274697163135957)⟩,⟨(-2149101907448954424148083761),(-2149101907447628561883048160)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-7632252038868798871702542241),(-7632252038867063601850655550)⟩,⟨(-591529025356352000652255866),(-591529025354616730742706155)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-9524777370545644116210946469),(-9524777370543958521744438160)⟩,⟨2142544725231371122023653400,2142544725233056716961847959⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-10369611625332138602807461055),(-10369611625330931765238992143)⟩,⟨5721450740155007624575263818,5721450740156214463138360684⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-9740102950134310569047870979),(-9740102950133635095118337376)⟩,⟨9235421411868025285013482859,9235421411868700760440404736⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-7782085389717587538743049284),(-7782085389717262039831372289)⟩,⟨11416256158714633152145149929,11416256158714958652803704410⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-5184720314167411607869366096),(-5184720314167242206413101170)⟩,⟨11174173919857115677972182385,11174173919857285080805266189⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2742827320815150988569307864),(-2742827320815071813584338899)⟩,⟨8161440733735529432337027941,8161440733735608608161013892⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-823701326336251490939737656),(-823701326336228797806208583)⟩,⟨2989029413823895841402358881,2989029413823918534815404042⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2623715435469186885439105),(-2623715435469186882584829)⟩,⟨5534802789505145184536287,5534802789505145187631765⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-6689075373698811739393350),(-6689075373698811730383544)⟩,⟨17653782066748372221127013,17653782066748372230991934⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-6920557114301382639563578),(-6920557114301382623083987)⟩,⟨32800008980713758171867766,32800008980713758190128915⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-3177775311313974648212),(-3177775311313948390821)⟩,⟨52415483900557778752016469,52415483900557778781437572⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨18062357170327546543163212,18062357170327546582707981⟩,⟨76288386157044411381604691,76288386157044411426130184⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨51642119302842134826815339,51642119302842134885974039⟩,⟨100857410372974354161097120,100857410372974354227348862⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨104430500722289769404907458,104430500722289769517071419⟩,⟨118103837907568200987546256,118103837907568201107321950⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨176743951717296147990541036,176743951717296148322196232⟩,⟨116323020518246819216340002,116323020518246819554162219⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨261851492999343489758582049,261851492999343491842129840⟩,⟨83371602390597537715351137,83371602390597539802111482⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨344335590092238344926484392,344335590092238362238417519⟩,⟨12796167785997883820486476,12796167785997901132382447⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨403285288841078740452372330,403285288841078854018365195⟩,⟨(-88483043383780751461209143),(-88483043383780637897370292)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨420024332475324182663795922,420024332475324687266615923⟩,⟨(-195667515637364108879738811),(-195667515637363604279300197)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨385941998497803735757816713,385941998497805175273127651⟩,⟨(-271155290203447805048696718),(-271155290203446365534494350)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨305636834968096770635657674,305636834968099369238172243⟩,⟨(-280660624987178588159723034),(-280660624987175989556628571)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨193578743741344053126353951,193578743741346853580986497⟩,⟨(-211112628821491071090664350),(-211112628821488270634707593)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨65893590298479019170617814,65893590298480253470388374⟩,⟨(-78343507545458065237921638),(-78343507545456830937491168)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-30681420129237330193547012544635),(-30681420129235699343290625145627)⟩,⟨372122525496930367454087939401890,372122525496931998303391809809068⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 14) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_14 (tableDensity false) (fullFactor true 0 14) density0_contains hk0_1_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-55831148224647864813636893443202),(-55831148224647864760795130458731)⟩,⟨(-10271747926401004071626730196638),(-10271747926401004024119732897542)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_14 0 14 ha0_1_14_contains + def realAnswer : RBox := ⟨(-86512568353885195007184005987837),(-86512568353883564104085655604358)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_14 +namespace hm0_1_1_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2879374095960997738778674310107,2879374095961013612746681707494⟩,⟨6738242584629444508592843015437,6738242584629460382303899492561⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨11400623396119389242790089385199,11400623396119426112005464134199⟩,⟨19640875876274473197833475819798,19640875876274510066040687279519⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨27736783589612731519359920913863,27736783589612766393834764658721⟩,⟨28804213946579938034659545916398,28804213946579972906776936517906⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨53662480407679297542448002271623,53662480407679324824631869781402⟩,⟨25774723926165938480569938342315,25774723926165965760192936120593⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨80719042142751204550804233857937,80719042142751219420498191489343⟩,⟨(-2167933290463147385141831398642),(-2167933290463132515788148151633)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨83904364316048473970465046056621,83904364316048478502521782904763⟩,⟨(-59967975308765254010606447999422),(-59967975308765249473824929495007)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨32117814334915144716658120473377,32117814334915145759330064038186⟩,⟨(-123462476986502641419466819811730),(-123462476986502640370736399911027)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-74551117767267123751643703888648),(-74551117767267123385481238189765)⟩,⟨(-136056234657514058493546555749716),(-136056234657514058130277476991949)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-175381537893437150815704711314998),(-175381537893437150624483184493925)⟩,⟨(-55110467824454918410597855616938),(-55110467824454918230722275446850)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-188438757593088778377218357836096),(-188438757593088778198003875803690)⟩,⟨86369876156299521121022898023836,86369876156299521298698830622578⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-97160556306263675337009856312206),(-97160556306263675200518789324658)⟩,⟨194315109850340279879255658036146,194315109850340280027686780703933⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨29066045163986398629131865669034,29066045163986398742443001380511⟩,⟨206045989363225786919932253609362,206045989363225787043472690062456⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨109886402012344914942248796737951,109886402012344915045039707733674⟩,⟨142462712449874025951468842861251,142462712449874026054061057234226⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨120597794842631912905920427639489,120597794842631912976838179986120⟩,⟨65869825589453626956306278249581,65869825589453627021473567683236⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨83965448017164252830777110802160,83965448017164252868837925064367⟩,⟨17799549356968467125186415226748,17799549356968467157461088056297⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨29112955569725858938747592077221,29112955569725858950319058701609⟩,⟨1704332573875008931702846134110,1704332573875008940960208256840⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨249554061325491534868128085154,249554061325492945650153221879⟩,⟨298951873757480021746911500372,298951873757481432521065656129⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨864375120359604803067198758861,864375120359610570418160853365⟩,⟨840411883808817590866813500133,840411883808823358201785575573⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1808006116953777260547209578941,1808006116953793862050582139266⟩,⟨1143272744810765966000788253459,1143272744810782567506101793028⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3187983540119092876805117451859,3187983540119137741347094910653⟩,⟨830690830107164868752778149563,830690830107209733371475132641⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨4771189682659017688164863143595,4771189682659122830535897691887⟩,⟨(-710995833386163537709126067106),(-710995833386058395095998578520)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨5615206200256087259264851696637,5615206200256380898938189353889⟩,⟨(-4078035268858124387599695448059),(-4078035268857830747614444142007)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨3907104182713487429345641185690,3907104182714223357390428589964⟩,⟨(-9060487140287433639787022447488),(-9060487140286697711640175426040)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2238279641113695154852569600139),(-2238279641112538558631085453469)⟩,⟨(-13562225485977734229299070018976),(-13562225485976577633459441019586)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-12653250834899194073184178134839),(-12653250834897840611815943332835)⟩,⟨(-13547925663118763017081920923947),(-13547925663117409556512624714592)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-23260477977289829928245239942436),(-23260477977288170826448152867530)⟩,⟨(-5583275589751192633604974629193),(-5583275589749533532060337277540)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-27656604994238657241594670246013),(-27656604994237444609055789531351)⟩,⟨9142842482289483090434859284037,9142842482290695723650274566256⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-22416482540719668153477743505908),(-22416482540719044555954990660992)⟩,⟨23940500151005255131020942095429,23940500151005878729854900404010⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-10786864686695274668499814834075),(-10786864686694880049902041201659)⟩,⟨31359572095420872474760785381013,31359572095421267094032174729834⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-70828792880405232942106676579),(-70828792880203815103401402247)⟩,⟨28855605900174195984671835209849,28855605900174397402533945728505⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨4374213374939752894693706777989,4374213374939837873920623104651⟩,⟨19230752365524322414529788743502,19230752365524407393515856345984⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2331163000898508968827214592341,2331163000898531623710327568164⟩,⟨6610390354677737013173481085466,6610390354677759667926300804286⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨12219760018064629183913832286,12219760018064629213439145783⟩,⟨(-16120787869579928629597148151),(-16120787869579928599654331436)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨34772085682325731108850476751,34772085682325731203521158649⟩,⟨(-53375861213214919635387850800),(-53375861213214919539266091935)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨49438462808567281747784125073,49438462808567281934092831905⟩,⟨(-105179447645688631180001045753),(-105179447645688630991302413899)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨43494167103472680390062036244,43494167103472680721964292133⟩,⟨(-178401656413232666645461777722),(-178401656413232666310714159086)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-6362295575901183401988483923),(-6362295575901182841098434136)⟩,⟨(-271060276337072760126289399135),(-271060276337072759563033228893)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-132390028190867250524860655874),(-132390028190867249614942685088)⟩,⟨(-360947215113676552304002774860),(-360947215113676551393581949357)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-360246031498309269589588308730),(-360246031498309268153156953678)⟩,⟨(-392658722837159287711252807290),(-392658722837159286279209650718)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-675015727479251425166655752952),(-675015727479251422813783316795)⟩,⟨(-277877183153891872849804553897),(-277877183153891870508659743504)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-984533075400485814122614287806),(-984533075400485807121933373168)⟩,⟨67074417097268065724894006616,67074417097268072715224164340⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1125012638913608054503184445464),(-1125012638913608009106508544972)⟩,⟨641776147320521745490582672559,641776147320521790883983721293⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-950345862630251712913525943270),(-950345862630251429866362673446)⟩,⟨1294796238207366191781836826690,1294796238207366474831254618755⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-466603134339644752215885798122),(-466603134339643609190502682243)⟩,⟨1763228388223880499432560850599,1763228388223881642461378764045⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨118423288704646419252207641084,118423288704649650321698952153⟩,⟨1836541160756771711126744964720,1836541160756774942198271676589⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨513366205239688739800104876184,513366205239695888471610911296⟩,⟨1506278917921142939958432473428,1506278917921150088628938666882⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨537534669867585903815210482636,537534669867594563453450673481⟩,⟨940165226716767774686253033573,940165226716776434322652380012⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨223451329515919456963670234330,223451329515923470165606304615⟩,⟨312778344990238406753661241640,312778344990242419954705056219⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-711114193022922706892565400),(-711114193022917398432334165)⟩,⟨818805927662763247792167570,818805927662768556211027093⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2063821364399282532191585949),(-2063821364399269187537547682)⟩,⟨2641308491395114522063860773,2641308491395127866598974912⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-3137262692339977741754681466),(-3137262692339962595506898038)⟩,⟨5021029355335832798071748649,5021029355335847944143979463⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3512899996388488661956387276),(-3512899996388477462172494920)⟩,⟨8323770907966816289444763900,8323770907966827489046211798⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2432489469010056190405248953),(-2432489469010050551162375615)⟩,⟨12815407261090306552394052257,12815407261090312191553599069⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1245471406697655704972031034,1245471406697657646244301950⟩,⟨18413551904717168141556732124,18413551904717170083015535902⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨8876740151915119943959780377,8876740151915120438706431004⟩,⟨24258198364311833533616731193,24258198364311834029070477324⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨21480655538123583193896582809,21480655538123583332907097184⟩,⟨28307966315851716318723451472,28307966315851716459254020877⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨38730289627075598529280802104,38730289627075598630820619496⟩,⟨27449216891415008632593817478,27449216891415008736131944361⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨57900835127900072425439336311,57900835127900072557027821906⟩,⟨18655244938014816239651837704,18655244938014816372731674459⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨73828439857468343695935092103,73828439857468343868509293281⟩,⟨1214790186079159010096829079,1214790186079159183163162959⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨80765420289024224854014237809,80765420289024225064367040268⟩,⟨(-21161451302941321832784761780),(-21161451302941321623142154818)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨75491360021810690213842404664,75491360021810690442486535733⟩,⟨(-40472778521560381999105234080),(-40472778521560381772196495733)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨59300235179798446018365426299,59300235179798446229993798901⟩,⟨(-47849804876524162394164108038),(-47849804876524162184682709539)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨36786622986765430789562483907,36786622986765430940889642729⟩,⟨(-38483281116322876918262908121),(-38483281116322876768682745663)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨12312680185013124596458726064,12312680185013124651432241224⟩,⟨(-14704393181073816196692416850),(-14704393181073816142385407480)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨11105101162167770297058389,11105101162169174900403412⟩,⟨(-58518997869203940287222034),(-58518997869202535680362849)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨25303545091903632684404963,25303545091909104014746047⟩,⟨(-185724232063942190779524223),(-185724232063936719437177613)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨12448402315690819052093467,12448402315705415514666671⟩,⟨(-341047096803917672301907297),(-341047096803903075814593667)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-55803757876545691020650833),(-55803757876508785968222371)⟩,⟨(-534522510765808340331578361),(-534522510765771435233819616)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-223026738610339195668997530),(-223026738610240706334345837)⟩,⟨(-759592817839571379396704680),(-759592817839472889992617483)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-547926387833245434965381873),(-547926387832971604897152216)⟩,⟨(-982734272388646089544286081),(-982734272388372259393110272)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-1089160392241384132088852178),(-1089160392240757236557254678)⟩,⟨(-1133550451385673930123320336),(-1133550451385047034505579446)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1871575738268378219590157331),(-1871575738267288827891855200)⟩,⟨(-1103214552842849310162446268),(-1103214552841759918400833166)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2842385465531758939027452300),(-2842385465530334300474192957)⟩,⟨(-769871554717881698248035374),(-769871554716457059689328709)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-3839445329082220262981783041),(-3839445329080837883900815473)⟩,⟨(-65276260668527941800734456),(-65276260667145562800439721)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4604613303154976315037872850),(-4604613303153987821835309878)⟩,⟨937739725719062416892037285,937739725720050909914503044⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-4866382313778726484873609101),(-4866382313778173961142991207)⟩,⟨1984551728474124495207768412,1984551728474677018667116761⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-4475066413618577417440478876),(-4475066413618311508045777394)⟩,⟨2708835306414983428208343809,2708835306415249337287281722⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-3500148860193735215085414642),(-3500148860193596974925442896)⟩,⟨2788312252358028111069512157,2788312252358166350984263723⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2176571810340211014408432131),(-2176571810340146452240082171)⟩,⟨2096077934554696530222260885,2096077934554761092243123311⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-731072518584709205954657934),(-731072518584690708357932224)⟩,⟨778430740354338912143036557,778430740354357409691449293⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-70074154684978341221541),(-70074154684978339644831)⟩,⟨168128832489703618405001,168128832489703620199347⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-60120019453276043739886),(-60120019453276038774229)⟩,⟨547916018400614179371424,547916018400614185079388⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨560125384731084188167130,560125384731084197160336⟩,⟨856834532419839295726696,856834532419839306212140⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2792244298044005242623640,2792244298044005256747862⟩,⟨440864790898022490618861,440864790898022507360474⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨8521063782881001948807696,8521063782881001970195774⟩,⟨(-1977176598924568121746592),(-1977176598924568096144260)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨20240416698375086230948767,20240416698375086264083009⟩,⟨(-8100755191630184135878443),(-8100755191630184096352442)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨39812063825815467460597268,39812063825815467532182089⟩,⟨(-20054910211440136531517647),(-20054910211440136452496257)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨66942974099067393383788762,66942974099067393632397277⟩,⟨(-40519458819730887619491568),(-40519458819730887364319513)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨98074287347687624644270970,98074287347687626331602474⟩,⟨(-71841788985097489291064235),(-71841788985097487599893297)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨126026573166778315109398602,126026573166778329255580296⟩,⟨(-113710738867682441184085489),(-113710738867682427037599977)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨141410039584187065998603926,141410039584187158751893181⟩,⟨(-160675535268917993630194508),(-160675535268917900880160994)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨136810858664442775848096036,136810858664443187930559703⟩,⟨(-201500807328556548068146104),(-201500807328556135991645427)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨112269654312389650829492888,112269654312390826849196064⟩,⟨(-221198417657201050284926733),(-221198417657199874272626587)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨76657830519867393927157252,76657830519869517875433082⟩,⟨(-205400000568145289452226640),(-205400000568143165510969451)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨41536718950364535731561924,41536718950366825517614718⟩,⟨(-147175304114870191916893285),(-147175304114867902135799583)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12700076404610199036863572,12700076404611208459722825⟩,⟨(-53638695001632978728962953),(-53638695001631969307856222)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨9133387730265441418222661811631,9133387730266788176397104987167⟩,⟨83527798448912520463281368298316,83527798448913867221151640508099⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 14) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_14 (tableDensity true) (fullFactor true 0 14) density1_contains hk0_1_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨73009963063001053917962862907571,73009963063001053987063629887263⟩,⟨13432285749909005262310419942940,13432285749909005324434954872527⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_14 0 14 ha0_1_14_contains + def realAnswer : RBox := ⟨82143350793266495336185424719202,82143350793267842163460834874430⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_14 +namespace hm0_0_1_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2106783928425224293648830612641),(-2106783928425212433948051746180)⟩,⟨(-24262953750813140479539862083118),(-24262953750813128620001268759043)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16776682580722968843874231951120),(-16776682580722939675741233770224)⟩,⟨(-73431344971193317769260002139566),(-73431344971193288601054346146634)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-63403635885752283365750949171783),(-63403635885752252847521534470653)⟩,⟨(-116953923674808145520438908029989),(-116953923674808115000228554842820)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-157462591137591219340849506892000),(-157462591137591201058674088721041)⟩,⟨(-126388700121941734515515283213237),(-126388700121941716226614261482220)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-281373916527497770967475853980640),(-281373916527497761312951811426282)⟩,⟨(-47498260357784617191304166941561),(-47498260357784607529912420967333)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-347797140376384821256982124238540),(-347797140376384817446319744638102)⟩,⟨161803568579550308216479790575642,161803568579550312026934237342422⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-217773024086209794203855716893637),(-217773024086209793125633472217377)⟩,⟨440553584937789239003098834243025,440553584937789240071156913074303⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨158400195563721420473440460072127,158400195563721421057195296801267⟩,⟨576364851917805488104556899684147,576364851917805488683032921724462⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨585316403217022771949963817332582,585316403217022772369430518853476⟩,⟨359339452028711414109929327033243,359339452028711414533784928016935⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨727651746929609715949223276273799,727651746929609716319069039574767⟩,⟨(-144923632648490609538645151907414),(-144923632648490609163095175184231)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨461488169202233936686560682387383,461488169202233936985289466119747⟩,⟨(-591109959162335006910993630993650),(-591109959162335006608708283407017)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨12825883230963674759337972547779,12825883230963674984650400809515⟩,⟨(-704509669248698106234382835446226),(-704509669248698106008077725727302)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-307854443396918879900279434071010),(-307854443396918879714426630952201)⟩,⟨(-523711757592358186174560301322694),(-523711757592358185990270132448589)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-382576919888803336008306862300337),(-382576919888803335885403943730014)⟩,⟨(-266288019982404866432209983554347),(-266288019982404866313175128762416)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-278245662329260425323967441166182),(-278245662329260425259599517120116)⟩,⟨(-89678328637143768872047159260172),(-89678328637143768811434990930831)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-98186162381239510695809992535230),(-98186162381239510676512722091874)⟩,⟨(-15955929065132481903244951446557),(-15955929065132481885443798996952)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-445612754378925004153955440357),(-445612754378924298109278356990)⟩,⟨(-1100351349765825833634145045665),(-1100351349765825127523039381341)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1734170670382984895988832372700),(-1734170670382982227118239840056)⟩,⟨(-3312756159178532544503873427910),(-3312756159178529875396179116719)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-4277221369529727491974021987642),(-4277221369529720114346534886675)⟩,⟨(-5342670637504136185883213371843),(-5342670637504128807794092473314)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-8957518750438399935779921691495),(-8957518750438374812666338619052)⟩,⟨(-6283844089938362631376201762569),(-6283844089938337507772212675454)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16073905014872409869415875179502),(-16073905014872331410476479155229)⟩,⟨(-3985529443625034763420083418781),(-3985529443624956304305553117561)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-23809697121598571543832949610541),(-23809697121598376734038147459289)⟩,⟨4862174736389006159752512053073,4862174736389200968830963761362⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-26365962976693341224844026434770),(-26365962976692979774361717621059)⟩,⟨22629472459519716565220424595180,22629472459520078013706626574378⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-14563624592752929602304550423672),(-14563624592752169162488262676069)⟩,⟨45960848123746689766917743173216,45960848123747450205625386404108⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨17434066216443674985260494314028,17434066216444689578057717908111⟩,⟨61911703058212804060281519021828,61911703058213818654647896590556⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨61730357236260682834745621445328,61730357236261559491904744601273⟩,⟨53151069499476430285043660190967,53151069499477306946233322393200⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨95504457734093512678087403820947,95504457734094342285436633381860⟩,⟨13970604295856424886881474967627,13970604295857254495715657693421⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨97886954112250880546270187086378,97886954112251390956512198543584⟩,⟨(-38668385399972355987326906063821),(-38668385399971845579337476953526)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨69799930064747055742700845902825,69799930064747279715441596288541⟩,⟨(-76258962819679710187517206388949),(-76258962819679486219462322763583)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨32568581876715100965232845737496,32568581876715221680067414230381⟩,⟨(-81908688373111096486800405973154),(-81908688373110975774930044498809)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨7446590104019462628448720671474,7446590104019520478294636900623⟩,⟨(-59102859402369661883293931575661),(-59102859402369604034536662547604)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-98424643756344016792177380954),(-98424643756327618234346655925)⟩,⟨(-21072872929683390855533517048351),(-21072872929683374457192029856845)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-32021981630895991905150106483),(-32021981630895991858668718935)⟩,⟨13916842451292737571735142440,13916842451292737616157686979⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-97250512424852937724849495469),(-97250512424852937574559386234)⟩,⟨51865861297660630716172744005,51865861297660630860998248193⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-161932394660708031563125592122),(-161932394660708031265205293184)⟩,⟨122480694313828649646733050280,122480694313828649938603365073⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-210393503186950644581278488440),(-210393503186950644039005026588)⟩,⟨253146711353231231732954232455,253146711353231232275500881125⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-198772585974794995025686055564),(-198772585974794994061130496420)⟩,⟨469894617290154719512155043214,469894617290154720496819638706⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-41760707380160882422213914795),(-41760707380160880732692250955)⟩,⟨773111479263197002689903005313,773111479263197004440074043332⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨379112050138642416871172288117,379112050138642419861103746651⟩,⟨1089874287770212856646474677768,1089874287770212859731985736689⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1151348751630912829838689322542,1151348751630912835265379764441⟩,⟨1223963604817294851663574658619,1223963604817294857151124887106⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2201526873920253044778756464851,2201526873920253055690069570091⟩,⟨873341486529316252230299380451,873341486529316263108876071121⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨3184307689286938151551684231610,3184307689286938183507975806607⟩,⟨(-202115351352532957614823173582),(-202115351352532925837790241216)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨3570551139012452462810301013289,3570551139012452612020420013849⟩,⟨(-1902649315055504291628103497282),(-1902649315055504142678435354128)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3010894642526718882185960248398,3010894642526719645507088037110⟩,⟨(-3655659081947418065858199299077),(-3655659081947417302679245435354)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1707937247347379174839842263108,1707937247347381580904683581847⟩,⟨(-4678477900368977535006049721727),(-4678477900368975128936649716287)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨364771889849794408517679146612,364771889849798906320396721012⟩,⟨(-4485922056363311886406241889690),(-4485922056363307388498872235833)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-332679775238614085475706677423),(-332679775238609262793331832784)⟩,⟨(-3153903633758416539399758392992),(-3153903633758411716600717039525)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-228127544668641533743192447441),(-228127544668639438672098361260)⟩,⟨(-1123562107131394188474868325702),(-1123562107131392093354667611527)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1021505447079376834614783157,1021505447079379139123416959⟩,⟨(-253581843816886453876203717),(-253581843816884149422273883)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨3164758933109850064249162545,3164758933109855790276250798⟩,⟨(-982624480247966554470756305),(-982624480247960828575680540)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨5550616257247298029814521656,5550616257247304384635090876⟩,⟨(-2440510164838974427163829368),(-2440510164838968072441044364)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨8118620670649203024633361220,8118620670649207573763249727⟩,⟨(-5306975129744967112554922377),(-5306975129744962563253427582)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨10351025666881340654072683145,10351025666881342850167117775⟩,⟨(-10459724319270991944480511687),(-10459724319270989747516937451)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨10925022479523129016357072387,10925022479523129738917644329⟩,⟨(-18787071098338849431201697254),(-18787071098338848706389566887)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7453231492877705845527307773,7453231492877706038835057078⟩,⟨(-30603945524353210211159511747),(-30603945524353210013480408451)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3246988695522981707616486174),(-3246988695522981606232125709)⟩,⟨(-44630929607106287804185846365),(-44630929607106287698028486898)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-23788187528112534292120523814),(-23788187528112534176606884324)⟩,⟨(-57038150691128314287355219538),(-57038150691128314168485418947)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-53698797949008405199404732935),(-53698797949008405036013638001)⟩,⟨(-61775686403182833817614458414),(-61775686403182833654378260289)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-87149300356534716515142135540),(-87149300356534716291650848773)⟩,⟨(-53361022529117477702448834439),(-53361022529117477484420028679)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-113509955206235233807271343744),(-113509955206235233528275365318)⟩,⟨(-31424278100230158712114369771),(-31424278100230158444265472476)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-121968292630689897157241570615),(-121968292630689896848437216053)⟩,⟨(-3489655294491234355067456818),(-3489655294491234060228362861)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-107426442487834105760302866644),(-107426442487834105468006857844)⟩,⟨17795014428765413535262411819,17795014428765413817272903651⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-72709087034027266616295050408),(-72709087034027266404739141998)⟩,⟨22386131774382590929033299600,22386131774382591134756010992⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-25556522585246177983126031728),(-25556522585246177905915855152)⟩,⟨9848786082046490194312504853,9848786082046490269684304328⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-50022497339496493404084011),(-50022497339496070719402027)⟩,⟨(-3375331881245711711223874),(-3375331881245289019452774)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-154996356185514849300726822),(-154996356185513217481532564)⟩,⟨(-577967765529896478410812),(-577967765528264636325862)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-272458610592280785699547881),(-272458610592276431682028937)⟩,⟨33583433927493060114891818,33583433927497414175662763⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-402393469170292179957654194),(-402393469170279133806249077)⟩,⟨127932359612047405718266180,127932359612060451929423790⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-528293696346560841022262958),(-528293696346521678124194832)⟩,⟨318628414440176009159647234,318628414440215172126358950⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-605086825809164705977365183),(-605086825809058587777235050)⟩,⟨641473769489137031789331216,641473769489243150053388615⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-550093929679692724714135044),(-550093929679456402371772787)⟩,⟨1112127562060638295700748942,1112127562060874618080208197⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-251477274929172072086531246),(-251477274928773564322888060)⟩,⟨1694196788546368386350673571,1694196788546766894089254196⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨389953912055501741903655104,389953912056004470245481929⟩,⟨2269036774986837635028942977,2269036774987340363236042682⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1384995674795989129416227474,1384995674796455256157423369⟩,⟨2640818615728500902635630599,2640818615728967029083354801⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨2580855748237316030639065356,2580855748237630505559339405⟩,⟨2611075643043474680139282673,2611075643043789154581785673⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨3651142384491974417767785132,3651142384492176966742978524⟩,⟨2110568338259916102954729978,2110568338260118651425760099⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨4195822285531567316388938033,4195822285531690903973549707⟩,⟨1296542514248457568854761896,1296542514248581156044045678⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨3919571015224188430771862933,3919571015224253213987425946⟩,⟨501515857454417442557988279,501515857454482225510914055⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨2779368443021261701669487702,2779368443021291160258916832⟩,⟨30848293101646153922630839,30848293101675612372212975⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1003045219315589984123521527,1003045219315598314482605277⟩,⟨(-47442438511559279031591322),(-47442438511550948714598470)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1366386744418427383067293,1366386744418427383818113⟩,⟨561956078154658706425022,561956078154658707103911⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4350322559050006404736848,4350322559050006407132231⟩,⟨1381999092459502119627078,1381999092459502121772257⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨8053235678085337984068749,8053235678085337988510844⟩,⟨1210395210024283694002912,1210395210024283697935530⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨12795502114251625151363391,12795502114251625158534443⟩,⟨(-830011374782866631112252),(-830011374782866624828794)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨18457082420818559909245707,18457082420818559920108259⟩,⟨(-5812634351029932436558137),(-5812634351029932427074864)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨24023226475505921546242190,24023226475505921563306984⟩,⟨(-14896423728437605288722624),(-14896423728437605273448247)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨27262759856507236954996400,27262759856507236987277545⟩,⟨(-28998417182003396451528764),(-28998417182003396420988014)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨24924147942552870667277552,24924147942552870758435763⟩,⟨(-48028061250634000312329579),(-48028061250634000222489526)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨13680074917013886068505209,13680074917013886628533576⟩,⟨(-69892860374304892772900849),(-69892860374304892213416489)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-8072851738911994532645099),(-8072851738911989926640485)⟩,⟨(-90133099885147282890638443),(-90133099885147278284429876)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-38011366706769124785214063),(-38011366706769094865949227)⟩,⟨(-103028495440457273328603929),(-103028495440457243408776514)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-68684306520221239500173452),(-68684306520221108163009985)⟩,⟨(-104053744140864110295339291),(-104053744140863978957795301)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-89097771514862744254440356),(-89097771514862374779525445)⟩,⟨(-92152918689721495037157031),(-92152918689721125562409718)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-89435790582506174008854313),(-89435790582505516457000290)⟩,⟨(-70138080222699937810871402),(-70138080222699280259719348)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-66223257078039423161597963),(-66223257078038722969439349)⟩,⟨(-42862064921731992155874391),(-42862064921731291964511730)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-24404938300276292099983254),(-24404938300275985626180053)⟩,⟨(-14272870977012600289145049),(-14272870977012293815687729)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨15315353079062089849624824739868,15315353079062957387315493993158⟩,⟨(-215964772209562004224426022845145),(-215964772209561136687213804569992)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 15) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_15 (tableDensity false) (fullFactor true 0 15) density0_contains hk0_1_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨32812675123455327174330162101469,32812675123455327213262394977881⟩,⟨2096400153488396237315233627104,2096400153488396272772806224982⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_15 0 15 ha0_1_15_contains + def realAnswer : RBox := ⟨48128028202517417023954886841337,48128028202518284600577988971039⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_15 +namespace hm0_1_1_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨190376400906319720298431803151,190376400906329417946506239087⟩,⟨(-4160661720077486998307214493030),(-4160661720077477300634145453384)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1090289804480147620443196706707),(-1090289804480123789029602932106)⟩,⟨(-12895543462825189076073559143198),(-12895543462825165244734006815410)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-7651706286399168729110213357569),(-7651706286399143848633000136317)⟩,⟨(-21584533945595838882637631421552),(-21584533945595814002800492250559)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-22641874916633043833163889249413),(-22641874916633029021158358610173)⟩,⟨(-25804547976320724811662236912705),(-25804547976320710001554873040344)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-44165364977004915493561062111085),(-44165364977004907791624436678614)⟩,⟨(-15936580253946967261625794680147),(-15936580253946959561479668652561)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-58110212444237320758385483714240),(-58110212444237317875239728225867)⟩,⟨16886212452695125830090080648855,16886212452695128714150404449379⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-39633761020082435243675332900922),(-39633761020082434613253134083132)⟩,⟨64318682308299096234928775152539,64318682308299096869901378390655⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨22623449202797582667628088316553,22623449202797582891265892025000⟩,⟨89891122030419366493190164610610,89891122030419366717612990173493⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨96364806448411745576324809697919,96364806448411745702085977921183⟩,⟨54509103556023735476157421589237,54509103556023735595474437809756⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨121330494398248069235823801692348,121330494398248069348000178764814⟩,⟨(-32718658482927934756799546301824),(-32718658482927934647780339915016)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨73460518367436903786008823403987,73460518367436903877026403311412⟩,⟨(-110121467994904386088092404872789),(-110121467994904385991259332307867)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-6783648463202470941925761658487),(-6783648463202470873399550561322)⟩,⟨(-127064664011938499119389328434949),(-127064664011938499043634108404982)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-62499881730950120496500991529176),(-62499881730950120432843513399064)⟩,⟨(-90853477478305481638253112311181),(-90853477478305481574052680023512)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-72816329099824777036688801589841),(-72816329099824776992353934342781)⟩,⟨(-42549261831843569044705220999083),(-42549261831843569003649931920958)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-51442082826597762119343998522067),(-51442082826597762095608458708036)⟩,⟨(-11512311590175059786155027547630),(-11512311590175059765922337534378)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-17882717454807640848332765530967),(-17882717454807640841151368704856)⟩,⟨(-1087628222225522810877151155026),(-1087628222225522805114970572638)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨20480657763387331488292865989,20480657763387910943630603791⟩,⟨(-184013200877615359141766563256),(-184013200877614779694720470743)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨623186004609725129566449480,623186004611917376272077541⟩,⟨(-575316649129018990257497306474),(-575316649129016798040714593251)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-222442227293862283095842488998),(-222442227293856213504451324552)⟩,⟨(-1003893058555988618647586099904),(-1003893058555982549115573625527)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-828473569608342405019975520816),(-828473569608321698446307024330)⟩,⟨(-1369078256756308660711923554189),(-1369078256756287954203805563736)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1957661706640183876884132664180),(-1957661706640119124519852827369)⟩,⟨(-1343647600676145565892912373484),(-1343647600676080813560221952823)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-3453672512133101404388265889103),(-3453672512132940467128748171307)⟩,⟨(-327495410439550915243519711991),(-327495410439389977906392387732)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-4469609476435130805694109500888),(-4469609476434831922232512336370)⟩,⟨2278639675180245962539012664874,2278639675180544846252372331522⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-3382244369897073647731972969648),(-3382244369896444492409797870386)⟩,⟨6258600852984534085120235663028,6258600852985163240597293160919⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1236821183015253467963505826142,1236821183016092857757509130024⟩,⟨9686871823223498968714312701936,9686871823224338358323899639308⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨8698145683704335992928068085324,8698145683705060795906053178249⟩,⟨9413391103933061705886252487822,9413391103933786508324975509086⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨15411118850476896141976835463445,15411118850477581334047184036630⟩,⟨3710338169917580106356365009687,3710338169918265298218872052171⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨17317109076408633957112912016895,17317109076409054909750954799866⟩,⟨(-5238796078426580606426078588030),(-5238796078426159653442205226510)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨13638451361650173359841421065215,13638451361650357722365969923861⟩,⟨(-12500752599457430322119074177596),(-12500752599457245958876446295866)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨7477528642577710632566910974874,7477528642577809822215073614319⟩,⟨(-14412428153984907030344748241677),(-14412428153984807840242124706992)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2626397219500750945356675574227,2626397219500798411051858782721⟩,⟨(-10848373084742454901314743354258),(-10848373084742407435458781854371)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨454437514553075619498975248915,454437514553089061941944333871⟩,⟨(-3952547954938002988161432755944),(-3952547954937989545689291943732)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-7803840444772192764887104766),(-7803840444772192749617980848)⟩,⟨(-1112815410056886779395508067),(-1112815410056886764223782867)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-24860985380462420150505341404),(-24860985380462420100439961045)⟩,⟨(-1647729981290205151172391544),(-1647729981290205101376824788)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-45638583011014462809332616312),(-45638583011014462711121108361)⟩,⟨3669170831313442586812110659,3669170831313442684713653010⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-69996387709603177270526197092),(-69996387709603177098192084511)⟩,⟨21103089913659545940414485105,21103089913659546112704076977⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-92030213077007527229727235884),(-92030213077007526942596327317)⟩,⟨59170769335822977246187476346,59170769335822977534069540400⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-95657015639239190336309875275),(-95657015639239189879143123821)⟩,⟨125284314460928771162237925204,125284314460928771621678195156⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-52728323058728496724020519279),(-52728323058728495987547647792)⟩,⟨216056492861802115235156529528,216056492861802115975444814190⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨68493117316816785446752099544,68493117316816786785322580658⟩,⟨302857488270491354123499318761,302857488270491355464663538970⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨277691226777223682101459102948,277691226777223685739303669305⟩,⟨325727052289132679818547151875,325727052289132683455877971810⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨529850233400732420854533064669,529850233400732438573788100403⟩,⟨217347652577502692437058753626,217347652577502710153016667504⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨722121481947226478321800307554,722121481947226587906014438999⟩,⟨(-39219720160494169015015249364),(-39219720160494059433625927211)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨751249447369663082619240573975,751249447369663689447161102240⟩,⟨(-363958081875797421601412671555),(-363958081875796814774106835526)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨598856092638161202114937875141,598856092638163147727779173214⟩,⟨(-608934520576451927331813904226),(-608934520576449981717883764099)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨356217229165034996676002424506,356217229165038652462360095889⟩,⟨(-656164224774075848442948166442),(-656164224774072192655497072811)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨149108477548504481435386492708,149108477548508409022228427516⟩,⟨(-489752980774102364757198604843),(-489752980774098437170066259328)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨34269467886143996186280538753,34269467886145703679108563879⟩,⟨(-179164534976508026313163203286),(-179164534976506318820454554921)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨324406130285713552262262412,324406130285715488238770263⟩,⟨136158044529688885180986738,136158044529690821163577846⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1027673373486358944310352527,1027673373486363751137810470⟩,⟨366238277279036397072004627,366238277279041203914210823⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1887800776550236661722331234,1887800776550241988152992473⟩,⟨444483857612169946627577857,444483857612175273069518436⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨2981575946813744008047454689,2981575946813747810728435414⟩,⟨187671808028803687917328902,187671808028807490581167761⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4309316403874670681303464992,4309316403874672507193476091⟩,⟨(-699329037180347299275727262),(-699329037180345473474725248)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨5694881977118176343974249187,5694881977118176934052301352⟩,⟨(-2613959274211934343266260719),(-2613959274211933753415075737)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨6643050447237710963872066703,6643050447237711106834358060⟩,⟨(-5942512525060825118304741274),(-5942512525060824975775161402)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨6253962533969330060634010617,6253962533969330115146166957⟩,⟨(-10795264046063137568792407869),(-10795264046063137514731790051)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3397489530488286154557369424,3397489530488286201631450228⟩,⟨(-16623575446166182088966912962),(-16623575446166182042167131051)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2687068670751362811840223173),(-2687068670751362751325709588)⟩,⟨(-21968328951635855316935246795),(-21968328951635855256334742808)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-11507151179899411169671219407),(-11507151179899411089935551311)⟩,⟨(-24780795819959339601053847060),(-24780795819959339520736055944)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-20775661092155444057296564412),(-20775661092155443959384992345)⟩,⟨(-23507960950467459114315371347),(-23507960950467459015324323259)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-26972365924677074626958341620),(-26972365924677074518438778243)⟩,⟨(-18333740172805911419315240899),(-18333740172805911309501596789)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-27014851199055881940971579014),(-27014851199055881836270629835)⟩,⟨(-11386215563388269126777961879),(-11386215563388269021168607744)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-19926713787309086271568974151),(-19926713787309086194599751964)⟩,⟨(-5344111790876243937610119715),(-5344111790876243860152146886)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-7322310518465526958523432509),(-7322310518465526930192699492)⟩,⟨(-1425133272092340671592912931),(-1425133272092340643114374430)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-16471102840415381831083057),(-16471102840415034450110288)⟩,⟨(-266593317385222310268586),(-266593317384874930635769)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-51947740501169156234362927),(-51947740501167815036689691)⟩,⟨2000389890598690354555625,2000389890600031547746456⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-94215945890808960039451209),(-94215945890805380980642060)⟩,⟨13509648275456020400110572,13509648275459599450132123⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-144787278626876544192018405),(-144787278626865818361708258)⟩,⟨43245296083400840843072381,43245296083411566660451373⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-199375107328818960532736608),(-199375107328786759080917272)⟩,⟨104110267583114302065977903,104110267583146503501611295⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-244284206693003533886278481),(-244284206692916279468432944)⟩,⟨212324750216113075281807886,212324750216200329682190468⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-253511195328604624664535757),(-253511195328410354358931820)⟩,⟨382112789408198622555222039,382112789408392892847728446⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-189708490871426102256368538),(-189708490871098668771213823)⟩,⟨614742243716530487048138811,614742243716857920533733603⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-15046369150794363236098015),(-15046369150381627331876800)⟩,⟨885601843287496756168729243,885601843287909492097476783⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨284184538887740870244561636,284184538888123148765149046⟩,⟨1138061341311098387992119739,1138061341311480666569047345⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨667817391639832683299563283,667817391640090263364779590⟩,⟨1294708842762771518631147141,1294708842763029098786389590⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1031880151884372287867942410,1031880151884537962686967817⟩,⟨1289202464558068133434244962,1289202464558233808347434755⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1241300779701318389452105430,1241300779701419349858348957⟩,⟨1106254901572442126477718991,1106254901572543086958035444⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1192013713056932636547477423,1192013713056985502572192911⟩,⟨799828608716028515026462166,799828608716081381100193632⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨860190152203850202857631154,860190152203874224131914094⟩,⟨460070673739234125279420491,460070673739258146579743323⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨313239534448827140032514025,313239534448833930133074723⟩,⟨146653904816579953744793904,146653904816586743853098510⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨41384268300124417924131,41384268300124418353487⟩,⟨14751287318164039020813,14751287318164039389571⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨133062663526707562104337,133062663526707563470383⟩,⟨7272569458966135143652,7272569458966136304219⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨199701639426742459655154,199701639426742462163081⟩,⟨(-148126682173142584056425),(-148126682173142581957882)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨62914312582244721854978,62914312582244725851778⟩,⟨(-688864321480666255365984),(-688864321480666252081096)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-640564135210505916387704),(-640564135210505910293026)⟩,⟨(-2063105107375566083405307),(-2063105107375566078450574)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-2429297687817291001525688),(-2429297687817290991490299)⟩,⟨(-4869285476582189188277188),(-4869285476582189179809275)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-5971011185571254781812380),(-5971011185571254760660408)⟩,⟨(-9546384046244851713416719),(-9546384046244851693881245)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-12078747440610670888349303),(-12078747440610670819829480)⟩,⟨(-15965478267712908873289923),(-15965478267712908806033179)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-21416981319985083262071503),(-21416981319985082809062883)⟩,⟨(-23122906833611156367444234),(-23122906833611155914933205)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-33804696086268295129972258),(-33804696086268291367657467)⟩,⟨(-29076736207186315896938671),(-29076736207186312134139681)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-47490608760713407304495809),(-47490608760713382871173835)⟩,⟨(-31409798923373855079124901),(-31409798923373830644363885)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-59040787972374583699319065),(-59040787972374476447740401)⟩,⟨(-28450765476978920697919599),(-28450765476978813444198311)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-64125795449660084118895975),(-64125795449659782280601738)⟩,⟨(-20796442233308578070076347),(-20796442233308276229311725)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-58921730500176318738649936),(-58921730500175781300227212)⟩,⟨(-11593559602771886090348108),(-11593559602771348649672411)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-41873710107564827668118256),(-41873710107564255162469987)⟩,⟨(-4514587189720939406156732),(-4514587189720366898952475)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-15193663781973844691087288),(-15193663781973594055544676)⟩,⟨(-949124127056085093632535),(-949124127055834457547555)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-2526956750667135403293058481095),(-2526956750666419181710651105960)⟩,⟨(-48715905501835503306831122884515),(-48715905501834787085460330179656)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 15) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_15 (tableDensity true) (fullFactor true 0 15) density1_contains hk0_1_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-42908882853749274048112362663382),(-42908882853749273997200981209613)⟩,⟨(-2741446354561748972087515832669),(-2741446354561748925719920896982)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_15 0 15 ha0_1_15_contains + def realAnswer : RBox := ⟨(-45435839604416409451405521144477),(-45435839604415693178911532315573)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_15 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_6.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_6.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a96945a8bb0bbc1d2f19b14b7a1980e50b2a400 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_6.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_1_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-4607406904232488895954709903187),(-4607406904232483386158836349899)⟩,⟨12132225063884437968030169679875,12132225063884443477395698106900⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-8662102065290652598909497638804),(-8662102065290638148329582845034)⟩,⟨39297092035611116747506892561350,39297092035611131197063831002012⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨5064517052751607103498938780523,5064517052751624059183166106241⟩,⟨71242610485378351994798768990750,71242610485378368949766720647247⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨51534675085141993449883346588123,51534675085142005288165071955791⟩,⟨96219092927355450144931246659186,96219092927355461984407241208398⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨133399571373414267183880403747604,133399571373414272056844722712679⟩,⟨80004560865714900607474443797707,80004560865714905485246833675161⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨210015075198160867322334653853124,210015075198160869384834444814101⟩,⟨(-20616467801290750971151352521345),(-20616467801290748905833789582243)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨187357215945472103834776798818701,187357215945472104525078379262295⟩,⟨(-198392491920471503250482615637088),(-198392491920471502563390673685047)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-4491418670517650731677524193086),(-4491418670517650375581631654025)⟩,⟨(-334807827776526178377308018706641),(-334807827776526178026067194262937)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-280781982030854064790275106955137),(-280781982030854064514834222749231)⟩,⟨(-267440189125633107260416543140361),(-267440189125633106984576785947414)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-421436094747094710782764194182113),(-421436094747094710557413450369197)⟩,⟨12680272151627332408425257533501,12680272151627332637288222842028⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-303528829532028546011312253654274),(-303528829532028545824508229973129)⟩,⟨302201780186276011925362373009611,302201780186276012114380635580712⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-42344741005079431172331506672073),(-42344741005079431037869274931052)⟩,⟨401678497966816093904745906676983,401678497966816094040362928117310⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨160250851945342589941827290234135,160250851945342590052096067565605⟩,⟨310089541371190763419810210896594,310089541371190763529451944948442⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨215604845706183010524226065997138,215604845706183010597315045827535⟩,⟨159510301252705846152238173690232,159510301252705846223209376886380⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨159615747509371185087481427704796,159615747509371185125558120165165⟩,⟨53436547062378816712527502308981,53436547062378816748460544685997⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨56528352969893467158603020312010,56528352969893467169950551615092⟩,⟨9317988614181958013130594852467,9317988614181958023615662889960⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-216559264339758430690482107248),(-216559264339758069409387668158)⟩,⟨482811342418659383969984610559,482811342418659745238093760258⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-523484244688907767356006696409),(-523484244688906272438034646020)⟩,⟨1588880983402028000659360745180,1588880983402029495553388716281⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-350110659833815632092748762150),(-350110659833811253805078267494)⟩,⟨3064318879007447746835660957786,3064318879007452125141653988480⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨928243531611674697853336814568,928243531611686639708724389591⟩,⟨4895908267880172726190343846210,4895908267880184668214351966438⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨4177711749575587013774709928114,4177711749575615424762591691448⟩,⟨6399993363872758511602505878322,6399993363872786923060532276306⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨9877223193078107677384461888707,9877223193078196592318252610534⟩,⟨5671678315990645659376174577158,5671678315990734574749715925493⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨16560978244737556867876073214537,16560978244737772324756861541680⟩,⟨(-282364666172601944859158478969),(-282364666172386488130237414076)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨19242772153948810164249033966513,19242772153949123454453150542569⟩,⟨(-13303002154113718626435868100002),(-13303002154113405337443351411648)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨10886934599902434820862777466507,10886934599902927089846160986860⟩,⟨(-29840696538214397323226206546876),(-29840696538213905055143569592283)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-10936635713404826631354672663725),(-10936635713404296067737659270760)⟩,⟨(-39426807898029023493389731831793),(-39426807898028492928944552617156)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-37632665007698307437052801526841),(-37632665007697958804236994079239)⟩,⟨(-31752406465132186596725798411905),(-31752406465131837961574876356167)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-53827037518695266089199192263030),(-53827037518694999547763136732257)⟩,⟨(-8043158362406695589893174632045),(-8043158362406429047523705142418)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-51111747158421566115659667296800),(-51111747158421420432343174820609)⟩,⟨17619473412255813088481031133702,17619473412255958770965007460416⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-35072350205140189797848699246623),(-35072350205140129225805511024298)⟩,⟨30525635319179658820108194240040,30525635319179719390357074867378⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-17492911513310529231886018039137),(-17492911513310505219812146595067)⟩,⟨26323976408722437285638710924145,26323976408722461296303410520513⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-4865782277010377711557136141913),(-4865782277010370357796862990769)⟩,⟨10102974979480993106075968870404,10102974979481000459415074573845⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨10124653715819079487970092928,10124653715819079509708557546⟩,⟨7758550507554910975174538330,7758550507554910996668241481⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨34032431915658200790354572298,34032431915658200861239328406⟩,⟨21795526149356611965582711656,21795526149356612035231716181⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨68963827632408806101914422210,68963827632408806245000023225⟩,⟨29449097279877012525722829862,29449097279877012664894126791⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨121264157366765136085845785898,121264157366765136352194603261⟩,⟨19743282179527147909590764345,19743282179527148165969935204⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨190916609505533317315813496653,190916609505533317804444048426⟩,⟨(-28437608882242907549208611926),(-28437608882242907079541165112)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨259264474329015996178948815698,259264474329015997079539161767⟩,⟨(-146154351370625340469586344415),(-146154351370625339587130379433)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨272149859663013575934440122946,272149859663013577564093048950⟩,⟨(-360327663115552025703795937409),(-360327663115552024078717306451)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨135088103246515334387249248679,135088103246515337293312643613⟩,⟨(-656435515639793466699132938224),(-656435515639793463764681359113)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-247914553698488111739414264162),(-247914553698488106299927734566)⟩,⟨(-930732173569604544763938827023),(-930732173569604539250443285610)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-878658469847238909247205302097),(-878658469847238892926321598350)⟩,⟨(-988699401108548924069520766413),(-988699401108548907691340168313)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1577205151037721288562511558562),(-1577205151037721210472667121421)⟩,⟨(-655157816584670335054628244110),(-655157816584670256968866106188)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2031654846069107087711204631124),(-2031654846069106775012200678542)⟩,⟨42579741960815388013018778797,42579741960815700632556256174⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-2012837576171245372654560351739),(-2012837576171244570609614209296)⟩,⟨802552026842129404318824605881,802552026842130206231266322896⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1559233804606941785471515972214),(-1559233804606940043406600846332)⟩,⟨1219844213489403857226172506591,1219844213489405599194435926279⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-915962833349166034826522279479),(-915962833349163850672393513043)⟩,⟨1066055810333553889928277768891,1066055810333556074036484516739⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-291776850013635145167961248953),(-291776850013634118094458079189)⟩,⟨418356328393820962696858990254,418356328393821989758034826301⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-170324207373551140776793606),(-170324207373550432594513004)⟩,⟨(-271029904660406030213173637),(-271029904660405322039081195)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-589154198683316575870284957),(-589154198683314838345761570)⟩,⟨(-821778340230226931971730091),(-821778340230225194485682841)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1257683305348635807135779511),(-1257683305348633928155202688)⟩,⟨(-1373230035381005208582411440),(-1373230035381003329716922276)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-2384076359331808669496428960),(-2384076359331807379027427914)⟩,⟨(-1832401946148151179400595495),(-1832401946148149889215211284)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-4193953811886666301438015572),(-4193953811886665715974430559)⟩,⟨(-1931907208875387140243235634),(-1931907208875386555387170377)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-6825247177114910657891163722),(-6825247177114910459217222516)⟩,⟨(-1128729751747602709500113415),(-1128729751747602511794754768)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-10089680105193980385522254488),(-10089680105193980309985397969)⟩,⟨1423616073327384199016223319,1423616073327384273610731528⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-13136766181589821061128118195),(-13136766181589821018625730786)⟩,⟨6661345652345012002576367592,6661345652345012044564994636⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-14276179380769407258238510549),(-14276179380769407209572529760)⟩,⟨15001297593930259512211199121,15001297593930259561445009015⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-11429206956992633812499791908),(-11429206956992633743911971262)⟩,⟨25472665404886625168734138844,25472665404886625239655215912⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-3474946281487414289854119904),(-3474946281487414195283302918)⟩,⟨35279068580575348496029832862,35279068580575348594808500875⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨8140230896224612849819951072,8140230896224612974073468907⟩,⟨40684741275048444366041808345,40684741275048444494038134431⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨19065791304438616789913510613,19065791304438616933165827095⟩,⟨39159784275989401546085300719,39159784275989401691655810984⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨23991699238172637261503699857,23991699238172637399499574941⟩,⟨31096459992321511787244120135,31096459992321511926109484107⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨19817866022282588917028924386,19817866022282589018206770588⟩,⟨19266030902080495468010443941,19266030902080495569166114266⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨7650936635095811722835522758,7650936635095811760009446894⟩,⟨6419304020511964524711387321,6419304020511964561761328464⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1349247573776671694844344,1349247573776774575019974⟩,⟨12929167192517614043019082,12929167192517716921235602⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨6824869642282106990126690,6824869642282534553653386⟩,⟨39718892510205972971513694,39718892510206400529295163⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨21317309054695422202344990,21317309054696712902263661⟩,⟨68535998049814047214305660,68535998049815337905131874⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨52778201656648604832108497,52778201656652493918199978⟩,⟨97985204721791478445017879,97985204721795367519827280⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨110606215836392270164271133,110606215836403685576310743⟩,⟨121520100784084575077687631,121520100784095990478725401⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨202823583689224150206380086,202823583689254328456922038⟩,⟨124146731824569333862167567,124146731824599512106347389⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨329595130239816755406904029,329595130239882067648130688⟩,⟨80551453220648670959693452,80551453220713983206959980⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨473713922289732788139850320,473713922289839061287543890⟩,⟨(-40837880990879304410503979),(-40837880990773031232703349)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨593316717514276583376227282,593316717514404303494953642⟩,⟨(-263379934321313768352452090),(-263379934321186048164985924)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨627795018745297951766243211,627795018745411665513795964⟩,⟨(-578802690207397869144142460),(-578802690207284155279788746)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨526247119692291238410512497,526247119692390154050533590⟩,⟨(-928135694537674426105058194),(-928135694537575510346482923)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨290747023371953738534938076,290747023372024375581983958⟩,⟨(-1207725269794325422991805455),(-1207725269794254785854095606)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1397276093517507587564064,1397276093558616528178083⟩,⟨(-1308635994107972101636661352),(-1308635994107930992644278353)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-212653955578234546672982131),(-212653955578213744849648351)⟩,⟨(-1169172844545090166930441406),(-1169172844545069365091499504)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-250222235385272100285093120),(-250222235385262870944002644)⟩,⟨(-803151911312533191189032038),(-803151911312523961851778349)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-108386007971339332123440153),(-108386007971336755672082769)⟩,⟨(-284985703357102300280967970),(-284985703357099723833694172)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨110692888026560325379522,110692888026560325530602⟩,⟨(-315222424983861970460067),(-315222424983861970289628)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨258986432175000278023678,258986432175000278501470⟩,⟨(-1001730309163640932786351),(-1001730309163640932242087)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨167472350729869837355823,167472350729869838233468⟩,⟨(-1847159250239076014755116),(-1847159250239076013744239)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-380115991381406242827905),(-380115991381406241422316)⟩,⟨(-2916028376390992210899755),(-2916028376390992209265211)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1651420244046669091618129),(-1651420244046669089463856)⟩,⟨(-4162150377913219103629671),(-4162150377913219101128659)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-3931583556173747334560984),(-3931583556173747330710643)⟩,⟨(-5314781260384436321968613),(-5314781260384436317725532)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-7428639351594309292075802),(-7428639351594309284357146)⟩,⟨(-5793172594656501964912605),(-5793172594656501956828207)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-12070114942763012497050648),(-12070114942763012474435932)⟩,⟨(-4755021829447713969157850),(-4755021829447713946295040)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-17250847703727947778180254),(-17250847703727947639211914)⟩,⟨(-1353528444962805955202250),(-1353528444962805816173343)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-21763844218011232366780157),(-21763844218011231236322287)⟩,⟨4771492365515405486306483,4771492365515406616668733⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-24149300338721253620419641),(-24149300338721246374601275)⟩,⟨12909923107842193075066216,12909923107842200320752547⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-23416941403288953908836867),(-23416941403288922628631369)⟩,⟨20995346280607855309629792,20995346280607886589811257⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-19663689208607360499013502),(-19663689208607274216558760)⟩,⟨26073940786101003428897166,26073940786101089711517697⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-14046777096230059833002553),(-14046777096229909405884126)⟩,⟨25583356077596318441858885,25583356077596468869296501⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-8057974699588282515319835),(-8057974699588124331277064)⟩,⟨18705453768200112285055127,18705453768200270469410652⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-2572458389475020862440468),(-2572458389474948880582234)⟩,⟨6853178049696237209937522,6853178049696309191920635⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-7541205252910534460823692983180),(-7541205252910100368469727230775)⟩,⟨118441682137385200493861582523369,118441682137385634585931013522621⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 16) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_16 (tableDensity false) (fullFactor true 0 16) density0_contains hk0_1_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-19235897115693432574292300631496),(-19235897115693432547323442280629)⟩,⟨1240528106568646707178839770050,1240528106568646732033895945916⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_16 0 16 ha0_1_16_contains + def realAnswer : RBox := ⟨(-26777102368603967035116093614676),(-26777102368603532915793069511404)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_16 +namespace hm0_1_1_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1054839205201618390709686036677),(-1054839205201613889843493650243)⟩,⟨1952718374305158165396404113240,1952718374305162666364463862113⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-2417607946488868707778339354354),(-2417607946488856913239121682360)⟩,⟨6477467989666614349784763864138,6477467989666626144560531838840⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1045603865829121150741710276433),(-1045603865829107342772327054700)⟩,⟨12250495717566608067801173024670,12250495717566621875898597138259⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨5792601388016604943988763405475,5792601388016614525758721964859⟩,⟨17631297339390141594401543908140,17631297339390151175710747349982⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨19251290075055008510531922431171,19251290075055012365591431044200⟩,⟨16864099059150772406027664520083,16864099059150776259637726166582⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨33234440301222925576402256735041,33234440301222927105912031080314⟩,⟨1825389303605737628322846360138,1825389303605739157231344162686⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨31506215249560521936102107643412,31506215249560522331136232333250⟩,⟨(-27681178297526341178804440058309),(-27681178297526340781733172102727)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨419664961524649484245135434308,419664961524649606788098473346⟩,⟨(-51911474572407007957748271030027),(-51911474572407007833377956770660)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-46777922574759445108560762633878),(-46777922574759445029418965015531)⟩,⟨(-41446733877120749396175674099737),(-41446733877120749319735178640686)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-71072558881657263476480911407134),(-71072558881657263411414214600310)⟩,⟨6920886921942248313020592364242,6920886921942248375084969848033⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-49448998850575230200805267053151),(-49448998850575230144619594444828)⟩,⟨57194155802374612713876204846709,57194155802374612772455005403151⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2439618775246414553319680830209),(-2439618775246414513604707962491)⟩,⟨72899504434886866836569768135111,72899504434886866880791968227986⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨33016914949777824018698105060171,33016914949777824055596079833132⟩,⟨54078094092574327275927174772883,54078094092574327313519358714549⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨41170456723091679310193878586348,41170456723091679336161978985564⟩,⟨25681634539825480688351783978173,25681634539825480712578645795558⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨29542231761930277453279886768054,29542231761930277467154384344565⟩,⟨6961811669217982313179395143324,6961811669217982325066625606191⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨10297908286608153598947123872879,10297908286608153603125138631520⟩,⟨649784708511049909880680834937,649784708511049913242715111380⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-65521702959442166728788464603),(-65521702959441870470071399455)⟩,⟨50175635168932741376600413910,50175635168933037637263780621⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-184926733923335669927313141996),(-184926733923334442483144697486)⟩,⟨179025170814961926730691108044,179025170814963154178912930362⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-250355742781323072589022868307),(-250355742781319471190625667966)⟩,⟨389900845755285067792429925881,389900845755288669190675156676⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-164342594094857508522984328272),(-164342594094847669656858629356)⟩,⟨709925661004799072054982598146,709925661004808910902364504351⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨239008330732065177097940648341,239008330732088614692745862653⟩,⟨1069268167801386143228983213572,1069268167801409580765273857838⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1112529370220895118684645499532,1112529370220968564799075373627⟩,⟨1185476202508765228344409627813,1185476202508838674400099186601⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨2333343977570947198769539376334,2333343977571125354384494920745⟩,⟨523359099331095031084026148108,523359099331273186709520758807⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨3156536280564890535655838757367,3156536280565149704372743524272⟩,⟨(-1396121306779082444884848235844),(-1396121306778823276016724725907)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨2300041003754648889724745433605,2300041003755056114779355832727⟩,⟨(-4238628923377411811204781026371),(-4238628923377004586028438112478)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1004824055280872910394946737346),(-1004824055280434262159503786811)⟩,⟨(-6358516253859852735597821900545),(-6358516253859414087467396550137)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-5681756969055810490316232702817),(-5681756969055522606528376503313)⟩,⟨(-5753989792380478666074586444205),(-5753989792380190782613524671245)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-9108251693410424685342098644155),(-9108251693410204906288915923584)⟩,⟨(-2139014248849841636095288324826),(-2139014248849621857172888656665)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-9388169212641314256949611324775),(-9388169212641194349341341314596)⟩,⟨2340694080311310880007226035874,2340694080311430787755936513219⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-6990281432643566482655603608287),(-6990281432643516743248229849987)⟩,⟨4949222382212942501721445760818,4949222382212992241417297728274⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3809325141069246552764666888611),(-3809325141069226881719704998000)⟩,⟨4534483208310506130221384805459,4534483208310525801490484101057⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1138861207974353202313633408871),(-1138861207974347183532513007026)⟩,⟨1784725147817500775630689216661,1784725147817506794479067569804⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1028809595113385752762205630,1028809595113385759891841841⟩,⟨2689751880235035833636116607,2689751880235035840755712423⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨3932968299720343450005740121,3932968299720343473379275162⟩,⟨8245984252244105663100604367,8245984252244105686419189711⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨9546347623054592096387787495,9546347623054592142255219797⟩,⟨13958178300945180703706561117,13958178300945180749399630016⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨20040533799505121426807098127,20040533799505121507204617669⟩,⟨18520163279069773400373541289,18520163279069773480339095574⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨37244721136962862114203928814,37244721136962862250194854124⟩,⟨18056293774362194608194080686,18056293774362194743415816704⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨60368750623024262626626390631,60368750623024262859893684332⟩,⟨5137016773849369025972871431,5137016773849369258498464688⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨81747645011055235696447029191,81747645011055236087373044136⟩,⟨(-29817414219533761694202488606),(-29817414219533761303551408693)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨83067029320567474566847018533,83067029320567475237581252623⟩,⟨(-91824009105940391788410349966),(-91824009105940391116723221104)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨39140179873580741272851231367,39140179873580742782363539495⟩,⟨(-169593225984387210777744956739),(-169593225984387209266046832799)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-64215922148441930204641606367),(-64215922148441921661786976450)⟩,⟨(-228547042759841747228250036785),(-228547042759841738684140329364)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-206232775601164576524226844387),(-206232775601164519942015496703)⟩,⟨(-225069773464428846149464239957),(-225069773464428789567304017444)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-328522162653268402452735003476),(-328522162653268156881072815611)⟩,⟨(-142687568987480258431110152117),(-142687568987480012859998995933)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-371153414751543287717750272555),(-371153414751542644156380522190)⟩,⟨(-17704974291963706420017058151),(-17704974291963062859118786666)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-318379969013170310335010762999),(-318379969013168898332504217388)⟩,⟨80491898256352390026489271744,80491898256353802029135156034⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-203264191798618916221200404088),(-203264191798617139562648986621)⟩,⟨100792883168984998875975478723,100792883168986775534895490050⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-68213165648641478109345717594),(-68213165648640641658480285513)⟩,⟨43962010408054011766922114303,43962010408054848217977642963⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨8513316208421141195795288,8513316208421736109088557⟩,⟨(-106662065107384203349845579),(-106662065107383608435792724)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨7126831678692269808758930,7126831678693728333354707⟩,⟨(-332815931909382268607904255),(-332815931909380810079545905)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-57092802223075753648712274),(-57092802223074178949664350)⟩,⟨(-592854321812422641669719053),(-592854321812421066959046169)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-250282822201981052251604831),(-250282822201979974048907130)⟩,⟨(-891659565931838715510999371),(-891659565931837637279374031)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-667953901102876110963347503),(-667953901102875625360378809)⟩,⟨(-1195914640748435365026331889),(-1195914640748434879362014729)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1421216421014529839154659401),(-1421216421014529679007906943)⟩,⟨(-1399403002802010609396191800),(-1399403002802010449153568036)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2581044675074485655886257336),(-2581044675074485601690321499)⟩,⟨(-1285065296587691583581478837),(-1285065296587691529296381137)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-4072562519993773762110656470),(-4072562519993773740468843203)⟩,⟨(-525929747245413024286428109),(-525929747245413002605249274)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-5556449626770871351278671647),(-5556449626770871332152743304)⟩,⟨1204150214839422971414405558,1204150214839422990471197763⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-6415128678602428810787784564),(-6415128678602428785351212076)⟩,⟨3978896285060755645620105930,3978896285060755670821745412⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-5995313242098720716790734879),(-5995313242098720682136179938)⟩,⟨7340952921148563243356558743,7340952921148563277613734192⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-4093772868329231065913936344),(-4093772868329231020610973615)⟩,⟨10265646560714685987362866057,10265646560714686032336559575⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1339049208376513302271146381),(-1339049208376513249989493086)⟩,⟨11564091440828686897912779260,11564091440828686950020545403⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨993581726916690303674348837,993581726916690354300302749⟩,⟨10527409200773000254080294040,10527409200773000304672724761⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1773076718242246510856739445,1773076718242246548203368744⟩,⟨7282581842270349689006164784,7282581842270349726385062617⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨836677871334748262890898527,836677871334748276668927445⟩,⟨2588302100701386814335911520,2588302100701386828135481411⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨660112609660312381446199,660112609660396930817233⟩,⟨4219893116492831476600344,4219893116492916026367403⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨2849362648108837072012588,2849362648109188481678190⟩,⟨13213446045548182238697263,13213446045548533649574381⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨7859734465714545679652161,7859734465715606641530767⟩,⟨23612280210827548831494992,23612280210828609795406579⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨18268943928029874726878910,18268943928033072103859098⟩,⟨35394631572330450818897388,35394631572333648198659620⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨37526146548491618816954827,37526146548501005049625771⟩,⟨46700217118933463876704699,46700217118942850112551521⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨69572813722678648406572415,69572813722703462096539967⟩,⟨52709234582474963276722435,52709234582499776969196647⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨117091976004922684227699967,117091976004976374607398380⟩,⟨44896527661470687775705670,44896527661524378155326486⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨178218987358138769105815839,178218987358226088508620257⟩,⟨11776934332320486202779518,11776934332407805600095371⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨243148423332704999891917882,243148423332809857553085521⟩,⟨(-57077347152950550914428654),(-57077347152845693267178292)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨293757681772194517995061278,293757681772287776067908150⟩,⟨(-162947864278846257644060869),(-162947864278752999594544280)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨309349995423632283689223172,309349995423713300647532442⟩,⟨(-289086144662896420681322330),(-289086144662815403746167172)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨277866524682592126193585691,277866524682649904182643088⟩,⟨(-399248262524743061565530576),(-399248262524685283594450514)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨206266978468204629243804191,206266978468238211843814631⟩,⟨(-450494973049341867502916634),(-450494973049308284913600627)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨120898772965203496122472274,120898772965220471309232213⟩,⟨(-414418866163386604159054662),(-414418866163369628975961388)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨52283476089861925437473619,52283476089869451184904037⟩,⟨(-290565199505309119902787131),(-290565199505301594155186065)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨12750282494351240799237449,12750282494353340830172090⟩,⟨(-104241554196999195306664405),(-104241554196997095275188068)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨2840124574743672004605,2840124574743672085163⟩,⟨(-9520292867645193494574),(-9520292867645193398517)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-2650898613076429232),(-2650898613076175997)⟩,⟨(-30204139845866499688657),(-30204139845866499383086)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-36362127680303834969384),(-36362127680303834512669)⟩,⟨(-43398237381038117372739),(-43398237381038116812432)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-158637197224225734851370),(-158637197224225734140089)⟩,⟨(-4054150891415890454787),(-4054150891415889564503)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-465559463805114150569136),(-465559463805114149481028)⟩,⟨182778649895272285466969,182778649895272286835558⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1088976764670750581706973),(-1088976764670750579563524)⟩,⟨659971516178102886646661,659971516178102889121754⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-2120628956930891705759068),(-2120628956930891700821564)⟩,⟨1616354678868378673413050,1616354678868378678667986⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-3509836475343459940052706),(-3509836475343459923190187)⟩,⟨3276934964438357463148674,3276934964438357480218891⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-4986015893808030524877341),(-4986015893808030412671267)⟩,⟨5815427113005701215404769,5815427113005701327612953⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-6054117678320903583504623),(-6054117678320902660387588)⟩,⟨9161365976384941468858555,9161365976384942391722930⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-6137365597085448564939110),(-6137365597085442648047218)⟩,⟨12804891544138762495902735,12804891544138768412304123⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-4911485877488151566363310),(-4911485877488126023011182)⟩,⟨15787033369959775910237102,15787033369959801452929719⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2694460306099277179935563),(-2694460306099206693072149)⟩,⟨16963006291321371951692959,16963006291321442437830265⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-483375538190533273916475),(-483375538190410325620897)⟩,⟨15413049885708418973911497,15413049885708541921562999⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨655048584086679874779075,655048584086809212105363⟩,⟨10854435394088787898912295,10854435394088917235803928⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨423741761826060956721348,423741761826119823694036⟩,⟨3918689372875064713701214,3918689372875123580532534⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨13106228737228004369433704865,13106228737586257517147502457⟩,⟨26268521831457345857860173711319,26268521831457704110920822442404⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 16) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_16 (tableDensity true) (fullFactor true 0 16) density1_contains hk0_1_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨25154634689752950254192193751592,25154634689752950289459162364264⟩,⟨(-1622229062435922649582787006198),(-1622229062435922617080021237757)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_16 0 16 ha0_1_16_contains + def realAnswer : RBox := ⟨25167740918490178258561527456457,25167740918490536546976409866721⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_16 +namespace hm0_0_1_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨4725287004327339612161432151021,4725287004327342235570412819433⟩,⟨(-4475873791824333698630497706284),(-4475873791824331075453174209829)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨12381540224858989029184030281605,12381540224858994945335329436384⟩,⟨(-16002349287303364542938565150420),(-16002349287303358627638160272734)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨12537697696275387009523452389328,12537697696275394341425088697372⟩,⟨(-33840066697401282049594828598304),(-33840066697401274718883293122010)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-4937826330158052511140489359093),(-4937826330158046393676232208277)⟩,⟨(-55311726009934828762886862606411),(-55311726009934822646029540433582)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-48776504677647962422465193418525),(-48776504677647959497517267686657)⟩,⟨(-63156354824139260508139344023999),(-63156354824139257581960105353199)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-106126421972622889127715000940189),(-106126421972622888160592314785165)⟩,⟨(-25933910928390629600023008311255),(-25933910928390628630177164901788)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-123995982806225041189622723005147),(-123995982806225040782752171075089)⟩,⟨70397252572942934642690002077687,70397252572942935049531439083753⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-42180685541149360070065777593322),(-42180685541149359861186135820092)⟩,⟨171393130925969775220865757340664,171393130925969775426830488553060⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨116207781121923237148711856139747,116207781121923237317789911997360⟩,⟨170110414108451574700243721585136,170110414108451574868659245199538⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨223375482494403090250481620543059,223375482494403090381846072015414⟩,⟨30657148512354035846829296095558,30657148512354035979801224486414⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨182074288746654581795690456858514,182074288746654581904948671429644⟩,⟨(-140876330585456757264746130543970),(-140876330585456757154237609275813)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨41543774320902970409092654016454,41543774320902970485465240662221⟩,⟨(-213885349972041042028916402153287),(-213885349972041041951654925715181)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-77403032099581949016052720294978),(-77403032099581948954537764238983)⟩,⟨(-172142548880497359872697690407139),(-172142548880497359811371230050615)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-114206612296189067304515219101213),(-114206612296189067263634852411927)⟩,⟨(-89712394826155957589899772305165),(-89712394826155957550105720764542)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-86164088964111161145790980198540),(-86164088964111161124600640331164)⟩,⟨(-29929957011589666139500789893535),(-29929957011589666119461561165711)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-30630239919252814324680358096796),(-30630239919252814318402266965704)⟩,⟨(-5120448131121017591022732976486),(-5120448131121017585212566969797)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨209076048112939512696620507088,209076048112939648612034141079⟩,⟨(-74602145064209183105649385487),(-74602145064209047201837914906)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨633667897550603835504195322965,633667897550604351466733708256⟩,⟨(-307671635209523327147867034918),(-307671635209522811228254644634)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1026830610482588752267846056074,1026830610482590170821435659729⟩,⟨(-810512836977840107584951153044),(-810512836977838689119334485419)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1178130335159869774916456923523,1178130335159874758766251802382⟩,⟨(-1781567341012993743567900985733),(-1781567341012988759808449556041)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨565060293149165840572156882341,565060293149181673014632521052⟩,⟨(-3271198870443021218095561876065),(-3271198870443005385664497766517)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1613489621857718352977050256636),(-1613489621857680052868338998839)⟩,⟨(-4757966535375365336658958374423),(-4757966535375327036346724731179)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-5800973315708515535251085762462),(-5800973315708433191220246628961)⟩,⟨(-4644110131077621628616895448511),(-4644110131077539284206417394353)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-10666704341097433899833923731318),(-10666704341097259552335340584427)⟩,⟨(-577316858640280556720515473252),(-577316858640106209215989621196)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-12211634096261372461765645608747),(-12211634096261168404956496578699)⟩,⟨8296389721695079716532062008194,8296389721695283772641049856392⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-6059445305397138441106900380510),(-6059445305396896228665067681867)⟩,⟨18366938888804314563968953086251,18366938888804556775883381308795⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨7310833345682018579803181231184,7310833345682220073068226147532⟩,⟨22480027612242627023098091255267,22480027612242828516838639564135⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨20714298007822473665222375879988,20714298007822580657697699276759⟩,⟨16505974969083299237840502004368,16505974969083406231527875877722⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨26244538135150253825819287604653,26244538135150324336786711937921⟩,⟨4386703170873746750332527751536,4386703170873817261819367817966⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨22420834761830185651202734010173,22420834761830221580634874765391⟩,⟨(-5488488623788175606957639211401),(-5488488623788139677687726185055)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨13672208630911445848891623094977,13672208630911460552630641238076⟩,⟨(-7884607072287070327587646882848),(-7884607072287055624230126847915)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨4407409206885608145531357399412,4407409206885611957012491249073⟩,⟨(-3480732901415571476154129170371),(-3480732901415567664856447066314)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨641903043300317017674407664,641903043300317026977215957⟩,⟨(-4338597432135021769997164014),(-4338597432135021760276768079)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨813875433144963218632609617,813875433144963248878920062⟩,⟨(-13923086060784106397253438734),(-13923086060784106365543112646)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3019075748472652699909829083),(-3019075748472652637714099889)⟩,⟨(-25891222977874623202727931683),(-25891222977874623137899935201)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-15634106864473594820374505032),(-15634106864473594699555429636)⟩,⟨(-40229198786257609796769531827),(-40229198786257609672804368901)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-44063821561887076509521446961),(-44063821561887076278277519467)⟩,⟨(-52745048367864675638383414028),(-52745048367864675404924099080)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-95000402500303826427069397900),(-95000402500303825989106686700)⟩,⟨(-50688202028015943346042014960),(-50688202028015942910042814663)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-166029358113903934854724032213),(-166029358113903934041282515753)⟩,⟨(-9580391536500572496028445574),(-9580391536500571694040678280)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-230704180619838665649791566464),(-230704180619838664160411013894)⟩,⟨100305621265550342301151284508,100305621265550343771654261624⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-229627276702551416819300741179),(-229627276702551413930376944487)⟩,⟨288406662675570556006975558406,288406662675570558887817356022⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-92913305527704475157572971212),(-92913305527704467658382769485)⟩,⟨507631540813744026971165522367,507631540813744034486054797310⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨196530356027034523769025667045,196530356027034550469562764722⟩,⟨649429637125568311021790001906,649429637125568337767019721187⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨547829229964726257494064829848,547829229964726387429552926415⟩,⟨610991310948476778911130180321,610991310948476908882764434795⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨794332577613883021735832079525,794332577613883454474986206504⟩,⟨395461820759431963106573929359,395461820759432395854354388828⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨808852958770675222740523134190,808852958770676061917741644964⟩,⟨132097485344905136024859111145,132097485344905975188800994590⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨585633705069945654620395004406,585633705069946572017241447510⟩,⟨(-27005625518025600303511876197),(-27005625518024682925486776753)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨211089637660034595500362874683,211089637660034997078417489032⟩,⟨(-32437509905386790927574354255),(-32437509905386389357910586951)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-58465667824889280872334705),(-58465667824889096355656631)⟩,⟨70551909068712494673230371,70551909068712679199144128⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-170575321205073947279547682),(-170575321205073501960398953)⟩,⟨235006476028942074582875298,235006476028942519934626585⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-258993173106224718197655537),(-258993173106224253541830051)⟩,⟨471824875984189529499038109,471824875984189994226654288⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-274936544021172703283504779),(-274936544021172396502546385)⟩,⟨833159181619876466863457400,833159181619876773780283194⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-113233732265038542777976969),(-113233732265038369717818731)⟩,⟨1358965333718718751147744002,1358965333718718924380696617⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨409673578463598148506516148,409673578463598221809692514⟩,⟨2031693843582191154287742832,2031693843582191227751827335⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1539575179433665201493979872,1539575179433665227690335184⟩,⟨2693436499515267971707212609,2693436499515267997957605342⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨3475833349985837810985326414,3475833349985837826389192822⟩,⟨2956178917728825738294710293,2956178917728825753482148130⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨6145054832787035048882488200,6145054832787035068132011221⟩,⟨2212142174027738829505879894,2212142174027738848062379509⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨8962233313090305316713241486,8962233313090305345707016756⟩,⟨(-105429172966848687319733849),(-105429172966848659365585781)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨10860315319089179816188010975,10860315319089179858380768170⟩,⟨(-4002438561918281139692322682),(-4002438561918281098268048764)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨10824761211773701882831489131,10824761211773701938345170562⟩,⟨(-8489283606941074933501314670),(-8489283606941074878210373281)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨8691148416147251040135779916,8691148416147251104156212072⟩,⟨(-11771438346324227047402351935),(-11771438346324226982961634156)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨5444860294932222907600823379,5444860294932222969421109042⟩,⟨(-12170694062718370322036814615),(-12170694062718370259389706384)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2524775168414773618559134399,2524775168414773663962670235⟩,⟨(-9107303363775842270728132723),(-9107303363775842224538094067)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨658128672361969403917790134,658128672361969420620473355⟩,⟨(-3363818745644573536453161728),(-3363818745644573519431208222)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨3052743247758223267153019,3052743247758251892909806⟩,⟨(-862432993066096405688396),(-862432993066067779567821)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨9284272814362827039989028,9284272814362945176541909⟩,⟨(-3326730727002742517028993),(-3326730727002624379439145)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨15662258940715196556739136,15662258940715548672050104⟩,⟨(-8163299340681425190617811),(-8163299340681073073779480)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨21462800653744492337529102,21462800653745535456942477⟩,⟨(-17368242290661032762773590),(-17368242290659989641748278)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨24488774536382588931325834,24488774536385587885559454⟩,⟨(-33121280099388603573240973),(-33121280099385604618046968)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨20257838232242627888645585,20257838232250355872503136⟩,⟨(-56854756145867505528803638),(-56854756145859777546096623)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1747914179796782605285876,1747914179812959588674225⟩,⟨(-87309570977642535944269999),(-87309570977626358966511838)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-39005898000080202950250090),(-39005898000055079777315693)⟩,⟨(-117946947704784937321484871),(-117946947704759814162027822)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-106352136679994263078456624),(-106352136679964887124179355)⟩,⟨(-135516240379816174539229160),(-135516240379786798609006637)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-194472998261958705449070143),(-194472998261924112828563423)⟩,⟨(-123051489985632689813889436),(-123051489985598097218159924)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-283445063576273887094201779),(-283445063576242908316532437)⟩,⟨(-69466770637550162656280650),(-69466770637519183896761798)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-343925613660684500628404639),(-343925613660663481870474729)⟩,⟨17784982617573151048887093,17784982617594169800139628⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-350888422486919389371398604),(-350888422486907676580571242)⟩,⟨107613633262068016938619617,107613633262079729735403343⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-297234668820178982991698020),(-297234668820173271661187410)⟩,⟨157437695718978147510900438,157437695718983858855728784⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-195696811006941008478223650),(-195696811006938545514866507)⟩,⟨138279203544175554220649379,138279203544178017198254949⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-67774471021842581793480299),(-67774471021841905019870026)⟩,⟨54760872752933118953446788,54760872752933795732954739⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-68231867530875170150773),(-68231867530875170114411)⟩,⟨(-20007065207018439716898),(-20007065207018439685306)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-216406189533535283927357),(-216406189533535283811171)⟩,⟨(-43507751467731305927050),(-43507751467731305827102)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-397371535656996163549250),(-397371535656996163333174)⟩,⟨(-12580083242080952789265),(-12580083242080952605365)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-622785409517812642868520),(-622785409517812642518698)⟩,⟨122668923870406903345160,122668923870406903640252⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-877984584901509573379532),(-877984584901509572816839)⟩,⟨424503262555358554783088,424503262555358555270061⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1095190896385791574468943),(-1095190896385791573480323)⟩,⟨958182178961885100104558,958182178961885101013520⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1132579163417057753652114),(-1132579163417057751758959)⟩,⟨1766681523584690133585256,1766681523584690135408187⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-786010339155807695280993),(-786010339155807689929742)⟩,⟨2819838723644841763894835,2819838723644841769206635⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨145225217670802874611876,145225217670802906680932⟩,⟨3954303906464351766549272,3954303906464351798620965⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1733255450670162606256341,1733255450670162863091807⟩,⟨4863511687543512906788564,4863511687543513163656032⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨3778094071215877788759499,3778094071215879406002462⟩,⟨5198758214510880994830500,5198758214510882612101327⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨5747672560550794691174733,5747672560550801513968411⟩,⟨4766589020577546567698900,4766589020577553390480235⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6909295923730005217737575,6909295923730023567933829⟩,⟨3685696935109831098849340,3685696935109849448976499⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨6651867014707482504116626,6651867014707518492295963⟩,⟨2346910980104830275696768,2346910980104866263777297⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨4808559866275303091977934,4808559866275346309176487⟩,⟨1172066013705963229818273,1172066013706006446935076⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1752028366219499510407395,1752028366219519609877079⟩,⟨335116001292787500063880,335116001292807599502191⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3796788992603585668035189745026,3796788992603790277204464071703⟩,⟨(-61413485406283218566519354036889),(-61413485406283013957524679561108)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 17) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_17 (tableDensity false) (fullFactor true 0 17) density0_contains hk0_1_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨11159582465256544360213244431198,11159582465256544377840203062509⟩,⟨(-1704498146833345377963795072825),(-1704498146833345361524991126406)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_17 0 17 ha0_1_17_contains + def realAnswer : RBox := ⟨14956371457860130028248334176224,14956371457860334655044767134212⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_17 +namespace hm0_1_1_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨902048941391294594004027668309,902048941391296734668986384667⟩,⟨(-652132885001323384402967495993),(-652132885001321243679000744395)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨2490865644670597099751360568007,2490865644670601918592220757870⟩,⟨(-2425070846542218494600098558910),(-2425070846542213675546789584503)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨3037969621159671314935449248085,3037969621159677269929085656685⟩,⟨(-5419098867130074886833167950288),(-5419098867130068931547850472804)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨804517432080978814521032809485,804517432080983751088389844321⟩,⟨(-9407632909782464226140819723966),(-9407632909782459289463837918797)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-6043430023966143287890774496167),(-6043430023966140982104747216073)⟩,⟨(-11655076513285518211832344787770),(-11655076513285515906529840034349)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-15918671668394526428105637675345),(-15918671668394525736950110111179)⟩,⟨(-6589559850193432817456488882067),(-6589559850193432127132062679835)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-19975452378503933520761380903271),(-19975452378503933296511352925021)⟩,⟨8998492723762769455771029031736,8998492723762769680479633573076⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-7103708825694182123873354520892),(-7103708825694182058386925748977)⟩,⟨26420900327116341588553482565581,26420900327116341655536159545308⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨19707867406057137459253882242022,19707867406057137505428374602056⟩,⟨26717210690745141865042394774868,26717210690745141910470801834652⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨38093471714082595564317952043107,38093471714082595600515467398210⟩,⟨2640795042071248642969813041131,2640795042071248677097251451323⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨30191778155610841738226193034276,30191778155610841770501629012180⟩,⟨(-27200195590935138475271022559425),(-27200195590935138442232275785120)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨4719284195880490941480732177345,4719284195880490963527035861146⟩,⟨(-39063446695507024203454961079578),(-39063446695507024178887517251072)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16235935896782933329065502022038),(-16235935896782933308967278585216)⟩,⟨(-30169683611405870563289951203312),(-30169683611405870542610136553484)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-21882283071478147951685885601778),(-21882283071478147937378786456873)⟩,⟨(-14544840399268641367413772067321),(-14544840399268641353969626544280)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-15965200072320085977404940514853),(-15965200072320085969773012353451)⟩,⟨(-3952723599610874803596318435712),(-3952723599610874797025079415422)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-5581264396410060549853653268303),(-5581264396410060547566096811554)⟩,⟨(-364891838268383502467749532055),(-364891838268383500621739457254)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨34217108926125900269145087365,34217108926126011456786573570⟩,⟨5272789293449471007716946923,5272789293449582196792196404⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨108323134119486426717152551914,108323134119486849357349978663⟩,⟨3395556738376203084735441882,3395556738376625730320966190⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨192154238409470299132059472892,192154238409471463835904874965⟩,⟨(-41188688236314117351437350623),(-41188688236312952636286483174)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨262644936077592236723574895938,262644936077596340399685879012⟩,⟨(-168970449319348087011183104891),(-168970449319343983322906563232)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨240303063373671803831245148263,240303063373684863590479942766⟩,⟨(-410689622846272207559202237592),(-410689622846259147796457300930)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-22336949435914975725407132070),(-22336949435883346710048512786)⟩,⟨(-716680750659633609983704388810),(-716680750659601980991998828794)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-656120924269405826631401428075),(-656120924269337750721562675018)⟩,⟨(-848653353061277216209263429958),(-848653353061209140348391401573)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1529879321482560063123166818605),(-1529879321482415840021854804366)⟩,⟨(-378247732565146772222431631670),(-378247732565002549126132292026)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2018509369309914911436683791139),(-2018509369309746130874955441276)⟩,⟨973961993235679480552754754912,973961993235848261203163742018⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1275020539370202798423545455314),(-1275020539370002580089795747146)⟩,⟨2762848291756059749746336445709,2762848291756259968152013849752⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨861277830466711595745811528298,861277830466877968917295854221⟩,⟨3785531705214683604775641991977,3785531705214849977880728897845⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨3316026295236886476325266216517,3316026295236974657569505071688⟩,⟨3120526520313990083068734897262,3120526520314078264135341815343⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨4610484807782257722671816033770,4610484807782315730727586627408⟩,⟨1192861379752972216202327216883,1192861379753030224183144942152⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨4210605514655131044502410533332,4210605514655160539722722987761⟩,⟨(-593319253814664108798313645542),(-593319253814634613545538193568)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2711144133200370760400033436434,2711144133200382802298987893683⟩,⟨(-1181321170499334267496184195999),(-1181321170499322225530472216009)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨904328596244666572811347843999,904328596244669688673607406709⟩,⟨(-553599466124925968592519612702),(-553599466124922852698957143243)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨636759497321328889261561735,636759497321328892306360890⟩,⟨(-758283862680482551715713714),(-758283862680482548651814420)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1817834519928047388660209326,1817834519928047398638875996⟩,⟨(-2576024041439062600020018753),(-2576024041439062589972065128)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨2563688409321454625440020382,2563688409321454645466367431⟩,⟨(-5289761395573108017880543991),(-5289761395573107997731745792)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨2035572715312801122368887062,2035572715312801159311811073⟩,⟨(-9367362846496740279834686028),(-9367362846496740242749093387)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1421505409308983907272366660),(-1421505409308983841817876587)⟩,⟨(-14668500344437809890662535872),(-14668500344437809825107099697)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-10167265671714455258217601753),(-10167265671714455146055000822)⟩,⟨(-19416665465183624042392847931),(-19416665465183623930283400126)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-25856613671417205142213004243),(-25856613671417204956050333445)⟩,⟨(-18925701427142119041040478769),(-18925701427142118855315647330)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-46124468588153971039255531745),(-46124468588153970718254004181)⟩,⟨(-5668185881131730259666080061),(-5668185881131729939390600855)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-61055456924966506478019863468),(-61055456924966505703140580616)⟩,⟨26629980254278849978947896741,26629980254278850753518332910⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-54834981929764350994216097170),(-54834981929764347486406991685)⟩,⟨74638707110640278251663761926,74638707110640281759720179068⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-17101244345999385781579554115),(-17101244345999367941993319638)⟩,⟨120063840316246807956472905158,120063840316246825796540462010⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨42771679078331724459041426434,42771679078331825096262492440⟩,⟨138167380523769806971815769401,138167380523769907609233053246⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨95877702704162830760444441686,95877702704163177616459058628⟩,⟨118137987604963702431621759155,118137987604964049287493352193⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨113850668653995741429761738661,113850668653996420560424859197⟩,⟨74292293430538605305216404939,74292293430539284435656167407⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨88746767840774821083557174594,88746767840775566049031453009⟩,⟨32855442381368282710745998023,32855442381369027676141888484⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨33031042604687910467236374073,33031042604688236960280237818⟩,⟨7972520787255303619309391841,7972520787255630112365268606⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-29764523008419853370603346),(-29764523008419698371716642)⟩,⟨7223714258792723969670309,7223714258792878967611026⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-91344103267573872684597167),(-91344103267573498889401426)⟩,⟨28208678932199335865865374,28208678932199709657708274⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-156957468351413249486331391),(-156957468351412860113002483)⟩,⟨70707559807992101740207717,70707559807992491106156891⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-221448774512615402685462027),(-221448774512615146449318981)⟩,⟨154834968699419371404226207,154834968699419627626477878⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-264570365667219277218570984),(-264570365667219133716895787)⟩,⟨306002034481623645848275085,306002034481623789332628566⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-240811597343751552435484829),(-240811597343751493163573591)⟩,⟨546851512114080017610497300,546851512114080076867081906⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-72652857890575798514341635),(-72652857890575779859718927)⟩,⟨874815912455586756832092044,874815912455586775483106197⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨337187541339844727104336960,337187541339844734527535345⟩,⟨1226579822968964815767016120,1226579822968964823213702024⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1054150504891290388586009512,1054150504891290395648145556⟩,⟨1450417413816495722726245868,1450417413816495729857108098⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2024204759879443645122345934,2024204759879443655240478994⟩,⟨1332339590372287922852100380,1332339590372287933067899555⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3010489839797179578338849608,3010489839797179593179779462⟩,⟨716204900888252020646728036,716204900888252035550940020⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3650010849599898650873909883,3650010849599898670638353643⟩,⟨(-322557239522429773810270534),(-322557239522429754039872803)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨3651271585812291359961889478,3651271585812291383104194959⟩,⟨(-1401312879222446610043597896),(-1401312879222446586953231201)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2988578887073512026615586846,2988578887073512049314470632⟩,⟨(-1988506161018509439803087084),(-1988506161018509417189088647)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1893195082643152221576231922,1893195082643152238465712292⟩,⟨(-1727516204193495363457682760),(-1727516204193495346644565183)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨638578612051350326972201036,638578612051350333231848614⟩,⟨(-680992643614417484530471059),(-680992643614417478301105278)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨987229107650485986964195,987229107650509512761558⟩,⟨(-334323989211203031381241),(-334323989211179505666396)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨3064165460787358379856795,3064165460787455476316063⟩,⟨(-1246277602321443434362761),(-1246277602321346338152069)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨5373638545538915869361438,5373638545539205311934197⟩,⟨(-2937362802366916031928090),(-2937362802366626589757989)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨7789928070583271742827498,7789928070584129336078244⟩,⟨(-6080003243258672158143338),(-6080003243257814565396521)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨9654629143989241142632111,9654629143991707010059074⟩,⟨(-11504245601995774078262837),(-11504245601993308211262752)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨9464609709277838657548495,9464609709284192895393457⟩,⟨(-20030894380347454808800102),(-20030894380341100570976286)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4711095770410497837404730,4711095770423796244426387⟩,⟨(-31931862683759209497943035),(-31931862683745911089951660)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-7775542906818500191822072),(-7775542906797857678449920)⟩,⟨(-46016495114118643253948109),(-46016495114098000737808336)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-30500531887896176003754445),(-30500531887872058716853179)⟩,⟨(-58849862921687872077892771),(-58849862921663754785906763)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-62914747231691357996201063),(-62914747231662988904992538)⟩,⟨(-65113988531379211653299273),(-65113988531350842556900970)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-99106722978554611029916911),(-99106722978529237706795748)⟩,⟨(-59931018421365079709524373),(-59931018421339706382546399)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-128002822870433769058744082),(-128002822870416576602972217)⟩,⟨(-42447586908486606451958855),(-42447586908469413994538316)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-137773062625589508680580500),(-137773062625579940323713709)⟩,⟨(-18124445270699482171380251),(-18124445270689913815280542)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-122153466683524301146630073),(-122153466683519640506658824)⟩,⟨2845778028861431255054441,2845778028866091892689688⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-83329230526006662682100279),(-83329230526004654393278216)⟩,⟨11324667160299409759255526,11324667160301418045704227⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-29445955110906516612104905),(-29445955110905965003107624)⟩,⟨5799127007452364007816678,5799127007452915615839832⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2055098689488863083185),(-2055098689488863063007)⟩,⟨(-497320191326209374140),(-497320191326209357634)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-6433514971199849521485),(-6433514971199849457345)⟩,⟨352769955427482682946,352769955427482734726⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-8823383812064222898504),(-8823383812064222781126)⟩,⟨8329818270824563341358,8329818270824563434386⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1369664486059761224208,1369664486059761409922⟩,⟨34235828151161846280656,34235828151161846424499⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨47129075526192725764022,47129075526192726067191⟩,⟨98269601441710772279913,98269601441710772523398⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨164530131296446976658580,164530131296446977230218⟩,⟨227105744494968315992629,227105744494968316499939⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨402294924064659329936787,402294924064659331155318⟩,⟨437399696815412939590804,437399696815412940753470⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨817604791244776283870501,817604791244776287832945⟩,⟨711709447059862417690619,711709447059862421627108⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1452320908019648436000830,1452320908019648461814127⟩,⟨980458394382086282984117,980458394382086308823623⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2283445449523677050924978,2283445449523677260488177⟩,⟨1124309152585279052869470,1124309152585279262520500⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨3174565337329859229673700,3174565337329860550008995⟩,⟨1015281349204513188699804,1015281349204514509178051⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨3878999179130689526786354,3878999179130695097800459⟩,⟨602798449644083430038563,602798449644089001233111⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨4118607953569291807883049,4118607953569306798120538⟩,⟨5921346034826663595656,5921346034841654024814⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨3694716189315961499286768,3694716189315990913178356⟩,⟨(-488993017851529083821829),(-488993017851499669789048)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2574132397357188266112960,2574132397357223602031582⟩,⟨(-597160033124526036164343),(-597160033124490700171561)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨923661970231408645219204,923661970231425082562948⟩,⟨(-263421944203466997256431),(-263421944203450559891016)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨562300531457080876082621879298,562300531457249659676281677688⟩,⟨(-13199814464771159881659573872793),(-13199814464770991098078353933027)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 17) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_17 (tableDensity true) (fullFactor true 0 17) density1_contains hk0_1_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-14593300146873942647944880927896),(-14593300146873942624894242717720)⟩,⟨2228959115089759318917296088377,2228959115089759340414193556771⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_17 0 17 ha0_1_17_contains + def realAnswer : RBox := ⟨(-14030999615416861771862359048598),(-14030999615416692965217861040032)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_17 +namespace hm0_0_1_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2937095393325332615767225093555),(-2937095393325331124044785034128)⟩,⟨936764289203055545471706421725,936764289203057037171504042011⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-8563038265419823355591920061647),(-8563038265419819779764413026024)⟩,⟨4357547711861713768608543503205,4357547711861717344282467065383⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-12118260428239731390249433295440),(-12118260428239727918606398174594)⟩,⟨12235479212116021049242651764124,12235479212116024520321913675685⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-8231005934197999928332521413462),(-8231005934197997407696161483953)⟩,⟨25380021307311450206831467167163,25380021307311452726644482107916⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨10859936143358967097490279002733,10859936143358968608855416117673⟩,⟨37103345061354494284227427467259,37103345061354495795464092122898⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨44760150725407285477100395328080,44760150725407285984879612035498⟩,⟨29142198941604755701159584235872,29142198941604756210204193120280⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨68678763628183144086492571052036,68678763628183144302335305289129⟩,⟨(-15270816898209420011128740358432),(-15270816898209419794596247657572)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨41811493554508440945526139604406,41811493554508441066033676305931⟩,⟨(-77274863339319181007404791692838),(-77274863339319180888054639047264)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-39194331411992905277583290502884),(-39194331411992905180641687562381)⟩,⟨(-95634022815009035121269814665499),(-95634022815009035025031798886802)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-108674991503683532436703680539713),(-108674991503683532362980701700685)⟩,⟨(-33953425670816084336386487315264),(-33953425670816084262096755477674)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-100584863883187183776752475550900),(-100584863883187183716689574816023)⟩,⟨59456077688633855081326171556725,59456077688633855142035603720930⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-30528914662671517635856182940241),(-30528914662671517594537967484471)⟩,⟨106712112639099292710956074263918,106712112639099292752837084790153⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨34686181492991408775201768055571,34686181492991408807584703852062⟩,⟨89925986721538278446450481453458,89925986721538278478815854002708⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨57055446317423837202604577746859,57055446317423837224185690593635⟩,⟨47547017941287669361258088873676,47547017941287669382315614098532⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨43922290475017821926469153778242,43922290475017821937602297266579⟩,⟨15813610202774156650763502577196,15813610202774156661313079819605⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨15675010453386045539541409480426,15675010453386045542820740901002⟩,⟨2656972881631617831852774199039,2656972881631617834892344629919⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-78665760562452910011127421117),(-78665760562452850351898297717)⟩,⟨(-39336644437314986795785229769),(-39336644437314927134020902085)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-263291120506059901506046750781),(-263291120506059651329946651939)⟩,⟨(-95659702074694896635311970153),(-95659702074694646454323966785)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-520217337900251024713635727546),(-520217337900250278133960659423)⟩,⟨(-63047649439880116071487051154),(-63047649439879369494549735452)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-844715003899605591812578641138),(-844715003899603536971251542102)⟩,⟨184397676230318271980172481947,184397676230320326790030466373⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1083689294423299728567868610170),(-1083689294423294605918918530612)⟩,⟨824574377677101954641683212589,824574377677107077206526830747⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-806509185551829216871485770089),(-806509185551812099641971184734)⟩,⟨1931312780308137986016246970116,1931312780308155103188840708855⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨636787836838618533282923693215,636787836838657998242473372627⟩,⟨3083340830020955748457256190914,3083340830020995213498977951495⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨3484718114031701802027408147086,3484718114031764527703906132251⟩,⟨3012925822026137342080446241617,3012925822026200067992613502960⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨6477413415378310082452120504347,6477413415378416603904306914417⟩,⟨177203974656833358170012510201,177203974656939879630155903249⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨6804783323259519386875173643917,6804783323259616261292475756935⟩,⟨(-5313713824522713065805660675440),(-5313713824522616191787162674920)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2558109522831906631771709789664,2558109522831996227122483160152⟩,⟨(-10407792971897743500136056118517),(-10407792971897653905027949628684)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-4442399528137565412441180680523),(-4442399528137506290821063177984)⟩,⟨(-11333526171330831569188385143991),(-11333526171330772447309995998365)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-9746599622065058382162442993068),(-9746599622065031416408691767898)⟩,⟨(-7613845830293950062868796111818),(-7613845830293923096560345675692)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-10522438998998381514083734044114),(-10522438998998365664201931279372)⟩,⟨(-2530773494640447851704153027636),(-2530773494640432001553201792152)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-7429050521177475621221716458756),(-7429050521177468138350742841061)⟩,⟨460701940814042801934144902957,460701940814050284850336709920⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-2595311820023207423352191082628),(-2595311820023205335198797017004)⟩,⟨566625131507682639390378267148,566625131507684727534608364216⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1332892043895445773473925879),(-1332892043895445769299990422)⟩,⟨501828911143716546525220878,501828911143716550605321989⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4087524056615630231310474449),(-4087524056615630217576219703)⟩,⟨1988883879574124455397749420,1988883879574124468882459450⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-6885613663653035031517149402),(-6885613663653035003195677827)⟩,⟨5081421092763976551550758146,5081421092763976579602134543⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-8870319046757835891689888047),(-8870319046757835837059064290)⟩,⟨11241356602586886762035288285,11241356602586886816735184053⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-7417007013036384053361287632),(-7417007013036383948878841368)⟩,⟨21889882483305246693845996050,21889882483305246799489584094⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2840080828104069486713407590,2840080828104069685777605184⟩,⟨36682234048771828038567096856,36682234048771828240957101381⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨29326302193149620013285965230,29326302193149620396289296110⟩,⟨49861144378352824650085816243,49861144378352825036620715109⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨76145416117166250435805069203,76145416117166251160241666969⟩,⟨46424528615701806069320199777,46424528615701806793948070929⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨133181921351241441012390009879,133181921351241442387902930641⟩,⟨4566151797922031892047552049,4566151797922033260358466389⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨168466662202606291565168692921,168466662202606294797856512697⟩,⟨(-88194334182041237277809672464),(-88194334182041234057666860017)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨141494080079933895243169497390,141494080079933908431005206528⟩,⟨(-211643231881129687779123586870),(-211643231881129674595940443886)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨40511681774702818664143994226,40511681774702871747036692781⟩,⟨(-310344933788864871501294170620),(-310344933788864818410598803986)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-90728946242584676668254699382),(-90728946242584540466354579942)⟩,⟨(-330947149895075235713382682171),(-330947149895075099492576578351)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-176456020334716438354893256585),(-176456020334716168500161089281)⟩,⟨(-267475916859355877014858892192),(-267475916859355607142539660035)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-165991364273376559365404481326),(-165991364273376207619594807287)⟩,⟨(-160574228985181581694684395942),(-160574228985181229940220264231)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-66882522273811083024526075610),(-66882522273810914931849893689)⟩,⟨(-51570410837114327916249269166),(-51570410837114159821196865284)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨23056505478947068987721347,23056505478947108965937014⟩,⟨9055716362911276950358861,9055716362911316924461021⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨75081015483952690265532458,75081015483952790812247257⟩,⟨23794350851007553239401609,23794350851007653773281945⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨144692522570807702296150152,144692522570807825944744879⟩,⟨25541883008165348389103419,25541883008165472017006710⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨241731615743858935561438039,241731615743859036705324523⟩,⟨(-4312036646397548031224712),(-4312036646397446913051658)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨367034662990219807369089486,367034662990219864271301850⟩,⟨(-99777727714824081432617769),(-99777727714824024553078715)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨496279385790137406960067770,496279385790137429380528906⟩,⟨(-312441905690157218530473054),(-312441905690157196110207271)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨555635205809112207218624550,555635205809112214981508611⟩,⟨(-697936615109675000834016441),(-697936615109674993014157788)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨404723025698176093464836835,404723025698176098450499934⟩,⟨(-1272193604595310536497178792),(-1272193604595310531347938736)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-135292439142657546170120657),(-135292439142657539121040913)⟩,⟨(-1940635693934972032296187067),(-1940635693934972025036106000)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1170589581610433389630959416),(-1170589581610433378337257802)⟩,⟨(-2452419549022890750512041925),(-2452419549022890739085505354)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-2571255492386146906146121918),(-2571255492386146889189279831)⟩,⟨(-2475270570394885265347875322),(-2475270570394885248438972813)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-3900820362539265972065223095),(-3900820362539265949114214066)⟩,⟨(-1827430038739408982738066398),(-1827430038739408960076221383)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-4587523087661496983518017948),(-4587523087661496956449660122)⟩,⟨(-713254520966221731240829076),(-713254520966221704667753227)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-4263606455917045620242561771),(-4263606455917045593524832051)⟩,⟨308961457407407703363261548,308961457407407729628748258⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2971351659883609046790695478),(-2971351659883609026830742780)⟩,⟨697031489148563606517479354,697031489148563626215457221⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1057468951833349141467122898),(-1057468951833349134063381566)⟩,⟨340683922243304675540271594,340683922243304682860800341⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-315827311040948342718226),(-315827311040941127095422)⟩,⟨(-659374627711973316241435),(-659374627711966100673618)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1128557686051307991598158),(-1128557686051278389797199)⟩,⟨(-1980387351567116952413552),(-1980387351567087350759801)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-2514713769433781949265532),(-2514713769433694710665357)⟩,⟨(-3244227159243161649183490),(-3244227159243074410770376)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-4930239639685091408123535),(-4930239639684837129151827)⟩,⟨(-4188011691964909857081829),(-4188011691964655578220496)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-8819403858734237889933065),(-8819403858733522561175239)⟩,⟨(-4161940068926946667111079),(-4161940068926231338154926)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-14335624936996080768761015),(-14335624936994291291761807)⟩,⟨(-1951210681277737351762746),(-1951210681275947873839651)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-20805585908440563654386207),(-20805585908436974901112452)⟩,⟨4210886134963605677628744,4210886134967194433193347⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-26089086301122867572892172),(-26089086301117475401959283)⟩,⟨16096431105747944666028547,16096431105753336841323845⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-26394076992417577170382474),(-26394076992409262532793504)⟩,⟨34167550297535696793762216,34167550297544011436099952⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-17438489110352950150791129),(-17438489110343029774569566)⟩,⟨55921766520538570226130471,55921766520548490605772488⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨2648774616031100238478330,2648774616039515240011624⟩,⟨75342009760242493724099239,75342009760250908726231522⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨30036699070369920042241112,30036699070375348321007888⟩,⟨85020611226436944099246154,85020611226442372374722295⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨54590774156913226909358634,54590774156916104436669859⟩,⟨80440866297349728311041328,80440866297352605831469575⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨64142421456507108426560930,64142421456508445492368562⟩,⟨63010287232327839112616064,63010287232329176169926744⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨51608345816754901264748211,51608345816755454876260323⟩,⟨38627974660504994133074180,38627974660505547737573558⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨19734781274645774762042986,19734781274645923266545193⟩,⟨12790138436358438905279454,12790138436358587407066195⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-3296559779924519461396),(-3296559779924519455159)⟩,⟨13907023404132024287563,13907023404132024294887⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-6373711848081364507285),(-6373711848081364487569)⟩,⟨44016706727936843388206,44016706727936843411598⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2183108802086333187716,2183108802086333224029⟩,⟨80456934454010943952706,80456934454010943996249⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨33184069552925253307828,33184069552925253366942⟩,⟨125072548056106964828711,125072548056106964899851⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨100195575535777923392196,100195575535777923499625⟩,⟨173779469739895033149116,173779469739895033271295⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨217151816272108020381244,217151816272108020582388⟩,⟨210623000573790110254950,210623000573790110471138⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨392065509705930617919910,392065509705930618324885⟩,⟨203019874464347988921838,203019874464347989338899⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨615032910356926350158334,615032910356926351326199⟩,⟨104549372853278242547934,104549372853278243720572⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨844774737057644062894333,844774737057644069797171⟩,⟨(-129184137345164071461861),(-129184137345164064563133)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1008028344860340465764426,1008028344860340519952560⟩,⟨(-510641613184143978240116),(-510641613184143924060967)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1026622972876448429649766,1026622972876448762727242⟩,⟨(-987489112083763260680368),(-987489112083762927608146)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨867750020424110873346572,867750020424112244554681⟩,⟨(-1431900955409637120098937),(-1431900955409635748883958)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨581237194487455668449452,581237194487460091800059⟩,⟨(-1675483287746223776853334),(-1675483287746219353483403)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨282294063709206579453032,282294063709215835520124⟩,⟨(-1585120722310610975380557),(-1585120722310601719289471)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨81041994754062374807673,81041994754073361509280⟩,⟨(-1133002558775769895023798),(-1133002558775758908302973)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨7753702228840082686350,7753702228845163833313⟩,⟨(-410459594504547002963776),(-410459594504541921809549)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1951539062000421868155145617797),(-1951539062000330727356712374282)⟩,⟨30120821879519480113874963835828,30120821879519571254587744146441⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 18) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_18 (tableDensity false) (fullFactor true 0 18) density0_contains hk0_1_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-6250725494067333863759554601083),(-6250725494067333852850246350933)⟩,⟨1148739611890442252020691139646,1148739611890442262308526163127⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_18 0 18 ha0_1_18_contains + def realAnswer : RBox := ⟨(-8202264556067755731914800218880),(-8202264556067664580206858725215)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_18 +namespace hm0_1_1_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-519045721843248869947748787422),(-519045721843247653180140195336)⟩,⟨92524770681336647836357623400,92524770681337864611697218458⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1561525516861409902049062883953),(-1561525516861406989892462134990)⟩,⟨535668614509281024065287108509,535668614509283936268091216461⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2388409028653047429955536899470),(-2388409028653044616868996485261)⟩,⟨1756343475840397392492899611405,1756343475840400205732092936459⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-2127120123547357526283289380448),(-2127120123547355506023146061508)⟩,⟨4007080754609801776480131521192,4007080754609803796950032192842⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨668884493284559745848458930523,668884493284560927860677957304⟩,⟨6324816631412980699330791441304,6324816631412981881322920571327⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨6275362943560575445803670064442,6275362943560575799914936572741⟩,⟨5616119826336873245935861569663,5616119826336873599575588576395⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨10722321160656515706475335681700,10722321160656515817491001985205⟩,⟨(-1355057045078364961545152385363),(-1355057045078364850635847806706)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨6731711825898582964452719156640,6731711825898583000409002957827⟩,⟨(-11835046361215794718671588721280),(-11835046361215794681917657459743)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-6872629165722073706671706999235),(-6872629165722073681758033912145)⟩,⟨(-15169075261458720032206526923000),(-15169075261458720007295477441076)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-18749416806035032611844908794225),(-18749416806035032592354192727804)⟩,⟨(-4498070642401939036275522207207),(-4498070642401939017925898167760)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16920261110037702601550627772945),(-16920261110037702584205745678038)⟩,⟨11794933577291430744542802263940,11794933577291430762001899598259⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-4119423748636930664166309597121),(-4119423748636930652446652323300)⟩,⟨19616674762173278100205460106644,19616674762173278113205991605451⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨7440577599529518883723538996327,7440577599529518894047921698728⟩,⟨15834446311064030331312959400250,15834446311064030342039061831448⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨10970739977607978481892188626565,10970739977607978489332601285388⟩,⟨7758325287273079843946192592850,7758325287273079850986651790987⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨8147357562990025181623508240461,8147357562990025185587724941391⟩,⟨2114871995504254894524968400031,2114871995504254897954722503701⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨2856864217384457775283926109394,2856864217384457776466750629601⟩,⟨193289547174033576888127515233,193289547174033577845297746215⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-7874645383223888729319660019),(-7874645383223840007184015244)⟩,⟨(-11231496814087394229943432562),(-11231496814087345508176964204)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-29026988863456310130854532573),(-29026988863456105369456676524)⟩,⟨(-31857131921953379040773412970),(-31857131921953174280160642296)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-65944121898133721748395277096),(-65944121898133108928267419427)⟩,⟨(-42984157943605197051772014747),(-42984157943604584231663379240)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-123890045589129052541735049634),(-123890045589127361913176019090)⟩,⟨(-25102166459414933061927401589),(-25102166459413242429809642741)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-186890186665629755734092130680),(-186890186665625533754213458340)⟩,⟨56204730433125754815991945566,56204730433129976806446389806⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-190400117748833058667106996607),(-190400117748818925698228707694)⟩,⟨230097927412474229715609947697,230097927412488362692468851711⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-15344576112050264215050189806),(-15344576112017642514598264051)⟩,⟨454183638100589936509248916920,454183638100622558200786928476⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨421837829225297021735127908881,421837829225348897010862218583⟩,⟨532764965858610084018431505470,532764965858661959263926960335⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨968719358048162587489956055526,968719358048250687073174097026⟩,⟨170670413323100484858439160671,170670413323188584438869403203⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1158385971064993194107406091070,1158385971065073255496074182780⟩,⟨(-709305084555258952946408851368),(-709305084555178891504815199499)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨573005761884238707748871063925,573005761884312665418974224818⟩,⟨(-1664308811310481609148665515521),(-1664308811310407651444645977980)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-601365123945460692916212880443),(-601365123945411972851198433865)⟩,⟨(-2004573723494081686811135806195),(-2004573723494032966785819180852)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1618736529351471434471433589554),(-1618736529351449273600251673756)⟩,⟨(-1509987768968828901632795208797),(-1509987768968806740846160680629)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1882190614591688348695747336868),(-1882190614591675351789304084290)⟩,⟨(-657520678883376195049006823574),(-657520678883363198182950319191)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1392968177817480543181016565538),(-1392968177817474420892340316272)⟩,⟨(-70038556496442639700781035737),(-70038556496436517417193463289)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-499237123607034827669767096586),(-499237123607033121979617291228)⟩,⟨47981067069288679795900945341,47981067069290385488471444767⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-315666055924334164763184141),(-315666055924334163443617255)⟩,⟨(-61212472467450053022674069),(-61212472467450051707519232)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1022137361655746925475620085),(-1022137361655746921081010247)⟩,⟨(-105952707948032615219217874),(-105952707948032610836851408)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1925323479683633400858037950),(-1925323479683633391957737575)⟩,⟨131838876508340944785048092,131838876508340953671599971⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3020873467432289465233557395),(-3020873467432289448851579084)⟩,⟨994595226978197330535901003,994595226978197346918511905⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-3961034314345550486604357251),(-3961034314345550457554620201)⟩,⟨2978032075344116400680634222,2978032075344116429775022972⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-3727852568038181138001627370),(-3727852568038181088067096750)⟩,⟨6494342333211639749048235520,6494342333211639799109327008⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-474372018245558254427353005),(-474372018245558167454072718)⟩,⟨11133755414969418796693339237,11133755414969418883812072329⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨7765167165411512494072559892,7765167165411512648435185590⟩,⟨14526777167704013739470829053,14526777167704013893861520507⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨20877193199868616634615386766,20877193199868616958420799921⟩,⟨11990230771239383051458512046,11990230771239383375066137738⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨34109548419826307088585736825,34109548419826308371382352617⟩,⟨(-1014232257025068407877853866),(-1014232257025067125338018925)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨38883135760011337431442661890,38883135760011346098940733403⟩,⟨(-23633898036765928064483787880),(-23633898036765919397034656828)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨29327735864187348719249161712,29327735864187389143717179096⟩,⟨(-46718489188832039947337898780),(-46718489188831999522805772445)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨9349302235039914060245009127,9349302235040021793372516065⟩,⟨(-58090430379294209223283951606),(-58090430379294101490076483421)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-8828063356920339360917322201),(-8828063356920122356446005513)⟩,⟨(-52412082260383155262719240188),(-52412082260382938258259550852)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-14562594507024911219443858490),(-14562594507024626347193828463)⟩,⟨(-34316841915537512433636495798),(-34316841915537227561444025821)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-6730782704495038449068133177),(-6730782704494902011178421975)⟩,⟨(-11629997265875668891431798266),(-11629997265875532453573779338)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨4369044855533817988886538,4369044855533851563920677⟩,⟨7033713495403694278551313,7033713495403727854013123⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨15075816537977111914382718,15075816537977196286394695⟩,⟨21096409345544672739282698,21096409345544757112629876⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨32050217103074681866504399,32050217103074785439021967⟩,⟨34367335390571152146385537,34367335390571255721047280⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨60423581689574406552528995,60423581689574490986655246⟩,⟨43508673511157021740215492,43508673511157106176977846⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨105414928758062967634614336,105414928758063014759082459⟩,⟨40204725840002694183018595,40204725840002741309711225⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨168834720247071945036186030,168834720247071963051621528⟩,⟨8772661998039692962392262,8772661998039710977652440⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨241414671104741630261797449,241414671104741635605097481⟩,⟨(-73696489733521294069313838),(-73696489733521288731959020)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨292864047309251131823865956,292864047309251134100840449⟩,⟨(-229662927297448277926248168),(-229662927297448275665456114)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨268686936948297173698623463,268686936948297176337470361⟩,⟨(-461543231663016619742533408),(-461543231663016617123458704)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨108747090846281791583812232,108747090846281795635469467⟩,⟨(-726622502503469345885217143),(-726622502503469341843826314)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-206150842937703055245589729),(-206150842937703049258297252)⟩,⟨(-931667418075560711378393913),(-931667418075560705383412201)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-605366668694740332751657554),(-605366668694740324679121881)⟩,⟨(-974689980353259341261637092),(-974689980353259333159638139)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-930792196175872694851885704),(-930792196175872685277713913)⟩,⟨(-820634620968848992106749530),(-820634620968848982485701647)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1015112469534035242945790287),(-1015112469534035233355897447)⟩,⟨(-542331767860012494507379195),(-542331767860012484876558271)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-782929594900193218630362649),(-782929594900193211357585975)⟩,⟨(-268408674127642673361476246),(-268408674127642666066110382)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-293309916923145430302425080),(-293309916923145427582146838)⟩,⟨(-74391010169130813735559989),(-74391010169130811008375577)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-114721931570899545586266),(-114721931570893615579552)⟩,⟨(-211057946899754394803385),(-211057946899748464781444)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-406240498394058161280831),(-406240498394033831792248)⟩,⟨(-647679963342916785023900),(-647679963342892455490686)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-894051683509522669838743),(-894051683509450959149361)⟩,⟨(-1107467171309106221275161),(-1107467171309034510520755)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1737965494620517468128310),(-1737965494620308414959930)⟩,⟨(-1529854319633858325077443),(-1529854319633649271847483)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-3116293638777788439750438),(-3116293638777200266592488)⟩,⟨(-1712555100577055390620773),(-1712555100576467217456495)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-5165499055070151700668366),(-5165499055068680325506812)⟩,⟨(-1233643676524667587931565),(-1233643676523196212914084)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-7825299183599510992030712),(-7825299183596560826921083)⟩,⟨573948353162607881812657,573948353165558046465366⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-10604046821770777270733616),(-10604046821766346798128195)⟩,⟨4493382603434295150862697,4493382603438725622525880⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-12426942676813185630774323),(-12426942676806359538594619)⟩,⟨11027296151435013216113947,11027296151441839307233847⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-11865285919862845914983802),(-11865285919854710253941643)⟩,⟨19760130110061388383731679,19760130110069524043977017⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7936981538658201664537971),(-7936981538651309280759560)⟩,⟨28849371482026761361060498,28849371482033653744618759⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1142523012991477709489131),(-1142523012987037599172059)⟩,⟨35292603449519061443670758,35292603449523501554507363⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨6147057912877019271245922,6147057912879369949120048⟩,⟨36290775826673275521806795,36290775826675626200873436⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨10597867599392268124091216,10597867599393359182704095⟩,⟨30895267687399354210127262,30895267687400445270215125⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨9803400344902792269656444,9803400344903243651428934⟩,⟨20388923297328341822353110,20388923297328793205331569⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨3958621378174382963898623,3958621378174503991124001⟩,⟨7066844200367266057757035,7066844200367387085441771⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-78153048615650012962),(-78153048615650009771)⟩,⟨417757478745229377600,417757478745229381604⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨141821055192209635229,141821055192209645187⟩,⟨1290336703347258583516,1290336703347258596202⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1788793700558311966460,1788793700558311984256⟩,⟨1683006513837219524696,1683006513837219547838⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨6948066380454527311675,6948066380454527339465⟩,⟨(-735964596925121520864),(-735964596925121484058)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨19461690209391959892432,19461690209391959946411⟩,⟨(-11150128573022122162338),(-11150128573022122097100)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨44272249922638775342139,44272249922638775454414⟩,⟨(-37982372899644009221341),(-37982372899644009097585)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨83866393922310556536452,83866393922310556792872⟩,⟨(-92811961879343912832663),(-92811961879343912567573)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨132924761343989343772215,132924761343989344631202⟩,⟨(-189055354483327952226666),(-189055354483327951366609)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨174429226513090691861063,174429226513090697407477⟩,⟨(-335993053940068427672727),(-335993053940068422137576)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨181116684471749841287698,181116684471749885486671⟩,⟨(-526912584052343522470343),(-526912584052343478296558)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨126532576354930248032776,126532576354930519936214⟩,⟨(-727939637913836122349120),(-727939637913835850482772)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨5898353979121574037671,5898353979122693630750⟩,⟨(-880254618411894803420305),(-880254618411893683871730)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-143688078444056941255539),(-143688078444053327774957)⟩,⟨(-921615934472997385564047),(-921615934472993772119466)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-246948364158636543851191),(-246948364158628978637626)⟩,⟨(-814071977159026650886179),(-814071977159019085692734)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-233727500544013121881632),(-233727500544004138747116)⟩,⟨(-559618794759578595717195),(-559618794759569612591011)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-95736608427692055021924),(-95736608427687899655980)⟩,⟨(-199246608110696429227626),(-199246608110692273863556)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-473792640216830491133162632710),(-473792640216755355686609471637)⟩,⟨6228056680271894204435365588833,6228056680271969339883174424532⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 18) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_18 (tableDensity true) (fullFactor true 0 18) density1_contains hk0_1_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨8174025646088051961419552920452,8174025646088051975685571401416⟩,⟨(-1502197954010578343018841905627),(-1502197954010578329565519182614)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_18 0 18 ha0_1_18_contains + def realAnswer : RBox := ⟨7700233005871221470286290287742,7700233005871296619999061929779⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_18 +namespace hm0_0_1_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1369684350212524711259464129405,1369684350212525360417873720233⟩,⟨194150931821601815113283668648,194150931821602464300165868009⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨4320502992750957560055350920915,4320502992750959227972799553561⟩,⟨(-126108273490378470847907287647),(-126108273490376802882774739231)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨7273584405281029166627488511541,7273584405281031023095368440289⟩,⟨(-2774942169039205444009000471973),(-2774942169039203587596940600602)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨7973135360775907704962450230944,7973135360775908863434874386437⟩,⟨(-9160362963918337936860128748164),(-9160362963918336778764317802450)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1560984551834330008254036762570,1560984551834330655401144556346⟩,⟨(-17673508711078370434174500086042),(-17673508711078369787395647220490)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-15092558779310076129655378560490),(-15092558779310075859059167011202)⟩,⟨(-19596944013617780486930386849807),(-19596944013617780216077335335815)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-32782119592215359941105639597946),(-32782119592215359835835583642379)⟩,⟨(-2585454655700991369417565557776),(-2585454655700991263536573871761)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-28254898030555409563180143756124),(-28254898030555409496256706472276)⟩,⟨30295942096046089302453248733119,30295942096046089369107038214764⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨8727978751325512985438524249967,8727978751325513037740135666308⟩,⟨48332149432725642300493551558568,48332149432725642352305991483793⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨48573498052537075251437477605330,48573498052537075291129755962063⟩,⟨24625295649413307656258259216020,24625295649413307696082100787670⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨51536345073501620279253333823976,51536345073501620310423350864915⟩,⟨(-22351300728719377536964330477450),(-22351300728719377505486284856719)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨19139690783988302414916672819481,19139690783988302436222697089457⟩,⟨(-50023679274833496572805581590689),(-50023679274833496551187072406584)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-14388415165320334028737658608119),(-14388415165320334012599396225338)⟩,⟨(-44349617615624139973065707674337),(-44349617615624139956897149717970)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-26964388590659170918460665046006),(-26964388590659170907673977426142)⟩,⟨(-23823715595034715439827134231657),(-23823715595034715429278147820024)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-21207709683381270243422304740257),(-21207709683381270237883095020458)⟩,⟨(-7906556097409380067608511160973),(-7906556097409380062349465418667)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-7599432113179685219971597342748),(-7599432113179685218349331334678)⟩,⟨(-1305883112845800871735086819047),(-1305883112845800870229203829114)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨9777843757136669007876420282,9777843757136689836924588332⟩,⟨31532089206932434761749768164,31532089206932455592398487879⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨43208035258583253164411891741,43208035258583332612720971664⟩,⟨96288228198964153107890327980,96288228198964232562364414041⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨122145759565551714497267420360,122145759565551932069470877389⟩,⟨156928618843056088852363157156,156928618843056306437882975266⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨281512937698185886543545051141,281512937698186672884292239679⟩,⟨175178719448272137682717045236,175178719448272924036637418494⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨526589061515532661644356727169,526589061515535189814486357298⟩,⟨52202335294510345149553534706,52202335294512873317720082186⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨742734379727676048914267892743,742734379727681937335781951530⟩,⟨(-361319774854621956216356538304),(-361319774854616067836725502096)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨592801182393906412037674750882,592801182393921713992364839582⟩,⟨(-1115992331927067175124616405369),(-1115992331927051873216800374306)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-372285148911209035990939489612),(-372285148911179244181506426308)⟩,⟨(-1844675823046102876037041025094),(-1844675823046073084186466653143)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2142612656667097891214685759606),(-2142612656667060416642485902094)⟩,⟨(-1633392192050043779399455165748),(-1633392192050006304699610758579)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-3640986004840874829288319959396),(-3640986004840826168912021705009)⟩,⟨269610357638842215913321592170,269610357638890876274021494830⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-3290384023420293667955135730190),(-3290384023420260141466995835304)⟩,⟨3218996195784201101071026474641,3218996195784234627348097462348⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-796173353939375812060784249424),(-796173353939349907449926509930)⟩,⟨5239786781709623763500976640833,5239786781709649668019813184654⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2171484762677113943328697178017,2171484762677128353625305149620⟩,⟨4994316531444684782296103816169,4994316531444699192706457695902⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨3638828028359223179651176764267,3638828028359229065097859083704⟩,⟨3141047603715995097262436974856,3141047603716000982921621248399⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨3064043827050961866215318221563,3064043827050964761363064287155⟩,⟨1292661505341309283978165140100,1292661505341312179241874697819⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1156667507509523743191811597474,1156667507509524619696700059278⟩,⟨281277985733702797084387145851,281277985733703673619674043309⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨334060133467733551777202056,334060133467733553475473419⟩,⟨283520843559507630799548070,283520843559507632492947987⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1153111022165054720206326762,1153111022165054725832854896⟩,⟨800285250168893728243298808,800285250168893733835260271⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨2435275222422418782493590472,2435275222422418794262301249⟩,⟨1073943024763520755763140495,1073943024763520767397738590⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨4459323836987702772032962358,4459323836987702795158502687⟩,⟨609919480462136324578783848,609919480462136347323656677⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨7183270785037678679509016479,7183270785037678724925688586⟩,⟨(-1617581864066678396189339881),(-1617581864066678351457672468)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨9518915761795743362160524418,9518915761795743451672549336⟩,⟨(-7157480694556516605319404402),(-7157480694556516516328939973)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨8286751274561577314168316374,8286751274561577488413597533⟩,⟨(-17165813897982367311777609959),(-17165813897982367137206965589)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1967371134418733535380932386),(-1967371134418733204030090642)⟩,⟨(-29886200990553612088808024808),(-29886200990553611755262187408)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-25915729730764650830294848128),(-25915729730764650190908730861)⟩,⟨(-37561283988691564204267252987),(-37561283988691563562349203386)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-60469532159222864700361373635),(-60469532159222863213943509463)⟩,⟨(-27376812840733077909076595821),(-27376812840733076422854770013)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-90055286020680803045148785184),(-90055286020680798453698913269)⟩,⟨8889841212504574809075466419,8889841212504579395808518556⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-94570307033034450375295714570),(-94570307033034432588029457301)⟩,⟨61999665465431210860195520670,61999665465431228641045843248⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-68233494076857350536345872435),(-68233494076857288719399175739)⟩,⟨105596623324805195951991249777,105596623324805257766393554921⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-28507025709049534525088669224),(-28507025709049410202704929258)⟩,⟨115216304774266717774095777705,115216304774266842097548732723⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1111785405863332779720544215),(-1111785405863194091016540874)⟩,⟨86183539608107617488840390215,86183539608107756179898467819⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨3304684515183851790064855374,3304684515183912996708670193⟩,⟨31467392682045859859821630225,31467392682045921067593620480⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨358321767356907200036957,358321767356919681698479⟩,⟨(-6334104644215353614190257),(-6334104644215341131786021)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-284379362736004163302657),(-284379362735972063435112)⟩,⟨(-20236034938929568957715823),(-20236034938929536855751582)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-5775038507477043055948651),(-5775038507477005147112767)⟩,⟨(-37557085854321093540380809),(-37557085854321055628636189)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-21905505774635397916809020),(-21905505774635368518732600)⟩,⟨(-59194511437727456022063933),(-59194511437727426621781300)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-57907297860335613812652742),(-57907297860335598272880723)⟩,⟨(-82146042515282620850557826),(-82146042515282605312698992)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-125527128402153533629228402),(-125527128402153527883182203)⟩,⟨(-94631484718004751330561778),(-94631484718004745596956239)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-232655778365362602275620922),(-232655778365362600236930256)⟩,⟨(-70229883397434814150208012),(-70229883397434812143862930)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-368581891882579449947739005),(-368581891882579448195906236)⟩,⟨32825008101352516375078471,32825008101352518088386736⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-485684187925532220312056443),(-485684187925532217674728758)⟩,⟨255826660988443609698649764,255826660988443612315410476⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-497948376320064795596695809),(-497948376320064791359368507)⟩,⟨601088264816821240413827359,601088264816821244677238147⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-323036516525637834322639859),(-323036516525637827913190486)⟩,⟨991331044954817396683914482,991331044954817403191300795⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨37759923802057419973125088,37759923802057428825119671⟩,⟨1277320082348923566811481049,1277320082348923575805240467⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨448945301424808235886316146,448945301424808246657829588⟩,⟨1321336153211618712706955925,1321336153211618723578935918⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨695588978654335032079505196,695588978654335042912824374⟩,⟨1096380010595345352901386682,1096380010595345363782751140⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨623565447297073131599005389,623565447297073139778403621⟩,⟨695000336638982606621283887,695000336638982614810858894⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨248629442360086613335013075,248629442360086616386262816⟩,⟨233603050280550545289873160,233603050280550548340143203⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-130101996979664764679534),(-130101996979663100400960)⟩,⟨92497784805228908051264,92497784805230572335734⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-384322025588528617882960),(-384322025588521828893712)⟩,⟨318406580104531736865169,318406580104538525867691⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-604345723553586948015802),(-604345723553567164638388)⟩,⟨671960710157194145920086,671960710157213929303071⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-710819979591824399832459),(-710819979591767724745523)⟩,⟨1247582936238472059906618,1247582936238528734958610⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-530893792323955405113893),(-530893792323799925695432)⟩,⟨2121912776689719052922533,2121912776689874532203239⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨235548780703578833830176,235548780703953459342018⟩,⟨3277074147762666669992675,3277074147763041295157004⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1990788322656589504729398,1990788322657306756425371⟩,⟨4464661528024091285988193,4464661528024808536980133⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨5071849325338998991420151,5071849325340393624748690⟩,⟨5062985266447028813974613,5062985266448423446459401⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨9401605219617197654050323,9401605219619412051011654⟩,⟨4086733372708762744294948,4086733372710977140623452⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨14114020712245125529138694,14114020712247624112787281⟩,⟨570204613190836341258402,570204613193334924833106⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨17566821686457379335499244,17566821686459385103502774⟩,⟨(-5639899997702217626351109),(-5639899997700211857479161)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨18105078283588541145539028,18105078283589758763149134⟩,⟨(-13133136952898698554128811),(-13133136952897480934516735)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨15260854036142930426421291,15260854036143532674286073⟩,⟨(-19032269847326615709501861),(-19032269847326013458729639)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨10298072211604286406537267,10298072211604589774498754⟩,⟨(-20308962234916282378715144),(-20308962234915979008104174)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨5314504092463930308745462,5314504092464080727801600⟩,⟨(-15546078706430661722460422),(-15546078706430511301791404)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1539314689812904849985240,1539314689812949127130393⟩,⟨(-5812768865765821748331435),(-5812768865765777470652626)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨2677540594850758901809,2677540594850758903214⟩,⟨487969653334822177709,487969653334822178883⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨8455942216043813402043,8455942216043813406507⟩,⟨756290010014138906674,756290010014138910362⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨15379670337716802902794,15379670337716802911101⟩,⟨(-1324482288315683155674),(-1324482288315683148885)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨23688971834424988006404,23688971834424988020556⟩,⟨(-7961302149382400271321),(-7961302149382400259506)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨32356831815947790154116,32356831815947790179174⟩,⟨(-21931807882501954493739),(-21931807882501954471368)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨37843938533599276121314,37843938533599276165908⟩,⟨(-46018198772904388228340),(-46018198772904388186382)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨33090723495774619799853,33090723495774619886512⟩,⟨(-81542119539217661543220),(-81542119539217661458388)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨8167857182855155114729,8167857182855155356215⟩,⟨(-125690137704674587358072),(-125690137704674587116802)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-46101289469352561472507),(-46101289469352560084220)⟩,⟨(-168668429388369421029992),(-168668429388369419640152)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-131412529199612869125290),(-131412529199612858496126)⟩,⟨(-193966858802074353439821),(-193966858802074342808423)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-234959609918440871183079),(-234959609918440807934189)⟩,⟨(-185107580703294476405525),(-185107580703294413155766)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-327969490914907188708068),(-327969490914906880917198)⟩,⟨(-137613967478435125088804),(-137613967478434817300049)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-374490674972487362414401),(-374490674972486307094827)⟩,⟨(-67287837542476475278936),(-67287837542475419963976)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-348133632048048703365963),(-348133632048046529626386)⟩,⟨(-4628009878062808653296),(-4628009878060634919107)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-245829480236068372043852),(-245829480236065818029604)⟩,⟨23739997809158635723893,23739997809161189734175⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-88488474710564540960237),(-88488474710563365797624)⟩,⟨13483683552180883734441,13483683552182058895665⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨993184968361124093080225332330,993184968361162638360829875646⟩,⟨(-13989776098389798795712351110577),(-13989776098389760250466230869205)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 19) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_19 (tableDensity false) (fullFactor true 0 19) density0_contains hk0_1_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨3302464185650742547880410771926,3302464185650742554293522747382⟩,⟨(-556983815484256208645298316957),(-556983815484256202540367349968)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_19 0 19 ha0_1_19_contains + def realAnswer : RBox := ⟨4295649154011866640960536104256,4295649154011905192654452623028⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_19 +namespace hm0_1_1_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨227812820312012253631907029762,227812820312012782302849527989⟩,⟨63821545735778521530512437346,63821545735779050195100965017⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨738098205822653648760543761371,738098205822655005055217646764⟩,⟨82328152328598302719139503359,82328152328599659004689110896⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1311283229938560042664910287233,1311283229938561545359967557795⟩,⟨(-277167576904551002179280335378),(-277167576904549499462450870902)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1605491587382348450546466497622,1605491587382349373854225732099⟩,⟨(-1298602302085252921526934166505),(-1298602302085251998110767106781)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨771682036931224509600473458338,771682036931225007179321057520⟩,⟨(-2814817088723031548175487590593),(-2814817088723031050505375916148)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1880747434856116412056577163682),(-1880747434856116226903604769153)⟩,⟨(-3415813954551356978682005781703),(-3415813954551356793668345628307)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-4975788513281882967522483357191),(-4975788513281882918876224684014)⟩,⟨(-863136327898883376091518239849),(-863136327898883327644964972097)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-4475316008174076845668040721817),(-4475316008174076826442455637430)⟩,⟨4600628603356987597325748058871,4600628603356987616851666379906⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1690569872758320988236980268216,1690569872758321000780064020730⟩,⟨7729847905446103761923079334655,7729847905446103774642774488878⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨8488291613638498501458990231650,8488291613638498511567752305539⟩,⟨3605334013859619462380735660442,3605334013859619471962090496634⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨8776119747672234991984489003389,8776119747672235000745469933352⟩,⟨(-4616432371088601566257319006515),(-4616432371088601557574371580749)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨2800516810041397537264023419533,2800516810041397543226287230603⟩,⟨(-9258406183358172649678573024928),(-9258406183358172643121173905340)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-3177353941047808606493740070712),(-3177353941047808601475993348684)⟩,⟨(-7844215052263364989933843658204),(-7844215052263364984671542113107)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-5203996031655877916984084352234),(-5203996031655877913320294273145)⟩,⟨(-3910554606371933816633258700222),(-3910554606371933813142978552700)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-3938335304089930280331089774676),(-3938335304089930278380657271751)⟩,⟨(-1069816107166517341102945995298),(-1069816107166517339407537359484)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-1385359591657027453542829038946),(-1385359591657027452963455810794)⟩,⟨(-96890091482637325900790656939),(-96890091482637325430668079312)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-997362013578117360080179247),(-997362013578100422194174868)⟩,⟨5051188802311242827539384844,5051188802311259765229893849⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-998851114651898228316961455),(-998851114651833483882198575)⟩,⟨16205968952868209996736515510,16205968952868274740402003825⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨6061432988176392936883166053,6061432988176570901926869865⟩,⟨29248843261729868537254990471,29248843261730046500588964475⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨27342072656394711291383485748,27342072656395357545885989272⟩,⟨40022817265282846430685091686,40022817265283492683398853243⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨68044821648758066470888848603,68044821648760149716912947678⟩,⟨33464226030161964835605103983,33464226030164048081533072898⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨116393295730967258795244282700,116393295730972117620168969963⟩,⟨(-18446728129930015860960784774),(-18446728129925157030970611035)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨121021102309682941455253283310,121021102309695586628943972795⟩,⟨(-136437799741519210997521609657),(-136437799741506565817575311688)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-3086197453706811689135168019),(-3086197453682176560073013117)⟩,⟨(-277563056343435474925736197920),(-277563056343410839801174821940)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-285438277955269029200849587661),(-285438277955238045638751355930)⟩,⟨(-292864776163705267621404739489),(-292864776163674284075916272811)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-573923478091531573719393942127),(-573923478091491363882612272118)⟩,⟨(-22665145308318880493434042386),(-22665145308278670655032521379)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-585930174944363286625492370113),(-585930174944335624840087856908)⟩,⟨477717678621853318612290398402,477717678621880980427228035686⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-210215156999835777779574608749),(-210215156999814441862181706972)⟩,⟨886641752608548393425794917358,886641752608569729356056509578⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨309139354230861732592696243516,309139354230873571553339746236⟩,⟨924475146073722981908449938643,924475146073734820850460415210⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨609234870724755158266885593257,609234870724759973574516401586⟩,⟨642718618496580929053458768060,642718618496585744327563393869⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨543428346533555418788788584828,543428346533557781035750158234⟩,⟨304963516316910192715727055623,304963516316912554944536342710⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨210519448418587411288678209104,210519448418588125385466709774⟩,⟨78684782483504262524362391424,78684782483504976616441307528⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨30688059351733330386115709,30688059351733330923599476⟩,⟨94041204181836515177453602,94041204181836515714757382⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨125884235622745299268221380,125884235622745301062084223⟩,⟨291265069286124129498154298,291265069286124131290511745⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨332962320425372866058767080,332962320425372869709273789⟩,⟨499394843018085959655784317,499394843018085963300333270⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨751094485888630071369434686,751094485888630078133092372⟩,⟨659643819854047904323353837,659643819854047911070483313⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1467249924056125373033683648,1467249924056125385306991186⟩,⟨582663618034270558705102407,582663618034270570950505473⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2421102999033577180698453805,2421102999033577202837617851⟩,⟨(-112152296236774282449220080),(-112152296236774260332416572)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨3136314403787089891401177205,3136314403787089930364230925⟩,⟨(-1908925482378262517117415890),(-1908925482378262478145119827)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨2488421567528269090017338315,2488421567528269157697624938⟩,⟨(-4939773032545628529085587300),(-4939773032545628461325707613)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-961846763112200289706908706),(-961846763112200147462284693)⟩,⟨(-8187252035341037313115850138),(-8187252035341037170790783198)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-7610849011556002787193808907),(-7610849011556002235429662696)⟩,⟨(-9162567153043153904742414922),(-9162567153043153352972591550)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-15264000164288568024928057188),(-15264000164288565324321867215)⟩,⟨(-5347052733161406523863905269),(-5347052733161403823308947039)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-19707288195976404935389093775),(-19707288195976391892053902396)⟩,⟨2968143738014959925874937188,2968143738014972969171901318⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-18148598730920774277666845344),(-18148598730920725600975632444)⟩,⟨11630746171984228342614851036,11630746171984277019318187482⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-12052446725088023145649030101),(-12052446725087923383558578133)⟩,⟨15565468674039606938553215714,15565468674039706700677657632⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-5591047352530960867405161102),(-5591047352530848875015956394)⟩,⟨12739399642354227045016143991,12739399642354339037420464715⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1413808025618961706196157598),(-1413808025618912176013268090)⟩,⟨4831506871016948104016933952,4831506871016997634199562558⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1361668829059802824643560,1361668829059813307986308⟩,⟨(-1625765190944405155457936),(-1625765190944394672193815)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨3921942763175094759980261,3921942763175121698878583⟩,⟨(-5386015644818481587313355),(-5386015644818454648637342)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨5751558263629865626662925,5751558263629897383335490⟩,⟨(-10705699266323666162485880),(-10705699266323634406120767)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨5511526082361516765226944,5511526082361541304403476⟩,⟨(-18639808786343359693069603),(-18639808786343335154121844)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨470706107946558830915196,470706107946571682000411⟩,⟨(-29806593693614435808264923),(-29806593693614422956974308)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-13868261933532568568167123),(-13868261933532564007509869)⟩,⟨(-43142376167912447676890157),(-43142376167912443114965986)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-42993089695146612619705104),(-42993089695146611327708184)⟩,⟨(-53660600581885399610830709),(-53660600581885398315620846)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-90082168294508341353044735),(-90082168294508340610697648)⟩,⟨(-50264919340223451242289954),(-50264919340223450496310242)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-149752383794974534723347972),(-149752383794974533764703113)⟩,⟨(-16844263294200558089130600),(-16844263294200557128961055)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-202513511447455145718516806),(-202513511447455144215099215)⟩,⟨59344165551784928928628312,59344165551784930428985685⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-218636276764224192551973075),(-218636276764224190279750829)⟩,⟨172907117752694117907146276,172907117752694120169777146⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-177135142436181678788785269),(-177135142436181675634175078)⟩,⟨290646041092383750299009046,290646041092383753440592245⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-88952280134059066360733524),(-88952280134059062488111776)⟩,⟨362235011978478118695089750,362235011978478122559384641⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨822907793052839401202123,822907793052843339838090⟩,⟨349574117253478453517788030,349574117253478457453451769⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨42987165246028468955185234,42987165246028471959458371⟩,⟨249539814370244222756202547,249539814370244225760625513⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨23572432441444722693440563,23572432441444723820993207⟩,⟨89879365990245156571484467,89879365990245157699495964⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-41136704632119750321667),(-41136704632118382561273)⟩,⟨32539801965598073821949,32539801965599441580116⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-124285396636920813768278),(-124285396636915233932546)⟩,⟨112147387892474916366506,112147387892480496196289⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-204914341857658661069387),(-204914341857642398998897)⟩,⟨237108973566581066461649,237108973566597328525462⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-262268829392038768476681),(-262268829391992173619549)⟩,⟨442006001639751759577748,442006001639798354434498⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-240855879940049304570681),(-240855879939921463120365)⟩,⟨760351347592863870002600,760351347592991711473021⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-33080402987188288043269),(-33080402986880257306982)⟩,⟨1205625162115706293995783,1205625162116014324797521⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨521796264160361572388460,521796264160951194154480⟩,⟨1729996745611608768415402,1729996745612198390330726⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1595514762582187197297057,1595514762583333077814489⟩,⟨2168849678917068798334695,2168849678918214679045456⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨3262027084546520024464501,3262027084548337991652408⟩,⟨2218932507780473007585485,2218932507782290974932341⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨5343731485882965228644144,5343731485885014316384670⟩,⟨1530333149755944679122374,1530333149757993766903930⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨7323054052265442907468003,7323054052267085757408153⟩,⟨(-50944010552360626616215),(-50944010550717776821177)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨8474892948618230918839746,8474892948619226882271847⟩,⟨(-2213758068879523457329538),(-2213758068878527494253482)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨8249955708490785965783473,8249955708491277942950936⟩,⟨(-4153409676381632528606930),(-4153409676381140551961751)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6646418760594721568463477,6646418760594969108832141⟩,⟨(-4923937950864937321588679),(-4923937950864689781690416)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4174097225576633936485604,4174097225576756576416500⟩,⟨(-3977624794267604891917344),(-3977624794267482252269820)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1402666911912047926787663,1402666911912084011423424⟩,⟨(-1523841205163287070758435),(-1523841205163250986215012)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨80222406135629270876,80222406135629271635⟩,⟨10688074708168235278,10688074708168235870⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨244433777429412928416,244433777429412930795⟩,⟨(-40491880617578327093),(-40491880617578325278)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨301856335092378429025,301856335092378433340⟩,⟨(-361516422607052929176),(-361516422607052925965)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-229801518215873539105),(-229801518215873531895)⟩,⟨(-1330081132067978700425),(-1330081132067978694926)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-2445262955141960929166),(-2445262955141960915912)⟩,⟨(-3625526273683347402019),(-3625526273683347390737)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-8175208481132704346358),(-8175208481132704321131)⟩,⟨(-8080614515338452860444),(-8080614515338452837090)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-19972219034830602689664),(-19972219034830602635391)⟩,⟨(-14945343862966612414801),(-14945343862966612361646)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-40755205542677251294558),(-40755205542677251119381)⟩,⟨(-22760247935398450220005),(-22760247935398450044151)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-72411211453163658717099),(-72411211453163657607564)⟩,⟨(-27574548212694104192588),(-27574548212694103079647)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-113140085629233316520497),(-113140085629233307862647)⟩,⟨(-23477798384094604243091),(-23477798384094595578885)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-155076851846144072547729),(-155076851846144020936595)⟩,⟨(-5375199632136284746282),(-5375199632136233126401)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-185155480961367990965620),(-185155480961367739671276)⟩,⟨26240384146508725257495,26240384146508976560087⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-190537239905183688120372),(-190537239905182826032870)⟩,⟨61197590777528310791771,61197590777529172884049⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-165043680460650336256660),(-165043680460648559619391)⟩,⟨81252510148323908758632,81252510148325685397488⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-111487835738837312905346),(-111487835738835224659103)⟩,⟨70413235437571994566515,70413235437574082812809⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-39281856408611590318890),(-39281856408610629273798)⟩,⟨27926645715472199570215,27926645715473160615163⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨275452271791863845003298553219,275452271791895594417497187254⟩,⟨(-2778522008930802102863834302769),(-2778522008930770353450460172545)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 19) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_19 (tableDensity true) (fullFactor true 0 19) density1_contains hk0_1_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4318607012004817186383837438884),(-4318607012004817177997460240211)⟩,⟨728363451017873495629711149958,728363451017873503613082414482⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_19 0 19 ha0_1_19_contains + def realAnswer : RBox := ⟨(-4043154740212953341380638885665),(-4043154740212921583579863052957)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_19 +namespace hm0_0_1_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-489906821197881199965676711371),(-489906821197880986274495445960)⟩,⟨(-328277894648205388653586766297),(-328277894648205174936272855230)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1692405377201840677767586442171),(-1692405377201840074835726371309)⟩,⟨(-740320111346677611949093449810),(-740320111346677008951111580942)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-3336962638546598190256656909097),(-3336962638546597409941128978230)⟩,⟨(-204677095044082321635471120930),(-204677095044081541261146444289)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-4723575675098293850289906432083),(-4723575675098293262690762402714)⟩,⟨2293465027339372917854095568036,2293465027339373505407242444958⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-3439908618192892464445446945323),(-3439908618192892202073530414473)⟩,⟨6927729481844952939714709853901,6927729481844953201853200844409⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨3411903951468711882784522629395,3411903951468712011043889325875⟩,⟨10332298130972524427559569074935,10332298130972524555770455065065⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨13578586552110469153636009108217,13578586552110469206238974386181⟩,⟨5362631130494125788011711695508,5362631130494125840908022448618⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨15662663540112061265700640593780,15662663540112061301054124015165⟩,⟨(-9945048277998896301430364724790),(-9945048277998896266049924207097)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨700030674723322405095685189072,700030674723322431942528869957⟩,⟨(-22157211224695996894148981671714),(-22157211224695996867561531971799)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-19911240371876116530766352195712),(-19911240371876116510310664770935)⟩,⟨(-14687532664372793937442540787315),(-14687532664372793916994904014063)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-24621024293859592012961506539001),(-24621024293859591997631201505655)⟩,⟨7202882412229675958512927044811,7202882412229675973978929473684⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-10727280626830640002845002202004),(-10727280626830639992365912734872)⟩,⟨22083142609101610578387616387558,22083142609101610589023373648640⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨5493719446759167793171441443084,5493719446759167800807346989349⟩,⟨20709207419447969160719601254550,20709207419447969168387518575191⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨12087742420028294729027019027042,12087742420028294734145933347603⟩,⟨11318102764868017603877169179630,11318102764868017608894242712850⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨9726505950258789952273578106399,9726505950258789954890789063883⟩,⟨3751530561397881739667239519481,3751530561397881742156722706477⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨3500056054079186657072796959596,3500056054079186657834959204522⟩,⟨609629996176109106750309811755,609629996176109107458804182864⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨5702937573892758026757490837,5702937573892765984706771676⟩,⟨(-10298445858159009227369913251),(-10298445858159001269809796725)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨13964823022129464180167697090,13964823022129497992214359962⟩,⟨(-35096920311346184820272522462),(-35096920311346151009002668762)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨9106489545940477635948550418,9106489545940580393313107928⟩,⟨(-71111621767213235164792664872),(-71111621767213132407104275047)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-29021941632933783075431648593),(-29021941632933498216023571869)⟩,⟨(-117254461793476194313745590108),(-117254461793475909449633488629)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-129220458638733837825585328942),(-129220458638733081550334790430)⟩,⟨(-146503195528572591489012946009),(-146503195528571835202036212710)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-298458685560753879184035787017),(-298458685560751271133255477385)⟩,⟨(-82471947860811673010247448662),(-82471947860809064954721787836)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-445505618695436301123291909715),(-445505618695430702703759498322)⟩,⟨183471335334425571846230513199,183471335334431170245497699537⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-323874079327728757083520732533),(-323874079327717802148817518619)⟩,⟨654533112512899103726091540513,654533112512910058634487310289⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨309944104407290301967815265359,309944104407307003645899077424⟩,⟨1017976254100093388451296479056,1017976254100110090157096115130⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1276320267457598950929032180054,1276320267457615937427461688554⟩,⟨722401503670881718962822685764,722401503670898705520840461574⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1833086958018159399443308021134,1833086958018175719187575429870⟩,⟨(-408297220127987887365041048047),(-408297220127971567644787473492)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1369920194917908219928305617607,1369920194917917258808320376893⟩,⟨(-1711171907161412715199971100462),(-1711171907161403676417687147995)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨198679547158069932654246608141,198679547158076093728855730641⟩,⟨(-2269330725882668898151709678344),(-2269330725882662737109351433561)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-757288511374696673086833562274),(-757288511374693583277333861510)⟩,⟨(-1881631207272777360785901508042),(-1881631207272774270942649357507)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-920513180097470291533831443337),(-920513180097469089204987396892)⟩,⟨(-1070044513979494115571997359531),(-1070044513979492913191920226003)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-390164018012849590708035541290),(-390164018012849293023638931884)⟩,⟨(-323364093250190345079344898219),(-323364093250190047372023969363)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨25036101727980949466992428,25036101727980950118683720⟩,⟨(-125584700509386498399195920),(-125584700509386497736170622)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨39241594419330967168258619,39241594419330969329465503⟩,⟨(-409857349762237560869664098),(-409857349762237558667171356)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-81928246095040844653604147),(-81928246095040840080240604)⟩,⟨(-782122244856686191514613718),(-782122244856686186861114596)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-518662795786746324600325662),(-518662795786746315361548054)⟩,⟨(-1239820151362123516379628476),(-1239820151362123507047376098)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1550861602979173390530733251),(-1550861602979173371879761570)⟩,⟨(-1600267109012843079899136673),(-1600267109012843061200360215)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-3429472159173095765602203377),(-3429472159173095727963942957)⟩,⟨(-1285179745640492086872582406),(-1285179745640492049370474160)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-5908812692445055811127409105),(-5908812692445055736037021949)⟩,⟨830867773944530564185240960,830867773944530638768930844⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-7435878915673806784861389974),(-7435878915673806637496551085)⟩,⟨6001514459365482779219949599,6001514459365482926149604165⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4789949183849918223410100529),(-4789949183849917937720142677)⟩,⟨14051506960877854895898750520,14051506960877855181880823703⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨5196752125878593358440090039,5196752125878593951287609489⟩,⟨21389492165578479617907027870,21389492165578480212257786807⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨21623750024872971819088496869,21623750024872973724817076915⟩,⟨21590478066748796225179198397,21590478066748798132075884017⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨37298646101066478498651242368,37298646101066485823799189694⟩,⟨10739257403021330852378657371,10739257403021338177130918909⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨43227289460461203196982932680,43227289460461222511748586298⟩,⟨(-6794308337936117372002610560),(-6794308337936098059261858295)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨36600848973015958242692249335,36600848973015992628667973750⟩,⟨(-20116318651057346969184812658),(-20116318651057312585658141243)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨22503935640979980460134580274,22503935640980026136811854866⟩,⟨(-20673098711866393374280084536),(-20673098711866347698890565844)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨7294804262349769778319204153,7294804262349791965791717599⟩,⟨(-8578884825682016834852694047),(-8578884825681994647740962267)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1491234044887566383773198),(-1491234044887562991287542)⟩,⟨398667458590701432404007,398667458590704824816074⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-4665593695308804713797033),(-4665593695308796141247984)⟩,⟨1624248304093190439495636,1624248304093199011888228⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-8281245548582897909319495),(-8281245548582888121592535)⟩,⟨4310036330580836577990951,4310036330580846365713931⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-12062585446661626298719406),(-12062585446661619074020282)⟩,⟨9976951364430968852220913,9976951364430976077605958⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-14414793101003414951510720),(-14414793101003411380484993)⟩,⟨20706084163723770035488933,20706084163723773608942475⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-11178245451422312694767144),(-11178245451422311446797471)⟩,⟨38439980318304907090153462,38439980318304908343772617⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨5407542323373690926846269,5407542323373691529822099⟩,⟨62661174825612010657429096,62661174825612011266824414⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨45487906240761143247681922,45487906240761143826951510⟩,⟨86170161669483228014741359,86170161669483228597083321⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨115277136633151870017795894,115277136633151870927321255⟩,⟨91466216083253944144539574,91466216083253945047408235⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨205933365810398377874103219,205933365810398379389565156⟩,⟨54373424445248137154127848,54373424445248138646021508⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨286667829229529783608470348,286667829229529785991233660⟩,⟨(-39347547418892205971215545),(-39347547418892203617075502)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨316517545500755798812491504,316517545500755802188581728⟩,⟨(-171787258566690862603298790),(-171787258566690859243372142)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨274961320316607356231257993,274961320316607360373351202⟩,⟨(-288444857679820769197954186),(-288444857679820765053234878)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨183685344318773425599461452,183685344318773429798496286⟩,⟨(-326543476354376894655131333),(-326543476354376890438550970)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨90159614884905504254064567,90159614884905507442546150⟩,⟨(-255969188468380998638963610),(-255969188468380995430746794)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨24561123272597680682339820,24561123272597681875297039⟩,⟨(-96443058685899695766286750),(-96443058685899694564875703)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨23507025003788856400188,23507025003789209923891⟩,⟨23319533929022055447182,23319533929022408970898⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨79064905429894108632492,79064905429895542131081⟩,⟨67276408756029017137033,67276408756030450636808⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨160804902704556820204743,160804902704560946187858⟩,⟨99373519282252705210413,99373519282256831199788⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨286285796454749892915727,286285796454761477847249⟩,⟨98566110426868940048572,98566110426880524999663⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨465500681169978070097707,465500681170008868455754⟩,⟨23007207753097838213133,23007207753128636619201⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨681442417582356012512859,681442417582426506761391⟩,⟨(-195076286421150891652463),(-195076286421080397302530)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨858303721844238822227809,858303721844406242199354⟩,⟨(-637997003063506237562533),(-637997003063338817452569)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨833285387416871844604969,833285387417220547226917⟩,⟨(-1355999616168349462981110),(-1355999616168000760246014)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨373685474378488334389008,373685474379011581368049⟩,⟨(-2282001884511789868835938),(-2282001884511266621832696)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-711109985844412318821897),(-711109985843854447324493)⟩,⟨(-3156854932589310673210134),(-3156854932588752801868802)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-2372997558977681652948039),(-2372997558977262764167264)⟩,⟨(-3573382168011408605446825),(-3573382168010989717088995)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-4179100528400569771768328),(-4179100528400327172027460)⟩,⟨(-3211741307779827304710018),(-3211741307779584705644831)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-5406826683188253930453123),(-5406826683188098386548980)⟩,⟨(-2141775028727975741240028),(-2141775028727820197928548)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-5406538884115373005783677),(-5406538884115284636898379)⟩,⟨(-883998484235617203574189),(-883998484235528835083500)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-3977358358995126277518813),(-3977358358995084206212571)⟩,⟨(-64706529326124382603880),(-64706529326082311501097)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1458244087741081943770500),(-1458244087741069797608128)⟩,⟨83637273248520431463114,83637273248532577566766⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨62745814857689094604,62745814857689094827⟩,⟨(-488343167011039758219),(-488343167011039757954)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨53254531005737940535,53254531005737941201⟩,⟨(-1538595477314212261733),(-1538595477314212260917)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-405537910731898880064),(-405537910731898878836)⟩,⟨(-2783182361461866108604),(-2783182361461866107081)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1739419620685794610171),(-1739419620685794607844)⟩,⟨(-4242451658020572577631),(-4242451658020572574896)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-4484343721932122451999),(-4484343721932122447590)⟩,⟨(-5679360606187673093632),(-5679360606187673088764)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-9160641192408986448088),(-9160641192408986439784)⟩,⟨(-6352351687882523849867),(-6352351687882523841139)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-15952008934065570752978),(-15952008934065570736183)⟩,⟨(-4815703933146478623092),(-4815703933146478606068)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-24140689237126799612581),(-24140689237126799565581)⟩,⟨932771431023711806274,932771431023711853174⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-31539251549551102604087),(-31539251549551102341662)⟩,⟨12666592594839810175578,12666592594839810437570⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-34632336340896005092523),(-34632336340896003151603)⟩,⟨30501453507484821547236,30501453507484823487656⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-30149786258868243834816),(-30149786258868231259058)⟩,⟨51492682304990505382719,51492682304990517958373⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-17738319916825359253323),(-17738319916825290383433)⟩,⟨69550316678874284964250,69550316678874353834686⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1677604499222883833646),(-1677604499222652313740)⟩,⟨77533264783934134433514,77533264783934365954426⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨10664535123852015051755,10664535123852485125845⟩,⟨70724210124906166773638,70724210124906636848695⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨13309390307260612200035,13309390307261159062084⟩,⟨49246569081315092161496,49246569081315639024171⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨5855356369467336894514,5855356369467587222048⟩,⟨17591449722448204072075,17591449722448454399814⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-484474265458980765784080034708),(-484474265458965260477490601063)⟩,⟨6165255120522591888307167616557,6165255120522607393601716393010⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 20) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_20 (tableDensity false) (fullFactor true 0 20) density0_contains hk0_1_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1623758900417341388802750421162),(-1623758900417341385212757163378)⟩,⟨204717164411552944133505034867,204717164411552947577896939991⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_20 0 20 ha0_1_20_contains + def realAnswer : RBox := ⟨(-2108233165876322154586930455870),(-2108233165876306645690147764441)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_20 +namespace hm0_1_1_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-75643070264710395695689090790),(-75643070264710222403843224989)⟩,⟨(-66706225796973999904729240175),(-66706225796973826619242736925)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-270157903364491086845417222754),(-270157903364490598508668116981)⟩,⟨(-166610000117663044349570952515),(-166610000117662556028762990767)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-562034644503526607514651190761),(-562034644503525978276622391118)⟩,⟨(-124169146614735039732968970491),(-124169146614734410507771809448)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-858696331691145152314356261368),(-858696331691144685314841091457)⟩,⟨244583751681628615493073722736,244583751681629082511609440167⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-760297890863534687465658376822),(-760297890863534490491545645850)⟩,⟨1020173803813876083360464716887,1020173803813876280403058484865⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨283209982030025215798467408234,283209982030025300421735519774⟩,⟨1691490544727426028824274378163,1691490544727426113441185164884⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1999275625549205090722802180674,1999275625549205113213081955914⟩,⟨1013439685786108509395675896447,1013439685786108531761669139648⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨2457684997407144013470414517408,2457684997407144023176042523536⟩,⟨(-1489427691574973773752840369430),(-1489427691574973763980625273355)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-18889439151082439726254611226),(-18889439151082433706516695187)⟩,⟨(-3570892427067214792936990585743),(-3570892427067214786766639711707)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3532297249135278263258839296636),(-3532297249135278258225576844924)⟩,⟨(-2253168369947292281622158786650),(-2253168369947292276793416657848)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-4238559199442675448046689421160),(-4238559199442675443869920555491)⟩,⟨1594216318030558170656042991984,1594216318030558174736718755735⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1646496456921671709835579619900),(-1646496456921671706934605473158)⟩,⟨4116742660000451399449612341175,4116742660000451402604232692374⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1261860168546903511614848505128,1261860168546903513928733739700⟩,⟨3678653673536338911921702207684,3678653673536338914370774060249⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2341947095729007063845741521140,2341947095729007065558784203710⟩,⟨1868134137458847453389473692011,1868134137458847455032074851948⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1808283212705997076611116774521,1808283212705997077522626625794⟩,⟨513153814365162596193647797148,513153814365162596989605632064⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨638198892508809794388304322435,638198892508809794657886574224⟩,⟨46090693364496395603684463690,46090693364496395823018304463⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1546250977390683309758817261,1546250977390689754563926363⟩,⟨(-989860037996091949536166700),(-989860037996085504675619590)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨4411701025605190028620856210,4411701025605217525329621488⟩,⟨(-3782352547694928871304110164),(-3782352547694901374475256423)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨5940931194136037539071911931,5940931194136121535803157475⟩,⟨(-8980789962473829772535871371),(-8980789962473745775795913351)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3024985931268309311687597629,3024985931268543035812012944⟩,⟨(-17395340537006267291043727665),(-17395340537006033567459195082)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-9980114229659762804872366376),(-9980114229659140584375767664)⟩,⟨(-26149166066354951744648384356),(-26149166066354329525640971600)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-37306099708478421691426370390),(-37306099708476270210996429651)⟩,⟨(-23654271593325979386808698198),(-23654271593323827907123498735)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-68710667800617016688229333436),(-68710667800612392471558490323)⟩,⟨10629782033348394325371715415,10629782033353018544446916672⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-64958194007522040192970158262),(-64958194007512984572903068399)⟩,⟨85916171446069076226381003606,85916171446078131849944110045⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨23947178854392684788173006508,23947178854406491029960123205⟩,⟨159727769466743454156744795534,159727769466757260395225673886⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨186660006942093759235387026288,186660006942107788640213765139⟩,⟨135603701729356512006311094880,135603701729370541403121306823⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨305881850412104737151276443670,305881850412118199240575664201⟩,⟨(-39643510308031424468771035187),(-39643510308017962376111283387)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨258817998740161749693103235827,258817998740169186027927586155⟩,⟨(-273964138040998157197134539167),(-273964138040990720847983558948)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨70872013612579780700344184495,70872013612584837162945996537⟩,⟨(-401563711299771138984942739246),(-401563711299766082517835892373)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-104213050448102162339984626091),(-104213050448099635633786628624)⟩,⟨(-358856592677300851952998961996),(-358856592677298325252753514283)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-148965382726854458867364107397),(-148965382726853480650292426543)⟩,⟨(-218555668066557566501742617192),(-218555668066556588293147196361)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-65884801186031361689765386454),(-65884801186031120598455487790)⟩,⟨(-69373929159818546530982613936),(-69373929159818305443413953829)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨19672924799057993268931891,19672924799057993474505336⟩,⟨(-21185434972916894302866267),(-21185434972916894096775542)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨56447723713769503575081553,56447723713769504262795433⟩,⟨(-74007577234393710636158625),(-74007577234393709946493613)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨79217004503952305398163951,79217004503952306817118824⟩,⟨(-158668864893023958697220173),(-158668864893023957274539616)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨55951595663883600690496440,55951595663883603407368467⟩,⟨(-293195950966198204736377124),(-293195950966198202015250166)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-80895939493273000168330891),(-80895939493272995103692289)⟩,⟨(-470877063087427235086099738),(-470877063087427230019145707)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-429202752076791743953074518),(-429202752076791734734004884)⟩,⟨(-609240200770768536944557369),(-609240200770768527730076055)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1042334279469858710045336275),(-1042334279469858693648585572)⟩,⟨(-483888810854116815299973582),(-483888810854116798923071075)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1745470406258840634502523826),(-1745470406258840604815817052)⟩,⟨257894749016373208437934511,257894749016373238106720801⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1952284683119712410457361194),(-1952284683119712350260123456)⟩,⟨1838157389073479064228510454,1838157389073479124431540667⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-839340283712643589248643826),(-839340283712643412356628381)⟩,⟨3859452423704741673263847792,3859452423704741850184544046⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1876856928149955657360124660,1876856928149956716878320589⟩,⟨5128540028545248936480870767,5128540028545249996011613282⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨5182163469997605412134031796,5182163469997610679181292151⟩,⟨4464935457475145060934829266,4464935457475150327977068802⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨7227613044241329441497971484,7227613044241344334394871973⟩,⟨2010687884850375720478285810,2010687884850390613364639415⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨6901140837734660223214308675,6901140837734687429718258797⟩,⟨(-596317250268357237004050356),(-596317250268330030499893814)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨4646162008724592605678708093,4646162008724629265794645655⟩,⟨(-1655786437223947443729622488),(-1655786437223910783606491586)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1591839771868338228194613670,1591839771868356114962378055⟩,⟨(-822274615316985313221329350),(-822274615316967426449319848)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-479268166508835317246846),(-479268166508832468174259)⟩,⟨(-191139482608797395341028),(-191139482608794546260219)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1549632696609684358937048),(-1549632696609677165578901)⟩,⟨(-493717654354184632780755),(-493717654354177439404847)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-2944825916117154130957220),(-2944825916117145933571284)⟩,⟨(-492505045334191873053171),(-492505045334183675665083)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-4814734990419976410808740),(-4814734990419970384083744)⟩,⟨236565158884179577185622,236565158884185603841075⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-7072202127079550240982566),(-7072202127079547296171768)⟩,⟨2444654585674377061218773,2444654585674380005783330⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-9016305325274619948004871),(-9016305325274618975424068)⟩,⟨7202003505147220482756561,7202003505147221454775421⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-8781018878787686927224221),(-8781018878787686552122111)⟩,⟨15476627898489365137836109,15476627898489365512324670⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3038390836482550821653730),(-3038390836482550576582341)⟩,⟨26992244357778684168053319,26992244357778684412894902⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨12062450097828131834428089,12062450097828132160055262⟩,⟨38553632748203576943920757,38553632748203577270280656⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨37913853415236475056957882,37913853415236475581816210⟩,⟨43339126240345864481825966,43339126240345865008983226⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨69646993521635933616541486,69646993521635934443719583⟩,⟨33664438391290713277271529,33664438391290714107031549⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨95617838428023562186372629,95617838428023563373369507⟩,⟨7630089675755696904628195,7630089675755698092770671⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨103433592170498839897967776,103433592170498841377313998⟩,⟨(-25422710567559553700777413),(-25422710567559552222081291)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨88743965827484030741834569,88743965827484032266179061⟩,⟨(-47952258366431564193328903),(-47952258366431562670891924)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨57619036524329143807316903,57619036524329144980604084⟩,⟨(-45785824159302771867891176),(-45785824159302770696564511)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨19621975925232738978658596,19621975925232739421037353⟩,⟨(-18700990407804510925283737),(-18700990407804510483718692)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨8105727774939484571173,8105727774939775107333⟩,⟨7256889923032876735852,7256889923033167272214⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨27449549772503424930874,27449549772504603111922⟩,⟨21426295914007074180353,21426295914008252361784⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨56433517034194779871054,56433517034198171452031⟩,⟨33350502107038555618449,33350502107041947199160⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨101840152047398951263739,101840152047408475695345⟩,⟨37086208245618930785257,37086208245628455214112⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨168909724968448698266580,168909724968474021918218⟩,⟨18830245647003619426364,18830245647028943069255⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨256021865873274196584655,256021865873332159558554⟩,⟨(-46481278661767703638672),(-46481278661709740685398)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨344503433053849431038154,344503433053987058467126⟩,⟨(-193922680933841994781728),(-193922680933704367383921)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨386643756818041253881714,386643756818327761443733⟩,⟨(-456201383509275682789045),(-456201383508989175256341)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨304863033261724678183724,304863033262154253246586⟩,⟨(-836138708324495773288715),(-836138708324066198236653)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨21687447028110512493928,21687447028568024875307⟩,⟨(-1273313076640888545794932),(-1273313076640431033386939)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-474523421390174755756361),(-474523421389831658253806)⟩,⟨(-1635291095197741871392408),(-1635291095197398773812072)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1067274710438163017245660),(-1067274710437964584886096)⟩,⟨(-1766850830722901018009769),(-1766850830722702585525944)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1524944851280086295005588),(-1524944851279959236553670)⟩,⟨(-1588372178381165063725569),(-1588372178381038005163971)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1612664627454033799574883),(-1612664627453961693490589)⟩,⟨(-1165985723934742902078255),(-1165985723934670795920920)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1227529821987184453760011),(-1227529821987150152999484)⟩,⟨(-664839295420642550105203),(-664839295420608249306864)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-457744345686445139825192),(-457744345686435241441044)⟩,⟨(-208742132420596171651983),(-208742132420586273257002)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1169439617420877247,1169439617420877362⟩,⟨(-14593934631310116178),(-14593934631310116034)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-9754138407437248799),(-9754138407437248476)⟩,⟨(-43853815756529229454),(-43853815756529229023)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-68997097351221935569),(-68997097351221935003)⟩,⟨(-50993520674126942732),(-50993520674126941954)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-240819932477666821964),(-240819932477666820870)⟩,⟨58077216415611481463,58077216415611482850⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-636646067723900010827),(-636646067723900008596)⟩,⟨500760129771041320058,500760129771041322613⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1382026174300037307513),(-1382026174300037302919)⟩,⟨1649409113966246973051,1649409113966246977919⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-2470077991185620462812),(-2470077991185620452413)⟩,⟨4028785227974214130645,4028785227974214141139⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-3535925490906487790472),(-3535925490906487756579)⟩,⟨8229704093793538470420,8229704093793538504011⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3710287465573169592185),(-3710287465573169382941)⟩,⟨14602005814898772117365,14602005814898772325744⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1776400829078655964966),(-1776400829078654384992)⟩,⟨22696174049339309474743,22696174049339311053265⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨3177853514971730469480,3177853514971740730728⟩,⟨30795055779282012948356,30795055779282023207896⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨10730122797846238128264,10730122797846294358143⟩,⟨36183758544400502399007,36183758544400558627773⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨18360626047335298547346,18360626047335487675241⟩,⟨36424412177709840499728,36424412177710029627265⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨21971453191675469895906,21971453191675854094682⟩,⟨30748183768446585807356,30748183768446970006234⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨18183669774034519308861,18183669774034966439703⟩,⟨20277956846213135135204,20277956846213582266285⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨7078399800381755907804,7078399800381960624382⟩,⟨7039867751680547881439,7039867751680752598132⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-131589620922921421305306964735),(-131589620922908664263165582138)⟩,⟨1179512422820775211323256091967,1179512422820787968363218617228⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 20) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_20 (tableDensity true) (fullFactor true 0 20) density1_contains hk0_1_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨2123377023622677196047451675186,2123377023622677200742058243058⟩,⟨(-267707061153569239140326767680),(-267707061153569234636121968672)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_20 0 20 ha0_1_20_contains + def realAnswer : RBox := ⟨1991787402699755774742044710451,1991787402699768536478992660920⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_20 +namespace hm0_0_1_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨121218885962150292954567757078,121218885962150402903946775434⟩,⟨206470356110582174016333792499,206470356110582283970744968929⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨494014140245581298079981797249,494014140245581551457070302463⟩,⟨566780077410751605180437883107,566780077410751858581140509627⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1208397913376633589759235963416,1208397913376633854049723616281⟩,⟨639840022053202700573428519313,639840022053202964915650013623⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨2159512148122871934326591134514,2159512148122872177063315205327⟩,⟨(-106930324129336372782676652328),(-106930324129336130017676557297)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2377394036848584731449204701465,2377394036848584855147500159346⟩,⟨(-2158553444128855584987615944129),(-2158553444128855461353174808188)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨83496279154222833786765330390,83496279154222887330567062607⟩,⟨(-4557402429818519190827536983196),(-4557402429818519137365450228908)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-4824322687792976520981916114970),(-4824322687792976494764408314327)⟩,⟨(-3849527816197624617409326804009),(-3849527816197624591103218740682)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-7531997893194813209048256253243),(-7531997893194813191404868729979)⟩,⟨2423292195014981240015812556921,2423292195014981257722153651379⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-2281140475581662673887745932449),(-2281140475581662660596408642458)⟩,⟨9250784642797643839471954976167,9250784642797643852663216598951⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨7443412071154582927366629443190,7443412071154582937442750028764⟩,⟨7692431487543515548406418816300,7692431487543515558450071872924⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨11012912814481799048963595131289,11012912814481799056137233470806⟩,⟨(-1777572964217359577113424757351),(-1777572964217359569884818373268)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨5500075535846758758469210769053,5500075535846758763389767946259⟩,⟨(-9197370044910340889840799915710),(-9197370044910340884848524410302)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1907751490901203142570641651873),(-1907751490901203139131369238807)⟩,⟨(-9179911078422301949690935312683),(-9179911078422301946229651797057)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-5152444174990221776120244215402),(-5152444174990221773807940374230)⟩,⟨(-5111565092791360899650627170187),(-5111565092791360897379560040329)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-4247768108784529610963265219818),(-4247768108784529609785975252778)⟩,⟨(-1693587471229957154958515134358),(-1693587471229957153836661326579)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-1535240833031299817272372831331),(-1535240833031299816931452354769)⟩,⟨(-270995640607091675454503203708),(-270995640607091675137151663680)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3864870732030220657331471613),(-3864870732030218045934071959)⟩,⟨1022539928476087981491414555,1022539928476090592710455659⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-11900717830820512417516737666),(-11900717830820502409339962316)⟩,⟨4914459447138041332906196126,4914459447138051340363998716⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-19525584609768033301436635921),(-19525584609768005992260568656)⟩,⟨14988301192555143479857270124,14988301192555170787393294255⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-21144881405210956090627911638),(-21144881405210854945194964597)⟩,⟨36184182342385905957758217096,36184182342386007101635628355⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1807983840540193738681148149),(-1807983840539866472410264597)⟩,⟨68655064318447756821704004481,68655064318448084088718237721⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨60483383488194147914822900222,60483383488194916709344822380⟩,⟨92536701693765508593254873431,92536701693766277393976248820⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨167073351283274737798678001593,167073351283276989376426183654⟩,⟨51882064734909501893502763006,51882064734911753474832384072⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨242685418266317797568585771400,242685418266321684293507026602⟩,⟨(-118062515427426120187142720428),(-118062515427422233473673671681)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨129026430109591715359377697218,129026430109597969267733761488⟩,⟨(-378875255837899100809740507095),(-378875255837892846912063630725)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-252522310595898810393135299496),(-252522310595892003085458453113)⟩,⟨(-500979985712467985096711578809),(-500979985712461177769209935353)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-688855285855745867899290281153),(-688855285855739991996390498542)⟩,⟨(-240600141928611222697665274066),(-240600141928605346773139794376)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-804468061076944709562495943757),(-804468061076940504400721950721)⟩,⟨313385471720616091518760509529,313385471720620296662342942381⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-500909590365862648553989296850),(-500909590365860618903147761297)⟩,⟨756688592909010623298697216098,756688592909012652910664324804⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-76022850475425680529028751529),(-76022850475424427752126183733)⟩,⟨811511883208055341675935818048,811511883208056594440127713993⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨140759193508769113272855373450,140759193508769689733392427290⟩,⟨552929915719478011872757381061,552929915719478588336909934294⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨84757357456639324198297131813,84757357456639481306050677134⟩,⟨187152883075342383069285963699,187152883075342540180534639738⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-33942515768890403220512465),(-33942515768890402972738475)⟩,⟨10879959654568779054692708,10879959654568779299877639⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-105224077220455590379422412),(-105224077220455589550741897)⟩,⟨46461313077968224635800361,46461313077968225457564389⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-179574981170477956069087268),(-179574981170477954300154612)⟩,⟨129313951307743315552127490,129313951307743317313690805⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-228976845540842726277306450),(-228976845540842722688589282)⟩,⟨305997420234936898651344498,305997420234936902243446035⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-160657736004656040342287417),(-160657736004656033030030628)⟩,⟨621906641561354703216681299,621906641561354710568029607⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨222573605228864765109582223,222573605228864780115717451⟩,⟨1049241210735426180368033605,1049241210735426195470607923⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1185269516011533853440458803,1185269516011533884301500685⟩,⟨1326525945838563028957686869,1326525945838563059883250186⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨2791707279502665952631884260,2791707279502666014604737009⟩,⟨797742756613546683257722728,797742756613546745135619890⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨4380356627769773129735149269,4380356627769773250733105038⟩,⟨(-1402479160268943241330155514),(-1402479160268943120673062720)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨4310899406663775075070623711,4310899406663775332929733101⟩,⟨(-5453528589420942093783117812),(-5453528589420941836094481181)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨949618559010610278667830880,949618559010610978887815482⟩,⟨(-9780767765292943377018532326),(-9780767765292942676472306865)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-5287622614136841783873910206),(-5287622614136839648139320215)⟩,⟨(-11533441060983645999310219474),(-11533441060983643862788762101)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-11229989711463466237826663375),(-11229989711463458982966418235)⟩,⟨(-9179712546827621408402344195),(-9179712546827614153099909975)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-13271806340885315973594750123),(-13271806340885300924610540766)⟩,⟨(-4444314846353014045298152619),(-4444314846352998996338005255)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-10291594591225627892160175353),(-10291594591225610775280148700)⟩,⟨(-740703079501581644401810067),(-740703079501564527753202079)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3810881081380514193706392719),(-3810881081380506577730060659)⟩,⟨216694586063515882147891495,216694586063523498002299947⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨195714054606899331109053,195714054606900120998811⟩,⟨299393271002361324112544,299393271002362113991585⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨700517047025201122594895,700517047025203083744543⟩,⟨910149141290363891042380,910149141290365852138948⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1577929621183606683394222,1577929621183608842717316⟩,⟨1510592856639381848176215,1510592856639384007331305⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3165431210431303975921168,3165431210431305478104005⟩,⟨1910879738283920223801883,1910879738283921725548682⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨5829784222333984205531246,5829784222333984922680579⟩,⟨1547688357515842621754111,1547688357515843338015235⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨9677974773573673829371619,9677974773573674178316455⟩,⟨(-776170556014458057410312),(-776170556014457709436918)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨13853130078589964919499994,13853130078589965099976710⟩,⟨(-6956610098172843747519726),(-6956610098172843567491855)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨15519648046200496535547622,15519648046200496715791191⟩,⟨(-18874870324237118461568879),(-18874870324237118280085239)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨9492033878373793409345485,9492033878373793703641897⟩,⟨(-36351083982220581264718513),(-36351083982220580965963479)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-9669533433504588100240649),(-9669533433504587587833134)⟩,⟨(-54500412532393756435676439),(-54500412532393755918115848)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-42414331571289584152736845),(-42414331571289583320898290)⟩,⟨(-63639798518244696506296244),(-63639798518244695672417955)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-79457665647270819417067880),(-79457665647270818209441199)⟩,⟨(-55039771025432266260710515),(-55039771025432265056745102)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-104166338298284528114644298),(-104166338298284526603012089)⟩,⟨(-29913758040758010017717876),(-29913758040758008515635305)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-102941613161818338089532339),(-102941613161818336532282698)⟩,⟨(-1992115313047454512349617),(-1992115313047452966633877)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-74133610355761250994308575),(-74133610355761249796510293)⟩,⟨12131789060409038404032131,12131789060409039594724662⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-26752100741720238601139142),(-26752100741720238150064828)⟩,⟨6988205010222863649125384,6988205010222864097920264⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨3747400387869196082150,3747400387869265515930⟩,⟨(-5361275087229074367426),(-5361275087229004933893)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨10416423138044066533580,10416423138044346164299⟩,⟨(-17732931942145921911556),(-17732931942145642281841)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨13777929847095026611779,13777929847095819812846⟩,⟨(-35045022403085057078855),(-35045022403084263880465)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨8801887315186547005642,8801887315188719114779⟩,⟨(-60165487084866955876614),(-60165487084864783773714)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-13798408576696949883401),(-13798408576691413544220)⟩,⟨(-93568193317975754714261),(-93568193317970218388228)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-68012982161827518298769),(-68012982161812869472770)⟩,⟨(-128780590377581211295595),(-128780590377566562490217)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-168725407889136047387058),(-168725407889096473119873)⟩,⟨(-145545626248628540799508),(-145545626248588966551197)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-319813052206419465818719),(-319813052206341465920697)⟩,⟨(-105093203445259517550019),(-105093203445181517659351)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-494954112031854134250194),(-494954112031743473938654)⟩,⟨42400424707570458781440,42400424707681119113420⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-625072969208586369908447),(-625072969208476088264756)⟩,⟨328233976881174390109463,328233976881284671822634⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-618406414352604504212038),(-618406414352524204236406)⟩,⟨720914498797918312065370,720914498797998612165965⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-424706620210665148530699),(-424706620210602343394846)⟩,⟨1104011883594306875625034,1104011883594369680873593⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-103465648473265548927410),(-103465648473224992530488)⟩,⟨1316306925915048698765172,1316306925915089255232677⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨181567102130402182191373,181567102130424061972124⟩,⟨1242052476317792221422882,1242052476317814101228074⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨268325248575506495717423,268325248575516557891799⟩,⟨877139328176924630963317,877139328176934693134359⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨123281007483940962586728,123281007483943815937621⟩,⟨314615064107477376979227,314615064107480230324997⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-84587938177429657295),(-84587938177429657234)⟩,⟨(-6382107175297982491),(-6382107175297982441)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-265827965933788140652),(-265827965933788140498)⟩,⟨5318904198430863531,5318904198430863657⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-477983957144332207226),(-477983957144332206945)⟩,⟨98625922952814930680,98625922952814930913⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-720044106815882095602),(-720044106815882095091)⟩,⟨351373158717612860523,351373158717612860972⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-941250442967825182267),(-941250442967825181355)⟩,⟨861265118629686768748,861265118629686769584⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-994537242467454941194),(-994537242467454939559)⟩,⟨1719533420856670683196,1719533420856670684767⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-599479547588649777177),(-599479547588649773996)⟩,⟨2944536381838418057024,2944536381838418060187⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨625243564756276484763,625243564756276493389⟩,⟨4368579391755063984781,4368579391755063993449⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2999956431582322335639,2999956431582322382101⟩,⟨5530610500518238576264,5530610500518238622829⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨6496524665257646288307,6496524665257646623762⟩,⟨5722232512621921401736,5722232512621921737295⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨10476226071719312182571,10476226071719314812678⟩,⟨4332125927201762315920,4332125927201764946022⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨13723390063344308549749,13723390063344322796967⟩,⟨1406585880887147119632,1406585880887161366723⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨14917927691757214872529,14917927691757261905676⟩,⟨(-2019035240947271551896),(-2019035240947224518917)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨13315252786997500783341,13315252786997594912430⟩,⟨(-4303820401209473568895),(-4303820401209379439947)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨9114852730968911022393,9114852730969019380539⟩,⟨(-4198356929816873319386),(-4198356929816764961314)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3224615555640946706020,3224615555640996026319⟩,⟨(-1725861799185752425953),(-1725861799185703105677)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨222064938913632133172006268206,222064938913638086317304499852⟩,⟨(-2584791820637538638098316371576),(-2584791820637532684957289498984)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 21) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_21 (tableDensity false) (fullFactor true 0 21) density0_contains hk0_1_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨739871213328095623773237700616,739871213328095625692030790986⟩,⟨(-52851875974801875285044392992),(-52851875974801873432780220442)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_21 0 21 ha0_1_21_contains + def realAnswer : RBox := ⟨961936152241727756945143968822,961936152241733712009435290838⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_21 +namespace hm0_1_1_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨15890353904564240243452226234,15890353904564329356075805340⟩,⟨37737165163608748382405423066,37737165163608837493612103021⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨70436487860608640379889116763,70436487860608844948859036702⟩,⟨108298777706314086904999661096,108298777706314291467722962981⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨188380690073968315215843091101,188380690073968526482825175696⟩,⟨141183615011267473384916263067,141183615011267684638907958709⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨364778903801494672179555114535,364778903801494863439107690065⟩,⟨45877361482109697010535323577,45877361482109888264496042480⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨448205148155402996346696350917,448205148155403088133937327312⟩,⟨(-279443506892868445589198069102),(-279443506892868353779166882126)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨122553256636718442313067669225,122553256636718475337339875086⟩,⟨(-707782607827301329535036376490),(-707782607827301296489758519898)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-682433920892408137583279866804),(-682433920892408126964916546147)⟩,⟨(-657089245978595576251089044518),(-657089245978595565681572011618)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1173908187372396079474929502843),(-1173908187372396074940611077657)⟩,⟨351008861483117104224325275943,351008861483117108753962439302⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-311901770715941712955355990492),(-311901770715941710109782035362)⟩,⟨1502536407133623730895769026623,1502536407133623733823620081683⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1345888819629143232211417858355,1345888819629143234610598155486⟩,⟨1213977754773663710223451146552,1213977754773663712559356068266⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1915002918027091181249595934846,1915002918027091183137380485137⟩,⟨(-459082223953750567609474547500),(-459082223953750565789080447923)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨871639254123536146100758069364,871639254123536147450292275912⟩,⟨(-1727992126995969848570639086081),(-1727992126995969847122090243717)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-463840602562758718853049148326),(-463840602562758717837975572672)⟩,⟨(-1637451587207173838341878733915),(-1637451587207173837257815020388)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1002345574652336698319891499899),(-1002345574652336697557447762553)⟩,⟨(-848079908458328433049482911462),(-848079908458328432313751938375)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-790614523008244095939718400915),(-790614523008244095534081434163)⟩,⟨(-234017962681263702626133383375),(-234017962681263702270337599046)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-279999518960774206074788065574),(-279999518960774205955332473649)⟩,⟨(-20860541075561998587374973282),(-20860541075561998489929661858)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-606069398558944249700886754),(-606069398558942151199644395)⟩,⟨(-146381703076053568939091478),(-146381703076051470416363714)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1972434026579702890830023283),(-1972434026579694818211549591)⟩,⟨(-181470422807794991514985700),(-181470422807786918807377861)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-3624920893895481413906670068),(-3624920893895459246679515291)⟩,⟨725823424855207317555488894,725823424855229484993020200⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-4959664308539610471730688522),(-4959664308539527657451035813)⟩,⟨3594571011003122174010917233,3594571011003204988503802376⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-3690250714781967191192520059),(-3690250714781698086651351310)⟩,⟨9120444016456649613594545352,9120444016456918718086383008⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨4411131550429417713734144823,4411131550430051096325849536⟩,⟨15139085832232213791616844906,15139085832232847173441043472⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨21675039142753818129037476467,21675039142755677265731103669⟩,⟨12937806146179798167991492982,12937806146181657304165987452⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨38411187061970262279907935329,38411187061973473495028410550⟩,⟨(-10425860391923436766328218066),(-10425860391920225549817993644)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨27771446715884918285775039793,27771446715890085811003365831⟩,⟨(-54025854727571407630850489541),(-54025854727566240104174079444)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-30579108802229388168161917523),(-30579108802223768031981039837)⟩,⟨(-82788962652232803015164282617),(-82788962652227182881582212797)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-109121747900140260991955345402),(-109121747900135417915841648275)⟩,⟨(-49538684134783880054156757077),(-49538684134779036981063616251)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-142264364425520162366825789783),(-142264364425516704279599869712)⟩,⟨42406541675858315083186572145,42406541675861773173211652397⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-101137230837810818335953999365),(-101137230837809156930542666385)⟩,⟨127122168332750294048667616453,127122168332751955459973554135⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-28858621655913800806500556840),(-28858621655912778606217201116)⟩,⟨147368548272818472726726826617,147368548272819494928827683764⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨14615350205279138841488687306,14615350205279607182766429056⟩,⟨105913154956975632036834129793,105913154956976100377337840851⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨11689151044770511241629372135,11689151044770638427196119386⟩,⟨36986149337454731248797758783,36986149337454858433713875522⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-7813828825432069127578311),(-7813828825432069050633755)⟩,⟨(-1923995404169341784012282),(-1923995404169341707188859)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-25747470730695676165452466),(-25747470730695675905302477)⟩,⟨(-3637460511501670079642699),(-3637460511501669819830272)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-49824330065020908920615626),(-49824330065020908377359181)⟩,⟨2825740765716525630643584,2825740765716526173527076⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-79921990083726240128325188),(-79921990083726239081657035)⟩,⟨28591886605698828058009287,28591886605698829104763597⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-103679534173770629606076180),(-103679534173770627635797395)⟩,⟨90628738216878324745329473,90628738216878326717139947⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-82882320736044047942536152),(-82882320736044044293612346)⟩,⟨201883910029489532497870637,201883910029489536150521194⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨52833352266976766218349113,52833352266976772958646197⟩,⟨338453360282530562444206378,338453360282530569187351204⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨369325614790618367198835204,369325614790618379491056638⟩,⟨388497712813453564967707524,388497712813453577256943196⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨817687084084453867414121454,817687084084453891062856414⟩,⟨146313239099626906283464692,146313239099626929922056313⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1123415682179491803055878269,1123415682179491877036725574⟩,⟨(-541898564375647672094827370),(-541898564375647598118228911)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨891041025349845158942184510,891041025349845506009408107⟩,⟨(-1513359746571885126792991562),(-1513359746571884779722228895)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2265360120720999979366423,2265360120722416340980306⟩,⟨(-2235950762174657987808540087),(-2235950762174656571442256291)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1100003265856122156001903027),(-1100003265856116641593254421)⟩,⟨(-2230070203197005451092217750),(-2230070203196999936684016432)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1714922602692767741100710297),(-1714922602692755864982934513)⟩,⟨(-1564336778536487959598155541),(-1564336778536476083484327563)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1482924428647059407855436603),(-1482924428647045736593160955)⟩,⟨(-758004630158729270516300272),(-758004630158715599256257885)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-574037170555530176645281875),(-574037170555524069802299158)⟩,⟨(-198234106079251278850284984),(-198234106079245172007454104)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-7377617406457440493385),(-7377617406456777204930)⟩,⟨119335408786629623862376,119335408786630287151848⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4732674667883762814196,4732674667885408150184⟩,⟨378072782929565576775482,378072782929567222116725⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨112393592754758052403223,112393592754759860096398⟩,⟨689504683016886696195519,689504683016888503905766⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨428341298390220423424057,428341298390221674596684⟩,⟨1054927378947765608026630,1054927378947766859243774⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1126824905372912469447736,1126824905372913056562910⟩,⟨1389332048501955040276897,1389332048501955627481479⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨2409245976635523974383609,2409245976635524242983378⟩,⟨1423912779177428524167378,1423912779177428792861377⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨4344674584011605454556912,4344674584011605563385901⟩,⟨598076454580770734434157,598076454580770843298684⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨6537310500113595434791282,6537310500113595508061945⟩,⟨(-1914017028761592075108489),(-1914017028761592001971128)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨7763642006079113466110180,7763642006079113571098096⟩,⟨(-6788907212417756572512792),(-6788907212417756467961684)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨6079118169824126912070412,6079118169824127091868918⟩,⟨(-13673519952963467566407115),(-13673519952963467387074673)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-24929352283995132863029),(-24929352283994841849213)⟩,⟨(-20445321103537719037001454),(-20445321103537718746102405)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-9743173403146876926107773),(-9743173403146876502077922)⟩,⟨(-23830107838959313876250530),(-23830107838959313451802956)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-19162255385663380663409131),(-19162255385663380127195108)⟩,⟨(-21723026178832870739908720),(-21723026178832870202765801)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-23151553966690491779829581),(-23151553966690491219644978)⟩,⟨(-15245609641148823345411530),(-15245609641148822784163760)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-18775528189737943050310954),(-18775528189737942613282830)⟩,⟨(-7904238536664729472145694),(-7904238536664729034490831)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-7184316612371686855693415),(-7184316612371686689775006)⟩,⟨(-2258199659394183947098395),(-2258199659394183780985992)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1139539594514620154789,1139539594514677217223⟩,⟨(-1822271031871567741822),(-1822271031871510679375)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨3239690893770664347182,3239690893770894172198⟩,⟨(-6090398294200642690155),(-6090398294200412865041)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨4536691547804856870499,4536691547805508882569⟩,⟨(-12245238433207921642438),(-12245238433207269629985)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨3530911927898202374839,3530911927899988142579⟩,⟨(-21478897479718839836948),(-21478897479717054068101)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-2919405719934349694134),(-2919405719929797514380)⟩,⟨(-34367312517762824580953),(-34367312517758272398580)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-20161199394001898908536),(-20161199393989854170520)⟩,⟨(-49518641929930973245371),(-49518641929918928502887)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-55084832259129021039778),(-55084832259096489030026)⟩,⟨(-61245824825673210747959),(-61245824825640678733410)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-112804453035596554801624),(-112804453035532466930988)⟩,⟨(-57235089180629536027249),(-57235089180565448153915)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-190217363891862047285591),(-190217363891771197079558)⟩,⟨(-19447864132308364484977),(-19447864132217514282294)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-269583258932625447605382),(-269583258932535004681762)⟩,⟨67370023916121195442502,67370023916211638352806⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-319882145421786815407956),(-319882145421721045923613)⟩,⟨199622387355694784254042,199622387355760553714656⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-312204679230188100015237),(-312204679230136730254316)⟩,⟨342275256443811992364524,342275256443863362103850⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-242794217593343694032502),(-242794217593310564803798)⟩,⟨437003593979008682205621,437003593979041811420276⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-142923812015821897099686),(-142923812015804044191280)⟩,⟨432992548426674902423539,432992548426692755326647⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-58660851446264406035659),(-58660851446256202697281)⟩,⟨316514180960958585356145,316514180960966788694555⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-12971808443261485399129),(-12971808443259160252823)⟩,⟨115661080371217136296818,115661080371219461443826⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2521477136460797062),(-2521477136460797023)⟩,⟨(-69285769129383198),(-69285769129383167)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-7469642704854774544),(-7469642704854774458)⟩,⟨2095935004340462691,2095935004340462756⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-8122821451151704337),(-8122821451151704185)⟩,⟨12473437988247878523,12473437988247878640⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨12887534211048634736,12887534211048634996⟩,⟨41337114949103321925,41337114949103322140⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨96304318140328244183,96304318140328244660⟩,⟨105551407338618161883,105551407338618162310⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨313305837344018460483,313305837344018461385⟩,⟨221431738363373537616,221431738363373538483⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨764926846426346956836,764926846426346958767⟩,⟨376664835457157430569,376664835457157432501⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1562692036416328596631,1562692036416328602719⟩,⟨487287476509669739688,487287476509669745862⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2765032390083580987925,2765032390083581024655⟩,⟨372131706116507568806,372131706116507605734⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨4266674119439932613764,4266674119439932886220⟩,⟨(-206722426854543896618),(-206722426854543623861)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨5713497575029009480029,5713497575029011625685⟩,⟨(-1400178225475681685997),(-1400178225475679540094)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨6576152501862083776235,6576152501862095408093⟩,⟨(-3062269720124694025354),(-3062269720124682393392)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6430443339982449463527,6430443339982487884051⟩,⟨(-4620318259521023610067),(-4620318259520985189565)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨5238757006493662615006,5238757006493739547384⟩,⟨(-5217802196914139172445),(-5217802196914062240156)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨3336087661130095542066,3336087661130184138357⟩,⟨(-4192691642505288290629),(-4192691642505199694430)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1132320729202499130407,1132320729202539464082⟩,⟨(-1611285128022015877571),(-1611285128021975543933)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨54579084260027861350506162715,54579084260032751758403434482⟩,⟨(-479154901915427069199465829875),(-479154901915422178793139988739)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 21) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_21 (tableDensity true) (fullFactor true 0 21) density1_contains hk0_1_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-967523894352125048981886418981),(-967523894352125046472695454652)⟩,⟨69113991659356296027481826732,69113991659356298449673436989⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_21 0 21 ha0_1_21_contains + def realAnswer : RBox := ⟨(-912944810092097187631480256266),(-912944810092092294714192020170)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_21 +namespace hm0_0_1_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-7537946949064206467598959937),(-7537946949064160640326642318)⟩,⟨(-92479543586103036694423278737),(-92479543586102990867799671716)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-79429392184313711652451050288),(-79429392184313597007481996438)⟩,⟨(-281098380876537832565778683739),(-281098380876537717919616886089)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-326495283248770740194388872216),(-326495283248770621551036399554)⟩,⟨(-422295890093014801724915669163),(-422295890093014683068356882960)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-797388795693987898615451312662),(-797388795693987815696544246370)⟩,⟨(-293802685898365080641421289021),(-293802685898364997695412277773)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1188817814060779667077575019263),(-1188817814060779612808046449729)⟩,⟨453611538649136893497447901294,453611538649136947766341130173⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-634347911856066758972601955670),(-634347911856066736752032962126)⟩,⟨1708491654420512642356100390768,1708491654420512664531691102312⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1406190603207264700018761910868,1406190603207264712531068123921⟩,⟨2055290553835512523338264263881,2055290553835512535859014995739⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨3215145465298818100905349412077,3215145465298818109282911259798⟩,⟨(-183119527098119872647535478486),(-183119527098119864226207123372)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1706605508410120128188139170872,1706605508410120134532326702338⟩,⟨(-3515972851233866918563203526348),(-3515972851233866912249074810791)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2505331801262790021002486212480),(-2505331801262790016278781434844)⟩,⟨(-3640955009503783818974998151146),(-3640955009503783814272839097116)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-4626986525333328478966437201221),(-4626986525333328475740539075326)⟩,⟨164215641801123819604731258158,164215641801123822847973265348⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2614752231133276126632259828554),(-2614752231133276124423586598046)⟩,⟨3618857625989281567635906874463,3618857625989281569874879885990⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨587188245983613209163695481004,587188245983613210641821049398⟩,⟨3872007664916315364214966990041,3872007664916315365705652382177⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2092868265365696577798139845536,2092868265365696578794666743274⟩,⟨2199791549930129288398372298742,2199791549930129289379104774704⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1770479701546687576023251770355,1770479701546687576528579737326⟩,⟨729112448538795552199879682497,729112448538795552682250490284⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨642793668530795262577991084571,642793668530795262723513303352⟩,⟨114968824740926335267864801195,114968824740926335403507124185⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1106358333673051228339031353,1106358333673052108277871247⟩,⟨674926604971509669632705582,674926604971510549619798779⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨3844010737042719318321391016,3844010737042723101616204585⟩,⟨1665478205769152566088217414,1665478205769156349482147668⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨7994766944778242673021462649,7994766944778254361654890841⟩,⟨1078069621457965039330294739,1078069621457976727932921053⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨13374698973392875530223147134,13374698973392908081879417109⟩,⟨(-3708871964783820882744280851),(-3708871964783788331663642221)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨16133025811418905081392209740,16133025811418997810092100534⟩,⟨(-16459078673919744734354343214),(-16459078673919652006962141653)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨5379812978429394353859621756,5379812978429716025965382268⟩,⟨(-37287074989852525323276841466),(-37287074989852203651291525469)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-33128166180732494135638432543),(-33128166180731825694108050871)⟩,⟨(-50780513512028884395147479651),(-50780513512028215950463397815)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-93189977960253812544912054911),(-93189977960252272302089294484)⟩,⟨(-19438811693436346174480059303),(-19438811693434805930304676830)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-117037916533835121537763186377),(-117037916533833086891082399813)⟩,⟨83357617958596931562779187250,83357617958598966202818202517⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-24903465029226388256865281003),(-24903465029223689429472737492)⟩,⟨203323211774324937467719487764,203323211774327636292704454676⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨170074584702521687779113399759,170074584702523736232857804037⟩,⟨210461935997339763060555969659,210461935997341811525808344643⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨320794687202550756993120339311,320794687202552343858488561280⟩,⟨49370123605564883592112731697,49370123605566470463172216072⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨304662925326483118265240916124,304662925326484012614898170079⟩,⟨(-161982778760331348049918520968),(-161982778760330453709349603003)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨168555554636778588090253026119,168555554636778980284690659715⟩,⟨(-263304704745936953393258349410),(-263304704745936561212188786993)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨46293279566298339064631782553,46293279566298550875256133973⟩,⟨(-215228985274484595823752071792),(-215228985274484384018353320592)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2246294640141302527172506689,2246294640141365469888260808⟩,⟨(-79478050660732461487605602250),(-79478050660732398545875027926)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨6905768823747202989995868,6905768823747203078451973⟩,⟨6480403100364789861623475,6480403100364789950050973⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨24534719424303667893816160,24534719424303668191401232⟩,⟨18409954185992539558569203,18409954185992539855582196⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨54103559299120117940989548,54103559299120118583826414⟩,⟨24614171379057609130643176,24614171379057609770591725⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨103114331941243750616601279,103114331941243751942051260⟩,⟨11410359794574852235146331,11410359794574853551468069⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨169063906353972094495329678,169063906353972097257891607⟩,⟨(-51467180218438774367144276),(-51467180218438771619690668)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨213865668711941697428242118,213865668711941703236050434⟩,⟨(-210162630258628977205304087),(-210162630258628971405211839)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨126216370166187192276354941,126216370166187204415664576⟩,⟨(-490244399661584028804307320),(-490244399661584016642753534)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-276969364029362793335967742),(-276969364029362768485902880)⟩,⟨(-795236834477789454925190175),(-795236834477789430010019883)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1105073604231863314867923628),(-1105073604231863265080245779)⟩,⟨(-793030809359798928792169564),(-793030809359798878982671301)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2095546553473016745644828984),(-2095546553473016644575577417)⟩,⟨(-11066356885023974334990743),(-11066356885023873368545411)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2504603691390847414442815952),(-2504603691390847162511417637)⟩,⟨1681051666507415257200030446,1681051666507415508962027931⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1652724655730379245479019940),(-1652724655730378383894649698)⟩,⟨3597377665169480050240384131,3597377665169480911805797917⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨203588032304906655919508626,203588032304908929089846847⟩,⟨4584685252488712891428746924,4584685252488715164768386745⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1833808931131869075085164674,1833808931131872864202091714⟩,⟨4084369455438858825067847884,4084369455438862614447967327⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨2101699398380909505897071022,2101699398380914417173179763⟩,⟨2577363112211423503830287280,2577363112211428415261568878⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨901523371630782488223341190,901523371630784910477146750⟩,⟨844098186612032527205239058,844098186612034949503340208⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨49382983305224407573007,49382983305224565656650⟩,⟨(-61812373458955721593786),(-61812373458955563501850)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨142617572954052663588787,142617572954053047407095⟩,⟨(-211236501634196737621083),(-211236501634196353772294)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨206166967425789457215070,206166967425789859370937⟩,⟨(-442196690287715752254712),(-442196690287715350027482)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨170897739206385827490852,170897739206386128514857⟩,⟨(-815951434614795196596336),(-815951434614794895450278)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-122601927134679193587700),(-122601927134678998282918)⟩,⟨(-1371013997335092993845121),(-1371013997335092798409310)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-963663611013889130942601),(-963663611013889038678500)⟩,⟨(-2030650715869993216286474),(-2030650715869993123962144)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2727258607392016152729942),(-2727258607392016105011412)⟩,⟨(-2421443612640212302609774),(-2421443612640212255082844)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-5603356646206069415792251),(-5603356646206069362142950)⟩,⟨(-1679227846973545221524070),(-1679227846973545168594939)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-9038986255677806336667895),(-9038986255677806241753930)⟩,⟨1458260475573936061274082,1458260475573936155323071⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-11259241000157228516795955),(-11259241000157228347856245)⟩,⟨7858985323006465505357217,7858985323006465674040947⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-9777831004864808524835486),(-9777831004864808246687293)⟩,⟨16634057955190091195129420,16634057955190091474369995⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-3407299019552745200587755),(-3407299019552744790480861)⟩,⟨24528241636682471247411107,24528241636682471660253059⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨5650079189005457749902403,5650079189005458274389082⟩,⟨27561028945115609273197996,27561028945115609800205276⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨12321214521014270004550477,12321214521014270554485807⟩,⟨24034384151335536614527260,24034384151335537165841098⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨12217556367545703617242619,12217556367545704044468832⟩,⟨15642313002992702368692806,15642313002992702796364133⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨5053727766882049294313407,5053727766882049456030920⟩,⟨5313015580380703812417066,5313015580380703974183554⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1116654710517641293230),(-1116654710517628660032)⟩,⟨(-523902030608556759353),(-523902030608544126068)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-3643533636945602208872),(-3643533636945551751495)⟩,⟨(-1359781929499640583751),(-1359781929499590126046)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-7023726071629033695072),(-7023726071628893163627)⟩,⟨(-1391885074893715571891),(-1391885074893575039682)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-11646556936088816703276),(-11646556936088444433605)⟩,⟨478546031721716615523,478546031722088886790⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-17258461359894305121153),(-17258461359893278625846)⟩,⟨6148321748095725377975,6148321748096751876024⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-21974598431004886166726),(-21974598431001607491921)⟩,⟨18247886864211946424259,18247886864215225101918⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-20932409477518906769408),(-20932409477510481669258)⟩,⟨39062103366049946532331,39062103366058371634131⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-5697242913635719194277),(-5697242913619968496301)⟩,⟨67727751298094958564452,67727751298110709260530⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨33324236099884614471277,33324236099905565225945⟩,⟨96264015333963678999233,96264015333984629744717⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨99744509056914668081853,99744509056934575265332⟩,⟨108029099922863507573651,108029099922883414737434⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨182192405075838921720544,182192405075858392454053⟩,⟨84307878963242740050156,84307878963262210764111⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨252610615596469907935813,252610615596484984759067⟩,⟨20050649017209398257907,20050649017224475069872⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨279234392430463480794121,279234392430472630063868⟩,⟨(-62528619964695109854523),(-62528619964685960584309)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨246925745279773716720251,246925745279778412066793⟩,⟨(-120007747316905521620376),(-120007747316900826263858)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨165484311146524068781899,165484311146526147968321⟩,⟨(-115662575016437084978476),(-115662575016435005780225)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨57567022659715805006126,57567022659716382297390⟩,⟨(-47475869092639457401325),(-47475869092638880104890)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-318415119464499865),(-318415119464499844)⟩,⟨13947131507978820350,13947131507978820372⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3267364919087835049,3267364919087835085⟩,⟨43709664425153168963,43709664425153169002⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨20960214970737064248,20960214970737064300⟩,⟨78075613177356727192,78075613177356727255⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨66272965589398850689,66272965589398850782⟩,⟨116045751875240825320,116045751875240825421⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨156070752034310771452,156070752034310771612⟩,⟨147459412393305462707,147459412393305462879⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨305349215398024675859,305349215398024676154⟩,⟨144651675351156441293,144651675351156441598⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨514226909371336500198,514226909371336500775⟩,⟨56003998214575070092,56003998214575070670⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨746390876981688793583,746390876981688795111⟩,⟨(-187185910888658189214),(-187185910888658187701)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨909925350748484052939,909925350748484060720⟩,⟨(-638882067057980053675),(-638882067057980045918)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨869525028994668932323,869525028994668995187⟩,⟨(-1283424867297835804298),(-1283424867297835741449)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨517584656702604491765,517584656702605009036⟩,⟨(-1989711562848094946839),(-1989711562848094429564)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-115012278908027987941),(-115012278908025245789)⟩,⟨(-2528288964126060136660),(-2528288964126057394489)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-799491544970468270562),(-799491544970459381267)⟩,⟨(-2672351233260689328359),(-2672351233260680439042)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1196577348062121155415),(-1196577348062103640218)⟩,⟨(-2323341170476718106669),(-2323341170476700591455)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1062959169471163221953),(-1062959169471143299748)⟩,⟨(-1555972619778843161652),(-1555972619778823239444)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-423081778797948449176),(-423081778797939441723)⟩,⟨(-543422304138226549402),(-543422304138217541948)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-94919687222230904686574219783),(-94919687222228722027388968905)⟩,⟨1034013139172928310992899396978,1034013139172930493650407998330⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 22) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_22 (tableDensity false) (fullFactor true 0 22) density0_contains hk0_1_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-313030892515952151890991420412),(-313030892515952150910374976035)⟩,⟨4817713416864723929702177885,4817713416864724881331561369⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_22 0 22 ha0_1_22_contains + def realAnswer : RBox := ⟨(-407950579738183056577665640195),(-407950579738180872937663944940)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_22 +namespace hm0_1_1_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨809014663300737082694813558,809014663300774126873559380⟩,⟨(-15847659005504566052270120426),(-15847659005504529007988298691)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-6761810623856112193507169264),(-6761810623856019827751799662)⟩,⟨(-49734683360261900992557917708),(-49734683360261808627323547375)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-44218354995182264366753779166),(-44218354995182169864113910644)⟩,⟨(-80568739105287125959576333051),(-80568739105287031460736449563)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-124846451690324008432405640101),(-124846451690323944326157853420)⟩,⟨(-72759049360160705211354749362),(-72759049360160641112085747645)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-205721200621627266700886317128),(-205721200621627227101902574744)⟩,⟨38438931361285337160731835363,38438931361285376761932927392⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-139859616304163561749009203055),(-139859616304163549027088566353)⟩,⟨250783137146669238199576136739,250783137146669250936279331838⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨185574989741640778433025912492,185574989741640783193863535279⟩,⟨334061469567043624407313664151,334061469567043629157049990969⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨498246235694580819274583086401,498246235694580821261711628850⟩,⟨(-18106648854470224654539904207),(-18106648854470222682580294282)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨253518680053829524256096688445,253518680053829525571625320494⟩,⟨(-576060956477664809590596978801),(-576060956477664808240249836585)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-465186376315513763569690241827),(-465186376315513762484640232281)⟩,⟨(-586179829765096885007454502662),(-586179829765096883935938213540)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-812304452305222955131689891338),(-812304452305222954310364948477)⟩,⟨90416610697724099125497608657,90416610697724099910130110578⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-424118306871485597386405535268),(-424118306871485596785812546409)⟩,⟨685768653556616561809793985006,685768653556616562445510690529⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨156264398290984109202276958269,156264398290984109626907209683⟩,⟨693462116010197122047369576771,693462116010197122504847296768⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨408898264996767326776388963638,408898264996767327100165912318⟩,⟨366753299824130259882700714425,366753299824130260197056607949⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨329908286440542579385658666327,329908286440542579557943475674⟩,⟨101708074322828542603967727181,101708074322828542755741264228⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨117260608945043557670039267189,117260608945043557720562407887⟩,⟨9003848308593581482588498269,9003848308593581523908845770⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨101721436182643806739681868,101721436182644507640858349⟩,⟨174654267524718928404037865,174654267524719629298458740⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨404519051975347568221286239,404519051975350606030783958⟩,⟨501697260178474460330697954,501697260178477498125313065⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1005944954568307924125121011,1005944954568317400119437895⟩,⟨675155045669575662750453841,675155045669585138743114912⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2007261571657017041671208561,2007261571657043600340917887⟩,⟨291631290427007257838647449,291631290427033816575277875⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨2990558739029715667855501791,2990558739029791700905431001⟩,⟨(-1398067717561056742749761112),(-1398067717560980709532002887)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨2281617285292520728922649287,2281617285292785622854171833⟩,⟨(-4864372826543505539608409562),(-4864372826543240645641252926)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-2926535358741118175054593525),(-2926535358740566875406391035)⟩,⟨(-8243428480995111642442988067),(-8243428480994560343184532042)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-12966505568061847612491510752),(-12966505568060575552445644857)⟩,⟨(-5379026275387863411835451499),(-5379026275386591351993077185)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-19417774041833596673481663694),(-19417774041831916747837268089)⟩,⟨9923613218254265896861576676,9923613218255945823347631134⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-7496245686327263186780367418),(-7496245686325036179352791991)⟩,⟨31339239960713044547414872994,31339239960715271555183953277⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨24714338939816713653448052971,24714338939818400283395902064⟩,⟨36936890487683191299767653858,36936890487684877928106401274⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨54285532519884637392299906453,54285532519885940665180584857⟩,⟨12960665633099631555289474085,12960665633100934827375867775⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨56859942744944549377139219858,56859942744945280664508533109⟩,⟨(-24136242213950230800364023714),(-24136242213949499511536088960)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨35741227045484711494210181752,35741227045485029688533130295⟩,⟨(-45172199914340231138232436656),(-45172199914339912941826109654)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨13133708348283872790230944489,13133708348284044018711712022⟩,⟨(-39107710616278712471599212953),(-39107710616278541242325197239)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2204570710733802424318280259,2204570710733853151148882022⟩,⟨(-14848795028835136080036993507),(-14848795028835085353068011642)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨561105417483500635239481,561105417483500662749148⟩,⟨2063143142881139648526632,2063143142881139676035981⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨2513443997688956375176232,2513443997688956468518396⟩,⟨6462739139899605496386377,6462739139899605589704485⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨7305398211412828387784212,7305398211412828584139213⟩,⟨11239018420616764723965323,11239018420616764920192391⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨17695665014106494115704327,17695665014106494498065456⟩,⟨14756684823794124181049853,14756684823794124563013870⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨36146155473883022730398879,36146155473883023466797210⟩,⟨11348803917629861305365843,11348803917629862041145138⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨60038109103237669706638138,60038109103237671111727646⟩,⟨(-10800878895063426493504546),(-10800878895063425088779957)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨71686016286494718780333012,71686016286494721410819485⟩,⟨(-66037282927307596716678215),(-66037282927307594085384217)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨30454453267360508915459836,30454453267360513774548900⟩,⟨(-152430552312047409943658837),(-152430552312047405082097079)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-109367068025614347208490319),(-109367068025614337602295476)⟩,⟨(-219936364554033684725290506),(-219936364554033675118176997)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-337276824472135470628406249),(-337276824472135445926609562)⟩,⟨(-166134361884048415061756549),(-166134361884048390361758502)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-532542170114199956423004750),(-532542170114199847900113469)⟩,⟨83636689824526317241421494,83636689824526425762487808⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-529423776542483861504635501),(-529423776542483302258666720)⟩,⟨454334388640729518016692640,454334388640730077262816642⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-293961574125050031338627617),(-293961574125048357681640748)⟩,⟨729742457293705113686632768,729742457293706787344749383⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨4160547580152670201548021,4160547580155578137158414⟩,⟨742482721385458170630323471,742482721385461078566049423⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨150089986237649393553391672,150089986237653263803396855⟩,⟨515358023837130569191149054,515358023837134439440419952⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨81728167836487554084683638,81728167836489480227927895⟩,⟨178689632655939063618012516,178689632655940989760790121⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨25584255526779747104319,25584255526779879825330⟩,⟨(-6696423371319980955653),(-6696423371319848235493)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨79283701827627618956421,79283701827627940876092⟩,⟨(-27464710331717774712904),(-27464710331717452796373)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨137752427778708392731581,137752427778708729183428⟩,⟨(-73279402034375694810637),(-73279402034375358366137)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨192592593179655684111187,192592593179655934446230⟩,⟨(-169711443745144403584715),(-169711443745144153262161)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨210114671732214923153233,210114671732215083007894⟩,⟨(-349977225185409758118473),(-349977225185409598276849)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨110077854017021711771973,110077854017021782260306⟩,⟨(-638435321961909899086815),(-638435321961909828603655)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-247797003082844995652979),(-247797003082844968463422)⟩,⟨(-1001580482693970361982225),(-1001580482693970334772325)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1027565207993493287725085),(-1027565207993493267307219)⟩,⟨(-1266048943703867311224946),(-1266048943703867290735975)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2277183158999568430834331),(-2277183158999568397691324)⟩,⟨(-1063529007189657437735329),(-1063529007189657404512993)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-3711491107912164690515655),(-3711491107912164631776813)⟩,⟨57273443647071833883514,57273443647071892634182⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-4638436028257061656106715),(-4638436028257061558959541)⟩,⟨2256266894114441080603077,2256266894114441177635077⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-4323721105443352583148846),(-4323721105443352438619777)⟩,⟨4980875631962883293411610,4980875631962883437682309⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-2691790184959387452475608),(-2691790184959387265296906)⟩,⟨7021418940404154274985383,7021418940404154461943410⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-648218588378341251038785),(-648218588378341052008788)⟩,⟨7242668422494192502872639,7242668422494192701801636⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨550276933945125440707670,550276933945125597216674⟩,⟨5354379372282221068828827,5354379372282221225320856⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨397434947025647587449232,397434947025647647109942⟩,⟨1957232258924406343675228,1957232258924406403339817⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-375231589491968554121),(-375231589491958171826)⟩,⟨(-153139604761350834612),(-153139604761340452327)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1240341473780812597503),(-1240341473780771127147)⟩,⟨(-404098072317612841117),(-404098072317571370813)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-2444885448101041637916),(-2444885448100926120770)⟩,⟨(-434432438834930936690),(-434432438834815419679)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-4171798097650245352352),(-4171798097649939296075)⟩,⟨97563002050859126514,97563002051165182479⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-6420323074869130418383),(-6420323074868286393846)⟩,⟨1849874756753186098175,1849874756754030122129⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-8691783347080517440052),(-8691783347077821603477)⟩,⟨5866698069455197062759,5866698069457892898639⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-9499277306545045293229),(-9499277306538119433380)⟩,⟨13348635452632261536821,13348635452639187396126⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-5971281220014171037949),(-5971281220001229598765)⟩,⟨24832731318846864876791,24832731318859806316199⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨5700704963373612024417,5700704963390812301152⟩,⟨38796685422845227626725,38796685422862427905272⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨28093951055687642808105,28093951055703968628552⟩,⟨50599491029903019648860,50599491029919345473241⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨58999074206080774725122,58999074206096721792773⟩,⟨53585848097454508460540,53585848097470455532077⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨89302192075445093667277,89302192075457425372688⟩,⟨43308033902359000519912,43308033902371332227717⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨105997609462957163768529,105997609462964637430718⟩,⟨22422214149174747387552,22422214149182221049913⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨99720225277539361692462,99720225277543192730160⟩,⟨1159654279351804545406,1159654279355635581507⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨70256897643932294838757,70256897643933989779246⟩,⟨(-9175998836933005108285),(-9175998836931310169763)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨25165628854362670823902,25165628854363141187053⟩,⟨(-5218763700603285638130),(-5218763700602815275835)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨10377425002244498,10377425002244516⟩,⟨414702151349971340,414702151349971357⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨412293488938501113,412293488938501142⟩,⟨1210559695102554740,1210559695102554767⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2141737987495296928,2141737987495296962⟩,⟨1220531690696443184,1220531690696443225⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨6741139506050036009,6741139506050036062⟩,⟨(-2597563283787865697),(-2597563283787865633)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨16540646230794157341,16540646230794157429⟩,⟨(-17471546617300342442),(-17471546617300342347)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨33179840195639518571,33179840195639518736⟩,⟨(-56234274771061415149),(-56234274771061414979)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨52430698496624935066,52430698496624935420⟩,⟨(-137165658568404068200),(-137165658568404067851)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨56367969696462967530,56367969696462968604⟩,⟨(-279925848346911369830),(-279925848346911368776)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨9225707082283774797,9225707082283780928⟩,⟨(-493083369675074811992),(-493083369675074805902)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-133178998506032977708),(-133178998506032926642)⟩,⟨(-753416856768789607916),(-753416856768789556902)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-393626934211115076408),(-393626934211114654396)⟩,⟨(-991701282875506107040),(-991701282875505685058)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-733100698115264914942),(-733100698115262676212)⟩,⟨(-1110843573312593957517),(-1110843573312591718792)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1031013938398086812444),(-1031013938398079551070)⟩,⟨(-1043899913117179623450),(-1043899913117172362057)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1120291764129676147430),(-1120291764129661832313)⟩,⟨(-807307688819759299718),(-807307688819744984573)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-880806819177780195291),(-880806819177763906560)⟩,⟨(-486251756255298969639),(-486251756255282680890)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-335123355521616527249),(-335123355521609161098)⟩,⟨(-158778243641162475721),(-158778243641155109560)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-20161637281063286519277840603),(-20161637281061497284909433297)⟩,⟨187158593559329779601060441675,187158593559331568834740071758⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 22) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_22 (tableDensity true) (fullFactor true 0 22) density1_contains hk0_1_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨409348090213168197344336507123,409348090213168198626681088231⟩,⟨(-6300086775900024844818195636),(-6300086775900023600379771081)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_22 0 22 ha0_1_22_contains + def realAnswer : RBox := ⟨389186452932104910824958666520,389186452932106701341871654934⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_22 +namespace hm0_0_1_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-12380624594235464982963249667),(-12380624594235450098542595377)⟩,⟨32089320755828756552673015059,32089320755828771435943399952⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-17950168629780784665680597415),(-17950168629780743984366382704)⟩,⟨107056339524188966803436700957,107056339524189007482301521308⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨45922697163233786127866693662,45922697163233835493365884749⟩,⟨193956661559555567029121221929,193956661559555616394496323224⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨232545681752709311240681166236,232545681752709344398537723652⟩,⟨219031560589284510206872289935,219031560589284543373938831937⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨482222668194705093158844742576,482222668194705113416767586848⟩,⟨3909875597851348647776605941,3909875597851368914029935358⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨445020913714187632342227178032,445020913714187642116091360373⟩,⟨(-536304239945024073489656842040),(-536304239945024063729330630480)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-286577642711234666433299576403),(-286577642711234660824104865807)⟩,⟨(-917253730585543660804321751936),(-917253730585543655202032072858)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1229178382691575898881398908334),(-1229178382691575895014957831910)⟩,⟨(-245862086302244589557817752325),(-245862086302244585672534400735)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-942380905189787915706936907544),(-942380905189787912793269102044)⟩,⟨1209364032034827452773113252815,1209364032034827455681071960136⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨737796865730711612666987084603,737796865730711614776998310032⟩,⟨1581587898534173091961441416013,1581587898534173094060462675476⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1830483155633617999459520327905,1830483155633618000857794144646⟩,⟨163432167445520255540386759364,163432167445520256942862862972⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1162851766200427727554211143060,1162851766200427728501480406253⟩,⟨(-1346304025665456507210051832100),(-1346304025665456506251129063504)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-150138398871091257652396298875),(-150138398871091257043231163148)⟩,⟨(-1557332361490141232371687381292),(-1557332361490141231755898163429)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-811681373829630463195093646253),(-811681373829630462784491112872)⟩,⟨(-904055562286175946366634718475),(-904055562286175945961755966682)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-705740367520265875464673766193),(-705740367520265875257272296590)⟩,⟨(-299977816506215179298501435320),(-299977816506215179100189777368)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-257429587703380579241262617112),(-257429587703380579181863708016)⟩,⟨(-46646577949439934344604158208),(-46646577949439934289166659126)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-86364249897559759356636753),(-86364249897559484702076576)⟩,⟨(-392458051994837026353745382),(-392458051994836751682843364)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-461099110684050765202805542),(-461099110684049708459921458)⟩,⟨(-1219543441425785219157908220),(-1219543441425784162345638815)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1526529174183674567919411582),(-1526529174183671696269628231)⟩,⟨(-2016173890602355359193340417),(-2016173890602352487376094523)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-3856497484114397506958624596),(-3856497484114386673144389938)⟩,⟨(-2111294063680318324342118871),(-2111294063680307490376380312)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-7389741318767116341190874849),(-7389741318767081292768574644)⟩,⟨343103903090419086570524808,343103903090454134860572738⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-9349210798421153765232250739),(-9349210798421066508164013811)⟩,⟨7961119737186656142959364293,7961119737186743399337822073⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-2276551028789951650209192985),(-2276551028789686562386082070)⟩,⟨19969161092428186817558657508,19969161092428451905319129484⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨20857619595121057197561780659,20857619595121505167177941298⟩,⟨24422147458646595752371714036,24422147458647043723603415868⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨49337493599516540586989539015,49337493599517353842201921741⟩,⟨231168516078016913229271516,231168516078830168410297505⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨46658262438727315480025913426,46658262438728133906116553954⟩,⟨(-54224454492881753699535605277),(-54224454492880935276695957011)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-11931514230090663842185799676),(-11931514230089820548307123008)⟩,⟨(-95232501027176358391905336144),(-95232501027175515097506802487)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-90982500981853642139507255999),(-90982500981853149412038911016)⟩,⟨(-73095373217299978897850260885),(-73095373217299486165316125749)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-125484261185045815313313992350),(-125484261185045469356235178737)⟩,⟨(-1088079270273923293911469668),(-1088079270273577335743120676)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-99231206020675169248476204540),(-99231206020675000477283211662)⟩,⟨57527257909263189332398669059,57527257909263358100580686115⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-50645701917583848203989569195),(-50645701917583784292168567294)⟩,⟨63535089626670295211719570691,63535089626670359119919225889⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-13637121982303482354157165219),(-13637121982303462803948652963)⟩,⟨26082629931380192402645834244,26082629931380211951697501215⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨587654325010502940650886,587654325010502970819644⟩,⟨(-2333921678373509380836023),(-2333921678373509350470913)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1033409151317333999629700,1033409151317334101432008⟩,⟨(-7755580033287820164098781),(-7755580033287820061549701)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1415124745552926484176076),(-1415124745552926262092408)⟩,⟨(-15205813701048394771123892),(-15205813701048394547478777)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-11033389352329452327160588),(-11033389352329451859943155)⟩,⟨(-24573344271221154408048982),(-24573344271221153939050145)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-34752001121370423949508160),(-34752001121370422954619633)⟩,⟨(-30908373945812137397959343),(-30908373945812136402589601)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-78130409617416353772578865),(-78130409617416351634429127)⟩,⟨(-18000283382219887202172880),(-18000283382219885068477124)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-130012792213019318362595709),(-130012792213019313782787517)⟩,⟨45651286159341862841752923,45651286159341867410558738⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-136131271357862764098432763),(-136131271357862754483189333)⟩,⟨189845608230083065511293896,189845608230083075123760534⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨6194692687947224525242796,6194692687947243969793933⟩,⟨384698829576120656419301930,384698829576120675886711955⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨369716321502440190424570703,369716321502440230101269555⟩,⟨477924804442991534102960794,477924804442991573810151397⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨848250389587297544121577293,848250389587297639061297621⟩,⟨254692173956581785740932293,254692173956581880669093792⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨1135625223258901383366906148,1135625223258901626005542277⟩,⟨(-326131495787691030298612744),(-326131495787690787729551161)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨993141277393251747572576777,993141277393252474670128650⟩,⟨(-970890653173155185194115111),(-970890653173154458152590830)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨538036834513309232827468387,538036834513310764125291215⟩,⟨(-1259810383696971082709796639),(-1259810383696969551419662214)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨133687653267427974768855244,133687653267429743356959446⟩,⟨(-1016524726838304060088850022),(-1016524726838302291482835463)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3428306952400174400600040),(-3428306952399381858879987)⟩,⟨(-382200078760016418641945162),(-382200078760015626089463828)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-15687384276743902456867),(-15687384276743875742483)⟩,⟨(-5839274393049955943246),(-5839274393049929231683)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-52099303328973763453253),(-52099303328973692254837)⟩,⟨(-14580948848781000259367),(-14580948848780929069471)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-103616542490836934922952),(-103616542490836843132839)⟩,⟨(-11332163899939588149569),(-11332163899939496372890)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-178266732905891272821847),(-178266732905891193612550)⟩,⟨23344279212395922959646,23344279212396002153829⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-272116413177982660513804),(-272116413177982613295660)⟩,⟨127408615310958996957868,127408615310959044169593⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-344559472404799049558176),(-344559472404799028671040)⟩,⟨359192061168356663508872,359192061168356684422733⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-278871588676762583581105),(-278871588676762572096252)⟩,⟨771918664922869305548736,771918664922869317136708⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨141547482684300857412003,141547482684300872947246⟩,⟨1331902376962693862909021,1331902376962693878580066⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1161374280354913239567678,1161374280354913268425275⟩,⟨1790637981493364146487695,1790637981493364175387555⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2815044265603236704625611,2815044265603236757516629⟩,⟨1640198334558280667354840,1640198334558280720036308⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4641489329194954218088835,4641489329194954307574595⟩,⟨371446599036340074679911,371446599036340163630345⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨5741553623941344788971139,5741553623941344924468002⟩,⟨(-1965230237613581647653697),(-1965230237613581512588120)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨5414171551368264989802973,5414171551368265165725597⟩,⟨(-4414848046790195703898583),(-4414848046790195528084018)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨3848823093885838370313226,3848823093885838556768633⟩,⟨(-5577796405725349956628267),(-5577796405725349769960666)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1984958087465229335020480,1984958087465229480993841⟩,⟨(-4606851603805356183623569),(-4606851603805356037339704)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨559494763662176061487083,559494763662176116957778⟩,⟨(-1773930721523874867339307),(-1773930721523874811726360)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-58767600079057132366),(-58767600079055003367)⟩,⟨214574011825863582422,214574011825865711401⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-128204957248626261740),(-128204957248617848641)⟩,⟨691650928498081470578,691650928498089883597⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-21715516730585506710),(-21715516730562638866)⟩,⟨1302155807471833948329,1302155807471856815994⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨481876028445119785752,481876028445183079497⟩,⟨2082329969647501757998,2082329969647565051419⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1739669680374828880824,1739669680375045327056⟩,⟨2914957096013983805769,2914957096014200251620⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨4197953713153495977371,4197953713154162606346⟩,⟨3330283640613278626136,3330283640613945254822⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨8120793659501238879752,8120793659502869888407⟩,⟨2265533773959835113901,2265533773961466122643⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨12979139064702974242774,12979139064705851361639⟩,⟨(-1957403993237893820769),(-1957403993235016700905)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨16701587635609881360971,16701587635613433715022⟩,⟨(-10968814818382402209787),(-10968814818378849853099)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨15638059691832038534607,15638059691836425350368⟩,⟨(-24766423140288707694995),(-24766423140284320876077)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨6376265894478831142613,6376265894483222938647⟩,⟨(-40082678954689945867878),(-40082678954685554069958)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-10766142985104643562570),(-10766142985101475240314)⟩,⟨(-50797492412817615873341),(-50797492412814447551661)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-29424985739014666429002),(-29424985739012862524412)⟩,⟨(-51505430473237660134709),(-51505430473235856233500)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-39553962258638823478473),(-39553962258637951719534)⟩,⟨(-41646252162085471670203),(-41646252162084599916371)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-33900121953537442025082),(-33900121953537075296620)⟩,⟨(-25645115989778818235763),(-25645115989778451511893)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-13311755386159440724553),(-13311755386159342007146)⟩,⟨(-8438887759422722025688),(-8438887759422623310124)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨2193607382746105114,2193607382746105130⟩,⟨(-65069477147327726),(-65069477147327709)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨6854033630090524040,6854033630090524057⟩,⟨(-890649769440819520),(-890649769440819497)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨12153499571153555428,12153499571153555454⟩,⟨(-4042059629520672785),(-4042059629520672764)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨17789466638010059020,17789466638010059051⟩,⟨(-11752051861171893455),(-11752051861171893428)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨21849508640667239313,21849508640667239353⟩,⟨(-26782266900176557136),(-26782266900176557096)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨19387488484837734275,19387488484837734341⟩,⟨(-51440288045819638569),(-51440288045819638506)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨1370777059468534983,1370777059468535096⟩,⟨(-85159820246042992517),(-85159820246042992408)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-43925494446741746878),(-43925494446741746616)⟩,⟨(-120593409133086737059),(-120593409133086736793)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-124945170487994547797),(-124945170487994546552)⟩,⟨(-140372346860833596475),(-140372346860833595222)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-236882706174666495603),(-236882706174666483836)⟩,⟨(-119970017363503949606),(-119970017363503937832)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-354207552142140197149),(-354207552142140102113)⟩,⟨(-41579338656166377680),(-41579338656166282645)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-435883962741883014720),(-435883962741882521503)⟩,⟨85219269896428623085,85219269896429116299⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-445832140304016267720),(-445832140304014699864)⟩,⟨213648261613125776968,213648261613127344816⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-374850472372430181458),(-374850472372427147249)⟩,⟨278260695932918497189,278260695932921531398⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-243686602788996227779),(-243686602788992826336)⟩,⟨234888173466250678270,234888173466254079716⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-83565599188412037845),(-83565599188410512657)⟩,⟨91672685899637963436,91672685899639488624⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨37839623834406691077979557247,37839623834407459045445127107⟩,⟨(-395888410498161426028593907791),(-395888410498160658061814276685)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 23) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_23 (tableDensity false) (fullFactor true 0 23) density0_contains hk0_1_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨123666430682154447557868876659,123666430682154448037949199832⟩,⟨4272215257482800075383499019,4272215257482800543412528448⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_23 0 23 ha0_1_23_contains + def realAnswer : RBox := ⟨161506054516561138635748433906,161506054516561907083494326939⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_23 +namespace hm0_1_1_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2822946100053541941512351388),(-2822946100053529994658425845)⟩,⟨5160559710911301231975781943,5160559710911313179102222941⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5625817927661448284142367267),(-5625817927661415722232396337)⟩,⟨17783836945373794549842919071,17783836945373827112309099242⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨2614768356595363728001952833,2614768356595402842417408942⟩,⟨34218904581773694861785765439,34218904581773733976054418135⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨32467368867133757476686974358,32467368867133782771878833304⟩,⟨43551687503272412373122024597,43551687503272437665617749950⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨77914083628630954738682864162,77914083628630968973204046607⟩,⟨14823480443942809400843966092,14823480443942823633451583022⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨82183288936285718202662503039,82183288936285723549911151792⟩,⟨(-72789383951109206378752780439),(-72789383951109201026038125933)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-30716274785492980587368822327),(-30716274785492978642559069048)⟩,⟨(-144191671250370343331963735343),(-144191671250370341386993795148)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-189439415629144164185025864447),(-189439415629144163320093820624)⟩,⟨(-41930091639411178511830800798),(-41930091639411177656317612111)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-144325139227704981950614734998),(-144325139227704981360837621482)⟩,⟨200281102768110063467659580981,200281102768110064069263249558⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨142907722699080999152980038681,142907722699080999618919755499⟩,⟨258630745754951942732752739001,258630745754951943198564311884⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨324396222945978559356242353400,324396222945978559701606607136⟩,⟨4397486868871181059769915354,4397486868871181388260856747⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨192018664890499002230959587641,192018664890499002485895433420⟩,⟨(-257596876275301447911895856999),(-257596876275301447645702270924)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-47272911797661119435703970751),(-47272911797661119264987810189)⟩,⟨(-280019520325912529071402095386),(-280019520325912528886123279322)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-159307645216779867587478249448),(-159307645216779867456019013257)⟩,⟨(-151416800221855198140250456819),(-151416800221855198011854299879)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-131658705821698548670762952490),(-131658705821698548600780429266)⟩,⟨(-42219572188214266120744629973),(-42219572188214266058832255989)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-46971978799132295172083268581),(-46971978799132295151645121364)⟩,⟨(-3714008676154520248069236629),(-3714008676154520231311555371)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨17260978138521624597767395,17260978138521840383910381⟩,⟨(-60247200591919870042476649),(-60247200591919654258269492)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨24388755867414923300819533,24388755867415759187054422⟩,⟨(-199078825055296964205966581),(-199078825055296128328272328)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-72086463589870028626734066),(-72086463589867731926459981)⟩,⟨(-372857009037950723719611108),(-372857009037948427040798251)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-391419775262089845282312740),(-391419775262081039851893535)⟩,⟨(-509444005376695137604499969),(-509444005376686332195076175)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1008441292262051127326428384),(-1008441292262022430644656191)⟩,⟨(-324862720144161553245484532),(-324862720144132856551640263)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1605783086481800371355619960),(-1605783086481728694768729973)⟩,⟨698294584374400866940222982,698294584374472543614016147⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-994980496919744097118980181),(-994980496919525574276356918)⟩,⟨2723289101434816421461552708,2723289101435034944321567061⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨2350559431284535422868097987,2350559431284904930277806696⟩,⟨4111109037215471985373484242,4111109037215841492579581813⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨7402093034612603300430198373,7402093034613274472188978145⟩,⟨1125997842535756948088032495,1125997842536428119837917105⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨8252593529630386368775625742,8252593529631060820099525954⟩,⟨(-7649743728790725446815331081),(-7649743728790050995057160572)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-548602268999743147057513048),(-548602268999049278320769969)⟩,⟨(-15754128395206310583675949460),(-15754128395205616715012531072)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-14569595197222214955489433423),(-14569595197221811385334757054)⟩,⟨(-13802266417773420646460574168),(-13802266417773017077048684825)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-22363144890341642076182883972),(-22363144890341359813596503277)⟩,⟨(-2149836074928704946740907596),(-2149836074928422684295330657)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-19249714994343501928038650045),(-19249714994343365288676791259)⟩,⟨8722921072289176409191942848,8722921072289313049058312379⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-10763268784443598292464949875),(-10763268784443547193034588742)⟩,⟨10769281649540952887831593295,10769281649541003987843047728⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-3141748066361454132727724716),(-3141748066361438562176345776)⟩,⟨4583525793102774404468837361,4583525793102789975205508419⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨389141025134889501875841,389141025134889511239438⟩,⟨(-379241092583800002734753),(-379241092583799993362216)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1124008587647592126199712,1124008587647592158089037⟩,⟨(-1365713837338798467645766),(-1365713837338798435721204)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1574100245087748061116902,1574100245087748128933087⟩,⟨(-3063245829227291656412379),(-3063245829227291588523645)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨970241351438868328616296,970241351438868463715482⟩,⟨(-5903334895449171617693149),(-5903334895449171482512537)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-2409178283135519203401650),(-2409178283135518937975218)⟩,⟨(-9674494455371584010416417),(-9674494455371583744962721)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-11065062647618946622835597),(-11065062647618946108490055)⟩,⟨(-11982452646808171851902346),(-11982452646808171337716617)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-25786297376557134394569060),(-25786297376557133410462315)⟩,⟨(-6221990582208327183670880),(-6221990582208326200003790)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-39432120114552743932206795),(-39432120114552742061222705)⟩,⟨17438403314633681321301187,17438403314633683192126742⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-31508480063288629841325954),(-31508480063288626251693178)⟩,⟨61916223098536537329163111,61916223098536540919428209⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨22178786900096297098479274,22178786900096306100835727⟩,⟨106108441698424758090734293,106108441698424767093746896⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨118252390118820975339178987,118252390118821012698113106⟩,⟨105196739555055236836004914,105196739555055274194811394⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨205827977502039227784185054,205827977502039365252535655⟩,⟨31380481769212621826366991,31380481769212759294317147⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨223916172783173489088702049,223916172783174004878894899⟩,⟨(-80901274255672963773236072),(-80901274255672447983091566)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨166106679413860831926767319,166106679413862001806630804⟩,⟨(-154973453063409120956525742),(-154973453063407951076302573)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨83864329156472066395898755,83864329156473449352714949⟩,⟨(-142653919499211923071159191),(-142653919499210540114079757)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨22575574729581530738381486,22575574729582155102287283⟩,⟨(-56465509961449540874215161),(-56465509961448916510275839)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-3036973830669481397489),(-3036973830669458981592)⟩,⟨(-4699335007190354134307),(-4699335007190331718117)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-10841312371617091512970),(-10841312371617031834534)⟩,⟨(-14130570853876781538522),(-14130570853876721859195)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-24285384240974749829262),(-24285384240974673085861)⟩,⟨(-22833246642277704956916),(-22833246642277628212117)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-48263912563811046917615),(-48263912563810981084400)⟩,⟨(-27112527338771359508655),(-27112527338771293673890)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-87463387265541537605603),(-87463387265541499090305)⟩,⟨(-17002276079620785317180),(-17002276079620746801278)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-140809262885036587918240),(-140809262885036572310993)⟩,⟨27423781730910083141789,27423781730910098746259⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-188711587720000248658589),(-188711587720000242638971)⟩,⟨135269690067055252784389,135269690067055258793727⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-176360380759447809363487),(-176360380759447803505361)⟩,⟨329071298126030969192513,329071298126030975037881⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-12611380289373699182248),(-12611380289373689074642)⟩,⟨585713291258881287251993,585713291258881297357288⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨382504243488494294537657,382504243488494312829351⟩,⟨793341948903568103854681,793341948903568122168191⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨978344287739014118775336,978344287739014149748718⟩,⟨769547989742370175769065,769547989742370206792820⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1567240283834846071666000,1567240283834846119102449⟩,⟨395283895298380275819008,395283895298380323291278⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1854708244366314644360815,1854708244366314706911601⟩,⟨(-215742779802496059768883),(-215742779802495997215879)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1677791857931845987421544,1677791857931846054813705⟩,⟨(-716940295260636555955017),(-716940295260636488588421)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1120214305434034407076374,1120214305434034460563889⟩,⟨(-771811315442665013540574),(-771811315442664960084835)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨385776729678215017390750,385776729678215037875045⟩,⟨(-328391281503436719693769),(-328391281503436699223411)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-15676344147650483517),(-15676344147648733874)⟩,⟨71399266316660494519,71399266316662244163⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-33167888564435435469),(-33167888564428520944)⟩,⟨233616764967110677423,233616764967117591961⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1402323855459141710,1402323855477938865⟩,⟨451661786652355347566,451661786652374144759⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨159296980552648362108,159296980552700397823⟩,⟨748439529458008745470,748439529458060781251⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨567677847321567712036,567677847321745682083⟩,⟨1100232078078204418529,1100232078078382388667⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1412421301338607546653,1412421301339155670809⟩,⟨1369472073852940728133,1369472073853488852374⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2872541744725189704471,2872541744726530477036⟩,⟨1209870187192732413321,1209870187194073185896⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨4932726393152812902291,4932726393155176870865⟩,⟨11775993449949732414,11775993452313700798⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨7103746927232001738674,7103746927234918178134⟩,⟨(-2950895901680354111964),(-2950895901677437673055)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨8287043238957285214542,8287043238960882716141⟩,⟨(-8016960388337590061417),(-8016960388333992560481)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨7179967281727564248917,7179967281731161277709⟩,⟨(-14426661817159459392842),(-14426661817155862364464)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨3312068642918721920348,3312068642921313365733⟩,⟨(-20066735297419867022793),(-20066735297417275577358)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-2023468168647668691831),(-2023468168646195192353)⟩,⟨(-22368007457643759453096),(-22368007457642285953045)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-6077282613946548251311),(-6077282613945837022794)⟩,⟨(-19958547689434164672565),(-19958547689433453443163)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-6394366026972001632229),(-6394366026971702734264)⟩,⟨(-13477376206813571096697),(-13477376206813272197943)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-2700442887851227756500),(-2700442887851147347728)⟩,⟨(-4709385714588456522686),(-4709385714588376113598)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨65060070436271654,65060070436271672⟩,⟨(-5052844441449664),(-5052844441449647)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨187032071900716701,187032071900716719⟩,⟨(-75345877225344282),(-75345877225344264)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨172912202206539746,172912202206539767⟩,⟨(-350123256749010173),(-350123256749010152)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-484166777160939631),(-484166777160939609)⟩,⟨(-1046340846172352648),(-1046340846172352627)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-3001216248304191704),(-3001216248304191673)⟩,⟨(-2451292870365972527),(-2451292870365972495)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-9566853751593044595),(-9566853751593044555)⟩,⟨(-4631294364354421461),(-4631294364354421420)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-23297325748201666433),(-23297325748201666362)⟩,⟨(-6513624371176605840),(-6513624371176605766)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-47430075613495653185),(-47430075613495653001)⟩,⟨(-4525453729786230188),(-4525453729786230003)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-82998515178250827066),(-82998515178250826094)⟩,⟨8025143987727156288,8025143987727157267⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-125164481712857784720),(-125164481712857775170)⟩,⟨38927923064126352998,38927923064126362560⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-161064101726442226738),(-161064101726442149212)⟩,⟨91236105667219280565,91236105667219358092⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-173915230188366560271),(-173915230188366157622)⟩,⟨155918860595391095970,155918860595391498617⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-154349159369848881797),(-154349159369847601099)⟩,⟨209289280841225371817,209289280841226652509⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-109832987265061488258),(-109832987265059008445)⟩,⟨220874132347342400163,220874132347344879969⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-59706576972706803913),(-59706576972704022861)⟩,⟨170562800182296549539,170562800182299330584⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-17967374003465400835),(-17967374003464153572)⟩,⟨64330739502255080038,64330739502256327300⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨6740544251335932830937196077,6740544251336560573337116407⟩,⟨(-70544815406414222116918092162),(-70544815406413594374732940109)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 23) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_23 (tableDensity true) (fullFactor true 0 23) density1_contains hk0_1_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-161717640122817355126548953626),(-161717640122817354498751607939)⟩,⟨(-5586743029015969941385614125),(-5586743029015969329347652563)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_23 0 23 ha0_1_23_contains + def realAnswer : RBox := ⟨(-154977095871481422295711757549),(-154977095871480793925314491532)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_23 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_7.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_7.lean new file mode 100644 index 0000000000000000000000000000000000000000..00cc3d9edf914c80a8b36f63bb1332308a5bdfba --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments0_7.lean @@ -0,0 +1,4721 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders0 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm0_0_1_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨8914914793596189654618641798,8914914793596194753850365061⟩,⟨(-8355639163937835098354592535),(-8355639163937829999553793891)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨22070745152774759004124915005,22070745152774770887586780477⟩,⟨(-31738309341413207800812859695),(-31738309341413195918965568918)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨13690925751046332184212043524,13690925751046348676893574275⟩,⟨(-69996832416971908069279304036),(-69996832416971891578367560855)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-46177540061589417416280106324),(-46177540061589403588475284542)⟩,⟨(-105409925175347631944490325010),(-105409925175347618115925871554)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-162598289690799077071734113767),(-162598289690799069940975559288)⟩,⟨(-65071249699201608141700307567),(-65071249699201601005927124403)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-218878897640079934790230293870),(-218878897640079930635531461395)⟩,⟨131526843724936753930161370848,131526843724936758083526344831⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨2020265219439727051688471735,2020265219439729438701279906⟩,⟨355323732313308743727444075745,355323732313308746108697025015⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨420648064225645025501614403722,420648064225645027232881639752⟩,⟨204055644577644575559149886723,204055644577644577296350594490⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨441204099669689820309915713625,441204099669689821596915285569⟩,⟨(-370748706799248700739837558707),(-370748706799248699452255312001)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-176330790523721903261707055007),(-176330790523721902360507528338)⟩,⟨(-636341736468891297205954590599),(-636341736468891296309668795928)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-683101514331049255307854252737),(-683101514331049254723616529749)⟩,⟨(-148129502790081096549655774909),(-148129502790081095964861702285)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-486841606190580635266488870503),(-486841606190580634878014492838)⟩,⟨473657301728838909352250746971,473657301728838909744900342608⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨24983575604132283036179955948,24983575604132283277783843344⟩,⟨598430270922568311841767722717,598430270922568312086479019625⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨301104305640110726189110599916,301104305640110726351171011936⟩,⟨355510530214763367261713794484,355510530214763367421812844704⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨269552871400247426939257333855,269552871400247427020807642572⟩,⟨118177072310134874657412046026,118177072310134874735514720971⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨98800438666172233528135812827,98800438666172233551364585360⟩,⟨18134473162791787740438906164,18134473162791787762145540541⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-66416587194331984977379207),(-66416587194331902117681160)⟩,⟨99236009732032379108789960,99236009732032461963551334⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-165273341628915789482309874),(-165273341628915430281580683)⟩,⟨351993073737259773845686326,351993073737260133036021585⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-106482462915665750189962310),(-106482462915664626890373874)⟩,⟨752215965285016738316467188,752215965285017861618432168⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨392558291558115796469535610,392558291558118926686019885⟩,⟨1275627814321744787854631194,1275627814321747918129823186⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1736662129295765346540988270,1736662129295774919694081657⟩,⟨1470351263276201848746387310,1470351263276211422018388691⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨3835038175667431287800698520,3835038175667464011516013545⟩,⟨63903491661951041463033230,63903491661983765144052591⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨4602002158737440740168067983,4602002158737512692799709484⟩,⟨(-4425254356754055780021614885),(-4425254356753983827723268880)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-504750328389722599484305444),(-504750328389552946470137115)⟩,⟨(-10370912279158351197994331179),(-10370912279158181544891829654)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-13135207500162720589077889240),(-13135207500162485600842919571)⟩,⟨(-9539860323805912190591685585),(-9539860323805677201637460078)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-23060637436690402220436694743),(-23060637436690090645255194954)⟩,⟨6424308720083071020205052987,6424308720083382594902044770⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-13607905505886142559149584957),(-13607905505885887494303764979)⟩,⟨29647877068579075265598890183,29647877068579330329289962193⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨14539827968065557058514946310,14539827968065754258995183264⟩,⟨37493812725865574886685887718,37493812725865772088009245026⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨38255290969864731999871414464,38255290969864833914140852423⟩,⟨21196417369897337607476583977,21196417369897439523484788464⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨40278142472757791982143994846,40278142472757856274315020078⟩,⟨(-1991797594134501337594688572),(-1991797594134437045182010243)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨26040545282507999473436849879,26040545282508028035162331327⟩,⟨(-12154205892422715519124334542),(-12154205892422686957932782717)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨8402560547636357772279397205,8402560547636365315588537776⟩,⟨(-6198063615361649218748779979),(-6198063615361641675758637456)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-566422691382947252599269),(-566422691382947242598624)⟩,⟨150869126919579485651101,150869126919579495605316⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1776997865925270638102686),(-1776997865925270604131264)⟩,⟨707295642176367559603674,707295642176367593450253⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3076455958534435234334844),(-3076455958534435159478812)⟩,⟨2161979380875174118255001,2161979380875174192979364⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3875409039709789659118420),(-3875409039709789500085395)⟩,⟨5468605814697881282965021,5468605814697881442084658⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-2082904333341178045525063),(-2082904333341177702098652)⟩,⟨11543093964849509869881202,11543093964849510214142891⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨6877158663957118961024328,6877158663957119714369087⟩,⟨19360348019707862779036847,19360348019707863534042961⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨28757835887521084874321196,28757835887521086529508922⟩,⟨21562942958093087103540743,21562942958093088759077665⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨62103294285886981992521622,62103294285886985547336682⟩,⟨524283461825592867133882,524283461825596417893540⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨82727760246674005179920640,82727760246674012541435112⟩,⟨(-63511620097394461691396376),(-63511620097394454335103582)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨41077789616135712862346469,41077789616135727841769870⟩,⟨(-161830340927126007423506967),(-161830340927125992440282917)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-96206566250792776833808399),(-96206566250792744845699487)⟩,⟨(-229879740521972882369901608),(-229879740521972850365933491)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-282523122285103220242378537),(-282523122285103129190495259)⟩,⟨(-185409149041922511878234770),(-185409149041922420819700080)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-401902518042685461748715999),(-401902518042685230997365258)⟩,⟨(-26966388739027251120376362),(-26966388739027020379926377)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-378480448687841750594683223),(-378480448687841379011833172)⟩,⟨134543760781841934314391235,134543760781842305874744139⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-245620223027615702555147209),(-245620223027615252739307784)⟩,⟨177281446301062983071737687,177281446301063432872124434⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-81347130558112119699442183),(-81347130558111895336164536)⟩,⟨78951363149783124289542086,78951363149783348648329186⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-130954396058053518010),(-130954396058046768296)⟩,⟨3391403407457916810090,3391403407457923560190⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨529015204050597371694,529015204050615107543⟩,⟨10992671799092779393432,10992671799092797130344⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨4624183146196375302235,4624183146196397019449⟩,⟨20833816228219531325150,20833816228219553043686⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨16725708281754304465922,16725708281754322020702⟩,⟨33181064526178325992669,33181064526178343547770⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨44500015558468706185247,44500015558468715905179⟩,⟨44390044647715860220473,44390044647715869936756⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨97227997161945903816661,97227997161945907931453⟩,⟨41276036722745612469188,41276036722745616570540⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨176911609465941426570809,176911609465941429518437⟩,⟨(-5797484507032353743593),(-5797484507032350815652)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨257510822554279019089162,257510822554279023527093⟩,⟨(-141674627736033092394798),(-141674627736033087965091)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨261264660930572853166729,261264660930572861582063⟩,⟨(-398828621511161049403235),(-398828621511161040957920)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨69294173687907459158591,69294173687907474944923⟩,⟨(-737601161248689926347069),(-737601161248689910473298)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-391162129062499021601570),(-391162129062498994090494)⟩,⟨(-1003300009998970809225116),(-1003300009998970781645661)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1020012886600220814747545),(-1020012886600220772141248)⟩,⟨(-995354816485526727425444),(-995354816485526684830143)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1528040819580804306701528),(-1528040819580804250333961)⟩,⟨(-654745103561577381977619),(-654745103561577325723209)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1619530657270917153658926),(-1619530657270917093044161)⟩,⟨(-180355404037797778812679),(-180355404037797718373508)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-1209585477609361195381082),(-1209585477609361147418536)⟩,⟨114101199576877781018699,114101199576877828856222⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-443225206174263518047982),(-443225206174263499719804)⟩,⟨89550363806125403984064,89550363806125422271667⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨38278959849945954962,38278959849946286325⟩,⟨3684872447772899676,3684872447773231047⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨121928290673565579585,121928290673566870134⟩,⟨1141678453477565341,1141678453478855909⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨224020139003475818614,224020139003479516841⟩,⟨(-36679112339009190483),(-36679112339005492225)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨343890773421189666725,343890773421202269044⟩,⟨(-151007489989169212510),(-151007489989156610151)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨447587238131426324635,447587238131468401948⟩,⟨(-403729649850602935186),(-403729649850560857837)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨430694494052904848515,430694494053028832338⟩,⟨(-861739413738667077863),(-861739413738543094033)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨80133710312158484352,80133710312446635329⟩,⟨(-1534977370238211574697),(-1534977370237923423808)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-908569964155185084030),(-908569964154712018854)⟩,⟨(-2252986603090247386527),(-2252986603089774321641)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2769137199755811289345),(-2769137199755126650862)⟩,⟨(-2537661598707410600347),(-2537661598706725962328)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-5340134830102468353008),(-5340134830101524043406)⟩,⟨(-1658463530721157606510),(-1658463530720213297234)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7809002108538088183576),(-7809002108537213031696)⟩,⟨925114620003709594734,925114620004584746681⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-8963583443555809033557),(-8963583443555222370333)⟩,⟨4861229969094969676910,4861229969095556340807⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-8058171994936973927968),(-8058171994936665567800)⟩,⟨8598382025756036609278,8598382025756344970711⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-5560175512930961591118),(-5560175512930811476485)⟩,⟨10084063253661378055448,10084063253661528171457⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2815628003051618354587),(-2815628003051540131999)⟩,⟨8101270385356301943830,8101270385356380167268⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-785733720362101987920),(-785733720362078340609)⟩,⟨3092187378439670508941,3092187378439694156530⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-27143172653246595),(-27143172653246579)⟩,⟨(-329724906770766866),(-329724906770766850)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-190926049185979597),(-190926049185979580)⟩,⟨(-1026866293653996412),(-1026866293653996396)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-721117192052128414),(-721117192052128396)⟩,⟨(-1806069553725349989),(-1806069553725349972)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1969505408093360689),(-1969505408093360671)⟩,⟨(-2597635155657500753),(-2597635155657500735)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-4365755129420076484),(-4365755129420076461)⟩,⟨(-3061569418915817063),(-3061569418915817043)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-8241220999970823040),(-8241220999970823017)⟩,⟨(-2355817013900118953),(-2355817013900118929)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-13400438735240284722),(-13400438735240284688)⟩,⟨1024627272605942280,1024627272605942310⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-18445996839721842677),(-18445996839721842622)⟩,⟨8976979900097375841,8976979900097375894⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-20261018512463299610),(-20261018512463299386)⟩,⟨22718302478339376461,22718302478339376685⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-14621644119516247724),(-14621644119516245634)⟩,⟨41060166660227287367,41060166660227289458⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1233562747378810071,1233562747378826464⟩,⟨59275465085256009252,59275465085256025647⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨24958542427818840948,24958542427818924102⟩,⟨70398753655428520258,70398753655428603415⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨47626704382990186424,47626704382990444906⟩,⟨69158538613480001253,69158538613480259736⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨57417653652042820542,57417653652043309959⟩,⟨55591813305506495831,55591813305506985248⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨46864902173271698065,46864902173272236675⟩,⟨34608872106178858209,34608872106179396819⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨18037036711523676048,18037036711523914945⟩,⟨11537362123839579022,11537362123839817922⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-14130619358572919752450611550),(-14130619358572660161113999847)⟩,⟨145483423657057458271501097386,145483423657057717862550631493⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 24) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_24 (tableDensity false) (fullFactor true 0 24) density0_contains hk0_1_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-45980399031996614585028965148),(-45980399031996614359490832386)⟩,⟨(-3336091205277960775632638279),(-3336091205277960554856210994)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_24 0 24 ha0_1_24_contains + def realAnswer : RBox := ⟨(-60111018390569534337579576698),(-60111018390569274520504832233)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_24 +namespace hm0_1_1_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1699853979503373160460690425,1699853979503377221062426373⟩,⟨(-1215319288479528578552552626),(-1215319288479524517840878400)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨4517685413340990210993134916,4517685413340999586020390893⟩,⟨(-4869983587140973522299987365),(-4869983587140964146872644297)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨4204028696247364452012844129,4204028696247377340117478771⟩,⟨(-11538752193084643989859818823),(-11538752193084631101340636651)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-4616039736533423838658931418),(-4616039736533413393042898106)⟩,⟨(-19017060495648892763280623907),(-19017060495648882318012835009)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-24392299517952312345887985779),(-24392299517952307606120544473)⟩,⟨(-15315868445499269382606496239),(-15315868445499264644270230970)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-37234300499454633861937428074),(-37234300499454631697652600725)⟩,⟨15205825205880726729011977565,15205825205880728894308232800⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-4747144686215208207112187756),(-4747144686215207474986850607)⟩,⟨54290747527879395658950808541,54290747527879396392770230553⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨64440742110418942579117387877,64440742110418942950531863776⟩,⟨32888222241145655422076285437,32888222241145655789588906704⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨68727292639084264827772662849,68727292639084265083075665349⟩,⟨(-62325439810269991978594180257),(-62325439810269991720311263793)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-37159323729433872397142699164),(-37159323729433872206273109416)⟩,⟨(-105439647805821250847689992936),(-105439647805821250654880845254)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-122222033974547510873774158926),(-122222033974547510733463201105)⟩,⟨(-16966238940862668456766086749),(-16966238940862668323302615970)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-81555067100481289114583210645),(-81555067100481289011350052786)⟩,⟨91639953783651690984458227336,91639953783651691090896025623⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨12242950144495064799136081172,12242950144495064865383032344⟩,⟨108022941505410991106866448697,108022941505410991179121997523⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨59383731372911082490850803182,59383731372911082541980730562⟩,⟨59800961016679053412532682015,59800961016679053462760624312⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨50344865172605980708550777416,50344865172605980735789621807⟩,⟨16772205363623467875941540509,16772205363623467900139012855⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨18031803536459127972745707444,18031803536459127980668571471⟩,⟨1466942795522939316952334688,1466942795522939323464621913⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16472182138372234568801718),(-16472182138372170702113303)⟩,⟨8687941286931791204321266,8687941286931855071691155⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-47677195331966741804529970),(-47677195331966460521010948)⟩,⟨36126587685100104039349288,36126587685100385324393512⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-64197834359319528856358507),(-64197834359318632868307188)⟩,⟨94301218313954034256731069,94301218313954930245001082⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-22612955750315190512846067),(-22612955750312665100849254)⟩,⟨193690368299580515676162543,193690368299583041081256466⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨159144074903520415411599082,159144074903528214366784768⟩,⟨284338584375703178445344247,284338584375710977385085494⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨520510823393892993553831129,520510823393919845142115023⟩,⟨167736667707024733963563010,167736667707051585554040701⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨794943240986872827594121589,794943240986932009976860625⟩,⟨(-464890173928845031156344218),(-464890173928785848731366474)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨211601283698924617943460660,211601283699064465705112887⟩,⟨(-1516187887139986722603487207),(-1516187887139846874849075319)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1761183911408792773835847184),(-1761183911408599144873370984)⟩,⟨(-1722413242399698878178834680),(-1722413242399505249310020486)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-3717989088251577104949688794),(-3717989088251320537385751786)⟩,⟨596586041063514256413089778,596586041063770824039160205⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2662192876611279740397511739),(-2662192876611070355761077387)⟩,⟨4649817645674124695548457878,4649817645674334080346169802⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1967618644842508973100072001,1967618644842670279999192964⟩,⟨6629811341566286434665815899,6629811341566447741435077939⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨6493078409490911875559633078,6493078409490994521547391677⟩,⟨4376415915671607024161173507,4376415915671689669886743431⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨7421213412011228128592547539,7421213412011279969019947983⟩,⟨374909409822858167357656495,374909409822910007757619401⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨5104075465441906020750880118,5104075465441928817740967327⟩,⟨(-1717342222073963183471633898),(-1717342222073940386385300035)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1714257388361704793297206034,1714257388361710757303463267⟩,⟨(-973362068782426190455805339),(-973362068782420226394558008)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-126763577411625895702926),(-126763577411625892619996)⟩,⟨(-38008764880169396917978),(-38008764880169393837209)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-425592457883127008189927),(-425592457883126997609846)⟩,⟨(-76280580370825615135752),(-76280580370825604561736)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-847130507691603383401412),(-847130507691603360638587)⟩,⟨38210645488676698091662,38210645488676720847858⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1388240357161043953372593),(-1388240357161043907541368)⟩,⟨537350676279087598129476,537350676279087643963435⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1765434665962426657404389),(-1765434665962426566073157)⟩,⟨1790282222536783316060845,1790282222536783407425240⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1064263087880947306444479),(-1064263087880947125576661)⟩,⟨4041235143190812842047490,4041235143190813022980986⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨2391364516019581543053248,2391364516019581898483857⟩,⟨6492006852180108558820808,6492006852180108914272274⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨9825565651734888360724035,9825565651734889045669302⟩,⟨5899863458115056283835604,5899863458115056968636727⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨18565189199840842271499515,18565189199840843612310608⟩,⟨(-3147764153405750171743834),(-3147764153405748831101758)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨19316439873445325824300645,19316439873445328968093872⟩,⟨(-22890566368226804356878307),(-22890566368226801213034758)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1735690847992123466643080,1735690847992133680452860⟩,⟨(-44497935745201557309557552),(-44497935745201547095580024)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-31582498063619657236723678),(-31582498063619607352766330)⟩,⟨(-50481904494199866830411670),(-50481904494199816946432227)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-60778667812201236099154399),(-60778667812201079565397427)⟩,⟨(-32763013206151683132740644),(-32763013206151526599083749)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-66423087392548376200669102),(-66423087392548106147867143)⟩,⟨(-4984632106322512947680295),(-4984632106322242894901442)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-47662766163445855482393023),(-47662766163445513845981223)⟩,⟨10882688547262415276311678,10882688547262756912785719⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16741662477370489356998540),(-16741662477370315769097856)⟩,⟨6708954862081882943467008,6708954862082056531410534⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-712747514254395249746),(-712747514254389585661)⟩,⟨882626755903071805542,882626755903077469587⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2031911297507811527776),(-2031911297507796660779)⟩,⟨2999559697227907877063,2999559697227922743949⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-2827965961915692955237),(-2827965961915674800504)⟩,⟨6211047876881569415312,6211047876881587569900⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1993722097281876457554),(-1993722097281861883074)⟩,⟨11265657466150703396112,11265657466150717970556⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2909021971493155832632,2909021971493163706849⟩,⟨18409566149568598734619,18409566149568606609205⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨16053480682450725130468,16053480682450728064736⟩,⟨25864768983188780368989,25864768983188783304604⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨42170921867680978781297,42170921867680980224809⟩,⟨26997594892374542852110,26997594892374544297523⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨81555269637749420902278,81555269637749422548189⟩,⟨7763127872183579028599,7763127872183580675103⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨120847480784229346464921,120847480784229349397715⟩,⟨(-50231070828412371498740),(-50231070828412368569087)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨127114678844595196916586,127114678844595202391658⟩,⟨(-154754210444500654686013),(-154754210444500649219278)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨61385598729054748851628,61385598729054758421143⟩,⟨(-281237801804954182593224),(-281237801804954173029265)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-83132108526058670517844),(-83132108526058655585215)⟩,⟨(-370368365418467598426332),(-370368365418467583491304)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-250047438628173870989245),(-250047438628173850982939)⟩,⟨(-367291007467210263296895),(-367291007467210243279122)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-342830367643103558021293),(-342830367643103536185261)⟩,⟨(-273772299028356034358924),(-273772299028356012506446)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-294259710892648194347957),(-294259710892648176833599)⟩,⟨(-148221822304431060462461),(-148221822304431042936864)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-115233841480011979594491),(-115233841480011972848280)⟩,⟨(-43465985617519814654824),(-43465985617519807905093)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨12622984368129183036,12622984368129455358⟩,⟨565532138349204059,565532138349476380⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨40879915848117013209,40879915848118073889⟩,⟨(-1344943440463655673),(-1344943440462594996)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨77428459170766814136,77428459170769854068⟩,⟨(-14255379601026955273),(-14255379601023915350)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨124062207738861157002,124062207738871517815⟩,⟨(-51875964507587644684),(-51875964507577283880)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨172025076803204567710,172025076803239165251⟩,⟨(-136893631640490363511),(-136893631640455765982)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨188731441397590927428,188731441397692870954⟩,⟨(-299148275461103138093),(-299148275461001194570)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨101039731210990626918,101039731211227501797⟩,⟨(-559228033382279315633),(-559228033382042440738)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-209243604253118871097),(-209243604252730178945)⟩,⟨(-888685056230116020254),(-888685056229727328043)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-865411154868628597929),(-865411154868066540961)⟩,⟨(-1158545814284723323151),(-1158545814284161266080)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1888240005761331635400),(-1888240005760557228927)⟩,⟨(-1131702062523651243298),(-1131702062522876836747)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-3068438292409493676768),(-3068438292408776895636)⟩,⟨(-578058975120703689072),(-578058975119986907945)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-3963195479493930917167),(-3963195479493451074965)⟩,⟨495632367665086030387,495632367665565872477⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-4128595106422086387579),(-4128595106421834517947)⟩,⟨1691837241943866549855,1691837241944118419262⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-3445633820399443430148),(-3445633820399320975167)⟩,⟨2371423626349877540503,2371423626349999995241⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2189615624789730892251),(-2189615624789667143962)⟩,⟨2065072273026131055152,2065072273026194803291⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-736078017838382672464),(-736078017838363411547)⟩,⟨815940590220696260386,815940590220715521253⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1275267642804058),(-1275267642804042)⟩,⟨(-9754499973159794),(-9754499973159778)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-12913149537155744),(-12913149537155728)⟩,⟨(-27596292878507667),(-27596292878507650)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-54612867252805876),(-54612867252805860)⟩,⟨(-23055592792486115),(-23055592792486099)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-154830871971340533),(-154830871971340517)⟩,⟨84379837824781286,84379837824781303⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-343487347406746873),(-343487347406746855)⟩,⟨489665903000007039,489665903000007058⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-597478948023843224),(-597478948023843204)⟩,⟨1546778116919973937,1546778116919973955⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-684190018616838564),(-684190018616838541)⟩,⟨3757290706419192861,3757290706419192884⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨64639831013142403,64639831013142446⟩,⟨7618540798651200717,7618540798651200758⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2836622513932122515,2836622513932122693⟩,⟨13210393739710514824,13210393739710515002⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨8934831957483029427,8934831957483031128⟩,⟨19578670904818288034,19578670904818289733⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨18698180715623772062,18698180715623785436⟩,⟨24445971567340364959,24445971567340378332⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨30238734165481040659,30238734165481108543⟩,⟨25076123475266303887,25076123475266371771⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨39194058851390964225,39194058851391175362⟩,⟨20368761093507934685,20368761093508145819⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨40362332488592594253,40362332488592994237⟩,⟨12418112974845282372,12418112974845682357⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨30662441637131943791,30662441637132384156⟩,⟨5232788590013407872,5232788590013848238⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨11468873316862920396,11468873316863115763⟩,⟨1176817868649386321,1176817868649581688⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-2069461994526207021266092817),(-2069461994525995652327515566)⟩,⟨25715606549030167590119850316,25715606549030378959018247267⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 24) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_24 (tableDensity true) (fullFactor true 0 24) density1_contains hk0_1_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨60128214118764803393180319274,60128214118764803688114800578⟩,⟨4362580806901948417888891300,4362580806901948706596526980⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_24 0 24 ha0_1_24_contains + def realAnswer : RBox := ⟨58058752124238596371814226457,58058752124238808035887285012⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_24 +namespace hm0_0_1_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-3976505238381315158434794238),(-3976505238381313069554464814)⟩,⟨1245246645123459932396798341,1245246645123462021247910159⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-11458437890224310178151556449),(-11458437890224305124329624136)⟩,⟨6586073639513791741100944574,6586073639513796794669743876⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-14211129123511279335809305230),(-14211129123511274255827822905)⟩,⟨19957707580489497854577625467,19957707580489502933642127885⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨418215941102946793732516464,418215941102951603328205941⟩,⟨39794188146621350080198850961,39794188146621354889190766893⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨44540425644319238839867760325,44540425644319241644205220795⟩,⟨41759820369468915149130762165,41759820369468917954866352495⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨87950915010804845182289024788,87950915010804846808198703066⟩,⟨(-18203784933922637239318198299),(-18203784933922635612573033267)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨36228346131144903566950841013,36228346131144904576149773303⟩,⟨(-120796669633818835072571791557),(-120796669633818834065756346056)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-127383569873294798282765171583),(-127383569873294797534806355122)⟩,⟨(-108567906739435576607102907954),(-108567906739435575857884828928)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-183560618136103715454234331043),(-183560618136103714908185241196)⟩,⟨97650022800356264939439422940,97650022800356265486594906549⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨24942402502393306504319121023,24942402502393306874385035096⟩,⟨238506209911858903435323054212,238506209911858903803566197743⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨240741137496125659789474073394,240741137496125660024796093674⟩,⟨84619856544109731768320874258,84619856544109732003473064910⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨192789083670214130978738521476,192789083670214131131376234852⟩,⟨(-157495085116913118317497120250),(-157495085116913118163452173431)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2785476718907756237127211088,2785476718907756329426912885⟩,⟨(-220088669487661740058495273154),(-220088669487661739964868194807)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-107012654982330745454414151844),(-107012654982330745393034914692)⟩,⟨(-134011013684307267928631733432),(-134011013684307267867886872907)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-98819343839136161818189963846),(-98819343839136161787416668656)⟩,⟨(-44658050720639335043435448313),(-44658050720639335013916932178)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-36402185817911134163287293677),(-36402185817911134154569008396)⟩,⟨(-6766933742312033146805434217),(-6766933742312033138648610304)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨33546316842749048142386638,33546316842749073047258838⟩,⟨(-5916465946109844076402032),(-5916465946109819172778222)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨105283038903340044365893742,105283038903340140351841714⟩,⟨(-36222698288605367380855014),(-36222698288605271400535236)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨175539946988922501023117541,175539946988922759957054550⟩,⟨(-131110721291758672506485763),(-131110721291758413586965320)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨177112415327521327505758522,177112415327522313343092771⟩,⟨(-346280784540443093932811406),(-346280784540442108107829951)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-80013156870380480116614314),(-80013156870377317307503049)⟩,⟨(-667138567022439905754693518),(-667138567022436742928891734)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-850369775483602155870183869),(-850369775483593594209458144)⟩,⟨(-774318365776225024522630616),(-774318365776216462801860835)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1941449182937883691115561573),(-1941449182937858255121921842)⟩,⟨144823327708790994153607134,144823327708816430119434362⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1844570633795775214484297760),(-1844570633795727990135581958)⟩,⟨2642174360393433106438191641,2642174360393480330645026297⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1609514176965281720185559054,1609514176965362043943289606⟩,⟨4868358094859862583470442867,4868358094859942907371239150⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨7307312984658586201057937667,7307312984658682696136903852⟩,⟨2395386833582762417143058029,2395386833582858912431531570⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨8869830937920406852733013513,8869830937920491025753853628⟩,⟨(-5883019798868625292810793978),(-5883019798868541120193667444)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨2040958685606038061339100174,2040958685606103485222462553⟩,⟨(-13144157060106322070817091388),(-13144157060106256647168719062)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-7865993535687260241426951686),(-7865993535687222981642068476)⟩,⟨(-12337909959796657282591465898),(-12337909959796620022342756705)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-12391628247959699093089058643),(-12391628247959680383071813708)⟩,⟨(-5631215279983449316772051836),(-5631215279983430606258177970)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-9754451610407650486562848704),(-9754451610407640354813922818)⟩,⟨(-238275824241235951754538851),(-238275824241225819890792772)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-3497104723551950197536905386),(-3497104723551947249318977533)⟩,⟨643762527729056702860745345,643762527729059651074061044⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨95139084401407244101731,95139084401407247265524⟩,⟨98649935486696274439718,98649935486696277604203⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨348793188581120362918832,348793188581120373724083⟩,⟨282466876896198661897969,282466876896198672697536⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨804722996785591350363244,804722996785591374429757⟩,⟨377315410918612974983701,377315410918612999008610⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1595385899938705976719984,1595385899938706028626227⟩,⟨134699925065217635241953,134699925065217687002265⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨2647763676177241193434649,2647763676177241307817263⟩,⟨(-1026728634381541834669499),(-1026728634381541720504123)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨3105462050412683328686255,3105462050412683584902435⟩,⟨(-3987591405021458572630814),(-3987591405021458316449320)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨481973560666145280135150,481973560666145854311309⟩,⟨(-8988010737501195532749227),(-8988010737501194957950560)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-9018691607603690580942259),(-9018691607603689317811409)⟩,⟨(-13034289156967597725542285),(-13034289156967596461549753)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-26103584317447485109326914),(-26103584317447482438639520)⟩,⟨(-7430640585989042645321325),(-7430640585989039975332370)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-40524164704987346289167210),(-40524164704987340864979213)⟩,⟨17868285150810919815685619,17868285150810925236950565⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-31459501307094250640196337),(-31459501307094238872424460)⟩,⟨59507370216048330392704387,59507370216048342159967845⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨11997135075176213785701773,11997135075176240630635553⟩,⟨92004441257075367149270666,92004441257075393998713545⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨69005840673393737796326811,69005840673393803063170319⟩,⟨88406061674705363605054418,88406061674705428877469406⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨100080929207638076872882837,100080929207638212163244641⟩,⟨52618494556239022678863959,52618494556239157970686599⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨84375205699814555352300682,84375205699814712505868802⟩,⟨16196233769366846471414162,16196233769367003623914008⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨32252304002629201796390125,32252304002629272524817868⟩,⟨1253887168579945917705218,1253887168580016645348510⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨635045018789532287124,635045018789533745772⟩,⟨(-182025120588721331681),(-182025120588719873061)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨2004477346425027703767,2004477346425031450926⟩,⟨(-775307557016131724310),(-775307557016127977203)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨3585171499145979623882,3585171499145984018850⟩,⟨(-2177292240953776361788),(-2177292240953771966756)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨5117382931597989832653,5117382931597993169273⟩,⟨(-5307269174747486146866),(-5307269174747482809735)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨5323840844246074777369,5323840844246076480404⟩,⟨(-11445053446848038374512),(-11445053446848036669830)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨823851449382603517007,823851449382604390497⟩,⟨(-21503154493583969167211),(-21503154493583968291117)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-14683323482627267197697),(-14683323482627266432570)⟩,⟨(-33576998615407284567650),(-33576998615407283801055)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-48503886543263461370051),(-48503886543263460169993)⟩,⟨(-38480592350259686315512),(-38480592350259685118814)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-100871194964044107224173),(-100871194964044104854511)⟩,⟨(-16734417248722351677909),(-16734417248722349320699)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-152451309021241951246672),(-152451309021241946656711)⟩,⟨53975778159897359944213,53975778159897364523353⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-162509590159407542289176),(-162509590159407534134372)⟩,⟨175355433067553805120811,175355433067553813279651⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-96572555880151443812267),(-96572555880151430959248)⟩,⟨306456026761392179997914,306456026761392192879517⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨29253418843304720753480,29253418843304738055566⟩,⟨378638567098282086048708,378638567098282103390699⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨140295931875828466283351,140295931875828485183757⟩,⟨349020954046424019913758,349020954046424038838460⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨158327069555838478819341,158327069555838493923971⟩,⟨233955849474534134621034,233955849474534149735081⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨68324563025189029637720,68324563025189035437953⟩,⟨80423008440105556089352,80423008440105561891297⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-480631906134523915),(-480631906134474709)⟩,⟨(-6363245007536779963),(-6363245007536730761)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-3323912970089376632),(-3323912970089161919)⟩,⟨(-20016541643560854643),(-20016541643560639928)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-12712769794794801096),(-12712769794794096552)⟩,⟨(-35794445067944864845),(-35794445067944160307)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-35782404813811702977),(-35782404813809363455)⟩,⟨(-52287985632419086407),(-52287985632416746889)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-82354975815102076768),(-82354975815094557681)⟩,⟨(-61444114249884047654),(-61444114249876528571)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-160841234245933181251),(-160841234245911986919)⟩,⟨(-42149674776017100373),(-42149674775995906040)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-265242936303387774849),(-265242936303341390288)⟩,⟨44924390925768276737,44924390925814661324⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-352036793287848829308),(-352036793287770980405)⟩,⟨249732796473751585364,249732796473829434332⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-321317153841080951558),(-321317153840939087311)⟩,⟨596807721190022062947,596807721190163927247⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-39961362218302822397),(-39961362218121957615)⟩,⟨1024027147601115039713,1024027147601295904502⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨560971345372237141434,560971345372392199955⟩,⟨1350770684594947176618,1350770684595102235051⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1358811241293895228921,1358811241293990074240⟩,⟨1359769293784819854736,1359769293784914699832⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨2019556086350212836837,2019556086350269467754⟩,⟨986012244485854102886,986012244485910733547⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2173653655189687015972,2173653655189722152835⟩,⟨433020007913696067667,433020007913731204358⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1660880725391036373934,1660880725391053917319⟩,⟨35452248592057467024,35452248592075010325⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨618585797084720474712,618585797084725646117⟩,⟨(-41713416394918740763),(-41713416394913569380)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-47447247014954730),(-47447247014954713)⟩,⟨6426050774052957,6426050774052973⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-147235327304973854),(-147235327304973838)⟩,⟨35788184136929898,35788184136929914⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-256622938076342621),(-256622938076342605)⟩,⟨120402716554977673,120402716554977689⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-361721022211649940),(-361721022211649924)⟩,⟨313213651151199291,313213651151199307⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-405223776604103421),(-405223776604103404)⟩,⟨677816500964523397,677816500964523415⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-250383260112189131),(-250383260112189112)⟩,⟨1258319286373840104,1258319286373840121⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨341916035274906228,341916035274906247⟩,⟨2006960057199125070,2006960057199125089⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1662910786476579880,1662910786476579901⟩,⟨2672775328042148941,2672775328042148963⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨3871582078748015443,3871582078748015493⟩,⟨2723643672489685510,2723643672489685561⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨6709634977621584465,6709634977621584825⟩,⟨1467896318073525301,1467896318073525662⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨9343369638780173907,9343369638780176581⟩,⟨(-1493348153713018699),(-1493348153713016028)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨10649233001177883286,10649233001177896461⟩,⟨(-5657689864452852477),(-5657689864452839301)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨9931399849324468219,9931399849324508070⟩,⟨(-9425734783554742836),(-9425734783554702986)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨7483956451733858105,7483956451733931472⟩,⟨(-10793796951441134646),(-10793796951441061279)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨4346103793808653890,4346103793808732657⟩,⟨(-8590039964718045934),(-8590039964717967168)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1378245035564207131,1378245035564241560⟩,⟨(-3269338113953582854),(-3269338113953548426)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨4977434305893864454283736582,4977434305893948856167826581⟩,⟨(-51445719120221342676930690474),(-51445719120221258275151819213)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 25) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_25 (tableDensity false) (fullFactor true 0 25) density0_contains hk0_1_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨16241812354000770286292451874,16241812354000770388132807005⟩,⟨1526829917636168138343717607,1526829917636168238389440209⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_25 0 25 ha0_1_25_contains + def realAnswer : RBox := ⟨21219246659894634740476188456,21219246659894719244400633586⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_25 +namespace hm0_1_1_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-702218779965189708653003785),(-702218779965188050469845371)⟩,⟨121368314388299199555584970,121368314388300857748845400⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-2107854857887947146388610325),(-2107854857887943169647306439)⟩,⟨845356417264111145316146337,845356417264115122131018647⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2951975005479916813232139970),(-2951975005479912932445446905)⟩,⟨3013840921736647150348037485,3013840921736651031371605848⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1107016813672695490583440858),(-1107016813672691948997581406)⟩,⟨6676245613131068666121292630,6676245613131072207833932103⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨5975837149578286004409195645,5975837149578287804794356080⟩,⟨8068254256994093859769715120,8068254256994095659684540788⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨14125430750163971749127271927,14125430750163972526545977082⟩,⟨(-715850335592609511098466964),(-715850335592608733787766388)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨7248718160241243843822862126,7248718160241244128548936687⟩,⟨(-17927045439840815805879686800),(-17927045439840815520200260241)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-19365953914778018019372614696),(-19365953914778017864817723155)⟩,⟨(-17188788915150118948232115377),(-17188788915150118794883148592)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-28929597854678375612598574751),(-28929597854678375506650090975)⟩,⟨16828852067659121916059511458,16828852067659122022371628479⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨6984896403190534093207514157,6984896403190534168648600335⟩,⟨39993505584519721237040217922,39993505584519721313832408863⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨43508053134078931021637728389,43508053134078931076692220642⟩,⟨11680470317488186129151500889,11680470317488186181704680359⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨32685107977549682050615739042,32685107977549682090586108616⟩,⟨(-30873722864172569966579422100),(-30873722864172569925846440242)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2334710892900141919302744121),(-2334710892900141894480381861)⟩,⟨(-39882373159431607643705662679),(-39882373159431607616555303280)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-21213993334731883676854645222),(-21213993334731883657770941269)⟩,⟨(-22634710721672937023491369350),(-22634710721672937004638862083)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-18478393674041635961842622176),(-18478393674041635951666076241)⟩,⟨(-6388201129553453811169325578),(-6388201129553453802092553179)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-6645194780241390862378651233),(-6645194780241390859430380048)⟩,⟨(-555793469687472855895042853),(-555793469687472853465758195)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨5041033740434182191219924,5041033740434200939939823⟩,⟨1676507151250659496084751,1676507151250678244949483⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨16929415226103555158701095,16929415226103628312190560⟩,⟨2593684423931593240786829,2593684423931666394963578⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨32340101592834203495748856,32340101592834404708280510⟩,⟨(-6032951258467491533223749),(-6032951258467290318846263)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨44066583800877817538538712,44066583800878607343986969⟩,⟨(-35873549513526268423971423),(-35873549513525478616789527)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨22734174522277744746741015,22734174522280312017522974⟩,⟨(-93478589743086177402019286),(-93478589743083610132951294)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-83899793869897498074396749),(-83899793869890503709546719)⟩,⟨(-140861661355502050450292567),(-140861661355495056093136734)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-277103649761992666546891144),(-277103649761971770648436756)⟩,⟨(-45303426356390717104497080),(-45303426356369821203445541)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-339663919896079094472349807),(-339663919896040252275089356)⟩,⟨332126642507538551793430493,332126642507577394009094351⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨134180824259646356202205085,134180824259712461882168312⟩,⟨766371388239515386033553570,766371388239581491696213288⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1099874177311946920372383021,1099874177312026224827962076⟩,⟨503360422615231614431297336,503360422615310918858410950⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1537421876743571859218775102,1537421876743640801269127868⟩,⟨(-832147195207752492000168452),(-832147195207683549893368969)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨533464421535235219642764160,533464421535288561146710052⟩,⟨(-2224510926355841853844851770),(-2224510926355788512308180614)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1211029618870809642353643608),(-1211029618870779543351554023)⟩,⟨(-2323140107993003247676019652),(-2323140107992973148747243852)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-2168527328623898358339323581),(-2168527328623883448299633861)⟩,⟨(-1260100698453172340849980688),(-1260100698453157430886751321)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1811492188836108180077029853),(-1811492188836100162464796510)⟩,⟨(-248883586145166264502430553),(-248883586145158246906013558)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-670027104870354345074052443),(-670027104870352029251369811)⟩,⟨42209111082200424901844829,42209111082202740726492020⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨6621450901609187605583,6621450901609188581932⟩,⟨30225341489542529520963,30225341489542530497363⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨33255621624456741223045,33255621624456744588156⟩,⟨95860815620974346310878,95860815620974349675765⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨107293546474567235124515,107293546474567242427203⟩,⟨169307397456427843743742,169307397456427851044595⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨278883714165026345116997,278883714165026360006852⟩,⟨220603393613425543927256,220603393613425558810749⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨592689209471414682586794,592689209471414712887899⟩,⟨138799316376670048660108,138799316376670078952236⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨978860410890723370122922,978860410890723431506059⟩,⟨(-313806074854585053665945),(-313806074854584992285328)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1017863030014720726465131,1017863030014720849309488⟩,⟨(-1401628291097060268481957),(-1401628291097060145613770)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-213244586291849013019079),(-213244586291848770210957)⟩,⟨(-2916746328488653080681546),(-2916746328488652837838766)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-3537627068317469865326162),(-3537627068317469386479222)⟩,⟨(-3389850965687168023545936),(-3389850965687167544714456)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-7939101976837828895097885),(-7939101976837827855578584)⟩,⟨(-293995902534530741643864),(-293995902534529702182884)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-9581709278819102127044376),(-9581709278819098574626313)⟩,⟨7270974359853481607768484,7270974359853485160181559⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-4852657850428369705784436),(-4852657850428357256980886)⟩,⟨15612292162624646633706606,15612292162624659082536467⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨4482044189442020910794522,4482044189442061680670257⟩,⟨18693319021045737772394093,18693319021045778542281005⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨11647070638530967435587326,11647070638531064638194540⟩,⟨14692934146673488783084314,14692934146673585985665003⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨11519115243884780380780263,11519115243884898409354294⟩,⟨7718794578716733603859984,7718794578716851632409079⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨4671675429949877979541924,4671675429949931852178357⟩,⟨2132208071847968272025893,2132208071848022144657955⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨206544062431950167264,206544062431951391037⟩,⟨78114936370160644474,78114936370161868254⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨681035282524310166845,681035282524313306872⟩,⟨191734906934651278154,191734906934654418185⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1334639520255527966404,1334639520255531637773⟩,⟨133811065570669320656,133811065570672992024⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨2240311196356823246683,2240311196356826010042⟩,⟨(-365042386621518762845),(-365042386621515999538)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨3274693908969408030994,3274693908969409392915⟩,⟨(-1812299964359295077947),(-1812299964359293716190)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3763655070325233940487,3763655070325234541937⟩,⟨(-4928824283207750506464),(-4928824283207749905267)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1957570144796266047415,1957570144796266416331⟩,⟨(-10180084067007990979409),(-10180084067007990610614)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-5136629897712109980763),(-5136629897712109545054)⟩,⟨(-16475228257842242224156),(-16475228257842241788085)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-20316764772098096200454),(-20316764772098095384506)⟩,⟨(-19362438379612444531084),(-19362438379612443713932)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-42316819755649478350556),(-42316819755649476767481)⟩,⟨(-10972892986713552925156),(-10972892986713551341168)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-62125063589374446295698),(-62125063589374443464835)⟩,⟨14989524460553818598653,14989524460553821428929⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-66071859140338355169581),(-66071859140338350661935)⟩,⟨54387021608729969160047,54387021608729973664904⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-47872345171881639034078),(-47872345171881632879943)⟩,⟨89505425470887191139852,89505425470887197290368⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-18205899150092477102011),(-18205899150092470276053)⟩,⟨99626732679281979578098,99626732679281986402111⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2625868449211691549548,2625868449211697075946⟩,⟨76564313203916270106164,76564313203916275632024⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4129900085576320041535,4129900085576322179547⟩,⟨28443966118260960541583,28443966118260962679564⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-264712701578245190),(-264712701578204750)⟩,⟨(-2079984869036800590),(-2079984869036760152)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1397649920008262147),(-1397649920008085676)⟩,⟨(-6661454474153176232),(-6661454474152999758)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-4653923013920840584),(-4653923013920261457)⟩,⟨(-12325126676230063936),(-12325126676229484808)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-12477932175915949988),(-12477932175914026595)⟩,⟨(-18945899497616770798),(-18945899497614847401)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-28597051937463220667),(-28597051937457038205)⟩,⟨(-24223708201193325135),(-24223708201187142673)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-57228994497641086445),(-57228994497623659795)⟩,⟨(-21258633636485266969),(-21258633636467840320)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-99381515028651050906),(-99381515028612920396)⟩,⟨4093750928648617608,4093750928686748113⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-145005553422125574132),(-145005553422061611059)⟩,⟨72730960710810375614,72730960710874338679⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-164373735815832018191),(-164373735815715553432)⟩,⟨202710828046245449242,202710828046361913990⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-110682585904118223904),(-110682585903969900072)⟩,⟨388014631879314821871,388014631879463145700⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨51863652731398871937,51863652731525870530⟩,⟨578489020141499612954,578489020141626611567⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨301825261445547750903,301825261445625324930⟩,⟨689852276674076293473,689852276674153867539⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨540089552152921003126,540089552152967255064⟩,⟨657559770429558931509,657559770429605183493⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨635604848131051208278,635604848131079870343⟩,⟨494093724387883825402,494093724387912487501⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨511190033254926793229,511190033254941089475⟩,⟨280277185069112071935,280277185069126368199⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨195174438207343044964,195174438207347256653⟩,⟨86649656782334035561,86649656782338247255⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1400067909944787),(-1400067909944771)⟩,⟨258372341389865,258372341389881⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3894671487355955),(-3894671487355939)⟩,⟨2089243487633618,2089243487633634⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-2882726878522511),(-2882726878522495)⟩,⟨8144098506749969,8144098506749985⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨13852686991094646,13852686991094662⟩,⟨21871805991406935,21871805991406952⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨76085418915376664,76085418915376680⟩,⟨45456301937364934,45456301937364953⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨238221848494114010,238221848494114026⟩,⟨70148076110558779,70148076110558796⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨576596129187977161,576596129187977178⟩,⟨50638685200339375,50638685200339392⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1162226165237843503,1162226165237843523⟩,⟨(-130855802562283834),(-130855802562283815)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1990644942322809638,1990644942322809681⟩,⟨(-674435254037171936),(-674435254037171893)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2883400504147772873,2883400504147773166⟩,⟨(-1786715188729449521),(-1786715188729449223)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨3455711198318860169,3455711198318862351⟩,⟨(-3491435976629978955),(-3491435976629976776)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨3286754313678336043,3286754313678346799⟩,⟨(-5424542803162103102),(-5424542803162092343)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2286806021583322825,2286806021583355373⟩,⟨(-6829889953888747741),(-6829889953888715190)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨937434654337379595,937434654337439557⟩,⟨(-6876680835649310993),(-6876680835649251031)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨6844228963069512,6844228963133913⟩,⟨(-5140047171870022155),(-5140047171869957760)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-129529540592745902),(-129529540592717741)⟩,⟨(-1906038326918541411),(-1906038326918513255)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨594068916575190513800657135,594068916575258873010280181⟩,⟨(-9073637504415138621831788882),(-9073637504415070262627798055)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 25) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_25 (tableDensity true) (fullFactor true 0 25) density1_contains hk0_1_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-21239293078308699738327516852),(-21239293078308699605151667836)⟩,⟨(-1996623738447296927124652581),(-1996623738447296796295630717)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_25 0 25 ha0_1_25_contains + def realAnswer : RBox := ⟨(-20645224161733509224626859717),(-20645224161733440732041387655)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_25 +namespace hm0_0_1_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1351849039792560507779243543,1351849039792561178961800563⟩,⟨198880625579834231507577718,198880625579834902718687604⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨4330614395141106787778251599,4330614395141108567731551851⟩,⟨(-347970335139625580976159524),(-347970335139623800988328569)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨6996622610246437422562265221,6996622610246439441577715175⟩,⟨(-4065873741741359770334111777),(-4065873741741357751454737545)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨5053163912261852500929626053,5053163912261853974214142474⟩,⟨(-12229195236690203810272361440),(-12229195236690202337411268058)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-8811844014294460132696188980),(-8811844014294459052405702685)⟩,⟨(-18470170771373465793180246443),(-18470170771373464712796503635)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-30104013999086714137838581719),(-30104013999086713534958975222)⟩,⟨(-4022455781439430818768492627),(-4022455781439430215253045572)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-23882587818286688429822993986),(-23882587818286688011740530858)⟩,⟨35795943351390740059005855985,35795943351390740476424436306⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨33041099163293223109356941576,33041099163293223420691834153⟩,⟨47186255755736766961276026717,47186255755736767272622587870⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨69327118044787229880204193146,69327118044787230102643558558⟩,⟨(-19861850572696031195506727160),(-19861850572696030972439672535)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨5177253848949929979021349763,5177253848949930125884069041⟩,⟨(-83566387554746642382162640854),(-83566387554746642235847913645)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-80156797054851625593356544204),(-80156797054851625501962588167)⟩,⟨(-39957944528804578930799142417),(-39957944528804578839589544440)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-72481728312142652379811294945),(-72481728312142652322235484685)⟩,⟨49406809637207381692677361688,49406809637207381750698418101⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-5208882727265669461309928258),(-5208882727265669427308534324)⟩,⟨77594608506372858991012366647,77594608506372859025539634386⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨36489882131482734682876131567,36489882131482734705220187754⟩,⟨48504676141517343092584747343,48504676141517343114735839517⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨34828417045534369199994771451,34828417045534369211157153928⟩,⟨16214407286363444737516094399,16214407286363444748239558087⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨12896137501323604744829591399,12896137501323604747975107521⟩,⟨2427603901559319875114924628,2427603901559319878061308011⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-7539750441274126900047434),(-7539750441274120044966682)⟩,⟨(-5518651729746743576245595),(-5518651729746736720740854)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-27341921737886906192917954),(-27341921737886876448673464)⟩,⟨(-13857055841871898786923655),(-13857055841871869041766600)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-60099988806645803414621733),(-60099988806645710066907888)⟩,⟨(-8906426931601113407070335),(-8906426931601020059505164)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-103219019098071089907234034),(-103219019098070831199727840)⟩,⟨34978690009833892123109371,34978690009834150825549963⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-112307578733807151501810475),(-112307578733806306974343849)⟩,⟨154208386976086550459031893,154208386976087394977564469⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨36496543866436649421477079,36496543866439441069869414⟩,⟨329557882359600220422864148,329557882359603012078188857⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨465614217765986280589167205,465614217765993102286880157⟩,⟨330167423095999566056765153,330167423096006387780067758⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨917606619537229228344949151,917606619537244115867764857⟩,⟨(-287209456036153844061807261),(-287209456036138956568425401)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨466032315107303019417520066,466032315107327708634838523⟩,⟨(-1485747163805002638410879308),(-1485747163804977949232137946)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1466792292997565459207931632),(-1466792292997537255547044655)⟩,⟨(-1867993116360400103765879488),(-1867993116360371900003528540)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-3337260060179714118547621158),(-3337260060179684593711692455)⟩,⟨103058799101000410374420777,103058799101029935216803509⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-2653287017988135143059858041),(-2653287017988116709013902020)⟩,⟨3294775461900769185367724536,3294775461900787619235074896⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨330879095793012875715932152,330879095793026174399053420⟩,⟨4695206020425779441860309984,4695206020425792740528711015⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨2737226417811005118047390604,2737226417811011380252576014⟩,⟨3466848222447290773501755813,3466848222447297035864073594⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2817370550322776836368151376,2817370550322779641709976328⟩,⟨1486598076166477899135243404,1486598076166480704603293463⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1121771652097829718947454270,1121771652097830629334824949⟩,⟨312211252415012772075630423,312211252415013682495030764⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨9003527246708751815320,9003527246708752777875⟩,⟨(-29466713251983327347635),(-29466713251983326382782)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨17076820860779451285166,17076820860779454585945⟩,⟨(-99824356557446475290139),(-99824356557446471980193)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-16417356008868571650187),(-16417356008868564227879)⟩,⟨(-201334818022004682735056),(-201334818022004675292100)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-159319164082775810059889),(-159319164082775793781999)⟩,⟨(-331435729515278116141331),(-331435729515278099840412)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-525348933600434511958688),(-525348933600434475395159)⟩,⟨(-401354373385825221310432),(-401354373385825184747552)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1190239906339986244893454),(-1190239906339986161231676)⟩,⟨(-111970499921586924647707),(-111970499921586841073254)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1862970662359171305843139),(-1862970662359171113809911)⟩,⟨1107386953168843987424279,1107386953168844179326089⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1339959868204147936120634),(-1339959868204147503964480)⟩,⟨3651461938809499306907125,3651461938809499739153375⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2401720031372036126770344,2401720031372037058515719⟩,⟨6352062725794763937349667,6352062725794764869573622⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨9958484980191855360456031,9958484980191857288794452⟩,⟨5331756477574205487035084,5331756477574207415426940⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨17126863411858817834176825,17126863411858821714651148⟩,⟨(-3505226750809416150491047),(-3505226750809412271047250)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨16346599322174406388904438,16346599322174415462810686⟩,⟨(-18242344703829516090460262),(-18242344703829507017390021)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨5322421178181515976445995,5322421178181537058109359⟩,⟨(-29547646233627102409552912),(-29547646233627081327382446)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-7902587354923273386520092),(-7902587354923240110778258)⟩,⟨(-29565974715448716783661185),(-29565974715448683506363729)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-12571343895073570581914145),(-12571343895073534242944508)⟩,⟨(-19772823657617077368536698),(-19772823657617041028275263)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-5844099477009531051515515),(-5844099477009512893331621)⟩,⟨(-6628006993047931398559268),(-6628006993047913239993040)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-69495787177295108030),(-69495787177294835139)⟩,⟨(-102261990235782961294),(-102261990235782688410)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-256897763862603639236),(-256897763862602953796)⟩,⟨(-311234900065842686163),(-311234900065842000743)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-607504453122435527491),(-607504453122434760061)⟩,⟨(-509262526966685105071),(-509262526966684337715)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1278221225857625419472),(-1278221225857624879779)⟩,⟨(-586925160721126780785),(-586925160721126241293)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2428301249439533622836),(-2428301249439533294347)⟩,⟨(-210811116227948715730),(-210811116227948387551)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-3994796960812501678364),(-3994796960812501469751)⟩,⟨1345687746232642334355,1345687746232642542752⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-5125716325601464917876),(-5125716325601464733352)⟩,⟨5191549258184006169902,5191549258184006354727⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3387014079601983133682),(-3387014079601982823588)⟩,⟨12075009061381031890411,12075009061381032202042⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨5240789751852810921640,5240789751852811562485⟩,⟨20423121932972022269261,20423121932972022911782⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨23735161129943651039263,23735161129943652315204⟩,⟨24268657087144722836189,24268657087144724111688⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨48822737828172572163208,48822737828172574486533⟩,⟨14872718507936670598713,14872718507936672917086⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨68735061979562207472229,68735061979562211219091⟩,⟨(-11279297487188463340756),(-11279297487188459600517)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨70718442389042967307930,70718442389042972443761⟩,⟨(-44244217348301940535659),(-44244217348301935402873)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨53498073077659996864437,53498073077660002543822⟩,⟨(-64102383592847372916039),(-64102383592847367235356)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨28881856175082874340457,28881856175082878918444⟩,⟨(-56166680156404580409550),(-56166680156404575828351)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨8379001803437668439359,8379001803437670205055⟩,⟨(-22148355457075651775162),(-22148355457075650007861)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-987357354612127427),(-987357354612118390)⟩,⟨248695231758827475,248695231758836514⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-3062434429031874540),(-3062434429031835687)⟩,⟨1078058895367793870,1078058895367832721⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-5303064485227463015),(-5303064485227338546)⟩,⟨3038057575762596197,3038057575762720671⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-7259060356325189311),(-7259060356324788329)⟩,⟨7275300635137800189,7275300635138201168⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-7251114467470455527),(-7251114467469213585)⟩,⟨15200803581735065775,15200803581736307721⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1353697073771689611),(-1353697073768357360)⟩,⟨27560640491567210691,27560640491570542938⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨17118146091080194351,17118146091087035325⟩,⟨41912733552766400260,41912733552773241228⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨55433049899798694199,55433049899813642090⟩,⟨48626378218945755088,48626378218960702973⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨114073207278517650680,114073207278544022765⟩,⟨28633900167164186650,28633900167190558733⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨176116947572006277540,176116947572037355931⟩,⟨(-39966043256045464260),(-39966043256014385860)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨205139195593731796127,205139195593756065551⟩,⟨(-162309057783236410573),(-162309057783212141119)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨166331004195193803276,166331004195210697000⟩,⟨(-306199494759263281142),(-306199494759246387380)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨63780449385877421953,63780449385889717984⟩,⟨(-407161900458866265340),(-407161900458853969283)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-45287989072903292706),(-45287989072896179857)⟩,⟨(-407669452525331994467),(-407669452525324881608)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-89012150307866887514),(-89012150307863491617)⟩,⟨(-296323272283380540207),(-296323272283377144313)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-43346264047666447653),(-43346264047665469254)⟩,⟨(-107431853427746140686),(-107431853427745162287)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1239357643643565,1239357643643581⟩,⟨6546636770922919,6546636770922935⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨6105841940533085,6105841940533101⟩,⟨20235040858706804,20235040858706820⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨18960126382384947,18960126382384963⟩,⟨34913056267005974,34913056267005990⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨47425036550173666,47425036550173682⟩,⟨48075275919252882,48075275919252898⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨100463850918571344,100463850918571361⟩,⟨50535742579942205,50535742579942223⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨183450226302462578,183450226302462594⟩,⟨21075550045726400,21075550045726416⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨286483782429243607,286483782429243624⟩,⟨(-76578698641400224),(-76578698641400208)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨366848869467380238,366848869467380255⟩,⟨(-284843781790194609),(-284843781790194593)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨337982081444394773,337982081444394796⟩,⟨(-621883641891616680),(-621883641891616658)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨92122366391277644,92122366391277714⟩,⟨(-1036611844840475200),(-1036611844840475129)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-423805256274319342),(-423805256274318919)⟩,⟨(-1388754617417816406),(-1388754617417815982)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1111961858933337508),(-1111961858933335536)⟩,⟨(-1505953035931055016),(-1505953035931053039)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1702097823135364759),(-1702097823135359016)⟩,⟨(-1308225279020924137),(-1308225279020918389)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1874992519772657693),(-1874992519772647360)⟩,⟨(-890183622537141434),(-890183622537131101)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1460970605940713568),(-1460970605940700792)⟩,⟨(-453046251634113090),(-453046251634100315)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-550567380429003242),(-550567380428997027)⟩,⟨(-128246630192412509),(-128246630192406295)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1668080852586692205878867880),(-1668080852586665717046165797)⟩,⟨17542266206692357454402320872,17542266206692383943201674911⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 26) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_26 (tableDensity false) (fullFactor true 0 26) density0_contains hk0_1_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-5506708101056395674258506000),(-5506708101056395629993746198)⟩,⟨(-529020573177356727121725920),(-529020573177356683507132050)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_26 0 26 ha0_1_26_contains + def realAnswer : RBox := ⟨(-7174788953643087880237373880),(-7174788953643061346939911995)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_26 +namespace hm0_1_1_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨224685345829528867456789583,224685345829529394097780977⟩,⟨64220760593230389665983388,64220760593230916300588429⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨745219178780664897328322146,745219178780666284152925259⟩,⟨44824390794449237486912132,44824390794450624305831034⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1299059623213547317573554884,1299059623213548849113357347⟩,⟨(-504085500826905018993924891),(-504085500826903487411731833)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1208051206721625887984330954,1208051206721626922101838737⟩,⟨(-1898375143501611958953939809),(-1898375143501610924726090890)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-881133001592459150115951141),(-881133001592458481208836148)⟩,⟨(-3247699993203744382197836675),(-3247699993203743713351212536)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-4587118317731797765846231373),(-4587118317731797510638882980)⟩,⟨(-1350758936560738204889526794),(-1350758936560737949863309456)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-4153917614716661946795448401),(-4153917614716661835443105842)⟩,⟨5124187241259006972613731183,5124187241259007084301794304⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4964083923656688001200379157,4964083923656688063162966094⟩,⟨7398693437895979951331248104,7398693437895980013050533139⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨11027715529411040736179910259,11027715529411040778177425692⟩,⟨(-3620375602178222563779940658),(-3620375602178222521917611158)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-99631760174087081586574636),(-99631760174087052509246686)⟩,⟨(-14173808187347933700027970505),(-14173808187347933670321818591)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-14644614142415929232988145725),(-14644614142415929212128958424)⟩,⟨(-5961641698842796434675114010),(-5961641698842796414643700446)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-12415469073809666662023296924),(-12415469073809666647193120967)⟩,⟨9841616016848649411146051535,9841616016848649426097073405⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨57840865506623129030048422,57840865506623138018703894⟩,⟨14115335853325518944477378530,14115335853325518954317735642⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨7273641231482320177008931191,7273641231482320183855275569⟩,⟨8224491138183743473192361128,8224491138183743479992705897⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨6520360978254774404105938616,6520360978254774407761227152⟩,⟨2336737979854598701731554282,2336737979854598705004661298⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨2354723553961259161773381972,2354723553961259162828237613⟩,⟨202328641230967507155892142,202328641230967508027146267⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-625044341534064562315286),(-625044341534059599199924)⟩,⟨(-1316333075392875031685006),(-1316333075392870068627491)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2733201543040044254246193),(-2733201543040022053416624)⟩,⟨(-3842092982689773840745327),(-3842092982689751640047195)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-7507019356742756933254611),(-7507019356742684780524307)⟩,⟨(-5182406216063661023194587),(-5182406216063588870486722)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-15858592181913126326936620),(-15858592181912922226559999)⟩,⟨(-1399231217543833977800739),(-1399231217543629876822481)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-22791949170520665521889345),(-22791949170519985980378767)⟩,⟨15045463175504563150388300,15045463175505242693076192⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-8674401469179466360310011),(-8674401469177192465032901)⟩,⟨46459138651946155730619641,46459138651948429625194577⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨54128033575700040842079565,54128033575705624255644904⟩,⟨62013164282523259584091386,62013164282528842994328593⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨140780492773427372946670899,140780492773439593165257728⟩,⟨(-16452168311788419860916733),(-16452168311776199638888917)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨102712737246011444734059516,102712737246031720986004329⟩,⟨(-212762314277107129335177673),(-212762314277086853077978510)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-196342816427209412242418753),(-196342816427186300149777217)⟩,⟨(-317816602511810237561868129),(-317816602511787125482677168)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-547471906236983267840853123),(-547471906236959135902049755)⟩,⟨(-32069922648786600438778200),(-32069922648762468500839839)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-500788479602147533087626540),(-500788479602132601694742054)⟩,⟨527767428895404966431860220,527767428895419897850939092⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-14003001417140110581547770),(-14003001417129416607722344)⟩,⟨842677761448445928633643919,842677761448456622608670785⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨438212077419050541584910014,438212077419055481976912135⟩,⟨685931044281808808067490052,685931044281813748434005861⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨493496422223147547452548486,493496422223149717003521367⟩,⟨335905897283935425150914791,335905897283937594681967789⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨203286387148017517370312728,203286387148018218655496602⟩,⟨83700331482485101355447323,83700331482485802635636551⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨5217677468035263514638,5217677468035263811393⟩,⟨(-4600644605523674822714),(-4600644605523674525858)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨15192674093936718172210,15192674093936719199485⟩,⟨(-17127992531676801723441),(-17127992531676800695737)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨21285780259826661431784,21285780259826663683494⟩,⟨(-40277941000280623025690),(-40277941000280620773022)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨11152095236368247920049,11152095236368252594135⟩,⟨(-80907493179121779568406),(-80907493179121774893259)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-44356607624171443347480),(-44356607624171433663114)⟩,⟨(-134583056471748806387051),(-134583056471748796702604)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-187073839430225591170024),(-187073839430225571185313)⟩,⟨(-155271871932355262382744),(-155271871932355242401266)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-416720136234984461113050),(-416720136234984420124696)⟩,⟨(-15948626367518133600913),(-15948626367518092617974)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-554872421694264329574624),(-554872421694264246770716)⟩,⟨454979270807600574256445,454979270807600657062871⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-153086672691082634623193),(-153086672691082470070308)⟩,⟨1216211640362667882969948,1216211640362668047537196⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1188738096540835937855644,1188738096540836297534419⟩,⟨1640805218039440136977182,1640805218039440496658729⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨3039060416795306131939280,3039060416795307083981954⟩,⟨722713850805802166498537,722713850805803118530140⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3959863507856408226688280,3959863507856412106200883⟩,⟨(-1716815657120924339801292),(-1716815657120920460292955)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨2929816564686663257806270,2929816564686675735866905⟩,⟨(-4230480449051273693674228),(-4230480449051261215606361)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨785038575229343302544640,785038575229365398069931⟩,⟨(-5013429592341474250488028),(-5013429592341452154959945)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-623331746552426531774949),(-623331746552400836067979)⟩,⟨(-3729750814924452484650114),(-3729750814924426788947594)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-459973087165904188078582),(-459973087165890867742105)⟩,⟨(-1328521261402081335030436),(-1328521261402068014697291)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1810882152468133948,1810882152468362811⟩,⟨(-41289396183671581816),(-41289396183671352952)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-6180741348890286204),(-6180741348889712164)⟩,⟨(-132707548121128410429),(-132707548121127836386)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-57153698912162558406),(-57153698912161918253)⟩,⟨(-246964979241983025695),(-246964979241982385535)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-206927392665414039210),(-206927392665413594671)⟩,⟨(-380381089258852124744),(-380381089258851680185)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-544955790802736188019),(-544955790802735928880)⟩,⟨(-474646221115873618819),(-474646221115873359650)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1164398406284217819792),(-1164398406284217678232)⟩,⟨(-346130453742305742345),(-346130453742305600767)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2026705000376011071468),(-2026705000376010986973)⟩,⟨388826536347112591693,388826536347112676155⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2674817079746083037497),(-2674817079746082926974)⟩,⟨2250279179068546284120,2250279179068546394493⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1961473040624455972805),(-1961473040624455751371)⟩,⟨5444671168793462544769,5444671168793462766057⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1645222422668615808617,1645222422668616248776⟩,⟨9027088484360133412836,9027088484360133853064⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨8667694396139777052241,8667694396139777856468⟩,⟨10535116101686597806630,10535116101686598611342⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨16982824002494178835904,16982824002494180146055⟩,⟨7465437933669755855883,7465437933669757166624⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨22295017384194571859065,22295017384194573682414⟩,⟨204549967201819779911,204549967201821603452⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨21391556360370156650326,21391556360370158699813⟩,⟨(-6908634060464123194839),(-6908634060464121145551)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨14732781668646705045293,14732781668646706720081⟩,⟨(-8735078164202336456226),(-8735078164202334781773)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨5138148874218275859046,5138148874218276510049⟩,⟨(-3898511389967545335352),(-3898511389967544684509)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-319815051289773095),(-319815051289765667)⟩,⟨98210534136090112,98210534136097538⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1011113635260434102),(-1011113635260402168)⟩,⟨404717101438398531,404717101438430465⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-1818151391955587733),(-1818151391955485416)⟩,⟨1089916943520259326,1089916943520361644⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-2645051352291987682),(-2645051352291658026)⟩,⟨2558514019403793600,2558514019404123263⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-2982474128673257498),(-2982474128672236328)⟩,⟨5370634107635008045,5370634107636029218⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1498905803925372819),(-1498905803922632942)⟩,⟨10020460538306973860,10020460538309713739⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4321586120894402963,4321586120900026584⟩,⟨16172397160127906946,16172397160133530561⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨17825576915053264971,17825576915065546498⟩,⟨21223241794917580818,21223241794929862347⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨41101060390190585703,41101060390212236208⟩,⟨19019698157173607615,19019698157195258121⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨71102329262052251715,71102329262077738628⟩,⟨1121807064189758888,1121807064215245798⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨97037093670958695892,97037093670978573403⟩,⟨(-37087450111755811929),(-37087450111735934427)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨104359314165075101812,104359314165088918157⟩,⟨(-87984369112707570800),(-87984369112693754463)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨86093947445663179651,86093947445673222136⟩,⟨(-130143518596615133088),(-130143518596605090605)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨51584367310034720894,51584367310040522718⟩,⟨(-139773875889697501637),(-139773875889691699817)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨20333534744531477904,20333534744534244851⟩,⟨(-106656998767001712578),(-106656998766998945633)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨4049098629302444483,4049098629303241134⟩,⟨(-39695320294941548887),(-39695320294940752236)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨46126585001593,46126585001609⟩,⟨192673449721323,192673449721339⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨320674435972162,320674435972178⟩,⟨526480061328961,526480061328977⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1163164167414652,1163164167414668⟩,⟨335649854705294,335649854705310⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2952931328362701,2952931328362717⟩,⟨(-2153937004904434),(-2153937004904418)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5666525347256582,5666525347256598⟩,⟨(-11285265704658562),(-11285265704658546)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨7248658498687393,7248658498687409⟩,⟨(-35019320861491138),(-35019320861491121)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-417315416006869),(-417315416006852)⟩,⟨(-84349933882479135),(-84349933882479119)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-36962659976426842),(-36962659976426825)⟩,⟨(-168633256439201816),(-168633256439201800)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-134426588558539632),(-134426588558539614)⟩,⟨(-284181803056715461),(-284181803056715441)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-323814668452002688),(-323814668452002629)⟩,⟨(-399294996789669511),(-399294996789669450)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-603535317042434476),(-603535317042434130)⟩,⟨(-451848308287283720),(-451848308287283372)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-908031503142144550),(-908031503142142936)⟩,⟨(-380858252383113643),(-380858252383112028)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1113599754750276987),(-1113599754750272293)⟩,⟨(-187598895799658329),(-187598895799653634)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1096330374885805135),(-1096330374885796690)⟩,⟨30167824164278783,30167824164287228⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-805420893320122910),(-805420893320112462)⟩,⟨135247196225080373,135247196225090821⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-295816418603770288),(-295816418603765203)⟩,⟨71751443669174335,71751443669179421⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-163514014905088596095589730),(-163514014905067296017774482)⟩,⟨3098655039326880309474448847,3098655039326901609550097378⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 26) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_26 (tableDensity true) (fullFactor true 0 26) density1_contains hk0_1_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨7201079824458363516145668105,7201079824458363574030354000⟩,⟨691796134155004893817018835,691796134155004950851487741⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_26 0 26 ha0_1_26_contains + def realAnswer : RBox := ⟨7037565809553274919950078375,7037565809553296278112579518⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_26 +namespace hm0_0_1_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-357171280711285086527124222),(-357171280711284917288632491)⟩,⟨(-242062311535196716291594394),(-242062311535196547033958011)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1286476679219204681447615512),(-1286476679219204179137954509)⟩,⟨(-486147389703714752281760665),(-486147389703714249926408760)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2560643857524045509950156821),(-2560643857524044824173365795)⟩,⟨259100500104122880633817931,259100500104123566432142674⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-3021692489338085642910013557),(-3021692489338085119239735053)⟩,⟨2969276750585167674108638188,2969276750585168197665880016⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨480030856858057894714153106,480030856858058265833452532⟩,⟨6587241634643232020570113719,6587241634643232391599356139⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨8817959431324103859957008325,8817959431324104090583252825⟩,⟨4475781860016198015450337875,4475781860016198246299977124⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨10943526463469120199954999541,10943526463469120367348274015⟩,⟨(-8950004411102234452569995523),(-8950004411102234285275201775)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-6668069796047419206637276437),(-6668069796047419081944774281)⟩,⟨(-17885586800810336424355038294),(-17885586800810336299795739467)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-24025155751581543775419238097),(-24025155751581543687988403092)⟩,⟨1665287888523243120027439409,1665287888523243207706835213⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-6358943392321661877099766180),(-6358943392321661820754837237)⟩,⟨27417359139556115798060694404,27417359139556115854264994431⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨25203004307345976345187677037,25203004307345976379431216582⟩,⟨16760143030701525076247561190,16760143030701525110391702064⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨25950107419228311120200989670,25950107419228311141089013810⟩,⟨(-14571275809304380549883428164),(-14571275809304380528863758183)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨3204036950555238336516539915,3204036950555238348608988056⟩,⟨(-26263514988892372879262753101),(-26263514988892372866975288810)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-11953632654917929374168539440),(-11953632654917929366338710935)⟩,⟨(-16883046988129226842317474969),(-16883046988129226834542477166)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-11818476843917869437066305469),(-11818476843917869433168488221)⟩,⟨(-5664945011098371741120334656),(-5664945011098371737370295452)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-4399449858772107786645116419),(-4399449858772107785552531718)⟩,⟨(-838507942379089806000604958),(-838507942379089804976029111)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨326150785487959045378292,326150785487961055201896⟩,⟨2446347591027405591770227,2446347591027407601674205⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨2411487022502160618861968,2411487022502168345595303⟩,⟨7760372637643399336005689,7760372637643407063127775⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨9624270766932852017806307,9624270766932872592993133⟩,⟨13060635212715054803990913,13060635212715075380237958⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨26548832307717613171863455,26548832307717690996611796⟩,⟨12645217633255557629900902,12645217633255635455502595⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨51191316848942212028278773,51191316848942457019179090⟩,⟨(-9981995797792459565072237),(-9981995797792214575824152)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨52845085566728646344596882,52845085566729374177593531⟩,⟨(-75368255620109122027637065),(-75368255620108394198779136)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-41866334110403876871897560),(-41866334110401858327702522)⟩,⟨(-155610707055456450919414612),(-155610707055454432370202400)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-259073697667715403217690118),(-259073697667711027582693641)⟩,⟨(-95905180517024026806102725),(-95905180517019651163579566)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-364196820853824791444219897),(-364196820853818079575267533)⟩,⟨273268078299967682556873276,273268078299974394405592130⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨54618130157452739681270765,54618130157462249153958153⟩,⟨704204686031425542686517032,704204686031435052162348472⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨873302567284610708198583542,873302567284618639782194073⟩,⟨504451997600892250706237462,504451997600900182328772753⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1208262509941376603732926233,1208262509941383064610627881⟩,⟨(-467215578063274517114439445),(-467215578063268056263814901)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨603561385593666235588266637,603561385593669847268855172⟩,⟨(-1327161552113092306897889798),(-1327161552113088695269608736)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-263984407924747783370274729),(-263984407924745496413402103)⟩,⟨(-1354886613019212879739365435),(-1354886613019210592777323905)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-585282667670633281089721420),(-585282667670632304119772771)⟩,⟨(-812630839278863356430545290),(-812630839278862379429742741)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-274844616741340980475227462),(-274844616741340731228192023)⟩,⟨(-243472664882514750808661397),(-243472664882514501545694352)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-6523237144150178056824),(-6523237144150177773450)⟩,⟨1393338135885937990664,1393338135885938273465⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-20732126503632254101614),(-20732126503632253124291)⟩,⟨7377157050058042174544,7377157050058043150322⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-36459053949229981311984),(-36459053949229979091915)⟩,⟨25006212488072913479857,25006212488072915698300⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-45276821001683127477470),(-45276821001683122548336)⟩,⟨67568257116450283547802,67568257116450288478321⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-15364129750378144861268),(-15364129750378133608725)⟩,⟨147407993130604044407030,147407993130604055671608⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨124323578335790691928961,124323578335790718229303⟩,⟨242263940218066363084674,242263940218066389403007⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨453659990559900157447551,453659990559900219245135⟩,⟨216095190756669648495275,216095190756669710283978⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨887703320477297292390815,887703320477297434770393⟩,⟨(-238219820198330539043239),(-238219820198330396733684)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨883531138522914889415151,883531138522915203700406⟩,⟨(-1377172524583217934243961),(-1377172524583217619974825)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-476101836528915773827769),(-476101836528915120374849)⟩,⟨(-2733158208558735724174629),(-2733158208558735070547879)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-3397794336808484980168989),(-3397794336808483638748699)⟩,⟨(-2751378627418591213886862),(-2751378627418589872344794)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-6225743194814573543415174),(-6225743194814570738621738)⟩,⟨(-125181762300335955953594),(-125181762300333151378843)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-6591656384319844157299262),(-6591656384319838551229280)⟩,⟨4056127379027684048481514,4056127379027689654119019⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4266487240271267749345695),(-4266487240271256950150228)⟩,⟨6739516014567749162027991,6739516014567759961062845⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1513416098583385142428434),(-1513416098583372743955098)⟩,⟨5964324495186850339276141,5964324495186862737794524⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-201681682667430750318183),(-201681682667425177180023)⟩,⟨2320860251363540167085456,2320860251363545740271132⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-13594774578606676571),(-13594774578606632298)⟩,⟨17656290230191596874,17656290230191641149⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-38747333507344272487),(-38747333507344164386)⟩,⟨61835323166402694069,61835323166402802175⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-52206515175563924405),(-52206515175563809316)⟩,⟨134490596692552172493,134490596692552287602⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-24178736010112498372),(-24178736010112395529)⟩,⟨257264903617816992688,257264903617817095561⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨117493657184956251348,117493657184956324250⟩,⟨437741417183793173652,437741417183793246581⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨505034736854229781894,505034736854229825498⟩,⟨614192858935547810185,614192858935547853764⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1288482024382885206205,1288482024382885248441⟩,⟨543905190070498564071,543905190070498606143⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2427448252594334696329,2427448252594334775214⟩,⟨(-302028718741587380015),(-302028718741587301371)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3289940891968329906129,3289940891968330073886⟩,⟨(-2589582068091586542969),(-2589582068091586375220)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2432818831334634025369,2432818831334634366659⟩,⟨(-6415553131762476592586),(-6415553131762476250654)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1630617267698267926037),(-1630617267698267289443)⟩,⟨(-10364330594676239272279),(-10364330594676238634676)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-8573609631492612793501),(-8573609631492611743779)⟩,⟨(-11743853719638515983544),(-11743853719638514933499)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-15226194439780507636796),(-15226194439780506171768)⟩,⟨(-8916363739658106212639),(-8916363739658104748439)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-17481839425364901397185),(-17481839425364899754222)⟩,⟨(-3586180590021648972097),(-3586180590021647330845)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-13592601467426997230041),(-13592601467426995892722)⟩,⟨352750581157417555761,352750581157418891583⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-5064643522678351150487),(-5064643522678350632033)⟩,⟨730318376300405946568,730318376300406464530⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨63520817817544697,63520817817546238⟩,⟨142967857034175158,142967857034176699⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨245257928443272335,245257928443278842⟩,⟨435998814178005264,435998814178011776⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨609469580968395457,609469580968415861⟩,⟨724716218577973440,724716218577993841⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1326840964713377689,1326840964713441518⟩,⟨903629131045299436,903629131045363261⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2576161060013934976,2576161060014124982⟩,⟨655553480711489329,655553480711679336⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨4354727474937892417,4354727474938372455⟩,⟨(-694569627695372893),(-694569627694892856)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨6023202796812312105,6023202796813450256⟩,⟨(-4189565357901719616),(-4189565357900581466)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨5669841027948198282,5669841027950916784⟩,⟨(-10724451162297853772),(-10724451162295135268)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-40507101706037347),(-40507101701606322)⟩,⟨(-19652020938331825008),(-19652020938327393988)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-14296803426651457833),(-14296803426646677400)⟩,⟨(-27107254750859527031),(-27107254750854746601)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-36516833483740968790),(-36516833483737062669)⟩,⟨(-26383380386686597023),(-26383380386682690903)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-59496442607462813900),(-59496442607459351714)⟩,⟨(-12647434502717578930),(-12647434502714116747)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-72029110962778070955),(-72029110962775753942)⟩,⟨10403230762419130601,10403230762421447612⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-66807730196846359680),(-66807730196845101666)⟩,⟨29668069708819800732,29668069708821058750⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-45642405331839938193),(-45642405331839365134)⟩,⟨31559979440024925105,31559979440025498170⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-15947261062079789184),(-15947261062079628344)⟩,⟨13423170309091339067,13423170309091499909⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨867351979237167,867351979237183⟩,⟨(-211868992131620),(-211868992131604)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2669262931400076,2669262931400092⟩,⟨(-967326169382873),(-967326169382856)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨4553458526890556,4553458526890572⟩,⟨(-2831525788639936),(-2831525788639919)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨6101716757430876,6101716757430892⟩,⟨(-6855898696407269),(-6855898696407253)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5909904856176027,5909904856176043⟩,⟨(-14244095354126442),(-14244095354126426)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨827283461602027,827283461602043⟩,⟨(-25579506216825117),(-25579506216825101)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-14406042174807396),(-14406042174807380)⟩,⟨(-39019757417650241),(-39019757417650225)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-45648272589080838),(-45648272589080820)⟩,⟨(-47653442221703988),(-47653442221703972)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-94545887791540876),(-94545887791540860)⟩,⟨(-38043185417067575),(-38043185417067558)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-151737588844091919),(-151737588844091893)⟩,⟨5789168465836087,5789168465836113⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-194677327337691072),(-194677327337690995)⟩,⟨90207827394097394,90207827394097468⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-198213086306715488),(-198213086306715197)⟩,⟨197542847771283882,197542847771284174⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-155125137832906805),(-155125137832906011)⟩,⟨284585964997533114,284585964997533908⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-87362958591128656),(-87362958591126941)⟩,⟨303522128478097876,303522128478099593⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-31034135897546254),(-31034135897544044)⟩,⟨231967999268816189,231967999268818400⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-5092736186740429),(-5092736186739362)⟩,⟨86585921981680805,86585921981681874⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨536982678290375634913654561,536982678290383676949950677⟩,⟨(-5777129141845556854073140248),(-5777129141845548812046409006)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 27) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_27 (tableDensity false) (fullFactor true 0 27) density0_contains hk0_1_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨1810108806980452802591225322,1810108806980452821136067547⟩,⟨143137697844743656048492028,143137697844743674366218462⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_27 0 27 ha0_1_27_contains + def realAnswer : RBox := ⟨2347091485270828437404879883,2347091485270836498186018224⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_27 +namespace hm0_1_1_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-55087545718316140680070068),(-55087545718316011809779632)⟩,⟨(-49095652037921657822469241),(-49095652037921528956840558)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-207220261892319830176687064),(-207220261892319448648159352)⟩,⟨(-113624373786536978718304723),(-113624373786536597200697772)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-442511239248864482131536367),(-442511239248863971745092274)⟩,⟨(-24558700980566953278532651),(-24558700980566442895518058)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-593903699044737004724664211),(-593903699044736648138399277)⟩,⟨407794379132181980546661227,407794379132182337166528067⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-116603098427558910502460261),(-116603098427558696830544744)⟩,⟨1079710929959794953421073874,1079710929959795167111178621⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1263930980860259015933484783,1263930980860259105709026838⟩,⟨908669644515144996943321217,908669644515145086640071134⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1796987980654923292234740858,1796987980654923334360319999⟩,⟨(-1210270242928426474528942577),(-1210270242928426432325508872)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-976263871033660011931898310),(-976263871033659988118159846)⟩,⟨(-2785534227912581410537269245),(-2785534227912581386726763630)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3853046304651015976694300992),(-3853046304651015960602463943)⟩,⟨416272411113548875779779181,416272411113548891750590234⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-753432289887146060427391659),(-753432289887146049525204808)⟩,⟨4704561275861226875357310294,4704561275861226886498971302⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨4661076755212792311014537504,4661076755212792318647378326⟩,⟨2612666418336294814433341548,2612666418336294821819065778⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨4485449358223562431686227036,4485449358223562436969795783⟩,⟨(-2962143888851014317696134565),(-2962143888851014312422267287)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨241313347092657233932214433,241313347092657237081369387⟩,⟨(-4796167659464599893617690638),(-4796167659464599890173341966)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-2396889557086772920061959709),(-2396889557086772917697587253)⟩,⟨(-2873349005101072664945789561),(-2873349005101072662584846047)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-2215235423814146770354972723),(-2215235423814146769090827852)⟩,⟨(-822165964786399190476645745),(-822165964786399189340322016)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-803486764810851617533976920),(-803486764810851617170562356)⟩,⟨(-70876895516547328281338215),(-70876895516547327980469746)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-136704875345120583399570),(-136704875345119182993200)⟩,⟨359802128049309331427911,359802128049310731825200⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-226385534666085852395001),(-226385534666080350158609)⟩,⟨1229322959140121332636069,1229322959140126834825406⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨431180232992767352056949,431180232992782501512622⟩,⟨2397239671229976203228372,2397239671229991352548426⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2804822510792648659094256,2804822510792709303334355⟩,⟨3252904974354182014218960,3252904974354242658337503⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨7363671681604163108954650,7363671681604358505760002⟩,⟨1228035232271583381299498,1228035232271778778285688⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨10327238532769484702333559,10327238532770073194424874⟩,⟨(-8090034381330663612599097),(-8090034381330075119966439)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-617475642798712528917998),(-617475642797066521565961)⟩,⟨(-23227463263925009210476023),(-23227463263923363203695077)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-34896816861461523592306136),(-34896816861457942813186103)⟩,⟨(-20984505130817046973932054),(-20984505130813466195839470)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-60687650583284596502758978),(-60687650583279105290532217)⟩,⟨33001056722741630038529424,33001056722747121253322547⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-3854680248992544402436220),(-3854680248984768050720488)⟩,⟨111028006365915340386849215,111028006365923116738217555⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨135488612697262857911010897,135488612697269301899557906⟩,⟨95311328998447107390181005,95311328998453551373289759⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨213639245570173426210593660,213639245570178640413030411⟩,⟨(-63259457061891846295101708),(-63259457061886632088490868)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨128296574882619306551252100,128296574882622171272814097⟩,⟨(-227372044227891839958257648),(-227372044227888975228859469)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-23527676151883820266452385),(-23527676151882028104142811)⟩,⟨(-253280306777634912822345200),(-253280306777633120661257791)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-91959841265336740719665612),(-91959841265335995209677741)⟩,⟨(-163603315708712731148963592),(-163603315708711985644194131)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-46060313567215399780358979),(-46060313567215214716895689)⟩,⟨(-51809834115953673815040269),(-51809834115953488754191235)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1419161702047141615863),(-1419161702047141528743)⟩,⟨(-503905897860896333668),(-503905897860896246573)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4861005808544576058390),(-4861005808544575754958)⟩,⟨(-1057980286092235944709),(-1057980286092235641348)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-9964970381391822142003),(-9964970381391821469642)⟩,⟨335304683999633586003,335304683999634258284⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-16670756636845830589640),(-16670756636845829176201)⟩,⟨6956548554413127917622,6956548554413129331110⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-20559903718217024902084),(-20559903718217021925601)⟩,⟨24214052320887829284618,24214052320887832261582⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-6898597363977980047710),(-6898597363977973767571)⟩,⟨54938383859668484949082,54938383859668491229951⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨50668751401116242681693,50668751401116255858398⟩,⟨82335702907348627914252,82335702907348641090699⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨163389066317170713861782,163389066317170741039205⟩,⟨45235986325887941194168,45235986325887968368968⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨257196771591855932355346,257196771591855987603265⟩,⟨(-145126498642860066232541),(-145126498642860010985442)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨137400370414000852938992,137400370414000967097673⟩,⟨(-478254720884669988241915),(-478254720884669874080032)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-343167821030383775104610),(-343167821030383460872733)⟩,⟨(-701809728917116915529662),(-701809728917116601296506)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-987372599164815265556109),(-987372599164814241618694)⟩,⟨(-478414183089302565720338),(-478414183089301541784312)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1316308955944982644053890),(-1316308955944979790701312)⟩,⟨164188717597610978518886,164188717597613831870299⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1099036250486009941182372),(-1099036250486002993358550)⟩,⟨735695103089119569206856,735695103089126517032316⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-600381891790720932753916),(-600381891790712285914085)⟩,⟨791019563059596288355747,791019563059604935197483⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-169837579155498553100430),(-169837579155494564619063)⟩,⟨329439096068345783108227,329439096068349771590017⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-7170981881349578428),(-7170981881349541325)⟩,⟨2014870657440196751,2014870657440233859⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-22417865916444304200),(-22417865916444213766)⟩,⟨8631060299278045234,8631060299278135671⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-39213050838272269416),(-39213050838272173659)⟩,⟨24300263410046635464,24300263410046731219⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-53394464537925287683),(-53394464537925203247)⟩,⟨58966270394749662858,58966270394749747290⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-48308536929809116073),(-48308536929809058750)⟩,⟨125389202178650574445,125389202178650631766⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨17009901105229317082,17009901105229345603⟩,⟨228502995239547490190,228502995239547518713⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨213183540421565594079,213183540421565611983⟩,⟨333241402394565913562,333241402394565931483⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨606573868825338086458,606573868825338114171⟩,⟨311290142938998224142,311290142938998251879⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1146342866494357211266,1146342866494357269051⟩,⟨(-80195417727520265747),(-80195417727520207960)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1515522125617930916761,1515522125617931034509⟩,⟨(-1069000709524627248245),(-1069000709524627130560)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1170588562524483768194,1170588562524483988979⟩,⟨(-2548423345177290719611),(-2548423345177290498918)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-208294311710108667100),(-208294311710108299624)⟩,⟨(-3866949763846340609680),(-3866949763846340242216)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-2147677997202533919145),(-2147677997202533399169)⟩,⟨(-4198655393724092469095),(-4198655393724091949026)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-3465209693793089624968),(-3465209693793089032720)⟩,⟨(-3328395099308845575829),(-3328395099308844983415)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-3172727105695961986571),(-3172727105695961497988)⟩,⟨(-1879072147719749506431),(-1879072147719749017710)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1274367750581876073584),(-1274367750581875882672)⟩,⟨(-564276899454746023675),(-564276899454745832724)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨23248129692465364,23248129692466636⟩,⟨45846219289157021,45846219289158292⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨88380188624191765,88380188624197118⟩,⟨142653424961780350,142653424961785704⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨216331067519806268,216331067519823039⟩,⟨247144188148132897,247144188148149669⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨469300294207226479,469300294207278956⟩,⟨331963908931747817,331963908931800292⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨923145528856380070,923145528856536303⟩,⟨296769831918748105,296769831918904335⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1616451344347866174,1616451344348260876⟩,⟨(-95040308560901709),(-95040308560507007)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2404985696205690228,2404985696206625833⟩,⟨(-1255428064501901732),(-1255428064500966127)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨2717520275887196190,2717520275889429785⟩,⟨(-3661717360311718575),(-3661717360309484982)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1395403556415156570,1395403556418794288⟩,⟨(-7438224319503022950),(-7438224319499385233)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-2943168370043318741),(-2943168370039398372)⟩,⟨(-11704074348744784461),(-11704074348740864091)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-10695967281445221884),(-10695967281442022841)⟩,⟨(-14343313844042538642),(-14343313844039339599)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-19901440839217965042),(-19901440839215133525)⟩,⟨(-13103221779027884431),(-13103221779025052912)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-26438486126171461720),(-26438486126169569421)⟩,⟨(-7765657554191117258),(-7765657554189224959)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-26523037184715123580),(-26523037184714097569)⟩,⟨(-1229052223123542066),(-1229052223122516053)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-19321786258188210151),(-19321786258187743355)⟩,⟨2423193995815347117,2423193995815813912⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-7014964315705267272),(-7014964315705136365)⟩,⟨1528326678156262066,1528326678156392972⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨25458824672893,25458824672909⟩,⟨(-7527180882640),(-7527180882624)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨68252455222509,68252455222525⟩,⟨(-46873266852854),(-46873266852838)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨35915323021313,35915323021329⟩,⟨(-159366021158169),(-159366021158153)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-318520413480379),(-318520413480363)⟩,⟨(-381381413312916),(-381381413312900)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1601095899371110),(-1601095899371094)⟩,⟨(-662134694745333),(-662134694745317)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-4922399519145718),(-4922399519145701)⟩,⟨(-602663268307762),(-602663268307746)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-11781020510836548),(-11781020510836532)⟩,⟨1152485488832338,1152485488832355⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-23297146883285977),(-23297146883285961)⟩,⟨7706481107163921,7706481107163937⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-38434986229286520),(-38434986229286502)⟩,⟨23938651560705542,23938651560705558⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-51837389585640428),(-51837389585640404)⟩,⟨54241895390104388,54241895390104411⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-53910440583152466),(-53910440583152401)⟩,⟨97515617100226352,97515617100226416⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-36351541607637092),(-36351541607636853)⟩,⟨142646909386078303,142646909386078540⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1822078284567312),(-1822078284566662)⟩,⟨170494413711854877,170494413711855527⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨31603697544526815,31603697544528220⟩,⟨163875828125525753,163875828125527160⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨40972866050189266,40972866050191077⟩,⟨118049827996843459,118049827996845269⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨18533484463788316,18533484463789194⟩,⟨42868693061007863,42868693061008744⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨44581411765760006841852876,44581411765766410910826230⟩,⟨(-1023586353669083923203795223),(-1023586353669077519136457467)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 27) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_27 (tableDensity true) (fullFactor true 0 27) density1_contains hk0_1_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-2367065362974438304562549869),(-2367065362974438280311602344)⟩,⟨(-187180066412357112632747220),(-187180066412357088678797267)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_27 0 27 ha0_1_27_contains + def realAnswer : RBox := ⟨(-2322483951208678297820696993),(-2322483951208671869300776114)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_27 +namespace hm0_0_1_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨65921048868377570279389367,65921048868377636071006069⟩,⟨113643748162520389871493024,113643748162520455665831089⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨291631298691114800966289194,291631298691114954365739316⟩,⟨301947390261084487459611939,301947390261084640873574389⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨748062977242226120033936994,748062977242226312348995287⟩,⟨251820837499097771455258945,251820837499097963795233694⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1217246937287626073013803415,1217246937287626260494206131⟩,⟨(-478266437755017346871147651),(-478266437755017159396586761)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨606607398619290198573370137,606607398619290319999380484⟩,⟨(-1963746776049432182574152532),(-1963746776049432061202644963)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-2148389360632707487091373030),(-2148389360632707399746687026)⟩,⟨(-2240932175141385946931880713),(-2240932175141385859540910561)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-4144009976493873135087872076),(-4144009976493873070551331332)⟩,⟨1697056178832027134121972256,1697056178832027198678055504⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨626454270527421602439395233,626454270527421650596455454⟩,⟨6066003500302998151996441698,6066003500302998200079063851⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨7677285100717140478491062016,7677285100717140511755600565⟩,⟨1086209054685656427195738092,1086209054685656460536709336⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨3500694615822194385854636666,3500694615822194406759512264⟩,⟨(-8423223993164273487752900598),(-8423223993164273466875930133)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-7470777132751922674973288713),(-7470777132751922662586240967)⟩,⟨(-6437332541277921035426859245),(-6437332541277921023082327621)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-8869593770602920524861979603),(-8869593770602920517561123206)⟩,⟨4014132222946440011662159532,4014132222946440018999071166⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1517610539062860466396706118),(-1517610539062860462241907634)⟩,⟨8545643685933701995310837780,8545643685933701999533880670⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨3766440429165706668725891546,3766440429165706671370727060⟩,⟨5659288284927616369848430540,5659288284927616372478894237⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨3866524051520546491830139290,3866524051520546493142242282⟩,⟨1907191082733011681778765671,1907191082733011683042913489⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1447237346601369740126873470,1447237346601369740492737807⟩,⟨279240034709977826735874670,279240034709977827079342291⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨392260344186536555779280,392260344186537074049753⟩,⟨(-491199001296407272086070),(-491199001296406753846609)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨994420065013774581748198,994420065013776804503243⟩,⟨(-1823989982061636364888632),(-1823989982061634142201687)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨638858890120200750347173,638858890120207646180182⟩,⟨(-4128268596140985580467054),(-4128268596140978684626634)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-2660035171017318382440933),(-2660035171017299550502015)⟩,⟨(-7173708018263435626518216),(-7173708018263416794204778)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-11677433386334596338821818),(-11677433386334531601943492)⟩,⟨(-7258235343329343923081490),(-7258235343329279185644235)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-23948099487084825026171006),(-23948099487084622002819955)⟩,⟨5799057039209649308862344,5799057039209852331412016⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-18216611381227809360876424),(-18216611381227247455583766)⟩,⟨39904991792400854698173975,39904991792401416602073932⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨40554538383305721817599223,40554538383306853870675934⟩,⟨64904270609980784553548617,64904270609981916610068447⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨128347514731662850740789726,128347514731664995569801387⟩,⟨(-2655734175049158290787732),(-2655734175047013462126504)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨99006427026774234453784991,99006427026776719071720843⟩,⟨(-176687157517290803610403496),(-176687157517288319000091485)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-138855537101771075768562697),(-138855537101768634358256798)⟩,⟨(-258840480646028860478553813),(-258840480646026419058712547)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-377939984204250537411518280),(-377939984204248617608736684)⟩,⟨(-58984102153708163591298985),(-58984102153706243781725112)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-347491294231369210680393193),(-347491294231368090588905471)⟩,⟨262438731694158034800685059,262438731694159154876516045⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-116329309485471939827085153),(-116329309485471291607144559)⟩,⟨399348227285346133164762588,399348227285346781373098726⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨49293187930993208715837519,49293187930993549437582044⟩,⟨299562677069287679166788454,299562677069288019888719377⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨42690335679119612575433714,42690335679119709800704322⟩,⟨103163547213948620567027520,103163547213948717793964380⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨915474289495978228467,915474289495978308756⟩,⟨1049262545754267694392,1049262545754267774699⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨3473535129960317544556,3473535129960317822869⟩,⟨3032052153684835798424,3032052153684836076704⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨8402387480831204109401,8402387480831204748096⟩,⟨4056563616026750370699,4056563616026751008975⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨17317821549956106596301,17317821549956108035191⟩,⟨1005507598537857482012,1005507598537858919286⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨28921228973654055580601,28921228973654058928271⟩,⟨(-13782785434778624952216),(-13782785434778621606688)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨30166324938385880163640,30166324938385888148387⟩,⟨(-51642155092730479864800),(-51642155092730471879314)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-16287069313824475059616),(-16287069313824455886834)⟩,⟨(-111160026615755241071999),(-111160026615755221890145)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-160898866038123422915043),(-160898866038123377662656)⟩,⟨(-134058624130134861954251),(-134058624130134816697410)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-379255396377363280363790),(-379255396377363178304943)⟩,⟨26043933625612137730242,26043933625612239765139⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-440217176558004076848851),(-440217176558003859942792)⟩,⟨487746667206228705504755,487746667206228922389907⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨8087892432146628112666,8087892432147062160688⟩,⟨1054320056777032111559604,1054320056777032545653389⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨972220060949124802842929,972220060949125677646462⟩,⟨1176789906953322073064295,1176789906953322947940468⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1843966467716059039552999,1843966467716060848515785⟩,⟨548838556878739976528302,548838556878741785478605⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1971976462733821480879885,1971976462733824233973162⟩,⟨(-360661897673376797212380),(-360661897673374044208829)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1361868412882771248134851,1361868412882773991542994⟩,⟨(-757281085973883081624513),(-757281085973880338306035)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨462429352626635897203323,462429352626637230197601⟩,⟨(-369992671126406408009518),(-369992671126405075042973)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3653068068686298642,3653068068686304893⟩,⟨1285707878990980567,1285707878990986821⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨12362620876506652570,12362620876506669902⟩,⟨3009295696791563398,3009295696791580727⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨25294412145877864618,25294412145877887998⟩,⟨1085437871060084378,1085437871060107752⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨44430394402316887828,44430394402316909158⟩,⟨(-11016977562763969410),(-11016977562763948082)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨66560911318886352806,66560911318886366685⟩,⟨(-46627993531421973276),(-46627993531421959395)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨71784485313925121148,71784485313925129378⟩,⟨(-125570061847300786961),(-125570061847300778714)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨5120555737656376898,5120555737656386487⟩,⟨(-258485126810198752858),(-258485126810198743240)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-229047767003668224827),(-229047767003668205491)⟩,⟨(-399025348158378917507),(-399025348158378898159)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-708018832419835811072),(-708018832419835768780)⟩,⟨(-376062752913941128873),(-376062752913941086648)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1333886933781887610333),(-1333886933781887521914)⟩,⟨95747741551015580334,95747741551015668615⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1707240275975868754405),(-1707240275975868585588)⟩,⟨1187753112035608803799,1187753112035608972568⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1331267295038324378309),(-1331267295038324094587)⟩,⟨2606655335537521446905,2606655335537521730805⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-171802416925914262042),(-171802416925913859375)⟩,⟨3594842368986381757292,3594842368986382160353⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1054671768968100183055,1054671768968100641164⟩,⟨3523690791807590759527,3523690791807591217921⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1419344984343564742574,1419344984343565119135⟩,⟨2440002101380557669040,2440002101380558045719⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨643655602022129561693,643655602022129708386⟩,⟨850040837911960958658,850040837911961105379⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨19267159159338853,19267159159339114⟩,⟨(-12885457407592256),(-12885457407592002)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨57496498730918075,57496498730919103⟩,⟨(-47100470322707024),(-47100470322705996)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨90333955978378582,90333955978381711⟩,⟨(-108879975511927515),(-108879975511924384)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨96709769714382792,96709769714392266⟩,⟨(-221613084432324584),(-221613084432315114)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨21532123803222002,21532123803248903⟩,⟨(-404017634537847125),(-404017634537820223)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-242844018722522810),(-242844018722455575)⟩,⟨(-634685840013218472),(-634685840013151239)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-844363615456991361),(-844363615456789713)⟩,⟨(-775663076454902348),(-775663076454700699)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1863405675582020105),(-1863405675581571115)⟩,⟨(-480860019600657011),(-480860019600208024)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-3067935765072662069),(-3067935765071987762)⟩,⟨783673006782696376,783673006783370681⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-3677651403286900725),(-3677651403286210687)⟩,⟨3409394008459453758,3409394008460143798⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-2564508167067219780),(-2564508167066466322)⟩,⟨7028403610088442229,7028403610089195685⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨805208472342643184,805208472343265100⟩,⟨10206649476364568138,10206649476365190054⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨5303975437199843250,5303975437200227798⟩,⟨11200038543356036628,11200038543356421171⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨8332310787959309375,8332310787959503766⟩,⟨9400825993523993707,9400825993524188094⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨7624384897831116800,7624384897831200098⟩,⟨5828165472565905785,5828165472565989084⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨3073881570480079828,3073881570480102355⟩,⟨1905646270004680031,1905646270004702557⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-33218817844270),(-33218817844254)⟩,⟨(-110486693699580),(-110486693699564)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-143983912724697),(-143983912724681)⟩,⟨(-338390012329037),(-338390012329021)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-402710805617250),(-402710805617234)⟩,⟨(-569919216833407),(-569919216833391)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-948505451488941),(-948505451488925)⟩,⟨(-739647766557260),(-739647766557244)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1935391293575539),(-1935391293575521)⟩,⟨(-642432505147094),(-642432505147078)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-3416193182978533),(-3416193182978517)⟩,⟨170063562239669,170063562239686⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-5075081110509546),(-5075081110509529)⟩,⟨2427636163162059,2427636163162075⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-5846304577053876),(-5846304577053860)⟩,⟨6896448514989153,6896448514989169⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3736869209949537),(-3736869209949520)⟩,⟨13647708827346268,13647708827346284⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨3507732566828795,3507732566828813⟩,⟨21074990958104556,21074990958104574⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨16541450483851160,16541450483851183⟩,⟨25712678197897677,25712678197897701⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨32370688742048630,32370688742048681⟩,⟨24070773368596027,24070773368596078⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨44442007253813945,44442007253814079⟩,⟨15862124350792943,15862124350793078⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨46028069680932209,46028069680932507⟩,⟨5421465271915241,5421465271915535⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨34508510865792703,34508510865793069⟩,⟨(-1198130906559160),(-1198130906558791)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12753159654446830,12753159654447011⟩,⟨(-1426038730401600),(-1426038730401418)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-167627516669486393708221794),(-167627516669484027001161940)⟩,⟨1839545027108398763724106882,1839545027108401130428447058⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 28) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_28 (tableDensity false) (fullFactor true 0 28) density0_contains hk0_1_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-581619506584913201494577423),(-581619506584913193995956545)⟩,⟨(-27716676122846519756772335),(-27716676122846512335186830)⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_28 0 28 ha0_1_28_contains + def realAnswer : RBox := ⟨(-749247023254399595302799217),(-749247023254397220897118485)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_28 +namespace hm0_1_1_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨8610917852995636596518960,8610917852995686519854041⟩,⟨20753151397876709385234337,20753151397876759307802229⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨42369203949839976570927087,42369203949840090075961332⟩,⟨58383994725283081696226418,58383994725283195197493854⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨120498858902603398713408893,120498858902603535465789122⟩,⟨62888524342872283435671917,62888524342872420181991680⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨218003374011816789007235428,218003374011816913287452777⟩,⟨(-44047676287005174240762445),(-44047676287005049957362012)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨156057026324489874805341523,156057026324489937865053796⟩,⟨(-299733390741260950017775053),(-299733390741260886942982010)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-280144484407257346782450414),(-280144484407257315014647468)⟩,⟨(-400303682158287724932426498),(-400303682158287693185146994)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-656255365942690283012085040),(-656255365942690267820160841)⟩,⟨200071562236605088086714176,200071562236605103284005751⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨78458439090288181893161004,78458439090288190725631655⟩,⟨939492633665232987168099742,939492633665232996023744234⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1241100651849718476291515883,1241100651849718482289623820⟩,⟨126916879400862431671388184,126916879400862437614683544⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨492431100071076260592906871,492431100071076264564204943⟩,⟨(-1463464265592684829416241243),(-1463464265592684825366150958)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1401478636714327362798474769),(-1401478636714327360099479356)⟩,⟨(-1032933639199343657498229956),(-1032933639199343654864545237)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1545643184613518330717543551),(-1545643184613518328906613292)⟩,⟨838451340329389808447536805,838451340329389810238663975⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-164530299119053016312230548),(-164530299119053015244586053)⟩,⟨1566692282782583323605988416,1566692282782583324770951005⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨760063040839031010070309784,760063040839031010857427589⟩,⟨966586044864934263245318568,966586044864934264035343340⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨725612232357748570951909899,725612232357748571373435060⟩,⟨278645633495182363290208002,278645633495182363670533964⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨264374924956456467951787068,264374924956456468072510580⟩,⟨23925833634165925140474374,23925833634165925240652047⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨90246378761433467475788,90246378761433802543223⟩,⟨(-38292250897398986246827),(-38292250897398651175205)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨265832384207737921886307,265832384207739440919987⟩,⟨(-177316918725200148969982),(-177316918725198629926643)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨359588626179895820171112,359588626179900844594704⟩,⟨(-513797128116410461585477),(-513797128116405437160004)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨66584591715237090788579,66584591715251314951429⟩,⟨(-1115413249005252126596037),(-1115413249005237902478065)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1201648286866808765283195),(-1201648286866757882194157)⟩,⟨(-1558246388929328061481711),(-1558246388929277178467710)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-3505492864316142003697873),(-3505492864315979152976299)⟩,⟨(-200360914312817486994964),(-200360914312654636183268)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3899340981015566862517837),(-3899340981015111142113289)⟩,⟨4979326273951992772302719,4979326273952448492896281⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨4097695376654375488967033,4097695376655296628990759⟩,⟨10509391078032687462799927,10509391078033608602398757⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨19324213876954043684157739,19324213876955793732155938⟩,⟨2424403470085093321304089,2424403470086843369315777⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨18579076366545361834075439,18579076366547381466635409⟩,⟨(-25876343350562292795412358),(-25876343350560273161828423)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-18935003199738468527590316),(-18935003199736495145754806)⟩,⟨(-44376684710325971353567221),(-44376684710323997973065901)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-63972329807173959243189047),(-63972329807172422497547541)⟩,⟨(-15370655116986017802526277),(-15370655116984481057828511)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-66068641369528471429610475),(-66068641369527593552138857)⟩,⟨41422189945786992215952458,41422189945787870095872239⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-28661582805098830079701020),(-28661582805098333190302031)⟩,⟨71092251530370013762675097,71092251530370510653828864⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2900356667538171091302403,2900356667538427740706418⟩,⟨56820765096419019083920036,56820765096419275733196826⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5688042348699245147248268,5688042348699317007874876⟩,⟨20297488781390304405658167,20297488781390376265969789⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨51882328059603259186,51882328059603283892⟩,⟨310072553193498133164,310072553193498157871⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨305036174856842430037,305036174856842516465⟩,⟨996722264196232058458,996722264196232144881⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1106051598019848872907,1106051598019849066186⟩,⟨1790119290237155208903,1790119290237155402166⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨3082908718063937820312,3082908718063938232137⟩,⟨2310482114045799539765,2310482114045799951515⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨6783511803386591902033,6783511803386592786305⟩,⟨1063173815559842980140,1063173815559843864322⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨10986176996865527693074,10986176996865529597791⟩,⟨(-5212355755835393099842),(-5212355755835391195110)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨8992538116716241678517,8992538116716245760696⟩,⟨(-19651844372363693422167),(-19651844372363689339627)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-13022229339565584532876),(-13022229339565575901270)⟩,⟨(-36363114616312262654548),(-36363114616312254022726)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-62696357052423037335894),(-62696357052423019571469)⟩,⟨(-27851510850075156135432),(-27851510850075138371676)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-109239024896556150298997),(-109239024896556112880405)⟩,⟨44187871063615418965473,44187871063615456383570⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-78135783214518430638263),(-78135783214518341701766)⟩,⟨171421456647098603815744,171421456647098692752736⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨68975089657511087551378,68975089657511363770978⟩,⟨259950000714288501163108,259950000714288777383129⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨248571511707756969735431,248571511707757841277434⟩,⟨216638697499162407594329,216638697499163279135913⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨323188220652150359194778,323188220652151942751624⟩,⟨77605876774202146295461,77605876774203729852054⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨250043582271332223933676,250043582271333934583902⟩,⟨(-26791760789449432400868),(-26791760789447721750376)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨90409851910733498442850,90409851910734384431608⟩,⟨(-26535804441261014783959),(-26535804441260128794978)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨721999413640149088,721999413640154321⟩,⟨1074471143779267025,1074471143779272258⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨2661265781615330865,2661265781615345343⟩,⟨3234365322933279864,3234365322933294344⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨6250615068465930893,6250615068465950326⟩,⟨5144699986842276423,5144699986842295857⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨12984123734670829505,12984123734670846983⟩,⟨5475987468644036588,5475987468644054070⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨24088418318795830858,24088418318795841631⟩,⟨455504364248328944,455504364248339717⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨37750455975297080942,37750455975297085985⟩,⟨(-17661084957873720471),(-17661084957873715426)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨42611277477729196678,42611277477729200554⟩,⟨(-59428245269843329192),(-59428245269843325318)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨9845718917647619702,9845718917647626489⟩,⟨(-127853366066874223525),(-127853366066874216737)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-102682905197481435729),(-102682905197481421205)⟩,⟨(-194602792850677322666),(-194602792850677308135)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-313257912951858241452),(-313257912951858211033)⟩,⟨(-180350419867273674896),(-180350419867273644457)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-555773555336176875476),(-555773555336176816999)⟩,⟨11785754761941562502,11785754761941620982⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-675773538146137800226),(-675773538146137700904)⟩,⟨388561701366718641177,388561701366718740479⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-555740596693673255933),(-555740596693673112905)⟩,⟨785134570944577311554,785134570944577454543⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-266146609388066717779),(-266146609388066552473)⟩,⟨953861978470673416040,953861978470673581319⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-25866155240497428664),(-25866155240497290960)⟩,⟨765078822351050555042,765078822351050692737⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨25535416918608038818,25535416918608092878⟩,⟨289282732601482170913,289282732601482224971⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨6105777684661840,6105777684662052⟩,⟨(-4552303531560913),(-4552303531560702)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨18603195112665251,18603195112666098⟩,⟨(-16601426599716967),(-16601426599716118)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨30581150100737298,30581150100739873⟩,⟨(-38379795002794749),(-38379795002792171)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨36037364232766925,36037364232774716⟩,⟨(-78732165854513609),(-78732165854505819)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨16956036656492602,16956036656514723⟩,⟨(-146615506022635114),(-146615506022612990)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-65589153619456058),(-65589153619400774)⟩,⟨(-240764867916948683),(-240764867916893398)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-273491385224204855),(-273491385224039089)⟩,⟨(-323966926938142847),(-323966926937977082)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-664995915462649930),(-664995915462281031)⟩,⟨(-284833112639913779),(-284833112639544878)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1217108839280387891),(-1217108839279834305)⟩,⟨76241482504127405,76241482504680993⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1725111756964503940),(-1725111756963938062)⟩,⟨961621189068246154,961621189068812030⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1808618538853184927),(-1808618538852567860)⟩,⟨2357856006287971894,2357856006288588961⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1162946823839747500),(-1162946823839238877)⟩,⟨3838600800095526207,3838600800096034829⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨61347870461743152,61347870462057190⟩,⟨4691771479078801699,4691771479079115734⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1177179550608034634,1177179550608193137⟩,⟨4408318796842917778,4408318796843076281⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1428073709280434578,1428073709280502394⟩,⟨3049944595665176779,3049944595665244592⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨630470362047235343,630470362047253662⟩,⟨1074359081501654692,1074359081501673010⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1143897377640),(-1143897377624)⟩,⟨(-3234138188531),(-3234138188515)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-6545187220162),(-6545187220146)⟩,⟨(-8494632163789),(-8494632163773)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-20977444244554),(-20977444244538)⟩,⟨(-3436612370272),(-3436612370256)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-47150571314126),(-47150571314110)⟩,⟨44945192474428,44945192474444⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-71871854994773),(-71871854994757)⟩,⟨217671909601459,217671909601475⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-26205389842468),(-26205389842452)⟩,⟨662621449468127,662621449468143⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨302687185430529,302687185430546⟩,⟨1572982881599375,1572982881599391⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1381179653356156,1381179653356172⟩,⟨3066711108382634,3066711108382650⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨3916555047893383,3916555047893399⟩,⟨4920596331790333,4920596331790349⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨8494157738181607,8494157738181626⟩,⟨6272155524919082,6272155524919099⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨14820069340818062,14820069340818083⟩,⟨5703366453984405,5703366453984431⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨21110987564690303,21110987564690349⟩,⟨2158403093754251,2158403093754296⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨24561508850481574,24561508850481684⟩,⟨(-3599968570297372),(-3599968570297259)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨22975538950233213,22975538950233458⟩,⟨(-8478541733512378),(-8478541733512136)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨16163638782975435,16163638782975736⟩,⟨(-8867584141938286),(-8867584141937986)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨5786747751226666,5786747751226818⟩,⟨(-3776176606942547),(-3776176606942395)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-12432922750830269995731511),(-12432922750828409918466049)⟩,⟨326880074940886793319874548,326880074940888653396357221⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 28) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_28 (tableDensity true) (fullFactor true 0 28) density1_contains hk0_1_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨760579354764886484456250867,760579354764886494262139706⟩,⟨36244884160645439207552009,36244884160645448912702284⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_28 0 28 ha0_1_28_contains + def realAnswer : RBox := ⟨748146432014056214360519356,748146432014058084443673657⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_28 +namespace hm0_0_1_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2936085595772021845024328),(-2936085595772000683312705)⟩,⟨(-38512753087764233163719077),(-38512753087764212002290208)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-39685884131229925372942513),(-39685884131229870758174181)⟩,⟨(-117178049721235316692892372),(-117178049721235262077231405)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-170965258979597828371852859),(-170965258979597769134600520)⟩,⟨(-159350974169774946719906914),(-159350974169774887474880574)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-389650251766172421143236996),(-389650251766172363001011955)⟩,⟨(-10856655307945055608480900),(-10856655307944997459547571)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-384363914544710295801888154),(-384363914544710253412901412)⟩,⟨483265066809714472621241764,483265066809714514995153287⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨390160091480807518755860197,390160091480807550648134775⟩,⟨856144640779447240973526382,856144640779447272865966773⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1363541526086208708483482783,1363541526086208732470782156⟩,⟨(-125701538062315505347166961),(-125701538062315481341182453)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨282854476858129218926499040,282854476858129236964556380⟩,⟨(-1859382915796720222766166009),(-1859382915796720204753609474)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-2263600632325840153324845279),(-2263600632325840141074124012)⟩,⟨(-826897161616122856181805630),(-826897161616122843911695105)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1515498051170829145662183985),(-1515498051170829138157757302)⟩,⟨2418250240717780188550917273,2418250240717780196052778996⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨2080585528183145630569960317,2080585528183145634900420820⟩,⟨2300612212620335966519649092,2300612212620335970834038448⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨2900289301614790324610693873,2900289301614790327073075108⟩,⟨(-1020589769910109802006063143),(-1020589769910109799534691946)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨626958252443259284487521260,626958252443259285867803200⟩,⟨(-2676335854957977520830999628),(-2676335854957977519428054326)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1142681360150150023284759784),(-1142681360150150022422445741)⟩,⟨(-1829330205038805357977078276),(-1829330205038805357118151216)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1221138471845172689132793951),(-1221138471845172688706455569)⟩,⟨(-619532768527881282779133709),(-619532768527881282367813239)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-459661489526847619038816160),(-459661489526847618920554429)⟩,⟨(-89772874056020626449237754),(-89772874056020626338097233)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-153953864083671790099401),(-153953864083671640133663)⟩,⟨13972804352486592557860,13972804352486742519203⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-494022471230971404846724),(-494022471230970833213698)⟩,⟨137382169180737932684692,137382169180738504294602⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-839965313571174584265192),(-839965313571173093697004)⟩,⟨610748227803826190084337,610748227803827680585170⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-776806528841332992895191),(-776806528841327527863280)⟩,⟨1757988396663768033598393,1757988396663773498579873⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨920059768896680275978632,920059768896696920654679⟩,⟨3376431198545231326330360,3376431198545247971140640⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨5636538858452175530327503,5636538858452229475142888⟩,⟨2963558065780949879051666,2963558065781003824091395⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨10373107028633772667882049,10373107028633911951538745⟩,⟨(-5031041401550395903313439),(-5031041401550256620165933)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨2026883894393880851623955,2026883894394224138314218⟩,⟨(-20369172892835276385561201),(-20369172892834933098969786)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-28796601716875951058989429),(-28796601716875415440125138)⟩,⟨(-19794986260890695166138992),(-19794986260890159545842329)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-49939328913758658693062819),(-49939328913757948633139742)⟩,⟨25492383121392644403544576,25492383121393354461555045⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-5128413328294089547296703),(-5128413328293351536014833)⟩,⟨82434298204616536252498688,82434298204617274263020906⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨84890821061595538046918735,84890821061596038689700022⟩,⟨68444209993957253625599241,68444209993957754272852441⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨124165705335250405577543140,124165705335250776920704448⟩,⟨(-18734616762189179701599626),(-18734616762188808358749988)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨83307967960878528723145473,83307967960878705463405599⟩,⟨(-87771403854823138393525486),(-87771403854822961658236073)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨26088827374419015805003022,26088827374419110928028592⟩,⟨(-84942580716187399055161964),(-84942580716187303934712945)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2002708997829371508376670,2002708997829401649191668⟩,⟨(-32716834620547685428277649),(-32716834620547655287937887)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨95294990025746451084,95294990025746473061⟩,⟨(-263997951161276576156),(-263997951161276554157)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨191100185224161656961,191100185224161733469⟩,⟨(-912966302528735284461),(-912966302528735207872)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-133101481414689272580),(-133101481414689095318)⟩,⟨(-1896549452984977142570),(-1896549452984976965110)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1631775238441437419613),(-1631775238441437014159)⟩,⟨(-3177638054162802293652),(-3177638054162801887989)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-5602437763176536343674),(-5602437763176535382927)⟩,⟨(-3650184205816136994072),(-3650184205816136033406)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-12672974383476401092624),(-12672974383476398752527)⟩,⟨499186224464880924836,499186224464883263871⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-17981247341795213710597),(-17981247341795207959755)⟩,⟨16273292330160157350316,16273292330160163100296⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-3709684834664833918573),(-3709684834664820032191)⟩,⟨45924368758732167671263,45924368758732181560266⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨55430738025563446334341,55430738025563478394693⟩,⟨64800203560587257909885,64800203560587289974015⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨149864757891676238398142,149864757891676307575889⟩,⟨10512960518217513632313,10512960518217582803735⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨188380648524480708326727,188380648524480847841088⟩,⟨(-157410384348385249805301),(-157410384348385110302428)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨60997964177717806049865,60997964177718079368331⟩,⟨(-356088256578518209221020),(-356088256578517935895018)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-196938560496090259748361),(-196938560496089780799677)⟩,⟨(-417641913407877383904484),(-417641913407876904929118)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-388835140479639849429680),(-388835140479639034668631)⟩,⟨(-292304020323855891291948),(-292304020323855076517662)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-363149307675451031524643),(-363149307675450128778269)⟩,⟨(-115254476277375327897694),(-115254476277374425152140)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-144051131789821052513072),(-144051131789820650679192)⟩,⟨(-19492859151303044882713),(-19492859151302643051223)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨13429984774622789,13429984774624115⟩,⟨(-649699087724608721),(-649699087724607396)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-175913549226125949),(-175913549226122413)⟩,⟨(-2134779335459361773),(-2134779335459358236)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1204110940890439092),(-1204110940890434607)⟩,⟨(-4117356911839010290),(-4117356911839005804)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-4289829356778886338),(-4289829356778882535)⟩,⟨(-6549907181591787857),(-6549907181591784052)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-11525326426368365532),(-11525326426368363214)⟩,⟨(-8069530104579569924),(-8069530104579567610)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-25094298309783988066),(-25094298309783986522)⟩,⟨(-3946648817916037420),(-3946648817916035880)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-43188180665824394154),(-43188180665824391934)⟩,⟨16249696789576692650,16249696789576694867⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-50720525562469816390),(-50720525562469811808)⟩,⟨66396941880383550927,66396941880383555513⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-10735450788066965006),(-10735450788066954718)⟩,⟨147825329485719679351,147825329485719689656⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨121938107327931954021,121938107327931976116⟩,⟨220149528152774578727,220149528152774600835⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨347179748592404537139,347179748592404580324⟩,⟨194704594257926120310,194704594257926163471⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨568855851064013811424,568855851064013885555⟩,⟨2359856433596288798,2359856433596362865⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨642960661044731991003,642960661044732098141⟩,⟨(-298208757755333076498),(-298208757755332969402)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨518291456609076538039,518291456609076661534⟩,⟨(-516834146548681470540),(-516834146548681347046)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨292370638693397795305,292370638693397897734⟩,⟨(-484414346519021681459),(-484414346519021579006)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨87040886528916878285,87040886528916918377⟩,⟨(-196058477925717883427),(-196058477925717843319)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2286279753201406),(-2286279753201353)⟩,⟨(-2401513038245932),(-2401513038245881)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-8082222175882322),(-8082222175882156)⟩,⟨(-6954405367036084),(-6954405367035921)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-17775370726013765),(-17775370726013303)⟩,⟨(-10026251875181398),(-10026251875180939)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-34277032064849414),(-34277032064848095)⟩,⟨(-7847261543019370),(-7847261543018050)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-58851589542834642),(-58851589542831121)⟩,⟨8456246032618199,8456246032621720⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-84976188431444988),(-84976188431434090)⟩,⟨54795056958706735,54795056958717636⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-86401551692897551),(-86401551692864729)⟩,⟨149875672015199166,149875672015231989⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-5518706443394358),(-5518706443326601)⟩,⟨294715270395044433,294715270395112191⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨235370864333299234,235370864333391572⟩,⟨432734147794202599,432734147794294938⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨670894044769492423,670894044769610776⟩,⟨421524657990367178,421524657990485527⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1196366217310175758,1196366217310307274⟩,⟨88735756809876604,88735756810008117⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1553158253736497988,1553158253736597140⟩,⟨(-596945983915118049),(-596945983915018895)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1503021432769378982,1503021432769435001⟩,⟨(-1375527975975027534),(-1375527975974971514)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1068539471773818355,1068539471773845572⟩,⟨(-1789581146547000386),(-1789581146546973167)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨533639248998626300,533639248998640900⟩,⟨(-1511008751321218965),(-1511008751321204363)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨143304668619310066,143304668619314612⟩,⟨(-588682611075809780),(-588682611075805233)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-13548134848012),(-13548134847996)⟩,⟨4861841309424,4861841309440⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-41273586220974),(-41273586220958)⟩,⟨20290404120391,20290404120407⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-68515286941856),(-68515286941840)⟩,⟨54726560045104,54726560045120⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-85602527345190),(-85602527345174)⟩,⟨125842138137997,125842138138013⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-63830393398500),(-63830393398484)⟩,⟨252410575160358,252410575160374⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨58017271522488,58017271522504⟩,⟨437539393516093,437539393516109⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨376904808070712,376904808070730⟩,⟨630638028956433,630638028956449⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨987464488472471,987464488472487⟩,⟨674741578597928,674741578597944⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1875070271197812,1875070271197828⟩,⟨287105462077102,287105462077119⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2779736726652670,2779736726652687⟩,⟨(-834803509103612),(-834803509103596)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨3191525406564402,3191525406564419⟩,⟨(-2740059572316158),(-2740059572316140)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨2650583522804831,2650583522804851⟩,⟨(-4949371059842103),(-4949371059842084)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1230373863932863,1230373863932898⟩,⟨(-6518013780455524),(-6518013780455490)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-300432185147367),(-300432185147308)⟩,⟨(-6559350989125061),(-6559350989125004)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-988826041957540),(-988826041957472)⟩,⟨(-4818340271420474),(-4818340271420407)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-509172072058761),(-509172072058720)⟩,⟨(-1761003971983696),(-1761003971983657)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨51135666375061797003964843,51135666375062473745981335⟩,⟨(-566754997441387011405715900),(-566754997441386334664569105)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 29) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_29 (tableDensity false) (fullFactor true 0 29) density0_contains hk0_1_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨183546502996908857116406850,183546502996908860045986206⟩,⟨1864749738453178227054945,1864749738453181131421286⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_29 0 29 ha0_1_29_contains + def realAnswer : RBox := ⟨234682169371970654020371693,234682169371971333891967541⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_29 +namespace hm0_1_1_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨371315160027395970478319,371315160027411745701080⟩,⟨(-6595190391474752659288967),(-6595190391474736884020062)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-3937915766196283713723961),(-3937915766196243746964137)⟩,⟨(-20892206755919057960369480),(-20892206755919017993929580)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-24810674576433226742428612),(-24810674576433186353084085)⟩,⟨(-31690566899443332955027360),(-31690566899443292567768285)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-64930046316293002222681100),(-64930046316292966036117095)⟩,⟨(-13360045197396766579912627),(-13360045197396730394818822)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-76430974039171182618857788),(-76430974039171162077367777)⟩,⟨66814152802895344131092460,66814152802895364677451418⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨40033244804445302394347946,40033244804445313097964451⟩,⟨142535548501655977890459908,142535548501655988591959068⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨209735762567774868502223703,209735762567774873722569264⟩,⟨169002651448241816342170,169002651448247032037414⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨49289844142354685912839868,49289844142354689135173253⟩,⟨(-286478010197060757930561012),(-286478010197060754696049988)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-369054151455975516975397697),(-369054151455975514804729315)⟩,⟨(-118775395043483781387111892),(-118775395043483779235457197)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-227482376389784869844972920),(-227482376389784868440726778)⟩,⟨426161391105372528300252515,426161391105372529727108806⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨397171214732925270839543637,397171214732925271762794766⟩,⟨377021646165309802433461673,377021646165309803342278552⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨509208013356852601642530130,509208013356852602240715138⟩,⟨(-221587243555619652759793517),(-221587243555619652173087002)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨78986859709660370020161264,78986859709660370370605220⟩,⟨(-492609759059383200567195253),(-492609759059383200186153500)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-232191169896427598795734967),(-232191169896427598542808691)⟩,⟨(-313507522779402210549299297),(-313507522779402210294169210)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-229445491623704637724805459),(-229445491623704637589112499)⟩,⟨(-91089641987497924163272790),(-91089641987497924040393452)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-83988307554044671387967359),(-83988307554044671349249048)⟩,⟨(-7793153107139638832502859),(-7793153107139638800300863)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-22156975507580357826544),(-22156975507580266217171)⟩,⟨(-9502048901825521736580),(-9502048901825430126730)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-77101234623498384181353),(-77101234623498022196941)⟩,⟨(-16608720115548462754694),(-16608720115548100767509)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-153610293422787263966232),(-153610293422786267427523)⟩,⟨26618969488654691109584,26618969488655687656897⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-207257889613002140116533),(-207257889612998097998335)⟩,⟨189254312602587950977491,189254312602591993103003⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-45846592167505939891667),(-45846592167493123249375)⟩,⟨498670368930902008099868,498670368930914824726850⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨645911351904737236383536,645911351904780017261035⟩,⟨637217349474016313696570,637217349474059094543795⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1623496290326953522437396,1623496290327065364963775⟩,⟨(-355568600780400038864522),(-355568600780288196276766)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨850313245331770707028697,850313245332048894723183⟩,⟨(-2894432060439107205878195),(-2894432060438829018163978)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-3887506838257140377084329),(-3887506838256706596006392)⟩,⟨(-3603926202786454485627715),(-3603926202786020704736496)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-8252659205996679449980120),(-8252659205996105734822741)⟩,⟨3108221227835292036823015,3108221227835865752232093⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2041662904639925019466542),(-2041662904639332278685114)⟩,⟨13412239550472645373296645,13412239550473238114183049⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨13603247143552779629958456,13603247143553174258379076⟩,⟨12914106874944625867761078,12914106874945020495525709⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨22443260164108270684205390,22443260164108559005235346⟩,⟨(-1415350714426513185463729),(-1415350714426224864356262)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨16887326816107300191045837,16887326816107431297371052⟩,⟨(-14566211619228796143271467),(-14566211619228665036156409)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨6639066110107651301975113,6639066110107720286542687⟩,⟨(-15272219734076097032084460),(-15272219734076028047119102)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1109572431764626389102631,1109572431764648001793755⟩,⟨(-6088332916215218928598864),(-6088332916215197315839096)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨49559479956330322287,49559479956330329056⟩,⟨(-39487025258458699199),(-39487025258458692427)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨145655855855330704792,145655855855330728549⟩,⟨(-152480845600222605545),(-152480845600222581784)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨204630867451259798045,204630867451259851687⟩,⟨(-376798698413136551567),(-376798698413136497914)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨87717126296365199235,87717126296365315330⟩,⟨(-788470253663997673602),(-788470253663997557498)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-548899362287275289470),(-548899362287275035764)⟩,⟨(-1323732997140426040183),(-1323732997140425786481)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-2184785375390901729958),(-2184785375390901172491)⟩,⟨(-1369226068862394786051),(-1369226068862394228627)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-4604231877866852078714),(-4604231877866850855233)⟩,⟨747319844634906005193,747319844634907228634⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-4886931602761202502234),(-4886931602761199858412)⟩,⟨6949928891214729014485,6949928891214731658401⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨3373991254741793571656,3373991254741799140100⟩,⟨15012969102623792058694,15012969102623797627264⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨23351988899637907603008,23351988899637919174086⟩,⟨13438283324071220237887,13438283324071231808862⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨42379910615771637143935,42379910615771663919200⟩,⟨(-11306917168147376427294),(-11306917168147349652151)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨35983016625681829287558,35983016625681906074806⟩,⟨(-52504103820636012754426),(-52504103820635935967124)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1029717435060377960702),(-1029717435060192177990)⟩,⟨(-79125580280833340654501),(-79125580280833154871703)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-39342971351292889994571),(-39342971351292452620267)⟩,⟨(-70402489776814939766274),(-70402489776814502392055)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-46705356331782933074802),(-46705356331782378975898)⟩,⟨(-39988224798993686799078),(-39988224798993132700296)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-20026299518717787374080),(-20026299518717529546721)⟩,⟨(-11568111090253047573539),(-11568111090252789746213)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨133419404316353985,133419404316355100⟩,⟨(-171414644558704809),(-171414644558703698)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨375339980781496879,375339980781499834⟩,⟨(-596926738296445014),(-596926738296442059)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨484840607928712897,484840607928716625⟩,⟨(-1283130566880085567),(-1283130566880081839)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨150180828253652420,150180828253655524⟩,⟨(-2405497435568058818),(-2405497435568055713)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1351349382561552576),(-1351349382561550818)⟩,⟨(-3945813201942893711),(-3945813201942891955)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-5255213267317242385),(-5255213267317241510)⟩,⟨(-5094634315110478880),(-5094634315110478004)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-12669748367281348988),(-12669748367281348095)⟩,⟨(-3132636777426498130),(-3132636777426497238)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-22100772768233953364),(-22100772768233951763)⟩,⟨7335937311967271459,7335937311967273062⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-25245434447960511451),(-25245434447960507909)⟩,⟨31895833286252418439,31895833286252421981⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-5993497989711010328),(-5993497989711002709)⟩,⟨67755883785201270593,67755883785201278213⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨48472033870627607187,48472033870627622143⟩,⟨94708360894171333789,94708360894171348749⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨126648207269970358264,126648207269970384191⟩,⟨83142816559509374804,83142816559509400738⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨187736548891964372167,187736548891964410196⟩,⟨25292436183457269494,25292436183457307525⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨192271835678632041500,192271835678632086051⟩,⟨(-43213254029420916495),(-43213254029420871947)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨137003701029250295401,137003701029250332863⟩,⟨(-69097825719881646254),(-69097825719881608795)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨48452898698492760765,48452898698492775551⟩,⟨(-32647849964595834194),(-32647849964595819413)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-790619080017914),(-790619080017871)⟩,⟨(-749604242594700),(-749604242594653)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-2807504803297222),(-2807504803297086)⟩,⟨(-2216334593905102),(-2216334593904966)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-6233581723348747),(-6233581723348368)⟩,⟨(-3355304885642964),(-3355304885642580)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-12223381357503548),(-12223381357502459)⟩,⟨(-3028231772872643),(-3028231772871552)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-21619519244205025),(-21619519244202132)⟩,⟨1750346617570432,1750346617573324⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-33049514134815394),(-33049514134806425)⟩,⟨16922551485887562,16922551485896527⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-38696907975907820),(-38696907975880837)⟩,⟨50941779657806668,50941779657833650⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-18843204222016089),(-18843204221960413)⟩,⟨109200039167921081,109200039167976752⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨57987942451803420,57987942451879230⟩,⟨180653743075874331,180653743075950143⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨217408276747150629,217408276747247684⟩,⟨223881272603953374,223881272604050428⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨442780574295105876,442780574295213585⟩,⟨176125828767251408,176125828767359116⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨651858019852950018,651858019853031108⟩,⟨3947616355759315,3947616355840405⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨734229628980160143,734229628980205883⟩,⟨(-236698625243623999),(-236698625243578255)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨638101815734700137,638101815734722324⟩,⟨(-407393487362407462),(-407393487362385273)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨411048511941419448,411048511941431335⟩,⟨(-383747461948880417),(-383747461948868530)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨138219270139032113,138219270139035816⟩,⟨(-156343683063865673),(-156343683063861972)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-395450049905),(-395450049889)⟩,⟨163687169481,163687169497⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1015911085968),(-1015911085952)⟩,⟨875346061438,875346061454⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-274848514634),(-274848514618)⟩,⟨2656452646431,2656452646447⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨6068088651974,6068088651990⟩,⟨5582016868487,5582016868503⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨28403037278168,28403037278184⟩,⟨7121963978021,7121963978037⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨85539295353294,85539295353310⟩,⟨(-3662404354856),(-3662404354840)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨200981816335601,200981816335617⟩,⟨(-58384780329140),(-58384780329124)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨384736878033655,384736878033672⟩,⟨(-223825020442480),(-223825020442463)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨595084968700963,595084968700980⟩,⟨(-597614869225395),(-597614869225379)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨699558481354607,699558481354623⟩,⟨(-1252635045784453),(-1252635045784437)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨497496867502173,497496867502190⟩,⟨(-2127643814328857),(-2127643814328840)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-135140082916019),(-135140082915998)⟩,⟨(-2950625834981300),(-2950625834981277)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1037108790391515),(-1037108790391486)⟩,⟨(-3331849310498875),(-3331849310498842)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1713598495472307),(-1713598495472255)⟩,⟨(-3017039560961206),(-3017039560961154)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1629833333854390),(-1629833333854328)⟩,⟨(-2059383787230537),(-2059383787230479)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-671578334014369),(-671578334014336)⟩,⟨(-723386101435571),(-723386101435533)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3604409670087412859826406,3604409670087935435036412⟩,⟨(-100890911122696178415916368),(-100890911122695655840955169)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 29) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_29 (tableDensity true) (fullFactor true 0 29) density1_contains hk0_1_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-240022350072880816983212731),(-240022350072880813152224343)⟩,⟨(-2438518888746467633397066),(-2438518888746463835379544)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_29 0 29 ha0_1_29_contains + def realAnswer : RBox := ⟨(-236417940402793404223386325),(-236417940402792877617187931)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_29 +namespace hm0_0_1_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk0_1_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-4004707894251317471806719),(-4004707894251311941942453)⟩,⟨10220196784360446639541133,10220196784360452169035234⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-4040814225867591921585851),(-4040814225867576093689897)⟩,⟨35012442015702176758990832,35012442015702192586195039⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨25742928907510800034896921,25742928907510820438357788⟩,⟨61741569761114661342565101,61741569761114681746623957⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨102076493670478392017357287,102076493670478409107968706⟩,⟨46820664430979218249403807,46820664430979235343555923⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨155013547793777397972240941,155013547793777412678472374⟩,⟨(-90131131213764358022928497),(-90131131213764343318308458)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-25031918056685703003150649),(-25031918056685691903713507)⟩,⟨(-274469860056856915031188282),(-274469860056856903935581045)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-396250600026690621044463757),(-396250600026690612315851462)⟩,⟨(-82286871433609961553502283),(-82286871433609952817897820)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-220774126933315888123687870),(-220774126933315881575079813)⟩,⟨515322426739456200142342483,515322426739456206684250518⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨613393999566168806938970272,613393999566168811307547342⟩,⟨384453378757948856465105774,384453378757948860837364159⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨572725024946823406833905122,572725024946823409441991761⟩,⟨(-645539592300737638056827441),(-645539592300737635447539748)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-540915162931325600743271197),(-540915162931325599280268520)⟩,⟨(-772445493882887784199601083),(-772445493882887782741878113)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-908941998568636368022447333),(-908941998568636367218808070)⟩,⟨233780620986021388986170201,233780620986021389791619016⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-236148883284149333635567828),(-236148883284149333191813024)⟩,⟨807657897695656832722831537,807657897695656833173754831⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨334108983471392701731771306,334108983471392702003464535⟩,⟨570923066889307435294326596,570923066889307435565345239⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨372743463711980606284617630,372743463711980606418493224⟩,⟨194417365225194653937056209,194417365225194654066387757⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨141127015285819767809567182,141127015285819767846511473⟩,⟨27895083732102852669496403,27895083732102852704251973⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨27727051386382164454927,27727051386382201872816⟩,⟨24118057372287208344803,24118057372287245764645⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨105611476024765662550425,105611476024765818666121⟩,⟨61762501748982406850266,61762501748982562970339⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨246396737905310325075282,246396737905310793831737⟩,⟨39727684207572919984252,39727684207573388740436⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨432785125494635431661483,432785125494636678924595⟩,⟨(-174669772784828796325709),(-174669772784827549086552)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨399532417187771169389382,399532417187775571592392⟩,⟨(-762692116888635805812911),(-762692116888631403639061)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-568149017343098858493639),(-568149017343085908957038)⟩,⟨(-1485977437905388817588724),(-1485977437905375867983780)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-2845341245155906023083679),(-2845341245155865975820746)⟩,⟨(-694149569370675890537745),(-694149569370635843231104)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-3633284036587687869371150),(-3633284036587606879309438)⟩,⟨3847788328092309053946625,3847788328092390043765957⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨3116086324846372667138892,3116086324846520207198045⟩,⟨8649956833944823934318094,8649956833944971474649455⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨14902864935747681436393629,14902864935747885407731122⟩,⟨1736033342716195638889991,1736033342716399610398601⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨12980391882684899676730629,12980391882685083722800849⟩,⟨(-18315030029287079685436306),(-18315030029286895640260575)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-10826325410368543828554605),(-10826325410368387502351005)⟩,⟨(-28030372104997181690693418),(-28030372104997025363862419)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-32912088965528207130286635),(-32912088965528111436271619)⟩,⟨(-11913047405094187853866618),(-11913047405094092158752525)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-32133077687225863352722732),(-32133077687225802893563576)⟩,⟨11209421791264491745791705,11209421791264552204491334⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-17303065078816529645166469),(-17303065078816504209788835)⟩,⟨18239402895117862700844176,18239402895117888135175623⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-4578745891013056517095965),(-4578745891013048831802237)⟩,⟨8097483895148210455150796,8097483895148218140063065⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-53982700384771069344),(-53982700384771063509)⟩,⟨8742879812015345951,8742879812015351779⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-173989437885958300677),(-173989437885958280285)⟩,⟨54769803846083182595,54769803846083202971⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-311192804061079812419),(-311192804061079764719)⟩,⟨208329344694810702826,208329344694810750511⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-380088446126506092672),(-380088446126505982111)⟩,⟨600944739215575959337,600944739215576069911⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-38833888860590901733),(-38833888860590635232)⟩,⟨1348500788394670734442,1348500788394671001063⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1483986105311475247241,1483986105311475910193⟩,⟨2134718730527547014430,2134718730527547677506⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨4909339071167325836614,4909339071167327503455⟩,⟨1227711049569647165499,1227711049569648832114⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨8436436537033725471380,8436436537033729593168⟩,⟨(-4983092260499075145584),(-4983092260499071024399)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨4107723004201715884982,4107723004201725619403⟩,⟨(-18028409077530231398197),(-18028409077530221663189)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-18591095900556080033370),(-18591095900556058612133)⟩,⟨(-27513584539222083616481),(-27513584539222062193424)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-54296710579755237894083),(-54296710579755194451200)⟩,⟨(-10231392054791406675964),(-10231392054791363234403)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-70848031149582863163763),(-70848031149582781706386)⟩,⟨42569900893951846053503,42569900893951927506258⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-41737362648098761661994),(-41737362648098611589292)⟩,⟨98660231031902812313736,98660231031902962386012⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨11470048582678518926514,11470048582678735058643⟩,⟨113527013147550726097920,113527013147550942234435⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨39061873918487638212140,39061873918487840476972⟩,⟨81137418541292354920732,81137418541292557190775⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨20235897615587521964084,20235897615587614776570⟩,⟨27930434257234015187634,27930434257234108001854⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-100790072910376519),(-100790072910376270)⟩,⟨30855588505385697,30855588505385950⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-320632067467266189),(-320632067467265561)⟩,⟨136777711102097390,136777711102098021⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-575138352198615376),(-575138352198614620)⟩,⟨403623787768852368,403623787768853124⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-787729532685637925),(-787729532685637324)⟩,⟨1027334140584971249,1027334140584971851⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-609681234105836530),(-609681234105836161)⟩,⟨2274274239615228358,2274274239615228727⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨887954576870124845,887954576870125184⟩,⟨4220297538548240183,4220297538548240522⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨5365858323979856314,5365858323979856810⟩,⟨5881403632896025464,5881403632896025961⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨14193572140548651556,14193572140548652615⟩,⟨3698697242732567071,3698697242732568130⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨24942279602195297872,24942279602195300313⟩,⟨(-8916268740244028978),(-8916268740244026536)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨26999418177288923964,26999418177288929314⟩,⟨(-36971761962761052036),(-36971761962761046680)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4358814135886101004,4358814135886111685⟩,⟨(-73514721278376075762),(-73514721278376065075)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-47822497981687940107),(-47822497981687921382)⟩,⟨(-95578389925070867971),(-95578389925070849242)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-107044615319583277247),(-107044615319583249708)⟩,⟨(-82132532319698133174),(-82132532319698105639)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-134774558847429983069),(-134774558847429950887)⟩,⟨(-40750897139516567238),(-40750897139516535068)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-109534155252432851343),(-109534155252432824397)⟩,⟨(-4615237482742787619),(-4615237482742760682)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-41559881808325146560),(-41559881808325135953)⟩,⟨3627847733884016339,3627847733884026943⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-273314280535895),(-273314280535871)⟩,⟨368152193882695,368152193882715⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-755876905949867),(-755876905949829)⟩,⟨1270769490228039,1270769490228076⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-934425314982352),(-934425314982275)⟩,⟨2688003292682706,2688003292682785⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-190887411666144),(-190887411665959)⟩,⟨4939660389073175,4939660389073358⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2806180380002267,2806180380002766⟩,⟨7966238994410028,7966238994410527⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨10228226703518661,10228226703520424⟩,⟨10338153085391206,10338153085392971⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨24084014171626042,24084014171630960⟩,⟨7525474160826041,7525474160830960⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨42638401961734789,42638401961744140⟩,⟨(-9317155205416842),(-9317155205407491)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨54391824937081558,54391824937094837⟩,⟨(-50293098258833239),(-50293098258819960)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨35607979188858008,35607979188878414⟩,⟨(-115653842732594715),(-115653842732574313)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-37275118707394021),(-37275118707373499)⟩,⟨(-182173507034550708),(-182173507034530184)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-159272918706087671),(-159272918706073661)⟩,⟨(-207279709411716432),(-207279709411702422)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-279255602680279771),(-279255602680271870)⟩,⟨(-163915440439979876),(-163915440439971971)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-325431124112915843),(-325431124112910616)⟩,⟨(-76527977743074562),(-76527977743069339)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-258571499279052470),(-258571499279049720)⟩,⟨(-6808041577180997),(-6808041577178247)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-97821022570877805),(-97821022570876967)⟩,⟨7584719812301339,7584719812302180⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨671259617777,671259617793⟩,⟨1600938524282,1600938524298⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2721725291103,2721725291119⟩,⟨4848340951181,4848340951197⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨7125425709129,7125425709145⟩,⟨7917182662405,7917182662422⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨16040078674033,16040078674049⟩,⟨9449178598997,9449178599013⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨31642683186216,31642683186232⟩,⟨5590508303542,5590508303559⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨53800545835435,53800545835452⟩,⟨(-11688845799975),(-11688845799958)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨74873485720847,74873485720863⟩,⟨(-54733438045150),(-54733438045134)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨72739241768652,72739241768668⟩,⟨(-134529100097272),(-134529100097255)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨8992477555656,8992477555672⟩,⟨(-245656981954068),(-245656981954051)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-154924638319031),(-154924638319014)⟩,⟨(-348235240207635),(-348235240207619)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-419263801173531),(-419263801173514)⟩,⟨(-370382175130070),(-370382175130054)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-711132708320527),(-711132708320508)⟩,⟨(-254709462504797),(-254709462504781)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-900914090659872),(-900914090659855)⟩,⟨(-27309588161421),(-27309588161402)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-879748075310153),(-879748075310129)⟩,⟨186401652270286,186401652270307⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-631463731113448),(-631463731113426)⟩,⟨245007653138556,245007653138576⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-227760952679432),(-227760952679409)⟩,⟨110461729813074,110461729813093⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-15310421550986289786755808),(-15310421550986101062604124)⟩,⟨169034975218614661961860878,169034975218614850685732309⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk0_1_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 0 30) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk0_1_30 (tableDensity false) (fullFactor true 0 30) density0_contains hk0_1_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-56912468009981344739561534),(-56912468009981343632501925)⟩,⟨1365092672477098654713804,1365092672477099753808273⟩⟩ +lemma atomChecked : tableAtomBox false ha0_1_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 0 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha0_1_30 0 30 ha0_1_30_contains + def realAnswer : RBox := ⟨(-72222889560967634626317342),(-72222889560967444595106049)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 0 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_0_1_30 +namespace hm0_1_1_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk0_1_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-909529028503182050975579),(-909529028503178113122316)⟩,⟨1642230083307680735695459,1642230083307684673636492⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1528699545732703388938075),(-1528699545732692233077743)⟩,⟨5860670484505767035959970,5860670484505778191973620⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨2723756953120490340243767,2723756953120503969239817⟩,⟨11193332332735449315687388,11193332332735462944465287⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨15706630570553461112499233,15706630570553470791519575⟩,⟨10865471216036840089183388,10865471216036849767268931⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨27731092861633460157626617,27731092861633466860772962⟩,⟨(-9997708631838619770760705),(-9997708631838613066871705)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2726490282039311044021415,2726490282039314359670080⟩,⟨(-43275239236894854012997283),(-43275239236894850696538328)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-59249351479989555657100724),(-59249351479989553853276625)⟩,⟨(-18162580035089020872635867),(-18162580035089019071423240)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-35640238124239536870204215),(-35640238124239535722327937)⟩,⟨78955769326981197671714369,78955769326981198823791654⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨101008322297694513156253152,101008322297694513918426365⟩,⟨57935959778346448312616782,57935959778346449069370939⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨89095587458192728232569064,89095587458192728714338216⟩,⟨(-115751416186992251313630105),(-115751416186992250826313263)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-105617098307944453008614554),(-105617098307944452703467222)⟩,⟨(-128695256721785973761173457),(-128695256721785973458286018)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-160703967727954619252490743),(-160703967727954619061283656)⟩,⟨53946625982738539545795891,53946625982738539731996427⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-32335734895315553209338260),(-32335734895315553097900973)⟩,⟨149262425662131194651563590,149262425662131194772191862⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨68403519474979891299633799,68403519474979891378176270⟩,⟨98164129673139613448374528,98164129673139613527986062⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨70123056638463425638702849,70123056638463425680922668⟩,⟨28757462584002076694815553,28757462584002076733185402⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨25792363539701092849206993,25792363539701092861210084⟩,⟨2452297239216599937210346,2452297239216599947215647⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2014938875135906313240,2014938875135926411568⟩,⟨5365241100956663838201,5365241100956683936267⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨9967139631445656466101,9967139631445748325988⟩,⟨15961277738489095476783,15961277738489187336056⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨30556360285409574459958,30556360285409881932768⟩,⟨21674947997943019513465,21674947997943326986145⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨68112704057141464938492,68112704057142333517159⟩,⟨2117798604555762527257,2117798604556631108823⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨91748714009979029936181,91748714009982342089280⟩,⟨(-82205989292737212759577),(-82205989292733900602462)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16016336767574352477577),(-16016336767564287518517)⟩,⟨(-226070711621075701092642),(-226070711621065636141660)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-375403754431494815919413),(-375403754431462896565908)⟩,⟨(-193117437426523673698860),(-193117437426491754352066)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-631222936138701419393658),(-631222936138636540743276)⟩,⟨457973743053958684809034,457973743054023563490263⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨277887406977771197745512,277887406977889812133134⟩,⟨1366709984150087404183782,1366709984150206018538095⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2298856354818442729158814,2298856354818606379078138⟩,⟨532418871455014314842652,532418871455177964737906⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2390525871449092902334103,2390525871449238582375334⟩,⟨(-2807559040754256070747024),(-2807559040754110390580781)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1467294759556443157097593),(-1467294759556321133381134)⟩,⟨(-4956222341805868708561387),(-4956222341805746684941718)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-5687440844958523500246581),(-5687440844958451340441566)⟩,⟨(-2635987916581825736898256),(-2635987916581753577256540)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-6098274854154994915451376),(-6098274854154950599056823)⟩,⟨1466050620027340337650437,1466050620027384654127807⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3604733379376261488889742),(-3604733379376244076489244)⟩,⟨3034152071642869873570468,3034152071642887286140848⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1040056245397755126590883),(-1040056245397750009143644)⟩,⟨1415257864900173895401290,1415257864900179012909792⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-11414385640319831196),(-11414385640319829392)⟩,⟨(-4706066495098452947),(-4706066495098451144)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-39942934688372599152),(-39942934688372592821)⟩,⟨(-10250439592565661224),(-10250439592565654892)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-84437611549042966409),(-84437611549042951977)⟩,⟨1886153395012040549,1886153395012054984⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-144090863118469107442),(-144090863118469075795)⟩,⟨64621732305128056263,64621732305128087909⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-170121546197312758560),(-170121546197312688216)⟩,⟨233754192001657352633,233754192001657422980⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨4335143263790553492,4335143263790711408⟩,⟨528471306781310679286,528471306781310837207⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨664095838406295494412,664095838406295848754⟩,⟨711374620127574789765,711374620127575144100⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1806530289510277670204,1806530289510278454131⟩,⟨(-2347999139431732053),(-2347999139430948148)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2175997296688494894649,2175997296688496578994⟩,⟨(-2528869934538509697346),(-2528869934538508012985)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-843457298753983601658),(-843457298753980069950)⟩,⟨(-5894695134189080750900),(-5894695134189077219151)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-8025247341999996512768),(-8025247341999988688395)⟩,⟨(-5748679752700855587114),(-5748679752700847762759)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-14474069411366229954922),(-14474069411366210727784)⟩,⟨1596461942414027745483,1596461942414046972593⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-13520438218178435322198),(-13520438218178380094360)⟩,⟨12418154667287416975777,12418154667287472203631⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-5877279446715552561369),(-5877279446715451660203)⟩,⟨17980750098793035307530,17980750098793136208712⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨696112696682885036691,696112696682988998143⟩,⟨14515273893512330518613,14515273893512434480052⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1291941207957443729310,1291941207957495914222⟩,⟨5333166261112840858274,5333166261112893043175⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-33173867922872864),(-33173867922872650)⟩,⟨(-11871259505109729),(-11871259505109517)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-111451760262918224),(-111451760262917698)⟩,⟨(-27313246529529766),(-27313246529529239)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-224534703825445648),(-224534703825445019)⟩,⟨(-7611443861050848),(-7611443861050220)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-383576918637018696),(-383576918637018208)⟩,⟨107988213429409920,107988213429410410⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-543218670640220063),(-543218670640219793)⟩,⟨438247983283901034,438247983283901306⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-491330403741578902),(-491330403741578710)⟩,⟨1141296488519948271,1141296488519948468⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨308237107460352086,308237107460352290⟩,⟨2230503722710796057,2230503722710796259⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2688923766837165764,2688923766837166139⟩,⟨3078915770873109094,3078915770873109468⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨7036723903637838684,7036723903637839530⟩,⟨1824842395788154515,1824842395788155362⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨11640215503243734536,11640215503243736386⟩,⟨(-4196024583913626459),(-4196024583913624611)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨11847073984596386750,11847073984596390459⟩,⟨(-15718680013183872069),(-15718680013183868361)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3204785562708831705,3204785562708838265⟩,⟨(-28281890268400163417),(-28281890268400156856)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-12302944799444949890),(-12302944799444940107)⟩,⟨(-33898289807783307131),(-33898289807783297351)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-24832947739816103694),(-24832947739816092079)⟩,⟨(-28643085848506639691),(-28643085848506628078)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-24491911531748298754),(-24491911531748288895)⟩,⟨(-16854949592611173772),(-16854949592611163914)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-10115131432603911602),(-10115131432603907685)⟩,⟨(-5176135476603227450),(-5176135476603223535)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-83496624646706),(-83496624646684)⟩,⟨125404301084717,125404301084737⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-235334672509225),(-235334672509193)⟩,⟨436646523358288,436646523358318⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-305641320898376),(-305641320898311)⟩,⟨938688083391109,938688083391174⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-99857472228494),(-99857472228341)⟩,⟨1767586443061529,1767586443061685⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨841857462942549,841857462942965⟩,⟨2964127174673202,2964127174673615⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨3360307699761615,3360307699763068⟩,⟨4150972063660009,4150972063661462⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨8483348506841131,8483348506845176⟩,⟨3886104874474194,3886104874478242⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨16376059126054751,16376059126062432⟩,⟨(-1032561188363967),(-1032561188356282)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨24196653770435769,24196653770446670⟩,⟨(-15125551309318594),(-15125551309307692)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨24418265230273178,24418265230289913⟩,⟨(-40937459553638224),(-40937459553621488)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨7580687500584276,7580687500601084⟩,⟨(-73477316263691515),(-73477316263674703)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-28507688151293026),(-28507688151281568)⟩,⟨(-98366006450595507),(-98366006450584046)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-70302329069462349),(-70302329069455894)⟩,⟨(-100446557991608441),(-100446557991601985)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-93236923698198373),(-93236923698194114)⟩,⟨(-77788418931122099),(-77788418931117841)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-79368636341278694),(-79368636341276457)⟩,⟨(-44039683559712851),(-44039683559710612)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-31022689548747834),(-31022689548747150)⟩,⟨(-13401522158531965),(-13401522158531281)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨22216108665,22216108681⟩,⟨46590651027,46590651043⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨112371533704,112371533720⟩,⟨116835276366,116835276382⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨324030004653,324030004669⟩,⟨14204315227,14204315243⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨632808705161,632808705177⟩,⟨(-785665760709),(-785665760693)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨620424930369,620424930386⟩,⟨(-3562278047561),(-3562278047545)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1333540267918),(-1333540267902)⟩,⟨(-10602088042055),(-10602088042039)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-9690532545141),(-9690532545125)⟩,⟨(-24593346352615),(-24593346352599)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-33577130014192),(-33577130014176)⟩,⟨(-45988357419394),(-45988357419378)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-85829087217470),(-85829087217454)⟩,⟨(-67719427755309),(-67719427755293)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-174829564646695),(-174829564646679)⟩,⟨(-70352596591578),(-70352596591562)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-289409664575176),(-289409664575159)⟩,⟨(-26702558699383),(-26702558699367)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-390007351359039),(-390007351359022)⟩,⟨76398655903015,76398655903031⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-425305962206866),(-425305962206846)⟩,⟨209663494193018,209663494193036⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-369634013793839),(-369634013793820)⟩,⟨298639944044376,298639944044397⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-242142503547550),(-242142503547528)⟩,⟨268623189193497,268623189193518⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-82750000463392),(-82750000463375)⟩,⟨108308668173885,108308668173904⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1076860194139078951698327),(-1076860194138936595021506)⟩,⟨30101627075929975912623048,30101627075930118269241299⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk0_1_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 0 30) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk0_1_30 (tableDensity true) (fullFactor true 0 30) density1_contains hk0_1_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨74423996628437141673271748,74423996628437143120965083⟩,⟨(-1785121187085438139595434),(-1785121187085436702318052)⟩⟩ +lemma atomChecked : tableAtomBox true ha0_1_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 0 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha0_1_30 0 30 ha0_1_30_contains + def realAnswer : RBox := ⟨73347136434298062621573421,73347136434298206625943577⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 0 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm0_1_1_30 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_0.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_0.lean new file mode 100644 index 0000000000000000000000000000000000000000..859513cd5ebff3c6441359d6815034d68b441b36 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_0.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨53120899936953143701172623042,53120899936953205104689835378⟩,⟨119309646649030956100449375270,119309646649031017506316454930⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨165304816364233514307552361553,165304816364233658681579029471⟩,⟨350145629043643266357957186402,350145629043643410739116368654⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨293643136501110290528505528357,293643136501110435039406004206⟩,⟨557946014793178282275829901375,557946014793178426798836382640⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨443619290880370851162218729987,443619290880370941250986948520⟩,⟨729632134772976007389501406595,729632134772976097495467900136⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨612670764841530174222368582526,612670764841530211407001357151⟩,⟨854643400991507020121129502487,854643400991507057327900670423⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨789481556964474137067628974258,789481556964474147477644258396⟩,⟨924475754036635921401452731621,924475754036635931837899643607⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨957246720095271276779044163728,957246720095271278983642550468⟩,⟨933539468823124468853259864476,933539468823124471087273896305⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1097739901136957907616038199521,1097739901136957908148713264327⟩,⟨882479552890041640454574637489,882479552890041641018129572828⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1193781976540600947903096606116,1193781976540600948174425482493⟩,⟨780323558188568586360923789115,780323558188568586662996003592⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1231430040242348516127295179469,1231430040242348516342118990660⟩,⟨643372836358556676035312300607,643372836358556676279201687590⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1202093645296529209593658481259,1202093645296529209773313364158⟩,⟨492087604094018163182206006435,492087604094018163387968756301⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1103332903880449548434223922437,1103332903880449548580350123460⟩,⟨347024735543901589314006434742,347024735543901589482097755425⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨938296434030799075364806337401,938296434030799075477706526628⟩,⟨224133554688926963192683466315,224133554688926963322700901006⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨715314362238235526074179208834,715314362238235526153680936027⟩,⟨130861191663485411065660466866,130861191663485411157327142790⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨447703425405895184890733379697,447703425405895184937722835143⟩,⟨65511356103477067543281785186,65511356103477067597508779460⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨152303074611714150764755555410,152303074611714150780190257572⟩,⟨19534568219305364349383410202,19534568219305364367245602406⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-47056722869561684985462158389),(-47056722869561609635181757182)⟩,⟨100935613136237012741964264139,100935613136237088089253488584⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-135044645874321417865404647427),(-135044645874321130788592029683)⟩,⟨301459899343432179515412753855,301459899343432466583723768840⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-205159457296416221914486981346),(-205159457296415484448900605306)⟩,⟨496882004007291383955344101522,496882004007292121408305458028⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-247652101639610617445891664166),(-247652101639608826401228924431)⟩,⟨681659908814767874368140531450,681659908814769665398087697628⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-255906400845931830009738597277),(-255906400845927725392959895350)⟩,⟨847989278126798479360914468461,847989278126802583963226582414⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-227718948627606021280045901035),(-227718948627597629731830669194)⟩,⟨986713508374275892726011077671,986713508374284284262205174029⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-166585883638182536836453118074),(-166585883638168315823482619512)⟩,⟨1088772231965777338122595139561,1088772231965791559127711736087⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-81945971779341781475415236894),(-81945971779323119447948131075)⟩,⟨1146334765156250014449765056080,1146334765156268676474499725885⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨12483943970959711590691435902,12483943970978676461345944286⟩,⟨1153918832395268447170562926896,1153918832395287412043688132919⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨101496877197185587090968689314,101496877197200501212263155898⟩,⟨1109679445608385233245696092413,1109679445608400147373930786547⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨171284755916302472969371527342,171284755916311540329574594118⟩,⟨1016211334177702726416953934534,1016211334177711793787221105555⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨211658133926676824360780504321,211658133926681371529720360452⟩,⟨880442688028941744485037292782,880442688028946291665477431686⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨217035766079831303558678695502,217035766079833328882478340719⟩,⟨712248730914266168184872696195,712248730914268193519852553177⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨186849431710466381648135435938,186849431710467228570252621970⟩,⟨521878219952253147889709111956,521878219952253994821095577558⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨125991480201336115923482776322,125991480201336448513422163015⟩,⟨317880751048533367989293449600,317880751048533700585331748172⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨44415660512251430725479817562,44415660512251518112386768831⟩,⟨106667756034050937567467131492,106667756034051024956498703738⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-79606260413926762677100149981),(-79606260413926762658530140917)⟩,⟨(-1072909342475473279734962269),(-1072909342475473269978130955)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-236869586109566903824450892082),(-236869586109566903768514056251)⟩,⟨2380826774969770143427923529,2380826774969770173357332156⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-387842498848941385922340714012),(-387842498848941385829058511112)⟩,⟨21681727973356974039973055295,21681727973356974091769984446⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-527646151986321989469919757110),(-527646151986321989339799531855)⟩,⟨64013114338109944816579029562,64013114338109944892413524436⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-650005109822468809591293054592),(-650005109822468809425835734298)⟩,⟨131485382410361825487129208109,131485382410361825589143993137⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-746803822526568891766702812910),(-746803822526568891565843526141)⟩,⟨220535717018612469481293636137,220535717018612469614357822838⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-809380565391002386285823268416),(-809380565391002386041918631067)⟩,⟨323035440098395087719418718585,323035440098395087895516407123⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-831392121605228075968621812471),(-831392121605228075611864394568)⟩,⟨427566233227702171600601426691,427566233227702171893577030112⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-811041785528168840127355182512),(-811041785528168839056912509904)⟩,⟨520543299629543601409033422686,520543299629543602422985222198⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-751739859920478225592192378459),(-751739859920478219545176198982)⟩,⟨588033189805529043872833352191,588033189805529049872423210087⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-661474905998265311897737311287),(-661474905998265279990795266635)⟩,⟨617956486181475220638355899438,617956486181475252507433757742⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-550895457799312007906136244256),(-550895457799311886906710673468)⟩,⟨601773554085007249362790691612,601773554085007370333295587970⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-430190767790576821833123151304),(-430190767790576514955441281289)⟩,⟨535705217456689298545021293684,535705217456689605401803717816⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-306391409137036328734314626639),(-306391409137035818615307195061)⟩,⟨422095951041226467150308198323,422095951041226977255407216420⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-182952541310702748061657800762),(-182952541310702226166850944433)⟩,⟨269847252567398868140477505827,269847252567399390027391386782⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-60761705633202141847582942584),(-60761705633201917670610170907)⟩,⟨92753951684528130473613282204,92753951684528354648044206604⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-29306781408476371244114241742),(-29306781408476273129401799660)⟩,⟨(-34905404969405124987957637739),(-34905404969405026876064545658)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-89396501728931818029104778580),(-89396501728931588727599285337)⟩,⟨(-102676572617537681038714145742),(-102676572617537451745869603543)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-153219876757997628420306951683),(-153219876757997401350480614569)⟩,⟨(-164190842547721011150593749074),(-164190842547720784095800977330)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-221438288383864229109051269191),(-221438288383864089391524893391)⟩,⟨(-215184862978019102567996322775),(-215184862978018962872578314220)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-292630233166266928075977269306),(-292630233166266871138896044194)⟩,⟨(-251352242898610753058924234198),(-251352242898610696151657281041)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-363620250774544653202895027261),(-363620250774544637460856315350)⟩,⟨(-269074876255752847091534351565),(-269074876255752831387295814573)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-429804770395318894416315240481),(-429804770395318891192051696360)⟩,⟨(-266872872774561156807812512499),(-266872872774561153629027619294)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-485105582327003676668121938865),(-485105582327003676000816967613)⟩,⟨(-246276433735286368790578827412),(-246276433735286368175351578524)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-522543210132766145817321706260),(-522543210132766145546744516708)⟩,⟨(-211406221477041752151441729919),(-211406221477041751937634355910)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-535670217559562113509553092930),(-535670217559562113309932148468)⟩,⟨(-167998392811235499458689056261),(-167998392811235499317858806888)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-520090371743723253683493115844),(-520090371743723253515537591433)⟩,⟨(-122316897487107773936710754213),(-122316897487107773826372968220)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-474514569793667992438397083909),(-474514569793667992298929068734)⟩,⟨(-80105260253554353749714122966),(-80105260253554353663337576729)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-400941790508548629964013049775),(-400941790508548629854034686103)⟩,⟨(-45796245880418324286697383847),(-45796245880418324222051360158)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-303903665694060992611334513375),(-303903665694060992532295459571)⟩,⟨(-21832081695068801592673570165),(-21832081695068801548287867965)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-189440769935571197885100968875),(-189440769935571197837624192375)⟩,⟨(-8081594515430936174870705940),(-8081594515430936149127772505)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-64317046967626097918621042325),(-64317046967626097902834157672)⟩,⟨(-1784169303599346946352244214),(-1784169303599346937955860144)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨23613357818565049538650743431,23613357818565341564035399891⟩,⟨(-15543294580380716086139092286),(-15543294580380424059067845510)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨68157413740144251670366217740,68157413740145366306471680452⟩,⟨(-48288612565964237060495852388),(-48288612565963122419597325165)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨104821483750875308068531377291,104821483750878181412307346074⟩,⟨(-85574775938896385262159827509),(-85574775938893511911184991491)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨129289745899603236381968340934,129289745899610248724690722741⟩,⟨(-129037038469275470066669769645),(-129037038469268457715407045080)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨138697587860131622175305978156,138697587860147790411275677922⟩,⟨(-178005147793815172022353097707),(-178005147793799003777757265377)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨131803736308676550790634460100,131803736308709817984367777532⟩,⟨(-228936514346928092834531261509),(-228936514346894825633424092622)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨108963407455024430834320160151,108963407455081082365485391620⟩,⟨(-276155604121191357414887340888),(-276155604121134705878769414762)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨72538850106181016358729270388,72538850106255761513770782597⟩,⟨(-313484237584999828257731966690),(-313484237584925083100966166558)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨27257526754592672466879519661,27257526754669095341153632200⟩,⟨(-335688204006959435399068073567),(-335688204006883012526653637754)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-20193311636794027220366627827),(-20193311636733534765907291840)⟩,⟨(-339510138637518769684434753810),(-339510138637458277235281363800)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-62147992298772473772349769514),(-62147992298735448600890222962)⟩,⟨(-324258490474519073299996263191),(-324258490474482048136595394283)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-91121350826231878779926249544),(-91121350826213189048110705191)⟩,⟨(-291502882929599576025790116428),(-291502882929580886303581456745)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-101399182176591182165903340990),(-101399182176582806944966149405)⟩,⟨(-243789080405164697372249111088),(-243789080405156322160987614640)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-91036887053524660971224488534),(-91036887053521139770165422547)⟩,⟨(-183701875530333015874268872992),(-183701875530329494681465549355)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-62646113912315273339434604733),(-62646113912313883964032481292)⟩,⟨(-114155973704611366186724925719),(-114155973704609976816862588078)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-22263960693599398107656749964),(-22263960693599031542803720803)⟩,⟨(-38701685475217449957622660865),(-38701685475217083394719596280)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨114640351183450726909282274,114640351183450728866188364⟩,⟨7554766214630580346184046768,7554766214630580348957187278⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1684090172253202379261562017,1684090172253202385379088054⟩,⟨22391923108995802116141162856,22391923108995802124656656394⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨6960499341024307004865145022,6960499341024307015849563168⟩,⟨36449727954902121155596939528,36449727954902121170248555969⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨17276110702479222552385574215,17276110702479222569331014535⟩,⟨49282738011436065330196209014,49282738011436065351619888908⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨32311883011449364074717419527,32311883011449364099174892346⟩,⟨60084198629351943056779969344,60084198629351943085945818726⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨50348654973259165954687118132,50348654973259165989673407057⟩,⟨67190905849891837173580646465,67190905849891837213093473638⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨69299846798944862892448349871,69299846798944862948385412615⟩,⟨68593712469517619349579030398,68593712469517619409544901381⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨87176367434902486385393752607,87176367434902486526785839603⟩,⟨63289179613253092607216396784,63289179613253092751775496046⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨101909446058781216285578093993,101909446058781217043548201119⟩,⟨51953022315400896722408509985,51953022315400897482437453577⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨111474136135998379077304763386,111474136135998384283215403019⟩,⟨36708810103788802474969238383,36708810103788807681913431175⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨114259472468600412792447619232,114259472468600441541999923987⟩,⟨20598083761319231611222799213,20598083761319260361049902817⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨109204358917284345832024160988,109204358917284456970312544018⟩,⟨6831064336054616542955275691,6831064336054727681098706016⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨95832541302157585699180841793,95832541302157871196849408690⟩,⟨(-2288536065101323977358375566),(-2288536065101038480018754139)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨74626071701118684994737119203,74626071701119164191418475306⟩,⟨(-6151246529511603441234375557),(-6151246529511124244898053807)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨47267457712045954845090780946,47267457712046448649561741144⟩,⟨(-5597376788399175155573183353),(-5597376788398681351350033392)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨16160671190842655554839451826,16160671190842868673160603294⟩,⟨(-2192566080174523118164333722),(-2192566080174309999932108304)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-118244841969982757154618284471),(-118244841969899079047340499916)⟩,⟨3246923381172445081331098266133,3246923381172528759295764721657⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 0) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_0 (tableDensity false) (fullFactor false 1 0) density0_contains hk1_0_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1633606471),1806106055⟩,⟨(-22516660498395404817716612206),(-22516660498395404814197451266)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_0 1 0 ha1_0_0_contains + def realAnswer : RBox := ⟨(-118244841969982757156351890942),(-118244841969899079045434393861)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_0 +namespace hm1_1_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨6312519776955755448513283305,6312519776955805750648648765⟩,⟨21423955859287446365726541336,21423955859287496667322202081⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨19707528271786810000044699001,19707528271786928227445211995⟩,⟨63526899907932748431849251526,63526899907932866657605262498⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨35011112721121808956315623334,35011112721121927203754926480⟩,⟨102685709138611265202924433321,102685709138611383447541059636⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨52885306155924022073440483954,52885306155924095696611866737⟩,⟨135174996130829231018648898874,135174996130829304637721693026⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨74446472278151847985968393480,74446472278151878309033710612⟩,⟨156353712810284193013445921443,156353712810284223331056790645⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨101367491530388953011538100030,101367491530388961452011487540⟩,⟨163383706839235780415855446145,163383706839235788849502531710⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨133594321720474449912030409766,133594321720474451652469308991⟩,⟨157214746849078760272756556176,157214746849078762005112438639⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨167482609636987548318641227174,167482609636987548693820426699⟩,⟨141345344251991381292677154190,141345344251991381658801735069⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨196849664825713949736187721214,196849664825713949899943218989⟩,⟨119652712021257396019552772702,119652712021257396173699284376⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨215260083775700450134728601045,215260083775700450257559252171⟩,⟨95442986363670153989653560728,95442986363670154102671048595⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨217928489418514336959781023026,217928489418514337061140099293⟩,⟨71158991787306010783665216782,71158991787306010875414235993⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨203154202090813980392548864970,203154202090813980474424626217⟩,⟨48371432118761696359672543490,48371432118761696432625720909⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨172812168216088346736172546105,172812168216088346799139772375⟩,⟨28475224336184385849077022278,28475224336184385904374167918⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨130933428110163610433240393281,130933428110163610477319052699⟩,⟨13347614563210891618540491642,13347614563210891656690664763⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨81487975285151496288889073870,81487975285151496314778215056⟩,⟨4374799138020398760629791007,4374799138020398782765855758⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨27645710357000874893510260919,27645710357000874901998971730⟩,⟨752384034471432665501746025,752384034471432672697809781⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-13942963380693734044019013897),(-13942963380693672001293296136)⟩,⟨10357896967309561753408820361,10357896967309623796513539419⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-39965588260455618715224941447),(-39965588260455382247691465546)⟩,⟨31425805175237974684015308669,31425805175238211152618324190⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-60656240946511162924453989149),(-60656240946510555046568053700)⟩,⟨53437692873918765553910275612,53437692873919373433372450163⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-73461930307780054071850440694),(-73461930307778576466271688428)⟩,⟨76736993662640636907068831667,76736993662642114514464324506⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-77253255547682270147892700357),(-77253255547678880879371525752)⟩,⟨101118741280105638868270728791,101118741280109028138556974562⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-72514561371352201043125276186),(-72514561371345266291110525383)⟩,⟨125392060384221023763036433543,125392060384227958516493345615⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-60795593399826413527290421548),(-60795593399814651081734724490)⟩,⟨147237761423308303266403625748,147237761423320065712873457910⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-43988098018619320310977936548),(-43988098018603877371606681630)⟩,⟨163987504464105779465990336609,163987504464121222405627135566⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-24278269273214406793793949495),(-24278269273198713857192821769)⟩,⟨173664675434935620830405165732,173664675434951313766612306585⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-4399532268341080687978817781),(-4399532268328746380220818360)⟩,⟨175332613744563257589987907122,175332613744575591896766038630⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨12483800995401668651454751568,12483800995409160239684812148⟩,⟨168746542849180078317965325887,168746542849187569904777227828⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨23531810233845096835241985008,23531810233848849043285485055⟩,⟨153765323919405718778862696979,153765323919409470985256260618⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨27385504444537731285651257768,27385504444539400280719285330⟩,⟨130301910088564298188982277700,130301910088565967182420449946⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨24582930826487532709730700726,24582930826488229770452520993⟩,⟨99049721177051091229301706335,99049721177051788288654760015⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨16779551774867742954797386101,16779551774868016439629359468⟩,⟨61819686386230253512572815336,61819686386230526996495764778⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5932135071328552192195624971,5932135071328624013652972097⟩,⟨20992309993223917659961590886,20992309993223989481099105766⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-15179774434696695788672780567),(-15179774434696695781928228365)⟩,⟨(-9625024387919737941015766748),(-9625024387919737934674683890)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-45760248206218648661472737174),(-45760248206218648640792997650)⟩,⟨(-27806514064781908044794330295),(-27806514064781908025344311445)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-76390593789921760238514046636),(-76390593789921760203019087426)⟩,⟨(-42854325457093167920271334135),(-42854325457093167886690662023)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-105626471729156440694876249427),(-105626471729156440643569576695)⟩,⟨(-52747933091969634535710740474),(-52747933091969634486790800737)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-131160053785483131839029142946),(-131160053785483131771094858579)⟩,⟨(-55232178826612686175892446861),(-55232178826612686110509724222)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-151212596539049235069905189626),(-151212596539049234982684958780)⟩,⟨(-48434791424623471586342736343),(-48434791424623471501747024083)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-165164031003458245776859630962),(-165164031003458245660775843870)⟩,⟨(-32439879476558617120168257019),(-32439879476558617006766004764)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-172832830755053116216355442427),(-172832830755053116009330733877)⟩,⟨(-9985267273458234861251123595),(-9985267273458234656662747918)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-173842975008464575975263668687),(-173842975008464575180055842852)⟩,⟨14411474777992339042708306146,14411474777992339836159528198⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-167663749001236745090504954314),(-167663749001236740226146332760)⟩,⟨35837982061948088495387743695,35837982061948093358700639280⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-153860107400590882499127315753),(-153860107400590856544163439097)⟩,⟨50312081645574291021079689723,50312081645574316975514608958⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-132554361888688253821332427720),(-132554361888688155198857802534)⟩,⟨55938022533337013803872285038,55938022533337112426042038493⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-105233590071682363894504118678),(-105233590071682113526453827923)⟩,⟨53158977490889256101140998050,53158977490889506469008475239⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-74829740101534742990425811760),(-74829740101534326501367217102)⟩,⟨43545978240474628254003885881,43545978240475044742973123744⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-44194467918007254283718211047),(-44194467918006827965368354227)⟩,⟨28606754024690324194623321516,28606754024690750512940777885⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-14545861020367861405581833417),(-14545861020367678236351823541)⟩,⟨9984630360953658340559551135,9984630360953841509786728776⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-879111969817871991323667215),(-879111969817789555183349366)⟩,⟨(-15209854844860457639048429794),(-15209854844860375202617561033)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3273953820290479142236900349),(-3273953820290286613645246149)⟩,⟨(-44706910975001620183341568527),(-44706910975001427653857251831)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-7577316603303228514668985178),(-7577316603303038126696415624)⟩,⟨(-71457834489413932995862266158),(-71457834489413742606346496859)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-14994496403470635497827785363),(-14994496403470518612352621503)⟩,⟨(-93978519920414972506833377802),(-93978519920414855619099437948)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-26288667639564897496063883598),(-26288667639564850028821014458)⟩,⟨(-111479671973065826543558330928),(-111479671973065779073299032921)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-41060588985854620270461835520),(-41060588985854607239822302498)⟩,⟨(-123891792938210475960154927885),(-123891792938210462925721284581)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-57503863497410986464393096857),(-57503863497410983867245680905)⟩,⟨(-131181046981529077539630129901),(-131181046981529074937924140263)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-73221125791751965326964470711),(-73221125791751964858815144678)⟩,⟨(-132901091958899405939965750477),(-132901091958899405466636238300)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-86127322657350064486753939358),(-86127322657350064349476718380)⟩,⟨(-128655872743438077846226874436),(-128655872743438077703354020023)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-94683953051533934534732833399),(-94683953051533934453620767610)⟩,⟨(-118729480517075263554892724232),(-118729480517075263468046045206)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-97731059686378248137643884858),(-97731059686378248076029266132)⟩,⟨(-104255322932836225392059673594),(-104255322932836225324911118455)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-94296899670499623332534202565),(-94296899670499623284649726877)⟩,⟨(-86860216444157533629654743279),(-86860216444157533576721903990)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-83713836535186922158731904286),(-83713836535186922122862025897)⟩,⟨(-68017013581565242053421992563),(-68017013581565242013270979929)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-66042109527277829083559488287),(-66042109527277829058910735339)⟩,⟨(-48648623271575349736967668645),(-48648623271575349709070087508)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-42338574154426433367942628116),(-42338574154426433353654844027)⟩,⟨(-29176275612762726940282050162),(-29176275612762726923967083777)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-14583166467598555853770999519),(-14583166467598555849111161696)⟩,⟨(-9717806201197724126206020322),(-9717806201197724120860470862)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨7486999770056941551635745410,7486999770057181552446894693⟩,⟨(-5497177579735092376295987768),(-5497177579734852375793994481)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨22151679791482604331680836646,22151679791483520459024786959⟩,⟨(-17142258682994990820157450348),(-17142258682994074693713073785)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨35728867743316774080786973718,35728867743319136011649117760⟩,⟨(-30370075161005354830810320858),(-30370075161002992901321622214)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨47027005833313429636903648886,47027005833319194797332366186⟩,⟨(-45342933907460105794997835621),(-45342933907454340636234124158)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨54390840957582336586845681879,54390840957595630821305276575⟩,⟨(-61659303023080283871495040550),(-61659303023066989638745396418)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨56383066052525369976829888918,56383066052552723622971428692⟩,⟨(-78824899737973995201706173325),(-78824899737946641557073175922)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨52758605485132081336950007439,52758605485178652500520382556⟩,⟨(-96138602034531532982426617357),(-96138602034484961819922612166)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨44687994255736354978113289219,44687994255797770117357675182⟩,⟨(-112189671473388575912080835613),(-112189671473327160773247942008)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨34230705673576470843896233961,34230705673639214467229623311⟩,⟨(-124813518613282969463769134545),(-124813518613220225840097076859)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨23654192307135077303256708624,23654192307184688996279809996⟩,⟨(-131517120872192174469338733208),(-131517120872142562775311599899)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨14715304995004810161476204152,14715304995035137171713505750⟩,⟨(-130059645824143769838186440038),(-130059645824113442826473519815)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨8040016242166558671414479152,8040016242181846717511708781⟩,⟨(-119271130318063780457674433579),(-119271130318048492409855206250)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3298421980375103088351030008,3298421980381945250284996733⟩,⟨(-99921794409342402228575230690),(-99921794409335560064926988818)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨227747973297799734956159825,227747973300673352259036629⟩,⟨(-74496028277350390503161938131),(-74496028277347516884426636272)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1008260512592199258279213798),(-1008260512591066243623621068)⟩,⟨(-45695027080401132530283961364),(-45695027080399999514682761867)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-567689880086112290536100833),(-567689880085813475362676974)⟩,⟨(-15368377041998846131282244010),(-15368377041998547315782065675)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨14102021606455677369493718,14102021606455678620998173⟩,⟨224261194746750556045999846,224261194746750557886331420⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨210493012806101473423616541,210493012806101477356120837⟩,⟨621555316342902053040609481,621555316342902058729429239⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨935387941829450623974707121,935387941829450631102133991⟩,⟨641922486172829622398157748,641922486172829632295998870⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2759293604900282392679793646,2759293604900282403829661801⟩,⟨(-481003293607761092439234362),(-481003293607761077736858911)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨6682116216667076388133817752,6682116216667076404622324873⟩,⟨(-3517961914144615020001450570),(-3517961914144614999496815577)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨13676747270575762169264260707,13676747270575762193821607632⟩,⟨(-8363670454725494889482409017),(-8363670454725494860648645185)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨23587268523890466668046198396,23587268523890466709917743957⟩,⟨(-13917749816915625515479165367),(-13917749816915625469234484229)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨34782359382105124410897893697,34782359382105124524537724749⟩,⟨(-18976430590020244513609395384),(-18976430590020244395828889469)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨44914957082431099509019384828,44914957082431100131855769379⟩,⟨(-22852361970484960092368437697),(-22852361970484959465975129851)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨51789713750936871625802201126,51789713750936875889979355163⟩,⟨(-25332383376909916805060658991),(-25332383376909912538033499302)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨53946934320673382132976108428,53946934320673405625122658829⟩,⟨(-26479904676529258460405688939),(-26479904676529234966087839224)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨51064263636421480671538955764,51064263636421571443994738640⟩,⟨(-26380858057868202226456718507),(-26380858057868111452361483959)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨43917272346170714800223737441,43917272346170948049768235766⟩,⟨(-24732215494498296611791338334),(-24732215494498063361065835466)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨33661000229037920719103905985,33661000229038312395792388600⟩,⟨(-20778507856001441195494497011),(-20778507856001049518032665215)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨21187261988112282353886178657,21187261988112686118291179275⟩,⟨(-14029003405897210224217936196),(-14029003405896806459382708532)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨7239431247193434554980163568,7239431247193608847569041497⟩,⟨(-4970320911725889812434181468),(-4970320911725715519710583163)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-44079102188169106559356192041),(-44079102188100321756885720206)⟩,⟨52037151810326914878357498310,52037151810395699677024883393⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 0) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_0 (tableDensity true) (fullFactor false 1 0) density1_contains hk1_0_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-2361830995),2136254616⟩,⟨29444863728670913987796667041,29444863728670913992398646731⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_0 1 0 ha1_0_0_contains + def realAnswer : RBox := ⟨(-44079102188169106561818023036),(-44079102188100321754649465590)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_0 +namespace hm1_0_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-62171009855601579030614672868),(-62171009855601547029625434634)⟩,⟨27680080035565356534646958146,27680080035565388534429317038⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-178973993149932979778120505033),(-178973993149932905916796450534)⟩,⟨84476603352289551394095554040,84476603352289625251833813554⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-274300851346119464889253918058),(-274300851346119393660625893804)⟩,⟨144286204424265686798138105231,144286204424265758020939033284⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-338034053040642168996186336344),(-338034053040642127030467091213)⟩,⟨205337343596114431142842052952,205337343596114473100821975936⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-365135376458380806471869832079),(-365135376458380790427401363208)⟩,⟨261409739860828346489058387648,261409739860828362524457142753⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-355785387459172753489338628339),(-355785387459172749413989128773)⟩,⟨303300770639297507390638282771,303300770639297511456434492990⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-315321639846726055512839364533),(-315321639846726054742488181357)⟩,⟨322595330185076887739307113032,322595330185076888500644399427⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-253976864510728750808707114930),(-253976864510728750642244246841)⟩,⟨314997327373582011212384418834,314997327373582011371253904114⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-184818540058006583933800948712),(-184818540058006583860012501836)⟩,⟨281654252615704768259039506980,281654252615704768327250848050⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-120222706648974626684049077386),(-120222706648974626636725599208)⟩,⟨228931790659398341828211616891,228931790659398341872208721525⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-68766543082890832871682969546),(-68766543082890832841557496750)⟩,⟨166833327526677730533212694576,166833327526677730562103167028⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-33756961842249258404660227686),(-33756961842249258387300318274)⟩,⟨106336792567404518386476005723,106336792567404518404252264021⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-13685750002397880778232804733),(-13685750002397880769622021562)⟩,⟨56592132802216927569092997352,56592132802216927579087748568⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-4251236375062619751061732392),(-4251236375062619747673759925)⟩,⟨22874741803684412478190006814,22874741803684412483195636930⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-831382983735718235330098354),(-831382983735718234425151328)⟩,⟨5578409017730055281890532179,5578409017730055284030573611⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-49594740393543661068789369),(-49594740393543660956055475)⟩,⟨382219054951144470591746885,382219054951144471159100753⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-105445882695487667543709262167),(-105445882695487588833090987259)⟩,⟨(-49159823746869786655805578452),(-49159823746869707942028850800)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-311923005125310494945999099529),(-311923005125310198036910592989)⟩,⟨(-139741879596196768632415119553),(-139741879596196471714435083715)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-504405669102616904182213562023),(-504405669102616156323521781394)⟩,⟨(-208308721701501569405684652775),(-208308721701500821534037713024)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-672624896323527615414658626831),(-672624896323525851035561150118)⟩,⟨(-244473031088542130277066248845),(-244473031088540365883290266235)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-806113173532028746919559069875),(-806113173532024853103789666887)⟩,⟨(-243455754982859623867599128847),(-243455754982855730037928721753)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-896081553441601750240448874507),(-896081553441594145639608053844)⟩,⟨(-207080886589188258949916137861),(-207080886589180654338041468250)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-937399510953190888894563007452),(-937399510953178664833524793229)⟩,⟨(-143782391536386286541630593595),(-143782391536374062473757504857)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-929556907418652591274838191243),(-929556907418637466037139155572)⟩,⟨(-66851240042884155595191635386),(-66851240042869030355241719712)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-876800489338212559565311752082),(-876800489338198142912832040348)⟩,⟨9084180629029413141775544985,9084180629043829792396739263⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-787627827863549837926226005760),(-787627827863539232619999653629)⟩,⟨71681197347552890329139290826,71681197347563495630470309334⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-673355797730893503107955801352),(-673355797730887478114964180105)⟩,⟨113209289860081820643244001654,113209289860087845629633282340⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-546011671275227683290792604774),(-546011671275224854588566987113)⟩,⟨131061543037601393558526707167,131061543037604222253731103943⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-415978398519265325505475655364),(-415978398519264139406081582403)⟩,⟨126641623148391877971619484972,126641623148393064064628270442⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-289979131808150532291902200399),(-289979131808150060833184472569)⟩,⟨103773122177488459327636361147,103773122177488930781351178284⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-170410866307168814402737656919),(-170410866307168635958847596282)⟩,⟨67530367728977571520182381591,67530367728977749960913735977⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-56119104189373879446537602827),(-56119104189373833465016061981)⟩,⟨23367124927467408025582317109,23367124927467454006027111320⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1683020166990756340351309270,1683020166990756355660091387⟩,⟨(-124845241358368358880422436495),(-124845241358368358850900823908)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-3699793503053039411390702387),(-3699793503053039364731618781)⟩,⟨(-369117096298883640185647656838),(-369117096298883640097287647306)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-33318952088891655381497399567),(-33318952088891655301690625616)⟩,⟨(-596794973566070768966793345840),(-596794973566070768821276359044)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-96577662323826927242231354767),(-96577662323826927127377034653)⟩,⟨(-796940208966602645458486312134),(-796940208966602645259205005579)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-193654813341098453751162839778),(-193654813341098453600103565505)⟩,⟨(-958271084592915763155121991461),(-958271084592915762907699061151)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-315486628633907318452464936123),(-315486628633907318260813030934)⟩,⟨(-1069275631152944000059694884657),(-1069275631152943999767902569410)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-446930807145299089427772681413),(-446930807145299089182312954272)⟩,⟨(-1120712643062806535491562409661),(-1120712643062806535149108540547)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-570207048247706137234627329567),(-570207048247706136842072984251)⟩,⟨(-1109586998839653043584446632019),(-1109586998839653043103801378331)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-667702508316370807550889755960),(-667702508316370806253108094113)⟩,⟨(-1041046031879998275862673909507),(-1041046031879998274489709423035)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-724909992316816421213760196491),(-724909992316816413853997980897)⟩,⟨(-927299383174879220337877893333),(-927299383174879212917337220861)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-732731707105303201411715863824),(-732731707105303163795454475510)⟩,⟨(-784750752748212895833831236354),(-784750752748212858170818677904)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-688069244799419304382455620981),(-688069244799419166538563631903)⟩,⟨(-630158413142015889942208436814),(-630158413142015752063835972798)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-593242557346961134785979469391),(-593242557346960795717223013877)⟩,⟨(-476531464711331736851354130520),(-476531464711331397758441614208)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-455492976599524583703113478402),(-455492976599524033864527105561)⟩,⟨(-330686079379628259412017545337),(-330686079379627709557751589133)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-285940454703090202027977537449),(-285940454703089649240177607803)⟩,⟨(-193875162691787140508646188613),(-193875162691786587712102790153)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-97364287393888539583211421519),(-97364287393888304275792666892)⟩,⟨(-63782302739143857884964182293),(-63782302739143622574754886446)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨73018105386950800700483463832,73018105386951005944262839923⟩,⟨(-61306201007770013029540967670),(-61306201007769807779797004651)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨213765833874744006558006194264,213765833874744484032431877279⟩,⟨(-186111664649014374195979535359),(-186111664649013896703311360298)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨338629724410137832482800409594,338629724410138301049705097437⟩,⟨(-315977032323191308116604753543),(-315977032323190839518308844434)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨437705164466067318884339443867,437705164466067603383273853624⟩,⟨(-450358720506009737551697865243),(-450358720506009453007183746867)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨502215442395688610687862948938,502215442395688724618976414222⟩,⟨(-584559696448206072450206479910),(-584559696448205958458627128023)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨526230208693988564277310256602,526230208693988595078106945339⟩,⟨(-710910507242783339700298499644),(-710910507242783308824322618740)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨509367836182775156381346718015,509367836182775162471083835707⟩,⟨(-820016923934543254067756210630),(-820016923934543247889537078298)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨457756362871903606483067457021,457756362871903607631715333076⟩,⟨(-901228534070262890263551054558),(-901228534070262889015954746637)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨382176833157895151868586008685,382176833157895152257104125385⟩,⟨(-944111274603743670858802764475),(-944111274603743670365040433699)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨295312630217820600610909789113,295312630217820600859778653262⟩,⟨(-941025723332690374790487646726),(-941025723332690374435272097126)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨209255112743986587420933834724,209255112743986587610616373900⟩,⟨(-889148034470400332861264422807),(-889148034470400332569789252833)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨133645965634405953606805880512,133645965634405953751505805177⟩,⟨(-791108419420562648513952212250),(-791108419420562648277466699535)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨74752397016664181203488967935,74752397016664181309333978464⟩,⟨(-653987088327840536527735666344),(-653987088327840536344981390343)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨35014174759281465969465042580,35014174759281466040796713382⟩,⟨(-487092251014320187612459292764),(-487092251014320187483211531599)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨12800489312345404166890061763,12800489312345404207717950593⟩,⟨(-299934017481749362513761547353),(-299934017481749362436988864047)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨2807246846108832728408486636,2807246846108832741633765919⟩,⟨(-101190417137587585536824250378),(-101190417137587585511441883609)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨40653059571654022140096468577,40653059571654785916346730759⟩,⟨61760454670500486793238522990,61760454670501250565158096781⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨125812756073652613668393839755,125812756073655517386196063355⟩,⟨177588794410589150441960145095,177588794410592054147497348505⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨221276314705027957959073960728,221276314705035385274051656192⟩,⟨271080319107343760840708755954,271080319107351188137386472351⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨329982204343348722744486373719,329982204343366645618005667362⟩,⟨330708127156357099218441834382,330708127156375022070459451758⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨448763645604850874181305293331,448763645604891608792298864347⟩,⟨349792783580053597371201922962,349792783580094331960744690650⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨567438331600908035399393831740,567438331600990438228079984977⟩,⟨326852147402465077002653452851,326852147402547479813272740899⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨671452700848586380360754327104,671452700848724063619447781824⟩,⟨265130140083413327329311795331,265130140083551010576068591549⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨746531530781148505434038876077,746531530781326492615796265808⟩,⟨172951965166812442082593592249,172951965166990429260261388002⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨782289626203310835334497789025,782289626203488972898771311178⟩,⟨63728162403556492908573557531,63728162403734630477151116693⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨774215358732879349035770216519,774215358733017384349039002996⟩,⟨(-45858969071797617346064018469),(-45858969071659582020714746236)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨724154652945107418695768406136,724154652945190178859486953231⟩,⟨(-138637008336265380369244634646),(-138637008336182620187485503569)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨638635054179927463862368460817,638635054179968447688730426756⟩,⟨(-199522668313789476488047343737),(-199522668313748492640508768738)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨525303837745183496289464737799,525303837745201556690333146936⟩,⟨(-218428582132422733391800088257),(-218428582132404672969884700675)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨390622246995278524114902520754,390622246995286015280751994310⟩,⟨(-193555491203134115481336605039),(-193555491203126624297719023510)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨240510836396221390989084774619,240510836396224318815772196517⟩,⟨(-131981058225898430470312277914),(-131981058225895502631791083320)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨81153773358289108267722115405,81153773358289876935500421693⟩,⟨(-46685206155711947802478844356),(-46685206155711179130551398150)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-23715026418803238325763439244),(-23715026418803238316982751013)⟩,⟨359769947475031816024219589,359769947475031822168232473⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-70066938078233892774176425654),(-70066938078233892747305718062)⟩,⟨5267237039019460321909766705,5267237039019460341068545759⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-113342782788130917279285392430),(-113342782788130917233355015310)⟩,⟨21633798698259948423433385382,21633798698259948457657930578⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-151849147529492420363403423823),(-151849147529492420296878116728)⟩,⟨53207337786263907757172385494,53207337786263907809553829429⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-182962379450741467536512834319),(-182962379450741467447042470931)⟩,⟨98353642080971854072500292588,98353642080971854147292940683⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-201757597480570250574681027458),(-201757597480570250455249342034)⟩,⟨151126451432704718203787245055,151126451432704718309328834369⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-202748098414951724674541427245),(-202748098414951724496486482946)⟩,⟨204750738355666779842791606093,204750738355666780008724907924⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-183917679482359328512937150558),(-183917679482359328092633605326)⟩,⟨253212535816419330051470505361,253212535816419330462471287114⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-148341418977933190645231174311),(-148341418977933188480654953096)⟩,⟨290814225816428511182657722495,290814225816428513341383969981⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-102994942808383005805992958566),(-102994942808382991242852184907)⟩,⟨312538177688999430012726214291,312538177688999444573110949216⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-56838498318750950457009039278),(-56838498318750871367229898639)⟩,⟨314968956074902601289335113221,314968956074902680378580330591⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-18578009408812320642552483445),(-18578009408812019434798273528)⟩,⟨296408135666033400734751405009,296408135666033701943154211227⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6110633820540503482204232211,6110633820541267396697821051⟩,⟨256662164251175474416228991756,256662164251176238331842190634⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨16293463590432261447683342350,16293463590433530679649530540⟩,⟨197754601823486954502602225984,197754601823488223735669274233⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨14722052169842761435587518562,14722052169844060138740319731⟩,⟨124334402666540708013666855829,124334402666542006717587607806⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨5745567475732324622575154005,5745567475732883089304215868⟩,⟨42349079501940581260310431711,42349079501941139727311602170⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1225758922461319426927642474142),(-1225758922461149016326210107335)⟩,⟨(-2364385504000101227394281875644),(-2364385503999930816500404063537)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 1) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_1 (tableDensity false) (fullFactor false 1 1) density0_contains hk1_0_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-3830363889),4122875485⟩,⟨41818114715378378765384021726,41818114715378378773103596798⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_1 1 1 ha1_0_1_contains + def realAnswer : RBox := ⟨(-1225758922461319426931572838031),(-1225758922461149016321987231850)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_1 +namespace hm1_1_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-11163747849206759288809911271),(-11163747849206733074812610087)⟩,⟨3289301870356979038135307646,3289301870357005252414274704⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-32470125052417095698478075373),(-32470125052417035217810382080)⟩,⟨10071174834220024393917961681,10071174834220084875427745319⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-50480278773711849939056196243),(-50480278773711791662183167887)⟩,⟨17203421221710620396948324234,17203421221710678675212422117⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-62626193338364258936041674569),(-62626193338364224649380429471)⟩,⟨24478266927481647586928919771,24478266927481681875496464271⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-66812621676254862891613718127),(-66812621676254849818586464525)⟩,⟨31755566235843121374288300724,31755566235843134449664623485⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-62905282304009921443226040944),(-62905282304009918150706807007)⟩,⟨38915397722455786128344797633,38915397722455789423536364175⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-53135359038419462995874523064),(-53135359038419462399221724304)⟩,⟨44972467179478903220146585132,44972467179478903819628526411⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-40707902373614612237236489048),(-40707902373614612129763780075)⟩,⟨47998281730675812795761587888,47998281730675812906021311115⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-28359165892724968422933951199),(-28359165892724968385913370090)⟩,⟨46385887824816892784702336078,46385887824816892824282934258⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-17845569029278777966794655786),(-17845569029278777945414449262)⟩,⟨39976470582410298405325034592,39976470582410298428925275063⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-9950957159078135433364199403),(-9950957159078135420365369992)⟩,⟨30224455401012534187710000638,30224455401012534202517301221⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-4714084368941940695286684770),(-4714084368941940688068744043)⟩,⟨19575278273702965221293570018,19575278273702965229876972528⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1749792130461167023130050908),(-1749792130461167019684562498)⟩,⟨10425125534027094368743345971,10425125534027094373133877473⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-442041558056853377871787722),(-442041558056853376599683488)⟩,⟨4188854080272561191619741100,4188854080272561193482606093⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-58441447691732763459565506),(-58441447691732763166962940)⟩,⟨1015773452686076735688195471,1015773452686076736294227463⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-2046734475817908359646077),(-2046734475817908338871631)⟩,⟨69394192549311339843881214,69394192549311339961146552⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-10820701736512018287748472907),(-10820701736511953475430667553)⟩,⟨(-14566118923546701807102730648),(-14566118923546636995162325904)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-32515621576172856270848920249),(-32515621576172611696924631938)⟩,⟨(-41355780933636574539356764232),(-41355780933636329966487674743)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-54242680738050722210289503653),(-54242680738050105755587065675)⟩,⟨(-61587330995136482466026533297),(-61587330995135866012851218308)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-75709020279662836342089595690),(-75709020279661380726961532811)⟩,⟨(-72517357109094516199448521604),(-72517357109093060586034121597)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-96104533726621295146265381558),(-96104533726618079938797393248)⟩,⟨(-73486920562023511585456903479),(-73486920562020296379596936782)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-113844180745544761527414524231),(-113844180745538477122876706878)⟩,⟨(-65919843770740504715571325943),(-65919843770734220312292651003)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-126731342902096110453235972363),(-126731342902085999752214226216)⟩,⟨(-52421284772830614107277084471),(-52421284772820503407015274333)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-132939642001114085304425878122),(-132939642001101569096001834785)⟩,⟨(-35754489050937300346193116614),(-35754489050924784137978568945)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-131922225791020709656575247338),(-131922225791008780236804019840)⟩,⟨(-18532437288252657954800553805),(-18532437288240728534738641047)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-124412520448037540990469325660),(-124412520448028770135997282478)⟩,⟨(-3198982528102636059750545583),(-3198982528093865204597069343)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-111781631393846122207578718223),(-111781631393841144245671621489)⟩,⟨8212427009696283075397889975,8212427009701261038233630128⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-95333266323960374414010083685),(-95333266323958040234299952575)⟩,⟨14555015597494630290337386857,14555015597496964471066072076⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-76085927979277478722990012167),(-76085927979276501304771086337)⟩,⟨15974448430143633843577954622,15974448430144611262749578293⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-55030375513551618023261578366),(-55030375513551229993521135939)⟩,⟨13651900140820313245151316455,13651900140820701275655180402⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-33139182390020441266746392908),(-33139182390020294538374409733)⟩,⟨8993584466349112310741033418,8993584466349259039602799137⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-11044238695367418092234960385),(-11044238695367380302413297896)⟩,⟨3120900086212296420727236513,3120900086212334210718086680⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨15094832985587270668272260314,15094832985587270678265415068⟩,⟨(-23806154820896442679182130538),(-23806154820896442668528808969)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨43332800581506413514560893662,43332800581506413545014953654⟩,⟨(-71307796457727409050074413373),(-71307796457727409017619257882)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨65949059073191605552648344413,65949059073191605604559841407⟩,⟨(-117543479008805271561745472581),(-117543479008805271506741448678)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨79686780223921898601439697347,79686780223921898675655098569⟩,⟨(-159531374757199197541875438401),(-159531374757199197463844059442)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨81463698883376926711486540665,81463698883376926808277734414⟩,⟨(-193361071825570857023855894286),(-193361071825570856923028649494)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨69412752609170499806577881449,69412752609170499928136684633⟩,⟨(-216504324382411461331801277656),(-216504324382411461206137660120)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨45006450336244417879939110294,45006450336244418037330896159⟩,⟨(-228686750092131056295709438058),(-228686750092131056134183547868)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨13429774992326828374343126959,13429774992326828647143903522⟩,⟨(-230646795215623287993972092251),(-230646795215623287717423313379)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-18394485313803713815900419551),(-18394485313803712802518319139)⟩,⟨(-223116638069016628705411399084),(-223116638069016627689226143267)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-44117007632643724311951490305),(-44117007632643718348752227303)⟩,⟨(-206790384685945113378652745886),(-206790384685945107413602045373)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-59620942110606229101686269192),(-59620942110606198469579698051)⟩,⟨(-182511073927953121076388071302),(-182511073927953090443128582027)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-63943223979329111288234191332),(-63943223979328998912934587671)⟩,⟨(-151614835547664372067969236737),(-151614835547664259691869741725)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-58861667087464633174779276347),(-58861667087464356527861551232)⟩,⟨(-116567672801845881891429823497),(-116567672801845605243962412875)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-46988583240521098245338113420),(-46988583240520649317443491249)⟩,⟨(-80764508481824183707433899323),(-80764508481823734779212722839)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-30312024825524930247029684669),(-30312024825524478687943166340)⟩,⟨(-46833618276564429208197214850),(-46833618276563977648948378421)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-10480882551287626720437072316),(-10480882551287434455086819444)⟩,⟨(-15268999200418618794475395483),(-15268999200418426529081539849)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨31817275397815084100736978807,31817275397815256552373732507⟩,⟨(-1838953865221164854458751886),(-1838953865220992403440691465)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨93076886026113021722825945528,93076886026113422642002417786⟩,⟨(-6814852733138916214270629356),(-6814852733138515296985086203)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨147375676034548302642804164257,147375676034548695544789508250⟩,⟨(-15621454250896366599992393124),(-15621454250895973701242137787)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨191158755082854704234449825081,191158755082854942284248056144⟩,⟨(-30483312632836207354958806032),(-30483312632835969309821740057)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨222733359775300349007276132075,222733359775300444044919014820⟩,⟨(-52491948742076801121970198185),(-52491948742076706090423350506)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨242271595040572096003326771710,242271595040572121567443541002⟩,⟨(-80246392701290017372060043330),(-80246392701289991815419190315)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨250336371826828321388906568851,250336371826828326372740669892⟩,⟨(-109677069382976624986565014065),(-109677069382976620011459035379)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨246964118115793266892425682720,246964118115793267775933394784⟩,⟨(-135998520531816628350587089616),(-135998520531816627476696863920)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨232508686461373429675498193769,232508686461373429935097515532⟩,⟨(-155583456819344993251388788715),(-155583456819344993001848652738)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨208625436621250732950529275155,208625436621250733104130857588⟩,⟨(-166308809869323461320561616006),(-166308809869323461176934971832)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨178273192635148350791082308347,178273192635148350906756822971⟩,⟨(-167059758040063598370555450834),(-167059758040063598264194697056)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨144837096101464430701847251458,144837096101464430790827351937⟩,⟨(-157194750044968136820257307652),(-157194750044968136739511612273)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨110956828712990287860564871770,110956828712990287926631007685⟩,⟨(-136537637055099386302571733516),(-136537637055099386243295503297)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨77978025190937325440114955048,77978025190937325485241465204⟩,⟨(-105846721410325094935635083069),(-105846721410325094895544691109)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨46194674947494591955520858958,46194674947494591981599388967⟩,⟨(-67031847811642701827558196636),(-67031847811642701804571896606)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨15289124519363030491418152945,15289124519363030499910672758⟩,⟨(-22943743756175111753551126682),(-22943743756175111746095837321)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨14377710207917912799149558150,14377710207918540503505641059⟩,⟨19582119241913427406453614230,19582119241914055111643211905⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨44662934675297323967067538395,44662934675299710540474009845⟩,⟨57716701068955633882472558159,57716701068958020458294162744⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨78530184841088345406470788973,78530184841094450748772972105⟩,⟨92394766801260656600042982574,92394766801266761946004214134⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨115955732750264285085470626076,115955732750279020255917742888⟩,⟨120280508190007989782822511588,120280508190022724957654932836⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨155450072011578252720920763601,155450072011611746482637494777⟩,⟨137158415842492568727385133866,137158415842526062493538266268⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨195373638861618343513506876392,195373638861686098475879593136⟩,⟨139800120907656755255859309389,139800120907724510222073731855⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨233746311309342933217529100960,233746311309456117668491293566⟩,⟨128337771140816584089177183144,128337771140929768542796831965⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨267152243965111456558501091815,267152243965257701752909630441⟩,⟨106479599033043504447208059194,106479599033189749642619650587⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨290844279019369024325084403553,290844279019515276556180853535⟩,⟨79823521117348834604650087885,79823521117495086834942809225⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨299888916264790975237057857628,299888916264904182429035305902⟩,⟨53979888550095142325124131506,53979888550208349514766344099⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨290443382198571653633077269224,290443382198639441963098976330⟩,⟨32888342941688463303531012916,32888342941756251630186793729⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨261299367049673922477614132027,261299367049707446994412701969⟩,⟨17629173512201201734002045928,17629173512234726246939726688⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨215307923814608569883903800614,215307923814623324423684871271⟩,⟨7115875709198026390285765037,7115875709212780926281020601⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨158409833032850543301213021044,158409833032856656789130859985⟩,⟨488541935369617273862828926,488541935375730758656227364⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨96273745990785294212747439121,96273745990787681822979220939⟩,⟨(-2123079029154101158957513033),(-2123079029151713550769375694)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨32226059940818738156737888159,32226059940819364760774649283⟩,⟨(-1190341993573931097315007827),(-1190341993573304493981046566)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-703975079335267614072967224),(-703975079335267608293801973)⟩,⟨44255643246211007270374839,44255643246211011199074731⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1945038231387370296806208235),(-1945038231387370278999311234)⟩,⟨658340380472417937647425063,658340380472417949954388854⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1997352116441889211963713968),(-1997352116441889181180207126)⟩,⟨2907057904275771098003687414,2907057904275771120174512309⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1476978049915286464469344512,1476978049915286509772094586⟩,⟨8496509140684942112807268968,8496509140684942147185745325⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨10700900786866594379344246382,10700900786866594441806463291⟩,⟨20333493455087488295786878976,20333493455087488346058401245⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨25095666230708327360469191174,25095666230708327447105684158⟩,⟨41038901134801094128055808083,41038901134801094201924133654⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨41113868800201651614034559523,41113868800201651750753571535⟩,⟨69671436557555579278920986466,69671436557555579402853694111⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨55115103065199032306166561314,55115103065199032647953315863⟩,⟨101010002952542694307926112984,101010002952542694637902837962⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨65211092162586062014068939966,65211092162586063797411119562⟩,⟨128157499050920992596382260406,128157499050920994369868694356⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨71022643135010814011514600274,71022643135010825945286756076⟩,⟨145194980651867265943269538803,145194980651867277869392257498⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨72991964712869511391671680872,72991964712869576023270738229⟩,⟨148710546436770816285281818388,148710546436770880911241311824⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨71599494154123945411428833802,71599494154124191427813293745⟩,⟨138604331930404932869861744900,138604331930405178882105370734⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨66233663587601325997744041228,66233663587601950113583724337⟩,⟨117623215340333294603174535883,117623215340333918716099582852⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨55058694452593576555814022979,55058694452594613978678389559⟩,⟨89200363815408705109876018052,89200363815409742530868787879⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨36901600879851244350797085175,36901600879852306250370825894⟩,⟨55731964837040240713370156254,55731964837041302611918118783⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨13024700049772682401179878653,13024700049773139127339315406⟩,⟨18970946826289420870186539790,18970946826289877596028015690⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨687802679173375102626238298179,687802679173515071201800604834⟩,⟨(-267351014885275817407723947554),(-267351014885135848856742483925)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 1) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_1 (tableDensity true) (fullFactor false 1 1) density1_contains hk1_0_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-5391452557),5008937393⟩,⟨(-54685226935494803010981626582),(-54685226935494803000886797642)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_1 1 1 ha1_0_1_contains + def realAnswer : RBox := ⟨687802679173375102620746845622,687802679173515071206909542227⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_1 +namespace hm1_0_0_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-7211782288781844090409648859),(-7211782288781835752174333805)⟩,⟨(-16198456462300619164261628724),(-16198456462300610825716453277)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-21586786306445755205190458021),(-21586786306445736312087664072)⟩,⟨(-45743749804609464537138659931),(-45743749804609445643134677038)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-35455780508662094663647530773),(-35455780508662077108987022061)⟩,⟨(-67440287535897653644934303107),(-67440287535897636088871660909)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-47541569849809619955566729911),(-47541569849809610181027695739)⟩,⟨(-78336638413355433154187051040),(-78336638413355423377907190737)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-55808123856623340271188244008),(-55808123856623336811433778523)⟩,⟨(-78055502832445310650817067256),(-78055502832445307189206232033)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-58327639831669951472297933438),(-58327639831669950677549700215)⟩,⟨(-68540735680630977766504140748),(-68540735680630976970033575806)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-54453562808190121607363021522),(-54453562808190121475731201831)⟩,⟨(-53346464046040988055179259880),(-53346464046040987922176400052)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-45313107535327727501886797211),(-45313107535327727478167010889)⟩,⟨(-36642572685387514996770400516),(-36642572685387514972138593368)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-33355127705176368048135883916),(-33355127705176368039564351832)⟩,⟨(-21971317262704833022297666761),(-21971317262704833013261284484)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-21403258409155678873475042483),(-21403258409155678868986603416)⟩,⟨(-11296820348721567860228673360),(-11296820348721567855619723016)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-11679213126067454596908515351),(-11679213126067454594614073050)⟩,⟨(-4846552800375268034640166198),(-4846552800375268032422166911)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-5196311550158206818622322546),(-5196311550158206817578476296)⟩,⟨(-1664421439556992489804523069),(-1664421439556992488900292801)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1747915499094829776386804548),(-1747915499094829775984544599)⟩,⟨(-427640335707701580577687787),(-427640335707701580288620806)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-383124563493157838991233711),(-383124563493157838869959053)⟩,⟨(-72218102052610109108015715),(-72218102052610109044113372)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-38876105451550072803541232),(-38876105451550072780103622)⟩,⟨(-5877006078668921787511121),(-5877006078668921779896331)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-638851087501164476870185),(-638851087501164475478008)⟩,⟨(-83367949124661902203708),(-83367949124661901956331)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨25678508341209095856682616874,25678508341209136970467942707⟩,⟨(-55078951500949807778590801957),(-55078951500949766666472832459)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨72302491493847032632760885437,72302491493847186183638507792⟩,⟨(-161377408575172954803772014693),(-161377408575172801257543622899)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨105758144244837876937021932496,105758144244838256166911277040⟩,⟨(-256033695788287724699873442520),(-256033695788287345476630652554)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨120678262787910808022284946146,120678262787911677169008435035⟩,⟨(-331884803901540901960108889305),(-331884803901540032820706072789)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨115822092639811708494438579662,115822092639813555689823914305⟩,⟨(-383207898194313268907549742583),(-383207898194311421718843527504)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨94175825762452194147221495186,94175825762455640582308674354⟩,⟨(-406971061146043184637524972997),(-406971061146039738207502291895)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨62066512827983775971212506396,62066512827989031143784915122⟩,⟨(-403645095183125883941215185485),(-403645095183120628771617463324)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨27276405124517879313675445524,27276405124524010682728262536⟩,⟨(-377010524364077255094991218790),(-377010524364071123726865693437)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-3300023980960296612653213725),(-3300023980954814978822975791)⟩,⟨(-333241536265219858063663928322),(-333241536265214376429134484369)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-25321610376173613409353530827),(-25321610376169841267281880596)⟩,⟨(-279632144874842931759591743954),(-279632144874839159615792865192)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-37426723922803384656889147352),(-37426723922801382190155169224)⟩,⟨(-223173857208291552971236782765),(-223173857208289550502336300898)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-40591272112170038869162684775),(-40591272112169158743824179493)⟩,⟨(-169363665080965043455454484260),(-169363665080964163327972227071)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-36957583186569776831407497310),(-36957583186569429437662795741)⟩,⟨(-121504364887667744354422302852),(-121504364887667396958854482319)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-28821482301253779846327878123),(-28821482301253648604692874861)⟩,⟨(-80575432825953658373565586781),(-80575432825953527130581337992)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-18099012794630159029223991115),(-18099012794630111157789047254)⟩,⟨(-45680218356942917976749608530),(-45680218356942870104497625957)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-6146780735901410080772034381),(-6146780735901397983895570850)⟩,⟨(-14762556955030158863455649916),(-14762556955030146766306734985)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨97896493695307395441768363853,97896493695307395465230050287⟩,⟨1320036573230415706753839369,1320036573230415718763832866⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨287602275773504022877530904654,287602275773504022947307146364⟩,⟨(-2874730331695943973550042511),(-2874730331695943937179703121)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨459170344444489382063357277212,459170344444489382176839203220⟩,⟨(-25601590040362983442726209795),(-25601590040362983381243635537)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨601859967217183813839861530186,601859967217183813992439273265⟩,⟨(-72856895973581050433095105913),(-72856895973581050346117307407)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨706408800587960260754697087291,706408800587960260939667114561⟩,⟨(-142618163765144719807882365632),(-142618163765144719696037749064)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨765559278266469729282775973869,765559278266469729494694573939⟩,⟨(-225677737321316160969816075251),(-225677737321316160831793365660)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨775981038389028209826387753819,775981038389028210066775972273⟩,⟨(-309204328154884334570218982129),(-309204328154884334399139777119)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨740524771731284018206143335890,740524771731284018529930226660⟩,⟨(-380263315779308659400910177995),(-380263315779308659137894590246)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨668226490995617798443796142178,668226490995617799324412878292⟩,⟨(-428288252116235388798061556440),(-428288252116235387967418502371)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨572004546638602421439953349607,572004546638602425993529513748⟩,⟨(-446882605914338154323377088774),(-446882605914338149808696677280)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨465556675623799634687135237726,465556675623799656918282846165⟩,⟨(-434464750395956731672947597499),(-434464750395956709470621575888)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨360448842316100518505676623744,360448842316100597068848216792⟩,⟨(-393409248601025760238615855397),(-393409248601025681695967267520)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨263950941454819081083119589282,263950941454819268440962752569⟩,⟨(-328503401725713974219651031923),(-328503401725713786875744877322)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨178461013469087021168810379373,178461013469087317523247038566⟩,⟨(-245776469319861121378594646381),(-245776469319860825032980497602)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨102726627389232848530505094247,102726627389233141299271328942⟩,⟨(-151499197831502559734769031646),(-151499197831502266970836578700)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨33476593689931645227091113562,33476593689931768725501648851⟩,⟨(-51101986915426055137641245339),(-51101986915425931640759553414)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨64122566472075955106298797877,64122566472076169791112463541⟩,⟨76372789067872865788519247257,76372789067873080467024394695⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨193730728793128923604578353620,193730728793129420767056396090⟩,⟨222524110009801478206529182664,222524110009801975349797735313⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨325814858402013185925910306435,325814858402013669448566313287⟩,⟨349201569196692502102161144037,349201569196692985592048243828⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨457977006653250150010751653011,457977006653250439764003343222⟩,⟨445175096079366032298808157539,445175096079366322005082932486⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨583878867826674375679218086570,583878867826674489791738213842⟩,⟨501743284709959390541601697205,501743284709959504592819092191⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨694978095417838811229533253356,694978095417838841510314927409⟩,⟨514597530919824649623395094724,514597530919824679829435330166⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨782290896179079168393758995078,782290896179079174313252907803⟩,⟨486130026913029829587871209143,486130026913029835421319686755⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨837203103037594565137953306008,837203103037594566304242211781⟩,⟨425444678219248523153609150902,425444678219248524225938270737⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨852948786580065474101301577414,852948786580065474551808374531⟩,⟨345469450207902839096755694777,345469450207902839449765819282⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨826615712943008515352370113447,826615712943008515668382879321⟩,⟨259571461726045602378394669232,259571461726045602598297475898⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨760089259101121172345154223441,760089259101121172598029904050⟩,⟨179003193706132490080249616126,179003193706132490243297463737⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨659497074641349489548071783535,659497074641349489748519839927⟩,⟨111491270883168109386117279416,111491270883168109507323154562⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨533385724034998162396058383551,533385724034998162547855717747⟩,⟨61010489526643941665533550626,61010489526643941752185668653⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨390359469418814998629565479933,390359469418814998735201241890⟩,⟨28078291587792400162391377543,28078291587792400219710315444⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨237438529699284318051770020790,237438529699284318113816262053⟩,⟨10137461210467770192558338015,10137461210467770224934719136⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨79601829169750955905518438334,79601829169750955925914112412⟩,⟨2208490373722752381841263722,2208490373722752392256935273⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-80766889580881017748720946297),(-80766889580880018952462368721)⟩,⟨53163495973104562193154622362,53163495973105560994971270041⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-231360491191799328885173019959),(-231360491191795546696301710138)⟩,⟨163898812497672870215201499330,163898812497676652419760160336⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-350524865319528134375153122086),(-350524865319518534909410940590)⟩,⟨286086421567105245024949445710,286086421567114844513944607637⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-422962138137004619813009176829),(-422962138136981714996222796487)⟩,⟨421932026084687376042337957356,421932026084710280886184609445⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-441094547269795119536930453172),(-441094547269743804720784579453)⟩,⟨565694152574051558051840161666,565694152574102872894652113695⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-405281634476186716607153813715),(-405281634476084657991580508681)⟩,⟨703241158744832771248029789809,703241158744934829885733230590⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-322568582452995890776099306789),(-322568582452828575705912632061)⟩,⟨816322341537603352080744825984,816322341537770667165314863869⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-206189413827134819840653015080),(-206189413826922895514609132825)⟩,⟨888929200457275577832653212862,888929200457487502163546652391⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-74500499195948989444645545908),(-74500499195741366750980267419)⟩,⟨911562329986038414790582137221,911562329986246037479266740670⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨52073922807432557536917358672,52073922807590052173846758103⟩,⟨882790262524686630432861829580,882790262524844125056038566056⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨154637750926976028143841676751,154637750927068525709015130785⟩,⟨808641642602614215460811516770,808641642602706713005791408616⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨218446976808431309657441705214,218446976808476246642211801496⟩,⟨699591422018959483228244314989,699591422019004420189675021798⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨235267903617782098755482213433,235267903617801571965883838712⟩,⟨565959211120745173968615887888,565959211120764647156128224893⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨205763461928124058563762672530,205763461928132027211944422285⟩,⟨415312524028240959487360322306,415312524028248928116424369235⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨139027554023909400341740295660,139027554023912485279645690297⟩,⟨253362572887141913433923326440,253362572887144998359191759830⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨48947030143717173891263406193,48947030143717979828886269073⟩,⟨85085933358666420723080566181,85085933358667226656290083257⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-564523886771782033897733051),(-564523886771782024252687323)⟩,⟨(-37221707556311963255682100564),(-37221707556311963241781832982)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-8237038748336737823715376693),(-8237038748336737793714774303)⟩,⟨(-109624015366444108500336245417),(-109624015366444108457943769054)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-33619965003397406857658667529),(-33619965003397406804341394356)⟩,⟨(-176224236448297866529577179318),(-176224236448297866457589477082)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-81935294818555996843985402973),(-81935294818555996763025454551)⟩,⟨(-233939693845302271810759797839),(-233939693845302271707477145356)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-149690651037528275441667342023),(-149690651037528275327307665242)⟩,⟨(-278573272231754290750875841036),(-278573272231754290613650015580)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-226814722113242157202431793327),(-226814722113242157043241488559)⟩,⟨(-302919676109615643374250815117),(-302919676109615643193758095828)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-302481349415144624560419247258),(-302481349415144624314302946150)⟩,⟨(-299646497862372796679006358246),(-299646497862372796414659471382)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-367750064482391482703617818934),(-367750064482391482106250430196)⟩,⟨(-267238232822342075254510757985),(-267238232822342074643481174452)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-414952499714436773497465513204),(-414952499714436770423323746691)⟩,⟨(-211785148565260876266994037391),(-211785148565260873184540630690)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-438140186414389566197222399650),(-438140186414389545834847747527)⟩,⟨(-144491529601610407344351172811),(-144491529601610386978311172141)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-434133203958443456579399406033),(-434133203958443347791073169762)⟩,⟨(-78421965044739793568406060639),(-78421965044739684779651843520)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-402270298548576652347296780650),(-402270298548576244171254876089)⟩,⟨(-25263068890599191801342570227),(-25263068890598783626527094514)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-343705141545692144972174965196),(-343705141545691122943040279586)⟩,⟨8158041813253643042598395148,8158041813254665069914256258⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-262020712951800392044550751259),(-262020712951798711144485206895)⟩,⟨21579263373951473465675121772,21579263373953154364034886740⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-163527779763558321480312920345),(-163527779763556613682561974189)⟩,⟨19360800830788062607904237908,19360800830789770404492455998⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-55487951571466278905103931850),(-55487951571465547186017937078)⟩,⟨7528064026890054038762676914,7528064026890785757440939245⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1703493716650124112208428543319,1703493716650314607160236254560⟩,⟨444262439525994481698761182771,444262439526184976417155476314⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 2) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_2 (tableDensity false) (fullFactor false 1 2) density0_contains hk1_0_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-22919455250350083737094632206),(-22919455250350083727080895917)⟩,⟨3819909208391680617095397668,3819909208391680627182572795⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_2 1 2 ha1_0_2_contains + def realAnswer : RBox := ⟨1680574261399774028471233911113,1680574261399964523433255358643⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_2 +namespace hm1_1_0_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-856994551001052623741617082),(-856994551001045793080194504)⟩,⟨(-2908665109095788178225407484),(-2908665109095781347637484415)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-2573526940611575638825253575),(-2573526940611560167501978686)⟩,⟨(-8298715448969470967982407360),(-8298715448969455496874748328)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-4227474664223109931858415608),(-4227474664223095567823906289)⟩,⟨(-12410541737185905145471215121),(-12410541737185890781779541746)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-5667277467567264442630255971),(-5667277467567256454923958552)⟩,⟨(-14513211380003971203436015335),(-14513211380003963216173197249)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-6777616672788115822916271743),(-6777616672788113002031318458)⟩,⟨(-14285291762013248773657258511),(-14285291762013245953278414396)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-7478493636223967347973086707),(-7478493636223966704114226091)⟩,⟨(-12123633508197391855700683730),(-12123633508197391212365185779)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-7582982934274023406563688285),(-7582982934274023303171752880)⟩,⟨(-8995046367732923679764150594),(-8995046367732923576867240106)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-6895920753641934841648551079),(-6895920753641934825411280569)⟩,⟨(-5877277688851509092349023506),(-5877277688851509076539365998)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-5486481509946350015061697998),(-5486481509946350010262917865)⟩,⟨(-3373660327246803668751811748),(-3373660327246803664290239303)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3733579614144043769407289607),(-3733579614144043767130244925)⟩,⟨(-1677872939847817176487027292),(-1677872939847817174453721313)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2114421152281099791458761474),(-2114421152281099790371364817)⟩,⟨(-701798170019674138908718951),(-701798170019674137980257281)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-956366295531943656812353712),(-956366295531943656360090885)⟩,⟨(-232841377274312853999164450),(-232841377274312853637427455)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-322054964188093173095718535),(-322054964188093172942698635)⟩,⟨(-54995774662779347814121108),(-54995774662779347704355811)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-70185424508529857768773246),(-70185424508529857730680022)⟩,⟨(-7634837465799031042987801),(-7634837465799031020838466)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7081323424578317676595435),(-7081323424578317670817153)⟩,⟨(-428801655599287600584789),(-428801655599287598440019)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-115999560470716674849701),(-115999560470716674573104)⟩,⟨(-3552191911134144630011),(-3552191911134144592464)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨7608577217240367872732978113,7608577217240401725175860945⟩,⟨(-5652103451848652270601091917),(-5652103451848618417970758905)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨21397533510987271502783362133,21397533510987397982958412876⟩,⟨(-16821905214363852262273660198),(-16821905214363725781579319448)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨31267829327126891608322942436,31267829327127204197560887666⟩,⟨(-27531195146419736863262851788),(-27531195146419424273286816844)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨35795692889329734413612089274,35795692889330451451412977027⟩,⟨(-37350783435628847701434478700),(-37350783435628130662827071874)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨34957139053572462894129588149,34957139053573988151519518625⟩,⟨(-45676084844890774871564119586),(-45676084844889249613443075682)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨29968579002593552023103653812,29968579002596400123177769235⟩,⟨(-51690550070677271752585456267),(-51690550070674423651962537134)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨22606291458995209886707911869,22606291458999556498462275036⟩,⟨(-54555197616801074055381623820),(-54555197616796727443311799910)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨14535699741147782998716359215,14535699741152856728398057907⟩,⟨(-53902789995495227962707983144),(-53902789995490154232943760810)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨7075703618947572588178512173,7075703618952108510390229075⟩,⟨(-50125340337232364032334368590),(-50125340337227828110229877439)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1162797452439581522926346618,1162797452442701193784598316⟩,⟨(-44157868986797198518536962331),(-44157868986794078847915661129)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2702179302814694340456702076),(-2702179302813039853196425352)⟩,⟨(-37037722308427590583617401626),(-37037722308425936096661234900)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-4502826935267683040006070341),(-4502826935266956774625473517)⟩,⟨(-29562973416523131348598787194),(-29562973416522405083532665249)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-4660286491118784082931344161),(-4660286491118497806485112083)⟩,⟨(-22219790080270025851574799134),(-22219790080269739575407068550)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-3791323337712983040989689812),(-3791323337712875022497687407)⟩,⟨(-15289385722812803656657909794),(-15289385722812695638378831649)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-2410366661562382975661337437),(-2410366661562343612005848280)⟩,⟨(-8882896795581422697575687179),(-8882896795581383334052150123)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-820959976505269032401139882),(-820959976505259090426788986)⟩,⟨(-2905257446936704557676576649),(-2905257446936694615746973948)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨18667388359810016139454264179,18667388359810016147867542013⟩,⟨11836550610692683794770027927,11836550610692683802644145930⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨55559580530565921346303121469,55559580530565921371769881728⟩,⟨33764495618831256108887003046,33764495618831256132728513717⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨90434909132613649306882736128,90434909132613649349499392180⟩,⟨50745957557331194427048458308,50745957557331194467172735997⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨120477567242185755085877396575,120477567242185755145215019301⟩,⟨60194086970249070779362394132,60194086970249070835658731328⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨142538637494698064854162767192,142538637494698064928987073198⟩,⟨60080293461530362919653903327,60080293461530362991300757663⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨155006961483811410395822818743,155006961483811410486352371596⟩,⟨49742390138700597065032144235,49742390138700597152374520726⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨158336809378683827737224613539,158336809378683827849611884292⟩,⟨31223651823637274949113242059,31223651823637275058346773176⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨153918709299029395847857951305,153918709299029396032591534633⟩,⟨9031786393445244759721548944,9031786393445244941622808258⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨143196979486858690665269437491,143196979486858691314636785659⟩,⟨(-11740350746837603200211748135),(-11740350746837602552995330203)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨127540659550362963888157308391,127540659550362967545976899251⟩,⟨(-27157778102341045655843033095),(-27157778102341041999511577477)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨108261707541668235441313444076,108261707541668253520647269285⟩,⟨(-35330313161602114621110376897),(-35330313161602096542772049325)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨86716694473710803604757098163,86716694473710867634525840538⟩,⟨(-36550659609430241366143998425),(-36550659609430177337090780839)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨64565866958651829281907785843,64565866958651982134998707482⟩,⟨(-32590395372119577453602927960),(-32590395372119424601008803890)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨43586798989033039762086681056,43586798989033281718954710373⟩,⟨(-25352732134665756234861129666),(-25352732134665514278293541206)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨24815591895168255898672455506,24815591895168495049857280896⟩,⟨(-16059737481432925732078051587),(-16059737481432686581047052704)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨8014059073626076830317444640,8014059073626177737144931344⟩,⟨(-5500910077010351323953448467),(-5500910077010250417170172142)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1923391472192101411713167456,1923391472192281789929083556⟩,⟨33279065047974489861921670215,33279065047974670240796098879⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨7092710554850210605934322670,7092710554850628038343121611⟩,⟨96890428483227636816741264943,96890428483228054251152260833⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨16102837154726975022306743374,16102837154727380434337631285⟩,⟨151976603376598375412400555701,151976603376598780827821533287⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨30986432778075953581073207438,30986432778076195983440455731⟩,⟨194419144026024262294327746135,194419144026024504701503465525⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨52408401768396262667330964514,52408401768396357798879704117⟩,⟨222514887934990742027461435666,222514887934990837165169495744⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨78417874168631822019412436002,78417874168631847082157365457⟩,⟨236892755170122207893181276096,236892755170122232963291477086⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨104599218833399421171064738445,104599218833399425936446736882⟩,⟨238874997001987623462747650178,238874997001987628236485849701⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨126307501855849782883920151404,126307501855849783699599974681⟩,⟨229475539113211352457085077531,229475539113211353281693498846⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨140535050415272937603566417200,140535050415272937830378723935⟩,⟨210110393761401340986595701599,210110393761401341222450195274⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨146067059011161252458374243600,146067059011161252585535812090⟩,⟨183304911984705332510711629870,183304911984705332646548452814⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨142792812917123252251558669688,142792812917123252343356802266⟩,⟨152429525655277398970558211254,152429525655277399070192712469⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨131029496608237057888936377983,131029496608237057957009935703⟩,⟨120761671342190542200746941279,120761671342190542275533285102⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨111350426395867858295257885756,111350426395867858344229250215⟩,⟨90505479368364514139907274950,90505479368364514194258985492⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨84822701511838164159004009482,84822701511838164191600541601⟩,⟨62495986185195603252617231708,62495986185195603289112710878⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨53063922467822108863610008774,53063922467822108882095745685⟩,⟨36570186309630175726648763781,36570186309630175747489552065⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨18048748995918708975904593987,18048748995918708981866821307⟩,⟨12027278647044109066621256837,12027278647044109073366697901⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-25608356016992977847065162476),(-25608356016992156987495064004)⟩,⟨18802249973162791689298880806,18802249973163612547746364733⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-75191286837557546249390257385),(-75191286837554437642533106674)⟩,⟨58183206150480121691578358903,58183206150483230295196302524⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-119467190879748762304077001372),(-119467190879740871405075160380)⟩,⟨101531435958385135572759312441,101531435958393026466891188605⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-153822201056582408502307431571),(-153822201056563577436239985225)⟩,⟨148269106806028381199586489220,148269106806047212259883616353⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-172941038331461344950837700410),(-172941038331419151663729966859)⟩,⟨195957623935134539098363802884,195957623935176732379720830787⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-173319887392335919880801865854),(-173319887392252003096779971301)⟩,⟨242131068186304004733542365827,242131068186387921512675706209⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-156099075495281423372062946925),(-156099075495143879583189601307)⟩,⟨284168823029511041130866657527,284168823029648584916430376501⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-126861091174351548508877288730),(-126861091174177418269103925398)⟩,⟨318090976322781844262295633634,318090976322955974500846901302⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-93075009643945837379981586706),(-93075009643775377354791365536)⟩,⟨338880618873416612532508419052,338880618873587072558651930386⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-61594564378027234331819850549),(-61594564377898067663065939464)⟩,⟨341920586596600121548416691634,341920586596729288219885263334⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-36753551782619149343033947853),(-36753551782543385021973794268)⟩,⟨324313633073525122121899961020,324313633073600886446797341997⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-19328070665580423328788047267),(-19328070665543665105408904535)⟩,⟨286235303674433316257303503103,286235303674470074485008664632⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-7675877684498427087457930827),(-7675877684482518346558596016)⟩,⟨231973316762163802293434106953,231973316762179711038511315373⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-523950773491128973663904867),(-523950773484625830203495039)⟩,⟨168424715466598690940740235202,168424715466605194087606066773⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨2235276454546587635784412742,2235276454549103356253517952⟩,⟨101418832750021734798147299700,101418832750024250520823377416⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1247965468046272534929582498,1247965468046929516166580488⟩,⟨33787544070472515089018152600,33787544070473172071010484030⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-69442605055469375135799895),(-69442605055469368969347239)⟩,⟨(-1104919239348304505132840731),(-1104919239348304496058727720)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1029518195093085996161757295),(-1029518195093085976904103210)⟩,⟨(-3043317852794258750637595182),(-3043317852794258722768356260)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-4517390863097742822493236732),(-4517390863097742788010409723)⟩,⟨(-3107410631223889041915574934),(-3107410631223888994045073641)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-13081484667049752940880339677),(-13081484667049752887880220986)⟩,⟨2267613950058345089303036134,2267613950058345159099828656⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-30937551562511312514359683334),(-30937551562511312437722913035)⟩,⟨16275157095544301029939466134,16275157095544301125078393829⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-61572483185437120704443399794),(-61572483185437120593344294835)⟩,⟨37651175176368568209958327001,37651175176368568340118415838⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-102899134406541161864185960796),(-102899134406541161680772616238)⟩,⟨60727796227262051079398152507,60727796227262051281502525720⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-146673210289790937049736802766),(-146673210289790936570646438856)⟩,⟨80040135445191753829974461105,80040135445191754325902046741⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-182843093284189617555688648618),(-182843093284189615030683927402)⟩,⟨93045072136739813400761226996,93045072136739815939408721462⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-203535764231769008546296894032),(-203535764231768991868346469644)⟩,⟨99563158113135230235557845162,99563158113135246923753743220⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-204972914553825668140636464164),(-204972914553825579247175046862)⟩,⟨100603574569175954371233195339,100603574569176043271991077716⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-188111017809591842574103457322),(-188111017809591509196512393034)⟩,⟨97164741291076212973804738329,97164741291076546356596035497⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-157516504469441095475189020283),(-157516504469440260486450955973)⟩,⟨88689022008340791772189653631,88689022008341626764498148710⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-118189594722587561353145214458),(-118189594722586187452653760560)⟩,⟨72947509625216192720545904553,72947509625217566623281669884⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-73300178522794728358376286084),(-73300178522793331960512491543)⟩,⟨48532733662058495449967190595,48532733662059891849040813846⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-24856713241325085934703000795),(-24856713241324487519821726235)⟩,⟨17065584502706626361470587036,17065584502707224776722514062⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨24506821277223636715783774797,24506821277380056924018364102⟩,⟨966908065558721641826752728991,966908065558878062069839800952⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 2) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_2 (tableDensity true) (fullFactor false 1 2) density1_contains hk1_0_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨29971595327380878720028863892,29971595327380878733123749808⟩,⟨(-4995265887896813127854133655),(-4995265887896813114663212335)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_2 1 2 ha1_0_2_contains + def realAnswer : RBox := ⟨54478416604604515435712638689,54478416604760935657242113910⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_2 +namespace hm1_0_0_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2813658789607566709707642405,2813658789607568158243502402⟩,⟨(-1252650623884262723730665460),(-1252650623884261275247831111)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨7794942995824437811983593165,7794942995824441034313229945⟩,⟨(-3677721952583751250514982786),(-3677721952583748028336308428)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨11056244391577665201860862098,11056244391577668087174593676⟩,⟨(-5809587676634360328681242768),(-5809587676634357443592387695)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨12107538812620525478705997046,12107538812620526997601444244⟩,⟨(-7341179424393070435575650211),(-7341179424393068916941156668)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨11131962452044500919021056861,11131962452044501417234904948⟩,⟨(-7948635334218508184524740900),(-7948635334218507686563964008)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨8812805092199562250543980942,8812805092199562354415797480⟩,⟨(-7486561194518554672222757548),(-7486561194518554568557361290)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨6027290379054803089300313836,6027290379054803104629775302⟩,⟨(-6138531010066962489181548885),(-6138531010066962473989824919)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨3533521991447148391368885408,3533521991447148393803333714⟩,⟨(-4356944606322401775606147667),(-4356944606322401773242248684)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1747917929182682274667717468,1747917929182682275407450745⟩,⟨(-2643540302250958258390993722),(-2643540302250958257672821903)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨711635544517191818673488143,711635544517191818973908908⟩,⟨(-1341624375023903542605157458),(-1341624375023903542300576024)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨229629745279225878504838629,229629745279225878614341036⟩,⟨(-549763967315321679291939430),(-549763967315321679171362672)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨55425138687157417539851672,55425138687157417571528597⟩,⟨(-171569865088750119137329215),(-171569865088750119097241902)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨9100659788413774053480922,9100659788413774060041597⟩,⟨(-36801883548899712183937301),(-36801883548899712173586418)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨849953705525139536435618,849953705525139537257436⟩,⟨(-4454509295654517503389098),(-4454509295654517501577286)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨29894784677025380581397,29894784677025380625630⟩,⟨(-195708804398209579773934),(-195708804398209579618557)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨104738191244981903107,104738191244981903508⟩,⟨(-799909650651730134604),(-799909650651730132288)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨19180118013037391901365716077,19180118013037406217176518738⟩,⟨8942085953204126849085076126,8942085953204141165482616446⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨55661419681329697187486258584,55661419681329750125906686173⟩,⟨24939983052343592089506542514,24939983052343645029547490161⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨86644999038275263679365245485,86644999038275391882690582335⟩,⟨35797226081850646947704086367,35797226081850775153302600101⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨109181679385764724165462874721,109181679385765009618231148141⟩,⟨39716869037788188046203457475,39716869037788473501405750917⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨121463104248660904426953148758,121463104248661488702283967490⟩,⟨36739555152696381959112538012,36739555152696966236582917520⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨123247392173733749683360196825,123247392173734791183932829244⟩,⟨28558538742191455522521015174,28558538742192497024643579453⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨115904569839960137591421868481,115904569839961644139000974837⟩,⟨17866169255183284156940604244,17866169255184790705382998880⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨101972376886953265253427242334,101972376886954922789558987578⟩,⟨7421614616629942082680184516,7421614616631599619066659544⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨84467346538079230660107474238,84467346538080620693904907087⟩,⟨(-797839327231156977509967039),(-797839327229766943887952487)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨66211616906700744342436105277,66211616906701639153017926132⟩,⟨(-5965548590568359330945429443),(-5965548590567464520770066646)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨49330862645829704858529924998,49330862645830148719586329150⟩,⟨(-8251957667770211423717575787),(-8251957667769767563135303235)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨35034394307698978030169081769,35034394307699160653091559285⟩,⟨(-8383897496853349289846007785),(-8383897496853166667359977418)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨23666477634824225061269838558,23666477634824292910467813744⟩,⟨(-7192027741776784003479546921),(-7192027741776716154628536239)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨14928479506230415917546758998,14928479506230440277926775034⟩,⟨(-5337339241983883889053362097),(-5337339241983859528915766347)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨8163861362268404880525916880,8163861362268413443059772295⟩,⟨(-3234053730093841990602552600),(-3234053730093833428209416326)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2588954775311751091299203546,2588954775311753213051733875⟩,⟨(-1077958855672083500629756779),(-1077958855672081378923114107)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-690226605506775657783941658),(-690226605506775651502578189)⟩,⟨51176595502264171505264994175,51176595502264171517693256078⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1489105283725316386451106348,1489105283725316405351476933⟩,⟨149393778019955482521368871612,149393778019955482558096610641⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨13114733040110819223776568348,13114733040110819255354204821⟩,⟨235526705112670283488998858951,235526705112670283547988900876⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨36642883294830204383349618115,36642883294830204427262183178⟩,⟨303033515341342663401330457253,303033515341342663479198579289⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨70025443850871946268765853888,70025443850871946323974241406⟩,⟨347183163309527476558785832121,347183163309527476650960471354⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨107631895154447637946997258890,107631895154447638013266565734⟩,⟨365437175465099201575355777689,365437175465099201677949073897⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨142627987651763889017708149293,142627987651763889097203863906⟩,⟨358230044391870595902659020702,358230044391870596015143989474⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨169082129879393572831597527578,169082129879393572949091476857⟩,⟨329518128987603025593047922568,329518128987603025738465332287⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨183170308937213033005038650769,183170308937213033359521153996⟩,⟨285984966327784909630422968960,285984966327784910007027337175⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨183682880074099141929420038150,183682880074099143775924375416⟩,⟨235258223217133822248172649775,235258223217133824111252172638⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨171761300772854486034919717899,171761300772854494772215405307⟩,⟨184151191300380979816511042319,184151191300380988565636933808⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨149971623506778113666065626518,149971623506778143504253302305⟩,⟨137464195727524795179971542293,137464195727524825026291350502⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨121279481150300440080073183759,121279481150300509092918661470⟩,⟨97475329472240197404723993541,97475329472240266422922042063⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨88414963314868122318854159481,88414963314868228803819696028⟩,⟨64209256636417937208112829670,64209256636418043696382459743⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨53513200593994704984686039763,53513200593994808354209595804⟩,⟨36287725422352796386336142617,36287725422352899757638206672⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨17880738358959379724006452086,17880738358959422934171829195⟩,⟨11713640551052907183887421758,11713640551052950394610216342⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-53254423830151240422744991163),(-53254423830151090724720121925)⟩,⟨44712230607271480858172977138,44712230607271630560645489195⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-154428139176576554170923798667),(-154428139176576209087909340858)⟩,⟨134441706605341638615672456967,134441706605341983712170353317⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-240071715672954300161041683182),(-240071715672953967565243652483)⟩,⟨223975211676298151626709887412,223975211676298484245309428216⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-301854756896016229481356050318),(-301854756896016032804771633523)⟩,⟨310489377020371734211058305601,310489377020371930919915506632⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-334191975190868732089434261680),(-334191975190868655972868919548)⟩,⟨388811942779679944570978702113,388811942779680020728970156489⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-335496232605194588922985297448),(-335496232605194569173712874775)⟩,⟨452955304741002135675335144218,452955304741002155474133001280⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-309318534401463426482545475416),(-309318534401463422757082421690)⟩,⟨497561021806978585290796240995,497561021806978589072025520608⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-263625668953184464612503336037),(-263625668953184463945085500333)⟩,⟨518516638632348087359307106033,518516638632348088086181487514⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-208205575540568578596046886830),(-208205575540568578382206791954)⟩,⟨513759967238440586268574130027,513759967238440586542593256199⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-152113796128576907887570679016),(-152113796128576907758027241965)⟩,⟨484108513557046391767359904461,484108513557046391954766382038⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-102089076798853821143436370294),(-102089076798853821049997788669)⟩,⟨433200667624346657392690114972,433200667624346657538925462108⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-62009009184729166931819931140),(-62009009184729166864133639213)⟩,⟨366537900442478231345578582244,366537900442478231458821048107⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-33197605604187765818715787019),(-33197605604187765771421688776)⟩,⟨290025845778289031408732200995,290025845778289031492763504552⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-15011159250491340744097638342),(-15011159250491340713391227976)⟩,⟨208561993922063915884259810154,208561993922063915941797300108⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-5352340002782839964123896527),(-5352340002782839947007556241)⟩,⟨125310826772860823703810593297,125310826772860823737226552700⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1158295912521367388389705976),(-1158295912521367382921078917)⟩,⟨41746091111456366065672116406,41746091111456366076593089555⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-46349248949227445699540816805),(-46349248949226574933725879565)⟩,⟨(-70414987297951450906470973100),(-70414987297950580145409867920)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-142343243098653608540060452434),(-142343243098650324219562948908)⟩,⟨(-200942941420657815755726387478),(-200942941420654531448600707217)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-246587725514617041654389125471),(-246587725514608770307493679357)⟩,⟨(-302170155404022951382476874322),(-302170155404014680055273086859)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-359673995503664137813037272825),(-359673995503644623130547244687)⟩,⟨(-360639001965085004022096014358),(-360639001965065489362304101889)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-475404585431294802808874188077),(-475404585431251706516958928012)⟩,⟨(-370825997029122890961740613136),(-370825997029079794691920604543)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-581046162446967613402318256019),(-581046162446883342440424111325)⟩,⟨(-335029613601373405710164411938),(-335029613601289134766339310819)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-661654654215250639746791131593),(-661654654215115085752608132774)⟩,⟨(-261642502519876042502570345376),(-261642502519740488519940812656)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-705685993558728853118017986495),(-705685993558560625196882345545)⟩,⟨(-163882269777982336701870975329),(-163882269777814108784568995467)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-708159707970095837246367989164),(-708159707969934505441654424692)⟩,⟨(-58064207885365564057015826731),(-58064207885204232248459771953)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-671086865461305779839639661257),(-671086865461185977176857099512)⟩,⟨39421607420206583696658037542,39421607420326386369878394464⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-602010995079621495207693244626),(-602010995079552572504995418245)⟩,⟨114993925000949521635839565757,114993925001018444353606572415⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-510924535499877802327121407224),(-510924535499844953855357963896)⟩,⟨159448440695330944361797125548,159448440695363792850708860037⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-406515081314620531274724405521),(-406515081314606533355599147244)⟩,⟨168940135928469824574130367180,168940135928483822509849559525⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-294378771342778363758821847224),(-294378771342772712682977955964)⟩,⟨145829175459330386086472003614,145829175459336037176027238086⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-177934767578354275070651852691),(-177934767578352108092870656694)⟩,⟨97633914051592613460147029933,97633914051594780446923040911⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-59472441012540527159932061166),(-59472441012539963822805250537)⟩,⟨34212306875725722154146159835,34212306875726285494401913802⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨38947340333403840962036110520,38947340333403840976704923360⟩,⟨(-590538973928021500326250791),(-590538973928021490232205700)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨114342538520220667492309323047,114342538520220667536893228987⟩,⟨(-8587540849633901228489001953),(-8587540849633901197170498425)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨182662049735260715114504893544,182662049735260715189719057278⟩,⟨(-34831530085389507550257606024),(-34831530085389507494883524136)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨240274809563649805402496261467,240274809563649805509390598421⟩,⟨(-84116886634119024962578445190),(-84116886634119024879158498485)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨282769098496366810342854211405,282769098496366810483162611308⟩,⟨(-151884584915430803140972220331),(-151884584915430803024400707847)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨303208931622502037433049417535,303208931622502037614892792576⟩,⟨(-226944090842618407356294810886),(-226944090842618407196222697258)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨295243464520289075173841165571,295243464520289075435480760193⟩,⟨(-297913641272601943355845819916),(-297913641272601943112480365111)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨258877041249488419539393415526,258877041249488420131611606514⟩,⟨(-356073925612077680543588792910),(-356073925612077679964746240414)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨201580615424988690137589566181,201580615424988693064030858992⟩,⟨(-394731144233190565928113561474),(-394731144233190563009545614466)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨135141426608128613826642794052,135141426608128632814516001360⟩,⟨(-409489615604921939468230868602),(-409489615604921920483598378619)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨72135811423530397165113369472,72135811423530496927060580190⟩,⟨(-398930011216649729838244617747),(-398930011216649630076407927709)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨22902763258982291166491859721,22902763258982659925007530600⟩,⟨(-363967206009833684861609187555),(-363967206009833316101670733475)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-7260984237682450233603324729),(-7260984237681538655113761737)⟩,⟨(-306848689078821247253514618807),(-306848689078820335673116036170)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-19053355668801910244531874865),(-19053355668800426177275648302)⟩,⟨(-231449578534668289798901808516),(-231449578534666805729920496937)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-16974155403606809355233891283),(-16974155403605312181232568217)⟩,⟨(-143384321370493030199723598860),(-143384321370491533024568881591)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-6575708490380721267108488818),(-6575708490380082121439084005)⟩,⟨(-48468801736877098831887762055),(-48468801736876459685817477527)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-754851122848659785254898197641),(-754851122848512588266090928966)⟩,⟨586066042111081134082941068339,586066042111228331189769831315⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 3) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_3 (tableDensity false) (fullFactor false 1 3) density0_contains hk1_0_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-18929147600076571115008488567),(-18929147600076571106005754767)⟩,⟨(-25644013782660850703848252400),(-25644013782660850694442610273)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_3 1 3 ha1_0_3_contains + def realAnswer : RBox := ⟨(-773780270448736356370006686208),(-773780270448589159371996683733)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_3 +namespace hm1_1_0_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨505230440849965583427402882,505230440849966770001886248⟩,⟨(-148855358932101516799979390),(-148855358932100330212709703)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨1414090258641558213458401749,1414090258641560852008187327⟩,⟨(-438446539913158318548908153),(-438446539913155679962314829)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨2034490534938358865775789218,2034490534938361226413303949⟩,⟨(-692696856324533538496578957),(-692696856324531177802724793)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨2243145086509750896192604108,2243145086509752137119341484⟩,⟨(-875094866864487422747034686),(-875094866864486181751492296)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2037688909602779566721058246,2037688909602779972625573972⟩,⟨(-965059503140114177449494772),(-965059503140113771472245245)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1559488661075623382349202708,1559488661075623466232060225⟩,⟨(-959212462993748346046184782),(-959212462993748262094956260)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1016918002280524649212348236,1016918002280524661059145772⟩,⟨(-853896030223237697912428730),(-853896030223237686007888746)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨567153722551755203737139156,567153722551755205291004722⟩,⟨(-662220795917677843492069349),(-662220795917677841894565115)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨268571288982403813611975881,268571288982403813971705476⟩,⟨(-434293497070077764308798098),(-434293497070077763919696662)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨105758222944501713965263227,105758222944501714094865000⟩,⟨(-233791808480464685989669325),(-233791808480464685842570340)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨33272685896744043558360980,33272685896744043602928794⟩,⟨(-99463034440878785786587206),(-99463034440878785733056412)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨7766320390012709148089245,7766320390012709160326545⟩,⟨(-31570096292167004672714132),(-31570096292167004656729479)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1176508210292738206626357,1176508210292738209006522⟩,⟨(-6781967295377525058197800),(-6781967295377525054625983)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨91102364680337909192271,91102364680337909459286⟩,⟨(-816304478399508436565241),(-816304478399508436048368)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨2238349814873373424998,2238349814873373436310⟩,⟨(-35657396259344916326056),(-35657396259344916290137)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨4545148400627318163,4545148400627318227⟩,⟨(-145252982718543604903),(-145252982718543604437)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1968223221082865109491963309,1968223221082876897403195738⟩,⟨2649553094148198640652455112,2649553094148210428501783664⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨5801957104956657195504501864,5801957104956700802332119023⟩,⟨7380867563938679918424016193,7380867563938723525081710071⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨9316186983055531086842258178,9316186983055636763206334870⟩,⟨10583596396173873513822523028,10583596396173979189949374051⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨12285696572922662487963645670,12285696572922897985192088218⟩,⟨11780601422414682668845925284,11780601422414918165821901501⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨14474560037515332711589929089,14474560037515815156919161089⟩,⟨11087482712844687322647252896,11087482712845169767755330202⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨15649833118754918488960817115,15649833118755779172561143311⟩,⟨9084766140822015326502989937,9084766140822876009944128701⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨15660808807098919005724918172,15660808807100165084159708541⟩,⟨6500930654200219649267315573,6500930654201465727614930061⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨14575371365859928620763964024,14575371365861300236012135254⟩,⟨3940846321489848627231523510,3940846321491220242458056315⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨12701885470762835841548051066,12701885470763986063062280615⟩,⟨1801634866753452353492744073,1801634866754602575033339617⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨10452816966062175811945632137,10452816966062915848915452044⟩,⟨281727270251093057294387884,281727270251833094319137046⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨8184552775009833081895294029,8184552775010199812488865367⟩,⟨(-592945118269873971279369096),(-592945118269507240619391834)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨6113753777277765556683224054,6113753777277916254639883938⟩,⟨(-928992289452318357840969619),(-928992289452167659819563990)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨4327093463820340671693719714,4327093463820396583974734958⟩,⟨(-906608488674277193364197281),(-906608488674221281028893907)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨2832400403713550909097035177,2832400403713570958665651953⟩,⟨(-702045995827616879762073285),(-702045995827596830153860588)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1587464454882567636241349725,1587464454882574676848405443⟩,⟨(-430695142249824617284141721),(-430695142249817576653385737)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨509501519574464601006404047,509501519574466344733591716⟩,⟨(-143971366452902625577292933),(-143971366452900881842215184)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-6187726604462921802310363053),(-6187726604462921798174175901)⟩,⟨9758587980293868687498992409,9758587980293868691928268510⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-17539443460055879934236158932),(-17539443460055879921793174121)⟩,⟨28859774556840155915775488472,28859774556840155929097019065⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-26032264216026040127262053988),(-26032264216026040106586401143)⟩,⟨46386469576368231803700168346,46386469576368231825712216072⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-30314250397930248769572909181),(-30314250397930248741103200147)⟩,⟨60658512189840567519964838452,60658512189840567550046060002⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-29541643560244555486808137127),(-29541643560244555451450303460)⟩,⟨70053686469080375288470897707,70053686469080375325489703970⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-23766119179166237526624528408),(-23766119179166237484783446937)⟩,⟨73991287317050488454119867771,73991287317050488497600780139⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-14442575836897139154267231819),(-14442575836897139103721768094)⟩,⟨73093180056856394611356866919,73093180056856394663492588598⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-4049609136511939169578515539),(-4049609136511939088708010453)⟩,⟨68485231289911772347423424264,68485231289911772429701359654⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨4996060390787952304253473989,4996060390787952579859172875⟩,⟨61277573653777680200514425349,61277573653777680477191010047⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨11146716427333316541312059509,11146716427333318036066954182⟩,⟨52448471841625850799723150789,52448471841625852295232317331⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨13959087282609654382887779525,13959087282609661496587169078⟩,⟨42817539075699921925919784549,42817539075699929040136103719⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨13929897751646605391853420959,13929897751646629715691650907⟩,⟨33068598519464753579734057042,33068598519464777903943528804⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨12030580190217435032337850185,12030580190217491338812657950⟩,⟨23843373103586285657344661445,23843373103586341964073966971⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨9119773242268028848989194364,9119773242268115790009793072⟩,⟨15682533820406880223807879020,15682533820406967164981273632⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨5672543043994738191853522085,5672543043994822631372017938⟩,⟨8766120269499909334571794415,8766120269499993774168588811⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1924778691532845351336220273,1924778691532880657397038373⟩,⟨2804168274159856211688697344,2804168274159891517772446807⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-23205353818236679315107865683),(-23205353818236553534707465557)⟩,⟨1341138056868629299150763548,1341138056868755079084040304⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-67240431853472660075474471857),(-67240431853472370320943378377)⟩,⟨4921285627965968978836444207,4921285627966258731954593624⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-104481971363746270849523128424),(-104481971363745991961486690714)⟩,⟨11066161183930502157345825049,11066161183930781043014492913⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-131826231237808365696515001254),(-131826231237808201130321430265)⟩,⟨20999013475978503855341992993,20999013475978668418229190332⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-148202603797035282571731009641),(-148202603797035219077920326184)⟩,⟨34884458008935772021067934979,34884458008935835510730138267⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-154429090004395187014744556118),(-154429090004395170623678756025)⟩,⟨51089606743474723100493467169,51089606743474739486721756580⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-151967264841161836071770665714),(-151967264841161833023300623191)⟩,⟨66507953191452976956175144293,66507953191452979999311446771⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-142159176817687573245002102474),(-142159176817687572731887330550)⟩,⟨78209594150435870990610805389,78209594150435871498199089763⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-126588252625003559558708671177),(-126588252625003559415848776499)⟩,⟨84633714372190125990521425828,84633714372190126127962310190⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-107378622347589401537381029650),(-107378622347589401457294836548)⟩,⟨85531523975632287121721793717,85531523975632287196778098537⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-86893268668463817891291074588),(-86893268668463817834078439746)⟩,⟨81371973620288955578263061524,81371973620288955631080894490⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-67128594893454830200020565709),(-67128594893454830158116842720)⟩,⟨72816408931463010311074838296,72816408931463010349331927582⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-49217415641050314215593865405),(-49217415641050314185785461633)⟩,⟨60541682791542790132849495051,60541682791542790159817908340⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-33392502700521970411453569171),(-33392502700521970391777973115)⟩,⟨45317270416615074262601120278,45317270416615074280266770107⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-19300757824015999515512656457),(-19300757824015999504410208310)⟩,⟨28004604246635977540985638189,28004604246635977550894188315⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-6307557753172499980967901993),(-6307557753172499977396380899)⟩,⟨9465401374329569406118825248,9465401374329569409296763914⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-16392258432886925735524916816),(-16392258432886210102663712235)⟩,⟨(-22326085352187808434983935107),(-22326085352187092801115588436)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-50531007877630034049271738912),(-50531007877627334658184003907)⟩,⟨(-65304551916283264932294901670),(-65304551916280565538313224997)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-87513757247205696663402962573),(-87513757247198897519042887042)⟩,⟨(-102982119242306801010799323254),(-102982119242300001862121631725)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-126393195782206455073246949458),(-126393195782190411214011091963)⟩,⟨(-131146699645600457642392281632),(-131146699645584413778098473148)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-164683868696695079120105066377),(-164683868696659643490905459320)⟩,⟨(-145375530928151486068051564195),(-145375530928116050433885906044)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-200057954028261440899505824296),(-200057954028192149865536586111)⟩,⟨(-143255061422394526175129474541),(-143255061422325235137015662963)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-230319934620086572419822585761),(-230319934619975138235526478521)⟩,⟨(-126581300345962979349272460835),(-126581300345851545162229753294)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-252504535353636337881711338497),(-252504535353498111178759889278)⟩,⟨(-100766388944363644190594287519),(-100766388944225417486650520485)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-263244304063623313465601677018),(-263244304063490858427710191895)⟩,⟨(-72353776129513168105987757898),(-72353776129380713068849747589)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-259905539461600835571156759162),(-259905539461502581143475864556)⟩,⟨(-46857386140566116410713931440),(-46857386140467861985136079775)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-241430683304483257323500758550),(-241430683304426802922007512108)⟩,⟨(-27382932597316009777606605326),(-27382932597259555379028503681)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-209039612307114649622024454389),(-209039612307087779671529345101)⟩,⟨(-14127499747009037418173682366),(-14127499746982167470908443503)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-166622258801722702888410526956),(-166622258801711267183208136630)⟩,⟨(-5520062784391076790471299654),(-5520062784379641088340895933)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-119383117036039656246927467600),(-119383117036035044437084086462)⟩,⟨(-374593035038778796429873609),(-374593035034166989059469143)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-71226218528810409597537555402),(-71226218528808642450751026707)⟩,⟨1568941480275379689051574937,1568941480277146834250151611⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-23616470217226614564068154198),(-23616470217226155342063147970)⟩,⟨872252712063680134692193122,872252712064139356156327193⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1156145835501058470015629011,1156145835501058479514063331⟩,⟨(-72642729372476090803097524),(-72642729372476084350556525)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3174505154058320148920657005,3174505154058320177999123291⟩,⟨(-1073314553844804974833488466),(-1073314553844804954744164714)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨3222948483482921813350807266,3222948483482921862979045918⟩,⟨(-4679855734074955012433164715),(-4679855734074954976678349227)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2320983253634308391101825260),(-2320983253634308319411765412)⟩,⟨(-13427222218312834957759348632),(-13427222218312834903286621046)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-16502298255010672753241153843),(-16502298255010672656633095109)⟩,⟨(-31381564090956964801538100978),(-31381564090956964723650997554)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-37659545488086314986768507456),(-37659545488086314856400509852)⟩,⟨(-61587758793820106406445763647),(-61587758793820106295047835265)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-59800565830865818485810294683),(-59800565830865818286632493637)⟩,⟨(-101318152524452088664950123503),(-101318152524452088483985900955)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-77493422034756465409907161380),(-77493422034756464930172288139)⟩,⟨(-141989758714811181000068162077),(-141989758714811180536331187970)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-88508614526234932893205869828),(-88508614526234930483916106363)⟩,⟨(-173913517031090254822828787944),(-173913517031090252426117526319)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-93050838211168085977505128762),(-93050838211168070419313587163)⟩,⟨(-190217135067996106832444987135),(-190217135067996091283382163745)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-92442191030672563642326337692),(-92442191030672482118738456246)⟩,⟨(-188351736441045860411476993696),(-188351736441045778894155794235)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-87907086944614323947414974867),(-87907086944614022759100079408)⟩,⟨(-170203347953857263950222486703),(-170203347953856962766233050394)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-79172621125936460458556668416),(-79172621125935715703336230623)⟩,⟨(-140628437325358884387271067942),(-140628437325358139634941158328)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-64432766090364939595224210369),(-64432766090363726575566913481)⟩,⟨(-104400747113879206628149112573),(-104400747113877993610266215597)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-42553393341461815650422865440),(-42553393341460591469672626285)⟩,⟨(-64271081400908560248304008716),(-64271081400907336068492424255)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-14906767500604919683306426797),(-14906767500604396976332992974)⟩,⟨(-21712371974907291621831176733),(-21712371974906768915141365279)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-763773091907805945472121779195),(-763773091907685086015643162703)⟩,⟨(-157910004404689489098645993993),(-157910004404568629672641838327)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 3) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_3 (tableDensity true) (fullFactor false 1 3) density1_contains hk1_0_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨24753500707792439138622910080,24753500707792439150395715819⟩,⟨33534479561941112446578798049,33534479561941112458878483908⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_3 1 3 ha1_0_3_contains + def realAnswer : RBox := ⟨(-739019591200013506333598869115),(-739019591199892646865147446884)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_3 +namespace hm1_0_0_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨163185632172452920528355673,163185632172453109248023456⟩,⟨366550515395601109092671864,366550515395601297819143789⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨469960831542267887105474349,469960831542268299286012198⟩,⟨996290487751582280568299088,996290487751582692767799325⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨714088578544510425761483437,714088578544510781451371001⟩,⟨1359703599185545203356858078,1359703599185545559073789048⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨850544963129599341632346859,850544963129599518658195723⟩,⟨1404059294998462092601394045,1404059294998462269656569393⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨849687395359829017640861725,849687395359829071427955076⟩,⟨1191543777879891850812434047,1191543777879891904625374894⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨721519812661027403766936721,721519812661027413917787123⟩,⟨850812988770191801877726924,850812988770191812047068602⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨519900977131458159877659209,519900977131458161194263038⟩,⟨511622113310191052012561907,511622113310191053339418978⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨315009330733236464085679066,315009330733236464262591933⟩,⟨256211083198152926537941233,256211083198152926718729051⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨157730158306889788068936263,157730158306889788114087265⟩,⟨104679563524702127174655595,104679563524702127220194318⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨63424520641801975909874903,63424520641801975925359229⟩,⟨33804619107582261731310075,33804619107582261746054035⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨19570255327595169535510541,19570255327595169540242674⟩,⟨8225560390046914204995346,8225560390046914209073478⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨4302879428076653300346627,4302879428076653301489341⟩,⟨1401174665323812446682847,1401174665323812447522389⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨593046113634482231816975,593046113634482232012931⟩,⟨148073571792346221168248,148073571792346221281461⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨40184469335234684483335,40184469335234684503111⟩,⟨7745901379127739935664,7745901379127739943777⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨780951450863332788429,780951450863332789206⟩,⟨120188677737643106970,120188677737643107188⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨800273825945284902,800273825945284920⟩,⟨105018116332366459,105018116332366475⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-2335446826177485247255988581),(-2335446826177481508370796264)⟩,⟨5009322370616418260516785624,5009322370616421999247141022⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-6452199317608563767891523862),(-6452199317608550078475156236)⟩,⟨14399073684185039291756949600,14399073684185052980749723082⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-9087964614895970004249311709),(-9087964614895937496050536698)⟩,⟨21992348390442163843203147996,21992348390442196350818872503⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-9804406595922319549137381095),(-9804406595922249228516017310)⟩,⟨26940934514865037091709195843,26940934514865107411723607101⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-8741781292735628207853308936),(-8741781292735489580634182504)⟩,⟨28878742803170906686135230872,28878742803171045312840295269⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-6496537718870419467961997977),(-6496537718870183365833127483)⟩,⟨27999006515435393795880731794,27999006515435629897653800305⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3858158545378449484200101692),(-3858158545378125475451703009)⟩,⟨24967770426976974419691439660,24967770426977298428251895171⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1514937852753306533843711197),(-1514937852752970354103601765)⟩,⟨20692621890911736577008961590,20692621890912072756696578923⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨144395749746833986590885462,144395749747098448065838466⟩,⟨16063575677308494670414133486,16063575677308759131922102860⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1054473472818743834469929397,1054473472818903093291518859⟩,⟨11762904756906066338473326064,11762904756906225597366683930⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1365087043974942772945450590,1365087043975016589128205123⟩,⟨8181313057909075738519728207,8181313057909149554780334632⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1299175245153616250175543713,1299175245153644679537778612⟩,⟨5437225350966994781039952576,5437225350967023210468842848⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1049959027874764601895147551,1049959027874774542946084379⟩,⟨3458186443352208412643308705,3458186443352218353743760354⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨741417575598551785808083538,741417575598555177494586760⟩,⟨2074712884670865307347341320,2074712884670868699066487301⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨433439678343162872750126294,433439678343164021439589659⟩,⟨1094339680143030648634870958,1094339680143031797342487426⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨141782030676248265688115705,141782030676248544789481392⟩,⟨340527261587461989532523862,340527261587462268639676227⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-20064912861905522949011066060),(-20064912861905522944074236599)⟩,⟨(-270681788322743422089996595),(-270681788322743419626076485)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-58201912972555441912442358189),(-58201912972555441897945624648)⟩,⟨578515341133413923763567380,578515341133413931130006879⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-90610109305534652989050432089),(-90610109305534652966055914066)⟩,⟨5038733806252022566168639009,5038733806252022578332600042⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-114436319062587140002718334157),(-114436319062587139972917609934)⟩,⟨13822485894306240580729956716,13822485894306240597357997715⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-127981903318692471798200056538),(-127981903318692471763755142770)⟩,⟨25788372330521221768883521183,25788372330521221789323007678⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-130841008632533942739175980218),(-130841008632533942701930066799)⟩,⟨38502622459355463314322972748,38502622459355463338187430745⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-124045057957824921324890338815),(-124045057957824921285417275693)⟩,⟨49348096884947117799784620829,49348096884947117827490544629⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-109984888142909172093799423409),(-109984888142909172044815967512)⟩,⟨56392968745716974630198780129,56392968745716974669567795536⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-91808092035634736170871233653),(-91808092035634736050059983445)⟩,⟨58761420661836003717457498283,58761420661836003830931295663⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-72578576733102418819929768227),(-72578576733102418248155259336)⟩,⟨56632052043818193061762756433,56632052043818193628245395418⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-54637415689630175278087486135),(-54637415689630172695374254986)⟩,⟨50934239491152356210844867264,50934239491152358789920527111⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-39322409010008373055329132221),(-39322409010008364550527779722)⟩,⟨42882317347697814098388655513,42882317347697822600776413043⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-26999677665593193404641195044),(-26999677665593174334824205052)⟩,⟨33583595857544877741862434801,33583595857544896810139820480⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-17327315840648778591771826217),(-17327315840648749892481715247)⟩,⟨23855614913189005904863477135,23855614913189034603226922083⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-9614016139128581649395852203),(-9614016139128554275060915569)⟩,⟨14176855266084557643195056861,14176855266084585017039987529⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3074005301877735380339494710),(-3074005301877724041103841448)⟩,⟨4692401856174047158186654838,4692401856174058497270129244⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-23383162486576966400454236932),(-23383162486576888108327060345)⟩,⟨(-27850577221538261880502069368),(-27850577221538183590726374910)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-69973344088165131048958732432),(-69973344088164951391251354344)⟩,⟨(-80378317734016998838279033774),(-80378317734016819187668944422)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-115476934893176035422357065253),(-115476934893175863812460018748)⟩,⟨(-123786142086907428720126848723),(-123786142086907257122127619261)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-157877526894381605845401224162),(-157877526894381505686508107975)⟩,⟨(-153509649990087514254923196570),(-153509649990087414112655858202)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-194192256815093032262735583449),(-194192256815092994141074544089)⟩,⟨(-166949809243496375146523551919),(-166949809243496337045854273212)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-221421687838829131063033095109),(-221421687838829121353722904913)⟩,⟨(-164054497086771909566068654909),(-164054497086771899881365247483)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-237361108934281183977017062307),(-237361108934281182165422271097)⟩,⟨(-147619768113587830729797398995),(-147619768113587828945301021108)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-240870191387658097709529086857),(-240870191387658097369758070520)⟩,⟨(-122523866272856330440156634774),(-122523866272856330128591743976)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-232106668783226877342328204874),(-232106668783226877217328260833)⟩,⟨(-94116328601485221399321523353),(-94116328601485221302165487119)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-212652849196646638588179397098),(-212652849196646638504833137164)⟩,⟨(-66860482367053519148015315405),(-66860482367053519090778280964)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-185182591415137687642331842129),(-185182591415137687578916742500)⟩,⟨(-43670088043921519351147419678),(-43670088043921519310985592333)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-152794094699546706899139339997),(-152794094699546706851167839293)⟩,⟨(-25867242475016187134255094987),(-25867242475016187105905162433)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-118278998321451426444981616106),(-118278998321451426410103262744)⟩,⟨(-13548286966091454601882768797),(-13548286966091454582522729656)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-83574751882499803977192642360),(-83574751882499803953696226197)⟩,⟨(-6019037769485351226310744768),(-6019037769485351213973230481)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-49601002047708934898264695500),(-49601002047708934884772523848)⟩,⟨(-2119446982443163906857047131),(-2119446982443163900070368694)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-16419888966327694539352833176),(-16419888966327694534968916612)⟩,⟨(-455622501875875568139302900),(-455622501875875565985874341)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨46042431288599601770584279644,46042431288600171124732213757⟩,⟨(-30306324322514902913178804808),(-30306324322514333555982534871)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨130893702984169662384386286826,130893702984171801364494667521⟩,⟨(-92717208382646503515652633357),(-92717208382644364526998741107)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨195365881309649854796019663309,195365881309655200042183937242⟩,⟨(-159407987980214564989839850511),(-159407987980209219731172722155)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨230627445270474791435978074803,230627445270487261311902740224⟩,⟨(-229954910163652079800807636684),(-229954910163639609910607387747)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨233818471357531443292755747036,233818471357558589339212710192⟩,⟨(-299650647949945842314126760823),(-299650647949918696253941626799)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨207722086593037461505406554232,207722086593089650521963573076⟩,⟨(-360072755814264525909531051327),(-360072755814212336881910680202)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨159173328465244056267775533664,159173328465326425552640234165⟩,⟨(-402232367934587901390145008756),(-402232367934505532098320620130)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨97695558496876042626878908472,97695558496976202326436208164⟩,⟨(-420178332545167691923827149448),(-420178332545067532221997019168)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨33941563824471468613965412342,33941563824565493665626764449⟩,⟨(-412624131308136900746883531797),(-412624131308042875697445500816)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-22383032875652974444636202389),(-22383032875584623429446594267)⟩,⟨(-382629031117295205219358156041),(-382629031117226854210110140053)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-64137176547069807550621782650),(-64137176547031288974753064310)⟩,⟨(-336146666761500147014107225931),(-336146666761461628446672501150)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-87290601635135253312234455480),(-87290601635117243895845160381)⟩,⟨(-279860833618959092604973905032),(-279860833618941083198033990185)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-90985557649504280010226278590),(-90985557649496733264422283659)⟩,⟨(-218996757331233818263539240932),(-218996757331226271526757069328)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-77515134664035990584575090716),(-77515134664032984884984642488)⟩,⟨(-156496229312686238748576890807),(-156496229312683233056360866594)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-51423730945298130395515276602),(-51423730945296988755598981142)⟩,⟨(-93722148372255538276468100724),(-93722148372254396641352749171)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-17934936425124526812004537678),(-17934936425124231486052442078)⟩,⟨(-31177065195575256527013091350),(-31177065195574961202724417299)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨463314755369981417257617890,463314755369981425180578336⟩,⟨30564737767511234570071947072,30564737767511234581681006460⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨6714729266255287625387018327,6714729266255287649907750535⟩,⟨89448288293847776640894653064,89448288293847776676058800898⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨27065197135461039047075302504,27065197135461039090207943013⟩,⟨142002000067476196141457881442,142002000067476196200393376316⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨64768011266162396915667135738,64768011266162396980132892660⟩,⟨185087825852335555251468101379,185087825852335555334438227835⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨115584616363443393787228901877,115584616363443393876347850738⟩,⟨215274122022655411905321615488,215274122022655412012912513081⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨170308344046960039412464247788,170308344046960039533182644190⟩,⟨227628133959064695465029874902,227628133959064695602429556229⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨220066210639882374459580662953,220066210639882374640065946178⟩,⟨218183834334690230830719083880,218183834334690231024939311397⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨258583001483876252097906508037,258583001483876252518586649865⟩,⟨188087889065280840911209632646,188087889065280841341710581848⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨281628885378927323574694242165,281628885378927325652896828816⟩,⟨143904620866720297777995149839,143904620866720299861791762673⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨287041711884926499774628127746,287041711884926513050000551407⟩,⟨94799652779587765144180301290,94799652779587778421694995632⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨274942192422208292608536705289,274942192422208361223114968859⟩,⟨49766226303938782536632900209,49766226303938851151092610015⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨246987801016243326233327151827,246987801016243576099974636398⟩,⟨15572452740208007866776107037,15572452740208257732245663815⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨205460861423229616191017678689,205460861423230225998880844718⟩,⟨(-4846938139871042450525603262),(-4846938139870432644131658754)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨153335047380006036434680181948,153335047380007019156239229035⟩,⟨(-12617418701824675067108355154),(-12617418701823692346836816633)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨94291861420835555824588929306,94291861420836540223663904298⟩,⟨(-11161317050831931421286505816),(-11161317050830947023058072184)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨31753183222434866794209001518,31753183222435285507993415167⟩,⟨(-4307876018496489251303949192),(-4307876018496070537811462874)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-12883592493210058119564431601),(-12883592493123560270427431525)⟩,⟨(-479503174981029986651269601749),(-479503174980943488842880409523)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 4) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_4 (tableDensity false) (fullFactor false 1 4) density0_contains hk1_0_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨29247805196765215183139634210,29247805196765215190064225291⟩,⟨(-21985530137787495989500681907),(-21985530137787495983310095550)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_4 1 4 ha1_0_4_contains + def realAnswer : RBox := ⟨16364212703555157063475202609,16364212703641654919736793766⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_4 +namespace hm1_1_0_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨19391682669549086286904683,19391682669549240883959410⟩,⟨65818791759018160607859974,65818791759018315203246417⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨56026880333630046002666032,56026880333630383528313103⟩,⟨180732079980885226718932765,180732079980885564239866948⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨85143976432371168820384664,85143976432371459857575773⟩,⟨250189451282054023026175251,250189451282054314056421235⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨101385309019945997440161066,101385309019946142098984987⟩,⟨260129571282988979297957975,260129571282989123948772790⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨103134315379130948792322279,103134315379130992640532701⟩,⟨218150502304514966763730402,218150502304515010604097031⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨92379321912466317641827531,92379321912466325859211422⟩,⟨150620793342763177296364852,150620793342763185507045880⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨72242130219583249711424043,72242130219583250740836741⟩,⟨86372755780845262115519059,86372755780845263139879687⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨47819056403582350945462706,47819056403582351063584748⟩,⟨41151892095338853568187974,41151892095338853682975625⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨25881229185396180971394681,25881229185396180995130681⟩,⟨16094907064534531495907289,16094907064534531517735807⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨11041214940486766923168947,11041214940486766930326526⟩,⟨5026659716680978157178723,5026659716680978163406453⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3538322580515210460124705,3538322580515210462112141⟩,⟨1192593511115703004665030,1192593511115703006282004⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨791593842431753362209551,791593842431753362636106⟩,⟨196632705349966515241025,196632705349966515555189⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨109305283116339580480274,109305283116339580543262⟩,⟨19230783521087413735759,19230783521087413775224⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨7366012859697538856061,7366012859697538861368⟩,⟨839550898255308306466,839550898255308308974⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨142312097210509081998,142312097210509082182⟩,⟨9162335900422376300,9162335900422376364⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨145325172396030556,145325172396030572⟩,⟨4611286857585646,4611286857585662⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-691996497802494628420204883),(-691996497802491549905497340)⟩,⟨514044475235926079849181761,514044475235929158379176256⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1909500781228882296328164686),(-1909500781228871020412153245)⟩,⟨1500868280359491546351444499,1500868280359502822309036228⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-2686893848736635254026289054),(-2686893848736608458565128705)⟩,⟨2364465935411258692155703094,2364465935411285487673888057⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-2908067798199363864436011557),(-2908067798199305851013599840)⟩,⟨3031100612026325704359898174,3031100612026383717841429719⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-2637871954702439040491732747),(-2637871954702324574694394943)⟩,⟨3440692697743553613702325721,3440692697743668079549722575⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2065909637135697945638874609),(-2065909637135502834827442351)⟩,⟨3554340172620717190958549043,3554340172620912301804545166⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1402485852013721657328948856),(-1402485852013453668085427805)⟩,⟨3372645074205027335227899761,3372645074205295324489460009⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-801573207806221403115598610),(-801573207805943214008305273)⟩,⟨2956868694325910954662418577,2956868694326189143773960081⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-344171954348762631155335454),(-344171954348543794928563299)⟩,⟨2414920663313180074348778607,2414920663313398910570688867⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-51185319257422349251362497),(-51185319257290636499879965)⟩,⟨1856487773575413600973901205,1856487773575545313715833643⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨97617122643017141599325639,97617122643078131051722284⟩,⟨1356984178849962930255772198,1356984178850023919697291372⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨143795732362974460671979389,143795732362997920395246475⟩,⟨948585125055505455844307515,948585125055528915557574319⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨132312209714950763674916041,132312209714958955844598414⟩,⟨632158133512749026253065401,632158133512757218414809248⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨97514645608893538733594262,97514645608896330258683405⟩,⟨393594288684947593097367124,393594288684950384616933040⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨57722604961311674010553096,57722604961312618542113947⟩,⟨212785722399635465155656190,212785722399636409684024278⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨18936286369606272181615446,18936286369606501560219695⟩,⟨67014825056424904164223968,67014825056425133541784843⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-3826062268203322301695674942),(-3826062268203322299946873786)⟩,⟨(-2426044187948876369303956832),(-2426044187948876367674473123)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-11243239620815716519859746838),(-11243239620815716514633645841)⟩,⟨(-6833385270006173909992259061),(-6833385270006173905121796417)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-17845006212752574689011528176),(-17845006212752574680484641072)⟩,⟨(-10015960411755956937397096310),(-10015960411755956929406629090)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-22906319918583909981793725090),(-22906319918583909970356568421)⟩,⟨(-11450324683942212723793425564),(-11450324683942212712995127573)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-25823596989986182715799150703),(-25823596989986182702062848769)⟩,⟨(-10894930227361773914726616033),(-10894930227361773901639197358)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-26491541314553230417116558785),(-26491541314553230401453119820)⟩,⟨(-8516999121459572457624561098),(-8516999121459572442590626001)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-25309199538621033996167110469),(-25309199538621033978026596321)⟩,⟨(-5010834382714982342602306260),(-5010834382714982325058926884)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-22856854469184122945699707243),(-22856854469184122918212096653)⟩,⟨(-1361882125117957174878195541),(-1361882125117957147909395708)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-19669239083357551636795757219),(-19669239083357551548371457002)⟩,⟨1594704447138769421572937660,1594704447138769509605244865⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-16178392705969660093950148513),(-16178392705969659635314950713)⟩,⟨3431759287716362690538943188,3431759287716363148897603431⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-12702295281690617085828362298),(-12702295281690614986018772448)⟩,⟨4136947395934680432464359297,4136947395934682532084054251⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-9458742949063135729896180335),(-9458742949063128798877940337)⟩,⟨3982036073394691225314859565,3982036073394698156198774253⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-6604269064526098322316527787),(-6604269064526082764898381547)⟩,⟨3331009802796028330740135928,3331009802796043888068110834⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4232108983736345232166571695),(-4232108983736321801098687630)⟩,⟨2460496146947784588194025977,2460496146947808019208612220⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2322515348233294673830112617),(-2322515348233272312990345304)⟩,⟨1502745876216732876116114390,1502745876216755236928788769⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-735898115855585281809717429),(-735898115855576016912000637)⟩,⟨505113698080371745173146611,505113698080381010062887276⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-701359618560775312304591282),(-701359618560709531360266277)⟩,⟨(-12135753416968954038615939115),(-12135753416968888257423166459)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2560990705981185057425065064),(-2560990705981034211644699453)⟩,⟨(-34997999462560380699932208289),(-34997999462560229853404213263)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-5703714222491551467630793462),(-5703714222491407580530488585)⟩,⟨(-53873129603248319865652629846),(-53873129603248175977312309668)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-10673248413927626079560149457),(-10673248413927542288642406194)⟩,⟨(-67040175646129696116413098667),(-67040175646129612323790513461)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-17415599083977395310280715572),(-17415599083977363530153182135)⟩,⟨(-74033463599961870640980426836),(-74033463599961838858757479844)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-24964940495814470629488549428),(-24964940495814462594091654129)⟩,⟨(-75506965366745981066828080115),(-75506965366745973029048225009)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-31717853753709875379896155599),(-31717853753709873922338207708)⟩,⟨(-72512775107420531670022274955),(-72512775107420530209910789834)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-36322804443476504948170061109),(-36322804443476504711259211625)⟩,⟨(-66054418703845077126379564747),(-66054418703845076886902979735)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-38228933810051558072249566493),(-38228933810051558009783953856)⟩,⟨(-57204382154366963037539028425),(-57204382154366962972637541534)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-37565533034828238938723192266),(-37565533034828238905496904163)⟩,⟨(-47179240408646135849989836562),(-47179240408646135814576338247)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-34780023667416414364861967802),(-34780023667416414342070365431)⟩,⟨(-37152638656938252421486865664),(-37152638656938252396847067970)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-30350867851699848586454042588),(-30350867851699848570330015121)⟩,⟨(-27987728355668714059416350791),(-27987728355668714041807266147)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-24688386995413466963572653933),(-24688386995413466952435493717)⟩,⟨(-20074204884658974207803944334),(-20074204884658974195543436021)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-18158704523806967125056792573),(-18158704523806967117877692473)⟩,⟨(-13381823152942565988401692433),(-13381823152942565980446487258)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-11084701021338761534117530492),(-11084701021338761530135130565)⟩,⟨(-7639870611871763650751668481),(-7639870611871763646316090933)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-3722996212375605609170364818),(-3722996212375605607900283059)⟩,⟨(-2480942671157328848989252686),(-2480942671157328847571114825)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨14598386534259605519902620863,14598386534260073442804898658⟩,⟨(-10718380208768386667074814647),(-10718380208767918744849658100)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨42538466705621603509338481427,42538466705623361551082551241⟩,⟨(-32914003655796001811673306901),(-32914003655794243771866847042)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨66579329113770081756470939869,66579329113774475624030499205⟩,⟨(-56573955783777230587559224119),(-56573955783772836722868426132)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨83861535417796668780723966736,83861535417806920814733975237⟩,⟨(-80809760252665299563053247337),(-80809760252655047532365967310)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨91654699156632789718556534651,91654699156655110379985998071⟩,⟨(-103803055792359335501098006231),(-103803055792337014842882721363)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨88806508646931610749502189512,88806508646974522711738940750⟩,⟨(-123975081978982415916370149432),(-123975081978939503956767231790)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨76986517253284588754663859585,76986517253352301700215739801⟩,⟨(-140011139505343332800803761413),(-140011139505275619856960627253)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨60031704870126624193242033468,60031704870208921835557431004⟩,⟨(-150336644347147364522361222732),(-150336644347065066880649938973)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨42185939469576981162255956489,42185939469654176808282113021⟩,⟨(-153373314490244131085499696341),(-153373314490166935439027061115)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨26735696461946204619956996039,26735696462002261833103988219⟩,⟨(-148178022755016818414959436730),(-148178022754960761200590959937)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨15301585321862173060006828834,15301585321893723583345265451⟩,⟨(-134801828139687155383724768869),(-134801828139655604858726008219)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨7744883199724443263165666381,7744883199739174930055733628⟩,⟨(-114500414822469626713956747965),(-114500414822454895045258924557)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨2977342389857499173341174022,2977342389863664543393839889⟩,⟨(-89763027450751328784965520312),(-89763027450745163413219626287)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨200845693116027797091845516,200845693118480725250533768⟩,⟨(-63466702300262108488873958300),(-63466702300259655559369147485)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-825933704907560301602498215),(-825933704906629311344524949)⟩,⟨(-37516665642045958318968548583),(-37516665642045027327854145821)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-457239307173849258230507205),(-457239307173608515678028746)⟩,⟨(-12380404068307269817645440001),(-12380404068307029074802650058)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨56992751785783945565081309,56992751785783950629008949⟩,⟨907310753243773191155540571,907310753243773198612489286⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨839231917384786539051409342,839231917384786554769118706⟩,⟨2483515261231809584623177467,2483515261231809607378339470⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨3636139986304660762537306496,3636139986304660790342723213⟩,⟨2507097965839394584154857236,2507097965839394622742946573⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨10336665777537966999169353636,10336665777537967041159364694⟩,⟨(-1781702573945921378136923410),(-1781702573945921322910423130)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨23874289923400466251034807759,23874289923400466310403795318⟩,⟨(-12549620562833057851119872779),(-12549620562833057777544032957)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨46203135145388829483989884636,46203135145388829567764116738⟩,⟨(-28251458442201938464736802717),(-28251458442201938366802944074)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨74822792961715011263778404481,74822792961715011397691746808⟩,⟨(-44166622481870090898820420585),(-44166622481870090751596930525)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨103094520140356427142929291843,103094520140356427479594872445⟩,⟨(-56272242535554659411871254753),(-56272242535554659063809068310)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨124068314737753135966723378283,124068314737753137672966811021⟩,⟨(-63146676099385972911921127362),(-63146676099385971196988197531)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨133330908908314063692289942669,133330908908314074564965878832⟩,⟨(-65225021645138003942300034553),(-65225021645137993063538258202)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨129811673324097235443189644712,129811673324097291509218192021⟩,⟨(-63708595718104788537855460694),(-63708595718104732467809898282)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨115502377076226283283740237448,115502377076226487361505221661⟩,⟨(-59649670288843843458319794126),(-59649670288843639377877212511)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨94164417743022445652827159606,94164417743022943859411170878⟩,⟨(-53008653504698287862062814228),(-53008653504697789653742275144)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨69165932667061201189259986213,69165932667062004425565426486⟩,⟨(-42684220012048196382705496598),(-42684220012047393145362370553)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨42265752104734633004567397188,42265752104735437907781616955⟩,⟨(-27983115226992262824530321215),(-27983115226991457920779155533)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨14224343613708893261718851290,14224343613709235694337863128⟩,⟨(-9765785561868653450509632859),(-9765785561868311017731111468)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨172189824979719381609353568915,172189824979790403557019485751⟩,⟨(-441724277998217428612836794872),(-441724277998146406644707945299)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 4) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_4 (tableDensity true) (fullFactor false 1 4) density1_contains hk1_0_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-38247129872692973710083986919),(-38247129872692973701028752429)⟩,⟨28750308641722110132020894181,28750308641722110140116276340⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_4 1 4 ha1_0_4_contains + def realAnswer : RBox := ⟨133942695107026407899169581996,133942695107097429856090733322⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_4 +namespace hm1_0_0_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-38202305287926685943444392),(-38202305287926666272295758)⟩,⟨17006980311425917762660754,17006980311425937433111066⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-101877808738627864620320412),(-101877808738627822434629142)⟩,⟨48046861730524324918231282,48046861730524367102017474⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-133800546267144503963921815),(-133800546267144468873387402)⟩,⟨70232165102468001218537485,70232165102468036306470770⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-130311265622032093098353433),(-130311265622032076580896121)⟩,⟨78867181968869794973478084,78867181968869811488299951⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-102104703624581457425603407),(-102104703624581452772787791)⟩,⟨72715187313884828513236593,72715187313884833163942857⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-65786070177296228636446473),(-65786070177296227839232202)⟩,⟨55692716147636786258472405,55692716147636787054366937⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-34802308246867339959552429),(-34802308246867339867557003)⟩,⟨35287232083357439337407097,35287232083357439428801662⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-14899360980823853715247518),(-14899360980823853704487437)⟩,⟨18266815779900964242798359,18266815779900964253404055⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-5033501405608857614422566),(-5033501405608857612173855)⟩,⟨7556954314526246808983164,7556954314526246811255767⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1291399929557803668556706),(-1291399929557803667975571)⟩,⟨2411675302658721858173538,2411675302658721858803136⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-237520326216355724985987),(-237520326216355724863776)⟩,⟨561756317651955819896334,561756317651955820044610⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-28658567691471286851308),(-28658567691471286833344)⟩,⟨87359437943250010197203,87359437943250010223145⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1960446070169519492465),(-1960446070169519490864)⟩,⟨7784934197255104585093,7784934197255104588053⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-57956523650728826915),(-57956523650728826832)⟩,⟨298167772173175415826,298167772173175416013⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-400882898201944499),(-400882898201944481)⟩,⟨2590544594790368546,2590544594790368566⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-87581485577929),(-87581485577913)⟩,⟨666364295536889,666364295536905⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1046640429499767080427936225),(-1046640429499766299298226041)⟩,⟨(-487968678228330033253630253),(-487968678228329252091234972)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2979972699850832366456247525),(-2979972699850829534611587116)⟩,⟨(-1335416838976582866311136727),(-1335416838976580034377904135)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-4465912001770616808530491789),(-4465912001770610214041102575)⟩,⟨(-1845841026323919548104234930),(-1845841026323912953495214355)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-5318690679792691423570802676),(-5318690679792677563919622182)⟩,⟨(-1936407086777904499968606236),(-1936407086777890640196345790)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-5493698893691030644883730973),(-5493698893691004328382266677)⟩,⟨(-1664248450264041414903570105),(-1664248450264015098303291181)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-5089637017281357659702130978),(-5089637017281314832714117273)⟩,⟨(-1182512872503480517975483276),(-1182512872503437690922118518)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-4303936467084919052041977307),(-4303936467084863290287921450)⟩,⟨(-666701550318504852975048270),(-666701550318449091188252191)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-3360321972199868591824347716),(-3360321972199814027176439686)⟩,⟨(-247459486588171192908000210),(-247459486588116628251436784)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2444824238131091800276931742),(-2444824238131051533234722732)⟩,⟨20862776220033961800980414,20862776220074228838216656⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1672463329160199830060722332),(-1672463329160177145311588385)⟩,⟨149168278585467426006727661,149168278585490110745719417⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1085886873446052428475018390),(-1085886873446042604016650132)⟩,⟨180726044560614775388377371,180726044560624599836515072⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-675300140245230874076204359),(-675300140245227332373864047)⟩,⟨161111559140827913103573517,161111559140831454797768432⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-404356819259332750040399052),(-404356819259331584515060202)⟩,⟨122657818227170616545081001,122657818227171782064768065⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-230705840950687298020560772),(-230705840950686920176947821)⟩,⟨82406073181875753740668311,82406073181876131580767689⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-117361718717143086927883907),(-117361718717142963636098746)⟩,⟨46475910697616478369793624,46475910697616601659708029⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-35832125870987250123939683),(-35832125870987220751470219)⟩,⟨14918785425248226481495327,14918785425248255853382082⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨84921315275163008255053303,84921315275163009028249288⟩,⟨(-6293518613473388302918000545),(-6293518613473388301349433548)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-179801890442941642325484308),(-179801890442941640028605934)⟩,⟨(-18139916707894564720768167969),(-18139916707894564716191323789)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1548750845457652904176425271),(-1548750845457652900427843628)⟩,⟨(-27887658227003535107170668988),(-27887658227003535100001080425)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-4171468365936898343413533101),(-4171468365936898338376277151)⟩,⟨(-34573538129057365496942911466),(-34573538129057365487820212028)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-7598148400939091659546285654),(-7598148400939091653492337605)⟩,⟨(-37744575332055539795089272602),(-37744575332055539784793158966)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-11019589982145660729936552090),(-11019589982145660723061167745)⟩,⟨(-37480122878573158652647801837),(-37480122878573158641831490879)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-13660646956778828191787655521),(-13660646956778828184062396139)⟩,⟨(-34366253135565263947975611367),(-34366253135565263936895015770)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-15048558769767646130634624763),(-15048558769767646120080370410)⟩,⟨(-29371720681314788286060494999),(-29371720681314788272860072861)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-15082610404047752839828962229),(-15082610404047752810765600807)⟩,⟨(-23581185752842365558601642312),(-23581185752842365527593052081)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-13970212785733789643118889022),(-13970212785733789504070843213)⟩,⟨(-17915092635109482914416979414),(-17915092635109482774018672742)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-12084725104343344700907904752),(-12084725104343344091807902958)⟩,⟨(-12970242237898388961052796921),(-12970242237898388351058988811)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-9810265021256899396995109728),(-9810265021256897458611084159)⟩,⟨(-8999614134008251826069717121),(-8999614134008249887113300852)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-7440261206813699117925568726),(-7440261206813694902776399725)⟩,⟨(-5983337834382728520488231828),(-5983337834382724304985240963)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-5149482136447770016955711224),(-5149482136447763829191448327)⟩,⟨(-3740873494253777063913641938),(-3740873494253770875941752357)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3004664551237630330827627699),(-3004664551237624531519782014)⟩,⟨(-2037731941263886010647680530),(-2037731941263880211231988733)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-985135021715056875000665500),(-985135021715054494541218944)⟩,⟨(-645369062518228351627727525),(-645369062518225971135094076)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨11652065183742988518331921289,11652065183743021273831058616⟩,⟨(-9782961694710294221598802708),(-9782961694710261465105193399)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨33469037155770152281439673784,33469037155770227102804539697⟩,⟨(-29135540200029768536618995794),(-29135540200029693712265850143)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨51062021622183809860067192166,51062021622183880687662879151⟩,⟨(-47630537901178285278728764127),(-47630537901178214446167116860)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨62455768259814296149165682856,62455768259814336941719877667⟩,⟨(-64223371999412080233804744039),(-64223371999412039434399582802)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨66723684227031461862444133396,66723684227031477120137410502⟩,⟨(-77594049717725572111231116700),(-77594049717725556845029684954)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨64179730653152057388717874596,64179730653152061188232616177⟩,⟨(-86595287746599642989800602738),(-86595287746599639180507327481)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨56363360967234642054520395161,56363360967234642738369431846⟩,⟨(-90591329190400365865870365396),(-90591329190400365171490073659)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨45558644426293455860638534090,45558644426293455976999920010⟩,⟨(-89520115086238466792368405898),(-89520115086238466665306362005)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨34037387151509655516971272643,34037387151509655552286165296⟩,⟨(-83894549983820843681891087165),(-83894549983820843636275042349)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨23511933375865942221745045347,23511933375865942241977320537⟩,⟨(-74733931858486285772356109629),(-74733931858486285742705095447)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨14945272946496470189114085269,14945272946496470202924463049⟩,⟨(-63332471167314254302138593221),(-63332471167314254280141802006)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨8632877834314119654991419535,8632877834314119664491042414⟩,⟨(-50957092333873291935217747646),(-50957092333873291918963899859)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4423500662139270027424279105,4423500662139270033764520155⟩,⟨(-38590723177324115210025957820),(-38590723177324115198447725504)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1930802734852468530109755749,1930802734852468534075481885⟩,⟨(-26792498751436410006394787632),(-26792498751436409998721212822)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨671420377223984250741609160,671420377223984252894371612⟩,⟨(-15706719302577992993243030728),(-15706719302577992988886560097)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨143377550429127490183014544,143377550429127490861393690⟩,⟨(-5166720509588631413235312135),(-5166720509588631411828043667)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨15853090964778532289785299917,15853090964778830112883405387⟩,⟨24084715011532964124807779449,24084715011533261946342725729⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨48314223317879311309353818935,48314223317880425764484626040⟩,⟨68211235797021660970887061542,68211235797022775421650553126⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨82440733219256902505835828398,82440733219259665973030988620⟩,⟨101050627122153358017457963969,101050627122156121478304454346⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨117617558252778456564612996212,117617558252784831260672187130⟩,⟨117989973177302748125308868066,117989973177309122814187323267⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨151100526776925250799149386297,151100526776938930369090618587⟩,⟨117946848480635785700364800597,117946848480649465263483806550⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨178513835556843669819901585784,178513835556869527065630641649⟩,⟨103034835270800894094946992746,103034835270826751335257716645⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨195626343820373761193733442330,195626343820413803849035559514⟩,⟨77470576433061890350639543998,77470576433101933002587989602⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨200153119117606189206909663644,200153119117653897554995924176⟩,⟨46593315297971588084210078744,46593315298019296431218409841⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨192346957675446441125125179268,192346957675490281500445019525⟩,⟨15872958993049015654909117641,15872958993092856031258123179⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨174535507551649379143501942388,174535507551680577363953465533⟩,⟨(-10167234762783975184355845526),(-10167234762752776961198509734)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨150161286971659049166058773826,150161286971676271118860089886⟩,⟨(-28618646142357553200952940295),(-28618646142340331244375270733)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨122639195235681098469654518417,122639195235688997706559634100⟩,⟨(-38231065294787750015755464226),(-38231065294779850774684859932)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨94383683399290806189041101450,94383683399294061203556961222⟩,⟨(-39202185028113834297365534307),(-39202185028110579278925966474)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨66557334339281906325640570238,66557334339283185272333770923⟩,⟨(-32962735010529980256077368472),(-32962735010528701306211605190)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨39492574298220050438677582503,39492574298220531601376138290⟩,⟨(-21667971406804771520416870940),(-21667971406804290355668679680)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨13075096161020450580848120183,13075096161020574437732718674⟩,⟨(-7521552959800158837684173869),(-7521552959800034980092260245)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-19189056506644287137525771324),(-19189056506644287130176257681)⟩,⟨290799560606418636458299381,290799560606418641433375812⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-55979245741360709411249528632),(-55979245741360709389063276756)⟩,⟨4200286415415631259158542325,4200286415415631274517296762⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-88314652600499147544552846225),(-88314652600499147507610933571)⟩,⟨16824489986431047839294114702,16824489986431047866172005609⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-114062130029531164839769746859),(-114062130029531164788251905564)⟩,⟨39896230303871640399439185215,39896230303871640439293607934⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-131113619612219350715701159655),(-131113619612219350649701683099)⟩,⟨70369167790643542518332807443,70369167790643542572837588617⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-136712444918717981206115386261),(-136712444918717981123062756462)⟩,⟨102247125594399558595217621585,102247125594399558668049042059⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-128992588438366546778194228814),(-128992588438366546662855279396)⟩,⟨130051766151922140369375805619,130051766151922140476458122035⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-109327444890442513103175199957),(-109327444890442512852813385303)⟩,⟨150231457924456601975141599851,150231457924456602219735115866⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-82186812532215986031324033358),(-82186812532215984844266374568)⟩,⟨160751309154323998180271334371,160751309154323999364149109412⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-53201741147580723514355225870),(-53201741147580716086614293176)⟩,⟨160971195311217832312133850255,160971195311217839738745828165⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-27467415648317237064771839882),(-27467415648317199310600727947)⟩,⟨151595313025270927303164161577,151595313025270965057507923238⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-8470757145600431019755066058),(-8470757145600295573346463067)⟩,⟨134086926963841491264988867962,134086926963841626712152246034⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2588395245197957004750863596,2588395245198283355750991241⟩,⟨110059934406098288332339742732,110059934406098614684229185188⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨6684400491490793460404303573,6684400491491314054422501042⟩,⟨81267979040769021310660793290,81267979040769541905438034786⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨5871294354565153325348690653,5871294354565671123511346408⟩,⟨49606421161146607697065366725,49606421161147125495719706701⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨2257740162101136616520224349,2257740162101356060757175045⟩,⟨16641879570449318751217226215,16641879570449538195622532836⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨204155425664314145291468487963,204155425664355052928157874080⟩,⟨118135973024807813756398753914,118135973024848721401463652986⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 5) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_5 (tableDensity false) (fullFactor false 1 5) density0_contains hk1_0_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨15421672956801917426994369829,15421672956801917430453163856⟩,⟨24805036725820210949022041446,24805036725820210953204543731⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_5 1 5 ha1_0_5_contains + def realAnswer : RBox := ⟨219577098621116062718362857792,219577098621156970358711037936⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_5 +namespace hm1_1_0_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-6859676473392144431349976),(-6859676473392128317794351)⟩,⟨2020969914418727824812290,2020969914418743938542048⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-18480509283273727158850168),(-18480509283273692616144351)⟩,⟨5727918370492626495438931,5727918370492661038627531⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-24618371979295983449116604),(-24618371979295954739928068)⟩,⟨8374171032063134470498100,8374171032063163180371678⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-24142870009913389758211681),(-24142870009913376263937526)⟩,⟨9400753169942466576938440,9400753169942480071958694⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-18696980205498439942291389),(-18696980205498436151908248)⟩,⟨8823731670272670979130973,8823731670272674770191199⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-11651075989837154572512963),(-11651075989837153928973510)⟩,⟨7125588890103808238165647,7125588890103808882231124⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-5878902469068486164459647),(-5878902469068486093506871)⟩,⟨4898018717073532316318445,4898018717073532387624911⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-2394714785649622027878934),(-2394714785649622021081147)⟩,⟨2769512275512965408670262,2769512275512965415671624⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-774423332399247106063694),(-774423332399247105000471)⟩,⟨1238507444400055631483057,1238507444400055632644960⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-192133519932629683183417),(-192133519932629682942790)⟩,⟨419421673477746068897529,419421673477746069177332⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-34457222484848125188128),(-34457222484848125140833)⟩,⟨101502012922800509517709,101502012922800509577080⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-4027297601264741608593),(-4027297601264741602055)⟩,⟨16068119211947707591454,16068119211947707600637⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-255625577892022601445),(-255625577892022600899)⟩,⟨1435045258655164480028,1435045258655164480943⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-6337897923464303597),(-6337897923464303562)⟩,⟨54668259596559465218,54668259596559465277⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-30955262588378807),(-30955262588378790)⟩,⟨472135823463072046,472135823463072062⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-3877163623895),(-3877163623878)⟩,⟨121011521999759,121011521999775⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-107403357908440980746098233),(-107403357908440337553941123)⟩,⟨(-144585914229868319681667674),(-144585914229867676492520592)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-310604756239829594514218695),(-310604756239827261863090785)⟩,⟨(-395211633932733192460832493),(-395211633932730859817817775)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-480107379385380599559159430),(-480107379385375163844078624)⟩,⟨(-545730423064747035263954497),(-545730423064741599559805629)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-598315331515327319836362265),(-598315331515315885769908600)⟩,⟨(-574342106285502082862310273),(-574342106285490648806900002)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-654393699635022382700854661),(-654393699635000652904965045)⟩,⟨(-502142265960514416313006235),(-502142265960492686526158559)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-645933268994445987405211508),(-645933268994410595997100464)⟩,⟨(-375913036042730224242563495),(-375913036042694832840443374)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-581211359146160426522886516),(-581211359146114305841990236)⟩,⟨(-242117705836628887576291020),(-242117705836582766898375748)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-480039530134415976431257409),(-480039530134370824183904222)⟩,⟨(-130474344404817353135098885),(-130474344404772200888411676)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-367442858251526612018026439),(-367442858251493291858240611)⟩,⟨(-52616673344910807283842468),(-52616673344877487123339492)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-263883816340128188884608065),(-263883816340109427717158016)⟩,⟨(-7438554370542464000370816),(-7438554370523702831592480)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-180057900076752229843920557),(-180057900076744112503990584)⟩,⟨12861105537605440143972641,12861105537613557485328286⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-117782751350307430324885158),(-117782751350304507726788026)⟩,⟨17812128548897376255655198,17812128548900298854988328⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-73902119831141563088839508),(-73902119831140602611035425)⟩,⟨15451895471431105360386555,15451895471432065839119522⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-43762399534029750351632880),(-43762399534029439371460632)⟩,⟨10837581319967009636490861,10837581319967320617279534⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-22819112693814167362712794),(-22819112693814065986199275)⟩,⟨6189273530304695947450844,6189273530304797324308459⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-7051630705033643765643256),(-7051630705033619626792998)⟩,⟨1992538706262288497134672,1992538706262312636095306⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨760950931731447581199341090,760950931731447581712888172⟩,⟨(-1200072383877228909904415630),(-1200072383877228909352061897)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨2129851309047679202376938015,2129851309047679203902042239⟩,⟨(-3504154765347742454571102089),(-3504154765347742452930989218)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨3082990177515642839186636105,3082990177515642841657079257⟩,⟨(-5492132166539346602495003397),(-5492132166539346599852603227)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨3460154187340494542504645351,3460154187340494545781263091⟩,⟨(-6920311040897729785835870077),(-6920311040897729782357090147)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨3214623724979499529711560975,3214623724979499533587089660⟩,⟨(-7615852822397104839912141365),(-7615852822397104835834453884)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2441969945105585544593670802,2441969945105585548915454986⟩,⟨(-7588568212388825031636856989),(-7588568212388825027122616171)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1390940241398672504685804653,1390940241398672509557475447⟩,⟨(-7011569554833913425578538852),(-7011569554833913420528571392)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨366421988410479460785062878,366421988410479467980860813⟩,⟨(-6103496671417081848260835219),(-6103496671417081840913404308)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-407256092036528495270577345),(-407256092036528472772767356)⟩,⟨(-5051502094040044116835092416),(-5051502094040044094224227003)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-845342378446741312343819385),(-845342378446741199888249609)⟩,⟨(-3992867912462734787630920321),(-3992867912462734675096278238)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-980946144815708687443625137),(-980946144815708191624961748)⟩,⟨(-3014984364256224036813261270),(-3014984364256223540940853665)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-910742765658576235215508101),(-910742765658574655148458608)⟩,⟨(-2164633184387989214134940349),(-2164633184387987634030712014)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-737881066146587169955597929),(-737881066146583730960011069)⟩,⟨(-1463534234473099995910068064),(-1463534234473096556890137201)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-531091607081834416353602823),(-531091607081829364331502684)⟩,⟨(-913703994410136039614152364),(-913703994410130987577940264)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-318486039054977208827062586),(-318486039054972471575041190)⟩,⟨(-492273961310438459982035348),(-492273961310433722722925721)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-106044537302023452051966340),(-106044537302021507040991151)⟩,⟨(-154497736653921604643141793),(-154497736653919659630080934)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨5077331120434555659059846416,5077331120434583181105415060⟩,⟨(-293425749405564916819517315),(-293425749405537394879632092)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨14572960185330948843457484171,14572960185331011668417034641⟩,⟨(-1066176860193109516275047731),(-1066176860193046691631887902)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨22222760123722321946331492444,22222760123722381336716389235⟩,⟨(-2351870607031663036501577965),(-2351870607031603646636085863)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨27275182839867855820182776151,27275182839867889952805429647⟩,⟨(-4340037541565060992382817174),(-4340037541565026860463291949)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨29587242861486875444964620305,29587242861486888172373785096⟩,⟨(-6955830050352378624403885744),(-6955830050352365897841372677)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨29536172027796999006606582176,29536172027797002159952730620⟩,⟨(-9759728199595371607101892265),(-9759728199595368454694822684)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨27681705710419853838045753179,27681705710419854397544983852⟩,⟨(-12101739532066004527236924809),(-12101739532066003968715761141)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨24555344763595402025140132953,24555344763595402114557533022⟩,⟨(-13496336396086211632966130077),(-13496336396086211544501745765)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨20681590252978625288466940754,20681590252978625312055743454⟩,⟨(-13815281303438918403448782792),(-13815281303438918380735985708)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨16584491608784521989133875742,16584491608784522001661825095⟩,⟨(-13199912263384452049964217346),(-13199912263384452038197131783)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨12708912747775227562047456371,12708912747775227570536804967⟩,⟨(-11893238887704417910642651621),(-11893238887704417902774981832)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨9335511335353519986998924028,9335511335353519992918682238⟩,⟨(-10120998606111820884168378967),(-10120998606111820878732207500)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨6550315719438476194164674045,6550315719438476198198821141⟩,⟨(-8054438908684775731498609529),(-8054438908684775727819608788)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨4290222311325080769776811143,4290222311325080772349805713⟩,⟨(-5821088197136597033435728314),(-5821088197136597031102142800)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2419306110172182801963299023,2419306110172182803380847197⟩,⟨(-3510037087636750839572846555),(-3510037087636750838292661133)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨780661165892179251444107946,780661165892179251894546459⟩,⟨(-1171484395317611437971441385),(-1171484395317611437565466379)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨5606730024814004329524481227,5606730024814249093327273555⟩,⟨7636375161629401211501553291,7636375161629645975668265011⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨17151204686580430881571064745,17151204686581346854747762255⟩,⟨22167227304561522972637232910,22167227304562438946851017464⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨29258354837393334198531763871,29258354837395605800263257762⟩,⟨34435797475234650425231081924,34435797475236922028486359810⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨41333270056006998529233609652,41333270056012239438793797256⟩,⟨42900670076110772269208195884,42900670076116013180513426316⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨52344146487512555319655651666,52344146487523803248994655981⟩,⟨46229271639181396469595598988,46229271639192644400597792203⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨61463174284440852085998753316,61463174284462112976757293721⟩,⟨44043475407026524135529759668,44043475407047785027626580703⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨68092352353898740060115880630,68092352353931657759554111849⟩,⟨37459709765014340125494079408,37459709765047257825782396541⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨71608912868352413529717353206,71608912868391613816386756993⟩,⟨28612255847570566788624004416,28612255847609767075587540795⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨71490431035925667730518431077,71490431035961661244660179831⟩,⟨19678018689074791598280477603,19678018689110785112210654815⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨67586312410159069293829816306,67586312410184656173367292980⟩,⟨12204259271849099021562836589,12204259271874685900532937983⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨60214888059770497192048626793,60214888059784603709562523103⟩,⟨6840651027344852308602670824,6840651027358958825360340639⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨50174993703345868857705199973,50174993703352330434417800935⟩,⟨3396768182056469851307974921,3396768182062931427211497425⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨38686565603135408626124152883,38686565603138067841957221358⟩,⟨1284727582825596298199299590,1284727582828255513286119970⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨26992530659380100459366125549,26992530659381144201723180380⟩,⟨86144625554660236640437880,86144625555703978411617674⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨15808853182999283494438501235,15808853182999675877471271282⟩,⟨(-347836618416203515512685395),(-347836618415811132849232858)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨5192121477075688930768601911,5192121477075789896564204524⟩,⟨(-191749826922168871498024209),(-191749826922067905827012869)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-569625701025629672656682805),(-569625701025629667973293019)⟩,⟨35771499666916090088921025,35771499666916093268241307⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1554348601968375480831725770),(-1554348601968375466586178475)⟩,⟨524961764569313872387822487,524961764569313882225756695⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1560203299312809143214634367),(-1560203299312809119211390420)⟩,⟨2260168313199035743951958835,2260168313199035761250767229⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1094176613327007719156829687,1094176613327007753192156802⟩,⟨6366029633971406680620827473,6366029633971406706515246337⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨7635059198094069730690768188,7635059198094069775519101812⟩,⟨14530558334502553411076068594,14530558334502553447279371507⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨16955268066085003866203134120,16955268066085003925059328522⟩,⟨27729787091456889885388652233,27729787091456889935789671870⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨26096540360908734299006807573,26096540360908734386065666146⟩,⟨44205917652288564308229518506,44205917652288564387507585917⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨32690735490051507654818946016,32690735490051507856847928142⟩,⟨59884607383511490616613900486,59884607383511490812150097862⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨36042670376284540553742940949,36042670376284541530317640949⟩,⟨70809238199590533865839004717,70809238199590534837616372218⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨36577095410023437741893549867,36577095410023443827434637459⟩,⟨74767535787563816024678082494,74767535787563822106981867849⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨35125744840271885248659042992,35125744840271916100215590371⟩,⟨71574374253476157753877496831,71574374253476188603385689291⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨32380973358105658806105365412,32380973358105769433254548486⟩,⟨62706336380477677679085550521,62706336380477788304920997877⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨28393167112224561217886837963,28393167112224827844480948886⟩,⟨50442408212034467881603668953,50442408212034734507374142929⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨22621474800603638978967156036,22621474800604064492003618298⟩,⟨36658429894093241988759009398,36658429894093667501318564733⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨14721398422671873283226543534,14721398422672296666300401152⟩,⟨22235798955791795350403564482,22235798955792218733237199970⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨5118244270203110745246503010,5118244270203290211371052395⟩,⟨7454994344735269719109541146,7454994344735449185164274749⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨205932432588399290162943355531,205932432588432880092112562826⟩,⟨112522065524056378766821148355,112522065524089968684688568279⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 5) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_5 (tableDensity true) (fullFactor false 1 5) density1_contains hk1_0_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-20166803097356353562900291196),(-20166803097356353558377252854)⟩,⟨(-32437355718380275861882864878),(-32437355718380275856413438814)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_5 1 5 ha1_0_5_contains + def realAnswer : RBox := ⟨185765629491042936599943064335,185765629491076526533835309972⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_5 +namespace hm1_0_0_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1477047963241007887673887),(-1477047963241006179100886)⟩,⟨(-3317931424483630766496807),(-3317931424483629057864094)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-4093716281101691599153920),(-4093716281101688001225080)⟩,⟨(-8682054953273637566251646),(-8682054953273633968163345)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-5757393594593084212208247),(-5757393594593081327204305)⟩,⟨(-10974309200722031335322191),(-10974309200722028450109818)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-6096652240393316025368529),(-6096652240393314740992457)⟩,⟨(-10082626143032708816713544),(-10082626143032707532140207)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-5189411436247015512576574),(-5189411436247015177269748)⟩,⟨(-7296358628386956747612634),(-7296358628386956412162561)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-3586398348466245132239435),(-3586398348466245080190338)⟩,⟨(-4243638893360144084533912),(-4243638893360144032406712)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-1999293939591449175708805),(-1999293939591449170415594)⟩,⟨(-1976140537801498223249988),(-1976140537801498217928077)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-884936534114979504015274),(-884936534114979503484739)⟩,⟨(-723811573776023152577266),(-723811573776023152042624)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-302812434298640382790608),(-302812434298640382695176)⟩,⟨(-202409992846850410319710),(-202409992846850410226914)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-76818200976937386389840),(-76818200976937386368483)⟩,⟨(-41319121944319352835727),(-41319121944319352816552)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-13538882901477438287546),(-13538882901477438283661)⟩,⟨(-5756697140591157429478),(-5756697140591157426393)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1494240942965329999834),(-1494240942965329999325)⟩,⟨(-493524924418957068034),(-493524924418957067694)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-86525300502560677781),(-86525300502560677727)⟩,⟨(-21952940314389808333),(-21952940314389808296)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1885432486654255218),(-1885432486654255198)⟩,⟨(-368987318540295653),(-368987318540295636)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7359794583573819),(-7359794583573802)⟩,⟨(-1143644745173666),(-1143644745173648)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-474998002815),(-474998002796)⟩,⟨(-62501266439),(-62501266423)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨84963715335143196365792344,84963715335143332372432629⟩,⟨(-182236605842737122619059648),(-182236605842736986618168455)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨230330865538690699681766362,230330865538691187892444627⟩,⟨(-513944519652959499416654329),(-513944519652959011221408211)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨312436045825233309926426049,312436045825234424796387751⟩,⟨(-755767003195921886436278539),(-755767003195920771586770894)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨318735019106527950571292087,318735019106530227172542710⟩,⟨(-875094086845833438993178801),(-875094086845831162412056434)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨264068879893953888196130782,264068879893958052014985928⟩,⟨(-871029367359226856227514518),(-871029367359222692424489010)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨179405699750299565577194956,179405699750306040638977521⟩,⟨(-771150171591539932444949647),(-771150171591533457393171093)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨96031536909641204867230739,96031536909649204162615602⟩,⟨(-618425511269554676540937793),(-618425511269546677250306825)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨33694111252795838584791756,33694111252803221218069415⟩,⟨(-454890762501726759406439993),(-454890762501719376774351893)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2506065895049246686608162),(-2506065895044135574775552)⟩,⟨(-310194060309042246193516224),(-310194060309037135081059286)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-17591471089590135286420875),(-17591471089587441583206892)⟩,⟨(-198238761641312149592834499),(-198238761641309455888425593)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-19946514805201334369673889),(-19946514805200244325387606)⟩,⟨(-120152207078496052782033328),(-120152207078494962736626272)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16655264801049719239869098),(-16655264801049351437935601)⟩,⟨(-69916802128066745092665247),(-69916802128066377289902112)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-11943969624838687139555784),(-11943969624838573237209342)⟩,⟨(-39410440846534316744111353),(-39410440846534202841227437)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-7633831404467756378041702),(-7633831404467721295963187)⟩,⟨(-21381886709762474508835543),(-21381886709762439426442140)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-4153112731518546249479505),(-4153112731518535221431876)⟩,⟨(-10489319571832668393363393),(-10489319571832657365155359)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1308180820254080595433957),(-1308180820254078019565061)⟩,⟨(-3142065961836738226698314),(-3142065961836735650780619)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1645011306024314713763334663,1645011306024314714178581061⟩,⟨22202070998642768243148378,22202070998642768445343938⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨4711458448130765024155931686,4711458448130765025359893581⟩,⟨(-46568503750354834837250529),(-46568503750354834240434867)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨7152783857566904602722063338,7152783857566904604584661452⟩,⟨(-396705896988953187054393083),(-396705896988953186091707957)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨8704809377658296893002848950,8704809377658296895329761881⟩,⟨(-1049123997730910200504425270),(-1049123997730910199232749454)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨9276952861367650763609655968,9276952861367650766174063678⟩,⟨(-1865675794612839519793026691),(-1865675794612839518298718820)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨8947729396672194537467079618,8947729396672194540084368610⟩,⟨(-2628422325173621322601549737),(-2628422325173621320950813547)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨7935035915035224300948347040,7935035915035224303540210901⟩,⟨(-3151636421096533720977868865),(-3151636421096533719182746130)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨6537280953743035299783757372,6537280953743035302748323307⟩,⟨(-3346850629802963162810908945),(-3346850629802963160452802221)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨5048076714588458052208901784,5048076714588458058842334459⟩,⟨(-3226535988467456964359631782),(-3226535988467456958155590889)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨3685575840413679575313282451,3685575840413679604045671977⟩,⟨(-2872232542498139722234813432),(-2872232542498139693789266671)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2566120588629415104291200962,2566120588629415224363106038⟩,⟨(-2389653419237763750832872240),(-2389653419237763630943798992)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨1716602119308627599799189496,1716602119308627968209120132⟩,⟨(-1870446648000428319102518082),(-1870446648000427950805581699)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1105040755706850592564582486,1105040755706851369171195307⟩,⟨(-1373722626446723155116816411),(-1373722626446722378577883418)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨673056607986426635223313658,673056607986427747113997776⟩,⟨(-926346266719516282951356225),(-926346266719515171099389409)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨359927583890011179171099936,359927583890012203055071294⟩,⟨(-530686397471590507730783059),(-530686397471589483866565031)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨112909699299903584897891780,112909699299904001354234301⟩,⟨(-172351829333108422558406624),(-172351829333108006108086841)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3410801301583451870985057855,3410801301583463291762862372⟩,⟨4062473787887543530018098431,4062473787887554950445463999⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨10109603404862433849795469706,10109603404862459819121078046⟩,⟨11613633695708171797157987382,11613633695708197765435219967⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨16371913349965731201714271021,16371913349965755565633226173⟩,⟨17552852135661400413495537236,17552852135661424775687455076⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨21771777192493153854002406270,21771777192493167703869725563⟩,⟨21175682164097495307241445480,21175682164097509154756551312⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨25837940398468828313923221459,25837940398468833408659801054⟩,⟨22223223462788503590127025638,22223223462788508681990410191⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨28223211064322719325422162773,28223211064322720570898931470⟩,⟨20924045540353442541371663743,20924045540353443783610874820⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨28814183870200921275453381807,28814183870200921497258047382⟩,⟨17934603777122802926153772739,17934603777122803144548753325⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨27727082906035426255927110765,27727082906035426295525426901⟩,⟨14117790817903102402417114842,14117790817903102438633711907⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨25271289979870911932201995102,25271289979870911946073825678⟩,⟨10258758521618140026150290964,10258758521618140036847790232⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨21888265954566838283409874477,21888265954566838292199598907⟩,⟨6890549450922102151473197563,6890549450922102157433208813⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨18050810541029510406311879253,18050810541029510412669338232⟩,⟨4262529197963138881534884375,4262529197963138885492479532⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨14162563082156555301741347102,14162563082156555306329735962⟩,⟨2401042902998692601566704881,2401042902998692604219431778⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨10492797804281558261868476179,10492797804281558265070564122⟩,⟨1203595742773523471045933590,1203595742773523472776285154⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨7157779340633548218472763862,7157779340633548220560490206⟩,⟨516149490162040271566309455,516149490162040272628599167⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨4144789305792926941565251950,4144789305792926942737036940⟩,⟨177250855700018901448642909,177250855700018902017700469⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1354811403290570920713084202,1354811403290570921089390127⟩,⟨37598997554297191078462320,37598997554297191256549705⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-10498896674935666264436925464),(-10498896674935536442348043615)⟩,⟨6910564477152283561534789171,6910564477152413384291379579⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-29621906946304734715009915264),(-29621906946304250838042109953)⟩,⟨20980198337702287106778901816,20980198337702770985605977097⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-43556323162442586099002411134),(-43556323162441395512964175396)⟩,⟨35530025427966434079641090957,35530025427967624668364833387⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-50304148344875821335955673808),(-50304148344873105645041165424)⟩,⟨50133291850047952184572539951,50133291850050667878496167945⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-49581710974134559869990233957),(-49581710974128815196166555238)⟩,⟨63495713205764565778554448935,63495713205770310455202779929⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-42590836545667270400644287190),(-42590836545656594222546596934)⟩,⟨73753776151118610506263743996,73753776151129286686572484138⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-31422194818232150480868767302),(-31422194818215928134621227613)⟩,⟨79288665072670079641444514325,79288665072686301989038634098⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-18518554902065384502963562137),(-18518554902046446642859220832)⟩,⟨79455943785342651604833035651,79455943785361589465363379055⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-6186077714006611896183414436),(-6186077713989576947043621340)⟩,⟨74722616923441876620837073234,74722616923458911569579866520⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨3848707213781475470147218810,3848707213793342715815923662⟩,⟨66347586404585387177917328762,66347586404597254422559147691⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨10641955127853692159963051519,10641955127860109099510933965⟩,⟨55901145284445673791699473843,55901145284452090729838273215⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨13953905837317536457320028090,13953905837320423819970750653⟩,⟨44786490245667790910749195174,44786490245670678271869754399⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨14075863509136523388675094090,14075863509137693356577432654⟩,⟨33898707634360684948303940549,33898707634361854914784323588⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨11681090468462090282168569298,11681090468462543790008552294⟩,⟨23589100508657555890195593249,23589100508658009396898324896⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨7608402509280245315513305447,7608402509280414312514438624⟩,⟨13867852316493816619227934271,13867852316493985615499991169⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2628658413388147264386584291,2628658413388190551897235657⟩,⟨4569550828685995277542852624,4569550828686038564802915773⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-152100336652245530558399885),(-152100336652245527955060339)⟩,⟨(-10039345845728784081975684094),(-10039345845728784078098566760)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-2189519310693452735689014582),(-2189519310693452727672280877)⟩,⟨(-29194538988065444501479692022),(-29194538988065444489815386854)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-8715523145047479328316687893),(-8715523145047479314359345230)⟩,⟨(-45771168978081263355155307666),(-45771168978081263335859802755)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-20479806993246151969511807287),(-20479806993246151948979345368)⟩,⟨(-58577101595870983192417556908),(-58577101595870983165761766895)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-35701758269789226192780511225),(-35701758269789226165001619361)⟩,⟨(-66547026463177834593635669075),(-66547026463177834559898576552)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-51155601222272753408890904324),(-51155601222272753372274093154)⟩,⟨(-68425360096810729048970902074),(-68425360096810729007136893091)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-64048332315432755450129782437),(-64048332315432755397185917141)⟩,⟨(-63552936281699146304797047917),(-63552936281699146247717973037)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-72736377847350408871722467668),(-72736377847350408753208913442)⟩,⟨(-52957490402354219912733377357),(-52957490402354219791396598498)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-76464900518125924346215062699),(-76464900518125923784190145678)⟩,⟨(-39116475804598578380476931964),(-39116475804598577816945586129)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-75228280064242972261073308317),(-75228280064242968798786424070)⟩,⟨(-24881385183432141803907181899),(-24881385183432138341126468391)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-69656014880110190114452066410),(-69656014880110172802549199392)⟩,⟨(-12633653033567552808539854083),(-12633653033567535496765574048)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-60662991632050460865709159993),(-60662991632050399678959077785)⟩,⟨(-3839832380044989760711020292),(-3839832380044928574354554159)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-49130759084131551575327370940),(-49130759084131406028385518090)⟩,⟨1151896885107411193481190835,1151896885107556739980393788⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-35893784063366202631478936794),(-35893784063365972809888504757)⟩,⟨2951046718695883992594310761,2951046718696113813815635114⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-21748108588248507984079642599),(-21748108588248281012991249940)⟩,⟨2573784424290627320295795068,2573784424290854291148317763⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-7268358945092604113269634914),(-7268358945092508272420287113)⟩,⟨986060603444510229193191689,986060603444606069962302884⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-88782973905632627309035540364),(-88782973905616452331911918986)⟩,⟨63836952485261903112519715375,63836952485278078090064931282⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 6) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_6 (tableDensity false) (fullFactor false 1 6) density0_contains hk1_0_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-16151808288097071857775839679),(-16151808288097071855636162069)⟩,⟨7985415443625704405222192040,7985415443625704406849125361⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_6 1 6 ha1_0_6_contains + def realAnswer : RBox := ⟨(-104934782193729699166911380043),(-104934782193713524187448081055)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_6 +namespace hm1_1_0_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-175519874382759633496672),(-175519874382758233867341)⟩,⟨(-595771137148820671729693),(-595771137148819272115508)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-488030028765008188333879),(-488030028765005242101410)⟩,⟨(-1574859990602959597888653),(-1574859990602956651697400)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-686492201677040072649403),(-686492201677037712081787)⟩,⟨(-2019088374592154868647674),(-2019088374592152508136380)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-726685424418488367601939),(-726685424418487318099691)⟩,⟨(-1868026913905302550385748),(-1868026913905301500941442)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-629548472134519330916402),(-629548472134519057608078)⟩,⟨(-1336320936855612153439834),(-1336320936855611880180244)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-458541793322664153945554),(-458541793322664111840314)⟩,⟨(-751882651268924147974027),(-751882651268924105903206)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-277215125754436452467834),(-277215125754436448346450)⟩,⟨(-334013007347342606539828),(-334013007347342602439080)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-134005616328147967662717),(-134005616328147967316207)⟩,⟨(-116412745257386647953560),(-116412745257386647617401)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-49569906563797297003440),(-49569906563797296955884)⟩,⟨(-31161225306594509059390),(-31161225306594509016081)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-13346941836563598027029),(-13346941836563598017860)⟩,⟨(-6150683821819304142680),(-6150683821819304134878)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2444822557341124694743),(-2444822557341124693241)⟩,⟨(-835583302798066219283),(-835583302798066218107)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-274784553120176116234),(-274784553120176116052)⟩,⟨(-69439242774375100651),(-69439242774375100519)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-15951559601487271761),(-15951559601487271735)⟩,⟨(-2872265954869232836),(-2872265954869232813)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-345754124690796534),(-345754124690796518)⟩,⟨(-40638318953911254),(-40638318953911238)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1341484485953919),(-1341484485953903)⟩,⟨(-89150465659372),(-89150465659356)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-86261342063),(-86261342046)⟩,⟨(-2783382152),(-2783382136)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨25174894570331187808150140,25174894570331299792096439⟩,⟨(-18700559887651028038305952),(-18700559887650916053867598)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨68165687445727190518933527,68165687445727592653044307⟩,⟨(-53567311217417602612235119),(-53567311217417200476809975)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨92372988634617485750407031,92372988634618404695155947⟩,⟨(-81242432696300707528191368),(-81242432696299788581702149)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨94535424356011362785739654,94535424356013240932719513⟩,⟨(-98427822313034264873153055),(-98427822313032386724459682)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨79667432707797369571893102,79667432707800807651763975⟩,⟨(-103732243872229709212836167),(-103732243872226271131608131)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨57012554088797859763672160,57012554088803210599560123⟩,⟨(-97841788802493428982629103),(-97841788802488078145877873)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨34840797443088053684604774,34840797443094669891941568⟩,⟨(-83489749333201573202091828),(-83489749333194956994345324)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨17703673264383051463322999,17703673264389160582367859⟩,⟨(-64965536738568385475721947),(-64965536738562276356590262)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨6705607846403538773729197,6705607846407768121456935⟩,⟨(-46607675536296893731064660),(-46607675536292664383425066)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨900726208962256649216994,900726208964484456483862⟩,⟨(-31269699182598133858734664),(-31269699182595906051621746)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1412540840457533481788948),(-1412540840456632839644744)⟩,⟨(-19917532148686080111855209),(-19917532148685179469866747)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1839291093402376142947182),(-1839291093402072631785301)⟩,⟨(-12191371543162837866778565),(-12191371543162534355744020)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1504159975754136122535358),(-1504159975754042257834035)⟩,⟨(-7201423716448181715647911),(-7201423716448087851037181)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1003880155231166300059890),(-1003880155231137425823077)⟩,⟨(-4055462251525534178136004),(-4055462251525505303956532)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-553069865407571112982133),(-553069865407562045069029)⟩,⟨(-2039396040618575245970707),(-2039396040618566178088510)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-174719249268902745043467),(-174719249268900628114652)⟩,⟨(-618344163942379280970889),(-618344163942377164051802)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨313676492529494940277795684,313676492529494940423171585⟩,⟨198899514319297911329536229,198899514319297911464407607⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨910116815249096105210886002,910116815249096105639800772⟩,⟨553203232908846593735924126,553203232908846594133885901⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1408616967759313219673339687,1408616967759313220355699954⟩,⟨790823076391832060752904486,790823076391832061389401188⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1742333937408877295428749515,1742333937408877296310511094⟩,⟨871381915928813461374779591,871381915928813462203338296⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1871824700506480354934928326,1871824700506480355943678824⟩,⟨790461048257913706514167053,790461048257913707470579804⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1811620297205446013550521821,1811620297205446014634749363⟩,⟨583509749012994235775109683,583509749012994236810497187⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1618885392073804338425818319,1618885392073804339597423377⟩,⟨321787052061336337051323786,321787052061336338178793819⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1358352228234900024800925044,1358352228234900026437771068⟩,⟨82161395010691343207926606,82161395010691344808114836⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1081257700117746402124118841,1081257700117746406942910664⟩,⟨(-86679981783125105552727282),(-86679981783125100760783005)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨821315970357311033555539538,821315970357311056568618210⟩,⟨(-173549461323984203163260046),(-173549461323984180168671086)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨596429348106853814442759099,596429348106853912037443555⟩,⟨(-193856919560973441250587793),(-193856919560973343668250022)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨412854658989812698296490554,412854658989812998512422539⟩,⟨(-173599437861981680109871237),(-173599437861981379902258124)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨270290526612130516430669128,270290526612131149980302143⟩,⟨(-136221827481244042041472491),(-136221827481243408497141055)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨164395919724638429945534741,164395919724639337718831596⟩,⟨(-95532919894293093329850760),(-95532919894292185559561756)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨86952286342308711649168210,86952286342309548006774130⟩,⟨(-56249819209441767280027967),(-56249819209440930923911781)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨27030005246869738625252869,27030005246870078895512616⟩,⟨(-18552696279648072009733316),(-18552696279647731739910393)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨102299767974296802177635210,102299767974306397883815608⟩,⟨1770203487454585925009724869,1770203487454595520753357718⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨369888722014863698757855957,369888722014885503325417934⟩,⟨5056766912324668990597861413,5056766912324690795276973293⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨808151458471169975968433912,808151458471190403994522833⟩,⟨7639193380908638856290101616,7639193380908659284497452982⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1470680281931025039514404646,1470680281931036626005936607⟩,⟨9247581827951848409520246560,9247581827951859996253399249⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2315220640104192520706516974,2315220640104196767862269677⟩,⟨9854030060467960066746055951,9854030060467964314186860583⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3179676209252614464351796432,3179676209252615495005069309⟩,⟨9628518078631779348018703063,9628518078631780378980370690⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨3847993960829924772419842929,3847993960829924950777393570⟩,⟨8806711452410339269058305833,8806711452410339447728061436⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨4179250156217606226794931515,4179250156217606254323955769⟩,⟨7607397979525562958136526509,7607397979525562985960564710⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨4160780516173516215636090972,4160780516173516222518391769⟩,⟨6231405986825284095678744329,6231405986825284102823590779⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨3865444495329725951697292388,3865444495329725955170074702⟩,⟨4858477932672946345532086862,4858477932672946349225433709⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3389334410099835372227969989,3389334410099835374491174658⟩,⟨3623023002278103293543356859,3623023002278103295980790057⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2812644059629702042380548885,2812644059629702043907765592⟩,⟨2595061750318705325866206179,2595061750318705327524583536⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2189832919317084549626105558,2189832919317084550638738508⟩,⟨1781226756151500426600319343,1781226756151500427706427918⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1555071859214542539338267296,1555071859214542539970274236⟩,⟨1146228672476646881022515945,1146228672476646881715973234⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨926235391364287228129713296,926235391364287228472580440⟩,⟨638436318540337862366428982,638436318540337862743923935⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨307184672761908956339469420,307184672761908956447583071⟩,⟨204704572515925510583067542,204704572515925510702283368⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-3328806423138355411209838571),(-3328806423138248717145308920)⟩,⟨2444043982305831127854157811,2444043982305937821755812986⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-9626332299544492067507216415),(-9626332299544094366000301519)⟩,⟨7447808104059068118110057969,7447808104059465819154717771⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-14842353893981742045534830504),(-14842353893980763367442296502)⟩,⟨12609711918216786589672164457,12609711918217765267090673442⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-18288998740665965930724672028),(-18288998740663733242581153594)⟩,⟨17618150031634285516483414516,17618150031636518203863707887⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-19431531139977381093802727734),(-19431531139972657574060525630)⟩,⟨21996509991982000958056085568,21996509991986724477081535823⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-18203256618087908686117103138),(-18203256618079130290032941424)⟩,⟨25393720506093316259910149469,25393720506102094655427945610⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-15189641220634246030207943862),(-15189641220620910184420772467)⟩,⟨27597359982323290608104432487,27597359982336626453539323502⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-11364719408402196184837266084),(-11364719408386635587053910341)⟩,⟨28425272383833904481526185285,28425272383849465079190236238⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-7649461860370615954928694257),(-7649461860356630018077051832)⟩,⟨27770396891192237368834843089,27770396891206223305770002348⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-4642656783649301428404824025),(-4642656783639568617015209570)⟩,⟨25690299642383341379461834953,25690299642393074191070997840⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-2548541622178130056625301183),(-2548541622172873925398534440)⟩,⟨22415350432606743915853919437,22415350432612000047367614245⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1241501277038149661871635989),(-1241501277035787795909696149)⟩,⟨18323066443440207689716030239,18323066443442569555979600335⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-461976172548734694488740409),(-461976172547778877939524594)⟩,⟨13894721281436681490135309815,13894721281437637306958469354⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-30788316917020244614319714),(-30788316916650139888785249)⟩,⟨9566755858828812765427401555,9566755858829182870365319519⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨122074750783885917934154798,122074750784023732469277604⟩,⟨5551330129799783182850191929,5551330129799920997517963047⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨67010886481113383815487598,67010886481148670720720319⟩,⟨1814570436190379419723393723,1814570436190414706673161735⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-18709986912586876346387293),(-18709986912586874682974994)⟩,⟨(-298017618665463166797991194),(-298017618665463164346794086)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-273648345611049250227234598),(-273648345611049245095808662)⟩,⟨(-810680235307766185089349622),(-810680235307766177657483380)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1170743608835892701612261947),(-1170743608835892692643682711)⟩,⟨(-809117867302020738127645557),(-809117867302020725685146405)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-3267228370186933259231251236),(-3267228370186933245923997728)⟩,⟨559960533503301712129222295,559960533503301729608960733⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-7369853811344734287098739801),(-7369853811344734268701190273)⟩,⟨3870959667013072647568232395,3870959667013072670329383736⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-13869105127975781212328635479),(-13869105127975781187059377040)⟩,⟨8479987466265823047714067684,8479987466265823077190688816⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-21764842016527524172971121558),(-21764842016527524133859203118)⟩,⟨12849916517446634768178779209,12849916517446634811080754446⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-28988428163190654628184834256),(-28988428163190654533542410252)⟩,⟨15826504851097299440919704477,15826504851097299538643555846⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-33678227331702876428564170480),(-33678227331702875967329570518)⟩,⟨17144061082786317722157887728,17144061082786318185597147178⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-34940175903160961316283831253),(-34940175903160958480794587047)⟩,⟨17093618499757700881500138229,17093618499757703718420247165⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-32887421950395757776544843167),(-32887421950395743630857968517)⟩,⟨16139182310771993131303479852,16139182310772007277855030128⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-28369937697506037173127065741),(-28369937697505987199222444244)⟩,⟨14648670548978415461260103521,14648670548978465435695774566⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-22517951470646649499080093721),(-22517951470646530589012607550)⟩,⟨12673745683325579770948980862,12673745683325698681336555770⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-16191133008071774008281687860),(-16191133008071586161770906476)⟩,⟨9990707388914760135486657392,9990707388914947982175799254⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-9748477325075202040044842540),(-9748477325075016455104740358)⟩,⟨6453896293083306991207333460,6453896293083492576234223197⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3255976697027269795156135999),(-3255976697027191414591082542)⟩,⟨2235392143757436005679786427,2235392143757514386269312081⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-55755124625465649355532200538),(-55755124625452367200805344896)⟩,⟨81303384071443184845807960365,81303384071456467005855821829⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 6) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_6 (tableDensity true) (fullFactor false 1 6) density1_contains hk1_0_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨21121595453665401657370365783,21121595453665401660168405734⟩,⟨(-10442466349356690378187317780),(-10442466349356690376059789590)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_6 1 6 ha1_0_6_contains + def realAnswer : RBox := ⟨(-34633529171800247698261834755),(-34633529171786965540536939162)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_6 +namespace hm1_0_0_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨247002753917859926529220,247002753917860053740118⟩,⟨(-109955901150258322811005),(-109955901150258195604484)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨634233574475300914996944,634233574475301178061194⟩,⟨(-298988340444514697435237),(-298988340444514434382423)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨771678636490320408703874,771678636490320612080976⟩,⟨(-404628104711974327837199),(-404628104711974124474410)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨668951159346683312792284,668951159346683398454397⟩,⟨(-404125845222166910594851),(-404125845222166824945384)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨447222779074741910534920,447222779074741931277059⟩,⟨(-317666353053966914599754),(-317666353053966893865939)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨234896954595567453552804,234896954595567456476879⟩,⟨(-198179818027363846281262),(-198179818027363843361126)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨96339083798316107216867,96339083798316107481092⟩,⟨(-97257565381347231371898),(-97257565381347231108812)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨30212259182337428886939,30212259182337428909767⟩,⟨(-36837135673231477246263),(-36837135673231477223468)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨7000582793491279318783,7000582793491279322089⟩,⟨(-10437278141945904239071),(-10437278141945904235611)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1138634445051675865071,1138634445051675865634⟩,⟨(-2107838323041641835292),(-2107838323041641834653)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨120397767400700923400,120397767400700923485⟩,⟨(-281672183403624519451),(-281672183403624519346)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨7353200273700368091,7353200273700368114⟩,⟨(-22126479937769236182),(-22126479937769236155)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨213429232993158426,213429232993158442⟩,⟨(-835759523664615358),(-835759523664615340)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2047647750295560,2047647750295577⟩,⟨(-10404932031154770),(-10404932031154754)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨2850992178690,2850992178707⟩,⟨(-18288415339165),(-18288415339149)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨38968076,38968092⟩,⟨(-295892684),(-295892665)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨27197424014351957446771967,27197424014351977742956093⟩,⟨12680287095106337943387977,12680287095106358240438780⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨75976777918845587016013595,75976777918845659156374727⟩,⟨34052429632273734408290932,34052429632273806550956543⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨109632508923995718378342317,109632508923995879934981538⟩,⟨45331656273075500652930849,45331656273075662212567469⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨123423294546580274430623347,123423294546580594988129910⟩,⟨44973333604634928850293144,44973333604635249410667792⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨118390406348803317889974393,118390406348803882654641058⟩,⟨35919597276965313569432458,35919597276965878336272824⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨100169012173108615580600793,100169012173109454868458736⟩,⟨23334968996445983941242742,23334968996446823230413508⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨76186604536340159819393024,76186604536341143685687633⟩,⟨11859359201564239312355792,11859359201565223179242184⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨52799316538102966668817940,52799316538103823125237624⟩,⟨3933488716988396122600353,3933488716989252579160196⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨33746886931458275724438361,33746886931458832004517778⟩,⟨(-257352254093732858410004),(-257352254093176578397790)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨20148578810306670006366508,20148578810306944280685039⟩,⟨(-1778884013075437084771599),(-1778884013075162810573789)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨11399832242036608457983741,11399832242036712161481516⟩,⟨(-1887702857832998646731994),(-1887702857832894943339504)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨6206768327684507785464973,6206768327684540535403942⟩,⟨(-1476306667994380882769500),(-1476306667994348132902975)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨3293230947533363881791362,3293230947533373425284273⟩,⟨(-997165071609960830170283),(-997165071609951286721165)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1698848586476723980223850,1698848586476726772674443⟩,⟨(-606243808013231273895114),(-606243808013228481468683)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨803617074666891096347472,803617074666891941930681⟩,⟨(-318127011325947814485295),(-318127011325946968913857)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨236164443163441674378692,236164443163441868011977⟩,⟨(-98323782641881576651801),(-98323782641881383022011)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4975352079147501676397779),(-4975352079147501631075969)⟩,⟨368551202860722618376415919,368551202860722618470625010⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨10338164075955006895981453,10338164075955007028904027⟩,⟨1048894831878257539887011771,1048894831878257540158434537⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨87099804966707007419975353,87099804966707007631890190⟩,⟨1572534827475570657887828810,1572534827475570658302530106⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨226169599505806366022814048,226169599505806366297997793⟩,⟨1878644691165575367384215122,1878644691165575367892882077⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨392684377259466516934153808,392684377259466517250315140⟩,⟨1954498893301612366398789839,1954498893301612366946187452⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨537420115499308045199744538,537420115499308045539470210⟩,⟨1831107422736916531773718687,1831107422736916532316509967⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨623303263153255057390860560,623303263153255057748422000⟩,⟨1570594315243537961994215545,1570594315243537962513833975⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨638092548607707896429587305,638092548607707896881231974⟩,⟨1247299367176980486375726157,1247299367176980486946421710⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨591707027066375957803684835,591707027066375958939000907⟩,⟨926395151508027167250504375,926395151508027168467001293⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨506228347870518749606914609,506228347870518754595410022⟩,⟨649982581130791398803759958,649982581130791403844440958⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨405078024193451592397941693,405078024193451612626819478⟩,⟨435222628720975091097306489,435222628720975111358210281⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨305707742572274617554846064,305707742572274677540910081⟩,⟨280680212340967554690856318,280680212340967614696019971⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨217417374254621778473068373,217417374254621901103101372⟩,⟨174943304786241564339400904,174943304786241686980518105⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨142841521272983943222408106,142841521272984114472666127⟩,⟨103800979652559640124483327,103800979652559811380922411⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨80341557992676059437492692,80341557992676214379389840⟩,⟨54493353642770605815539301,54493353642770760760533757⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨25845805430082948786185942,25845805430083011234345981⟩,⟨16932005211208226071039178,16932005211208288520134869⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1214036254185990338597896304),(-1214036254185986925616601516)⟩,⟨1019285638005672613467442173,1019285638005676026554573746⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3454204808908312970572652175),(-3454204808908305245266657203)⟩,⟨3006770067872357002978145092,3006770067872364728599361149⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-5171964692507370658470791821),(-5171964692507363475762084722)⟩,⟨4823603018016863409730503087,4823603018016870592953962858⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-6154102148618732697888617938),(-6154102148618728668634045794)⟩,⟨6326406618352500743787886790,6326406618352504773734597359⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-6344559626854513583303794637),(-6344559626854512126736294069)⟩,⟨7374877046652518403491433000,7374877046652519860890458063⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-5847441498892242648035608781),(-5847441498892242299897135984)⟩,⟨7884807635979128287664976631,7884807635979128636722044620⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-4891743435032250073315148364),(-4891743435032250013529452967)⟩,⟨7856029177577969220252841360,7856029177577969280984525222⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3750101078204288901544562758),(-3750101078204288891882292422)⟩,⟨7361531150551597805190021681,7361531150551597815768019991⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2650422948958983708566361481),(-2650422948958983705788712125)⟩,⟨6525338609932592099092673062,6525338609932592102708381555⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1731013541823638541351631846),(-1731013541823638539846693376)⟩,⟨5495234480471771128162329103,5495234480471771130395537341⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1042099153035332505531296808),(-1042099153035332504559164399)⟩,⟨4410069428554185889545728572,4410069428554185891120444468⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-572423616353491265811565339),(-572423616353491265176607245)⟩,⟨3374059024818393292035344567,3374059024818393293145370609⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-280712962333970458239291545),(-280712962333970457834504643)⟩,⟨2445497662091351995399504360,2445497662091351996158374949⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-118269921917648894942430338),(-118269921917648894698524099)⟩,⟨1639097588758195712697514706,1639097588758195713184223156⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-40108690245984927914618522),(-40108690245984927785683166)⟩,⟨937509841264803151202480560,937509841264803151472541526⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-8451327867371728785924263),(-8451327867371728745851712)⟩,⟨304506308723180721790885226,304506308723180721877102761⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2582060644706589867239505932),(-2582060644706541361110344922)⟩,⟨(-3922826989213116209059119945),(-3922826989213067703174325171)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-7809056496885041891072629418),(-7809056496884861811259510770)⟩,⟨(-11026165249978362314125194344),(-11026165249978182234990262505)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-13125188659897933320447799315),(-13125188659897493651758597934)⟩,⟨(-16092361189718030292726637234),(-16092361189717590625010784144)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-18316366845025939120515384067),(-18316366845024947464379879389)⟩,⟨(-18383218038775065792900478242),(-18383218038774074137845499704)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-22870989778232422741140661045),(-22870989778230354883180302332)⟩,⟨(-17865648069019156727198119441),(-17865648069017088870239974869)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-26119319474311051770153524923),(-26119319474307273312298802076)⟩,⟨(-15090839261877089012731208872),(-15090839261873310555649732441)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-27546268383409076286579700351),(-27546268383403442864421448934)⟩,⟨(-10924559370954410374765954545),(-10924559370948776953071105276)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-27037105283447633475937134517),(-27037105283441189749682566439)⟩,⟨(-6308987867822178112434243356),(-6308987867815734386323974897)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-24882231797068713451786849587),(-24882231797063039603461972583)⟩,⟨(-2066515641761193000793334614),(-2066515641755519152337191653)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-21619038613999615520572501787),(-21619038613995746156539266184)⟩,⟨1248790185596350253141745091,1248790185600219617509030114⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-17838216641738957477081651020),(-17838216641736908010040044796)⟩,⟨3392042817777562797263514753,3392042817779612264755792021⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-14019411739690158755778704239),(-14019411739689254103358698064)⟩,⟨4365561531334202252080531993,4365561531335106904982323522⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-10435921354176375840842045246),(-10435921354176015382467579092)⟩,⟨4332127576489592407652059700,4332127576489952866468195454⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-7166130568558327389629337205),(-7166130568558189550424047125)⟩,⟨3548145392733832459742779634,3548145392733970299297453469⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-4174053240133256441866386747),(-4174053240133205565358716325)⟩,⟨2289937969436491904296709070,2289937969436542781026634737⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1368849022952465454958654100),(-1368849022952452487542181600)⟩,⟨787434081852439554220715709,787434081852452521713270232⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨4502052050846960446910481817,4502052050846960448663486255⟩,⟨(-68189872119178768790825199),(-68189872119178767623168644)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨13050592466425610363588155877,13050592466425610368844209804⟩,⟨(-978301199510256269280120241),(-978301199510256265693443175)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨20333242295875654465437280199,20333242295875654474075457495⟩,⟨(-3869905053218082082648554876),(-3869905053218082076436101019)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨25785259977725210265841959737,25785259977725210277663070413⟩,⟨(-9011083455939872129330788969),(-9011083455939872120263925142)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨28951350363361536301577766297,28951350363361536316359037825⟩,⟨(-15525874276729763471708992581),(-15525874276729763459573831507)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨29355367207377537130459971925,29355367207377537148521259716⟩,⟨(-21937980239101531584886380945),(-21937980239101531569106880903)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨26839202809607225135944631697,26839202809607225160156695476⟩,⟨(-27037251349308538185198098630),(-27037251349308538162760830688)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨21988210061360921964806006926,21988210061360922015211944914⟩,⟨(-30186085262857054376416893481),(-30186085262857054327195292351)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨15958127727161354838906744602,15958127727161355068219710075⟩,⟨(-31177011368671939553688612205),(-31177011368671939324987393005)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨9974412384153297133592737801,9974412384153298517337538234⟩,⟨(-30135497055620737260970799197),(-30135497055620735877410316908)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨4980840022786919118593681646,4980840022786925922840334432⟩,⟨(-27434332504361615072611028952),(-27434332504361608268294346643)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1491975092651864841811432580,1491975092651888533826850005⟩,⟨(-23524593022500309717432051384),(-23524593022500286025243777849)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-439390799264005542312145818),(-439390799263949903623753654)⟩,⟨(-18799064346855289303330904888),(-18799064346855233664455670481)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1116723975781948306999685573),(-1116723975781861343454354904)⟩,⟨(-13588616610384857482645488239),(-13588616610384770518947602850)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-967085438943769179108562677),(-967085438943683901692690784)⟩,⟨(-8172585175680156919406428732),(-8172585175680071641894288801)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-369136167739183998215803111),(-369136167739148120090431073)⟩,⟨(-2720969670928967041916134310),(-2720969670928931163758214222)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-14052303362329738588218154105),(-14052303362324243841350513667)⟩,⟨(-43463739832454165367846696100),(-43463739832448670622321320605)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 7) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_7 (tableDensity false) (fullFactor false 1 7) density0_contains hk1_0_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-3327541872566209321304847382),(-3327541872566209320644015794)⟩,⟨(-8512513999966307925168124629),(-8512513999966307924218838849)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_7 1 7 ha1_0_7_contains + def realAnswer : RBox := ⟨(-17379845234895947909623001487),(-17379845234890453161894529461)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_7 +namespace hm1_1_0_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨44351860276727614605767,44351860276727718809170⟩,⟨(-13066200112791023096426),(-13066200112790918891896)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨115041286881361004648181,115041286881361220049766⟩,⟨(-35643477070219653767062),(-35643477070219438362459)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨141968276265144307592677,141968276265144473982869⟩,⟨(-48246925190876776840003),(-48246925190876610445837)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨123938513104413168757429,123938513104413238738972⟩,⟨(-48168207151856563156630),(-48168207151856493171227)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨81923163270018744866479,81923163270018761762393⟩,⟨(-38527163716584953716445),(-38527163716584936817523)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨41635774292553224750894,41635774292553227110418⟩,⟨(-25320975437134140140127),(-25320975437134137778673)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨16293019351935318640083,16293019351935318843498⟩,⟨(-13471205573970285805072),(-13471205573970285600625)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4862291381379351881669,4862291381379351895958⟩,⟨(-5571551267802062018168),(-5571551267802062003427)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1078407675062281514361,1078407675062281515894⟩,⟨(-1706620315788412209265),(-1706620315788412207573)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨169580842078746671196,169580842078746671424⟩,⟨(-365894253671089009689),(-365894253671089009413)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨17484594495419756407,17484594495419756448⟩,⟨(-50834630722520114328),(-50834630722520114283)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1035742780845015944,1035742780845015960⟩,⟨(-4068230099162760261),(-4068230099162760240)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨28005808139070691,28005808139070707⟩,⟨(-154093035327472712),(-154093035327472696)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨226800934794955,226800934794971⟩,⟨(-1908369099311000),(-1908369099310984)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨223855690438,223855690454⟩,⟨(-3333729679786),(-3333729679770)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1743183,1743199⟩,⟨(-53736072),(-53736053)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2790907235793451489822600,2790907235793468201831347⟩,⟨3757191905399305879110086,3757191905399322591050179⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨7918670519907625155779968,7918670519907684578909571⟩,⟨10077727025964705262279433,10077727025964764685227287⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨11784227757791157804865164,11784227757791290972059589⟩,⟨13402488503481824043205092,13402488503481957210162992⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨13880273577115783340146213,13880273577116047794803972⟩,⟨13338614006154681144010568,13338614006154945598441262⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨14096272375248047040637287,14096272375248513369111426⟩,⟨10835530679141166587153995,10835530679141632915454089⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨12705844390642639646291562,12705844390643333211884538⟩,⟨7413014884859036544514662,7413014884859730110001296⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨10282579863986331913305851,10282579863987145665386547⟩,⟨4298501898133013651978287,4298501898133827404010817⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨7538488445955914553766153,7538488445956623269362103⟩,⟨2059641890682598722012865,2059641890683307437599132⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨5069204444216316170068397,5069204444216776481809829⟩,⟨732745335316072170368922,732745335316532482119637⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨3177305045118508152285874,3177305045118734989628971⟩,⟨93475555696567578570552,93475555696794415928937⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1889203835380846172027425,1889203835380931856765178⟩,⟨(-133023811476861121861051),(-133023811476775437108715)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1081989446261636212988025,1081989446261663238406936⟩,⟨(-162848760090342519866326),(-162848760090315494436165)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨601650638681937336331357,601650638681945200920880⟩,⟨(-125536815551774818501445),(-125536815551766953904348)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨322181703415178474423943,322181703415180772718880⟩,⟨(-79717332549259859650081),(-79717332549257561350574)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨156237536406997570672044,156237536406998265944435⟩,⟨(-42364426170544440645340),(-42364426170543745370572)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨46475862952167287122442,46475862952167446251121⟩,⟨(-13132010884383871407340),(-13132010884383712277924)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-44561968960295092905200938),(-44561968960295092874840833)⟩,⟨70276493515168038882833785,70276493515168038915628257⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-123161972624283417444029335),(-123161972624283417355021076)⟩,⟨202613090529622000360256275,202613090529622000456396331⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-173879599494227680800215007),(-173879599494227680659652135)⟩,⟨309675584374913741726945069,309675584374913741877977667⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-188101180773506370897103681),(-188101180773506370717513588)⟩,⟨376016686456481376053981438,376016686456481376245550542⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-166613377863422149639296579),(-166613377863422149436979881)⟩,⟨394358380575037170803206446,394358380575037171017108040⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-119521051164292855740650655),(-119521051164292855528019596)⟩,⟨370735067662114874576345712,370735067662114874799563566⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-63815276072511516473717111),(-63815276072511516250036178)⟩,⟨320416891900072814101939071,320416891900072814334942413⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-15791839248257275423732023),(-15791839248257275118680959)⟩,⟨259150429598255511444848232,259150429598255511757447900⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨15814975960287142604695050,15814975960287143479661501⟩,⟨198402886393225065917032098,198402886393225066797410454⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨30543811475500571888602046,30543811475500575919244247⟩,⟨144825735568604998174449655,144825735568605002208744328⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨32841493186870347716498557,32841493186870364179930754⟩,⟨101143605796231290268849033,101143605796231306734665746⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨28365953897000051729267901,28365953897000100623967973⟩,⟨67500420029548943219643065,67500420029548992115903972⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨21557151161140536203520905,21557151161140636250897619⟩,⟨42790071228000386648814526,42790071228000486697158100⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨14730177614084378094044264,14730177614084517910323050⟩,⟨25354078083559954937831390,25354078083560094754646373⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨8515540026068994891454384,8515540026069121457229984⟩,⟨13164836566641169868552049,13164836566641296434589193⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2782145269430738946470992,2782145269430789970981622⟩,⟨4053443956806629639159690,4053443956806680663746617⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-529010527690914218741994596),(-529010527690911351066657831)⟩,⟨30570637304561919997501871,30570637304564787661465161⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1504018396144145463889665343),(-1504018396144138977213445471)⟩,⟨109993740425325546729092122,109993740425332033371609577⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-2250894697168667677285556942),(-2250894697168661654430548544)⟩,⟨238029193740832336367730996,238029193740838359168530513⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-2687516473517402673442319531),(-2687516473517399302011424767)⟩,⟨427174606957225764072361884,427174606957229135432099333⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2813135678031739286784283665),(-2813135678031738071771972481)⟩,⟨660546126416787793765291239,660546126416789008695347334⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-2690525973928153198469316937),(-2690525973928152909545651216)⟩,⟨887974554314343990608427224,887974554314344279445283668⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2401661136853453470802075150),(-2401661136853453421894623184)⟩,⟨1048812836242471487884161996,1048812836242471536706187940⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2020256990767662903676076474),(-2020256990767662896254574416)⟩,⟨1109331251236964982236744813,1109331251236964989579962738⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1609422582182290519431527861),(-1609422582182290517576501180)⟩,⟨1074167142133499392954161413,1074167142133499394741737904⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1220055529597997655628973480),(-1220055529597997654695668029)⟩,⟨970307075467346690677339650,970307075467346691555841305⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-885344278165112119221092492),(-885344278165112118621236539)⟩,⟨827955815145482364390799546,827955815145482364948810995⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-618345000896265595616822258),(-618345000896265595218614399)⟩,⟨670007707362342970160208397,670007707362342970527940578⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-415186988548713837952208597),(-415186988548713837692263562)⟩,⟨510333685820784497132988779,510333685820784497371867287⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-262496884645012178962956490),(-262496884645012178802768851)⟩,⟨356088678910085433602266474,356088678910085433748956673⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-144411156708103582658745295),(-144411156708103582572585373)⟩,⟨209501645319055538163119756,209501645319055538241813676⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-46009349037017929330650601),(-46009349037017929303607971)⟩,⟨69042443639212912077158994,69042443639212912101831495⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-913191231671422323666153741),(-913191231671382459255779099)⟩,⟨(-1243778852312128055597897349),(-1243778852312088191125083083)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-2772149927183363355411404045),(-2772149927183215347446103314)⟩,⟨(-3583147716824146161799335069),(-3583147716823998153657546151)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-4658185613473386412968493487),(-4658185613473025000387440442)⟩,⟨(-5483423430639804151169174282),(-5483423430639442738332732492)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-6436946361691169235806801026),(-6436946361690353953317216119)⟩,⟨(-6683051817364425532088236822),(-6683051817363610249312706405)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-7923217320759107212432366961),(-7923217320757406931322844210)⟩,⟨(-7000984336002065673208374185),(-7000984336000365391834245667)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-8992965120706922432995966341),(-8992965120703815628835483970)⟩,⟨(-6448842624959460544346175106),(-6448842624956353739980348450)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-9587483921232828155046350799),(-9587483921228197105878788081)⟩,⟨(-5279568681888107621903170868),(-5279568681883476572610525605)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-9671903862096905792715154545),(-9671903862091611195363681643)⟩,⟨(-3869322901726258431078749860),(-3869322901720963833685810000)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-9246700077305663411585048398),(-9246700077301005092818324226)⟩,⟨(-2548887748333831554721290202),(-2548887748329173235982814317)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-8370463453413628633472782395),(-8370463453410455203414752691)⟩,⟨(-1513879824110232002243483087),(-1513879824107058572258249479)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7152455833324383237865129123),(-7152455833322704510149030617)⟩,⟨(-813867588930190385320991933),(-813867588928511657698175322)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-5735535920199216734787423722),(-5735535920198476726165804827)⟩,⟨(-388949395763290751908026973),(-388949395762550743382754422)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-4277607520913023320273578137),(-4277607520912728839488233658)⟩,⟨(-142393055724049715629537253),(-142393055723755234930350388)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2906321483318008473035414558),(-2906321483317895982953283780)⟩,⟨(-9431282203096587277350363),(-9431282202984097261178955)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1670893445926405807284680309),(-1670893445926364318027375453)⟩,⟨36722419272451260042739186,36722419272492749259226986⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-543570943821980027121806526),(-543570943821969456333317199)⟩,⟨20072855686046740690999567,20072855686057311465850645⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨133643427923547033134619230,133643427923547034234256390⟩,⟨(-8388090183744948024031287),(-8388090183744947278065633)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨362413830851352090156501642,362413830851352093479809896⟩,⟨(-122267747477890284670979152),(-122267747477890282376806156)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨359664487273944967808523027,359664487273944973336939786⟩,⟨(-519802176037552364928116535),(-519802176037552360942585014)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-245628987656427755420837643),(-245628987656427747726043920)⟩,⟨(-1437300047777189559865666881),(-1437300047777189554003917687)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1682223791223795765497193344),(-1682223791223795755591278757)⟩,⟨(-3204015711923467353118410116),(-3204015711923467345104776810)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-3635356314904915737690369050),(-3635356314904915725036483804)⟩,⟨(-5945818153912829065005415212),(-5945818153912829054146049707)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-5423513913045751078262269788),(-5423513913045751060140336403)⟩,⟨(-9185307565163467854519988744),(-9185307565163467837980331203)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-6567644730075489129109695030),(-6567644730075489088591320088)⟩,⟨(-12028138597075310303269246321),(-12028138597075310264003914976)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-6989968014219395732752331129),(-6989968014219395544238297831)⟩,⟨(-13730085695099577549413806092),(-13730085695099577361767172221)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-6847358466300957515634015093),(-6847358466300956382039669436)⟩,⟨(-13995916931567016726471232290),(-13995916931567015593417205579)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-6356242309921464892546778707),(-6356242309921459332404503075)⟩,⟨(-12952840453057953826178901559),(-12952840453057948266347043953)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-5680249885319977344899281692),(-5680249885319957994301349713)⟩,⟨(-11001863208031052149844199543),(-11001863208031032799427650814)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-4849027846890380525763648007),(-4849027846890335069427583495)⟩,⟨(-8616293433673640165171002002),(-8616293433673594708939204349)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-3782054465638602195296282283),(-3782054465638531114812780775)⟩,⟨(-6129666349410590201247926105),(-6129666349410519120819727835)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-2425209521585984157154673177),(-2425209521585914429230628364)⟩,⟨(-3663322887174952514352933143),(-3663322887174882786454538513)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-836834881144277117215515848),(-836834881144247775337369026)⟩,⟨(-1218901468459290004694263652),(-1218901468459260662823024577)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-28011642881168045001745820550),(-28011642881163532747825583635)⟩,⟨(-22757854248321392816798615121),(-22757854248316880565063417964)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 7) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_7 (tableDensity true) (fullFactor false 1 7) density1_contains hk1_0_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨4351400910278889111611405269,4351400910278889112475569653⟩,⟨11131749076879018054747712341,11131749076879018055989086053⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_7 1 7 ha1_0_7_contains + def realAnswer : RBox := ⟨(-23660241970889155890234415281),(-23660241970884643635250013982)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_7 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_1.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_1.lean new file mode 100644 index 0000000000000000000000000000000000000000..405aac17e0455257fa99a034265db2403d4e9d49 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_1.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_0_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨7162322690769969064224,7162322690769977351224⟩,⟨16089686508702427121050,16089686508702435408331⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨19108623087702555829675,19108623087702572659200⟩,⟨40542872246956271326687,40542872246956288156930⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨24887493732273351814003,24887493732273364359505⟩,⟨47488715189191635424361,47488715189191647970719⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨23449105552612017610490,23449105552612022609982⟩,⟨38850656666958519879521,38850656666958524879720⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨17026983230404532679703,17026983230404533802203⟩,⟨24002239781942666950603,24002239781942668073522⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨9592938307135077831931,9592938307135077975422⟩,⟨11389390767913505810875,11389390767913505954538⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨4146698675024842625676,4146698675024842637148⟩,⟨4116282302274834404859,4116282302274834416371⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1344981838295665263093,1344981838295665263969⟩,⟨1106038965087446325329,1106038965087446326197⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨315860228812267967772,315860228812267967901⟩,⟨212559483575131964541,212559483575131964661⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨50850530458278661411,50850530458278661447⟩,⟨27581171562817495443,27581171562817495475⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨5161620001910374320,5161620001910374342⟩,⟨2217111094059641163,2217111094059641182⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨289287783869010870,289287783869010888⟩,⟨96674086297497023,96674086297497042⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨7148266299088815,7148266299088834⟩,⟨1835756098826675,1835756098826692⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨50979004054706,50979004054725⟩,⟨10078397587120,10078397587137⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨40383191177,40383191193⟩,⟨6311448111,6311448129⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨163627,163649⟩,⟨21560,21576⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1655897929301808415362414),(-1655897929301805764942711)⟩,⟨3551638959043459050975932,3551638959043461701281324⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-4405138657768130761851103),(-4405138657768121433764090)⟩,⟨9827906682241708910292439,9827906682241718238078372⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-5755333409516789769962148),(-5755333409516769283362854)⟩,⟨13916155577169243523443232,13916155577169264009658201⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-5552995917457293528814925),(-5552995917457254030407369)⟩,⟨15233044281842125838601422,15233044281842165336651392⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-4275782243086465583628059),(-4275782243086398546284806)⟩,⟨14082208164243710442255781,14082208164243777479337837⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2656277256081777325544371),(-2656277256081682116935805)⟩,⟨11387405633956893197752697,11387405633956988406210492⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1281822120690660378501864),(-1281822120690554466467410)⟩,⟨8214745012573018729499591,8214745012573124641469568⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-401910706562296016703544),(-401910706562209050986137)⟩,⟨5364124803071120827444776,5364124803071207793147729⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨23056325924463492090891,23056325924516487485399⟩,⟨3213680243294729063442136,3213680243294782058842977⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨157459236190988192130205,157459236191012637314354⟩,⟨1792579232253604699493730,1792579232253629144688556⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨156377883053257125566499,156377883053265761482291⟩,⟨946757945226793920798262,946757945226802556722714⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨114539811911040285615239,114539811911042838031799⟩,⟨482284338593112908333586,482284338593115460755683⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨72862661491895309048779,72862661491896008877802⟩,⟨240852983037239876083406,240852983037240575915545⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨42133569472580182739431,42133569472580377253915⟩,⟨118124308006936882025952,118124308006937076542061⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨21323732047560887961832,21323732047560944695058⟩,⟨53874940323308149426876,53874940323308206160853⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨6466372394009930997678,6466372394009943733659⟩,⟨15531916826351844337179,15531916826351857073380⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-72249559079981467324352251),(-72249559079981467305653153)⟩,⟨(-975579239295318512892123),(-975579239295318504003152)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-204324230447782862188234511),(-204324230447782862134701290)⟩,⟨2008179351042340902104717,2008179351042340928008823⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-302511856903678460841227097),(-302511856903678460760447885)⟩,⟨16733315096806176638142007,16733315096806176678960148⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-354776476842697643557858125),(-354776476842697643460574381)⟩,⟨42664438734344200549574275,42664438734344200601680317⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-360329326479016518804232160),(-360329326479016518702002317)⟩,⟨72324421839261345392214595,72324421839261345450747452⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-327913100563053176703634457),(-327913100563053176605147270)⟩,⟨96156047170300931543260586,96156047170300931604439848⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-272039743828183732649161115),(-272039743828183732558015244)⟩,⟨107873800771348258044323424,107873800771348258106644924⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-208259502485529231256484452),(-208259502485529231160351222)⟩,⟨106461300345741151791601952,106461300345741151867299692⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-148775489994852640717348343),(-148775489994852640522114454)⟩,⟨94960276110351869362266706,94960276110351869544080746⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-100314317072088157436357456),(-100314317072088156662484877)⟩,⟨78079750535418037225224673,78079750535418037990796484⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-64596067915903435810332486),(-64596067915903432818531149)⟩,⟨60090093428647762066239846,60090093428647765053136847⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-40161057580119185587170289),(-40161057580119177034633995)⟩,⟨43723900393419447396578490,43723900393419455946292604⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-24235692544538670148648740),(-24235692544538653201003955)⟩,⟨30111236921203622279695654,30111236921203639225753686⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-14008042007279342822466022),(-14008042007279319741305114)⟩,⟨19273550542301914625699062,19273550542301937705997489⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-7219167350748320131318661),(-7219167350748299614051937)⟩,⟨10642844460745063807049390,10642844460745084323891663⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2221746031687347222815171),(-2221746031687339028895452)⟩,⟨3391353967134663361960473,3391353967134671555753157⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-266528497086402926993632599),(-266528497086402034495473644)⟩,⟨(-317454144150791259555974640),(-317454144150790367085781097)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-782485351018853376363691014),(-782485351018851365345350822)⟩,⟨(-898954980693999439055886515),(-898954980693997428120468768)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1243531214040350268247639075),(-1243531214040348415123645968)⟩,⟨(-1333449025671244642662892848),(-1333449025671242789673129907)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1608561272777491732209555168),(-1608561272777490706156705706)⟩,⟨(-1564981715135349513909342139),(-1564981715135348488034671941)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1841933454699291223802457649),(-1841933454699290859001458653)⟩,⟨(-1584959413025270991341454465),(-1584959413025270626750989572)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1927538826982033573082440174),(-1927538826982033487480894251)⟩,⟨(-1429925492390492993805403604),(-1429925492390492908431866669)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-1874268307632905512554829083),(-1874268307632905498004055122)⟩,⟨(-1167528149069664110618403192),(-1167528149069664096297220090)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1710280659242601727995088502),(-1710280659242601725522504441)⟩,⟨(-871674424031932029283392922),(-871674424031932027027708688)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1474400619908718289322980108),(-1474400619908718288498363572)⟩,⟨(-599200482672188168196382185),(-599200482672188167565282081)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1207250173911075522666654925),(-1207250173911075522170225223)⟩,⟨(-380524818035614351457507161),(-380524818035614351124989544)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-942817039074235315238352748),(-942817039074235314897102954)⟩,⟨(-222937789878428053065627664),(-222937789878428052856677526)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-703383100290194056904702991),(-703383100290194056669775921)⟩,⟨(-119416209583182429661625986),(-119416209583182429528636032)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-498730122486786485499015004),(-498730122486786485341687513)⟩,⟨(-57288360926948799381685467),(-57288360926948799298826982)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-328433597301424671787157400),(-328433597301424671687904422)⟩,⟨(-23713145327636385051523362),(-23713145327636385002520951)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-185549784649215935628521643),(-185549784649215935574079267)⟩,⟨(-7941449490933442694269332),(-7941449490933442668707112)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-59885567012274476132410054),(-59885567012274476115131723)⟩,⟨(-1662195306468942176158902),(-1662195306468942168269044)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1282516122601516567921212591,1282516122601532425922717383⟩,⟨(-844165383124033813224057600),(-844165383124017955144333662)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨3591246464420082946663773655,3591246464420141587622855041⟩,⟨(-2543295197168004958161555046),(-2543295197167946316986110758)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨5202349631810595163884246716,5202349631810737232953510250⟩,⟨(-4242548320528162832071224659),(-4242548320528020762693388436)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨5878319079898627259795980807,5878319079898944110526140483⟩,⟨(-5855531678625659944018759311),(-5855531678625343092949203851)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨5632912121020591279101479773,5632912121021242596130594230⟩,⟨(-7208459843876427622494341554),(-7208459843875776305154152749)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨4678758024304104389363297071,4678758024305274516560334311⟩,⟨(-8093931289974133094197339145),(-8093931289972962966763722784)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨3323485994057869713402343356,3323485994059581515156005866⟩,⟨(-8374081528855810160930026291),(-8374081528854098359036838879)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1880772331993534032713066194,1880772331995452558830951429⟩,⟨(-8050421265434922718902120077),(-8050421265433004192741468225)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨604063608559867366749810765,604063608561521002222220361⟩,⟨(-7250232521376803326920153025),(-7250232521375149691485720843)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-354553293673442540358615176),(-354553293672338579257444210)⟩,⟨(-6164138343763026602336348680),(-6164138343761922641330264058)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-946070825485394425423921356),(-946070825484821660291142587)⟩,⟨(-4980867694863145293252396142),(-4980867694862572528245741081)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1195099941609672796009624473),(-1195099941609424778618888510)⟩,⟨(-3840010532360684517646697603),(-3840010532360436500388691452)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1166658341344426756747214758),(-1166658341344329582003999270)⟩,⟨(-2811219341325032076220972132),(-2811219341324934901597785799)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-943044404539937294576331415),(-943044404539900636004087052)⟩,⟨(-1904893808182857346864766922),(-1904893808182820688386431099)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-603064564759905792950691353),(-603064564759892390962891572)⟩,⟨(-1099300979332784619664507145),(-1099300979332771217735982214)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-206396591648134740718028444),(-206396591648131341667173392)⟩,⟨(-358794558332248670325577511),(-358794558332245271294930963)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨26749624545180954375817374,26749624545180954834072700⟩,⟨1766541129393769391372282968,1766541129393769392065766485⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨382476861731057218625124515,382476861731057220029215647⟩,⟨5104670384663545247974329911,5104670384663545250046579416⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1503548008580922141783524171,1503548008580922144203056046⟩,⟨7903719195128573396571482686,7903719195128573399955032085⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨3469286483888001978063999295,3469286483888001981567317677⟩,⟨9931783103136880785922413139,9931783103136880790509247289⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5907947665408435359647679701,5907947665408435364286220804⟩,⟨11021054766284074438730672601,11021054766284074444397083708⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨8232207253081470461179227128,8232207253081470467129157471⟩,⟨11019811562394073659343269365,11019811562394073666166124487⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨9987004269697801433117839196,9987004269697801441438075235⟩,⟨9917942154407923925171635785,9917942154407923934158239168⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨10961780419393181780728154530,10961780419393181798616202239⟩,⟨7988614764830546210237003869,7988614764830546228559754438⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨11123114857925801867853818738,11123114857925801949286826095⟩,⟨5696703581942616405636754430,5696703581942616487287149262⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨10563180248724607740815823245,10563180248724608224599153994⟩,⟨3498798846495956058479569826,3498798846495956542322784369⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨9454704016121908713763740906,9454704016121911053898800716⟩,⟨1718278569830664115902964722,1718278569830666456007214760⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨7982449218362520780261488992,7982449218362528807536380164⟩,⟨507253416176157313286891677,507253416176165340496271236⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6294081654633031310484973454,6294081654633049921358216838⟩,⟨(-146655209274945204750327035),(-146655209274926593945488531)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨4501345018919714362214949312,4501345018919743155828373563⟩,⟨(-369765657414648609517005423),(-369765657414619815958362476)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2687241062280076069861149180,2687241062280104105322376239⟩,⟨(-317955780384904222507823960),(-317955780384876187080760455)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨891290383143368772983968108,891290383143380525146947510⟩,⟨(-120914330649100653401600873),(-120914330649088901250105481)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨16907190941578326860765384320,16907190941579963398196786257⟩,⟨(-1368579985293918479989480652),(-1368579985292281941791049576)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 8) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_8 (tableDensity false) (fullFactor false 1 8) density0_contains hk1_0_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨3774213400146128454350003846,3774213400146128454721889967⟩,⟨(-1170054074655807285544968933),(-1170054074655807285308718910)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_8 1 8 ha1_0_8_contains + def realAnswer : RBox := ⟨20681404341724455315015388166,20681404341726091853018676224⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_8 +namespace hm1_1_0_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨851106110462198173083,851106110462204961565⟩,⟨2889053729368058306639,2889053729368065095044⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨2277992059096975632551,2277992059096989413575⟩,⟨7353669438125083671637,7353669438125097452472⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨2967554177390099777777,2967554177390110042595⟩,⟨8736187708419805767782,8736187708419816032354⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨2794853847906600171230,2794853847906604256312⟩,⟨7198011138181944469083,7198011138181948553936⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2064520597333758017127,2064520597333758931949⟩,⟨4397562494966874809139,4397562494966875723799⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1224831114768553233935,1224831114768553349938⟩,⟨2019599377757105717181,2019599377757105833086⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨573765644641315561477,573765644641315570377⟩,⟨696551887441625790763,696551887441625799617⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨203187201561689330377,203187201561689330942⟩,⟨178116558870508776941,178116558870508777491⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨51589827725410254710,51589827725410254777⟩,⟨32763224458165194659,32763224458165194721⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨8819234751891514401,8819234751891514425⟩,⟨4109746107161077691,4109746107161077715⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨931037467291478575,931037467291478592⟩,⟨322128521743826103,322128521743826119⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨53180213548855664,53180213548855681⟩,⟨13630499354035907,13630499354035923⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1318066403567957,1318066403567973⟩,⟨241479759631443,241479759631459⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨9351239864278,9351239864294⟩,⟨1121427240259,1121427240276⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨7361771729,7361771745⟩,⟨498385416,498385432⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨29707,29729⟩,⟨965,981⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-490645681562262140056524),(-490645681562259957794681)⟩,⟨364455978814192942822398,364455978814195125092582⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1303691627513744902310769),(-1303691627513737218919263)⟩,⟨1024283602245664263062894,1024283602245671946476287⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1701587711159597779629370),(-1701587711159580893430232)⟩,⟨1495711536537624014330857,1495711536537640900557994⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1646925041380714355080379),(-1646925041380681769984843)⟩,⟨1712873934989215775902450,1712873934989248361024206⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1289702639384487472322783),(-1289702639384432119748653)⟩,⟨1676352799568751489539800,1676352799568806842133390⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-843558285440694440359219),(-843558285440615762920921)⟩,⟨1444041958801131721067530,1444041958801210398517252⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-464160346284600071197199),(-464160346284512472142207)⟩,⟨1108397418270627947568324,1108397418270715546628259⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-209731755146474298714839),(-209731755146402334916427)⟩,⟨765658677113820689874605,765658677113892653673959⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-70084462795764472811661),(-70084462795720620011848)⟩,⟨482604375294689815002038,482604375294733667800994⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-8487195856125041068565),(-8487195856104823697429)⟩,⟨282600332405911014798238,282600332405931232168046⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨10965261815426027519714,10965261815433162970605⟩,⟨156854276398545193097067,156854276398552328546765⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨12620385800488559305952,12620385800490665590488⟩,⟨84051892176490973432957,84051892176493079716625⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨9169966243161387233857,9169966243161963953228⟩,⟨43993604557533867799682,43993604557534444518502⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨5539873160218388400267,5539873160218548494811⟩,⟨22399452651070024339776,22399452651070184434003⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2839608737892036995202,2839608737892083644070⟩,⟨10473817705959656142564,10473817705959702791272⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨863640591424059652563,863640591424070119184⟩,⟨3056581576546745799397,3056581576546756265973⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-13776744911639804959388641),(-13776744911639804952915758)⟩,⟨(-8735815299627788542183320),(-8735815299627788536203526)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-39468371688823074180228466),(-39468371688823074161373354)⟩,⟨(-23992743309132119275114444),(-23992743309132119257695510)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-59571422733502073862658301),(-59571422733502073833408377)⟩,⟨(-33452984850596812213241664),(-33452984850596812186080195)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-71008055294010120886650504),(-71008055294010120850233430)⟩,⟨(-35530328435961082109151552),(-35530328435961082075090496)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-72702789464561577684343956),(-72702789464561577644655894)⟩,⟨(-30730749087437567371860770),(-30730749087437567334411351)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-66390223196804027752878900),(-66390223196804027712666005)⟩,⟨(-21423180945871872183784463),(-21423180945871872145573375)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-55496800402697546423193153),(-55496800402697546382643573)⟩,⟨(-11074686454554994285426065),(-11074686454554994246592721)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-43266533308628052166966714),(-43266533308628052114723177)⟩,⟨(-2656017940911016879150965),(-2656017940911016828260265)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-31858962732420252568332142),(-31858962732420252427576458)⟩,⟨2525060634360523713312177,2525060634360523853120925⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-22348384992027041751619697),(-22348384992027041132720275)⟩,⟨4704217872123798151789019,4704217872123798770064345⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-15009911388702309018751898),(-15009911388702306587688068)⟩,⟨4868831821942373105472106,4868831821942375536138938⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-9657550053289543382124877),(-9657550053289536413189026)⟩,⟨4055998589756422850259587,4055998589756429818943407⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-5927809783083597217586912),(-5927809783083583392197282)⟩,⟨2985212103826222887706023,2985212103826236712944041⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-3421611721395259473707083),(-3421611721395240629957619)⟩,⟨1987417328237119851922000,1987417328237138695589341⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1744074786842761775695017),(-1744074786842745016332324)⟩,⟨1128024241091844867372260,1128024241091861626695535⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-531876855573135015217185),(-531876855573128320320488)⟩,⟨365057645151229668916430,365057645151236363801702⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-7993603391737530325128514),(-7993603391736780451921492)⟩,⟨(-138329146825158073626612375),(-138329146825157323750383978)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-28620336703399592724691174),(-28620336703397904219765709)⟩,⟨(-391420221995517717697118971),(-391420221995516029183285972)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-61345210693178862996496638),(-61345210693177309238177660)⟩,⟨(-580331123278466051499566885),(-580331123278464497727065456)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-108569992859838663388576866),(-108569992859837805017682290)⟩,⟨(-683425796294605810604961871),(-683425796294604952215733704)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-164905865976748883055226884),(-164905865976748578949087155)⟩,⟨(-702731987064033740755510320),(-702731987064033436628603439)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-216992858624532661587759296),(-216992858624532590757775479)⟩,⟨(-657873297615220826733757676),(-657873297615220755882392536)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-250145954027229430031839990),(-250145954027229418337727055)⟩,⟨(-573114724697144258344187596),(-573114724697144246629620832)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-257667341461258860169321575),(-257667341461258858455324677)⟩,⟨(-469474821372521041860081641),(-469474821372521040127906642)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-242664216218137748081409771),(-242664216218137747675136259)⟩,⟨(-363739849312785123032618275),(-363739849312785122611181357)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-213135185120578788778147957),(-213135185120578788583692926)⟩,⟨(-268098926363555113652225724),(-268098926363555113445855915)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-176983670735541806781394366),(-176983670735541806661012939)⟩,⟨(-189315644603073203028905001),(-189315644603073202899731840)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-139660396930837143140520033),(-139660396930837143063048527)⟩,⟨(-128926565823671283968098514),(-128926565823671283884434507)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-104068644877665583191112873),(-104068644877665583141811227)⟩,⟨(-84681909831019282285215251),(-84681909831019282231763931)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-71348054161528799959452889),(-71348054161528799929666454)⟩,⟨(-52600914467365465863135746),(-52600914467365465830759818)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-41463384398654301134502915),(-41463384398654301118702204)⟩,⟨(-28582166883142580189035853),(-28582166883142580171830010)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-13578168245456517387825992),(-13578168245456517382900430)⟩,⟨(-9048426303989197933166293),(-9048426303989197927799226)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨406636147015843219445087278,406636147015856252312467043⟩,⟨(-298553821334487358676271220),(-298553821334474325829822769)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1167018677167669701939190362,1167018677167717899293527452⟩,⟨(-902847046472334596021616193),(-902847046472286398726202263)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1772605082900606729744517624,1772605082900723512426905280⟩,⟨(-1505704056032400953260136620),(-1505704056032284170662368251)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨2136847911390498531251781356,2136847911390759027971879549⟩,⟨(-2057848350321584293648899842),(-2057848350321323797022485826)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2207131150279906588311657899,2207131150280442129256821788⟩,⟨(-2497274764815836894893088007),(-2497274764815301354033352076)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1999099818695398069329447531,1999099818696360196629123137⟩,⟨(-2786759878339085646900743960),(-2786759878338123519666181626)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1605728165775166847986898010,1605728165776574064271383934⟩,⟨(-2914503019434484057711945193),(-2914503019433076841466305584)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1152751503558898763338110904,1152751503560475154823950268⟩,⟨(-2879678007251721523702169192),(-2879678007250145132228937518)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨743182838776194040400037529,743182838777551703442149696⟩,⟨(-2694119215458862224301875735),(-2694119215457504561251406142)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨431957198675475315703847233,431957198676380722982747268⟩,⟨(-2386462396843479596895207220),(-2386462396842574189595193499)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨227425066384195720711512851,227425066384664876116966087⟩,⟨(-1997044207439229332623473567),(-1997044207438760177191493464)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨106624873570565489162031784,106624873570768368446750409⟩,⟨(-1570976576266599343287374738),(-1570976576266396463975738650)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨38403745280344326636924667,38403745280423714693350574⟩,⟨(-1152307274652279739058168920),(-1152307274652200350978043263)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2527771844163498848415098,2527771844193415704408364⟩,⟨(-772565533412000651452817065),(-772565533411970734578907987)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-9665992622333889044241552),(-9665992622322959922098063)⟩,⟨(-440058394860780511556706527),(-440058394860769582423578447)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-5261156496578992105576162),(-5261156496576221285449084)⟩,⟨(-142477700166587071980166390),(-142477700166584301156386606)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨3290491797095382590392300,3290491797095382883107923⟩,⟨52439847292444332884281785,52439847292444333315928730⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨47801306760210908023595364,47801306760210908921071801⟩,⟨141764929072779723444846413,141764929072779724745172293⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨201941007548299948840310593,201941007548299950390050547⟩,⟨139892146356715332513557328,139892146356715334662893002⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨553257546866654316835587825,553257546866654319094906129⟩,⟨(-94277672497107588737184068),(-94277672497107585773233677)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1218833663760729498904318970,1218833663760729501958617621⟩,⟨(-639679792171876225274988279),(-639679792171876221502668519)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2230441979527967348834851461,2230441979527967352918327775⟩,⟨(-1363687405691243343975817448),(-1363687405691243339222622782)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨3391952870388255366293770189,3391952870388255372413892415⟩,⟨(-2002991654345925980064280219),(-2002991654345925973366212342)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨4367081750152219060258049856,4367081750152219074512558940⟩,⟨(-2384808146096697104258302991),(-2384808146096697089558115500)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨4897978083966056650549254735,4897978083966056717349545614⟩,⟨(-2493769174853800702850359363),(-2493769174853800635751840406)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨4905651784622963761516899081,4905651784622964157695324066⟩,⟨(-2400110458465841015709594991),(-2400110458465840619353295479)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨4463935997539038382774910789,4463935997539040294898502710⟩,⟨(-2190469129180334706551616954),(-2190469129180332794331432884)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨3733273832602212112934112066,3733273832602218669139082025⟩,⟨(-1927313802873706561084309852),(-1927313802873700004826125209)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2884864771703030513272449416,2884864771703045718096113286⟩,⟨(-1623370880832721878522921848),(-1623370880832706673670446341)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨2030521011223180014725829998,2030521011223203549386247095⟩,⟨(-1252767206355563172216405959),(-1252767206355539637541717650)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨1204544424293137338133113831,1204544424293160261564226909⟩,⟨(-797417487894464084752834644),(-797417487894441161315577143)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨399267626251105300833577022,399267626251114911984767667⟩,⟨(-274115765024029242324415800),(-274115765024019631171700637)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨7983058897775504900991784256,7983058897776848878784932167⟩,⟨(-8594303798213597567839514457),(-8594303798212253589250891722)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 8) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_8 (tableDensity true) (fullFactor false 1 8) density1_contains hk1_0_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4935509830960321825405548418),(-4935509830960321824919235798)⟩,⟨1530070713011440296172940113,1530070713011440296481882451⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_8 1 8 ha1_0_8_contains + def realAnswer : RBox := ⟨3047549066815183075486235838,3047549066816527053965696369⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_8 +namespace hm1_0_0_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-931631557469965960199),(-931631557469965480285)⟩,⟨414705740821208674989,414705740821209154886⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-2303869024421066840240),(-2303869024421065883041)⟩,⟨1085631846983429209558,1085631846983430166718⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2598233992066866182374),(-2598233992066865494242)⟩,⟨1360944990385739801609,1360944990385740489697⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-2006430796138718648947),(-2006430796138718389398)⟩,⟨1209927192457117392382,1209927192457117651897⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1145847635864747909035),(-1145847635864747854949)⟩,⟨811811421938379485859,811811421938379539928⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-491407110130024931514),(-491407110130024925221)⟩,⟨413208980245005110703,413208980245005116995⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-156585763510479415613),(-156585763510479415151)⟩,⟨157413473035317893270,157413473035317893736⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-36074436550643619902),(-36074436550643619858)⟩,⟨43754071751656748265,43754071751656748313⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-5755140604527944088),(-5755140604527944066)⟩,⟨8524815549056397538,8524815549056397561⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-596444209790112473),(-596444209790112456)⟩,⟨1095406399023142975,1095406399023142995⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-36502081631338579),(-36502081631338562)⟩,⟨84595149823963662,84595149823963679⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1138338368275300),(-1138338368275281)⟩,⟨3389380704074237,3389380704074259⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-14168957978647),(-14168957978631)⟩,⟨54905338604501,54905338604519⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-44583621495),(-44583621478)⟩,⟨224662487597,224662487615⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-12565214),(-12565198)⟩,⟨80230819,80230835⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-25),(-9)⟩,⟨69,96⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-412266608092062136110798),(-412266608092061828482858)⟩,⟨(-192214589855367323625803),(-192214589855367015984464)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1130045994092966683490284),(-1130045994092965611394091)⟩,⟨(-506554291330229478880433),(-506554291330228406749274)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1570243880726026492721765),(-1570243880726024183495776)⟩,⟨(-649542010457998013269428),(-649542010457995703999642)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1671332467411537913678602),(-1671332467411533587228373)⟩,⟨(-609517213345983926399799),(-609517213345979599909944)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1489137780475806470626408),(-1489137780475799396506372)⟩,⟨(-452489877566551860963470),(-452489877566544786815530)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1150939265098083663493964),(-1150939265098074061166953)⟩,⟨(-268827613709495601080303),(-268827613709485998737899)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-787540540235348269386395),(-787540540235338132193512)⟩,⟨(-123183435715042566409171),(-123183435715032429210044)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-484571421151912321076522),(-484571421151904469108741)⟩,⟨(-36512983587986443062863),(-36512983587978591093761)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-272131699342155296448493),(-272131699342150807049433)⟩,⟨1829989024510989530766,1829989024515478929296⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-141817275363696728592675),(-141817275363694791218847)⟩,⟨12393770045614626417038,12393770045616563790026⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-69918484763619594053623),(-69918484763618954570361)⟩,⟨11519440200821004836398,11519440200821644319026⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-33322174526908127893647),(-33322174526907951013346)⟩,⟨7901878799681333738934,7901878799681510618861⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-15661737445374279497782),(-15661737445374233869590)⟩,⟨4733712199816820395858,4733712199816866023855⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-7301954899882935633015),(-7301954899882923587118)⟩,⟨2603303030418197583990,2603303030418209629788⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3210699502563433741138),(-3210699502563430357321)⟩,⟨1270577450487040578522,1270577450487043962297⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-908001065004793677683),(-908001065004792933022)⟩,⟨378018977166081352447,378018977166082097099⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨170039220069412641851656,170039220069412643401354⟩,⟨(-12589845945833789085235119),(-12589845945833789081936503)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-346743980670138512055762),(-346743980670138507568413)⟩,⟨(-35380060290109845093179835),(-35380060290109845083795886)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-2857607068882433644423673),(-2857607068882433637434919)⟩,⟨(-51729813283143458089881101),(-51729813283143458075896400)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-7154210007036386905362606),(-7154210007036386896592352)⟩,⟨(-59556502379515493477383410),(-59556502379515493460846975)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-11841307472867594453545922),(-11841307472867594443913112)⟩,⟨(-59052365949422777736446840),(-59052365949422777719477966)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-15294054441836005267309929),(-15294054441836005257516260)⟩,⟨(-52201991269916311469672601),(-52201991269916311453789545)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-16596834784128856121896834),(-16596834784128856112240860)⟩,⟨(-41888352573312825149938938),(-41888352573312825135728378)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-15790650210209086719838579),(-15790650210209086708559815)⟩,⟨(-30912838107954223480461525),(-30912838107954223466066625)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-13548200876004548767162880),(-13548200876004548741277986)⟩,⟨(-21240788527705516367107745),(-21240788527705516339252259)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-10706187543286273900850029),(-10706187543286273796401302)⟩,⟨(-13763481359605788104404390),(-13763481359605787998782904)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-7924409133807303091873997),(-7924409133807302699803064)⟩,⟨(-8523152423869874303589313),(-8523152423869873910851344)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-5559325378695633939069797),(-5559325378695632855788221)⟩,⟨(-5108448856276983417164467),(-5108448856276982333512547)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-3707161513573872449873880),(-3707161513573870368173322)⟩,⟨(-2984640424906101715952828),(-2984640424906099634050554)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-2311716403930450975296314),(-2311716403930448210157299)⟩,⟨(-1680424314522716141901548),(-1680424314522713376655668)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1253227098407386005877325),(-1253227098407383590935094)⟩,⟨(-850129866687830694179142),(-850129866687828279185265)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-395552808916153355805775),(-395552808916152400156351)⟩,⟨(-259136586869901040747802),(-259136586869900085083063)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨73786690344047329410518151,73786690344047536854680561⟩,⟨(-61949681930909924403857738),(-61949681930909716953127730)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨207958714372591848193917663,207958714372592313490498109⟩,⟨(-181009569738976802051420754),(-181009569738976336735452524)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨305597445149793602607670148,305597445149794027530512933⟩,⟨(-284966796497406548162949797),(-284966796497406123208997230)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨353761472781661619512422363,353761472781661851689882354⟩,⟨(-363558936791922255545616599),(-363558936791922023327389446)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨351962552173804147570683410,351962552173804228692974052⟩,⟨(-408935458619026970800691870),(-408935458619026889631026244)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨310833371097994241615504040,310833371097994260226017684⟩,⟨(-418872588814029061453500427),(-418872588814029042792689615)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨247709269943936333132463546,247709269943936336181950871⟩,⟨(-397495083429379877747146453),(-397495083429379874648140959)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨180110955157014801893199121,180110955157014802361305304⟩,⟨(-353216745834975562850397396),(-353216745834975562336639010)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨120421799410852195114798674,120421799410852195242261710⟩,⟨(-296144845379946729518115741),(-296144845379946729350949044)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨74360244330374520229788590,74360244330374520295097798⟩,⟨(-235767485686671612507876365),(-235767485686671612409791560)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨42396568278325936813524760,42396568278325936853447714⟩,⟨(-179176937128405517871656692),(-179176937128405517805930906)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨22145043448054929390922681,22145043448054929415682842⟩,⟨(-130346398231125780800468605),(-130346398231125780756280797)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨10392782541410259070356098,10392782541410259085432775⟩,⟨(-90411935701318446604005841),(-90411935701318446575019904)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨4226291791622200861324106,4226291791622200870075282⟩,⟨(-58498674550772546557428224),(-58498674550772546539441920)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1397692570247682761516424,1397692570247682766021232⟩,⟨(-32643426626466358394703661),(-32643426626466358384951092)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨290594235146558739307698,290594235146558740688536⟩,⟨(-10468775378326176101121117),(-10468775378326176098044266)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨245321860652653383257899869,245321860652657991679303564⟩,⟨372712640843759181751870037,372712640843763790151028664⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨736281066718210954289756330,736281066718227928475536793⟩,⟨1039715650042822701836990149,1039715650042839675961440395⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1218985869550870744683829028,1218985869550911550870373411⟩,⟨1494961227824337055045708048,1494961227824377861145331024⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1663974444734429782328250546,1663974444734519774031466806⟩,⟨1670852364324980535672384905,1670852364325070527280871221⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2019558329927682232952066236,2019558329927864589276337705⟩,⟨1578714266282068055755879378,1578714266282250411994345983⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨2229547103988887069269916042,2229547103989209184359509922⟩,⟨1289457883669671699131605442,1289457883669993814156869674⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2262943752341359616144208203,2262943752341821993702178136⟩,⟨898764060606490451165108174,898764060606952828685740075⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨2130791989995717857902612765,2130791989996225622322732947⟩,⟨498397777714574062670344959,498397777715081827079199139⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1877929582598137982711929237,1877929582598566399410431807⟩,⟨156959166398083720233781718,156959166398512136942051025⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1562329193330250000509903704,1562329193330529983554464051⟩,⟨(-89480924176247420116453103),(-89480924175967437047833403)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1236291380479020432715539809,1236291380479162722549306967⟩,⟨(-234556696356991378215394095),(-234556696356849088350251674)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨934962786702421598259167129,934962786702482040557609336⟩,⟨(-290822197260293408791256533),(-290822197260232966460311417)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨673153902820237058864600195,673153902820260345463958227⟩,⟨(-279281283254409700633631198),(-279281283254386414005280121)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨450099950058907629981108067,450099950058916296170008880⟩,⟨(-222799913042219685643922066),(-222799913042211019432587376)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨257350208541181534757660283,257350208541184672856107227⟩,⟨(-141173500053488884708308585),(-141173500053485746595811864)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨83595678898875406591848482,83595678898876198553923865⟩,⟨(-48088199702682779825737755),(-48088199702681987858891930)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-616147321042466768039981993),(-616147321042466767796140152)⟩,⟨9327452454559115207433424,9327452454559115367296235⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1774816571351104139225341115),(-1774816571351104138499159196)⟩,⟨132918658201350987569797447,132918658201350988058388993⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-2730901447596751048078752263),(-2730901447596751046900747109)⟩,⟨519258788568906489683379778,519258788568906490520999110⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-3400434700041659663999806442),(-3400434700041659662417846069)⟩,⟨1187284347558142120921847377,1187284347558142122125075670⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-3729332314794717063095100010),(-3729332314794717061164304664)⟩,⟨1998346319890804612446535668,1998346319890804614022556725⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-3677193355084846724891287272),(-3677193355084846722600306456)⟩,⟨2745943414940366550628389227,2745943414940366552622622576⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-3257848753311977053457568312),(-3257848753311977050492684106)⟩,⟨3279180654270995459994608443,3279180654270995462737143239⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-2579951958218209706565579773),(-2579951958218209700645073983)⟩,⟨3538457687023848005039501122,3538457687023848010818187041⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1807690988626468888154644321),(-1807690988626468862311427401)⟩,⟨3527584076547214433694674434,3527584076547214459469219644⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1090960266544945506031991776),(-1090960266544945355644955262)⟩,⟨3291315772729172996378583796,3291315772729173146748430458⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-526915895390403654850436371),(-526915895390402939454453713)⟩,⟨2896400854248517884869855060,2896400854248518600277319549⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-153299910538379956092666881),(-153299910538377538507497116)⟩,⟨2407716697649851970115670889,2407716697649854387722668460⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨43510355120829246369693468,43510355120834779947337184⟩,⟨1873187769780946420650695370,1873187769780951954250437594⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨108832275150927269025572859,108832275150935743326347605⟩,⟨1325439287210121856741853294,1325439287210130331060008951⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨92921718785115353331058835,92921718785123546066804427⟩,⟨785420860767404045785954744,785420860767412238532419067⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨35205990118398809766006798,35205990118402231550305216⟩,⟨259514931171362133986814216,259514931171365555774695879⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-549820288392811543807744879),(-549820288392377468755701989)⟩,⟨5594608980025807461621720097,5594608980026241536362854653⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 9) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_9 (tableDensity false) (fullFactor false 1 9) density0_contains hk1_0_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨357662548203131991169391136,357662548203131991244845019⟩,⟨1446730841301445719820310307,1446730841301445719950769792⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_9 1 9 ha1_0_9_contains + def realAnswer : RBox := ⟨(-192157740189679552738353743),(-192157740189245477410856970)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_9 +namespace hm1_1_0_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-167282387725474063843),(-167282387725473670727)⟩,⟨49279799668875863424,49279799668876256545⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-417861607487162685855),(-417861607487161902088)⟩,⟨129420294151059834917,129420294151060618696⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-477954457714318483741),(-477954457714317920757)⟩,⟨162278860236988699552,162278860236989262548⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-371741022309844504527),(-371741022309844292493)⟩,⟨144205279939169974729,144205279939170186775⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-209973155978948393459),(-209973155978948349406)⟩,⟨98406409722744517097,98406409722744561159⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-87172461996443299682),(-87172461996443294603)⟩,⟨52723127352899844934,52723127352899850019⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-26512167363383381705),(-26512167363383381345)⟩,⟨21758548560677311044,21758548560677311406⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-5813026687215294277),(-5813026687215294240)⟩,⟨6602363697626501891,6602363697626501923⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-887585336400224637),(-887585336400224620)⟩,⟨1390878173096720222,1390878173096720240⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-88914225693578780),(-88914225693578764)⟩,⟨189821452150444530,189821452150444547⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-5305766079998887),(-5305766079998870)⟩,⟨15251291839614453,15251291839614469⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-160638703359428),(-160638703359412)⟩,⟨622977698915626,622977698915643⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1867726815941),(-1867726815925)⟩,⟨10124656362404,10124656362421⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-4979431917),(-4979431901)⟩,⟨41214844339,41214844355⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-996757),(-996741)⟩,⟨14626656,14626672⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨3,29⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-42305133153457550992329),(-42305133153457297691439)⟩,⟨(-56953562284576035025055),(-56953562284575781725062)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-117772287992987067475641),(-117772287992986184379874)⟩,⟨(-149913968021569262673704),(-149913968021568379580264)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-168757267327518145168929),(-168757267327516241743809)⟩,⟨(-192039734589714359469788),(-192039734589712456047601)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-187905459664691576728786),(-187905459664688007504609)⟩,⟨(-180768741649716143226277),(-180768741649712574004778)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-177229719726178790806959),(-177229719726172949718937)⟩,⟨(-136470354645479114548193),(-136470354645473273462102)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-145912500435704358019051),(-145912500435696422974321)⟩,⟨(-85343473116330982140521),(-85343473116323047096877)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-106231314181820087423729),(-106231314181811703052892)⟩,⟨(-44563546908233564153282),(-44563546908225179782892)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-69147238834229639592542),(-69147238834223142127798)⟩,⟨(-18989757722363957383920),(-18989757722357459919262)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-40855511765535573023728),(-40855511765531858116832)⟩,⟨(-5960495704001336639610),(-5960495703997621732643)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-22351350040850634840792),(-22351350040849032531645)⟩,⟨(-684913127826479349901),(-684913127824877040648)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-11580491094319940575428),(-11580491094319412198161)⟩,⟨803729621740325123241,803729621740853500596⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-5805838195623569099288),(-5805838195623423135122)⟩,⟨869669744365512755855,869669744365658720083⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2860177629950355825613),(-2860177629950318224128)⟩,⟨595556816681220730572,595556816681258332096⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1384488268513576256713),(-1384488268513566342480)⟩,⟨342264938647742882216,342264938647752796465⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-624165649067772811576),(-624165649067770029292)⟩,⟨169196328190613354986,169196328190616137280⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-178687954124524697457),(-178687954124524085499)⟩,⟨50487703367761965746,50487703367762577709⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1522265348017129424702945,1522265348017129425749863⟩,⟨(-2400661883917899157492961),(-2400661883917899156357359)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨4154645261784201470770146,4154645261784201473800240⟩,⟨(-6834105645381589209126340),(-6834105645381589205839442)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨5721072922771795209593139,5721072922771795214258492⟩,⟨(-10186508652573148249005899),(-10186508652573148243970702)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨5965832524618652288023883,5965832524618652293766244⟩,⟨(-11919891907094198012628380),(-11919891907094198006474764)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨5038597904328396921939825,5038597904328396928101880⟩,⟨(-11914740355307937458244558),(-11914740355307937451698773)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨3413548907841577268895829,3413548907841577275000060⟩,⟨(-10568855398836741586467927),(-10568855398836741580028163)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1708552032206376926160709,1708552032206376932154099⟩,⟨(-8545020461836461925095449),(-8545020461836461918822178)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨397101933306807141212378,397101933306807148759978⟩,⟨(-6421733198585228864608455),(-6421733198585228856846339)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-358400215857016924884399),(-358400215857016905024341)⟩,⟨(-4547989989614222154535190),(-4547989989614222134528840)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-644103025557265565180418),(-644103025557265480868604)⟩,⟨(-3065849412957161263960927),(-3065849412957161179555207)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-641691615611390555264094),(-641691615611390236238114)⟩,⟨(-1980238279033162869379474),(-1980238279033162550295427)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-515571532670802252247135),(-515571532670801369313228)⟩,⟨(-1228338440980913751644426),(-1228338440980912868674809)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-367483288964320059088038),(-367483288964318360776992)⟩,⟨(-730001867853098360469593),(-730001867853096662137698)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-238361295597088056544085),(-238361295597085798988364)⟩,⟨(-410467856494698667935062),(-410467856494696410368317)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-132824830020267546959772),(-132824830020265574304277)⟩,⟨(-205385284607060928356796),(-205385284607058955696094)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-42578601686807713990448),(-42578601686806933161802)⟩,⟨(-62036360888448709976995),(-62036360888447929146852)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨32152205345346219057088905,32152205345346393356883983⟩,⟨(-1857925885286711096802981),(-1857925885286536797721177)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨90548798494527316610182257,90548798494527707303811922⟩,⟨(-6619585839902333138210688),(-6619585839901942446673211)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨132999185497199310618257024,132999185497199666925578286⟩,⟨(-14053467633698123914287213),(-14053467633697767610263505)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨154485706195709919436252091,154485706195710113708338993⟩,⟨(-24528491511861383176087335),(-24528491511861188908198595)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨156045206541895735354919902,156045206541895803023836647⟩,⟨(-36595752202234887893992605),(-36595752202234820229736081)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨142992768755267811390092728,142992768755267826834711721⟩,⟨(-47136473411004409979533831),(-47136473411004394539595981)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨121574554114217299370477823,121574554114217301864750716⟩,⟨(-53034719164318893980645676),(-53034719164318891490726220)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨96982327639881182415892616,96982327639881182775277148⟩,⟨(-53202516411166844461111464),(-53202516411166844105479305)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨73078197156975705942013538,73078197156975706027123357⟩,⟨(-48732181224949953058208414),(-48732181224949952976128894)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨52370421384205207131695891,52370421384205207172258595⟩,⟨(-41617569528145409728776162),(-41617569528145409690515962)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨35985990119678501089934708,35985990119678501114660402⟩,⟨(-33630393582779444917569357),(-33630393582779444894485246)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨23895811875879035266363367,23895811875879035281988004⟩,⟨(-25878232758891768661940933),(-25878232758891768647434106)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨15353215873201410070783715,15353215873201410080553134⟩,⟨(-18864590933055418781493331),(-18864590933055418772449627)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨9369536626110335274100820,9369536626110335279917029⟩,⟨(-12707548812376507118135054),(-12707548812376507112759585)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨5028520451642858465120984,5028520451642858468174952⟩,⟨(-7294452917302192263662701),(-7294452917302192260843180)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1581786493343923295118751,1581786493343923296065516⟩,⟨(-2373635680388920550759804),(-2373635680388920549885916)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨86762317937519821747726711,86762317937523609144651316⟩,⟨118172495089813140296160036,118172495089816927699317894⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨261372747923802051778180137,261372747923816002892489804⟩,⟨337862161537913610221515541,337862161537927561353301350⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨432626463058326159850015296,432626463058359702980283291⟩,⟨509357643115634631366788712,509357643115668174521964270⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨584790298136721812348355508,584790298136795798308062056⟩,⟨607331359051629460497287380,607331359051703446484261929⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨699660709571951094604300228,699660709572101035722544722⟩,⟨618519715335253471400036230,618519715335403412542783872⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨767636611597773247931123173,767636611598038104328707098⟩,⟨550866818326230150133934368,550866818326495006549862817⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨787565248333860162773497968,787565248334240268426340947⟩,⟨434117880773220450532660905,434117880773600556196223868⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨762149085390893971212721227,762149085391311185443056368⟩,⟨305281367140847416773005041,305281367141264631006746627⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨697768922242588561544872312,697768922242940299605819284⟩,⟨192621685347969499903321303,192621685348321237962071120⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨604816824821900478342964947,604816824822130105318919883⟩,⟨109560480708708114981919729,109560480708937741952432864⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨495658360392325006377035251,495658360392441557132579395⟩,⟨56491729021195785755649302,56491729021312336504490219⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨382494060129106968284088975,382494060129156410469763534⟩,⟨25982615423696027245935825,25982615423745469424928200⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨275925202199282610100199373,275925202199301634418168514⟩,⟨9206897349228984462645699,9206897349248008774822428⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨182548868505084952131273610,182548868505092024586915368⟩,⟨602181243982952827236359,602181243990025278554480⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨103019904708498197952351251,103019904708500757039247454⟩,⟨(-2261573962611298397778849),(-2261573962608739313509138)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨33195960778497474804742256,33195960778498120396701889⟩,⟨(-1225747347500393328771059),(-1225747347499747737680631)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-18290382999079912142833143),(-18290382999079911992222574)⟩,⟨1147376821750207724964720,1147376821750207827063502⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-49292532796008623506490881),(-49292532796008623054237259)⟩,⟨16611766789489968207605118,16611766789489968519686724⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-48365818339322799034432810),(-48365818339322798291657492)⟩,⟨69736556382972381255654059,69736556382972381791303703⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨32165071953970785981152246,32165071953970786995989031⟩,⟨189303497936202531499097103,189303497936202532273163872⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨216219400460292111114346487,216219400460292112391300955⟩,⟨412142795874975022571816126,412142795874975023606590143⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨454713843658443198186057279,454713843658443199773149839⟩,⟨743747969041507822875072248,743747969041507824239996999⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨657559228765631445365028280,657559228765631447565682268⟩,⟨1113430892821813896137471900,1113430892821813898150497544⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨769760859588022583085755862,769760859588022587826566248⟩,⟨1409427656242935015409081541,1409427656242935020009044103⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨790854011531834292759186258,790854011531834313988698878⟩,⟨1553171522285375899786805352,1553171522285375920925300292⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨747821464840922512356646051,747821464840922635545336908⟩,⟨1528447746649577092324787082,1528447746649577215461644083⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨671013145098560359058756694,671013145098560943641527484⟩,⟨1367502356756928292020045374,1367502356756928876576407978⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨581289671918813649351085466,581289671918815623920068309⟩,⟨1126078384323886530543076019,1126078384323888505098521776⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨483096212897468416665855466,483096212897472937541648595⟩,⟨858584891284976165168081153,858584891284980686037114683⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨368861609110446179120962102,368861609110453105662609790⟩,⟨597900093629874376928988144,597900093629881303467625821⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨233061684183904277706864989,233061684183910976574059949⟩,⟨352061939745678368462664208,352061939745685067328732536⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨79813409322130037135856756,79813409322132835541426348⟩,⟨116253812717789204061109745,116253812717792002466450392⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2382765772165663859702471480,2382765772166020352360779171⟩,⟨2469669902266045029735666433,2469669902266401522134021388⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 9) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_9 (tableDensity true) (fullFactor false 1 9) density1_contains hk1_0_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-467712563034864911627874255),(-467712563034864911529203794)⟩,⟨(-1891878792471121326089468190),(-1891878792471121325918867325)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_9 1 9 ha1_0_9_contains + def realAnswer : RBox := ⟨1915053209130798947974597225,1915053209131155440931575377⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_9 +namespace hm1_0_0_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-21610860742019637846),(-21610860742019612819)⟩,⟨(-48549711470635707814),(-48549711470635682787)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-55514803816288432000),(-55514803816288382987)⟩,⟨(-117834931610852641720),(-117834931610852592704)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-66992957185077034804),(-66992957185077000817)⟩,⟨(-127966067953999468689),(-127966067953999434698)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-56209518517150911094),(-56209518517150898950)⟩,⟨(-93296653073495326358),(-93296653073495314212)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-34859127498866414514),(-34859127498866412151)⟩,⟨(-49265369870309357427),(-49265369870309355064)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16036268540529799525),(-16036268540529799260)⟩,⟨(-19102446960519934536),(-19102446960519934270)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-5386716712618761032),(-5386716712618760996)⟩,⟨(-5369390865892521921),(-5369390865892521886)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1283985933172806030),(-1283985933172806012)⟩,⟨(-1061296901645288553),(-1061296901645288533)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-207729517692483030),(-207729517692483008)⟩,⟨(-140669223534265708),(-140669223534265687)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-21328769136100074),(-21328769136100054)⟩,⟨(-11655839213093626),(-11655839213093607)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1254920844754554),(-1254920844754537)⟩,⟨(-543759624885441),(-543759624885421)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-36000654197795),(-36000654197777)⟩,⟨(-12145245205895),(-12145245205877)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-382905442592),(-382905442574)⟩,⟨(-99228992945),(-99228992928)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-899787057),(-899787041)⟩,⟨(-179127401),(-179127385)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-144873),(-144857)⟩,⟨(-22736),(-22720)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨20080867800948210932707,20080867800948243070662⟩,⟨(-43069601218177833779041),(-43069601218177801642498)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨52425475944460843617044,52425475944460954522584⟩,⟨(-116944874006171190943097),(-116944874006171080041208)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨65979174404427718355157,65979174404427952639002⟩,⟨(-159469590089852794137750),(-159469590089852559858399)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨60217943283791408303030,60217943283791834856257⟩,⟨(-165051914267518580757867),(-165051914267518154208590)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨43102871731239918273835,43102871731240590222844⟩,⟨(-141743715720012469969398),(-141743715720011798023068)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨24490821328646459236394,24490821328647331021806⟩,⟨(-104715523991051934402793),(-104715523991051062618796)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨10656860274809072028116,10656860274809945500676⟩,⟨(-67968831068479798126898),(-67968831068478924654885)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨2986242337270717123347,2986242337271355374272⟩,⟨(-39409378470601287391350),(-39409378470600649140532)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-130225161907802838160),(-130225161907460434923)⟩,⟨(-20747104047885345767163),(-20747104047885003363887)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-878311956541813167207),(-878311956541674925612)⟩,⟨(-10101619707353639732838),(-10101619707353501491183)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-764005633476748352590),(-764005633476705719379)⟩,⟨(-4648918209360363713890),(-4648918209360321080638)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-490786936818769869842),(-490786936818758834519)⟩,⟨(-2072767166425848671329),(-2072767166425837635980)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-276854973348495699573),(-276854973348493021510)⟩,⟨(-916812683302793917617),(-916812683302791239543)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-144787700282882654389),(-144787700282881982905)⟩,⟨(-406302209614672456826),(-406302209614671785336)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-68141131639640936417),(-68141131639640754754)⟩,⟨(-172219665591502613660),(-172219665591502431994)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-19888969532127442884),(-19888969532127403687)⟩,⟨(-47774202657453464716),(-47774202657453425514)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1974460771171771408314076,1974460771171771408837711⟩,⟨26673408377428092387096,26673408377428092630264⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨5513699174387259981982695,5513699174387259983462936⟩,⟨(-53883741593639163054761),(-53883741593639162355136)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨7961425417203722228797233,7961425417203722230975921⟩,⟨(-439211590664386705617615),(-439211590664386704540656)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨8998347875835092598763589,8998347875835092601293102⟩,⟨(-1079732611837903522518121),(-1079732611837903521189526)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨8710508748735731220267387,8710508748735731222802098⟩,⟨(-1744948973054406280052171),(-1744948973054406278625360)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨7479864451649318825822247,7479864451649318828127378⟩,⟨(-2189510561303993126134734),(-2189510561303993124723656)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨5805528585993512210717437,5805528585993512212711348⟩,⟨(-2298382424186478871958671),(-2298382424186478870612116)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨4130168939047429977663567,4130168939047429979603594⟩,⟨(-2108159260140489402821453),(-2108159260140489401308826)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2729662483797578735098446,2729662483797578738675903⟩,⟨(-1739885581608241149074877),(-1739885581608241145757686)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1699780292502543193809947,1699780292502543206785725⟩,⟨(-1321389128121887236741732),(-1321389128121887223914971)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1012252681272622908878409,1012252681272622955283391⟩,⟨(-940644883737721802563084),(-940644883737721756239691)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨584868858663375837899113,584868858663375961484885⟩,⟨(-636225432217250024885974),(-636225432217249901343904)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨330827860064094737040887,330827860064094967229678⟩,⟨(-410797691292000444946832),(-410797691292000214781097)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨181434987015973638274028,181434987015973936448387⟩,⟨(-249555976390311608526891),(-249555976390311310364434)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨90101715525579804161713,90101715525580059998029⟩,⟨(-132816326900156799291526),(-132816326900156543460858)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨27202347785275576311541,27202347785275676625829⟩,⟨(-41522085492965018861613),(-41522085492964918548982)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨12959171234969136327004176,12959171234969179724565237⟩,⟨15435396061680652813223202,15435396061680696209396262⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨37685233522641098556765438,37685233522641195456863788⟩,⟨43297284470752707248296882,43297284470752804144315991⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨58773194622235111355308419,58773194622235199060759509⟩,⟨63033363917494617864266789,63033363917494705563229508⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨73954359689167083299798540,73954359689167130601203839⟩,⟨71971992583112209122934331,71971992583112256415946003⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨81713218052575442910857566,81713218052575459165846788⟩,⟨70344710516337719700663263,70344710516337735946059532⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨81926149998420319565257777,81926149998420323226581373⟩,⟨60814003358432450105450777,60814003358432453756790545⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨75874895991462001201240617,75874895991462001795285206⟩,⟨47302422082711965513326527,47302422082711966097761299⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨65657580401073180035013301,65657580401073180131090912⟩,⟨33496193282454184903475800,33496193282454184990908204⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨53538239675286143115398824,53538239675286143145897597⟩,⟨21782566746068636915460374,21782566746068636938630621⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨41442042344911693966705539,41442042344911693984145995⟩,⟨13078830869699178393507233,13078830869699178405052220⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨30648166752385109423860191,30648166752385109435251923⟩,⟨7256798784936679334238836,7256798784936679341104162⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨21740474305709327665821301,21740474305709327673300236⟩,⟨3696173191945477215830109,3696173191945477219979126⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨14751724140715813002764746,14751724140715813007569992⟩,⟨1696890478141398079418559,1696890478141398081887605⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨9377675237545264611241096,9377675237545264614173780⟩,⟨677922862747885699509183,677922862747885700915773⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨5168645256604978330749480,5168645256604978332321326⟩,⟨221395681816608515593435,221395681816608516307939⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1647071579458377611874401,1647071579458377612367368⟩,⟨45723009769026590385784,45723009769026590603296⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-97482813195629948955766283),(-97482813195628743657964073)⟩,⟨64163434585078803285659374,64163434585080008589152593⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-270911622869113075879804930),(-270911622869108653893635647)⟩,⟨191837798514770430994365209,191837798514774852996173578⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-386639287791927051971361824),(-386639287791916503336463832)⟩,⟨315221773602900717185306024,315221773602911265842231462⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-427436231742444059684060670),(-427436231742421055990587383)⟩,⟨425574224878513616527115841,425574224878536620244377652⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-398222207464956069821537549),(-398222207464910118277575698)⟩,⟨509239103097161438603780890,509239103097207390169038591⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-319843955060737483737927011),(-319843955060657676319623391)⟩,⟨552749431662042299844081478,552749431662122107278125471⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-218753233029157566041607250),(-218753233029045158090039711)⟩,⟨550386188452997155922217712,550386188453109563882777142⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-118870559682086280577223319),(-118870559681965327834049555)⟩,⟨507601112879017141704172229,507601112879138094450016871⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-36706731985350280764840998),(-36706731985250383726216523)⟩,⟨437790630641425439862445295,437790630641525336898809195⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨20325036751688833326415040,20325036751752743299683723⟩,⟨356395256955315947165968128,356395256955379857133757791⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨52339422952341892133916929,52339422952373706863229652⟩,⟨276181107835701965805557938,276181107835733780527845978⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨63694968736628841675962142,63694968736642098949208319⟩,⟨204885181684196768125666145,204885181684210025391749075⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨60171479925883416306874657,60171479925888438695397785⟩,⟨145072379913036223450073914,145072379913041245832294522⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨47374546210705099266577405,47374546210706943135640527⟩,⟨95718157902594038302943738,95718157902595882167184086⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨29743143362325364075279483,29743143362326025395940457⟩,⟨54222151351729741602918537,54222151351730402920582795⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨10083637664463879246665968,10083637664464045319675288⟩,⟨17529298096285513320075956,17529298096285679392071943⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2927190369847414968495611),(-2927190369847414918304133)⟩,⟨(-193414031482627506000953012),(-193414031482627505923792555)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-41572865661098641518977900),(-41572865661098641365961041)⟩,⟨(-555370199107074618115037584),(-555370199107074617886021789)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-161396833888737472734698439),(-161396833888737472473720216)⟩,⟨(-849229836600485356224572770),(-849229836600485355855474896)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-365692269894567270015364554),(-365692269894567269643437770)⟩,⟨(-1047823620434564043162890761),(-1047823620434564042671868306)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-608349906222576484769866257),(-608349906222576484287937901)⟩,⟨(-1135762767500310716548423508),(-1135762767500310715956328191)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-824361191445153710136604274),(-824361191445153709535041914)⟩,⟨(-1104356883320629436601089500),(-1104356883320629435908764711)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-969053811567917420562002447),(-969053811567917419748395658)⟩,⟨(-963147233554429723902535788),(-963147233554429723022169479)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1028017603862223550637486678),(-1028017603862223548957332150)⟩,⟨(-749903401967674997742667706),(-749903401967674996020873774)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1006890788792760419402991897),(-1006890788792760412060640631)⟩,⟨(-516272119863264079772214896),(-516272119863264072410338382)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-922992073325727315807767550),(-922992073325727273742584897)⟩,⟨(-306162656961505844965198030),(-306162656961505802895605909)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-798585861090653865005431007),(-798585861090653668163687872)⟩,⟨(-145425575887098055564184391),(-145425575887097858726169955)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-653619214514391469339489932),(-653619214514390814020241184)⟩,⟨(-41697244395984705488622923),(-41697244395984050175860913)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-501739263689847180110799910),(-501739263689845699310980102)⟩,⟨11618000366555965047601436,11618000366557445841035931⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-351255302748530545551854924),(-351255302748528300849211983)⟩,⟨28829312096878405287400047,28829312096880649985105510⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-206605511095796045539600106),(-206605511095793890799054897)⟩,⟨24440574215097994506864679,24440574215100149244397373⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-68006139361274301564340539),(-68006139361273404897718179)⟩,⟨9225671596300699386469697,9225671596301596052090312⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1629639224603767187832424131),(-1629639224603663378449418800)⟩,⟨(-398661842542597602515412585),(-398661842542493793028176558)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 10) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_10 (tableDensity false) (fullFactor false 1 10) density0_contains hk1_0_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-489111514053367585396039828),(-489111514053367585354599848)⟩,⟨96999166175934232179448493,96999166175934232201236727⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_10 1 10 ha1_0_10_contains + def realAnswer : RBox := ⟨(-2118750738657134773328463959),(-2118750738657030963704018648)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_10 +namespace hm1_1_0_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2568029524822662653),(-2568029524822642149)⟩,⟨(-8717474232652598569),(-8717474232652578066)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-6617982412489807848),(-6617982412489767711)⟩,⟨(-21371442706175234314),(-21371442706175194178)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-7988300577852720572),(-7988300577852692760)⟩,⟨(-23538556210555381423),(-23538556210555353612)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-6699170598757859048),(-6699170598757849126)⟩,⟨(-17285597453716018202),(-17285597453716008277)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-4224473332244235718),(-4224473332244233793)⟩,⟨(-9029307632872626395),(-9029307632872624468)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-2044773565021246831),(-2044773565021246617)⟩,⟨(-3389982896478212746),(-3389982896478212526)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-743833591870088013),(-743833591870087985)⟩,⟨(-909615091465336474),(-909615091465336446)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-193532835297856670),(-193532835297856653)⟩,⟨(-171120057596984236),(-171120057596984219)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-33857413824633138),(-33857413824633122)⟩,⟨(-21706588231971428),(-21706588231971411)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3693078454303479),(-3693078454303462)⟩,⟨(-1738334314534104),(-1738334314534088)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-226137294836891),(-226137294836875)⟩,⟨(-79069848476102),(-79069848476086)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-6616067979647),(-6616067979631)⟩,⟨(-1715212818861),(-1715212818845)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-70612503513),(-70612503497)⟩,⟨(-13103524071),(-13103524055)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-165082358),(-165082342)⟩,⟨(-20068267),(-20068251)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-26420),(-26404)⟩,⟨(-1819),(-1803)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨5950002485563527649878,5950002485563554110925⟩,⟨(-4419614554431525484369),(-4419614554431499023233)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨15515268287152647440536,15515268287152738790916⟩,⟨(-12187537936549682953624),(-12187537936549591603020)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨19507011066122259311546,19507011066122452419969⟩,⟨(-17137208246695456167023),(-17137208246695263058326)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨17858878676582968225275,17858878676583320117312⟩,⟨(-18553891903148739819214),(-18553891903148387926932)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨12998441029757471604937,12998441029758026427647⟩,⟨(-16866020107538333036068),(-16866020107537778213189)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨7772402046434981698995,7772402046435702109217⟩,⟨(-13272002497957833831520),(-13272002497957113421203)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨3851649564557779283964,3851649564558501721182⟩,⟨(-9165749047030295517265),(-9165749047029573080007)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨1547930976091561750448,1547930976092089899064⟩,⟨(-5622089249049914121640),(-5622089249049385973016)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨456382190440535486719,456382190440818820415⟩,⟨(-3113955578160066941589),(-3113955578159783607902)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨49740638337677791890,49740638337792125407⟩,⟨(-1591646090496772707384),(-1591646090496658373872)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-53039320243207989443),(-53039320243172763239)⟩,⟨(-769777137242955821172),(-769777137242920594970)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-53954113725904045958),(-53954113725894939374)⟩,⟨(-361052059799181622898),(-361052059799172516318)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-34820287637303091205),(-34820287637300884236)⟩,⟨(-167397697320947434875),(-167397697320945227908)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-19034237360356828916),(-19034237360356276250)⟩,⟨(-77028494276372185140),(-77028494276371632476)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-9073892599637648956),(-9073892599637499583)⟩,⟨(-33478419873957208904),(-33478419873957059530)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-2656341906651870420),(-2656341906651838204)⟩,⟨(-9401569263240298241),(-9401569263240266024)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨376494170146496686123391,376494170146496686302700⟩,⟨238737234307959968992530,238737234307959969157499⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1065025407670468006565974,1065025407670468007081655⟩,⟨647491078832596336516371,647491078832596336990762⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1567704316669553289588901,1567704316669553290368994⟩,⟨880585416870261712115099,880585416870261712836314⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1800927536976888604125854,1800927536976888605061691⟩,⟨901575390682751220997500,901575390682751221868826⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1757464718215239472267323,1757464718215239473238994⟩,⟨743557460018313823979928,743557460018313824892512⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1514363552538128185878281,1514363552538128186806485⟩,⟨489559955207149957613045,489559955207149958490760⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1184256748297908404155795,1184256748297908405029341⟩,⟨237251981666693032085678,237251981666693032918273⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨857921141992095590828149,857921141992095591866232⟩,⟨53436824157841187766014,53436824157841188773603⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨584395063266003085619306,584395063266003088178910⟩,⟨(-45788152303376507732670),(-45788152303376505193293)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨378577427016946502307462,378577427016946512668871⟩,⟨(-79382001005876628179559),(-79382001005876617830769)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨235153452271519830938925,235153452271519868635758⟩,⟨(-76124190870830217458453),(-76124190870830179769191)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨140622456676663781703352,140622456676663882398546⟩,⟨(-58988289831833677592636),(-58988289831833576901947)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨80914647848952729869992,80914647848952917646207⟩,⟨(-40716795070043769315928),(-40716795070043581542267)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨44318814001639828726459,44318814001640072156578⟩,⟨(-25730190726025681061476),(-25730190726025437632676)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨21768232290674856474086,21768232290675065450332⟩,⟨(-14076339535778956560541),(-14076339535778747584908)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨6512157089135765541502,6512157089135847503524⟩,⟨(-4469559005834599164198),(-4469559005834517202349)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨388648406226081233987090,388648406226117696372643⟩,⟨6725902267787079801593829,6725902267787116264130895⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1377942964693684382094708,1377942964693765741921114⟩,⟨18852392769664559277238376,18852392769664640637506956⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2897568856964973328296868,2897568856965046865194990⟩,⟨27432763891914642342399626,27432763891914715879987656⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨4987507440113183619984607,4987507440113223191093848⟩,⟨31429463622687273301015048,31429463622687312872989361⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨7309403008829557450384684,7309403008829571000676586⟩,⟨31186585992292858130204922,31186585992292871681437950⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨9215745933055241500766585,9215745933055244530000396⟩,⟨27973554800331732412993049,27973554800331735443149249⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨10120300239752947816133896,10120300239752948293294737⟩,⟨23211868537117276535747915,23211868537117277013742742⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨9887230686342095599145585,9887230686342095665558785⟩,⟨18031942848614884419746167,18031942848614884486856543⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨8808403891611926613300536,8808403891611926628225350⟩,⟨13214657894908925468284210,13214657894908925483754083⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨7314234980464297507232591,7314234980464297514007800⟩,⟨9207624200214394733040443,9207624200214394740216102⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨5751729291929919927906066,5751729291929919931889898⟩,⟨6156700850393228476287841,6156700850393228480547473⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨4315775565313189920926001,4315775565313189923370672⟩,⟨3986245115398900324908047,3986245115398900327534202⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨3077738679508580825073244,3077738679508580826566144⟩,⟨2505329756131421560414465,2505329756131421562021446⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2037005290137972211718788,2037005290137972212591754⟩,⟨1502081991868575483235637,1502081991868575484175970⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1154958560387689744380640,1154958560387689744833375⟩,⟨796216161677449358734793,796216161677449359222629⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨373447721415309265152048,373447721415309265291570⟩,⟨248865989045276978704869,248865989045276978855182⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-30907898056960408458122747),(-30907898056959417886824968)⟩,⟨22692497697770053294661196,22692497697771043864289336⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-88032896842652684834089432),(-88032896842649050378525331)⟩,⟨68100470600580308225011457,68100470600583942675913242⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-131728372476428252956654200),(-131728372476419581840546119)⟩,⟨111874782454556068757998433,111874782454564739867511824⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-155355323497582758939612505),(-155355323497563846613878115)⟩,⟨149566833003024933703405504,149566833003043846022000667⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-156002068243027410984557613),(-156002068242989627653560003)⟩,⟨176424978102269637693937272,176424978102307421018612651⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-136619661418206670466803040),(-136619661418141049469391462)⟩,⟨190312069179487998626169694,190312069179553619618931866⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-105633194066006584770581802),(-105633194065914177763174761)⟩,⟨191542778491010608042444466,191542778491103015047189977⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-72765210844370770178904362),(-72765210844271386955647119)⟩,⟨181549479975414476625029574,181549479975513859847458684⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-44933913019404184054826588),(-44933913019322166593573942)⟩,⟨162654558247392547072495775,162654558247474564534268129⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-25010711821389472095996746),(-25010711821337056481910551)⟩,⟨137959730318744222376879292,137959730318796637992227447⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-12629564604131672981577174),(-12629564604105613229490409)⟩,⟨110722143336355544486770324,110722143336381604240381115⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-5698507532532052577479200),(-5698507532521208030068708)⟩,⟨83817362307721158227598005,83817362307732002776500913⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1986565971890529990863202),(-1986565971886426880099533)⟩,⟨59465511973643752033046292,59465511973647855145083590⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-129102387461487393748653),(-129102387459982620522816)⟩,⟨38821305207905171673555264,38821305207906676447719778⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨476232824743310546654911,476232824743849843882432⟩,⟨21705824529615255959708443,21705824529615795257500929⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨257017928747595739470406,257017928747731117889534⟩,⟨6960914594031588928733736,6960914594031724307338934⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-360075773925513727666449),(-360075773925513695615720)⟩,⟨(-5741518685311365478964587),(-5741518685311365431668539)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-5195592872364890901264949),(-5195592872364890803595990)⟩,⟨(-15425412356843390497691323),(-15425412356843390356126540)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-21674099557722025137627985),(-21674099557722024971000257)⟩,⟨(-15049712693207583345282854),(-15049712693207583114259719)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-58295677093525988205036380),(-58295677093525987966351294)⟩,⟨9876467920809258880944196,9876467920809259193672964⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-125429441783827950027099526),(-125429441783827949711579767)⟩,⟨65777125600537513882278926,65777125600537514271315432⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-223208765953205046626676914),(-223208765953205046216061257)⟩,⟨136462103449280105268697572,136462103449280105745643228⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-328949409995670872021852448),(-328949409995670871425930754)⟩,⟨194286670743686686495608368,194286670743686687146346461⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-409400020499803061912138667),(-409400020499803060576126484)⟩,⟨223620605492928184338916956,223620605492928185714973278⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-443277844461387673445465492),(-443277844461387667425098455)⟩,⟨225730596179763170451735596,225730596179763176497065657⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-428605779336406285192615175),(-428605779336406250746725389)⟩,⟨209709539762843163507861797,209709539762843197967281123⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-377042598524259498584193715),(-377042598524259337746437391)⟩,⟨185002309296907501808922818,185002309296907662653082836⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-305701520746104925523850675),(-305701520746104390299586112)⟩,⟨157791279684773735603873678,157791279684774270831130585⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-229979357557154081025112441),(-229979357557152871234855015)⟩,⟨129388999403878708801089701,129388999403879918592671457⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-158451103538676138179337594),(-158451103538674303458288074)⟩,⟨97746688061249087781235480,97746688061250922502766701⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-92610237628500712977321792),(-92610237628498951136670427)⟩,⟨61305532718797741352819160,61305532718799503193590832⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-30464422804115518475399101),(-30464422804114785163935037)⟩,⟨20915119647552685236813245,20915119647553418548280976⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-685771053797433572870037684),(-685771053797348313712569291)⟩,⟨603628886412233356350819238,603628886412318615585305192⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 10) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_10 (tableDensity true) (fullFactor false 1 10) density1_contains hk1_0_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨639607364531326842386784416,639607364531326842440975160⟩,⟨(-126845063460837072878540335),(-126845063460837072850048030)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_10 1 10 ha1_0_10_contains + def realAnswer : RBox := ⟨(-46163689266106730583253268),(-46163689266021471171594131)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_10 +namespace hm1_0_0_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2300063223729731234,2300063223729732435⟩,⟨(-1023799094952935222),(-1023799094952934022)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨5479338062034951277,5479338062034953574⟩,⟨(-2580910137529840457),(-2580910137529838161)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨5730660709244530396,5730660709244531937⟩,⟨(-2998551622521088188),(-2998551622521086646)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨3945371348903144199,3945371348903144733⟩,⟨(-2374883055724906549),(-2374883055724906019)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1926896891303122349,1926896891303122461⟩,⟨(-1361708868358430911),(-1361708868358430800)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨675773695257266843,675773695257266869⟩,⟨(-566384291675588867),(-566384291675588842)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨167638367353242671,167638367353242690⟩,⟨(-167841908186159885),(-167841908186159863)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨28445736639982574,28445736639982595⟩,⟨(-34330341222879518),(-34330341222879497)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3134850605866680,3134850605866697⟩,⟨(-4615757881152370),(-4615757881152349)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨207870067144535,207870067144555⟩,⟨(-379074756714341),(-379074756714319)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨7399996522846,7399996522864⟩,⟨(-17012510054800),(-17012510054782)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨118512121649,118512121669⟩,⟨(-349886805044),(-349886805026)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨636198068,636198086⟩,⟨(-2446041974),(-2446041956)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨659260,659276⟩,⟨(-3302746),(-3302730)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨34,51⟩,⟨(-252),(-230)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨4090455648790781845599,4090455648790784897585⟩,⟨1907158341594194075189,1907158341594197127310⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨11002238088012588279804,11002238088012598709208⟩,⟨4932573159774291041266,4932573159774301471015⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨14723680153374357670703,14723680153374379279451⟩,⟨6093042006358735298136,6093042006358756907299⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨14819195104691176214055,14819195104691214448353⟩,⟨5408937072005105202218,5408937072005143436878⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨12267109770468900141945,12267109770468958173812⟩,⟨3733122460998707213330,3733122460998765245433⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨8662941211275208852281,8662941211275280819985⟩,⟨2028739472327172550333,2028739472327244518152⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨5334198310914569709567,5334198310914638148565⟩,⟨838345002366206863134,838345002366275302177⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨2914663863111709010733,2914663863111756189991⟩,⟨222088672215598843119,222088672215646022383⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1438473217287445535228,1438473217287469284568⟩,⟨(-8387800329165092686),(-8387800329141343348)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨654376898215752408499,654376898215761379363⟩,⟨(-56606877956624293013),(-56606877956615322152)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨281114114070756331285,281114114070758916120⟩,⟨(-46082430683044031210),(-46082430683041446378)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨117251631464738124652,117251631464738750758⟩,⟨(-27720993459164077705),(-27720993459163451605)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨48802097424952746465,48802097424952889410⟩,⟨(-14723837731448252102),(-14723837731448109157)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨20555784532365724554,20555784532365758606⟩,⟨(-7321731438114366662),(-7321731438114332613)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨8398482583953070572,8398482583953079453⟩,⟨(-3322405205240606223),(-3322405205240597343)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2285131147098249474,2285131147098251365⟩,⟨(-951308891922829126),(-951308891922827237)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-3803781700640180651849),(-3803781700640180617149)⟩,⟨281503816530907715246593,281503816530907715322163⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨7612262162228193043886,7612262162228193143061⟩,⟨781156720508085921291900,781156720508085921504150⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨61370639404043459288148,61370639404043459439032⟩,⟨1113927601251581656577094,1113927601251581656885630⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨148147545138410664624368,148147545138410664807357⟩,⟨1236005482827225852352879,1236005482827225852704606⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨233775507014338034877156,233775507014338035069302⟩,⟨1168108147292442536810615,1168108147292442537154790⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨284980173220901288693499,284980173220901288878345⟩,⟨974413989349074337035300,974413989349074337339417⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨289382212880769200990929,289382212880769201161664⟩,⟨731547558076295357326555,731547558076295357580892⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨255897913274124217512301,255897913274124217696754⟩,⟨501714160090907627067770,501714160090907627305489⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨203153311453954906842391,203153311453954907228919⟩,⟨318941506539885208422868,318941506539885208840625⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨148282810267403013709171,148282810267403015141346⟩,⟨190862713852430919271458,190862713852430920720838⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨101518233340757334899456,101518233340757339875610⟩,⟨109304197554090198618166,109304197554090203603383⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨66198851811309251632444,66198851811309264442101⟩,⟨60880502513662810817714,60880502513662823632056⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨41385941390054917206043,41385941390054940342720⟩,⟨33338832224256280346540,33338832224256303485611⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨24492142908630274783215,24492142908630304012242⟩,⟨17809366563979334530146,17809366563979363760379⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨12796393442094982285422,12796393442095006923859⟩,⟨8681510020359360179047,8681510020359384818042⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨3962433462418762010522,3962433462418771582934⟩,⟨2595925245832883059027,2595925245832892631604⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-2935384839821913789480871),(-2935384839821905536531712)⟩,⟨2464466382095941671477221,2464466382095949924693025⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-8195082946613567785076898),(-8195082946613549441199033)⟩,⟨7132635740260889317849699,7132635740260907662507738⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-11819620160258418198662839),(-11819620160258401743925413)⟩,⟨11019873466962892290849207,11019873466962908746816707⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-13311685543820347788416597),(-13311685543820339030721030)⟩,⟨13676320893522421482303325,13676320893522430241569764⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-12781679082196045712620434),(-12781679082196042755013945)⟩,⟨14844014569989472017611753,14844014569989474976983870⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-10816980972308598639692448),(-10816980972308597988409537)⟩,⟨14567658420164200202588962,14567658420164200855673154⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-8212124064338066310791362),(-8212124064338066208962405)⟩,⟨13167265668920560842425561,13167265668920560945949542⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-5663501907428199445786861),(-5663501907428199430940246)⟩,⟨11095910410254575353334987,11095910410254575369669493⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-3582191059924230902716809),(-3582191059924230898887647)⟩,⟨8799541038336267495202994,8799541038336267500261429⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2091375904499828448863329),(-2091375904499828447007922)⟩,⟨6622680104649897552076609,6622680104649897554895598⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1129253878456298135211121),(-1129253878456298134137805)⟩,⟨4766058766301605375562662,4766058766301605377357411⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-560861189266747083585773),(-560861189266747082953704)⟩,⟨3296603104312453971421546,3296603104312453972572128⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-251881982406677962728022),(-251881982406677962360413)⟩,⟨2188171939218823568376363,2188171939218823569100408⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-98859035149937902587834),(-98859035149937902382289)⟩,⟨1366658062417297878235026,1366658062417297878669629⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-31881375455872114422261),(-31881375455872114319221)⟩,⟨743991912518652830339949,743991912518652830570200⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-6540189099462231175756),(-6540189099462231144599)⟩,⟨235579093869512212494963,235579093869512212566752⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-15256201069642298543473033),(-15256201069642011962011688)⟩,⟨(-23178719113974686550093998),(-23178719113974399969955580)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-45439466504990637150315788),(-45439466504989589883441675)⟩,⟨(-64172533751995614130862419),(-64172533751994566867611977)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-74104437273945677712644585),(-74104437273943198699911909)⟩,⟨(-90905989785976461679332637),(-90905989785973982671672517)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-98950304338260896607714486),(-98950304338255550882449178)⟩,⟨(-99407173324556160768377213),(-99407173324550815048540731)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-116735599620233352564155611),(-116735599620222825775786300)⟩,⟨(-91319516331434096076214591),(-91319516331423569292648966)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-124583140565295721313507653),(-124583140565277745241151620)⟩,⟨(-72125417081710192793567317),(-72125417081692216724711943)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-121697957726008900696399895),(-121697957725984056824766959)⟩,⟨(-48404416626525726710806298),(-48404416626500882841141765)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-109932963930449570703226660),(-109932963930423377239865041)⟩,⟨(-25774819733924044951655527),(-25774819733897851488869509)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-92785094049311384615027126),(-92785094049290207675000219)⟩,⟨(-7804130974182858579803964),(-7804130974161681639301397)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-73912055287676204685706925),(-73912055287662942071989668)⟩,⟨4197096800986990282138660,4197096801000252896990249⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-56090483522201922833845029),(-56090483522195455816056063)⟩,⟨10617731815331241163829747,10617731815337708183048530⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-40817451789632146119466938),(-40817451789629502580616216)⟩,⟨12682409355066856825439627,12682409355069500365725492⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-28423047349735662404050426),(-28423047349734677647835088)⟩,⟨11785691864709062387793444,11785691864710047145254199⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-18505110243491111977478942),(-18505110243490755327989046)⟩,⟨9157714208726841499489241,9157714208727198149921562⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-10385755192060830513939209),(-10385755192060703817975305)⟩,⟨5696782818686136891328597,5696782818686263587873487⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-3341586789192578836797056),(-3341586789192547177887892)⟩,⟨1922221658852310603937720,1922221658852342263042533⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨55194880474262187311990125,55194880474262187334185433⟩,⟨(-835114967191437585103099),(-835114967191437570777258)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨157986435508122368270627523,157986435508122368336282450⟩,⟨(-11820667825818579089713124),(-11820667825818579046147879)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨240078880274030216366850805,240078880274030216471979382⟩,⟨(-45605326748126036138420801),(-45605326748126036064499615)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨293530521610900138373539650,293530521610900138512086118⟩,⟨(-102397200817516940158946435),(-102397200817516940054432852)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨314454340942525143212440501,314454340942525143377499556⟩,⟨(-168364109604650014122902397),(-168364109604650013988932352)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨301521231718104983318239494,301521231718104983508433351⟩,⟨(-224987798653345236354881151),(-224987798653345236189916522)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨258864002709179731947512697,258864002709179732185157061⟩,⟨(-260344072647384184558902049),(-260344072647384184339476208)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨198160638085829769726072480,198160638085829770181293793⟩,⟨(-271522321573711287894286832),(-271522321573711287450179252)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨134045382220538694319257003,134045382220538696225810505⟩,⟨(-261280025190134308109508734),(-261280025190134306208002494)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨78111256351515757939820878,78111256351515768638820906⟩,⟨(-235312368709123076281994374),(-235312368709123065584013911)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨36488570007151099038536381,36488570007151148275069623⟩,⟨(-200171199387096404762937628),(-200171199387096355525328761)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨10310652134944397989451737,10310652134944559473614854⟩,⟨(-161309240784165638703917676),(-161309240784165477218015218)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2820191287449134525262867),(-2820191287448774282402796)⟩,⟨(-122176449856089164299107777),(-122176449856088804054579340)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-6942583215363075757663518),(-6942583215362535224784828)⟩,⟨(-84624527574196764370342309),(-84624527574196223836194253)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-5844051609051898813869848),(-5844051609051383622866691)⟩,⟨(-49407154506902076549309311),(-49407154506901561357539608)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-2197793408358600422439580),(-2197793408358386815255342)⟩,⟨(-16200981991463725006084037),(-16200981991463511398646200)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨158408028620037517920947001,158408028620060127743981301⟩,⟨(-426641403276536394480062219),(-426641403276513784687571322)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 11) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_11 (tableDensity false) (fullFactor false 1 11) density0_contains hk1_0_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-23687354313445331962055891),(-23687354313445331956311134)⟩,⟨(-148068244402214326940918701),(-148068244402214326928892220)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_11 1 11 ha1_0_11_contains + def realAnswer : RBox := ⟨134720674306592185858891110,134720674306614795887670167⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_11 +namespace hm1_1_0_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨412992138340827712,412992138340828699⟩,⟨(-121658301925738458),(-121658301925737470)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨993740507725779719,993740507725781603⟩,⟨(-307671075799827166),(-307671075799825283)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1054062727007077644,1054062727007078908⟩,⟨(-357553173200909568),(-357553173200908304)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨730984415526041133,730984415526041568⟩,⟨(-283036729160475163),(-283036729160474727)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨353220640375452565,353220640375452656⟩,⟨(-164979259361130390),(-164979259361130296)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨119971403093689389,119971403093689412⟩,⟨(-72171801132646341),(-72171801132646320)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨28414530667114356,28414530667114373⟩,⟨(-23153891837874981),(-23153891837874964)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4589173630874408,4589173630874425⟩,⟨(-5168912320828689),(-5168912320828673)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨483991397245509,483991397245525⟩,⟨(-751566314761667),(-751566314761651)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨31014106050439,31014106050455⟩,⟨(-65587147844425),(-65587147844409)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1076451523941,1076451523957⟩,⟨(-3064314463914),(-3064314463898)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨16748197891,16748197907⟩,⟨(-64292390621),(-64292390604)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨84140136,84140152⟩,⟨(-451101600),(-451101584)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨74044,74060⟩,⟨(-606000),(-605984)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1,17⟩,⟨(-58),(-36)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨419743395000501876725,419743395000504389713⟩,⟨565095108595437218978,565095108595439731959⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1146578065353585605826,1146578065353594196562⟩,⟨1459792911514760740584,1459792911514769331304⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1582141817407623538222,1582141817407641349533⟩,⟨1801432649311228262005,1801432649311246073291⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1665624272077728047795,1665624272077759590004⟩,⟨1604098877533968909870,1604098877534000452058⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1459346185339239301213,1459346185339287217678⟩,⟨1125675162993235643384,1125675162993283559837⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1097681361344195224324,1097681361344254695542⟩,⟨643627239962521861620,643627239962581332830⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨719127989934845681709,719127989934902286498⟩,⟨302714572389944087744,302714572390000692528⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨415688651730971525581,415688651731010566069⟩,⟨114742577470215672686,114742577470254713174⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨215844328039413014577,215844328039432666834⟩,⟨31777823253854887292,31777823253874539550⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨103077749200326921857,103077749200334341289⟩,⟨3283679927045471716,3283679927052891150⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨46534441837943339016,46534441837945474778⟩,⟨(-3183085461631067108),(-3183085461628931348)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨20418621134300674398,20418621134301191075⟩,⟨(-3044022569695974320),(-3044022569695457643)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨8908886598389860732,8908886598389978534⟩,⟨(-1851227518680859056),(-1851227518680741256)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨3896623682439728164,3896623682439756188⟩,⟨(-962462317911335679),(-962462317911307655)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1632544612944960675,1632544612944967981⟩,⟨(-442416578892248773),(-442416578892241468)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨449692885290400587,449692885290402145⟩,⟨(-127055340935683169),(-127055340935681614)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-34037498831993492604130),(-34037498831993492580486)⟩,⟨53677613442832787639813,53677613442832787665561⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-91736937021704836752317),(-91736937021704836684786)⟩,⟨150885968984059760470420,150885968984059760543981⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-123220138486765417850373),(-123220138486765417749007)⟩,⟨219340668751674112622978,219340668751674112732858⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-123867390694910589512788),(-123867390694910589392581)⟩,⟨247368378174094068521611,247368378174094068651004⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-99759076440181895221851),(-99759076440181895098966)⟩,⟨235679581568496859214711,235679581568496859345847⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-63833397186156302249687),(-63833397186156302134937)⟩,⟨197276554980300618543135,197276554980300618664779⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-29953047332085905649015),(-29953047332085905543847)⟩,⟨149221353786522755100759,149221353786522755211362⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-6537498819946827654222),(-6537498819946827531908)⟩,⟨104208264292653544793658,104208264292653544919893⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨5318527119510661815206,5318527119510662110431⟩,⟨68274332012779784190129,68274332012779784487885⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨8895131603150378245764,8895131603150379400694⟩,⟨42503289439754743244091,42503289439754744400551⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨8210668809091948235172,8210668809091952283409⟩,⟨25388940331121642605580,25388940331121646654708⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨6136110901555450734538,6136110901555461174512⟩,⟨14636647949205473786455,14636647949205484226941⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨4101549487927579168067,4101549487927598043204⟩,⟨8153959752769760159524,8153959752769779034942⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨2525083100056831379630,2525083100056855242955⟩,⟨4350332463733644834780,4350332463733668698246⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1356171559022435449661,1356171559022455575533⟩,⟨2097449070836061539289,2097449070836081665228⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨426526573971846932006,426526573971854753266⟩,⟨621457682823244568908,621457682823252390186⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1279080447868618273697374),(-1279080447868611339368843)⟩,⟨73908249927352631750993,73908249927359566050276⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3568284110443196179503368),(-3568284110443180776778473)⟩,⟨260759905482790018248160,260759905482805420888114⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-5144017294810081698052252),(-5144017294810067900370044)⟩,⟨543120595176227286059648,543120595176241083610659⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-5813024732872672848113075),(-5813024732872665520188527)⟩,⟨921961460168894206084251,921961460168901533846771⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-5666393477779041593614725),(-5666393477779039126505458)⟩,⟨1327255709105708952266208,1327255709105711419202702⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-4975168599514475555007287),(-4975168599514475014531276)⟩,⟨1638062497432105999567950,1638062497432106539878735⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-4029105177155936898681197),(-4029105177155936815403505)⟩,⟨1755729701667421523122628,1755729701667421606255069⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3048083388366215349740078),(-3048083388366215338346826)⟩,⟨1670519895180589743913578,1670519895180589755189067⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2172500875425798207112326),(-2172500875425798204555979)⟩,⟨1447486896268775077157821,1447486896268775079625036⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1471785112697307821660052),(-1471785112697307820506016)⟩,⟨1168682462257104685368352,1168682462257104686459077⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-957624117153455863123177),(-957624117153455862456043)⟩,⟨894329290752467578877277,894329290752467579502301⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-604552239098049038512732),(-604552239098049038111451)⟩,⟨654351015373280193562758,654351015373280193937271⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-371665340422570191917444),(-371665340422570191677137)⟩,⟨456496814947059788143663,456496814947059788367693⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-218919615233382230344302),(-218919615233382230206087)⟩,⟨296850680014676191945638,296850680014676192074510⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-114612572194513995279811),(-114612572194513995208961)⟩,⟨166245762112045838960900,166245762112045839026985⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-35595157221553882363809),(-35595157221553882342105)⟩,⟨53413771957131898530787,53413771957131898551042⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-5395614357212295578935138),(-5395614357212060054136495)⟩,⟨(-7349029396737462741599269),(-7349029396737227216394280)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-16130521740253960781358865),(-16130521740253100031021547)⟩,⟨(-20852538071420022678835573),(-20852538071419161927368118)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-26300366116794268555844280),(-26300366116792230781051603)⟩,⟨(-30970362716914116709295638),(-30970362716912078932916483)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-34776317234070767021968417),(-34776317234066372078394905)⟩,⟨(-36127650372907491681238792),(-36127650372903096735966899)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-40443514785303850403535384),(-40443514785295194833044386)⟩,⟨(-35770364766196398318324880),(-35770364766187742746351639)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-42893976280783396713939276),(-42893976280768616037597037)⟩,⟨(-30803428175198243305122242),(-30803428175183462627709188)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-42351327487606691552419479),(-42351327487586268185252685)⟩,⟨(-23367649628934457267545612),(-23367649628914033899778293)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-39316419515876622551966560),(-39316419515855100148784226)⟩,⟨(-15767795151564948526497775),(-15767795151543426123132465)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-34470331308587937933770539),(-34470331308570551213286204)⟩,⟨(-9529445792602254725989692),(-9529445792584868005617076)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-28609140754009165064119394),(-28609140753998287738619430)⟩,⟨(-5190651485080016936807843),(-5190651485069139611573853)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-22485814531604180122645378),(-22485814531598882912890047)⟩,⟨(-2566927789744037668592630),(-2566927789738740459152204)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-16697920725148845968058263),(-16697920725146683528173762)⟩,⟨(-1136208683683263308204537),(-1136208683681100868622950)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-11650766159978215345184315),(-11650766159977410832427909)⟩,⟨(-389679399540001274365180),(-389679399539196761863261)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-7505387084178013756375155),(-7505387084177722695188953)⟩,⟨(-25160789186182984933249),(-25160789185891923932239)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-4157579358408827505103868),(-4157579358408724185828935)⟩,⟨91166830803679749793497,91166830803783068957996⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1326951009307394111032788),(-1326951009307368303322262)⟩,⟨48992928258456990725514,48992928258482798399840⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1638468786722913916981763,1638468786722913930483879⟩,⟨(-102728065309283893098823),(-102728065309283883952149)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4388342902500153758203794,4388342902500153798488166⟩,⟨(-1477278698469892853943406),(-1477278698469892826155672)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨4257230293472907038443108,4257230293472907103765653⟩,⟨(-6123941358252867189153476),(-6123941358252867142031551)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2756925499096399560962443),(-2756925499096399473353049)⟩,⟨(-16320193015432781528709898),(-16320193015432781461801158)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-18191484488353004730848381),(-18191484488353004623098160)⟩,⟨(-34702804993589816304563512),(-34702804993589816217101497)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-37230707936894061892809536),(-37230707936894061762507754)⟩,⟨(-60899272015953554867165996),(-60899272015953554754867153)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-52187721325934199214699451),(-52187721325934199039764023)⟩,⟨(-88351139097374379286989648),(-88351139097374379126611718)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-59059020004365142059836633),(-59059020004365141696726320)⟩,⟨(-108111362926646322632991066),(-108111362926646322280226087)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-58573796946202280350744322),(-58573796946202278785732032)⟩,⟨(-115014199806716192961363470),(-115014199806716191402565207)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-53463429670565099134971617),(-53463429670565090371787370)⟩,⟨(-109265687521157358265639083),(-109265687521157349505647586)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-46370342746361558406742332),(-46370342746361518173912496)⟩,⟨(-94508261118322435105032368),(-94508261118322394873587697)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-38939324354651016919021577),(-38939324354650885026977401)⟩,⟨(-75446931617127123135087015),(-75446931617126991243612854)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-31504581955293889169970937),(-31504581955293594855937931)⟩,⟨(-56002460578083778940398177),(-56002460578083484626569227)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-23547834014297823933068447),(-23547834014297382124504667)⟩,⟨(-38174401183455689742381730),(-38174401183455247933857869)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-14660099960738851854779185),(-14660099960738430604299745)⟩,⟨(-22146616755781305896115300),(-22146616755780884645622528)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-4982557178144787495717754),(-4982557178144612803425352)⟩,⟨(-7257485056292690149386855),(-7257485056292515457081910)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-140948868271354180974211354),(-140948868271335610664305678)⟩,⟨(-173125165912330867743078095),(-173125165912312297454031861)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 11) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_11 (tableDensity true) (fullFactor false 1 11) density1_contains hk1_0_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨30975771025274664865945329,30975771025274664873457703⟩,⟨193627704218280273676243672,193627704218280273691970609⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_11 1 11 ha1_0_11_contains + def realAnswer : RBox := ⟨(-109973097246079516208266025),(-109973097246060945690847975)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_11 +namespace hm1_0_0_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨44460280771137227,44460280771137294⟩,⟨99886702749816237,99886702749816305⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨109996508256595945,109996508256596059⟩,⟨233573735508708895,233573735508709012⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨123052841762886674,123052841762886755⟩,⟨235294487465496246,235294487465496329⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨92015212076534792,92015212076534831⟩,⟨153000475531995301,153000475531995340⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨48793279106124363,48793279106124383⟩,⟨69131862137635107,69131862137635127⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨18356549919272304,18356549919272322⟩,⟨21936899646692486,21936899646692506⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨4801316628277571,4801316628277589⟩,⟨4804919019963412,4804919019963430⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨843230493797325,843230493797343⟩,⟨700347280936340,700347280936361⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨94290022174504,94290022174525⟩,⟨64217702146778,64217702146796⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨6199408031651,6199408031669⟩,⟨3410470833756,3410470833774⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨212431807809,212431807829⟩,⟨92729349037,92729349054⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨3135241324,3135241343⟩,⟨1065763735,1065763751⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨14417398,14417415⟩,⟨3761763,3761781⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨11178,11196⟩,⟨2231,2247⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-14),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-166036395912980730813),(-166036395912980465096)⟩,⟨356110514560744609478,356110514560744875182⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-425425562286419017636),(-425425562286418118512)⟩,⟨948854864374739075254,948854864374739974351⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-515814134062677855960),(-515814134062676028830)⟩,⟨1246197029800661456143,1246197029800663283236⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-445397798749589778003),(-445397798749586636095)⟩,⟨1219773178120648149093,1219773178120651290975⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-296422327775037102782),(-296422327775032507888)⟩,⟨973316763194454592739,973316763194459187616⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-154080053828448129043),(-154080053828442681900)⟩,⟨657081410080500810486,657081410080506257622⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-60469485021496217904),(-60469485021491301051)⟩,⟨383843948113256140821,383843948113261057672⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-15144479496583438103),(-15144479496580240216)⟩,⟨197664179559163521327,197664179559166719213⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨492731436886663328,492731436888173880⟩,⟨91456660010249021508,91456660010250532063⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨3345560440916823262,3345560440917357107⟩,⟨38872563565182713572,38872563565183247417⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2548892742625329273,2548892742625472999⟩,⟨15587895829552585554,15587895829552729282⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1435758663704995542,1435758663705028130⟩,⟨6081936738726039102,6081936738726071691⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨717979044242690832,717979044242697844⟩,⟨2381865796219093587,2381865796219100598⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨339449448610062518,339449448610064117⟩,⟨953449589202250496,953449589202252096⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨148502928309432949,148502928309433366⟩,⟨375455103384272473,375455103384272887⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨41710514561115282,41710514561115378⟩,⟨100194418482105170,100194418482105269⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-36790176665909921094821),(-36790176665909921084814)⟩,⟨(-497238148032836592305),(-497238148032836587754)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-101449056111824937111709),(-101449056111824937083801)⟩,⟨985782315054361186270,985782315054361199170⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-142870786453418798226758),(-142870786453418798186700)⟩,⟨7860808440789998676811,7860808440789998696201⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-155634600590851684002082),(-155634600590851683957244)⟩,⟨18633761988903366177988,18633761988903366201105⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-143601838878514859777511),(-143601838878514859734661)⟩,⟨28711284340394351665279,28711284340394351689012⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-116369857196940844653487),(-116369857196940844616696)⟩,⟨34003964865006943251110,34003964865006943273322⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-84508371015063627176253),(-84508371015063627146502)⟩,⟨33402424979425327139476,33402424979425327159332⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-55873842488840773884087),(-55873842488840773857368)⟩,⟨28476989638626965754810,28476989638626965775447⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-34164960381545964563330),(-34164960381545964518589)⟩,⟨21746798907505628811436,21746798907505628852740⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-19647949189141403700679),(-19647949189141403552244)⟩,⟨15255243255439850170471,15255243255439850317088⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-10820516614141152968933),(-10820516614141152477939)⟩,⟨10044446530050963398874,10044446530050963888948⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-5809681154877343357147),(-5809681154877342139049)⟩,⟨6314579942906218268503,6314579942906219486140⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-3079931298394951146078),(-3079931298394949013757)⟩,⟨3822259245315235556409,3822259245315237688505⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1602527067708177876250),(-1602527067708175249457)⟩,⟨2203510377414509084808,2203510377414511711491⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-766789273504526637843),(-766789273504524462611)⟩,⟨1130166050500059985689,1130166050500062160868⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-227085936053022748643),(-227085936053021911280)⟩,⟨346622755108778237555,346622755108779074905⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-429615770099604614336608),(-429615770099603175562120)⟩,⟨(-511710069140807457873876),(-511710069140806019146336)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1237491327836415300678814),(-1237491327836412117153634)⟩,⟨(-1421868169140994030861033),(-1421868169140990847472613)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1894045097030758597094306),(-1894045097030755766768064)⟩,⟨(-2031668973549455908262426),(-2031668973549453078149929)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-2318437809093226404599700),(-2318437809093224917700606)⟩,⟨(-2256956686618140140414441),(-2256956686618138653784802)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2471929399805932915009352),(-2471929399805932421112191)⟩,⟨(-2128972061046492064961140),(-2128972061046491571361829)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-2374584711323995341677600),(-2374584711323995234888287)⟩,⟨(-1763758678437206079397134),(-1763758678437205972905675)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2094731390961431844683608),(-2094731390961431828145246)⟩,⟨(-1306961299452383408329477),(-1306961299452383392065121)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1719014712940823990410275),(-1719014712940823987864522)⟩,⟨(-877835241487964128262070),(-877835241487964125950986)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1325855155727041973801343),(-1325855155727041973032280)⟩,⟨(-540042916045858500763420),(-540042916045858500183305)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-970210339618261438171942),(-970210339618261437754276)⟩,⟨(-306573364647243013301462),(-306573364647243013028103)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-679439651810020515292841),(-679439651810020515033659)⟩,⟨(-161092128877153856181315),(-161092128877153856027481)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-458243267695981792148191),(-458243267695981791985947)⟩,⟨(-78017110227960087964489),(-78017110227960087876207)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-297540351498003349650425),(-297540351498003349550426)⟩,⟨(-34274080858536419049314),(-34274080858536418999128)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-182576209479507315895354),(-182576209479507315836319)⟩,⟨(-13215142646567673775802),(-13215142646567673748254)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-98168991835931943296044),(-98168991835931943265124)⟩,⟨(-4208424019531907696922),(-4208424019531907683288)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-30886793638204950968858),(-30886793638204950959264)⟩,⟨(-857546350999235958252),(-857546350999235954150)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨5051988850056709483722073,5051988850056771944786845⟩,⟨(-3325192379186837494910635),(-3325192379186775033564111)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨13934242131339810635740639,13934242131340037992022705⟩,⟨(-9866085679995495982067933),(-9866085679995268625016589)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨19592669199692710941883209,19592669199693244982186651⟩,⟨(-15969334281608086970216736),(-15969334281607552928842979)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨21192460217163905272966248,21192460217165044032454742⟩,⟨(-21089982951780044393317198),(-21089982951778905632693430)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨19196499180501366170010449,19196499180503576776866261⟩,⟨(-24530434813385395950757660),(-24530434813383185342908848)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨14909457733589345521531618,14909457733593057192734531⟩,⟨(-25740304737175297366412011),(-25740304737171585694495555)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨9818413891429550704232105,9818413891434584174013573⟩,⟨(-24667501822672650562818780),(-24667501822667617092642366)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨5123233864551847076393646,5123233864557047011895516⟩,⟨(-21825353612953853608840777),(-21825353612948653673225202)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1520993131170793251399354,1520993131174908559163608⟩,⟨(-18026801177224155161568497),(-18026801177220039853895992)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-794488369744827442994177),(-794488369742304441896326)⟩,⟨(-14051631589129203825638589),(-14051631589126680824756016)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1974515003951130212438883),(-1974515003949925160326378)⟩,⟨(-10442647272523894143922451),(-10442647272522689092076726)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2314843281429264185561302),(-2314843281428780970470284)⟩,⟨(-7454258744992945497424711),(-7454258744992462282597257)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-2116114309182387424764986),(-2116114309182210427054493)⟩,⟨(-5104770229707957733031026),(-5104770229707780735546116)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1622726059285893366231986),(-1622726059285830129207336)⟩,⟨(-3279481025469082014963160),(-3279481025469018778107303)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1000197355546112778791116),(-1000197355546090528757406)⟩,⟨(-1823528931632092322667878),(-1823528931632070072737402)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-335893304288756601478243),(-335893304288751069125638)⟩,⟨(-583919003769158280119927),(-583919003769152747801945)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨218400217782387094703091,218400217782387098451294⟩,⟨14438469118662919886126343,14438469118662919891978454⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3080961188015944838998061,3080961188015944850367864⟩,⟨41197350384798136277067640,41197350384798136294320292⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨11812713291969503665717447,11812713291969503684910539⟩,⟨62215169691857112362706542,62215169691857112390153201⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨26283051243063264832328662,26283051243063264859250092⟩,⟨75376125387641425819823522,75376125387641425855656461⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨42713297288538689472630050,42713297288538689506768358⟩,⟨79807757516706800210326027,79807757516706800252503823⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨56288541234675871832002820,56288541234675871873470602⟩,⟨75465066088407888622864598,75465066088407888670759098⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨64116361466096380766816293,64116361466096380821063329⟩,⟨63778159144091332744740719,63778159144091332803544367⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨65740513253212799894902589,65740513253212800002511970⟩,⟨48001183023409438777907330,48001183023409438888235704⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨62151701216794667535341509,62151701216794667986763762⟩,⟨31904200262177946079884000,31904200262177946532502338⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨54993837546424063127219428,54993837546424065621251156⟩,⟨18268263271854061618301324,18268263271854064112546935⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨45994162314364793538096198,45994162314364804828172247⟩,⟨8392542825715354482484360,8392542825715365772280887⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨36493273097266332545597765,36493273097266369023924648⟩,⟨2337127210892953242710025,2337127210892989720612101⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨27271792083030253382414091,27271792083030333719299977⟩,⟨(-627535483501565498389874),(-627535483501485161901731)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨18688914063953914411904679,18688914063954033728772355⟩,⟨(-1532576904926543297703072),(-1532576904926423981133360)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨10830546657641125591449092,10830546657641238507436826⟩,⟨(-1280941425694222045335180),(-1280941425694109129525595)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3537904688469482102627475,3537904688469528748509458⟩,⟨(-479940404589898809367549),(-479940404589852163544206)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨101816515523237213008813297,101816515523241735128713367⟩,⟨49376626739590018575454584,49376626739594540703398213⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 12) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_12 (tableDensity false) (fullFactor false 1 12) density0_contains hk1_0_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨40616493024030407623652924,40616493024030407626865386⟩,⟨(-5267581095613204334899062),(-5267581095613204333504589)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_12 1 12 ha1_0_12_contains + def realAnswer : RBox := ⟨142433008547267620532466221,142433008547272142855578753⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_12 +namespace hm1_1_0_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨5283214838948784,5283214838948844⟩,⟨17935260109614599,17935260109614658⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨13112625838147029,13112625838147125⟩,⟨42359811990866993,42359811990867090⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨14673191886845355,14673191886845422⟩,⟨43276318490329566,43276318490329631⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨10966038000839985,10966038000840020⟩,⟨28347501504036400,28347501504036433⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨5910107536475268,5910107536475287⟩,⟨12674761510782040,12674761510782060⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2337577888789823,2337577888789839⟩,⟨3895980965282310,3895980965282326⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨661705524124076,661705524124093⟩,⟨814858234575130,814858234575147⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨126825891480539,126825891480556⟩,⟨113051359816316,113051359816332⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨15338274217986,15338274218003⟩,⟨9919590954264,9919590954280⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1071849126523,1071849126539⟩,⟨509036131713,509036131729⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨38247886516,38247886532⟩,⟨13493531692,13493531710⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨576036688,576036705⟩,⟨150704143,150704159⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2658970,2658986⟩,⟨498155,498171⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2045,2064⟩,⟨246,262⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-14),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-49196954652735179871),(-49196954652734961091)⟩,⟨36542278060269499201,36542278060269717983⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-125904746752682425321),(-125904746752681684736)⟩,⟨98880392428497879627,98880392428498620216⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-152502548816320813577),(-152502548816319307580)⟩,⟨133900624997785935320,133900624997787441322⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-132086441275893933635),(-132086441275891341682)⟩,⟨137078562332759209061,137078562332761801017⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-89373286187902249473),(-89373286187898455534)⟩,⟨115765116536322458915,115765116536326252855⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-48866538422805150267),(-48866538422800648996)⟩,⟨83236903516956200493,83236903516960701768⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-21814384506483801845),(-21814384506479735212)⟩,⟨51733396344314990473,51733396344319057107⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-7799048853292309425),(-7799048853289663197)⟩,⟨28183160197550896815,28183160197553543042⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2028950727529855939),(-2028950727528605971)⟩,⟨13719513249493773140,13719513249495023106⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-198697292080757847),(-198697292080316323)⟩,⟨6121562433258350235,6121562433258791760⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨175172387988705476,175172387988824232⟩,⟨2579638086652512133,2579638086652630891⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨157481001878559946,157481001878586844⟩,⟨1058859077779128794,1058859077779155687⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨90242145456620522,90242145456626302⟩,⟨434728995523610638,434728995523616414⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨44618112225049310,44618112225050627⟩,⟨180719257030822250,180719257030823568⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨19774627616142186,19774627616142528⟩,⟨72980071096228252,72980071096228596⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5570787542614810,5570787542614895⟩,⟨19717252590761388,19717252590761471⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-7015198263072658636083),(-7015198263072658632682)⟩,⟨(-4448431719889217035913),(-4448431719889217032792)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-19595325185942793552216),(-19595325185942793542585)⟩,⟨(-11914324139571281208852),(-11914324139571281200027)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-28131604815589689701238),(-28131604815589689687039)⟩,⟨(-15805644703964527449496),(-15805644703964527436423)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-31147289722426315308929),(-31147289722426315292516)⟩,⟨(-15600552889703913113329),(-15600552889703913098114)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-28973083391298160912207),(-28973083391298160895972)⟩,⟨(-12269516395971264076446),(-12269516395971264061267)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-23559605850234356384796),(-23559605850234356370171)⟩,⟨(-7630208262664075195879),(-7630208262664075182112)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-17237428994349028899225),(-17237428994349028886373)⟩,⟨(-3466775128925785891018),(-3466775128925785878822)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-11604346056501542039484),(-11604346056501542025395)⟩,⟨(-733194125546389753249),(-733194125546389739625)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-7312675239233470099735),(-7312675239233470067966)⟩,⟨566353193232563423019,566353193232563454499⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-4374801202170776679481),(-4374801202170776561133)⟩,⟨913798620514709012154,913798620514709130332⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2513050029446261206781),(-2513050029446260808035)⟩,⟨811891506114733889491,811891506114734288139⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1396635068929671881005),(-1396635068929670888595)⟩,⟨585160774146019188320,585160774146020180680⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-753272835568387403444),(-753272835568385664051)⟩,⟨378760610407115526313,378760610407117265677⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-391458943707524210169),(-391458943707522065675)⟩,⟨227163140187881706515,227163140187883850994⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-185258536840481257516),(-185258536840479480723)⟩,⟨119772768173557072403,119772768173558849191⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-54363889043173807495),(-54363889043173123326)⟩,⟨37311248077426842892,37311248077427527057⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-12883699678399782577789),(-12883699678398573729685)⟩,⟨(-222975329766529377220805),(-222975329766528168367524)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-45233861334462596322546),(-45233861334459923355647)⟩,⟨(-619106917472773053102167),(-619106917472770380120312)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-93320088649680521043221),(-93320088649678147949157)⟩,⟨(-884202356554966682306849),(-884202356554964309189917)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-156229340312183595089801),(-156229340312182351192235)⟩,⟨(-985571253697698436042483),(-985571253697697192117103)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-220929082614874106492406),(-220929082614873694782447)⟩,⟨(-943781002931319606247667),(-943781002931319194508640)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-266907719691666895835666),(-266907719691666807490623)⟩,⟨(-811145230348228731385643),(-811145230348228643013469)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-279226846333693690006911),(-279226846333693676729697)⟩,⟨(-641124387301659777239012),(-641124387301659763938611)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-258742186611216419064783),(-258742186611216417309892)⟩,⟨(-472334499256651481243038),(-472334499256651479469910)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-218058099482740118409896),(-218058099482740118036003)⟩,⟨(-327419112336302211097829),(-327419112336302210710575)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-171184199890770195598367),(-171184199890770195437393)⟩,⟨(-215665473779861191403470),(-215665473779861191233321)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-127477375197707357257785),(-127477375197707357167883)⟩,⟨(-136545887854255443081540),(-136545887854255442985749)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-90948285476075271138266),(-90948285476075271085665)⟩,⟨(-84049551599890469383126),(-84049551599890469326911)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-62068255511991567562193),(-62068255511991567531369)⟩,⟨(-50543460353329306269668),(-50543460353329306236717)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-39655513963979806679945),(-39655513963979806662491)⟩,⟨(-29247944159110691251927),(-29247944159110691233298)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-21935593665677248308882),(-21935593665677248300027)⟩,⟨(-15123355338698504858803),(-15123355338698504849359)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-7003070329762661724620),(-7003070329762661721910)⟩,⟨(-4666895631424980113238),(-4666895631424980110355)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1601777061245142607294904,1601777061245193940763767⟩,⟨(-1176010163354428106492060),(-1176010163354376773113801)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4527781590561275964669601,4527781590561462830024829⟩,⟨(-3502348299757568306130446),(-3502348299757381441026205)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨6674640021566238082379212,6674640021566677070333665⟩,⟨(-5667688541845770979525740),(-5667688541845331991920965)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨7701415634160044347274213,7701415634160980570036361⟩,⟨(-7412234595951180626551330),(-7412234595950244404159368)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨7518595252997086151463358,7518595252998903806792931⟩,⟨(-8498808958835994210086708),(-8498808958834176555075544)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨6366610400153886734388752,6366610400156938626408790⟩,⟨(-8862366994255770471895281),(-8862366994252718580101224)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4738661075918477690090230,4738661075922615550394679⟩,⟨(-8584092712894834254520052),(-8584092712890696394339768)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨3132174406140089256552812,3132174406144361896551785⟩,⟨(-7805143746992923770805576),(-7805143746988651130843653)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1852633416318172631168115,1852633416321551392512922⟩,⟨(-6696585196471154157848828),(-6696585196467775396482016)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨987519057781907410388503,987519057783976652502106⟩,⟨(-5438578671551252393493177),(-5438578671549183151328199)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨478260805653700126497213,478260805654687200616718⟩,⟨(-4186093986420492983710310),(-4186093986419505909531178)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨207671981504880056692798,207671981505275331705838⟩,⟨(-3049397439401430950179090),(-3049397439401035675109714)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨70069784091295529493259,70069784091440130643642⟩,⟨(-2092490340265310902044828),(-2092490340265166300847847)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨4494710541176359298896,4494710541227966817495⟩,⟨(-1330124085197099993081493),(-1330124085197048385529418)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-15998067162762773772819),(-15998067162744629197616)⟩,⟨(-729991910304331581881447),(-729991910304313437286467)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-8560813205812072793101),(-8560813205807562965429)⟩,⟨(-231875636220760303190145),(-231875636220755793356021)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨26865554915970072593571,26865554915970074986341⟩,⟨428608809755650797286730,428608809755650800820120⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨385036516794817748965374,385036516794817756212444⟩,⟨1144396649988048505026965,1144396649988048515535218⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1586114376685575066752222,1586114376685575078967757⟩,⟨1103924742396527022537223,1103924742396527039468300⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨4188220953249864277889888,4188220953249864295083037⟩,⟨(-705437839984818535402448),(-705437839984818512904187)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨8801305826220071175256633,8801305826220071197480955⟩,⟨(-4611885714190440939319330),(-4611885714190440911962669)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨15231142651806472799810638,15231142651806472827964127⟩,⟨(-9311293246988942366896408),(-9311293246988942334263868)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨21752867719903893767778586,21752867719903893807344370⟩,⟨(-12850350959531750065329360),(-12850350959531750022220097)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨26170821920387032182420513,26170821920387032267805913⟩,⟨(-14298260349355402488739901),(-14298260349355402400905657)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨27355827366822395839134756,27355827366822396209115449⟩,⟨(-13932828500033651306313655),(-13932828500033650934917506)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨25534776397014111558152521,25534776397014113600318554⟩,⟨(-12494472738848790133509214),(-12494472738848788090656966)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨21715521543621022426372280,21715521543621031651309135⟩,⟨(-10654292623773012188593640),(-10654292623773002963389057)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨17068866961108958066840686,17068866961108987859979116⟩,⟨(-8808723352437533241389663),(-8808723352437503448160401)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨12500924236406277663185454,12500924236406343297025404⟩,⟨(-7031805629193790541343094),(-7031805629193724907484036)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨8430700101081616640963036,8430700101081714165192513⟩,⟨(-5200131484255689045349256),(-5200131484255591521127782)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨4854766840820414208866310,4854766840820506535458559⟩,⟨(-3213562772257535084133852),(-3213562772257442757553755)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1584860048368812447214056,1584860048368850595115076⟩,⟨(-1088067405025789877214226),(-1088067405025751729318880)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨40128281248508696542497364,40128281248512410874922008⟩,⟨(-30549839188294080258341616),(-30549839188290365920716027)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 12) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_12 (tableDensity true) (fullFactor false 1 12) density1_contains hk1_0_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-53113875492962840742823967),(-53113875492962840738623054)⟩,⟨6888375278878805666890616,6888375278878805668714158⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_12 1 12 ha1_0_12_contains + def realAnswer : RBox := ⟨(-12985594244454144300326603),(-12985594244450429763701046)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_12 +namespace hm1_0_0_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-4004209739803344),(-4004209739803326)⟩,⟨1782259335872835,1782259335872853⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-9191538421999241),(-9191538421999217)⟩,⟨4327661520500198,4327661520500219⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-8919534405630483),(-8919534405630464)⟩,⟨4662252009053209,4662252009053231⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-5479060959198005),(-5479060959197987)⟩,⟨3292210745703615,3292210745703636⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-2290996465830685),(-2290996465830668)⟩,⟨1614981079478686,1614981079478706⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-658005926264558),(-658005926264542)⟩,⟨549746463034722,549746463034740⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-127313143880340),(-127313143880319)⟩,⟨126974092454257,126974092454277⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-15948516864130),(-15948516864111)⟩,⟨19158448810675,19158448810692⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1217532824957),(-1217532824940)⟩,⟨1782930207532,1782930207552⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-51824530601),(-51824530582)⟩,⟨93921267336,93921267354⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1077020926),(-1077020908)⟩,⟨2459352705,2459352723⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-8889462),(-8889444)⟩,⟨26067199,26067219⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-20650),(-20631)⟩,⟨78880,78897⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-20),(-4)⟩,⟨23,47⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-28617825522185860441),(-28617825522185839077)⟩,⟨(-13343156183714802968),(-13343156183714781600)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-75537723444112893708),(-75537723444112822145)⟩,⟨(-33870294480895681313),(-33870294480895609747)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-97367794086845817656),(-97367794086845675034)⟩,⟨(-40309787756250797961),(-40309787756250655334)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-92685193516415180599),(-92685193516414942243)⟩,⟨(-33857954476070733052),(-33857954476070494690)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-71296136255085866689),(-71296136255085530797)⟩,⟨(-21729438789956066428),(-21729438789955730535)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-46014923347086684655),(-46014923347086303991)⟩,⟨(-10804131115870498041),(-10804131115870117373)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-25503067837805474013),(-25503067837805147845)⟩,⟨(-4027128427135076380),(-4027128427134750210)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-12377811480255368312),(-12377811480255168148)⟩,⟨(-953529522782631315),(-953529522782431150)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-5369375040723309082),(-5369375040723220347)⟩,⟨26560242391265692,26560242391354430⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-2132368009731533458),(-2132368009731504108)⟩,⟨182588870990540006,182588870990569359⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-798163660238151759),(-798163660238144363)⟩,⟨130188042415415232,130188042415422628⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-291303199117144116),(-291303199117142534)⟩,⟨68665237786500315,68665237786501897⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-107335414391471258),(-107335414391470924)⟩,⟨32325905905820028,32325905905820363⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-40828790269543628),(-40828790269543545)⟩,⟨14529207806884373,14529207806884456⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-15494612717792565),(-15494612717792530)⟩,⟨6127495921029514,6127495921029545⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-4055245012856316),(-4055245012856296)⟩,⟨1688148747605485,1688148747605504⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨60000039339552636942,60000039339552637504⟩,⟨(-4438310914881372388262),(-4438310914881372387026)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-117838186114324216087),(-117838186114324214523)⟩,⟨(-12161832938268510195292),(-12161832938268510191892)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-929436989745586017970),(-929436989745586015656)⟩,⟨(-16915182730532382087070),(-16915182730532382082254)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2163520125523770332191),(-2163520125523770329482)⟩,⟨(-18090330412454983287277),(-18090330412454983281990)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-3255142698879321456197),(-3255142698879321453477)⟩,⟨(-16296742294500748004295),(-16296742294500747999359)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-3745572699851221369937),(-3745572699851221367459)⟩,⟨(-12829540779989073121456),(-12829540779989073117334)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-3559321440824386160265),(-3559321440824386158117)⟩,⟨(-9012383159499751358181),(-9012383159499751354954)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-2925578915122374633150),(-2925578915122374631009)⟩,⟨(-5744479902473077056952),(-5744479902473077054167)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-2149123485432395290426),(-2149123485432395286339)⟩,⟨(-3378663406919138787923),(-3378663406919138783486)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1448912273237775403826),(-1448912273237775389954)⟩,⟨(-1867271714656376234952),(-1867271714656376220901)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-917482860999944557557),(-917482860999944512987)⟩,⟨(-988891751485155739108),(-988891751485155694452)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-556057183549564774271),(-556057183549564667404)⟩,⟨(-511808023007744837028),(-511808023007744730120)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-325878962956772047363),(-325878962956771865970)⟩,⟨(-262663924786141068589),(-262663924786140887176)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-183003487336529399671),(-183003487336529181757)⟩,⟨(-133112298302922252294),(-133112298302922034367)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-92138669439326752592),(-92138669439326575313)⟩,⟨(-62517526494594139403),(-62517526494593962120)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-27989225099455425436),(-27989225099455357810)⟩,⟨(-18336946247266573480),(-18336946247266505855)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨82341918230560451471498,82341918230560682990195⟩,⟨(-69131444672343439689865),(-69131444672343208163539)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨227722030928188874055790,227722030928189384006076⟩,⟨(-198186478798997301126167),(-198186478798996791153750)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨322363025597167344267825,322363025597167793591336⟩,⟨(-300501658993459287768079),(-300501658993458838410287)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨353232375354003763679117,353232375354003996628873⟩,⟨(-362801220356442605662358),(-362801220356442372669940)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨327343748809977397142449,327343748809977473185449⟩,⟨(-379990585651389971377009),(-379990585651389895287630)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨265478482217495927023457,265478482217495943097095⟩,⟨(-357308004008144470689482),(-357308004008144454570385)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨192013377047584429367279,192013377047584431765346⟩,⟨(-307625814968596409435126),(-307625814968596406996183)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨125604661063643705113810,125604661063643705445917⟩,⟨(-245844935399499075027597),(-245844935399499074661337)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨75157798459110336914001,75157798459110336995142⟩,⟨(-184416043933363436702496),(-184416043933363436594554)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨41486070002810592381914,41486070002810592419105⟩,⟨(-131209096300719176141581),(-131209096300719176084454)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨21213859459508464138798,21213859459508464159164⟩,⟨(-89413979476189651758649),(-89413979476189651724087)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨10018025947660244861890,10018025947660244873285⟩,⟨(-58800869265701151277015),(-58800869265701151255890)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4305131208360343244168,4305131208360343250506⟩,⟨(-37347583974578693994985),(-37347583974578693982224)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1630696694027056496544,1630696694027056499965⟩,⟨(-22515137133264582758029),(-22515137133264582750619)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨512793983642344935620,512793983642344937297⟩,⟨(-11956980726343130386861),(-11956980726343130383017)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨103791827462385642938,103791827462385643450⟩,⟨(-3738067733807558535659),(-3738067733807558534463)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨668998548678348763945424,668998548678361330395743⟩,⟨1016420371218872397115376,1016420371218884963510333⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1977404933174008462260706,1977404933174054023817508⟩,⟨2792907741777626759234187,2792907741777672320640320⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨3176657974404668909634950,3176657974404775106590096⟩,⟨3897945429569989608864665,3897945429570095805611438⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨4149340302508945226913844,4149340302509169151561046⟩,⟨4170505909022732370344550,4170505909022956294772690⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨4758323689085980862503974,4758323689086409385583427⟩,⟨3725008100370174207533851,3725008100370602730423875⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨4909282066467611534668152,4909282066468318982026590⟩,⟨2845018690876526416314451,2845018690877233863538663⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4615509120427985356387385,4615509120428926743385404⟩,⟨1838442088547556350289131,1838442088548497737214006⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨3999899396309491915158497,3999899396310444837048376⟩,⟨940040071742452624766145,940040071743405546635294⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨3233063829165589679343889,3233063829166327917275202⟩,⟨273640417636227182940737,273640417636965420888386⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨2465998394660057182749593,2465998394660500240030845⟩,⟨(-138826856216951794496966),(-138826856216508737177998)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1794670360064978044798457,1794670360065185325848422⟩,⟨(-338954541600023581531196),(-338954541599816300435282)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1256645338137696340957076,1256645338137777875957035⟩,⟨(-390023762560977060095071),(-390023762560895525050431)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨846306875425213124846204,846306875425242491286113⟩,⟨(-350727058647593608566019),(-350727058647564242088399)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨536489372364115261986323,536489372364125612010818⟩,⟨(-265427484379126189155440),(-265427484379115839103043)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨295547254664245424317923,295547254664249031218848⟩,⟨(-162099410728763943995479),(-162099410728760337077624)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨94186915453473333612309,94186915453474226005866⟩,⟨(-54179791229313067879035),(-54179791229312175479821)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-3486434298169990220387335),(-3486434298169990218963110)⟩,⟨52722721697930291019286,52722721697930291924535⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-9916478629494588774312156),(-9916478629494588770127513)⟩,⟨741257429155299792847345,741257429155299795586429⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-14882596183464391069931159),(-14882596183464391063316993)⟩,⟨2824383992611412960134614,2824383992611412964734631⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-17867190480386287530823624),(-17867190480386287522269227)⟩,⟨6227379427788721426061646,6227379427788721432462835⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-18697202059600503347977614),(-18697202059600503338029234)⟩,⟨10002778300054669153911797,10002778300054669161941736⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-17434924410441445929067959),(-17434924410441445917935160)⟩,⟨12999512789237110122210147,12999512789237110131832195⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-14505078527190171373733423),(-14505078527190171360302048)⟩,⟨14575983620981352892865991,14575983620981352905245577⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-10733353133297948919201687),(-10733353133297948894518474)⟩,⟨14692972361562091134159528,14692972361562091158228730⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-7009598349740447321722048),(-7009598349740447222532825)⟩,⟨13647379079166494253082242,13647379079166494352009805⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-3943933445682050681679390),(-3943933445682050144916016)⟩,⟨11864030007706531587446708,11864030007706532124169189⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1781875685302444042443603),(-1781875685302441652809562)⟩,⟨9755542741617511436381123,9755542741617513826081309⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-489015301713672234875447),(-489015301713664628551096)⟩,⟨7621000219912717899493141,7621000219912725505912739⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨128895274896856587650497,128895274896873125282472⟩,⟨5619311008883935390597406,5619311008883951928316557⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨312294462604445864496676,312294462604470176472166⟩,⟨3809892951354068670761724,3809892951354092982801553⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨259169293700634400811618,259169293700657245239118⟩,⟨2191542827698757646280882,2191542827698780490746476⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨96744388979590497983997,96744388979599900578294⟩,⟨713163231663103935967055,713163231663113338573834⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-13190753352288485703882757),(-13190753352287649339566746)⟩,⟨22379147373333883401016169,22379147373334719763396744⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 13) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_13 (tableDensity false) (fullFactor false 1 13) density0_contains hk1_0_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨1076248158015973525305591,1076248158015973525619405⟩,⟨10192364869661754709891200,10192364869661754710685895⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_13 1 13 ha1_0_13_contains + def realAnswer : RBox := ⟨(-12114505194272512278577166),(-12114505194271675713947341)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_13 +namespace hm1_1_0_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-718976691978755),(-718976691978738)⟩,⟨211785406052159,211785406052176⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1666876239701767),(-1666876239701750)⟩,⟨515894663540261,515894663540278⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1640429508400974),(-1640429508400957)⟩,⟨555945886118394,555945886118414⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1015148993151944),(-1015148993151926)⟩,⟨392344388681856,392344388681872⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-420106023107385),(-420106023107369)⟩,⟨195566495443755,195566495443773⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-116905122544867),(-116905122544851)⟩,⟨69961751930030,69961751930046⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-21601923910207),(-21601923910191)⟩,⟨17482749342433,17482749342450⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-2575842190204),(-2575842190188)⟩,⟨2878571413159,2878571413176⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-188160201826),(-188160201810)⟩,⟨289767457199,289767457216⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-7737956853),(-7737956837)⟩,⟨16227630062,16227630078⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-156770913),(-156770897)⟩,⟨442634119,442634135⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1257683),(-1257667)⟩,⟨4788775,4788791⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2745),(-2729)⟩,⟨14542,14558⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-4),19⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-2936608766345817711),(-2936608766345800115)⟩,⟨(-3953608104176312351),(-3953608104176294756)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-7871583198615932721),(-7871583198615873774)⟩,⟨(-10023936390461306650),(-10023936390461247700)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-10461118012035107687),(-10461118012034990129)⟩,⟨(-11917753113878596171),(-11917753113878478609)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-10414512215694919071),(-10414512215694722433)⟩,⟨(-10040651356776262519),(-10040651356776065882)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-8478072263623012792),(-8478072263622735448)⟩,⟨(-6550907659135465928),(-6550907659135188583)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-5827490200271342490),(-5827490200271027926)⟩,⟨(-3425412152036801097),(-3425412152036486534)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3436278849098940054),(-3436278849098670285)⟩,⟨(-1451448078909375356),(-1451448078909105587)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1764363747491396549),(-1764363747491230914)⟩,⟨(-489472376665823631),(-489472376665657997)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-805252778271934471),(-805252778271861043)⟩,⟨(-119617797306006092),(-119617797305932664)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-335709861184221182),(-335709861184196907)⟩,⟨(-11097749167660971),(-11097749167636694)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-132051514081415589),(-132051514081409477)⟩,⟨8901780872719421,8901780872725533⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-50702672156542389),(-50702672156541082)⟩,⟨7523009853011081,7523009853012387⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-19586690354281216),(-19586690354280937)⟩,⟨4061695643781579,4061695643781856⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-7737944451596053),(-7737944451595983)⟩,⟨1909607815583405,1909607815583477⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3011681570152842),(-3011681570152813)⟩,⟨815926106765932,815926106765964⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-798027678766975),(-798027678766957)⟩,⟨225466195972992,225466195973011⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨536654136554419422938,536654136554419423329⟩,⟨(-846301213540719336438),(-846301213540719336006)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1428353721224749921089,1428353721224749922165⟩,⟨(-2349077144201353051346),(-2349077144201353050169)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1871498605524722895920,1871498605524722897489⟩,⟨(-3330555235570511788902),(-3330555235570511787196)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1813750282055384441580,1813750282055384443368⟩,⟨(-3620353075298937997821),(-3620353075298937995886)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1393047835994212924608,1393047835994212926353⟩,⟨(-3287996309708179663001),(-3287996309708179661132)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨841971832763309126433,841971832763309127972⟩,⟨(-2597372244095477300241),(-2597372244095477298603)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨370416329193981181731,370416329193981183048⟩,⟨(-1838217079340237133795),(-1838217079340237132406)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨75908262507014474891,75908262507014476309⟩,⟨(-1192969275951359272008),(-1192969275951359270543)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-55675956127831658343),(-55675956127831655229)⟩,⟨(-723085018357180268089),(-723085018357180264946)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-86664827363329809492),(-86664827363329798316)⟩,⟨(-415708016146733244340),(-415708016146733233145)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-74115236838888774501),(-74115236838888738245)⟩,⟨(-229639924961910150923),(-229639924961910114655)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-51515537887650798074),(-51515537887650710982)⟩,⟨(-123028297556930624483),(-123028297556930537385)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-32288700977762267962),(-32288700977762119986)⟩,⟨(-64239890787453018088),(-64239890787452870106)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-18864965551697050395),(-18864965551696872488)⟩,⟨(-32516656733171368935),(-32516656733171191025)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-9764422241675775361),(-9764422241675630552)⟩,⟨(-15104627926391296691),(-15104627926391151877)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3012813000560087718),(-3012813000560032460)⟩,⟨(-4389834940258296420),(-4389834940258241164)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨35880118668567692124255,35880118668567886651708⟩,⟨(-2073129195691975734088),(-2073129195691781207483)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨99154316518177226916778,99154316518177655104484⟩,⟨(-7243129315210478689835),(-7243129315210050504558)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨140295507126325521459492,140295507126325898228212⟩,⟨(-14801196847191453952627),(-14801196847191077187585)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨154248515152420323894000,154248515152420518813015⟩,⟨(-24437653888156728755105),(-24437653888156533840500)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨145106808135071044905889,145106808135071108337576⟩,⟨(-33947142729979591122717),(-33947142729979527695546)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨122080569784744336890248,122080569784744350228811⟩,⟨(-40146616573705543934311),(-40146616573705530599862)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨94175430331491459257954,94175430331491461218873⟩,⟨(-40993820147705590631496),(-40993820147705588673994)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨67567432992597971726791,67567432992597971981539⟩,⟨(-36995413423375209145662),(-36995413423375208893521)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨45552744468021676396328,45552744468021676450495⟩,⟨(-30324692327766124565945),(-30324692327766124513632)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨29173105585108480436130,29173105585108480459300⟩,⟨(-23147111123992461889404),(-23147111123992461867461)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨17973188676292279650929,17973188676292279663641⟩,⟨(-16773815057762896853697),(-16773815057762896841751)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨10786862387289529556808,10786862387289529564091⟩,⟨(-11669076933922596506290),(-11669076933922596499461)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨6344977245434355403808,6344977245434355407992⟩,⟨(-7790288737893831295366),(-7790288737893831291437)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨3607049460251145765789,3607049460251145768118⟩,⟨(-4890071558298973341886),(-4890071558298973339689)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1842065778422894068357,1842065778422894069529⟩,⟨(-2671709808242417095944),(-2671709808242417094835)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨564811488956523274204,564811488956523274571⟩,⟨(-847543482141467249812),(-847543482141467249465)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨236602470448259884940155,236602470448270212579848⟩,⟨322264288216737773534659,322264288216748101192992⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨701955083306412372369432,701955083306449819477064⟩,⟨907509306563674527180176,907509306563711974339232⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1127434200344753899650099,1127434200344841194644849⟩,⟨1327854377713046536954700,1327854377713133832020557⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1458338878656894524709677,1458338878657078622423385⟩,⟨1515462267336210790921358,1515462267336394888709513⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1648595282110619712604695,1648595282110972062309791⟩,⟨1458803575240488620841897,1458803575240840970610101⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1690258204388646385174464,1690258204389228078031270⟩,⟨1214695204032516830217509,1214695204033098523118321⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1606106535600670195613800,1606106535601444081187645⟩,⟨887051225589404771648502,887051225590178657246034⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1430349915360860861033024,1430349915361643850877930⟩,⟨574348024007599476652033,574348024008382466503862⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1200926723732904296564632,1200926723733510407764758⟩,⟨332480532609700135235602,332480532610306246431724⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨954378367791491318663525,954378367791854693380725⟩,⟨173429643545498153437323,173429643545861528145365⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨719386005621823631954646,719386005621993419020017⟩,⟨82256122251689020829646,82256122251858807884594⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨514061819815125762527561,514061819815192459185291⟩,⟨35038618437138486557358,35038618437205183205420⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨346911377102030573617535,346911377102054565077716⟩,⟨11630527985926597212582,11630527985950588664891⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨217597435375352061235549,217597435375360507888905⟩,⟨741128562141761878498,741128562150208526270⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨118313755926955196022203,118313755926958137414049⟩,⟨(-2591419696488802372615),(-2591419696485860984035)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨37401881359541232548390,37401881359541960009475⟩,⟨(-1380812609182824398496),(-1380812609182096938475)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-103495627090325466292679),(-103495627090325465439138)⟩,⟨6485455394245591466273,6485455394245592044083⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-275480779590552858085582),(-275480779590552855555323)⟩,⟨92636048234594915931363,92636048234594917676031⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-264235784883815020626249),(-264235784883815016575389)⟩,⟨379208404951176591084580,379208404951176594007677⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨166620816411293337375431,166620816411293342708655⟩,⟨992146241103719767033219,992146241103719771111433⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1079276051676578844065469,1079276051676578850476858⟩,⟨2060504392040801864699397,2060504392040801869912311⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2149634632881977722425737,2149634632881977729969661⟩,⟨3516404755655700308729434,3516404755655700315244719⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨2920851154442219689972774,2920851154442219699779216⟩,⟨4943888492755847172014231,4943888492755847181024576⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨3195428960738841659860376,3195428960738841679473138⟩,⟨5848067490265379344927618,5848067490265379364005560⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨3059318014717396670412898,3059318014717396751771873⟩,⟨6006170495517898490975670,6006170495517898572037600⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2695429615345882210321108,2695429615345882649922934⟩,⟨5508447889808380104203477,5508447889808380543670195⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨2259729976722382790333115,2259729976722384742954538⟩,⟨4605940761362700354698996,4605940761362702307274357⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1839429424229375333093216,1839429424229381545524911⟩,⟨3564621208688728804194579,3564621208688735016615267⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1448782588917689475077935,1448782588917702986091461⟩,⟨2575848715709804721813387,2575848715709818232828426⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1060031040273823399350198,1060031040273843270898237⟩,⟨1718683647731905539369669,1718683647731925410922764⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨650243011675980269505928,650243011675998948441903⟩,⟨982354893894599750070105,982354893894618429010407⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨219329644981503206365671,219329644981510895995745⟩,⟨319472669824513423403823,319472669824521113035633⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨6181968555042725784287310,6181968555043412772790601⟩,⟨8606833874870803130940197,8606833874871490118242438⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 13) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_13 (tableDensity true) (fullFactor false 1 13) density1_contains hk1_0_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1407401437405503841194606),(-1407401437405503840784234)⟩,⟨(-13328477137249986929358478),(-13328477137249986928319262)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_13 1 13 ha1_0_13_contains + def realAnswer : RBox := ⟨4774567117637221843092704,4774567117637909032006367⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_13 +namespace hm1_0_0_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-66341953562281),(-66341953562265)⟩,⟨(-149054337144073),(-149054337144057)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-158115133671903),(-158115133671885)⟩,⟨(-335890782278521),(-335890782278505)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-164059359831687),(-164059359831670)⟩,⟨(-314031442228936),(-314031442228918)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-109421500677769),(-109421500677750)⟩,⟨(-182265396386504),(-182265396386487)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-49668499410950),(-49668499410929)⟩,⟨(-70545787931753),(-70545787931735)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-15303664935916),(-15303664935893)⟩,⟨(-18345707637169),(-18345707637147)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-3122670587764),(-3122670587745)⟩,⟨(-3136863648454),(-3136863648435)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-405010200289),(-405010200269)⟩,⟨(-337895869256),(-337895869236)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-31388296908),(-31388296889)⟩,⟨(-21488889191),(-21488889172)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1325690804),(-1325690786)⟩,⟨(-733558386),(-733558368)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-26545223),(-26545205)⟩,⟨(-11659400),(-11659382)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-202187),(-202170)⟩,⟨(-69152),(-69135)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-412),(-395)⟩,⟨(-116),(-99)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨995703399836391958,995703399836393567⟩,⟨(-2135524778637474011),(-2135524778637472403)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨2504016169361269662,2504016169361274966⟩,⟨(-5584068928973705705),(-5584068928973700402)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨2925252743572130831,2925252743572141186⟩,⟨(-7064470899785470932),(-7064470899785460578)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2390161410226655126,2390161410226671932⟩,⟨(-6540272297253938508),(-6540272297253921698)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1479320441473523450,1479320441473546269⟩,⟨(-4850147103422404027),(-4850147103422381207)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨703612542180691889,703612542180716612⟩,⟨(-2992823293191654698),(-2992823293191629975)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨249101927957398511,249101927957418622⟩,⟨(-1573835300304501129),(-1573835300304481018)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨55762469686703999,55762469686715654⟩,⟨(-719967430585181544),(-719967430585169888)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1320123366050830),(-1320123366045972)⟩,⟨(-292821849856717469),(-292821849856712609)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-9256841759277294),(-9256841759275777)⟩,⟨(-108657888294017840),(-108657888294016323)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-6176904263044577),(-6176904263044203)⟩,⟨(-37964041235233209),(-37964041235232836)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-3050367176584201),(-3050367176584112)⟩,⟨(-12960017836900466),(-12960017836900377)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1351807658599448),(-1351807658599419)⟩,⟨(-4492547697877286),(-4492547697877256)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-577552624213000),(-577552624212978)⟩,⟨(-1623744272518670),(-1623744272518652)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-234786994543614),(-234786994543595)⟩,⟨(-593808431544894),(-593808431544876)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-63444571513875),(-63444571513859)⟩,⟨(-152408525638603),(-152408525638586)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨497186419321965694003,497186419321965694156⟩,⟨6722863480222420113,6722863480222420194⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1353844123414888073586,1353844123414888073983⟩,⟨(-13079954392555803699),(-13079954392555803509)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1859662614489105827424,1859662614489105827974⟩,⟨(-102046073665247224381),(-102046073665247224112)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1952624981357705817636,1952624981357705818230⟩,⟨(-233266880166247963072),(-233266880166247962764)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1717445014567787537623,1717445014567787538163⟩,⟨(-342711495060990800214),(-342711495060990799912)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1313507982248472729112,1313507982248472729557⟩,⟨(-383140512597764914182),(-383140512597764913912)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨892564608553219656616,892564608553219656954⟩,⟨(-352222311911638341703),(-352222311911638341475)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨548479248788670773654,548479248788670773940⟩,⟨(-279124095051563031802),(-279124095051563031577)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨310298987235011890329,310298987235011890752⟩,⟨(-197241975097070332002),(-197241975097070331613)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨164804575628527012480,164804575628527013729⟩,⟨(-127801810091349881985),(-127801810091349880752)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨83929846090026350670,83929846090026354459⟩,⟨(-77828245867370480070),(-77828245867370476289)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨41871637748749253223,41871637748749261951⟩,⟨(-45472914770980275719),(-45472914770980266994)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨20802041877926130875,20802041877926145225⟩,⟨(-25801133652999491785),(-25801133652999477440)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨10267490423985015212,10267490423985032015⟩,⟨(-14113573652160114740),(-14113573652160097937)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨4733146697545697689,4733146697545711119⟩,⟨(-6975318507882718149),(-6975318507882704718)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1374927903854711641,1374927903854716726⟩,⟨(-2098653888885126001),(-2098653888885120914)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨10329673025176151714923,10329673025176186310747⟩,⟨12303637339966929547085,12303637339966964141763⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨29472911535422353847368,29472911535422429705524⟩,⟨33866313615225007717661,33866313615225083572495⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨44271445905558640014861,44271445905558706262172⟩,⟨47496079925184260712934,47496079925184326955137⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨52718927791172777181503,52718927791172811083567⟩,⟨51336032451095858764007,51336032451095892659799⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨54242426896244918488991,54242426896244929374278⟩,⟨46737727490244099566357,46737727490244110444941⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨49926646411367706526715,49926646411367708786084⟩,⟨37106838890509929320148,37106838890509931573077⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨41952352000438805946061,41952352000438806280074⟩,⟨26196252721290526993597,26196252721290527321948⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨32650163395536505031564,32650163395536505080513⟩,⟨16689397884327382048082,16689397884327382092411⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨23820193083798188252444,23820193083798188266521⟩,⟨9713225115521861841991,9713225115521861852544⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨16478030892086404018226,16478030892086404025497⟩,⟨5213304647611198195178,5213304647611198199889⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨10926986381358702008512,10926986381358702012801⟩,⟨2594209664463047068213,2594209664463047070730⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨7006595271080838307589,7006595271080838310153⟩,⟨1194564647854819747819,1194564647854819749196⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4353201621471964438543,4353201621471964440066⟩,⟨502153197378887349642,502153197378887350396⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2578270732490183346097,2578270732490183346975⟩,⟨186852016179054604752,186852016179054605163⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1352344166100189128730,1352344166100189129185⟩,⟨58020940249330628408,58020940249330628614⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨420085015075462537716,420085015075462537868⟩,⟨11664990632957710964,11664990632957711037⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-189888991214170593595222),(-189888991214168245976965)⟩,⟨124982447217044337150475,124982447217046684778828⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-519812023688491120330060),(-519812023688482642127892)⟩,⟨368012727269390235237595,368012727269398713467148⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-720105898961670363396737),(-720105898961650753882778)⟩,⟨586776312308680946295842,586776312308700555847450⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-762109259798036703574777),(-762109259797995815937449)⟩,⟨758059044796492489403777,758059044796533377080341⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-671207160474474241482982),(-671207160474397104853123)⟩,⟨857091024142619101008158,857091024142696237671559⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-504121915416564053367610),(-504121915416438841411407)⟩,⟨869459983808627238034161,869459983808752450013805⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-319659967410216285925200),(-319659967410052793078074)⟩,⟨801943998268471885881780,801943998268635378741483⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-160169414733572405443199),(-160169414733410243722408)⟩,⟨680720282658925150657423,680720282659087312381724⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-45715229730029241489880),(-45715229729906264810039)⟩,⟨538446373464677311689110,538446373464800288366248⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨22526009516346629811067,22526009516418879168129⟩,⟨401874821336140746921314,401874821336212996272243⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨54032149411502005571064,54032149411535114349375⟩,⟨286410439462373552674456,286410439462406661445419⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨61022165291369471138760,61022165291382246547744⟩,⟨196719806887843510013992,196719806887856285415943⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨53978766135059135193659,53978766135063659576242⟩,⟨130287595693355428901846,130287595693359953278575⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨40314989433319845297081,40314989433321418314526⟩,⟨81496151581046020664541,81496151581047593677701⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨24394632960736770487751,24394632960737313436625⟩,⟨44479338368540287994417,44479338368540830940714⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨8115005732439427320895,8115005732439560987855⟩,⟨14107305201995764292091,14107305201995897958191⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-11818380112076521689227),(-11818380112076521486200)⟩,⟨(-781730813988499081359932),(-781730813988499081038087)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-165602897638477372419795),(-165602897638477371807054)⟩,⟨(-2216469751449895759907840),(-2216469751449895758965394)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-627068853739040853148218),(-627068853739040852124467)⟩,⟨(-3305815438954626400332544),(-3305815438954626398852561)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1370105932195827590028992),(-1370105932195827588615672)⟩,⟨(-3932765603582637100193721),(-3932765603582637098297469)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-2175201914454079825151673),(-2175201914454079823397803)⟩,⟨(-4067518683288347601571088),(-4067518683288347599392254)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-2787774466175008394480415),(-2787774466175008392407221)⟩,⟨(-3740396610941033228072893),(-3740396610941033225670014)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-3077032802202855065018280),(-3077032802202855062394929)⟩,⟨(-3063327243941817996701640),(-3063327243941817993852883)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-3049387907074742221107978),(-3049387907074742216108774)⟩,⟨(-2228667288486503463030251),(-2228667288486503457902297)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-2782738092747533441609206),(-2782738092747533421477600)⟩,⟨(-1430095641713543173450732),(-1430095641713543153265966)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-2376713353995027515104901),(-2376713353995027407848621)⟩,⟨(-790656747861155755603248),(-790656747861155648339826)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1921432710027651616143470),(-1921432710027651146450505)⟩,⟨(-351306156474260553478276),(-351306156474260083799689)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1477862875515235159220414),(-1477862875515233686405555)⟩,⟨(-95013176054039368484118),(-95013176054037895688997)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1075160003920397686545237),(-1075160003920394525310974)⟩,⟨24583975293452462389099,24583975293455623605681⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-721206775989134323932477),(-721206775989129723917718)⟩,⟨59091435327198360435582,59091435327202960437482⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-411780729710361415845822),(-411780729710357124208278)⟩,⟨48691627184134290509965,48691627184138582139965⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-133489531443010710469591),(-133489531443008950526233)⟩,⟨18108384510117552908600,18108384510119312849496⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-4566583072963896475902506),(-4566583072963752587211863)⟩,⟨(-3137240321658726815577430),(-3137240321658582926456562)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 14) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_14 (tableDensity false) (fullFactor false 1 14) density0_contains hk1_0_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-2358233789545934952650487),(-2358233789545934952467463)⟩,⟨203495557511320762569717,203495557511320762635583⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_14 1 14 ha1_0_14_contains + def realAnswer : RBox := ⟨(-6924816862509831528552993),(-6924816862509687439679326)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_14 +namespace hm1_1_0_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-7883379773978),(-7883379773962)⟩,⟨(-26763357983511),(-26763357983495)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-18848559517712),(-18848559517696)⟩,⟨(-60911371589104),(-60911371589088)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-19563276753392),(-19563276753376)⟩,⟨(-57751782791305),(-57751782791289)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-13039842485569),(-13039842485553)⟩,⟨(-33769871264825),(-33769871264809)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-6013137046396),(-6013137046380)⟩,⟨(-12938308076867),(-12938308076851)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1946353146799),(-1946353146783)⟩,⟨(-3260598156720),(-3260598156704)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-429556991210),(-429556991194)⟩,⟨(-532515364148),(-532515364132)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-60792856014),(-60792855997)⟩,⟨(-54602168672),(-54602168653)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-5096894362),(-5096894346)⟩,⟨(-3322455038),(-3322455022)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-228906871),(-228906854)⟩,⟨(-109565134),(-109565118)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-4775948),(-4775932)⟩,⟨(-1697620),(-1697604)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-37146),(-37130)⟩,⟨(-9795),(-9779)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-85),(-68)⟩,⟨(-27),(-11)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨295029310967108623,295029310967109952⟩,⟨(-219135486670071641),(-219135486670070314)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨741066643739593080,741066643739597453⟩,⟨(-581884483892640980),(-581884483892636609)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨864862924243373279,864862924243381813⟩,⟨(-758943265507990560),(-758943265507982024)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨708793016005707391,708793016005721261⟩,⟨(-734788913299593021),(-734788913299579155)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨445935015558553380,445935015558572222⟩,⟨(-576625480075838213),(-576625480075819369)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨223005327751699535,223005327751719968⟩,⟨(-378922475373977096),(-378922475373956666)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨89698611559441340,89698611559457976⟩,⟨(-211999770709225357),(-211999770709208723)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨28533868125982572,28533868125992217⟩,⟨(-102598314051836426),(-102598314051826780)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨6550478551157065,6550478551161086⟩,⟨(-43903360378690050),(-43903360378686031)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨575533479040946,575533479042199⟩,⟨(-17101995730215136),(-17101995730213882)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-420203676184885),(-420203676184580)⟩,⟨(-6279206829122841),(-6279206829122538)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-333822287422795),(-333822287422721)⟩,⟨(-2255179633581630),(-2255179633581556)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-169797311105234),(-169797311105208)⟩,⟨(-819648720173285),(-819648720173257)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-75903185102131),(-75903185102113)⟩,⟨(-307701240162421),(-307701240162400)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-31263409401772),(-31263409401756)⟩,⟨(-115413539362010),(-115413539361994)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-8473539801227),(-8473539801211)⟩,⟨(-29992184753891),(-29992184753875)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨94803782138364696776,94803782138364696837⟩,⟨60117058079376437891,60117058079376437952⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨261493375834711714421,261493375834711714569⟩,⟨159008644647958499794,159008644647958499930⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨366153324499877720664,366153324499877720865⟩,⟨205774232085764638989,205774232085764639177⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨390763138535409550901,390763138535409551127⟩,⟨195815427949881438335,195815427949881438542⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨346504733907603431084,346504733907603431296⟩,⟨146874215050818011217,146874215050818011414⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨265920228722077775847,265920228722077776031⟩,⟨86279736610569672101,86279736610569672275⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨182046043249955175287,182046043249955175441⟩,⟨36754593833407483108,36754593833407483252⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨113895153942772132815,113895153942772132969⟩,⟨7297921114948242961,7297921114948243111⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨66400904417736038402,66400904417736038704⟩,⟨(-5082881351113936919),(-5082881351113936624)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨36685131016381580727,36685131016381581725⟩,⟨(-7633205334254191095),(-7633205334254190101)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨19487704229008264746,19487704229008267820⟩,⟨(-6283251228321982444),(-6283251228321979368)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨10064337479365021075,10064337479365028189⟩,⟨(-4211721823562479595),(-4211721823562472484)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨5087488136995898017,5087488136995909721⟩,⟨(-2556128301300649646),(-2556128301300637941)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨2508180898306707868,2508180898306721586⟩,⟨(-1454814254754898153),(-1454814254754884433)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1143573942363871725,1143573942363882697⟩,⟨(-739192320719514927),(-739192320719503953)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨329156173301098026,329156173301102184⟩,⟨(-225902333651170396),(-225902333651166238)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨309761662669107778637,309761662669136845759⟩,⟨5361254833242049137346,5361254833242078204593⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1076975857623157490346,1076975857623221182668⟩,⟨14746017836998151480980,14746017836998215173670⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2179911042520505448547,2179911042520560993739⟩,⟨20670744911629176989334,20670744911629232535072⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3549612330932436996909,3549612330932465358347⟩,⟨22417051147380067232155,22417051147380095594240⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4843764709971521869483,4843764709971530943253⟩,⟨20717331589752354296003,20717331589752363370422⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨5607526507451770037809,5607526507451771906781⟩,⟨17061963049959926665810,17061963049959928535359⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨5588802108183749132182,5588802108183749400193⟩,⟨12846119385476472395381,12846119385476472663861⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨4912142801376048530351,4912142801376048564006⟩,⟨8975682745005727290698,8975682745005727324697⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3916197506892485760961,3916197506892485767770⟩,⟨5885304146511608303486,5885304146511608310534⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2906519812110112207615,2906519812110112210403⟩,⟨3664611293916059196717,3664611293916059199660⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2049609257001213840254,2049609257001213841745⟩,⟨2196908624985734179858,2196908624985734181435⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1390318022746940229701,1390318022746940230537⟩,⟨1285554376506689937910,1285554376506689938800⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨907961042124049189787,907961042124049190263⟩,⟨739647457301358616922,739647457301358617427⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨559951436438497116392,559951436438497116661⟩,⟨413078274025780454380,413078274025780454663⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨302167451861858561771,302167451861858561912⟩,⟨208343816507990478091,208343816507990478240⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨95246970781957457691,95246970781957457745⟩,⟨63473820481004720430,63473820481004720484⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-60205718402655951108093),(-60205718402654021724583)⟩,⟨44202102183776071567755,44202102183778000947707⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-168901380757097560756454),(-168901380757090592478767)⟩,⟨130639890500832732950694,130639890500839701218604⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-245296594479834994969680),(-245296594479818875704940)⟩,⟨208254743666032280663358,208254743666048399914676⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-276911399601075051599435),(-276911399601041436142231)⟩,⟨266433545961608841701078,266433545961642457144384⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-262833746932865089170097),(-262833746932801664156565)⟩,⟨296957480473771462948112,296957480473834887950032⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-215205613222843074130444),(-215205613222740119574997)⟩,⟨299353054684357480555953,299353054684460435103444⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-154195464576480045496292),(-154195464576345642917295)⟩,⟨279051457522960846296623,279051457523095248871424⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-97799347671936017438637),(-97799347671802773433792)⟩,⟨243408389762502087820462,243408389762635331824106⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-55408351577918638313358),(-55408351577817671314519)⟩,⟨199991807280860459195600,199991807280961426195114⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-28283477630476951512833),(-28283477630417695874958)⟩,⟨155520536233566211503246,155520536233625467142635⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-13137156604459796088288),(-13137156604432676132575)⟩,⟨114800841432421777109709,114800841432448897067112⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-5489625425440023438381),(-5489625425429572980274)⟩,⟨80471809547076481833479,80471809547086932293127⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1792630628098124888666),(-1792630628094428611041)⟩,⟨53406872879100904952566,53406872879104601231425⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-113469085058697219176),(-113469085057413483349)⟩,⟨33054863058937298304096,33054863058938582040788⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨389784890915621050915,389784890916063817775⟩,⟨17806130532042976464420,17806130532043419231783⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨206809264571224927803,206809264571333889507⟩,⟨5602054132948288242781,5602054132948397204648⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1453786111505125959633),(-1453786111505125830060)⟩,⟨(-23205894631367826829651),(-23205894631367826638187)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-20695415961433018139021),(-20695415961433017748996)⟩,⟨(-61577514492212804329791),(-61577514492212803764045)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-84185792884445595479529),(-84185792884445594829999)⟩,⟨(-58730143461238076937864),(-58730143461238076037884)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-218243357587987135549876),(-218243357587987134651602)⟩,⟨36543820904212139200708,36543820904212140374668⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-447941504120690601372948),(-447941504120690600237527)⟩,⟨234534956047506956225989,234534956047506957621279⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-753856436530042562236280),(-753856436530042560836184)⟩,⟨460832032662888737595256,460832032662888739214711⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1043388445445812541478961),(-1043388445445812539573549)⟩,⟨616494307208187547566387,616494307208187549637861⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1213483310391909318182461),(-1213483310391909314224173)⟩,⟨663134400478592889276954,663134400478592893343646⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1224538066056847354990201),(-1224538066056847338497904)⟩,⟨623787684926988535796833,623787684926988552346896⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1103450313660818809968208),(-1103450313660818722149710)⟩,⟨539963522539066554351836,539963522539066642194809⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-907175775465244622953248),(-907175775465244239178594)⟩,⟨445054816897571603616441,445054816897571987398055⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-691265819516457661416231),(-691265819516456458520541)⟩,⟨356677989310314523064791,356677989310315725961069⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-492855059652510031320969),(-492855059652507448652920)⟩,⟨277178937279844094528358,277178937279846677195071⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-325346821670675531750854),(-325346821670671771910827)⟩,⟨200650923152687578161884,200650923152691338000306⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-184580118931634535250050),(-184580118931631026163099)⟩,⟨122174641067916056203003,122174641067919565288791⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-59798729020385398719836),(-59798729020383959404687)⟩,⟨41053890511893207786558,41053890511894647101270⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1719145496287977838189830),(-1719145496287859644229348)⟩,⟨1173607189398513239334493,1173607189398631433553213⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 14) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_14 (tableDensity true) (fullFactor false 1 14) density1_contains hk1_0_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨3083844186329299553226683,3083844186329299553466022⟩,⟨(-266109575207111766523455),(-266109575207111766437323)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_14 1 14 ha1_0_14_contains + def realAnswer : RBox := ⟨1364698690041321615036853,1364698690041440009236674⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_14 +namespace hm1_0_0_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨5178602022425,5178602022441⟩,⟨(-2304866277067),(-2304866277050)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨11457109546468,11457109546485⟩,⟨(-5392135410343),(-5392135410323)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨10321094556286,10321094556307⟩,⟨(-5389254089859),(-5389254089839)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨5661184488835,5661184488853⟩,⟨(-3395667501142),(-3395667501125)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2028786049819,2028786049835⟩,⟨(-1426655539332),(-1426655539314)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨477861974643,477861974662⟩,⟨(-398019022748),(-398019022730)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨72236649393,72236649411⟩,⟨(-71779170926),(-71779170907)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨6694068644,6694068662⟩,⟨(-8006679207),(-8006679188)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨354828955,354828972⟩,⟨(-517046338),(-517046321)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨9719415,9719432⟩,⟨(-17519013),(-17518992)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨118200,118219⟩,⟨(-268415),(-268392)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨493,512⟩,⟨(-1479),(-1461)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),12⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨148733982613950540,148733982613950667⟩,⟨69348810968328094,69348810968328221⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨385284805615651102,385284805615651482⟩,⟨172782402316266990,172782402316267371⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨478410920823234541,478410920823235258⟩,⟨198140534147426722,198140534147427439⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨430781345720558550,430781345720559671⟩,⟨157495805006602612,157495805006603732⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨307994004565684808,307994004565686271⟩,⟨94009862878042919,94009862878044384⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨181713609700512699,181713609700514211⟩,⟨42775849179383143,42775849179384660⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨90672629181883931,90672629181885105⟩,⟨14384732506655293,14384732506656467⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨39098097811464533,39098097811465183⟩,⟨3044375068876579,3044375068877228⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨14909910158092378,14909910158092645⟩,⟨(-60724403928431),(-60724403928167)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨5169646332228590,5169646332228679⟩,⟨(-438183296694048),(-438183296693957)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1685968063025393,1685968063025429⟩,⟨(-273635052444236),(-273635052444202)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨538323773638754,538323773638773⟩,⟨(-126516707293432),(-126516707293412)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨175544503001444,175544503001465⟩,⟨(-52774659593863),(-52774659593843)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨60279878411288,60279878411304⟩,⟨(-21431141009698),(-21431141009680)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨21241067646797,21241067646814⟩,⟨(-8397102759538),(-8397102759521)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5346154154972,5346154154989⟩,⟨(-2225452249363),(-2225452249346)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-703062884130329749),(-703062884130329726)⟩,⟨51982592877972246303,51982592877972246336⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1355074013770488222,1355074013770488258⟩,⟨140662509952073232477,140662509952073232531⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨10457255610026864677,10457255610026864719⟩,⟨190825888142631862959,190825888142631863031⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨23474612903112929541,23474612903112929588⟩,⟨196718240436274376890,196718240436274376965⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨33678287750667632729,33678287750667632771⟩,⟨168938084662675189631,168938084662675189698⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨36582260716842603709,36582260716842603748⟩,⟨125523986938449008677,125523986938449008735⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨32534817600673996051,32534817600673996086⟩,⟨82512767474083743637,82512767474083743684⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨24858333038697875225,24858333038697875259⟩,⟨48883055727555891690,48883055727555891733⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨16897817952828373856,16897817952828373903⟩,⟨26601647653925870215,26601647653925870269⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨10522652807912435514,10522652807912435631⟩,⟨13577624351507212354,13577624351507212472⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨6162617756755460207,6162617756755460519⟩,⟨6649245301933106157,6649245301933106471⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3471090015815203805,3471090015815204484⟩,⟨3197512504946149212,3197512504946149891⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1906728928528909210,1906728928528910285⟩,⟨1537726352787320004,1537726352787321077⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1015943212705341402,1015943212705342626⟩,⟨739205504766227006,739205504766228229⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨492867334718872206,492867334718873169⟩,⟨334458333306123918,334458333306124884⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨146868400929904431,146868400929904800⟩,⟨96221127227615495,96221127227615865⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1715864728800440972781),(-1715864728800436148080)⟩,⟨1440570445905867476725,1440570445905872301589⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-4700774562455845184231),(-4700774562455834653033)⟩,⟨4090822924078952386613,4090822924078962918276⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-6531486562496836498025),(-6531486562496827383113)⟩,⟨6087546219509548877226,6087546219509557992851⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-6963540051032692308698),(-6963540051032687705330)⟩,⟨7150071709666872484589,7150071709666877088820⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-6228479417142336179613),(-6228479417142334727036)⟩,⟨7226971518647383662687,7226971518647385116166⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-4840993542561949653089),(-4840993542561949358338)⟩,⟨6511455361203845981288,6511455361203846276888⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-3335855392719622832004),(-3335855392719622790031)⟩,⟨5340112341598811770409,5340112341598811813116⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2069851416276900399389),(-2069851416276900393852)⟩,⟨4047373738018961554471,4047373738018961560589⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1171703964850782856282),(-1171703964850782854987)⟩,⟨2871820178350436753046,2871820178350436754771⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-611488450315062843217),(-611488450315062842648)⟩,⟨1931574381195397593352,1931574381195397594231⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-296109196437449344889),(-296109196437449344585)⟩,⟨1246399479715985151103,1246399479715985151612⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-132951672770477384418),(-132951672770477384250)⟩,⟨779268988927010229358,779268988927010229663⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-54668452274154495563),(-54668452274154495466)⟩,⟨473593936617025729967,473593936617025730150⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-19983295008404176881),(-19983295008404176821)⟩,⟨275567128270861636896,275567128270861637004⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-6127262302427606122),(-6127262302427606087)⟩,⟨142755516110214620978,142755516110214621042⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1223609303701807623),(-1223609303701807601)⟩,⟨44062015298272979147,44062015298272979173⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-21792636855375715522480),(-21792636855375306183602)⟩,⟨(-33110300580079353832642),(-33110300580078944495485)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-63924599864435102387153),(-63924599864433629906020)⟩,⟨(-90297142240494481351138),(-90297142240493008874647)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-101161350701851776409036),(-101161350701848396825687)⟩,⟨(-124164346403073678850129),(-124164346403070299273128)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-129261629630517889678498),(-129261629630510921399875)⟩,⟨(-129983530028725705275431),(-129983530028718737003367)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-144093901334951440330145),(-144093901334938480686199)⟩,⟨(-112883786247799927005612),(-112883786247786967367211)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-143724226682202049802036),(-143724226682181365241181)⟩,⟨(-83374771967919324282747),(-83374771967898639725712)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-130052859993219969318443),(-130052859993193467190542)⟩,⟨(-51877336238912510193074),(-51877336238886008067192)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-108128856129437341389183),(-108128856129411584549754)⟩,⟨(-25472130816692478166971),(-25472130816666721328100)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-83699844539265924224041),(-83699844539246803560885)⟩,⟨(-7128376951296240928304),(-7128376951277120264733)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-61128287324569918482826),(-61128287324558921816280)⟩,⟨3411468349382898108090,3411468349393894775566⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-42662325119245089455646),(-42662325119240153428387)⟩,⟨8039226607439193420328,8039226607444129448686⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-28742994589569839290927),(-28742994589567970962635)⟩,⟨8911128277484455901151,8911128277486324230478⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-18720750627210590512061),(-18720750627209939916748)⟩,⟨7753925503408040398208,7753925503408690994372⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-11554589338826470493753),(-11554589338826247360300)⟩,⟨5715163355673098042900,5715163355673321176964⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-6247816774003223525604),(-6247816774003147244291)⟩,⟨3426460408748883984035,3426460408748960265717⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1972125429024203085168),(-1972125429024184398866)⟩,⟨1134428994081261913885,1134428994081280600309⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨163594932081450022052068,163594932081450022119955⟩,⟨(-2472606029855169560525),(-2472606029855169518017)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨462384993332403456154686,462384993332403456352789⟩,⟨(-34530614365355255641593),(-34530614365355255513645)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨685357968555271866497029,685357968555271866806108⟩,⟨(-129940816145534909652462),(-129940816145534909439801)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨807942874301921856464513,807942874301921856856825⟩,⟨(-281347914630961175397527),(-281347914630961175106276)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨825896016462316783259115,825896016462316783704493⟩,⟨(-441490497550035151461053),(-441490497550035151103509)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨748962669288018680510927,748962669288018680994984⟩,⟨(-557998633549636710381049),(-557998633549636709964126)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨603828158337528115858197,603828158337528116422139⟩,⟨(-606279789748250227696633),(-606279789748250227177761)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨431919542899822245630174,431919542899822246624525⟩,⟨(-590695394628004460444951),(-590695394628004459475793)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨272323525667245194952133,272323525667245198785957⟩,⟨(-529594800435379899410155),(-529594800435379895586410)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨147942830164060960536842,147942830164060980543159⟩,⟨(-444395030071109257717117),(-444395030071109237711940)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨64645766625676072509308,64645766625676158671299⟩,⟨(-353220094540989831615413),(-353220094540989745450528)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨17230106427619185212082,17230106427619451378849⟩,⟨(-267485824889095656037398),(-267485824889095389866831)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-4376279808345935022776),(-4376279808345371025378)⟩,⟨(-192001768427687573899229),(-192001768427687009898495)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-10435770127020599896301),(-10435770127019787560653)⟩,⟨(-127422641040779688294335),(-127422641040778875956297)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-8538133870600431064542),(-8538133870599678572000)⟩,⟨(-72213768220111746670344),(-72213768220110994176412)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3163519662617503976545),(-3163519662617196518833)⟩,⟨(-23320742942796326304640),(-23320742942796018846477)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨678361787270052349158667,678361787270075494163275⟩,⟨(-870598559927300667858934),(-870598559927277522943364)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 15) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_15 (tableDensity false) (fullFactor false 1 15) density0_contains hk1_0_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-35821480759333264281021),(-35821480759333264268060)⟩,⟨(-506393260298752914587702),(-506393260298752914548281)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_15 1 15 ha1_0_15_contains + def realAnswer : RBox := ⟨642540306510718984877646,642540306510742329895215⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_15 +namespace hm1_1_0_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨929836337626,929836337642⟩,⟨(-273885466644),(-273885466628)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨2077593206213,2077593206229⟩,⟨(-642780197343),(-642780197327)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1897994455475,1897994455491⟩,⟨(-642647819899),(-642647819883)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1048899527112,1048899527128⟩,⟨(-404654952200),(-404654952183)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨372146111230,372146111248⟩,⟨(-172676689064),(-172676689048)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨84961303727,84961303744⟩,⟨(-50589799996),(-50589799980)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨12268893055,12268893071⟩,⟨(-9865139328),(-9865139312)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1082272521,1082272538⟩,⟨(-1200671168),(-1200671152)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨54884831,54884847⟩,⟨(-83889575),(-83889559)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1452156,1452174⟩,⟨(-3023221),(-3023203)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨17209,17225⟩,⟨(-48281),(-48265)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨64,80⟩,⟨(-280),(-263)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),12⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨15262193069088732,15262193069088843⟩,⟨20548225370900516,20548225370900622⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨40147240503101742,40147240503102061⟩,⟨51135258036969121,51135258036969436⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨51392255811122928,51392255811123522⟩,⟨58581060269741391,58581060269741982⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨48390703202904418,48390703202905345⟩,⟨46703803548582971,46703803548583901⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨36609111230023067,36609111230024274⟩,⟨28336048415809866,28336048415811076⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨23000831765691848,23000831765693102⟩,⟨13553137879011953,13553137879013207⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨12210485898968683,12210485898969654⟩,⟨5175071918797189,5175071918798163⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨5570147813807510,5570147813808049⟩,⟨1552957023629545,1552957023630083⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨2234888228976448,2234888228976671⟩,⟨334906189601082,334906189601303⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨813449805486542,813449805486620⟩,⟨27856320045473,27856320045551⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨278781164720197,278781164720225⟩,⟨(-18519799049757),(-18519799049724)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨93650414886917,93650414886936⟩,⟨(-13829940753867),(-13829940753845)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨32021356173001,32021356173019⟩,⟨(-6626753646614),(-6626753646598)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨11421854656920,11421854656936⟩,⟨(-2816306753970),(-2816306753954)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨4128277057103,4128277057119⟩,⟨(-1118114483798),(-1118114483782)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1052054658160,1052054658176⟩,⟨(-297227072378),(-297227072362)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-6285475005537682357),(-6285475005537682335)⟩,⟨9912050578027356900,9912050578027356919⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-16521358926840374758),(-16521358926840374728)⟩,⟨27168406835998706495,27168406835998706523⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-21117286717284767362),(-21117286717284767329)⟩,⟨37571193261846551145,37571193261846551181⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-19731934925437968596),(-19731934925437968562)⟩,⟨39366762312806356029,39366762312806356062⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-14453980065200049093),(-14453980065200049059)⟩,⟨34083933002165471628,34083933002165471663⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-8252613558360914372),(-8252613558360914341)⟩,⟨25412124310473382128,25412124310473382160⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-3404171873418397358),(-3404171873418397326)⟩,⟨16828569914689365583,16828569914689365613⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-654893489211025751),(-654893489211025726)⟩,⟨10150092128548855085,10150092128548855114⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨433147541256313961,433147541256314005⟩,⟨5691824665727501783,5691824665727501825⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨627572877552903862,627572877552903958⟩,⟨3021931948945190596,3021931948945190692⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨497221822943222996,497221822943223256⟩,⟨1543697972918009809,1543697972918010068⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨321411150030542421,321411150030542975⟩,⟨768501739724013356,768501739724013912⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨188878474583595016,188878474583595898⟩,⟨376070762436037364,376070762436038241⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨104716208008409138,104716208008410138⟩,⟨180578721458559182,180578721458560183⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨52229062553298586,52229062553299376⟩,⟨80809486058982075,80809486058982868⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨15809089515802839,15809089515803145⟩,⟨23035275921931207,23035275921931511⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-747680432606811259242),(-747680432606807205415)⟩,⟨43198229715197536154,43198229715201589963⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2046805170428908795487),(-2046805170428899952801)⟩,⟨149459769972458392274,149459769972467234912⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-2842563793203596496892),(-2842563793203588853802)⟩,⟨299655611140959855581,299655611140967498594⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3040758686744954589384),(-3040758686744950737540)⟩,⟨481225137963558781113,481225137963562632868⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2760773429305867258395),(-2760773429305866046719)⟩,⟨645080313069294733937,645080313069295945522⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-2225704026070068648465),(-2225704026070068403875)⟩,⟨731054488369774150414,731054488369774394929⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-1635561030045156111843),(-1635561030045156077522)⟩,⟨711180179940099930683,711180179940099964946⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1112913262468166033541),(-1112913262468166029296)⟩,⟨608776646960823186061,608776646960823190266⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-709722450239797683873),(-709722450239797683004)⟩,⟨472061097105165301589,472061097105165302428⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-429672742947745471151),(-429672742947745470791)⟩,⟨340654859209092008222,340654859209092008566⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-250645919240980592293),(-250645919240980592096)⟩,⟨233761090493809875445,233761090493809875629⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-143002220271453313050),(-143002220271453312937)⟩,⟨154614034218220655206,154614034218220655317⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-80476766982839895188),(-80476766982839895116)⟩,⟨98771573643134046194,98771573643134046261⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-44152730913501070851),(-44152730913501070807)⟩,⟨59845360431798255638,59845360431798255682⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-21993586676466362533),(-21993586676466362501)⟩,⟨31896721362088195600,31896721362088195630⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-6657679733029128674),(-6657679733029128653)⟩,⟨9990276302812344661,9990276302812344682⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-7707321633562354774313),(-7707321633562018362400)⟩,⟨(-10497846387971380921203),(-10497846387971044508652)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-22692390389660591736370),(-22692390389659381502358)⟩,⟨(-29339537717693812955169),(-29339537717692602719426)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-35903644040387322315605),(-35903644040384544264118)⟩,⟨(-42293391746741117404172),(-42293391746738339350321)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-45432011756824307107860),(-45432011756818578200077)⟩,⟨(-47225780260093947141389),(-47225780260088218231185)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-49925241788391367951097),(-49925241788380711989317)⟩,⟨(-44198861639620866531427),(-44198861639610210567653)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-49483807839137869627273),(-49483807839120861910776)⟩,⟨(-35586769088280823535200),(-35586769088263815817362)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-45252824584409790991098),(-45252824584388004374674)⟩,⟨(-25017608535762170253299),(-25017608535740383636181)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-38661803130394746521329),(-38661803130373582782959)⟩,⟨(-15543537232635482376051),(-15543537232614318637485)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-31085792090155155431363),(-31085792090139456850700)⟩,⟨(-8618624418200102952260),(-8618624418184404371701)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-23654204175239023454631),(-23654204175230004468817)⟩,⟨(-4305220015089158604768),(-4305220015080139619191)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-17099353319188463124199),(-17099353319184419931566)⟩,⟨(-1958329046592678921253),(-1958329046588635728877)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-11757655744159246576784),(-11757655744157718254897)⟩,⟨(-802761555803537706374),(-802761555802009384715)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-7673981343038083524160),(-7673981343037552006758)⟩,⟨(-257885172322188928790),(-257885172321657411566)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-4686605374018619231490),(-4686605374018437132058)⟩,⟨(-16213455737152996913),(-16213455736970897609)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2501165565978294832837),(-2501165565978232626167)⟩,⟨54720582615884387526,54720582615946594124⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-783137710466285271774),(-783137710466270039084)⟩,⟨28909609070198723157,28909609070213955826⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨4856367011140698315922,4856367011140698356020⟩,⟨(-304156703216494273732),(-304156703216494246604)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨12846670732346425249558,12846670732346425367634⟩,⟨(-4315248388683803423639),(-4315248388683803342249)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨12183419903457824855170,12183419903457825041799⟩,⟨(-17443696362797461852254),(-17443696362797461717538)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-7480562919114387698993),(-7480562919114387457794)⟩,⟨(-44807124817969132336306),(-44807124817969132151630)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-47569120699026838353764),(-47569120699026838070342)⟩,⟨(-90889110626951574729271),(-90889110626951574498439)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-92207340410070091411673),(-92207340410070091087186)⟩,⟨(-150842358781647740484308),(-150842358781647740203478)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-121449402985013829369911),(-121449402985013828961496)⟩,⟨(-205527552273159036020519),(-205527552273159035644426)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-128446369155308149338170),(-128446369155308148551123)⟩,⟨(-235019077999396727065329),(-235019077999396726298782)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-118712722944541913254693),(-118712722944541910112428)⟩,⟨(-233021082431963803612268),(-233021082431963800480465)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-100959843740257565205724),(-100959843740257548822429)⟩,⟨(-206311828670806214623864),(-206311828670806198244659)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-81811989851912431831014),(-81811989851912361427249)⟩,⟨(-166767343891093983895384),(-166767343891093913492512)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-64552634456796580236073),(-64552634456796362846487)⟩,⟨(-125118417003726411992861),(-125118417003726194603102)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-49494773249151346475870),(-49494773249150885698945)⟩,⟨(-88015707169880380796857),(-88015707169879920019508)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-35448962034625973843052),(-35448962034625309876196)⟩,⟨(-57482675108213434991255),(-57482675108212771023999)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-21425175239654620885810),(-21425175239654005604434)⟩,⟨(-32369751261043565281462),(-32369751261042949999816)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-7172130988365484231324),(-7172130988365232786321)⟩,⟨(-10446891991369185290169),(-10446891991368933845070)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-209888756684888781033979),(-209888756684869768558531)⟩,⟨(-321496188114507135272713),(-321496188114488122849198)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 15) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_15 (tableDensity true) (fullFactor false 1 15) density1_contains hk1_0_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨46843474839128114812079,46843474839128114829028⟩,⟨662206571159907657486213,662206571159907657537764⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_15 1 15 ha1_0_15_contains + def realAnswer : RBox := ⟨(-163045281845760766221900),(-163045281845741553729503)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_15 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_2.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_2.lean new file mode 100644 index 0000000000000000000000000000000000000000..e017efdc276193c26607690576bc2c489a74575b --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_2.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_0_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨75071973183,75071973199⟩,⟨168676691600,168676691616⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨172404979137,172404979153⟩,⟨366398431715,366398431732⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨166001845514,166001845532⟩,⟨318078440782,318078440800⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨98829928657,98829928673⟩,⟨164910613853,164910613870⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨38442611396,38442611412⟩,⟨54733191363,54733191385⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨9714356615,9714356634⟩,⟨11680456551,11680456571⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1548992881,1548992900⟩,⟨1561622828,1561622845⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨148669471,148669488⟩,⟨124550125,124550142⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨8003802,8003824⟩,⟨5505213,5505232⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨217664,217684⟩,⟨121050,121071⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨2542,2561⟩,⟨1117,1134⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2),23⟩,⟨1,17⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4528143242674505),(-4528143242674483)⟩,⟨9711535627762413,9711535627762437⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-11177395204910301),(-11177395204910258)⟩,⟨24922506879785164,24922506879785206⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-12582727517116785),(-12582727517116724)⟩,⟨30374850361432561,30374850361432622⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-9730169748844602),(-9730169748844515)⟩,⟨26602838287334760,26602838287334847⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-5601654035742098),(-5601654035741995)⟩,⟨18338440105305254,18338440105305359⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2438479511398736),(-2438479511398630)⟩,⟨10345512788219010,10345512788219113⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-778938721685148),(-778938721685070)⟩,⟨4898658419270165,4898658419270245⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-155860432225161),(-155860432225110)⟩,⟨1991158751592978,1991158751593029⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨2591771001962,2591771001994⟩,⟨711986617566682,711986617566712⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨19453042324404,19453042324430⟩,⟨230671636584644,230671636584667⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨11368613222272,11368613222293⟩,⟨70219226867654,70219226867676⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨4921053215527,4921053215549⟩,⟨20969725862668,20969725862687⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1932041295898,1932041295916⟩,⟨6432216138280,6432216138297⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨745654199280,745654199297⟩,⟨2098287621581,2098287621598⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨281568323962,281568323978⟩,⟨712369205480,712369205497⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨73184084594,73184084610⟩,⟨175811890780,175811890796⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-5095282463821347207),(-5095282463821347190)⟩,⟨(-68929586366238729),(-68929586366238713)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-13701326893313238530),(-13701326893313238513)⟩,⟨131610609901428221,131610609901428238⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-18357797978547057988),(-18357797978547057969)⟩,⟨1004659129615989182,1004659129615989203⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-18580541096352584910),(-18580541096352584885)⟩,⟨2214784754277512914,2214784754277512935⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-15580071373034244009),(-15580071373034243983)⟩,⟨3102905356184981385,3102905356184981402⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-11246764024939150259),(-11246764024939150238)⟩,⟨3274840162448735166,3274840162448735187⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-7151852240163557618),(-7151852240163557599)⟩,⟨2817709426154009267,2817709426154009285⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-4084882130315850490),(-4084882130315850470)⟩,⟨2075727145025204071,2075727145025204090⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-2138276294179493285),(-2138276294179493266)⟩,⟨1357343053153635111,1357343053153635131⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1048830827907907415),(-1048830827907907391)⟩,⟨812346276603562345,812346276603562372⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-493913519946464377),(-493913519946464339)⟩,⟨457526583312102679,457526583312102719⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-228938278641633045),(-228938278641632979)⟩,⟨248423764908305969,248423764908306034⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-106574709084847140),(-106574709084847049)⟩,⟨132111703194488949,132111703194489039⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-49894804308378508),(-49894804308378410)⟩,⟨68563214536553286,68563214536553384⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-22157076267384483),(-22157076267384401)⟩,⟨32649340404972044,32649340404972125⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-6312960250001418),(-6312960250001379)⟩,⟨9635805221893339,9635805221893379⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-188344919922253579201),(-188344919922252948350)⟩,⟨(-224338626445221616424),(-224338626445220985597)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-532318356383590048140),(-532318356383588677355)⟩,⟨(-611707834265175553753),(-611707834265174183032)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-784760380542320269966),(-784760380542319094023)⟩,⟨(-842059024788751950727),(-842059024788750774881)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-909148281668327104893),(-909148281668326518649)⟩,⟨(-885560686849089739235),(-885560686849089153107)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-902732385538319690750),(-902732385538319508782)⟩,⟨(-778183227790811630913),(-778183227790811449060)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-796185473398781594282),(-796185473398781558011)⟩,⟨(-592114151478571748340),(-592114151478571712170)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-637293511131588748910),(-637293511131588743775)⟩,⟨(-398263117278892990203),(-398263117278892985159)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-470391636040744627387),(-470391636040744626658)⟩,⟨(-240677627338738662370),(-240677627338738661708)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-324615360894871705886),(-324615360894871705673)⟩,⟨(-132517073934896529348),(-132517073934896529187)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-212283767448234496649),(-212283767448234496536)⟩,⟨(-67245342366003910409),(-67245342366003910329)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-133293960248731432535),(-133293960248731432462)⟩,⟨(-31687984149408550144),(-31687984149408550098)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-81256725373621949002),(-81256725373621948954)⟩,⟨(-13872957737532588880),(-13872957737532588848)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-48304663123223392338),(-48304663123223392305)⟩,⟨(-5579849835133294875),(-5579849835133294848)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-27612502522204134215),(-27612502522204134190)⟩,⟨(-2003621191166061955),(-2003621191166061933)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-14127750887203245191),(-14127750887203245171)⟩,⟨(-606628135682304236),(-606628135682304217)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-4332745371804776387),(-4332745371804776369)⟩,⟨(-120329686895717706),(-120329686895717687)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨5412499491631756516936,5412499491631823429296⟩,⟨(-3562393986561421360121),(-3562393986561354447488)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨14705308650381406849626,14705308650381646603394⟩,⟨(-10409878301947275004273),(-10409878301947035249766)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨20071132062508581179868,20071132062509127229692⟩,⟨(-16350502154782890831342),(-16350502154782344780515)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨20784352748958391266170,20784352748959504625182⟩,⟨(-20663949533472040503107),(-20663949533470927143066)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨17798634147583815669712,17798634147585856962041⟩,⟨(-22711427868735754444794),(-22711427868733713151611)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨12927568784073746880233,12927568784076950417838⟩,⟨(-22273764683810074435112),(-22273764683806870896923)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨7893192365316658641913,7893192365320686262311⟩,⟨(-19773416036427030001785),(-19773416036423002381086)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨3797850806638721806885,3797850806642557328531⟩,⟨(-16102833864531432068718),(-16102833864527596546989)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1042086944700489677201,1042086944703276898429⟩,⟨(-12198188865455302161154),(-12198188865452514939985)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-484372253799589330522),(-484372253798020139865)⟩,⟨(-8717291552073461614127),(-8717291552071892423605)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1121403862030650229908),(-1121403862029960311632)⟩,⟨(-5957804026642108199426),(-5957804026641418281300)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1220002762807034656892),(-1220002762806778494912)⟩,⟨(-3937304378851015630064),(-3937304378850759468228)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1044238704220582476309),(-1044238704220494767558)⟩,⟨(-2521871371485187621864),(-2521871371485099913227)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-759568042952559436280),(-759568042952529762410)⟩,⟨(-1535846681972722799556),(-1535846681972693125765)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-451201178866292292219),(-451201178866282244786)⟩,⟨(-822756511360793477735),(-822756511360783430352)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-148674774204818602742),(-148674774204816153666)⟩,⟨(-258461872772716216527),(-258461872772713767470)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨484979332600678114452,484979332600678122805⟩,⟨32096215623036604189863,32096215623036604203296⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨6750138447766784095136,6750138447766784120192⟩,⟨90431085846894400558161,90431085846894400597205⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨25243485648952250307172,25243485648952250348597⟩,⟨133207840151094548041874,133207840151094548102393⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨54163720730572452006732,54163720730572452063013⟩,⟨155610372766294537940364,155610372766294538016461⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨84007970944696047569685,84007970944696047638029⟩,⟨157216659556111478825452,157216659556111478910811⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨104709979414652301963718,104709979414652302042335⟩,⟨140598962392089161553076,140598962392089161644506⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨111994131616764882173951,111994131616764882270174⟩,⟨111587226482800128043916,111587226482800128148589⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨107274597342860864149587,107274597342860864325744⟩,⟨78477066048200306508304,78477066048200306689081⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨94492619885366468600981,94492619885366469281890⟩,⟨48616966453546649054602,48616966453546649737301⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨77901154538046194670057,77901154538046198168256⟩,⟨25952660617376353782563,25952660617376357280930⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨60876069093633043014293,60876069093633057833569⟩,⟨11152567912358541938469,11152567912358556757203⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨45388556330133676653742,45388556330133721751038⟩,⟨2929336808784605115957,2929336808784650212569⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨32145038780682689348054,32145038780682783684415⟩,⟨(-730348939914594959772),(-730348939914500623999)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨21106085073608820203413,21106085073608954692990⟩,⟨(-1727820728275878371907),(-1727820728275743882745)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨11872616187887349087112,11872616187887472783049⟩,⟨(-1403602265020853503518),(-1403602265020729807822)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3819521541671985815925,3819521541672036171188⟩,⟨(-518122887569876275006),(-518122887569825919820)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨155878147757367053325436,155878147757370549647382⟩,⟨135148439366707462070773,135148439366710958409969⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 16) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_16 (tableDensity false) (fullFactor false 1 16) density0_contains hk1_0_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨101483743164828845087718,101483743164828845095691⟩,⟨(-5900423093866128969247),(-5900423093866128966845)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_16 1 16 ha1_0_16_contains + def realAnswer : RBox := ⟨257361890922195798413154,257361890922199494743073⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_16 +namespace hm1_1_0_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨8920724877,8920724893⟩,⟨30286357462,30286357478⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨20551734126,20551734142⟩,⟨66439174782,66439174798⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨19795253543,19795253561⟩,⟨58489834109,58489834126⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨11777100212,11777100228⟩,⟨30554590513,30554590530⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨4651826660,4651826676⟩,⟨10041480123,10041480139⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1233988999,1233989016⟩,⟨2077452560,2077452577⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨212703584,212703600⟩,⟨265356110,265356126⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨22273767,22273783⟩,⟨20146580,20146597⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1297569,1297586⟩,⟨851887,851903⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨37534,37552⟩,⟨18083,18100⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨452,468⟩,⟨157,174⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-8),16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1341700507961612),(-1341700507961587)⟩,⟨996536665228343,996536665228367⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-3307976058176648),(-3307976058176612)⟩,⟨2596888819935097,2596888819935133⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-3720135054934402),(-3720135054934350)⟩,⟨3262704144286139,3262704144286193⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-2885325215233645),(-2885325215233573)⟩,⟨2987936702139048,2987936702139119⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1688258350844618),(-1688258350844531)⟩,⟨2179302610907510,2179302610907595⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-772361782458391),(-772361782458305)⟩,⟨1309167702987657,1309167702987746⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-279980189187915),(-279980189187845)⟩,⟨659500379598671,659500379598738⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-79260711248535),(-79260711248492)⟩,⟨283596809736321,283596809736362⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16057548319897),(-16057548319871)⟩,⟨106693966739050,106693966739075⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1263955945629),(-1263955945612)⟩,⟨36286857717668,36286857717685⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨765492461337,765492461353⟩,⟨11607874929595,11607874929612⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨537329449586,537329449604⟩,⟨3647121215913,3647121215929⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨242522232041,242522232057⟩,⟨1173088905057,1173088905073⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨97980216337,97980216353⟩,⟨397541126919,397541126935⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨37491697708,37491697724⟩,⟨138445787800,138445787816⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨9774316699,9774316715⟩,⟨34597367640,34597367656⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-971567549643728069),(-971567549643728052)⟩,⟨(-616098474651457703),(-616098474651457686)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2646319149285428151),(-2646319149285428134)⟩,⟨(-1609330942680131891),(-1609330942680131873)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3614324635243683533),(-3614324635243683514)⟩,⟨(-2031727149699567478),(-2031727149699567461)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3718208530103301502),(-3718208530103301484)⟩,⟨(-1864147540531030623),(-1864147540531030605)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-3143311239813401231),(-3143311239813401213)⟩,⟨(-1333601780450542941),(-1333601780450542923)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-2276865768231288332),(-2276865768231288316)⟩,⟨(-740082387143673524),(-740082387143673506)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1458576167827097700),(-1458576167827097681)⟩,⟨(-295613325806402024),(-295613325806402007)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-848121080054803968),(-848121080054803950)⟩,⟨(-55098270692262313),(-55098270692262297)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-457463326501620612),(-457463326501620594)⟩,⟨34608278619968304,34608278619968324⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-233403078213954711),(-233403078213954687)⟩,⟨48378124863958384,48378124863958407⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-114653348052706746),(-114653348052706711)⟩,⟨36892595864802104,36892595864802138⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-55019725884311659),(-55019725884311605)⟩,⟨22997279541851048,22997279541851104⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-26063799840688940),(-26063799840688866)⟩,⟨13085324441573930,13085324441574007⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-12188872192982577),(-12188872192982495)⟩,⟨7066584935394065,7066584935394148⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-5353512366645223),(-5353512366645155)⟩,⟨3459755452669274,3459755452669343⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1511321750776605),(-1511321750776572)⟩,⟨1037206190262712,1037206190262747⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-5647753275185194429),(-5647753275184664394)⟩,⟨(-97754568515850778096),(-97754568515850248056)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-19445349970708706047),(-19445349970707555105)⟩,⟨(-266349187495641499679),(-266349187495640348731)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-38617331894077262212),(-38617331894076276240)⟩,⟨(-366471781218366442101),(-366471781218365456120)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-61164038820136492251),(-61164038820136001820)⟩,⟨(-386692641661123118042),(-386692641661122627595)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-80543403062335033806),(-80543403062334882123)⟩,⟨(-344915830583846962236),(-344915830583846810541)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-89354964121639467479),(-89354964121639437473)⟩,⟨(-272205109717398511686),(-272205109717398481678)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-84846829492273818355),(-84846829492273814236)⟩,⟨(-195234465909886081912),(-195234465909886077788)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-70736467551184664048),(-70736467551184663543)⟩,⟨(-129375892485076838515),(-129375892485076838005)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-53349672015184885146),(-53349672015184885036)⟩,⟨(-80243138005324997824),(-80243138005324997710)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-37433046504167572061),(-37433046504167572008)⟩,⟨(-47233137209951263942),(-47233137209951263889)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-24995957739305710193),(-24995957739305710157)⟩,⟨(-26810538423781713035),(-26810538423781713000)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-16120379718706363780),(-16120379718706363755)⟩,⟨(-14913741304428448534),(-14913741304428448509)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-10073544809565414445),(-10073544809565414423)⟩,⟨(-8209218511567026418),(-8209218511567026396)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-5996392929837376257),(-5996392929837376239)⟩,⟨(-4424480080569391150),(-4424480080569391132)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-3156595050428236835),(-3156595050428236816)⟩,⟨(-2176636786327905312),(-2176636786327905295)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-982370857347705867),(-982370857347705851)⟩,⟨(-654670547489475415),(-654670547489475399)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1716066420873938830081,1716066420873993821800⟩,⟨(-1259898186102421387952),(-1259898186102366396342)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4777996062380568800578,4777996062380765855359⟩,⟨(-3695363280896011884817),(-3695363280895814830327)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨6836407435064273834372,6836407435064722693957⟩,⟨(-5803053643785027448266),(-5803053643784578589075)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨7550827479391918753320,7550827479392834092509⟩,⟨(-7262934756102631106517),(-7262934756101715767724)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨6968209310849392716050,6968209310851071152869⟩,⟨(-7869121877790691042224),(-7869121877789012605721)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨5517047259837834932700,5517047259840469017152⟩,⟨(-7668771567880967775960),(-7668771567878333691723)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨3805447757766978713927,3805447757770289703883⟩,⟨(-6880072805628941077563),(-6880072805625630087718)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨2316068024386362846840,2316068024389514400882⟩,⟨(-5757268336539722668169),(-5757268336536571114157)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1256865700356898357860,1256865700359186745580⟩,⟨(-4530020827395007225137),(-4530020827392718837399)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨614391835983268366073,614391835984555350293⟩,⟨(-3373004076782957642794),(-3373004076781670658543)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨273687886633529816393,273687886634094942473⟩,⟨(-2387813052488394068387),(-2387813052487828942269)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨110055821150313934420,110055821150523479191⟩,⟨(-1610574291509900385247),(-1610574291509690840445)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨34780882532867295300,34780882532938950775⟩,⟨(-1033769722507594186761),(-1033769722507522531262)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2171813599792924107,2171813599817140916⟩,⟨(-622955956696052913629),(-622955956696028696801)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-7201938229083273914),(-7201938229075080374)⟩,⟨(-329373311303955865425),(-329373311303947671879)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-3788662594782790992),(-3788662594780794570)⟩,⟨(-102636174373477261892),(-102636174373475265468)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨59657576426704090455,59657576426704095789⟩,⟨952787505214932097506,952787505214932105391⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨843547296967843498380,843547296967843514312⟩,⟨2512644903807888470710,2512644903807888493825⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨3388531999691431621667,3388531999691431647869⟩,⟨2369466557637798900872,2369466557637798937166⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨8624388683878752414141,8624388683878752449748⟩,⟨(-1435571136857994178638),(-1435571136857994132170)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨17289391049102625592251,17289391049102625636257⟩,⟨(-9045231249009488033378),(-9045231249009487979391)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨28296802620009269864985,28296802620009269917805⟩,⟨(-17296875615457127528390),(-17296875615457127467425)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨37955546612207199525269,37955546612207199594876⟩,⟨(-22430702125069326881365),(-22430702125069326805860)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨42673160371627279604132,42673160371627279743313⟩,⟨(-23325152380486704111868),(-23325152380486703969052)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨41572001109503056861373,41572001109503057418944⟩,⟨(-21180710866403461781384),(-21180710866403461222042)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨36164109945162883090554,36164109945162885954616⟩,⟨(-17697635100803083384840),(-17697635100803080520146)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨28741640092207602184606,28741640092207614292958⟩,⟨(-14099424764010709558938),(-14099424764010697450503)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨21231288815302159121115,21231288815302195953413⟩,⟨(-10952937554531005236404),(-10952937554530968404185)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨14735936495032795788526,14735936495032872859375⟩,⟨(-8285811679170130007174),(-8285811679170052936429)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨9521418447418808931399,9521418447418918856844⟩,⟨(-5871379683947729349222),(-5871379683947619423862)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨5321894179932311538501,5321894179932412679271⟩,⟨(-3522411789765200925309),(-3522411789765099784592)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1711014399332312488013,1711014399332353669497⟩,⟨(-1174663608388616895815),(-1174663608388575714347)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨56546216940718067158893,56546216940720939297327⟩,⟨(-35487044872065097252695),(-35487044872062225104464)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 16) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_16 (tableDensity true) (fullFactor false 1 16) density1_contains hk1_0_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-132709510292468489740519),(-132709510292468489730093)⟩,⟨7715937891978784033566,7715937891978784036708⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_16 1 16 ha1_0_16_contains + def realAnswer : RBox := ⟨(-76163293351750522581626),(-76163293351747450432766)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_16 +namespace hm1_0_0_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-5170969972),(-5170969956)⟩,⟨2301358785,2301358801⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-11028931776),(-11028931759)⟩,⟨5188481014,5188481031⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-9227796564),(-9227796548)⟩,⟨4813414658,4813414675⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-4522999842),(-4522999824)⟩,⟨2708265464,2708265481⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1390627018),(-1390627000)⟩,⟨975570353,975570375⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-268966112),(-268966093)⟩,⟨223366232,223366250⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-31815120),(-31815102)⟩,⟨31503693,31503712⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-2184814),(-2184795)⟩,⟨2602794,2602814⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-80571),(-80553)⟩,⟨116861,116885⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1430),(-1412)⟩,⟨2543,2562⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-23),(-5)⟩,⟨13,33⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-596811938105761),(-596811938105745)⟩,⟨(-278274356867927),(-278274356867911)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1517330124492940),(-1517330124492921)⟩,⟨(-680550264599820),(-680550264599803)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1815175387947902),(-1815175387947880)⟩,⟨(-752086070306055),(-752086070306034)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1546353588686033),(-1546353588686014)⟩,⟨(-565823798314147),(-565823798314124)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1027814908590443),(-1027814908590419)⟩,⟨(-314188594730380),(-314188594730355)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-554465103364699),(-554465103364676)⟩,⟨(-130856203662141),(-130856203662115)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-249150252726109),(-249150252726087)⟩,⟨(-39708233821494),(-39708233821473)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-95469039688610),(-95469039688592)⟩,⟨(-7511967384972),(-7511967384949)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-32010508496243),(-32010508496224)⟩,⟨102778107158,102778107179⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-9690805946682),(-9690805946664)⟩,⟨813125313227,813125313246⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2753538378165),(-2753538378149)⟩,⟨444710300054,444710300073⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-769045499913),(-769045499894)⟩,⟨180211185376,180211185396⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-221876913854),(-221876913834)⟩,⟨66586645324,66586645343⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-68753554974),(-68753554957)⟩,⟨24421238934,24421238951⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-22487050455),(-22487050439)⟩,⟨8886623351,8886623367⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-5441634256),(-5441634240)⟩,⟨2265110250,2265110267⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨6360460793437398,6360460793437415⟩,⟨(-470056455854289085),(-470056455854289069)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-12030665736530600),(-12030665736530583)⟩,⟨(-1256091408237059281),(-1256091408237059264)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-90844602336790681),(-90844602336790665)⟩,⟨(-1662202088472282889),(-1662202088472282871)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-196676346929349307),(-196676346929349290)⟩,⟨(-1651808863334797141),(-1651808863334797124)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-269081620355043094),(-269081620355043078)⟩,⟨(-1352409544366976729),(-1352409544366976710)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-275941196163486956),(-275941196163486937)⟩,⟨(-948494938477998837),(-948494938477998820)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-229699517978133681),(-229699517978133663)⟩,⟨(-583487415334598849),(-583487415334598833)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-163151780873610332),(-163151780873610313)⟩,⟨(-321309383062498819),(-321309383062498802)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-102630398147482518),(-102630398147482501)⟩,⟨(-161787828227675460),(-161787828227675441)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-59031597281541141),(-59031597281541122)⟩,⟨(-76262995757174759),(-76262995757174740)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-31973503826353663),(-31973503826353647)⟩,⟨(-34534387457937421),(-34534387457937403)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16735330568727917),(-16735330568727899)⟩,⟨(-15429012311945315),(-15429012311945294)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-8615798690984093),(-8615798690984067)⟩,⟨(-6952339939418423),(-6952339939418400)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4355138579911741),(-4355138579911719)⟩,⟨(-3169819031065132),(-3169819031065108)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2035621148653260),(-2035621148653239)⟩,⟨(-1381532294390510),(-1381532294390490)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-595003532099790),(-595003532099773)⟩,⟨(-389823084973072),(-389823084973052)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨27605545586924545790,27605545586924623430⟩,⟨(-23176325928119368729),(-23176325928119291086)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨74918930053716851598,74918930053717019527⟩,⟨(-65193622011319076415),(-65193622011318908476)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨102176034069796430735,102176034069796573512⟩,⟨(-95215550560598289710),(-95215550560598146919)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨105995354896915770107,105995354896915840362⟩,⟨(-108802612979382765473),(-108802612979382695203)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨91509643659215779743,91509643659215801183⟩,⟨(-106132142172727810320),(-106132142172727788864)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨68165799976440519189,68165799976440523378⟩,⟨(-91630638495056488123),(-91630638495056483921)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨44753555375031484534,44753555375031485117⟩,⟨(-71585223840654885003),(-71585223840654884409)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨26340866805679142251,26340866805679142337⟩,⟨(-51456940556424507671),(-51456940556424507575)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨14106686133178443161,14106686133178443195⟩,⟨(-34536673359952418547),(-34536673359952418509)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨6960407870569618222,6960407870569618247⟩,⟨(-21959432674071405545),(-21959432674071405519)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3191780095475525250,3191780095475525269⟩,⟨(-13417135245649935809),(-13417135245649935785)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1362495829136082953,1362495829136082971⟩,⟨(-7974850803330629684),(-7974850803330629664)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨536035058767505471,536035058767505489⟩,⟨(-4637216055099875198),(-4637216055099875180)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨189078920483880850,189078920483880867⟩,⟨(-2604134283321648283),(-2604134283321648265)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨56526588487937566,56526588487937582⟩,⟨(-1315913693054807584),(-1315913693054807566)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨11137154071167754,11137154071167770⟩,⟨(-400989873482143962),(-400989873482143946)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨548081710740444775348,548081710740455069842⟩,⟨832729227190053592347,832729227190063886795⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1595495287197247461055,1595495287197284202500⟩,⟨2253961644125430212118,2253961644125466953446⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨2487263436128903119665,2487263436128986157727⟩,⟨3053662515103182505705,3053662515103265543624⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨3109094590157198876311,3109094590157366302201⟩,⟨3127962611400890212364,3127962611401057638104⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨3369172502635160231954,3369172502635462851937⟩,⟨2641324048885638190097,2641324048885940809956⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨3248929737992868588940,3248929737993335567007⟩,⟨1886609190382728141428,1886609190383195119412⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2829627125530341275598,2829627125530917381122⟩,⟨1130350351446675244907,1130350351447251350388⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨2257098836039431448165,2257098836039969028989⟩,⟨532963188626165783027,532963188626703363843⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1673224964100955888199,1673224964101338297088⟩,⟨143383950896964049947,143383950897346458846⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1170061261015523224377,1170061261015733979239⟩,⟨(-64728836543178715424),(-64728836542967960547)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨783093640615348309051,783093640615439070805⟩,⟨(-147229680699739753307),(-147229680699648991530)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨507631774576156989052,507631774576190045651⟩,⟨(-157206955361651362599),(-157206955361618305982)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨319743608266404328560,319743608266415457483⟩,⟨(-132360141745679815779),(-132360141745668686838)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨192139621889448797951,192139621889452512090⟩,⟨(-95012433954637789540),(-95012433954634075388)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨101973478231248046450,101973478231249292011⟩,⟨(-55920055744886246638),(-55920055744885001071)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨31880836527474829628,31880836527475131735⟩,⟨(-18338699120881031216),(-18338699120880729104)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-5926645700802201576336),(-5926645700802201573823)⟩,⟨89528778971754279721,89528778971754281279⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-16645760382122666564890),(-16645760382122666557636)⟩,⟨1241917772662672219707,1241917772662672224336⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-24367745398530187609004),(-24367745398530187597840)⟩,⟨4615579259052014094410,4615579259052014102013⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-28207949092508212476379),(-28207949092508212462476)⟩,⟨9814050810312200705957,9814050810312200716203⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-28167539932094487335306),(-28167539932094487319900)⟩,⟨15045158499125649389880,15045158499125649402188⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-24841811860918269148145),(-24841811860918269131879)⟩,⟨18493633109653659347912,18493633109653659361877⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-19408704024061667773217),(-19408704024061667754918)⟩,⟨19471456370477713703981,19471456370477713720788⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-13420377269922104311602),(-13420377269922104280658)⟩,⟨18336328500119221700152,18336328500119221730294⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-8169076142823448762259),(-8169076142823448647826)⟩,⟨15868455129317401322883,15868455129317401437018⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-4285008118315403626886),(-4285008118315403051108)⟩,⟨12852887035025945378654,12852887035025945954407⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1810880914354404877046),(-1810880914354402478278)⟩,⟨9874805684316539296096,9874805684316541694958⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-468735292548853899442),(-468735292548846708049)⟩,⟨7248876734859647300672,7248876734859654492179⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨114717018875261101039,114717018875275951923⟩,⟨5065228711105457551635,5065228711105472402614⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨269244507251477434208,269244507251498390445⟩,⟨3290355546442166405340,3290355546442187361647⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨217168771469555594002,217168771469574731249⟩,⟨1837151897556825137308,1837151897556844274594⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨79866786362748129401,79866786362755891424⟩,⟨588771445332359719649,588771445332367481684⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-25041384873521769923022),(-25041384873521271965422)⟩,⟨26326291211918424858779,26326291211918922813250⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 17) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_17 (tableDensity false) (fullFactor false 1 17) density0_contains hk1_0_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨913416241216351424594,913416241216351425016⟩,⟨19071726649954635692944,19071726649954635694465⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_17 1 17 ha1_0_17_contains + def realAnswer : RBox := ⟨(-24127968632305518498428),(-24127968632304820540406)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_17 +namespace hm1_1_0_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-928457395),(-928457379)⟩,⟨273467484,273467500⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1999812433),(-1999812417)⟩,⟨618494531,618494547⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1696763058),(-1696763041)⟩,⟨573991127,573991143⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-838022331),(-838022314)⟩,⟨322724152,322724168⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-255168007),(-255167990)⟩,⟨118023058,118023075⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-47853991),(-47853975)⟩,⟨28356860,28356877⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-5408614),(-5408597)⟩,⟨4322325,4322342⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-353576),(-353559)⟩,⟨389600,389617⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-12479),(-12463)⟩,⟨18923,18940⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-222),(-205)⟩,⟨431,448⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-3),17⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-61240892965704),(-61240892965688)⟩,⟨(-82453432777454),(-82453432777438)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-158099148399599),(-158099148399581)⟩,⟨(-201410804894268),(-201410804894252)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-194961618342894),(-194961618342878)⟩,⟨(-222357344399586),(-222357344399569)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-173656362343085),(-173656362343066)⟩,⟨(-167782511833117),(-167782511833098)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-122117673351707),(-122117673351684)⟩,⟨(-94682563987277),(-94682563987256)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-70146346946645),(-70146346946628)⟩,⟨(-41434046991064),(-41434046991044)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-33533658681944),(-33533658681923)⟩,⟨(-14259933800693),(-14259933800672)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-13593868180993),(-13593868180976)⟩,⟨(-3808508253116),(-3808508253100)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-4795662873488),(-4795662873472)⟩,⟨(-724835541003),(-724835540987)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1524056922848),(-1524056922832)⟩,⟨(-53975646352),(-53975646335)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-455062768704),(-455062768687)⟩,⟨29790223635,29790223651⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-133721583000),(-133721582984)⟩,⟨19655114186,19655114202⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-40457648830),(-40457648814)⟩,⟨8355691213,8355691230⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-13024622169),(-13024622153)⟩,⟨3208742943,3208742961⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-4370078548),(-4370078531)⟩,⟨1183266556,1183266572⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1070833993),(-1070833977)⟩,⟨302523264,302523280⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨56837320271226696,56837320271226712⟩,⟨(-89630108669416322),(-89630108669416306)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨147543236432226954,147543236432226970⟩,⟨(-242602135055753151),(-242602135055753135)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨183980829507874310,183980829507874327⟩,⟨(-327249711000933028),(-327249711000933011)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨165759526523385172,165759526523385189⟩,⟨(-330541121798770057),(-330541121798770041)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨115814102481834701,115814102481834717⟩,⟨(-272848754172258679),(-272848754172258662)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨62470385004897390,62470385004897406⟩,⟨(-192017350525882711),(-192017350525882695)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨24162887096777023,24162887096777039⟩,⟨(-118994432893474997),(-118994432893474979)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨4363155872308006,4363155872308023⟩,⟨(-66706557479516405),(-66706557479516388)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-2602809349208041),(-2602809349208025)⟩,⟨(-34608912027066372),(-34608912027066354)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-3510438016328613),(-3510438016328597)⟩,⟨(-16968967262666532),(-16968967262666515)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2576625171827100),(-2576625171827084)⟩,⟨(-8015554330572654),(-8015554330572636)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1548837954158869),(-1548837954158850)⟩,⟨(-3707708564607173),(-3707708564607154)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-853273946906032),(-853273946906010)⟩,⟨(-1700229826011699),(-1700229826011678)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-448842888937979),(-448842888937956)⟩,⟨(-774371698898252),(-774371698898231)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-215703277575822),(-215703277575804)⟩,⟨(-333805455004789),(-333805455004766)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-64046474220575),(-64046474220558)⟩,⟨(-93323782217883),(-93323782217866)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨12028995988642294967,12028995988642360208⟩,⟨(-694955107673754794),(-694955107673689557)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨32621141373381763122,32621141373381904130⟩,⟨(-2381113602530474590),(-2381113602530333580)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨44467925410661379886,44467925410661499612⟩,⟨(-4684013177615624379),(-4684013177615504654)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨46283918386248501200,46283918386248559987⟩,⟨(-7316851820543162616),(-7316851820543103827)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨40558387064602984578,40558387064603002468⟩,⟨(-9465234663951842154),(-9465234663951824268)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨31333964702015334999,31333964702015338478⟩,⟨(-10279640500307928925),(-10279640500307925447)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨21935165474089372346,21935165474089372826⟩,⟨(-9527663857693049934),(-9527663857693049454)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨14156091644525599796,14156091644525599867⟩,⟨(-7736185948732420773),(-7736185948732420702)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨8539387835119428925,8539387835119428951⟩,⟨(-5674988331505217235),(-5674988331505217209)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨4887138253570210161,4887138253570210179⟩,⟨(-3871638525011062410),(-3871638525011062390)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2699270691359688105,2699270691359688124⟩,⟨(-2515726983817848337),(-2515726983817848319)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1463934648762462122,1463934648762462140⟩,⟨(-1581950860304471129),(-1581950860304471112)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨788167326265188891,788167326265188908⟩,⟨(-966981222291488664),(-966981222291488644)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨417297858609868162,417297858609868178⟩,⟨(-565495215480385022),(-565495215480385006)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨202744983107310747,202744983107310764⟩,⟨(-294012602679145775),(-294012602679145759)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨60589048842622964,60589048842622980⟩,⟨(-90916952320744444),(-90916952320744428)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨193837862690437870496,193837862690446330944⟩,⟨264021422816669165254,264021422816677625721⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨566377863410205592302,566377863410235790130⟩,⟨732336275823023904631,732336275823054102506⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨882772619577145498226,882772619577213756332⟩,⟨1040058030141236000322,1040058030141304258484⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1092796293641278905348,1092796293641416552989⟩,⟨1136283851584987056103,1136283851585124703806⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1167380238885721984271,1167380238885970811030⟩,⟨1033977806445501438010,1033977806445750264817⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1118591575879096571520,1118591575879480540633⟩,⟨805022098508007551476,805022098508391520618⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨984523528283401566715,984523528283875166580⟩,⟨544817795647137545261,544817795647611145141⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨806934752161470102264,806934752161911819729⟩,⟨324817995017647167321,324817995018088884789⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨621336350575754246686,621336350576068215783⟩,⟨172515351695568811575,172515351695882780669⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨452702710572393752048,452702710572566604710⟩,⟨82524485276266399818,82524485276439252474⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨313838887070477514107,313838887070551859089⟩,⟨36000693892779927730,36000693892854272708⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨207646020916890035410,207646020916917076333⟩,⟨14201095169636722234,14201095169663763151⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨131070856996136397469,131070856996145489505⟩,⟨4415025957576470973,4415025957585563007⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨77934906063013945671,77934906063016976791⟩,⟨273790635204260046,273790635207291166⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨40823217623833418554,40823217623834434302⟩,⟨(-892114965276648178),(-892114965275632434)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨12660009819552653167,12660009819552899445⟩,⟨(-467305517615514597),(-467305517615268323)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-175934803172938850586),(-175934803172938849116)⟩,⟨11012982339067811790,11012982339067812791⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-462533839048543883049),(-462533839048543878781)⟩,⟨155197550418545360005,155197550418545362951⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-433715514971476678355),(-433715514971476671702)⟩,⟨619523537441161986385,619523537441161991192⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨259289561388358878123,259289561388358886559⟩,⟨1562372383690901468986,1562372383690901475456⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1618791904161414799263,1618791904161414808949⟩,⟨3095455910487680412697,3095455910487680420603⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨3053858767570534745324,3053858767570534756119⟩,⟨4996093838794681151829,4996093838794681161192⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨3899162256571530052213,3899162256571530065362⟩,⟨6597226741369819262848,6597226741369819274983⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨3986661049093226409828,3986661049093226434228⟩,⟨7292705265247272864407,7292705265247272888204⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨3556856745380897132402,3556856745380897226124⟩,⟨6980543183639028523959,6980543183639028617400⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2919872605412550160054,2919872605412550631517⟩,⟨5966415878976404172293,5966415878976404643665⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨2287002315015756315198,2287002315015758275229⟩,⟨4662220736298706443342,4662220736298708403366⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1749145815594609398872,1749145815594615272365⟩,⟨3390862796414048320862,3390862796414054194372⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1305530937925993569826,1305530937926005702738⟩,⟨2322050597692875128543,2322050597692887261473⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨915273470246550218791,915273470246567347466⟩,⟨1484363941777575742260,1484363941777592870951⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨545039636842506453353,545039636842522101064⟩,⟨823503262925836042970,823503262925851690692⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨181071462537303753649,181071462537310101582⟩,⟨263749361991398043656,263749361991404391595⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨5689965410324704918497,5689965410325113987255⟩,⟨9390641546052138091531,9390641546052547158555⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 17) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_17 (tableDensity true) (fullFactor false 1 17) density1_contains hk1_0_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1194467392359844171174),(-1194467392359844170623)⟩,⟨(-24939950234556062061992),(-24939950234556062060004)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_17 1 17 ha1_0_17_contains + def realAnswer : RBox := ⟨4495498017964760747323,4495498017965369816632⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_17 +namespace hm1_0_0_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-66630126),(-66630110)⟩,⟨(-149716178),(-149716161)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-147481458),(-147481441)⟩,⟨(-313559469),(-313559450)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-131842316),(-131842299)⟩,⟨(-252884435),(-252884419)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-70119298),(-70119282)⟩,⟨(-117204742),(-117204725)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-23396892),(-23396872)⟩,⟨(-33390083),(-33390065)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-4855254),(-4855236)⟩,⟨(-5854810),(-5854790)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-605939),(-605920)⟩,⟨(-612949),(-612931)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-43122),(-43101)⟩,⟨(-36264),(-36247)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1626),(-1605)⟩,⟨(-1126),(-1106)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-40),(-18)⟩,⟨(-28),(-10)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨16151150606394,16151150606411⟩,⟨(-34638920113367),(-34638920113351)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨39134848880558,39134848880574⟩,⟨(-87247361434734),(-87247361434718)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨42457744562722,42457744562739⟩,⟨(-102451839973641),(-102451839973624)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨31078255739127,31078255739145⟩,⟨(-84899409558656),(-84899409558639)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨16645657175733,16645657175751⟩,⟨(-54413292354566),(-54413292354549)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨6633292407100,6633292407118⟩,⟨(-28071074636187),(-28071074636170)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1912221260152,1912221260174⟩,⟨(-11971083958877),(-11971083958857)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨342023307641,342023307658⟩,⟨(-4324442093497),(-4324442093478)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-3786204804),(-3786204787)⟩,⟨(-1359694844298),(-1359694844279)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-32112244659),(-32112244641)⟩,⟨(-384646681691),(-384646681670)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16435592125),(-16435592105)⟩,⟨(-102013753484),(-102013753466)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-6234814365),(-6234814343)⟩,⟨(-26645617421),(-26645617404)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2167916319),(-2167916299)⟩,⟨(-7230136126),(-7230136109)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-755511606),(-755511589)⟩,⟨(-2127981860),(-2127981844)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-264907185),(-264907169)⟩,⟨(-670445893),(-670445877)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-66212777),(-66212760)⟩,⟨(-159070689),(-159070673)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨40955154095977434,40955154095977450⟩,⟨554304301668657,554304301668673⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨108757588154549531,108757588154549548⟩,⟨(-1038639031980655),(-1038639031980639)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨142145251366112444,142145251366112461⟩,⟨(-7758258882453559),(-7758258882453543)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨138692915594913108,138692915594913124⟩,⟨(-16495505417100305),(-16495505417100288)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨110878985052850822,110878985052850839⟩,⟨(-22039506835229795),(-22039506835229778)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨75553453922185531,75553453922185549⟩,⟨(-21961154926719919),(-21961154926719903)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨44964036529704096,44964036529704115⟩,⟨(-17686639046349574),(-17686639046349554)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨23872351666292734,23872351666292752⟩,⟨(-12112727006024697),(-12112727006024677)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨11562714568150899,11562714568150916⟩,⟨(-7329849105826345),(-7329849105826328)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨5237864194584173,5237864194584193⟩,⟨(-4051916569287733),(-4051916569287716)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2280762691356263,2280762691356282⟩,⟨(-2110533128973361),(-2110533128973343)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨982147346498938,982147346498956⟩,⟨(-1064865172034389),(-1064865172034371)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨428365899610087,428365899610104⟩,⟨(-530709698972332),(-530709698972315)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨190198884050241,190198884050258⟩,⟨(-261280619678969),(-261280619678953)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨81356665396171,81356665396189⟩,⟨(-119867932734637),(-119867932734620)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨22734179945329,22734179945346⟩,⟨(-34699907337488),(-34699907337472)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨2693468447693347209,2693468447693356246⟩,⟨3208228089520590509,3208228089520599543⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨7540793335126703926,7540793335126723369⟩,⟨8665973371165252418,8665973371165271861⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨10910887235852161040,10910887235852177425⟩,⟨11709461206021050310,11709461206021066698⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨12297860407209558316,12297860407209566283⟩,⟨11982320805260211676,11982320805260219643⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨11784886713086772064,11784886713086774467⟩,⟨10163478470093477338,10163478470093479738⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨9960079351281169297,9960079351281169772⟩,⟨7411790281829169613,7411790281829170083⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7594643606114614525,7594643606114614602⟩,⟨4749904742530666648,4749904742530666726⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨5316572551601017744,5316572551601017770⟩,⟨2722873740268308499,2722873740268308526⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3470538544950949192,3470538544950949215⟩,⟨1418347669880731555,1418347669880731572⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2145506062066381203,2145506062066381221⟩,⟨680473162495695631,680473162495695650⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1275588410986288531,1275588410986288548⟩,⟨303649278744068360,303649278744068378⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨739234933227477520,739234933227477539⟩,⟨126385567015521219,126385567015521235⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨420451879815772186,420451879815772203⟩,⟨48635587294637413,48635587294637429⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨231955984446264465,231955984446264482⟩,⟨16852135377375491,16852135377375507⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨115760764420668832,115760764420668848⟩,⟨4974649701281263,4974649701281279⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨35049386970343570,35049386970343587⟩,⟨973536970440582,973536970440599⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-121000257940356854501),(-121000257940355358677)⟩,⟨79638894024721996749,79638894024723492576⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-326284536320068278959),(-326284536320062961268)⟩,⟨230952673108178964658,230952673108184282359⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-438782976220276181191),(-438782976220264255033)⟩,⟨357348567420737669107,357348567420749595285⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-444599352524356803209),(-444599352524333024316)⟩,⟨441811268936098661986,441811268936122440899⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-370204714377414187273),(-370204714377371815660)⟩,⟨472049321821676399448,472049321821718771081⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-260037072516281776890),(-260037072516217485708)⟩,⟨447584880558524707348,447584880558588998540⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-152884748490932889486),(-152884748490855059573)⟩,⟨382443930256481418127,382443930256559248047⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-70639650353807129452),(-70639650353735966176)⟩,⟨298807673975278572041,298807673975349735319⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-18633126583767103931),(-18633126583717550008)⟩,⟨216773874902768423780,216773874902817977704⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨8169629295620973403,8169629295647707921⟩,⟨148329884750473327629,148329884750500062146⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨18256587543122022774,18256587543133299925⟩,⟨97214784286350960252,97214784286362237402⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨19132462892711923064,19132462892715952009⟩,⟨61813991409518863017,61813991409522891957⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨15845257134377594880,15845257134378928566⟩,⟨38288242361068276227,38288242361069609909⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨11224713900008130274,11224713900008569347⟩,⟨22702154374308990079,22702154374309429153⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨6545505362954021129,6545505362954166978⟩,⟨11936619617129671252,11936619617129817096⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2136369580997808675,2136369580997843887⟩,⟨3713979932046475932,3713979932046511140⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-15609125369156665433),(-15609125369156665147)⟩,⟨(-1033571702740967808703),(-1033571702740967808250)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-215799356757256660181),(-215799356757256659358)⟩,⟨(-2893788354284368978444),(-2893788354284368977161)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-797042753658150130332),(-797042753658150129004)⟩,⟨(-4209974900114355648060),(-4209974900114355646102)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1679455467849570302597),(-1679455467849570300824)⟩,⟨(-4829308102152674309228),(-4829308102152674306819)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-2544810996711765627620),(-2544810996711765625518)⟩,⟨(-4766304534144110341106),(-4766304534144110338468)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-3084899218220713282502),(-3084899218220713280148)⟩,⟨(-4145424225231129984814),(-4145424225231129982070)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-3197333607686842578145),(-3197333607686842575360)⟩,⟨(-3188341796253700737120),(-3188341796253700734091)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-2960161464000706782769),(-2960161464000706777887)⟩,⟨(-2167574838326193789916),(-2167574838326193784902)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-2516861615915047378344),(-2516861615915047360264)⟩,⟨(-1296420133034029950015),(-1296420133034029931887)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-2002833899566669124195),(-2002833899566669034686)⟩,⟨(-668203197434194743700),(-668203197434194654188)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1512852633571128451936),(-1512852633571128085174)⟩,⟨(-277709333787026809953),(-277709333787026443209)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1093400230375258721329),(-1093400230375257638206)⟩,⟨(-70838333924047993637),(-70838333924046910537)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-753816953053966597766),(-753816953053964389683)⟩,⟨17017775015326747638,17017775015328955704⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-484459404753439994310),(-484459404753436910259)⟩,⟨39625465523509154994,39625465523512239038⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-268485771226011278653),(-268485771226008482348)⟩,⟨31734251366846455104,31734251366849251402⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-85715835554460803711),(-85715835554459673687)⟩,⟨11627228062231467959,11627228062232597981⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-4209675701016504313948),(-4209675701016437218595)⟩,⟨(-4345490686529970060522),(-4345490686529902964650)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 18) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_18 (tableDensity false) (fullFactor false 1 18) density0_contains hk1_0_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-3374986251039467393071),(-3374986251039467392796)⟩,⟨133397974364361408054,133397974364361408125⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_18 1 18 ha1_0_18_contains + def realAnswer : RBox := ⟨(-7584661952056071707019),(-7584661952055804611391)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_18 +namespace hm1_1_0_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-7917562),(-7917546)⟩,⟨(-26881702),(-26881686)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-17580458),(-17580442)⟩,⟨(-56853996),(-56853980)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-15722102),(-15722086)⟩,⟨(-46496735),(-46496719)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-8355428),(-8355412)⟩,⟨(-21715776),(-21715759)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-2829872),(-2829856)⟩,⟨(-6127747),(-6127731)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-616036),(-616019)⟩,⟨(-1042034),(-1042018)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-83074),(-83058)⟩,⟨(-104256),(-104240)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-6455),(-6439)⟩,⟨(-5878),(-5861)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-270),(-254)⟩,⟨(-181),(-165)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-17),2⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨4785630313920,4785630313936⟩,⟨(-3554405689634),(-3554405689618)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨11582092414021,11582092414037⟩,⟨(-9090537743146),(-9090537743130)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨12552807672264,12552807672281⟩,⟨(-11003156719473),(-11003156719457)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨9215380688898,9215380688914⟩,⟨(-9532902343822),(-9532902343805)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨5015771344061,5015771344077⟩,⟨(-6463642431448),(-6463642431431)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨2099686716934,2099686716950⟩,⟨(-3550404945844),(-3550404945826)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨686106611207,686106611223⟩,⟨(-1610776898583),(-1610776898566)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨172883860475,172883860491⟩,⟨(-615596798904),(-615596798888)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨30910619466,30910619482⟩,⟨(-203650928740),(-203650928723)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2176855296,2176855312⟩,⟨(-60477013389),(-60477013373)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1095318157),(-1095318141)⟩,⟨(-16854789607),(-16854789589)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-679250387),(-679250371)⟩,⟨(-4631994730),(-4631994714)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-271955744),(-271955728)⟩,⟨(-1318116093),(-1318116077)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-99260114),(-99260098)⟩,⟨(-403079753),(-403079737)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-35272331),(-35272314)⟩,⟨(-130287476),(-130287460)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-8843237),(-8843221)⟩,⟨(-31302645),(-31302628)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨7809291434287897,7809291434287913⟩,⟨4952150556843094,4952150556843110⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨21005195312809855,21005195312809871⟩,⟨12775354294616902,12775354294616918⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨27984443925125167,27984443925125183⟩,⟨15734937874063850,15734937874063866⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨27753023409939785,27753023409939801⟩,⟨13920975150728424,13920975150728440⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨22369629726175904,22369629726175921⟩,⟨9499453019299523,9499453019299539⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨15295208491013996,15295208491014013⟩,⟨4980570709490979,4980570709490995⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨9169487470396255,9169487470396271⟩,⟨1865482195574753,1865482195574770⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨4955725265350897,4955725265350913⟩,⟨326335408336407,326335408336424⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2473157110470015,2473157110470034⟩,⟨(-184896397049657),(-184896397049641)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1165296331435172,1165296331435190⟩,⟨(-240605931810056),(-240605931810040)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨529307466097557,529307466097574⟩,⟨(-169977547183401),(-169977547183385)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨235999792242084,235999792242102⟩,⟨(-98526892390043),(-98526892390027)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨104757366351512,104757366351528⟩,⟨(-52553271476883),(-52553271476867)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨46465408354371,46465408354387⟩,⟨(-26926105713088),(-26926105713072)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨19657648031993,19657648032009⟩,⟨(-12701400457543),(-12701400457527)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨5442581863137,5442581863153⟩,⟨(-3735103093498),(-3735103093482)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨80763365807197715,80763365807205313⟩,⟨1397971510173700946,1397971510173708543⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨275373865741527363,275373865741543692⟩,⟨3773333475556865364,3773333475556881694⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨536581013012169740,536581013012183484⟩,⟨5096060345377553440,5096060345377567182⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨826681037916247023,826681037916253690⟩,⟨5232147033191584234,5232147033191590901⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1050566079418406436,1050566079418408442⟩,⟨4504418721728062152,4504418721728064160⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1116947662758662550,1116947662758662946⟩,⟨3406669301853557083,3406669301853557476⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1010502542029511941,1010502542029512004⟩,⟨2327691171227346153,2327691171227346223⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨799123519023600602,799123519023600624⟩,⟨1462974161362514776,1462974161362514797⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨570168467679111594,570168467679111612⟩,⟨858322227323349541,858322227323349557⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨378215045549983674,378215045549983691⟩,⟨477602527558148787,477602527558148805⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨239143584540916999,239143584540917016⟩,⟨256678013451624018,256678013451624034⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨146624794204131631,146624794204131647⟩,⟨135722973591098647,135722973591098663⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨87668681301976523,87668681301976539⟩,⟨71470315390147814,71470315390147831⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨50367731751539834,50367731751539851⟩,⟨37171891211881593,37171891211881609⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨25863817389622533,25863817389622549⟩,⟨17835852363805227,17835852363805243⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨7946777451446058,7946777451446074⟩,⟨5295930161825889,5295930161825905⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-38363726836532163175),(-38363726836530933834)⟩,⟨28165555646716411466,28165555646717640801⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-106011480735614926705),(-106011480735610556070)⟩,⟨81984734864931408835,81984734864935779465⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-149439969595257864253),(-149439969595248060808)⟩,⟨126829620228316269555,126829620228326072994⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-161495846147457811947),(-161495846147438262330)⟩,⟨155291803530719523433,155291803530739073046⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-144906051569788767131),(-144906051569753927407)⟩,⟨163562494936119654892,163562494936154494610⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-110942308895110875368),(-110942308895058012420)⟩,⟨154101082976781655248,154101082976834518191⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-73669495158450114992),(-73669495158386133202)⟩,⟨133060832541566894803,133060832541630876593⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-43025061853529861552),(-43025061853471388297)⟩,⟨106820177305557155360,106820177305615628611⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-22364536677238303341),(-22364536677197618024)⟩,⟨80490935106822460837,80490935106863146155⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-10469184277311608490),(-10469184277289681869)⟩,⟨57385526672513198114,57385526672535124738⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4472567307475843461),(-4472567307466606075)⟩,⟨38958688801278133935,38958688801287371323⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1730686324770645273),(-1730686324767349514)⟩,⟨25284515802786211069,25284515802789506830⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-529309520607695946),(-529309520606606361)⟩,⟨15695425118011034454,15695425118012124040⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-32596384882987204),(-32596384882628870)⟩,⟨9208475992706357122,9208475992706715455⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨104368722243313219,104368722243432156⟩,⟨4778639564799395401,4778639564799514337⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨54436790243757720,54436790243786424⟩,⟨1474837772471484428,1474837772471513131⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1920086334273644174),(-1920086334273643986)⟩,⟨(-30682021796865648808),(-30682021796865648540)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-26967297530205849437),(-26967297530205848913)⟩,⟨(-80414271393754994285),(-80414271393754993528)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-106975058847316044820),(-106975058847316043977)⟩,⟨(-74978662636910257919),(-74978662636910256757)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-267313647874105257094),(-267313647874105255971)⟩,⟨44230368862848762848,44230368862848764306⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-523422018819642080050),(-523422018819642078695)⟩,⟨273617916908149702833,273617916908149704487⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-833121491021637682960),(-833121491021637681381)⟩,⟨509230856855008389432,509230856855008391250⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1083013545068883430525),(-1083013545068883428517)⟩,⟨640156352712186792239,640156352712186794414⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1177090989208864645063),(-1177090989208864641209)⟩,⟨643549053282828554897,643549053282828558847⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1107045400908435022141),(-1107045400908435007339)⟩,⟨564131233284981309648,564131233284981324493⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-929686882533450539538),(-929686882533450466257)⟩,⟨454988084025331881828,454988084025331955122⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-714266396019936748491),(-714266396019936448824)⟩,⟨350362758934418418108,350362758934418717774⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-511479428676113757279),(-511479428676112872659)⟩,⟨263818675691116397834,263818675691117282449⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-345579004501863504897),(-345579004501861700942)⟩,⟨194276836162631952038,194276836162633755993⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-218553898363520212262),(-218553898363517691504)⟩,⟨134753794628692889207,134753794628695409966⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-120348861302444662985),(-120348861302442376567)⟩,⟨79651437708262541586,79651437708264828000⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-38397744950974903974),(-38397744950973979820)⟩,⟨26361071138276197655,26361071138277121813⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1477522043586281716764),(-1477522043586226597033)⟩,⟨867545236051383778632,867545236051438898648⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 18) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_18 (tableDensity true) (fullFactor false 1 18) density1_contains hk1_0_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨4413443559051611205964,4413443559051611206323⟩,⟨(-174443504938011072163),(-174443504938011072070)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_18 1 18 ha1_0_18_contains + def realAnswer : RBox := ⟨2935921515465229489200,2935921515465484609290⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_18 +namespace hm1_0_0_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨4106639,4106656⟩,⟨(-1827600),(-1827583)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨8446077,8446094⟩,⟨(-3971776),(-3971759)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨6566711,6566729⟩,⟨(-3421850),(-3421833)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨2878355,2878371⟩,⟨(-1720562),(-1720544)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨759983,760002⟩,⟨(-531934),(-531914)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨120836,120857⟩,⟨(-100083),(-100064)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨11193,11211⟩,⟨(-11063),(-11045)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨562,581⟩,⟨(-689),(-669)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨8,26⟩,⟨(-30),(-11)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1904631325076,1904631325092⟩,⟨888082847472,888082847488⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨4752814610137,4752814610153⟩,⟨2132030696472,2132030696489⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨5478480490808,5478480490826⟩,⟨2270833955396,2270833955412⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨4416294010826,4416294010842⟩,⟨1617294434285,1617294434303⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨2729448882897,2729448882915⟩,⟨835584018570,835584018588⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1346630957692,1346630957710⟩,⟨318614539544,318614539560⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨545048863571,545048863588⟩,⟨87260489023,87260489044⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨185630797322,185630797340⟩,⟨14756491759,14756491778⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨54734321970,54734321988⟩,⟨(-129274329),(-129274309)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨14469103024,14469103043⟩,⟨(-1201902224),(-1201902205)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨3581789127,3581789143⟩,⟨(-575670003),(-575669983)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨874894079,874894097⟩,⟨(-204420815),(-204420797)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨223257250,223257267⟩,⟨(-66884361),(-66884343)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨62405878,62405894⟩,⟨(-22146251),(-22146235)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨18938303,18938320⟩,⟨(-7481655),(-7481638)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨4405267,4405283⟩,⟨(-1833662),(-1833645)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-45764336178224),(-45764336178208)⟩,⟨3380542344913114,3380542344913130⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨84949009155839,84949009155855⟩,⟨8921134442571081,8921134442571097⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨627706534556687,627706534556703⟩,⟨11516185900964303,11516185900964320⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1310733810811338,1310733810811356⟩,⟨11032762997738429,11032762997738446⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1710269409750289,1710269409750306⟩,⟨8612613173863597,8612613173863613⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1655954760234972,1655954760234988⟩,⟨5702009311244465,5702009311244483⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1290310758139829,1290310758139846⟩,⟨3282935219770760,3282935219770776⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨852045893592849,852045893592865⟩,⟨1680495144118055,1680495144118074⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨496008421609763,496008421609780⟩,⟨782975226961479,782975226961498⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨263518694751393,263518694751409⟩,⟨340854381160543,340854381160559⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨131997143473994,131997143474014⟩,⟨142717847014865,142717847014884⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨64197265454489,64197265454506⟩,⟨59234723545705,59234723545721⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨30971923721758,30971923721774⟩,⟨25006232618224,25006232618241⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨14850781206201,14850781206220⟩,⟨10812304825250,10812304825266⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨6687057861005,6687057861024⟩,⟨4538906457322,4538906457340⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1917153179265,1917153179281⟩,⟨1256061083126,1256061083142⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-353226477806895696),(-353226477806894689)⟩,⟨296550258421794789,296550258421795801⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-949650675878174475),(-949650675878172328)⟩,⟨826322761207908508,826322761207910652⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1271301714230378765),(-1271301714230376972)⟩,⟨1184502848211427295,1184502848211429089⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1283285065819536308),(-1283285065819535442)⟩,⟨1316885173066496658,1316885173066497528⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1069426310014145346),(-1069426310014145075)⟩,⟨1239758084024834892,1239758084024835161⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-763515162745275277),(-763515162745275214)⟩,⟨1025706196544761314,1025706196544761382⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-477622319780017759),(-477622319780017733)⟩,⟨763368077016660540,763368077016660560⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-266667743739032307),(-266667743739032289)⟩,⟨520433684808590265,520433684808590286⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-135109958010417826),(-135109958010417810)⟩,⟨330415662322362281,330415662322362299⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-63028007511206240),(-63028007511206224)⟩,⟨198602691150991209,198602691150991227⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-27368747785470838),(-27368747785470822)⟩,⟨114896085354660586,114896085354660605⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-11107042017913406),(-11107042017913389)⟩,⟨64920451136152366,64920451136152382⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-4180689236379770),(-4180689236379754)⟩,⟨36116731348500009,36116731348500027⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1422962878762781),(-1422962878762765)⟩,⟨19573787682164651,19573787682164667⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-414757475169637),(-414757475169621)⟩,⟨9647559270389742,9647559270389758⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-80621326089841),(-80621326089825)⟩,⟨2902329515517455,2902329515517471⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-10962867551687489483),(-10962867551687283558)⟩,⟨(-16656656180928455733),(-16656656180928249811)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-31671639311699861323),(-31671639311699132169)⟩,⟨(-44747269858942139803),(-44747269858941410651)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-48638969187581170343),(-48638969187579547597)⟩,⟨(-59731105193769252897),(-59731105193767630155)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-59479098979158308439),(-59479098979155108900)⟩,⟨(-59868835079845469720),(-59868835079842270183)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-62658402215562766436),(-62658402215557145850)⟩,⟨(-49157516787841322291),(-49157516787835701709)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-58417285841911525545),(-58417285841903139873)⟩,⟨(-33956217010054783916),(-33956217010046398246)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-48971101376545260064),(-48971101376535298554)⟩,⟨(-19590630942772653566),(-19590630942762692054)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-37477300328493702158),(-37477300328484777243)⟩,⟨(-8870218907972959360),(-8870218907964034445)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-26606983730078682359),(-26606983730072598702)⟩,⟨(-2294045221860827896),(-2294045221854744237)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-17814934178341415709),(-17814934178338202759)⟩,⟨976866941783411740,976866941786624691⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-11433640957186302585),(-11433640957184975087)⟩,⟨2144752812987656715,2144752812988984212⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-7131082127150384901),(-7131082127149919675)⟩,⟨2205975434492710416,2205975434493175645⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-4343662687565533606),(-4343662687565382175)⟩,⟨1797084409171458107,1797084409171609543⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2541211272028969545),(-2541211272028920358)⟩,⟨1256300932415802616,1256300932415851803⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1323720151071345142),(-1323720151071328953)⟩,⟨725837622844938710,725837622844954902⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-409891118128649049),(-409891118128645147)⟩,⟨235778041901266754,235778041901270655⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨170762007597873842345,170762007597873842432⟩,⟨(-2578181224946576213),(-2578181224946576151)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨476595142058783709940,476595142058783710167⟩,⟨(-35524426842383884812),(-35524426842383884664)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨689072231506105629786,689072231506105630122⟩,⟨(-130394125278572576031),(-130394125278572575798)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨783287574680741516281,783287574680741516690⟩,⟨(-272277372503198269472),(-272277372503198269172)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨764081450200167320740,764081450200167321180⟩,⟨(-407792543541914228176),(-407792543541914227824)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨655362726987922792119,655362726987922792566⟩,⟨(-487513662040584997976),(-487513662040584997585)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨496205952984217544761,496205952984217545248⟩,⟨(-497400598298189309823),(-497400598298189309374)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨331675479303918672211,331675479303918672993⟩,⟨(-452739552431816498283),(-452739552431816497521)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨194916588441663838482,194916588441663841214⟩,⟨(-378193832594591780348),(-378193832594591777622)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨98717708005156981810,98717708005156995002⟩,⟨(-295678064888731638317),(-295678064888731625125)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨40347729986770636147,40347729986770689280⟩,⟨(-219580256250484945861),(-219580256250484892726)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨10142238902954301701,10142238902954456261⟩,⟨(-156247901767344008638),(-156247901767343854082)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2391650193729805778),(-2391650193729494741)⟩,⟨(-106281325491990188976),(-106281325491989877939)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-5524891383244589291),(-5524891383244159297)⟩,⟨(-67576214265577139719),(-67576214265576709723)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-4393182016013084624),(-4393182016012697525)⟩,⟨(-37172138184336703769),(-37172138184336316668)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1603633826555670393),(-1603633826555514525)⟩,⟨(-11822094409283919735),(-11822094409283763871)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨710117131958923444716,710117131958932024399⟩,⟨(-639382680397466491648),(-639382680397457912031)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 19) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_19 (tableDensity false) (fullFactor false 1 19) density0_contains hk1_0_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-18440582161090640481),(-18440582161090640469)⟩,⟨(-564446039720823486597),(-564446039720823486549)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_19 1 19 ha1_0_19_contains + def realAnswer : RBox := ⟨691676549797732804235,691676549797941383930⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_19 +namespace hm1_1_0_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨737341,737357⟩,⟨(-217176),(-217160)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨1531368,1531384⟩,⟨(-473457),(-473441)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1207323,1207339⟩,⟨(-408064),(-408048)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨533297,533314⟩,⟨(-205025),(-205009)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨139489,139505⟩,⟨(-64329),(-64312)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨21507,21526⟩,⟨(-12698),(-12682)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1898,1915⟩,⟨(-1521),(-1504)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨85,101⟩,⟨(-109),(-93)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),2⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨195439441299,195439441315⟩,⟨263141464946,263141464962⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨495194683388,495194683404⟩,⟨630982950852,630982950868⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨588335015550,588335015566⟩,⟨671381481769,671381481785⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨495812129589,495812129605⟩,⟨479553355913,479553355929⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨324157638157,324157638173⟩,⟨251758605269,251758605286⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨170276968387,170276968403⟩,⟨100821752529,100821752545⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨73319633801,73319633817⟩,⟨31281767920,31281767937⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨26418175418,26418175435⟩,⟨7437002497,7437002514⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨8195858028,8195858044⟩,⟨1249179476,1249179492⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2274353543,2274353560⟩,⟨83171029,83171045⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨591629792,591629809⟩,⟨(-38166569),(-38166552)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨152051716,152051732⟩,⟨(-22245677),(-22245661)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨40694133,40694149⟩,⟨(-8387676),(-8387659)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨11819566,11819582⟩,⟨(-2909386),(-2909370)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨3680116,3680132⟩,⟨(-996175),(-996158)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨866879,866895⟩,⟨(-244906),(-244890)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-408764676444672),(-408764676444656)⟩,⟨644597492096965,644597492096981⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1047969856951590),(-1047969856951573)⟩,⟨1722983122437518,1722983122437534⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1274926789332783),(-1274926789332767)⟩,⟨2267158439692375,2267158439692391⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1107633887230352),(-1107633887230335)⟩,⟨2207652093587402,2207652093587418⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-738210244601128),(-738210244601111)⟩,⟨1737561964355056,1737561964355072⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-376215982731281),(-376215982731265)⟩,⟨1154315790326556,1154315790326572⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-136456166472038),(-136456166472022)⟩,⟨669463268107292,669463268107308⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-23124415107036),(-23124415107020)⟩,⟨348831976764780,348831976764796⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨12444599199686,12444599199702⟩,⟨167451826869661,167451826869677⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨15625234655192,15625234655208⟩,⟨75821401586665,75821401586681⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨10624354725268,10624354725284⟩,⟨33117112559062,33117112559078⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨5938343175754,5938343175770⟩,⟨14232425009956,14232425009972⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨3066625598840,3066625598856⟩,⟨6115204575309,6115204575325⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1530346060479,1530346060495⟩,⟨2641477100595,2641477100611⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨708553230378,708553230394⟩,⟨1096719765846,1096719765862⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨206361980852,206361980868⟩,⟨300702705932,300702705948⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-153916923227420600),(-153916923227419749)⟩,⟨8891830593294939,8891830593295787⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-413496628013778591),(-413496628013776785)⟩,⟨30170747334606701,30170747334608506⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-553281445600870555),(-553281445600869050)⟩,⟨58233961105872356,58233961105873862⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-560348035656375066),(-560348035656374338)⟩,⟨88487065554532282,88487065554533009⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-473947069719199218),(-473947069719198992)⟩,⟨110471036434333196,110471036434333421⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-350899397714615178),(-350899397714615122)⟩,⟨114980940642846880,114980940642846936⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-234019625219740577),(-234019625219740552)⟩,⟨101538569998662740,101538569998662763⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-143243748711979566),(-143243748711979549)⟩,⟨78207223792663331,78207223792663348⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-81737473528787012),(-81737473528786995)⟩,⟨54273631243144348,54273631243144365⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-44220659059505968),(-44220659059505952)⟩,⟨35004963296953929,35004963296953945⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-23124623946006418),(-23124623946006401)⟩,⟨21537630588395528,21537630588395545⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-11921313214741332),(-11921313214741315)⟩,⟨12875408531478025,12875408531478041⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-6139967981132040),(-6139967981132024)⟩,⟨7530158227878898,7530158227878914⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-3136969037973983),(-3136969037973967)⟩,⟨4250137143387296,4250137143387312⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-1486482186126766),(-1486482186126750)⟩,⟨2155467081854859,2155467081854875⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-438540426691831),(-438540426691815)⟩,⟨658046378719862,658046378719878⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-3877189885631775484),(-3877189885631606250)⟩,⟨(-5281064232588060706),(-5281064232587891466)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-11242937697065668462),(-11242937697065069166)⟩,⟨(-14538357222377787594),(-14538357222377188298)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-17262933026232391817),(-17262933026231057898)⟩,⟨(-20342204798074649022),(-20342204798073315105)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-20906560574528885684),(-20906560574526255210)⟩,⟨(-21745059397401121248),(-21745059397398490772)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-21711154834327909223),(-21711154834323287745)⟩,⟨(-19239314226749896962),(-19239314226745275479)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-20112716130344792410),(-20112716130337897348)⟩,⟨(-14484962510286253653),(-14484962510279358594)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-17037580677810270950),(-17037580677802081862)⟩,⟨(-9437510835078176611),(-9437510835069987526)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-13396877130525633207),(-13396877130518299794)⟩,⟨(-5399307264148814916),(-5399307264141481507)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-9878779842531393254),(-9878779842526398371)⟩,⟨(-2746804873601837410),(-2746804873596842526)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-6891712846860561196),(-6891712846857926052)⟩,⟨(-1258281924776045554),(-1258281924773410409)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-4581793697196423777),(-4581793697195336392)⟩,⟨(-526424485242807714),(-526424485241720324)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2916864992263074973),(-2916864992262694404)⟩,⟨(-199822809811511110),(-199822809811130539)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1780603100996403970),(-1780603100996280250)⟩,⟨(-60119091069394559),(-60119091069270839)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1030782558426262421),(-1030782558426222276)⟩,⟨(-3676359220006592),(-3676359219966447)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-529934288497403042),(-529934288497389836)⟩,⟨11567526587206801,11567526587220003⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-162769703327960580),(-162769703327957396)⟩,⟨6007630608952695,6007630608955876⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨5069150496317921755,5069150496317921811⟩,⟨(-317143296298512168),(-317143296298512124)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨13244710336828772593,13244710336828772730⟩,⟨(-4439250169096977204),(-4439250169096977106)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨12279799193365284355,12279799193365284559⟩,⟨(-17499605131335084501),(-17499605131335084348)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-7147822690693188420),(-7147822690693188172)⟩,⟨(-43329187695730040637),(-43329187695730040442)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-43814987618620745879),(-43814987618620745600)⟩,⟨(-83850235170752096065),(-83850235170752095833)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-80446553783504286429),(-80446553783504286129)⟩,⟨(-131617339725471697877),(-131617339725471697611)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-99570253212612558401),(-99570253212612558049)⟩,⟨(-168436098259390052338),(-168436098259390052009)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-98420145747432432232),(-98420145747432431612)⟩,⟨(-179995403589472673522),(-179995403589472672919)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-84766515239348568866),(-84766515239348566628)⟩,⟨(-166330563004567773123),(-166330563004567770891)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-67168566271312804968),(-67168566271312794161)⟩,⟨(-137242875815934563571),(-137242875815934552768)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-50850810492626458199),(-50850810492626414777)⟩,⟨(-103670738345711769972),(-103670738345711726558)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-37697422704336363593),(-37697422704336237359)⟩,⟨(-73092481363988845862),(-73092481363988719628)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-27389184936503912953),(-27389184936503658838)⟩,⟨(-48724482942180712799),(-48724482942180458684)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-18795463571012408862),(-18795463571012057403)⟩,⟨(-30485872152881158484),(-30485872152880807023)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-11027554476680638923),(-11027554476680322406)⟩,⟨(-16662444130978528933),(-16662444130978212415)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3635759379368420131),(-3635759379368292659)⟩,⟨(-5295891242667330757),(-5295891242667203285)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-126086498460787332848),(-126086498460780284377)⟩,⟨(-220915770718850909422),(-220915770718843860985)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 19) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_19 (tableDensity true) (fullFactor false 1 19) density1_contains hk1_0_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨24114607441426222151,24114607441426222167⟩,⟨738121744250307636256,738121744250307636319⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_19 1 19 ha1_0_19_contains + def realAnswer : RBox := ⟨(-101971891019461110697),(-101971891019254062210)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_19 +namespace hm1_0_0_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨47615,47631⟩,⟨107005,107021⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨101613,101631⟩,⟨216135,216152⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨84378,84396⟩,⟨162016,162034⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨40114,40133⟩,⟨67169,67187⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨11486,11506⟩,⟨16433,16451⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1953,1971⟩,⟨2362,2380⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨180,201⟩,⟨186,203⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,22⟩,⟨3,20⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-46390380503),(-46390380487)⟩,⟨99490574507,99490574523⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-110345412212),(-110345412195)⟩,⟨245969068560,245969068576⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-115387190522),(-115387190505)⟩,⟨278319954744,278319954762⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-79961914351),(-79961914333)⟩,⟨218259600249,218259600268⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-39853127613),(-39853127596)⟩,⟨130085622420,130085622437⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-14541454962),(-14541454944)⟩,⟨61382869745,61382869762⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3783754059),(-3783754038)⟩,⟨23581490321,23581490340⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-604977709),(-604977690)⟩,⟨7572270262,7572270282⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨4067668,4067686⟩,⟨2093875665,2093875685⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨42752056,42752072⟩,⟨517251832,517251854⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨19162202,19162221⟩,⟨119513871,119513891⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨6369270,6369289⟩,⟨27298867,27298884⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1960811,1960829⟩,⟨6550779,6550796⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨616800,616816⟩,⟨1738882,1738900⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨200739,200756⟩,⟨508232,508248⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨48233,48249⟩,⟨115890,115907⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-265086841664265),(-265086841664249)⟩,⟨(-3589467585124),(-3589467585107)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-695196368166617),(-695196368166600)⟩,⟨6600477997182,6600477997198⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-886374909288820),(-886374909288803)⟩,⟨48248185569816,48248185569833⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-833785832922133),(-833785832922117)⟩,⟨98947190767241,98947190767257⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-635579663220736),(-635579663220719)⟩,⟨126088853825751,126088853825770⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-408846655086942),(-408846655086925)⟩,⟨118631791662527,118631791662544⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-227733620244392),(-227733620244376)⟩,⟨89435869819436,89435869819453⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-112396849156890),(-112396849156872)⟩,⟨56945523657283,56945523657300⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-50374995557178),(-50374995557161)⟩,⟨31890595660352,31890595660370⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-21074744809116),(-21074744809098)⟩,⟨16283280528137,16283280528157⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-8484980766295),(-8484980766276)⟩,⟨7843535882919,7843535882940⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-3394234752284),(-3394234752268)⟩,⟨3677093127333,3677093127349⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1386870056408),(-1386870056391)⟩,⟨1717250563767,1717250563786⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-583942520378),(-583942520360)⟩,⟨801923556360,801923556378⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-240569196545),(-240569196528)⟩,⟨354403375344,354403375362⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-65927507297),(-65927507281)⟩,⟨100625891730,100625891747⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-31017624497471169),(-31017624497471051)⟩,⟨(-36945800214069430),(-36945800214069310)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-86021664615032528),(-86021664615032290)⟩,⟨(-98863472762322439),(-98863472762322201)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-122163286872851985),(-122163286872851785)⟩,⟨(-131126027066906378),(-131126027066906179)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-133967381786752048),(-133967381786751945)⟩,⟨(-130568411789959997),(-130568411789959893)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-123904258565818210),(-123904258565818166)⟩,⟨(-106904757290456472),(-106904757290456431)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-100351978703966573),(-100351978703966552)⟩,⟨(-74723093885529354),(-74723093885529332)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-72896697033075958),(-72896697033075939)⟩,⟨(-45627991119631153),(-45627991119631136)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-48400471128087415),(-48400471128087397)⟩,⟨(-24812108029427645),(-24812108029427629)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-29886594125949389),(-29886594125949370)⟩,⟨(-12227667668805119),(-12227667668805102)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-17465938578314023),(-17465938578314005)⟩,⟨(-5546347332822354),(-5546347332822337)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-9832149394970457),(-9832149394970440)⟩,⟨(-2343611573904621),(-2343611573904604)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-5416570367380861),(-5416570367380845)⟩,⟨(-927347802184189),(-927347802184173)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-2947395675882083),(-2947395675882066)⟩,⟨(-341412203112082),(-341412203112066)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1569191499952287),(-1569191499952271)⟩,⟨(-114146789308889),(-114146789308872)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-763836337405532),(-763836337405516)⟩,⟨(-32851305063913),(-32851305063897)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-228316334040659),(-228316334040643)⟩,⟨(-6342659462654),(-6342659462638)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨2178276893234014056,2178276893234040998⟩,⟨(-1433662257724264689),(-1433662257724237744)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨5829903641739116201,5829903641739211195⟩,⟨(-4126129702674144566),(-4126129702674049572)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨7724637019668852093,7724637019669061866⟩,⟨(-6289316308418042155),(-6289316308417832380)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨7658825904019681903,7658825904020090904⟩,⟨(-7607140045757724728),(-7607140045757315726)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨6201123119461459501,6201123119462167820⟩,⟨(-7901394772518102305),(-7901394772517393988)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨4212488531778901142,4212488531779940262⟩,⟨(-7243407487516754416),(-7243407487515715295)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨2384901982229781702,2384901982230992989⟩,⟨(-5957309989045147866),(-5957309989043936580)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1058179328292012680,1058179328293076081⟩,⟨(-4465652475120583093),(-4465652475119519694)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨268320542456190696,268320542456900277⟩,⟨(-3102595315807077184),(-3102595315806367605)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-110969009064318860),(-110969009063952009)⟩,⟨(-2032731310664043311),(-2032731310663676458)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-239371811600187843),(-239371811600039372)⟩,⟨(-1277541708201295585),(-1277541708201147112)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-241638335308024004),(-241638335307972956)⟩,⟨(-781554817663355018),(-781554817663303969)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-193628588474156180),(-193628588474139833)⟩,⟨(-468143022684795795),(-468143022684779446)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-133579664892089357),(-133579664892084109)⟩,⟨(-270235707149919516),(-270235707149914268)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-76464732620306381),(-76464732620304660)⟩,⟨(-139455745323364929),(-139455745323363208)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-24720322912915543),(-24720322912915120)⟩,⟨(-42975533280120073),(-42975533280119651)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨404549790406980769,404549790406980791⟩,⟨26801900518862793376,26801900518862793402⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨5555566432579551906,5555566432579551942⟩,⟨74568752891382040149,74568752891382040196⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨20265631339495034669,20265631339495034717⟩,⟨107145954051712344752,107145954051712344818⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨41935534183882881763,41935534183882881823⟩,⟨120693861622152421807,120693861622152421885⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨62080143541407462724,62080143541407462792⟩,⟨116366299765727707691,116366299765727707774⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨73192127229067875327,73192127229067875399⟩,⟨98429716807887965465,98429716807887965547⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨73511991318979867319,73511991318979867401⟩,⟨73365608686210220805,73365608686210220891⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨65783380657680547852,65783380657680547978⟩,⟨48215559378612367690,48215559378612367820⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨53988922435481567849,53988922435481568251⟩,⟨27841122235629493957,27841122235629494361⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨41469414942809250975,41469414942809252834⟩,⟨13855298253553399654,13855298253553401513⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨30277725113610310349,30277725113610317678⟩,⟨5569041655312608530,5569041655312615854⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨21211945971314117006,21211945971314137969⟩,⟨1379522652625035089,1379522652625056055⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨14235638307392429448,14235638307392471085⟩,⟨(-319313434775373853),(-319313434775332217)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨8954821447514106471,8954821447514163438⟩,⟨(-731812217225280937),(-731812217225223970)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨4889208653292608114,4889208653292659032⟩,⟨(-577769875990593864),(-577769875990542943)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1549000368213113282,1549000368213133716⟩,⟨(-210115438348349495),(-210115438348329057)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨92501816976303517201,92501816976304561440⟩,⟨109763979168141712512,109763979168142756746⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 20) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_20 (tableDensity false) (fullFactor false 1 20) density0_contains hk1_0_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨89502790755250420904,89502790755250420913⟩,⟨(-2420087938498221619),(-2420087938498221616)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_20 1 20 ha1_0_20_contains + def realAnswer : RBox := ⟨182004607731453938105,182004607731654982353⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_20 +namespace hm1_1_0_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨5649,5665⟩,⟨19205,19221⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨12107,12123⟩,⟨39180,39196⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨10055,10071⟩,⟨29778,29795⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨4771,4787⟩,⟨12439,12455⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1380,1396⟩,⟨3010,3026⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨241,257⟩,⟨413,430⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨18,35⟩,⟨24,41⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-3),16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-13745605235),(-13745605219)⟩,⟨10208968565,10208968581⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-32657223585),(-32657223569)⟩,⟨25626743737,25626743753⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-34114703741),(-34114703725)⟩,⟨29886564627,29886564643⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-23709492597),(-23709492581)⟩,⟨24500296385,24500296401⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-12006439995),(-12006439979)⟩,⟨15446135751,15446135768⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-4600031477),(-4600031461)⟩,⟨7759673455,7759673471⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1355253262),(-1355253246)⟩,⟨3171317217,3171317233⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-304010677),(-304010661)⟩,⟨1077373296,1077373312⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-47972688),(-47972672)⟩,⟨313455728,313455744⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-3018795),(-3018778)⟩,⟨81284438,81284455⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1263872,1263888⟩,⟨19735795,19735812⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨692342,692359⟩,⟨4743231,4743247⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨245811,245827⟩,⟨1193814,1193830⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨81016,81032⟩,⟨329300,329316⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨26721,26737⟩,⟨98749,98765⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨6436,6452⟩,⟨22798,22814⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-50546322852730),(-50546322852714)⟩,⟨(-32053602936043),(-32053602936027)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-134264814741726),(-134264814741710)⟩,⟨(-81667924777409),(-81667924777393)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-174493614844629),(-174493614844613)⟩,⟨(-98138160081859),(-98138160081843)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-166836541446011),(-166836541445995)⟩,⟨(-83726494394298),(-83726494394282)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-128224542567033),(-128224542567017)⟩,⟨(-54501757198118),(-54501757198102)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-82766161227144),(-82766161227128)⟩,⟨(-26999341823271),(-26999341823255)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-46438300111965),(-46438300111947)⟩,⟨(-9483300563745),(-9483300563729)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-23329223681054),(-23329223681037)⟩,⟨(-1556771932196),(-1556771932180)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-10772265064922),(-10772265064906)⟩,⟨795801231952,795801231969⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-4687337564421),(-4687337564405)⟩,⟨964110077046,964110077062⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1968663325875),(-1968663325859)⟩,⟨630941181125,630941181141⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-815477607019),(-815477607003)⟩,⟨340049492255,340049492271⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-339149774702),(-339149774685)⟩,⟨170010657154,170010657170⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-142661054367),(-142661054351)⟩,⟨82631825164,82631825180⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-58128681907),(-58128681891)⟩,⟨37551221022,37551221038⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-15783166253),(-15783166237)⟩,⟨10831315623,10831315639⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-930018874749513),(-930018874749413)⟩,⟨(-16098975468709449),(-16098975468709347)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3140326883055571),(-3140326883055369)⟩,⟨(-43047130290364488),(-43047130290364285)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-6004072162301821),(-6004072162301650)⟩,⟨(-57067152233587114),(-57067152233586943)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-8998174543127378),(-8998174543127291)⟩,⟨(-57012299359579432),(-57012299359579344)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-11035988736869826),(-11035988736869790)⟩,⟨(-47376025965279323),(-47376025965279283)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-11245058557487449),(-11245058557487428)⟩,⟨(-34338234913864178),(-34338234913864158)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-9693307909635819),(-9693307909635802)⟩,⟨(-22352512421232751),(-22352512421232734)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-7271607781860941),(-7271607781860924)⟩,⟨(-13324934782161061),(-13324934782161045)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4908250203892084),(-4908250203892068)⟩,⟨(-7395098180294451),(-7395098180294435)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-3078023611685500),(-3078023611685483)⟩,⟨(-3889869792335083),(-3889869792335067)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1842832017419705),(-1842832017419689)⟩,⟨(-1979288638108204),(-1979288638108188)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1074134037692923),(-1074134037692907)⟩,⟨(-994806383992113),(-994806383992096)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-614471318555510),(-614471318555493)⟩,⟨(-501123003692918),(-501123003692901)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-340710317299852),(-340710317299836)⟩,⟨(-251499761400637),(-251499761400621)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-170654189891242),(-170654189891226)⟩,⟨(-117693461887493),(-117693461887477)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-51766157369361),(-51766157369345)⟩,⟨(-34498561959321),(-34498561959305)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨690630648836149462,690630648836171606⟩,⟨(-507036888718769239),(-507036888718747097)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1894098470841849649,1894098470841927727⟩,⟨(-1464709149569023186),(-1464709149568945110)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨2630607339319976313,2630607339320148754⟩,⟨(-2232210960169981467),(-2232210960169809025)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨2781565299691686198,2781565299692022456⟩,⟨(-2673905689903693997),(-2673905689903357737)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2426750388640463304,2426750388641045716⟩,⟨(-2737881390787805165),(-2737881390787222753)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1796689457916803093,1796689457917657505⟩,⟨(-2493855810767676859),(-2493855810766822449)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1148590653358451092,1148590653359446857⟩,⟨(-2072544476428310457),(-2072544476427314689)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨643716111259555105,643716111260428882⟩,⟨(-1596224414802331691),(-1596224414801457914)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨320505977975318648,320505977975901241⟩,⟨(-1151862005546421176),(-1151862005545838586)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨143675540532790201,143675540533091084⟩,⟨(-786307085677365890),(-786307085677065009)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨58864456422812915,58864456422934535⟩,⟨(-511923471401129351),(-511923471401007730)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨21918287523963446,21918287524005207⟩,⟨(-319678455280208051),(-319678455280166288)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨6487032153912384,6487032153925744⟩,⟨(-191907948544830197),(-191907948544816839)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨393884736652364,393884736656650⟩,⟨(-109616168992151364),(-109616168992147081)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1217968191137185),(-1217968191135780)⟩,⟨(-55829684250024425),(-55829684250023020)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-629850885382551),(-629850885382205)⟩,⟨(-17065802043742931),(-17065802043742583)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨49763851039209609,49763851039209630⟩,⟨795628063745976063,795628063745976083⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨694234421785209703,694234421785209731⟩,⟨2072412544474053404,2072412544474053438⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2719566349098321766,2719566349098321803⟩,⟨1910602683182657968,1910602683182658012⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨6672176118587407078,6672176118587407123⟩,⟨(-1097360550292665922),(-1097360550292665869)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨12761044327569762323,12761044327569762372⟩,⟨(-6665461336092184544),(-6665461336092184485)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨19753752302096974064,19753752302096974113⟩,⟨(-12073462840059742013),(-12073462840059741956)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨24886852065182771401,24886852065182771462⟩,⟨(-14713183960747109015),(-14713183960747108948)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨26148543413511696324,26148543413511696426⟩,⟨(-14299506712920015420),(-14299506712920015316)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨23741808246892140496,23741808246892140829⟩,⟨(-12100508595297304793),(-12100508595297304459)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨19247642282756268237,19247642282756269763⟩,⟨(-9420344106879001490),(-9420344106878999964)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨14295042431100542422,14295042431100548408⟩,⟨(-7011503056959853373),(-7011503056959847389)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨9923126295419405005,9923126295419422132⟩,⟨(-5117396705226049188),(-5117396705226032064)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6526435470524249143,6526435470524283161⟩,⟨(-3668310821215855841),(-3668310821215821821)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨4039850523952125963,4039850523952172528⟩,⟨(-2490529493419173754),(-2490529493419127189)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2191594428024867908,2191594428024909545⟩,⟨(-1450405926561113121),(-1450405926561071482)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨693898795301162461,693898795301179176⟩,⟨(-476377181694448068),(-476377181694431349)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨31472791972357328384,31472791972358186311⟩,⟨(-17505738919898734541),(-17505738919897876627)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 20) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_20 (tableDensity true) (fullFactor false 1 20) density1_contains hk1_0_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-117042110987635165809),(-117042110987635165798)⟩,⟨3164730381113059037,3164730381113059041⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_20 1 20 ha1_0_20_contains + def realAnswer : RBox := ⟨(-85569319015377837425),(-85569319015176979487)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_20 +namespace hm1_0_0_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2665),(-2649)⟩,⟨1172,1189⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5278),(-5261)⟩,⟨2467,2486⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-3816),(-3799)⟩,⟨1973,1991⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1504),(-1484)⟩,⟨882,902⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-351),(-331)⟩,⟨229,245⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-53),(-35)⟩,⟨27,46⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-7),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4949536009),(-4949535993)⟩,⟨(-2307883708),(-2307883692)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-12123506823),(-12123506807)⟩,⟨(-5439177580),(-5439177563)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-13466648147),(-13466648130)⟩,⟨(-5584195932),(-5584195913)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-10273958691),(-10273958673)⟩,⟨(-3765528215),(-3765528198)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-5905475823),(-5905475806)⟩,⟨(-1810525497),(-1810525477)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2665271805),(-2665271787)⟩,⟨(-632182608),(-632182590)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-971912819),(-971912796)⟩,⟨(-156293221),(-156293204)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-294268931),(-294268908)⟩,⟨(-23627100),(-23627080)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-76313390),(-76313369)⟩,⟨116532,116550⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-17616887),(-17616870)⟩,⟨1448834,1448852⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-3799272),(-3799252)⟩,⟨607688,607708⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-811494),(-811472)⟩,⟨189053,189072⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-183113),(-183095)⟩,⟨54751,54769⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-46161),(-46145)⟩,⟨16353,16372⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-12999),(-12983)⟩,⟨5122,5140⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-2913),(-2895)⟩,⟨1200,1216⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨268129099822,268129099838⟩,⟨(-19797075143647),(-19797075143631)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-488430680637),(-488430680621)⟩,⟨(-51595151736888),(-51595151736872)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3532029970887),(-3532029970871)⟩,⟨(-64974928211616),(-64974928211599)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-7114094466266),(-7114094466249)⟩,⟨(-60013924367261),(-60013924367243)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-8853713572847),(-8853713572831)⟩,⟨(-44672622944090),(-44672622944072)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-8094687769230),(-8094687769213)⟩,⟨(-27921511717976),(-27921511717959)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-5904519849687),(-5904519849671)⟩,⟨(-15046891359998),(-15046891359981)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-3625089416928),(-3625089416909)⟩,⟨(-7160325563208),(-7160325563191)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1953002198426),(-1953002198407)⟩,⟨(-3087078809841),(-3087078809825)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-958382478640),(-958382478623)⟩,⟨(-1241142011738),(-1241142011719)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-443936859021),(-443936859004)⟩,⟨(-480490457830),(-480490457812)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-200606928005),(-200606927988)⟩,⟨(-185250829957),(-185250829939)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-90686059644),(-90686059626)⟩,⟨(-73259583077),(-73259583058)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-41242529151),(-41242529134)⟩,⟨(-30036581049),(-30036581033)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-17888684886),(-17888684870)⟩,⟨(-12143575803),(-12143575787)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-5030071928),(-5030071912)⟩,⟨(-3295596828),(-3295596811)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3680338904429494,3680338904429518⟩,⟨(-3089795026428398),(-3089795026428370)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨9802128374821176,9802128374821216⟩,⟨(-8528615087290227),(-8528615087290195)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨12880858730591933,12880858730591966⟩,⟨(-11999439527829282),(-11999439527829248)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨12652401851625352,12652401851625375⟩,⟨(-12979863835185203),(-12979863835185177)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨10178129138583131,10178129138583150⟩,⟨(-11793979048089161),(-11793979048089141)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨6965009797903251,6965009797903269⟩,⟨(-9351015134090556),(-9351015134090540)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨4151568062358217,4151568062358233⟩,⟨(-6630038289092587),(-6630038289092569)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2198842283072351,2198842283072367⟩,⟨(-4287176634454069),(-4287176634454052)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1053994973430548,1053994973430567⟩,⟨(-2574727831972123),(-2574727831972107)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨464856056436084,464856056436101⟩,⟨(-1462975995238008),(-1462975995237991)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨191139928179550,191139928179567⟩,⟨(-801359404889119),(-801359404889102)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨73742394593452,73742394593468⟩,⟨(-430425642723243),(-430425642723226)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨26554290341408,26554290341426⟩,⟨(-229083280185224),(-229083280185207)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨8720721441005,8720721441021⟩,⟨(-119810779847942),(-119810779847925)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2478134155830,2478134155847⟩,⟨(-57596628162643),(-57596628162627)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨475230074294,475230074310⟩,⟨(-17105600085255),(-17105600085239)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨178558435063959097,178558435063962467⟩,⟨271299617548624149,271299617548627518⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨511949457669424019,511949457669435819⟩,⟨723382649638622122,723382649638633921⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨774526650012403703,774526650012429538⟩,⟨951413821574717507,951413821574743344⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨926605716964101124,926605716964150931⟩,⟨933125565018622571,933125565018672380⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨948959776696092453,948959776696177480⟩,⟨745024042073688527,745024042073773552⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨855395823383972314,855395823384094963⟩,⟨497714902434073438,497714902434196087⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨690217302424968710,690217302425109002⟩,⟨276514284469234177,276514284469374469⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨506790774193372510,506790774193493197⟩,⟨120229325212007175,120229325212127866⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨344573986229797267,344573986229876105⟩,⟨29890187068786576,29890187068865415⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨220903707441318813,220903707441358720⟩,⟨(-12005723845652570),(-12005723845612663)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨135953694181718817,135953694181734644⟩,⟨(-25444504003878307),(-25444504003862481)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨81580412073926820,81580412073932172⟩,⟨(-25208875035182060),(-25208875035176711)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨48052934067408371,48052934067410065⟩,⟨(-19869612395877832),(-19869612395876136)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨27369070455078882,27369070455079428⟩,⟨(-13527027659671141),(-13527027659670593)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨13992301116776892,13992301116777083⟩,⟨(-7671766475685904),(-7671766475685720)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨4291261187863560,4291261187863618⟩,⟨(-2468401659916402),(-2468401659916344)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-4006366934057931506),(-4006366934057931488)⟩,⟨60456260659791460,60456260659791477⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-11111576127084524587),(-11111576127084524569)⟩,⟨827448624536987123,827448624536987144⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-15867177644859202742),(-15867177644859202716)⟩,⟨2999680861517679784,2999680861517679806⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-17711846705492639185),(-17711846705492639158)⟩,⟨6151308031167167425,6151308031167167446⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-16878412093268407016),(-16878412093268406991)⟩,⟨9000837583216697583,9000837583216697606⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-14079575663090749062),(-14079575663090749037)⟩,⟨10465519993139038356,10465519993139038382⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-10331030071574572841),(-10331030071574572814)⟩,⟨10347387132711125451,10347387132711125478⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-6675483387778219096),(-6675483387778219063)⟩,⟨9103444448162803097,9103444448162803124⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3787447810235525960),(-3787447810235525894)⟩,⟨7340355268960675010,7340355268960675078⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1852072903454618834),(-1852072903454618572)⟩,⟨5539345167497749167,5539345167497749430⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-732085221153304605),(-732085221153303628)⟩,⟨3976249065320204596,3976249065320205574⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-178706529569208204),(-178706529569205484)⟩,⟨2742617286716507178,2742617286716509899⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨40602096770576486,40602096770581806⟩,⟨1815987871988887225,1815987871988892544⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨92318599493834617,92318599493841815⟩,⟨1130143792948273775,1130143792948280976⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨72367312721028451,72367312721034840⟩,⟨612451153007886608,612451153007893001⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨26219327714995476,26219327714998041⟩,⟨193294480025849121,193294480025851687⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-16107710386474343945),(-16107710386474222482)⟩,⟨12779046030491468899,12779046030491590384⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 21) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_21 (tableDensity false) (fullFactor false 1 21) density0_contains hk1_0_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨302321100221965790,302321100221965792⟩,⟨13494458465799728564,13494458465799728567⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_21 1 21 ha1_0_21_contains + def realAnswer : RBox := ⟨(-15805389286352378155),(-15805389286152256690)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_21 +namespace hm1_1_0_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-486),(-470)⟩,⟨131,147⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-962),(-946)⟩,⟨288,304⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-709),(-692)⟩,⟨229,245⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-285),(-269)⟩,⟨98,115⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-71),(-54)⟩,⟨20,37⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-18),(-2)⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-7),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-507882283),(-507882267)⟩,⟨(-683832886),(-683832870)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1263074680),(-1263074664)⟩,⟨(-1609752190),(-1609752174)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1445966654),(-1445966638)⟩,⟨(-1650990913),(-1650990897)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1153120626),(-1153120610)⟩,⟨(-1116493648),(-1116493632)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-701059690),(-701059674)⟩,⟨(-545399046),(-545399030)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-336842760),(-336842744)⟩,⟨(-199922098),(-199922082)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-130671250),(-130671234)⟩,⟨(-55932657),(-55932641)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-41857445),(-41857428)⟩,⟨(-11838953),(-11838936)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-11421361),(-11421345)⟩,⟨(-1755103),(-1755087)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-2767742),(-2767726)⟩,⟨(-104359),(-104343)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-627234),(-627218)⟩,⟨39865,39882⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-140970),(-140954)⟩,⟨20519,20537⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-33371),(-33355)⟩,⟨6854,6870⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-8749),(-8733)⟩,⟨2141,2157⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-2531),(-2515)⟩,⟨676,692⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-580),(-564)⟩,⟨155,171⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨2393819590010,2393819590026⟩,⟨(-3774866460633),(-3774866460617)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨6061334269134,6061334269150⟩,⟨(-9964543332996),(-9964543332980)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨7194657376514,7194657376531⟩,⟨(-12790772573116),(-12790772573098)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨6027771145675,6027771145691⟩,⟨(-12008230542742),(-12008230542726)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨3832454038693,3832454038709⟩,⟨(-9012357813919),(-9012357813903)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1845499402499,1845499402515⟩,⟨(-5652322780574),(-5652322780558)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨627736040636,627736040652⟩,⟨(-3068179241836),(-3068179241819)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨99819155214,99819155232⟩,⟨(-1486093592480),(-1486093592463)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-48471534652),(-48471534636)⟩,⟨(-660070084461),(-660070084444)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-56662221427),(-56662221411)⟩,⟨(-276011111395),(-276011111378)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-35689256219),(-35689256202)⟩,⟨(-111468440256),(-111468440240)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-18546942251),(-18546942235)⟩,⟨(-44503894403),(-44503894386)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-8977036203),(-8977036187)⟩,⟨(-17914852533),(-17914852517)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-4249459696),(-4249459680)⟩,⟨(-7338251160),(-7338251144)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1895367575),(-1895367559)⟩,⟨(-2934290192),(-2934290176)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-541432432),(-541432416)⟩,⟨(-788973569),(-788973553)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1603692183351062,1603692183351086⟩,⟨(-92641004110999),(-92641004110972)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4268044917702640,4268044917702675⟩,⟨(-311297895510964),(-311297895510930)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨5605856031190633,5605856031190665⟩,⟨(-589564209947388),(-589564209947356)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨5524578381356067,5524578381356090⟩,⟨(-871462959986769),(-871462959986749)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4510370262735784,4510370262735802⟩,⟨(-1050023280922550),(-1050023280922534)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3200391325140704,3200391325140720⟩,⟨(-1047436016954424),(-1047436016954408)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2033455243596625,2033455243596641⟩,⟨(-881347921571372),(-881347921571355)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1180570563733921,1180570563733937⟩,⟨(-643949349176091),(-643949349176075)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨637243786647600,637243786647616⟩,⟨(-422769548151080),(-422769548151064)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨325899147472534,325899147472550⟩,⟨(-257782139010529),(-257782139010512)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨161353757840564,161353757840580⟩,⟨(-150179023940568),(-150179023940552)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨79064919152249,79064919152268⟩,⟨(-85346727803091),(-85346727803075)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨38953589180223,38953589180239⟩,⟨(-47755577683227),(-47755577683211)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨19203650099003,19203650099019⟩,⟨(-26012764449791),(-26012764449775)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨8874805613751,8874805613767⟩,⟨(-12867862239340),(-12867862239324)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨2584659973808,2584659973824⟩,⟨(-3878344833556),(-3878344833540)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨63149930427242142,63149930427244917⟩,⟨86016363714669245,86016363714672016⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨181733446748590386,181733446748600085⟩,⟨235018283205116663,235018283205126362⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨274896834632058848,274896834632080090⟩,⟨323987221201354343,323987221201375586⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨325706264161245012,325706264161285964⟩,⟨338871023533253340,338871023533294291⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨328825837815380738,328825837815450654⟩,⟨291527932836576689,291527932836646602⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨294506326426264883,294506326426365728⟩,⟨212251719515892859,212251719515993709⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨240118225324594674,240118225324710008⟩,⟨133136831270865783,133136831270981116⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨181138807145903835,181138807146003005⟩,⟨73093302358271627,73093302358370795⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨127916183774390517,127916183774455249⟩,⟨35618198406983245,35618198407047978⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨85444576481517899,85444576481550628⟩,⟨15624803254519387,15624803254552122⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨54475340290516157,54475340290529127⟩,⟨6268954635719300,6268954635732269⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨33368205323593896,33368205323598270⟩,⟨2289760790276946,2289760790281324⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨19698705517563760,19698705517565147⟩,⟨666649752748671,666649752750058⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨11101905584706111,11101905584706563⟩,⟨40189306585170,40189306585619⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨5601712594318562,5601712594318718⟩,⟨(-122136025374362),(-122136025374207)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1704082995811984,1704082995812034⟩,⟨(-62890228707247),(-62890228707199)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-118931198308265166),(-118931198308265150)⟩,⟨7436750119594316,7436750119594332⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-308831414200723829),(-308831414200723808)⟩,⟨103398465282292028,103398465282292045⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-283114516993658674),(-283114516993658654)⟩,⟨402516659185365314,402516659185365333⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨160448017302688183,160448017302688208⟩,⟨978518616710470156,978518616710470177⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨965726600655755015,965726600655755036⟩,⟨1849630097128703023,1849630097128703046⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨1725738654675476182,1725738654675476206⟩,⟨2823611367205488379,2823611367205488401⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨2070638647619002906,2070638647619002929⟩,⟨3502074380531779747,3502074380531779766⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1978699778094968558,1978699778094968584⟩,⟨3617890265382499687,3617890265382499713⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1645148558096805220,1645148558096805279⟩,⟨3227585316953502099,3227585316953502159⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1258314439253460215,1258314439253460435⟩,⟨2570910640368877577,2570910640368877793⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨920756460566056192,920756460566056993⟩,⟨1877306058763966190,1877306058763966989⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨661614335979750539,661614335979752763⟩,⟨1283047408206837071,1283047408206839297⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨467917375683892801,467917375683897150⟩,⟨832570216911248438,832570216911252787⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨314299754327894198,314299754327900085⟩,⟨509853810676727567,509853810676733460⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨181681947342689101,181681947342694332⟩,⟨274532348416204389,274532348416209618⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨59445310727927838,59445310727929938⟩,⟨86589262839324027,86589262839326127⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2326361195959082190,2326361195959182014⟩,⟨4282524112218858770,4282524112218958617⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 21) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_21 (tableDensity true) (fullFactor false 1 21) density1_contains hk1_0_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-395342977213339882),(-395342977213339880)⟩,⟨(-17646599532199645049),(-17646599532199645046)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_21 1 21 ha1_0_21_contains + def realAnswer : RBox := ⟨1931018218645742308,1931018218845842134⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_21 +namespace hm1_0_0_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-37),(-20)⟩,⟨(-69),(-53)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-64),(-48)⟩,⟨(-128),(-112)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-55),(-37)⟩,⟨(-95),(-76)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-27),(-9)⟩,⟨(-42),(-24)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),2⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨109596662,109596678⟩,⟨(-235041471),(-235041453)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨255927068,255927085⟩,⟨(-570400745),(-570400728)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨257976649,257976665⟩,⟨(-622001625),(-622001606)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨169278986,169279004⟩,⟨(-461675886),(-461675868)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨78524003,78524021⟩,⟨(-255939588),(-255939569)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨26239458,26239476⟩,⟨(-110488493),(-110488476)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨6163872,6163892⟩,⟨(-38246253),(-38246236)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨881000,881018⟩,⟨(-10919183),(-10919164)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2972),(-2953)⟩,⟨(-2655798),(-2655779)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-46897),(-46878)⟩,⟨(-572947),(-572928)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-18415),(-18394)⟩,⟨(-115335),(-115317)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-5367),(-5350)⟩,⟨(-23042),(-23024)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1468),(-1451)⟩,⟨(-4895),(-4877)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-424),(-406)⟩,⟨(-1176),(-1159)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-133),(-117)⟩,⟨(-324),(-308)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-37),(-21)⟩,⟨(-78),(-61)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1411272488367,1411272488383⟩,⟨19118544362,19118544378⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨3655192003065,3655192003082⟩,⟨(-34500617432),(-34500617416)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨4546525577022,4546525577039⟩,⟨(-246815684429),(-246815684412)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨4123468971345,4123468971361⟩,⟨(-488257472876),(-488257472859)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨2997334389279,2997334389298⟩,⟨(-593467232820),(-593467232804)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1820326108134,1820326108151⟩,⟨(-527267957456),(-527267957439)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨949089161008,949089161024⟩,⟨(-372133450086),(-372133450068)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨435470671269,435470671290⟩,⟨(-220305926114),(-220305926097)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨180605857704,180605857723⟩,⟨(-114181335382),(-114181335365)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨69780175352,69780175372⟩,⟨(-53850292783),(-53850292767)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨25975609614,25975609630⟩,⟨(-23987128508),(-23987128488)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨9651993559,9651993579⟩,⟨(-10447833476),(-10447833458)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨3694197685,3694197704⟩,⟨(-4571667509),(-4571667492)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1474841541,1474841558⟩,⟨(-2024753479),(-2024753462)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨585136038,585136055⟩,⟨(-861911527),(-861911509)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨157252990,157253006⟩,⟨(-240013737),(-240013721)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨293797182713660,293797182713679⟩,⟨349951104987658,349951104987675⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨807137721111495,807137721111512⟩,⟨927691050827756,927691050827774⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1125078377141427,1125078377141446⟩,⟨1207820195139525,1207820195139543⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1200458130653797,1200458130653813⟩,⟨1170344219570115,1170344219570132⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1071630851953196,1071630851953213⟩,⟨925016626831356,925016626831375⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨831777815862755,831777815862772⟩,⟨619732415861491,619732415861510⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨575631347145300,575631347145316⟩,⟨360589377980562,360589377980578⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨362507200786323,362507200786342⟩,⟨186014841373460,186014841373479⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨211744043103038,211744043103058⟩,⟨86727724241886,86727724241903⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨116978706569180,116978706569198⟩,⟨37192358667816,37192358667833⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨62348745385607,62348745385624⟩,⟨14881206419333,14881206419350⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨32650411605368,32650411605384⟩,⟨5597679856535,5597679856552⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨16996488043962,16996488043979⟩,⟨1971518038358,1971518038374⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨8732138720497,8732138720513⟩,⟨635983160365,635983160382⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨4145659241973,4145659241989⟩,⟨178441839694,178441839710⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1223310284135,1223310284151⟩,⟨33988610912,33988610928⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-32253884406430595),(-32253884406430179)⟩,⟨21228076127455667,21228076127456082⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-85678645062958003),(-85678645062956591)⟩,⟨60633004723564755,60633004723566168⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-111856335732814553),(-111856335732811501)⟩,⟨91047716937012148,91047716937015200⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-108522649850556391),(-108522649850550588)⟩,⟨107738514758017892,107738514758023694⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-85442833742441530),(-85442833742431775)⟩,⟨108792099394708475,108792099394718233⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-56134639662272104),(-56134639662258271)⟩,⟨96427277501137454,96427277501151284⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-30603804945348172),(-30603804945332648)⟩,⟨76336580715102953,76336580715118478⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-13039880949436881),(-13039880949423791)⟩,⟨54901667054893410,54901667054906499⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-3178425049126407),(-3178425049118033)⟩,⟨36530330837890259,36530330837898635⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1239884609086644,1239884609090802⟩,⟨22916020598219933,22916020598224089⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨2581820919893702,2581820919895325⟩,⟨13810780633569601,13810780633571221⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨2510437857969783,2510437857970330⟩,⟨8128692477198794,8128692477199342⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1946319507350163,1946319507350346⟩,⟨4708321039558060,4708321039558242⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1307572203786579,1307572203786646⟩,⟨2645931689256417,2645931689256484⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨734730366623460,734730366623493⟩,⟨1340109505330826,1340109505330857⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨235274219039737,235274219039760⟩,⟨409020846568059,409020846568082⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-8623970415145400),(-8623970415145384)⟩,⟨(-571653097231136919),(-571653097231136903)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-117638931866604858),(-117638931866604842)⟩,⟨(-1580490474156904620),(-1580490474156904604)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-423827060487050177),(-423827060487050161)⟩,⟨(-2242964422347681502),(-2242964422347681485)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-861297828174398076),(-861297828174398059)⟩,⟨(-2481093524185788083),(-2481093524185788066)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1245706791328617959),(-1245706791328617940)⟩,⟨(-2336892050453419025),(-2336892050453419009)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1428440087801747834),(-1428440087801747818)⟩,⟨(-1922461439936236488),(-1922461439936236469)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1390303915719480515),(-1390303915719480499)⟩,⟨(-1388676793092184065),(-1388676793092184047)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1202549660174864646),(-1202549660174864629)⟩,⟨(-882238076830520723),(-882238076830520702)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-952659301035317424),(-952659301035317400)⟩,⟨(-491829372912143716),(-491829372912143693)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-706311981526759604),(-706311981526759557)⟩,⟨(-236323853300562780),(-236323853300562733)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-498459882988915320),(-498459882988915186)⟩,⟨(-91864671104481274),(-91864671104481135)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-338496509417568945),(-338496509417568597)⟩,⟨(-22098077406699896),(-22098077406699546)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-221131631277178829),(-221131631277178165)⟩,⟨4928075770239430,4928075770240092⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-136147631584296072),(-136147631584295190)⟩,⟨11116762162275708,11116762162276592⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-73232204929207185),(-73232204929206408)⟩,⟨8652224185522850,8652224185523627⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-23024177725980852),(-23024177725980533)⟩,⟨3123071205646228,3123071205646546⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1689543926088583497),(-1689543926088569741)⟩,⟨(-2251213312027333997),(-2251213312027320272)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 22) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_22 (tableDensity false) (fullFactor false 1 22) density0_contains hk1_0_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1939500660400705385),(-1939500660400705383)⟩,⟨36034701563044891,36034701563044892⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_22 1 22 ha1_0_22_contains + def realAnswer : RBox := ⟨(-3629044586589288882),(-3629044586389275124)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_22 +namespace hm1_1_0_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-21),(-5)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-32),(-16)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-24),(-8)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),2⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨32473823,32473839⟩,⟨(-24118031),(-24118015)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨75743047,75743063⟩,⟨(-59424937),(-59424920)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨76271877,76271893⟩,⟨(-66781700),(-66781683)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨50190861,50190877⟩,⟨(-51809960),(-51809943)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨23652125,23652142⟩,⟨(-30377186),(-30377169)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨8295434,8295450⟩,⟨(-13960242),(-13960226)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨2203989,2204006⟩,⟨(-5140759),(-5140742)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨440196,440212⟩,⟨(-1552780),(-1552763)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨61302,61318⟩,⟨(-397384),(-397368)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨3436,3452⟩,⟨(-89996),(-89980)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1210),(-1194)⟩,⟨(-19042),(-19026)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-591),(-575)⟩,⟨(-4010),(-3994)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-194),(-177)⟩,⟨(-900),(-884)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-62),(-46)⟩,⟨(-231),(-215)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-24),(-8)⟩,⟨(-70),(-54)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-22),(-6)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨269098081479,269098081495⟩,⟨170648691992,170648692008⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨705915121869,705915121886⟩,⟨429422551660,429422551676⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨894992699009,894992699025⟩,⟨503486430488,503486430504⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨825049580560,825049580578⟩,⟨414251099070,414251099086⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨604683305383,604683305399⟩,⟨257255862753,257255862770⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨368496104855,368496104871⟩,⟨120421835667,120421835683⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨193519970904,193519970921⟩,⟨39667198921,39667198938⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨90373201677,90373201693⟩,⟨6109747289,6109747305⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨38612211518,38612211534⟩,⟨(-2818470270),(-2818470254)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨15515956062,15515956080⟩,⟨(-3179166888),(-3179166872)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨6025313359,6025313375⟩,⟨(-1927233096),(-1927233079)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2318582931,2318582948⟩,⟨(-965698800),(-965698784)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨903362280,903362297⟩,⟨(-452498477),(-452498461)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨360324804,360324820⟩,⟨(-208609781),(-208609765)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨141390202,141390218⟩,⟨(-91320141),(-91320125)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨37646803,37646819⟩,⟨(-25834787),(-25834771)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨8808694856841,8808694856857⟩,⟨152489734270119,152489734270135⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨29456148735172,29456148735190⟩,⟨403935678476309,403935678476327⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨55260889347065,55260889347082⟩,⟨525653106368413,525653106368430⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨80565529524007,80565529524023⟩,⟨511017190215750,511017190215766⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨95366836926178,95366836926194⟩,⟨409898608762890,409898608762906⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨93134182578551,93134182578567⟩,⟨284736973401593,284736973401609⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨76496764198960,76496764198976⟩,⟨176588727571589,176588727571605⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨54437295501247,54437295501265⟩,⟨99848632375445,99848632375461⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨34762081148817,34762081148834⟩,⟨52419402695722,52419402695738⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨20609057483377,20609057483393⟩,⟨26064869510287,26064869510303⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨11683000380852,11683000380868⟩,⟨12556552289648,12556552289666⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨6473394854870,6473394854886⟩,⟨5998543152326,5998543152342⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨3542888335695,3542888335711⟩,⟨2890423153586,2890423153602⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1895800021074,1895800021090⟩,⟨1399699351681,1399699351697⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨926180533983,926180533999⟩,⟨638800366790,638800366807⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨277360041590,277360041606⟩,⟨184842921058,184842921074⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-10226171156408231),(-10226171156407888)⟩,⟨7507631409353916,7507631409354258⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-27835468580100120),(-27835468580098958)⟩,⟨21523660046482168,21523660046483329⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-38088993383304792),(-38088993383302284)⟩,⟨32314988596528789,32314988596531300⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-39407785694041979),(-39407785694037207)⟩,⟨37871157607511107,37871157607515881⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-33430332108965120),(-33430332108957095)⟩,⟨37698385456900467,37698385456908492⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-23935244631603853),(-23935244631592476)⟩,⟨33199114239486701,33199114239498075⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-14731337309412427),(-14731337309399663)⟩,⟨26555692193360776,26555692193373542⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-7922706114208720),(-7922706114197965)⟩,⟨19621948779321465,19621948779332222⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-3778514889463567),(-3778514889456688)⟩,⟨13560144864266051,13560144864272930⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1622030424800350),(-1622030424796937)⟩,⟨8863188985992919,8863188985996333⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-637305897570542),(-637305897569210)⟩,⟨5533579594636789,5533579594638124⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-228339707224461),(-228339707224010)⟩,⟨3324762879442277,3324762879442726⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-65396321667612),(-65396321667464)⟩,⟨1930132880176976,1930132880177126⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-3914067165364),(-3914067165305)⟩,⟨1073301416745060,1073301416745117⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨11690953413213,11690953413241⟩,⟨536506375165459,536506375165489⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨5994119875342,5994119875361⟩,⟨162424523894390,162424523894407⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1060838009291681),(-1060838009291665)⟩,⟨(-16969857758552049),(-16969857758552033)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-14700069283354089),(-14700069283354073)⟩,⟨(-43930298143761809),(-43930298143761793)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-56867844272070223),(-56867844272070207)⟩,⟨(-40045382203814453),(-40045382203814436)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-136984439238671493),(-136984439238671477)⟩,⟨22393124665435097,22393124665435113⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-255909377230971866),(-255909377230971850)⟩,⟨133561274026407898,133561274026407916⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-385269809037215100),(-385269809037215084)⟩,⟨235463118478047924,235463118478047940⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-470421633097453603),(-470421633097453585)⟩,⟨278168837875256794,278168837875256811⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-477827335662120291),(-477827335662120272)⟩,⟨261364417047377364,261364417047377381⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-418841572302635315),(-418841572302635292)⟩,⟨213508282973322592,213508282973322614⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-327796300166419205),(-327796300166419163)⟩,⟨160442428151483881,160442428151483922⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-235337426238282925),(-235337426238282812)⟩,⟨115420972690982739,115420972690982852⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-158358423819230556),(-158358423819230267)⟩,⟨81651663257103671,81651663257103961⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-101383579083027569),(-101383579083027028)⟩,⟨56973664993204924,56973664993205463⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-61422240797316801),(-61422240797316078)⟩,⟨37861342709262869,37861342709263594⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-32826503898068396),(-32826503898067755)⟩,⟨21723597943678680,21723597943679316⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-10314037293479827),(-10314037293479564)⟩,⟨7080778326509364,7080778326509629⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-557773262037600306),(-557773262037588963)⟩,⟨296435473001167009,296435473001178321⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 22) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_22 (tableDensity true) (fullFactor false 1 22) density1_contains hk1_0_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨2536270094370153194,2536270094370153195⟩,⟨(-47122302043981782),(-47122302043981781)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_22 1 22 ha1_0_22_contains + def realAnswer : RBox := ⟨1978496832232552888,1978496832432564232⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_22 +namespace hm1_0_0_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),7⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨10676277,10676293⟩,⟨4978237,4978253⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨25670482,25670499⟩,⟨11518640,11518656⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨27481372,27481389⟩,⟨11400262,11400278⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨19845839,19845855⟩,⟨7279682,7279698⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨10611445,10611461⟩,⟨3258012,3258029⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨4381982,4382001⟩,⟨1041932,1041951⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1439960,1439978⟩,⟨232567,232585⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨387659,387677⟩,⟨31421,31440⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨88428,88445⟩,⟨(-72),(-53)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨17819,17838⟩,⟨(-1462),(-1442)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨3340,3358⟩,⟨(-544),(-525)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨616,635⟩,⟨(-153),(-137)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨115,134⟩,⟨(-46),(-30)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨19,37⟩,⟨(-18),(-1)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1303949849),(-1303949832)⟩,⟨96231207044,96231207061⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨2331016787,2331016803⟩,⟨247690658355,247690658371⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨16497735934,16497735952⟩,⟨304310663490,304310663507⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨32054537733,32054537749⟩,⟨271009701995,271009702012⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨38052986639,38052986656⟩,⟨192375346089,192375346108⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨32854367666,32854367684⟩,⟨113524451542,113524451560⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨22436352279,22436352296⟩,⟨57267199104,57267199121⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨12807963009,12807963028⟩,⟨25335566821,25335566838⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨6386131575,6386131593⟩,⟨10108003876,10108003896⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨2894593495,2894593511⟩,⟨3753116924,3753116942⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1239884248,1239884266⟩,⟨1343358302,1343358319⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨520527519,520527539⟩,⟨481072535,481072552⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨220462203,220462220⟩,⟨178197246,178197262⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨95084939,95084956⟩,⟨69271223,69271240⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨39723617,39723634⟩,⟨26969254,26969270⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨10954521,10954537⟩,⟨7177266,7177282⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-31828925528857),(-31828925528841)⟩,⟨26721487879716,26721487879732⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-83981385603484),(-83981385603468)⟩,⟨73065685477144,73065685477160⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-108332693508118),(-108332693508102)⟩,⟨100903072078557,100903072078575⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-103551944597937),(-103551944597921)⟩,⟨106200836910648,106200836910665⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-80415542432765),(-80415542432748)⟩,⟨93140598293586,93140598293602⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-52747331619265),(-52747331619249)⟩,⟨70773369383072,70773369383089⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-29959312292201),(-29959312292184)⟩,⟨47806973539214,47806973539230⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-15052976709050),(-15052976709033)⟩,⟨29321323020399,29321323020415⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-6826530384899),(-6826530384883)⟩,⟨16657669179658,16657669179674⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2846498207745),(-2846498207727)⟩,⟨8947443405830,8947443405847⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1108265918739),(-1108265918723)⟩,⟨4640318658184,4640318658200⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-406455776531),(-406455776515)⟩,⟨2369158780768,2369158780784⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-140015273993),(-140015273976)⟩,⟨1206240930391,1206240930408⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-44365106455),(-44365106438)⟩,⟨608763167279,608763167296⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-12290413422),(-12290413405)⟩,⟨285422477666,285422477682⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2325188275),(-2325188259)⟩,⟨83681633781,83681633797⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2413992293982758),(-2413992293982697)⟩,⟨(-3667835472489520),(-3667835472489460)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-6868898778979678),(-6868898778979507)⟩,⟨(-9706733655881423),(-9706733655881249)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-10237637586302714),(-10237637586302356)⟩,⟨(-12579103984216182),(-12579103984215824)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-11982506351189275),(-11982506351188618)⟩,⟨(-12072614421146972),(-12072614421146311)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-11930280304382330),(-11930280304381244)⟩,⟨(-9373130101441213),(-9373130101440129)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-10397752641838519),(-10397752641837014)⟩,⟨(-6056027425552367),(-6056027425550860)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-8075864111889975),(-8075864111888319)⟩,⟨(-3239979816409621),(-3239979816407964)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-5689231863561830),(-5689231863560460)⟩,⟨(-1352842132688513),(-1352842132687142)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-3704560588686100),(-3704560588685233)⟩,⟨(-323297343738343),(-323297343737477)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-2273980779630411),(-2273980779629983)⟩,⟨122483817949622,122483817950052⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1342007516902324),(-1342007516902153)⟩,⟨250592242555267,250592242555440⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-774750855297325),(-774750855297261)⟩,⟨239139929027432,239139929027500⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-441281025617657),(-441281025617626)⟩,⟨182365184255094,182365184255126⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-244679003563797),(-244679003563777)⟩,⟨120900608083632,120900608083651⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-122768818610121),(-122768818610102)⟩,⟨67306537620357,67306537620375⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-37290738925513),(-37290738925496)⟩,⟨21450029931662,21450029931679⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨78020608986228764,78020608986228780⟩,⟨(-1176706467000046),(-1176706467000030)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨215032329885179699,215032329885179715⟩,⟨(-15997667977187827),(-15997667977187811)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨303278839466481778,303278839466481794⟩,⟨(-57279505404161783),(-57279505404161766)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨332446131804991338,332446131804991354⟩,⟨(-115355429993283182),(-115355429993283166)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨309490019598565323,309490019598565339⟩,⟨(-164911015131501184),(-164911015131501167)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨251089572188446616,251089572188446632⟩,⟨(-186494596787060515),(-186494596787060499)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨178551459667288123,178551459667288139⟩,⟨(-178687247735011224),(-178687247735011208)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨111530760807892347,111530760807892363⟩,⟨(-151951935279713108),(-151951935279713090)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨61092566428597012,61092566428597028⟩,⟨(-118267245152727503),(-118267245152727486)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨28844468427761358,28844468427761378⟩,⟨(-86147081916379455),(-86147081916379436)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨11026542027500926,11026542027500957⟩,⟨(-59771115599816563),(-59771115599816535)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨2613781396702446,2613781396702503⟩,⟨(-39961860272349512),(-39961860272349457)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-572139798373865),(-572139798373772)⟩,⟨(-25756624845377332),(-25756624845377243)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1280457616600685),(-1280457616600568)⟩,⟨(-15688604728780240),(-15688604728780123)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-989484691124012),(-989484691123909)⟩,⟨(-8375847547656318),(-8375847547656216)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-355825605961415),(-355825605961366)⟩,⟨(-2623274774310476),(-2623274774310427)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨300460766682438557,300460766682440257⟩,⟨(-214204838303323707),(-214204838303321971)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 23) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_23 (tableDensity false) (fullFactor false 1 23) density0_contains hk1_0_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4106998856611946),(-4106998856611944)⟩,⟨(-266342252630024228),(-266342252630024226)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_23 1 23 ha1_0_23_contains + def realAnswer : RBox := ⟨296353767725826611,296353767925828313⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_23 +namespace hm1_1_0_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),7⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1095501,1095517⟩,⟨1475064,1475080⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨2674296,2674312⟩,⟨3409010,3409026⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨2950330,2950346⟩,⟨3370532,3370548⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2226811,2226827⟩,⟨2158362,2158378⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1259194,1259210⟩,⟨981243,981260⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨553516,553532⟩,⟨329295,329311⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨193490,193506⟩,⟨83083,83100⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨55106,55122⟩,⟨15653,15669⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨13221,13238⟩,⟨2041,2058⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2790,2806⟩,⟨100,116⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨545,561⟩,⟨(-44),(-28)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨99,116⟩,⟨(-23),(-7)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨14,30⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-11636161097),(-11636161081)⟩,⟨18349102395,18349102411⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-29100442298),(-29100442282)⟩,⟨47834991679,47834991695⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-33703041665),(-33703041649)⟩,⟨59902633080,59902633096⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-27232145590),(-27232145573)⟩,⟨54224116521,54224116538⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-16518616085),(-16518616068)⟩,⟨38809496295,38809496311⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-7516666852),(-7516666836)⟩,⟨22980993884,22980993901⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-2397844220),(-2397844204)⟩,⟨11676417393,11676417410⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-357726567),(-357726551)⟩,⟨5257495072,5257495089⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨156777240,156777256⟩,⟨2160772027,2160772043⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨170641220,170641237⟩,⟨834411330,834411347⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨99558237,99558254⟩,⟨311567858,311567874⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨48100358,48100374⟩,⟨115553735,115553752⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨21818584,21818600⟩,⟨43574839,43574855⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨9795982,9795998⟩,⟨16924202,16924218⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨4208629,4208645⟩,⟨6516838,6516854⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1179120,1179136⟩,⟨1718255,1718271⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-13869322767370),(-13869322767354)⟩,⟨801152016426,801152016442⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-36567236104178),(-36567236104162)⟩,⟨2666075391564,2666075391580⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-47147244502355),(-47147244502338)⟩,⟨4954552227314,4954552227330⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-45214308419046),(-45214308419030)⟩,⟨7124487739163,7124487739179⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-35632770697602),(-35632770697586)⟩,⟨8285234924963,8285234924979⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-24232516326200),(-24232516326184)⟩,⟨7921451241337,7921451241353⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-14669307665188),(-14669307665172)⟩,⟨6351221497258,6351221497274⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-8078184857070),(-8078184857053)⟩,⟨4402132814486,4402132814502⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4124786717259),(-4124786717243)⟩,⟨2734205162137,2734205162154⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1994115162031),(-1994115162015)⟩,⟨1576108319167,1576108319183⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-934719485105),(-934719485089)⟩,⟨869399303565,869399303581⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-435334048174),(-435334048158)⟩,⟨469669500106,469669500122⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-205156083363),(-205156083347)⟩,⟨251420057255,251420057272⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-97586273743),(-97586273727)⟩,⟨132160465116,132160465133⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-43981444615),(-43981444598)⟩,⟨63765082264,63765082280⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-12644377126),(-12644377110)⟩,⟨18973024967,18973024983⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-853744632532763),(-853744632532710)⟩,⟨(-1162893687441643),(-1162893687441590)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-2438335192695073),(-2438335192694930)⟩,⟨(-3153489909503159),(-3153489909503011)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-3633592919021369),(-3633592919021073)⟩,⟨(-4283207364765772),(-4283207364765480)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-4212032586906333),(-4212032586905789)⟩,⟨(-4383593591808274),(-4383593591807730)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-4134122140692693),(-4134122140691799)⟩,⟨(-3666949141650739),(-3666949141649846)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-3579852799903113),(-3579852799901871)⟩,⟨(-2581851140815950),(-2581851140814711)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2809309474231389),(-2809309474230023)⟩,⟨(-1559176797495428),(-1559176797494063)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2033218580504644),(-2033218580503517)⟩,⟨(-821448750700493),(-821448750699365)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1375039499755987),(-1375039499755274)⟩,⟨(-383426304657052),(-383426304656338)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-879441448762692),(-879441448762339)⟩,⟨(-161069888366677),(-161069888366324)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-537677532434718),(-537677532434575)⟩,⟨(-61974035243222),(-61974035243078)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-316880178854136),(-316880178854078)⟩,⟨(-21781049840182),(-21781049840123)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-180900494259444),(-180900494259415)⟩,⟨(-6136363320574),(-6136363320543)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-99253394409726),(-99253394409706)⟩,⟨(-364603635872),(-364603635852)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-49150234552779),(-49150234552762)⟩,⟨1070416067311,1070416067328⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-14808378733495),(-14808378733479)⟩,⟨546465470036,546465470052⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨2316090612786621,2316090612786637⟩,⟨(-144747096415578),(-144747096415562)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨5977264647131422,5977264647131438⟩,⟨(-1999034278903881),(-1999034278903865)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨5418006544324447,5418006544324463⟩,⟨(-7685048430452540),(-7685048430452524)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2989431341500420),(-2989431341500404)⟩,⟨(-18343075978815821),(-18343075978815805)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-17668819198173169),(-17668819198173152)⟩,⟨(-33867910222866708),(-33867910222866692)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-30730786614332547),(-30730786614332531)⟩,⟨(-50283790136904583),(-50283790136904567)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-35745170810687523),(-35745170810687507)⟩,⟨(-60444105650110865),(-60444105650110849)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-33023184544092691),(-33023184544092675)⟩,⟨(-60366018801454231),(-60366018801454215)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-26505174684383429),(-26505174684383411)⟩,⟨(-51990999973171385),(-51990999973171368)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-19568391574531715),(-19568391574531698)⟩,⟨(-39978542955406625),(-39978542955406606)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-13839781068608650),(-13839781068608620)⟩,⟨(-28219637357972408),(-28219637357972378)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-9638905005761545),(-9638905005761496)⟩,⟨(-18695717922690977),(-18695717922690929)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-6635586452308129),(-6635586452308053)⟩,⟨(-11809038021601160),(-11809038021601081)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-4362604369898240),(-4362604369898142)⟩,⟨(-7077884750755454),(-7077884750755354)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-2484549976880693),(-2484549976880605)⟩,⟨(-3754496798335382),(-3754496798335294)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-806750739867784),(-806750739867741)⟩,⟨(-1175136537014905),(-1175136537014863)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-36278086869917489),(-36278086869916051)⟩,⟨(-69672007685617286),(-69672007685615812)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 23) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_23 (tableDensity true) (fullFactor false 1 23) density1_contains hk1_0_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨5370690812492543,5370690812492544⟩,⟨348293714977723988,348293714977723990⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_23 1 23 ha1_0_23_contains + def realAnswer : RBox := ⟨(-30907396157424946),(-30907395957423507)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_23 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_3.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_3.lean new file mode 100644 index 0000000000000000000000000000000000000000..ef94763a865025f4551fb07b53e7f85cf9207272 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_3.lean @@ -0,0 +1,4721 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_0_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-216715),(-216698)⟩,⟨464734,464751⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-496842),(-496826)⟩,⟨1107158,1107174⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-482831),(-482811)⟩,⟨1163643,1163660⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-300048),(-300029)⟩,⟨817623,817639⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-129570),(-129553)⟩,⟨421675,421695⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-39667),(-39650)⟩,⟨166570,166589⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-8421),(-8404)⟩,⟨51961,51980⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1086),(-1065)⟩,⟨13184,13205⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-8),11⟩,⟨2815,2834⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨34,53⟩,⟨523,542⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨5,23⟩,⟨84,101⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨6,25⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-9),16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-6288368090),(-6288368074)⟩,⟨(-85228319),(-85228303)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-16085291697),(-16085291680)⟩,⟨150931628,150931644⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-19520015139),(-19520015122)⟩,⟨1056819737,1056819753⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-17070257888),(-17070257872)⟩,⟨2016801884,2016801900⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-11833298317),(-11833298298)⟩,⟨2338423753,2338423770⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-6785490405),(-6785490389)⟩,⟨1962036148,1962036165⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-3311808339),(-3311808321)⟩,⟨1296483129,1296483145⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1412763579),(-1412763561)⟩,⟨713677477,713677495⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-542213059),(-542213040)⟩,⟨342335975,342335991⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-193474244),(-193474226)⟩,⟨149127918,149127939⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-66586280),(-66586262)⟩,⟨61425881,61425898⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-22980664),(-22980648)⟩,⟨24855345,24855365⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-8238142),(-8238123)⟩,⟨10189208,10189224⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-3118144),(-3118127)⟩,⟨4279422,4279438⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1191264),(-1191248)⟩,⟨1754514,1754530⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-313942),(-313925)⟩,⟨479139,479155⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-2329112401374),(-2329112401358)⟩,⟨(-2774299789106),(-2774299789090)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-6338663834587),(-6338663834571)⟩,⟨(-7285865357838),(-7285865357821)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-8672564574452),(-8672564574436)⟩,⟨(-9311900530407),(-9311900530391)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-9003982599655),(-9003982599637)⟩,⟨(-8780690185864),(-8780690185848)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-7758245814244),(-7758245814226)⟩,⟨(-6699788022525),(-6699788022508)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-5771226321073),(-5771226321057)⟩,⟨(-4302613133318),(-4302613133302)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-3805206232982),(-3805206232966)⟩,⟨(-2385561415519),(-2385561415503)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2272970813454),(-2272970813438)⟩,⟨(-1167455011471),(-1167455011455)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1255920427119),(-1255920427102)⟩,⟨(-514975367263),(-514975367246)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-655896538245),(-655896538226)⟩,⟨(-208790992443),(-208790992426)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-330985759958),(-330985759940)⟩,⟨(-79102575507),(-79102575490)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-164754157854),(-164754157836)⟩,⟨(-28284901842),(-28284901824)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-82042660134),(-82042660117)⟩,⟨(-9529725795),(-9529725779)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-40672499732),(-40672499715)⟩,⟨(-2965936776),(-2965936759)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-18832263346),(-18832263329)⟩,⟨(-811252342),(-811252326)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-5485808413),(-5485808397)⟩,⟨(-152440305),(-152440289)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨399718634033032,399718634033050⟩,⟨(-263073952277420),(-263073952277399)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1053880593066907,1053880593066938⟩,⟨(-745732232191699),(-745732232191669)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1355684284646690,1355684284646742⟩,⟨(-1103189675188625),(-1103189675188572)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1287077376109180,1287077376109265⟩,⟨(-1277164311984351),(-1277164311984262)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨985414697030818,985414697030948⟩,⟨(-1253803335456068),(-1253803335455939)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨626142326348692,626142326348860⟩,⟨(-1074502912813401),(-1074502912813233)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨328730451795890,328730451796077⟩,⟨(-818797446256039),(-818797446255856)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨134509390990517,134509390990668⟩,⟨(-565008186933541),(-565008186933391)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨31515254948692,31515254948792⟩,⟨(-360042285313959),(-360042285313863)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-11595846442824),(-11595846442770)⟩,⟨(-216255665820475),(-216255665820420)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-23309892311975),(-23309892311942)⟩,⟨(-124974933128641),(-124974933128613)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-21831474823763),(-21831474823741)⟩,⟨(-70767156804552),(-70767156804531)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-16375498372304),(-16375498372282)⟩,⟨(-39635944710213),(-39635944710196)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-10713035474371),(-10713035474355)⟩,⟨(-21683831418461),(-21683831418444)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-5908876396440),(-5908876396423)⟩,⟨(-10778399066128),(-10778399066112)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1874123754513),(-1874123754497)⟩,⟨(-3258166962928),(-3258166962912)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨153867067960462,153867067960478⟩,⟨10204760049022440,10204760049022456⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2084873011846843,2084873011846859⟩,⟨28037097327438454,28037097327438470⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨7418712384458425,7418712384458441⟩,⟨39298919251242646,39298919251242664⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨14806189265228843,14806189265228859⟩,⟨42689398919034194,42689398919034210⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨20922143371331971,20922143371331987⟩,⟨39280528743860481,39280528743860498⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨23334324448793942,23334324448793958⟩,⟨31428556034057423,31428556034057439⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨22009181173471705,22009181173471722⟩,⟨22001487735216278,22001487735216294⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨18400818366461281,18400818366461297⟩,⟨13512355394019231,13512355394019247⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨14070820738710728,14070820738710746⟩,⟨7272606948564842,7272606948564858⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨10069598727531001,10069598727531019⟩,⟨3373997484306757,3373997484306775⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨6868766875222589,6868766875222606⟩,⟨1268398770224752,1268398770224770⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨4521280615820088,4521280615820112⟩,⟨296282822783782,296282822783799⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2875073420719929,2875073420719954⟩,⟨(-63656762888300),(-63656762888275)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1732519551413727,1732519551413756⟩,⟨(-141342132250467),(-141342132250439)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨918064441743443,918064441743467⟩,⟨(-108444652684309),(-108444652684280)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨286431095255093,286431095255116⟩,⟨(-38851629235837),(-38851629235816)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨26089189851262168,26089189851262640⟩,⟨38386647188058391,38386647188058806⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 24) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_24 (tableDensity false) (fullFactor false 1 24) density0_contains hk1_0_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨35019580788114933,35019580788114934⟩,⟨(-448467332641068),(-448467332641066)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_24 1 24 ha1_0_24_contains + def realAnswer : RBox := ⟨61108770539377101,61108770739377574⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_24 +namespace hm1_1_0_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-64221),(-64205)⟩,⟨47677,47693⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-147050),(-147034)⟩,⟨115332,115348⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-142757),(-142741)⟩,⟨124910,124926⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-88964),(-88948)⟩,⟨91721,91739⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-39027),(-39010)⟩,⟨50022,50038⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-12538),(-12522)⟩,⟨21030,21046⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3009),(-2993)⟩,⟨6974,6990⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-542),(-525)⟩,⟨1866,1882⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-73),(-57)⟩,⟨413,429⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-12),5⟩,⟨76,92⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨0,16⟩,⟨6,23⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-2),16⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-10),16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1199046466),(-1199046450)⟩,⟨(-760384851),(-760384835)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-3106410193),(-3106410177)⟩,⟨(-1889879918),(-1889879902)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-3842357618),(-3842357602)⟩,⟨(-2162100327),(-2162100311)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3415372378),(-3415372362)⟩,⟨(-1715667234),(-1715667218)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-2387207765),(-2387207749)⟩,⟨(-1016538401),(-1016538384)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1373587543),(-1373587527)⟩,⟨(-449671880),(-449671864)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-675233250),(-675233233)⟩,⟨(-138920688),(-138920672)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-293146944),(-293146928)⟩,⟨(-20073333),(-20073316)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-115894934),(-115894918)⟩,⟨8358281,8358297⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-43008390),(-43008374)⟩,⟨8778631,8778647⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-15441619),(-15441602)⟩,⟨4929325,4929341⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-5519560),(-5519543)⟩,⟨2296215,2296231⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-2014460),(-2014444)⟩,⟨1008279,1008295⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-761837),(-761820)⟩,⟨440847,440865⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-287867),(-287851)⟩,⟨185876,185892⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-75163),(-75147)⟩,⟨51565,51581⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-69828883178),(-69828883161)⟩,⟨(-1208889775985),(-1208889775969)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-231252971003),(-231252970987)⟩,⟨(-3172418645933),(-3172418645917)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-425708659035),(-425708659019)⟩,⟨(-4052611096593),(-4052611096576)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-603787079385),(-603787079369)⟩,⟨(-3833911039389),(-3833911039373)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-689831498317),(-689831498301)⟩,⟨(-2968611582082),(-2968611582066)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-645708019289),(-645708019272)⟩,⟨(-1976463315870),(-1976463315854)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-505372601679),(-505372601663)⟩,⟨(-1167874699821),(-1167874699803)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-341171877281),(-341171877264)⟩,⟨(-626366684518),(-626366684502)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-206111106879),(-206111106862)⟩,⟨(-311068182419),(-311068182403)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-115520304154),(-115520304138)⟩,⟨(-146214001305),(-146214001289)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-62004853285),(-62004853269)⟩,⟨(-66685812930),(-66685812914)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-32657984772),(-32657984756)⟩,⟨(-30278621257),(-30278621241)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-17099098363),(-17099098347)⟩,⟨(-13955266370),(-13955266354)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-8829484701),(-8829484685)⟩,⟨(-6520298080),(-6520298064)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4207169202),(-4207169186)⟩,⟨(-2901974545),(-2901974529)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1243787613),(-1243787596)⟩,⟨(-828913138),(-828913122)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨126731243392157,126731243392176⟩,⟨(-93040011860214),(-93040011860192)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨342375063774053,342375063774083⟩,⟨(-264721040807943),(-264721040807914)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨461592183306571,461592183306615⟩,⟨(-391550947165775),(-391550947165728)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨467305544001366,467305544001438⟩,⟨(-448949286456774),(-448949286456702)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨385473478780943,385473478781049⟩,⟨(-434479549773961),(-434479549773853)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨266902683455533,266902683455677⟩,⟨(-369940933929732),(-369940933929589)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨158153757847677,158153757847829⟩,⟨(-284821478869541),(-284821478869390)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨81624416385140,81624416385268⟩,⟨(-201910561059952),(-201910561059829)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨37288590476487,37288590476569⟩,⟨(-133628705951038),(-133628705950952)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨15328595438358,15328595438409⟩,⟨(-83629018167361),(-83629018167312)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨5775669894409,5775669894436⟩,⟨(-50068994884012),(-50068994883984)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1991149878450,1991149878471⟩,⟨(-28943948892752),(-28943948892730)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨551813969388,551813969406⟩,⟨(-16248641849635),(-16248641849618)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨32546983908,32546983924⟩,⟨(-8796102362087),(-8796102362070)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-93923355912),(-93923355896)⟩,⟨(-4315138061126),(-4315138061110)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-47743782889),(-47743782873)⟩,⟨(-1293838961119),(-1293838961103)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨18927240691848,18927240691864⟩,⟨302935086520781,302935086520797⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨260518411647247,260518411647263⟩,⟨779396088966756,779396088966772⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨995279685469112,995279685469128⟩,⟨702498066883040,702498066883056⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2353930468951626,2353930468951642⟩,⟨(-382452708062184),(-382452708062168)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨4295495175780185,4295495175780201⟩,⟨(-2240045653297831),(-2240045653297815)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨6289494704529716,6289494704529732⟩,⟨(-3843696916364139),(-3843696916364123)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨7442984727943595,7442984727943611⟩,⟨(-4402027649351694),(-4402027649351678)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨7308727457267588,7308727457267604⟩,⟨(-3998702757174739),(-3998702757174723)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨6184927944282187,6184927944282203⟩,⟨(-3153368273571115),(-3153368273571099)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨4672802975493431,4672802975493447⟩,⟨(-2287276336798553),(-2287276336798537)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨3242934026732027,3242934026732043⟩,⟨(-1590376649174253),(-1590376649174235)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨2115277643186676,2115277643186697⟩,⟨(-1090472322794661),(-1090472322794640)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1318206125007720,1318206125007745⟩,⟨(-740638670266066),(-740638670266040)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨781629442342059,781629442342084⟩,⟨(-481742814856936),(-481742814856911)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨411525351155677,411525351155700⟩,⟨(-272321209729589),(-272321209729563)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨128311235861437,128311235861455⟩,⟨(-88087538203946),(-88087538203924)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨8361330145924187,8361330145924623⟩,⟨(-4270385363827664),(-4270385363827279)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 24) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_24 (tableDensity true) (fullFactor false 1 24) density1_contains hk1_0_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-45794836415227222),(-45794836415227220)⟩,⟨586457281146010,586457281146011⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_24 1 24 ha1_0_24_contains + def realAnswer : RBox := ⟨(-37433506369303035),(-37433506169302597)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_24 +namespace hm1_0_0_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-19429),(-19413)⟩,⟨(-9065),(-9049)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-45849),(-45832)⟩,⟨(-20582),(-20566)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-47313),(-47296)⟩,⟨(-19641),(-19621)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-32349),(-32329)⟩,⟨(-11880),(-11862)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16097),(-16079)⟩,⟨(-4956),(-4935)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-6088),(-6070)⟩,⟨(-1460),(-1439)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1811),(-1790)⟩,⟨(-304),(-284)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-439),(-422)⟩,⟨(-45),(-26)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-96),(-78)⟩,⟨(-9),13⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-24),(-5)⟩,⟨(-6),16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨5347833,5347849⟩,⟨(-394485994),(-394485978)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-9381809),(-9381792)⟩,⟨(-1002819515),(-1002819499)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-64991591),(-64991575)⟩,⟨(-1202051883),(-1202051864)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-121821725),(-121821707)⟩,⟨(-1032245706),(-1032245689)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-137960513),(-137960497)⟩,⟨(-698809808),(-698809792)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-112493568),(-112493550)⟩,⟨(-389385026),(-389385008)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-71927864),(-71927848)⟩,⟨(-183882033),(-183882015)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-38180935),(-38180919)⟩,⟨(-75636253),(-75636235)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-17619511),(-17619493)⟩,⟨(-27925445),(-27925426)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-7376618),(-7376601)⟩,⟨(-9575907),(-9575891)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2921764),(-2921745)⟩,⟨(-3168837),(-3168820)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1139495),(-1139478)⟩,⟨(-1053977),(-1053959)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-452126),(-452110)⟩,⟨(-365653),(-365633)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-184913),(-184897)⟩,⟨(-134759),(-134740)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-74404),(-74387)⟩,⟨(-50524),(-50507)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-20129),(-20113)⟩,⟨(-13190),(-13172)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨232143346185,232143346201⟩,⟨(-194890962189),(-194890962173)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨606809431199,606809431216⟩,⟨(-527904122620),(-527904122604)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨768410489333,768410489349⟩,⟨(-715594304796),(-715594304780)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨714791586881,714791586899⟩,⟨(-732861277258),(-732861277242)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨535879769591,535879769607⟩,⟨(-620402263022),(-620402263005)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨336941291518,336941291535⟩,⟨(-451810845676),(-451810845659)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨182365973850,182365973867⟩,⟨(-290776889871),(-290776889854)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨86927155725,86927155742⟩,⟨(-169161732062),(-169161732045)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨37296820288,37296820304⟩,⟨(-90909540989),(-90909540971)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨14703164804,14703164821⟩,⟨(-46160503985),(-46160503968)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨5420416510,5420416526⟩,⟨(-22665579683),(-22665579664)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1889673528,1889673545⟩,⟨(-10999423404),(-10999423388)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨622687768,622687784⟩,⟨(-5357113359),(-5357113343)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨190353692,190353708⟩,⟨(-2608751748),(-2608751732)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨51406694,51406711⟩,⟨(-1192864965),(-1192864948)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨9594288,9594304⟩,⟨(-345241288),(-345241272)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨27522709441952,27522709441968⟩,⟨41818678884713,41818678884730⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨77723280630881,77723280630900⟩,⟨109845459670357,109845459670375⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨114123481012770,114123481012793⟩,⟨140262569168701,140262569168718⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨130684157217851,130684157217877⟩,⟨131730094696765,131730094696785⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨126499355354591,126499355354618⟩,⟨99456562609864,99456562609892⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨106600412080023,106600412080055⟩,⟨62150016961788,62150016961820⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨79698428947688,79698428947720⟩,⟨32020118616194,32020118616227⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨53869565912001,53869565912030⟩,⟨12839398779910,12839398779941⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨33593762605701,33593762605726⟩,⟨2949325024105,2949325024128⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨19744036292703,19744036292723⟩,⟨(-1053918786964),(-1053918786941)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨11173178727188,11173178727208⟩,⟨(-2081606779891),(-2081606779874)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨6205608490318,6205608490336⟩,⟨(-1913361589428),(-1913361589411)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3417768023726,3417768023742⟩,⟨(-1411648470038),(-1411648470020)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1844808206743,1844808206759⟩,⟨(-911323335933),(-911323335917)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨908434195084,908434195100⟩,⟨(-497995701302),(-497995701286)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨273285834982,273285835000⟩,⟨(-157195484924),(-157195484907)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1281349441738330),(-1281349441738314)⟩,⟨19314991002720,19314991002736⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3509412247618559),(-3509412247618543)⟩,⟨260840183624274,260840183624291⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-4888690194682156),(-4888690194682140)⟩,⟨922425173718498,922425173718514⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-5262523403026184),(-5262523403026168)⟩,⟨1824415505365694,1824415505365711⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-4786139107711550),(-4786139107711534)⟩,⟨2548238057682609,2548238057682625⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-3776587275112203),(-3776587275112186)⟩,⟨2802874178047496,2802874178047512⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-2602685783789606),(-2602685783789590)⟩,⟨2602527690311728,2602527690311744⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1571627461908201),(-1571627461908185)⟩,⟨2139194936546402,2139194936546418⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-831140275022115),(-831140275022099)⟩,⟨1607152517669435,1607152517669451⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-378886234625182),(-378886234625166)⟩,⟨1129967586902799,1129967586902815⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-140072401258616),(-140072401258598)⟩,⟨757786894023873,757786894023889⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-32241909106810),(-32241909106793)⟩,⟨491084387254943,491084387254959⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6799221371781,6799221371801⟩,⟨308095580788564,308095580788581⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨14977945520280,14977945520297⟩,⟨183673371671312,183673371671328⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨11409840962513,11409840962531⟩,⟨96602854016789,96602854016805⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨4072420723652,4072420723670⟩,⟨30023955624163,30023955624179⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-4704448360375703),(-4704448360375418)⟩,⟨3057562395904246,3057562395904591⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 25) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_25 (tableDensity false) (fullFactor false 1 25) density0_contains hk1_0_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨47002139241058,47002139241059⟩,⟨4416981328593884,4416981328593885⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_25 1 25 ha1_0_25_contains + def realAnswer : RBox := ⟨(-4657446321134645),(-4657446121134359)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_25 +namespace hm1_1_0_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-2001),(-1985)⟩,⟨(-2691),(-2675)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-4784),(-4768)⟩,⟨(-6096),(-6080)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-5086),(-5070)⟩,⟨(-5812),(-5795)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-3637),(-3621)⟩,⟨(-3528),(-3512)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1916),(-1900)⟩,⟨(-1499),(-1483)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-776),(-759)⟩,⟨(-466),(-450)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-249),(-233)⟩,⟨(-113),(-97)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-69),(-53)⟩,⟨(-26),(-9)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-21),(-5)⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),13⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨47701133,47701149⟩,⟨(-75219225),(-75219209)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨117826591,117826607⟩,⟨(-193662903),(-193662887)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨133156571,133156587⟩,⟨(-236608176),(-236608160)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨103770005,103770021⟩,⟨(-206524422),(-206524405)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨60057905,60057921⟩,⟨(-140974066),(-140974050)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨25826817,25826834⟩,⟨(-78822481),(-78822465)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨7727222,7727238⟩,⟨(-37489789),(-37489773)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1081381,1081399⟩,⟨(-15693283),(-15693267)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-427839),(-427823)⟩,⟨(-5968238),(-5968221)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-433615),(-433599)⟩,⟨(-2128401),(-2128385)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-234336),(-234320)⟩,⟨(-734783),(-734767)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-105251),(-105235)⟩,⟨(-253133),(-253117)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-44745),(-44728)⟩,⟨(-89417),(-89400)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-19056),(-19039)⟩,⟨(-32931),(-32915)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-7890),(-7874)⟩,⟨(-12214),(-12198)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2172),(-2156)⟩,⟨(-3164),(-3147)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨101155521773,101155521789⟩,⟨(-5842876449),(-5842876433)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨264217711734,264217711750⟩,⟨(-19256408365),(-19256408349)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨334418052116,334418052132⟩,⟨(-35115327959),(-35115327943)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨312096256500,312096256516⟩,⟨(-49124078868),(-49124078852)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨237433733777,237433733793⟩,⟨(-55139978703),(-55139978685)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨154763737564,154763737580⟩,⟨(-50531014080),(-50531014064)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨89264232595,89264232612⟩,⟨(-38606549048),(-38606549032)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨46627410586,46627410603⟩,⟨(-25385247108),(-25385247090)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨22522102611,22522102627⟩,⟨(-14916648451),(-14916648435)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨10292628976,10292628992⟩,⟨(-8128857553),(-8128857537)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4567530575,4567530591⟩,⟨(-4245493528),(-4245493511)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2021812024,2021812040⟩,⟨(-2180106881),(-2180106865)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨911333301,911333317⟩,⟨(-1116431193),(-1116431177)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨418239966,418239983⟩,⟨(-566302610),(-566302594)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨183819720,183819736⟩,⟨(-266484196),(-266484180)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨52166552,52166568⟩,⟨(-78275800),(-78275784)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨9733810648153,9733810648169⟩,⟨13258632847994,13258632848010⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨27590268504394,27590268504410⟩,⟨35684960195112,35684960195130⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨40505562757027,40505562757044⟩,⟨47755365011359,47755365011379⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨45938827566009,45938827566030⟩,⟨47824299674961,47824299674981⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨43836461896545,43836461896568⟩,⟨38901305249406,38901305249433⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨36701413135858,36701413135886⟩,⟨26488521673122,26488521673151⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨27722456682380,27722456682410⟩,⟨15401011672295,15401011672323⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨19249597772695,19249597772723⟩,⟨7786584595500,7786584595527⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨12467308835898,12467308835922⟩,⟨3481432154650,3481432154673⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨7634750261330,7634750261349⟩,⟨1400482280410,1400482280428⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨4476120181675,4476120181692⟩,⟨516749798684,516749798701⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨2538069039804,2538069039820⟩,⟨174747707838,174747707854⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1401114996100,1401114996116⟩,⟨47637923495,47637923512⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨748360848923,748360848940⟩,⟨2789025532,2789025548⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨363694578668,363694578684⟩,⟨(-7911658204),(-7911658188)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨108523645956,108523645973⟩,⟨(-4004445321),(-4004445305)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-38037759912344),(-38037759912328)⟩,⟨2375943142146,2375943142162⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-97563192062538),(-97563192062522)⟩,⟨32593317083065,32593317083081⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-87442769639622),(-87442769639606)⟩,⟨123741962242639,123741962242655⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨46971755006700,46971755006716⟩,⟨289994841904083,289994841904099⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨272636015138563,272636015138579⟩,⟨523016449898628,523016449898644⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨461534220514162,461534220514178⟩,⟨755236325056972,755236325056988⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨520438338545131,520438338545147⟩,⟨879875934826238,879875934826254⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨464837982505512,464837982505528⟩,⟨849519448038793,849519448038809⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨360164936270969,360164936270985⟩,⟨706356322596413,706356322596429⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨256663657716661,256663657716677⟩,⟨524336637077549,524336637077565⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨175449314456678,175449314456694⟩,⟨357771456328154,357771456328170⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨118435122381602,118435122381618⟩,⟨229758455421848,229758455421864⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨79361526172424,79361526172442⟩,⟨141263079273710,141263079273726⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨51069181538229,51069181538246⟩,⟨82865272748573,82865272748589⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨28654153756250,28654153756266⟩,⟨43302586508855,43302586508871⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨9233384875092,9233384875109⟩,⟨13449694254548,13449694254564⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨484167275126509,484167275126782⟩,⟨965643139298499,965643139298835⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 25) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_25 (tableDensity true) (fullFactor false 1 25) density1_contains hk1_0_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-61464335930615),(-61464335930614)⟩,⟨(-5776052506622773),(-5776052506622771)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_25 1 25 ha1_0_25_contains + def realAnswer : RBox := ⟨422702839195894,422703039196168⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_25 +namespace hm1_0_0_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨356,372⟩,⟨(-789),(-773)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨812,828⟩,⟨(-1832),(-1815)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨760,777⟩,⟨(-1859),(-1842)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨443,461⟩,⟨(-1240),(-1221)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨172,189⟩,⟨(-601),(-582)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨43,59⟩,⟨(-223),(-206)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨2,19⟩,⟨(-69),(-50)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-11),16⟩,⟨(-22),(-5)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨23795348,23795365⟩,⟨322649,322665⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨60115504,60115520⟩,⟨(-560744),(-560727)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨71177336,71177354⟩,⟨(-3843165),(-3843149)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨60021826,60021842⟩,⟨(-7075708),(-7075690)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨39682977,39682993⟩,⟨(-7826711),(-7826695)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨21487136,21487155⟩,⟨(-6202274),(-6202256)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨9818001,9818020⟩,⟨(-3837419),(-3837403)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨3894092,3894110⟩,⟨(-1964312),(-1964296)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1383082,1383100⟩,⟨(-872090),(-872072)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨455771,455791⟩,⟨(-350903),(-350887)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨145013,145031⟩,⟨(-133655),(-133638)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨46472,46493⟩,⟨(-50243),(-50224)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨15596,15614⟩,⟨(-19300),(-19282)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5591,5609⟩,⟨(-7691),(-7673)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨2052,2069⟩,⟨(-3042),(-3025)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨522,539⟩,⟨(-822),(-806)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨15680496853,15680496869⟩,⟨18677810276,18677810292⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨42274734750,42274734767⟩,⟨48595046903,48595046919⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨56775087864,56775087880⟩,⟨60970511214,60970511230⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨57356777910,57356777928⟩,⟨55950763191,55950763208⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨47705005668,47705005684⟩,⟨41214905431,41214905448⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨34011901774,34011901790⟩,⟨25372409161,25372409177⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨21366417350,21366417366⟩,⟨13405618249,13405618266⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨12106085502,12106085518⟩,⟨6223915751,6223915767⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨6327783778,6327783795⟩,⟨2597475391,2597475407⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨3123920302,3123920319⟩,⟨995642603,995642619⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1492504857,1492504875⟩,⟨357162164,357162181⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨706138957,706138973⟩,⟨121396165,121396184⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨336358779,336358798⟩,⟨39123754,39123771⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨160893844,160893861⟩,⟨11747214,11747230⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨72652377,72652393⟩,⟨3132220,3132237⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨20891598,20891614⟩,⟨580614,580630⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-4206811148769),(-4206811148752)⟩,⟨2768670763016,2768670763032⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-11008816960854),(-11008816960838)⟩,⟨7789098048504,7789098048520⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-13953874660347),(-13953874660330)⟩,⟨11351928399303,11351928399320⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-12963963435061),(-12963963435045)⟩,⟨12857945924763,12857945924780⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-9652132942282),(-9652132942266)⟩,⟨12272209087392,12272209087409⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-5931817945697),(-5931817945680)⟩,⟨10169246175225,10169246175246⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2999070728502),(-2999070728482)⟩,⟨7459406267893,7459406267911⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1178470611842),(-1178470611825)⟩,⟨4938729620391,4938729620412⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-265401243720),(-265401243703)⟩,⟨3014029709628,3014029709645⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨92106065764,92106065782⟩,⟨1733355078875,1733355078892⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨178746824646,178746824662⟩,⟨960532048925,960532048941⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨161246185498,161246185517⟩,⟨523257375140,523257375157⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨117012824410,117012824426⟩,⟨283381034832,283381034848⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨74542466136,74542466152⟩,⟨150916848870,150916848887⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨40356616077,40356616093⟩,⟨73620904200,73620904216⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨12677941313,12677941329⟩,⟨22040821376,22040821392⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2331363883114),(-2331363883098)⟩,⟨(-154703138196501),(-154703138196485)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-31378832157378),(-31378832157362)⟩,⟨(-422379860745263),(-422379860745247)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-110281464582405),(-110281464582389)⟩,⟨(-584754084163737),(-584754084163721)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-216159757759645),(-216159757759629)⟩,⟨(-623790435834169),(-623790435834153)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-298432807279870),(-298432807279854)⟩,⟨(-560745826110705),(-560745826110689)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-323732865403565),(-323732865403549)⟩,⟨(-436364479651211),(-436364479651195)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-295912563647144),(-295912563647127)⟩,⟨(-296051930887381),(-296051930887365)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-239134000061386),(-239134000061370)⟩,⟨(-175770395433775),(-175770395433759)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-176511453120782),(-176511453120766)⟩,⟨(-91334828331024),(-91334828331008)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-121926317526629),(-121926317526613)⟩,⟨(-40911949111005),(-40911949110989)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-80388092515431),(-80388092515415)⟩,⟨(-14873906059553),(-14873906059536)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-51289104302338),(-51289104302322)⟩,⟨(-3373708101590),(-3373708101574)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-31746362144606),(-31746362144590)⟩,⟨698299084898,698299084916⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-18723365292002),(-18723365291985)⟩,⟨1526168410854,1526168410870⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-9774050156495),(-9774050156479)⟩,⟨1154300419624,1154300419640⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3026094235788),(-3026094235772)⟩,⟨410452433599,410452433616⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-345322059186858),(-345322059186520)⟩,⟨(-554103741560130),(-554103741559858)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 26) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_26 (tableDensity false) (fullFactor false 1 26) density0_contains hk1_0_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-535347276983672),(-535347276983670)⟩,⟨4735860653366,4735860653367⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_26 1 26 ha1_0_26_contains + def realAnswer : RBox := ⟨(-880669436170530),(-880669236170190)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_26 +namespace hm1_1_0_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨101,117⟩,⟨(-89),(-73)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨235,252⟩,⟨(-199),(-183)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨218,235⟩,⟨(-208),(-192)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨125,142⟩,⟨(-146),(-130)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨47,63⟩,⟨(-77),(-61)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨7,23⟩,⟨(-36),(-19)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2),16⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨4537200,4537216⟩,⟨2877334,2877350⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨11609237,11609253⟩,⟨7063532,7063548⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨14009961,14009977⟩,⟨7885411,7885429⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨12008469,12008485⟩,⟨6035220,6035236⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨8005343,8005359⟩,⟨3411985,3412001⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨4349553,4349570⟩,⟨1426410,1426426⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨2001614,2001630⟩,⟨413312,413330⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨807895,807911⟩,⟨56011,56027⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨295552,295569⟩,⟨(-21066),(-21050)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨101284,101300⟩,⟨(-20606),(-20590)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨33613,33632⟩,⟨(-10721),(-10705)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨11155,11172⟩,⟨(-4646),(-4630)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨3809,3826⟩,⟨(-1918),(-1902)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1360,1376⟩,⟨(-800),(-784)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨492,508⟩,⟨(-327),(-311)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨122,138⟩,⟨(-95),(-79)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨470094501,470094517⟩,⟨8138780811,8138780827⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1541813169,1541813185⟩,⟨21159327616,21159327632⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2785175537,2785175553⟩,⟨26534816734,26534816750⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3843092910,3843092926⟩,⟨24429292964,24429292980⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨4238097748,4238097764⟩,⟨18260477910,18260477926⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3802468875,3802468893⟩,⟨11652933522,11652933538⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2835962786,2835962803⟩,⟨6560677359,6560677375⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1816280996,1816281012⟩,⟨3337698510,3337698526⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1038092500,1038092516⟩,⟨1568039099,1568039115⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨550040926,550040942⟩,⟨696719021,696719040⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨279525969,279525986⟩,⟨300829699,300829715⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨139943569,139943585⟩,⟨129817145,129817161⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨70092498,70092515⟩,⟨57226486,57226503⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨34925006,34925022⟩,⟨25796350,25796366⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨16230150,16230166⟩,⟨11195929,11195945⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4736690,4736706⟩,⟨3156759,3156775⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1333768899998),(-1333768899982)⟩,⟨979180652434,979180652450⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-3576318133405),(-3576318133389)⟩,⟨2764975137258,2764975137274⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-4750679113745),(-4750679113729)⟩,⟨4029126215810,4029126215827⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-4706182508561),(-4706182508544)⟩,⟨4519964386371,4519964386389⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-3774933611521),(-3774933611502)⟩,⟨4252821854268,4252821854284⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-2527789795619),(-2527789795603)⟩,⟨3501158587434,3501158587450⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-1442115267455),(-1442115267436)⟩,⟨2594609053881,2594609053900⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-714260487915),(-714260487897)⟩,⟨1764685645870,1764685645887⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-312552666183),(-312552666167)⟩,⟨1118483159914,1118483159930⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-123036940408),(-123036940391)⟩,⟨670217639475,670217639491⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-44456885517),(-44456885501)⟩,⟨384783020616,384783020632⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-14746767251),(-14746767235)⟩,⟨214006734116,214006734132⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-3954457176),(-3954457160)⟩,⟨116173031438,116173031454⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-229795741),(-229795725)⟩,⟨61221384556,61221384572⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨640810746,640810762⟩,⟨29474565942,29474565958⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨322949610,322949626⟩,⟨8752565988,8752566005⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-286781745639),(-286781745623)⟩,⟨(-4592477545888),(-4592477545872)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3920902919455),(-3920902919439)⟩,⟨(-11743059171539),(-11743059171523)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-14793046203680),(-14793046203664)⟩,⟨(-10465771910410),(-10465771910394)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-34352434727893),(-34352434727876)⟩,⟨5547037860764,5547037860780⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-61233652979675),(-61233652979659)⟩,⟨31906710143825,31906710143841⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-87201665179601),(-87201665179585)⟩,⟨53288491082645,53288491082661⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-100016653380198),(-100016653380182)⟩,⟨59164656861062,59164656861078⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-94947303288687),(-94947303288671)⟩,⟨51959125270757,51959125270773⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-77569531933589),(-77569531933573)⟩,⟨39555447376780,39555447376796⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-56574482167623),(-56574482167607)⟩,⟨27694133297411,27694133297428⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-37953302905345),(-37953302905329)⟩,⟨18611428072901,18611428072917⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-23996612698422),(-23996612698406)⟩,⟨12368605072772,12368605072788⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-14556131741135),(-14556131741119)⟩,⟨8176842264827,8176842264843⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-8447221385544),(-8447221385528)⟩,⟨5205617007501,5205617007518⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-4381258696417),(-4381258696401)⟩,⟨2899088829062,2899088829078⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1355585543166),(-1355585543150)⟩,⟨930623890515,930623890531⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-107481184119231),(-107481184118902)⟩,⟨52939837988687,52939837988951⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 26) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_26 (tableDensity true) (fullFactor false 1 26) density1_contains hk1_0_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨700069516055569,700069516055571⟩,⟨(-6193048546711),(-6193048546709)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_26 1 26 ha1_0_26_contains + def realAnswer : RBox := ⟨592588231936338,592588431936669⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_26 +namespace hm1_0_0_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨23,39⟩,⟨7,23⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨61,77⟩,⟨24,41⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨61,78⟩,⟨18,37⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨37,55⟩,⟨7,25⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨11,30⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨0,16⟩,⟨(-8),16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-18754),(-18738)⟩,⟨1382166,1382182⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨32265,32281⟩,⟨3470261,3470278⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨218836,218853⟩,⟨4058617,4058633⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨395759,395775⟩,⟨3360937,3360954⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨427591,427608⟩,⟨2170117,2170133⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨329313,329329⟩,⟨1141876,1141898⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨197159,197175⟩,⟨504838,504856⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨97316,97335⟩,⟨193075,193092⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨41561,41579⟩,⟨65964,65981⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨16067,16085⟩,⟨20884,20901⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨5879,5896⟩,⟨6383,6402⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2125,2142⟩,⟨1965,1982⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨786,802⟩,⟨635,651⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨300,319⟩,⟨214,232⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨111,127⟩,⟨73,89⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨25,41⟩,⟨13,30⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1447123091),(-1447123075)⟩,⟨1214892158,1214892174⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-3747512723),(-3747512707)⟩,⟨3260004168,3260004184⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-4658658820),(-4658658804)⟩,⟨4337737650,4337737667⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-4217463372),(-4217463355)⟩,⟨4322813290,4322813306⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-3052564208),(-3052564192)⟩,⟨3532467552,3532467568⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1839914341),(-1839914324)⟩,⟨2465663450,2465663468⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-948992100),(-948992083)⟩,⟨1511946923,1511946941⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-429148631),(-429148615)⟩,⟨834337134,834337151⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-174208057),(-174208040)⟩,⟨424161734,424161751⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-64928089),(-64928071)⟩,⟨203594672,203594691⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-22663764),(-22663748)⟩,⟨94645273,94645289⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-7510219),(-7510202)⟩,⟨43655599,43655617⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-2367205),(-2367189)⟩,⟨20337535,20337551⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-698123),(-698107)⟩,⟨9555720,9555740⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-183790),(-183774)⟩,⟨4261087,4261103⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-33842),(-33826)⟩,⟨1217386,1217402⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-268201474099),(-268201474083)⟩,⟨(-407516727695),(-407516727679)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-751681703705),(-751681703689)⟩,⟨(-1062453548171),(-1062453548155)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-1087369158105),(-1087369158089)⟩,⟨(-1336781935597),(-1336781935581)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1218247858385),(-1218247858367)⟩,⟨(-1228587115859),(-1228587115843)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1146504175536),(-1146504175520)⟩,⟨(-902051846821),(-902051846805)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-934200604656),(-934200604639)⟩,⟨(-545199761261),(-545199761245)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-672330621590),(-672330621573)⟩,⟨(-270504285887),(-270504285869)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-436026586195),(-436026586178)⟩,⟨(-104164012243),(-104164012227)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-260413235432),(-260413235415)⟩,⟨(-22998772586),(-22998772568)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-146543037463),(-146543037446)⟩,⟨7751551796,7751551813⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-79519046481),(-79519046463)⟩,⟨14780942253,14780942270⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-42488130065),(-42488130048)⟩,⟨13085887768,13085887784⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-22626466210),(-22626466194)⟩,⟨9340242426,9340242442⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-11888812126),(-11888812110)⟩,⟨5871502650,5871502666⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-5745399120),(-5745399103)⟩,⟨3149309009,3149309025⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1711781075),(-1711781059)⟩,⟨984616690,984616707⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨17986238135191,17986238135207⟩,⟨(-270978767616),(-270978767600)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨48953350121637,48953350121653⟩,⟨(-3635041452627),(-3635041452611)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨67354369172633,67354369172649⟩,⟨(-12696546086342),(-12696546086326)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨71202784270177,71202784270194⟩,⟨(-24662635931021),(-24662635931005)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨63264844215627,63264844215643⟩,⟨(-33656488080142),(-33656488080125)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨48553097782744,48553097782760⟩,⟨(-36007064761209),(-36007064761193)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨32428991091826,32428991091842⟩,⟨(-32400442488812),(-32400442488796)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨18930510828951,18930510828968⟩,⟨(-25742632421180),(-25742632421164)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨9665388005356,9665388005372⟩,⟨(-18668513509451),(-18668513509435)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨4254139158977,4254139158993⟩,⟨(-12669208826034),(-12669208826018)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1520954077050,1520954077066⟩,⟨(-8212125842314),(-8212125842298)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨339945774833,339945774849⟩,⟨(-5158356401673),(-5158356401657)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-69061234904),(-69061234887)⟩,⟨(-3150049312459),(-3150049312443)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-149749438775),(-149749438759)⟩,⟨(-1837952160600),(-1837952160584)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-112452432178),(-112452432162)⟩,⟨(-952291499659),(-952291499643)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-39836644246),(-39836644230)⟩,⟨(-293701864193),(-293701864177)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨62829567095133,62829567095400⟩,⟨(-37636170948315),(-37636170947976)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 27) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_27 (tableDensity false) (fullFactor false 1 27) density0_contains hk1_0_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-459443650423),(-459443650422)⟩,⟨(-62449696101934),(-62449696101932)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_27 1 27 ha1_0_27_contains + def realAnswer : RBox := ⟨62370023444710,62370223444978⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_27 +namespace hm1_1_0_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨0,16⟩,⟨(-10),16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-167142),(-167126)⟩,⟨263539,263555⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-407780),(-407764)⟩,⟨670144,670160⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-449690),(-449674)⟩,⟨798839,798855⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-338028),(-338012)⟩,⟨672398,672414⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-186681),(-186665)⟩,⟨437774,437790⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-75877),(-75861)⟩,⟨231136,231153⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-21300),(-21282)⟩,⟨102910,102926⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-2801),(-2785)⟩,⟨40048,40064⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨991,1007⟩,⟨14089,14105⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨934,951⟩,⟨4633,4649⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨463,480⟩,⟨1474,1490⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨189,205⟩,⟨466,482⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨71,87⟩,⟨149,165⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨23,39⟩,⟨47,63⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨3,20⟩,⟨10,26⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨0,16⟩,⟨0,16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-630578136),(-630578120)⟩,⟨36421123,36421139⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1631748517),(-1631748501)⟩,⟨118877486,118877502⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-2027481926),(-2027481910)⟩,⟨212727153,212727169⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1841416225),(-1841416208)⟩,⟨289525033,289525049⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1352400870),(-1352400854)⟩,⟨313688829,313688847⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-844947719),(-844947703)⟩,⟨275551030,275551049⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-464357812),(-464357795)⟩,⟨200619530,200619547⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-230085345),(-230085329)⟩,⟨125147166,125147182⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-105133797),(-105133781)⟩,⟨69572663,69572679⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-45417787),(-45417770)⟩,⟨35842444,35842461⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-19080699),(-19080681)⟩,⟨17723533,17723549⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-8027001),(-8026985)⟩,⟨8650822,8650838⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-3460521),(-3460505)⟩,⟨4237740,4237756⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1532185),(-1532169)⟩,⟨2074153,2074169⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-656670),(-656654)⟩,⟨951881,951897⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-183961),(-183945)⟩,⟨276010,276026⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-94853305570),(-94853305554)⟩,⟨(-129202865382),(-129202865366)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-266831621397),(-266831621381)⟩,⟨(-345142017545),(-345142017529)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-385940013121),(-385940013104)⟩,⟨(-455094882598),(-455094882582)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-428258039598),(-428258039582)⟩,⟨(-445968611285),(-445968611269)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-397317183871),(-397317183855)⟩,⟨(-352754736830),(-352754736813)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-321634252665),(-321634252649)⟩,⟨(-232298045934),(-232298045917)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-233849418889),(-233849418873)⟩,⟨(-130039290826),(-130039290810)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-155789801695),(-155789801679)⟩,⟨(-63094549623),(-63094549606)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-96630196694),(-96630196678)⟩,⟨(-27021824829),(-27021824813)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-56658224247),(-56658224231)⟩,⟨(-10409238705),(-10409238689)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-31853287779),(-31853287762)⟩,⟨(-3683167037),(-3683167021)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-17376916748),(-17376916731)⟩,⟨(-1198402956),(-1198402940)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-9275869010),(-9275868994)⟩,⟨(-316109661),(-316109645)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-4822913375),(-4822913359)⟩,⟨(-18231508),(-18231490)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-2300220093),(-2300220077)⟩,⟨49980809,49980825⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-679760945),(-679760929)⟩,⟨25080540,25080556⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨533935535911,533935535927⟩,⟨(-33333169414),(-33333169398)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1361090145479,1361090145495⟩,⟨(-454207110113),(-454207110097)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1206230031851,1206230031867⟩,⟨(-1702981418596),(-1702981418580)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-630802886203),(-630802886187)⟩,⟨(-3918666506882),(-3918666506866)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-3595805581400),(-3595805581384)⟩,⟨(-6903679505162),(-6903679505146)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-5924894300036),(-5924894300020)⟩,⟨(-9695816870019),(-9695816870003)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-6477014845089),(-6477014845072)⟩,⟨(-10948199123335),(-10948199123319)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-5592972850047),(-5592972850031)⟩,⟨(-10219099162315),(-10219099162299)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-4183427269318),(-4183427269302)⟩,⟨(-8203129432979),(-8203129432963)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-2877608787002),(-2877608786986)⟩,⟨(-5878297154969),(-5878297154953)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1901196370778),(-1901196370762)⟩,⟨(-3877150814935),(-3877150814919)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1243879173517),(-1243879173501)⟩,⟨(-2413490624627),(-2413490624611)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-811290018676),(-811290018660)⟩,⟨(-1444369046113),(-1444369046097)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-510973189493),(-510973189477)⟩,⟨(-829216182757),(-829216182741)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-282453003575),(-282453003559)⟩,⟨(-426869077221),(-426869077205)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-90322754225),(-90322754209)⟩,⟨(-131568269161),(-131568269145)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-5589110749604),(-5589110749341)⟩,⟨(-11545754209690),(-11545754209358)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 27) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_27 (tableDensity true) (fullFactor false 1 27) density1_contains hk1_0_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨600810927475,600810927477⟩,⟨81664987210219,81664987210221⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_27 1 27 ha1_0_27_contains + def realAnswer : RBox := ⟨(-4988399822129),(-4988199821864)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_27 +namespace hm1_0_0_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),2⟩,⟨0,16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-77424),(-77408)⟩,⟨(-1059),(-1043)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-193184),(-193167)⟩,⟨1784,1800⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-223176),(-223156)⟩,⟨12010,12027⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-181491),(-181475)⟩,⟨21337,21354⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-114454),(-114438)⟩,⟨22521,22538⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-58529),(-58512)⟩,⟨16854,16871⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-25044),(-25028)⟩,⟨9762,9779⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-9243),(-9225)⟩,⟨4643,4660⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-3044),(-3027)⟩,⟨1900,1920⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-933),(-913)⟩,⟨700,718⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-281),(-264)⟩,⟨242,258⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-90),(-72)⟩,⟨78,97⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-36),(-17)⟩,⟨23,40⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨2,19⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-90765671),(-90765655)⟩,⟨(-108116246),(-108116230)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-242416967),(-242416951)⟩,⟨(-278677439),(-278677422)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-319579887),(-319579871)⟩,⟨(-343251661),(-343251644)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-314168855),(-314168839)⟩,⟨(-306557183),(-306557167)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-252238987),(-252238971)⟩,⟨(-218019333),(-218019317)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-172369907),(-172369891)⟩,⟨(-128664304),(-128664286)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-103174069),(-103174052)⟩,⟨(-64783919),(-64783903)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-55451312),(-55451293)⟩,⟨(-28535383),(-28535367)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-27418601),(-27418584)⟩,⟨(-11267265),(-11267249)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-12795769),(-12795753)⟩,⟨(-4083146),(-4083129)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-5787795),(-5787778)⟩,⟨(-1386854),(-1386837)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-2602658),(-2602641)⟩,⟨(-448056),(-448040)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1185815),(-1185798)⟩,⟨(-138124),(-138107)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-547279),(-547261)⟩,⟨(-40012),(-39996)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-241002),(-240985)⟩,⟨(-10408),(-10392)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-68413),(-68395)⟩,⟨(-1908),(-1892)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨38066568556,38066568572⟩,⟨(-25052834654),(-25052834638)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨98874923450,98874923466⟩,⟨(-69949996740),(-69949996724)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨123490966349,123490966365⟩,⟨(-100436891034),(-100436891018)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨112275662698,112275662715⟩,⟨(-111304128544),(-111304128528)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨81293196623,81293196639⟩,⟨(-103286400236),(-103286400220)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨48321556559,48321556576⟩,⟨(-82757845154),(-82757845138)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨23527803685,23527803701⟩,⟨(-58436175977),(-58436175961)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨8878459727,8878459743⟩,⟨(-37122119755),(-37122119739)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1921869322,1921869339⟩,⟨(-21697083044),(-21697083027)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-629078124),(-629078107)⟩,⟨(-11947169516),(-11947169500)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1178653650),(-1178653633)⟩,⟨(-6348202781),(-6348202763)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1024081278),(-1024081262)⟩,⟨(-3326881187),(-3326881170)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-718946830),(-718946814)⟩,⟨(-1742114022),(-1742114006)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-445969504),(-445969487)⟩,⟨(-903128565),(-903128549)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-236986364),(-236986347)⟩,⟨(-432361283),(-432361266)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-73738048),(-73738032)⟩,⟨(-128196045),(-128196029)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨30371501035,30371501052⟩,⟨2016449637591,2016449637607⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨406058327333,406058327349⟩,⟨5471018491222,5471018491238⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1409537068529,1409537068545⟩,⟨7481112615009,7481112615025⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2713400154289,2713400154305⟩,⟨7837273123928,7837273123944⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨3660183385226,3660183385242⟩,⟨6882887059175,6882887059191⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨3861913440796,3861913440812⟩,⟨5209527397928,5209527397944⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨3421008194695,3421008194711⟩,⟨3425425279988,3425425280004⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨2672276458968,2672276458984⟩,⟨1966054517665,1966054517681⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨1903986124852,1903986124868⟩,⟨986322840907,986322840923⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨1269457717508,1269457717524⟩,⟨426569230634,426569230650⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨808974532731,808974532747⟩,⟨149976049144,149976049160⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨500277491653,500277491669⟩,⟨33031121235,33031121251⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨301405918015,301405918031⟩,⟨(-6586184971),(-6586184955)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨173977555608,173977555624⟩,⟨(-14168916035),(-14168916019)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨89468908579,89468908595⟩,⟨(-10563935447),(-10563935431)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨27487600029,27487600045⟩,⟨(-3728280036),(-3728280020)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨3963421038754,3963421039100⟩,⟨6869039104824,6869039105090⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 28) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_28 (tableDensity false) (fullFactor false 1 28) density0_contains hk1_0_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨7021731002963,7021731002964⟩,⟨(-42975943975),(-42975943973)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_28 1 28 ha1_0_28_contains + def realAnswer : RBox := ⟨10985052041717,10985252042064⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_28 +namespace hm1_1_0_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),5⟩,⟨0,16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨0,16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-14769),(-14753)⟩,⟨(-9369),(-9353)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-37313),(-37296)⟩,⟨(-22709),(-22693)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-43933),(-43917)⟩,⟨(-24736),(-24720)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-36316),(-36300)⟩,⟨(-18262),(-18246)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-23095),(-23079)⟩,⟨(-9857),(-9840)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-11856),(-11840)⟩,⟨(-3899),(-3883)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-5112),(-5096)⟩,⟨(-1064),(-1048)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1924),(-1908)⟩,⟨(-143),(-127)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-657),(-639)⟩,⟨39,56⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-213),(-196)⟩,⟨34,50⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-72),(-56)⟩,⟨12,28⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-26),(-10)⟩,⟨0,16⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨0,16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-2721001),(-2720985)⟩,⟨(-47111233),(-47111217)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-8838439),(-8838422)⟩,⟨(-121342291),(-121342275)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-15667663),(-15667647)⟩,⟨(-149385544),(-149385528)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-21033253),(-21033237)⟩,⟨(-133846779),(-133846763)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-22389644),(-22389628)⟩,⟨(-96586956),(-96586940)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-19255885),(-19255869)⟩,⟨(-59081170),(-59081153)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-13685967),(-13685950)⟩,⟨(-31694644),(-31694628)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-8315569),(-8315552)⟩,⟨(-15295481),(-15295465)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4496513),(-4496497)⟩,⟨(-6797696),(-6797680)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2252345),(-2252329)⟩,⟨(-2855145),(-2855129)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1083707),(-1083691)⟩,⟨(-1167079),(-1167063)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-515698),(-515681)⟩,⟨(-478637),(-478621)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-247076),(-247060)⟩,⟨(-201800),(-201784)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-118796),(-118780)⟩,⟨(-87764),(-87748)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-53842),(-53826)⟩,⟨(-37147),(-37131)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-15517),(-15501)⟩,⟨(-10344),(-10328)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨12068952256,12068952272⟩,⟨(-8860290942),(-8860290926)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨32119326606,32119326622⟩,⟨(-24830774747),(-24830774731)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨42039455520,42039455536⟩,⟨(-35648201503),(-35648201487)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨40752227049,40752227066⟩,⟨(-39127994565),(-39127994549)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨31787101104,31787101120⟩,⟨(-35794154783),(-35794154767)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨20585795648,20585795664⟩,⟨(-28492493487),(-28492493470)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨11307568593,11307568610⟩,⟨(-20324550398),(-20324550382)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨5374632603,5374632619⟩,⟨(-13262726257),(-13262726241)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨2252830153,2252830169⟩,⟨(-8050430225),(-8050430208)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨849227534,849227550⟩,⟨(-4618833237),(-4618833221)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨294254807,294254823⟩,⟨(-2542804497),(-2542804481)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨93912999,93913015⟩,⟨(-1360615505),(-1360615488)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨24366968,24366984⟩,⟨(-714196610),(-714196594)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1394721,1394738⟩,⟨(-366375274),(-366375258)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-3759110),(-3759094)⟩,⟨(-173100734),(-173100718)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1878222),(-1878206)⟩,⟨(-50907646),(-50907630)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨3736005509,3736005525⟩,⟨59859961837,59859961853⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨50737402263,50737402279⟩,⟨152124467548,152124467564⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨189047106936,189047106952⟩,⟨134059213366,134059213382⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨431051111912,431051111928⟩,⟨(-69172032956),(-69172032940)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨750555580889,750555580905⟩,⟨(-390770620791),(-390770620775)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨1039579959214,1039579959230⟩,⟨(-635245518854),(-635245518838)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨1155656309529,1155656309545⟩,⟨(-683759000220),(-683759000204)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1060619013358,1060619013374⟩,⟨(-580551018779),(-580551018763)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨836537010579,836537010595⟩,⟨(-426653525597),(-426653525581)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨588978163665,588978163683⟩,⟨(-288331731209),(-288331731193)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨381936519827,381936519843⟩,⟨(-187279246971),(-187279246955)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨234074804899,234074804915⟩,⟨(-120628264597),(-120628264580)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨138204250817,138204250833⟩,⟨(-77620725392),(-77620725376)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨78492902855,78492902872⟩,⟨(-48365173381),(-48365173365)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨40104894715,40104894731⟩,⟨(-26536140657),(-26536140641)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12313492748,12313492764⟩,⟨(-8453294751),(-8453294735)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1198508178692,1198508179030⟩,⟨(-570367861915),(-570367861653)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 28) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_28 (tableDensity true) (fullFactor false 1 28) density1_contains hk1_0_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-9182263619260),(-9182263619259)⟩,⟨56199311350,56199311351⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_28 1 28 ha1_0_28_contains + def realAnswer : RBox := ⟨(-7983855440568),(-7983655440229)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_28 +namespace hm1_0_0_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨48,64⟩,⟨(-4194),(-4178)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-106),(-89)⟩,⟨(-10392),(-10374)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-645),(-629)⟩,⟨(-11857),(-11840)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1121),(-1104)⟩,⟨(-9471),(-9454)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1155),(-1139)⟩,⟨(-5837),(-5820)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-842),(-825)⟩,⟨(-2907),(-2888)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-476),(-459)⟩,⟨(-1208),(-1192)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-224),(-205)⟩,⟨(-437),(-417)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-94),(-76)⟩,⟨(-144),(-126)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-40),(-22)⟩,⟨(-48),(-31)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-17),0⟩,⟨(-19),(-2)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),7⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨7798950,7798966⟩,⟨(-6547359),(-6547343)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨20008853,20008869⟩,⟨(-17404836),(-17404819)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨24419072,24419089⟩,⟨(-22733207),(-22733190)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨21514965,21514982⟩,⟨(-22045967),(-22045949)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨15034842,15034859⟩,⟨(-17390837),(-17390821)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨8687542,8687559⟩,⟨(-11635055),(-11635038)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨4270258,4270274⟩,⟨(-6798114),(-6798097)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1832077,1832093⟩,⟨(-3558521),(-3558504)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨703640,703657⟩,⟨(-1711390),(-1711373)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨247928,247947⟩,⟨(-776529),(-776512)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨81934,81951⟩,⟨(-341762),(-341745)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨25801,25817⟩,⟨(-149829),(-149812)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨7771,7789⟩,⟨(-66766),(-66750)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨2206,2222⟩,⟨(-30270),(-30254)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨560,577⟩,⟨(-13168),(-13152)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨97,113⟩,⟨(-3720),(-3704)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨2259502093,2259502109⟩,⟨3433224357,3433224373⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨6284961594,6284961610⟩,⟨8884307427,8884307443⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨8957208710,8957208726⟩,⟨11014707783,11014707799⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨9818671827,9818671844⟩,⟨9906747774,9906747790⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨8984202744,8984202761⟩,⟨7073684587,7073684604⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨7078645150,7078645166⟩,⟨4135212896,4135212915⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨4904053914,4904053933⟩,⟨1975889687,1975889703⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨3051609242,3051609259⟩,⟨730689394,730689410⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1745487325,1745487342⟩,⟨155065355,155065372⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨940462151,940462172⟩,⟨(-49293585),(-49293568)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨489333578,489333594⟩,⟨(-90749642),(-90749626)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨251523547,251523564⟩,⟨(-77381561),(-77381545)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨129510381,129510399⟩,⟨(-53432277),(-53432260)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨66240758,66240774⟩,⟨(-32705883),(-32705866)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨31414859,31414875⟩,⟨(-17218425),(-17218409)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨9269597,9269613⟩,⟨(-5331838),(-5331822)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-218270249958),(-218270249942)⟩,⟨3286679403,3286679419⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-590357108391),(-590357108375)⟩,⟨43795373831,43795373847⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-802285276503),(-802285276487)⟩,⟨151087853437,151087853453⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-832907989140),(-832907989124)⟩,⟨288238644513,288238644529⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-723011072495),(-723011072479)⟩,⟨384328870300,384328870317⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-539694303188),(-539694303172)⟩,⟨399931430845,399931430861⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-349353720681),(-349353720665)⟩,⟨348760442727,348760442743⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-197151319182),(-197151319166)⟩,⟨267843378176,267843378192⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-97182953859),(-97182953843)⟩,⟨187494833775,187494833791⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-41298849723),(-41298849707)⟩,⟨122816859227,122816859243⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-14278965407),(-14278965390)⟩,⟨76945598186,76945598202⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-3098866005),(-3098865989)⟩,⟨46846620557,46846620573⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨606449313,606449329⟩,⟨27845276399,27845276415⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1294407521,1294407537⟩,⟨15900664532,15900664548⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨958172728,958172744⟩,⟨8115878910,8115878926⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨336894916,336894932⟩,⟨2483859961,2483859977⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-725098003560),(-725098003294)⟩,⟨403765737730,403765738091⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 29) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_29 (tableDensity false) (fullFactor false 1 29) density0_contains hk1_0_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨3880985209,3880985210⟩,⟨762014319019,762014319020⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_29 1 29 ha1_0_29_contains + def realAnswer : RBox := ⟨(-721317018351),(-721117018084)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_29 +namespace hm1_1_0_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨498,514⟩,⟨(-807),(-791)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1213,1229⟩,⟨(-2013),(-1997)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1302,1318⟩,⟨(-2339),(-2323)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨944,960⟩,⟨(-1900),(-1884)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨493,509⟩,⟨(-1183),(-1167)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨183,201⟩,⟨(-594),(-577)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨43,59⟩,⟨(-253),(-237)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1),16⟩,⟨(-97),(-81)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-16),0⟩,⟨(-37),(-21)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16),0⟩,⟨(-16),0⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-16),3⟩,⟨(-16),7⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),0⟩,⟨(-16),16⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3398358,3398375⟩,⟨(-196281),(-196265)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨8712295,8712311⟩,⟨(-634478),(-634462)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨10627344,10627361⟩,⟨(-1114175),(-1114159)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨9393613,9393629⟩,⟨(-1475362),(-1475346)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨6660470,6660486⟩,⟨(-1543020),(-1543003)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3988835,3988851⟩,⟨(-1299291),(-1299275)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2088817,2088833⟩,⟨(-901497),(-901481)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨981791,981809⟩,⟨(-533526),(-533508)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨424386,424402⟩,⟨(-280616),(-280600)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨173300,173316⟩,⟨(-136673),(-136656)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨68920,68936⟩,⟨(-63989),(-63973)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨27547,27563⟩,⟨(-29690),(-29674)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨11356,11372⟩,⟨(-13916),(-13900)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨4846,4862⟩,⟨(-6577),(-6560)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨2018,2034⟩,⟨(-2949),(-2933)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨553,569⟩,⟨(-848),(-832)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨799104647,799104663⟩,⟨1088496800,1088496816⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨2231025090,2231025106⟩,⟨2885999414,2885999430⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨3179205649,3179205665⟩,⟨3749517524,3749517540⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨3451719572,3451719588⟩,⟨3595540840,3595540856⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨3113549502,3113549518⟩,⟨2765653822,2765653838⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨2437084384,2437084401⟩,⟨1761414404,1761414420⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1705611717,1705611733⟩,⟨949375821,949375837⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1090191964,1090191982⟩,⟨442060497,442060513⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨647593385,647593401⟩,⟨181350512,181350528⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨363561674,363561691⟩,⟨66896755,66896771⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨195995580,195995596⟩,⟨22698630,22698646⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨102865507,102865523⟩,⟨7105902,7105918⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨53094441,53094458⟩,⟨1813555,1813571⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨26872458,26872474⟩,⟨103006,103022⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨12577372,12577389⟩,⟨(-272985),(-272969)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨3681026,3681042⟩,⟨(-135813),(-135797)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-6479539941),(-6479539925)⟩,⟨404295115,404295131⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-16416179592),(-16416179576)⟩,⟨5472216713,5472216729⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-14385506379),(-14385506363)⟩,⟨20262465755,20262465771⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨7323623553,7323623569⟩,⟨45780783362,45780783378⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨41002792946,41002792962⟩,⟨78786386536,78786386552⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨65761352182,65761352198⟩,⟨107621629555,107621629572⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨69694922403,69694922419⟩,⟨117783549918,117783549934⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨58184749297,58184749313⟩,⟨106286306599,106286306615⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨42013604352,42013604369⟩,⟨82368707880,82368707896⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨27894856874,27894856890⟩,⟨56979397557,56979397573⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨17812383081,17812383097⟩,⟨36327820813,36327820829⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨11295037323,11295037339⟩,⟨21919538214,21919538230⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨7170420273,7170420289⟩,⟨12768208364,12768208380⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨4420082938,4420082954⟩,⟨7173911927,7173911943⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2407079924,2407079940⟩,⟨3637987922,3637987938⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨763862187,763862203⟩,⟨1112683171,1112683187⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨56320640643,56320640906⟩,⟨120365877557,120365877913⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 29) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_29 (tableDensity true) (fullFactor false 1 29) density1_contains hk1_0_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-5075134505),(-5075134504)⟩,⟨(-996480263334),(-996480263332)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_29 1 29 ha1_0_29_contains + def realAnswer : RBox := ⟨51145506138,51345506402⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_29 +namespace hm1_0_0_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_0_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨210,228⟩,⟨0,16⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨533,549⟩,⟨(-13),5⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨598,616⟩,⟨(-41),(-24)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨468,487⟩,⟨(-64),(-48)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨279,295⟩,⟨(-64),(-48)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨130,147⟩,⟨(-49),(-31)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨46,65⟩,⟨(-31),(-14)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨8,27⟩,⟨(-16),0⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨0,16⟩,⟨(-16),0⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-8),16⟩,⟨(-16),0⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨456541,456557⟩,⟨543816,543832⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1207958,1207974⟩,⟨1388733,1388749⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1563223,1563239⟩,⟨1679288,1679305⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1495472,1495488⟩,⟨1459666,1459683⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1159086,1159104⟩,⟨1002283,1002299⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨759218,759234⟩,⟨567055,567071⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨433010,433026⟩,⟨272099,272116⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨220755,220773⟩,⟨113704,113721⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨103256,103273⟩,⟨42474,42490⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨45547,45563⟩,⟨14547,14564⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨19500,19518⟩,⟨4673,4690⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨8330,8347⟩,⟨1428,1446⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨3623,3642⟩,⟨415,431⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1610,1626⟩,⟨110,127⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨687,703⟩,⟨22,38⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨187,203⟩,⟨0,16⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-299321236),(-299321220)⟩,⟨196990591,196990607⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-771682979),(-771682963)⟩,⟨545877851,545877867⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-949709220),(-949709204)⟩,⟨772203944,772203960⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-845004662),(-845004646)⟩,⟨837291678,837291694⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-595007826),(-595007809)⟩,⟨755442737,755442753⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-342092251),(-342092235)⟩,⟨585301644,585301660⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-160411237),(-160411219)⟩,⟨397850515,397850532⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-58132630),(-58132614)⟩,⟨242503557,242503575⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-12094683),(-12094665)⟩,⟨135745603,135745619⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨3733891,3733907⟩,⟨71566657,71566673⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨6754517,6754534⟩,⟨36462838,36462854⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨5652340,5652358⟩,⟨18382655,18382671⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3838792,3838808⟩,⟨9307159,9307176⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2318601,2318618⟩,⟨4696580,4696596⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1209311,1209327⟩,⟨2206484,2206500⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨372672,372688⟩,⟨647918,647934⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-343815338),(-343815322)⟩,⟨(-22839076932),(-22839076916)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-4566101153),(-4566101137)⟩,⟨(-61579898755),(-61579898739)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-15655302103),(-15655302087)⟩,⟨(-83170702883),(-83170702867)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-29598607995),(-29598607979)⟩,⟨(-85567692884),(-85567692868)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-39010902625),(-39010902609)⟩,⟨(-73417918029),(-73417918013)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-40036253640),(-40036253624)⟩,⟨(-54048316393),(-54048316377)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-34370588170),(-34370588154)⟩,⟨(-34443141917),(-34443141901)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-25951845246),(-25951845230)⟩,⟨(-19111352518),(-19111352501)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-17848553283),(-17848553265)⟩,⟨(-9256546817),(-9256546801)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-11486439720),(-11486439704)⟩,⟨(-3865215179),(-3865215163)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-7074880215),(-7074880199)⟩,⟨(-1314187389),(-1314187373)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-4240625906),(-4240625889)⟩,⟨(-281037839),(-281037822)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2486756922),(-2486756906)⟩,⟨53979984,53980000⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-1404808306),(-1404808290)⟩,⟨114310231,114310247⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-711667086),(-711667070)⟩,⟨84011693,84011709⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-216967298),(-216967282)⟩,⟨29427759,29427775⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-39834368660),(-39834368290)⟩,⟨(-73998965013),(-73998964750)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_0_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 1 30) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_0_30 (tableDensity false) (fullFactor false 1 30) density0_contains hk1_0_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-79915327593),(-79915327592)⟩,⟨338770845,338770847⟩⟩ +lemma atomChecked : tableAtomBox false ha1_0_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 1 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha1_0_30 1 30 ha1_0_30_contains + def realAnswer : RBox := ⟨(-119849696253),(-119649695882)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 1 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_0_30 +namespace hm1_1_0_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_0_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨34,50⟩,⟨18,35⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨97,114⟩,⟨57,73⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨112,128⟩,⟨61,77⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨87,103⟩,⟨40,56⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨49,65⟩,⟨17,35⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨21,37⟩,⟨0,16⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1,18⟩,⟨0,16⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨0,16⟩,⟨(-7),16⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨0,16⟩,⟨(-16),12⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨0,16⟩,⟨(-16),16⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-11),16⟩,⟨(-16),5⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16),16⟩,⟨(-16),0⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨13678,13694⟩,⟨236962,236978⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨44020,44036⟩,⟨604681,604697⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨76583,76600⟩,⟨730834,730850⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨100029,100045⟩,⟨637292,637308⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨102788,102805⟩,⟨443993,444009⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨84741,84757⟩,⟨260334,260351⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨57397,57413⟩,⟨133073,133089⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨33082,33098⟩,⟨60919,60936⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨16922,16938⟩,⟨25606,25622⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨8009,8025⟩,⟨10162,10178⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3643,3659⟩,⟨3925,3942⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1643,1659⟩,⟨1526,1543⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨750,767⟩,⟨609,625⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨342,359⟩,⟨253,269⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨147,163⟩,⟨97,114⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨36,52⟩,⟨21,37⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-94899005),(-94898989)⟩,⟨69668454,69668470⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-250670937),(-250670921)⟩,⟨193774465,193774481⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-323276095),(-323276079)⟩,⟨274081359,274081375⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-306661778),(-306661762)⟩,⟨294351309,294351325⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-232611005),(-232610989)⟩,⟨261809278,261809294⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-145694765),(-145694749)⟩,⟨201511253,201511269⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-77054526),(-77054510)⟩,⟨138366401,138366417⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-35148551),(-35148535)⟩,⟨86629578,86629594⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-14112457),(-14112441)⟩,⟨50359272,50359288⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-5094241),(-5094223)⟩,⟨27664129,27664145⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1692657),(-1692640)⟩,⟨14603965,14603981⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-519767),(-519751)⟩,⟨7517824,7517840⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-130488),(-130472)⟩,⟨3815613,3815629⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-7365),(-7349)⟩,⟨1905323,1905339⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨19154,19170⟩,⟨883399,883415⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨9484,9500⟩,⟨257287,257303⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-42292793),(-42292777)⟩,⟨(-677998520),(-677998504)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-570526510),(-570526494)⟩,⟨(-1712468814),(-1712468798)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-2099391319),(-2099391303)⟩,⟨(-1492218117),(-1492218101)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-4700221960),(-4700221944)⟩,⟨749543386,749543402⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-7994702466),(-7994702450)⟩,⟨4158986607,4158986623⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-10770258085),(-10770258068)⟩,⟨6580890896,6580890912⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-11604521320),(-11604521304)⟩,⟨6867297283,6867297299⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-10296343952),(-10296343936)⟩,⟨5637229844,5637229860⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-7840207333),(-7840207317)⟩,⟨3999380567,3999380583⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-5328736167),(-5328736151)⟩,⟨2608816581,2608816597⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-3340210835),(-3340210819)⟩,⟨1637724311,1637724327⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1984232302),(-1984232286)⟩,⟨1022376063,1022376079⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1140303783),(-1140303767)⟩,⟨640314858,640314874⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-633813427),(-633813411)⟩,⟨390488117,390488133⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-319009075),(-319009059)⟩,⟨211067393,211067409⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-97193830),(-97193814)⟩,⟨66723810,66723826⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-11708161088),(-11708160731)⟩,⟨5386417165,5386417439⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_0_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 1 30) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_0_30 (tableDensity true) (fullFactor false 1 30) density1_contains hk1_0_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨104504659158,104504659160⟩,⟨(-443008030),(-443008029)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_0_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 1 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha1_0_30 1 30 ha1_0_30_contains + def realAnswer : RBox := ⟨92696498070,92896498429⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 1 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_0_30 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_4.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_4.lean new file mode 100644 index 0000000000000000000000000000000000000000..f18fc1a0adfc7fc3b26cce18fd4fbbfd376de4a2 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_4.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-144312892740622400451439759),(-144312892740622336311156980)⟩,⟨(-71537028892799394186136253),(-71537028892799330039739232)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-401674134429779925919243981),(-401674134429779785765962151)⟩,⟨(-215056157190509073875542677),(-215056157190508933704335673)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-575296231799293701812477012),(-575296231799293581127702666)⟩,⟨(-357426841587539993106170354),(-357426841587539872393308033)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-638181520263654915399869517),(-638181520263654846172478564)⟩,⟨(-492053437912766332344368927),(-492053437912766263088579091)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-590242132179494961305051272),(-590242132179494933164668729)⟩,⟨(-606442990281667840420075367),(-606442990281667812261586213)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-452617080284373895309576345),(-452617080284373887761425983)⟩,⟨(-682575697515622996946572430),(-682575697515622989391965969)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-261956330077002710587566872),(-261956330077002709031147261)⟩,⟨(-702724157297277859453236650),(-702724157297277857899408300)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-61446062252852136941239500),(-61446062252852136518167316)⟩,⟨(-660141599379416669074304054),(-660141599379416668658433133)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨111549596721030392598425070,111549596721030392821435657⟩,⟨(-563869231945865047461539160),(-563869231945865047245776724)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨233665529119934037993277998,233665529119934038158645502⟩,⟨(-434596318026736139904865232),(-434596318026736139740846616)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨297016196478082646428023352,297016196478082646565715002⟩,⟨(-297057315188082001477410166),(-297057315188082001339030036)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨306031715295677191591114921,306031715295677191697004025⟩,⟨(-173219771044220160291187674),(-173219771044220160185309016)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨272166512029448726455515774,272166512029448726530315719⟩,⟨(-78272835460373404091699718),(-78272835460373404018272852)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨209191422158538373311592259,209191422158538373359248988⟩,⟨(-19333449169462174567334665),(-19333449169462174521745905)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨129959838281281401631775791,129959838281281401657535905⟩,⟨5054155827992210733084257,5054155827992210757101093⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨43857466137948805409920668,43857466137948805417955967⟩,⟨4672348988834133989685293,4672348988834133997056129⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1668436313680505630049335137),(-1668436313680504555411858143)⟩,⟨609770593222383328153565106,609770593222384402696999604⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-4733059874879583389169705884),(-4733059874879579479552476935)⟩,⟨1732771230456114883239631942,1732771230456118792593184886⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-7055296706356270682104637024),(-7055296706356261499932394522)⟩,⟨2580165007076513451134377213,2580165007076522632924900643⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-8373506490116157676417864296),(-8373506490116138063248032646)⟩,⟨3025475165808078630748301743,3025475165808098243487528454⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-8676995839226753489904813002),(-8676995839226715223923539993)⟩,⟨3030116693403686678590506325,3030116693403724944160804352⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-8163656595219832056883635087),(-8163656595219767158164648614)⟩,⟨2657635917140543267300725544,2657635917140608165678893647⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-7136717556105008781836638430),(-7136717556104919272667709682)⟩,⟨2045450940314909706760223593,2045450940314999215684045196⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-5890450308406113004592773120),(-5890450308406018666039524467)⟩,⟨1351796050346170519324639730,1351796050346264857729332307⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-4639895465375762587437907062),(-4639895465375686414575905265)⟩,⟨711296218361891787343998239,711296218361967960137786120⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-3509994049831524378162327444),(-3509994049831476943390708497)⟩,⟨210242803984710319069628500,210242803984757753828821249⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-2556880492042179808083393856),(-2556880492042156995012545618)⟩,⟨(-118566338056379449098223982),(-118566338056356636008211418)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1792962454451575911533792565),(-1792962454451566811628624893)⟩,⟨(-285499606559898668959396496),(-285499606559889569022286246)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1203537114926723976670931872),(-1203537114926720703315022893)⟩,⟨(-325952229722067569168898521),(-325952229722064295780585972)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-756901181915075906582305999),(-756901181915074768802210426)⟩,⟨(-281201651565495315459274779),(-281201651565494177653177457)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-413227973272027753909991536),(-413227973272027364982301006)⟩,⟨(-185770312008894494072919414),(-185770312008894105128844596)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-130920051903690295587517977),(-130920051903690200797342327)⟩,⟨(-64506388192623830839852337),(-64506388192623736044121543)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-7328008146993923007275258886),(-7328008146993923004195771261)⟩,⟨(-4133671610161325215058012014),(-4133671610161325212329677960)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-21478914486740238077957142565),(-21478914486740238068951734687)⟩,⟨(-11457569182719354604444432090),(-11457569182719354596495721651)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-34089814081333231345732170050),(-34089814081333231331380538422)⟩,⟨(-16237348893150637201836277625),(-16237348893150637189229176138)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-44153053789067111608797460647),(-44153053789067111590018036313)⟩,⟨(-17681319606440240647133536015),(-17681319606440240630725665418)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-50763587544564579394227083183),(-50763587544564579372274834644)⟩,⟨(-15996515620503580484050377623),(-15996515620503580464956137350)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-53343363269079599727022119160),(-53343363269079599703103637021)⟩,⟨(-12161057508918313585649541748),(-12161057508918313564831959640)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-51939819886019831175419923439),(-51939819886019831150329949282)⟩,⟨(-7453569138949906248354157528),(-7453569138949906226353443535)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-47314210683192898070399774396),(-47314210683192898041959070658)⟩,⟨(-3032975212926692988450355992),(-3032975212926692962847318906)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-40678107863207192598692147121),(-40678107863207192545161987685)⟩,⟨337804796585152061277118342,337804796585152112395617581⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-33282074606125134044842465124),(-33282074606125133839738612360)⟩,⟨2390467847846845942685336489,2390467847846846145870758218⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-26095192429150795483184129303),(-26095192429150794635818292067)⟩,⟨3253125081442493093078608237,3253125081442493939002789994⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-19667717249144241874351926355),(-19667717249144239221950279492)⟩,⟨3248929294104953645040266234,3248929294104956296404999945⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-14161409619868379897860644453),(-14161409619868374152090518347)⟩,⟨2726712227991774313449168122,2726712227991780058509435422⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-9484684106353911146884379420),(-9484684106353902698110166969)⟩,⟨1972372994850560638377900707,1972372994850569086699678352⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-5433815866039999448048674416),(-5433815866039991502549251895)⟩,⟨1167524827791843750955989399,1167524827791851696206130553⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1767432520807945718782593505),(-1767432520807942449315649709)⟩,⟨383770537929177053854970079,383770537929180323242814804⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1477042420301113951046820162),(-1477042420301082739110731274)⟩,⟨(-14740572021198027517765056339),(-14740572021197996304578037415)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-5223428227995051932405036691),(-5223428227994979617690729452)⟩,⟨(-43232259068043908502391211927),(-43232259068043836184141136090)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-11050511458753153935442720482),(-11050511458753083573685204797)⟩,⟨(-68690599390943186985966590345),(-68690599390943116618997368800)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-19489803303983137637685849207),(-19489803303983095495149415933)⟩,⟨(-89101007886953924866079066451),(-89101007886953882717513627411)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-30152288004459250546817295497),(-30152288004459233992600960230)⟩,⟨(-102683497382250683940265173136),(-102683497382250667380135141389)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-41858342007549635839003563144),(-41858342007549631468657359792)⟩,⟨(-108395225557965025744692253228),(-108395225557965021369390171384)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-52862782620611094192257025268),(-52862782620611093340870366227)⟩,⟨(-106392642157592461250011126236),(-106392642157592460395149067268)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-61230103614235909825940257855),(-61230103614235909653766007249)⟩,⟨(-97997336057882323242081471285),(-97997336057882323068079339681)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-65442765104019103251286126984),(-65442765104019103180091955134)⟩,⟨(-85245485572581458310237999137),(-85245485572581458238715415957)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-64889928372227120782322544990),(-64889928372227120730476481235)⟩,⟨(-70357089554123710276452209040),(-70357089554123710225412611712)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-59937619120182882257904699818),(-59937619120182882215858817128)⟩,⟨(-55269739894720873093672572333),(-55269739894720873053115124072)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-51628315342697093800540486697),(-51628315342697093767047637651)⟩,⟨(-41342907302194372367333723869),(-41342907302194372335580418375)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-41210454191392571061671335932),(-41210454191392571036293628967)⟩,⟨(-29281439215749107371338052212),(-29281439215749107347608334579)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-29735985141168120521083687494),(-29735985141168120503439106482)⟩,⟨(-19205610559055564850933815453),(-19205610559055564834604780357)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-17880388242117752689886779777),(-17880388242117752679539747427)⟩,⟨(-10797917873435545627046530416),(-10797917873435545617537467990)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-5956414911665558938052092007),(-5956414911665558934655391845)⟩,⟨(-3473755840506456747541718386),(-3473755840506456744431132981)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨17294673731728879457538898282,17294673731729032192982511078⟩,⟨2097942737797872871768468855,2097942737798025609484262574⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨50823335891329605245758970938,50823335891330176454516238909⟩,⟨4342945243163285327200997941,4342945243163856542713243387⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨81135843225330644741025771330,81135843225332058965269364226⟩,⟨1176692324969019235927309139,1176692324970433471299876036⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨106186285707952048582796396365,106186285707955300226807796744⟩,⟨(-9487851383613453516490016711),(-9487851383610201857205799588)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨124050896592639522546945677241,124050896592646457832820809282⟩,⟨(-27594671551648573200227474450),(-27594671551641637895288148855)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨133001271518111557381303857520,133001271518124544315556586179⟩,⟨(-50857513486441911283053376072),(-50857513486428924326593465345)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨131958838640708388388837918016,131958838640729680445177639814⟩,⟨(-75559886610058873207290931223),(-75559886610037581128179267932)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨121243287230893852733392220603,121243287230921743695169406647⟩,⟨(-97633280728879787243204714989),(-97633280728851896260222753114)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨102874137947929920873712217531,102874137947958055861384893952⟩,⟨(-113558759295413601317966525087),(-113558759295385466311430228430)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨80151159013561045360598218893,80151159013582896560133010376⟩,⟨(-121073594882496188112564127258),(-121073594882474336896969517594)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨56843880143446004397899197086,56843880143459070488202301506⟩,⟨(-119497391476132103916469102945),(-119497391476119037813121084037)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨36308280443562187600965695078,36308280443568616201268532932⟩,⟨(-109461802015760502021717585030),(-109461802015754073411371196216)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨20656982976497943986241392852,20656982976500752437860719815⟩,⟨(-92285980303477573386623208950),(-92285980303474764927706080064)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨10315521599412789888491685446,10315521599413944444293051379⟩,⟨(-69584007962938271239431741213),(-69584007962937116678737223307)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4345561698624381101966801521,4345561698624829078482020771⟩,⟨(-43123424696863351296297681237),(-43123424696862903316989168693)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1136586222516551343744503173,1136586222516668477306375160⟩,⟨(-14585093531428779371594652890),(-14585093531428662237126778986)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-4349300248201765902195482613),(-4349300248201765898987645625)⟩,⟨5102955719954065128049855502,5102955719954065131271960139⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-11942203800838333546410611330),(-11942203800838333536627221657)⟩,⟨15822591972759740379464296608,15822591972759740389330383724⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-16500945345679050387562886093),(-16500945345679050370864638957)⟩,⟨27907099771237290694574896852,27907099771237290711512225725⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-16945629631154344864271574285),(-16945629631154344840177471230)⟩,⟨41604816239943385673597294321,41604816239943385698182990909⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-13203594452766757611873267649),(-13203594452766757579737304989)⟩,⟨55962686606726543243582667028,55962686606726543276506317163⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-5707315380320950721996072111),(-5707315380320950679990805257)⟩,⟨68782322411512317195689405177,68782322411512317238769886554⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨5021957523172496827958562176,5021957523172496887860773516⟩,⟨77691021174354033161758023337,77691021174354033222963326708⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨17975884109552464435971097601,17975884109552464565872177691⟩,⟨81294963148351206939650605490,81294963148351207070887831327⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨31330878046419146151611038355,31330878046419146758170244734⟩,⟨79403931682822982548404735581,79403931682822983156062198147⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨42826472499251813617691713689,42826472499251817405511023520⟩,⟨72798100935367411927862878683,72798100935367415716355031185⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨50357530971273004546641796582,50357530971273023853166589029⟩,⟨62933509232789625647710392559,62933509232789644954433112925⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨52387606375349398599484070292,52387606375349468030546700708⟩,⟨51450051357645131901565363537,51450051357645201332451542901⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨48288580847857533617328439768,48288580847857701106924820712⟩,⟨39560714172275101409014652885,39560714172275268898202876312⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨38594837044475716856218117572,38594837044475984081010108055⟩,⟨27835621624003256545938541253,27835621624003523770260244434⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨24756324314451499578124117298,24756324314451765277482711349⟩,⟨16463372210495908037251148475,16463372210496173736246243405⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨8507420220358507605760345641,8507420220358620172445551991⟩,⟨5436653516486909188406867812,5436653516487021754956406504⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨40082156811814036708273370668,40082156811839063318810883654⟩,⟨(-202361171095831272120664880204),(-202361171095806245477320985603)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 0) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_0 (tableDensity false) (fullFactor true 1 0) density0_contains hk1_1_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨3996945478438807200847239445,3996945478438807207089363645⟩,⟨(-1830973894742064691529737567),(-1830973894742064684743588549)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_0 1 0 ha1_1_0_contains + def realAnswer : RBox := ⟨44079102290252843909020610113,44079102290277870526000247299⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_0 +namespace hm1_1_1_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-22849007093146667965756984),(-22849007093146615439477084)⟩,⟨(-15383293643670567905448685),(-15383293643670515380645341)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-63151039529352454791589395),(-63151039529352340069787320)⟩,⟨(-46218784746193741101175552),(-46218784746193626383771985)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-88243766472495003444015698),(-88243766472494904762893272)⟩,⟨(-76092040879444490102151255),(-76092040879444391428187958)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-92484850156743459315830232),(-92484850156743402826222158)⟩,⟨(-101055394616034095146148912),(-101055394616034038664487672)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-78168537060192460318139475),(-78168537060192437459863877)⟩,⟨(-115501290352606224434816393),(-115501290352606201583012137)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-54592916127452524258162780),(-54592916127452518238155829)⟩,⟨(-117702659868277346829389259),(-117702659868277340813138435)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-30087618585923410223102984),(-30087618585923409097316040)⟩,⟨(-111988562860094240228841087),(-111988562860094239103468075)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-6943918580013303307000080),(-6943918580013303093513858)⟩,⟨(-103106174552862869170910781),(-103106174552862868954506979)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨15224728918933227982427749,15224728918933228058155799⟩,⟨(-91672596267734587471251483),(-91672596267734587389950943)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨34937503328960861375357678,34937503328960861428405208⟩,⟨(-75995315817876979964462704),(-75995315817876979906316395)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨48510214974247396592452552,48510214974247396639761211⟩,⟨(-56050582193996793288130981),(-56050582193996793238713216)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨52903952870166094496243340,52903952870166094534433726⟩,⟨(-35092598957477868217860101),(-35092598957477868180063541)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨48281453061275560300194684,48281453061275560328057303⟩,⟨(-17690488980427393356658187),(-17690488980427393330661136)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨37471921274540014631091234,37471921274540014649137447⟩,⟨(-6493018364464840490355130),(-6493018364464840474548450)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨23426856512754814842449139,23426856512754814852278515⟩,⟨(-1238419756943312423390845),(-1238419756943312415279337)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨7943851850558006596963116,7943851850558006600041294⟩,⟨45889055046714769097454,45889055046714771537158⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-274141667452766900708526990),(-274141667452766016124128647)⟩,⟨(-40097409323612479159672336),(-40097409323611594563625038)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-769077945770383243578190943),(-769077945770380023966191527)⟩,⟨(-102435703858498035919167519),(-102435703858494816274780526)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1123645133148655079116747905),(-1123645133148647511683816442)⟩,⟨(-120280938375954471336939551),(-120280938375946903857592609)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1301731604988515376568103807),(-1301731604988499197450682561)⟩,⟨(-89835449087837673250225278),(-89835449087821494081218214)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1320782927178340969337997607),(-1320782927178309374364980823)⟩,⟨(-31959891070030644518753724),(-31959891069999049497290463)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1228428439181016001330639281),(-1228428439180962371730458103)⟩,⟨19757105514731327719086068,19757105514784957358649485⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1073140987356439710517954009),(-1073140987356365678487808263)⟩,⟨40927568552189172509732250,40927568552263204567593846⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-892349818120931228465828619),(-892349818120853164470786094)⟩,⟨30016667025342037796625033,30016667025420101807848102⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-713177002432992654274815628),(-713177002432929623975431513)⟩,⟨829767322876781692441692,829767322939811998989485⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-552323345235914583811567094),(-552323345235875354493206827)⟩,⟨(-31878942677694733368812941),(-31878942677655504049427523)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-415881694102349538715424514),(-415881694102330690471521447)⟩,⟨(-58810090743458066498659061),(-58810090743439218257512175)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-302533618285471324872728616),(-302533618285463816161400289)⟩,⟨(-74883457062787190755097296),(-74883457062779682048328936)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-209066905123812865601511980),(-209066905123810168416091514)⟩,⟨(-77130176006141076070115310),(-77130176006138378889487106)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-133397266582394635419287968),(-133397266582393699157766936)⟩,⟨(-65487631245841136238274210),(-65487631245840199980731682)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-73012444440579798167501036),(-73012444440579478465618210)⟩,⟨(-43253210943256713999016417),(-43253210943256394299703821)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-23093739591216675296737215),(-23093739591216597425569647)⟩,⟨(-15030042481345147289030615),(-15030042481345069418750333)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-919953222116643345597756760),(-919953222116643344384914447)⟩,⟨(-1661843012691721324839131714),(-1661843012691721323641791293)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2756679326646094269834868435),(-2756679326646094266256454287)⟩,⟨(-4762528207977207386638327649),(-4762528207977207383108210937)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-4517609538037979632665235323),(-4517609538037979626955343197)⟩,⟨(-7217288063038397888105087489),(-7217288063038397882472654874)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-6020119136050360618793758515),(-6020119136050360611384802404)⟩,⟨(-8684260882128732465335871045),(-8684260882128732458026797958)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-7073341185968550824324080308),(-7073341185968550815817213057)⟩,⟨(-8974553300212337446821492145),(-8974553300212337438424162966)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-7604906194026217840675693773),(-7604906194026217831566968538)⟩,⟨(-8172861784532067776111760655),(-8172861784532067767117235524)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-7647444313220039953480659016),(-7647444313220039943823962041)⟩,⟨(-6661783489607057878643325702),(-6661783489607057869102989602)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-7263221480372835303186330874),(-7263221480372835290526871748)⟩,⟨(-4940892884397195304448981951),(-4940892884397195291892308561)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-6532443588956100138133135659),(-6532443588956100104099804764)⟩,⟨(-3402622793484781472368686064),(-3402622793484781438404935375)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-5563038484922649121923764810),(-5563038484922648963022667335)⟩,⟨(-2234448904635238405182857638),(-2234448904635238246319035165)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-4477032348850505768584813497),(-4477032348850505084816785627)⟩,⟨(-1441325451617161740360894338),(-1441325451617161056608466040)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-3392333072227285327141229153),(-3392333072227283169949221550)⟩,⟨(-925831845363500940616259948),(-925831845363498783431467068)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-2406962056543380672379822449),(-2406962056543375988379191348)⟩,⟨(-579346811956965828438126812),(-579346811956961144440828403)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1572950734562830679618710653),(-1572950734562823784232870677)⟩,⟨(-336730691078419154496754782),(-336730691078412259111893140)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-881624318256280329147951605),(-881624318256273840306138267)⟩,⟨(-168575315992347325641631997),(-168575315992340836799752869)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-283357785522423733335317307),(-283357785522421062452610150)⟩,⟨(-50243414110891213894719261),(-50243414110888543011750907)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨2549548371491904970193423842,2549548371491931194844980914⟩,⟨(-4245347770324873049433340435),(-4245347770324846824916701216)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨7162485121342086603211344928,7162485121342147321836103328⟩,⟨(-12422175190743518409718414455),(-12422175190743457691473326630)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨10393819710300370866619270471,10393819710300429863240731042⟩,⟨(-19689173737472689759447442013),(-19689173737472630763377455102)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨11624126355001466218612216565,11624126355001501475821521057⟩,⟨(-25600956890550292875589021896),(-25600956890550257619000832552)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨10720009545522081583054781513,10720009545522095384938604621⟩,⟨(-29918832348381417122764573295),(-29918832348381403321459915380)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨8143316075818792402083410995,8143316075818796019906125974⟩,⟨(-32527843538674941950999678852),(-32527843538674938333626681664)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨4725712382392509217811233484,4725712382392509903174410130⟩,⟨(-33304507045287502683332237910),(-33304507045287501998246520797)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1257495521422559579322994528,1257495521422559699873245593⟩,⟨(-32208283735191108066518158536),(-32208283735191107946068088688)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1719357208545296819664138056),(-1719357208545296782408682496)⟩,⟨(-29471708133795977902247019482),(-29471708133795977864942375649)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-3901628079137616020366024443),(-3901628079137615997503992853)⟩,⟨(-25598387440910947218614332063),(-25598387440910947195599755698)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-5164887629564873321060647791),(-5164887629564873303793791724)⟩,⟨(-21187522847672457750565700674),(-21187522847672457733093666501)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-5515636408010551358909236712),(-5515636408010551345697861790)⟩,⟨(-16735392953787638466984804793),(-16735392953787638453558680445)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-5066959142061954816715978561),(-5066959142061954806953740808)⟩,⟨(-12525672237213068804661099251),(-12525672237213068794706560226)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-4008349038208515134133214865),(-4008349038208515127463055387)⟩,⟨(-8645454964118402086933584083),(-8645454964118402080115203346)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2548829117576786684189197467),(-2548829117576786680322406028)⟩,⟨(-5058224096729319803951026409),(-5058224096729319799991773509)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-871833350697943947283002505),(-871833350697943946020488813)⟩,⟨(-1663413829434929129265873606),(-1663413829434929127972174982)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨5710167146394813048278878429,5710167146394938573927408475⟩,⟨397666249600534730858857200,397666249600660256068394882⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨17088257437361288307813062261,17088257437361757788774461219⟩,⟨735691743093230431029291703,735691743093699910653915569⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨28117576769926451799376215501,28117576769927614312864342528⟩,⟨(-152259971524498123021768615),(-152259971523335611773832336)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨38025896365216242623997195420,38025896365218915945290425488⟩,⟨(-2742045813238082239549119801),(-2742045813235408921395136490)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨45725144563340015058214215136,45725144563345717554254566800⟩,⟨(-7289841235995799023493785386),(-7289841235990096531426255136)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨50391199699632973936174442097,50391199699643652334632007787⟩,⟨(-13773665955304023693985247716),(-13773665955293345300242302591)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨51863470794027025232392646557,51863470794044528661940188463⟩,⟨(-21565550503082136133210496356),(-21565550503064632708669667235)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨50508943362753843221415360683,50508943362776760136349791357⟩,⟨(-29352689542810081258508657766),(-29352689542787164348333833766)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨46930581196491210705551385068,46930581196514309724555150891⟩,⟨(-35552414865568986578625473722),(-35552414865545887563780994253)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨41778835723582461466407395112,41778835723600382334797880968⟩,⟨(-38842801355438822525822866197),(-38842801355420901660802493985)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨35595524045426998724290877334,35595524045437701078222932049⟩,⟨(-38541290745685211502117645876),(-38541290745674509150783576677)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨28747242694654213489939779152,28747242694659472044345046809⟩,⟨(-34812256943053615515756069379),(-34812256943048356963300828513)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨21595163039334688242254160062,21595163039336982617847663714⟩,⟨(-28572551337728702859397159003),(-28572551337726408485195788837)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨14650258176937666303904830122,14650258176938608524292276112⟩,⟨(-20949306004456190769414810769),(-20949306004455248549936764595)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨8340986712889980132519011250,8340986712890345449034810002⟩,⟨(-12723743729736496093536497738),(-12723743729736130777528196223)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2688946119866954249646976248,2688946119867049733581112000⟩,⟨(-4261554509758643089128244329),(-4261554509758547605355159596)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-121979774637886539831549349),(-121979774637886537916552812)⟩,⟨157745424275718289440347902,157745424275718291403357318⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-223088503618374933829032474),(-223088503618374927968825719)⟩,⟨534667477027125051619593836,534667477027125057646114324⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨241214789403229818020419283,241214789403229828058037575⟩,⟨961155883354138381674530630,961155883354138392048733249⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2049283830386843019127434454,2049283830386843033704043983⟩,⟨1262100241629757782238093384,1262100241629757797389321163⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨6173968958730315702135937927,6173968958730315722042013010⟩,⟨1514456485254941032884953757,1514456485254941053646298463⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨12959401040089581444374004642,12959401040089581471616970925⟩,⟨2314292231927181475785496681,2314292231927181504214150373⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨21445692215015857682532984853,21445692215015857724582085578⟩,⟨4178280464067672788157209491,4178280464067672831765881438⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨29830918283869917791719541122,29830918283869917892693109670⟩,⟨6834535022324210108281969814,6834535022324210211108005926⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨36401565147324484961353647485,36401565147324485455999276598⟩,⟨9384064348876955448572691295,9384064348876955945170430635⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨40028999040376645443460475546,40028999040376648542181313962⟩,⟨10884461464214546187338708374,10884461464214549287932184069⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨40305628620828583014882263588,40305628620828598786864317350⟩,⟨10762433468019009151369113422,10762433468019024925025141249⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨37494335485283600633278841296,37494335485283657337203331890⟩,⟨9050294837167372594771978280,9050294837167429300148137180⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨32185942703767944515309543627,32185942703768081349153082466⟩,⟨6433681617587637520993655300,6433681617587774356021126552⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨24840879967393365605360140024,24840879967393584021231623278⟩,⟨3856584434753849083460942443,3856584434754067500190059453⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨15758212770854324105784639769,15758212770854541355668507658⟩,⟨1897921324246689293114507256,1897921324246906543511261533⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨5408122438331626848029918803,5408122438331718906774990738⟩,⟨552657939268952457871078524,552657939269044516782679326⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨123471616912439879590176627908,123471616912460425033558476061⟩,⟨(-98344683772844875485520468906),(-98344683772824330046637368756)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 0) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_0 (tableDensity true) (fullFactor true 1 0) density1_contains hk1_1_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-5226774856419978655424552458),(-5226774856419978647261774658)⟩,⟨2394350477739623049280077333,2394350477739623058154272202⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_0 1 0 ha1_1_0_contains + def realAnswer : RBox := ⟨118244842056019900934652075450,118244842056040446386396701403⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_0 +namespace hm1_0_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨843088589212980180685770324,843088589212980766024280238⟩,⟨1084052016390588155137261494,1084052016390588740519943216⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨2318287610579884794391901735,2318287610579886141302124791⟩,⟨3130365323178865008753754170,3130365323178866355778290439⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨3231338643617155144846005195,3231338643617156434850058024⟩,⟨4841861878502973468567592228,4841861878502974758709036701⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨3407809284906755126402153546,3407809284906755877236694508⟩,⟨6088778211810074850663135421,6088778211810075601601342342⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2861630473422298491392861560,2861630473422298773076950877⟩,⟨6817352147613898010985336796,6817352147613898292694744469⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1760888830118019917073951270,1760888830118019987309007251⟩,⟨7008465834665513625009705620,7008465834665513695188642196⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨381841051407163730887877983,381841051407163744748204952⟩,⟨6672339196004614795582635253,6672339196004614809331843491⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-972802234900680488919667482),(-972802234900680485057198770)⟩,⟨5883651142590081713026408853,5883651142590081716761579458⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-2065093922079596499778486036),(-2065093922079596497589486965)⟩,⟨4785483784073045438305609895,4785483784073045440408699924⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2764593563201799128436938233),(-2764593563201799126724246079)⟩,⟨3554433283835351452618612062,3554433283835351454330825687⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-3042543455744043695597616938),(-3042543455744043694235330949)⟩,⟨2361141645229584099206790217,2361141645229584100585777047⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2942001958267160618333021147),(-2942001958267160617316449167)⟩,⟨1341451952218846482944283010,1341451952218846483968405848⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2542028107786792133963418970),(-2542028107786792133257484401)⟩,⟨582924846541544004796783009,582924846541544005494464107⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1932002692333443094155340817),(-1932002692333443093708520720)⟩,⟨122281491061120736657757436,122281491061120737087341869⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1197083375146187000389526356),(-1197083375146187000148016471)⟩,⟨(-60078629222315040989975166),(-60078629222315040764102531)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-404066393944869500452213902),(-404066393944869500376744816)⟩,⟨(-43974983490166823598634319),(-43974983490166823529271838)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨11373880619626247309576620279,11373880619626255835718397505⟩,⟨5579338999632106094273507590,5579338999632114620779102225⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨32492598725669933002285632563,32492598725669964068121423700⟩,⟨15686077932816339649811684297,15686077932816370716674418393⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨49041616655346845722694654386,49041616655346918812520337587⟩,⟨23012407250075453297571870287,23012407250075526388914853611⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨59092466275378272133570161618,59092466275378428220507711300⟩,⟨26805622987530414928977835471,26805622987530571017711034805⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨62130840434186888574570002179,62130840434187191662331133317⟩,⟨27361653994584066657046775899,27361653994584369746693450817⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨59082493989400894368083654597,59082493989401402493577895477⟩,⟨25665929218038602153968036075,25665929218039110281310634894⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨51849578727308121087256276955,51849578727308808176940046676⟩,⟨22866623039795751156025159837,22866623039796438247446353516⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨42571538867103822723553614217,42571538867104526682649042418⟩,⟨19833265028830719698755024748,19833265028831423659436003368⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨33028015906254886076900644589,33028015906255434066572896692⟩,⟨16975943795004768713978825707,16975943795005316705058895213⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨24385270536582458825734666281,24385270536582785620531783016⟩,⟨14351521654957198703949228418,14351521654957525499955464514⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨17217203958293146247685558520,17217203958293295873076722248⟩,⟨11880606043207323166091954217,11880606043207472792480205575⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨11654672934836905265211285991,11654672934836962026755699989⟩,⟨9502936545390930759996103225,9502936545390987522320493333⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨7545581602117959085254330852,7545581602117981067813759426⟩,⟨7217466017783085569783497443,7217466017783107552846366738⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨4588986093915279823480015669,4588986093915288522978611824⟩,⟨5042441426095930249771513671,5042441426095938949555258244⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2439482285583659895685747656,2439482285583663174106486708⟩,⟨2974448177482363191538864797,2974448177482366470102135634⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨761363243559182415508782219,761363243559183258021639292⟩,⟨982094537044063359512791553,982094537044064202068529814⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-326704960724590742622046092),(-326704960724590729093751430)⟩,⟨49177646432858325091255866677,49177646432858325110160957291⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨3011144281878528657879137512,3011144281878528698174528435⟩,⟨142785167715121009357072678935,142785167715121009412792476401⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨16684413581786212202656594761,16684413581786212269943472120⟩,⟨222499439755153329729274755712,222499439755153329819814093799⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨42611458210029249199479352092,42611458210029249293499609415⟩,⟨280804420422729022688000097847,280804420422729022809975188005⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨77188613524459211367513388118,77188613524459211486124956270⟩,⟨312758815003669556727006675750,312758815003669556874809945345⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨112848019055608048717354076466,112848019055608048857455996648⟩,⟨316979994503165823806513432848,316979994503165823973802003120⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨141477295571480723729421342879,141477295571480723888197960362⟩,⟨296470123880615921362017047704,296470123880615921543953990965⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨157455266228095435751604675160,157455266228095435943745035050⟩,⟨258317712568649284756620880088,258317712568649284967035451474⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨159047212400663304039734234102,159047212400663304416006427397⟩,⟨211572410897124503519695702749,211572410897124503909453460084⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨148127795002195456193206735911,148127795002195457679348553141⟩,⟨164450087953047399889672300773,164450087953047401385300806797⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨128659615222254212446755576807,128659615222254218783958838657⟩,⟨122462543890151393772316099030,122462543890151400115981167257⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨104830271775159491141373597331,104830271775159511475780088164⟩,⟨87994084657060075828979959899,87994084657060096167725215427⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨79809408775379001526607015012,79809408775379046310214700600⟩,⟨60918221352066012218355240851,60918221352066057004817467576⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨55445100898193032783227190169,55445100898193099281735648327⟩,⟨39684071277894131305721650592,39684071277894197806020566287⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨32450724231164753276497928805,32450724231164816130883201160⟩,⟨22364992949714794086755245262,22364992949714856942124940752⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨10657844181865336459583815376,10657844181865362376306903695⟩,⟨7221612194058077743371201598,7221612194058103660407250703⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-65894076211332605957014997393),(-65894076211332445192876644620)⟩,⟨29237155076121130040570153396,29237155076121290804090267703⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-192245134542158415263498230176),(-192245134542158043084147084993)⟩,⟨90768550885465712747963161294,90768550885466084926262640719⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-302167650483901125011331985570),(-302167650483900763501087852118)⟩,⟨159857512565250523070793718853,159857512565250884581731183833⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-385280573821106828081354426018),(-385280573821106612177364427461)⟩,⟨237052429740189004635489795103,237052429740189220544828282993⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-432928064242236970943489920590),(-432928064242236886496383801932)⟩,⟨318075204515746475217147034842,318075204515746559677065039309⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-440635792321051329762413739770),(-440635792321051307593659744697)⟩,⟨394886325845774999218655523223,394886325845775021409604642108⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-410614284879838753513069081547),(-410614284879838749213487308456)⟩,⟨457534058920876287923379159030,457534058920876292254734889390⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-351805785072014767572795985930),(-351805785072014766695738316148)⟩,⟨496373349696203263480830290564,496373349696203264397655273153⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-277178525506791770185757355635),(-277178525506791769816353030892)⟩,⟨504980153679185545794364987286,504980153679185546208548809483⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-200122819019511208275004637964),(-200122819019511208005294905372)⟩,⟨482365276682374865421770832145,482365276682374865737577350418⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-131334133011991105925527988975),(-131334133011991105707257228889)⟩,⟨432973578427430401677023195107,432973578427430401939090604561⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-77097178790478688364730186066),(-77097178790478688190932753332)⟩,⟨364692492539003660738664843127,364692492539003660951046629035⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-39295541553969631772203177590),(-39295541553969631640332643382)⟩,⟨286011836503001854790318593417,286011836503001854953551473732⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-16478908325858142931053598482),(-16478908325858142839119421879)⟩,⟨203614155378019459085353954979,203614155378019459200204681027⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-5163873878273701102528279544),(-5163873878273701048484881747)⟩,⟨121306691139903102334553842517,121306691139903102402486970304⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-929504472236181869233510212),(-929504472236181851426366046)⟩,⟨40219254037761090289813745687,40219254037761090312236977641⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-3657913324276279295279769952),(-3657913324275730243141077237)⟩,⟨(-72180094717085949806778134419),(-72180094717085400766198610508)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-18778941725506245638257407534),(-18778941725504161542314998223)⟩,⟨(-211368381086796409927823548510),(-211368381086794325865683147355)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-55519330475557326858698287693),(-55519330475551908348148032521)⟩,⟨(-334863875997560331139659476230),(-334863875997554912681869877327)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-122152874473955164385397505015),(-122152874473941803342639163978)⟩,⟨(-432657604822912152481740108847),(-432657604822898791505830491920)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-217971572410628039631564554989),(-217971572410596939631781282587)⟩,⟨(-495694546199616369122007651510),(-495694546199585269197416774815)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-332407367005870120795301712489),(-332407367005805726742716114459)⟩,⟨(-516581814624633406527723989455),(-516581814624569012552265103677)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-448132615281521087440662594012),(-448132615281411297319433672442)⟩,⟨(-491596822008193269600541575271),(-491596822008083479552417659806)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-546077587325355715528107328772),(-546077587325211592542913625791)⟩,⟨(-423866148341908001060952065938),(-423866148341763878140418478553)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-610084827268670885164244429848),(-610084827268525266003447885732)⟩,⟨(-324688309275074183525679218732),(-324688309274928564418405521633)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-630609439725465848011166107505),(-630609439725352651639548711330)⟩,⟨(-211457265560142293455777333894),(-211457265560029097125407883934)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-606426471854136503269090519453),(-606426471854068811107077412519)⟩,⟨(-103530968130533271133732315498),(-103530968130465579000977500964)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-543156818409875627727590724010),(-543156818409842345389675170355)⟩,⟨(-17819014310444267046144821700),(-17819014310410984727011925358)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-449470818924981217786421021926),(-449470818924966695820591190526)⟩,⟨35196303817326253643140908560,35196303817340775598204214495⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-334145947660042386444895372256),(-334145947660036425217541687667)⟩,⟨53871379525729975843376448253,53871379525735937065354992204⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-205147920186113449217017546080),(-205147920186111139207872578720)⟩,⟨44289162164948588993391906453,44289162164950899000314280383⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-69061608177373404853563894461),(-69061608177372801306557342511)⟩,⟨16782465020504905162989486846,16782465020505508709430037293⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨19262917850381345379819862982,19262917850381345391663196692⟩,⟨14746065846948797574247284197,14746065846948797585827435044⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨59661343789390475586930903418,59661343789390475623280340790⟩,⟨40117035187901185228083868189,40117035187901185263484788015⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨105042959633779617600997442598,105042959633779617663670860891⟩,⟨54059405805966808606912389353,54059405805966808667636868700⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨156359868702024233232824771605,156359868702024233324354351869⟩,⟨52175615448853949699508393083,52175615448853949787760492410⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨210174625849887895031017731419,210174625849887895154453461716⟩,⟨33761976339338794874711990021,33761976339338794993457890844⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨258238455267148992556899004733,258238455267148992719460666215⟩,⟨312663515237195862112056535,312663515237196018687600933⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨291187710436486359830571815226,291187710436486360062076864012⟩,⟨(-45930825850657534895168509873),(-45930825850657534670610772227)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨303055915410376359490375743966,303055915410376359982947923908⟩,⟨(-100650537006395023079473018114),(-100650537006395022593821600815)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨292681911824441697252570945870,292681911824441699509914839499⟩,⟨(-156270706009168190203622238778),(-156270706009168187951825859769)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨263240769616064076428413585390,263240769616064090441549012130⟩,⟨(-203414505855433086428405244221),(-203414505855433072418533113215)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨221227458896148743387776924988,221227458896148814542475154166⟩,⟨(-233324179015956909028250699364),(-233324179015956837874320125827)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨174372919901793400315466346864,174372919901793654975603970944⟩,⟨(-239592749090178570025422072300),(-239592749090178315364107730715)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨128731799243877076889773469069,128731799243877687721485130656⟩,⟨(-219482449812709823649318573795),(-219482449812709212815255206562)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨87143486181174436014150492154,87143486181175405033168088537⟩,⟨(-175006167518212029433471967428),(-175006167518211060411831980551)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨49993734460381355938435653686,49993734460382314955209473424⟩,⟨(-112182731960723642321841803599),(-112182731960722683303067286279)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨16231112238822836100547402022,16231112238823241335843533552⟩,⟨(-38546948717131004959197080004),(-38546948717130599723158179697)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-691531862240898338834785871128),(-691531862240771282453591648676)⟩,⟨448487283939324918718964113350,448487283939451975089355871441⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 1) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_1 (tableDensity false) (fullFactor true 1 1) density0_contains hk1_1_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨3729183071596926178252232218,3729183071596926214156928845⟩,⟨(-13497664989784452456054402277),(-13497664989784452422447517742)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_1 1 1 ha1_1_1_contains + def realAnswer : RBox := ⟨(-687802679169301412656633638910),(-687802679169174356239334719831)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_1 +namespace hm1_1_1_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨118454119845964960676043036,118454119845965439971595984⟩,⟨202789885337915002746037915,202789885337915482031010687⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨319130051542706841947928906,319130051542707944311071706⟩,⟨588057519177677263677510345,588057519177678366012785788⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨420054124658794251267109887,420054124658795305904574974⟩,⟨909135570402087445567620730,909135570402088500169799930⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨392613206031767508965309732,392613206031768121478113048⟩,⟨1119286904030916239787248965,1119286904030916852269269734⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨266405629454150833846531502,266405629454151062432988348⟩,⟨1188938423374750199207813544,1188938423374750427777665188⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨108383421415906894721143011,108383421415906950465241929⟩,⟨1139454936841662919194954987,1139454936841662974942571367⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-38382113733263527825821631),(-38382113733263518076328037)⟩,⟨1032406658399139243007326229,1032406658399139252782094205⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-174855031488371896233188134),(-174855031488371894459905704)⟩,⟨912715123312800984213729688,912715123312800986032106519⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-309736909108487066013847812),(-309736909108487065327148140)⟩,⟨783522187373140640661027854,783522187373140641400245687⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-430008422557119878308755305),(-430008422557119877759295877)⟩,⟨630613474898548725119616022,630613474898548725704949160⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-505523089526451965439475954),(-505523089526451964978943284)⟩,⟨454217964450426047671636755,454217964450426048144594118⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-512705877861344586820694089),(-512705877861344586461371410)⟩,⟨279074970700934850199126088,279074970700934850551279359⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-452855839277421799457708771),(-452855839277421799199714237)⟩,⟨138396778896444795811324081,138396778896444796050699548⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-346875716531125501227091649),(-346875716531125501060611410)⟩,⟨49808210103972344273845460,49808210103972344419252153⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-216009449397623223118825258),(-216009449397623223027892578)⟩,⟨8977467201682082385447087,8977467201682082460463163⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-73204684711347027810127600),(-73204684711347027781551294)⟩,⟨(-589069015778831841876887),(-589069015778831819191877)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1146648481812861334220569716,1146648481812868352457087489⟩,⟨1609160611043608048250542182,1609160611043615066439755639⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨3306411652065614812516898882,3306411652065640395409224753⟩,⟨4462491694343018185454031558,4462491694343043768213507447⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨5090854022066226657347800069,5090854022066286893415631318⟩,⟨6362619528604526946454418502,6362619528604587182326549422⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨6336246235115100251879802533,6336246235115229008634014155⟩,⟨7089917105482753038997644666,7089917105482881795520937360⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨6971349393856449510168430440,6971349393856699757938742410⟩,⟨6827166043857963986644734870,6827166043858214234172173602⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨6999566364080802847734713213,6999566364081222738433830838⟩,⟨5996413229501655260541705364,5996413229502075151001361973⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨6493851732835768357906134991,6493851732836336638052586136⟩,⟨5000935753389061424315612756,5000935753389629704234233172⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨5614888647569743082513583045,5614888647570325596109742964⟩,⟨4075030368595615682969316350,4075030368596198196355339385⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨4573242781241320672168791144,4573242781241774110744911578⟩,⟨3303558136013541740622144642,3303558136013995179009853388⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨3545897771807687750836494412,3545897771807958012835278394⟩,⟨2691544590671877333974103553,2691544590672147595807809264⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2629806300456999854281668974,2629806300457123473032559009⟩,⟨2206121883966230773892010822,2206121883966354392502841786⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1855710180963832958251504785,1855710180963879792424685569⟩,⟨1794649201048541505668352317,1794649201048588339728562872⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1228755435750768028636717800,1228755435750786140115621361⟩,⟨1404563866067626718533925461,1404563866067644829937945194⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨747105274943799828724109868,747105274943806986544063517⟩,⟨1008199300243712170610235400,1008199300243719328386803052⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨391611594085517168703240258,391611594085519863217840634⟩,⟨604851123557284901393791056,604851123557287595886299758⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨120680212895448671307808067,120680212895449363338951155⟩,⟨201183581309721881371085372,201183581309722573395475376⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-5881315918008895290995200611),(-5881315918008895284775479962)⟩,⟨9417244471129658781329313235,9417244471129658787794422849⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-16458613957127338588466787600),(-16458613957127338569835635995)⟩,⟨27772772839509494459361948279,27772772839509494478720518247⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-23775445157264621744729112758),(-23775445157264621714033423338)⟩,⟨44342117854289745324294034683,44342117854289745356060150342⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-26487191954887798870898174003),(-26487191954887798829263267399)⟩,⟨57272277428089273804037640911,57272277428089273846899646804⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-24114484748470014801394947511),(-24114484748470014751007957675)⟩,⟨64818860155910392428269040096,64818860155910392479828420178⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-17335679214290689270127730006),(-17335679214290689213226084830)⟩,⟨66423420924689200046422173706,66423420924689200104383073361⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-8159941845410964840266128919),(-8159941845410964776923977747)⟩,⟨62958496482115008727568400180,62958496482115008791836891503⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨788613850506294277375365170,788613850506294363392358903⟩,⟨56038328109008681421324800581,56038328109008681508058747146⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨7451562350982696675453145087,7451562350982696912455628241⟩,⟨47336399846323361834588068219,47336399846323362072033923470⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨10974116041185393406382359088,10974116041185394553438459383⟩,⟨38217798457027718968566068310,38217798457027720115856945141⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨11623375506113702079701629334,11623375506113707188362223570⟩,⟨29564806704085037733479472088,29564806704085042842252086868⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨10333719217275540338717080620,10333719217275556871588592736⟩,⟨21819075358310502760105206825,21819075358310519293038826715⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨8147361093401416618945765987,8147361093401453122373309560⟩,⟨15187677131912652922122549526,15187677131912689425584695628⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5758709725776757501044984015,5758709725776811769583897379⟩,⟨9747088694082029973137102980,9747088694082084241691950971⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨3417355501434836919546015708,3417355501434888248481677881⟩,⟨5369604124519637412074136039,5369604124519688741015350048⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1132798954226769252733347366,1132798954226790423760868308⟩,⟨1706722281486212268075738865,1706722281486233439103904064⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-23500415670438684423009973843),(-23500415670438549351250764512)⟩,⟨(-5331526477521932131147084455),(-5331526477521797059304003444)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-68578111578534006354607681272),(-68578111578533693868256541355)⟩,⟨(-14055508493727927195568259288),(-14055508493727614709057777154)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-108018055129018290009056715209),(-108018055129017986908609172663)⟩,⟨(-17280917931893712007500834759),(-17280917931893408907069935404)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-138879164172055898704459075748),(-138879164172055718094438837414)⟩,⟨(-12535452444739371477644056188),(-12535452444739190868153489319)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-159526087326414718157594106097),(-159526087326414647768810733517)⟩,⟨630819377351593973331558621,630819377351664360758139578⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-169575011172816049795447041390),(-169575011172816031458072599278)⟩,⟨19906844349246269755275929416,19906844349246288090275916493⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-169185431085591402495176998570),(-169185431085591399042656178638)⟩,⟨40916996505551044963825026711,40916996505551048412952803468⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-159022476764040426022670504875),(-159022476764040425410026800597)⟩,⟨59260388692492514013212334743,59260388692492514621675558950⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-140912567696430631922676462386),(-140912567696430631723614106613)⟩,⟨71991300032076964856921863268,71991300032076965051365858574⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-117883181080981653343810196776),(-117883181080981653215739634552)⟩,⟨77870389529881001337465699080,77870389529881001460876996516⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-93374809967253077160533158303),(-93374809967253077060887258226)⟩,⟨76987274524258813945499722674,76987274524258814040824995940⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-70228442623021651840537005032),(-70228442623021651762427388106)⟩,⟨70209048358351184420394933137,70209048358351184494764951239⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-50012285437078938037631480386),(-50012285437078937978664586260)⟩,⟨58759083327106600033960620612,58759083327106600089928572968⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-33014945771705442793080567451),(-33014945771705442752008829404)⟩,⟨43979707230905625428230146518,43979707230905625467137622970⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-18679866118434281149178014585),(-18679866118434281125009751571)⟩,⟨27112199748990933837481084869,27112199748990933860348830879⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-6033837547589623920162528224),(-6033837547589623912195769876)⟩,⟨9146182093766125375755685624,9146182093766125383293229295⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2413671770855227013789372421),(-2413671770854775786073828259)⟩,⟨(-23622995196018545299015591561),(-23622995196018094069049093268)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-9283103732301238596197878888),(-9283103732299525693204998683)⟩,⟨(-70547700513378483571110678266),(-70547700513376770661371355460)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-21546370689407046042074623650),(-21546370689402591994751264744)⟩,⟨(-115634302603623035177863454371),(-115634302603618581119792175533)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-41026363711389393271210587162),(-41026363711378408623501174596)⟩,⟨(-155456910880787446930439104868),(-155456910880776462268743806285)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-68297060308736402755048228564),(-68297060308710831043235339121)⟩,⟨(-185107754393619881323523071047),(-185107754393594309595633646652)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-102737036421800720462326931426),(-102737036421747773127796403116)⟩,⟨(-200593510082475391450693024342),(-200593510082422444099167101358)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-141409151821942210572419489198),(-141409151821851956191459615811)⟩,⟨(-200955038727148469062226849509),(-200955038727058214664523912128)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-178584305095847463551940974749),(-178584305095729043426213638993)⟩,⟨(-188189959008493056540779924392),(-188189959008374636399933155456)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-207251210637716722843788873602),(-207251210637597168604335223360)⟩,⟨(-166062071553308621754058838971),(-166062071553189067502286234056)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-221330125732730997276973341285),(-221330125732638161383525928334)⟩,⟨(-138955693610821793648985454747),(-138955693610728957746450333965)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-217382498993148608343365188959),(-217382498993093162166382079531)⟩,⟨(-110655006395787957652901901052),(-110655006395732511469735782230)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-195721958397980754824179068027),(-195721958397953530123618329028)⟩,⟨(-83413526864556213156988596577),(-83413526864528988452481317101)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-160456323035691432800504833578),(-160456323035679569054818419770)⟩,⟨(-58375608307585310637600615042),(-58375608307573446889627941311)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-117384087223736243742477383916),(-117384087223731378872138498122)⟩,⟨(-36734895944384191943555107024),(-36734895944379327072056774565)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-71055552979508294455396593916),(-71055552979506410699142870847)⟩,⟨(-19452779293689420656075456340),(-19452779293687536899328654151)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-23738754395519730903050672990),(-23738754395519238913149141579)⟩,⟨(-5978899742732469425381818796),(-5978899742731977435351524242)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨593098751579506679043582247,593098751579506686186153154⟩,⟨410780532409442715455647426,410780532409442722283966652⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1980230859674492614500571768,1980230859674492636470298050⟩,⟨701872252742989656726405582,701872252742989677655029457⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨3443662329489388907991715197,3443662329489388945932077727⟩,⟨(-1084243977371527999065466346),(-1084243977371527963100762984)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨4130827780513446402565188294,4130827780513446458228050479⟩,⟨(-7808152385630221162236027748),(-7808152385630221109753273127)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨3929839276029285979904889255,3929839276029286056667994211⟩,⟨(-23216601892587477517473813144),(-23216601892587477445261138468)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨4669791071146644663047777475,4669791071146644768873526472⟩,⟨(-49060864043195957875473890753),(-49060864043195957775774141560)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨8297963072565588709462622210,8297963072565588872476575151⟩,⟨(-82354396250870639433014646111),(-82354396250870639277884975586)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨14311651532862087749349198455,14311651532862088132654914702⟩,⟨(-116553325770524212774979399626),(-116553325770524212400896930419)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨20072368018319022067246740376,20072368018319023908848003518⟩,⟨(-144777248461652548152257076188),(-144777248461652546320267295004)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨22719027650625475706783479553,22719027650625487172017879062⟩,⟨(-161842668503760385498015095166),(-161842668503760374041925160338)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨20564111252222105767556800781,20564111252222163897527361839⟩,⟨(-165166516835481857198387297079),(-165166516835481799076543623287)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨13940778124022149304722159932,13940778124022357286223923569⟩,⟨(-155044389793878452901662199954),(-155044389793878244927192602696)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨5536376239404567664357595304,5536376239405066697032308261⟩,⟨(-133676760562478618282104716169),(-133676760562478119255164257731)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-909462331411750600574735149),(-909462331410958572454437237)⟩,⟨(-103276789101129340695360685002),(-103276789101128548671391895736)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-3131203331396136855942464297),(-3131203331395352711912409149)⟩,⟨(-65493374882141545317296889504),(-65493374882140761175747259299)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1536081363635567064229201825),(-1536081363635235656263569236)⟩,⟨(-22468079816838786418550088767),(-22468079816838455011388465964)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-532399472701993199269866870647),(-532399472701888894459000045262)⟩,⟨(-310135446717172004923211436105),(-310135446717067700108543120921)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 1) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_1 (tableDensity true) (fullFactor true 1 1) density1_contains hk1_1_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4876624016703672741589830028),(-4876624016703672694637534439)⟩,⟨17650792678948899321662138586,17650792678948899365609602977⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_1 1 1 ha1_1_1_contains + def realAnswer : RBox := ⟨(-537276096718696872011556700675),(-537276096718592567153537579701)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_1 +namespace hm1_0_1_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1228587748151593927683392160),(-1228587748151591078574056036)⟩,⟨(-5724100760705929066635657195),(-5724100760705926217503825434)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-3237378960104212246293476909),(-3237378960104205784243156990)⟩,⟨(-16333669737618166318093847095),(-16333669737618159856011757036)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-4038086521785299330975748313),(-4038086521785293308166327238)⟩,⟨(-24686546547196582886352784085),(-24686546547196576863592210086)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-3212754558846296521620028354),(-3212754558846293143871619334)⟩,⟨(-30035233377203862908326262274),(-30035233377203859530807165397)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-743793804236002339700675664),(-743793804236001126309598651)⟩,⟨(-32286885145208479585388482177),(-32286885145208478372473882735)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2965136972726996462862164725,2965136972726996752545741495⟩,⟨(-31737937405681683071921524660),(-31737937405681682782950985226)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨7147468434596206510811286235,7147468434596206566946552878⟩,⟨(-28904107762128452557744401582),(-28904107762128452502451922272)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨10945970589115030197471387331,10945970589115030214542093096⟩,⟨(-24480599080458570404746220585),(-24480599080458570388420825276)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨13716760942696495940216937558,13716760942696495951428138740⟩,⟨(-19237164924544965742162640808),(-19237164924544965731254240282)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨15142353021168344300418100281,15142353021168344308972684636⟩,⟨(-13883615566798326771807636540),(-13883615566798326763205044533)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨15189911395749900215197229116,15189911395749900221823736329⟩,⟨(-8991690849471151426509746492),(-8991690849471151419761411877)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨14010037552167654111602787145,14010037552167654116451029530⟩,⟨(-4964748664051760894258612659),(-4964748664051760889340762562)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨11833140141297191393479209982,11833140141297191396804738866⟩,⟨(-2041066651349323956265118370),(-2041066651349323952957082690)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨8913716652795817916516587275,8913716652795817918611010347⟩,⟨(-305505636060012478086237828),(-305505636060012476062697155)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨5512489264301230519787374934,5512489264301230520919485460⟩,⟨339003805814301986791540210,339003805814301987853591781⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1861353776187706380983840854,1861353776187706381338154061⟩,⟨206849334718146050125795572,206849334718146050452049055⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-13707877167502081269318600964),(-13707877167502053296322986404)⟩,⟨(-43044691197234052863167870080),(-43044691197234024887954899032)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-40665362910384126986666879735),(-40665362910384025093284347856)⟩,⟨(-122571890754656661914067873222),(-122571890754656560014289995426)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-65641427541412407599881037088),(-65641427541412167785753214356)⟩,⟨(-183961072854947186322862612115),(-183961072854946946498949271364)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-86031302865555629057289062203),(-86031302865555115445193281382)⟩,⟨(-220243536248235709730901079485),(-220243536248235196106841374128)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-98840977058738627612145871922),(-98840977058737622051048352667)⟩,⟨(-230420406544184581900478664112),(-230420406544183576326686618478)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-102167812370010863636995053377),(-102167812370009148536639517214)⟩,⟨(-218989284635118490141979860831),(-218989284635116775029564368981)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-96210976582082906164194160998),(-96210976582080515673081479311)⟩,⟨(-193681400672337436375594810611),(-193681400672335045874097510312)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-83182952860771566508071351926),(-83182952860768998926112937901)⟩,⟨(-162406543284280960625230170168),(-162406543284278393035108993577)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-66419175440886389633044812340),(-66419175440884250737414343814)⟩,⟨(-131003161882696434428693439737),(-131003161882694295527180570701)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-49223997695617458595178616726),(-49223997695616064533079621058)⟩,⟨(-102640858371574749212299475445),(-102640858371573355146295287737)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-34006151014614728806841308728),(-34006151014614016373831006398)⟩,⟨(-78414977025196743501569830813),(-78414977025196031066167886894)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-21976710877144793912720144768),(-21976710877144488032420985576)⟩,⟨(-58267370767424911280435751534),(-58267370767424605398792146438)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-13293486525222299806817583382),(-13293486525222180523346497510)⟩,⟨(-41647642406614969750514644133),(-41647642406614850466360373034)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-7445602537778545702982298138),(-7445602537778500846882886751)⟩,⟨(-27804747100200042758237889176),(-27804747100199997901832867143)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3651714828431073704502112192),(-3651714828431057355310590847)⟩,⟨(-15917785244014927068728552972),(-15917785244014910719422711843)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1081732346393513980107317530),(-1081732346393509847233306394)⟩,⟨(-5178361581297351901892213857),(-5178361581297347768991194505)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨126113600159292107039413201858,126113600159292107099621559128⟩,⟨(-68947304507809696046034850283),(-68947304507809695992007748623)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨360986020605439352612990461150,360986020605439352790155015088⟩,⟨(-212581837081966871353814992321),(-212581837081966871193540004957)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨546227637768902431573517574509,546227637768902431860312712408⟩,⟨(-369081842246438146484715709925),(-369081842246438146220717635780)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨658261726484639364750997530714,658261726484639365135091314002⟩,⟨(-534628162727160396589086042082),(-534628162727160396227297785672)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨686696444188823750849551354802,686696444188823751311526133604⟩,⟨(-691991875224800153125549259299),(-691991875224800152679203950851)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨636414665050437530205039754864,636414665050437530724595713460⟩,⟨(-815700597458891314031316747307),(-815700597458891313516663522160)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨526633311861496389615472091976,526633311861496390178348980305⟩,⟨(-883154431788525412347976462541),(-883154431788525411778405695009)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨386392562061209626180018871549,386392562061209626838208218268⟩,⟨(-884434395626534245805046956684),(-884434395626534245130731299425)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨246058937768238420842045990160,246058937768238422119935319952⟩,⟨(-825184789040742517604472557652),(-825184789040742516304959167736)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨128494172625531623081342530740,128494172625531628125732658612⟩,⟨(-722674480268822913339833079452),(-722674480268822908272413898438)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨44714733169517853880771014686,44714733169517875188732377383⟩,⟨(-598198903657223835652743971021),(-598198903657223814323451197330)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-4945999059240409166262055557),(-4945999059240341473566467744)⟩,⟨(-469817995027060654500186676377),(-469817995027060586789550070824)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-26780885922441060723062257977),(-26780885922440912715127388895)⟩,⟨(-348464758550592935939042880586),(-348464758550592787917271953508)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-29526100728931033327810465771),(-29526100728930814491023716550)⟩,⟨(-238119636816113483722363304412),(-238119636816113264875952230352)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-21196522590514986557879115372),(-21196522590514780133424728026)⟩,⟨(-138117125138400497937170228550),(-138117125138400291507095171085)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-7568179252991815712669827819),(-7568179252991730657988501321)⟩,⟨(-45190524967337346104252465859),(-45190524967337261047734702300)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨117663519350480407651458058401,117663519350480781257912296769⟩,⟨130076514667793944071814287846,130076514667794317666253961780⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨358269618751632878173399005541,358269618751633740721094260745⟩,⟨375436362845954545978615953606,375436362845955408488863068979⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨610421794040878585369254946212,610421794040879418371039960092⟩,⟨576795418172637638827325147131,576795418172638471762673055755⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨870183761873498675879522057149,870183761873499168763615162959⟩,⟨707978956047354923990093822735,707978956047355416774592759767⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1121076760301073663680369718248,1121076760301073853893394628183⟩,⟨749161360002679206708163294536,749161360002679396785764283794⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1337706748497412393041674483882,1337706748497412442147432236973⟩,⟨692832823875341516992120695992,692832823875341565927481907151⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1492503121189904293934208704673,1492503121189904303394555751253⟩,⟨550059504062942989930969566477,550059504062942999191614575169⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1562781853177408624532804476994,1562781853177408626612510901527⟩,⟨350728188413439556731769988103,350728188413439558593053672410⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1537898632269011182661876576046,1537898632269011183727075715080⟩,⟨135470073316817470118547535058,135470073316817470984849653642⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1423611242449689766772241075405,1423611242449689767653589650537⟩,⟨(-56006199651267413686260906591),(-56006199651267412962224433738)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1240209652323067774444583249742,1240209652323067775209887186633⟩,⟨(-194969905388088843466835848618),(-194969905388088842818626025469)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1015432486177137529056802813911,1015432486177137529696807665318⟩,⟨(-268585663798344049517843603430),(-268585663798344048960121716576)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨775840144936829866780881755330,775840144936829867283677604768⟩,⟨(-278565024498710128858811849761),(-278565024498710128410483034764)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨540112528364532602955280506875,540112528364532603314136815196⟩,⟨(-236015641391575420426969638779),(-236015641391575420101522322000)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨316483598423717025669266754094,316483598423717025883294836205⟩,⟨(-156092421911834698767114508378),(-156092421911834698570854133029)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨104000677905534647741987325420,104000677905534647812828879181⟩,⟨(-54376586087109093134396763129),(-54376586087109093069081871151)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-146232852278449306334474893939),(-146232852278448001835105500440)⟩,⟨33005390245126340007053722915,33005390245127644526014053507⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-426272430200140954291857430586),(-426272430200135947793534696812)⟩,⟨114526356864521618136613215983,114526356864526624691210901241⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-668564983300378516857759446691),(-668564983300365485804551121673)⟩,⟨238840311768508644658986580424,238840311768521675798720152901⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-848864814354884077876937371876),(-848864814354851905798405783828)⟩,⟨421878011062049295749000212791,421878011062081467934406480263⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-945808276445240203854169072809),(-945808276445165221972809209589)⟩,⟨660617877644948445057803848233,660617877645023427054594280973⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-943525841225203946769479566844),(-943525841225048535602491810919)⟩,⟨930312707202864783430927938147,930312707203020194708943945587⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-836415786306450267581194184689),(-836415786306185191857397246151)⟩,⟨1190541400294407179913033702904,1190541400294672255731919658450⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-635989555279893428595715159916),(-635989555279545661530160896340)⟩,⟨1396932645850518386560734797226,1396932645850866153697215291716⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-373565619599026013954430307251),(-373565619598675290621625087344)⟩,⟨1513124844627671134439343210697,1513124844628021857814690838669⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-94806626767590460928070536996),(-94806626767318725632089957972)⟩,⟨1520407366643841279589215005064,1520407366644113014899277611151⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨151099843834032481398550428988,151099843834194212257118046992⟩,⟨1422043402445016195085168113841,1422043402445177925933464068763⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨322630940244048619199409933693,322630940244127669134139753102⟩,⟨1239128187034317763934022904512,1239128187034396813841741478987⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨395140441173536453840936911365,395140441173570722129552858818⟩,⟨999393754907640218467393121344,999393754907674486721714323144⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨366491205345537908514374454317,366491205345551888291980799281⟩,⟨727106684941777909926390006879,727106684941791889671641552723⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨254986820079611110896410630719,254986820079616501423333679725⟩,⟨439528589437778123126654476223,439528589437783513630824508716⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨90903640078137770448113831367,90903640078139174989208317620⟩,⟨146766766417923134553721109809,146766766417924539086653101503⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨24811725284730350267384496844,24811725284730350288240344383⟩,⟨(-36198722474303574420602311888),(-36198722474303574398890234188)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨66737931681074400587543484469,66737931681074400651439542248⟩,⟨(-111995077488122091879973658371),(-111995077488122091813190876437)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨87097053817707653456895988853,87097053817707653567007211693⟩,⟨(-196832240249712703696317648109),(-196832240249712703580712724333)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨76969222851785651865404999644,76969222851785652026490452243⟩,⟨(-292452646352533598923326600392),(-292452646352533598753564190643)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨34175633077132503565538996412,34175633077132503784002486886⟩,⟨(-392549709841422536036469550916),(-392549709841422535806108930735)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-38792517466747077025402495455),(-38792517466747076735190488006)⟩,⟨(-481550975282398015847225874178),(-481550975282398015542246972724)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-137193434800454828215675318130),(-137193434800454827797938329090)⟩,⟨(-540978048411776132282608572782),(-540978048411776131848050489900)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-251788239309518193886807498797),(-251788239309518192989085194238)⟩,⟨(-558234787310518107587470041952),(-558234787310518106673194069178)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-366764732124555351716446711901),(-366764732124555347605090014019)⟩,⟨(-530339838442117995041451410784),(-530339838442117990916958414086)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-462650069648293743911263748550),(-462650069648293718568415348855)⟩,⟨(-463906445097131685137222621286),(-463906445097131659786770603786)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-521356186779883743147546154741),(-521356186779883615678191552647)⟩,⟨(-373470128549843486744807071005),(-373470128549843359273842498726)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-529852806673494508449103639341),(-529852806673494042121243868510)⟩,⟨(-277115084604485489113020183480),(-277115084604485022788130354905)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-482635126002665832155475650746),(-482635126002664606015323123401)⟩,⟨(-189710194453252400287292653313),(-189710194453251174152456409730)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-383766536617794787224974807786),(-383766536617792689275313852610)⟩,⟨(-118363067972445091310199194205),(-118363067972442993366014681858)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-245695847586928382385337481468),(-245695847586926194863218728724)⟩,⟨(-63153170103709692119292234894),(-63153170103707504601131189301)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-84381660747483416689027762621),(-84381660747482467320375867360)⟩,⟨(-19618854751345284410013874283),(-19618854751344335042790714911)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1739753875783434847047470074997,1739753875783741015603533636220⟩,⟨241010609169240710483052146456,241010609169546878904532003204⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 2) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_2 (tableDensity false) (fullFactor true 1 2) density0_contains hk1_1_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-46155683587825365956377631845),(-46155683587825365859148901946)⟩,⟨(-19552242702175213855307713016),(-19552242702175213754163499415)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_2 1 2 ha1_1_2_contains + def realAnswer : RBox := ⟨1693598192195609481090992443152,1693598192195915649744484734274⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_2 +namespace hm1_1_1_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-79094148089538496047385322),(-79094148089536163132336694)⟩,⟨(-998054477855853016804791979),(-998054477855850683895018154)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-158461680193882553794304884),(-158461680193877265149657547)⟩,⟨(-2855724640712662128702716342),(-2855724640712656840065668542)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-27755962339346309465926355),(-27755962339341385896549288)⟩,⟨(-4303650032624027708065793624),(-4303650032624022784485608643)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨340640834134277038824136080,340640834134279793660298154⟩,⟨(-5123730338532539358646258035),(-5123730338532536603756917343)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨816635279638320809137241491,816635279638321792870124256⟩,⟨(-5258779239098154517515709211),(-5258779239098153533670406430)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1222293098486968878527003095,1222293098486969107220375959⟩,⟨(-4897917529636980768650435132),(-4897917529636980539781210942)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1520329306550637339587305166,1520329306550637377774264872⟩,⟨(-4343137350179050319924264500),(-4343137350179050281505703173)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1801236164778977597520948540,1801236164778977604677603792⟩,⟨(-3769680978989167801810360755),(-3769680978989167794404020280)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨2119141907509506807867765733,2119141907509506811452795113⟩,⟨(-3176734696644477656402601304),(-3176734696644477652638294734)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨2413905395070954532762077437,2413905395070954535501633574⟩,⟨(-2509541256401520640970407698),(-2509541256401520638121136019)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨2559161241312034411313110577,2559161241312034413517365286⟩,⟨(-1775806715594473192908940600),(-1775806715594473190680539232)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨2459672715672892022078503059,2459672715672892023757518079⟩,⟨(-1072760496663316947144268106),(-1072760496663316945514270188)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2116705229492498900280023625,2116705229492498901471873223⟩,⟨(-522442867626205183836369082),(-522442867626205182736579608)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1604068020530281574578653019,1604068020530281575346257859⟩,⟨(-183108630087086327083656257),(-183108630087086326415057670)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨995725457684666528493129903,995725457684666528913758347⟩,⟨(-30139274476019275935954282),(-30139274476019275589047228)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨337297899229394253282335299,337297899229394253414977126⟩,⟨3479954104068916829317359,3479954104068916934779428⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1312167575983853693144238235,1312167575983876720782282998⟩,⟨(-6922537387388424768060193304),(-6922537387388401740696341299)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨3226389273069032877285697694,3226389273069116792620939760⟩,⟨(-19614806943677736729241678311),(-19614806943677652814690940317)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨3356728177814011330934239718,3356728177814208979935011085⟩,⟨(-29186040974794304387699366989),(-29186040974794106739888081826)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1496529263987208897599578047,1496529263987632589260230386⟩,⟨(-34613307549160814905366068723),(-34613307549160391215145935699)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1626264434646004144721503777),(-1626264434645173881356304379)⟩,⟨(-35994593233432805988611831270),(-35994593233431975726766684701)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-4758080648103146164255233576),(-4758080648101728876566160943)⟩,⟨(-34242056177140102340506266288),(-34242056177138685054258211368)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-6833962991691936576622378138),(-6833962991689959432154223573)⟩,⟨(-30520073335243143127721522616),(-30520073335241165984502234411)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-7491705791154799147656181166),(-7491705791152674513431846366)⟩,⟨(-25890471921147490147378882865),(-25890471921145365514146997022)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-6988597134313032616321840271),(-6988597134311262770270864648)⟩,⟨(-21189816855609947333504413212),(-21189816855608177488191247855)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-5803308934717836835074397439),(-5803308934716683938732165677)⟩,⟨(-16942854401001613799343671816),(-16942854401000460903518231070)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-4349826932560225054999578597),(-4349826932559636453743591693)⟩,⟨(-13333969976804451374779089525),(-13333969976803862773857527267)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-2915018774703417254128762424),(-2915018774703164869046482978)⟩,⟨(-10285977357055077383926588986),(-10285977357054824999040295755)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-1706329897583086747548118953),(-1706329897582988465954574901)⟩,⟨(-7625264652775483400379230145),(-7625264652775385118887856388)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-849567653117087298998475830),(-849567653117050390820087199)⟩,⟨(-5229349648190377924547516516),(-5229349648190341016415208459)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-345526739536618722750668587),(-345526739536605285119368229)⟩,⟨(-3039483400405765241162689190),(-3039483400405751803548540921)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-86563302011743887828929025),(-86563302011740493077725763)⟩,⟨(-994980116902611527145836580),(-994980116902608132398659998)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨32406754520431028707841147925,32406754520431028730905050192⟩,⟨1664029804424741837271799517,1664029804424741860048359618⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨94671187187746338100967818698,94671187187746338169830606648⟩,⟨2258294884616628068510221203,2258294884616628136560719352⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨148601280456021230286948608282,148601280456021230399413000559⟩,⟨(-4041407998687598883421045942),(-4041407998687598772036751097)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨187494373483877240419668597421,187494373483877240570383970987⟩,⟨(-18489829498336735859540663586),(-18489829498336735709852395635)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨205477211791399888903277440016,205477211791399889083084326464⟩,⟨(-39738209127868480196108060495),(-39738209127868480016990462270)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨200948257899963750303651055031,200948257899963750503960012329⟩,⟨(-64558166262391559309076094355),(-64558166262391559109046818799)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨178133096191198696716490865388,178133096191198696936791591285⟩,⟨(-88015272524265565338572415844),(-88015272524265565118104901133)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨144918110367320391054290567733,144918110367320391351523503859⟩,⟨(-104683742246711503482941583400),(-104683742246711503185208764241)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨109428089490279871844782614852,109428089490279872662241730663⟩,⟨(-111008202366074977415224639177),(-111008202366074976597216838578)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨77634543626016770346212107380,77634543626016774260094280879⟩,⟨(-106582028123839446121764860021),(-106582028123839442207496574338)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨52381247091356740808515983159,52381247091356758008134101844⟩,⟨(-93624291840177061143870133518),(-93624291840177043944061310794)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨33769514748156274376285690795,33769514748156329435184303553⟩,⟨(-75683236437810360845629173225),(-75683236437810305786631785827)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨20559661091906863370427889939,20559661091906984031293954663⟩,⟨(-56358161646062637834144446033),(-56358161646062517173225824604)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨11491424941284153595236245065,11491424941284332199321124341⟩,⟨(-38145085357141601318260269946),(-38145085357141422714159729474)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨5546066794982533004058919341,5546066794982701586028148697⟩,⟨(-21874150345254629138894934409),(-21874150345254460556929002304)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1615020830754005363326582180,1615020830754074846453126267⟩,⟨(-7109447716977627048388793372),(-7109447716977557565268738924)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨5540520680510830739047824425,5540520680511144630750305027⟩,⟨58368931771588856842831561151,58368931771589170735753794925⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨20238772432515664199595468120,20238772432516388382157716748⟩,⟨169675932512882907147411828530,169675932512883631333788727350⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨45055131443117540561697147058,45055131443118238930539261796⟩,⟨264935511731859986382353721614,264935511731860684757970712989⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨84275738274793100154695220864,84275738274793512396369690047⟩,⟨335360461232131809164408752300,335360461232132221416245936764⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨138036226783217072279866702103,138036226783217230724426538026⟩,⟨375828239787175139324979664029,375828239787175297783274709045⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨200370216744768617617429539728,200370216744768658099297649894⟩,⟨385758645171956783355252935829,385758645171956823854279435523⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨260047827793860702766365378930,260047827793860710198742520342⟩,⟨367683350368282666235441364048,367683350368282673687858575556⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨305337555497003738612716550020,305337555497003739904352372375⟩,⟨326118071062519753463261772974,326118071062519754776567297779⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨328583579350879611779937070126,328583579350879612237379482652⟩,⟨268093651768989069729036663640,268093651768989070205936101232⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨327680542807105974599725325548,327680542807105974931275264419⟩,⟨202915537701650084068016313616,202915537701650084414686820959⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨305103145713190771401906522116,305103145713190771681942679274⟩,⟨140242363274750522014153916735,140242363274750522305156892408⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨265736420753501320162129192576,265736420753501320395410572024⟩,⟨87651547329293816123263933453,87651547329293816364076624491⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨214822415453756642402055901127,214822415453756642586059456400⟩,⟨48917208443745403566909242685,48917208443745403755784373045⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨156865608811646694274916598097,156865608811646694406871338808⟩,⟨23901292928379674249252514757,23901292928379674384123011698⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨95188215442301977459827028720,95188215442301977538811577301⟩,⟨9795687479112980028105760581,9795687479112980108609832568⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨31866161371714876111526234303,31866161371714876137726423183⟩,⟨2500413776748205753090634566,2500413776748205779756680416⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-47428679504455794635165441919),(-47428679504454722533905100053)⟩,⟨13288407011709291219725915319,13288407011710363317069152608⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-141192432088576101641415167735),(-141192432088571986766782452350)⟩,⟨44403727371781229052150119025,44403727371785343915229714516⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-229991843275790703702213993056),(-229991843275779991990066368047)⟩,⟨87366282397628636677671367627,87366282397639348371647778747⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-306137766873202007213028034315),(-306137766873175557121253108197)⟩,⟨145651862566563135614658179140,145651862566589585683293934798⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-358637551602490029987739085291),(-358637551602428376615814748499)⟩,⟨219315292750508691235587285540,219315292750570344581820382276⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-378056521465338494415824536906),(-378056521465210709060590849495)⟩,⟨305640833277527232974193395416,305640833277655018303703155719⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-361801004471033766261399003769),(-361801004470815857214956531112)⟩,⟨397483306176952699136218855186,397483306177170608159509930258⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-315113096763155757633575463320),(-315113096762870011134168778632)⟩,⟨482261808974042963006724491724,482261808974328709488138753523⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-248874325162130101941772796932),(-248874325161842155758223505222)⟩,⟨544811218602227113764118762288,544811218602515059936463616774⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-176565406933469015750704217461),(-176565406933246156978342821354)⟩,⟨571972418289177177941513427584,571972418289400036709337746554⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-110421369575391857455967628053),(-110421369575259384746513875685)⟩,⟨556198636217264594559705236428,556198636217397067269853918814⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-57750320864168925589569801841),(-57750320864104263307075628595)⟩,⟨497963372154441587417422623324,497963372154506249703975792482⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-20596940111056916056643022572),(-20596940111028920524758456218)⟩,⟨406481963035672512983347838587,406481963035700508520827785957⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1093736194267975780204819554,1093736194279384449100287699⟩,⟨295895586475197979633709284919,295895586475209388307948477049⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨8170757603268752196083398202,8170757603273148019378786643⟩,⟨178178211093711387262578508170,178178211093715783089629292529⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨4124994757317963535481881416,4124994757319108459314183409⟩,⟨59320791432895829491466780989,59320791432896974416629724069⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨685802426788795528020727280,685802426788795540158348269⟩,⟨(-1110439950166225390615787699),(-1110439950166225377657030846)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1074566095473824529276649120,1074566095473824566527297244⟩,⟨(-3654741141327770696809754792),(-3654741141327770656882728319)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-2342444398537794260381972797),(-2342444398537794196192879609)⟩,⟨(-6145340697624183033225248139),(-6145340697624182964083734417)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-14794027217299006641960691509),(-14794027217299006547910411123)⟩,⟨(-6627904156896003885479302085),(-6627904156896003783651552407)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-43414024203767870541605718812),(-43414024203767870411357717750)⟩,⟨(-4127908075507817586303641494),(-4127908075507817445111003845)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-92240085075860802004082525889),(-92240085075860801822927526883)⟩,⟨(-1204721444351972536713689718),(-1204721444351972341004894155)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-156778467580965587645651554893),(-156778467580965587362089087734)⟩,⟨(-1316671156340386655814513528),(-1316671156340386353680731559)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-225250098470886746753127271929),(-225250098470886746068712255848)⟩,⟨(-4305259547641048383096094795),(-4305259547641047677064580808)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-284074518514388385643685591281),(-284074518514388382308077856025)⟩,⟨(-6592935649323314702188004735),(-6592935649323311344107881783)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-321906051635733449125998282597),(-321906051635733428413783491855)⟩,⟨(-4317582531909343557085723188),(-4317582531909322823495333702)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-331998940326035682137276208475),(-331998940326035578026870289358)⟩,⟨4388862698740224543805600971,4388862698740328673240981469⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-313616447441144275955458956984),(-313616447441143895130789047338)⟩,⟨18058248964877142104933048477,18058248964877522945702667821⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-270893765418421862868957964043),(-270893765418420861164617218081)⟩,⟨31158453377102768134295375874,31158453377103769850284829359⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-209045968574654481216689340458),(-209045968574652766467794207743)⟩,⟨36237263253562836412495326816,36237263253564551168933367903⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-132302242487115297228642535238),(-132302242487113508599383197253)⟩,⟨28948579911709790697581509748,28948579911711579330981981893⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-45328240914831790079352703835),(-45328240914831013673207885966)⟩,⟨11013782802100367912401908788,11013782802101144319825864367⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-150983373698336744135066649485),(-150983373698085393556200890202)⟩,⟨1133658338586844792076623418962,1133658338587096142686546732040⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 2) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_2 (tableDensity true) (fullFactor true 1 2) density1_contains hk1_1_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨60357432384079324585040871776,60357432384079324712186133950⟩,⟨25568317379767587216983037696,25568317379767587349248547790⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_2 1 2 ha1_1_2_contains + def realAnswer : RBox := ⟨(-90625941314257419550125777709),(-90625941314006068843914756252)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_2 +namespace hm1_0_1_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-3925171984469409546405756405),(-3925171984469402053153593859)⟩,⟨16168936176788982558586980347,16168936176788990051420897297⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-11560763239762043479068358761),(-11560763239762026597682240169)⟩,⟨46022943925112392176275494706,46022943925112409056438552216⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-18712917944314170475334975608),(-18712917944314154951441714723)⟩,⟨69174125733882651268163126949,69174125733882666790121417222⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-25519283275936609101549948202),(-25519283275936600567994647257)⟩,⟨83354758576763325579685831983,83354758576763334110743962568⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-32360422782486994194129747822),(-32360422782486991207602490475)⟩,⟨88294086148061835407436436364,88294086148061838391073641084⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-39277870128305399106789088113),(-39277870128305398412136797281)⟩,⟨85102792026417425405086838107,85102792026417426096535544456⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-45607260811584998061642018590),(-45607260811584997907190041198)⟩,⟨75751465815272047247566847287,75751465815272047399346587605⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-50353507515256677041654014459),(-50353507515256676984775142399)⟩,⟨62650573984493517334551394276,62650573984493517389785914517⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-52747619212722903930536208046),(-52747619212722903893842468316)⟩,⟨48105392235144442667394791544,48105392235144442703511392745⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-52447630368412881904924747711),(-52447630368412881877276951432)⟩,⟨33944705147256487455800980968,33944705147256487483733894380⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-49480533085394232584953171027),(-49480533085394232563779207229)⟩,⟨21448534219561359441166218093,21448534219561359462841932347⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-44093033886671011725078756557),(-44093033886671011709754276999)⟩,⟨11415661371600952794954614969,11415661371600952810597730304⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-36606862001424354661529252696),(-36606862001424354651101551001)⟩,⟨4273026989195328531343116521,4273026989195328541780732542⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-27392836421178655996669238999),(-27392836421178655990124900257)⟩,⟨145565300158823380513341968,145565300158823386866560917⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-16920683629169309812695318062),(-16920683629169309809157402678)⟩,⟨(-1232210649084185619059487285),(-1232210649084185615730592313)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-5716245214447337762555181667),(-5716245214447337761446520831)⟩,⟨(-648376216672085001856661055),(-648376216672085000833953526)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-51310706671901387652724929030),(-51310706671901316302915707161)⟩,⟨94340329930989442791975467328,94340329930989514138247697961⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-142392627371269346186437968573),(-142392627371269083157032519592)⟩,⟨273278771599568248079295997577,273278771599568511098987668460⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-202754359767057431152930235701),(-202754359767056798370025494833)⟩,⟨423451658683630723807836343153,423451658683631356577224733575⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-223739301073911003858226323100),(-223739301073909609880444773936)⟩,⟨529032801964728859222762854557,529032801964730253186093482901⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-209037823123573527429235023151),(-209037823123570715721531334370)⟩,⟨580823191446297084798890506753,580823191446299896493560258184⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-171563218913656467958620738159),(-171563218913651542930165161207)⟩,⟨579452639877989919735275664739,579452639877994844753291868611⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-127172311201229469322064526118),(-127172311201222471378190628177)⟩,⟨535279629079667172895891617718,535279629079674170831967536411⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-88329503580611515869648745712),(-88329503580603929806233095754)⟩,⟨464266459439824900717934452088,464266459439832486775536027138⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-60722511356728187198492254158),(-60722511356721877568777363153)⟩,⟨382472012763678384415547946040,382472012763684694040616151011⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-43932708824968937551816832952),(-43932708824964870583276292775)⟩,⟨302108859070307680679114733123,302108859070311747643630647938⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-34403687403802066441978050734),(-34403687403800025030415898143)⟩,⟨230246292680602747607342801617,230246292680604789015313119527⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-28295947793419563097130979021),(-28295947793418705176182941405)⟩,⟨169569347126280862446946767129,169569347126281720364772872510⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-23002382586770228762250370695),(-23002382586769901288551210124)⟩,⟨119834132259473997507491832218,119834132259474324978656445914⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-17287443230094610104068094938),(-17287443230094489227634037929)⟩,⟨79147147305919878990822982331,79147147305919999865396606275⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-10801708691180821715187912710),(-10801708691180778254092872817)⟩,⟨44940932238127672039170092914,44940932238127715499131465370⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-3679498488691913896308961213),(-3679498488691902988584672270)⟩,⟨14556027272816458149829719445,14556027272816469057173516194⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-236743065697809887628730810407),(-236743065697809887520577025109)⟩,⟨(-149592079255351371737723750832),(-149592079255351371639182384983)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-707898236374675763979090785742),(-707898236374675763660099317029)⟩,⟨(-412350517208938811333417115757),(-412350517208938811045453050554)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1165134005407322802349130441059),(-1165134005407322801831998620274)⟩,⟨(-573173230893109305415817525520),(-573173230893109304956320807200)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1581493697633479801127475598845),(-1581493697633479800425148096290)⟩,⟨(-590079223353262950407813762951),(-590079223353262949795637866291)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1913112785112366128798069436369),(-1913112785112366127930156839914)⟩,⟨(-456504997317942045455956031187),(-456504997317942044713389145228)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-2110992074247188304826798611111),(-2110992074247188303821428901189)⟩,⟨(-203862388739348490451896532052),(-203862388739348489602171174972)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-2143004366639197170080770983241),(-2143004366639197168961898910454)⟩,⟨107707266192848041883418360874,107707266192848042826414132709⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-2011958272922958666909289066587),(-2011958272922958665607637348757)⟩,⟨407192070086617831680713568679,407192070086617832801334129561⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1756408609263362157547079614884),(-1756408609263362155115878541234)⟩,⟨634541040757834812158019329742,634541040757834814438159485531⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1435113004147783334793209046915),(-1435113004147783324999081363327)⟩,⟨757597113934824187984355109393,757597113934824197669471235610⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1105749251205156404859789863162),(-1105749251205156360465495738150)⟩,⟨775422542013418955015687692227,775422542013418999335437688427⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-808798812746314754403806992945),(-808798812746314603467717466649)⟩,⟨708533096173377492555625037915,708533096173377643442575508194⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-561897993791497277773116520143),(-561897993791496929654261417003)⟩,⟨584837989738017648615932567983,584837989738017996703618593113⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-363857625734254891369248330179),(-363857625734254356505884611038)⟩,⟨429512721275164400453782087811,429512721275164935298449020687⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-203232112770389240952429418275),(-203232112770388723870286478030)⟩,⟨260359099821361187978705548681,260359099821361705050970191943⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-65222389459343878648602145965),(-65222389459343663030995889814)⟩,⟨86980550817999172964485763423,86980550817999388579024007755⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨140803619380753495123573797154,140803619380754011978798510437⟩,⟨(-247219764502368146241290356572),(-247219764502367629346536277637)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨395885025579336441781994575532,395885025579337627436667713847⟩,⟨(-745971578476272524190651210141),(-745971578476271338415949220523)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨573352395987528626728331460961,573352395987529756361515738320⟩,⟨(-1250287836289227162541084885705),(-1250287836289226032704295472152)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨630215899078541631778024046881,630215899078542285400536463683⟩,⟨(-1744266682842047961884070602090),(-1744266682842047307972208930767)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨538516821331513335382176766367,538516821331513595470162761472⟩,⟨(-2190945031508227703656443457854),(-2190945031508227443225090778957)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨295020911900761317467680646370,295020911900761394172482642383⟩,⟨(-2539988024244312260423378845282),(-2539988024244312183379129970810)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-69264772945728803122349284078),(-69264772945728786296521892256)⟩,⟨(-2742843112150098215609911445763),(-2742843112150098198480140299320)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-489671844905748697115990260865),(-489671844905748693191431412322)⟩,⟨(-2767982657450391238709552919521),(-2767982657450391234539865276280)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-884248634117692726025968522006),(-884248634117692724143279869231)⟩,⟨(-2612851065360462667180364288518),(-2612851065360462665123048741922)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1178042473796582230101402450083),(-1178042473796582228584537257054)⟩,⟨(-2307917300322579896838089350890),(-2307917300322579895216315292652)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1323567276027318850068161416088),(-1323567276027318848746169825374)⟩,⟨(-1908253575470249127279778801420),(-1908253575470249125911580308227)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1309249880741832116428490946622),(-1309249880741832115316701852548)⟩,⟨(-1476188756506683764955713417056),(-1476188756506683763839280090927)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1153682139984031350802254156591),(-1153682139984031349925747551989)⟩,⟨(-1063627692232536726232907651615),(-1063627692232536725374950729923)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-891459945533655297377894608503),(-891459945533655296751583484588)⟩,⟨(-700601746593836605018207650128),(-700601746593836604417322719351)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-559703966590133176642851811956),(-559703966590133176269336729889)⟩,⟨(-392729422364723509776508988881),(-392729422364723509423126494738)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-190388236218765883531447717767),(-190388236218765883407855972144)⟩,⟨(-125874536797885309521237684210),(-125874536797885309405149089004)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨79452858797992652748112349879,79452858797994649595240793991⟩,⟨191471409368049786882952593239,191471409368051783710105366704⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨258674773451801125613978434946,258674773451808791010727260406⟩,⟨554728679725933996188902738345,554728679725941661529107579697⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨493533072384287579944072053523,493533072384307538377878154733⟩,⟨858126749456450340718783403982,858126749456470299068451882859⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨803540148562870963890315762077,803540148562920248762175348374⟩,⟨1062909916449017373780119995795,1062909916449066658554078306348⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1181318618835860758193458874204,1181318618835975590818775977559⟩,⟨1135584481075181890795149189923,1135584481075296723325428334129⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1587684255546983102008817300870,1587684255547220818561848535929⟩,⟨1053527749212915911417886984211,1053527749213153627896630774916⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1959729848792944774024951004591,1959729848793349159023307580721⟩,⟨812948657980382659302716658322,812948657980787044262656269759⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨2229256604005577514152654049071,2229256604006105632162734160797⟩,⟨438838507355097908192484207517,438838507355626026210112902063⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨2343180440430566144813438775793,2343180440431095056753829350640⟩,⟨(-11778547647248226271756846542),(-11778547646719314274280676541)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨2280119427866258665738972849475,2280119427866664577290811214603⟩,⟨(-459887555007783356102008374140),(-459887555007377444447486974627)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨2057346167206705594665563220365,2057346167206944279068462289724⟩,⟨(-823736767051909616229561396503),(-823736767051670931690382830491)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1722753056690782519621150923983,1722753056690897540472910359188⟩,⟨(-1037939506209472559611868986539),(-1037939506209357538608812313103)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1333381606188745616431095921415,1333381606188794729410910736199⟩,⟨(-1067065136550038963201959492226),(-1067065136549989850076728656129)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨933963759445465307834504797077,933963759445485058127812529777⟩,⟨(-912754133786320774195462859801),(-912754133786301023782098742918)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨548205821319027160621762602856,548205821319034689986746426035⟩,⟨(-610061101493784745348686766359),(-610061101493777215904881924715)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨180122713067021145205493108220,180122713067023094619529370642⟩,⟨(-213808305407136423036046413092),(-213808305407134473594570161602)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-45166189689784161703347186467),(-45166189689784161676874499037)⟩,⟨(-27592566652673446440967448227),(-27592566652673446415981519243)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-139591763468461225806204732758),(-139591763468461225724617123149)⟩,⟨(-73175437380858735575002928852),(-73175437380858735498300269049)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-244875016597972323199278878117),(-244875016597972323057533975871)⟩,⟨(-91582792294308967939269568412),(-91582792294308967806524630381)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-363035485772508716778674885456),(-363035485772508716569498383249)⟩,⟨(-70805218506936070737512101437),(-70805218506936070542145640193)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-486206511418538888096163063068),(-486206511418538887810795114334)⟩,⟨(-6998202181574055584032571994),(-6998202181574055317213103923)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-594646410360036906779987910675),(-594646410360036906400652657169)⟩,⟨97182559952028343219768493205,97182559952028343576392923981⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-664019710144453358673443988010),(-664019710144453358133714413217)⟩,⟨235118600003147084494684920043,235118600003147085008769491995⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-676779791583385210125856754714),(-676779791583385209007655984947)⟩,⟨393643100776016059958157446177,393643100776016061051248359622⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-628250308108047296805464761261),(-628250308108047291874311265385)⟩,⟨550676273070299291606577625444,550676273070299296517869933216⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-527801327854443945765258517402),(-527801327854443915126618318448)⟩,⟨679252796701581041846315008190,679252796701581072473658080663⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-397127671665550261322344514510),(-397127671665550085574562574289)⟩,⟨754671124641694399464888997160,754671124641694575210819191503⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-264157105295500338180161114454),(-264157105295499630438361015387)⟩,⟨759760096201787659236687370062,759760096201788366982474815214⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-152784380069095502615205378880),(-152784380069093629549556456208)⟩,⟨687834785342186935205162783452,687834785342188808277384156046⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-74746304878167309716731909481),(-74746304878164101541482197098)⟩,⟨544887991393333286448114130296,544887991393336494629904716119⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-29292511632568039186070306081),(-29292511632564692026786079337)⟩,⟨348092119118354300753594934087,348092119118357647917504968840⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-6975751601249086360317561301),(-6975751601247633330235003862)⟩,⟨119424977671296754826669963358,119424977671298207858403588130⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1816740374980571693698412451687),(-1816740374980107389513936250487)⟩,⟨(-1852026701703304274165311645679),(-1852026701702839969816876936274)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 3) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_3 (tableDensity false) (fullFactor true 1 3) density0_contains hk1_1_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-11176879606754503020036331479),(-11176879606754502814248143108)⟩,⟨105472558490690134166067178825,105472558490690134367963372852⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_3 1 3 ha1_1_3_contains + def realAnswer : RBox := ⟨(-1827917254587326196718548783166),(-1827917254586861892328084393595)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_3 +namespace hm1_1_1_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1030254994018659579210719498),(-1030254994018653443696326059)⟩,⟨2652330394576410708788403700,2652330394576416844404024180⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-3071206220893102709020472623),(-3071206220893088893523077738)⟩,⟨7550046090354853812155256226,7550046090354867627953137728⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-5026334779728645971808648575),(-5026334779728633282348658000)⟩,⟨11258400994082919026443718595,11258400994082931716394843756⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-6712838525917992897480462016),(-6712838525917985939704974517)⟩,⟨13211997364915547558273626212,13211997364915554516716561487⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-7813204219140601008906555321),(-7813204219140598590686507959)⟩,⟨13381071224311839913161274619,13381071224311842332202615015⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-8181528662252999296264228295),(-8181528662252998751997530290)⟩,⟨12382376081452246116364861930,12382376081452246661558070683⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-8117226545128227020683085855),(-8117226545128226917916109538)⟩,⟨10988814473038557768980795444,10988814473038557872541268521⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-8086038315875456708128331332),(-8086038315875456683358488191)⟩,⟨9558317106664841964537601494,9558317106664841989843898547⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-8276532398216225952221720796),(-8276532398216225940235252178)⟩,⟨8037232093424304858523714183,8037232093424304870831554412⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-8509726714889626613456818928),(-8509726714889626604634125478)⟩,⟨6300910075323632665742583227,6300910075323632674723709474⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-8435678891208880824195752440),(-8435678891208880817268734892)⟩,⟨4405412039024597925570374480,4405412039024597932469209771⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-7794866889955130953033353915),(-7794866889955130947836514036)⟩,⟨2618477830413978796430564105,2618477830413978801429133348⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-6574503133296348721877187921),(-6574503133296348718214319489)⟩,⟨1246528581860166539641795642,1246528581860166543003611419⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-4940764831270225056688460409),(-4940764831270225054329848216)⟩,⟨419521097786438593952378761,419521097786438596001321914⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-3059520632596378492597160762),(-3059520632596378491299978782)⟩,⟨58084241532398156038909197,58084241532398157108498050⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-1036082070252726499566033830),(-1036082070252726499155589744)⟩,⟨(-13041715017259570289668749),(-13041715017259569962820377)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-14037614496732576508263079827),(-14037614496732517781679498860)⟩,⟨9137444798500571365423622547,9137444798500630092465171658⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-38956590041902433074348138432),(-38956590041902216480681789889)⟩,⟨27058270481544940029318835200,27058270481545156624237593359⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-55479075500085118704111173942),(-55479075500084597221442507066)⟩,⟨43682157553802709296463503119,43682157553803230780873775507⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-61281829612384181661400762845),(-61281829612383031781207160674)⟩,⟨57676024913513565757166879285,57676024913514715639228142255⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-57512277382946727823173004702),(-57512277382944406318662932322)⟩,⟨67525478752016141189651858890,67525478752018462695872212650⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-47821451891759815531774286352),(-47821451891755745723647367225)⟩,⟨72010605540454835093469100386,72010605540458904903009651517⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-36306480474750537176213918047),(-36306480474744749286624982939)⟩,⟨70790471940407170839184996267,70790471940412958729888986662⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-25861588190929584627989747551),(-25861588190923307289271322824)⟩,⟨64832791497438630342928309105,64832791497444907682526229653⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-17831141815036050824412303466),(-17831141815030829870901261876)⟩,⟨56058193327842818364833591439,56058193327848039319051288771⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-12413638333695546412287745535),(-12413638333692182998074189920)⟩,⟨46396427281763753722607074420,46396427281767117137407949281⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-9156296637892454992270128180),(-9156296637890768394711039435)⟩,⟨37088906833787485549292085709,37088906833789172147359933666⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-7294999778069500750601958145),(-7294999778068792858015190621)⟩,⟨28599230946235949998300042684,28599230946236657891332162452⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-5993934370432164250406787574),(-5993934370431894427814150735)⟩,⟨20970708443731828287848901612,20970708443732098110815749007⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-4628363281824792285764200822),(-4628363281824692824972603944)⟩,⟨14174883644022983185770888803,14174883644023082646847529164⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-2954010138208344550222595548),(-2954010138208308828471348848)⟩,⟨8138341439889095257846878464,8138341439889130979776612921⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1016399055494075989816451408),(-1016399055494067030153264926)⟩,⟨2646014733938940727231325565,2646014733938949686955553850⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-27821953715874018222163785558),(-27821953715874018179646390682)⟩,⟨(-56774157724405243586889976766),(-56774157724405243544794759925)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-86709460483494847361365676938),(-86709460483494847235068836744)⟩,⟨(-163633971269712910874576589089),(-163633971269712910749693245371)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-152190062027072380919629939325),(-152190062027072380715598967375)⟩,⟨(-250151414675218424629016178838),(-250151414675218424427542181402)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-220881557296707730601932762089),(-220881557296707730330162843650)⟩,⟨(-303068438507747041229574781195),(-303068438507747040961620377628)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-284155156029595800583662806759),(-284155156029595800259911769404)⟩,⟨(-312279347001057261995763891267),(-312279347001057261676891347444)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-332620349204756411825143835926),(-332620349204756411466073749100)⟩,⟨(-276621850841869964626375947221),(-276621850841869964273152382732)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-358934624344316763063001178233),(-358934624344316762673271280807)⟩,⟨(-207425650196438771873097876352),(-207425650196438771490180156854)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-359207759960303290907476941461),(-359207759960303290405193554754)⟩,⟨(-124496829391878243555475698800),(-124496829391878243059984955297)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-334635051370400601407682012599),(-334635051370400599990295691430)⟩,⟨(-47743754502883219744189238474),(-47743754502883218331435878593)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-291356332409123539007454776322),(-291356332409123531561780490376)⟩,⟨9379856441386161309777265512,9379856441386168753064388813⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-237790990910260139760462521299),(-237790990910260104063597356859)⟩,⟨42310472674854059521857747994,42310472674854095217677444069⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-181783439297664291382649604636),(-181783439297664168731637855575)⟩,⟨54081484977654667358739460456,54081484977654790009210760953⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-129337284860251487925484466796),(-129337284860251204218640672514)⟩,⟨51487063508832560630482802946,51487063508832844337040040819⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-84074476558944677429961166057),(-84074476558944240965916758218)⟩,⟨40816360173178763549634170946,40816360173179200013553722477⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-46618277752124488601724109563),(-46618277752124066353014402063)⟩,⟨25917886493419110929502698348,25917886493419533178172631699⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-14854077965137472371069100573),(-14854077965137296241541908074)⟩,⟨8865309052010229908117599196,8865309052010406037642412495⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨87130738612441523296892331808,87130738612441957563818710120⟩,⟨(-38115631438479572370975908360),(-38115631438479138108149889340)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨251637671029783038825648884381,251637671029784034352863570159⟩,⟨(-118342112254592853179296859746),(-118342112254591857664526120862)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨387191777803136148363136602824,387191777803137095537855155227⟩,⟨(-209290067752453935514138718335),(-209290067752452988360410330446)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨477396886446557834389307711276,477396886446558381234665556588⟩,⟨(-314441734078157107801392756855),(-314441734078156560985629093912)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨512343856340461406954479129312,512343856340461623798104093376⟩,⟨(-431589292458449700998725662657),(-431589292458449484189684960434)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨491738784026471373694305214553,491738784026471437179899444155⟩,⟨(-550041435224181612180299734452),(-550041435224181548728321342802)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨423667971053284138500328075400,423667971053284152024249336897⟩,⟨(-651083907822086038038596187287),(-651083907822086024544314784530)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨321455784796361044519412739511,321455784796361047253457919211⟩,⟨(-715111974987186257799453109552),(-715111974987186255088647432137)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨202246520482779032336573286924,202246520482779033330299011482⟩,⟨(-730192890966384808521756724890),(-730192890966384807543873048009)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨85184960007554410419214087968,85184960007554411102576996598⟩,⟨(-695767813070389862375381840244),(-695767813070389861700796496565)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-12194466750042350800750766961),(-12194466750042350245837400680)⟩,⟨(-621018907961194801103702318445),(-621018907961194800551814567935)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-77699112907316673642981895049),(-77699112907316673195923509447)⟩,⟨(-519871961745107950956696813655),(-519871961745107950508829036937)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-106762885339333768901410971073),(-106762885339333768558818827913)⟩,⟨(-405577368432429272003262006666),(-405577368432429271657902613608)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-102234202583364272043913176360),(-102234202583364271804020163786)⟩,⟨(-287598328442409367776307924580),(-287598328442409367533298791072)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-71895384173672253881907002399),(-71895384173672253740765185188)⟩,⟨(-170903419842150990846642097778),(-170903419842150990703185536016)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-25719653544675428303131279170),(-25719653544675428256734194404)⟩,⟨(-56593222826495058876554699808),(-56593222826495058829317239618)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨29289856116252755376681238262,29289856116254396457624954960⟩,⟨61492110051246784108958775734,61492110051248425194018974416⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨94518052348414254823575238257,94518052348420554991413102298⟩,⟨182190829947176790290771181546,182190829947183090470595535489⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨176925406857538028741163639509,176925406857554434747224543125⟩,⟨293922520316120309608802388580,293922520316136715633194470737⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨280826672895889666431456353228,280826672895930185572241497439⟩,⟨385044622728645404258635529686,385044622728685923421616350241⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨404499249350773785466391240084,404499249350868205712478201985⟩,⟨439232256808249935908788706962,439232256808344356177441645533⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨541697952211398545644319588189,541697952211594005689979786917⟩,⟨441965508948463375977488901478,441965508948658836042385170993⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨680486917415450842023760137982,680486917415783272050412089564⟩,⟨388936985728449649977986967100,388936985728782080016656797039⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨802288325673891933070891025213,802288325674325866904083706198⟩,⟨289149527550975681890716907712,289149527551409615725594219987⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨885800577164869704782723675617,885800577165303945259273306687⟩,⟨162522053461397689414623180899,162522053461831929881670985803⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨913434306373076563800946211047,913434306373409465176575123441⟩,⟨34882155656921784193508248227,34882155657254685550390804418⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨876086099877190884414801614428,876086099877386389611959566253⟩,⟨(-69283791934695031184622638958),(-69283791934499526012118187345)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨775837715890970429881283723279,775837715891064516328306330388⟩,⟨(-134762498996067325689750455307),(-134762498995973239269820459394)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨627042008200708722499027180178,627042008200748845540743354180⟩,⟨(-158565271801867914621271363819),(-158565271801827791605417443862)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨451842143761683841804224692803,451842143761699959760637867975⟩,⟨(-145083143159606451639782905879),(-145083143159590333704323941248)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨269556540001950711122262142046,269556540001956851141400550497⟩,⟨(-101115785753547922946845222349),(-101115785753541782941247858273)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨89225096974003606196038373642,89225096974005195288448472852⟩,⟨(-36216426579132338894447396025),(-36216426579130749806665376081)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1380758155687989320060913727),(-1380758155687989304429619631)⟩,⟨(-755694120627049119663765306),(-755694120627049105324715067)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-4482246236104097236313324059),(-4482246236104097188080963626)⟩,⟨(-1055619277560229918903713814),(-1055619277560229874850403828)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-7281787577658962401736518527),(-7281787577658962318020847837)⟩,⟨3280921814329437846844342153,3280921814329437922921747877⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-6908292743261900229619312525),(-6908292743261900105945225396)⟩,⟨18590967343692582289076670537,18590967343692582400899722484⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-1179235097523512678660947750),(-1179235097523512506415450929)⟩,⟨53832117198253361789046081395,53832117198253361944740407551⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨7913156951270274260657019712,7913156951270274500372146311⟩,⟨114842119559041634419455091675,114842119559041634637271583174⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨16541452371379563819286174379,16541452371379564189359602746⟩,⟨197293278472545830587679000098,197293278472545830929883025232⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨24171344303039556337716065472,24171344303039557193655787915⟩,⟨287138406895725423749227814374,287138406895725424572739005684⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨33607083629769861758011233646,33607083629769865763001276604⟩,⟨366739925645713541315808216435,366739925645713545287030054748⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨47532909440808970473587981265,47532909440808995521344564125⟩,⟨420101142959912532954635366629,420101142959912557970713634508⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨66129822361461715485924490765,66129822361461859044033374998⟩,⟨436587444683447629075058025521,436587444683447772608906902029⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨85915909584015853186028239104,85915909584016431185915646649⟩,⟨413785153235193514441438219789,413785153235194092423706132719⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨98980803563071192480784128659,98980803563072722717601454034⟩,⟨357032889873331763385778208333,357032889873333293610505415057⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨95383774668252968141200352264,95383774668255590343585785126⟩,⟨274454272459844178814991679975,274454272459846801009903675158⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨69702035030611300049631275164,69702035030614036866791622031⟩,⟨172976535112487598236932076284,172976535112490335050161728200⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨25584845642997155358782433874,25584845642998343669002326253⟩,⟨59114869112074286518093373580,59114869112075474827134449381⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1275815688523019725741817910898,1275815688523400924882729211952⟩,⟨(-347627372674875228061553370020),(-347627372674494029007075655744)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 3) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_3 (tableDensity true) (fullFactor true 1 3) density1_contains hk1_1_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨14615919485755888295555264064,14615919485755888564662895011⟩,⟨(-137925653410902483404259795267),(-137925653410902483140241695387)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_3 1 3 ha1_1_3_contains + def realAnswer : RBox := ⟨1290431608008775614037273174962,1290431608009156813447492106963⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_3 +namespace hm1_0_1_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨22512938242263772133888711134,22512938242263785035003755997⟩,⟨(-27403675170532136762084316636),(-27403675170532123862536635276)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨64391279995815822273053800602,64391279995815851961373652886⟩,⟨(-78358221513496221280588227234),(-78358221513496191596585319496)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨98063380369026991708591988292,98063380369027020258393580050⟩,⟨(-118693171927155936492314228116),(-118693171927155907948525311779)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨121648227612125085312365296135,121648227612125102186277948526⟩,⟨(-144218305469014550522153349456),(-144218305469014533654490564870)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨136263030185927505355696339391,136263030185927511923862178413⟩,⟨(-153621052268111826772249028912),(-153621052268111820209340609515)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨144113985380067112463001793486,144113985380067114225472708041⟩,⟨(-148149443433702787354795355769),(-148149443433702785596516604990)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨146809392672557740243014107679,146809392672557740641863935261⟩,⟨(-131226429214203437444598565946),(-131226429214203437048890116952)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨145197144787655388567952157640,145197144787655388703401094570⟩,⟨(-107500562652230478492468047889),(-107500562652230478358971631973)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨139768311210460484768559554014,139768311210460484854781885283⟩,⟨(-81420277905250657088349740531),(-81420277905250657002634881488)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨130839587071979006126048605738,130839587071979006191342450219⟩,⟨(-56370799328345445082262230475),(-56370799328345445016036408871)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨118620468769511387088169124009,118620468769511387138246491143⟩,⟨(-34572466247411413074506308206),(-34572466247411413023006371713)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨103224770375455498360209815240,103224770375455498396343944738⟩,⟨(-17307679976984149923387904943),(-17307679976984149886285000756)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨84672372586995827134026061007,84672372586995827158514332556⟩,⟨(-5222647741720100071667524029),(-5222647741720100047009015350)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨63080521635993193115724602896,63080521635993193131060065380⟩,⟨1490908658022138808129049776,1490908658022138823086368340⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨38948190777814696984940257985,38948190777814696993232321019⟩,⟨3278130394919271998260132824,3278130394919272006085043923⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨13165914532267159744251512416,13165914532267159746852625816⟩,⟨1523646869647863765818724269,1523646869647863768222372821⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨184726591282644335041228200991,184726591282644456145164200398⟩,⟨(-50372699234706301612767463145),(-50372699234706180517474636275)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨528477446832757937604631319171,528477446832758379731434022841⟩,⟨(-157571359444508429200195440193),(-157571359444507987099138979199)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨799327626325625757859731468608,799327626325626801690979204385⟩,⟨(-278233996130699059463347188466),(-278233996130698015673902534271)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨964618159739826051492882099021,964618159739828290623938818572⟩,⟨(-405817433427711516937670052127),(-405817433427709277861881583168)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1013784015965425573474162802707,1013784015965429945935823927864⟩,⟨(-520981030152657437514050670180),(-520981030152653065116589086166)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨961102138215448683134423636024,961102138215456076574566308814⟩,⟨(-600743252328355425308819592059),(-600743252328348031936004657023)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨839865064056265014788574494099,839865064056275168478158428823⟩,⟨(-629679125811818964013880418044),(-629679125811808810388820970771)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨689190192019322932175031734772,689190192019333640634621206582⟩,⟨(-606333000973523686311951024881),(-606333000973512977909440550554)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨540716833642267565673498965528,540716833642276622656539308687⟩,⟨(-542197069774688525248923516823),(-542197069774679468311530178780)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨412150608621426260979430079248,412150608621432313144341012904⟩,⟨(-455117536087054187173541456815),(-455117536087048135043039519842)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨308439007422737179176826442059,308439007422740287071515596822⟩,⟨(-361940892654331483472041203497),(-361940892654328375602922760746)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨226912761492639646011860069096,226912761492640967747700919827⟩,⟨(-274204855336650964753487102133),(-274204855336649643036351648998)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨162234758732766847695958242266,162234758732767355488200863788⟩,⟨(-197283249722648210844071556197),(-197283249722647703065049534802)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨109075238525146838984207853013,109075238525147033125062789849⟩,⟨(-131699199215298646842585455673),(-131699199215298452710196771374)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨62998095553947112559432400524,62998095553947185040985504248⟩,⟨(-75211386451939657983433606489),(-75211386451939585506521612511)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨20615338164336136197257552024,20615338164336154777840395486⟩,⟨(-24419701252602258672630160524),(-24419701252602240093519905007)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-23138354332822141900507590549),(-23138354332822141777483513067)⟩,⟨408575947450908840227948759408,408575947450908840394176952085⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-19601639714819275510442172290),(-19601639714819275150395676664)⟩,⟨1201388973421403614736986206007,1201388973421403615227817606251⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨119298471340702617772527413196,119298471340702618387873432258⟩,⟨1914499407586106838492026736798,1914499407586106839310030022314⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨437420309520000935085184137185,437420309520000935998407972917⟩,⟨2481711268866051586491058976168,2481711268866051587645415532621⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨916705693984929439937640950400,916705693984929441170624489253⟩,⟨2831309289637001172374551716567,2831309289637001173851734337920⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1476848037207555417457318832220,1476848037207555419016385223281⟩,⟨2906900773307100977252347480959,2906900773307100979023684963940⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨2000625257449527307223213761798,2000625257449527309105649875551⟩,⟨2697127038706557369464037192790,2697127038706557371503368077793⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨2374627542331077162439583131225,2374627542331077164837371802621⟩,⟨2254478330175999303639416733686,2254478330175999306129916957673⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2528190078440917375894735545273,2528190078440917380735839112901⟩,⟨1683843366649708283831898687726,1683843366649708288706952714640⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨2453299715279942392217882186841,2453299715279942411830282321224⟩,⟨1105350117180409428214872566761,1105350117180409447818083682735⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2195970663019359083666003400659,2195970663019359169455881605010⟩,⟨614778524295255091149623456595,614778524295255176905407190910⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨1826845482489082012360625274891,1826845482489082292997889040722⟩,⟨261993074399107029584359749001,261993074399107310178266460534⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1410574750554065341342469427817,1410574750554065967433841752263⟩,⟨51737692788765297331941347355,51737692788765923381721643193⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨989591147261349028890011629363,989591147261349966088118205352⟩,⟨(-41375859467083361357544525621),(-41375859467082424192382571306)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨582994078581966406507688614925,582994078581967296457312843579⟩,⟨(-54343717566017331768868935625),(-54343717566016441840006307645)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨192121395650321134771241186410,192121395650321502498240778040⟩,⟨(-22786629251283439250891764681),(-22786629251283071530921626525)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-339213016775653827803530780145),(-339213016775653205959356216126)⟩,⟨(-68759604879412162507511466518),(-68759604879411540713495308646)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1016390823633065702527665975393),(-1016390823633064224319527987534)⟩,⟨(-171343901302779511064087409378),(-171343901302778032999441817985)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1680668338824075120389070911361),(-1680668338824073610679184561396)⟩,⟨(-173441400190395949127277575604),(-173441400190394439633614166326)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-2299492523382249609223916697644),(-2299492523382248642959292652256)⟩,⟨(-23981026025386517178163994980),(-23981026025385551170653564284)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2815144555820753611039251066542),(-2815144555820753200457739110797)⟩,⟨302658317341459965167154597122,302658317341460375489929934194⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-3156706315794710008802620044718),(-3156706315794709890686356387702)⟩,⟨794816000298309273240414962048,794816000298309391137692484460⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-3264255878554240548822845351774),(-3264255878554240523569093181156)⟩,⟨1394152241178333182094319489113,1394152241178333207203248597160⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3113018210865423310813783179512),(-3113018210865423305115786023488)⟩,⟨1999782413287706649751798099553,1999782413287706655400651052894⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2728244597403908202076726235080),(-2728244597403908199440917544321)⟩,⟨2493959138346692102751997445766,2493959138346692105439712673434⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2184186906085253959874770729214),(-2184186906085253957806785467531)⟩,⟨2778888027966648082368733224646,2778888027966648084574087397636⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1583663361588871725273607330448),(-1583663361588871723499449308432)⟩,⟨2805849409219217146310944494247,2805849409219217148278607107792⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1026669172299452459282061563385),(-1026669172299452457800012103601)⟩,⟨2583436865878862201879108912682,2583436865878862203575771384872⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-583506114579352785039801847754),(-583506114579352783871827984959)⟩,⟨2162919403145552067450767811770,2162919403145552068821222687709⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-282109457057635157006338813709),(-282109457057635156168874192180)⟩,⟨1611239418875139555137288026189,1611239418875139556137851782605⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-110157379290035285491584933128),(-110157379290035284990068997277)⟩,⟨987484707768759610676352397136,987484707768759611282793303126⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-26373105102449942364815787032),(-26373105102449942198444044255)⟩,⟨331857977547509835050336120416,331857977547509835252745803118⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨181620428119887267436612682470,181620428119889477819865954189⟩,⟨(-115056093343841380700244089628),(-115056093343839170304163151658)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨521695614576760740778385326356,521695614576769224219961858467⟩,⟨(-364776383568709060174494728654),(-364776383568700576697949082018)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨791294369343866437698472556688,791294369343888513505920964108⟩,⟨(-667520776825431785465187175519),(-667520776825409709610266810590)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨944490628935919079008377192336,944490628935973522312129688448⟩,⟨(-1039839284167504766000136027143),(-1039839284167450322651269228707)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨942257155946778846546110458224,942257155946905380538700495126⟩,⟨(-1469390413964106431703050666546),(-1469390413963979897685725197487)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨760777559572115078063340273252,760777559572375877040438443130⟩,⟨(-1909033353161384392323234536765),(-1909033353161123593360684204193)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨401654957699723567973172396347,401654957700164144082399153252⟩,⟨(-2285327384625360829433602495173),(-2285327384624920253393265486495)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-97166411458681060403835106668),(-97166411458111585469290390428)⟩,⟨(-2520538595715938799236568158625),(-2520538595715369324434364257464)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-659148196217754556729483991061),(-659148196217192489386649774864)⟩,⟨(-2558641240118452127383580158996),(-2558641240117890060237431424762)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1183423479024857188645214168536),(-1183423479024434073009246924768)⟩,⟨(-2386428702783009576525603047233),(-2386428702782586461141459918951)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1570776111764730350183320871439),(-1570776111764487539689910925411)⟩,⟨(-2041335723343315090972477243324),(-2041335723343072280765664172533)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1748158969658315560622643758267),(-1748158969658201888774208630699)⟩,⟨(-1599402785506008422089755571789),(-1599402785505894750533520024075)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1682781821875128986571858922094),(-1682781821875081397701328313134)⟩,⟨(-1145051752917261004546400874624),(-1145051752917213415938523876514)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1386130159659661826044485688947),(-1386130159659641043811937864625)⟩,⟨(-739050008033011065980085981768),(-739050008032990283935009234409)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-907016964079471663187205993294),(-907016964079463111828894095677)⟩,⟨(-403936832595770346858570057004),(-403936832595761795609897770069)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-314826338907836533075289741214),(-314826338907834231439325159070)⟩,⟨(-127184688335730592049012984067),(-127184688335728290449034404341)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-22780829541185338967003619687),(-22780829541185338944602461888)⟩,⟨42106688289800533756350213245,42106688289800533780501974277⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-59344666101093950284641635119),(-59344666101093950215748394697)⟩,⟨129996638130709539906622768606,129996638130709539981192698387⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-70197708690497020242884518785),(-70197708690497020123189505039)⟩,⟨227587128275957421925155921380,227587128275957422055133115364⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-43270228493044276948031663815),(-43270228493044276770915258539)⟩,⟨336522860045245875831956644262,336522860045245876024607119134⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨26119897246155933374619961067,26119897246155933617998980699⟩,⟨449289929755538125946568231564,449289929755538126210582334039⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨135957851285017782909287188160,135957851285017783236129354869⟩,⟨546968450188357273954802247766,546968450188357274306734049076⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨279353785700817779329252319875,279353785700817779799967190559⟩,⟨605481617615989556536960161408,605481617615989557035893647195⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨442243988876446775752559145184,442243988876446776737746641742⟩,⟨606643686785924565977783932569,606643686785924566990556178505⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨601444939892687715282711280682,601444939892687719918465538312⟩,⟨545246822928362756716468242095,545246822928362761373044601561⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨728965465432207143599433791900,728965465432207176925529750505⟩,⟨431411305014813452846055206135,431411305014813486181966683685⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨799736637563577961657835248371,799736637563578155792910828659⟩,⟨289376138234031227185764305946,289376138234031421321996715017⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨797353901272131823249459543518,797353901272132606123407837185⟩,⟨151135151917373357145747984546,151135151917374140015988071144⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨716600437335640617040346576029,716600437335642690424018184126⟩,⟨44931343707478717375812522947,44931343707480790753871875813⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨564703780526101538548642691404,564703780526105090598501295531⟩,⟨(-14980291954114103703627234119),(-14980291954110551659081127657)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨359502125720069931671305938237,359502125720073637415542757124⟩,⟨(-30155931126560792469899699271),(-30155931126557086729283706542)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨123121295093460946795032049994,123121295093462555337648626664⟩,⟨(-13816786854720794517972313114),(-13816786854719185976621388788)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨503666533245272030226745418415,503666533245769149209675804315⟩,⟨2778393080610132109040978671446,2778393080610629227830568327904⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 4) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_4 (tableDensity false) (fullFactor true 1 4) density0_contains hk1_1_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨150405897470215938238081824792,150405897470215938579872927945⟩,⟨(-29991942607520721048750605397),(-29991942607520720706407241235)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_4 1 4 ha1_1_4_contains + def realAnswer : RBox := ⟨654072430715487968464727243207,654072430715985087789648732260⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_4 +namespace hm1_1_1_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨4434725090056173278893548146,4434725090056183840614004740⟩,⟨(-4137360523097339445299477683),(-4137360523097328883204065779)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨12833132296156929766310907213,12833132296156954058584193133⟩,⟨(-11781429820165716841610958980),(-11781429820165692548287658853)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨19835764329850201615285602056,19835764329850224948618095790⟩,⟨(-17558292499984446758119892080),(-17558292499984423423257082136)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨24593560395226452696793797928,24593560395226466455418663535⟩,⟨(-20590140273732791975290700372),(-20590140273732778214904557521)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨26563883559361501574685681003,26563883559361506897855917225⟩,⟨(-20955250489681630608405320931),(-20955250489681625283481161189)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨26094898252160643848235007445,26094898252160645239157441611⟩,⟨(-19740481656021049365371990294),(-19740481656021047972938947350)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨24484810853159598607985955127,24484810853159598882409261233⟩,⟨(-18046118204629207863904846110),(-18046118204629207588396992831)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨23022564494177760350035005200,23022564494177760411459733959⟩,⟨(-16170202862576727695340520937),(-16170202862576727633325381469)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨22158056878754924064424298519,22158056878754924093038379468⟩,⟨(-13861415834686968511250852148),(-13861415834686968482444621785)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨21527821840069635897599455728,21527821840069635918321807964⟩,⟨(-10933355970897095214140565654),(-10933355970897095193469891545)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨20436896713491202565127373782,20436896713491202581222975821⟩,⟨(-7598375521420148280135065698),(-7598375521420148264337719354)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨18368508063112553168756620447,18368508063112553180746022010⟩,⟨(-4434883109527636237864548559),(-4434883109527636226437756870)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨15266975990216728338602158631,15266975990216728347027525982⟩,⟨(-2039085051651012376201677862),(-2039085051651012368509557146)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨11403622135821988466036319596,11403622135821988471469809752⟩,⟨(-636468803184735457036688100),(-636468803184735452328668556)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨7049635033817641315821300522,7049635033817641318821706046⟩,⟨(-54324018721811181323962674),(-54324018721811178850423938)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨2386893063545395817316331520,2386893063545395818268862361⟩,⟨35464534174351554569434164,35464534174351555329133192⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨29080818718370888456107428679,29080818718370988138030205935⟩,⟨6791176758131903246037581091,6791176758132002929027003928⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨83296140707770207478227386944,83296140707770571561369511922⟩,⟨16331474929964768045564099049,16331474929965132131859760564⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨126336849829000864037420271830,126336849829001724283423788100⟩,⟨15527358645688634191842665990,15527358645689494442925889643⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨153282974492310459801465688121,153282974492312306840840135509⟩,⟨2660706040367463601321560020,2660706040369310647381515509⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨162679032038572771374562330590,162679032038576381489913228034⟩,⟨(-18746692482648655014484963154),(-18746692482645044891351577069)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨156638943596149130547083309342,156638943596155240050082878378⟩,⟨(-41731874212964093406049341084),(-41731874212957983894827169574)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨139624400014251035635896533102,139624400014259433475130576637⟩,⟨(-59497218872557845118591933500),(-59497218872549447271348331647)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨116958209924351960572753173921,116958209924360821511956942210⟩,⟨(-68546710785354198904790601526),(-68546710785345337958360844125)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨93540698808024705505400371726,93540698808032199643472439089⟩,⟨(-69122809145246090077292697488),(-69122809145238595933278415142)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨72744916060145994296175132775,72744916060150999359323745466⟩,⟨(-63548891325648936702137792134),(-63548891325643931634335695350)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨55942503644610493224348066714,55942503644613060841341677113⟩,⟨(-54405508157437383339929847789),(-54405508157434815719347575751)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨42784432793346358302661467248,42784432793347448825752725208⟩,⟨(-43631339696008788181045790704),(-43631339696007697655245467232)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨32009241887130248949441961311,32009241887130667298167822146⟩,⟨(-32557374948326217469698701915),(-32557374948325799119006132328)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨22408777654508184977068658757,22408777654508344696226365298⟩,⟨(-22104119773551767602357712847),(-22104119773551607881910698367)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨13305140919494519733141097113,13305140919494579296017330021⟩,⟨(-12677288056653777452339251442),(-12677288056653717888742032971)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨4412454807113809121689293712,4412454807113824380709730953⟩,⟨(-4114943699700420710751336303),(-4114943699700405451498269274)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-52790182212971877495277963151),(-52790182212971877440172217439)⟩,⟨75823619516471699961252644977,75823619516471700018328487636⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-147113569893852832709065575064),(-147113569893852832545961044684)⟩,⟨228318819551119871380621002676,228318819551119871549888769588⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-209214782915032964431466918691),(-209214782915032964156783328700)⟩,⟨378601417901077365512867256128,378601417901077365796878648821⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-222883124484353032445154396570),(-222883124484353032051964416677)⟩,⟨513576898232045371609425467484,513576898232045372013209507290⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-179751741919070404748352304919),(-179751741919070404241971879562)⟩,⟨613013396206846183552742174983,613013396206846184068955008735⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-84549145479315759913566620515),(-84549145479315759303531696228)⟩,⟨659641420774087573123436305381,659641420774087573741817111881⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨41451023877466886181437421365,41451023877466886904314264960⟩,⟨647383874296054239726884177985,647383874296054240456151579877⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨166416351308720360688559647139,166416351308720361726469531983⟩,⟨583042469617514942377030315526,583042469617514943418794828576⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨261090350425901690239810081870,261090350425901693237733428945⟩,⟨483796991642363814532377344510,483796991642363817531750208173⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨309135071698664239164698623196,309135071698664254244517360596⟩,⟨371535855832117429505830493446,371535855832117444585877941372⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨309675149176102991777115437556,309675149176103060886062774025⟩,⟨265344143332900535454452721086,265344143332900604563313303217⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨273569963810610832401746624860,273569963810611060537817822911⟩,⟨176402997950927799948190143189,176402997950928028084152832077⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨216736083898060770870444210973,216736083898061281180240884785⟩,⟨108260602829234491738945378489,108260602829235002048642613456⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨153053290001960996582438522973,153053290001961761406802938095⟩,⟨60111662937016896883822224991,60111662937017661708156529787⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨90114588982319786234692401091,90114588982320512992781822669⟩,⟨28634044883764283285641459903,28634044883765010043751177754⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨29657698630120081845407916091,29657698630120382235953165102⟩,⟨8248098123721075514775122705,8248098123721375905347101265⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-77163330894344054301180799422),(-77163330894343531867128004306)⟩,⟨(-86205897630086511047862034016),(-86205897630085988608544093513)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-233931890594846370504580554835),(-233931890594845129475687725533)⟩,⟨(-245891241260092193056812387802),(-245891241260090952012877936736)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-396260394278828313605401637026),(-396260394278827047971136805831)⟩,⟨(-367782722913985127945930685194),(-367782722913983862289179790364)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-563342947251784594531915811746),(-563342947251783786409026050925)⟩,⟨(-430126926117527166471915212153),(-430126926117526358322659056275)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-728420062191336915058586093094),(-728420062191336573024694807802)⟩,⟨(-419630441120414467775000032509),(-419630441120414125715353702820)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-876588034009147020193405052750),(-876588034009146922673882874795)⟩,⟨(-337185977241506793222242360728),(-337185977241506695681925666426)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-985160602703840102531153718982),(-985160602703840082399684643452)⟩,⟨(-198152696027569351177151494662),(-198152696027569331033186350502)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1031623964945163732237122204646),(-1031623964945163728353952454309)⟩,⟨(-27403888100947889455090573340),(-27403888100947885569600430457)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1004784134130433694376663274592),(-1004784134130433693024294438589)⟩,⟨145712449217600901134844397906,145712449217600902479575683357⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-910302217466993450345886298447),(-910302217466993449414776996451)⟩,⟨292450622471883238238647730526,292450622471883239154209616176⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-768218585034811940453581350870),(-768218585034811939681519409880)⟩,⟨390392113216234125008288772327,390392113216234125760137320566⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-604727735816342123626405913078),(-604727735816342122987471262953)⟩,⟨427502314246377919531599089449,427502314246377920149038832603⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-442679443192227099206537724342),(-442679443192227098702701899206)⟩,⟨403162645537486651997807480978,403162645537486652481887996234⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-295780229677791663402235402214),(-295780229677791663039613749389)⟩,⟨326227229849798498824035404278,326227229849798499171057127739⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-167703657524145252172414500642),(-167703657524145251954294543109)⟩,⟨210883382870933484198447487783,210883382870933484406660008722⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-54102369962117073822610608398),(-54102369962117073750026032148)⟩,⟨72761085744042936029304999892,72761085744042936098516990540⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨57661228866460074072653173264,57661228866461890663272921376⟩,⟨(-40806901420030357306409783103),(-40806901420028540718555895197)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨169623568804934199395432092607,169623568804941171962432810854⟩,⟨(-129600576847336018499439836915),(-129600576847329045940241651787)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨269574564913673064412137878090,269574564913691210990423403922⟩,⟨(-236756955285266195003132935511),(-236756955285248048435918579588)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨344170687972682401197536817629,344170687972727161378049701333⟩,⟨(-366070530312226951186242130468),(-366070530312182191017192888748)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨375334735297932621862886543256,375334735298036663532812444626⟩,⟨(-513577148070598049612250575876),(-513577148070494007950296897067)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨346702337698930824108043449660,346702337699145263485694135764⟩,⟨(-669609929444532336724584613398),(-669609929444317897347264820728)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨253342449244714519098675908989,253342449245076700572959391416⟩,⟨(-818942396220178718293158594873),(-818942396219816536807207378849)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨106790861885000657774761351321,106790861885468573197497116356⟩,⟨(-940795034994378584800069876198),(-940795034993910669351029477557)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-66599936390824390763619616439),(-66599936390362928990373629390)⟩,⟨(-1013391136488167451621809001552),(-1013391136487705989808458030823)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-231645701837795356666515419132),(-231645701837448345102593087826)⟩,⟨(-1020961779003348753752289627367),(-1020961779003001742138667192654)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-353962709725983673265934865953),(-353962709725784788071419895761)⟩,⟨(-958215800465992555052418441002),(-958215800465793669803749809599)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-411399340550453087735544386097),(-411399340550360104727703333638)⟩,⟨(-831508439747188560328777097831),(-831508439747095577267025144856)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-400299127283314103588075762591),(-400299127283275226029610851001)⟩,⟨(-658779045580412062450384347759),(-658779045580373184844151957990)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-330604574283567536092489516852),(-330604574283550576279823790298)⟩,⟨(-465349472062480568141694255613),(-465349472062463608295661189817)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-216952254332395861217954557724),(-216952254332388887909498175758)⟩,⟨(-272759296377043412145838933860),(-272759296377036438818210607215)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-75499294272983014222778321215),(-75499294272981138045943029817)⟩,⟨(-89320259553202166918633094959),(-89320259553200290735625069681)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-617074025847719560294004649),(-617074025847719547630001284)⟩,⟨1283055274224921988255589167,1283055274224922002358309279⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-733565017882793331974747893),(-733565017882793293037733578)⟩,⟨4109848074292500481027248132,4109848074292500524597543501⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨3375202171376382705355123074,3375202171376382772703594813⟩,⟨6444077779332485103998778009,6444077779332485179760304767⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨17436666941184193659805539586,17436666941184193759017330517⟩,⟨5210049778640603319629366327,5210049778640603431813446832⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨49797091849384993677059879433,49797091849384993815770278025⟩,⟨(-2542162063126940435157968343),(-2542162063126940278387302374)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨106516505050809068080919931526,106516505050809068275786832488⟩,⟨(-16171391074258625382801023139),(-16171391074258625164072648305)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨184624146536576282614333616139,184624146536576282920797905512⟩,⟨(-32778897075291907652743980330),(-32778897075291907315904022043)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨271594805542467519015491016255,271594805542467519747312780400⟩,⟨(-51416791354612462188500063556),(-51416791354612461421264879547)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨350414013669260566821153197221,350414013669260570560412551293⟩,⟨(-73221989734081462668140930157),(-73221989734081458893782438995)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨404601523209458632591334875215,404601523209458659814302644105⟩,⟨(-98485826918755841902901081312),(-98485826918755814652527913273)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨422363053429088805766037842799,422363053429088964323038699457⟩,⟨(-124869808847377810631337560234),(-124869808847377652054838900226)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨400270126592351765558426155074,400270126592352404898235095710⟩,⟨(-146995311896426111168317112077),(-146995311896425471815154691244)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨343755706419333731455990153118,343755706419335425330332355716⟩,⟨(-156147322633062912701207301675),(-156147322633061218818383258608)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨262284388366337634253394924596,262284388366340537509823716920⟩,⟨(-142378365878649748291029358197),(-142378365878646845029830445232)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨164127309411579359531694147084,164127309411582389539979023752⟩,⟨(-100784582469390249026953548196),(-100784582469387219016396272928)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨55853774263128866214874522351,55853774263130181703266698919⟩,⟨(-36478507386272733083423621027),(-36478507386271417594398976882)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-621464019911512007553007560401),(-621464019911103834034416813384)⟩,⟨(-875182672802576096384817099062),(-875182672802167922749966655231)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 4) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_4 (tableDensity true) (fullFactor true 1 4) density1_contains hk1_1_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-196684635153359304296756905774),(-196684635153359303849799309344)⟩,⟨39220232640604019385301777000,39220232640604019832981560904⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_4 1 4 ha1_1_4_contains + def realAnswer : RBox := ⟨(-818148655064871311849864466175),(-818148655064463137884116122728)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_4 +namespace hm1_0_1_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-54882412831736683748466104389),(-54882412831736655406777876609)⟩,⟨25402215554088584090462548694,25402215554088612431045251495⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-156808634583068106627249647221),(-156808634583068041833696360152)⟩,⟨74047726316790715401390744902,74047726316790780191904666571⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-237817952678520305974553492119),(-237817952678520244498216094474)⟩,⟨116053002075012265624285856612,116053002075012327096459901555⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-291756122343187927704154129428),(-291756122343187892106017440959)⟩,⟨146922280493159477482992939272,146922280493159513077087485988⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-319644598837598302050463936044),(-319644598837598288567609307521)⟩,⟨162759146511529788232494886264,162759146511529801712866871088⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-326650400814052567610676385280),(-326650400814052564121486845619)⟩,⟨161871127674039054480198301537,161871127674039057968650661523⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-318823163029385921794501798466),(-318823163029385921049135725850)⟩,⟨146229343868843604856445847678,146229343868843605601708306016⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-301523318161459246700253347817),(-301523318161459246457672945906)⟩,⟨120746925227010701766285962080,120746925227010702008699831107⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-278675036093568901475341828629),(-278675036093568901319577062455)⟩,⟨90995434457368043401497725191,90995434457368043557800162558⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-252463836656081344195963972270),(-252463836656081344075497168729)⟩,⟨61578783621235971316456317826,61578783621235971439064218680⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-223602745078429103011860599696),(-223602745078429102918246978948)⟩,⟨35671306275022813012224401738,35671306275022813108895628372⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-191796560431245273612117991756),(-191796560431245273544290332430)⟩,⟨15169309601821843402810752630,15169309601821843472840636912⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-156199483873823995260381686530),(-156199483873823995214435028250)⟩,⟨1094909019364912100301021567,1094909019364912146833493389⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-116108025839230788730038313652),(-116108025839230788701291221970)⟩,⟨(-6109824918331486004927036555),(-6109824918331485976760897662)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-71710794794839878207476691972),(-71710794794839878191929127181)⟩,⟨(-6850633590883567877563161857),(-6850633590883567862849792274)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-24259295757254033992347746902),(-24259295757254033987466831777)⟩,⟨(-2863264331899310745441254928),(-2863264331899310740923245360)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-234212542687624262192092950149),(-234212542687624083432418181531)⟩,⟨(-140465578337796618105371272018),(-140465578337796439335565838916)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-688705351023530486325539164732),(-688705351023529818921211754439)⟩,⟨(-386050360266009394416179561865),(-386050360266008726984573612667)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1096813023585584515257444366430),(-1096813023585582871891393819313)⟩,⟨(-535628176848369259689200508736),(-535628176848367616287068792124)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1419738208063272223629351916160),(-1419738208063268492093316309129)⟩,⟨(-557531637384908127526103098956),(-557531637384904395955578822947)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1619997151473373108157296680060),(-1619997151473365325914051511690)⟩,⟨(-458589850360923239173863329809),(-458589850360915456906491091694)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1677242178669583948794682434518),(-1677242178669569858097313783928)⟩,⟨(-280288912294765028636523583751),(-280288912294750937929685004722)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1600038494410698447186027536537),(-1600038494410677802659201893495)⟩,⟨(-81317880099280528052719354313),(-81317880099259883530406008999)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1423679772682219025059715985132),(-1423679772682196020870580254137)⟩,⟨86055088283481419087679122110,86055088283504423262631095390⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1195657819557766849756449785955),(-1195657819557747220567269470841)⟩,⟨193304826673027298883672367469,193304826673046928054512334553⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-958703587507292487982369215007),(-958703587507279511885136937395)⟩,⟨238177473741489912597437498259,238177473741502888676461945333⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-740543058560498393196868619414),(-740543058560491699152107145450)⟩,⟨235325347908358545580029910276,235325347908365239609023358955⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-552990164162663451681716602644),(-552990164162660551097578187853)⟩,⟨204113249861905431867805006114,204113249861908332439538181525⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-396557230065199998074682732357),(-396557230065198853945879770355)⟩,⟨160253315720739547688399059394,160253315720740691808230964826⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-265687115842240573642038085071),(-265687115842240137680728426307)⟩,⟨113096383175410987030459211045,113096383175411422985876348968⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-152647107042220568472178603727),(-152647107042220407638338587582)⟩,⟨66738529659304984938560300790,66738529659305145769117325845⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-49775113485682980412033882496),(-49775113485682939456566430745)⟩,⟨21998567394467992312339370716,21998567394468033266759625237⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨430700993793347721914692095918,430700993793347722129490604680⟩,⟨(-208257437411683240986359400953),(-208257437411683240795641418965)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1240706607299311342282629236987,1240706607299311342921754903952⟩,⟨(-669494448525496088380965911278),(-669494448525496087806505221601)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1894172723550770351808588987004,1894172723550770352866567869735⟩,⟨(-1245494619738522487034258618099),(-1245494619738522486058980799141)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨2290036581576118439539198385974,2290036581576118440999302077832⟩,⟨(-1952782329991647533009756833940),(-1952782329991647531618085965795)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨2348896013376593878056595645363,2348896013376593879871155187973⟩,⟨(-2731290315888256818148229182382),(-2731290315888256816353328782418)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2042249691731007012164376229228,2042249691731007014265827620782⟩,⟨(-3451191814408861968640999620458),(-3451191814408861966485030167993)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1420052756449250832483561598380,1420052756449250834805479240384⟩,⟨(-3957348283538958080610772019206),(-3957348283538958078151368576794)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨614941444430084629560351613213,614941444430084632280890780945⟩,⟨(-4132829739821518234333099680765),(-4132829739821518231404184164266)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-193906674969901874788211677375),(-193906674969901869547586443338)⟩,⟨(-3947818309377886266523817156453),(-3947818309377886261031882857401)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-843306817516408939688159185249),(-843306817516408919859166310943)⟩,⟨(-3468223669661970306684863091160),(-3468223669661970286594691247923)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1237308018571882836676121380543),(-1237308018571882748050435603182)⟩,⟨(-2820893129248642537430845184772),(-2820893129248642448584422970192)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1360093674608332005168968596102),(-1360093674608331678348003611454)⟩,⟨(-2138119112982506034322176948962),(-2138119112982505707352697982243)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1254168691096270125172942539893),(-1254168691096269325141410709919)⟩,⟨(-1513072468473425115039484957870),(-1513072468473424314913768685360)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-986834663191215168918361134467),(-986834663191213887840998735550)⟩,⟨(-984808153480922686747302083065),(-984808153480921405614256230612)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-623136016861626056823140234571),(-623136016861624785648895727045)⟩,⟨(-548859328690255249065555660969),(-548859328690253977862471811832)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-212197247903899609579112125032),(-212197247903899072798207381197)⟩,⟨(-175592021892871605003638152502),(-175592021892871068213901703891)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨39569076393732851091328225506,39569076393733565010878582752⟩,⟨334514591423082142526140382950,334514591423082856472813617266⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨154262165026341931459778712910,154262165026343618983978510501⟩,⟨994520956019742573522261305731,994520956019744261120584892442⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨369310759191077748744026943262,369310759191079453490804112285⟩,⟨1618756617935107835022587660248,1618756617935109539869383285666⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨730266120810280643160767069552,730266120810281717193514114986⟩,⟨2161052194738199017532378591398,2161052194738200091658811701968⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1249827101473129899140338805265,1249827101473130346302958930475⟩,⟨2553081333487843297928087453195,2553081333487843745139370189096⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1896435196800968600677499506636,1896435196800968726146470226903⟩,⟨2719228742617301846984486788033,2719228742617301972418847056763⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2588994401030499186688461597908,2588994401030499212876092549750⟩,⟨2606180360990678322903327775515,2606180360990678348945918131024⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨3207228482846177193071431216009,3207228482846177199122085993610⟩,⟨2212208609103211148784271810921,2212208609103211154570861715320⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3624738493349505077989637211307,3624738493349505081059184929712⟩,⟨1601067880793593705282069253037,1601067880793593707982223141577⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨3752449999646325059344028222629,3752449999646325061903324623453⟩,⟨892057706001172725634620656609,892057706001172727753301088666⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨3568809167792076745889439245713,3568809167792076748195465312521⟩,⟨226068599700620291613172561026,226068599700620293484833500675⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3121019610313613589688083991398,3121019610313613591762561894107⟩,⟨(-277761139741801847170424772643),(-277761139741801845417188638863)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2498189105970607709425083601530,2498189105970607711149641879460⟩,⟨(-552938328592600222177941089328),(-552938328592600220670154496820)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1792398379629945071675233547930,1792398379629945072956331633279⟩,⟨(-592864028278686966271815908889),(-592864028278686965123850481677)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1068531170135303086917029479892,1068531170135303087700703836853⟩,⟨(-438807151658366592975955431945),(-438807151658366592262386000814)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨353809041128815997120319871876,353809041128815997382887480530⟩,⟨(-160368132941676763234160078679),(-160368132941676762993185674524)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-119758578704929191701751839138),(-119758578704927295783083405425)⟩,⟨(-132205703629576524937398954517),(-132205703629574629022581268235)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-374015637935510029361462784407),(-374015637935502758530789892711)⟩,⟨(-375014418947629707928283475321),(-375014418947622437106188763253)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-667316311702015646898438364775),(-667316311701996760732855176325)⟩,⟨(-552117872700877815026818810980),(-552117872700858928866103821934)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1009256270661532459119979709915),(-1009256270661486036203046862496)⟩,⟨(-620555738764276916674095584695),(-620555738764230493745321486757)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1384350888331621461564691501581),(-1384350888331514164835585676968)⟩,⟨(-544482513617231264599008922265),(-544482513617123967825487024981)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1746785900944059552370108525733),(-1746785900943840330365397590098)⟩,⟨(-304477427329658745243044240356),(-304477427329439523145170270589)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2028053809674038024154248976327),(-2028053809673672531683940267799)⟩,⟨91935180638327333986417034694,91935180638692826610669991145⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2158262308542317188662619570033),(-2158262308541853680514082714895)⟩,⟨600725678115331566834589468591,600725678115795075204084419340⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2092494127497205874944120178807),(-2092494127496760561981741867482)⟩,⟨1141176861884362405900865692651,1141176861884807719149093811197⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1831912830451055487127139485038),(-1831912830450731660631125994865)⟩,⟨1612332857115717275022948757880,1612332857116041101856165808427⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1430055856113155129142315126987),(-1430055856112950254151140602602)⟩,⟨1921132729369019048624213048010,1921132729369223923928010327046⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-978158229191796545828486154111),(-978158229191681976211210586741)⟩,⟨2007452285879792851040008401303,2007452285879907420900695181087⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-571781767392111743511609160728),(-571781767392056516843213189348)⟩,⟨1854569752327629438653145983527,1854569752327684665496472269353⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-274751440105819044098503524688),(-274751440105794661712891419077)⟩,⟨1486439652422608895372136976962,1486439652422633277871864149294⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-101646506268396414274704590568),(-101646506268386505513477139546)⟩,⟨956194947965454052816471328083,956194947965463961640762135248⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-22343420039230330272339429593),(-22343420039227679790046806995)⟩,⟨329156199140124248674790001823,329156199140126899177063128814⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨31291860636656495242144936936,31291860636656495259732691608⟩,⟨14863718977393755860688738385,14863718977393755876720434612⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨96500727946596451691074489637,96500727946596451745467270742⟩,⟨37837992014861100587172383566,37837992014861100636557788530⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨168578168760902006173782435686,168578168760902006268868300278⟩,⟨41338337789260745163658709375,41338337789260745249764218594⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨248495899206243271215874505882,248495899206243271357348168382⟩,⟨15708342968457819553656848576,15708342968457819681684946752⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨330394304160765070325407294691,330394304160765070520003203337⟩,⟨(-43378870258306552788729674758),(-43378870258306552611885731449)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨399647735444207724501480549073,399647735444207724761264637079⟩,⟨(-134784561525303617519334727947),(-134784561525303617281059115303)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨437161118396724534437321770761,437161118396724534803402201311⟩,⟨(-252780332125701025977691399261),(-252780332125701025635765027710)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨427954112326352345297520119677,427954112326352346069100837834⟩,⟨(-385352966074341125428393343942),(-385352966074341124679166884677)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨367568199596537696322217647332,367568199596537700299442558829⟩,⟨(-512991442147922191003691117635),(-512991442147922187040734498633)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨264856318025443959153527525503,264856318025443987798275336839⟩,⟨(-612474385303776137134526430892),(-612474385303776108496087702718)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨141408073571385396738832500595,141408073571385563760083148294⟩,⟨(-663651417404162409685618770339),(-663651417404162242664826130665)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨26207018583825285989149114920,26207018583825959682995626436⟩,⟨(-654512314642203053475149809562),(-654512314642202379778780964563)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-54561670283716815715837518485),(-54561670283715032364652686053)⟩,⟨(-582789598390645271924895036617),(-582789598390643488570307200035)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-87379207048511314147759652539),(-87379207048508261765120430536)⟩,⟨(-455876466752367978005209333281),(-455876466752364925619640208366)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-74126475167740795170049821841),(-74126475167737613698373925176)⟩,⟨(-288701037990445232838374511927),(-288701037990442051364862615374)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-28550407317591434767866347543),(-28550407317590054601641228074)⟩,⟨(-98599129583113732636109399269),(-98599129583112352469275698591)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨682572478614283339469238093906,682572478614707855209796013264⟩,⟨(-2188674976239149194311381787739),(-2188674976238724678393094362421)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 5) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_5 (tableDensity false) (fullFactor true 1 5) density0_contains hk1_1_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-66864778925623034013232615730),(-66864778925623033513130943963)⟩,⟨(-177504083723144903010774182615),(-177504083723144902511448841666)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_5 1 5 ha1_1_5_contains + def realAnswer : RBox := ⟨615707699688660305455905478176,615707699689084821696765069301⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_5 +namespace hm1_1_1_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-9876753922236181845369432527),(-9876753922236158640881712129)⟩,⟨3067633048553829494255601789,3067633048553852699007729345⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-28448620343544785973047354415),(-28448620343544732951158446998)⟩,⟨8829608152563716493465180950,8829608152563769516095429284⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-43521747977212693951999201488),(-43521747977212643703451076148)⟩,⟨13379967694011337767571845884,13379967694011388017198840785⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-53161415642145677814579823131),(-53161415642145648787246838703)⟩,⟨16060340019972006481161256366,16060340019972035509722468900⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-56569761948738805913002140351),(-56569761948738794982825752617)⟩,⟨17101751697806024197414157008,17101751697806035128794338192⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-54981834251791485052983072600),(-54981834251791482288386375095)⟩,⟨17517369842753891101816049466,17517369842753893867413044584⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-51142990110741930516612537767),(-51142990110741929991463468261)⟩,⟨17849201649991834675492823442,17849201649991835201184733272⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-47397491335373420801354446745),(-47397491335373420687781335333)⟩,⟨17626425972848159417892452224,17626425972848159531348062020⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-44533531318992405726240052699),(-44533531318992405673939583936)⟩,⟨16121984693703726829551563841,16121984693703726881207260403⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-42039607700915118037157785222),(-42039607700915117999221504829)⟩,⟨13121345757093175409584242257,13121345757093175446670850705⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-38899713826499734467513132657),(-38899713826499734437997932345)⟩,⟨9135512682090693173102902219,9135512682090693201650152212⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-34346653590873510741955340611),(-34346653590873510719959590430)⟩,⟨5182049645332343364095139772,5182049645332343384867921307⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-28273743016145155107213534760),(-28273743016145155091740419497)⟩,⟨2215004497751277447778124838,2215004497751277461831335488⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-21037734554040752072396389321),(-21037734554040752062386233453)⟩,⟨564047428841810071438059777,564047428841810080090280453⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-12992959885933496478161858002),(-12992959885933496472609656903)⟩,⟨(-46393549577264905784902705),(-46393549577264901208248832)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-4399048726235925021201155576),(-4399048726235925019432739729)⟩,⟨(-75349902078570492921625610),(-75349902078570491509052633)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-21714558880169025234462596292),(-21714558880168878098554728208)⟩,⟨(-36644662102272892191950868108),(-36644662102272745057350457361)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-66241323119044944892028524660),(-66241323119044395306521692320)⟩,⟨(-101879623001799187988073330362),(-101879623001798638406073823564)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-112434693368977813604422429215),(-112434693368976459283074705254)⟩,⟨(-145095634805096607697266536596),(-145095634805095253380563621860)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-157290014976182917206723347054),(-157290014976179839088780395540)⟩,⟨(-158671056523797156688452550178),(-158671056523794078574994288011)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-194597433802435268531775878425),(-194597433802428843067086764393)⟩,⟨(-143615995079942645593791733684),(-143615995079936220132381777699)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-217491495099594585103878141862),(-217491495099582941210283561258)⟩,⟨(-108775230797261923625033273675),(-108775230797250279733007378414)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-221866799914935678702513818202),(-221866799914918603919735618126)⟩,⟨(-66489880598299044882221129142),(-66489880598281970099381145764)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-208816489763543070320924499366),(-208816489763524034734640806473)⟩,⟨(-27490968248924655271632684981),(-27490968248905619684106476696)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-183947818742633686191798387208),(-183947818742617443867022947543)⟩,⟨1851429389350160304014215030,1851429389366402630761109138⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-154153151854343110706806109836),(-154153151854332379440668478759)⟩,⟨19650033649885166506813292983,19650033649895897775271065643⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-124596214051279247220298598742),(-124596214051273716750513062110)⟩,⟨27111989996933785863866768577,27111989996939316335852502386⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-97558170998190240402117704217),(-97558170998187847146769976959)⟩,⟨26938217035932611200070677476,26938217035935004457230108710⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-73145845599493861445393388224),(-73145845599492918797292773249)⟩,⟨22260076691073954820918414592,22260076691074897470359013172⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-50747963748397551485638573907),(-50747963748397192795546294145)⟩,⟨15806018214829207629017722468,15806018214829566320003923461⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-29814717742582299473323827316),(-29814717742582167294796924079)⟩,⟨9218681093854450049812058268,9218681093854582228844369754⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-9824266405372425914125773545),(-9824266405372392277230815493)⟩,⟨3006713122649725512541193460,3006713122649759149599786496⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨107455744845205732321967510340,107455744845205732402425527771⟩,⟨10915009237876726636996372315,10915009237876726716339601480⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨318091994376831560657383816899,318091994376831560900842340484⟩,⟨19504689235434001673442280217,19504689235434001913801304176⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨511156817101781057010787821840,511156817101781057418417207646⟩,⟨(-7448938329860627669164031864),(-7448938329860627265446795784)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨663652800200675919417600664633,663652800200675919982177294342⟩,⟨(-81444667104232024495765703241),(-81444667104232023934372235601)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨746841302492543568725540321242,746841302492543569423763625248⟩,⟨(-200354890603619318403264181569),(-200354890603619317706065800643)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨740359187554242647426639552717,740359187554242648230073617196⟩,⟨(-347498281542669763952879524359),(-347498281542669763147732250059)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨645517805914235697137546954044,645517805914235698040788956877⟩,⟨(-492723594669910759084682551884),(-492723594669910758176426853279)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨487046998892881236498087709257,487046998892881237719535329755⟩,⟨(-601037292781172131735453727089),(-601037292781172130506564261233)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨304169408217151796073266623400,304169408217151799371218046260⟩,⟨(-647368819873544699095560489492),(-647368819873544695790303536726)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨136736710025010225016298818954,136736710025010240181468723060⟩,⟨(-626324030188850798913915495853),(-626324030188850783743445266460)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨12191548359560849899901165676,12191548359560921138391686808⟩,⟨(-550704642624490851994314058632),(-550704642624490780753096201342)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-60700860070486833509023322556),(-60700860070486567974923200270)⟩,⟨(-442796699415749326344475417417),(-442796699415749060809010104975)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-88498002270665322990628944961),(-88498002270664671032913957435)⟩,⟨(-325484504256365389197620878862),(-325484504256364737239203486794)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-83775610658838926162334589664),(-83775610658837880804224895401)⟩,⟨(-215754183345334102628106883477),(-215754183345333057269706629728)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-58093777090996115485404453106),(-58093777090995077471432289242)⟩,⟨(-120857307814873414416360030409),(-120857307814872376402305201857)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-20632585907337001769415535459),(-20632585907336563303198985880)⟩,⟨(-38663111823554170520792751511),(-38663111823553732054577946562)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-56237176002051458216848965867),(-56237176002050858379755278464)⟩,⟨97549729201578024172750446641,97549729201578624006910721547⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-155790453380375067947085812366),(-155790453380373651054237285815)⟩,⟨292477453013876653713936627651,292477453013878070598793774520⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-217126587712895848809242484904),(-217126587712894419478940826931)⟩,⟨484870398167839942103190290511,484870398167841371422844457829⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-218365827248006662739743122437),(-218365827248005764282847576709)⟩,⟨668268346584247866503377792536,668268346584248764950582623276⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-146540563206153205940830322136),(-146540563206152833273345173334)⟩,⟨831110401477832017327508614872,831110401477832389990500309104⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-4676785750334163731628932158),(-4676785750334060081990652625)⟩,⟨956451834852220634762148838170,956451834852220738416289204073⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨186130184140568108739267433035,186130184140568129534891795823⟩,⟨1023184414735052949677553750486,1023184414735052970489130323464⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨392342512527214279391145430186,392342512527214283326123914096⟩,⟨1013377675523902752360141739884,1013377675523902756322777171175⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨576559202203964116583295018901,576559202203964117963388296986⟩,⟨923133729155813626971192578242,923133729155813628388731160705⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨706266453921826684514078079790,706266453921826685462902202151⟩,⟨767943849979917229140867811395,767943849979917230133174546996⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨761340578823711568089428992361,761340578823711568891039037975⟩,⟨578828607564883668473989973242,578828607564883669317312633218⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨737122659869048577788534008879,737122659869048578516929784967⟩,⟨391649895615307050016660621947,391649895615307050775239924120⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨642217994831486762663291348329,642217994831486763278353332967⟩,⟨234967661361930190364501490844,234967661361930190999478780244⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨493216230847326806164677473924,493216230847326806627593186338⟩,⟨122638846670787622892211906145,122638846670787623367057897577⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨308663099454423000296223340727,308663099454423000581991605911⟩,⟨53324356165519039241608725881,53324356165519039533524031974⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨104846078402959977604486821705,104846078402959977700704883216⟩,⟨14187450961746235258068912586,14187450961746235356150452236⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-41519302068995651712547499273),(-41519302068994093570711184789)⟩,⟨(-41367658536765062279459026842),(-41367658536763504136662725319)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-130621686794471567641856746562),(-130621686794465591744392963062)⟩,⟨(-120350157394198711720284612527),(-120350157394192735820467334903)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-235043565161495067572765582032),(-235043565161479542944264047443)⟩,⟨(-186708212714099343802515659011),(-186708212714083819171931874576)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-357139142064670805923248841998),(-357139142064632639667006370668)⟩,⟨(-228150803871226411263381506876),(-228150803871188245008032009601)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-491484669777421504775671712554),(-491484669777333280805929787630)⟩,⟨(-228787018978381746432300045775),(-228787018978293522469929568575)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-626854752810783864342704442483),(-626854752810603611159965312457)⟩,⟨(-174256647667184044194671937771),(-174256647667003791029532451875)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-747600267950813093056624484973),(-747600267950512634858483689772)⟩,⟨(-60504746304470038814517920664),(-60504746304169580648076005247)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-834955895226777506457327598057),(-834955895226396659201618816076)⟩,⟨100590326371919124530918117277,100590326372299971739250505682⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-871760761184141827034812743500),(-871760761183776220410689604009)⟩,⟨281889799257130010920237143812,281889799257495617483646085470⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-848850345979014371004518819928),(-848850345978748788787442091275)⟩,⟨446711286515329484525142573619,446711286515595066673882058528⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-768193780330350623161962711881),(-768193780330182814076538585813)⟩,⟨558705452955351627691026054644,558705452955519436715920403062⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-641586689855399895700848425691),(-641586689855306179700585829830)⟩,⟨594042663614826979639691675337,594042663614920695593632867611⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-488191923601736752094049927424),(-488191923601691634880858559612)⟩,⟨549449290392112412874522024389,549449290392157530054734027835⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-330714199267647172497851327643),(-330714199267627274440760152137)⟩,⟨438592470776840621366892520850,438592470776860519402860098700⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-186609139710788666182457985304),(-186609139710780585822455445030)⟩,⟨281247708419022861341945865953,281247708419030941690469267900⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-59676862646713751373708599939),(-59676862646711590790479326664)⟩,⟨96704907683223150846238796655,96704907683225311425901767413⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨950580452662538750925668781,950580452662538761076708436⟩,⟨397199104711646522953885828,397199104711646531871460810⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3005426287154436430467417519,3005426287154436461861141210⟩,⟨368372483169010699734179868,368372483169010727164836865⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨4541860105577361579434934758,4541860105577361634095527715⟩,⟨(-2732677079335468132119082579),(-2732677079335468084629106893)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2979376182877151686749978429,2979376182877151767811035639⟩,⟨(-13022362536450789609384359631),(-13022362536450789539346200561)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-4566048004167667767889802281),(-4566048004167667654357595563)⟩,⟨(-36655583184840790809232720965),(-36655583184840790711035230465)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-18591261670286043671269959101),(-18591261670286043512732536933)⟩,⟨(-78494650297151844116458592916),(-78494650297151843978191894883)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-37594413351032578467911488771),(-37594413351032578225067563078)⟩,⟨(-137009398858087601914118458256),(-137009398858087601697124616351)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-60708496005442984340711887820),(-60708496005442983760295501030)⟩,⟨(-203257711445585008128415016498),(-203257711445585007576467751188)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-87736809329501629199052359306),(-87736809329501625975941362065)⟩,⟨(-264194516633110801380397670057),(-264194516633110798181103100193)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-117090367234759792632062113409),(-117090367234759769217791635542)⟩,⟨(-306513891963867016086813640685),(-306513891963866992690172728220)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-144783104596229960435362107831),(-144783104596229824009320748082)⟩,⟨(-320237088386390924624109141794),(-320237088386390788209737968569)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-164770743879095966458543483246),(-164770743879095416270080662554)⟩,⟨(-302190401893765080183867154728),(-302190401893764530002560550437)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-169279212926181428739582821065),(-169279212926179971802337990931)⟩,⟨(-257072356739293014426221142626),(-257072356739291557492776483657)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-150387261658082942444329116976),(-150387261658080447584219488197)⟩,⟨(-193698347215123033460032597509),(-193698347215120538601507631144)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-104728667967275990933206252287),(-104728667967273389594716654731)⟩,⟨(-119807758195876757237984987514),(-119807758195874155899949657175)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-37620867018437362908249746060),(-37620867018436234188454708738)⟩,⟨(-40492236298281355455250841195),(-40492236298280226735514619743)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-461926746259588703553884503773),(-461926746259240103177740956208)⟩,⟨552324873980077313033350812892,552324873980425913348232378644⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 5) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_5 (tableDensity true) (fullFactor true 1 5) density1_contains hk1_1_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨87438557056583966901786619029,87438557056583967555765728262⟩,⟨232120724868727949438048485256,232120724868727950091012392650⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_5 1 5 ha1_1_5_contains + def realAnswer : RBox := ⟨(-374488189203004736652197884744),(-374488189202656135621875227946)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_5 +namespace hm1_0_1_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨85925892504492082474856811349,85925892504492123757197578244⟩,⟨1382670058797645828606062570,1382670058797687111901304327⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨247086084866007756119680488252,247086084866007850681202457667⟩,⟨141199570822071218211342044,141199570822165782374164259⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨378862696991066711486501461445,378862696991066801469994626506⟩,⟨(-10505432858115703031072136130),(-10505432858115613043730491038)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨470351973292573998402812401522,470351973292574050636163693820⟩,⟨(-29653455950378920702323936198),(-29653455950378868464223506104)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨519653847578707155372437524921,519653847578707175174566805112⟩,⟨(-50453253127282513592403005020),(-50453253127282493784324568417)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨531882664637886801502429028111,531882664637886806637000369479⟩,⟨(-64683140518912146648862318499),(-64683140518912141507102807663)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨516163370752295558567037149559,516163370752295559673149257544⟩,⟨(-67854659181760306809901945641),(-67854659181760305696769953976)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨482775051929144075669561816586,482775051929144076013987640489⟩,⟨(-60442264174482116751123963490),(-60442264174482116401958203606)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨440294942560449695838225024280,440294942560449696063805465280⟩,⟨(-45868239148345610219783006865),(-45868239148345609991268047061)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨393928728924161998411764955746,393928728924161998592873616947⟩,⟨(-28298888806168387001042338624),(-28298888806168386816131117221)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨345566141113337571171804365809,345566141113337571316023530600⟩,⟨(-11345937541586648158146424560),(-11345937541586648008654855946)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨294675225520505376127928093631,294675225520505376233552399224⟩,⟨2433439500099857856803524886,2433439500099857966421019695⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨239392296308125739991698796415,239392296308125740063455012443⟩,⟨11398292240509082067857901696,11398292240509082140930790828⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨177936863178483338150850172638,177936863178483338195754992979⟩,⟨14536638420007369494258074162,14536638420007369538450725742⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨110011555632164605906938470637,110011555632164605931231123271⟩,⟨11762505656877885901128273066,11762505656877885924181246280⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨37249555078789302849773222603,37249555078789302857403787382⟩,⟨4482225025194894837903836224,4482225025194894844978621182⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨72149573576069377503309181994,72149573576069586744857962907⟩,⟨316498309942348897375191350412,316498309942349106630087736519⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨241455918022276290581317867702,241455918022277056999622838292⟩,⟨910479090584702126026872331829,910479090584702892486444995882⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨471577082373620588768431150499,471577082373622405782808292446⟩,⟨1389070613543587407109504462568,1389070613543589224195303113629⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨762522243215941005447260054534,762522243215944905142177610717⟩,⟨1688348364290165412997227887119,1688348364290169312794044344532⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1073360913924995472667399787733,1073360913925003017153843210733⟩,⟨1772796479224371747473937430594,1772796479224379292088384621669⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1338593529303970354217885913686,1338593529303983208218067306839⟩,⟨1651705382620281210501106090903,1651705382620294064641788173819⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1498062462844441758255726877055,1498062462844462442890413639686⟩,⟨1381102353782967703736393085896,1381102353782988388488550383604⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨1523378842555507269300086287944,1523378842555532759194551230553⟩,⟨1043726111084568122548201144186,1043726111084593612529529551814⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1426060321981826172464020471761,1426060321981849811816397558074⟩,⟨717392221653398218806423789760,717392221653421858218373846211⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1245029304909585415107442858809,1245029304909602087265207229521⟩,⟨451358159796681003201315613959,451358159796697675397866124875⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1025208123482196167916069195414,1025208123482205191496856223929⟩,⟨261334507770913746628742632865,261334507770922770234029010019⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨801444255551035484782377214412,801444255551039526775585766452⟩,⟨139423704006468201022823912624,139423704006472243031231711029⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨592919272868510865082445016666,592919272868512493705032189735⟩,⟨68155823916804947961204307235,68155823916806576592989593607⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨405202261394759822647960551803,405202261394760451028084174845⟩,⟨30113217882394412133472263360,30113217882395040518982770359⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨235461904538630128653274503076,235461904538630362006013447346⟩,⟨11593732800134030156748840819,11593732800134263512324259898⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨77169687162669305107620481709,77169687162669364693785782082⟩,⟨2885841839037808697356519614,2885841839037868284410160390⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-381086626105178840584422652308),(-381086626105178840384609948461)⟩,⟨(-268311597868877991845038228819),(-268311597868877991657704348531)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-1164383571812617829351030014018),(-1164383571812617828755536448397)⟩,⟨(-737848177287288081522967627431),(-737848177287288080971913827967)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1990825884683657491862009420293),(-1990825884683657490875560010238)⟩,⟨(-1010516538730924281953155506910),(-1010516538730924281061648086744)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2830654331147222210690422875722),(-2830654331147222209295284648179)⟩,⟨(-979321463168186160449137823519),(-979321463168186159224435512280)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-3585761981890088426104128979353),(-3585761981890088424283363893975)⟩,⟨(-589047040220670108379214122009),(-589047040220670106825329994645)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-4107964663810504812142650545959),(-4107964663810504809915624548639)⟩,⟨132005679307580427510732584874,132005679307580429372271217116⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-4257086288575033545109411382045),(-4257086288575033542444801639284)⟩,⟨1058055793793827234184069800591,1058055793793827236446550116865⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-3973130256238110233908467252179),(-3973130256238110230424694482426)⟩,⟨1988848188366925853966997949229,1988848188366925857140786382160⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-3316887975561706849338913489344),(-3316887975561706842367319857068)⟩,⟨2714197035345812965711109258043,2714197035345812972483662700305⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-2451102512650414117762731782899),(-2451102512650414088877735127065)⟩,⟨3091584486278762007871014028521,3091584486278762036658494001938⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1573538576553470116904620519917),(-1573538576553469983902639534780)⟩,⟨3089661220979993632726094434285,3089661220979993765706517831733⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-843526712742233643452474733810),(-843526712742233188993350720792)⟩,⟨2774052218572233754935835968641,2774052218572234209418948665496⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-340474424167453327522608838347),(-340474424167452282624324552056)⟩,⟨2254640757566956670130029303983,2254640757566957715071587497707⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-64922392122022881372341870069),(-64922392122021287950539582990)⟩,⟨1634046574437598302747787456945,1634046574437599896212434071116⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨33012251162000970145461805362,33012251162002498468343580998⟩,⟨980824481612588158924787153509,980824481612589687277670097426⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨22912452351412937544984539084,22912452351413571705075696657⟩,⟨325951733937509009384292832497,325951733937509643555005327602⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨247694322754724671856755074470,247694322754725281140717742356⟩,⟨(-115243590955482823960353914660),(-115243590955482214677569264574)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨728314092430026327009355221560,728314092430027758871437073221⟩,⟨(-374354245105837212677073365941),(-374354245105835780812427495028)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1158123292516883540521327899181,1158123292516884970133519669412⟩,⟨(-712372445236372860073963177407),(-712372445236371430438031204206)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1487080636503772055617459418089,1487080636503772940166348551979⟩,⟨(-1159371987561955733763049460949),(-1159371987561954849143280860944)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1651080266997597219247354905286,1651080266997597578255338297976⟩,⟨(-1711668172459716575028468713239),(-1711668172459716215872966283890)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨1587366170388719057757399575719,1587366170388719155033099911180⟩,⟨(-2323053550546445267104011205567),(-2323053550546445169578476893902)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1263531609617262870101493218188,1263531609617262889445589256468⟩,⟨(-2905437325104003279547083932457),(-2905437325104003259838003420295)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨705344480258386658811106452053,705344480258386663029657966978⟩,⟨(-3345406476958916931417883575593),(-3345406476958916926735871414070)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨5604008259055464717962108534,5604008259055467090592026087⟩,⟨(-3539982098183474381029146597591),(-3539982098183474378243370683603)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-694781221965605236547399790366),(-694781221965605234336569099780)⟩,⟨(-3437945766533096092329393958132),(-3437945766533096089815719945989)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1249383209781657492758458824817),(-1249383209781657490630159701291)⟩,⟨(-3062354511601869145256374020377),(-3062354511601869142939288390819)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1552896887822110503502616456395),(-1552896887822110501574174727219)⟩,⟨(-2500011106787355707289757577293),(-2500011106787355705270175333678)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1567300333209451647666102575305),(-1567300333209451646060009222353)⟩,⟨(-1863872433850724818561958244851),(-1863872433850724816933411584876)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1317917349249365109193758474344),(-1317917349249365108001357309570)⟩,⟨(-1249044909255363358367152158795),(-1249044909255363357188159069582)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-869905431352501022373351737382),(-869905431352501021645094109279)⟩,⟨(-703985143245179277574426644944),(-703985143245179276866868538618)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-302895775098022306597139044171),(-302895775098022306353436033028)⟩,⟨(-225691065419356893547247765549),(-225691065419356893312611098061)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-75951261979357960060552206130),(-75951261979356644752566402051)⟩,⟨97176797181982873890696981323,97176797181984189196607744888⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-211234780246634177115207771353),(-211234780246629140767443822682)⟩,⟨300396196938386416298233284735,300396196938391452637649384570⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-296028988932403147718892126801),(-296028988932390110828947286393)⟩,⟨526297563435891141940113182687,526297563435904178809225483903⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-297355638534296554200426682809),(-297355638534264702812176644102)⟩,⟨777800867386760055176597840986,777800867386791906521983304523⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-188336084842303794850678088214),(-188336084842230894128916209069)⟩,⟨1039519902690530505866274320204,1039519902690603406511459409715⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨43471874548301548779641106969,43471874548448259067530887023⟩,⟨1274163236394102393338317368786,1274163236394249103504403787346⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨387118018830648063635140840011,387118018830887166260342726406⟩,⟨1428667027823350099403902479746,1428667027823589201854196999973⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨801400978129302274621552583708,801400978129595495610898933489⟩,⟨1451604174410282239786625596533,1451604174410575460544894329832⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1216654140106302438839885968890,1216654140106608637110015066673⟩,⟨1315289522030791074094012176712,1315289522031097272117014917704⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1550589515767100294334909494403,1550589515767378972850309944226⟩,⟨1032952951711001911289208136996,1032952951711280589597257572589⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1733598932335046808913486232508,1733598932335236619639206997935⟩,⟨662085512044863496633816001094,662085512045053307202259363843⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1729778017272408332550490758393,1729778017272511870523199771537⟩,⟨289450774317150957992460876133,289450774317254495860342354442⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1542017060173742683837457083278,1542017060173791584455366817893⟩,⟨960386886599074626540328427,960386886647975184904255018⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1202837804195987735812936735055,1202837804196008977525188535503⟩,⟨(-150278271536442748387808185686),(-150278271536421506702824738851)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨759451975649306389534878440277,759451975649314922824128675140⟩,⟨(-159626155855600774546245797666),(-159626155855592241266108842402)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨258930923267032067609439885706,258930923267034336365378500270⟩,⟨(-65669945214846277654144936337),(-65669945214844008899908974273)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨7960939239429459129100031710,7960939239429459138639993942⟩,⟨(-19313613796063617218863693887),(-19313613796063617208214034765)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨19655465946775913451668476488,19655465946775913481099093745⟩,⟨(-59491468782753540397691558629),(-59491468782753540364706999006)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨19054305988762645669461735043,19054305988762645720937598497⟩,⟨(-103677922094738460245127267882),(-103677922094738460187316458178)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-247964502989850284193859912),(-247964502989850207332839403)⟩,⟨(-152269850734579451801355872205),(-152269850734579451715061038509)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-41460838294398275083619748742),(-41460838294398274976998684548)⟩,⟨(-201388230472196985115235409417),(-201388230472196984996200573907)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-104103166452372688136364240566),(-104103166452372687992451853465)⟩,⟨(-241534659820558861942143100113),(-241534659820558861783213869422)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-184200047989759118494595500037),(-184200047989759118281748175160)⟩,⟨(-260062636453614342129872061157),(-260062636453614341900807689157)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-273200011111925795313528905243),(-273200011111925794792232179517)⟩,⟨(-246746869002753511534078312191),(-246746869002753510999959341859)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-357400507075558024506330990252),(-357400507075558021732295593853)⟩,⟨(-198509395588783618591629625726),(-198509395588783615809805766049)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-420769735617836386565359571127),(-420769735617836366498739604208)⟩,⟨(-121861262234548746925169488251),(-121861262234548726855378286093)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-449957038668877666755835173614),(-449957038668877549744949179558)⟩,⟨(-32755094395806667397686367831),(-32755094395806550386752040323)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-438056644565326374476210718229),(-438056644565325903094920044389)⟩,⟨47185823082379001184085706718,47185823082379472564119537485⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-385356509711644974378905826757),(-385356509711643729169205496304)⟩,⟨98122494091264333853712259817,98122494091265579062053221075⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-298326101987946258491639581276),(-298326101987944132306463729126)⟩,⟨109654597712696965806766477799,109654597712699091991065134282⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-187469145385412354181690942081),(-187469145385410142741994928747)⟩,⟨83488208801433330162204333197,83488208801435541601532823537⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-63757224205767461175345936838),(-63757224205766503003522574677)⟩,⟨30951790694600437659789010575,30951790694601395831531624604⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-747616995563170471656133723463),(-747616995562852258234410051229)⟩,⟨1215771098278928532033138239654,1215771098279246745448720328809⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 6) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_6 (tableDensity false) (fullFactor true 1 6) density0_contains hk1_1_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-207368877810849428351328131914),(-207368877810849427694545584752)⟩,⟨121399183840485335661276479695,121399183840485336317470947688⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_6 1 6 ha1_1_6_contains + def realAnswer : RBox := ⟨(-954985873374019900007561855377),(-954985873373701685928855635981)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_6 +namespace hm1_1_1_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨14534756733911140978829881538,14534756733911174779906096947⟩,⟨2173398523093121125009484364,2173398523093154925853575520⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨42022847287994096518015708742,42022847287994173903130150141⟩,⟨5956330053418322010911405993,5956330053418399395376238760⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨64681537519305898555000146844,64681537519305972106820625659⟩,⟨8326484323743194329246645175,8326484323743267880110708229⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨79636565167076529470156345924,79636565167076572059962503573⟩,⟨8812914231366577924708709944,8812914231366620513369158129⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨85735334624000046466868938745,85735334624000062510951857889⟩,⟨6934565103361593685286096827,6934565103361609728132088316⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨84756323872550612417641522126,84756323872550616469828098650⟩,⟨2603560887800276756833309042,2603560887800280807743851726⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨80324700412364143002099724485,80324700412364143771383650933⟩,⟨(-2932652094404653669410360704),(-2932652094404652901561160984)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨75356574756759493085305479920,75356574756759493249724849629⟩,⟨(-7547758885526102878507898930),(-7547758885526102716024338143)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨70851112437304867679987686528,70851112437304867756331925056⟩,⟨(-9676013045490936675881409154),(-9676013045490936601973999963)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨66317956658507764252785992669,66317956658507764309207584504⟩,⟨(-9020592745565609380251101098),(-9020592745565609326238511932)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨60676592892095361553007266744,60676592892095361597514098430⟩,⟨(-6419222300083828857439679120),(-6419222300083828815033174904)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨53099282591112765188071071964,53099282591112765221502288944⟩,⟨(-3328336476179535816149765199),(-3328336476179535784866603126)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨43500892711090706170441927736,43500892711090706194076139015⟩,⟨(-1026522069800634604337281076),(-1026522069800634582981662618)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨32314121165886758449000490125,32314121165886758464363587352⟩,⟨69271014481875603939179901,69271014481875617186725738⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨19952924149421743271741232513,19952924149421743280303445912⟩,⟨296259448665540506073363911,296259448665540513130595298⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨6756166677591792106114589864,6756166677591792108850481523⟩,⟨131066257446092429403227947,131066257446092431591912717⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-13577703100614726628357116385),(-13577703100614554396683532249)⟩,⟨48774870755497618458835441074,48774870755497790688865768360⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-32226753271699021291208710643),(-32226753271698390150577759899)⟩,⟨141351633313789203596183074075,141351633313789834731767850256⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-28593269854355557898965438372),(-28593269854354060435928247794)⟩,⟨218728718991553899116454091695,218728718991555396570815422156⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2348095723393223932096917496,2348095723396440768272134317⟩,⟨271319008008143237871956040277,271319008008146454695752299137⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨54621742034663844634996146192,54621742034670073705101442941⟩,⟨292603816622095981356755028077,292603816622102210411187049875⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨113597427894138757913289293233,113597427894149379729350859585⟩,⟨281960671119500513099099348942,281960671119511134897748759805⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨162822096736630869451683414548,162822096736647977339095185982⟩,⟨245437184419297698353320819288,245437184419314806225931146801⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨191563658362496001568844971151,191563658362517093871818618364⟩,⟨194038096894150991724965677531,194038096894172084016712625871⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨197855322327760988416042826649,197855322327780548753041294978⟩,⟨140108606146731791242163693046,140108606146751351571189499576⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨186265358021377806427822511359,186265358021391594207596161363⟩,⟨93298472895508781312047060967,93298472895522569086455125582⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨163512814522284200647601176728,163512814522291655709085858360⟩,⟨58369634522458110608034453744,58369634522465565666065925278⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨135116050846657665815937753211,135116050846661000892396319583⟩,⟨35411151771244558316100955198,35411151771247893390392768688⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨104502287394220992514701646163,104502287394222334373536771040⟩,⟨21511167802563400023640613043,21511167802564741881121549522⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨73657320061093401803094690845,73657320061093918823935152357⟩,⟨12997126431882710280806166054,12997126431883227300818532124⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨43586389203577690919458244076,43586389203577882702849889585⟩,⟨7100186951153159432527675935,7100186951153351215467770675⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨14401095150923302028880631264,14401095150923350968802402595⟩,⟨2272756135529818305469679235,2272756135529867245246816778⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-41530026501847784652521202894),(-41530026501847784575028264116)⟩,⟨(-96679934903353338729866851214),(-96679934903353338652916937160)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-135512079958150756166146097589),(-135512079958150755933914597289)⟩,⟨(-280599170285579720115215044102),(-280599170285579719884997067785)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-256252237382407200247957662571),(-256252237382407199866807442629)⟩,⟨(-433373658374018122896267913154),(-433373658374018122519321603949)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-404680599048842190708992803909),(-404680599048842190186741584912)⟩,⟨(-528257793219349504416738927940),(-528257793219349503901724371339)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-564631677223115618610593931355),(-564631677223115617966253922167)⟩,⟨(-538081019061205405999146199038),(-538081019061205405365298682316)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-707630023269028417730226767337),(-707630023269028416996272328331)⟩,⟨(-449166724102250767067557215312),(-449166724102250766347488613640)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-801227779210361552140023195996),(-801227779210361551287080358163)⟩,⟨(-275111181871192600090768032642),(-275111181871192599253629358407)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-820537842329113153936108581424),(-820537842329113152614352080783)⟩,⟨(-56865164114000536991295395412),(-56865164114000535681557465319)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-760413935856828622516899545797),(-760413935856828618451602373102)⟩,⟨152179268592706602272231487553,152179268592706606330900535338⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-638957087842385413129941639820),(-638957087842385391184616630225)⟩,⟨306298042794019763452033493810,306298042794019785394640842511⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-488188156859725146291349469834),(-488188156859725039368129329701)⟩,⟨382225050682750474045094033849,382225050682750580967471764639⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-339317723691853889535482179659),(-339317723691853520263238593413)⟩,⟨382576314905753632821267241906,382576314905754002093240260515⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-213330492090574251335781459067),(-213330492090573399790781211234)⟩,⟨328074247245420704677482951080,328074247245421556222459931563⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-119495326429849311340125819835),(-119495326429848011071072332946)⟩,⟨243760802513701550854742559025,243760802513702851123788513114⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-56860226500116219854526614410),(-56860226500114971831055420118)⟩,⟨147922066020297002491404491114,147922066020298250514830942170⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16311742982845366285129900580),(-16311742982844848265238526923)⟩,⟨49365746828405402842952377750,49365746828405920862799846584⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨89404401501278265209180328393,89404401501278777115314114835⟩,⟨18610048794951174599564818895,18610048794951686505895837429⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨265813263880998963892246741508,265813263881000166082503209210⟩,⟨45229638024599943309102694968,45229638024601145499283744316⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨433132516084596116268609529515,433132516084597314863463712857⟩,⟨40790254867528529147061114948,40790254867529727739673757103⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨581004496564896140097227270059,581004496564896880005545681212⟩,⟨(-11893698017430048137800103895),(-11893698017429308236665124864)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨695408429597270667426624835119,695408429597270966617942471575⟩,⟨(-121969370017273450666077025771),(-121969370017273151489854343263)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨760389912613532872846478827213,760389912613532953248445211596⟩,⟨(-284018611671447225265028813547),(-284018611671447144888446442618)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨760656469281517461164829239003,760656469281517476624948758337⟩,⟨(-475227491013927059298140753416),(-475227491013927043874812881939)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨687616017421298951077279638561,687616017421298953959084635892⟩,⟨(-660641477735300418286604652457),(-660641477735300415450734807868)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨547534682318792786334797814936,547534682318792787570109052859⟩,⟨(-803464755593372627772913053423),(-803464755593372626577676808424)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨364582598754940917312659082496,364582598754940918309877912788⟩,⟨(-875900619124962879977250495192),(-875900619124962879008467570561)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨175225406996032063162787514221,175225406996032064059846397655⟩,⟨(-867015905469105848739047722593),(-867015905469105847858689873737)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨16707051326441528721200317560,16707051326441529500132361251⟩,⟨(-783825139661603973958859159114),(-783825139661603973187070291694)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-84779006317242214455602346287),(-84779006317242213824981705663)⟩,⟨(-645325160522304553183770080760),(-645325160522304552553865503869)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-120501656091718829708056287007),(-120501656091718829249052330337)⟩,⟨(-473731595267045765947513650657),(-473731595267045765486153634491)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-98247843422732854405111121998),(-98247843422732854128373791702)⟩,⟨(-287116512387951113074061979996),(-287116512387951112794705838521)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-37238671442446221506116351995),(-37238671442446221414079968106)⟩,⟨(-95904939654254868241188336238),(-95904939654254868148078540104)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-23288396060665360612417888423),(-23288396060664279639408789693)⟩,⟨33163820937742820891641356246,33163820937743901864940475626⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-66519872710880350936047506939),(-66519872710876211562089441300)⟩,⟨103638642826098623851591199677,103638642826102763226871141291⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-98947564752729537739565050798),(-98947564752718821287747789382)⟩,⟨184417838048011476029914664922,184417838048022192485393742956⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-111144575618160006020036499959),(-111144575618133819667831178032)⟩,⟨276360770747468968830715336887,276360770747495155191040088306⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-91597891283681625928024580510),(-91597891283621683892459594092)⟩,⟨373969078238664667354114123021,373969078238724609404895710642⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-30150569340824702608479160755),(-30150569340704071571417587586)⟩,⟨466854174808086917932898504414,466854174808207548995080789520⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨75520900905526716225364559758,75520900905723273884177607582⟩,⟨541644622645897616316236421146,541644622646094174012875458582⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨215118335467304031185220012009,215118335467544960195138708457⟩,⟨584135424564844904134798570331,584135424565085833195802293872⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨365822018421592614522427747202,365822018421844001579738990729⟩,⟨583622389703407832702983122853,583622389703659219814325077304⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨496963458476193750998413874025,496963458476422300547704840969⟩,⟨537984217285113057054140319214,537984217285341606647239803688⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨578320141851815182564271340262,578320141851970653096856418296⟩,⟨455349755382510387069379655179,455349755382665857633828549352⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨590312534423394954863168116408,590312534423479647221095513000⟩,⟨350921343827166165504083519571,350921343827250857883039410611⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨531311627084308629595984240770,531311627084348578715709914462⟩,⟨242428013240986936751803570085,242428013241026885883559865273⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨415413444184882213704916867056,415413444184899548639593577189⟩,⟨146504158318428823099673184292,146504158318446158039970788111⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨262328558489433322374898947061,262328558489440281017663523389⟩,⟨73378564485158577553121950851,73378564485165536197886083336⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨89443826111231507805351323222,89443826111233357200032942751⟩,⟨21579824229467317171386239757,21579824229469166566484562525⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨209112994374566793542614163,209112994374566798756906897⟩,⟨(-584985246536022653155777251),(-584985246536022647083736513)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨123053880669155443591266580,123053880669155459632321092⟩,⟨(-1825942833658537100206185457),(-1825942833658537081412683001)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1819486473214185790628975497),(-1819486473214185762852349835)⟩,⟨(-2654920131226375842102198484),(-2654920131226375809354370389)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-8068220934000218195177066295),(-8068220934000218154214499013)⟩,⟨(-1297685471298322742288128276),(-1297685471298322693692924031)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-22363897162406963844281352581),(-22363897162406963786775816599)⟩,⟨4460392949189920771089274392,4460392949189920839219400635⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-47863086314323501390766943468),(-47863086314323501309790436996)⟩,⟨15568224052235480700222905084,15568224052235480795265455521⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-83957912330674521822038097318),(-83957912330674521689509092022)⟩,⟨31593635906440167048186615403,31593635906440167197962005557⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-125298159439960338490387710424),(-125298159439960338105065632632)⟩,⟨52004712969815561940592076355,52004712969815562342094562327⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-163578335140794011257043391903),(-163578335140794009016156073636)⟩,⟨76071696505346563100494807009,76071696505346565354251579568⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-189993954330034918563101083554),(-189993954330034902168067470244)⟩,⟨101597547831598341184676000596,101597547831598357588563917829⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-197779831555067289534386968644),(-197779831555067193964569918045)⟩,⟨124489678385721547174042290899,124489678385721642748976161842⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-184808867147262924268561010242),(-184808867147262539309198317586)⟩,⟨139460733762298030557129899692,139460733762298415518868607137⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-154664560695167681393265690050),(-154664560695166664103427823890)⟩,⟨140734733422540670806914708311,140734733422541688097259027261⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-114182628963747618526923501663),(-114182628963745880695441166419)⟩,⟨123120536113949558505830209047,123120536113951296336858555125⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-69299975379022876060210099388),(-69299975379021067872136389287)⟩,⟨84859875483768978565307913667,84859875483770786752765476126⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-23156878186379415532168141612),(-23156878186378631925809050750)⟩,⟨30332659616336245954913118537,30332659616337029561011542212⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨455700513678610579323642551946,455700513678871872201037251876⟩,⟨167896824469368102910958145497,167896824469629395786161824146⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 6) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_6 (tableDensity true) (fullFactor true 1 6) density1_contains hk1_1_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨271174686368033866985174995446,271174686368033867844044480195⟩,⟨(-158752778868326978261308162361),(-158752778868326977403207704216)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_6 1 6 ha1_1_6_contains + def realAnswer : RBox := ⟨726875200046644446308717547392,726875200046905740045181732071⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_6 +namespace hm1_0_1_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-93526674780040825483016460860),(-93526674780040783964866126289)⟩,⟨(-46999540751100171575815362524),(-46999540751100130053663522720)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-272721808408494127255675342618),(-272721808408494031232237834162)⟩,⟨(-129162681497181861423000876997),(-129162681497181765388470477186)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-428812831814894146395623619175),(-428812831814894053407631609353)⟩,⟨(-180556715242376661024453736238),(-180556715242376568020596580505)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-549307963459861770722434014580),(-549307963459861715516476444057)⟩,⟨(-194648596617651531285085183233),(-194648596617651476061203649382)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-626429367249172846815389640264),(-626429367249172825356660941089)⟩,⟨(-178334065928495091749534570902),(-178334065928495070272587358394)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-658938512341888632386600738370),(-658938512341888626655994186729)⟩,⟨(-145956684646222051900393227680),(-145956684646222046151426474321)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-652835705304342944886365842213),(-652835705304342943580070685703)⟩,⟨(-111082671813525139601738723931),(-111082671813525138278489575931)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-619201592144853379546600135911),(-619201592144853379106603433939)⟩,⟨(-82046988211393627257219845030),(-82046988211393626804784270733)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-569540730222474602157058099497),(-569540730222474601886499936991)⟩,⟨(-61725670429519574327024161924),(-61725670429519574050082653090)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-512051620349265146844766408133),(-512051620349265146616437006032)⟩,⟨(-49190110360491215166064529565),(-49190110360491214932238741832)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-450535265018531676966105631011),(-450535265018531676777629259716)⟩,⟨(-41806748857287920075198974271),(-41806748857287919879153378631)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-385078225869422555109217332437),(-385078225869422554968808327584)⟩,⟨(-36859191171306639247054778122),(-36859191171306639100629190377)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-313520158292675978401913745791),(-313520158292675978305959651163)⟩,⟨(-32140681526692732811490423639),(-32140681526692732713257268881)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-233528262138190480669084508653),(-233528262138190480608962198470)⟩,⟨(-25899485901029776215143211286),(-25899485901029776155719052394)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-144638174471530264461306753899),(-144638174471530264428773001199)⟩,⟨(-17116060710273464765050699857),(-17116060710273464734093748003)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-49024614610112103433519144752),(-49024614610112103423296502109)⟩,⟨(-6012035128376356930176872871),(-6012035128376356920683774509)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨181883616945819078782024841245,181883616945819291654776660106⟩,⟨(-276221477583590283582505398420),(-276221477583590070723375317209)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨496423981442102762883263751001,496423981442103568568742784186⟩,⟨(-825488283017035965743731016623),(-825488283017035160094415505747)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨673457326123073586045550449917,673457326123075618397775455343⟩,⟨(-1352730670200996954017250579742),(-1352730670200994921710842162829)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨657911387258927595863085654987,657911387258932348565360355627⟩,⟨(-1812881885928331926421182751102),(-1812881885928327173757543806986)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨447277322137734817520779530140,447277322137745019372333944290⟩,⟨(-2140217408695784843130856294011),(-2140217408695774641295596337993)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨97924589860749593953091134340,97924589860768489640531240755⟩,⟨(-2276094426325683835286945241229),(-2276094426325664939585265011329)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-292488870252507218990658117018),(-292488870252479200343202503875)⟩,⟨(-2201696996560238605276519266209),(-2201696996560210586585200110215)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-623482439999479933646524044261),(-623482439999448767196150522757)⟩,⟨(-1952020622366793046566868946857),(-1952020622366761880051888369139)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-830199193557853379357389107838),(-830199193557827231058698721960)⟩,⟨(-1600794410420891931144778846467),(-1600794410420865782772708892843)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-898683965200104510708938742425),(-898683965200087748193233445129)⟩,⟨(-1227919596322925993246014036680),(-1227919596322909230658161705406)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-854160388986701889470638099359),(-854160388986693590185087618984)⟩,⟨(-891508260151728727444039611411),(-891508260151720428094308924579)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-737164752899870259143722462071),(-737164752899866708210926844330)⟩,⟨(-618412765930088121948802867537),(-618412765930084570965325064309)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-583872297176831056420346092064),(-583872297176829546125253365631)⟩,⟨(-410605166152262229141425068857),(-410605166152260718812148553068)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-417584821790527488416270256540),(-417584821790526881883427156222)⟩,⟨(-256472356047452605854754466441),(-256472356047451999300330561550)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-249472305257278569132610837138),(-249472305257278338341014862087)⟩,⟨(-139726095360432522522011574854),(-139726095360432291718587646282)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-82836221233596744112932140082),(-82836221233596684500202420852)⟩,⟨(-44280033949192502441586432981),(-44280033949192442825100361810)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-41366847257106175363569958050),(-41366847257106175222930426067)⟩,⟨386975287672656105764100473697,386975287672656105943446148234⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-61966427173717433865653746031),(-61966427173717433450449667288)⟩,⟨1153630767124055715033747589331,1153630767124055715569674990365⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨93736240213673821548570874390,93736240213673822257141361057⟩,⟨1882319402831710293135950830477,1882319402831710294045199359569⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨504094585631460570550891731369,504094585631460571657136303674⟩,⟨2504939285491863300129603419989,2504939285491863301473083757279⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1178997593883004958904303036915,1178997593883004960487899536672⟩,⟨2912252816074050748042172845702,2912252816074050749855152817714⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2034669739526331139531748969116,2034669739526331141646105765507⟩,⟨2982784148129316497212161772606,2982784148129316499500783157146⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨2899540652866542064698223534063,2899540652866542067363836893619⟩,⟨2642172753695606672573280253385,2642172753695606675321716927907⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨3563968727346684346414645236156,3563968727346684349860790576867⟩,⟨1922971662121417264838863874758,1922971662121417268261411594539⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨3861211467004356725733764853548,3861211467004356732356257647472⟩,⟨978511996921247887441555378623,978511996921247893944683653853⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨3737825948206255272410225338780,3737825948206255297324309752314⟩,⟨31235698534058011597467333853,31235698534058036327509449591⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨3267916866483164364497667082738,3267916866483164466834564220686⟩,⟨(-715023052391167316432242315170),(-715023052391167214305825052876)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2603455910840952643721229150398,2603455910840952975310683186540⟩,⟨(-1143667253402218999525676258594),(-1143667253402218668130110854496)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1898058187163086146077024447693,1898058187163087007930798212920⟩,⟨(-1240750174253800026435707707879),(-1240750174253799164710707935576)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1252259140401706014130680279451,1252259140401707464030281338900⟩,⟨(-1065449244282396328557700097334),(-1065449244282394878734378866343)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨700136667999102095024811285952,700136667999103577213414423982⟩,⟨(-705769169701476439480614802336),(-705769169701474957331207171647)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨223839520761257977754725878195,223839520761258612463394089042⟩,⟨(-245561166015729268468502834281),(-245561166015728633771742286779)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-129897717114363444467474592372),(-129897717114363042264168636023)⟩,⟨(-138540930858096666028784193141),(-138540930858096263839272792845)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-407978872737773839761682578313),(-407978872737772901994666118108)⟩,⟨(-399666889686938613648405906740),(-399666889686937675927022492233)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-734742423293459752144328164203),(-734742423293458831200529643036)⟩,⟨(-609108492503537755288413538281),(-609108492503536834433953450238)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1123170883385904321332946173161),(-1123170883385903766619394708508)⟩,⟨(-723503298426778216050911553507),(-723503298426777661487425903913)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-1557798156429929805614139725395),(-1557798156429929589353046728951)⟩,⟨(-694142438438332601482920357776),(-694142438438332385450339820428)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1989519522070483784294329865721),(-1989519522070483727129091121981)⟩,⟨(-480606586113897400569123489422),(-480606586113897343705033148913)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2340983357832324722391785962808),(-2340983357832324708284493185856)⟩,⟨(-74171708910659141266677775763),(-74171708910659127440979334854)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2526141151281559417152321207803),(-2526141151281559413116685657096)⟩,⟨481321112878299895647954299563,481321112878299899465071614788⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2482947125499295006498139193021),(-2482947125499295004212344742831)⟩,⟨1087514772234575953017526275352,1087514772234575955173422900376⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2205417133453696059903941090908),(-2205417133453696057961206418026)⟩,⟨1615650089568654332191796232454,1615650089568654334101812039493⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1753915148848730627429363158382),(-1753915148848730625697705249967)⟩,⟨1949039877751897274112334020759,1949039877751897275898011723504⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1234130183309065015813416071636),(-1234130183309065014265894404434)⟩,⟨2022612051699304048088128292919,2022612051699304049750994587647⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-755753195452749871227126159106),(-755753195452749869936480958652)⟩,⟨1837322540529651874286674047112,1837322540529651875717710053175⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-393173621794449480222606154442),(-393173621794449479258211840657)⟩,⟨1444347314001520953356762956811,1444347314001520954450410265546⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-165996892224535632184695884602),(-165996892224535631591511158906)⟩,⟨914326988541606924342439434042,914326988541606925025071832785⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-42528274457612294287857426188),(-42528274457612294088490932722)⟩,⟨311947517348501353359970304979,311947517348501353591085116194⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨64422770858353874049138379857,64422770858354633350061439834⟩,⟨34532565829423518810084468424,34532565829424278114991135987⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨197551882245303456891159815210,197551882245306356707836351003⟩,⟨92759831238865660257517947551,92759831238868560087449272636⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨340963119596381946330555101773,340963119596389409835842181533⟩,⟨118132631320267662719477382103,118132631320275126251209220633⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨493630493724548095176165209800,493630493724566149454093291229⟩,⟨89328745042108847411507069775,89328745042126901735063385476⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨642997193564975143861372200655,642997193565015810028013994187⟩,⟨(-10471543439930981919587184840),(-10471543439890315680825415364)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨763053551740523738964297611020,763053551740603554696169658951⟩,⟨(-187386626366935635307339392755),(-187386626366855819469946811943)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨818813468030757690169441585362,818813468030887801306158784188⟩,⟨(-430405296689646419876264332258),(-430405296689516308601669481443)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨778623030798971614431780710713,778623030799169236333919396879⟩,⟨(-707314894588938211993484400511),(-707314894588740589959107957488)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨629893430822690420162928772866,629893430822923887323065694370⟩,⟨(-967499567547694686995652579160),(-967499567547461219726469129903)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨390716180881873193037610617616,390716180882079853655078945584⟩,⟨(-1154940129987288802974457492345),(-1154940129987082142280522691354)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨110418189816425709203674058503,110418189816562956078647420394⟩,⟨(-1227538239089297086132975516727),(-1227538239089159839218344528155)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-143490393373484962413340830004),(-143490393373411841545825127976)⟩,⟨(-1171903708766682419179608475589),(-1171903708766609298306292568031)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-308181250838522124070837984151),(-308181250838488336747267033418)⟩,⟨(-1003961887958954504585586082937),(-1003961887958920717279949883516)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-348376320469296464657715789490),(-348376320469282066122696763399)⟩,⟨(-756878173642837383722124677135),(-756878173642822985214801670989)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-266859718166249773040701335676),(-266859718166244072362331088522)⟩,⟨(-465810326479230586296757955134),(-465810326479224885641853609564)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-99190826287267423916198079934),(-99190826287265920269235237864)⟩,⟨(-156626537898231379349725669921),(-156626537898229875711824535305)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-10184713003260814714181514785),(-10184713003260814708666078085)⟩,⟨(-3585481711735678638956238030),(-3585481711735678634101126415)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-31332608146689876935076442413),(-31332608146689876917971257571)⟩,⟨(-8487010062219456842896106871),(-8487010062219456827899105353)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-54459816327805298462338499143),(-54459816327805298432291395246)⟩,⟨(-6734384518195148913062366624),(-6734384518195148886758665039)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-79641537407313924653947782949),(-79641537407313924608974726061)⟩,⟨5295642605830925656354934275,5295642605830925695771403231⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-104642183491242360731989468129),(-104642183491242360669831962088)⟩,⟨29586002433376572949763185811,29586002433376573004621376159⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-124134070579985384074220652159),(-124134070579985383990582617702)⟩,⟨65994159947407852342118221029,65994159947407852417051186972⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-130924212234936506579811208033),(-130924212234936506448012987952)⟩,⟨112146826521431416738391397525,112146826521431416862082948642⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-119061359265195588448005878573),(-119061359265195588134747769719)⟩,⟨162824980114334191774271946946,162824980114334192081454029908⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-86779068912130119292189372599),(-86779068912130117653450206319)⟩,⟨209772248848082612896158316045,209772248848082614531434137738⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-38206841595559585001159301805),(-38206841595559573177018503337)⟩,⟨243517120365454059394325891913,243517120365454071217242125103⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨16603159372106108815194222819,16603159372106177629554969837⟩,⟨256568289378984451352440292356,256568289378984520166891309436⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨63985936028853177853790132148,63985936028853454194030790134⟩,⟨245823795873774385412497185839,245823795873774661753151141446⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨91305581114889581185636743811,91305581114890308169962787550⟩,⟨212793797885418871149743904891,212793797885419598134239104277⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨91898463487417661168576038706,91898463487418897112416895027⟩,⟨162341555970050875746308591502,162341555970052111689942906863⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨67040370788609409708798806799,67040370788610690524377250936⟩,⟨100861744849583792698317228179,100861744849585073513545688145⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨24440278028848646627009403799,24440278028849200415915219178⟩,⟨34086471171700577790231196878,34086471171701131578971191301⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨323069659408552603633606317149,323069659408777441740161643268⟩,⟨(-770645017498851614302646346852),(-770645017498626776154146797585)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 7) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_7 (tableDensity false) (fullFactor true 1 7) density0_contains hk1_1_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨211892757358957129743619790060,211892757358957130532509028272⟩,⟨177346271492481110004654137201,177346271492481110790779938632⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_7 1 7 ha1_1_7_contains + def realAnswer : RBox := ⟨534962416767509733377126107209,534962416767734572272770671540⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_7 +namespace hm1_1_1_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-14793858373015374749085111134),(-14793858373015340754453611429)⟩,⟨(-10077793031583062933083750366),(-10077793031583028939419303188)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-43286084019861908531864949779),(-43286084019861829949553235071)⟩,⟨(-28517098691370719209692336182),(-28517098691370640630105816114)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-68073964324472268977736141091),(-68073964324472192971728621702)⟩,⟨(-42139674660443332110823220194),(-42139674660443256108852615452)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-86286732684231699215784304550),(-86286732684231654210738324575)⟩,⟨(-48694648411956255710970615297),(-48694648411956210710725279066)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-96385079486436826245176774505),(-96385079486436808876819850825)⟩,⟨(-47148153765178575259736194285),(-47148153765178557896443335126)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-99574851170773519525278870392),(-99574851170773515029745160090)⟩,⟨(-38597391008717415277360576811),(-38597391008717410786716855010)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-98709785217077593860285645862),(-98709785217077592980206527486)⟩,⟨(-26548198850862580953596506275),(-26548198850862580078065676982)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-96017803685940771580041125070),(-96017803685940771382378829827)⟩,⟨(-15132785150956002277577057610),(-15132785150956002084443338753)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-92261831581920593126855761256),(-92261831581920593035256882160)⟩,⟨(-7009705107406049895757859673),(-7009705107406049809063998113)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-87124666846161020954153880772),(-87124666846161020884070695506)⟩,⟨(-2799026766809811701633557739),(-2799026766809811636061915302)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-79832752686664721262837026338),(-79832752686664721206069242306)⟩,⟨(-1583908245046149916487204201),(-1583908245046149863241429222)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-69820842903805515491952935686),(-69820842903805515448650191758)⟩,⟨(-1713226142324493958358483182),(-1713226142324493918214863109)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-57192586214784168400297355022),(-57192586214784168369413078888)⟩,⟨(-1772913719737142847137313394),(-1772913719737142819371378774)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-42506733900584448188655000589),(-42506733900584448168451109538)⟩,⟨(-1321977828412804124245433155),(-1321977828412804106863205924)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-26260104173107875299154603367),(-26260104173107875287836395399)⟩,⟨(-686142245581017430083830880),(-686142245581017420755312078)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-8893898462152149584982367213),(-8893898462152149581354452531)⟩,⟨(-192735349228878783614140309),(-192735349228878780707487591)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨45443029694695222762818372939,45443029694695397949360265845⟩,⟨(-24405731978217711258648235730),(-24405731978217536070352908707)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨126701620617819589124872780010,126701620617820252502796658731⟩,⟨(-76981856606388977570658806396),(-76981856606388314188096045670)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨180664442045462775798365200538,180664442045464450576632361051⟩,⟨(-137797015348297148156527240188),(-137797015348295473372367150512)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨195325893116260844230636282934,195325893116264764575432798534⟩,⟨(-204000131687989985064913869104),(-204000131687986064715054702090)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨168342296722199867029105996972,168342296722208290140412287644⟩,⟨(-265053011122669277097098812746),(-265053011122660853983360194034)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨108917100101487230210352086303,108917100101502844625830126222⟩,⟨(-306945793210866969657645611573),(-306945793210851355243333821647)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨34623773639266277599523244825,34623773639289451327395487941⟩,⟨(-319147096057943257416110208664),(-319147096057920083692918096567)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-35667854938515869632955943568),(-35667854938490080043306331381)⟩,⟨(-300436867160647479661740477872),(-300436867160621690079530785279)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-88350801708232899412764238924),(-88350801708211263045201386319)⟩,⟨(-259205424588749031308675947775),(-259205424588727394950332928562)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-117972898602253597806154609337),(-117972898602239735386506313932)⟩,⟨(-208267094428759983280614476483),(-208267094428746120870647606644)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-125957062227539281697717546823),(-125957062227532425204093230334)⟩,⟨(-158701544161564941293216487545),(-158701544161558084808595537921)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-117229128762654877167818722796),(-117229128762651947490650830674)⟩,⟨(-116430687491814168365563630933),(-116430687491811238695735023714)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-97486830456766612894962894463),(-97486830456765368646775603669)⟩,⟨(-82345019875765162036575780123),(-82345019875763917793470477107)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-71749553165038363976475408311),(-71749553165037864977878531029)⟩,⟨(-54683559781389778743144655553),(-54683559781389279747838976357)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-43505836213515914299187399932),(-43505836213515724634341920947)⟩,⟨(-31245340673472728342172178076),(-31245340673472538679174246569)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-14534406985146190377248107738),(-14534406985146141417763990602)⟩,⟨(-10159480861306312070011930050),(-10159480861306263111126379795)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-53739565379507172177736506970),(-53739565379507172117886515424)⟩,⟨69513592380419937571036361517,69513592380419937632649027982⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-149552525898100242599741359576),(-149552525898100242421041910490)⟩,⟨214095975587776573128197322323,214095975587776573312580150519⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-210202117709875905524246607332),(-210202117709875905223140800249)⟩,⟨369381675032685124505565397182,369381675032685124815904775895⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-213440092149289431126879118150),(-213440092149289430675467032391)⟩,⟨526013525698315538273475703146,526013525698315538735318288973⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-143149453561734153880868682971),(-143149453561734153267768558068)⟩,⟨658968293465934033712010020379,658968293465934034334370045087⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨631348563660821348226643318,631348563660822123860929582⟩,⟨736228954147190040612182746742,736228954147190041394772943504⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨192833673817835968121799835511,192833673817835969075269692615⟩,⟨732509702437300571775318401962,732509702437300572732360169085⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨387117568748342171965423045312,387117568748342173346745457130⟩,⟨641854824963287162892615079503,641854824963287164273537647932⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨533913489072472517236029466757,533913489072472521120643891252⟩,⟨484033444654273684069282355756,484033444654273687950796111774⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨600987441804807442683921007807,600987441804807461529251374525⟩,⟨299073402913475395359151403292,299073402913475414201058472485⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨583747003417526148552333681919,583747003417526230533069411962⟩,⟨130587518910281349168308893188,130587518910281431146645981005⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨501432251438189158125692514402,501432251438189427105207839586⟩,⟨8263070288114064501158165629,8263070288114333479134068315⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨384655565858674448962077568295,384655565858675150961811700370⟩,⟨(-59021505482940960602596292929),(-59021505482940258603670854763)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨261623702809649905032922533533,261623702809651087914862174554⟩,⟨(-77748786258051326788116358262),(-77748786258050143906494940247)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨148550682522559371302439777060,148550682522560581487951244615⟩,⟨(-60849150924017048329636383838),(-60849150924015838144202754296)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨47780115300345818678213829643,47780115300346337090544343161⟩,⟨(-22630047434941748308022496491),(-22630047434941229895680499352)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-7127334635464112803973571362),(-7127334635463774891927016407)⟩,⟨(-63081583603374737636360601922),(-63081583603374399722911134871)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-28539172434557351035110798887),(-28539172434556563719859047144)⟩,⟨(-185871972320627490819564243672),(-185871972320626703499650804514)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-70579040009286768449408516439),(-70579040009285996393818222212)⟩,⟨(-297095609794030798984134244908),(-297095609794030026919405087380)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-143801328727455630898990213384),(-143801328727455167016173280883)⟩,⟨(-385802899859883590762672471776),(-385802899859883126864529299680)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-252350806463865670493673041907),(-252350806463865490467835944905)⟩,⟨(-438898701175072824855638485108),(-438898701175072644806720974008)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-389270568555607950060677542212),(-389270568555607903101575120865)⟩,⟨(-443949461361565843708841040191),(-443949461361565796719743569588)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-534229824569732478284625815662),(-534229824569732467297891194853)⟩,⟨(-392666264176612703956892110940),(-392666264176612692942533455497)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-657948109639183592780166925911),(-657948109639183590234117526645)⟩,⟨(-285453724483871296212957906812),(-285453724483871293646246855984)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-731952349449929338210125286067),(-731952349449929337144465369067)⟩,⟨(-136064261025069626232052300507),(-136064261025069625155137414530)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-738939584364909836992004157022),(-738939584364909836180847375581)⟩,⟨28399792549234186494666239885,28399792549234187307142922715⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-679205795851874429497806099667),(-679205795851874428787166686996)⟩,⟨174342296130911776281548924453,174342296130911776985105947181⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-569489799529408102294021843246),(-569489799529408101660362800941)⟩,⟨272154312865769405905025126363,272154312865769406526324605248⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-434602140130637374845006259127),(-434602140130637374313580157468)⟩,⟨305059848003872992568332226575,305059848003872993085626653855⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-297071739275327191016901578402),(-297071739275327190616713005134)⟩,⟨272285792982621934311481393741,272285792982621934699091575678⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-169975645437370802470466549615),(-169975645437370802222493340776)⟩,⟨186033655191599997917186849403,186033655191599998156620760781⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-54949324803080892833736120631),(-54949324803080892750001084685)⟩,⟨65829335016355538183574390264,65829335016355538264313182821⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨21719852325486664284977523509,21719852325487288311445347766⟩,⟨10248209945732430304648126765,10248209945733054330378357235⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨67504151272845818332230900109,67504151272848201699889020680⟩,⟨28281600660184698868183929573,28281600660187082233307805275⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨118971323031460060205568945906,118971323031466195298194092680⟩,⟨38583156647820538909581465028,38583156647826673997002711745⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨176012531099358085775066071488,176012531099372928980034582125⟩,⟨34994685320680112563498692351,34994685320694955759187654411⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨234149792323060807983778073359,234149792323094245465522187035⟩,⟨10478372677297266559161147033,10478372677330704025860927803⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨285423401898652317443141191135,285423401898717945212079684721⟩,⟨(-40857345512335040670783774621),(-40857345512269412924421275275)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨320136335772048320680406971616,320136335772155280144940782610⟩,⟨(-119718560685833660204424820974),(-119718560685726700770578355681)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨329074184954747664066615269593,329074184954910040706453469658⟩,⟨(-218361607416862493946674548000),(-218361607416700117337185312912)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨306972173681290171160476320997,306972173681481846994593458930⟩,⟨(-320591183723668459672427174485),(-320591183723476783863199358656)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨256078374573628481979810393655,256078374573797968843029607726⟩,⟨(-405181409185004762834519450235),(-405181409184835275988308016381)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨186762909972957877279138508496,186762909973070294074620529449⟩,⟨(-451824264497770262494948019746),(-451824264497657845708321007149)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨113843543870935681598554605406,113843543870995493427617974131⟩,⟨(-448088628795173307249549550050),(-448088628795113495422588319412)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨51435894359989573833857840295,51435894360017176257898045935⟩,⟨(-394401753092226022740746263676),(-394401753092198420314155819235)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨9691762016585643024039595512,9691762016597393360511066560⟩,⟨(-302615171321002764718109598298),(-302615171320991014377165761703)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-7594734223801827271844881652),(-7594734223797178565840878571)⟩,⟨(-188279048785569916015621577557),(-188279048785565267305760365271)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-5065934253371974557793955557),(-5065934253370748859346410824)⟩,⟨(-63655851412668363010826486346),(-63655851412667137310901237858)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-307612546045377502690442298),(-307612546045377499585946568)⟩,⟨(-92071845522510419040650668),(-92071845522510416437170223)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-948018932193462951284340863),(-948018932193462941670542888)⟩,⟨(-11962508495880646518884209),(-11962508495880638511835176)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1323376635147570235712305275),(-1323376635147570218956465829)⟩,⟨1027041095409273379836433157,1027041095409273393692458579⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-402264432504126899853556297),(-402264432504126874997457921)⟩,⟨4265898765245086714521297689,4265898765245086734925563406⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨3216506775075152711250713070,3216506775075152746086613530⟩,⟨11630621929488405055652219928,11630621929488405084282814583⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨10392979160757768173402891039,10392979160757768222405296421⟩,⟨24830510408217490418219585826,24830510408217490459109592640⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨21206522313308630304100034384,21206522313308630390032394088⟩,⟨43672478981936047912095358843,43672478981936047989475161302⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨35430519593329776902118468407,35430519593329777137348919267⟩,⟨65381951212392012859934771214,65381951212392013087571067459⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨52375415110300711588377831217,52375415110300712915520257581⟩,⟨85429034603422191176580994264,85429034603422192498073000748⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨70184517449188237774380010498,70184517449188247437862309240⟩,⟨98888158039902875302129012239,98888158039902884962206946624⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨85705739447849332863597561764,85705739447849389070153445168⟩,⟨101964761260837634809032312342,101964761260837691014190426575⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨95174370622343265205302855345,95174370622343490882391819850⟩,⟨93601663876580431363982061247,93601663876580657041086007555⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨94947926234472176836464191567,94947926234472770754653093870⟩,⟨76240388379989662140743477541,76240388379990256059802961466⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨82173324677868345014336154183,82173324677869355208007630777⟩,⟨54412772338700269950839656246,54412772338701280145631041271⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨56202236571932049123968644194,56202236571933096384039988403⟩,⟨31967212553953180194731995720,31967212553954227455676077740⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨20011810880829147751515305952,20011810880829600647354251963⟩,⟨10467804810406638212394111186,10467804810407091108550977296⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-119524184851393248215590343373),(-119524184851208588314668354376)⟩,⟨(-271926420661005848601544752518),(-271926420660821188730347214343)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 7) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_7 (tableDensity true) (fullFactor true 1 7) density1_contains hk1_1_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-277090528854020863004050267740),(-277090528854020861972425879309)⟩,⟨(-231914355028629144880250688980),(-231914355028629143852240025571)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_7 1 7 ha1_1_7_contains + def realAnswer : RBox := ⟨(-396614713705414111219740611113),(-396614713705229450286994233685)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_7 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_5.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_5.lean new file mode 100644 index 0000000000000000000000000000000000000000..61d20b465b5be28aa579ea8026a6b80206800b14 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_5.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_1_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨68003567383545438949733446814,68003567383545486655912245798⟩,⟨88430311058176776428579561401,88430311058176824138308893839⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨204453433366061226803092874563,204453433366061335471933005899⟩,⟨249365298236187612299358608859,249365298236187720978561995231⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨339207730069293205818241424588,339207730069293308090262049028⟩,⟨367021853224374084608059560175,367021853224374186896189770197⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨463911600707445910294620097989,463911600707445968722197115227⟩,⟨427025106991221809579342685975,427025106991221868026504790543⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨565321854484729939419671589288,565321854484729961179012787609⟩,⟨431035810348005834974698285349,431035810348005856755240663201⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨631389257468334905036624468234,631389257468334910645166470007⟩,⟨393146952793913076881642670139,393146952793913082513894608060⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨657808087614268115373401586507,657808087614268116666989170743⟩,⟨332262302688425924034945511342,332262302688425925353002117513⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨649386988107073083611809660989,649386988107073084094476763172⟩,⟨265386535326950072585700877015,265386535326950073088813213184⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨615734719429004994457832800597,615734719429004994757737504701⟩,⟨203816379000382203809390335767,203816379000382204120354845829⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨565979591191137081683339299050,565979591191137081929756000999⟩,⟨152513353674084191088105976144,152513353674084191341200486419⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨505798058717012329381779517723,505798058717012329595224321524⟩,⟨111966131622829335842364886222,111966131622829336065095188509⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨436901083744486119153830337586,436901083744486119316543501177⟩,⟨80669602519279441327252930478,80669602519279441497714031752⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨358170720050759007142485058319,358170720050759007254654515263⟩,⟨56601704403643752914565803479,56601704403643753029983231963⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨267938829503431653349421216347,267938829503431653419855464725⟩,⟨37592133143588689620245396692,37592133143588689690153510620⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨166369272793523663486164106883,166369272793523663524287743422⟩,⟨21592033545119346687688222755,21592033545119346724059677368⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨56456288829469620366885170582,56456288829469620378865771381⟩,⟨7053515100853016076904168165,7053515100853016088046863475⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-289958756402096600393091393011),(-289958756402096407085947153279)⟩,⟨53378602922300623711806638705,53378602922300817008035478730⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-839466938089776610750989887625),(-839466938089775899700047223638)⟩,⟨195424647739018725111322108409,195424647739019436127014963539⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1293000753696716034501364702672),(-1293000753696714340122346378271)⟩,⟨428031852553074209274281958744,428031852553075903587939120111⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1581546425883956565929137157959),(-1581546425883952931908791553502)⟩,⟨764683284937969588095602873436,764683284937973222015511882216⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-1649257099388256298060692931184),(-1649257099388249317588780124934)⟩,⟨1163498756172529266874773997218,1163498756172536247212725917298⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1482324832877901716985083939654),(-1482324832877887625464952658851)⟩,⟨1537948170690107744834240157670,1537948170690121836227903593658⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1128360485959487594039280675253),(-1128360485959463329016626375013)⟩,⟨1792753569872133547133466107023,1792753569872157812064381517748⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-685366599818529680988145926743),(-685366599818498863054011816774)⟩,⟨1867775687542989632778790058842,1867775687543020450659739972500⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-262356728117672231626625883428),(-262356728117643161824168946280)⟩,⟨1762836758533570154115417024442,1762836758533599223897816034009⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨62227014089918252999806435596,62227014089938850880957958677⟩,⟨1528448821795826103327186358129,1528448821795846701211190811523⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨258954392869532926084207521932,258954392869544015512777600589⟩,⟨1233742058175668320663326774119,1233742058175679410107588040313⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨338707506461868436939358450604,338707506461873344710205611758⟩,⟨936428723974220812952040810024,936428723974225720743341532783⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨331259836559260660487766037756,331259836559262608383396124294⟩,⟨669475991861167129142893865892,669475991861169077058115802892⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨267410902662054721979689766010,267410902662055462768403036982⟩,⟨442652590271989018172399650745,442652590271989758976526912405⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨171067738105546978005495418833,171067738105547250086399857392⟩,⟨250643183800057388951526583789,250643183800057661042060263716⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨58600723371686784456440700995,58600723371686853523672180989⟩,⟨80988537930144608588634355295,80988537930144677659118049799⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨261856802488128888981135311069,261856802488128889129305837343⟩,⟨(-110855095897871336134892516951),(-110855095897871336003080754366)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨760084806827079364344804391266,760084806827079364791418127695⟩,⟨(-374217551112328644643596814259),(-374217551112328644240478823926)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1172554431128486746809350806255,1172554431128486747569102685544⟩,⟨(-750294234998131825249502056575),(-750294234998131824543130302609)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1420863964489578187181997156219,1420863964489578188270855845897⟩,⟨(-1272283348518620563134532002707),(-1272283348518620562082127743688)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1416791029455979952374550514377,1416791029455979953785553137606⟩,⟨(-1908514146696721866324977768150),(-1908514146696721864901583574280)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1095059024595375269397469985632,1095059024595375271092873002810⟩,⟨(-2550239370610648659960794032900),(-2550239370610648658177177183726)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨460872459725036150937035299974,460872459725036152872507360560⟩,⟨(-3034702549639791936840771290394),(-3034702549639791934727893803361)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-377594779337584485613955549411),(-377594779337584483172734974641)⟩,⟨(-3207445532343868908984002622617),(-3207445532343868906284777745932)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1227584095016699497472472521683),(-1227584095016699492585688440322)⟩,⟨(-2997592580237057155633889891964),(-2997592580237057150497252883749)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1884459780237128177534811478055),(-1884459780237128155951997688566)⟩,⟨(-2459839064635398133322581966004),(-2459839064635398111581219575064)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2215485287759863112087769690261),(-2215485287759863005445147766141)⟩,⟨(-1751126270281395820101300210939),(-1751126270281395713382110329404)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2199614376046433906688922891682),(-2199614376046433520898948406309)⟩,⟨(-1056378134778358281184110739508),(-1056378134778357895376773764903)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1905363076790569633062543765715),(-1905363076790568710535473882531)⟩,⟨(-512880578459213709306096981256),(-512880578459212786795327929772)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1435832385254969710743950481478),(-1435832385254968269443321060186)⟩,⟨(-174768457209085347879656624432),(-174768457209083906606465299976)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-880879056449933826527266156549),(-880879056449932425904130853902)⟩,⟨(-22576903854742425362604188764),(-22576903854741024762007122191)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-295571557304133102626867786138),(-295571557304132518262963096165)⟩,⟨6594384141990554598834552429,6594384141991138954282997144⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-55367187886735051160623809948),(-55367187886734844001851109085)⟩,⟨101385252796348327661171737697,101385252796348534836406917161⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-152914966074023314751585015439),(-152914966074022838020480611176)⟩,⟨313193222413844208126047859074,313193222413844684908981289935⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-209238964259189770279672177209),(-209238964259189314952868855765)⟩,⟨547553052085404852940255042588,547553052085405308360773522996⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-193588013102134218747879190320),(-193588013102133923367868828936)⟩,⟨805355967138685378066697728132,805355967138685673572301608446⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-75865180768677403157288324759),(-75865180768677263530334497182)⟩,⟨1067440569675158344100276022349,1067440569675158483860330943550⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨162967219268758399302919351542,162967219268758444001875292278⟩,⟨1292558454618842667611755018170,1292558454618842712428823828597⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨515099397902283689785776469239,515099397902283700428308240398⟩,⟨1424754079943657740111149016642,1424754079943657750832440712001⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨933736787769820869641491200771,933736787769820872426302284400⟩,⟨1411571299890786095590970598033,1411571299890786098393613669148⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1336884349327160458662801694110,1336884349327160460261809512448⟩,⟨1229323518726473507353893760117,1229323518726473508896234297694⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1631261342079241281585785533939,1631261342079241283070495407141⟩,⟨903120166998335780159069085759,903120166998335781516201765042⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1746962638966139964953397889612,1746962638966139966392534014788⟩,⟨506187273789976052946354437526,506187273789976054205988627707⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1663673032366148040391099905242,1663673032366148041719072718063⟩,⟨134582992855779618897097849693,134582992855779620029555607704⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1412257355679120861274556436284,1412257355679120862443921334760⟩,⟨(-129109121864530428810066826458),(-129109121864530427785285742435)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1052069763279628235408302467470,1052069763279628236319341421913⟩,⟨(-243050040691933276144864847520),(-243050040691933275324217152836)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨640676370774439529418647797095,640676370774439529993066840446⟩,⟨(-213153941347739095702774183971),(-213153941347739095176102543585)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨214120247962980738432344498324,214120247962980738627625881866⟩,⟨(-82895017185634247249596444473),(-82895017185634247068982908246)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨11948583033919131469781022256,11948583033919503205555277500⟩,⟨(-35971365506973046391940621524),(-35971365506972674659592140021)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨29736845994052122950279121410,29736845994053536849597938993⟩,⟨(-109525731794919051634991576100),(-109525731794917637746648225240)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨29067823524478307345351942493,29067823524481913892028692854⟩,⟨(-186431511571162306319052342352),(-186431511571158699793044675597)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1882792000347842421806050947),(-1882792000339254140214281190)⟩,⟨(-264426885362059665772772935948),(-264426885362051077524795549286)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-72012855136792440752648413197),(-72012855136773589012345092526)⟩,⟨(-334872597000567275008437031743),(-334872597000548423318632406287)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-183362173095969545785859188369),(-183362173095928893949148414773)⟩,⟨(-381984587988158319959703644142),(-381984587988117668185554696349)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-327159214965641928030145071462),(-327159214965559874777146085422)⟩,⟨(-385804885674101007267615532615),(-385804885674018954073523233473)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-481837623139835264146848302369),(-481837623139710002621286069321)⟩,⟨(-329859354304368229283647145361),(-329859354304242967805779026984)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-615807194901614245914102165795),(-615807194901470177114943167409)⟩,⟨(-210831449118752955116809893964),(-210831449118608886347304174786)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-696674165375407848474463769082),(-696674165375283620054666565230)⟩,⟨(-45161962763127753990849933803),(-45161962763003525577971509121)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-703971575109417142168714033608),(-703971575109336856552555853747)⟩,⟨132055156372273996317327260543,132055156372354281949918137143⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-637955096959424171187757996486),(-637955096959382607698220001460)⟩,⟨276891776889376130987247008612,276891776889417694511954382948⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-517826427744616191381462460995),(-517826427744597541712265356658)⟩,⟨351465354185399716369074381165,351465354185418366083037375761⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-370581937216716477242323297513),(-370581937216708746989646470630)⟩,⟨337328045810213379386805721172,337328045810221109682653104639⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-218494386159459530269979856745),(-218494386159456537250825731137)⟩,⟨240513718710751319893722329265,240513718710754312943809389193⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-71671907745081161086244910090),(-71671907745080381544125404079)⟩,⟨86823033666519723847426402633,86823033666520503400754890187⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1377732295610739197368839342),(-1377732295610739195211680140)⟩,⟨4684864901494237353896359607,4684864901494237356390469327⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3066892663911265811300686289),(-3066892663911265804630211318)⟩,⟨14393196735217934402183729940,14393196735217934409927728995⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1606221275029483598037255222),(-1606221275029483586309638575)⟩,⟨24943259089821561088479390425,24943259089821561102108550493⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨4788339372652197839131422978,4788339372652197856757305794⟩,⟨36294629039048319307855207322,36294629039048319328298364202⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨17164265363757547015778775827,17164265363757547040365209405⟩,⟨47306199083430055434160521445,47306199083430055462445076289⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨35501321132979349844562545733,35501321132979349881285358506⟩,⟨55345452182561611743443390780,55345452182561611784113101006⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨58552892099698966173476805036,58552892099698966236359254272⟩,⟨56827037891263577207411515408,56827037891263577273698836544⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨83530911685112204475728100741,83530911685112204631944029887⟩,⟨48735901818098696881593121372,48735901818098697040234509833⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨106080061217695212925235435288,106080061217695213755577479114⟩,⟨30212941638944729282642492898,30212941638944730114228043441⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨121313345976366992687730843838,121313345976366998676824516746⟩,⟨3558800995718999897886852496,3558800995719005887304495507⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨125601816440068709315568355766,125601816440068744038173082127⟩,⟨(-25713785953105296331866357177),(-25713785953105261609352268947)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨117926805577310439900849657779,117926805577310578557080349858⟩,⟨(-50136560582450189527975117106),(-50136560582450050871773405837)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨99877463157579474713322614428,99877463157579837022615611736⟩,⟨(-62802670595183566211439771705),(-62802670595183203901893106082)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨74615427620529334635988759758,74615427620529946349134432384⟩,⟨(-60089768254179499632015440351),(-60089768254178887918376913211)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨45575986800585280403925139259,45575986800585910688362039387⟩,⟨(-42823710358386037933228051919),(-42823710358385407648309365784)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨15253819414920744667592987810,15253819414921016289578895057⟩,⟨(-15461183276516006675994878524),(-15461183276515735053810174070)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-51816598705134353444936067849),(-51816598704990836351187850686)⟩,⟨671894986011356215170388485255,671894986011499732280098328077⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 8) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_8 (tableDensity false) (fullFactor true 1 8) density0_contains hk1_1_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨61352840181628718751463626520,61352840181628719621599769910⟩,⟨(-249668728122603495176144619193),(-249668728122603494308342549976)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_8 1 8 ha1_1_8_contains + def realAnswer : RBox := ⟨9536241476494365306427558671,9536241476637883270511919224⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_8 +namespace hm1_1_1_8 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_8 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨9532328842196488867192373451,9532328842196527922705158345⟩,⟨16525119074979826023052909054,16525119074979865077714701391⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨28788789516203381019714387297,28788789516203469936379335865⟩,⟨47323872116676780689202065830,47323872116676869603339657488⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨47864735059525179809921868676,47864735059525263391956886092⟩,⟨71447608958464844720358936506,71447608958464928298275486851⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨65172033825139797557284912544,65172033825139845187695770567⟩,⟨85112685952947356067729290987,85112685952947403692595213775⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨79109003947530010234872678215,79109003947530027840938741292⟩,⟨86348514505609397492724407732,86348514505609415092111865755⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨89329513128246324198702125358,89329513128246328574417572518⟩,⟨76596647559204568126679995785,76596647559204572495174786506⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨96240434855112107267870731278,96240434855112108106275631663⟩,⟨60592518810090241311533812849,60592518810090242142768371963⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨99996037030114721655915383080,99996037030114721852545020008⟩,⟨43747061539585964067635390702,43747061539585964257306719111⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨100448102709943242527288557679,100448102709943242623152284898⟩,⟨29683765203391894621386111006,29683765203391894710169414303⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨97357397217734871519953812780,97357397217734871594042347478⟩,⟨19672650719473017230083087876,19672650719473017297603739224⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨90460641708076293690729586289,90460641708076293753237131350⟩,⟨13214249234171029118356559258,13214249234171029176007556864⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨79715212779579929313449806423,79715212779579929362249010189⟩,⟨8937414956033230826318386017,8937414956033230871127264014⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨65593793697254601766243270859,65593793697254601801492199220⟩,⟨5626309558964064979387454326,5626309558964065010919652351⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨48882081545941188298216798133,48882081545941188321458746690⟩,⟨2938186811124270228695542395,2938186811124270248648258726⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨30236575139192434040734040146,30236575139192434053825725841⟩,⟨1131327485925506417969959427,1131327485925506428760384539⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨10244459505635464806871100643,10244459505635464811080438845⟩,⟨245270235906165180546159898,245270235906165183923662421⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-43741087202991078064883131672),(-43741087202990918978825498206)⟩,⟨(-14184450936777684962123833422),(-14184450936777525874726323942)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-128375156304457185933442930478),(-128375156304456600477776998258)⟩,⟨(-33419655959700315232824246634),(-33419655959699729772856292102)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-202850714079286598014445290772),(-202850714079285201773268270206)⟩,⟨(-28089342938287600080001018191),(-28089342938286203830887027968)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-257080955283359513644734741051),(-257080955283356516198196440794)⟩,⟨8955949752912537626761401381,8955949752915535085549390964⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-280470731513151059202860798673),(-280470731513145296132282130110)⟩,⟨72994381324401536893004525928,72994381324407299980119664998⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-267078557415223839782429861960),(-267078557415212195499963974480)⟩,⟨147966123927034329175266324555,147966123927045973473506967727⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-219984172989736106703935761891),(-219984172989716037734101469955)⟩,⟨212895329783551029052296292408,212895329783571098033876649050⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-151651254345987998915967883459),(-151651254345962497949922226557)⟩,⟨251538665059949257098131234750,251538665059974758071377119829⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-79338959217580755009612738727),(-79338959217556701374108739422)⟩,⟨258749903613745260753210652201,258749903613769314391787626137⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-18166886306261070895903282657),(-18166886306244036626119720825)⟩,⟨239933236948760903693474337743,239933236948777937963117528103⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨23511722966960977774917811988,23511722966970139446387029696⟩,⟨205534213476702521546971160048,205534213476711683216261053593⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨44490584570871023012908456948,44490584570875072258174895673⟩,⟨165109529191089402719797484030,165109529191093451962071088911⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨48422381581187693218319952573,48422381581189297994627695630⟩,⟨124455600686922350837422479453,124455600686923955610805909258⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨40810919228663585908882568427,40810919228664195334489973964⟩,⟨86013503601817428060630303671,86013503601818037483894188729⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨26584005697184940662213863278,26584005697185164232655667617⟩,⟨50247096300841356078877581856,50247096300841579647828631569⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨9167574201424767886785848122,9167574201424824601223963924⟩,⟨16496836599155232105907541939,16496836599155288819833793823⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨63466071688781309145209398881,63466071688781309198868776151⟩,⟨9666636019630319145679690186,9666636019630319198584134545⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨190585337773123920255373925000,190585337773123920420068119377⟩,⟨18849204986764749423016714756,18849204986764749585631802318⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨313921188449576340326508700314,313921188449576340609606515551⟩,⟨(-656640656803451778312096409),(-656640656803451497735516514)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨419201993429505836823134805365,419201993429505837228943946415⟩,⟨(-61719302097887158410153952155),(-61719302097887158006063684705)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨482020767987698557675518427980,482020767987698558195598473705⟩,⟨(-167018435343595663522802750917),(-167018435343595663002382914927)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨477205262489996261687030914443,477205262489996262301495385575⟩,⟨(-304093623730983224652675529969),(-304093623730983224035101493455)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨393051735151589918274783899123,393051735151589918972707982519⟩,⟨(-443509704256957770219936717262),(-443509704256957769515299370081)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨241581327647215880599024519740,241581327647215881536066008749⟩,⟨(-546685319400759842590199235864),(-546685319400759841643592053096)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨58215918434950586912363815473,58215918434950589632494848900⟩,⟨(-583081432880096684421570446566),(-583081432880096681693712067702)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-110744499237170733702387303460),(-110744499237170717553533171070)⟩,⟨(-545324067064013481540268313896),(-545324067064013465387653334952)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-227084216155470545222163666812),(-227084216155470459798995387576)⟩,⟨(-451009295597985093360777719477),(-451009295597985007936158173677)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-274800383238245615506664190651),(-274800383238245302355284496275)⟩,⟨(-331167327408600767515586558885),(-331167327408600454363615651443)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-261218374281910076730015905453),(-261218374281909325208991370554)⟩,⟨(-215462466493126262336389038248),(-215462466493125510815185947948)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-206270028874345969282299140014),(-206270028874344793383032602058)⟩,⟨(-122875847394988579517421243646),(-122875847394987403618097567088)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-129553480795144051705269178839),(-129553480795142908111201664317)⟩,⟨(-58831514747168773283363863856),(-58831514747167629689246704115)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-43907872470722680301359742714),(-43907872470722203009334415027)⟩,⟨(-16879144160037127593081726796),(-16879144160036650301017889051)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-35095528863664448208628067951),(-35095528863664274155560698952)⟩,⟨16105887386863659787604161663,16105887386863833838963156155⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-102144750801787630777375086011),(-102144750801787230504806252377)⟩,⟨52304353329680466327726838956,52304353329680866594918172396⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-158859938940512124197133568046),(-158859938940511742434346367310)⟩,⟨99683031698359800316327750830,99683031698360182069444212303⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-196353672152005835513134562339),(-196353672152005588434942309829)⟩,⟨163088250141458390360412391187,163088250141458637425752193114⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-204830250617602505068833374754),(-204830250617602388718111442918)⟩,⟨242798526910021378558638235104,242798526910021494896013186107⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-176364757461467754414715369787),(-176364757461467717498385063947)⟩,⟨331855547517761979267001800443,331855547517762016171876784947⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-108285496918415575693120346669),(-108285496918415567235887160997)⟩,⟨414955800187717440698301778064,414955800187717449148449430716⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-6247748435817239565052533836),(-6247748435817237729078915963)⟩,⟨471963680634692863110033962300,471963680634692864945380879728⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨114030041325788259204894653364,114030041325788259950328964659⟩,⟨485595879874037566981469311756,485595879874037567733580027782⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨228991927745678661838748924837,228991927745678662414952235297⟩,⟨449345910822962552627426340234,449345910822962553216881266173⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨314090404617195867782200698959,314090404617195868297531429354⟩,⟨371402752870056370699894977567,371402752870056371232891346868⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨351838785624125288960279497637,351838785624125289417084550558⟩,⟨271846783852822037694845702098,271846783852822038170325293543⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨336656324210970032137579368534,336656324210970032546316462092⟩,⟨174137791718671842483453405210,174137791718671842905705388628⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨274422849180278074571515935120,274422849180278074896437197406⟩,⟨95865208378839080966569108472,95865208378839081299737118770⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨177868600952639606527882774420,177868600952639606735607407793⟩,⟨43441241968620322979157548370,43441241968620323191144786676⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨61402986446073887361515456961,61402986446073887432652135542⟩,⟨11852859062714522649214150070,11852859062714522721639216634⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨3315972263963511917257637562,3315972263963817423018700336⟩,⟨(-12004322668422803168129921086),(-12004322668422497661701888565)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨8412221793342880905013733785,8412221793344042983608282864⟩,⟨(-37118693450215693316914886670),(-37118693450214531236125736779)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨8786210060810809785594764698,8786210060813774392775233296⟩,⟨(-64808078721560210958306627281),(-64808078721557246346902493823)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨958272277936260049863497045,958272277943320817079216271⟩,⟨(-94597346252821471652487730430),(-94597346252814410878217810551)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-18753595908619135909700704231),(-18753595908603635242464369328)⟩,⟨(-123430496678456357449351516442),(-123430496678440856771310495663)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-53154843186006778691496093322),(-53154843185973353206868209071)⟩,⟨(-146126054394441467224749033869),(-146126054394408041726400870820)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-101994991386956724559134349972),(-101994991386889271960117502179)⟩,⟨(-156627141990909818543721646139),(-156627141990842365931085010393)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-160131072620155463124809849852),(-160131072620052541527337581652)⟩,⟨(-149750897944671986179150206332),(-149750897944569064570207479605)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-217626570996085332216631290008),(-217626570995967051974615180186)⟩,⟨(-123586215212463526297870773981),(-123586215212345246048526341530)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-262045578261177525502855078466),(-262045578261075642840171257648)⟩,⟨(-81691906827223228506034597371),(-81691906827121345841096681863)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-282202090778362248477074561624),(-282202090778296487583737114010)⟩,⟨(-33142611041351805538659887352),(-33142611041286044647831831910)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-272133595418761623391950051125),(-272133595418727624945951496586)⟩,⟨10554504549350956075655003476,10554504549384954515592042982⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-233658857846813771406128085475),(-233658857846798535585936109590)⟩,⟨39800596318620076367118743802,39800596318635312179446657139⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-175251482153872262367384607490),(-175251482153865953856695801991)⟩,⟨49452706527369691582277156329,49452706527376000085462624721⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-107007155084265125888497638269),(-107007155084262685178952859395)⟩,⟨39471586477223930744891560985,39471586477226371449128004320⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-35783795853875142072142439260),(-35783795853874506626564064462)⟩,⟨14942822017518697540503921514,14942822017519332984191818935⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-34284161355529739866717121),(-34284161355529738733894322)⟩,⟨141112957919299167152493450,141112957919299168537362105⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨18069497719657094338690793,18069497719657097820229151⟩,⟨429394019522293984020905473,429394019522293988310597512⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨502548888443684335947255341,502548888443684341962353282⟩,⟨573959786111583581747708882,573959786111583589221242244⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1965051015737499133291326772,1965051015737499142122056948⟩,⟨56131658314592436077104378,56131658314592447148126706⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5262290766240592389636629668,5262290766240592401995444581⟩,⟨(-1877900657467277155450549314),(-1877900657467277139963586640)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨11182635090752849313927564385,11182635090752849333921734840⟩,⟨(-5798325602425573128703528545),(-5798325602425573105057973915)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨19669391040800171134700936410,19669391040800171174256799901⟩,⟨(-11903029445424553072722084374),(-11903029445424553029602819738)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨29442212641536138747202602325,29442212641536138863146502218⟩,⟨(-20134777672651393045987738992),(-20134777672651392927046976711)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨38334453061452262887848884250,38334453061452263558973218552⟩,⟨(-30041459695383728483282791356),(-30041459695383727810167644992)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨43962370012992323248002980667,43962370012992328141511756939⟩,⟨(-40419227160885339934993592794),(-40419227160885335040598845087)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨44527508457390583964105899253,44527508457390612324224615962⟩,⟨(-49297630110110318324438153515),(-49297630110110289964374577662)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨39663664278567977772910783662,39663664278568091008119893999⟩,⟨(-54425668688434268059761982795),(-54425668688434154825237577260)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨30859452945161354680497350371,30859452945161650673296422892⟩,⟨(-53826203110950592566583645643),(-53826203110950296574789974256)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨20731382450969419556146237964,20731382450969919537680203740⟩,⟨(-46173947478688050472346053230),(-46173947478687550491792166691)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨11432953380934399526904174732,11432953380934914879911082961⟩,⟨(-31369385958779341926920764961),(-31369385958778826574602566409)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨3588096159509258429916412223,3588096159509480566101160809⟩,⟨(-11130730351814291379425353592),(-11130730351814069243480920922)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨40474536739090715765270514556,40474536739208640384182391360⟩,⟨164487685413289198482691416150,164487685413407123118496489584⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_8 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 8) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_8 (tableDensity true) (fullFactor true 1 8) density1_contains hk1_1_8_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-80230637160591402582092006806),(-80230637160591401444221665449)⟩,⟨326489875237250723326294103815,326489875237250724461112194329⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_8 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 8) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_8 1 8 ha1_1_8_contains + def realAnswer : RBox := ⟨(-39756100421500686816921492250),(-39756100421382761059939274089)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 8) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_8 +namespace hm1_0_1_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-21614408115520065344518841719),(-21614408115520013887390093852)⟩,⟨(-103445632609825846738887848739),(-103445632609825795281392095457)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-74304407802635845644419930296),(-74304407802635727115538041619)⟩,⟨(-297150278881233134446245990104),(-297150278881233015915813653226)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-150017367626386170832684813266),(-150017367626386056990877793585)⟩,⟨(-452959830675875254316162383349),(-452959830675875140470715044808)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-249097533162091697760780997353),(-249097533162091631009283677684)⟩,⟨(-552832552685891675022776583134),(-552832552685891608265248860460)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-357732391992589412812168739769),(-357732391992589387290444103943)⟩,⟨(-589629448099679192105438796104),(-589629448099679166576484955524)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-455256937284531052012641520550),(-455256937284531045331515113705)⟩,⟨(-568771531310795995569777674462),(-568771531310795988879073403528)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-524892863931179913335264534148),(-524892863931179911803513831276)⟩,⟨(-505764046564106811668674541535),(-505764046564106810122709501137)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-559937551946471638683246968507),(-559937551946471638119887889795)⟩,⟨(-420494676615632833116153644288),(-420494676615632832537927722889)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-562649400612637636019331675505),(-562649400612637635668341892788)⟩,⟨(-330658003413561309606145779315),(-330658003413561309245983555767)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-539436141255083378980140022473),(-539436141255083378720247729496)⟩,⟨(-247802078231360436157225485873),(-247802078231360435893845864270)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-496411186234907710891556769081),(-496411186234907710664814043189)⟩,⟨(-177360190683041909999827546623),(-177360190683041909765279539907)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-437123835667006262651457877098),(-437123835667006262477049253433)⟩,⟨(-120848702782826045823603646497),(-120848702782826045641532693071)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-362581057291882907709039948559),(-362581057291882907589122232522)⟩,⟨(-77775464491285145657674724337),(-77775464491285145534252057585)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-273018049953386980055547809923),(-273018049953386979980916322462)⟩,⟨(-46395361665481242013654775947),(-46395361665481241939431206167)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-170077998803659707592380751781),(-170077998803659707552373616408)⟩,⟨(-24025857034476677092037270299),(-24025857034476677053792299861)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-57790297070159048608230842563),(-57790297070159048595732974037)⟩,⟨(-7353444095900559317353115736),(-7353444095900559305712899159)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨189547780614887344185442548764,189547780614887491745329260539⟩,⟨136578498914057249509900444644,136578498914057397080348766088⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨576443662926594426922437881315,576443662926594993689481853760⟩,⟨371043296279362056710158053423,371043296279362623504964266036⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨973143691433363072589366415497,973143691433364538670287179789⟩,⟨493690396292273554481433436170,493690396292275020596257950564⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1349282533364723045993588307632,1349282533364726574091430135112⟩,⟨449986525051080152459114653990,449986525051083680581742184038⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨1640836606787089880418150816419,1640836606787097640073158706626⟩,⟨224442639649149156489638247289,224442639649156916145497907268⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1774426301572967233427560105945,1774426301572981780598261059482⟩,⟨(-142087057698052000813666427453),(-142087057698037453675020061153)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1707191943012827177607601406776,1707191943012848569481289556667⟩,⟨(-556856317016812165090748663044),(-556856317016790773281668415622)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨1456156231724596970660617238689,1456156231724619882344534086666⟩,⟨(-909614434299946773718788539733),(-909614434299923862122463804319)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1094173565437707463734509083581,1094173565437726647442619813568⟩,⟨(-1119827686733022103048492647717),(-1119827686733002919430191021022)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨714811440717334055243391830185,714811440717349543298137545057⟩,⟨(-1165036330096201859360884833560),(-1165036330096186371366448376599)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨392447132451954240689564588527,392447132451963619515198411729⟩,⟨(-1074623336204234905304076726449),(-1074623336204225526513444810999)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨162726082714936033403412784486,162726082714940565346941678464⟩,⟨(-901434713293127708714107483459),(-901434713293123176788136477219)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨27012941150320735878820608623,27012941150322653587618198094⟩,⟨(-694236073021508295025023602522),(-694236073021506377323131480885)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-32418756197603727385294056184),(-32418756197602965034457333793)⟩,⟨(-484017559166178906426160714267),(-484017559166178144076912673440)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-39253038615500213582451943866),(-39253038615499925734810258476)⟩,⟨(-283560661898627577058729240100),(-283560661898627289210833878327)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-16264789321609193088322932488),(-16264789321609119046168946743)⟩,⟨(-93160908671430397274209252832),(-93160908671430323231786459079)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-145513011543535476046011909604),(-145513011543535475948350746613)⟩,⟨(-113721300597507680008902190846),(-113721300597507679914779869208)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-455128887239070568843500203863),(-455128887239070568548636366281)⟩,⟨(-312796807266995484509098753999),(-312796807266995484228907529943)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-809802871034686690214712299973),(-809802871034686689711855958655)⟩,⟨(-423737361548403026316184186918),(-423737361548403025850508462023)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1205578467826030824745080153749),(-1205578467826030823999747400082)⟩,⟨(-384568695068708894184829132531),(-384568695068708893515932513025)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1591785081575972348326095060417),(-1591785081575972347295786986753)⟩,⟨(-145270313923302922728383261821),(-145270313923302921830486085992)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1871770856851989690551528814144),(-1871770856851989689201374845889)⟩,⟨304069885795199667229536649169,304069885795199668397380089655⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1933712279966818062140083833538),(-1933712279966818060363969680294)⟩,⟨904759541474249984654850032327,904759541474249986278266027936⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1707144187357056486160283218663),(-1707144187357056483782596502269)⟩,⟨1525423395780008313109324869393,1525423395780008315398266007002⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1214111646728364337732879994262),(-1214111646728364333210883214467)⟩,⟨2002037773394639652542937869709,2002037773394639657050605205422⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-575780436893325190222506526182),(-575780436893325173064258947130)⟩,⟨2209519956366523751628505848930,2209519956366523768837951335523⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨37580161238191422690367971460,37580161238191496421279153070⟩,⟨2118676903526219501053581240680,2118676903526219574879057368895⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨481154594602640382069701297917,481154594602640614665174168919⟩,⟨1797959895062624017806363510027,1797959895062624250513580657880⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨685706286254375232140099657096,685706286254375767875194416094⟩,⟨1363467300121562970113811037576,1363467300121563505946702430996⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨660499138325785448416870383984,660499138325786397563610190622⟩,⟨918179877056869662733587642948,918179877056870611939744979197⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨463055810316700083460878624321,463055810316701087331224449794⟩,⟨517271109615427521973151713564,517271109615428525874032552590⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨165071654550771900038831169588,165071654550772336648565680133⟩,⟨165609851218626001972114252627,165609851218626438591091108257⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨61426063367066769793988609487,61426063367066883458821641375⟩,⟨11311825050914249289844004663,11311825050914362945832297131⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨187382519815311787635041959905,187382519815312064683779607682⟩,⟨25124783991556123287555446082,25124783991556400311164501857⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨319785140892437299344376387387,319785140892437595458714480438⟩,⟨12103416226063474816292348968,12103416226063770893649173464⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨454158659380502638768275190713,454158659380502839669222251459⟩,⟨(-45787301706371423778179741562),(-45787301706371222918339763543)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨574072705732421015717648031701,574072705732421106596282498675⟩,⟨(-163403761438607756000145708456),(-163403761438607665155571635557)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨651103180359079947703306552228,651103180359079975455463221773⟩,⟨(-345541207992956284917879917060),(-345541207992956257177947841267)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨651690464646164917063471272102,651690464646164923374148502502⟩,⟨(-578007045575566444832814014420),(-578007045575566438498309017722)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨551022131227091603371101841174,551022131227091604990433610942⟩,⟨(-822601718924109528873821542538),(-822601718924109527184823879622)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨349466602398490431082063200106,349466602398490431990624497448⟩,⟨(-1023639977791815351762840306202),(-1023639977791815350737283118061)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨82068947756656952412683095396,82068947756656953251306502040⟩,⟨(-1127395623069807489084092144294),(-1127395623069807488106393976793)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-188342071213789041645099661982),(-188342071213789040745856674014)⟩,⟨(-1105547170527854174073660098721),(-1105547170527854173071852225658)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-393928360330000938059859327595),(-393928360330000937169403252466)⟩,⟨(-968066261983883826409430796777),(-968066261983883825457700921505)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-487543233704785848694963559459),(-487543233704785847902012630629)⟩,⟨(-756302138363548246349959322181),(-756302138363548245529954001766)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-456452046435386243341929603191),(-456452046435386242724062475729)⟩,⟨(-520570628069810823035794140179),(-520570628069810822412603207354)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-319427560808378301299203970198),(-319427560808378300909867781069)⟩,⟨(-296881744078849235992189583520),(-296881744078849235606115192767)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-114172911148766498604810756815),(-114172911148766498472527814752)⟩,⟨(-95495684682983227891881139519),(-95495684682983227761840364752)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-17277072075012831486121932380),(-17277072075012675304555537065)⟩,⟨(-2599688860971646083108038611),(-2599688860971489899384729256)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-52241246596238410573973369651),(-52241246596237820248896963361)⟩,⟨(-4779604285049245589233996564),(-4779604285048655257357770746)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-87673179130786254678268095022),(-87673179130784769741341737359)⟩,⟨2121070685881484240897348499,2121070685882969190316509181⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-121596034665361977918293096836),(-121596034665358440840656641398)⟩,⟨23798999447470684241666189682,23798999447474221338640968340⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-148899933819454357367575833697),(-148899933819445020202337107188)⟩,⟨64252383522764743357312741998,64252383522774080545147248760⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-161160250811365187240153927684),(-161160250811342621285241376545)⟩,⟨123611229615071183682493458205,123611229615093749659517968383⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-148423074946019608858472160655),(-148423074945975172611217604893)⟩,⟨196027930721396885315696810507,196027930721441321580811098674⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-103446047659755372793909743959),(-103446047659689224539275250388)⟩,⟨268917931740855175864975170533,268917931740921324129277290336⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-26901812720847000431371177733),(-26901812720772947692374306015)⟩,⟨325092657111010818333408193499,325092657111084871070460559470⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨69473040720509750651811426739,69473040720571698643101413028⟩,⟨348479196399065150419516068487,348479196399127098395326847948⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨164457456849861892242498542379,164457456849900533898623069297⟩,⟨331433825250442019682059425089,331433825250480661309905964794⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨233794743924251659350050714621,233794743924270854316523016226⟩,⟨279165941068755855901437195311,279165941068775050830748610089⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨258607536583854077617988970406,258607536583862300881725550624⟩,⟨207418586506527294242996245223,207418586506535517467005014941⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨231791352585368581269597076995,231791352585372016747066207546⟩,⟨134332823620511049705043911801,134332823620514485149489689775⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨159321308583345776452437588458,159321308583347273735536720928⟩,⟨71986469987602527329879672433,71986469987604024593559043372⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨56572683043515123363780359089,56572683043515538352189416232⟩,⟨22198851265044459664744218418,22198851265044874646793835336⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1909821015858302171897991832,1909821015858302172898445904⟩,⟨454309966990180450957839550,454309966990180451807846874⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨5858850026378673408274662568,5858850026378673411384070095⟩,⟨917604310241831473739314500,917604310241831476370072371⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨10119828063533431793717458841,10119828063533431799198484629⟩,⟨56410384375556948382999023,56410384375556953017490685⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨14639863192906216014429491389,14639863192906216022663676713⟩,⟨(-2906087179102897079875849491),(-2906087179102897072894566793)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨18896756331064760238786662637,18896756331064760250548487887⟩,⟨(-8452238996736982165487743893),(-8452238996736982155282042230)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨21727662579021513682995648973,21727662579021513700879702932⟩,⟨(-16588384876846925909664646305),(-16588384876846925893271930965)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨21542407905624529960695816510,21542407905624529990044705460⟩,⟨(-26728888953423187474454879350),(-26728888953423187446343642906)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨16990574569393732201750683220,16990574569393732272321341591⟩,⟨(-37549428728799721809328749062),(-37549428728799721739572432641)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨7714415024473926856632530495,7714415024473927226383674735⟩,⟨(-47007570758470941084498284095),(-47007570758470940715087987849)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-5144103965810359815954242262),(-5144103965810357163664290018)⟩,⟨(-52866841394452857998428442619),(-52866841394452855346158340499)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-18912142013185026700616631053),(-18912142013185011423794822732)⟩,⟨(-53588587076000727075556983573),(-53588587076000711798680198707)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-30003313186771944640614508485),(-30003313186771884167044969953)⟩,⟨(-49005809292390983724665967918),(-49005809292390923251171011380)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-35127009374974261590858828159),(-35127009374974105191423381558)⟩,⟨(-40265985796254698416076943511),(-40265985796254542016915307744)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-32591203058287532375387660665),(-32591203058287271065814490343)⟩,⟨(-29162603224330327970990344820),(-29162603224330066661819971742)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-22871439566737806167632575434),(-22871439566737539267517243163)⟩,⟨(-17346199752703750494348033897),(-17346199752703483594590871726)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-8202507445669214062829365718),(-8202507445669099618094859771)⟩,⟨(-5715169032796652118255537210),(-5715169032796537673663678019)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-23946669801187466096591422003),(-23946669801106607214617777547)⟩,⟨(-603349486048186027252280042503),(-603349486048105168396074338682)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 9) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_9 (tableDensity false) (fullFactor true 1 9) density0_contains hk1_1_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-193363686324792982625177329319),(-193363686324792981738196996610)⟩,⟨47060873050266836552975334877,47060873050266837437964764583⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_9 1 9 ha1_1_9_contains + def realAnswer : RBox := ⟨(-217310356125980448721868751322),(-217310356125899588952714774157)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_9 +namespace hm1_1_1_9 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_9 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1329695868217593738458372891),(-1329695868217551614289738141)⟩,⟨(-18023701342796008639269227634),(-18023701342795966515186658463)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5504303979231882393364344210),(-5504303979231785415722778124)⟩,⟨(-52327617198010556634252505141),(-52327617198010459656988541625)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-13408316499285693973543593661),(-13408316499285600948777551594)⟩,⟨(-81008108477537342603311286266),(-81008108477537249579509994841)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-25504112499531594899812540509),(-25504112499531540504194916205)⟩,⟨(-99887246578383606396903488963),(-99887246578383552003170117219)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-40819969803992152157860250565),(-40819969803992131511137416972)⟩,⟨(-106016282453239049174981259766),(-106016282453239028531332766205)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-57563018447313636510591800661),(-57563018447313631271523211586)⟩,⟨(-99833585399296890958269632981),(-99833585399296885723387196298)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-73286144477763927438779484419),(-73286144477763926428124027232)⟩,⟨(-85297030928287377056086155617),(-85297030928287376050120554733)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-85483475132002910159503303140),(-85483475132002909926961156988)⟩,⟨(-67504922801241092029727335397),(-67504922801241091802174918705)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-92538959289158509668994417105),(-92538959289158509559135951817)⟩,⟨(-50408572202286083773079632390),(-50408572202286083669004251716)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-93900975361476066702022799661),(-93900975361476066622940471230)⟩,⟨(-36054697620792304122367666399),(-36054697620792304049648107219)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-89651275885149594720380198045),(-89651275885149594654038590260)⟩,⟨(-24834795439581335441614825232),(-24834795439581335380080286798)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-80270950274109219151975176667),(-80270950274109219100217579775)⟩,⟨(-16167670036039277204500316132),(-16167670036039277156650312189)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-66665136120092489125903561725),(-66665136120092489088740611222)⟩,⟨(-9403835510481883554733093369),(-9403835510481883521242619833)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-49923697257285041241694348168),(-49923697257285041217396606192)⟩,⟨(-4453904997023244577302092360),(-4453904997023244556312248435)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-30942428728598740986277704694),(-30942428728598740972693456292)⟩,⟨(-1507276817531089650548904582),(-1507276817531089639306920248)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-10488911689919668979021171238),(-10488911689919668974671839555)⟩,⟨(-274948118702761199484238621),(-274948118702761195986076778)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨15874671725462222549505391772,15874671725462343974127594803⟩,⟨32798021650397953929708924355,32798021650398075352974517475⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨52009107421306964396953790495,52009107421307431018662196573⟩,⟨91796276444190627775409275526,91796276444191094393563563122⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨98505288841351066845377907821,98505288841352274912888786037⟩,⟨131196466849162210763573576087,131196466849163418826727333733⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨154148239244706503115523484120,154148239244709413213077708316⟩,⟨140026767066018014202189802956,140026767066020924296463786479⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨209151152031289978585732814841,209151152031296385143078661287⟩,⟨113086989628317696210869153603,113086989628324102767769493351⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨248401366080989238935838723143,248401366081001259735389247588⟩,⟨54997707080708929510403473529,54997707080720950313411938612⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨258746658842165996797484961260,258746658842183689300555920759⟩,⟨(-19549334982197683446461910179),(-19549334982179990935921016540)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨236508922628568182822355528344,236508922628587141266430613547⟩,⟨(-91092071373792062130975403348),(-91092071373773103676061998651)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨189634895446658760869328751660,189634895446674633839869421545⟩,⟨(-143370234940591847887912635650),(-143370234940575974905683092724)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨132906666283985945440192853417,132906666283998753431672622585⟩,⟨(-168991959337569463623583256366),(-168991959337556655623894854080)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨80475972278350896306791201547,80475972278358644484062517506⟩,⟨(-169621531250533770113472214040),(-169621531250526021931279233799)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨40794402564542064532032720640,40794402564545803639526572005⟩,⟨(-151920584547678218385840217467),(-151920584547674479275845055173)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨15765124117838006249068218824,15765124117839586140990134506⟩,⟨(-123215061088741445442745272165),(-123215061088739865549812933980)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨2992335236594691116061112031,2992335236595318270558568489⟩,⟨(-89256321856800033571549823247),(-89256321856799406416802577844)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1356463030958562601569845316),(-1356463030958326082029038289)⟩,⟨(-53609066698652123450198827840),(-53609066698651886930686156014)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-958311761789871864341948102),(-958311761789811067132375964)⟩,⟨(-17828580976782725428716850711),(-17828580976782664631545339142)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-14524292130841082020960931164),(-14524292130841081984339417389)⟩,⟨(-39083049987352029907045390184),(-39083049987352029870575316925)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-50057663938002870268092454651),(-50057663938002870157032011238)⟩,⟨(-114363925154166204879720584702),(-114363925154166204769319825424)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-102690724831879664896058482227),(-102690724831879664709716345470)⟩,⟨(-178705476561444651120951962630),(-178705476561444650936252772325)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-176305888124724760918419919416),(-176305888124724760654282370489)⟩,⟨(-218979214631062234797911150949),(-218979214631062234537028545028)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-264621243737714653487014876942),(-264621243737714653148260405650)⟩,⟨(-218287386250003414809739236456),(-218287386250003414476231344471)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-350276036602031912265659838291),(-350276036602031911856234829981)⟩,⟨(-163575160578674754607193216074),(-163575160578674754204757537722)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-408263790921819728062845885992),(-408263790921819727518381953973)⟩,⟨(-56223764232919454397586258923),(-56223764232919453859219961998)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-415513037784329961825113091174),(-415513037784329960981352214308)⟩,⟨82484501070997134790806202263,82484501070997135630963217246⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-363800589642736112370659600250),(-363800589642736109899131276839)⟩,⟨216836050151621277868051908099,216836050151621280338802072549⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-266710136850861084560392218938),(-266710136850861071810118849998)⟩,⟨311398088689073459111719109165,311398088689073471862706145001⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-153717772553911180623379332813),(-153717772553911121688847805559)⟩,⟨346303586463320288890026555005,346303586463320347825507106541⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-55198776521706340898384563360),(-55198776521706152336573098255)⟩,⟨323555450303263950361322367693,323555450303264138923919639671⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨10257210740100721519298038677,10257210740101157640825692503⟩,⟨261692489738350574889256665774,261692489738351011011313914208⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨38666541471004430702037568671,38666541471005204854479081781⟩,⟨183715145516445401417937547196,183715145516446175570579602143⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨36272843605438911396440125349,36272843605439730916153771364⟩,⟨106071183875236177084299770353,106071183875236996604052808810⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨14297968588266493160913930146,14297968588266849728330014515⟩,⟨34347374559905898014911026024,34347374559906254582312441931⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨14200571804657295450592806263,14200571804657390942071172565⟩,⟨15305186460085615865755701623,15305186460085711358163349209⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨44400683188468032577649517766,44400683188468265165773449596⟩,⟨43630120723420237084441175612,43630120723420469675203759475⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨79403062785119629326056796934,79403062785119877553844244987⟩,⟨64638138493352768233208601183,64638138493353016464852718634⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨120547390914083882023968933951,120547390914084050027303073634⟩,⟨72478029525399327964641780988,72478029525399495972197540203⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨166270535140810838147111751421,166270535140810913832849317842⟩,⟨61172769427068119068400356249,61172769427068194757476532062⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨210934465805564441792920722415,210934465805564464673862095579⟩,⟨26722212595387686715309350382,26722212595387709597208768655⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨244695746795069845544047467207,244695746795069850525701587751⟩,⟨(-30339820620803438646425791937),(-30339820620803433667531297669)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨256122497554261269309146582388,256122497554261270361847733495⟩,⟨(-103168580364873802618788006886),(-103168580364873801573354605433)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨237357344470331881785717097843,237357344470331882228715838209⟩,⟨(-178627401756260546451814884449),(-178627401756260546020526611456)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨189028240256483408313672151483,189028240256483408678904241280⟩,⟨(-240297796585765415274280799640),(-240297796585765414922566969304)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨121754576324566468264694206482,121754576324566468635053888594⟩,⟨(-274083374735131834654847104591),(-274083374735131834294073975662)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨52756468676583849320781531555,52756468676583849674456507782⟩,⟨(-273363461638676727365171073950),(-273363461638676727016919242984)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-983054896864628914176636724),(-983054896864628606438189281)⟩,⟨(-240494031395260329208192254777),(-240494031395260328902562537082)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-29097523251016307484901392573),(-29097523251016307248656950585)⟩,⟨(-184100264386671521328797990177),(-184100264386671521092666296215)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-30543150750575124601534385573),(-30543150750575124453975333819)⟩,⟨(-114242770231607471348171370585),(-114242770231607471200052368549)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-12528455273554257724971721341),(-12528455273554257675029901615)⟩,⟨(-38555633975181196010181337585),(-38555633975181195959943043738)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-5712916560164138340063795888),(-5712916560164009982705519416)⟩,⟨(-562573964067695627068685497),(-562573964067567270140843854)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-17571818398372119290838716044),(-17571818398371634099308898787)⟩,⟨(-861433166460037688452195235),(-861433166459552498313957812)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-30369358971887059261821844430),(-30369358971885838623275168279)⟩,⟨1340431362158156272954658200,1340431362159376908906554774⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-43644173566367806824992902462),(-43644173566364898835477060956)⟩,⟨7762293642592896213269288267,7762293642595804198694212571⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-55602817788923860842242829403),(-55602817788916183410863695831)⟩,⟨20064230548180532873661976370,20064230548188210300111493606⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-63326319794177227904142457179),(-63326319794158673286306223004)⟩,⟨39315893195298138581251831235,39315893195316693194028644980⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-63520721165479721092399651108),(-63520721165443191832927972107)⟩,⟨64960500480059985554650745966,64960500480096514809748204823⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-53647666279545231913038931378),(-53647666279490880861639979985)⟩,⟨93948912040286119497142144165,93948912040340470545902839819⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-33360782971061570311653109652),(-33360782971000772995451149877)⟩,⟨120917799150262604212698938923,120917799150323401528867481645⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-5690273608092518580501242254),(-5690273608041713413671835605)⟩,⟨139603495791559193275964985228,139603495791609998445582173140⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨23122688321920722121401835790,23122688321952373100422915688⟩,⟨144957219450012454812162349724,144957219450044105796378581555⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨45716442505141837583101982166,45716442505157538873944188189⟩,⟨135072847387748324427276248530,135072847387764025724888416651⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨56540977462279276942451434637,56540977462285994908672406323⟩,⟨112103037067001985440271516440,112103037067008703413677395367⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨53519312753908366346235591542,53519312753911169906225789566⟩,⟨81317280019466906476864486823,81317280019469710042713433806⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨37936165472750671582660106341,37936165472751892540115683564⟩,⟨48233959785387072951985689123,48233959785388293912834420919⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨13671943038503942482503612425,13671943038504280753843237992⟩,⟨15850657510573554360469706782,15850657510573892632900693646⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨57373258085901245345610532,57373258085901245893121598⟩,⟨10787324078248881545804374,10787324078248881982036805⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨172361916378095428259964299,172361916378095429955854028⟩,⟨(-16725248493579410913835477),(-16725248493579409574774366)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨219903969918908179590604718,219903969918908182542035277⟩,⟨(-216822414484886487320314722),(-216822414484886485013065997)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-29587642721738147817645689),(-29587642721738143456773259)⟩,⟨(-801163917623216582544272050),(-801163917623216579173884156)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-928744586695969640880734830),(-928744586695969634543412050)⟩,⟨(-2103696794324135696409238773),(-2103696794324135691380611575)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-2784655702917165875756445395),(-2784655702917165865389375804)⟩,⟨(-4438523050640184788189426603),(-4438523050640184779192628153)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-5751289667788598059619416105),(-5751289667788598040587948697)⟩,⟨(-7783263960154396063562891860),(-7783263960154396045814693120)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-9832473156913764646195947792),(-9832473156913764593395756653)⟩,⟨(-11601198426786015924675946983),(-11601198426786015872866473174)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-14789583842737129507745628817),(-14789583842737129208654235063)⟩,⟨(-14966761691941041077896074801),(-14966761691941040779330418875)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-19975924072543719864870542883),(-19975924072543717697797322791)⟩,⟨(-16864302708504754462628298506),(-16864302708504752295595885193)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-24349244290735486144159334502),(-24349244290735473667041675076)⟩,⟨(-16564107883841706059668236961),(-16564107883841693582200032985)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-26753218273464411127332441352),(-26753218273464361741729991915)⟩,⟨(-14011847452735441683656769186),(-14011847452735392297458338528)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-26254143545499295683511947434),(-26254143545499167912345208876)⟩,⟨(-10019499060887665432254995350),(-10019499060887537660397519269)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-22334117753030567674787833865),(-22334117753030354095574814003)⟩,⟨(-5920503002155184182176104388),(-5920503002154970602349495799)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-15072526128332423766983111249),(-15072526128332205536594277145)⟩,⟨(-2771459723418791806161558978),(-2771459723418573575360797678)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-5329028709632283134227953747),(-5329028709632189540065225169)⟩,⟨(-760444059290405743958228900),(-760444059290312149654857064)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-42870258472003499293899537462),(-42870258471937018992370713828)⟩,⟨(-136417080253307319842971811137),(-136417080253240839553607920933)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_9 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 9) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_9 (tableDensity true) (fullFactor true 1 9) density1_contains hk1_1_9_contains +noncomputable def atomAnswer : CBox := ⟨⟨252860205193960053042257610952,252860205193960054202154969110⟩,⟨(-61541141681118172034261615224),(-61541141681118170876967745609)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_9 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 9) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_9 1 9 ha1_1_9_contains + def realAnswer : RBox := ⟨209989946721956553748258073490,209989946722023035209884255282⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 9) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_9 +namespace hm1_0_1_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-21731866792778407888585846599),(-21731866792778367392372773683)⟩,⟨87442596968751742437182966661,87442596968751782931100763745⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-51169424446144750319255341879),(-51169424446144655377128825706)⟩,⟨256798331306189122685309703718,256798331306189217621451475891⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-43528292999334820111851503330),(-43528292999334725946404828680)⟩,⟨407682761761935832219784395320,407682761761935926377795060780⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨10462692072135681689470624793,10462692072135739248353541723⟩,⟨524677062738386471615085810414,524677062738386529167415898828⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨102670346767861775532205783844,102670346767861798577117122313⟩,⟨593286742385406420028497633684,593286742385406443068651578749⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨211840607032375443444750399513,211840607032375449762366916068⟩,⟨606214441153820549543464409645,606214441153820555858685290801⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨313823214304646383707465441123,313823214304646385187460206937⟩,⟨567811624327040176187900413820,567811624327040177670567324346⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨390873000239218345719814518994,390873000239218346277723131560⟩,⟨492780322043610902824098161023,492780322043610903389379627772⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨435204334137160346214342107103,435204334137160346573848758083⟩,⟨399707840930614039373608481892,399707840930614039738702065000⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨447108835860538012274883894488,447108835860538012535652577413⟩,⟨304562969843955285260123963269,304562969843955285521517406263⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨430704094594624332331227185240,430704094594624332550234131630⟩,⟨217928416172960201460201009089,217928416172960201684070666263⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨390363654106566085188593321506,390363654106566085358800664080⟩,⟨145533641298483490632422304826,145533641298483490808987250805⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨329290170530227654365919580504,329290170530227654482516298456⟩,⟨89669946265858796950793541520,89669946265858797070583849805⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨250148737431426119539064247948,250148737431426119610757696113⟩,⟨49994788781252714497846574522,49994788781252714569215530163⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨156459829378477038923205944630,156459829378477038961116763352⟩,⟨23903946611277164095439305603,23903946611277164131740284426⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨53239874240397516577477990947,53239874240397516589217768856⟩,⟨6897270785740121749094619072,6897270785740121760043293540⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-23246257399494510962072369575),(-23246257399494400064029352561)⟩,⟨(-164987231317960390007307096651),(-164987231317960279103788714749)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-96649210611872823994631398140),(-96649210611872413969348061964)⟩,⟨(-481113454751010801804663030522),(-481113454751010391760757424753)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-241651733342918233078657027211),(-241651733342917250088578136102)⟩,⟨(-748792627742094463969925290167),(-748792627742093480942633508339)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-475539121073637895125404154353),(-475539121073635790860942294010)⟩,⟨(-920898790649049085900000606230),(-920898790649046981574061929115)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-773340187779346061220806894219),(-773340187779341768012015449336)⟩,⟨(-947402602999340247767737817851),(-947402602999335954478112201590)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1067730794710415926041944869937),(-1067730794710406325129641212532)⟩,⟨(-801505661127316816554799116361),(-801505661127307215576534015541)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1273068721683694532601954011948),(-1273068721683677583053385133738)⟩,⟨(-506034653463157602155390385920),(-506034653463140652569168926647)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1326409117693513753665259005532),(-1326409117693492127701892618450)⟩,⟨(-136146270338149981675004565253),(-136146270338128355705318494536)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1219666893069805705906885982437),(-1219666893069785681609627014733)⟩,⟨210642734312828717590948965883,210642734312848741868443012529⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-999247405942458749556133993102),(-999247405942445172364443835673)⟩,⟨457732038062962104737563847263,457732038062975681893093713261⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-736006168894394151605932255184),(-736006168894387344915290163751)⟩,⟨575584413257032538727423301322,575584413257039345375362909387⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-490934151760703774549337619348),(-490934151760700926378766021946)⟩,⟨577923458602127829157344724950,577923458602130677288737322355⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-297622172858310962743482369883),(-297622172858309660911372492668)⟩,⟨499648818074959001734825757001,499648818074960303541601526570⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-163110340885140029987221502374),(-163110340885139473254445118682)⟩,⟨375636483067326896437555409254,375636483067327453155735733325⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-77322751759719101546188449242),(-77322751759718881832178685094)⟩,⟨230411124450164705163798297427,230411124450164924870479258832⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-22304141921930772355509381427),(-22304141921930714643761962352)⟩,⟨77367991296409886272779547562,77367991296409943982317921953⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-16815565738921614572060142692),(-16815565738921614517981949735)⟩,⟨106631462688861000852842721938,106631462688861000916970047600⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-29429059211389099524240568537),(-29429059211389099362109381026)⟩,⟨322647601794096084673009296883,322647601794096084867506793029⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨20204312086574509082393666555,20204312086574509364219512134⟩,⟨539685039362948228085423550808,539685039362948228424614467842⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨167088145047133282589115031836,167088145047133283045755106363⟩,⟨736929530366367696319602024004,736929530366367696844187639562⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨426526778747196248560299964639,426526778747196249247045740459⟩,⟨868273274016854719210533996669,868273274016854719958742284733⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨775652846976597285772869610665,775652846976597286733974910259⟩,⟨870696057912665405243696259057,870696057912665406240439623624⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1142939921143676185900959617331,1142939921143676187157909782570⟩,⟨692514812334809373903489075449,692514812334809375153253256275⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1422299945316288871155984304970,1422299945316288872777098107434⟩,⟨332149634944444125824709452987,332149634944444127387800393396⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1516746015449265570581358489515,1516746015449265573346157555296⟩,⟨(-139798223458819427535709584132),(-139798223458819424874403033778)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1390314745079145929204392733443,1390314745079145939027026196958⟩,⟨(-599837445538349922381148662040),(-599837445538349912669534920713)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1090417455501204752072000812778,1090417455501204803588940271961⟩,⟨(-926682094455316137384126498704),(-926682094455316085934072059253)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨721477145434001983718665797784,721477145434002183298004368124⟩,⟨(-1054477297162745266856606178295),(-1054477297162745067305778400344)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨389975204727801863333193087243,389975204727802364080032419735⟩,⟨(-988222109558260822447426095827),(-988222109558260321703292239359)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨160056002418776302661815229278,160056002418777108510632219420⟩,⟨(-779752421180542541502762002875),(-779752421180541735644693885330)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨41726344764976269026067850651,41726344764977064749109865043⟩,⟨(-490517607384220010637125440905),(-490517607384219214903992544740)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨4253970328223937073113893804,4253970328224271289347338745⟩,⟨(-166387506401179374192410526675),(-166387506401179039972076827226)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-4109445875527012979859122746),(-4109445875526948199584280343)⟩,⟨(-30114395735685162904938652079),(-30114395735685098122343016744)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-17216479807540850080145166790),(-17216479807540693983090814986)⟩,⟨(-90679607127951525795949033464),(-90679607127951369692821728491)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-44866114548382772060947315341),(-44866114548382608816699129966)⟩,⟨(-150701024169182735428804521856),(-150701024169182572177470223902)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-95789612121360865142368265494),(-95789612121360757747801112079)⟩,⟨(-205130317684376117815603769699),(-205130317684376010417581803018)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-175451555522417339422631283421),(-175451555522417292719806308177)⟩,⟨(-242877628732685603468174648354),(-242877628732685556771888317120)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-282098814410391965595041764054),(-282098814410391952000570520476)⟩,⟨(-247602081341153828756688440459),(-247602081341153815185989759905)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-402587174249742044371780149389),(-402587174249742041405010348307)⟩,⟨(-202763138539617162997584392738),(-202763138539617160077981167265)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-511519689212956693174065832557),(-511519689212956692347795556841)⟩,⟨(-100482306844169741353193827365),(-100482306844169740596567852268)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-577649514387699802249773737779),(-577649514387699801646235987616)⟩,⟨49559453804443330041343895375,49559453804443330584826578059⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-577139350380197739460406353585),(-577139350380197738854234748815)⟩,⟨217466089494799809759431468126,217466089494799810328649175870⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-506672833812372102137579146774),(-506672833812372101537227736019)⟩,⟨361380646413027079876905397400,361380646413027080466239376973⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-387096935406871088280616306177),(-387096935406871087727152087014)⟩,⟨443926623360079155944232474952,443926623360079156509066936788⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-253868918153068312790268650479),(-253868918153068312304783374439)⟩,⟨446762336725621437002672127894,446762336725621437513776202722⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-140029975370932365843187155401),(-140029975370932365460979125479)⟩,⟨374189858472642662070302372471,374189858472642662481384832234⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-62233291138094748062441118274),(-62233291138094747819154034917)⟩,⟨245728637484199980399521352087,245728637484199980664727556813⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-16544246163317837792727562607),(-16544246163317837709568450240)⟩,⟨85251149554631639809207257709,85251149554631639900452740772⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨159464907557816691106532696,159464907557873294306263036⟩,⟨7246308376722206711866056282,7246308376722263313951003448⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1801530789153764178192703582,1801530789153979802203934115⟩,⟨21749254470376989077405322844,21749254470377204697988316206⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨7398105986424065515916419780,7398105986424674709007463043⟩,⟨35931883112351809618465722324,35931883112352418806151013732⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨19354118268912478471721803633,19354118268914173174034425327⟩,⟨48533925838915835919503824516,48533925838917530615119061615⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨39186459559327730272123301813,39186459559332237487495509142⟩,⟨56917662728828187289784022009,56917662728832694498186413870⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨66466424440046703505680619498,66466424440057359712748184209⟩,⟨57096831101380525555660166752,57096831101391181756962872102⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨97834038996845416684119535947,97834038996865915279993484019⟩,⟨44705980001945386612322817378,44705980001965885205429429879⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨126805376315197495562310637398,126805376315227211192121312618⟩,⟨17108522077982301795009560055,17108522078012017426886991290⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨145139925626188740200299378013,145139925626220948046295129718⟩,⟨(-24133365187760480217695124977),(-24133365187728272363310557237)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨145974002484794576897074798808,145974002484820445977358632605⟩,⟨(-72019619028736564042499338077),(-72019619028710694946902650232)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨127512578137984276948847336767,127512578137999582496497297800⟩,⟨(-115453613623307715331832805520),(-115453613623292409762812740043)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨94883193723476230707175119865,94883193723484150017111055393⟩,⟨(-142972276057836372374057882493),(-142972276057828453042120261598)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨58252962252605902787214880041,58252962252610176484713831353⟩,⟨(-146917652798144143259876658213),(-146917652798139869546226159244)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨27895416207170174918857371701,27895416207172215111106944938⟩,⟨(-125847322386649981279644899020),(-125847322386647941076955944530)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨9401771916813951016228974237,9401771916814820755163697148⟩,⟨(-84134160199221270303406973256),(-84134160199220400558851417124)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1704727335520345547859006023,1704727335520583523398312373⟩,⟨(-29474823562199240673023158368),(-29474823562199002695745315775)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨127901881436094471275423327,127901881436094471576169961⟩,⟨(-698660887315768928884094332),(-698660887315768928523654747)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨216368846986659848312112117,216368846986659849243550122⟩,⟨(-2139852635124405908789679486),(-2139852635124405907668507532)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-195953981431580754098513776),(-195953981431580752455030162)⟩,⟨(-3682449600677620458965781796),(-3682449600677620456987051205)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1411913229895976366084420846),(-1411913229895976363581747025)⟩,⟨(-5291485680049286325787932509),(-5291485680049286322794627056)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-3628036959630331616145054827),(-3628036959630331612119329573)⟩,⟨(-6750732697240833716134617389),(-6750732697240833711569358275)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-6849912274861653069085220020),(-6849912274861653062558188203)⟩,⟨(-7595827999824142645506601011),(-7595827999824142638481521253)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-10828410413350286031575658299),(-10828410413350286020372585477)⟩,⟨(-7191793042551664266231676701),(-7191793042551664254638035363)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-14997345899492372913078170517),(-14997345899492372885354420652)⟩,⟨(-4997493154130908523339862377),(-4997493154130908495391384548)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-18494994935048448673437653720),(-18494994935048448527526309907)⟩,⟨(-885260793506756152203017608),(-885260793506756006237002274)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-20402549328948092992362573376),(-20402549328948091952369665260)⟩,⟨4634171729418794399677182944,4634171729418795439630581633⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-20143564863459284627153150097),(-20143564863459278695379670520)⟩,⟨10400665183894569372844795610,10400665183894575304592446032⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-17784872930227059320864750459),(-17784872930227036140060428361)⟩,⟨14881798706074764748766606320,14881798706074787929638034986⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-13988674591999765709910610157),(-13988674591999706660587087716)⟩,⟨16694902860652727408493127447,16694902860652786457992628700⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-9651333450302376052975879973),(-9651333450302278922289900640)⟩,⟨15155760718823163325646518279,15155760718823260456565123210⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-5488648375101467023179129699),(-5488648375101369118915331514)⟩,⟨10511544926076751469106330000,10511544926076849373566682489⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1758197609609540453654342712),(-1758197609609498795350740534)⟩,⟨3749740746587525207648520256,3749740746587566866028734444⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨19160141902133783010018056677,19160141902177459356744134056⟩,⟨489309673128834342201876025666,489309673128878018543487803761⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 10) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_10 (tableDensity false) (fullFactor true 1 10) density0_contains hk1_1_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨94282177907632673814756003807,94282177907632674653395396113⟩,⟨104460388539100487391365920705,104460388539100488227689703308⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_10 1 10 ha1_1_10_contains + def realAnswer : RBox := ⟨113442319809766456824674060484,113442319809810134010239530169⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_10 +namespace hm1_1_1_10 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_10 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-5657179270741662862722953026),(-5657179270741629715704908805)⟩,⟨14332767172763799320902137195,14332767172763832468475571366⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-14869420073914781744079190298),(-14869420073914704077055015505)⟩,⟨42451988378720077851987228709,42451988378720155520480976219⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-18286750998515034412107347130),(-18286750998514957485333401802)⟩,⟨68144879659099493109330527396,68144879659099570037976337933⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-13639530802245014069004990719),(-13639530802244967192099058682)⟩,⟨88174697142164408269412264664,88174697142164455147939521354⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-648824691805141610304188358),(-648824691805123002489097247)⟩,⟨99173021026583848452603175312,99173021026583867061160740455⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨18595072701971060638075382073,18595072701971065566769882981⟩,⟨99843845313932567181637373754,99843845313932572109770596178⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨39958648204020408558591059058,39958648204020409539249111034⟩,⟨91742445914635482099654615370,91742445914635483078651146565⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨58917628143131703874235573024,58917628143131704104149916464⟩,⟨78080578602492391667810724395,78080578602492391895357454299⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨72336279026949830003514521381,72336279026949830114033365818⟩,⟨62198213796192867291397593098,62198213796192867398420985197⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨78909029320643403561184912285,78909029320643403639851212450⟩,⟨46637036458879020882104126103,46637036458879020955977325279⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨78612158985820173567594592024,78612158985820173632039304024⟩,⟨32811319607746067570178498889,32811319607746067630694351263⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨72167323727807068023049856629,72167323727807068073360417655⟩,⟨21209458041510312352475031845,21209458041510312399570358667⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨60789280547475798329516506814,60789280547475798365323674115⟩,⟨11987583516952188933309698358,11987583516952188965973103277⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨45848211651277599654230339178,45848211651277599677320472338⟩,⟨5431629963389766481190031897,5431629963389766501334004764⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨28494223826397247867822401174,28494223826397247880563783295⟩,⟨1710248824514623264437161524,1710248824514623275044121898⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨9665210902895025339829395055,9665210902895025343877553830⟩,⟨275313085719849515814620728,275313085719849519079666762⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨9048687656862889607895487620,9048687656862980858545617460⟩,⟨(-24360049768369932298514615375),(-24360049768369841048534115809)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨21245213164689733604858474607,21245213164690071161953314211⟩,⟨(-72472394129952133235190631220),(-72472394129951795680363473758)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨17106143492023517839049552750,17106143492024327795236597255⟩,⟨(-117045667172890444220934407873),(-117045667172889634269264654655)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-9272775025626103747065464778),(-9272775025624368194324417400)⟩,⟨(-151450074124729275831481429216),(-151450074124727540286266004138)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-56040185350019888551420914707),(-56040185350016344157400808719)⟩,⟨(-166369282433519085940026331515),(-166369282433515541556036108077)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-112273222265614012534436586159),(-112273222265606079095153638648)⟩,⟨(-154254504083833736095948378557),(-154254504083825802664956922851)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-161314468794262547430445204311),(-161314468794248529054545942322)⟩,⟨(-114703744898935570463089881771),(-114703744898921552092173616753)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-188430798277699778254850832804),(-188430798277681883585265043942)⟩,⟨(-56818570264011926523983425441),(-56818570263994031855640378011)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-187884108039182201198678481307),(-187884108039165632439146081798)⟩,⟨4046050892738718019230987263,4046050892755286780938812515⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-164442991985124253502033720168),(-164442991985113025615646778160)⟩,⟨53328008418224834743133976713,53328008418236062634304406662⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-129009461566718670378442922066),(-129009461566713047268030863333)⟩,⟨82870990970715813238926851338,82870990970721436355326565222⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-92305754198318450639897462983),(-92305754198316101014949589211)⟩,⟨91859498232211590118434481952,91859498232213939749056971405⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-60886899101898489022283274790),(-60886899101897416672920075924)⟩,⟨84297841515319694588880906010,84297841515320766942007294353⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-36807330028650624798053340616),(-36807330028650166852939574393)⟩,⟨65799588589208275707871662629,65799588589208733655215803149⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-19228905864995794556336818406),(-19228905864995614044565063736)⟩,⟨41269551410139540575382118560,41269551410139721088304987994⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-5917260333972742870754234596),(-5917260333972695490179055688)⟩,⟨14002604067035323348937261980,14002604067035370729866448388⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-15849589337946760129027088271),(-15849589337946760107761246625)⟩,⟨18513662663952187660448114460,18513662663952187682170913959⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-44150734535915448777903489387),(-44150734535915448713510118107)⟩,⟨58435120823773974107120342379,58435120823773974173035766254⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-61543160965219239857980909474),(-61543160965219239747856567181)⟩,⟨105097488486853220599614466621,105097488486853220712376746412⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-59331012141171982280504681499),(-59331012141171982109617985898)⟩,⟨157039961890238615892246346541,157039961890238616066122809526⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-29421182403720733606464287556),(-29421182403720733364097005535)⟩,⟨205507300953569293791261588238,205507300953569294036117843107⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨30747462027265243508045937072,30747462027265243826005181616⟩,⟨235700677971420756760574527591,235700677971420757080003243456⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨112544462437269690526675867546,112544462437269690924234820184⟩,⟨232083715593556051733137689660,232083715593556052130535194631⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨195364251334195564311008546963,195364251334195564864573091483⟩,⟨186686189337940361142446612094,186686189337940361693992371749⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨254142445736176213723976796772,254142445736176215084707023155⟩,⟨106316459696424480315841131711,106316459696424481673553626121⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨271592893994912486188505685120,271592893994912493157316555971⟩,⟨12497382980590826931963090063,12497382980590833898398740083⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨246664291137734704910790501796,246664291137734745794259504688⟩,⟨(-67977362560369770294695981878),(-67977362560369729412246904478)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨193222867754062735914553223016,193222867754062897573060197066⟩,⟨(-115891151283197608865773577457),(-115891151283197447207757831746)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨131115453008658948192092480799,131115453008659355830945495958⟩,⟨(-126653834068321091541895672660),(-126653834068320683903222581988)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨76619748725752856377453291265,76619748725753513622576768748⟩,⟨(-107634384958246078124260765260),(-107634384958245420879196232478)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨37094843531740556366831582929,37094843531741205933328511097⟩,⟨(-70302242842001950728453690738),(-70302242842001301161989680724)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨10674499100880268416924425195,10674499100880541350428681062⟩,⟨(-24236034054432531878011473393),(-24236034054432258944528163250)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨4916080053277439481026580757,4916080053277493907813174040⟩,⟨(-8891118525713969369772255316),(-8891118525713914943237073169)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨13375551330072281191912756340,13375551330072412249273781149⟩,⟨(-27288466829909978573367197095),(-27288466829909847516663270356)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨17536879949726009001260389133,17536879949726145859723085744⟩,⟨(-47150298528177508799771606860),(-47150298528177371942069979609)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨14198229258092586539897773790,14198229258092676357623596315⟩,⟨(-68299987025474160885808314317),(-68299987025474071068445983927)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨380062285309927382613602450,380062285309966272533424107⟩,⟨(-88928864125059044099957357675),(-88928864125059005209341603729)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-25366675144844322666513221153),(-25366675144844311484988600119)⟩,⟨(-105250526069018581721884752795),(-105250526069018570537906964238)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-61396930789625258823258913931),(-61396930789625256534672658132)⟩,⟨(-111845449776027162768360030290),(-111845449776027160474994688130)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-102151275659380850159290072884),(-102151275659380849688282236917)⟩,⟨(-103437361656742397741018016344),(-103437361656742397263115192320)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-138875769753156578819617433884),(-138875769753156578569029497470)⟩,⟨(-77882464532124773592798764899),(-77882464532124773336447497307)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-162280968617776562657815917117),(-162280968617776562425446443142)⟩,⟨(-38603848926563869942135512243),(-38603848926563869706447001523)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-166336813308279815001544755079),(-166336813308279814772561156391)⟩,⟨5454035335367249213103012430,5454035335367249442760887103⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-150932386311014066842838677319),(-150932386311014066629528784810)⟩,⟨42843317619922978585585177795,42843317619922978797404279567⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-121462711724959490084409881989),(-121462711724959489894968951225)⟩,⟨64095484373490502418046904702,64095484373490502604765914662⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-85650770527379674558933749243),(-85650770527379674408063128908)⟩,⟨65059087259222655449036015568,65059087259222655597030528051⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-49727958496338673429644538402),(-49727958496338673332646009896)⟩,⟨47456960176238466443233498035,47456960176238466538111732556⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-16152645627664732720825661546),(-16152645627664732687470175187)⟩,⟨17278187307458525553597628021,17278187307458525586182585868⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨174157980821666239851168192,174157980821712757936301264⟩,⟨2375088878514563933987252239,2375088878514610452294740712⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨911761267420648638630364155,911761267420825857873629684⟩,⟨7261955035394558466088142565,7261955035394735686031595412⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨2812088756257597149931381348,2812088756258097910040061102⟩,⟨12401905534761473449729567884,12401905534761974210971213389⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨6623620122109344936446150727,6623620122110738220432231905⟩,⟨17482012974975984052826781214,17482012974977377338271014430⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨12990766555216870808064754795,12990766555220576830467775351⟩,⟨21581210244032832292038157594,21581210244036538316024963474⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨22209342218898983200952488931,22209342218907745146988003912⟩,⟨23257023799442971447939790026,23257023799451733395385721997⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨33786764090485332480549886622,33786764090502183560330627394⟩,⟨20937335413863702376468753563,20937335413880553457066322699⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨46099326980217620089592050636,46099326980242036124057724989⟩,⟨13543124989493097416953948452,13543124989517513451165161891⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨56568214327144537940493647203,56568214327170980668100785362⟩,⟨1238638654425068513919141375,1238638654451511239880466621⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨62455493181035015090225200702,62455493181056231104820385353⟩,⟨(-14016051285701878160984215888),(-14016051285680662149397482202)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨61942355834179998704295424356,61942355834192535412667159306⟩,⟨(-28655943656813568590903949690),(-28655943656801031886592090289)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨54927357751238145618426469654,54927357751244623377222900819⟩,⟨(-38715323043044403778213316394),(-38715323043037926023528009579)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨43156252635921635832896054986,43156252635925127164469805465⟩,⟨(-41477818838416185807140619228),(-41477818838412694478572691941)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨29511833667990813363360790448,29511833667992478307366327496⟩,⟨(-36372174815074590535560958810),(-36372174815072925593474097292)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨16563241101835067008983470887,16563241101835776248722826842⟩,⟨(-24670189743897352451222773415),(-24670189743896643212504938502)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨5253693645437306754347800008,5253693645437500740023891995⟩,⟨(-8707062275132470995962322892),(-8707062275132277010596858517)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨2808507424008754873776481,2808507424008755024245930⟩,⟨(-20934148324264510361318595),(-20934148324264510167097383)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-9472216691385422830109600),(-9472216691385422369057299)⟩,⟨(-62080889411788027910206787),(-62080889411788027308824100)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-83595277447432103973034548),(-83595277447432103181820129)⟩,⟨(-75304031659509157521283341),(-75304031659509156476573671)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-292715998054588660645959580),(-292715998054588659482052578)⟩,⟨30077588127090357911900257,30077588127090359461735487⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-752080761913888839454925765),(-752080761913888837457910962)⟩,⟨399930873819974949341318918,399930873819974951789305123⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-1570705015408104303603414431),(-1570705015408104300001016683)⟩,⟨1175068618008762950213882282,1175068618008762954270373206⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-2735530905538665945605223390),(-2735530905538665938517290214)⟩,⟨2441080225850796352485283036,2441080225850796359973466198⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-4038952123843681727149853011),(-4038952123843681706560955854)⟩,⟨4211689073331037359949940270,4211689073331037380805465250⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-5122675119024170441651102302),(-5122675119024170323750570482)⟩,⟨6379193078747003452687839445,6379193078747003570661248728⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-5600404139075176481999383862),(-5600404139075175632329885935)⟩,⟨8644201654482852018127296279,8644201654482852867677679255⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-5217323124367957981273414670),(-5217323124367953136550840977)⟩,⟨10527796951721180199495816845,10527796951721185043953411664⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-4008871682533351187608709340),(-4008871682533332256928078797)⟩,⟨11510777116089436115416124566,11510777116089455045747564067⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-2371816588232989991292616807),(-2371816588232941750538277205)⟩,⟨11206440086598278540179518522,11206440086598326780565566893⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-912187930337287902836385356),(-912187930337208513828491819)⟩,⟨9448992310698052166123607465,9448992310698131554816353356⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-89799220608026063160348163),(-89799220607946011927842731)⟩,⟨6330279339953496429557343780,6330279339953576480581350603⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨63231680949030306671012478,63231680949064375284388498⟩,⟨2229087000459893529872728192,2229087000459927598415322443⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨12930476867483417628172283405,12930476867519362816805519245⟩,⟨119306089524767368666783050186,119306089524803313849972698446⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_10 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 10) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_10 (tableDensity true) (fullFactor true 1 10) density1_contains hk1_1_10_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-123292078802288882239055517993),(-123292078802288881142373235747)⟩,⟨(-136602046551131407682363458172),(-136602046551131406588709280922)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_10 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 10) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_10 1 10 ha1_1_10_contains + def realAnswer : RBox := ⟨(-110361601934805464610983234588),(-110361601934769518325467716502)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 10) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_10 +namespace hm1_0_1_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨44624558825802847958872533345,44624558825802873508661623778⟩,⟨(-53721168189922702528956448699),(-53721168189922676982234880072)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨121262545786867541004152673214,121262545786867598184520150143⟩,⟨(-163416735765346524349396382099),(-163416735765346467178152329166)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨162602584563325223553054697362,162602584563325281056672032269⟩,⟨(-275910845444794665278869255985),(-275910845444794607788263025500)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨154453754548884838695117843561,154453754548884876494643475615⟩,⟨(-382888246503062348097041229371),(-382888246503062310311044060810)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨96136092200956621605850100784,96136092200956637951475069464⟩,⟨(-468065960152968027215645606068),(-468065960152968010881970937672)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1321989808252649487770701531,1321989808252654342227635216⟩,⟨(-514515239806149781447950321200),(-514515239806149776603141171115)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-107318635600431429976130987325),(-107318635600431428747598126402)⟩,⟨(-513776119677806174511458669008),(-513776119677806173288266521853)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-206834844953403616514645975496),(-206834844953403616036220661567)⟩,⟨(-470027214213697423432071223995),(-470027214213697422952871819034)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-281115273444917540714802057880),(-281115273444917540392356290176)⟩,⟨(-396828361456377129238532165286),(-396828361456377128913861749573)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-323169780899866974106896752129),(-323169780899866973866422619726)⟩,⟨(-310439761733811227329181779341),(-310439761733811227089480869878)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-333021743433806733464386522586),(-333021743433806733273904697044)⟩,⟨(-224749753165603347507325943035),(-224749753165603347314754516857)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-314149866773103088013390297773),(-314149866773103087863329536876)⟩,⟨(-149421389211864293175102018364),(-149421389211864293020340617566)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-270981619302884965501184487778),(-270981619302884965398469023655)⟩,⟨(-89927844880951015842448108531),(-89927844880951015737093370679)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-208169628450338722771339246179),(-208169628450338722708817501344)⟩,⟨(-47906435100133771136512415199),(-47906435100133771074217981855)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-130828356583176750847999155572),(-130828356583176750815357039767)⟩,⟨(-21499794846822808333307688608),(-21499794846822808302002027761)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-44588556448814655441370902962),(-44588556448814655431348663958)⟩,⟨(-5879423339566343263008486417),(-5879423339566343253649612518)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-66781118432735656236662560534),(-66781118432735589407337402106)⟩,⟨84908521971531582551140790987,84908521971531649375156980688⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-180937878663969216777742094060),(-180937878663968956020169779566)⟩,⟨263132713863972354745008175418,263132713863972615488717814533⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-236770781654792193381026764815),(-236770781654791501077286945317)⟩,⟨458198173275209096235629870396,458198173275209788522963711934⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-199948277147282852106112957149),(-199948277147281139196071233985)⟩,⟨656797525124305898791832643463,656797525124307611691719647135⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-53836072360240889220477865785),(-53836072360237046692164314588)⟩,⟨819201033434421568544406685450,819201033434425411078015910836⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨183622234250070255296060707348,183622234250077465090585864816⟩,⟨891539346167614014760699521596,891539346167621224582092898642⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨454575012580040641494929860104,454575012580050901558318446028⟩,⟨834265387338433895891672475885,834265387338444156003400199445⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨680463002099799929744151195666,680463002099811671388896119634⟩,⟨650418632644666211342998459068,650418632644677953042042728878⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨799030689825657177585391007567,799030689825670411383697358464⟩,⟨390762496317796458492749033765,390762496317809692323543169645⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨792962933970823796808469092164,792962933970834424946848922234⟩,⟨129006151664571893047247294252,129006151664582521197410244843⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨689710792749519131281495318353,689710792749525292083221532888⟩,⟨(-73952180278308961987140524195),(-73952180278302801188556570835)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨537767246267550167769554968426,537767246267552984028192272444⟩,⟨(-190874876456044185789833061674),(-190874876456041369542650361758)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨380648896837858514074711563823,380648896837859632577059993983⟩,⟨(-225736070842486466643840702594),(-225736070842485348155370677710)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨243458882057831752145896483546,243458882057832169495702887380⟩,⟨(-198744978358882395457243360808),(-198744978358881978119576251639)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨132600074291535043353523974925,132600074291535192917723557850⟩,⟨(-132679172942858593120527117420),(-132679172942858443564328481385)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨41755835763931155973120501102,41755835763931193315273250732⟩,⟨(-46266610464914707489221136723),(-46266610464914670149834272361)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨53873805440931526070134918168,53873805440931526110305199418⟩,⟨(-19699143291372933550920029813),(-19699143291372933514454240723)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨157758986518842882664859393743,157758986518842882787768534515⟩,⟨(-70492183638116587984690940869),(-70492183638116587871584927848)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨246269596222543071437778754302,246269596222543071654080658413⟩,⟨(-153349714875060048964120717763),(-153349714875060048759477149157)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨298804870181694660799117982884,298804870181694661125075677479⟩,⟨(-281027014709047574526170275656),(-281027014709047574206545578068)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨285655840377582660900480078282,285655840377582661349477536445⟩,⟨(-449095800622508666189062741363),(-449095800622508665731592570649)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨177835691405910811188322122709,177835691405910811765058664089⟩,⟨(-627130411850967221677136278006),(-627130411850967221068107443578)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-33248783620712906347742412199),(-33248783620712905605840217899)⟩,⟨(-759732426730960058197976425203),(-759732426730960057394406985148)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-316399642321556522636243734576),(-316399642321556521598115813484)⟩,⟨(-785772997341628262673052181808),(-785772997341628261568499091250)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-600060717106857361376597493514),(-600060717106857359361786457716)⟩,⟨(-671813659246824745623231785909),(-671813659246824743570936507762)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-800580130006612012667731132923),(-800580130006612005170264531276)⟩,⟨(-438576494019798751493136261214),(-438576494019798743990499457494)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-864359706542927284361533273355),(-864359706542927250850597628208)⟩,⟨(-156982452012306587548247232386),(-156982452012306554058959980775)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-792577115234856891942848915141),(-792577115234856781141187246951)⟩,⟨86955678153798699113262639760,86955678153798809877413115489⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-630808778604651906115792871873),(-630808778604651667211537516319)⟩,⟨232505355197237166085373767379,232505355197237404948222597302⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-436202876374327316016690568561),(-436202876374326912936360542733)⟩,⟨262845520850580494678655080531,262845520850580897729286159911⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-248556053341072055179237467583),(-248556053341071612045820579146)⟩,⟨197296047681738667466406932630,197296047681739110584470506119⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-79833708579003312825223485768),(-79833708579003116762721424204)⟩,⟨72297993011854893521207559905,72297993011855089579064869773⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-12087156058231961220594436519),(-12087156058231931239902670689)⟩,⟨5888941170164318536715646719,5888941170164348517408647976⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-35780584534182407383007544964),(-35780584534182335914699488518)⟩,⟨19945954071649753519298212241,19945954071649824988071600640⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-57302678815139734664522056538),(-57302678815139661527420679831)⟩,⟨40612125974019455379984175291,40612125974019528519403293603⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-73048604694127150426394439142),(-73048604694127103901204840273)⟩,⟨71301044800041518873999250561,71301044800041565405630936111⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-76852734505766540724803708439),(-76852734505766521454062052343)⟩,⟨113089190762433575731253381460,113089190762433595015486722541⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-60852480582159994671545192498),(-60852480582159989446090390312)⟩,⟨162753310115432959697291048445,162753310115432964946249263434⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-18601392561979916084698267858),(-18601392561979914851894623386)⟩,⟨211236657467139018651177577181,211236657467139019911374361960⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨50138279437236541949824710890,50138279437236542388083945555⟩,⟨244425130929086166115350708156,244425130929086166574215978086⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨135496070815275647170732193881,135496070815275647486313011825⟩,⟨247896640188628828036130391099,247896640188628828360755868536⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨218042343189785960258084887439,218042343189785960583104513337⟩,⟨214573563799761309903299293668,214573563799761310222919368005⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨275472400064936391503786418234,275472400064936391854748589298⟩,⟨150624786862622530969623419984,150624786862622531301019923116⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨292382367470252982987323789448,292382367470252983339335690669⟩,⟨74615420669948991737575813300,74615420669948992060242224567⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨266597559003474138377962328060,266597559003474138699463332729⟩,⟨9403296282576266246966833634,9403296282576266538042339912⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨207698170539168382157210146506,207698170539168382419851432603⟩,⟨(-28161971678532024804166078701),(-28161971678532024561683090673)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨129694483637214158087635389992,129694483637214158258836779104⟩,⟨(-33496426773237269270366586311),(-33496426773237269109935224518)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨43819923020916129973498974674,43819923020916130032663397927⟩,⟨(-14190976473156650116214969440),(-14190976473156650060365837657)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨2682562980158284511473311921,2682562980158307808202854779⟩,⟨(-525251632524527625967057529),(-525251632524504328868646248)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨7983496216876368927905361909,7983496216876462335311063675⟩,⟨(-2094111657074074432688237985),(-2094111657073981024229942793)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨12945778971285690125367115378,12945778971285953482883657054⟩,⟨(-5199683363925009381126627578),(-5199683363924746022030677910)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨16911358588387039755675448131,16911358588387761111940557543⟩,⟨(-10735774746528734801785193515),(-10735774746528013443709346053)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨18677784301399432243845184667,18677784301401316344108077581⟩,⟨(-19175450608632932447935492239),(-19175450608631048346092477557)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨16563228546280012767279132878,16563228546284374912329940309⟩,⟨(-30110598813386270357736838808),(-30110598813381908211987807677)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨8882198197999856954243548773,8882198198008038880030630582⟩,⟨(-41846250260773418120833048901),(-41846250260765236195992487783)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-5107925073111583233907058767),(-5107925073100098165841900796)⟩,⟨(-51404261221491696415629302554),(-51404261221480211350912447156)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-24166632617884836466818818966),(-24166632617872921445377862993)⟩,⟨(-55278916164415742283466329553),(-55278916164403827268331940717)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-44692526024751971496820916327),(-44692526024742862806522818966)⟩,⟨(-50965071961295873999075266711),(-50965071961286765317997452437)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-61606470684387827536063263171),(-61606470684381241176944116531)⟩,⟨(-38603085413140534858526837018),(-38603085413133948508006794051)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-70265575379548770866448227026),(-70265575379544671842235860386)⟩,⟨(-21595318822298568405435477904),(-21595318822294469387371206450)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-68283256494687133672003436255),(-68283256494685009629978766408)⟩,⟨(-5402854886344917278674042397),(-5402854886342793240269268981)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-56159786751032499710376730543),(-56159786751031518041568267569)⟩,⟨5010499815808000543470077560,5010499815808982210652461191⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-36510924257894568188242721398),(-36510924257894158809821388795)⟩,⟨7469909868689244241482229450,7469909868689653619430929359⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-12606461791238395075223787499),(-12606461791238284325247343724)⟩,⟨3331854801900264905170921208,3331854801900375655087535664⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-231691873896070432961555625),(-231691873896070432843741588)⟩,⟨(-29957148367983726341772321),(-29957148367983726245264179)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-708361478299173241154267256),(-708361478299173240787556272)⟩,⟨(-32738607705657300720237830),(-32738607705657300421204274)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1213960205350854958480858235),(-1213960205350854957833094904)⟩,⟨136417824946713834402883071,136417824946713834931129934⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1730892229860753646058294109),(-1730892229860753645032794977)⟩,⟨584292604148749114347959682,584292604148749115212460303⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-2177550843881000644277811002),(-2177550843881000642667991312)⟩,⟨1382568810202731714075646477,1382568810202731715519313055⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-2384817070764130972925552443),(-2384817070764130970433744595)⟩,⟨2533248154385610398669536255,2533248154385610401013547116⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-2122270377676913033489032314),(-2122270377676913029358385128)⟩,⟨3939456009131795249766938239,3939456009131795253791253610⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1194090312449728114376620053),(-1194090312449728104415733660)⟩,⟨5381199775236891761812798483,5381199775236891771726763927⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨438240707000352601221552901,438240707000352652918827860⟩,⟨6528241462111126663575801941,6528241462111126715281449535⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2567018172846590094712457817,2567018172846590459326800026⟩,⟨7038449883311349256269298172,7038449883311349620914253194⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨4736821486468933839339202808,4736821486468935890098382950⟩,⟨6719933605399598719562337769,6719933605399600770331627877⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨6359100437618502472970129817,6359100437618510340545859235⟩,⟨5652360847965154259400357466,5652360847965162126938496878⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6916883509607059667486709688,6916883509607079268587397008⟩,⟨4159250073995205753313289413,4159250073995225354328913631⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨6170306698751060978122949242,6170306698751093557740419759⟩,⟨2639014117402339604384937441,2639014117402372183898331720⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨4236210000794222443701634551,4236210000794259061978721562⟩,⟨1373599551349941661537720192,1373599551349978279736569558⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨1503869892998496692704757162,1503869892998513280192183596⟩,⟨413533190784189852803377633,413533190784206440262246972⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-2109399772950272262346795134),(-2109399772927821608198229682)⟩,⟨(-353159785202631620171340853208),(-353159785202609169516296464993)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 11) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_11 (tableDensity false) (fullFactor true 1 11) density0_contains hk1_1_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨22252347638244984728453643050,22252347638244985466052715907⟩,⟨(-92334771656312833480284752362),(-92334771656312832745290720003)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_11 1 11 ha1_1_11_contains + def realAnswer : RBox := ⟨20142947865294712466006847916,20142947865317163857954486225⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_11 +namespace hm1_1_1_11 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_11 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨8776977595349205620343797959,8776977595349226525293090772⟩,⟨(-8099774363504373681359824199),(-8099774363504352775676700469)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨24550269105116833223891358974,24550269105116879977303791337⟩,⟨(-24885524712130759877154835509),(-24885524712130713121523590770)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨35012490041956786452130264429,35012490041956833400905956097⟩,⟨(-42564169748086071363969716248),(-42564169748086024411883398143)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨37102747902849778741038523914,37102747902849809490738798683⟩,⟨(-59590212319239357431208933797),(-59590212319239326677876912502)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨29234113351479095624696679110,29234113351479108781324500206⟩,⟨(-73071176505361365200625068409),(-73071176505361352040765417635)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨12536331755449887252493228924,12536331755449890995534867232⟩,⟨(-80387647491128465889882226640),(-80387647491128462144668508609)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-9030806868174284777767715553),(-9030806868174283984406743130)⟩,⟨(-80430934421035183782236703587),(-80430934421035182987987372784)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-30394316666230763392096801471),(-30394316666230763198122303218)⟩,⟨(-73830672204961223597246447831),(-73830672204961223403347816795)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-47463057332937516561136810962),(-47463057332937516464311350438)⟩,⟨(-62529330989152669143963351461),(-62529330989152669048441328780)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-58022975976077205556085630235),(-58022975976077205485541383551)⟩,⟨(-48965123911986093110862878441),(-48965123911986093043184287012)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-61511678804009002827543071982),(-61511678804009002771403482339)⟩,⟨(-35263054392402877011555047383),(-35263054392402876958239055891)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-58492821542816878840292240004),(-58492821542816878796177534238)⟩,⟨(-22883958172117195037718806967),(-22883958172117194995955687745)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-50232880232834328192305771311),(-50232880232834328161053688485)⟩,⟨(-12786946845446773137632102390),(-12786946845446773108804235375)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-38243649378343353082186359257),(-38243649378343353062262482250)⟩,⟨(-5657192199840707918443804010),(-5657192199840707900900146997)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-23850892504304077990626275571),(-23850892504304077979764614420)⟩,⟨(-1701631244525151996527852851),(-1701631244525151987433870819)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-8096486085161748251674167296),(-8096486085161748248249092465)⟩,⟨(-249023448730312163084446997),(-249023448730312160314361423)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-15460261146849999071114932295),(-15460261146849944102688408367)⟩,⟨6695643579109214461047246862,6695643579109269430154464789⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-43477067043907693755838604110),(-43477067043907479144217893206)⟩,⟨22912127206475772502284995364,22912127206475987115677344619⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-62348713384040661119928663626),(-62348713384040090766177334466)⟩,⟨46087543817577678496575038062,46087543817578248852433139731⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-65588305951594817652790401679),(-65588305951593404933360480967)⟩,⟨76149290440166037816457194667,76149290440167450537249152610⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-48612164162024660360152757892),(-48612164162021488056841322665)⟩,⟨107337585650418174773956636940,107337585650421347076793044181⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-12270462363058991879482271734),(-12270462363053034408383655907)⟩,⟨129478721736970193640246102606,129478721736976151108294773700⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨35187872054452623886146852682,35187872054461109316564641443⟩,⟨132667689505854028224671118121,132667689505862513649225594170⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨80442551184636555988716983926,80442551184646271465245608346⟩,⟨113270212318742836913608260431,113270212318752552383221355636⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨111134541435374220258231425105,111134541435385170028320780256⟩,⟨76715984502461934960951202323,76715984502472884726691302949⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨121539146644830048488257748806,121539146644838837451012632201⟩,⟨34565032093699526746698879651,34565032093708315707762356042⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨113824788689933933051430866527,113824788689939022584792690132⟩,⟨(-1622659332852706372279966046),(-1622659332847616838490578725)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨94769273951433444870745223398,94769273951435768249915263477⟩,⟨(-24962236980875352181574248285),(-24962236980873028800724811878)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨71356693200868447530110416307,71356693200869368839290629741⟩,⟨(-34209333065881314961127429575),(-34209333065880393649876676100)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨48263153610396722307237366380,48263153610397065532309689995⟩,⟨(-31917250601489873635559549747),(-31917250601489530408639423251)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨27468432364603026233140816365,27468432364603149064268458694⟩,⟨(-21916898506949653273682922151),(-21916898506949530441313200977)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨8865671536712176202769812463,8865671536712206844775818615⟩,⟨(-7735956259468206733516971556),(-7735956259468176091074160105)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨12689660591190884492698109319,12689660591190884506581806407⟩,⟨2586393855911113765892711620,2586393855911113779605868100⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨38700720805649458991170782115,38700720805649459034411723217⟩,⟨5290844531168865597376067428,5290844531168865640149455904⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨65420875345405926952613353393,65420875345405927029032967899⟩,⟨670597505840920088229421758,670597505840920164099156942⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨89808567019529985351654344980,89808567019529985465459067468⟩,⟨(-15462933791986476462878364664),(-15462933791986476349378261216)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨104959333238486951822794273810,104959333238486951974913202061⟩,⟨(-45044729878577692063281113037),(-45044729878577691910857456316)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨101927869476251726434914246101,101927869476251726621258499937⟩,⟨(-85225212045733365476474726010),(-85225212045733365288957469711)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨74294816741163668652141529358,74294816741163668875137802405⟩,⟨(-126559202311253737140364313677),(-126559202311253736914978768923)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨23488170287251561687190188032,23488170287251562014898386706⟩,⟨(-154925337897006160381670164531),(-154925337897006160051412240455)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-38873651082565653170162236382),(-38873651082565652194463172614)⟩,⟨(-158192558298036110220165526900),(-158192558298036109243198670159)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-94743064683213019668322816552),(-94743064683213014329229950482)⟩,⟨(-133735637782959390500119549914),(-133735637782959385160757065341)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-128276557176866744662173845874),(-128276557176866718158919709620)⟩,⟨(-90641833041224804720155259182),(-90641833041224778217048729394)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-133409021290966447172667237827),(-133409021290966357603257271973)⟩,⟨(-44395947792655848680163180858),(-44395947792655759110978553079)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-115042077184656866868124314622),(-115042077184656672655942920345)⟩,⟨(-8499997899850393613763738603),(-8499997899850199401786358576)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-83853791589966369397613683976),(-83853791589966040871508591835)⟩,⟨10630596002440069262250589794,10630596002440397788274302197⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-49379291173428362194893914731),(-49379291173428000585546950720)⟩,⟨13680072304920946715608218799,13680072304921308324944090344⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16117959223021889365992576241),(-16117959223021729296630029740)⟩,⟨5821305599138370081283703469,5821305599138530150656027843⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-4415785288462569297877871606),(-4415785288462544109722317899)⟩,⟨(-837099448000427087590611543),(-837099448000401899431591697)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-13365318176612914627856512585),(-13365318176612854626112566450)⟩,⟨(-1813056395068042208147968526),(-1813056395067982206443189605)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-22460738498585091659566721219),(-22460738498585030346548904762)⟩,⟨(-649355304464522355439306422),(-649355304464461042650739749)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-31181389796071362738400098021),(-31181389796071323829656282370)⟩,⟨4121865271987855281964181313,4121865271987894190052260320⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-38202864781922455708800480599),(-38202864781922439661813105717)⟩,⟨13686920735723499944526231279,13686920735723515990145185962⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-41388829688750592922031940467),(-41388829688750588621828267305)⟩,⟨28258335845535175111443129679,28258335845535179409295339579⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-38206957099491116565525690314),(-38206957099491115608083197181)⟩,⟨46288428305240420281236589357,46288428305240421235978589892⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-26800153882825884530945482779),(-26800153882825884259970348163)⟩,⟨64213193252633629643225555124,64213193252633629912258282385⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-7474847285725131457967492013),(-7474847285725131315355394297)⟩,⟨77223294058292395733969378888,77223294058292395875871348486⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨16397719717925542834661916774,16397719717925542961672175831⟩,⟨81095853073784189941344211821,81095853073784190069096643713⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨39040776325906097549626811305,39040776325906097677731346489⟩,⟨74328044272399319581583319385,74328044272399319711720742175⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨54426889938925137355307586202,54426889938925137479075693863⟩,⟨59148631927581689511187340630,59148631927581689637815060767⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨58693163245917987194524869734,58693163245917987306299003819⟩,⟨40477280340487143815402129451,40477280340487143930055235534⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨51328835026851557456939322701,51328835026851557550143399352⟩,⟨23436331255482904984357773120,23436331255482905079424844780⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨34614882658171957376478611542,34614882658171957438246936067⟩,⟨11010463654969952165324231953,11010463654969952228066927441⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨12164889404158227390237194296,12164889404158227411770700094⟩,⟨3065696236783775689903990351,3065696236783775711732630326⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨871414043008783110934889466,871414043008802257250183101⟩,⟨(-217456414571613299283974153),(-217456414571594153043737066)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨2645381692224924154106012467,2645381692225000926057440838⟩,⟨(-814795372099338336540306389),(-814795372099261564809707211)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨4450899452707476456675222196,4450899452707692940003103498⟩,⟨(-1891525491055183914233724296),(-1891525491054967431247501000)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨6116546819714843631566452425,6116546819715436690280214989⟩,⟨(-3736120507913474084605622667),(-3736120507912881026302462247)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨7223105508789379969471543480,7223105508790929158151823135⟩,⟨(-6561167978268111848486712141),(-6561167978266562660191005342)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨7138947192104170529109739093,7138947192107757255630600405⟩,⟨(-10397933651658125688333850382),(-10397933651654538962033168889)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨5202124802959191594946831362,5202124802965917635479034377⟩,⟨(-14928068833367923823761575272),(-14928068833361197783095630615)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1019946362973970788576738378,1019946362983407583078232290⟩,⟨(-19371971203069439748468509748),(-19371971203060002953287779614)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-5186907319051720993091829637),(-5186907319041938694725147138)⟩,⟨(-22615676156632004304911301441),(-22615676156622222005224204382)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-12364406763280829805713417099),(-12364406763273359497347473249)⟩,⟨(-23617502802723213737030238803),(-23617502802715743426799135328)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-18770138334727732359894687984),(-18770138334722337695937907790)⟩,⟨(-21906181329095465746060343277),(-21906181329090071080420207788)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-22580334058461962139509402920),(-22580334058458609254988236402)⟩,⟨(-17859429110128048226711190422),(-17859429110124695340987430199)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-22681599558945903317494002478),(-22681599558944168113682404687)⟩,⟨(-12591295445683462444151590719),(-12591295445681727239628736808)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-19067044132007688393252285360),(-19067044132006887284239281373)⟩,⟨(-7495808943634610906298441812),(-7495808943633809796960562197)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-12577709949998172159071791378),(-12577709949997838329477925956)⟩,⟨(-3592049808806452619069218395),(-3592049808806118789373301982)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-4376304291793552083140419547),(-4376304291793461806549025945)⟩,⟨(-1009660701805701062008307022),(-1009660701805610785400598717)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-6924522634493180850987991),(-6924522634493180788552335)⟩,⟨(-561245939787623906262039),(-561245939787623859325346)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-20265273592529679115187353),(-20265273592529678921997143)⟩,⟨4236639068485512583001064,4236639068485512726461865⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-23259620121738981440949392),(-23259620121738981106234578)⟩,⟨29114362394373955656232704,29114362394373955901046337⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨16406270495891498308894942,16406270495891498834083023⟩,⟨96804588621648461008359946,96804588621648461407639350⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨152786801508691817500666402,152786801508691818360281267⟩,⟨242760379247658385272745388,242760379247658385994395817⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨442363617244677771840961958,442363617244677773272872337⟩,⟨500018482626416487352842134,500018482626416488651234051⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨923914309524228637783549382,923914309524228640438543172⟩,⟨860708663033613380395706502,860708663033613382943510813⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1606632066433395873941881639,1606632066433395881350477608⟩,⟨1249936799561209707934942715,1249936799561209715290918881⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2447491159989434213969625854,2447491159989434255709192005⟩,⟨1540569392215268446266246879,1540569392215268488026530005⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨3324061849641402540342241806,3324061849641402838133078588⟩,⟨1599995379139609305928434939,1599995379139609603809120525⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨4041599884475831135846401606,4041599884475832810607266962⟩,⟨1352003874406666478662137610,1352003874406668153561956185⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨4393598341021615084163007447,4393598341021621508931349662⟩,⟨834903556220859348718244000,834903556220865773651868875⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨4238882476522541613169117746,4238882476522557625958048377⟩,⟨222969868484976301615399793,222969868484992314572130840⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨3537741701071121936871941814,3537741701071148565240641357⟩,⟨(-236157023759149111092132539),(-236157023759122482586902061)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2349627619945183008426855459,2349627619945212949134204987⟩,⟨(-363471821397045673851704752),(-363471821397015733068668259)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨823333797374903344539287119,823333797374916909901767389⟩,⟨(-165578276566432942903490411),(-165578276566419377518025745)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨11174216474641056262317669172,11174216474659548210119571674⟩,⟨(-78528003475889803674855951788),(-78528003475871311726259565521)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_11 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 11) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_11 (tableDensity true) (fullFactor true 1 11) density1_contains hk1_1_11_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-29099223834628057917145859262),(-29099223834628056952593225527)⟩,⟨120745470627486012051534018466,120745470627486013012680060781⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_11 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 11) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_11 1 11 ha1_1_11_contains + def realAnswer : RBox := ⟨(-17925007359987001654928190090),(-17925007359968508742373653853)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 11) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_11 +namespace hm1_0_1_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-45142663436531994112002159849),(-45142663436531970804899366331)⟩,⟨20597501342470760640764892017,20597501342470783946977806376⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-127858595233653176517916087982),(-127858595233653123119769827568)⟩,⟨68314367998637001490644781900,68314367998637054885809574980⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-187674964861905190566368285471),(-187674964861905140095877163316)⟩,⟨131759788806327834449696046826,131759788806327884914487680293⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-210816675831615521170701407643),(-210816675831615492638109193863)⟩,⟨210245197926955656338674580438,210245197926955684862645490128⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-189452789330180335644181898498),(-189452789330180325407397168753)⟩,⟨291417389180657562541659729365,291417389180657572766761864912⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-126456356946110964925982700330),(-126456356946110961907845894213)⟩,⟨356059475831320951856243009248,356059475831320954862462283889⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-36140925056345033223345599765),(-36140925056345032335150658838)⟩,⟨387506724929830484614864441522,387506724929830485494224838854⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨60680663147253083484473452365,60680663147253083851471495403⟩,⟨379441237726319343838874671310,379441237726319344202523870646⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨144484724483921421906813445854,144484724483921422164151434052⟩,⟨337164757032242369614987972481,337164757032242369872179949039⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨202681174803181452141926954491,202681174803181452342228976153⟩,⟨273245940225598300186217007788,273245940225598300385158770908⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨230648908340292409992922880940,230648908340292410146211610572⟩,⟨201841044472795260335531830672,201841044472795260489125879014⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨229574485529870567551917546084,229574485529870567672525464731⟩,⟨134841209085176052093609413413,134841209085176052217323204430⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨203725916730968605247394805855,203725916730968605330090197572⟩,⟨80186037313055343604478882376,80186037313055343689168911783⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨158652884464522837798037787667,158652884464522837847951900030⟩,⟨41377823128886184979825553690,41377823128886185029600357200⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨100264955133257875388764140479,100264955133257875414515253254⟩,⟨17640047325668466099221242541,17640047325668466123955724981⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨34230892611610270761947866267,34230892611610270769788638869⟩,⟨4592740585997442061496840340,4592740585997442068827726696⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨63892191853822601401367344596,63892191853822644709731439343⟩,⟨(-6275325395479974009070023121),(-6275325395479930702544839965)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨187815611870747606886670693601,187815611870747767973175787064⟩,⟨(-31815725812940397504040209618),(-31815725812940236424196157683)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨295622027814894910412878319911,295622027814895299276619211165⟩,⟨(-92985313622025759917272148892),(-92985313622025371067974796035)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨365223131633574050492046353964,365223131633574880222276962293⟩,⟨(-201011702509364524125577098402),(-201011702509363694420955924414)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨367893884187162489679373811416,367893884187164346795319122622⟩,⟨(-346196973784452769542143394025),(-346196973784450912457805947915)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨282927523304031236858307600557,282927523304035603101827827879⟩,⟨(-493512127761890074885249569662),(-493512127761885708663819250877)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨116757268560620528723382245461,116757268560628300985534260028⟩,⟨(-592545410781758801490591588893),(-592545410781751029234903455350)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-89536228232008990268624914783),(-89536228231999281133122348814)⟩,⟨(-602496094995690932999100079235),(-602496094995681223852899004986)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-275829356790335557221078523208),(-275829356790327109438628340741)⟩,⟨(-516890953577186299379475154136),(-516890953577177851572696220118)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-393101527417019347388811781453),(-393101527417013861274477798407)⟩,⟨(-367688441629204386738495555862),(-367688441629198900595183846432)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-425041847997992666286858514053),(-425041847997988993048755570085)⟩,⟨(-205310359430582918829623703744),(-205310359430579245573737406955)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-386936994705132566250878239851),(-386936994705130626954150868442)⟩,⟨(-72173911172338520073136784031),(-72173911172336580768690279013)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-308471094240564720712930878255),(-308471094240563863231292161488)⟩,⟨11426270414500771700460841900,11426270414501629183452762321⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-216312504770165397616989134271),(-216312504770165051237035429325)⟩,⟨45683105341827109994254585947,45683105341827456372707841090⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-125789991005527671161814435471),(-125789991005527540177430152663)⟩,⟨42297972588459044068390464328,42297972588459175050946554919⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-41013975979336010050654593704),(-41013975979335976436024661114)⟩,⟨16528105555626965886835650124,16528105555626999500711277886⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-21129694577397183556766257904),(-21129694577397183535111301835)⟩,⟨(-18282539342529510957654769266),(-18282539342529510936321198486)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-67787944245877071116289645933),(-67787944245877071049862920794)⟩,⟨(-50407283300874027282095520372),(-50407283300874027217431744339)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-125753954355954928857034630394),(-125753954355954928739415654918)⟩,⟨(-67776269491467026801769325750),(-67776269491467026689700245457)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-195927316915047939875299698438),(-195927316915047939691315213429)⟩,⟨(-57240029873529343455947212513),(-57240029873529343285007237754)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-268386212291152270445293747816),(-268386212291152270174375531975)⟩,⟨(-5049078817577033122020158440),(-5049078817577032875760604371)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-320033451401198932967169065425),(-320033451401198932580148966152)⟩,⟨95672579984822832227260488523,95672579984822832585248652767⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-319983993239839881767874515592),(-319983993239839881232090039956)⟩,⟨234431332009546653670599223346,234431332009546654187482578600⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-245171501521615554329784032199),(-245171501521615553604414436375)⟩,⟨377742641930549304255029632544,377742641930549304978222831356⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-99181972989129695514867148875),(-99181972989129694305859674955)⟩,⟨478125778417920456322784843539,478125778417920457548890086375⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨80974840656388890861191260556,80974840656388894377650365012⟩,⟨497899039705834749342961984231,497899039705834752892685588462⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨240104461923965508789082137732,240104461923965525181474370823⟩,⟨432139899603473384967892058823,432139899603473401392106626509⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨333057240276032472999373461556,333057240276032541966420557184⟩,⟨311612265421871727279609248742,311612265421871796263472391508⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨344341886658190047801770667487,344341886658190231028742891149⟩,⟨183062639260563047985247395953,183062639260563231217409046531⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨286732400661979375012920699176,286732400661979680332817857066⟩,⟨83600681773033299409702152645,83600681773033604728343354177⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨185575972073497570628246883547,185575972073497877808934988302⟩,⟨26921871050684267438429312121,26921871050684574616239198063⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨63716314793244997866724998248,63716314793245127900375288636⟩,⟨4686822671421434419722051119,4686822671421564452055555423⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3799825168000668952053489029,3799825168000680429445656582⟩,⟨3910085392422703389332305383,3910085392422714866305521641⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨12292290324839670595015206789,12292290324839697596469591793⟩,⟨11253910043719250084822536553,11253910043719277084816086741⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨23287655622044674479384024844,23287655622044701350363016447⟩,⟨16873462190986080049420973651,16873462190986106917298539797⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨37784679299702025433509893507,37784679299702041743525722283⟩,⟨18770686228313435133977778936,18770686228313451438312661446⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨55439894582647879529077190398,55439894582647886175186524376⟩,⟨14070032844849496592183887106,14070032844849503229732070714⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨73732500298461918550357277099,73732500298461920921720107999⟩,⟨(-354123357451027543553917820),(-354123357451025180494554380)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨87600713519740762387062440361,87600713519740763046988665551⟩,⟨(-26231386435250615299045302968),(-26231386435250614644867623200)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨90436889011991699376296562227,90436889011991699596593670826⟩,⟨(-61694017052273718613420363429),(-61694017052273718393957035583)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨76958663313713068451936389151,76958663313713068611234457325⟩,⟨(-100005184747809033034142352821),(-100005184747809032868749202655)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨46943511846851991914530256765,46943511846851992078883392769⟩,⟨(-130931386754017951010421760015),(-130931386754017950832669862128)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨7178364096742294866915251524,7178364096742295042335115840⟩,⟨(-145012319943117695183557096902),(-145012319943117694991079662396)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-30569472379626158191325696991),(-30569472379626158003480640693)⟩,⟨(-138374050038894619709420148829),(-138374050038894619509597442970)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-54788859080428546222281711261),(-54788859080428546043047736883)⟩,⟨(-114515306766029948361389502988),(-114515306766029948175758207853)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-59190072271190718933976883615),(-59190072271190718786715128709)⟩,⟨(-81584379797982748702900586995),(-81584379797982748553353129057)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-44396133653418113918807774789),(-44396133653418113822631241339)⟩,⟨(-47318279960066666155367553524),(-47318279960066666058959701534)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-16343967216312406852333816733),(-16343967216312406819063573383)⟩,⟨(-15309692516014687911004906240),(-15309692516014687877870785586)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-337057793296424509417261029),(-337057793296415533768692063)⟩,⟨(-882837851377331959106341290),(-882837851377322983553525152)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1193871393256449634310094543),(-1193871393256413838190784737)⟩,⟨(-2600352695682101957384635845),(-2600352695682066161530636330)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-2586621722951921092456322521),(-2586621722951821169631865712)⟩,⟨(-4118314427394606522165402061),(-4118314427394506599710152129)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-4807767413207943181462830765),(-4807767413207673269505529699)⟩,⟨(-5141869748024399249929426421),(-5141869748024129338323527561)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-7968335748874059645261054060),(-7968335748873367139740594452)⟩,⟨(-5182388949937659760405753688),(-5182388949936967255030946833)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-11817349493865066090970657371),(-11817349493863499153909525715)⟩,⟨(-3604679446256453329565616756),(-3604679446254886392186810596)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-15594528245861321178861802482),(-15594528245858471055715649950)⟩,⟨161396996870930656843971163,161396996873780781061587126⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-18071781741971922523226302181),(-18071781741968091639818864384)⟩,⟨6235118214691880142985985050,6235118214695711028493600523⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-17920716842200634251864874140),(-17920716842196775479087613413)⟩,⟨13895320005265788164301569136,13895320005269646940247745384⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-14380492856462493227467420109),(-14380492856458643397941138679)⟩,⟨21512350298566982116764071516,21512350298570831949183090728⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7905466471264768829753502089),(-7905466471261803622680665395)⟩,⟨27034680625023784649922128359,27034680625026749858968393993⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-300697173655460613534010202),(-300697173653700149389247403)⟩,⟨28865220984506552267721885186,28865220984508312732750410156⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨5927554196572048796792895725,5927554196572926199715976839⟩,⟨26559183816819223583277486736,26559183816820100986136932081⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨8722579789197019267938792568,8722579789197411909792391192⟩,⟨20856687105845798528740394983,20856687105846191169986434598⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨7405669986094753709632775793,7405669986094913555415851779⟩,⟨13088412645071490629114023973,13088412645071650474253650227⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2868874672947147701487911318,2868874672947190381028984651⟩,⟨4431323365096420669006787316,4431323365096463348280767795⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-5355568904360919429499983),(-5355568904360919401179774)⟩,⟨70234422737412931541048938,70234422737412931576278232⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1801145120538050006406208,1801145120538050094178837⟩,⟨214308831919216583773279618,214308831919216583882989304⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨62997061798139167493102615,62997061798139167653346905⟩,⟨365565394081467353710992111,365565394081467353908608596⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨212566585634191172934288286,212566585634191173216157251⟩,⟨516582013442953408597981967,516582013442953408925749275⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨474137218269499984088047891,474137218269499984559359637⟩,⟨639115065424969949833282046,639115065424969950350802351⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨847990288417614993499184810,847990288417614994265408977⟩,⟨676593894141784436035933283,676593894141784436841168821⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨1299442234916184214147940673,1299442234916184215462816425⟩,⟨552459211695098114823701003,552459211695098116162944915⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨1750195435496424006350213317,1750195435496424009568491964⟩,⟨202246214005194709001776717,202246214005194712224828728⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨2084400534517786552546287255,2084400534517786569122469366⟩,⟨(-383418835410352619516753871),(-383418835410352602952200950)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2185692466419393330157278443,2185692466419393445343796625⟩,⟨(-1127142274407189014296384165),(-1127142274407188899125086128)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨1997245344135613709938284781,1997245344135614345157975796⟩,⟨(-1865857173372355838320149192),(-1865857173372355203104020258)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1566199746745801277112825614,1566199746745803650191973551⟩,⟨(-2394695516800983770246559519),(-2394695516800981397151316731)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1030488868177758991328032772,1030488868177765495424349895⟩,⟨(-2540561844911256747438757395),(-2540561844911250243311024017)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨548948620477989857782610856,548948620478002466293680174⟩,⟨(-2231114778214498512985130225),(-2231114778214485904441334719)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨222874249563630363086621634,222874249563644581266130409⟩,⟨(-1516787977776072550358935779),(-1516787977776058332155938950)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨52814257109558379359716763,52814257109564786921138998⟩,⟨(-535838470600122144897017074),(-535838470600115737327189293)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-3802376523168135102817142537),(-3802376523156363537200619409)⟩,⟨230950622631600930207933659792,230950622631612701767336677694⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 12) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_12 (tableDensity false) (fullFactor true 1 12) density0_contains hk1_1_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-49222994366024818966146916102),(-49222994366024818360832591326)⟩,⟨29552562733597423688780222158,29552562733597424292209242789⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_12 1 12 ha1_1_12_contains + def realAnswer : RBox := ⟨(-53025370889192954069064058639),(-53025370889181181897933210735)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_12 +namespace hm1_1_1_12 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_12 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-8117355137760872566224584476),(-8117355137760853495001339764)⟩,⟨2472996864984305633851732474,2472996864984324705287785012⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-23389157640942011589706603268),(-23389157640941967925030833543)⟩,⟨8550469095258519331271635021,8550469095258562996675217232⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-35426332418619732745992704954),(-35426332418619691540649108384)⟩,⟨17387781152864062823962878611,17387781152864104030773441175⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-41477949614347414228612030275),(-41477949614347391024773087489)⟩,⟨29021511067668219018610542547,29021511067668242224904020599⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-39211529495664002078683655610),(-39211529495663993870764819137)⟩,⟨41708323200225334141680116721,41708323200225342353118650667⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-28297310950862476545353774718),(-28297310950862474264849903312)⟩,⟨52610927050558216261870221197,52610927050558218545716297230⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-11159610561431434187215978622),(-11159610561431433647062435881)⟩,⟨58952670392025858382239548090,58952670392025858924688333320⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨8021703830771225479144484657,8021703830771225621692607754⟩,⟨59190132146868116914540416284,59190132146868117058430156188⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨25109673688626532770713254190,25109673688626532845675270122⟩,⟨53616913032692956786535797342,53616913032692956861752489500⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨37252333805915760224038284952,37252333805915760280877674905⟩,⟨43981081917674543630401830846,43981081917674543686001884082⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨43202013100927472476416307143,43202013100927472521144168108⟩,⟨32546517104255419154652248097,32546517104255419197645578403⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨43075399386294159301001368165,43075399386294159336214389100⟩,⟨21340708160498038041725605445,21340708160498038075407706447⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨37927393309687228079803443955,37927393309687228104724930632⟩,⟨11890932781657848021787734932,11890932781657848045014013352⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨29215872223355019764349568159,29215872223355019780090924462⟩,⟨5189666263754321981089484404,5189666263754321995072233021⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨18297925527119265597127298953,18297925527119265605612889836⟩,⟨1512985646725185357064783971,1512985646725185364208825076⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨6217134587334201568037706706,6217134587334201570693930760⟩,⟨205347695766948012073996633,205347695766948014228051585⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨9231237720708417654477164232,9231237720708453272349627689⟩,⟨3878270583395340538800183331,3878270583395376156896468727⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨27867166526768879977162574781,27867166526769012538263254844⟩,⟨9099360486006865834007024213,9099360486006998395916725741⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨46043261629188964249301025935,46043261629189284565348319592⟩,⟨7079340303172931665040710373,7079340303173251982840699013⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨60784912962300249791922444784,60784912962300933983910064771⟩,⟨(-5340636283794507356322805500),(-5340636283793823161189446364)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨66901720152890242662761867419,66901720152891775690762300953⟩,⟨(-27926759519696680030042606980),(-27926759519695146998105270862)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨59311659486538521766551685746,59311659486542129483692260341⟩,⟨(-55558153381840904232434986263),(-55558153381837296512485036484)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨36689775915103986099075935288,36689775915110414035125156666⟩,⟨(-79149166652950664710078831772),(-79149166652944236773060405377)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨3843792675625515560681292987,3843792675633549256682164663⟩,⟨(-89808489057819939561336634011),(-89808489057811905866453688147)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-29745691163998947401721903477),(-29745691163991957726984041788)⟩,⟨(-83823716949092346538644323850),(-83823716949085356866969764286)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-54739880332146753826346563056),(-54739880332142217351371811906)⟩,⟨(-64576877455761046338919782550),(-64576877455756509867859523934)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-66346673147313318328951650822),(-66346673147310284040812600209)⟩,⟨(-39986805889812286674358779811),(-39986805889809252388716708373)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-65191879080306687590528635058),(-65191879080305087769055077868)⟩,⟨(-17889062525155397818315665489),(-17889062525153797997941041093)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-55126613749037343046358612354),(-55126613749036636761790195951)⟩,⟨(-2821949411620011078911902890),(-2821949411619304794537120096)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-40468865784730580085694109176),(-40468865784730295229758687751)⟩,⟨4380566184271949828618285670,4380566184272234684779377677⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-24304541258834923928163525065),(-24304541258834816354610693299)⟩,⟨5234944519685315553028965179,5234944519685423126861752315⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-8059261408148155120589248405),(-8059261408148127536337583184)⟩,⟨2177930269406714096333121873,2177930269406741680702425912⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1899715225949630140469121509),(-1899715225949630132783225304)⟩,⟨(-6015388324679260514142058961),(-6015388324679260506469374802)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-6999976199389480398817591440),(-6999976199389480375138021797)⟩,⟨(-17767063101274084307223190123),(-17767063101274084283621934208)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-15706536498017965271241739694),(-15706536498017965230262990792)⟩,⟨(-28128023639504952937052136748),(-28128023639504952896318083540)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-29291971724221285840067309394),(-29291971724221285779396655306)⟩,⟨(-34616961273695768960644899697),(-34616961273695768900531189295)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-46955320010362981226352178726),(-46955320010362981144535398397)⟩,⟨(-33364102782068497127632820906),(-33364102782068497046799227653)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-64878622664772499201580566741),(-64878622664772499092121080429)⟩,⟨(-20616614523766068341336514638),(-20616614523766068233005080598)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-76411824523505425166725167825),(-76411824523505425017556873097)⟩,⟨4412548789230593140117171663,4412548789230593288516851754⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-74565281798251106888676501867),(-74565281798251106668912861412)⟩,⟨37114324257499850979110510868,37114324257499851198734494660⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-56379178794630622629444180681),(-56379178794630622084260184999)⟩,⟨67952847229313985326988028975,67952847229313985872624134816⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-26070766832613792636105244644),(-26070766832613790268078414087)⟩,⟨86729889506579469020967126698,86729889506579471389644969116⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨6327758279678473710232187049,6327758279678486503570807068⟩,⟨88159172530325845930859579525,88159172530325858724613017502⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨30435012741457796114342842947,30435012741457851754644307961⟩,⟨74445915634072836180404517695,74445915634072891820926661073⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨40772510746447387642473031198,40772510746447536592460200118⟩,⟨53054442011000167217878774886,53054442011000316167961793016⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨37914419935262604177115729351,37914419935262853024756814216⟩,⟨31930595526645865956212158527,31930595526646114803885503181⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨25894584638703576854858590800,25894584638703827502865206303⟩,⟨15689400792423092881288372024,15689400792423343529309451734⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨9096209345334609030784050515,9096209345334715182899170315⟩,⟨4537797282798855085462850407,4537797282798961237585709244⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨236968497344463261180804782,236968497344472903442229089⟩,⟨1807077024340179524323200417,1807077024340189166627327586⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1015197961866269206467554736,1015197961866291874251714077⟩,⟨5392529867336186417670177398,5392529867336209085603991975⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2703814516677981145189917867,2703814516678003668665537094⟩,⟨8794044578749597108687828278,8794044578749619632481508854⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨5862093716220265232801853832,5862093716220278866400940496⟩,⟨11602440438255946116641952519,11602440438255959750821575024⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨10835773301283533477117056281,10835773301283539000480339305⟩,⟨13066299417212888023571401597,13066299417212893547796833220⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨17440467311842204210157017082,17440467311842206150722944071⟩,⟨12167317677968156485588276938,12167317677968158426969472968⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨24637665744196927564106337576,24637665744196928069877386340⟩,⟨7926825595970908842225342653,7926825595970909348527045493⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨30528513354605513778085176834,30528513354605513909548652089⟩,⟨(-28703736736569826544002922),(-28703736736569695069969534)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨32914457034179202151198727005,32914457034179202221384488953⟩,⟨(-10840649179206742365309426707),(-10840649179206742295789227168)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨30337842520998415139846381160,30337842520998415205782260650⟩,⟨(-22241699173139951466890477921),(-22241699173139951402296423537)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨23068610596411636228035382491,23068610596411636296642549083⟩,⟨(-31227917448315672879121727221),(-31227917448315672812150601374)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨13284947051300759914441319052,13284947051300759986386217250⟩,⟨(-35332617144168493319145308335),(-35332617144168493248305415796)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4136381330406045505883093859,4136381330406045573688978381⟩,⟨(-33675734288165560619405382355),(-33675734288165560552151901935)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1750581904194871041163819771),(-1750581904194870985781114440)⟩,⟨(-27078400761705905512302019671),(-27078400761705905457082569542)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-3372019178773749125320300056),(-3372019178773749089220896006)⟩,⟨(-17268969986581535101882013900),(-17268969986581535065768157865)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1556266623454986146564658685),(-1556266623454986134079098838)⟩,⟨(-5897575565680188548877204121),(-5897575565680188536366208834)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-125444504734278627601569750),(-125444504734271251127102262)⟩,⟨(-284024162610772058767812361),(-284024162610764682273254724)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-436887000213049865111679324),(-436887000213020444477898425)⟩,⟨(-854402826510607918321406650),(-854402826510578497630046278)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-924954925496332142330756063),(-924954925496250004989743369)⟩,⟨(-1409531585553350105678077394),(-1409531585553267968253622631)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1688237274805661483718822123),(-1688237274805439577846239306)⟩,⟨(-1869396882345690507030369408),(-1869396882345468601071768692)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-2783990998281435910160799553),(-2783990998280866502728845519)⟩,⟨(-2063297349249666138163267951),(-2063297349249096730682768463)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-4185707602380593686731198649),(-4185707602379305289600075832)⟩,⟨(-1744346693684913713587185909),(-1744346693683625316501817879)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-5724770073584712975029564391),(-5724770073582369997675044070)⟩,⟨(-666109453288264883033460604),(-666109453285921905894455753)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-7062729294174281327485395028),(-7062729294171133642544865755)⟩,⟨1289389566168096081393518930,1289389566171243765881161997⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-7765100386237267294428805441),(-7765100386234099240408415425)⟩,⟨3972114775502558173222939480,3972114775505726226560266679⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-7489151110903965515767691019),(-7489151110900808244201799100)⟩,⟨6891467426778353985109486614,6891467426781511256065951622⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-6192244699422705820730024097),(-6192244699420277102606701655)⟩,⟨9305338415882760585924562348,9305338415885189303642641084⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-4209549614935259077924547815),(-4209549614933819061211240445)⟩,⟨10493031834046948777498813065,10493031834048388794021529227⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-2131399847375518780908526973),(-2131399847374801998296915632)⟩,⟨10083638237783426833498580137,10083638237784143616102215452⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-553931246191169013795918137),(-553931246190848592080730147)⟩,⟨8195866481485116501065904328,8195866481485436922876517024⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨184177194526257204996194981,184177194526387550610842057⟩,⟨5275100528214984818912820604,5275100528215115164633073845⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨162367697849749063259224274,162367697849783852401296089⟩,⟨1811006470910740834211022236,1811006470910775623396746656⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-59452595677045344641656),(-59452595677045331298376)⟩,⟨2093779531793736960734598,2093779531793736979072181⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1613124943415088759876529,1613124943415088800524624⟩,⟨6045084075407556914136987,6045084075407556970816294⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨9241641288434989409896413,9241641288434989482318987⟩,⟨6526445942324300062251027,6526445942324300162642087⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨29217245101659437187672292,29217245101659437319120377⟩,⟨(-6945296056516160901453307),(-6945296056516160734325223)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨71295453824899983453755937,71295453824899983690607972⟩,⟨(-52503326026183521133161470),(-52503326026183520858229977)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨144163892115640436702298587,144163892115640437127513877⟩,⟨(-150323939803590711974891179),(-150323939803590711514844308)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨243708594770909644680670594,243708594770909645512564021⟩,⟨(-315476469086832595072477166),(-315476469086832594216680999)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨344573314678946964691680455,344573314678946967075477780⟩,⟨(-552230768391844690492056519),(-552230768391844688104468761)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨405039744717020861056197041,405039744717020874434354890⟩,⟨(-845017811239114980167282859),(-845017811239114966810706517)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨383655845261938813432952170,383655845261938907513783938⟩,⟨(-1148844988051948791514056417),(-1148844988051948697477587938)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨261365596209113045208152747,261365596209113563956602762⟩,⟨(-1392657588207023382177363272),(-1392657588207022863488508857)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨60790064916447203079454004,60790064916449140942125247⟩,⟨(-1502934410358559839484315583),(-1502934410358557901689288562)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-148935120099058824685353069),(-148935120099053511214827464)⟩,⟨(-1434175995877242488848240650),(-1434175995877237175436933850)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-276224895506370593400920730),(-276224895506360287967131287)⟩,⟨(-1182089659097709477353037485),(-1182089659097699171955692677)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-258355891388108273009448547),(-258355891388096647561073078)⟩,⟨(-776645411560715497572704594),(-776645411560703872142902209)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-104451006225201994062077642),(-104451006225196753899974863)⟩,⟨(-270452314751819334236653291),(-270452314751814094079942891)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-13370904017209326188683151982),(-13370904017199622086091857613)⟩,⟨40773503022913090744929021208,40773503022922794847830648294⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_12 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 12) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_12 (tableDensity true) (fullFactor true 1 12) density1_contains hk1_1_12_contains +noncomputable def atomAnswer : CBox := ⟨⟨64368531094032454779550311734,64368531094032455571115197979⟩,⟨(-38645658959319708689812086724),(-38645658959319707900712598207)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_12 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 12) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_12 1 12 ha1_1_12_contains + def realAnswer : RBox := ⟨50997627076823128590767159752,50997627076832833485123340366⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 12) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_12 +namespace hm1_0_1_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨32535330415089175191712456061,32535330415089190823095220475⟩,⟨699941520370406731195360500,699941520370422362951083709⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨95210208258413069569998162950,95210208258413106318564730641⟩,⟨(-4670501002316113738888720826),(-4670501002316076989602444923)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨148939642980012017151164231673,148939642980012053604085860603⟩,⟨(-28023740832533259472805411989),(-28023740832533223019794199374)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨183990972315941017167948063481,183990972315941039192092690700⟩,⟨(-73647956957862462239878047806),(-73647956957862440217224514424)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨189866433652860604353998539227,189866433652860612878136762776⟩,⟨(-135695859795091744723616494701),(-135695859795091736202769324847)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨161017631692799310889975483137,161017631692799313116988780349⟩,⟨(-199161679034586242693805067976),(-199161679034586240473264705949)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨101717537926787343385220190764,101717537926787343952553218730⟩,⟨(-246160739138266078650018736429),(-246160739138266078091271289513)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨25787892747920893686464937742,25787892747920893951188837121⟩,⟨(-264122899927603789072653006957),(-264122899927603788812867453633)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-49084708810084232125516148621),(-49084708810084231940426172382)⟩,⟨(-250599874107089997883637224508),(-250599874107089997699891029480)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-108162947063580666195318876824),(-108162947063580666044260413417)⟩,⟨(-212428953580986615383471133066),(-212428953580986615233855130525)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-143381249491505171844022206703),(-143381249491505171728828806203)⟩,⟨(-161280165599280345420062605334),(-161280165599280345305394382825)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-153272410294385445826806801374),(-153272410294385445737758950055)⟩,⟨(-108995994488497078962877959797),(-108995994488497078871999376295)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-140885731827070601607079862127),(-140885731827070601545791712698)⟩,⟨(-64531382819308641297357555209),(-64531382819308641234681361002)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-111509322096398101556961292538),(-111509322096398101520222825488)⟩,⟨(-32554862248301756338558802896),(-32554862248301756301893397997)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-70920359127037888959654373835),(-70920359127037888940910852933)⟩,⟨(-13303140845149471007891999710),(-13303140845149470989862042266)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-24257604409053793794956347490),(-24257604409053793789295615370)⟩,⟨(-3310698847131624572059302385),(-3310698847131624566760331311)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-26742818643200531756859073825),(-26742818643200510457361625329)⟩,⟨(-22917933476986849969974320384),(-22917933476986828668610304799)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-84580720005871012355038713614),(-84580720005870927834187877725)⟩,⟨(-62032691773880038539017679633),(-62032691773879954013312457160)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-152114142763687234849490506050),(-152114142763687004308762210256)⟩,⟨(-80032440794514414141885064796),(-80032440794514183595563886177)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-225259560630363128914647996931),(-225259560630362542962300953202)⟩,⟨(-62092895497868653829212452340),(-62092895497868067874031281871)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-286926358995670238037108926942),(-286926358995668903552128967142)⟩,⟨1415695618824652652480632709,1415695618825987133613537489⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-310794884311925637972814657615),(-310794884311923162837604124496)⟩,⟨105293812275923485272460959423,105293812275925960394368681010⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-274895228754406722851586668278),(-274895228754403202114695271847)⟩,⟨223611373118575755950542529860,223611373118579276666125018420⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-178491744356902581556149253993),(-178491744356897292556257134233)⟩,⟨317007974213709762190405421878,317007974213715051175659579004⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-48106680060840478208593956253),(-48106680060834659975181346445)⟩,⟨352938702108249691672698187894,352938702108255509902445461512⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨75285876032607191871587157569,75285876032611574989037061288⟩,⟨324234247907088936498784816724,324234247907093319621927773115⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨158513670712755009233343816178,158513670712757311279409538192⟩,⟨250548333623251216850463800699,250548333623253518908094907378⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨190076194037799233354040479157,190076194037800193919903388720⟩,⟨163317252190784552115636783524,163317252190785512694154091593⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨177974775180390108237588204726,177974775180390575316594037475⟩,⟨88441128825538759509428254594,88441128825539226596177269747⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨138419461262832682653287189844,138419461262832891618740345329⟩,⟨38061313773904271133127624136,38061313773904480102395348518⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨85857039936219678128521351204,85857039936219762220886799439⟩,⟨11830104153443974543432913111,11830104153444058637358099075⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨28888830056563529508033810869,28888830056563551742545590875⟩,⟨2038315545208861538205923478,2038315545208883773115360186⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-2573712963788037454882459385),(-2573712963788037444332276419)⟩,⟨12296837407303653717822571780,12296837407303653729459425124⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4874034010904205342239071546),(-4874034010904205309963240408)⟩,⟨37809081684842284227518429228,37809081684842284263422380961⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1637469095337698977338582435,1637469095337699035364299534⟩,⟨64912322688029997467220514314,64912322688029997532096471528⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨22977819255737025668692535554,22977819255737025765722584030⟩,⟨90898071503890129579845489597,90898071503890129685023608459⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨63060977837962930416830445838,63060977837962930569402037537⟩,⟨107889421563423979478889033146,107889421563423979638168394674⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨119462908727790560267055284066,119462908727790560491539222893⟩,⟨103399112256800171299847967213,103399112256800171526271817371⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨179421446664669413471369727027,179421446664669413780147522848⟩,⟨65467994474664526286501505639,65467994474664526589201746293⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨220839757130855724662921862393,220839757130855725079121572033⟩,⟨(-8102529080289729093693031670),(-8102529080289728693203691414)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨221812829106703379120241360153,221812829106703379816689585794⟩,⟨(-102469934259277617463675254043),(-102469934259277616785030705529)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨174845005266310117757944514089,174845005266310120050698261774⟩,⟨(-188776547564408782325089221440),(-188776547564408780040919401172)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨94479746317110104581411760751,94479746317110114998704161410⟩,⟨(-238778115200864170797891595844),(-238778115200864160379636811862)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨10284126349381303456509753380,10284126349381339699345796918⟩,⟨(-240612437288205089010524974978),(-240612437288205052759749072597)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-49724168043711344929078969258),(-49724168043711263852370301837)⟩,⟨(-202804630492324074160369552102),(-202804630492323993072565811988)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-71940072745248600308696221980),(-71940072745248477725969675178)⟩,⟨(-144798439337668113292688091608),(-144798439337667990700010960654)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-58739682436532340494469971123),(-58739682436532203181843495491)⟩,⟨(-83732855711976268140389954799),(-83732855711976130822382708395)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-22214525974160276914438461427),(-22214525974160215001532942823)⟩,⟨(-27023341042389881318042680709),(-27023341042389819403506163315)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨945991480900031734669801350,945991480900035346028132661⟩,⟨(-1808415761280485113812137796),(-1808415761280481502155650776)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨2554346601163708469760342647,2554346601163716796010346583⟩,⟨(-5713747359893408134219636500),(-5713747359893399806998346966)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨3210079971365434211046629804,3210079971365442584276790922⟩,⟨(-10384568507497172556347620487),(-10384568507497164181373959726)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨2000660875217757009890730087,2000660875217763236680711919⟩,⟨(-15971652628979545197415951080),(-15971652628979538968487337339)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2201274701563840071980844481),(-2201274701563836928818372724)⟩,⟨(-21976321243700807778675868069),(-21976321243700804633462016059)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-10375235406686277497064505288),(-10375235406686276427343694255)⟩,⟨(-26953779642099830112617447259),(-26953779642099829041659245225)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-22597286952886784303595414483),(-22597286952886784025152314299)⟩,⟨(-28536180623748392518606867167),(-28536180623748392240720550659)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-37190637718467607602150206650),(-37190637718467607505788045754)⟩,⟨(-24140066485973222572311991965),(-24140066485973222479191076144)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-50523587904103046038996633329),(-50523587904103045961448593573)⟩,⟨(-12425674433293732989171136560),(-12425674433293732917919417790)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-58146515754005943005200810227),(-58146515754005942916619792869)⟩,⟨5183901388053097586099299432,5183901388053097668646700544⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-57048399157498014784078063914),(-57048399157498014684782437139)⟩,⟨24220454095174649348508465902,24220454095174649444406465933⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-47582983563028107575263769059),(-47582983563028107473707105002)⟩,⟨38854266409922645813945514835,38854266409922645914926598099⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-33436626562158652968392572282),(-33436626562158652874912535049)⟩,⟨44627937364696730453934654430,44627937364696730549011099420⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-19472276691658127104150128268),(-19472276691658127027104565913)⟩,⟨40282979890387911734401373392,40282979890387911814024061750⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-9028269468335776377791476889),(-9028269468335776326903863729)⟩,⟨27571638731692281854461735994,27571638731692281907562617727⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2465727703376874818498352226),(-2465727703376874800779880965)⟩,⟨9743411266918286460445902802,9743411266918286479019652782⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-259259851907477639195353416),(-259259851907474564733182902)⟩,⟨154023858126020860203036587,154023858126023934684850214⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-753488413134031868152187871),(-753488413134019666343742414)⟩,⟨520259015792232500010238580,520259015792244701869506946⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-1155945434924853799610051690),(-1155945434924820061858787940)⟩,⟨1054840059877265515215218928,1054840059877299253023715081⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1350400530919328255347275623),(-1350400530919238409344384697)⟩,⟨1841432407581472679367617118,1841432407581562525388909360⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1158560817241436545466768124),(-1158560817241210553288127046)⟩,⟨2892234515837376951697992129,2892234515837602943787298815⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-365262374001116244267719432),(-365262374000618944340758209)⟩,⟨4083798275785472041247474686,4083798275785969340885741768⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1195865033961232090195162732,1195865033962100356023770408⟩,⟨5110066049635635061032765290,5110066049636503326274482959⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨3499104079142913285642520018,3499104079144054642446961054⟩,⟨5514084884303688687243256033,5514084884304830043118290601⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨6197201542970338195407148630,6197201542971851136503696868⟩,⟨4847583024229399243382277953,4847583024230912183607866790⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨8633209162118956826869791360,8633209162120496656342785301⟩,⟨2933911628386034826815766112,2933911628387574655712566300⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨10072823768065336406614705079,10072823768066465153435740446⟩,⟨92565094056659885581248261,92565094057788632238339089⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨10063966794877774326780516097,10063966794878414877489375843⟩,⟨(-2865268757312437549260900694),(-2865268757311796998288315474)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨8669592809214396891947516021,8669592809214702605377861855⟩,⟨(-4942549913403994587067344075),(-4942549913403688873061962498)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6382112591411088588461957037,6382112591411219989356144414⟩,⟨(-5411091334017100717477972576),(-5411091334016969315911245350)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨3788573469100401458275696413,3788573469100453223681616674⟩,⟨(-4126025100533806990852560485),(-4126025100533755224917950756)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1240584050896782329561729527,1240584050896795892118456239⟩,⟨(-1533860140294481923817291744),(-1533860140294468361061234189)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨19598533789329449578996289,19598533789329449588701107⟩,⟨463136508640499479248919,463136508640499486901405⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨59671680302113069481363275,59671680302113069511807554⟩,⟨(-3763988384571346277389703),(-3763988384571346253371932)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨101255614468205227557101041,101255614468205227614602209⟩,⟨(-23644629999629383470638114),(-23644629999629383423117522)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨141615110829443368035468792,141615110829443368131748549⟩,⟨(-69316908244850743108627212),(-69316908244850743024298908)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨171738959754910962249063596,171738959754910962401872695⟩,⟨(-147872269205618671157443668),(-147872269205618671016280350)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨174145856087098685462409285,174145856087098685701256861⟩,⟨(-259166849028826485964826801),(-259166849028826485735090178)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨125400471667067351570540214,125400471667067351968636758⟩,⟨(-391702857436507936073384955),(-391702857436507935679643188)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨6084291363942192524364860,6084291363942193478116096⟩,⟨(-519789206485410280206975908),(-519789206485410279251597324)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-185345848480745466933627199),(-185345848480745462099874737)⟩,⟨(-605985072140904265580928640),(-605985072140904260741082937)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-422299028133396046054488495),(-422299028133396013084701991)⟩,⟨(-613912951576850044513631745),(-613912951576850011537757465)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-651137149942098768556629039),(-651137149942098591685494497)⟩,⟨(-528679980132162103691499186),(-528679980132161926819123477)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-806784640300178767885310999),(-806784640300178028507268578)⟩,⟨(-371728379441027516112776757),(-371728379441026776740013545)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-837138785344632765328425802),(-837138785344630470838639266)⟩,⟨(-195369465227190364030659546),(-195369465227188069549794658)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-723916737064459414833555182),(-723916737064455026742052973)⟩,⟨(-56829523238312898590631431),(-56829523238308510507852860)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-487052605194274783448834477),(-487052605194269879715427833)⟩,⟨10604423076560913743543984,10604423076565817471004056⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-171136990641291561770285470),(-171136990641289361756945034)⟩,⟨12318161280804445392884207,12318161280806645404162759⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2217997850365122827393224460,2217997850371224110839943291⟩,⟨(-141929399103679541373625308176),(-141929399103673440092093447836)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 13) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_13 (tableDensity false) (fullFactor true 1 13) density0_contains hk1_1_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨28494123232316597014493600449,28494123232316597479673419172⟩,⟨1763757356661817472515247259,1763757356661817936663051245⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_13 1 13 ha1_1_13_contains + def realAnswer : RBox := ⟨30712121082681719841786824909,30712121082687821590613362463⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_13 +namespace hm1_1_1_13 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_13 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨5499583853925662005372415911,5499583853925674794147137419⟩,⟨852836892413203333606124515,852836892413216122290169732⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨16307748365082206114582639886,16307748365082236160010803686⟩,⟨1491553939742799556868333210,1491553939742829602119555110⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨26070760195108738620500313248,26070760195108768375766716449⟩,⟨(-785720759850707893823814076),(-785720759850678138567303175)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨32976381582189001498436890773,32976381582189019403011459607⟩,⟨(-6930935410277897743081047619),(-6930935410277879838019390832)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨34734751135830956749852864938,34734751135830963592323974771⟩,⟨(-16450764103649996585525717410),(-16450764103649989741761101348)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨29934233818118552449430890124,29934233818118554128552213562⟩,⟨(-27256480832272457029444137181),(-27256480832272455348176961870)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨19171825602754773751796480994,19171825602754774069593091744⟩,⟨(-36299927198035733957875739591),(-36299927198035733637597586118)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4980578279814891925073581654,4980578279814892018563178732⟩,⟨(-40940192832366438727850632899),(-40940192832366438632538597197)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-9264392040925730329948820310),(-9264392040925730278113505095)⟩,⟨(-40155319285978937234901420713),(-40155319285978937182030926022)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-20613349120087438509071833617),(-20613349120087438467700487930)⟩,⟨(-34726760662995637244202679470),(-34726760662995637203014507241)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-27321769269056672757187431105),(-27321769269056672724292720817)⟩,⟨(-26531739849075412445938206187),(-26531739849075412413916573055)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-29003007935790493860089429210),(-29003007935790493834306181403)⟩,⟨(-17663602613549353503596711476),(-17663602613549353478696607213)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-26345428173888359236679148312),(-26345428173888359218389851151)⟩,⟨(-9867172135214326232906868690),(-9867172135214326215697710412)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-20583725678394274602501960551),(-20583725678394274591034025504)⟩,⟨(-4274081594895966675867943617),(-4274081594895966665596359745)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-12956116806375904965817249064),(-12956116806375904959699331749)⟩,⟨(-1218506283141187268045232534),(-1218506283141187262866852161)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-4406754685561834795538633479),(-4406754685561834793637255857)⟩,⟨(-155567193258955928689533627),(-155567193258955927143540253)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1969059381276691585762159949),(-1969059381276674077502321007)⟩,⟨(-5127897008527887106007680006),(-5127897008527869597986795898)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-7087349898144232731432335764),(-7087349898144163202077799908)⟩,⟨(-14502240531113714580883591563),(-14502240531113645052148505034)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-15203415043405154381348988577),(-15203415043404964510348334377)⟩,⟨(-20889052370801165776767677694),(-20889052370800975906484708007)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-26494527241562909066784827933),(-26494527241562425895888764794)⟩,⟨(-21621225573172617283737999507),(-21621225573172134113229386930)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-38609748109353068310328726782),(-38609748109351966724115569477)⟩,⟨(-14295239436561797212481129902),(-14295239436560695625858735840)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-46853078774526426263303273773),(-46853078774524381246413058121)⟩,⟨1370192350113806253593293811,1370192350115851272042344663⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-46229875351892704326502321492),(-46229875351889792774580750259)⟩,⟨21961772148667358153212767202,21961772148670269707787418839⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-34706088640665581582852879976),(-34706088640661205443188129545)⟩,⟨40956867638124723764626955974,40956867638129099906204089381⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-15177688082612746335780791320),(-15177688082607932449734408573)⟩,⟨51899134276260197859085332022,51899134276265011745700158489⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨5885094305009479432793342614,5885094305013103878290879995⟩,⟨52017731688438557689900034953,52017731688442182134673527889⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨22114703036799195180588633241,22114703036801096737164078772⟩,⟨43339836166397119288709137456,43339836166399020843663841260⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨30199545458882560354934558042,30199545458883352623429771523⟩,⟨30669460013038471439551044362,30669460013039263706213051389⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨30311985286425528057964241525,30311985286425912692610623081⟩,⟨18555016077418690519973441741,18555016077419075153470864534⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨24656617414657221569150619283,24656617414657393384292522378⟩,⟨9524191750780680899768382803,9524191750780852714326691676⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨15735189228913039628103101109,15735189228913108674907549084⟩,⟨4003617184326155704746570493,4003617184326224751304599007⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5369683911052139708900060744,5369683911052157950044650687⟩,⟨1030378027523525535217682822,1030378027523543776297821973⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1949800179762866499522342952),(-1949800179762866495737775739)⟩,⟨2059939874947075766376421916,2059939874947075770210318085⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-5447554066504327809534724693),(-5447554066504327797856348856)⟩,⟨6677595376935537808792489318,6677595376935537820641274011⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-7553865967177745387151284387),(-7553865967177745366606054063)⟩,⟨12544788926229920683616963451,12544788926229920704477017074⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-6882124623439350916080611718),(-6882124623439350883282207243)⟩,⟨19659391420916638976720716929,19659391420916639009877972888⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1878057844017419391191553775),(-1878057844017419342916983642)⟩,⟨26749075078731614170870568386,26749075078731614219417868203⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨8249301029437552017986580111,8249301029437552083520883719⟩,⟨31121931489820595924124454602,31121931489820595989748945141⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨22189949620555823597598822405,22189949620555823681019474383⟩,⟨29416567632267198131782632337,29416567632267198214981615298⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨35931122891012794391112208231,35931122891012794502149920685⟩,⟨19469635672552999954979009842,19469635672553000065442440235⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨44109337447969459936371581170,44109337447969460203803703088⟩,⟨2439087487566772860789040132,2439087487566773127664995844⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨43058006547221070437978507983,43058006547221071944199790085⟩,⟨(-16725453301890166013901522277),(-16725453301890164507906831972)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨33323465064097676542411273389,33323465064097684634175957678⟩,⟨(-31579016814472488570198927495),(-31579016814472480478462965596)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨19357607205665729401834190733,19357607205665758553918886511⟩,⟨(-37797267362203811951251322400),(-37797267362203782799134908371)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨6643917921577216996613460036,6643917921577282783759048612⟩,⟨(-35204399370078141523887664435),(-35204399370078075736690644132)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1202958335893116903584167950),(-1202958335893017119792639120)⟩,⟨(-26805828461045615205357312996),(-26805828461045515421543087730)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3459584812223071281845473090),(-3459584812222959313815132886)⟩,⟨(-16147651331031289338560451694),(-16147651331031177370528780353)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1638080252748933953532373931),(-1638080252748883435108367083)⟩,⟨(-5319465105613830102633819501),(-5319465105613779584213963359)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨614853527128815211790836906,614853527128818245800234365⟩,⟨(-295588521069962013184818420),(-295588521069958979206380997)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1801455385980343516017938621,1801455385980350506180986738⟩,⟨(-1000573481293459638865925972),(-1000573481293452648803740972)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2818947579751318844541590113,2818947579751325863389114759⟩,⟨(-2035909743013296521697443704),(-2035909743013289503030079151)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3439962588725059636967161953,3439962588725064843094026082⟩,⟨(-3572264419824018372046928289),(-3572264419824013166139069073)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨3313941951203503921657270339,3313941951203506537067782628⟩,⟨(-5654779693231681621353541925),(-5654779693231679006147213834)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨2032554175510579476520835727,2032554175510580354232854351⟩,⟨(-8077509429423409569248163242),(-8077509429423408691648851639)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-695245048454893514014753905),(-695245048454893301654568520)⟩,⟨(-10278465927000335119416204938),(-10278465927000334906983242848)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-4784166978287431871127648406),(-4784166978287431817557482675)⟩,⟨(-11400783744770873118540476956),(-11400783744770873064633483653)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-9558774736281688859409334850),(-9558774736281688829465642196)⟩,⟨(-10619305275941073263082411263),(-10619305275941073232514607143)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-13816810925838647524845268718),(-13816810925838647493084402786)⟩,⟨(-7638398454084397670078114980),(-7638398454084397637740707595)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-16288929017663264625885972633),(-16288929017663264590031199989)⟩,⟨(-3053051894519917504170945744),(-3053051894519917468017328179)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-16268511623997329713095266930),(-16268511623997329675909780132)⟩,⟨1758874011057080749839198351,1758874011057080787042346363⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-13952072889327140088546415007),(-13952072889327140053743681865)⟩,⟨5240952092551151099512549935,5240952092551151134126874709⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-10221614043244009184559711916),(-10221614043244009155437517888)⟩,⟨6372246857680007309335521399,6372246857680007338192171346⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-6049380434343749143509301492),(-6049380434343749124039045634)⟩,⟨5029970516634589229142074261,5029970516634589248394701677⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1978750340357886524994670798),(-1978750340357886518167462108)⟩,⟨1891561353483498855119616698,1891561353483498861864403120⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-82483033644541020329800456),(-82483033644538493612440037)⟩,⟨54900044661047615460977690,54900044661050142174021040⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-245107918522948479826425326),(-245107918522938451157393502)⟩,⟨185007854863083832274034756,185007854863093860931382627⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-393376191553520744438652581),(-393376191553493011660113769)⟩,⟨373600258209603018013574403,373600258209630750777793320⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-494576131125202342342365194),(-494576131125128476156970244)⟩,⟨650474105734399687651813714,650474105734473553829469527⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-486073894764402505624721334),(-486073894764216685343999385)⟩,⟨1026625909864974882349731271,1026625909865160702644389543⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-281291864700764667196414428),(-281291864700355767853668029)⟩,⟨1478397520973214292433787035,1478397520973623191832997845⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨200738237621679486769583123,200738237622393255346276063⟩,⟨1929150069793889200395350181,1929150069794602969097700356⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨986187063929906491090478018,986187063930844292353029984⟩,⟨2245724692018312960799186712,2245724692019250762268455846⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1996181313779267575574081592,1996181313780509677392184099⟩,⟨2274818647936718166994709436,2274818647937960269008432282⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨3028553837313194733082156277,3028553837314457563616342958⟩,⟨1921320011365410327530716114,1921320011366673158192806218⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨3804703098805783362331877401,3804703098806707891207111174⟩,⟨1226918734983898870149343949,1226918734984823399065965880⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨4080408272776249463884058387,4080408272776773420579362260⟩,⟨383988364037147033805425515,383988364037670990460132479⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨3764270761905270026917877268,3764270761905519775859677879⟩,⟨(-340387351562118558570794917),(-340387351561868809728404970)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2953446034198775092924410405,2953446034198882324537230257⟩,⟨(-721539497664318175329482613),(-721539497664210943833133047)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨1848236101956277527641889024,1848236101956319739219429866⟩,⟨(-670447120672640958764082117),(-670447120672598747277234874)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨624370735939424875034004289,624370735939435930068299434⟩,⟨(-268094588284364141337757937),(-268094588284353086337099839)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨582789847624182444776178,582789847624182449730408⟩,⟨(-14048460774979050528244),(-14048460774979047049577)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨1659197458428750551315436,1659197458428750566748781⟩,⟨(-541486290639266050350801),(-541486290639266039591006)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1672603480267365234715276,1672603480267365263757639⟩,⟨(-2693682001288179387022141),(-2693682001288179365407684)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2496699562070564312205193),(-2496699562070564263366626)⟩,⟨(-8103080831409228200384448),(-8103080831409228160774580)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-16402510110589954914602779),(-16402510110589954833917540)⟩,⟨(-19169050670935020445360343),(-19169050670935020374185607)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-46546828712173621490410423),(-46546828712173621354883514)⟩,⟨(-37829365686413233559271387),(-37829365686413233431747445)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-98089723822366537711997219),(-98089723822366537459363702)⟩,⟨(-62249582637038552053516193),(-62249582637038551804901022)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-172625037665764077034460690),(-172625037665764076331387370)⟩,⟨(-84350457186124291095338506),(-84350457186124290389540022)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-264963916912793748416109280),(-264963916912793744524848536)⟩,⟨(-91387166873501633565354121),(-91387166873501629663303250)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-360053708765197208850578826),(-360053708765197181946998813)⟩,⟨(-71480197085305795671634883),(-71480197085305768750358794)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-434379732375932354839863301),(-434379732375932210444196217)⟩,⟨(-20949151064607474973796031),(-20949151064607330555912709)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-464319326538546266953929328),(-464319326538545663218608547)⟩,⟨49851214562995384813313458,49851214562995988570131712⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-436977134932810973491755394),(-436977134932809099053238083)⟩,⟨116019394885618097814163667,116019394885619972266898102⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-354482307889752470991119067),(-354482307889748884453395317)⟩,⟨146733752709819208324989713,146733752709822794870606003⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-229635404665384039111438137),(-229635404665380029603906737)⟩,⟨122133333837448813695143136,122133333837452823206227638⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-79305058392526200184903479),(-79305058392524400998540500)⟩,⟨47393723276851022561240866,47393723276852821748531021⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨7121545280278775883156778944,7121545280283809171330078588⟩,⟨(-18826685042314172183705095693),(-18826685042309138895052276663)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_13 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 13) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_13 (tableDensity true) (fullFactor true 1 13) density1_contains hk1_1_13_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-37261545765337089011880625071),(-37261545765337088403568554434)⟩,⟨(-2306451927942377301790143935),(-2306451927942376694827631032)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_13 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 13) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_13 1 13 ha1_1_13_contains + def realAnswer : RBox := ⟨(-30140000485058313128823846127),(-30140000485053279232138475846)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 13) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_13 +namespace hm1_0_1_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-17659890369077246271681242522),(-17659890369077238430808207361)⟩,⟨(-8994619312662886096024335234),(-8994619312662878254387542754)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-53775113800901348799167816421),(-53775113800901329667157319874)⟩,⟨(-22272430529071799532107361988),(-22272430529071780398110863008)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-90337711898138550093961697303),(-90337711898138529831508930939)⟩,⟨(-22119391901672890086802792570),(-22119391901672869821953000565)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-122457768473438540631373225895),(-122457768473438527338251589439)⟩,⟨(-2756862352680938646780890413),(-2756862352680925351840955903)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-141077919821295420567909646213),(-141077919821295414930761607143)⟩,⟨35533869213625067440691776033,35533869213625073078468442468⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-137208884777748065967414408956),(-137208884777748064356276715130)⟩,⟨84566150590007981883151125450,84566150590007983493177778250⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-107808312542790409544395188330),(-107808312542790409123813209869)⟩,⟨130455603625591729751004108155,130455603625591730167690725933⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-58853087154742228084653334368),(-58853087154742227903021017852)⟩,⟨159655818973119820588366086278,159655818973119820765454599641⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-2964289275039657152582467341),(-2964289275039657030345129007)⟩,⟨165019293421450178227790564582,165019293421450178348377227221⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨46383758999069948616267006690,46383758999069948720421171768⟩,⟨147975762595493675181276361191,147975762595493675284213527545⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨79834374830223950421369558736,79834374830223950502201914189⟩,⟨116306928062629752134234669924,116306928062629752214315790841⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨93929909240877261059100583427,93929909240877261119892820289⟩,⟨79958922112913007701013907796,79958922112913007762760093893⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨90138193166959978902311799781,90138193166959978944385589922⟩,⟨47393029688231698961363411315,47393029688231699004331814587⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨72707331768910972686021450073,72707331768910972711101964253⟩,⟨23529280866971037981965255596,23529280866971038007015017134⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨46574088662289233555521105751,46574088662289233568183889758⟩,⟨9280908479238944625608328955,9280908479238944637806236677⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨15962094944959504489585697446,15962094944959504493379608797⟩,⟨2215438086168764478050962889,2215438086168764481606545943⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1001210480006746306341300672,1001210480006758554670064719⟩,⟨17913094194820252322774364808,17913094194820264571540441133⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨7345396436476101854063643142,7345396436476147721661683052⟩,⟨53124658269560778131428403438,53124658269560824000740335681⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨25940623419378229325744618405,25940623419378340906882685014⟩,⟨84636847594439201776286043788,84636847594439313361489432502⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨61451586501027769043365403979,61451586501028006294186838449⟩,⟨104939001041363441532554248247,104939001041363678791091092803⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨111228293548544200777526473704,111228293548544787801093546946⟩,⟨102605608714093526763012240370,102605608714094113795242076954⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨162101984401493438076166723575,162101984401494851369850657656⟩,⟨67936670580928884220170158036,67936670580930297518711863743⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨193044428127234739843149206115,193044428127237235144814371740⟩,⟨2004470322588624889928799760,2004470322591120190343837069⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨186003655534935289112230653880,186003655534938247732627330752⟩,⟨(-78149091036749616981673985905),(-78149091036746658369078546179)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨138675815072397616351664268897,138675815072400183456580845176⟩,⟨(-145606594769031421476462100467),(-145606594769028854382532788559)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨67754571285501400112372113993,67754571285503778826355833556⟩,⟨(-178709756200801901880189091814),(-178709756200799523172038666198)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1289029761092210133820306005),(-1289029761090676289403669445)⟩,⟨(-172900048369813352999015652542),(-172900048369811819155178848174)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-48792667477342602703266487036),(-48792667477341870595443961526)⟩,⟨(-139881090479934851115394651724),(-139881090479934119004661615630)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-68200900236711011587781243269),(-68200900236710722360812196195)⟩,⟨(-97283322009550239777562652575),(-97283322009549950546276645352)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-63638538171686240514160973452),(-63638538171686136732062694611)⟩,⟨(-58668939221570253559080889232),(-58668939221570149772943799699)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-43429068305640613723706506008),(-43429068305640574253975319615)⟩,⟨(-29598416462602603497668401465),(-29598416462602564025508026219)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-15249735133952904632311119968),(-15249735133952893703946793779)⟩,⟨(-8811762863963773814397641587),(-8811762863963762885295890160)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨5010089909788969519424532363,5010089909788969525458512016⟩,⟨(-1553331295334972474944233104),(-1553331295334972469285140502)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨14817421314548029290390588939,14817421314548029309157820224⟩,⟨(-5969708687177465370724898804),(-5969708687177465352948767517)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨23438830738368456135308616928,23438830738368456169633750997⟩,⟨(-14202777686272187085171012924),(-14202777686272187051996904199)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨28443945045841805687922475277,28443945045841805742841091040⟩,⟨(-28108499893497919848513430019),(-28108499893497919794063306893)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨25617233179054020633774793324,25617233179054020715548775955⟩,⟨(-47561485610200929003351312982),(-47561485610200928920140177691)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨10131268510677728683310709340,10131268510677728800003504851⟩,⟨(-68650257255239396111060436583),(-68650257255239395989738303788)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-20200447316030792995450838321),(-20200447316030792828447757907)⟩,⟨(-82967055821167014638319197293),(-82967055821167014463797453941)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-60870218650064428207717621202),(-60870218650064427961613664695)⟩,⟨(-80215771140950590383947159083),(-80215771140950590132939755811)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-99593134006488208345035190920),(-99593134006488207933417088298)⟩,⟨(-54492744727996716509327508821),(-54492744727996716097618452785)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-121435940448449723752453244676),(-121435940448449722642618037505)⟩,⟨(-10292334246656044052171911456),(-10292334246656042947338084012)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-117946109912446555015620368363),(-117946109912446551011436532465)⟩,⟨37803002411438775008092031804,37803002411438779003857364868⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-92789486337895917361926099290),(-92789486337895900393298238440)⟩,⟨73026114146826235351481168483,73026114146826252314155522409⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-58727622261743776112188304175),(-58727622261743727995620318763)⟩,⟨85612236844581936400733672514,85612236844581984514823693090⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-29000467973594804495135800067),(-29000467973594721068253158435)⟩,⟨75924823257668133420052287675,75924823257668216846672295829⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-10456362091250894207300544501),(-10456362091250808467716110750)⟩,⟨50737973386781396478117692318,50737973386781482218227894963⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2151938315734834656551435477),(-2151938315734798038318948229)⟩,⟨17655576439843577657600430197,17655576439843614276127097814⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-699836741781522918230150149),(-699836741781521611094421628)⟩,⟨(-115973026043767838153217252),(-115973026043766531115586193)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2171735123107723040275471931),(-2171735123107719776669662644)⟩,⟨(-216737283844253201869703869),(-216737283844249938539934909)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-3813318125993788051416618809),(-3813318125993784413444752116)⟩,⟨104620988160602160356060367,104620988160605797936376025⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-5574989043478043718735403536),(-5574989043478041122693263689)⟩,⟨1199107001324352175310702664,1199107001324354770971427534⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-7136939966899439180978188714),(-7136939966899437947659023479)⟩,⟨3432021340956453813437869606,3432021340956455046607882410⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-7827180580597826450062640010),(-7827180580597826057119990579)⟩,⟨7006466183979183843606865966,7006466183979184236939246972⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-6710274935674900861149278078),(-6710274935674900764795836648)⟩,⟨11661482999417131070225757651,11661482999417131167842327247⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-2973503755111718763053370527),(-2973503755111718728318075137)⟩,⟨16407306061961620097534172842,16407306061961620134457961900⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨3441642429430236953959061942,3441642429430236987634577394⟩,⟨19620287826936504137801910575,19620287826936504173260951367⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨11346762100085878475590837320,11346762100085878515939324970⟩,⟨19719248492634743333072039768,19719248492634743374143822528⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨18496688951964263111601127650,18496688951964263158145480837⟩,⟨16167051757299745511108141198,16167051757299745557080814178⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨22592282026679666058609543831,22592282026679666109404837197⟩,⟨10053170345885658003708214600,10053170345885658052761235069⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨22450170522757846274018637267,22450170522757846323537826498⟩,⟨3656346962059848749708430221,3656346962059848796836382024⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨18425701036177382512856703688,18425701036177382554837261777⟩,⟨(-785995638789608398399700125),(-785995638789608358407298649)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨11841555919821350570961554507,11841555919821350599237640096⟩,⟨(-2208258063723995646108662244),(-2208258063723995618913164755)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨4050898388151662734621951959,4050898388151662744557725449⟩,⟨(-1064671281343325491295625590),(-1064671281343325481694272651)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨58071849045771966747079371,58071849045772913386675216⟩,⟨67916522072811908443227239,67916522072812855080377805⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨191002589844029525618493247,191002589844033263890166464⟩,⟨193776171918038463100909769,193776171918042201367977546⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨371611980415996681007414304,371611980416006912855499475⟩,⟨283795809650328573354402053,283795809650338805204190072⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨620398218034657097085448515,620398218034683910976692919⟩,⟨297037098492326220020060558,297037098492353033934561633⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨932058577117430742203965019,932058577117496585523107292⟩,⟨174762322653221276223904060,174762322653287119610704658⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1254735285008087600798766098,1254735285008227276795728608⟩,⟨(-148349239907930811879827603),(-148349239907791135741443045)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1477078582878163651670860767,1477078582878400694973267423⟩,⟨(-712511909212690562215470008),(-712511909212453518675397898)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨1445187367707147081075625092,1445187367707553416836113303⟩,⟨(-1484203510025222059011182236),(-1484203510024815723012452356)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1025110683464795038452655311,1025110683465342507275935502⟩,⟨(-2318361281210680607717741724),(-2318361281210133138733862708)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨196471381657108643382443265,196471381657638256565622625⟩,⟨(-2977024992745983985152757204),(-2977024992745454371938752778)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-879811658698870188812319157),(-879811658698500765981294770)⟩,⟨(-3227391924650692304095588205),(-3227391924650322881394531780)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-1886324264070905680387345759),(-1886324264070706903870767565)⟩,⟨(-2974414591848901183083203048),(-2974414591848702406845332075)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-2477057418526236628839459328),(-2477057418526147156116010445)⟩,⟨(-2326532834838920567352913215),(-2326532834838831094996520544)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2435797334913141660151732923),(-2435797334913104664394367631)⟩,⟨(-1528493322108707109944359699),(-1528493322108670114540747399)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1761343622561255021868184911),(-1761343622561238520843563248)⟩,⟨(-807110635204712755938655154),(-807110635204696255130583535)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-639736016105991105273040923),(-639736016105986396479540654)⟩,⟨(-243665956795057840698509583),(-243665956795053131975755355)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-146154973158637067991047),(-146154973158637066017747)⟩,⟨(-5064250772252082325894946),(-5064250772252082323377173)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1817106115058246487066214),(-1817106115058246480516184)⟩,⟨(-15381962643401052662676514),(-15381962643401052654524785)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-7691299036057805847041206),(-7691299036057805833922690)⟩,⟨(-25948142271685082028608228),(-25948142271685082013057849)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-20534019003981598384978565),(-20534019003981598361681612)⟩,⟨(-35861526732710471975543396),(-35861526732710471949391090)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-42295374510943828735949228),(-42295374510943828696905329)⟩,⟨(-42459291937744128087076619),(-42459291937744128045370962)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-72838344198144044490704630),(-72838344198144044427111877)⟩,⟨(-40726581468170256843140948),(-40726581468170256777696982)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-108617695715980807155885515),(-108617695715980807047125309)⟩,⟨(-24020252313530739572496611),(-24020252313530739463312372)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-141819838084657568937370977),(-141819838084657568676406750)⟩,⟨13035980239268657979024382,13035980239268658238714772⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-161237461387762376523785845),(-161237461387762375228134654)⟩,⟨70416286109841990133387138,70416286109841991426644692⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-156364877347150054145567494),(-156364877347150045559054380)⟩,⟨139650996063978194868305378,139650996063978203452708810⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-123806207655914568293273718),(-123806207655914519313487273)⟩,⟨204433113514299800277368801,204433113514299849256765131⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-71824695863454983566517154),(-71824695863454745861341832)⟩,⟨245792906155045845748793913,245792906155046083455410872⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-18304415698378480118200241),(-18304415698377753663399094)⟩,⟨249617349806702533125746251,249617349806703259582732236⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨18000660818199899695215915,18000660818201271653236042⟩,⟨212334878415547247051757251,212334878415548619011721522⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨27068853502237131175386915,27068853502238651310675860⟩,⟨141179000893832012421882748,141179000893833532558377933⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12164774415638198986921142,12164774415638877981625102⟩,⟨49291918931008467327029666,49291918931009146322125220⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1003170548811008565583271521),(-1003170548807914671628433509)⟩,⟨84014297310145801312598326941,84014297310148895206837714297⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 14) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_14 (tableDensity false) (fullFactor true 1 14) density0_contains hk1_1_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-9936665555120681368613580155),(-9936665555120681032472334221)⟩,⟨(-4272766134487843408376369690),(-4272766134487843072956324538)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_14 1 14 ha1_1_14_contains + def realAnswer : RBox := ⟨(-10939836103931689934296851676),(-10939836103928595704000767730)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_14 +namespace hm1_1_1_14 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_14 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-2790734292432132811086901378),(-2790734292432126399115969310)⟩,⟨(-1923274601653206674859795155),(-1923274601653200263073349189)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-8612699697201758463896819488),(-8612699697201742829627259971)⟩,⟨(-5079839036334873657797166399),(-5079839036334858024015335116)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-14768292100280217824300646133),(-14768292100280201295328122653)⟩,⟨(-6174322925584255357565800804),(-6174322925584238829199814465)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-20427576363080997048506429871),(-20427576363080986254168963218)⟩,⟨(-4059101554699178829219535367),(-4059101554699168035339427802)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-23902009263346638037819854970),(-23902009263346633525228910044)⟩,⟨1638326189232178877385630095,1638326189232183389965338856⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-23462942647567018493214051801),(-23462942647567017278048897854)⟩,⟨9918929946964850076294626170,9918929946964851292111260914⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-18426410278027053715912971863),(-18426410278027053477769863401)⟩,⟨18453031019124026916438420530,18453031019124027155824869507⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-9726735246369173685500906667),(-9726735246369173628416752651)⟩,⟨24583533921694943594966590144,24583533921694943653629219827⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨414529460789015511352950529,414529460789015543776485342⟩,⟨26628099189674102506342441889,26628099189674102539956883102⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨9466972430206978125444091494,9466972430206978152880900506⟩,⟨24504842060318232600654403562,24504842060318232628423710418⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨15557790601512824225163826048,15557790601512824247576260303⟩,⟨19436524523351279549736435292,19436524523351279571828697607⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨17943505971314354556983024667,17943505971314354574413624119⟩,⟨13194898449108401974241091577,13194898449108401991227039625⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨16934344466527253150318717739,16934344466527253162747471226⟩,⟨7418657066192565782080844047,7418657066192565793880683548⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨13453893767179493797939812350,13453893767179493805689885668⟩,⟨3202252987095823707684539455,3202252987095823714680959485⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨8517280447891606168530578687,8517280447891606172625458698⟩,⟨898020593710607258320049403,898020593710607261804129441⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨2900412807907590637771677376,2900412807907590639035420940⟩,⟨108983058294517372690239791,108983058294517373720446114⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1191344094757266244833828341),(-1191344094757256179870053999)⟩,⟨2531858330362703914190540582,2531858330362713979101432209⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2799103308750459273813905292),(-2799103308750421553906505188)⟩,⟨7763698128704672367860114787,7763698128704710087559997114⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-2118578236895876799289881763),(-2118578236895784930825842719)⟩,⟨13135406805753967619637932251,13135406805754059487608826926⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2029299180244660213814948758,2029299180244855783081090846⟩,⟨17679747662743123761082924850,17679747662743319329398330187⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨9759118403777966928757188769,9759118403778451428025867571⟩,⟨19393522754678751754333883542,19393522754679236252519878130⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨19293375055356816146018635999,19293375055357983802824129614⟩,⟨16059636834306300309936125006,16059636834307467966110815674⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨27016066359449011837928774417,27016066359451075390964173912⟩,⟨6888183149382525142621881919,6888183149384588695751118658⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨29128761227363088645633325959,29128761227365536518962749360⟩,⟨(-6139470059726366976086878512),(-6139470059723919101826443950)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨24096065166630497412617910854,24096065166632621195902888986⟩,⟨(-18734987493327732042001388369),(-18734987493325608257286562823)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨13819270524856288270123081066,13819270524858255100851633586⟩,⟨(-26692098173278548112131582923),(-26692098173276581280600136924)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2399701499846542909484753203,2399701499847809852690691283⟩,⟨(-28274254833991949385235452953),(-28274254833990682441945358496)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-6355446574822796544906704311),(-6355446574822192703755783046)⟩,⟨(-24639520915326028469055585895),(-24639520915325424628332254107)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-10619934164485947566219821445),(-10619934164485709431052969351)⟩,⟨(-18402992052561288305254790828),(-18402992052561050170731773294)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-10577733623762229784391657823),(-10577733623762144502483559728)⟩,⟨(-11921165900267180761069201746),(-11921165900267095479776393811)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-7464054208269039073240825404),(-7464054208269006693071456331)⟩,⟨(-6421298124126720045579932352),(-6421298124126687665788792606)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-2660940795403184805249385618),(-2660940795403175847073983343)⟩,⟨(-1994043328012836827032304265),(-1994043328012827868974175927)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1147133041927465223242447174,1147133041927465225227358362⟩,⟨294101526134513430566824897,294101526134513432534511293⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨3557272063539793566921632434,3557272063539793573193521590⟩,⟨622011886297037176384643577,622011886297037182609349898⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨6179054622318090674458080596,6179054622318090685866774348⟩,⟨138767388479128754552785510,138767388479128765907258258⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨8715501463377420369539695922,8715501463377420387282986529⟩,⟨(-1722168872260225839043187220),(-1722168872260225821323165012)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨10294047607567448387701873883,10294047607567448412744534832⟩,⟨(-5328150899182266658007305513),(-5328150899182266632910516780)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨9584749263824855991926866197,9584749263824856024810860989⟩,⟨(-10395428060979105482340576703),(-10395428060979105449285108775)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨5428889367182351564926667506,5428889367182351607676765067⟩,⟨(-15551335637976294484644816504),(-15551335637976294441599247615)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-2152950938111517347967683772),(-2152950938111517283473922521)⟩,⟨(-18493959029035157316027437542),(-18493959029035157251337459733)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-11284796608699261390429980981),(-11284796608699261236357001020)⟩,⟨(-17142563875131996834404541642),(-17142563875131996680311127148)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-18789982017792380888194003165),(-18789982017792380203943228772)⟩,⟨(-11204854141779633971682449654),(-11204854141779633287518339560)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-21968926687235987815291809552),(-21968926687235984805112817657)⟩,⟨(-2767815414191104300334350990),(-2767815414191101290254201222)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-20242473295426462275596216645),(-20242473295426448711334245627)⟩,⟨4870810138636917632795814163,4870810138636931196995353700⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-15253805060765291685324406565),(-15253805060765252683827742014)⟩,⟨9196223684365845985505502579,9196223684365884986969603919⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-9496570364683076836281463925),(-9496570364683008931030899956)⟩,⟨9577637090092254238767290744,9577637090092322144006382375⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-4749771317308357612021990052),(-4749771317308287710514009450)⟩,⟨6884462958971735368039181067,6884462958971805269542649324⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1383003799646890813496047557),(-1383003799646860940733152934)⟩,⟨2468985823913724464232155171,2468985823913754336992984174⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-164366092298223884712177668),(-164366092298222786664880883)⟩,⟨(-170916580298841371880121526),(-170916580298840273822506749)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-529258145862867159627848276),(-529258145862864420076129771)⟩,⟨(-486059632361917580771653762),(-486059632361914841190890729)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-994571971259239350034959803),(-994571971259236300970586450)⟩,⟨(-707186416107403728864714508),(-707186416107400679759360427)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1596848209536169604565280871),(-1596848209536167434590320112)⟩,⟨(-732516242599697302817461618),(-732516242599695132803227821)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-2311288168145532361104162700),(-2311288168145531335580683359)⟩,⟨(-424668373706441377474565031),(-424668373706440351937199948)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-3009022869105942361274353413),(-3009022869105942039829106121)⟩,⟨351103625684788202249134928,351103625684788523652690042⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-3434596838488031864848487084),(-3434596838488031792394152811)⟩,⟨1643879350490512433822303373,1643879350490512506147852165⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3260231383762484207447694405),(-3260231383762484188580997949)⟩,⟨3315140162982620218688351360,3315140162982620237338643037⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2246114785576659456698481236),(-2246114785576659442745605806)⟩,⟨4987640887177322134121655357,4987640887177322147905793312⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-441385788531085016531733528),(-441385788531085001288740896)⟩,⟨6136740754965762820546682740,6136740754965762835732731826⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1725037339746117481600723202,1725037339746117498485568880⟩,⟨6338279200504135019441934071,6338279200504135036398717466⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨3582486770632756071652959401,3582486770632756089671586537⟩,⟨5527226154848727777494539222,5527226154848727795689578456⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4530533298751758861436593500,4530533298751758878873292536⟩,⟨4053557271353000439054873411,4053557271353000456720870967⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨4307607538449209782802746773,4307607538449209797737258684⟩,⟨2468840925905426438336109863,2468840925905426453456188721⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨3037904198961305862403974711,3037904198961305872633602350⟩,⟨1200488758556066197634850123,1200488758556066207963257612⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1088807397103966938538312941,1088807397103966942165438826⟩,⟨340447559162349964904738760,340447559162349968561952381⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨20197498799505022188419692,20197498799505800170171951⟩,⟨21309542005823426705463458,21309542005824204687828051⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨66748968572842614993415295,66748968572845687467062288⟩,⟨62224866913447628540492878,62224866913450701015476237⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨130768687520779146314223062,130768687520787556984653959⟩,⟨95803115257557773204483776,95803115257566183875264776⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨220140105511088747866201417,220140105511110792691096184⟩,⟨110132065362537866763531722,110132065362559911584531865⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨335284006819867747272830032,335284006819921886442144399⟩,⟨84389877784441188447891817,84389877784495327603946473⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨463686308784959973744311056,463686308785074820902803044⟩,⟨(-8735785518169662999617044),(-8735785518054815870618240)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨574717004323902335035108609,574717004324097199163304611⟩,⟨(-192518348548847620159059689),(-192518348548652756083412210)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨620806961029710756909396208,620806961030044620833296947⟩,⟨(-469041368930839496385284168),(-469041368930505632516470893)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨553094059028530193694134085,553094059028979659504662572⟩,⟨(-803120510933261426524613848),(-803120510932811960752192708)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨350976613974708623224973814,350976613975142966812658004⟩,⟨(-1119951795171380185654804628),(-1119951795170945842077005218)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨48713313167435670540201871,48713313167738257207849961⟩,⟨(-1326756983954103352470215368),(-1326756983953800765780394523)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-265808630481429670136457450),(-265808630481267074742279283)⟩,⟨(-1353728192884519372274449876),(-1353728192884356776830410971)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-487766512122265064028666346),(-487766512122191970645657569)⟩,⟨(-1191074966640014625219814549),(-1191074966639941531770788010)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-543215764355927569349816116),(-543215764355897379263486560)⟩,⟨(-892573350418776583852407498),(-892573350418746393703462338)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-417512399777092902438433644),(-417512399777079447343986235)⟩,⟨(-536762132232912228692739542),(-536762132232898773560469505)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-155785794255832499346765792),(-155785794255828661270487148)⟩,⟨(-176999278384574049935355931),(-176999278384570211846926259)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-11527321052372237842849),(-11527321052372236967064)⟩,⟨(-150214065629862521769814),(-150214065629862520504506)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-163543143368205855715495),(-163543143368205852767897)⟩,⟨(-421474193597686938275712),(-421474193597686934169509)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-725518850478672881565434),(-725518850478672875548929)⟩,⟨(-393026868848533282853981),(-393026868848533275038508)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-2076985376285353623505575),(-2076985376285353612508197)⟩,⟨792239791538167685966445,792239791538167699151779⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-4741618620209216999471803),(-4741618620209216979756051)⟩,⟨4698416519680658102165132,4698416519680658124029944⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-9061764593116894695762131),(-9061764593116894660507639)⟩,⟨13234401749953311168518700,13234401749953311205357756⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-14327348104122964511251625),(-14327348104122964442808844)⟩,⟨27983321556802198975880294,27983321556802199044605568⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-18114042749893679550227280),(-18114042749893679358140431)⟩,⟨49447543130777529323508707,49447543130777529513806862⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-16779617862329354431068209),(-16779617862329353388767858)⟩,⟨76014833732923687577297943,76014833732923688615449517⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-7186988731714342555648544),(-7186988731714335551323789)⟩,⟨103054132648536097435822554,103054132648536104434033362⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨11035278305163118525999746,11035278305163158511950263⟩,⟨123445509132241414134805453,123445509132241454113919153⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨33874564411364313831482373,33874564411364507935378555⟩,⟨130295653961565444192780707,130295653961565638291768353⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨53144247797038434715767044,53144247797039028182943227⟩,⟨120434972455764198411712984,120434972455764791876044999⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨59364038177789881139078934,59364038177791002488952493⟩,⟨95666632776843471630027120,95666632776844592978640353⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨46841188534654237760091832,46841188534655480689620624⟩,⟨60795194548400844583955107,60795194548402087513111001⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨17793990276835512325361045,17793990276836067611982228⟩,⟨20753864707210340771882021,20753864707210896058454325⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1940196519126610870193117233),(-1940196519124057416499882932)⟩,⟨8566459066667627108866735530,8566459066670180562333565538⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_14 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 14) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_14 (tableDensity true) (fullFactor true 1 14) density1_contains hk1_1_14_contains +noncomputable def atomAnswer : CBox := ⟨⟨12994101110542429042463821674,12994101110542429482033143280⟩,⟨5587463406637948633865962858,5587463406637949072492175748⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_14 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 14) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_14 1 14 ha1_1_14_contains + def realAnswer : RBox := ⟨11053904591415818172170704441,11053904591418372065633260348⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 14) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_14 +namespace hm1_0_1_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨6818644749813460973861353672,6818644749813465815189083436⟩,⟨8966732292502992781597901390,8966732292502997623280615726⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨22279216576243202233398392779,22279216576243213116522988123⟩,⟨24574318297761135017881500337,24574318297761145902163665266⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨41879236237332847127071235580,41879236237332856918384239382⟩,⟨32921823922728567386255753357,32921823922728577179704856188⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨64347643800154903704736875128,64347643800154909957467297117⟩,⟨29179259945115363137275771197,29179259945115369392457312745⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨83960039750998084189890117404,83960039750998087208596703348⟩,⟨10719204631279128233160828248,10719204631279131253718828683⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨92503416047120312660302179747,92503416047120313637159174379⟩,⟨(-20087798163772413207218500324),(-20087798163772412229477995023)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨83859698727998250959766836891,83859698727998251239170445783⟩,⟨(-55115838776366124081829866044),(-55115838776366123803228556091)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨58237945954588809599984838333,58237945954588809725428053564⟩,⟨(-83512667090138576440943575375),(-83512667090138576317754238137)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨22625111848029294802307781440,22625111848029294879654666667⟩,⟨(-96939798691965066102287798698),(-96939798691965066026451869777)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-12818998474464206082755608765),(-12818998474464206016549239784)⟩,⟨(-93264923031709812298478913975),(-93264923031709812233153288148)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-39465837793296732133475862174),(-39465837793296732080447673525)⟩,⟨(-76476621671570324276537603833),(-76476621671570324224183364008)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-53019963535780164156580103288),(-53019963535780164117987023205)⟩,⟨(-53755197323795156520609380025),(-53755197323795156481587478798)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-53617608004051526221345605297),(-53617608004051526194448276249)⟩,⟨(-32037537649852171450801005553),(-32037537649852171423366977267)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-44204197026860915682629806022),(-44204197026860915666666497122)⟩,⟨(-15731476210071809887277765390),(-15731476210071809871322451858)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-28542413655133356060247027534),(-28542413655133356052265996111)⟩,⟨(-6022953039647551680250373093),(-6022953039647551672551891910)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-9803149455331841289716130041),(-9803149455331841287343513066)⟩,⟨(-1383302518163115518886214736),(-1383302518163115516660137772)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨5818111785231929459690053160,5818111785231934495969260990⟩,⟨(-6237846983182189510343945703),(-6237846983182184474548867850)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨15755861448411620506292704227,15755861448411640851120928100⟩,⟨(-20167842431253092621341905536),(-20167842431253072277770411114)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨20086892125118016947672764847,20086892125118074000710831152⟩,⟨(-37511441290619612107976922106),(-37511441290619555056354015694)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨14171149519751024643228548469,14171149519751173448429571151⟩,⟨(-57344857435907797912106656808),(-57344857435907649107463436747)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-5635506645812770996734734719),(-5635506645812428593181114945)⟩,⟨(-74272775253602701180076296879),(-74272775253602358775008959903)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-38256582587123458653113136813),(-38256582587122839810162990602)⟩,⟨(-79096025530773391789743111187),(-79096025530772772942320066815)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-74850931645642327396299026531),(-74850931645641284051220938149)⟩,⟨(-63502377241986752823376205532),(-63502377241985709472963873196)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-100846072846512879763401074261),(-100846072846511219651498030253)⟩,⟨(-27084089779205494633201616125),(-27084089779203834519306642089)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-104139284720391089808040961447),(-104139284720389379696520893643)⟩,⟨19415537133298238217795225758,19415537133299948327513377380⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-83474673390269083013954976678),(-83474673390267940453550489770)⟩,⟨59336877584084962325522510848,59336877584086104881174927952⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-49116580050170862500192454113),(-49116580050170176668676422688)⟩,⟨80272626322712574398770865164,80272626322713260226115135095⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-15410368276775461498336487005),(-15410368276775060347692221112)⟩,⟨80269349941801058042631972744,80269349941801459191640401042⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨7494242578491314330090507421,7494242578491498749794272032⟩,⟨65862255064508080598455178657,65862255064508265018240055513⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨16682408060286202041558861859,16682408060286276696541116351⟩,⟨45761306144560845465803374940,45761306144560920121600292065⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨14554244827695120192887487859,14554244827695148014658411182⟩,⟨25941530801741261303251603319,25941530801741289125801527009⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨5589518235423235526820646160,5589518235423242572759480602⟩,⟨8288447207061560332983449654,8288447207061567379227426564⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1477078253831180135133494724),(-1477078253831180132292431920)⟩,⟨(-1412886223961287391463308843),(-1412886223961287388630042692)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4871470212070652111478735178),(-4871470212070652102610978928)⟩,⟨(-3912090215516819163138060007),(-3912090215516819154364950893)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-9440973033177497237033216746),(-9440973033177497220670050844)⟩,⟨(-5236781932101341813559676245),(-5236781932101341797596327388)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-15386346454351654518593533820),(-15386346454351654491529153761)⟩,⟨(-4083779560828689668663123822),(-4083779560828689642671836444)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-21764302934055156819624856868),(-21764302934055156776971186488)⟩,⟨1171625531035154644015022123,1171625531035154684554694285⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-25968752007824819693674286339),(-25968752007824819628190226535)⟩,⟨11611285364739770673877964916,11611285364739770737326453454⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-24109986437626909444692655890),(-24109986437626909348930196012)⟩,⟨26235992946353159618362505539,26235992946353159713346228909⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-13028387269073798366926740444),(-13028387269073798232821165655)⟩,⟨40794036013445944168426385382,40794036013445944303798117799⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨6714118994829043425879935118,6714118994829043627617375218⟩,⟨48770098917537514660187399966,48770098917537514865460415965⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨29437340598341511757155030476,29437340598341512292333885023⟩,⟨45120037664803907341095132454,45120037664803907879439319284⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨46830977831142298097172949310,46830977831142300467141235606⟩,⟨30256770275775557514782581465,30256770275775559885713404798⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨53014528388395002953118059019,53014528388395011594097895328⟩,⟨10442714064508561946639924548,10442714064508570586638467311⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨47782459060620806502990356490,47782459060620826677194661018⟩,⟨(-6144715075916959273498266223),(-6144715075916939101407481322)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨35410965725830810119667595529,35410965725830839668082644641⟩,⟨(-14143070918447673963356111379),(-14143070918447644417201139235)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨20844178491341576992301925514,20844178491341608466896346999⟩,⟨(-12853884075460217262347280648),(-12853884075460185789140077575)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨6769024491809147900736801850,6769024491809162389215876010⟩,⟨(-5041761977325097516647194565),(-5041761977325083028590270679)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨35190296888410711249763836,35190296888411204404828111⟩,⟨227424081379506685022481626,227424081379507178194159490⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨156033340999364767448993169,156033340999365977930071985⟩,⟨692995634395505856782408384,692995634395507067304591082⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨433956192785749513104307399,433956192785750819955661064⟩,⟨1171807612105690925936572180,1171807612105692232824988942⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨982894906068197291801080541,982894906068198183319279883⟩,⟨1609088933859562163747610434,1609088933859563055245348768⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1894996042235037499649034467,1894996042235037899058441856⟩,⟨1852756536977635954580585656,1852756536977636353829859575⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3166587016573077938177465572,3166587016573078056502678875⟩,⟨1640314400785904786593841960,1640314400785904904516587513⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨4593974392360597488903630859,4593974392360597519062557173⟩,⟨662532404115190369652333637,662532404115190399188070529⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨5715302837610245938553209845,5715302837610245954056289780⟩,⟨(-1261378342977059202110719348),(-1261378342977059187076028018)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨5920624708259847417157892560,5920624708259847432101167477⟩,⟨(-3951334048645291497708871459),(-3951334048645291482876589347)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨4777002863537205281149640688,4777002863537205299032171147⟩,⟨(-6757318323370472045673864840),(-6757318323370472027392739712)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2399942051243750739795436290,2399942051243750760728902674⟩,⟨(-8765705095788599242491636019),(-8765705095788599220641284667)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-452540186042430953580218441),(-452540186042430930400435071)⟩,⟨(-9279210037437366582486293605),(-9279210037437366558306330224)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-2725106894330748351193192203),(-2725106894330748327680089128)⟩,⟨(-8219433842398653854380598110),(-8219433842398653830262630580)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-3620674197222602987794220329),(-3620674197222602967480698255)⟩,⟨(-6101645198564826829320805711),(-6101645198564826808741572708)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2953905051128353991746352002),(-2953905051128353978002640740)⟩,⟨(-3614365109525694828351742980),(-3614365109525694814539950934)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1124571175390196086997631348),(-1124571175390196082156310669)⟩,⟨(-1178739468612850873894786659),(-1178739468612850869048700559)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨15769696921758272712613059,15769696921758536699707084⟩,⟨(-19028381405233146983857585),(-19028381405232882997034095)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨43766397118009799491698670,43766397118010836161847157⟩,⟨(-61472429333607590241138792),(-61472429333606553572643508)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨59439328875826966740914121,59439328875829770996289953⟩,⟨(-116063489935952827605019491),(-116063489935950023355316122)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨49769182374404431894314812,49769182374411638279615791⟩,⟨(-186864631827628639825276450),(-186864631827621433454343166)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-2781183040822189600798053),(-2781183040805039064219801)⟩,⟨(-269375638283203205953739664),(-269375638283186055447096681)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-115897263988653411609542090),(-115897263988618405238101573)⟩,⟨(-344415921618912240013625818),(-344415921618877233695493359)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-296657929163756897927702990),(-296657929163680692461200745)⟩,⟨(-375178521410938330199501130),(-375178521410862124791966496)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-526432191340247790544174075),(-526432191340112901041881260)⟩,⟨(-314689029886365100176896782),(-314689029886230210717281997)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-751411073581672858012957893),(-751411073581500192599696352)⟩,⟨(-128059987788632881097687045),(-128059987788460215693824528)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-893724873175201203093351880),(-893724873175042563208842327)⟩,⟨177290838146390904449424938,177290838146549544373317178⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-888487485546058743247732824),(-888487485545954497480294881)⟩,⟨534401746484602434915966198,534401746484706680777899837⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-727769300465283117563101756),(-727769300465230791398233037)⟩,⟨833489704235573691230901297,833489704235626017534818569⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-475117196320060572482857405),(-475117196320033070441018190)⟩,⟨969967766376828288899707441,969967766376855791064238476⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-231111229016025658962998740),(-231111229016011355372695843)⟩,⟨892994799892579255836999595,892994799892593559506979042⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-72745438373605629805574125),(-72745438373599223206302599)⟩,⟨621208529966519912277088638,621208529966526318918405414⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-10584502749443811459676688),(-10584502749442018494377032)⟩,⟨221463627001681569138616998,221463627001683362116606045⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1217996378407420056173480),(-1217996378407420055543212)⟩,⟨99280170910684457690576,99280170910684458196089⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3689596824213252075211515),(-3689596824213252073167776)⟩,⟨641634045360553215903342,641634045360553217581777⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-6182975131139955855338347),(-6182975131139955851427297)⟩,⟨2235419982293755272506902,2235419982293755275869640⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-8428601033992373186582764),(-8428601033992373179978065)⟩,⟨5580923897515881671483369,5580923897515881677460497⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-9694618388417189069794955),(-9694618388417189059216161)⟩,⟨11171963287296806166824479,11171963287296806176853235⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-8639928058560890995770463),(-8639928058560890979115295)⟩,⟨18939043059233124057936534,18939043059233124074279018⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-3513126842447044412575889),(-3513126842447044384795096)⟩,⟨27861602816620457981515767,27861602816620458009381157⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨7058388530994572195712956,7058388530994572261203060⟩,⟨35726866399621705711756860,35726866399621705777781285⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨22919855277434228314969856,22919855277434228633845586⟩,⟨39413652583941627905858016,39413652583941628225527964⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨41558822411862891476241368,41558822411862893550551769⟩,⟨36107706471844374048290664,36107706471844376123249506⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨58369266439125172944860305,58369266439125187290376883⟩,⟨25165884908660765412840538,25165884908660779758429274⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨68253207591623324355332094,68253207591623393652724063⟩,⟨9397390022834804379968598,9397390022834873677017586⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨67781141180860559069622338,67781141180860767538908519⟩,⟨(-5631148362589887201339060),(-5631148362589678732502377)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨56588485062050152430499353,56588485062050541302916239⟩,⟨(-14298461733271318452508393),(-14298461733270929580424695)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨37091700594060269167808385,37091700594060696217129421⟩,⟨(-13838913972552150367236811),(-13838913972551723318075996)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12848017469493642029373786,12848017469493831872656055⟩,⟨(-5615599815441961688815536),(-5615599815441771845573785)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1487390878374355092190701607,1487390878375870454534879009⟩,⟨(-47521015610851956530677778889),(-47521015610850441168400171908)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 15) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_15 (tableDensity false) (fullFactor true 1 15) density0_contains hk1_1_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨3555534123829665646865874879,3555534123829665875912645640⟩,⟨397138423961903719831787997,397138423961903948365892955⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_15 1 15 ha1_1_15_contains + def realAnswer : RBox := ⟨5042925002204020738956576486,5042925002205536330547524649⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_15 +namespace hm1_1_1_15 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_15 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨953558518091248590815542830,953558518091252548169740761⟩,⟨1673909485753068280346543157,1673909485753072237615661183⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨3199836207109716549753158451,3199836207109725437576626079⟩,⟨4715234421505644432544404643,4715234421505653320085700383⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨6240823707237537156650896584,6240823707237545133876819081⟩,⟨6716563542849034995281950447,6716563542849042971963970410⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨9919176582134570624460485481,9919176582134575687825160264⟩,⟨6777795976527072211762163091,6777795976527077274467483807⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨13292960625545602063942670019,13292960625545604466076315163⟩,⟨4190642687574796126877315922,4190642687574798528528322702⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨14929940242984980307345211331,14929940242984981033601871152⟩,⟨(-917488828223231573137432289),(-917488828223230846974448760)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨13658766457578244655068096782,13658766457578244812880752404⟩,⟨(-7240292385290204457035407471),(-7240292385290204298862971027)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨9348155684279401472264690470,9348155684279401511652553772⟩,⟨(-12756930183925558940988800007),(-12756930183925558900828458756)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3120718619954104675225480439,3120718619954104694167232861⟩,⟨(-15753933633614780697721357379),(-15753933633614780677804175266)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-3194509276028412250656023775),(-3194509276028412233957100542)⟩,⟨(-15623796605348816160539323710),(-15623796605348816143368742793)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-7938290067996873963757353424),(-7938290067996873949556488326)⟩,⟨(-12948300851723393845003042918),(-12948300851723393830836398019)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-10239585212378998449497098050),(-10239585212378998438555880429)⟩,⟨(-9000465980975285647038610533),(-9000465980975285636285032076)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-10122724910639298049227196113),(-10122724910639298041364382564)⟩,⟨(-5109378061531442720831615274),(-5109378061531442713303653799)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-8199879722848430026493928133),(-8199879722848430021610230136)⟩,⟨(-2204204885023768396089327290),(-2204204885023768391647425740)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-5225182593773941032054314494),(-5225182593773941029496793971)⟩,⟨(-610554138489256112791435290),(-610554138489256110604408151)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-1781699862699496610611937195),(-1781699862699496609828041386)⟩,⟨(-70997939301054798843675997),(-70997939301054798203013934)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1260907969277859507661250908,1260907969277863640927187782⟩,⟨(-424242680077399078260558850),(-424242680077394944932727317)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨3589253670911732651690168050,3589253670911749368076103051⟩,⟨(-1620844998437144447932300235),(-1620844998437127731386213345)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨5197981650256952309203325696,5197981650256999263898609694⟩,⟨(-3725380012474016586196256010),(-3725380012473969631319502833)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨5283836055376421661112645906,5283836055376544315303768089⟩,⟨(-6840072619812376501974403467),(-6840072619812253847704755666)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨2990859280014283344749052328,2990859280014565922784679549⟩,⟨(-10257822206638169038983910537),(-10257822206637886461117343383)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1915605165385523861108863345),(-1915605165385012654124243326)⟩,⟨(-12399758202167867474229176308),(-12399758202167356267781903465)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-8328888433590143542910859940),(-8328888433589280802034331917)⟩,⟨(-11468933487711277391139051970),(-11468933487710414650936527317)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-13856833529652799895675587346),(-13856833529651426417248009205)⟩,⟨(-6732310930378096347964741046),(-6732310930376722869817430126)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16068923630187394620222604402),(-16068923630185979833164703497)⟩,⟨571892857912895354634220461,571892857914310141895079295⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-14112888651558323158968796984),(-14112888651557378507755154778)⟩,⟨7760829678646743568568789662,7760829678647688220420223273⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-9236672953576421684560324674),(-9236672953575855308169892217)⟩,⟨12377816655257868749893075874,12377816655258435126868726924⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-3781968861037000261946891327),(-3781968861036669444187673682)⟩,⟨13520606245825630392509717284,13520606245825961210501661840⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨300199794420570024736732389,300199794420721848421873148⟩,⟨11851451217423041304880281465,11851451217423193128551666957⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨2213327004362526685333457590,2213327004362588029441201940⟩,⟨8691346296596885988148149018,8691346296596947332132253973⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2165347048719146176557241546,2165347048719168997594685959⟩,⟨5134803572783408401540866744,5134803572783431222457894909⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨861804784460400532358229130,861804784460406305324106728⟩,⟨1679166458078597110274565600,1679166458078602883192444985⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-116846502304426713129598478),(-116846502304426712179316557)⟩,⟨(-446435487542639128786245330),(-446435487542639127836217881)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-468471992455955014195300392),(-468471992455955011212654777)⟩,⟨(-1332434115161906509811015247),(-1332434115161906506832484845)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1161094089385619194867940897),(-1161094089385619189507524720)⟩,⟨(-2140057298047675586021091687),(-2140057298047675580678260894)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2350338149336053198118435797),(-2350338149336053189762045168)⟩,⟨(-2642575978893466028934099809),(-2642575978893466020623634433)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-3997968972379029607482242796),(-3997968972379029595420580455)⟩,⟨(-2425989533018472009038919714),(-2425989533018471997061841712)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-5704164499802174724248070615),(-5704164499802174706962307060)⟩,⟨(-1025867083807890973883593258),(-1025867083807890956677709554)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-6653744932815574381422584073),(-6653744932815574357613099745)⟩,⟨1719278282925261950599207466,1719278282925261974375286295⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-5907809023243535648925597074),(-5907809023243535615732755196)⟩,⟨5270392318839831575528922955,5270392318839831608763916218⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-3060691619660029538798856510),(-3060691619660029475577053157)⟩,⟨8356004443195593580206011486,8356004443195593643531313658⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1205212057217585586539118383,1205212057217585891690200186⟩,⟨9594917148955981724088649697,9594917148955982029312366287⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨5308750168261236965745895672,5308750168261238741885635122⟩,⟨8435985278367291210523125836,8435985278367292986684438751⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨7725228658333198719319358190,7725228658333205598538339721⟩,⟨5575495402647182542635276281,5575495402647189421855255804⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨7897755464929439769820515830,7897755464929456071935517641⟩,⟨2435785331774087403828032384,2435785331774103705934516080⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨6323408369339705223817900847,6323408369339729216385211638⟩,⟨229802840783122075188911171,229802840783146067751549834⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨3908209898037542893347018546,3908209898037568515704813272⟩,⟨(-598194089224671022979512184),(-598194089224645400621496990)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1300889028546350409009044299,1300889028546362216334384090⟩,⟨(-333371059300721836128963531),(-333371059300710028802389131)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-36012881777393850148185903),(-36012881777393435852789512)⟩,⟨67975652154381470068963098,67975652154381884362556176⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-95782360601653759660289593),(-95782360601652743491887738)⟩,⟨213363336508974698247160636,213363336508975714411093883⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-114643829264797906244625846),(-114643829264796810900212612)⟩,⟨382946886197395157545709872,382946886197396252886069930⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-54303549919374506259901095),(-54303549919373761137554545)⟩,⟨578335115467261949174422770,578335115467262694298782748⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨130487192413923892912527444,130487192413924224689607421⟩,⟨775490026887954629774442963,775490026887954961567911848⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨473850791926715796181413245,473850791926715892178269049⟩,⟨912700728673562506733347610,912700728673562602770704138⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨965148306668938331533887620,965148306668938352974756631⟩,⟨891023480590524743222999482,891023480590524764725548838⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨1515245292482111096863881157,1515245292482111104762351602⟩,⟨606197637912053747821265943,606197637912053755763736125⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1954528517169617090351195015,1954528517169617096265290631⟩,⟨16227970529092677709493344,16227970529092683629582520⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨2093258284210057596633411643,2093258284210057603302527266⟩,⟨(-791416010037640025317875131),(-791416010037640018692190291)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1832102722827767968369115587,1832102722827767976096733609⟩,⟨(-1596470156662754755946795070),(-1596470156662754748309228020)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1247351878553739007561281225,1247351878553739016098226263⟩,⟨(-2137186735874434330615010086),(-2137186735874434322172478172)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨568745854014455073979647123,568745854014455082637326399⟩,⟨(-2243391817374207224812195453),(-2243391817374207216208967343)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨52533263322495221866919173,52533263322495229373006181⟩,⟨(-1909352835682947653474995483),(-1909352835682947645990623771)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-157167775407668164316295723),(-157167775407668159213539140)⟩,⟨(-1256026343304231003574191254),(-1256026343304230998475350119)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-88947456698606129644889241),(-88947456698606127841447372)⟩,⟨(-434712888914805643363685679),(-434712888914805641559793735)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨4854690772909655357504489,4854690772909872311429314⟩,⟨(-6509091418143464547438349),(-6509091418143247593491456)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨13794440039938912392258981,13794440039939764427310940⟩,⟨(-21219305928376515829161711),(-21219305928375663793870751)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨19802026238686853416799683,19802026238689158534790127⟩,⟨(-40642050319039250805783745),(-40642050319036945686781364)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨18969355801295094145077145,18969355801301018801427684⟩,⟨(-66555836352531520956416549),(-66555836352525596297242512)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨5000559547055257499461040,5000559547069359363743567⟩,⟨(-98094190085044769888687533),(-98094190085030668018198751)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-29854354214624891460462885),(-29854354214596107890539264)⟩,⟨(-130007459620937985812870632),(-130007459620909202231466118)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-91314212499048533239809518),(-91314212498985888230042969)⟩,⟨(-151368100893769248404525623),(-151368100893706603381265284)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-177604832068454847513105817),(-177604832068344015918985985)⟩,⟨(-146726467292672403614793610),(-146726467292561572010250255)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-274907522992818890924073291),(-274907522992677134027569436)⟩,⟨(-102095862206236129982208797),(-102095862206094373082587271)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-358143834013913247072728226),(-358143834013783143482132250)⟩,⟨(-15056354800076156178591020),(-15056354799946052595069763)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-399874203542970799005864363),(-399874203542885412838719102)⟩,⟨97253467058982380035596763,97253467059067766185146895⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-384117532975083327795725578),(-384117532975040525795491052)⟩,⟨200770707436933831426609358,200770707436976633401206356⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-316221216297455542325238552),(-316221216297433075548325121)⟩,⟨259506623429901568165663265,259506623429924034919969036⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-220233388929220674736629573),(-220233388929209002372212116)⟩,⟨252643777860316795807747193,252643777860328468157605907⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-123339806090928896220646620),(-123339806090923672134843209)⟩,⟨181598388852690330996157591,181598388852695555074328564⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-38797020462056646294383784),(-38797020462055184851775913)⟩,⟨65778465859065671222382650,65778465859067132662720003⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-36036441770213823685809),(-36036441770213823370457)⟩,⟨4677507761370502641362,4677507761370502867959⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-99582962472756417546350),(-99582962472756416521820)⟩,⟨45049103968086089836261,45049103968086090598079⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-84865044309789518403845),(-84865044309789516449323)⟩,⟨181559041344245618543038,181559041344245620094691⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨226717347703848587500374,226717347703848590806990⟩,⟨494441737819149324447331,494441737819149327277434⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1242630008611847944622835,1242630008611847950123603⟩,⟨1083117945789911779287030,1083117945789911784350476⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨3477397876593606367779062,3477397876593606377068310⟩,⟨1983274258946434157333829,1983274258946434166368633⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨7371173842253972480169346,7371173842253972497488854⟩,⟨2951734428710932195307373,2951734428710932212758979⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨13060221406268970208021731,13060221406268970255629767⟩,⟨3303607362919417300431577,3303607362919417348757415⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨20073562282094947552183857,20073562282094947806923871⟩,⟨2061955464016156601946617,2061955464016156858044722⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨27090391142540862109959029,27090391142540863799022131⟩,⟨(-1538994809236812315089756),(-1538994809236810624159363)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨32124182755691682700568420,32124182755691694409926727⟩,⟨(-7404040763397650031121592),(-7404040763397638320202854)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨33339594430642865355637642,33339594430642921940237133⟩,⟨(-14165200099493051551685858),(-14165200099492994966132929)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨30085898580475270193028750,30085898580475440497289256⟩,⟨(-19353557390775705962831758),(-19353557390775535658150907)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨23218872988468127921235252,23218872988468445758916020⟩,⟨(-20294795681799848620739547),(-20294795681799530782996237)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨14355522832589625772752114,14355522832589974946142194⟩,⟨(-15513548063275907670476120),(-15513548063275558497161670)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨4817084967778301804794180,4817084967778457059663500⟩,⟨(-5813618932344312267453233),(-5813618932344157012629340)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-513867490184716577818846100),(-513867490183465515420874590)⟩,⟨(-4181317785359224640407762224),(-4181317785357973578198606759)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_15 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 15) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_15 (tableDensity true) (fullFactor true 1 15) density1_contains hk1_1_15_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4649544623469563068501151990),(-4649544623469562768978451765)⟩,⟨(-519334862104028240170783094),(-519334862104027941318491996)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_15 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 15) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_15 1 15 ha1_1_15_contains + def realAnswer : RBox := ⟨(-5163412113654279646419998090),(-5163412113653028284299326355)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 15) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_15 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_6.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_6.lean new file mode 100644 index 0000000000000000000000000000000000000000..f17f77583ca04264507515adde6de8e2de4858e3 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_6.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_1_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1195968626899915498653716763),(-1195968626899912568550712156)⟩,⟨(-5882364934421743553528053463),(-5882364934421740623406348528)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5148720062340645595048312035),(-5148720062340638755945311066)⟩,⟨(-16957135621138560571967030041),(-16957135621138553732717994337)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-13170662886061830145633413693),(-13170662886061823515772850421)⟩,⟨(-25390588857379387709610768635),(-25390588857379381079260985559)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-25814859245542216414827770575),(-25814859245542212627139059861)⟩,⟨(-28165370044902653029334073558),(-28165370044902649240620535668)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-40496672938112937176676674497),(-40496672938112935787362134666)⟩,⟨(-22158005120605054102168260044),(-22158005120605052711295278559)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-51709420628091920925760848539),(-51709420628091920424967071012)⟩,⟨(-6476784150701432949907242558),(-6476784150701432447876925094)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-53561240900929900010249226891),(-53561240900929899844201717533)⟩,⟨15564057011802948462454805220,15564057011802948628868857351⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-43448816519480366076674745445),(-43448816519480365996670132200)⟩,⟨37054333362649666789255088869,37054333362649666868530912354⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-23999457236757709840004347876),(-23999457236757709791317115851)⟩,⟨50903702807108864411302134729,50903702807108864459123342040⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1635352628334399478817147832),(-1635352628334399439729260129)⟩,⟨53545602045513049536447002878,53545602045513049574969936736⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨16934418832488624032466445645,16934418832488624064950072369⟩,⟨46206897894105660347080686927,46206897894105660379067604380⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨27624726448945553822381716939,27624726448945553845399594832⟩,⟨33370925585121170577908947803,33370925585121170601085110133⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨29777856714020564844894731241,29777856714020564860982468257⟩,⟨20072802106160461710518143774,20072802106160461726906882735⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨25170605839435428509590026632,25170605839435428519105803258⟩,⟨9786757923860672602328782019,9786757923860672611846360540⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨16396235751308643278325479445,16396235751308643283039399356⟩,⟨3653394629194248696320708939,3653394629194248700873698285⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨5644293774409259256372084163,5644293774409259257762779149⟩,⟨809525638984116254448820854,809525638984116255755046677⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3801733125714957657860368576),(-3801733125714955033038628344)⟩,⟨52350880068451449503454699,52350880068454074248911703⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-11384229746793650642854518341),(-11384229746793640739888858147)⟩,⟨1222998908857850156516858390,1222998908857860059151377236⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-18373345670547437818705986362),(-18373345670547413525667933449)⟩,⟨5485832784280954557063776723,5485832784280978849234237150⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-22839458639402156587637543169),(-22839458639402104503515925915)⟩,⟨14209390391864769940116270954,14209390391864822022499523715⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-21456491419316211775325814534),(-21456491419316071801494874739)⟩,⟨26851522130329668566581466611,26851522130329808538646779434⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-11095774776173365191187127708),(-11095774776173024212017228125)⟩,⟨39651310351572100377045543918,39651310351572441355556989019⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨8107460784010100815805709838,8107460784010687316089725981⟩,⟨46079335211940229678230488337,46079335211940816179611205218⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨30595128497123733926335134451,30595128497124389548438533760⟩,⟨40380594105409074079403515975,40380594105409729704283406007⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨47310886503624631825894884143,47310886503625414901933746282⟩,⟨22332352494277242360540282190,22332352494278025438437795705⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨51426658057899406805889619663,51426658057900098042766593812⟩,⟨(-1420326638231594954220912226),(-1420326638230903717379538768)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨42912141767838746042352122835,42912141767839137782897817873⟩,⟨(-21540195206411021831610487084),(-21540195206410630092600094164)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨27712548928776865361521140115,27712548928777030765100978139⟩,⟨(-31923184544251546987829851500),(-31923184544251381586334093896)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨13014393081857121963535746560,13014393081857206958189454463⟩,⟨(-32135654824677762840908117114),(-32135654824677677847437166413)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨3250090309884564319943836198,3250090309884603507704486493⟩,⟨(-25488827851167798484045467771),(-25488827851167759296720887400)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-788761755552249851393513849),(-788761755552234000459589493)⟩,⟨(-15763044051215537487250858162),(-15763044051215521636399134516)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-741300902296414076402736656),(-741300902296409894417814492)⟩,⟨(-5267866340470694858326346033),(-5267866340470690676338347714)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-189244992599783865685723083),(-189244992599783864430860411)⟩,⟨722354005572228973484043170,722354005572228974798409482⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-377178574044975876650905732),(-377178574044975872730500062)⟩,⟨2259593014130448960268128144,2259593014130448964395437524⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨52466625159061975009043136,52466625159061982337654409⟩,⟨3986747245457352377325044402,3986747245457352385070423723⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1598907851613280040240541994,1598907851613280052906133610⟩,⟨5721820361138041986249590593,5721820361138041999413088753⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨4666318748929153146098690847,4666318748929153166949277989⟩,⟨6796453264814833292178579796,6796453264814833313387612443⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨9124441958064356736550306594,9124441958064356769079263567⟩,⟨6021121453102221290950216733,6021121453102221323410120324⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨13773149117217204546860718223,13773149117217204595012661917⟩,⟨2142950551736442587146717082,2142950551736442634501000996⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨16293291847960619777308696293,16293291847960619847757326266⟩,⟨(-5102386842409809608555146650),(-5102386842409809539496621532)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨14307190122904421967984628011,14307190122904422080478663878⟩,⟨(-13994661718699090331335736977),(-13994661718699090219571603083)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨7234850858045461439021535945,7234850858045461706362076097⟩,⟨(-21121380329108888268284647049),(-21121380329108888000636716568)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2664012276720105962915495465),(-2664012276720105071838057438)⟩,⟨(-23378087415261364457095212138),(-23378087415261363564755821948)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-11419024461208263367117017196),(-11419024461208260236612584439)⟩,⟨(-20172090984796557682075075521),(-20172090984796554550133796749)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-15842796720230780762756956258),(-15842796720230771268527751439)⟩,⟨(-13720090244795115257096894407),(-13720090244795105762154468818)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-15131090984774905989194659026),(-15131090984774888785015161290)⟩,⟨(-7233522267732042242016902529),(-7233522267732025037658980446)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-10481325660847879821237620460),(-10481325660847861718652104753)⟩,⟨(-2815000849457441036635554574),(-2815000849457422934103398643)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3701373341037027297098215082),(-3701373341037019489438751757)⟩,⟨(-632101429363536327338281605),(-632101429363528519725497327)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨62361630807882852327417847,62361630807883008335678697⟩,⟨(-31776181700967866652763882),(-31776181700967710644189188)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨185636384500121565221163160,185636384500121942178450597⟩,⟨(-111883136481481956011520994),(-111883136481481579049988657)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨297918731392531783120808263,297918731392532177390056021⟩,⟨(-241864265240968301778285451),(-241864265240967907490445952)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨370213610881224669736650633,370213610881224925591527952⟩,⟨(-452295044607736969474847970),(-452295044607736713568558900)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨343343194243830835677561818,343343194243830941921164640⟩,⟨(-757285489539749044438184256),(-757285489539748938084262273)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨130449844611688396986384823,130449844611688430860511557⟩,⟨(-1127464306650179265230891643),(-1127464306650179231206169914)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-350613760598259680176458000),(-350613760598259668402498598)⟩,⟨(-1459643615163945199875743128),(-1459643615163945187991600617)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1109282179573913060163622448),(-1109282179573913054248585857)⟩,⟨(-1574439756411556287314867160),(-1574439756411556281391127399)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2010918773378535001334368953),(-2010918773378534995160253068)⟩,⟨(-1281535576859415506279908729),(-1281535576859415500261264282)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-2775297831083325070601701179),(-2775297831083325062812188453)⟩,⟨(-510843432639529732067402454),(-510843432639529724609035035)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-3098949403757820106377640038),(-3098949403757820096764122576)⟩,⟨576287704481068508492936567,576287704481068517825092917⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-2845839272548101356838024935),(-2845839272548101346018425203)⟩,⟨1614986622063091381760559756,1614986622063091392456985756⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-2149348662478414867362743892),(-2149348662478414856578321827)⟩,⟨2220827032306874797372860078,2220827032306874808181164024⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1320727024530053200380820173),(-1320727024530053191113217358)⟩,⟨2191765334958858523737313516,2191765334958858533113734655⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-636555816112693060395105051),(-636555816112693054063027111)⟩,⟨1571816425875996791871896899,1571816425875996798315484862⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-177846462508109929734271555),(-177846462508109927490280489)⟩,⟨566814433365191153820954492,566814433365191156110576069⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-5558644439614419256356552),(-5558644439614352249931816)⟩,⟨(-3187617299450474367407315),(-3187617299450407360670371)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-17711161877994471029535243),(-17711161877994209656690486)⟩,⟨(-8442535047845023514906935),(-8442535047844762140887395)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-32625597412909174118709204),(-32625597412908477294016275)⟩,⟨(-9892221037960232631261342),(-9892221037959535803780344)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-50828823494464593434871093),(-50828823494462847663309502)⟩,⟨(-3770601864907071447664853),(-3770601864905325670392360)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-70227396001097921829028832),(-70227396001093935827826702)⟩,⟨14676293130284259627937290,14676293130288245639639159⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-84465515594111086367456932),(-84465515594100963120763994)⟩,⟨49665101907137656355569385,49665101907147779615293577⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-82446400988081452729464614),(-82446400988058023770966714)⟩,⟨101514696818089264984531173,101514696818112693953498612⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-51193043634944784788942462),(-51193043634905321919299449)⟩,⟨162353537293608363181871448,162353537293647826055038659⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨16905246760526872249301356,16905246760574853793525277⟩,⟨214217850745282204698702087,214217850745330186234475363⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨115248833799419595511481755,115248833799461047750450346⟩,⟨234026767406175814687080063,234026767406217266901569950⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨219635944075810716440732367,219635944075836440334319128⟩,⟨206218214558461225176844522,206218214558486949030749710⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨296234739176290828656798708,296234739176307613368397335⟩,⟨135833502627489679478739900,135833502627506464155943511⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨317873729296591558193343028,317873729296601248881266494⟩,⟨50275900740595487323175252,50275900740605177989634096⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨276985470151521765551939272,276985470151526557697439734⟩,⟨(-14948880194172296030769340),(-14948880194167503895013072)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨185645934598893363832473064,185645934598895441184292684⟩,⟨(-36964235090049695907102600),(-36964235090047618557862256)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨64910393846536593385426513,64910393846537165200562667⟩,⟨(-17853173971123087386707138),(-17853173971122515571760905)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨36866922332429627161935,36866922332429627282762⟩,⟨273869384613513336189658,273869384613513336337132⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨190861851978445067972618,190861851978445068373924⟩,⟨827147544045926194838637,827147544045926195317511⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨590936734039170458491109,590936734039170459295511⟩,⟨1375822606626593805619465,1375822606626593806538617⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1402463830172884472925553,1402463830172884474356740⟩,⟨1845952019179707198622885,1845952019179707200181084⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨2741049117390348118250035,2741049117390348120654002⟩,⟨2049736895955462168669479,2049736895955462171175239⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨4579428011431445965260684,4579428011431445969178790⟩,⟨1651622452189262044978153,1651622452189262048933941⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨6642439196472427946537454,6642439196472427953191535⟩,⟨220580674755213096421627,220580674755213103010401⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨8344283631405471811567407,8344283631405471827206627⟩,⟨(-2567209827062451007844653),(-2567209827062450992382444)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨8873130057554088539959132,8873130057554088612733626⟩,⟨(-6630033805894112216904303),(-6630033805894112144362635)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨7527470162748762112795454,7527470162748762649658631⟩,⟨(-11271040734149816533765906),(-11271040734149815997064282)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨4220899526829795488018778,4220899526829799378350010⟩,⟨(-15276086900907274416628206),(-15276086900907270526304961)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-185422652469430092145403),(-185422652469411646494885)⟩,⟨(-17377496745360621079887530),(-17377496745360602634166944)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-4101754174850119414031275),(-4101754174850064784192827)⟩,⟨(-16835089481488999293332056),(-16835089481488944663422364)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-5979966764287069774643012),(-5979966764286969209979228)⟩,⟨(-13742834430943581834374864),(-13742834430943481269682466)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-5121182608225837908133447),(-5121182608225728575526807)⟩,⟨(-8846101124842875363894480),(-8846101124842766031294500)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1996100201600625079653183),(-1996100201600576744316552)⟩,⟨(-3032396208945854327698404),(-3032396208945805992369974)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-1916593162920642154112478578),(-1916593162919925830107297984)⟩,⟨25054318613774845440576654469,25054318613775561764490358217⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 16) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_16 (tableDensity false) (fullFactor true 1 16) density0_contains hk1_1_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-2517751149641087094942836280),(-2517751149641086947354058371)⟩,⟨988856984101999729291379326,988856984101999876576047078⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_16 1 16 ha1_1_16_contains + def realAnswer : RBox := ⟨(-4434344312561729249155314858),(-4434344312561012777361356355)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_16 +namespace hm1_1_1_16 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_16 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-70002394314499955327684840),(-70002394314497560999317626)⟩,⟨(-1024169285314453542233423717),(-1024169285314451147909428064)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-468698077647547107674156211),(-468698077647541524245703660)⟩,⟨(-3008214615010377797920324748),(-3008214615010372214527529834)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1560865097215913262182203356),(-1560865097215907862162884442)⟩,⟨(-4669113377083126228486250376),(-4669113377083120828593976357)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-3495405339227440188799903451),(-3495405339227437124853407678)⟩,⟨(-5475930887388998752209645703),(-5475930887388995688556803896)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-5914390967698334044318484225),(-5914390967698332950389217693)⟩,⟨(-4774596006682771808771257832),(-4774596006682770715299696745)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-7919382735413418229254000223),(-7919382735413417867675929163)⟩,⟨(-2252824155897466593670983339),(-2252824155897466232404456496)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-8437690358156826986570603239),(-8437690358156826896376985325)⟩,⟨1612195617948128375174422960,1612195617948128465333751524⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-6879907555191753853930943909),(-6879907555191753828862649005)⟩,⟨5595781754140192958106832391,5595781754140192983419600634⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3590598329047867439427117360),(-3590598329047867427866594987)⟩,⟨8337983363272796280072870862,8337983363272796292183897672⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨315193705374652914111112771,315193705374652923498092637⟩,⟨9068633567457556340272665238,9068633567457556350074650715⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3580873117292635253840363204,3580873117292635262221660217⟩,⟨7912631368372849787178276835,7912631368372849795633625506⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨5404246093647275017861672895,5404246093647275024290463768⟩,⟨5655244314179233718688502917,5655244314179233725059565598⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨5651269335291887680812079064,5651269335291887685464346136⟩,⟨3250456285405698627175118690,3250456285405698631664736835⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨4680921262282661831823234572,4680921262282661834705742164⟩,⟨1404664826527683669934261619,1404664826527683672574766678⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨3004766919860412758238089347,3004766919860412759735271640⟩,⟨385486011870932230474515775,385486011870932231761083049⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1026071373075141445821868282,1026071373075141446277696772⟩,⟨43220430957483561848773525,43220430957483562222245065⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-525460221825524838152161477),(-525460221825522685037025246)⟩,⟨(-274810987601010861529248233),(-274810987601008708404973094)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1638512421229302432369557202),(-1638512421229294300405974130)⟩,⟨(-647647492201106817277808979),(-647647492201098685274281696)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-2841489687758282687112170480),(-2841489687758262707193691877)⟩,⟨(-479501373225102724869682417),(-479501373225082744845998033)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-3896373804754491819791831294),(-3896373804754448919597564146)⟩,⟨553395156587714588382908229,553395156587757488791928231⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-4235350501861480562989929873),(-4235350501861365079841731755)⟩,⟨2522886972817909952372979637,2522886972818025435742731336⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-3172395535920262815903922887),(-3172395535919981158562191147)⟩,⟨4949557457703908645642140727,4949557457704190303073694814⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-437761244436821021291017715),(-437761244436336075734917120)⟩,⟨6741058978523817233181124930,6741058978524302178616285953⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨3308929164208233494953997500,3308929164208775841879403800⟩,⟨6701432021807517615983161089,6701432021808059962560752016⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨6599643714640968728004621037,6599643714641616503615933730⟩,⟨4415234160686600290417477203,4415234160687248065779795895⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨8059388305275666873105125318,8059388305276238351037229677⟩,⟨706362366434307128182896839,706362366434878606112871162⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨7337061732307269252862352267,7337061732307592747296501253⟩,⟨(-2874350514719895741739416317),(-2874350514719572247090282035)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨5198392557028275955727708405,5198392557028412303124064325⟩,⟨(-5070314771101339744549278953),(-5070314771101203396850948980)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2823324521987525457037188404,2823324521987595395533515301⟩,⟨(-5521077335554829764913656132),(-5521077335554759826242072830)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1064952237695630381885364066,1064952237695662567503983994⟩,⟨(-4610154501345461479240940675),(-4610154501345429293555495102)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨183806838153363509466860370,183806838153376505015551470⟩,⟨(-2951167364622525939118776553),(-2951167364622512943556665618)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-20751113117644336785655764),(-20751113117640912018355450)⟩,⟨(-1004140437841534410076449383),(-1004140437841530985309382117)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-121855162269823934979501376),(-121855162269823934561780750)⟩,⟨116504526059708049115220920,116504526059708049535637277⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-342061866923315456509801955),(-342061866923315455193675824)⟩,⟨388827221498827134270394339,388827221498827135596225497⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-473137183569460844819460649),(-473137183569460842419133044)⟩,⟨764632838850347248765248634,764632838850347251184718230⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-405124043099425253324798360),(-405124043099425249378741683)⟩,⟨1256132659529938393829668657,1256132659529938397797675003⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨4241882757970807108672768,4241882757970813147003506⟩,⟨1768764677246384031784053523,1768764677246384037837039418⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨844684535701521731242931746,844684535701521739817751859⟩,⟨2060667163927864697535339542,2060667163927864706108697632⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨2004578189439742431428768447,2004578189439742442859181810⟩,⟨1790804489191923808070676877,1790804489191923819470824276⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨3073061812433959460217612377,3073061812433959476022968982⟩,⟨718677035489006591923126527,718677035489006607675693756⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨3469875667648863702366984670,3469875667648863736043359984⟩,⟨(-1022162578351243906408234500),(-1022162578351243872757067804)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨2827053322538548001901910531,2827053322538548145460701902⟩,⟨(-2840093692899107796932282755),(-2840093692899107653371079846)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1331253024692305460470998531,1331253024692306099234481876⟩,⟨(-3990026605229740199467313829),(-3990026605229739560690234047)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-344525231037514273319358406),(-344525231037511817606945992)⟩,⟨(-4072380681207312215120034192),(-4072380681207309759394931181)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1498709287457929575589113326),(-1498709287457921924893455966)⟩,⟨(-3268023220473873535810700781),(-3268023220473865885107722054)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-1810900773394390060034173988),(-1810900773394376094189724602)⟩,⟨(-2113181335927004454689386263),(-2113181335926990488842031130)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1380852703818736814163138037),(-1380852703818722080465005821)⟩,⟨(-1078542333269464301497715890),(-1078542333269449567798533803)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-506674665420162678881777953),(-506674665420156318194611832)⟩,⟨(-316574595614614346387965829),(-316574595614607985700383430)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨23060755162691711684887444,23060755162691842739059689⟩,⟨3945653755255192985626566,3945653755255324039784505⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨70997731830864348068374801,70997731830864664494523865⟩,⟨7197011143707692718363561,7197011143708009144118276⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨122673048179430830751973964,122673048179431161179391396⟩,⟨(-4460996512524430725716543),(-4460996512524100300168024)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨174772737306108228504895134,174772737306108442299784098⟩,⟨(-43300385362674029641542980),(-43300385362673815851896630)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨214691766176244155604077215,214691766176244243778939609⟩,⟨(-121543879705121669114442062),(-121543879705121580950720210)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨218049321113338696952180546,218049321113338724343587407⟩,⟨(-244056732214381922041916453),(-244056732214381894665417372)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨152244558303746113633476405,152244558303746122141564948⟩,⟨(-396601370169399717430444376),(-396601370169399708932707748)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-8578802169707442830766644),(-8578802169707439832723021)⟩,⟨(-536956030045556250760805065),(-536956030045556247762387060)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-258946747777844466816310641),(-258946747777844464478539986)⟩,⟨(-601396046345199554049080233),(-601396046345199551694980298)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-544637749884524425425576193),(-544637749884524422702268909)⟩,⟨(-534503401614466597612314845),(-534503401614466594856503263)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-775311524172111146194882007),(-775311524172111142827828930)⟩,⟨(-330463595492345595938192178),(-330463595492345592544897987)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-869951291686679469809061095),(-869951291686679465960317389)⟩,⟨(-53002904695533814214846790),(-53002904695533810355972603)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-803624162183384049349626369),(-803624162183384045446856429)⟩,⟨190994536772828537249169667,190994536772828541147731421⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-615621616226498541812417052),(-615621616226498538401880280)⟩,⟨309185795690435151718175502,309185795690435155116894615⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-372852582459491103168944454),(-372852582459491100807138354)⟩,⟨269182669400790158626141708,269182669400790160976749215⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-123051109384239750652235640),(-123051109384239749808830769)⟩,⟨105062144023669056595768498,105062144023669057434716187⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1877603966899934937978234),(-1877603966899879869619119)⟩,⟨(-952514733534557443448840),(-952514733534502375145331)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-6054641673258789831263533),(-6054641673258575009450628)⟩,⟨(-2577996356512785075497329),(-2577996356512570253904511)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-11377858440536026122852069),(-11377858440535453326535497)⟩,⟨(-3203743042367811054390119),(-3203743042367238258622062)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-18165322896069041989368281),(-18165322896067606718046765)⟩,⟨(-1665291181609201816606763),(-1665291181607766546462705)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-25886321873467640792350061),(-25886321873464363335479156)⟩,⟨3772868708413205318364547,3772868708416482772998616⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-32654797069382087003622541),(-32654797069373763291499813)⟩,⟨15080387772444403319488525,15080387772452727028715960⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-34955794870646684059483929),(-34955794870627424148087254)⟩,⟨33385576609299756664368367,33385576609319016573241807⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-28226019712122089814233243),(-28226019712089665164300844)⟩,⟨57380016227836056916610920,57380016227868481565475903⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-8917147930983532485518855),(-8917147930944139869336506)⟩,⟨82195481557994266760860642,82195481558033659378599742⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨22368491410624234963575733,22368491410658230935826724⟩,⟨100171906402585005059323035,100171906402619001036377288⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨58786161638638156883595940,58786161638659226783423676⟩,⟨104143366935512190448267345,104143366935533260355680536⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨88811718851322191784247751,88811718851335920871041731⟩,⟨91701227531911818441143038,91701227531925547534503243⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨101616842945128046578255024,101616842945135963040919875⟩,⟨67312363560801269517985490,67312363560809185984800205⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨92440896255008250439672921,92440896255012161016000130⟩,⟨40160371787335152708362079,40160371787339063286597801⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨63784739331124428982094679,63784739331126122871612342⟩,⟨18585180737493976857811284,18585180737495670747878647⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨22645373909498070803770280,22645373909498536877153251⟩,⟨4986334138268621586964673,4986334138269087660411468⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1483789367923014446795,1483789367923014501381⟩,⟨8082156034708266819570,8082156034708266892993⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨11428965003777966038357,11428965003777966221688⟩,⟨21978809026751715169310,21978809026751715408066⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨42413332619252641738878,42413332619252642111608⟩,⟨16843605496736281587412,16843605496736282043801⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨109776065529435065014552,109776065529435065693091⟩,⟨(-59325301837602019215452),(-59325301837602018441555)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨229085279029034260736773,229085279029034261948452⟩,⟨(-305223583497541741915327),(-305223583497541740624533)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨395777142633028699408236,395777142633028701565044⟩,⟨(-848975341134460392636777),(-848975341134460390453777)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨535020136363125959450576,535020136363125963591366⟩,⟨(-1802380432789770890014266),(-1802380432789770885952556)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨464722249590658821207375,464722249590658832525153⟩,⟨(-3197280246738866069524419),(-3197280246738866058438568)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-61598551073206510553455),(-61598551073206452563757)⟩,⟨(-4903615779665228643853862),(-4903615779665228586259744)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1216908578005434058050227),(-1216908578005433620753919)⟩,⟨(-6569899681783020215166057),(-6569899681783019778325010)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-2926072213790309486011820),(-2926072213790306310276566)⟩,⟨(-7682376946543231187151661),(-7682376946543228011717972)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-4769870484323234410900830),(-4769870484323219349065941)⟩,⟨(-7793889810502945242002529),(-7793889810502930180314149)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-6062187992174561511628520),(-6062187992174516883176575)⟩,⟨(-6805305410419096493037835),(-6805305410419051864604422)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-6109461782778068504867996),(-6109461782777986310513979)⟩,⟨(-5037927035331105387288407),(-5037927035331023192880763)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-4567854786676990743494416),(-4567854786676901348866172)⟩,⟨(-2986014753310763365656942),(-2986014753310673970965920)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1694638295282241279356633),(-1694638295282201750564070)⟩,⟨(-974402620837907198578405),(-974402620837867669759955)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1110891195639715851541468940,1110891195640307265309026126⟩,⟨2327179235139581371575494382,2327179235140172785346602527⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_16 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 16) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_16 (tableDensity true) (fullFactor true 1 16) density1_contains hk1_1_16_contains +noncomputable def atomAnswer : CBox := ⟨⟨3292443811069113700386076332,3292443811069113893386785904⟩,⟨(-1293120671517999838599446178),(-1293120671517999645996419118)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_16 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 16) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_16 1 16 ha1_1_16_contains + def realAnswer : RBox := ⟨4403335006708829551827545272,4403335006709421158795812030⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 16) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_16 +namespace hm1_0_1_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-741857808995819479988478551),(-741857808995818125781003610)⟩,⟨2917682407030673796084649027,2917682407030675150214443269⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1304088259685605201862337007),(-1304088259685601905794399149)⟩,⟨8814985377528153547434294130,8814985377528156843325325451⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨758028574689736436225641656,758028574689739885100931120⟩,⟨14434727082076655071439085509,14434727082076658520187843570⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨6460878941997323441713866143,6460878941997325629155774928⟩,⟨18338511033503472796350512115,18338511033503474983891953839⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨15200475290759494586644473804,15200475290759495451539623607⟩,⟨18174759228970409535807224785,18174759228970410401132323941⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨24157262360258568098802071054,24157262360258568337126198119⟩,⟨12058598162703315422797195571,12058598162703315661988482416⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨29170521374209032666899054705,29170521374209032756806501336⟩,⟨460566928802817004698626943,460566928802817095178229152⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨27131951579065281153823786707,27131951579065281200613446427⟩,⟨(-13122365033986722365872496075),(-13122365033986722319161876644)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨18161663453516457756975228215,18161663453516457786787841108⟩,⟨(-23802350789994380626425598942),(-23802350789994380596947007283)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨5631990075698521147240139332,5631990075698521168952987782⟩,⟨(-28127926170115853695001629426),(-28127926170115853673599741973)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-5939429717063735646908721512),(-5939429717063735628303974594)⟩,⟨(-25808007929570762864460260474),(-25808007929570762846177640991)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-13293604783807537584531155038),(-13293604783807537571541254318)⟩,⟨(-19247311419226055965728045398),(-19247311419226055952698991218)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-15496766663437743933105144281),(-15496766663437743924065479101)⟩,⟨(-11723159368435174720258519984),(-11723159368435174711060443181)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-13475957508486903185534338784),(-13475957508486903180200656591)⟩,⟨(-5693582112829832842177224386),(-5693582112829832836839027582)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-8863479523207434196675571747),(-8863479523207434194056151477)⟩,⟨(-2080078923189475313791236576),(-2080078923189475311258047023)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-3058592584895469490005361361),(-3058592584895469489238347884)⟩,⟨(-445762289653198071813358473),(-445762289653198071092169877)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1119630968277410819484653113,1119630968277411738091705797⟩,⟨1136011310968907250004246450,1136011310968908168707659516⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨3707294210580762814510061655,3707294210580766595753701890⟩,⟨3081991337623715689135608704,3081991337623719470629369817⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨7141373625852627525619683968,7141373625852638434235476305⟩,⟨3890629211982535978354076478,3890629211982546887246101306⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨11261832968049494547846296298,11261832968049523711199622992⟩,⟨2464091914020666458729836696,2464091914020695622160795665⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨14766530352669184909563694729,14766530352669252365742665412⟩,⟨(-2182939777239187689773085452),(-2182939777239120233999506444)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨15242736804552669895553161875,15242736804552790199064817894⟩,⟨(-9870761453613849121577944107),(-9870761453613728819131919127)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨10406938315233755942058360625,10406938315234003891530963539⟩,⟨(-18225947787838899585222992313),(-18225947787838651636586191386)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨266782060537775984585263739,266782060538152256442988304⟩,⟨(-23131101563115268299589128327),(-23131101563114892027654863876)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-11754028914747165692985312548),(-11754028914746817491025700961)⟩,⟨(-21286011086221665831264210881),(-21286011086221317628270115339)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-20571773449937649216027813519),(-20571773449937377482405740780)⟩,⟨(-12973348037820959719087412338),(-12973348037820687984370906984)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-22959437580881210016722893375),(-22959437580881007842228701644)⟩,⟨(-2099341200262372239455611335),(-2099341200262170064704927829)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-19461768985171594655215396966),(-19461768985171492811172661748)⟩,⟨6681666915342610905208123874,6681666915342712748854582012⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-13185013234941188040824696215),(-13185013234941148267204034852)⟩,⟨10836653373748746798758418425,10836653373748786571677226106⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-7237270783885132492121420260),(-7237270783885117321695477764)⟩,⟨10506153096830407854473996893,10506153096830423024306001402⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-3150905036623304017872745602),(-3150905036623297207677608491)⟩,⟨7224338460800760049363546162,7224338460800766859278534709⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-822183510307413415504227919),(-822183510307411525522633073)⟩,⟨2534273384457287412705707071,2534273384457289302608717425⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨248724473648054002646168231,248724473648054003232298792⟩,⟨(-63705842200286458360360976),(-63705842200286457794303715)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨743760301441831334447875786,743760301441831336301086337⟩,⟨(-267970890886453147855264350),(-267970890886453146055224151)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨1193775629835632391916947859,1193775629835632395437484776⟩,⟨(-703900504733867941203665235),(-703900504733867937743808362)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1447199884383530384729866951,1447199884383530390707945257⟩,⟨(-1503397826211624038284458450),(-1503397826211624032322959764)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1199956039855665549163257527,1199956039855665558794552057⟩,⟨(-2678350258784152033248888552),(-2678350258784152023508378340)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨64042992814075344947808597,64042992814075360063454636⟩,⟨(-3953521625349150169512138937),(-3953521625349150154068993425)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-2160630035571289678310568560),(-2160630035571289654764251031)⟩,⟨(-4654959433395252943920495842),(-4654959433395252920004693625)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-5082193696393269879814693944),(-5082193696393269844192194368)⟩,⟨(-3900645393197288002788634418),(-3900645393197287967068743684)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-7561084893914591540689588244),(-7561084893914591486109068833)⟩,⟨(-1210974112218655321998157446),(-1210974112218655267725766351)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-8230126747404569299781224834),(-8230126747404569190657696648)⟩,⟨2844591824163168396978935655,2844591824163168505477756821⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-6506898089485846373678876284),(-6506898089485845954251466092)⟩,⟨6708004490143022122458122920,6708004490143022541535207169⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-3174331990862329254534566298),(-3174331990862327682408553050)⟩,⟨8804119845807351499319125940,8804119845807353071472834942⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨133013995951963765586750947,133013995951967596561833288⟩,⟨8579847061714342051139964813,8579847061714345882407191624⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨2044708763116413784341303044,2044708763116419534878511116⟩,⟨6634634132283532699259170528,6634634132283538450169420085⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨2144184834644519682199692493,2144184834644525284530420989⟩,⟨3986669899944476764310266003,3986669899944482366911513417⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨877778711588280830363962289,877778711588283442953592223⟩,⟨1304408452588796054958143368,1304408452588798667631563462⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-14217370824407499267027474),(-14217370824407457354491430)⟩,⟨(-14115443318784790914233976),(-14115443318784749003320957)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-47307333463217181146495741),(-47307333463217081742556966)⟩,⟨(-40452837131416013694984868),(-40452837131415914296979351)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-93874694211194246331773752),(-93874694211194146449222717)⟩,⟨(-59065614060306751289940644),(-59065614060306651420884444)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-160222455529602499815934632),(-160222455529602438644186593)⟩,⟨(-58377420068178728028028836),(-58377420068178666882223911)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-244794217255090354297739934),(-244794217255090322751231005)⟩,⟨(-18929964022562890752697186),(-18929964022562859237016362)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-329604276792278644354230979),(-329604276792278631921330467)⟩,⟨83322737234555141800590835,83322737234555154210616580⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-373288527706688106181808411),(-373288527706688102181921339)⟩,⟨263549579103226995799037789,263549579103226999800457787⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-317053488362371754215497823),(-317053488362371752133274368)⟩,⟨505251036984555205902815931,505251036984555208030369419⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-114153591707408317273773546),(-114153591707408314984348376)⟩,⟨743122950187922035469811239,743122950187922037852322196⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨225261714339099329692225477,225261714339099332791624484⟩,⟨877218492014422525080323509,877218492014422528250507159⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨610339479047072016599804983,610339479047072020538713464⟩,⟨828346632037907197328834050,828346632037907201283274648⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨903041697244164995252603886,903041697244164999818735596⟩,⟨600909495627953480600225557,600909495627953485121047440⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨995581357527810939298546424,995581357527810944046160741⟩,⟨294282436755056067583837731,294282436755056072241461183⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨867572889080153356907437255,867572889080153361111288127⟩,⟨42870320069050328945194621,42870320069050333052137839⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨575943956480441583658798969,575943956480441586573298935⟩,⟨(-67130697978751228770368313),(-67130697978751225913032484)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨199782072537315498041417942,199782072537315499081825080⟩,⟨(-40672252024563176918351399),(-40672252024563175895774903)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-535176680557973937002031),(-535176680557958415851087)⟩,⟨1469244688398550376270101,1469244688398565897288289⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-1284930399053058600882070),(-1284930399052998570441662)⟩,⟨4626254374121497253310510,4626254374121557283290610⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-966598297888068555286283),(-966598297887911526037550)⟩,⟨8333156923166387373969825,8333156923166544402234567⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1415813375473836886463606,1415813375474216761370387⟩,⟨12563950844422775622116463,12563950844423155495176934⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨7031662672995270152320589,7031662672996309119256564⟩,⟨16551538106563357767548978,16551538106564396731952780⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨16739837396968931881725160,16739837396971834149170885⟩,⟨18388029604728011064606857,18388029604730913329762917⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨30119380932511086177167438,30119380932517492892474404⟩,⟨15014590705324383143629818,15014590705330789857812751⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨44355400283193298668136719,44355400283203577750614387⟩,⟨3202744523403997921411760,3202744523414277005182734⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨54005266094610979990415042,54005266094622751815339322⟩,⟨(-18278026248049197744005910),(-18278026248037425914035435)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨52875509224476484028347805,52875509224486068948784655⟩,⟨(-46319341525934731296205994),(-46319341525925146366386925)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨37936054312984530663865407,37936054312992370738880506⟩,⟨(-73140286546710313714100732),(-73140286546702473630428934)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨12788703021889909404443662,12788703021895233559265916⟩,⟨(-89427370047277669092459976),(-89427370047272344932615615)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-12751861371192864460483279),(-12751861371189967193691569)⟩,⟨(-89346235113018643301490155),(-89346235113015746033583820)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-27737117511342580098236905),(-27737117511341211580055444)⟩,⟨(-73446374929361967141392166),(-73446374929360598624820467)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-26305358619893020854253650),(-26305358619892447183366016)⟩,⟨(-47065477115199595121643239),(-47065477115199021453012840)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-10616624105349845383038845),(-10616624105349690332811319)⟩,⟨(-16043968063881041603016611),(-16043968063880886553795213)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨57795454981512743550264,57795454981512743582657⟩,⟨(-10893025457985045806095),(-10893025457985045779022)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨173977777528613095954158,173977777528613096059471⟩,⟨(-50287317449159862521034),(-50287317449159862431105)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨286958811013404674205680,286958811013404674408372⟩,⟨(-143771121101333730598737),(-143771121101333730418377)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨377978744442792495763438,377978744442792496108290⟩,⟨(-327899784235805505477322),(-327899784235805505156109)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨401887333438450290461266,401887333438450291017846⟩,⟨(-627768570385124688679121),(-627768570385124688139032)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨279877749945993165109939,279877749945993165990479⟩,⟨(-1034297564230988081079023),(-1034297564230988080198905)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-87382936321365214918886),(-87382936321365213450058)⟩,⟨(-1477804861599418432658326),(-1477804861599418431164931)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-770538365980063415275554),(-770538365980063411853468)⟩,⟨(-1812821869522039093482117),(-1812821869522039090009447)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1738788711699005431148653),(-1738788711699005415445616)⟩,⟨(-1841481823626021178380345),(-1841481823626021162616603)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-2810801270845967441483048),(-2810801270845967305432116)⟩,⟨(-1400682846170263364076005),(-1400682846170263227993205)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-3686746147861966014738608),(-3686746147861965045510367)⟩,⟨(-489772075527850451493017),(-489772075527849482264846)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-4074167532272314778987150),(-4074167532272310266305535)⟩,⟨649884920706663208389300,649884920706667721059199⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-3834660537878381862128261),(-3834660537878368719220395)⟩,⟨1599154380882363704044405,1599154380882376846946734⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-3042890897129735077726815),(-3042890897129711248231256)⟩,⟨1964841216670137318518168,1964841216670161148021454⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1911789132217850617932360),(-1911789132217825021398900)⟩,⟨1585755288087712216865027,1585755288087737813412218⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-645939711180799913010321),(-645939711180788673772699)⟩,⟨604488792721670089238243,604488792721681328482535⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨1581777454147141975736981429,1581777454147464849031317039⟩,⟨(-12129184561954003348691420180),(-12129184561953680475435739386)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 17) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_17 (tableDensity false) (fullFactor true 1 17) density0_contains hk1_1_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨1999940176776273458762854516,1999940176776273548951563952⟩,⟨(-537135231382993321538373414),(-537135231382993231518060212)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_17 1 17 ha1_1_17_contains + def realAnswer : RBox := ⟨3581717630923415434399835945,3581717630923738398082880991⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_17 +namespace hm1_1_1_17 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_17 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-191599304999108992769831109),(-191599304999107887223497637)⟩,⟨477867486755907192878084324,477867486755908298443213463⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-433498613051928446654392199),(-433498613051925758448767897)⟩,⟨1468231227472652737286470576,1468231227472655425535516707⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-256907930438564049483180163),(-256907930438561243624003689)⟩,⟨2474649447133915883329953064,2474649447133918689220173877⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨542763344742504564316123633,542763344742506330874497495⟩,⟨3261293459286428683410073293,3261293459286430449933214990⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨1931304413894660813344047663,1931304413894661493522916519⟩,⟨3389547337092815417549243227,3389547337092816097572206086⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨3482069455098823948880041085,3482069455098824114117707392⟩,⟨2462879038430099720175069019,2462879038430099885157466391⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨4465033778958671507382161951,4465033778958671552378294417⟩,⟨492089614670069842014671291,492089614670069886868760891⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨4258701977517931044584735595,4258701977517931058858134713⟩,⟨(-1939343511850230162633281739),(-1939343511850230148339195686)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨2796555986540007359964931900,2796555986540007367067634277⟩,⟨(-3936797138720015923548706215),(-3936797138720015916228502354)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨640268281136049635771079331,640268281136049640738412645⟩,⟨(-4816455802138580487610721653),(-4816455802138580482355906379)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1381179489933926532577507431),(-1381179489933926527958039777)⟩,⟨(-4465055294442707940325729434),(-4465055294442707935616481127)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2641772653810223107204878563),(-2641772653810223103646997596)⟩,⟨(-3295628428875805594947964938),(-3295628428875805591393711020)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2957439842318170960081067910),(-2957439842318170957496059436)⟩,⟨(-1922807024060288038903754284),(-1922807024060288036390300770)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-2512539704797207147888388435),(-2512539704797207146288495676)⟩,⟨(-833918338939464237372072900),(-833918338939464235896493244)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1626029925403415497317904458),(-1626029925403415496493177365)⟩,⟨(-227266101058101510887787580),(-227266101058101510175708065)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-556145813862959576787687884),(-556145813862959576538234995)⟩,⟨(-24690923879787517884412933),(-24690923879787517679527788)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨69343383837110086465588920,69343383837110838161530115⟩,⟨238902549047416216994299059,238902549047416968677935329⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨284643585506883653797807870,284643585506886753849277386⟩,⟨685059146009957564941913811,685059146009960664961547127⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨704722303732796857188926700,704722303732805822897969230⟩,⟨998440524665767400903024780,998440524665776366576668593⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1361874557573828772695823846,1361874557573852791917453310⟩,⟨994740867378179564096230814,994740867378203583306359105⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨2092478396764529549131648519,2092478396764585190846100761⟩,⟨451615955922715351247746430,451615955922770993008543090⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨2493221723335665746820154635,2493221723335765085617474961⟩,⟨(-710552796045549465157543604),(-710552796045450126229829231)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨2082334646724488522431233324,2082334646724693509841074774⟩,⟨(-2200985536494492345484400095),(-2200985536494287357966969453)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨681719140043050124379975299,681719140043361377238679033⟩,⟨(-3343496273248451100530472445),(-3343496273248139847673203259)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1286429600998857122130186866),(-1286429600998569116000993218)⟩,⟨(-3458779901022593253049302264),(-3458779901022305247050682404)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-2979783966018597058179384569),(-2979783966018372456516246687)⟩,⟨(-2397444900570905019225791212),(-2397444900570680417711237028)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-3720662227625336010174366318),(-3720662227625169081199969186)⟩,⟨(-688090738911697042730783806),(-688090738911530113792625729)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-3426727317558405388108509965),(-3426727317558321437976954835)⟩,⟨867197560279282199740152938,867197560279366149930047671⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2519279837437395052102686104),(-2519279837437362342616440075)⟩,⟨1723916813703231015803014961,1723916813703263725393909224⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1519512340316191937390647744),(-1519512340316179495722940014)⟩,⟨1791719476317062064610463895,1791719476317074506368713702⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-738147176874935104045080972),(-738147176874929528511021554)⟩,⟨1278891698841542779818217333,1278891698841548355396180429⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-210994711385064227791784934),(-210994711385062682268321818)⟩,⟨456621635069347833991897898,456621635069349379527942487⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨55362674558376416655670086,55362674558376416841600219⟩,⟨17178901814059769835833337,17178901814059770020842642⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨174778853921210249098169008,174778853921210249693975497⟩,⟨37306087329609304965714811,37306087329609305558993975⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨312355958767339457969222926,312355958767339459085108214⟩,⟨10786667231089317923825374,10786667231089319036855518⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨452424611076437249565388547,452424611076437251383302322⟩,⟨(-101133699957402614588601399),(-101133699957402612771562104)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨536704389491239605467580527,536704389491239608200236724⟩,⟨(-329239771467453535613295881),(-329239771467453532876444843)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨464542292965129111436074165,464542292965129115317784753⟩,⟨(-657969973820152982100805427),(-657969973820152978206786164)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨138333906184865710017883893,138333906184865715503468419⟩,⟨(-979793926087806285706917933),(-979793926087806280206604680)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-442452673630434585400579196),(-442452673630434577436513996)⟩,⟨(-1098274654070262054896754894),(-1098274654070262046928164276)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1104475473071810743336163993),(-1104475473071810728744704116)⟩,⟨(-833796562891192787186552433),(-833796562891192772603354779)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1551576104773795058139898607),(-1551576104773795009068639073)⟩,⟨(-187518258845332470603575247),(-187518258845332421545257632)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-1560469767689580375524023456),(-1560469767689580082745817026)⟩,⟨596503294659534793259341726,596503294659535086031744698⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1156667074270733741004927705),(-1156667074270732513690583150)⟩,⟨1176767748284614901860485352,1176767748284616129173266819⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-588950022290341606241533150),(-588950022290338534252961365)⟩,⟨1349008748211628308040194624,1349008748211631380029614746⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-134948209162463877416115993),(-134948209162459227950415905)⟩,⟨1144049140574879595824100461,1144049140574884245290554300⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨67677958565772755878198812,67677958565777301447007635⟩,⟨727666381884597486827897967,727666381884602032396574495⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨50435939292778955086006064,50435939292781078922266415⟩,⟨245019867369991072237415980,245019867369993196073403408⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-989393655062177495296872),(-989393655062142289909288)⟩,⟨(-6623444010155984424190186),(-6623444010155949218636851)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-4470412727384833795030275),(-4470412727384750364277180)⟩,⟨(-19999851740863485592466660),(-19999851740863402161104315)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-12617297391996739861740979),(-12617297391996656178060482)⟩,⟨(-33159246304709575654213427),(-33159246304709491969146339)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-28759612843465750730309667),(-28759612843465699667666113)⟩,⟨(-43957347754180970643038824),(-43957347754180919577742949)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-55376960614769463221645762),(-55376960614769437105276168)⟩,⟨(-47327348766216948479272036),(-47327348766216922359811608)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-91520776114580730437906174),(-91520776114580720421025812)⟩,⟨(-35117797836507055484219262),(-35117797836507045465168436)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-129299159187896147388349654),(-129299159187896144562686634)⟩,⟨1613602275300956824962592,1613602275300959650241501⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-152362323493437469054665503),(-152362323493437468051416379)⟩,⟨66687017871951908629943919,66687017871951909628500319⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-140608480279555350533623987),(-140608480279555349662946016)⟩,⟨151154027526765406840894480,151154027526765407702417470⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-82280340172400232236950370),(-82280340172400231111763227)⟩,⟨230670715345472059270562584,230670715345472060389171929⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨13264305628483081702789266,13264305628483083107131046⟩,⟨274785183277937812515260371,274785183277937813918754340⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨114273427174080580080622432,114273427174080581696774173⟩,⟨265355729558141519202012375,265355729558141520823144232⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨181908691157895728702001802,181908691157895730386053632⟩,⟨209513612094266540175147640,209513612094266541868020330⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨191350169821506822875092804,191350169821506824380019892⟩,⟨134425645744166567696902632,134425645744166569210950746⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨141950165076701296166814961,141950165076701297225397586⟩,⟨67636599099954589216370391,67636599099954590280222453⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨51985412229662394708057684,51985412229662395089253610⟩,⟨19521142084680338459738612,19521142084680338842552660⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-150907505587942549000247),(-150907505587929793272992)⟩,⟨491115561459008088679825,491115561459020844432511⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-364994293241934770102370),(-364994293241885431667672)⟩,⟨1568484383867591124408803,1568484383867640462934649⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-277516545753008261496248),(-277516545752879183060101)⟩,⟨2895434177786949316914043,2895434177787078395551183⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨428481030820513473833781,428481030820825782582890⟩,⟨4504962765643763016289767,4504962765644075325427878⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨2189356614707536400971726,2189356614708390681852677⟩,⟨6181166207354378404437742,6181166207355232685868256⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨5448323883306595867490971,5448323883308982217817359⟩,⟨7324223034953137675940843,7324223034955524026801018⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨10345476058126824704017436,10345476058132091385495092⟩,⟨6907777022312096345871991,6907777022317363027660105⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨16289462747715621842045239,16289462747724067667711793⟩,⟨3707713857148220038520414,3707713857156665863966836⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨21725353806642650270373833,21725353806652314934462896⟩,⟨(-3050588548326861212876986),(-3050588548317196549828007)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨24516026208526865044820242,24516026208534725845370222⟩,⟨(-12808358584107852059251915),(-12808358584099991260599699)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨23039408719120705315957591,23039408719127126754439259⟩,⟨(-23216563305068227509374099),(-23216563305061806072609992)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨17387194291851527558358368,17387194291855882497691789⟩,⟨(-30822209685415204936929509),(-30822209685410849998610528)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨9659693596175054391301235,9659693596177421214524228⟩,⟨(-32789038548194747646652531),(-32789038548192380823700638)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨2924679292746716197673305,2924679292747832950963254⟩,⟨(-28375348672817801964885075),(-28375348672816685211353976)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-559662039726340906966344),(-559662039725873143683097)⟩,⟨(-18915693458597252201129266),(-18915693458596784437476238)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-657778444959781435736717),(-657778444959655063242954)⟩,⟨(-6593750310048373711539512),(-6593750310048247338880999)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1701163861736884051471,1701163861736884067519⟩,⟨(-405600292016445587964),(-405600292016445575656)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4548228828663833327076,4548228828663833379265⟩,⟨(-2690669549733833357666),(-2690669549733833316384)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨3065440445215883584111,3065440445215883684032⟩,⟨(-9287405311055386533259),(-9287405311055386449470)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-14333578090482267391444),(-14333578090482267221701)⟩,⟨(-22811651299181766835145),(-22811651299181766682895)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-69973987997300398109430),(-69973987997300397825751)⟩,⟨(-44927329239746732976152),(-44927329239746732704805)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-193482490878147199436099),(-193482490878147198956051)⟩,⟨(-71531514865218313171583),(-71531514865218312689934)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-410955467810854101846152),(-410955467810854100954532)⟩,⟨(-81680991274173120346464),(-81680991274173119426776)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-728672004923339734656334),(-728672004923339732248499)⟩,⟨(-29817234743337017973368),(-29817234743337015500258)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1112577665689987339286003),(-1112577665689987326900393)⟩,⟨142637657110732555249359,142637657110732567737532⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1474936641231873235443993),(-1474936641231873124704622)⟩,⟨471770684981982104854469,471770684981982215683126⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1691985045866427579441085),(-1691985045866426788337654)⟩,⟨927257845587486212876808,927257845587487004029795⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1663938878329625477080795),(-1663938878329621792342711)⟩,⟨1392002841955138996882234,1392002841955142681632801⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-1385979796762781044799700),(-1385979796762770308140410)⟩,⟨1689600029014305308596995,1689600029014316045240162⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-961917779555293297563267),(-961917779555273821131577)⟩,⟨1654474498983408455615598,1654474498983427932018486⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-530183725011884326671019),(-530183725011863397999780)⟩,⟨1215535230444520515449370,1215535230444541444095716⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-164112878157593554174476),(-164112878157584362708959)⟩,⟨447192434968119923202952,447192434968129114659059⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-873423657428035309958964846),(-873423657427768757388107231)⟩,⟨(-1418537333128575436440854344),(-1418537333128308883875599982)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_17 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 17) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_17 (tableDensity true) (fullFactor true 1 17) density1_contains hk1_1_17_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-2615306385015126948628968245),(-2615306385015126830689886675)⟩,⟨702407610270068071985155662,702407610270068189704026773⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_17 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 17) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_17 1 17 ha1_1_17_contains + def realAnswer : RBox := ⟨(-3488730042443162258687933091),(-3488730042442895587977993906)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 17) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_17 +namespace hm1_0_1_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨917056916983601478970216347,917056916983602006046826467⟩,⟨(-1091972269215849285552835246),(-1091972269215848758538471354)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨2349173241590454827395112858,2349173241590456042886564306⟩,⟨(-3519764314297249264599963921),(-3519764314297248049293767120)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨2517526993953464636994304440,2517526993953466037017855216⟩,⟨(-6422839662644081378923541028),(-6422839662644079979127058560)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨601189967435596191710002434,601189967435597200775247306⟩,⟨(-9325332774461733128509775727),(-9325332774461732119604744032)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-3644694365901931271390340511),(-3644694365901930813323964789)⟩,⟨(-10890698048506195124749117830),(-10890698048506194666690237319)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-9191005131071081068826519703),(-9191005131071080930011094435)⟩,⟨(-9488077315527204142638124439),(-9488077315527204003576402898)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-13703941807691394490030363709),(-13703941807691394444580945234)⟩,⟨(-4454875473205821072417673501),(-4454875473205821026539539769)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-14736408925351791561067611884),(-14736408925351791535303680829)⟩,⟨2908981678845937778110547662,2908981678845937803988260622⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-11427429614366386427542873740),(-11427429614366386410553629772)⟩,⟨9779551264208111274109628511,9779551264208111291004141049⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-5173031714840246335883841028),(-5173031714840246324071752288)⟩,⟨13551595043235347751368051263,13551595043235347763056724945⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1358736507942704814357633392,1358736507942704824369705376⟩,⟨13388784587793780486275017404,13388784587793780496098467672⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨5899954739846556558117060276,5899954739846556565066265980⟩,⟨10366336100576586088037387014,10366336100576586094982949241⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨7580601429274751058991398770,7580601429274751063780606923⟩,⟨6413064784848700974157555416,6413064784848700979025254236⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨6807017849195838836590832596,6807017849195838839411824678⟩,⟨3110895935857931513278897250,3110895935857931516104042102⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨4524556639991912634029853554,4524556639991912635404020908⟩,⟨1115769139742383567016347280,1115769139742383568346896462⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1565334083622873225902263353,1565334083622873226301701397⟩,⟨231763002142001938165912238,231763002142001938541871743⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨17876981233826208071017239,17876981233826649295003738⟩,⟨(-631703040331340810212587584),(-631703040331340368978668716)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-146854898611497906164870267),(-146854898611496228264712252)⟩,⟨(-1911561210548130347725808483),(-1911561210548128669776068965)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-909551464245027749858048570),(-909551464245023597477847839)⟩,⟨(-3127906494462001568567419141),(-3127906494461997416042018466)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-2570758181544154997954988294),(-2570758181544145931276563893)⟩,⟨(-3894154786208313100911559845),(-3894154786208304033929633215)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-5042459318443477936163834466),(-5042459318443451937108817070)⟩,⟨(-3472152726727310592024877181),(-3472152726727284592693048061)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-7480575283937049609786458193),(-7480575283936986131264684530)⟩,⟨(-1119333528062188443753840881),(-1119333528062124965201294344)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-8324090501913238441069837087),(-8324090501913134318234382041)⟩,⟨3124554276162293931340012825,3124554276162398053823928025⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-6204904693093605568811127210),(-6204904693093471292508816333)⟩,⟨7810221539506560246186617459,7810221539506694521978100089⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1284141603917029136992053598),(-1284141603916854457905886292)⟩,⟨10595129113238048349698054240,10595129113238223028687055971⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨4407529940833538948529603596,4407529940833673912300228064⟩,⟨9923111613531806944683084358,9923111613531941908800529135⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨8338505729999181820291297509,8338505729999255279403117169⟩,⟨6306151623712443765147065959,6306151623712517224763243263⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨9280603357417113408983759429,9280603357417159684542156228⟩,⟨1827212068891275246840320734,1827212068891321522591451800⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨7791440558313929848386936711,7791440558313951861027974505⟩,⟨(-1497914476755425332466487356),(-1497914476755403319879803699)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨5274760279551425413163084605,5274760279551434216024087581⟩,⟨(-2821787772298023884752356526),(-2821787772298015082048944087)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨2847250193469241921178829181,2847250193469245094329080339⟩,⟨(-2389708560974196417912276066),(-2389708560974193244902138177)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨874781701778565241483775549,874781701778566023429900712⟩,⟨(-907164958623181710955850290),(-907164958623180929063455175)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-57301074393471080759059155),(-57301074393471080514492998)⟩,⟨(-60565943451414104324810493),(-60565943451414104079920650)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-194767161104225583440757233),(-194767161104225582664260296)⟩,⟨(-168686873680602574485434373),(-168686873680602573711363261)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-395163096493392022244363772),(-395163096493392020754875166)⟩,⟨(-225418174333359879834643758),(-225418174333359878361183553)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-673321063653660800559719260),(-673321063653660797964234820)⟩,⟨(-160762893215046078617251771),(-160762893215046076070852509)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-978825615850946506549429793),(-978825615850946502186913262)⟩,⟨124748085867758371632706908,124748085867758375899868153⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1150812069399523076570453508),(-1150812069399523069434741213)⟩,⟨707088916777908744856643712,707088916777908751918243127⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-928524513657469472347399152),(-928524513657469461192641308)⟩,⟨1523866402840283394313021848,1523866402840283405476475292⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-94959462935941615191426062),(-94959462935941598506304047)⟩,⟨2268358413555016323810455457,2268358413555016340636581148⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1275049779958422027710886977,1275049779958422053530148823⟩,⟨2455711816003435558548166705,2455711816003435584556122869⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨2691500755602144755273162929,2691500755602144808834201198⟩,⟨1744789498017892530306145831,1744789498017892583912940915⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨3493482082238555891358750007,3493482082238556055105109022⟩,⟨290487575566423347976550966,290487575566423511602047273⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3335279234964257617773528614,3335279234964258100742204949⟩,⟨(-1269363809178306764928264873),(-1269363809178306282186653869)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨2439612617487741977320087863,2439612617487743438246381250⟩,⟨(-2248968840860999864328743528),(-2248968840860998403547413918)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1364951593627018501081547231,1364951593627021274904336749⟩,⟨(-2346060007954575766897282120),(-2346060007954572993123258101)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨563456229787125287143539239,563456229787128280393789186⟩,⟨(-1691835597514061661265562827),(-1691835597514058668015901346)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨133861144454847490364880218,133861144454848795046006914⟩,⟨(-607168553538116890040599469),(-607168553538115585354315538)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-2424178711007625286349495),(-2424178711007615831751934)⟩,⟨4843355855673363423854354,4843355855673372879262285⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-6363862492867315288931575),(-6363862492867293468407348)⟩,⟨15636945986295696878171595,15636945986295718701420729⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-7029955598467995960519480),(-7029955598467971617935670)⟩,⟨29447981480002629875828836,29447981480002654222997665⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-603955205379012897859048),(-603955205378993481961156)⟩,⟨46983495667738208310583076,46983495667738227731761033⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨18352285464784863513814025,18352285464784873858990187⟩,⟨65966950402836916987665097,65966950402836927336828700⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨55132348903463224921759309,55132348903463228658426260⟩,⟨78807406140095818550351123,78807406140095822286006137⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨110100412205450525613138564,110100412205450526780313023⟩,⟨71659450852149338865310460,71659450852149340021583197⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨172141622428577163848970240,172141622428577164556930773⟩,⟨28441411423960308701599966,28441411423960309387109141⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨216206355759896142094580739,216206355759896142989964809⟩,⟨(-58117748301796387622288422),(-58117748301796386743616134)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨212630324624111722533677690,212630324624111723741915758⟩,⟨(-173641898995103358044120519),(-173641898995103356836567592)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨147768728755880469196787657,147768728755880470753425742⟩,⟨(-280683734321778137629839150),(-280683734321778136052591118)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨40528312002502027310982493,40528312002502029148263182⟩,⟨(-337168370391850295264185680),(-337168370391850293389175281)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-63579094813981361852866482),(-63579094813981359898551930)⟩,⟨(-323160860219197561727488537),(-323160860219197559744159504)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-119516431368106877588165393),(-119516431368106875821839434)⟩,⟨(-251524480736170888178018544),(-251524480736170886397245689)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-108319593976366129480829895),(-108319593976366128246395896)⟩,⟨(-152737167293945115710606348),(-152737167293945114471392193)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-42860525961497176142265412),(-42860525961497175700060886)⟩,⟨(-50299634260698344211525193),(-50299634260698343768533051)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨354692412728934437467794,354692412728937718423325⟩,⟨63796053000468799254055,63796053000472080252270⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1104468587095588238838512,1104468587095600784933523⟩,⟨107490367178844504896408,107490367178857051134413⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨1945669832848653146772520,1945669832848685113557303⟩,⟨(-123607992092195583426529),(-123607992092163616350211)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨2831175183290317509031882,2831175183290408542864265⟩,⟨(-871103028544217703754246),(-871103028544126669495975)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨3519716869819358057240932,3519716869819636888821682⟩,⟨(-2394881793100510504729113),(-2394881793100231672712507)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨3488578714704912819670631,3488578714705658588716022⟩,⟨(-4832344164135620814740703),(-4832344164134875045410885)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1966160388804890854970726,1966160388806464790449845⟩,⟨(-7939711728054290184995371),(-7939711728052716249635262)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1762373825861263938675966),(-1762373825858872747423828)⟩,⟨(-10829508920680620659485192),(-10829508920678229469079354)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-7757601695669785122107069),(-7757601695667238793380502)⟩,⟨(-11997572946546291583954241),(-11997572946543745257100884)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-14869662710818044836443309),(-14869662710815395256492200)⟩,⟨(-9946533086554069872284497),(-9946533086551420294338138)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-20844283694501222170263793),(-20844283694498930853177546)⟩,⟨(-4290910175032612942699317),(-4290910175030321626777275)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-23399117756252647933801285),(-23399117756251192590385737)⟩,⟨3437540543247236487443408,3437540543248691830848526⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-21622797725406229294540445),(-21622797725405482031817460)⟩,⟨10190540335798143045775215,10190540335798890309536260⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-16471738103612672520803888),(-16471738103612337600776784)⟩,⟨13003705518589065365434215,13003705518589400287025550⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-9866004239058079676807321),(-9866004239057945190798851)⟩,⟨10632612091488794639917620,10632612091488929127283342⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-3224681016756434138304801),(-3224681016756398693505547)⟩,⟨4069748306512474476665911,4069748306512509921997418⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2795924172098591102774),(-2795924172098591097056)⟩,⟨(-11486324632509509630340),(-11486324632509509623629)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-12030137748090775330662),(-12030137748090775311691)⟩,⟨(-34449045397716195091618),(-34449045397716195069795)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-32467607677985015166345),(-32467607677985015128287)⟩,⟨(-56282534526758073085494),(-56282534526758073043391)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-71697200181733561966220),(-71697200181733561898378)⟩,⟨(-72556832258960630477400),(-72556832258960630405534)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-134780027411359111667552),(-134780027411359111553385)⟩,⟨(-73069252104771593480879),(-73069252104771593364511)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-219043497499490874060402),(-219043497499490873874458)⟩,⟨(-40397343431950935932463),(-40397343431950935748072)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-307870690163325405033685),(-307870690163325404715623)⟩,⟨46952479065588550987502,46952479065588551298304⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-367275073126151892036187),(-367275073126151891313716)⟩,⟨203216268229376217668173,203216268229376218377720⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-351938251573978091269423),(-351938251573978087696341)⟩,⟨418656529667080388089315,418656529667080391649173⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-226435314502212156914132),(-226435314502212124931460)⟩,⟨648871281236993784438541,648871281236993816415693⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨4497696247449289552550,4497696247449512758874⟩,⟨824266039165386271233458,824266039165386494440141⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨278405634261940278187805,278405634261941297770136⟩,⟨882139112747647623082903,882139112747648642666579⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨492757724262977638331785,492757724262980551637895⟩,⟨801512031575635036600592,801512031575637949905172⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨555203775906978528436078,555203775906983714476845⟩,⟨612587724921961877866864,612587724921967063902442⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨432055706324084234417024,432055706324089720867009⟩,⟨371868761417069441255014,371868761417074927699061⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨162278619987982476552747,162278619987984864427609⟩,⟨122964161928911632172508,122964161928914020044772⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-924112858865094688515485272),(-924112858864955191262524124)⟩,⟨5421628588345681451503634863,5421628588345820948744841363⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 18) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_18 (tableDensity false) (fullFactor true 1 18) density0_contains hk1_1_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1211280744282986785933082848),(-1211280744282986733524106576)⟩,⟨(-3548976872869409392059175),(-3548976872869357076010791)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_18 1 18 ha1_1_18_contains + def realAnswer : RBox := ⟨(-2135393603148081474548568120),(-2135393603147941924686630700)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_18 +namespace hm1_1_1_18 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_18 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨180101335237160734155599054,180101335237161163580974240⟩,⟨(-164418531380790802080085263),(-164418531380790372639818452)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨484143901247568312280730700,484143901247569301016473848⟩,⟨(-542359571025236765795705018),(-542359571025235777014788341)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨599760437961959243634017189,599760437961960379455122668⟩,⟨(-1024832752732896317592680596),(-1024832752732895181713920987)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨375018417190031990684310132,375018417190032802347550511⟩,⟨(-1544111303403774559846548725),(-1544111303403773748142535071)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-271768579487114452246488667),(-271768579487114094497754413)⟩,⟨(-1871184399865997831138395189),(-1871184399865997473402190678)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1206774511713161920573289160),(-1206774511713161824864538841)⟩,⟨(-1701916473756280278359584527),(-1701916473756280182742258381)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-2035882743693989106201736748),(-2035882743693989085964461722)⟩,⟨(-880652337689969512059385949),(-880652337689969491944008355)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-2297308612028132526605347196),(-2297308612028132519177815173)⟩,⟨398795106928102264843581509,398795106928102272226513445⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1787631928135301601611103373),(-1787631928135301597590698289)⟩,⟨1639452950138301499631338891,1639452950138301503714174414⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-723726365759795102184896675),(-723726365759795099534711548)⟩,⟨2347767740177271633624899104,2347767740177271636427502900⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨413620879357327794178867511,413620879357327796567673202⟩,⟨2338786127994827624284136144,2338786127994827626743297784⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1196006154262404676929130301,1196006154262404678789080117⟩,⟨1791154642556654819199666174,1791154642556654821071858251⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1455439300028351972721769487,1455439300028351974075536993⟩,⟨1063422669842908344024094878,1063422669842908345349827399⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1272478288314085908648419932,1272478288314085909486401341⟩,⟨463611292728542084862541286,463611292728542085640454716⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨830921302996201303400315995,830921302996201303829292747⟩,⟨125701302326778146443818860,125701302326778146815912990⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨284690650954330038035335918,284690650954330038164257410⟩,⟨13286852384739085482009261,13286852384739085588152948⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨49309017485283631439080696,49309017485283992143375329⟩,⟨(-85339692315640360388030806),(-85339692315639999684908779)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨116716503051953802685947345,116716503051955176702114104⟩,⟨(-270929760334710138605310110),(-270929760334708764595096382)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨84911344427165624389568460,84911344427169032703639558⟩,⟨(-482063461923722695295936185),(-482063461923719286999465924)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-114161388438398909711109242),(-114161388438391452386247425)⟩,⟨(-672932163583174397812536341),(-672932163583166940525244608)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-501811200661992714556363752),(-501811200661971279441904634)⟩,⟨(-720297649139265818340626478),(-720297649139244383261079104)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-974308491330656914441990156),(-974308491330604501008602128)⟩,⟨(-465208265429310318638606116),(-465208265429257905210794127)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1274152343922191469870339595),(-1274152343922105406681778810)⟩,⟨154064466733793792899272608,154064466733879856129320081⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1115777655831400596630969204),(-1115777655831289550640825284)⟩,⟨959003309540806877920519803,959003309540917923976184213⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-430308733304963858760457455),(-430308733304819391678619259)⟩,⟨1561423528391268575282922151,1561423528391413042380112304⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨509896617945431358985790672,509896617945542903376423255⟩,⟨1629458563946393896716045436,1629458563946505441060784103⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1268163251651349494841891586,1268163251651410118839658869⟩,⟨1155723551235196287783665291,1155723551235256911710688651⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1562925200896061933326219553,1562925200896100063714166469⟩,⟨444583081760547211279801308,444583081760585341640347401⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1411800215919442609419273996,1411800215919460708186490069⟩,⟨(-144727126198707664789387740),(-144727126198689566013878584)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1018451437609534021283718374,1018451437609541239031175225⟩,⟨(-419933595753979465777162005),(-419933595753972248005731095)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨580212514728465098536642755,580212514728467692448534074⟩,⟨(-385189773366147097884334090),(-385189773366144503950709092)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨184342433100770453212334588,184342433100771091013341639⟩,⟨(-150426146719107215396359349),(-150426146719106577586869713)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-3851961107842760184976809),(-3851961107842760106639578)⟩,⟨(-18425436384622339368156182),(-18425436384622339289800258)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-17264765366232452802602044),(-17264765366232452552085617)⟩,⟨(-55630273798655248207726317),(-55630273798655247957310303)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-47840910319096537574646378),(-47840910319096537106805297)⟩,⟨(-90763316552982618564470245),(-90763316552982618097332288)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-105035979435304883477149181),(-105035979435304882708442917)⟩,⟨(-112329596906776986665156787),(-112329596906776985898555771)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-188476945768336438540456215),(-188476945768336437351340675)⟩,⟨(-96370010772152954851106478),(-96370010772152953665813162)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-274792090268874649490603478),(-274792090268874647700614842)⟩,⟨(-13111485320215332592083359),(-13111485320215330805044125)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-309967963246956780773812792),(-309967963246956778219829215)⟩,⟨149229334499788027874550521,149229334499788030428720464⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-228174438488763761566146724),(-228174438488763758018602483)⟩,⟨352065961977020185487265029,352065961977020189039884468⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4445258925415861771021751),(-4445258925415855533131036)⟩,⟨499980649535801421551905665,499980649535801427795761164⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨297260790873902132269784503,297260790873902155624540965⟩,⟨492961161004048157579162444,492961161004048180935499061⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨544283740741003282013864743,544283740741003390173880517⟩,⟨310521915614656197276745476,310521915614656305435693929⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨627748583941061205995808423,627748583941061570983174523⟩,⟨42195881321456701677601433,42195881321457066663270155⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨540696716222071502902873349,540696716222072665629838787⟩,⟨(-177728365809396953536347835),(-177728365809395790810575040)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨364569250981053409938071469,364569250981055649441103535⟩,⟨(-264403419406409625047530000),(-264403419406407385545050464)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨190302585092184412979772843,190302585092186841024861950⟩,⟨(-216007918145106387951656900),(-216007918145103959906756812)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨56371682327726461735891819,56371682327727521759682882⟩,⟨(-81291626392459647590010606),(-81291626392458587566285025)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-1617400156693698195394264),(-1617400156693690254231664)⟩,⟨813502112007962237728379,813502112007970178806784⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-4764960615002664188290124),(-4764960615002645875618282)⟩,⟨2861723538375001190520398,2861723538375019502909050⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-7463891657996946829124868),(-7463891657996926436945960)⟩,⟨6170764395844645132242357,6170764395844665523946687⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-8815674160318776754508170),(-8815674160318760543968042)⟩,⟨11479053121011300885158205,11479053121011317095157133⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-7131077395558012789060024),(-7131077395558004220546814)⟩,⟨19021347110286710789830461,19021347110286719357952427⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-98726786133835727047625),(-98726786133832730301821)⟩,⟨27730191536449599315333791,27730191536449602312210524⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨14185558184938549297200093,14185558184938550082725873⟩,⟨34360274111141237322256960,34360274111141238108902876⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨35208057310256680179897257,35208057310256680484351486⟩,⟨33569798310329228641491073,33569798310329228948162413⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨58069801675286682082600689,58069801675286682408732157⟩,⟨20167880083315300672198917,20167880083315300999879685⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨73926447561209261103155525,73926447561209261533177587⟩,⟨(-6730886678992468421808236),(-6730886678992467991909264)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨74450987437205203886162358,74450987437205204440321580⟩,⟨(-40617708845093948930395455),(-40617708845093948378364952)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨58036971441235784879374997,58036971441235785537565145⟩,⟨(-69377430880337513074796714),(-69377430880337512420223850)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨32169706259587323346587482,32169706259587324052761834⟩,⟨(-81936123797908286454814467),(-81936123797908285751316347)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨8933190788782106628050920,8933190788782107272766939⟩,⟨(-74435909344553534663092835),(-74435909344553534019622725)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2851195355325775359313307),(-2851195355325774904521273)⟩,⟨(-50697437343151234872611982),(-50697437343151234418174899)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2612409049807155991581209),(-2612409049807155827747145)⟩,⟨(-17808338432766735410325215),(-17808338432766735246529751)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨117461392209894493944964,117461392209897190356453⟩,⟨14969879848355022548968,14969879848357718952019⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨371639173661715354789847,371639173661725666396761⟩,⟨20360595098520627860396,20360595098530939438224⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨673652458090839608028696,673652458090865884975642⟩,⟨(-56291991013598422329276),(-56291991013572145442582)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨1018644462991790422247618,1018644462991865265083917⟩,⟨(-294115105137429715263859),(-294115105137354872518676)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1334627151858250791220465,1334627151858480058376977⟩,⟨(-792975505570761994322243),(-792975505570532727264165)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨1449723391112773796459649,1449723391113386995543451⟩,⟨(-1638780728958441490058910),(-1638780728957828291048076)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨1090668378280907330050384,1090668378282201195334901⟩,⟨(-2819964258352781575019000),(-2819964258351487709722551)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-39534352988562536139946),(-39534352986597804401005)⟩,⟨(-4121832555942332778442153),(-4121832555940368046527451)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2075559547363682694716902),(-2075559547361592152501307)⟩,⟨(-5091143746391927641748947),(-5091143746389837099133649)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-4763801480492258923055620),(-4763801480490086025982436)⟩,⟨(-5183527302331964862502946),(-5183527302329791965007998)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7389302177321944803910733),(-7389302177320068080662142)⟩,⟨(-4096445498983124489482189),(-4096445498981247765989287)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-9029796751669037083720170),(-9029796751667846668737175)⟩,⟨(-2074283700799992199243154),(-2074283700798801784237377)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-9052812174763934224343501),(-9052812174763323775249806)⟩,⟨109331751392286893630171,109331751392897342549207⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-7466229540191387608807446),(-7466229540191114308129299)⟩,⟨1547985914115022728230510,1547985914115296028638927⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-4794840732554892993398768),(-4794840732554783339712554)⟩,⟨1710609439460624269313264,1710609439460733922766752⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-1636230314403592665550152),(-1636230314403563778321531)⟩,⟨722061304999327633181153,722061304999356520319914⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-99354567904484906259),(-99354567904484903641)⟩,⟨(-337191214790903638848),(-337191214790903635537)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-591366457176259555013),(-591366457176259546270)⟩,⟨(-885321480595178996667),(-885321480595178985919)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1913256878631647289165),(-1913256878631647271463)⟩,⟨(-508099067778742243463),(-508099067778742222867)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-4450144527742405012740),(-4450144527742404980636)⟩,⟨3221217880994839589372,3221217880994839624394⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-8169315959358386807661),(-8169315959358386750568)⟩,⟨15036734954462793280087,15036734954462793338693⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-11526387106016154944923),(-11526387106016154843926)⟩,⟨41327079984628586657624,41327079984628586756759⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-9139739133814321413136),(-9139739133814321220770)⟩,⟨87713262519802057256322,87713262519802057440648⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨9721285954685923924710,9721285954685924429583⟩,⟨155166404155489135146001,155166404155489135634325⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨58181491273072626950248,58181491273072629774351⟩,⟨235219517941060379712885,235219517941060382514971⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨143154729586088868713839,143154729586088894755603⟩,⟨307243355181427029979017,307243355181427056005368⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨254981666931483665674182,254981666931483847857474⟩,⟨343352632648100103685342,343352632648100285862436⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨363556041960778563665223,363556041960779396165498⟩,⟨323188395499967545235162,323188395499968377737553⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨426772317567984132198068,426772317567986512089534⟩,⟨250567756867782224627538,250567756867784604527079⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨408252257668451406482371,408252257668455645115784⟩,⟨155390624801975660639967,155390624801979899283268⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨295364189746812935984010,295364189746817421872166⟩,⟨73413743420504089176469,73413743420508575072306⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨107828105046569888151539,107828105046571840945899⟩,⟨19802217098055396404548,19802217098057349201702⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨478024217441530999872191365,478024217441646132856216120⟩,⟨845856867724998938822067139,845856867725114071797309023⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_18 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 18) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_18 (tableDensity true) (fullFactor true 1 18) density1_contains hk1_1_18_contains +noncomputable def atomAnswer : CBox := ⟨⟨1583982511754674959223831677,1583982511754675027758646801⟩,⟨4640969756829159253244880,4640969756829227666538921⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_18 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 18) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_18 1 18 ha1_1_18_contains + def realAnswer : RBox := ⟨2062006729196205958996023042,2062006729196321160714862921⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 18) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_18 +namespace hm1_0_1_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-583567226226566358631322745),(-583567226226566055920524049)⟩,⟨262482313663423908748630435,262482313663424211448174307⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1632299180517532066557521207),(-1632299180517531372829979134)⟩,⟨979838328617946951480614805,979838328617947645163265876⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2236532043189921559258203510),(-2236532043189920920689919813)⟩,⟨2174039000058013483757755976,2174039000058014122221562512⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-1917175947055804846492986249),(-1917175947055804470333728077)⟩,⟨3798124316766538194718120154,3798124316766538570725234651⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-266575248777268630627945610),(-266575248777268429848325101)⟩,⟨5266429998297109570463262832,5266429998297109771144979636⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨2559042980298894873060681308,2559042980298894944995782513⟩,⟨5561633726242528670630512546,5561633726242528742571703679⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨5515294693111521856852830972,5515294693111521881600968197⟩,⟨3877391533562555892155854669,3877391533562555917080192034⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨7078038543919414065286251130,7078038543919414078851913320⟩,⟨429649504515690801748191845,429649504515690815437472463⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨6292134199820779918527378776,6292134199820779927560539683⟩,⟨(-3410812437244750383222290690),(-3410812437244750374198380337)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨3522184175953440946583285153,3522184175953440952840694698⟩,⟨(-5988616219038189056749827115),(-5988616219038189050523457941)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨154807954810844056439866788,154807954810844061524924045⟩,⟨(-6475997371740604718131244700),(-6475997371740604713147412024)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-2403939778149383751248033657),(-2403939778149383747717321249)⟩,⟨(-5235837166578473476621647744),(-5235837166578473473104241525)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-3494930054170741637313430561),(-3494930054170741634913253630)⟩,⟨(-3299661570932529808568208315),(-3299661570932529806131309686)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-3253995618080341258391193295),(-3253995618080341256978870335)⟩,⟨(-1602428343472537788031501719),(-1602428343472537786616258216)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-2187770081316510426323688700),(-2187770081316510425640982299)⟩,⟨(-565740764460933156949054605),(-565740764460933156287240830)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-758941545438698891728815629),(-758941545438698891531792753)⟩,⟨(-114129711230345123597290706),(-114129711230345123411663765)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-175795336071306167803939014),(-175795336071306034366922718)⟩,⟨159256660307949117686527552,159256660307949251108371399⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-478366666805636313169543720),(-478366666805635753283525810)⟩,⟨541160854163355276932159310,541160854163355836778736390⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-599081603296797144422247660),(-599081603296795482890929723)⟩,⟨1081226949650036205413004771,1081226949650037866901472529⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-335076017016775313607143280),(-335076017016770767739758730)⟩,⟨1757590788878594310486927386,1757590788878598856347147736⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨514583508108380727583907732,514583508108391239192716172⟩,⟨2322476423746644099841935448,2322476423746654611531292621⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1920756529202394170425934123,1920756529202414126445817143⟩,⟨2284341071785755327704016779,2284341071785775283902141152⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨3371335818774148955798364695,3371335818774194036707625392⟩,⟨1168736047594020312581301530,1168736047594065393574715572⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨3958104521181494986552878318,3958104521181558604076262423⟩,⟨(-967466729213000290543571863),(-967466729212936673123847537)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨3010655856456983090717363092,3010655856457042095554670271⟩,⟨(-3260047535413625127199790746),(-3260047535413566122592574539)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨786243539227332175102102542,786243539227392593291223515⟩,⟨(-4524148827417967422386097621),(-4524148827417907004268858062)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1611644267870385415287606766),(-1611644267870347385902523909)⟩,⟨(-4191722036283565364965854940),(-4191722036283527335469936875)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-3098121130960524365410685749),(-3098121130960507901287415710)⟩,⟨(-2714251034157998102149322582),(-2714251034157981637828009337)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-3329699335393252031370359062),(-3329699335393243143651664369)⟩,⟨(-1059402356730087736076362778),(-1059402356730078848256202267)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-2657037507602236639423756367),(-2657037507602232472081660444)⟩,⟨39545431675818441560916380,39545431675822608921660650⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1614433295561170471452369356),(-1614433295561168799663005389)⟩,⟨389937137550322183696241337,389937137550323855472707441⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-530476653120179012451584143),(-530476653120178576153274397)⟩,⟨193672310936273747554914075,193672310936274183844833049⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-7730074977778229210242631),(-7730074977778229113179274)⟩,⟨24457669379720078356797211,24457669379720078455724754⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-16003702187196638077261735),(-16003702187196637768165742)⟩,⟨77931452191751904512426223,77931452191751904828312028⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨174984780121740946717443,174984780121741546326749⟩,⟨141482761721526737681258509,141482761721526738295503607⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨63799925894993598399409453,63799925894993599474563432⟩,⟨207987981563596530989661686,207987981563596532082356038⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨196346404067142920598973871,196346404067142922458453292⟩,⟨245414940877960594356949014,245414940877960596226797336⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨393084958393497743460573551,393084958393497746552503669⟩,⟨191154090892230783219819623,191154090892230786300866473⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨587310525385590663282472332,587310525385590668243492420⟩,⟨(-24571737051099929230141246),(-24571737051099924315874130)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨641281289650091896212557228,641281289650091903970357892⟩,⟨(-411963714181045588965433702),(-411963714181045581251852053)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨415490715306768986331169451,415490715306768998380400965⟩,⟨(-851212015914074098162283152),(-851212015914074086108531104)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-98146045365208543293895730),(-98146045365208521982709970)⟩,⟨(-1114994364426676064905143077),(-1114994364426676043528244456)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-707830102559004506483674795),(-707830102559004444933258969)⟩,⟨(-1025079739156324599983398770),(-1025079739156324538363142120)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-1132936579159584026044440417),(-1132936579159583798354485146)⟩,⟨(-615075787795877994892841700),(-615075787795877767187047760)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1209806507200446800067437687),(-1209806507200446224678116686)⟩,⟨(-117405736178738905587706002),(-117405736178738330227316730)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-981496979677316549032247806),(-981496979677315659599467837)⟩,⟨217419794197609418277799114,217419794197610307662729048⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-603679945241116584506790850),(-603679945241115755354058090)⟩,⟨280056190870552924470956012,280056190870553753584090090⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-199248931825369661823628539),(-199248931825369287294924811)⟩,⟨120651362609955728600041851,120651362609956103115597101⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1372327903160012325659392,1372327903160014913419277⟩,⟨202244511507147138005130,202244511507149725577869⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4328589293330027137661336,4328589293330033750157830⟩,⟨284172424186035372969230,284172424186041984945716⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨7795579084782198269417160,7795579084782205933972187⟩,⟨(-726647505548087971308528),(-726647505548080307452118)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨11628580713270322233048997,11628580713270327948721792⟩,⟨(-3901583397970109544018997),(-3901583397970103828857643)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨14724670922871963945249587,14724670922871966769277749⟩,⟨(-10509651559076385660414687),(-10509651559076382836017267)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨14500747492847026085480092,14500747492847027026906786⟩,⟨(-21311023626412076388706176),(-21311023626412075444986128)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7033158583295478651083900,7033158583295478951997160⟩,⟨(-35080302402724365469889447),(-35080302402724365164182013)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-11162479838339445476581019),(-11162479838339445236248864)⟩,⟨(-47042290986336850751130243),(-47042290986336850507060702)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-39599162876342913078493046),(-39599162876342912761484415)⟩,⟨(-49202149543072393846971713),(-49202149543072393530063898)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-70898294693850537502722788),(-70898294693850537052375845)⟩,⟨(-34466200680167319421747126),(-34466200680167318977522270)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-92592374650968742612974578),(-92592374650968742012491226)⟩,⟨(-3088918885916078583967442),(-3088918885916077993981562)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-94688432102881930398493060),(-94688432102881929667329664)⟩,⟨34341614977101033825842835,34341614977101034550480298⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-77221754882210850573021623),(-77221754882210849791511475)⟩,⟨61930819564652064252436828,61930819564652065032646547⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-50117783347913903223776468),(-50117783347913902516728195)⟩,⟨68129639047586991448046074,68129639047586992157423576⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-25076398584357209583615361),(-25076398584357209086225294)⟩,⟨51504982167416740716034931,51504982167416741216571372⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-7152415562830918711143597),(-7152415562830918531996571)⟩,⟨18990188786724560752517745,18990188786724560933050411⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨519705962026794989766,519705962027425711506⟩,⟨(-78685140062841961907945),(-78685140062841331197950)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-18662655762480922175639),(-18662655762478499687199)⟩,⟨(-242252753136584198256385),(-242252753136581775805839)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-103019896257948360618288),(-103019896257940964075451)⟩,⟨(-416688849047975747427497),(-416688849047968350944956)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-306384049040414690318918),(-306384049040391799421836)⟩,⟨(-581706513000945056068231),(-581706513000922165241819)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-680386802057022440635797),(-680386802056954922802691)⟩,⟨(-669831597128275112530565),(-669831597128207594755264)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-1236655152123596470966856),(-1236655152123422989513814)⟩,⟨(-549686583053925967944852),(-549686583053752486494116)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-1882875064684827503990456),(-1882875064684478691633175)⟩,⟨(-43359370975000650337795),(-43359370974651837864560)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2367320123288512191414764),(-2367320123288017473936047)⟩,⟨986311440483871782718713,986311440484366500507459⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2309837719036987186886738),(-2309837719036371546207204)⟩,⟨2483684361275089583799244,2483684361275705224904648⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-1388217149585050769534221),(-1388217149584324760613370)⟩,⟨4083743525673992896489205,4083743525674718905683565⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨377048311246796276279648,377048311247380007970928⟩,⟨5193804271414123382020546,5193804271414707113712005⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨2465512276685224418452604,2465512276685571051618996⟩,⟨5322459382640875479637068,5322459382641222112481049⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨4040227919411713731915726,4040227919411879668369323⟩,⟨4432977064751775337876821,4432977064751941273757126⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨4400201818064078590072369,4400201818064148275463555⟩,⟨2980224796464089837716522,2980224796464159522468095⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨3352581875123610988956115,3352581875123642304650891⟩,⟨1557464152538383526565086,1557464152538414841844203⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1245391620954248003593350,1245391620954257203359537⟩,⟨460110382448389597572045,460110382448398797202774⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-2156352324020524843152),(-2156352324020524841828)⟩,⟨646419275780085197844,646419275780085198993⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-6440591130717313575423),(-6440591130717313571140)⟩,⟨2651784991262879709197,2651784991262879712987⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-10409829311137878793445),(-10409829311137878785171)⟩,⟨6850267709344152355636,6850267709344152363229⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-13085263872264586133725),(-13085263872264586119566)⟩,⟨14725727092790521511614,14725727092790521525148⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-12293551430838838241657),(-12293551430838838218669)⟩,⟨27227179117653906441714,27227179117653906464507⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-4399557478204550407351),(-4399557478204550370775)⟩,⟨43643641247607915556029,43643641247607915593234⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨14973255964356546161540,14973255964356546223915⟩,⟨60234814839608114117805,60234814839608114182034⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨48465197002517367589901,48465197002517367728711⟩,⟨69509972126820439288623,69509972126820439430436⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨93351125571463917142737,93351125571463917932193⟩,⟨61691404654698654643141,61691404654698655435006⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨139373149888258588445735,139373149888258595427077⟩,⟨29587091042155126474123,29587091042155133456296⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨171304884714906917231886,171304884714906964966992⟩,⟨(-24666398937091326703958),(-24666398937091278968986)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨176647894672531034171848,176647894672531247637350⟩,⟨(-86040861677041498527656),(-86040861677041285062135)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨153424046408410705319237,153424046408411301478701⟩,⟨(-131168224113604276906559),(-131168224113603680746154)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨111233000955909807837489,111233000955910844668541⟩,⟨(-139954629091777163625470),(-139954629091776126792563)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨64041065816423288194975,64041065816424363187430⟩,⟨(-106115332030049848730715),(-106115332030048773736408)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨20433715148524971078433,20433715148525433340928⟩,⟨(-39410003937811228091795),(-39410003937810765828533)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨409623477348308514642732887,409623477348365882763915252⟩,⟨(-2286952280330902874040347792),(-2286952280330845505926784236)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 19) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_19 (tableDensity false) (fullFactor true 1 19) density0_contains hk1_1_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨551794145682255948338835998,551794145682255977367412519⟩,⟨163519604404076537734901953,163519604404076566717693985⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_19 1 19 ha1_1_19_contains + def realAnswer : RBox := ⟨961417623030564462881568885,961417623030621860231327771⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_19 +namespace hm1_1_1_19 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_19 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-104850137010293228196172873),(-104850137010292981598623137)⟩,⟨31327938007342072362059130,31327938007342318962300223⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-301210111588101918810153595),(-301210111588101354634223549)⟩,⟨127494177012447406756125437,127494177012447970943021183⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-438425524769952738484102560),(-438425524769952221656509259)⟩,⟨309888199684982400150825059,309888199684982917005150031⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-432860932913077840682129591),(-432860932913077540737038578)⟩,⟨579690896046622509890538028,579690896046622809876700979⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-197402879329974783006301785),(-197402879329974628563052784)⟩,⟨845399068685995211489909267,845399068685995365957397070⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨265727673043294598023196810,265727673043294646526010545⟩,⟨929521786475535877686333990,929521786475535926175268371⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨789074737177695073830017620,789074737177695084471067774⟩,⟨673701055210848854864546672,673701055210848865450748688⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1096651968228271694525672073,1096651968228271698112070369⟩,⟨91781842733328183678282528,91781842733328187219228235⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨994969435379131823489096798,994969435379131825587587848⟩,⟨(-584683056304721890964011714),(-584683056304721888859588660)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨528525622369906044845949244,528525622369906046250511025⟩,⟨(-1051288619982923198945079557),(-1051288619982923197475618908)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-57272994039211202096124910),(-57272994039211200932145593)⟩,⟨(-1141828033951903016770832219),(-1141828033951903015561583031)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-500375339915904551445529195),(-500375339915904550524586266)⟩,⟨(-912080235304053956449884027),(-912080235304053955516296767)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-675428958684077931953210608),(-675428958684077931282836047)⟩,⟨(-552382394436696843868419960),(-552382394436696843207440969)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-609927225191332013959341768),(-609927225191332013543851066)⟩,⟨(-242422394033588016648596138),(-242422394033588016260478899)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-402204729464270206355838706),(-402204729464270206144494624)⟩,⟨(-65491179970969848846065549),(-65491179970969848661923485)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-138061839995215507559834696),(-138061839995215507496716474)⟩,⟨(-6757625862480365371446791),(-6757625862480365319357070)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-35930758450966810410191042),(-35930758450966701912380743)⟩,⟨8809398366421493359739693,8809398366421601859485446⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-103875547734902121040335966),(-103875547734901664162162704)⟩,⟨39509934141932307492062632,39509934141932764375250655⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-152501838109499260744285188),(-152501838109497898938074386)⟩,⟨106017358792912490989289141,106017358792913852800987709⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-148585521414471707385990345),(-148585521414467969306577185)⟩,⟨215421472945230297109858350,215421472945234035190458222⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-47992404008372474971686036),(-47992404008363813341898676)⟩,⟨337650846632001446645693836,337650846632010108266114824⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨166781881724412040026049733,166781881724428506881568649⟩,⟨391948588945508619539384840,391948588945525086372846723⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨432929629516194510915968052,432929629516231766202215954⟩,⟨278921961258600814866354531,278921961258638070141305854⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨600174777802877697207162403,600174777802930302106633306⟩,⟨(-30277086581201717335829167),(-30277086581149112424607870)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨524870268444094937274110027,524870268444143718613196610⟩,⟨(-421843140758925552133073411),(-421843140758876770764043123)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨204143114522923379340352917,204143114522973302496451781⟩,⟨(-692589544183684829430750504),(-692589544183634906264459805)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-200611196166578236667533027),(-200611196166546855427437529)⟩,⟨(-709214890498990300877825608),(-709214890498958919653231776)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-491950204543311677219996493),(-491950204543298123673180216)⟩,⟨(-508638712232434966629636668),(-508638712232421413111521499)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-576731299073428968013480162),(-576731299073421667960852377)⟩,⟨(-240955767396155389069181090),(-240955767396148089031561705)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-487599005411062931999402632),(-487599005411059518085669733)⟩,⟨(-41657106695937903438031128),(-41657106695934489527173152)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-308751985691772732268895178),(-308751985691771366578867215)⟩,⟨38739334024021150249043147,38739334024022515941019662⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-103788757300147777528924318),(-103788757300147421812678415)⟩,⟨24401858297869848843614413,24401858297870204561165609⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4380119612622519348956431),(-4380119612622519318047467)⟩,⟨3788166111319851847866798,3788166111319851878860020⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-12372754387812651498080831),(-12372754387812651398771737)⟩,⟨13052957185379771771597443,13052957185379771871224543⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-17113420134204112870997766),(-17113420134204112683175912)⟩,⟨26930790464208540561723824,26930790464208540750217455⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-13680211378523721834664905),(-13680211378523721515126120)⟩,⟨46354151236923408768312547,46354151236923409088625405⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨5070983820889485057842377,5070983820889485569346685⟩,⟨67231337267066108808796664,67231337267066109320728570⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨44189815542936842521344511,44189815542936843290459597⟩,⟨77275885129822434487889689,77275885129822435256637500⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨97584797502471709215423264,97584797502471710315593531⟩,⟨57582916188585052598954580,57582916188585053697312243⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨140727167661983101821820344,140727167661983103424438214⟩,⟨(-5325899544077972835868879),(-5325899544077971234997332)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨138393443692503321949284962,138393443692503324725076258⟩,⟨(-100681947246183930817479388),(-100681947246183928041707194)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨71733287683995730553667588,71733287683995738182135668⟩,⟨(-187620647699556182266324571),(-187620647699556174636623151)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-37415899959379352763813933),(-37415899959379315115835886)⟩,⟨(-219505549873307121635919435),(-219505549873307083986968301)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-136199365983487915272909358),(-136199365983487744182394333)⟩,⟨(-181938508310470621591280332),(-181938508310470450500364766)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-180516927661600727096678317),(-180516927661600272555050173)⟩,⟨(-104310118807070879187299525),(-104310118807070424645694678)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-163521489028090899305108324),(-163521489028090186102976723)⟩,⟨(-32878333340296639537162057),(-32878333340295926335119524)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-107371761654635724126507884),(-107371761654635055705795357)⟩,⟨3612278553435488297203850,3612278553436156717941996⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-36615669015375417324315304),(-36615669015375114454640207)⟩,⟨5727156220377850961659061,5727156220378153831380866⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨327335699024684038180364,327335699024686211389889⟩,⟨328410400503176151783507,328410400503178325012739⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨1083997554579226280823206,1083997554579231829480058⟩,⟨929868896136162409751967,929868896136167958463654⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨2131506779802090222822251,2131506779802096642570822⟩,⟨1314756867425246261255759,1314756867425252681077791⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3588189378343750693594216,3588189378343755463692011⟩,⟨1182591472455134570186120,1182591472455139340336825⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨5366483934908650323811146,5366483934908652658683809⟩,⟨54488295467586032932195,54488295467588367765425⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨6957055063045205871708927,6957055063045206618779022⟩,⟨(-2613151945440945787876306),(-2613151945440945041038987)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨7263673312082474446224826,7263673312082474637756737⟩,⟨(-7052295955747771736723418),(-7052295955747771545667606)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨4810266672497468417452821,4810266672497468522207026⟩,⟨(-12592696016274180938728569),(-12592696016274180834324071)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-1399357639597817062573168),(-1399357639597816946990444)⟩,⟨(-17284660099871851912883263),(-17284660099871851797247358)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-10670540352099152481364250),(-10670540352099152324106979)⟩,⟨(-18452815424213985646096795),(-18452815424213985488213265)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-20157444673465785506440761),(-20157444673465785298341261)⟩,⟨(-14394305423074932428009465),(-14394305423074932218904705)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-26126811765040637871871411),(-26126811765040637615012367)⟩,⟨(-6091555171404102663450782),(-6091555171404102406006493)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-26302993360770019860757928),(-26302993360770019581545648)⟩,⟨2840564321932415737840356,2840564321932416017120061⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-21199594415742499211893417),(-21199594415742498954970289)⟩,⟨8309065691785011272108369,8309065691785011528757972⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-13186213029038989264334846),(-13186213029038989081068351)⟩,⟨8212495332262688286011883,8212495332262688468953239⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-4398137012699764121536230),(-4398137012699764055007698)⟩,⟨3347189892480770031247828,3347189892480770097638749⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1152570568960749362251),(-1152570568960231024778)⟩,⟨(-25828500553653166478540),(-25828500553652648138727)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-9689313013572570008110),(-9689313013570579013294)⟩,⟨(-80917113813819548883572),(-80917113813817557881042)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-38593874996696593080927),(-38593874996690513120861)⟩,⟨(-143747158248387551419850),(-143747158248381471447109)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-106027265553933071676785),(-106027265553914252188249)⟩,⟨(-210101174072152560364122),(-210101174072133740859918)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-232668401511754613196507),(-232668401511699097285698)⟩,⟨(-259032509563283415648222),(-259032509563227899723483)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-431837056639653070345651),(-431837056639510427475725)⟩,⟨(-245690900810376221518658),(-245690900810233578645593)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-688460773150467131026400),(-688460773150180386847532)⟩,⟨(-103583479776615483211167),(-103583479776328739055284)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-935219338946061360439708),(-935219338945654871995339)⟩,⟨231859251052855790515121,231859251053262278892022⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-1051071841703652288818271),(-1051071841703146865142474)⟩,⟨774030325860600007884683,774030325861105431466347⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-909961635565473365456803),(-909961635564877966831675)⟩,⟨1433040998318907546050310,1433040998319502944614734⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-472950349169290708194367),(-472950349168812594561420)⟩,⟨2012732813666566266126689,2012732813667044379754595⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨142482033404916993543087,142482033405200526731560⟩,⟨2293581390969392850788732,2293581390969676384033050⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨694439850273732569390756,694439850273868123549439⟩,⟨2162939794553399775499584,2162939794553535329760657⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨945307672378290528185567,945307672378347389786284⟩,⟨1683701121001270024570749,1683701121001326886284438⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨791162838729422046190688,791162838729447577541306⟩,⟨1028300935967618176296887,1028300935967643707720070⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨305555635627722286994549,305555635627729784216647⟩,⟨340230791228113947092130,340230791228121444337512⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-63128296930628920273),(-63128296930628919619)⟩,⟨22262211392996335040,22262211392996335570⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-162553811606373948423),(-162553811606373946323)⟩,⟨121939962697430074863,121939962697430076617⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-75539795742277368996),(-75539795742277364981)⟩,⟨371997300465509742344,371997300465509745878⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨677260880855553562435,677260880855553569265⟩,⟨817069653461820598377,817069653461820604768⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨3040064228152818135269,3040064228152818146697⟩,⟨1374307590154892240772,1374307590154892252103⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨8302100785732468795908,8302100785732468815228⟩,⟨1595367094461103878308,1595367094461103898293⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨17583467803029079556063,17583467803029079591993⟩,⟨200939402553508025615,200939402553508063564⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨30967498594977212102375,30967498594977212195515⟩,⟨(-5190252970689594054656),(-5190252970689593957689)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨46454164524307177602318,46454164524307178223663⟩,⟨(-17352070731989190167327),(-17352070731989189542027)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨59458797665816444909441,59458797665816450590532⟩,⟨(-37484973543386460455468),(-37484973543386454772067)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨64085599699938069631809,64085599699938108589419⟩,⟨(-62919777622277610187373),(-62919777622277571229469)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨56559454431645897142277,56559454431646071434083⟩,⟨(-86478668017270365660431),(-86478668017270191370079)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨38867887265504947976987,38867887265505434976020⟩,⟨(-98805335488110367739119),(-98805335488109880742700)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨18834901699287283399812,18834901699288130812129⟩,⟨(-92561692535615708838205),(-92561692535614861428658)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨5020006481443706718515,5020006481444585659904⟩,⟨(-65982592472001441767851),(-65982592472000562828516)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨275341195440478568412,275341195440856602785⟩,⟨(-23901695100490551437990),(-23901695100490173404355)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-202923274738217060995021080),(-202923274738169731596412635)⟩,⟨(-457357690475329573087515925),(-457357690475282243687074349)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_19 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 19) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_19 (tableDensity true) (fullFactor true 1 19) density1_contains hk1_1_19_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-721576959738334739634308678),(-721576959738334701673862459)⟩,⟨(-213833328836100125707753673),(-213833328836100087807179477)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_19 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 19) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_19 1 19 ha1_1_19_contains + def realAnswer : RBox := ⟨(-924500234476551800729329758),(-924500234476504433170275094)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 19) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_19 +namespace hm1_0_1_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨272680115247871516270992592,272680115247871648120438690⟩,⟨7332889613462120352587510,7332889613462252205255567⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨809689092031671101203278054,809689092031671418835305556⟩,⟨(-80414172277883815443683599),(-80414172277883497808100997)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1260616708545770832636920331,1260616708545771155057169100⟩,⟨(-453379760724123092847488641),(-453379760724122770439416024)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1407044383762736408057876001,1407044383762736598792371727⟩,⟨(-1185860571397321293048311428),(-1185860571397321102359216144)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨946324485417063812636467247,946324485417063888365429622⟩,⟨(-2096279040095686235116972517),(-2096279040095686159462206590)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-250423084569571957158592826),(-250423084569571924616154997)⟩,⟨(-2683500569263695943014851135),(-2683500569263695910512088293)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-1836184126369929424999145587),(-1836184126369929412030607564)⟩,⟨(-2367553090236568610396752042),(-2367553090236568597392554592)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-3022172329271871844709153751),(-3022172329271871837748594297)⟩,⟨(-988403580782367039421593908),(-988403580782367032384088488)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3103778954610931117209634542),(-3103778954610931112690367249)⟩,⟨911633514068064381679871356,911633514068064386210993526⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2032904372504324487812051633),(-2032904372504324484630507058)⟩,⟨2420325346939944113217514703,2420325346939944116398030100⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-439421374153768915518452882),(-439421374153768913056343776)⟩,⟨2929049369880411547915169119,2929049369880411550329736654⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨890099944086791564982982645,890099944086791566689778746⟩,⟨2489051088583383440615529183,2489051088583383442310831429⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨1522030349595028517575002476,1522030349595028518716205671⟩,⟨1602577511551552235856331012,1602577511551552237013797609⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1476156493708463949577926313,1476156493708463950249122957⟩,⟨780750622853662912575889970,780750622853662913248855382⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨1004813738503833658419166170,1004813738503833658741271995⟩,⟨271954528157514300702845769,271954528157514301015449070⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨349566807133352730732920244,349566807133352730825222486⟩,⟨53379559467091732408019859,53379559467091732495067462⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨84374726023703377138914232,84374726023703436994919562⟩,⟨5945569462415487523168310,5945569462415547378214225⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨258226845263962589102820340,258226845263962818565501271⟩,⟨(-11980405865060639637781664),(-11980405865060410180989760)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨428750880023606706491876091,428750880023607279365098446⟩,⟨(-121388965295516078778141546),(-121388965295515505924484907)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨534003178845353085504631858,534003178845354366724838107⟩,⟨(-373689326743820509663568406),(-373689326743819228485668178)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨445108181930586709490918385,445108181930590575273619486⟩,⟨(-756855231806337625023043612),(-756855231806333759274416947)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨26719796441112052839628792,26719796441121419840804782⟩,⟨(-1118391342665411797745934075),(-1118391342665402430735865411)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-704492309970118279706380353),(-704492309970103692356365497)⟩,⟨(-1163642036018541251063551470),(-1163642036018526663641807817)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1443747982081711410439609539),(-1443747982081687370739124770)⟩,⟨(-644540295451035246687109572),(-644540295451011206934913184)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1717678806495369400443299766),(-1717678806495341164320739974)⟩,⟨348579563435739904841620160,348579563435768140932166174⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1273610969307282950624861925),(-1273610969307262934112153360)⟩,⟨1334553140428656455425770277,1334553140428676471846590326⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-344462631335758765110903399),(-344462631335743036078115493)⟩,⟨1799843459637911535776284719,1799843459637927264774767277⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨546239638447341712131826107,546239638447350166371177121⟩,⟨1613908759775216987949172598,1613908759775225442220744223⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1012178097516272538857191595,1012178097516275811620792245⟩,⟨1054710869073952987535059524,1054710869073956260364440220⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1004092837333811394567268534,1004092837333812872052524662⟩,⟨499275066713854013728348175,499275066713855491257161576⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨687313682459314088376154570,687313682459314758925742090⟩,⟨156772313342479551422643236,156772313342480221989006810⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨239120883016174926866855754,239120883016175112126884688⟩,⟨24827543402095389695433769,24827543402095574959294863⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨7345844446861891312846101,7345844446861891351323342⟩,⟨(-1495523134200212002676124),(-1495523134200211964833815)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨22233569648519886181935037,22233569648519886305526369⟩,⟨(-7089903352503219140690535),(-7089903352503219018788112)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨36256583304474124259377430,36256583304474124502434236⟩,⟨(-20802104534515035142099187),(-20802104534515034900946210)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨43850100359324509697848681,43850100359324510133219390⟩,⟨(-47915782332602316687508267),(-47915782332602316252405813)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨32427999828234614909721464,32427999828234615662691222⟩,⟨(-89402041552149810760684288),(-89402041552149810003173158)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-15373053205579614655691408),(-15373053205579613378352730)⟩,⟨(-133495052254215669089159518),(-133495052254215667799735660)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-108514428668278444589326600),(-108514428668278442464292643)⟩,⟨(-148535709254641067752655355),(-148535709254641065618793949)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-225127120433698965772266064),(-225127120433698962391407091)⟩,⟨(-91708946228913477039614083),(-91708946228913473663492473)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-302842066951253585513563855),(-302842066951253580295123467)⟩,⟨56292982995858306376494370,56292982995858311572541145⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-271286503785253291444447493),(-271286503785253281999903772)⟩,⟨253147991066991200477625413,253147991066991209906839622⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-115854989569921065452482053),(-115854989569921040514597747)⟩,⟨404257649772408005348904332,404257649772408030292693417⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨93273117409086739898156524,93273117409086807260152380⟩,⟨432444948182343861065501105,432444948182343928452157382⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨250089700340852802113942191,250089700340852983344040476⟩,⟨341144740942729961028173815,341144740942730142280592908⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨290358565488700071370989435,290358565488700431503545170⟩,⟨202006962402746574369183222,202006962402746934510629083⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨219053731049767122319263197,219053731049767521074755596⟩,⟨87637017125974831415513853,87637017125975230172321022⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨80011040842737370800008507,80011040842737546510757168⟩,⟨21700392043217526792103928,21700392043217702502509417⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-57572401843167482610564),(-57572401843166755415311)⟩,⟨(-332557940467252142508783),(-332557940467251415290578)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-267508052936279608011588),(-267508052936277790991927)⟩,⟨(-1024545459882607881535083),(-1024545459882606064462645)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-784734236897452471221169),(-784734236897450451091093)⟩,⟨(-1756118678485333337363745),(-1756118678485331317206614)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1865674880792478323183249),(-1865674880792476902749732)⟩,⟨(-2402399209266299636349335),(-2402399209266298216028419)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-3741546580806048628154569),(-3741546580806047979098056)⟩,⟨(-2572537944284038276237823),(-2572537944284037627623743)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-6383235349149753723851435),(-6383235349149753515596657)⟩,⟨(-1525313614187441634027320),(-1525313614187441426689104)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-9105498105717557984043157),(-9105498105717557889025192)⟩,⟨1669115275725292196175571,1669115275725292290419949⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-10286337600316406254501225),(-10286337600316406175317592)⟩,⟨7495982963341351376537385,7495982963341351455705174⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-7785989853623554777755534),(-7785989853623554669966047)⟩,⟨15029291301263610405467817,15029291301263610514640937⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-407362220108389667197071),(-407362220108389510440848)⟩,⟨21501587916517407641144098,21501587916517407800361080⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨10433121146328951565971258,10433121146328951782772105⟩,⟨23492389075334663836452711,23492389075334664054594516⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨20663445054478525573623963,20663445054478525843143556⟩,⟨19454726190094083909708114,19454726190094084178864543⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨25885466864305135279955911,25885466864305135575747405⟩,⟨11347037265782500176695852,11347037265782500470596834⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨24160378493924779536584751,24160378493924779810635321⟩,⟨3435480980918671168295433,3435480980918671439806415⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨16630113008138168216212977,16630113008138168411600967⟩,⟨(-794738203290462215434924),(-794738203290462021828334)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨5857834420675283644298825,5857834420675283715100160⟩,⟨(-853425498321027650115297),(-853425498321027579875103)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-16100583678789932537404),(-16100583678789796466332)⟩,⟨2676850212287177182698,2676850212287313256059⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-48958384873111224048406),(-48958384873110653291210)⟩,⟨12542460720641968612239,12542460720642539375944⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-81927338354907700397958),(-81927338354905960773878)⟩,⟨36715396175442655255588,36715396175444394889138⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-108567717244323354848925),(-108567717244318129026018)⟩,⟨86203955832477618739912,86203955832482844572246⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-111789235231948943485475),(-111789235231934047118780)⟩,⟨169955278459936050189882,169955278459950946559997⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-61203278294906440515456),(-61203278294869728552175)⟩,⟨285441756183198075845051,285441756183234787795455⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨80528489808339418702399,80528489808409063155454⟩,⟨404026852213283571073172,404026852213353215482785⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨334689937550352121506815,334689937550454562445554⟩,⟨460734632493477992249532,460734632493580433109965⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨670774025160125058759940,670774025160284975278533⟩,⟨367700621675837885875806,367700621675997802332861⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨985805923428090007691161,985805923428264967302494⟩,⟨64931705121627914711435,64931705121802874312404⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨1137981537687110184641991,1137981537687241056637500⟩,⟨(-412803388976451991776650),(-412803388976321119714875)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1037465295910880625391595,1037465295910952239900366⟩,⟨(-913161071778342467445489),(-913161071778270852790219)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨726516691780798664895822,726516691780833271138080⟩,⟨(-1231382955585652644315343),(-1231382955585618037898480)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨363293284343633841268699,363293284343653236072726⟩,⟨(-1225831705919749816917719),(-1225831705919730421996552)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨108713706834541428868173,108713706834550571200389⟩,⟨(-888400105463430679602226),(-888400105463421537209119)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨12165414946994068014346,12165414946996684879762⟩,⟨(-322271493032815441721847),(-322271493032812824838505)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨137241930030215566891,137241930030215567121⟩,⟨383422490489727918385,383422490489727918644⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨543894543241775297319,543894543241775298047⟩,⟨1139940540230539516116,1139940540230539516924⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1357384562041085616250,1357384562041085617696⟩,⟨1820047079150301660703,1820047079150301662255⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2851671811680478308258,2851671811680478310826⟩,⟨2220489899237945410681,2220489899237945413331⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5192081175810674423638,5192081175810674427955⟩,⟨1903677636288037152555,1903677636288037156865⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨8205212507598871223053,8205212507598871230174⟩,⟨152130617406011105065,152130617406011112002⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨11094640167664756245509,11094640167664756257795⟩,⟨(-3874319631448260112781),(-3874319631448260100921)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨12299150929637867822074,12299150929637867849954⟩,⟨(-10622676389354593059918),(-10622676389354593032642)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨9827250418087127719127,9827250418087127884101⟩,⟨(-19400298738302624992981),(-19400298738302624828393)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨2314788717420888756190,2314788717420890178713⟩,⟨(-27966124288686821074917),(-27966124288686819652502)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-9559804113017524729608),(-9559804113017515216788)⟩,⟨(-33172534319686255537230),(-33172534319686246024371)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-22414698061300996242194),(-22414698061300954742504)⟩,⟨(-32706079025408574741404),(-32706079025408533241785)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-31271103103220079625231),(-31271103103219966989097)⟩,⟨(-26731696488823756370007),(-26731696488823643734190)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-32076415824907964835761),(-32076415824907774895390)⟩,⟨(-17883074325625947493443),(-17883074325625757553581)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-23818612826063359526156),(-23818612826063158614469)⟩,⟨(-9384189562254422545760),(-9384189562254221634533)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-8761727933170431315691),(-8761727933170336648952)⟩,⟨(-2789508042779886760179),(-2789508042779792093613)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-143320629466984491454904614),(-143320629466961953945413733)⟩,⟨934277348678190782969303982,934277348678213320474467913⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 20) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_20 (tableDensity false) (fullFactor true 1 20) density0_contains hk1_1_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-194762186266801584638025216),(-194762186266801569277692182)⟩,⟨(-119950344245346030204356719),(-119950344245346014864446137)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_20 1 20 ha1_1_20_contains + def realAnswer : RBox := ⟨(-338082815733786076192929830),(-338082815733763523123105915)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_20 +namespace hm1_1_1_20 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_20 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨46059716974391380983310637,46059716974391488230413262⟩,⟨7396203701646081310140309,7396203701646188556459830⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨139675163577326822158281744,139675163577327080095320958⟩,⟨5761770113031768509654059,5761770113032026445820615⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨226485949278144360012984379,226485949278144620653721518⟩,⟨(-43390702819872295341691515),(-43390702819872034697725535)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨270563521578932826186908529,270563521578932977924107472⟩,⟨(-157187801117699985224873408),(-157187801117699833474569346)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨214717501074755083386175659,214717501074755140009134810⟩,⟨(-311864211280690561515506933),(-311864211280690504871210186)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨25442075854403091869224952,25442075854403112757026047⟩,⟨(-424763788203141111908936844),(-424763788203141091013540376)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-247108133519359476635437579),(-247108133519359471222456702)⟩,⟨(-389154275125074694797442829),(-389154275125074689398283433)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-465305935992792691330897362),(-465305935992792689631819178)⟩,⟨(-163973509730411927485443868),(-163973509730411925813725034)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-494986798876838207504027490),(-494986798876838206484093725)⟩,⟨164269709300873919988326412,164269709300873921000015511⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-316498485102397171712194616),(-316498485102397170997673340)⟩,⟨431709545188799683199174652,431709545188799683936488535⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-39054634762457440171934412),(-39054634762457439626585818)⟩,⟨521270886218021583440409129,521270886218021584010247877⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨192376768807927735686092503,192376768807927736119085021⟩,⟨436842246330615464090518350,436842246330615464532329588⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨296280564677196878151690377,296280564677196878466499519⟩,⟨270541901978014015871487451,270541901978014016183911724⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨277454287633070005267525647,277454287633070005463091557⟩,⟨119680939637663419366356225,119680939637663419550131823⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨184924680199594146089646540,184924680199594146188544277⟩,⟨32255247908953058631093589,32255247908953058717637912⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨63605508378373723318850572,63605508378373723348205561⟩,⟨3258004294277511009366326,3258004294277511033648615⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨11134607821997252021868300,11134607821997300623211023⟩,⟨7074148161485192255945883,7074148161485240857398922⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨36035232820395654585503781,36035232820395841444592999⟩,⟨16836978871849240440053187,16836978871849427299845292⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨65851659942956846603887493,65851659942957314901800022⟩,⟨12081274783700629732893736,12081274783701098033177115⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨93507755819925827038962454,93507755819926877766114971⟩,⟨(-18485255873946969957916292),(-18485255873945919225517722)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨97870338086659859784343396,97870338086663042497794334⟩,⟨(-79141856361738920990977503),(-79141856361735738273199680)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨50312920949299765960324630,50312920949307493714604356⟩,⟨(-151505251368158552526793156),(-151505251368150824773321483)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-59117502284849378571770395),(-59117502284837330492319090)⟩,⟨(-187196032241180854419430547),(-187196032241168806348745955)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-191235830270061079450201421),(-191235830270041207426334832)⟩,⟨(-133392662911585207946978539),(-133392662911565335929977538)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-265583414717244993093858408),(-265583414717221651996664758)⟩,⟨13880936889930976175936076,13880936889954317276815057⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-222905303943894527470544351),(-222905303943877997649340554)⟩,⟨185607440724061825342525076,185607440724078355176131325⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-83215538750249626920086860),(-83215538750236653601513666)⟩,⟨289012525538295577403291068,289012525538308550726687214⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨70674443271349532439161813,70674443271356490669539937⟩,⟨284069029979682714371623977,284069029979689672597248500⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨163857985256122422644114901,163857985256125106178030943⟩,⟨203803269653944710572457137,203803269653947394096568037⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨174808076266190410293186230,174808076266191617407016989⟩,⟨109965651218123466127291196,109965651218124673234472277⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨124677709652840739109421942,124677709652841285503804331⟩,⟨43602079028901241459535521,43602079028901787851277596⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨44268384511198636709323877,44268384511198787377801879⟩,⟨10019971306440248799292398,10019971306440399467151321⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1589420165073278632351090,1589420165073278644321984⟩,⟨581579009036203258604876,581579009036203270546678⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨5114929547719937456778983,5114929547719937495680028⟩,⟨1292037558427160705403554,1292037558427160744224428⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨9417017954617713046805407,9417017954617713121813404⟩,⟨437706056093020084131483,437706056093020159049998⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨13998432345386911454014162,13998432345386911581974824⟩,⟨(-3500137990762777785168395),(-3500137990762777657224251)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨16564594610373821281852501,16564594610373821486870637⟩,⟨(-11907435721613488822102177),(-11907435721613488616907284)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨12736571807532918472086264,12736571807532918786084658⟩,⟨(-24219354651933377447504598),(-24219354651933377133047397)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1984139282432511440275121),(-1984139282432510969532327)⟩,⟨(-35397302208831343002260697),(-35397302208831342531159332)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-27205166747259465058551995),(-27205166747259464370995607)⟩,⟨(-35729120777316124954525750),(-35729120777316124267113419)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-53098586091974030429210818),(-53098586091974029350754542)⟩,⟨(-16653968616195896887410009),(-16653968616195895809614390)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-63651303195797319513595873),(-63651303195797316358142981)⟩,⟨19541935801159735417323475,19541935801159738572390715⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-49258702915334646716102645),(-49258702915334632303621439)⟩,⟨56778029609849596842216528,56778029609849611254708451⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-16898938206416849987691065),(-16898938206416802017371543)⟩,⟨76136770919130733663608905,76136770919130781634082223⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨14791973069537870593692543,14791973069538011184155853⟩,⟨71027210742493284444983592,71027210742493425035599138⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨30498949949345286379072238,30498949949345573977745534⟩,⟨50137045591684321475150237,50137045591684609073901443⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨27041817337628137673894905,27041817337628458977215548⟩,⟨26821672889076650123290758,26821672889076971426638504⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨10467105079176343907951005,10467105079176485904739718⟩,⟨8026194192120593856596644,8026194192120735853393606⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨51022876575164201361926,51022876575164812080768⟩,⟨(-100620515428976130876873),(-100620515428975520160529)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨131918654245554912088213,131918654245556436785350⟩,⟨(-322696919650901930298481),(-322696919650900405607120)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨137520254216853869016204,137520254216855560869788⟩,⟨(-599681077784847779938482),(-599681077784846088088024)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-17043020057266762268474),(-17043020057265577576132)⟩,⟨(-936720611564110983004679),(-936720611564109798300940)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-447162672636064815276277),(-447162672636064280688217)⟩,⟨(-1270554452590092417158619),(-1270554452590091882525687)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-1250746211557878399519417),(-1250746211557878238479970)⟩,⟨(-1419703291829711252158838),(-1419703291829711091028201)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2390641843177805587729678),(-2390641843177805529101866)⟩,⟨(-1070500956917443576505480),(-1070500956917443517804046)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-3546794597936410640995905),(-3546794597936410607672034)⟩,⟨113073661197630051238968,113073661197630084556448⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4087520727064811413429687),(-4087520727064811374509300)⟩,⟨2211277587065269205072582,2211277587065269243851072⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-3345302714898666193557684),(-3345302714898666138233239)⟩,⟨4756171084654290954085045,4756171084654291009171525⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1154757563210464223718968),(-1154757563210464147509842)⟩,⟨6774598796446981633580055,6774598796446981709672117⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1786103777971148607706026,1786103777971148702642374⟩,⟨7345007121274223117725344,7345007121274223212715040⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4198261018956599325679822,4198261018956599430760425⟩,⟨6279620021239401311622375,6279620021239401416894653⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨5006817383332055144853811,5006817383332055243405177⟩,⟨4253737663022174701308820,4253737663022174800101855⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨3933879740060279670932981,3933879740060279742108221⟩,⟨2215587673096044901881656,2215587673096044973222250⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1475204128781486963449494,1475204128781486989456716⟩,⟨650636254210074976687238,650636254210075002745753⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-5238245866164499237549),(-5238245866164387409940)⟩,⟨1149122441336593142411,1149122441336704969557⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-16228896249787111512354),(-16228896249786642410376)⟩,⟨4897508038415938698781,4897508038416407799397⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-28150150225633226074067),(-28150150225631796091332)⟩,⟨13295063094552184958024,13295063094553614938702⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-39395939909464132761418),(-39395939909459836401392)⟩,⟨30176170480686645235073,30176170480690941592897⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-44496156218196267655650),(-44496156218184019256833)⟩,⟨59362375656125251225802,59362375656137499623533⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-32721659888962747652192),(-32721659888932561728475)⟩,⟨102061434037874138168381,102061434037904324094388⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨10713714293560435851541,10713714293617687713472⟩,⟨151919335085280732733809,151919335085337984604995⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨98137776202872213680803,98137776202956383394324⟩,⟨190134021800647394019675,190134021800731563750799⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨227373226001006971594644,227373226001138259223320⟩,⟨187034241677697140000212,187034241677828427643138⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨371036167795722049554288,371036167795865534514082⟩,⟨116359482368509922864768,116359482368653407827880⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨480185148314523482908767,480185148314630676111431⟩,⟨(-21451193954132214763345),(-21451193954025021572487)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨508666852666305972125111,508666852666364550334929⟩,⟨(-185624747657036967033278),(-185624747656978388850156)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨444071324907327477198433,444071324907355745950749⟩,⟨(-309890532431754312213706),(-309890532431726043493300)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨317334756139342841305146,317334756139358666768851⟩,⟨(-339242100407003953487472),(-339242100406988128045060)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨177858986465252068335112,177858986465259522056925⟩,⟨(-258925424297540752387939),(-258925424297533298677165)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨55471146097164761332634,55471146097166893907330⟩,⟨(-96239124206120999309174),(-96239124206118866737694)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨4620913435003776691,4620913435003776805⟩,⟨11193071666211195125,11193071666211195261⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨23688671435556118445,23688671435556118786⟩,⟨28221709931830532863,28221709931830533262⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨68460952806158357112,68460952806158357787⟩,⟨9724564995509433281,9724564995509434034⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨141484541459244051680,141484541459244052894⟩,⟨(-133850289770311010960),(-133850289770311009689)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨212724320536319002262,212724320536319004400⟩,⟨(-580148533996771521533),(-580148533996771519417)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨170088119308018011126,170088119308018014886⟩,⟨(-1573346987524797502353),(-1573346987524797498774)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-269496567644202546555),(-269496567644202539483)⟩,⟨(-3320126224117794086244),(-3320126224117794079626)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1604456797504521621282),(-1604456797504521602466)⟩,⟨(-5806914631569955915974),(-5806914631569955897919)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-4387897793320253945291),(-4387897793320253815176)⟩,⟨(-8584798232841054548075),(-8584798232841054418587)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-8803294322405525994347),(-8803294322405524836933)⟩,⟨(-10688107720210438083850),(-10688107720210436926713)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-14185949945032760143717),(-14185949945032752381037)⟩,⟨(-10944007632009784854014),(-10944007632009777091192)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-18939749976302084237365),(-18939749976302050355411)⟩,⟨(-8725197788412788637181),(-8725197788412754754737)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-21124891430973212653201),(-21124891430973120644587)⟩,⟨(-4694248962158179068200),(-4694248962158087058890)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-19390496358288381571809),(-19390496358288226335749)⟩,⟨(-733103254625057430740),(-733103254624902193982)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-13610800763939818596167),(-13610800763939654328027)⟩,⟨1252309613776512078129,1252309613776676346752⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-4888998533263167264293),(-4888998533263089847391)⟩,⟨781883709453261229351,781883709453338646403⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨69766006868206792418539658,69766006868225374434083079⟩,⟨220121303891301611145106836,220121303891320193162618216⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_20 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 20) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_20 (tableDensity true) (fullFactor true 1 20) density1_contains hk1_1_20_contains +noncomputable def atomAnswer : CBox := ⟨⟨254689012810432821363135930,254689012810432841449725282⟩,⟨156858142474683250207352640,156858142474683270267235710⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_20 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 20) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_20 1 20 ha1_1_20_contains + def realAnswer : RBox := ⟨324455019678639613681675588,324455019678658215983808361⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 20) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_20 +namespace hm1_0_1_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-98413007553530264069321429),(-98413007553530219910921556)⟩,⟨(-50791474724887001443400223),(-50791474724886957280698654)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-311942251767338170844870844),(-311942251767338057448526903)⟩,⟨(-111272109660014915798154725),(-111272109660014802391419093)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-546201130706752405819329846),(-546201130706752277443015670)⟩,⟨(-44185165616536861827890904),(-44185165616536733442409736)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-724674031225398718204351413),(-724674031225398630669779462)⟩,⟨222023521857877125749939777,222023521857877213282436999⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-683616568599001605701946400),(-683616568599001569272154439)⟩,⟨667321498306353532789584229,667321498306353569197966206⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-274142822717295978789278393),(-274142822717295965738524522)⟩,⟨1096107807261654530088553714,1096107807261654543107461956⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨448257898087938230262603907,448257898087938236552082080⟩,⟨1186050996660205982301818650,1186050996660205988587819174⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨1141958293408110715992395232,1141958293408110719514868416⟩,⟨734344548350997294915591873,734344548350997298468485876⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1388375282238759941182696397,1388375282238759943337497709⟩,⟨(-103879559825299724895016834),(-103879559825299722728177420)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1042653415150424150611471671,1042653415150424152152234910⟩,⟨(-887627560628814570654286395),(-887627560628814569109639576)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨348804430379694788540613070,348804430379694789685408121⟩,⟨(-1241486870147978578070557349),(-1241486870147978576944509968)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-292970878612095952098697039),(-292970878612095951312026373)⟩,⟨(-1117201376840690439992031081),(-1117201376840690439212780893)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-627284229818557963890203959),(-627284229818557963374056692)⟩,⟨(-737034044886611992070521812),(-737034044886611991547540760)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-637054869314904806405341836),(-637054869314904806101773626)⟩,⟨(-360889410051323082980618065),(-360889410051323082676085911)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-439455022212433539526927952),(-439455022212433539382242155)⟩,⟨(-124271050628923191204009132),(-124271050628923191063437555)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-153341503510410023123857457),(-153341503510410023082683172)⟩,⟨(-23771850572006332571043355),(-23771850572006332532176546)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-18373487433726570053117178),(-18373487433726554195587935)⟩,⟨(-22080384047309422703202745),(-22080384047309406843737440)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-64219592369928891893649966),(-64219592369928824104066874)⟩,⟨(-60330177322769975762877445),(-60330177322769907968247423)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-133291956133762005708302448),(-133291956133761798988148654)⟩,⟨(-75084634586827916872910437),(-75084634586827710147347997)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-223178535775118448587454511),(-223178535775117871043070567)⟩,⟨(-36292156892361036025112283),(-36292156892360458480444614)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-295800370966029031739181753),(-295800370966027704756454583)⟩,⟨88129589215089390136979063,88129589215090717107239516⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-271285321253619166627439311),(-271285321253616363431048133)⟩,⟨293054129615419230780155403,293054129615422033954361403⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-72924511083278658972022838),(-72924511083272227427953467)⟩,⟨488440172407210556363257107,488440172407216987904114548⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨275689833253944255835056919,275689833253952457857507430⟩,⟨515123464124303306053784372,515123464124311508102870332⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨600699085991611459472165441,600699085991621407645435711⟩,⟨271582879645527433652693131,271582879645537381848587385⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨688916221800597199359490154,688916221800606516404785686⟩,⟨(-153251957962819226303265347),(-153251957962809909269447354)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨482873756883111384645037625,482873756883116482499625908⟩,⟨(-523371520842404783138255968),(-523371520842399685317863576)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨132411267294304430450993657,132411267294307709449340022⟩,⟨(-658021563440381270093291553),(-658021563440377991108838093)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-153625303751220373232907309),(-153625303751218766518526113)⟩,⟨(-561793103482585666409502831),(-561793103482584059687862355)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-266620912505213832979254272),(-266620912505213207627828136)⟩,⟨(-363335603991852912053690115),(-363335603991852286686289172)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-220602054919227289829766739),(-220602054919227072988375803)⟩,⟨(-180408139798391759806373745),(-180408139798391542951642658)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-82737312761292347435933209),(-82737312761292287418278284)⟩,⟨(-51523520920863130775661037),(-51523520920863070753746849)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1356655024026984448028525),(-1356655024026984433814176)⟩,⟨(-1585379645851483893570972),(-1585379645851483879332484)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4766261193263737237000905),(-4766261193263737191136427)⟩,⟨(-4448000057026701865778885),(-4448000057026701819938369)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-10146578112210567910136703),(-10146578112210567819053764)⟩,⟨(-5948236867485167955421532),(-5948236867485167864731975)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-18066220299084903048941547),(-18066220299084902882472753)⟩,⟨(-3832846752480121363721857),(-3832846752480121198627049)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-26859058976832874495753486),(-26859058976832874199045763)⟩,⟨5448473118227235849424294,5448473118227236143593779⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-30543601028475738478679928),(-30543601028475737962048367)⟩,⟨24799938879870982193312923,24799938879870982708481859⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-18832264049121005212058612),(-18832264049121004344831758)⟩,⟨51487245892207878990018276,51487245892207879858974907⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨16558032869543947428796963,16558032869543948832681676⟩,⟨71955021372728034479862651,71955021372728035889609985⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨69864200703981615204225050,69864200703981617442389055⟩,⟨64961045551033176253289624,64961045551033178494412013⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨115706766621736320493613137,115706766621736324308742385⟩,⟨18300534832074337000129491,18300534832074340811388925⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨124085396965772164440212454,124085396965772172712056223⟩,⟨(-53684248404918560769036866),(-53684248404918552506041608)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨87325844908193000603046045,87325844908193028048189307⟩,⟨(-115230958193934497045580483),(-115230958193934469604365851)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨29064768429533776780164995,29064768429533847371033867⟩,⟨(-137146028528365818762351261),(-137146028528365748169621436)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-16202954335216167413855530),(-16202954335216055420160468)⟩,⟨(-117416352011904274102395080),(-117416352011904162103823710)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-29200876581107235700064215),(-29200876581107131345175113)⟩,⟨(-74118049613813336031406701),(-74118049613813231672013098)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-13388715164571677301192264),(-13388715164571633467895184)⟩,⟨(-24705492737284589303119581),(-24705492737284545468151295)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-69035560741708039835095),(-69035560741707865552048)⟩,⟨36748493452939040440811,36748493452939214724549⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-206402114789569280134573),(-206402114789568853554465)⟩,⟨134155360175475325187569,134155360175475751774521⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-330047613764263946705651),(-330047613764263491848001)⟩,⟨305958466623281500738980,305958466623281955625326⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-390022456794201272405751),(-390022456794200973415097)⟩,⟨603312429180206644982684,603312429180206944053703⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-272442663272950423721935),(-272442663272950292416057)⟩,⟨1050643660742670026246431,1050643660742670157710226⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨203771997342503514794819,203771997342503573930870⟩,⟨1578316324009079401798145,1578316324009079461077899⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1212680031622978203715586,1212680031622978231112527⟩,⟨1932092597100915763058525,1932092597100915790474368⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2730074838227569631406668,2730074838227569655939400⟩,⟨1652187210047649881175443,1652187210047649905455969⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨4311722522294447416844272,4311722522294447452567009⟩,⟨271121662399521624191161,271121662399521659398499⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨5113816107414520097284454,5113816107414520151205323⟩,⟨(-2251025009835582740579444),(-2251025009835582686942191)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨4383676872995345402928788,4383676872995345478200270⟩,⟨(-5188491331799158633337907),(-5188491331799158557887437)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2160636365199086686722943,2160636365199086782229708⟩,⟨(-7303045379588003833064531),(-7303045379588003736862103)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-526923382583916210822718),(-526923382583916104165010)⟩,⟨(-7667414340487695988729786),(-7667414340487695881269689)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-2310474618397602205187403),(-2310474618397602104642978)⟩,⟨(-6295243228903632817260550),(-6295243228903632716274874)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2403254454424947053037689),(-2403254454424946980626639)⟩,⟨(-3932130265836058368162091),(-3932130265836058295583549)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-994725615727285167159184),(-994725615727285140812306)⟩,⟨(-1309721655136236228043566),(-1309721655136236201662360)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1063416063032247155506,1063416063032277322697⟩,⟨3043873031545537258165,3043873031545567425008⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4125407560284755019427,4125407560284880150246⟩,⟨9122499890725415550208,9122499890725540680081⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨10101642543707446572782,10101642543707820396707⟩,⟨14757464907905191312067,14757464907905565134785⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨21050051492684556797360,21050051492685649993649⟩,⟨18218091994526138866314,18218091994527232061867⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨38240456922620062481751,38240456922623072959596⟩,⟨15541171104052096957753,15541171104055107436725⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨59974170254602150860695,59974170254609223299514⟩,⟨248479234859477465933,248479234866549910018⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨78487083652511629262465,78487083652524400012466⟩,⟨(-34723969512742599897895),(-34723969512729829135879)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨78412962884839527615045,78412962884864086058632⟩,⟨(-91405233692833407237402),(-91405233692808848781357)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨41237446660270294162636,41237446660307152557255⟩,⟨(-159044872232298845729701),(-159044872232261987330105)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-42007359772502563713730),(-42007359772465099757919)⟩,⟨(-211377912938884378653688),(-211377912938846914707174)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-156491700008176333288411),(-156491700008150599513069)⟩,⟨(-217571262086946019657698),(-217571262086920285910621)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-262597977790536093450137),(-262597977790521462149436)⟩,⟨(-165021191149197852273771),(-165021191149183221011338)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-315708368033999808892172),(-315708368033990386319151)⟩,⟨(-75366085072659528040240),(-75366085072650105493142)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-292884175483821297568228),(-292884175483816282154400)⟩,⟨5593635603543069090670,5593635603548084492390⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-202613830429971894296882),(-202613830429969631130080)⟩,⟨39253986337632662620876,39253986337634925784673⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-71734293644550647240189),(-71734293644550013384910)⟩,⟨20505991462840387342939,20505991462841021198138⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨64728552842978586492,64728552842978586548⟩,⟨(-27078109674871001689),(-27078109674871001632)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨191451192306484977708,191451192306484977864⟩,⟨(-104537184863424399593),(-104537184863424399451)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨301433560616263025590,301433560616263025875⟩,⟨(-253686345102084395320),(-253686345102084395045)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨354859212173279584082,354859212173279584568⟩,⟨(-522388297823331074933),(-522388297823331074460)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨268243334207395305637,268243334207395306417⟩,⟨(-937319377093951792450),(-937319377093951791663)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-92657287761104630971),(-92657287761104629699)⟩,⟨(-1459320855120658103654),(-1459320855120658102342)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-880126161012933612074),(-880126161012933609924)⟩,⟨(-1927637102794527334350),(-1927637102794527332110)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-2162066121383160839384),(-2162066121383160834063)⟩,⟨(-2033906744711070051544),(-2033906744711070046118)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3776213722897620145782),(-3776213722897620113602)⟩,⟨(-1394524915951132773201),(-1394524915951132740967)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-5258597010293929454208),(-5258597010293929182755)⟩,⟨231741173670850325801,231741173670850597260⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-5993186587202956606635),(-5993186587202954835822)⟩,⟨2663299349677895239796,2663299349677897010601⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-5583822779499968850377),(-5583822779499961353901)⟩,⟨5185177799031646100552,5185177799031653597055⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-4181630490646963661395),(-4181630490646944057738)⟩,⟨6803036762942990360046,6803036762943009963781⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-2434198648666550458209),(-2434198648666513893406)⟩,⟨6760025891630127846822,6760025891630164411730⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1038122857892098148158),(-1038122857892053159862)⟩,⟨4927892747101697431789,4927892747101742420164⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-249746725009089102872),(-249746725009067995851)⟩,⟨1796617894404731236238,1796617894404752343286⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨40616145128023554322641629,40616145128032017879585096⟩,⟨(-375679835923704258685738553),(-375679835923695795129693104)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 21) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_21 (tableDensity false) (fullFactor true 1 21) density0_contains hk1_1_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨54872525793450678214481978,54872525793450685995800070⟩,⟨52491600772809933901045764,52491600772809941673594326⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_21 1 21 ha1_1_21_contains + def realAnswer : RBox := ⟨95488670921474232437123607,95488670921482703975385166⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_21 +namespace hm1_1_1_21 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_21 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-15537040219313802683825660),(-15537040219313766911801478)⟩,⟨(-10830987531939262884587192),(-10830987531939227113601572)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-50396513420445314864625261),(-50396513420445223147946412)⟩,⟨(-26420116737649660687047127),(-26420116737649568972919130)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-91700680090264029551150989),(-91700680090263926188868701)⟩,⟨(-22119333479998036939160109),(-22119333479997933579172769)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-127908397056252985226918943),(-127908397056252915903732897)⟩,⟨15844037312867713112314770,15844037312867782436388808⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-130296333626403308654826253),(-130296333626403281650189197)⟩,⟨88056804421110028259825895,88056804421110055271699878⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-69133493777900109951443535),(-69133493777900102281138432)⟩,⟨164415167354252212987296359,164415167354252220666188386⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨51543266392677688335960384,51543266392677690784840802⟩,⟨188098034437004432883033919,188098034437004435331306795⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨174524788570649536451746225,174524788570649537283340779⟩,⟨117882543534922644069257901,117882543534922644890209530⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨223081936850775801273960168,223081936850775801741284601⟩,⟨(-24556012857538724534518814),(-24556012857538724075246578)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨166242331877880855213530661,166242331877880855556307201⟩,⟨(-161666548880501868929021788),(-161666548880501868579823036)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨45139195034657618182143502,45139195034657618431585016⟩,⟨(-223074008543495320138060281),(-223074008543495319877361183)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-67165556521665110806152558),(-67165556521665110612352964)⟩,⟨(-197447104623651555458292031),(-197447104623651555259366460)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-123094496236479077127026765),(-123094496236479076986461469)⟩,⟨(-125360887722847284526090967),(-125360887722847284385718162)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-120079147034277842588266353),(-120079147034277842500660547)⟩,⟨(-55968985645021734119486823),(-55968985645021734036689420)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-80963613948707741124315333),(-80963613948707741080248495)⟩,⟨(-15064281964039215449485459),(-15064281964039215410759585)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-27907665813507262538665877),(-27907665813507262525664347)⟩,⟨(-1493011188929369501636489),(-1493011188929369490857074)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-882904903255725035072179),(-882904903255712303294024)⟩,⟨(-4392107852649301531782707),(-4392107852649288800251292)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-4433525504170918108833611),(-4433525504170863298650722)⟩,⟨(-12811695895530590464122944),(-12811695895530535654581128)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-12986216340174707302313495),(-12986216340174538794637777)⟩,⟨(-18963954657599998873515591),(-18963954657599830366532142)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-27717905065661890625559862),(-27717905065661417209425440)⟩,⟨(-18025756813322979750043568),(-18025756813322506333982944)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-44131143729263396924078288),(-44131143729262305846913798)⟩,⟨(-3075225612653855206911491),(-3075225612652764128276140)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-49239059024229834774546807),(-49239059024227524767752818)⟩,⟨28672294806861043906519350,28672294806863353916081646⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-26867400978437610550885994),(-26867400978432299661915924)⟩,⟨66003165637820050623918293,66003165637825361513428514⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨25654358535095317457388064,25654358535102093777108818⟩,⟨82244157816821549287244550,82244157816828325603707518⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨84077244093222612448827961,84077244093230831871481038⟩,⟨54182734554142169081938427,54182734554150388501557415⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨110360599434467130796700403,110360599434474823505472826⟩,⟨(-11589922305953821638418755),(-11589922305946128928178045)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨86736682887100082056009269,86736682887104282197211799⟩,⟨(-78331141753683270099497856),(-78331141753679069953497709)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨31978018471866275096142904,31978018471868971162433090⟩,⟨(-110800110041873149268958444),(-110800110041870453200694527)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-18587018098808483774011036),(-18587018098807166971746335)⟩,⟨(-102523085453584984270912214),(-102523085453583667469743026)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-42174810639936130055442262),(-42174810639935620171198786)⟩,⟨(-71486680263387715966970045),(-71486680263387206085159575)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-37289562051354888786443991),(-37289562051354713156451053)⟩,⟨(-38215290237859237356544390),(-38215290237859061728625332)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-14353762418110235012083997),(-14353762418110186532216284)⟩,⟨(-11515189703148504531391895),(-11515189703148456052200310)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-73282350200766597167251),(-73282350200766592720975)⟩,⟨(-465356123631062719839570),(-465356123631062715392103)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-384305260527509433715215),(-384305260527509419247717)⟩,⟨(-1422815091906244464668845),(-1422815091906244450202130)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1208901519795597844955628),(-1208901519795597816967277)⟩,⟨(-2361104540020703227557112),(-2361104540020703199585968)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2876759412572300114242460),(-2876759412572300065932935)⟩,⟨(-2925288171086815142469186),(-2925288171086815094218707)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-5415725879250200772755607),(-5415725879250200693303754)⟩,⟨(-2286587870867690142297182),(-2286587870867690062947154)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-7983406924772415614443874),(-7983406924772415488439252)⟩,⟨665079516931461882696436,665079516931462008641266⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-8441097010256862406642678),(-8441097010256862216457105)⟩,⟨6352672738415357522744957,6352672738415357712993737⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-4121336271379561376648592),(-4121336271379561097858998)⟩,⟨13000467737513489900499083,13000467737513490179508613⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨5650715546919512765153521,5650715546919513221024745⟩,⟨16280192950895577669991473,16280192950895578125967904⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨17231591767999607288837456,17231591767999608401989531⟩,⟨12037648940335493153302932,12037648940335494266394623⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨24156670645418905433090135,24156670645418909510784348⟩,⟨656617748867434864176945,656617748867438941762854⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨22471733051051166753307681,22471733051051185922514828⟩,⟨(-12027098946035610336150062),(-12027098946035591167004977)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨14284746505817219811152886,14284746505817274014083236⟩,⟨(-19341082060857510037500675),(-19341082060857455834578762)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5421849786151992616356888,5421849786152081032685456⟩,⟨(-18902051982862789018680369),(-18902051982862700602344476)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨327223816781882845694072,327223816781965993957111⟩,⟨(-12855800468063706149676893),(-12855800468063623001416768)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-478834255378218310453867),(-478834255378183243244158)⟩,⟨(-4445180095895194647047172),(-4445180095895159579843839)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-25842618079898535883347),(-25842618079898389533322)⟩,⟨(-3946900327913450092653),(-3946900327913303742680)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-80863428988502810399807),(-80863428988502452506971)⟩,⟨(-5435930006072434613977),(-5435930006072076721803)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-143203527587068073394135),(-143203527587067692577696)⟩,⟨14636885763818593181696,14636885763818973995226⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-207483533431787314625382),(-207483533431787065523727)⟩,⟨76861276107665872658748,76861276107666121752199⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-248924177304699649429732),(-248924177304699541821468)⟩,⟨204190212135994642141896,204190212135994749734264⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-214143871235036850982851),(-214143871235036805338759)⟩,⟨405730971326685517012040,405730971326685562642210⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-26981692511355243544981),(-26981692511355227033409)⟩,⟨644873163660751096613963,644873163660751113124850⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨369807010170386631970215,369807010170386641746817⟩,⟨809169445924089683199041,809169445924089693001653⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨937232642444694487669518,937232642444694500151198⟩,⟨726994838416991387840921,726994838416991400372885⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1486464747597561380325771,1486464747597561399083522⟩,⟨269549682961942506119530,269549682961942524902118⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1743954540636286268389703,1743954540636286294719473⟩,⟨(-506218696077834899163423),(-506218696077834872855349)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1543330482689597428649720,1543330482689597462374982⟩,⟨(-1316329727165558801933534),(-1316329727165558768276494)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨984281081995574394944213,984281081995574433095098⟩,⟨(-1802862167547408984379111),(-1802862167547408946303418)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨378533941160081579278176,378533941160081615732751⟩,⟨(-1765203751520976660097656),(-1765203751520976623682316)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨15087068295803283768639,15087068295803310332631⟩,⟨(-1249612757913428821628369),(-1249612757913428795077943)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-40034535397463527914170),(-40034535397463518182708)⟩,⟨(-446150950440781993560252),(-446150950440781983831161)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨400135648954912113769,400135648954936905693⟩,⟨980938479698097195222,980938479698121987220⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1511900224139155591493,1511900224139258434463⟩,⟨2998634461948242606206,2998634461948345449381⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨3604275018053049230473,3604275018053356514228⟩,⟨5046729266268833242560,5046729266269140526589⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨7420706246538305185215,7420706246539203943524⟩,⟨6652333257268985447911,6652333257269884206420⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨13572294065680977126053,13572294065683452461100⟩,⟨6513780210574203507939,6513780210576678842810⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨21902638237070900523452,21902638237076715744094⟩,⟨2268645919380834556185,2268645919386649775760⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨30402242833457940390656,30402242833468438692034⟩,⟨(-9078389180733621600138),(-9078389180723123301404)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨34318060766698987343949,34318060766719165467729⟩,⟨(-29496470955598416309351),(-29496470955578238188488)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨26974671416265758177497,26974671416296018212440⟩,⟨(-57202083798286945503792),(-57202083798256685470158)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨3562078894465168731699,3562078894495893238626⟩,⟨(-84758302939522470999403),(-84758302939491746490809)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-33488447515801800674951),(-33488447515780722820966)⟩,⟨(-101017480311020955874113),(-101017480310999878014814)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-72352226905009710933861),(-72352226904997743679442)⟩,⟨(-97624581789866905224756),(-97624581789854937963165)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-96898491743884824950995),(-96898491743877127996708)⟩,⟨(-75654186605665662061144),(-75654186605657965101917)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-96072219660705703380553),(-96072219660701611047356)⟩,⟨(-45802005880772829398940),(-45802005880768737063404)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-69433985098973010419665),(-69433985098971165345386)⟩,⟨(-20627054181924736217829),(-20627054181922891142917)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-25150498245063418034750),(-25150498245062901518543)⟩,⟨(-5274275923674933773424),(-5274275923674417257168)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1884012208159255658,1884012208159255697⟩,⟨(-896210635091249565),(-896210635091249530)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨4642601220460736493,4642601220460736578⟩,⟨(-4351062615978398694),(-4351062615978398619)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨980902293773549233,980902293773549380⟩,⟨(-11956431857434958619),(-11956431857434958485)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-24965033770571118154),(-24965033770571117921)⟩,⟨(-23142960646736416632),(-23142960646736416403)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-104802480179231006372),(-104802480179231005988)⟩,⟨(-29945418685984785774),(-29945418685984785381)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-282035469938168105189),(-282035469938168104550)⟩,⟨(-7195590143145859297),(-7195590143145858614)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-591937424808065571231),(-591937424808065570069)⟩,⟨103704715514415508761,103704715514415510017⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1025115789694624493997),(-1025115789694624490485)⟩,⟨401283645860646575014,401283645860646578658⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1485814417759884364653),(-1485814417759884339364)⟩,⟨989589282658453485735,989589282658453511116⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-1780846314504059070563),(-1780846314504058849837)⟩,⟨1891505463611301992145,1891505463611302212890⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-1690273634785711694329),(-1690273634785710249493)⟩,⟨2954861104836791206836,2954861104836792651605⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1123691287598605996734),(-1123691287598599876597)⟩,⟨3847076189380328083861,3847076189380334203871⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-262471877693321802494),(-262471877693305789440)⟩,⟨4192369484857657125235,4192369484857673138119⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨473958996799593640234,473958996799623524276⟩,⟨3766662617281010158544,3766662617281040042453⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨689773308995163509856,689773308995200293065⟩,⟨2598806498550379494371,2598806498550416277511⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨315280266126404041052,315280266126421302068⟩,⟨924413933796729142798,924413933796746403797⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-19788723380537943710860368),(-19788723380530971529690597)⟩,⟨(-95466070166456385082264342),(-95466070166449412901040557)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_21 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 21) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_21 (tableDensity true) (fullFactor true 1 21) density1_contains hk1_1_21_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-71756379883743204763738553),(-71756379883743194588168741)⟩,⟨(-68642862549059154496238733),(-68642862549059144332136768)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_21 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 21) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_21 1 21 ha1_1_21_contains + def realAnswer : RBox := ⟨(-91545103264281148574598921),(-91545103264274166017859338)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 21) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_21 +namespace hm1_0_1_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨25795464642691979965051089,25795464642691998736587077⟩,⟨34302091936473676923749334,34302091936473695696624360⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨91093454473528090538208511,91093454473528132172566593⟩,⟨90885915423428689701798817,90885915423428731340994480⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨187076896782927572052967728,187076896782927612771580690⟩,⟨103825170827836346424979349,103825170827836387151909771⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨296311525473684373038132911,296311525473684405711138086⟩,⟨31428387017645274458592619,31428387017645307137373622⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨348846489147237845805247700,348846489147237862146769417⟩,⟨(-147478349858262999005620416),(-147478349858262982665263419)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨248940906601250386644119708,248940906601250392421211174⟩,⟨(-377371860519165542899686975),(-377371860519165537135291586)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-32293372021029125282999023),(-32293372021029122418755581)⟩,⟨(-511093250737755638579202960),(-511093250737755635723300317)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-374697101649110724392677054),(-374697101649110722686650200)⟩,⟨(-407088910594236715643627378),(-407088910594236713929922644)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-566576918783868213611811814),(-566576918783868212617832460)⟩,⟨(-77685591464521904317549975),(-77685591464521903315898344)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-486065812083162370899447060),(-486065812083162370188022121)⟩,⟨290292146726667898703513618,290292146726667899417845651⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-208111033917350883884727737),(-208111033917350883373618074)⟩,⟨493805786554838575425027390,493805786554838575929945272⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨81250609404594956985927428,81250609404594957332274859⟩,⟨474746779873570359799142917,474746779873570360141379601⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨245016771992228087745063123,245016771992228087967661378⟩,⟨321878311358871912475808099,321878311358871912701136155⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨262132763052695435876382774,262132763052695436007348680⟩,⟨158678212644527151512153560,158678212644527151643602658⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨183431461799396100254994635,183431461799396100317011089⟩,⟨54111279439057557739954671,54111279439057557800271635⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨64207066292898278435832141,64207066292898278453360718⟩,⟨10103026836972030990744445,10103026836972031007305820⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-1044473372243695525274622),(-1044473372243688806676122)⟩,⟨9252959093821370096478560,9252959093821376815141766⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨461021711730027930866597,461021711730053879604902⟩,⟨28664856441298346124285375,28664856441298372073587964⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨13319829630108682760299474,13319829630108748060579991⟩,⟨48333338049108683088708647,48333338049108748391157408⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨44585197909245418735393537,44585197909245568701694850⟩,⟨60152821670287327393263096,60152821670287477364384113⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨92797864764504291343306509,92797864764504761853467101⟩,⟨45975018022364833577669633,45975018022365304091162875⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨135373534992590146595252452,135373534992591265963067938⟩,⟨(-13729884488721815144781906),(-13729884488720695779669117)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨127515731879382198725194802,127515731879384031855072363⟩,⟨(-114135531692472401420182226),(-114135531692470568299793927)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨34457358314372774250195514,34457358314376116433953858⟩,⟨(-203170613375632104347416698),(-203170613375628762165887800)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-117897931324453089719459562),(-117897931324449700660840440)⟩,⟨(-205214034959308855586790532),(-205214034959305466517941576)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-240188405531815558503804135),(-240188405531812373066644705)⟩,⟨(-93404576547357308097734698),(-93404576547354122652512231)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-254575838324970344796870282),(-254575838324968047025262091)⟩,⟨70354188959850202472159877,70354188959852500239224999⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-167069576699674517403161517),(-167069576699673484625706988)⟩,⟨189168665274739402680649831,189168665274740435446277151⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-50693993677188511322706419),(-50693993677187928452770438)⟩,⟨215611106343272638975728134,215611106343273221840400946⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨26994185722366063946211102,26994185722366338622671490⟩,⟨170759312885816233821053488,170759312885816508498048043⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨45245964919450091563929986,45245964919450199437296090⟩,⟨100222930376818825650715376,100222930376818933526332485⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨20046808847333880507492747,20046808847333908097130845⟩,⟨31952757180957784510061160,31952757180957812100773646⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-193230856702035856272846),(-193230856702035851247753)⟩,⟨519629425716751867354490,519629425716751872415892⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-412615241092970976827359),(-412615241092970960548150)⟩,⟨1688793646636875308787712,1688793646636875325206450⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-33318826319257199849599),(-33318826319257167186194)⟩,⟨3158803750826517285231530,3158803750826517318217881⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨1591231661950574474717586,1591231661950574535655012⟩,⟨4753266326118654097707334,4753266326118654159032523⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨5129246162263062557457213,5129246162263062668443101⟩,⟨5524857105125452782731913,5524857105125452893885587⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨10432593983843646290426785,10432593983843646487361906⟩,⟨3473675422011882277503970,3473675422011882473964372⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨15154193309070677138088391,15154193309070677478376929⟩,⟨(-3686388586369200290180288),(-3686388586369199951197413)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨14299798105269657619207391,14299798105269658185941364⟩,⟨(-15930167257558164848109132),(-15930167257558164281914994)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨3123997720345504258392352,3123997720345505162648057⟩,⟨(-28028555215769803220232703),(-28028555215769802314690147)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-17120246586011831212172589),(-17120246586011829711467104)⟩,⟨(-30872750203690969129084972),(-30872750203690967626125883)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-36897446611697903384364424),(-36897446611697900039066634)⟩,⟨(-18974066381322159784556673),(-18974066381322156438972735)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-45018659897380145601340490),(-45018659897380137123820682)⟩,⟨2768829660645583637847844,2768829660645592113449620⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-38475900852455104456953930),(-38475900852455085359219892)⟩,⟨22059057638372214160070244,22059057638372233255182423⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-24094154561039298709832243),(-24094154561039259998825270)⟩,⟨29272280141734600217898471,29272280141734638927688788⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-10927157947659559633875167),(-10927157947659515747103902)⟩,⟨23234087397920499884006047,23234087397920543770500203⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2796841706461452019426323),(-2796841706461432478295646)⟩,⟨8650954367200017652316636,8650954367200037193447093⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨12492139340558481796881,12492139340558517771155⟩,⟨11966063026765618623090,11966063026765654595893⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨42700123418235839289583,42700123418235925240584⟩,⟨34071918408680203206488,34071918408680289151869⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨88403852022685359305785,88403852022685446220818⟩,⟨47830481606340710495830,47830481606340797397290⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨157423327526502137934377,157423327526502196231095⟩,⟨38067818612033303345738,38067818612033361618278⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨246545762423877456047516,246545762423877491582841⟩,⟨(-23471017416566781868134),(-23471017416566746356073)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨324769579535920472003902,324769579535920487438682⟩,⟨(-173808847334054670832669),(-173808847334054655403782)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨316561068993789631244420,316561068993789638345911⟩,⟨(-433227009009362973881617),(-433227009009362966741493)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨112115256288404206762436,112115256288404213902782⟩,⟨(-755417317072283612805562),(-755417317072283605569072)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-363340733566211758344839),(-363340733566211747123642)⟩,⟨(-987863077456239510612306),(-987863077456239499328999)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1039479570781138264611733),(-1039479570781138247151738)⟩,⟨(-916256636691777938108536),(-916256636691777920687342)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-1659966368217681554750771),(-1659966368217681529540843)⟩,⟨(-424092484593482681563994),(-424092484593482656529885)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-1919314313302095929986688),(-1919314313302095897172402)⟩,⟨349292401803434005160796,349292401803434037799512⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1700286193348522952309275),(-1700286193348522915042520)⟩,⟨1043351424678453359199977,1043351424678453396399396⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1167766037772311686181133),(-1167766037772311650793341)⟩,⟨1315376858554459196061508,1315376858554459231471528⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-606415409076300506133649),(-606415409076300480485361)⟩,⟨1055845845719418542171573,1055845845719418567873329⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-176399666311113166084538),(-176399666311113156706526)⟩,⟨398892469749392614325401,398892469749392623729383⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨531376826563990517470,531376826563996659067⟩,⟨(-295463160438994117196),(-295463160438987975557)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1564029630915890427318,1564029630915915655845⟩,⟨(-1066828341697971112153),(-1066828341697945883518)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨2419346952585072616909,2419346952585146613601⟩,⟨(-2389565793557648227422),(-2389565793557574230634)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨2684247598604237456422,2684247598604448123229⟩,⟨(-4612123102839561682272),(-4612123102839351015549)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨1511572903977475166656,1511572903978033510442⟩,⟨(-7850983848213741728081),(-7850983848213183384855)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-2370701235829585367997),(-2370701235828350201146)⟩,⟨(-11519910292817499693505),(-11519910292816264528154)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-10142402053216110406915),(-10142402053213435400296)⟩,⟨(-13726481397764042688701),(-13726481397761367684287)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-21614107546546310566438),(-21614107546540848996109)⟩,⟨(-11128933076241913923027),(-11128933076236452354077)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-33686536962725987982696),(-33686536962718376905009)⟩,⟨(-199193080817314140753),(-199193080809703062332)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-40247295761715777448146),(-40247295761708652463703)⟩,⟨19848217994659635219428,19848217994666760208082⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-35245459040806617461358),(-35245459040801740025281)⟩,⟨44334923928055575793525,44334923928060453236898⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-17914692963795095955577),(-17914692963791386010031)⟩,⟨63972392284161821696413,63972392284165531647237⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨4525325933343314348957,4525325933345548113028⟩,⟨70191432500648306568774,70191432500650540334731⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨20537344180276684567379,20537344180277804011583⟩,⟨60686196432697400464365,60686196432698519907665⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨21957505405791139901762,21957505405791623799301⟩,⟨39766294144992298174090,39766294144992782069769⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨9229085813355612107680,9229085813355744504504⟩,⟨13647652835022796039759,13647652835022928435700⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-5005505731349373990),(-5005505731349373969)⟩,⟨(-10396911681275805541),(-10396911681275805515)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-18930205355029627716),(-18930205355029627678)⟩,⟨(-30573669248004863748),(-30573669248004863709)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-44880642604774810739),(-44880642604774810681)⟩,⟨(-47372524427949978200),(-47372524427949978138)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-90784030928807713271),(-90784030928807713177)⟩,⟨(-53410985122771467793),(-53410985122771467700)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-160600370102923063763),(-160600370102923063614)⟩,⟨(-33562873978595337810),(-33562873978595337662)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-246080368790446946259),(-246080368790446946019)⟩,⟨36027787089593412994,36027787089593413226⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-316405301676033217448),(-316405301676033217047)⟩,⟨181449243470993641049,181449243470993641433⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-313743445040025096959),(-313743445040025095926)⟩,⟨411600719901232008557,411600719901232009572⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-168109493424259768110),(-168109493424259762171)⟩,⟨691106695053113390499,691106695053113396434⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨160088423105244576213,160088423105244624877⟩,⟨928770164437990577019,928770164437990625685⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨627478421810408009354,627478421810408317700⟩,⟨1010259962585892515410,1010259962585892823757⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1091513446635183253227,1091513446635184510146⟩,⟨873320040115473874973,873320040115475131886⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1365657270710905830258,1365657270710909391726⟩,⟨569306231157597371503,569306231157600932951⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1319467390081954255936,1319467390081961951900⟩,⟨243736714808514706718,243736714808522402665⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨944889666326484064670,944889666326493353998⟩,⟨37759117001934589545,37759117001943878857⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨341384038654077182413,341384038654081500205⟩,⟨(-10920946848820496775),(-10920946848816178984)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-9662632296429623675006084),(-9662632296426582083556347)⟩,⟨148764963259627327141772643,148764963259630368733209141⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 22) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_22 (tableDensity false) (fullFactor true 1 22) density0_contains hk1_1_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-13403390211880415842460358),(-13403390211880412061118917)⟩,⟨(-15300821202971964555112932),(-15300821202971960777627328)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_22 1 22 ha1_1_22_contains + def realAnswer : RBox := ⟨(-23066022508310039617466442),(-23066022508306994044675264)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_22 +namespace hm1_1_1_22 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_22 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨3598869912098204802717805,3598869912098219971691992⟩,⟨6397047838510793684510930,6397047838510808853164198⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨13314906058125678258730243,13314906058125711765961524⟩,⟨17649254465139581989084527,17649254465139615495137085⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨29036830600391072243496156,29036830600391104711235157⟩,⟨22659177617937335286871917,22659177617937367752499435⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨48701369525960106335788604,48701369525960131913709193⟩,⟨13992907485154438587097072,13992907485154464163534704⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨60828731727801813427083449,60828731727801825375797248⟩,⟨(-13656402647378074947463059),(-13656402647378062997891234)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨47910922633004708423645709,47910922633004711647424083⟩,⟨(-52874881726507287994528691),(-52874881726507284766760431)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨2422424395873494815435431,2422424395873495814749613⟩,⟨(-78715433097493462437212998),(-78715433097493461435956146)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-56679108400989786978713468),(-56679108400989786586664088)⟩,⟨(-64420780983332202395515728),(-64420780983332202006135896)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-91702039315330569274594154),(-91702039315330569068802012)⟩,⟨(-9303216484369113315875953),(-9303216484369113114903896)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-78868775288433379202307220),(-78868775288433379046704296)⟩,⟨54508811929108036505978636,54508811929108036662649879⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-30154435752810476182660228),(-30154435752810476071941899)⟩,⟨89640777754301447733983727,89640777754301447849256829⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨20755959625502351704207055,20755959625502351786974277⟩,⟨84461250470293834801252814,84461250470293834886664470⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨48518708251143220988992626,48518708251143221048813285⟩,⟨55120617160793199479621874,55120617160793199539718846⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨49554274826085330934885102,49554274826085330972320419⟩,⟨24866116239316139296288740,24866116239316139331864769⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨33831237505222744582927167,33831237505222744601666535⟩,⟨6690116976192053618915857,6690116976192053635451890⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨11688154035602129299736284,11688154035602129305232689⟩,⟨651906726440514921406531,651906726440514925973790⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-829626018330145815378254),(-829626018330140432232474)⟩,⟨1191960187830751258263191,1191960187830756641401980⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-1987330398638506986924647),(-1987330398638486084745523)⟩,⟨3937801854540788641522012,3937801854540809543634313⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-1410962266426882080145861),(-1410962266426829124692109)⟩,⟨7398406642858555007418724,7398406642858607962609838⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2415295582698249948522413,2415295582698372246855948⟩,⟨10677862515931244020734631,10677862515931366318469591⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨10135141404361124286488315,10135141404361510611601476⟩,⟨10841716530087858166070294,10841716530088244490756147⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨19041866382376654589484276,19041866382377576467249250⟩,⟨3770240409810679146870999,3770240409811601024932730⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨21764685237428227897239620,21764685237429739834614114⟩,⟨(-11660517454018292110409596),(-11660517454016780171851595)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨10615105724063051793659194,10615105724065812102313293⟩,⟨(-28469237003076611763428591),(-28469237003073851454429949)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-13110548987698393472838007),(-13110548987695595268990074)⟩,⟨(-33427605681122374345615004),(-33427605681119576143061024)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-35846626662396669804850985),(-35846626662394041865142795)⟩,⟨(-18889703839176675084087559),(-18889703839174047145484567)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-42658240659663989250693980),(-42658240659662096757817255)⟩,⟨7704048433943867843484541,7704048433945760336995384⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-31280261044596204665430416),(-31280261044595357385259890)⟩,⟨30033424644366363244903893,30033424644367210526788785⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-12406434476232542174346109),(-12406434476232065560836536)⟩,⟨37634206591040987438307706,37634206591041464052593953⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1806393566895709636710097,1806393566895933235678377⟩,⟨31789563768557457435571968,31789563768557681034460557⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨6322674214980050631734964,6322674214980137953610296⟩,⟨19609011869472726991238205,19609011869472814312766405⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨3040975528177761962259916,3040975528177784199248954⟩,⟨6439712288826101539546402,6439712288826123776366552⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-98636135060492470994969),(-98636135060492469428628)⟩,⟨77052875669264982558956,77052875669264984126933⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-280762258233949920200457),(-280762258233949915078862)⟩,⟨275008071818023883336510,275008071818023888464630⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-389200469398202877595786),(-389200469398202867576563)⟩,⟨596749963558894742263821,596749963558894752297857⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-288115867309179473204640),(-288115867309179455493000)⟩,⟨1075632438174426935151829,1075632438174426952880603⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨239341816306140938880603,239341816306140968681226⟩,⟨1599198542219568334483810,1599198542219568364291458⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1355579980325887462638937,1355579980325887510364388⟩,⟨1781586548103450211309507,1781586548103450259018021⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨2836509044350260894238931,2836509044350260967865479⟩,⟨991927392490739916470936,991927392490739990046162⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨3769659737790277365997254,3769659737790277477798892⟩,⟨(-1191407801824442536506041),(-1191407801824442424727691)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨2870445386784590868822418,2870445386784591043492917⟩,⟨(-4208128944667458242429588),(-4208128944667458067724136)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-338397619419782876098694),(-338397619419782494059673)⟩,⟨(-6324946747629251442344992),(-6324946747629251060255746)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-4548582965992929096222516),(-4548582965992927517059183)⟩,⟨(-5856861855395416540963149),(-5856861855395414961789388)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-7414320479499221560008611),(-7414320479499216051628109)⟩,⟨(-2871413162019707033209390),(-2871413162019701524838214)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-7573264142138771364525940),(-7573264142138757293987008)⟩,⟨708026346015202171869388,708026346015216242392987⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-5620005989266946300999757),(-5620005989266916061495753)⟩,⟨2823942816151532327125468,2823942816151562566621042⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-3087343012239454216785256),(-3087343012239419321490760)⟩,⟨2765271889334185860205356,2765271889334220755496687⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-934125979639630406226935),(-934125979639614781188363)⟩,⟨1104507928037404080709804,1104507928037419705747527⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨956518559274189839787,956518559274220041498⟩,⟨5702717169492659757506,5702717169492689959368⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4516206726706032591868,4516206726706104678090⟩,⟨17408588171921241803240,17408588171921313890042⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨13377101121096775243976,13377101121096847950492⟩,⟨29233782943021181186188,29233782943021253894103⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨31803419421964489895434,31803419421964538346172⟩,⟨38426579839178845601464,38426579839178894054675⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨63187395088025807795291,63187395088025836850582⟩,⟨37464350668626858169369,37464350668626887226976⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨105386774172193548010292,105386774172193559784945⟩,⟨12991226241347873144811,12991226241347884919924⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨143251418935443645957655,143251418935443649989138⟩,⟨(-50259295719447895200195),(-50259295719447891172721)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨144387979445837789348921,144387979445837792094511⟩,⟨(-156470793871817590258793),(-156470793871817587522681)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨69957195169665695110743,69957195169665699072004⟩,⟨(-280382581550980396465513),(-280382581550980392509831)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-94233319310274095609869),(-94233319310274089545588)⟩,⟨(-362599645485377422628939),(-362599645485377416559993)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-306773603820251161012586),(-306773603820251152278958)⟩,⟨(-340121679700260412181902),(-340121679700260403431042)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-479185822121506870449467),(-479185822121506858970132)⟩,⟨(-200866595904613937562018),(-200866595904613926066382)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-533071552383571877753631),(-533071552383571864504402)⟩,⟨(-9569419232803067950718),(-9569419232803054696086)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-454865293080327267499002),(-454865293080327254705202)⟩,⟨131677756575073607588134,131677756575073620378764⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-291525478309335309749963),(-291525478309335300347503)⟩,⟨155042000158261430878932,155042000158261440275644⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-98420659500691570013149),(-98420659500691566548016)⟩,⟨66523195116347225101362,66523195116347228563865⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨169398496942814324914,169398496942819372239⟩,⟨(-105889447713556327558),(-105889447713551280244)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨509014963619756734800,509014963619777469837⟩,⟨(-379707776767139055138),(-379707776767118320126)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨822324726360996793531,822324726361057618991⟩,⟨(-845225898991919629267),(-845225898991858803838)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨989663106528193856063,989663106528367053033⟩,⟨(-1634129444601959019209),(-1634129444601785822230)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨726204667192956421691,726204667193415513203⟩,⟨(-2824185181820916517054),(-2824185181820457425432)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-447693713709545096983),(-447693713708529499062)⟩,⟨(-4295076485519944334620),(-4295076485518928736382)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-3080216494977378733764),(-3080216494975179751462)⟩,⟨(-5506859962945357197402),(-5506859962943158214601)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-7396380509712066519576),(-7396380509707579076752)⟩,⟨(-5361993744510610020104),(-5361993744506122576936)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-12727310947656639720131),(-12727310947650391139603)⟩,⟨(-2485862945993501300458),(-2485862945987252720044)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-17240658434235931388301),(-17240658434230088083142)⟩,⟨3853999174435060305862,3853999174440903610200⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-18619250939560216175403),(-18619250939556221348072)⟩,⟨12618432032480137390980,12618432032484132216902⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-15650468475649250050002),(-15650468475646215596240)⟩,⟨20798682006805812825626,20798682006808847278355⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-9490677196190007754798),(-9490677196188183079396)⟩,⟨24892401582312745269322,24892401582314569944323⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-3194861832031803399774),(-3194861832030890016434)⟩,⟨23056660035451524529398,23056660035452437912856⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨388179394643177564947,388179394643572037125⟩,⟨15938074055336505764481,15938074055336900236963⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨619862345482650224426,619862345482758098645⟩,⟨5640715423339610209465,5640715423339718083832⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-163441320929436552),(-163441320929436532)⟩,⟨(-301679824814347876),(-301679824814347856)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-757988480408060815),(-757988480408060789)⟩,⟨(-724920171833884580),(-724920171833884549)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1986194629775742679),(-1986194629775742642)⟩,⟨(-44907802950337860),(-44907802950337823)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-3579874504071126511),(-3579874504071126457)⟩,⟨4409244332773457675,4409244332773457727⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-3738988093408922447),(-3738988093408922367)⟩,⟨17967495074646369030,17967495074646369108⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2720309011685229290,2720309011685229421⟩,⟨47933832573974398911,47933832573974399030⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨27194831046977617567,27194831046977617792⟩,⟨99853057711093042071,99853057711093042280⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨88103960642378289146,88103960642378289840⟩,⟨170612058069349749325,170612058069349749999⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨203905142130349584153,203905142130349588819⟩,⟨240794292948206916204,240794292948206920860⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨376297105722406338900,376297105722406378449⟩,⟨273629976210842793198,273629976210842832748⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨572863484221754701755,572863484221754953273⟩,⟨230191520673091712261,230191520673091963796⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨728419798719121759392,728419798719122785402⟩,⟨100162323327177070113,100162323327178096158⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨774905153556853065887,774905153556855974925⟩,⟨(-72761038345499898628),(-72761038345496989558)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨679751207650973210613,679751207650979500396⟩,⟨(-201470460033567585355),(-201470460033561295553)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨459529384901064870661,459529384901072465737⟩,⟨(-209154163642715675913),(-209154163642708080831)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨161506173663488951922,161506173663492482939⟩,⟨(-87978083509626142200),(-87978083509622611182)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨4518018148823045605282315,4518018148825548197682421⟩,⟨38128746853567322789392309,38128746853569825381523120⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_22 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 22) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_22 (tableDensity true) (fullFactor true 1 22) density1_contains hk1_1_22_contains +noncomputable def atomAnswer : CBox := ⟨⟨17527510277074385003001660,17527510277074389947832775⟩,⟨20008766188501794863051122,20008766188501799802839987⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_22 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 22) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_22 1 22 ha1_1_22_contains + def realAnswer : RBox := ⟨22045528425897430508283975,22045528425899938245515196⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 22) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_22 +namespace hm1_0_1_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-3086257427469952655190105),(-3086257427469944753392140)⟩,⟨(-15607462071572053164700545),(-15607462071572045262858659)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-16169754371404816538133776),(-16169754371404797847477764)⟩,⟨(-45004794804416468558516023),(-45004794804416449867313696)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-47603104755254661219721534),(-47603104755254643198836037)⟩,⟨(-64175519462880229354460650),(-64175519462880211331476068)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-97865384198923512127228367),(-97865384198923501539123026)⟩,⟨(-54562261805611432991299473),(-54562261805611422399221992)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-143560350647417923974427300),(-143560350647417917761195559)⟩,⟨3828065881223424750713405,3828065881223430966114692⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-137762771340681862072745877),(-137762771340681859441174489)⟩,⟨104652173431400779143187474,104652173431400781772594541⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-46075600248623819313410593),(-46075600248623818060574995)⟩,⟨192378597655073818121850706,192378597655073819369354105⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨101239819634421849719616380,101239819634421850503268776⟩,⟨190389106530448530327791584,190389106530448531112270671⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨211250385183996101618189555,211250385183996102066421198⟩,⟨76432016472023315694302751,76432016472023316145814401⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨208593471727248171684085166,208593471727248171996677659⟩,⟨(-81275817514937425427344881),(-81275817514937425113166378)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨106517525273595635746846047,106517525273595635967130081⟩,⟨(-184414174627814301114332716),(-184414174627814300895732497)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-15841834251842795536973770),(-15841834251842795391066061)⟩,⟨(-191450148801682354448011654),(-191450148801682354304151854)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-90796424307851211303115380),(-90796424307851211211374326)⟩,⟨(-133819085080565273760431859),(-133819085080565273667652403)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-103049899045006803620129152),(-103049899045006803566119486)⟩,⟨(-66524441801301742717137091),(-66524441801301742662901740)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-73225373166679245737316343),(-73225373166679245711898139)⟩,⟨(-22501116941454810936799269),(-22501116941454810912052228)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-25715664204587794818680364),(-25715664204587794811544032)⟩,⟨(-4106213188281540671007771),(-4106213188281540664259220)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨2295099766107512572469646,2295099766107514156852398⟩,⟨(-1751883829930947255808399),(-1751883829930945671629828)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨6302833667363874868015898,6302833667363881749017022⟩,⟨(-6314871363160976585479051),(-6314871363160969705012313)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨7808050913948125123226817,7808050913948146607819078⟩,⟨(-13638474906712522851651763),(-13638474906712501367625765)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3165189305997387648204778,3165189305997448722997395⟩,⟨(-23503493788837040873457930),(-23503493788836979798629465)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-11749558870093093795035149),(-11749558870092955330934413)⟩,⟨(-31090667896325381077826840),(-31090667896325242612173283)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-36046632453117482954420066),(-36046632453117151200256654)⟩,⟨(-25827702296252389479695566),(-25827702296252057723425735)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-56681339113105945883124419),(-56681339113105210193158471)⟩,⟨2136507682598967708484229,2136507682599703397836244⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-51172484895260689076689459),(-51172484895259745486067227)⟩,⟨47054482077264713586019236,47054482077265657173002565⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-8367431459196783462628415),(-8367431459195447763513881)⟩,⟨80833203917129717721907828,80833203917131053420397114⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨51578843140314541058442958,51578843140315579050909643⟩,⟨73760955251707273343224380,73760955251708311339659877⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨89882317384701675802238054,89882317384702456164298527⟩,⟨26458687408401526524513566,26458687408402306889017032⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨86086255228366242132581851,86086255228366694901416057⟩,⟨(-28771536638246751228364733),(-28771536638246298461219053)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨53650911254456219784387682,53650911254456399299264680⟩,⟨(-60103350616712646154876649),(-60103350616712466643707115)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨19922010362952773904141650,19922010362952865380481574⟩,⟨(-60223842981385804139974571),(-60223842981385712665535459)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1507996413345093810216208,1507996413345134994394534⟩,⟨(-40557545182173722954146044),(-40557545182173681770423713)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1488524058175360252354651),(-1488524058175348990669586)⟩,⟨(-13883780807407827332500668),(-13883780807407816070839106)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨139291281226306991549453,139291281226306993282682⟩,⟨(-21187413316252747874622),(-21187413316252746154212)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨427172324658759861552942,427172324658759867205764⟩,⟨(-118966911840246099267153),(-118966911840246093648646)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨708622121740663091469344,708622121740663102946548⟩,⟨(-395587172244504651985992),(-395587172244504640547163)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨853784923340821060888186,853784923340821082458441⟩,⟨(-982071192979774643222690),(-982071192979774621652789)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨537343115766490761904197,537343115766490801606994⟩,⟨(-1909397624260719549184274),(-1909397624260719509366104)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-715914749684097342251389),(-715914749684097270174496)⟩,⟨(-2850880127824606987758827),(-2850880127824606915427035)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-3125830025943622358684748),(-3125830025943622230849254)⟩,⟨(-2870404891781814169122257),(-2870404891781814041193490)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-5894951684430720024399036),(-5894951684430719807241376)⟩,⟨(-700871839722752958387983),(-700871839722752741544918)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-6892029023476890106254391),(-6892029023476889751567547)⟩,⟨4011651362655828380192687,4011651362655828734376114⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-3973846320129570164755766),(-3973846320129569574674866)⟩,⟨9367550960795655140484105,9367550960795655730620762⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2569676250822749596077285,2569676250822750684041012⟩,⟨11904433112226829162147671,11904433112226830250849386⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨9382498450073919226747435,9382498450073922127146474⟩,⟨9648846337763654615746125,9648846337763657516701316⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨12735935598891058739702727,12735935598891066060283317⟩,⟨4231569548058194663324230,4231569548058201983870009⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨11581175830597381600145998,11581175830597393404964840⟩,⟨(-653233238552548370759391),(-653233238552536566339635)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨7522774324862544646533276,7522774324862555798847115⟩,⟨(-2461908291207235835128767),(-2461908291207224683230229)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2535135319725055082896893,2535135319725059559510552⟩,⟨(-1220810757872047631521901),(-1220810757872043155076212)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1579227432846525569717,1579227432846531875117⟩,⟨(-3301643542924052654571),(-3301643542924046348616)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4003443441377395166343,4003443441377409988540⟩,⟨(-10882417501677371953489),(-10882417501677357129390)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨3603566272588616111942,3603566272588634287795⟩,⟨(-21168213222642060829902),(-21168213222642042651043)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-3465238783669695535398),(-3465238783669680270526)⟩,⟨(-34753437868686347808323),(-34753437868686332540291)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-23198223685411275869733),(-23198223685411267292848)⟩,⟨(-48822071840253885946146),(-48822071840253877368178)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-61507046276420109867562),(-61507046276420106415402)⟩,⟨(-53552378774620177886730),(-53552378774620174439782)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-116915521131837974935303),(-116915521131837973206347)⟩,⟨(-30069496776931056847567),(-30069496776931055134394)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-169403335977349082782760),(-169403335977349080662068)⟩,⟨43182633271603057492316,43182633271603059600001⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-176481712944590418608130),(-176481712944590415201842)⟩,⟨170359521883344746887668,170359521883344750298671⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-93602957534501256623438),(-93602957534501251204132)⟩,⟨315091852452761621571322,315091852452761627024879⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨82648452652893433452071,82648452652893441480613⟩,⟨405012430658339025811725,405012430658339033876106⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨288401137796336005065001,288401137796336015754370⟩,⟨381171924869802239531571,381171924869802250228461⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨425162880485414991871751,425162880485415004244132⟩,⟨254057263317216388442106,254057263317216400791623⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨429388143783377534990653,429388143783377546957646⟩,⟨101893698376484287288971,101893698376484299215753⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨307654616034323143167340,307654616034323151947998⟩,⟨6301016866689129830116,6301016866689138576503⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨110205561817836613508527,110205561817836616736552⟩,⟨(-9779937666599925164942),(-9779937666599921948180)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-68855222401281928266),(-68855222401280771220)⟩,⟨(-85352944799332523596),(-85352944799331366553)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-239003874970479901279),(-239003874970475192394)⟩,⟨(-245236943785687991067),(-245236943785683282188)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-505993182342286824646),(-505993182342273266609)⟩,⟨(-355635151157213589818),(-355635151157200031776)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-922191256115197875427),(-922191256115160387330)⟩,⟨(-326979254762685252885),(-326979254762647764736)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1481247994171491017050),(-1481247994171396139604)⟩,⟨8333245112703562085,8333245112798439694⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-2023254029563857952799),(-2023254029563640345231)⟩,⟨879576036224594465372,879576036224812073258⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2127361244559890281020),(-2127361244559314060792)⟩,⟨2452201424706054364760,2452201424706630585269⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1124511162574019671536),(-1124511162572924973025)⟩,⟨4557549434123781305313,4557549434124876003859⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1582632558642753909442,1582632558644166162364⟩,⟨6414210737427078495114,6414210737428490747558⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨5894779572592502860501,5894779572593739727287⟩,⟨6718613013475788176451,6718613013477025042065⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨10562616640964257066724,10562616640965392553649⟩,⟨4416815213141500841118,4416815213142636327004⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨13609938864532077679033,13609938864532904500169⟩,⟨(-204035729920783315631),(-204035729919956494851)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨13628876241264069699526,13628876241264531623829⟩,⟨(-5178495674562283451883),(-5178495674561821527159)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨10801571010301752078772,10801571010301969114269⟩,⟨(-7934540784838433053614),(-7934540784838216017196)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨6541041986130935057466,6541041986131024049283⟩,⟨(-6977074547638553078522),(-6977074547638464085817)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2133711595618873415270,2133711595618897012086⟩,⟨(-2749093113362441292731),(-2749093113362417695554)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1591963424654050400),(-1591963424654050383)⟩,⟨872117251985902475,872117251985902495⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-4650910834527314191),(-4650910834527314173)⟩,⟨3243711458208598777,3243711458208598798⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-7074558122401266668),(-7074558122401266644)⟩,⟨7539389662074314468,7539389662074314488⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-7563605566104868935),(-7563605566104868907)⟩,⟨15005714617087152254,15005714617087152282⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-3509865353518197646),(-3509865353518197607)⟩,⟨26175998634027538450,26175998634027538490⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨9120067969056059538,9120067969056059592⟩,⟨39419724675123270505,39419724675123270560⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨34552763553653323754,34552763553653323832⟩,⟨49114948550669674386,49114948550669674470⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨73686014766642979179,73686014766642979373⟩,⟨44944756004017658062,44944756004017658257⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨119293571222581968668,119293571222581969713⟩,⟨14801146517092429224,14801146517092430268⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨154328397650721877660,154328397650721885884⟩,⟨(-47293656126967694111),(-47293656126967685888)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨158642854794080011220,158642854794080061473⟩,⟨(-131851895085787290746),(-131851895085787240497)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨123407367853024484775,123407367853024688769⟩,⟨(-211987181780478517950),(-211987181780478313956)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨62021248225205971172,62021248225206674579⟩,⟨(-254780932437519414461),(-254780932437518711049)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨4718980823944346399,4718980823945840652⟩,⟨(-239639108656846429566),(-239639108656844935311)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-21638919008507419449),(-21638919008505646630)⟩,⟨(-168463732261043385506),(-168463732261041612684)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-12347636391904736304),(-12347636391903919209)⟩,⟨(-60267745947378814123),(-60267745947377997027)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2166362552976170374770811,2166362552977218031200866⟩,⟨(-57456739967962925644621885),(-57456739967961877988276743)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 23) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_23 (tableDensity false) (fullFactor true 1 23) density0_contains hk1_1_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨3778425382416942516018152,3778425382416944281763309⟩,⟨2261987839578227469491457,2261987839578229233600924⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_23 1 23 ha1_1_23_contains + def realAnswer : RBox := ⟨5944787935393112790788963,5944787935394162412964175⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_23 +namespace hm1_1_1_23 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_23 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-171004899122586413627214),(-171004899122580043350356)⟩,⟨(-2715458168414847044005555),(-2715458168414840673738923)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1670256683877956646323725),(-1670256683877941630834862)⟩,⟨(-8044798110367772430718200),(-8044798110367757415362883)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-6378889816158577356716968),(-6378889816158563030820482)⟩,⟨(-12186934401198550111045550),(-12186934401198535785689503)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-14782978713580100231705603),(-14782978713580092124485442)⟩,⟨(-12022409481406628441502035),(-12022409481406620335359320)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-23363398232785992776340793),(-23363398232785988382066930)⟩,⟨(-3592538054314779259242904),(-3592538054314774865464774)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-24003881151779171854318011),(-24003881151779170424003389)⟩,⟨13005305505912015998424438,13005305505912017429661344⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-9823984948501834343907368),(-9823984948501833961451742)⟩,⟨28782548298745864421922992,28782548298745864805863524⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨15035414965875245542458381,15035414965875245715241274⟩,⟨29861945576705920995360535,29861945576705921167872298⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨34457805953734932707244332,34457805953734932797145910⟩,⟨11105743957431971281376505,11105743957431971369202896⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨34328058495265105618427481,34328058495265105685314253⟩,⟨(-16081269655366238971400654),(-16081269655366238904739632)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨16326147577412024202393349,16326147577412024250059157⟩,⟨(-33856472779674751553628781),(-33856472779674751504340241)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-5323340401777696076598552),(-5323340401777696042798813)⟩,⟨(-34278935981344752620104405),(-34278935981344752585058850)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-18167090414627524499468847),(-18167090414627524475151359)⟩,⟨(-23058704434619981020769177),(-23058704434619980996198739)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-19539694743197858122014056),(-19539694743197858106722500)⟩,⟨(-10522901307768242936913361),(-10522901307768242922304078)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-13520005172427202747325836),(-13520005172427202739704763)⟩,⟨(-2832292089861009494825687),(-2832292089861009488073703)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-4682310355132219789019965),(-4682310355132219786797502)⟩,⟨(-271818948164284302017492),(-271818948164284300166643)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨444813481473239710083197,444813481473240949476899⟩,⟨(-70106618405086365007191),(-70106618405085125587485)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1310211210816774053624000,1310211210816779513954907⟩,⟨(-409435168445547188306149),(-409435168445541727907421)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1957073413600682159242686,1957073413600699482401514⟩,⟨(-1320255885236587642278582),(-1320255885236570319047315)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1810005328906736428310515,1810005328906786177137348⟩,⟨(-2957210263923274948646483),(-2957210263923225199819951)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-10908122992832701542360),(-10908122992719361065753)⟩,⟨(-4762406219260074794848867),(-4762406219259961454557750)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-3841215585805696506608304),(-3841215585805423790746626)⟩,⟨(-5025388878221557636927133),(-5025388878221284921330652)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-8019039843008978504551859),(-8019039843008371997297881)⟩,⟨(-1629212151155008747638531),(-1629212151154402240326194)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-8712004606237889680871607),(-8712004606237111399507578)⟩,⟨5398441108109375627705229,5398441108110153909528687⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-3058381465599343995016199),(-3058381465598241700606312)⟩,⟨11943078365072304413762251,11943078365073406708273426⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨6738269065174531339460665,6738269065175386685306527⟩,⟨12443653503849051066798317,12443653503849906412111759⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨14297461863382535820027103,14297461863383177640581163⟩,⟨5662432279248789659220455,5662432279249431479431759⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨15147811950000250650477508,15147811950000621849565061⟩,⟨(-3712881240590238884045846),(-3712881240589867684708640)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨10501569437543203014274805,10501569437543349124193839⟩,⟨(-9874038414023674965995358),(-9874038414023528855524113)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨4758344433693491671973964,4758344433693565747781613⟩,⟨(-10670633796226186033341912),(-10670633796226111957243785)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1131168047235715158474680,1131168047235748345188266⟩,⟨(-7519800208692904429407703),(-7519800208692871242621539)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨32504094790526119679300,32504094790535159722399⟩,⟨(-2636062951773460461379228),(-2636062951773451421331741)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨29290087519269022446037,29290087519269022980736⟩,⟨12406651528187415134904,12406651528187415669016⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨96215119101273310855400,96215119101273312617856⟩,⟨28137240147808544238259,28137240147808545999086⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨182724683752816303422013,182724683752816306920283⟩,⟨10653189509134271429546,10653189509134274926013⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨278587738949232098686367,278587738949232104926427⟩,⟨(-77210458565956849846380),(-77210458565956843606437)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨326305301319553647418646,326305301319553658031546⟩,⟨(-272992488633581051569467),(-272992488633581040952027)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨206866223694610259753325,206866223694610277152585⟩,⟨(-561490288749084539375500),(-561490288749084521966441)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-204559236861047076891617),(-204559236861047049238307)⟩,⟨(-791543546740908422533703),(-791543546740908394876402)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-871672700585766861979543),(-871672700585766819675418)⟩,⟨(-664698252381116879594074),(-664698252381116837301061)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-1439085712685972581731923),(-1439085712685972515331667)⟩,⟨56946293914843678472016,56946293914843744856168⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1376413867149900777767173),(-1376413867149900636955078)⟩,⟨1199328386940858828991545,1199328386940858969802762⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-481176270464527912982224),(-481176270464527498397055)⟩,⟨2122810582444112946279052,2122810582444113360872557⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨792170331176971345591581,792170331176973120414364⟩,⟨2236239075336010867207509,2236239075336012642037124⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1686882235420462301614481,1686882235420467630032990⟩,⟨1565750782070077452913443,1565750782070082781333811⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1800772585793199377342942,1800772585793208426888556⟩,⟨678177844711404788084685,678177844711413837629959⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1273164777173372161408679,1273164777173380857004395⟩,⟨107831215794210816478164,107831215794219512074119⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨446892906766272616232465,446892906766276124971383⟩,⟨(-26603745478798102672459),(-26603745478794593932877)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1082914283243396267739,1082914283243401559623⟩,⟨(-569189662873172378478),(-569189662873167086651)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨3204055695658297323199,3204055695658309748327⟩,⟨(-2075388821720202391677),(-2075388821720189966746)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨4994827700107731540896,4994827700107746737863⟩,⟨(-4713705371981125050329),(-4713705371981109853674)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨5555911941624936883437,5555911941624949571757⟩,⟨(-9209885034055042516778),(-9209885034055029828784)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2973346955842374268568,2973346955842381264134⟩,⟨(-15753804785736428610852),(-15753804785736421615388)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-5596390230610545599641),(-5596390230610543030500)⟩,⟨(-22832200541937650655222),(-22832200541937648085542)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-22437004849639645817447),(-22437004849639644931157)⟩,⟨(-25751643670761429567102),(-25751643670761428679241)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-45810075839994435373011),(-45810075839994434576524)⟩,⟨(-16636062805083444015813),(-16636062805083443218113)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-66362958259767685562699),(-66362958259767684369955)⟩,⟨11443893699163772704897,11443893699163773897021⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-68655633838251336893986),(-68655633838251335009539)⟩,⟨56428531171456770716248,56428531171456772597296⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-41549433132964406444877),(-41549433132964403646388)⟩,⟨102396601199887567204855,102396601199887570000010⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨9003425443538859072851,9003425443538862824548⟩,⟨126984634670701867208500,126984634670701870959752⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨59223271288781312088919,59223271288781316483183⟩,⟨118383966328838585973617,118383966328838590370337⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨83118435181654512482705,83118435181654516794089⟩,⟨84894689025385535979629,84894689025385540294896⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨69748405000401025443034,69748405000401028647346⟩,⟨45811232847949052744066,45811232847949055951579⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨26845540973878420662748,26845540973878421850176⟩,⟨13688818286702773528051,13688818286702774716520⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-24029632565987418786),(-24029632565986467902)⟩,⟨(-26850038890857170330),(-26850038890856219444)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-83576669781245146590),(-83576669781241276432)⟩,⟨(-78796015555076093535),(-78796015555072223375)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-177901398848230029312),(-177901398848218884605)⟩,⟨(-119813792055081793455),(-119813792055070648747)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-328068995916850595005),(-328068995916819774688)⟩,⟨(-122819250576048170836),(-122819250576017350530)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-539441991293712882224),(-539441991293634870407)⟩,⟨(-30178619842091831054),(-30178619842013819268)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-771211223911885227532),(-771211223911706303251)⟩,⟨247852723916680580148,247852723916859504358⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-894533425173066574740),(-894533425172592893168)⟩,⟨800253327865015900531,800253327865489582035⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-676721366207653862539),(-676721366206754411737)⟩,⟨1629129471710410127506,1629129471711309578293⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨139573098760595400560,139573098761754845029⟩,⟨2539569997775273916363,2539569997776433360929⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1630879806927061747570,1630879806928076108944⟩,⟨3118235022104600031484,3118235022105614393096⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨3478725952990539465652,3478725952991469462837⟩,⟨2928057823009899533112,2928057823010829530506⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨4996773666896462976453,4996773666897139254585⟩,⟨1864514193939293432720,1864514193939969710930⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨5510162460610441470709,5510162460610818792640⟩,⟨361958485870345082868,361958485870722404730⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨4799628527985300675490,4799628527985477749743⟩,⟨(-821436090627848520961),(-821436090627671446865)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨3167174780839115595460,3167174780839188131181⟩,⟨(-1111358907663091002410),(-1111358907663018466843)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1091690875947860941745,1091690875947880163688⟩,⟨(-494892203795175492918),(-494892203795156271037)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-46042034637781690),(-46042034637781673)⟩,⟨28164887646008363,28164887646008379⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-107593731741208508),(-107593731741208488)⟩,⟨125583575679479975,125583575679479994⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨11531130259507490,11531130259507512⟩,⟨314492942113967340,314492942113967359⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨739585681419850812,739585681419850832⟩,⟨523945670095518723,523945670095518745⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨2930039361807559926,2930039361807559952⟩,⟨389054939657168963,389054939657168989⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨7739778335628709128,7739778335628709161⟩,⟨(-1082073743925346707),(-1082073743925346671)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨15964094979527363199,15964094979527363246⟩,⟨(-5979525569557133749),(-5979525569557133697)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨26792707877153363047,26792707877153363180⟩,⟨(-17564104177145148365),(-17564104177145148228)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨36481084511615114886,36481084511615115705⟩,⟨(-38920320165306269736),(-38920320165306268917)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨38362016867635200497,38362016867635207174⟩,⟨(-69863374554980410796),(-69863374554980404118)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨25930059256795506920,25930059256795547900⟩,⟨(-103915229261650052556),(-103915229261650011576)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1406687798650656917),(-1406687798650490409)⟩,⟨(-129020743489312153244),(-129020743489311986743)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-34098166374276237689),(-34098166374275663131)⟩,⟨(-133660947451307396140),(-133660947451306821584)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-55214185911939779793),(-55214185911938558569)⟩,⟨(-113977389381501560939),(-113977389381500339714)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-50815538656869418701),(-50815538656867969219)⟩,⟨(-75108848878926970967),(-75108848878925521491)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-20541862134497463329),(-20541862134496795124)⟩,⟨(-25987241084615865182),(-25987241084615196978)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-668018525197755004979539),(-668018525196894429782842)⟩,⟨(-14292102319570927068758451),(-14292102319570066493659501)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_23 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 23) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_23 (tableDensity true) (fullFactor true 1 23) density1_contains hk1_1_23_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4941017807776004060767403),(-4941017807776001751716045)⟩,⟨(-2957984097909992074708901),(-2957984097909989767796521)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_23 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 23) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_23 1 23 ha1_1_23_contains + def realAnswer : RBox := ⟨(-5609036332973759165746942),(-5609036332972896081498887)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 23) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_23 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_7.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_7.lean new file mode 100644 index 0000000000000000000000000000000000000000..f3ec23aa3f26975fef6c2159bfc5b6a1387f0a5b --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments1_7.lean @@ -0,0 +1,4721 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders1 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm1_0_1_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-1422020998061805642480385),(-1422020998061803042640563)⟩,⟨5470017044318116555709499,5470017044318119155401646⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1643991677831508604358099),(-1643991677831502038236638)⟩,⟨16951874755189394435315626,16951874755189401001151358⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨6025671655663224016420411,6025671655663231161519577⟩,⟨27954208032373421119721084,27954208032373428264847153⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨24732796109525710787362730,24732796109525715314299543⟩,⟨31913893267124877748431639,31913893267124882276277540⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨49078547261314477346188814,49078547261314479421152192⟩,⟨17726311664317202581295048,17726311664317204657828071⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨60382832608210731602224260,60382832608210732692328041⟩,⟨(-19456455279461222314902128),(-19456455279461221224500977)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨37216059124402767528762487,37216059124402768083645596⟩,⟨(-63056205046244919592676208),(-63056205046244919039751220)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-18634414491500173555716333),(-18634414491500173210649606)⟩,⟨(-78339410434590476849728481),(-78339410434590476505172991)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-71733548069051343389008899),(-71733548069051343192682131)⟩,⟨(-44772716961000502127201671),(-44772716961000501929815098)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-83048438553969573349446900),(-83048438553969573218327877)⟩,⟨17245426672826540259933840,17245426672826540391795645⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-48995963834391963165240097),(-48995963834391963073677086)⟩,⟨64626515826567418820830105,64626515826567418912064035⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-320969665550960386549814),(-320969665550960327600848)⟩,⟨73419240536556480841940045,73419240536556480899970513⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨31939355037883695891696922,31939355037883695927989597⟩,⟨53081477127989494012578836,53081477127989494049242443⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨38775658943152488008476001,38775658943152488029808141⟩,⟨26650652801927187682100633,26650652801927187703531828⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨28009094914772720248201632,28009094914772720258182450⟩,⟨8953448657130186053402296,8953448657130186063129235⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨9870206133065429531050794,9870206133065429533834579⟩,⟨1599032598713404445339291,1599032598713404447974085⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-847760673718619065145552),(-847760673718618425546497)⟩,⟨(-131991853477927006870264),(-131991853477926367273391)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2660704666713505472137007),(-2660704666713502988058081)⟩,⟨(-37692986801276924722860),(-37692986801274440688030)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-4559752632869529115838892),(-4559752632869522829061506)⟩,⟨1222765879506645645206327,1222765879506651931782635⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-5663475445624370250495695),(-5663475445624355426466280)⟩,⟨4443424586344547863254835,4443424586344562686827174⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-3868393723898384842250739),(-3868393723898337055502420)⟩,⟨9461826829440599954564456,9461826829440647741053501⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨3108183184381036172238377,3108183184381146442329025⟩,⟨13495743204935691997722653,13495743204935802268248827⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨14291228794229715588975802,14291228794229920272372718⟩,⟨10969198906330822566863892,10969198906331027251143880⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨22393196623150478726953669,22393196623150843364031858⟩,⟨(-1892400558587582790212430),(-1892400558587218153398247)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨17784778137043408948318870,17784778137043780378295371⟩,⟨(-19967065232217262069456090),(-19967065232216890640788053)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-622202215603039544769658),(-622202215602633987336946)⟩,⟨(-30116050093238082718466928),(-30116050093237677161033595)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-21209257129849998961814142),(-21209257129849761503419164)⟩,⟨(-23762662820235881539679439),(-23762662820235644079836805)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-30644108195190197523664772),(-30644108195190044278467840)⟩,⟨(-6282075031527359032135750),(-6282075031527205786282542)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-26434948688725900551798198),(-26434948688725823462115556)⟩,⟨9478739588996571094918968,9478739588996648184095274⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-15933493682032112601410287),(-15933493682032083664638726)⟩,⟨15608524172033626627884296,15608524172033655563685896⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-6861871329635722670641926),(-6861871329635710556862027)⟩,⟨12608996542528297603101594,12608996542528309716297379⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-1683210400829427372115361),(-1683210400829423778820741)⟩,⟨4658787533432329352276432,4658787533432332945414913⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-20982493487341743844042),(-20982493487341743275622)⟩,⟨(-27151983416549931312993),(-27151983416549930743914)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-76450641946713999784254),(-76450641946713997921624)⟩,⟨(-76838421330103495997304),(-76838421330103494134449)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-171179147137086724003224),(-171179147137086720184465)⟩,⟨(-103058432890100857850419),(-103058432890100854037991)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-318323051150434833272627),(-318323051150434825973184)⟩,⟨(-59070681247727192104031),(-59070681247727184829801)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-481511851262682839556978),(-481511851262682825805376)⟩,⟨135289738306797824945361,135289738306797838653877⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-517269639526324344825423),(-517269639526324319332692)⟩,⟨547237913221968779906094,547237913221968805384694⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-169103362566831945611787),(-169103362566831899636951)⟩,⟨1093649629380275904785285,1093649629380275950823449⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨749329667505719782584216,749329667505719862701648⟩,⟨1388345657264088490722323,1388345657264088570943968⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1985722507773741484382490,1985722507773741617927594⟩,⟨852332438296650171804719,852332438296650305326928⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨2714752287701310480418258,2714752287701310697238583⟩,⟨(-728416325462544357987526),(-728416325462544141356487)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2128855092172030543719165,2128855092172030956851056⟩,⟨(-2683998971757580160562380),(-2683998971757579747524645)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨343444139980523830744616,343444139980524766993957⟩,⟨(-3833131197769602395280625),(-3833131197769601458922399)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1546667913532043263193689),(-1546667913532041430410568)⟩,⟨(-3571229706993017446682732),(-3571229706993015613666424)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-2443018894587841732419085),(-2443018894587838182961000)⟩,⟨(-2366141446754290787745645),(-2366141446754287238155585)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-2053782465450698741808661),(-2053782465450694650700173)⟩,⟨(-1118323398733403717803431),(-1118323398733399626657592)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-780876336028623672511477),(-780876336028621835494507)⟩,⟨(-294400877781655950015489),(-294400877781654112995023)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-735957709503561584924),(-735957709503560182488)⟩,⟨(-95025249017798550883),(-95025249017797148547)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-2357558121344454823300),(-2357558121344451157970)⟩,⟨(-74397930752137662568),(-74397930752133997507)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-4340839804031113770153),(-4340839804031109361706)⟩,⟨694803523250634423408,694803523250638831525⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-6542343386666238693730),(-6542343386666235270282)⟩,⟨3048448003846848491074,3048448003846851914411⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-7939319362631819750606),(-7939319362631817986535)⟩,⟨8049207097861517052165,8049207097861518816911⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-5986988162860116133822),(-5986988162860115461059)⟩,⟨16234863120296815960678,16234863120296816635720⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨3312750606311959821843,3312750606311960271507⟩,⟨25817477057670461747527,25817477057670462199619⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨23105394212837179062738,23105394212837179657405⟩,⟨30610229534457798968780,30610229534457799563364⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨50715957452115269307207,50715957452115270301892⟩,⟨20710253973017465518824,20710253973017466508146⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨73940194780803773414435,73940194780803775048715⟩,⟨(-10797422477594585883666),(-10797422477594584256491)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨75924116844338423625357,75924116844338426095759⟩,⟨(-58051578235357819007081),(-58051578235357816537833)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨49355317613739198969200,49355317613739202317776⟩,⟨(-100797570262973842037098),(-100797570262973838681314)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨6689681352904436380721,6689681352904440326626⟩,⟨(-117654945354144006075047),(-117654945354144002116297)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-27284599489976742888326),(-27284599489976739014951)⟩,⟨(-102541826905977907497866),(-102541826905977903616089)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-34441250913840545168983),(-34441250913840542297706)⟩,⟨(-66092760617998885884317),(-66092760617998883009539)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-15039604990928659805886),(-15039604990928658745478)⟩,⟨(-22298159062654313970095),(-22298159062654312908888)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-12508004274427297376),(-12508004274427094706)⟩,⟨14243355375711023837,14243355375711226508⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-34698976949440179463),(-34698976949439362619)⟩,⟨48159554090520163373,48159554090520980216⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-45297387265333591930),(-45297387265331287070)⟩,⟨97819999260639397257,97819999260641702114⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-26437701929037219103),(-26437701929031061210)⟩,⟨169881669043611056574,169881669043617214451⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨52631015352689074238,52631015352703919583⟩,⟨257682020387297442457,257682020387312287764⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨229541272678718995104,229541272678762686344⟩,⟨323411126035562551119,323411126035606242312⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨520829921655351804261,520829921655464254021⟩,⟨280953084525655715753,280953084525768165492⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨868619916490636584368,868619916490835580322⟩,⟨7194196079127086174,7194196079326082168⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨1095706158131650298652,1095706158131884426943⟩,⟨(-584104392174912466855),(-584104392174678338417)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨947146770253720596927,947146770253972343097⟩,⟨(-1418990473972810564905),(-1418990473972558818545)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨266416677866015052608,266416677866257759068⟩,⟨(-2201826166139433726890),(-2201826166139191020342)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-797603004065513126761),(-797603004065351000816)⟩,⟨(-2550850119286693502951),(-2550850119286531377087)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1779945310969128981304),(-1779945310969045530058)⟩,⟨(-2284609949763401167762),(-2284609949763317716756)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2171147244330634906053),(-2171147244330598800947)⟩,⟨(-1583009283574954637293),(-1583009283574918532502)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1745808734693816038078),(-1745808734693799769789)⟩,⟨(-821915509256056648528),(-821915509256040380459)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-663190925401465589755),(-663190925401460669766)⟩,⟨(-237480601102424309780),(-237480601102419389862)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨143883296158900955,143883296158900971⟩,⟨232767253713749349,232767253713749365⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨527806747868974127,527806747868974143⟩,⟨675020689461634329,675020689461634345⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨1205875041524235037,1205875041524235054⟩,⟨1005011958796024939,1005011958796024956⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2364422141608030273,2364422141608030291⟩,⟨1005124306822859318,1005124306822859336⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨4066655499927293990,4066655499927294007⟩,⟨246544164049314146,246544164049314167⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨6008778751897483797,6008778751897483819⟩,⟨(-1920539634365305058),(-1920539634365305035)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨7213261384254018410,7213261384254018435⟩,⟨(-6143671166310290446),(-6143671166310290420)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨5926596329966106623,5926596329966106670⟩,⟨(-12456573455680177244),(-12456573455680177196)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨160548748544490823,160548748544491011⟩,⟨(-19469043037605475421),(-19469043037605475238)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-10900793598857660479),(-10900793598857659160)⟩,⟨(-24146119389990967830),(-24146119389990966506)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-25328741492717900991),(-25328741492717893328)⟩,⟨(-23113601330354521598),(-23113601330354513935)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-38313024800101182417),(-38313024800101145823)⟩,⟨(-15282995069277367353),(-15282995069277330758)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-44384798680412643574),(-44384798680412513535)⟩,⟨(-3674168436472435857),(-3674168436472305819)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-40610849120808197816),(-40610849120807928335)⟩,⟨5859374582123542836,5859374582123812317⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-27968738330922539322),(-27968738330922224763)⟩,⟨8512222232979903257,8512222232980217813⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-9891850939622865676),(-9891850939622721895)⟩,⟨3861596456944528147,3861596456944671924⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-610511704233459017835440),(-610511704233112163653949)⟩,⟨21416111201534525282196878,21416111201534872136295710⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 24) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_24 (tableDensity false) (fullFactor true 1 24) density0_contains hk1_1_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1666837143709902032259228),(-1666837143709901238648602)⟩,⟨529532722967106974178227,529532722967107767137803⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_24 1 24 ha1_1_24_contains + def realAnswer : RBox := ⟨(-2277348847943361150094668),(-2277348847943013302302551)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_24 +namespace hm1_1_1_24 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_24 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-364496615825039044108861),(-364496615825036962730114)⟩,⟨895204509943441793382937,895204509943443874797416⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-686742466574737734462041),(-686742466574732494257460)⟩,⟨2844535091527475793395450,2844535091527481033670120⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨276970033210476871781029,276970033210482519699728⟩,⟨4915207846318919748299341,4915207846318925396208315⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨3201550440302325517901896,3201550440302328960205118⟩,⟨6074244504075003458382787,6074244504075006900421439⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨7427761841869076286531180,7427761841869077664573950⟩,⟨4311615914768013096815804,4311615914768014474417162⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨9883791677282052788437027,9883791677282053345387188⟩,⟨(-1579878017804940404599787),(-1579878017804939847620022)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨6602950223537318009750225,6602950223537318169674658⟩,⟨(-9113346486003597803620755),(-9113346486003597643097853)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-2619071156345705816770786),(-2619071156345705744760428)⟩,⟨(-12204493310026419870120085),(-12204493310026419797915856)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-11807690835554288574301948),(-11807690835554288535797726)⟩,⟨(-6798538552756093534952747),(-6798538552756093497143208)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-13836074693157378055475399),(-13836074693157378028135029)⟩,⟨3851406267256243506665830,3851406267256243533676158⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-7773662603593297703594837),(-7773662603593297683804034)⟩,⟨12018926795369011980035758,12018926795369012000334199⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨889914372463338644533164,889914372463338657802660⟩,⟨13228275571572578573874948,13228275571572578587682390⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨6468062110620357754362886,6468062110620357763839365⟩,⟨9199123504597375562552572,9199123504597375572179167⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨7375398145609404867974243,7375398145609404873956691⟩,⟨4251507128615195031278439,4251507128615195037023205⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨5177120747946906085589863,5177120747946906088559610⟩,⟨1145611756796291877472571,1145611756796291880113931⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1797579359396827705865508,1797579359396827706726672⟩,⟨108448371191281556902877,108448371191281557621608⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-106515038810745767220000),(-106515038810745267878332)⟩,⟨(-80990106297426175235979),(-80990106297425675894143)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-359736619846380750575981),(-359736619846378791716300)⟩,⟨(-195424946278959896672556),(-195424946278957937807710)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-695633823550309793972495),(-695633823550304775548950)⟩,⟨(-137659276993757445043655),(-137659276993752426595762)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1019606950941052837440977),(-1019606950941040881172296)⟩,⟨260235393132357792819314,260235393132369749144842⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-995126208418076161543148),(-995126208418037133756970)⟩,⟨1074456176141894219809208,1074456176141933247629126⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-138122213738093045834723),(-138122213738002559918303)⟩,⟨1970315543413881155484756,1970315543413971641350810⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1630347556209692828634296,1630347556209861237035294⟩,⟨2023654772860788351081985,2023654772860956759371028⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨3294886320829609989832888,3294886320829910576115388⟩,⟨344912847526916194289909,344912847527216780598193⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨3113473735528016299657603,3113473735528322286130798⟩,⟨(-2599888123845609051596718),(-2599888123845303064953214)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨440383584040016940179756,440383584040350900377569⟩,⟨(-4715258627137716592764076),(-4715258627137382632563039)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-3113632408242756949839210),(-3113632408242562117050263)⟩,⟨(-4199255039447122349627481),(-4199255039446927517041620)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-5159502268343135246198285),(-5159502268343009929304308)⟩,⟨(-1507473277570783716628154),(-1507473277570658399827344)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-4859859172948270054254497),(-4859859172948207385934612)⟩,⟨1276725104309456338767005,1276725104309519007162982⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-3207084974031789240798999),(-3207084974031765997865069)⟩,⟨2567710324810814981498822,2567710324810838224580583⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1541996770000992607197254),(-1541996770000982965847261)⟩,⟨2203838550554767596855369,2203838550554777238296624⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-420075951788724871523959),(-420075951788722019749925)⟩,⟨835570379023350897385378,835570379023353749184391⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-822002401205706780022),(-822002401205706604160)⟩,⟨(-7703447820933929860756),(-7703447820933929684865)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-5508610346744729640603),(-5508610346744729059110)⟩,⟨(-23876840721162874274397),(-23876840721162873692884)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-20065107620052420061575),(-20065107620052418899649)⟩,⟨(-40350257775733279011682),(-40350257775733277850033)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-51718064951693736859170),(-51718064951693734759276)⟩,⟨(-49981786640293777705652),(-49981786640293775606842)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-101621652376333104298568),(-101621652376333100645841)⟩,⟨(-34350728478031503372393),(-34350728478031499721396)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-149768666042778418947368),(-149768666042778412811837)⟩,⟨32617898921660936271016,32617898921660942405924⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-141913331865558806162170),(-141913331865558796266920)⟩,⟨159049712814952762356091,159049712814952772253751⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-11128597355921320433985),(-11128597355921304914224)⟩,⟨291064086575207931640213,291064086575207947164042⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨244702849208278066710538,244702849208278091297099⟩,⟨303961636669228351050250,303961636669228375636491⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨495120144498013494132337,495120144498013539107152⟩,⟨95558842206921545798800,95558842206921590769821⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨547325531350218681632376,547325531350218831175465⟩,⟨(-274408137626077173027039),(-274408137626077023485674)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨337276101367732468675136,337276101367732994484569⟩,⟨(-588586137046512552051776),(-588586137046512026242118)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨12502109704763863823990,12502109704765095909643⟩,⟨(-667272834436847548954265),(-667272834436846316867406)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-211792609335387336241343),(-211792609335384681901136)⟩,⟨(-522905516623296948252155),(-522905516623294293911219)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-234823529360623928015461),(-234823529360620759023746)⟩,⟨(-295552153911783834516090),(-295552153911780665524066)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-97164424545230181147334),(-97164424545228742542318)⟩,⟨(-90492519810206284139733),(-90492519810204845534642)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-178227744713011990610),(-178227744713010813895)⟩,⟨(-172521359886673978342),(-172521359886672801617)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-606225496033511257527),(-606225496033508185484)⟩,⟨(-485291815979018738097),(-485291815979015666025)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1242530248100446453666),(-1242530248100442768813)⟩,⟨(-658024874084088955839),(-658024874084085270953)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-2175636348578276093365),(-2175636348578273251295)⟩,⟨(-455024312133354680355),(-455024312133351838274)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-3309108937304192801074),(-3309108937304191371748)⟩,⟨541256933932177142274,541256933932178571530⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-4106730861752198240917),(-4106730861752197761257)⟩,⟨2830314549530470685444,2830314549530471164873⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-3366142194275207228059),(-3366142194275207004151)⟩,⟨6549732015524520667272,6549732015524520890944⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨519668162185263054117,519668162185263274943⟩,⟨10678930281136502249465,10678930281136502470321⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨8318491134192153763239,8318491134192154107328⟩,⟨12529348151410697984751,12529348151410698329385⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨18199140120685007652804,18199140120685008216251⟩,⟨8770702953334479966035,8770702953334480530154⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨25494090281006797977795,25494090281006798835665⟩,⟨(-1685323692284970909205),(-1685323692284970051286)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨25660232522012998373615,25660232522012999548724⟩,⟨(-15330535099071798950740),(-15330535099071797776370)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨18430524258532704605708,18430524258532706010363⟩,⟨(-25539752868527118112924),(-25539752868527116709483)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨8521563714192851592533,8521563714192852992448⟩,⟨(-27266281837202690648203),(-27266281837202689249051)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨1620676422356639479460,1620676422356640530610⟩,⟨(-20145606306443058202294),(-20145606306443057151438)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-244158095793227528741),(-244158095793227137656)⟩,⟨(-7321487371092272711900),(-7321487371092272320876)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-3864890939274337585),(-3864890939274171023)⟩,⟨4884197264274224932,4884197264274391495⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-10945610241013311231),(-10945610241012639880)⟩,⟨16632307798132513040,16632307798133184389⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-15030664140710476534),(-15030664140708581948)⟩,⟨34231539973725210986,34231539973727105578⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-10528445252405438588),(-10528445252400375987)⟩,⟨60649674665229832986,60649674665234895588⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨13380434935113976497,13380434935126182836⟩,⟨94995292336582436630,94995292336594642976⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨72115007159532494822,72115007159568419130⟩,⟨126514814707798644214,126514814707834568531⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨177936407897740242921,177936407897832682291⟩,⟨127325920050178829256,127325920050271268631⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨322283557719574139313,322283557719737643364⟩,⟨52040489459575347802,52040489459738851848⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨456319712567073316522,456319712567265534729⟩,⟨(-142524591302828694811),(-142524591302636476636)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨494300900684192570881,494300900684399020501⟩,⟨(-454877305171328913003),(-454877305171122463425)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨362492354571727274279,362492354571926059714⟩,⟨(-802870874364429158255),(-802870874364230372842)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨72387251075655251195,72387251075787857760⟩,⟨(-1044741144810093682663),(-1044741144809961076087)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-253364644860945997924),(-253364644860877833423)⟩,⟨(-1067263469592391874094),(-1067263469592323709552)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-447939286521596225282),(-447939286521566771894)⟩,⟨(-867375119176542207370),(-867375119176512753925)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-410166710833610032849),(-410166710833596775654)⟩,⟨(-538871695419143822719),(-538871695419130565485)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-163921399727033358373),(-163921399727029351243)⟩,⟨(-178882629321407759937),(-178882629321403752795)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨4604244401617672,4604244401617688⟩,⟨6708622397122362,6708622397122378⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨19836422350687682,19836422350687698⟩,⟨15195729462934398,15195729462934415⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨47554209677135858,47554209677135874⟩,⟨(-4574963510278102),(-4574963510278086)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨72543094345038414,72543094345038431⟩,⟨(-118119403057072581),(-118119403057072564)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨26825993892967124,26825993892967140⟩,⟨(-455417466008684553),(-455417466008684535)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-267401396071593523),(-267401396071593503)⟩,⟨(-1189417993941283523),(-1189417993941283503)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1172689711495181254),(-1172689711495181232)⟩,⟨(-2422122755258598442),(-2422122755258598422)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-3236363605143774472),(-3236363605143774434)⟩,⟨(-3970474459629271829),(-3970474459629271794)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-6943115008411627494),(-6943115008411627345)⟩,⟨(-5147164718935746944),(-5147164718935746799)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-12172747071721482460),(-12172747071721481388)⟩,⟨(-4799314000973831022),(-4799314000973829949)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-17703772014988553267),(-17703772014988547021)⟩,⟨(-1901080533644607447),(-1901080533644601193)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-21427074072768888506),(-21427074072768858639)⟩,⟨3424288736282577659,3424288736282607525⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-21524866770008183819),(-21524866770008077603)⟩,⟨9251995642798528035,9251995642798634253⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-17719491713833131169),(-17719491713832910929)⟩,⟨12492845343991122788,12492845343991343032⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-11287036429810544668),(-11287036429810287482)⟩,⟨10781931588025994546,10781931588026251733⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3820669739541130872),(-3820669739541013292)⟩,⟨4253905665189053825,4253905665189171404⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-70294417689789589891075),(-70294417689505324063615)⟩,⟨5082395487980003134972166,5082395487980287400778472⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_24 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 24) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_24 (tableDensity true) (fullFactor true 1 24) density1_contains hk1_1_24_contains +noncomputable def atomAnswer : CBox := ⟨⟨2179710111005255465925095,2179710111005256503723605⟩,⟨(-692465868495448618564819),(-692465868495447581617681)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_24 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 24) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_24 1 24 ha1_1_24_contains + def realAnswer : RBox := ⟨2109415693315465776034020,2109415693315751279659990⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 24) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_24 +namespace hm1_0_1_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1247446319928586450439013,1247446319928587195342467⟩,⟨(-1469363023932038249618960),(-1469363023932037504799121)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨2985175020383598855864888,2985175020383600667691426⟩,⟨(-4999576422841500357251915),(-4999576422841498545667815)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨2082365803078084168377719,2082365803078086448287834⟩,⟨(-9601328892309097665142883),(-9601328892309095385472317)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-3542493890021052042723045),(-3542493890021050313262301)⟩,⟨(-13509805873642653089967707),(-13509805873642651360501557)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-13685488226834216685117662),(-13685488226834215869733027)⟩,⟨(-11998518963581856836604085),(-11998518963581856020745512)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-22322480644246484232141544),(-22322480644246483817513373)⟩,⟨(-584087249437770591284451),(-584087249437770176213747)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-19217606794506900025144966),(-19217606794506899786101767)⟩,⟨17532259372346026701538485,17532259372346026940170303⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-623518293481481342367668),(-623518293481481196088542)⟩,⟨28856852832540727326751689,28856852832540727472562431⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨21958388769438027276401767,21958388769438027359481363⟩,⟨21239983117128231231471973,21239983117128231314799458⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨30824328995139845379629469,30824328995139845432347868⟩,⟨(-1171604195573941428198369),(-1171604195573941375169579)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨20712262697787856072179760,20712262697787856108782796⟩,⟨(-21208182824131878145494846),(-21208182824131878108907674)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨2455405234918256061363951,2455405234918256084308882⟩,⟨(-26822748233836030973237406),(-26822748233836030950658902)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-10664896579593995634211706),(-10664896579593995620407974)⟩,⟨(-20130236668932815907869035),(-20130236668932815893941343)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-13989128549535294271032242),(-13989128549535294262948409)⟩,⟨(-10222445971847798255499392),(-10222445971847798247374444)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-10283488936913530142640462),(-10283488936913530138879228)⟩,⟨(-3415432503771129304957069),(-3415432503771129301287979)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-3636829103445941455157977),(-3636829103445941454115689)⟩,⟨(-597662659660749903339647),(-597662659660749902352313)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨140194165831697882941912,140194165831698021968846⟩,⟨200621516319860152175256,200621516319860291219988⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨522727057774303095563539,522727057774303696568200⟩,⟨554267340276298511223908,554267340276299112276152⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨1176803141903035959911478,1176803141903037866339870⟩,⟨684488962593781174746313,684488962593783081224668⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨2085716205013427360055388,2085716205013432841682498⟩,⟨222683742250015813145771,222683742250021294763872⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨2739044582304289568748380,2739044582304301796966834⟩,⟨(-1267219826787819989810284),(-1267219826787807761750201)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨1976958260066432506876842,1976958260066465623111496⟩,⟨(-3651069687742131471859784),(-3651069687742098355777968)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1219823859589182319074408),(-1219823859589113732412795)⟩,⟨(-5355666876749190768078274),(-5355666876749122181264304)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-5853155858374097043350063),(-5853155858373996083105452)⟩,⟨(-3791269581639974834048622),(-3791269581639873873498209)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-8244312719119109078596392),(-8244312719118972823796873)⟩,⟨1832662410109452902295725,1832662410109589156928564⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-5212507587037163948071656),(-5212507587037052092400793)⟩,⟨8153329075360023848773538,8153329075360135704026841⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1788457700080136458772827,1788457700080228696466021⟩,⟨10238662046868785960553495,10238662046868878198346761⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨7733111556196424467927443,7733111556196468082307047⟩,⟨6877219771715065121875146,6877219771715108736727084⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨9286563520190151165503885,9286563520190176805728080⟩,⟨1436258647863505837491109,1436258647863531477887404⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨7195203619390782556701936,7195203619390794586097558⟩,⟨(-2216952443301378416497872),(-2216952443301366387201241)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨3991867044849391970699917,3991867044849396543796114⟩,⟨(-2797148308872467605335007),(-2797148308872463032397055)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1210419491717715467906447,1210419491717716603913362⟩,⟨(-1175077222398650370592618),(-1175077222398649234654610)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-3167902943347116093879),(-3167902943347115914697)⟩,⟨7371141597672659717120,7371141597672659896765⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-6947821539405622285583),(-6947821539405621695811)⟩,⟨24468292121554385635278,24468292121554386226959⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1048004418696271168858),(-1048004418696269947685)⟩,⟨47213702851775163153972,47213702851775164379917⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨26420565120547608701421,26420565120547611075335⟩,⟨72672737363116072466345,72672737363116074845981⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨88699403803199592449573,88699403803199597007602⟩,⟨82402707033281426701364,82402707033281431260764⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨181869610727609972566066,181869610727609981190248⟩,⟨34917627550674145523759,34917627550674154136663⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨251103019971104800386722,251103019971104816354937⟩,⟨(-117014828280981631130412),(-117014828280981615181888)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨179599074824402748297614,179599074824402776746304⟩,⟨(-360202959252578568534296),(-360202959252578540081757)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-129712007153743269550206),(-129712007153743221382664)⟩,⟨(-546954393789843220254617),(-546954393789843172046798)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-595501628280137869759549),(-595501628280137789752815)⟩,⟨(-448232043546874666569701),(-448232043546874586546329)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-924943870650908017843076),(-924943870650907879544736)⟩,⟨15864838914915024362837,15864838914915162620165⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-859369463882005770182892),(-859369463882005484804838)⟩,⟨614455441934852752542115,614455441934853037863138⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-454170035809638748918821),(-454170035809638081124804)⟩,⟨983611290172229767392369,983611290172230435177607⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-23313001857631422184218),(-23313001857630348921036)⟩,⟨957008567796977531116392,957008567796978604405850⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨168764717974613577050322,168764717974614599113633⟩,⟨641424011220140431958013,641424011220141454053292⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨92736508032452016421075,92736508032452427903834⟩,⟨218766703830913585690682,218766703830913997186931⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨27184664559794187077,27184664559794500274⟩,⟨141859376187644291954,141859376187644605158⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨131461221523021559777,131461221523022356089⟩,⟨441459630719292964789,441459630719293761119⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨403617714611499354749,403617714611500265097⟩,⟨763938706864859271096,763938706864860181439⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨999620767392499811980,999620767392500470099⟩,⟨1025281957973339870847,1025281957973340528875⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2063688133400405968266,2063688133400406277927⟩,⟨945958855902179464301,945958855902179773667⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3524369112267791107388,3524369112267791256232⟩,⟨(-34576395829449423586),(-34576395829449275131)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨4709992741726926396482,4709992741726926512192⟩,⟨(-2616153004138987768717),(-2616153004138987653114)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨4063428503831326851374,4063428503831327011050⟩,⟨(-6980342631798613604927),(-6980342631798613444583)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-325563726944855003977),(-325563726944854726480)⟩,⟨(-11740590534904389096762),(-11740590534904388817974)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-8921007094032995594372),(-8921007094032995124420)⟩,⟨(-13651325951726958038037),(-13651325951726957567732)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-18947462079568689226478),(-18947462079568688496606)⟩,⟨(-9541134161444923590420),(-9541134161444922861994)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-25296504180610155119218),(-25296504180610154106166)⟩,⟨314908822120820106753,314908822120821117092⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-24522410512750987605677),(-24522410512750986389364)⟩,⟨11099891931079533139011,11099891931079534353875⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-17868811087265685583637),(-17868811087265684376148)⟩,⟨16750926146214470263105,16750926146214471470538⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-9634144574226272009672),(-9634144574226271107697)⟩,⟨14403322633741884717423,14403322633741885619969⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-2856820154328907168240),(-2856820154328906833630)⟩,⟨5589038832810913589972,5589038832810913924898⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨2682849322345892442,2682849322345925543⟩,⟨1642146071718558128,1642146071718591226⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨8892287831604355338,8892287831604487271⟩,⟨4300215946643844819,4300215946643976752⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨17455813880606670462,17455813880607034022⟩,⟨4544641011659911491,4544641011660275052⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨28986766766399628993,28986766766400559126⟩,⟨(-927300153325895665),(-927300153324965529)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨41336086230414026369,41336086230416641076⟩,⟨(-17347514549717989901),(-17347514549715375188)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨46470293056104555595,46470293056112875240⟩,⟨(-50246346886139478980),(-50246346886131159332)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨28098491545357100412,28098491545377127161⟩,⟨(-99674274899362110020),(-99674274899342083267)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-34484435673038016279),(-34484435673005221342)⟩,⟨(-150408915342448124830),(-150408915342415329907)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-150674466128092120193),(-150674466128052190295)⟩,⟨(-165794007293627816996),(-165794007293587887123)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-296107308338310783392),(-296107308338258313896)⟩,⟨(-100259039727295752636),(-100259039727243283163)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-407503370576563500033),(-407503370576517527762)⟩,⟨63784477933454655188,63784477933500627468⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-418299996460215370950),(-418299996460187356773)⟩,⟨280762946097695991390,280762946097724005609⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-316461676562576634196),(-316461676562563167698)⟩,⟨452633821792057553382,452633821792071019948⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-164020852552073932951),(-164020852552066268527)⟩,⟨490436940266061587548,490436940266069252024⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-47288429738884002046),(-47288429738880192740)⟩,⟨370748118432618352870,370748118432622162200⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-3790558897998478692),(-3790558897997363407)⟩,⟨136836491740274564224,136836491740275679519⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨32548203455232594,32548203455232610⟩,⟨(-22561757584170238),(-22561757584170222)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨93600195583235885,93600195583235901⟩,⟨(-81800535573016991),(-81800535573016975)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨135905313270895526,135905313270895542⟩,⟨(-184073794675809634),(-184073794675809618)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨124698349346892592,124698349346892608⟩,⟨(-355879471947876760),(-355879471947876743)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-7362255138715988),(-7362255138715969)⟩,⟨(-603302620797707587),(-603302620797707570)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-360170478756327886),(-360170478756327870)⟩,⟨(-872779652760092045),(-872779652760092029)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-1027467743528660122),(-1027467743528660104)⟩,⟨(-1002036502296190532),(-1002036502296190514)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-1995047557412396782),(-1995047557412396763)⟩,⟨(-706713477839931099),(-706713477839931078)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3010007692751245791),(-3010007692751245746)⟩,⟨323232911879242086,323232911879242129⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-3557020149966158751),(-3557020149966158538)⟩,⟨2184661403119328812,2184661403119329025⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-3098780777154440313),(-3098780777154439139)⟩,⟨4509897716686155597,4509897716686156772⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-1530473250830869656),(-1530473250830863139)⟩,⟨6480765056755156403,6480765056755162920⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨534080985026058973,534080985026081391⟩,⟨7242036316718657163,7242036316718679583⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨2033151480725155817,2033151480725201187⟩,⟨6429319221193405005,6429319221193450377⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2158235777369696406,2158235777369748491⟩,⟨4322008216055573646,4322008216055625728⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨908132214756108920,908132214756132520⟩,⟨1507150841627999291,1507150841628022892⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨252267445362985750983431,252267445363096220978933⟩,⟨(-7653362181927198713024114),(-7653362181927088243068003)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 25) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_25 (tableDensity false) (fullFactor true 1 25) density0_contains hk1_1_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨897619658696858459680295,897619658696858803509369⟩,⟨(-550661901341208085442039),(-550661901341207741858919)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_25 1 25 ha1_1_25_contains + def realAnswer : RBox := ⟨1149887104059844110663726,1149887104059955124488302⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_25 +namespace hm1_1_1_25 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_25 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨244627232426011406593850,244627232426011994855109⟩,⟨(-220942229562804547668329),(-220942229562803959387065)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨627924310375313957496354,627924310375315379340991⟩,⟨(-778905147699461119871487),(-778905147699459697967614)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨611016093874709909925268,611016093874711685642186⟩,⟨(-1577177181642729132201313),(-1577177181642727356423974)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-194904402746824895144720),(-194904402746823598610900)⟩,⟨(-2367181460956000589907844),(-2367181460955999293381534)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-1863731739932890289064146),(-1863731739932889765370747)⟩,⟨(-2344986237915343638291555),(-2344986237915343114750138)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-3465953335718669666291934),(-3465953335718669476471457)⟩,⟨(-628740082152876336663539),(-628740082152876146945461)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-3192353304471324588735775),(-3192353304471324522331700)⟩,⟨2405632744870722949456999,2405632744870723016007714⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-194919368405256878063928),(-194919368405256849397960)⟩,⟨4468891633753448087055946,4468891633753448115892178⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3657807786545496298214260,3657807786545496314206558⟩,⟨3293145283040064924494377,3293145283040064940315101⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨5194123484598003245838471,5194123484598003256519902⟩,⟨(-546970595895808448526178),(-546970595895808438050081)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3366140832987799402198020,3366140832987799410062887⟩,⟨(-4005545721740798418914951),(-4005545721740798410910410)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨95837435244505578413134,95837435244505583470867⟩,⟨(-4863019224195002845528257),(-4863019224195002840260305)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2190769833325152212886201),(-2190769833325152209339627)⟩,⟨(-3507255835790621404281518),(-3507255835790621400660768)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-2669460887331417650098358),(-2669460887331417647852762)⟩,⟨(-1643406071320645954018227),(-1643406071320645951851215)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1902858760662816849248698),(-1902858760662816848137931)⟩,⟨(-443626546968401064755185),(-443626546968401063763484)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-662497423030162309021302),(-662497423030162308700980)⟩,⟨(-41478141925053398323460),(-41478141925053398055542)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨4352448594586447361597,4352448594586550852889⟩,⟨37922232247780969076301,37922232247781072565326⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨31562318628280204881694,31562318628280664664122⟩,⟨112882888400686860500356,112882888400687320276754⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨113189234208998689103867,113189234209000193878402⟩,⟨170298814926971801820818,170298814926973306588966⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨265804764677794483056577,265804764677798892777186⟩,⟨152797510281439455282675,152797510281443865004026⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨431122070622302612118637,431122070622312529189229⟩,⟨(-32132979132108323168005),(-32132979132098406078297)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨421626722142350068834793,421626722142377165392820⟩,⟨(-415661500596561134174269),(-415661500596534037596749)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨11021102930618057096824,11021102930674402476891⟩,⟨(-792152228264557201667245),(-792152228264500856304590)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-742795971479742043201217),(-742795971479658999994371)⟩,⟨(-710590783646176315435276),(-710590783646093272268034)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1277809877621439941181939),(-1277809877621327793078517)⟩,⟨91516102678906055502046,91516102679018203625048⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-959518936548700753705974),(-959518936548608892889286)⟩,⟨1180629155183046755997630,1180629155183138616870935⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨140442354699597736695340,140442354699673333441450⟩,⟨1700120013358274287535589,1700120013358349884267773⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨1227672476691392117275379,1227672476691427594049851⟩,⟨1286604522088721760478539,1286604522088757237184535⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨1632944423885728265982664,1632944423885749006516653⟩,⟨400929443219097165176231,400929443219117905684915⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1359470699083778965130100,1359470699083788605702572⟩,⟨(-274088358115087040892670),(-274088358115077400305161)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨801911086806788159175539,801911086806791774239966⟩,⟨(-437127313662524271959259),(-437127313662520656870309)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨253274443110679452552638,253274443110680340085844⟩,⟨(-193120576010337516726812),(-193120576010336629182729)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1481269308963150431036),(-1481269308963150375691)⟩,⟨1042521724946089657145,1042521724946089712512⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4254108748109954581124),(-4254108748109954397235)⟩,⟨3868787425784700308950,3868787425784700492929⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-5922450895377140111742),(-5922450895377139740492)⟩,⟨8852673810474901410415,8852673810474901781884⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-4019726846364650223388),(-4019726846364649539970)⟩,⟨16701153652438488765324,16701153652438489448996⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨5722872387871074473844,5722872387871075685181⟩,⟨25326485415079700236758,25326485415079701448160⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨26559993707523242749228,26559993707523244817358⟩,⟨26744780186068236004709,26744780186068238072426⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨52837275069400190096961,52837275069400193519125⟩,⟨7395879781930055000069,7395879781930058421447⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨62346390923495051787840,62346390923495057277210⟩,⟨(-40415538401024806376773),(-40415538401024800887321)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨25567280495656954880982,25567280495656963518964⟩,⟨(-98224807161867595302513),(-98224807161867586663334)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-60888625810608092018864),(-60888625810608075849843)⟩,⟨(-119038595736944134097647),(-119038595736944117928127)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-151070007572464581961988),(-151070007572464540312362)⟩,⟨(-67165005158745099326474),(-67165005158745057677260)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-182872672427385097481266),(-182872672427384956800322)⟩,⟨35113331432373647368521,35113331432373788048889⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-140799749979485643420625),(-140799749979485202101275)⟩,⟨121203720353121444037215,121203720353121885356332⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-67768714597618909405221),(-67768714597618129918514)⟩,⟨143603532994239379000913,143603532994240158487611⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-15311229348551706997317),(-15311229348550941278299)⟩,⟨105959433793026903860753,105959433793027669579751⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨439212025011698093412,439212025012009248899⟩,⟨37802282462660558204506,37802282462660869359940⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-21061333720776369085),(-21061333720776106318)⟩,⟨43446139636489118537,43446139636489381306⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-52580593836171200235),(-52580593836170532930)⟩,⟨142235751677123026108,142235751677123693412⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-43946070844670885030),(-43946070844670124549)⟩,⟨272814859558339008394,272814859558339768878⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨57372695923852318120,57372695923852863130⟩,⟨437201324546640429125,437201324546640974142⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨329152928995612071122,329152928995612318434⟩,⟨587297887817371056817,587297887817371304159⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨835974001349406279353,835974001349406381845⟩,⟨577164954488509812785,577164954488509915313⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨1517324908269326212888,1517324908269326268705⟩,⟨145110229854064416230,145110229854064472054⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2031697860784237578074,2031697860784237636128⟩,⟨(-970537064063670619763),(-970537064063670561776)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1738070757113126728605,1738070757113126824770⟩,⟨(-2715773876074676019846),(-2715773876074675923806)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨67366069581338764110,67366069581338926544⟩,⟨(-4408289512601310093815),(-4408289512601309931406)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-2805686964032678394608),(-2805686964032678141729)⟩,⟨(-4928326720901619087244),(-4928326720901618834213)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-5692503610243193218816),(-5692503610243192864725)⟩,⟨(-3604435316345411682157),(-3604435316345411327807)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-7120347786248384953169),(-7120347786248384521435)⟩,⟨(-1026967458478219655561),(-1026967458478219223699)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-6475065895072407681090),(-6475065895072407245349)⟩,⟨1246344206794468837007,1246344206794469272739⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4289589490024512385003),(-4289589490024512054980)⟩,⟨1918703974276890451918,1918703974276890781879⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1467901018693676974021),(-1467901018693676850621)⟩,⟨876348736061612952752,876348736061613076122⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨907975096536571941,907975096536599147⟩,⟨493742899649677826,493742899649705030⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨3041187253119713347,3041187253119821783⟩,⟨1315004987575805683,1315004987575914118⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨6084324760912072737,6084324760912371586⟩,⟨1455256831771482059,1455256831771780904⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨10383190074885198970,10383190074885963660⟩,⟨(-150236902827190000),(-150236902826425308)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨15439348231013696245,15439348231015846155⟩,⟨(-5388126174435052725),(-5388126174432902816)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨18807448662333759340,18807448662340600022⟩,⟨(-16670136208830507808),(-16670136208823667122)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨14953319782181908449,14953319782198371470⟩,⟨(-35250333847825770789),(-35250333847809307772)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-4262009176321936422),(-4262009176294990544)⟩,⟨(-57840400107022247152),(-57840400106995301271)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-45132570225400732572),(-45132570225367951475)⟩,⟨(-73513692453247432170),(-73513692453214651068)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-103980277385632884040),(-103980277385589854956)⟩,⟨(-65898558133033636346),(-65898558132990607260)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-162033763446066874400),(-162033763446029221274)⟩,⟨(-24241070558453761165),(-24241070558416108039)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-192704497695789337821),(-192704497695766424593)⟩,⟨42852507695243954245,42852507695266867468⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-180296455853492533564),(-180296455853481534715)⟩,⟨106069349732184868072,106069349732195866911⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-133048430397334673470),(-133048430397328421471)⟩,⟨132655066389380526278,132655066389386778268⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-74826936408147102185),(-74826936408143997968)⟩,⟨107734254934036313390,107734254934039417601⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-23134331346153478138),(-23134331346152569828)⟩,⟨41083580179618133115,41083580179619041426⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨934590138841264,934590138841280⟩,⟨(-716358518218199),(-716358518218183)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2043624969277836,2043624969277852⟩,⟨(-2993646942971504),(-2993646942971488)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1076039348045180),(-1076039348045164)⟩,⟨(-6878569661189609),(-6878569661189593)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-18003218519517038),(-18003218519517022)⟩,⟨(-9490785236060046),(-9490785236060030)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-67590030566918036),(-67590030566918020)⟩,⟨969983405425821,969983405425838⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-174229339933357257),(-174229339933357241)⟩,⟨54543652481025058,54543652481025074⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-349072830000707704),(-349072830000707688)⟩,⟨210872524507186013,210872524507186031⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-554789251884682512),(-554789251884682492)⟩,⟨557153514020571811,557153514020571830⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-671204449648325050),(-671204449648325016)⟩,⟨1164767122496389807,1164767122496389846⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-508056935937491639),(-508056935937491466)⟩,⟨1998614513127274927,1998614513127275101⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨86981248407239157,86981248407240117⟩,⟨2840430197119239762,2840430197119240723⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1055520042984900531,1055520042984905849⟩,⟨3340403856599998422,3340403856600003742⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2036140570148190846,2036140570148209159⟩,⟨3232330406608186620,3232330406608204935⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨2498427204917693634,2498427204917730714⟩,⟨2540317423849936179,2540317423849973263⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2067950719914993247,2067950719915035837⟩,⟨1541558574888523661,1541558574888566249⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨801896924709575107,801896924709594408⟩,⟨504639120521519757,504639120521539061⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨115191104964737281612889,115191104964827534686320⟩,⟨(-1720867037620522584648957),(-1720867037620432331579096)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_25 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 25) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_25 (tableDensity true) (fullFactor true 1 25) density1_contains hk1_1_25_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-1173810322911276896896868),(-1173810322911276447274232)⟩,⟨720096332523117816277048,720096332523118265578051⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_25 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 25) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_25 1 25 ha1_1_25_contains + def realAnswer : RBox := ⟨(-1058619217946539715283979),(-1058619217946448812587912)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 25) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_25 +namespace hm1_0_1_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-577803246998630596050651),(-577803246998630283890060)⟩,⟨256190718465965911863360,256190718465966224013050⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-1589643097963460580457473),(-1589643097963459861166630)⟩,⟨1066506864306435752360279,1066506864306436471600264⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-1936681514910098714846129),(-1936681514910098046593805)⟩,⟨2604226796760217390583280,2604226796760218058709326⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-677522362335190302185030),(-677522362335189751609589)⟩,⟨4595474276751067970710213,4595474276751068521185521⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2806706307203604345866664,2806706307203604667615283⟩,⟨5419868940054111182700348,5419868940054111504491690⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨7061732783979845313397525,7061732783979845468437303⟩,⟨2690107379788954826670240,2690107379788954981928483⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨8032917559676379573956643,8032917559676379672364974⟩,⟨(-3797448485743805120772801),(-3797448485743805022375478)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨2716891148965137485777676,2716891148965137546096846⟩,⟨(-9568143940982078131122371),(-9568143940982078071020041)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-5915045910588555310784086),(-5915045910588555277067182)⟩,⟨(-8809415499510981511344352),(-8809415499510981477594675)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-10695593929285781672404123),(-10695593929285781651848333)⟩,⟨(-1384410538268702906190799),(-1384410538268702885527202)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-8150167928319312318452586),(-8150167928319312304369135)⟩,⟨6488589149144080496066275,6488589149144080510177547⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1683900627279677082284498),(-1683900627279677073674735)⟩,⟨9349863510071110520266621,9349863510071110528743216⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨3377643360201870890735462,3377643360201870895790168⟩,⟨7312010631159078612384731,7312010631159078617477963⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨4846353973044056367949093,4846353973044056370893052⟩,⟨3761028206512412327878953,3761028206512412330839118⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨3629784193490154291427420,3629784193490154292789923⟩,⟨1251138602254028685102756,1251138602254028686433121⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨1288496328132775269060904,1288496328132775269436079⟩,⟨214751269270497624629321,214751269270497624985008⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨13107231789396554897744,13107231789396607986980⟩,⟨(-65842215396282082389895),(-65842215396282029300786)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨9305579475703116004674,9305579475703322485155⟩,⟨(-209539653394511755824135),(-209539653394511549340834)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-95286678150589373465754),(-95286678150588850466298)⟩,⟨(-365268530951937285192466),(-365268530951936762177175)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-375373440089112032117573),(-375373440089110770718890)⟩,⟨(-452185860244491991268034),(-452185860244490729832702)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-814321595060995310268947),(-814321595060991187900686)⟩,⟨(-266231014488517056410875),(-266231014488512934026853)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1123456858739083095991797),(-1123456858739073999606164)⟩,⟨412602204085036097815547,412602204085045194150276⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-726624458940160920185438),(-726624458940141090812638)⟩,⟨1436944107550339509468606,1436944107550359338784081⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨688070397938065719494493,688070397938097427610489⟩,⟨1963625583004574773185954,1963625583004606481371683⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨2356681633918381981278296,2356681633918421279810554⟩,⟨1011866134807600901325479,1011866134807640199942093⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨2738237083679523984762585,2738237083679561618614089⟩,⟨(-1198563773234766364386698),(-1198563773234728730629188)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1217842714969136851363591,1217842714969163067099105⟩,⟨(-3025040311323506365674460),(-3025040311323480150046957)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-1033268182896575830458668),(-1033268182896559200341179)⟩,⟨(-3125415694361647604529837),(-3125415694361630974351992)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2404717660308045511272818),(-2404717660308038572189511)⟩,⟨(-1832388981671385063611756),(-1832388981671378124392121)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-2405305897327957215299080),(-2405305897327953392536464)⟩,⟨(-430994546749036875330659),(-430994546749033052517974)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-1573538570394517693725094),(-1573538570394515998072457)⟩,⟨237819576506508495861837,237819576506510191511732⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-524888011695683931779990),(-524888011695683474734083)⟩,⟨172240807046506366476412,172240807046506823515334⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨1794503374527984654743,1794503374527984709468⟩,⟨(-181983609771780513155),(-181983609771780458606)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨5582012406993331612375,5582012406993331793521⟩,⟨(-1334071891877281996423),(-1334071891877281815751)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨9431244748192795508496,9431244748192795887628⟩,⟨(-5122401364449325729880),(-5122401364449325351274)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨11302263258934145941106,11302263258934146686413⟩,⟨(-13697271798342160881009),(-13697271798342160135636)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨5606442773943511793281,5606442773943513245936⟩,⟨(-27615678965278093177885),(-27615678965278091723307)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-16159786388151880180843),(-16159786388151877370522)⟩,⟨(-40701666213420949397036),(-40701666213420946583384)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-57015675620486685476533),(-57015675620486680151774)⟩,⟨(-34577375539575386108129),(-34577375539575380783705)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-97612260621915681097615),(-97612260621915671389465)⟩,⟨14841742503053475637344,14841742503053485338082⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-90529741455548593514432),(-90529741455548576659329)⟩,⟨107576586492223335822506,107576586492223352674056⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨3474510689805655147174,3474510689805683014006⟩,⟨190006678354909157440501,190006678354909185317132⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨155639755472008100063197,155639755472008147846483⟩,⟨182943559061754326341864,182943559061754374136407⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨270856121539481851847478,270856121539481946748329⟩,⟨66261957221816583992613,66261957221816678889717⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨277301642932828011992496,277301642932828178863580⟩,⟨(-84864774822084060225240),(-84864774822083893370435)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨194657979154741891662524,194657979154742179791753⟩,⟨(-170977770908194896050998),(-170977770908194607933490)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨95712495120293307582933,95712495120293639911457⟩,⟨(-153478941538367044385565),(-153478941538366712060859)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨25833064756583077113030,25833064756583226880820⟩,⟨(-59702189823972540049661),(-59702189823972390282416)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨23631774290173614136,23631774290173674453⟩,⟨(-13128167925140225067),(-13128167925140164750)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨70871992159612498802,70871992159612648287⟩,⟨(-49576223405975930881),(-49576223405975781393)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨112177424829345073997,112177424829345236302⟩,⟨(-118645960960704067671),(-118645960960703905359)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨121603512222961376647,121603512222961484504⟩,⟨(-244598700883130076585),(-244598700883129968693)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨35486611445897543382,35486611445897603028⟩,⟨(-436867699447807284206),(-436867699447807224503)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-251525733513594563138),(-251525733513594528234)⟩,⟨(-642839504878601599019),(-642839504878601564084)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-830884633504705439057),(-830884633504705411397)⟩,⟨(-677880906386304119772),(-677880906386304092176)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1621773706521865222223),(-1621773706521865180610)⟩,⟨(-212152478257110521137),(-212152478257110479725)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-2187356124860303887407),(-2187356124860303812046)⟩,⟨1038306698596372001130,1038306698596372076385⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1812249174778372077326),(-1812249174778371946934)⟩,⟨2902842346132183261339,2902842346132183391932⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-67527380928416664370),(-67527380928416457283)⟩,⟨4527168729392427097873,4527168729392427305452⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2533328882284977763869,2533328882284978057791⟩,⟨4862918289448112782756,4862918289448113076916⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨4656274168911792329424,4656274168911792688565⟩,⟨3642748366205008675758,3642748366205009034750⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨5152139509536545473922,5152139509536545835996⟩,⟨1733711705987852731348,1733711705987853092999⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨3858799020774300833587,3858799020774301107018⟩,⟨343012785906720751825,343012785906721024838⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1407775678092811343517,1407775678092811445496⟩,⟨(-45565454235145681508),(-45565454235145579681)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨185184839522705441,185184839522710495⟩,⟨(-466478242540850504),(-466478242540845453)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨431464274097946204,431464274097966049⟩,⟨(-1520414200097110783),(-1520414200097090939)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨219533746183170624,219533746183223696⟩,⟨(-2893807213493717655),(-2893807213493664583)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1019014508541098335),(-1019014508540957619)⟩,⟨(-4592310729927030534),(-4592310729926889818)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-4107424766571962336),(-4107424766571478800)⟩,⟨(-6091795245186519913),(-6091795245186036377)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-9745762832426771006),(-9745762832425320196)⟩,⟨(-5830887944832419283),(-5830887944830968474)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-17399422657588922798),(-17399422657585657011)⟩,⟨(-954766334477296513),(-954766334474030725)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-23629426016929124015),(-23629426016924199095)⟩,⟨11679828412268956283,11679828412273881210⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-21469060442668076132),(-21469060442660274966)⟩,⟨32399587502315208598,32399587502323009767⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-3541945428350626778),(-3541945428340894356)⟩,⟨54967979514437041823,54967979514446774247⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨30812466022407511420,30812466022415264092⟩,⟨67012565060641315027,67012565060649067698⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨70332955369488453526,70332955369492804347⟩,⟨58232108517497609076,58232108517501959888⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨96400799341030276106,96400799341033089374⟩,⟨31025837291411342049,31025837291414155307⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨95689530820788039387,95689530820789661687⟩,⟨1481518231230903239,1481518231232525534⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨68404410238693061343,68404410238693824594⟩,⟨(-12892338861019216919),(-12892338861018453669)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨24521113435422613999,24521113435422831549⟩,⟨(-7276670560987330738),(-7276670560987113186)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-3372906910119761),(-3372906910119745)⟩,⟨(-4358387629255154),(-4358387629255138)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-12106158103142378),(-12106158103142362)⟩,⟨(-12414066212059042),(-12414066212059026)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-26873580342479287),(-26873580342479271)⟩,⟨(-17498126198303241),(-17498126198303225)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-51261514116590725),(-51261514116590707)⟩,⟨(-14302209507875373),(-14302209507875356)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-85604972423911951),(-85604972423911935)⟩,⟨7291482002496100,7291482002496116⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-120937725971232183),(-120937725971232167)⟩,⟨61953619013669441,61953619013669458⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-131502375056886487),(-131502375056886470)⟩,⟨162481587335919277,162481587335919294⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-73243891678610044),(-73243891678610028)⟩,⟨303539629278530044,303539629278530061⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨99755127459388336,99755127459388355⟩,⟨441479794439627215,441479794439627235⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨396457654186853380,396457654186853422⟩,⟨492747666704329741,492747666704329783⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨750722397179069579,750722397179069782⟩,⟨375988617120837106,375988617120837313⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1029997271101528385,1029997271101529482⟩,⟨86974350439494532,86974350439495629⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1108547878603735801,1108547878603739434⟩,⟨(-259362244926468411),(-259362244926464781)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨950361502997917774,950361502997924935⟩,⟨(-481885393577135299),(-481885393577128141)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨619839245583394638,619839245583402711⟩,⟨(-452724202521272072),(-452724202521263999)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨212176750576856764,212176750576860394⟩,⟨(-183257913212127368),(-183257913212123738)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-118663930416764353073552),(-118663930416730409987487)⟩,⟨2616694391468331540184639,2616694391468365483256149⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 26) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_26 (tableDensity false) (fullFactor true 1 26) density0_contains hk1_1_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-446492930578168441846998),(-446492930578168298053733)⟩,⟨249701934579198972900221,249701934579199116605658⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_26 1 26 ha1_1_26_contains + def realAnswer : RBox := ⟨(-565156860994932894920550),(-565156860994898608041220)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_26 +namespace hm1_1_1_26 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_26 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-103732100967795345719133),(-103732100967795099585687)⟩,⟨30392170413745727296569,30392170413745973432622⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-296061836871311506608944),(-296061836871310944610350)⟩,⟨143277728060783615187468,143277728060784177198486⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-399059180537256420118543),(-399059180537255912401923)⟩,⟨391089950294319652646554,391089950294320160395325⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-249049270082767975545960),(-249049270082767576451269)⟩,⟨749697034979640206015905,749697034979640605136488⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨295187883048404984821830,295187883048405185794368⟩,⟨960092164472610354810425,960092164472610555762042⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1035878836700796099805275,1035878836700796162546993⟩,⟨589460699147429129122265,589460699147429191801674⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1283238046255739491042791,1283238046255739516813958⟩,⟨(-465265233351011117812258),(-465265233351011092026969)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨453217463204504418177117,453217463204504429529658⟩,⟨(-1472929498410142328684883),(-1472929498410142317254110)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1003269631183826720991377),(-1003269631183826714639988)⟩,⟨(-1383844108619490691005376),(-1383844108619490684679255)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1822503693947560594987769),(-1822503693947560590925004)⟩,⟨(-112420235467956035994978),(-112420235467956032024557)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1348883693240044953091987),(-1348883693240044950095765)⟩,⟨1249533550875159917122327,1249533550875159920150069⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-182481921865792098670124),(-182481921865792096799898)⟩,⟨1705871059982509107636398,1705871059982509109582129⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨705907096473866544370416,705907096473866545647105⟩,⟨1280349766779937352934382,1280349766779937354243772⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨927920090570314750551931,927920090570314751361996⟩,⟨608936735621388131861300,608936735621388132646733⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨672398551657971447112706,672398551657971447512129⟩,⟨164772862069203949942635,164772862069203950300561⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨234770748899755403036994,234770748899755403151561⟩,⟨15233788968090936349676,15233788968090936445704⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨6681969727503523830717,6681969727503563284311⟩,⟨(-8060713304160857136396),(-8060713304160817682774)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨16253143574366319884196,16253143574366476237197⟩,⟨(-27875847918444724938391),(-27875847918444568585718)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨11385916082195926956149,11385916082196331937127⟩,⟨(-55541526154907683760460),(-55541526154907278781398)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-23529894607041549152961),(-23529894607040553081975)⟩,⟨(-82604786233290637125602),(-82604786233289641059181)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-95809911563969493517116),(-95809911563966161735181)⟩,⟨(-76666332671152048511018),(-76666332671148716731185)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-170377437501857228043398),(-170377437501849821395509)⟩,⟨9520324396651452066926,9520324396658858720873⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-150641305804927055209830),(-150641305804910812207205)⟩,⟨176721004869319124856771,176721004869335367866832⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨45439913086431465383130,45439913086457493316427⟩,⟨303287247270406223943643,303287247270432251868669⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨331103090860659791111558,331103090860692054799596⟩,⟨204207920966412173077044,204207920966444436753749⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨449038031085842682221226,449038031085873530708066⟩,⟨(-138472973948907802436216),(-138472973948876953936917)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨243875211406176134673540,243875211406197529230274⟩,⟨(-476439973772886377989350),(-476439973772864983417471)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-133066956209778403762853),(-133066956209764903703838)⟩,⟨(-549817334727845086011183),(-549817334727831585961114)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-400098157430566282579545),(-400098157430560733722751)⟩,⟨(-364144784101546685486530),(-364144784101541136650018)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-432938990707416991244205),(-432938990707413958333106)⟩,⟨(-123188264635321931117424),(-123188264635318898213983)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-297976123385349253827665),(-297976123385347922940488)⟩,⟨11294264966267620830947,11294264966268951718489⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-102261222480114638528290),(-102261222480114283039428)⟩,⟨20510531567519414211749,20510531567519769701696⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨366583534086639148637,366583534086639165473⟩,⟨177329561948193413923,177329561948193430754⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨1230972972727167689387,1230972972727167745659⟩,⟨410033739009011079741,410033739009011135995⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨2414695096971746375594,2414695096971746490561⟩,⟨169030070700234426365,169030070700234541310⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨3773462478563789836539,3773462478563790050695⟩,⟨(-1150625405838256221298),(-1150625405838256007137)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨4336422375294309077860,4336422375294309463199⟩,⟨(-4208889605791813307373),(-4208889605791812921958)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨1956337340095798165685,1956337340095798838947⟩,⟨(-8694851533316772664701),(-8694851533316771991306)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-5590206894050534335270),(-5590206894050533195141)⟩,⟨(-11559282064632305327735),(-11559282064632304187612)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-16908419473201221989037),(-16908419473201220127050)⟩,⟨(-6797053399293320941874),(-6797053399293319080162)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-23537450548600101157168),(-23537450548600098151537)⟩,⟨9504623956147831669341,9504623956147834674842⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-14348243281812535001524),(-14348243281812529835074)⟩,⟨30922306526887397510493,30922306526887402677118⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨11425888301477433170769,11425888301477446132515⟩,⟨41376518236185664871972,41376518236185677833885⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨38493570856335741783548,38493570856335784920592⟩,⟨30558680506504400238510,30558680506504443375583⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨49303407527080216646311,49303407527080313686343⟩,⟨6472693708416543207706,6472693708416640247662⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨41001883751779893401365,41001883751780091629413⟩,⟨(-12868920203519897168463),(-12868920203519698940466)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨23890248511663336539044,23890248511663581334851⟩,⟨(-16782683758419766989985),(-16782683758419522194203)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨7407975143554962395838,7407975143555075070484⟩,⟨(-7227921609729314753508),(-7227921609729202078863)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨8955856304493170244,8955856304493220832⟩,⟨1204094312295557223,1204094312295607813⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨28458409259073190278,28458409259073315482⟩,⟨943032110793077985,943032110793203190⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨51488278952236816593,51488278952236952012⟩,⟨(-8712249161227221351),(-8712249161227085931)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨75100365626267828098,75100365626267917009⟩,⟨(-37880091119470191498),(-37880091119470102590)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨84845479090653344186,84845479090653391287⟩,⟨(-98466182538767399543),(-98466182538767352443)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨47507422424796794754,47507422424796818492⟩,⟨(-193195266956477869607),(-193195266956477845873)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-85027281202792204658),(-85027281202792192074)⟩,⟨(-291200722097171392881),(-291200722097171380291)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-340342589714771745758),(-340342589714771731039)⟩,⟨(-303399533378133359347),(-303399533378133344608)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-656834689241269364014),(-656834689241269338019)⟩,⟨(-101865773050854679870),(-101865773050854653864)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-845267550002656557511),(-845267550002656512479)⟩,⟨376034514995608501988,376034514995608547000⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-685075661529985947082),(-685075661529985875194)⟩,⟨997766803182984364358,997766803182984436198⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-140901910563428118610),(-140901910563428015655)⟩,⟨1453505558595965068079,1453505558595965171016⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨524895862116002090779,524895862116002218284⟩,⟨1490282027574132101988,1490282027574132229511⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨923921768297712126888,923921768297712257421⟩,⟨1134982431173822062884,1134982431173822193454⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨836775061888078264888,836775061888078364772⟩,⟨635215051866153064036,635215051866153163959⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨331444723117148225399,331444723117148262948⟩,⟨193175655202880012600,193175655202880050164⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨52922561665748402,52922561665752558⟩,⟨(-156186309678702731),(-156186309678698577)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨123027903897062112,123027903897078426⟩,⟨(-515683398273176908),(-515683398273160592)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨56129012494511535,56129012494555163⟩,⟨(-1004999610550216757),(-1004999610550173130)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-336009476568474495),(-336009476568358806)⟩,⟨(-1650542056164420396),(-1650542056164304706)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1358706334085152483),(-1358706334084754899)⟩,⟨(-2310297513195698964),(-2310297513195301377)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-3349105987672464356),(-3349105987671271451)⟩,⟨(-2485205967389644520),(-2485205967388451616)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-6337785993497301327),(-6337785993494616677)⟩,⟨(-1161538553495084552),(-1161538553492399903)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-9443375420867363304),(-9443375420863316750)⟩,⟨2996197220077767656,2996197220081814210⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-10443508769482308079),(-10443508769475903655)⟩,⟨10720976952146601121,10720976952153005546⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-6468547301375926096),(-6468547301367944689)⟩,⟨20705280724094129687,20705280724102111092⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨3714554992826945902,3714554992833295661⟩,⟨29063094826640588828,29063094826646938588⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨17368841487877339212,17368841487880897666⟩,⟨31283754604423056657,31283754604426615110⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨28317329718106545850,28317329718108843490⟩,⟨25872297435256481102,25872297435258778748⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨30845162812344541378,30845162812345864663⟩,⟨16044877161624837813,16044877161626161099⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨23381793166145000303,23381793166145622202⟩,⟨7077447674912257340,7077447674912879240⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨8640094605644268536,8640094605644445681⟩,⟨1721606657149016944,1721606657149194091⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-106371885995586),(-106371885995570)⟩,⟨(-124644640408437),(-124644640408421)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-432511206828245),(-432511206828229)⟩,⟨(-261783482298185),(-261783482298169)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-953257368808658),(-953257368808642)⟩,⟨207615610450750,207615610450766⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1170298922481857),(-1170298922481841)⟩,⟨2623953002065771,2623953002065787⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨842089858802346,842089858802362⟩,⟨9593876676845382,9593876676845398⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨9889169462595515,9889169462595531⟩,⟨24358026902775916,24358026902775932⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨35297487660600411,35297487660600427⟩,⟨47808664067565193,47808664067565209⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨90263571278286739,90263571278286756⟩,⟨72934167422073145,72934167422073161⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨184582989339979172,184582989339979195⟩,⟨79699108995806293,79699108995806313⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨310171688871646298,310171688871646340⟩,⟨38119486526127995,38119486526128036⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨429945926387014651,429945926387014821⟩,⟨(-73015771420960873),(-73015771420960704)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨488816085687034804,488816085687035705⟩,⟨(-238335888557768684),(-238335888557767786)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨450943831275893326,450943831275896292⟩,⟨(-394179079942388864),(-394179079942385897)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨332037863805616275,332037863805622130⟩,⟨(-454713680347385799),(-454713680347379943)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨186654406455836235,186654406455842836⟩,⟨(-364844752966263524),(-364844752966256920)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨57615379814723525,57615379814726495⟩,⟨(-139535299095860107),(-139535299095857137)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-62331821216838560345008),(-62331821216810947900231)⟩,⟨555443563645691128468560,555443563645718740912812⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_26 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 26) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_26 (tableDensity true) (fullFactor true 1 26) density1_contains hk1_1_26_contains +noncomputable def atomAnswer : CBox := ⟨⟨583875370756066235916420,583875370756066423953766⟩,⟨(-326533299065106537099707),(-326533299065106349177212)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_26 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 26) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_26 1 26 ha1_1_26_contains + def realAnswer : RBox := ⟨521543549539227575571412,521543549539255576053535⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 26) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_26 +namespace hm1_0_1_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨199481079378502829205059,199481079378502930933331⟩,⟨6428796198859231979636,6428796198859333710335⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨599240890890567712652419,599240890890567964696307⟩,⟨(-90170490428669282872451),(-90170490428669030827865)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨903224885123785614390630,903224885123785876006606⟩,⟨(-499926419253209650470534),(-499926419253209388873792)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨776507388645457620485892,776507388645457786150288⟩,⟨(-1268899675186151680941105),(-1268899675186151515328062)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-206018687498067096226968),(-206018687498066984414208)⟩,⟨(-1960025420797069175620917),(-1960025420797069063830835)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1880550516874542298159524),(-1880550516874542237224063)⟩,⟨(-1589485587826975528121275),(-1589485587826975467129158)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-2891978103190357074584543),(-2891978103190357035802188)⟩,⟨418456206204811783591956,418456206204811822411358⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-1673035377158008107539589),(-1673035377158008083380582)⟩,⟨2844524172717912288077282,2844524172717912312166368⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1318290881567759877694189,1318290881567759890819606⟩,⟨3294473773405713310812966,3294473773405713323931467⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨3473193786414743179709977,3473193786414743187508040⟩,⟨1056874479856993141176036,1056874479856993149005261⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3009558874068921233442235,3009558874068921238664437⟩,⟨(-1835055669652588980568787),(-1835055669652588975326976)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨845264963217853186096947,845264963217853189212916⟩,⟨(-3113730890041282418907245),(-3113730890041282415835991)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1012684167957433165631476),(-1012684167957433163846867)⟩,⟨(-2548221414150162708807796),(-2548221414150162707012205)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1614547444628631727054296),(-1614547444628631726022397)⟩,⟨(-1329484989806757210466399),(-1329484989806757209428410)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1233566286327171827294195),(-1233566286327171826819033)⟩,⟨(-440806779046937598106910),(-440806779046937597642534)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-439592241168685621560719),(-439592241168685621430690)⟩,⟨(-74291887527111555898760),(-74291887527111555775392)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-14949346569452649207605),(-14949346569452637812731)⟩,⟨9537295293389948324378,9537295293389959717995⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-41586059152968450449946),(-41586059152968403800224)⟩,⟨36911827849068767596543,36911827849068814242653⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-51267529231439080486104),(-51267529231438932455796)⟩,⟨86782810533463307270446,86782810533463455296990⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-12465739513919195986976),(-12465739513918769863992)⟩,⟨158063698543385957684680,158063698543386383808786⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨113421257261125346600585,113421257261126300753501⟩,⟨204895620618719527372887,204895620618720481538923⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨309659840605137138908268,309659840605139930393703⟩,⟨120285216348168204114109,120285216348170995607959⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨416744101558135843540059,416744101558141161755873⟩,⟨(-181426692522076828403917),(-181426692522071510207699)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨189075979269037363189649,189075979269046886807604⟩,⟨(-567069313689853961600369),(-567069313689844437997033)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-386248698996452434161538),(-386248698996441425858331)⟩,⟨(-642829495750730085809690),(-642829495750719077474424)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-875150613580508213122525),(-875150613580496422754532)⟩,⟨(-156263867277338155934922),(-156263867277326365552585)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-794592255419912906737859),(-794592255419905158130920)⟩,⟨582369010848286639757198,582369010848294388323486⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-205508253753479325276861),(-205508253753474318713745)⟩,⟨987058461923130897545564,987058461923135904087285⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨383635337531748377119821,383635337531750961217529⟩,⟨854448649053094646309353,854448649053097230429086⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨606367351386979157058265,606367351386980162598770⟩,⟨464292100654734165560352,464292100654735171135452⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨476296320178183253329897,476296320178183747796343⟩,⟨153197220408660598813215,153197220408661093294367⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨172580285536965251323846,172580285536965395982546⟩,⟨23692363758759003794733,23692363758759148456590⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-223066579464542965687),(-223066579464542949628)⟩,⟨(-320497000605300999437),(-320497000605300983370)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-846234574060050987251),(-846234574060050933858)⟩,⟨(-915936867591727464414),(-915936867591727411015)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1998091997659357365440),(-1998091997659357252617)⟩,⟨(-1234625768189268614166),(-1234625768189268501411)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-3878487750615908717108),(-3878487750615908491893)⟩,⟨(-616558428360292084018),(-616558428360291859124)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-5937012380457097700322),(-5937012380457097252478)⟩,⟨2154194304210390364269,2154194304210390811621⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-5835903563131764460330),(-5835903563131763576535)⟩,⟨8085919646019095010657,8085919646019095894456⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨687290713039582184547,687290713039583894270⟩,⟨15440283253478002314151,15440283253478004025061⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨16141608724036987034140,16141608724036990230091⟩,⟨16834244511308939895419,16834244511308943092184⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨33800862190476626692978,33800862190476632353068⟩,⟨2067537537296273126151,2067537537296278784507⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨36225082701853667888951,36225082701853677428147⟩,⟨(-29406262343786762141468),(-29406262343786752604538)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨10633993519907386413785,10633993519907402376237⟩,⟨(-59104337816216770183385),(-59104337816216754219456)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-32114221182330150396929),(-32114221182330122757520)⟩,⟨(-63178777180116722920498),(-63178777180116695276843)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-63949642057655515531536),(-63949642057655459414351)⟩,⟨(-38700490871273398494404),(-38700490871273342375826)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-67150497746660246808481),(-67150497746660159590831)⟩,⟨(-7074912671636164763568),(-7074912671636077547289)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-46569383211153805536012),(-46569383211153722706838)⟩,⟨9358350701823791620156,9358350701823874447258⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-16091661528590869648589),(-16091661528590836237730)⟩,⟨5930632401676225649297,5930632401676259059235⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-3578274181466899062),(-3578274181466888959)⟩,⟨(-3306693328016719067),(-3306693328016708964)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-12549416205426829299),(-12549416205426805003)⟩,⟨(-9332160360504761242),(-9332160360504736947)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-27008891254506592617),(-27008891254506567911)⟩,⟨(-12387399432799442769),(-12387399432799418069)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-49789158803334827886),(-49789158803334808239)⟩,⟨(-6238515490518771120),(-6238515490518751478)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-78587652997965903304),(-78587652997965890051)⟩,⟨21557722441404657414,21557722441404670662⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-96478532361612542438),(-96478532361612535206)⟩,⟨87414762365380813478,87414762365380820711⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-61685034688690375380),(-61685034688690369095)⟩,⟨196045496433005613373,196045496433005619683⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨84172106138911410457,84172106138911420983⟩,⟨307635945682556279943,307635945682556290494⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨363866481346725932601,363866481346725952256⟩,⟨314071475047011640247,314071475047011659883⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨686186851957169484943,686186851957169519910⟩,⟨85643385511594633364,85643385511594668249⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨843204722645681976114,843204722645682033004⟩,⟨(-393577611613167315199),(-393577611613167258355)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨667439241662458920641,667439241662459002882⟩,⟨(-929637539222346247711),(-929637539222346165432)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨226276064401692844026,226276064401692946300⟩,⟨(-1229688693505475632131),(-1229688693505475529732)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-194829294389655270109),(-194829294389655165549)⟩,⟨(-1145359335817015804134),(-1145359335817015699468)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-334147570107090760913),(-334147570107090681167)⟩,⟨(-764151156006147268918),(-764151156006147189124)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-155761455517680277893),(-155761455517680248001)⟩,⟨(-261484882148322388161),(-261484882148322358256)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-75475546586878050),(-75475546586877319)⟩,⟨(-15814757746178735),(-15814757746178005)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-242234219860106751),(-242234219860103969)⟩,⟨(-24937508192866230),(-24937508192863449)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-447239430611127544),(-447239430611120205)⟩,⟨46350139663281563,46350139663288903⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-675360135107868942),(-675360135107844372)⟩,⟨289326020952543217,289326020952567784⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-816855957227103984),(-816855957227021554)⟩,⟨823005143443003385,823005143443085815⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-591373306138640796),(-591373306138407675)⟩,⟨1715676454082105210,1715676454082338333⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨464245454584632406,464245454585119150⟩,⟨2785142451066906241,2785142451067392981⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨2769151437501525273,2769151437502336684⟩,⟨3336101273581874994,3336101273582686409⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨6127555535654501638,6127555535655933662⟩,⟨2148502125451040545,2148502125452472566⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨9163468663691351256,9163468663692972919⟩,⟨(-1836692682571879874),(-1836692682570258208)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨9658910641402864508,9658910641404023764⟩,⟨(-8247110292500180205),(-8247110292499020947)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨6256322008545687917,6256322008546513319⟩,⟨(-14657724614393527569),(-14657724614392702167)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨224756938306715383,224756938307273693⟩,⟨(-17880258624712405218),(-17880258624711846907)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-4906019775783787218),(-4906019775783488760)⟩,⟨(-16333519670415762463),(-16333519670415464006)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-5979031805305520200),(-5979031805305386929)⟩,⟨(-10959084561363375851),(-10959084561363242579)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-2616257568636318128),(-2616257568636281194)⟩,⟨(-3786337553204500321),(-3786337553204463384)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-559524581502544),(-559524581502528)⟩,⟨481995721691303,481995721691319⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1576260523663352),(-1576260523663336)⟩,⟨1714762379660728,1714762379660744⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-2144288095752351),(-2144288095752335)⟩,⟨3759482780044659,3759482780044675⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-1487455164573337),(-1487455164573321)⟩,⟨7078074519470851,7078074519470867⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1850780293429301,1850780293429317⟩,⟨11634666183254091,11634666183254107⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨9930877608367172,9930877608367188⟩,⟨16000272062450122,16000272062450138⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨24394226492102624,24394226492102640⟩,⟨16260128308052140,16260128308052157⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨43968406172832222,43968406172832238⟩,⟨5886078815286877,5886078815286893⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨61486962148306338,61486962148306356⟩,⟨(-21577323049074651),(-21577323049074635)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨63999651000575052,63999651000575072⟩,⟨(-66466439062443067),(-66466439062443048)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨39800404285868964,39800404285869011⟩,⟨(-117502645605684477),(-117502645605684430)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-9795815600490292),(-9795815600490105)⟩,⟨(-154199518844173485),(-154199518844173301)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-64720200751447965),(-64720200751447404)⟩,⟨(-159229815660798181),(-159229815660797617)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-95823602534631559),(-95823602534630489)⟩,⟨(-130797853133567361),(-130797853133566290)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-84125557536479087),(-84125557536477909)⟩,⟨(-81944399757915624),(-81944399757914443)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-33222596855546381),(-33222596855545852)⟩,⟨(-27324711654841405),(-27324711654840873)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨52261922269665791495862,52261922269675855673426⟩,⟨(-856647369022512218609406),(-856647369022502154436645)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 27) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_27 (tableDensity false) (fullFactor true 1 27) density0_contains hk1_1_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨193388578819572139883676,193388578819572198006638⟩,⟨(-82285009575875532016923),(-82285009575875473924071)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_27 1 27 ha1_1_27_contains + def realAnswer : RBox := ⟨245650501089237831379538,245650501089248153680064⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_27 +namespace hm1_1_1_27 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_27 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨33671695354263039628963,33671695354263118939048⟩,⟨5591117227854523074766,5591117227854602384259⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨104117878716263622516666,104117878716263817559925⟩,⟨(-951885663541314779970),(-951885663541119736880)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨166996701298839560290995,166996701298839757923379⟩,⟨(-60855812810298510210601),(-60855812810298312573218)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨167503775770887877243712,167503775770887991338783⟩,⟨(-189610081493534100647552),(-189610081493533986538484)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨24276450122420385034321,24276450122420450491822⟩,⟨(-323408614302657718980319),(-323408614302657653518339)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-254748196476450863390467),(-254748196476450840091921)⟩,⟨(-293033274441092664894840),(-293033274441092641615391)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-448223589402486457385146),(-448223589402486448054621)⟩,⟨22409123755118964317731,22409123755118973640412⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-268648209293077131386211),(-268648209293077126932980)⟩,⟨434898881102492355927667,434898881102492360405979⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨231393627357940848863008,231393627357940851274068⟩,⟨522576196804308596026746,522576196804308598441286⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨598718825544709413220454,598718825544709414731602⟩,⟨138979648955227618687571,138979648955227620164942⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨505456073128872973517717,505456073128872974614244⟩,⟨(-362739058392437957166424),(-362739058392437956065533)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨111992074715315279148622,111992074715315279818624⟩,⟨(-571783940197669543252646),(-571783940197669542557463)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-216234317107027319387934),(-216234317107027318945183)⟩,⟨(-448316625947851316824558),(-448316625947851316368562)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-310220684067202880174826),(-310220684067202879893567)⟩,⟨(-216662175123587349712826),(-216662175123587349438868)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-228766037919445742617802),(-228766037919445742479508)⟩,⟨(-58800560335773516441485),(-58800560335773516317109)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-80114360654446531061948),(-80114360654446531022480)⟩,⟨(-5381103387423977648336),(-5381103387423977615187)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-2758321599489405046067),(-2758321599489397253489)⟩,⟨199571188491166243775,199571188491174036512⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-8304070664470723271263),(-8304070664470689990581)⟩,⟨2053558300801816350785,2053558300801849631925⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-12663644023826738040107),(-12663644023826625889197)⟩,⟨8293536929665964116512,8293536929666076267904⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-10986957802456658664455),(-10986957802456324136555)⟩,⟨20399703467101405236824,20399703467101739764615⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨4903931999774589868251,4903931999775349825194⟩,⟨33177679301859126883580,33177679301859886838929⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨37221728055203437886487,37221728055205701491534⟩,⟨29280778925530039164064,29280778925532302768011⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨64561917780618148694575,64561917780622484285952⟩,⟨(-11282419964488178908993),(-11282419964483843315259)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨43007086711629456582529,43007086711637252401275⟩,⟨(-76884797319060419210628),(-76884797319052623389888)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-43676413547414811046493),(-43676413547405805939443)⟩,⟨(-105022787820352540472074),(-105022787820343535369090)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-133916779514621677362332),(-133916779514612040634442)⟩,⟨(-39962581820874545534225),(-39962581820864908808348)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-138499994454290516111378),(-138499994454284224086245)⟩,⟨83447527362955210193021,83447527362961502223850⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-49047414456976161558273),(-49047414456972123651369)⟩,⟨166183265005922281346594,166183265005926319256539⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨55077185503623355071845,55077185503625413404099⟩,⟨158302872434398804590939,158302872434400862919894⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨102614045221462895242024,102614045221463675152530⟩,⟨96239305970740235423733,96239305970741015328966⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨85475562836418876867972,85475562836419256820914⟩,⟨38509907560430228830658,38509907560430608781295⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨31820584828277730373648,31820584828277840800442⟩,⟨8313932807453072578743,8313932807453183005031⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4971271364729115519),(-4971271364729110564)⟩,⟨(-88018777344119719457),(-88018777344119714502)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-53167048404428761053),(-53167048404428744446)⟩,⟨(-276856256286688526408),(-276856256286688509801)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-230351732405552454338),(-230351732405552420143)⟩,⟨(-477035554090301612517),(-477035554090301578324)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-642701553338406044339),(-642701553338405979772)⟩,⟨(-589957604598808927373),(-589957604598808862820)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1311591843649820015181),(-1311591843649819896651)⟩,⟨(-337748007943202366482),(-337748007943202247972)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1908733902825823182450),(-1908733902825822970991)⟩,⟨688741106776299625790,688741106776299837251⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1506225070304772427000),(-1506225070304772061717)⟩,⟨2566300727812961100923,2566300727812961466250⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨986646229429688215060,986646229429688827461⟩,⟨4189415551998210810727,4189415551998211423158⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨5216413538137620815985,5216413538137621811687⟩,⟨3187439917137216433013,3187439917137217428667⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨8150184731742384958125,8150184731742386676137⟩,⟨(-1901293808074450378122),(-1901293808074448660166)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨6178863378817414268555,6178863378817418129588⟩,⟨(-8774730798992284363344),(-8774730798992280502300)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-489209293136715874762),(-489209293136705613340)⟩,⟨(-12481893453243378961395),(-12481893453243368699936)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-7226438939219921038346),(-7226438939219889491001)⟩,⟨(-10585164213237072266322),(-10585164213237040718952)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-9710080649099130982518),(-9710080649099073399939)⟩,⟨(-5580229298005239043633),(-5580229298005181461054)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-7510360196980673713880),(-7510360196980615945799)⟩,⟨(-1541898033206816323929),(-1541898033206758555847)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2726789038022143415557),(-2726789038022119727304)⟩,⟨(-98808493151126877185),(-98808493151103188929)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-298132145197207451),(-298132145197198982)⟩,⟨(-1601097915948570805),(-1601097915948562333)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-1461601532644562234),(-1461601532644541903)⟩,⟨(-4936716177060088128),(-4936716177060067796)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-4513867674431525937),(-4513867674431505376)⟩,⟨(-8362409019309732587),(-8362409019309712024)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-11124928273741421305),(-11124928273741405185)⟩,⟨(-10721794008243855943),(-10721794008243839821)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-22594366253139360584),(-22594366253139350164)⟩,⟨(-8568348641085776190),(-8568348641085765768)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-37241190516617869830),(-37241190516617865099)⟩,⟨4568401117527535094,4568401117527539827⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-45802092012521437283),(-45802092012521434617)⟩,⟨35810329321205115362,35810329321205118025⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-28889170073018642359),(-28889170073018638632)⟩,⟨84083118827615417743,84083118827615421470⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨34130732849319724666,34130732849319731439⟩,⟨127457551022922131946,127457551022922138720⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨140751133676940153090,140751133676940165126⟩,⟨123026068458302693597,123026068458302705641⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨245945478831057810099,245945478831057829811⟩,⟨37185828771427864197,37185828771427883914⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨284022977605526862604,284022977605526891404⟩,⟨(-110564079400096591287),(-110564079400096562494)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨227838101665185262888,227838101665185299229⟩,⟨(-244450085732358999492),(-244450085732358963164)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨120204345170618890176,120204345170618927923⟩,⟨(-288766251400966501951),(-288766251400966464216)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨33446814402265368635,33446814402265397810⟩,⟨(-223684505337101554062),(-223684505337101524891)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1891236431722571717,1891236431722582745⟩,⟨(-82876106927662567712),(-82876106927662556686)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-25032853409092671),(-25032853409092069)⟩,⟨(-3920239747310841),(-3920239747310240)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-81538913846774481),(-81538913846772188)⟩,⟨(-4920022841018160),(-4920022841015871)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-154773917681897934),(-154773917681891899)⟩,⟨19164279098954025,19164279098960062⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-243623067534409122),(-243623067534388918)⟩,⟨99347811405390433,99347811405410634⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-315928736114068681),(-315928736114000900)⟩,⟨281315558539708517,281315558539776299⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-278536663628578004),(-278536663628386321)⟩,⟨605429306045429081,605429306045620767⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨40403944597114336,40403944597514463⟩,⟨1043311217575142527,1043311217575542657⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨839230156632139569,839230156632806251⟩,⟨1397032600019379088,1397032600020045770⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨2164674613408055834,2164674613409231474⟩,⟨1251933672707633051,1251933672708808688⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨3677788522859132984,3677788522860462896⟩,⟨149757073153683282,149757073155013192⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨4641902449230854537,4641902449231804011⟩,⟨(-1977776800943800958),(-1977776800942851486)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨4374199993031056460,4374199993031731502⟩,⟨(-4457855662865106870),(-4457855662864431825)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨2894487935773940299,2894487935774396274⟩,⟨(-6123150805175034955),(-6123150805174578981)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1063043400607991049,1063043400608234475⟩,⟨(-6104016442153025542),(-6104016442152782118)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-84188116673431866),(-84188116673323301)⟩,⟨(-4380468116453235829),(-4380468116453127265)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-188955757821446265),(-188955757821416199)⟩,⟨(-1573885920466698632),(-1573885920466668565)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-15931784261957),(-15931784261941)⟩,⟨15110771913107,15110771913123⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-31931633880458),(-31931633880442)⟩,⟨59927534655212,59927534655228⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨35586432224808,35586432224824⟩,⟨126745470386647,126745470386663⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨366377869997447,366377869997463⟩,⟨135359375399005,135359375399021⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1304272411199383,1304272411199399⟩,⟨(-211502262934088),(-211502262934072)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨3253420618668217,3253420618668233⟩,⟨(-1644239630703888),(-1644239630703872)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨6222001924334133,6222001924334149⟩,⟨(-5551947160443305),(-5551947160443289)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨8982418021253028,8982418021253044⟩,⟨(-13832896121604872),(-13832896121604856)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨8346364706351312,8346364706351328⟩,⟨(-27726791250375256),(-27726791250375240)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-200060131522269),(-200060131522249)⟩,⟨(-45603218057077337),(-45603218057077317)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-19405060693641738),(-19405060693641698)⟩,⟨(-61455598177351908),(-61455598177351868)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-45988448902614324),(-45988448902614170)⟩,⟨(-67036698909239682),(-67036698909239530)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-69378646780582282),(-69378646780581818)⟩,⟨(-57994410514266139),(-57994410514265676)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-76475589109449838),(-76475589109448960)⟩,⟨(-38627426580560136),(-38627426580559258)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-59805986967156305),(-59805986967155337)⟩,⟨(-18840242568263451),(-18840242568262484)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-22596514560703251),(-22596514560702813)⟩,⟨(-5088134855896030),(-5088134855895593)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨25027667423270840033115,25027667423278978994862⟩,⟨(-171422228498372819473602),(-171422228498364680511906)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_27 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 27) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_27 (tableDensity true) (fullFactor true 1 27) density1_contains hk1_1_27_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-252892756917902105085603),(-252892756917902029078654)⟩,⟨107603474060760235131477,107603474060760311099054⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_27 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 27) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_27 1 27 ha1_1_27_contains + def realAnswer : RBox := ⟨(-227865089494631365052488),(-227865089494622950083792)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 27) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_27 +namespace hm1_0_1_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-53854958922004758186032),(-53854958922004731872602)⟩,⟨(-28158976001996137300022),(-28158976001996110984211)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-177138881705246873677534),(-177138881705246802629003)⟩,⟨(-53288736560268696602382),(-53288736560268625548577)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-315641643662472798286434),(-315641643662472712990879)⟩,⟨25209827714546833426968,25209827714546918724795⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-374181841613699917942243),(-374181841613699856788519)⟩,⟨266503229708543247569594,266503229708543308713967⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-162676422626974675856477),(-162676422626974640485615)⟩,⟨591645337230813252964238,591645337230813288318256⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨392003670806887872392328,392003670806887895650668⟩,⟨666898285039798593596653,666898285039798616860105⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨915550021154050553804764,915550021154050568610067⟩,⟨142244684400505729975184,142244684400505744802604⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨747340190615813312397151,747340190615813321743291⟩,⟨(-745546335427885475517347),(-745546335427885466187020)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-193587583849867366543688),(-193587583849867361611195)⟩,⟨(-1127569587283666159148972),(-1127569587283666154224678)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-1054722223221345980439250),(-1054722223221345977568036)⟩,⟨(-525217380797652085631510),(-525217380797652082752976)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1048685126457292328973382),(-1048685126457292327105074)⟩,⟨471783919585599539347579,471783919585599541225264⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-364199567288018386654665),(-364199567288018385566121)⟩,⟨991727750223405614223838,991727750223405615298438⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨286402916735549771345097,286402916735549771953249⟩,⟨853332202758945218093660,853332202758945218704622⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨517924451114378831279785,517924451114378831628400⟩,⟨452219351908485486565152,452219351908485486915954⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨404185943091601231602958,404185943091601231762713⟩,⟨149590062275991813538820,149590062275991813695085⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨144617064144786281614242,144617064144786281657696⟩,⟨24778296293160752173921,24778296293160752215185⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨4388623922696449703957,4388623922696453678764⟩,⟨1067202620343478779686,1067202620343482754523⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨14175057961793116951195,14175057961793132320654⟩,⟨1058895661013622977389,1058895661013638346701⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨25155124520991576116862,25155124520991614751026⟩,⟨(-6381565219952303801515),(-6381565219952265168425)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨30994868195855123039673,30994868195855217494831⟩,⟨(-27216778542615366176507),(-27216778542615271723865)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨14889946137850029808080,14889946137850337435842⟩,⟨(-59907005210692602417025),(-59907005210692294789961)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-40891828103664851103247),(-40891828103664189769877)⟩,⟨(-78950027917253342909162),(-78950027917252681571295)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-118847811895506310824513),(-118847811895504684788425)⟩,⟨(-34345789972119737444969),(-34345789972118111406540)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-137573586320794355415027),(-137573586320791965963240)⟩,⟨92152260966665638266937,92152260966668027710860⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-17536084432962224004057),(-17536084432958694166940)⟩,⟨210712790348978133356018,210712790348981663191854⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨183751166167605860386761,183751166167608855732819⟩,⟨176714505235847730154382,176714505235850725512083⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨286118648547712851881608,286118648547715448420819⟩,⟨(-22067713345611117036797),(-22067713345608520498169)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨198513869644258724723425,198513869644260037358133⟩,⟨(-221927026884407158765237),(-221927026884405846143754)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨21131980075479615593831,21131980075480418209224⟩,⟨(-278991805352197207008603),(-278991805352196404396773)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-98276951157420289457833),(-98276951157419916021463)⟩,⟨(-208114906523982812093278),(-208114906523982438651624)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-108641308206305381472059),(-108641308206305244429759)⟩,⟨(-105848471690460010680891),(-105848471690459873632024)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-44016050476785650590130),(-44016050476785614165653)⟩,⟨(-29467115480993746833276),(-29467115480993710406386)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-35880872679072387287),(-35880872679072382729)⟩,⟨73194650622998137283,73194650622998141839⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-80613613664545620045),(-80613613664545604855)⟩,⟨248527947148651151869,248527947148651167073⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-16700765700875346835),(-16700765700875314434)⟩,⟨495373752732582662950,495373752732582695398⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨306441984934347294126,306441984934347359783⟩,⟨779385285682461987357,779385285682462053074⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨1066229207629044472124,1066229207629044605059⟩,⟨852248333275894671899,852248333275894804834⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2185990413187038322224,2185990413187038590095⟩,⟨125656677628395589775,125656677628395857478⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨2782660179125669997105,2782660179125670527919⟩,⟨(-2046794398924165072716),(-2046794398924164542070)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1017952178945342192970,1017952178945343207193⟩,⟨(-5213884690995701654985),(-5213884690995700640526)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-4293398383104624281252),(-4293398383104622442846)⟩,⟨(-6589558535807426961216),(-6589558535807425122358)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-10767084984522653574003),(-10767084984522650431690)⟩,⟨(-2467177618757151884121),(-2467177618757148742088)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-12636376527192653011363),(-12636376527192647857131)⟩,⟨7066723534978677816129,7066723534978682969501⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-6608093000333312730158),(-6608093000333303637123)⟩,⟨16063511602457959235916,16063511602457968328919⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨3425106065972387216865,3425106065972401958409⟩,⟨18259888973514299357906,18259888973514314100349⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨10135757304131163774621,10135757304131185463276⟩,⟨13609121728291090768232,13609121728291112457762⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨9813812609556297962493,9813812609556322334184⟩,⟨6955251941185957782541,6955251941185982154547⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨3913895485594960584097,3913895485594971510570⟩,⟨1920687429792375216971,1920687429792386143498⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-351619437940473814),(-351619437940472356)⟩,⟨770286226526633892,770286226526635351⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-853692227959877160),(-853692227959873615)⟩,⟨2589711924926205342,2589711924926208886⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-534266224391100742),(-534266224391096075)⟩,⟨5186855081830485292,5186855081830489961⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1871046667180954534,1871046667180958673⟩,⟨8689270060499328494,8689270060499332632⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨8447617632418626768,8447617632418629298⟩,⟨11919953413091509657,11919953413091512188⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨21094437884008368686,21094437884008370051⟩,⟨10752915025619323143,10752915025619324508⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨37877132254195616890,37877132254195618359⟩,⟨(-2834817882235263065),(-2834817882235261602)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨47220775767658597706,47220775767658600297⟩,⟨(-36972917044583177807),(-36972917044583175219)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨26883520927642395806,26883520927642400757⟩,⟨(-87997573513269491874),(-87997573513269486918)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-41081077216165919139),(-41081077216165910105)⟩,⟨(-128329306747100540291),(-128329306747100531250)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-143115089046960998874),(-143115089046960983829)⟩,⟨(-116305525963349933138),(-116305525963349918096)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-227571413263656628072),(-227571413263656605828)⟩,⟨(-35508252229175341550),(-35508252229175319331)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-243608974051905390779),(-243608974051905362611)⟩,⟨75343655517864613837,75343655517864641988⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-188920702283560555365),(-188920702283560526187)⟩,⟨147106120967447911903,147106120967447941076⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-105836481504868674241),(-105836481504868651795)⟩,⟨137023334833861500939,137023334833861523389⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-31988358139917367971),(-31988358139917359516)⟩,⟨54761392057257432104,54761392057257440564⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-401957832930306),(-401957832930196)⟩,⟨11418266323637812,11418266323637922⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨2578954745476469,2578954745476853⟩,⟨36088486619810021,36088486619810398⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨18710159511571706,18710159511572921⟩,⟨64517148819377910,64517148819379125⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨61672522990716610,61672522990720702⟩,⟨91880237376671663,91880237376675754⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨147057170526172885,147057170526185892⟩,⟨97553672136704495,97553672136717502⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨277453631021146100,277453631021180690⟩,⟨34771816765476789,34771816765511379⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨408854707205092290,408854707205159791⟩,⟨(-165765721735795404),(-165765721735727905)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨413015255557889004,413015255558034187⟩,⟨(-549853290867910914),(-549853290867765729)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨93214241746910394,93214241747147754⟩,⟨(-1041898345169673282),(-1041898345169435922)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-678841223664479523),(-678841223664237088)⟩,⟨(-1370106555977812117),(-1370106555977569680)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-1754384199771516707),(-1754384199771329228)⟩,⟨(-1170362450237578905),(-1170362450237391424)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-2664462876016210853),(-2664462876016052902)⟩,⟨(-308467716919223708),(-308467716919065757)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-2920774059400805949),(-2920774059400708788)⟩,⟨859686007668151094,859686007668248256⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-2420294208374036953),(-2420294208373988831)⟩,⟨1652526273770648486,1652526273770696607⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-1484547125010936159),(-1484547125010915958)⟩,⟨1567590984331258736,1567590984331278937⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-483247342944941300),(-483247342944935893)⟩,⟨635699780537014235,635699780537019638⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨65989250370727,65989250370743⟩,⟨68933639343591,68933639343607⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨232923715030906,232923715030922⟩,⟨191739574224902,191739574224918⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨504828731973231,504828731973247⟩,⟨249814974953024,249814974953040⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨938277417745442,938277417745460⟩,⟨134307038666977,134307038666993⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1516537509999134,1516537509999150⟩,⟨(-355965154897760),(-355965154897744)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨2022242857536941,2022242857536957⟩,⟨(-1497979218432501),(-1497979218432484)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨1884920491338254,1884920491338270⟩,⟨(-3488187147970071),(-3488187147970054)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨178402345707642,178402345707660⟩,⟨(-6074513162095878),(-6074513162095862)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3957760110034850),(-3957760110034834)⟩,⟨(-8134968024576616),(-8134968024576600)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-10414395461287449),(-10414395461287432)⟩,⟨(-7749044211487277),(-7749044211487260)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-17362111221176622),(-17362111221176600)⟩,⟨(-3318238127422028),(-3318238127422010)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-21776578640323652),(-21776578640323610)⟩,⟨4667517517251777,4667517517251822⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-21432379282066053),(-21432379282065957)⟩,⟨12914369306834202,12914369306834296⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-16656138681111976),(-16656138681111817)⟩,⟨16988812697370806,16988812697370971⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-9848551402346917),(-9848551402346741)⟩,⟨14255568992339059,14255568992339231⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-3152277691527016),(-3152277691526932)⟩,⟨5528754590957508,5528754590957593⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-20661696435976089233251),(-20661696435973196947434)⟩,⟨269136366855827260243635,269136366855830152528158⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 28) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_28 (tableDensity false) (fullFactor true 1 28) density0_contains hk1_1_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-73805630219023571190789),(-73805630219023548456638)⟩,⟨21232325072263367358745,21232325072263390082958⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_28 1 28 ha1_1_28_contains + def realAnswer : RBox := ⟨(-94467326654999760424040),(-94467326654996645404072)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_28 +namespace hm1_1_1_28 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_28 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-8494299691821416460945),(-8494299691821396535458)⟩,⟨(-5988852999199872332305),(-5988852999199852407394)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-28858556282810164984348),(-28858556282810111401025)⟩,⟨(-13320088008065520724113),(-13320088008065467142082)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-54359747554987180302672),(-54359747554987117168543)⟩,⟨(-4159984073791766239524),(-4159984073791703105947)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-70539422325665964795204),(-70539422325665923433725)⟩,⟨33589783058054454388093,33589783058054495752320⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-43743215024440491103338),(-43743215024440472633945)⟩,⟨91001052692542633658137,91001052692542652132146⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨44996353020765280481753,44996353020765288873213⟩,⟨113361247135425952149708,113361247135425960538339⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨137915319851747116757103,137915319851747120013437⟩,⟨34900147685611457406158,34900147685611460656499⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨118195382463835100373666,118195382463835102069802⟩,⟨(-112940307119168987107230),(-112940307119168985405433)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-37766042008543409341023),(-37766042008543408459321)⟩,⟨(-180325426598836189736494),(-180325426598836188849923)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-184147927617934431869460),(-184147927617934431322153)⟩,⟨(-76671475383873661042835),(-76671475383873660506103)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-178332250877483913780209),(-178332250877483913393974)⟩,⟨96912020522588718001767,96912020522588718387297⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-52771547100261160443487),(-52771547100261160211049)⟩,⟨183346381437531949666799,183346381437531949907059⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨62865044683062736416616,62865044683062736564733⟩,⟨150808179756351953021846,150808179756351953174979⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨99880234379466660134919,99880234379466660229048⟩,⟨74143481153433941123124,74143481153433941215215⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨75040672346541301579007,75040672346541301625178⟩,⟨20192258771708095183736,20192258771708095225409⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨26362069412767331885498,26362069412767331898615⟩,⟨1830801075560132094705,1830801075560132105745⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨522915666082799514901,522915666082802215567⟩,⟨471930313775645529853,471930313775648230514⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨1854957230586291541659,1854957230586302342801⟩,⟨1157954022761283986108,1157954022761294787265⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨3812555486735098460910,3812555486735126714013⟩,⟨808395178756743766344,808395178756772019574⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨5748518667478611582047,5748518667478683241762⟩,⟨(-1811436742334103291478),(-1811436742334031631448)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨5008195300933140499037,5008195300933384109154⟩,⟨(-7283115257041659963088),(-7283115257041416352871)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2293256492222063704244),(-2293256492221533574886)⟩,⟨(-12464157359548020267454),(-12464157359547490138643)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-15489630755901170437421),(-15489630755899849730325)⟩,⟨(-8843802496205605095235),(-8843802496204284388460)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-22454365838293107400492),(-22454365838291163256325)⟩,⟨9550981402304174876878,9550981402306119022023⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-7304573210931715479633),(-7304573210928835673566)⟩,⟨31223824533230979278918,31223824533233859085202⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨25564269608375022128155,25564269608377453897402⟩,⟨30862922646139814710920,30862922646142246478598⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨47097466566322940814475,47097466566325041881661⟩,⟨616536496383226132073,616536496385327199339⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨37113062006756571188782,37113062006757616659689⟩,⟨(-35233149546577812643990),(-35233149546576767171160)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨8111813522160831848002,8111813522161464427484⟩,⟨(-49410330196648659842268),(-49410330196648027262269)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-14192237639427831692831),(-14192237639427543700221)⟩,⟨(-39952032013475280191269),(-39952032013474992199466)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-18010723595820461330698),(-18010723595820359462153)⟩,⟨(-21986673618594326858017),(-21986673618594224990494)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-7590135860453096059029),(-7590135860453069556215)⟩,⟨(-6511637350739831812562),(-6511637350739805310124)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-15559517632660274180),(-15559517632660272766)⟩,⟨9828709280086231174,9828709280086232585⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-45138886700150158084),(-45138886700150153356)⟩,⟨38097272707629898901,38097272707629903630⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-63230425541956923682),(-63230425541956913859)⟩,⟨92190919521271473592,92190919521271483416⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-38857692423262709605),(-38857692423262690769)⟩,⟨181937617918743681145,181937617918743699985⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨85462677942862086699,85462677942862121888⟩,⟨279945676102528289936,279945676102528325124⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨352817636934502777893,352817636934502841875⟩,⟨272036355361049829194,272036355361049893170⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨663816366365704814562,663816366365704927838⟩,⟨(-39156115738371519047),(-39156115738371405777)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨650672538998209934648,650672538998210128524⟩,⟨(-733097821748680227629),(-733097821748680033747)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-127733589400235562056),(-127733589400235240287)⟩,⟨(-1413848801218955965963),(-1413848801218955644178)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1543141675742916046310),(-1543141675742915499775)⟩,⟨(-1242541914466968928116),(-1242541914466968381587)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-2580102538129729776899),(-2580102538129728684193)⟩,⟨192327133516816011696,192327133516817104393⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-2241230295503424105125),(-2241230295503420937569)⟩,⟨2085373531333554299273,2085373531333557466825⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-763942723210304373605),(-763942723210297343264)⟩,⟨3092426561512872280124,3092426561512879310473⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨623781749677131162706,623781749677144031745⟩,⟨2744358443423153209184,2744358443423166078230⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨1020459431716677391712,1020459431716693759084⟩,⟨1651670369435892662196,1651670369435909029569⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨460119822794976217985,460119822794983848249⟩,⟨519078159131168444818,519078159131176075081⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-248140486977481901),(-248140486977480678)⟩,⟨136153086853181638,136153086853182860⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-736393756039794343),(-736393756039791381)⟩,⟨513386297271452974,513386297271455934⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-1134810496694158179),(-1134810496694154295)⟩,⟨1221854454038338930,1221854454038342815⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-1141454068583055804),(-1141454068583052409)⟩,⟨2487338785501105574,2487338785501108968⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-59256847873600000),(-59256847873598035)⟩,⟨4331613200669713988,4331613200669715955⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨3182772667735558894,3182772667735559729⟩,⟨6035511160587369718,6035511160587370554⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨9283063036350702039,9283063036350702641⟩,⟨5410327930007935150,5410327930007935752⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨16680876836593071576,16680876836593072496⟩,⟨(-1106580489448992603),(-1106580489448991684)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨19684148247403378246,19684148247403379959⟩,⟨(-15826908204667606360),(-15826908204667604650)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨10217870357548115715,10217870357548118840⟩,⟨(-34962530191495115244),(-34962530191495112119)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-14643448047260189631),(-14643448047260184410)⟩,⟨(-47069410997217760102),(-47069410997217754880)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-45640788644150375915),(-45640788644150368128)⟩,⟨(-40981520507751241541),(-40981520507751233754)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-65711495532262863225),(-65711495532262853222)⟩,⟨(-18066023185229786508),(-18066023185229776503)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-64149181923950955644),(-64149181923950945112)⟩,⟨6349782989809335741,6349782989809346273⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-44065859427257364818),(-44065859427257356596)⟩,⟨16208535783516364783,16208535783516372998⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-15304879853341959720),(-15304879853341956592)⟩,⟨8008133048698023099,8008133048698026226⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨60125652112786,60125652112877⟩,⟨3753608610730726,3753608610730822⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1376574124634255,1376574124634569⟩,⟨12058657772071848,12058657772072166⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨6934468437163783,6934468437164783⟩,⟨22244817762383088,22244817762384087⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨21504599349380498,21504599349383864⟩,⟨33286163493813390,33286163493816757⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨51355297616547610,51355297616558305⟩,⟨38829484979742859,38829484979753554⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨100125803540064802,100125803540093243⟩,⟨22807177543879975,22807177543908417⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨157716077627743418,157716077627798909⟩,⟨(-41737626838237115),(-41737626838181624)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨184740226762764250,184740226762883537⟩,⟨(-180830819092261773),(-180830819092142484)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨109930674989838250,109930674990033117⟩,⟨(-387592818826117339),(-387592818825922470)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-132284379802031044),(-132284379801832221)⟩,⟨(-587570987754786668),(-587570987754587845)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-525856433792704496),(-525856433792550951)⟩,⟨(-652326362824156449),(-652326362824002904)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-928541639529450032),(-928541639529320851)⟩,⟨(-492724967575459900),(-492724967575330719)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-1141449452893903199),(-1141449452893823844)⟩,⟨(-164155567586660056),(-164155567586580704)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-1055034149988315569),(-1055034149988276327)⟩,⟨143103355200814682,143103355200853924⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-716228308794964081),(-716228308794947632)⟩,⟨247216411083630997,247216411083647446⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-249348843573856862),(-249348843573852467)⟩,⟨116066874684735793,116066874684740192⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨2057881834235,2057881834251⟩,⟨1953367355759,1953367355775⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨7976110499286,7976110499302⟩,⟨3705027810324,3705027810340⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨16188725431540,16188725431556⟩,⟨(-5599449470901),(-5599449470885)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨14555796369253,14555796369269⟩,⟨(-49088772281832),(-49088772281816)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-40530079792770),(-40530079792754)⟩,⟨(-170042160662027),(-170042160662011)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-254872980339531),(-254872980339515)⟩,⟨(-415471725657540),(-415471725657524)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-825864675056247),(-825864675056231)⟩,⟨(-768834539327827),(-768834539327811)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-2013081934683228),(-2013081934683212)⟩,⟨(-1028170830411193),(-1028170830411177)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3958338360827705),(-3958338360827689)⟩,⟨(-708702588511797),(-708702588511781)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-6362200355926309),(-6362200355926293)⟩,⟨838788103890770,838788103890787⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-8295218509075595),(-8295218509075577)⟩,⟨3940759678270148,3940759678270168⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-8582973854482995),(-8582973854482961)⟩,⟨7978547680228885,7978547680228922⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-6768789987142778),(-6768789987142699)⟩,⟨11291050854116910,11291050854116990⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-3771718769714424),(-3771718769714292)⟩,⟨11992702163907907,11992702163908043⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1267810024601731),(-1267810024601586)⟩,⟨9163859108052182,9163859108052322⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-175974493545536),(-175974493545463)⟩,⟨3422367566770706,3422367566770781⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-8336475506188311087456),(-8336475506185990788019)⟩,⟨50916153798752818003590,50916153798755138302900⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_28 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 28) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_28 (tableDensity true) (fullFactor true 1 28) density1_contains hk1_1_28_contains +noncomputable def atomAnswer : CBox := ⟨⟨96515054901800024904834,96515054901800054634108⟩,⟨(-27765348171421356262330),(-27765348171421326546052)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_28 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 28) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_28 1 28 ha1_1_28_contains + def realAnswer : RBox := ⟨88178579395611613817378,88178579395614163846089⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 28) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_28 +namespace hm1_0_1_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨10662292451483733073974,10662292451483741766854⟩,⟨14336516914325028771265,14336516914325037464700⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨40488098695048191913328,40488098695048211368874⟩,⟨36510259702668789571455,36510259702668809029187⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨88211391981317690635946,88211391981317713647520⟩,⟨31810327661311505756222,31810327661311528770765⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨133772983286503610563822,133772983286503630926900⟩,⟨(-29377537256589094475587),(-29377537256589074112245)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨110341234702787874030952,110341234702787886268072⟩,⟨(-147791105353152472407768),(-147791105353152460175738)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-45183234403937560564311),(-45183234403937552189052)⟩,⟨(-230233859670719523370234),(-230233859670719514997359)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-255144734681577398556755),(-255144734681577392984181)⟩,⟨(-123845398032740779926118),(-123845398032740774346209)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-281368885572917112998035),(-281368885572917109507860)⟩,⟨164606634803954315593347,164606634803954319081840⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-14426011131048909556704),(-14426011131048907759568)⟩,⟨355791017722179346127558,355791017722179347920551⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨298592748304654337663110,298592748304654338688134⟩,⟨217071358579956430922464,217071358579956431948656⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨346191349599022845290983,346191349599022845936648⟩,⟨(-106325934793322564869486),(-106325934793322564220027)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨141894237506741064369779,141894237506741064737171⟩,⟨(-302338746306127265454168),(-302338746306127265090823)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-75913941681254148765474),(-75913941681254148565221)⟩,⟨(-274974826253497816372705),(-274974826253497816171843)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-160171675101654082630582),(-160171675101654082516913)⟩,⟨(-148223622506821417343511),(-148223622506821417229087)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-127847057728941778433737),(-127847057728941778381883)⟩,⟨(-48961247975357478906415),(-48961247975357478855652)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-45935246450876714758970),(-45935246450876714744944)⟩,⟨(-7977784665925112756742),(-7977784665925112743412)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-557497674845220038841),(-557497674845219161537)⟩,⟨(-960650597677859549508),(-960650597677858672129)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-2248787779200621646026),(-2248787779200618284991)⟩,⟨(-2692966005316962466708),(-2692966005316959105433)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-5532523930372302626962),(-5532523930372292260565)⟩,⟨(-3318502486933377320467),(-3318502486933366953823)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-10347278012362951091093),(-10347278012362921702554)⟩,⟨(-526933034195682217503),(-526933034195652829064)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-13157040119964040669763),(-13157040119963973808140)⟩,⟨8583627452879494301087,8583627452879561161805⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-5559550195797602066717),(-5559550195797400107141)⟩,⟨22292162861675259347327,22292162861675461306593⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨18292415886797856059627,18292415886798233548286⟩,⟨26873519690111639528097,26873519690112017018403⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨44180238709670411683556,44180238709671152652048⟩,⟨3029399654377269453811,3029399654378010422393⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨37384733607530409802727,37384733607531259206081⟩,⟨(-43758985340600659511137),(-43758985340599810110428)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-15115665790992505179782),(-15115665790991549906833)⟩,⟨(-68943871824099424943429),(-68943871824098469669354)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-71641348043167968038472),(-71641348043167320445029)⟩,⟨(-37155606224988139651920),(-37155606224987492055399)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-80679275706388397675244),(-80679275706387955071114)⟩,⟨26431444309666542251309,26431444309666984853903⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-43760467062356464745440),(-43760467062356265367486)⟩,⟨67798546214174380998223,67798546214174580372724⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-2339424342791324592131),(-2339424342791209432265)⟩,⟨66925014676378125921246,66925014676378241080405⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨14690432850271193412409,14690432850271243719387⟩,⟨41896621272171847754303,41896621272171898061931⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨7826048854086195981867,7826048854086209363977⟩,⟨13438271008882541700131,13438271008882555082652⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨16408793781050121094,16408793781050122355⟩,⟨(-840643800969982878),(-840643800969981622)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨51825882339843673777,51825882339843677971⟩,⟨(-10377504419135411961),(-10377504419135407773)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨89292123523492182789,89292123523492191814⟩,⟨(-47180185485677173959),(-47180185485677164940)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨106247419294796432398,106247419294796450910⟩,⟨(-135805890480048847258),(-135805890480048828739)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨35756788721791532770,35756788721791570882⟩,⟨(-282576531235402476886),(-282576531235402438754)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-226768091037426504324),(-226768091037426425879)⟩,⟨(-405040300319090630881),(-405040300319090552407)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-701038529905731352628),(-701038529905731193660)⟩,⟨(-253380090275860340763),(-253380090275860181816)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1066333061946456333742),(-1066333061946456022590)⟩,⟨477288391191771816652,477288391191772127722⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-612497931988539512141),(-612497931988538935308)⟩,⟨1653785997460869361944,1653785997460869938806⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1072023737968277702837,1072023737968278703963⟩,⟨2286016268535024864618,2286016268535025865901⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨3138466887829656947043,3138466887829658606883⟩,⟨1227768501512037366014,1227768501512039025843⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3901433663348759763480,3901433663348762398217⟩,⟨(-1293052339507852293011),(-1293052339507849658520)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨2718291076675612737258,2718291076675617274210⟩,⟨(-3533720119370042839852),(-3533720119370038303032)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨759405602506842697622,759405602506849294116⟩,⟨(-4046681319010260130777),(-4046681319010253534228)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-408588339265427423087),(-408588339265421269963)⟩,⟨(-2912440544758835617176),(-2912440544758829463940)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-321626763895703139373),(-321626763895700664233)⟩,⟨(-1020636342385197363084),(-1020636342385194887892)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨141216278309894003,141216278309894290⟩,⟨15665921811087895,15665921811088184⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨459044782427681248,459044782427681995⟩,⟨(-1174329475388266),(-1174329475387521)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨861247005223414005,861247005223414933⟩,⟨(-196885659997965217),(-196885659997964290)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1296899814196652243,1296899814196653003⟩,⟨(-793082070046564428),(-793082070046563670)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1439252755760822951,1439252755760823387⟩,⟨(-2079475364593645057),(-2079475364593644624)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨448764064816827009,448764064816827282⟩,⟨(-4133247183811472163),(-4133247183811471890)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-2974254959560737959),(-2974254959560737610)⟩,⟨(-6090274125332032012),(-6090274125332031665)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-9506680635188153165),(-9506680635188152538)⟩,⟨(-5308447147257193400),(-5308447147257192777)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-16885754437659808958),(-16885754437659807740)⟩,⟨2021338813844391834,2021338813844393054⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-18654409722487771823),(-18654409722487769555)⟩,⟨17165319136543853712,17165319136543855982⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-8068854363835807681),(-8068854363835803827)⟩,⟨34352403541130684523,34352403541130688382⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨13787391062476366572,13787391062476372385⟩,⟨42579816176420165210,42579816176420171028⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨35379693663425298263,35379693663425305753⟩,⟨35628050309495433007,35628050309495440497⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨43579722634941441739,43579722634941449603⟩,⟨19256935201995770176,19256935201995778036⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨34277595408771425147,34277595408771431261⟩,⟨5418773770091101622,5418773770091107732⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨12755465548212275232,12755465548212277553⟩,⟨303556475623188340,303556475623190660⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨1619282516614693,1619282516614721⟩,⟨(-221870571394503),(-221870571394474)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨5034876018800018,5034876018800094⟩,⟨(-1260280555420548),(-1260280555420475)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨8677264104975450,8677264104975658⟩,⟨(-4312762807330796),(-4312762807330588)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨11467525463246948,11467525463247593⟩,⟨(-11289387220937516),(-11289387220936876)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨9853137728418550,9853137728420467⟩,⟨(-23986128383713066),(-23986128383711146)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-3432769185875166),(-3432769185870425)⟩,⟨(-41458467187554233),(-41458467187549498)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-37868324198232471),(-37868324198222028)⟩,⟨(-54734621825026756),(-54734621825016310)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-96570116163384760),(-96570116163360668)⟩,⟨(-42021263257480955),(-42021263257456865)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-160660403680686765),(-160660403680651050)⟩,⟨25732260436513299,25732260436549014⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-181235591765415401),(-181235591765381442)⟩,⟨159678339843136770,159678339843170727⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-103949118255308660),(-103949118255273944)⟩,⟨321734570365846110,321734570365880824⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨74997935508415926,74997935508442590⟩,⟨429365913406519312,429365913406545978⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨276430535137271553,276430535137286474⟩,⟨417274228245744976,417274228245759898⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨382800444555739667,382800444555746394⟩,⟨299819446608785817,299819446608792544⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨325386324967500669,325386324967503718⟩,⟨155191520141347363,155191520141350409⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨126386762685634530,126386762685635488⟩,⟨43830253163636195,43830253163637155⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨8156556538736,8156556538752⟩,⟨(-8672751357032),(-8672751357016)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨22353133304819,22353133304835⟩,⟨(-30395369816296),(-30395369816279)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨27606405669933,27606405669949⟩,⟨(-65170121491302),(-65170121491286)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨9250458099229,9250458099245⟩,⟨(-119574023670330),(-119574023670314)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-59409085718857),(-59409085718841)⟩,⟨(-189793264679646),(-189793264679630)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-214030835019721),(-214030835019704)⟩,⟨(-244201896641075),(-244201896641059)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-476281732878121),(-476281732878105)⟩,⟨(-202995713752080),(-202995713752064)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-801602025765674),(-801602025765658)⟩,⟨59736145496455,59736145496471⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-1022152999809982),(-1022152999809966)⟩,⟨652468014647229,652468014647245⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-865208817436162),(-865208817436146)⟩,⟨1536409787477971,1536409787477987⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-124140714765026),(-124140714765009)⟩,⟨2428553789111486,2428553789111505⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1088559954252638,1088559954252658⟩,⟨2902042379685673,2902042379685693⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨2261956960253259,2261956960253285⟩,⟨2693376796234211,2693376796234240⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨2757930134519989,2757930134520028⟩,⟨1937832251835047,1937832251835082⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨2236394638198060,2236394638198096⟩,⟨1044280561002100,1044280561002134⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨854610012058350,854610012058375⟩,⟨310102790309234,310102790309262⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨7373306877346076401314,7373306877346882447997⟩,⟨(-81361650522747594127657),(-81361650522746788081248)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 29) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_29 (tableDensity false) (fullFactor true 1 29) density0_contains hk1_1_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨25340672187614061683987,25340672187614070297920⟩,⟨(-4088704358650542604561),(-4088704358650533993867)⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_29 1 29 ha1_1_29_contains + def realAnswer : RBox := ⟨32713979064960038085301,32713979064961052745917⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_29 +namespace hm1_1_1_29 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_29 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨1484015291737854376040,1484015291737860857056⟩,⟨2670979999805514429504,2670979999805520910385⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨6011962737694754706996,6011962737694768837005⟩,⟨7184134884766169920619,7184134884766184050091⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨14152115098248366580804,14152115098248382805789⟩,⟨7771670244528376819350,7771670244528393043584⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨23273341428677859771116,23273341428677873042978⟩,⟨(-969745690150627197783),(-969745690150613925932)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨22213043461396426023037,22213043461396431964047⟩,⟨(-20677542619157541309354),(-20677542619157535366767)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-1484809778073282467901),(-1484809778073279732105)⟩,⟨(-36955525603614099084502),(-36955525603614096348397)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-37215074125197163389160),(-37215074125197162217556)⟩,⟨(-22591369964818779402427),(-22591369964818778233028)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-44098424225766958652153),(-44098424225766958029669)⟩,⟨24548634396901041843179,24548634396901042466267⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-222979963302289375704),(-222979963302289062118)⟩,⟨57334085454399135833023,57334085454399136149072⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨52917089697728757336099,52917089697728757528694⟩,⟨33244483293055055406515,33244483293055055596278⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨59522721702873775393206,59522721702873775524388⟩,⟨(-23301557048299863558098),(-23301557048299863427814)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨21645447829099258623603,21645447829099258701677⟩,⟨(-56295914133086694375795),(-56295914133086694295456)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-17292211130054318135414),(-17292211130054318087551)⟩,⟨(-48806713758138655990778),(-48806713758138655941125)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-31007616347992365920275),(-31007616347992365889868)⟩,⟨(-24438913494675386748154),(-24438913494675386718277)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-23762723780578627316376),(-23762723780578627301485)⟩,⟨(-6682263758217018763433),(-6682263758217018749948)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-8375402153791333098178),(-8375402153791333093964)⟩,⟨(-600763838679342064631),(-600763838679342061076)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-5227686038228826617),(-5227686038228303062)⟩,⟨(-173142709996988256056),(-173142709996987732510)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-113698808599512301577),(-113698808599510181550)⟩,⟨(-527600437056745668849),(-527600437056743548855)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-525327729729797278797),(-525327729729789996968)⟩,⟨(-813985401948208927011),(-813985401948201645214)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1352192230320359855922),(-1352192230320337837301)⟩,⟨(-680400635138426792937),(-680400635138404774307)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-2195179747818320704462),(-2195179747818269243042)⟩,⟨489366192194101252614,489366192194152714146⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-1684187446393515668314),(-1684187446393354754625)⟩,⟨2808024219535821935859,2808024219535982849590⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1652321069576912765195,1652321069577216004406⟩,⟨4385533990257783114699,4385533990258086353706⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨6312029626660892901371,6312029626661493600294⟩,⟨1654447900324961915978,1654447900325562614874⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨6578033837147492064762,6578033837148179289884⟩,⟨(-5736521792286926331532),(-5736521792286239106062)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1139049311596350802131),(-1139049311595578250559)⟩,⟨(-11036338195890571030760),(-11036338195889798479335)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-11163848798164794426593),(-11163848798164276549181)⟩,⟨(-7129853276597338058046),(-7129853276596820181062)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-14190264040883655312417),(-14190264040883304777301)⟩,⟨3398940023536666722026,3398940023537017257369⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-8857153820041355565357),(-8857153820041202546795)⟩,⟨11407038267934195984579,11407038267934349003649⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1657539159610368400326),(-1657539159610281206107)⟩,⟨12224795981914379571227,12224795981914466765557⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1857302262223234404832,1857302262223271526896⟩,⟨8109346366644072656835,8109346366644109778804⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨1165552892218520523000,1165552892218530173713⟩,⟨2694777888361815826376,2694777888361825477026⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨3254591614604084303,3254591614604084701⟩,⟨1779816231491382075,1779816231491382475⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨11189287239375015223,11189287239375016535⟩,⟨4192745858653557366,4192745858653558677⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨22702324694612449873,22702324694612452614⟩,⟨1852032901189129051,1852032901189131793⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨36337863479416347696,36337863479416353013⟩,⟨(-12115942189472171023),(-12115942189472165705)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨40552336605481219830,40552336605481229914⟩,⟨(-45668939577485591179),(-45668939577485581091)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨8403734425609464110,8403734425609482850⟩,⟨(-94065775428343145080),(-94065775428343126337)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-86675390766865608017),(-86675390766865574116)⟩,⟨(-114333867927870308550),(-114333867927870274648)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-214177250255564622704),(-214177250255564563328)⟩,⟨(-24136733538524165927),(-24136733538524106557)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-237439144565711312716),(-237439144565711212204)⟩,⟨211968650466813059653,211968650466813160166⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-6392266706178655678),(-6392266706178486910)⟩,⟨452787586483471374200,452787586483471542971⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨415925669003288725452,415925669003289058834⟩,⟨435513593059567506977,435513593059567840360⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨719909974079294254144,719909974079294984236⟩,⟨80336541262182779409,80336541262183509502⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨675347286735903981249,675347286735905988268⟩,⟨(-358005846692966246922),(-358005846692964239904)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨386792612484295395228,386792612484299121550⟩,⟨(-562735773061376563898),(-562735773061372837573)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨122690458113834758160,122690458113838561026⟩,⟨(-458548540111496698199),(-458548540111492895334)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨14294175778223647464,14294175778225219839⟩,⟨(-169656307800593825716),(-169656307800592253342)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨34711224005572454,34711224005572699⟩,⟨32415594773952232,32415594773952478⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨121123510655045349,121123510655045972⟩,⟨90370018864176770,90370018864177394⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨257844924859315150,257844924859315923⟩,⟨115491893703402622,115491893703403394⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨465996237155618969,465996237155619590⟩,⟨43699947599907055,43699947599907678⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨708113968613879339,708113968613879672⟩,⟨(-246620787984486055),(-246620787984485721)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨792020915918971927,792020915918972088⟩,⟨(-898931605434616479),(-898931605434616318)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨282920012165609255,282920012165609402⟩,⟨(-1896225119742436015),(-1896225119742435866)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-1356859924326991643),(-1356859924326991416)⟩,⟨(-2714862449210536948),(-2714862449210536721)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-4144997767467760060),(-4144997767467759634)⟩,⟨(-2147298178420020316),(-2147298178420019886)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-6776025814166370222),(-6776025814166369432)⟩,⟨1021940477181447702,1021940477181448493⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-6879959392043136327),(-6879959392043134982)⟩,⟨6452275555174935176,6452275555174936524⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-3107036285032916632),(-3107036285032914585)⟩,⟨11507212725065092355,11507212725065094400⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2845434400747827400,2845434400747830069⟩,⟨13114049488669298385,13114049488669301054⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨7155606318008573879,7155606318008576726⟩,⟨10645757168625937512,10645757168625940359⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨7091153019990057418,7091153019990059663⟩,⟨6187280014970594542,6187280014970596788⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨2899476932881781341,2899476932881782207⟩,⟨1915625197766857366,1915625197766858234⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨527629230520586,527629230520615⟩,⟨(-100038485098214),(-100038485098189)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1669602340874495,1669602340874558⟩,⟨(-493866327359140),(-493866327359078)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨2979517420548581,2979517420548755⟩,⟨(-1555666485248380),(-1555666485248205)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨4177285763500943,4177285763501473⟩,⟨(-3970278312447477),(-3970278312446945)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨4127692311231648,4127692311233226⟩,⟨(-8512930151342287),(-8512930151340708)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨255271565638393,255271565642293⟩,⟨(-15275935639605900),(-15275935639602001)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-11338422827188253),(-11338422827179666)⟩,⟨(-21846271331550641),(-21846271331542054)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-33496251103556533),(-33496251103536736)⟩,⟨(-21108045184393779),(-21108045184373984)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-62645643613121414),(-62645643613092094)⟩,⟨(-1776401834177868),(-1776401834148545)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-84237857559703252),(-84237857559675397)⟩,⟨44243863923593051,44243863923620904⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-77686790105597893),(-77686790105569457)⟩,⟨109602046802498049,109602046802526483⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-33898717372421387),(-33898717372399576)⟩,⟨167424808653727210,167424808653749020⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨29441644474967530,29441644474979718⟩,⟨187281082028247603,187281082028259789⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨75571210101825025,75571210101830514⟩,⟨159666053725693963,159666053725699453⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨76112670524678471,76112670524680954⟩,⟨101060429721707099,101060429721709581⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨31467948219951643,31467948219952425⟩,⟨33655506759295376,33655506759296160⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨229897163843,229897163859⟩,⟨(-269175589704),(-269175589688)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨408075025280,408075025296⟩,⟨(-1021255895266),(-1021255895250)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-822745999497),(-822745999481)⟩,⟨(-1988576093722),(-1988576093706)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-6320617707311),(-6320617707295)⟩,⟨(-1430775308919),(-1430775308903)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-21283386061637),(-21283386061621)⟩,⟨6752608523369,6752608523385⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-50750412120510),(-50750412120493)⟩,⟨37203534932315,37203534932331⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-90035364309867),(-90035364309851)⟩,⟨116722504488280,116722504488296⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-107738058218361),(-107738058218345)⟩,⟨279040152337231,279040152337247⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-33359475272202),(-33359475272186)⟩,⟨538174049576699,538174049576715⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨222294764747484,222294764747500⟩,⟨843073670229367,843073670229383⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨693702452488779,693702452488795⟩,⟨1056110794357513,1056110794357529⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨1274102522346557,1274102522346579⟩,⟨1018200352742175,1018200352742192⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨1715831019144449,1715831019144473⟩,⟨692913288881180,692913288881204⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1763263312911667,1763263312911699⟩,⟨251525897311066,251525897311098⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨1317230364650436,1317230364650467⟩,⟨(-39834060650961),(-39834060650928)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨486082722125666,486082722125688⟩,⟨(-57986524883249),(-57986524883224)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2392517104199589209490,2392517104200228805585⟩,⟨(-14683129133695488042267),(-14683129133694848446275)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_29 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 29) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_29 (tableDensity true) (fullFactor true 1 29) density1_contains hk1_1_29_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-33137802091495322697280),(-33137802091495311432907)⟩,⟨5346767238235313684288,5346767238235324944426⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_29 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 29) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_29 1 29 ha1_1_29_contains + def realAnswer : RBox := ⟨(-30745284987295833487790),(-30745284987294982627322)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 29) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_29 +namespace hm1_0_1_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk1_1_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-958514579536332956225),(-958514579536330109057)⟩,⟨(-4986329157257325669411),(-4986329157257322822229)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-5983517624825090219069),(-5983517624825083294435)⟩,⟨(-14333542496848247497144),(-14333542496848240572282)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-19235878435210682224234),(-19235878435210675324049)⟩,⟨(-18722636878255253015132),(-18722636878255246114017)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-38785644049289017360850),(-38785644049289011471904)⟩,⟨(-7318483256846068589058),(-7318483256846062699176)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-45499934498751540168715),(-45499934498751535851994)⟩,⟨28306584347311113608695,28306584347311117924814⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-9854275398926712984371),(-9854275398926710090107)⟩,⟨68072413719275475803721,68072413719275478696337⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨61418838675490932673219,61418838675490934712930⟩,⟨57169791616964791031570,57169791616964793072863⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨93648974252654066504674,93648974252654067765192⟩,⟨(-26376079520817525727399),(-26376079520817524466396)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨26606650011185806865123,26606650011185807501337⟩,⟨(-103759110689732417838425),(-103759110689732417203630)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-78270766076262515792289),(-78270766076262515437687)⟩,⟨(-79812116310875754143459),(-79812116310875753788903)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-108586989780659725904592),(-108586989780659725688721)⟩,⟨19002488184163830910538,19002488184163831127786⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-51205270361995236366737),(-51205270361995236246826)⟩,⟨88271817443663236687558,88271817443663236806382⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨18636732314082526925958,18636732314082526989756⟩,⟨85374014448723752243326,85374014448723752307213⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨47806989354940424654790,47806989354940424690612⟩,⟨46876743326797242062916,46876743326797242098985⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨39084743441524590954610,39084743441524590970885⟩,⟨15475362399535071399375,15475362399535071415321⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨14104128516716753606840,14104128516716753611225⟩,⟨2482519935005282905930,2482519935005282910101⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-73116525239984308816),(-73116525239984029331)⟩,⟨253712146551123287565,253712146551123567045⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-87493145403185264477),(-87493145403184200851)⟩,⟨832498347636671368988,832498347636672432621⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨371223347900885964221,371223347900888585476⟩,⟨1505205532693482897589,1505205532693485518909⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨1711931681353287793597,1711931681353294192019⟩,⟨1843210343711522122439,1843210343711528521011⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨3808107453629611578559,3808107453629631868012⟩,⟨657617321564213349494,657617321564233638962⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨4722792550502750219857,4722792550502794385077⟩,⟨(-3259955633740333959016),(-3259955633740289794107)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨775713545293655067183,775713545293767850736⟩,⟨(-8220726023975703816721),(-8220726023975591033179)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-8553289356829374543725),(-8553289356829203556877)⟩,⟨(-7608585798705945313852),(-7608585798705774326462)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-14708981099300835038063),(-14708981099300584992624)⟩,⟨3598413729371768453946,3598413729372018499057⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-6885800786116350895783),(-6885800786116108891755)⟩,⟨17588381586991016322682,17588381586991258326119⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨11222849984154192314402,11222849984154377424478⟩,⟨18849779894136583492248,18849779894136768603117⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨22895242992499036682237,22895242992499157602289⟩,⟨4826871234746651725318,4826871234746772645873⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨19741382901509741040829,19741382901509805475732⟩,⟨(-10787309301484309734210),(-10787309301484245299958)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨9211779195175236435585,9211779195175264777508⟩,⟨(-16428234299297638946050),(-16428234299297610604901)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1552818732371112742598,1552818732371127447960⟩,⟨(-12465708982491868464593),(-12465708982491853759442)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-325639515579357875009),(-325639515579353619747)⟩,⟨(-4401351536428806667475),(-4401351536428802412231)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1695485229232179486),(-1695485229232179141)⟩,⟨(-2715429457897850249),(-2715429457897849905)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-6728697025560765357),(-6728697025560764232)⟩,⟨(-7845621668189385130),(-7845621668189384001)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-16800821343880911160),(-16800821343880908725)⟩,⟨(-10648162751786762788),(-10648162751786760349)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-34021975922633925505),(-34021975922633920449)⟩,⟨(-4501950158722361114),(-4501950158722356062)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-52398723927927904870),(-52398723927927894279)⟩,⟨23565030047947433441,23565030047947444028⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-44984219831631886973),(-44984219831631864743)⟩,⟨83822178938407743564,83822178938407765790⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨37418075316269632065,37418075316269678111⟩,⟨150923654666889617089,150923654666889663144⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨213502549528110218026,213502549528110310308⟩,⟨126877219939577940157,126877219939578032439⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨366947496500516779577,366947496500516954556⟩,⟨(-107118373694341385824),(-107118373694341210875)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨251894414860086505707,251894414860086815819⟩,⟨(-497779776095573166748),(-497779776095572856637)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-235049015321441767515),(-235049015321441258453)⟩,⟨(-720937107057342716386),(-720937107057342207277)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-806169869529445163183),(-806169869529444334242)⟩,⟨(-483675729680408094982),(-483675729680407266028)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-1031355711944377368681),(-1031355711944376115857)⟩,⟨76466409065625908934,76466409065627161713⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-818383408496427352543),(-818383408496425751632)⟩,⟨512697557773382498372,512697557773384099228⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-434614608878895944777),(-434614608878894260841)⟩,⟨542455519791025062987,542455519791026746905⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-122628017051752475424),(-122628017051751733859)⟩,⟨222329476436189587196,222329476436190328759⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-4742531656720729),(-4742531656720664)⟩,⟨(-22553302347420354),(-22553302347420287)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-23750623092969997),(-23750623092969852)⟩,⟨(-70826802740051328),(-70826802740051180)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-75894991480566853),(-75894991480566681)⟩,⟨(-123195748310536831),(-123195748310536663)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-194604853249783591),(-194604853249783458)⟩,⟨(-159040830152348740),(-159040830152348607)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-409322286903006387),(-409322286903006306)⟩,⟨(-107378849758654201),(-107378849758654120)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-682856652573449262),(-682856652573449196)⟩,⟨178117341546601264,178117341546601336⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-785606712261134175),(-785606712261134085)⟩,⟨865819133383336070,865819133383336161⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-213485074273079723),(-213485074273079569)⟩,⟨1898966862151176172,1898966862151176327⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1548683803084468226,1548683803084468525⟩,⟨2614128282600509624,2614128282600509924⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨4259091919900062874,4259091919900063434⟩,⟨1764955034208550718,1764955034208551277⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨6368210192496871695,6368210192496872661⟩,⟨(-1431157519654374786),(-1431157519654373822)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨5970100310995492047,5970100310995493524⟩,⟨(-5919178439005673971),(-5919178439005672491)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨2887460266580916934,2887460266580918870⟩,⟨(-9110618841337006370),(-9110618841337004432)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-705481400649452946),(-705481400649450888)⟩,⟨(-9137341559892628221),(-9137341559892626159)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2268404051313978410),(-2268404051313976790)⟩,⟨(-6329765113813439771),(-6329765113813438152)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1148241031080508146),(-1148241031080507521)⟩,⟨(-2199708095508898631),(-2199708095508898005)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-68414643584393),(-68414643584375)⟩,⟨(-215408161631704),(-215408161631688)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-292955198355176),(-292955198355153)⟩,⟨(-657414858884591),(-657414858884565)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-807198770660997),(-807198770660953)⟩,⟨(-1083549363749996),(-1083549363749951)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-1858273124204916),(-1858273124204808)⟩,⟨(-1289939058200834),(-1289939058200729)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-3614376531320121),(-3614376531319842)⟩,⟨(-709368071854023),(-709368071853748)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-5733017885762450),(-5733017885761829)⟩,⟨1710335892588154,1710335892588776⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-6584008048110683),(-6584008048108961)⟩,⟨7131868388349215,7131868388350937⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-2738899766252776),(-2738899766249117)⟩,⟨15348681444174845,15348681444178505⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨9682242270006976,9682242270011851⟩,⟨22467234076876580,22467234076881453⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨30725238438506099,30725238438511561⟩,⟨20407000953260488,20407000953265947⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨52364774710877786,52364774710883595⟩,⟨1920920141270250,1920920141276058⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨61315851134474939,61315851134478952⟩,⟨(-30465711696982301),(-30465711696978286)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨50438460648958895,50438460648960922⟩,⟨(-61506129827896986),(-61506129827894958)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨27262399432658259,27262399432659405⟩,⟨(-73064831589509603),(-73064831589508457)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨7651050424302410,7651050424303021⟩,⟨(-57683530927264938),(-57683530927264325)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨382257721132791,382257721132985⟩,⟨(-21659336008066247),(-21659336008066052)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-1096123236591),(-1096123236575)⟩,⟨(-927481767710),(-927481767694)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-3816625457903),(-3816625457886)⟩,⟨(-2497682705994),(-2497682705978)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-8099466363299),(-8099466363283)⟩,⟨(-2881973085926),(-2881973085910)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-14668120226089),(-14668120226073)⟩,⟨(-179407375003),(-179407374986)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-22827219288797),(-22827219288781)⟩,⟨9016580797525,9016580797541⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-28166949426442),(-28166949426426)⟩,⟨29104355916994,29104355917010⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-19957947017523),(-19957947017507)⟩,⟨62230933709233,62230933709249⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨18213569945859,18213569945875⟩,⟨101151870109323,101151870109339⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨99226775235909,99226775235925⟩,⟨121835872169096,121835872169112⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨214493445244892,214493445244908⟩,⟨87173734584888,87173734584905⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨322165591526467,322165591526483⟩,⟨(-28008000799804),(-28008000799788)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨364607212529904,364607212529923⟩,⟨(-202319022153749),(-202319022153733)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨313674591197322,313674591197339⟩,⟨(-360556586045483),(-360556586045466)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨200568766229130,200568766229149⟩,⟨(-415767259490652),(-415767259490632)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨90377283004516,90377283004536⟩,⟨(-327638453767794),(-327638453767776)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨22225624705660,22225624705676⟩,⟨(-123556981361598),(-123556981361580)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-2402423245483968326264),(-2402423245483749951641)⟩,⟨23730616897788935785459,23730616897789154160021⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk1_1_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false true 1 30) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk1_1_30 (tableDensity false) (fullFactor true 1 30) density0_contains hk1_1_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-7961783367136325293241),(-7961783367136322128463)⟩,⟨383084095562158069049,383084095562161232797⟩⟩ +lemma atomChecked : tableAtomBox false ha1_1_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false true 1 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains false true ha1_1_30 1 30 ha1_1_30_contains + def realAnswer : RBox := ⟨(-10364206612620393619505),(-10364206612619972080104)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false true 1 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_0_1_30 +namespace hm1_1_1_30 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk1_1_30 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-49976147928759555625),(-49976147928757466029)⟩,⟨(-866933676479846631454),(-866933676479844541860)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-673860980063564123775),(-673860980063559137005)⟩,⟨(-2582440350105276758008),(-2582440350105271771293)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-2770639667724763111131),(-2770639667724758451367)⟩,⟨(-3699506549681649709663),(-3699506549681645050135)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-6280061404926754268109),(-6280061404926750728703)⟩,⟨(-2371654002033978533021),(-2371654002033974993858)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-8198921961261256085544),(-8198921961261254086505)⟩,⟨3242118541991881229005,3242118541991883228288⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-3177463253437469110339),(-3177463253437468282431)⟩,⟨10364415596566477896563,10364415596566478724891⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨8563595374008844214227,8563595374008844629826⟩,⟨9616514343125908064059,9616514343125908479124⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨14579310657922476537292,14579310657922476757153⟩,⟨(-3774236348318782641012),(-3774236348318782421330)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨3665101355018082409596,3665101355018082518923⟩,⟨(-16850759631726925910410),(-16850759631726925800208)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-14135335106880668881752),(-14135335106880668815993)⟩,⟨(-12580773224774217034014),(-12580773224774216968873)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-18859768989452791620530),(-18859768989452791577475)⟩,⟨4785714908736592795892,4785714908736592838467⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-8080295830255254466192),(-8080295830255254440796)⟩,⟨16563419643724317796749,16563419643724317822754⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨4475649846844101619215,4475649846844101634181⟩,⟨15216972875332416860585,15216972875332416876154⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨9292414010072584666432,9292414010072584675931⟩,⟨7769646475907352060519,7769646475907352069891⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨7272879688592633286123,7272879688592633290772⟩,⟨2133923011996778560127,2133923011996778564350⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨2572205073369922644113,2572205073369922645431⟩,⟨190372843081370920324,190372843081370921442⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-28849535207546630378),(-28849535207546467081)⟩,⟨29383179940590484116,29383179940590647411⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-71450738053185419645),(-71450738053184762344)⟩,⟨107126057763785899064,107126057763786556362⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-49800370539658807619),(-49800370539657076284)⟩,⟨227398471234914826694,227398471234916558022⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨120192405056312039549,120192405056316553227⟩,⟨347283015366860683166,347283015366865196828⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨477384741552243201271,477384741552258650366⟩,⟨279494345380935625689,279494345380951074777⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨779165164982116725929,779165164982151109082⟩,⟨(-248226998980671473020),(-248226998980637089828)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨387124986409754574575,387124986409844638989⟩,⟨(-1125524491414303021371),(-1125524491414212956954)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1028852500827274627505),(-1028852500827137664305)⟩,⟨(-1336528056331692184671),(-1336528056331555221540)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2286217137718843890743),(-2286217137718642737486)⟩,⟨214297214870755976669,214297214870957129967⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1386758090552150524391),(-1386758090551956893628)⟩,⟨2625264602487879597167,2625264602488073228010⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨1557326210833061025539,1557326210833207536544⟩,⟨3246655022633477192987,3246655022633623703879⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨3854750510286505479304,3854750510286599716499⟩,⟨1146791672354427216294,1146791672354521453418⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨3687678068328595403887,3687678068328644236135⟩,⟨(-1616434070228950850490),(-1616434070228902018145)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1990174344004840501321,1990174344004860952950⟩,⟨(-2842421641627630889722),(-2842421641627610437976)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨550415970081729902746,550415970081740385986⟩,⟨(-2288688399377245765673),(-2288688399377235282397)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨37714878937355950117,37714878937358936429⟩,⟨(-832396501192965863292),(-832396501192962876978)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-4728017788740111),(-4728017788739995)⟩,⟨(-722737259445107945),(-722737259445107827)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-355577866725429134),(-355577866725428772)⟩,⟨(-2309449394599047306),(-2309449394599046945)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1904376223251581733),(-1904376223251580987)⟩,⟨(-4062068099789190777),(-4062068099789190027)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-5748179556481003225),(-5748179556481001768)⟩,⟨(-5007942724043898581),(-5007942724043897125)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-12125025857438942481),(-12125025857438939675)⟩,⟨(-2177665148738675883),(-2177665148738673073)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-17176847469035003815),(-17176847469034998502)⟩,⟨8913778509431864458,8913778509431869773⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-9762361110505364382),(-9762361110505354561)⟩,⟨28286574948636864546,28286574948636874366⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨22025386116919995492,22025386116920013100⟩,⟨40169888960303075615,40169888960303093221⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨67563428296541262837,67563428296541293179⟩,⟨13924185754008247188,13924185754008277527⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨79662258281178395979,79662258281178447659⟩,⟨(-60528600229324160707),(-60528600229324109026)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨16266186248717927438,16266186248718019110⟩,⟨(-134518612918920515322),(-134518612918920423655)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-93443389118811528316),(-93443389118811310376)⟩,⟨(-136821869831142275263),(-136821869831142057324)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-166328149208279619390),(-166328149208279152582)⟩,⟨(-61410535596442674805),(-61410535596442208000)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-158521343627361346778),(-158521343627360589860)⟩,⟨22817375899306334205,22817375899307091124⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-98747528169802899842),(-98747528169801933107)⟩,⟨53242512210834407958,53242512210835374689⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-31476729925367001335),(-31476729925366546379)⟩,⟨25320337238540692865,25320337238541147823⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨3235720627045050,3235720627045105⟩,⟨(-6991217987417988),(-6991217987417933)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨7736398743361822,7736398743361946⟩,⟨(-23343974700497141),(-23343974700497017)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨4331359928110264,4331359928110409⟩,⟨(-46069309822209531),(-46069309822209387)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-18636528755163202),(-18636528755163092)⟩,⟨(-75098819211840190),(-75098819211840083)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-79278500280619662),(-79278500280619597)⟩,⟨(-97240816289435566),(-97240816289435503)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-190390823632864041),(-190390823632863997)⟩,⟨(-71437471628151587),(-71437471628151541)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-321871766411387842),(-321871766411387798)⟩,⟨75880011684377102,75880011684377146⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-347205563429085572),(-347205563429085509)⟩,⟨403928288755921585,403928288755921648⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-51932804504711226),(-51932804504711113)⟩,⟨832400685820411295,832400685820411408⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨686877567371074944,686877567371075148⟩,⟨1039835709337762302,1039835709337762508⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1629247298696540926,1629247298696541271⟩,⟨623879019611391233,623879019611391577⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨2192356474322903882,2192356474322904410⟩,⟨(-454147269201050141),(-454147269201049610)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨1960735829276785955,1960735829276786653⟩,⟨(-1636994108665769991),(-1636994108665769293)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨1152159683764315281,1152159683764316034⟩,⟨(-2181788452822641351),(-2181788452822640601)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨391747987130636560,391747987130637161⟩,⟨(-1780859929704104505),(-1780859929704103902)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨53310333810267597,53310333810267838⟩,⟨(-673733792705858107),(-673733792705857868)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-26072732123921),(-26072732123902)⟩,⟨(-69534783532733),(-69534783532712)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-107521412769733),(-107521412769713)⟩,⟨(-216183838076816),(-216183838076796)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-287440763155873),(-287440763155833)⟩,⟨(-370215219107760),(-370215219107721)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-657308610461964),(-657308610461872)⟩,⟨(-473624227046226),(-473624227046138)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-1300274493666164),(-1300274493665935)⟩,⟨(-339693340980087),(-339693340979861)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-2157497022653787),(-2157497022653271)⟩,⟨416209345434954,416209345435470⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-2748248486882653),(-2748248486881236)⟩,⟨2309202799684581,2309202799686003⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-1890969317871504),(-1890969317868493)⟩,⟨5548231023678229,5548231023681236⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨2053880891788189,2053880891792194⟩,⟨9197408880587252,9197408880591254⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨9860644702265177,9860644702269658⟩,⟨10673404486460622,10673404486465103⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨19623836058033722,19623836058038479⟩,⟨6960718063496931,6960718063501692⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨26729690044225506,26729690044228788⟩,⟨(-2367592191761066),(-2367592191757781)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨27066349903939998,27066349903941654⟩,⟨(-13232133270381761),(-13232133270380103)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨20742631734516214,20742631734517149⟩,⟨(-19297728021319918),(-19297728021318982)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨11734239446826256,11734239446826757⟩,⟨(-16712941569033828),(-16712941569033327)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨3595536329266054,3595536329266215⟩,⟨(-6537877809682240),(-6537877809682079)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-33873118538),(-33873118522)⟩,⟨(-25984607435),(-25984607419)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-125963970302),(-125963970286)⟩,⟨(-42503600410),(-42503600394)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-235157300088),(-235157300072)⟩,⟨114053545095,114053545111⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-123942682298),(-123942682282)⟩,⟨783152034003,783152034019⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨1023898682163,1023898682179⟩,⟨2559961552338,2559961552354⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨5148113758755,5148113758771⟩,⟨5930219253238,5930219253254⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨15729641969901,15729641969917⟩,⟨9958244087087,9958244087103⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨36929117095487,36929117095503⟩,⟨10010267041746,10010267041762⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨69792082988429,69792082988445⟩,⟨(-3728661132398),(-3728661132381)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨106148697275551,106148697275567⟩,⟨(-42958170745366),(-42958170745349)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨126471194493067,126471194493083⟩,⟨(-110670589102150),(-110670589102134)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨110275691360399,110275691360417⟩,⟨(-189707401358145),(-189707401358127)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨56726314635828,56726314635845⟩,⟨(-244956410859333),(-244956410859317)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-5202480782582),(-5202480782563)⟩,⟨(-243872519195194),(-243872519195174)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-35686171641714),(-35686171641695)⟩,⟨(-177925306360541),(-177925306360524)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-19254576714025),(-19254576714009)⟩,⟨(-64797789808931),(-64797789808914)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-603010047335126214095),(-603010047334955492784)⟩,⟨4145214284902427068539,4145214284902597789812⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk1_1_30 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true true 1 30) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk1_1_30 (tableDensity true) (fullFactor true 1 30) density1_contains hk1_1_30_contains +noncomputable def atomAnswer : CBox := ⟨⟨10411562864716728937221,10411562864716733075777⟩,⟨(-500956124965903150581),(-500956124965899013372)⟩⟩ +lemma atomChecked : tableAtomBox true ha1_1_30 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true true 1 30) := by + rw [← atomChecked] + exact @fullAtomBox_contains true true ha1_1_30 1 30 ha1_1_30_contains + def realAnswer : RBox := ⟨9808552817381502723126,9808552817381877582993⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true true 1 30) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm1_1_1_30 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments3_0.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments3_0.lean new file mode 100644 index 0000000000000000000000000000000000000000..b6eadd387f7258c56f3e2d042bbf5e7803a0f604 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/HighMoments3_0.lean @@ -0,0 +1,5393 @@ +import OAI.Analysis.PlanarPacking.Certificate.TableDensityValues +import OAI.Analysis.PlanarPacking.Certificate.HighHeaders3 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid Numerical +namespace hm3_0_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-76232057695463846844199712320),(-76232057695463801528014751964)⟩,⟨106041665428336539468478252975,106041665428336584778416842650⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-212548636740098799135982816914),(-212548636740098689331616430502)⟩,⟨323597096120572184333153800601,323597096120572294119815182859⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-301452647174763209990027659391),(-301452647174763093887720271487)⟩,⟨553541828502337965057472854703,553541828502338081133563092485⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-316615658653572062577946250127),(-316615658653571984884133131586)⟩,⟨792532980780144743067568410705,792532980780144820731088374425⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-241720273227196184623895994008),(-241720273227196149967645144318)⟩,⟨1022542252183858210414824755145,1022542252183858245041825809732⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-75655447245989969738713647678),(-75655447245989959258756433472)⟩,⟨1212123184487941481270396789503,1212123184487941491727011338014⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨164097606791142910098032637163,164097606791142912493898247069⟩,⟨1325413376748059561527139222072,1325413376748059563909108095080⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨441312843469115261700220099796,441312843469115262331076230675⟩,⟨1335681540781118839089765191080,1335681540781118839717491524837⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨707051933311744443287363484577,707051933311744443627868111364⟩,⟨1236500935921179103362763502216,1236500935921179103710146201593⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨912033387267749873413111586990,912033387267749873684501872593⟩,⟨1045931282179503267494208156764,1045931282179503267780231222938⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨1019985418247339296376020111827,1019985418247339296598512024931⟩,⟨802119117503401023486407924561,802119117503401023728214535183⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1015544969484726082555022479326,1015544969484726082729378561539⟩,⟨551693255905118205623798734858,551693255905118205818813351732⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨904015497802997231779946243088,904015497802997231908375674422⟩,⟨335315460665714363356619360720,335315460665714363504007034450⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨705286831840289909908756205039,705286831840289909994843231074⟩,⟨176286300239125010251654258220,176286300239125010352817531787⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨445885406656819273807964310154,445885406656819273856792165695⟩,⟨76643102450028055054824444132,76643102450028055113287802922⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨152201330577284136957309927183,152201330577284136972974627065⟩,⟨20298666459835558909942904508,20298666459835558928939613561⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-64341149715187222738896219412),(-64341149715187167197250108562)⟩,⟨(-90897133045747541773512370189),(-90897133045747486223726910986)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-200149836598294209611819800225),(-200149836598293992231454095554)⟩,⟨(-262745064484678604568707440872),(-262745064484678387165049833127)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-354248437340664717657454282496),(-354248437340664131959367853144)⟩,⟨(-404164569862442860907135654747),(-404164569862442275174027129987)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-529794599885172570853806687852),(-529794599885171062374052443963)⟩,⟨(-494815656716462424066241431901),(-494815656716460915545007549855)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-718541571104193647269151593222),(-718541571104189978316405502066)⟩,⟨(-516942016208652822272075195853),(-516942016208649153277858437562)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-900936463174339918677657225564),(-900936463174332020191656291478)⟩,⟨(-460410223889233623806316589629),(-460410223889225725285344065485)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-1050150875233874294268381365902),(-1050150875233860396783301076892)⟩,⟨(-328381399435345847467283264175),(-328381399435331949959140448081)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-1139371847963651643379911756711),(-1139371847963633044273162772164)⟩,⟨(-140167759823916345024377563114),(-140167759823897745909651605949)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1150473846511735816626587813434),(-1150473846511716916218863075897)⟩,⟨71340539657008526159886828247,71340539657027426560137964232⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1080578235666301661998796763199),(-1080578235666287088284397138388)⟩,⟨267308700048666449926502510548,267308700048681023620352782809⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-943207188027341671537074226218),(-943207188027333137820874471266)⟩,⟨412915176262691990941389860807,412915176262700524628315087219⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-763537411511169928434603902816),(-763537411511165864281694907706)⟩,⟨485652823249221236784613120674,485652823249225300904760084211⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-569892044367165585475746178519),(-569892044367163879780128271706)⟩,⟨478647546659453322847679930561,478647546659455028512148333188⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-384751000875681918348870344446),(-384751000875681245714225567161)⟩,⟨398841525270068663989310215584,398841525270069336598657976042⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-218895126169059100979364826104),(-218895126169058849111571935892)⟩,⟨262647071493789767314245102667,262647071493790019165656373140⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-70628467723233979387388650916),(-70628467723233914963560849392)⟩,⟨91444386145787333416659607395,91444386145787397834829472305⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨79609526486762008226157737435,79609526486762008245839252663⟩,⟨672938421700919874600298043,672938421700919885512951242⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨236707065283587584764632311488,236707065283587584824468844081⟩,⟨(-8292211637998615627105774604),(-8292211637998615592608397277)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨385532881915377512234476571874,385532881915377512336107421207⟩,⟨(-46463283303732005149501515226),(-46463283303732005086461403259)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨515779206433472020360706626891,515779206433472020505636026449⟩,⟨(-127112083631594880502073157486),(-127112083631594880403703171701)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨612166030228292219833515090657,612166030228292220021485529919⟩,⟨(-253634238697467855579179040916),(-253634238697467855438786507534)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨656857975679454393259892032352,656857975679454393491079701329⟩,⟨(-416714168702606627326681038782),(-416714168702606627136248688553)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨635507022642966253005752838823,635507022642966253287104704297⟩,⟨(-594812464826889475356016699198),(-594812464826889475102007173684)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨544810463308179279296915774362,544810463308179279705205545279⟩,⟨(-758305500281668416417770476977),(-758305500281668416019264643425)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨397100007093782946716043692975,397100007093782947915914862154⟩,⟨(-876791779803141994365411892309),(-876791779803141993157028312739)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨219084275545312892276502500296,219084275545312898746638770849⟩,⟨(-927800578204333940685923697071),(-927800578204333934191813824739)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨45150908374705209844061768179,45150908374705241842567610768⟩,⟨(-903211879309706788997286205911),(-903211879309706756964540441527)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-91980181428409624885010752561),(-91980181428409512260225162196)⟩,⟨(-810046767137852174994956916375),(-810046767137852062331734449510)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-169861203995777358582824639416),(-169861203995777094098523512105)⟩,⟨(-665382363787725971592711659434),(-665382363787725707071683332351)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-181416319726957158710874462391),(-181416319726956749025070334483)⟩,⟨(-488863468709170791332362422307),(-488863468709170381616682228922)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-134850866992383908830705891212),(-134850866992383511980072950227)⟩,⟨(-296789485671972556623842077253),(-296789485671972159753851906981)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-49448372795823964504161321268),(-49448372795823799078724674359)⟩,⟨(-99246532345427883241795426799),(-99246532345427717809697316931)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-15359926471177437732539057136),(-15359926471177365333980794541)⟩,⟨42910354185846257279224850776,42910354185846329685389801058⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-40988255928897234267356296522),(-40988255928897059907143005652)⟩,⟨129808980513867645360116550266,129808980513867819742173985836⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-51672774538340383134903355515),(-51672774538340200763316420338)⟩,⟨218490310067764781000982636187,218490310067764963405728049772⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-38954371977690400968205704786),(-38954371977690280543489113511)⟩,⟨306155626061696475035632921172,306155626061696595500188174485⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2750426670979376427262166385,2750426670979429422717592742⟩,⟨385477714776534451028168957686,385477714776534504064261245959⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨74102754122778029796607240796,74102754122778045575708070319⟩,⟨445815687897195261927793183033,445815687897195277741997045679⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨168789317312833407692003290198,168789317312833411132879402222⟩,⟨476345567601688988834127787537,476345567601688992298837607126⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨273136420640529698865929321768,273136420640529699607774325415⟩,⟨469771200172681631787577473522,469771200172681632537995722040⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨368773591721032296075517476883,368773591721032296383178756216⟩,⟨425468931552544195205315596107,425468931552544195504887671763⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨437496332052659595730263857159,437496332052659595961610418892⟩,⟨350875530260993212875697487961,350875530260993213083827535622⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨466223739346213507705737641834,466223739346213507901892269024⟩,⟨260003936504513238923424069625,260003936504513239085323390219⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨450070345630773941305811239952,450070345630773941467826152925⟩,⟨169460036527627848132454148670,169460036527627848254886518459⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨392340091156867030045348352626,392340091156867030171247464807⟩,⟨93695122790408876960789656411,93695122790408877047944894864⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨301812797040240171877703734977,301812797040240171966547136086⟩,⟨41210310144757791330065342388,41210310144757791386732194351⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨189163070931658151998499546320,189163070931658152051007004112⟩,⟨12800166815075983000249120112,12800166815075983031596120094⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨64306607137691418370125789620,64306607137691418387421541727⟩,⟨2107006658342471374073343709,2107006658342471384016734327⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1795856677973524097330249310),(-1795856677973308826234662489)⟩,⟨(-28212233075793944766390918951),(-28212233075793729499944600344)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-9810616085039529890412386970),(-9810616085038685815364009431)⟩,⟨(-82937829388970586681490548537),(-82937829388969742619748744794)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-30188919618983220793934173777),(-30188919618980938668450422785)⟩,⟨(-131845202959257271112317497760),(-131845202959254989007080608151)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-67981129887493251787322436326),(-67981129887487345522867480150)⟩,⟨(-169387477710889259021746595969),(-169387477710883352781720737924)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-123231936684417269488245601993),(-123231936684402816844156876121)⟩,⟨(-188733407263703010061017142397),(-188733407263688557442057973778)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-189784995905289897778956805613),(-189784995905258584598469572562)⟩,⟨(-183212842915831599614026280193),(-183212842915800286455395798513)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-256216657098682238508324006508),(-256216657098626875111994230111)⟩,⟨(-149010465556109366465419526524),(-149010465556054003083987982231)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-308881676405252298010855143306),(-308881676405177804547765961980)⟩,⟨(-88184001370469903248166419573),(-88184001370395409790362192993)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-336087888411491174330588645017),(-336087888411415011745349118914)⟩,⟨(-9931683378441413731165322468),(-9931683378365251140426190828)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-332057937378184387510413092252),(-332057937378125276888416190533)⟩,⟨71152148043187219913188334120,71152148043246330550957549588⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-298976968492564573097952128060),(-298976968492529728027500507848)⟩,⟨139078012733096693897181282299,139078012733131538991359224376⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-245846300725681587505877230945),(-245846300725664883719200423361)⟩,⟨180722378908115490740588010619,180722378908132194555131822046⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-184367266842096359838684438444),(-184367266842089306707084119688)⟩,⟨188784575853541275878672329517,188784575853548329037869237860⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-124199147357918210951266686571),(-124199147357915414556249786476)⟩,⟨163041091719065717516882019967,163041091719068513935070752903⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-70280970111763228159128935280),(-70280970111762176087002957558)⟩,⟨109603313103910198173889603173,109603313103911250261371164888⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-22577870388446680319190377249),(-22577870388446410105901759205)⟩,⟨38518754882956814697893638265,38518754882957084916550410423⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨152580394370847595869468720,152580394370847598042166497⟩,⟨7553872668250438349762116650,7553872668250438352746916000⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨2242028014426447766165704799,2242028014426447773135560240⟩,⟨22337159250922175891616448942,22337159250922175900922779675⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨9277235515305090551924034620,9277235515305090564991824125⟩,⟨35905320968407720376444662192,35905320968407720392924456836⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨23080251022288853839168156528,23080251022288853860324299944⟩,⟨46786331449323132944529461735,46786331449323132969527862553⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨43209254082849885474787213488,43209254082849885506581300418⟩,⟨52680854104107388333049143952,52680854104107388368373306815⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨66784277723613897467744738385,66784277723613897514173793210⟩,⟨50686228729922908542938531525,50686228729922908592093998083⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨89380308393312739054968127303,89380308393312739128159969301⟩,⟨38574062218023844434115143920,38574062218023844508932406621⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨106250731528487912881161277759,106250731528487913054673442276⟩,⟨16594522766857397748038299818,16594522766857397922040541409⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨113572387883772627532080179020,113572387883772628396189952866⟩,⟨(-11825207471563506562670228763),(-11825207471563505698869411033)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨109773123472754527392398729378,109773123472754532976559306459⟩,⟨(-40980863193802286881925983760),(-40980863193802281298291043399)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨96254088903147796543997179058,96254088903147825386035721542⟩,⟨(-64646761973880895121378176186),(-64646761973880866279605890421)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨76772873366186274306595626219,76772873366186377754376096846⟩,⟨(-77819500751669109650711404971),(-77819500751669006202763222861)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨55681947795973662636325352923,55681947795973908685098392191⟩,⟨(-77963278276215401884012324051),(-77963278276215155834696875515)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨36232166985035252441638041184,36232166985035637280618133782⟩,⟨(-65505338224050438393857906700),(-65505338224050053554172333285)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨19866969281957227075531197395,19866969281957602560667328989⟩,⟨(-43248003254868055257352810420),(-43248003254867679771635185482)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨6257075306673185391992215534,6257075306673342657305853949⟩,⟨(-15060468431831885211857708908),(-15060468431831727946320612574)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨16488691224104454950703232564,16488691224184751120767620230⟩,⟨1162942111463461978195768980312,1162942111463542274365635086015⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 0) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_0 (tableDensity false) (fullFactor false 3 0) density0_contains hk3_0_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-5506294250),5506294250⟩,⟨22516660498395404810607042579,22516660498395404821361172660⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_0 3 0 ha3_0_0_contains + def realAnswer : RBox := ⟨16488691224104454945096938314,16488691224184751126373914480⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_0 +namespace hm3_1_0_0 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_0 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-15315779090563646383249479714),(-15315779090563609264827225214)⟩,⟨16255781899089872017251227777,16255781899089909137124905962⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-43925197856202648743187910850),(-43925197856202558839115854604)⟩,⟨49938395189092572026326742578,49938395189092661934534197366⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-66034158039358802688897371729),(-66034158039358707709789439110)⟩,⟨86046712109763362872337029881,86046712109763457857655745270⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-76271560507769787510944544961),(-76271560507769724046234661087)⟩,⟨123417001882426043839189194332,123417001882426107311274444596⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-68965268317283511068292768122),(-68965268317283482839614759081)⟩,⟨158686680271695918550221849935,158686680271695946786346911352⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-40799653825754155579604423059),(-40799653825754147115902963407)⟩,⟨187633398919845872557915374776,187633398919845881028004264910⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨6079241476524991611472743935,6079241476524993471658944532⟩,⟨205864115522242022237703996977,205864115522242024102256183476⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨63700920550145329617032235747,63700920550145330036338506797⟩,⟨209273970475600752703233625969,209273970475600753124272223414⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨120720273713764361938900134157,120720273713764362126379609456⟩,⟨195750445446567935199822551112,195750445446567935386324245757⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨165650373921089063667731587388,165650373921089063809780614919⟩,⟨166907510019416307984953582551,166907510019416308123681098996⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨189890428513360607770493678271,189890428513360607886956434873⟩,⟨128027275300339000243378889885,128027275300339000354844726206⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨189975217921766919337562822944,189975217921766919429638586490⟩,⟨86341717728794915913736378323,86341717728794915999981003934⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨168035515851628676338468240007,168035515851628676407080674193⟩,⟨49051589977727110028817116139,49051589977727110091719993346⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨129769449746229406298143605560,129769449746229406344541614267⟩,⟨21688268117419485492936956841,21688268117419485534577912535⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨81342787278785398974089779334,81342787278785399000551110708⟩,⟨6404345739299668867737397127,6404345739299668891063455954⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨27641152928493616583715770596,27641152928493616592246564118⟩,⟨891157048856201833673337483,891157048856201841103600150⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-2085227669125241699889914903),(-2085227669125195964151689895)⟩,⟨(-17243396292387911779333835877),(-17243396292387866044659215830)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-8482587013878367728824831222),(-8482587013878188661375949460)⟩,⟨(-50121390247316857694919336202),(-50121390247316678630495420264)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-20973764073098324761282372943),(-20973764073097841967338073523)⟩,⟨(-78037735132225384834775218723),(-78037735132224902045353871670)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-41756594997515016037227456657),(-41756594997513771526737089226)⟩,⟨(-97598721537892454784956789579),(-97598721537891210279781395800)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-70485831085030313794128184358),(-70485831085027284238644519848)⟩,⟨(-105784242356384003107409749218),(-105784242356380973557206427182)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-103859903838398694890841590669),(-103859903838392167574481336771)⟩,⟨(-100690467588941003116488979418),(-100690467588934475804551357079)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-136207113049908118409445597876),(-136207113049896623540908640609)⟩,⟨(-82144370287453035200336424776),(-82144370287441540334696387936)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-161296790867933757469710147554),(-161296790867918366606672630850)⟩,⟨(-52184429493692020092743188963),(-52184429493676629230657110444)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-174429693264212817645044391725),(-174429693264197178067815971477)⟩,⟨(-15305158471403570365518095240),(-15305158471387930787238894287)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-173763111437906514975483077854),(-173763111437894462198127044892)⟩,⟨22103862259019875188529132018,22103862259031927968705010416⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-160463401642649853185471243873),(-160463401642642802505417297549)⟩,⟨53148281792104378903863476474,53148281792111429588031333055⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-137683291217942665041997314632),(-137683291217939311420547582709)⟩,⟨72159371792480009431186278020,72159371792483363057389167128⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-109077011306489495824122785546),(-109077011306488090245286849581)⟩,⟨76262203561081290641098750126,76262203561082696224568232551⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-77846383891739054842279409328),(-77846383891738501251102252812)⟩,⟨65959997821343103441551992200,65959997821343657036563410666⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-46262210531148854604440022517),(-46262210531148647511593095622)⟩,⟨44299124358392698486154352040,44299124358392905581516659032⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-15291946970161821431910447484),(-15291946970161768488622497030)⟩,⟨15556851491177735322642366845,15556851491177788266809249601⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨15227758436897518658138306198,15227758436897518665240708117⟩,⟨9548505680442365682258551448,9548505680442365688959548221⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨46435295325708049436216873846,46435295325708049458355634743⟩,⟨26652596205014379860449545323,26652596205014379881389991425⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨78956615227314356376379199928,78956615227314356415501711286⟩,⟨37865739592329227381103406110,37865739592329227418443871154⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨111159323351953173055615884462,111159323351953173114153117533⟩,⟨39619047545421987556593264082,39619047545421987613079651852⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨139210362747317127069512031357,139210362747317127149537399152⟩,⟨29040416971746742152527965275,29040416971746742230635828166⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨158521346652015446745785490079,158521346652015446850711719726⟩,⟨5108349758363686220190696385,5108349758363686323517803708⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨165412849056865364729235030955,165412849056865364869365742599⟩,⟨(-29798932247107460033042288174),(-29798932247107459894020586043)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨158180790043953337430380854301,158180790043953337675292328399⟩,⟨(-69654351077557888049746591688),(-69654351077557887805268757471)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨137849826020260044075253301276,137849826020260044975978411136⟩,⟨(-106440079663700399672285251991),(-106440079663700398771391503127)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨108344086149040271259642482233,108344086149040276473299921106⟩,⟨(-132578584187258252253080541428),(-132578584187258247039039582500)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨75441681498635146864569490860,75441681498635172901359185166⟩,⟨(-143031831279615254957927570233),(-143031831279615228920843127055)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨44849322410033589705838316886,44849322410033681507402825198⟩,⟨(-136591149474873056100908443189),(-136591149474872964299179094202)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨20710918673503531225535641283,20710918673503747009037372466⟩,⟨(-116002516400915505808522866535),(-116002516400915290024951117027)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5247467716914917026827686848,5247467716915251517484957586⟩,⟨(-86391243466682065172992435181),(-86391243466681730682366088879)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-1362909092872205133785873471),(-1362909092871880959388555145)⟩,⟨(-52620336476047723591534870499),(-52620336476047399417211961361)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-1285580707500180865164685167),(-1285580707500045700059818416)⟩,⟨(-17595800262504228912989845658),(-17595800262504093747932677098)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-12690277629266980452510522017),(-12690277629266919619769586567)⟩,⟨8429978012638732540305433608,8429978012638793372260467669⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-36437617919129749955892458331),(-36437617919129603548419241343)⟩,⟨26102586348105487184925613458,26102586348105633590142469603⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-55258160393150458746759526315),(-55258160393150305822332836807)⟩,⟨45906679144446519543174458590,45906679144446672464192245559⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-66096714135183265095572775345),(-66096714135183164332109664179)⟩,⟨68400483861985850939877329847,68400483861985951699268377861⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-66742184948310661854876546144),(-66742184948310617652389593076)⟩,⟨92968457451271088164108999785,92968457451271132362489385836⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-56614181418916505138780104587),(-56614181418916492054776034388)⟩,⟨117450577738860149124706805880,117450577738860162205198349739⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-37000869178279133496444932882),(-37000869178279130702958454016)⟩,⟨138197982240781040728536307714,138197982240781043519652238648⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-10741792283547769603252470642),(-10741792283547769064174670728)⟩,⟨151176049396543916412241658734,151176049396543916950488618942⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨18139196724375053893521795570,18139196724375054063678074869⟩,⟨153577356614103763563245207811,153577356614103763734224545207⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨44978946702068745865299862867,44978946702068745969707679821⟩,⟨144876894763055364573739798400,144876894763055364680437674559⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨65333376973633302767265856569,65333376973633302846517404306⟩,⟨126942428097585779177356103130,126942428097585779259921907033⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨75845983420667256433481588592,75845983420667256493761931243⟩,⟨103249864890479515603427375046,103249864890479515667489787956⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨74882639762196611054625678195,74882639762196611098315804272⟩,⟨77561984933406426326183953393,77561984933406426373545052008⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨62781731943778968313248677958,62781731943778968342225235532⟩,⟨52756535641466124362795135044,52756535641466124394793950374⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨41594643859940781578986980599,41594643859940781595290400270⟩,⟨30219079683435643459171068134,30219079683435643477449696373⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨14534062111975602543260013014,14534062111975602548487093920⟩,⟨9790760987486216828014097748,9790760987486216833923455636⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1063607681591479215176315987),(-1063607681591302298519189803)⟩,⟨(-9227147374512512247168500912),(-9227147374512335329675415865)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-4462204805022511057779255647),(-4462204805021817317084519268)⟩,⟨(-27648554084572366293614014716),(-27648554084571672550470247371)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-11374222192042003947817775191),(-11374222192040128022784003410)⟩,⟨(-45476675713488458284007716672),(-45476675713486582355189161213)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-23277519430497438708188350284),(-23277519430492582921951592201)⟩,⟨(-60999162955817586085730394280),(-60999162955812730294833922464)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-40646014687901250187613040715),(-40646014687889366607646313825)⟩,⟨(-71389646459467815465261598115),(-71389646459455931880432549207)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-62693232137546058943683624052),(-62693232137520311999270731406)⟩,⟨(-73754597411148100724785897489),(-73754597411122353776027485415)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-86994655138631895043329031789),(-86994655138586382867425383516)⟩,⟨(-66513868517489950213129026432),(-66513868517444438034138228699)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-109630443833407877773063523174),(-109630443833346669487717365553)⟩,⟨(-50224135557950172347106194620),(-50224135557888964060606100895)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-126251328019087488229010426197),(-126251328019024958260496325248)⟩,⟨(-27700098743663610654929812173),(-27700098743601080687503111966)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-133443787930812876771128997053),(-133443787930764398216969773470)⟩,⟨(-3488009910633418595062955953),(-3488009910584940043961983959)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-129630274473519028884767544367),(-129630274473490487427429540136)⟩,⟨17391918985440633372088395753,17391918985469174825021212422⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-115357729859070616727124365841),(-115357729859056953075813542590)⟩,⟨31115593776258391195122137265,31115593776272054841388730618⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-93183416509457270590410470541),(-93183416509451508472544641368)⟩,⟨36127031202729364411876476428,36127031202735126524816555977⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-66854148548912713931324237230),(-66854148548910431805522033272)⟩,⟨32831196744908921528400838721,32831196744911203650158776097⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-39645223726830261916554897731),(-39645223726829403961826925133)⟩,⟨22736205008653725062811110172,22736205008654583014905325845⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-13066328583648066254318846102),(-13066328583647845981151086912)⟩,⟨8110192950265996455692010624,8110192950266216727956342812⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨15226142902558213549676498,15226142902558214816698675⟩,⟨224163110719035309541763249,224163110719035311394596225⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨225672591551128308100692841,225672591551128312194204620⟩,⟨615460130449120481579237356,615460130449120487383479806⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨971761574589681992874518059,971761574589682000638844731⟩,⟨577658937379671880848021676,577658937379671891187728351⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2669346811819489223419384901,2669346811819489236210871734⟩,⟨(-819370387262569955974565034),(-819370387262569940140697738)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨5853504948676815381296287142,5853504948676815401203047848⟩,⟨(-4756411098658523826401053290),(-4756411098658523803493558897)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨10805221828321395523887098549,10805221828321395554589952030⟩,⟨(-11834085667045721860582485138),(-11834085667045721827322583541)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨16837407258227781395414630861,16837407258227781447961132236⟩,⟨(-21595102008454090836152488095),(-21595102008454090781869400097)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨22252690376648009824057714600,22252690376648009960893912593⟩,⟨(-32776228358476162452994854726),(-32776228358476162315557964142)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨25196967338067884238909714074,25196967338067884946330960729⟩,⟨(-43629275461024237608790217782),(-43629275461024236901952954489)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨24539140454693403844758865062,24539140454693408416412457575⟩,⟨(-52148916903995874316880916288),(-52148916903995869746729195661)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨20286376519829758912066448776,20286376519829782477727560636⟩,⟨(-56540907893296217949469511938),(-56540907893296194385854464972)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨13615630080244235444307143489,13615630080244319933509092639⟩,⟨(-55813044208831438456478740336),(-55813044208831353969545052260)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨6590281977332844182874738105,6590281977333045200733898212⟩,⟨(-49949579853063196002688892910),(-49949579853062994987003025799)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨1360421123370114033176245680,1360421123370428583559164095⟩,⟨(-39524368258263900656579467806),(-39524368258263586107946419529)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-924686817656845207621132149),(-924686817656538189336386789)⟩,⟨(-25391538836198116835372740189),(-25391538836197809818205900315)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-640813145754311524425729825),(-640813145754182909844924674)⟩,⟨(-8757915016000346746296472950),(-8757915016000218132091347771)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-32830528330751116801287990986),(-32830528330685109088560173405)⟩,⟨226177743084379756153697254195,226177743084445763866111715642⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_0 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 0) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_0 (tableDensity true) (fullFactor false 3 0) density1_contains hk3_0_0_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-7200538635),7200538634⟩,⟨(-29444863728670913997164610401),(-29444863728670913983101517218)⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_0 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 0) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_0 3 0 ha3_0_0_contains + def realAnswer : RBox := ⟨(-32830528330751116808588529621),(-32830528330685109081259634771)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 0) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_0 +namespace hm3_0_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-55256309831371515140115380750),(-55256309831371491527616797882)⟩,⟨(-39724507713328272925839308869),(-39724507713328249310133020279)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-165381118602286249031810054255),(-165381118602286192874118598672)⟩,⟨(-108663525336376899909212425265),(-108663525336376843742619252831)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-272042734869115044488607253651),(-272042734869114987295319118879)⟩,⟨(-148298169120909379098508870091),(-148298169120909321892595305952)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-366969048554852862429344460083),(-366969048554852826274014019209)⟩,⟨(-146938933521759296034361653142),(-146938933521759259865384421050)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-436544073393843968820274059496),(-436544073393843953896182139433)⟩,⟨(-103766312078488216181638924760),(-103766312078488201245541342020)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-466091275048210447053503631542),(-466091275048210442972138156037)⟩,⟨(-29910525559439000619149235414),(-29910525559438996529323666318)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-447292604584220062162286783542),(-447292604584220061340604494998)⟩,⟨54323546196492536798015360299,54323546196492537623967072689⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-384093765859977931934325594320),(-384093765859977931748124713374)⟩,⟨125649554012885193662908713590,125649554012885193849856913121⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-292674045346426849654529822326),(-292674045346426849568817345200)⟩,⟨165957500228130765689459752038,165957500228130765773840857096⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-195384029481550862299187570617),(-195384029481550862242878492850)⟩,⟨168910851719975483359967976428,168910851719975483414420511318⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-112123132431680086827739775106),(-112123132431680086791661383539)⟩,⟨141156878142553013427911338080,141156878142553013462761473967⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-53741990228955340983244669258),(-53741990228955340962621240376)⟩,⟨97671990209726168739370018018,97671990209726168759912939654⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-20549399951321718381331299249),(-20549399951321718371292490027)⟩,⟨54445305418453433860901778657,54445305418453433871874267265⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-5772254279105710046182058196),(-5772254279105710042329743304)⟩,⟨22532686930695886010980054519,22532686930695886016218460448⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-986503711161760444336736337),(-986503711161760443338944659)⟩,⟨5552556540816089914104038532,5552556540816089916273263713⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-52148862283588649781843923),(-52148862283588649663545816)⟩,⟨381875987652714735719213036,381875987652714736287544565⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨94959443925525291837990574001,94959443925525349867137001958⟩,⟨(-67215636556583614122914446641),(-67215636556583556102363066980)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨271880682197107160450766885921,271880682197107385297226173756⟩,⟨(-207082158001943188487882565437),(-207082158001942963665784726098)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨410357094191654925948863774587,410357094191655519884761934197⟩,⟨(-359554128377429250794691782710),(-359554128377428656894732897722)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨488445514952780221665857266227,488445514952781707499712034552⟩,⟨(-522644845756349181094201425844),(-522644845756347695301722868990)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨491778311168283488889891353889,491778311168286968791659335074⟩,⟨(-682862245475615000473544938876),(-682862245475611520611627161689)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨418696966116029122380338097017,418696966116036278849058395180⟩,⟨(-817958976002531431535489759419),(-817958976002524275098869946590)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨283499815904896526773857444673,283499815904908471085549312973⟩,⟨(-903962345406304751689016504161),(-903962345406292807397396296201)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨114555925578308255584314960934,114555925578323329023536153961⟩,⟨(-923829454275991052733270986400),(-923829454275975979300622956361)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-53308377038568647352139298850),(-53308377038554278884058808582)⟩,⟨(-874234224940061377693928981261),(-874234224940047009220225386139)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-188942446748629067560543954352),(-188942446748618702570553474332)⟩,⟨(-767133581930435911096915341655),(-767133581930425546092428994603)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-273004798765137629861894870462),(-273004798765131958023239702020)⟩,⟨(-625192359179174860264766130886),(-625192359179169188406905310191)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-300792268108607821319170507186),(-300792268108605292367627732822)⟩,⟨(-473703870788180209497538602650),(-473703870788177680525995428253)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-279341060249700832267373311168),(-279341060249699833104288417040)⟩,⟨(-332966372522237199411528114365),(-332966372522236200230658345819)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-221533205842688453097500809667),(-221533205842688078606136077461)⟩,⟨(-213845482762834118049306523174),(-213845482762833743544296324608)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-140782639553016977362492007808),(-140782639553016842227766873406)⟩,⟨(-117361492453645755571107762532),(-117361492453645620427905847421)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-48109229721944490982442779179),(-48109229721944457087075832200)⟩,⟨(-37159036821766611816666394960),(-37159036821766577918435060111)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1056085025258880301608218314),(-1056085025258880284484854684)⟩,⟨124850362627673129342055219650,124850362627673129373319963773⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨12902869451459569916951456971,12902869451459569970756578318⟩,⟨368864399074015945743803595418,368864399074015945838238755569⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨71414350089509139529098999794,71414350089509139626323539328⟩,⟨593248358250252801086783089168,593248358250252801245136599402⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨191790367896892677481906071933,191790367896892677631103470623⟩,⟨779051840795520198413507296398,779051840795520198635125531374⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨373576490357689486594142028046,373576490357689486802391225222⟩,⟨902589012179085649879430959549,902589012179085650159968324399⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨596162675973138546199536811309,596162675973138546474349665998⟩,⟨940708640670058086490330316600,940708640670058086825376538697⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨823018509430791522614280693112,823018509430791522969078965075⟩,⟨880327619937419219052452893168,880327619937419219446410724146⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨1011427202701396063647973218691,1011427202701396064183121246398⟩,⟨727634832541583240104478020526,727634832541583240653194628858⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨1124882356577363080521075846393,1124882356577363082069819358356⟩,⟨510345140402437014162754211813,510345140402437015700224589521⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨1144037219153792342092964205943,1144037219153792350062935136728⟩,⟨270902140416520791510185233461,270902140416520799449478136048⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨1071243497515753704598225916167,1071243497515753742417506392500⟩,⟨54144221459024863449355462798,54144221459024901226387942133⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨926431707389022219745965711828,926431707389022348152941398746⟩,⟨(-104785748233328776021407401624),(-104785748233328647660252581335)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨736986315009514773772350436958,736986315009515066116338283311⟩,⟨(-187906252741629826560332478160),(-187906252741629534258806532436)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨527604494989111370293018914123,527604494989111811977841786110⟩,⟨(-195693767048195949175035165792),(-195693767048195507523914415745)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨314504391762496100230329692440,314504391762496520621866238617⟩,⟨(-142876115608008154876946473473),(-142876115608007734506872680101)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨104180165274877581607832376972,104180165274877755256972056353⟩,⟨(-51905569403999581902909872132),(-51905569403999408261091324210)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-89763282213712017730518014755),(-89763282213711866261845215407)⟩,⟨(-32131498518061142872766668787),(-32131498518060991420185805861)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-270247134597172591896546254344),(-270247134597172228776599288598)⟩,⟨(-85342716657406153298083107649),(-85342716657405790224146467826)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-450591123126499101159408360264),(-450591123126498724759226313850)⟩,⟨(-106606371153169886614682689618),(-106606371153169510283744578460)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-622687813275371879600176072907),(-622687813275371634289939384035)⟩,⟨(-79330466491209389368948892531),(-79330466491209144140864211193)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-770107108611397832815165112353),(-770107108611397726646357149772)⟩,⟨5308455344939644376086391243,5308455344939750462445381840⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-871753271984560178843968799788),(-871753271984560147830382826279)⟩,⟨144611574017088263056519010593,144611574017088294000242237596⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-909039397870669932646417997571),(-909039397870669926008664142682)⟩,⟨321710799795123380622691196706,321710799795123387214018324610⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-873046732429289283068317851130),(-873046732429289281666418339762)⟩,⟨507107044878053182830168796487,507107044878053184215721803050⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-769073106097090795248919728993),(-769073106097090794703689198410)⟩,⟨666003452936034185566822495339,666003452936034186126999098628⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-616740004920513125650606428176),(-616740004920513125282016320838)⟩,⟨768353049532921468742441503824,768353049532921469152990307227⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-444798357605760706312563382916),(-444798357605760706033582340665)⟩,⟨796930096648789520251702495089,796930096648789520591177881743⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-282733642036947149673212548876),(-282733642036947149467637509501)⟩,⟨750292630672402100350311677721,750292630672402100624305774079⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-152950215766844293176789733837),(-152950215766844293033812751136)⟩,⟨639933755588422084632939667477,639933755588422084841643347749⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-66102587867205324788553604017),(-66102587867205324697367113854)⟩,⟨483735623454022379132711497532,483735623454022379277673336708⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-20278182520137429865833092153),(-20278182520137429816090699680)⟩,⟨299493746189185639006201449397,299493746189185639090940191769⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-3315437845826599478587304235),(-3315437845826599462925300257)⟩,⟨101173982273312300982159178510,101173982273312301009915551370⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨73788645744012452669809689470,73788645744013015682979259843⟩,⟨(-4696714060648457806329797770),(-4696714060647894781220646182)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨216097419872213704003492213296,216097419872215902805050402503⟩,⟨(-25553448681961789771275331269),(-25553448681959590935662503143)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨340956454123352321885068674542,340956454123358220648480122892⟩,⟨(-78032455188612419012106113318),(-78032455188606520197219878899)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨433254285312576769786276680468,433254285312591864608014685890⟩,⟨(-173784862349892423174519190868),(-173784862349877328291270672905)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨475961902980112719553683977010,475961902980149129119402517066⟩,⟨(-310586127361644587249285658828),(-310586127361608177621071163190)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨454333355892065133804938229972,454333355892142691120135106627⟩,⟨(-470295355891870877425933336465),(-470295355891793320057180016323)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨362601952795635242042331463240,362601952795769787944456958445⟩,⟨(-622883642169756172676993997398),(-622883642169621626738958504709)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨210342725489855720081125559179,210342725490033104656521611906⟩,⟨(-735522059683860619996104283822),(-735522059683683235408172216638)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨23497145369535319500079098415,23497145369712853693363738985⟩,⟨(-783227230784037485392009115403),(-783227230783859951211451469485)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-161934183780826964225324280611),(-161934183780692074856459474831)⟩,⟨(-757278461018110547800800935046),(-757278461017975658467846488856)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-310345006288995971824181372669),(-310345006288918078668277498423)⟩,⟨(-667779538062179318999881973093),(-667779538062101425897093681231)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-395765510168108316038852922430),(-395765510168071683931486207660)⟩,⟨(-538691654114930323657860931309),(-538691654114893691611921668768)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-406694447990075224442438148989),(-406694447990060013802247912934)⟩,⟨(-397321992863323549833957483044),(-397321992863308339253794855942)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-346655163342519174085008127714),(-346655163342513224543223199961)⟩,⟨(-264122876366326577372567844574),(-264122876366320627880650996320)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-230911474932765162289258171716),(-230911474932762945170750112307)⟩,⟨(-148079007554745458539869485654),(-148079007554743241454160762302)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-80769905531557215202724085587),(-80769905531556648563363810123)⟩,⟨(-47343925220943086916680519321),(-47343925220942520288741664015)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-23712222617088992800635026090),(-23712222617088992791189931031)⟩,⟨478835241743589414237589340,478835241743589421059354855⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-69895719827901138583177212810),(-69895719827901138553831952512)⟩,⟨7012267559591114617639411452,7012267559591114639470435997⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-111651474940403645575055196238),(-111651474940403645523439029801)⟩,⟨28834371451575955298601512337,28834371451575955339326105679⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-144164152110801982909272672247),(-144164152110801982831726307298)⟩,⟨71082894698855372676594059823,71082894698855372742004284521⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-160437267680893165006628983682),(-160437267680893164898385079660)⟩,⟨131524192429555944075754816686,131524192429555944172992097399⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-152236791370978468540639456939),(-152236791370978468392211383174)⟩,⟨200463557661586515420732769995,200463557661586515560791862370⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-114083106354248819406163671180),(-114083106354248819184153489562)⟩,⟨264094634165652537077665033936,264094634165652537294780237321⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-48324657753790354305155391942),(-48324657753790353799296165332)⟩,⟨308648660421688902511986115063,308648660421688903016400094813⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨33624118642046412097091039675,33624118642046414557403335160⟩,⟨324147721228975442906519538308,324147721228975445367702900597⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨114794799130614447723916301192,114794799130614463341914775940⟩,⟨307832312558639326395772514377,307832312558639342015165509245⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨178131873231110924823738079887,178131873231111004173620379088⟩,⟨265397109648964120411622758757,265397109648964199762028525982⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨211177494211243318426176656840,211177494211243598817176231525⟩,⟨208428958131784544093333092216,208428958131784824483528900349⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨208783079371049802649011716235,208783079371050461061354292304⟩,⟨149157983785063865309265884522,149157983785064523719726618708⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨173577821406126033548349971281,173577821406127052912062877061⟩,⟨96025226451532772547656710875,96025226451533791909090185142⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨113759920806792654537627248162,113759920806793642084839350322⟩,⟨52261853033558680047656020116,52261853033559667593046949916⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨39465940262994629074598718481,39465940262995041182983161385⟩,⟨16396794177223587214796291196,16396794177223999322490190413⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨85975378783143523823830383077,85975378783307103439866007360⟩,⟨(-101682524015329748402284234136),(-101682524015166168792651814143)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 1) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_1 (tableDensity false) (fullFactor false 3 1) density0_contains hk3_0_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-11885724760),11679412698⟩,⟨41818114715378378756943821594,41818114715378378781118037335⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_1 3 1 ha3_0_1_contains + def realAnswer : RBox := ⟨85975378783143523811844658317,85975378783307103451645420058⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_1 +namespace hm3_1_0_1 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_1 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-8470553509382366809873235406),(-8470553509382347465601995691)⟩,⟨(-7980959282968788243167405156),(-7980959282968768899653665953)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-25521546100146949571217727951),(-25521546100146903581985795651)⟩,⟨(-22454010291645764987636443028),(-22454010291645719000522599318)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-42287449426046256395238854424),(-42287449426046209594301729781)⟩,⟨(-32475195181511478289454929375),(-32475195181511431491580624935)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-57146681442994619453479236676),(-57146681442994589905504316293)⟩,⟨(-35372138948941434022801621010),(-35372138948941404478261586754)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-67748840743391409840267718474),(-67748840743391397671647773384)⟩,⟨(-29548751967377320569203688768),(-29548751967377308403798185803)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-72149683576573332165531038201),(-72149683576573328860828422342)⟩,⟨(-15853307160841170868149807230),(-15853307160841167565956679859)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-69468241831437798510333049555),(-69468241831437797868505184343)⟩,⟨1831891934400900484777148337,1831891934400901125068396225⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-60170465133036503534665287996),(-60170465133036503411061064020)⟩,⟨18056292323062130863508922945,18056292323062130986575483660⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-46324974677347545923027440490),(-46324974677347545878124763872)⟩,⟨28287131286226108519406293449,28287131286226108564573791469⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-31175318447130640239032464240),(-31175318447130640212647881341)⟩,⟨30652543750248985528888464244,30652543750248985556041586595⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-17899360425483467991061336134),(-17899360425483467975135792943)⟩,⟨26269806619683701404760932341,26269806619683701421659223328⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-8421397127808525568865416398),(-8421397127808525560231023855)⟩,⟨18272634165689637224937833999,18272634165689637234509828362⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-3020419618484340559866042251),(-3020419618484340555884820016)⟩,⟨10124488396286601049540014612,10124488396286601054277609761⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-721454888608754079103502207),(-721454888608754077687520438)⟩,⟨4148550307101819456124871398,4148550307101819458065515689⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-86735329939035022395554303),(-86735329939035022080189200)⟩,⟨1013630688255572280585833973,1013630688255572281199937621⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-2510673525841185314454853),(-2510673525841185292575476)⟩,⟨69378240903115723462727678,69378240903115723580139914⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨18014006614550851933513278397,18014006614550899709270804414⟩,⟨(-2178244454577950745413864719),(-2178244454577902968595942394)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨51863573857964964281364325707,51863573857965149475323528224⟩,⟨(-8772887992713286786637796222),(-8772887992713101589690511256)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨79230894039836658132471844118,79230894039837147681208564207⟩,⟨(-21274428129855141673208718763),(-21274428129854652120084432749)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨96334982549163555888370558871,96334982549164781672310216090⟩,⟨(-41164538373752792051426728786),(-41164538373751566262466998803)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨100618030091414141890811906187,100618030091417015294027817618⟩,⟨(-66942034188095453197017504544),(-66942034188092579788984189643)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨91533683855229392787934673923,91533683855235306845100661926⟩,⟨(-94240411997419051949303339736),(-94240411997413137888269587662)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨70850159092810752849654809745,70850159092820632156618972386⟩,⟨(-117190007420028876045641216424),(-117190007420018996736263508667)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨42468702518826901426836351761,42468702518839374756224586672⟩,⟨(-130730861224922319306620232927),(-130730861224909845976477819642)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨11791542335761976290772172711,11791542335773865832767762441⟩,⟨(-132501262376270235881472073560),(-132501262376258346340248815403)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-15538585631336033112365466770),(-15538585631327460991391364177)⟩,⟨(-123319271644815944212606278290),(-123319271644807372093591789261)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-35096647036636558662404370791),(-35096647036631872460911923007)⟩,⟨(-106326625705698479636810953603),(-106326625705693793438012047265)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-44669596498669977834549098250),(-44669596498667890985205368450)⟩,⟨(-85392574691891044948102629286),(-85392574691888958101693278963)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-44496667053419641966280195981),(-44496667053418818585227557738)⟩,⟨(-63712161201128217553249361699),(-63712161201127394174905333036)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-36633364825690196297559738636),(-36633364825689888070631638630)⟩,⟨(-43259208175985536989701984256),(-43259208175985228764912498044)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-23744234296866543190735480681),(-23744234296866432071301523579)⟩,⟨(-24801662278136902895291237669),(-24801662278136791777212571814)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-8184490338832863339818766899),(-8184490338832835482113544921)⟩,⟨(-8045316631916484142574311755),(-8045316631916456285334026226)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-14974893815685232889942226494),(-14974893815685232879384273934)⟩,⟨23881367734185044977151249419,23881367734185044988365993574⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-41536369695363620529760182833),(-41536369695363620496978719888)⟩,⟨72358788263370760242288152273,72358788263370760277019600576⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-58280689849042051381530467612),(-58280689849042051323813283160)⟩,⟨121488716041879659105686989495,121488716041879659166283016694⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-59877171831017932008864564104),(-59877171831017931923169174018)⟩,⟨167883239592342552245063997553,167883239592342552334038150146⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-42886472913921864289769885173),(-42886472913921864174118191514)⟩,⟨205228915954410504824528796907,205228915954410504943213327062⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-7429930381619992955224478582),(-7429930381619992806682160920)⟩,⟨226984857994270382192547131741,226984857994270382343587378360⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨41109568634470032735233620700,41109568634470032928328391352⟩,⟨229075978483263104243676913440,229075978483263104438475946841⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨92792839608829658967921223162,92792839608829659294191307431⟩,⟨211171195706613601638042201606,211171195706613601964964196679⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨136464089563165888646674408772,136464089563165889797812056298⟩,⟨177023065786068922119231939625,177023065786068923270064900097⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨163408424495172455204638704324,163408424495172461599438925133⟩,⟨133733380835425368328416571256,133733380835425374722451133202⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨169597670832901191595462299302,169597670832901222331896032357⟩,⟨89580350786632190383946879948,89580350786632221119544978672⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨156195205701691560028140821482,156195205701691664654594877002⟩,⟨51362945396785780342801248998,51362945396785884968454020519⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨128479160431471877777312946262,128479160431472116254150545032⟩,⟨22980159935801682149550012386,22980159935801920625687479876⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨93236333372677791174268756003,93236333372678151761847089563⟩,⟨5681224942951734681304628879,5681224942952095268411305662⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨55761122342729466453563202646,55761122342729809839479625456⟩,⟨(-1439772660092100493107067040),(-1439772660091757107433082727)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨18470505391678563411452630218,18470505391678705289742624753⟩,⟨(-1349308998181881728043627587),(-1349308998181739849812699209)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-17634454788014647779227194930),(-17634454788014520523173762861)⟩,⟨(-26546667594167267398794515960),(-26546667594167140141067792419)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-54341433101716638055850035931),(-54341433101716333193109279361)⟩,⟨(-75862397572923541719738367570),(-75862397572923236852218183757)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-94668145650098038719037824348),(-94668145650097723160169097439)⟩,⟨(-113973083678889288335381320195),(-113973083678888972769365721366)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-139106437078976444444092007839),(-139106437078976239261338771218)⟩,⟨(-134467217525176170684959064881),(-134467217525175965493800332950)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-185706815604296971795647480098),(-185706815604296883319272918643)⟩,⟨(-133394462105290141073374558195),(-133394462105290052588695961917)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-229623101291513628293445614053),(-229623101291513602642224664438)⟩,⟨(-110784014318716953184878524407),(-110784014318716927526729439666)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-263675225658220874042178361776),(-263675225658220868696130439749)⟩,⟨(-70711282650994203572636866489),(-70711282650994198222041798243)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-280883678696926565303230793155),(-280883678696926564298659617294)⟩,⟨(-20081028740507507583581330691),(-20081028740507506577459125994)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-277524514646856814744306376753),(-277524514646856814433668484530)⟩,⟨32655200416289580444903920932,32655200416289580754069866429⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-254564741143694140450176248504),(-254564741143694140261477379624)⟩,⟨78916131912623371712670583551,78916131912623371897392175372⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-217073973677240369965152057457),(-217073973677240369822925929998)⟩,⟨111619802737815644565757493274,111619802737815644702409822199⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-172178024086607286879327460187),(-172178024086607286771649309187)⟩,⟨126402158333473021017705422397,126402158333473021119217052626⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-126537739748850576506182605774),(-126537739748850576428271267958)⟩,⟨122117756706570828502102734059,122117756706570828574192969062⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-84567922702812756846923203706),(-84567922702812756795186467473)⟩,⟨100615616629939174768013880509,100615616629939174815066058232⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-47847208707858435997729266807),(-47847208707858435968532377770)⟩,⟨65852873935801486903969815466,65852873935801486930153815536⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-15403965311261864987339324669),(-15403965311261864977959121784)⟩,⟨22866446424385625898121539665,22866446424385625906469708458⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨24133418475174700063159820803,24133418475175162777412949438⟩,⟨(-2781754058020288788522098514),(-2781754058019826076523618451)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨72038326765827035820943498390,72038326765828843038439021432⟩,⟨(-11623945850926922163162857301),(-11623945850925114952244756771)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨117600682634863750399715061742,117600682634868599281179990985⟩,⟨(-29403238163137385203531224393),(-29403238163132536332153259370)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨156014218900167047067505436406,156014218900179457210305207057⟩,⟨(-59509906595328903810483297525),(-59509906595316493679961193930)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨180023139962673328699641016191,180023139962703266256793939157⟩,⟨(-102443847263372723959489951641),(-102443847263342786414957642200)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨182876589509463471220258089484,182876589509527241997143212204⟩,⟨(-155352712191286102037765330487),(-155352712191222331271952205892)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨161815657183530240525471634188,161815657183640845774842060989⟩,⟨(-211477985716095334339166991804),(-211477985715984729097494865920)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨119709909021768758431073911134,119709909021914508388784517016⟩,⟨(-261032873906190815355403289920),(-261032873906045065400509837222)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨64660263263626769428213730404,64660263263772526372302840850⟩,⟨(-294185596583850010886689165669),(-294185596583704253940022530970)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨8049328606673751543272965514,8049328606784378924396191541⟩,⟨(-304287165366517922284713591274),(-304287165366407294896480434346)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-38768808732008370664555842209),(-38768808731944568606268157237)⟩,⟨(-289496918251595220607868637595),(-289496918251531418539535714785)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-68123684403533764649063359355),(-68123684403503799690327433241)⟩,⟨(-252738900031721325136994861258),(-252738900031691360166952466591)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-77820980636550535398315269816),(-77820980636538108974788938814)⟩,⟨(-200798017080245923769502440832),(-200798017080233497335101002362)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-69802602246644300652392791372),(-69802602246639445303100156516)⟩,⟨(-142165066042577313169798179013),(-142165066042572457811686431183)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-47899845300821571645362158218),(-47899845300819763638529170425)⟩,⟨(-83528973624519896158045191338),(-83528973624518088145521582933)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-17006222786375503407091990258),(-17006222786375041503842892237)⟩,⟨(-27398937225001532075158560183),(-27398937225001070169966814970)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-703667307810478422894797820),(-703667307810478417076394315)⟩,⟨47783419382561285118432283,47783419382561289095846767⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1925981870627986252922434361),(-1925981870627986234754459136)⟩,⟨705819583461529853442741390,705819583461529866253454505⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1797714658093383411873303383),(-1797714658093383379715825033)⟩,⟨3020192664331373780309675128,3020192664331373804460408508⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨2518464213697351361410744222,2518464213697351410201433508⟩,⟨8220166255938971569313499705,8220166255938971608747646337⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨14468049388254441341760405914,14468049388254441411548346583⟩,⟨17814035135004859041612736988,17814035135004859102290293362⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨35505517527199166446919429472,35505517527199166546874442333⟩,⟨32426603450902219056592315930,32426603450902219148909131219⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨63784076619032372401788606904,63784076619032372562326726176⟩,⟨49740946851910528296957183979,49740946851910528452412475722⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨95180235176499655074952559692,95180235176499655473904675087⟩,⟨64634260176500914567012917919,64634260176500914964244820331⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨124482846060457474281412865639,124482846060457476294082109147⟩,⟨71911195089173834166334629864,71911195089173836180615415178⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨146193837481999626201615105760,146193837481999638984353420331⟩,⟨68816209192785437989335527699,68816209192785450776100519515⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨155852251768935040636800810156,155852251768935105465009227116⟩,⟨55942708849109437999636506310,55942708849109502833160550916⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨151486263257182875793300581708,151486263257183104790936590326⟩,⟨36976455565044511870298726617,36976455565044740873668759633⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨133774489340692416903233331529,133774489340692954807900655602⟩,⟨17664594480127729553480388085,17664594480128267463520900217⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨104735961383286266189585636930,104735961383287099365790230317⟩,⟨3611865365594524892630137160,3611865365595358073080719513⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨66790632218189429950045295793,66790632218190237421117069774⟩,⟨(-2430597052725352850482399407),(-2430597052724545376736176673)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨22950120808422141839738212903,22950120808422478868343719483⟩,⟨(-1679183158371476063542295557),(-1679183158371139034046542296)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨15618856323518824745970366668,15618856323653187203120179327⟩,⟨(-227456892497481691947459528023),(-227456892497347329490890426389)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_1 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 1) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_1 (tableDensity true) (fullFactor false 3 1) density1_contains hk3_0_1_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-15273078143),15542870840⟩,⟨(-54685226935494803021462048823),(-54685226935494802989849612853)⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_1 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 1) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_1 3 1 ha3_0_1_contains + def realAnswer : RBox := ⟨15618856323518824730597288525,15618856323653187218763050167⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 1) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_1 +namespace hm3_0_0_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨10350295619138436689729397753,10350295619138442843224850437⟩,⟨(-14396620780980054577711626907),(-14396620780980048425039631444)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨27778567089655753395708499203,27778567089655767761744574772⟩,⟨(-42263732599351718203024158101),(-42263732599351703839225447077)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨36484583788163543445049929858,36484583788163557541063700722⟩,⟨(-66862269371907604144295487147),(-66862269371907590051321123633)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨34110423572460159645013394984,34110423572460168067204833473⟩,⟨(-84994255301686097899565445111),(-84994255301686089480446864844)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨22287734904435528168969720822,22287734904435531389631325719⟩,⟨(-93251495182873594611928858768),(-93251495182873591393729020062)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨5914657324742519492054199559,5914657324742520290870684798⟩,⟨(-89714744588655592761987072693),(-89714744588655591964699649348)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-9004820118042116892851169686),(-9004820118042116750286592856)⟩,⟨(-75607336132188456626560595474),(-75607336132188456484646087226)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-17933552617269252492559688106),(-17933552617269252464814561698)⟩,⟨(-55370127899087341828827036039),(-55370127899087341801166223710)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-19552209832515976164877314945),(-19552209832515976154409163685)⟩,⟨(-34770867012578385386775851887),(-34770867012578385376182090223)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-15732151710609215130048718089),(-15732151710609215124588795609)⟩,⟨(-18353600444302714953101493491),(-18353600444302714947545330308)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-9853909510036462836354854150),(-9853909510036462833642421522)⟩,⟨(-7904349184373901722547380523),(-7904349184373901719846471161)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-4763137460905402435184857050),(-4763137460905402434003711616)⟩,⟨(-2653356809354101377765354743),(-2653356809354101376669159817)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-1679255879230398698035621131),(-1679255879230398697601959610)⟩,⟨(-644280903336911494534190208),(-644280903336911494189339956)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-377065501554492348761756840),(-377065501554492348636234281)⟩,⟨(-98735498301641492120038780),(-98735498301641492045688012)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-38678027743661582891922678),(-38678027743661582868241907)⟩,⟨(-7048167419977767001560972),(-7048167419977766993022995)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-638203458902363785782945),(-638203458902363784388540)⟩,⟨(-88164833299835768064751),(-88164833299835767803588)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨35109338837294567961800015599,35109338837294598266904916932⟩,⟨49601747416627932719949623054,49601747416627963029592144891⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨107129134392715174928035236159,107129134392715291189312356401⟩,⟨140669391168246661504500656724,140669391168246777778516609262⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨182478237087424809025102052906,182478237087425110147390909608⟩,⟨208332060198894410664450487202,208332060198894711805178413645⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨257819063640389522153196794177,257819063640390253940968222015⟩,⟨241100423927684851490962877529,241100423927685583299370532783⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨324524156488511045648528565928,324524156488512696139744296188⟩,⟨233953402644427838799727007661,233953402644429489310090252134⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨371388409440335526834407707023,371388409440338769540953473241⟩,⟨190420258621744084751670494955,190420258621747327472950747315⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨389167150023530444244474126350,389167150023535578416483050552⟩,⟨122408187385974048107943107756,122408187385979182288688273652⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨374654529855061616438622276549,374654529855067726476164303496⟩,⟨46824313718505770186860125066,46824313718511880227110905324⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨332285595443300214399740476707,332285595443305678027687147584⟩,⟨(-19919066879171791315209563612),(-19919066879166327689378892813)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨272413148488776361146915326273,272413148488780048443542256277⟩,⟨(-66800909142026311068512054148),(-66800909142022623777000169514)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨207280318382843353471460571746,207280318382845239055671399046⟩,⟨(-90285193638089640093482185736),(-90285193638087754515573772718)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨146994377697843325416637397688,146994377697844112517658986641⟩,⟨(-93180403895160031658065139736),(-93180403895159244563149630900)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨97294868766049935796977835982,97294868766050228525562126334⟩,⟨(-81533422352126286845544045234),(-81533422352125994122036059114)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨59437239089307010367743670107,59437239089307114640960789614⟩,⟨(-61534067702192191069150827631),(-61534067702192086799611459251)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨31463930012869770791151275696,31463930012869807049939872913⟩,⟨(-37733186296176625499438245435),(-37733186296176589242840197163)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨9775126742483458265367093101,9775126742483467183641469779⟩,⟨(-12655317448150321941431527540),(-12655317448150313023881106765)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-97900508825426496518994490560),(-97900508825426496494165960547)⟩,⟨(-828690987277522216221219728),(-828690987277522202786827994)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-287405820565236896871162304276),(-287405820565236896796653931973)⟩,⟨10038633115662267979644668492,10038633115662268021604480015⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-456447231392872018363179905948),(-456447231392872018239829325328)⟩,⟨54883201257427249677160922061,54883201257427249752134630150⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-588376923327152390954196060817),(-588376923327152390784772061932)⟩,⟨144694844272861187302740950539,144694844272861187415885830476⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-665436985096147663455716000427),(-665436985096147663246390535070)⟩,⟨275135702446877534816423210308,275135702446877534970876339964⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-673666165413389953225467764799),(-673666165413389952982702601038)⟩,⟨426478415570295213633561077888,426478415570295213831853410792⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-609794448601124033337309970757),(-609794448601124033061500168744)⟩,⟨569448309541733121260063533309,569448309541733121507856243103⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-485963764695727135001435216438),(-485963764695727134632686828571)⟩,⟨674602163105505283740329306163,674602163105505284099677734830⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-327985098358190951429670937230),(-327985098358190950444502672653)⟩,⟨721680128130103873366779190897,721680128130103874359402317122⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-167508771531534777659644177389),(-167508771531534772788035443739)⟩,⟨705428130523712361870324538745,705428130523712366761535761782⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-32464417626606127819696769400),(-32464417626606105517727152264)⟩,⟨635344402621419397702029951311,635344402621419420030026016826⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨59692150325728493711138933750,59692150325728566866067920577⟩,⟨529822111471333610762195947216,529822111471333683944392935141⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨103941467926156900216392505818,103941467926157061749745828338⟩,⟨408177159341030873047192257199,408177159341031034605049361334⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨105551806547200259004541241834,105551806547200497069547895387⟩,⟨284719689119306078721511540740,284719689119306316805492146300⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨75690721650659616107734607240,75690721650659838753066613727⟩,⟨166641069154926229526745206784,166641069154926452183952663156⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨27242486415448301619613693435,27242486415448392752933201759⟩,⟨54679630495647059194492003561,54679630495647150331826478778⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨33608028407245787023545484772,33608028407245945437578565661⟩,⟨(-93887021405188655660475498909),(-93887021405188497229423297289)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨88847524626522176730387200767,88847524626522554750227839601⟩,⟨(-281312678541286087458415032008),(-281312678541285709390124902297)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨109971321561613508872884946099,109971321561613897164073245046⟩,⟨(-464630853042332672081322490199),(-464630853042332283717844370277)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨80779723276674437283384727083,80779723276674686974802472250⟩,⟨(-633253681663795032201806171228),(-633253681663794782425698698314)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-5116643684160790633602197159),(-5116643684160684448509288228)⟩,⟨(-769284881180818694365679976591),(-769284881180818588096962267973)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-141110530739980580117037911036),(-141110530739980549774645249451)⟩,⟨(-852356202386874915246472944121),(-852356202386874884834576361058)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-306605304587912257859892747045),(-306605304587912251546453134306)⟩,⟨(-867435384783974373600416912633),(-867435384783974367241773467309)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-470778535567181896107254848319),(-470778535567181894813297181166)⟩,⟨(-811308037486078650509681086826),(-811308037486078649200145938252)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-601439316519356987749250651235),(-601439316519356987239274565445)⟩,⟨(-695130117815816693650838585582),(-695130117815816693154660822631)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-674753776795858894552755944015),(-674753776795858894188489512658)⟩,⟨(-542062278990553964038474762010),(-542062278990553963712093135353)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-681147719498462204298969344695),(-681147719498462204005239865568)⟩,⟨(-380488464261317353269759858021),(-380488464261317353029392035621)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-625419418582357449717578660216),(-625419418582357449485930272828)⟩,⟨(-235872787909959764226456935396),(-235872787909959764053866402993)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-521905302731731609836284454774),(-521905302731731609663338914561)⟩,⟨(-124843887073292820106545253022),(-124843887073292819989268358194)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-387665101762951258822088919188),(-387665101762951258703859939448)⟩,⟨(-53016247679248619508574781116),(-53016247679248619435206939771)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-237089518835018693580761838675),(-237089518835018693512408444392)⟩,⟨(-16062585743558944093616107970),(-16062585743558944054149530604)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-79588892900354705607483465914),(-79588892900354705585220195784)⟩,⟨(-2608472334356272659842469913),(-2608472334356272647507727163)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨6141673183032310111128229234,6141673183033046385938866105⟩,⟨96496542660810289184649244454,96496542660811025444134351151⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨33279278077954426197043179537,33279278077957290214323343906⟩,⟨281525462393263239400873193399,281525462393266103374590657682⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨100850032670424257757433867033,100850032670431881410304048737⟩,⟨440866050017638093202222848345,440866050017645716789678389723⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨222132066116306881890128410123,222132066116326171450127682293⟩,⟨554089948651161790827856147301,554089948651181080310434948141⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨391398962300804972531431696151,391398962300850835680560838112⟩,⟨600170311756437864265038782135,600170311756483727336470146075⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨582722050981886683393182247406,582722050981982734131118311952⟩,⟨563346083940273117892957026560,563346083940369168565285829304⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨757166068279608679516548307919,757166068279772173941245849598⟩,⟨441192353345383572628469101175,441192353345547067009892002432⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨875761404359371975169628143669,875761404359583178136366637995⟩,⟨250871142095436579870590542764,250871142095647782822461800791⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨912662024545193573715206020688,912662024545400497025272319373⟩,⟨27790571331523944075254443645,27790571331730867400047030615⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨863543138808512467661121723273,863543138808666380959342897437⟩,⟨(-184278236509000364871139578043),(-184278236508846451532037083149)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨745784348694079447523110804759,745784348694166512025492709387⟩,⟨(-346270555094297310113826976918),(-346270555094210245551989979145)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨590199202820563142623126747819,590199202820603311427906321755⟩,⟨(-433356881759909935437956768592),(-433356881759869766565476340980)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨428133895124199329952230574231,428133895124215731603785758084⟩,⟨(-438074718937292421538908158858),(-438074718937276019822072688111)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨280845898435300813637149434709,280845898435307142647634311433⟩,⟨(-368530076602667785808258036643),(-368530076602661456744120029070)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨155998724468870266010649481775,155998724468872602109628018666⟩,⟨(-243242329572288537427489436707),(-243242329572286201293487857026)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨49638169644454275879445265163,49638169644454869979341544580⟩,⟨(-84683172678924497951466761205),(-84683172678923903839422760934)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-751352170252477169633310313),(-751352170252477158923931508)⟩,⟨(-37217308621369500155096963246),(-37217308621369500140153893663)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-10965959726557983935770144894),(-10965959726557983901580511789)⟩,⟨(-109356359570065657066229528852),(-109356359570065657019965571954)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-44809952207629940502061312551),(-44809952207629940438604171735)⟩,⟨(-173597034064938620034202026954),(-173597034064938619953372643513)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-109462061129270004592696181931),(-109462061129270004491579626379)⟩,⟨(-222110758484582707280702250572),(-222110758484582707160430214909)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-200175337232554550727434026045),(-200175337232554550578742727189)⟩,⟨(-244305818659310924047390580012),(-244305818659310923881548997563)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-300867152414262801674053539571),(-300867152414262801462801881319)⟩,⟨(-228626934219634455493321845935),(-228626934219634455269230965259)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-390173012771113063634595279764),(-390173012771113063312569254535)⟩,⟨(-168704623793720241632640432687),(-168704623793720241303245773256)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-448309541096600369537487626331),(-448309541096600368804282114305)⟩,⟨(-70364153286192650517003491504),(-70364153286192649781667169954)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-462588373997833068368019320490),(-462588373997833064862922849158)⟩,⟨47804467587093301087038743236,47804467587093304590907301954⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-431631795205759709815069459716),(-431631795205759687970176167627)⟩,⟨160784407580621929444663859359,160784407580621951287712803406⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-365891978868827287741744943497),(-365891978868827178584904638284)⟩,⟨245423471340701373512267030509,245423471340701482668675381050⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-282934563911744831023095620467),(-282934563911744451024857850591)⟩,⟨286539494937742605918896061085,286539494937742985918697194206⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-199780873203137199425903382720),(-199780873203136318483845635099)⟩,⟨279560510553350255081918658378,279560510553351136027070805266⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-127247533471316150337311348086),(-127247533471314800285944914659)⟩,⟨229977198412956184344942437413,229977198412957534399872109933⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-68739939755016402799535403277),(-68739939755015104148289938643)⟩,⟨149617936603795930435437623264,149617936603797229089461811223⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-21484074264657120701955690531),(-21484074264656580745626040878)⟩,⟨51710241358224768664832195471,51710241358225308622204169294⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-275432676998581592431046636279),(-275432676998398724477193830400)⟩,⟨62535643213685090370097649495,62535643213867958338995611303⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 2) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_2 (tableDensity false) (fullFactor false 3 2) density0_contains hk3_0_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-22919455250350083746733163124),(-22919455250350083716693981134)⟩,⟨(-3819909208391680636345302438),(-3819909208391680607948076045)⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_2 3 2 ha3_0_2_contains + def realAnswer : RBox := ⟨(-298352132248931676177879799403),(-298352132248748808193787811534)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_2 +namespace hm3_1_0_2 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_2 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2079430671699758373441441650,2079430671699763413720384068⟩,⟨(-2206932576493703726004766362),(-2206932576493698685528152543)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨5739508549244696792063725465,5739508549244708554393400598⟩,⟨(-6521987910159890793548662700),(-6521987910159879030676526462)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨7987152598812542450911192090,7987152598812553982243795624⟩,⟨(-10393120717298714725064771809),(-10393120717298703192976821399)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨8205532426688999900619144518,8205532426689006780189868669⟩,⟨(-13235947912216276456607472893),(-13235947912216269576236608119)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨6334636345667183036276098679,6334636345667185659380395473⟩,⟨(-14472519362598783187557135423),(-14472519362598780563758725319)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨3083158354782960413270340627,3083158354782961058101004894⟩,⟨(-13887608408001370884207443248),(-13887608408001370238883535877)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-272660421743965002787853790),(-272660421743964892430755047)⟩,⟨(-11741513273622926154437528194),(-11741513273622926043810015971)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-2565476902698535757336170673),(-2565476902698535739235629222)⟩,⟨(-8672731713557408132559508857),(-8672731713557408114375597938)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-3326942246237469397783710900),(-3326942246237469392324510422)⟩,⟨(-5502623637135997288491597285),(-5502623637135997283067362370)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2852485754462723213901011669),(-2852485754462723211293702704)⟩,⟨(-2928144051181064017838314010),(-2928144051181064015316297108)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-1833195239135378611265809885),(-1833195239135378610032437248)⟩,⟨(-1262068025692793016911169974),(-1262068025692793015764598662)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-891157462572193838181715952),(-891157462572193837680908383)⟩,⟨(-416276692555875056514682923),(-416276692555875056077160819)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-312396845379619640608190445),(-312396845379619640444264713)⟩,⟨(-95112028424972369604981497),(-95112028424972369476312245)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-69462615855496087044296098),(-69462615855496087004845845)⟩,⟨(-12508152687291545797078551),(-12508152687291545771986565)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7064480633569690495572022),(-7064480633569690489732199)⟩,⟨(-642488389863287534527405),(-642488389863287532170142)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-115968802107049993536516),(-115968802107049993259630)⟩,⟨(-4423589456343184766692),(-4423589456343184726468)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨1137707415027065831728109630,1137707415027090786268980529⟩,⟨9409545851055790930332206398,9409545851055815884345688262⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨4536638985668947238399939793,4536638985669043008162861556⟩,⟨26833618730634229560592123853,26833618730634325328882537614⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨10790202737622494277340287657,10790202737622742492300916090⟩,⟨40223042527150638143891677887,40223042527150886356728745980⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨20292253453772809144431150753,20292253453773412872222324394⟩,⟨47548092578572894390197750604,47548092578573498115622822237⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨31792770205818730137008911058,31792770205820092983689858960⟩,⟨47858954921978463520972708438,47858954921979826365459908189⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨42764720442593806806828675599,42764720442596486559922510309⟩,⟨41613327334088939910198539565,41613327334091619661603548701⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨50427612604524469900393639811,50427612604528716438183161535⟩,⟨30562530559664407497015287260,30562530559668654033800530396⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨52996028808126877681045235863,52996028808131933755898861182⟩,⟨17286349975586237195822581469,17286349975591293270377592360⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨50344532844859181270272233214,50344532844863702287866852521⟩,⟨4543069063015563159375261692,4543069063020084177253637943⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨43777075014129101734354838174,43777075014132151233973416792⟩,⟨(-5463369291262166668564243101),(-5463369291259117168264768469)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨35240828530392880371488471028,35240828530394438286805276927⟩,⟨(-11592481587902516405458305705),(-11592481587900958489259542365)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨26489658608820202606633144889,26489658608820852107226041221⟩,⟨(-13830822097157697333231597703),(-13830822097157047831732687054)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨18612014133623855041802666527,18612014133624096266688910670⟩,⟨(-12984566568481367152241791148),(-12984566568481125926563692206)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨12021453430216273046511849422,12021453430216358865366033863⟩,⟨(-10174458344329779933929548024),(-10174458344329694114478865885)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨6648643140130367725442003941,6648643140130397538180445997⟩,⟨(-6363836746118160846814880758),(-6363836746118131033711309332)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2116395276405708945473348946,2116395276405716274369178653⟩,⟨(-2152954543671536357695874131),(-2152954543671529028677076406)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-18726334938416018273928596150),(-18726334938416018265074916399)⟩,⟨(-11742551293237422335691383723),(-11742551293237422327374109077)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-56377739130507891239030199647),(-56377739130507891211787753633)⟩,⟨(-32366135501023274033806338670),(-32366135501023274008147631907)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-93467853804231892457614588972),(-93467853804231892410687737901)⟩,⟨(-44851999316297868323767359945),(-44851999316297868279160652333)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-126781395457674308700020782743),(-126781395457674308632402472464)⟩,⟨(-45248593566743735293250017187),(-45248593566743735228244755661)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-151287002784763779320243739493),(-151287002784763779232232006702)⟩,⟨(-31668867678973193952821523061),(-31668867678973193867197377896)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-162521941511713367200787018352),(-162521941511713367092070723115)⟩,⟨(-5402417554606485681094363035),(-5402417554606485574315751454)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-158637234255693506814918287115),(-158637234255693506679508736327)⟩,⟨28359263948295430262607142020,28359263948295430396719602430⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-140973754007482912069586439478),(-140973754007482911851361182319)⟩,⟨61816193394053776654874286998,61816193394053776872615098927⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-113679017840670621262096565049),(-113679017840670620526809185332)⟩,⟨87489955776350738154895327302,87489955776350738890434073294⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-82546976492670125126320376244),(-82546976492670121205045986665)⟩,⟨100716927028211521430450532347,100716927028211525352376666689⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-53190737544323099138264110444),(-53190737544323080995112069157)⟩,⟨100560971549335600765172517454,100560971549335618909107613068⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-29414155899190855864133528550),(-29414155899190796238014661549)⟩,⟨89315362216682682458576299499,89315362216682742085503225222⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-12749886829715974080216160791),(-12749886829715842293527507355)⟩,⟨71153963245090633045614489592,71153963245090764833035430562⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-3075514056569551646449897494),(-3075514056569357278704987767)⟩,⟨50313989546529577388381924650,50313989546529771756653808849⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨760490868071443292585313889,760490868071625163278204059⟩,⟨29545171653302256225463291689,29545171653302438096454857607⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨708099535051352399754154643,708099535051426862281346416⟩,⟨9694364897921978160439992154,9694364897922052623055465199⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨27766370355036334065503091918,27766370355036467172580776677⟩,⟨(-18444540649332241450555266932),(-18444540649332108345258371129)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨78972338752173237768821125867,78972338752173555186352050054⟩,⟨(-56565350540072026381164314970),(-56565350540071708968693831251)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨117539309290888035636600811664,117539309290888361232148503735⟩,⟨(-97612812038978429123562292405),(-97612812038978103535504559214)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨136783018680310222990712803951,136783018680310431916976805112⟩,⟨(-141453765383313426144298321883),(-141453765383313217226708004343)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨133308953369009387382497033823,133308953369009475949622131439⟩,⟨(-185483065275380267573951551919),(-185483065275380179015221629369)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨108397189634397564393601500917,108397189634397589552810198128⟩,⟨(-224473612721406266719776757950),(-224473612721406241567400593028)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨67570688120217399999666415397,67570688120217405124118749750⟩,⟨(-251553756725975308343648543386),(-251553756725975303223557582802)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨18770514324178030627050837710,18770514324178031565997329599⟩,⟨(-260955964975357641499039724371),(-260955964975357640561541057311)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-29395408279913839189180162842),(-29395408279913838908299572759)⟩,⟨(-250769251859708549649749536712),(-250769251859708549367552705885)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-69234044589988237619764706097),(-69234044589988237456354523748)⟩,⟨(-223663700792723968802522469323),(-223663700792723968635658561556)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-95354774331032100697247047626),(-95354774331032100579434857120)⟩,⟨(-185611098068858262845274085322),(-185611098068858262722775774124)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-105333553449843684891436641541),(-105333553449843684805968722689)⟩,⟨(-143567562871359911714347568519),(-143567562871359911623854620178)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-99577411908621980991608692933),(-99577411908621980932138831328)⟩,⟨(-103222785590717653547114552909),(-103222785590717653483032889607)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-80626109886056268713698950022),(-80626109886056268675502927214)⟩,⟨(-67781826001911046190579101628),(-67781826001911046148756574426)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-52129702998612112974505563922),(-52129702998612112953483318800)⟩,⟨(-37879581627123720416383903593),(-37879581627123720393067079041)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-17987910392597848676012814294),(-17987910392597848669347859540)⟩,⟨(-12117666238600669819390893086),(-12117666238600669811946648991)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨3637693732419032580634319258,3637693732419637674757044088⟩,⟨31560245094544649470273363907,31560245094545254567433791654⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨15140102666968730363812968489,15140102666971084283733237588⟩,⟨93848209598578880445753090362,93848209598581234374498088163⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨38005086303437530384383175423,38005086303443797085007767591⟩,⟨152056199622318260325024408224,152056199622324527039078851571⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨76070735361765906329659493763,76070735361781765075242494076⟩,⟨199517193024756753615605866497,199517193024772612377350244676⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨129101902857093554370633933742,129101902857131264997468448167⟩,⟨226986665239567508161019312010,226986665239605218804220084657⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨192485921790960867624138942868,192485921791039844386012328861⟩,⟨226730063204976382281491396679,226730063205055359057460541379⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨257052841767583883004697249418,257052841767718285802405788165⟩,⟨196840052530975972553587594838,196840052531110375360889559358⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨310774786385068669430526752842,310774786385242206818507091723⟩,⟨142670443380688875923546106693,142670443380862413314963857641⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨342763164207896775801594666286,342763164208066661745749801026⟩,⟨75470944276113331597387867347,75470944276283217538489354387⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨346940987013205883280260556253,346940987013332113145652130008⟩,⟨9286834792003817881579723448,9286834792130047738709640380⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨323270625864688590259062184365,323270625864759904757380503833⟩,⟨(-43211633839133722010309198637),(-43211633839062407523439274474)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨276872162721113489323285127123,276872162721146347421114178726⟩,⟨(-74576120032346332444923192043),(-74576120032313474359759323064)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨216350765419679443753445440558,216350765419692843263988678492⟩,⟨(-83818390419751088366852635294),(-83818390419737688868307646518)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨151158330628728230788383286951,151158330628733395874063135533⟩,⟨(-74204659405212817167608139677),(-74204659405207652091538089596)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨87994438106801367661630670819,87994438106803272728769308802⟩,⟨(-50457072642594099131450575661),(-50457072642592194070455862871)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨28726589616854678248819804115,28726589616855162548631713837⟩,⟨(-17830139972237579909497333196),(-17830139972237095611772782050)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-74978131452388515457517379),(-74978131452388509214600150)⟩,⟨(-1104436371125306121964474762),(-1104436371125306112828783039)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1103771852892711386372352475),(-1103771852892711366326648692)⟩,⟨(-3013528329457948244481480779),(-3013528329457948216047458259)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-4693336059603673410781438695),(-4693336059603673373221159537)⟩,⟨(-2797318153567389920875498287),(-2797318153567389870868820619)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-12656980613034191480816275828),(-12656980613034191420031149586)⟩,⟨3870462803775957448867656538,3870462803775957524040451121⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-27107197629089123699756812534),(-27107197629089123607280523417)⟩,⟨22004740935508645874122931599,22004740935508645980429117932⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-48657222967437889890389767294),(-48657222967437889751599432399)⟩,⟨53264143827753834581634669453,53264143827753834731833054424⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-73473842773012530824202146115),(-73473842773012530594245394850)⟩,⟨94199610387466188640529833971,94199610387466188877924518323⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-93869418583022283917831332849),(-93869418583022283341239198941)⟩,⟨138202414555148461916524091692,138202414555148462495578655561⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-102618637790556806123197647787),(-102618637790556803255440983078)⟩,⟨177591638244503065368605421838,177591638244503068234140589055⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-96494633163419903602821559582),(-96494633163419885720352725781)⟩,⟨204924494416713729129753105035,204924494416713747006834548994⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-77136893740140362779309254258),(-77136893740140273592994241945)⟩,⟨214804359303635366528677457628,214804359303635455708112604655⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-50210018180995528236575618420),(-50210018180995217880931296704)⟩,⟨205583612654823827442281791424,205583612654824137790717370180⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-23674367652382435372916216222),(-23674367652381715659230616221)⟩,⟨179138978628543795532889142290,179138978628544515239978263782⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-4794697209289374319452004064),(-4794697209288270848576834522)⟩,⟨138771319694254874089236477427,138771319694255977555003869499⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨3194494964345356013512797213,3194494964346417864888144268⟩,⟨87844231387194348559819182242,87844231387195410408027039319⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨2200061712812902515419811948,2200061712813344101882526873⟩,⟨30070410854400573110627421298,30070410854401014696047144991⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨258995033992541095703348006546,258995033992691257757014917675⟩,⟨143786587877685199081693134338,143786587877835361139446459075⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_2 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 2) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_2 (tableDensity true) (fullFactor false 3 2) density1_contains hk3_0_2_contains +noncomputable def atomAnswer : CBox := ⟨⟨29971595327380878706445975329,29971595327380878745727982546⟩,⟨4995265887896813102701330212,4995265887896813139836164727⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_2 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 2) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_2 3 2 ha3_0_2_contains + def realAnswer : RBox := ⟨288966629319921974409693981875,288966629320072136502842900221⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 2) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_2 +namespace hm3_0_0_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2500640942201640796438307147,2500640942201641865241308068⟩,⟨1797873245202120950789491769,1797873245202122019733390178⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨7200938890180970370139059279,7200938890180972819588468965⟩,⟨4734511695604854966064594152,4734511695604857415888821314⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨10957742710711297377672202001,10957742710711299693221404790⟩,⟨5985198136794741744779295516,5985198136794744060816189730⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨13129142372373900312816459399,13129142372373901620303784411⟩,⟨5281061208546984500894088453,5281061208546985808842519079⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨13289315421446379504681438580,13289315421446379967622170695⟩,⟨3193582125348725677011842852,3193582125348726140288764611⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨11525572178132392889749645279,11525572178132392993681839340⟩,⟨780004920202851871445807210,780004920202851975561660137⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨8534982644209510353518671494,8534982644209510369880446132⟩,⟨(-996577897734618678452500627),(-996577897734618662025488844)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨5335149058593054690739525717,5335149058593054693483367321⟩,⟨(-1710822381009438796935459714),(-1710822381009438794185884861)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨2764421510116412940787074034,2764421510116412941661682834⟩,⟨(-1541631707994523568736868958),(-1541631707994523567869866077)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1155810035121416157194867307,1155810035121416157561338592⟩,⟨(-982456739299374630562096769),(-982456739299374630197019518)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨374601210785278600561977511,374601210785278600697308977⟩,⟨(-462563620667062899008052371),(-462563620667062898867775206)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨88467382381778541286205018,88467382381778541325286351⟩,⟨(-156957253805031050339336952),(-156957253805031050294652269)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨13752899054640870503715056,13752899054640870511694502⟩,⟨(-35309874519235294746591685),(-35309874519235294735555938)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨1168810767846765437455977,1168810767846765438430092⟩,⟨(-4380680219202089093736925),(-4380680219202089091871957)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨36125185069723117934278,36125185069723117984534⟩,⟨(-194643866405447561129381),(-194643866405447560972595)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨111136802615555920850,111136802615555921272⟩,⟨(-799042861315113171140),(-799042861315113168816)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-17272904159871445413911499279),(-17272904159871434859718828409)⟩,⟨12226004724593443588404601143,12226004724593454141000404191⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-48521818971599041071852588759),(-48521818971599000985601168268)⟩,⟨36947811399697763598439912011,36947811399697803680250910180⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-70514666838287323126517490298),(-70514666838287221331083800858)⟩,⟨61742906953791688430512200195,61742906953791790219639352671⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-79346484085969369257042237624),(-79346484085969128947134805906)⟩,⟨84795212529148998756032138786,84795212529149239059078161274⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-74209665990093459731867322100),(-74209665990092937768862137207)⟩,⟨102832979762510966016585494817,102832979762511487973456931035⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-57746213787617450140807740445),(-57746213787616470386360267333)⟩,⟨112440651744840254948235751274,112440651744841234698173763989⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-35244381829013726089633709868),(-35244381829012254434963789404)⟩,⟨111724361426778037516780395012,111724361426779509168914782296⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-12762843835425501409796535582),(-12762843835423849728970378804)⟩,⟨101326176315284449819482888995,101326176315286101499564723489⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨4962436386235168084058886540,4962436386236553629945290076⟩,⟨84229927710825398018953223732,84229927710826783565370619530⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨15751102634997246673958000607,15751102634998121503674199020⟩,⟨64515773955108222758500526754,64515773955109097589420522868⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨19913086185024316074360878301,19913086185024734132313582438⟩,⟨45833052148999525662711166914,45833052148999943722043183824⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨19250343263538358730472574308,19250343263538522097474838818⟩,⟨30419368377993199851053417098,30419368377993363219298706042⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨15869281339437871229081814873,15869281339437928415845543988⟩,⟨18958320706335352376183904816,18958320706335409563913401362⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨11396447003653586448794637089,11396447003653605806254963965⟩,⟨11015242812859961341154113442,11015242812859980699274780804⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨6742709131674617175480087555,6742709131674623660978493597⟩,⟨5623890396910575078296831943,5623890396910581564172132895⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2219369971363440606766196034,2219369971363442170860085133⟩,⟨1714321875158763681979109693,1714321875158765246194780529⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨433506141645605512970846295,433506141645605519997618518⟩,⟨(-51178694106921436216754989325),(-51178694106921436203612203813)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-5206836669332420273949132177),(-5206836669332420252134165244)⟩,⟨(-149291957107789241743045477799),(-149291957107789241703860379866)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-28119687113644886815564562366),(-28119687113644886777020717991)⟩,⟨(-234132799175526132569013972167),(-234132799175526132504965841967)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-72778715511727949631792083894),(-72778715511727949574588606706)⟩,⟨(-296258201909250390303791275092),(-296258201909250390217452646024)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-135097986409111200528625771918),(-135097986409111200452255701793)⟩,⟨(-327083499010520788738973767961),(-327083499010520788634856216891)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-203410726606103970927602723843),(-203410726606103970832216274219)⟩,⟨(-321646628386473471331160095824),(-321646628386473471213900101595)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-262695684558983961339939698611),(-262695684558983961224564995178)⟩,⟨(-281628413247805282609047281609),(-281628413247805282480320280771)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-300000692357121069243752881069),(-300000692357121069082873918055)⟩,⟨(-216399039666601182989400956257),(-216399039666601182824184357668)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-308708179262654614414270471577),(-308708179262654613990082323724)⟩,⟨(-140542898606795678731455155043),(-140542898606795678310549615372)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-290022192204853029492450798308),(-290022192204853027491033007476)⟩,⟨(-69059768128127098699683438497),(-69059768128127096706605713853)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-251241509322652227544500055150),(-251241509322652218755436330021)⟩,⟨(-12976936667379613289284129953),(-12976936667379604510894951166)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-202022073164866741622279174868),(-202022073164866713814164869043)⟩,⟨22671390634419680644889939199,22671390634419708442201995572⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-150722413716875891497217113770),(-150722413716875831972030918974)⟩,⟨38333265293869006249804607149,38333265293869065765578634245⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-102436176573692536827134381930),(-102436176573692451266412682385)⟩,⟨37956060410622480848923861892,37956060410622566402536195561⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-58864469468820243739149425648),(-58864469468820165118725495011)⟩,⟨26732619366000241657766511488,26732619366000320273817769378⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-19132673715883263336420255388),(-19132673715883231448251931733)⟩,⟨9532111012415504919512517704,9532111012415536806215653473⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨65466835161661424817475827975,65466835161661535293170577281⟩,⟨23434950442874305712008613706,23434950442874416175705001486⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨195221704301343960357799778523,195221704301344222780242673836⟩,⟨61664438743557080484696627680,61664438743557342873131856733⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨319409006426029020421432395728,319409006426029287562426138585⟩,⟨75629175730334898422398008565,75629175730335165513085590566⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨429341681710955906570057919565,429341681710956076122352212430⟩,⟨54838048355591609269749841727,54838048355591778763849455297⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨512325776403697674625018198379,512325776403697745539628418114⟩,⟨(-3283604152325275245550791115),(-3283604152325204387474786907)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨555618502983778849876580257851,555618502983778869758603343162⟩,⟨(-91799906833709704956348871387),(-91799906833709685120412796222)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨551853934789493527371299413652,551853934789493531432323084567⟩,⟨(-194816525705380325653245350684),(-194816525705380321621554780949)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨502654964250256517528514723426,502654964250256518344050376773⟩,⟨(-291386482676400994770451409843),(-291386482676400993964808322441)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨418891951490573456987622272903,418891951490573457288653596366⟩,⟨(-362113375253657381887112043208),(-362113375253657381577593641082)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨317638399359575280034282580112,317638399359575280226955179050⟩,⟨(-395063289484902097632460282762),(-395063289484902097417000721231)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨216996933383411849861612066237,216996933383411849999678781252⟩,⟨(-388147111305872220833828538622),(-388147111305872220664411687756)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨131191914829846387206697904471,131191914829846387303297423750⟩,⟨(-347569115050339887411166737444),(-347569115050339887280621682341)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨67937141812486344533913417507,67937141812486344598044905890⟩,⟨(-283773277261808971510230181710),(-283773277261808971414708333148)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨28347592762649077134524955973,28347592762649077173879380916⟩,⟨(-207120122362639833473615411656),(-207120122362639833409349691411)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨8482300571180658628944405346,8482300571180658649820204400⟩,⟨(-125126380965604381326425646060),(-125126380965604381289680523515)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨1368171934344731970943599054,1368171934344731977419818214⟩,⟨(-41739302812689267574473522224),(-41739302812689267562573074471)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-84128440972772446006691227979),(-84128440972771804129231211056)⟩,⟨5354120681156176823152750516,5354120681156818713722593995⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-244509477848260699696718205098),(-244509477848258212776065709408)⟩,⟨28894031777705227677256587240,28894031777707714635046799413⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-380037358384573580167983277041),(-380037358384567011616127374374)⟩,⟨86893766800888345692349362531,86893766800894914299608238467⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-472424325918730560816345982217),(-472424325918714127409668638804)⟩,⟨189288859229660246480945650200,189288859229676679952570415342⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-504538677036261959919075405341),(-504538677036223445069211167833)⟩,⟨328832597866005512807151242117,328832597866044027721401415719⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-465689682187175256220608126130),(-465689682187095951588715841386)⟩,⟨481363220062473714841388959541,481363220062553019526853898924⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-357889543562765447843548479602),(-357889543562632995872108067241)⟩,⟨613618936051307827241639747776,613618936051440279247843921362⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-199479439664324363947281686542),(-199479439664156711743770267690)⟩,⟨695186262289934476928207560104,695186262290102129143473144573⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-21908429992097716785057023048),(-21908429991936925409413901645)⟩,⟨709019539719987245020102877087,709019539720148036384386150089⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨139808416856230673183299779549,139808416856347757838176423423⟩,⟨656504792230721305412817862268,656504792230838390036666802179⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨257578512678442706199721110796,257578512678507585583782278347⟩,⟨555286276202623578928866673259,555286276202688458268559766797⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨316354442510736052138812128894,316354442510765417652074523077⟩,⟨431099506776486256510989631922,431099506776515621974509910214⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨314590127189895718925684477582,314590127189907509850350494787⟩,⟨307562635134104441977235154586,307562635134116232854576455616⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨261193042419787847464386808500,261193042419792336042474909098⟩,⟨199087298129650657058606508359,199087298129655145598216125537⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨170821816255016291127392551705,170821816255017932159651718119⟩,⟨109561795511331184280602526695,109561795511332825287934479400⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨59190718773849148970084803327,59190718773849564248082402637⟩,⟨34695743902478610990980380665,34695743902479026260366250820⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨38942739287535425734227310590,38942739287535425749987258341⟩,⟨(-785976906366004290868593965),(-785976906366004279660273630)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨114063597382424152404238886721,114063597382424152452860798474⟩,⟨(-11432580698566515954597323120),(-11432580698566515918901000662)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨179941385016643198074799148442,179941385016643198159179516426⟩,⟨(-46424720233687624160941451162),(-46424720233687624095022222922)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨228136444552913168897849958616,228136444552913169022204280721⟩,⟨(-112376322399784082428200246928),(-112376322399784082323991261414)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨248014575056314562045422319198,248014575056314562214809600222⟩,⟨(-203109521623523020625239305075),(-203109521623523020473658769498)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨228903284638717705750803012606,228903284638717705976349007670⟩,⟨(-301044709092678478206641717914),(-301044709092678477994221844377)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨166322516630972809348558183632,166322516630972809674373579981⟩,⟨(-384302789426380721224837087858),(-384302789426380720906414636697)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨68304846715760841338476375480,68304846715760842051103957120⟩,⟨(-434121627675106477594088476466),(-434121627675106476883555064998)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-45310644652904217792099033742),(-45310644652904214465311316429)⟩,⟨(-440115552762749949449090679188),(-440115552762749946121149021122)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-150136055993042539587947386413),(-150136055993042519221305371195)⟩,⟨(-403489676771207906977385069282),(-403489676771207886609122275664)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-225428539836161284737385864093),(-225428539836161184629208991507)⟩,⟨(-336300894657994506854187975450),(-336300894657994406745879724980)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-259201646203058319354819751508),(-259201646203057976019461479380)⟩,⟨(-256053297061256020204378737397),(-256053297061255676870862045847)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-249557374763788400065503405377),(-249557374763787614262612244604)⟩,⟨(-178391995134966202923952202381),(-178391995134965417124336105237)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-203136080192564239557764750559),(-203136080192563047532672472372)⟩,⟨(-112415227553917002847067415296),(-112415227553915810825602199005)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-131186135168506853385240462228),(-131186135168505714869723234275)⟩,⟨(-60275855820757855119647697660),(-60275855820756716606903115450)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-45168903579183455243589294311),(-45168903579182983597353652178)⟩,⟨(-18766497179473952569700512164),(-18766497179473480924495480430)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨77085591731020151328813989526,77085591731161438199299310059⟩,⟨(-241045965657726372776926326922),(-241045965657585085920392104279)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 3) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_3 (tableDensity false) (fullFactor false 3 3) density0_contains hk3_0_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨18929147600076571098622863801,18929147600076571122708662652⟩,⟨(-25644013782660850711975538516),(-25644013782660850685480552923)⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_3 3 3 ha3_0_3_contains + def realAnswer : RBox := ⟨96014739331096722427336853327,96014739331238009322107972711⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_3 +namespace hm3_1_0_3 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_3 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨383334957437781799006029006,383334957437782674600315303⟩,⟨361198452876487774216139862,361198452876488649776037470⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨1111200285918711178022521104,1111200285918713183924476517⟩,⟨978126043046778525814386091,978126043046780531623716221⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1703242308290100004599275294,1703242308290101899363284028⟩,⟨1309869174913960040964051526,1309869174913961935603849321⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨2044587463777526909961404093,2044587463777527978456872653⟩,⟨1269513231444131413582184379,1269513231444132481953349200⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2062554816568872101438733668,2062554816568872478843786723⟩,⟨905972501528996079967003937,905972501528996457272080451⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨1784129689306124875842464444,1784129689306124959934425975⟩,⟨400144368665530942115563207,400144368665531026142855098⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1325344117471721496955956844,1325344117471721509686020012⟩,⟨(-26628849867769731454805295),(-26628849867769718756471157)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨835529662219662646689793952,835529662219662648477094375⟩,⟨(-243619430109516492390357364),(-243619430109516490611669691)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨437404091792772769407776977,437404091792772769846100116⟩,⟨(-261869621104188542525653398),(-261869621104188542084306852)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨184377327017252575935520167,184377327017252576097051374⟩,⟨(-177982318265516224880823998),(-177982318265516224713144909)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨59821233876816864507511205,59821233876816864562963255⟩,⟨(-86023708653738875748764067),(-86023708653738875688383270)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨13894688047372330315483398,13894688047372330330437818⟩,⟨(-29367670622648853101194960),(-29367670622648853083601103)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨2038191236677434370279468,2038191236677434373106725⟩,⟨(-6571264584573564064990265),(-6571264584573564061185362)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨149721774717672710576411,149721774717672710883731⟩,⟨(-807408909416497028965963),(-807408909416497028432768)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨3375393883081875838733,3375393883081875851377⟩,⟨(-35565228269194430618765),(-35565228269194430582513)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨5707580892465315630,5707580892465315700⟩,⟨(-145211252438234451768),(-145211252438234451304)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3276699243614517285738181888),(-3276699243614508596478013786)⟩,⟨396154077477800768374662050,396154077477809457809253655⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-9255763699285964653286547973),(-9255763699285931636651783411)⟩,⟨1564018810305245871878703747,1564018810305278888996030745⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-13613960076521854259661715718),(-13613960076521770355902218979)⟩,⟨3648633677802351992439563546,3648633677802435896882637932⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-15646963632263142845672155363),(-15646963632262944596155470722)⟩,⟨6669371910964461990642413973,6669371910964660240900960487⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-15178255310194839382371281264),(-15178255310194408393335636564)⟩,⟨10067670854283476041449845174,10067670854283907031150222896⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-12614831255989419685591762715),(-12614831255988610030090523302)⟩,⟨12939934606432576248561148657,12939934606433385904553219473⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-8791473187764395579781738170),(-8791473187763178362721978391)⟩,⟨14470116091183477837502318703,14470116091184695054840321156⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-4692258262815291465583416841),(-4692258262813924697325978876)⟩,⟨14327157383111786106967843967,14327157383113152875304021129⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-1167111491622778989234085394),(-1167111491621632481994598968)⟩,⟨12757216600354136296599517447,12757216600355282803769522442⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨1281018108518036776666197699,1281018108518760289978829824⟩,⟨10364384197177695481782835302,10364384197178418994937746803⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨2553646589380975441527663286,2553646589381320854472134743⟩,⟨7789808054302956333363137916,7789808054303301746115050525⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨2855877206034939970055025808,2855877206035074779350565907⟩,⟨5480100879548381194211731652,5480100879548516003320729594⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2526667208550883077399877896,2526667208550930203651298756⟩,⟨3625642354738896194053823529,3625642354738943320150879065⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1884181912193381554036722784,1884181912193397486251877491⟩,⟨2227472606049195762123571984,2227472606049211694227796478⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1137146606677578158443861700,1137146606677583491308727979⟩,⟨1188288269542849393436673956,1188288269542854726235958201⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨377563586270973275460624333,377563586270974560919969167⟩,⟨371161095311177923175681571,371161095311179208613344869⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨6138613504598578364437748509,6138613504598578368805744587⟩,⟨(-9789386779219441630401933505),(-9789386779219441625742344981)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨16813773438344600988875209748,16813773438344601002264083570⟩,⟨(-29284381740434487713250024164),(-29284381740434487699005041517)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨23012115593782627965313361105,23012115593782627988296198374⟩,⟨(-47940906790242270723601891434),(-47940906790242270699375011009)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨22796814769426668520333913676,22796814769426668553208157955⟩,⟨(-63830638761889604972037779548),(-63830638761889604937778950195)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨15591149899734982935846447712,15591149899734982978110032783⟩,⟨(-74353172156466812292369921884),(-74353172156466812248858228658)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨2618376988663549036671525791,2618376988663549087846225768⟩,⟨(-77583938810838508060433617567),(-77583938810838508008262658229)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-13043546576050929436240857351),(-13043546576050929374137189204)⟩,⟨(-73246131581779137449942650311),(-73246131581779137387186016566)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-27456833826773641135040270094),(-27456833826773641038153134862)⟩,⟨(-62748477543010239072146926843),(-62748477543010238975022018018)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-37399295675963462173462337675),(-37399295675963461860099467851)⟩,⟨(-48673913186766592451541401383),(-48673913186766592138309632004)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-41390074498680145557339405019),(-41390074498680143953611142986)⟩,⟨(-33972531607190437481466031399),(-33972531607190435878079207531)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-39755770133278191275941059909),(-39755770133278184134837002013)⟩,⟨(-21058128587022444319650390924),(-21058128587022437178969327894)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-34051534272766234768163772359),(-34051534272766212111679634524)⟩,⟨(-11230884251152112287383949219),(-11230884251152089631341069212)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-26272739308289737445500758342),(-26272739308289688889774866315)⟩,⟨(-4716261540130344611167254662),(-4716261540130296055838875412)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-18101691796474683026092661513),(-18101691796474613176071149787)⟩,⟨(-1109981303533344438755068293),(-1109981303533274589021138568)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-10436560374138549582151970433),(-10436560374138485363642931122)⟩,⟨267797100081208496521903642,267797100081272714865316046⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-3392106753278259271403208191),(-3392106753278233217656149864)⟩,⟨247734653786460664980890745,247734653786486718677016609⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨12861232793226964759301749027,12861232793227057574944160639⟩,⟨19361417985555617855288584322,19361417985555710672194084753⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨39253687769505168128013561180,39253687769505388448151710360⟩,⟨54806746404152794042088801951,54806746404153014365797943376⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨67100147675486788972550024668,67100147675487012932386987710⟩,⟨80812336790435111073031565337,80812336790435335038100280750⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨95895839954358030804062995047,95895839954358172620549892613⟩,⟨92761102331351391614564594954,92761102331351533437017399533⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨123510428265707638702348765786,123510428265707697798234096801⟩,⟨88818555262629301236944444830,88818555262629360338487484763⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨146299570038640614628717067387,146299570038640631071513380380⟩,⟨70710958428011301118151336412,70710958428011317565439802987⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨160001805177027263259794036493,160001805177027266529065754357⟩,⟨43048646272817560718104030032,43048646272817563990164696707⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨161638160094059822832490411891,161638160094059823415787887969⟩,⟨11697313423917942927063907398,11697313423917943511262423985⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨151072256579359052280646528241,151072256579359052451559700136⟩,⟨(-17641613331675691341351009657),(-17641613331675691171222529354)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨131017595294611889162816891098,131017595294611889261189472470⟩,⟨(-40495782742237011386695946751),(-40495782742237011290322724412)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨105811794491796517196489494621,105811794491796517266827724030⟩,⟨(-54309704272848094688026929205),(-54309704272848094620314782789)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨79811237938317541726172002274,79811237938317541776871528390⟩,⟨(-58520505479286246100898005589),(-58520505479286246052927171720)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨56137640327893130819879437059,56137640327893130855016085882⟩,⟨(-54133478548723562350923271146),(-54133478548723562318220483521)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨36219112835843862651598462720,36219112835843862674136023569⟩,⟨(-43072786503836687985845769222),(-43072786503836687965177571038)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨19992433941036111965657427479,19992433941036111978070559942⟩,⟨(-27511083773494761980874462015),(-27511083773494761969624548634)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨6354985275127350773899235459,6354985275127350777837498693⟩,⟨(-9433478429282517837275366266),(-9433478429282517833728713102)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-27515079029410683088814616025),(-27515079029410155559952285564)⟩,⟨3171337087326721016733931373,3171337087327248542870135492⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-81507633756722850870787366980),(-81507633756720806846221679453)⟩,⟨13146615535364851406588516110,13146615535366895423267564018⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-131072117284953501137157737089),(-131072117284948101680906426253)⟩,⟨32749157351276685975958475215,32749157351282085420299186059⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-170102637289537226083108877022),(-170102637289523715434308354258)⟩,⟨64827679273624457563445122588,64827679273637968198074457490⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-190805110539000379089713828710),(-190805110538968710483037873693)⟩,⟨108466843261608556529115636432,108466843261640225121652938326⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-187404845177202029274151817888),(-187404845177136821767298676848)⟩,⟨159000978323945181513694480437,159000978324010389008591695083⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-159635592432303890499259357418),(-159635592432195006471491473731)⟩,⟨208306607130569562994621348415,208306607130678447014423165182⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-113360805012748722337604155376),(-113360805012610968773762677166)⟩,⟨246673007108987438187995004175,246673007109125191749041420172⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-58728237705547359337958487342),(-58728237705415347921218379449)⟩,⟨266252017313458050589864390263,266252017313590062009015424481⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-7142361151766653226402288929),(-7142361151670627692314021146)⟩,⟨263726046404532958072874597279,263726046404628983613360569799⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨32110048389084179506742503820,32110048389137322255404316775⟩,⟨240664522674195783769729811152,240664522674248926527086520373⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨54427928694489256390945316877,54427928694513277388181777010⟩,⟨202212054968272132686467236026,202212054968296153693157296437⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨60186469177357534776796694465,60186469177367167468877739188⟩,⟨155408373102696626045473202494,155408373102706258746374396981⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨52590117200486176958068654096,52590117200489840036993757153⟩,⟨107148152172938098184703360559,107148152172941761270605317807⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨35434028688502993501695561541,35434028688504331723887941962⟩,⟨61799340699822002070489428088,61799340699823340297101441707⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨12462655449664439270243097287,12462655449664777789038659468⟩,⟨20079059676676420811872108558,20079059676676759332162026540⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨1155640781754310315372726624,1155640781754310324935586829⟩,⟨(-78433356972894911205920795),(-78433356972894904673365010)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨3143459811440495900299913988,3143459811440495929967321932⟩,⟨(-1150732519135062593677355018),(-1150732519135062572766163072)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨2901840546518348980156094143,2901840546518349031998482707⟩,⟨(-4862274484876301652187891526),(-4862274484876301613244120743)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-3965521813382766452261479318),(-3965521813382766375047316993)⟩,⟨(-12992486740036726474355943031),(-12992486740036726411891280991)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-22311920780633765641231141351),(-22311920780633765533274144787)⟩,⟨(-27499302790543562379608847714),(-27499302790543562285648141340)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-53270989288547431087820345710),(-53270989288547430937353175676)⟩,⟨(-48675453101200395176460877344),(-48675453101200395037352682059)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-92747989516228257774087436395),(-92747989516228257540051930609)⟩,⟨(-72355254753737149475347608862),(-72355254753737149248567731359)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-133784035028638522568573505060),(-133784035028638522008250787849)⟩,⟨(-90887739466093262881926155562),(-90887739466093262323952701058)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-168910152903379366286746919376),(-168910152903379363566813935103)⟩,⟨(-97628412416605234742578728418),(-97628412416605232020606237356)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-191504265006893123970926805603),(-191504265006893107302771279419)⟩,⟨(-90205978812930787904732616440),(-90205978812930771231782141733)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-197374727870820095028500719045),(-197374727870820013241784926515)⟩,⟨(-70908643540291588657870104247),(-70908643540291506865242469845)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-186003094701443786647613266396),(-186003094701443506243757252515)⟩,⟨(-45453965198906068148668044298),(-45453965198905787738807975335)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-159926691256228110387115833653),(-159926691256227468409192240617)⟩,⟨(-21152751942681670181475233686),(-21152751942681028198197066739)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-122578798005007328253337076033),(-122578798005006353953656458627)⟩,⟨(-4243273262170377740953987559),(-4243273262169403437219093596)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-77023072154045039195253916239),(-77023072154044108285041718886)⟩,⟨2798988579165566765163327975,2798988579166497677845960611⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-26266525039566991664596149162),(-26266525039566605945126874993)⟩,⟨1921677605905718803888903757,1921677605906104524161393885⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-189925832930077180459558166439),(-189925832929961170710252147018)⟩,⟨213402041012394921406282033558,213402041012510931148050916609⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_3 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 3) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_3 (tableDensity true) (fullFactor false 3 3) density1_contains hk3_0_3_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-24753500707792439160465174237),(-24753500707792439128968360355)⟩,⟨33534479561941112434859184591,33534479561941112469506473444⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_3 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 3) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_3 3 3 ha3_0_3_contains + def realAnswer : RBox := ⟨(-214679333637869619620123340676),(-214679333637753609839120507373)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 3) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_3 +namespace hm3_0_0_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-234223244651647270191999815),(-234223244651647130923612406)⟩,⟨325766721919073108637018580,325766721919073247887328807⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-605246600688997188638653249),(-605246600688996875292414008)⟩,⟨920242464115073051288241449,920242464115073364587396895⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-736538700564476892945657343),(-736538700564476607488708164)⟩,⟨1347130186057950744782906244,1347130186057951030181179564⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-613466678386692843421118413),(-613466678386692691021448082)⟩,⟨1521675647662189865653788287,1521675647662190018001586235⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-343433600503685463819921640),(-343433600503685413808095290)⟩,⟨1421412917243565878315823028,1421412917243565928293255282⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-77175817090109276150435046),(-77175817090109265963149351)⟩,⟨1111775944174842058834914067,1111775944174842069005717716⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨82843392868471534046078333,82843392868471535467536003⟩,⟨723860208573502126198103498,723860208573502127614724616⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨122723934377213371432866440,122723934377213371637561474⟩,⟨386535710090101124843550097,386535710090101125048012565⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨91514472107377819148454823,91514472107377819202395266⟩,⟨165452431100262986174592225,165452431100262986228857477⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨46274517550342971793217835,46274517550342971811542027⟩,⟨54887165476970752084289328,54887165476970752102469594⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨16422047777162086601606290,16422047777162086607040134⟩,⟨13421669764747932254562746,13421669764747932259669982⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨3929017124749286518225817,3929017124749286519485300⟩,⟨2239083898001458859882548,2239083898001458860934369⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨568317838899330754698523,568317838899330754905869⟩,⟨224374000668110705302197,224374000668110705442186⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨39492408395557727837137,39492408395557727857428⟩,⟨10702538671876117309222,10702538671876117318986⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨776501877660674820678,776501877660674821462⟩,⟨146020391636538436441,146020391636538436687⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨799369522303629464,799369522303629481⟩,⟨111677926386281827,111677926386281843⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-3193070907566920325900412498),(-3193070907566917569991177533)⟩,⟨(-4511239099363309077644643346),(-4511239099363306321313979541)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-9557373792816453658793902579),(-9557373792816443294773440796)⟩,⟨(-12552876868536114510842379598),(-12552876868536104145661162730)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-15669126697266475678995954043),(-15669126697266449871771182269)⟩,⟨(-17901297502700467662678933277),(-17901297502700441853836533716)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-20918383124541220850400364925),(-20918383124541161662472728977)⟩,⟨(-19586541605641903227328026349),(-19586541605641844037689378048)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-24442284007209070559408967352),(-24442284007208946742808277180)⟩,⟨(-17656927716103806686672703282),(-17656927716103682868598261026)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-25536950321857793649192823767),(-25536950321857571588178679610)⟩,⟨(-13136607233140235512539241039),(-13136607233140013450489875798)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-24062341771035026094614500470),(-24062341771034709635727882013)⟩,⟨(-7612777161398987344507951446),(-7612777161398670885069294443)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-20559670634989938482823629947),(-20559670634989603509088126414)⟩,⟨(-2609739527868136787278639207),(-2609739527867801813389709083)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-16019346740824481331544370101),(-16019346740824217708904635286)⟩,⟨927310233057736084394449863,927310233057999706934219847⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-11464014307714301316443139473),(-11464014307714145587450452847)⟩,⟨2786559785846070409202707465,2786559785846226137982820446⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-7603752411794016807724601790),(-7603752411793947264797061365)⟩,⟨3295255382928411018243670009,3295255382928480560944720262⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-4722887100730896688004471546),(-4722887100730871248585530625)⟩,⟨2983739217185408150178709956,2983739217185433589407831209⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-2771293347599023529250189357),(-2771293347599015147990688784)⟩,⟨2317138686282328449298852518,2317138686282336830420578335⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-1531295019535837006558621949),(-1531295019535834310798753987)⟩,⟨1583262350519076998207838995,1583262350519079693878853644⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-753962550828069972675203686),(-753962550828069102488182759)⟩,⟨903721174510642906341463029,903721174510643776479917188⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-225489788824663949388581100),(-225489788824663743620991755)⟩,⟨291911303317281737628562086,291911303317281943380814737⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨20065735527171420062562672444,20065735527171420067779642456⟩,⟨170082379993936423615575023,170082379993936426372057312⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨58162333198873974610097142893,58162333198873974625550949693⟩,⟨(-2025521913805294354838793175),(-2025521913805294346332521841)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨90074966103431197136584649884,90074966103431197161523566546⟩,⟨(-10805656747192518276585130329),(-10805656747192518261723496366)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨111882749996737688688810237523,111882749996737688721805396569⟩,⟨(-27455750607461890460258925010),(-27455750607461890438568080600)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨120586212456213809448670166453,120586212456213809487507589851⟩,⟨(-49755129731380259997963510933),(-49755129731380259969642053961)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨115188848485772903563881343336,115188848485772903606357893457⟩,⟨(-72769219017330622462244924212),(-72769219017330622427831141022)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨97560903300545427641871596284,97560903300545427686930779507⟩,⟨(-90898775871903489753855580959),(-90898775871903489713565236464)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨72280350859684741858386313826,72280350859684741913909146739⟩,⟨(-100071576916814956585200308660),(-100071576916814956531177478059)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨45173190806669663459725947998,45173190806669663594616729920⟩,⟨(-99053492156460622995834808265),(-99053492156460622859861161580)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨21356371079548090246779826608,21356371079548090858411814840⟩,⟨(-89439225859600732791381341965),(-89439225859600732177091102240)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨3890440464952726541520718019,3890440464952729133284665924⟩,⟨(-74522473009539669490242099514),(-74522473009539666895198647487)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-6458589653733061224037611321),(-6458589653733053301507120998)⟩,⟨(-57779283125447375249857494706),(-57779283125447367324121846353)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-10603633203071837682331963047),(-10603633203071821235081477790)⟩,⟨(-41744509271610820102439456033),(-41744509271610803652481420675)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-10237075305828047843965142427),(-10237075305828024783915082831)⟩,⟨(-27641944021463724116991395743),(-27641944021463701054946587654)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-7081231033725151686676785079),(-7081231033725130866845187915)⟩,⟨(-15595266785297516479853196340),(-15595266785297495658816032482)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-2501459799020823129360987876),(-2501459799020814761698881176)⟩,⟨(-5020972547181515015898938379),(-5020972547181506647836491178)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-12255936841128988782354842541),(-12255936841128931011743500448)⟩,⟨34237228612104929678223200873,34237228612104987455177860525⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-32098692117926633336295789122),(-32098692117926496740327582880)⟩,⟨101608491134473990921607520439,101608491134474127535476506423⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-39009056783917615021559155990),(-39009056783917477228901863463)⟩,⟨164684411652447052002887186813,164684411652447189821796812414⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-27921028065909828703189443725),(-27921028065909742410178502703)⟩,⟨218322691850208143012633570341,218322691850208229335631328839⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨1578243635317092090724470815,1578243635317127554865759922⟩,⟨255906125959478839920252249121,255906125959478875413053091189⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨44792371697419157066349572399,44792371697419166792336021665⟩,⟨271651950594498453499221654187,271651950594498463248122574759⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨92844584990271940176678273291,92844584990271942107707291398⟩,⟨263327520080012076009532290074,263327520080012077954832968009⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨135272784097615235024875729107,135272784097615235401097149689⟩,⟨233583732362401876147338067931,233583732362401876528269479330⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨163526172049314429554726333751,163526172049314429695618818523⟩,⟨189333673078270952841589799336,189333673078270952978569460494⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨173491180489833797796587386247,173491180489833797892165410887⟩,⟨139606634221089925705382069662,139606634221089925790688014657⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨165896761064501653282461587006,165896761064501653355742276194⟩,⟨92822226336422342583822036174,92822226336422342643301290311⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨144874734413335106118010672056,144874734413335106173178962792⟩,⟨54729021270481331085683306718,54729021270481331126233889782⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨115724922854059368471715578616,115724922854059368511276468660⟩,⟨27728256976794818400336961068,27728256976794818426639357868⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨82996036772003436425479912102,82996036772003436451672414786⟩,⟨11368222698139332966541234612,11368222698139332982373626557⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨49527894467203951071767228265,49527894467203951086577356712⟩,⟨3359511592309247485838641848,3359511592309247494120353829⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨16417217348482794970506684132,16417217348482794975275870571⟩,⟨538216168746758839547557152,538216168746758842097756771⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-3500668633034264703047351203),(-3500668633033844998722838558)⟩,⟨(-55009199414398847805250730198),(-55009199414398428109333971093)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-18815024658770538152605672862),(-18815024658768918493466530863)⟩,⟨(-159270798467060703655110309573),(-159270798467059084019708089407)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-56152039922348005801268508642),(-56152039922343761093074621732)⟩,⟨(-245702933449340180514129865743),(-245702933449335935841117658580)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-120977850288775547227269330509),(-120977850288765046889266223835)⟩,⟨(-302100419864971704364211577609),(-302100419864961204067060755420)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-207204966620280944609231950949),(-207204966620256686107945107561)⟩,⟨(-318115315585483792838884152036),(-318115315585459534377605502487)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-298234286003079391989255624738),(-298234286003030281979126507624)⟩,⟨(-288729492524426317317015044349),(-288729492524377207339690638388)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-372977197964660724950197452010),(-372977197964580244591600814983)⟩,⟨(-217743774628686455707581872635),(-217743774628605975369928614166)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-413898989403436899252179722325),(-413898989403337084150507208633)⟩,⟨(-118965843610982084379489347264),(-118965843610882269284786246518)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-413128324418093404709641550529),(-413128324417999692882433393996)⟩,⟨(-12951241491481928340685102244),(-12951241491388216506904665918)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-374342996529294279583561744514),(-374342996529227475766930070276)⟩,⟨79555260573114217190766974377,79555260573181021025060915529⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-310096348284856512768286282403),(-310096348284820251131318531181)⟩,⟨143707522057257499269236361170,143707522057293760931036534479⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-236172588005152231249193783787),(-236172588005136130075483141711)⟩,⟨173210889260065183257892002663,173210889260081284459012431904⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-165713163840664067056007711495),(-165713163840657709738331848830)⟩,⟨169438251747107970652849290553,169438251747114327996254115545⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-105848556797286009115922902499),(-105848556797283621633743070911)⟩,⟨138840508717156467403603235554,138840508717158854906477107169⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-57711225686846688670006701727),(-57711225686845824114561845019)⟩,⟨89972664290964553468506094262,89972664290965418037254860112⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-18188551662015951783789990134),(-18188551662015734082088098909)⟩,⟨31029271321400907385008340733,31029271321401125091288084122⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨616648033196309924139932663,616648033196309932937813441⟩,⟨30561128435023466956751026582,30561128435023466969216367157⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨8939307744611798011405634425,8939307744611798039357689911⟩,⟨89230261271793894325178409374,89230261271793894363501333071⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨36073431445623473235302954085,36073431445623473286660484996⟩,⟨139888901895117161096594885516,139888901895117161162657389622⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨86526913304365479534525085930,86526913304365479615071630718⟩,⟨175745828448366623605783290413,175745828448366623702211232767⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨154567190205014176838275867539,154567190205014176954169364032⟩,⟨188837376125763813580980599241,188837376125763813710733860395⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨225921013728368012354282539007,225921013728368012514477553366⟩,⟨171888189263617974216036437468,171888189263617974386292092243⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨283897148651302353663686139492,283897148651302353899832331197⟩,⟨122983270308470941230289800297,122983270308470941471997579933⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨315295115112391012322909558930,315295115112391012839344962308⟩,⟨49730342953657924688822568061,49730342953657925206801439370⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨314059186492454475818648068351,314059186492454478188513647641⟩,⟨(-32210591830994485890027499907),(-32210591830994483520975223137)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨282893991638574804556584372332,282893991638574818800483492513⟩,⟨(-105147261580477240067979523507),(-105147261580477225825144632110)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨231832388856398054100529060180,231832388856398122959288428988⟩,⟨(-155300399515891437256131356220),(-155300399515891368397279881227)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨173797562077502754035674588455,173797562077502986694331368310⟩,⟨(-175857117422713012359907657853),(-175857117422712779699711682710)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨119471245833056992094691780200,119471245833057517800352553047⟩,⟨(-167082733690610285249076938307),(-167082733690609759540880275076)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨74484374531883377019733231665,74484374531884166392378137257⟩,⟨(-134571663850302576880176929555),(-134571663850301787504811469919)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨39640583748055689854385277318,39640583748056438447226152225⟩,⟨(-86268974062665116179250515333),(-86268974062664367584365226086)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨12294508920585405089519916242,12294508920585714071823106355⟩,⟨(-29591292047485757085560745445),(-29591292047485448102503669989)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨131844853960303397505990660609,131844853960386400065233865623⟩,⟨69319223301321892901685983964,69319223301404895470791741067⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 4) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_4 (tableDensity false) (fullFactor false 3 4) density0_contains hk3_0_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨29247805196765215177193547597,29247805196765215195365968619⟩,⟨21985530137787495978731152494,21985530137787495994575168991⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_4 3 4 ha3_0_4_contains + def realAnswer : RBox := ⟨161092659157068612683084208206,161092659157151615260699834242⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_4 +namespace hm3_1_0_4 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_4 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-47055666069518459885709850),(-47055666069518345813000273)⟩,⟨49938143589056788762550001,49938143589056902839746521⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-125027852854850230451761600),(-125027852854849973898500592)⟩,⟨142002687816494734467631513,142002687816494991032755110⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-161143204726626335010981781),(-161143204726626101493275294)⟩,⟨209389724377204638918810839,209389724377204872451839283⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-147368508810728395120011652),(-147368508810728270636753529)⟩,⟨236971024719468791419437192,236971024719468915917183646⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-97245524823223054269947922),(-97245524823223013540671614)⟩,⟨220616343045931946126936017,220616343045931986867018245⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-38987759794293159337414319),(-38987759794293151117440338)⟩,⟨172100286933510484942757319,172100286933510493169094317⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨1909242510423549503752552,1909242510423550601121230⟩,⟨112394999372097256954663173,112394999372097258054824687⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨17394752531000353818522679,17394752531000353949890934⟩,⟨60525824188462178043043969,60525824188462178175079239⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨15518524749447053260746928,15518524749447053287594371⟩,⟨26174435010653995678049074,26174435010653995704702971⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨8376016715335949074073018,8376016715335949082197592⟩,⟨8754727243567208814090639,8754727243567208821888517⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨3052975068768118475100731,3052975068768118477331157⟩,⟨2143666032461228526642605,2143666032461228528668813⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨735182627214442096372033,735182627214442096839066⟩,⟨352026190733242720855998,352026190733242721243643⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨105801243146164432695256,105801243146164432762050⟩,⟨33366065185302996171813,33366065185302996219261⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨7281962588339450197338,7281962588339450202798⟩,⟨1383262273617342508118,1383262273617342511043⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨141922126435872004582,141922126435872004769⟩,⟨13877412279943417908,13877412279943417976⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨145281225600643110,145281225600643126⟩,⟨5821220029701486,5821220029701502⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-103456972357812662915597129),(-103456972357810393596606719)⟩,⟨(-855788792233370484423128318),(-855788792233368215147282161)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-404406721358900667026327373),(-404406721358892129765067695)⟩,⟨(-2394495378461601518396383657),(-2394495378461592981253405069)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-925363588807007188495053872),(-925363588806985915757198026)⟩,⟨(-3456015934143380044972082140),(-3456015934143358772398828228)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-1644143721291431293107722058),(-1644143721291382463179773204)⟩,⟨(-3862134905933593691409607682),(-3862134905933544861655691485)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-2391406357268402575365311110),(-2391406357268300338003698609)⟩,⟨(-3610806259071328330074141071),(-3610806259071226092863279960)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-2937169800071411556822526231),(-2937169800071228048501041824)⟩,⟨(-2868668059201543667828529103),(-2868668059201360159613848123)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-3114970236825025771427521937),(-3114970236824764026277105764)⟩,⟨(-1897186494428927167125474992),(-1897186494428665422032796958)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2905899918598073666820975759),(-2905899918597796475841624225)⟩,⟨(-955556992555924078433245160),(-955556992555646887469446994)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-2425398946552376265717327500),(-2425398946552158123857545289)⟩,⟨(-224911541927365672334266689),(-224911541927147530461728554)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-1841083532283697718185112238),(-1841083532283568924795828373)⟩,⟨225345692360876123445345204,225345692361004916862028338⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-1291921733244559480245813368),(-1291921733244502021528279639)⟩,⟨422057555900988648155786597,422057555901046106904857415⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-850567854262995311625181263),(-850567854262974319264258997)⟩,⟨442424583287954740828271127,442424583287975733218006781⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-529845773948499479972753365),(-529845773948492573289487026)⟩,⟨368843184092811449738604279,368843184092818356444444770⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-309597331713068756844515619),(-309597331713066538182450324)⟩,⟨261736275054667758765767269,261736275054669977443306763⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-159294089237663627607958801),(-159294089237662912128265830)⟩,⟨152406320074354739954573908,152406320074355455443101738⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-48819424491305058359459364),(-48819424491304889265525709)⟩,⟨49660362909608654868823710,49660362909608823965624445⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨3838131245398736049402355915,3838131245398736051241490168⟩,⟨2406798585970357357841278416,2406798585970357359561704060⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨11408512414447329062070379042,11408512414447329067656664837⟩,⟨6550947028907017558018797345,6550947028907017563258525957⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨18442525216990135898659415594,18442525216990135908039897928⟩,⟨8855262161501600669283628421,8855262161501600678164757099⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨24103541131453934435047986347,24103541131453934448065895108⟩,⟨8614320858169872519292717276,8614320858169872531761724419⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨27408465176329982947684334802,27408465176329982963818372499⟩,⟨5757177683012816069381020683,5757177683012816085027436215⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨27779783827263898427081779332,27779783827263898445859716498⟩,⟨951638145473606499678462179,951638145473606518074144316⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨25367094868075109299318122406,25367094868075109321133885947⟩,⟨(-4499847578028759166185975762),(-4499847578028759144615115913)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨20949899190830993072544051996,20949899190830993104968576744⟩,⟨(-9147694699848539981994497508),(-9147694699848539949656826437)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨15632562089884843921849562183,15632562089884844021939684668⟩,⟨(-11991862109123148133752147232),(-11991862109123148033612501554)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨10487512302508985455153577216,10487512302508985946922466700⟩,⟨(-12758752241094164118035870572),(-12758752241094163626139135633)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨6253403800899341219628984358,6253403800899343327650913129⟩,⟨(-11789205380326921401086387460),(-11789205380326919292905468484)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨3216436945339359814678524938,3216436945339366271717453179⟩,⟨(-9737596504248588681772209679),(-9737596504248582224569068086)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1308519358779380435271857358,1308519358779393853450526031⟩,⟨(-7276189282525920802109369074),(-7276189282525907383785429020)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨300461137628026189506038997,300461137628045016648871319⟩,⟨(-4884599242705807247504044812),(-4884599242705788420257177152)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-70726480189127642445138895),(-70726480189110635597215951)⟩,⟨(-2765009609956602098365031518),(-2765009609956585091457301243)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-65004181580695123933306873),(-65004181580688286973882188)⟩,⟨(-890188025275111238641061728),(-890188025275104401663011203)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-10125504722729821345719430635),(-10125504722729772804074171746)⟩,⟨6726030393307284563666535429,6726030393307333104640067417⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-28527003159016822940008620554),(-28527003159016708242322723103)⟩,⟨20430243961109252828738413541,20430243961109367524534866448⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-41671430863179943389252283395),(-41671430863179827845029410477)⟩,⟨34594443483961525598600033106,34594443483961641140082750903⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-47181320175262861399134834266),(-47181320175262789194177594775)⟩,⟨48759081443537804212149406658,48759081443537876414029579681⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-44383696719176876469045722146),(-44383696719176846888962959413)⟩,⟨61684841953601286196700053687,61684841953601315773923413635⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-34596781932330296009421400540),(-34596781932330287945063681718)⟩,⟨71515694745222888240314964049,71515694745222896302457611041⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-20570491315630947273474573248),(-20570491315630945706448606269)⟩,⟨76331548447523384723202771252,76331548447523386288891086522⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-5467242488972116751238101385),(-5467242488972116478615404193)⟩,⟨75094655903974812970971876594,75094655903974813243173985485⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨7941112791786355695172780204,7941112791786355772460433616⟩,⟨68262967250427517421302687834,68262967250427517498941202716⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨17765958113774201141380317950,17765958113774201184009033397⟩,⟨57564285088633359821525926106,57564285088633359865022695585⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨23200576463362465480761612192,23200576463362465509949260634⟩,⟨45242926324806057426619374625,45242926324806057456910556786⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨24385463728168639372212014208,24385463728168639392404582245⟩,⟨33277706790243961543389848145,33277706790243961564693203481⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨22072251936795447145140908969,22072251936795447158627237615⟩,⟨22898568160364215998325078940,22898568160364216012773931177⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨17258367118618800350695304240,17258367118618800359081933534⟩,⟨14515493835738152661610174582,14515493835738152670718572593⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨10889165582320366839369944742,10889165582320366843884355704⟩,⟨7913901078354757965665313747,7913901078354757970621248943⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨3710433362498890279763419859,3710433362498890281178597557⟩,⟨2499607050763820366249429086,2499607050763820367811920861⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-2073576568459137173738989912),(-2073576568458792247347960989)⟩,⟨(-17991300522524196538671099949),(-17991300522523851610446682520)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-8561729995261448686729545743),(-8561729995260117498043810338)⟩,⟨(-53092480988634928185347292577),(-53092480988633596991379532374)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-21165225786033479385816900320),(-21165225786029990204402274233)⟩,⟨(-84738527736012009174307403479),(-84738527736008519984976514548)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-41435289220826912513462481073),(-41435289220818279754225455792)⟩,⟨(-108769934169263596817563907205),(-108769934169254964049014281179)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-68348892024262874336724885233),(-68348892024242927972720024718)⟩,⟨(-120295623596470285069896644013),(-120295623596450338696737460859)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-98508531012440248390717262896),(-98508531012399868164801159522)⟩,⟨(-116178495918718388109673968453),(-116178495918678007876156752862)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-126607548469425931011166621426),(-126607548469359770972345202866)⟩,⟨(-97100579745051438182479782888),(-97100579744985278138699657814)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-146850451237552380040782020050),(-146850451237470365607581841856)⟩,⟨(-67556841601980198285343049650),(-67556841601898183850438949267)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-155120865990374047307340405938),(-155120865990297108768586895652)⟩,⟨(-34276108953999182708692341304),(-34276108953922244171365939440)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-150358643981399462737891979501),(-150358643981344674278258804903)⟩,⟨(-4119415265275603908074221043),(-4119415265220815452155505389)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-134379789294878790565744874530),(-134379789294849088543329238805)⟩,⟨17895993913979512467919964005,17895993914009214485384750434⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-110766354034197566282391724209),(-110766354034184395465462699297)⟩,⟨29793170827944148346200767352,29793170827957319157839905579⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-83725909754035203591244689294),(-83725909754030009895939502416)⟩,⟨32413645106440401457330111519,32413645106445595147774904754⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-56964358316376251246159929711),(-56964358316374302826486437547)⟩,⟨27953939722799464001939946278,27953939722801412417816569413⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-32551838765263395505203935753),(-32551838765262690467918266719)⟩,⟨18663026771954753926530537391,18663026771955458961433090834⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-10526018784112788155952252275),(-10526018784112610689373303843)⟩,⟨6533229196521204877172777319,6533229196521382342949809066⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨61535866159171990372418486,61535866159171995499143508⟩,⟨906914559263452714183311766,906914559263452721690814012⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨899769858269492149911819271,899769858269492166272383166⟩,⟨2459249652093620261250189331,2459249652093620284465951851⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨3777988493692643969220965566,3777988493692643999504768613⟩,⟨2257710866245853730427694507,2257710866245853770737018158⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨10002754926461468209379466194,10002754926461468257522802792⟩,⟨(-3047197771431745163058065717),(-3047197771431745103574323480)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨20923099174713694741987658674,20923099174713694813590168775⟩,⟨(-16967763798427968289253335582),(-16967763798427968207027238984)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨36520947832753136825558419931,36520947832753136930130037183⟩,⟨(-39959110412205886162290468079),(-39959110412205886049236300234)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨53441487972655139834938373937,53441487972655140002677006932⟩,⟨(-68490603751647330836059827975),(-68490603751647330663013263580)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨66002263397403491385392838467,66002263397403491790370566538⟩,⟨(-97132659607982332708900601973),(-97132659607982332302242394581)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨69662486873669726775449766502,69662486873669728713195845802⟩,⟨(-120492984054036442181442223797),(-120492984054036440245098966530)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨63246974824066786407958918884,63246974824066798067143653876⟩,⟨(-134225591378928430366255627321),(-134225591378928418710264055780)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨48888544186176401683415055421,48888544186176457943449267112⟩,⟨(-136022566633331717494210005565),(-136022566633331661237967886870)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨30861852128934247734483961349,30861852128934437752730275332⟩,⟨(-126217857938867104558435095862),(-126217857938866914543911633426)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨14174953927478749619531937922,14174953927479179110508343558⟩,⟨(-107082474813543636031572849894),(-107082474813543206543823970191)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨2816459552396345925267432495,2816459552396991121871015333⟩,⟨(-81207336425526145729932804393),(-81207336425525500535712092372)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-1839340974783184386321516505),(-1839340974782572294505061323)⟩,⟨(-50651329125533173775058340165),(-50651329125532561684664684627)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1258889439002249461086821803),(-1258889439001996769621288282)⟩,⟨(-17207876318051973237326798418),(-17207876318051720546316825439)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-126859038911447546403319803009),(-126859038911379392808320427191)⟩,⟨(-162700379323545824835226946426),(-162700379323477671232622865021)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_4 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 4) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_4 (tableDensity true) (fullFactor false 3 4) density1_contains hk3_0_4_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-38247129872692973717017035886),(-38247129872692973693253100704)⟩,⟨(-28750308641722110146752144065),(-28750308641722110126033045570)⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_4 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 4) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_4 3 4 ha3_0_4_contains + def realAnswer : RBox := ⟨(-165106168784140520120436838895),(-165106168784072366501473527895)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 4) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_4 +namespace hm3_0_0_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-33951223494194675405411838),(-33951223494194660891382144)⟩,⟨(-24411487711066154360695903),(-24411487711066139844811184)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-94088381910878117352373013),(-94088381910878085291876313)⟩,⟨(-61902763851878022976129820),(-61902763851877990910902519)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-132518092819394562276697528),(-132518092819394534130285042)⟩,⟨(-72525222360529672434272842),(-72525222360529644282214207)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-141148148185396908053545147),(-141148148185396893846946568)⟩,⟨(-57032760557471776276084899),(-57032760557471762064820194)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-121712849998128178405669381),(-121712849998128174086665702)⟩,⟨(-29565549368384244982629281),(-29565549368384240660814366)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-85892251756499059954001407),(-85892251756499059157015474)⟩,⟨(-6110982819610612750244643),(-6110982819610611952080808)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-49197348301567782056391522),(-49197348301567781958146293)⟩,⟨5517614169796150907513800,5517614169796151006040060⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-22460376962985020344845497),(-22460376962985020332637290)⟩,⟨7060974726087006017734036,7060974726087006029944587⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-7950871956468937837701475),(-7950871956468937835002325)⟩,⟨4362451951876432748808961,4362451951876432751498216⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-2096159680601118592670893),(-2096159680601118591947228)⟩,⟨1753247299061822073179986,1753247299061822073916764⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-387644570732918649685141),(-387644570732918649530261)⟩,⟨470174420445681415288099,470174420445681415456517⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-45844770637446778891863),(-45844770637446778869051)⟩,⟨79628549349456129471398,79628549349456129499737⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-2977650829430132606985),(-2977650829430132604983)⟩,⟨7452227349289563012841,7452227349289563015957⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-80386969601577126424),(-80386969601577126330)⟩,⟨292870876559868742910,292870876559868743101⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-488942884690663182),(-488942884690663163)⟩,⟨2575287620043552588,2575287620043552606⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-93278115005441),(-93278115005425)⟩,⟨665589435180253,665589435180270⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨942577670478900556786420220,942577670478901132661696088⟩,⟨(-667149839015117001586177465),(-667149839015116425799867530)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨2598046485031162754153507122,2598046485031164898306447800⟩,⟨(-1977815976104661932727056076),(-1977815976104659788816836905)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨3635799950656506728203349444,3635799950656511963230384258⟩,⟨(-3181361038449165472732759439),(-3181361038449160238037643238)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨3868270887071547501455656991,3868270887071559165474812708⟩,⟨(-4128707210578109512180352117),(-4128707210578097848502530214)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨3361413798535625764783166720,3361413798535649265443974551⟩,⟨(-4648403604216532374720123127),(-4648403604216508874342609108)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨2391226659848002241070527588,2391226659848042513682872422⟩,⟨(-4640812697233268131628736769),(-4640812697233227859206538955)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨1315825625423264654593406021,1315825625423319109420924723⟩,⟨(-4147007265602999954638683123),(-4147007265602945499907337439)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨427020012682718824686849288,427020012682773190656032912⟩,⟨(-3338435412381486872721897752),(-3338435412381432506778019695)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-138639547899618472853713896),(-138639547899578331303392564)⟩,⟨(-2438231985026904366213028966),(-2438231985026864224647647722)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-394533401550574624616668754),(-394533401550552439000193299)⟩,⟨(-1630304759542277990861066318),(-1630304759542255805214547640)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-436412167343319059085690907),(-436412167343309801079325428)⟩,⟨(-1009564162721655107236488155),(-1009564162721645849200358371)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-370101127893283278155144346),(-370101127893280108048883602)⟩,⟨(-586815001346913187847311519),(-586815001346910017717856851)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-270737636037081648710870493),(-270737636037080665819164993)⟩,⟨(-324165163699103094823075555),(-324165163699102111915649835)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-175992654742099442025427605),(-175992654742099141665846279)⟩,⟨(-170326275455011466420152299),(-170326275455011166051014416)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-96906363034423515238181146),(-96906363034423421837348005)⟩,⟨(-80868698936225114108064317),(-80868698936225020702232136)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-30716051419381515571222695),(-30716051419381493918144957)⟩,⟨(-23727646274082968022174727),(-23727646274082946367554863)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-53384299487912757745799528),(-53384299487912756880742524)⟩,⟨6293776605292192811054719061,6293776605292192812711153042⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨630365277860674593915828511,630365277860674596569311293⟩,⟨18127608318066519905918103983,18127608318066519910793153365⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨3321928036375867092870411230,3321928036375867097454703915⟩,⟨27723295231706466880945816682,27723295231706466888713380744⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨8286451679556159189669649564,8286451679556159196249648687⟩,⟨33803572465956762258855981145,33803572465956762268942478534⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨14660293155812630989523988259,14660293155812630997926380262⟩,⟨35567448069956285349643000979,35567448069956285361231619430⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨20827991323572870345481370539,20827991323572870355414186704⟩,⟨33004087823930923233858403339,33004087823930923246167172390⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨25165081023627218419864217541,25165081023627218431120347971⟩,⟨27040217110991998258966374067,27040217110991998271584084590⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨26708033524978588940683388521,26708033524978588955197118912⟩,⟨19316449249703555672234391190,19316449249703555687162782363⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨25429535188559963499452385448,25429535188559963534326408430⟩,⟨11617115123079920050418705345,11617115123079920085007252941⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨22068452251955049464898709474,22068452251955049615751397963⟩,⟨5284125342207481859140133867,5284125342207482009315716188⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨17685832132682962486122047425,17685832132682963099156353891⟩,⟨933074936969334962768154145,933074936969335574997339801⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨13221439962415090816593654948,13221439962415092623927764395⟩,⟨(-1472057199061505281422678872),(-1472057199061503474848428723)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨9250005016384632787657290354,9250005016384636424704769580⟩,⟨(-2346682027036644513314967860),(-2346682027036640876889747668)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨5967492592819432893347101177,5967492592819437866468209987⟩,⟨(-2208913487943336124616720748),(-2208913487943331151942718289)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨3305441604884897981244722507,3305441604884902392542938652⟩,⟨(-1500628249872906585009981209),(-1500628249872902173977266559)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨1054121908132977698955559668,1054121908132979455710008850⟩,⟨(-525156536100746725253470290),(-525156536100744968586393965)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-14324057428725648326520931718),(-14324057428725624153398750062)⟩,⟨(-5127659561103475693455721469),(-5127659561103451523016106247)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-42308120885225315351624236188),(-42308120885225258455795566810)⟩,⟨(-13366931371052723415106396855),(-13366931371052666526814831950)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-67928617034087265956373325170),(-67928617034087209074758228467)⟩,⟨(-16096683780188525328149533045),(-16096683780188468457492847039)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-88816554137591191844283629985),(-88816554137591156684343022672)⟩,⟨(-11373112023091367230512069622),(-11373112023091332082931013979)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-102263192217703817310211820801),(-102263192217703803098454329514)⟩,⟨605947427040978926394659422,605947427040993126531227738⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-106257165929910160962769802143),(-106257165929910157138421666326)⟩,⟨17485322197022363221438140920,17485322197022367036673814443⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-100526871170520907154206786563),(-100526871170520906408708282894)⟩,⟨35399796849514258113720667153,35399796849514258853665771402⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-86842504548171625625217572541),(-86842504548171625482867601326)⟩,⟨50242180211430610539966094874,50242180211430610680522710833⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-68465587888218108337883894577),(-68465587888218108288018479630)⟩,⟨59081111977429834266923927423,59081111977429834318231673404⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-49090455269023896722078604497),(-49090455269023896691862895702)⟩,⟨60954564288135437128042810258,60954564288135437161960444976⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-31766205861720141140401797604),(-31766205861720141119902691660)⟩,⟨56727634784772626515828793817,56727634784772626541184548807⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-18265786391296955487739299549),(-18265786391296955474121331556)⟩,⟨48311943367749216622880681395,48311943367749216641529339285⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-9054029107391261243957702310),(-9054029107391261235327652723)⟩,⟨37756057950604741269621885180,37756057950604741282726712806⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-3647261183820900171423363327),(-3647261183820900166327786278)⟩,⟨26606675392636336735238595400,26606675392636336743776469918⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-1064465620356311070932746339),(-1064465620356311068304359792)⟩,⟨15683537428784566607934638098,15683537428784566612708516351⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-169380397433667388229492874),(-169380397433667387426120780)⟩,⟨5165879350897148967665642973,5165879350897148969194146233⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨28775171965540998880254023496,28775171965541218417131115520⟩,⟨(-1831065871438367147321847544),(-1831065871438147606132673649)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨82998029426107034027585313615,82998029426107877874658578939⟩,⟨(-9801500308316940500056073492),(-9801500308316096640849892589)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨127083021576202301288237149772,127083021576204495668728615924⟩,⟨(-29029229622453456508322421038),(-29029229622451262109964060712)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨154549009181924181821363345216,154549009181929549311638769602⟩,⟨(-61856082287251284741410861674),(-61856082287245917230583924140)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨160462507019339899779830587262,160462507019352123319604484799⟩,⟨(-104453811034178026329535435905),(-104453811034165802769877332149)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨143214698187971030491896779786,143214698187995360524085328128⟩,⟨(-147823737607135855061714819854),(-147823737607111525013458415886)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨105985608804059594465269218885,105985608804098716880107843838⟩,⟨(-181372089136807327547457320327),(-181372089136768205122525676459)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨56761236569896213399427358773,56761236569943756727583968144⟩,⟨(-197148773590920473791521845044),(-197148773590872930460059473264)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨6123912359175557252320158413,6123912359219252401015304564⟩,⟨(-192583468779172513553349616350),(-192583468779128818407696423158)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-36216756798638646458157674461),(-36216756798608152823130218663)⟩,⟨(-170768669009243808503393612290),(-170768669009213314876409637803)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-64143685332333707744224975075),(-64143685332317493635586581542)⟩,⟨(-138541893807475918030195152340),(-138541893807459703932675698484)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-75871415618609026688079279952),(-75871415618601963831515136898)⟩,⟨(-103510218828317111013665256592),(-103510218828310048169183908194)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-73008938535942734331662705565),(-73008938535939992117023587348)⟩,⟨(-71429669573759632897399384433),(-71429669573756890693949860162)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-59042595088543597208098317803),(-59042595088542581255205888970)⟩,⟨(-45021604989863901515862140940),(-45021604989862885571872114991)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-37911381932879098342052940031),(-37911381932878733945954951271)⟩,⟨(-24319421632793116829485847851),(-24319421632792752439067242960)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-13013069029532118681363701910),(-13013069029532027376653111582)⟩,⟨(-7627991947034300330507750188),(-7627991947034209027743595670)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-19186791407342916707889967667),(-19186791407342916700002872379)⟩,⟨387039209054299147971753750,387039209054299153496414536⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-55842913478959121066592386090),(-55842913478959121042429340212)⟩,⟨5591833214885841410444673860,5591833214885841427954989999⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-87001678365386110207506491361),(-87001678365386110166131382534)⟩,⟨22424237675161372814351903186,22424237675161372846361876028⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-108310207422145807337725339121),(-108310207422145807277909019253)⟩,⟨53299303617098847633914652771,53299303617098847683720035471⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-115025675870002620276997930171),(-115025675870002620197485536339)⟩,⟨94102331025326007395761332828,94102331025326007466647460840⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-103261433206368746216799126740),(-103261433206368746113985106345)⟩,⟨135637691415020924507336341511,135637691415020924603983815072⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-72751285103350294093345988908),(-72751285103350293949895372113)⟩,⟨167783184903818873004969481382,167783184903818873145073808430⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-28966096210697805078514224419),(-28966096210697804777308643982)⟩,⟨183199449601285585041288781340,183199449601285585341584382977⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨18318613762054556754664812590,18318613762054558104327459625⟩,⟨179290712395388521135901053863,179290712395388522486022267045⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨58913056618055970762403926087,58913056618055978730839040351⟩,⟨158677751378643525545451545159,158677751378643533514443311191⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨85592526950040107789166111809,85592526950040145681263821672⟩,⟨127855634871816147131550515035,127855634871816185023496932551⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨95450850113151905083979903494,95450850113152031215253051595⟩,⟨94374496998723370788210978830,94374496998723496918491518426⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨89492788577175900646062730831,89492788577176182011648453911⟩,⟨64009836640783461501757517924,64009836640783742865801218477⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨71320300687319937708868085264,71320300687320355899864822565⟩,⟨39481913239932212297335302993,39481913239932630486721836466⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨45385013778542472720402093555,45385013778542866493365050145⟩,⟨20855847300645673204087693249,20855847300646066975858796773⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨15508808269461344345431341664,15508808269461506281308543082⟩,⟨6443610404897629576864425748,6443610404897791512305265719⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-30157542393150964220652652084),(-30157542393111725616675552249)⟩,⟨68630541578381154612428771343,68630541578420393210689852422⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 5) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_5 (tableDensity false) (fullFactor false 3 5) density0_contains hk3_0_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-15421672956801917433216814321),(-15421672956801917424683941296)⟩,⟨24805036725820210945815234011,24805036725820210956035284480⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_5 3 5 ha3_0_5_contains + def realAnswer : RBox := ⟨(-45579215349952881653969466405),(-45579215349913643041259493545)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_5 +namespace hm3_1_0_5 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_5 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨(-5204508154434191206285765),(-5204508154434179316115049)⟩,⟨(-4904235315902631888234256),(-4904235315902619998531897)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨(-14518487262224457734035501),(-14518487262224431479410699)⟩,⟨(-12786134466812318296386019),(-12786134466812292042976697)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨(-20597353286820025452080925),(-20597353286820002420916151)⟩,⟨(-15862542243006178439905561),(-15862542243006155410253090)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨(-21981236570969144357487903),(-21981236570969132748197843)⟩,⟨(-13691064807803485393240688),(-13691064807803473785302070)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨(-18891583190704706405423235),(-18891583190704702884975225)⟩,⟨(-8356260798317777476718009),(-8356260798317773957204870)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨(-13295932819362953350968505),(-13295932819362952706571207)⟩,⟨(-3041950782883392967084603),(-3041950782883392323188474)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-7638370423394626802927072),(-7638370423394626726762607)⟩,⟨106269883236142092684090,106269883236142168651833⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-3516453907513761377330379),(-3516453907513761369511117)⟩,⟨996135212605709945581535,996135212605709953359492⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-1257610323309251552738192),(-1257610323309251551437324)⟩,⟨738502402331859942275494,738502402331859943586182⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-334309023225999272048090),(-334309023225999271745475)⟩,⟨317086296231552509433231,317086296231552509749579⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-61921766796096288750734),(-61921766796096288691072)⟩,⟨87379237777582593174114,87379237777582593240432⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-7214261755889335030418),(-7214261755889335022281)⟩,⟨14900463641448276569721,14900463641448276579729⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-444105643477443918330),(-444105643477443917663)⟩,⟨1387762727519057556111,1387762727519057557070⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-10463718153133260617),(-10463718153133260579)⟩,⟨54020882073579509965,54020882073579510026⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-47030976690421186),(-47030976690421170)⟩,⟨470786237330200161,470786237330200178⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-4912139988152),(-4912139988136)⟩,⟨120973608048404,120973608048420⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨178808198316330532003918244,178808198316331006117720436⟩,⟨(-21614550860067566610732112),(-21614550860067092488419060)⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨495579349701638484185297226,495579349701640250181276432⟩,⟨(-83655043086532531679358531),(-83655043086530765660256848)⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨701903526722072437149311094,701903526722076752030151745⟩,⟨(-187760735131932861075022438),(-187760735131928546162565928)⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨762700256879029777803763565,762700256879039400249114918⟩,⟨(-324282532862764623902855951),(-324282532862755001424930796)⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨687288136573489263599524123,687288136573508668144591010⟩,⟨(-454496178035809361552808255),(-454496178035789956980454170)⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨521984404540835871997305000,521984404540869152440796613⟩,⟨(-533464199510476007955980089),(-533464199510442727493932139)⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨327614218076566017500576689,327614218076611057176322250⟩,⟨(-536590186604019170146400269),(-536590186603974130461084100)⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨155723911193540741416831931,155723911193585729200943877⟩,⟨(-471665112353299743913374447),(-471665112353254756126807835)⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨34679739425727033424689584,34679739425760249723825895⟩,⟨(-369030733226436768996955311),(-369030733226403552699691809)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨(-31722860211149911681101987),(-31722860211131563287152437)⟩,⟨(-261736978183136526019670032),(-261736978183118177629528100)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨(-55826206542961125007638391),(-55826206542953475657099532)⟩,⟨(-171475789566614100729239073),(-171475789566606451382833059)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨(-54849909244232041325444316),(-54849909244229425346927464)⟩,⟨(-105649153211665065068647000),(-105649153211662449093691500)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨(-43086111280341486921923167),(-43086111280340676938911275)⟩,⟨(-61960576997935754423070401),(-61960576997934944442700066)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨(-29091308572666291935939252),(-29091308572666044724646969)⟩,⟨(-34430247287017759657520641),(-34430247287017512447955440)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨(-16342078765507413793568439),(-16342078765507336993402323)⟩,⟨(-17084225205049555631785745),(-17084225205049478832571807)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨(-5225440934950434687788221),(-5225440934950416892472638)⟩,⟨(-5137077646686169525441534),(-5137077646686151730429247)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-754917618343252027102556163),(-754917618343252026560466836)⟩,⟨1203855915647711891917665801,1203855915647711892498363886⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-2041908425054765879698757732),(-2041908425054765878058327344)⟩,⟨3555619331780962305664149358,3555619331780962307416652291⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-2726121171519455929360243777),(-2726121171519455926614736878)⟩,⟨5675882794640663165155390965,5675882794640663168060974731⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-2604200473005358988883362195),(-2604200473005358985099758799)⟩,⟨7281808116025084221996109824,7281808116025084225953413448⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1700809456218402813995953136),(-1700809456218402809361797321)⟩,⟨8083249419825133356122234035,8083249419825133360908322631⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-276654830430852618732136673),(-276654830430852613441659613)⟩,⟨7958144494117225108140426745,7958144494117225113547729376⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨1242024464052859214965439078,1242024464052859220959877681⟩,⟨7028974034793469736656796741,7028974034793469742724305563⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨2438454610646749700026318278,2438454610646749708661998597⟩,⟨5596328062595721887592125458,5596328062595721896253021780⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨3076497467695242157615172340,3076497467695242183219309427⟩,⟨4017081617113791455445808325,4017081617113791481035344343⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨3146785811198107198490395369,3146785811198107319204472424⟩,⟨2590380226200743612823504333,2590380226200743733500500058⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨2797121049420821566120999008,2797121049420822064073593008⟩,⟨1485780786070580096833876512,1485780786070580594740805808⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨2227922819756122360621372839,2227922819756123833025744823⟩,⟨737001371181038005349455613,737001371181039477707568758⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨1612217766282718313282207817,1612217766282721279999844552⟩,⟨290456965001606089895050167,290456965001609056572709038⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨1054500497122623760230948364,1054500497122627820127201166⟩,⟨65067531104474285961455980,65067531104478345829544573⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨586047754225597450781279170,586047754225601053974669763⟩,⟨(-14943463070989724238467241),(-14943463070986121061128310)⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨186889454047442375190583833,186889454047443810511420649⟩,⟨(-13645411401676975509164695),(-13645411401675540193342483)⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨(-2814007471620945991724093263),(-2814007471620925682843600835)⟩,⟨(-4236296947318206318140092094),(-4236296947318186008973892053)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨(-8506648215669841088661376986),(-8506648215669793321148730512)⟩,⟨(-11878732731015201518355854930),(-11878732731015153750043638276)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨(-14268692075154278912808058320),(-14268692075154231225745838513)⟩,⟨(-17190721348544556157611425610),(-17190721348544508469401328940)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨(-19834007845513521273150134635),(-19834007845513491864907618456)⟩,⟨(-19198772728093094425543359244),(-19198772728093065016031392668)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-24646625993488617028688151811),(-24646625993488605185720468583)⟩,⟨(-17743828654309982711388149771),(-17743828654309970867264450731)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-27968485904338666554637939951),(-27968485904338663392126629014)⟩,⟨(-13542338544679064847479979124),(-13542338544679061684094871691)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-29133797564110554528674473661),(-29133797564110553928787825179)⟩,⟨(-7863982102778519090747954268),(-7863982102778518490348019751)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-27912025000782383016342060927),(-27912025000782382914716376892)⟩,⟨(-2044332436345183812038713227),(-2044332436345183710255962807)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-24677680379977539168883786770),(-24677680379977539140668402548)⟩,⟨2859812087070660480666488486,2859812087070660508756363917⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-20234603148415866202211479668),(-20234603148415866186824968961)⟩,⟨6235696525798386845806987861,6235696525798386860892000976⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-15476846464509982579530265291),(-15476846464509982569094278692)⟩,⟨7929306314015281295974381198,7929306314015281306039456199⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-11100769207245963758560526636),(-11100769207245963751399484997)⟩,⟨8129508975087422480532237476,8129508975087422487331714382⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-7472515297584457573671670424),(-7472515297584457568918515159)⟩,⟨7199986595568533576628050922,7199986595568533581076962164⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-4653974591654990476610932819),(-4653974591654990473666207603)⟩,⟨5532158745603268825942935192,5532158745603268828665028868⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-2506159688092373727127555211),(-2506159688092373725544735813)⟩,⟨3448058945180436478182078134,3448058945180436479631069484⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-786537235246878352062336668),(-786537235246878351566442623)⟩,⟨1167529239313389132432143872,1167529239313389132883797265⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨9411188478551364545599198399,9411188478551544972529074096⟩,⟨(-1084645618052485992525179330),(-1084645618052305566580945047)⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨27666799317522148948778729355,27666799317522842514668797108⟩,⟨(-4460671483823609780409223625),(-4460671483822916217347120907)⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨43827293616191703178945957885,43827293616193506994515831478⟩,⟨(-10943059876778684266444008267),(-10943059876776880455080218320)⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨55641970960329749834019882503,55641970960334162689247746153⟩,⟨(-21187320678773974723507098064),(-21187320678769561873171598633)⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨60674826281681078145430029989,60674826281691128875798657713⟩,⟨(-34455995675026708821863950347),(-34455995675016658096233906979)⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨57619917490250655579135699267,57619917490270660729795031875⟩,⟨(-48825852843859117498162591955),(-48825852843839112351367037350)⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨47251812271580723046095180161,47251812271612884219919446610⟩,⟨(-61563145248640433748508797619),(-61563145248608272577152760093)⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨32209350315306543547320902865,32209350315345608216426252055⟩,⟨(-69941585683856920224260197251),(-69941585683817855555985543587)⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨16004500065763019213344719969,16004500065798893515252101264⟩,⟨(-72302748794543332439448871345),(-72302748794507458136865915892)⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨1900548004012672964240646409,1900548004037682048380247878⟩,⟨(-68582049735552640295871910681),(-68582049735527631210007598944)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨(-7979469648443367994882179121),(-7979469648430086949086959090)⟩,⟨(-60028931282515073765779268757),(-60028931282501792717729672519)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨(-13047078489330860897785412005),(-13047078489325083457358101026)⟩,⟨(-48541195605208261765147223953),(-48541195605202484322352922535)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨(-13965454108485859897733336439),(-13965454108483619617171146335)⟩,⟨(-36086398598997778313541641583),(-36086398598995538030837826497)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨(-11887117545327684202816500911),(-11887117545326855093885440075)⟩,⟨(-24227933968718438769175815521),(-24227933968717609658592594419)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨(-7863853496365742689557679654),(-7863853496365445533371041008)⟩,⟨(-13716995539697038820748852405),(-13716995539696741663534759511)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨(-2739904297709410073726726258),(-2739904297709335645677526191)⟩,⟨(-4414434775849558065239548763),(-4414434775849483636846266174)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-569377062640897643734681861),(-569377062640897639019557505)⟩,⟨38622989009244048003889781,38622989009244051222637888⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-1539175425792268367645428753),(-1539175425792268353111699211)⟩,⟨562832544748111450852441957,562832544748111461092642729⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1405254295408154886556880845),(-1405254295408154861483190928)⟩,⟨2348409637323378899286994509,2348409637323378918126728806⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨1873236099800677257100311166,1873236099800677293760388472⟩,⟨6160853468412215795241040281,6160853468412215824925655421⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨10323047890771677140502273440,10323047890771677190605293625⟩,⟨12735803251104707715403316472,12735803251104707759055406844⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨23979428484556836136167866540,23979428484556836204123969587⟩,⟨21921595451928978276274646433,21921595451928978339163153107⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨40462928078215898461064648281,40462928078215898563427745525⟩,⟨31578164020982324310516316097,31578164020982324409773202558⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨56419252643004484657477002561,56419252643004484893591236519⟩,⟨38345414315828373402079489157,38345414315828373637232348928⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨68765286281950466010314444581,68765286281950467113140275557⟩,⟨39767034869989693649629622988,39767034869989694753226489241⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨75265027453267086666350241942,75265027453267093187293360396⟩,⟨35476860740682124921045248729,35476860740682131443685082054⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨74994614808888586446139632510,74994614808888617403028524360⟩,⟨26965883124872789483452781818,26965883124872820442277031645⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨68520279161755329794307370268,68520279161755432806051825701⟩,⟨16763694214303204896613258349,16763694214303307910188103852⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨57360266461727827020359381075,57360266461728056887327912644⟩,⟨7599262476209206931645586857,7599262476209436800151410720⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨43039593894791209816628413138,43039593894791551623913603740⟩,⟨1495538034597284744234672438,1495538034597626552622181119⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨26647225554617025080514708190,26647225554617347049819021546⟩,⟨(-966972871297341721524785233),(-966972871297019751578104193)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨9018660735773287914250112983,9018660735773420347836788552⟩,⟨(-659758159318530980732579083),(-659758159318398546944169824)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨102945612667924275531173418279,102945612667956495623524486493⟩,⟨(-56597007894462168494393573878),(-56597007894429948407444015121)⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_5 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 5) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_5 (tableDensity true) (fullFactor false 3 5) density1_contains hk3_0_5_contains +noncomputable def atomAnswer : CBox := ⟨⟨20166803097356353555355923234,20166803097356353566514295651⟩,⟨(-32437355718380275865584602781),(-32437355718380275852219921399)⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_5 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 5) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_5 3 5 ha3_0_5_contains + def realAnswer : RBox := ⟨123112415765280629086429341513,123112415765312849190138782144⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 5) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_5 +namespace hm3_0_0_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨2120218404784761739526340,2120218404784763000356460⟩,⟨(-2948670465161205649184653),(-2948670465161204388513129)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨5276391137139227721093466,5276391137139230455689388⟩,⟨(-8017132722024546122308515),(-8017132722024543388108577)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨5952338262036153846663237,5952338262036156160765352⟩,⟨(-10865422195522580113859552),(-10865422195522577800210061)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨4420275730443596845117555,4420275730443597949867819⟩,⟨(-10915006827622157578027660),(-10915006827622156473626990)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨2122430076829356853371854,2122430076829357164791404⟩,⟨(-8691177095864359756440491),(-8691177095864359445212130)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨403381839611586588947481,403381839611586641107492⟩,⟨(-5536022803522163235314014),(-5536022803522163183223765)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-306709387486320092570132),(-306709387486320086872059)⟩,⟨(-2791154058092902418444111),(-2791154058092902412759256)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-339416542825831519282279),(-339416542825831518674310)⟩,⟨(-1090280525593477250276341),(-1090280525593477249667917)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-173941724248595684084856),(-173941724248595683972911)⟩,⟨(-319533265182129968293814),(-319533265182129968181678)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-55651107124546694756720),(-55651107124546694731975)⟩,⟨(-67048200309234297766721),(-67048200309234297742625)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-11303836943281337970189),(-11303836943281337965816)⟩,⟨(-9397015856120440387110),(-9397015856120440383164)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-1359779897539548698459),(-1359779897539548697908)⟩,⟨(-790236394105963445604),(-790236394105963445172)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-82747483263909158792),(-82747483263909158737)⟩,⟨(-33411441907086660781),(-33411441907086660739)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-1851088742767452476),(-1851088742767452458)⟩,⟨(-513377263810671990),(-513377263810671973)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-7315366705645012),(-7315366705644995)⟩,⟨(-1398921842517928),(-1398921842517912)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-474434129693),(-474434129676)⟩,⟨(-66641293934),(-66641293918)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨116160318532125313359593967,116160318532125413607969674⟩,⟨164118687365008066089791228,164118687365008166353816317⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨341082479728769492389187140,341082479728769861971436458⟩,⟨448101899117974799337451490,448101899117975168961992682⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨538294988119697899661917534,538294988119698784533897165⟩,⟨615395935337504407913347789,615395935337505292842079222⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨679137966342914775482859541,679137966342916691040609480⟩,⟨636698425258414884029353002,636698425258416799643847130⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨736796043148767003026475330,736796043148770720530005247⟩,⟨533346750918653284345724497,533346750918657001894637426⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨702954257170499686824551722,702954257170505774485324322⟩,⟨362797774259917644445534765,362797774259923732135416062⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨595754312591344644709521681,595754312591352455391483309⟩,⟨189576189963752470654482575,189576189963760281350409464⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨451887796110666998420119211,451887796110674353764772571⟩,⟨58240937976549849741941598,58240937976557205090073803⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨309375169198254686864591179,309375169198259782333625709⟩,⟨(-17274640629537149780081584),(-17274640629532054312938278)⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨193281556076852512300897517,193281556076855147175203292⟩,⟨(-46567868046343999839272121),(-46567868046341364968506272)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨111744180900871228783935408,111744180900872256240345519⟩,⟨(-48182647367535731443864402),(-48182647367534703990715141)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨60779829356180682220228560,60779829356181011530261402⟩,⟨(-38268881241720628517713452),(-38268881241720299210042752)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨31606754783919310625210440,31606754783919406706990344⟩,⟨(-26367911739663104120309665),(-26367911739663008040024132)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨15790325455895017761785774,15790325455895045655994132⟩,⟨(-16305088825753595585848000),(-16305088825753567692495405)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨7228657368017068995170574,7228657368017077350844775⟩,⟨(-8659976081689036349142756),(-8659976081689027993896645)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨2080676068117106895164461,2080676068117108794257255⟩,⟨(-2693406440552916239600000),(-2693406440552914340636147)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-1645078728969343321858628636),(-1645078728969343321420415750)⟩,⟨(-13963255769990995883088423),(-13963255769990995656856848)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-4708268750167828627532145691),(-4708268750167828626250754115)⟩,⟨163481545850106155159976349,163481545850106155849762484⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-7110714647849509638435839457),(-7110714647849509636419988193)⟩,⟨851052630379534303955453511,851052630379534305133876365⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-8511332335829479576279126411),(-8511332335829479573709879625)⟩,⟨2084198180382888541547241606,2084198180382888543210652111⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-8742840269474900499672981468),(-8742840269474900496791618951)⟩,⟨3599913270296812171974054265,3599913270296812174051426337⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-7880969256008487426514274027),(-7880969256008487423542086756)⟩,⟨4968229588882571784334136872,4968229588882571786723245644⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-6246090399747515050468541552),(-6246090399747515047524179201)⟩,⟨5806341933644283155010598981,5806341933644283157631221499⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-4302344099657967865478129925),(-4302344099657967862133046679)⟩,⟨5940794429568866597153077452,5940794429568866600402704355⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-2489947054856902814162256760),(-2489947054856902806770224434)⟩,⟨5441050703736249050822522969,5441050703736249058277211296⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-1089659072530261481837256362),(-1089659072530261451105970473)⟩,⟨4538282187563976104892352776,4538282187563976135767225247⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-186489595820137555205845623),(-186489595820137434674614670)⟩,⟨3498121149737654563621270352,3498121149737654684317042181⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨279619878907484766175527643,279619878907485109502089206⟩,⟨2521432736397971149966355517,2521432736397971493442863070⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨432815957471189662041698814,432815957471190332088258481⟩,⟨1708183081584325683096541377,1708183081584326353262128231⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨397208312379748290965905826,397208312379749184593079203⟩,⟨1073623570701106472450993129,1073623570701107366161568121⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨265010660120786659223030022,265010660120787438028861569⟩,⟨583837574714014045915997967,583837574714014824770487280⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨91876321880034034961925229,91876321880034342284431823⟩,⟨184422289899361910372543937,184422289899362217710918227⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1787766579232066537118123568,1787766579232074964275356185⟩,⟨(-4994045166232761596318907798),(-4994045166232753168216409513)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4638704346456859335801660857,4638704346456879079499147545⟩,⟨(-14680406112600638025451472876),(-14680406112600618279109723773)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨5535170723594056703638736378,5535170723594076263871221716⟩,⟨(-23349455929727858401911033539),(-23349455929727838837867096699)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨3860597092809870467326697867,3860597092809882397391244993⟩,⟨(-30110429194061986169725493253),(-30110429194061974235416402909)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨(-193556385004710022878158178),(-193556385004705284526284950)⟩,⟨(-34055790139298669569613239168),(-34055790139298664827335311321)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨(-5688264547138120062657052105),(-5688264547138118815432824057)⟩,⟨(-34637111119476718195927838442),(-34637111119476716945684433077)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨(-11248306889052087079082244062),(-11248306889052086842790805153)⟩,⟨(-31982370450011754691115616391),(-31982370450011754453023876396)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨(-15551501586683219210546266161),(-15551501586683219166784507156)⟩,⟨(-26907166463813084822047753279),(-26907166463813084777717163397)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-17789244799614416603093045827),(-17789244799614416587522605493)⟩,⟨(-20633086755335995820126535648),(-20633086755335995804998911856)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-17847686608474047426473143481),(-17847686608474047416443213897)⟩,⟨(-14385824187360689659076941072),(-14385824187360689650158077746)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-16165734114226719433463261847),(-16165734114226719426152749918)⟩,⟨(-9059879735603112302273759256),(-9059879735603112296386322285)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-13426274015480010403628401846),(-13426274015480010398375908266)⟩,⟨(-5080399841950456926981270987),(-5080399841950456923170177978)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-10265485479378020866347530371),(-10265485479378020862730681737)⟩,⟨(-2463734874718389867277700463),(-2463734874718389864918015239)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-7108055830473088477709536829),(-7108055830473088475390911919)⟩,⟨(-975141905462566760921581552),(-975141905462566759554914004)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-4138663602906211380729576386),(-4138663602906211379447626948)⟩,⟨(-281066385301917930560165992),(-281066385301917929865014880)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-1354590704212793684563926666),(-1354590704212793684155829413)⟩,⟨(-44421034222794444237086527),(-44421034222794444026185830)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨798134010326152611649644955,798134010326248310664483510⟩,⟨12543519744207403296496034654,12543519744207498993668659140⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨4255006341671684278474056787,4255006341672050662290315262⟩,⟨36042867652963318882383270179,36042867652963685261033462157⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨12506255877423587563658372469,12506255877424532940489425270⟩,⟨54775535174684364486628258947,54775535174685309855900493169⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨26356240680872628658529190830,26356240680874915136601445717⟩,⟨65887906231985404647222171073,65887906231987691116681141063⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨43880949968550255733010375076,43880949968555388586890606243⟩,⟨67451282556513037381900964628,67451282556518170227547501659⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨61060660952546348166692957266,61060660952556393086273503130⟩,⟨59199046225654540885647654765,59199046225664585798670748936⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨73500796092970426002722910548,73500796092986274748724182559⟩,⟨42991363309426178360223471830,42991363309442027102171735795⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨78258062156905180281559118032,78258062156924052290528272999⟩,⟨22569168315279144116322417183,22569168315298016123984960958⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨74815066849334786466975917319,74815066849351765299949975839⟩,⟨2412653512820033197236416892,2412653512837012031383779531⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨64920537436190432040008538898,64920537436202031881110658951⟩,⟨(-13739916035743737268338052638),(-13739916035732137424183323101)⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨51582110348674636536544922617,51582110348680678405404109760⟩,⟨(-23859516148427369692888030780),(-23859516148421327819879950089)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨37806589620230117790342909006,37806589620232699645865413634⟩,⟨(-27695658563466964333863587301),(-27695658563464382473902559293)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨25658261916564203652749575026,25658261916565189369545870309⟩,⟨(-26216069216347220921135190654),(-26216069216346235200283868657)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨15958071832074896814886945642,15958071832075257080412911102⟩,⟨(-20923681262079337742224348968),(-20923681262078977473507330784)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨8540174415423722422483890379,8540174415423850408223938854⟩,⟨(-13312180735347696555373125986),(-13312180735347568567612989406)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨2665884283057667900351146139,2665884283057699810217666114⟩,⟨(-4547857525361322766519443016),(-4547857525361290855963387976)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-202437698535879573011827218),(-202437698535879570120801621)⟩,⟨(-10038161260272601340610681458),(-10038161260272601336452314920)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-2914902317559527916985157139),(-2914902317559527907844172960)⟩,⟨(-29123498441856509000468808048),(-29123498441856508987773586310)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-11616325123008703422503324449),(-11616325123008703405877453511)⟩,⟨(-45091318539414011591216586647),(-45091318539414011569623096773)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-27359903084561743499027819630),(-27359903084561743473363953422)⟩,⟨(-55625832305999385570968168088),(-55625832305999385540048111745)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-47742841211294732429900180257),(-47742841211294732393769273536)⟩,⟨(-58388387097028911751735011656),(-58388387097028911711131890744)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-67862687055878604562663408588),(-67862687055878604514073224168)⟩,⟨(-51696021752975003963890837523),(-51696021752975003912152027825)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-82635092036880612926348602815),(-82635092036880612857078742440)⟩,⟨(-35864410830083044969661754091),(-35864410830083044898714464784)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-88707625965957191196300247030),(-88707625965957191050783766161)⟩,⟨(-14060015885305716096442263473),(-14060015885305715950478746407)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-85297117672721232485311990189),(-85297117672721231844321407777)⟩,⟨8681818820096033223904839994,8681818820096033864679964771⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-74171683081453849552437394206),(-74171683081453845837031622576)⟩,⟨27507717149368052924200408452,27507717149368056639364729826⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-58761662606720461197911022603),(-58761662606720443821420343863)⟩,⟨39312213313431868735490174800,39312213313431886112096459762⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-42706309827228718011495086983),(-42706309827228661028481100046)⟩,⟨43174376659478955425223633208,43174376659479012408757642260⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-28579465835205729674698716275),(-28579465835205604182012758475)⟩,⟨39945566217882085445139852646,39945566217882210938596088822⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-17440259963717362265165115853),(-17440259963717177642231670736)⟩,⟨31498833090743519043633589093,31498833090743703667352532261⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-9143985814133150111837586744),(-9143985814132977502855140114)⟩,⟨19897120018086060814667271608,19897120018086233424223224797⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-2814273154871006297447797028),(-2814273154870935573076444733)⟩,⟨6773479362219699206716172333,6773479362219769931296121488⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-36147122781366022684091081357),(-36147122781350516038318972696)⟩,⟨(-9576113568665196979828125652),(-9576113568649690331226694230)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 6) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_6 (tableDensity false) (fullFactor false 3 6) density0_contains hk3_0_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-16151808288097071859058776250),(-16151808288097071854176804195)⟩,⟨(-7985415443625704408135604415),(-7985415443625704404238104181)⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_6 3 6 ha3_0_6_contains + def realAnswer : RBox := ⟨(-52298931069463094543249857607),(-52298931069447587892395776891)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_6 +namespace hm3_1_0_6 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_6 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨425944263736597767666398,425944263736598800385738⟩,⟨(-452011091091631868288480),(-452011091091630835528399)⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨1089735389569277161491432,1089735389569279400433660⟩,⟨(-1237073524239690979497758),(-1237073524239688740451738)⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨1301484251048062195956303,1301484251048064088987578⟩,⟨(-1688780778026819016963711),(-1688780778026817123808022)⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨1060383333655113521981899,1060383333655114424346420⟩,⟨(-1699826846479386964238968),(-1699826846479386061769358)⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨598781530386120612984272,598781530386120866581891⟩,⟨(-1349040462844774600845041),(-1349040462844774347179981)⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨197974742528633387978440,197974742528633430048814⟩,⟨(-856965424860174219566887),(-856965424860174177463599)⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨(-4712390933165390709234),(-4712390933165386321003)⟩,⟨(-433321348076955858452303),(-433321348076955854052520)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨(-47658457923040391127384),(-47658457923040390742845)⟩,⟨(-170672727802501511080026),(-170672727802501510693356)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨(-29396339387580736400807),(-29396339387580736347304)⟩,⟨(-50533156258797966578717),(-50533156258797966525628)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨(-10056694832687703526653),(-10056694832687703516329)⟩,⟨(-10692128662148801234364),(-10692128662148801224515)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨(-2100069196156831753307),(-2100069196156831751636)⟩,⟨(-1501250954127868426157),(-1501250954127868424666)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨(-254457868102677600597),(-254457868102677600401)⟩,⟨(-124455910879428470093),(-124455910879428469931)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨(-15413345820261567795),(-15413345820261567768)⟩,⟨(-4995769611582909901),(-4995769611582909877)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨(-341535472377799936),(-341535472377799918)⟩,⟨(-67202266489972308),(-67202266489972291)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨(-1337526746361870),(-1337526746361854)⟩,⟨(-135757039616070),(-135757039616054)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨(-86233609372),(-86233609355)⟩,⟨(-3535568655),(-3535568639)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨3763156238876224656567273,3763156238876307204238657⟩,⟨31133492805921380718997909,31133492805921463265275112⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨14420888831981928343005995,14420888831982232780681694⟩,⟨85474903533201498980752899,85474903533201803414674750⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨31749446165676473537604213,31749446165677202927176575⟩,⟨118800507539477571324905399,118800507539478300709433772⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨53304645760871440981931216,53304645760873021302213225⟩,⟨125527293189149873965976516,125527293189151454281192958⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨71992683359322662088380425,71992683359325731669416199⟩,⟨109032132737302638113838907,109032132737305707690769295⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨80758734187938464012460241,80758734187943494732971577⟩,⟨79166543802224102025423049,79166543802229132743253420⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨77049026220970959339526726,77049026220977419555823999⟩,⟨47157214215797648128231687,47157214215804108343209140⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨63818690032041803755183422,63818690032047890289520755⟩,⟨21154656262151707416856169,21154656262157793950871120⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨46808250568157398854856948,46808250568161615253674942⟩,⟨4456900244394988623745109,4456900244399205022792150⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨31020344140028566553292396,31020344140030745705404955⟩,⟨(-3722668039170576189257481),(-3722668039168397036704008)⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨18973825523672156843720720,18973825523673005772670361⟩,⟨(-6155865474341266116463863),(-6155865474340417187062812)⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨10939264577320741717331569,10939264577321013463867863⟩,⟨(-5668631937390087261859504),(-5668631937389815514956295)⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨6039645486517226250317433,6039645486517305428318583⟩,⟨(-4195303147498435294366586),(-4195303147498356116107788)⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨3191316315433928023031191,3191316315433950980500469⟩,⟨(-2694942957343123119500333),(-2694942957343100161870399)⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨1526994389201133801891929,1526994389201140671980755⟩,⟨(-1460354139114319973630553),(-1460354139114313103456203)⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨450465607147692605246502,450465607147694165842847⟩,⟨(-458203109065232493840726),(-458203109065230933217644)⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨(-314664916576846036909991946),(-314664916576846036757204565)⟩,⟨(-197323358073836503502520037),(-197323358073836503360183643)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-923471602012630524097449369),(-923471602012630523639309852)⟩,⟨(-530384077362562116686957604),(-530384077362562116258981087)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-1455707466272100212411877816),(-1455707466272100211661895204)⟩,⟨(-699385312708984668278482867),(-699385312708984667571195948)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-1833298123104513385737407064),(-1833298123104513384734926519)⟩,⟨(-656089413197707279077240340),(-656089413197707278120474129)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-1986698890589995520157398460),(-1986698890589995518974226321)⟩,⟨(-418740476009317292477886669),(-418740476009317291334053994)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1899981816839075908310424901),(-1899981816839075907012779292)⟩,⟨(-67013527000014328135407138),(-67013527000014326867402175)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1623218698960912336626934555),(-1623218698960912335220535840)⟩,⟨285707498802122194929862139,285707498802122196318181052⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1245935555599854897173384501),(-1245935555599854895245295132)⟩,⟨541736793428278297321589484,541736793428278299243611904⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-860332686311143954929126523),(-860332686311143949476465972)⟩,⟨657812349673467967579046903,657812349673467973035229536⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-533248539496000279026810941),(-533248539496000254346097912)⟩,⟨646847507304067280032650450,646847507304067304722121961⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-294213928294909132865948852),(-294213928294909034852024644)⟩,⟨553106933754852004865314470,553106933754852102889835328⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-140741568157095232067957447),(-140741568157094952264474071)⟩,⟨424825456202496330009827480,424825456202496609823785622⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-53731813942479527917168986),(-53731813942478981283850134)⟩,⟨297709883579110182193233291,297709883579110728835371721⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-11742821276894232073612332),(-11742821276893502488340312)⟩,⟨189714917212987983536543467,189714917212988713127908524⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨2631129755278275624926663,2631129755278911795088203⟩,⟨103513081807386906215355059,103513081807387542388947923⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨2386995199865433781585846,2386995199865684884365314⟩,⟨32696963371287714766318258,32696963371287965870168238⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1476981550831330070271014320,1476981550831337151174201674⟩,⟨(-981094019678751382230231146),(-981094019678744301428284174)⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4121968512938673496408560758,4121968512938690074927267178⟩,⟨(-2951644115940985857051970083),(-2951644115940969278815159479)⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨5909809671167166437920855415,5909809671167182839943599145⟩,⟨(-4904397866414254431296767365),(-4904397866414238029674649969)⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨6510356955627118048050526424,6510356955627128030477771862⟩,⟨(-6723469365652162936663468198),(-6723469365652152954672581796)⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨5911586540438599140524690409,5911586540438603092718225480⟩,⟨(-8206716860387846808466442426),(-8206716860387842856662343033)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨4417630177109536189678296846,4417630177109537223795736813⟩,⟨(-9115376215258645690609882950),(-9115376215258644656779687030)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2505427117904855639550330694,2505427117904855831259709413⟩,⟨(-9266862565629916332760900235),(-9266862565629916141215663019)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨637036673624449106982877194,637036673624449138651244009⟩,⟨(-8646086934471421768209380292),(-8646086934471421736589895730)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨(-858292947237259216360345012),(-858292947237259207852395071)⟩,⟨(-7434829079778488979740206515),(-7434829079778488971194841797)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨(-1824011661753693749928596356),(-1824011661753693745480074435)⟩,⟨(-5927657519259670742367657811),(-5927657519259670737831872866)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨(-2258475981837772142477903366),(-2258475981837772139585562029)⟩,⟨(-4412230506634931658733007453),(-4412230506634931655736796575)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨(-2258586502308616378609917637),(-2258586502308616376702004292)⟩,⟨(-3085971076905413546539289097),(-3085971076905413544533350555)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨(-1957265914572634976451319338),(-1957265914572634975228408746)⟩,⟨(-2032162216719788251393323838),(-2032162216719788250090350537)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨(-1477802944486698492339873716),(-1477802944486698491603700703)⟩,⟨(-1243492441879817957058184799),(-1243492441879817956264871906)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨(-909864468479856511193381701),(-909864468479856510805879476)⟩,⟨(-661376567968666477736738985),(-661376567968666477315500605)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨(-306147005628297995844691515),(-306147005628297995724594317)⟩,⟨(-206246199358092379723009376),(-206246199358092379591865645)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨472796814264741242946810019,472796814264819891445290909⟩,⟨4102468650610957009770091975,4102468650611035658709824029⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨1936684452323219627212717154,1936684452323520755958561112⟩,⟨12014473710420927828411327048,12014473710421228958418007355⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨4714943656309971156923895041,4714943656310748263423754789⟩,⟨18889927847116832288538676022,18889927847117609396899561392⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨9028305368748764335594418761,9028305368750644142451106759⟩,⟨23720330293354552007095622619,23720330293356431816092708681⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨14475239154963366117519243313,14475239154967586565669213998⟩,⟨25503213631601216764609077438,25503213631605437214801814859⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨20167708363764913234654391533,20167708363773172573578728200⟩,⟨23814980154746697925251917225,23814980154754957265812050772⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨24946832790017144235685550766,24946832790030172940389677222⟩,⟨19162334894168181835459032243,19162334894181210541186529042⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨27760735197277352718255752881,27760735197292859196011660917⟩,⟨12797630075039534231933389370,12797630075055040710026664642⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨28085065279202833593944987273,28085065279216773468281724588⟩,⟨6227697322687068089004359583,6227697322701007963074676892⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨26069216036348096783308004956,26069216036357610313312588954⟩,⟨730636633795526773695731260,730636633805040303033169790⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨22347081128039588777801047770,22347081128044537713506995374⟩,⟨(-2964997721260116710202809698),(-2964997721255167775352007480)⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨17727342372725610960053269025,17727342372727722935077806095⟩,⟨(-4761460945860042031455868130),(-4761460945857930057313567052)⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨12961467629736976212342551060,12961467629737781509022244750⟩,⟨(-5014287177386687688774775055),(-5014287177385882392881095502)⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨8587227476474979547619395627,8587227476475273560072083354⟩,⟨(-4212437833639349160317879779),(-4212437833639055148463987637)⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4816848908020701737150812746,4816848908020806108430262736⟩,⟨(-2761272732454045674966131528),(-2761272732453941304055640101)⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1542783653232889567926981262,1542783653232915580281853440⟩,⟨(-957550866133599230464829714),(-957550866133573218232925852)⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨(-20201436746326723850080720),(-20201436746326722166039195)⟩,⟨(-297887587554390787554060044),(-297887587554390785086261999)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨(-293390763565713095295992819),(-293390763565713089954801117)⟩,⟨(-802773792525779658923309235),(-802773792525779651341187806)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨(-1216488224400541047386640504),(-1216488224400541037619670603)⟩,⟨(-728890189368372567937122082),(-728890189368372554939856643)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-3162167019778657912440634559),(-3162167019778657897187859216)⟩,⟨959632041270909064393717151,959632041270909083222012948⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-6460281414341755736628699211),(-6460281414341755714451564191)⟩,⟨5233783208804675706653264093,5233783208804675732094737422⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-10965517435598617703861760024),(-10965517435598617672344107290)⟩,⟨11991916233233114838886020864,11991916233233114872926541290⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-15549765745622587733370926269),(-15549765745622587684425068990)⟩,⟨19921049488293444573165072045,19921049488293444623625605290⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-18565125421831365182317469755),(-18565125421831365068528621290)⟩,⟨27309843266270210844498545818,27309843266270210958745571004⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-18918108027578187297927276713),(-18918108027578186774141976498)⟩,⟨32704462158928281219091021694,32704462158928281742523599659⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-16583659213358804443311586049),(-16583659213358801402378254457)⟩,⟨35170692073288522104383095794,35170692073288525144567313903⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-12395115245494206468538802305),(-12395115245494192271546463801)⟩,⟨34457015029150923613334853823,34457015029150937809509285438⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-7588287377886460641372292704),(-7588287377886414102107483182)⟩,⟨30998729324127220767447289558,30998729324127267305970226771⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-3395040865753333512758782560),(-3395040865753230987995418568)⟩,⟨25605189855321388408741634710,25605189855321490932904257784⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-661776892021504718480076029),(-661776892021353816456116896)⟩,⟨19009155434398779392761212326,19009155434398930294369234453⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨423629335956708150913586620,423629335956849285677775489⟩,⟨11682426568097960932338430913,11682426568098102066867536332⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨288138197625532915883404121,288138197625590755568169468⟩,⟨3938906847658561317820560221,3938906847658619157433389261⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨19594314614777107143356648652,19594314614789840718185447713⟩,⟨51566609115385877723419340575,51566609115398611301249563843⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_6 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 6) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_6 (tableDensity true) (fullFactor false 3 6) density1_contains hk3_0_6_contains +noncomputable def atomAnswer : CBox := ⟨⟨21121595453665401655461974717,21121595453665401661846092020⟩,⟨10442466349356690374772905468,10442466349356690379869636542⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_6 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 6) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_6 3 6 ha3_0_6_contains + def realAnswer : RBox := ⟨40715910068442508798718623369,40715910068455242380131539733⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 6) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_6 +namespace hm3_0_0_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density0 j i k).mul (hk3_0_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨219509643764799869256580,219509643764799963114837⟩,⟨157842338711688159340292,157842338711688253210171⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨585579594664646045990560,585579594664646245872581⟩,⟨385520625496756909041476,385520625496757108951905⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨763762276567600256880260,763762276567600419925839⟩,⟨418818080835307143408777,418818080835307306485447⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨723773280062329189117704,723773280062329262734844⟩,⟨293764565048909848333722,293764565048909921973297⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨532328433935258413014719,532328433935258432249688⟩,⟨130682188954901140241569,130682188954901159487662⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨306181690146243238278134,306181690146243241198927⟩,⟨22831370999304260635972,22831370999304263560283⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨135958253343927805630820,135958253343927805913129⟩,⟨(-14636094789610756415773),(-14636094789610756132957)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨45474269961890499490964,45474269961890499517013⟩,⟨(-14020342315184519283411),(-14020342315184519257407)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨11044980694598665506169,11044980694598665510188⟩,⟨(-5966353537163068514904),(-5966353537163068510886)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨1847127762863694769155,1847127762863694769861⟩,⟨(-1521895777505722766169),(-1521895777505722765437)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨196566989784287889311,196566989784287889415⟩,⟨(-234625924945451423674),(-234625924945451423557)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨11784027601898881688,11784027601898881713⟩,⟨(-20105100732603831730),(-20105100732603831702)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨325397296682440361,325397296682440379⟩,⟨(-798589128306554634),(-798589128306554616)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨2856031741797286,2856031741797304⟩,⟨(-10211515611714347),(-10211515611714330)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨3495174985937,3495174985954⟩,⟨(-18175902011715),(-18175902011699)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨41584686,41584703⟩,⟨(-295535932),(-295535913)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-24493619385617619513735189),(-24493619385617604550831539)⟩,⟨17335894104015932529235921,17335894104015947489780291⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-66247169246710281310051712),(-66247169246710226693223614)⟩,⟨50418929597875774015345952,50418929597875828625858343⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-89285901497967519962219299),(-89285901497967391737692730)⟩,⟨78073092263888661285231323,78073092263888789501441055⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-89834439598509997512337729),(-89834439598509727825422261)⟩,⟨95762247160847902061621723,95762247160848171740451548⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-72545838140280790002974537),(-72545838140280285866105890)⟩,⟨100116709295499075386602679,100116709295499579517239319⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-47189894677090213848749356),(-47189894677089424921293521)⟩,⟨91285638421122247946115738,91285638421123036869751537⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-23417113153685098089859304),(-23417113153684137556271830)⟩,⟨73378585687784120164989781,73378585687785080696838688⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-6810373646274242238647139),(-6810373646273388994234798)⟩,⟨52446096773574140011549180,52446096773574993255551515⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨1845118086361988709314661,1845118086362543317200207⟩,⟨33659686648938489949134714,33659686648939044557223890⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨4713145794691934771904221,4713145794692203099839238⟩,⟨19648773736682563245754733,19648773736682831574047424⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨4561470623986820151463851,4561470623986917924391031⟩,⟨10605589575056794810965323,10605589575056892584198834⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨3392901210486306680406963,3392901210486336011048369⟩,⟨5397794617788464802103185,5397794617788494132950828⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨2201748240457557893426557,2201748240457565945761952⟩,⟨2642149365051389006413637,2642149365051397058870759⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨1295010116616466863303697,1295010116616469083946897⟩,⟨1254935800659863369389132,1254935800659865590097950⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨663379577439376740236168,663379577439377380926653⟩,⟨553880102408567950809129,553880102408568591530977⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨202439330869106464818797,202439330869106607566878⟩,⟨156390646022649936683559,156390646022650079440859⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨3130496450236377485995659,3130496450236377536708181⟩,⟨(-368566305851963161820864869),(-368566305851963161721510402)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨(-36341325479743614940076426),(-36341325479743614786378408)⟩,⟨(-1048186310888567609709851065),(-1048186310888567609421195481)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨(-186889210360749744232155539),(-186889210360749743972506023)⟩,⟨(-1563305173791003638654059072),(-1563305173791003638205691284)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨(-449344079520051250578436558),(-449344079520051250217997494)⟩,⟨(-1836971540282007053740786076),(-1836971540282007053179889998)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨(-757740474856767445207038149),(-757740474856767444766803333)⟩,⟨(-1842178076704157785804958766),(-1842178076704157785190935313)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨(-1015886034380590906025963923),(-1015886034380590905533405246)⟩,⟨(-1613171565245419858455915223),(-1613171565245419857840781324)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-1148432082989751691706553136),(-1148432082989751691183576644)⟩,⟨(-1236814256460060517578226473),(-1236814256460060516989313761)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-1132799427260314840708880286),(-1132799427260314840085180686)⟩,⟨(-821463261802697298125837467),(-821463261802697297483315249)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-998015460625419312968220196),(-998015460625419311602153830)⟩,⟨(-457499410160021923684754863),(-457499410160021922330465079)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-800057699702203256112188737),(-800057699702203250695114952)⟩,⟨(-192625727768345927183705733),(-192625727768345921792707415)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-593129760575150271443938909),(-593129760575150251073463771)⟩,⟨(-31948308689198555390643778),(-31948308689198535048963452)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-412204247326100019590937800),(-412204247326099963634512703)⟩,⟨45530493403351936345652235,45530493403351992276742064⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-270402773389739000038823783),(-270402773389738894186896237)⟩,⟨68428375871970882381953114,68428375871970988214387826⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-165570698009360403613567815),(-165570698009360265944659150)⟩,⟨61225060472604925788226993,61225060472605063443817161⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-88392399241475960870035466),(-88392399241475842999150083)⟩,⟨40115656003639900367794986,40115656003640018231046842⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-27656041311290833359654004),(-27656041311290787272854274)⟩,⟨13777564747229342220948489,13777564747229388305281487⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨1492424245880464762773446120,1492424245880467281495749566⟩,⟨534263940372612758957151022,534263940372615277393983370⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨4366238538137573403233562251,4366238538137579277422520851⟩,⟨1379801833672119964801761904,1379801833672125838195646390⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨6879532499792475458073514780,6879532499792481225783210599⟩,⟨1631487414064178382204629044,1631487414064184148778183835⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨8749886348914832394813701786,8749886348914835867043047311⟩,⟨1123288559489990231680634603,1123288559489993702660724321⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨9721426174892893171820257241,9721426174892894528234496724⟩,⟨(-52901052511288661759750981),(-52901052511287306482231423)⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨9678266605073616161874616468,9678266605073616512224124916⟩,⟨(-1586196511317156526314391599),(-1586196511317156176822130923)⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨8722001249825878633167985432,8722001249825878698347898894⟩,⟨(-3063728099393384762063248047),(-3063728099393384697383452594)⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨7146343833075527775508456742,7146343833075527787342131205⟩,⟨(-4126258716087700277428655654),(-4126258716087700265749581822)⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨5330130959361544094377990325,5330130959361544098311720650⟩,⟨(-4591433356786215655016877313),(-4591433356786215650966677191)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨3613712104105804425340296141,3613712104105804427596842373⟩,⟨(-4479597140308376322707513628),(-4479597140308376320165310320)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨2214918084029005786717949290,2214918084029005788167302741⟩,⟨(-3948886261620744829461818702),(-3948886261620744827655313995)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨1211241304887973004830674900,1211241304887973005744879649⟩,⟨(-3198380301521305907157592672),(-3198380301521305905889707505)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨574663038251182493925617687,574663038251182494478652180⟩,⟨(-2392433642597216763048500641),(-2392433642597216762193039058)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨223475484247320890193594568,223475484247320890507782532⟩,⟨(-1627692893492235129351439206),(-1627692893492235128811857155)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨63612491413848998991700934,63612491413848999149289449⟩,⟨(-936122385844180853978970724),(-936122385844180853683987993)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨9985452524578399545251619,9985452524578399592707768⟩,⟨(-304456675036259868153348894),(-304456675036259868059985680)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-4686776578260783422181430499),(-4686776578260747666581088773)⟩,⟨298195446850172605230422011,298195446850208361505084624⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-13416068938627375216240173775),(-13416068938627238867557223043)⟩,⟨1583296347957069623922994773,1583296347957205974490621177⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-20236811639441241985792217884),(-20236811639440892887806073803)⟩,⟨4618228257826792474358486239,4618228257827141575084689160⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-24077102933784691280153246703),(-24077102933783856410902493417)⟩,⟨9625947447787886541968424564,9625947447788721414312473077⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-24303507083023532028456730365),(-24303507083021684541598533659)⟩,⟨15801190674859240021697540629,15801190674861087511477464689⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-20975240529423311364395726751),(-20975240529419756568325310815)⟩,⟨21619417871220052233194753193,21619417871223607031558676779⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-14948001899443753981926480280),(-14948001899438250574380853343)⟩,⟨25531804041390477074886702491,25531804041395980483827249130⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-7692151623164279411127162708),(-7692151623157858210327481807)⟩,⟨26627711999451158535773684747,26627711999457579737016009396⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-814602940221329573274085820),(-814602940215674310127257880)⟩,⟨24913205768155040972602692859,24913205768160696235361616361⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨4468141886441099658921185985,4468141886444882034918066869⟩,⟨21155627065512346502058562461,21155627065516128877062413096⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨7607415553451590257981886917,7607415553453520081890684452⟩,⟨16462093413948648048723325525,16462093413950577871305155330⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨8665830285737953295852800026,8665830285738762297869055542⟩,⟨11836321967431840037433913024,11836321967432649038052662288⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨8069015342475034864532993319,8069015342475338580492898272⟩,⟨7900184643272106119974279658,7900184643272409834674691925⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨6355776643461503394122601660,6355776643461612899967816444⟩,⟨4848391973664337558998227457,4848391973664447063863137086⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨4006672146397448596466171968,4006672146397487128164522835⟩,⟨2570604411513691177375184612,2570604411513729708457759332⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨1362345886527510864219404463,1362345886527520423582906026⟩,⟨798593515524080207129043241,798593515524089766283207228⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨4501521045618304166986686168,4501521045618304168865812788⟩,⟨(-90757200343920609530885825),(-90757200343920608234150059)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨13018862637516736817979439461,13018862637516736823696322156⟩,⟨(-1302410034631080444657602377),(-1302410034631080440567396964)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨20031507311178763438616202659,20031507311178763448275395793⟩,⟨(-5157926227447053479190417144),(-5157926227447053471788641693)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨24487299057473006262148970966,24487299057473006275848302144⟩,⟨(-12038288005732453323639547160),(-12038288005732453312304617674)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨25404898648193775124949977968,25404898648193775142721585350⟩,⟨(-20762297420761059805136479868),(-20762297420761059789351412942)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨22183875216395620356875887102,22183875216395620379192507623⟩,⟨(-29103356122930420750561477304),(-29103356122930420729622393261)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨15154777994820983262182857084,15154777994820983292259219489⟩,⟨(-34885401963993912431815261613),(-34885401963993912402459473094)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨5849832319925192773108093496,5849832319925192833738493897⟩,⟨(-36818159481142795123913940457),(-36818159481142795063471760701)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-3526854184871411341332194587),(-3526854184871411080566545692)⟩,⟨(-34783689471437907359268629692),(-34783689471437907098416211464)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-11009343345220689797436302120),(-11009343345220688312711770180)⟩,⟨(-29718334520558435779074803212),(-29718334520558434294261009071)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-15476828718778158758149810078),(-15476828718778151927796183853)⟩,⟨(-23148943255254547164196493137),(-23148943255254540333906515053)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-16739143570189032627344124243),(-16739143570189010560696551734)⟩,⟨(-16564957418962782353375201559),(-16564957418962760286956773483)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-15282966155186743681432066451),(-15282966155186695704826229609)⟩,⟨(-10937549034613840331014816499),(-10937549034613792354735041511)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-11924274843839188565223439506),(-11924274843839118700736262179)⟩,⟨(-6603344029009930731338327760),(-6603344029009860867176650681)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-7476913108255912544994466032),(-7476913108255847690789838811)⟩,⟨(-3436351756262929958340861692),(-3436351756262865104370905721)⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-2535703905126686852739799605),(-2535703905126660376822375074)⟩,⟨(-1053553427805919571557552183),(-1053553427805893095724961795)⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨2927663951076233424554276337,2927663951081497619873320032⟩,⟨(-17667215524640810083572020640),(-17667215524635545889490338586)⟩⟩ +lemma checked : cachedMomentRuleBox density0 hk3_0_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule false false 3 7) := by + rw [← checked] + exact @cached_density_rule_contains density0 hk3_0_7 (tableDensity false) (fullFactor false 3 7) density0_contains hk3_0_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨3327541872566209320280787944,3327541872566209321828890547⟩,⟨(-8512513999966307925674363850),(-8512513999966307923643274707)⟩⟩ +lemma atomChecked : tableAtomBox false ha3_0_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom false false 3 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains false false ha3_0_7 3 7 ha3_0_7_contains + def realAnswer : RBox := ⟨6255205823642442744735064281,6255205823647706941802210579⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment false false 3 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_0_0_7 +namespace hm3_1_0_7 +noncomputable def chunk (j : Fin 6) (i : Fin 16) : CBox := finSum (fun k => (density1 j i k).mul (hk3_0_7 j i k)) +noncomputable def s0_0 : CBox := ⟨⟨33649223296916595658363,33649223296916672547929⟩,⟨31709602797750617790722,31709602797750694677253⟩⟩ +lemma c0_0 : chunk 0 0 = s0_0 := by decide +kernel +noncomputable def s0_1 : CBox := ⟨⟨90355260661377929464930,90355260661378093147969⟩,⟨79613473389861662409044,79613473389861826084484⟩⟩ +lemma c0_1 : chunk 0 1 = s0_1 := by decide +kernel +noncomputable def s0_2 : CBox := ⟨⟨118706716677397879764366,118706716677398013176011⟩,⟨91547112645499254374624,91547112645499387777494⟩⟩ +lemma c0_2 : chunk 0 2 = s0_2 := by decide +kernel +noncomputable def s0_3 : CBox := ⟨⟨112716348366785420626184,112716348366785480781687⟩,⟨70423134155458348638206,70423134155458408786703⟩⟩ +lemma c0_3 : chunk 0 3 = s0_3 := by decide +kernel +noncomputable def s0_4 : CBox := ⟨⟨82630510512264232805494,82630510512264248481693⟩,⟨36801932984316304912220,36801932984316320584248⟩⟩ +lemma c0_4 : chunk 0 4 = s0_4 := by decide +kernel +noncomputable def s0_5 : CBox := ⟨⟨47396399749064822929873,47396399749064825289924⟩,⟨11054214431568864650976,11054214431568867009172⟩⟩ +lemma c0_5 : chunk 0 5 = s0_5 := by decide +kernel +noncomputable def s0_6 : CBox := ⟨⟨21105696536472316110051,21105696536472316328191⟩,⟨(-166304176363673140665),(-166304176363672923101)⟩⟩ +lemma c0_6 : chunk 0 6 = s0_6 := by decide +kernel +noncomputable def s0_7 : CBox := ⟨⟨7117556664249748398656,7117556664249748415092⟩,⟨(-1959357594964006357419),(-1959357594964006341078)⟩⟩ +lemma c0_7 : chunk 0 7 = s0_7 := by decide +kernel +noncomputable def s0_8 : CBox := ⟨⟨1746450914953960692895,1746450914953960694772⟩,⟨(-1006647229224731650577),(-1006647229224731648683)⟩⟩ +lemma c0_8 : chunk 0 8 = s0_8 := by decide +kernel +noncomputable def s0_9 : CBox := ⟨⟨294529565953556620600,294529565953556620891⟩,⟨(-274804497731719397010),(-274804497731719396705)⟩⟩ +lemma c0_9 : chunk 0 9 = s0_9 := by decide +kernel +noncomputable def s0_10 : CBox := ⟨⟨31406705587760685762,31406705587760685811⟩,⟨(-43576085216940496395),(-43576085216940496344)⟩⟩ +lemma c0_10 : chunk 0 10 = s0_10 := by decide +kernel +noncomputable def s0_11 : CBox := ⟨⟨1857245674332322154,1857245674332322172⟩,⟨(-3762415048354450956),(-3762415048354450936)⟩⟩ +lemma c0_11 : chunk 0 11 = s0_11 := by decide +kernel +noncomputable def s0_12 : CBox := ⟨⟨48758641247336310,48758641247336327⟩,⟨(-148786355640093527),(-148786355640093510)⟩⟩ +lemma c0_12 : chunk 0 12 = s0_12 := by decide +kernel +noncomputable def s0_13 : CBox := ⟨⟨375545698304040,375545698304056⟩,⟨(-1884513783953056),(-1884513783953040)⟩⟩ +lemma c0_13 : chunk 0 13 = s0_13 := by decide +kernel +noncomputable def s0_14 : CBox := ⟨⟨341475169196,341475169212⟩,⟨(-3323651241092),(-3323651241076)⟩⟩ +lemma c0_14 : chunk 0 14 = s0_14 := by decide +kernel +noncomputable def s0_15 : CBox := ⟨⟨2218592,2218608⟩,⟨(-53718456),(-53718436)⟩⟩ +lemma c0_15 : chunk 0 15 = s0_15 := by decide +kernel +noncomputable def s0 : Fin 16 → CBox := ![s0_0,s0_1,s0_2,s0_3,s0_4,s0_5,s0_6,s0_7,s0_8,s0_9,s0_10,s0_11,s0_12,s0_13,s0_14,s0_15] +lemma s0_eq (i : Fin 16) : chunk 0 i = s0 i := by + fin_cases i + · exact c0_0 + · exact c0_1 + · exact c0_2 + · exact c0_3 + · exact c0_4 + · exact c0_5 + · exact c0_6 + · exact c0_7 + · exact c0_8 + · exact c0_9 + · exact c0_10 + · exact c0_11 + · exact c0_12 + · exact c0_13 + · exact c0_14 + · exact c0_15 +noncomputable def s1_0 : CBox := ⟨⟨(-4646461119607759792967380),(-4646461119607747474223478)⟩,⟨561580893999083277082344,561580893999095596021228⟩⟩ +lemma c1_0 : chunk 1 0 = s1_0 := by decide +kernel +noncomputable def s1_1 : CBox := ⟨⟨(-12636439196269589930701910),(-12636439196269544946811650)⟩,⟨2130848288911027206771861,2130848288911072191182456⟩⟩ +lemma c1_1 : chunk 1 1 = s1_1 := by decide +kernel +noncomputable def s1_2 : CBox := ⟨⟨(-17235853623812486167043600),(-17235853623812380480979168)⟩,⟨4601940584565791472412297,4601940584565897159163945⟩⟩ +lemma c1_2 : chunk 1 2 = s1_2 := by decide +kernel +noncomputable def s1_3 : CBox := ⟨⟨(-17709841377128107637330390),(-17709841377127885155853778)⟩,⟨7511017429063774528055023,7511017429063997010204585⟩⟩ +lemma c1_3 : chunk 1 3 = s1_3 := by decide +kernel +noncomputable def s1_4 : CBox := ⟨⟨(-14828100314212883857443018),(-14828100314212467593564669)⟩,⟨9776023109827801239104248,9776023109828217503510494⟩⟩ +lemma c1_4 : chunk 1 4 = s1_4 := by decide +kernel +noncomputable def s1_5 : CBox := ⟨⟨(-10293592924644617128874411),(-10293592924643965181347822)⟩,⟨10481323810887996188290023,10481323810888648136147824⟩⟩ +lemma c1_5 : chunk 1 5 = s1_5 := by decide +kernel +noncomputable def s1_6 : CBox := ⟨⟨(-5819694873286035448421510),(-5819694873285240995504987)⟩,⟨9485527859643104848295150,9485527859643899301367388⟩⟩ +lemma c1_6 : chunk 1 6 = s1_6 := by decide +kernel +noncomputable def s1_7 : CBox := ⟨⟨(-2464008455789496490730614),(-2464008455788790433955709)⟩,⟨7403843517265555964570227,7403843517266262021381367⟩⟩ +lemma c1_7 : chunk 1 7 = s1_7 := by decide +kernel +noncomputable def s1_8 : CBox := ⟨⟨(-491040147255260925370015),(-491040147254801997602503)⟩,⟨5090926769504275109391450,5090926769504734037134959⟩⟩ +lemma c1_8 : chunk 1 8 = s1_8 := by decide +kernel +noncomputable def s1_9 : CBox := ⟨⟨374567973976005564334748,374567973976227484083441⟩,⟨3152477690937612906302156,3152477690937834826007091⟩⟩ +lemma c1_9 : chunk 1 9 = s1_9 := by decide +kernel +noncomputable def s1_10 : CBox := ⟨⟨582048686550062137573596,582048686550142922550498⟩,⟨1800223461015295556695456,1800223461015376341630086⟩⟩ +lemma c1_10 : chunk 1 10 = s1_10 := by decide +kernel +noncomputable def s1_11 : CBox := ⟨⟨502320218246341404376790,502320218246365608352204⟩,⟨971201448746387258606320,971201448746411462549323⟩⟩ +lemma c1_11 : chunk 1 11 = s1_11 := by decide +kernel +noncomputable def s1_12 : CBox := ⟨⟨350230738224511128243430,350230738224517764068542⟩,⟨504744577153808797122186,504744577153815432925754⟩⟩ +lemma c1_12 : chunk 1 12 = s1_12 := by decide +kernel +noncomputable def s1_13 : CBox := ⟨⟨214021440375853939281167,214021440375855766980026⟩,⟨253583329464653854160661,253583329464655681846709⟩⟩ +lemma c1_13 : chunk 1 13 = s1_13 := by decide +kernel +noncomputable def s1_14 : CBox := ⟨⟨111863932564629267792761,111863932564629794602619⟩,⟨116993184162774580205699,116993184162775107008973⟩⟩ +lemma c1_14 : chunk 1 14 = s1_14 := by decide +kernel +noncomputable def s1_15 : CBox := ⟨⟨34438926924333143615036,34438926924333260928237⟩,⟨33858182090002192019038,33858182090002309330222⟩⟩ +lemma c1_15 : chunk 1 15 = s1_15 := by decide +kernel +noncomputable def s1 : Fin 16 → CBox := ![s1_0,s1_1,s1_2,s1_3,s1_4,s1_5,s1_6,s1_7,s1_8,s1_9,s1_10,s1_11,s1_12,s1_13,s1_14,s1_15] +lemma s1_eq (i : Fin 16) : chunk 1 i = s1 i := by + fin_cases i + · exact c1_0 + · exact c1_1 + · exact c1_2 + · exact c1_3 + · exact c1_4 + · exact c1_5 + · exact c1_6 + · exact c1_7 + · exact c1_8 + · exact c1_9 + · exact c1_10 + · exact c1_11 + · exact c1_12 + · exact c1_13 + · exact c1_14 + · exact c1_15 +noncomputable def s2_0 : CBox := ⟨⟨44209032842200120803986763,44209032842200120836020370⟩,⟨(-70497824734344638986552239),(-70497824734344638952096663)⟩⟩ +lemma c2_0 : chunk 2 0 = s2_0 := by decide +kernel +noncomputable def s2_1 : CBox := ⟨⟨118086756365342727651083201,118086756365342727746787131⟩,⟨(-205583537107670261791997072),(-205583537107670261689343308)⟩⟩ +lemma c2_1 : chunk 2 1 = s2_1 := by decide +kernel +noncomputable def s2_2 : CBox := ⟨⟨153797732364281647816369253,153797732364281647972548015⟩,⟨(-320019847367868611481705457),(-320019847367868611315779909)⟩⟩ +lemma c2_2 : chunk 2 2 = s2_2 := by decide +kernel +noncomputable def s2_3 : CBox := ⟨⟨141684170862957388764350132,141684170862957388971730243⟩,⟨(-395636994045851591065336306),(-395636994045851590847662761)⟩⟩ +lemma c2_3 : chunk 2 3 = s2_3 := by decide +kernel +noncomputable def s2_4 : CBox := ⟨⟨88371427981388254017445998,88371427981388254259451368⟩,⟨(-418559660885240872779632124),(-418559660885240872528917703)⟩⟩ +lemma c2_4 : chunk 2 4 = s2_4 := by decide +kernel +noncomputable def s2_5 : CBox := ⟨⟨13911730201677859834103831,13911730201677860094616458⟩,⟨(-388844684374177749633342983),(-388844684374177749366405999)⟩⟩ +lemma c2_5 : chunk 2 5 = s2_5 := by decide +kernel +noncomputable def s2_6 : CBox := ⟨⟨(-56338705170182037967456204),(-56338705170182037691827694)⟩,⟨(-321336779787753525899508920),(-321336779787753525620062166)⟩⟩ +lemma c2_6 : chunk 2 6 = s2_6 := by decide +kernel +noncomputable def s2_7 : CBox := ⟨⟨(-103173258956085455626454257),(-103173258956085455259738990)⟩,⟨(-237789988081864429539018832),(-237789988081864429171058379)⟩⟩ +lemma c2_7 : chunk 2 7 = s2_7 := by decide +kernel +noncomputable def s2_8 : CBox := ⟨⟨(-120575058144722999517930833),(-120575058144722998521201855)⟩,⟨(-157954435579793767648967880),(-157954435579793766652956857)⟩⟩ +lemma c2_8 : chunk 2 8 = s2_8 := by decide +kernel +noncomputable def s2_9 : CBox := ⟨⟨(-113984769279752840069964701),(-113984769279752835741136720)⟩,⟨(-94103397621204658535831168),(-94103397621204654208745944)⟩⟩ +lemma c2_9 : chunk 2 9 = s2_9 := by decide +kernel +noncomputable def s2_10 : CBox := ⟨⟨(-93758896627366256565568261),(-93758896627366240023768687)⟩,⟨(-49943191347621203697593269),(-49943191347621187157854942)⟩⟩ +lemma c2_10 : chunk 2 10 = s2_10 := by decide +kernel +noncomputable def s2_11 : CBox := ⟨⟨(-69441225605874731890515368),(-69441225605874686307203433)⟩,⟨(-23039426742134149800448667),(-23039426742134104219118869)⟩⟩ +lemma c2_11 : chunk 2 11 = s2_11 := by decide +kernel +noncomputable def s2_12 : CBox := ⟨⟨(-47124535105126790352830208),(-47124535105126704012546575)⟩,⟨(-8520471999753357392099561),(-8520471999753271053439326)⟩⟩ +lemma c2_12 : chunk 2 12 = s2_12 := by decide +kernel +noncomputable def s2_13 : CBox := ⟨⟨(-29256843135864406187042040),(-29256843135864293800181268)⟩,⟨(-1816548881577923009686526),(-1816548881577810623923568)⟩⟩ +lemma c2_13 : chunk 2 13 = s2_13 := by decide +kernel +noncomputable def s2_14 : CBox := ⟨⟨(-15671760938187497909513202),(-15671760938187401632189075)⟩,⟨397090536378913469102841,397090536379009745817225⟩⟩ +lemma c2_14 : chunk 2 14 = s2_14 := by decide +kernel +noncomputable def s2_15 : CBox := ⟨⟨(-4903250492322722955935426),(-4903250492322685301877385)⟩,⟨357907242275408625915826,357907242275446279784363⟩⟩ +lemma c2_15 : chunk 2 15 = s2_15 := by decide +kernel +noncomputable def s2 : Fin 16 → CBox := ![s2_0,s2_1,s2_2,s2_3,s2_4,s2_5,s2_6,s2_7,s2_8,s2_9,s2_10,s2_11,s2_12,s2_13,s2_14,s2_15] +lemma s2_eq (i : Fin 16) : chunk 2 i = s2 i := by + fin_cases i + · exact c2_0 + · exact c2_1 + · exact c2_2 + · exact c2_3 + · exact c2_4 + · exact c2_5 + · exact c2_6 + · exact c2_7 + · exact c2_8 + · exact c2_9 + · exact c2_10 + · exact c2_11 + · exact c2_12 + · exact c2_13 + · exact c2_14 + · exact c2_15 +noncomputable def s3_0 : CBox := ⟨⟨293190185706940597093546909,293190185706942713174743717⟩,⟨441384587484820319865471710,441384587484822435977410141⟩⟩ +lemma c3_0 : chunk 3 0 = s3_0 := by decide +kernel +noncomputable def s3_1 : CBox := ⟨⟨877858598685433408027919333,877858598685438339755655345⟩,⟨1226010765334746025033797513,1226010765334750956846699906⟩⟩ +lemma c3_1 : chunk 3 1 = s3_1 := by decide +kernel +noncomputable def s3_2 : CBox := ⟨⟨1444925289351033873232049714,1444925289351038708617390340⟩,⟨1741450159948450462446984982,1741450159948455297952149967⟩⟩ +lemma c3_2 : chunk 3 2 = s3_2 := by decide +kernel +noncomputable def s3_3 : CBox := ⟨⟨1953614280766838465760636046,1953614280766841369965467334⟩,⟨1892337266337480076361010559,1892337266337482980694387709⟩⟩ +lemma c3_3 : chunk 3 3 = s3_3 := by decide +kernel +noncomputable def s3_4 : CBox := ⟨⟨2342334084705542796577256776,2342334084705543926884249521⟩,⟨1688216218407332617801684959,1688216218407333748221119218⟩⟩ +lemma c3_4 : chunk 3 4 = s3_4 := by decide +kernel +noncomputable def s3_5 : CBox := ⟨⟨2546553127290885234298169061,2546553127290885523990001319⟩,⟨1235256666160809667255758001,1235256666160809957028526808⟩⟩ +lemma c3_5 : chunk 3 5 = s3_5 := by decide +kernel +noncomputable def s3_6 : CBox := ⟨⟨2526651795176413474035761120,2526651795176413526461694060⟩,⟨684221701392100571500201350,684221701392100623971128254⟩⟩ +lemma c3_6 : chunk 3 6 = s3_6 := by decide +kernel +noncomputable def s3_7 : CBox := ⟨⟨2295769251338618730209797675,2295769251338618738642752762⟩,⟨170153752744189179569522435,170153752744189188015518056⟩⟩ +lemma c3_7 : chunk 3 7 = s3_7 := by decide +kernel +noncomputable def s3_8 : CBox := ⟨⟨1920081066775425650631689897,1920081066775425652850119397⟩,⟨(-220805577257695794746156696),(-220805577257695792537287625)⟩⟩ +lemma c3_8 : chunk 3 8 = s3_8 := by decide +kernel +noncomputable def s3_9 : CBox := ⟨⟨1488513547818741961550251362,1488513547818741962696367397⟩,⟨(-457352482626109954794399605),(-457352482626109953669931668)⟩⟩ +lemma c3_9 : chunk 3 9 = s3_9 := by decide +kernel +noncomputable def s3_10 : CBox := ⟨⟨1078232167775977791814845115,1078232167775977792552184733⟩,⟨(-551409300924079430967725820),(-551409300924079430255313188)⟩⟩ +lemma c3_10 : chunk 3 10 = s3_10 := by decide +kernel +noncomputable def s3_11 : CBox := ⟨⟨735367054958794937955277796,735367054958794938436900695⟩,⟨(-537876684471014982288360139),(-537876684471014981829504381)⟩⟩ +lemma c3_11 : chunk 3 11 = s3_11 := by decide +kernel +noncomputable def s3_12 : CBox := ⟨⟨473715347993864281466566439,473715347993864281772712588⟩,⟨(-456074233419558366570640134),(-456074233419558366282534188)⟩⟩ +lemma c3_12 : chunk 3 12 = s3_12 := by decide +kernel +noncomputable def s3_13 : CBox := ⟨⟨284789318088031786093395117,284789318088031786276574324⟩,⟨(-338376224821319846146763149),(-338376224821319845976133700)⟩⟩ +lemma c3_13 : chunk 3 13 = s3_13 := by decide +kernel +noncomputable def s3_14 : CBox := ⟨⟨149604709719502168581300431,149604709719502168677384268⟩,⟨(-205795147450408754845521059),(-205795147450408754756710858)⟩⟩ +lemma c3_14 : chunk 3 14 = s3_14 := by decide +kernel +noncomputable def s3_15 : CBox := ⟨⟨46356026066195711580214941,46356026066195711609940417⟩,⟨(-68809094632763746037573489),(-68809094632763746010206266)⟩⟩ +lemma c3_15 : chunk 3 15 = s3_15 := by decide +kernel +noncomputable def s3 : Fin 16 → CBox := ![s3_0,s3_1,s3_2,s3_3,s3_4,s3_5,s3_6,s3_7,s3_8,s3_9,s3_10,s3_11,s3_12,s3_13,s3_14,s3_15] +lemma s3_eq (i : Fin 16) : chunk 3 i = s3 i := by + fin_cases i + · exact c3_0 + · exact c3_1 + · exact c3_2 + · exact c3_3 + · exact c3_4 + · exact c3_5 + · exact c3_6 + · exact c3_7 + · exact c3_8 + · exact c3_9 + · exact c3_10 + · exact c3_11 + · exact c3_12 + · exact c3_13 + · exact c3_14 + · exact c3_15 +noncomputable def s4_0 : CBox := ⟨⟨(-1532849138230105268759365712),(-1532849138230075882945174713)⟩,⟨176650373357098906908036303,176650373357128292553025051⟩⟩ +lemma c4_0 : chunk 4 0 = s4_0 := by decide +kernel +noncomputable def s4_1 : CBox := ⟨⟨(-4472032707107389227737949172),(-4472032707107277161518702196)⟩,⟨720728777542008873704136159,720728777542120939441873717⟩⟩ +lemma c4_1 : chunk 4 1 = s4_1 := by decide +kernel +noncomputable def s4_2 : CBox := ⟨⟨(-6978664302104332167298181066),(-6978664302104045203346240982)⟩,⟨1741287805262181467292069101,1741287805262468430538677227⟩⟩ +lemma c4_2 : chunk 4 2 = s4_2 := by decide +kernel +noncomputable def s4_3 : CBox := ⟨⟨(-8667582854323784129963100038),(-8667582854323097746691635175)⟩,⟨3297580708558846807103968038,3297580708559533189573297547⟩⟩ +lemma c4_3 : chunk 4 3 = s4_3 := by decide +kernel +noncomputable def s4_4 : CBox := ⟨⟨(-9188473851192314757930410372),(-9188473851190795673630835766)⟩,⟨5212532417131429441841429474,5212532417132948525386633334⟩⟩ +lemma c4_4 : chunk 4 4 = s4_4 := by decide +kernel +noncomputable def s4_5 : CBox := ⟨⟨(-8437095719832759483841227369),(-8437095719829836583991239588)⟩,⟨7140497094738601279492779551,7140497094741524178749466866⟩⟩ +lemma c4_5 : chunk 4 5 = s4_5 := by decide +kernel +noncomputable def s4_6 : CBox := ⟨⟨(-6661102807636027733207560202),(-6661102807631503568588210556)⟩,⟨8665186367063042391305523139,8665186367067566555561331725⟩⟩ +lemma c4_6 : chunk 4 6 = s4_6 := by decide +kernel +noncomputable def s4_7 : CBox := ⟨⟨(-4358595209557696162415338192),(-4358595209552420077063384973)⟩,⟨9444874915515380984119965332,9444874915520657069354517151⟩⟩ +lemma c4_7 : chunk 4 7 = s4_7 := by decide +kernel +noncomputable def s4_8 : CBox := ⟨⟨(-2077218064187079497870680479),(-2077218064182436435163051747)⟩,⟨9351183157664278817928713701,9351183157668921880726370602⟩⟩ +lemma c4_8 : chunk 4 8 = s4_8 := by decide +kernel +noncomputable def s4_9 : CBox := ⟨⟨(-240734791201645353238695338),(-240734791198543258031976865)⟩,⟨8494061184042867731789128206,8494061184045969827216977209⟩⟩ +lemma c4_9 : chunk 4 9 = s4_9 := by decide +kernel +noncomputable def s4_10 : CBox := ⟨⟨944368115046165788083478678,944368115047746522006280130⟩,⟨7130976275603932875393349508,7130976275605513609594097456⟩⟩ +lemma c4_10 : chunk 4 10 = s4_10 := by decide +kernel +noncomputable def s4_11 : CBox := ⟨⟨1489470975975542099550979539,1489470975976203868432417308⟩,⟨5549346008991038195456465304,5549346008991699964619646293⟩⟩ +lemma c4_11 : chunk 4 11 = s4_11 := by decide +kernel +noncomputable def s4_12 : CBox := ⟨⟨1543209025240001341619138649,1543209025240249466165442201⟩,⟨3990490149164454386543349573,3990490149164702511336811748⟩⟩ +lemma c4_12 : chunk 4 12 = s4_12 := by decide +kernel +noncomputable def s4_13 : CBox := ⟨⟨1279523667648914552549090634,1279523667649003919276490276⟩,⟨2608839875441893275040460665,2608839875441982641953790159⟩⟩ +lemma c4_13 : chunk 4 13 = s4_13 := by decide +kernel +noncomputable def s4_14 : CBox := ⟨⟨831071149928610542208302434,831071149928641963870825769⟩,⟨1449846622857976079952161419,1449846622858007501728194886⟩⟩ +lemma c4_14 : chunk 4 14 = s4_14 := by decide +kernel +noncomputable def s4_15 : CBox := ⟨⟨286841331774675323033818479,286841331774683115447761303⟩,⟨462155759452731597824300021,462155759452739390275892870⟩⟩ +lemma c4_15 : chunk 4 15 = s4_15 := by decide +kernel +noncomputable def s4 : Fin 16 → CBox := ![s4_0,s4_1,s4_2,s4_3,s4_4,s4_5,s4_6,s4_7,s4_8,s4_9,s4_10,s4_11,s4_12,s4_13,s4_14,s4_15] +lemma s4_eq (i : Fin 16) : chunk 4 i = s4 i := by + fin_cases i + · exact c4_0 + · exact c4_1 + · exact c4_2 + · exact c4_3 + · exact c4_4 + · exact c4_5 + · exact c4_6 + · exact c4_7 + · exact c4_8 + · exact c4_9 + · exact c4_10 + · exact c4_11 + · exact c4_12 + · exact c4_13 + · exact c4_14 + · exact c4_15 +noncomputable def s5_0 : CBox := ⟨⟨133585139860689380369609910,133585139860689381476690720⟩,⟨(-9056740137373824624979405),(-9056740137373823869762161)⟩⟩ +lemma c5_0 : chunk 5 0 = s5_0 := by decide +kernel +noncomputable def s5_1 : CBox := ⟨⟨358882490715910208601256148,358882490715910211991714337⟩,⟨(-131089408603047430973565356),(-131089408603047428585634168)⟩⟩ +lemma c5_1 : chunk 5 1 = s5_1 := by decide +kernel +noncomputable def s5_2 : CBox := ⟨⟨324059179527000381345149197,324059179527000387120005491⟩,⟨(-540128700334405923656842484),(-540128700334405919316738871)⟩⟩ +lemma c5_2 : chunk 5 2 = s5_2 := by decide +kernel +noncomputable def s5_3 : CBox := ⟨⟨(-421377908881336194353348837),(-421377908881336186064663580)⟩,⟨(-1391188128903802005018501098),(-1391188128903801998300764102)⟩⟩ +lemma c5_3 : chunk 5 3 = s5_3 := by decide +kernel +noncomputable def s5_4 : CBox := ⟨⟨(-2274481638194303411070724073),(-2274481638194303399997369928)⟩,⟨(-2808896646124601766653132014),(-2808896646124601756995650312)⟩⟩ +lemma c5_4 : chunk 5 4 = s5_4 := by decide +kernel +noncomputable def s5_5 : CBox := ⟨⟨(-5140431167849332151917418354),(-5140431167849332137301563754)⟩,⟨(-4701618790908783649987295240),(-4701618790908783636448000509)⟩⟩ +lemma c5_5 : chunk 5 5 = s5_5 := by decide +kernel +noncomputable def s5_6 : CBox := ⟨⟨(-8406789600276406358215920474),(-8406789600276406336894177719)⟩,⟨(-6563325231442495268799407556),(-6563325231442495248110696181)⟩⟩ +lemma c5_6 : chunk 5 6 = s5_6 := by decide +kernel +noncomputable def s5_7 : CBox := ⟨⟨(-11331186225195650428507525706),(-11331186225195650381123471702)⟩,⟨(-7704538781526318001711462123),(-7704538781526317954514512445)⟩⟩ +lemma c5_7 : chunk 5 7 = s5_7 := by decide +kernel +noncomputable def s5_8 : CBox := ⟨⟨(-13332435369005559460742489645),(-13332435369005559247792171232)⟩,⟨(-7714306724055170966845551594),(-7714306724055170753757108033)⟩⟩ +lemma c5_8 : chunk 5 8 = s5_8 := by decide +kernel +noncomputable def s5_9 : CBox := ⟨⟨(-14087465113762803372436580412),(-14087465113762802157504014138)⟩,⟨(-6644766972097911157148030115),(-6644766972097909941932897210)⟩⟩ +lemma c5_9 : chunk 5 9 = s5_9 := by decide +kernel +noncomputable def s5_10 : CBox := ⟨⟨(-13570259192035704312582708897),(-13570259192035698732415016880)⟩,⟨(-4883703850893493795368059194),(-4883703850893488214906305135)⟩⟩ +lemma c5_10 : chunk 5 10 = s5_10 := by decide +kernel +noncomputable def s5_11 : CBox := ⟨⟨(-12020694686758350949757196525),(-12020694686758332927929816871)⟩,⟨(-2944276251025164127249498233),(-2944276251025146105167843185)⟩⟩ +lemma c5_11 : chunk 5 11 = s5_11 := by decide +kernel +noncomputable def s5_12 : CBox := ⟨⟨(-9797231648182822126629623227),(-9797231648182782931308324476)⟩,⟨(-1300100096995020562896970074),(-1300100096994981367378515004)⟩⟩ +lemma c5_12 : chunk 5 12 = s5_12 := by decide +kernel +noncomputable def s5_13 : CBox := ⟨⟨(-7196373462910935227642519990),(-7196373462910878124161349486)⟩,⟨(-251003849282194972085266922),(-251003849282137868473478510)⟩⟩ +lemma c5_13 : chunk 5 13 = s5_13 := by decide +kernel +noncomputable def s5_14 : CBox := ⟨⟨(-4390040107777626085946566734),(-4390040107777573057799960453)⟩,⟨159078656225729530850608671,159078656225782559068067865⟩⟩ +lemma c5_14 : chunk 5 14 = s5_14 := by decide +kernel +noncomputable def s5_15 : CBox := ⟨⟨(-1474560897390450905344673834),(-1474560897390429252948946979)⟩,⟨107862440541627847345442790,107862440541649499762045839⟩⟩ +lemma c5_15 : chunk 5 15 = s5_15 := by decide +kernel +noncomputable def s5 : Fin 16 → CBox := ![s5_0,s5_1,s5_2,s5_3,s5_4,s5_5,s5_6,s5_7,s5_8,s5_9,s5_10,s5_11,s5_12,s5_13,s5_14,s5_15] +lemma s5_eq (i : Fin 16) : chunk 5 i = s5 i := by + fin_cases i + · exact c5_0 + · exact c5_1 + · exact c5_2 + · exact c5_3 + · exact c5_4 + · exact c5_5 + · exact c5_6 + · exact c5_7 + · exact c5_8 + · exact c5_9 + · exact c5_10 + · exact c5_11 + · exact c5_12 + · exact c5_13 + · exact c5_14 + · exact c5_15 +noncomputable def sums : Fin 6 → Fin 16 → CBox := ![s0,s1,s2,s3,s4,s5] +lemma sums_eq (j : Fin 6) (i : Fin 16) : chunk j i = sums j i := by + fin_cases j + · exact s0_eq i + · exact s1_eq i + · exact s2_eq i + · exact s3_eq i + · exact s4_eq i + · exact s5_eq i +noncomputable def ans : CBox := ⟨⟨(-21431119462767569215851788740),(-21431119462763246224782801656)⟩,⟨5288168801209847219770212566,5288168801214170209459738994⟩⟩ +lemma checked : cachedMomentRuleBox density1 hk3_0_7 = ans := by + change (finSum (fun j => (finSum (fun i => chunk j i)).scale 1 6)) = ans + simp_rw [sums_eq] + decide +kernel +lemma contains : ans.Contains (fullMomentRule true false 3 7) := by + rw [← checked] + exact @cached_density_rule_contains density1 hk3_0_7 (tableDensity true) (fullFactor false 3 7) density1_contains hk3_0_7_contains +noncomputable def atomAnswer : CBox := ⟨⟨(-4351400910278889113160856870),(-4351400910278889111136415004)⟩,⟨11131749076879018053995051540,11131749076879018056651091189⟩⟩ +lemma atomChecked : tableAtomBox true ha3_0_7 = atomAnswer := by decide +kernel +lemma atomContains : atomAnswer.Contains (fullMomentAtom true false 3 7) := by + rw [← atomChecked] + exact @fullAtomBox_contains true false ha3_0_7 3 7 ha3_0_7_contains + def realAnswer : RBox := ⟨(-25782520373046458329112645610),(-25782520373042135335819216660)⟩ +lemma realChecked : inflate (atomAnswer.add ans).re = realAnswer := by decide +kernel +lemma realContains : realAnswer.Contains (fullMoment true false 3 7) := by + rw [← realChecked] + exact fullMoment_contains atomContains contains (by norm_num) (by norm_num) +end hm3_1_0_7 +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues10.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues10.lean new file mode 100644 index 0000000000000000000000000000000000000000..082b62a4831e71f61241945ac0115e9260589b2c --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues10.lean @@ -0,0 +1,3941 @@ +import OAI.Analysis.PlanarPacking.Grid +import OAI.Analysis.PlanarPacking.Certificate.TransformedPowers10 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid IntegerAlpha IntegerCompact +noncomputable def kernel0_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans0 j i k) +noncomputable def kernel0_0_r0_0 : Fin 16 → CBox := ![⟨⟨2459723972788753827453440368550,2459723972788753827538647753780⟩,⟨1024875342076841814988952621372,1024875342076841815024455431020⟩⟩,⟨⟨2459778767205941797004422540690,2459778767205941797089632180420⟩,⟨1024821000648014976348954936866,1024821000648014976384456514467⟩⟩,⟨⟨2459888342733773335824931173699,2459888342733773335910145314530⟩,⟨1024712313555039836432400037341,1024712313555039836467899137201⟩⟩,⟨⟨2460052672758385581263607727066,2460052672758385581348828614472⟩,⟨1024549272335344907041004717300,1024549272335344907076500093267⟩⟩,⟨⟨2460271717357056916181061244625,2460271717357056916266291122403⟩,⟨1024331864315250260880391670362,1024331864315250260915882075550⟩⟩,⟨⟨2460545423295916105652500870684,2460545423295916105737741980410⟩,⟨1024060072634176680250278674094,1024060072634176680285762860716⟩⟩,⟨⟨2460873724026924337575237952273,2460873724026924337660492532596⟩,⟨1023733876276918457733538182303,1023733876276918457769014901155⟩⟩,⟨⟨2461256539684161442602263130730,2461256539684161442687533417071⟩,⟨1023353250113974580280738371531,1023353250113974580316206372323⟩⟩,⟨⟨2461693777079455347853865426578,2461693777079455347939153650027⟩,⟨1022918164949931622707197594510,1022918164949931622742655624459⟩⟩,⟨⟨2462185329697401571079323171722,2462185329697401571164631559536⟩,⟨1022428587579890212631229324797,1022428587579890212666676130516⟩⟩,⟨⟨2462731077689827281728060733246,2462731077689827281813391506436⟩,⟨1021884480853925394774591949615,1021884480853925394810026273402⟩⟩,⟨⟨2463330887869762136982048705244,2463330887869762137067404080792⟩,⟨1021285803749569606924935188242,1021285803749569606960355773034⟩⟩,⟨⟨2463984613704985738273906345208,2463984613704985738359288531237⟩,⟨1020632511452305271467540110813,1020632511452305271502945692032⟩⟩,⟨⟨2464692095311229141059389070189,2464692095311229141144800271722⟩,⟨1019924555444052194129363659492,1019924555444052194164752976488⟩⟩,⟨⟨2465453159445115381314985158905,2465453159445115381400427568925⟩,⟨1019161883599633034520093131732,1019161883599633034555464912225⟩⟩,⟨⟨2466267619496931449852304968833,2466267619496931449937780778040⟩,⟨1018344440291198060480238764483,1018344440291198060515591743251⟩⟩] +lemma kernel0_0_r0_0_eq : ∀ k : Fin 16, kernel0_0Expr 0 0 k = kernel0_0_r0_0 k := by decide +kernel +noncomputable def kernel0_0_r0_1 : Fin 16 → CBox := ![⟨⟨2467135275483331543297371641482,2467135275483331543382883023986⟩,⟨1017472166500588209654882858358,1017472166500588209690215751898⟩⟩,⟨⟨2468055914040078741428342853922,2468055914040078741513891985232⟩,⟨1016544999939613146847874577474,1016544999939613146883186117754⟩⟩,⟨⟨2469029308414939497172650360096,2469029308414939497258239394194⟩,⟨1015562875178218514587282194741,1015562875178218514622571088014⟩⟩,⟨⟨2470055218460852470310213838050,2470055218460852470395844931944⟩,⟨1014525723780513917252929239330,1014525723780513917288194212111⟩⟩,⟨⟨2471133390629500280877384003173,2471133390629500280963059285313⟩,⟨1013433474448630346701424437244,1013433474448630346736664179078⟩⟩,⟨⟨2472263557965419695154728893300,2472263557965419695240450502989⟩,⟨1012286053174372740535490714053,1012286053174372740570703950863⟩⟩,⟨⟨2473445440100792577350292811700,2473445440100792577436062852181⟩,⟨1011083383398630154332436078265,1011083383398630154367621486997⟩⟩,⟨⟨2474678743251066634708494780059,2474678743251066634794315367916⟩,⟨1009825386178502617995301190226,1009825386178502618030457490538⟩⟩,⟨⟨2475963160211561543474197063526,2475963160211561543560070268354⟩,⟨1008511980362100126065052504667,1008511980362100126100178348937⟩⟩,⟨⟨2477298370355222458245423896459,2477298370355222458331351815927⟩,⟨1007143082770965374928080894521,1007143082770965374963175006711⟩⟩,⟨⟨2478684039631689167707337887840,2478684039631689167793322562103⟩,⟨1005718608390067799443186101439,1005718608390067799478247120668⟩⟩,⟨⟨2480119820567855255127523791878,2480119820567855255213567290758⟩,⟨1004238470565312171176448588135,1004238470565312171211475229976⟩⟩,⟨⟨2481605352270097541501741058226,2481605352270097541587845379929⟩,⟨1002702581208500494288352625113,1002702581208500494323343496042⟩⟩,⟨⟨2483140260428361821683356443718,2483140260428361821769523638057⟩,⟨1001110851009681167850234856491,1001110851009681167885188681897⟩⟩,⟨⟨2484724157322296437643691567990,2484724157322296437729923599129⟩,⟨999463189656814370260109279744,999463189656814370295024651769⟩⟩,⟨⟨2486356641829630556255381804395,2486356641829630556341680689495⟩,⟨997759506062677358394544199618,997759506062677358429419834034⟩⟩] +lemma kernel0_0_r0_1_eq : ∀ k : Fin 16, kernel0_0Expr 0 1 k = kernel0_0_r0_1 k := by decide +kernel +noncomputable def kernel0_0_r0_2 : Fin 16 → CBox := ![⟨⟨2488037299436999119359645791594,2488037299436999119446013441331⟩,⟨995999708598927857748564620515,995999708598927857783399063095⟩⟩,⟨⟨2489765702253421298705247817171,2489765702253421298791686230757⟩,⟨994183705337237947348222724469,994183705337237947383014712398⟩⟩,⟨⟨2491541409026643904618401966152,2491541409026643904704913018197⟩,⟨992311404297404812665191792112,992311404297404812699939860843⟩⟩,⟨⟨2493363965162565551631664916737,2493363965162565551718250566309⟩,⟨990382713702338449872490720143,990382713702338449907193591411⟩⟩,⟨⟨2495232902747961463101570384723,2495232902747961463188232443249⟩,⟨988397542239819855098984435970,988397542239819855133640588599⟩⟩,⟨⟨2497147740576732586117059030809,2497147740576732586203799439587⟩,⟨986355799330916423234359254132,986355799330916423268967439980⟩⟩,⟨⟨2499107984179906173505590636845,2499107984179906173592411166958⟩,⟨984257395404934213527630757279,984257395404934213562189445022⟩⟩,⟨⟨2501113125859618156992339470745,2501113125859618157079242018133⟩,⟨982102242180779415819346213886,982102242180779415853854138540⟩⟩,⟨⟨2503162644727310469848379955890,2503162644727310469935366212384⟩,⟨979890252954593774776753653582,979890252954593774811209205398⟩⟩,⟨⟨2505256006746378963772605229481,2505256006746378963859677079763⟩,⟨977621342893520903936753384288,977621342893520903971155349237⟩⟩,⟨⟨2507392664779509688227603549366,2507392664779509688314762646521⟩,⟨975295429335452351655635580302,975295429335452351689982349867⟩⟩,⟨⟨2509572058640943045809070414683,2509572058640943045896318586867⟩,⟨972912432094593973175856249540,972912432094593973210146580882⟩⟩,⟨⟨2511793615153906689207765683252,2511793615153906689295104493530⟩,⟨970472273772684623940379197336,970472273772684623974611391579⟩⟩,⟨⟨2514056748213458968620789720609,2514056748213458968708220987165⟩,⟨967974880075690427065663876690,967974880075690427099836753636⟩⟩,⟨⟨2516360858854985257791586924204,2516360858854985257879112167419⟩,⟨965420180135788891660021930649,965420180135788891694133794035⟩⟩,⟨⟨2518705335328589566969588302634,2518705335328589567057209278599⟩,⟨962808106838447978685397014156,962808106838447978719446653715⟩⟩] +lemma kernel0_0_r0_2_eq : ∀ k : Fin 16, kernel0_0Expr 0 2 k = kernel0_0_r0_2 k := by decide +kernel +noncomputable def kernel0_0_r0_3 : Fin 16 → CBox := ![⟨⟨2521089553179623476854558512877,2521089553179623476942276629011⟩,⟨960138597154395838674381013003,960138597154395838708366607272⟩⟩,⟨⟨2523512875335593584066250855512,2523512875335593584154067871451⟩,⟨957411592476267393341159363731,957411592476267393375079800338⟩⟩,⟨⟨2525974652199687321118797258296,2525974652199687321206714546853⟩,⟨954627038959704214635251339956,954627038959704214669104824348⟩⟩,⟨⟨2528474221751155187827342074893,2528474221751155187915361316223⟩,⟨951784887868674284922505242453,951784887868674284956290608888⟩⟩,⟨⟨2531010909652785092425602433502,2531010909652785092513724877553⟩,⟨948885095924768216762644220777,948885095924768216796359539195⟩⟩,⟨⟨2533584029365701635735241036799,2533584029365701635823468367866⟩,⟨945927625660218387398415488523,945927625660218387432059702656⟩⟩,⟨⟨2536192882271719767292106775856,2536192882271719767380440204226⟩,⟨942912445774377219980594358171,942912445774377220014165564638⟩⟩,⟨⟨2538836757803478285745507340450,2538836757803478285833948466822⟩,⟨939839531493380540317974865873,939839531493380540351471956983⟩⟩,⟨⟨2541514933582574135077111620413,2541514933582574135165661502374⟩,⟨936708864932711575339246184799,936708864932711575372667073058⟩⟩,⟨⟨2544226675565913351910755068212,2544226675565913351999415331444⟩,⟨933520435462370759437097845401,933520435462370759470441583275⟩⟩,⟨⟨2546971238200488836857851704294,2546971238200488836946623381819⟩,⟨930274240074346100548947933099,930274240074346100582212498144⟩⟩,⟨⟨2549747864586788844777733215788,2549747864586788844866617825696⟩,⟨926970283752068453471840402524,926970283752068453505024760090⟩⟩,⟨⟨2552555786651033206278174614486,2552555786651033206367173028041⟩,⟨923608579841525678890330988094,923608579841525678923432922099⟩⟩,⟨⟨2555394225326426798006931274844,2555394225326426798096045035541⟩,⟨920189150423699359386465301262,920189150423699359419483949807⟩⟩,⟨⟨2558262390743611665658141259725,2558262390743611665747371208925⟩,⟨916712026687977525829547699795,916712026687977525862480911423⟩⟩,⟨⟨2561159482430490465686685344766,2561159482430490465776032915284⟩,⟨913177249306186747558503990739,913177249306186747591350820400⟩⟩] +lemma kernel0_0_r0_3_eq : ∀ k : Fin 16, kernel0_0Expr 0 3 k = kernel0_0_r0_3 k := by decide +kernel +noncomputable def kernel0_0_r0_4 : Fin 16 → CBox := ![⟨⟨2564084689521584525300318029595,2564084689521584525389783858803⟩,⟨909584868806876987193742783307,909584868806876987226500811606⟩⟩,⟨⟨2567037190977079822538262805168,2567037190977079822627848385286⟩,⟨905934945949482846194267732420,905934945949482846226936265134⟩⟩,⟨⟨2570016155811703557724469310336,2570016155811703557814175277216⟩,⟨902227552097975261722059510464,902227552097975261754636257749⟩⟩,⟨⟨2573020743333562724384917167343,2573020743333562724474744866229⟩,⟨898462769593608391105985094907,898462769593608391138469219132⟩⟩,⟨⟨2576050103393064193502375858013,2576050103393064193592325718237⟩,⟨894640692126357370063671942876,894640692126357370096060887858⟩⟩,⟨⟨2579103376642023303065147296098,2579103376642023303155220717239⟩,⟨890761425104633888353911275562,890761425104633888386204457866⟩⟩,⟨⟨2582179694803054800292716135527,2582179694803054800382913534900⟩,⟨886825086022858125785484193491,886825086022858125817679175946⟩⟩,⟨⟨2585278180949326223532393243086,2585278180949326223622715876553⟩,⟨882831804826457567083563039933,882831804826457567115659111661⟩⟩,⟨⟨2588397949794739443321983611787,2588397949794739443412431640079⟩,⟨878781724273855600993152786809,878781724273855601025147151054⟩⟩,⟨⟨2591538107994591118134565917822,2591538107994591118225140694337⟩,⟨874675000295005642459917318669,874675000295005642491809617632⟩⟩,⟨⟨2594697754456747272475944519211,2594697754456747272566646230709⟩,⟨870511802346019832245058885993,870511802346019832276846527048⟩⟩,⟨⟨2597875980663351087941653618058,2597875980663351088032483429699⟩,⟨866292313759435201457151188446,866292313759435201488833607876⟩⟩,⟨⟨2601071871003066328289183748345,2601071871003066328380141590651⟩,⟨862016732089654574739666097829,862016732089654574771240347931⟩⟩,⟨⟨2604284503113841616395650684125,2604284503113841616486737813541⟩,⟨857685269453094460600544130841,857685269453094460632010003395⟩⟩,⟨⟨2607512948236163065161822599238,2607512948236163065253038961224⟩,⟨853298152862567775687431117177,853298152862567775718785856507⟩⟩,⟨⟨2610756271576744559184523203861,2610756271576744559275869872148⟩,⟨848855624555425506360125006057,848855624555425506391368217394⟩⟩] +lemma kernel0_0_r0_4_eq : ∀ k : Fin 16, kernel0_0Expr 0 4 k = kernel0_0_r0_4 k := by decide +kernel +noncomputable def kernel0_0_r0_5 : Fin 16 → CBox := ![⟨⟨2614013532682586314748865764807,2614013532682586314840342359891⟩,⟨844357942314978359798586203841,844357942314978359829714639436⟩⟩,⟨⟨2617283785825313240002279949024,2617283785825313240093887699791⟩,⟨839805379784717131525006796777,839805379784717131556020561724⟩⟩,⟨⟨2620566080395685104894681757089,2620566080395685104986420358641⟩,⟨835198226774848949189258478524,835198226774848949220154647679⟩⟩,⟨⟨2623859461308150643645976765190,2623859461308150643737847199579⟩,⟨830536789560665775361150246540,830536789560665775391928616509⟩⟩,⟨⟨2627162969415297485372734990480,2627162969415297485464736643307⟩,⟨825821391172261595349420078035,825821391172261595380077262500⟩⟩,⟨⟨2630475641932029277481072835435,2630475641932029277573206824759⟩,⟨821052371675115608899725572362,821052371675115608930261845702⟩⟩,⟨⟨2633796512869280570059935751353,2633796512869280570152201514484⟩,⟨816230088441060514748024932698,816230088441060514778437194285⟩⟩,⟨⟨2637124613477059008426345581393,2637124613477059008518744009278⟩,⟨811354916409157650565987662151,811354916409157650596275923746⟩⟩,⟨⟨2640458972696583177855175102186,2640458972696583177947705247172⟩,⟨806427248336004352231762384581,806427248336004352261922923760⟩⟩,⟨⟨2643798617621263104011915229798,2643798617621263104104578191998⟩,⟨801447495035003448095609287013,801447495035003448125642762860⟩⟩,⟨⟨2647142573966248981229364158877,2647142573966248981322159112711⟩,⟨796416085604130326441375688622,796416085604130326471278820355⟩⟩,⟨⟨2650489866546252226860794503269,2650489866546252226953722249573⟩,⟨791333467641739525930724580027,791333467641739525960497618510⟩⟩,⟨⟨2653839519761321493536769880094,2653839519761321493629829228534⟩,⟨786200107449960315375574327864,786200107449960315405213406035⟩⟩,⟨⟨2657190558090234863873645436859,2657190558090234863966837376296⟩,⟨781016490225239264150249698174,781016490225239264179755688993⟩⟩,⟨⟨2660542006591148157119654732981,2660542006591148157212978171833⟩,⟨775783120235597368744547908399,775783120235597368773917346612⟩⟩,⟨⟨2663892891409118148803764423060,2663892891409118148897220073991⟩,⟨770500520984179902438035338138,770500520984179902467268738693⟩⟩] +lemma kernel0_0_r0_5_eq : ∀ k : Fin 16, kernel0_0Expr 0 5 k = kernel0_0_r0_5 k := by decide +kernel +noncomputable def kernel0_0_r0_6 : Fin 16 → CBox := ![⟨⟨2667242240290098598287600753773,2667242240290098598381187057222⟩,⟨765169235358688799036688607259,765169235358688799065781684161⟩⟩,⟨⟨2670589083100986351861075733797,2670589083100986351954793694577⟩,⟨759789825766300070256598352339,759789825766300070285552487051⟩⟩,⟨⟨2673932452355274498187941962112,2673932452355274498281790222431⟩,⟨754362874253682488768674287441,754362874253682488797485827467⟩⟩,⟨⟨2677271383743849656714199055881,2677271383743849656808178242589⟩,⟨748888982611748541037422344598,748888982611748541066092093503⟩⟩,⟨⟨2680604916670451036828496459302,2680604916670451036922604795013⟩,⟨743368772464784458513875293988,743368772464784458542398867548⟩⟩,⟨⟨2683932094791289975157565841200,2683932094791289975251804198931⟩,⟨737802885343622961729896445047,737802885343622961758275435916⟩⟩,⟨⟨2687251966558310299559330223187,2687251966558310299653696980980⟩,⟨732191982742540185209671212234,732191982742540185237901777754⟩⟩,⟨⟨2690563585765552140221364849318,2690563585765552140315860551643⟩,⟨726536746159577074199300940805,726536746159577074227384198674⟩⟩,⟨⟨2693866012098064769560496221924,2693866012098064769655118723569⟩,⟨720837877120005335826163035196,720837877120005335854094155062⟩⟩,⟨⟨2697158311682797761605600865683,2697158311682797761700351065521⟩,⟨715096097182678762690843667821,715096097182678762718624823086⟩⟩,⟨⟨2700439557640884275738466078842,2700439557640884275833342096159⟩,⟨709312147929032397754977331619,709312147929032397782604488309⟩⟩,⟨⟨2703708830640715645599317510062,2703708830640715645694319810783⟩,⟨703486790934514543842273432578,703486790934514543869748046865⟩⟩,⟨⟨2706965219451192746960041070286,2706965219451192747055167301995⟩,⟨697620807722260003695583937143,697620807722260003722901075919⟩⟩,⟨⟨2710207821494526882314486361628,2710207821494526882409737299074⟩,⟨691714999698837128394418527234,691714999698837128421580625796⟩⟩,⟨⟨2713435743397951207043286119668,2713435743397951207138659631180⟩,⟨685770188071926210636607332403,685770188071926210663610163783⟩⟩,⟨⟨2716648101543693082584750571470,2716648101543693082680247049363⟩,⟨679787213749812439128546864956,679787213749812439155392248745⟩⟩] +lemma kernel0_0_r0_6_eq : ∀ k : Fin 16, kernel0_0Expr 0 6 k = kernel0_0_r0_6 k := by decide +kernel +noncomputable def kernel0_0_r0_7 : Fin 16 → CBox := ![⟨⟨2719844022616548224249943870894,2719844022616548224345560574645⟩,⟨673766937222602982000625307640,673766937222602982027307755248⟩⟩,⟨⟨2723022644148389160958214020930,2723022644148389161053951797270⟩,⟨667710238425104738441990415405,667710238425104738468513098301⟩⟩,⟨⟨2726183115058933384447859115477,2726183115058933384543715593397⟩,⟨661618016581326833207515268711,661618016581326833233873767332⟩⟩,⟨⟨2729324596192090676833965871923,2729324596192090676929941375082⟩,⟨655491190030599969897881184438,655491190030599969924077704505⟩⟩,⟨⟨2732446260847204505119435881939,2732446260847204505215527520875⟩,⟨649330696035333244742568624017,649330696035333244768597656017⟩⟩,⟨⟨2735547295304499093567903976221,2735547295304499093664112448192⟩,⟨643137490570457889162763855648,643137490570457889188628797547⟩⟩,⟨⟨2738626899344041860451452605422,2738626899344041860547775313721⟩,⟨636912548094636590322672634649,636912548094636590348368873172⟩⟩,⟨⟨2741684286757530361720495319446,2741684286757530361816932525495⟩,⟨630656861303346465581192825143,630656861303346465606722975769⟩⟩,⟨⟨2744718685852213743961261322660,2744718685852213744057809780599⟩,⟨624371440863973368552525793273,624371440863973368577883768304⟩⟩,⟨⟨2747729339946260992025717027207,2747729339946260992122377514991⟩,⟨618057315133084908850108496129,618057315133084908875298497234⟩⟩,⟨⟨2750715507854891978277261765792,2750715507854891978374031478521⟩,⟨611715529856079300392255540376,611715529856079300417272761624⟩⟩,⟨⟨2753676464366592491619848451174,2753676464366592491716727594176⟩,⟨605347147849436838898078000651,605347147849436838922925487695⟩⟩,⟨⟨2756611500708741052170749736746,2756611500708741052267734947800⟩,⟨598953248665830371306515020504,598953248665830371331186661533⟩⟩,⟨⟨2759519925001983403978198777893,2759519925001983404075290699971⟩,⟨592534928242380480883875316533,592534928242380480908375585778⟩⟩,⟨⟨2762401062702700121454160734447,2762401062702700121551356373970⟩,⟨586093298532370193766025011093,586093298532370193790348909252⟩⟩,⟨⟨2765254257032923758506965859962,2765254257032923758604265373442⟩,⟨579629487120762737357910283817,579629487120762737382061307548⟩⟩] +lemma kernel0_0_r0_7_eq : ∀ k : Fin 16, kernel0_0Expr 0 7 k = kernel0_0_r0_7 k := by decide +kernel +noncomputable def kernel0_0_r0_8 : Fin 16 → CBox := ![⟨⟨2768078869397074401433251877222,2768078869397074401530651539043⟩,⟨573144636823894170153483493575,573144636823894170177454786502⟩⟩,⟨⟨2770874279784896341553287613362,2770874279784896341650788209131⟩,⟨566639905273740478224137541621,566639905273740478247934589515⟩⟩,⟨⟨2773639887159993840812424139945,2773639887159993840910022510425⟩,⟨560116464487185918547420879090,560116464487185918571038491100⟩⟩,⟨⟨2776375109833380597981090802797,2776375109833380598078787062546⟩,⟨553575500420745907114211591710,553575500420745907137653732024⟩⟩,⟨⟨2779079385821475504957202162704,2779079385821475505054992566599⟩,⟨547018212511223525178013996425,547018212511223525201273926097⟩⟩,⟨⟨2781752173187996577792651758007,2781752173187996577890536918268⟩,⟨540445813202803676418522790340,540445813202803676441606161308⟩⟩,⟨⟨2784392950369225516790946817906,2784392950369225516888923433987⟩,⟨533859527461112999312245900355,533859527461112999335147328886⟩⟩,⟨⟨2787001216482137151395348844845,2787001216482137151493416997345⟩,⟨527260592274796752857788302308,527260592274796752880512237700⟩⟩,⟨⟨2789576491614911011447578222670,2789576491614911011545733873752⟩,⟨520650256145185982594050722125,520650256145185982616589682309⟩⟩,⟨⟨2792118317099366385531707885679,2792118317099366385629951783647⟩,⟨514029778564649272830995399664,514029778564649272853356077095⟩⟩,⟨⟨2794626255764887424419268057092,2794626255764887424517596787533⟩,⟨507400429484243238362836030417,507400429484243238385012850025⟩⟩,⟨⟨2797099892173431064280459768284,2797099892173431064378873384982⟩,⟨500763488771294546007180121415,500763488771294546029178029862⟩⟩,⟨⟨2799538832835237717991367611321,2799538832835237718089862097425⟩,⟨494120245657563627889193944486,494120245657563627911005548458⟩⟩,⟨⟨2801942706404892747920157018634,2801942706404892748018732978233⟩,⟨487471998178656302896966842923,487471998178656302918599059168⟩⟩,⟨⟨2804311163857415621325374730444,2804311163857415621424028663318⟩,⟨480820052605364212472837255244,480820052605364212494284315597⟩⟩,⟨⟨2806643878644083288439055049157,2806643878644083288537786990335⟩,⟨474165722867628258242258268818,474165722867628258263525630221⟩⟩] +lemma kernel0_0_r0_8_eq : ∀ k : Fin 16, kernel0_0Expr 0 8 k = kernel0_0_r0_8 k := by decide +kernel +noncomputable def kernel0_0_r0_9 : Fin 16 → CBox := ![⟨⟨2808940546827724639374689879518,2808940546827724639473495533608⟩,⟨467510329971831062536146042348,467510329971831062557225356182⟩⟩,⟨⟨2811200887197253812852340801006,2811200887197253812951220966936⟩,⟨460855201412134823667618458669,460855201412134823688517915793⟩⟩,⟨⟨2813424641361241569032235542520,2813424641361241569131186664828⟩,⟨454201670576589775474892671144,454201670576589775495606312160⟩⟩,⟨⟨2815611573820355820454652979808,2815611573820355820553675081463⟩,⟨447551076148745759418400608060,447551076148745759438934406564⟩⟩,⟨⟨2817761472018534657760899927764,2817761472018534657859988847937⟩,⟨440904761505505156493785344789,440904761505505156514131224611⟩⟩,⟨⟨2819874146372787727991880455105,2819874146372787728091036808658⟩,⟨434264074111959589337511327440,434264074111959589357677537241⟩⟩,⟨⟨2821949430281554539527994326411,2821949430281554539627214532644⟩,⟨427630364913955381040224516424,427630364913955381060204902562⟩⟩,⟨⟨2823987180111581095391215824028,2823987180111581095490499901566⟩,⟨421004987729133740200586783829,421004987729133740220387844850⟩⟩,⟨⟨2825987275163309111785737471729,2825987275163309111885081074115⟩,⟨414389298637191030500252371580,414389298637191030519865080793⟩⟩,⟨⟨2827949617614804877698832852091,2827949617614804877798236771570⟩,⟨407784655370102281397312272209,407784655370102281416746158189⟩⟩,⟨⟨2829874132444287470911812848729,2829874132444287471011273510991⟩,⟨401192416703047313223595516907,401192416703047313242844233066⟩⟩,⟨⟨2831760767331348483490910608550,2831760767331348483590428033842⟩,⟨394613941846773498745475156202,394613941846773498764545726865⟩⟩,⟨⟨2833609492536987544474961770146,2833609492536987544574531790074⟩,⟨388050589842122282669043123727,388050589842122282687926757516⟩⟩,⟨⟨2835420300762619679214979975218,2835420300762619679314603229534⟩,⟨381503718957438153950347722215,381503718957438153969054046845⟩⟩,⟨⟨2837193206988241835539574474688,2837193206988241835639247425744⟩,⟨374974686089568841064899087036,374974686089568841083421559601⟩⟩,⟨⟨2838928248289976660519062726689,2838928248289976660618785403000⟩,⟨368464846169154110060993535013,368464846169154110079339708125⟩⟩] +lemma kernel0_0_r0_9_eq : ∀ k : Fin 16, kernel0_0Expr 0 9 k = kernel0_0_r0_9 k := by decide +kernel +noncomputable def kernel0_0_r0_10 : Fin 16 → CBox := ![⟨⟨2840625483637241754265593003497,2840625483637241754365361067202⟩,⟨361975551570887726093665659034,361975551570887726111825476188⟩⟩,⟨⟨2842284993669822087669748317751,2842284993669822087769562644625⟩,⟨355508151529422932224942540335,355508151529422932242927220846⟩⟩,⟨⟨2843906880455151980766977660958,2843906880455151980866834781125⟩,⟨349063991561576249604898983663,349063991561576249622701790691⟩⟩,⟨⟨2845491267226140932112109597038,2845491267226140932212009551910⟩,⟨342644412895467559543600577327,342644412895467559561229585454⟩⟩,⟨⟨2847038298099904604930603379413,2847038298099904605030542130763⟩,⟨336250751907216342865436615298,336250751907216342882882286131⟩⟩,⟨⟨2848548137777788354176620943726,2848548137777788354276599163311⟩,⟨329884339565794681082475411272,329884339565794681099748773724⟩⟩,⟨⟨2850020971227095764863709929016,2850020971227095764963724242972⟩,⟨323546500886617226232732656775,323546500886617226249826775599⟩⟩,⟨⟨2851457003344958714849996612565,2851457003344958714950047080641⟩,⟨317238554394426883469547066774,317238554394426883486470536207⟩⟩,⟨⟨2852856458604808427313717815987,2852856458604808427413800342827⟩,⟨310961811596012487036943276938,310961811596012487053685356914⟩⟩,⟨⟨2854219580685928796182308505448,2854219580685928796282423953824⟩,⟨304717576463271352837806446209,304717576463271352854379680634⟩⟩,⟨⟨2855546632086593912702235805937,2855546632086593912802380926269⟩,⟨298507144927105328179486870493,298507144927105328195884128212⟩⟩,⟨⟨2856837893721311158355127638601,2856837893721311158455302512183⟩,⟨292331804382613902031572836365,292331804382613902047803219271⟩⟩,⟨⟨2858093664502709427980088275532,2858093664502709428080289123991⟩,⟨286192833206022159325909895173,286192833206022159341963084676⟩⟩,⟨⟨2859314260908628981184707659606,2859314260908628981284935187307⟩,⟨280091500283754933759887470737,280091500283754933775775897685⟩⟩,⟨⟨2860500016534985068270086017368,2860500016534985068370337123919⟩,⟨274029064554041509459338043660,274029064554041509475054377680⟩⟩,⟨⟨2861651281634991821736845832327,2861651281634991821837120624372⟩,⟨268006774561407717596436827256,268006774561407717611990669271⟩⟩] +lemma kernel0_0_r0_10_eq : ∀ k : Fin 16, kernel0_0Expr 0 10 k = kernel0_0_r0_10 k := by decide +kernel +noncomputable def kernel0_0_r0_11 : Fin 16 → CBox := ![⟨⟨2862768422645345933174549784653,2862768422645345933274844449636⟩,⟨262025868024384344895473985513,262025868024384344910853450447⟩⟩,⟨⟨2863851821699981339546035656584,2863851821699981339646351125247⟩,⟨256087571416732492244260806195,256087571416732492259480179787⟩⟩,⟨⟨2864901876132016518477712951920,2864901876132016518578046296966⟩,⟨250193099562457968538825945618,250193099562457968553877703569⟩⟩,⟨⟨2865918997964525039342787585661,2865918997964525039443138940602⟩,⟨244343655244858052160927895409,244343655244858052175822118316⟩⟩,⟨⟨2866903613390767740048820613480,2866903613390767740149186574270⟩,⟨238540428829815074167160791586,238540428829815074181886354888⟩⟩,⟨⟨2867856162244531306970982815036,2867856162244531307071364112021⟩,⟨232784597903522346456036200846,232784597903522346470606911269⟩⟩,⟨⟨2868777097461223139834917295757,2868777097461223139935311194475⟩,⟨227077326924799046800109524026,227077326924799046814517660315⟩⟩,⟨⟨2869666884530376200814144653258,2869666884530376200914551316406⟩,⟨221419766892121851200474730519,221419766892121851214730839987⟩⟩,⟨⟨2870526000940220097628193756875,2870526000940220097728609844434⟩,⟨215813055025472441439760345599,215813055025472441453851817180⟩⟩,⟨⟨2871354935614975957509480168028,2871354935614975957609906581920⟩,⟨210258314463071579050876373961,210258314463071579064818758002⟩⟩,⟨⟨2872154188345532739421517262534,2872154188345532739521951479040⟩,⟨204756653973042291247259133758,204756653973042291261044519391⟩⟩,⟨⟨2872924269214161535923309761107,2872924269214161536023751972267⟩,⟨199309167680016922551761116158,199309167680016922565400492616⟩⟩,⟨⟨2873665698013922166656292150366,2873665698013922166756739417951⟩,⟨193916934806675428446372615875,193916934806675428459854032890⟩⟩,⟨⟨2874379003663412998463002951013,2874379003663412998563456019986⟩,⟨188581019430175382377262667155,188581019430175382390601260502⟩⟩,⟨⟨2875064723617510481122350814553,2875064723617510481222807385440⟩,⟨183302470253407790300235577974,183302470253407790313423247339⟩⟩,⟨⟨2875723403274739403497351371288,2875723403274739403597811666386⟩,⟨178082320390987010306802111767,178082320390987010319850269460⟩⟩] +lemma kernel0_0_r0_11_eq : ∀ k : Fin 16, kernel0_0Expr 0 11 k = kernel0_0_r0_11 k := by decide +kernel +noncomputable def kernel0_0_r0_12 : Fin 16 → CBox := ![⟨⟨2876355595381908395619867587842,2876355595381908395720328739031⟩,⟨172921587169857908556726982820,172921587169857908569621676618⟩⟩,⟨⟨2876961859436637772938970376247,2876961859436637773039433323799⟩,⟨167821271944378893653172083075,167821271944378893665930669252⟩⟩,⟨⟨2877542761088398486447558953336,2877542761088398486548021633473⟩,⟨162782359925715703628618777330,162782359925715703641232979099⟩⟩,⟨⟨2878098871538671755025541357066,2878098871538671755126004021133⟩,⟨157805820025357813702065182644,157805820025357813714546802933⟩⟩,⟨⟨2878630766940828963766076188522,2878630766940828963866536428316⟩,⟨152892604712547126665387423217,152892604712547126677723684375⟩⟩,⟨⟨2879139027800320665053625400168,2879139027800320665154083959782⟩,⟨148043649885387235777226914789,148043649885387235789434207377⟩⟩,⟨⟨2879624238375752069393916939927,2879624238375752069494371997570⟩,⟨143259874755381043871340387514,143259874755381043883410260214⟩⟩,⟨⟨2880086986081410312783262360008,2880086986081410312883714196077⟩,⟨138542181745124910369509158723,138542181745124910381453783071⟩⟩,⟨⟨2880527860891796089538287085283,2880527860891796089638733443867⟩,⟨133891456398868805255075605536,133891456398868805266880419478⟩⟩,⟨⟨2880947454748698997035363123797,2880947454748698997135804873534⟩,⟨129308567305634197941944544332,129308567305634197953627902526⟩⟩,⟨⟨2881346360971342204839766590603,2881346360971342204940202155638⟩,⟨124794366034564618441924764106,124794366034564618453478057218⟩⟩,⟨⟨2881725173670107888211391886079,2881725173670107888311821574101⟩,⟨120349687082168014356562844043,120349687082168014367998575442⟩⟩,⟨⟨2882084487164340307610201741994,2882084487164340307710623707111⟩,⟨115975347831095203120281910212,115975347831095203131586486814⟩⟩,⟨⟨2882424895404708523743989218978,2882424895404708523844404188824⟩,⟨111672148520084894840956201772,111672148520084894852147176810⟩⟩,⟨⟨2882746991400595563386296066268,2882746991400595563486702710284⟩,⟨107440872224692944468196261085,107440872224692944479264875087⟩⟩,⟨⟨2883051366652965445291869884766,2883051366652965445392268536998⟩,⟨103282284848411687600002889879,103282284848411687610961949916⟩⟩] +lemma kernel0_0_r0_12_eq : ∀ k : Fin 16, kernel0_0Expr 0 12 k = kernel0_0_r0_12 k := by decide +kernel +noncomputable def kernel0_0_r0_13 : Fin 16 → CBox := ![⟨⟨2883338610593143887710916813414,2883338610593143887811305779631⟩,⟨99197135123774424133077268884,99197135123774424143910868614⟩⟩,⟨⟨2883609310027932797777265336044,2883609310027932797877645466544⟩,⟨95186154623030337770088876494,95186154623030337780817020868⟩⟩,⟨⟨2883864048591462835674881012916,2883864048591462835775251219200⟩,⟨91250057777966374312924797585,91250057777966374323538601248⟩⟩,⟨⟨2884103406204172498829874694804,2884103406204172498930235335021⟩,⟨87389541908444842589305734252,87389541908444842599818263913⟩⟩,⟨⟨2884327958539286327774802986237,2884327958539286327875152776715⟩,⟨83605287259218741500434196563,83605287259218741510831084409⟩⟩,⟨⟨2884538276497149038509746530746,2884538276497149038610086168114⟩,⟨79897957044581045695981049106,79897957044581045706280890590⟩⟩,⟨⟨2884734925687756677141514699067,2884734925687756677241843329222⟩,⟨76268197500399389503650365854,76268197500399389513844161025⟩⟩,⟨⟨2884918465921810310510836273018,2884918465921810310611154276986⟩,⟨72716637943083760872954275830,72716637943083760883055320140⟩⟩,⟨⟨2885089450710602348723149133765,2885089450710602348823455417034⟩,⟨69243890835031939464442852232,69243890835031939474434708723⟩⟩,⟨⟨2885248426775030377330733201169,2885248426775030377431028526207⟩,⟨65850551856095469292552653750,65850551856095469302456088000⟩⟩,⟨⟨2885395933564018391705732219954,2885395933564018391806015956775⟩,⟨62537199980607928750811401421,62537199980607928760617328312⟩⟩,⟨⟨2885532502782610605161495500548,2885532502782610605261768050909⟩,⟨59304397559517130341849107043,59304397559517130351571002664⟩⟩,⟨⟨2885658657929988574781864898880,2885658657929988574882125508314⟩,⟨56152690407163628754254042834,56152690407163628763876826888⟩⟩,⟨⟨2885774913847648281721171287950,2885774913847648281821420612002⟩,⟨53082607892249517764983197451,53082607892249517774526369468⟩⟩,⟨⟨2885881776277960040792588041217,2885881776277960040892825660159⟩,⟨50094663032543931557511908060,50094663032543931566966316446⟩⟩,⟨⟨2885979741433320720137214065326,2885979741433320720237440400155⟩,⟨47189352592874911366392537294,47189352592874911375771801896⟩⟩] +lemma kernel0_0_r0_13_eq : ∀ k : Fin 16, kernel0_0Expr 0 13 k = kernel0_0_r0_13 k := by decide +kernel +noncomputable def kernel0_0_r0_14 : Fin 16 → CBox := ![⟨⟨2886069295576094746137784653435,2886069295576094746237999117021⟩,⟨44367157185961330120492663360,44367157185961330129778930330⟩⟩,⟨⟨2886150914609527769793416359216,2886150914609527769893619664267⟩,⟨41628541375643361592684395355,41628541375643361601900002161⟩⟩,⟨⟨2886225063679804694602706398765,2886225063679804694702898319502⟩,⟨38973953782075511620059596293,38973953782075511629195364227⟩⟩,⟨⟨2886292196789412026534643017263,2886292196789412026634823991669⟩,⟨36403827188452471990748237253,36403827188452471999817873578⟩⟩,⟨⟨2886352756421953215667358618341,2886352756421953215767528357775⟩,⟨33918578648844987068283637034,33918578648844987077271448452⟩⟩,⟨⟨2886407173178554826179813261818,2886407173178554826279972375926⟩,⟨31518609596730513404938162756,31518609596730513413864383641⟩⟩,⟨⟨2886455865425991004126385458486,2886455865425991004226533896134⟩,⟨29204305953811677633912028458,29204305953811677642767475068⟩⟩,⟨⟨2886499238956643816278922605832,2886499238956643816379060820646⟩,⟨26976038238724371941239099932,26976038238724371950037528276⟩⟩,⟨⟨2886537686660407611729838514623,2886537686660407611829966383106⟩,⟨24834161675246743560788068980,24834161675246743569511472178⟩⟩,⟨⟨2886571588208636612377482745211,2886571588208636612477600892622⟩,⟨22779016299630309274381632029,22779016299630309283052591743⟩⟩,⟨⟨2886601309750226468393643070056,2886601309750226468493751598534⟩,⟨20810927066684932274483506086,20810927066684932283092877828⟩⟩,⟨⟨2886627203619912517955577720562,2886627203619912518055677097230⟩,⟨18930203954260411624945442668,18930203954260411633506971656⟩⟩,⟨⟨2886649608058859962740752554199,2886649608058859962840842865484⟩,⟨17137142065778928885599185076,17137142065778928894096687440⟩⟩,⟨⟨2886668846947614105995942457232,2886668846947614106096024268773⟩,⟨15432021730484547519060256967,15432021730484547527514516556⟩⟩,⟨⟨2886685229551472190764819573474,2886685229551472190864893117379⟩,⟨13815108601088344110286575334,13815108601088344118688517808⟩⟩,⟨⟨2886699050278332212811530595764,2886699050278332212911596350948⟩,⟨12286653748500542230667759955,12286653748500542239031073923⟩⟩] +lemma kernel0_0_r0_14_eq : ∀ k : Fin 16, kernel0_0Expr 0 14 k = kernel0_0_r0_14 k := by decide +kernel +noncomputable def kernel0_0_r0_15 : Fin 16 → CBox := ![⟨⟨2886710588449068355060901802548,2886710588449068355160959980847⟩,⟨10846893753354196425035330389,10846893753354196433340848040⟩⟩,⟨⟨2886720108080477385632454449662,2886720108080477385732505620883⟩,⟨9496050794038512188608286894,9496050794038512196879781003⟩⟩,⟨⟨2886727857680835465983565170229,2886727857680835466083609671576⟩,⟨8234332730973765291882288775,8234332730973765300110809584⟩⟩,⟨⟨2886734070058100314140587974358,2886734070058100314240626293970⟩,⟨7061933186873978231281751461,7061933186873978239480862946⟩⟩,⟨⟨2886738962140789544037141421593,2886738962140789544137173908131⟩,⟨5979031622758001237578221294,5979031622758001245731413182⟩⟩,⟨⟨2886742734811562237928678567310,2886742734811562238028705749860⟩,⟨4985793409484408938799604004,4985793409484408946927989290⟩⟩,⟨⟨2886745572753527385899733666466,2886745572753527385999755961341⟩,⟨4082369894600640699811653033,4082369894600640707906440865⟩⟩,⟨⟨2886747644309299724742657680111,2886747644309299724842675582398⟩,⟨3268898464312062553536774043,3268898464312062561611355848⟩⟩,⟨⟨2886749101352820707087316617860,2886749101352820707187330555601⟩,⟨2545502600392091655798625721,2545502600392091663833998593⟩⟩,⟨⟨2886750079173959808804280576875,2886750079173959808904291070416⟩,⟨1912291931870180918420369527,1912291931870180926440119632⟩⟩,⟨⟨2886750696375909115750791726654,2886750696375909115850799244761⟩,⟨1369362281350292895255930151,1369362281350292903251484613⟩⟩,⟨⟨2886751054785382096474047872523,2886751054785382096574052913852⟩,⟨916795705828479482306167345,916795705828479490290673562⟩⟩,⟨⟨2886751239375625641434840968110,2886751239375625641534844014719⟩,⟨554660531894309271527316053,554660531894309279484124933⟩⟩,⟨⟨2886751318202252806957684460038,2886751318202252807057686016054⟩,⟨283011385217129510608921881,283011385217129518559236777⟩⟩,⟨⟨2886751342351902218205843251799,2886751342351902218305843811668⟩,⟨101889214234496900786339479,101889214234496908721848345⟩⟩,⟨⟨2886751345903728734315683452211,2886751345903728734415683514489⟩,⟨11321307976543490696569092,11321307976543498630119723⟩⟩] +lemma kernel0_0_r0_15_eq : ∀ k : Fin 16, kernel0_0Expr 0 15 k = kernel0_0_r0_15 k := by decide +kernel +noncomputable def kernel0_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel0_0_r0_0,kernel0_0_r0_1,kernel0_0_r0_2,kernel0_0_r0_3,kernel0_0_r0_4,kernel0_0_r0_5,kernel0_0_r0_6,kernel0_0_r0_7,kernel0_0_r0_8,kernel0_0_r0_9,kernel0_0_r0_10,kernel0_0_r0_11,kernel0_0_r0_12,kernel0_0_r0_13,kernel0_0_r0_14,kernel0_0_r0_15] +lemma kernel0_0_r0_eq (i k : Fin 16) : kernel0_0Expr 0 i k = kernel0_0_r0 i k := by + fin_cases i + · exact kernel0_0_r0_0_eq k + · exact kernel0_0_r0_1_eq k + · exact kernel0_0_r0_2_eq k + · exact kernel0_0_r0_3_eq k + · exact kernel0_0_r0_4_eq k + · exact kernel0_0_r0_5_eq k + · exact kernel0_0_r0_6_eq k + · exact kernel0_0_r0_7_eq k + · exact kernel0_0_r0_8_eq k + · exact kernel0_0_r0_9_eq k + · exact kernel0_0_r0_10_eq k + · exact kernel0_0_r0_11_eq k + · exact kernel0_0_r0_12_eq k + · exact kernel0_0_r0_13_eq k + · exact kernel0_0_r0_14_eq k + · exact kernel0_0_r0_15_eq k +noncomputable def kernel0_0_r1_0 : Fin 16 → CBox := ![⟨⟨1703663103940905670664679262911,1703663103940905670723695929431⟩,⟨1419712571830655861455358675328,1419712571830655861504539045459⟩⟩,⟨⟨1703715678415708468813345492119,1703715678415708468872364321816⟩,⟨1419702931919201917849777008452,1419702931919201917898957677239⟩⟩,⟨⟨1703820823243414341187747257719,1703820823243414341246770406596⟩,⟨1419683646815201244737535972687,1419683646815201244786717225529⟩⟩,⟨⟨1703978530177566743204134786413,1703978530177566743263164410207⟩,⟨1419654705958707518975694855399,1419654705958707519024876977288⟩⟩,⟨⟨1704188786841840052920751103836,1704188786841840052979789357932⟩,⟨1419616093515401096278878384789,1419616093515401096328061660134⟩⟩,⟨⟨1704451576722076029860001530243,1704451576722076029919050569490⟩,⟨1419567788383313629394688021951,1419567788383313629443872734332⟩⟩,⟨⟨1704766879155674807365748046061,1704766879155674807424810024571⟩,⟨1419509764201802232990277324806,1419509764201802233039463756577⟩⟩,⟨⟨1705134669318348184789364501396,1705134669318348184848441572666⟩,⟨1419441989362780041094414320152,1419441989362780041143602752760⟩⟩,⟨⟨1705554918208244941702755417168,1705554918208244941761849733356⟩,⟨1419364427024211692414678926755,1419364427024211692463869639385⟩⟩,⟨⟨1706027592627459861730015761301,1706027592627459861789129474202⟩,⟨1419277035125883953635971507335,1419277035125883953685164778786⟩⟩,⟨⟨1706552655160940130304300197325,1706552655160940130363435456394⟩,⟨1419179766407463347935090807507,1419179766407463347984286912576⟩⟩,⟨⟨1707130064152804760489587789350,1707130064152804760548746744305⟩,⟨1419072568428854292430807664437,1419072568428854292480006878782⟩⟩,⟨⟨1707759773680094705713455672214,1707759773680094705772640468723⟩,⟨1418955383592872861124276333843,1418955383592872861173478926031⟩⟩,⟨⟨1708441733523973339544008159112,1708441733523973339603220944786⟩,⟨1418828149170252876043644202060,1418828149170252876092850444726⟩⟩,⟨⟨1709175889138399022165153751806,1709175889138399022224396668012⟩,⟨1418690797327002585738093243746,1418690797327002585787303398491⟩⟩,⟨⟨1709962181616293532552859903557,1709962181616293532612135095180⟩,⟨1418543255154131713892765698951,1418543255154131713941980034470⟩⟩] +lemma kernel0_0_r1_0_eq : ∀ k : Fin 16, kernel0_0Expr 1 0 k = kernel0_0_r1_0 k := by decide +kernel +noncomputable def kernel0_0_r1_1 : Fin 16 → CBox := ![⟨⟨1710800547653232226058009007365,1710800547653232226117318609477⟩,⟨1418385444699770148551345237525,1418385444699770148600564005012⟩⟩,⟨⟨1711690919508683880613748611708,1711690919508683880673094767305⟩,⟨1418217283003700991101696343175,1418217283003700991150919809153⟩⟩,⟨⟨1712633224964830322482771599199,1712633224964830322542156437407⟩,⟨1418038682134332090634486071552,1418038682134332090683714477710⟩⟩,⟨⟨1713627387282998075633725133287,1713627387282998075693150793652⟩,⟨1417849549228131550324683865787,1417849549228131550373917473892⟩⟩,⟨⟨1714673325157736458685454841915,1714673325157736458744923444025⟩,⟨1417649786531554004876660069387,1417649786531554004925899105308⟩⟩,⟨⟨1715770952668578760984720388911,1715770952668578761044234071186⟩,⟨1417439291445485728545634560188,1417439291445485728594879285553⟩⟩,⟨⟨1716920179229525365784736475020,1716920179229525365844297349493⟩,⟨1417217956572237838496150545676,1417217956572237838545401174516⟩⟩,⟨⟨1718120909536289954554941112731,1718120909536289954614551313507⟩,⟨1416985669765118004940748390077,1416985669765118004990005178335⟩⟩,⟨⟨1719373043511352222945943093247,1719373043511352223005604718104⟩,⟨1416742314180612164241750414010,1416742314180612164291013551970⟩⟩,⟨⟨1720676476246862866502867912570,1720676476246862866562583096597⟩,⟨1416487768333208750542962321703,1416487768333208750592232069800⟩⟩,⟨⟨1722031097945448953379957887608,1722031097945448953439728720054⟩,⟨1416221906152898912077979271509,1416221906152898912127255807249⟩⟩,⟨⟨1723436793858970192436736964669,1723436793858970192496565574540⟩,⟨1415944597045387056595367492744,1415944597045387056644651068498⟩⟩,⟨⟨1724893444225279028424932326660,1724893444225279028484820783953⟩,⟨1415655705955046872833249198520,1415655705955046872882539959794⟩⟩,⟨⟨1726400924203039951588762816628,1726400924203039951648713253560⟩,⟨1415355093430658698120718059683,1415355093430658698170016268394⟩⟩,⟨⟨1727959103804665896825137229090,1727959103804665896885151705705⟩,⟨1415042615693964742406194589914,1415042615693964742455500377248⟩⟩,⟨⟨1729567847827432127346967806253,1729567847827432127407048447196⟩,⟨1414718124711079232712163244885,1414718124711079232761476863040⟩⟩] +lemma kernel0_0_r1_1_eq : ∀ k : Fin 16, kernel0_0Expr 1 1 k = kernel0_0_r1_1 k := by decide +kernel +noncomputable def kernel0_0_r1_2 : Fin 16 → CBox := ![⟨⟨1731227015782830549154069356560,1731227015782830549214218194324⟩,⟨1414381468266791005567350995941,1414381468266791005616672530052⟩⟩,⟨⟨1732936461824229984956959395246,1732936461824229985017178562938⟩,⟨1414032490041796444727152469595,1414032490041796444776482192256⟩⟩,⟨⟨1734696034672910548750920956523,1734696034672910548811212477701⟩,⟨1413671029692900933800992221586,1413671029692900933850330206832⟩⟩,⟨⟨1736505577542542904042790918654,1736505577542542904103156914718⟩,⟨1413296922936227164589903165571,1413296922936227164639249669964⟩⟩,⟨⟨1738364928062185858636908998766,1738364928062185858697351458877⟩,⟨1412910001633468708320950081975,1412910001633468708370305122485⟩⟩,⟨⟨1740273918197878445533093925755,1740273918197878445593614983295⟩,⟨1412510093881227214868162123729,1412510093881227214917525985196⟩⟩,⟨⟨1742232374172905361313768131203,1742232374172905361374369765142⟩,⟨1412097024103471450798124418925,1412097024103471450847497106506⟩⟩,⟨⟨1744240116386817378620692854484,1744240116386817378681377184343⟩,⟨1411670613147156117009330465836,1411670613147156117058712246029⟩⟩,⟨⟨1746296959333291115945738636957,1746296959333291116006507593928⟩,⟨1411230678381037997203127393594,1411230678381037997252518191839⟩⟩,⟨⟨1748402711516915333761048800243,1748402711516915333821904525633⟩,⟨1410777033797726475811684746420,1410777033797726475861084877138⟩⟩,⟨⟨1750557175368993728537872375795,1750557175368993728598816795018⟩,⟨1410309490119004824729908478130,1410309490119004824779317864975⟩⟩,⟨⟨1752760147162457012761000012972,1752760147162457012822035245391⟩,⟨1409827854904457888711138276082,1409827854904457888760557202243⟩⟩,⟨⟨1755011416925979896708084203959,1755011416925979896769212118660⟩,⟨1409331932663440896100138992306,1409331932663440896149567288344⟩⟩,⟨⟨1757310768357401423357038836708,1757310768357401423418261579516⟩,⟨1408821524970423081262136640522,1408821524970423081311574648051⟩⟩,⟨⟨1759657978736549947889196580835,1759657978736549947950516013736⟩,⟨1408296430583738624266175238755,1408296430583738624315622786412⟩⟩,⟨⟨1762052818837576894198607656074,1762052818837576894260025900260⟩,⟨1407756445567776088820301727895,1407756445567776088869759123430⟩⟩] +lemma kernel0_0_r1_2_eq : ∀ k : Fin 16, kernel0_0Expr 1 2 k = kernel0_0_r1_2 k := by decide +kernel +noncomputable def kernel0_0_r1_3 : Fin 16 → CBox := ![⟨⟨1764495052840906258672182026045,1764495052840906258733700865699⟩,⟨1407201363418636067954700116207,1407201363418636068004167058666⟩⟩,⟨⟨1766984438244909662087905983986,1766984438244909662149527584019⟩,⟨1406630975193285125432710863372,1406630975193285125482187752636⟩⟩,⟨⟨1769520725777419569347041177952,1769520725777419569408767326230⟩,⟨1406045069642232346383312089256,1406045069642232346432798644783⟩⟩,⟨⟨1772103659307196099208888029622,1772103659307196099270720851342⟩,⟨1405443433345752880368471005072,1405443433345752880417967568012⟩⟩,⟨⟨1774732975755465627270470345880,1774732975755465627332411542463⟩,⟨1404825850853680771346634213847,1404825850853680771396140361469⟩⟩,⟨⟨1777408405007652139904573590239,1777408405007652139966625334738⟩,⟨1404192104828791119250747573561,1404192104828791119300263749229⟩⟩,⟨⟨1780129669825425019253966495080,1780129669825425019316130489678⟩,⟨1403541976193789204820938007863,1403541976193789204870463806946⟩⟩,⟨⟨1782896485759189623934481754087,1782896485759189623996760130426⟩,⟨1402875244281921630762671545600,1402875244281921630812207352671⟩⟩,⟨⟨1785708561061149670825439675845,1785708561061149670887834019332⟩,⟨1402191686991221786289737347173,1402191686991221786339282563986⟩⟩,⟨⟨1788565596599073013969473185976,1788565596599073014031985701496⟩,⟨1401491080942399026926944405092,1401491080942399026976499567408⟩⟩,⟨⟨1791467285770894950662261562940,1791467285770894950724893854565⟩,⟨1400773201640377875595755062836,1400773201640377875645319626430⟩⟩,⟨⟨1794413314420295655538115314292,1794413314420295655600869522676⟩,⟨1400037823639490293245977266052,1400037823639490293295551669901⟩⟩,⟨⟨1797403360753390743862813384911,1797403360753390743925690987928⟩,⟨1399284720712320636656874227790,1399284720712320636706457721149⟩⟩,⟨⟨1800437095256676288111202444116,1800437095256676288174205659947⟩,⟨1398513666022199316827229756883,1398513666022199316876822940803⟩⟩,⟨⟨1803514180616371849790043648589,1803514180616371849853173969958⟩,⟨1397724432299337393225982055232,1397724432299337393275584229886⟩⟩,⟨⟨1806634271639307233707036375531,1806634271639307233770295954904⟩,⟨1396916792020590387024424197233,1396916792020590387074035868117⟩⟩] +lemma kernel0_0_r1_3_eq : ∀ k : Fin 16, kernel0_0Expr 1 3 k = kernel0_0_r1_3 k := by decide +kernel +noncomputable def kernel0_0_r1_4 : Fin 16 → CBox := ![⟨⟨1809797015175500716620085914948,1809797015175500716683476072670⟩,⟨1396090517592835470558318596155,1396090517592835470607938778221⟩⟩,⟨⟨1813002050042578438367633960851,1813002050042578438431156967405⟩,⟨1395245381539941891310668006882,1395245381539941891360297444318⟩⟩,⟨⟨1816249006952186462940478119647,1816249006952186463004135342486⟩,⟨1394381156693310017674627305531,1394381156693310017724265126645⟩⟩,⟨⟨1819537508438548711099016615409,1819537508438548711162810221605⟩,⟨1393497616385949752053655974692,1393497616385949752103302764381⟩⟩,⟨⟨1822867168789325526505255698623,1822867168789325526569186878620⟩,⟨1392594534650064246293789344929,1392594534650064246343443943297⟩⟩,⟨⟨1826237593978929055227145165883,1826237593978929055291216203636⟩,⟨1391671686418099877257420929885,1391671686418099877307084162108⟩⟩,⟨⟨1829648381604452885065491101161,1829648381604452885129703224051⟩,⟨1390728847727218299218073247055,1390728847727218299267744052795⟩⟩,⟨⟨1833099120824374497531772084007,1833099120824374497596127476797⟩,⟨1389765795927141087818116431708,1389765795927141087867795489373⟩⟩,⟨⟨1836589392300190022469322774850,1836589392300190022533822429187⟩,⟨1388782309891312031197161386207,1388782309891312031246847247598⟩⟩,⟨⟨1840118768141141544202213144335,1840118768141141544266859414295⟩,⟨1387778170231316511667437909282,1387778170231316511717131591328⟩⟩,⟨⟨1843686811852197779621538232023,1843686811852197779686332189610⟩,⟨1386753159514491660586854043782,1386753159514491660636554280794⟩⟩,⟨⟨1847293078285449323671599228345,1847293078285449323736543079061⟩,⟨1385707062484655064980110272961,1385707062484655065029817851653⟩⟩,⟨⟨1850937113595079827186349888245,1850937113595079827251444464055⟩,⟨1384639666285873762632376676444,1384639666285873762682089942076⟩⟩,⟨⟨1854618455196074426897690041630,1854618455196074426962937715374⟩,⟨1383550760689189089018576970122,1383550760689189089068297048546⟩⟩,⟨⟨1858336631726826478708804583828,1858336631726826478774206256122⟩,⟨1382440138322206641276110094409,1382440138322206641325835497599⟩⟩,⟨⟨1862091163015803144112857439487,1862091163015803144178415339856⟩,⟨1381307594901454208782390234915,1381307594901454208832121873845⟩⟩] +lemma kernel0_0_r1_4_eq : ∀ k : Fin 16, kernel0_0Expr 1 4 k = kernel0_0_r1_4 k := by decide +kernel +noncomputable def kernel0_0_r1_5 : Fin 16 → CBox := ![⟨⟨1865881560052429637184012516189,1865881560052429637249727219210⟩,⟨1380152929467403994632718260234,1380152929467403994682454111240⟩⟩,⟨⟨1869707324962350947278462930093,1869707324962350947344336911692⟩,⟨1378975944622048825875810609651,1378975944622048825925552068622⟩⟩,⟨⟨1873567950987228602056161083713,1873567950987228602122195056841⟩,⟨1377776446768915331781927699768,1377776446768915331831673039856⟩⟩,⟨⟨1877462922469228518494907721843,1877462922469228518561103943195⟩,⟨1376554246355390268303863474339,1376554246355390268353613747138⟩⟩,⟨⟨1881391714840354198305851327872,1881391714840354198372210193860⟩,⟨1375309158117229293442178823380,1375309158117229293491931791072⟩⟩,⟨⟨1885353794616777450960081420467,1885353794616777451026605418103⟩,⟨1374041001325110563226365858008,1374041001325110563276123032919⟩⟩,⟨⟨1889348619398316465122236056453,1889348619398316465188925694140⟩,⟨1372749600033088532840459525332,1372749600033088532890218925098⟩⟩,⟨⟨1893375637873208390753869078521,1893375637873208390820726643604⟩,⟨1371434783328796324001301324568,1371434783328796324051064159049⟩⟩,⟨⟨1897434289828320633002949340078,1897434289828320633069974922208⟩,⟨1370096385585237970560038332291,1370096385585237970609801934697⟩⟩,⟨⟨1901524006164941789191919255620,1901524006164941789259115467419⟩,⟨1368734246714004792526414082004,1368734246714004792576180296484⟩⟩,⟨⟨1905644208920289576199823945632,1905644208920289576267191074079⟩,⟨1367348212419743087948936998362,1367348212419743087998703571195⟩⟩,⟨⟨1909794311294869192276518196401,1909794311294869192344058562788⟩,⟨1365938134455693286499874725040,1365938134455693286549643042169⟩⟩,⟨⟨1913973717685811330369017261739,1913973717685811330436730745548⟩,⟨1364503870880113692914951468251,1364503870880113692964718620236⟩⟩,⟨⟨1918181823726314505528450741468,1918181823726314505596339971343⟩,⟨1363045286313394977831919793880,1363045286313394977881687773902⟩⟩,⟨⟨1922418016331311473694012536614,1922418016331311473762077560862⟩,⟨1361562252195664663753726933378,1361562252195664663803493200531⟩⟩,⟨⟨1926681673749474300595698791448,1926681673749474300663941968976⟩,⟨1360054647044674020985530894321,1360054647044674021035297029676⟩⟩] +lemma kernel0_0_r1_5_eq : ∀ k : Fin 16, kernel0_0Expr 1 5 k = kernel0_0_r1_5 k := by decide +kernel +noncomputable def kernel0_0_r1_6 : Fin 16 → CBox := ![⟨⟨1930972165621667085882092694805,1930972165621667085950513518102⟩,⟨1358522356713753049050585510614,1358522356713753049100348064485⟩⟩,⟨⟨1935288853045949457825281199733,1935288853045949457893882475905⟩,⟨1356965274649612590273468875129,1356965274649612590323230289802⟩⟩,⟨⟨1939631088649227727842549329503,1939631088649227727911330851486⟩,⟨1355383302149766121300167026467,1355383302149766121349924459525⟩⟩,⟨⟨1943998216665644032197231759452,1943998216665644032266195927074⟩,⟨1353776348619337413011538947231,1353776348619337413061294193652⟩⟩,⟨⟨1948389573021786892060575781355,1948389573021786892129721873928⟩,⟨1352144331827014057590304776072,1352144331827014057640054168687⟩⟩,⟨⟨1952804485428799394994509769582,1952804485428799395063840586611⟩,⟨1350487178159900851693188985333,1350487178159900851742935099454⟩⟩,⟨⟨1957242273481453644145819725661,1957242273481453644215334787669⟩,⟨1348804822877021215249452407076,1348804822877021215299192084281⟩⟩,⟨⟨1961702248764252240280074942588,1961702248764252240349776694218⟩,⟨1347097210361209235016903625772,1347097210361209235066638895133⟩⟩,⟨⟨1966183714964609361471936849799,1966183714964609361541824133931⟩,⟨1345364294369129569463681537740,1345364294369129569513408137333⟩⟩,⟨⟨1970685967993155492062993878254,1970685967993155492133069696091⟩,⟨1343606038279157355668373152730,1343606038279157355718094172836⟩⟩,⟨⟨1975208296111201033690344406109,1975208296111201033760607989746⟩,⟨1341822415336845438622849476820,1341822415336845438672561430532⟩⟩,⟨⟨1979749980065384915124356547945,1979749980065384915194810390303⟩,⟨1340013408897701717425592553614,1340013408897701717475297723652⟩⟩,⟨⟨1984310293229524913749501153631,1984310293229524913820143851394⟩,⟨1338179012666995190119460610033,1338179012666995190169154490029⟩⟩,⟨⟨1988888501753676720278976101934,1988888501753676720349810656607⟩,⟨1336319230936305397953567004141,1336319230936305398003252858457⟩⟩,⟨⟨1993483864720398831307947427823,1993483864720398831378972767111⟩,⟨1334434078816526439016308239504,1334434078816526439065982240338⟩⟩,⟨⟨1998095634308210154277794591838,1998095634308210154349013260998⟩,⟨1332523582467033558597597972488,1332523582467033558647262676955⟩⟩] +lemma kernel0_0_r1_6_eq : ∀ k : Fin 16, kernel0_0Expr 1 6 k = kernel0_0_r1_6 k := by decide +kernel +noncomputable def kernel0_0_r1_7 : Fin 16 → CBox := ![⟨⟨2002723055962216770144750866856,2002723055962216770216160927025⟩,⟨1330587779320717547051541758990,1330587779320717547101191925047⟩⟩,⟨⟨2007365368571873635422248222113,2007365368571873635493852951577⟩,⟨1328626718304589802692766366100,1328626718304589802742405930175⟩⟩,⟨⟨2012021804655836133295681456946,2012021804655836133367479464746⟩,⟨1326640460055658964239354356583,1326640460055658964288979140353⟩⟩,⟨⟨2016691590553845320276144711321,2016691590553845320348138598417⟩,⟨1324629077131778500833722448105,1324629077131778500883335302445⟩⟩,⟨⟨2021373946625579478524343113628,2021373946625579478596530716034⟩,⟨1322592654217163583435463768188,1322592654217163583485059273849⟩⟩,⟨⟨2026068087456393193749456142791,2026068087456393193821840696489⟩,⟨1320531288322274964406080659814,1320531288322274964455662879945⟩⟩,⟨⟨2030773222069853654714098277495,2030773222069853654786678058487⟩,⟨1318445088977767476659453749070,1318445088977767476709018144590⟩⟩,⟨⟨2035488554146972234102284153471,2035488554146972234175061822972⟩,⟨1316334178422201143273163916215,1316334178422201143322713653005⟩⟩,⟨⟨2040213282252017684050381435113,2040213282252017684123354249004⟩,⟨1314198691783213775491737019055,1314198691783213775541265895618⟩⟩,⟨⟨2044946600064785486152030029006,2044946600064785486225201524982⟩,⟨1312038777251855343188917332521,1312038777251855343238430152502⟩⟩,⟨⟨2049687696619186059269235288179,2049687696619186059342603397296⟩,⟨1309854596249786337651322598289,1309854596249786337700814455131⟩⟩,⟨⟨2054435756548002673898977403703,2054435756548002673972544850823⟩,⟨1307646323589044821465916282345,1307646323589044821515390675823⟩⟩,⟨⟨2059189960333658074836219519102,2059189960333658074909983308907⟩,⟨1305414147624089882650028340208,1305414147624089882699478873519⟩⟩,⟨⟨2063949484564817000853467400863,2063949484564817000927431037880⟩,⟨1303158270395832787049059502046,1303158270395832787098491148051⟩⟩,⟨⟨2068713502198640038172303615238,2068713502198640038246464673899⟩,⟨1300878907767371260264187590044,1300878907767371260313595067514⟩⟩,⟨⟨2073481182828492581329509429539,2073481182828492581403870703084⟩,⟨1298576289551147032450073160330,1298576289551147032499460323524⟩⟩] +lemma kernel0_0_r1_7_eq : ∀ k : Fin 16, kernel0_0Expr 1 7 k = kernel0_0_r1_7 k := by decide +kernel +noncomputable def kernel0_0_r1_8 : Fin 16 → CBox := ![⟨⟨2078251692956901128874196278768,2078251692956901128948754062773⟩,⟨1296250659627252049350065445035,1296250659627252049399424918066⟩⟩,⟨⟨2083024196273537740870186009886,2083024196273537740944944226441⟩,⟨1293902276052614592591817108613,1293902276052614592641154829687⟩⟩,⟨⟨2087797853938002259502586967821,2087797853938002259577542826227⟩,⟨1291531411160802961754687234030,1291531411160802961803997544335⟩⟩,⟨⟨2092571824867160872583331071573,2092571824867160872658487436660⟩,⟨1289138351652191348731421845035,1289138351652191348780708970586⟩⟩,⟨⟨2097345266026788812018261976941,2097345266026788812093614963134⟩,⟨1286723398674240078581793997576,1286723398674240078631050511701⟩⟩,⟨⟨2102117332727254455064450026980,2102117332727254455140003441881⟩,⟨1284286867891650495975195169863,1284286867891650496024427062779⟩⟩,⟨⟨2106887178922971865231311750112,2106887178922971865307062429312⟩,⟨1281829089546163436399028446346,1281829089546163436448229677176⟩⟩,⟨⟨2111653957515338901660455058891,2111653957515338901736405943966⟩,⟨1279350408505779428900416364129,1279350408505779428949591550369⟩⟩,⟨⟨2116416820658868470295389766318,2116416820658868470371536244878⟩,⟨1276851184303188522923399854399,1276851184303188522972540581094⟩⟩,⟨⟨2121174920070211316400785583768,2121174920070211316477131890712⟩,⟨1274331791163207904847729606163,1274331791163207904896842866441⟩⟩,⟨⟨2125927407339759994928336964386,2125927407339759995004879556931⟩,⟨1271792618019036257527312944269,1271792618019036257576392315751⟩⟩,⟨⟨2130673434245515331303254037123,2130673434245515331379995936814⟩,⟨1269234068517145104220286296725,1269234068517145104269336803759⟩⟩,⟨⟨2135412153068888828304932521529,2135412153068888828381868907526⟩,⟨1266656561010639150922132180425,1266656561010639150971145325978⟩⟩,⟨⟨2140142716912107112046485031851,2140142716912107112123620050153⟩,⟨1264060528540929880766162391277,1264060528540929880815145285636⟩⟩,⟨⟨2144864280016877668053339280717,2144864280016877668130669005581⟩,⟨1261446418807579341762446574589,1261446418807579341811392412782⟩⟩,⟨⟨2149575998083968822651916925201,2149575998083968822729444463295⟩,⟨1258814694126184184067932661821,1258814694126184184116846892549⟩⟩] +lemma kernel0_0_r1_8_eq : ∀ k : Fin 16, kernel0_0Expr 1 8 k = kernel0_0_r1_8 k := by decide +kernel +noncomputable def kernel0_0_r1_9 : Fin 16 → CBox := ![⟨⟨2154277028593351199873761731242,2154277028593351199951481391708⟩,⟨1256165831374183523060678365263,1256165831374183523109551268395⟩⟩,⟨⟨2158966531124542753340761184996,2158966531124542753418677685109⟩,⟨1253500321924488106097696258394,1253500321924488106146536213781⟩⟩,⟨⟨2163643667676794958422598186584,2163643667676794958500707217837⟩,⟨1250818671566842518916786043792,1250818671566842518965585868862⟩⟩,⟨⟨2168307602988753873365605911816,2168307602988753873443910668623⟩,⟨1248121400416846755780888736775,1248121400416846755829654316313⟩⟩,⟨⟨2172957504857226558726480022777,2172957504857226558804974722054⟩,⟨1245409042812578367946235169273,1245409042812578367994956910423⟩⟩,⟨⟨2177592544454680800482261913402,2177592544454680800560951073294⟩,⟨1242682147198771568922368087398,1242682147198771568971054312049⟩⟩,⟨⟨2182211896645104230256638013178,2182211896645104230335516941915⟩,⟨1239941275998525082196722082055,1239941275998525082245365231652⟩⟩,⟨⟨2186814740297847791194106512824,2186814740297847791273178497897⟩,⟨1237187005472526136466932367949,1237187005472526136515538778449⟩⟩,⟨⟨2191400258599078073410422921680,2191400258599078073489681314360⟩,⟨1234419925565793812836611896786,1234419925565793812885170763349⟩⟩,⟨⟨2195967639360463350148445119409,2195967639360463350227895014787⟩,⟨1231640639741960894880499465678,1231640639741960894929020402284⟩⟩,⟨⟨2200516075324719194423700233710,2200516075324719194503336561398⟩,⟨1228849764805129432191854644692,1228849764805129432240329725093⟩⟩,⟨⟨2205044764467641353793961320624,2205044764467641353873787463553⟩,⟨1226047930709351366532534386563,1226047930709351366580970406080⟩⟩,⟨⟨2209552910296256113710564682132,2209552910296256113790573886084⟩,⟨1223235780355801751996235217568,1223235780355801752044621474532⟩⟩,⟨⟨2214039722142721691473891797979,2214039722142721691554088985964⟩,⟨1220413969377728291196693067375,1220413969377728291245039174577⟩⟩,⟨⟨2218504415453618274841095443559,2218504415453618274921475170836⟩,⟨1217583165913277072601845543842,1217583165913277072650143212390⟩⟩,⟨⟨2222946212074269151457551679677,2222946212074269151538117429381⟩,⟨1214744050366310493731568573299,1214744050366310493779825068815⟩⟩] +lemma kernel0_0_r1_9_eq : ∀ k : Fin 16, kernel0_0Expr 1 9 k = kernel0_0_r1_9 k := by decide +kernel +noncomputable def kernel0_0_r1_10 : Fin 16 → CBox := ![⟨⟨2227364340527740965036463896106,2227364340527740965117207860407⟩,⟨1211897315155349354909206235348,1211897315155349354957409310668⟩⟩,⟨⟨2231758036288177477000934519165,2231758036288177477081862403382⟩,⟨1209043664450786972522524008135,1209043664450786972570684932288⟩⟩,⟨⟨2236126542048128301406572954399,2236126542048128301487678949606⟩,⟨1206183813900538853382461188763,1206183813900538853430571323236⟩⟩,⟨⟨2240469107979541907523454302656,2240469107979541907604741992937⟩,⟨1203318490344306957121316188843,1203318490344306957169383271743⟩⟩,⟨⟨2244784991988100737493754130440,2244784991988100737575215802606⟩,⟨1200448431516652816408176785189,1200448431516652816456189009108⟩⟩,⟨⟨2249073459960585552905102368053,2249073459960585552986743377771⟩,⟨1197574385739088750370399892046,1197574385739088750418368219927⟩⟩,⟨⟨2253333786004966088755862346182,2253333786004966088837676528267⟩,⟨1194697111601411060946420609753,1194697111601411060994336060297⟩⟩,⟨⟨2257565252682925738909714284519,2257565252682925738991705328747⟩,⟨1191817377632513411684093264711,1191817377632513411731964055855⟩⟩,⟨⟨2261767151234539304505463866120,2261767151234539304587623069385⟩,⟨1188935961960932521368725564288,1188935961960932521416538434791⟩⟩,⟨⟨2265938781794834784701708156287,2265938781794834784784041618594⟩,⟨1186053651965391829458554713149,1186053651965391829506322219445⟩⟩,⟨⟨2270079453601982754487489741378,2270079453601982754569990955651⟩,⟨1183171243915621876398430397058,1183171243915621876446143230823⟩⟩,⟨⟨2274188485196870032127806844309,2274188485196870032210479605836⟩,⟨1180289542603748760488790456685,1180289542603748760536457312807⟩⟩,⟨⟨2278265204613828062415546042084,2278265204613828062498381708329⟩,⟨1177409360966554156469501000696,1177409360966554156517108979711⟩⟩,⟨⟨2282308949562300702853285441555,2282308949562300702936289824884⟩,⟨1174531519698921983143609937135,1174531519698921983191171392532⟩⟩,⟨⟨2286319067599250868167508321396,2286319067599250868250674585145⟩,⟨1171656846858797863565868382788,1171656846858797863613373689357⟩⟩,⟨⟨2290294916292120732624144896272,2290294916292120732707476944361⟩,⟨1168786177463998008534249564418,1168786177463998008581707895190⟩⟩] +lemma kernel0_0_r1_10_eq : ∀ k : Fin 16, kernel0_0Expr 1 10 k = kernel0_0_r1_10 k := by decide +kernel +noncomputable def kernel0_0_r1_11 : Fin 16 → CBox := ![⟨⟨2294235863372175876510651085835,2294235863372175876594139085784⟩,⟨1165920353081214051044785551798,1165920353081214051092182174842⟩⟩,⟨⟨2298141286878079858600788741257,2298141286878079858684439480194⟩,⟨1163060221407569646481870108320,1163060221407569646529219370731⟩⟩,⟨⟨2302010575289562164941803453077,2302010575289562165025609784022⟩,⟨1160206635845093312958643966410,1160206635845093313005935946445⟩⟩,⟨⟨2305843127651059289319841356539,2305843127651059289403807289336⟩,⟨1157360455068480002650941992256,1157360455068480002698186330441⟩⟩,⟨⟨2309638353685225804709999321846,2309638353685225804794115333628⟩,⟨1154522542586521254412910696694,1154522542586521254460093431226⟩⟩,⟨⟨2313395673896229649482047688010,2313395673896229649566320062643⟩,⟨1151693766297590468664324056986,1151693766297590468711458944133⟩⟩,⟨⟨2317114519662763437955236355971,2317114519662763438039657651015⟩,⟨1148874998039575857795021291792,1148874998039575857842098124512⟩⟩,⟨⟨2320794333320721372304577714811,2320794333320721372389152048214⟩,⟨1146067113134658951513262466906,1146067113134658951560291349547⟩⟩,⟨⟨2324434568235509241560708769124,2324434568235509241645425518259⟩,⟨1143270989929341171146147819812,1143270989929341171193113076696⟩⟩,⟨⟨2328034688863973002899329576867,2328034688863973002984195944937⟩,⟨1140487509330124926461303467221,1140487509330124926508220745725⟩⟩,⟨⟨2331594170805949509738789593235,2331594170805949509823797864570⟩,⟨1137717554335258931813041047780,1137717554335258931859899878272⟩⟩,⟨⟨2335112500845461039405695839597,2335112500845461039490850235628⟩,⟨1134962009562959986116481665272,1134962009562959986163292598869⟩⟩,⟨⟨2338589176981593339365160131619,2338589176981593339450450311228⟩,⟨1132221760776525316203659193859,1132221760776525316250407245488⟩⟩,⟨⟨2342023708449114914470319545126,2342023708449114914555752270934⟩,⟨1129497694406750750459889585775,1129497694406750750506589902045⟩⟩,⟨⟨2345415615728913177868269601744,2345415615728913177953836902804⟩,⟨1126790697072070476253519952939,1126790697072070476300161815937⟩⟩,⟨⟨2348764430548340845005516127289,2348764430548340845091222328134⟩,⟨1124101655096833949519898667900,1124101655096833949566493064528⟩⟩] +lemma kernel0_0_r1_11_eq : ∀ k : Fin 16, kernel0_0Expr 1 11 k = kernel0_0_r1_11 k := by decide +kernel +noncomputable def kernel0_0_r1_12 : Fin 16 → CBox := ![⟨⟨2352069695871583524023230643242,2352069695871583524109064020330⟩,⟨1121431454028134678846284884923,1121431454028134678892814572552⟩⟩,⟨⟨2355330965880176807769672886295,2355330965880176807855641438887⟩,⟨1118780978151604112313018920073,1118780978151604112359501485475⟩⟩,⟨⟨2358547805943818264479658073595,2358547805943818264565753601377⟩,⟨1116151110006581727783830853220,1116151110006581727830255358004⟩⟩,⟨⟨2361719792581636518525246528761,2361719792581636518611473450783⟩,⟨1113542729901069682654301902208,1113542729901069682700679742358⟩⟩,⟨⟨2364846513414096073132171094263,2364846513414096073218518327496⟩,⟨1110956715426877035284055642563,1110956715426877035330370865962⟩⟩,⟨⟨2367927567105732618238967763964,2367927567105732618325442543289⟩,⟨1108393940975354627057592662168,1108393940975354627103861758637⟩⟩,⟨⟨2370962563298929254554949937118,2370962563298929254641543851479⟩,⟨1105855277254117232340603262072,1105855277254117232386815087359⟩⟩,⟨⟨2373951122538959316384986263486,2373951122538959316471703824519⟩,⟨1103341590805144566017489976586,1103341590805144566063656319760⟩⟩,⟨⟨2376892876190536259285515846027,2376892876190536259372344769059⟩,⟨1100853743524647208607113102173,1100853743524647208653216023184⟩⟩,⟨⟨2379787466346125363835934899082,2379787466346125363922883508962⟩,⟨1098392592185077492141708021935,1098392592185077492187766179896⟩⟩,⟨⟨2382634545726285764949610610692,2382634545726285765036670312621⟩,⟨1095958987959658912129879372792,1095958987959658912175881447177⟩⟩,⟨⟨2385433777572324519922432458890,2385433777572324520009607846058⟩,⟨1093553775949800719047531160186,1093553775949800719093489299976⟩⟩,⟨⟨2388184835531557052111798627287,2388184835531557052199077956308⟩,⟨1091177794715757024809438050423,1091177794715757024855335400225⟩⟩,⟨⟨2390887403535480326661191820000,2390887403535480326748582781656⟩,⟨1088831875810882064202734312928,1088831875810882064248588632360⟩⟩,⟨⟨2393541175671176507604283358669,2393541175671176507691777194914⟩,⟨1086516843319825207569277001626,1086516843319825207615076812382⟩⟩,⟨⟨2396145856046275591260119513760,2396145856046275591347720893555⟩,⟨1084233513401000958859796457738,1084233513401000958905554244136⟩⟩] +lemma kernel0_0_r1_12_eq : ∀ k : Fin 16, kernel0_0Expr 1 12 k = kernel0_0_r1_12 k := by decide +kernel +noncomputable def kernel0_0_r1_13 : Fin 16 → CBox := ![⟨⟨2398701158647815590054055810870,2398701158647815590141751500262⟩,⟨1081982693833660522684562367034,1081982693833660522730258721168⟩⟩,⟨⟨2401206807195348236494840286307,2401206807195348236582639384192⟩,⟨1079765183569882615542510759275,1079765183569882615588166161785⟩⟩,⟨⟨2403662534988646873492123382977,2403662534988646873580016997476⟩,⟨1077581772291792060554030486408,1077581772291792060599633336397⟩⟩,⟨⟨2406068084750381180757437678476,2406068084750381180845430538421⟩,⟨1075433239974305372296470590534,1075433239974305372342033664280⟩⟩,⟨⟨2408423208464130645708540820075,2408423208464130645796620612095⟩,⟨1073320356453693039194296501292,1073320356453693039239802124279⟩⟩,⟨⟨2410727667208115210861671295417,2410727667208115210949846132238⟩,⟨1071243881002238575575698880758,1071243881002238575621165970080⟩⟩,⟨⟨2412981230985027309668327336617,2412981230985027309756588212346⟩,⟨1069204561909264673876562910719,1069204561909264673921979761978⟩⟩,⟨⟨2415183678548354532380749495937,2415183678548354532469101191259⟩,⟨1067203136068786969008734885050,1067203136068786969054114536738⟩⟩,⟨⟨2417334797225586437772161866807,2417334797225586437860590765029⟩,⟨1065240328574046060526137358538,1065240328574046060571459871663⟩⟩,⟨⟨2419434382738702542031791616382,2419434382738702542120307075499⟩,⟨1063316852319158552177494923020,1063316852319158552222781628146⟩⟩,⟨⟨2421482239022341271189978238134,2421482239022341271278571167622⟩,⟨1061433407608117990238953223052,1061433407608117990284192349756⟩⟩,⟨⟨2423478178040051657905183579124,2423478178040051657993858792512⟩,⟨1059590681771366738333972544970,1059590681771366738379177344045⟩⟩,⟨⟨2425422019599030798837155330534,2425422019599030798925900034752⟩,⟨1057789348790150042999170457686,1057789348790150043044322529602⟩⟩,⟨⟨2427313591163750568139762017475,2427313591163750568228584701318⟩,⟨1056030068928853845744452038113,1056030068928853845789571317673⟩⟩,⟨⟨2429152727668876810317599991559,2429152727668876810406491500786⟩,⟨1054313488375518307387004358595,1054313488375518307432079033102⟩⟩,⟨⟨2430939271331883217715724155064,2430939271331883217804689323559⟩,⟨1052640238890709551434028713107,1052640238890709551479072207168⟩⟩] +lemma kernel0_0_r1_13_eq : ∀ k : Fin 16, kernel0_0Expr 1 13 k = kernel0_0_r1_13 k := by decide +kernel +noncomputable def kernel0_0_r1_14 : Fin 16 → CBox := ![⟨⟨2432673071465760341545896108410,2432673071465760341634920434865⟩,⟨1051010937464922826429692814935,1051010937464922826474683694032⟩⟩,⟨⟨2434353984292217699211151838832,2434353984292217699300245479136⟩,⟨1049426185984681152336757235470,1049426185984681152381718588841⟩⟩,⟨⟨2435981872755773734658413765132,2435981872755773734747567533204⟩,⟨1047886570907484571701130416112,1047886570907484571746050433860⟩⟩,⟨⟨2437556606339124473658577848969,2437556606339124473747796574058⟩,⟨1046392662945756389637335693681,1046392662945756389682227913087⟩⟩,⟨⟨2439078060880177104530343665095,2439078060880177104619614171525⟩,⟨1044945016759924273208721937096,1044945016759924273253567354152⟩⟩,⟨⟨2440546118391129420222083989465,2440546118391129420311415075855⟩,⟨1043544170660765804690812767333,1043544170660765804735632153038⟩⟩,⟨⟨2441960666879970094213286268792,2441960666879970094302668736646⟩,⟨1042190646321140057108030041096,1042190646321140057152811612526⟩⟩,⟨⟨2443321600174768145731072784658,2443321600174768145820511444125⟩,⟨1040884948497218995374054327878,1040884948497218995418811692595⟩⟩,⟨⟨2444628817751112695550489281436,2444628817751112695639969549792⟩,⟨1039627564759325011827473131309,1039627564759325011872184762342⟩⟩,⟨⟨2445882224563056239263782228715,2445882224563056239353314281292⟩,⟨1038418965232473688831896442443,1038418965232473688876585719367⟩⟩,⟨⟨2447081730877906188266630556982,2447081730877906188356205214236⟩,⟨1037259602346713949712366504955,1037259602346713949757021719126⟩⟩,⟨⟨2448227252115200368458762149216,2448227252115200368548384174332⟩,⟨1036149910597351117342674990339,1036149910597351117387309753162⟩⟩,⟨⟨2449318708690192542120570134651,2449318708690192542210226063817⟩,⟨1035090306315132050317352397150,1035090306315132050361947231900⟩⟩,⟨⟨2450356025862163849563526524293,2450356025862163849653225388474⟩,⟨1034081187446465471398514376827,1034081187446465471443090684982⟩⟩,⟨⟨2451339133587865374500494021954,2451339133587865374590226682305⟩,⟨1033122933343744841834338467353,1033122933343744841878884645715⟩⟩,⟨⟨2452267966380385841711260176289,2452267966380385841801031329050⟩,⟨1032215904565835666682890285333,1032215904565835666727419897117⟩⟩] +lemma kernel0_0_r1_14_eq : ∀ k : Fin 16, kernel0_0Expr 1 14 k = kernel0_0_r1_14 k := by decide +kernel +noncomputable def kernel0_0_r1_15 : Fin 16 → CBox := ![⟨⟨2453142463173726779043793157491,2453142463173726779133587534730⟩,⟨1031360442688783937427940496188,1031360442688783937472430796730⟩⟩,⟨⟨2453962567193355340084510167108,2453962567193355340174338577579⟩,⟨1030556870126797524459689254260,1030556870126797524504164958039⟩⟩,⟨⟨2454728225832992411341834581932,2454728225832992411431687962034⟩,⟨1029805489963547717510783843674,1029805489963547717555233508880⟩⟩,⟨⟨2455439390537880641261218246585,2455439390537880641351101191721⟩,⟨1029106585793833769601357166042,1029106585793833769645794230473⟩⟩,⟨⟨2456096016694763650892905441530,2456096016694763650982804304776⟩,⟨1028460421575649220846249101454,1028460421575649220890653781446⟩⟩,⟨⟨2456698063528793940913804366150,2456698063528793941003728311002⟩,⟨1027867241492684952723875142256,1027867241492684952768269220590⟩⟩,⟨⟨2457245494007572920563850496289,2457245494007572920653790555743⟩,⟨1027327269827300339998524638854,1027327269827300340042896867921⟩⟩,⟨⟨2457738274752512074716429862792,2457738274752512074806390509251⟩,⟨1026840710843990514167384863303,1026840710843990514211748499840⟩⟩,⟨⟨2458176375957689579779564797921,2458176375957689579869530880802⟩,⟨1026407748683374615728558627606,1026407748683374615772891153267⟩⟩,⟨⟨2458559771316361701604089524052,2458559771316361701694071683715⟩,⟨1026028547266726978373364961379,1026028547266726978417690895963⟩⟩,⟨⟨2458888437955273083389912434212,2458888437955273083479901835747⟩,⟨1025703250211070441092013331497,1025703250211070441136321680995⟩⟩,⟨⟨2459162356376894583187694245988,2459162356376894583277695201940⟩,⟨1025431980754848407970752079868,1025431980754848408015055837874⟩⟩,⟨⟨2459381510409701673556093666443,2459381510409701673646092454717⟩,⟨1025214841694189853190705577248,1025214841694189853234984836100⟩⟩,⟨⟨2459545887166590594906739469344,2459545887166590594996745274111⟩,⟨1025051915329779182741459799545,1025051915329779182785736450379⟩⟩,⟨⟨2459655477011513483780114121480,2459655477011513483870118265297⟩,⟨1024943263424340696344123785987,1024943263424340696388387129513⟩⟩,⟨⟨2459710273534397602534229816111,2459710273534397602624236424033⟩,⟨1024888927170745324204397834586,1024888927170745324248660536347⟩⟩] +lemma kernel0_0_r1_15_eq : ∀ k : Fin 16, kernel0_0Expr 1 15 k = kernel0_0_r1_15 k := by decide +kernel +noncomputable def kernel0_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel0_0_r1_0,kernel0_0_r1_1,kernel0_0_r1_2,kernel0_0_r1_3,kernel0_0_r1_4,kernel0_0_r1_5,kernel0_0_r1_6,kernel0_0_r1_7,kernel0_0_r1_8,kernel0_0_r1_9,kernel0_0_r1_10,kernel0_0_r1_11,kernel0_0_r1_12,kernel0_0_r1_13,kernel0_0_r1_14,kernel0_0_r1_15] +lemma kernel0_0_r1_eq (i k : Fin 16) : kernel0_0Expr 1 i k = kernel0_0_r1 i k := by + fin_cases i + · exact kernel0_0_r1_0_eq k + · exact kernel0_0_r1_1_eq k + · exact kernel0_0_r1_2_eq k + · exact kernel0_0_r1_3_eq k + · exact kernel0_0_r1_4_eq k + · exact kernel0_0_r1_5_eq k + · exact kernel0_0_r1_6_eq k + · exact kernel0_0_r1_7_eq k + · exact kernel0_0_r1_8_eq k + · exact kernel0_0_r1_9_eq k + · exact kernel0_0_r1_10_eq k + · exact kernel0_0_r1_11_eq k + · exact kernel0_0_r1_12_eq k + · exact kernel0_0_r1_13_eq k + · exact kernel0_0_r1_14_eq k + · exact kernel0_0_r1_15_eq k +noncomputable def kernel0_0_r2_0 : Fin 16 → CBox := ![⟨⟨1126541420937200586103049971099,1126541420937200586142074540439⟩,⟨1408172358083190888880114347657,1408172358083190888928894936804⟩⟩,⟨⟨1126575903250441722928081860094,1126575903250441722967107848216⟩,⟨1408180116049219383639052768240,1408180116049219383687834136354⟩⟩,⟨⟨1126644866419905264649498643380,1126644866419905264688527464402⟩,⟨1408195628992252322791603113933,1408195628992252322840386029340⟩⟩,⟨⟨1126748307530045840593194404156,1126748307530045840632227472174⟩,⟨1408218890934684645194137197591,1408218890934684645242922428481⟩⟩,⟨⟨1126886222203776032162895540807,1126886222203776032201934269823⟩,⟨1408249892911217139634160076130,1408249892911217139682948390375⟩⟩,⟨⟨1127058604597944271125905221460,1127058604597944271164951025387⟩,⟨1408288622970188689167498721259,1408288622970188689216290886379⟩⟩,⟨⟨1127265447397307262365159586095,1127265447397307262404213878645⟩,⟨1408335066175356241426431003279,1408335066175356241475227786146⟩⟩,⟨⟨1127506741806998558004654543871,1127506741806998558043718738724⟩,⟨1408389204608125625378460413735,1408389204608125625427262580934⟩⟩,⟨⟨1127782477543495323342903293062,1127782477543495323381978803419⟩,⟨1408451017370237110877653786027,1408451017370237110926462102789⟩⟩,⟨⟨1128092642824085753079905006748,1128092642824085753118993246056⟩,⟨1408520480586910380360360605973,1408520480586910380409175837811⟩⟩,⟨⟨1128437224354840019791079538897,1128437224354840019830181919587⟩,⟨1408597567410454351610463110597,1408597567410454351659286020391⟩⟩,⟨⟨1128816207317088066374798769530,1128816207317088066413916704823⟩,⟨1408682248024348056064325634488,1408682248024348056113156986556⟩⟩,⟨⟨1129229575352407991159661885420,1129229575352407991198796786521⟩,⟨1408774489647799538041890445436,1408774489647799538090730999132⟩⟩,⟨⟨1129677310546129219376713651649,1129677310546129219415866931754⟩,⟨1408874256540790495967597353738,1408874256540790496016447872538⟩⟩,⟨⟨1130159393409355108644582949211,1130159393409355108683756018187⟩,⟨1408981510009615136461628965888,1408981510009615136510490205258⟩⟩,⟨⟨1130675802859510099836132003221,1130675802859510099875326274097⟩,⟨1409096208412922455504850421241,1409096208412922455553723143385⟩⟩] +lemma kernel0_0_r2_0_eq : ∀ k : Fin 16, kernel0_0Expr 2 0 k = kernel0_0_r2_0 k := by decide +kernel +noncomputable def kernel0_0_r2_1 : Fin 16 → CBox := ![⟨⟨1131226516199416999036576383238,1131226516199416999075793263492⟩,⟨1409218307168271897062854844848,1409218307168271897111739798861⟩⟩,⟨⟨1131811509094910462095765164319,1131811509094910462135006067583⟩,⟨1409347758759213067934469407166,1409347758759213067983367355623⟩⟩,⟨⟨1132430755550993251338525279325,1132430755550993251377791611154⟩,⟨1409484512742900907491182752260,1409484512742900907540094438876⟩⟩,⟨⟨1133084227886542345129130995330,1133084227886542345168424169208⟩,⟨1409628515758258421702992274259,1409628515758258421751918460203⟩⟩,⟨⟨1133771896707572505975625056223,1133771896707572506014946473663⟩,⟨1409779711534699791692433941085,1409779711534699791741375359830⟩⟩,⟨⟨1134493730879065452476309700722,1134493730879065452515660776834⟩,⟨1409938040901427357292919193687,1409938040901427357341876608969⟩⟩,⟨⟨1135249697495373335405220580568,1135249697495373335444602714373⟩,⟨1410103441797316654961513764425,1410103441797316655010487902936⟩⟩,⟨⟨1136039761849205789336998899495,1136039761849205789376413505869⟩,⟨1410275849281404356141324559563,1410275849281404356190316183359⟩⟩,⟨⟨1136863887399210419134352193152,1136863887399210419173800664503⟩,⟨1410455195543994605995111186838,1410455195543994606044121006500⟩⟩,⟨⟨1137722035736157186050756484553,1137722035736157186090240239273⟩,⟨1410641409918399902528277375245,1410641409918399902577306159625⟩⟩,⟨⟨1138614166547737781800719838186,1138614166547737781840240266050⟩,⟨1410834418893333281652283686798,1410834418893333281701332139396⟩⟩,⟨⟨1139540237581991721357825221550,1139540237581991721397383740099⟩,⟨1411034146125969183851968541386,1411034146125969183901037427970⟩⟩,⟨⟨1140500204609371547067904378242,1140500204609371547107502367828⟩,⟨1411240512455690971931884125035,1411240512455690971980974126719⟩⟩,⟨⟨1141494021383460218493467200162,1141494021383460218533106083847⟩,⟨1411453435918543645923058174298,1411453435918543645972170068221⟩⟩,⟨⟨1142521639600354464788111682993,1142521639600354464827792838083⟩,⟨1411672831762410859703585618341,1411672831762410859752720077738⟩⟩,⟨⟨1143583008856728599856373189984,1143583008856728599896098038254⟩,⟨1411898612462935883270272895756,1411898612462935883319430693798⟩⟩] +lemma kernel0_0_r2_1_eq : ∀ k : Fin 16, kernel0_0Expr 2 1 k = kernel0_0_r2_1 k := by decide +kernel +noncomputable def kernel0_0_r2_2 : Fin 16 → CBox := ![⟨⟨1144678076606594045572064541155,1144678076606594045611834445499⟩,⟨1412130687740206673915232713766,1412130687740206673964414490275⟩⟩,⟨⟨1145806788116770575358001167761,1145806788116770575397817559512⟩,⟨1412368964576225717806584338759,1412368964576225717855790887538⟩⟩,⟨⟨1146969086421086079886377052093,1146969086421086079926241292317⟩,⟨1412613347233185779616616557554,1412613347233185779665848513557⟩⟩,⟨⟨1148164912273322468917283966637,1148164912273322468957197483166⟩,⟨1412863737272573150828897114263,1412863737272573150878155262575⟩⟩,⟨⟨1149394204098926158687469820217,1149394204098926158727433955734⟩,⟨1413120033575120416107600218949,1413120033575120416156885152557⟩⟩,⟨⟨1150656897945502453084207672550,1150656897945502453124223867352⟩,⟨1413382132361631160522441474904,1413382132361631160571754006328⟩⟩,⟨⟨1151952927432114009337243189068,1151952927432114009377312783696⟩,⟨1413649927214699417361014947799,1413649927214699417410355664885⟩⟩,⟨⟨1153282223697404485335713352948,1153282223697404485375837783379⟩,⟨1413923309101347005572654432122,1413923309101347005622024137204⟩⟩,⟨⟨1154644715346569396078568633917,1154644715346569396118749213932⟩,⟨1414202166396602226396093339597,1414202166396602226445492560351⟩⟩,⟨⟨1156040328397197161297593276396,1156040328397197161337831461565⟩,⟨1414486384908043679225963113861,1414486384908043679275392696434⟩⟩,⟨⟨1157468986224004305000104463298,1157468986224004305040401568729⟩,⟨1414775847901333216047068797618,1414775847901333216096529272946⟩⟩,⟨⟨1158930609502489770557509773874,1158930609502489770597867246047⟩,⟨1415070436126762280565526180734,1415070436126762280615018374600⟩⟩,⟨⟨1160425116151534341952926517030,1160425116151534341993345639146⟩,⟨1415370027846836071227066651767,1415370027846836071276591024249⟩⟩,⟨⟨1161952421274972212773815008274,1161952421274972212814297250138⟩,⟨1415674498864920125350779197813,1415674498864920125400336627371⟩⟩,⟨⟨1163512437102162819310756109406,1163512437102162819351302755244⟩,⟨1415983722554974043319180472782,1415983722554974043368771422852⟩⟩,⟨⟨1165105072927592152454570212110,1165105072927592152495182721472⟩,⟨1416297569892397155834351002726,1416297569892397155883976329525⟩⟩] +lemma kernel0_0_r2_2_eq : ∀ k : Fin 16, kernel0_0Expr 2 2 k = kernel0_0_r2_2 k := by decide +kernel +noncomputable def kernel0_0_r2_3 : Fin 16 → CBox := ![⟨⟨1166730235049533884659069011868,1166730235049533884699748623251⟩,⟨1416615909486010982341889521364,1416615909486010982391549587711⟩⟩,⟨⟨1168387826707801792676524365769,1168387826707801792717272574216⟩,⟨1416938607611203333493624815064,1416938607611203333543320557653⟩⟩,⟨⟨1170077748020626123628591785707,1170077748020626123669409838493⟩,⟨1417265528244258873609506673134,1417265528244258873659238476475⟩⟩,⟨⟨1171799895920687740726475530735,1171799895920687740767364903264⟩,⟨1417596533097900879143107951707,1417596533097900879192876710192⟩⟩,⟨⟨1173554164090345095006494439781,1173554164090345095047456328258⟩,⟨1417931481658068804781445321640,1417931481658068804831251308703⟩⟩,⟨⟨1175340442896090300131162691853,1175340442896090300172198610700⟩,⟨1418270231221956098641918762240,1418270231221956098691762961324⟩⟩,⟨⟨1177158619322271837874138237943,1177158619322271837915249390786⟩,⟨1418612636937332490689193171561,1418612636937332490739075875949⟩⟩,⟨⟨1179008576904122691533089874082,1179008576904122691574277755167⟩,⟨1418958551843174712606114401090,1418958551843174712656036551899⟩⟩,⟨⟨1180890195660133992289574413921,1180890195660133992330840155944⟩,⟨1419307826911629291542892623915,1419307826911629291592854361024⟩⟩,⟨⟨1182803352023815568468148736731,1182803352023815568509493890741⟩,⟨1419660311091330693072706449320,1419660311091330693122708843242⟩⟩,⟨⟨1184747918774886108662180199871,1184747918774886108703605918533⟩,⟨1420015851352097668945255571215,1420015851352097668995298810989⟩⟩,⟨⟨1186723764969936985628764098540,1186723764969936985670271898108⟩,⟨1420374292731030191512364058625,1420374292731030191562449141359⟩⟩,⟨⟨1188730755872615137459597243237,1188730755872615137501188199439⟩,⟨1420735478380028827679191199970,1420735478380028827729318150179⟩⟩,⟨⟨1190768752883371764469099440418,1190768752883371764510775130074⟩,⟨1421099249614757819610193327264,1421099249614757819660363280685⟩⟩,⟨⟨1192837613468824973075593985958,1192837613468824973117355502824⟩,⟨1421465445965072495915761952455,1421465445965072495965974980100⟩⟩,⟨⟨1194937191090785880164378138311,1194937191090785880206227024023⟩,⟨1421833905226930934418284808689,1421833905226930934468541973719⟩⟩] +lemma kernel0_0_r2_3_eq : ∀ k : Fin 16, kernel0_0Expr 2 3 k = kernel0_0_r2_3 k := by decide +kernel +noncomputable def kernel0_0_r2_4 : Fin 16 → CBox := ![⟨⟨1197067335134999081398951433007,1197067335134999081440888673537⟩,⟨1422204463515809034634472359349,1422204463515809034684773502832⟩⟩,⟨⟨1199227890839649782981012324873,1199227890839649783023039550612⟩,⟨1422576955321637333642075878784,1422576955321637333692422265742⟩⟩,⟨⟨1201418699223691296649631356632,1201418699223691296691749593874⟩,⟨1422951213565277011895159565240,1422951213565277011945551134264⟩⟩,⟨⟨1203639597015048000359297323377,1203639597015048000401508142584⟩,⟨1423327069656551584732684099519,1423327069656551584783121990420⟩⟩,⟨⟨1205890416578750270094719780771,1205890416578750270137024097450⟩,⟨1423704353553849759763684369957,1423704353553849759814168287904⟩⟩,⟨⟨1208170985845059289581955494478,1208170985845059289624354968147⟩,⟨1424082893825313859040577609195,1424082893825313859091108897528⟩⟩,⟨⟨1210481128237641042060734747763,1210481128237641042103230327987⟩,⟨1424462517711627057045998135266,1424462517711627057096576584956⟩⟩,⟨⟨1212820662601850179517718023737,1212820662601850179560311313487⟩,⟨1424843051190411470183094791284,1424843051190411470233721630266⟩⟩,⟨⟨1215189403133185847477368795763,1215189403133185847520060593960⟩,⟨1425224319042247849914659611240,1425224319042247849965334313430⟩⟩,⟨⟨1217587159305982915146137140783,1217587159305982915188929176129⟩,⟨1425606144918326279263462226833,1425606144918326279314186305126⟩⟩,⟨⟨1220013735802403418855455738335,1220013735802403418898348873862⟩,⟨1425988351409735850472096860363,1425988351409735850522869942541⟩⟩,⟨⟨1222468932441794368708505832113,1222468932441794368751501707020⟩,⟨1426370760118399809725030678913,1426370760118399809775854092945⟩⟩,⟨⟨1224952544110479391375775499547,1224952544110479391418874823060⟩,⟨1426753191729661092556488954144,1426753191729661092607362008050⟩⟩,⟨⟨1227464360692052983290083810505,1227464360692052983333288347482⟩,⟨1427135466086521540607635128260,1427135466086521540658559435885⟩⟩,⟨⟨1230004166998247425164638388474,1230004166998247425207948904910⟩,⟨1427517402265536386568297572703,1427517402265536386619272582362⟩⟩,⟨⟨1232571742700443657818722556062,1232571742700443657862140731295⟩,⟨1427898818654363819371803219654,1427898818654363819422830372048⟩⟩] +lemma kernel0_0_r2_4_eq : ∀ k : Fin 16, kernel0_0Expr 2 4 k = kernel0_0_r2_4 k := by decide +kernel +noncomputable def kernel0_0_r2_5 : Fin 16 → CBox := ![⟨⟨1235166862261898637688259414971,1235166862261898637731785801916⟩,⟨1428279533030967596058972066684,1428279533030967596110050366516⟩⟩,⟨⟨1237789294870762874992101873365,1237789294870762875035738332440⟩,⟨1428659362644468750370453120959,1428659362644468750421584416283⟩⟩,⟨⟨1240438804373963005118724102699,1240438804373963005162471291897⟩,⟨1429038124297640461382274384541,1429038124297640461433457927798⟩⟩,⟨⟨1243115149212025351125230152123,1243115149212025351169089794759⟩,⟨1429415634431038088825709114252,1429415634431038088876946471802⟩⟩,⟨⟨1245818082354917498973244105331,1245818082354917499017216652077⟩,⟨1429791709208754255735004824109,1429791709208754255786294822709⟩⟩,⟨⟨1248547351238985923879818882219,1248547351238985923923906228051⟩,⟨1430166164605786664503916797395,1430166164605786664555261391303⟩⟩,⟨⟨1251302697705068672500739647323,1251302697705068672544942330503⟩,⟨1430538816497004070222665770740,1430538816497004070274063999363⟩⟩,⟨⟨1254083857937863018107968300500,1254083857937863018152288092455⟩,⟨1430909480747693506393911539021,1430909480747693506445365108251⟩⟩,⟨⟨1256890562406628860953196438307,1256890562406628860997633598332⟩,⟨1431277973305669464043579607921,1431277973305669464095086983467⟩⟩,⟨⟨1259722535807309440073806174616,1259722535807309440118362713002⟩,⟨1431644110294923267279547985694,1431644110294923267331111406989⟩⟩,⟨⟨1262579497006151652319155205506,1262579497006151652363831528733⟩,⟨1432007708110788368119570226424,1432007708110788368171188502865⟩⟩,⟨⟨1265461158984908935759173200676,1265461158984908935803971132211⟩,⟨1432368583516594702706487335179,1432368583516594702758162326006⟩⟩,⟨⟨1268367228787710264279158962906,1268367228787710264324078636594⟩,⟨1432726553741782611842218779847,1432726553741782611893948741185⟩⟩,⟨⟨1271297407469679314457843381252,1271297407469679314502886848971⟩,⟨1433081436581444133285598661690,1433081436581444133337385964617⟩⟩,⟨⟨1274251390047388301170781588405,1274251390047388301215949112100⟩,⟨1433433050497256723856096499870,1433433050497256723907939706175⟩⟩,⟨⟨1277228865451231331174234751048,1277228865451231331219528210453⟩,⟨1433781214719771668651830478921,1433781214719771668703731615952⟩⟩] +lemma kernel0_0_r2_5_eq : ∀ k : Fin 16, kernel0_0Expr 2 5 k = kernel0_0_r2_5 k := by decide +kernel +noncomputable def kernel0_0_r2_6 : Fin 16 → CBox := ![⟨⟨1280229516479802390647731974922,1280229516479802390693151253806⟩,⟨1434125749352016585419038673662,1434125749352016585470995532692⟩⟩,⟨⟨1283253019756363259783197210515,1283253019756363259828744517433⟩,⟨1434466475474368537303309246423,1434466475474368537355324581357⟩⟩,⟨⟨1286299045687486731527097960052,1286299045687486731572773399516⟩,⟨1434803215250651330084823648536,1434803215250651330136895756571⟩⟩,⟨⟨1289367258423960499087218046443,1289367258423960499133023558370⟩,⟨1435135792035407593978535943843,1435135792035407594030667034818⟩⟩,⟨⟨1292457315824036964451835743634,1292457315824036964497771081470⟩,⟨1435464030482293238809496730650,1435464030482293238861684397244⟩⟩,⟨⟨1295568869419114004658101922500,1295568869419114004704169323446⟩,⟨1435787756653538828713194292700,1435787756653538828765441404529⟩⟩,⟨⟨1298701564381931410699300770435,1298701564381931410745500167939⟩,⟨1436106798130419352537962967840,1436106798130419352590267539784⟩⟩,⟨⟨1301855039497367282688802193021,1301855039497367282735135591457⟩,⟨1436420984124670773134343676918,1436420984124670773186708116757⟩⟩,⟨⟨1305028927135918121225966210454,1305028927135918121272433073175⟩,⟨1436730145590788627214243198113,1436730145590788627266664574251⟩⟩,⟨⟨1308222853229945695984320665699,1308222853229945696030923407811⟩,⟨1437034115339140822173906655810,1437034115339140822226388275446⟩⟩,⟨⟨1311436437252772995650282566085,1311436437252772995697020936413⟩,⟨1437332728149823642134818934576,1437332728149823642187358513584⟩⟩,⟨⟨1314669292200710665915539914453,1314669292200710665962415985701⟩,⟨1437625820887186837609875200141,1437625820887186837662475359041⟩⟩,⟨⟨1317921024578094321863756116442,1317921024578094321910769193563⟩,⟨1437913232614950536998831350834,1437913232614950537051488924151⟩⟩,⟨⟨1321191234385411975561929882866,1321191234385411975609082418362⟩,⟨1438194804711833589107824439150,1438194804711833589160542881327⟩⟩,⟨⟨1324479515110599546924767783186,1324479515110599546972059327065⟩,⟨1438470380987609829819862098123,1438470380987609829872638808745⟩⟩,⟨⟨1327785453723581024121624292361,1327785453723581024169056989896⟩,⟨1438739807799505668852966118859,1438739807799505668905803946968⟩⟩] +lemma kernel0_0_r2_6_eq : ∀ k : Fin 16, kernel0_0Expr 2 6 k = kernel0_0_r2_6 k := by decide +kernel +noncomputable def kernel0_0_r2_7 : Fin 16 → CBox := ![⟨⟨1331108630674128307306442044382,1331108630674128307354014831414⟩,⟨1439002934168849320350235562636,1439002934168849320403130681704⟩⟩,⟨⟨1334448619893114104861434932926,1334448619893114104909150498621⟩,⟨1439259611897878960146198387432,1439259611897878960199154822680⟩⟩,⟨⟨1337804988797229453480838472269,1337804988797229453528696154111⟩,⟨1439509695686614089408836808333,1439509695686614089461851627516⟩⟩,⟨⟨1341177298297235501354956384923,1341177298297235501402958404310⟩,⟨1439753043249691425585708608516,1439753043249691425638784903695⟩⟩,⟨⟨1344565102809817126779619497130,1344565102809817126827764639380⟩,⟨1439989515433063733952907877155,1439989515433063734006041630678⟩⟩,⟨⟨1347967950273103762314763734900,1347967950273103762363054698708⟩,⟨1440218976330457163479830902499,1440218976330457163533026242504⟩⟩,⟨⟨1351385382165920457032650152528,1351385382165920457081086048385⟩,⟨1440441293399479866208625243441,1440441293399479866261878889340⟩⟩,⟨⟨1354816933530829736607212643888,1354816933530829736655795773570⟩,⟨1440656337577271967043181291886,1440656337577271967096496594799⟩⟩,⟨⟨1358262133001022213479270382122,1358262133001022213527999117794⟩,⟨1440863983395584317985689037494,1440863983395584318039061259090⟩⟩,⟨⟨1361720502831111157876751967292,1361720502831111157925629267753⟩,⟨1441064109095170924768624392802,1441064109095170924822058290391⟩⟩,⟨⟨1365191558931883366183940973786,1365191558931883366232965708951⟩,⟨1441256596739377481894992750497,1441256596739377481948484681021⟩⟩,⟨⟨1368674810909055657475961371053,1368674810909055657525135926353⟩,⟨1441441332326806101759058201472,1441441332326806101812611789178⟩⟩,⟨⟨1372169762106083193737118436520,1372169762106083193786441004751⟩,⟨1441618205902934082248897453040,1441618205902934082302507736392⟩⟩,⟨⟨1375675909651062556478666837253,1375675909651062556528140395097⟩,⟨1441787111670562432522398892582,1441787111670562432576070763920⟩⟩,⟨⟨1379192744507769124625769021906,1379192744507769124675392184487⟩,⟨1441947948098967875991154220276,1441947948098967876044883659068⟩⟩,⟨⟨1382719751530864788469615370838,1382719751530864788519390611274⟩,⟨1442100618031630180412106638183,1442100618031630180465897557368⟩⟩] +lemma kernel0_0_r2_7_eq : ∀ k : Fin 16, kernel0_0Expr 2 7 k = kernel0_0_r2_7 k := by decide +kernel +noncomputable def kernel0_0_r2_8 : Fin 16 → CBox := ![⟨⟨1386256409525308405350731707413,1386256409525308405400656694348⟩,⟨1442245028792404934805968692303,1442245028792404934859815216069⟩⟩,⟨⟨1389802191309997658084064032714,1389802191309997658134142093889⟩,⟨1442381092290010309063962059300,1442381092290010309117869904752⟩⟩,⟨⟨1393356563785667120847929909031,1393356563785667120898159392100⟩,⟨1442508725120694901859907436358,1442508725120694901913872193930⟩⟩,⟨⟨1396918988007063373591109913513,1396918988007063373641493381956⟩,⟨1442627848668952513038793570875,1442627848668952513092819454898⟩⟩,⟨⟨1400488919259413939581026114194,1400488919259413939631561096241⟩,⟨1442738389206148575068078171777,1442738389206148575122159191159⟩⟩,⟨⟨1404065807139202656496093769286,1404065807139202656546783551162⟩,⟨1442840277986922051328466688891,1442840277986922051382608589004⟩⟩,⟨⟨1407649095639259834789455551526,1407649095639259834840298199808⟩,⟨1442933451343225863733088472341,1442933451343225863787286441270⟩⟩,⟨⟨1411238223238171213604048212471,1411238223238171213655046384881⟩,⟨1443017850775868354950738082704,1443017850775868355004996651180⟩⟩,⟨⟨1414832622994005300332867947746,1414832622994005300384018614558⟩,⟨1443093423043417927709271780323,1443093423043417927763584009795⟩⟩,⟨⟨1418431722642354181365770271060,1418431722642354181417077083039⟩,⟨1443160120248332841368920502255,1443160120248332841423292997626⟩⟩,⟨⟨1422034944698678325350537387121,1422034944698678325401998118203⟩,⟨1443217899920178190021864704814,1443217899920178190076292242711⟩⟩,⟨⟨1425641706564941273448755490810,1425641706564941273500372895184⟩,⟨1443266725095792342347881273194,1443266725095792342402368712111⟩⟩,⟨⟨1429251420640515430926357133589,1429251420640515430978128005309⟩,⟨1443306564396265596584464590173,1443306564396265596639004830872⟩⟩,⟨⟨1432863494437335448623435045344,1432863494437335448675363011691⟩,⟨1443337392100594499170477140000,1443337392100594499225076867333⟩⟩,⟨⟨1436477330699270919323700496309,1436477330699270919375783026439⟩,⟨1443359188215876197461425256777,1443359188215876197516078825458⟩⟩,⟨⟨1440092327525685320986389104913,1440092327525685321038629052844⟩,⟨1443371938543908349582701804953,1443371938543908349637414414569⟩⟩] +lemma kernel0_0_r2_8_eq : ∀ k : Fin 16, kernel0_0Expr 2 8 k = kernel0_0_r2_8 k := by decide +kernel +noncomputable def kernel0_0_r2_9 : Fin 16 → CBox := ![⟨⟨1443707878499143324663288028105,1443707878499143324715681495327⟩,⟨1443375634744061501781575087790,1443375634744061501836338456917⟩⟩,⟨⟨1447323372817223758387430884417,1447323372817223758439981979059⟩,⟨1443370274392292468938617253678,1443370274392292468993439165966⟩⟩,⟨⟨1450938195428390688292664460664,1450938195428390688345370337720⟩,⟨1443355861036169120149349996427,1443355861036169120204224379455⟩⟩,⟨⟨1454551727171870253805702114222,1454551727171870253858565728744⟩,⟨1443332404245779080974754715635,1443332404245779081029687118688⟩⟩,⟨⟨1458163344921476084221571972198,1458163344921476084274589320469⟩,⟨1443299919660397219100455099918,1443299919660397219155437248800⟩⟩,⟨⟨1461772421733321338758199998808,1461772421733321338811375078841⟩,⟨1443258429030789382261378256284,1443258429030789382316417854575⟩⟩,⟨⟨1465378326997350660844123830207,1465378326997350660897453472332⟩,⟨1443207960257032707398336471041,1443207960257032707453427011240⟩⟩,⟨⟨1468980426592620629585205417808,1468980426592620629638692681196⟩,⟨1443148547421735918607639380596,1443148547421735918662786773540⟩⟩,⟨⟨1472578083046252636819774792709,1472578083046252636873414954646⟩,⟨1443080230818546378482169843154,1443080230818546378537364614576⟩⟩,⟨⟨1476170655695977526693895689212,1476170655695977526747693240251⟩,⟨1443003056975834252329038435865,1443003056975834252384289413973⟩⟩,⟨⟨1479757500856186816079126118425,1479757500856186816133077557273⟩,⟨1442917078675447986333258539803,1442917078675447986388558780454⟩⟩,⟨⟨1483337971987400878216017672931,1483337971987400878270126163269⟩,⟨1442822354966439387295365913875,1442822354966439387350721695373⟩⟩,⟨⟨1486911419869060128463855650863,1486911419869060128518116335232⟩,⟨1442718951173660920804009356870,1442718951173660920859411175175⟩⟩,⟨⟨1490477192775541009669296829154,1490477192775541009723714104335⟩,⟨1442606938901142413726265087099,1442606938901142413781721735890⟩⟩,⟨⟨1494034636655294445035834931160,1494034636655294445090404956406⟩,⟨1442486396030159152235564270854,1442486396030159152291068365222⟩⟩,⟨⟨1497583095313000417955311323385,1497583095313000418010037369114⟩,⟨1442357406711908404182211176465,1442357406711908404237769371079⟩⟩] +lemma kernel0_0_r2_9_eq : ∀ k : Fin 16, kernel0_0Expr 2 9 k = kernel0_0_r2_9 k := by decide +kernel +noncomputable def kernel0_0_r2_10 : Fin 16 → CBox := ![⟨⟨1501121910594628460366311330935,1501121910594628460421187637271⟩,⟨1442220061354716659785598363559,1442220061354716659841199625497⟩⟩,⟨⟨1504650422575290092954472207295,1504650422575290093009503834826⟩,⟨1442074456605705372136541077940,1442074456605705372192195662303⟩⟩,⟨⟨1508167969749765670807251527994,1508167969749765670862434293207⟩,⟨1441920695326848683000500491161,1441920695326848683056200576061⟩⟩,⟨⟨1511673889225584655626353117628,1511673889225584655681690396441⟩,⟨1441758886565362533477524663786,1441758886565362533533277281595⟩⟩,⟨⟨1515167516918535068646656562978,1515167516918535068702142600215⟩,⟨1441589145518370676194695042933,1441589145518370676250489422445⟩⟩,⟨⟨1518648187750474785055991840845,1518648187750474785111631455736⟩,⟨1441411593491799418300097753118,1441411593491799418355943835114⟩⟩,⟨⟨1522115235849314418655292276434,1522115235849314418711080937518⟩,⟨1441226357853459424453156937870,1441226357853459424509046462387⟩⟩,⟨⟨1525567994751038822066375622032,1525567994751038822122316812438⟩,⟨1441033571980279587572336341704,1441033571980279587628276725177⟩⟩,⟨⟨1529005797603631699904046943236,1529005797603631699960134019908⟩,⟨1440833375199664823082503540452,1440833375199664823138482539962⟩⟩,⟨⟨1532427977372765506465549275685,1532427977372765506521787700666⟩,⟨1440625912724956650053681331137,1440625912724956650109710303029⟩⟩,⟨⟨1535833867049116681680103253533,1535833867049116681736488147505⟩,⟨1440411335584982579694180633528,1440411335584982579750250887715⟩⟩,⟨⟨1539222799857164374843896393637,1539222799857164374900431344631⟩,⟨1440189800547687627423392035872,1440189800547687627479511370431⟩⟩,⟨⟨1542594109465329120071873870208,1542594109465329120128552193914⟩,⟨1439961470037848688013660193923,1439961470037848688069816548645⟩⟩,⟨⟨1545947130197306464922681498185,1545947130197306464979508456427⟩,⟨1439726512048880052427176929669,1439726512048880052483381435925⟩⟩,⟨⟨1549281197244449318238902723025,1549281197244449318295873087390⟩,⟨1439485100048745987942633993908,1439485100048745987998877535307⟩⟩,⟨⟨1552595646879051778256629570058,1552595646879051778313747033697⟩,⟨1439237412880004037537987431296,1439237412880004037594278189208⟩⟩] +lemma kernel0_0_r2_10_eq : ∀ k : Fin 16, kernel0_0Expr 2 10 k = kernel0_0_r2_10 k := by decide +kernel +noncomputable def kernel0_0_r2_11 : Fin 16 → CBox := ![⟨⟨1555889816668386430249632786567,1555889816668386430306889572716⟩,⟨1438983634654010507483995098181,1438983634654010507540319168453⟩⟩,⟨⟨1559163045689346566546034618478,1559163045689346566603436833397⟩,⟨1438723954639327490589424952999,1438723954639327490645795264310⟩⟩,⟨⟨1562414674743544482228676178574,1562414674743544482286218249724⟩,⟨1438458567144378703107189925870,1438458567144378703163596949834⟩⟩,⟨⟨1565644046572716938105601170338,1565644046572716938163286891318⟩,⟨1438187671394409382274606764818,1438187671394409382331059057281⟩⟩,⟨⟨1568850506074289058870210976526,1568850506074289058928032720066⟩,⟨1437911471402813484901379602206,1437911471402813484957863814668⟩⟩,⟨⟨1572033400516948348361382978074,1572033400516948348419346461084⟩,⟨1437630175836899431212048965655,1437630175836899431268577441415⟩⟩,⟨⟨1575192079756081154422882399568,1575192079756081154480981707503⟩,⟨1437343997878173638007413055464,1437343997878173638063975861219⟩⟩,⟨⟨1578325896448924801324128150257,1578325896448924801382367176560⟩,⟨1437053155077229066708874036730,1437053155077229066765480100902⟩⟩,⟨⟨1581434206269289725652827421296,1581434206269289725711197483948⟩,⟨1436757869203333960474432191627,1436757869203333960531066411697⟩⟩,⟨⟨1584516368121707298971338561258,1584516368121707299029846187584⟩,⟨1436458366088823845745938303507,1436458366088823845802614741532⟩⟩,⟨⟨1587571744354860593632061442411,1587571744354860593690700385118⟩,⟨1436154875468407712704480505670,1436154875468407712761188842468⟩⟩,⟨⟨1590599700974157142607285649665,1590599700974157142666059895694⟩,⟨1435847630813507051585092216996,1435847630813507051641841739553⟩⟩,⟨⟨1593599607853304754997716123664,1593599607853304755056617105716⟩,⟨1435536869161754093097156716194,1435536869161754093153932806912⟩⟩,⟨⟨1596570838944753670398793918206,1596570838944753670457827814354⟩,⟨1435222830941783166860476509011,1435222830941783166917292724528⟩⟩,⟨⟨1599512772488870761264918434312,1599512772488870761324078671340⟩,⟨1434905759793456537472872432414,1434905759793456537529718080188⟩⟩,⟨⟨1602424791221714115954271048688,1602424791221714116013561704336⟩,⟨1434585902383673389403581172204,1434585902383673389460465889796⟩⟩] +lemma kernel0_0_r2_11_eq : ∀ k : Fin 16, kernel0_0Expr 2 11 k = kernel0_0_r2_11 k := by decide +kernel +noncomputable def kernel0_0_r2_12 : Fin 16 → CBox := ![⟨⟨1605306282581279148814006186350,1605306282581279148873417357353⟩,⟨1434263508217917795385839611027,1434263508217917795442746501641⟩⟩,⟨⟨1608156638912090379465031428214,1608156638912090379524570391486⟩,⟨1433938829447708504616817305426,1433938829447708504673762177020⟩⟩,⟨⟨1610975257668016192816927188695,1610975257668016192876587060274⟩,⟨1433612120674120213385580963761,1433612120674120213442552776981⟩⟩,⟨⟨1613761541613187225219902718343,1613761541613187225279687657019⟩,⟨1433283638747552618556202780161,1433283638747552618613211500676⟩⟩,⟨⟨1616514899020902510989852050664,1616514899020902511049752574196⟩,⟨1432953642563929990782469698121,1432953642563929990839499485573⟩⟩,⟨⟨1619234743870411157313029200139,1619234743870411157373051941992⟩,⟨1432622392857520226929085238382,1432622392857520226986150833906⟩⟩,⟨⟨1621920496041461083812853070481,1621920496041461083872990846301⟩,⟨1432290151990568337821823009608,1432290151990568337878913042519⟩⟩,⟨⟨1624571581506510255012678297515,1624571581506510255072935343362⟩,⟨1431957183739945086461486226016,1431957183739945086518610977977⟩⟩,⟨⟨1627187432520499838368904860817,1627187432520499838429270485458⟩,⟨1431623753081017001978827573914,1431623753081017002035969169023⟩⟩,⟨⟨1629767487808092825969536137340,1629767487808092826030017960363⟩,⟨1431290125968949245113080146315,1431290125968949245170255341869⟩⟩,⟨⟨1632311192748285852603904920032,1632311192748285852664495476153⟩,⟨1430956569117657781597638420249,1430956569117657781654835545114⟩⟩,⟨⟨1634817999556306214673810674012,1634817999556306214734514264891⟩,⟨1430623349776632020779250004824,1430623349776632020836479628552⟩⟩,⟨⟨1637287367462710431097271892589,1637287367462710431158078164411⟩,⟨1430290735505853488870226102961,1430290735505853488927471227599⟩⟩,⟨⟨1639718762889605076552069463136,1639718762889605076612985490392⟩,⟨1429958993949040220778391797085,1429958993949040220835668295803⟩⟩,⟨⟨1642111659623915046597923203872,1642111659623915046658941255983⟩,⟨1429628392605450363396017743544,1429628392605450363453313666518⟩⟩,⟨⟨1644465538987628870805360763256,1644465538987628870866485200622⟩,⟨1429299198600481979061406692043,1429299198600481979118732876804⟩⟩] +lemma kernel0_0_r2_12_eq : ∀ k : Fin 16, kernel0_0Expr 2 12 k = kernel0_0_r2_12 k := by decide +kernel +noncomputable def kernel0_0_r2_13 : Fin 16 → CBox := ![⟨⟨1646779890004955161376234148598,1646779890004955161437453123186⟩,⟨1428971678455309213745328227079,1428971678455309213802665098347⟩⟩,⟨⟨1649054209566328758243660868262,1649054209566328758304982742912⟩,⟨1428646097855797844078904762908,1428646097855797844136270754641⟩⟩,⟨⟨1651288002589209594721895729365,1651288002589209594783312533945⟩,⟨1428322721420945734975792689219,1428322721420945735033175611848⟩⟩,⟨⟨1653480782175621747968863768532,1653480782175621748030379906413⟩,⟨1428001812471095920281755691459,1428001812471095920339166612864⟩⟩,⟨⟨1655632069766384543498531045829,1655632069766384543560135359888⟩,⟨1427683632796171858220423841347,1427683632796171858277844702244⟩⟩,⟨⟨1657741395291991940591832020708,1657741395291991940653531995940⟩,⟨1427368442424185907641697294263,1427368442424185907699145010325⟩⟩,⟨⟨1659808297320100723787294827753,1659808297320100723849082273502⟩,⟨1427056499390273217110123323342,1427056499390273217167585489899⟩⟩,⟨⟨1661832323199592253036298777615,1661832323199592253098178131846⟩,⟨1426748059506504014222939959921,1426748059506504014280427850612⟩⟩,⟨⟨1663813029201176670245254864741,1663813029201176670307213630352⟩,⟨1426443376132727725392468619144,1426443376132727725449961873641⟩⟩,⟨⟨1665749980654512511807701318321,1665749980654512511869748137158⟩,⟨1426142699948702445468107232168,1426142699948702445525625053037⟩⟩,⟨⟨1667642752081818624753495302440,1667642752081818624815621793299⟩,⟨1425846278727763011446645047889,1425846278727763011504174858824⟩⟩,⟨⟨1669490927327959118133725715251,1669490927327959118195936332464⟩,⟨1425554357112280315183404986389,1425554357112280315240958222879⟩⟩,⟨⟨1671294099686985791506088889284,1671294099686985791568371759660⟩,⟨1425267176391163517148071633354,1425267176391163517205629291600⟩⟩,⟨⟨1673051872025126059667177237145,1673051872025126059729540214143⟩,⟨1424984974279655498147472878232,1424984974279655498205052799506⟩⟩,⟨⟨1674763856900207828406595646316,1674763856900207828469030182434⟩,⟨1424707984701670210442107372163,1424707984701670210499696839804⟩⟩,⟨⟨1676429676677516061900674706841,1676429676677516061963185260800⟩,⟨1424436437574918566272486460586,1424436437574918566330097038975⟩⟩] +lemma kernel0_0_r2_13_eq : ∀ k : Fin 16, kernel0_0Expr 2 13 k = kernel0_0_r2_13 k := by decide +kernel +noncomputable def kernel0_0_r2_14 : Fin 16 → CBox := ![⟨⟨1678048963642078910877550356168,1678048963642078910940123331474⟩,⟨1424170558599067133518311806509,1424170558599067133575921455834⟩⟩,⟨⟨1679621360107384234938478631111,1679621360107384235001123445785⟩,⟨1423910569047171198623263485297,1423910569047171198680893065089⟩⟩,⟨⟨1681146518520530146119930274110,1681146518520530146182638250889⟩,⟨1423656685560620710160901893647,1423656685560620710218538599594⟩⟩,⟨⟨1682624101563815818291698453409,1682624101563815818354474032124⟩,⟨1423409119947834237144157414450,1423409119947834237201812885060⟩⟩,⟨⟨1684053782252781243353104831562,1684053782252781243415935536389⟩,⟨1423168078986932369556068470674,1423168078986932369613722909775⟩⟩,⟨⟨1685435244030706866150493282093,1685435244030706866213387272964⟩,⟨1422933764232617960253638752378,1422933764232617960311310767887⟩⟩,⟨⟨1686768180859586092044486677711,1686768180859586092107435174424⟩,⟨1422706371827486263498351855678,1422706371827486263556028589042⟩⟩,⟨⟨1688052297307585531273911751683,1688052297307585531336919161840⟩,⟨1422486092317983372475464721323,1422486092317983372533157848308⟩⟩,⟨⟨1689287308633009520596293545551,1689287308633009520659345956881⟩,⟨1422273110475226403299781786091,1422273110475226403357468981055⟩⟩,⟨⟨1690472940864786943768234075650,1690472940864786943831340954751⟩,⟨1422067605120893623601896568845,1422067605120893623659598947699⟩⟩,⟨⟨1691608930879499657641167048668,1691608930879499657704319552199⟩,⟨1421869748958387187682430014955,1421869748958387187740134721291⟩⟩,⟨⟨1692695026474972920106311457421,1692695026474972920169513935330⟩,⟨1421679708409465325624752793989,1421679708409465325682471480838⟩⟩,⟨⟨1693730986440449110686348775143,1693730986440449110749588279063⟩,⟨1421497643456534749246211728326,1421497643456534749303923978680⟩⟩,⟨⟨1694716580623366735832342501614,1694716580623366735895627424090⟩,⟨1421323707490787692258527484611,1421323707490787692316252488283⟩⟩,⟨⟨1695651589992767221264903335039,1695651589992767221328224801786⟩,⟨1421158047166361404741652514057,1421158047166361404799377458094⟩⟩,⟨⟨1696535806699352316036731482129,1696535806699352316100093767704⟩,⟨1421000802260691082554155352459,1421000802260691082611891821002⟩⟩] +lemma kernel0_0_r2_14_eq : ∀ k : Fin 16, kernel0_0Expr 2 14 k = kernel0_0_r2_14 k := by decide +kernel +noncomputable def kernel0_0_r2_15 : Fin 16 → CBox := ![⟨⟨1697369034132215071135653856311,1697369034132215071199042213828⟩,⟨1420852105541220140439679599591,1420852105541220140497403941450⟩⟩,⟨⟨1698151086972267313827974392564,1698151086972267313891398913122⟩,⟨1420712082638624443439878621774,1420712082638624443497613231220⟩⟩,⟨⟨1698881791242386322671948893610,1698881791242386322735400717808⟩,⟨1420580851926699605141049509517,1420580851926699605198781682880⟩⟩,⟨⟨1699560984354303022972394191641,1699560984354303023035877488107⟩,⟨1420458524409052753845493889671,1420458524409052753903235071691⟩⟩,⟨⟨1700188515152253474795549161791,1700188515152253474859050666012⟩,⟨1420345203612732269771831950111,1420345203612732269829561314069⟩⟩,⟨⟨1700764243953414722518480545378,1700764243953414722582008786261⟩,⟨1420240985488920918849714707246,1420240985488920918907451795779⟩⟩,⟨⟨1701288042585145223832364495374,1701288042585145223895910662636⟩,⟨1420145958320809562771733431153,1420145958320809562829465693574⟩⟩,⟨⟨1701759794419049085285880153397,1701759794419049085349448290668⟩,⟨1420060202638760222052544271830,1420060202638760222110282963907⟩⟩,⟨⟨1702179394401882209498763147958,1702179394401882209562338504704⟩,⟨1419983791142858720435372579546,1419983791142858720493094180663⟩⟩,⟨⟨1702546749083317215237232025112,1702546749083317215300824548666⟩,⟨1419916788632948456728915795760,1419916788632948456786642504374⟩⟩,⟨⟨1702861776640582635219572098597,1702861776640582635283173076294⟩,⟨1419859251946228045834387287806,1419859251946228045892106775928⟩⟩,⟨⟨1703124406899990437824323269733,1703124406899990437887936587585⟩,⟨1419811229902486656223950814162,1419811229902486656281674073469⟩⟩,⟨⟨1703334581355364368200785222938,1703334581355364368264397471616⟩,⟨1419772763257041858454535955938,1419772763257041858512241982421⟩⟩,⟨⟨1703492253183379972366677966173,1703492253183379972430297702340⟩,⟨1419743884661435700525718696557,1419743884661435700583427131864⟩⟩,⟨⟨1703597387255825465759550868951,1703597387255825465823169516545⟩,⟨1419724618631935553178855111650,1419724618631935553236553902364⟩⟩,⟨⟨1703649960148790846684016481094,1703649960148790846747637745166⟩,⟨1419714981525877033809772762662,1419714981525877033867472578173⟩⟩] +lemma kernel0_0_r2_15_eq : ∀ k : Fin 16, kernel0_0Expr 2 15 k = kernel0_0_r2_15 k := by decide +kernel +noncomputable def kernel0_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel0_0_r2_0,kernel0_0_r2_1,kernel0_0_r2_2,kernel0_0_r2_3,kernel0_0_r2_4,kernel0_0_r2_5,kernel0_0_r2_6,kernel0_0_r2_7,kernel0_0_r2_8,kernel0_0_r2_9,kernel0_0_r2_10,kernel0_0_r2_11,kernel0_0_r2_12,kernel0_0_r2_13,kernel0_0_r2_14,kernel0_0_r2_15] +lemma kernel0_0_r2_eq (i k : Fin 16) : kernel0_0Expr 2 i k = kernel0_0_r2 i k := by + fin_cases i + · exact kernel0_0_r2_0_eq k + · exact kernel0_0_r2_1_eq k + · exact kernel0_0_r2_2_eq k + · exact kernel0_0_r2_3_eq k + · exact kernel0_0_r2_4_eq k + · exact kernel0_0_r2_5_eq k + · exact kernel0_0_r2_6_eq k + · exact kernel0_0_r2_7_eq k + · exact kernel0_0_r2_8_eq k + · exact kernel0_0_r2_9_eq k + · exact kernel0_0_r2_10_eq k + · exact kernel0_0_r2_11_eq k + · exact kernel0_0_r2_12_eq k + · exact kernel0_0_r2_13_eq k + · exact kernel0_0_r2_14_eq k + · exact kernel0_0_r2_15_eq k +noncomputable def kernel0_0_r3_0 : Fin 16 → CBox := ![⟨⟨764142706418912115983658537579,764142706418912116010129235685⟩,⟨1273568180537665873715765538027,1273568180537665873759883285091⟩⟩,⟨⟨764163860305767553508781906462,764163860305767553535253474945⟩,⟨1273579462328589746567997296725,1273579462328589746612115819835⟩⟩,⟨⟨764206167212529829343282338043,764206167212529829369755644434⟩,⟨1273602024094248280498982997113,1273602024094248280543103064324⟩⟩,⟨⟨764269625404502255288174165016,764269625404502255314650076816⟩,⟨1273635862202294033466611706023,1273635862202294033510734085295⟩⟩,⟨⟨764354232277641230771367729810,764354232277641230797847114478⟩,⟨1273680971204283632191478659357,1273680971204283632235604118483⟩⟩,⟨⟨764459984356158398512684994302,764459984356158398539168719246⟩,⟨1273737343835772060608687750483,1273737343835772060652817057072⟩⟩,⟨⟨764586877289324249226888427791,764586877289324249253377360302⟩,⟨1273804971016439945207321073116,1273804971016439945251454994386⟩⟩,⟨⟨764734905847473803813695730007,764734905847473803840190737363⟩,⟨1273883841850255179848336422012,1273883841850255179892475725077⟩⟩,⟨⟨764904063917215161494954217210,764904063917215161521456166406⟩,⟨1273973943625670567173676299263,1273973943625670567217821750356⟩⟩,⟨⟨765094344495841864300039286303,765094344495841864326549044490⟩,⟨1274075261815859487486324603691,1274075261815859487530476969395⟩⟩,⟨⟨765305739684950192554097687815,765305739684950192580616121544⟩,⟨1274187780078991938837299672209,1274187780078991938881459717329⟩⟩,⟨⟨765538240683262672971324178319,765538240683262672997852154632⟩,⟨1274311480258553623842987890684,1274311480258553623887156381280⟩⟩,⟨⟨765791837778659250976470256885,765791837778659251003008641598⟩,⟨1274446342383711089313748978709,1274446342383711089357926677304⟩⟩,⟨⟨766066520339417752349461548380,766066520339417752376011208561⟩,⟨1274592344669726253937991500900,1274592344669726253982179173384⟩⟩,⟨⟨766362276804665436585069328078,766362276804665436611631128762⟩,⟨1274749463518423986866836746639,1274749463518423986911035153092⟩⟩,⟨⟨766679094674043625853958564291,766679094674043625880533372475⟩,⟨1274917673518716725910861178999,1274917673518716725955071084857⟩⟩] +lemma kernel0_0_r3_0_eq : ∀ k : Fin 16, kernel0_0Expr 3 0 k = kernel0_0_r3_0 k := by decide +kernel +noncomputable def kernel0_0_r3_1 : Fin 16 → CBox := ![⟨⟨767016960496587579511917956654,767016960496587579538506635953⟩,⟨1275096947447190448015535199782,1275096947447190448059757360876⟩⟩,⟨⟨767375859858823975096024833364,767375859858823975122628251196⟩,⟨1275287256268756626544284228281,1275287256268756626588519410936⟩⟩,⟨⟨767755777372088553031496848655,767755777372088553058115867510⟩,⟨1275488569137375129480763957834,1275488569137375129525012914460⟩⟩,⟨⟨768156696659066684208508160013,768156696659066684235143647268⟩,⟨1275700853396853329772529064017,1275700853396853329816792560533⟩⟩,⟨⟨768578600339559827527311184902,768578600339559827553964000630⟩,⟨1275924074581727013478382838695,1275924074581727013522661620488⟩⟩,⟨⟨769021470015481058800788407347,769021470015481058827459419997⟩,⟨1276158196418228982946612685452,1276158196418228982990907521151⟩⟩,⟨⟨769485286255083073389040456767,769485286255083073415730524948⟩,⟨1276403180825351560729691374644,1276403180825351560774003005283⟩⟩,⟨⟨769970028576422292958180958789,769970028576422292984890950886⟩,⟨1276658987916009505114539889666,1276658987916009505158869083425⟩⟩,⟨⟨770475675430062942136544393684,770475675430062942163275164331⟩,⟨1276925575998310149790519797375,1276925575998310149834867283972⟩⟩,⟨⟨771002204181025203910995596788,771002204181025203937748016619⟩,⟨1277202901576937878056798286516,1277202901576937878101164840168⟩⟩,⟨⟨771549591089981813682091327081,771549591089981813708866249211⟩,⟨1277490919354660335845612421922,1277490919354660335889998767923⟩⟩,⟨⟨772117811293707711290327076514,772117811293707711317125371154⟩,⟨1277789582233964077459141842278,1277789582233964077503548753472⟩⟩,⟨⟨772706838784787638339698187710,772706838784787638366520702302⟩,⟨1278098841318827623027718739531,1278098841318827623072146925292⟩⟩,⟨⟨773316646390586845074175471545,773316646390586845101023079807⟩,⟨1278418645916640187029903655416,1278418645916640187074353898220⟩⟩,⟨⟨773947205751490357193584879916,773947205751490357220458427549⟩,⟨1278748943540274612495683252101,1278748943540274612540156256432⟩⟩,⟨⟨774598487298416548604698172233,774598487298416548631598532290⟩,⟨1279089679910323315458848124040,1279089679910323315503344670466⟩⟩] +lemma kernel0_0_r3_1_eq : ∀ k : Fin 16, kernel0_0Expr 3 1 k = kernel0_0_r3_1 k := by decide +kernel +noncomputable def kernel0_0_r3_2 : Fin 16 → CBox := ![⟨⟨775270460229611071458242841315,775270460229611071485170850805⟩,⟨1279440798957506308540472230433,1279440798957506308584992999329⟩⟩,⟨⟨775963092486727510179878185445,775963092486727510206834723435⟩,⟨1279802242825260630930001194908,1279802242825260630974546983599⟩⟩,⟨⟨776676350730201451808958431867,776676350730201451835944334403⟩,⟨1280173951872520764171989103984,1280173951872520764216560590358⟩⟩,⟨⟨777410200313925001047672235981,777410200313925001074688380155⟩,⟨1280555864676699858743665856224,1280555864676699858788263832253⟩⟩,⟨⟨778164605259229115217446032196,778164605259229115244493242941⟩,⟨1280947918036881835090316194808,1280947918036881835134941307885⟩⟩,⟨⟨778939528228181492029218963888,778939528228181492056298126143⟩,⟨1281350046977234654231257968693,1281350046977234654275911032838⟩⟩,⟨⟨779734930496208111895973030089,779734930496208111923084967676⟩,⟨1281762184750655276908679405484,1281762184750655276953361065515⟩⟩,⟨⟨780550771924046916632454378976,780550771924046916659599974397⟩,⟨1282184262842657046164671269584,1282184262842657046209382333174⟩⟩,⟨⟨781387010929042497966512204951,781387010929042497993692265827⟩,⟨1282616210975510435828755507110,1282616210975510435873496574941⟩⟩,⟨⟨782243604455791072481825533794,782243604455791072509040954886⟩,⟨1283057957112648306299727380405,1283057957112648306344499294693⟩⟩,⟨⟨783120507946145434559979399460,783120507946145434587230989459⟩,⟨1283509427463346998822866373850,1283509427463346998867669739161⟩⟩,⟨⟨784017675308590005711243565728,784017675308590005738532214083⟩,⟨1283970546487694779798304474386,1283970546487694779843140119011⟩⟩,⟨⟨784935058886996537481011396848,784935058886996537508337892930⟩,⟨1284441236901859317101155860520,1284441236901859317146024336862⟩⟩,⟨⟨785872609428771475977595153139,785872609428771476004960401015⟩,⟨1284921419683666030532459865649,1284921419683666030577362043390⟩⟩,⟨⟨786830276052406459053055672993,786830276052406459080460462969⟩,⟨1285411014078499307926881887322,1285411014078499307971818322918⟩⟩,⟨⟨787808006214443892328488492372,787808006214443892355933722541⟩,⟨1285909937605538716684746415776,1285909937605538716729717963645⟩⟩] +lemma kernel0_0_r3_2_eq : ∀ k : Fin 16, kernel0_0Expr 3 2 k = kernel0_0_r3_2 k := by decide +kernel +noncomputable def kernel0_0_r3_3 : Fin 16 → CBox := ![⟨⟨788805745675870037614884957307,788805745675870037642371390234⟩,⟨1286418106064342467130500537464,1286418106064342467175507679456⟩⟩,⟨⟨789823438467948546845396741385,789823438467948546872925297318⟩,⟨1286935433541790498677438125350,1286935433541790498722481778429⟩⟩,⟨⟨790861026857507886387734326141,790861026857507886415305773394⟩,⟨1287461832419399661842404604392,1287461832419399661887485268382⟩⟩,⟨⟨791918451311696620507003556907,791918451311696620534618804061⟩,⟨1287997213381023558240201800824,1287997213381023558285320362340⟩⟩,⟨⟨792995650462221058736548934516,792995650462221058764208718937⟩,⟨1288541485420949676325059818611,1288541485420949676370216695008⟩⟩,⟨⟨794092561069080319900056767529,794092561069080319927762022186⟩,⟨1289094555852406522359404253799,1289094555852406522404600400819⟩⟩,⟨⟨795209117983814425399954300536,795209117983814425427705767778⟩,⟨1289656330316493493396507858504,1289656330316493493441743710142⟩⟩,⟨⟨796345254112281606006814050833,796345254112281606034612651715⟩,⟨1290226712791546271477007845468,1290226712791546271522284327183⟩⟩,⟨⟨797500900376981589587187696489,797500900376981589615034130271⟩,⟨1290805605602950535269272872124,1290805605602950535314590303351⟩⟩,⟨⟨798675985678942231800727776318,798675985678942231828622999454⟩,⟨1291392909433416786536457494039,1291392909433416786581816900031⟩⟩,⟨⟨799870436859187457561073593980,799870436859187457589018318506⟩,⟨1291988523333729073592605548504,1291988523333729073638007287593⟩⟩,⟨⟨801084178659805097739208553704,801084178659805097767203715269⟩,⟨1292592344733980361818456943490,1292592344733980361863901987150⟩⟩,⟨⟨802317133684633832913521420290,802317133684633832941567684213⟩,⟨1293204269455307251846095077323,1293204269455307251891583660842⟩⟩,⟨⟨803569222359589093627750989096,803569222359589093655849328838⟩,⟨1293824191722136678691774090308,1293824191722136678737307292066⟩⟩,⟨⟨804840362892648414265262752521,804840362892648414293413845068⟩,⟨1294452004174957139420991803256,1294452004174957139466569895428⟩⟩,⟨⟨806130471233517394912593245123,806130471233517394940798042979⟩,⟨1295087597883626892374087841519,1295087597883626892419711849346⟩⟩] +lemma kernel0_0_r3_3_eq : ∀ k : Fin 16, kernel0_0Expr 3 3 k = kernel0_0_r3_3 k := by decide +kernel +noncomputable def kernel0_0_r3_4 : Fin 16 → CBox := ![⟨⟨807439461032998092061169280730,807439461032998092089428395288⟩,⟨1295730862361231447072758056499,1295730862361231447118428079426⟩⟩,⟨⟨808767243602082334244465169834,808767243602082334272779608847⟩,⟨1296381685578502520180716875451,1296381685578502520226434093669⟩⟩,⟨⟨810113727870793142255570995950,810113727870793142283941396269⟩,⟨1297039953978810468823981335495,1297039953978810468869745924019⟩⟩,⟨⟨811478820346798124929564223026,811478820346798124957991556338⟩,⟨1297705552493742027713469020167,1297705552493742027759282066132⟩⟩,⟨⟨812862425073819420063457692940,812862425073819420091942528734⟩,⟨1298378364559274970388828112106,1298378364559274970434689615009⟩⟩,⟨⟨814264443589865455305367907011,814264443589865455333911272522⟩,⟨1299058272132561087061279796699,1299058272132561087107190999967⟩⟩,⟨⟨815684774885310515159314930553,815684774885310515187917416985⟩,⟨1299745155709328621529663902445,1299745155709328621575624872246⟩⟩,⟨⟨817123315360848816971473095430,817123315360848817000135696148⟩,⟨1300438894341915037045261228571,1300438894341915037091273122681⟩⟩,⟨⟨818579958785350520199525289122,818579958785350520228248503522⟩,⟨1301139365657940685389063995807,1301139365657940685435126641144⟩⟩,⟨⟨820054596253647818693412692642,820054596253647818722197592326⟩,⟨1301846445879633634397346786993,1301846445879633634443461559544⟩⟩,⟨⟨821547116144279994370014702284,821547116144279994398861826951⟩,⟨1302560009843815566342579656624,1302560009843815566388746501598⟩⟩,⟨⟨823057404077227041745018358887,823057404077227041773928726116⟩,⟨1303279931022558292580779320384,1303279931022558292626999475251⟩⟩,⟨⟨824585342871662205453361863449,824585342871662205482335919232⟩,⟨1304006081544520038368156494457,1304006081544520038414429662790⟩⟩,⟨⟨826130812503754506267903913164,826130812503754506296942753451⟩,⟨1304738332216970235406641976262,1304738332216970235452969614591⟩⟩,⟨⟨827693690064553064299058577239,827693690064553064328162683928⟩,⟨1305476552548511118201397376060,1305476552548511118247779295861⟩⟩,⟨⟨829273849717985760072582465940,829273849717985760101752883506⟩,⟨1306220610772503953431634858954,1306220610772503953478072387031⟩⟩] +lemma kernel0_0_r3_4_eq : ∀ k : Fin 16, kernel0_0Expr 3 4 k = kernel0_0_r3_4 k := by decide +kernel +noncomputable def kernel0_0_r3_5 : Fin 16 → CBox := ![⟨⟨830871162659005504047186681792,830871162659005504076423762007⟩,⟨1306970373871207239005206066387,1306970373871207239051698678027⟩⟩,⟨⟨832485497071918111819067234957,832485497071918111848372134946⟩,⟨1307725707600633691073534657408,1307725707600633691120083990941⟩⟩,⟨⟨834116718088926504700386396638,834116718088926504729759533925⟩,⟨1308486476516132292844817273388,1308486476516132292891422993588⟩⟩,⟨⟨835764687748926672449705898411,835764687748926672479148347018⟩,⟨1309252543998701108401989640380,1309252543998701108448653173122⟩⟩,⟨⟨837429264956591545534485116433,837429264956591545563997167331⟩,⟨1310023772282035967795901010041,1310023772282035967842621697046⟩⟩,⟨⟨839110305441779627243153080278,839110305441779627272735914543⟩,⟨1310800022480319506369300962010,1310800022480319506416080526031⟩⟩,⟨⟨840807661719305930025999578240,840807661719305930055653541968⟩,⟨1311581154616754391539650890158,1311581154616754391586488835596⟩⟩,⟨⟨842521183049113444384806174900,842521183049113444414532374499⟩,⟨1312367027652843894136160961221,1312367027652843894183058823438⟩⟩,⟨⟨844250715396884041172012418034,844250715396884041201811028916⟩,⟨1313157499518422258900792200603,1313157499518422258947749047591⟩⟩,⟨⟨845996101395128367990041621736,845996101395128368019913898993⟩,⟨1313952427142436600021925415145,1313952427142436600068943190228⟩⟩,⟨⟨847757180304794946157812354285,847757180304794946187758565292⟩,⟨1314751666484481292718919149488,1314751666484481292765997182963⟩⟩,⟨⟨849533787977439305061972539226,849533787977439305091993825538⟩,⟨1315555072567085051131452010226,1315555072567085051178591957317⟩⟩,⟨⟨851325756817994604234094016512,851325756817994604264190478691⟩,⟨1316362499508750076337187382229,1316362499508750076384388151613⟩⟩,⟨⟨853132915748185788763863683701,853132915748185788794036605786⟩,⟨1317173800557741826526234255233,1317173800557741826573497893747⟩⟩,⟨⟨854955090170629899218833338367,854955090170629899249082901268⟩,⟨1317988828126627104558480778851,1317988828126627104605806428357⟩⟩,⟨⟨856792101933665711616421035541,856792101933665711646748418889⟩,⟨1318807433827557276734737940003,1318807433827557276782127386570⟩⟩] +lemma kernel0_0_r3_5_eq : ∀ k : Fin 16, kernel0_0Expr 3 5 k = kernel0_0_r3_5 k := by decide +kernel +noncomputable def kernel0_0_r3_6 : Fin 16 → CBox := ![⟨⟨858643769296956414684883539163,858643769296956414715288691872⟩,⟨1319629468508292531099032132331,1319629468508292531146483929486⟩⟩,⟨⟨860509906897909539138375640687,860509906897909539168859947086⟩,⟨1320454782288962154492309838390,1320454782288962154539826327876⟩⟩,⟨⟨862390325718958835441082662926,862390325718958835471646209585⟩,⟨1321283224599554855495340174955,1321283224599554855542920296128⟩⟩,⟨⟨864284833055753250995506668711,864284833055753251026150676089⟩,⟨1322114644218132185992701461574,1322114644218132186040347142020⟩⟩,⟨⟨866193232486298583296435220964,866193232486298583327159560253⟩,⟨1322948889309757118088587721771,1322948889309757118136297361807⟩⟩,⟨⟨868115323841097780770684022169,868115323841097780801490099386⟩,⟨1323785807466128816303691223327,1323785807466128816351467255558⟩⟩,⟨⟨870050903174336226191794370530,870050903174336226222682169505⟩,⟨1324625245745913608244428060977,1324625245745913608292269207398⟩⟩,⟨⟨871999762736158667132042719067,871999762736158667163013504086⟩,⟨1325467050715761101194298648038,1325467050715761101242206989208⟩⟩,⟨⟨873961690946084752303381455751,873961690946084752334434921541⟩,⟨1326311068491993318336384655673,1326311068491993318384358188227⟩⟩,⟨⟨875936472367610390257442692621,875936472367610390288580359454⟩,⟨1327157144782953637651200321471,1327157144782953637699241814551⟩⟩,⟨⟨877923887684042366180393289430,877923887684042366211615030012⟩,⟨1328005124932001210093538560533,1328005124932001210141646504554⟩⟩,⟨⟨879923713675613831856796792277,879923713675613831888103917454⟩,⟨1328854853961135412656317143136,1328854853961135412704493782501⟩⟩,⟨⟨881935723197928421724778031532,881935723197928421756170140869⟩,⟨1329706176615233757673493307020,1329706176615233757721736455116⟩⟩,⟨⟨883959685161780842754392677404,883959685161780842785871318989⟩,⟨1330558937406885533565899919805,1330558937406885533614212459945⟩⟩,⟨⟨885995364514401836122566136025,885995364514401836154131062577⟩,⟨1331412980661802295635862345295,1331412980661802295684242521397⟩⟩,⟨⟨888042522222175412823692069630,888042522222175412855344641512⟩,⟨1332268150564785159984499764304,1332268150564785160032949996199⟩⟩] +lemma kernel0_0_r3_6_eq : ∀ k : Fin 16, kernel0_0Expr 3 6 k = kernel0_0_r3_6 k := by decide +kernel +noncomputable def kernel0_0_r3_7 : Fin 16 → CBox := ![⟨⟨890100915254876221963666546942,890100915254876221995406137952⟩,⟨1333124291206227680749694992975,1333124291206227680798212581505⟩⟩,⟨⟨892170296571474818085242091867,892170296571474818117070401609⟩,⟨1333981246629131912305396013948,1333981246629131912353984280659⟩⟩,⟨⟨894250415107558451046803388261,894250415107558451078720040829⟩,⟨1334838860876614075559830579590,1334838860876614075608487508132⟩⟩,⟨⟨896341015764414807345503599570,896341015764414807377510007377⟩,⟨1335696978039875062847978665243,1335696978039875062896706861393⟩⟩,⟨⟨898441839399825884002110880596,898441839399825884034206326775⟩,⟨1336555442306609831009972725098,1336555442306609831058769335354⟩⟩,⟨⟨900552622820618873917964983612,900552622820618873950151179053⟩,⟨1337414098009828549028131069962,1337414098009828549076999495037⟩⟩,⟨⟨902673098777020583734058210392,902673098777020583766334641330⟩,⟨1338272789677061187075408593293,1338272789677061187124346541746⟩⟩,⟨⟨904802995958861490482937697727,904802995958861490515305831577⟩,⟨1339131362079916060086478059353,1339131362079916060135488334601⟩⟩,⟨⟨906942038993675070599769019060,906942038993675070632227885005⟩,⟨1339989660283961673142995630609,1339989660283961673192074815590⟩⟩,⟨⟨909089948446737503086507678276,909089948446737503119059154260⟩,⟨1340847529698900060270890558069,1340847529698900060320042536312⟩⟩,⟨⟨911246440823092256807647303542,911246440823092256840290729162⟩,⟨1341704816128998664943086809669,1341704816128998664992309001473⟩⟩,⟨⟨913411228571603419114023691811,913411228571603419146760591814⟩,⟨1342561365823746681984169429792,1342561365823746682033464846310⟩⟩,⟨⟨915584020091080908395668064433,915584020091080908428497358711⟩,⟨1343417025528700669055704821482,1343417025528700669105069862016⟩⟩,⟨⟨917764519738519935988727119066,917764519738519936021650702634⟩,⟨1344271642536483143882023201099,1344271642536483143931461851595⟩⟩,⟨⟨919952427839496242422754899132,919952427839496242455771955670⟩,⟨1345125064737896813322270695506,1345125064737896813371780073944⟩⟩,⟨⟨922147440700757728699124833444,922147440700757728732236947794⟩,⟨1345977140673116034811983856047,1345977140673116034861567192523⟩⟩] +lemma kernel0_0_r3_7_eq : ∀ k : Fin 16, kernel0_0Expr 3 7 k = kernel0_0_r3_7 k := by decide +kernel +noncomputable def kernel0_0_r3_8 : Fin 16 → CBox := ![⟨⟨924349250625052134637549728725,924349250625052134670755496375⟩,⟨1346827719582916092130840736441,1346827719582916092180493711156⟩⟩,⟨⟨926557545928229382910290925078,926557545928229382943592465680⟩,⟨1347676651459899878478822762702,1347676651459899878528549994836⟩⟩,⟨⟨928772010958656108897477972383,928772010958656108930874305227⟩,⟨1348523787099680623065670979538,1348523787099680623115469273087⟩⟩,⟨⟨930992326118978732740154604174,930992326118978732773647376086⟩,⟨1349368978151978375464927183678,1349368978151978375514799996631⟩⟩,⟨⟨933218167890270200845712482282,933218167890270200879300202511⟩,⟨1350212077171587077499037236404,1350212077171587077548980143056⟩⟩,⟨⟨935449208858594229628659520602,935449208858594229662344289425⟩,⟨1351052937669168208061783878700,1351052937669168208111801516740⟩⟩,⟨⟨937685117744019524577345348487,937685117744019524611126011620⟩,⟨1351891414161826184711480105492,1351891414161826184761568951723⟩⟩,⟨⟨939925559432115023069345997852,939925559432115023103224266727⟩,⟨1352727362223419949744541882207,1352727362223419949794705633233⟩⟩,⟨⟨942170195007955720079037437231,942170195007955720113011473509⟩,⟨1353560638534564460440496741252,1353560638534564460490730219050⟩⟩,⟨⟨944418681792667082515767074888,944418681792667082549839212936⟩,⟨1354391100932275145898392776864,1354391100932275145948701279118⟩⟩,⟨⟨946670673382534441009255652782,946670673382534441043424556703⟩,⟨1355218608459207788984514146087,1355218608459207789034893812277⟩⟩,⟨⟨948925819690702068254797485700,948925819690702068289064933042⟩,⟨1356043021412445743978121400230,1356043021412445744028576173403⟩⟩,⟨⟨951183766991484911406460758687,951183766991484911440824800863⟩,⟨1356864201391785911098811844689,1356864201391785911149336399755⟩⟩,⟨⟨953444157967314143451887515668,953444157967314143486350479202⟩,⟨1357682011347474460747015160225,1357682011347474460797614851330⟩⟩,⟨⟨955706631758335836137604428681,955706631758335836172164787464⟩,⟨1358496315627342935461757667439,1358496315627342935512428285293⟩⟩,⟨⟨957970824014680136089039100224,957970824014680136123698700149⟩,⟨1359306980023295058713574416112,1359306980023295058764320159643⟩⟩] +lemma kernel0_0_r3_8_eq : ∀ k : Fin 16, kernel0_0Expr 3 8 k = kernel0_0_r3_8 k := by decide +kernel +noncomputable def kernel0_0_r3_9 : Fin 16 → CBox := ![⟨⟨960236366951416347666037927311,960236366951416347700794385094⟩,⟨1360113871817094349059200807311,1360113871817094349110015408392⟩⟩,⟨⟨962502889406207292324364161191,962502889406207292359220111299⟩,⟨1360916859825402478169582511900,1360916859825402478220472170340⟩⟩,⟨⟨964770016899674226459336911933,964770016899674226494290631081⟩,⟨1361715814444018224006830308411,1361715814444018224057790458749⟩⟩,⟨⟨967037371698481459661913923490,967037371698481459696967326670⟩,⟨1362510607691266858083522129097,1362510607691266858134557231758⟩⟩,⟨⟨969304572881147624922200610047,969304572881147624957351246015⟩,⟨1363301113250489870309879135372,1363301113250489870360982898892⟩⟩,⟨⟨971571236406588313599855381287,971571236406588313635105822450⟩,⟨1364087206511585078337019506712,1364087206511585078388198061018⟩⟩,⟨⟨973836975185392503101009107244,973836975185392503136357425301⟩,⟨1364868764611547392344310685963,1364868764611547392395559099733⟩⟩,⟨⟨976101399153832876436359910827,976101399153832876471808091799⟩,⟨1365645666473960812582194596428,1365645666473960812633517599828⟩⟩,⟨⟨978364115350607762586292875881,978364115350607762621838013559⟩,⟨1366417792847392627229933205108,1366417792847392627281323540084⟩⟩,⟨⟨980624727996310017385475862801,980624727996310017421120845997⟩,⟨1367185026342641253686026440331,1367185026342641253737491103203⟩⟩,⟨⟨982882838575615719096587371091,982882838575615719132330060721⟩,⟨1367947251468789728562745207405,1367947251468789728614278896178⟩⟩,⟨⟨985138045922183073716946663844,985138045922183073752789117109⟩,⟨1368704354668017501539840838166,1368704354668017501591448556364⟩⟩,⟨⟨987389946306249415207460694950,987389946306249415243399916510⟩,⟨1369456224349123926825769434358,1369456224349123926877443865188⟩⟩,⟨⟨989638133524911648207765906272,989638133524911648243804732819⟩,⟨1370202750919717674092584721767,1370202750919717674144332824586⟩⟩,⟨⟨991882198995072918461200160931,991882198995072918497336236169⟩,⟨1370943826817027199039459324301,1370943826817027199091275419626⟩⟩,⟨⟨994121731849035712267553115712,994121731849035712303788569281⟩,⟨1371679346537288422668066490739,1371679346537288422719955861430⟩⟩] +lemma kernel0_0_r3_9_eq : ∀ k : Fin 16, kernel0_0Expr 3 9 k = kernel0_0_r3_9 k := by decide +kernel +noncomputable def kernel0_0_r3_10 : Fin 16 → CBox := ![⟨⟨996356319032718984048270087352,996356319032718984084601348815⟩,⟨1372409206663666868208309765105,1372409206663666868260263860607⟩⟩,⟨⟨998585545406474293867251847529,998585545406474293903682179084⟩,⟨1373133305892672695512706535415,1373133305892672695564733445608⟩⟩,⟨⟨1000808993848473307896581939461,1000808993848473307933108763896⟩,⟨1373851545059028354547591310233,1373851545059028354599684977516⟩⟩,⟨⟨1003026245360636377815238686021,1003026245360636377851864204403⟩,⟨1374563827158949952054251384685,1374563827158949952106417371339⟩⟩,⟨⟨1005236879177069273508403215616,1005236879177069273545123853392⟩,⟨1375270057371804888036578264569,1375270057371804888088808182693⟩⟩,⟨⟨1007440472874972500778622347626,1007440472874972500815441221141⟩,⟨1375970143080109870747939718090,1375970143080109870800241399472⟩⟩,⟨⟨1009636602487984995720238814747,1009636602487984995757153120901⟩,⟨1376663993887835059383494049310,1376663993887835059435861053895⟩⟩,⟨⟨1011824842621921353617698635787,1011824842621921353654710647912⟩,⟨1377351521636981811603694202094,1377351521636981811656132375725⟩⟩,⟨⟨1014004766572859126412953156338,1014004766572859126450058728747⟩,⟨1378032640422403326973673941453,1378032640422403327026173696460⟩⟩,⟨⟨1016175946447530112677921783375,1016175946447530112715124445911⟩,⟨1378707266604839375834051606087,1378707266604839375886621870879⟩⟩,⟨⟨1018337953285966971373343568823,1018337953285966971410640290794⟩,⟨1379375318822138284235121427685,1379375318822138284287755382593⟩⟩,⟨⟨1020490357186353919231706798757,1020490357186353919269099923931⟩,⟨1380036717998641407358667825071,1380036717998641407411371596755⟩⟩,⟨⟨1022632727432027725126784749413,1022632727432027725164270095853⟩,⟨1380691387352707464090019881984,1380691387352707464142783978039⟩⟩,⟨⟨1024764632620572697034049093033,1024764632620572697071630069627⟩,⟨1381339252402356321634116294670,1381339252402356321686949452569⟩⟩,⟨⟨1026885640794950871877357879984,1026885640794950871915031225857⟩,⟨1381980240969014108621242541420,1381980240969014108674137561713⟩⟩,⟨⟨1028995319576606169404094346197,1028995319576606169441862475322⟩,⟨1382614283179343895127601623103,1382614283179343895180564913861⟩⟩] +lemma kernel0_0_r3_10_eq : ∀ k : Fin 16, kernel0_0Expr 3 10 k = kernel0_0_r3_10 k := by decide +kernel +noncomputable def kernel0_0_r3_11 : Fin 16 → CBox := ![⟨⟨1031093236300478861906492291493,1031093236300478861944350315035⟩,⟨1383241311465148605334992637015,1383241311465148605388013202676⟩⟩,⟨⟨1033178958151864345740938229122,1033178958151864345778890098915⟩,⟨1383861260561335319848594981565,1383861260561335319901682959161⟩⟩,⟨⟨1035252052305047881769091318211,1035252052305047881807133544543⟩,⟨1384474067501932676449876873896,1384474067501932676503024692494⟩⟩,⟨⟨1037312086063644703573824834573,1037312086063644703611959898221⟩,⟨1385079671614155686542435932020,1385079671614155686595650273580⟩⟩,⟨⟨1039358627002572678041491395681,1039358627002572678079714489910⟩,⟨1385678014510514945812647511644,1385678014510514945865917765051⟩⟩,⟨⟨1041391243111582546025154080988,1041391243111582546063468914967⟩,⟨1386269040078969927537058893590,1386269040078969927590394718706⟩⟩,⟨⟨1043409502940268674603513744086,1043409502940268674641916598842⟩,⟨1386852694471128801200264837635,1386852694471128801253658295014⟩⟩,⟨⟨1045412975744481220126974754909,1045412975744481220165468177175⟩,⟨1387428926088500013131814087818,1387428926088500013185272131321⟩⟩,⟨⟨1047401231634058635897021841268,1047401231634058635935600335482⟩,⟨1387997685566803695047431240010,1387997685566803695100941816411⟩⟩,⟨⟨1049373841721797562951811352286,1049373841721797562990479150352⟩,⟨1388558925758353825838819939998,1388558925758353825892394050455⟩⟩,⟨⟨1051330378273575319911151029358,1051330378273575319949904187249⟩,⟨1389112601712524956692758522317,1389112601712524956746387871653⟩⟩,⟨⟨1053270414859538460928405178397,1053270414859538460967246304241⟩,⟨1389658670654320214479175460126,1389658670654320214532867262692⟩⟩,⟨⟨1055193526506269202140617630967,1055193526506269202179541286609⟩,⟨1390197091961060218039190037306,1390197091961060218092932566049⟩⟩,⟨⟨1057099289849839929103407908489,1057099289849839929142418106869⟩,⟨1390727827137215471108093209624,1390727827137215471161897048915⟩⟩,⟨⟨1058987283289664492909509268766,1058987283289664492948601843538⟩,⟨1391250839787407728592091014709,1391250839787407728645947521665⟩⟩,⟨⟨1060857087143053583241047644630,1060857087143053583280225263094⟩,⟨1391766095587608764142252811600,1391766095587608764196169454568⟩⟩] +lemma kernel0_0_r3_11_eq : ∀ k : Fin 16, kernel0_0Expr 3 11 k = kernel0_0_r3_11 k := by decide +kernel +noncomputable def kernel0_0_r3_12 : Fin 16 → CBox := ![⟨⟨1062708283800380134571460483939,1062708283800380134610716832801⟩,⟨1392273562254567890706342281623,1392273562254567890760305466433⟩⟩,⟨⟨1064540457880759479036547825455,1064540457880759479075887626992⟩,⟨1392773209513502496179712973376,1392773209513502496233735052344⟩⟩,⟨⟨1066353196388147807904792599687,1066353196388147807944211473521⟩,⟨1393265009064088747547893071452,1393265009064088747601965073700⟩⟩,⟨⟨1068146088867761444704782393319,1068146088867761444744283059150⟩,⟨1393748934544792483089155291262,1393748934544792483143284921313⟩⟩,⟨⟨1069918727562718468362621209046,1069918727562718468402197605791⟩,⟨1394224961495583147323384827615,1394224961495583147377559270413⟩⟩,⟨⟨1071670707570803355450837135407,1071670707570803355490493575517⟩,⟨1394693067319076421465807435274,1394693067319076421520038178901⟩⟩,⟨⟨1073401627001254537975278518302,1073401627001254538015010412701⟩,⟨1395153231240153957176338854083,1395153231240153957230616611034⟩⟩,⟨⟨1075111087131474097983915060203,1075111087131474098023725178083⟩,⟨1395605434264111327396537845628,1395605434264111327450870547204⟩⟩,⟨⟨1076798692563558243462372744537,1076798692563558243502254225968⟩,⟨1396049659133387959069177604069,1396049659133387959123550754838⟩⟩,⟨⟨1078464051380546732109187458900,1078464051380546732149145255036⟩,⟨1396485890282935402606698204304,1396485890282935402661124879076⟩⟩,⟨⟨1080106775302289031118446882906,1080106775302289031158476207475⟩,⟨1396914113794282816234999339489,1396914113794282816289469958447⟩⟩,⟨⟨1081726479840824722332254984613,1081726479840824722372358648285⟩,⟨1397334317348360993973229643459,1397334317348360994027752342671⟩⟩,⟨⟨1083322784455175483192073386048,1083322784455175483232244726721⟩,⟨1397746490177148638288787644245,1397746490177148638343348568064⟩⟩,⟨⟨1084895312705445894786084255437,1084895312705445894826327875201⟩,⟨1398150623014206866754988541710,1398150623014206866809600043451⟩⟩,⟨⟨1086443692406130348771797983364,1086443692406130348812108908031⟩,⟨1398546708044170140818156937806,1398546708044170140872809162967⟩⟩,⟨⟨1087967555778523444705227227291,1087967555778523444745608304144⟩,⟨1398934738851263908658229146952,1398934738851263908712930421087⟩⟩] +lemma kernel0_0_r3_12_eq : ∀ k : Fin 16, kernel0_0Expr 3 12 k = kernel0_0_r3_12 k := by decide +kernel +noncomputable def kernel0_0_r3_13 : Fin 16 → CBox := ![⟨⟨1089466539602131487835563575702,1089466539602131487876007154825⟩,⟨1399314710366921257855478252266,1399314710366921257910212602550⟩⟩,⟨⟨1090940285364983014083895358057,1090940285364983014124406877622⟩,⟨1399686618816572772064226422352,1399686618816572772119008229525⟩⟩,⟨⟨1092388439412736682930406778145,1092388439412736682970981092148⟩,⟨1400050461665685574226511515254,1400050461665685574281330682065⟩⟩,⟨⟨1093810653096485389361129861704,1093810653096485389401769843477⟩,⟨1400406237565129212302764091850,1400406237565129212357629104151⟩⟩,⟨⟨1095206582919156051814974175447,1095206582919156051855672602253⟩,⟨1400753946295947597524614749823,1400753946295947597579510788941⟩⟩,⟨⟨1096575890680405233037408239960,1096575890680405233078169983245⟩,⟨1401093588713617635470052630981,1401093588713617635524992848439⟩⟩,⟨⟨1097918243619911543580981128904,1097918243619911543621800882948⟩,⟨1401425166691876492736668555138,1401425166691876492791642632147⟩⟩,⟨⟨1099233314558966661969677591249,1099233314558966662010558249663⟩,⟨1401748683066200612794699971423,1401748683066200612849716535439⟩⟩,⟨⟨1100520782040267779730332271675,1100520782040267779771265720763⟩,⟨1402064141577020630142770999822,1402064141577020630197813334237⟩⟩,⟨⟨1101780330465815341951986958563,1101780330465815341992978822711⟩,⟨1402371546812757228830286564887,1402371546812757228885369636498⟩⟩,⟨⟨1103011650232821103030108931371,1103011650232821103071153764698⟩,⟨1402670904152763746692909091274,1402670904152763746748022396671⟩⟩,⟨⟨1104214437867532750963149031108,1104214437867532751004249735420⟩,⟨1402962219710261937493729354211,1402962219710261937548881628546⟩⟩,⟨⟨1105388396156882670089095391520,1105388396156882670130244239104⟩,⟨1403245500275357767091439243371,1403245500275357767146614804779⟩⟩,⟨⟨1106533234277869809497778921276,1106533234277869809538981025227⟩,⟨1403520753258224434585514298680,1403520753258224434640727008791⟩⟩,⟨⟨1107648667924585100482192556480,1107648667924585100523442346950⟩,⟨1403787986632539973247758884747,1403787986632539973302998083334⟩⟩,⟨⟨1108734419432792419188022406476,1108734419432792419229322785484⟩,⟨1404047208879266797384130943511,1404047208879266797439405448401⟩⟩] +lemma kernel0_0_r3_13_eq : ∀ k : Fin 16, kernel0_0Expr 3 13 k = kernel0_0_r3_13 k := by decide +kernel +noncomputable def kernel0_0_r3_14 : Fin 16 → CBox := ![⟨⟨1109790217901978717921360354424,1109790217901978717962702452004⟩,⟨1404298428930860418851707460768,1404298428930860418906999103743⟩⟩,⟨⟨1110815799314788648168236689478,1110815799314788648209626639281⟩,⟨1404541656115994259879912565868,1404541656115994259935237617613⟩⟩,⟨⟨1111810906653760768015603998793,1111810906653760768057036131561⟩,⟨1404776900104887036546481107003,1404776900104887036601828796091⟩⟩,⟨⟨1112775290015284264056499713603,1112775290015284264097976916340⟩,⟨1405004170855318579505061044378,1405004170855318579560440229037⟩⟩,⟨⟨1113708706720697020701963220425,1113708706720697020743477336481⟩,⟨1405223478559419195464650476145,1405223478559419195520044745408⟩⟩,⟨⟨1114610921424447835776816170336,1114610921424447835818372513792⟩,⟨1405434833591316754931943653822,1405434833591316754987367458180⟩⟩,⟨⟨1115481706219247608001045690608,1115481706219247608042638511344⟩,⟨1405638246455724619643842764270,1405638246455724619699285251763⟩⟩,⟨⟨1116320840738136407099149812804,1116320840738136407140781974114⟩,⟨1405833727737552298077106492053,1405833727737552298132576533524⟩⟩,⟨⟨1117128112253395478481279011001,1117128112253395478522941401397⟩,⟨1406021288052619340909976071066,1406021288052619340965455180687⟩⟩,⟨⟨1117903315772235429348627079137,1117903315772235429390325867026⟩,⟨1406200937999551462149491424426,1406200937999551462204996058890⟩⟩,⟨⟨1118646254129194089346858241941,1118646254129194089388587623717⟩,⟨1406372688112936197993226259976,1406372688112936198048745536512⟩⟩,⟨⟨1119356738075179834191991545115,1119356738075179834233754343866⟩,⟨1406536548817813596862749384903,1406536548817813596918292140775⟩⟩,⟨⟨1120034586363098502707905425156,1120034586363098502749693145454⟩,⟨1406692530385575473260401683246,1406692530385575473315950933481⟩⟩,⟨⟨1120679625830004424147294583697,1120679625830004424189112692325⟩,⟨1406840642891344658315622187408,1406840642891344658371192829903⟩⟩,⟨⟨1121291691475718501247850960136,1121291691475718501289693622675⟩,⟨1406980896172903444580152579669,1406980896172903444635733738857⟩⟩,⟨⟨1121870626537858762957563851072,1121870626537858762999433839008⟩,⟨1407113299791238055590754847645,1407113299791238055646355292270⟩⟩] +lemma kernel0_0_r3_14_eq : ∀ k : Fin 16, kernel0_0Expr 3 14 k = kernel0_0_r3_14 k := by decide +kernel +noncomputable def kernel0_0_r3_15 : Fin 16 → CBox := ![⟨⟨1122416282563231306933354206885,1122416282563231306975241835060⟩,⟨1407237862992763476039901622583,1407237862992763476095501732935⟩⟩,⟨⟨1122928519475532093592120942682,1122928519475532093634032790308⟩,⟨1407354594673290360468770585849,1407354594673290360524387833359⟩⟩,⟨⟨1123407205639312628524049460015,1123407205639312628565979693782⟩,⟨1407463503343793001902839488019,1407463503343793001958463062569⟩⟩,⟨⟨1123852217920165176349442688341,1123852217920165176391394008448⟩,⟨1407564597098034491742030594597,1407564597098034491797669142043⟩⟩,⟨⟨1124263441741085784534407531464,1124263441741085784576371214088⟩,⟨1407657883582102243717852813543,1407657883582102243773488966693⟩⟩,⟨⟨1124640771134976058234061900424,1124640771134976058276043502111⟩,⟨1407743369965903993313142083088,1407743369965903993368791010278⟩⟩,⟨⟨1124984108793247314898902797688,1124984108793247314940896510663⟩,⟨1407821062916671225425129559555,1407821062916671225480780556707⟩⟩,⟨⟨1125293366110493458189332721761,1125293366110493458231341162845⟩,⟨1407890968574513733184507495682,1407890968574513733240169048400⟩⟩,⟨⟨1125568463225201642760396387679,1125568463225201642802409851865⟩,⟨1407953092530065675885403664859,1407953092530065675941056217032⟩⟩,⟨⟨1125809329056472552801321987534,1125809329056472552843346961530⟩,⟨1408007439804260090294856780470,1408007439804260090350517637726⟩⟩,⟨⟨1126015901336724885974234473811,1126015901336724886016265209395⟩,⟨1408054014830265323746280176868,1408054014830265323801938803072⟩⟩,⟨⟨1126188126640361418754324112121,1126188126640361418796363121874⟩,⟨1408092821437613306097880181999,1408092821437613306153544844728⟩⟩,⟨⟨1126325960408376827320799155297,1126325960408376827362837609405⟩,⟨1408123862838545967731203225694,1408123862838545967786856387892⟩⟩,⟨⟨1126429366968890248299626362185,1126429366968890248341669835979⟩,⟨1408147141616602449289509962128,1408147141616602449345166865867⟩⟩,⟨⟨1126498319553588384055841337445,1126498319553588384097884170068⟩,⟨1408162659717466042949148288661,1408162659717466043004798613334⟩⟩,⟨⟨1126532800310067786134606508592,1126532800310067786176651093660⟩,⟨1408170418442086061920429659657,1408170418442086061976081410749⟩⟩] +lemma kernel0_0_r3_15_eq : ∀ k : Fin 16, kernel0_0Expr 3 15 k = kernel0_0_r3_15 k := by decide +kernel +noncomputable def kernel0_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel0_0_r3_0,kernel0_0_r3_1,kernel0_0_r3_2,kernel0_0_r3_3,kernel0_0_r3_4,kernel0_0_r3_5,kernel0_0_r3_6,kernel0_0_r3_7,kernel0_0_r3_8,kernel0_0_r3_9,kernel0_0_r3_10,kernel0_0_r3_11,kernel0_0_r3_12,kernel0_0_r3_13,kernel0_0_r3_14,kernel0_0_r3_15] +lemma kernel0_0_r3_eq (i k : Fin 16) : kernel0_0Expr 3 i k = kernel0_0_r3 i k := by + fin_cases i + · exact kernel0_0_r3_0_eq k + · exact kernel0_0_r3_1_eq k + · exact kernel0_0_r3_2_eq k + · exact kernel0_0_r3_3_eq k + · exact kernel0_0_r3_4_eq k + · exact kernel0_0_r3_5_eq k + · exact kernel0_0_r3_6_eq k + · exact kernel0_0_r3_7_eq k + · exact kernel0_0_r3_8_eq k + · exact kernel0_0_r3_9_eq k + · exact kernel0_0_r3_10_eq k + · exact kernel0_0_r3_11_eq k + · exact kernel0_0_r3_12_eq k + · exact kernel0_0_r3_13_eq k + · exact kernel0_0_r3_14_eq k + · exact kernel0_0_r3_15_eq k +noncomputable def kernel0_0_r4_0 : Fin 16 → CBox := ![⟨⟨540563674655571831184242340284,540563674655571831202968026697⟩,⟨1126172202207772256841505735509,1126172202207772256880517523405⟩⟩,⟨⟨540576907237531164880475678770,540576907237531164899201909639⟩,⟨1126182810168014195352662746315,1126182810168014195391675191291⟩⟩,⟨⟨540603371754237357076320650082,540603371754237357095047968075⟩,⟨1126204024803495000001850789524,1126204024803495000040864542645⟩⟩,⟨⟨540643066910826902347979805994,540643066910826902366708753750⟩,⟨1126235843544152600525281505193,1126235843544152600564297217452⟩⟩,⟨⟨540695990763908255857143804198,540695990763908255875874924319⟩,⟨1126278262534754253248582608094,1126278262534754253287600930381⟩⟩,⟨⟨540762140720246571935104407119,540762140720246571953838242151⟩,⟨1126331276634729466545570373209,1126331276634729466584591956269⟩⟩,⟨⟨540841513535010493782253393017,540841513535010493800990485411⟩,⟨1126394879417948053624111721672,1126394879417948053663137215965⟩⟩,⟨⟨540934105309581399584156721589,540934105309581399602897613757⟩,⟨1126469063172444014206458454516,1126469063172444014245488510436⟩⟩,⟨⟨541039911488925613024106473567,541039911488925613042851707707⟩,⟨1126553818900086121691881998997,1126553818900086121730917266277⟩⟩,⟨⟨541158926858530189751622298942,541158926858530189770372417314⟩,⟨1126649136316196267160472409508,1126649136316196267199513538168⟩⟩,⟨⟨541291145540902996025544852599,541291145540902996044300397042⟩,⟨1126755003849116786046900771537,1126755003849116786085948410267⟩⟩,⟨⟨541436560991637901667098029897,541436560991637901685859542506⟩,⟨1126871408639728167429108102659,1126871408639728167468162901107⟩⟩,⟨⟨541595165995046016809638043096,541595165995046016828406065147⟩,⟨1126998336540918719585462624325,1126998336540918719624525229499⟩⟩,⟨⟨541766952659354010893742468348,541766952659354010912517541838⟩,⟨1127135772117007938719806024358,1127135772117007938758877085806⟩⟩,⟨⟨541951912411470663103612007672,541951912411470663122394673268⟩,⟨1127283698643125500480415214531,1127283698643125500519495377468⟩⟩,⟨⟨542150035991322906146913298943,542150035991322906165704098469⟩,⟨1127442098104547966048052957185,1127442098104547966087142870860⟩⟩] +lemma kernel0_0_r4_0_eq : ∀ k : Fin 16, kernel0_0Expr 4 0 k = kernel0_0_r4_0 k := by decide +kernel +noncomputable def kernel0_0_r4_1 : Fin 16 → CBox := ![⟨⟨542361313445762740117149158622,542361313445762740135948631711⟩,⟨1127610951195995466080016835214,1127610951195995466119117141683⟩⟩,⟨⟨542585734122046510315735237617,542585734122046510334543926206⟩,⟨1127790237320890796609553052193,1127790237320890796648664401423⟩⟩,⟨⟨542823286660888162518734271695,542823286660888162537552714551⟩,⟨1127979934590583531049247957751,1127979934590583531088370989265⟩⟩,⟨⟨543073958989088211417251821743,543073958989088211436080560610⟩,⟨1128180019823541921666905557351,1128180019823541921706040920868⟩⟩,⟨⟨543337738311740283005326886115,543337738311740283024166458075⟩,⟨1128390468544515532224474456956,1128390468544515532263622786776⟩⟩,⟨⟨543614611104017219696982713490,543614611104017219715833660764⟩,⟨1128611254983671710823825222230,1128611254983671710862987170149⟩⟩,⟨⟨543904563102538868084723348095,543904563102538868103586206655⟩,⟨1128842352075709178314001535939,1128842352075709178353177733055⟩⟩,⟨⟨544207579296323803662340065365,544207579296323803681215377189⟩,⟨1129083731458952172806625652614,1129083731458952172845816750458⟩⟩,⟨⟨544523643917327384679804466002,544523643917327384698692764360⟩,⟨1129335363474428754840205549555,1129335363474428754879412170759⟩⟩,⟨⟨544852740430568668728666013367,544852740430568668747567841420⟩,⟨1129597217164937040447943215446,1129597217164937040487166016145⟩⟩,⟨⟨545194851523848870820965143097,545194851523848870839881032938⟩,⟨1129869260274103290731945313845,1129869260274103290771184913427⟩⟩,⟨⟨545549959097064190768073987887,545549959097064190787004482173⟩,⟨1130151459245435946440926637908,1130151459245435946480183691539⟩⟩,⟨⟨545918044251115990729371452644,545918044251115990748317079677⟩,⟨1130443779221379854396685624778,1130443779221379854435960739955⟩⟩,⟨⟨546299087276421461021754407049,546299087276421461040715711420⟩,⟨1130746184042375089321499953169,1130746184042375089360793792369⟩⟩,⟨⟨546693067641028073793197210501,546693067641028073812174719161⟩,⟨1131058636245924929585303048693,1131058636245924929624616215812⟩⟩,⟨⟨547099963978335290096197609193,547099963978335290115191866048⟩,⟨1131381097065677698515611182842,1131381097065677698554944339001⟩⟩] +lemma kernel0_0_r4_1_eq : ∀ k : Fin 16, kernel0_0Expr 4 1 k = kernel0_0_r4_1 k := by decide +kernel +noncomputable def kernel0_0_r4_2 : Fin 16 → CBox := ![⟨⟨547519754074427156374849421843,547519754074427156393860948135⟩,⟨1131713526430527334088547670032,1131713526430527334127901401093⟩⟩,⟨⟨547952414855019601522646544073,547952414855019601541675887176⟩,⟨1132055882963737698936062687063,1132055882963737698975437666814⟩⟩,⟨⟨548397922372026425592222201214,548397922372026425611269881479⟩,⟨1132408123982095789548867064284,1132408123982095789588263876803⟩⟩,⟨⟨548856251789748156053172870922,548856251789748156072239434187⟩,⟨1132770205495099148209092057766,1132770205495099148248511372906⟩⟩,⟨⟨549327377370688137304608375812,549327377370688137323694335185⟩,⟨1133142082204182923429744192815,1133142082204182923469186571828⟩⟩,⟨⟨549811272461000414054133180614,549811272461000414073239086516⟩,⟨1133523707501992164384159233103,1133523707501992164423625362492⟩⟩,⟨⟨550307909475574169267688872700,550307909475574169286815237227⟩,⟨1133915033471705071848403802420,1133915033471705071887894241590⟩⟩,⟨⟨550817259882759682761949847559,550817259882759682781097219280⟩,⟨1134316010886413062419432182983,1134316010886413062458947613756⟩⟩,⟨⟨551339294188740987233154096721,551339294188740987252322977289⟩,⟨1134726589208563634074273990806,1134726589208563634113814939524⟩⟩,⟨⟨551873981921560614666981185138,551873981921560614686172130431⟩,⟨1135146716589472149359061923750,1135146716589472149398629098267⟩⟩,⟨⟨552421291614802047719912885387,552421291614802047739126397388⟩,⟨1135576339868908777495767938612,1135576339868908777535361868288⟩⟩,⟨⟨552981190790935717862614982463,552981190790935717881851613379⟩,⟨1136015404574766958319554253015,1136015404574766958359175635336⟩⟩,⟨⟨553553645944334624881790514055,553553645944334624901050753461⟩,⟨1136463854922819869057180302566,1136463854922819869096829627797⟩⟩,⟨⟨554138622523965890792226863976,554138622523965890811511272837⟩,⟨1136921633816571489369526311416,1136921633816571489409204308224⟩⟩,⟨⟨554736084915764805350666482907,554736084915764805369975551020⟩,⟨1137388682847208970647759931497,1137388682847208970687467093287⟩⟩,⟨⟨555345996424698170214339742163,555345996424698170233674026390⟩,⟨1137864942293663122107944314358,1137864942293663122147681358426⟩⟩] +lemma kernel0_0_r4_2_eq : ∀ k : Fin 16, kernel0_0Expr 4 2 k = kernel0_0_r4_2 k := by decide +kernel +noncomputable def kernel0_0_r4_3 : Fin 16 → CBox := ![⟨⟨555968319256524004367259190359,555968319256524004386619162829⟩,⟨1138350351122783928604258170384,1138350351122783928644025534193⟩⟩,⟨⟨556603014499254934755179816386,556603014499254934774566047390⟩,⟨1138844846989638113104143945919,1138844846989638113143942393825⟩⟩,⟨⟨557250042104332863124401979054,557250042104332863143814943934⟩,⟨1139348366237935850263843145079,1139348366237935850303673128148⟩⟩,⟨⟨557909360867522772839332218133,557909360867522772858772479506⟩,⟨1139860843900593826330758058218,1139860843900593826370620318091⟩⟩,⟨⟨558580928409533817937684173324,558580928409533817957152186859⟩,⟨1140382213700441924497563545328,1140382213700441924537458471227⟩⟩,⟨⟨559264701156376120838561313099,559264701156376120858057656214⟩,⟨1140912408051080893656559746407,1140912408051080893696488131969⟩⟩,⟨⟨559960634319461994904664946837,559960634319461994924190077925⟩,⟨1141451358057898432063149090409,1141451358057898432103111337454⟩⟩,⟨⟨560668681875460603421485249412,560668681875460603441039738051⟩,⟨1141998993519251185523553081782,1141998993519251185563549961275⟩⟩,⟨⟨561388796545915367427935439370,561388796545915367447519716716⟩,⟨1142555242927820222180535659048,1142555242927820222220567486867⟩⟩,⟨⟨562120929776633741136892229123,562120929776633741156506886396⟩,⟨1143120033472147602586246033258,1143120033472147602626313655384⟩⟩,⟨⟨562865031716859285330648305769,562865031716859285350293781697⟩,⟨1143693291038361714325644816762,1143693291038361714365748578365⟩⟩,⟨⟨563621051198236286002861388825,563621051198236286022538261235⟩,⟨1144274940212099084787831100314,1144274940212099084827971807042⟩⟩,⟨⟨564388935713577487529751637640,564388935713577487549460315781⟩,⟨1144864904280630423575017484875,1144864904280630423615195389606⟩⟩,⟨⟨565168631395445836660295299739,565168631395445836680036384560⟩,⟨1145463105235198677287726151261,1145463105235198677327942139966⟩⟩,⟨⟨565960082994561465475626836644,565960082994561465495400744271⟩,⟨1146069463773576903827007892782,1146069463773576903867262246107⟩⟩,⟨⟨566763233858045478025471144050,566763233858045478045278461945⟩,⟨1146683899302853790706507189918,1146683899302853790746800753975⟩⟩] +lemma kernel0_0_r4_3_eq : ∀ k : Fin 16, kernel0_0Expr 4 3 k = kernel0_0_r4_3 k := by decide +kernel +noncomputable def kernel0_0_r4_4 : Fin 16 → CBox := ![⟨⟨567578025907512446433622365770,567578025907512446453463468848⟩,⟨1147306329942454651965267447220,1147306329942454652005600373045⟩⟩,⟨⟨568404399617023867690118328033,568404399617023867709993837713⟩,⟨1147936672527405740912638128542,1147936672527405740953011378616⟩⟩,⟨⟨569242293990915181914840459823,569242293990915181934750766481⟩,⟨1148574842611849710916482201162,1148574842611849710956895983312⟩⟩,⟨⟨570091646541509306370628842109,570091646541509306390574544278⟩,⟨1149220754472820043562928971223,1149220754472820043603384178083⟩⟩,⟨⟨570952393266729996693064093552,570952393266729996713045539321⟩,⟨1149874321114282242569474815089,1149874321114282242609971522770⟩⟩,⟨⟨571824468627628707442526077808,571824468627628707462543899836⟩,⟨1150535454271449562624321815982,1150535454271449562664861034456⟩⟩,⟨⟨572707805525838987909762296907,572707805525838987929816856421⟩,⟨1151204064415381004656846828607,1151204064415381004697428684073⟩⟩,⟨⟨573602335280972815840530177483,573602335280972815860622085629⟩,⟨1151880060757869262723041796611,1151880060757869262763667234723⟩⟩,⟨⟨574507987607973641093075311298,574507987607973641113204871860⟩,⟨1152563351256626252525034161230,1152563351256626252565703128625⟩⟩,⟨⟨575424690594441282892772721431,575424690594441282912940593766⟩,⟨1153253842620773787388398600889,1153253842620773787429112206984⟩⟩,⟨⟨576352370677944197972914097709,576352370677944197993120610308⟩,⟨1153951440316646894112314976179,1153951440316646894153073256418⟩⟩,⟨⟨577290952623335012144078302436,577290952623335012164324080624⟩,⟨1154656048573917178307823372454,1154656048573917178348627332212⟩⟩,⟨⟨578240359500085584354395611998,578240359500085584374680925706⟩,⟨1155367570392043556476097845764,1155367570392043556516947339132⟩⟩,⟨⟨579200512659658249709637888746,579200512659658249729963411567⟩,⟨1156085907547057569985256719890,1156085907547057570026152916580⟩⟩,⟨⟨580171331712930265818459867703,580171331712930265838825891546⟩,⟨1156810960598690384120890380061,1156810960598690384161833215110⟩⟩,⟨⟨581152734507688864799837660045,581152734507688864820244826087⟩,⟨1157542628897848453359377616416,1157542628897848453400368162071⟩⟩] +lemma kernel0_0_r4_4_eq : ∀ k : Fin 16, kernel0_0Expr 4 4 k = kernel0_0_r4_4 k := by decide +kernel +noncomputable def kernel0_0_r4_5 : Fin 16 → CBox := ![⟨⟨582144637106214690904932222642,582144637106214690925380741671⟩,⟨1158280810594444701799265259265,1158280810594444701840303198217⟩⟩,⟨⟨583146953762971780514846804195,583146953762971780535337386929⟩,⟨1159025402645591925147847863315,1159025402645591925188934501473⟩⟩,⟨⟨584159596902422616812222276842,584159596902422616832755174600⟩,⟨1159776300824164967670164221662,1159776300824164967711299383845⟩⟩,⟨⟨585182477096987165204016283517,585182477096987165224592154985⟩,⟨1160533399727738063948029634688,1160533399727738063989214467197⟩⟩,⟨⟨586215503045165167093537639121,586215503045165167114156656801⟩,⟨1161296592787903561060101855168,1161296592787903561101335940309⟩⟩,⟨⟨587258581549841338342957181558,587258581549841338363620070169⟩,⟨1162065772279978051783852182432,1162065772279978051825136889088⟩⟩,⟨⟨588311617496793484197159866801,588311617496793484217866832788⟩,⟨1162840829333101753552114693910,1162840829333101753593449726319⟩⟩,⟨⟨589374513833423904003047641050,589374513833423904023799362392⟩,⟨1163621653940736761098268848077,1163621653940736761139655434289⟩⟩,⟨⟨590447171547734816185741346908,590447171547734816206537923948⟩,⟨1164408134971569582936028006475,1164408134971569582977465523115⟩⟩,⟨⟨591529489647568886048581472888,591529489647568886069423675431⟩,⟨1165200160180823142996798713797,1165200160180823143038288694743⟩⟩,⟨⟨592621365140136285445376814556,592621365140136285466264799758⟩,⟨1165997616221983188858883661550,1165997616221983188900425680034⟩⟩,⟨⟨593722693011850053613164741332,593722693011850053634099208194⟩,⟨1166800388658943797032621971430,1166800388658943797074217344863⟩⟩,⟨⟨594833366208491861818716503709,594833366208491861839697505795⟩,⟨1167608361978576403714193290608,1167608361978576403755841275660⟩⟩,⟨⟨595953275615730610314051727719,595953275615730610335080051979⟩,⟨1168421419603726516304864801044,1168421419603726516346567008580⟩⟩,⟨⟨597082310040016603752884433344,597082310040016603773960182962⟩,⟨1169239443906641976846021666996,1169239443906641976887777528333⟩⟩,⟨⟨598220356189874360014817120261,598220356189874360035941017109⟩,⟨1170062316222836353395127074573,1170062316222836353436938004552⟩⟩] +lemma kernel0_0_r4_5_eq : ∀ k : Fin 16, kernel0_0Expr 4 5 k = kernel0_0_r4_5 k := by decide +kernel +noncomputable def kernel0_0_r4_6 : Fin 16 → CBox := ![⟨⟨599367298657617406627630017440,599367298657617406648802020855⟩,⟨1170889916865390729334366570505,1170889916865390729376231558744⟩⟩,⟨⟨600523019901508707967842321915,600523019901508707989063280225⟩,⟨1171722125139696843751633625997,1171722125139696843793554503756⟩⟩,⟨⟨601687400228390644441639427557,601687400228390644462909385231⟩,⟨1172558819358644208472316608092,1172558819358644208514292654029⟩⟩,⟨⟨602860317776808731176740840903,602860317776808731198060544424⟩,⟨1173399876858253489179815129963,1173399876858253489221847864147⟩⟩,⟨⟨604041648500653517654973308314,604041648500653517676342668736⟩,⟨1174245174013758089493955967340,1174245174013758089536044263638⟩⟩,⟨⟨605231266153345350439678652947,605231266153345350461098531305⟩,⟨1175094586256135518051893486508,1175094586256135518094039243270⟩⟩,⟨⟨606429042272586907947515992595,606429042272586907968986369595⟩,⟨1175947988089089749750541487020,1175947988089089749792743818906⟩⟩,⟨⟨607634846165708628318776994283,607634846165708628340298642914⟩,⟨1176805253106485413580304174749,1176805253106485413622564715420⟩⟩,⟨⟨608848544895632348085477268859,608848544895632348107049990942⟩,⟨1177666254010234251147554325979,1177666254010234251189871645417⟩⟩,⟨⟨610070003267478649747913163010,610070003267478649769537889620⟩,⟨1178530862628633892311897137244,1178530862628633892354273384953⟩⟩,⟨⟨611299083815843579769358023814,611299083815843579791034666859⟩,⟨1179398949935158587642081587300,1179398949935158587684515703001⟩⟩,⟨⟨612535646792770544102914692133,612535646792770544124644052845⟩,⟨1180270386067701121933817317520,1180270386067701121976311056372⟩⟩,⟨⟨613779550156443315390027563227,613779550156443315411809384674⟩,⟨1181145040348264709171171305730,1181145040348264709213723098919⟩⟩,⟨⟨615030649560626193631588476345,615030649560626193653423706186⟩,⟨1182022781303103237412704185604,1182022781303103237455316266707⟩⟩,⟨⟨616288798344877449645348013434,616288798344877449667236489467⟩,⟨1182903476683307792531763164842,1182903476683307792574434287171⟩⟩,⟨⟨617553847525562247204591577164,617553847525562247226534130744⟩,⟨1183786993485836942950096592107,1183786993485836942992828640717⟩⟩] +lemma kernel0_0_r4_6_eq : ∀ k : Fin 16, kernel0_0Expr 4 6 k = kernel0_0_r4_6 k := by decide +kernel +noncomputable def kernel0_0_r4_7 : Fin 16 → CBox := ![⟨⟨618825645787691284623301453796,618825645787691284645297688688⟩,⟨1184673197974987813913903990612,1184673197974987813956695010573⟩⟩,⟨⟨620104039477611418937470426227,620104039477611418959521383189⟩,⟨1185561955704304519935496857918,1185561955704304519978349409674⟩⟩,⟨⟨621388872596574534962462310291,621388872596574534984567747842⟩,⟨1186453131538920058251939870736,1186453131538920058294852510514⟩⟩,⟨⟨622679986795210896621649705897,622679986795210896643810487129⟩,⟨1187346589678327295049540163880,1187346589678327295092514914225⟩⟩,⟨⟨623977221368933168290954494384,623977221368933168313170167432⟩,⟨1188242193679574200311015583147,1188242193679574200354050371311⟩⟩,⟨⟨625280413254297218747304795140,625280413254297218769576407238⟩,⟨1189139806480878007026585724655,1189139806480878007069683168318⟩⟩,⟨⟨626589397026345718919334035515,626589397026345718941661260377⟩,⟨1190039290425652486762667154187,1190039290425652486805825600991⟩⟩,⟨⟨627904004896960416303219206314,627904004896960416325602940655⟩,⟨1190940507286942046818139844672,1190940507286942046861361463092⟩⟩,⟨⟨629224066714248812929226410920,629224066714248812951666046613⟩,⟨1191843318292255865059001530706,1191843318292255865102283822805⟩⟩,⟨⟨630549409962990789467104145530,630549409962990789489600832518⟩,⟨1192747584148794787671712925451,1192747584148794787715058868585⟩⟩,⟨⟨631879859766170504782877324315,631879859766170504805430646267⟩,⟨1193653165069063223201630020425,1193653165069063223245037743339⟩⟩,⟨⟨633215238887618657369416072811,633215238887618657392026961558⟩,⟨1194559920796857774055741740593,1194559920796857774099213564914⟩⟩,⟨⟨634555367735789921955823156490,634555367735789921978490937113⟩,⟨1195467710633623854881199973396,1195467710633623854924733260504⟩⟩,⟨⟨635900064368700070669015969675,635900064368700070691741802292⟩,⟨1196376393465171056636158720764,1196376393465171056679756521991⟩⟩,⟨⟨637249144500046952815356814800,637249144500046952838140187489⟩,⟨1197285827788737526521489677136,1197285827788737526565149891317⟩⟩,⟨⟨638602421506539140140472618505,638602421506539140163314499972⟩,⟨1198195871740393148034011982706,1198195871740393148077737092632⟩⟩] +lemma kernel0_0_r4_7_eq : ∀ k : Fin 16, kernel0_0Expr 4 7 k = kernel0_0_r4_7 k := by decide +kernel +noncomputable def kernel0_0_r4_8 : Fin 16 → CBox := ![⟨⟨639959706436455644812666215690,639959706436455644835565731776⟩,⟨1199106383122770823045905400254,1199106383122770823089692224461⟩⟩,⟨⟨641320808019459684893717173282,641320808019459684916675622324⟩,⟨1200017219433114679839421375380,1200017219433114679883273436967⟩⟩,⟨⟨642685532677689006279894989607,642685532677689006302911759037⟩,⟨1200928237891633558275919262840,1200928237891633558319834221430⟩⟩,⟨⟨644053684538144770621950015114,644053684538144770645026111744⟩,⟨1201839295470147656612623106616,1201839295470147656656603612507⟩⟩,⟨⟨645425065446400485211129099491,645425065446400485234263596901⟩,⟨1202750248921015764772236047447,1202750248921015764816278835690⟩⟩,⟨⟨646799474981651882934828458915,646799474981651882958022643280⟩,⟨1203660954806330057003563398886,1203660954806330057047672002862⟩⟩,⟨⟨648176710473128057889135245205,648176710473128057912388397820⟩,⟨1204571269527364973740371155095,1204571269527364973784542984741⟩⟩,⟨⟨649556567017883524859178497912,649556567017883524882491665350⟩,⟨1205481049354266288973370324355,1205481049354266289017608205061⟩⟩,⟨⟨650938837499990198461294320426,650938837499990198484666363189⟩,⟨1206390150455966036506491327121,1206390150455966036550791424901⟩⟩,⟨⟨652323312611147580150549125804,652323312611147580173981474106⟩,⟨1207298428930308556987650325729,1207298428930308557032016665079⟩⟩,⟨⟨653709780872728698450046091814,653709780872728698473537916013⟩,⟨1208205740834372528503957376984,1208205740834372528548387109913⟩⟩,⟨⟨655098028659278569622502594207,655098028659278569646054981628⟩,⟨1209111942214973457729932013595,1209111942214973457774428146041⟩⟩,⟨⟨656487840223481132600728956837,656487840223481132624340701210⟩,⟨1210016889139330737032739558070,1210016889139330737077298140411⟩⟩,⟨⟨657878997722609763396759318112,657878997722609763420431844727⟩,⟨1210920437725883016484670340043,1210920437725883016529295434674⟩⟩,⟨⟨659271281246475590550384123941,659271281246475590574116487072⟩,⟨1211822444175235299319501481975,1211822444175235299364189973725⟩⟩,⟨⟨660664468846886914644391764483,660664468846886914668185093616⟩,⟨1212722764801220845896965856160,1212722764801220845941720938129⟩⟩] +lemma kernel0_0_r4_8_eq : ∀ k : Fin 16, kernel0_0Expr 4 8 k = kernel0_0_r4_8 k := by decide +kernel +noncomputable def kernel0_0_r4_9 : Fin 16 → CBox := ![⟨⟨662058336568632081752256942003,662058336568632081776109764580⟩,⟨1213621256062060665600229172902,1213621256062060665645046181812⟩⟩,⟨⟨663452658481997173199846924721,663452658481997173223760855497⟩,⟨1214517774591603089163759669991,1214517774591603089208643297916⟩⟩,⟨⟨664847206716828852582397529697,664847206716828852606371502697⟩,⟨1215412177230625646578199774921,1215412177230625646623146633225⟩⟩,⟨⟨666241751498151656009261420564,666241751498151656033296607948⟩,⟨1216304321058181228791631553724,1216304321058181228836645026442⟩⟩,⟨⟨667636061183347923542277995553,667636061183347923566372884228⟩,⟨1217194063422970285751117230570,1217194063422970285796192630197⟩⟩,⟨⟨669029902300907449302488565467,669029902300907449326644732010⟩,⟨1218081261974720609709531309799,1218081261974720609754673270582⟩⟩,⟨⟨670423039590752775361994876130,670423039590752775386211129613⟩,⟨1218965774695556071941716864240,1218965774695556071986921716085⟩⟩,⟨⟨671815236046144870994801092127,671815236046144871019078648591⟩,⟨1219847459931335523823813268041,1219847459931335523869084591611⟩⟩,⟨⟨673206252957172724879444196578,673206252957172724903781264517⟩,⟨1220726176422942940354303912210,1220726176422942940399636286942⟩⟩,⟨⟨674595849955829134238830428933,674595849955829134263228779533⟩,⟨1221601783337509776325507303736,1221601783337509776370906008404⟩⟩,⟨⟨675983785062673702546304178247,675983785062673702570762492154⟩,⟨1222474140299550423146534002931,1222474140299550423191995081562⟩⟩,⟨⟨677369814735082757263837902157,677369814735082757288357439428⟩,⟨1223343107421991598391149226365,1223343107421991598436676458527⟩⟩,⟨⟨678753693917084572116123199603,678753693917084572140702115282⟩,⟨1224208545337076471075560032711,1224208545337076471121147945472⟩⟩,⟨⟨680135176090776925715507439631,680135176090776925740147472960⟩,⟨1225070315227124323997166655634,1225070315227124324042820493745⟩⟩,⟨⟨681514013329322651074225506891,681514013329322651098925206210⟩,⟨1225928278855126580677190010962,1225928278855126580722905526673⟩⟩,⟨⟨682889956351517429872754084097,682889956351517429897514754253⟩,⟨1226782298595160078990599596170,1226782298595160079036380771955⟩⟩] +lemma kernel0_0_r4_9_eq : ∀ k : Fin 16, kernel0_0Expr 4 9 k = kernel0_0_r4_9 k := by decide +kernel +noncomputable def kernel0_0_r4_10 : Fin 16 → CBox := ![⟨⟨684262754577922662560421158226,684262754577922662585240602275⟩,⟨1227632237462598556830093400298,1227632237462598556875933827638⟩⟩,⟨⟨685632156188554801772525561380,685632156188554801797405780127⟩,⟨1228477959144103427477905495374,1228477959144103427523811261261⟩⟩,⟨⟨686997908182121073544664309843,686997908182121073569603717081⟩,⟨1229319328027375064037765098853,1229319328027375064083731662469⟩⟩,⟨⟨688359756436790029836817989563,688359756436790029861817934328⟩,⟨1230156209230645983539575129452,1230156209230645983585606675818⟩⟩,⟨⟨689717445772483878453191929545,689717445772483878478250213694⟩,⟨1230988468631897522344387536436,1230988468631897522390477769327⟩⟩,⟨⟨691070720014678024121729767532,691070720014678024146848302407⟩,⟨1231815972897781825358412108773,1231815972897781825404566914198⟩⟩,⟨⟨692419322059691728898419791713,692419322059691728923596853524⟩,⟨1232638589512231232362713774571,1232638589512231232408928314589⟩⟩,⟨⟨693762993941452262858029368144,693762993941452262883266350619⟩,⟨1233456186804737435465404715449,1233456186804737435511683380293⟩⟩,⟨⟨695101476899713368948900672020,695101476899713368974195027596⟩,⟨1234268633978283102207006505844,1234268633978283102253342087224⟩⟩,⟨⟨696434511449707310698195240248,696434511449707310723549134337⟩,⟨1235075801136909009050619619713,1235075801136909009097018819954⟩⟩,⟨⟨697761837453208209976520379627,697761837453208210001931949803⟩,⟨1235877559312900109653373762608,1235877559312900109699831447999⟩⟩,⟨⟨699083194190982816132637297614,699083194190982816158107981164⟩,⟨1236673780493574371160645185091,1236673780493574371207165948615⟩⟩,⟨⟨700398320436603279398178875056,700398320436603279423706103382⟩,⟨1237464337647658649437503270648,1237464337647658649484079964189⟩⟩,⟨⟨701706954531594932486333269841,701706954531594932511919134250⟩,⟨1238249104751236340228337513014,1238249104751236340274976687499⟩⟩,⟨⟨703008834461890516751906717984,703008834461890516777549215773⟩,⟨1239027956813252037221386997793,1239027956813252037268083222827⟩⟩,⟨⟨704303697935560725161001942312,704303697935560725186702554174⟩,⟨1239800769900558949322570965915,1239800769900558949369329037338⟩⟩] +lemma kernel0_0_r4_10_eq : ∀ k : Fin 16, kernel0_0Expr 4 10 k = kernel0_0_r4_10 k := by decide +kernel +noncomputable def kernel0_0_r4_11 : Fin 16 → CBox := ![⟨⟨705591282461789375685917345488,705591282461789375711673070081⟩,⟨1240567421162495377474905415967,1240567421162495377521717043519⟩⟩,⟨⟨706871325431059977670967853580,706871325431059977696781115617⟩,⟨1241327788854977125384855134951,1241327788854977125431727913347⟩⟩,⟨⟨708143564196518912308671705463,708143564196518912334540362743⟩,⟨1242081752364093317754171356989,1242081752364093317801099564684⟩⟩,⟨⟨709407736156478918744309261372,709407736156478918770234835874⟩,⟨1242829192229193723211364175594,1242829192229193723258352805300⟩⟩,⟨⟨710663578838025061629249869315,710663578838025061655229411109⟩,⟨1243569990165456326168424948178,1243569990165456326215465985855⟩⟩,⟨⟨711910829981683856321755983901,711910829981683856347791768898⟩,⟨1244304029085924561301953785569,1244304029085924561349054458631⟩⟩,⟨⟨713149227627114746550863572144,713149227627114746576953318315⟩,⟨1245031193123004315212907535933,1245031193123004315260061833284⟩⟩,⟨⟨714378510199781668382705616888,714378510199781668408850886932⟩,⟨1245751367649411510926431097945,1245751367649411510973644207385⟩⟩,⟨⟨715598416598560995930559096433,715598416598560995956756518674⟩,⟨1246464439298561821059456104287,1246464439298561821106718913641⟩⟩,⟨⟨716808686284240750599147713804,716808686284240750625399885023⟩,⟨1247170295984394803450262003040,1247170295984394803497582739756⟩⟩,⟨⟨718009059368864568914683956076,718009059368864568940988456884⟩,⟨1247868826920625517492268697092,1247868826920625517539641069521⟩⟩,⟨⟨719199276705872566319160367150,719199276705872566345518798137⟩,⟨1248559922639417458963984446508,1248559922639417459011413828772⟩⟩,⟨⟨720379079980989907842118783108,720379079980989907868527808589⟩,⟨1249243475009471444363041247482,1249243475009471444410518758854⟩⟩,⟨⟨721548211803812603429120188941,721548211803812603455582271436⟩,⟨1249919377253525881143155852940,1249919377253525881190689398359⟩⟩,⟨⟨722706415800038788006210993113,722706415800038788032723577456⟩,⟨1250587523965264676277577000366,1250587523965264676325160013201⟩⟩,⟨⟨723853436704292526170575531470,723853436704292526197140254720⟩,⟨1251247811125629860639860457871,1251247811125629860687498493520⟩⟩] +lemma kernel0_0_r4_11_eq : ∀ k : Fin 16, kernel0_0Expr 4 11 k = kernel0_0_r4_11 k := by decide +kernel +noncomputable def kernel0_0_r4_12 : Fin 16 → CBox := ![⟨⟨724989020453486000767212623686,724989020453486000793825613935⟩,⟨1251900136118536839168190148873,1251900136118536839215872906985⟩⟩,⟨⟨726112914280664805553735140964,726112914280664805580399295940⟩,⟨1252544397745991014985087548529,1252544397745991015032824255514⟩⟩,⟨⟨727224866809279966647391286358,727224866809279966674103920067⟩,⟨1253180496242605377866443721876,1253180496242605377914227550549⟩⟩,⟨⟨728324628147829267425309469468,728324628147829267452072251243⟩,⟨1253808333289519491942763607297,1253808333289519491990600280874⟩⟩,⟨⟨729411949984809448901475159001,729411949984809448928284372114⟩,⟨1254427812027721162493888212171,1254427812027721162541768002111⟩⟩,⟨⟨730486585683919904173083168594,730486585683919904199941459400⟩,⟨1255038837070772905361157324849,1255038837070772905409088797952⟩⟩,⟨⟨731548290379457583103714665444,731548290379457583130619220279⟩,⟨1255641314516946183023725214522,1255641314516946183071701291375⟩⟩,⟨⟨732596821071841973723275079783,732596821071841973750227598407⟩,⟨1256235151960767206925623417430,1256235151960767206973649981967⟩⟩,⟨⟨733631936723208231547600047804,733631936723208231574596323824⟩,⟨1256820258503978934344259084614,1256820258503978934392325128019⟩⟩,⟨⟨734653398353005788762826511254,734653398353005788789869582780⟩,⟨1257396544765924708097203171738,1257396544765924708145318446603⟩⟩,⟨⟨735660969133539093523754888755,735660969133539093550841821385⟩,⟨1257963922893359796829937838471,1257963922893359796878095031347⟩⟩,⟨⟨736654414485386506953536011228,736654414485386506980668530177⟩,⟨1258522306569697890650900670712,1258522306569697890699105809774⟩⟩,⟨⟨737633502172632823203807142423,737633502172632823230981162811⟩,⟨1259071611023700389629768569806,1259071611023700389678011113299⟩⟩,⟨⟨738598002397850377462741591864,738598002397850377489959937663⟩,⟨1259611753037617089309224490716,1259611753037617089357513638896⟩⟩,⟨⟨739547687896763269328068243740,739547687896763269355327865364⟩,⟨1260142650954787616078408334778,1260142650954787616126736553436⟩⟩,⟨⟨740482334032528855655290089720,740482334032528855682592734819⟩,⟨1260664224686713694217942487176,1260664224686713694266315937427⟩⟩] +lemma kernel0_0_r4_12_eq : ∀ k : Fin 16, kernel0_0Expr 4 12 k = kernel0_0_r4_12 k := by decide +kernel +noncomputable def kernel0_0_r4_13 : Fin 16 → CBox := ![⟨⟨741401718889570358926974344935,741401718889570358954315322791⟩,⟨1261176395719613033882494183723,1261176395719613033930900713703⟩⟩,⟨⟨742305623366894195358644033888,742305623366894195386026681213⟩,⟨1261679087120466313499423922827,1261679087120466313547874251747⟩⟩,⟨⟨743193831270825452263949231945,743193831270825452291370393734⟩,⟨1262172223542569389334304490562,1262172223542569389382790887706⟩⟩,⟨⟨744066129407094837458235729885,744066129407094837485697169680⟩,⟨1262655731230603497650867969418,1262655731230603497699396707082⟩⟩,⟨⟨744922307672210385405166901311,744922307672210385432664190321⟩,⟨1263129538025236819370495604227,1263129538025236819419055385996⟩⟩,⟨⟨745762159144047236030131204653,745762159144047236057667331883⟩,⟨1263593573367271351862633561935,1263593573367271351911234172250⟩⟩,⟨⟨746585480171588903165961405813,746585480171588903193533118175⟩,⟨1264047768301349575981724438267,1264047768301349576030357966262⟩⟩,⟨⟨747392070463753620891927828479,747392070463753620919536901826⟩,⟨1264492055479235917279110298979,1264492055479235917327783114421⟩⟩,⟨⟨748181733177239597909130305995,748181733177239597936771764874⟩,⟨1264926369162688477101313378864,1264926369162688477150012740470⟩⟩,⟨⟨748954275003323322796933014537,748954275003323322824610309640⟩,⟨1265350645225936950751222778481,1265350645225936950799959831188⟩⟩,⟨⟨749709506253545446648940511098,749709506253545446676650303148⟩,⟨1265764821157783054827706146904,1265764821157783054876472828026⟩⟩,⟨⟨750447240944219224224268387385,750447240944219224252012457110⟩,⟨1266168836063340153142893191280,1266168836063340153191695942969⟩⟩,⟨⟨751167296879697020300899512088,751167296879697020328673120495⟩,⟨1266562630665429099203600321633,1266562630665429099252427169574⟩⟩,⟨⟨751869495734330984210449096645,751869495734330984238255380685⟩,⟨1266946147305647602179603787261,1266946147305647602228465035540⟩⟩,⟨⟨752553663133064662294395412891,752553663133064662322230956957⟩,⟨1267319329945130671707460991496,1267319329945130671756348447220⟩⟩,⟨⟨753219628730593054874882488729,753219628730593054902749073506⟩,⟨1267682124165019904028769665511,1267682124165019904077689824912⟩⟩] +lemma kernel0_0_r4_13_eq : ∀ k : Fin 16, kernel0_0Expr 4 13 k = kernel0_0_r4_13 k := by decide +kernel +noncomputable def kernel0_0_r4_14 : Fin 16 → CBox := ![⟨⟨753867226289029430802063554475,753867226289029430829955739996⟩,⟨1268034477166659537172078460882,1268034477166659537221017461678⟩⟩,⟨⟨754496293754018088146294369124,754496293754018088174215918158⟩,⟨1268376337771537325593537122860,1268376337771537325642507079236⟩⟩,⟨⟨755106673329233193469495055238,755106673329233193497442490883⟩,⟨1268707656420988364434996626756,1268707656420988364483989250904⟩⟩,⟨⟨755698211549204843557507506025,755698211549204843585482599556⟩,⟨1269028385175680029985955306179,1269028385175680030034977117155⟩⟩,⟨⟨756270759350414571648529944074,756270759350414571676527692663⟩,⟨1269338477714896195804830606468,1269338477714896195853869056153⟩⟩,⟨⟨756824172140603664077705602340,756824172140603664105729265905⟩,⟨1269637889335638833130247475372,1269637889335638833179313298552⟩⟩,⟨⟨757358309866238861805608642632,757358309866238861833654694315⟩,⟨1269926576951565009672967700858,1269926576951565009722052538909⟩⟩,⟨⟨757873037078081293344275726447,757873037078081293372345922777⟩,⟨1270204499091777162712058707450,1270204499091777162761169082032⟩⟩,⟨⟨758368222994805819882198641970,758368222994805819910287394021⟩,⟨1270471615899484340828505000654,1270471615899484340877626787607⟩⟩,⟨⟨758843741564619368591046979906,758843741564619368619158071481⟩,⟨1270727889130551883909849760993,1270727889130551883958995203298⟩⟩,⟨⟨759299471524828284735378480201,759299471524828284763508351286⟩,⟨1270973282151956743680199221650,1270973282151956743729359928541⟩⟩,⟨⟨759735296459306245777920427453,759735296459306245806070809711⟩,⟨1271207759940165337490619750998,1271207759940165337539802212698⟩⟩,⟨⟨760151104853815849569077007261,760151104853815849597242689284⟩,⟨1271431289079450477099526888724,1271431289079450477148718104727⟩⟩,⟨⟨760546790149138612238742671984,760546790149138612266927007044⟩,⟨1271643837760163522442938965156,1271643837760163522492149997221⟩⟩,⟨⟨760922250791969787800964703635,760922250791969787829164112489⟩,⟨1271845375776977478813992819938,1271845375776977478863215275109⟩⟩,⟨⟨761277390283536148889049958410,761277390283536148917266140888⟩,⟨1272035874527116285418190477067,1272035874527116285467430788675⟩⟩] +lemma kernel0_0_r4_14_eq : ∀ k : Fin 16, kernel0_0Expr 4 14 k = kernel0_0_r4_14 k := by decide +kernel +noncomputable def kernel0_0_r4_15 : Fin 16 → CBox := ![⟨⟨761612117225896644538298309775,761612117225896644566525324285⟩,⟨1272215307008585035031382477777,1272215307008585035080625648876⟩⟩,⟨⟨761926345365887674531054229690,761926345365887674559296111784⟩,⟨1272383647818415319647471557718,1272383647818415319696730588625⟩⟩,⟨⟨762219993636676588451781311411,762219993636676588480034482238⟩,⟨1272540873150939316850518077835,1272540873150939316899784618749⟩⟩,⟨⟨762492986196888929139393138655,762492986196888929167659254160⟩,⟨1272686960796105617563667611533,1272686960796105617612947998828⟩⟩,⟨⟨762745252467276892479575639452,762745252467276892507849347461⟩,⟨1272821890137849149293264752156,1272821890137849149342545683194⟩⟩,⟨⟨762976727164898466200498594126,762976727164898466228783302750⟩,⟨1272945642152526871565435003386,1272945642152526871614727736850⟩⟩,⟨⟨763187350334778737215317009273,763187350334778737243609155094⟩,⟨1273058199407430213597089485551,1273058199407430213646385746904⟩⟩,⟨⟨763377067379026917734889765526,763377067379026917763190953217⟩,⟨1273159546059384490084917350111,1273159546059384490134223351580⟩⟩,⟨⟨763545829083384732446670228027,763545829083384732474974503270⟩,⟨1273249667853444771144582181702,1273249667853444771193882963628⟩⟩,⟨⟨763693591641183930066726493358,763693591641183930095037834806⟩,⟨1273328552121696898767087269378,1273328552121696898816395701848⟩⟩,⟨⟨763820316674692830026210374928,763820316674692830054525255537⟩,⟨1273396187782171536628138072451,1273396187782171536677446004461⟩⟩,⟨⟨763925971253833986416929929235,763925971253833986445249889649⟩,⟨1273452565337878314695878143820,1273452565337878314745191620929⟩⟩,⟨⟨764010527912257244024898599281,764010527912257244053218221936⟩,⟨1273497676875966286897439164030,1273497676875966286946744748253⟩⟩,⟨⟨764073964660754672725845243049,764073964660754672754167947471⟩,⟨1273531516067016061237314894230,1273531516067016061286623896461⟩⟩,⟨⟨764116264998006094076490941644,764116264998006094104813254293⟩,⟨1273554078164468089369317144087,1273554078164468089418621574343⟩⟩,⟨⟨764137417918646154959511861203,764137417918646154987835249708⟩,⟨1273565360004190718902945724841,1273565360004190718952251429867⟩⟩] +lemma kernel0_0_r4_15_eq : ∀ k : Fin 16, kernel0_0Expr 4 15 k = kernel0_0_r4_15 k := by decide +kernel +noncomputable def kernel0_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel0_0_r4_0,kernel0_0_r4_1,kernel0_0_r4_2,kernel0_0_r4_3,kernel0_0_r4_4,kernel0_0_r4_5,kernel0_0_r4_6,kernel0_0_r4_7,kernel0_0_r4_8,kernel0_0_r4_9,kernel0_0_r4_10,kernel0_0_r4_11,kernel0_0_r4_12,kernel0_0_r4_13,kernel0_0_r4_14,kernel0_0_r4_15] +lemma kernel0_0_r4_eq (i k : Fin 16) : kernel0_0Expr 4 i k = kernel0_0_r4 i k := by + fin_cases i + · exact kernel0_0_r4_0_eq k + · exact kernel0_0_r4_1_eq k + · exact kernel0_0_r4_2_eq k + · exact kernel0_0_r4_3_eq k + · exact kernel0_0_r4_4_eq k + · exact kernel0_0_r4_5_eq k + · exact kernel0_0_r4_6_eq k + · exact kernel0_0_r4_7_eq k + · exact kernel0_0_r4_8_eq k + · exact kernel0_0_r4_9_eq k + · exact kernel0_0_r4_10_eq k + · exact kernel0_0_r4_11_eq k + · exact kernel0_0_r4_12_eq k + · exact kernel0_0_r4_13_eq k + · exact kernel0_0_r4_14_eq k + · exact kernel0_0_r4_15_eq k +noncomputable def kernel0_0_r5_0 : Fin 16 → CBox := ![⟨⟨398173676380927874230867124866,398173676380927874244660273062⟩,⟨995432629388375199109241251539,995432629388375199143724078719⟩⟩,⟨⟨398182291805002096205851760064,398182291805002096219645262743⟩,⟨995441675485669299348000699134,995441675485669299382484061019⟩⟩,⟨⟨398199522149743572854440870987,398199522149743572868235081461⟩,⟨995459766681401279075913832062,995459766681401279110398258751⟩⟩,⟨⟨398225366408088282561191178116,398225366408088282574986449676⟩,⟨995486900977797622355398115604,995486900977797622389884137152⟩⟩,⟨⟨398259823068815049838384246863,398259823068815049852180932760⟩,⟨995523075378045479500665491464,995523075378045479535153637826⟩⟩,⟨⟨398302890115795582245776437479,398302890115795582259574890913⟩,⟨995568285886109885008764779392,995568285886109885043255580405⟩⟩,⟨⟨398354565026994867546426106178,398354565026994867560226680267⟩,⟨995622527506490562851764755515,995622527506490562886258740782⟩⟩,⟨⟨398414844773222229858569022971,398414844773222229872372070785⟩,⟨995685794243918760196676098667,995685794243918760231173797726⟩⟩,⟨⟨398483725816633418921305423012,398483725816633418935111297455⟩,⟨995758079102994660736051167670,995758079102994660770553109542⟩⟩,⟨⟨398561204108984182393977006828,398561204108984182407786060814⟩,⟨995839374087766038827459225105,995839374087766038861965939007⟩⟩,⟨⟨398647275089635847443534828956,398647275089635847457347415086⟩,⟨995929670201248925533119920291,995929670201248925567631934394⟩⟩,⟨⟨398741933683313514828432710842,398741933683313514842249181850⟩,⟨996028957444891167400322707508,996028957444891167434840550694⟩⟩,⟨⟨398845174297617546348564737966,398845174297617546362385446010⟩,⟨996137224817979868406744231241,996137224817979868441268430354⟩⟩,⟨⟨398956990820289104984791320175,398956990820289104998616617833⟩,⟨996254460316993814889648821679,996254460316993814924179905461⟩⟩,⟨⟨399077376616230586384226447179,399077376616230586398056686113⟩,⟨996380650934902092460761598018,996380650934902092495300091865⟩⟩,⟨⟨399206324524281860643432482696,399206324524281860657268015272⟩,⟨996515782660410212855099195593,996515782660410212889645627961⟩⟩] +lemma kernel0_0_r5_0_eq : ∀ k : Fin 16, kernel0_0Expr 5 0 k = kernel0_0_r5_0 k := by decide +kernel +noncomputable def kernel0_0_r5_1 : Fin 16 → CBox := ![⟨⟨399343826853753324684828048460,399343826853753324698669225556⟩,⟨996659840477155177347132992866,996659840477155177381687886664⟩⟩,⟨⟨399489875380716847994807738150,399489875380716848008654912083⟩,⟨996812808362851011765316340241,996812808362851011799880224383⟩⟩,⟨⟨399644461344055778177067372448,399644461344055778190920893409⟩,⟨996974669288386416219200737479,996974669288386416253774132861⟩⟩,⟨⟨399807575441275257752021161933,399807575441275257765881381980⟩,⟨997145405216876280393991919384,997145405216876280428575354642⟩⟩,⟨⟨399979207824074189982319114080,399979207824074189996186382164⟩,⟨997324997102668922636208364208,997324997102668922670802356151⟩⟩,⟨⟨400159348093680279303296844708,400159348093680279317171513051⟩,⟨997513424890311018020642443209,997513424890311018055247521961⟩⟩,⟨⟨400347985295949661262233220002,400347985295949661276115636679⟩,⟨997710667513472287121351806292,997710667513472287155968486105⟩⟩,⟨⟨400545107916232727796517767572,400545107916232727810408284480⟩,⟨997916702893832123274845137372,997916702893832123309473948049⟩⟩,⟨⟨400750703874007846281549924970,400750703874007846295448888260⟩,⟨998131507939930441687487281286,998131507939930441722128730515⟩⟩,⟨⟨400964760517284765125959645817,400964760517284765139867407977⟩,⟨998355058545985138765480704180,998355058545985138800135325152⟩⟩,⟨⟨401187264616779594854247008736,401187264616779594868163914967⟩,⟨998587329590678654497106513433,998587329590678654531774811226⟩⟩,⟨⟨401418202359863351662912302255,401418202359863351676838704529⟩,⟨998828294935916234554167566897,998828294935916234588850073841⟩⟩,⟨⟨401657559344286150431236399550,401657559344286150445172640403⟩,⟨999077927425558591962073607599,999077927425558591996770819547⟩⟩,⟨⟨401905320571679236175533657251,401905320571679236189480089707⟩,⟨999336198884131770673357644545,999336198884131770708070099265⟩⟩,⟨⟨402161470440837147017094158494,402161470440837147031051124002⟩,⟨999603080115517115123493998978,999603080115517115158222189438⟩⟩,⟨⟨402425992740782407947897198606,402425992740782407961865049526⟩,⟨999878540901624350804793942112,999878540901624350839538404893⟩⟩] +lemma kernel0_0_r5_1_eq : ∀ k : Fin 16, kernel0_0Expr 5 1 k = kernel0_0_r5_1 k := by decide +kernel +noncomputable def kernel0_0_r5_2 : Fin 16 → CBox := ![⟨⟨402698870643615263080715406521,402698870643615263094694480365⟩,⟨1000162550001050881016154518171,1000162550001050881050915732302⟩⟩,⟨⟨402980086697151064714980582885,402980086697151064728971234038⟩,⟨1000455075147730504183927216563,1000455075147730504218705728144⟩⟩,⟨⟨403269622817348050487508838344,403269622817348050501511403503⟩,⟨1000756083049574854450653887021,1000756083049574854485450173553⟩⟩,⟨⟨403567460280528355155734090711,403567460280528355169748923017⟩,⟨1001065539387110965540441016241,1001065539387110965575255620641⟩⟩,⟨⟨403873579715395221225289886245,403873579715395221239317317439⟩,⟨1001383408812118454176901838224,1001383408812118454211735220396⟩⟩,⟨⟨404187961094849492725253620809,404187961094849492739294006754⟩,⟨1001709654946269914494476792920,1001709654946269914529329508310⟩⟩,⟨⟨404510583727608598991468368783,404510583727608599005522040304⟩,⟨1002044240379778208887124865871,1002044240379778208921997372790⟩⟩,⟨⟨404841426249631360375989035732,404841426249631360390056347216⟩,⟨1002387126670054433518392721136,1002387126670054433553285571260⟩⟩,⟨⟨405180466615352075390191253975,405180466615352075404272529196⟩,⟨1002738274340380428210204927509,1002738274340380428245118553716⟩⟩,⟨⟨405527682088727478938043651058,405527682088727478952139248867⟩,⟨1003097642878599790568792441491,1003097642878599790603727415123⟩⟩,⟨⟨405883049234100294028231228493,405883049234100294042341472596⟩,⟨1003465190735831442927346967712,1003465190735831442962303723753⟩⟩,⟨⟨406246543906883234688976870188,406246543906883234703102116759⟩,⟨1003840875325209887916531182143,1003840875325209887951510283798⟩⟩,⟨⟨406618141244067455763140422842,406618141244067455777280987243⟩,⟨1004224653020656374144112397153,1004224653020656374179114249367⟩⟩,⟨⟨406997815654559585844778763129,406997815654559585858935006911⟩,⟨1004616479155685277499868462258,1004616479155685277534893651803⟩⟩,⟨⟨407385540809351622838680287001,407385540809351622852852525371⟩,⟨1005016308022250085925659949334,1005016308022250085960708883331⟩⟩,⟨⟨407781289631528117483693284393,407781289631528117497881875921⟩,⟨1005424092869633456025247114146,1005424092869633456060320370446⟩⟩] +lemma kernel0_0_r5_2_eq : ∀ k : Fin 16, kernel0_0Expr 5 2 k = kernel0_0_r5_2 k := by decide +kernel +noncomputable def kernel0_0_r5_3 : Fin 16 → CBox := ![⟨⟨408185034286115218676452200077,408185034286115218690657448197⟩,⟨1005839785903385888554146253974,1005839785903385888589244196791⟩⟩,⟨⟨408596746169776305556959272067,408596746169776305571181543737⟩,⟨1006263338284317646544665693407,1006263338284317646579788936243⟩⟩,⟨⟨409016395900359085058936403731,409016395900359085073176004153⟩,⟨1006694700127548614501419839151,1006694700127548614536568756374⟩⟩,⟨⟨409443953306299189968234871688,409443953306299189982492162502⟩,⟨1007133820501620869662352357413,1007133820501620869697527544925⟩⟩,⟨⟨409879387415885471448823801108,409879387415885471463099074433⟩,⟨1007580647427678806672046037908,1007580647427678806707247822654⟩⟩,⟨⟨410322666446392341459380432624,410322666446392341473674059353⟩,⟨1008035127878721725068472102198,1008035127878721725103701119476⟩⟩,⟨⟨410773757793084684460006064378,410773757793084684474318338065⟩,⟨1008497207778933854650244865996,1008497207778933854685501452113⟩⟩,⟨⟨411232628018101024257970867045,411232628018101024272302153139⟩,⟨1008966832003096856976106284183,1008966832003096857011391056838⟩⟩,⟨⟨411699242839220800717539423131,411699242839220800731889997202⟩,⟨1009443944376089901857413862799,1009443944376089901892727092518⟩⟩,⟨⟨412173567118521782309576192496,412173567118521782323946433652⟩,⟨1009928487672482475641935956923,1009928487672482475677278318304⟩⟩,⟨⟨412655564850933814043209880966,412655564850933814057600069340⟩,⟨1010420403616225133255969483327,1010420403616225133291341268969⟩⟩,⟨⟨413145199152695276139313873367,413145199152695276153724379015⟩,⟨1010919632880443458273007308458,1010919632880443458308409161890⟩⟩,⟨⟨413642432249718806802306757561,413642432249718806816737841178⟩,⟨1011426115087340544611023769077,1011426115087340544646455912271⟩⟩,⟨⟨414147225465873022544396353156,414147225465873022558848399390⟩,⟨1011939788808213359725868772883,1011939788808213359761331910259⟩⟩,⟨⟨414659539211187151629599928605,414659539211187151644073202255⟩,⟨1012460591563588392263249897839,1012460591563588392298744272274⟩⟩,⟨⟨415179332969985680241336240028,415179332969985680255831116616⟩,⟨1012988459823482026953381105244,1012988459823482026988907390420⟩⟩] +lemma kernel0_0_r5_3_eq : ∀ k : Fin 16, kernel0_0Expr 5 3 k = kernel0_0_r5_3 k := by decide +kernel +noncomputable def kernel0_0_r5_4 : Fin 16 → CBox := ![⟨⟨415706565288960296837601034918,415706565288960296852117752225⟩,⟨1013523329007791125976920422550,1013523329007791126012478762296⟩⟩,⟨⟨416241193765186607734879500438,416241193765186607749418455561⟩,⟨1014065133486819328993959217614,1014065133486819329029550373925⟩⟩,⟨⟨416783175034093286141763810123,416783175034093286156325250495⟩,⟨1014613806581944613404792659385,1014613806581944613440416819086⟩⟩,⟨⟨417332464757391507523897074380,417332464757391507538481381882⟩,⟨1015169280566433682096832854031,1015169280566433682132490725504⟩⟩,⟨⟨417889017610972716193855931708,417889017610972716208463326077⟩,⟨1015731486666408767821058207528,1015731486666408767856749876968⟩⟩,⟨⟨418452787272782961245597638664,418452787272782961260228523439⟩,⟨1016300355061972461328486094112,1016300355061972461364212358904⟩⟩,⟨⟨419023726410682234247935915780,419023726410682234262590518836⟩,⟨1016875814888496184377216653301,1016875814888496184412977637491⟩⟩,⟨⟨419601786670297436321955076402,419601786670297436336633786951⟩,⟨1017457794238077938588806285537,1017457794238077938624602737091⟩⟩,⟨⟨420186918662877798192035630185,420186918662877798206738638636⟩,⟨1018046220161174966784894050291,1018046220161174966820725956228⟩⟩,⟨⟨420779071953161773349762912133,420779071953161773364490638431⟩,⟨1018641018668416964767581135188,1018641018668416964803449367760⟩⟩,⟨⟨421378195047264621426715038874,421378195047264621441467689038⟩,⟨1019242114732605478417539064241,1019242114732605478453443677769⟩⟩,⟨⟨421984235380596096049934691960,421984235380596096064712663520⟩,⟨1019849432290905113370743171796,1019849432290905113406684958861⟩⟩,⟨⟨422597139305817848658398146078,422597139305817848673201606898⟩,⟨1020462894247232172298105637407,1020462894247232172334084513970⟩⟩,⟨⟨423216852080850356787187673823,423216852080850356802017052169⟩,⟨1021082422474846317853619393927,1021082422474846317889636277198⟩⟩,⟨⟨423843317856939381967120841482,423843317856939381981976319066⟩,⟨1021707937819150837579349379010,1021707937819150837615404246255⟩⟩,⟨⟨424476479666792158421576322128,424476479666792158436458305848⟩,⟨1022339360100707060365101113335,1022339360100707060401194807067⟩⟩] +lemma kernel0_0_r5_4_eq : ∀ k : Fin 16, kernel0_0Expr 5 4 k = kernel0_0_r5_4 k := by decide +kernel +noncomputable def kernel0_0_r5_5 : Fin 16 → CBox := ![⟨⟨425116279412793708941028339743,425116279412793708955936958655⟩,⟨1022976608118468442364651431637,1022976608118468442400783736808⟩⟩,⟨⟨425762657855313878442718854543,425762657855313878457654559970⟩,⟨1023619599653239803479267218436,1023619599653239803515439154856⟩⟩,⟨⟨426415554601115868532909547747,426415554601115868547872494552⟩,⟨1024268251471367153546013265386,1024268251471367153582224725807⟩⟩,⟨⟨427074908091877247628779966277,427074908091877247643770571783⟩,⟨1024922479328663500129141938171,1024922479328663500165393820434⟩⟩,⟨⟨427740655592834600604471971567,427740655592834600619490339518⟩,⟨1025582197974575977227204477737,1025582197974575977263496489809⟩⟩,⟨⟨428412733181563169230899694450,428412733181563169245946284291⟩,⟨1026247321156599576199416041163,1026247321156599576235749249640⟩⟩,⟨⟨429091075736903019603459711407,429091075736903019618534648445⟩,⟨1026917761624942696709238840977,1026917761624942696745613046224⟩⟩,⟨⟨429775616928043455009259224758,429775616928043455024362937865⟩,⟨1027593431137449666412104148235,1027593431137449666448520309149⟩⟩,⟨⟨430466289203777571981558649795,430466289203777571996691195663⟩,⟨1028274240464785303413224094876,1028274240464785303449681762414⟩⟩,⟨⟨431163023781939033321539711567,431163023781939033336701577759⟩,⟨1028960099395886515130632476783,1028960099395886515167132841772⟩⟩,⟨⟨431865750639033304326354716656,431865750639033304341545996151⟩,⟨1029650916743685841063161850528,1029650916743685841099704613052⟩⟩,⟨⟨432574398500075767030222766462,432574398500075767045443900784⟩,⟨1030346600351111755033321565199,1030346600351111755069907750877⟩⟩,⟨⟨433288894828649291617379815338,433288894828649291632630830548⟩,⟨1031047057097370444707016008652,1031047057097370444743645076642⟩⟩,⟨⟨434009165817194003970078208351,434009165817194003985359602119⟩,⟨1031752192904513682547399556406,1031752192904513682584072754722⟩⟩,⟨⟨434735136377542143232873264820,434735136377542143248185094858⟩,⟨1032461912744297292806865888367,1032461912744297292843582808526⟩⟩,⟨⟨435466730131711052960783687141,435466730131711052976126408809⟩,⟨1033176120645334603673369430672,1033176120645334603710131171029⟩⟩] +lemma kernel0_0_r5_5_eq : ∀ k : Fin 16, kernel0_0Expr 5 5 k = kernel0_0_r5_5 k := by decide +kernel +noncomputable def kernel0_0_r5_6 : Fin 16 → CBox := ![⟨⟨436203869402967493521958801137,436203869402967493537332379453⟩,⟨1033894719700549152245997057821,1033894719700549152282802874017⟩⟩,⟨⟨436946475207176601587552381871,436946475207176601602957353037⟩,⟨1034617612074930782607704691008,1034617612074930782644555997044⟩⟩,⟨⟨437694467244448954399288176624,437694467244448954414724560136⟩,⟨1035344699013599143885590130207,1035344699013599143922486400921⟩⟩,⟨⟨438447763891099321690016614184,438447763891099321705484880343⟩,⟨1036075880850178455843435425705,1036075880850178455880377837962⟩⟩,⟨⟨439206282191930806270825865638,439206282191930806286325948060⟩,⟨1036811057015487264247942667522,1036811057015487264284930388423⟩⟩,⟨⟨439969937852858185011788508001,439969937852858185027320950117⟩,⟨1037550126046546757007287934480,1037550126046546757044322427390⟩⟩,⟨⟨440738645233884364849943504660,440738645233884364865508284611⟩,⟨1038292985595911054925008656552,1038292985595911054962089271030⟩⟩,⟨⟨441512317342443963171637454397,441512317342443963187235058640⟩,⟨1039039532441322727878741065440,1039039532441322727915869063069⟩⟩,⟨⟨442290865827128108047754489534,442290865827128108063384781290⟩,⟨1039789662495696618365839686391,1039789662495696618403014002957⟩⟩,⟨⟨443074200971804630957757539662,443074200971804630973421106381⟩,⟨1040543270817434879709023741695,1040543270817434879746246029501⟩⟩,⟨⟨443862231690147892427852072702,443862231690147892443548848061⟩,⟨1041300251621075955846920455097,1041300251621075955884189930163⟩⟩,⟨⟨444654865520592539034277558834,444654865520592539050008046560⟩,⟨1042060498288280043617804269170,1042060498288280043655122283624⟩⟩,⟨⟨445452008621725538088075402083,445452008621725538103839427521⟩,⟨1042823903379153386860895635668,1042823903379153386898261019335⟩⟩,⟨⟨446253565768130873625491428762,446253565768130873641289589074⟩,⟨1043590358643913554598627426874,1043590358643913554636041893985⟩⟩,⟨⟨447059440346701313681525590545,447059440346701313697357771667⟩,⟨1044359755034897653125842990952,1044359755034897653163305615304⟩⟩,⟨⟨447869534353431673826865771984,447869534353431673842732496123⟩,⟨1045131982718915214128195187313,1045131982718915214165707417795⟩⟩] +lemma kernel0_0_r5_6_eq : ∀ k : Fin 16, kernel0_0Expr 5 6 k = kernel0_0_r5_6 k := by decide +kernel +noncomputable def kernel0_0_r5_7 : Fin 16 → CBox := ![⟨⟨448683748390708005205949964942,448683748390708005221850968124⟩,⟨1045906931089947288102777004574,1045906931089947288140337377493⟩⟩,⟨⟨449501981665107126433714920299,449501981665107126449650858409⟩,⟨1046684488782193054489859297343,1046684488782193054527469772852⟩⟩,⟨⟨450324131985720897301243561747,450324131985720897317214269814⟩,⟨1047464543683465037186852022083,1047464543683465037224511523683⟩⟩,⟨⟨451150095763019597920118386583,451150095763019597936124406334⟩,⟨1048246982948933786655616450460,1048246982948933786693326529376⟩⟩,⟨⟨451979768008268729320448315954,451979768008268729336489347832⟩,⟨1049031693015222657814243045470,1049031693015222657852002148022⟩⟩,⟨⟨452813042333513490231993015435,452813042333513490248069718566⟩,⟨1049818559614853076496686692755,1049818559614853076534496820286⟩⟩,⟨⟨453649810952145109451411122843,453649810952145109467523277972⟩,⟨1050607467791040446651413738491,1050607467791040446689273655536⟩⟩,⟨⟨454489964680063123467989783562,454489964680063123484137953149⟩,⟨1051398301912840605826748269729,1051398301912840605864659636048⟩⟩,⟨⟨455333392937447584529642603935,455333392937447584545826388681⟩,⟨1052190945690646488060025804551,1052190945690646488097986743569⟩⟩,⟨⟨456179983751155064733289859942,456179983751155064749509983746⟩,⟨1052985282192034401264046593275,1052985282192034401302059376557⟩⟩,⟨⟨457029623757752186681283032136,457029623757752186697539218282⟩,⟨1053781193857959070812435063523,1053781193857959070850498288847⟩⟩,⟨⟨457882198207200260430815971498,457882198207200260447108804141⟩,⟨1054578562519296342499848974100,1054578562519296342537964415025⟩⟩,⟨⟨458737590967204439560113333540,458737590967204439576442370992⟩,⟨1055377269413732176638489234121,1055377269413732176676654906791⟩⟩,⟨⟨459595684528240625879431011632,459595684528240625895796983431⟩,⟨1056177195202996301003355024552,1056177195202996301041573254048⟩⟩,⟨⟨460456360009273152335538827389,460456360009273152351941395983⟩,⟨1056978219990438623919581816706,1056978219990438623957851025707⟩⟩,⟨⟨461319497164176056718222787024,461319497164176056734662559407⟩,⟨1057780223338946240269331202258,1057780223338946240307653284003⟩⟩] +lemma kernel0_0_r5_7_eq : ∀ k : Fin 16, kernel0_0Expr 5 7 k = kernel0_0_r5_7 k := by decide +kernel +noncomputable def kernel0_0_r5_8 : Fin 16 → CBox := ![⟨⟨462184974388870524614324398342,462184974388870524630800806133⟩,⟨1058583084289198592866026825753,1058583084289198592904399384616⟩⟩,⟨⟨463052668729190828422527734057,463052668729190828439041594137⟩,⟨1059386681378258079791554819577,1059386681378258079829980535144⟩⟩,⟨⟨463922455889490819911046920564,463922455889490819927597831511⟩,⟨1060190892658493125217701280517,1060190892658493125256178393374⟩⟩,⟨⟨464794210242002746558696181039,464794210242002746575284773483⟩,⟨1060995595716830457244567369174,1060995595716830457283097896797⟩⟩,⟨⟨465667804836959856574517389649,465667804836959856591143062453⟩,⟨1061800667694333061702300338683,1061800667694333061740881821495⟩⟩,⟨⟨466543111413493933868648415995,466543111413493933885311977460⟩,⟨1062605985306100006001337451209,1062605985306100006039972573643⟩⟩,⟨⟨467420000411318562194610949068,467420000411318562211311930594⟩,⟨1063411424861484052311110074349,1063411424861484052349796886967⟩⟩,⟨⟨468298340983208557069187525326,468298340983208557085926582257⟩,⟨1064216862284622704934326037342,1064216862284622704973066687398⟩⟩,⟨⟨469178001008285624791618190397,469178001008285624808394586629⟩,⟨1065022173135278063066603339598,1065022173135278063105394936187⟩⟩,⟨⟨470058847106119909843200767176,470058847106119909860015401940⟩,⟨1065827232629980577537270960289,1065827232629980577576116556316⟩⟩,⟨⟨470940744651656675090110869877,470940744651656675106963204534⟩,⟨1066631915663471538969951848712,1066631915663471539008849298481⟩⟩,⟨⟨471823557790976923499853412608,471823557790976923516744127869⟩,⟨1067436096830438855438134708741,1067436096830438855477086293178⟩⟩,⟨⟨472707149457900315504793016435,472707149457900315521721334560⟩,⟨1068239650447540410482660751627,1068239650447540410521663491505⟩⟩,⟨⟨473591381391438262720822206978,473591381391438262737789023299⟩,⟨1069042450575709027668594302429,1069042450575709027707651275986⟩⟩,⟨⟨474476114154104586499271871249,474476114154104586516276574022⟩,⟨1069844371042732806055018273167,1069844371042732806094127131477⟩⟩,⟨⟨475361207151090618827633105084,475361207151090618844676401296⟩,⟨1070645285466104332400595914031,1070645285466104332439759076438⟩⟩] +lemma kernel0_0_r5_8_eq : ∀ k : Fin 16, kernel0_0Expr 5 8 k = kernel0_0_r5_8 k := by decide +kernel +noncomputable def kernel0_0_r5_9 : Fin 16 → CBox := ![⟨⟨476246518650311093500762860404,476246518650311093517843804118⟩,⟨1071445067276132020999579209855,1071445067276132021038793156749⟩⟩,⟨⟨477131905803326627389767756860,477131905803326627406887363073⟩,⟨1072243589739306581106137339582,1072243589739306581145405621701⟩⟩,⟨⟨478017224667148025202094042323,478017224667148025219251623739⟩,⟨1073040725981915365328377737980,1073040725981915365367697798400⟩⟩,⟨⟨478902330226927056545735863430,478902330226927056562932153666⟩,⟨1073836349013897110524124445951,1073836349013897110563498845070⟩⟩,⟨⟨479787076419537751606985748743,479787076419537751624219777266⟩,⟨1074630331752929345973897355637,1074630331752929346013322554530⟩⟩,⟨⟨480671316158051641580820247441,480671316158051641598093004304⟩,⟨1075422547048740512304360574059,1075422547048740512343840076059⟩⟩,⟨⟨481554901357109732444744775602,481554901357109732462055495167⟩,⟨1076212867707638609146526307406,1076212867707638609186057341513⟩⟩,⟨⟨482437682959193346062503567411,482437682959193346079853010720⟩,⟨1077001166517247970190559260614,1077001166517247970230144532362⟩⟩,⟨⟨483319510961795291298985913315,483319510961795291316372934549⟩,⟨1077787316271445551491776828737,1077787316271445551531412244393⟩⟩,⟨⟨484200234445492140211014246462,484200234445492140228439958443⟩,⟨1078571189795487912931895031646,1078571189795487912971584577522⟩⟩,⟨⟨485079701602917680873883526346,485079701602917680891347083100⟩,⟨1079352659971319873980849651451,1079352659971319874020590339137⟩⟩,⟨⟨485957759768636899468004010410,485957759768636899485506200505⟩,⟨1080131599763055633663849996259,1080131599763055633703644677894⟩⟩,⟨⟨486834255449919110375939543611,486834255449919110393479188784⟩,⟨1080907882242622961233846404524,1080907882242622961273690945670⟩⟩,⟨⟨487709034358408104753972510154,487709034358408104771550702342⟩,⟨1081681380615560888788768397615,1081681380615560888828666754792⟩⟩,⟨⟨488581941442686425905302096841,488581941442686425922917907465⟩,⟨1082451968246961170253397920130,1082451968246961170293346883021⟩⟩,⟨⟨489452820921730104389577332455,489452820921730104407231578133⟩,⟨1083219518687543613052859074599,1083219518687543613092861644774⟩⟩] +lemma kernel0_0_r5_9_eq : ∀ k : Fin 16, kernel0_0Expr 5 9 k = kernel0_0_r5_9 k := by decide +kernel +noncomputable def kernel0_0_r5_10 : Fin 16 → CBox := ![⟨⟨490321516319249397785783225288,490321516319249397803474506510⟩,⟨1083983905699855239712244730889,1083983905699855239752296066465⟩⟩,⟨⟨491187870498910280046552035199,491187870498910280064281608887⟩,⟨1084745003284583096784564802675,1084745003284583096824669491659⟩⟩,⟨⟨492051725700430614139934779841,492051725700430614157701633585⟩,⟨1085502685706970398183614103398,1085502685706970398223768712573⟩⟩,⟨⟨492912923576544119900993225432,492912923576544119918798203540⟩,⟨1086256827523325569410389926973,1086256827523325569450597606843⟩⟩,⟨⟨493771305230824417475113230525,493771305230824417492954934415⟩,⟨1087007303607613648527624736103,1087007303607613648567880728174⟩⟩,⟨⟨494626711256360586224877515538,494626711256360586242757144954⟩,⟨1087753989178119399255771955710,1087753989178119399296080691870⟩⟩,⟨⟨495478981775274830322170468487,495478981775274830340086925442⟩,⟨1088496759824171401418297279307,1088496759824171401458655100315⟩⟩,⟨⟨496327956479071986317502793727,496327956479071986335456950560⟩,⟨1089235491532916304318541210328,1089235491532916304358951417438⟩⟩,⟨⟨497173474669809745660833249395,497173474669809745678823488530⟩,⟨1089970060716132359631508645878,1089970060716132359671965791176⟩⟩,⟨⟨498015375302077597363424505597,498015375302077597381452186802⟩,⟨1090700344237071292168431760771,1090700344237071292208940887331⟩⟩,⟨⟨498853497025771623688681444693,498853497025771623706745383911⟩,⟨1091426219437317519528012955224,1091426219437317519568570178776⟩⟩,⟨⟨499687678229651405919262305489,499687678229651405937363402403⟩,⟨1092147564163653695272851463705,1092147564163653695313460234229⟩⟩,⟨⟨500517757085664418872951007478,500517757085664418891087633127⟩,⟨1092864256794921524930131692677,1092864256794921524970786606064⟩⟩,⟨⟨501343571594022412961115716862,501343571594022412979289183695⟩,⟨1093576176268866789857425915988,1093576176268866789898131896399⟩⟩,⟨⟨502164959629013402256113330165,502164959629013402274322367179⟩,⟨1094283202108957510862321450852,1094283202108957510903074388256⟩⟩,⟨⟨502981758985531997335616776350,502981758985531997353862310488⟩,⟨1094985214451164191420462249189,1094985214451164191461265742194⟩⟩] +lemma kernel0_0_r5_10_eq : ∀ k : Fin 16, kernel0_0Expr 5 10 k = kernel0_0_r5_10 k := by decide +kernel +noncomputable def kernel0_0_r5_11 : Fin 16 → CBox := ![⟨⟨503793807426309943702512299591,503793807426309943720792430895⟩,⟨1095682094070691099381466831641,1095682094070691099422314613480⟩⟩,⟨⟨504600942729827851458678019474,504600942729827851476994270267⟩,⟨1096373722408647576143520262358,1096373722408647576184418039248⟩⟩,⟨⟨505403002738888230778654788116,505403002738888230797005801075⟩,⟨1097059981598648403351368030997,1097059981598648403392311471280⟩⟩,⟨⟨506199825409829081740816492722,506199825409829081759203220733⟩,⟨1097740754493332309141278509293,1097740754493332309182271355539⟩⟩,⟨⟨506991248862356427400840888208,506991248862356427419261465804⟩,⟨1098415924690787758711178730974,1098415924690787758752214922866⟩⟩,⟨⟨507777111429973326820148044801,507777111429973326838603900011⟩,⟨1099085376560875247401559232922,1099085376560875247442644194876⟩⟩,⟨⟨508557251710982061287882378305,508557251710982061306372067393⟩,⟨1099748995271435398378544297228,1099748995271435398419673477094⟩⟩,⟨⟨509331508620035353406038109580,509331508620035353424562611050⟩,⟨1100406666814372261236714865115,1100406666814372261277892148003⟩⟩,⟨⟨510099721440211656259032622563,510099721440211656277589807415⟩,⟨1101058278031601312186891375726,1101058278031601312228109872081⟩⟩,⟨⟨510861729875588739782760981229,510861729875588739801352479206⟩,⟨1101703716640851770740969584071,1101703716640851770782235466822⟩⟩,⟨⟨511617374104289004909740952084,511617374104289004928365234705⟩,⟨1102342871261312971709616421842,1102342871261312971750924925114⟩⟩,⟨⟨512366494831969174323850590924,512366494831969174342508660533⟩,⟨1102975631439114664624285708515,1102975631439114664665640853237⟩⟩,⟨⟨513108933345726242938125350818,513108933345726242956815103242⟩,⟨1103601887672631255098431636932,1103601887672631255139826705982⟩⟩,⟨⟨513844531568390822737194411267,513844531568390822755917391310⟩,⟨1104221531437600153848321998835,1104221531437600153889762917130⟩⟩,⟨⟨514573132113178286623191216219,514573132113178286641945811729⟩,⟨1104834455212044558777760100899,1104834455212044558819241893005⟩⟩,⟨⟨515294578338667405584251517043,515294578338667405603038753334⟩,⟨1105440552500991163349465754979,1105440552500991163390992573812⟩⟩] +lemma kernel0_0_r5_11_eq : ∀ k : Fin 16, kernel0_0Expr 5 11 k = kernel0_0_r5_11 k := by decide +kernel +noncomputable def kernel0_0_r5_12 : Fin 16 → CBox := ![⟨⟨516008714404075484073310451334,516008714404075484092127889147⟩,⟨1106039717860973460058384156311,1106039717860973460099948213674⟩⟩,⟨⟨516715385324798331135451197241,516715385324798331154300654770⟩,⟨1106631846924311490809764482907,1106631846924311490851372693880⟩⟩,⟨⟨517414437028182760735002915181,517414437028182760753882699784⟩,⟨1107216836423159085993602829656,1107216836423159086035250020094⟩⟩,⟨⟨518105716409498695073094354652,518105716409498695092005511988⟩,⟨1107794584213309830626348667021,1107794584213309830668039111666⟩⟩,⟨⟨518789071388077350598832265508,518789071388077350617772456069⟩,⟨1108364989297753198677213496356,1108364989297753198718939835507⟩⟩,⟨⟨519464350963581419028104582206,519464350963581419047075465765⟩,⟨1108927951849972505171803875202,1108927951849972505213572522232⟩⟩,⟨⟨520131405272372616096220962106,520131405272372616115220767560⟩,⟨1109483373236976539421373846956,1109483373236976539463179435296⟩⟩,⟨⟨520790085643941460061623724120,520790085643941460080653516317⟩,⟨1110031156042056961300583738673,1110031156042056961342430659554⟩⟩,⟨⟨521440244657363661198147209401,521440244657363661217204343390⟩,⟨1110571204087263765420903950559,1110571204087263765462783878447⟩⟩,⟨⟨522081736197747053683029747232,522081736197747053702116128587⟩,⟨1111103422455591344841414431175,1111103422455591344883334667157⟩⟩,⟨⟨522714415512632583395826377759,522714415512632583414940161287⟩,⟨1111627717512867916138842515392,1111627717512867916180797514160⟩⟩,⟨⟨523338139268312480143641104966,523338139268312480162783371594⟩,⟨1112143996929341300732070828288,1112143996929341300774065085228⟩⟩,⟨⟨523952765606028391638918166279,523952765606028391658086349495⟩,⟨1112652169700954292828085987722,1112652169700954292870111526726⟩⟩,⟨⟨524558154198011940056657679895,524558154198011940075853550473⟩,⟨1113152146170303081726870026227,1113152146170303081768933727807⟩⟩,⟨⟨525154166303329881027511383572,525154166303329881046733025717⟩,⟨1113643838047272434992610842192,1113643838047272435034706992344⟩⟩,⟨⟨525740664823495800277859733367,525740664823495800297108242194⟩,⟨1114127158429341588666712201657,1114127158429341588708845391497⟩⟩] +lemma kernel0_0_r5_12_eq : ∀ k : Fin 16, kernel0_0Expr 5 12 k = kernel0_0_r5_12 k := by decide +kernel +noncomputable def kernel0_0_r5_13 : Fin 16 → CBox := ![⟨⟨526317514357810075559659359460,526317514357810075578931790369⟩,⟨1114602021821555030766316746294,1114602021821555030808477786039⟩⟩,⟨⟨526884581258389661726611375868,526884581258389661745909821116⟩,⟨1115068344156152604283573435874,1115068344156152604325770344368⟩⟩,⟨⟨527441733684849125466230850088,527441733684849125485553329382⟩,⟨1115526042811853595284848800263,1115526042811853595327075713117⟩⟩,⟨⟨527988841658594263896327368128,527988841658594263915674986676⟩,⟨1115975036632789710018859861487,1115975036632789710061121449322⟩⟩,⟨⟨528525777116689588534619310119,528525777116689588553989289626⟩,⟨1116415245947082081700733902085,1116415245947082081743021616676⟩⟩,⟨⟨529052413965260943553206698865,529052413965260943572600913174⟩,⟨1116846592585057682374736889767,1116846592585057682417058042111⟩⟩,⟨⟨529568628132394555182581407224,529568628132394555201997816089⟩,⟨1117268999897100747513339904497,1117268999897100747555688492190⟩⟩,⟨⟨530074297620493878023147464330,530074297620493878042587180813⟩,⟨1117682392771135050335877886949,1117682392771135050378258649985⟩⟩,⟨⟨530569302558055714189160815142,530569302558055714208620720126⟩,⟨1118086697649733088792571296283,1118086697649733088834974597483⟩⟩,⟨⟨531053525250827232924573502688,531053525250827232944055759235⟩,⟨1118481842546848470338147424869,1118481842546848470380581594450⟩⟩,⟨⟨531526850232305711807079149489,531526850232305711826581664803⟩,⟨1118867757064167997610263892028,1118867757064167997652722811006⟩⟩,⟨⟨531989164313543056048886099321,531989164313543056068409989648⟩,⟨1119244372407080171543303147155,1119244372407080171585791606219⟩⟩,⟨⟨532440356632217429802320225341,532440356632217429821862521549⟩,⟨1119611621400257036919932106796,1119611621400257036962441043745⟩⟩,⟨⟨532880318700934652814106386713,532880318700934652833669054972⟩,⟨1119969438502846498540831539872,1119969438502846498583368648402⟩⟩,⟨⟨533308944454722377210256016307,533308944454722377229836917363⟩,⟨1120317759823272433749419508501,1120317759823272433791978569444⟩⟩,⟨⟨533726130297680462535800269068,533726130297680462555400519276⟩,⟨1120656523133640118675396584948,1120656523133640118717982426195⟩⟩] +lemma kernel0_0_r5_13_eq : ∀ k : Fin 16, kernel0_0Expr 5 13 k = kernel0_0_r5_13 k := by decide +kernel +noncomputable def kernel0_0_r5_14 : Fin 16 → CBox := ![⟨⟨534131775148751412258444400118,534131775148751412278060592879⟩,⟨1120985667883744670975227916483,1120985667883744671017830054074⟩⟩,⟨⟨534525780486575221545919945364,534525780486575221565554438702⟩,⟨1121305135214680390787809808827,1121305135214680390830437294158⟩⟩,⟨⟨534908050393393513952681203923,534908050393393513972331821427⟩,⟨1121614867972049053854444804179,1121614867972049053897091344569⟩⟩,⟨⟨535278491597968413346798576705,535278491597968413366466428970⟩,⟨1121914810718765376062230981841,1121914810718765376104901419171⟩⟩,⟨⟨535637013517482206552690243428,535637013517482206572372199140⟩,⟨1122204909747458026875346394300,1122204909747458026918031231212⟩⟩,⟨⟨535983528298384501295112457679,535983528298384501314810559698⟩,⟨1122485113092464720060390843464,1122485113092464720103098090603⟩⟩,⟨⟨536317950856154272556688050701,536317950856154272576400092454⟩,⟨1122755370541420053659913835139,1122755370541420053702637144653⟩⟩,⟨⟨536640198913944917793337399722,536640198913944917813064482693⟩,⟨1123015633646434907218175110848,1123015633646434907260919323716⟩⟩,⟨⟨536950193040081206915212369150,536950193040081206934950996424⟩,⟨1123265855734866332740466379039,1123265855734866332783220811256⟩⟩,⟨⟨537247856684377815798481645482,537247856684377815818234187747⟩,⟨1123505991919676996723640445477,1123505991919676996766414238821⟩⟩,⟨⟨537533116213249971548357834946,537533116213249971568122065844⟩,⟨1123735999109383343812651516786,1123735999109383343855438297505⟩⟩,⟨⟨537805900943587612928200482370,537805900943587612947977487938⟩,⟨1123955836017591758224144686242,1123955836017591758266949269188⟩⟩,⟨⟨538066143175365379387081577636,538066143175365379406868098410⟩,⟨1124165463172122097071896934517,1124165463172122097114709479205⟩⟩,⟨⟨538313778222961685984252468909,538313778222961686004050605920⟩,⟨1124364842923718060194751250647,1124364842923718060237580008097⟩⟩,⟨⟨538548744445161118193138956572,538548744445161118212946472247⟩,⟨1124553939454343944119956188157,1124553939454343944162794781475⟩⟩,⟨⟨538770983273815388984051374959,538770983273815389003869335514⟩,⟨1124732718785067403513473929145,1124732718785067403556327128300⟩⟩] +lemma kernel0_0_r5_14_eq : ∀ k : Fin 16, kernel0_0Expr 5 14 k = kernel0_0_r5_14 k := by decide +kernel +noncomputable def kernel0_0_r5_15 : Fin 16 → CBox := ![⟨⟨538980439241139139595308433002,538980439241139139615133123000⟩,⟨1124901148783527912022731481275,1124901148783527912065587943609⟩⟩,⟨⟨539177060005617933816463214170,539177060005617933836297161481⟩,⟨1125059199170990675979916675472,1125059199170990676022786107388⟩⟩,⟨⟨539360796376506892185232067446,539360796376506892205073035402⟩,⟨1125206841528985809206463969466,1125206841528985809249340025267⟩⟩,⟨⟨539531602336899535953735671704,539531602336899535973584699143⟩,⟨1125344049305532625366202019429,1125344049305532625409089394486⟩⟩,⟨⟨539689435065347559676892404264,539689435065347559696746145310⟩,⟨1125470797820948946206406157692,1125470797820948946249294782235⟩⟩,⟨⟨539834254956013424439264721626,539834254956013424459125311423⟩,⟨1125587064273245359874637115185,1125587064273245359917535384521⟩⟩,⟨⟨539966025637338859648699505838,539966025637338859668564717873⟩,⟨1125692827743104393601040291130,1125692827743104393643941915179⟩⟩,⟨⟨540084713989213578528570707885,540084713989213578548441548979⟩,⟨1125788069198444589706328661714,1125788069198444589749238241232⟩⟩,⟨⟨540190290158629749442231146237,540190290158629749462103894346⟩,⟨1125872771498569493472577535961,1125872771498569493515483754737⟩⟩,⟨⟨540282727573809020455723697067,540282727573809020475600844195⟩,⟨1125946919397901576251734831346,1125946919397901576294647294939⟩⟩,⟨⟨540362002956790166529320832631,540362002956790166549200175346⟩,⟨1126010499549301127659347936275,1126010499549301127702260446799⟩⟩,⟨⟨540428096334466715837101338080,540428096334466715856983843182⟩,⟨1126063500506970157196607538170,1126063500506970157239524570219⟩⟩,⟨⟨540480991048065212333061129749,540480991048065212352943411297⟩,⟨1126105912728941348567309437155,1126105912728941348610220818038⟩⟩,⟨⟨540520673761056084174748561955,540520673761056084194632762101⟩,⟨1126137728579152109723799552918,1126137728579152109766713715301⟩⟩,⟨⟨540547134465490410323712650277,540547134465490410343596599222⟩,⟨1126158942329103758717134550744,1126158942329103758760045417408⟩⟩,⟨⟨540560366486757208890486673710,540560366486757208910371292585⟩,⟨1126169550159105880179481653731,1126169550159105880222393549411⟩⟩] +lemma kernel0_0_r5_15_eq : ∀ k : Fin 16, kernel0_0Expr 5 15 k = kernel0_0_r5_15 k := by decide +kernel +noncomputable def kernel0_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel0_0_r5_0,kernel0_0_r5_1,kernel0_0_r5_2,kernel0_0_r5_3,kernel0_0_r5_4,kernel0_0_r5_5,kernel0_0_r5_6,kernel0_0_r5_7,kernel0_0_r5_8,kernel0_0_r5_9,kernel0_0_r5_10,kernel0_0_r5_11,kernel0_0_r5_12,kernel0_0_r5_13,kernel0_0_r5_14,kernel0_0_r5_15] +lemma kernel0_0_r5_eq (i k : Fin 16) : kernel0_0Expr 5 i k = kernel0_0_r5 i k := by + fin_cases i + · exact kernel0_0_r5_0_eq k + · exact kernel0_0_r5_1_eq k + · exact kernel0_0_r5_2_eq k + · exact kernel0_0_r5_3_eq k + · exact kernel0_0_r5_4_eq k + · exact kernel0_0_r5_5_eq k + · exact kernel0_0_r5_6_eq k + · exact kernel0_0_r5_7_eq k + · exact kernel0_0_r5_8_eq k + · exact kernel0_0_r5_9_eq k + · exact kernel0_0_r5_10_eq k + · exact kernel0_0_r5_11_eq k + · exact kernel0_0_r5_12_eq k + · exact kernel0_0_r5_13_eq k + · exact kernel0_0_r5_14_eq k + · exact kernel0_0_r5_15_eq k +noncomputable def kernel0_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel0_0_r0,kernel0_0_r1,kernel0_0_r2,kernel0_0_r3,kernel0_0_r4,kernel0_0_r5] +lemma kernel0_0_eq (j : Fin 6) (i k : Fin 16) : kernel0_0Expr j i k = kernel0_0 j i k := by + fin_cases j + · exact kernel0_0_r0_eq i k + · exact kernel0_0_r1_eq i k + · exact kernel0_0_r2_eq i k + · exact kernel0_0_r3_eq i k + · exact kernel0_0_r4_eq i k + · exact kernel0_0_r5_eq i k +lemma kernel0_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel0_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(0:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel0_0_eq] + unfold kernel0_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans0_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel0_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans0 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel0_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-15046551019780130376576884074229),(-15046551019780130375719516286696)⟩,⟨(-17001806733481751411674328821871),(-17001806733481751411031248743980)⟩⟩,⟨⟨(-15047864077642742081362520393851),(-15047864077642742080505122759075)⟩,⟨(-17001312667346306262853219140339),(-17001312667346306262210144310431)⟩⟩,⟨⟨(-15050490005171375099017422494576),(-15050490005171375098159965394772)⟩,⟨(-17000324236263867909090565138733),(-17000324236263867908447501095033)⟩⟩,⟨⟨(-15054428425795623599671187938885),(-15054428425795623598813641771190)⟩,⟨(-16998840842792949285024782754184),(-16998840842792949284381735060039)⟩⟩,⟨⟨(-15059678774217076667316224664432),(-15059678774217076666458559849436)⟩,⟨(-16996861591225506208060747690842),(-16996861591225506207417721948780)⟩⟩,⟨⟨(-15066240295878685122324567971073),(-15066240295878685121466754958966)⟩,⟨(-16994385288132419156408582628566),(-16994385288132419155765584491385)⟩⟩,⟨⟨(-15074112046258466884993201370671),(-15074112046258466884135210653684)⟩,⟨(-16991410443091564105387832216797),(-16991410443091564104744867406272)⟩⟩,⟨⟨(-15083292889988594496743736808614),(-15083292889988594495885538919776)⟩,⟨(-16987935269599122058254714064241),(-16987935269599122057611788372290)⟩⟩,⟨⟨(-15093781499801170686224670801447),(-15093781499801170685366236341205)⟩,⟨(-16983957686164935148167582246941),(-16983957686164935147524701572866)⟩⟩,⟨⟨(-15105576355302261031662159647747),(-15105576355302261030803459256847)⟩,⟨(-16979475317592872647769162660277),(-16979475317592872647126332979200)⟩⟩,⟨⟨(-15118675741576016989585615960984),(-15118675741576016988726620385799)⟩,⟨(-16974485496447322344861750443927),(-16974485496447322344218977891989)⟩⟩,⟨⟨(-15133077747620987985204271570746),(-15133077747620987984344951585154)⟩,⟨(-16968985264707070968822834623097),(-16968985264707070968180125402342)⟩⟩,⟨⟨(-15148780264620988031825868009928),(-15148780264620988030966194554208)⟩,⟨(-16962971375607981124193687472325),(-16962971375607981123551048027749)⟩⟩,⟨⟨(-15165780984053150593730717031240),(-15165780984053150592870661027863)⟩,⟨(-16956440295676010946142849997556),(-16956440295676010945500286788820)⟩⟩,⟨⟨(-15184077395636075242578731053834),(-15184077395636075241718263667195)⟩,⟨(-16949388206952255877636310578187),(-16949388206952255876993830408052)⟩⟩,⟨⟨(-15203666785121241179720959656755),(-15203666785121241178860051990579)⟩,⟨(-16941811009411819020144580454329),(-16941811009411819019502190091584)⟩⟩] +lemma kernel0_1_r0_0_eq : ∀ k : Fin 16, kernel0_1Expr 0 0 k = kernel0_1_r0_0 k := by decide +kernel +noncomputable def kernel0_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-15224546231931135986422538443742),(-15224546231931135985561161962533)⟩,⟨(-16933704323578436868406344204784),(-16933704323578436867764050915216)⟩⟩,⟨⟨(-15246712606647823082905723662010),(-15246712606647823082043849639540)⟩,⟨(-16925063493336900345029907311990),(-16925063493336900344387718168992)⟩⟩,⟨⟨(-15270162568355948366935058356454),(-15270162568355948366072658558583)⟩,⟨(-16915883588945416342797107399616),(-16915883588945416342155030143511)⟩⟩,⟨⟨(-15294892561844465383285877679744),(-15294892561844465382422923612482)⟩,⟨(-16906159410250151902440038167455),(-16906159410250151901798080262652)⟩⟩,⟨⟨(-15320898814671639143558787144158),(-15320898814671639142695250999822)⟩,⟨(-16895885490104291143597098163447),(-16895885490104291142955267990117)⟩⟩,⟨⟨(-15348177334098171343506815348670),(-15348177334098171342642668805326)⟩,⟨(-16885056097994013570575480000613),(-16885056097994013569933785346060)⟩⟩,⟨⟨(-15376723903893574158406366811268),(-15376723903893574157541582440091)⟩,⟨(-16873665243873870838773971983488),(-16873665243873870838132421814759)⟩⟩,⟨⟨(-15406534081021205954752690689905),(-15406534081021205953887240454509)⟩,⟨(-16861706682214096941552919393041),(-16861706682214096940911521968967)⟩⟩,⟨⟨(-15437603192207670028757397852696),(-15437603192207670027891254920400)⟩,⟨(-16849173916262433514258054238757),(-16849173916262433513616819392958)⟩⟩,⟨⟨(-15469926330402566728904830604460),(-15469926330402566728037967072721)⟩,⟨(-16836060202523087010070747113347),(-16836060202523087009429683389501)⟩⟩,⟨⟨(-15503498351134879870180501847725),(-15503498351134879869312891315756)⟩,⟨(-16822358555455457345202182990908),(-16822358555455457344561300886700)⟩⟩,⟨⟨(-15538313868772569998215466265806),(-15538313868772569997347081196158)⟩,⟨(-16808061752395287709376980215062),(-16808061752395287708736288853005)⟩⟩,⟨⟨(-15574367252692239575799583832612),(-15574367252692239574930398597074)⟩,⟨(-16793162338700882070336828459096),(-16793162338700882069696339434239)⟩⟩,⟨⟨(-15611652623366028270889287289462),(-15611652623366028270019274442083)⟩,⟨(-16777652633127019956385222045301),(-16777652633127019955744944714165)⟩⟩,⟨⟨(-15650163848373189917885977808222),(-15650163848373189917015112216886)⟩,⟨(-16761524733429166877722671485970),(-16761524733429166877082618193004)⟩⟩,⟨⟨(-15689894538344096059864218695076),(-15689894538344096058992473349190)⟩,⟨(-16744770522200532756721153589386),(-16744770522200532756081334358431)⟩⟩] +lemma kernel0_1_r0_1_eq : ∀ k : Fin 16, kernel0_1Expr 0 1 k = kernel0_1_r0_1 k := by decide +kernel +noncomputable def kernel0_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-15730838042844703878839374436471),(-15730838042844703877966725248746)⟩,⟨(-16727381672944469504513890776108),(-16727381672944469503874319395969)⟩⟩,⟨⟨(-15772987446209818366635207195886),(-15772987446209818365761627111413)⟩,⟨(-16709349656384621947142463656126),(-16709349656384621946503150206911)⟩⟩,⟨⟨(-15816335563333769324716072600831),(-15816335563333769323841538014953)⟩,⟨(-16690665747015153227306314981918),(-16690665747015153226667273981438)⟩⟩,⟨⟨(-15860874935427412713014688870134),(-15860874935427412712139173314446)⟩,⟨(-16671321029893256165225521154865),(-16671321029893256164586763533278)⟩⟩,⟨⟨(-15906597825750652461756493866884),(-15906597825750652460879975000781)⟩,⟨(-16651306407676035453447759649344),(-16651306407676035452809301643600)⟩⟩,⟨⟨(-15953496215329962543697483454990),(-15953496215329962542819934684734)⟩,⟨(-16630612607903701608400566669102),(-16630612607903701607762419146152)⟩⟩,⟨⟨(-16001561798670669264822386328136),(-16001561798670669263943785850309)⟩,⟨(-16609230190530855954741356593145),(-16609230190530855954103536576677)⟩⟩,⟨⟨(-16050785979474029717863380033873),(-16050785979474029716983701925767)⟩,⟨(-16587149555707466253878936866722),(-16587149555707466253241456163267)⟩⟩,⟨⟨(-16101159866369413464396541162676),(-16101159866369413463515765294394)⟩,⟨(-16564360951810934612781644137223),(-16564360951810934612144522001723)⟩⟩,⟨⟨(-16152674268672160038482579279699),(-16152674268672160037600679333898)⟩,⟨(-16540854483730442763744592855576),(-16540854483730442763107840659276)⟩⟩,⟨⟨(-16205319692177944030467289500623),(-16205319692177944029584245763474)⟩,⟨(-16516620121404524466154826424093),(-16516620121404524465518464032594)⟩⟩,⟨⟨(-16259086335004731508926799361824),(-16259086335004731508042586449510)⟩,⟨(-16491647708612560461674993242232),(-16491647708612560461039033272682)⟩⟩,⟨⟨(-16313964083493655530713412092727),(-16313964083493655529828012217174)⟩,⟨(-16465926972020617969749921331395),(-16465926972020617969114386186770)⟩⟩,⟨⟨(-16369942508180373597257209489985),(-16369942508180373596370596761304)⟩,⟨(-16439447530481764039604784407796),(-16439447530481764038969686084494)⟩⟩,⟨⟨(-16427010859848695229434754568704),(-16427010859848695228546911661541)⟩,⟨(-16412198904590670122959668499023),(-16412198904590670122325030039000)⟩⟩,⟨⟨(-16485158065678482410830604770755),(-16485158065678482409941506824203)⟩,⟨(-16384170526491993992641179075462),(-16384170526491993992007013803117)⟩⟩] +lemma kernel0_1_r0_2_eq : ∀ k : Fin 16, kernel0_1Expr 0 2 k = kernel0_1_r0_2 k := by decide +kernel +noncomputable def kernel0_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-16544372725500028516956634453150),(-16544372725500028516066266688370)⟩,⟨(-16355351749941674652098184740557),(-16355351749941674651464519013198)⟩⟩,⟨⟨(-16604643108167311504315865637305),(-16604643108167311503424202208517)⟩,⟨(-16325731860619906260123477242698),(-16325731860619906259490323086953)⟩⟩,⟨⟨(-16665957148062693550206751815822),(-16665957148062693549313778091876)⟩,⟨(-16295300086694168491806573835225),(-16295300086694168491173957796978)⟩⟩,⟨⟨(-16728302441745800960215051249280),(-16728302441745800959320742868595)⟩,⟨(-16264045609630283388922046489950),(-16264045609630283388289982459371)⟩⟩,⟨⟨(-16791666244759463922779015505589),(-16791666244759463921883360611677)⟩,⟨(-16231957575249042901328515090338),(-16231957575249042900697033194428)⟩⟩,⟨⟨(-16856035468605724498370789631007),(-16856035468605724497473762790257)⟩,⟨(-16199025105025507331536702756537),(-16199025105025507330905815397089)⟩⟩,⟨⟨(-16921396677905031979269165207904),(-16921396677905031978370754795725)⟩,⟨(-16165237307627613181184625824916),(-16165237307627613180554363371141)⟩⟩,⟨⟨(-16987736087751836327884249344231),(-16987736087751836326984431466943)⟩,⟨(-16130583290690249944655453781430),(-16130583290690249944025830506176)⟩⟩,⟨⟨(-17055039561279861672874302470229),(-17055039561279861671973069111400)⟩,⟨(-16095052172820469757783817820739),(-16095052172820469757154868729936)⟩⟩,⟨⟨(-17123292607450391685069909785614),(-17123292607450391684167235284269)⟩,⟨(-16058633095828982119280714709744),(-16058633095828982118652451581175)⟩⟩,⟨⟨(-17192480379076925942388138227446),(-17192480379076925941484014277415)⟩,⟨(-16021315237182558866304762690748),(-16021315237182558865677220019847)⟩⟩,⟨⟨(-17262587671099570002558189826341),(-17262587671099570001652592965224)⟩,⟨(-15983087822671432988761231628270),(-15983087822671432988134423846954)⟩⟩,⟨⟨(-17333598919122500722563523364403),(-17333598919122500721656449103482)⟩,⟨(-15943940139285219574266115466255),(-15943940139285219573640081944646)⟩⟩,⟨⟨(-17405498198227801297049229783580),(-17405498198227801296140652817100)⟩,⟨(-15903861548290319132990735502559),(-15903861548290319132365487955268)⟩⟩,⟨⟨(-17478269222078886457363117991271),(-17478269222078886456453033639843)⟩,⟨(-15862841498501183786395432394027),(-15862841498501183785771009726324)⟩⟩,⟨⟨(-17551895342326636226581354470062),(-17551895342326636225669739658872)⟩,⟨(-15820869539737236426358934892626),(-15820869539737236425735351426722)⟩⟩] +lemma kernel0_1_r0_3_eq : ∀ k : Fin 16, kernel0_1Expr 0 3 k = kernel0_1_r0_3 k := by decide +kernel +noncomputable def kernel0_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-17626359548331225542927425442970),(-17626359548331225542014280523632)⟩,⟨(-15777935336456633154607548562255),(-15777935336456633153984849653144)⟩⟩,⟨⟨(-17701644467212475960205895002337),(-17701644467212475959291193972055)⟩,⟨(-15734028681557451372934959572200),(-15734028681557451372313155236745)⟩⟩,⟨⟨(-17777732364241363567574725420685),(-17777732364241363566658467525656)⟩,⟨(-15689139510336271171590740661233),(-15689139510336271170969874471442)⟩⟩,⟨⟨(-17854605143585093349100617758361),(-17854605143585093348182780265702)⟩,⟨(-15643257914593497597706444708597),(-15643257914593497597086530567535)⟩⟩,⟨⟨(-17932244349417893587748163173939),(-17932244349417893586828750381464)⟩,⟨(-15596374156874147500179797868952),(-15596374156874147499560885789222)⟩⟩,⟨⟨(-18010631167409393831400275075540),(-18010631167409393830479261420719)⟩,⟨(-15548478684832198544229525328444),(-15548478684832198543611624861900)⟩⟩,⟨⟨(-18089746426602125670140327361925),(-18089746426602125669217716302771)⟩,⟨(-15499562145705971347890280030190),(-15499562145705971347273439645123)⟩⟩,⟨⟨(-18169570601689326487938004504465),(-18169570601689326487013773598187)⟩,⟨(-15449615400891390269602734548733),(-15449615400891390268986967371593)⟩⟩,⟨⟨(-18250083815703831891660668496834),(-18250083815703831890734827712258)⟩,⟨(-15398629540599345999087527967799),(-15398629540599345998472890855116)⟩⟩,⟨⟨(-18331265843128412215907926393275),(-18331265843128412214980449107723)⟩,⟨(-15346595898582765670709735310486),(-15346595898582765670096235002163)⟩⟩,⟨⟨(-18413096113437441976074725762460),(-18413096113437441975145619910793)⟩,⟨(-15293506066918385693153699884944),(-15293506066918385692541389937740)⟩⟩,⟨⟨(-18495553715079288115622533103882),(-18495553715079288114691776481151)⟩,⟨(-15239351910827620896605969670159),(-15239351910827620895994862035787)⟩⟩,⟨⟨(-18578617399908263192958584326398),(-18578617399908263192026191324883)⟩,⟨(-15184125583520333020778398384361),(-15184125583520333020168554915351)⟩⟩,⟨⟨(-18662265588074413215507068121851),(-18662265588074413214573012504123)⟩,⟨(-15127819541044724137589905430416),(-15127819541044724136981331649067)⟩⟩,⟨⟨(-18746476373378796706825104185590),(-18746476373378796705889398605182)⟩,⟨(-15070426557126018500617999920200),(-15070426557126018500010754629381)⟩⟩,⟨⟨(-18831227529101261962130617639407),(-18831227529101261961193240071026)⟩,⟨(-15011939737976051758618053329658),(-15011939737976051758012146859488)⟩⟩] +lemma kernel0_1_r0_4_eq : ∀ k : Fin 16, kernel0_1Expr 0 4 k = kernel0_1_r0_4 k := by decide +kernel +noncomputable def kernel0_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-18916496514307043610490986368064),(-18916496514307043609551957960354)⟩,⟨(-14952352537055361714465668341980),(-14952352537055361713861170618891)⟩⟩,⟨⟨(-19002260480637777992062296587801),(-19002260480637777991121589324098)⟩,⟨(-14891658769768872131460665123812),(-14891658769768872130857577053257)⟩⟩,⟨⟨(-19088496279591780046239963546263),(-19088496279591780045297595004642)⟩,⟨(-14829852628075782781662921194397),(-14829852628075782781061306934072)⟩⟩,⟨⟨(-19175180470297633101640362163698),(-19175180470297633100696310444322)⟩,⟨(-14766928694993827301255837624094),(-14766928694993827300655705401178)⟩⟩,⟨⟨(-19262289327784318015448041084598),(-19262289327784318014502331768060)⟩,⟨(-14702881958977637772505971273792),(-14702881958977637771907395701886)⟩⟩,⟨⟨(-19349798851750250528549349365292),(-19349798851750250527601955111779)⟩,⟨(-14637707828150563589566843542069),(-14637707828150563588969823869294)⟩⟩,⟨⟨(-19437684775832706633958968988353),(-19437684775832706633009912475319)⟩,⟨(-14571402144368934367802901009673),(-14571402144368934367207506821632)⟩⟩,⟨⟨(-19525922577378196500370470881809),(-19525922577378196499419730272277)⟩,⟨(-14503961197097434678159268564749),(-14503961197097434677565505453658)⟩⟩,⟨⟨(-19614487487713399503622802242179),(-19614487487713399502670410474100)⟩,⟨(-14435381737073974446970943571336),(-14435381737073974446378894859896)⟩⟩,⟨⟨(-19703354502915297802830217127149),(-19703354502915297801876144701674)⟩,⟨(-14365660989742195127652190840691),(-14365660989742195127061849610197)⟩⟩,⟨⟨(-19792498395078145414071039348197),(-19792498395078145413115314165877)⟩,⟨(-14294796668429550336021108880284),(-14294796668429550335432550161032)⟩⟩,⟨⟨(-19881893724073885794075785479761),(-19881893724073885793118385710845)⟩,⟨(-14222786987248742588814257382293),(-14222786987248742588227483573330)⟩⟩,⟨⟨(-19971514849801585610888655756461),(-19971514849801585609929618943360)⟩,⟨(-14149630673700187058601002252435),(-14149630673700187058016101325375)⟩⟩,⟨⟨(-20061335944920387857591400889174),(-20061335944920387856630698173098)⟩,⟨(-14075326980953110730303404472956),(-14075326980953110729720366807266)⟩⟩,⟨⟨(-20151331008059406113245388469395),(-20151331008059406112283053057529)⟩,⟨(-13999875699782882785359584889049),(-13999875699782882784778490940636)⟩⟩,⟨⟨(-20241473877496886067346639599178),(-20241473877496886066382649605573)⟩,⟨(-13923277170142211106695552628366),(-13923277170142211106116401000151)⟩⟩] +lemma kernel0_1_r0_5_eq : ∀ k : Fin 16, kernel0_1Expr 0 5 k = kernel0_1_r0_5 k := by decide +kernel +noncomputable def kernel0_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-20331738245299853031268301401223),(-20331738245299853030302702791794)⟩,⟨(-13845532292343932024516562572173),(-13845532292343932023939451425845)⟩⟩,⟨⟨(-20422097671914347823476259805292),(-20422097671914347822509020530486)⟩,⟨(-13766642537833267208079224098511),(-13766642537833267207504134928443)⟩⟩,⟨⟨(-20512525601195231019343321059679),(-20512525601195231018374479651628)⟩,⟨(-13686609959527624205174982669840),(-13686609959527624204602001277001)⟩⟩,⟨⟨(-20602995375863410101816461274771),(-20602995375863410100845995738555)⟩,⟨(-13605437201702276636392162703886),(-13605437201702276635821283279472)⟩⟩,⟨⟨(-20693480253377218644408337907500),(-20693480253377218643436298089514)⟩,⟨(-13523127509400577396919285675965),(-13523127509400577396350609792526)⟩⟩,⟨⟨(-20783953422203554509992585430539),(-20783953422203554509018940577126)⟩,⟨(-13439684737347734161031254746421),(-13439684737347734160464761040306)⟩⟩,⟨⟨(-20874388018473268453304271548267),(-20874388018473268452329065489943)⟩,⟨(-13355113358347611595453893057906),(-13355113358347611594889672570085)⟩⟩,⟨⟨(-20964757143004188845373031826247),(-20964757143004188844396242396201)⟩,⟨(-13269418471142519346746710440640),(-13269418471142519346184752294056)⟩⟩,⟨⟨(-21055033878674075934155115248162),(-21055033878674075933176800745360)⟩,⟨(-13182605807716499253259114077818),(-13182605807716499252699530243969)⟩⟩,⟨⟨(-21145191308124723611263255622190),(-21145191308124723610283381886716)⟩,⟨(-13094681740023239314950580548666),(-13094681740023239314393339049360)⟩⟩,⟨⟨(-21235202531777371604905725394358),(-21235202531777371603924341452244)⟩,⟨(-13005653286120415491158875850849),(-13005653286120415490604072799635)⟩⟩,⟨⟨(-21325040686138559926459985130833),(-21325040686138559925477068594019)⟩,⟨(-12915528115692994924396968346183),(-12915528115692994923844587146286)⟩⟩,⟨⟨(-21414678962374553838389619912298),(-21414678962374553837405232758642)⟩,⟨(-12824314554948825020366583537581),(-12824314554948825019816739277815)⟩⟩,⟨⟨(-21504090625131495159007480358935),(-21504090625131495158021589624761)⟩,⟨(-12732021590870681035641360657947),(-12732021590870681035094017163341)⟩⟩,⟨⟨(-21593249031577497932940489658931),(-21593249031577497931953149413028)⟩,⟨(-12638658874809849289404040792574),(-12638658874809849288859299068536)⟩⟩,⟨⟨(-21682127650642006901105796859447),(-21682127650642006900116984434741)⟩,⟨(-12544236725407282446638205203102),(-12544236725407282446096042253913)⟩⟩] +lemma kernel0_1_r0_6_eq : ∀ k : Fin 16, kernel0_1Expr 0 6 k = kernel0_1_r0_6 k := by decide +kernel +noncomputable def kernel0_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-21770700082426879278744912575524),(-21770700082426879277754699181976)⟩,⟨(-12448766130829375907087863257052),(-12448766130829375906548406358046)⟩⟩,⟨⟨(-21858940077762837508861164363188),(-21858940077762837507869512419065)⟩,⟨(-12352258750306478335006898435268),(-12352258750306478334470097298688)⟩⟩,⟨⟨(-21946821557884176235420871784331),(-21946821557884176234427840162056)⟩,⟨(-12254726914963362707007686854759),(-12254726914963362706473647135698)⟩⟩,⟨⟨(-22034318634193893973713634428097),(-22034318634193893972719200145494)⟩,⟨(-12156183627932044639914990848700),(-12156183627932044639383682505362)⟩⟩,⟨⟨(-22121405628090761969545833474461),(-22121405628090761968550069879433)⟩,⟨(-12056642563738539665322970081971),(-12056642563738539664794521353306)⟩⟩,⟨⟨(-22208057090829242531065500054657),(-22208057090829242530068371756629)⟩,⟨(-11956118066956397803087620960628),(-11956118066956397802561977735201)⟩⟩,⟨⟨(-22294247823382629539111137638249),(-22294247823382629538112708032267)⟩,⟨(-11854625150121139302130802197189),(-11854625150121139301608074552057)⟩⟩,⟨⟨(-22379952896279307586219592861340),(-22379952896279307585219838596116)⟩,⟨(-11752179490901036610828541362866),(-11752179490901036610308691535995)⟩⟩,⟨⟨(-22465147669381615777963416454664),(-22465147669381615776962419418992)⟩,⟨(-11648797428521041164410534526900),(-11648797428521041163893702867858)⟩⟩,⟨⟨(-22549807811576459980724914449478),(-22549807811576459979722634649907)⟩,⟨(-11544495959438035903427974590764),(-11544495959438035902914091154207)⟩⟩,⟨⟨(-22633909320346545341502213543192),(-22633909320346545340498718526139)⟩,⟨(-11439292732267001863806815250816),(-11439292732267001863295994253657)⟩⟩,⟨⟨(-22717428541190901145429074458066),(-22717428541190901144424340479696)⟩,⟨(-11333206041959115844404041097466),(-11333206041959115843896236444496)⟩⟩,⟨⟨(-22800342186863244193943652927404),(-22800342186863244192937763344064)⟩,⟨(-11226254823234242055793604528791),(-11226254823234242055288957079144)⟩⟩,⟨⟨(-22882627356396676319142182359840),(-22882627356396676318135099253262)⟩,⟨(-11118458643271739646752836947492),(-11118458643271739646251271599895)⟩⟩,⟨⟨(-22964261553883237585126840228075),(-22964261553883237584118634886229)⟩,⟨(-11009837693664975839737442836666),(-11009837693664975839239077697322)⟩⟩,⟨⟨(-23045222706976940092240809993608),(-23045222706976940091231458241867)⟩,⟨(-10900412781646406731794331400135),(-10900412781646406731299111418834)⟩⟩] +lemma kernel0_1_r0_7_eq : ∀ k : Fin 16, kernel0_1Expr 0 7 k = kernel0_1_r0_7 k := by decide +kernel +noncomputable def kernel0_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-23125489185089088753697796512079),(-23125489185089088752687390814595)⟩,⟨(-10790205320591560199489646970128),(-10790205320591560198997727926050)⟩⟩,⟨⟨(-23205039817244955339610386847559),(-23205039817244955338598883180689)⟩,⟨(-10679237319811723288523526078720),(-10679237319811723288034812458014)⟩⟩,⟨⟨(-23283853909571210583070115200468),(-23283853909571210582057588095626)⟩,⟨(-10567531373646595428677704184632),(-10567531373646595428192317681813)⟩⟩,⟨⟨(-23361911262383936033601022110071),(-23361911262383936032587446959255)⟩,⟨(-10455110649869614224581966962542),(-10455110649869614224099843042919)⟩⟩,⟨⟨(-23439192186847532153487094194508),(-23439192186847532152472562403585)⟩,⟨(-10341998877420087858009136494082),(-10341998877420087857530428040191)⟩⟩,⟨⟨(-23515677521175411120780746908125),(-23515677521175411119765218090862)⟩,⟨(-10228220333477672736941006917511),(-10228220333477672736465615041422)⟩⟩,⟨⟨(-23591348646344010877892314173819),(-23591348646344010876875865587192)⟩,⟨(-10113799829896112412774609774275),(-10113799829896112412302659529314)⟩⟩,⟨⟨(-23666187501292389806687692910167),(-23666187501292389805670299489573)⟩,⟨(-9998762699014499485543833715405),(-9998762699014499485075250541198)⟩⟩,⟨⟨(-23740176597580457394505150559030),(-23740176597580457393486911114804)⟩,⟨(-9883134778865631827185034015827),(-9883134778865631826719985108964)⟩⟩,⟨⟨(-23813299033479763473774770941458),(-23813299033479763472755639618223)⟩,⟨(-9766942397802303667367949605525),(-9766942397802303666906314774015)⟩⟩,⟨⟨(-23885538507471704888985317467700),(-23885538507471704887965373650032)⟩,⟨(-9650212358563596710900208282824),(-9650212358563596710442115664073)⟩⟩,⟨⟨(-23956879331129011318644884694008),(-23956879331129011317624102879307)⟩,⟨(-9532971921804412428074198166516),(-9532971921804412427619562754677)⟩⟩,⟨⟨(-24027306441357438747481780485384),(-24027306441357438746460257664403)⟩,⟨(-9415248789112610068287481759215),(-9415248789112610067836467964832)⟩⟩,⟨⟨(-24096805411975726787308199212281),(-24096805411975726786285892752623)⟩,⟨(-9297071085539182050527326421185),(-9297071085539182050079809143544)⟩⟩,⟨⟨(-24165362464613061488112245731177),(-24165362464613061487089236540890)⟩,⟨(-9178467341667905625777967358722),(-9178467341667905625334077630640)⟩⟩,⟨⟨(-24232964478904525043801318543594),(-24232964478904525042777580682669)⟩,⟨(-9059466475251853732741920976595),(-9059466475251853732301562931146)⟩⟩] +lemma kernel0_1_r0_8_eq : ∀ k : Fin 16, kernel0_1Expr 0 8 k = kernel0_1_r0_8 k := by decide +kernel +noncomputable def kernel0_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-24299599001966304248694530348780),(-24299599001966304247670168268011)⟩,⟨(-8940097772445025644313809563551),(-8940097772445025643877165693218)⟩⟩,⟨⟨(-24365254257133766875014630988273),(-24365254257133766873989595301503)⟩,⟨(-8820390868658166425581205451463),(-8820390868658166425148124393007)⟩⟩,⟨⟨(-24429919151946895312675820416611),(-24429919151946895311650192883045)⟩,⟨(-8700375729068580738313763929661),(-8700375729068580737884379373951)⟩⟩,⟨⟨(-24493583285368985672996194360014),(-24493583285368985671969948652651)⟩,⟨(-8580082628814408733665234001856),(-8580082628814408733239438958044)⟩⟩,⟨⟨(-24556236954225973795978667695622),(-24556236954225973794951903519272)⟩,⟨(-8459542132904417544789021207675),(-8459542132904417544366991293726)⟩⟩,⟨⟨(-24617871158855232779752218218620),(-24617871158855232778724891114326)⟩,⟨(-8338785075874869373331617153118),(-8338785075874869372913199174574)⟩⟩,⟨⟨(-24678477607954195228183687916834),(-24678477607954195227155879845670)⟩,⟨(-8217842541225454793800269755654),(-8217842541225454793385599950491)⟩⟩,⟨⟨(-24738048722620682760418702531522),(-24738048722620682759390386801217)⟩,⟨(-8096745840666626406138598462274),(-8096745840666626405727558437531)⟩⟩,⟨⟨(-24796577639578370750755562833188),(-24796577639578370749726844314602)⟩,⟨(-7975526493210932376083992625121),(-7975526493210932375676775563831)⟩⟩,⟨⟨(-24854058213582373030818616020722),(-24854058213582373029789444537773)⟩,⟨(-7854216204141131043305892516487),(-7854216204141131042902318702679)⟩⟩,⟨⟨(-24910485019001494626804371222215),(-24910485019001494625774828238220)⟩,⟨(-7732846843887966280833752859806),(-7732846843887966280433960912694)⟩⟩,⟨⟨(-24965853350575265758224696354403),(-24965853350575265757194754887471)⟩,⟨(-7611450426850498591927172819360),(-7611450426850498591531032841482)⟩⟩,⟨⟨(-25020159223345432544767380011536),(-25020159223345432543737139385105)⟩,⟨(-7490059090191819271352722915231),(-7490059090191819270960421715766)⟩⟩,⟨⟨(-25073399371763134447132942713087),(-25073399371763134446102357235122)⟩,⟨(-7368705072642824876494470546706),(-7368705072642824876105825542636)⟩⟩,⟨⟨(-25125571247974540757595272564777),(-25125571247974540756564422542046)⟩,⟨(-7247420693346497585563741916464),(-7247420693346497585178894070331)⟩⟩,⟨⟨(-25176673019289243887234520770902),(-25176673019289243886203378981578)⟩,⟨(-7126238330774824891845996257606),(-7126238330774824891464804057347)⟩⟩] +lemma kernel0_1_r0_9_eq : ∀ k : Fin 16, kernel0_1Expr 0 9 k = kernel0_1_r0_9 k := by decide +kernel +noncomputable def kernel0_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-25226703564837211298351981521524),(-25226703564837211297320652472727)⟩,⟨(-7005190401750100904519577497539),(-7005190401750100904142251326048)⟩⟩,⟨⟨(-25275662471421576348673233975649),(-25275662471421576347641664990718)⟩,⟨(-6884309340601882983519648179596),(-6884309340601882983145972649162)⟩⟩,⟨⟨(-25323550028575996829794275516811),(-25323550028575996828762545052548)⟩,⟨(-6763627578490333479162545270563),(-6763627578490333478792663568791)⟩⟩,⟨⟨(-25370367222836724529307648386314),(-25370367222836724528275729086895)⟩,⟨(-6643177522926059182446376013976),(-6643177522926059182080135106654)⟩⟩,⟨⟨(-25416115731240905825819228548606),(-25416115731240905824787216196150)⟩,⟨(-6522991537515873167268017465523),(-6522991537515873166905615600017)⟩⟩,⟨⟨(-25460797914063968423711479396516),(-25460797914063968422679327840102)⟩,⟨(-6403101921963147698839538238928),(-6403101921963147698480762851934)⟩⟩,⟨⟨(-25504416806810239332502284099097),(-25504416806810239331470069328683)⟩,⟨(-6283540892350605686126297074907),(-6283540892350605685771293632934)⟩⟩,⟨⟨(-25546976111472180786731905520486),(-25546976111472180785699600113531)⟩,⟨(-6164340561732514863174144740527),(-6164340561732514862822748725499)⟩⟩,⟨⟨(-25588480187074820901065317330805),(-25588480187074820900033019335954)⟩,⟨(-6045532921062306772066071364968),(-6045532921062306771718503182015)⟩⟩,⟨⟨(-25628934039523091608502841967727),(-25628934039523091607470500070116)⟩,⟨(-5927149820480645134163891860577),(-5927149820480645133819907734315)⟩⟩,⟨⟨(-25668343310770865225204806128593),(-25668343310770865224172493221246)⟩,⟨(-5809222950987918932177028689060),(-5809222950987918931836776313508)⟩⟩,⟨⟨(-25706714267331500460281033665428),(-25706714267331500459248722379599)⟩,⟨(-5691783826524038212643376783757),(-5691783826524038212306680412010)⟩⟩,⟨⟨(-25744053788150666734928643064946),(-25744053788150666733896422645729)⟩,⟨(-5574863766477269101045214414874),(-5574863766477269100712284292303)⟩⟩,⟨⟨(-25780369351863110444551585948677),(-25780369351863110443519410665221)⟩,⟨(-5458493878642662741655632640927),(-5458493878642662741326226251340)⟩⟩,⟨⟨(-25815669023455856705565483342454),(-25815669023455856704533422444841)⟩,⟨(-5342705042649414851771570709923),(-5342705042649414851445838070788)⟩⟩,⟨⟨(-25849961440361103856844082206945),(-25849961440361103855812108466705)⟩,⟨(-5227527893875242396292373321807),(-5227527893875242395970127666047)⟩⟩] +lemma kernel0_1_r0_10_eq : ∀ k : Fin 16, kernel0_1Expr 0 10 k = kernel0_1_r0_10 k := by decide +kernel +noncomputable def kernel0_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-25883255798002764482087398486592),(-25883255798002764481055603130660)⟩,⟨(-5112992807864585666970347280993),(-5112992807864585666651828253747)⟩⟩,⟨⟨(-25915561834821235197692827591906),(-25915561834821235196661159060093)⟩,⟨(-4999129885266141938733927502778),(-4999129885266141938418854762281)⟩⟩,⟨⟨(-25946889816801537389044099863274),(-25946889816801537388012623225383)⟩,⟨(-4885968937303915027357805044922),(-4885968937303915027046330885320)⟩⟩,⟨⟨(-25977250521530462215630555238408),(-25977250521530462214599243541606)⟩,⟨(-4773539471794627631687047677840),(-4773539471794627631378974753415)⟩⟩,⟨⟨(-26006655221808775537933498647295),(-26006655221808775536902431924783)⟩,⟨(-4661870679722994425014757955545),(-4661870679722994424710309182829)⟩⟩,⟨⟨(-26035115668844892193715522465184),(-26035115668844892192684656365011)⟩,⟨(-4550991422384997535352995856693),(-4550991422384997535051899486898)⟩⟩,⟨⟨(-26062644075056714760050002207326),(-26062644075056714759019397190462)⟩,⟨(-4440930219107946334557975040239),(-4440930219107946334260385786934)⟩⟩,⟨⟨(-26089253096508550309056047668402),(-26089253096508550308025677143592)⟩,⟨(-4331715235554744278037091842621),(-4331715235554744277742802110585)⟩⟩,⟨⟨(-26114955815010170657276990153532),(-26114955815010170656246933499657)⟩,⟨(-4223374272618430747312549792611),(-4223374272618430747021810416340)⟩⟩,⟨⟨(-26139765719905168397431118290871),(-26139765719905168396401327295451)⟩,⟨(-4115934755911719191741472978774),(-4115934755911719191453976797082)⟩⟩,⟨⟨(-26163696689575783972094049137551),(-26163696689575783971064579249869)⟩,⟨(-4009423725854917972709978487116),(-4009423725854917972425882590916)⟩⟩,⟨⟨(-26186762972691339784730216853302),(-26186762972691339783701041972015)⟩,⟨(-3903867828364300686467030866530),(-3903867828364300686186117986742)⟩⟩,⟨⟨(-26208979169227317613441445067148),(-26208979169227317612412633860520)⟩,⟨(-3799293306141691745852948540143),(-3799293306141691745575455022471)⟩⟩,⟨⟨(-26230360211281957339786723918679),(-26230360211281957338758234340205)⟩,⟨(-3695725990564753854965627662889),(-3695725990564753854691253769551)⟩⟩,⟨⟨(-26250921343717040333136284024743),(-26250921343717040332108166219563)⟩,⟨(-3593191294176209777061685424253),(-3593191294176209776790590738202)⟩⟩,⟨⟨(-26270678104649251992407505163307),(-26270678104649251991379733602516)⟩,⟨(-3491714203769004374315951294049),(-3491714203769004374047909338510)⟩⟩] +lemma kernel0_1_r0_11_eq : ∀ k : Fin 16, kernel0_1Expr 0 11 k = kernel0_1_r0_11 k := by decide +kernel +noncomputable def kernel0_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-26289646305818197328466849871282),(-26289646305818197327439492615344)⟩,⟨(-3391319274063217018246784270629),(-3391319274063217017982069690479)⟩⟩,⟨⟨(-26307842012856773579750566620985),(-26307842012856773578723577260583)⟩,⟨(-3292030621969371686241355087444),(-3292030621969371685979623535225)⟩⟩,⟨⟨(-26325281525489187305722338379108),(-26325281525489187304695761499696)⟩,⟨(-3193871921431664747489651683352),(-3193871921431664747231065106642)⟩⟩,⟨⟨(-26341981357681442905960326024717),(-26341981357681442904934136786539)⟩,⟨(-3096866398843540792472973015737),(-3096866398843540792217296470352)⟩⟩,⟨⟨(-26357958217768627854730259818972),(-26357958217768627853704513993443)⟩,⟨(-3001036829026996880028873844735),(-3001036829026996879776357638968)⟩⟩,⟨⟨(-26373228988582779975356946151143),(-26373228988582779974331604842823)⟩,⟨(-2906405531765987084061081674921),(-2906405531765987083811399924923)⟩⟩,⟨⟨(-26387810707604546711131173657581),(-26387810707604546710106275763166)⟩,⟨(-2812994368883333849756382964737),(-2812994368883333849509700078538)⟩⟩,⟨⟨(-26401720547161238524154651617815),(-26401720547161238523130173042332)⟩,⟨(-2720824741849631861303650958559),(-2720824741849631861059724059598)⟩⟩,⟨⟨(-26414975794693241240253755261491),(-26414975794693241239229748814119)⟩,⟨(-2629917589911755138395415613454),(-2629917589911755138154529245037)⟩⟩,⟨⟨(-26427593833110088339488558602352),(-26427593833110088338464983270047)⟩,⟨(-2540293388727749992559700556405),(-2540293388727749992321489526887)⟩⟩,⟨⟨(-26439592121256806850818716713007),(-26439592121256806849795605619903)⟩,⟨(-2451972149494116181308908099868),(-2451972149494116181073539087716)⟩⟩,⟨⟨(-26450988174510442617562809489815),(-26450988174510442616540139367816)⟩,⟨(-2364973418550746816097909636805),(-2364973418550746815865132657939)⟩⟩,⟨⟨(-26461799545525945205736429063280),(-26461799545525945204714242007398)⟩,⟨(-2279316277448114854537925912436),(-2279316277448114854308005555943)⟩⟩,⟨⟨(-26472043805149852544507397321915),(-26472043805149852543485658226613)⟩,⟨(-2195019343460660716280462204777),(-2195019343460660716053048641112)⟩⟩,⟨⟨(-26481738523519463386770957457309),(-26481738523519463385749693701795)⟩,⟨(-2112100770529751921722270660735),(-2112100770529751921497532816052)⟩⟩,⟨⟨(-26490901251364424673905485973347),(-26490901251364424672884675146220)⟩,⟨(-2030578250619051723947517691734),(-2030578250619051723725199124384)⟩⟩] +lemma kernel0_1_r0_12_eq : ∀ k : Fin 16, kernel0_1Expr 0 12 k = kernel0_1_r0_12 k := by decide +kernel +noncomputable def kernel0_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-26499549501526893634346129005158),(-26499549501526893633325810276569)⟩,⟨(-1950469015464649398900713833122),(-1950469015464649398681124039229)⟩⟩,⟨⟨(-26507700730715663620907957892625),(-26507700730715663619888094100519)⟩,⟨(-1871789838701869946685572801678),(-1871789838701869946468313240341)⟩⟩,⟨⟨(-26515372321508870897005817154234),(-26515372321508870895986430014368)⟩,⟨(-1794557038350295073646790128180),(-1794557038350295073432031621193)⟩⟩,⟨⟨(-26522581564619129329979478527995),(-26522581564619129328960546532125)⟩,⟨(-1718786479638189979442746802480),(-1718786479638189979230227409133)⟩⟩,⟨⟨(-26529345641434173659621174842109),(-26529345641434173658602726396669)⟩,⟨(-1644493578147241055818882458306),(-1644493578147241055608880782860)⟩⟩,⟨⟨(-26535681606845332000778394669740),(-26535681606845331999760398855526)⟩,⟨(-1571693303258267393953893026675),(-1571693303258267393746038016346)⟩⟩,⟨⟨(-26541606372375396724350525206529),(-26541606372375396723332998266752)⟩,⟨(-1500400181878373172495160049562),(-1500400181878373172289624316099)⟩⟩,⟨⟨(-26547136689616721944936156361147),(-26547136689616721943919077677626)⟩,⟨(-1430628302429857642394489490634),(-1430628302429857642191006283860)⟩⟩,⟨⟨(-26552289133989647515606205580143),(-26552289133989647514589599422139)⟩,⟨(-1362391319081093535605370675838),(-1362391319081093535404258917737)⟩⟩,⟨⟨(-26557080088830635563102335517767),(-26557080088830635562086170529229)⟩,⟨(-1295702456199522223907039507501),(-1295702456199522223707885158577)⟩⟩,⟨⟨(-26561525729818807942207933905062),(-26561525729818807941192221100557)⟩,⟨(-1230574513006893694187224322494),(-1230574513006893693990201309752)⟩⟩,⟨⟨(-26565642009748893175584324361347),(-26565642009748893174569044010389)⟩,⟨(-1167019868416900179761205189207),(-1167019868416900179566042972943)⟩⟩,⟨⟨(-26569444643657930980245781170695),(-26569444643657930979230948777163)⟩,⟨(-1105050486035412833722820171221),(-1105050486035412833529810608914)⟩⟩,⟨⟨(-26572949094312442743938358098909),(-26572949094312442742923947000143)⟩,⟨(-1044677919303629845666546753188),(-1044677919303629845475300574660)⟩⟩,⟨⟨(-26576170558062158557870519196003),(-26576170558062158556856535511264)⟩,⟨(-985913316764580546469927552522),(-985913316764580546280619723910)⟩⟩,⟨⟨(-26579123951065796764287280302263),(-26579123951065796763273705140551)⟩,⟨(-928767427433601947209726844420),(-928767427433601947022083824465)⟩⟩] +lemma kernel0_1_r0_13_eq : ∀ k : Fin 16, kernel0_1Expr 0 13 k = kernel0_1_r0_13 k := by decide +kernel +noncomputable def kernel0_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-26581823895893821440268192390757),(-26581823895893821439255037603670)⟩,⟨(-873250606253610425725870355753),(-873250606253610425540238372156)⟩⟩,⟨⟨(-26584284708512557689843984022795),(-26584284708512557688831222590998)⟩,⟨(-819372819616230500899702685398),(-819372819616230500715636456853)⟩⟩,⟨⟨(-26586520385653524808216018918152),(-26586520385653524807203652450862)⟩,⟨(-767143650930113404883248425780),(-767143650930113404700923259852)⟩⟩,⟨⟨(-26588544592571353945410287350742),(-26588544592571353944398297753856)⟩,⟨(-716572306218079059626361407214),(-716572306218079059445501922559)⟩⟩,⟨⟨(-26590370651193190342619729636185),(-26590370651193190341608121038990)⟩,⟨(-667667619725044671938092547496),(-667667619725044671759002253385)⟩⟩,⟨⟨(-26592011528662040935168243027095),(-26592011528662040934156992766099)⟩,⟨(-620438059519060075975026719695),(-620438059519060075797301668594)⟩⟩,⟨⟨(-26593479826276116388224854471482),(-26593479826276116387213960103971)⟩,⟨(-574891733068152782531535841828),(-574891733068152782355351310799)⟩⟩,⟨⟨(-26594787768825832619024978396663),(-26594787768825832618014422538797)⟩,⟨(-531036392776093068778488379676),(-531036392776093068603567950152)⟩⟩,⟨⟨(-26595947194329780616499812272934),(-26595947194329780615489595219849)⟩,⟨(-488879441460620011146586587286),(-488879441460620010973279208237)⟩⟩,⟨⟨(-26596969544170644843345580936077),(-26596969544170644842335680665443)⟩,⟨(-448427937758121805899876400055),(-448427937758121805727731857039)⟩⟩,⟨⟨(-26597865853631749540933850363464),(-26597865853631749539924260884762)⟩,⟨(-409688601439236744939443465992),(-409688601439236744768636182683)⟩⟩,⟨⟨(-26598646742834638598665522120967),(-26598646742834638597656226681249)⟩,⟨(-372667818620333560362156716045),(-372667818620333560192410440379)⟩⟩,⟨⟨(-26599322408077847945019394896388),(-26599322408077847944010388460008)⟩,⟨(-337371646856340298075638573192),(-337371646856340297907266294358)⟩⟩,⟨⟨(-26599902613576809224078470726299),(-26599902613576809223069734029851)⟩,⟨(-303805820100918244455354681335),(-303805820100918244287941555113)⟩⟩,⟨⟨(-26600396683604629306872646410592),(-26600396683604629305864170465376)⟩,⟨(-271975753520520566690308413395),(-271975753520520566524027437674)⟩⟩,⟨⟨(-26600813495033321335253334976475),(-26600813495033321334245103555812)⟩,⟨(-241886548149433134670857559438),(-241886548149433134505433573037)⟩⟩] +lemma kernel0_1_r0_14_eq : ∀ k : Fin 16, kernel0_1Expr 0 14 k = kernel0_1_r0_14 k := by decide +kernel +noncomputable def kernel0_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-26601161470274918810672346975549),(-26601161470274918809664352100769)⟩,⟨(-213542995373466409954329003828),(-213542995373466409790133708204)⟩⟩,⟨⟨(-26601448570621783948335009606080),(-26601448570621783947327232687067)⟩,⟨(-186949581230551298570049319357),(-186949581230551298406609013568)⟩⟩,⟨⟨(-26601682289985324273656094715686),(-26601682289985324272648524350847)⟩,⟨(-162110490517087495511402190307),(-162110490517087495348887399125)⟩⟩,⟨⟨(-26601869649032256329514708188110),(-26601869649032256328507328584688)⟩,⟨(-139029610689499169333112838692),(-139029610689499169171250845351)⟩⟩,⟨⟨(-26602017189717501412116297897198),(-26602017189717501411109097620979)⟩,⟨(-117710535551068957666271884912),(-117710535551068957505382056916)⟩⟩,⟨⟨(-26602130970212764422898581761021),(-26602130970212764421891544076181)⟩,⟨(-98156568714746323139494097722),(-98156568714746322979155096437)⟩⟩,⟨⟨(-26602216560229832120394905010202),(-26602216560229832119388016709708)⟩,⟨(-80370726833259549492092044223),(-80370726833259549332471259634)⟩⟩,⟨⟨(-26602279036737630133780246827924),(-26602279036737630132773492446657)⟩,⟨(-64355742588501274599730402093),(-64355742588501274440558513552)⟩⟩,⟨⟨(-26602322980072097865372466685677),(-26602322980072097864365832886646)⟩,⟨(-50114067432804733598211207404),(-50114067432804733439856652905)⟩⟩,⟨⟨(-26602352470437975624880527951274),(-26602352470437975623873998707563)⟩,⟨(-37647874075381130310292718329),(-37647874075381130152285470737)⟩⟩,⟨⟨(-26602371084801647725631922129759),(-26602371084801647724625483053216)⟩,⟨(-26959058707847111610064206319),(-26959058707847111452567364812)⟩⟩,⟨⟨(-26602381894174247517873274554692),(-26602381894174247516866910425033)⟩,⟨(-18049242963434561676465546289),(-18049242963434561519214596411)⟩⟩,⟨⟨(-26602387461284304089363860265425),(-26602387461284304088357556423698)⟩,⟨(-10919775605142264663534167746),(-10919775605142264506851208428)⟩⟩,⟨⟨(-26602389838639294252808696108078),(-26602389838639294251802437276492)⟩,⟨(-5571733938759834825962961916),(-5571733938759834669424879506)⟩⟩,⟨⟨(-26602390566975556061948373792880),(-26602390566975556060942145021832)⟩,⟨(-2005924947368135486043858434),(-2005924947368135329808618764)⟩⟩,⟨⟨(-26602390674096120030558903994840),(-26602390674096120029552690232913)⟩,⟨(-222886144596675634967206553),(-222886144596675478776195011)⟩⟩] +lemma kernel0_1_r0_15_eq : ∀ k : Fin 16, kernel0_1Expr 0 15 k = kernel0_1_r0_15 k := by decide +kernel +noncomputable def kernel0_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel0_1_r0_0,kernel0_1_r0_1,kernel0_1_r0_2,kernel0_1_r0_3,kernel0_1_r0_4,kernel0_1_r0_5,kernel0_1_r0_6,kernel0_1_r0_7,kernel0_1_r0_8,kernel0_1_r0_9,kernel0_1_r0_10,kernel0_1_r0_11,kernel0_1_r0_12,kernel0_1_r0_13,kernel0_1_r0_14,kernel0_1_r0_15] +lemma kernel0_1_r0_eq (i k : Fin 16) : kernel0_1Expr 0 i k = kernel0_1_r0 i k := by + fin_cases i + · exact kernel0_1_r0_0_eq k + · exact kernel0_1_r0_1_eq k + · exact kernel0_1_r0_2_eq k + · exact kernel0_1_r0_3_eq k + · exact kernel0_1_r0_4_eq k + · exact kernel0_1_r0_5_eq k + · exact kernel0_1_r0_6_eq k + · exact kernel0_1_r0_7_eq k + · exact kernel0_1_r0_8_eq k + · exact kernel0_1_r0_9_eq k + · exact kernel0_1_r0_10_eq k + · exact kernel0_1_r0_11_eq k + · exact kernel0_1_r0_12_eq k + · exact kernel0_1_r0_13_eq k + · exact kernel0_1_r0_14_eq k + · exact kernel0_1_r0_15_eq k +noncomputable def kernel0_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-1076373745610825912886861111614),(-1076373745610825912293027486953)⟩,⟨(-15764169186243310087260193745486),(-15764169186243310086663926596801)⟩⟩,⟨⟨(-1077056824380066557645744608739),(-1077056824380066557051882345695)⟩,⟨(-15764603675759034505644555178667),(-15764603675759034505048261049204)⟩⟩,⟨⟨(-1078423048679996882631314136957),(-1078423048679996882037394811100)⟩,⟨(-15765472531626272351456320145479),(-15765472531626272350859972275711)⟩⟩,⟨⟨(-1080472551951816199085773037874),(-1080472551951816198491768226200)⟩,⟨(-15766775507488214368815814785070),(-15766775507488214368219386421837)⟩⟩,⟨⟨(-1083205534153053635193897708422),(-1083205534153053634599778991038)⟩,⟨(-15768512233738757705407471441596),(-15768512233738757704810935842291)⟩⟩,⟨⟨(-1086622261512380224069633577919),(-1086622261512380223475372538678)⟩,⟨(-15770682217437660974221583526807),(-15770682217437660973624913962468)⟩⟩,⟨⟨(-1090723066202585219623222786953),(-1090723066202585219028791018111)⟩,⟨(-15773284842197787429390926227861),(-15773284842197787428794095990423)⟩⟩,⟨⟨(-1095508345931626131054468903176),(-1095508345931626130459837997677)⟩,⟨(-15776319368044753299785733514657),(-15776319368044753299188715911496)⟩⟩,⟨⟨(-1100978563451640275879829405575),(-1100978563451640275284970977212)⟩,⟨(-15779784931249377715939426352760),(-15779784931249377715342194729803)⟩⟩,⟨⟨(-1107134245985784584972222898328),(-1107134245985784584377108548494)⟩,⟨(-15783680544133410142060762145808),(-15783680544133410141463289855964)⟩⟩,⟨⟨(-1113975984572750076034843192861),(-1113975984572750075439444567411)⟩,⟨(-15788005094849090799147417874531),(-15788005094849090798549678338363)⟩⟩,⟨⟨(-1121504433328777969234879432694),(-1121504433328777968639168140275)⟩,⟨(-15792757347133179249689262943856),(-15792757347133179249091229568460)⟩⟩,⟨⟨(-1129720308626985975402157995354),(-1129720308626985974806105735234)⟩,⟨(-15797935940036166119334714664949),(-15797935940036166118736360977250)⟩⟩,⟨⟨(-1138624388193795968271699598752),(-1138624388193795967675277976520)⟩,⟨(-15803539387627462864173483273118),(-15803539387627462863574782733734)⟩⟩,⟨⟨(-1148217510122238182726637388489),(-1148217510122238182129818160152)⟩,⟨(-15809566078677444559457064170137),(-15809566078677444558857990425708)⟩⟩,⟨⟨(-1158500571801892385848692654336),(-1158500571801892385251447428340)⟩,⟨(-15816014276317300889365016032405),(-15816014276317300888765542613019)⟩⟩] +lemma kernel0_1_r1_0_eq : ∀ k : Fin 16, kernel0_1Expr 1 0 k = kernel0_1_r1_0 k := by decide +kernel +noncomputable def kernel0_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-1169474528765213271703332800901),(-1169474528765213271105633437973)⟩,⟨(-15822882117677730857525894662652),(-15822882117677730856925995393755)⟩⟩,⟨⟨(-1181140393449975758953811884118),(-1181140393449975758355629958948)⟩,⟨(-15830167613507597210806687441454),(-15830167613507597210206335895032)⟩⟩,⟨⟨(-1193499233877566047218947575780),(-1193499233877566046620255030797)⟩,⟨(-15837868647773737167209355438241),(-15837868647773737166608525604989)⟩⟩,⟨⟨(-1206552172246836337934686532527),(-1206552172246836337335454942791)⟩,⟨(-15845982977243206751532287181874),(-15845982977243206750930952720556)⟩⟩,⟨⟨(-1220300383443235172409634017878),(-1220300383443235171809835503271)⟩,⟨(-15854508231049316854637459325817),(-15854508231049316854035594500560)⟩⟩,⟨⟨(-1234745093462921507442745132106),(-1234745093462921506842351184914)⟩,⟨(-15863441910242900024213635128457),(-15863441910242900023611213609538)⟩⟩,⟨⟨(-1249887577751569060463353539786),(-1249887577751569059862336385391)⟩,⟨(-15872781387330327942719956535054),(-15872781387330327942116952796395)⟩⟩,⟨⟨(-1265729159457568234216267852358),(-1265729159457568233614598984042)⟩,⟨(-15882523905799880522731695068772),(-15882523905799880522128082887970)⟩⟩,⟨⟨(-1282271207599336197368351617893),(-1282271207599336196766003554318)⟩,⟨(-15892666579638148517060384646394),(-15892666579638148516456138909976)⟩⟩,⟨⟨(-1299515135146451573001456495427),(-1299515135146451572398400557609)⟩,⟨(-15903206392838232461279462774387),(-15903206392838232460674557199477)⟩⟩,⟨⟨(-1317462397014338791690232562475),(-1317462397014338791086441376997)⟩,⟨(-15914140198901581594535164044406),(-15914140198901581593929573750187)⟩⟩,⟨⟨(-1336114487972238618447832811102),(-1336114487972238617843277725982)⟩,⟨(-15925464720335397089794589070493),(-15925464720335397089188287927956)⟩⟩,⟨⟨(-1355472940464215780570455933805),(-1355472940464215779965109993007)⟩,⟨(-15937176548147604409938221772136),(-15937176548147604409331185461237)⟩⟩,⟨⟨(-1375539322342972122038129085905),(-1375539322342972121431963370409)⟩,⟨(-15949272141341479828009481413311),(-15949272141341479827401683666902)⟩⟩,⟨⟨(-1396315234516254403529504224088),(-1396315234516254402922491900702)⟩,⟨(-15961747826412096038652542976265),(-15961747826412096038043959742836)⟩⟩,⟨⟨(-1417802308505669867119266764083),(-1417802308505669866511378957265)⟩,⟨(-15974599796846831266761139658401),(-15974599796846831266151744861431)⟩⟩] +lemma kernel0_1_r1_1_eq : ∀ k : Fin 16, kernel0_1Expr 1 1 k = kernel0_1_r1_1 k := by decide +kernel +noncomputable def kernel0_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-1440002203917750100867904880369),(-1440002203917750100259115396254)⟩,⟨(-15987824112632265265190230353361),(-15987824112632265264580000751506)⟩⟩,⟨⟨(-1462916605827134677713052425084),(-1462916605827134677103331933330)⟩,⟨(-16001416699769863995541057562306),(-16001416699769863994929966767155)⟩⟩,⟨⟨(-1486547222071780609370856040475),(-1486547222071780608760178409447)⟩,⟨(-16015373349802932506770094131309),(-16015373349802932506158119128428)⟩⟩,⟨⟨(-1510895780460141950197512367231),(-1510895780460141949585848406007)⟩,⟨(-16029689719357392460553547870760),(-16029689719357392459940662580704)⟩⟩,⟨⟨(-1535964025890306005456983964106),(-1535964025890306004844308356011)⟩,⟨(-16044361329699016787290937551253),(-16044361329699016786677119972314)⟩⟩,⟨⟨(-1561753717381118636622014400821),(-1561753717381118636008297363218)⟩,⟨(-16059383566309828972031979627025),(-16059383566309828971417203245584)⟩⟩,⟨⟨(-1588266625015381202382495328839),(-1588266625015381201767711614642)⟩,⟨(-16074751678486448337382612301340),(-16074751678486448336766855370967)⟩⟩,⟨⟨(-1615504526795255812491195867717),(-1615504526795255811875315866248)⟩,⟨(-16090460778963235274669707351302),(-16090460778963235274052943720300)⟩⟩,⟨⟨(-1643469205410073881940673836103),(-1643469205410073881323673487245)⟩,⟨(-16106505843563161531494346991370),(-16106505843563161530876556332089)⟩⟩,⟨⟨(-1672162444916805529268198315283),(-1672162444916805528650047088432)⟩,⟨(-16122881710879400241505699835319),(-16122881710879400240886855241236)⟩⟩,⟨⟨(-1701586027333514233148744537363),(-1701586027333514232529418276084)⟩,⟨(-16139583081990698221036014193113),(-16139583081990698220416095441375)⟩⟩,⟨⟨(-1731741729146192407612678560488),(-1731741729146192406992147116775)⟩,⟨(-16156604520213658989441412988847),(-16156604520213658988820393771182)⟩⟩,⟨⟨(-1762631317729449233123270629520),(-1762631317729449232501511257614)⟩,⟨(-16173940450895128819946425167811),(-16173940450895128819324286934336)⟩⟩,⟨⟨(-1794256547681602235944450461086),(-1794256547681602235321431917842)⟩,⟨(-16191585161247939711969857679640),(-16191585161247939711346573202740)⟩⟩,⟨⟨(-1826619157074808781455038651200),(-1826619157074808780830738099518)⟩,⟨(-16209532800233322303003140474256),(-16209532800233322302378691334357)⟩⟩,⟨⟨(-1859720863620962869697275996024),(-1859720863620962869071662621272)⟩,⟨(-16227777378493358209137775258150),(-16227777378493358208512134891944)⟩⟩] +lemma kernel0_1_r1_2_eq : ∀ k : Fin 16, kernel0_1Expr 1 2 k = kernel0_1_r1_2 k := by decide +kernel +noncomputable def kernel0_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-1893563360754176415967901096246),(-1893563360754176415340954083693)⟩,⟨(-16246312768336894891794388788632),(-16246312768336894891167541106786)⟩⟩,⟨⟨(-1928148313630762578719214042044),(-1928148313630762578090900925881)⟩,⟨(-16265132703782396680258597638439),(-16265132703782396679630514597472)⟩⟩,⟨⟨(-1963477355047741664497501097328),(-1963477355047741663867800609428)⟩,⟨(-16284230780661252814332437598095),(-16284230780661252813703102883797)⟩⟩,⟨⟨(-1999552081280997687622397116298),(-1999552081280997686991277636315)⟩,⟨(-16303600456785107080967458211868),(-16303600456785107080336844894650)⟩⟩,⟨⟨(-2036374047844325772202732892872),(-2036374047844325771570175398443)⟩,⟨(-16323235052180813568804263265287),(-16323235052180813568172357617718)⟩⟩,⟨⟨(-2073944765170727225606747240096),(-2073944765170727224972718296443)⟩,⟨(-16343127749396659014536746590289),(-16343127749396659013903520045577)⟩⟩,⟨⟨(-2112265694217430243110330869936),(-2112265694217430242474811050727)⟩,⟨(-16363271593883523918544655579845),(-16363271593883523917910094255765)⟩⟩,⟨⟨(-2151338241996239767756877280207),(-2151338241996239767119834008625)⟩,⟨(-16383659494454681812483242378848),(-16383659494454681811847318852718)⟩⟩,⟨⟨(-2191163757030949958690022021714),(-2191163757030949958051438992081)⟩,⟨(-16404284223827958511727630938169),(-16404284223827958511090334850158)⟩⟩,⟨⟨(-2231743524743686932609565270251),(-2231743524743686931969407285265)⟩,⟨(-16425138419253990619560302563674),(-16425138419253990618921604025350)⟩⟩,⟨⟨(-2273078762772187839262292335056),(-2273078762772187838620542104335)⟩,⟨(-16446214583234334702713057263994),(-16446214583234334702072945174074)⟩⟩,⟨⟨(-2315170616220164800647552421134),(-2315170616220164800004176252650)⟩,⟨(-16467505084333185161025743138644),(-16467505084333185160384189441932)⟩⟩,⟨⟨(-2358020152843048656911583675108),(-2358020152843048656266567642029)⟩,⟨(-16489002158086459596658564194830),(-16489002158086459596015561592376)⟩⟩,⟨⟨(-2401628358171557675615792334146),(-2401628358171557674969099952633)⟩,⟨(-16510697908012005177700621720922),(-16510697908012005177056139518847)⟩⟩,⟨⟨(-2445996130575690234454088568696),(-2445996130575690233805704999095)⟩,⟨(-16532584306724667813227728225366),(-16532584306724667812581758473648)⟩⟩,⟨⟨(-2491124276271897802726707112344),(-2491124276271897802076597378297)⟩,⟨(-16554653197159947637629359333095),(-16554653197159947636981873188459)⟩⟩] +lemma kernel0_1_r1_3_eq : ∀ k : Fin 16, kernel0_1Expr 1 3 k = kernel0_1_r1_3 k := by decide +kernel +noncomputable def kernel0_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-2537013504276355128568431288114),(-2537013504276355127916585262939)⟩,⟨(-16576896293909939067632266895873),(-16576896293909939066983261649135)⟩⟩,⟨⟨(-2583664421307408173736855307419),(-2583664421307408173083233957565)⟩,⟨(-16599305184675221273628366806472),(-16599305184675221272977809654647)⟩⟩,⟨⟨(-2631077526640446794009829034297),(-2631077526640446793354420304090)⟩,⟨(-16621871331836325027799628529478),(-16621871331836325027147515062783)⟩⟩,⟨⟨(-2679253206918618190565441669351),(-2679253206918618189908209124182)⟩,⟨(-16644586074148354288671380704054),(-16644586074148354288017681124146)⟩⟩,⟨⟨(-2728191730922968486792788001285),(-2728191730922968486133724392197)⟩,⟨(-16667440628562285293133572804920),(-16667440628562285292478288070184)⟩⟩,⟨⟨(-2777893244305773127261520060811),(-2777893244305773126600584885512)⟩,⟨(-16690426092176402096242296080385),(-16690426092176402095585392417092)⟩⟩,⟨⟨(-2828357764290991843099438435236),(-2828357764290991842436622776251)⟩,⟨(-16713533444321255176570145900681),(-16713533444321255175911622848997)⟩⟩,⟨⟨(-2879585174345960353277699586897),(-2879585174345960352612965367347)⟩,⟨(-16736753548781448668759467555541),(-16736753548781448668099294176897)⟩⟩,⟨⟨(-2931575218828608427136442209085),(-2931575218828608426469787043389)⟩,⟨(-16760077156157471762650113262447),(-16760077156157471761988296308801)⟩⟩,⟨⟨(-2984327497614672053115449084527),(-2984327497614672052446829199305)⟩,⟨(-16783494906370690597749252142710),(-16783494906370690597085754978084)⟩⟩,⟨⟨(-3037841460709545855712212242688),(-3037841460709545855041622227047)⟩,⟨(-16806997331314508372481208827389),(-16806997331314508371816035364647)⟩⟩,⟨⟨(-3092116402849600171352719080199),(-3092116402849600170680119027964)⟩,⟨(-16830574857654583182304192664174),(-16830574857654583181637310627369)⟩⟩,⟨⟨(-3147151458097964909061210978998),(-3147151458097964908386602092837)⟩,⟨(-16854217809780865116590022871761),(-16854217809780865115921443503152)⟩⟩,⟨⟨(-3202945594439959039542650074927),(-3202945594439959038865986764058)⟩,⟨(-16877916412914076214208096239830),(-16877916412914076213537781559757)⟩⟩,⟨⟨(-3259497608383519813960074548895),(-3259497608383519813281355295106)⟩,⟨(-16901660796369108852423033188424),(-16901660796369108851750991921302)⟩⟩,⟨⟨(-3316806119570159130618873130563),(-3316806119570159129938056002807)⟩,⟨(-16925440996977659892161444917233),(-16925440996977659891487643233339)⟩⟩] +lemma kernel0_1_r1_4_eq : ∀ k : Fin 16, kernel0_1Expr 1 4 k = kernel0_1_r1_4 k := by decide +kernel +noncomputable def kernel0_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-3374869565402145345742077590289),(-3374869565402145345059170228739)⟩,⟨(-16949246962672249314296595583068),(-16949246962672249313621052260683)⟩⟩,⟨⟨(-3433686195691776748449335691283),(-3433686195691776747764288046464)⟩,⟨(-16973068556233593067400714228848),(-16973068556233593066723387134677)⟩⟩,⟨⟨(-3493254067338777358737297237502),(-3493254067338777358050112077147)⟩,⟨(-16996895559203110341628443068055),(-16996895559203110340949346181076)⟩⟩,⟨⟨(-3553571039042006114265409299294),(-3553571039042006113576042474143)⟩,⟨(-17020717675962145444843872051839),(-17020717675962145444162969763019)⟩⟩,⟨⟨(-3614634766051826326369663424982),(-3614634766051826325678126525011)⟩,⟨(-17044524537979273870663108749846),(-17044524537979273869980424770213)⟩⟩,⟨⟨(-3676442694969632934070656896567),(-3676442694969632933376898089436)⟩,⟨(-17068305708226841026125300109908),(-17068305708226841025440790950098)⟩⟩,⟨⟨(-3738992058601179981026277527533),(-3738992058601179980330304277116)⟩,⟨(-17092050685767650470482684268458),(-17092050685767650469796369618664)⟩⟩,⟨⟨(-3802279870870489287838885914544),(-3802279870870489287140651648606)⟩,⟨(-17115748910512476477637004244491),(-17115748910512476476948846465730)⟩⟩,⟨⟨(-3866302921801252885022197484125),(-3866302921801252884321721521838)⟩,⟨(-17139389768148823376146384682735),(-17139389768148823375456416461794)⟩⟩,⟨⟨(-3931057772572765796694634084012),(-3931057772572765795991859256860)⟩,⟨(-17162962595241091578453931740071),(-17162962595241091577762104410130)⟩⟩,⟨⟨(-3996540750657541602023609318027),(-3996540750657541601318548195597)⟩,⟨(-17186456684502037655086975286983),(-17186456684502037654393314700293)⟩⟩,⟨⟨(-4062747945047870226600101059420),(-4062747945047870225892704448728)⟩,⟨(-17209861290235133445318527245661),(-17209861290235133444622993475864)⟩⟩,⟨⟨(-4129675201578675002797867757222),(-4129675201578675002088159694049)⟩,⟨(-17233165633947137264732749510340),(-17233165633947137264035381028701)⟩⟩,⟨⟨(-4197318118354113559804069635601),(-4197318118354113559091990822195)⟩,⟨(-17256358910129889051147444058509),(-17256358910129889050448190373239)⟩⟩,⟨⟨(-4265672041285443935013184263363),(-4265672041285443934298752796360)⟩,⟨(-17279430292210031100433381952048),(-17279430292210031099732275534809)⟩⟩,⟨⟨(-4334732059747742817248698394067),(-4334732059747742816531862250934)⟩,⟨(-17302368938665037238911584269352),(-17302368938665037238208582621507)⟩⟩] +lemma kernel0_1_r1_5_eq : ∀ k : Fin 16, kernel0_1Expr 1 5 k = kernel0_1_r1_5 k := by decide +kernel +noncomputable def kernel0_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-4404493002363116423254293230675),(-4404493002363116422535086399647)⟩,⟨(-17325163999303606254798782423338),(-17325163999303606254093935419872)⟩⟩,⟨⟨(-4474949432918085564951064507873),(-4474949432918085564229420565257)⟩,⟨(-17347804621708140603382420564722),(-17347804621708140602675670463628)⟩⟩,⟨⟨(-4546095646422854389840115390797),(-4546095646422854389116058367981)⟩,⟨(-17370279957836689285587055041396),(-17370279957836689284878441369665)⟩⟩,⟨⟨(-4617925665320186487830452847392),(-4617925665320186487103927697146)⟩,⟨(-17392579170781384894557492323211),(-17392579170781384893846969722923)⟩⟩,⟨⟨(-4690433235851611987913212781548),(-4690433235851611987184258106724)⟩,⟨(-17414691441680049688008514546752),(-17414691441680049687296138572043)⟩⟩,⟨⟨(-4763611824588674369441898729404),(-4763611824588674368710446498277)⟩,⟨(-17436605976777284774504481588631),(-17436605976777284773790193067815)⟩⟩,⟨⟨(-4837454615136895458717971695105),(-4837454615136895457984052294262)⟩,⟨(-17458312014630990739382215995431),(-17458312014630990738666061952624)⟩⟩,⟨⟨(-4911954505020090969775188786003),(-4911954505020090969038743932942)⟩,⟨(-17479798833459897960929378455329),(-17479798833459897960211310351732)⟩⟩,⟨⟨(-4987104102752606503399766191678),(-4987104102752606502660845745977)⟩,⟨(-17501055758627311199666406711438),(-17501055758627311198946492936111)⟩⟩,⟨⟨(-5062895725106964695116976219116),(-5062895725106964694375504138290)⟩,⟨(-17522072170255896542192888269955),(-17522072170255896541471061210865)⟩⟩,⟨⟨(-5139321394584317788448542587501),(-5139321394584317787704556006779)⟩,⟨(-17542837510967960243167770949390),(-17542837510967960242444085532214)⟩⟩,⟨⟨(-5216372837094985927133786806115),(-5216372837094985926387224016290)⟩,⟨(-17563341293745289268677337491427),(-17563341293745289267951741676968)⟩⟩,⟨⟨(-5294041479856229570556077141326),(-5294041479856229569806993434649)⟩,⟨(-17583573109902243271169007341908),(-17583573109902243270441576044316)⟩⟩,⟨⟨(-5372318449514254342911805842451),(-5372318449514254342160123154314)⟩,⟨(-17603522637165408224013299527536),(-17603522637165408223283963028409)⟩⟩,⟨⟨(-5451194570497278075261175633295),(-5451194570497278074506938246137)⟩,⟨(-17623179647852743948580629339892),(-17623179647852743947849450867602)⟩⟩,⟨⟨(-5530660363606302583768146140780),(-5530660363606302583011288713012)⟩,⟨(-17642534017144782244776825412466),(-17642534017144782244043749072913)⟩⟩] +lemma kernel0_1_r1_6_eq : ∀ k : Fin 16, kernel0_1Expr 1 6 k = kernel0_1_r1_6 k := by decide +kernel +noncomputable def kernel0_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-5610706044850026689724888769559),(-5610706044850026688965480673413)⟩,⟨(-17661575731440060281655415515499),(-17661575731440060280920532123948)⟩⟩,⟨⟨(-5691321524530112021774202359790),(-5691321524530112021012155090874)⟩,⟨(-17680294896786606338123559689161),(-17680294896786606337386788126095)⟩⟩,⟨⟨(-5772496406582769196750055257009),(-5772496406582769195985420598602)⟩,⟨(-17698681747380932948069997185057),(-17698681747380932947331409324863)⟩⟩,⟨⟨(-5854219988182369057988769328584),(-5854219988182369057221478131241)⟩,⟨(-17716726654125637062955352620841),(-17716726654125637062214888373451)⟩⟩,⟨⟨(-5936481259612501822759923801051),(-5936481259612501821990050080128)⟩,⟨(-17734420133236359078752732587218),(-17734420133236359078010488354527)⟩⟩,⟨⟨(-6019268904409606378299246442637),(-6019268904409606377526700807877)⟩,⟨(-17751752854888513577918320128343),(-17751752854888513577174213614939)⟩⟩,⟨⟨(-6102571299783972755988487423476),(-6102571299783972755213329522874)⟩,⟨(-17768715651893875516251437920206),(-17768715651893875515505549991663)⟩⟩,⟨⟨(-6186376517322583256898887789914),(-6186376517322583256121044462579)⟩,⟨(-17785299528396787451610458831891),(-17785299528396787450862724810720)⟩⟩,⟨⟨(-6270672323977902116146900855958),(-6270672323977902115366461403976)⟩,⟨(-17801495668579447382331812365088),(-17801495668579447381582345850521)⟩⟩,⟨⟨(-6355446183346350362062268663203),(-6355446183346350361279132372203)⟩,⟨(-17817295445365443953143426980471),(-17817295445365443952392132891031)⟩⟩,⟨⟨(-6440685257239812100526681678819),(-6440685257239812099740916362353)⟩,⟨(-17832690429110427306010616562491),(-17832690429110427305257585022564)⟩⟩,⟨⟨(-6526376407553111354965794949236),(-6526376407553111354177323275005)⟩,⟨(-17847672396268540804552366341171),(-17847672396268540803797527723044)⟩⟩,⟨⟨(-6612506198429975407198143892868),(-6612506198429975406407060474823)⟩,⟨(-17862233338022992332140758892616),(-17862233338022992331384232987434)⟩⟩,⟨⟨(-6699060898729561971560946694842),(-6699060898729561970767149542781)⟩,⟨(-17876365468868914926789854507830),(-17876365468868914926031544259379)⟩⟩,⟨⟨(-6786026484795174221237159554067),(-6786026484795174220440724949969)⟩,⟨(-17890061235136456219697860057612),(-17890061235136456218937865110501)⟩⟩,⟨⟨(-6873388643526320466792039442214),(-6873388643526320465992885693896)⟩,⟨(-17903313323441845511586835147979),(-17903313323441845510825080511959)⟩⟩] +lemma kernel0_1_r1_7_eq : ∀ k : Fin 16, kernel0_1Expr 1 7 k = kernel0_1_r1_7 k := by decide +kernel +noncomputable def kernel0_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-6961132775754795025590132844615),(-6961132775754795024788373644880)⟩,⟨(-17916114669054017343437679050324),(-17916114669054017342674305858534)⟩⟩,⟨⟨(-7049243999924964446689155039678),(-7049243999924964445884673488551)⟩,⟨(-17928458464164222051842366136687),(-17928458464164222051077260081156)⟩⟩,⟨⟨(-7137707156077939763925880700270),(-7137707156077939763118761767005)⟩,⟨(-17940338166045927959696391999112),(-17940338166045927958929662406124)⟩⟩,⟨⟨(-7226506810138801898720481451546),(-7226506810138801897910638952826)⟩,⟨(-17951747505092217411236855705525),(-17951747505092217410468421856444)⟩⟩,⟨⟨(-7315627258505524843593629016510),(-7315627258505524842781179769853)⟩,⟨(-17962680492717800638035822768680),(-17962680492717800637265829403135)⟩⟩,⟨⟨(-7405052532937711006602704964099),(-7405052532937711005787533178027)⟩,⟨(-17973131429112718207282693884575),(-17973131429112718206511026918226)⟩⟩,⟨⟨(-7494766405742716321295218690600),(-7494766405742716320477418255640)⟩,⟨(-17983094910834775265200417675235),(-17983094910834775264427196288256)⟩⟩,⟨⟨(-7584752395256200715128720541165),(-7584752395256200714308200605873)⟩,⟨(-17992565838227749594126315646264),(-17992565838227749593351452960144)⟩⟩,⟨⟨(-7674993771613593620308068472126),(-7674993771613593619484965416649)⟩,⟨(-18001539422652441232647045808913),(-18001539422652441231870708397642)⟩⟩,⟨⟨(-7765473562808415789597480842334),(-7765473562808415788771663628769)⟩,⟨(-18010011193517684575000355888993),(-18010011193517684574222411444639)⟩⟩,⟨⟨(-7856174561032849173030449786662),(-7856174561032849172202021356298)⟩,⟨(-18017977005098524905596907337797),(-18017977005098524904817484946239)⟩⟩,⟨⟨(-7947079329295397484663699861543),(-7947079329295397483832564588697)⟩,⟨(-18025433043128870596504999191133),(-18025433043128870595724005448981)⟩⟩,⟨⟨(-8038170208309932839992404018024),(-8038170208309932839158702207692)⟩,⟨(-18032375831156069979034414721893),(-18032375831156069978252020495469)⟩⟩,⟨⟨(-8129429323649880001236927402153),(-8129429323649880000400528337151)⟩,⟨(-18038802236645028390680707064801),(-18038802236645028389896778920384)⟩⟩,⟨⟨(-8220838593160750879604250623775),(-8220838593160750878765266435347)⟩,⟨(-18044709476819676205065254863576),(-18044709476819676204279931852581)⟩⟩,⟨⟨(-8312379734623709579005847407307),(-8312379734623709578164177546463)⟩,⟨(-18050095124229822796205743243575),(-18050095124229822795418925014719)⟩⟩] +lemma kernel0_1_r1_8_eq : ∀ k : Fin 16, kernel0_1Expr 1 8 k = kernel0_1_r1_8 k := by decide +kernel +noncomputable def kernel0_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-8404034273662324005143824991726),(-8404034273662324004299633650393)⟩,⟨(-18054957112031684300188654579113),(-18054957112031684299400538655864)⟩⟩,⟨⟨(-8495783551884145494606391233941),(-8495783551884145493759528116386)⟩,⟨(-18059293738970654555910205582068),(-18059293738970654555120634780271)⟩⟩,⟨⟨(-8587608735248254628585405696924),(-8587608735248254627735992136036)⟩,⟨(-18063103674055198477643695367836),(-18063103674055198476852818621210)⟩⟩,⟨⟨(-8679490822649420967681213597412),(-8679490822649420966829144061338)⟩,⟨(-18066385960911084987480606886391),(-18066385960911084986688316567506)⟩⟩,⟨⟨(-8771410654709048449085743747728),(-8771410654709048448231182880184)⟩,⟨(-18069140021805542072448357544569),(-18069140021805542071654851344738)⟩⟩,⟨⟨(-8863348922762618178591301112733),(-8863348922762618177734102302384)⟩,⟨(-18071365661331308992237217994751),(-18071365661331308991442340885607)⟩⟩,⟨⟨(-8955286178032897856603145432309),(-8955286178032897855743439259126)⟩,⟨(-18073063069740979517864567798973),(-18073063069740979517068478553182)⟩⟩,⟨⟨(-9047202840977763598507296632501),(-9047202840977763597644972454400)⟩,⟨(-18074232825922474605075748803248),(-18074232825922474604278332109064)⟩⟩,⟨⟨(-9139079210801076907467027502776),(-9139079210801076906602273779046)⟩,⟨(-18074875900006952282769829383062),(-18074875900006952281971309510113)⟩⟩,⟨⟨(-9230895475114678451131747733755),(-9230895475114678450264398173557)⟩,⟨(-18074993655600955860133933385524),(-18074993655600955859334130725240)⟩⟩,⟨⟨(-9322631719739202452746022532732),(-9322631719739202451876216865624)⟩,⟨(-18074587851635117832397407940742),(-18074587851635117831596490904225)⟩⟩,⟨⟨(-9414267938631082246402736161727),(-9414267938631082245530358613893)⟩,⟨(-18073660643822275014830742999066),(-18073660643822275014028588304151)⟩⟩,⟨⟨(-9505784043922810119088941564122),(-9505784043922810118214181535612)⟩,⟨(-18072214585718409296148769970557),(-18072214585718409295345602382304)⟩⟩,⟨⟨(-9597159876063234155172850838105),(-9597159876063234154295545002027)⟩,⟨(-18070252629380406735395631647616),(-18070252629380406734591272420419)⟩⟩,⟨⟨(-9688375214044422525942859616152),(-9688375214044422525063156783506)⟩,⟨(-18067778125615224215259788141021),(-18067778125615224214454415164307)⟩⟩,⟨⟨(-9779409785701402563788209192779),(-9779409785701402562905988374459)⟩,⟨(-18064794823815666123519572632056),(-18064794823815666122713054301260)⟩⟩] +lemma kernel0_1_r1_9_eq : ∀ k : Fin 16, kernel0_1Expr 1 9 k = kernel0_1_r1_9 k := by decide +kernel +noncomputable def kernel0_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-9870243278070888980730522357095),(-9870243278070888979846002554285)⟩,⟨(-18061306871378602110794976856288),(-18061306871378602109987571199562)⟩⟩,⟨⟨(-9960855347794953599815798792880),(-9960855347794953598928790927271)⟩,⟨(-18057318812702099353825755276746),(-18057318812702099353017251290775)⟩⟩,⟨⟨(-10051225631555458738828673788883),(-10051225631555458737939335516889)⟩,⟨(-18052835587758597370208271829547),(-18052835587758597369398856539482)⟩⟩,⟨⟨(-10141333756524978596333704688634),(-10141333756524978595441909857342)⟩,⟨(-18047862530241918664001036765615),(-18047862530241918663190570057365)⟩⟩,⟨⟨(-10231159350819868217842593714126),(-10231159350819868216948556373037)⟩,⟨(-18042405365286582668790834945980),(-18042405365286582667979568387441)⟩⟩,⟨⟨(-10320682053941108339665155914989),(-10320682053941108338768695453603)⟩,⟨(-18036470206758571894777693985469),(-18036470206758571893965423303230)⟩⟩,⟨⟨(-10409881527188556988575433252117),(-10409881527188556987676716016405)⟩,⟨(-18030063554117386146733982895963),(-18030063554117386145920904011215)⟩⟩,⟨⟨(-10498737464034275417503538607022),(-10498737464034275416602433224312)⟩,⟨(-18023192288849911403057260642780),(-18023192288849911402243224635834)⟩⟩,⟨⟨(-10587229600440666931572004663929),(-10587229600440666930668753028990)⟩,⟨(-18015863670477322657180613960763),(-18015863670477322656365903785317)⟩⟩,⟨⟨(-10675337725109272443930659162837),(-10675337725109272443025056231431)⟩,⟨(-18008085332136932934832313257919),(-18008085332136932934016693173487)⟩⟩,⟨⟨(-10763041689646206123429182638853),(-10763041689646206122521403106732)⟩,⟨(-17999865275741592023347217193452),(-17999865275741592022530891579318)⟩⟩,⟨⟨(-10850321418630388069672409375960),(-10850321418630388068762316752508)⟩,⟨(-17991211866719926394683635020011),(-17991211866719926393866446055477)⟩⟩,⟨⟨(-10937156919570938275887475017607),(-10937156919570938274975307460411)⟩,⟨(-17982133828341394594180060019595),(-17982133828341394593362285414099)⟩⟩,⟨⟨(-11023528292740336804365300517785),(-11023528292740336803450859773512)⟩,⟨(-17972640235630808241684850583412),(-17972640235630808240866259061040)⟩⟩,⟨⟨(-11109415740870228579640588642527),(-11109415740870228578724057489501)⟩,⟨(-17962740508877636013784558814803),(-17962740508877636012965362873268)⟩⟩,⟨⟨(-11194799578697056867833159071321),(-11194799578697056866914395912064)⟩,⟨(-17952444406746064839722304048170),(-17952444406746064838902336787857)⟩⟩] +lemma kernel0_1_r1_10_eq : ∀ k : Fin 16, kernel0_1Expr 1 10 k = kernel0_1_r1_10 k := by decide +kernel +noncomputable def kernel0_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-11279660242345046615565701899672),(-11279660242345046614644978977049)⟩,⟨(-17941762018992437381178013195898),(-17941762018992437380357591237352)⟩⟩,⟨⟨(-11363978298534426522153094928732),(-11363978298534426521230182816377)⟩,⟨(-17930703758797316053695878744490),(-17930703758797316052874730811984)⟩⟩,⟨⟨(-11447734453603176065417708717100),(-11447734453603176064492797806617)⟩,⟨(-17919280354720039812166959268435),(-17919280354720039811345305418945)⟩⟩,⟨⟨(-11530909562331009646659664642712),(-11530909562331009645732608424668)⟩,⟨(-17907502842284239148311450392428),(-17907502842284239147489114710723)⟩⟩,⟨⟨(-11613484636554763420918577544352),(-11613484636554763419989637235562)⟩,⟨(-17895382555203355781151845280101),(-17895382555203355780329130496555)⟩⟩,⟨⟨(-11695440853564830000760071859410),(-11695440853564829999829031553323)⟩,⟨(-17882931116255774977013237374356),(-17882931116255774976189884308258)⟩⟩,⟨⟨(-11776759564272790745132303771537),(-11776759564272790744199361141582)⟩,⟨(-17870160427819719002127835689823),(-17870160427819719001304071574678)⟩⟩,⟨⟨(-11857422301140923367867263924410),(-11857422301140923366932267602529)⟩,⟨(-17857082662078568655467958670085),(-17857082662078568654643598502475)⟩⟩,⟨⟨(-11937410785864812645658874199635),(-11937410785864812644722117002573)⟩,⟨(-17843710250907775001878369249253),(-17843710250907775001053752099163)⟩⟩,⟨⟨(-12016706936800862525100535000012),(-12016706936800862524161771757143)⟩,⟨(-17830055875454994262906398148014),(-17830055875454994262081226471879)⟩⟩,⟨⟨(-12095292876131097310440597161999),(-12095292876131097309500032280738)⟩,⟨(-17816132455425524352531809418102),(-17816132455425524351706317004646)⟩⟩,⟨⟨(-12173150936758246187780841281260),(-12173150936758246186838318796385)⟩,⟨(-17801953138085540888814353513820),(-17801953138085540887988346477178)⟩⟩,⟨⟨(-12250263668924727385259038105389),(-12250263668924727384314840899074)⟩,⟨(-17787531286996022888390419729232),(-17787531286996022887564224426498)⟩⟩,⟨⟨(-12326613846549784014832324265179),(-12326613846549784013886219040452)⟩,⟨(-17772880470490623075789960507516),(-17772880470490623074963289503807)⟩⟩,⟨⟨(-12402184473279671283445600474710),(-12402184473279671282497797956119)⟩,⟨(-17758014449911074231322798946329),(-17758014449911074230495892133697)⟩⟩,⟨⟨(-12476958788246452461685524969480),(-12476958788246452460735864731425)⟩,⟨(-17742947167614030779411692948798),(-17742947167614030778584347652486)⟩⟩] +lemma kernel0_1_r1_11_eq : ∀ k : Fin 16, kernel0_1Expr 1 11 k = kernel0_1_r1_11 k := by decide +kernel +noncomputable def kernel0_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-12550920271531626893514248927156),(-12550920271531626892563054225048)⟩,⟨(-17727692734763523505994494536304),(-17727692734763523505167084346210)⟩⟩,⟨⟨(-12624052649331485540353844984854),(-12624052649331485539400843937548)⟩,⟨(-17712265418923454614326923947037),(-17712265418923454613499111484557)⟩⟩,⟨⟨(-12696339898821766184412292299892),(-12696339898821766183457701291181)⟩,⟨(-17696679631464780111281349538547),(-17696679631464780110453380073198)⟩⟩,⟨⟨(-12767766252719859573189668849292),(-12767766252719859572233323377678)⟩,⟨(-17680949914802216691337789250801),(-17680949914802216690509451744582)⟩⟩,⟨⟨(-12838316203543497575453556894296),(-12838316203543497574495759702382)⟩,⟨(-17665090929475470884063461791812),(-17665090929475470883235104458019)⟩⟩,⟨⟨(-12907974507565532953695753560717),(-12907974507565532952736254657173)⟩,⟨(-17649117441090119383528997651518),(-17649117441090119382700305250756)⟩⟩,⟨⟨(-12976726188465095769866225912705),(-12976726188465095768905246904389)⟩,⟨(-17633044307133371412513654439773),(-17633044307133371411684877169159)⟩⟩,⟨⟨(-13044556540676081882835093130822),(-13044556540676081881872465620778)⟩,⟨(-17616886463680017012972171045901),(-17616886463680017012143089724981)⟩⟩,⟨⟨(-13111451132434592648559456515538),(-13111451132434592647595518415686)⟩,⟨(-17600658912003909711201945912904),(-17600658912003909710372950283455)⟩⟩,⟨⟨(-13177395808527600012608648355426),(-13177395808527600011643115759724)⟩,⟨(-17584376705110348584050344281634),(-17584376705110348583221074370200)⟩⟩,⟨⟨(-13242376692745755944688179049704),(-13242376692745755943721278094812)⟩,⟨(-17568054934204713938511525885557),(-17568054934204713937682236067573)⟩⟩,⟨⟨(-13306380190043897906715128148275),(-13306380190043897905746686995888)⟩,⟨(-17551708715112673279003701883035),(-17551708715112673278174165423260)⟩⟩,⟨⟨(-13369392988413421120947217735622),(-13369392988413421119977557019839)⟩,⟨(-17535353174667210718405477773611),(-17535353174667210717576062845707)⟩⟩,⟨⟨(-13431402060471292219247808901035),(-13431402060471292218276662915432)⟩,⟨(-17519003437077644306018859344009),(-17519003437077644305189224013728)⟩⟩,⟨⟨(-13492394664771065875257825398363),(-13492394664771065874285424308390)⟩,⟨(-17502674610295682779878856664380),(-17502674610295682779049258974180)⟩⟩,⟨⟨(-13552358346841834778729466955769),(-13552358346841834777755635771891)⟩,⟨(-17486381772393436945453885218011),(-17486381772393436944624091306958)⟩⟩] +lemma kernel0_1_r1_12_eq : ∀ k : Fin 16, kernel0_1Expr 1 12 k = kernel0_1_r1_12 k := by decide +kernel +noncomputable def kernel0_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-13611280939961592404169141506187),(-13611280939961592403194244978608)⟩,⟨(-17470139957968142236754320843953),(-17470139957968142235924751827715)⟩⟩,⟨⟨(-13669150565672016124394896498548),(-13669150565672016123418625642975)⟩,⟨(-17453964144588169078486958188812),(-17453964144588169077657215835049)⟩⟩,⟨⟨(-13725955634042184068330856848903),(-13725955634042184067353445083486)⟩,⟨(-17437869239294697532877560670312),(-17437869239294697532047905846617)⟩⟩,⟨⟨(-13781684843689221543453586576393),(-13781684843689221542474856350297)⟩,⟨(-17421870065173213514564382616061),(-17421870065173213513734575165988)⟩⟩,⟨⟨(-13836327181564330738560858835728),(-13836327181564330737581146404749)⟩,⟨(-17405981348008746756586673650128),(-17405981348008746755757099465906)⟩⟩,⟨⟨(-13889871922513089775564289157060),(-13889871922513089774583314575465)⟩,⟨(-17390217703038516901787064052409),(-17390217703038516900957356552612)⟩⟩,⟨⟨(-13942308628619313056758447048455),(-13942308628619313055776446494806)⟩,⟨(-17374593621815384789361162613846),(-17374593621815384788531584995542)⟩⟩,⟨⟨(-13993627148342143408187874772441),(-13993627148342143407204668478662)⟩,⟨(-17359123459195222433050046270478),(-17359123459195222432220352650355)⟩⟩,⟨⟨(-14043817615456396987566592497312),(-14043817615456396986582555398647)⟩,⟨(-17343821420461018581479548241741),(-17343821420461018580650171397204)⟩⟩,⟨⟨(-14092870447806503630215073752622),(-14092870447806503629229887741443)⟩,⟨(-17328701548596228351257235885913),(-17328701548596228350427759096361)⟩⟩,⟨⟨(-14140776345884677658560603829160),(-14140776345884677657574507056372)⟩,⟨(-17313777711719556465512083904370),(-17313777711719556464682771836809)⟩⟩,⟨⟨(-14187526291244216676231497470610),(-14187526291244216675244308619632)⟩,⟨(-17299063590693035342004293515000),(-17299063590693035341174895558310)⟩⟩,⟨⟨(-14233111544759058088915016767585),(-14233111544759058087927085398813)⟩,⟨(-17284572666914922869016886892050),(-17284572666914922868187804315610)⟩⟩,⟨⟨(-14277523644740924708576324245926),(-14277523644740924707587357953287)⟩,⟨(-17270318210308601377973386072969),(-17270318210308601377144230402613)⟩⟩,⟨⟨(-14320754404925561557269189346851),(-14320754404925561556279427711374)⟩,⟨(-17256313267518310238562319833057),(-17256313267518310237733356644378)⟩⟩,⟨⟨(-14362795912339705726734624604109),(-14362795912339705725743885224976)⟩,⟨(-17242570650322190805277546180836),(-17242570650322190804448520916289)⟩⟩] +lemma kernel0_1_r1_13_eq : ∀ k : Fin 16, kernel0_1Expr 1 13 k = kernel0_1_r1_13 k := by decide +kernel +noncomputable def kernel0_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-14403640525060539787021960600165),(-14403640525060539786030644107263)⟩,⟨(-17229102924272765239813284744218),(-17229102924272765238984661345930)⟩⟩,⟨⟨(-14443280869879456768292202781544),(-14443280869879456767299966060526)⟩,⟨(-17215922397574611089504657028338),(-17215922397574611088675981536331)⟩⟩,⟨⟨(-14481709839882011239642752370183),(-14481709839882011238649835552479)⟩,⟨(-17203041110208632443236411475475),(-17203041110208632442407949389438)⟩⟩,⟨⟨(-14518920591955946628219876168254),(-14518920591955946627226096600652)⟩,⟨(-17190470823311966992012127226507),(-17190470823311966991183621304274)⟩⟩,⟨⟨(-14554906544239173885810469945228),(-14554906544239173884816187905490)⟩,⟨(-17178223008822207320860088163624),(-17178223008822207320031952284478)⟩⟩,⟨⟨(-14589661373519531214811381421511),(-14589661373519531213816294375154)⟩,⟨(-17166308839394255128241973760738),(-17166308839394255127413801306647)⟩⟩,⟨⟨(-14623179012598079176137866909416),(-14623179012598079175142215023952)⟩,⟨(-17154739178597769628988187072756),(-17154739178597769628160242928567)⟩⟩,⟨⟨(-14655453647627580549867199137942),(-14655453647627580548870800016603)⟩,⟨(-17143524571402816909091375148859),(-17143524571402816908263400279253)⟩⟩,⟨⟨(-14686479715437680300451494675932),(-14686479715437680299454750727072)⟩,⟨(-17132675234960976166887057456237),(-17132675234960976166059517810085)⟩⟩,⟨⟨(-14716251900858138468421832601214),(-14716251900858138467424399482253)⟩,⟨(-17122201049688812234363144334196),(-17122201049688812233535579056642)⟩⟩,⟨⟨(-14744765134051278383970262480387),(-14744765134051278382972379513949)⟩,⟨(-17112111550660282099705635787588),(-17112111550660282098878308146936)⟩⟩,⟨⟨(-14772014587864594944363393010445),(-14772014587864594943364878959653)⟩,⟨(-17102415919314306857875526488431),(-17102415919314306857048177055133)⟩⟩,⟨⟨(-14797995675214223538955782094882),(-14797995675214223537957005379156)⟩,⟨(-17093122975483410044235652311645),(-17093122975483410043408704693053)⟩⟩,⟨⟨(-14822704046509700314512514238910),(-14822704046509700313513164799660)⟩,⟨(-17084241169748999034983584731487),(-17084241169748999034156618529419)⟩⟩,⟨⟨(-14846135587130149668263881589085),(-14846135587130149667264197307745)⟩,⟨(-17075778576128548438827122778550),(-17075778576128548438000398990702)⟩⟩,⟨⟨(-14868286414961715999369277628311),(-14868286414961715998369079083888)⟩,⟨(-17067742885099633402231570484600),(-17067742885099633401404830399384)⟩⟩] +lemma kernel0_1_r1_14_eq : ∀ k : Fin 16, kernel0_1Expr 1 14 k = kernel0_1_r1_14 k := by decide +kernel +noncomputable def kernel0_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-14889152878005714745262067057087),(-14889152878005714744261776891700)⟩,⟨(-17060141396965456685139863380048),(-17060141396965456684313598053031)⟩⟩,⟨⟨(-14908731552066613520358969884016),(-14908731552066613519358224245794)⟩,⟨(-17052981015566216350015476607402),(-17052981015566216349189196914309)⟩⟩,⟨⟨(-14927019238528568739419613037503),(-14927019238528568738418647374247)⟩,⟨(-17046268242340370995300822971827),(-17046268242340370994474786484099)⟩⟩,⟨⟨(-14944012962228837458478794900456),(-14944012962228837457477432680235)⟩,⟨(-17040009170739576643703348267212),(-17040009170739576642877298633128)⟩⟩,⟨⟨(-14959709969435959345618700955589),(-14959709969435959344617315790467)⟩,⟨(-17034209481000793594340525004108),(-17034209481000793593514892076915)⟩⟩,⟨⟨(-14974107725940160773341062715111),(-14974107725940160772339340243483)⟩,⟨(-17028874435278792635584775483166),(-17028874435278792634759130435380)⟩⟩,⟨⟨(-14987203915262973101462422969749),(-14987203915262973100460595606962)⟩,⟨(-17024008873142027806122175833067),(-17024008873142027805296772143009)⟩⟩,⟨⟨(-14998996436992581415795587825299),(-14998996436992581414793482639811)⟩,⟨(-17019617207434587145468339346859),(-17019617207434587144642924225712)⟩⟩,⟨⟨(-15009483405250929446584284437618),(-15009483405250929445582320293828)⟩,⟨(-17015703420506683301302469597886),(-17015703420506683300477529356007)⟩⟩,⟨⟨(-15018663147298102274664611437775),(-15018663147298102273662429344453)⟩,⟨(-17012271060815902121153229825428),(-17012271060815902120328278907266)⟩⟩,⟨⟨(-15026534202278991923195276329218),(-15026534202278991922193104639177)⟩,⟨(-17009323239901189067250485950419),(-17009323239901189066425772531959)⟩⟩,⟨⟨(-15033095320116723224945804599517),(-15033095320116723223943475134643)⟩,⟨(-17006862629731320031782979320445),(-17006862629731320030958255930243)⟩⟩,⟨⟨(-15038345460556779659859534866333),(-15038345460556779658857423349562)⟩,⟨(-17004891460429374433812326213978),(-17004891460429374432988025188421)⟩⟩,⟨⟨(-15042283792365222397500761808782),(-15042283792365222396498553116182)⟩,⟨(-17003411518374503853475423830360),(-17003411518374503852651113813939)⟩⟩,⟨⟨(-15044909692683841787084503137418),(-15044909692683841786082420832919)⟩,⟨(-17002424144682068378709060186979),(-17002424144682068377884983228094)⟩⟩,⟨⟨(-15046222746544520256073878513458),(-15046222746544520255071760042075)⟩,⟨(-17001930234062994753672058386807),(-17001930234062994752847973733171)⟩⟩] +lemma kernel0_1_r1_15_eq : ∀ k : Fin 16, kernel0_1Expr 1 15 k = kernel0_1_r1_15 k := by decide +kernel +noncomputable def kernel0_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel0_1_r1_0,kernel0_1_r1_1,kernel0_1_r1_2,kernel0_1_r1_3,kernel0_1_r1_4,kernel0_1_r1_5,kernel0_1_r1_6,kernel0_1_r1_7,kernel0_1_r1_8,kernel0_1_r1_9,kernel0_1_r1_10,kernel0_1_r1_11,kernel0_1_r1_12,kernel0_1_r1_13,kernel0_1_r1_14,kernel0_1_r1_15] +lemma kernel0_1_r1_eq (i k : Fin 16) : kernel0_1Expr 1 i k = kernel0_1_r1 i k := by + fin_cases i + · exact kernel0_1_r1_0_eq k + · exact kernel0_1_r1_1_eq k + · exact kernel0_1_r1_2_eq k + · exact kernel0_1_r1_3_eq k + · exact kernel0_1_r1_4_eq k + · exact kernel0_1_r1_5_eq k + · exact kernel0_1_r1_6_eq k + · exact kernel0_1_r1_7_eq k + · exact kernel0_1_r1_8_eq k + · exact kernel0_1_r1_9_eq k + · exact kernel0_1_r1_10_eq k + · exact kernel0_1_r1_11_eq k + · exact kernel0_1_r1_12_eq k + · exact kernel0_1_r1_13_eq k + · exact kernel0_1_r1_14_eq k + · exact kernel0_1_r1_15_eq k +noncomputable def kernel0_1_r2_0 : Fin 16 → CBox := ![⟨⟨4005228899589941982968000051922,4005228899589941983360670504883⟩,⟨(-9739826033758414944842594685919),(-9739826033758414944474193613040)⟩⟩,⟨⟨4005069653422406110507657678176,4005069653422406110900346914475⟩,⟨(-9740231985699385433272154309429),(-9740231985699385432903732061196)⟩⟩,⟨⟨4004751116058077246463125308604,4004751116058077246855851971970⟩,⟨(-9741043865664232979613335802734),(-9741043865664232979244871323917)⟩⟩,⟨⟨4004273197456344140228620355188,4004273197456344140621403090566⟩,⟨(-9742261625793983356333636789287),(-9742261625793983355965109023550)⟩⟩,⟨⟨4003635762601065560393944164246,4003635762601065560786801616945⟩,⟨(-9743885194238219286584161385041),(-9743885194238219286215549275683)⟩⟩,⟨⟨4002838631554351939236486954899,4002838631554351939629437771614⟩,⟨(-9745914475080768288546757030144),(-9745914475080768288178039519200)⟩⟩,⟨⟨4001881579528358957138252711154,4001881579528358957531315537570⟩,⟨(-9748349348240678142752170032949),(-9748349348240678142383326063216)⟩⟩,⟨⟨4000764336975165568198593100654,4000764336975165568591786587671⟩,⟨(-9751189669348530115623067470170),(-9751189669348530115254075979866)⟩⟩,⟨⟨3999486589694826943074877400065,3999486589694826943468220191128⟩,⟨(-9754435269598152763337457037991),(-9754435269598152762968296971639)⟩⟩,⟨⟨3998047978961710679074065318348,3998047978961710679467576072627⟩,⟨(-9758085955573811935554846949288),(-9758085955573811935185497237767)⟩⟩,⟨⟨3996448101669242380185350726462,3996448101669242380579048081890⟩,⟨(-9762141509052965519105651667287),(-9762141509052965518736091259643)⟩⟩,⟨⟨3994686510493204320319419240779,3994686510493204320713321869170⟩,⟨(-9766601686784684527692432868048),(-9766601686784684527322640684045)⟩⟩,⟨⟨3992762714073748350485212839300,3992762714073748350879339363194⟩,⟨(-9771466220243855375001366746651),(-9771466220243855374631321748385)⟩⟩,⟨⟨3990676177216301473688665539589,3990676177216301474083034654034⟩,⟨(-9776734815361291585079247459189),(-9776734815361291584708928546229)⟩⟩,⟨⟨3988426321111559568361551708373,3988426321111559568756182021592⟩,⟨(-9782407152229896814754137660592),(-9782407152229896814383523807239)⟩⟩,⟨⟨3986012523574781570156025643182,3986012523574781570550935873430⟩,⟨(-9788482884787034907237709975496),(-9788482884787034906866780061235)⟩⟩] +lemma kernel0_1_r2_0_eq : ∀ k : Fin 16, kernel0_1Expr 2 0 k = kernel0_1_r2_0 k := by decide +kernel +noncomputable def kernel0_1_r2_1 : Fin 16 → CBox := ![⟨⟨3983434119304613000626247102065,3983434119304613001021455815884⟩,⟨(-9794961640473276782386497702674),(-9794961640473276782015230737736)⟩⟩,⟨⟨3980690400161684036908608296539,3980690400161684037304134263242⟩,⟨(-9801843019867708315488278862211),(-9801843019867708315116653682083)⟩⟩,⟨⟨3977780615467243325815395879152,3977780615467243326211257642317⟩,⟨(-9809126596299997980434475479151),(-9809126596299997980062471114079)⟩⟩,⟨⟨3974703972322104435118107867039,3974703972322104435514324228667⟩,⟨(-9816811915439437951736718016352),(-9816811915439437951364313273869)⟩⟩,⟨⟨3971459635946197180071547204121,3971459635946197180468136625861⟩,⟨(-9824898494861187589438619344252),(-9824898494861187589065793325779)⟩⟩,⟨⟨3968046730039031039760414054385,3968046730039031040157395429476⟩,⟨(-9833385823589963787305415299993),(-9833385823589963786932146734830)⟩⟩,⟨⟨3964464337161392460443367116783,3964464337161392460840758876109⟩,⟨(-9842273361621438562790551762032),(-9842273361621438562416819779001)⟩⟩,⟨⟨3960711499138612005976940428036,3960711499138612006374761504933⟩,⟨(-9851560539421620521480617844398),(-9851560539421620521106401139010)⟩⟩,⟨⟨3956787217485751032301357409928,3956787217485751032699626085370⟩,⟨(-9861246757404513452515132032776),(-9861246757404513452140409864680)⟩⟩,⟨⟨3952690453855070806950763963613,3952690453855070807349499329256⟩,⟨(-9871331385388362317528167055742),(-9871331385388362317152917984919)⟩⟩,⟨⟨3948420130506159738097276638920,3948420130506159738496496951144⟩,⟨(-9881813762030814295731555177216),(-9881813762030814295355758486483)⟩⟩,⟨⟨3943975130799106592622721048745,3943975130799106593022445430981⟩,⟨(-9892693194243340352673433020212),(-9892693194243340352297067243772)⟩⟩,⟨⟨3939354299711119240382391418521,3939354299711119240782637903100⟩,⟨(-9903968956585281019778664942360),(-9903968956585281019401709559465)⟩⟩,⟨⟨3934556444376999532801028510732,3934556444376999533201816450613⟩,⟨(-9915640290637898714770913541143),(-9915640290637898714393346889754)⟩⟩,⟨⟨3929580334653895378210134753850,3929580334653895378611482155431⟩,⟨(-9927706404358838007139984714711),(-9927706404358838006761786299978)⟩⟩,⟨⟨3924424703710760883253296619598,3924424703710760883655222865497⟩,⟨(-9940166471417414744434923624647),(-9940166471417414744056071761761)⟩⟩] +lemma kernel0_1_r2_1_eq : ∀ k : Fin 16, kernel0_1Expr 2 1 k = kernel0_1_r2_1 k := by decide +kernel +noncomputable def kernel0_1_r2_2 : Fin 16 → CBox := ![⟨⟨3919088248642964557979239456880,3919088248642964558381762190677⟩,⟨(-9953019630511174909590029453948),(-9953019630511174909210503966891)⟩⟩,⟨⟨3913569631112494000015188362200,3913569631112494000418327329546⟩,⟨(-9966264984664184480700736782075),(-9966264984664184480320515675223)⟩⟩,⟨⟨3907867478014213147957655884039,3907867478014213148361428751146⟩,⟨(-9979901600507532415289346870649),(-9979901600507532414908409953932)⟩⟩,⟨⟨3901980382168635092726647931037,3901980382168635093131074418796⟩,⟨(-9993928507542550182364361556163),(-9993928507542550181982686859897)⟩⟩,⟨⟨3895906903041679524413466910550,3895906903041679524818564214646⟩,⟨(-10008344697387273017245511611101),(-10008344697387273016863079360562)⟩⟩,⟨⟨3889645567491889136861831441544,3889645567491889137267619746438⟩,⟨(-10023149123006690274438930608533),(-10023149123006690274055718437187)⟩⟩,⟨⟨3883194870545583678071715306685,3883194870545583678478211834232⟩,⟨(-10038340697927354899456332839194),(-10038340697927354899072320957944)⟩⟩,⟨⟨3876553276200433786213522782383,3876553276200433786620747680781⟩,⟨(-10053918295436945126383699232184),(-10053918295436945125998865312419)⟩⟩,⟨⟨3869719218257939252823322390797,3869719218257939253231292172677⟩,⟨(-10069880747769395027513598401259),(-10069880747769395027127923280899)⟩⟩,⟨⟨3862691101185297870419763365191,3862691101185297870828498870637⟩,⟨(-10086226845276234485983655580196),(-10086226845276234485597116336582)⟩⟩,⟨⟨3855467301007151514751081569297,3855467301007151515160599455898⟩,⟨(-10102955335584803521800077520379),(-10102955335584803521412654877149)⟩⟩,⟨⟨3848046166227695545213381843196,3848046166227695545623702785526⟩,⟨(-10120064922744030663662349656044),(-10120064922744030663274020843309)⟩⟩,⟨⟨3840426018783635943455761402132,3840426018783635943866901207699⟩,⟨(-10137554266358490209478765442580),(-10137554266358490209089511939133)⟩⟩,⟨⟨3832605155028475812346524413253,3832605155028475812758504576523⟩,⟨(-10155421980711478741191085923614),(-10155421980711478740800884255221)⟩⟩,⟨⟨3824581846748608887690333842147,3824581846748608888103170321656⟩,⟨(-10173666633877877136252104239151),(-10173666633877877135860935769065)⟩⟩,⟨⟨3816354342211692535628032117451,3816354342211692536041746222594⟩,⟨(-10192286746827590528429777223949),(-10192286746827590528037618650859)⟩⟩] +lemma kernel0_1_r2_2_eq : ∀ k : Fin 16, kernel0_1Expr 2 2 k = kernel0_1_r2_2 k := by decide +kernel +noncomputable def kernel0_1_r2_3 : Fin 16 → CBox := ![⟨⟨3807920867247766281759744328241,3807920867247766282174350766941⟩,⟨(-10211280792520385191961595524057),(-10211280792520385191568429323149)⟩⟩,⟨⟨3799279626363574205997303336744,3799279626363574206412824621346⟩,⟨(-10230647194992968130623078845335),(-10230647194992968130228880677494)⟩⟩,⟨⟨3790428803890540502398112164173,3790428803890540502814563404193⟩,⟨(-10250384328439182219875101107162),(-10250384328439182219479853117852)⟩⟩,⟨⟨3781366565166837108406395524920,3781366565166837108823798781596⟩,⟨(-10270490516284217046437677814845),(-10270490516284217046041356073923)⟩⟩,⟨⟨3772091057753970515996693226025,3772091057753970516415062214642⟩,⟨(-10290964030253763083526261565118),(-10290964030253763083128849464406)⟩⟩,⟨⟨3762600412688301651565444884395,3762600412688301651984802993354⟩,⟨(-10311803089439064497262425792008),(-10311803089439064496863898255428)⟩⟩,⟨⟨3752892745767898015965203977473,3752892745767898016385565300569⟩,⟨(-10333005859358853663631465363791),(-10333005859358853663231805478952)⟩⟩,⟨⟨3742966158875101075377317979681,3742966158875101075798705456712⟩,⟨(-10354570451019178346481696861372),(-10354570451019178346080879963526)⟩⟩,⟨⟨3732818741335174153087540995317,3732818741335174153509966745468⟩,⟨(-10376494919972160403564803962001),(-10376494919972160403162814905498)⟩⟩,⟨⟨3722448571311376757861412826294,3722448571311376758284901672023⟩,⟨(-10398777265374752805040791649261),(-10398777265374752804637604135903)⟩⟩,⟨⟨3711853717236790363722480205017,3711853717236790364147045042459⟩,⟨(-10421415429048589620142611862372),(-10421415429048589619738210098236)⟩⟩,⟨⟨3701032239283198096873187804514,3701032239283198097298852586541⟩,⟨(-10444407294542051403115353486390),(-10444407294542051402709711959518)⟩⟩,⟨⟨3689982190867296557911997678792,3689982190867296558338773166055⟩,⟨(-10467750686195696036771891320532),(-10467750686195696036364996158391)⟩⟩,⟨⟨3678701620194492082470467237107,3678701620194492082898379399322⟩,⟨(-10491443368212232516053018957312),(-10491443368212232515644842895519)⟩⟩,⟨⟨3667188571840506093587218766659,3667188571840506094016279103919⟩,⟨(-10515483043732242317207216283076),(-10515483043732242316797744840176)⟩⟩,⟨⟨3655441088370984798958685515863,3655441088370984799388919137964⟩,⟨(-10539867353916879840334299795875),(-10539867353916879839923506491630)⟩⟩] +lemma kernel0_1_r2_3_eq : ∀ k : Fin 16, kernel0_1Expr 2 3 k = kernel0_1_r2_3 k := by decide +kernel +noncomputable def kernel0_1_r2_4 : Fin 16 → CBox := ![⟨⟨3643457211999277311970215306519,3643457211999277312401630669788⟩,⟨(-10564593877038809871159406498897),(-10564593877038809870747279591422)⟩⟩,⟨⟨3631234986282513305492735944182,3631234986282513305925361048022⟩,⟨(-10589660127582666016505290091871),(-10589660127582666016091800575898)⟩⟩,⟨⟨3618772457856076522446369051920,3618772457856076522880213786902⟩,⟨(-10615063555356339558920113995271),(-10615063555356339558505248912638)⟩⟩,⟨⟨3606067678206533850108883044110,3606067678206533850543973826566⟩,⟨(-10640801544614433078667799853645),(-10640801544614433078251531629297)⟩⟩,⟨⟨3593118705483041201699771690603,3593118705483041202136115300388⟩,⟨(-10666871413195237432680969448666),(-10666871413195237432263287942058)⟩⟩,⟨⟨3579923606347207127282339793743,3579923606347207127719965569363⟩,⟨(-10693270411672614184566494816871),(-10693270411672614184147369895386)⟩⟩,⟨⟨3566480457861352887832603768096,3566480457861352888271519759314⟩,⟨(-10719995722524188269430328984852),(-10719995722524188269009749443850)⟩⟩,⟨⟨3552787349415063665895660366348,3552787349415063666335894455455⟩,⟨(-10747044459317277471960256339284),(-10747044459317277471538193373032)⟩⟩,⟨⟨3538842384689879651384532898836,3538842384689879651826088847765⟩,⟨(-10774413665914006113485735514226),(-10774413665914006113062181804485)⟩⟩,⟨⟨3524643683661927933080226305675,3524643683661927933523136050529⟩,⟨(-10802100315697070099147047195866),(-10802100315697070098721970368272)⟩⟩,⟨⟨3510189384642246450275908646666,3510189384642246450720178151476⟩,⟨(-10830101310817639083394667538563),(-10830101310817639082968058388257)⟩⟩,⟨⟨3495477646354499723671670842484,3495477646354499724117329619506⟩,⟨(-10858413481466898882497079902882),(-10858413481466898882068908252596)⟩⟩,⟨⟨3480506650049732703050382902384,3480506650049732703497432559159⟩,⟨(-10887033585172753306536581366624),(-10887033585172753306106841984762)⟩⟩,⟨⟨3465274601657753858694260763028,3465274601657753859142734890552⟩,⟨(-10915958306123219208932592254380),(-10915958306123219208501251364941)⟩⟩,⟨⟨3449779733974681625635498959585,3449779733974681626085401173682⟩,⟨(-10945184254518061665862456449088),(-10945184254518061665429507112794)⟩⟩,⟨⟨3434020308886129511003175351301,3434020308886129511454536966827⟩,⟨(-10974707965950227706843516864903),(-10974707965950227706408927383238)⟩⟩] +lemma kernel0_1_r2_4_eq : ∀ k : Fin 16, kernel0_1Expr 2 4 k = kernel0_1_r2_4 k := by decide +kernel +noncomputable def kernel0_1_r2_5 : Fin 16 → CBox := ![⟨⟨3417994619625444626079736900873,3417994619625444626532555417824⟩,⟨(-11004525900818646825955912724309),(-11004525900818646825519681736982)⟩⟩,⟨⟨3401700993066352142344625325221,3401700993066352142798937837548⟩,⟨(-11034634443773974514658809568095),(-11034634443773974514220900245297)⟩⟩,⟨⟨3385137792049294236051257975761,3385137792049294236507065477333⟩,⟨(-11065029903198861175208598402288),(-11065029903198861174769006350346)⟩⟩,⟨⟨3368303417740686525363084067151,3368303417740686525820419849669⟩,⟨(-11095708510724332901280070623445),(-11095708510724332900838762469953)⟩⟩,⟨⟨3351196312024247869850221664282,3351196312024247870309080809160⟩,⟨(-11126666420783872652343289047483),(-11126666420783872651900265829293)⟩⟩,⟨⟨3333814959923490751923147475359,3333814959923490752383568799191⟩,⟨(-11157899710206790203619654097077),(-11157899710206790203174877524335)⟩⟩,⟨⟨3316157892054389357021538310510,3316157892054389357483519892050⟩,⟨(-11189404377852466827394130326972),(-11189404377852466826947598853112)⟩⟩,⟨⟨3298223687107170983435116812454,3298223687107170983898694105447⟩,⟨(-11221176344287055858161032550429),(-11221176344287055857712710964790)⟩⟩,⟨⟨3280010974356103618868664317890,3280010974356103619333827358959⟩,⟨(-11253211451504213018586505073665),(-11253211451504213018136399221072)⟩⟩,⟨⟨3261518436196078500737593306026,3261518436196078501204385132167⟩,⟨(-11285505462691420541958484525991),(-11285505462691420541506552404414)⟩⟩,⟨⟨3242744810704711318359683322133,3242744810704711318828098796489⟩,⟨(-11318054062043456627678249213545),(-11318054062043456627224492435716)⟩⟩,⟨⟨3223688894228609511627629262964,3223688894228609512097706183616⟩,⟨(-11350852854624546519427686515165),(-11350852854624546518972067868310)⟩⟩,⟨⟨3204349543992375972680844558656,3204349543992375973152569969798⟩,⟨(-11383897366280713413253894144494),(-11383897366280713412796422474587)⟩⟩,⟨⟨3184725680728841471189920269073,3184725680728841471663339269580⟩,⟨(-11417183043603826399982497322246),(-11417183043603826399523128858049)⟩⟩,⟨⟨3164816291328939413178600517090,3164816291328939413653704435215⟩,⟨(-11450705253948818641205410681486),(-11450705253948818640744150528122)⟩⟩,⟨⟨3144620431509557227294137933888,3144620431509557227770967105656⟩,⟨(-11484459285505521892152924121414),(-11484459285505521891689732887270)⟩⟩] +lemma kernel0_1_r2_5_eq : ∀ k : Fin 16, kernel0_1Expr 2 5 k = kernel0_1_r2_5 k := by decide +kernel +noncomputable def kernel0_1_r2_6 : Fin 16 → CBox := ![⟨⟨3124137228497618876957018737414,3124137228497618877435553522761⟩,⟨(-11518440347426533243463712818713),(-11518440347426533242998605757242)⟩⟩,⟨⟨3103365883728572854088058210879,3103365883728572854568349308786⟩,⟨(-11552643570012496486877156163659),(-11552643570012496486410084513502)⟩⟩,⟨⟨3082305675557379658647050452250,3082305675557379659129085334972⟩,⟨(-11587064004956143751511133276652),(-11587064004956143751042105973968)⟩⟩,⟨⟨3060955961980012352759632224687,3060955961980012353243453952294⟩,⟨(-11621696625646402947056408664466),(-11621696625646402946585383965984)⟩⟩,⟨⟨3039316183363403449619831143605,3039316183363403450105417072312⟩,⟨(-11656536327533833032802270925115),(-11656536327533833032329267193121)⟩⟩,⟨⟨3017385865181691312476597469331,3017385865181691312964000106516⟩,⟨(-11691577928558602157714817983593),(-11691577928558602157239784905834)⟩⟩,⟨⟨2995164620756539560525105337756,2995164620756539561014307957541⟩,⟨(-11726816169642173243956893973273),(-11726816169642173243479844678188)⟩⟩,⟨⟨2972652153999223874750786808938,2972652153999223875241835395118⟩,⟨(-11762245715243807578173636036035),(-11762245715243807577694526240103)⟩⟩,⟨⟨2949848262152102241487225662062,2949848262152102241980089818732⟩,⟨(-11797861153982939402652489404426),(-11797861153982939402171344983432)⟩⟩,⟨⟨2926752838527007243612918016694,2926752838527007244107656631418⟩,⟨(-11833656999328413340795320362021),(-11833656999328413340312085256179)⟩⟩,⟨⟨2903365875238022692836063654980,2903365875238022693332655466764⟩,⟨(-11869627690355511734916755805552),(-11869627690355511734431447695414)⟩⟩,⟨⟨2879687465926031879942040655047,2879687465926031880440534759055⟩,⟨(-11905767592571630614345628941562),(-11905767592571630613858200822092)⟩⟩,⟨⟨2855717808472351196072009874073,2855717808472351196572372165886⟩,⟨(-11942070998811391052110821750597),(-11942070998811391051621303356673)⟩⟩,⟨⟨2831457207698691043882370496148,2831457207698691044384662077930⟩,⟨(-11978532130201897122318272175133),(-11978532130201897121826605502550)⟩⟩,⟨⟨2806906078050616013211641213250,2806906078050616013715835932648⟩,⟨(-12015145137198772560433582986677),(-12015145137198772559939790648391)⟩⟩,⟨⟨2782064946261608445217109985848,2782064946261608445723260249736⟩,⟨(-12051904100693525587797910171687),(-12051904100693525587301942244025)⟩⟩] +lemma kernel0_1_r2_6_eq : ∀ k : Fin 16, kernel0_1Expr 2 6 k = kernel0_1_r2_6 k := by decide +kernel +noncomputable def kernel0_1_r2_7 : Fin 16 → CBox := ![⟨⟨2756934453994773958135341390625,2756934453994773958643403103616⟩,⟨(-12088803033192705232834628296334),(-12088803033192705232336524239227)⟩⟩,⟨⟨2731515360459164465405919065758,2731515360459164465915961626661⟩,⟨(-12125835880069222918194840298193),(-12125835880069222917694534526261)⟩⟩,⟨⟨2705808544997633893176770469046,2705808544997633893688762493456⟩,⟨(-12162996520886120150102129899494),(-12162996520886120149599650326454)⟩⟩,⟨⟨2679815009643084410693712460974,2679815009643084411207709847187⟩,⟨(-12200278770792966919170629034379),(-12200278770792966918665922635441)⟩⟩,⟨⟨2653535881639906735958056691915,2653535881639906736474012018473⟩,⟨(-12237676381994975988216270373149),(-12237676381994975987709380222184)⟩⟩,⟨⟨2626972415927367182579188139934,2626972415927367183097172325002⟩,⟨(-12275183045294815700990534224865),(-12275183045294815700481393399027)⟩⟩,⟨⟨2600125997581646783711001383299,2600125997581646784230977446260⟩,⟨(-12312792391706998407143721934563),(-12312792391706998406632364040130)⟩⟩,⟨⟨2572998144213194275934553854690,2572998144213194276456581385775⟩,⟨(-12350497994144613185935787559593),(-12350497994144613185422156263998)⟩⟩,⟨⟨2545590508316015158735476159255,2545590508316015159259496562414⟩,⟨(-12388293369178060399286510215509),(-12388293369178060398770659577890)⟩⟩,⟨⟨2517904879565483670132542857905,2517904879565483670658636199603⟩,⟨(-12426171978865331861003593978309),(-12426171978865331860485448609910)⟩⟩,⟨⟨2489943187061233539194707938843,2489943187061233539722831304239⟩,⟨(-12464127232653264233064836366764),(-12464127232653264232544435935208)⟩⟩,⟨⟨2461707501511656990893416490311,2461707501511656991423633331927⟩,⟨(-12502152489349074823621208104779),(-12502152489349074823098492786119)⟩⟩,⟨⟨2433200037356519882639387769002,2433200037356519883171635437895⟩,⟨(-12540241059161368449179231040339),(-12540241059161368448654259289707)⟩⟩,⟨⟨2404423154824184234253500240081,2404423154824184234787860716117⟩,⟨(-12578386205809681631697858560795),(-12578386205809681631170553237389)⟩⟩,⟨⟨2375379361919917957249825392482,2375379361919917957786249468334⟩,⟨(-12616581148701506338665521349734),(-12616581148701506338135928570678)⟩⟩,⟨⟨2346071316341765471533799858835,2346071316341765472072355040431⟩,⟨(-12654819065175609961116976081761),(-12654819065175609960585032323287)⟩⟩] +lemma kernel0_1_r2_7_eq : ∀ k : Fin 16, kernel0_1Expr 2 7 k = kernel0_1_r2_7 k := by decide +kernel +noncomputable def kernel0_1_r2_8 : Fin 16 → CBox := ![⟨⟨2316501827320452286719826345612,2316501827320452287260435601990⟩,⟨(-12693093092810341493207126843924),(-12693093092810341492672904727558)⟩⟩,⟨⟨2286673857379801681647766463070,2286673857379801682190523804629⟩,⟨(-12731396331795486171028725656260),(-12731396331795486170492136747876)⟩⟩,⟨⟨2256590524014152490616263336611,2256590524014152491161112949088⟩,⟨(-12769721847366102402584362752897),(-12769721847366102402045459966058)⟩⟩,⟨⟨2226255101279283839744990957451,2226255101279283840292004547998⟩,⟨(-12808062672296645940690264528783),(-12808062672296645940148980466731)⟩⟩,⟨⟨2195671021293375602512345339166,2195671021293375603061443134880⟩,⟨(-12846411809453557191874242616687),(-12846411809453557191330653161065)⟩⟩,⟨⟨2164841875644562479294388131280,2164841875644562479845664399100⟩,⟨(-12884762234404358602641876683197),(-12884762234404358602095893140750)⟩⟩,⟨⟨2133771416701675058997838966055,2133771416701675059551230939185⟩,⟨(-12923106898081180514693824731041),(-12923106898081180514145507187145)⟩⟩,⟨⟨2102463558824803086176342204616,2102463558824803086731925973088⟩,⟨(-12961438729496506036357816219655),(-12961438729496506035807093193946)⟩⟩,⟨⟨2070922379472364515445558511352,2070922379472364516003239030556⟩,⟨(-12999750638508798650248404674718),(-12999750638508798649695367233106)⟩⟩,⟨⟨2039152120201418853535988211776,2039152120201418854095872313847⟩,⟨(-13038035518635550785943263375960),(-13038035518635550785387810869651)⟩⟩,⟨⟨2007157187558024820194022953603,2007157187558024820756040632285⟩,⟨(-13076286249911167756794880296210),(-13076286249911167756237080300798)⟩⟩,⟨⟨1974942153854510539266568582412,1974942153854510539830800437644⟩,⟨(-13114495701786979623216285637764),(-13114495701786979622656062424921)⟩⟩,⟨⟨1942511757830599321732041214650,1942511757830599322298388502044⟩,⟨(-13152656736070554037138880112419),(-13152656736070554036576328994304)⟩⟩,⟨⟨1909870905195415627809290212262,1909870905195415628377860685335⟩,⟨(-13190762209901366284145643356139),(-13190762209901366283580662721280)⟩⟩,⟨⟨1877024669047483983392620079354,1877024669047483983963336182592⟩,⟨(-13228804978759768914407288088787),(-13228804978759768913839953340734)⟩⟩,⟨⟨1843978290169928447436761210686,1843978290169928448009708211239⟩,⟨(-13266777899506092886485660976593),(-13266777899506092885915891940446)⟩⟩] +lemma kernel0_1_r2_8_eq : ∀ k : Fin 16, kernel0_1Expr 2 8 k = kernel0_1_r2_8 k := by decide +kernel +noncomputable def kernel0_1_r2_9 : Fin 16 → CBox := ![⟨⟨1810737177198181634445048096730,1810737177198181635020108032412⟩,⟨(-13304673833446605385856894224274),(-13304673833446605385284805340952)⟩⟩,⟨⟨1777306906657620224816956192999,1777306906657620225394253001865⟩,⟨(-13342485649422946769206301010587),(-13342485649422946768631775071434)⟩⟩,⟨⟨1743693222868658262226002863815,1743693222868658262805451209940⟩,⟨(-13380206226921570771588804546543),(-13380206226921570771011925042874)⟩⟩,⟨⟨1709902037716950239741560057353,1709902037716950240323249961539⟩,⟨(-13417828459199618539645610218037),(-13417828459199618539066292392581)⟩⟩,⟨⟨1675939430286482894892298241272,1675939430286482895476110287007⟩,⟨(-13455345256423568560002839176946),(-13455345256423568559421199629583)⟩⟩,⟨⟨1641811646353467629491572245553,1641811646353467630077628778843⟩,⟨(-13492749548816921472966738917708),(-13492749548816921472382661788571)⟩⟩,⟨⟨1607525097739084385444186912378,1607525097739084386032394546322⟩,⟨(-13530034289813101427063680025284),(-13530034289813101426477257187286)⟩⟩,⟨⟨1573086361519272467031757521908,1573086361519272467622211168223⟩,⟨(-13567192459209684362246270183908),(-13567192459209684361657412108111)⟩⟩,⟨⟨1538502179089914009097695237587,1538502179089914009690255555934⟩,⟨(-13604217066319998722814901076508),(-13604217066319998722223744344809)⟩⟩,⟨⟨1503779455085911336722391417679,1503779455085911337317197379360⟩,⟨(-13641101153118085899937340533038),(-13641101153118085899343753043663)⟩⟩,⟨⟨1468925256152820115177770110104,1468925256152820115774720105971⟩,⟨(-13677837797372956481981885001589),(-13677837797372956481385967203410)⟩⟩,⟨⟨1433946809569865701459958254222,1433946809569865702059152136048⟩,⟨(-13714420115768034430671352470379),(-13714420115768034430073009954340)⟩⟩,⟨⟨1398851501723340215804942114881,1398851501723340216406238274666⟩,⟨(-13750841267001644871061161137379),(-13750841267001644870460533455767)⟩⟩,⟨⟨1363646876429552272046163661713,1363646876429552272649700046536⟩,⟨(-13787094454864372537927375432290),(-13787094454864372537324331193528)⟩⟩,⟨⟨1328340633106679742351200715095,1328340633106679742956867289265⟩,⟨(-13823172931289097299094615364180),(-13823172931289097298489263814618)⟩⟩,⟨⟨1292940624795058072388675513243,1292940624795058072996577165494⟩,⟨(-13859069999369500799606307373751),(-13859069999369500798998549066191)⟩⟩] +lemma kernel0_1_r2_9_eq : ∀ k : Fin 16, kernel0_1Expr 2 9 k = kernel0_1_r2_9 k := by decide +kernel +noncomputable def kernel0_1_r2_10 : Fin 16 → CBox := ![⟨⟨1257454856025622180480142477952,1257454856025622181090112208299⟩,⟨(-13894779016342834343614780136575),(-13894779016342834343004780079428)⟩⟩,⟨⟨1221891480536408528234626949779,1221891480536408528846824555006⟩,⟨(-13930293396532742838699341759753),(-13930293396532742838086947005643)⟩⟩,⟨⟨1186258798837215187240953949075,1186258798837215187855260890876⟩,⟨(-13965606614247953135232981312867),(-13965606614247953134618309997928)⟩⟩,⟨⟨1150565255622711281433568405012,1150565255622711282050094593538⟩,⟨(-14000712206632657545680047364553),(-14000712206632657545062994952159)⟩⟩,⟨⟨1114819437034482681797016072220,1114819437034482682415596493098⟩,⟨(-14035603776464454847620819102203),(-14035603776464454847001549438826)⟩⟩,⟨⟨1079030067772697883403353118071,1079030067772697884024142136114⟩,⟨(-14070274994895751759389639849937),(-14070274994895751758768004880228)⟩⟩,⟨⟨1043206008058276210086355518001,1043206008058276210709225951336⟩,⟨(-14104719604134577804344827490874),(-14104719604134577803720954390779)⟩⟩,⟨⟨1007356250446639467594574184929,1007356250446639468219641030540⟩,⟨(-14138931420060825700485666956336),(-14138931420060825699859445968140)⟩⟩,⟨⟨971489916494327493933467734077,971489916494327494560541054095⟩,⟨(-14172904334773997952840627340109),(-14172904334773997952212247468349)⟩⟩,⟨⟨935616253279957322967964204784,935616253279957323597219607199⟩,⟨(-14206632319068618187616677145621),(-14206632319068618186985969100926)⟩⟩,⟨⟨899744629781204467825678551736,899744629781204468456980220891⟩,⟨(-14240109424833552924186324858448),(-14240109424833552923553424854205)⟩⟩,⟨⟨863884533109682725562017289503,863884533109682726195485242855⟩,⟨(-14273329787371585881729240002941),(-14273329787371585881094033057103)⟩⟩,⟨⟨828045564605795484449533813692,828045564605795485084978726228⟩,⟨(-14306287627635692482933346221252),(-14306287627635692482296021477618)⟩⟩,⟨⟨792237435795826361168213597815,792237435795826361805806894951⟩,⟨(-14338977254378576841689847490854),(-14338977254378576841050239250445)⟩⟩,⟨⟨756469964213729690133158459008,756469964213729690772755650629⟩,⟨(-14371393066212157071959587017865),(-14371393066212157071317840573098)⟩⟩,⟨⟨720753069090271517577588808719,720753069090271518219314935172⟩,⟨(-14403529553573817070426248770960),(-14403529553573817069782243845589)⟩⟩] +lemma kernel0_1_r2_10_eq : ∀ k : Fin 16, kernel0_1Expr 2 10 k = kernel0_1_r2_10 k := by decide +kernel +noncomputable def kernel0_1_r2_11 : Fin 16 → CBox := ![⟨⟨685096766912358910036848984273,685096766912358910680483622278⟩,⟨(-14435381300596383818353512848004),(-14435381300596383817707469969222)⟩⟩,⟨⟨649511166855579167967024835772,649511166855579168612766724610⟩,⟨(-14466942986878938503317217486622),(-14466942986878938502668943471840)⟩⟩,⟨⟨614006466093150545473828098689,614006466093150546121524211998⟩,⟨(-14498209389155727137376001062116),(-14498209389155727136725650143091)⟩⟩,⟨⟨578592944984661930606200281713,578592944984661931255980527081⟩,⟨(-14529175382860601576498644154890),(-14529175382860601575846090849134)⟩⟩,⟨⟨543280962148150261907429049554,543280962148150262559079345314⟩,⟨(-14559835943584594632321653677306),(-14559835943584594631667112939149)⟩⟩,⟨⟨508080949419230882122921810496,508080949419230882776630980008⟩,⟨(-14590186148424412991768721987213),(-14590186148424412991112009798591)⟩⟩,⟨⟨473003406701157208417238278283,473003406701157209072844801380⟩,⟨(-14620221177219818578064464159924),(-14620221177219818577405743641637)⟩⟩,⟨⟨438058896709841693664618021417,438058896709841694322256630805⟩,⟨(-14649936313678062429544131414339),(-14649936313678062428883271857105)⟩⟩,⟨⟨403258039618019744376432784215,403258039618019745035859393713⟩,⟨(-14679326946383734748480231726481),(-14679326946383734747817478519704)⟩⟩,⟨⟨368611507602881743214033298360,368611507602881743875462971157⟩,⟨(-14708388569692600066792090617316),(-14708388569692600066127233045840)⟩⟩,⟨⟨334130019301635311139519230799,334130019301635311802782200871⟩,⟨(-14737116784508197053597387529212),(-14737116784508197052930597344392)⟩⟩,⟨⟨299824334179590168062405407105,299824334179590168727641007062⟩,⟨(-14765507298940197895692292063444),(-14765507298940197895023433494811)⟩⟩,⟨⟨265705246815481163002722527177,265705246815481163669691901149⟩,⟨(-14793555928843741941877974275399),(-14793555928843741941207288136285)⟩⟩,⟨⟨231783581108861017392320588213,231783581108861018061230026233⟩,⟨(-14821258598239181923723096703633),(-14821258598239181923050380276135)⟩⟩,⟨⟨198070184414502851545882502644,198070184414502852216554157674⟩,⟨(-14848611339611908040735124725873),(-14848611339611908040060558211653)⟩⟩,⟨⟨164575921608853459787140888833,164575921608853460459718568995⟩,⟨(-14875610294092145004140227192836),(-14875610294092145003463669832055)⟩⟩] +lemma kernel0_1_r2_11_eq : ∀ k : Fin 16, kernel0_1Expr 2 11 k = kernel0_1_r2_11 k := by decide +kernel +noncomputable def kernel0_1_r2_12 : Fin 16 → CBox := ![⟨⟨131311669093671401993747161493,131311669093671402667953443976⟩,⟨(-14902251711514849234334026388315),(-14902251711514849233655758091636)⟩⟩,⟨⟨98288308742069149136178480109,98288308742069149812254507121⟩,⟨(-14928531950360067254663945802053),(-14928531950360067253983728311588)⟩⟩,⟨⟨65516721792255641856273815039,65516721792255642534034066583⟩,⟨(-14954447477574351360450729599626),(-14954447477574351359768751140663)⟩⟩,⟨⟨33007782694344601980013870934,33007782694344602659606284353⟩,⟨(-14979994868274064300523247279218),(-14979994868274064299839362403072)⟩⟩,⟨⟨772352915654708686561284053,772352915654709367722804453⟩,⟨(-15005170805331640415638267053733),(-15005170805331640414952741852244)⟩⟩,⟨⟨(-31178725290019730694235874694),(-31178725290019730011281855324)⟩,⟨(-15029972078846105855560299265167),(-15029972078846105854872912425757)⟩⟩,⟨⟨(-62834635143644741244781202559),(-62834635143644740560227624900)⟩,⟨(-15054395585499394562455592039738),(-15054395585499394561766539537138)⟩⟩,⟨⟨(-94184591627130425501927899692),(-94184591627130424815622872353)⟩,⟨(-15078438327800229079237913952186),(-15078438327800229078547045787416)⟩⟩,⟨⟨(-125217847788875917814426335282),(-125217847788875917126667768733)⟩,⟨(-15102097413217565334341873961723),(-15102097413217565333649491719142)⟩⟩,⟨⟨(-155923701063069439489900555908),(-155923701063069438800433728066)⟩,⟨(-15125370053205827787841035340426),(-15125370053205827787146885461882)⟩⟩,⟨⟨(-186291499597125935357159521511),(-186291499597125934666184273439)⟩,⟨(-15148253562124385120279930283392),(-15148253562124385119584215947454)⟩⟩,⟨⟨(-216310648581641389544230012771),(-216310648581641388851590921627)⟩,⟨(-15170745356053936432981629612049),(-15170745356053936432284196665491)⟩⟩,⟨⟨(-245970616577247447434720149715),(-245970616577247446740703414685)⟩,⟨(-15192842951512693142006422170850),(-15192842951512693141307560888333)⟩⟩,⟨⟨(-275260941832762275192560704072),(-275260941832762274496926527621)⟩,⟨(-15214543964075451831433666878143),(-15214543964075451830733137868320)⟩⟩,⟨⟨(-304171238589053511245729837054),(-304171238589053510548684565610)⟩,⟨(-15235846106898857739826934404789),(-15235846106898857739124947628372)⟩⟩,⟨⟨(-332691203363056530065380960177),(-332691203363056529366765923941)⟩,⟨(-15256747189156356753540332733653),(-15256747189156356752836730151533)⟩⟩] +lemma kernel0_1_r2_12_eq : ∀ k : Fin 16, kernel0_1Expr 2 12 k = kernel0_1_r2_12 k := by decide +kernel +noncomputable def kernel0_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-360810621206425853791684962846),(-360810621206425853091829970803)⟩,⟨(-15277245114386525252648188182121),(-15277245114386525251943304479548)⟩⟩,⟨⟨(-388519371933339201208652908430),(-388519371933339200507277873964)⟩,⟨(-15297337878758651395916278263658),(-15297337878758651395209832598166)⟩⟩,⟨⟨(-415807436312022129898897461211),(-415807436312022129196214543954)⟩,⟨(-15317023569259617953417933264289),(-15317023569259617952710141655797)⟩⟩,⟨⟨(-442664902214616265260230305194),(-442664902214616264556078149556)⟩,⟨(-15336300361806305130580238862802),(-15336300361806305129870939944503)⟩⟩,⟨⟨(-469081970720075465234926524993),(-469081970720075464529612735585)⟩,⟨(-15355166519287891526736851214440),(-15355166519287891526026357629842)⟩⟩,⟨⟨(-495048962164841675981128586415),(-495048962164841675274398207743)⟩,⟨(-15373620389542582006875269131858),(-15373620389542582006163324579236)⟩⟩,⟨⟨(-520556322136125414529772900511),(-520556322136125413821843422286)⟩,⟨(-15391660403273432431614033071821),(-15391660403273432430900859117710)⟩⟩,⟨⟨(-545594627402694483802001592504),(-545594627402694483092709319064)⟩,⟨(-15409285071908072505432922780273),(-15409285071908072504718355083331)⟩⟩,⟨⟨(-570154591778158389458295202397),(-570154591778158388747986878847)⟩,⟨(-15426492985407249109153376805189),(-15426492985407249108437767985844)⟩⟩,⟨⟨(-594227071911824686895314051930),(-594227071911824686183698584986)⟩,⟨(-15443282810027223047534983150920),(-15443282810027223046818039521811)⟩⟩,⟨⟨(-617803073002296835361576475907),(-617803073002296834648875879112)⟩,⟨(-15459653286041151860872639058069),(-15459653286041151860154586892104)⟩⟩,⟨⟨(-640873754429080766361407644771),(-640873754429080765647456531358)⟩,⟨(-15475603225424679942199120482205),(-15475603225424679941479793134857)⟩⟩,⟨⟨(-663430435297568975002676249610),(-663430435297568974287801376362)⟩,⟨(-15491131509511034418572845300877),(-15491131509511034417852575425650)⟩⟩,⟨⟨(-685464599892876205062294986947),(-685464599892876204346227892058)⟩,⟨(-15506237086620990874093583202786),(-15506237086620990873372099275495)⟩⟩,⟨⟨(-706967903038109411547431148362),(-706967903038109410830397741718)⟩,⟨(-15520918969673126820973750865615),(-15520918969673126820251283206878)⟩⟩,⟨⟨(-727932175352766341124548645237),(-727932175352766340406382315651)⟩,⟨(-15535176233779822700128623861331),(-15535176233779822699405004022574)⟩⟩] +lemma kernel0_1_r2_13_eq : ∀ k : Fin 16, kernel0_1Expr 2 13 k = kernel0_1_r2_13 k := by decide +kernel +noncomputable def kernel0_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-748349428407071467383991479569),(-748349428407071466665069892075)⟩,⟨(-15549008013834499981203365787479),(-15549008013834499980478978419778)⟩⟩,⟨⟨(-768211859768174856092164687013),(-768211859768174855372171156396)⟩,⟨(-15562413502095603530947764587746),(-15562413502095603530222288445775)⟩⟩,⟨⟨(-787511857934258523286244013776),(-787511857934258522565407353570)⟩,⟨(-15575391945772840756014573101438),(-15575391945772840755288241523814)⟩⟩,⟨⟨(-806242007152715701930899000397),(-806242007152715701209052187007)⟩,⟨(-15587942644621183059878491870401),(-15587942644621183059151135465106)⟩⟩,⟨⟨(-824395092118690875286480014115),(-824395092118690874563965960654)⟩,⟨(-15600064948548115872466387584621),(-15600064948548115871738355882484)⟩⟩,⟨⟨(-841964102550392201551819176363),(-841964102550392200828358215602)⟩,⟨(-15611758255239591934677450232987),(-15611758255239591933948458948401)⟩⟩,⟨⟨(-858942237637712790078971442829),(-858942237637712789354794597162)⟩,⟨(-15623022007810098697990052404064),(-15623022007810098697260337168370)⟩⟩,⟨⟨(-875322910360822951868700085808),(-875322910360822951143640436994)⟩,⟨(-15633855692482194711754520897429),(-15633855692482194711023911948332)⟩⟩,⟨⟨(-891099751675521806273152943033),(-891099751675521805547595888816)⟩,⟨(-15644258836300801827285958524791),(-15644258836300801826554848869019)⟩⟩,⟨⟨(-906266614562263265687910701021),(-906266614562263264961536358574)⟩,⟨(-15654231004887460087748882661273),(-15654231004887460087016946438036)⟩⟩,⟨⟨(-920817577935898238620038847638),(-920817577935898237893079365524)⟩,⟨(-15663771800239660464243151926358),(-15663771800239660463510625939991)⟩⟩,⟨⟨(-934746950413301702009702887113),(-934746950413301701281992338399)⟩,⟨(-15672880858580267338168651098714),(-15672880858580267337435366173466)⟩⟩,⟨⟨(-948049273936179924607820339573),(-948049273936179923879714334030)⟩,⟨(-15681557848261928042371202920663),(-15681557848261928041637521843375)⟩⟩,⟨⟨(-960719327246479419090560046046),(-960719327246479418361770406155)⟩,⟨(-15689802467731241110540048406510),(-15689802467731241109805677101001)⟩⟩,⟨⟨(-972752129211945022094196102601),(-972752129211945021364955254421)⟩,⟨(-15697614443557318424036780696190),(-15697614443557318423301956260732)⟩⟩,⟨⟨(-984142941999499725660734210537),(-984142941999499724930877875136)⟩,⟨(-15704993528529229491759059571526),(-15704993528529229491023614149304)⟩⟩] +lemma kernel0_1_r2_14_eq : ∀ k : Fin 16, kernel0_1Expr 2 14 k = kernel0_1_r2_14 k := by decide +kernel +noncomputable def kernel0_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-994887274094243404367878508708),(-994887274094243403637815943592)⟩,⟨(-15711939499826658980553750829402),(-15711939499826658979818102100494)⟩⟩,⟨⟨(-1004980883161991309992512962939),(-1004980883161991309261904200989)⟩,⟨(-15718452157267941683922154361424),(-15718452157267941683185954932274)⟩⟩,⟨⟨(-1014419778753396066664799997316),(-1014419778753396065933876483296)⟩,⟨(-15724531321639462751116768857319),(-15724531321639462750380254823304)⟩⟩,⟨⟨(-1023200224847818837225680613267),(-1023200224847818836494280762837)⟩,⟨(-15730176833110225595171735582438),(-15730176833110225594434741541772)⟩⟩,⟨⟨(-1031318742235236304970913457360),(-1031318742235236304239401352664)⟩,⟨(-15735388549735195875877013120905),(-15735388549735195875139910701734)⟩⟩,⟨⟨(-1038772110734590098935058767423),(-1038772110734590098203141118465)⟩,⟨(-15740166346050827751212786140351),(-15740166346050827750475275254358)⟩⟩,⟨⟨(-1045557371247104275223217729464),(-1045557371247104274491124095070)⟩,⟨(-15744510111765968666150652688748),(-15744510111765968665412967496258)⟩⟩,⟨⟨(-1051671827643214456197638968882),(-1051671827643214455465211162045)⟩,⟨(-15748419750551121776697167117581),(-15748419750551121775959145462929)⟩⟩,⟨⟨(-1057113048481869242020357773071),(-1057113048481869241288004351699)⟩,⟨(-15751895178928821181853815886141),(-15751895178928821181115874916256)⟩⟩,⟨⟨(-1061878868561080576884750484518),(-1061878868561080576152135071751)⟩,⟨(-15754936325267644964558712197778),(-15754936325267644963820507523221)⟩⟩,⟨⟨(-1065967390298714919326705194569),(-1065967390298714918594054128673)⟩,⟨(-15757543128882155146589154503125),(-15757543128882155145850916978777)⟩⟩,⟨⟨(-1069376984942631387976384507548),(-1069376984942631387243544110932)⟩,⟨(-15759715539240812576848369987493),(-15759715539240812576109941914905)⟩⟩,⟨⟨(-1072106293609386597186916959786),(-1072106293609386596454255129266)⟩,⟨(-15761453515283669044128785016093),(-15761453515283669043390541997366)⟩⟩,⟨⟨(-1074154228150838736986645254151),(-1074154228150838736253867375351)⟩,⟨(-15762757024851389091602228373751),(-15762757024851389090863868550344)⟩⟩,⟨⟨(-1075519971848095672999681118076),(-1075519971848095672267009262814)⟩,⟨(-15763626044226900677340665505413),(-15763626044226900676602415354912)⟩⟩,⟨⟨(-1076202979932363536061308072185),(-1076202979932363535328593906130)⟩,⟨(-15764060557790717547516643965460),(-15764060557790717546778351174950)⟩⟩] +lemma kernel0_1_r2_15_eq : ∀ k : Fin 16, kernel0_1Expr 2 15 k = kernel0_1_r2_15 k := by decide +kernel +noncomputable def kernel0_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel0_1_r2_0,kernel0_1_r2_1,kernel0_1_r2_2,kernel0_1_r2_3,kernel0_1_r2_4,kernel0_1_r2_5,kernel0_1_r2_6,kernel0_1_r2_7,kernel0_1_r2_8,kernel0_1_r2_9,kernel0_1_r2_10,kernel0_1_r2_11,kernel0_1_r2_12,kernel0_1_r2_13,kernel0_1_r2_14,kernel0_1_r2_15] +lemma kernel0_1_r2_eq (i k : Fin 16) : kernel0_1Expr 2 i k = kernel0_1_r2 i k := by + fin_cases i + · exact kernel0_1_r2_0_eq k + · exact kernel0_1_r2_1_eq k + · exact kernel0_1_r2_2_eq k + · exact kernel0_1_r2_3_eq k + · exact kernel0_1_r2_4_eq k + · exact kernel0_1_r2_5_eq k + · exact kernel0_1_r2_6_eq k + · exact kernel0_1_r2_7_eq k + · exact kernel0_1_r2_8_eq k + · exact kernel0_1_r2_9_eq k + · exact kernel0_1_r2_10_eq k + · exact kernel0_1_r2_11_eq k + · exact kernel0_1_r2_12_eq k + · exact kernel0_1_r2_13_eq k + · exact kernel0_1_r2_14_eq k + · exact kernel0_1_r2_15_eq k +noncomputable def kernel0_1_r3_0 : Fin 16 → CBox := ![⟨⟨4725921836758698109577018853421,4725921836758698109843370530762⟩,⟨(-5460256939008135583140041498338),(-5460256939008135582933511723789)⟩⟩,⟨⟨4725935384694818945893911598279,4725935384694818946160274798593⟩,⟨(-5460500771615991662087684987324),(-5460500771615991661881143066985)⟩⟩,⟨⟨4725962460532855378448211839306,4725962460532855378714598000129⟩,⟨(-5460988431422265472034473921678),(-5460988431422265471827907769661)⟩⟩,⟨⟨4726003024207877801518005342492,4726003024207877801784425901909⟩,⟨(-5461719907595580205424307775623),(-5461719907595580205217705305098)⟩⟩,⟨⟨4726057015631200581068578278888,4726057015631200581335044675347⟩,⟨(-5462695183857622357054219028098),(-5462695183857622356847568151135)⟩⟩,⟨⟨4726124354700851027861534853686,4726124354700851028128058526646⟩,⟨(-5463914238445649338215073545417),(-5463914238445649338008362172270)⟩⟩,⟨⟨4726204941315558755602163283345,4726204941315558755868755671691⟩,⟨(-5465377044062508930852081493580),(-5465377044062508930645297533506)⟩⟩,⟨⟨4726298655392291737638046862390,4726298655392291737904719408305⟩,⟨(-5467083567814178602847645198457),(-5467083567814178602640776556746)⟩⟩,⟨⟨4726405356887371923766606800112,4726405356887371924033370941395⟩,⟨(-5469033771134834770741245388256),(-5469033771134834770534279971327)⟩⟩,⟨⟨4726524885821209806407369508992,4726524885821209806674236693159⟩,⟨(-5471227609699464201305317390197),(-5471227609699464201098243095434)⟩⟩,⟨⟨4726657062306703828552993238205,4726657062306703828819974900095⟩,⟨(-5473665033324031896304861601028),(-5473665033324031896097666332281)⟩⟩,⟨⟨4726801686581357000270887144935,4726801686581357000537994740301⟩,⟨(-5476345985853222013357949253701),(-5476345985853222013150620897319)⟩⟩,⟨⟨4726958539043169531745779318204,4726958539043169532013024272743⟩,⟨(-5479270405035770647917610393145),(-5479270405035770647710136853682)⟩⟩,⟨⟨4727127380290372694504928121456,4727127380290372694772321905758⟩,⟨(-5482438222387411644796749943505),(-5482438222387411644589119090596)⟩⟩,⟨⟨4727307951165075484024151538711,4727307951165075484291705570321⟩,⟨(-5485849363041459030084544116276),(-5485849363041459029876743853453)⟩⟩,⟨⟨4727499972800901971736511772090,4727499972800901972004237536415⟩,⟨(-5489503745587052163419985297594),(-5489503745587052163212003476749)⟩⟩] +lemma kernel0_1_r3_0_eq : ∀ k : Fin 16, kernel0_1Expr 3 0 k = kernel0_1_r3_0 k := by decide +kernel +noncomputable def kernel0_1_r3_1 : Fin 16 → CBox := ![⟨⟨4727703146674703497797755808395,4727703146674703498065664698092⟩,⟨(-5493401281895092313990406842335),(-5493401281895092313782231376795)⟩⟩,⟨⟨4727917154662436062914127410195,4727917154662436063182230942730⟩,⟨(-5497541876931902068826842495641),(-5497541876931902068618461206378)⟩⟩,⟨⟨4728141659099299423078913293232,4728141659099299423347222848073⟩,⟨(-5501925428560641796405568164621),(-5501925428560641796196968965548)⟩⟩,⟨⟨4728376302844240470013692925432,4728376302844240470282220040939⟩,⟨(-5506551827330520319574507561243),(-5506551827330520319365678249318)⟩⟩,⟨⟨4728620709348929487128620796205,4728620709348929487397376802577⟩,⟨(-5511420956253840006641229695704),(-5511420956253840006432158209997)⟩⟩,⟨⟨4728874482731323800394204713821,4728874482731323800663201206574⟩,⟨(-5516532690570919675212857391581),(-5516532690570919675003531478504)⟩⟩,⟨⟨4729137207853939189968343907387,4729137207853939190237592198883⟩,⟨(-5521886897502942027075219116457),(-5521886897502942026865626717153)⟩⟩,⟨⟨4729408450406955185874117640182,4729408450406955186143629351800⟩,⟨(-5527483435992775800918724516119),(-5527483435992775800708853347627)⟩⟩,⟨⟨4729687756996286033409059529423,4729687756996286033678845882846⟩,⟨(-5533322156433826449803641356421),(-5533322156433826449593479412725)⟩⟩,⟨⟨4729974655236754675016576817283,4729974655236754675286649532530⟩,⟨(-5539402900386972928501880602292),(-5539402900386972928291415518726)⟩⟩,⟨⟨4730268653850512548586799432115,4730268653850512548857169717384⟩,⟨(-5545725500285652118692096497558),(-5545725500285652118481316265557)⟩⟩,⟨⟨4730569242770853340883437683657,4730569242770853341154117280059⟩,⟨(-5552289779129156533687072732401),(-5552289779129156533475964959633)⟩⟩,⟨⟨4730875893251574052098839045074,4730875893251574052369839025062⟩,⟨(-5559095550164215235024103972301),(-5559095550164215234812656733634)⟩⟩,⟨⟨4731188057982041816276733050584,4731188057982041816548065298076⟩,⟨(-5566142616554932366745912753660),(-5566142616554932366534113542104)⟩⟩,⟨⟨4731505171208129875133039609903,4731505171208129875404715183527⟩,⟨(-5573430771041162375233392816726),(-5573430771041162375021229703569)⟩⟩,⟨⟨4731826648859190912033134029532,4731826648859190912305164833506⟩,⟨(-5580959795585405838497939229001),(-5580959795585405838285399678663)⟩⟩] +lemma kernel0_1_r3_1_eq : ∀ k : Fin 16, kernel0_1Expr 3 1 k = kernel0_1_r3_1 k := by decide +kernel +noncomputable def kernel0_1_r3_2 : Fin 16 → CBox := ![⟨⟨4732151888681240610690316356903,4732151888681240610962713229638⟩,⟨(-5588729461008314884147093585363),(-5588729461008314883934165811563)⟩⟩,⟨⟨4732480270376528801430097232176,4732480270376528801702872303076⟩,⟨(-5596739526612902434807282953531),(-5596739526612902434593954246043)⟩⟩,⟨⟨4732811155749679888264796134730,4732811155749679888537960258755⟩,⟨(-5604989739797554988370062028257),(-5604989739797554988156320574720)⟩⟩,⟨⟨4733143888860588403938332730070,4733143888860588404211898024307⟩,⟨(-5613479835657954322501875142759),(-5613479835657954322287708226217)⟩⟩,⟨⟨4733477796184259508675297599326,4733477796184259508949274632766⟩,⟨(-5622209536578019412615441923527),(-5622209536578019412400837920392)⟩⟩,⟨⟨4733812186777788022491671689743,4733812186777788022766072867219⟩,⟨(-5631178551809985973837219640099),(-5631178551809985973622165612817)⟩⟩,⟨⟨4734146352454673151234636351237,4734146352454673151509472261182⟩,⟨(-5640386577043747383998394232863),(-5640386577043747383782878529112)⟩⟩,⟨⟨4734479567966669423401657187601,4734479567966669423676940216166⟩,⟨(-5649833293965587319573883549890),(-5649833293965587319357893228915)⟩⟩,⟨⟨4734811091193377488380809694346,4734811091193377488656549998350⟩,⟨(-5659518369806441242694762241654),(-5659518369806441242478285943877)⟩⟩,⟨⟨4735140163339781326944479119303,4735140163339781327220689513542⟩,⟨(-5669441456879830917400348713480),(-5669441456879830917183373175791)⟩⟩,⟨⟨4735466009141941081263716548804,4735466009141941081540407283259⟩,⟨(-5679602192109623409331782496782),(-5679602192109623409114296278114)⟩⟩,⟨⟨4735787837081053113798915201601,4735787837081053114076098993986⟩,⟨(-5690000196547773536855985882372),(-5690000196547773536637975771566)⟩⟩,⟨⟨4736104839606091041340433813684,4736104839606091041618120396629⟩,⟨(-5700635074882216494488010739878),(-5700635074882216494269465650782)⟩⟩,⟨⟨4736416193365243351171205562513,4736416193365243351449408162111⟩,⟨(-5711506414935085362357821839524),(-5711506414935085362138728180280)⟩⟩,⟨⟨4736721059446364779536399965759,4736721059446364779815128412469⟩,⟨(-5722613787151436448799157387955),(-5722613787151436448579503987807)⟩⟩,⟨⟨4737018583626659906858953464162,4737018583626659907138220875908⟩,⟨(-5733956744078673886907598376318),(-5733956744078673886687371702966)⟩⟩] +lemma kernel0_1_r3_2_eq : ∀ k : Fin 16, kernel0_1Expr 3 2 k = kernel0_1_r3_2 k := by decide +kernel +noncomputable def kernel0_1_r3_3 : Fin 16 → CBox := ![⟨⟨4737307896631818387763548427176,4737307896631818388043363872231⟩,⟨(-5745534819836873619617369233738),(-5745534819836873619396558648518)⟩⟩,⟨⟨4737588114404821875108875179137,4737588114404821875389252520212⟩,⟨(-5757347529580215860469126744272),(-5757347529580215860247718163483)⟩⟩,⟨⟨4737858338384643003850328827170,4737858338384643004131277385074⟩,⟨(-5769394368949744307244483748059),(-5769394368949744307022466338236)⟩⟩,⟨⟨4738117655795056760475819759678,4738117655795056760757353126920⟩,⟨(-5781674813517679810942359479314),(-5781674813517679810719719332425)⟩⟩,⟨⟨4738365139943784164647579526187,4738365139943784164929706174333⟩,⟨(-5794188318223525860517584899030),(-5794188318223525860294311779121)⟩⟩,⟨⟨4738599850532187419088591414476,4738599850532187419371325758375⟩,⟨(-5806934316802213131160544620355),(-5806934316802213130936624010687)⟩⟩,⟨⟨4738820833975734529113557969207,4738820833975734529396908720065⟩,⟨(-5819912221204540456832292493970),(-5819912221204540456607713974101)⟩⟩,⟨⟨4739027123735449841874096496617,4739027123735449842158077802063⟩,⟨(-5833121421010179921826277836779),(-5833121421010179921601027064137)⟩⟩,⟨⟨4739217740660564994654864134275,4739217740660564994939483500742⟩,⟨(-5846561282833524316209406346031),(-5846561282833524315983473757956)⟩⟩,⟨⟨4739391693342582378667770055712,4739391693342582378953042796025⟩,⟨(-5860231149722665960348388922079),(-5860231149722665960121759318578)⟩⟩,⟨⟨4739547978480960406975059895002,4739547978480960407260994001372⟩,⟨(-5874130340551806867923031657545),(-5874130340551806867695695115587)⟩⟩,⟨⟨4739685581260626609666738898071,4739685581260626609953349159121⟩,⟨(-5888258149407411377744911425719),(-5888258149407411377516853105718)⟩⟩,⟨⟨4739803475741520853498950510548,4739803475741520853786243615896⟩,⟨(-5902613844968423734506133032010),(-5902613844968423734277343944960)⟩⟩,⟨⟨4739900625260366784208101194573,4739900625260366784496093182477⟩,⟨(-5917196669880884628721667143800),(-5917196669880884628492131529472)⟩⟩,⟨⟨4739975982844864905089212446944,4739975982844864905377910471246⟩,⟨(-5932005840127292407301001924481),(-5932005840127292407070710450923)⟩⟩,⟨⟨4740028491640495522733279945774,4740028491640495523022699528100⟩,⟨(-5947040544391066528335706835674),(-5947040544391066528104644099520)⟩⟩] +lemma kernel0_1_r3_3_eq : ∀ k : Fin 16, kernel0_1Expr 3 3 k = kernel0_1_r3_3 k := by decide +kernel +noncomputable def kernel0_1_r3_4 : Fin 16 → CBox := ![⟨⟨4740057085350114097789237679704,4740057085350114098079384114301⟩,⟨(-5962299943416482845993075522144),(-5962299943416482845761233536747)⟩⟩,⟨⟨4740060688686515323181883073338,4740060688686515323472773669978⟩,⟨(-5977783169364462462253717934407),(-5977783169364462462021079982676)⟩⟩,⟨⟨4740038217838135502546432494260,4740038217838135502838073440067⟩,⟨(-5993489325164608159217972044199),(-5993489325164608158984529487729)⟩⟩,⟨⟨4739988580948055506176736524521,4739988580948055506469144170131⟩,⟨(-6009417483863894815622043701205),(-6009417483863894815387780503282)⟩⟩,⟨⟨4739910678606458729289098083797,4739910678606458729582276716553⟩,⟨(-6025566687972432700022744150667),(-6025566687972432699787653056578)⟩⟩,⟨⟨4739803404356690056996149950079,4739803404356690057290117731326⟩,⟨(-6041935948806735105979282957170),(-6041935948806735105743346596536)⟩⟩,⟨⟨4739665645215052841588469486338,4739665645215052841883231497225⟩,⟨(-6058524245830934435799479937498),(-6058524245830934435562690478351)⟩⟩,⟨⟨4739496282204471310505039968730,4739496282204471310800613491440⟩,⟨(-6075330525996403532508530196247),(-6075330525996403532270870894192)⟩⟩,⟨⟨4739294190902135638202902061691,4739294190902135638499289554542⟩,⟨(-6092353703080251787282747624853),(-6092353703080251787044212571197)⟩⟩,⟨⟨4739058242001236123017978813307,4739058242001236123315200067971⟩,⟨(-6109592657023178293469834670998),(-6109592657023178293230405273215)⟩⟩,⟨⟨4738787301886881502643459046850,4738787301886881502941517890694⟩,⟨(-6127046233267177059449876106822),(-6127046233267177059209545461215)⟩⟩,⟨⟨4738480233226284411280652987639,4738480233226284411579567740244⟩,⟨(-6144713242093602011098202312744),(-6144713242093602010856952890462)⟩⟩,⟨⟨4738135895573284320777838230579,4738135895573284321077610054552⟩,⟨(-6162592457962112189776987846475),(-6162592457962112189534814711457)⟩⟩,⟨⟨4737753145987265010849010366524,4737753145987265011149660110114⟩,⟨(-6180682618851030162064490487661),(-6180682618851030161821374243475)⟩⟩,⟨⟨4737330839666509674244229019506,4737330839666509674545759097330⟩,⟨(-6198982425599659180465773334562),(-6198982425599659180221708138611)⟩⟩,⟨⟨4736867830596022176868741311375,4736867830596022177171171192431⟩,⟨(-6217490541253117046966608515000),(-6217490541253117046721575972589)⟩⟩] +lemma kernel0_1_r3_4_eq : ∀ k : Fin 16, kernel0_1Expr 3 4 k = kernel0_1_r3_4 k := by decide +kernel +noncomputable def kernel0_1_r3_5 : Fin 16 → CBox := ![⟨⟨4736362972209827756576488244452,4736362972209827756879816596041⟩,⟨(-6236205590410256909527303303444),(-6236205590410256909281300353496)⟩⟩,⟨⟨4735815118067750554919114169663,4735815118067750555223364039776⟩,⟨(-6255126158575257340723873416088),(-6255126158575257340476879016578)⟩⟩,⟨⟨4735223122546648831767108293834,4735223122546648832072280518481⟩,⟨(-6274250791513475982228958149906),(-6274250791513475981980967660356)⟩⟩,⟨⟨4734585841546071512769558556996,4734585841546071513075673867719⟩,⟨(-6293577994612172762448872828165),(-6293577994612172762199866905634)⟩⟩,⟨⟨4733902133208281864561971919794,4733902133208281864869027530168⟩,⟨(-6313106232246720180448619699357),(-6313106232246720180198596411962)⟩⟩,⟨⟨4733170858652575584143519603885,4733170858652575584451539672738⟩,⟨(-6332833927152929369675959805096),(-6332833927152929369424897266171)⟩⟩,⟨⟨4732390882723801429862309222182,4732390882723801430171292828679⟩,⟨(-6352759459806131581658692746122),(-6352759459806131581406587670651)⟩⟩,⟨⟨4731561074754972716218903948479,4731561074754972716528873207313⟩,⟨(-6372881167807665333902543159385),(-6372881167807665333649375167992)⟩⟩,⟨⟨4730680309343837548849244398795,4730680309343837549160193453557⟩,⟨(-6393197345279429718187269326135),(-6393197345279429717933038840509)⟩⟩,⟨⟨4729747467143254596629865176668,4729747467143254596941820842898⟩,⟨(-6413706242267174235338946742723),(-6413706242267174235083629884482)⟩⟩,⟨⟨4728761435665199493401211815996,4728761435665199493714171232387⟩,⟨(-6434406064153204979846654328967),(-6434406064153204979590249329245)⟩⟩,⟨⟨4727721110098204642406602100998,4727721110098204642720588885130⟩,⟨(-6455294971079196011451852255480),(-6455294971079196011194337610593)⟩⟩,⟨⟨4726625394138012273870503507379,4726625394138012274185509997901⟩,⟨(-6476371077379803289735346431751),(-6476371077379803289476724004556)⟩⟩,⟨⟨4725473200831197093508816782538,4725473200831197093824871130003⟩,⟨(-6497632451027786580094517752847),(-6497632451027786579834762653429)⟩⟩,⟨⟨4724263453431490772195261893522,4724263453431490772512359100456⟩,⟨(-6519077113091352233398525210466),(-6519077113091352233137637359256)⟩⟩,⟨⟨4722995086268515881263205196500,4722995086268515881581370510169⟩,⟨(-6540703037204436664877409614463),(-6540703037204436664615366289860)⟩⟩] +lemma kernel0_1_r3_5_eq : ∀ k : Fin 16, kernel0_1Expr 3 5 k = kernel0_1_r3_5 k := by decide +kernel +noncomputable def kernel0_1_r3_6 : Fin 16 → CBox := ![⟨⟨4721667045628611692559005050254,4721667045628611692878226726971⟩,⟨(-6562508149050656678138661905218),(-6562508149050656677875468148710)⟩⟩,⟨⟨4720278290647408557770816234223,4720278290647408558091125950393⟩,⟨(-6584490325861658465234342228429),(-6584490325861658464969970497223)⟩⟩,⟨⟨4718827794213781380006988333842,4718827794213781380328378757897⟩,⟨(-6606647395930602131038984625211),(-6606647395930602130773436707400)⟩⟩,⟨⟨4717314543884786016272934557731,4717314543884786016595432689622⟩,⟨(-6628977138141522907535654754322),(-6628977138141522907268906619152)⟩⟩,⟨⟨4715737542811155328531839324787,4715737542811155328855431608247⟩,⟨(-6651477281515313808786971265212),(-6651477281515313808519029463782)⟩⟩,⟨⟨4714095810672904061546709571660,4714095810672904061871428879090⟩,⟨(-6674145504773077298472631400693),(-6674145504773077298203467481715)⟩⟩,⟨⟨4712388384624563797816905951630,4712388384624563798142742405163⟩,⟨(-6696979435917595567307910449789),(-6696979435917595567037528261661)⟩⟩,⟨⟨4710614320249540955796458759278,4710614320249540956123441243410⟩,⟨(-6719976651833670216238884332061),(-6719976651833670215967258436334)⟩⟩,⟨⟨4708772692523062191425460040087,4708772692523062191753570249750⟩,⟨(-6743134677908082482362145420693),(-6743134677908082482089286134133)⟩⟩,⟨⟨4706862596783142671090652059242,4706862596783142671419926896522⟩,⟨(-6766450987669924597967631253238),(-6766450987669924597693507074778)⟩⟩,⟨⟨4704883149708983544807718572492,4704883149708983545138145402816⟩,⟨(-6789923002452051409576519340114),(-6789923002452051409301136373376)⟩⟩,⟨⟨4702833490306175602108686357693,4702833490306175602440296075013⟩,⟨(-6813548091074398974770145943593),(-6813548091074398974493477248441)⟩⟩,⟨⟨4700712780898056582328317773038,4700712780898056582661089818590⟩,⟨(-6837323569549913472307143555048),(-6837323569549913472029201364673)⟩⟩,⟨⟨4698520208122539980280703849821,4698520208122539980614676591618⟩,⟨(-6861246700813829378843267158768),(-6861246700813829378564018858705)⟩⟩,⟨⟨4696254983933703484329709854120,4696254983933703484664867676912⟩,⟨(-6885314694477030457949551483145),(-6885314694477030457669005640950)⟩⟩,⟨⟨4693916346607395455240830596146,4693916346607395455577206536519⟩,⟨(-6909524706604220649743805205662),(-6909524706604220649461933278449)⟩⟩] +lemma kernel0_1_r3_6_eq : ∀ k : Fin 16, kernel0_1Expr 3 6 k = kernel0_1_r3_6 k := by decide +kernel +noncomputable def kernel0_1_r3_7 : Fin 16 → CBox := ![⟨⟨4691503561750088151628013660181,4691503561750088151965581010251⟩,⟨(-6933873839517624419307706171953),(-6933873839517624419024525326853)⟩⟩,⟨⟨4689015923310176783914974844189,4689015923310176784253777213071⟩,⟨(-6958359141626927497601857104255),(-6958359141626927497317330730726)⟩⟩,⟨⟨4686452754590893988094606153181,4686452754590893988434624728672⟩,⟨(-6982977607286159209803874831039),(-6982977607286159209518014166907)⟩⟩,⟨⟨4683813409263980009648484114057,4683813409263980009989754195981⟩,⟨(-7007726176678206714535542856696),(-7007726176678206714248317663955)⟩⟩,⟨⟨4681097272383219835074776355712,4681097272383219835417269206802⟩,⟨(-7032601735727639456734364356169),(-7032601735727639456445793630749)⟩⟩,⟨⟨4678303761396929763619314571829,4678303761396929763963074857476⟩,⟨(-7057601116042508952268139159437),(-7057601116042508951978185487621)⟩⟩,⟨⟨4675432327158447536767134010417,4675432327158447537112139487971⟩,⟨(-7082721094885774661075658675799),(-7082721094885774660784336188420)⟩⟩,⟨⟨4672482454933652201194974375538,4672482454933652201541262742296⟩,⟨(-7107958395176991157029930060884),(-7107958395176991156737206721017)⟩⟩,⟨⟨4669453665404512437111680201115,4669453665404512437459215810673⟩,⟨(-7133309685524875058442868429393),(-7133309685524875058148768869533)⟩⟩,⟨⟨4666345515667635204551959454270,4666345515667635204900792771437⟩,⟨(-7158771580291352237050281812534),(-7158771580291352236754764161228)⟩⟩,⟨⟨4663157600226760312908452953096,4663157600226760313258558085293⟩,⟨(-7184340639687666671715397620879),(-7184340639687666671418479117105)⟩⟩,⟨⟨4659889551978120972667519853729,4659889551978120973018937011086⟩,⟨(-7210013369903111954753868360100),(-7210013369903111954455515077717)⟩⟩,⟨⟨4656541043187565612945130358170,4656541043187565613297821393231⟩,⟨(-7235786223266924895080568636624),(-7235786223266924894780807491181)⟩⟩,⟨⟨4653111786458312314953171460736,4653111786458312315307188159532⟩,⟨(-7261655598443857897360093385647),(-7261655598443857897058881496504)⟩⟩,⟨⟨4649601535688184191761949928239,4649601535688184192117262513536⟩,⟨(-7287617840663922836812311938580),(-7287617840663922836509669882571)⟩⟩,⟨⟨4646010087015152011143116136916,4646010087015152011499767460175⟩,⟨(-7313669241986774004930018705965),(-7313669241986774004625910566075)⟩⟩] +lemma kernel0_1_r3_7_eq : ∀ k : Fin 16, kernel0_1Expr 3 7 k = kernel0_1_r3_7 k := by decide +kernel +noncomputable def kernel0_1_r3_8 : Fin 16 → CBox := ![⟨⟨4642337279749989383910813300015,4642337279749989384268756270153⟩,⟨(-7339806041601171384657118134593),(-7339806041601171384351578178852)⟩⟩,⟨⟨4638582997294825998430666929222,4638582997294825998789960958280⟩,⟨(-7366024426159938040084525407924),(-7366024426159938039777504836354)⟩⟩,⟨⟨4634747168046365746464141306281,4634747168046365746824752521525⟩,⟨(-7392320530150796794003016827216),(-7392320530150796793694539768177)⟩⟩,⟨⟨4630829766282519229916843175010,4630829766282519230278817170892⟩,⟨(-7418690436303441638355523268907),(-7418690436303441638045551732576)⟩⟩,⟨⟨4626830813031184135890811310640,4626830813031184136254099279489⟩,⟨(-7445130176033168502521402021628),(-7445130176033168502209972044383)⟩⟩,⟨⟨4622750376919892391889219967059,4622750376919892392253881632104⟩,⟨(-7471635729921358120378040951961),(-7471635729921358120065103507047)⟩⟩,⟨⟨4618588575005029936762638488197,4618588575005029937128635648070⟩,⟨(-7498203028233070820334491589360),(-7498203028233070820020074589843)⟩⟩,⟨⟨4614345573579323437959641753474,4614345573579323438327022868130⟩,⟨(-7524827951471979147344255343364),(-7524827951471979147028318627136)⟩⟩,⟨⟨4610021588956278422875672644461,4610021588956278423244379351174⟩,⟨(-7551506330972829349807192337386),(-7551506330972829349489779921915)⟩⟩,⟨⟨4605616888230245141456261736715,4605616888230245141826361757169⟩,⟨(-7578233949531586968007707537814),(-7578233949531586967688764130084)⟩⟩,⟨⟨4601131790010782107237208477771,4601131790010782107608659082182⟩,⟨(-7605006542073385088234765621033),(-7605006542073385087914323127608)⟩⟩,⟨⟨4596566665129982741643810532294,4596566665129982742016663134160⟩,⟨(-7631819796358356325093941854621),(-7631819796358356324771957867436)⟩⟩,⟨⟨4591921937321427936792643146769,4591921937321427937166837027923⟩,⟨(-7658669353725391313978893853217),(-7658669353725391313655414755662)⟩⟩,⟨⟨4587198083869426718380114542973,4587198083869426718755718168456⟩,⟨(-7685550809873827489540835553929),(-7685550809873827489215805485534)⟩⟩,⟨⟨4582395636227208593409656053631,4582395636227208593786621947139⟩,⟨(-7712459715683032250614971992169),(-7712459715683032250288427077363)⟩⟩,⟨⟨4577515180602734665926121077349,4577515180602734666304503713275⟩,⟨(-7739391578069804326732018668082),(-7739391578069804326403914162541)⟩⟩] +lemma kernel0_1_r3_8_eq : ∀ k : Fin 16, kernel0_1Expr 3 8 k = kernel0_1_r3_8 k := by decide +kernel +noncomputable def kernel0_1_r3_9 : Fin 16 → CBox := ![⟨⟨4572557358510800253328978869556,4572557358510800253708705429473⟩,⟨(-7766341860883476328218803634168),(-7766341860883476327889196080300)⟩⟩,⟨⟨4567522867290109589020593618583,4567522867290109589401742874229⟩,⟨(-7793305985838560145917884647886),(-7793305985838560145586710023788)⟩⟩,⟨⟨4562412460584013303768890881465,4562412460584013304151410438458⟩,⟨(-7820279333484735135329008708962),(-7820279333484735134996307545160)⟩⟩,⟨⟨4557226948783611784487664677040,4557226948783611784871612132054⟩,⟨(-7847257244213936943648913705240),(-7847257244213936943314638866119)⟩⟩,⟨⟨4551967199431942257840660500048,4551967199431942258225962032196⟩,⟨(-7874235019304262489313023213726),(-7874235019304262488977232627211)⟩⟩,⟨⟨4546634137587984575999410818830,4546634137587984576386144384426⟩,⟨(-7901207922000364057055006894659),(-7901207922000364056717637204465)⟩⟩,⟨⟨4541228746149240227854808566173,4541228746149240228242916652786⟩,⟨(-7928171178629962804125217617911),(-7928171178629962803786313971454)⟩⟩,⟨⟨4535752066131661091564799147099,4535752066131661091954342567041⟩,⟨(-7955119979756069264026133679656),(-7955119979756069263685646468144)⟩⟩,⟨⟨4530205196905728909653369128562,4530205196905728910044261421599⟩,⟨(-7982049481364455763555771991561),(-7982049481364455763213769901486)⟩⟩,⟨⟨4524589296387513427439257431968,4524589296387513427831587187094⟩,⟨(-8008954806085883119300995032183),(-8008954806085883118957406204531)⟩⟩,⟨⟨4518905581183566606035669518988,4518905581183566606429373964832⟩,⟨(-8035831044452541634541335247350),(-8035831044452541634196209609571)⟩⟩,⟨⟨4513155326688542314168815842335,4513155326688542314563959043834⟩,⟨(-8062673256188124361521274704518),(-8062673256188124361174560136767)⟩⟩,⟨⟨4507339867134465425099760397047,4507339867134465425496254319034⟩,⟨(-8089476471530908912843268873080),(-8089476471530908912495035988576)⟩⟩,⟨⟨4501460595590611297133282588435,4501460595590611297531215368742⟩,⟨(-8116235692589182885647674626778),(-8116235692589182885297851941332)⟩⟩,⟨⟨4495518963912996194229101290386,4495518963912996194628404734235⟩,⟨(-8142945894728307290031936787253),(-8142945894728307289680579189144)⟩⟩,⟨⟨4489516482642521297128974800182,4489516482642521297529716291513⟩,⟨(-8169602027988672335782992100503),(-8169602027988672335430044896065)⟩⟩] +lemma kernel0_1_r3_9_eq : ∀ k : Fin 16, kernel0_1Expr 3 9 k = kernel0_1_r3_9 k := by decide +kernel +noncomputable def kernel0_1_r3_10 : Fin 16 → CBox := ![⟨⟨4483454720850857549493199314632,4483454720850857549895274614736⟩,⟨(-8196199018533760615837616986856),(-8196199018533760615483164600014)⟩⟩,⟨⟨4477335305933205656251120668886,4477335305933205656654631895467⟩,⟨(-8222731770127494217516575775269),(-8222731770127494217160535423045)⟩⟩,⟨⟨4471159923347115075242534122811,4471159923347115075647407571446⟩,⟨(-8249195165640004679455284265220),(-8249195165640004679097715912546)⟩⟩,⟨⟨4464930316296597784752274893069,4464930316296597785158581260727⟩,⟨(-8275584068580928078373259178661),(-8275584068580928078014105552846)⟩⟩,⟨⟨4458648285360826929153190537580,4458648285360826929560826625301⟩,⟨(-8301893324659291959311573459368),(-8301893324659291958950918865700)⟩⟩,⟨⟨4452315688066767096860081748091,4452315688066767097269146443921⟩,⟨(-8328117763369026398227597560063),(-8328117763369026397865361837141)⟩⟩,⟨⟨4445934438405141917315233820094,4445934438405141917725647780902⟩,⟨(-8354252199599098287635751518580),(-8354252199599098287271999855904)⟩⟩,⟨⟨4439506506289205818744843572332,4439506506289205819156680852723⟩,⟨(-8380291435267236043099856306853),(-8380291435267236042734528805478)⟩⟩,⟨⟨4433033916955850101780598770652,4433033916955850102193740129371⟩,⟨(-8406230260976181417286171123869),(-8406230260976181416919365939779)⟩⟩,⟨⟨4426518750308638885413654652438,4426518750308638885828212634421⟩,⟨(-8432063457691376052890701623197),(-8432063457691376052522327451427)⟩⟩,⟨⟨4419963140202437894757425967604,4419963140202437895173315555576⟩,⟨(-8457785798438962877102091312165),(-8457785798438962876732218635346)⟩⟩,⟨⟨4413369273669368402312397174931,4413369273669368402729695740619⟩,⟨(-8483392050022956506284498104269),(-8483392050022956505913064418641)⟩⟩,⟨⟨4406739390085889817505726800588,4406739390085889817924315205134⟩,⟨(-8508876974760412554775607097172),(-8508876974760412554402711250199)⟩⟩,⟨⟨4400075780280887349011854348346,4400075780280887349431842686945⟩,⟨(-8534235332233403186962340035059),(-8534235332233403186587892717892)⟩⟩,⟨⟨4393380785584715740845937561767,4393380785584715741267235075081⟩,⟨(-8559461881056585474049187236501),(-8559461881056585473673264316078)⟩⟩,⟨⟨4386656796819226200955552049758,4386656796819226201378239428870⟩,⟨(-8584551380659130168952811115452),(-8584551380659130168575347469069)⟩⟩] +lemma kernel0_1_r3_10_eq : ∀ k : Fin 16, kernel0_1Expr 3 10 k = kernel0_1_r3_10 k := by decide +kernel +noncomputable def kernel0_1_r3_11 : Fin 16 → CBox := ![⟨⟨4379906253228881189120415212318,4379906253228881189544353202075⟩,⟨(-8609498593079761442898169889568),(-8609498593079761442519281726971)⟩⟩,⟨⟨4373131641353140593241829803204,4373131641353140593667146078010⟩,⟨(-8634298284773642979304040400758),(-8634298284773642978923623931888)⟩⟩,⟨⟨4366335493840382878382581670021,4366335493840382878809179773936⟩,⟨(-8658945228429832633314169839529),(-8658945228429832632932306309172)⟩⟩,⟨⟨4359520388203705915168630971610,4359520388203705915596594815476⟩,⟨(-8683434204798016672720189373706),(-8683434204798016672336811109558)⟩⟩,⟨⟨4352688945519034252782532667697,4352688945519034253211726677370⟩,⟨(-8707760004523225446652523823545),(-8707760004523225446267744807061)⟩⟩,⟨⟨4345843829066042461786965143709,4345843829066042462217510879265⟩,⟨(-8731917429987225205536379757152),(-8731917429987225205150101218098)⟩⟩,⟨⟨4338987742912487694385843850769,4338987742912487694817639145422⟩,⟨(-8755901297155275737106706028893),(-8755901297155275736719014627510)⟩⟩,⟨⟨4332123430442628651605898587880,4332123430442628652039030543684⟩,⟨(-8779706437426940500783397172278),(-8779706437426940500394222697268)⟩⟩,⟨⟨4325253672830492561937586117405,4325253672830492562371899585986⟩,⟨(-8803327699489635042650679267245),(-8803327699489635042260152763269)⟩⟩,⟨⟨4318381287458836414668575521714,4318381287458836415104209026663⟩,⟨(-8826759951173600656031904434998),(-8826759951173600655639913035325)⟩⟩,⟨⟨4311509126284733401099992904670,4311509126284733401536838687160⟩,⟨(-8849998081306993512597221794816),(-8849998081306993512203857497038)⟩⟩,⟨⟨4304640074152800143125186342140,4304640074152800143563334548481⟩,⟨(-8873037001569784814504254560702),(-8873037001569784814109444723304)⟩⟩,⟨⟨4297777047057164674198141527978,4297777047057164674637439930191⟩,⟨(-8895871648345174891613675306716),(-8895871648345174891217549367790)⟩⟩,⟨⟨4290922990353359123601626055570,4290922990353359124042207758622⟩,⟨(-8918496984567233565696621594293),(-8918496984567233565299071154102)⟩⟩,⟨⟨4284080876921404480805788177007,4284080876921404481247539898232⟩,⟨(-8940908001563490496070575169240),(-8940908001563490495671697520513)⟩⟩,⟨⟨4277253705281437521147606413608,4277253705281437521590621260015⟩,⟨(-8963099720891212572626263212384),(-8963099720891212572225983339943)⟩⟩] +lemma kernel0_1_r3_11_eq : ∀ k : Fin 16, kernel0_1Expr 3 11 k = kernel0_1_r3_11 k := by decide +kernel +noncomputable def kernel0_1_r3_12 : Fin 16 → CBox := ![⟨⟨4270444497663311794966782385732,4270444497663311795410882907202⟩,⟨(-8985067196166120691165750998871),(-8985067196166120690764220249646)⟩⟩,⟨⟨4263656298031685357282818078697,4263656298031685357728159938792⟩,⟨(-9006805514882315384991911102677),(-9006805514882315384589002185255)⟩⟩,⟨⟨4256892170068187481799181392798,4256892170068187482245646013267⟩,⟨(-9028309800222199742667834312721),(-9028309800222199742263649632639)⟩⟩,⟨⟨4250155195112334799643914778495,4250155195112334800091598000120⟩,⟨(-9049575212855208756153508529403),(-9049575212855208755747970874629)⟩⟩,⟨⟨4243448470062943968900005522788,4243448470062943969348738648027⟩,⟨(-9070596952724176652039080198047),(-9070596952724176651632334399379)⟩⟩,⟨⟨4236775105241862955999724624571,4236775105241862956449652096037⟩,⟨(-9091370260818197792044742337700),(-9091370260818197791636670442527)⟩⟩,⟨⟨4230138222221916136538153806533,4230138222221916136989151883158⟩,⟨(-9111890420930862313013249568116),(-9111890420930862312603958985556)⟩⟩,⟨⟨4223540951621029545140059137827,4223540951621029545592226276154⟩,⟨(-9132152761402774732186496530148),(-9132152761402774731775907938000)⟩⟩,⟨⟨4216986430864571568344827687017,4216986430864571568797972211390⟩,⟨(-9152152656847292186968306290000),(-9152152656847292186556584651391)⟩⟩,⟨⟨4210477801918011030545669065023,4210477801918011030999955786429⟩,⟨(-9171885529858448721728404804915),(-9171885529858448721315414983918)⟩⟩,⟨⟨4204018208992058823608382624876,4204018208992058824063682950991⟩,⟨(-9191346852700062985589104468451),(-9191346852700062985174958611325)⟩⟩,⟨⟨4197610796222520832271061236694,4197610796222520832727475961017⟩,⟨(-9210532148975058769012593684289),(-9210532148975058768597210581309)⟩⟩,⟨⟨4191258705327148770189890224626,4191258705327148770647234713717⟩,⟨(-9229436995274060884462006459145),(-9229436995274060884045545917068)⟩⟩,⟨⟨4184965073241831530262712916414,4184965073241831530721142518696⟩,⟨(-9248057022802362885573965779551),(-9248057022802362885156300570299)⟩⟩,⟨⟨4178733029738522637081975766063,4178733029738522637541357275446⟩,⟨(-9266387918984397915623730410877),(-9266387918984397915204977206643)⟩⟩,⟨⟨4172565695027349243489347757211,4172565695027349243949784113720⟩,⟨(-9284425429044879472832926884674),(-9284425429044879472413002737930)⟩⟩] +lemma kernel0_1_r3_12_eq : ∀ k : Fin 16, kernel0_1Expr 3 12 k = kernel0_1_r3_12 k := by decide +kernel +noncomputable def kernel0_1_r3_13 : Fin 16 → CBox := ![⟨⟨4166466177345394717064818083094,4166466177345394717526095891487⟩,⟨(-9302165357565814968613539905864),(-9302165357565814968192629719155)⟩⟩,⟨⟨4160437570534690101448322948121,4160437570534690101910623790258⟩,⟨(-9319603570018631525074231957992),(-9319603570018631524652186246080)⟩⟩,⟨⟨4154482951611989503120853119793,4154482951611989503584039612338⟩,⟨(-9336735994270690398859775641458),(-9336735994270690398436715215662)⟩⟩,⟨⟨4148605378332940644319770476512,4148605378332940644783947336420⟩,⟨(-9353558622065503617864911642549),(-9353558622065503617440752119945)⟩⟩,⟨⟨4142807886753294341320875485453,4142807886753294341785843178694⟩,⟨(-9370067510476003763519945662016),(-9370067510476003763094860919745)⟩⟩,⟨⟨4137093488789825425278450462776,4137093488789825425744374442622⟩,⟨(-9386258783330255212387673351476),(-9386258783330255211961527493335)⟩⟩,⟨⟨4131465169783662538073011700006,4131465169783662538539750715278⟩,⟨(-9402128632609032455541673254285),(-9402128632609032455114590944659)⟩⟩,⟨⟨4125925886068745233211101763544,4125925886068745233678762076738⟩,⟨(-9417673319814728232514634638698),(-9417673319814728232086530246478)⟩⟩,⟨⟨4120478562548143824194558531183,4120478562548143824662914656169⟩,⟨(-9432889177311091039871753249451),(-9432889177311091039442823404551)⟩⟩,⟨⟨4115126090280990389869056712084,4115126090280990390338297713298⟩,⟨(-9447772609633327995989429344059),(-9447772609633327995559518008155)⟩⟩,⟨⟨4109871324082778215743769702764,4109871324082778216213750988785⟩,⟨(-9462320094768144959018416594613),(-9462320094768144958587651806617)⟩⟩,⟨⟨4104717080141791677598171298463,4104717080141791678069000249230⟩,⟨(-9476528185403331102682536125885),(-9476528185403331102250831362048)⟩⟩,⟨⟨4099666133654429122287380849041,4099666133654429122758844472976⟩,⟨(-9490393510146529756026833873245),(-9490393510146529755594375761552)⟩⟩,⟨⟨4094721216482177641937580811568,4094721216482177642409853588919⟩,⟨(-9503912774712871113584024571258),(-9503912774712871113150669413309)⟩⟩,⟨⟨4089885014832990751244019400748,4089885014832990751716953819901⟩,⟨(-9517082763081175330668072250745),(-9517082763081175330233951066600)⟩⟩,⟨⟨4085160166969807851014093355794,4085160166969807851487797603838⟩,⟨(-9529900338618466447950268368728),(-9529900338618466447515293999244)⟩⟩] +lemma kernel0_1_r3_13_eq : ∀ k : Fin 16, kernel0_1Expr 3 13 k = kernel0_1_r3_13 k := by decide +kernel +noncomputable def kernel0_1_r3_14 : Fin 16 → CBox := ![⟨⟨4080549260948937990332976267400,4080549260948937990807203685372⟩,⟨(-9542362445172568458055873572134),(-9542362445172568457620261986846)⟩⟩,⟨⟨4076054832391009828823644744749,4076054832391009829298601355935⟩,⟨(-9554466108132584557579265388886),(-9554466108132584557142845889088)⟩⟩,⟨⟨4071679362287164861718032438375,4071679362287164862193568477528⟩,⟨(-9566208435457089148846236974675),(-9566208435457089148409142951196)⟩⟩,⟨⟨4067425274843141924270101372372,4067425274843141924746325299240⟩,⟨(-9577586618669889400764007113858),(-9577586618669889400326151221765)⟩⟩,⟨⟨4063294935363867767015304900755,4063294935363867767491992274998⟩,⟨(-9588597933823239086814863206380),(-9588597933823239086376442956136)⟩⟩,⟨⟨4059290648181131126124457928092,4059290648181131126601790741175⟩,⟨(-9599239742428411936425634794801),(-9599239742428411935986499951055)⟩⟩,⟨⟨4055414654626876248255232859623,4055414654626876248733059573026⟩,⟨(-9609509492353564815618533346907),(-9609509492353564815178819214756)⟩⟩,⟨⟨4051669131054606319360015335912,4051669131054606319838444338941⟩,⟨(-9619404718688842652604764804341),(-9619404718688842652164384141077)⟩⟩,⟨⟨4048056186911337752173510451144,4048056186911337752652289130516⟩,⟨(-9628923044578697109049707086496),(-9628923044578697108608882011250)⟩⟩,⟨⟨4044577862862492875490377672023,4044577862862492875969714387716⟩,⟨(-9638062182021409540204183732632),(-9638062182021409539762741361334)⟩⟩,⟨⟨4041236128972061315311465944904,4041236128972061315791208127019⟩,⟨(-9646819932635825765942530164712),(-9646819932635825765500607030881)⟩⟩,⟨⟨4038032882940299346245280059419,4038032882940299346725535444353⟩,⟨(-9655194188395325576008888635487),(-9655194188395325575566398092002)⟩⟩,⟨⟨4034969948401171811171716222517,4034969948401171811652251314938⟩,⟨(-9663182932329063709510809494442),(-9663182932329063709067957675463)⟩⟩,⟨⟨4032049073281672955014445135220,4032049073281672955495447650302⟩,⟨(-9670784239190531281105798364141),(-9670784239190531280662430021500)⟩⟩,⟨⟨4029271928225090798258698395059,4029271928225090798740015326927⟩,⟨(-9677996276093497281636455347273),(-9677996276093497281192707678711)⟩⟩,⟨⟨4026640105080204597847025351667,4026640105080204598328763351279⟩,⟨(-9684817303115398873499039021151),(-9684817303115398873054826341322)⟩⟩] +lemma kernel0_1_r3_14_eq : ∀ k : Fin 16, kernel0_1Expr 3 14 k = kernel0_1_r3_14 k := by decide +kernel +noncomputable def kernel0_1_r3_15 : Fin 16 → CBox := ![⟨⟨4024155115458326623926803601208,4024155115458326624408693739641⟩,⟨(-9691245673868256752031109587189),(-9691245673868256751586668799176)⟩⟩,⟨⟨4021818389360018043310786241897,4021818389360018043793050209318⟩,⟨(-9697279836037197881842616864914),(-9697279836037197881397763495973)⟩⟩,⟨⟨4019631273873224273050089933350,4019631273873224273532575158984⟩,⟨(-9702918331886672476166316664220),(-9702918331886672475721187771361)⟩⟩,⟨⟨4017595031944487884370055413130,4017595031944487884852866776313⟩,⟨(-9708159798734455209469872432251),(-9708159798734455209024383875495)⟩⟩,⟨⟨4015710841224807137930701028966,4015710841224807138413598948463⟩,⟨(-9713002969393522386616645741328),(-9713002969393522386171009474766)⟩⟩,⟨⟨4013979792991615660508127606092,4013979792991615660991303260085⟩,⟨(-9717446672581897189876594941135),(-9717446672581897189430652656488)⟩⟩,⟨⟨4012402891148263780144512019221,4012402891148263780627813914128⟩,⟨(-9721489833300554248068479029605),(-9721489833300554247622367033054)⟩⟩,⟨⟨4010981051302284775424840088951,4010981051302284775908370872378⟩,⟨(-9725131473179472685770472776284),(-9725131473179472685324108863288)⟩⟩,⟨⟨4009715099923629922894948790333,4009715099923629923378439548109⟩,⟨(-9728370710791923585923863946074),(-9728370710791923585477485488105)⟩⟩,⟨⟨4008605773583954906677738651431,4008605773583954907161408849326⟩,⟨(-9731206761937073512434163742033),(-9731206761937073511987588069594)⟩⟩,⟨⟨4007653718277937051648758621090,4007653718277937052132458771623⟩,⟨(-9733638939890980471394855471427),(-9733638939890980470948217280971)⟩⟩,⟨⟨4006859488827498124910223819922,4006859488827498125394053612548⟩,⟨(-9735666655626052525575682931192),(-9735666655626052525128902571151)⟩⟩,⟨⟨4006223548369701291576427138841,4006223548369701292060144215615⟩,⟨(-9737289417999032306031457206475),(-9737289417999032305584749317131)⟩⟩,⟨⟨4005746267928983384472340393791,4005746267928983384956136870516⟩,⟨(-9738506833907562979931956335848),(-9738506833907562979485161745384)⟩⟩,⟨⟨4005427926074275130037670298015,4005427926074275130521399433625⟩,⟨(-9739318608415382930958695268241),(-9739318608415382930511946366850)⟩⟩,⟨⟨4005268708661452543257744255529,4005268708661452543741502238663⟩,⟨(-9739724544846187586618563827432),(-9739724544846187586171783975374)⟩⟩] +lemma kernel0_1_r3_15_eq : ∀ k : Fin 16, kernel0_1Expr 3 15 k = kernel0_1_r3_15 k := by decide +kernel +noncomputable def kernel0_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel0_1_r3_0,kernel0_1_r3_1,kernel0_1_r3_2,kernel0_1_r3_3,kernel0_1_r3_4,kernel0_1_r3_5,kernel0_1_r3_6,kernel0_1_r3_7,kernel0_1_r3_8,kernel0_1_r3_9,kernel0_1_r3_10,kernel0_1_r3_11,kernel0_1_r3_12,kernel0_1_r3_13,kernel0_1_r3_14,kernel0_1_r3_15] +lemma kernel0_1_r3_eq (i k : Fin 16) : kernel0_1Expr 3 i k = kernel0_1_r3 i k := by + fin_cases i + · exact kernel0_1_r3_0_eq k + · exact kernel0_1_r3_1_eq k + · exact kernel0_1_r3_2_eq k + · exact kernel0_1_r3_3_eq k + · exact kernel0_1_r3_4_eq k + · exact kernel0_1_r3_5_eq k + · exact kernel0_1_r3_6_eq k + · exact kernel0_1_r3_7_eq k + · exact kernel0_1_r3_8_eq k + · exact kernel0_1_r3_9_eq k + · exact kernel0_1_r3_10_eq k + · exact kernel0_1_r3_11_eq k + · exact kernel0_1_r3_12_eq k + · exact kernel0_1_r3_13_eq k + · exact kernel0_1_r3_14_eq k + · exact kernel0_1_r3_15_eq k +noncomputable def kernel0_1_r4_0 : Fin 16 → CBox := ![⟨⟨4220027291057539074955713624020,4220027291057539075144133935776⟩,⟨(-3001540750911125438172590079700),(-3001540750911125438059059261275)⟩⟩,⟨⟨4220078695988548493636954506256,4220078695988548493825382026090⟩,⟨(-3001677143049113927861903138124),(-3001677143049113927748365685660)⟩⟩,⟨⟨4220181495714272271135421504166,4220181495714272271323863386599⟩,⟨(-3001949924722092870607178235323),(-3001949924722092870493627545021)⟩⟩,⟨⟨4220335669962281093643536687448,4220335669962281093832000087196⟩,⟨(-3002359090717736094223759333083),(-3002359090717736094110188800697)⟩⟩,⟨⟨4220541188324335541703985621719,4220541188324335541892477693555⟩,⟨(-3002904633201729712654343572097),(-3002904633201729712540746592828)⟩⟩,⟨⟨4220798010256878652747324715745,4220798010256878652935852614708⟩,⟨(-3003586541698784310639786611971),(-3003586541698784310526156580179)⟩⟩,⟨⟨4221106085081704503086767431576,4221106085081704503275338311970⟩,⟨(-3004404803067320763389766903906),(-3004404803067320763276097213492)⟩⟩,⟨⟨4221465351986812944805789024547,4221465351986812944994410042299⟩,⟨(-3005359401467832202966011546236),(-3005359401467832202852295589149)⟩⟩,⟨⟨4221875740027463159018613230999,4221875740027463159207291538714⟩,⟨(-3006450318324925296245377183024),(-3006450318324925296131608351892)⟩⟩,⟨⟨4222337168127441207778797087727,4222337168127441207967539843529⟩,⟨(-3007677532283044669284594708135),(-3007677532283044669170766391073)⟩⟩,⟨⟨4222849545080559281367611003010,4222849545080559281556425356388⟩,⟨(-3009041019155885003005116887166),(-3009041019155885002891222475658)⟩⟩,⟨⟨4223412769552406844700833425918,4223412769552406844889726538675⟩,⟨(-3010540751869496038687600081307),(-3010540751869496038573632958115)⟩⟩,⟨⟨4224026730082376385014061323320,4224026730082376385203040337616⟩,⟨(-3012176700399086472131851961536),(-3012176700399086472017805518733)⟩⟩,⟨⟨4224691305085988951658325283051,4224691305085988951847397368187⟩,⟨(-3013948831699533485806926289704),(-3013948831699533485692793901877)⟩⟩,⟨⟨4225406362857547156563429701085,4225406362857547156752601992272⟩,⟨(-3015857109629605472179507172954),(-3015857109629605472065282231899)⟩⟩,⟨⟨4226171761573145769474447559615,4226171761573145769663727233390⟩,⟨(-3017901494869906341941652875305),(-3017901494869906341827328746923)⟩⟩] +lemma kernel0_1_r4_0_eq : ∀ k : Fin 16, kernel0_1Expr 4 0 k = kernel0_1_r4_0 k := by decide +kernel +noncomputable def kernel0_1_r4_1 : Fin 16 → CBox := ![⟨⟨4226987349294072494166973736140,4226987349294072494356367909926⟩,⟨(-3020081944834550691316996339685),(-3020081944834550691202566421038)⟩⟩,⟨⟨4227852963970633949186926596446,4227852963970633949376442464512⟩,⟨(-3022398413576580026241951164270),(-3022398413576580026127408805977)⟩⟩,⟨⟨4228768433446444297883566677360,4228768433446444298073211346383⟩,⟨(-3024850851687131211206182347987),(-3024850851687131211091520947764)⟩⟩,⟨⟨4229733575463216376204316359790,4229733575463216376394097034505⟩,⟨(-3027439206188369330079647882599),(-3027439206188369329964860779295)⟩⟩,⟨⟨4230748197666097551439840650446,4230748197666097551629764403957⟩,⟨(-3030163420420198218508838786158),(-3030163420420198218393919390551)⟩⟩,⟨⟨4231812097609594909336162612250,4231812097609594909526236682064⟩,⟨(-3033023433920763055558770277383),(-3033023433920763055443711903261)⟩⟩,⟨⟨4232925062764136709158456264857,4232925062764136709348687709967⟩,⟨(-3036019182300760589302918349261),(-3036019182300760589187714408831)⟩⟩,⟨⟨4234086870523319364769482328335,4234086870523319364959878399268⟩,⟨(-3039150597111573820077852085900),(-3039150597111573819962495878571)⟩⟩,⟨⟨4235297288211891502882374969979,4235297288211891503072942665659⟩,⟨(-3042417605707249279141210091712),(-3042417605707249279025695056823)⟩⟩,⟨⟨4236556073094528915605015384739,4236556073094528915795762013893⟩,⟨(-3045820131100336422477618779727),(-3045820131100336422361938175961)⟩⟩,⟨⟨4237862972385456461385824016222,4237862972385456461576756565827⟩,⟨(-3049358091811610112419013944411),(-3049358091811610112303161210296)⟩⟩,⟨⟨4239217723258975174602216635058,4239217723258975174793342423291⟩,⟨(-3053031401713698686467406779745),(-3053031401713698686351375160522)⟩⟩,⟨⟨4240620052860955017334200415227,4240620052860955017525526340450⟩,⟨(-3056839969868641716061749618677),(-3056839969868641715945532595459)⟩⟩,⟨⟨4242069678321355845292678355507,4242069678321355845484211821144⟩,⟨(-3060783700359403240793542558113),(-3060783700359403240677133318880)⟩⟩,⟨⟨4243566306767841261304156217678,4243566306767841261495904109370⟩,⟨(-3064862492115368028466801929947),(-3064862492115368028350193954591)⟩⟩,⟨⟨4245109635340552091991076745747,4245109635340552092183046475401⟩,⟨(-3069076238731850261073097769661),(-3069076238731850260956284232303)⟩⟩] +lemma kernel0_1_r4_1_eq : ∀ k : Fin 16, kernel0_1Expr 4 1 k = kernel0_1_r4_1 k := by decide +kernel +noncomputable def kernel0_1_r4_2 : Fin 16 → CBox := ![⟨⟨4246699351208108244049933199532,4246699351208108244242131510954⟩,⟨(-3073424828283645983801101140778),(-3073424828283645983684075593706)⟩⟩,⟨⟨4248335131584909673455628782215,4248335131584909673648063223483⟩,⟨(-3077908143132662681141332957279),(-3077908143132662681024088487201)⟩⟩,⟨⟨4250016643749809131565039862944,4250016643749809131757717183698⟩,⟨(-3082526059729661463424369726121),(-3082526059729661463306899872790)⟩⟩,⟨⟨4251743545066231233925717054479,4251743545066231234118644790406⟩,⟨(-3087278448410149561108948266508),(-3087278448410149560991246113898)⟩⟩,⟨⟨4253515483003814228002168356770,4253515483003814228195353074273⟩,⟨(-3092165173184463135095292527977),(-3092165173184463134977351711595)⟩⟩,⟨⟨4255332095161652612311095802323,4255332095161652612504545211799⟩,⟨(-3097186091522082821469669866506),(-3097186091522082821351483359860)⟩⟩,⟨⟨4257193009293220478820707951696,4257193009293220479014428626792⟩,⟨(-3102341054130226940485710142771),(-3102341054130226940367271567552)⟩⟩,⟨⟨4259097843333057110043243138178,4259097843333057110237242772487⟩,⟨(-3107629904726769914254320059896),(-3107629904726769914135622388709)⟩⟩,⟨⟨4261046205425297959072782423407,4261046205425297959267067316078⟩,⟨(-3113052479807536157440459843388),(-3113052479807536157321496846140)⟩⟩,⟨⟨4263037693954135671844165852656,4263037693954135672038743959463⟩,⟨(-3118608608408022532035073207929),(-3118608608408022531915837695561)⟩⟩,⟨⟨4265071897576297272979162020657,4265071897576297273174039693737⟩,⟨(-3124298111859605392651806072938),(-3124298111859605392532291774954)⟩⟩,⟨⟨4267148395255625026523189128601,4267148395255625026718374257528⟩,⟨(-3130120803540291294337192959061),(-3130120803540291294217392713408)⟩⟩,⟨⟨4269266756299849797355832354968,4269266756299849797551330963683⟩,⟨(-3136076488620073591998600802722),(-3136076488620073591878508518435)⟩⟩,⟨⟨4271426540399646974693878448586,4271426540399646974889698738134⟩,⟨(-3142164963800960430531857693672),(-3142164963800960430411466017726)⟩⟩,⟨⟨4273627297670066172428113832992,4273627297670066172624261882883⟩,⟨(-3148386017051743008715724097642),(-3148386017051743008595026897173)⟩⟩,⟨⟨4275868568694426988496555344120,4275868568694426988693039281963⟩,⟨(-3154739427337576498932709502765),(-3154739427337576498811699455630)⟩⟩] +lemma kernel0_1_r4_2_eq : ∀ k : Fin 16, kernel0_1Expr 4 2 k = kernel0_1_r4_2 k := by decide +kernel +noncomputable def kernel0_1_r4_3 : Fin 16 → CBox := ![⟨⟨4278149884570774083472034995680,4278149884570774083668860419998⟩,⟨(-3161224964344449619621889835556),(-3161224964344449619500561077628)⟩⟩,⟨⟨4280470766960985723331302253264,4280470766960985723528477750074⟩,⟨(-3167842388198622588756839019443),(-3167842388198622588635183951784)⟩⟩,⟨⟨4282830728142630719204952869916,4282830728142630719402484189629⟩,⟨(-3174591449181117035091788494958),(-3174591449181117034969801156047)⟩⟩,⟨⟨4285229271063669383942998522320,4285229271063669384140894076100⟩,⟨(-3181471887437345409780109120466),(-3181471887437345409657782000813)⟩⟩,⟨⟨4287665889400094707666105486073,4287665889400094707864370489140⟩,⟨(-3188483432681971524409492601915),(-3188483432681971524286820041614)⟩⟩,⟨⟨4290140067616610428143151418130,4290140067616610428341794787908⟩,⟨(-3195625803899098042499343030900),(-3195625803899098042376317214955)⟩⟩,⟨⟨4292651281030443032822050770949,4292651281030443033021077866316⟩,⟨(-3202898709037881069855125187812),(-3202898709037881069731740364155)⟩⟩,⟨⟨4295198995878384973571810903859,4295198995878384973771230469015⟩,⟨(-3210301844703676424457973327975),(-3210301844703676424334221770365)⟩⟩,⟨⟨4297782669387166498553421868438,4297782669387166498753238505782⟩,⟨(-3217834895844826718163256492404),(-3217834895844826718039132881291)⟩⟩,⟨⟨4300401749847253503969188138904,4300401749847253504169411312048⟩,⟨(-3225497535435203049551085929864),(-3225497535435203049426582108480)⟩⟩,⟨⟨4303055676690168677555130263883,4303055676690168677755764872096⟩,⟨(-3233289424152619888753778784537),(-3233289424152619888628889252681)⟩⟩,⟨⟨4305743880569432941362383549141,4305743880569432941563438722481⟩,⟨(-3241210210053246629688992355276),(-3241210210053246629563709138783)⟩⟩,⟨⟨4308465783445223799385092263075,4308465783445223799586572083893⟩,⟨(-3249259528242144291323834100771),(-3249259528242144291198152170148)⟩⟩,⟨⟨4311220798672846651685333648735,4311220798672846651887248018458⟩,⟨(-3257437000540060965611703827295),(-3257437000540060965485614746263)⟩⟩,⟨⟨4314008331095114446587662401012,4314008331095114446790015685419⟩,⟨(-3265742235146624833554888055880),(-3265742235146624833428386623101)⟩⟩,⟨⟨4316827777138730202018159029063,4316827777138730202220960800710⟩,⟨(-3274174826300078900168620397613),(-3274174826300078900041698357667)⟩⟩] +lemma kernel0_1_r4_3_eq : ∀ k : Fin 16, kernel0_1Expr 4 3 k = kernel0_1_r4_3 k := by decide +kernel +noncomputable def kernel0_1_r4_4 : Fin 16 → CBox := ![⟨⟨4319678524914765931910487973603,4319678524914765932113741435178⟩,⟨(-3282734353933707031407095710304),(-3282734353933707031279748539280)⟩⟩,⟨⟨4322559954323330359581507078240,4322559954323330359785222908341⟩,⟨(-3291420383329106408537471080447),(-3291420383329106408409689863331)⟩⟩,⟨⟨4325471437162516482911808541910,4325471437162516483115990493438⟩,⟨(-3300232464766467144913512694320),(-3300232464766467144785292580098)⟩⟩,⟨⟨4328412337241718571914837086116,4328412337241718572119495233412⟩,⟨(-3309170133172025533220622956392),(-3309170133172025533091955373658)⟩⟩,⟨⟨4331382010499406523759223339235,4331382010499406523964360247957⟩,⟨(-3318232907762863204360812019388),(-3318232907762863204231692813646)⟩⟩,⟨⟨4334379805125443669504358543201,4334379805125443669709985407003⟩,⟨(-3327420291689230378245013507895),(-3327420291689230378115433438479)⟩⟩,⟨⟨4337405061688032116778630775695,4337405061688032116984750648875⟩,⟨(-3336731771674577367582465327508),(-3336731771674577367452419950322)⟩⟩,⟨⟨4340457113265367519521195594749,4340457113265367519727819116616⟩,⟨(-3346166817653484553716052796979),(-3346166817653484553585533187683)⟩⟩,⟨⟨4343535285582082785972802577503,4343535285582082786179931166651⟩,⟨(-3355724882407687183747632548588),(-3355724882407687183616635230548)⟩⟩,⟨⟨4346638897150557665704519669098,4346638897150557665912165517931⟩,⟨(-3365405401200397535409685379315),(-3365405401200397535278200500677)⟩⟩,⟨⟨4349767259417168392110732934000,4349767259417168392318898307487⟩,⟨(-3375207791409133254827096700556),(-3375207791409133254695120285225)⟩⟩,⟨⟨4352919676913548595102116181702,4352919676913548595310812349481⟩,⟨(-3385131452157266986607378102508),(-3385131452157266986474900835030)⟩⟩,⟨⟨4356095447412929536511749511615,4356095447412929536720977078408⟩,⟨(-3395175763944518779400430330556),(-3395175763944518779267449224157)⟩⟩,⟨⟨4359293862091624354940959451994,4359293862091624355150731251464⟩,⟨(-3405340088276619156648963913622),(-3405340088276619156515468716111)⟩⟩,⟨⟨4362514205695717434577676290658,4362514205695717434787993701137⟩,⟨(-3415623767294377184840760060522),(-3415623767294377184706747330318)⟩⟩,⟨⟨4365755756713016231278375022688,4365755756713016231489250013356⟩,⟨(-3426026123402394342970437901452),(-3426026123402394342835897891608)⟩⟩] +lemma kernel0_1_r4_4_eq : ∀ k : Fin 16, kernel0_1Expr 4 4 k = kernel0_1_r4_4 k := by decide +kernel +noncomputable def kernel0_1_r4_5 : Fin 16 → CBox := ![⟨⟨4369017787550318896495212858466,4369017787550318896706644476741⟩,⟨(-3436546458897671489578376486806),(-3436546458897671489443307153544)⟩⟩,⟨⟨4372299564716046833267610600780,4372299564716046833479613031284⟩,⟨(-3447184055598362729776759849094),(-3447184055598362729641150117548)⟩⟩,⟨⟨4375600349008286896551210312143,4375600349008286896763783945295⟩,⟨(-3457938174472936495876292301059),(-3457938174472936495740139334859)⟩⟩,⟨⟨4378919395708283310963897272137,4378919395708283311177054846571⟩,⟨(-3468808055270010663033526989150),(-3468808055270010662896820569024)⟩⟩,⟨⟨4382255954779414521213824344281,4382255954779414521427563999181⟩,⟨(-3479792916149135016851754220649),(-3479792916149135016714492870893)⟩⟩,⟨⟨4385609271071685112965962727668,4385609271071685113180299321600⟩,⟨(-3490891953312800863858294818930),(-3490891953312800863720467045153)⟩⟩,⟨⟨4388978584531757643952893813906,4388978584531757644167826640863⟩,⟨(-3502104340639964018685614867464),(-3502104340639964018547218515318)⟩⟩,⟨⟨4392363130418543706331148117829,4392363130418543706546690760510⟩,⟨(-3513429229321373803714224498990),(-3513429229321373803575248833247)⟩⟩,⟨⟨4395762139524367801574121673534,4395762139524367801790270362449⟩,⟨(-3524865747497007047679258530413),(-3524865747497007047539703257983)⟩⟩,⟨⟨4399174838401711648897095220789,4399174838401711649113866447320⟩,⟨(-3536412999895912358771453916430),(-3536412999895912358631306548204)⟩⟩,⟨⟨4402600449595540368044413712243,4402600449595540368261805562342⟩,⟨(-3548070067478776164236759206075),(-3548070067478776164096018350304)⟩⟩,⟨⟨4406038191881205578356971069637,4406038191881205578574998044079⟩,⟨(-3559836007083528141255223114919),(-3559836007083528141113877477129)⟩⟩,⟨⟨4409487280507913839933445777772,4409487280507913840152102985922⟩,⟨(-3571709851074309701521667126041),(-3571709851074309701379717137524)⟩⟩,⟨⟨4412946927447742031397982377903,4412946927447742031617287123464⟩,⟨(-3583690606994135122737171108991),(-3583690606994135122594603778973)⟩⟩,⟨⟨4416416341650174214751886205312,4416416341650174214971835247564⟩,⟨(-3595777257221580732155312761950),(-3595777257221580732012127548098)⟩⟩,⟨⟨4419894729302127283956188211419,4419894729302127284176797047631⟩,⟨(-3607968758631843228153187873165),(-3607968758631843228009372875705)⟩⟩] +lemma kernel0_1_r4_5_eq : ∀ k : Fin 16, kernel0_1Expr 4 5 k = kernel0_1_r4_5 k := by decide +kernel +noncomputable def kernel0_1_r4_6 : Fin 16 → CBox := ![⟨⟨4423381294093425233703013175623,4423381294093425233924274385959⟩,⟨(-3620264042262513763006193766588),(-3620264042262513762861751012734)⟩⟩,⟨⟨4426875237487674222233600625263,4426875237487674222455533683023⟩,⟨(-3632662012984419790894937085354),(-3632662012984419790749852260254)⟩⟩,⟨⟨4430375758998482741527229785697,4430375758998482741749830003732⟩,⟨(-3645161549177891896697691286200),(-3645161549177891896551964786493)⟩⟩,⟨⟨4433882056470963154736154511604,4433882056470963154959438459747⟩,⟨(-3657761502414817850154972019538),(-3657761502414817850008591295437)⟩⟩,⟨⟨4437393326368442619955410453566,4437393326368442620179369592151⟩,⟨(-3670460697146850963177402474252),(-3670460697146850963030370311752)⟩⟩,⟨⟨4440908764064302997439826553035,4440908764064302997664481081041⟩,⟨(-3683257930400144451880521463404),(-3683257930400144451732823099865)⟩⟩,⟨⟨4444427564138860740948073696704,4444427564138860741173417352403⟩,⟨(-3696151971476987905695872837943),(-3696151971476987905547509705733)⟩⟩,⟨⟨4447948920681189010332921166769,4447948920681189010558971674145⟩,⟨(-3709141561664726129825372657787),(-3709141561664726129676331508893)⟩⟩,⟨⟨4451472027595775319746933322405,4451472027595775319973679208257⟩,⟨(-3722225413952344540465819683713),(-3722225413952344540316105194215)⟩⟩,⟨⟨4454996078913898962447291229154,4454996078913898962674755171858⟩,⟨(-3735402212755108940641245754488),(-3735402212755108940490841641700)⟩⟩,⟨⟨4458520269109603238346602624139,4458520269109603238574776660484⟩,⟨(-3748670613647650874089911342548),(-3748670613647650873938820172681)⟩⟩,⟨⟨4462043793420128163984513655277,4462043793420128164213416740640⟩,⟨(-3762029243105892831375556460071),(-3762029243105892831223764241199)⟩⟩,⟨⟨4465565848170659876949357326174,4465565848170659877178976601381⟩,⟨(-3775476698258210352134495776288),(-3775476698258210351982008147940)⟩⟩,⟨⟨4469085631103243369065153058867,4469085631103243369295512094906⟩,⟨(-3789011546646230516058927387296),(-3789011546646230515905727519067)⟩⟩,⟨⟨4472602341709695506637398194256,4472602341709695506868487191504⟩,⟨(-3802632325995668428825918535013),(-3802632325995668428672010232123)⟩⟩,⟨⟨4476115181568345534131446444169,4476115181568345534363285671787⟩,⟨(-3816337543997605073764680120256),(-3816337543997605073610048597771)⟩⟩] +lemma kernel0_1_r4_6_eq : ∀ k : Fin 16, kernel0_1Expr 4 6 k = kernel0_1_r4_6 k := by decide +kernel +noncomputable def kernel0_1_r4_7 : Fin 16 → CBox := ![⟨⟨4479623354684420422908720605849,4479623354684420423141293414984⟩,⟨(-3830125678100611301771446583614),(-3830125678100611301616099957029)⟩⟩,⟨⟨4483126067833882532787037422736,4483126067833882533020370610341⟩,⟨(-3843995175314123757133311027888),(-3843995175314123756977230476454)⟩⟩,⟨⟨4486622530910517115595991448090,4486622530910517115830073248142⟩,⟨(-3857944452023479171980790002901),(-3857944452023479171823980675095)⟩⟩,⟨⟨4490111957276057221583164630133,4490111957276057221818016700182⟩,⟨(-3871971893817013693732579832273),(-3871971893817013693575026105705)⟩⟩,⟨⟨4493593564113123587153719262014,4493593564113123587389323713089⟩,⟨(-3886075855325633725039811856169),(-3886075855325633724881522767721)⟩⟩,⟨⟨4497066572780747102284054069753,4497066572780747102520438338393⟩,⟨(-3900254660075264141572508091348),(-3900254660075264141413464431510)⟩⟩,⟨⟨4500530209172231494956042694059,4500530209172231495193192907399⟩,⟨(-3914506600352578697014896402102),(-3914506600352578696855104775291)⟩⟩,⟨⟨4503983704075103945633096463761,4503983704075103945871035750719⟩,⟨(-3928829937084415914693279300221),(-3928829937084415914532723196648)⟩⟩,⟨⟨4507426293532891475264301869310,4507426293532891475503008092211⟩,⟨(-3943222899731281789572262127580),(-3943222899731281789410953413581)⟩⟩,⟨⟨4510857219208451154252739334131,4510857219208451154492243497639⟩,⟨(-3957683686195338171564843796432),(-3957683686195338171402761045780)⟩⟩,⟨⟨4514275728748572476517992250521,4514275728748572476758278243200⟩,⟨(-3972210462743272760302502802690),(-3972210462743272760139654185027)⟩⟩,⟨⟨4517681076149560652012429697423,4517681076149560652253522190940⟩,⟨(-3986801363944443202291026179576),(-3986801363944443202127394254759)⟩⟩,⟨⟨4521072522123500113127588714544,4521072522123500113369464047134⟩,⟨(-4001454492624683833849389970362),(-4001454492624683833684987756865)⟩⟩,⟨⟨4524449334464888226144395570895,4524449334464888226387085550849⟩,⟨(-4016167919836159148074913684928),(-4016167919836159147909719269019)⟩⟩,⟨⟨4527810788417320069497886553138,4527810788417320069741372689499⟩,⟨(-4030939684843643072579647815766),(-4030939684843643072413671049188)⟩⟩,⟨⟨4531156167039896207824551498949,4531156167039896208068860085454⟩,⟨(-4045767795127597618825507946327),(-4045767795127597618658730410275)⟩⟩] +lemma kernel0_1_r4_7_eq : ∀ k : Fin 16, kernel0_1Expr 4 7 k = kernel0_1_r4_7 k := by decide +kernel +noncomputable def kernel0_1_r4_8 : Fin 16 → CBox := ![⟨⟨4534484761573016676620329832751,4534484761573016676865431715027⟩,⟨(-4060650226404418396146421816588),(-4060650226404418395978860221036)⟩⟩,⟨⟨4537795871803215919293793252374,4537795871803215919539724930316⟩,⟨(-4075584922664207867298488622906),(-4075584922664207867130118111682)⟩⟩,⟨⟨4541088806426685209212887054224,4541088806426685209459627530911⟩,⟨(-4090569796226430051681452006319),(-4090569796226430051512284222651)⟩⟩,⟨⟨4544362883411121167047882214306,4544362883411121167295459468421⟩,⟨(-4105602727813792652071206405353),(-4105602727813792651901221913583)⟩⟩,⟨⟨4547617430355531371583623193271,4547617430355531371832007036678⟩,⟨(-4120681566644694286450413497099),(-4120681566644694286279629906855)⟩⟩,⟨⟨4550851784847620783668863316686,4550851784847620783918090431018⟩,⟨(-4135804130544565644833767704355),(-4135804130544565644662160068859)⟩⟩,⟨⟨4554065294818375781696270504379,4554065294818375781946317246567⟩,⟨(-4150968206076423959244210957456),(-4150968206076423959071792830987)⟩⟩,⟨⟨4557257318893456066653772147857,4557257318893456066904668257090⟩,⟨(-4166171548690950171511671254237),(-4166171548690950171338422137654)⟩⟩,⟨⟨4560427226740998559091743817499,4560427226740998559343453246769⟩,⟨(-4181411882896387607578863354559),(-4181411882896387607404804868781)⟩⟩,⟨⟨4563574399415431703021543117439,4563574399415431703274107466157⟩,⟨(-4196686902448549818725955144241),(-4196686902448549818551059233251)⟩⟩,⟨⟨4566698229696893336442544200113,4566698229696893336695937059250⟩,⟨(-4211994270561213530774896832471),(-4211994270561213530599179069493)⟩⟩,⟨⟨4569798122425840508388596294958,4569798122425840508642849218609⟩,⟨(-4227331620137160354137696523267),(-4227331620137160353961135312170)⟩⟩,⟨⟨4572873494832435341405123117861,4572873494832435341660198637091⟩,⟨(-4242696554020118053801152214827),(-4242696554020118053623770382503)⟩⟩,⟨⟨4575923776860287279262167749906,4575923776860287279518107913380⟩,⟨(-4258086645267838763332644320544),(-4258086645267838763154413556271)⟩⟩,⟨⟨4578948411484128845209098360485,4578948411484128845465873861919⟩,⟨(-4273499437446537556162903506921),(-4273499437446537555983841519059)⟩⟩,⟨⟨4581946855020999388517425425681,4581946855020999388775069700107⟩,⟨(-4288932444946900267271033421365),(-4288932444946900267091117475397)⟩⟩] +lemma kernel0_1_r4_8_eq : ∀ k : Fin 16, kernel0_1Expr 4 8 k = kernel0_1_r4_8 k := by decide +kernel +noncomputable def kernel0_1_r4_9 : Fin 16 → CBox := ![⟨⟨4584918577434509238324348971610,4584918577434509238582817134314⟩,⟨(-4304383153321854396589318561155),(-4304383153321854396408576592391)⟩⟩,⟨⟨4587863062631755235230379147409,4587863062631755235489719581993⟩,⟨(-4319849019646281330714108360805),(-4319849019646281330532508008948)⟩⟩,⟨⟨4590779808752457793480816976284,4590779808752457793740997376145⟩,⟨(-4335327472898832001733636115881),(-4335327472898832001551197323169)⟩⟩,⟨⟨4593668328449889479956347723434,4593668328449889480217403442480⟩,⟨(-4350815914365991472186989540832),(-4350815914365991472003688410720)⟩⟩,⟨⟨4596528149163165599965354506321,4596528149163165600227240074424⟩,⟨(-4366311718068520805507922546335),(-4366311718068520805323787739279)⟩⟩,⟨⟨4599358813380468472499610358064,4599358813380468472762373649930⟩,⟨(-4381812231210386965087747913134),(-4381812231210386964902747438398)⟩⟩,⟨⟨4602159878892778976840176874205,4602159878892778977103782462186⟩,⟨(-4397314774650273396749820338426),(-4397314774650273396563976482626)⟩⟩,⟨⟨4604930919037691574867262940337,4604930919037691575131748154437⟩,⟨(-4412816643395745404539979308072),(-4412816643395745404353266975976)⟩⟩,⟨⟨4607671522932892374801112996193,4607671522932892375066424627019⟩,⟨(-4428315107120125444995677330465),(-4428315107120125444808130601189)⟩⟩,⟨⟨4610381295698883916930881232663,4610381295698883917197073686445⟩,⟨(-4443807410702114058272987046000),(-4443807410702114058084569716860)⟩⟩,⟨⟨4613059858670545243560138063159,4613059858670545243827172706124⟩,⟨(-4459290774788172344586520822140),(-4459290774788172344397257611485)⟩⟩,⟨⟨4615706849597121476038670445734,4615706849597121476306586606817⟩,⟨(-4474762396377661701339203320072),(-4474762396377661701149067919332)⟩⟩,⟨⟨4618321922830243572182941385106,4618321922830243572451684918902⟩,⟨(-4490219449430715981122667888479),(-4490219449430715980931695384648)⟩⟩,⟨⟨4620904749499586187037348991627,4620904749499586187306974021199⟩,⟨(-4505659085498800335530163672605),(-4505659085498800335338318095308)⟩⟩,⟨⟨4623455017675779616780442561610,4623455017675779617050907147280⟩,⟨(-4521078434377889797513542121450),(-4521078434377889797320850717267)⟩⟩,⟨⟨4625972432520200676090840166810,4625972432520200676362185676805⟩,⟨(-4536474604784179149885482881581),(-4536474604784179149691918102036)⟩⟩] +lemma kernel0_1_r4_9_eq : ∀ k : Fin 16, kernel0_1Expr 4 9 k = kernel0_1_r4_9 k := by decide +kernel +noncomputable def kernel0_1_r4_10 : Fin 16 → CBox := ![⟨⟨4628456716421277048345219825330,4628456716421277048617382190695⟩,⟨(-4551844685052213854498899152618),(-4551844685052213854304503043024)⟩⟩,⟨⟨4630907609116950158861428466997,4630907609116950159134470395246⟩,⟨(-4567185743855309801516893580988),(-4567185743855309801321624569142)⟩⟩,⟨⟨4633324867802952955574089356739,4633324867802952955847965549857⟩,⟨(-4582494830948107407759357207608),(-4582494830948107407563245132973)⟩⟩,⟨⟨4635708267226571138823554705128,4635708267226571139098308566845⟩,⟨(-4597768977931083174940897309500),(-4597768977931083174743913385733)⟩⟩,⟨⟨4638057599765569360346696232561,4638057599765569360622264363723⟩,⟨(-4613005199036819241023859343991),(-4613005199036819240826045615078)⟩⟩,⟨⟨4640372675491977707209663234287,4640372675491977707486106353411⟩,⟨(-4628200491937808749952691735680),(-4628200491937808749754007994349)⟩⟩,⟨⟨4642653322220448393566471717400,4642653322220448393843741088882⟩,⟨(-4643351838575552056422551720945),(-4643351838575552056223030480595)⟩⟩,⟨⟨4644899385540907994062381873594,4644899385540907994340522963660⟩,⟨(-4658456206010675903397587741955),(-4658456206010675903197198959596)⟩⟩,⟨⟨4647110728835246757769713621947,4647110728835246758048653210298⟩,⟨(-4673510547293784791709946641814),(-4673510547293784791508739355289)⟩⟩,⟨⟨4649287233277803529072616051105,4649287233277803529352423238188⟩,⟨(-4688511802356730834620545332585),(-4688511802356730834418473818724)⟩⟩,⟨⟨4651428797819422558219329941444,4651428797819422558499952531967⟩,⟨(-4703456898923965487511857335196),(-4703456898923965487308956822844)⟩⟩,⟨⟨4653535339154876993585491156785,4653535339154876993866976654088⟩,⟨(-4718342753443613696094850607226),(-4718342753443613695891089812336)⟩⟩,⟨⟨4655606791673473092240406427785,4655606791673473092522681702356⟩,⟨(-4733166272037888248123553988593),(-4733166272037888247918982367903)⟩⟩,⟨⟨4657643107392669145290227711783,4657643107392669145573360355652⟩,⟨(-4747924351472439476344605022355),(-4747924351472439476139177913939)⟩⟩,⟨⟨4659644255874563767733984157483,4659644255874563768017918472722⟩,⟨(-4762613880144212977145587048962),(-4762613880144212976939342450380)⟩⟩,⟨⟨4661610224125129525163704818281,4661610224125129525448490346346⟩,⟨(-4777231739087365713092578053390),(-4777231739087365712885483437088)⟩⟩] +lemma kernel0_1_r4_10_eq : ∀ k : Fin 16, kernel0_1Expr 4 10 k = kernel0_1_r4_10 k := by decide +kernel +noncomputable def kernel0_1_r4_11 : Fin 16 → CBox := ![⟨⟨4663541016476089835466473142861,4663541016476089835752024432833⟩,⟨(-4791774802996768791267737438211),(-4791774802996768791059851028956)⟩⟩,⟨⟨4665436654449359664569366361702,4665436654449359664855761791589⟩,⟨(-4806239941268603386000909045004),(-4806239941268603385792179002315)⟩⟩,⟨⟨4667297176603993701011636903519,4667297176603993701298817299265⟩,⟨(-4820624019057534737075966287753),(-4820624019057534736866433382048)⟩⟩,⟨⟨4669122638365609412508476955977,4669122638365609412796493835373⟩,⟨(-4834923898349927935444909932332),(-4834923898349927935234540431804)⟩⟩,⟨⟨4670913111838276624502061323140,4670913111838276624790831517051⟩,⟨(-4849136439052548340288735674116),(-4849136439052548340077586776762)⟩⟩,⟨⟨4672668685598889979836148219146,4672668685598889980125746348854⟩,⟨(-4863258500096168985989272885899),(-4863258500096168985777295334221)⟩⟩,⟨⟨4674389464474065802122054897994,4674389464474065802412418302718⟩,⟨(-4877286940553487266867973326338),(-4877286940553487266655210689685)⟩⟩,⟨⟨4676075569299630453209604983667,4676075569299630453500787139156⟩,⟨(-4891218620770733562587692014330),(-4891218620770733562374109366352)⟩⟩,⟨⟨4677727136662793205795024222547,4677727136662793206086929968969⟩,⟨(-4905050403512335318524507415220),(-4905050403512335318310170590010)⟩⟩,⟨⟨4679344318627122902212720349307,4679344318627122902505434712708⟩,⟨(-4918779155117981453216996327945),(-4918779155117981453001849087320)⟩⟩,⟨⟨4680927282440474194866439934253,4680927282440474195159896837442⟩,⟨(-4932401746671413858513092564880),(-4932401746671413858297181245196)⟩⟩,⟨⟨4682476210226035915970171400367,4682476210226035916264426186306⟩,⟨(-4945915055180255215845898507702),(-4945915055180255215629187046247)⟩⟩,⟨⟨4683991298656701056240440663767,4683991298656701056535399980651⟩,⟨(-4959315964766165401940410145227),(-4959315964766165401722963674014)⟩⟩,⟨⟨4685472758612984894449639214377,4685472758612984894745384759456⟩,⟨(-4972601367864602426082965699358),(-4972601367864602425864730294512)⟩⟩,⟨⟨4686920814824744961580871474847,4686920814824744961877333793864⟩,⟨(-4985768166433448154828215462666),(-4985768166433448154609240212759)⟩⟩,⟨⟨4688335705496983692775239647779,4688335705496983693072475898825⟩,⟨(-4998813273169744063651960934007),(-4998813273169744063432208671651)⟩⟩] +lemma kernel0_1_r4_11_eq : ∀ k : Fin 16, kernel0_1Expr 4 11 k = kernel0_1_r4_11 k := by decide +kernel +noncomputable def kernel0_1_r4_12 : Fin 16 → CBox := ![⟨⟨4689717681920041764326456454687,4689717681920041764624357826154⟩,⟨(-5011733612733767932503962130436),(-5011733612733767932283509067008)⟩⟩,⟨⟨4691067008064517177661796587615,4691067008064517177960458611264⟩,⟨(-5024526122979668796314434978638),(-5024526122979668796093217811398)⟩⟩,⟨⟨4692383960161272082730160630590,4692383960161272083029510612149⟩,⟨(-5037187756191864593949379070554),(-5037187756191864593727449554787)⟩⟩,⟨⟨4693668826266916073930260493748,4693668826266916074230357266475⟩,⟨(-5049715480326394850410480372315),(-5049715480326394850187800327222)⟩⟩,⟨⟨4694921905815181186512415145525,4694921905815181186813155275691⟩,⟨(-5062106280256409396513815128798),(-5062106280256409396290457615957)⟩⟩,⟨⟨4696143509154630013649322182924,4696143509154630013950794314664⟩,⟨(-5074357159020963595890407221362),(-5074357159020963595666313697782)⟩⟩,⟨⟨4697333957073164197162704987596,4697333957073164197464833265211⟩,⟨(-5086465139076280827655078051602),(-5086465139076280827430302889309)⟩⟩,⟨⟨4698493580309825961075511984382,4698493580309825961378356842992⟩,⟨(-5098427263548634079903991751735),(-5098427263548634079678495801990)⟩⟩,⟨⟨4699622719054410299573627716950,4699622719054410299877071634038⟩,⟨(-5110240597487990458380250436410),(-5110240597487990458154116964520)⟩⟩,⟨⟨4700721722435429842529954415822,4700721722435429842834098524451⟩,⟨(-5121902229121555218891811459642),(-5121902229121555218664973398712)⟩⟩,⟨⟨4701790947996998245664350902363,4701790947996998245969116373590⟩,⟨(-5133409271106345602678685661279),(-5133409271106345602451199870209)⟩⟩,⟨⟨4702830761165221132264031603172,4702830761165221132569480302271⟩,⟨(-5144758861779919300826487790162),(-5144758861779919300598314264920)⟩⟩,⟨⟨4703841534704706093327124817316,4703841534704706093633143542814⟩,⟨(-5155948166408377805509894227862),(-5155948166408377805281113770653)⟩⟩,⟨⟨4704823648165824977858752162349,4704823648165824978165436238785⟩,⟨(-5166974378430761229427913447164),(-5166974378430761229198463037934)⟩⟩,⟨⟨4705777487323382620570319338734,4705777487323382620877587106596⟩,⟨(-5177834720698948395943538811956),(-5177834720698948395713477693108)⟩⟩,⟨⟨4706703443607366207127520538830,4706703443607366207435435176157⟩,⟨(-5188526446712174125454013872115),(-5188526446712174125223301259473)⟩⟩] +lemma kernel0_1_r4_12_eq : ∀ k : Fin 16, kernel0_1Expr 4 12 k = kernel0_1_r4_12 k := by decide +kernel +noncomputable def kernel0_1_r4_13 : Fin 16 → CBox := ![⟨⟨4707601913526468615270321801292,4707601913526468615578752464150⟩,⟨(-5199046841845274671272663175264),(-5199046841845274671041392572309)⟩⟩,⟨⟨4708473298085097242795589528982,4708473298085097243104647627318⟩,⟨(-5209393224569772192307862404699),(-5209393224569772192075959719777)⟩⟩,⟨⟨4709318002194596991250336369633,4709318002194596991559937678584⟩,⟨(-5219562947666909990203065336142),(-5219562947666909989970592002045)⟩⟩,⟨⟨4710136434079432169526751799642,4710136434079432169836960582530⟩,⟨(-5229553399431751984144288755307),(-5229553399431751983911203358583)⟩⟩,⟨⟨4710929004679087068464826530061,4710929004679087068775520440120⟩,⟨(-5239362004867462544695124405346),(-5239362004867462544461515044047)⟩⟩,⟨⟨4711696127046458792022976613546,4711696127046458792334257163572⟩,⟨(-5248986226868886354948712962595),(-5248986226868886354714512439834)⟩⟩,⟨⟨4712438215743528570612516096137,4712438215743528570924296683519⟩,⟨(-5258423567394552407868314390479),(-5258423567394552407633586185169)⟩⟩,⟨⟨4713155686235109188008003317571,4713155686235109188320349148509⟩,⟨(-5267671568626231576579510927401),(-5267671568626231576344213088745)⟩⟩,⟨⟨4713848954281476287380486597260,4713848954281476287693259400353⟩,⟨(-5276727814115183402015437400420),(-5276727814115183401779669556647)⟩⟩,⟨⟨4714518435330700149408350255713,4714518435330700149721666020758⟩,⟨(-5285589929914234820992698171145),(-5285589929914234820756383104955)⟩⟩,⟨⟨4715164543911502023639778431559,4715164543911502023953548499725⟩,⟨(-5294255585694841497660653183585),(-5294255585694841497423856177697)⟩⟩,⟨⟨4715787693027465213501556795379,4715787693027465213815847053015⟩,⟨(-5302722495848291211408063256973),(-5302722495848291211170741998299)⟩⟩,⟨⟨4716388293553435838570335949561,4716388293553435838885015779704⟩,⟨(-5310988420570218382762428543544),(-5310988420570218382524677759919)⟩⟩,⟨⟨4716966753634951500803063188018,4716966753634951501118239630644⟩,⟨(-5319051166927609272641148644925),(-5319051166927609272402897384497)⟩⟩,⟨⟨4717523478091537943227577286504,4717523478091537943543159882763⟩,⟨(-5326908589907488655612114219473),(-5326908589907488655373429367168)⟩⟩,⟨⟨4718058867824714192028710085459,4718058867824714192344765211283⟩,⟨(-5334558593446490829820948428975),(-5334558593446490829581787434231)⟩⟩] +lemma kernel0_1_r4_13_eq : ∀ k : Fin 16, kernel0_1Expr 4 13 k = kernel0_1_r4_13 k := by decide +kernel +noncomputable def kernel0_1_r4_14 : Fin 16 → CBox := ![⟨⟨4718573319231545601107626860077,4718573319231545601424003237530⟩,⟨(-5341999131440530669307763007588),(-5341999131440530669068235430182)⟩⟩,⟨⟨4719067223624581660312118845711,4719067223624581660628942857679⟩,⟨(-5349228208733804032157044962911),(-5349228208733804031917066376731)⟩⟩,⟨⟨4719540966659011376208085081972,4719540966659011376525264877710⟩,⟨(-5356243882086361193127978763238),(-5356243882086361192887617343011)⟩⟩,⟨⟨4719994927767863482369685776055,4719994927767863482687287893124⟩,⟨(-5363044261119512054252403415662),(-5363044261119512054011616593526)⟩⟩,⟨⟨4720429479606071682995195241791,4720429479606071683313082019315⟩,⟨(-5369627509238337682855304734847),(-5369627509238337682614192911509)⟩⟩,⟨⟨4720844987504216580880216973110,4720844987504216581198500049427⟩,⟨(-5375991844530599214466833184273),(-5375991844530599214225322267039)⟩⟩,⟨⟨4721241808932745893539341790133,4721241808932745893857928216754⟩,⟨(-5382135540641352318511020493920),(-5382135540641352318269179710516)⟩⟩,⟨⟨4721620292977463028130284012614,4721620292977463028449240278492⟩,⟨(-5388056927622593237353528523303),(-5388056927622593237111315426470)⟩⟩,⟨⟨4721980779827061078858460792333,4721980779827061079177631943906⟩,⟨(-5393754392757280853680866676692),(-5393754392757280853438394112364)⟩⟩,⟨⟨4722323600273464845214657956401,4722323600273464845534171802523⟩,⟨(-5399226381357098296294414228882),(-5399226381357098296051596796417)⟩⟩,⟨⟨4722649075225727564686018594979,4722649075225727565005781544841⟩,⟨(-5404471397533337238884823548700),(-5404471397533337238641731174978)⟩⟩,⟨⟨4722957515238211731839219524421,4722957515238211732159297661281⟩,⟨(-5409488004940308258558872875054),(-5409488004940308258315463473451)⟩⟩,⟨⟨4723249220053764662680205013428,4723249220053764663000455100166⟩,⟨(-5414274827490701378878855596719),(-5414274827490701378635234072122)⟩⟩,⟨⟨4723524478162579388041292918989,4723524478162579388361830097322⟩,⟨(-5418830550042342203783744378809),(-5418830550042342203539834234332)⟩⟩,⟨⟨4723783566377410054850175855859,4723783566377410055170906258548⟩,⟨(-5423153919055810831609882954830),(-5423153919055810831365754522306)⟩⟩,⟨⟨4724026749425788315117332834558,4724026749425788315438321874548⟩,⟨(-5427243743222412999986118394095),(-5427243743222412999741730122504)⟩⟩] +lemma kernel0_1_r4_14_eq : ∀ k : Fin 16, kernel0_1Expr 4 14 k = kernel0_1_r4_14 k := by decide +kernel +noncomputable def kernel0_1_r4_15 : Fin 16 → CBox := ![⟨⟨4724254279559863228146563010269,4724254279559863228467645704286⟩,⟨(-5431098894062015629957725109589),(-5431098894062015629713197422255)⟩⟩,⟨⟨4724466396184462033686831485353,4724466396184462034008143813746⟩,⟨(-5434718306490282088520151404940),(-5434718306490282088275393175635)⟩⟩,⟨⟨4724663325503942817376620175086,4724663325503942817698068529735⟩,⟨(-5438100979354866049941763723714),(-5438100979354866049696845272680)⟩⟩,⟨⟨4724845280188382632619549751677,4724845280188382632941198454921⟩,⟨(-5441245975940146784910046549114),(-5441245975940146784664927144317)⟩⟩,⟨⟨4725012459059616115516430500795,4725012459059616115838132564228⟩,⟨(-5444152424440113019676534175116),(-5444152424440113019431321769681)⟩⟩,⟨⟨4725165046797610084842225052602,4725165046797610085164097737171⟩,⟨(-5446819518399027162032968771793),(-5446819518399027161787585409746)⟩⟩,⟨⟨4725303213667629113042781164303,4725303213667629113364731516483⟩,⟨(-5449246517119526664132673128210),(-5449246517119526663887188798379)⟩⟩,⟨⟨4725427115268615644960725141581,4725427115268615645282816111721⟩,⟨(-5451432746037844560914972936269),(-5451432746037844560669347911013)⟩⟩,⟨⟨4725536892303175988902177973040,4725536892303175989224244571943⟩,⟨(-5453377597065856764237068496429),(-5453377597065856763991423533935)⟩⟩,⟨⟨4725632670369530472238455940710,4725632670369530472560632781099⟩,⟨(-5455080528899689483856887354152),(-5455080528899689483611132289236)⟩⟩,⟨⟨4725714559775752305506909639365,4725714559775752305829104994047⟩,⟨(-5456541067294646164249065215574),(-5456541067294646164003269259958)⟩⟩,⟨⟨4725782655376585301220668543761,4725782655376585301542943546475⟩,⟨(-5457758805306239548040967362977),(-5457758805306239547795092092413)⟩⟩,⟨⟨4725837036433095614278934162739,4725837036433095614601140111664⟩,⟨(-5458733403497140879815456331922),(-5458733403497140879569611115283)⟩⟩,⟨⟨4725877766495377179392916922564,4725877766495377179715171651599⟩,⟨(-5459464590109884825394203118547),(-5459464590109884825148309603879)⟩⟩,⟨⟨4725904893308494588041443421584,4725904893308494588363656886071⟩,⟨(-5459952161205195378763001157878),(-5459952161205195378517127415161)⟩⟩,⟨⟨4725918448741810844972986378155,4725918448741810845295217563347⟩,⟨(-5460195980765824838859493657428),(-5460195980765824838613602784711)⟩⟩] +lemma kernel0_1_r4_15_eq : ∀ k : Fin 16, kernel0_1Expr 4 15 k = kernel0_1_r4_15 k := by decide +kernel +noncomputable def kernel0_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel0_1_r4_0,kernel0_1_r4_1,kernel0_1_r4_2,kernel0_1_r4_3,kernel0_1_r4_4,kernel0_1_r4_5,kernel0_1_r4_6,kernel0_1_r4_7,kernel0_1_r4_8,kernel0_1_r4_9,kernel0_1_r4_10,kernel0_1_r4_11,kernel0_1_r4_12,kernel0_1_r4_13,kernel0_1_r4_14,kernel0_1_r4_15] +lemma kernel0_1_r4_eq (i k : Fin 16) : kernel0_1Expr 4 i k = kernel0_1_r4 i k := by + fin_cases i + · exact kernel0_1_r4_0_eq k + · exact kernel0_1_r4_1_eq k + · exact kernel0_1_r4_2_eq k + · exact kernel0_1_r4_3_eq k + · exact kernel0_1_r4_4_eq k + · exact kernel0_1_r4_5_eq k + · exact kernel0_1_r4_6_eq k + · exact kernel0_1_r4_7_eq k + · exact kernel0_1_r4_8_eq k + · exact kernel0_1_r4_9_eq k + · exact kernel0_1_r4_10_eq k + · exact kernel0_1_r4_11_eq k + · exact kernel0_1_r4_12_eq k + · exact kernel0_1_r4_13_eq k + · exact kernel0_1_r4_14_eq k + · exact kernel0_1_r4_15_eq k +noncomputable def kernel0_1_r5_0 : Fin 16 → CBox := ![⟨⟨3519769265464296375663901003563,3519769265464296375802689449463⟩,⟨(-1624736758994089277899994433559),(-1624736758994089277838540101819)⟩⟩,⟨⟨3519820534929200818065236981253,3519820534929200818204030120175⟩,⟨(-1624813745635404184249225565265),(-1624813745635404184187767555584)⟩⟩,⟨⟨3519923067632320801006188192441,3519923067632320801144990682426⟩,⟨(-1624967717044432262301429694472),(-1624967717044432262239964344684)⟩⟩,⟨⟨3520076851119734402718495865124,3520076851119734402857312364290⟩,⟨(-1625198669470632050832009957536),(-1625198669470632050770533605255)⟩⟩,⟨⟨3520281866709199635062341720692,3520281866709199635201176886974⟩,⟨(-1625506597279846785197878087769),(-1625506597279846785136387070435)⟩⟩,⟨⟨3520538089488526847618284511171,3520538089488526847757143002442⟩,⟨(-1625891492944292051206466064348),(-1625891492944292051144956719081)⟩⟩,⟨⟨3520845488313414150120380200308,3520845488313414150259266673645⟩,⟨(-1626353347029207897042039182902),(-1626353347029207896980507846731)⟩⟩,⟨⟨3521204025804750609000151101733,3521204025804750609139070214930⟩,⟨(-1626892148176177047032940837484),(-1626892148176177046971383846603)⟩⟩,⟨⟨3521613658345393160694678556356,3521613658345393160833634964625⟩,⟨(-1627507883083111283748095736881),(-1627507883083111283686509428046)⟩⟩,⟨⟨3522074336076424369868247636351,3522074336076424370007245998027⟩,⟨(-1628200536480908495446516591426),(-1628200536480908495384897299272)⟩⟩,⟨⟨3522586002892899344513285515504,3522586002892899344652330482723⟩,⟨(-1628970091106783325827330476091),(-1628970091106783325765674537301)⟩⟩,⟨⟨3523148596439091301732326991077,3523148596439091301871423223408⟩,⟨(-1629816527674274813892898296331),(-1629816527674274813831202043338)⟩⟩,⟨⟨3523762048103246457548511310713,3523762048103246457687663454324⟩,⟨(-1630739824839934875091351185811),(-1630739824839934875029610956201)⟩⟩,⟨⟨3524426283011860091027030654840,3524426283011860091166243372801⟩,⟨(-1631739959166701952288344003548),(-1631739959166701952226556126201)⟩⟩,⟨⟨3525141220023486806981346909925,3525141220023486807120624842343⟩,⟨(-1632816905083964658064813886626),(-1632816905083964658002974699740)⟩⟩,⟨⟨3525906771722099192239884970307,3525906771722099192379232783379⟩,⟨(-1633970634844320739873671649925),(-1633970634844320739811777478674)⟩⟩] +lemma kernel0_1_r5_0_eq : ∀ k : Fin 16, kernel0_1Expr 5 0 k = kernel0_1_r5_0 k := by decide +kernel +noncomputable def kernel0_1_r5_1 : Fin 16 → CBox := ![⟨⟨3526722844410010227500728108397,3526722844410010227640150428937⟩,⟨(-1635201118477037228230212327314),(-1635201118477037228168259513488)⟩⟩,⟨⟨3527589338100375979827175656903,3527589338100375979966677160789⟩,⟨(-1636508323738218176865143163137),(-1636508323738218176803128024900)⟩⟩,⟨⟨3528506146509296259442404299965,3528506146509296259581989605071⟩,⟨(-1637892216057686974130999382344),(-1637892216057686974068918262812)⟩⟩,⟨⟨3529473157047532078255154024052,3529473157047532078394827810994⟩,⟨(-1639352758482590798405800029913),(-1639352758482590798343649242190)⟩⟩,⟨⟨3530490250811859896059140372588,3530490250811859896198907235224⟩,⟨(-1640889911617735408252406328656),(-1640889911617735408190182223739)⟩⟩,⟨⟨3531557302576083783144960843026,3531557302576083783284825480996⟩,⟨(-1642503633562659102124261692546),(-1642503633562659102061960571690)⟩⟩,⟨⟨3532674180781727764671068795393,3532674180781727764811035790933⟩,⟨(-1644193879845455353898689965082),(-1644193879845455353836308181262)⟩⟩,⟨⟨3533840747528431742063542639021,3533840747528431742203616697696⟩,⟨(-1645960603353354330891779350462),(-1645960603353354330829313198762)⟩⟩,⟨⟨3535056858564075509432603341613,3535056858564075509572789004031⟩,⟨(-1647803754260074231670291779881),(-1647803754260074231607737628677)⟩⟩,⟨⟨3536322363274656497961911895972,3536322363274656498102213902757⟩,⟨(-1649723279949954143313059593361),(-1649723279949954143250413718035)⟩⟩,⟨⟨3537637104673947987873491233308,3537637104673947988013914114445⟩,⟨(-1651719124938880913153480645604),(-1651719124938880913090739415578)⟩⟩,⟨⟨3539000919392965625298660713568,3539000919392965625439209212891⟩,⟨(-1653791230792023359800585936680),(-1653791230792023359737745621872)⟩⟩,⟨⟨3540413637669271169567889555245,3540413637669271169708568142023⟩,⟨(-1655939536038388013709897571988),(-1655939536038388013646954565519)⟩⟩,⟨⟨3541875083336143474415553062461,3541875083336143474556366532752⟩,⟨(-1658163976082211480053156510833),(-1658163976082211479990107054577)⟩⟩,⟨⟨3543385073811647773695375655922,3543385073811647773836328467519⟩,⟨(-1660464483111205457387672457805),(-1660464483111205457324512945930)⟩⟩,⟨⟨3544943420087635397704789474970,3544943420087635397845886426020⟩,⟨(-1662840986001671425893055268413),(-1662840986001671425829781937401)⟩⟩] +lemma kernel0_1_r5_1_eq : ∀ k : Fin 16, kernel0_1Expr 5 1 k = kernel0_1_r5_1 k := by decide +kernel +noncomputable def kernel0_1_r5_2 : Fin 16 → CBox := ![⟨⟨3546549926718707089376564320918,3546549926718707089517809773501⟩,⟨(-1665293410220503039937034905957),(-1665293410220503039873644189371)⟩⟩,⟨⟨3548204391811174119637301369611,3548204391811174119778700206824⟩,⟨(-1667821677724095322632908965769),(-1667821677724095322569397056629)⟩⟩,⟨⟨3549906607012052417346037762214,3549906607012052417487594346268⟩,⟨(-1670425706854180866005270275153),(-1670425706854180865941633602469)⟩⟩,⟨⟨3551656357498125930570849405458,3551656357498125930712568607534⟩,⟨(-1673105412230614390499043416314),(-1673105412230614390435278173738)⟩⟩,⟨⟨3553453421965116421662432955428,3553453421965116421804319014847⟩,⟨(-1675860704641128212923037533254),(-1675860704641128212859140201520)⟩⟩,⟨⟨3555297572616997867733052972676,3555297572616997867875110870118⟩,⟨(-1678691490928082413547308412407),(-1678691490928082413483275130040)⟩⟩,⟨⟨3557188575155494589805011648364,3557188575155494589947245623846⟩,⟨(-1681597673872234781966114401947),(-1681597673872234781901941644693)⟩⟩,⟨⟨3559126188769803167078803184159,3559126188769803167221218203143⟩,⟨(-1684579152073556958443924533286),(-1684579152073556958379608441522)⟩⟩,⟨⟨3561110166126579106477018969990,3561110166126579106619619090083⟩,⟨(-1687635819829124573683528974996),(-1687635819829124573619066103575)⟩⟩,⟨⟨3563140253360230130801086535156,3563140253360230130943876887640⟩,⟨(-1690767567008110626147269662759),(-1690767567008110626082656070690)⟩⟩,⟨⟨3565216190063558820415002257630,3565216190063558820557986930176⟩,⟨(-1693974278923912823028467883090),(-1693974278923912822963700106720)⟩⟩,⟨⟨3567337709278798192229928999688,3567337709278798192373113075932⟩,⟨(-1697255836203447149460894218988),(-1697255836203447149395968333867)⟩⟩,⟨⟨3569504537489084624758481171090,3569504537489084624901868521184⟩,⟨(-1700612114653641521264515557836),(-1700612114653641521199428195871)⟩⟩,⟨⟨3571716394610413337956391828804,3571716394610413338099987733730⟩,⟨(-1704042985125165020092504998371),(-1704042985125165020027252138857)⟩⟩,⟨⟨3573972993984122410257446962189,3573972993984122410401255323533⟩,⟨(-1707548313373429906843432216075),(-1707548313373429906778010471870)⟩⟩,⟨⟨3576274042369952061387406493350,3576274042369952061531432539374⟩,⟨(-1711127959916905360145995231919),(-1711127959916905360080400601155)⟩⟩] +lemma kernel0_1_r5_2_eq : ∀ k : Fin 16, kernel0_1Expr 5 2 k = kernel0_1_r5_2 k := by decide +kernel +noncomputable def kernel0_1_r5_3 : Fin 16 → CBox := ![⟨⟨3578619239939726646934255805367,3578619239939726647078503120857⟩,⟨(-1714781779892783692057566679826),(-1714781779892783691991795917319)⟩⟩,⟨⟨3581008280271707497943897634600,3581008280271707498088371740017⟩,⟨(-1718509622910041653219136421282),(-1718509622910041653153185384742)⟩⟩,⟨⟨3583440850345665394660025775245,3583440850345665394804730349078⟩,⟨(-1722311332899941354882822706540),(-1722311332899941354816688103223)⟩⟩,⟨⟨3585916630538722086562085272964,3585916630538722086707025716777⟩,⟨(-1726186747964017305704106134200),(-1726186747964017305637783871271)⟩⟩,⟨⟨3588435294622010859674988096574,3588435294622010859820167736841⟩,⟨(-1730135700219598087121518053609),(-1730135700219598087055004997492)⟩⟩,⟨⟨3590996509758206705299846519949,3590996509758206705445271080986⟩,⟨(-1734158015642913272603196954375),(-1734158015642913272536488857268)⟩⟩,⟨⟨3593599936499977160391569721281,3593599936499977160537242617661⟩,⟨(-1738253513909838333010091091954),(-1738253513909838332943184775670)⟩⟩,⟨⟨3596245228789405367306799990187,3596245228789405367452726828056⟩,⟨(-1742422008234332462710448863268),(-1742422008234332462643340129382)⟩⟩,⟨⟨3598932033958437338061392547865,3598932033958437338207576246501⟩,⟨(-1746663305204626508690333400268),(-1746663305204626508623019297644)⟩⟩,⟨⟨3601659992730405804045680905315,3601659992730405804192127531140⟩,⟨(-1750977204617220487458024669466),(-1750977204617220487390500780374)⟩⟩,⟨⟨3604428739222683384803936523133,3604428739222683384950649182613⟩,⟨(-1755363499308752531657809464861),(-1755363499308752531590072748001)⟩⟩,⟨⟨3607237900950518117429540299014,3607237900950518117576524836293⟩,⟨(-1759821974985803519513119695439),(-1759821974985803519445165831274)⟩⟩,⟨⟨3610087098832104649782048254196,3610087098832104649929307241498⟩,⟨(-1764352410052704104929971089906),(-1764352410052704104861797284055)⟩⟩,⟨⟨3612975947194944614505564515479,3612975947194944614653104290202⟩,⟨(-1768954575437413383623480909793),(-1768954575437413383555082607494)⟩⟩,⟨⟨3615904053783549865118225735592,3615904053783549865266049048264⟩,⟨(-1773628234415541000188338421702),(-1773628234415541000119712743212)⟩⟩,⟨⟨3618871019768542368640157628107,3618871019768542368788270596678⟩,⟨(-1778373142432587121712291288917),(-1778373142432587121643433777021)⟩⟩] +lemma kernel0_1_r5_3_eq : ∀ k : Fin 16, kernel0_1Expr 5 3 k = kernel0_1_r5_3 k := by decide +kernel +noncomputable def kernel0_1_r5_4 : Fin 16 → CBox := ![⟨⟨3621876439757204609716967858331,3621876439757204609865372475451⟩,⟨(-1783189046924477374308759461238),(-1783189046924477374239667590068)⟩⟩,⟨⟨3624919901805534367359696269639,3624919901805534367508399362442⟩,⟨(-1788075687136472558681662312934),(-1788075687136472558612331288349)⟩⟩,⟨⟨3628000987431857675643151578364,3628000987431857675792155490284⟩,⟨(-1793032793940535728272395926430),(-1793032793940535728202823057178)⟩⟩,⟨⟨3631119271632053672368981222605,3631119271632053672518292382914⟩,⟨(-1798060089651242027291964376931),(-1798060089651242027222145050850)⟩⟩,⟨⟨3634274322896444873201552189681,3634274322896444873351172168921⟩,⟨(-1803157287840319544499925008332),(-1803157287840319544429856897902)⟩⟩,⟨⟨3637465703228406181527771597096,3637465703228406181677707541535⟩,⟨(-1808324093149912340316157817768),(-1808324093149912340245835969383)⟩⟩,⟨⟨3640692968164745654695267378632,3640692968164745654845521169518⟩,⟨(-1813560201104659747969096677422),(-1813560201104659747898518617866)⟩⟩,⟨⟨3643955666797909693783393564888,3643955666797909693933971982920⟩,⟨(-1818865297922689031987943115834),(-1818865297922689031917104059580)⟩⟩,⟨⟨3647253341800064905117631585561,3647253341800064905268535450114⟩,⟨(-1824239060325621507391796773719),(-1824239060325621507320694751187)⟩⟩,⟨⟨3650585529449108395835109203326,3650585529449108395986346291518⟩,⟨(-1829681155347695278231340514752),(-1829681155347695278159970266104)⟩⟩,⟨⟨3653951759656657711463426950425,3653951759656657711614998623335⟩,⟨(-1835191240144110842372046792845),(-1835191240144110842300406094678)⟩⟩,⟨⟨3657351555998070999237386262233,3657351555998070999389299693400⟩,⟨(-1840768961798708928101244821542),(-1840768961798708928029328695995)⟩⟩,⟨⟨3660784435744547285339562492354,3660784435744547285491817966137⟩,⟨(-1846413957131093074677624703548),(-1846413957131093074605431442031)⟩⟩,⟨⟨3664249909897355986045525969388,3664249909897355986198131661704⟩,⟨(-1852125852503312640555978526309),(-1852125852503312640483502672493)⟩⟩,⟨⟨3667747483224243930567475069850,3667747483224243930720431759681⟩,⟨(-1857904263626225116797201552806),(-1857904263626225116724441167604)⟩⟩,⟨⟨3671276654298067255959035865134,3671276654298067256112351162563⟩,⟨(-1863748795365659836048025495199),(-1863748795365659835974975388390)⟩⟩] +lemma kernel0_1_r5_4_eq : ∀ k : Fin 16, kernel0_1Expr 5 4 k = kernel0_1_r5_4 k := by decide +kernel +noncomputable def kernel0_1_r5_5 : Fin 16 → CBox := ![⟨⟨3674836915537694540567094494044,3674836915537694540720767670023⟩,⟨(-1869659041548508396227995588064),(-1869659041548508396154654545880)⟩⟩,⟨⟨3678427753251226471055427523945,3678427753251226471209467610078⟩,⟨(-1875634584768870359321151007860),(-1875634584768870359247513160451)⟩⟩,⟨⟨3682048647681576187912020044443,3682048647681576188066427173357⟩,⟨(-1881674996194386035910290901514),(-1881674996194386035836354630696)⟩⟩,⟨⟨3685699073054453224593989315140,3685699073054453224748771577851⟩,⟨(-1887779835372891421631783085976),(-1887779835372891421557542968860)⟩⟩,⟨⟨3689378497628792645149445336177,3689378497628792645304601410187⟩,⟨(-1893948650039533608732098933391),(-1893948650039533608657554057716)⟩⟩,⟨⟨3693086383749669593458130967550,3693086383749669593613670302386⟩,⟨(-1900180975924488250382451567757),(-1900180975924488250307595858993)⟩⟩,⟨⟨3696822187903737993419139867667,3696822187903737993575061880951⟩,⟨(-1906476336561423903208382220672),(-1906476336561423903133214421214)⟩⟩,⟨⟨3700585360777230582847816051712,3700585360777230583004129362544⟩,⟨(-1912834243096861310316322596779),(-1912834243096861310240837029487)⟩⟩,⟨⟨3704375347316555823993190408052,3704375347316555824149892457789⟩,⟨(-1919254194100578908494360872102),(-1919254194100578908418557242799)⟩⟩,⟨⟨3708191586791525510028137191014,3708191586791525510185238463749⟩,⟨(-1925735675377219044623179182623),(-1925735675377219044547050916633)⟩⟩,⟨⟨3712033512861245079289370271648,3712033512861245079446869399808⟩,⟨(-1932278159779252562897458702582),(-1932278159779252562821004944366)⟩⟩,⟨⟨3715900553642696757265572833027,3715900553642696757423479010561⟩,⟨(-1938881107021462571321678471814),(-1938881107021462571244893268529)⟩⟩,⟨⟨3719792131782043670289669373863,3719792131782043670447979315118⟩,⟨(-1945543963497111308053459548275),(-1945543963497111307976342987630)⟩⟩,⟨⟨3723707664528681014656884642862,3723707664528681014815609336938⟩,⟨(-1952266162095957100325314231126),(-1952266162095957100247859493332)⟩⟩,⟨⟨3727646563812058220674993521547,3727646563812058220834130741116⟩,⟨(-1959047122024291435542898114900),(-1959047122024291435465104791151)⟩⟩,⟨⟨3731608236321293823310719003527,3731608236321293823470278567035⟩,⟨(-1965886248627169140258721961804),(-1965886248627169140180583800732)⟩⟩] +lemma kernel0_1_r5_5_eq : ∀ k : Fin 16, kernel0_1Expr 5 5 k = kernel0_1_r5_5 k := by decide +kernel +noncomputable def kernel0_1_r5_6 : Fin 16 → CBox := ![⟨⟨3735592083587602440131478438793,3735592083587602440291455430529⟩,⟨(-1972782933213007582444202743168),(-1972782933213007582365720662702)⟩⟩,⟨⟨3739597502069550863813005517512,3739597502069550863973412303231⟩,⟨(-1979736552880733670090532109571),(-1979736552880733670011698622533)⟩⟩,⟨⟨3743623883241157801411453372170,3743623883241157801572286790064⟩,⟨(-1986746470349660208794950988796),(-1986746470349660208715766178997)⟩⟩,⟨⟨3747670613682849236868151060445,3747670613682849237029421601377⟩,⟨(-1993812033792275896649505974685),(-1993812033792275896569963270237)⟩⟩,⟨⟨3751737075175278757983807328639,3751737075175278758145509355358⟩,⟨(-2000932576670135870344928388044),(-2000932576670135870265029106019)⟩⟩,⟨⟨3755822644796019475698156491993,3755822644796019475860302817400⟩,⟨(-2008107417573042265726344361437),(-2008107417573042265646080799316)⟩⟩,⟨⟨3759926695019131373454971966199,3759926695019131373617558414086⟩,⟨(-2015335860061706712780826029943),(-2015335860061706712700198813697)⟩⟩,⟨⟨3764048593817605059418346313753,3764048593817605059581384098947⟩,⟨(-2022617192514089042796281114730),(-2022617192514089042715283328131)⟩⟩,⟨⟨3768187704768679956222973770143,3768187704768679956386455372626⟩,⟨(-2029950687975608737715477777873),(-2029950687975608737634111718227)⟩⟩,⟨⟨3772343387162031953869004838574,3772343387162031954032944643030⟩,⟨(-2037335604013427791948395497766),(-2037335604013427791866652697148)⟩⟩,⟨⟨3776514996110822473590355917199,3776514996110822473754748654376⟩,⟨(-2044771182575005678458806376418),(-2044771182575005678376688053011)⟩⟩,⟨⟨3780701882665597746511926227092,3780701882665597746676783884380⟩,⟨(-2052256649851129007104267607658),(-2052256649851129007021766478466)⟩⟩,⟨⟨3784903393931023903349758274406,3784903393931023903515072445069⟩,⟨(-2059791216143620227225903340330),(-2059791216143620227143022206282)⟩⟩,⟨⟨3789118873185440203186361073672,3789118873185440203352146694689⟩,⟨(-2067374075737931351557185343753),(-2067374075737931351473915472356)⟩⟩,⟨⟨3793347660003209403569877321586,3793347660003209403736127947122⟩,⟨(-2075004406780830157817341756238),(-2075004406780830157733685011544)⟩⟩,⟨⟨3797589090379840894147127232333,3797589090379840894313855674266⟩,⟨(-2082681371163387651022528346632),(-2082681371163387650938477054723)⟩⟩] +lemma kernel0_1_r5_6_eq : ∀ k : Fin 16, kernel0_1Expr 5 6 k = kernel0_1_r5_6 k := by decide +kernel +noncomputable def kernel0_1_r5_7 : Fin 16 → CBox := ![⟨⟨3801842496859858785267928250989,3801842496859858785435123679759⟩,⟨(-2090404114409476736722268562513),(-2090404114409476736637826803615)⟩⟩,⟨⟨3806107208667383665222775217003,3806107208667383665390454615474⟩,⟨(-2098171765569993056188343501914),(-2098171765569993056103501539707)⟩⟩,⟨⟨3810382551839393218945388367017,3810382551839393219113544032807⟩,⟨(-2105983437123009762198883486149),(-2105983437123009762113643883542)⟩⟩,⟨⟨3814667849361623341283685053915,3814667849361623341452330670247⟩,⟨(-2113838224880078661650054298400),(-2113838224880078661564408968840)⟩⟩,⟨⟨3818962421307067783691033042188,3818962421307067783860156992872⟩,⟨(-2121735207898890612007378955889),(-2121735207898890611921332460601)⟩⟩,⟨⟨3823265584977030748996331676576,3823265584977030749165951332631⟩,⟨(-2129673448402508325848613176123),(-2129673448402508325762155598117)⟩⟩,⟨⟨3827576655044683199571714757549,3827576655044683199741821073757⟩,⟨(-2137651991705384804785497003542),(-2137651991705384804698631661819)⟩⟩,⟨⟨3831894943701069974730056661091,3831894943701069974900664244132⟩,⟨(-2145669866146380484300434057553),(-2145669866146380484213152428495)⟩⟩,⟨⟨3836219760803511128758440359526,3836219760803511128929534887152⟩,⟨(-2153726083028991818007951855639),(-2153726083028991817920259958647)⟩⟩,⟨⟨3840550414026337207033453764838,3840550414026337207205054867661⟩,⟨(-2161819636569003457173651639244),(-2161819636569003457085538440939)⟩⟩,⟨⟨3844886209013894479774938930787,3844886209013894479947036140363⟩,⟨(-2169949503849775382743414729716),(-2169949503849775382654884360508)⟩⟩,⟨⟨3849226449535752456970275232907,3849226449535752457142884124040⟩,⟨(-2178114644785375316544288280787),(-2178114644785375316455331759154)⟩⟩,⟨⟨3853570437644042319824941165318,3853570437644042319998046454970⟩,⟨(-2186314002091765469762645522517),(-2186314002091765469673269465869)⟩⟩,⟨⟨3857917473832851229926527326965,3857917473832851230100149137177⟩,⟨(-2194546501266251174507219136431),(-2194546501266251174417412282399)⟩⟩,⟨⟨3862266857199593823484733606389,3862266857199593823658859959338⟩,⟨(-2202811050575397182634642518685),(-2202811050575397182544409868318)⟩⟩,⟨⟨3866617885608278571026452486465,3866617885608278571201099974921⟩,⟨(-2211106541051615399671675890287),(-2211106541051615399581007980563)⟩⟩] +lemma kernel0_1_r5_7_eq : ∀ k : Fin 16, kernel0_1Expr 5 7 k = kernel0_1_r5_7 k := by decide +kernel +noncomputable def kernel0_1_r5_8 : Fin 16 → CBox := ![⟨⟨3870969855854583089440463622839,3870969855854583089615613475702⟩,⟨(-2219431846498625545450799845951),(-2219431846498625545359705190904)⟩⟩,⟨⟨3875322063832648940081236325257,3875322063832648940256911635504⟩,⟨(-2227785823505987692065582532982),(-2227785823505987691974048386165)⟩⟩,⟨⟨3879673804703502940697754331298,3879673804703502940873941535386⟩,⟨(-2236167311472902819284897172329),(-2236167311472902819192929460576)⟩⟩,⟨⟨3884024373065008567315012146045,3884024373065008567491728893778⟩,⟨(-2244575132641474443252015077718),(-2244575132641474443159603838242)⟩⟩,⟨⟨3888373063123247632045897462474,3888373063123247632223124342831⟩,⟨(-2253008092139621012035177740208),(-2253008092139621011942331954364)⟩⟩,⟨⟨3892719168865229101430290134827,3892719168865229101608050333727⟩,⟨(-2261464978033825117599262755161),(-2261464978033825117505969653095)⟩⟩,⟨⟨3897061984232818674661021903391,3897061984232818674839300186528⟩,⟨(-2269944561391901644563834111926),(-2269944561391901644470100606592)⟩⟩,⟨⟨3901400803297779579408277968479,3901400803297779579587093090014⟩,⟨(-2278445596355962758574187060979),(-2278445596355962758480002667200)⟩⟩,⟨⟨3905734920437811972406156575368,3905734920437811972585485416344⟩,⟨(-2286966820225753128466262397652),(-2286966820225753128371638153453)⟩⟩,⟨⟨3910063630513475360069258153437,3910063630513475360249127008276⟩,⟨(-2295506953552523974256204644692),(-2295506953552523974161126215116)⟩⟩,⟨⟨3914386229045875588749784909006,3914386229045875588930176800758⟩,⟨(-2304064700243609435319785910159),(-2304064700243609435224261248596)⟩⟩,⟨⟨3918702012394995202421052252541,3918702012394995202601987073491⟩,⟨(-2312638747677863358341720837165),(-2312638747677863358245738920141)⟩⟩,⟨⟨3923010277938543335176902053362,3923010277938543335358355805475⟩,⟨(-2321227766832108911522585219667),(-2321227766832108911426157707672)⟩⟩,⟨⟨3927310324251198804535897883515,3927310324251198804717897123621⟩,⟨(-2329830412418747439381123421641),(-2329830412418747439284235874645)⟩⟩,⟨⟨3931601451284117706666735295338,3931601451284117706849261224992⟩,⟨(-2338445323034666680977243077881),(-2338445323034666680879904548091)⟩⟩,⟨⟨3935882960544574593773966909731,3935882960544574593957040600354⟩,⟨(-2347071121321581883665935033407),(-2347071121321581883568133939252)⟩⟩] +lemma kernel0_1_r5_8_eq : ∀ k : Fin 16, kernel0_1Expr 5 8 k = kernel0_1_r5_8 k := by decide +kernel +noncomputable def kernel0_1_r5_9 : Fin 16 → CBox := ![⟨⟨3940154155275604244393964763482,3940154155275604244577557534161⟩,⟨(-2355706414137936455206999399331),(-2355706414137936455108750014036)⟩⟩,⟨⟨3944414340635509126537620719868,3944414340635509126721763129568⟩,⟨(-2364349792742481610322731622456),(-2364349792742481610224017465539)⟩⟩,⟨⟨3948662823877095908651821292474,3948662823877095908836492660349⟩,⟨(-2372999832989646985234967017409),(-2372999832989646985135798289356)⟩⟩,⟨⟨3952898914526502801282159890988,3952898914526502801467382490900⟩,⟨(-2381655095536806417457045775863),(-2381655095536806417357410326182)⟩⟩,⟨⟨3957121924561478119974293796578,3957121924561478120160038608133⟩,⟨(-2390314126063535020815761701645),(-2390314126063535020715674179178)⟩⟩,⟨⟨3961331168588969254029693256607,3961331168588969254215990491693⟩,⟨(-2398975455502945330517136677280),(-2398975455502945330416580817213)⟩⟩,⟨⟨3965525964021880212712518128929,3965525964021880212899345152110⟩,⟨(-2407637600285181653767127977881),(-2407637600285181653666115184468)⟩⟩,⟨⟨3969705631254855106632536057549,3969705631254855106819916380764⟩,⟨(-2416299062593142842282952682498),(-2416299062593142842181470218810)⟩⟩,⟨⟨3973869493838944313305065561948,3973869493838944313492965292007⟩,⟨(-2424958330630494508800822335994),(-2424958330630494508698887617573)⟩⟩,⟨⟨3978016878655009678034153391357,3978016878655009678222606859142⟩,⟨(-2433613878902022245781658051481),(-2433613878902022245679252695158)⟩⟩,⟨⟨3982147116085724919712703807146,3982147116085724919901686373311⟩,⟨(-2442264168506367676877261630204),(-2442264168506367676774398287538)⟩⟩,⟨⟨3986259540186027450992072830721,3986259540186027451181609258844⟩,⟨(-2450907647441179186854840341870),(-2450907647441179186751505683335)⟩⟩,⟨⟨3990353488851878088320811038221,3990353488851878088510866880503⟩,⟨(-2459542750920698940661803500083),(-2459542750920698940558015459692)⟩⟩,⟨⟨3994428303987185623996380278234,3994428303987185624186989661894⟩,⟨(-2468167901705797324792935481109),(-2468167901705797324688675823252)⟩⟩,⟨⟨3998483331668753963648376947120,3998483331668753963839513170047⟩,⟨(-2476781510446455232311393107961),(-2476781510446455232206675779765)⟩⟩,⟨⟨4002517922309110502099544973196,4002517922309110502291234075589⟩,⟨(-2485381976036683675558341608961),(-2485381976036683675453152675885)⟩⟩] +lemma kernel0_1_r5_9_eq : ∀ k : Fin 16, kernel0_1Expr 5 9 k = kernel0_1_r5_9 k := by decide +kernel +noncomputable def kernel0_1_r5_10 : Fin 16 → CBox := ![⟨⟨4006531430817075621537417556834,4006531430817075621729618850996⟩,⟨(-2493967685981859057109518503348),(-2493967685981859057003879445190)⟩⟩,⟨⟨4010523216755934651128333639429,4010523216755934651321086663126⟩,⟨(-2502537016778441069811994108373),(-2502537016778441069705883868759)⟩⟩,⟨⟨4014492644499075328914290862438,4014492644499075329107566821897⟩,⟨(-2511088334306028641223976473439),(-2511088334306028641117410327087)⟩⟩,⟨⟨4018439083382955756858251400551,4018439083382955757052077609460⟩,⟨(-2519619994231697597501219656187),(-2519619994231697597394183065725)⟩⟩,⟨⟨4022361907857270039559389478003,4022361907857270039753725716789⟩,⟨(-2528130342426551808278614553449),(-2528130342426551808171129002671)⟩⟩,⟨⟨4026260497632181247234015400285,4026260497632181247428899923887⟩,⟨(-2536617715394407499474350424095),(-2536617715394407499366395582097)⟩⟩,⟨⟨4030134237822494044312755675744,4030134237822494044508157552618⟩,⟨(-2545080440712518197802378399764),(-2545080440712518197693970909220)⟩⟩,⟨⟨4033982519088642276144391622014,4033982519088642276340339455796⟩,⟨(-2553516837484235412235785995840),(-2553516837484235412126910708066)⟩⟩,⟨⟨4037804737774370006971344330745,4037804737774370007167791742826⟩,⟨(-2561925216803487677328586688678),(-2561925216803487677219268646522)⟩⟩,⟨⟨4041600296040987951115969024784,4041600296040987951312959543308⟩,⟨(-2570303882230947995270701722308),(-2570303882230947995160917823059)⟩⟩,⟨⟨4045368601998090934176703453518,4045368601998090934374203999031⟩,⟨(-2578651130281747032373984280181),(-2578651130281747032263752554763)⟩⟩,⟨⟨4049109069830625959357874220271,4049109069830625959555914669831⟩,⟨(-2586965250924576666370458424446),(-2586965250924576666259763121735)⟩⟩,⟨⟨4052821119922204632628678056559,4052821119922204632827212137899⟩,⟨(-2595244528092015658874023095179),(-2595244528092015658762889475248)⟩⟩,⟨⟨4056504178974558115383999336966,4056504178974558115583069601446⟩,⟨(-2603487240201896358452249355114),(-2603487240201896358340654887071)⟩⟩,⟨⟨4060157680123037420211022948409,4060157680123037420410594145057⟩,⟨(-2611691660689518440194068087264),(-2611691660689518440082032216552)⟩⟩,⟨⟨4063781063048066739166587521841,4063781063048066739366690801216⟩,⟨(-2619856058550502774028073273314),(-2619856058550502773915579646043)⟩⟩] +lemma kernel0_1_r5_10_eq : ∀ k : Fin 16, kernel0_1Expr 5 10 k = kernel0_1_r5_10 k := by decide +kernel +noncomputable def kernel0_1_r5_11 : Fin 16 → CBox := ![⟨⟨4067373774082462588940353102297,4067373774082462589140934470517⟩,⟨(-2627978698894065603263735329265),(-2627978698894065603150813660699)⟩⟩,⟨⟨4070935266314536867081176613918,4070935266314536867282285403646⟩,⟨(-2636057843506480324131161695849),(-2636057843506480324017785843908)⟩⟩,⟨⟨4074464999686907431146523822609,4074464999686907431348122631248⟩,⟨(-2644091751424481304002294776566),(-2644091751424481303888485602621)⟩⟩,⟨⟨4077962441090945530612830626787,4077962441090945530814951838926⟩,⟨(-2652078679518351378270192898115),(-2652078679518351378155933466234)⟩⟩,⟨⟨4081427064456795331467642152784,4081427064456795331670233266069⟩,⟨(-2660016883084421941550396470050),(-2660016883084421941435715978611)⟩⟩,⟨⟨4084858350838906866780041451012,4084858350838906866983149405249⟩,⟨(-2667904616446701916163176342963),(-2667904616446701916048049994574)⟩⟩,⟨⟨4088255788497030013812012394553,4088255788497030014015597631454⟩,⟨(-2675740133567339358135812253903),(-2675740133567339358020262338482)⟩⟩,⟨⟨4091618872972623529386433991411,4091618872972623529590530117862⟩,⟨(-2683521688665607066752825586273),(-2683521688665607066636834591272)⟩⟩,⟨⟨4094947107160639759697312243622,4094947107160639759901859258329⟩,⟨(-2691247536845091316602929358497),(-2691247536845091316486530865830)⟩⟩,⟨⟨4098240001376652367390908156330,4098240001376652367595959530596⟩,⟨(-2698915934728750749827830864184),(-2698915934728750749710996570359)⟩⟩,⟨⟨4101497073419301275884497254636,4101497073419301276090011321200⟩,⟨(-2706525141101500569607548985920),(-2706525141101500569490302592554)⟩⟩,⟨⟨4104717848628036006306479582178,4104717848628036006512491112655⟩,⟨(-2714073417559965482569489420998),(-2714073417559965482451812868983)⟩⟩,⟨⟨4107901859936145663427528255613,4107901859936145663633978441650⟩,⟨(-2721559029169033366499029696027),(-2721559029169033366380956215643)⟩⟩,⟨⟨4111048647919071000302648919929,4111048647919071000509589113852⟩,⟨(-2728980245124830409115663196687),(-2728980245124830408997165691952)⟩⟩,⟨⟨4114157760838001243408003058492,4114157760838001243615389510655⟩,⟨(-2736335339423727492313007375124),(-2736335339423727492194110951318)⟩⟩,⟨⟨4117228754678765676740905057084,4117228754678765676948773670986⟩,⟨(-2743622591536976902567110092787),(-2743622591536976902447796160529)⟩⟩] +lemma kernel0_1_r5_11_eq : ∀ k : Fin 16, kernel0_1Expr 5 11 k = kernel0_1_r5_11 k := by decide +kernel +noncomputable def kernel0_1_r5_12 : Fin 16 → CBox := ![⟨⟨4120261193186037350173218623303,4120261193186037350381500921772⟩,⟨(-2750840287090568050442174356101),(-2750840287090568050322481762455)⟩⟩,⟨⟨4123254647892873679440341734329,4123254647892873679649097749983⟩,⟨(-2757986718549880798312865328160),(-2757986718549880798192762259914)⟩⟩,⟨⟨4126208698145626127316113340347,4126208698145626127525297328742⟩,⟨(-2765060185908705243375248670555),(-2765060185908705243254761592803)⟩⟩,⟨⟨4129122931124258582256617104003,4129122931124258582466266012387⟩,⟨(-2772058997382187400260119285165),(-2772058997382187400139229124552)⟩⟩,⟨⟨4131996941858121466325057981052,4131996941858121466535106768476⟩,⟨(-2778981470103251191297655465281),(-2778981470103251191176399478098)⟩⟩,⟨⟨4134830333237235992521982564594,4134830333237235992732486910540⟩,⟨(-2785825930822038499573545842693),(-2785825930822038499451894660491)⟩⟩,⟨⟨4137622716019150336546396836115,4137622716019150336757309051723⟩,⟨(-2792590716607900786834573171999),(-2792590716607900786712554593837)⟩⟩,⟨⟨4140373708831436773143615369585,4140373708831436773354973399716⟩,⟨(-2799274175553467941104688474260),(-2799274175553467940982282965747)⟩⟩,⟨⟨4143082938169906036095892573248,4143082938169906036307622580528⟩,⟨(-2805874667480312613158874552400),(-2805874667480312613036124538786)⟩⟩,⟨⟨4145750038392622277040098671608,4145750038392622277252264160986⟩,⟨(-2812390564645721341890140790266),(-2812390564645721341767012622021)⟩⟩,⟨⟨4148374651709809005098317058119,4148374651709809005310868514785⟩,⟨(-2818820252450077270686392760473),(-2818820252450077270562915504434)⟩⟩,⟨⟨4150956428169743270232465211471,4150956428169743270445441470212⟩,⟨(-2825162130144353234256195270506),(-2825162130144353234132348987861)⟩⟩,⟨⟨4153495025640742091810784576896,4153495025640742092024114567022⟩,⟨(-2831414611537208461362578610277),(-2831414611537208461238404484474)⟩⟩,⟨⟨4155990109789351713725083367959,4155990109789351713938826925952⟩,⟨(-2837576125701177106494160483828),(-2837576125701177106369626946068)⟩⟩,⟨⟨4158441354054856672315778113083,4158441354054856672529883987663⟩,⟨(-2843645117677432304825091667813),(-2843645117677432304700228999926)⟩⟩,⟨⟨4160848439620231877328176578557,4160848439620231877542684420895⟩,⟨(-2849620049178605451429493235004),(-2849620049178605451304281131166)⟩⟩] +lemma kernel0_1_r5_12_eq : ∀ k : Fin 16, kernel0_1Expr 5 12 k = kernel0_1_r5_12 k := by decide +kernel +noncomputable def kernel0_1_r5_13 : Fin 16 → CBox := ![⟨⟨4163211055379666913382542465242,4163211055379666913597370185737⟩,⟨(-2855499399289136948457064340073),(-2855499399289136948331550411821)⟩⟩,⟨⟨4165528897902797554518472307424,4165528897902797554733689817684⟩,⟨(-2861281665162631752964630001864),(-2861281665162631752838777112538)⟩⟩,⟨⟨4167801671395785032154465321760,4167801671395785032370019799782⟩,⟨(-2866965362715690702698717109180),(-2866965362715690702572556657461)⟩⟩,⟨⟨4170029087659388892544406331588,4170029087659388892760338102511⟩,⟨(-2872549027317686805940059874312),(-2872549027317686805813571262767)⟩⟩,⟨⟨4172210866044184309222874055194,4172210866044184309439106409586⟩,⟨(-2878031214475954462355301565257),(-2878031214475954462228529676788)⟩⟩,⟨⟨4174346733403079465184635641216,4174346733403079465401232262616⟩,⟨(-2883410500515858941654168326514),(-2883410500515858941527079541675)⟩⟩,⟨⟨4176436424041293075355340415939,4176436424041293075572247028096⟩,⟨(-2888685483255213391883079088356),(-2888685483255213391755705849237)⟩⟩,⟨⟨4178479679663956269549347679140,4178479679663956269766605192254⟩,⟨(-2893854782672511184720584677639),(-2893854782672511184592906140563)⟩⟩,⟨⟨4180476249321506887472878284597,4180476249321506887690400052832⟩,⟨(-2898917041568442535626953159677),(-2898917041568442535499020039645)⟩⟩,⟨⟨4182425889353047738950303514792,4182425889353047739168162281050⟩,⟨(-2903870926220166065722291981663),(-2903870926220166065594065623585)⟩⟩,⟨⟨4184328363327843543670920164910,4184328363327843543889060398737⟩,⟨(-2908715127027808302510145175551),(-2908715127027808302381658941831)⟩⟩,⟨⟨4186183441985134075331680197302,4186183441985134075550143229577⟩,⟨(-2913448359152667049821325970828),(-2913448359152667049692558858685)⟩⟩,⟨⟨4187990903172443485831094251553,4187990903172443486049798278132⟩,⟨(-2918069363146598094503716416861),(-2918069363146598094374716669443)⟩⟩,⟨⟨4189750531782567867680463319645,4189750531782567867899475457227⟩,⟨(-2922576905572068858400187339292),(-2922576905572068858270919495195)⟩⟩,⟨⟨4191462119689424819422336391123,4191462119689424819641600013469⟩,⟨(-2926969779612367348081782577804),(-2926969779612367347952280817326)⟩⟩,⟨⟨4193125465682950102814814049397,4193125465682950103034370789295⟩,⟨(-2931246805671460099765405958468),(-2931246805671460099635649181109)⟩⟩] +lemma kernel0_1_r5_13_eq : ∀ k : Fin 16, kernel0_1Expr 5 13 k = kernel0_1_r5_13 k := by decide +kernel +noncomputable def kernel0_1_r5_14 : Fin 16 → CBox := ![⟨⟨4194740375403227415996763806980,4194740375403227416216518958538⟩,⟨(-2935406831962998760038912543317),(-2935406831962998759908956488761)⟩⟩,⟨⟨4196306661274037848840416090536,4196306661274037849060448873331⟩,⟨(-2939448735087981480720212460001),(-2939448735087981480590014885398)⟩⟩,⟨⟨4197824142436015731231413397075,4197824142436015731451666342109⟩,⟨(-2943371420600582433737013513156),(-2943371420600582433606609258304)⟩⟩,⟨⟨4199292644679597329047652356832,4199292644679597329268167193913⟩,⟨(-2947173823561670463766142491238),(-2947173823561670463635510467247)⟩⟩,⟨⟨4200712000377948184092345758652,4200712000377948184313036347574⟩,⟨(-2950854909079546186028210392531),(-2950854909079546185897401717029)⟩⟩,⟨⟨4202082048420053832108770093029,4202082048420053832329706404242⟩,⟨(-2954413672837435696709919997894),(-2954413672837435696578897670620)⟩⟩,⟨⟨4203402634144157167226355467975,4203402634144157167447479371168⟩,⟨(-2957849141607288485689898216598),(-2957849141607288485558697616474)⟩⟩,⟨⟨4204673609271723852724626525209,4204673609271723852945979716154⟩,⟨(-2961160373749437116403744591425),(-2961160373749437116272344708735)⟩⟩,⟨⟨4205894831842114908859153052361,4205894831842114909080638597563⟩,⟨(-2964346459697686755744503246440),(-2964346459697686755612961486643)⟩⟩,⟨⟨4207066166148142941689616643695,4207066166148142941911314625763⟩,⟨(-2967406522429413686948413491527),(-2967406522429413686816687164845)⟩⟩,⟨⟨4208187482672685416446357382524,4208187482672685416668209291660⟩,⟨(-2970339717920263508699595995796),(-2970339717920263508567720840828)⟩⟩,⟨⟨4209258658026524930038093122111,4209258658026524930260140397162⟩,⟨(-2973145235583051801618827232159),(-2973145235583051801486782437240)⟩⟩,⟨⟨4210279574887582605945144950077,4210279574887582606167298019875⟩,⟨(-2975822298690482615478001565987),(-2975822298690482615345840530676)⟩⟩,⟨⟨4211250121941706528054979423099,4211250121941706528277310430214⟩,⟨(-2978370164781313182720362778969),(-2978370164781313182588047326794)⟩⟩,⟨⟨4212170193825172556088546092651,4212170193825172556310996373330⟩,⟨(-2980788126049606781205452376209),(-2980788126049606781073018456060)⟩⟩,⟨⟨4213039691069049933207272762214,4213039691069049933429883333387⟩,⟨(-2983075509716729635839040052722),(-2983075509716729635706467136845)⟩⟩] +lemma kernel0_1_r5_14_eq : ∀ k : Fin 16, kernel0_1Expr 5 14 k = kernel0_1_r5_14 k := by decide +kernel +noncomputable def kernel0_1_r5_15 : Fin 16 → CBox := ![⟨⟨4213858520045578816228986190535,4213858520045578816451653896536⟩,⟨(-2985231678385762148462951936102),(-2985231678385762148330301260453)⟩⟩,⟨⟨4214626592916701241584111891756,4214626592916701241806921907042⟩,⟨(-2987256030378009560952240808489),(-2987256030378009560819466826559)⟩⟩,⟨⟨4215343827584881097607982637601,4215343827584881097830876475777⟩,⟨(-2989148000051312370103256622144),(-2989148000051312369970395281951)⟩⟩,⟨⟨4216010147646342418753947288022,4216010147646342418976965281693⟩,⟨(-2990907058099872406170233579745),(-2990907058099872406037264777864)⟩⟩,⟨⟨4216625482346848763458577164395,4216625482346848763681627436104⟩,⟨(-2992532711835326440772125748400),(-2992532711835326440639104428880)⟩⟩,⟨⟨4217189766540139599127408140107,4217189766540139599350564143641⟩,⟨(-2994024505448815484726581681611),(-2994024505448815484593468957571)⟩⟩,⟨⟨4217702940649132510269463340536,4217702940649132510492667010534⟩,⟨(-2995382020253814551994443504069),(-2995382020253814551861275160159)⟩⟩,⟨⟨4218164950629992685147805210275,4218164950629992685371096019463⟩,⟨(-2996604874909504581647969622480),(-2996604874909504581514726070483)⟩⟩,⟨⟨4218575747939163539105044248170,4218575747939163539328319070916⟩,⟨(-2997692725624485404426378742360),(-2997692725624485404293121390911)⟩⟩,⟨⟨4218935289503444516278791184743,4218935289503444516502134325073⟩,⟨(-2998645266340646092389395260381),(-2998645266340646092256079069040)⟩⟩,⟨⟨4219243537693194093680258414483,4219243537693194093903612581728⟩,⟨(-2999462228897026717373475820296),(-2999462228897026717240136184389)⟩⟩,⟨⟨4219500460298727811050564322675,4219500460298727811273967851930⟩,⟨(-3000143383173523443975688371895),(-3000143383173523443842306366494)⟩⟩,⟨⟨4219706030509972785542660600353,4219706030509972785766020562819⟩,⟨(-3000688537214306972861510820164),(-3000688537214306972728142107380)⟩⟩,⟨⟨4219860226899431661550401225022,4219860226899431661773791424471⟩,⟨(-3001097537330842607242616717848),(-3001097537330842607109222224300)⟩⟩,⟨⟨4219963033408500312790237421240,4219963033408500313013601623057⟩,⟨(-3001370268184418616045967188915),(-3001370268184418615912581735423)⟩⟩,⟨⟨4220014439337174876237257676993,4220014439337174876460632871481⟩,⟨(-3001506652848108088020290199502),(-3001506652848108087886895632068)⟩⟩] +lemma kernel0_1_r5_15_eq : ∀ k : Fin 16, kernel0_1Expr 5 15 k = kernel0_1_r5_15 k := by decide +kernel +noncomputable def kernel0_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel0_1_r5_0,kernel0_1_r5_1,kernel0_1_r5_2,kernel0_1_r5_3,kernel0_1_r5_4,kernel0_1_r5_5,kernel0_1_r5_6,kernel0_1_r5_7,kernel0_1_r5_8,kernel0_1_r5_9,kernel0_1_r5_10,kernel0_1_r5_11,kernel0_1_r5_12,kernel0_1_r5_13,kernel0_1_r5_14,kernel0_1_r5_15] +lemma kernel0_1_r5_eq (i k : Fin 16) : kernel0_1Expr 5 i k = kernel0_1_r5 i k := by + fin_cases i + · exact kernel0_1_r5_0_eq k + · exact kernel0_1_r5_1_eq k + · exact kernel0_1_r5_2_eq k + · exact kernel0_1_r5_3_eq k + · exact kernel0_1_r5_4_eq k + · exact kernel0_1_r5_5_eq k + · exact kernel0_1_r5_6_eq k + · exact kernel0_1_r5_7_eq k + · exact kernel0_1_r5_8_eq k + · exact kernel0_1_r5_9_eq k + · exact kernel0_1_r5_10_eq k + · exact kernel0_1_r5_11_eq k + · exact kernel0_1_r5_12_eq k + · exact kernel0_1_r5_13_eq k + · exact kernel0_1_r5_14_eq k + · exact kernel0_1_r5_15_eq k +noncomputable def kernel0_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel0_1_r0,kernel0_1_r1,kernel0_1_r2,kernel0_1_r3,kernel0_1_r4,kernel0_1_r5] +lemma kernel0_1_eq (j : Fin 6) (i k : Fin 16) : kernel0_1Expr j i k = kernel0_1 j i k := by + fin_cases j + · exact kernel0_1_r0_eq i k + · exact kernel0_1_r1_eq i k + · exact kernel0_1_r2_eq i k + · exact kernel0_1_r3_eq i k + · exact kernel0_1_r4_eq i k + · exact kernel0_1_r5_eq i k +lemma kernel0_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel0_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(0:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel0_1_eq] + unfold kernel0_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans0_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel1_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans1 j i k) +noncomputable def kernel1_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-1227570411305908688298047004),(-1227570411305908688123041682)⟩,⟨225227498139545215585173569,225227498139545215752960741⟩⟩,⟨⟨(-1227378451857787104450007224),(-1227378451857787104275029941)⟩,⟨224976104722109510273819905,224976104722109510441573629⟩⟩,⟨⟨(-1226994571491451692968000523),(-1226994571491451692793079594)⟩,⟨224473545951546030875549840,224473545951546031043236388⟩⟩,⟨⟨(-1226418847292807511783750543),(-1226418847292807511608914280)⟩,⟨223720277666453836771822736,223720277666453836939408402⟩⟩,⟨⟨(-1225651394955857464798093293),(-1225651394955857464623370002)⟩,⟨222716982900228507089493282,222716982900228507256944377⟩⟩,⟨⟨(-1224692368860656776876160074),(-1224692368860656776701578044)⟩,⟨221464571013166277686015249,221464571013166277853298117⟩⟩,⟨⟨(-1223541962176885862642274843),(-1223541962176885862467862356)⟩,⟨219964176537778143023836936,219964176537778143190917957⟩⟩,⟨⟨(-1222200406992727664874356597),(-1222200406992727664700141911)⟩,⟨218217157739455497617002349,218217157739455497783847955⟩⟩,⟨⟨(-1220667974468657265923783582),(-1220667974468657265749794950)⟩,⟨216225094895153519415939915,216225094895153519582516573⟩⟩,⟨⟨(-1218944975015673456324086713),(-1218944975015673456150352338)⟩,⟨213989788293276004088071571,213989788293276004254345841⟩⟩,⟨⟨(-1217031758497424023008384096),(-1217031758497424022834932203)⟩,⟨211513255958454376363500508,211513255958454376529438969⟩⟩,⟨⟨(-1214928714455598846995988467),(-1214928714455598846822847184)⟩,⟨208797731105412794279096479,208797731105412794444665854⟩⟩,⟨⟨(-1212636272357887536949222852),(-1212636272357887536776420376)⟩,⟨205845659326599320925259601,205845659326599321090426599⟩⟩,⟨⟨(-1210154901867721339708355246),(-1210154901867721339535919595)⟩,⟨202659695518738802209753603,202659695518738802374485166⟩⟩,⟨⟨(-1207485113134942540794280306),(-1207485113134942540622239636)⟩,⟨199242700553925138003983811,199242700553925138168246809⟩⟩,⟨⟨(-1204627457106468586551946963),(-1204627457106468586380329166)⟩,⟨195597737701317895609353777,195597737701317895773115411⟩⟩] +lemma kernel1_0_r0_0_eq : ∀ k : Fin 16, kernel1_0Expr 0 0 k = kernel1_0_r0_0 k := by decide +kernel +noncomputable def kernel1_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-1201582525855942825888103571),(-1201582525855942825716936791)⟩,⟨191728068805939568543063615,191728068805939568706290900⟩⟩,⟨⟨(-1198350952931289195816548486),(-1198350952931289195645860425)⟩,⟨187637150231484165742052492,187637150231484165904712967⟩⟩,⟨⟨(-1194933413719014485508964467),(-1194933413719014485338783202)⟩,⟨183328628574444221308210192,183328628574444221470271095⟩⟩,⟨⟨(-1191330625824029144503946974),(-1191330625824029144334300027)⟩,⟨178806336157240800405830718,178806336157240800567259931⟩⟩,⟨⟨(-1187543349463686100379012861),(-1187543349463686100209928328)⟩,⟨174074286308398766112789051,174074286308398766273553968⟩⟩,⟨⟨(-1183572387874666879587121064),(-1183572387874666879418626159)⟩,⟨169136668438146656635687935,169136668438146656795756929⟩⟩,⟨⟨(-1179418587731275653850310302),(-1179418587731275653682433021)⟩,⟨163997842918136265007908423,163997842918136265167249180⟩⟩,⟨⟨(-1175082839573634846074680586),(-1175082839573634845907447903)⟩,⟨158662335774270750039027048,158662335774270750197608382⟩⟩,⟨⟨(-1170566078244210817210735218),(-1170566078244210817044175215)⟩,⟨153134833201901248762806877,153134833201901248920596591⟩⟩,⟨⟨(-1165869283331035121500493651),(-1165869283331035121334632818)⟩,⟨147420175912899994449701687,147420175912899994606669298⟩⟩,⟨⟨(-1160993479615926073559172948),(-1160993479615926073394039194)⟩,⟨141523353324342435797917851,141523353324342435954031563⟩⟩,⟨⟨(-1155939737525957135895004416),(-1155939737525957135730623953)⟩,⟨135449497598731446394432535,135449497598731446549662374⟩⟩,⟨⟨(-1150709173586363135505898130),(-1150709173586363135342299004)⟩,⟨129203877545873132559616581,129203877545873132713930850⟩⟩,⟨⟨(-1145302950873022784130018534),(-1145302950873022783967226301)⟩,⟨122791892396665795563491802,122791892396665795716861440⟩⟩,⟨⟨(-1139722279462606643503123126),(-1139722279462606643341165568)⟩,⟨116219065459191163874512954,116219065459191164026906781⟩⟩,⟨⟨(-1133968416878433781954951848),(-1133968416878433781793854191)⟩,⟨109491037667600044777702265,109491037667600044929091812⟩⟩] +lemma kernel1_0_r0_1_eq : ∀ k : Fin 16, kernel1_0Expr 0 1 k = kernel1_0_r0_1 k := by decide +kernel +noncomputable def kernel1_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-1128042668530038150095204417),(-1128042668530038149934994716)⟩,⟨102613561034363093136281871,102613561034363093286635956⟩⟩,⟨⟨(-1121946388144407398668106148),(-1121946388144407398508808689)⟩,⟨95592492016511576556102798,95592492016511576705394172⟩⟩,⟨⟨(-1115680978186822705910037373),(-1115680978186822705751679771)⟩,⟨88433784806523025221511873,88433784806523025369710080⟩⟩,⟨⟨(-1109247890269198405757138565),(-1109247890269198405599744795)⟩,⟨81143484558512760225466358,81143484558512760372544752⟩⟩,⟨⟨(-1102648625543795036900872269),(-1102648625543795036744470271)⟩,⟨73727720560374837939534533,73727720560374838085462628⟩⟩,⟨⟨(-1095884735080159083140064153),(-1095884735080159082984676744)⟩,⟨66192699362475341859213124,66192699362475342003965745⟩⟩,⟨⟨(-1088957820223127355396506924),(-1088957820223127355242161481)⟩,⟨58544697873437677288572084,58544697873437677432119615⟩⟩,⟨⟨(-1081869532929723871572617709),(-1081869532929723871419336685)⟩,⟨50790056433474123177844008,50790056433474123320161958⟩⟩,⟨⟨(-1074621576082772405595211366),(-1074621576082772405443022678)⟩,⟨42935171875610976484337624,42935171875610976625396155⟩⟩,⟨⟨(-1067215703779048770338133757),(-1067215703779048770187058294)⟩,⟨34986490585026853543066827,34986490585026853682843345⟩⟩,⟨⟨(-1059653721589803523237287213),(-1059653721589803523087352023)⟩,⟨26950501566575811479300356,26950501566575811617766228⟩⟩,⟨⟨(-1051937486791498273126366964),(-1051937486791498272977592692)⟩,⟨18833729530399693816332455,18833729530399693953465673⟩⟩,⟨⟨(-1044068908564617237746993489),(-1044068908564617237599407736)⟩,⟨10642728005348309233591303,10642728005348309369363014⟩⟩,⟨⟨(-1036049948158440248603436438),(-1036049948158440248457058068)⟩,⟨2384072489722586006324520,2384072489722586140714855⟩⟩,⟨⟨(-1027882619019694096667185978),(-1027882619019694096522041585)⟩,⟨(-5935646351364388011360444),(-5935646351364387878378974)⟩⟩,⟨⟨(-1019568986883036009378442959),(-1019568986883036009234551099)⟩,⟨(-14309829432949588263048547),(-14309829432949588131495147)⟩⟩] +lemma kernel1_0_r0_2_eq : ∀ k : Fin 16, kernel1_0Expr 0 2 k = kernel1_0_r0_2 k := by decide +kernel +noncomputable def kernel1_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-1011111169821366173137474863),(-1011111169821366172994863017)⟩,⟨(-22731875932697599470644893),(-22731875932697599340547592)⟩⟩,⟨⟨(-1002511338254015568133845632),(-1002511338254015567992530030)⟩,⟨(-31195189900350311368008522),(-31195189900350311239383818)⟩⟩,⟨⟨(-993771714910910940787832866),(-993771714910910940647839493)⟩,⟨(-39693186785883190207465212),(-39693186785883190080339265)⟩⟩,⟨⟨(-984894574750880454408824651),(-984894574750880454270169708)⟩,⟨(-48219299878391944656210645),(-48219299878391944530599556)⟩⟩,⟨⟨(-975882244832331355989063878),(-975882244832331355851774161)⟩,⟨(-56766986648033537071791723),(-56766986648033536947722107)⟩⟩,⟨⟨(-966737104134604775221695966),(-966737104134604775085785205)⟩,⟨(-65329734983655300545243614),(-65329734983655300422728707)⟩⟩,⟨⟨(-957461583328392403543893752),(-957461583328392403409387157)⟩,⟨(-73901069319064340846063332),(-73901069319064340725127780)⟩⟩,⟨⟨(-948058164493685132945866851),(-948058164493685132812778013)⟩,⟨(-82474556641215362182302763),(-82474556641215362062959280)⟩⟩,⟨⟨(-938529380783814587502853685),(-938529380783814587371209034)⟩,⟨(-91043812373927491765013925),(-91043812373927491647288024)⟩⟩,⟨⟨(-928877816034244651021800524),(-928877816034244650891610551)⟩,⟨(-99602506131078533483525076),(-99602506131078533367425967)⟩⟩,⟨⟨(-919106104314871353375939073),(-919106104314871353247228007)⟩,⟨(-108144367333567310153435434),(-108144367333567310038986028)⟩⟩,⟨⟨(-909216929424695574003183223),(-909216929424695573875961825)⟩,⟨(-116663190684680326873548874),(-116663190684680326760758274)⟩⟩,⟨⟨(-899213024327843679095236971),(-899213024327843678969530535)⟩,⟨(-125152841498846894247604627),(-125152841498846894136496459)⟩⟩,⟨⟨(-889097170530026133243991454),(-889097170530026133119807593)⟩,⟨(-133607260879116101452967335),(-133607260879116101343547142)⟩⟩,⟨⟨(-878872197394643000685817111),(-878872197394643000563178874)⟩,⟨(-142020470739038663156136745),(-142020470739038663048425504)⟩⟩,⟨⟨(-868540981397867741071102544),(-868540981397867740950017668)⟩,⟨(-150386578664985747880781935),(-150386578664985747774784944)⟩⟩] +lemma kernel1_0_r0_3_eq : ∀ k : Fin 16, kernel1_0Expr 0 3 k = kernel1_0_r0_3 k := by decide +kernel +noncomputable def kernel1_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-858106445322166458034943384),(-858106445322166457915436568)⟩,⟨(-158699782615284527299054480),(-158699782615284527194794021)⟩⟩,⟨⟨(-847571557387838408427071637),(-847571557387838408309146686)⟩,⟨(-166954375452895499227592211),(-166954375452895499125069233)⟩⟩,⟨⟨(-836939330322294744807603604),(-836939330322294744691282157)⟩,⟨(-175144749308698801962911980),(-175144749308698801862145310)⟩⟩,⟨⟨(-826212820366925750750969385),(-826212820366925750636256022)⟩,⟨(-183265399772794963153372874),(-183265399772794963054363876)⟩⟩,⟨⟨(-815395126221541834619477186),(-815395126221541834506394843)⟩,⟨(-191310929911559062812908841),(-191310929911559062715677299)⟩⟩,⟨⟨(-804489387926509861690876605),(-804489387926509861579426124)⟩,⟨(-199276054108515430096855243),(-199276054108515430001398375)⟩⟩,⟨⟨(-793498785682843609676177859),(-793498785682843609566379239)⟩,⟨(-207155601727422073859555245),(-207155601727422073765889520)⟩⟩,⟨⟨(-782426538610644807489831346),(-782426538610644807381685925)⟩,⟨(-214944520596269449733275432),(-214944520596269449641398217)⟩⟩,⟨⟨(-771275903446428938316031568),(-771275903446428938209561245)⟩,⟨(-222637880311206319482487259),(-222637880311206319392416612)⟩⟩,⟨⟨(-760050173180007332195286718),(-760050173180007332090488331)⟩,⟨(-230230875359705836345306969),(-230230875359705836257035355)⟩⟩,⟨⟨(-748752675631733619136126400),(-748752675631733619033018098)⟩,⟨(-237718828062577114675849057),(-237718828062577114589390401)⟩⟩,⟨⟨(-737386771971057943676158485),(-737386771971057943574738312)⟩,⟨(-245097191334710982347057946),(-245097191334710982262405609)⟩⟩,⟨⟨(-725955855177466044274599357),(-725955855177466044173540311)⟩,⟨(-252361551264722986062563682),(-252361551264722985977901963)⟩⟩,⟨⟨(-714463348445011972049617139),(-714463348445011971948833916)⟩,⟨(-259507629513921685732332900),(-259507629513921685647540736)⟩⟩,⟨⟨(-702912703531782468879166923),(-702912703531782468778688355)⟩,⟨(-266531285535285543435301873),(-266531285535285543350405314)⟩⟩,⟨⟨(-691307399055757461685765559),(-691307399055757461585599135)⟩,⟨(-273428518613377039691325404),(-273428518613377039606329005)⟩⟩] +lemma kernel1_0_r0_4_eq : ∀ k : Fin 16, kernel1_0Expr 0 4 k = kernel1_0_r0_4 k := by decide +kernel +noncomputable def kernel1_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-679650938738654387738668112),(-679650938738654387638847187)⟩,⟨(-280195469726357833925570079),(-280195469726357833840504749)⟩⟩,⟨⟨(-667946849599463789325972252),(-667946849599463789226500215)⟩,⟨(-286828423231493669588006294),(-286828423231493669502872739)⟩⟩,⟨⟨(-656198680099499465410227911),(-656198680099499465311135259)⟩,⟨(-293323808375752192050611001),(-293323808375752191965437530)⟩⟩,⟨⟨(-644409998240898120318664420),(-644409998240898120219957685)⟩,⟨(-299678200633300824471767656),(-299678200633300824386558482)⟩⟩,⟨⟨(-632584389620610600988246862),(-632584389620610600889960505)⟩,⟨(-305888322871905297720147916),(-305888322871905297634935658)⟩⟩,⟨⟨(-620725455442029180142505738),(-620725455442029180044642421)⟩,⟨(-311951046350412357004680392),(-311951046350412356919465695)⟩⟩,⟨⟨(-608836810486492658821355155),(-608836810486492658723946735)⟩,⟨(-317863391549672607430972729),(-317863391549672607345785895)⟩⟩,⟨⟨(-596922081047003084985103559),(-596922081047003084888155269)⟩,⟨(-323622528839421484301227407),(-323622528839421484216072036)⟩⟩,⟨⟨(-584984902826574394482428888),(-584984902826574394385977588)⟩,⟨(-329225778983788044221317938),(-329225778983788044136229714)⟩⟩,⟨⟨(-573028918803714078022686584),(-573028918803714077926732254)⟩,⟨(-334670613488242802162530146),(-334670613488242802077507736)⟩⟩,⟨⟨(-561057777067613887346081729),(-561057777067613887250657229)⟩,⟨(-339954654790927347164855085),(-339954654790927347079930479)⟩⟩,⟨⟨(-549075128625694463156664289),(-549075128625694463061773244)⟩,⟨(-345075676301430140262856742),(-345075676301430140178032670)⟩⟩,⟨⟨(-537084625186211467524830263),(-537084625186211467430509889)⟩,⟨(-350031602290184940456211876),(-350031602290184940371525065)⟩⟩,⟨⟨(-525089916918687228695323164),(-525089916918687228601572151)⟩,⟨(-354820507631770947040233140),(-354820507631770946955681745)⟩⟩,⟨⟨(-513094650194981974124113231),(-513094650194981974030965080)⟩,⟨(-359440617405487236983512283),(-359440617405487236899129654)⟩⟩,⟨⟨(-501102465313862378721666092),(-501102465313862378629122519)⟩,⟨(-363890306356658678480656220),(-363890306356658678396443967)⟩⟩] +lemma kernel1_0_r0_5_eq : ∀ k : Fin 16, kernel1_0Expr 0 5 k = kernel1_0_r0_5 k := by decide +kernel +noncomputable def kernel1_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-489116994211962353001544644),(-489116994211962352909644980)⟩,⟨(-368168098222206494927086755),(-368168098222206494843084444)⟩⟩,⟨⟨(-477141858164061725677169189),(-477141858164061725585908416)⟩,⟨(-372272664924084328300588659),(-372272664924084328216791554)⟩⟩,⟨⟨(-465180665475632744469031552),(-465180665475632744378443447)⟩,⟨(-376202825634240308508134596),(-376202825634240308424577059)⟩⟩,⟨⟨(-453237009170622155797820928),(-453237009170622155707905042)⟩,⟨(-379957545714817585184454598),(-379957545714817585101136911)⟩⟩,⟨⟨(-441314464677448077290292308),(-441314464677448077201087158)⟩,⟨(-383535935537350336602992111),(-383535935537350336519953753)⟩⟩,⟨⟨(-429416587516196014786798335),(-429416587516196014698297532)⟩,⟨(-386937249184749757215701436),(-386937249184749757132937164)⟩⟩,⟨⟨(-417546910989997284623651772),(-417546910989997284535889000)⟩,⟨(-390160883039905264086521751),(-390160883039905264004066593)⟩⟩,⟨⟨(-405708943883565886888455513),(-405708943883565886801427947)⟩,⟨(-393206374264750477451665701),(-393206374264750477369518412)⟩⟩,⟨⟨(-393906168171856657331950030),(-393906168171856657245697513)⟩,⟨(-396073399173661745686371030),(-396073399173661745604573162)⟩⟩,⟨⟨(-382142036741788441555122515),(-382142036741788441469634566)⟩,⟨(-398761771505069422004019014),(-398761771505069421922562111)⟩⟩,⟨⟨(-370419971129951236444796763),(-370419971129951236360106619)⟩,⟨(-401271440595169077856762073),(-401271440595169077775681469)⟩⟩,⟨⟨(-358743359279185895556636712),(-358743359279185895472738994)⟩,⟨(-403602489457621670256190603),(-403602489457621670175483375)⟩⟩,⟨⟨(-347115553316889274535912509),(-347115553316889274452845544)⟩,⟨(-405755132773128675328528677),(-405755132773128675248235592)⟩⟩,⟨⟨(-335539867357856788229247879),(-335539867357856788146999471)⟩,⟨(-407729714792760659779193309),(-407729714792760659699305086)⟩⟩,⟨⟨(-324019575334428461432867478),(-324019575334428461351470088)⟩,⟨(-409526707158905979190227629),(-409526707158905979110779570)⟩⟩,⟨⟨(-312557908856653887719906929),(-312557908856653887639352502)⟩,⟨(-411146706647690552196389465),(-411146706647690552117376842)⟩⟩] +lemma kernel1_0_r0_6_eq : ∀ k : Fin 16, kernel1_0Expr 0 6 k = kernel1_0_r0_6 k := by decide +kernel +noncomputable def kernel1_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-301158055105136280735014311),(-301158055105136280655342304)⟩,⟨(-412590432836700238163523015),(-412590432836700238084988412)⟩⟩,⟨⟨(-289823154759156231640203913),(-289823154759156231561397339)⟩,⟨(-413858725701814508563502696),(-413858725701814508485432941)⟩⟩,⟨⟨(-278556299962612102487794223),(-278556299962612102409884446)⟩,⟨(-414952543146934103729611294),(-414952543146934103652041308)⟩⟩,⟨⟨(-267360532330246420111980373),(-267360532330246420034956614)⟩,⟨(-415872958470356450951263419),(-415872958470356450874186595)⟩⟩,⟨⟨(-256238840996556424024483199),(-256238840996556423948382241)⟩,⟨(-416621157771521019353934435),(-416621157771521019277391379)⟩⟩,⟨⟨(-245194160709712302558311463),(-245194160709712302483115034)⟩,⟨(-417198437301812722426257528),(-417198437301812722350234621)⟩⟩,⟨⟨(-234229369972728863366809665),(-234229369972728863292547777)⟩,⟨(-417606200763075159199199896),(-417606200763075159123731378)⟩⟩,⟨⟨(-223347289234055667135760905),(-223347289234055667062420039)⟩,⟨(-417845956557447106723067346),(-417845956557447106648144683)⟩⟩,⟨⟨(-212550679129667246442319219),(-212550679129667246369936566)⟩,⟨(-417919314992095424313703826),(-417919314992095424239368632)⟩⟩,⟨⟨(-201842238778649173375056646),(-201842238778649173303609307)⟩,⟨(-417827985442375576688553813),(-417827985442375576614788676)⟩⟩,⟨⟨(-191224604134187666147205473),(-191224604134187666076721874)⟩,⟨(-417573773476907489252812693),(-417573773476907489179650884)⟩⟩,⟨⟨(-180700346391780370167366501),(-180700346391780370097830449)⟩,⟨(-417158577948009563279604939),(-417158577948009563207036005)⟩⟩,⟨⟨(-170271970456394143219150880),(-170271970456394143150596504)⟩,⟨(-416584388050887538785830040),(-416584388050887538713893116)⟩⟩,⟨⟨(-159941913470202343947366333),(-159941913470202343879769484)⟩,⟨(-415853280354927624406057369),(-415853280354927624334734517)⟩⟩,⟨⟨(-149712543402439489648970128),(-149712543402439489582357468)⟩,⟨(-414967415810395031300267583),(-414967415810395031229590858)⟩⟩,⟨⟨(-139586157702815430318437902),(-139586157702815430252790655)⟩,⟨(-413929036733789856154008986),(-413929036733789856083966032)⟩⟩] +lemma kernel1_0_r0_7_eq : ∀ k : Fin 16, kernel1_0Expr 0 7 k = kernel1_0_r0_7 k := by decide +kernel +noncomputable def kernel1_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-129564982019834592433737443),(-129564982019834592369090316)⟩,⟨(-412740463775062250320512060),(-412740463775062250251143028)⟩⟩,⟨⟨(-119651168985268583679491816),(-119651168985268583615815703)⟩,⟨(-411404092869838071825177749),(-411404092869838071756460452)⟩⟩,⟨⟨(-109846797065932718073363845),(-109846797065932718010683493)⟩,⟨(-409922392179754818458259590),(-409922392179754818390224637)⟩⟩,⟨⟨(-100153869483819012690798832),(-100153869483819012629093063)⟩,⟨(-408297899023955648576294731),(-408297899023955648508927949)⟩⟩,⟨⟨(-90574313205540108528772913),(-90574313205540108468072424)⟩,⟨(-406533216804736767919819118),(-406533216804736767853157105)⟩⟩,⟨⟨(-81109978001940558238782102),(-81109978001940558179057552)⟩,⟨(-404631011930290443973189293),(-404631011930290443907210128)⟩⟩,⟨⟨(-71762635578634174623060111),(-71762635578634174564334253)⟩,⟨(-402594010737432444687670947),(-402594010737432444622403634)⟩⟩,⟨⟨(-62533978778128810859617982),(-62533978778128810801867430)⟩,⟨(-400424996417148819117604935),(-400424996417148819053033561)⟩⟩,⟨⟨(-53425620854103204052053352),(-53425620854103203995308783)⟩,⟨(-398126805945742670328700881),(-398126805945742670264862294)⟩⟩,⟨⟨(-44439094818304508235044048),(-44439094818304508179271999)⟩,⟨(-395702327024306936273002488),(-395702327024306936209871126)⟩⟩,⟨⟨(-35575852860440014431864414),(-35575852860440014377085594)⟩,⟨(-393154495029194206909606238),(-393154495029194206847209345)⟩⟩,⟨⟨(-26837265841342439505804095),(-26837265841342439451993166)⟩,⟨(-390486289976099275184436922),(-390486289976099275122756986)⟩⟩,⟨⟨(-18224622859595190891964333),(-18224622859595190839148139)⟩,⟨(-387700733500314450312302701),(-387700733500314450251373013)⟩⟩,⟨⟨(-9739130891712302227140150),(-9739130891712302175285208)⟩,⟨(-384800885855661654607578751),(-384800885855661654547373968)⟩⟩,⟨⟨(-1381914505877399764448493),(-1381914505877399713573479)⟩,⟨(-381789842934548976544035253),(-381789842934548976484580783)⟩⟩,⟨⟨6845984350842791276044420,6845984350842791325966531⟩,⟨(-378670733311542656092087427),(-378670733311542656033364268)⟩⟩] +lemma kernel1_0_r0_8_eq : ∀ k : Fin 16, kernel1_0Expr 0 8 k = kernel1_0_r0_8 k := by decide +kernel +noncomputable def kernel1_0_r0_9 : Fin 16 → CBox := ![⟨⟨14943606491982156910321323,14943606491982156959263272⟩,⟨(-375446715312788424055541674),(-375446715312788423997583612)⟩⟩,⟨⟨22910075558113464066303926,22910075558113464114303201⟩,⟨(-372120974113558692990065704),(-372120974113558692932843591)⟩⟩,⟨⟨30744598010582352173069780,30744598010582352220109723⟩,⟨(-368696718866144289117453741),(-368696718866144289060991070)⟩⟩,⟨⟨38446463052960180238211227,38446463052960180284320225⟩,⟨(-365177179860251206552135671),(-365177179860251206496412126)⟩⟩,⟨⟨46015042480718910294760887,46015042480718910339916031⟩,⟨(-361565605718004239908052248),(-361565605718004239853097401)⟩⟩,⟨⟨53449790459709261958743559,53449790459709262002981145⟩,⟨(-357865260625600290791203943),(-357865260625600290736989728)⟩⟩,⟨⟨60750243234099369261653730,60750243234099369305446688⟩,⟨(-354079421603594629033916404),(-354079421603594628980366199)⟩⟩,⟨⟨67916018764505051330116856,67916018764505051373599657⟩,⟨(-350211375817743401755582335),(-350211375817743401702655592)⟩⟩,⟨⟨74946816297114519503825308,74946816297114519546965663⟩,⟨(-346264417932265203446940875),(-346264417932265203394671451)⟩⟩,⟨⟨81842415864679836749927512,81842415864679836792755193⟩,⟨(-342241847507323529624914465),(-342241847507323529573275221)⟩⟩,⟨⟨88602677720314677159878802,88602677720314677202371330⟩,⟨(-338146966442470417175338108),(-338146966442470417124352930)⟩⟩,⟨⟨95227541705102864927053602,95227541705102864969231493⟩,⟨(-333983076467729509174116047),(-333983076467729509123766281)⟩⟩,⟨⟨101717026550584768915550351,101717026550584768957384589⟩,⟨(-329753476683934154783800679),(-329753476683934154734116374)⟩⟩,⟨⟨108071229117248860364530721,108071229117248860406049153⟩,⟨(-325461461153872951188690083),(-325461461153872951139644747)⟩⟩,⟨⟨114290323570213581083694792,114290323570213581124876205⟩,⟨(-321110316545731341491584942),(-321110316545731341443200571)⟩⟩,⟨⟨120374560493340095185965858,120374560493340095226830805⟩,⟨(-316703319830253488914697457),(-316703319830253488866954169)⟩⟩] +lemma kernel1_0_r0_9_eq : ∀ k : Fin 16, kernel1_0Expr 0 9 k = kernel1_0_r0_9 k := by decide +kernel +noncomputable def kernel1_0_r0_10 : Fin 16 → CBox := ![⟨⟨126324265943069490168965269,126324265943069490209483589⟩,⟨(-312243736032983644406231753),(-312243736032983644359160278)⟩⟩,⟨⟨132139840443328537717876117,132139840443328537758078080⟩,⟨(-307734816042880604944544954),(-307734816042880604898115046)⟩⟩,⟨⟨137821757922896209069783229,137821757922896209109648924⟩,⟨(-303179794478532618914873555),(-303179794478532618869105353)⟩⟩,⟨⟨143370564596668755505128874,143370564596668755544678706⟩,⟨(-298581887613133230911713149),(-298581887613133230866585670)⟩⟩,⟨⟨148786877792304305993316836,148786877792304306032524590⟩,⟨(-293944291359311071870575415),(-293944291359311071826115064)⟩⟩,⟨⟨154071384723768598690410465,154071384723768598729303502⟩,⟨(-289270179314838495057237131),(-289270179314838495013415163)⟩⟩,⟨⟨159224841213341651242376352,159224841213341651280936074⟩,⟨(-284562700870175240577145905),(-284562700870175240533980692)⟩⟩,⟨⟨164248070363680889853705747,164248070363680889891952255⟩,⟨(-279824979378733990210330473),(-279824979378733990167800043)⟩⟩,⟨⟨169141961181569504719994008,169141961181569504757900645⟩,⟨(-275060110390684763178402878),(-275060110390684763136533962)⟩⟩,⟨⟨173907467155009588199756713,173907467155009588237352268⟩,⟨(-270271159951044617818361293),(-270271159951044617777122145)⟩⟩,⟨⟨178545604785347953086710617,178545604785347953123977817⟩,⟨(-265461162962728083309991704),(-265461162962728083269399041)⟩⟩,⟨⟨183057452076148435102075150,183057452076148435139033638⟩,⟨(-260633121615162172231158000),(-260633121615162172191188976)⟩⟩,⟨⟨187444146980547972269586605,187444146980547972306213165⟩,⟨(-255790003878997744915314943),(-255790003878997744875992698)⟩⟩,⟨⟨191706885808854842566345073,191706885808854842602665816⟩,⟨(-250934742067376440007756696),(-250934742067376439969050703)⟩⟩,⟨⟨195846921598166150923886118,195846921598166150959885113⟩,⟨(-246070231464139385475592964),(-246070231464139385437518416)⟩⟩,⟨⟨199865562445798010364030233,199865562445798010399726528⟩,⟨(-241199329019290497447362683),(-241199329019290497409895974)⟩⟩] +lemma kernel1_0_r0_10_eq : ∀ k : Fin 16, kernel1_0Expr 0 10 k = kernel1_0_r0_10 k := by decide +kernel +noncomputable def kernel1_0_r0_11 : Fin 16 → CBox := ![⟨⟨203764169808335885166779476,203764169808335885202149168⟩,⟨(-236324852111953401093331081),(-236324852111953401056496495)⟩⟩,⟨⟨207544156768124284115203921,207544156768124284150274554⟩,⟨(-231449577380986912412342839),(-231449577380986912376106526)⟩⟩,⟨⟨211206986269024438924649376,211206986269024438959406373⟩,⟨(-226576239623349650019278857),(-226576239623349649983654639)⟩⟩,⟨⟨214754169323275809037344500,214754169323275809071806187⟩,⟨(-221707530760229753239045381),(-221707530760229753204009016)⟩⟩,⟨⟨218187263191302253355203058,218187263191302253389349410⟩,⟨(-216846098870880922050267506),(-216846098870880922015839463)⟩⟩,⟨⟨221507869536306538682204775,221507869536306538716059999⟩,⟨(-211994547294031124346250874),(-211994547294031124312399274)⟩⟩,⟨⟨224717632555497552318763047,224717632555497552352313925⟩,⟨(-207155433796655398828145717),(-207155433796655398794883172)⟩⟩,⟨⟨227818237089793193208764804,227818237089793193242028854⟩,⟨(-202331269809829283393031697),(-202331269809829283360333424)⟩⟩,⟨⟨230811406713838475241332827,230811406713838475274289985⟩,⟨(-197524519731304588380016825),(-197524519731304588347904372)⟩⟩,⟨⟨233698901808172932820364102,233698901808172932853039164⟩,⟨(-192737600294374584162754444),(-192737600294374584131193240)⟩⟩,⟨⟨236482517615374019799338463,236482517615374019831719581⟩,⟨(-187972880002521259330468033),(-187972880002521259299469656)⟩⟩,⟨⟨239164082281993887561499831,239164082281993887593603632⟩,⟨(-183232678629263208338700216),(-183232678629263208308239454)⟩⟩,⟨⟨241745454888095767670555519,241745454888095767702365305⟩,⟨(-178519266782549008433822133),(-178519266782549008403917551)⟩⟩,⟨⟨244228523466183222382952759,244228523466183222414490367⟩,⟨(-173834865532967730300458937),(-173834865532967730271077648)⟩⟩,⟨⟨246615203011300817620427935,246615203011300817651682884⟩,⟨(-169181646104975583590577363),(-169181646104975583561730094)⟩⟩,⟨⟨248907433484068374877927798,248907433484068374908915770⟩,⟨(-164561729630265718387079258),(-164561729630265718358740451)⟩⟩] +lemma kernel1_0_r0_11_eq : ∀ k : Fin 16, kernel1_0Expr 0 11 k = kernel1_0_r0_11 k := by decide +kernel +noncomputable def kernel1_0_r0_12 : Fin 16 → CBox := ![⟨⟨251107177808392929975567184,251107177808392930006271228⟩,⟨(-159977186962336980470074629),(-159977186962336980442265072)⟩⟩,⟨⟨253216419865582928334675323,253216419865582928365117992⟩,⟨(-155430038551247048192915839),(-155430038551247048165599354)⟩⟩,⟨⟨255237162486568081080819109,255237162486568081110991298⟩,⟨(-150922254377465960319013793),(-150922254377465960292200423)⟩⟩,⟨⟨257171425443905757913963876,257171425443905757943880277⟩,⟨(-146455753943677677903441266),(-146455753943677677877105217)⟩⟩,⟨⟨259021243445230867075108541,259021243445230867104755919⟩,⟨(-142032406323310111699686691),(-142032406323310111673845428)⟩⟩,⟨⟨260788664129780937092279900,260788664129780937121677415⟩,⟨(-137654030264508093794827810),(-137654030264508093769447701)⟩⟩,⟨⟨262475746069601637902999060,262475746069601637932138975⟩,⟨(-133322394348199183840098480),(-133322394348199183815189074)⟩⟩,⟨⟨264084556777010330290124699,264084556777010330319020716⟩,⟨(-129039217198839083186883572),(-129039217198839083162418893)⟩⟩,⟨⟨265617170719866483358514174,265617170719866483387153492⟩,⟨(-124806167746361892261749499),(-124806167746361892237749081)⟩⟩,⟨⟨267075667346168022075694254,267075667346168022104096002⟩,⟨(-120624865537800596130939796),(-120624865537800596107367386)⟩⟩,⟨⟨268462129119461933659738689,268462129119461933687896492⟩,⟨(-116496881096985109354243277),(-116496881096985109331108074)⟩⟩,⟨⟨269778639566525846539085989,269778639566525846567012545⟩,⟨(-112423736330669063002892471),(-112423736330669062980168408)⟩⟩,⟨⟨271027281338744873067428107,271027281338744873095113684⟩,⟨(-108406904979382383055497765),(-108406904979382383033201986)⟩⟩,⟨⟨272210134288574851944631786,272210134288574851972092764⟩,⟨(-104447813111254698782742837),(-104447813111254698760841163)⟩⟩,⟨⟨273329273562449313467564698,273329273562449313494796046⟩,⟨(-100547839657004839906163839),(-100547839657004839884665279)⟩⟩,⟨⟨274386767711453095538172575,274386767711453095565186009⟩,⟨(-96708316984244238906007444),(-96708316984244238884885886)⟩⟩] +lemma kernel1_0_r0_12_eq : ∀ k : Fin 16, kernel1_0Expr 0 12 k = kernel1_0_r0_12 k := by decide +kernel +noncomputable def kernel1_0_r0_13 : Fin 16 → CBox := ![⟨⟨275384676821050635978798799,275384676821050636005584993⟩,⟨(-92930531509197055070688048),(-92930531509197055049963829)⟩⟩,⟨⟨276325050661121632114723016,276325050661121632141298362⟩,⟨(-89215724343897383188812735),(-89215724343897383168448355)⟩⟩,⟨⟨277209926857521066352326603,277209926857521066378687390⟩,⟨(-85565091976884103544179458),(-85565091976884103524183844)⟩⟩,⟨⟨278041329086344620590749587,278041329086344620616906579⟩,⟨(-81979786985376870006350316),(-81979786985376869986697398)⟩⟩,⟨⟨278821265292044315965763147,278821265292044315991710085⟩,⟨(-78460918776882515636410584),(-78460918776882515617117859)⟩⟩,⟨⟨279551725930502889878345932,279551725930502889904096456⟩,⟨(-75009554358149873331552044),(-75009554358149873312584901)⟩⟩,⟨⟨280234682238139030592178846,280234682238139030617730520⟩,⟨(-71626719129362752090812992),(-71626719129362752072180398)⟩⟩,⟨⟨280872084528079200624328426,280872084528079200649691118⟩,⟨(-68313397701435663129997205),(-68313397701435663111673171)⟩⟩,⟨⟨281465860514395461888930796,281465860514395461914099090⟩,⟨(-65070534734254935731779239),(-65070534734254935713784276)⟩⟩,⟨⟨282017913665372534532321565,282017913665372534557308669⟩,⟨(-61899035793689177269841229),(-61899035793689177252137896)⟩⟩,⟨⟨282530121586731342142187381,282530121586731342166992090⟩,⟨(-58799768225177687279911865),(-58799768225177687262509231)⟩⟩,⟨⟨283004334435700580929203455,283004334435700580953834784⟩,⟨(-55773562041693498531446960),(-55773562041693498514319179)⟩⟩,⟨⟨283442373366792459678355959,283442373366792459702810939⟩,⟨(-52821210823869249986970978),(-52821210823869249970136369)⟩⟩,⟨⟨283846029010103748382604691,283846029010103748406894422⟩,⟨(-49943472630069152660831860),(-49943472630069152644255481)⟩⟩,⟨⟨284217059982928701491731652,284217059982928701515856082⟩,⟨(-47141070914188938858668199),(-47141070914188938842359280)⟩⟩,⟨⟨284557191435436338807069936,284557191435436338831037308⟩,⟨(-44414695448967930777964356),(-44414695448967930761897225)⟩⟩] +lemma kernel1_0_r0_13_eq : ∀ k : Fin 16, kernel1_0Expr 0 13 k = kernel1_0_r0_13 k := by decide +kernel +noncomputable def kernel1_0_r0_14 : Fin 16 → CBox := ![⟨⟨284868113631131022431207778,284868113631131022455015885⟩,⟨(-41765003252603261902999744),(-41765003252603261887196989)⟩⟩,⟨⟨285151480562782307920696832,285151480562782307944356428⟩,⟨(-39192619516465862945148301),(-39192619516465862929571096)⟩⟩,⟨⟨285408908604477714708743234,285408908604477714732255341⟩,⟨(-36698138531731104900567094),(-36698138531731104885224842)⟩⟩,⟨⟨285641975200420394389505870,285641975200420394412878025⟩,⟨(-34282124612753989271579507),(-34282124612753989256446771)⟩⟩,⟨⟨285852217591062711500881815,285852217591062711524114000⟩,⟨(-31945113015039496066286635),(-31945113015039496051382806)⟩⟩,⟨⟨286041131577136522301857699,286041131577136522324958790⟩,⟨(-29687610845683142410786128),(-29687610845683142396076013)⟩⟩,⟨⟨286210170322111471291980543,286210170322111471314952535⟩,⟨(-27510097964184958978546048),(-27510097964184958964039224)⟩⟩,⟨⟨286360743193583947642146701,286360743193583947664996518⟩,⟨(-25413027871571940274373239),(-25413027871571940260044540)⟩⟩,⟨⟨286494214644071475207537179,286494214644071475230265725⟩,⟨(-23396828585799542106517172),(-23396828585799542092389639)⟩⟩,⟨⟨286611903131660267359065806,286611903131660267381681394⟩,⟨(-21461903501441950952441796),(-21461903501441950938477036)⟩⟩,⟨⟨286715080080927474517488824,286715080080927474539994308⟩,⟨(-19608632231723592524728084),(-19608632231723592510935815)⟩⟩,⟨⟨286804968884534297028573300,286804968884534297050975071⟩,⟨(-17837371430990629346518587),(-17837371430990629332873953)⟩⟩,⟨⟨286882743945861633898330026,286882743945861633920630473⟩,⟨(-16148455595770959728976968),(-16148455595770959715500428)⟩⟩,⟨⟨286949529763036289931733860,286949529763036289953940075⟩,⟨(-14542197842624404928242546),(-14542197842624404914898733)⟩⟩,⟨⟨287006400054672967021838223,287006400054672967043953790⟩,⟨(-13018890661041280755908278),(-13018890661041280742707007)⟩⟩,⟨⟨287054376927635312804832216,287054376927635312826863090⟩,⟨(-11578806639707309521067852),(-11578806639707309507984601)⟩⟩] +lemma kernel1_0_r0_14_eq : ∀ k : Fin 16, kernel1_0Expr 0 14 k = kernel1_0_r0_14 k := by decide +kernel +noncomputable def kernel1_0_r0_15 : Fin 16 → CBox := ![⟨⟨287094430087098180818261085,287094430087098180840210389⟩,⟨(-10222199164515744681007282),(-10222199164515744668067199)⟩⟩,⟨⟨287127476089172956028193543,287127476089172956050067906⟩,⟨(-8949303086773552710032883),(-8949303086773552697196332)⟩⟩,⟨⟨287154377636338299727905596,287154377636338299749709195⟩,⟨(-7760335360117415316892481),(-7760335360117415304169267)⟩⟩,⟨⟨287175942915899946299236416,287175942915899946320974846⟩,⟨(-6655495644727063442303312),(-6655495644727063429669311)⟩⟩,⟨⟨287192924981685215565174289,287192924981685215586851643⟩,⟨(-5634966877497908202282432),(-5634966877497908189758949)⟩⟩,⟨⟨287206021179160659423039214,287206021179160659444661323⟩,⟨(-4698915806911961703740336),(-4698915806911961691291930)⟩⟩,⟨⟨287215872614144707823510286,287215872614144707845081760⟩,⟨(-3847493491425504161850720),(-3847493491425504149487117)⟩⟩,⟨⟨287223063665271281512246438,287223063665271281533772610⟩,⟨(-3080835760273708165972213),(-3080835760273708153669703)⟩⟩,⟨⟨287228121540345058873142100,287228121540345058894627562⟩,⟨(-2399063635676325236682554),(-2399063635676325224466328)⟩⟩,⟨⟨287231515876714380512339575,287231515876714380533789793⟩,⟨(-1802283715514417132381227),(-1802283715514417120212250)⟩⟩,⟨⟨287233658385773604108328111,287233658385773604129747979⟩,⟨(-1290588515635812403779403),(-1290588515635812391667182)⟩⟩,⟨⟨287234902541693037335245860,287234902541693037356640533⟩,⟨(-864056771036320155350507),(-864056771036320143271802)⟩⟩,⟨⟨287235543314461329964742973,287235543314461329986117397⟩,⟨(-522753695254565972055067),(-522753695254565960031600)⟩⟩,⟨⟨287235816947312347217855507,287235816947312347239214826⟩,⟨(-266731197410453516736614),(-266731197410453504733027)⟩⟩,⟨⟨287235900778596022981913201,287235900778596023003262437⟩,⟨(-96028056410519762899870),(-96028056410519750925333)⟩⟩,⟨⟨287235913108140450031226051,287235913108140450052570254⟩,⟨(-10670051937659421484038),(-10670051937659409515813)⟩⟩] +lemma kernel1_0_r0_15_eq : ∀ k : Fin 16, kernel1_0Expr 0 15 k = kernel1_0_r0_15 k := by decide +kernel +noncomputable def kernel1_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel1_0_r0_0,kernel1_0_r0_1,kernel1_0_r0_2,kernel1_0_r0_3,kernel1_0_r0_4,kernel1_0_r0_5,kernel1_0_r0_6,kernel1_0_r0_7,kernel1_0_r0_8,kernel1_0_r0_9,kernel1_0_r0_10,kernel1_0_r0_11,kernel1_0_r0_12,kernel1_0_r0_13,kernel1_0_r0_14,kernel1_0_r0_15] +lemma kernel1_0_r0_eq (i k : Fin 16) : kernel1_0Expr 0 i k = kernel1_0_r0 i k := by + fin_cases i + · exact kernel1_0_r0_0_eq k + · exact kernel1_0_r0_1_eq k + · exact kernel1_0_r0_2_eq k + · exact kernel1_0_r0_3_eq k + · exact kernel1_0_r0_4_eq k + · exact kernel1_0_r0_5_eq k + · exact kernel1_0_r0_6_eq k + · exact kernel1_0_r0_7_eq k + · exact kernel1_0_r0_8_eq k + · exact kernel1_0_r0_9_eq k + · exact kernel1_0_r0_10_eq k + · exact kernel1_0_r0_11_eq k + · exact kernel1_0_r0_12_eq k + · exact kernel1_0_r0_13_eq k + · exact kernel1_0_r0_14_eq k + · exact kernel1_0_r0_15_eq k +noncomputable def kernel1_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4099417340367007860369823350),(-4099417340367007858134774581)⟩,⟨15599733409278095898213309431,15599733409278095900482793907⟩⟩,⟨⟨(-4098955447566270771423916535),(-4098955447566270769189032699)⟩,⟨15596931738208354133453140127,15596931738208354135722462941⟩⟩,⟨⟨(-4098032132482365818971640963),(-4098032132482365816737091048)⟩,⟨15591330001048699089757791022,15591330001048699092026786478⟩⟩,⟨⟨(-4096648335171068213143232067),(-4096648335171068210909185054)⟩,⟨15582931406246498927421700812,15582931406246498929690203220⟩⟩,⟨⟨(-4094805463270212450448305328),(-4094805463270212448214930226)⟩,⟨15571740762693681657149372821,15571740762693681659417216456⟩⟩,⟨⟨(-4092505389071914282458976942),(-4092505389071914280226442759)⟩,⟨15557764475196259936028715464,15557764475196259938295734601⟩⟩,⟨⟨(-4089750445630870953869980539),(-4089750445630870951638456378)⟩,⟨15541010538441154006053148404,15541010538441154008319177212⟩⟩,⟨⟨(-4086543421918984545019177987),(-4086543421918984542788832868)⟩,⟨15521488529466704233209583338,15521488529466704235474456066⟩⟩,⟨⟨(-4082887557039058920109988657),(-4082887557039058917880991885)⟩,⟨15499209598644862631320480450,15499209598644862633584031051⟩⟩,⟨⟨(-4078786533512789640674956569),(-4078786533512789638447477093)⟩,⟨15474186459184650557020661146,15474186459184650559282723920⟩⟩,⟨⟨(-4074244469660691112876260479),(-4074244469660691110650467930)⟩,⟨15446433375168067252131336051,15446433375168067254391744606⟩⟩,⟨⟨(-4069265911093979175318824528),(-4069265911093979173094887679)⟩,⟨15415966148131230811698775462,15415966148131230813957364248⟩⟩,⟨⟨(-4063855821340743418614062860),(-4063855821340743416392151987)⟩,⟨15382802102205129094379704394,15382802102205129096636306351⟩⟩,⟨⟨(-4058019571630995034992248091),(-4058019571630995032772531511)⟩,⟨15346960067831952578640474919,15346960067831952580894924923⟩⟩,⟨⟨(-4051762929867356379528518127),(-4051762929867356377311166731)⟩,⟨15308460364074573591678150849,15308460364074573593930281196⟩⟩,⟨⟨(-4045092048810261334307309046),(-4045092048810261332092490694)⟩,⟨15267324779538325952249631092,15267324779538325954499277079⟩⟩] +lemma kernel1_0_r1_0_eq : ∀ k : Fin 16, kernel1_0Expr 1 0 k = kernel1_0_r1_0 k := by decide +kernel +noncomputable def kernel1_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4038013453508554868550765189),(-4038013453508554866338652148)⟩,⟨15223576551925824984360352755,15223576551925824986607345274⟩⟩,⟨⟨(-4030534028008309980241419470),(-4030534028008309978032178385)⟩,⟨15177240346247149034795318031,15177240346247149037039493548⟩⟩,⟨⟨(-4022661001374514838229303646),(-4022661001374514836023107595)⟩,⟨15128342231709278863495902216,15128342231709278865737090777⟩⟩,⟨⟨(-4014401933062017037119578215),(-4014401933062017034916593124)⟩,⟨15076909657310259206507565385,15076909657310259208745604126⟩⟩,⟨⟨(-4005764697673740334998016600),(-4005764697673740332798417965)⟩,⟨15022971426165105901677015670,15022971426165105903911732189⟩⟩,⟨⟨(-3996757469145707273054442606),(-3996757469145707270858393970)⟩,⟨14966557668592030509483805315,14966557668592030511715039072⟩⟩,⟨⟨(-3987388704399804201251899568),(-3987388704399804199059577349)⟩,⟨14907699813989090472424731608,14907699813989090474652309234⟩⟩,⟨⟨(-3977667126506509313514644731),(-3977667126506509311326211477)⟩,⟨14846430561532894477842541471,14846430561532894480066303364⟩⟩,⟨⟨(-3967601707400965535491316414),(-3967601707400965533306952649)⟩,⟨14782783849732497588103052751,14782783849732497590322821403⟩⟩,⟨⟨(-3957201650196815075491793509),(-3957201650196815073311657492)⟩,⟨14716794824873106473586949163,14716794824873106475802569182⟩⟩,⟨⟨(-3946476371143118087074017461),(-3946476371143118084898290234)⟩,⟨14648499808385679154917062384,14648499808385679157128355690⟩⟩,⟨⟨(-3935435481270451529148577069),(-3935435481270451526977416035)⟩,⟨14577936263179943295278192616,14577936263179943297485004607⟩⟩,⟨⟨(-3924088767772923673531028622),(-3924088767772923671364620581)⟩,⟨14505142758979769389854389282,14505142758979769392056536091⟩⟩,⟨⟨(-3912446175173342935920196220),(-3912446175173342933758692287)⟩,⟨14430158936701217138102422257,14430158936701217140299755470⟩⟩,⟨⟨(-3900517786319145346886196800),(-3900517786319145344729783988)⟩,⟨14353025471914921678987457805,14353025471914921681179793277⟩⟩,⟨⟨(-3888313803256912012412403855),(-3888313803256912010261232335)⟩,⟨14273784037435797916266809468,14273784037435797918453999655⟩⟩] +lemma kernel1_0_r1_1_eq : ∀ k : Fin 16, kernel1_0Expr 1 1 k = kernel1_0_r1_1 k := by decide +kernel +noncomputable def kernel1_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-3875844528033395748629797848),(-3875844528033395746484063519)⟩,⟨14192477265084312443560704161,14192477265084312445742556013⟩⟩,⟨⟨(-3863120343470924559872721134),(-3863120343470924557732564269)⟩,⟨14109148706664800080698141058,14109148706664800082874516801⟩⟩,⟨⟨(-3850151693964859051975295401),(-3850151693964859049840910382)⟩,⟨14023842794207482152577429652,14023842794207482154748137671⟩⟩,⟨⟨(-3836949066350451967149337811),(-3836949066350451965020865196)⟩,⟨13936604799521972710359507816,13936604799521972712524409977⟩⟩,⟨⟨(-3823522970885991971919418810),(-3823522970885991969797063881)⟩,⟨13847480793111133192508366417,13847480793111133194667260189⟩⟩,⟨⟨(-3809883922398512250118788106),(-3809883922398512248002678920)⟩,⟨13756517602495151798310836520,13756517602495151800463596119⟩⟩,⟨⟨(-3796042421637609417425904027),(-3796042421637609415316243669)⟩,⟨13663762769996677334862847317,13663762769996677337009272316⟩⟩,⟨⟨(-3782008936882052291490067745),(-3782008936882052289386984576)⟩,⟨13569264510038724743716770351,13569264510038724745856734579⟩⟩,⟨⟨(-3767793885842866067149622209),(-3767793885842866065053335189)⟩,⟨13473071666007887187886509457,13473071666007887190019796615⟩⟩,⟨⟨(-3753407617905458833463212242),(-3753407617905458831373831533)⟩,⟨13375233666736133806549628154,13375233666736133808676130080⟩⟩,⟨⟨(-3738860396752117922927321863),(-3738860396752117920845060547)⟩,⟨13275800482655139418892020705,13275800482655139421011526856⟩⟩,⟨⟨(-3724162383404847508868349268),(-3724162383404847506793320748)⟩,⟨13174822581677679070270133782,13174822581677679072382532681⟩⟩,⟨⟨(-3709323619727050769259253084),(-3709323619727050767191688391)⟩,⟨13072350884861122970805351710,13072350884861122972910414876⟩⟩,⟨⟨(-3694354012420984804604341659),(-3694354012420984802544333085)⟩,⟨12968436721908482826279372066,12968436721908482828377008911⟩⟩,⟨⟨(-3679263317556239695240273264),(-3679263317556239693188045036)⟩,⟨12863131786562785713931442770,12863131786562785716021431485⟩⟩,⟨⟨(-3664061125662720324555986027),(-3664061125662720322511633744)⟩,⟨12756488091950783606430867233,12756488091950783608513113840⟩⟩] +lemma kernel1_0_r1_2_eq : ∀ k : Fin 16, kernel1_0Expr 1 2 k = kernel1_0_r1_2 k := by decide +kernel +noncomputable def kernel1_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-3648756847419746929894672784),(-3648756847419746927858446333)⟩,⟨12648557925932142697573344471,12648557925932142699647601551⟩⟩,⟨⟨(-3633359699970944138441716993),(-3633359699970944136413682179)⟩,⟨12539393806510294362781372932,12539393806510294364847576020⟩⟩,⟨⟨(-3617878693892565161289753030),(-3617878693892565159270146195)⟩,⟨12429048437361066674581830751,12429048437361066676639745789⟩⟩,⟨⟨(-3602322620840804785998061051),(-3602322620840804783986957114)⟩,⟨12317574663535049934587844019,12317574663535049936637397372⟩⟩,⟨⟨(-3586700041901499003471998393),(-3586700041901499001469660473)⟩,⟨12205025427389380013047118313,12205025427389380015088049197⟩⟩,⟨⟨(-3571019276663397926421996482),(-3571019276663397924428467575)⟩,⟨12091453724804248043486143877,12091453724804248045518410274⟩⟩,⟨⟨(-3555288393033939694762105810),(-3555288393033939692777635169)⟩,⟨11976912561738963163382205886,11976912561738963165405560686⟩⟩,⟨⟨(-3539515197814154073738324201),(-3539515197814154071762963230)⟩,⟨11861454911181805818315198389,11861454911181805820329591093⟩⟩,⟨⟨(-3523707228046993324500854331),(-3523707228046993322534889202)⟩,⟨11745133670547212302536953627,11745133670547212304542100311⟩⟩,⟨⟨(-3507871743151032660660791978),(-3507871743151032658704230896)⟩,⟨11628001619573026700601028129,11628001619573026702596921111⟩⟩,⟨⟨(-3492015717849111268594363894),(-3492015717849111266647469577)⟩,⟨11510111378769644601362381450,11510111378769644603348759997⟩⟩,⟨⟨(-3476145835899105576739753641),(-3476145835899105574802551279)⟩,⟨11391515368471854635629872286,11391515368471854637606711704⟩⟩,⟨⟨(-3460268484631647332758797031),(-3460268484631647330831586527)⟩,⟨11272265768543060186265325830,11272265768543060188232328298⟩⟩,⟨⟨(-3444389750297228187527381446),(-3444389750297228185610143395)⟩,⟨11152414478780336068821896001,11152414478780336070779081015⟩⟩,⟨⟨(-3428515414222777936305624327),(-3428515414222777934398635240)⟩,⟨11032013080067445508343664141,11032013080067445510290757005⟩⟩,⟨⟨(-3412650949775473286636745563),(-3412650949775473284740001861)⟩,⟨10911112796321513662239306210,10911112796321513664176310542⟩⟩] +lemma kernel1_0_r1_3_eq : ∀ k : Fin 16, kernel1_0Expr 1 3 k = kernel1_0_r1_3 k := by decide +kernel +noncomputable def kernel1_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-3396801520129235844895280089),(-3396801520129235843009110139)⟩,⟨10789764457277527968668376886,10789764457277527970594966323⟩⟩,⟨⟨(-3380971976827119620771146823),(-3380971976827119618895486589)⟩,⟨10668018462153215828560964005,10668018462153215830477202104⟩⟩,⟨⟨(-3365166859130577237550080002),(-3365166859130577235685219840)⟩,⟨10545924744235140030040305597,10545924744235140031945903633⟩⟩,⟨⟨(-3349390394144437485183117657),(-3349390394144437483329022973)⟩,⟨10423532736425055739410649585,10423532736425055741305641697⟩⟩,⟨⟨(-3333646497704331894721800408),(-3333646497704331892878810424)⟩,⟨10300891337783694014805149734,10300891337783694016689198498⟩⟩,⟨⟨(-3317938776011281401744813776),(-3317938776011281399912835338)⟩,⟨10178048881107180194608199516,10178048881107180196481397109⟩⟩,⟨⟨(-3302270527996202352618000703),(-3302270527996202350797337858)⟩,⟨10055053101569266050981439796,10055053101569266052843483600⟩⟩,⟨⟨(-3286644748395220208290093254),(-3286644748395220206480678401)⟩,⟨9931951106460457470498464325,9931951106460457472349420958⟩⟩,⟨⟨(-3271064131514895075478780381),(-3271064131514895073680983228)⟩,⟨9808789346052960114286030003,9808789346052960116125531456⟩⟩,⟨⟨(-3255531075664771022601808527),(-3255531075664771020815484937)⟩,⟨9685613585618149777213279444,9685613585618149779041468213⟩⟩,⟨⟨(-3240047688233065991952602110),(-3240047688233065990178069391)⟩,⟨9562468878621008017620623180,9562468878621008019437183171⟩⟩,⟨⟨(-3224615791379825550917053651),(-3224615791379825549154209591)⟩,⟨9439399541113653299333589352,9439399541113653301138621224⟩⟩,⟨⟨(-3209236928320475842008056167),(-3209236928320475840257279430)⟩,⟨9316449127347749809353627987,9316449127347749811146754532⟩⟩,⟨⟨(-3193912370171432544915785959),(-3193912370171432543176901146)⟩,⟨9193660406623196892934720238,9193660406623196894716114646⟩⟩,⟨⟨(-3178643123328256632867191815),(-3178643123328256631140528873)⟩,⟨9071075341388098431857581383,9071075341388098433626914692⟩⟩,⟨⟨(-3163429937345796886905379963),(-3163429937345796885190800821)⟩,⟨8948735066602590344966708843,8948735066602590346724116967⟩⟩] +lemma kernel1_0_r1_4_eq : ∀ k : Fin 16, kernel1_0Expr 1 4 k = kernel1_0_r1_4 k := by decide +kernel +noncomputable def kernel1_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-3148273313288825730133732481),(-3148273313288825728431651413)⟩,⟨8826679870376672659874010344,8826679870376672661619080386⟩⟩,⟨⟨(-3133173512520860666533950164),(-3133173512520860664844131890)⟩,⟨8704949175889757291591233691,8704949175889757293324197945⟩⟩,⟨⟨(-3118130565898169660840820661),(-3118130565898169659163606879)⟩,⟨8583581524597210789897683315,8583581524597210791618200820⟩⟩,⟨⟨(-3103144283335385879353000388),(-3103144283335385877688216416)⟩,⟨8462614560726749894585737544,8462614560726749896293980193⟩⟩,⟨⟨(-3088214263708705526891902098),(-3088214263708705525239963868)⟩,⟨8342085017065143736816969911,8342085017065143738512522846⟩⟩,⟨⟨(-3073339905062311765010300582),(-3073339905062311763370945603)⟩,⟨8222028702033296842757452997,8222028702033296844440575133⟩⟩,⟨⟨(-3058520415083457092077547495),(-3058520415083457090451128243)⟩,⟨8102480488045438525057512303,8102480488045438526727851641⟩⟩,⟨⟨(-3043754821811544835608151090),(-3043754821811544833994455850)⟩,⟨7983474301145833445871090938,7983474301145833447528855755⟩⟩,⟨⟨(-3029041984546575808410880562),(-3029041984546575806810360118)⟩,⟨7865043111914161594056303132,7865043111914161595701043631⟩⟩,⟨⟨(-3014380604922466512593198824),(-3014380604922466511005528773)⟩,⟨7747218927628499936619410793,7747218927628499938251446961⟩⟩,⟨⟨(-2999769238110997897259636290),(-2999769238110997895685178652)⟩,⟨7630032785672678655759866755,7630032785672678657378836785⟩⟩,⟨⟨(-2985206304122515521599114445),(-2985206304122515520037620631)⟩,⟨7513514748172687994307801645,7513514748172687995913950020⟩⟩,⟨⟨(-2970690099169969576281415485),(-2970690099169969574733334536)⟩,⟨7397693897844782855923410674,7397693897844782857516289007⟩⟩,⟨⟨(-2956218807063452722854236619),(-2956218807063452721319218160)⟩,⟨7282598335035976696030481797,7282598335035976697610435443⟩⟩,⟨⟨(-2941790510603060915856214159),(-2941790510603060914334628506)⟩,⟨7168255175935738829046703773,7168255175935738830613362353⟩⟩,⟨⟨(-2927403202938662736500690744),(-2927403202938662734992252900)⟩,⟨7054690551935914660817193190,7054690551935914662370836929⟩⟩] +lemma kernel1_0_r1_5_eq : ∀ k : Fin 16, kernel1_0Expr 1 5 k = kernel1_0_r1_5 k := by decide +kernel +noncomputable def kernel1_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-2913054798866011445769619052),(-2913054798866011444274818757)⟩,⟨6941929610114180767873614614,6941929610114180769413754404⟩⟩,⟨⟨(-2898743146029565837517387123),(-2898743146029565836035804603)⟩,⟨6829996514814730048472056303,6829996514814730049999105973⟩⟩,⟨⟨(-2884466036003395669896017113),(-2884466036003395668428029530)⟩,⟨6718914450298359837476255619,6718914450298359838989837683⟩⟩,⟨⟨(-2870221215222629389803152264),(-2870221215222629388348439241)⟩,⟨6608705624432710981306055803,6608705624432710982806485190⟩⟩,⟨⟨(-2856006395739050267018149524),(-2856006395739050265577187517)⟩,⟨6499391273392081074543709842,6499391273392081076030510347⟩⟩,⟨⟨(-2841819265775655993801886548),(-2841819265775655992374240585)⟩,⟨6390991667335012614250463129,6390991667335012615724063240⟩⟩,⟨⟨(-2827657500056260229643205896),(-2827657500056260228229258616)⟩,⟨6283526117026738558659784598,6283526117026738560119801094⟩⟩,⟨⟨(-2813518769887526335175574954),(-2813518769887526333774971879)⟩,⟨6177012981372555087402063987,6177012981372555088848845249⟩⟩,⟨⟨(-2799400752972177439085231521),(-2799400752972177437698485551)⟩,⟨6071469675827285231343808665,6071469675827285232776842042⟩⟩,⟨⟨(-2785301142933516783020790308),(-2785301142933516781647401149)⟩,⟨5966912681645198030986174859,5966912681645198032405953270⟩⟩,⟨⟨(-2771217658532811759563217626),(-2771217658532811758203571849)⟩,⟨5863357555934056136338784067,5863357555934056137744920117⟩⟩,⟨⟨(-2757148052562537996615437180),(-2757148052562537995269148017)⟩,⟨5760818942476380011647304918,5760818942476380013040178652⟩⟩,⟨⟨(-2743090120399940108554584186),(-2743090120399940107222148878)⟩,⟨5659310583280538487962541356,5659310583280538489341655431⟩⟩,⟨⟨(-2729041708206837280188734351),(-2729041708206837278869640303)⟩,⟨5558845330823902257873615122,5558845330823902259239474272⟩⟩,⟨⟨(-2715000720763078740554693263),(-2715000720763078739249329598)⟩,⟨5459435160950027595306970118,5459435160950027596659184182⟩⟩,⟨⟨(-2700965128922530629114294014),(-2700965128922530627822243637)⟩,⟨5361091186381670311943011661,5361091186381670313281990422⟩⟩] +lemma kernel1_0_r1_6_eq : ∀ k : Fin 16, kernel1_0Expr 1 6 k = kernel1_0_r1_6 k := by decide +kernel +noncomputable def kernel1_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-2686932976681946133044683389),(-2686932976681946131766486118)⟩,⟨5263823670811362587149841215,5263823670811362588475044887⟩⟩,⟨⟨(-2672902387854529647139081780),(-2672902387854529645874154635)⟩,⟨5167642043531315358381031357,5167642043531315359693034161⟩⟩,⟨⟨(-2658871572341447854369573242),(-2658871572341447853118306354)⟩,⟨5072554914564533652536216209,5072554914564533653834626787⟩⟩,⟨⟨(-2644838831995961053114829489),(-2644838831995961051876777895)⟩,⟨4978570090259248505648205639,4978570090259248506933461108⟩⟩,⟨⟨(-2630802566076242022197550683),(-2630802566076242020973225358)⟩,⟨4885694589309073621006776112,4885694589309073622278365157⟩⟩,⟨⟨(-2616761276284312737051710053),(-2616761276284312735840530820)⟩,⟨4793934659161684071976776285,4793934659161684073235270023⟩⟩,⟨⟨(-2602713571389857127022057153),(-2602713571389857125824413892)⟩,⟨4703295792779284361225512039,4703295792779284362470519220⟩⟩,⟨⟨(-2588658171438956882179578689),(-2588658171438956880995001022)⟩,⟨4613782745714680000674221464,4613782745714680001906204141⟩⟩,⟨⟨(-2574593911549043464633260894),(-2574593911549043463462296224)⟩,⟨4525399553467386300433724886,4525399553467386301652135520⟩⟩,⟨⟨(-2560519745292559648083165671),(-2560519745292559646925171980)⟩,⟨4438149549084895925061264877,4438149549084895926266735654⟩⟩,⟨⟨(-2546434747672975107315928798),(-2546434747672975106171294299)⟩,⟨4352035380974978541857114769,4352035380974978543049256009⟩⟩,⟨⟨(-2532338117697900130770227218),(-2532338117697900129638458984)⟩,⟨4267059030895696998408186361,4267059030895696999587482259⟩⟩,⟨⟨(-2518229180555087077494455856),(-2518229180555087076376071716)⟩,⟨4183221832090690299144770336,4183221832090690300310702657⟩⟩,⟨⟨(-2504107389398098707519381307),(-2504107389398098706413745674)⟩,⟨4100524487538189525083884641,4100524487538189526237078969⟩⟩,⟨⟨(-2489972326749354262148367547),(-2489972326749354261055865874)⟩,⟨4018967088283194050455913216,4018967088283194051595982587⟩⟩,⟨⟨(-2475823705529136752633630258),(-2475823705529136751553276076)⟩,⟨3938549131823237241826653237,3938549131823237242954415951⟩⟩] +lemma kernel1_0_r1_7_eq : ∀ k : Fin 16, kernel1_0Expr 1 7 k = kernel1_0_r1_7 k := by decide +kernel +noncomputable def kernel1_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-2461661369719957236032566496),(-2461661369719957234963052519)⟩,⟨3859269540519208583202004874,3859269540519208584318134095⟩⟩,⟨⟨(-2447485294676423122475394867),(-2447485294676423121416063561)⟩,⟨3781126680003768195189111100,3781126680003768196294259518⟩⟩,⟨⟨(-2433295587091447270004475385),(-2433295587091447268955754194)⟩,⟨3704118377560985405957193785,3704118377560985407050938398⟩⟩,⟨⟨(-2419092484630262568437657126),(-2419092484630262567399062197)⟩,⟨3628241940451950861382750492,3628241940451950862465572440⟩⟩,⟨⟨(-2404876355244272954024946371),(-2404876355244272952997042243)⟩,⟨3553494174162247200935288787,3553494174162247202006629537⟩⟩,⟨⟨(-2390647696177276656872662933),(-2390647696177276655854817166)⟩,⟨3479871400548312255400644325,3479871400548312256461133074⟩⟩,⟨⟨(-2376407132677041538490517481),(-2376407132677041537483152773)⟩,⟨3407369475860886850220777936,3407369475860886851269997333⟩⟩,⟨⟨(-2362155416425596439722608639),(-2362155416425596438725226563)⟩,⟨3335983808624902572723776942,3335983808624902573762223891⟩⟩,⟨⟨(-2347893423701927564649710028),(-2347893423701927563662911137)⟩,⟨3265709377356329385456646217,3265709377356329386483727290⟩⟩,⟨⟨(-2333622153291036316604414075),(-2333622153291036315627510709)⟩,⟨3196540748097665008981675758,3196540748097665009998076287⟩⟩,⟨⟨(-2319342724153526113270134689),(-2319342724153526112303543392)⟩,⟨3128472091754903999071873083,3128472091754904000077182699⟩⟩,⟨⟨(-2305056372870042150725233301),(-2305056372870042149768443751)⟩,⟨3061497201219971032294294158,3061497201219971033289022823⟩⟩,⟨⟨(-2290764450874991633457284017),(-2290764450874991632510855433)⟩,⟨2995609508263736908932036316,2995609508263736909915632394⟩⟩,⟨⟨(-2276468421494024555553389598),(-2276468421494024554616658672)⟩,⟨2930802100185854198492574361,2930802100185854199465700309⟩⟩,⟨⟨(-2262169856799758752249168461),(-2262169856799758751322544608)⟩,⟨2867067736208749507941979181,2867067736208749508904232500⟩⟩,⟨⟨(-2247870434300189797741539264),(-2247870434300189796824502650)⟩,⟨2804398863604188468356114708,2804398863604188469308015987⟩⟩] +lemma kernel1_0_r1_8_eq : ∀ k : Fin 16, kernel1_0Expr 1 8 k = kernel1_0_r1_8 k := by decide +kernel +noncomputable def kernel1_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-2233571933474138657511277437),(-2233571933474138656604431558)⟩,⟨2742787633541885341016796219,2742787633541885341957750527⟩⟩,⟨⟨(-2219276232167960144722932579),(-2219276232167960143825553312)⟩,⟨2682225916650659475779733159,2682225916650659476710464566⟩⟩,⟨⟨(-2204985302867565578786400387),(-2204985302867565577898888881)⟩,⟨2622705318283643756909045983,2622705318283643757829160907⟩⟩,⟨⟨(-2190701208859606048288935104),(-2190701208859606047410764660)⟩,⟨2564217193480023894275453069,2564217193480023895185480030⟩⟩,⟨⟨(-2176426100295420824136794278),(-2176426100295420823268512911)⟩,⟨2506752661616730414024549952,2506752661616730414923949721⟩⟩,⟨⟨(-2162162210171081257688952800),(-2162162210171081256829878066)⟩,⟨2450302620744416125335761552,2450302620744416126225217939⟩⟩,⟨⟨(-2147911850236556447106946547),(-2147911850236556446257470723)⟩,⟨2394857761602929537032488232,2394857761602929537911617086⟩⟩,⟨⟨(-2133677406846695573362212309),(-2133677406846695572521804018)⟩,⟨2340408581312338207927490732,2340408581312338208796826243⟩⟩,⟨⟨(-2119461336766365589570698642),(-2119461336766365588739940534)⟩,⟨2286945396736364560620322068,2286945396736364561479291055⟩⟩,⟨⟨(-2105266162941704360929764227),(-2105266162941704360107925942)⟩,⟨2234458357515869670214110592,2234458357515869671063445558⟩⟩,⟨⟨(-2091094470249050827402156830),(-2091094470249050826589620972)⟩,⟨2182937458770757527862152601,2182937458770757528701479521⟩⟩,⟨⟨(-2076948901232697680579126693),(-2076948901232697679775359632)⟩,⟨2132372553469373007556487145,2132372553469373008386343385⟩⟩,⟨⟨(-2062832151842180737271721274),(-2062832151842180736477255473)⟩,⟨2082753364465131121237321598,2082753364465131122057184262⟩⟩,⟨⟨(-2048746967179374919373892775),(-2048746967179374918588037442)⟩,⟨2034069496200743166212289451,2034069496200743167022852670⟩⟩,⟨⟨(-2034696137265211705717935237),(-2034696137265211704941062980)⟩,⟨1986310446080997221596327810,1986310446080997222397227911⟩⟩,⟨⟨(-2020682492835369223560609772),(-2020682492835369222792186662)⟩,⟨1939465615515606436819556150,1939465615515606437611331639⟩⟩] +lemma kernel1_0_r1_9_eq : ∀ k : Fin 16, kernel1_0Expr 1 9 k = kernel1_0_r1_9 k := by decide +kernel +noncomputable def kernel1_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-2006708901173815829051009511),(-2006708901173815828291614457)⟩,⟨1893524320634159094394457212,1893524320634159095176539235⟩⟩,⟨⟨(-1992778261992613034665007221),(-1992778261992613033913892815)⟩,⟨1848475802675690050194350945,1848475802675690050967490850⟩⟩,⟨⟨(-1978893503365905833133997428),(-1978893503365905832391525728)⟩,⟨1804309238055844487557780409,1804309238055844488321625330⟩⟩,⟨⟨(-1965057577725549603777080564),(-1965057577725549603042719528)⟩,⟨1761013748115022688209518950,1761013748115022688964606255⟩⟩,⟨⟨(-1951273457925344533473225886),(-1951273457925344532747489387)⟩,⟨1718578408551279527612365531,1718578408551279528358191278⟩⟩,⟨⟨(-1937544133380372407549551225),(-1937544133380372406831749684)⟩,⟨1676992258542105522767981444,1676992258542105523505240205⟩⟩,⟨⟨(-1923872606287458192597129657),(-1923872606287458191887614585)⟩,⟨1636244309559538439533241584,1636244309559538440261591195⟩⟩,⟨⟨(-1910261887932311410587667889),(-1910261887932311409885910682)⟩,⟨1596323553883346703304700435,1596323553883346704024675493⟩⟩,⟨⟨(-1896714995088441158285331879),(-1896714995088441157591880967)⟩,⟨1557218972817289198783007883,1557218972817289199494070075⟩⟩,⟨⟨(-1883234946512484924991702296),(-1883234946512484924305826666)⟩,⟨1518919544613691578805188020,1518919544613691579508073881⟩⟩,⟨⟨(-1869824759540146173606559794),(-1869824759540146172928600154)⟩,⟨1481414252111788048907353654,1481414252111788049601731895⟩⟩,⟨⟨(-1856487446786499946399616561),(-1856487446786499945729049523)⟩,⟨1444692090095460898414499630,1444692090095460899100900193⟩⟩,⟨⟨(-1843226012954000414069667242),(-1843226012954000413406986534)⟩,⟨1408742072376168973933376621,1408742072376168974611315677⟩⟩,⟨⟨(-1830043451751110088218011875),(-1830043451751110087562536875)⟩,⟨1373553238606992012243805692,1373553238606992012913970161⟩⟩,⟨⟨(-1816942742924068056525667012),(-1816942742924068055877727795)⟩,⟨1339114660833831447573962041,1339114660833831448236031242⟩⟩,⟨⟨(-1803926849403924682763991384),(-1803926849403924682123071014)⟩,⟨1305415449789901163662120654,1305415449789901164316618561⟩⟩] +lemma kernel1_0_r1_10_eq : ∀ k : Fin 16, kernel1_0Expr 1 10 k = kernel1_0_r1_10 k := by decide +kernel +noncomputable def kernel1_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-1790998714570593262072063616),(-1790998714570593261438701715)⟩,⟨1272444760939714849059857369,1272444760939714849706254244⟩⟩,⟨⟨(-1778161259635305576849395180),(-1778161259635305576222861082)⟩,⟨1240191800278831299493933382,1240191800278831300132966561⟩⟩,⟨⟨(-1765417381142508523943468054),(-1765417381142508523324081109)⟩,⟨1208645829895656343661212841,1208645829895656344292572264⟩⟩,⟨⟨(-1752769948591903269980915608),(-1752769948591903269368166769)⟩,⟨1177796173301621179307991173,1177796173301621179932193313⟩⟩,⟨⟨(-1740221802181006959287781880),(-1740221802181006958682144200)⟩,⟨1147632220536062902960315555,1147632220536062903576896875⟩⟩,⟨⟨(-1727775750668310002786226914),(-1727775750668310002187034772)⟩,⟨1118143433052124981147719227,1118143433052124981757352602⟩⟩,⟨⟨(-1715434569356809509464689763),(-1715434569356809508872252173)⟩,⟨1089319348389974396455723162,1089319348389974397058108689⟩⟩,⟨⟨(-1703200998197421519652570024),(-1703200998197421519066386620)⟩,⟨1061149584643599229612616153,1061149584643599230208261928⟩⟩,⟨⟨(-1691077740011511342491578636),(-1691077740011511341912158276)⟩,⟨1033623844727406496768776728,1033623844727406497357183169⟩⟩,⟨⟨(-1679067458831532419930051791),(-1679067458831532419356691475)⟩,⟨1006731920448786101086598898,1006731920448786101668476540⟩⟩,⟨⟨(-1667172778358529621308378170),(-1667172778358529620741376656)⟩,⟨980463696392743694574666653,980463696392743695149725611⟩⟩,⟨⟨(-1655396280535042559061613817),(-1655396280535042558500480448)⟩,⟨954809153624633956055170779,954809153624633956623909655⟩⟩,⟨⟨(-1643740504231738211520113759),(-1643740504231738210965301486)⟩,⟨929758373216947111274654916,929758373216947111836629614⟩⟩,⟨⟨(-1632207944045909612808046850),(-1632207944045909612258909093)⟩,⟨905301539606016248292522844,905301539606016248848387823⟩⟩,⟨⟨(-1620801049209798360566739250),(-1620801049209798360023564989)⟩,⟨881428943784421871898173650,881428943784421872447648501⟩⟩,⟨⟨(-1609522222606532910060644132),(-1609522222606532909522952873)⟩,⟨858130986334773910627586687,858130986334773911171159998⟩⟩] +lemma kernel1_0_r1_11_eq : ∀ k : Fin 16, kernel1_0Expr 1 11 k = kernel1_0_r1_11 k := by decide +kernel +noncomputable def kernel1_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-1598373819891321753856149119),(-1598373819891321753324444689)⟩,⟨835398180310450714193037114,835398180310450714730213514⟩⟩,⟨⟨(-1587358148715400294097899583),(-1587358148715400293571484759)⟩,⟨813221153968770092531152031,813221153968770093062636798⟩⟩,⟨⟨(-1576477468050102145315732685),(-1576477468050102144794886777)⟩,⟨791590653361959745115829152,791590653361959745641351206⟩⟩,⟨⟨(-1565733987608309390125485126),(-1565733987608309389609738549)⟩,⟨770497544791184066100345759,770497544791184066620382851⟩⟩,⟨⟨(-1555129867360431565625498377),(-1555129867360431565115285166)⟩,⟨749932817128771804187398934,749932817128771804701525021⟩⟩,⟨⟨(-1544667217141969492068112211),(-1544667217141969491562807244)⟩,⟨729887584013674884953919538,729887584013674885462767956⟩⟩,⟨⟨(-1534348096349637066823502654),(-1534348096349637066323376174)⟩,⟨710353085925073310135248861,710353085925073310638557212⟩⟩,⟨⟨(-1524174513722941429548130249),(-1524174513722941429052723653)⟩,⟨691320692138924839787072668,691320692138924840285307745⟩⟩,⟨⟨(-1514148427208059048942755860),(-1514148427208059048452541466)⟩,⟨672781902572141511627251839,672781902572141512119948784⟩⟩,⟨⟨(-1504271743900791876148017872),(-1504271743900791875662334087)⟩,⟨654728349518958296215255261,654728349518958296703083997⟩⟩,⟨⟨(-1494546320065343343333097509),(-1494546320065343342852205703)⟩,⟨637151799283942634171908395,637151799283942634654614993⟩⟩,⟨⟨(-1484973961225618248947200461),(-1484973961225618248470653391)⟩,⟨620044153715977528942352043,620044153715977529420391892⟩⟩,⟨⟨(-1475556422325723057153670175),(-1475556422325723056681884872)⟩,⟨603397451647435523208227393,603397451647435523681190465⟩⟩,⟨⟨(-1466295407956323446640932661),(-1466295407956323446173306087)⟩,⟨587203870242646488679227394,587203870242646489147725049⟩⟩,⟨⟨(-1457192572643503677534900188),(-1457192572643503677071685410)⟩,⟨571455726259648901207197141,571455726259648901670983327⟩⟩,⟨⟨(-1448249521196767115821600375),(-1448249521196767115362361366)⟩,⟨556145477229102324605542173,556145477229102325065060985⟩⟩] +lemma kernel1_0_r1_12_eq : ∀ k : Fin 16, kernel1_0Expr 1 12 k = kernel1_0_r1_12 k := by decide +kernel +noncomputable def kernel1_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-1439467809112818681636076805),(-1439467809112818681181282488)⟩,⟨541265722554128332603688577,541265722554128333058477472⟩⟩,⟨⟨(-1430848943031777698982823008),(-1430848943031777698531821090)⟩,⟨526809204534738182360878762,526809204534738182811598439⟩⟩,⟨⟨(-1422394381242483257333080379),(-1422394381242483256886115778)⟩,⟨512768809320398317852477279,512768809320398318298889416⟩⟩,⟨⟨(-1414105534233573397775311929),(-1414105534233573397331960027)⟩,⟨499137567794179310958978249,499137567794179311401515408⟩⟩,⟨⟨(-1405983765287043866243422910),(-1405983765287043865804085863)⟩,⟨485908656391830208355263233,485908656391830208793529247⟩⟩,⟨⟨(-1398030391111021503345196335),(-1398030391111021502909292609)⟩,⟨473075397859018492937996753,473075397859018493372581406⟩⟩,⟨⟨(-1390246682508521245392249420),(-1390246682508521244960016376)⟩,⟨460631261949876024202755188,460631261949876024633427287⟩⟩,⟨⟨(-1382633865078993887227638757),(-1382633865078993886798662771)⟩,⟨448569866069893413432375602,448569866069893413859556570⟩⟩,⟨⟨(-1375193119949513909089526117),(-1375193119949513908664251370)⟩,⟨436884975866109325049908723,436884975866109325473159728⟩⟩,⟨⟨(-1367925584532502514021635259),(-1367925584532502513599441424)⟩,⟨425570505767447171776004459,425570505767447172195954136⟩⟩,⟨⟨(-1360832353306930288341893147),(-1360832353306930287923010186)⟩,⟨414620519477959574895030374,414620519477959575311454522⟩⟩,⟨⟨(-1353914478619996326855511354),(-1353914478619996326439536614)⟩,⟨404029230425650769260351389,404029230425650769673660291⟩⟩,⟨⟨(-1347172971506336010394791160),(-1347172971506336009982114447)⟩,⟨393791002169458814886413804,393791002169458815296222670⟩⟩,⟨⟨(-1340608802521867651673175520),(-1340608802521867651263234940)⟩,⟨383900348766892995018020200,383900348766892995424898996⟩⟩,⟨⟨(-1334222902589448714044879865),(-1334222902589448713637898482)⟩,⟨374351935104737090220389332,374351935104737090624120368⟩⟩,⟨⟨(-1328016163853575046205904410),(-1328016163853575045801490035)⟩,⟨365140577195146269595230389,365140577195146269996213303⟩⟩] +lemma kernel1_0_r1_13_eq : ∀ k : Fin 16, kernel1_0Expr 1 13 k = kernel1_0_r1_13 k := by decide +kernel +noncomputable def kernel1_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-1321989440541421365352519813),(-1321989440541421364951121907)⟩,⟨356261242439384079537783002,356261242439384079935572657⟩⟩,⟨⟨(-1316143549827587874559618704),(-1316143549827587874160618967)⟩,⟨347709049861366379452666526,347709049861366379847889429⟩⟩,⟨⟨(-1310479272699986240964749177),(-1310479272699986240568363787)⟩,⟨339479270313101011516347175,339479270313101011908792158⟩⟩,⟨⟨(-1304997354824368024568478512),(-1304997354824368024174325702)⟩,⟨331567326654035434375835513,331567326654035434765891609⟩⟩,⟨⟨(-1299698507405069878425248842),(-1299698507405069878033708495)⟩,⟨323968793906249433388929796,323968793906249433776221279⟩⟩,⟨⟨(-1294583408039622295458092923),(-1294583408039622295068620320)⟩,⟨316679399387356276092757689,316679399387356276477837131⟩⟩,⟨⟨(-1289652701564942220727040831),(-1289652701564942220339845731)⟩,⟨309695022822903243890561841,309695022822903244273224167⟩⟩,⟨⟨(-1284907000892904356113901350),(-1284907000892904355728611781)⟩,⟨303011696439991271998651518,303011696439991272379275787⟩⟩,⟨⟨(-1280346887833161341671051548),(-1280346887833161341288094605)⟩,⟨296625605043763402322496941,296625605043763402700659614⟩⟩,⟨⟨(-1275972913901159098000720824),(-1275972913901159097619507742)⟩,⟨290533086078342831444161443,290533086078342831820459257⟩⟩,⟨⟨(-1271785601109370359182080567),(-1271785601109370358802814669)⟩,⟨284730629673733452637774972,284730629673733453012008998⟩⟩,⟨⟨(-1267785442739846726499637129),(-1267785442739846726121956102)⟩,⟨279214878680128882249420494,279214878680128882621959963⟩⟩,⟨⟨(-1263972904096267347899590332),(-1263972904096267347523866759)⟩,⟨273982628691009963936844306,273982628691009964307320093⟩⟩,⟨⟨(-1260348423233740502706256557),(-1260348423233740502331959664)⟩,⟨269030828056345597826675283,269030828056345598195625807⟩⟩,⟨⟨(-1256912411664692878746185188),(-1256912411664692878373512157)⟩,⟨264356577887147386278356365,264356577887147386645588596⟩⟩,⟨⟨(-1253665255039260109653560700),(-1253665255039260109282158340)⟩,⟨259957132052564966269904236,259957132052564966635778128⟩⟩] +lemma kernel1_0_r1_14_eq : ∀ k : Fin 16, kernel1_0Expr 1 14 k = kernel1_0_r1_14 k := by decide +kernel +noncomputable def kernel1_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-1250607313798671140144706459),(-1250607313798671139775011482)⟩,⟨255829897170645955338920492,255829897170645955703002190⟩⟩,⟨⟨(-1247738923800198159047518844),(-1247738923800198158678939120)⟩,⟨251972432593822120592809870,251972432593822120955699380⟩⟩,⟨⟨(-1245060396912323142129698493),(-1245060396912323141762424835)⟩,⟨248382450390121638039057845,248382450390121638400568326⟩⟩,⟨⟨(-1242572021578851443092271434),(-1242572021578851442725959780)⟩,⟨245057815321046094140787918,245057815321046094501270050⟩⟩,⟨⟨(-1240274063350782330282122197),(-1240274063350782329917140118)⟩,⟨241996544816990147306295829,241996544816990147665385013⟩⟩,⟨⟨(-1238166765384825862392815047),(-1238166765384825862028642536)⟩,⟨239196808951021470456925795,239196808951021470815149511⟩⟩,⟨⟨(-1236250348907535006665526306),(-1236250348907535006302348002)⟩,⟨236656930411778695782084116,236656930411778696139261558⟩⟩,⟨⟨(-1234525013644101410074475720),(-1234525013644101409711956205)⟩,⟨234375384476185540339129059,234375384476185540695602149⟩⟩,⟨⟨(-1232990938210942723586578421),(-1232990938210942723225139506)⟩,⟨232350798982620069611189893,232350798982620069966539341⟩⟩,⟨⟨(-1231648280471288841297519568),(-1231648280471288840936589412)⟩,⟨230581954305119120800853959,230581954305119121155659317⟩⟩,⟨⟨(-1230497177853053842619360628),(-1230497177853053842259117335)⟩,⟨229067783329139225866493211,229067783329139226220580129⟩⟩,⟨⟨(-1229537747628359812239648091),(-1229537747628359811879765021)⟩,⟨227807371429336915191534127,227807371429336915545235650⟩⟩,⟨⟨(-1228770087154158057271495291),(-1228770087154158056912337237)⟩,⟨226799956449773017186448596,226799956449773017539402658⟩⟩,⟨⟨(-1228194274073472544219628117),(-1228194274073472543860682608)⟩,⟨226044928686887469359541595,226044928686887469712268043⟩⟩,⟨⟨(-1227810366476869642334298761),(-1227810366476869641975737315)⟩,⟨225541830875533196212428451,225541830875533196564759505⟩⟩,⟨⟨(-1227618403023837488628989497),(-1227618403023837488270494043)⟩,⟨225290358178299763568824008,225290358178299763921084075⟩⟩] +lemma kernel1_0_r1_15_eq : ∀ k : Fin 16, kernel1_0Expr 1 15 k = kernel1_0_r1_15 k := by decide +kernel +noncomputable def kernel1_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel1_0_r1_0,kernel1_0_r1_1,kernel1_0_r1_2,kernel1_0_r1_3,kernel1_0_r1_4,kernel1_0_r1_5,kernel1_0_r1_6,kernel1_0_r1_7,kernel1_0_r1_8,kernel1_0_r1_9,kernel1_0_r1_10,kernel1_0_r1_11,kernel1_0_r1_12,kernel1_0_r1_13,kernel1_0_r1_14,kernel1_0_r1_15] +lemma kernel1_0_r1_eq (i k : Fin 16) : kernel1_0Expr 1 i k = kernel1_0_r1 i k := by + fin_cases i + · exact kernel1_0_r1_0_eq k + · exact kernel1_0_r1_1_eq k + · exact kernel1_0_r1_2_eq k + · exact kernel1_0_r1_3_eq k + · exact kernel1_0_r1_4_eq k + · exact kernel1_0_r1_5_eq k + · exact kernel1_0_r1_6_eq k + · exact kernel1_0_r1_7_eq k + · exact kernel1_0_r1_8_eq k + · exact kernel1_0_r1_9_eq k + · exact kernel1_0_r1_10_eq k + · exact kernel1_0_r1_11_eq k + · exact kernel1_0_r1_12_eq k + · exact kernel1_0_r1_13_eq k + · exact kernel1_0_r1_14_eq k + · exact kernel1_0_r1_15_eq k +noncomputable def kernel1_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-51035305542180368933959228947),(-51035305542180368921987178142)⟩,⟨93384299769814617372030433896,93384299769814617383695562259⟩⟩,⟨⟨(-51025931920881972224189598936),(-51025931920881972212217748126)⟩,⟨93376109085676836344519262932,93376109085676836356184271300⟩⟩,⟨⟨(-51007190001872665358600078750),(-51007190001872665346628647247)⟩,⟨93359728991417267698969093309,93359728991417267710633842490⟩⟩,⟨⟨(-50979090428064547721584814039),(-50979090428064547709614021519)⟩,⟨93335162036840841845195642699,93335162036840841856859993014⟩⟩,⟨⟨(-50941649153171264244259621281),(-50941649153171264232289688158)⟩,⟨93302412051081574452740355045,93302412051081574464404165892⟩⟩,⟨⟨(-50894887428930109687915920255),(-50894887428930109675947067807)⟩,⟨93261484147898453490743100882,93261484147898453502406230556⟩⟩,⟨⟨(-50838831788077364153311629208),(-50838831788077364141344080192)⟩,⟨93212384732709896096788174504,93212384732709896108450479512⟩⟩,⟨⟨(-50773514023087628270387031280),(-50773514023087628258421009361)⟩,⟨93155121511343939084778955192,93155121511343939096440290768⟩⟩,⟨⟨(-50698971160690654178099657088),(-50698971160690654166135388722)⟩,⟨93089703500475707377423827596,93089703500475707389084045769⟩⟩,⟨⟨(-50615245432181919376078445865),(-50615245432181919364116157525)⟩,⟨93016141039718144681567863827,93016141039718144693226816107⟩⟩,⟨⟨(-50522384239545969106263101877),(-50522384239545969094303025181)⟩,⟨92934445805326502099845109634,92934445805326502111502641874⟩⟩,⟨⟨(-50420440117414363188203040462),(-50420440117414363176245405097)⟩,⟨92844630825471674805352858193,92844630825471674817008817535⟩⟩,⟨⟨(-50309470690882909035700075353),(-50309470690882909023745120452)⟩,⟨92746710497032166029799710125,92746710497032166041453933675⟩⟩,⟨⟨(-50189538629215747507950287262),(-50189538629215747495998245204)⟩,⟨92640700603849252966238398012,92640700603849252977890728826⟩⟩,⟨⟨(-50060711595466785581246183196),(-50060711595466785569297301355)⟩,⟨92526618336384842191446398978,92526618336384842203096664458⟩⟩,⟨⟨(-49923062192051942527133456781),(-49923062192051942515187971237)⟩,⟨92404482312716544172185530055,92404482312716544183833567939⟩⟩] +lemma kernel1_0_r2_0_eq : ∀ k : Fin 16, kernel1_0Expr 2 0 k = kernel1_0_r2_0 k := by decide +kernel +noncomputable def kernel1_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-49776667902308696954300401015),(-49776667902308696942358571908)⟩,⟨92274312600799678496302448052,92274312600799678507948071336⟩⟩,⟨⟨(-49621611028082492936991751210),(-49621611028082492925053815397)⟩,⟨92136130741921254670874324846,92136130741921254682517368623⟩⟩,⟨⟨(-49457978623382686327061267233),(-49457978623382686315127495930)⟩,⟨91989959775266468490357380233,91989959775266468501997644542⟩⟩,⟨⟨(-49285862424153888612264871998),(-49285862424153888600335506163)⟩,⟨91835824263513921743685968808,91835824263513921755323282593⟩⟩,⟨⟨(-49105358774211796267186044018),(-49105358774211796255261374448)⟩,⟨91673750319371623838845462203,91673750319371623850479603911⟩⟩,⟨⟨(-48916568547395878895949575641),(-48916568547395878884029840409)⟩,⟨91503765632961877988661819114,91503765632961878000292618257⟩⟩,⟨⟨(-48719597065994639542307531930),(-48719597065994639530393035252)⟩,⟨91325899499959401888476667920,91325899499959401900103887260⟩⟩,⟨⟨(-48514554015502554783818198189),(-48514554015502554771909182755)⟩,⟨91140182850383493024550446080,91140182850383493036173908071⟩⟩,⟨⟨(-48301553355771249544349674648),(-48301553355771249532446474269)⟩,⟨90946648277941731293183997514,90946648277941731304803433016⟩⟩,⟨⟨(-48080713228620960321629548555),(-48080713228620960309732395610)⟩,⟨90745330069819625586496328811,90745330069819625598111567830⟩⟩,⟨⟨(-47852155861981888547998430198),(-47852155861981888536107672071)⟩,⟨90536264236807765180671997313,90536264236807765192282754506⟩⟩,⟨⟨(-47616007470638640332910903804),(-47616007470638640321026779849)⟩,⟨90319488543655439559204963643,90319488543655439570811059273⟩⟩,⟨⟨(-47372398153654586554037114280),(-47372398153654586542160011639)⟩,⟨90095042539537349749774352856,90095042539537349761375459269⟩⟩,⟨⟨(-47121461788556654273360764888),(-47121461788556654261490904664)⟩,⟨89862967588517957976337273537,89862967588517957987933226090⟩⟩,⟨⟨(-46863335922364772280857342012),(-46863335922364772268995125511)⟩,⟨89623306899896217624923756151,89623306899896217636514210085⟩⟩,⟨⟨(-46598161659553935159038661961),(-46598161659553935147184318609)⟩,⟨89376105558311898933525297082,89376105558311898945110076383⟩⟩] +lemma kernel1_0_r2_1_eq : ∀ k : Fin 16, kernel1_0Expr 2 1 k = kernel1_0_r2_1 k := by decide +kernel +noncomputable def kernel1_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-46326083547040615990068041009),(-46326083547040615978222029468)⟩,⟨89121410553493483702388583402,89121410553493483713967283268⟩⟩,⟨⟨(-46047249456289041497413872452),(-46047249456289041485576387940)⟩,⟨88859270809526650431604364283,88859270809526650443176839345⟩⟩,⟨⟨(-45761810462636638269381346633),(-45761810462636638257552855692)⟩,⟨88589737213521714844032524076,88589737213521714855598358399⟩⟩,⟨⟨(-45469920721941757445770691778),(-45469920721941757433951405633)⟩,⟨88312862643558034398036886389,88312862643558034409595915374⟩⟩,⟨⟨(-45171737344660580018643533560),(-45171737344660580006833988708)⟩,⟨88028701995783333203455333791,88028701995783333215007068742⟩⟩,⟨⟨(-44867420267463887341480321205),(-44867420267463887329680683152)⟩,⟨87737312210546159179337730957,87737312210546159190882049127⟩⟩,⟨⟨(-44557132122508142695350618551),(-44557132122508142683561430619)⟩,⟨87438752297440251147658644323,87438752297440251159195046729⟩⟩,⟨⟨(-44241038104479060485498479444),(-44241038104479060473719924993)⟩,⟨87133083359140471993427417335,87133083359140472004955760000⟩⟩,⟨⟨(-43919305835529530043157284951),(-43919305835529530031390004775)⟩,⟨86820368613911156499536207598,86820368613911156511055891321⟩⟩,⟨⟨(-43592105228237400866214237937),(-43592105228237400854458342597)⟩,⟨86500673416669229732980598123,86500673416669229744491547487⟩⟩,⟨⟨(-43259608346712214834222497925),(-43259608346712214822478619114)⟩,⟨86174065278486273931470668133,86174065278486273942972289303⟩⟩,⟨⟨(-42921989265983477502032171388),(-42921989265983477490300453629)⟩,⟨85840613884415857973211701948,85840613884415857984703882199⟩⟩,⟨⟨(-42579423929806483709598326550),(-42579423929806483697879512762)⟩,⟨85500391109534892188756536761,85500391109534892200238568288⟩⟩,⟨⟨(-42232090007025040853174874454),(-42232090007025040841469022356)⟩,⟨85153471033090530178439411342,85153471033090530189911263800⟩⟩,⟨⟨(-41880166746633654407858515425),(-41880166746633654396166356443)⟩,⟨84799929950647205306681602017,84799929950647205318142575268⟩⟩,⟨⟨(-41523834831684842632232022670),(-41523834831684842620553650397)⟩,⟨84439846384131758703737293020,84439846384131758715187317467⟩⟩] +lemma kernel1_0_r2_2_eq : ∀ k : Fin 16, kernel1_0Expr 2 2 k = kernel1_0_r2_2 k := by decide +kernel +noncomputable def kernel1_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-41163276232190218623042658713),(-41163276232190218611378958706)⟩,⟨84073301089678283125632023962,84073301089678283137070242902⟩⟩,⟨⟨(-40798674057166805710945321572),(-40798674057166805699296256845)⟩,⟨83700377063178267264038528712,83700377063178267275464998336⟩⟩,⟨⟨(-40430212405982724225319079195),(-40430212405982724213685491719)⟩,⟨83321159543445871562208244704,83321159543445871573622147791⟩⟩,⟨⟨(-40058076219158891524979832171),(-40058076219158891513361751724)⟩,⟨82935736012912691920513218585,82935736012912691931914541466⟩⟩,⟨⟨(-39682451128785700552950556935),(-39682451128785700541348989748)⟩,⟨82544196195771163640023318738,82544196195771163651411077577⟩⟩,⟨⟨(-39303523308715772785360527341),(-39303523308715772773775360910)⟩,⟨82146632053490815464016481073,82146632053490815475390799675⟩⟩,⟨⟨(-38921479324695807217867191991),(-38921479324695807206299389212)⟩,⟨81743137777636892682965618602,81743137777636892694325552426⟩⟩,⟨⟨(-38536505984602256088278652681),(-38536505984602256076728165761)⟩,⟨81333809779926418160703747660,81333809779926418172049352762⟩⟩,⟨⟨(-38148790188947038758800024727),(-38148790188947038747268038402)⟩,⟨80918746679462539165412217841,80918746679462539176742326009⟩⟩,⟨⟨(-37758518781820746288274785008),(-37758518781820746276761049309)⟩,⟨80498049287094003564129602628,80498049287094003575444466939⟩⟩,⟨⟨(-37365878402441779809992356375),(-37365878402441779798497964454)⟩,⟨80071820586852807964194004630,80071820586852807975492544146⟩⟩,⟨⟨(-36971055337480595432097660060),(-36971055337480595420622472578)⟩,⟨79640165714429448665443269725,79640165714429448676725624366⟩⟩,⟨⟨(-36574235374328687033166274833),(-36574235374328687021711613826)⟩,⟨79203191932651768959141570341,79203191932651768970406428613⟩⟩,⟨⟨(-36175603655482116630607713701),(-36175603655482116619173227654)⟩,⟨78761008603940117767151424981,78761008603940117778399133955⟩⟩,⟨⟨(-35775344534209291163889405652),(-35775344534209291152476326389)⟩,⟨78313727159718398541193102305,78313727159718398552422436579⟩⟩,⟨⟨(-35373641431672276437961130744),(-35373641431672276426569212935)⟩,⟨77861461066767576745327960453,77861461066767576756539158538⟩⟩] +lemma kernel1_0_r2_3_eq : ∀ k : Fin 16, kernel1_0Expr 2 3 k = kernel1_0_r2_3 k := by decide +kernel +noncomputable def kernel1_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-34970676695670226218574786927),(-34970676695670226207205576032)⟩,⟨77404325790515311497709496956,77404325790515311508901018948⟩⟩,⟨⟨(-34566631461172480441253686537),(-34566631461172480429906636736)⟩,⟨76942438755262563829836827843,76942438755262563841009207296⟩⟩,⟨⟨(-34161685512807545397314583322),(-34161685512807545385991072180)⟩,⟨76475919301355291766751076646,76475919301355291777902937059⟩⟩,⟨⟨(-33756017149472505677020503574),(-33756017149472505665720165632)⟩,⟨76004888639316651777428396562,76004888639316651788560089568⟩⟩,⟨⟨(-33349803051225428585726756600),(-33349803051225428574451274097)⟩,⟨75529469800962467386630884143,75529469800962467397740727809⟩⟩,⟨⟨(-32943218148621003671524068749),(-32943218148621003660272780708)⟩,⟨75049787587530078787842218773,75049787587530078798930855168⟩⟩,⟨⟨(-32536435494647010882618625211),(-32536435494647010871393060912)⟩,⟨74565968514858031737102033373,74565968514858031748167929433⟩⟩,⟨⟨(-32129626139416229718523189999),(-32129626139416229707322849777)⟩,⟨74078140755661379163093755100,74078140755661379174137390135⟩⟩,⟨⟨(-31722959007765088630298633304),(-31722959007765088619125451914)⟩,⟨73586434078954633927926954536,73586434078954633938946390214⟩⟩,⟨⟨(-31316600779906710039481349133),(-31316600779906710028334425856)⟩,⟨73090979786681605016683210377,73090979786681605027679321559⟩⟩,⟨⟨(-30910715775282033982554880846),(-30910715775282033971435901001)⟩,⟨72591910647618451067338017610,72591910647618451078309110917⟩⟩,⟨⟨(-30505465839748405988768374138),(-30505465839748405977676690539)⟩,⟨72089360828623273538408730668,72089360828623273549355426961⟩⟩,⟨⟨(-30101010236240396959617113826),(-30101010236240396948554802149)⟩,⟨71583465823312426004274252880,71583465823312426015194468752⟩⟩,⟨⟨(-29697505539032690299101221305),(-29697505539032690288067243561)⟩,⟨71074362378250415290344018366,71074362378250415301238760469⟩⟩,⟨⟨(-29295105531729631274053533897),(-29295105531729631263049734528)⟩,⟨70562188416746793881159159061,70562188416746793892026571226⟩⟩,⟨⟨(-28893961109100493660352254621),(-28893961109100493649377826098)⟩,⟨70047082960359771047011608478,70047082960359771057852466571⟩⟩] +lemma kernel1_0_r2_4_eq : ∀ k : Fin 16, kernel1_0Expr 2 4 k = kernel1_0_r2_4 k := by decide +kernel +noncomputable def kernel1_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-28494220182873688411327548796),(-28494220182873688400384867489)⟩,⟨69529186048212382634977323839,69529186048212382645789241342⟩⟩,⟨⟨(-28096027591597028776037212030),(-28096027591597028765124932516)⟩,⟨69008638654232937135935728326,69008638654232937146720013373⟩⟩,⟨⟨(-27699525014664787535127159671),(-27699525014664787524247286697)⟩,⟨68485582602437079708250520867,68485582602437079719005153964⟩⟩,⟨⟨(-27304850890605647456898742115),(-27304850890605647446050296359)⟩,⟨67960160480374168186815798574,67960160480374168197541722706⟩⟩,⟨⟨(-26912140339718769430875065462),(-26912140339718769420060536217)⟩,⟨67432515550865718323381841766,67432515550865718334076554386⟩⟩,⟨⟨(-26521525091138098780535198404),(-26521525091138098769753110641)⟩,⟨66902791662168432969633370168,66902791662168432980298305107⟩⟩,⟨⟨(-26133133414397714765079321258),(-26133133414397714754331840230)⟩,⟨66371133156698765870314638328,66371133156698765880947613217⟩⟩,⟨⟨(-25747090055563517985767424186),(-25747090055563517975053388076)⟩,⟨65837684778460070354190273350,65837684778460070364792409695⟩⟩,⟨⟨(-25363516177988862957093827606),(-25363516177988862946416041742)⟩,⟨65302591579317132671371017286,65302591579317132681939495435⟩⟩,⟨⟨(-24982529307743896981217195787),(-24982529307743896970573841163)⟩,⟨64765998824266276266938690680,64765998824266276277475283842⟩⟩,⟨⟨(-24604243283760380961059640980),(-24604243283760380950453041525)⟩,⟨64228051895852235270035227257,64228051895852235280537592667⟩⟩,⟨⟨(-24228768212725662915025230686),(-24228768212725662904454033280)⟩,⟨63688896197885622464566141527,63688896197885622475035588737⟩⟩,⟨⟨(-23856210428751271381272436020),(-23856210428751271370739549911)⟩,⟨63148677058617049778695296029,63148677058617049789128899619⟩⟩,⟨⟨(-23486672457833314870736746747),(-23486672457833314860240211088)⟩,⟨62607539633525789954878712403,62607539633525789965278384964⟩⟩,⟨⟨(-23120252987113536797183761804),(-23120252987113536786726056554)⟩,⟨62065628807882289936890614529,62065628807882289947253856182⟩⟩,⟨⟨(-22757046838941505053142030799),(-22757046838941505042721603620)⟩,⟨61523089099244854395209630136,61523089099244854405537947090⟩⟩] +lemma kernel1_0_r2_5_eq : ∀ k : Fin 16, kernel1_0Expr 2 5 k = kernel1_0_r2_5 k := by decide +kernel +noncomputable def kernel1_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-22397144949730034122532981756),(-22397144949730034112153114052)⟩,⟨60980064560051407863690310387,60980064560051407873980405579⟩⟩,⟨⟨(-22040634353587568083959078062),(-22040634353587568073617387593)⟩,⟨60436698680467413756218807028,60436698680467413766473010919⟩⟩,⟨⟨(-21687598170702917981646403623),(-21687598170702917971345521600)⟩,⟨59893134291650777091631454262,59893134291650777101847115235⟩⟩,⟨⟨(-21338115600449469811159934695),(-21338115600449469800898104149)⟩,⟨59349513469593885552420966113,59349513469593885562599793129⟩⟩,⟨⟨(-20992261919167782745702416835),(-20992261919167782735482959760)⟩,⟨58805977439701852473908272564,58805977439701852484046926990⟩⟩,⟨⟨(-20650108482577404059222744510),(-20650108482577404049043180002)⟩,⟨58262666482264518903295602391,58262666482264518913396512589⟩⟩,⟨⟨(-20311722732760760113987900607),(-20311722732760760103851006123)⟩,⟨57719719838977854836309837272,57719719838977854846370205453⟩⟩,⟨⟨(-19977168209654164095293910644),(-19977168209654164085197719951)⟩,⟨57177275620668078428828611643,57177275620668078438850354796⟩⟩,⟨⟨(-19646504566973332815683842335),(-19646504566973332805632042188)⟩,⟨56635470716369094111023862976,56635470716369094121003279275⟩⟩,⟨⟨(-19319787592493348303957944882),(-19319787592493348293947620988)⟩,⟨56094440703900745216510135121,56094440703900745226450084135⟩⟩,⟨⟨(-18997069232595755884402587335),(-18997069232595755874436656324)⟩,⟨55554319762091894456440050332,55554319762091894466337595681⟩⟩,⟨⟨(-18678397620988479211344485774),(-18678397620988479201420770249)⟩,⟨55015240584788498118306009844,55015240584788498128163279033⟩⟩,⟨⟨(-18363817111497473666740351667),(-18363817111497473656862567263)⟩,⟨54477334296782640328638356151,54477334296782640338451618542⟩⟩,⟨⟨(-18053368314822551227296669499),(-18053368314822551217461797202)⟩,⟨53940730371793956388684675613,53940730371793956398456895879⟩⟩,⟨⟨(-17747088139143610015203882492),(-17747088139143610005414971122)⟩,⟨53405556552630014540159592238,53405556552630014549887702841⟩⟩,⟨⟨(-17445009834457606921525312285),(-17445009834457606911779972298)⟩,⟨52871938773647060113308654579,52871938773647060122994995056⟩⟩] +lemma kernel1_0_r2_6_eq : ∀ k : Fin 16, kernel1_0Expr 2 6 k = kernel1_0_r2_6 k := by decide +kernel +noncomputable def kernel1_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-17147163040521037526213293047),(-17147163040521037516515665408)⟩,⟨52340001085627072454500900209,52340001085627072464141317416⟩⟩,⟨⟨(-16853573838267448496381399724),(-16853573838267448486727955031)⟩,⟨51809865583181361885880593010,51809865583181361895478560524⟩⟩,⟨⟨(-16564264804564616996051445873),(-16564264804564616986445356080)⟩,⟨51281652334784960656366409360,51281652334784960665918737918⟩⟩,⟨⟨(-16279255070171501412928019554),(-16279255070171501403366685024)⟩,⟨50755479315539858638549010466,50755479315539858648058250051⟩⟩,⟨⟨(-15998560380750908633158765458),(-15998560380750908623646266135)⟩,⟨50231462342758722357688106677,50231462342758722367150165608⟩⟩,⟨⟨(-15722193160790044570858609640),(-15722193160790044561391387722)⟩,⟨49709715014454136374033479822,49709715014454136383451861782⟩⟩,⟨⟨(-15450162580277724710387190700),(-15450162580277724700968533162)⟩,⟨49190348650811641173054371558,49190348650811641182425773992⟩⟩,⟨⟨(-15182474623984026671322810043),(-15182474623984026661949909420)⟩,⟨48673472238717934076006051170,48673472238717934085333232632⟩⟩,⟨⟨(-14919132163185572460696519149),(-14919132163185572451373856277)⟩,⟨48159192379408572127777619558,48159192379408572137056090824⟩⟩,⟨⟨(-14660135029677437899460718408),(-14660135029677437890184237898)⟩,⟨47647613239292391548587715444,47647613239292391557821477193⟩⟩,⟨⟨(-14405480091910903018881972401),(-14405480091910903009655066145)⟩,⟨47138836504002660388530758083,47138836504002660397716404817⟩⟩,⟨⟨(-14155161333094880890285950901),(-14155161333094880881105609214)⟩,⟨46632961335717732775575728068,46632961335717732784716221627⟩⟩,⟨⟨(-13909169931097892809536816052),(-13909169931097892800407447237)⟩,⟨46130084333786697816764341410,46130084333786697825855266122⟩⟩,⟨⟨(-13667494339986893010450211344),(-13667494339986893001367734026)⟩,⟨45630299498688236860131887963,45630299498688236869177272755⟩⟩,⟨⟨(-13430120373039082725207820804),(-13430120373039082716175723022)⟩,⟨45133698199343642261009716262,45133698199343642270006061643⟩⟩,⟨⟨(-13197031287063086661124946025),(-13197031287063086652140021369)⟩,⟨44640369143797731483424304176,44640369143797731492374770022⟩⟩] +lemma kernel1_0_r2_7_eq : ∀ k : Fin 16, kernel1_0Expr 2 7 k = kernel1_0_r2_7 k := by decide +kernel +noncomputable def kernel1_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-12968207867866488689741016741),(-12968207867866488680808157978)⟩,⟨44150398353274234331183025779,44150398353274234340082716148⟩⟩,⟨⟨(-12743628516707730307160901274),(-12743628516707730298275437284)⟩,⟨43663869139605159842896405263,43663869139605159851749938235⟩⟩,⟨⟨(-12523269337571756521652681310),(-12523269337571756512818185331)⟩,⟨43180862086026683789744927137,43180862086026683798548720287⟩⟩,⟨⟨(-12307104225110539343610352474),(-12307104225110539334823430445)⟩,⟨42701455031327257980637558074,42701455031327257989394960422⟩⟩,⟨⟨(-12095104953091707926886347217),(-12095104953091707918151694862)⟩,⟨42225723057326948135630901167,42225723057326948144337214564⟩⟩,⟨⟨(-11887241263200954480682491975),(-11887241263200954471995535007)⟩,⟨41753738479660476523004880348,41753738479660476531664629173⟩⟩,⟨⟨(-11683480954046653152158494746),(-11683480954046653143522883051)⟩,⟨41285570841830096550321140716,41285570841830096558930668225⟩⟩,⟨⟨(-11483789970218211031831981721),(-11483789970218211023244141433)⟩,⟨40821286912488275767981632724,40821286912488275776544469339⟩⟩,⟨⟨(-11288132491253051234731589666),(-11288132491253051226196646556)⟩,⟨40360950685904226975278464091,40360950685904226983789485698⟩⟩,⟨⟨(-11096471020370791835675781237),(-11096471020370791827188626008)⟩,⟨39904623385562618929019409497,39904623385562618937483675359⟩⟩,⟨⟨(-10908766472837114738262874501),(-10908766472837114729827222969)⟩,⟨39452363470837332042634857708,39452363470837332051048647479⟩⟩,⟨⟨(-10724978263823998145913464941),(-10724978263823998137525574780)⟩,⟨39004226646677912772577450972,39004226646677912780944465190⟩⟩,⟨⟨(-10545064395637397433999069505),(-10545064395637397425663882146)⟩,⟨38560265876241434277558044619,38560265876241434285873344493⟩⟩,⟨⟨(-10368981544188083679642400745),(-10368981544188083671354890624)⟩,⟨38120531396397800352025153369,38120531396397800360293717433⟩⟩,⟨⟨(-10196685144586168289770733796),(-10196685144586168281534674412)⟩,⟨37685070736032143298261869821,37685070736032143306479922340⟩⟩,⟨⟨(-10028129475744837181574656943),(-10028129475744837173386147572)⟩,⟨37253928737063871790262677359,37253928737063871798434078919⟩⟩] +lemma kernel1_0_r2_8_eq : ∀ k : Fin 16, kernel1_0Expr 2 8 k = kernel1_0_r2_8 k := by decide +kernel +noncomputable def kernel1_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-9863267743883969703514449650),(-9863267743883969695378952347)⟩,⟨36827147578098128131534535597,36827147578098128139653831303⟩⟩,⟨⟨(-9702052164829606705906113288),(-9702052164829606697817979852)⟩,⟨36404766800621920606900277057,36404766800621920614973067438⟩⟩,⟨⟨(-9544434045010639602220815625),(-9544434045010639594183866658)⟩,⟨35986823337654009627796487210,35986823337654009635818951631⟩⟩,⟨⟨(-9390363861059598672788484515),(-9390363861059598664798674380)⟩,⟨35573351544754748598573565612,35573351544754748606549711189⟩⟩,⟨⟨(-9239791337930005140158079331),(-9239791337930005132220553457)⟩,⟨35164383233299513210834834898,35164383233299513218759523673⟩⟩,⟨⟨(-9092665525448398780409022250),(-9092665525448398772518354885)⟩,⟨34759947705917096344600339096,34759947705917096352478952589⟩⟩,⟨⟨(-8948934873224842392535376194),(-8948934873224842384695427939)⟩,⟨34360071793992498909609606356,34360071793992498917438286041⟩⟩,⟨⟨(-8808547303851418043236151634),(-8808547303851418035442742822)⟩,⟨33964779897131907670033946885,33964779897131907677816835435⟩⟩,⟨⟨(-8671450284323949767065444728),(-8671450284323949759324179816)⟩,⟨33574094024486316157590813501,33574094024486316165322318000⟩⟩,⟨⟨(-8537590895627895944384812557),(-8537590895627895936689712649)⟩,⟨33188033837829209952728313584,33188033837829209960414368138⟩⟩,⟨⟨(-8406915900435035054904186468),(-8406915900435035047259142593)⟩,⟨32806616696282997677059233177,32806616696282997684695950794⟩⟩,⟨⟨(-8279371808863204664839483347),(-8279371808863204657240196101)⟩,⟨32429857702588417831754335989,32429857702588417839345980514⟩⟩,⟨⟨(-8154904942256929751054521324),(-8154904942256929743506302106)⟩,⟨32057769750810982095239876671,32057769750810982102781148538⟩⟩,⟨⟨(-8033461494952277893691894076),(-8033461494952277886188972046)⟩,⟨31690363575378619992682475177,31690363575378620000179103422⟩⟩,⟨⟨(-7914987593994691314384822373),(-7914987593994691306931112749)⟩,⟨31327647801345059338868606569,31327647801345059346316681835⟩⟩,⟨⟨(-7799429356783855811313651382),(-7799429356783855803904746566)⟩,⟨30969628995774102199478569648,30969628995774102206882465278⟩⟩] +lemma kernel1_0_r2_9_eq : ∀ k : Fin 16, kernel1_0Expr 2 9 k = kernel1_0_r2_9 k := by decide +kernel +noncomputable def kernel1_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-7686732946624861762305554013),(-7686732946624861754947352614)⟩,⟨30616311720140827337683244703,30616311720140827345037078400⟩⟩,⟨⟨(-7576844626169980785608781638),(-7576844626169980778294841427)⟩,⟨30267698583646856659071807391,30267698583646856666381978072⟩⟩,⟨⟨(-7469710808740312472699332560),(-7469710808740312465433583762)⟩,⟨29923790297348153972170111104,29923790297348153979432696059⟩⟩,⟨⟨(-7365278107521338820922013015),(-7365278107521338813699954960)⟩,⟨29584585728995367929041274933,29584585728995367936260741757⟩⟩,⟨⟨(-7263493382631050462561094773),(-7263493382631050455388169677)⟩,⟨29250081958488475403672202257,29250081958488475410843124335⟩⟩,⟨⟨(-7164303786063770271927229492),(-7164303786063770264797379139)⟩,⟨28920274333849414588025954308,28920274333849414595154349959⟩⟩,⟨⟨(-7067656804517089088359230215),(-7067656804517089081276395246)⟩,⟨28595156527618506266040625854,28595156527618506273122563455⟩⟩,⟨⟨(-6973500300113438670876741094),(-6973500300113438663836338572)⟩,⟨28274720593582734399977984127,28274720593582734407018014571⟩⟩,⟨⟨(-6881782549031753036177927931),(-6881782549031753029185892601)⟩,⟨27958957023746380536800738497,27958957023746380543792946427⟩⟩,⟨⟨(-6792452278068406341074584121),(-6792452278068406334124294099)⟩,⟨27647854805457067746913531575,27647854805457067753864497570⟩⟩,⟨⟨(-6705458699150159630600464792),(-6705458699150159623695863310)⟩,⟨27341401478602955962689547394,27341401478602955969595338575⟩⟩,⟨⟨(-6620751541825197107973600334),(-6620751541825197101110036576)⟩,⟨27039583192799628848244538848,27039583192799628855109774893⟩⟩,⟨⟨(-6538281083761482939260463464),(-6538281083761482932443481576)⟩,⟨26742384764488109958316050968,26742384764488109965135206491⟩⟩,⟨⟨(-6457998179284620632048323877),(-6457998179284620625271632828)⟩,⟨26449789733868430328596934422,26449789733868430335376261883⟩⟩,⟨⟨(-6379854285990148142885027762),(-6379854285990148136152569530)⟩,⟨26161780421596228370553734985,26161780421596228377289303947⟩⟩,⟨⟨(-6303801489467753235761113115),(-6303801489467753229068179437)⟩,⟨25878337985172983842803030999,25878337985172983849499519355⟩⟩] +lemma kernel1_0_r2_10_eq : ∀ k : Fin 16, kernel1_0Expr 2 10 k = kernel1_0_r2_10 k := by decide +kernel +noncomputable def kernel1_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-6229792526177246105525823270),(-6229792526177246098878583153)⟩,⟨25599442474963658838671303549,25599442474963658845322565258⟩⟩,⟨⟨(-6157780804518281445177645606),(-6157780804518281438569124664)⟩,⟨25325072889778728579231275066,25325072889778728585844243543⟩⟩,⟨⟨(-6087720424137782162336889130),(-6087720424137782155771020631)⟩,⟨25055207231960822097445594229,25055207231960822104016348771⟩⟩,⟨⟨(-6019566193520784629416158264),(-6019566193520784622888190642)⟩,⟨24789822561919446786476838558,24789822561919446793010101023⟩⟩,⟨⟨(-5953273645912004037713487856),(-5953273645912004031229042011)⟩,⟨24528895052060530818967453002,24528895052060530825457623821⟩⟩,⟨⟨(-5888799053616811996718826197),(-5888799053616811990271430136)⟩,⟨24272400040060773612333073472,24272400040060773618786586876⟩⟩,⟨⟨(-5826099440731531337213734056),(-5826099440731531330807310025)⟩,⟨24020312081440037263370950822,24020312081440037269783898025⟩⟩,⟨⟨(-5765132594353989945050759342),(-5765132594353989938680521215)⟩,⟨23772605001388232122264224600,23772605001388232128641362561⟩⟩,⟨⟨(-5705857074326141576874762628),(-5705857074326141570546864889)⟩,⟨23529251945806338830665472793,23529251945806338837000671937⟩⟩,⟨⟨(-5648232221561262556576508029),(-5648232221561262550283900241)⟩,⟨23290225431524359120412274177,23290225431524359126712544920⟩⟩,⟨⟨(-5592218165008774907742488812),(-5592218165008774901489075912)⟩,⟨23055497395662090879803327332,23055497395662090886064778955⟩⟩,⟨⟨(-5537775827310135009849207543),(-5537775827310135003630181508)⟩,⟨22825039244101672379647916572,22825039244101672385875328390⟩⟩,⟨⟨(-5484866929199468680601229215),(-5484866929199468674422269048)⟩,⟨22598821899043829569015615960,22598821899043829575203332382⟩⟩,⟨⟨(-5433453992702735293112000345),(-5433453992702735286966497510)⟩,⟨22376815845622682977155482171,22376815845622682983310074335⟩⟩,⟨⟨(-5383500343189171907041547528),(-5383500343189171900933387757)⟩,⟨22158991177556821489496177898,22158991177556821495613774941⟩⟩,⟨⟨(-5334970110328610329186889024),(-5334970110328610323111250223)⟩,⟨21945317641817124110598305110,21945317641817124116683700789⟩⟩] +lemma kernel1_0_r2_11_eq : ∀ k : Fin 16, kernel1_0Expr 2 11 k = kernel1_0_r2_11 k := by decide +kernel +noncomputable def kernel1_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-5287828228007982514862927222),(-5287828228007982508826206409)⟩,⟨21735764682294503302635874432,21735764682294503308682699492⟩⟩,⟨⟨(-5242040433259939830971929564),(-5242040433259939824966766721)⟩,⟨21530301482453350608855536650,21530301482453350614871110283⟩⟩,⟨⟨(-5197573264256016505179192832),(-5197573264256016499209448077)⟩,⟨21328897006958983541191572057,21328897006958983547172049547⟩⟩,⟨⟨(-5154394057416174161612342750),(-5154394057416174155673192128)⟩,⟨21131520042269819107664248192,21131520042269819113614425477⟩⟩,⟨⟨(-5112470943685879737250088826),(-5112470943685879731347253650)⟩,⟨20938139236187331319207930982,20938139236187331325122111823⟩⟩,⟨⟨(-5071772844031100272558180335),(-5071772844031100266684954928)⟩,⟨20748723136359085432764252756,20748723136359085438649105482⟩⟩,⟨⟨(-5032269464200751977419899397),(-5032269464200751971580117697)⟩,⟨20563240227732278874416651283,20563240227732278880268357808⟩⟩,⟨⟨(-4993931288805224385429063713),(-4993931288805224379617905633)⟩,⟨20381658968957256470104142333,20381658968957256475927494983⟩⟩,⟨⟨(-4956729574758619992296548808),(-4956729574758619986520319546)⟩,⟨20203947827742404913680902131,20203947827742404919469624365⟩⟩,⟨⟨(-4920636344131312046332137956),(-4920636344131312040583525999)⟩,⟨20030075315163667816882684176,20030075315163667822644047215⟩⟩,⟨⟨(-4885624376458334471697372419),(-4885624376458334465980180067)⟩,⟨19860010018933658062372996816,19860010018933658068103214565⟩⟩,⟨⟨(-4851667200547984428180964628),(-4851667200547984422490386115)⟩,⟨19693720635636978700668570162,19693720635636978706372420862⟩⟩,⟨⟨(-4818739085833845716172287321),(-4818739085833845710514076752)⟩,⟨19531176001939897789474184048,19531176001939897795145940013⟩⟩,⟨⟨(-4786815033312235885909830100),(-4786815033312235880277214696)⟩,⟨19372345124783957154920738961,19372345124783957160567135459⟩⟩,⟨⟨(-4755870766105847047950270188),(-4755870766105847042347019813)⟩,⟨19217197210574431115309961568,19217197210574431120927245229⟩⟩,⟨⟨(-4725882719693095321099086076),(-4725882719693095315520414445)⟩,⟨19065701693375790054108756478,19065701693375790059701686257⟩⟩] +lemma kernel1_0_r2_12_eq : ∀ k : Fin 16, kernel1_0Expr 2 12 k = kernel1_0_r2_12 k := by decide +kernel +noncomputable def kernel1_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4696828031841421670352620423),(-4696828031841421664805044220)⟩,⟨18917828262127466894791041080,18917828262127466900353131148⟩⟩,⟨⟨(-4668684532281502414587560859),(-4668684532281502409063531420)⟩,⟨18773546886894273756821742795,18773546886894273762360500312⟩⟩,⟨⟨(-4641430732158035506554132875),(-4641430732158035501057381537)⟩,⟨18632827844166773289625233069,18632827844166773295136943390⟩⟩,⟨⟨(-4615045813291473141312344172),(-4615045813291473135838114402)⟩,⟨18495641741227776486084868326,18495641741227776491574260862⟩⟩,⟨⟨(-4589509617283776414313762541),(-4589509617283776408867832766)⟩,⟨18361959539601918415037685107,18361959539601918420499008937⟩⟩,⟨⟨(-4564802634499977455311398544),(-4564802634499977449886954643)⟩,⟨18231752577605957657528729512,18231752577605957662968760982⟩⟩,⟨⟨(-4540905992956052282821186924),(-4540905992956052277421921681)⟩,⟨18104992592018056771307282269,18104992592018056776722345441⟩⟩,⟨⟨(-4517801447142336879040752848),(-4517801447142336873661943005)⟩,⟨17981651738884832421861840220,17981651738884832427256631419⟩⟩,⟨⟨(-4495471366810462749122769345),(-4495471366810462743770838139)⟩,⟨17861702613485417564562561174,17861702613485417569930688453⟩⟩,⟨⟨(-4473898725750549328770373989),(-4473898725750549323437857370)⟩,⟨17745118269472156959612391411,17745118269472156964961277572⟩⟩,⟨⟨(-4453067090584171623990783859),(-4453067090584171618681330335)⟩,⟨17631872237207864115553184353,17631872237207864120879197814⟩⟩,⟨⟨(-4432960609597424754210034301),(-4432960609597424748918963017)⟩,⟨17521938541319805284737775843,17521938541319805290045570735⟩⟩,⟨⟨(-4413564001637234739162253898),(-4413564001637234733895363605)⟩,⟨17415291717490747192155764437,17415291717490747197439570403⟩⟩,⟨⟨(-4394862545092918810874152867),(-4394862545092918805624606129)⟩,⟨17311906828507512588557280454,17311906828507512593823896857⟩⟩,⟨⟨(-4376842066983880413681663907),(-4376842066983880408453064103)⟩,⟨17211759479587534296924022686,17211759479587534302169863107⟩⟩,⟨⟨(-4359488932173235335402112738),(-4359488932173235330189825085)⟩,⟨17114825833003886967063062924,17114825833003886972292735638⟩⟩] +lemma kernel1_0_r2_13_eq : ∀ k : Fin 16, kernel1_0Expr 2 13 k = kernel1_0_r2_13 k := by decide +kernel +noncomputable def kernel1_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4342790032726107342803934459),(-4342790032726107337614643025)⟩,⟨17021082622029209040348658020,17021082622029209045555512374⟩⟩,⟨⟨(-4326732777430305329302660442),(-4326732777430305324128643103)⟩,⟨16930507164218808192315223211,16930507164218808197506938464⟩⟩,⟨⟨(-4311305081496100186031651383),(-4311305081496100180876459134)⟩,⟨16843077374053074459245766328,16843077374053074464418808404⟩⟩,⟨⟨(-4296495356450859062151998889),(-4296495356450859057011053068)⟩,⟨16758771774959109007705238948,16758771774959109012864160261⟩⟩,⟨⟨(-4282292500243367894190158723),(-4282292500243367889069272845)⟩,⟨16677569510731215658147773491,16677569510731215663286789618⟩⟩,⟨⟨(-4268685887571780400682977897),(-4268685887571780395575308177)⟩,⟨16599450356369599344974551553,16599450356369599350100467948⟩⟩,⟨⟨(-4255665360448273341707749259),(-4255665360448273336616793823)⟩,⟨16524394728356273137896364835,16524394728356273143005700216⟩⟩,⟨⟨(-4243221219012663768977291628),(-4243221219012663763898530662)⟩,⟨16452383694386795640670547675,16452383694386795645767795879⟩⟩,⟨⟨(-4231344212606454134145075005),(-4231344212606454129085039013)⟩,⟨16383398982576045825158281917,16383398982576045830236945626⟩⟩,⟨⟨(-4220025531118015241525373350),(-4220025531118015236476507973)⟩,⟨16317422990155794871884286468,16317422990155794876951877798⟩⟩,⟨⟨(-4209256796608894760073263905),(-4209256796608894755039007015)⟩,⟨16254438791681356512738045952,16254438791681356517791143722⟩⟩,⟨⟨(-4199030055230549864722098701),(-4199030055230549859697999066)⟩,⟨16194430146764090761814522049,16194430146764090766857551840⟩⟩,⟨⟨(-4189337769440145963295377529),(-4189337769440145958287260693)⟩,⟨16137381507346002747807104947,16137381507346002752834270837⟩⟩,⟨⟨(-4180172810523438684200136644),(-4180172810523438679201164620)⟩,⟨16083278024532120510143284166,16083278024532120515161385632⟩⟩,⟨⟨(-4171528451432162555882837902),(-4171528451432162550896385926)⟩,⟨16032105554995754891478696768,16032105554995754896484375072⟩⟩,⟨⟨(-4163398359942786216872731649),(-4163398359942786211894421414)⟩,⟨15983850666971142765306295075,15983850666971142770303903225⟩⟩] +lemma kernel1_0_r2_14_eq : ∀ k : Fin 16, kernel1_0Expr 2 14 k = kernel1_0_r2_14 k := by decide +kernel +noncomputable def kernel1_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4155776592142959585623263088),(-4155776592142959580659870743)⟩,⟨15938500645847353410795252258,15938500645847353415778049037⟩⟩,⟨⟨(-4148657586251472146834610318),(-4148657586251472141878358187)⟩,⟨15896043499376698435261654435,15896043499376698440237373851⟩⟩,⟨⟨(-4142036156777062257402904838),(-4142036156777062252457095772)⟩,⟨15856467962510229716315269179,15856467962510229721280624596⟩⟩,⟨⟨(-4135907489020963958212247010),(-4135907489020963953272587597)⟩,⟨15819763501872238779431264818,15819763501872238784390524774⟩⟩,⟨⟨(-4130267133927648953663812294),(-4130267133927648948736132339)⟩,⟨15785920319884986156770399608,15785920319884986161717764255⟩⟩,⟨⟨(-4125111003287815891496150566),(-4125111003287815886573634192)⟩,⟨15754929358554191829506717998,15754929358554191834448964662⟩⟩,⟨⟨(-4120435365297295491888199705),(-4120435365297295486974074403)⟩,⟨15726782302925109010430286999,15726782302925109015364204078⟩⟩,⟨⟨(-4116236840475177043630833142),(-4116236840475177038720895295)⟩,⟨15701471584218284380383993219,15701471584218284385313759916⟩⟩,⟨⟨(-4112512397944117870402506869),(-4112512397944117865503386082)⟩,⟨15678990382653379494255368213,15678990382653379499174389322⟩⟩,⟨⟨(-4109259352075471100291723977),(-4109259352075471095395820436)⟩,⟨15659332629968691403095983474,15659332629968691408011815944⟩⟩,⟨⟨(-4106475359501556940678864535),(-4106475359501556935789319375)⟩,⟨15642493011643266528827130831,15642493011643266533736649001⟩⟩,⟨⟨(-4104158416497107134362785127),(-4104158416497107129475497835)⟩,⟨15628466968827751356049385936,15628466968827751360956666446⟩⟩,⟨⟨(-4102306856731629790110480868),(-4102306856731629785231276643)⟩,⟨15617250699989367406836660685,15617250699989367411735908420⟩⟩,⟨⟨(-4100919349394170759221448572),(-4100919349394170754343551175)⟩,⟨15608841162275637032119942275,15608841162275637037017895046⟩⟩,⟨⟨(-4099994897691686566136957387),(-4099994897691686561263415614)⟩,⟨15603236072600721545891060182,15603236072600721550784684189⟩⟩,⟨⟨(-4099532837721990977487934342),(-4099532837721990972614758998)⟩,⟨15600433908457464872285456411,15600433908457464877178717566⟩⟩] +lemma kernel1_0_r2_15_eq : ∀ k : Fin 16, kernel1_0Expr 2 15 k = kernel1_0_r2_15 k := by decide +kernel +noncomputable def kernel1_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel1_0_r2_0,kernel1_0_r2_1,kernel1_0_r2_2,kernel1_0_r2_3,kernel1_0_r2_4,kernel1_0_r2_5,kernel1_0_r2_6,kernel1_0_r2_7,kernel1_0_r2_8,kernel1_0_r2_9,kernel1_0_r2_10,kernel1_0_r2_11,kernel1_0_r2_12,kernel1_0_r2_13,kernel1_0_r2_14,kernel1_0_r2_15] +lemma kernel1_0_r2_eq (i k : Fin 16) : kernel1_0Expr 2 i k = kernel1_0_r2 i k := by + fin_cases i + · exact kernel1_0_r2_0_eq k + · exact kernel1_0_r2_1_eq k + · exact kernel1_0_r2_2_eq k + · exact kernel1_0_r2_3_eq k + · exact kernel1_0_r2_4_eq k + · exact kernel1_0_r2_5_eq k + · exact kernel1_0_r2_6_eq k + · exact kernel1_0_r2_7_eq k + · exact kernel1_0_r2_8_eq k + · exact kernel1_0_r2_9_eq k + · exact kernel1_0_r2_10_eq k + · exact kernel1_0_r2_11_eq k + · exact kernel1_0_r2_12_eq k + · exact kernel1_0_r2_13_eq k + · exact kernel1_0_r2_14_eq k + · exact kernel1_0_r2_15_eq k +noncomputable def kernel1_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-294135959542638947866008734904),(-294135959542638947836690020489)⟩,⟨141368391007632342067028742544,141368391007632342092838671497⟩⟩,⟨⟨(-294110500435127137637522928171),(-294110500435127137608203872165)⟩,⟨141373979170562238334067449642,141373979170562238359877837655⟩⟩,⟨⟨(-294059587629447177043142230513),(-294059587629447177013822531890)⟩,⟨141385148781869828520277347346,141385148781869828546088613990⟩⟩,⟨⟨(-293983231945147953633973501607),(-293983231945147953604652860078)⟩,⟨141401886418180181565736101498,141401886418180181591548665719⟩⟩,⟨⟨(-293881449613701086979148990894),(-293881449613701086949827107101)⟩,⟨141424171958751377955975915989,141424171958751377981790195970⟩⟩,⟨⟨(-293754262281063116720594226344),(-293754262281063116691270802556)⟩,⟨141451978602650097915701639141,141451978602650097941518051658⟩⟩,⟨⟨(-293601697011065519848127818648),(-293601697011065519818802559466)⟩,⟨141485272891637417892668424318,141485272891637417918487384104⟩⟩,⟨⟨(-293423786289610130549069692011),(-293423786289610130519742303193)⟩,⟨141524014738751940854578115527,141524014738751940880400036465⟩⟩,⟨⟨(-293220568029642003277436585984),(-293220568029642003248106778621)⟩,⟨141568157462574132714658556039,141568157462574132740483847127⟩⟩,⟨⟨(-292992085576866276242682815660),(-292992085576866276213350299728)⟩,⟨141617647827152461213511677573,141617647827152461239340749268⟩⟩,⟨⟨(-292738387716170168151117983896),(-292738387716170168121782479378)⟩,⟨141672426087568630536695678037,141672426087568630562528931437⟩⟩,⟨⟨(-292459528678705885536814084925),(-292459528678705885507475306474)⟩,⟨141732426041115870710385555984,141732426041115870736223397833⟩⟩,⟨⟨(-292155568149584941158500659635),(-292155568149584941129158340779)⟩,⟨141797575084060871436858221967,141797575084060871462701041106⟩⟩,⟨⟨(-291826571276129195448397280090),(-291826571276129195419051138656)⟩,⟨141867794273956541751407563935,141867794273956541777255765028⟩⟩,⟨⟨(-291472608676618842574666743067),(-291472608676618842545316527366)⟩,⟨141942998397469326168484687120,141942998397469326194338645693⟩⟩,⟨⟨(-291093756449472579974448814528),(-291093756449472579945094247324)⟩,⟨142023096043681311548260484075,142023096043681311574120601153⟩⟩] +lemma kernel1_0_r3_0_eq : ∀ k : Fin 16, kernel1_0Expr 3 0 k = kernel1_0_r3_0 k := by decide +kernel +noncomputable def kernel1_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-290690096182790334832652792308),(-290690096182790334803293645994)⟩,⟨142107989682823813733875153040,142107989682823813759741781926⟩⟩,⟨⟨(-290261714964184182469177494336),(-290261714964184182439813490184)⟩,⟨142197575750395536352389108290,142197575750395536378262652779⟩⟩,⟨⟨(-289808705390818489435366520420),(-289808705390818489405997451149)⟩,⟨142291744736614743617842963397,142291744736614743643723758366⟩⟩,⟨⟨(-289331165579575857717147562206),(-289331165579575857687773154272)⟩,⟨142390381281151182433465514283,142390381281151182459353959927⟩⟩,⟨⟨(-288829199177261145122448543561),(-288829199177261145093068628002)⟩,⟨142493364273079724824137246194,142493364273079724850033641563⟩⟩,⟨⟨(-288302915370751699926206389413),(-288302915370751699896820682820)⟩,⟨142600566955993878372681122270,142600566955993878398585878735⟩⟩,⟨⟨(-287752428896997984285836580281),(-287752428896997984256444938818)⟩,⟨142711857038213428906456915406,142711857038213428932370309164⟩⟩,⟨⟨(-287177860052774979836151741324),(-287177860052774979806753887616)⟩,⟨142827096808016535612589494472,142827096808016535638511932690⟩⟩,⟨⟨(-286579334704081179110064025113),(-286579334704081179080659875010)⟩,⟨142946143253822593902381834155,142946143253822593928313536601⟩⟩,⟨⟨(-285956984295078576753187433809),(-285956984295078576723776684073)⟩,⟨143068848189248115987728148025,143068848189248116013669548828⟩⟩,⟨⟨(-285310945856463893494139181076),(-285310945856463893464721773036)⟩,⟨143195058382953754016901281535,143195058382953754042852577449⟩⟩,⟨⟨(-284641362013158301914562217666),(-284641362013158301885137858936)⟩,⟨143324615693196406951839962028,143324615693196406977801578455⟩⟩,⟨⟨(-283948380991200184463434740896),(-283948380991200184434003455206)⟩,⟨143457357206996111839480241447,143457357206996111865452296729⟩⟩,⟨⟨(-283232156623722948905230895867),(-283232156623722948875792347484)⟩,⟨143593115383823124909354087269,143593115383823124935337050945⟩⟩,⟨⟨(-282492848355897662285701038744),(-282492848355897662256255278783)⟩,⟨143731718203706250689618388748,143731718203706250715612354407⟩⟩,⟨⟨(-281730621248718249107385883872),(-281730621248718249077932590546)⟩,⟨143872989319659081250042071434,143872989319659081276047496965⟩⟩] +lemma kernel1_0_r3_1_eq : ∀ k : Fin 16, kernel1_0Expr 3 1 k = kernel1_0_r3_1 k := by decide +kernel +noncomputable def kernel1_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-280945645981505240035224604285),(-280945645981505240005763950322)⟩,⟨144016748214316366440994505341,144016748214316366467011367806⟩⟩,⟨⟨(-280138098853002561127378002742),(-280138098853002561097909588477)⟩,⟨144162810360668253806142482251,144162810360668253832171317382⟩⟩,⟨⟨(-279308161780940627034277317967),(-279308161780940627004801331029)⟩,⟨144310987386775618426916245123,144310987386775618452957017439⟩⟩,⟨⟨(-278456022299938051235202198530),(-278456022299938051205718270303)⟩,⟨144461087244345153553346527257,144461087244345153579399744197⟩⟩,⟨⟨(-277581873557613618248149608417),(-277581873557613618218658077408)⟩,⟨144612914381038318253969932600,144612914381038318280035413661⟩⟩,⟨⟨(-276685914308779782551138121231),(-276685914308779782521638515890)⟩,⟨144766269916383644761271752922,144766269916383644787350107770⟩⟩,⟨⟨(-275768348907588871997900542873),(-275768348907588871968393215990)⟩,⟨144920951821157302497788482806,144920951821157302523879518965⟩⟩,⟨⟨(-274829387297503384692017361486),(-274829387297503384662501877108)⟩,⟨145076755100092205249970014135,145076755100092205276074308499⟩⟩,⟨⟨(-273869244998962282058118972988),(-273869244998962282028595898420)⟩,⟨145233471977771340422431384214,145233471977771340448548537213⟩⟩,⟨⟨(-272888143094616001213396977434),(-272888143094616001183865713999)⟩,⟨145390892087556403056548987656,145390892087556403082679736561⟩⟩,⟨⟨(-271886308212004040208756450435),(-271886308212004040179217546812)⟩,⟨145548802663398241117337906776,145548802663398241143481871992⟩⟩,⟨⟨(-270863972503550413278699491028),(-270863972503550413249152420636)⟩,⟨145706988734371071690817288233,145706988734371071716975138554⟩⟩,⟨⟨(-269821373623754032380832007588),(-269821373623754032351277568227)⟩,⟨145865233321767919891564102192,145865233321767919917735217073⟩⟩,⟨⟨(-268758754703453147930394478405),(-268758754703453147900831949377)⟩,⟨146023317638590273591061114285,146023317638590273617246353288⟩⟩,⟨⟨(-267676364321045377071204254148),(-267676364321045377041634411774)⟩,⟨146181021291260548089582276439,146181021291260548115781041575⟩⟩,⟨⟨(-266574456470547562795531775810),(-266574456470547562765953977225)⟩,⟨146338122483381626506869723879,146338122483381626533082800416⟩⟩] +lemma kernel1_0_r3_2_eq : ∀ k : Fin 16, kernel1_0Expr 3 2 k = kernel1_0_r3_2 k := by decide +kernel +noncomputable def kernel1_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-265453290526382741826965759424),(-265453290526382741797381131355)⟩,⟨146494398221363495266385556615,146494398221363495292612006726⟩⟩,⟨⟨(-264313131204784852857079163973),(-264313131204784852827486770832)⟩,⟨146649624521732841242028513544,146649624521732841268269409037⟩⟩,⟨⟨(-263154248521715488251145088148),(-263154248521715488221545966703)⟩,⟨146803576619937429885379719946,146803576619937429911634211974⟩⟩,⟨⟨(-261976917747190979790096406470),(-261976917747190979760489769580)⟩,⟨146956029180453154198385009519,146956029180453154224654026508⟩⟩,⟨⟨(-260781419355922409762541163171),(-260781419355922409732928427899)⟩,⟨147106756507997845253548658892,147106756507997845279830982732⟩⟩,⟨⟨(-259568038974175749398502480167),(-259568038974175749368882538701)⟩,⟨147255532759652278798973525825,147255532759652278825270398339⟩⟩,⟨⟨(-258337067322764243134060733708),(-258337067322764243104434916832)⟩,⟨147402132157685312205846586900,147402132157685312232156875004⟩⟩,⟨⟨(-257088800156090374638443536513),(-257088800156090374608810882777)⟩,⟨147546329202876754648436479185,147546329202876754674761282964⟩⟩,⟨⟨(-255823538197160263269854603586),(-255823538197160263240216964326)⟩,⟨147687898888128424079173893407,147687898888128424105511573514⟩⟩,⟨⟨(-254541587068499141211709124636),(-254541587068499141182065078747)⟩,⟨147826616912150890459890150286,147826616912150890486242255135⟩⟩,⟨⟨(-253243257218902644735094874898),(-253243257218902644705446081017)⟩,⟨147962259893010659035879943755,147962259893010659062245022238⟩⟩,⟨⟨(-251928863845965009786719061018),(-251928863845965009757064351772)⟩,⟨148094605581320023362543873006,148094605581320023388923226747⟩⟩,⟨⟨(-250598726814331883550566804059),(-250598726814331883520908385870)⟩,⟨148223433072849528408745961664,148223433072849528435137606320⟩⟩,⟨⟨(-249253170569632340095059928808),(-249253170569632340065396147800)⟩,⟨148348523020340942335198149995,148348523020340942361603861137⟩⟩,⟨⟨(-247892524048051809195653877852),(-247892524048051809165986753856)⟩,⟨148469657844296854274988809458,148469657844296854301406784513⟩⟩,⟨⟨(-246517120581514981598704428688),(-246517120581514981569032555458)⟩,⟨148586621942521507196986219983,148586621942521507223417993152⟩⟩] +lemma kernel1_0_r3_3_eq : ∀ k : Fin 16, kernel1_0Expr 3 3 k = kernel1_0_r3_3 k := by decide +kernel +noncomputable def kernel1_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-245127297798455329235729425633),(-245127297798455329206055581585)⟩,⟨148699201898186252006527369902,148699201898186252032970399549⟩⟩,⟨⟨(-243723397520155662271912908230),(-243723397520155662242234989809)⟩,⟨148807186686192083399199698915,148807186686192083425656197907⟩⟩,⟨⟨(-242305765652652122646251821256),(-242305765652652122616572242163)⟩,⟨148910367877601101221213745916,148910367877601101247681527290⟩⟩,⟨⟨(-240874752074202171417824530551),(-240874752074202171388141611867)⟩,⟨149008539841908444359657604236,149008539841908444386138466507⟩⟩,⟨⟨(-239430710518325449490286629629),(-239430710518325449460603538809)⟩,⟨149101499946926278158946582896,149101499946926278185437604162⟩⟩,⟨⟨(-237973998452434862114548022009),(-237973998452434862084861621451)⟩,⟨149189048756051791168530676162,149189048756051791195035559955⟩⟩,⟨⟨(-236504976952083840211340830948),(-236504976952083840181628749371)⟩,⟨149270990222691882213712757490,149270990222691882240269408958⟩⟩,⟨⟨(-235024010570864448555576265409),(-235024010570864448525836419808)⟩,⟨149347131881618303245248425838,149347131881618303271859012627⟩⟩,⟨⟨(-233531467205999824096779598837),(-233531467205999824067015756472)⟩,⟨149417285037028475368754909090,149417285037028475395415891387⟩⟩,⟨⟨(-232027717959683318389771446558),(-232027717959683318359980588517)⟩,⟨149481264947089022342383348878,149481264947089022369097789235⟩⟩,⟨⟨(-230513136996225666910941978012),(-230513136996225666881127335017)⟩,⟨149538891004741274325040512436,149538891004741274351805375667⟩⟩,⟨⟨(-228988101395080495007677403043),(-228988101395080494977836587955)⟩,⟨149589986914550590581448034920,149589986914550590608265751459⟩⟩,⟨⟨(-227452990999827474920977999134),(-227452990999827474891115261259)⟩,⟨149634380865384338138568417737,149634380865384338165434941457⟩⟩,⟨⟨(-225908188263201449808490537213),(-225908188263201449778602565054)⟩,⟨149671905698706748041239275400,149671905698706748068157921025⟩⟩,⟨⟨(-224354078088264817624568017448),(-224354078088264817594658567535)⟩,⟨149702399072282654899146963544,149702399072282654926114147156⟩⟩,⟨⟨(-222791047665829398359609118471),(-222791047665829398329675463874)⟩,⟨149725703619086310862222046315,149725703619086310889240496473⟩⟩] +lemma kernel1_0_r3_4_eq : ∀ k : Fin 16, kernel1_0Expr 3 4 k = kernel1_0_r3_4 k := by decide +kernel +noncomputable def kernel1_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-221219486308242870456749973606),(-221219486308242870426797263218)⟩,⟨149741667101216052964925204880,149741667101216052991989961692⟩⟩,⟨⟨(-219639785279663633903422816091),(-219639785279663633873447021020)⟩,⟨149750142558620592811478319451,149750142558620592838593364808⟩⟩,⟨⟨(-218052337622956616030163772206),(-218052337622956616000169200852)⟩,⟨149750988452448088586092480905,149750988452448088613253656604⟩⟩,⟨⟨(-216457537983351058794612375859),(-216457537983351058764595926677)⟩,⟨149744068802834948969554693840,149744068802834948996765061467⟩⟩,⟨⟨(-214855782429009690567348791931),(-214855782429009690537316075923)⟩,⟨149729253320957503161274556349,149729253320957503188528668761⟩⟩,⟨⟨(-213247468268666868447626282669),(-213247468268666868417572980573)⟩,⟨149706417535176246086820299122,149706417535176246114122390220⟩⟩,⟨⟨(-211632993866501256265657818167),(-211632993866501256235588814588)⟩,⟨149675442911109327050952748853,149675442911109327078298062536⟩⟩,⟨⟨(-210012758454416356157137683209),(-210012758454416356127049466540)⟩,⟨149636216965479286389666497433,149636216965479286417058464176⟩⟩,⟨⟨(-208387161941909715618132544936),(-208387161941909715588031729258)⟩,⟨149588633373584749668947873654,149588633373584749696380031246⟩⟩,⟨⟨(-206756604723718865243922440017),(-206756604723718865213803862915)⟩,⟨149532592070256853027015431446,149532592070256853054492806777⟩⟩,⟨⟨(-205121487485438983263072979164),(-205121487485438983232942121421)⟩,⟨149467999344168585485298596133,149467999344168585512815816085⟩⟩,⟨⟨(-203482211007313910275541192923),(-203482211007313910245394099627)⟩,⟨149394767925373982359945460703,149394767925373982387506358691⟩⟩,⟨⟨(-201839175966408430580900554647),(-201839175966408430550744330460)⟩,⟨149312817065963174976203538032,149312817065963175003801137495⟩⟩,⟨⟨(-200192782737375675021408105740),(-200192782737375674991237242591)⟩,⟨149222072613728681209242422635,149222072613728681236882059724⟩⟩,⟨⟨(-198543431192039064911573281874),(-198543431192039064881393874952)⟩,⟨149122467078747993257802263609,149122467078747993285477931017⟩⟩,⟨⟨(-196891520498013388671951350126),(-196891520498013388641758967365)⟩,⟨149013939692797466660032392605,149013939692797466687748361673⟩⟩] +lemma kernel1_0_r3_5_eq : ∀ k : Fin 16, kernel1_0Expr 3 5 k = kernel1_0_r3_5 k := by decide +kernel +noncomputable def kernel1_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-195237448916594364336841556016),(-195237448916594364306644524271)⟩,⟨148896436461522719924190646003,148896436461522719951938711576⟩⟩,⟨⟨(-193581613600150375162556802549),(-193581613600150375132348520773)⟩,⟨148769910209301198225767868471,148769910209301198253554408267⟩⟩,⟨⟨(-191924410389253956085383961921),(-191924410389253956055171152094)⟩,⟨148634320616743217331767573986,148634320616743217359585935273⟩⟩,⟨⟨(-190266233609794040760922149117),(-190266233609794040730699872297)⟩,⟨148489634250788664169913970794,148489634250788664197768894083⟩⟩,⟨⟨(-188607475870312938452367052631),(-188607475870312938422144011234)⟩,⟨148335824587367566240532392035,148335824587367566268415271909⟩⟩,⟨⟨(-186948527859814484384297560803),(-186948527859814484354066888180)⟩,⟨148172872026603930457296636752,148172872026603930485214086428⟩⟩,⟨⟨(-185289778146291784825296299653),(-185289778146291784795065356075)⟩,⟨148000763900553569260312293424,148000763900553569288257004597⟩⟩,⟨⟨(-183631612976224448878491591411),(-183631612976224448848254900358)⟩,⟨147819494473478053468444401792,147819494473478053496421616629⟩⟩,⟨⟨(-181974416075296153852529207505),(-181974416075296153822296752402)⟩,⟨147629064934668432135008148080,147629064934668432163007976346⟩⟩,⟨⟨(-180318568450583822656619350929),(-180318568450583822626383074927)⟩,⟨147429483383843913830340190102,147429483383843913858370387451⟩⟩,⟨⟨(-178664448194469593845835525896),(-178664448194469593815603432345)⟩,⟨147220764809162284947040641101,147220764809162284975093240268⟩⟩,⟨⟨(-177012430290526133148948947147),(-177012430290526133118714996456)⟩,⟨147002931057890421999652832840,147002931057890422027733605276⟩⟩,⟨⟨(-175362886421624666463744179546),(-175362886421624666433518745067)⟩,⟨146776010799794809289798804779,146776010799794809317897448585⟩⟩,⟨⟨(-173716184780513406872601700512),(-173716184780513406842376404259)⟩,⟨146540039483323473262536093749,146540039483323473290660659715⟩⟩,⟨⟨(-172072689883111802249658897458),(-172072689883111802219442389853)⟩,⟨146295059284662162729287160477,146295059284662162757429019946⟩⟩,⟨⟨(-170432762384763247126138248547),(-170432762384763247095923901196)⟩,⟨146041119049758912112313297549,146041119049758912140478779318⟩⟩] +lemma kernel1_0_r3_6_eq : ∀ k : Fin 16, kernel1_0Expr 3 6 k = kernel1_0_r3_6 k := by decide +kernel +noncomputable def kernel1_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-168796758899685585878528361589),(-168796758899685585848328080779)⟩,⟨145778274229422295205148430283,145778274229422295233325702866⟩⟩,⟨⟨(-167165031823854888843045425921),(-167165031823854888812849347775)⟩,⟨145506586807609681959033504254,145506586807609681987232057148⟩⟩,⟨⟨(-165537929161553615085631028197),(-165537929161553615055448446476)⟩,⟨145226125223032623001634311643,145226125223032623029844860100⟩⟩,⟨⟨(-163915794355809393324009470386),(-163915794355809393293833148733)⟩,⟨144936964284217078757219328516,144936964284217078785448780459⟩⟩,⟨⟨(-162298966122945265553068428373),(-162298966122945265522910449203)⟩,⟨144639185078166555337255982877,144639185078166555365492307948⟩⟩,⟨⟨(-160687778291456357491406699390),(-160687778291456357461257045801)⟩,⟨144332874872786281454652584571,144332874872786281482905408688⟩⟩,⟨⟨(-159082559645421578818481204824),(-159082559645421578788349811168)⟩,⟨144018127013236333710497008751,144018127013236333738756395534⟩⟩,⟨⟨(-157483633772652128604070423565),(-157483633772652128573949424929)⟩,⟨143695040812391066606443956348,143695040812391066634717416145⟩⟩,⟨⟨(-155891318917771303120414009922),(-155891318917771303090317034277)⟩,⟨143363721435591304215815178028,143363721435591304244089140847⟩⟩,⟨⟨(-154305927840412391589056166295),(-154305927840412391558971651295)⟩,⟨143024279779884479125863753169,143024279779884479154149349432⟩⟩,⟨⟨(-152727767678713318951439073767),(-152727767678713318921377583236)⟩,⟨142676832347956238517999602414,142676832347956238546286256879⟩⟩,⟨⟨(-151157139818278173401527391348),(-151157139818278173371480419296)⟩,⟨142321501116964955590761666582,142321501116964955619057507478⟩⟩,⟨⟨(-149594339766766861384023137470),(-149594339766766861354004481235)⟩,⟨141958413402498066582315491975,141958413402498066610606761084⟩⟩,⟨⟨(-148039657034264886451498581914),(-148039657034264886421496485884)⟩,⟨141587701717876180241210642175,141587701717876180269508651844⟩⟩,⟨⟨(-146493375019575674322168476327),(-146493375019575674292194123924)⟩,⟨141209503629037459828185716200,141209503629037459856479263944⟩⟩,⟨⟨(-144955770902567989274092046629),(-144955770902567989244136277267)⟩,⟨140823961605240841051111271810,140823961605240841079409120181⟩⟩] +lemma kernel1_0_r3_7_eq : ∀ k : Fin 16, kernel1_0Expr 3 7 k = kernel1_0_r3_7 k := by decide +kernel +noncomputable def kernel1_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-143427115542700832202408078408),(-143427115542700832172486572010)⟩,⟨140431222865832207594766317054,140431222865832207623052839945⟩⟩,⟨⟨(-141907673383837804686987545393),(-141907673383837804657086612088)⟩,⟨140031439223322685428217749279,140031439223322685456506152782⟩⟩,⟨⟨(-140397702365452293486400574446),(-140397702365452293456531998023)⟩,⟨139624766923032725702330378144,139624766923032725730608853384⟩⟩,⟨⟨(-138897453840314003903248716926),(-138897453840314003873402678331)⟩,⟨139211366479559613203877820465,139211366479559613232155771270⟩⟩,⟨⟨(-137407172498736376958963176828),(-137407172498736376929155160089)⟩,⟨138791402510329454042515324952,138791402510329454070777299844⟩⟩,⟨⟨(-135927096299453293271696853568),(-135927096299453293241913299731)⟩,⟨138365043566497555189333757299,138365043566497555217592832025⟩⟩,⟨⟨(-134457456407182225332634006168),(-134457456407182225302887284546)⟩,⟨137932461961463404017711032508,137932461961463404045954808359⟩⟩,⟨⟨(-132998477136919679193597946634),(-132998477136919679163877572330)⟩,⟨137493833597268184170907314287,137493833597268184199145846669⟩⟩,⟨⟨(-131550375905003396254551958174),(-131550375905003396224875208515)⟩,⟨137049337789143922664769696008,137049337789143922692985755723⟩⟩,⟨⟨(-130113363186964395787184474890),(-130113363186964395757535906014)⟩,⟨136599157088483951613724092143,136599157088483951641932607823⟩⟩,⟨⟨(-128687642482180558920645045470),(-128687642482180558891037587464)⟩,⟨136143477104504387553691364207,136143477104504387581879373582⟩⟩,⟨⟨(-127273410285332114773582835397),(-127273410285332114744005341275)⟩,⟨135682486324865784946897084218,135682486324865784975075293532⟩⟩,⟨⟨(-125870856064648118710268841279),(-125870856064648118680738427413)⟩,⟨135216375935523012714136459090,135216375935523012742287783965⟩⟩,⟨⟨(-124480162246921840437666341368),(-124480162246921840408167613126)⟩,⟨134745339640069739848192786056,134745339640069739876332110293⟩⟩,⟨⟨(-123101504209261934485844319776),(-123101504209261934456390747968)⟩,⟨134269573478841706269839161353,134269573478841706297952980730⟩⟩,⟨⟨(-121735050277535375603359929822),(-121735050277535375573939705818)⟩,⟨133789275648040207658789128147,133789275648040207686888802099⟩⟩] +lemma kernel1_0_r3_8_eq : ∀ k : Fin 16, kernel1_0Expr 3 8 k = kernel1_0_r3_8 k := by decide +kernel +noncomputable def kernel1_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-120380961731447434159134078220),(-120380961731447434129766486319)⟩,⟨133304646319133949166571307155,133304646319133949194637607385⟩⟩,⟨⟨(-119039392816193468420783844169),(-119039392816193468391451190712)⟩,⟨132815887458793635358414725675,132815887458793635386464803219⟩⟩,⟨⟨(-117710490760607047365201840447),(-117710490760607047335918105978)⟩,⟨132323202649609376572838764873,132323202649609376600858605868⟩⟩,⟨⟨(-116394395801718914319300413580),(-116394395801718914290053140932)⟩,⟨131826796911836220673045176145,131826796911836220701046782922⟩⟩,⟨⟨(-115091241215631582044548129088),(-115091241215631582015355986302)⟩,⟨131326876526407880783570126120,131326876526407880811534867355⟩⟩,⟨⟨(-113801153354604936582761751807),(-113801153354604936553607514414)⟩,⟨130823648859453042217786459510,130823648859453042245731032901⟩⟩,⟨⟨(-112524251690239141802428390912),(-112524251690239141773326526803)⟩,⟨130317322188542514765929000713,130317322188542514793838906506⟩⟩,⟨⟨(-111260648862632399409449111153),(-111260648862632399380386521030)⟩,⟨129808105530888970300269334038,129808105530888970328157213538⟩⟩,⟨⟨(-110010450735382749182930853371),(-110010450735382749153928236656)⟩,⟨129296208473714091769606802405,129296208473714091797452016587⟩⟩,⟨⟨(-108773756456295108970981647058),(-108773756456295108942019584752)⟩,⟨128781841006990680543478076487,128781841006990680571299493836⟩⟩,⟨⟨(-107550658523647169716761056249),(-107550658523647169687854469808)⟩,⟨128265213358759648026341555075,128265213358759648054124224813⟩⟩,⟨⟨(-106341242857860592207240751559),(-106341242857860592178375919655)⟩,⟨127746535833213878544770794560,127746535833213878572527979327⟩⟩,⟨⟨(-105145588878417212569356416853),(-105145588878417212540553463729)⟩,⟨127226018651732718431873248034,127226018651732718459584869447⟩⟩,⟨⟨(-103963769585853664479299594193),(-103963769585853664450539501714)⟩,⟨126703871797042346265592173262,126703871797042346293276717099⟩⟩,⟨⟨(-102795851648661977743016139312),(-102795851648661977714314257332)⟩,⟨126180304860668537100662963317,126180304860668537128305054036⟩⟩,⟨⟨(-101641895494918323927779062150),(-101641895494918323899121061039)⟩,⟨125655526893839375365009198515,125655526893839375392622708457⟩⟩] +lemma kernel1_0_r3_9_eq : ∀ k : Fin 16, kernel1_0Expr 3 9 k = kernel1_0_r3_9 k := by decide +kernel +noncomputable def kernel1_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-100501955408457157071760274480),(-100501955408457157043168834354)⟩,⟨125129746261986323233482923587,125129746261986323261045251134⟩⟩,⟨⟨(-99376079629403546590155849916),(-99376079629403546561609210131)⟩,⟨124603170502982740265489403969,124603170502982740293021751036⟩⟩,⟨⟨(-98264310458872524170575146744),(-98264310458872524142089047381)⟩,⟨124076006189249502485198390094,124076006189249502512684995312⟩⟩,⟨⟨(-97166684367640768983234792693),(-97166684367640768954794324871)⟩,⟨123548458793847811440385859526,123548458793847811467841177947⟩⟩,⟨⟨(-96083232108592936645200244102),(-96083232108592936616826876341)⟩,⟨123020732560669642517442253670,123020732560669642544844875085⟩⟩,⟨⟨(-95013978832742396273587011694),(-95013978832742396245260003209)⟩,⟨122493030378826583103388291115,122493030378826583130758427103⟩⟩,⟨⟨(-93958944208624074340115701763),(-93958944208624074311851158563)⟩,⟨121965553661328080944971556780,121965553661328080972293085273⟩⟩,⟨⟨(-92918142544855510141996248510),(-92918142544855510113778700140)⟩,⟨121438502228130386722634761594,121438502228130386749922704290⟩⟩,⟨⟨(-91891582915661100349942807191),(-91891582915661100321795994987)⟩,⟨120912074193627757408271616554,120912074193627757435502319783⟩⟩,⟨⟨(-90879269289153842731684241235),(-90879269289153842703584951706)⟩,⟨120386465858647812806590366723,120386465858647812833786496614⟩⟩,⟨⟨(-89881200658168673898921069789),(-89881200658168673870885736743)⟩,⟨119861871607003330540252464271,119861871607003330567397576678⟩⟩,⟨⟨(-88897371173441723644480707111),(-88897371173441723616493332571)⟩,⟨119338483806643247649074308536,119338483806643247676183959326⟩⟩,⟨⟨(-87927770278930468768482999397),(-87927770278930468740566282969)⟩,⟨118816492715436232165587280799,118816492715436232192638843412⟩⟩,⟨⟨(-86972382849070850742182971268),(-86972382849070850714314541259)⟩,⟨118296086391610916873439633476,118296086391610916900454960291⟩⟩,⟨⟨(-86031189327768911547695517253),(-86031189327768911519892109677)⟩,⟨117777450608867770411384653611,117777450608867770438347004509⟩⟩,⟨⟨(-85104165868926386980305198150),(-85104165868926386952550311359)⟩,⟨117260768776168637440222741101,117260768776168637467148183429⟩⟩] +lemma kernel1_0_r3_10_eq : ∀ k : Fin 16, kernel1_0Expr 3 10 k = kernel1_0_r3_10 k := by decide +kernel +noncomputable def kernel1_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-84191284478301962086882877175),(-84191284478301962059202048501)⟩,⟨116746221862201228217636253746,116746221862201228244499360082⟩⟩,⟨⟨(-83292513156512523863392519856),(-83292513156512523835760335948)⟩,⟨116233988324507296036942228748,116233988324507296063767870788⟩⟩,⟨⟨(-82407816042981725682365671867),(-82407816042981725654799129922)⟩,⟨115724244043254924900104963175,115724244043254924926876146036⟩⟩,⟨⟨(-81537153560646489302988968480),(-81537153560646489275471104703)⟩,⟨115217162259627274700508449384,115217162259627274727241711501⟩⟩,⟨⟨(-80680482561235696235646808709),(-80680482561235696208201433048)⟩,⟨114712913518792311127283646955,114712913518792311153955267330⟩⟩,⟨⟨(-79837756470939242651297932811),(-79837756470939242623901161273)⟩,⟨114211665617410495332845834111,114211665617410495359479192148⟩⟩,⟨⟨(-79008925436289832432962585215),(-79008925436289832405631653653)⟩,⟨113713583555630135809648695575,113713583555630135836226564433⟩⟩,⟨⟨(-78193936470084342467976241627),(-78193936470084342440693749538)⟩,⟨113218829493513122381072220312,113218829493513122407611584750⟩⟩,⟨⟨(-77392733597176293666913321008),(-77392733597176293639705610059)⟩,⟨112727562711827079010988099455,112727562711827079037462739381⟩⟩,⟨⟨(-76605257999975881033143305206),(-76605257999975881005983761609)⟩,⟨112239939577133596360480461611,112239939577133596386916470098⟩⟩,⟨⟨(-75831448163499136800070761341),(-75831448163499136772976819938)⟩,⟨111756113511096143566864396887,111756113511096143593244354737⟩⟩,⟨⟨(-75071240019813102530094684754),(-75071240019813102503048552849)⟩,⟨111276234963925517304038568683,111276234963925517330379863161⟩⟩,⟨⟨(-74324567091729349445488899104),(-74324567091729349418515383912)⟩,⟨110800451391875269362199570385,110800451391875269388477499443⟩⟩,⟨⟨(-73591360635603791520112147164),(-73591360635603791493185981174)⟩,⟨110328907238694465170175205974,110328907238694465196414550147⟩⟩,⟨⟨(-72871549783106463510146317811),(-72871549783106463483285111727)⟩,⟨109861743920940367175880172928,109861743920940367202063343811⟩⟩,⟨⟨(-72165061681830766850851279415),(-72165061681830766824036878340)⟩,⟨109399099817049210008339145333,109399099817049210034483903000⟩⟩] +lemma kernel1_0_r3_11_eq : ∀ k : Fin 16, kernel1_0Expr 3 11 k = kernel1_0_r3_11 k := by decide +kernel +noncomputable def kernel1_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-71471821634617601155535884663),(-71471821634617601128796432213)⟩,⟨108941110260059139028710329523,108941110260059139054788676773⟩⟩,⟨⟨(-70791753237475779205468891255),(-70791753237475779178775598426)⟩,⟨108487907533875619375237706853,108487907533875619401277921573⟩⟩,⟨⟨(-70124778515986150464587461405),(-70124778515986150437958072021)⟩,⟨108039620872966187083118717242,108039620872966187109103084250⟩⟩,⟨⟨(-69470818060082914369553350181),(-69470818060082914342969398543)⟩,⟨107596376465368304538822391159,107596376465368304564768992302⟩⟩,⟨⟨(-68829791157111672479482813289),(-68829791157111672452969986895)⟩,⟨107158297458891295748475642713,107158297458891295774358911321⟩⟩,⟨⟨(-68201615923069831089190469544),(-68201615923069831062722265368)⟩,⟨106725503970390868151124448930,106725503970390868176970419982⟩⟩,⟨⟨(-67586209431941006735835104030),(-67586209431941006709429380112)⟩,⟨106298113097992571690889775831,106298113097992571716680626132⟩⟩,⟨⟨(-66983487843041090383074830502),(-66983487843041090356712839336)⟩,⟨105876238936138696528729442968,105876238936138696554483547072⟩⟩,⟨⟨(-66393366526299576793475427704),(-66393366526299576767185674532)⟩,⟨105459992593331561390008751398,105459992593331561415697759067⟩⟩,⟨⟨(-65815760185405649206644163985),(-65815760185405649180397163983)⟩,⟨105049482212444887729270185822,105049482212444887754923096434⟩⟩,⟨⟨(-65250582978754312112500960101),(-65250582978754312086314645046)⟩,⟨104644812993473982690100682982,104644812993473982715699605340⟩⟩,⟨⟨(-64697748638133573542063467005),(-64697748638133573515918859785)⟩,⟨104246087218594757751017071845,104246087218594757776580621056⟩⟩,⟨⟨(-64157170585099280504824440269),(-64157170585099280478748005794)⟩,⟨103853404279401181012664021215,103853404279401181038165867805⟩⟩,⟨⟨(-63628762044989695338287221904),(-63628762044989695312251368387)⟩,⟨103466860706190589904197898578,103466860706190589929665185043⟩⟩,⟨⟨(-63112436158537255899510291010),(-63112436158537255873533003003)⟩,⟨103086550199166367912409833521,103086550199166367937824621311⟩⟩,⟨⟨(-62608106091040178579787320203),(-62608106091040178553849424569)⟩,⟨102712563661427803690544302833,102712563661427803715925413727⟩⟩] +lemma kernel1_0_r3_12_eq : ∀ k : Fin 16, kernel1_0Expr 3 12 k = kernel1_0_r3_12 k := by decide +kernel +noncomputable def kernel1_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-62115685139061630674499503752),(-62115685139061630648631092128)⟩,⟨102344989233617493253501396816,102344989233617493278818916182⟩⟩,⟨⟨(-61635086834629109069441206158),(-61635086834629109043610921361)⟩,⟨101983912330097405364735820265,101983912330097405390020629966⟩⟩,⟨⟨(-61166225046911407643295082938),(-61166225046911407617520917932)⟩,⟨101629415676525695966351411431,101629415676525695991585569295⟩⟩,⟨⟨(-60709014081355129123058402917),(-60709014081355129097321047027)⟩,⟨101281579348707518779673636448,101281579348707518804876112308⟩⟩,⟨⟨(-60263368776267091993649056073),(-60263368776267091967975642924)⟩,⟨100940480812594425133942750105,100940480812594425159086558796⟩⟩,⟨⟨(-59829204596833193824437112488),(-59829204596833193798799124022)⟩,⟨100606194965308465766940007906,100606194965308465792053235798⟩⟩,⟨⟨(-59406437726568314119845951238),(-59406437726568314094261371024)⟩,⟨100278794177068789917257007003,100278794177068789942321725703⟩⟩,⟨⟨(-58994985156195668327773520400),(-58994985156195668302222932730)⟩,⟨99958348333900371689957413572,99958348333900371714992707953⟩⟩,⟨⟨(-58594764769957656432481747496),(-58594764769957656406995419658)⟩,⟨99644924881006469736314691244,99644924881006469761290477446⟩⟩,⟨⟨(-58205695429363681780208982597),(-58205695429363681754755154780)⟩,⟨99338588866688533195044048226,99338588866688533219991633202⟩⟩,⟨⟨(-57827697054383646244686829601),(-57827697054383646219283432286)⟩,⟨99039402986699494235515448001,99039402986699494260416960118⟩⟩,⟨⟨(-57460690702098854981437395046),(-57460690702098854956064966951)⟩,⟨98747427628918725270262604023,98747427628918725295137183444⟩⟩,⟨⟨(-57104598642824886891469210137),(-57104598642824886866155455819)⟩,⟨98462720918239377064138971900,98462720918239377088959073758⟩⟩,⟨⟨(-56759344433723605154950943959),(-56759344433723605129666578262)⟩,⟨98185338761561342928131063844,98185338761561342952925557190⟩⟩,⟨⟨(-56424852989923895995460918561),(-56424852989923895970223797382)⟩,⟨97915334892785704621253809525,97915334892785704646004900459⟩⟩,⟨⟨(-56101050653172933928267842979),(-56101050653172933903058497253)⟩,⟨97652760917709198486436156829,97652760917709198511163002427⟩⟩] +lemma kernel1_0_r3_13_eq : ∀ k : Fin 16, kernel1_0Expr 3 13 k = kernel1_0_r3_13 k := by decide +kernel +noncomputable def kernel1_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-55787865258041779367682799778),(-55787865258041779342533172545)⟩,⟨97397666358719987059802556105,97397666358719987084473417711⟩⟩,⟨⟨(-55485226195710921344135587941),(-55485226195710921319012080246)⟩,⟨97150098699198823619712267510,97150098699198823644360294878⟩⟩,⟨⟨(-55193064475362986387598197637),(-55193064475362986362518539625)⟩,⟨96910103427532546972079793954,96910103427532546996687321247⟩⟩,⟨⟨(-54911312783211246983890368375),(-54911312783211246958835151568)⟩,⟨96677724080649733681021818596,96677724080649733705607951119⟩⟩,⟨⟨(-54639905539193782416420255158),(-54639905539193782391417642647)⟩,⟨96453002286991257841949209593,96453002286991257866485953064⟩⟩,⟨⟨(-54378778951364174666185567070),(-54378778951364174641205686198)⟩,⟨96235977808831457661908814518,96235977808831457686425638675⟩⟩,⟨⟨(-54127871068010466103044835839),(-54127871068010466078105271453)⟩,⟨96026688583868577294889601449,96026688583868577319368987515⟩⟩,⟨⟨(-53887121827534768042407286744),(-53887121827534768017488727969)⟩,⟨95825170766006135738080788742,95825170766006135762541752558⟩⟩,⟨⟨(-53656473106126394243364270346),(-53656473106126394218498352871)⟩,⟨95631458765249866729194553149,95631458765249866753605663637⟩⟩,⟨⟨(-53435868763261705754246652740),(-53435868763261705729399992155)⟩,⟨95445585286647869525102107466,95445585286647869549496319556⟩⟩,⟨⟨(-53225254685063998089435776605),(-53225254685063998064625760855)⟩,⟨95267581368204605659938955497,95267581368204605684298948189⟩⟩,⟨⟨(-53024578825556743709664695633),(-53024578825556743684872181354)⟩,⟨95097476417702367175519687694,95097476417702367199864317104⟩⟩,⟨⟨(-52833791245843327548963103147),(-52833791245843327524216605847)⟩,⟨94935298248366823723289087559,94935298248366823747590013989⟩⟩,⟨⟨(-52652844151246086459029769456),(-52652844151246086434299006878)⟩,⟨94781073113316226107578188252,94781073113316226131865301438⟩⟩,⟨⟨(-52481691926436990670603698819),(-52481691926436990645905834095)⟩,⟨94634825738736799450461150855,94634825738736799474717354826⟩⟩,⟨⟨(-52320291168591692610706242713),(-52320291168591692586022346544)⟩,⟨94496579355729797787196631070,94496579355729797811440575046⟩⟩] +lemma kernel1_0_r3_14_eq : ∀ k : Fin 16, kernel1_0Expr 3 14 k = kernel1_0_r3_14 k := by decide +kernel +noncomputable def kernel1_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-52168600718597921709468737223),(-52168600718597921684831872972)⟩,⟨94366355730778611530934642058,94366355730778611555133483546⟩⟩,⟨⟨(-52026581690348329357944221489),(-52026581690348329333319557705)⟩,⟨94244175194787218240108412960,94244175194787218264296552548⟩⟩,⟨⟨(-51894197498146892221323990592),(-51894197498146892196728403219)⟩,⟨94130056670644144226745627242,94130056670644144250906255356⟩⟩,⟨⟨(-51771413882256871056890525670),(-51771413882256871032305381238)⟩,⟨94024017699268958858944626078,94024017699268958883096103013⟩⟩,⟨⟨(-51658198932617102498156674220),(-51658198932617102473610704957)⟩,⟨93926074464101154389178381352,93926074464101154413292155278⟩⟩,⟨⟨(-51554523110752079491908463912),(-51554523110752079467371189781)⟩,⟨93836241813994071559413509428,93836241813994071583519675584⟩⟩,⟨⟨(-51460359269899858816245536765),(-51460359269899858791733516887)⟩,⟨93754533284479315192597848712,93754533284479315216679912854⟩⟩,⟨⟨(-51375682673380328028590616125),(-51375682673380328004085562302)⟩,⟨93680961117369864866997481338,93680961117369864891073464799⟩⟩,⟨⟨(-51300471011224775996101887067),(-51300471011224775971636346896)⟩,⟨93615536278672824259131047299,93615536278672824283168620026⟩⟩,⟨⟨(-51234704415086047594661445696),(-51234704415086047570201162814)⟩,⟨93558268474785469760385134291,93558268474785469784418134907⟩⟩,⟨⟨(-51178365471446831000105449790),(-51178365471446830975666599196)⟩,⟨93509166166950955695924979258,93509166166950955719937295072⟩⟩,⟨⟨(-51131439233141832042437824162),(-51131439233141832018002550787)⟩,⟨93468236583952711290507968344,93468236583952711314517193676⟩⟩,⟨⟨(-51093913229207741171130969253),(-51093913229207741146728076330)⟩,⟨93435485733029225028496913029,93435485733029225052474427160⟩⟩,⟨⟨(-51065777473073001531604701810),(-51065777473073001507203737823)⟩,⟨93410918408993557011023066493,93410918408993557034998941223⟩⟩,⟨⟨(-51047024469097448331046570313),(-51047024469097448306663283899)⟩,⟨93394538201544551251520365552,93394538201544551275478911132⟩⟩,⟨⟨(-51037649217469916943934982905),(-51037649217469916919552015411)⟩,⟨93386347500759339630616054914,93386347500759339654574374935⟩⟩] +lemma kernel1_0_r3_15_eq : ∀ k : Fin 16, kernel1_0Expr 3 15 k = kernel1_0_r3_15 k := by decide +kernel +noncomputable def kernel1_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel1_0_r3_0,kernel1_0_r3_1,kernel1_0_r3_2,kernel1_0_r3_3,kernel1_0_r3_4,kernel1_0_r3_5,kernel1_0_r3_6,kernel1_0_r3_7,kernel1_0_r3_8,kernel1_0_r3_9,kernel1_0_r3_10,kernel1_0_r3_11,kernel1_0_r3_12,kernel1_0_r3_13,kernel1_0_r3_14,kernel1_0_r3_15] +lemma kernel1_0_r3_eq (i k : Fin 16) : kernel1_0Expr 3 i k = kernel1_0_r3 i k := by + fin_cases i + · exact kernel1_0_r3_0_eq k + · exact kernel1_0_r3_1_eq k + · exact kernel1_0_r3_2_eq k + · exact kernel1_0_r3_3_eq k + · exact kernel1_0_r3_4_eq k + · exact kernel1_0_r3_5_eq k + · exact kernel1_0_r3_6_eq k + · exact kernel1_0_r3_7_eq k + · exact kernel1_0_r3_8_eq k + · exact kernel1_0_r3_9_eq k + · exact kernel1_0_r3_10_eq k + · exact kernel1_0_r3_11_eq k + · exact kernel1_0_r3_12_eq k + · exact kernel1_0_r3_13_eq k + · exact kernel1_0_r3_14_eq k + · exact kernel1_0_r3_15_eq k +noncomputable def kernel1_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-607729013232032715820163380663),(-607729013232032715774099762963)⟩,⟨(-110316588469793141622747496340),(-110316588469793141579015506555)⟩⟩,⟨⟨(-607712171864288649645991733560),(-607712171864288649599926463108)⟩,⟨(-110285687455867237478349775232),(-110285687455867237434616574060)⟩⟩,⟨⟨(-607678486777009123092666233365),(-607678486777009123046597706886)⟩,⟨(-110223894186255529057681179274),(-110223894186255529013945604003)⟩⟩,⟨⟨(-607627953271362918859902465790),(-607627953271362918813829080670)⟩,⟨(-110131226175643583148860737437),(-110131226175643583105121625621)⟩⟩,⟨⟨(-607560564310978291604780174497),(-607560564310978291558700329557)⟩,⟨(-110007709691570364841528304590),(-110007709691570364797784494612)⟩⟩,⟨⟨(-607476310536182291979032202304),(-607476310536182291932944298045)⟩,⟨(-109853379749033134586356737534),(-109853379749033134542607068660)⟩⟩,⟨⟨(-607375180282968575663447880017),(-607375180282968575617350319804)⟩,⟨(-109668280103280929931352949077),(-109668280103280929887596262425)⟩⟩,⟨⟨(-607257159606678302557699315282),(-607257159606678302511590503809)⟩,⟨(-109452463240785488940448832583),(-109452463240785488896683969412)⟩⟩,⟨⟨(-607122232310374878054437346056),(-607122232310374878008315694402)⟩,⟨(-109205990368375737422491360018),(-109205990368375737378717166540)⟩⟩,⟨⟨(-606970379977889432221161229259),(-606970379977889432175025146906)⟩,⟨(-108928931400519261074799211038),(-108928931400519261031014530325)⟩⟩,⟨⟨(-606801582011510073293371874405),(-606801582011510073247219783217)⟩,⟨(-108621364944731523184622536010),(-108621364944731523140826221622)⟩⟩,⟨⟨(-606615815674284088782988579125),(-606615815674284088736818893969)⟩,⟨(-108283378285090975310087707028),(-108283378285090975266278603675)⟩⟩,⟨⟨(-606413056136898400447828534097),(-606413056136898400401639693176)⟩,⟨(-107915067363835649015844062390),(-107915067363835648972021035705)⟩⟩,⟨⟨(-606193276529099708169454825003),(-606193276529099708123245246942)⟩,⟨(-107516536761014317858212989110),(-107516536761014317814374883069)⟩⟩,⟨⟨(-605956447995611882375135894148),(-605956447995611882328904034652)⟩,⟨(-107087899672162886938694347616),(-107087899672162886894840040315)⟩⟩,⟨⟨(-605702539756504285062375989417),(-605702539756504285016120272898)⟩,⟨(-106629277883974308953234351142),(-106629277883974308909362687081)⟩⟩] +lemma kernel1_0_r4_0_eq : ∀ k : Fin 16, kernel1_0Expr 4 0 k = kernel1_0_r4_0 k := by decide +kernel +noncomputable def kernel1_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-605431519171960815919830338142),(-605431519171960815873549249729)⟩,⟨(-106140801747928047172546447679),(-106140801747928047128656328441)⟩⟩,⟨⟨(-605143351811395592806376434541),(-605143351811395592760068396473)⟩,⟨(-105622610151842913538774014784),(-105622610151842913494864276789)⟩⟩,⟨⟨(-604838001526857285422485133752),(-604838001526857285376148655544)⟩,⟨(-105074850489315010319445417619),(-105074850489315010275514980226)⟩⟩,⟨⟨(-604515430530660228018357360238),(-604515430530660227971990870299)⟩,⟨(-104497678627000502697956670131),(-104497678627000502654004369185)⟩⟩,⟨⟨(-604175599477176542236273005993),(-604175599477176542189875060799)⟩,⟨(-103891258869701053383421971684),(-103891258869701053339446765892)⟩⟩,⟨⟨(-603818467548719605665161500774),(-603818467548719605618730516289)⟩,⟨(-103255763923207964772182963715),(-103255763923207964728183669253)⟩⟩,⟨⟨(-603443992545445306567225674697),(-603443992545445306520760238137)⟩,⟨(-102591374854859405258688694077),(-102591374854859405214664292265)⟩⟩,⟨⟨(-603052130979193631890046340876),(-603052130979193631843544875365)⟩,⟨(-101898281051763549726099632271),(-101898281051763549682048938278)⟩⟩,⟨⟨(-602642838171189245677820577808),(-602642838171189245631281744214)⟩,⟨(-101176680176639045670385054515),(-101176680176639045626307113941)⟩⟩,⟨⟨(-602216068353515830128447009707),(-602216068353515830081869198851)⟩,⟨(-100426778121222931312677317465),(-100426778121222931268570904826)⟩⟩,⟨⟨(-601771774774275083812965724659),(-601771774774275083766347629092)⟩,⟨(-99648788957194985773846921924),(-99648788957194985729711104984)⟩⟩,⟨⟨(-601309909806337403207793706853),(-601309909806337403161133730717)⟩,⟨(-98842934884566489107485160859),(-98842934884566489063318717860)⟩⟩,⟨⟨(-600830425059587417144241112560),(-600830425059587417097538050563)⟩,⟨(-98009446177480516731704884499),(-98009446177480516687506974273)⟩⟩,⟨⟨(-600333271496563701742987908086),(-600333271496563701696240110741)⟩,⟨(-97148561127370193409338030801),(-97148561127370193365107368584)⟩⟩,⟨⟨(-599818399551388178799305027647),(-599818399551388178752511324359)⟩,⟨(-96260525983420791056524372595),(-96260525983420791012260141048)⟩⟩,⟨⟨(-599285759251876896583371576519),(-599285759251876896536530334772)⟩,⟨(-95345594890281176770291323368),(-95345594890281176725992243789)⟩⟩] +lemma kernel1_0_r4_1_eq : ∀ k : Fin 16, kernel1_0Expr 4 1 k = kernel1_0_r4_1 k := by decide +kernel +noncomputable def kernel1_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-598735300344720112026544498246),(-598735300344720111979654699460)⟩,⟨(-94404029822969906806957983659),(-94404029822969906762623377697)⟩⟩,⟨⟨(-598166972423615840929807134503),(-598166972423615840882867049679)⟩,⟨(-93436100518921222845807021064),(-93436100518921222801435503507)⟩⟩,⟨⟨(-597580725060237322049728487083),(-597580725060237322002737117535)⟩,⟨(-92442084407116342535898047594),(-92442084407116342491488948076)⟩⟩,⟨⟨(-596976507937911155828803995471),(-596976507937911155781759650762)⟩,⟨(-91422266534245750604710952265),(-91422266534245750560262911776)⟩⟩,⟨⟨(-596354270987879233522286047153),(-596354270987879233475187918883)⟩,⟨(-90376939487848693007184414682),(-90376939487848692962696938399)⟩⟩,⟨⟨(-595713964528013972154525687965),(-595713964528013972107371957452)⟩,⟨(-89306403316376757747591552723),(-89306403316376757703063142678)⟩⟩,⟨⟨(-595055539403852819974012892376),(-595055539403852819926802771578)⟩,⟨(-88210965446129294870471764103),(-88210965446129294825901932790)⟩⟩,⟨⟨(-594378947131814500961212149313),(-594378947131814500913943864282)⟩,⟨(-87090940595009487155365242462),(-87090940595009487110752523127)⟩⟩,⟨⟨(-593684140044456030799295555183),(-593684140044456030751968589453)⟩,⟨(-85946650683051134424716644953),(-85946650683051134380060804686)⟩⟩,⟨⟨(-592971071437626166090602560982),(-592971071437626166043214937679)⟩,⟨(-84778424739667659930835750734),(-84778424739667659886135109190)⟩⟩,⟨⟨(-592239695719367649252931747960),(-592239695719367649205482931024)⟩,⟨(-83586598807576488544030181924),(-83586598807576488499284473052)⟩⟩,⟨⟨(-591489968560417389430072439970),(-591489968560417389382560543236)⟩,⟨(-82371515843353784597886077886),(-82371515843353784553093696955)⟩⟩,⟨⟨(-590721847046150581070286860161),(-590721847046150581022711665993)⟩,⟨(-81133525614576573084899758788),(-81133525614576573040060739510)⟩⟩,⟨⟨(-589935289829811712924675746273),(-589935289829811712877035124961)⟩,⟨(-79872984593511501898269905305),(-79872984593511501853382388457)⟩⟩,⟨⟨(-589130257286872467633089946526),(-589130257286872467585383658983)⟩,⟨(-78590255847311935069960949380),(-78590255847311935025024932789)⟩⟩,⟨⟨(-588306711670353662504160791414),(-588306711670353662456386806330)⟩,⟨(-77285708924687697160781808061),(-77285708924687697115795514869)⟩⟩] +lemma kernel1_0_r4_2_eq : ∀ k : Fin 16, kernel1_0Expr 4 2 k = kernel1_0_r4_2 k := by decide +kernel +noncomputable def kernel1_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-587464617266945642417458968278),(-587464617266945642369617497421)⟩,⟨(-75959719739014616416724361991),(-75959719739014616371688219398)⟩⟩,⟨⟨(-586603940553758912979165914735),(-586603940553758912931254557062)⟩,⟨(-74612670447854037910399076762),(-74612670447854037865310928325)⟩⟩,⟨⟨(-585724650355534303271877439463),(-585724650355534303223896300296)⟩,⟨(-73244949328855696111351379855),(-73244949328855696066211532301)⟩⟩,⟨⟨(-584826718002139579987089217021),(-584826718002139579939036084404)⟩,⟨(-71856950652020747220444243342),(-71856950652020747175250711308)⟩⟩,⟨⟨(-583910117486177205739616412920),(-583910117486177205691491886091)⟩,⟨(-70449074548305362769636806684),(-70449074548305362724390367839)⟩⟩,⟨⟨(-582974825620525851334468389324),(-582974825620525851286269848678)⟩,⟨(-69021726874549074591932115657),(-69021726874549074546630367186)⟩⟩,⟨⟨(-582020822195636342140328317863),(-582020822195636342092056262890)⟩,⟨(-67575319074716034015421482156),(-67575319074716033970065087223)⟩⟩,⟨⟨(-581048090136400950006183454605),(-581048090136400949957835453329)⟩,⟨(-66110268037441501278089965165),(-66110268037441501232676690019)⟩⟩,⟨⟨(-580056615658413341838178022180),(-580056615658413341789755254466)⟩,⟨(-64626995949880210476795009066),(-64626995949880210431326170767)⟩⟩,⟨⟨(-579046388423435071523622500574),(-579046388423435071475121945859)⟩,⟨(-63125930147857756162967787873),(-63125930147857756117440556614)⟩⟩,⟨⟨(-578017401693883260807856510209),(-578017401693883260759279114116)⟩,⟨(-61607502962330814810296766618),(-61607502962330814764712211935)⟩⟩,⟨⟨(-576969652486153064402571331006),(-576969652486153064353914399746)⟩,⟨(-60072151562166842157373159626),(-60072151562166842111728757463)⟩⟩,⟨⟨(-575903141722587662357025647331),(-575903141722587662308290850522)⟩,⟨(-58520317793258869739553101789),(-58520317793258869693850617851)⟩⟩,⟨⟨(-574817874381907875778603470555),(-574817874381907875729787486830)⟩,⟨(-56952448013996154154565781767),(-56952448013996154108802057450)⟩⟩,⟨⟨(-573713859647913067438515224259),(-573713859647913067389619498889)⟩,⟨(-55368992927116703657109232014),(-55368992927116703611285794926)⟩⟩,⟨⟨(-572591111056264773578978241992),(-572591111056264773529999774357)⟩,⟨(-53770407407973110968612990662),(-53770407407973110922726981709)⟩⟩] +lemma kernel1_0_r4_3_eq : ∀ k : Fin 16, kernel1_0Expr 4 3 k = kernel1_0_r4_3 k := by decide +kernel +noncomputable def kernel1_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-571449646639164524103657059300),(-571449646639164524054598303839)⟩,⟨(-52157150329248650659239805597),(-52157150329248650613293728771)⟩⟩,⟨⟨(-570289489067737551828056399874),(-570289489067737551778913448393)⟩,⟨(-50529684382166245574885971299),(-50529684382166245528876057353)⟩⟩,⟨⟨(-569110665791934573897571659158),(-569110665791934573848346511757)⟩,⟨(-48888475894238660536659564694),(-48888475894238660490587852907)⟩⟩,⟨⟨(-567913209177764555890118365368),(-567913209177764555840807667498)⟩,⟨(-47233994643614133465897928877),(-47233994643614133419761178700)⟩⟩,⟨⟨(-566697156641672347255861003390),(-566697156641672347206467770403)⟩,⟨(-45566713670077594260816484534),(-45566713670077594214617717098)⟩⟩,⟨⟨(-565462550781876311036024768562),(-565462550781876310986544735785)⟩,⟨(-43887109082773639804147046293),(-43887109082773639757882108765)⟩⟩,⟨⟨(-564209439506482566323193979269),(-564209439506482566273629757762)⟩,⟨(-42195659864723518613806492473),(-42195659864723518567477990593)⟩⟩,⟨⟨(-562937876158194223376971194023),(-562937876158194223327319025973)⟩,⟨(-40492847674214519641108801777),(-40492847674214519594713065317)⟩⟩,⟨⟨(-561647919635436022984928140206),(-561647919635436022935192010561)⟩,⟨(-38779156643146344948250453721),(-38779156643146344901791422732)⟩⟩,⟨⟨(-560339634509717097420380328493),(-560339634509717097370555214437)⟩,⟨(-37055073172425263446580749879),(-37055073172425263400053493231)⟩⟩,⟨⟨(-559013091139057153595000574057),(-559013091139057153545089753863)⟩,⟨(-35321085724503080166834840843),(-35321085724503080120242585897)⟩⟩,⟨⟨(-557668365777304242648380659995),(-557668365777304242598379921730)⟩,⟨(-33577684613164199930717880509),(-33577684613164199884056478033)⟩⟩,⟨⟨(-556305540679175426656375624443),(-556305540679175426606289618656)⟩,⟨(-31825361790670302739880433122),(-31825361790670302693154442829)⟩⟩,⟨⟨(-554924704200855084235283524368),(-554924704200855084185106777699)⟩,⟨(-30064610632378367330014308159),(-30064610632378367283218324306)⟩⟩,⟨⟨(-553525950895989313864623597047),(-553525950895989313814360111736)⟩,⟨(-28295925718953965510948790723),(-28295925718953965464086718208)⟩⟩,⟨⟨(-552109381606918897456109563820),(-552109381606918897405754620795)⟩,⟨(-26519802616307889233468849647),(-26519802616307889186536009159)⟩⟩] +lemma kernel1_0_r4_4_eq : ∀ k : Fin 16, kernel1_0Expr 4 4 k = kernel1_0_r4_4 k := by decide +kernel +noncomputable def kernel1_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-550675103550997577157855756253),(-550675103550997577107415254904)⟩,⟨(-24736737653390250670480033294),(-24736737653390250623482177873)⟩⟩,⟨⟨(-549223230401846975068194294967),(-549223230401846975017661732974)⟩,⟨(-22947227697982198662037480958),(-22947227697982198614968162781)⟩⟩,⟨⟨(-547753882365404347257392987670),(-547753882365404347206773146935)⟩,⟨(-21151769930631308175479212872),(-21151769930631308128343069513)⟩⟩,⟨⟨(-546267186250624508404009982029),(-546267186250624508353297583232)⟩,⟨(-19350861616882508370906265965),(-19350861616882508323698037266)⟩⟩,⟨⟨(-544763275534702688903228457485),(-544763275534702688852430082971)⟩,⟨(-17544999877962104740730778656),(-17544999877962104693456855021)⟩⟩,⟨⟨(-543242290422690789253992967843),(-543242290422690789203101651662)⟩,⟨(-15734681460078006855727206252),(-15734681460078006808380655391)⟩⟩,⟨⟨(-541704377901385472919534716193),(-541704377901385472868556076050)⟩,⟨(-13920402502504680722927857140),(-13920402502504680675514105138)⟩⟩,⟨⟨(-540149691787372783995331004655),(-540149691787372783944259145541)⟩,⟨(-12102658304626588886479945000),(-12102658304626588838993098165)⟩⟩,⟨⟨(-538578392769120484484497789681),(-538578392769120484433340745477)⟩,⟨(-10281943092118947481504902663),(-10281943092118947433952744670)⟩⟩,⟨⟨(-536990648443016071604874847207),(-536990648443016071553624422145)⟩,⟨(-8458749782449502883841639186),(-8458749782449502836216002418)⟩⟩,⟨⟨(-535386633343255451414986109509),(-535386633343255451363648810255)⟩,⟨(-6633569749889696925215047506),(-6633569749889696877522199700)⟩⟩,⟨⟨(-533766528965494503476890194171),(-533766528965494503425459456087)⟩,⟨(-4806892590228034588717676641),(-4806892590228034540951039718)⟩⟩,⟨⟨(-532130523784183263846813306712),(-532130523784183263795297939863)⟩,⟨(-2979205885382677613249973023),(-2979205885382677565418061374)⟩⟩,⟨⟨(-530478813263510171223930734868),(-530478813263510171172321984759)⟩,⟨(-1150994968114247739680222053),(-1150994968114247691774294529)⟩⟩,⟨⟨(-528811599861891753669455826352),(-528811599861891753617761141441)⟩,⟨677257312956479039291335344,677257312956479087264116292⟩⟩,⟨⟨(-527129093029951270270062993343),(-527129093029951270218275083512)⟩,⟨2505070827817884013494040628,2505070827817884061540989858⟩⟩] +lemma kernel1_0_r4_5_eq : ∀ k : Fin 16, kernel1_0Expr 4 5 k = kernel1_0_r4_5 k := by decide +kernel +noncomputable def kernel1_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-525431509201938152067279955451),(-525431509201938152015409465016)⟩,⟨4331968398812586493310874679,4331968398812586541421707070⟩⟩,⟨⟨(-523719071780548597397878138017),(-523719071780548597345914695738)⟩,⟨6157476033444224536100935747,6157476033444224584286002131⟩⟩,⟨⟨(-521992011115116355674972597089),(-521992011115116355622924641329)⟩,⟨7981123156029346306538666444,7981123156029346354789861010⟩⟩,⟨⟨(-520250564473151567088714301018),(-520250564473151567036573763524)⟩,⟨9802442837975626295751283075,9802442837975626344076706406⟩⟩,⟨⟨(-518494976005214499556347249434),(-518494976005214499504125453207)⟩,⟨11620972026465758567601847783,11620972026465758615990576986⟩⟩,⟨⟨(-516725496703120123703461934703),(-516725496703120123651148037392)⟩,⟨13436251771324861528845218554,13436251771324861577308086410⟩⟩,⟨⟨(-514942384351478676294751214562),(-514942384351478676242354693405)⟩,⟨15247827449848064792300549188,15247827449848064840828456822⟩⟩,⟨⟨(-513145903472586666354415130423),(-513145903472586666301927083672)⟩,⟨17055248989364147170808794925,17055248989364147219410679967⟩⟩,⟨⟨(-511336325264692159669125198602),(-511336325264692159616558960753)⟩,⟨18858071087310663615383194431,18858071087310663664046186926⟩⟩,⟨⟨(-509513927533667619379846918142),(-509513927533667619327189840092)⟩,⟨20655853428595945120355330037,20655853428595945169092052044⟩⟩,⟨⟨(-507678994618133065388589395341),(-507678994618133065335852035200)⟩,⟨22448160900023685573156738869,22448160900023685621957055415⟩⟩,⟨⟨(-505831817308081825339072666218),(-505831817308081825286245238727)⟩,⟨24234563801556548683853826441,24234563801556548732727558044⟩⟩,⟨⟨(-503972692757070666580727600930),(-503972692757070666527824209570)⟩,⟨26014638054196341065607884337,26014638054196341114541430968⟩⟩,⟨⟨(-502101924388045603045490283114),(-502101924388045602992497700888)⟩,⟨27787965404259807910922443107,27787965404259807959929007132⟩⟩,⟨⟨(-500219821792884144297204022677),(-500219821792884144244133930696)⟩,⟨29554133623831018240229534584,29554133623831018289297901613⟩⟩,⟨⟨(-498326700625744176838077722852),(-498326700625744176784919399906)⟩,⟨31312736707173619139839758842,31312736707173619188980680298⟩⟩] +lemma kernel1_0_r4_6_eq : ∀ k : Fin 16, kernel1_0Expr 4 6 k = kernel1_0_r4_6 k := by decide +kernel +noncomputable def kernel1_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-496422882490319020547561615668),(-496422882490319020494331654138)⟩,⟨33063375062888953520337112059,33063375062888953569534569767⟩⟩,⟨⟨(-494508694821107466204994418207),(-494508694821107466151677288069)⟩,⟨34805655701609153467374383260,34805655701609153516643847681⟩⟩,⟨⟨(-492584470758816753621937211929),(-492584470758816753568545750322)⟩,⟨36539192419017839955957018919,36539192419017840005286161701⟩⟩,⟨⟨(-490650549020025474153659836691),(-490650549020025474100182342003)⟩,⟨38263605973994977246590990565,38263605973994977295991534076⟩⟩,⟨⟨(-488707273761242256449386621455),(-488707273761242256395840216509)⟩,⟨39978524261686743322025918350,39978524261686743371481343797⟩⟩,⟨⟨(-486754994437504800487587927480),(-486754994437504800433956717837)⟩,⟨41683582481305981843053512195,41683582481305981892579654069⟩⟩,⟨⟨(-484794065655672342599928858286),(-484794065655672342546226871725)⟩,⟨43378423298473890832434918949,43378423298473890882018298763⟩⟩,⟨⟨(-482824847022572943880651668227),(-482824847022572943826866174164)⟩,⟨45062697001919072107466150615,45062697001919072157119505653⟩⟩,⟨⟨(-480847702988175076916274824631),(-480847702988175076862425577129)⟩,⟨46736061654355905793436327961,46736061654355905843140578446⟩⟩,⟨⟨(-478863002683960822274415226927),(-478863002683960822220483859476)⟩,⟨48398183237370417431611656662,48398183237370417481385062415⟩⟩,⟨⟨(-476871119756685558145632233218),(-476871119756685558091633987853)⟩,⟨50048735790148361584411808856,50048735790148361634239715767⟩⟩,⟨⟨(-474872432197716315856203705388),(-474872432197716315802124784056)⟩,⟨51687401541887144751319251342,51687401541887144801215445661⟩⟩,⟨⟨(-472867322168147963064355305605),(-472867322168147963010216056925)⟩,⟨53313871037740440158923454942,53313871037740440208868288525⟩⟩,⟨⟨(-470856175819903048270528874787),(-470856175819903048216310473661)⟩,⟨54927843258151894911900219848,54927843258151894961912401741⟩⟩,⟨⟨(-468839383113027478367146899892),(-468839383113027478312865828057)⟩,⟨56529025731442182475367111215,56529025731442182525430784370⟩⟩,⟨⟨(-466817337629400189544066666969),(-466817337629400189489708016887)⟩,⟨58117134639521795963478545863,58117134639521796013608582995⟩⟩] +lemma kernel1_0_r4_7_eq : ∀ k : Fin 16, kernel1_0Expr 4 7 k = kernel1_0_r4_7 k := by decide +kernel +noncomputable def kernel1_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-464790436383080595883737314773),(-464790436383080595829324721658)⟩,⟨59691894916610394810920466600,59691894916610394861094013461⟩⟩,⟨⟨(-462759079627522845130621236397),(-462759079627522845076132709358)⟩,⟨61253040340852192824369794547,61253040340852192874608656169⟩⟩,⟨⟨(-460723670659890763925146850379),(-460723670659890763870600121490)⟩,⟨62800313618725792265491350628,62800313618725792315778454211⟩⟩,⟨⟨(-458684615622711822650972339864),(-458684615622711822596351363762)⟩,⟨64333466462156008650459465445,64333466462156008700810794311⟩⟩,⟨⟨(-456642323303112481265707439729),(-456642323303112481211035953919)⟩,⟨65852259658244575794123197138,65852259658244575844515805424⟩⟩,⟨⟨(-454597204929880881345905323847),(-454597204929880881291161341401)⟩,⟨67356463131546151037292160058,67356463131546151087747842336⟩⟩,⟨⟨(-452549673968606016351015685603),(-452549673968606016296218205820)⟩,⟨68845855998825736720628860785,68845855998825736771129309585⟩⟩,⟨⟨(-450500145915145233117655990058),(-450500145915145233062787794295)⟩,⟨70320226616243475391823188432,70320226616243475442385528905⟩⟩,⟨⟨(-448449038087674185224883117774),(-448449038087674185169971235442)⟩,⟨71779372618922742042288326628,71779372618922742092886398266⟩⟩,⟨⟨(-446396769417575166624981373181),(-446396769417575166570000615761)⟩,⟨73223100952867525509247015285,73223100952867525559905735289⟩⟩,⟨⟨(-444343760239421096443632086921),(-444343760239421096388602720458)⟩,⟨74651227899205241321331518718,74651227899205241372031343105⟩⟩,⟨⟨(-442290432080313298912968746873),(-442290432080313298857872360284)⟩,⟨76063579090741327666621361378,76063579090741327717380572526⟩⟩,⟨⟨(-440237207448831622978466373746),(-440237207448831622923330213981)⟩,⟨77459989520822222538050023217,77459989520822222588842251069⟩⟩,⟨⟨(-438184509623855372383476728880),(-438184509623855372328275450353)⟩,⟨78840303544513580996552301260,78840303544513581047402603984⟩⟩,⟨⟨(-436132762443512968351444337657),(-436132762443512968296199478599)⟩,⟨80204374872110844319410840450,80204374872110844370298429986⟩⟩,⟨⟨(-434082390094517243942852614616),(-434082390094517243887544546413)⟩,⟨81552066555009494958813904379,81552066555009495009758241727⟩⟩] +lemma kernel1_0_r4_8_eq : ∀ k : Fin 16, kernel1_0Expr 4 8 k = kernel1_0_r4_8 k := by decide +kernel +noncomputable def kernel1_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-432033816902141773560330321798),(-432033816902141773504990344027)⟩,⟨82883250963972500150970978163,82883250963972500201941731762⟩⟩,⟨⟨(-429987467121091675931644541618),(-429987467121091675876243308198)⟩,⟨84197809759842540214235078057,84197809759842540265261202209⟩⟩,⟨⟨(-427943764727519898441594033902),(-427943764727519898386154340624)⟩,⟨85495633856756612760763081336,85495633856756612811822556082⟩⟩,⟨⟨(-425903133212437100342215209680),(-425903133212437100286716204567)⟩,⟨86776623377930479164216496838,86776623377930479215329964587⟩⟩,⟨⟨(-423865995376759908758641852285),(-423865995376759908703114359569)⟩,⟨88040687604090152940701615459,88040687604090152991839207736⟩⟩,⟨⟨(-421832773128238532312843535165),(-421832773128238532257258702366)⟩,⟨89287744914637199853504119620,89287744914637199904694290228⟩⟩,⟨⟨(-419803887280500491535811399017),(-419803887280500491480193275908)⟩,⟨90517722721644005644003203362,90517722721644005695222701966⟩⟩,⟨⟨(-417779757354442573082551551368),(-417779757354442573026878046141)⟩,⟨91730557396784348932569340187,91730557396784348983840004048⟩⟩,⟨⟨(-415760801382198047236846192162),(-415760801382198047181152109441)⟩,⟨92926194191313574224202458866,92926194191313574275490526167⟩⟩,⟨⟨(-413747435713900717487482214881),(-413747435713900717431734733052)⟩,⟨94104587149221373932383391772,94104587149221373983721174953⟩⟩,⟨⟨(-411740074827461510275580245955),(-411740074827461510219804642859)⟩,⟨95265699013688640451207877203,95265699013688640502570919071⟩⟩,⟨⟨(-409739131141567076534057012005),(-409739131141567076478229962195)⟩,⟨96409501126988021866642610248,96409501126988021918053934484⟩⟩,⟨⟨(-407745014832103279464663873330),(-407745014832103279408819801408)⟩,⟨97535973323975691033999881593,97535973323975691085426091911⟩⟩,⟨⟨(-405758133652199501109854580946),(-405758133652199501053961024616)⟩,⟨98645103819329401454484363684,98645103819329401505957399310⟩⟩,⟨⟨(-403778892756082430478222339662),(-403778892756082430422305789846)⟩,⟨99736889088695139578875905478,99736889088695139630370115384⟩⟩,⟨⟨(-401807694526920415853317014705),(-401807694526920415797352908361)⟩,⟨100811333743911577727901596248,100811333743911577779441192324⟩⟩] +lemma kernel1_0_r4_9_eq : ∀ k : Fin 16, kernel1_0Expr 4 9 k = kernel1_0_r4_9 k := by decide +kernel +noncomputable def kernel1_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-399844938408831591741459403213),(-399844938408831591685487200470)⟩,⟨101868450402488071636469751644,101868450402488071688016411904⟩⟩,⟨⟨(-397891020743220845640113561643),(-397891020743220845584095740340)⟩,⟨102908259551518119628862321329,102908259551518119680452903431⟩⟩,⟨⟨(-395946334609602290962817398960),(-395946334609602290906781621138)⟩,⟨103930789406215995625572864485,103930789406215995677180563137⟩⟩,⟨⟨(-394011269671055280102402214126),(-394011269671055280046322702741)⟩,⟨104936075763269675681179321339,104936075763269675732829511836⟩⟩,⟨⟨(-392086212024453146267096992022),(-392086212024453146211011738423)⟩,⟨105924161849208188809291314619,105924161849208188860947100270⟩⟩,⟨⟨(-390171544055594825302671201265),(-390171544055594825246544092660)⟩,⟨106895098163986129864906736254,106895098163986129916603573149⟩⟩,⟨⟨(-388267644299360300454911352821),(-388267644299360300398771200962)⟩,⟨107848942319992268806432479488,107848942319992268858142427765⟩⟩,⟨⟨(-386374887305001455433673070436),(-386374887305001455377492889064)⟩,⟨108785758876692971506180164943,108785758876692971557929757199⟩⟩,⟨⟨(-384493643506670435896817636783),(-384493643506670435840640105355)⟩,⟨109705619171124508377783249913,109705619171124508429531002083⟩⟩,⟨⟨(-382624279099278028392561118238),(-382624279099278028336345376150)⟩,⟨110608601144451265589376390114,110608601144451265641162367617⟩⟩,⟨⟨(-380767155919764890738390564048),(-380767155919764890682166521555)⟩,⟨111494789164809387885367497518,111494789164809387937162674929⟩⟩,⟨⟨(-378922631333858730621867258489),(-378922631333858730565606755857)⟩,⟨112364273846657471583900725503,112364273846657471635732756715⟩⟩,⟨⟨(-377091058128380751638505025374),(-377091058128380751582249548475)⟩,⟨113217151866857591880021204438,113217151866857591931849758982⟩⟩,⟨⟨(-375272784409154889648148646453),(-375272784409154889591858439845)⟩,⟨114053525777711192055334050376,114053525777711192107198087959⟩⟩,⟨⟨(-373468153504563568622881146925),(-373468153504563568566587186245)⟩,⟨114873503817175186623831821303,114873503817175186675701262498⟩⟩,⟨⟨(-371677503874783935195187356174),(-371677503874783935138860328020)⟩,⟨115677199716484040002782827101,115677199716484040054686426979⟩⟩] +lemma kernel1_0_r4_10_eq : ∀ k : Fin 16, kernel1_0Expr 4 10 k = kernel1_0_r4_10 k := by decide +kernel +noncomputable def kernel1_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-369901169026728805663849084500),(-369901169026728805607536325238)⟩,⟨116464732505403582273372067438,116464732505403582325263773558⟩⟩,⟨⟨(-368139477434706898654552144614),(-368139477434706898598207963672)⟩,⟨117236226315341920341592761997,117236226315341920393517299236⟩⟩,⟨⟨(-366392752466807350873412451520),(-366392752466807350817068823543)⟩,⟨117991810180542003731371126113,117991810180542003783297425270⟩⟩,⟨⟨(-364661312317004041842614316780),(-364661312317004041786240829426)⟩,⟨118731617837579217742760906406,118731617837579217794718769836⟩⟩,⟨⟨(-362945469942965905002250581020),(-362945469942965904945892087336)⟩,⟨119455787523385812169149469193,119455787523385812221095254677⟩⟩,⟨⟨(-361245533009550195332193374765),(-361245533009550195275806553815)⟩,⟨120164461772022041485253635063,120164461772022041537229727685⟩⟩,⟨⟨(-359561803837946635254395404568),(-359561803837946635198013192283)⟩,⟨120857787210411603578478878919,120857787210411603630453256173⟩⟩,⟨⟨(-357894579360431487889369806026),(-357894579360431487832960719718)⟩,⟨121535914353256330709115780718,121535914353256330761119264164⟩⟩,⟨⟨(-356244151080681925879977885002),(-356244151080681925823592189841)⟩,⟨122198997397342121250745214248,122198997397342121302728868082⟩⟩,⟨⟨(-354610805039592590313435663637),(-354610805039592590257024521732)⟩,⟨122847194015444817402502850802,122847194015444817454514415511⟩⟩,⟨⟨(-352994821786527982302254486235),(-352994821786527982245851720591)⟩,⟨123480665150041146686599065137,123480665150041146738605637170⟩⟩,⟨⟨(-351396476355936313232922595092),(-351396476355936313176495719866)⟩,⟨124099574807025968465508689312,124099574807025968517542043975⟩⟩,⟨⟨(-349816038249242671391321895339),(-349816038249242671334918971786)⟩,⟨124704089849632916324995693100,124704089849632916377009030815⟩⟩,⟨⟨(-348253771421931854587522620608),(-348253771421931854531096888982)⟩,⟨125294379792751118858262836751,125294379792751118910301843942⟩⟩,⟨⟨(-346709934275723981580322241826),(-346709934275723981523908364059)⟩,⟨125870616597826031496640681069,125870616597826031548671620163⟩⟩,⟨⟨(-345184779655739039691011335562),(-345184779655739039634575866727)⟩,⟨126432974468527537284258967016,126432974468527537336314524430⟩⟩] +lemma kernel1_0_r4_11_eq : ∀ k : Fin 16, kernel1_0Expr 4 11 k = kernel1_0_r4_11 k := by decide +kernel +noncomputable def kernel1_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-343678554852539861210066542316),(-343678554852539861153664599080)⟩,⟨126981629647363391946776328484,126981629647363391998802809559⟩⟩,⟨⟨(-342191501608936655334927436101),(-342191501608936655278505092115)⟩,⟨127516760213410815573841189999,127516760213410815625891245095⟩⟩,⟨⟨(-340723856131430162785005013110),(-340723856131430162728597678494)⟩,⟨128038545881333587256551033841,128038545881333587308590180088⟩⟩,⟨⟨(-339275849106164753355790412344),(-339275849106164753299363771978)⟩,⟨128547167801846397768551298769,128547167801846397820613047584⟩⟩,⟨⟨(-337847705719257357995503753669),(-337847705719257357939108863585)⟩,⟨129042808363782476628006144036,129042808363782476680040747352⟩⟩,⟨⟨(-336439645681363021108258615132),(-336439645681363021051845477804)⟩,⟨129525650997914651424827618525,129525650997914651476883869748⟩⟩,⟨⟨(-335051883256333079384198075777),(-335051883256333079327802800127)⟩,⟨129995879982674036928235865491,129995879982674036980278585009⟩⟩,⟨⟨(-333684627293817523327569805393),(-333684627293817523271157256717)⟩,⟨130453680251904506899448494104,130453680251904506951511969781⟩⟩,⟨⟨(-332338081265658978713266736273),(-332338081265658978656894117593)⟩,⟨130899237204784990296839463092,130899237204784990348867939571⟩⟩,⟨⟨(-331012443305921958525882033426),(-331012443305921958469493088477)⟩,⟨131332736518045473054514314961,131332736518045473106562664653⟩⟩,⟨⟨(-329707906254397581758822561283),(-329707906254397581702454002021)⟩,⟨131754363960596393994023254745,131754363960596394046055695205⟩⟩,⟨⟨(-328424657703420833220058901847),(-328424657703420833163674873384)⟩,⟨132164305210684915552557919951,132164305210684915604609419551⟩⟩,⟨⟨(-327162880047834646866199631682),(-327162880047834646809853951605)⟩,⟨132562745675685343420787936522,132562745675685343472806027991⟩⟩,⟨⟨(-325922750537932632097497540851),(-325922750537932632041137216529)⟩,⟨132949870314624780035283831603,132949870314624780087320182206⟩⟩,⟨⟨(-324704441335210125100786836526),(-324704441335210125044449121182)⟩,⟨133325863463538940915895933817,133325863463538940967914219165⟩⟩,⟨⟨(-323508119570751432268440448580),(-323508119570751432212088835707)⟩,⟨133690908663746955362865635879,133690908663746955414901439131⟩⟩] +lemma kernel1_0_r4_12_eq : ∀ k : Fin 16, kernel1_0Expr 4 12 k = kernel1_0_r4_12 k := by decide +kernel +noncomputable def kernel1_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-322333947406079635840759797204),(-322333947406079635784455926492)⟩,⟨134045188493127928836514843099,134045188493127928888508058786⟩⟩,⟨⟨(-321182082096294148517092641973),(-321182082096294148460775601471)⟩,⟨134388884400476077701048946222,134388884400476077753058940959⟩⟩,⟨⟨(-320052676055320328581466269816),(-320052676055320328525173741526)⟩,⟨134722176543005371643640718822,134722176543005371695630736708⟩⟩,⟨⟨(-318945876923094894302304757912),(-318945876923094894245999705115)⟩,⟨135045243627068848102082607995,135045243627068848154088729901⟩⟩,⟨⟨(-317861827634510599705927645670),(-317861827634510599649666357291)⟩,⟨135358262752152108968888915427,135358262752152109020856240614⟩⟩,⟨⟨(-316800666489943646571108182511),(-316800666489943646514834992062)⟩,⟨135661409258194984556945585963,135661409258194984608928347228⟩⟩,⟨⟨(-315762527227187602511829493946),(-315762527227187602455582449282)⟩,⟨135954856576289964535399818798,135954856576289964587360890941⟩⟩,⟨⟨(-314747539094618164821681545456),(-314747539094618164765423155028)⟩,⟨136238776082800760809347731852,136238776082800760861323621346⟩⟩,⟨⟨(-313755826925413946526348359775),(-313755826925413946470141791644)⟩,⟨136513336956939292976763851696,136513336956939293028692941360⟩⟩,⟨⟨(-312787511212659556741644109558),(-312787511212659556685426742065)⟩,⟨136778706041834482186691897058,136778706041834482238635181086⟩⟩,⟨⟨(-311842708185158593621841445713),(-311842708185158593565651574314)⟩,⟨137035047709121512374537925913,137035047709121512426458026005⟩⟩,⟨⟨(-310921529883785756375903572274),(-310921529883785756319703382862)⟩,⟨137282523727075676656736966800,137282523727075676708670687584⟩⟩,⟨⟨(-310024084238209104321898166604),(-310024084238209104265746108912)⟩,⟨137521293132310578102769063456,137521293132310578154659376883⟩⟩,⟨⟨(-309150475143815536925171892337),(-309150475143815536869009988758)⟩,⟨137751512105056304394784522630,137751512105056304446687879295⟩⟩,⟨⟨(-308300802538674830306259398857),(-308300802538674830250126116037)⟩,⟨137973333848029250537810025313,137973333848029250589688869315⟩⟩,⟨⟨(-307475162480380033852950376362),(-307475162480380033796807671522)⟩,⟨138186908468901527553304969152,138186908468901527605196313299⟩⟩] +lemma kernel1_0_r4_13_eq : ∀ k : Fin 16, kernel1_0Expr 4 13 k = kernel1_0_r4_13 k := by decide +kernel +noncomputable def kernel1_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-306673647222604696340300661104),(-306673647222604696284216148409)⟩,⟨138392382866374372012375285089,138392382866374372064213160090⟩⟩,⟨⟨(-305896345291220245393204172956),(-305896345291220245337110669360)⟩,⟨138589900619856664639423952178,138589900619856664691273765782⟩⟩,⟨⟨(-305143341559819878292793025022),(-305143341559819878236729028238)⟩,⟨138779601882746578631416029748,138779601882746578683240186070⟩⟩,⟨⟨(-304414717324498527193368857668),(-304414717324498527137296255205)⟩,⟨138961623279311511656945605406,138961623279311511708781172104⟩⟩,⟨⟨(-303710550377741829034070906381),(-303710550377741828978049929820)⟩,⟨139136097805158810898879970093,139136097805158810950668165066⟩⟩,⟨⟨(-303030915081280551195544021660),(-303030915081280551139514832900)⟩,⟨139303154731287378457214993425,139303154731287378509014052353⟩⟩,⟨⟨(-302375882437770589803122870328),(-302375882437770589747123921117)⟩,⟨139462919511708044743859988932,139462919511708044795632352134⟩⟩,⟨⟨(-301745520161162460239500891597),(-301745520161162460183494098742)⟩,⟨139615513694618619312570856562,139615513694618619364353551680⟩⟩,⟨⟨(-301139892745628130809236078741),(-301139892745628130753289249244)⟩,⟨139761054837117770375298819121,139761054837117770427025674139⟩⟩,⟨⟨(-300559061532917102728720842809),(-300559061532917102672766561664)⟩,⟨139899656423440343918816808261,139899656423440343970553431589⟩⟩,⟨⟨(-300003084778017805048831348737),(-300003084778017804992907876270)⟩,⟨140031427786695408111312128845,140031427786695408163021139886⟩⟩,⟨⟨(-299472017713004644359592343221),(-299472017713004644303661793957)⟩,⟨140156474034087195230892338264,140156474034087195282610562174⟩⟩,⟨⟨(-298965912608955419024233930966),(-298965912608955418968357918868)⟩,⟨140274895975598207749538893493,140274895975598207801206187587⟩⟩,⟨⟨(-298484818835828269369111507648),(-298484818835828269313228822532)⟩,⟨140386790056113052993500708079,140386790056113053045176624008⟩⟩,⟨⟨(-298028782920191882099297457954),(-298028782920191882043446071682)⟩,⟨140492248290961066982010830619,140492248290961067033658262605⟩⟩,⟨⟨(-297597848600707292890109999634),(-297597848600707292834252347229)⟩,⟨140591358204855477105007208666,140591358204855477156662661397⟩⟩] +lemma kernel1_0_r4_14_eq : ∀ k : Fin 16, kernel1_0Expr 4 14 k = kernel1_0_r4_14 k := by decide +kernel +noncomputable def kernel1_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-297192056881264329562476646821),(-297192056881264329506684128351)⟩,⟨140684202774206729245757200002,140684202774206729297350989076⟩⟩,⟨⟨(-296811446081680503719202024520),(-296811446081680503663403692050)⟩,⟨140770860372787661315678428494,140770860372787661367279587164⟩⟩,⟨⟨(-296456051885874985702001492129),(-296456051885874985646234858241)⟩,⟨140851404720728435045179715053,140851404720728435096751579995⟩⟩,⟨⟨(-296125907387435181018788843522),(-296125907387435180963016861052)⟩,⟨140925904836819533931825858747,140925904836819533983404423566⟩⟩,⟨⟨(-295821043132498361040275654178),(-295821043132498360984560830854)⟩,⟨140994424994101689767534217792,140994424994101689819058459672⟩⟩,⟨⟨(-295541487159875782109028360158),(-295541487159875782053308704964)⟩,⟨141057024678722305044243162883,141057024678722305095773380326⟩⟩,⟨⟨(-295287265038351750823074213035),(-295287265038351750767386677416)⟩,⟨141113758552038785329922777054,141113758552038785381422849648⟩⟩,⟨⟨(-295058399901095154993251819612),(-295058399901095154937560005026)⟩,⟨141164676415950175631721694202,141164676415950175683226978672⟩⟩,⟨⟨(-294854912477126075697923463065),(-294854912477126075642298053618)⟩,⟨141209823181439598747603273952,141209823181439598799044776873⟩⟩,⟨⟨(-294676821119785222278782275216),(-294676821119785222223153204529)⟩,⟨141249238840311212286835089888,141249238840311212338280974642⟩⟩,⟨⟨(-294524141832159085545124453514),(-294524141832159085489527930651)⟩,⟨141282958440106724804413525587,141282958440106724855828392497⟩⟩,⟨⟨(-294396888289418881599023933844),(-294396888289418881543424418839)⟩,⟨141311012062187930491013645346,141311012062187930542432011326⟩⟩,⟨⟨(-294295071858036556445553172050),(-294295071858036556390013536470)⟩,⟨141333424802973226038529091252,141333424802973226089889574093⟩⟩,⟨⟨(-294218701611846336973004727857),(-294218701611846336917462843386)⟩,⟨141350216758317652412766142153,141350216758317652464129167236⟩⟩,⟨⟨(-294167784344925544172090579998),(-294167784344925544116581786009)⟩,⟨141361403011027647911287643621,141361403011027647962618657282⟩⟩,⟨⟨(-294142324581273626943203754060),(-294142324581273626887693527556)⟩,⟨141366993621503396516220084318,141366993621503396567552610969⟩⟩] +lemma kernel1_0_r4_15_eq : ∀ k : Fin 16, kernel1_0Expr 4 15 k = kernel1_0_r4_15 k := by decide +kernel +noncomputable def kernel1_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel1_0_r4_0,kernel1_0_r4_1,kernel1_0_r4_2,kernel1_0_r4_3,kernel1_0_r4_4,kernel1_0_r4_5,kernel1_0_r4_6,kernel1_0_r4_7,kernel1_0_r4_8,kernel1_0_r4_9,kernel1_0_r4_10,kernel1_0_r4_11,kernel1_0_r4_12,kernel1_0_r4_13,kernel1_0_r4_14,kernel1_0_r4_15] +lemma kernel1_0_r4_eq (i k : Fin 16) : kernel1_0Expr 4 i k = kernel1_0_r4 i k := by + fin_cases i + · exact kernel1_0_r4_0_eq k + · exact kernel1_0_r4_1_eq k + · exact kernel1_0_r4_2_eq k + · exact kernel1_0_r4_3_eq k + · exact kernel1_0_r4_4_eq k + · exact kernel1_0_r4_5_eq k + · exact kernel1_0_r4_6_eq k + · exact kernel1_0_r4_7_eq k + · exact kernel1_0_r4_8_eq k + · exact kernel1_0_r4_9_eq k + · exact kernel1_0_r4_10_eq k + · exact kernel1_0_r4_11_eq k + · exact kernel1_0_r4_12_eq k + · exact kernel1_0_r4_13_eq k + · exact kernel1_0_r4_14_eq k + · exact kernel1_0_r4_15_eq k +noncomputable def kernel1_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-667530606363152079801049988720),(-667530606363152079754354069896)⟩,⟨(-586476562346765004640983642235),(-586476562346765004586933761782)⟩⟩,⟨⟨(-667538748320163042302476878319),(-667538748320163042255778292662)⟩,⟨(-586439783938771040477160888668),(-586439783938771040423109276932)⟩⟩,⟨⟨(-667555025623196704614917954209),(-667555025623196704568214078328)⟩,⟨(-586366231425115334433135063623),(-586366231425115334379080033622)⟩⟩,⟨⟨(-667579425053723188939078775307),(-667579425053723188892366986063)⟩,⟨(-586255913412146306690884277383),(-586255913412146306636824142014)⟩⟩,⟨⟨(-667611926792564033415366940860),(-667611926792564033368644616502)⟩,⟨(-586108842813593440575707696728),(-586108842813593440521640769728)⟩⟩,⟨⟨(-667652504430231075153144124568),(-667652504430231075106408644135)⟩,⟨(-585925036855606867599811659704),(-585925036855606867545736254866)⟩⟩,⟨⟨(-667701124980710379873427879212),(-667701124980710379826676624445)⟩,⟨(-585704517083462422904063739514),(-585704517083462422849978172435)⟩⟩,⟨⟨(-667757748898690129168425910448),(-667757748898690129121656263363)⟩,⟨(-585447309369919848554365921708),(-585447309369919848500268507132)⟩⟩,⟨⟨(-667822330100231079781477714841),(-667822330100231079734687063010)⟩,⟨(-585153443925218757589351269129),(-585153443925218757535240326141)⟩⟩,⟨⟨(-667894815986877896542647835154),(-667894815986877896495833564178)⟩,⟨(-584822955308693917910623545495),(-584822955308693917856497389642)⟩⟩,⟨⟨(-667975147473209328489917315585),(-667975147473209328443076821248)⟩,⟨(-584455882441988374242994408329),(-584455882441988374188851363868)⟩⟩,⟨⟨(-668063259017824843130825536513),(-668063259017824843083956207784)⟩,⟨(-584052268623839900677262161607),(-584052268623839900623100543916)⟩⟩,⟨⟨(-668159078657764953663256656657),(-668159078657764953616355902372)⟩,⟨(-583612161546413267971866295425),(-583612161546413267917684438113)⟩⟩,⟨⟨(-668262528046362065233094731370),(-668262528046362065186159942534)⟩,⟨(-583135613313147821087729242714),(-583135613313147821033525458856)⟩⟩,⟨⟨(-668373522494518225970415862071),(-668373522494518225923444461509)⟩,⟨(-582622680458086895646683876554),(-582622680458086895592456509317)⟩⟩,⟨⟨(-668491971015405693683912096388),(-668491971015405693636901478482)⟩,⟨(-582073423966652659453101551647),(-582073423966652659398848912417)⟩⟩] +lemma kernel1_0_r5_0_eq : ∀ k : Fin 16, kernel1_0Expr 5 0 k = kernel1_0_r5_0 k := by decide +kernel +noncomputable def kernel1_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-668617776372585716839921674344),(-668617776372585716792869285876)⟩,⟨(-581487909297827049249292442020),(-581487909297827049195012892962)⟩⟩,⟨⟨(-668750835131540376013722170605),(-668750835131540375966625402335)⟩,⟨(-580866206407696585872483463620),(-580866206407696585818175306508)⟩⟩,⟨⟨(-668891037714611736659914807799),(-668891037714611736612771126078)⟩,⟨(-580208389774315995367282789838),(-580208389774315995312944400587)⟩⟩,⟨⟨(-669038268459341923172391351403),(-669038268459341923125198150280)⟩,⟨(-579514538423842741845112093007),(-579514538423842741790741770103)⟩⟩,⟨⟨(-669192405680207035248395458049),(-669192405680207035201150243129)⟩,⟨(-578784735957891792475442027797),(-578784735957891792421038180277)⟩⟩,⟨⟨(-669353321733737088086664777799),(-669353321733737088039364929690)⟩,⟨(-578019070582057188490338835448),(-578019070582057188435899740641)⟩⟩,⟨⟨(-669520883087013365588819203066),(-669520883087013365541462252398)⟩,⟨(-577217635135544291075809190463),(-577217635135544291021333275210)⟩⟩,⟨⟨(-669694950389533728255392509479),(-669694950389533728207975840848)⟩,⟨(-576380527121853910148171119305),(-576380527121853910093656656856)⟩⟩,⟨⟨(-669875378548435512745510343550),(-669875378548435512698031549876)⟩,⟨(-575507848740456909954797691524),(-575507848740456909900243163895)⟩⟩,⟨⟨(-670062016807064696093392420279),(-670062016807064696045848855017)⟩,⟨(-574599706919395320926325716535),(-574599706919395320871729356216)⟩⟩,⟨⟨(-670254708826878972461472056737),(-670254708826878972413861338405)⟩,⟨(-573656213348743475018783658417),(-573656213348743474964143964298)⟩⟩,⟨⟨(-670453292772671302305362916702),(-670453292772671302257682407835)⟩,⟨(-572677484514860224742683338195),(-572677484514860224687998542413)⟩⟩,⟨⟨(-670657601401099341312747111774),(-670657601401099341264994518366)⟩,⟨(-571663641735360907051646550923),(-571663641735360906996915231768)⟩⟩,⟨⟨(-670867462152504937981039185749),(-670867462152504937933211819753)⟩,⟨(-570614811194735375170655852911),(-570614811194735375115876180427)⟩⟩,⟨⟨(-671082697246006602889418134342),(-671082697246006602841513730079)⟩,⟨(-569531123980536147242725354333),(-569531123980536147187895924950)⟩⟩,⟨⟨(-671303123777846498424631748126),(-671303123777846498376647629636)⟩,⟨(-568412716120058513364605551672),(-568412716120058513309724536698)⟩⟩] +lemma kernel1_0_r5_1_eq : ∀ k : Fin 16, kernel1_0Expr 5 1 k = kernel1_0_r5_1 k := by decide +kernel +noncomputable def kernel1_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-671528553822972073920438254617),(-671528553822972073872372287772)⟩,⟨(-567259728617432305209790843429),(-567259728617432305154856962214)⟩⟩,⟨⟨(-671758794539830977015118962172),(-671758794539830976966968382349)⟩,⟨(-566072307491042968082004445017),(-566072307491042968027015766413)⟩⟩,⟨⟨(-671993648278356306836636652944),(-671993648278356306788399341333)⟩,⟨(-564850603811197587021920597684),(-564850603811197586966875844389)⟩⟩,⟨⟨(-672232912691117637881402098234),(-672232912691117637833075320809)⟩,⟨(-563594773737949609654756414661),(-563594773737949609599653674273)⟩⟩,⟨⟨(-672476380847611534829948899192),(-672476380847611534781530703248)⟩,⟨(-562304978558994181996855010541),(-562304978558994181941693162429)⟩⟩,⟨⟨(-672723841351663497894768554967),(-672723841351663497846256089575)⟩,⟨(-560981384727544272641971994384),(-560981384727544272586748993462)⟩⟩,⟨⟨(-672975078461911425664202668804),(-672975078461911425615593996692)⟩,⟨(-559624163900096108851047361069),(-559624163900096108795762088683)⟩⟩,⟨⟨(-673229872215338758026715332707),(-673229872215338757978007639105)⟩,⟨(-558233492973990888318752261361),(-558233492973990888263402695454)⟩⟩,⟨⟨(-673487998553823466064197046415),(-673487998553823466015388633528)⟩,⟨(-556809554124678266044510766136),(-556809554124678265989096018078)⟩⟩,⟨⟨(-673749229453666989424528937282),(-673749229453666989375616805968)⟩,⟨(-555352534842585750060924317339),(-555352534842585750005442162180)⟩⟩,⟨⟨(-674013333058065085460552275858),(-674013333058065085411534708920)⟩,⟨(-553862627969496876036044015983),(-553862627969496875980493530020)⟩⟩,⟨⟨(-674280073812480349401398509659),(-674280073812480349352272584787)⟩,⟨(-552340031734339872230979280937),(-552340031734339872175358302423)⟩⟩,⟨⟨(-674549212602873892260787390030),(-674549212602873892211551672767)⟩,⟨(-550784949788287476213198018470),(-550784949788287476157505896277)⟩⟩,⟨⟨(-674820506896751324557922309743),(-674820506896751324508573656313)⟩,⟨(-549197591239067626333415641795),(-549197591239067626277649972208)⟩⟩,⟨⟨(-675093710886975790919362913662),(-675093710886975790869899868912)⟩,⟨(-547578170684383927480096713254),(-547578170684383927424256807322)⟩⟩,⟨⟨(-675368575638298335153493266127),(-675368575638298335103912770559)⟩,⟨(-545926908244344085208074255014),(-545926908244344085152157778483)⟩⟩] +lemma kernel1_0_r5_2_eq : ∀ k : Fin 16, kernel1_0Expr 5 2 k = kernel1_0_r5_2 k := by decide +kernel +noncomputable def kernel1_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-675644849236553349572585357847),(-675644849236553349522886359111)⟩,⟨(-544244029592793918133998140683),(-544244029592793918078004798010)⟩⟩,⟨⟨(-675922276940464278533406779879),(-675922276940464278483585883187)⟩,⟨(-542529765987454098590390846230),(-542529765987454098534317943975)⟩⟩,⟨⟨(-676200601336002106951683812052),(-676200601336002106901739869140)⟩,⟨(-540784354298756438963924669800),(-540784354298756438907771796461)⟩⟩,⟨⟨(-676479562493236472718870771894),(-676479562493236472668800553146)⟩,⟨(-539008037037276338878400637998),(-539008037037276338822165250839)⟩⟩,⟨⟨(-676758898125616500536188565123),(-676758898125616500485991366393)⟩,⟨(-537201062379657939309745382177),(-537201062379657939253427503539)⟩⟩,⟨⟨(-677038343751615666929863344862),(-677038343751615666879535566112)⟩,⟨(-535363684192928596645840668169),(-535363684192928596589437359343)⟩⟩,⟨⟨(-677317632858672175595176920143),(-677317632858672175544717768039)⟩,⟨(-533496162057099495340312632759),(-533496162057099495283823805652)⟩⟩,⟨⟨(-677596497069353452430087250065),(-677596497069353452379493289060)⟩,⟨(-531598761285949564764776983644),(-531598761285949564708199848300)⟩⟩,⟨⟨(-677874666309670464576625151628),(-677874666309670464525896203717)⟩,⟨(-529671752945890356631974946768),(-529671752945890356575310021611)⟩⟩,⟨⟨(-678151868979464631623263698585),(-678151868979464631572395793315)⟩,⟨(-527715413872810176311816911767),(-527715413872810176255060842474)⟩⟩,⟨⟨(-678427832124787134182031950115),(-678427832124787134131024700154)⟩,⟨(-525730026686796546726942553328),(-525730026686796546670095624241)⟩⟩,⟨⟨(-678702281612187439900406536100),(-678702281612187439849256260875)⟩,⟨(-523715879804637019381725777556),(-523715879804637019324784909650)⟩⟩,⟨⟨(-678974942304824864367247237244),(-678974942304824864315954208946)⟩,⟨(-521673267449999435379148957765),(-521673267449999435322115085077)⟩⟩,⟨⟨(-679245538240313969294865552135),(-679245538240313969243425517389)⟩,⟨(-519602489661193981776793118408),(-519602489661193981719662558365)⟩⟩,⟨⟨(-679513792810211577973464564556),(-679513792810211577921877596098)⟩,⟨(-517503852296420786910330557685),(-517503852296420786853104019116)⟩⟩,⟨⟨(-679779428941050163659486657865),(-679779428941050163607748788224)⟩,⟨(-515377667036408353765182796380),(-515377667036408353707856866795)⟩⟩] +lemma kernel1_0_r5_3_eq : ∀ k : Fin 16, kernel1_0Expr 5 3 k = kernel1_0_r5_3 k := by decide +kernel +noncomputable def kernel1_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-680042169276819345820166291193),(-680042169276819345768278517445)⟩,⟨(-513224251384349844298120732881),(-513224251384349844240697038282)⟩⟩,⟨⟨(-680301736362794217735371635839),(-680301736362794217683329160001)⟩,⟨(-511043928663046100783278481639),(-511043928663046100725752743413)⟩⟩,⟨⟨(-680557852830606232746410448986),(-680557852830606232694213860407)⟩,⟨(-508837028009166323541202538088),(-508837028009166323483575944132)⟩⟩,⟨⟨(-680810241584449401493390359309),(-680810241584449401441035359152)⟩,⟨(-506603884364539518332664069015),(-506603884364539518274932826614)⟩⟩,⟨⟨(-681058625988311605002703543584),(-681058625988311604950191657870)⟩,⟨(-504344838464392181544414762518),(-504344838464392181486580987289)⟩⟩,⟨⟨(-681302730054117914821525359609),(-681302730054117914768851452421)⟩,⟨(-502060236822450207092173837985),(-502060236822450207034232864292)⟩⟩,⟨⟨(-681542278630669938024669073977),(-681542278630669937971834310191)⟩,⟨(-499750431712825675482717319626),(-499750431712825675424670871437)⟩⟩,⟨⟨(-681776997593262378439089121757),(-681776997593262378386088824181)⟩,⟨(-497415781148612022205024605421),(-497415781148612022146868460790)⟩⟩,⟨⟨(-682006614033855232548238874953),(-682006614033855232495075482787)⟩,⟨(-495056648857114078769383764060),(-495056648857114078711120915504)⟩⟩,⟨⟨(-682230856451677326053770167887),(-682230856451677326000437836005)⟩,⟨(-492673404251642634201414975981),(-492673404251642634143039992720)⟩⟩,⟨⟨(-682449454944134251868120519549),(-682449454944134251814621049201)⟩,⟨(-490266422399806476242095479387),(-490266422399806476183610680437)⟩⟩,⟨⟨(-682662141397891199339457331880),(-682662141397891199285785617918)⟩,⟨(-487836083988238338214319621721),(-487836083988238338155720304606)⟩⟩,⟨⟨(-682868649679998674773633235545),(-682868649679998674719792362154)⟩,⟨(-485382775283694797483532449776),(-485382775283694797424822208604)⟩⟩,⟨⟨(-683068715828926711858579635247),(-683068715828926711804563326312)⟩,⟨(-482906888090473942334619332266),(-482906888090473942275792253131)⟩⟩,⟨⟨(-683262078245370864478439495318),(-683262078245370864424250251317)⟩,⟨(-480408819704098543249133890025),(-480408819704098543190192948047)⟩⟩,⟨⟨(-683448477882691070698007790680),(-683448477882691070643640026592)⟩,⟨(-477888972861216529001548888524),(-477888972861216528942488847429)⟩⟩] +lemma kernel1_0_r5_4_eq : ∀ k : Fin 16, kernel1_0Expr 5 4 k = kernel1_0_r5_4 k := by decide +kernel +noncomputable def kernel1_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-683627658436842382460806533062),(-683627658436842382406264531860)⟩,⟨(-475347755685674774364716073726),(-475347755685674774305541687852)⟩⟩,⟨⟨(-683799366535654577806978365362),(-683799366535654577752254879428)⟩,⟨(-472785581630726550843986065590),(-472785581630726550784690389540)⟩⟩,⟨⟨(-683963351927315818163121883959),(-683963351927315818108220176177)⟩,⟨(-470202869417337470718290232664),(-470202869417337470658876959090)⟩⟩,⟨⟨(-684119367667913789404534781855),(-684119367667913789349448734942)⟩,⟨(-467600042968559363377426934462),(-467600042968559363317890239938)⟩⟩,⟨⟨(-684267170307886178775558074232),(-684267170307886178720292657782)⟩,⟨(-464977531339946256776805441047),(-464977531339946256717150718189)⟩⟩,⟨⟨(-684406520077230897108916288842),(-684406520077230897053463803030)⟩,⟨(-462335768645991490701207531469),(-462335768645991490641427330086)⟩⟩,⟨⟨(-684537181069325163719755628160),(-684537181069325163664120164343)⟩,⟨(-459675193982569957000642201828),(-459675193982569956940740996530)⟩⟩,⟨⟨(-684658921423201436333690975252),(-684658921423201436277865827588)⟩,⟨(-456996251345374539246553986683),(-456996251345374539186525310011)⟩⟩,⟨⟨(-684771513504127196746662133865),(-684771513504127196690653695577)⟩,⟨(-454299389544341004216824604709),(-454299389544341004156675230942)⟩⟩,⟨⟨(-684874734082334800733569625451),(-684874734082334800677369020603)⟩,⟨(-451585062114060873769488745450),(-451585062114060873709209987240)⟩⟩,⟨⟨(-684968364509746973944881605430),(-684968364509746973888493818688)⟩,⟨(-448853727220187171180397530676),(-448853727220187171119994707857)⟩⟩,⟨⟨(-685052190894543089857515342552),(-685052190894543089800933023857)⟩,⟨(-446105847561843383736466835067),(-446105847561843383675932780359)⟩⟩,⟨⟨(-685126004273411106736191280341),(-685126004273411106679421629797)⟩,⟨(-443341890270051505798854965422),(-443341890270051505738197208142)⟩⟩,⟨⟨(-685189600781329973211378164545),(-685189600781329973154411752286)⟩,⟨(-440562326802200615863668426844),(-440562326802200615802877673220)⟩⟩,⟨⟨(-685242781818727441403041893908),(-685242781818727441345884664940)⟩,⟨(-437767632832583089220129288179),(-437767632832583089159211768856)⟩⟩,⟨⟨(-685285354215858557128572923960),(-685285354215858557071216825591)⟩,⟨(-434958288139031246203957374265),(-434958288139031246142905164008)⟩⟩] +lemma kernel1_0_r5_5_eq : ∀ k : Fin 16, kernel1_0Expr 5 5 k = kernel1_0_r5_5 k := by decide +kernel +noncomputable def kernel1_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-685317130394250632918037714497),(-685317130394250632860491778621)⟩,⟨(-432134776485692976038744915681),(-432134776485692975977567331937)⟩⟩,⟨⟨(-685337928525061255271178526340),(-685337928525061255213431756805)⟩,⟨(-429297585501990648843524398268),(-429297585501990648782210519264)⟩⟩,⟨⟨(-685347572684196836418071259946),(-685347572684196836360130626382)⟩,⟨(-426447206557813424284767325150),(-426447206557813424223324355274)⟩⟩,⟨⟨(-685345893004040396003439887355),(-685345893004040395945296577343)⟩,⟨(-423584134634998875039694158428),(-423584134634998874978113358167)⟩⟩,⟨⟨(-685332725821638652420634052310),(-685332725821638652362297850444)⟩,⟨(-420708868195165656950362323183),(-420708868195165656888653706077)⟩⟩,⟨⟨(-685307913823200119382951464917),(-685307913823200119324410889029)⟩,⟨(-417821909043964765502653972010),(-417821909043964765440806081424)⟩⟩,⟨⟨(-685271306184757742714791044233),(-685271306184757742656054155139)⟩,⟨(-414923762191822709875430800075),(-414923762191822709813451879521)⟩⟩,⟨⟨(-685222758708851676809470381201),(-685222758708851676750527546470)⟩,⟨(-412014935711255700907329512097),(-412014935711255700845209948700)⟩⟩,⟨⟨(-685162133957090090810608448465),(-685162133957090090751471511238)⟩,⟨(-409095940590839677392178915074),(-409095940590839677329930733541)⟩⟩,⟨⟨(-685089301378448411937009251873),(-685089301378448411877664950450)⟩,⟨(-406167290585926675470926321073),(-406167290585926675408536227259)⟩⟩,⟨⟨(-685004137433170157607811826614),(-685004137433170157548269374931)⟩,⟨(-403229502066203667749489167607),(-403229502066203667686966505009)⟩⟩,⟨⟨(-684906525712135478763408602136),(-684906525712135478703657490972)⟩,⟨(-400283093860195551256842763167),(-400283093860195551194176990475)⟩⟩,⟨⟨(-684796357051566733138103160008),(-684796357051566733078156116735)⟩,⟨(-397328587096819435510950737374),(-397328587096819435448154704831)⟩⟩,⟨⟨(-684673529642943827830753273888),(-684673529642943827770596429351)⟩,⟨(-394366505044102762783731277294),(-394366505044102762720791037801)⟩⟩,⟨⟨(-684537949138005713422631638703),(-684537949138005713362275424200)⟩,⟨(-391397372945183071128886337563),(-391397372945183071065812397985)⟩⟩,⟨⟨(-684389528748718274664573332182),(-684389528748718274604006301536)⟩,⟨(-388421717851712375845997463827),(-388421717851712375782778296365)⟩⟩] +lemma kernel1_0_r5_6_eq : ∀ k : Fin 16, kernel1_0Expr 5 6 k = kernel1_0_r5_6 k := by decide +kernel +noncomputable def kernel1_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-684228189342092942418714421945),(-684228189342092942357951894346)⟩,⟨(-385440068454794185819032369188),(-385440068454794185755683366891)⟩⟩,⟨⟨(-684053859529744644580286354544),(-684053859529744644519312157945)⟩,⟨(-382452954913586076669624352292),(-382452954913586076606129211238)⟩⟩,⟨⟨(-683866475752082216066351772816),(-683866475752082216005177612904)⟩,⟨(-379460908681705502073500531849),(-379460908681705502009870978558)⟩⟩,⟨⟨(-683665982357029095049172432909),(-683665982357029094987785872021)⟩,⟨(-376464462331581127191553508310),(-376464462331581127127776976569)⟩⟩,⟨⟨(-683452331673177039298583929686),(-683452331673177039237000987914)⟩,⟨(-373464149376896403397793451053),(-373464149376896403333885972801)⟩⟩,⟨⟨(-683225484077280697114940779921),(-683225484077280697053144864411)⟩,⟨(-370460504093276360956579261905),(-370460504093276360892524074040)⟩⟩,⟨⟨(-682985408056006155682100310905),(-682985408056006155620104461880)⟩,⟨(-367454061337372665824318596691),(-367454061337372665760128705039)⟩⟩,⟨⟨(-682732080261852059027672661550),(-682732080261852058965463390786)⟩,⟨(-364445356364505858377319905507),(-364445356364505858312981649347)⟩⟩,⟨⟨(-682465485563167530904155366701),(-682465485563167530841751506474)⟩,⟨(-361434924645027355908570838267),(-361434924645027355844103009015)⟩⟩,⟨⟨(-682185617088196947055081669202),(-682185617088196946992464106172)⟩,⟨(-358423301679567247799124663140),(-358423301679567247734507931898)⟩⟩,⟨⟨(-681892476263087568260959757087),(-681892476263087568198142916677)⟩,⟨(-355411022813337133279212108402),(-355411022813337133214460810627)⟩⟩,⟨⟨(-681586072843802161547994420870),(-681586072843802161484963713259)⟩,⟨(-352398623049660237928562697714),(-352398623049660237863662030551)⟩⟩,⟨⟨(-681266424941884992794036908994),(-681266424941884992730811983689)⟩,⟨(-349386636862903788176675782041),(-349386636862903788111645291950)⟩⟩,⟨⟨(-680933559044035960039732232434),(-680933559044035959976293438419)⟩,⟨(-346375598010991115113155613649),(-346375598010991115047975402006)⟩⟩,⟨⟨(-680587510025454143030154424679),(-680587510025454142966517626318)⟩,⟨(-343366039347673192394302040132),(-343366039347673192328987825664)⟩⟩,⟨⟨(-680228321156918660386463144008),(-680228321156918660322612594469)⟩,⟨(-340358492634741280885310869151),(-340358492634741280819846655201)⟩⟩] +lemma kernel1_0_r5_7_eq : ∀ k : Fin 16, kernel1_0Expr 5 7 k = kernel1_0_r5_7 k := by decide +kernel +noncomputable def kernel1_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-679856044105581440455662602633),(-679856044105581440391621513739)⟩,⟨(-337353488354364048336069547514),(-337353488354364048270478388215)⟩⟩,⟨⟨(-679470738929453314063074618079),(-679470738929453313998820060471)⟩,⟨(-334351555521733949791859987623),(-334351555521733949726118669756)⟩⟩,⟨⟨(-679072474065571715502193708900),(-679072474065571715437743025980)⟩,⟨(-331353221498208788052026340154),(-331353221498208787986152005894)⟩⟩,⟨⟨(-678661326311845220233032499032),(-678661326311845220168368743548)⟩,⟨(-328359011805135218328960396607),(-328359011805135218262935816173)⟩⟩,⟨⟨(-678237380802577141720971546406),(-678237380802577141656118305573)⟩,⟨(-325369449938541512911705376884),(-325369449938541512845553916897)⟩⟩,⟨⟨(-677800730977677443175736290431),(-677800730977677443110670536936)⟩,⟨(-322385057184887156283057917230),(-322385057184887156216756243649)⟩⟩,⟨⟨(-677351478545579279950757928928),(-677351478545579279885498531869)⟩,⟨(-319406352438056795558187540403),(-319406352438056795491754265840)⟩⟩,⟨⟨(-676889733439883562148824721247),(-676889733439883562083353481656)⟩,⟨(-316433852017785722716382557218),(-316433852017785722649799171799)⟩⟩,⟨⟨(-676415613769762001490346674618),(-676415613769762001424690849600)⟩,⟨(-313468069489703411927141966792),(-313468069489703411860435448751)⟩⟩,⟨⟨(-675929245764156168547204570359),(-675929245764156168481337744276)⟩,⟨(-310509515487180676023595965656),(-310509515487180675956739569322)⟩⟩,⟨⟨(-675430763709817122734769524083),(-675430763709817122668712122003)⟩,⟨(-307558697535164740200590934407),(-307558697535164740133604773623)⟩⟩,⟨⟨(-674920309883237174635286311838),(-674920309883237174569018846607)⟩,⟨(-304616119876184958336037986633),(-304616119876184958268902239524)⟩⟩,⟨⟨(-674398034476532284911167756783),(-674398034476532284844718030481)⟩,⟨(-301682283298710018645867358355),(-301682283298710018578609487591)⟩⟩,⟨⟨(-673864095517340482884332703199),(-673864095517340482817674013602)⟩,⟨(-298757684968035302064383470301),(-298757684968035301996976428528)⟩⟩,⟨⟨(-673318658782808487473542772261),(-673318658782808487406697135701)⟩,⟨(-295842818259876570848593319884),(-295842818259876570781058758211)⟩⟩,⟨⟨(-672761897707745420349225144110),(-672761897707745420282171742525)⟩,⟨(-292938172596843379181708505749),(-292938172596843379114025252305)⟩⟩] +lemma kernel1_0_r5_8_eq : ∀ k : Fin 16, kernel1_0Expr 5 8 k = kernel1_0_r5_8 k := by decide +kernel +noncomputable def kernel1_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-672193993287029102750592377178),(-672193993287029102683363584112)⟩,⟨(-290044233287962515417379360517),(-290044233287962515349579387681)⟩⟩,⟨⟨(-671615133972356910441183001130),(-671615133972356910373747813544)⟩,⟨(-287161481371418411166200390043),(-287161481371418411098252340571)⟩⟩,⟨⟨(-671025515563439512971171705610),(-671025515563439512903553746183)⟩,⟨(-284290393460673790449263891339),(-284290393460673790381190969651)⟩⟩,⟨⟨(-670425341093742031219236556176),(-670425341093742031151413652238)⟩,⟨(-281431441594129888070274430042),(-281431441594129888002054095382)⟩⟩,⟨⟨(-669814820710883198814446365498),(-669814820710883198746450762630)⟩,⟨(-278585093088481346275631365304),(-278585093088481346207295405170)⟩⟩,⟨⟨(-669194171551808996510006578101),(-669194171551808996441807638559)⟩,⟨(-275751810395916409417579429850),(-275751810395916409349096845249)⟩⟩,⟨⟨(-668563617612862932247176457365),(-668563617612862932178799435584)⟩,⟨(-272932050965308285066556901911),(-272932050965308284997952477127)⟩⟩,⟨⟨(-667923389614880652240065882714),(-667923389614880652171487216026)⟩,⟨(-270126267107538534811272923355),(-270126267107538534742522718223)⟩⟩,⟨⟨(-667273724863441879060401527493),(-667273724863441878991658074779)⟩,⟨(-267334905865088107401219749113),(-267334905865088107332360099763)⟩⟩,⟨⟨(-666614867104417770981865186756),(-666614867104417770912921947265)⟩,⟨(-264558408886026140068956690666),(-264558408886026139999952240963)⟩⟩,⟨⟨(-665947066374956672795651764727),(-665947066374956672726535626237)⟩,⟨(-261797212302520940505130078197),(-261797212302520940436007195245)⟩⟩,⟨⟨(-665270578850055872479965793028),(-665270578850055872410651790891)⟩,⟨(-259051746613991632268853952952),(-259051746613991632199587289997)⟩⟩,⟨⟨(-664585666684871381565689099693),(-664585666684871381496214104396)⟩,⟨(-256322436575012811114644937229),(-256322436575012811045270789582)⟩⟩,⟨⟨(-663892597852921911422627151972),(-663892597852921911352956367859)⟩,⟨(-253609701088078230001480666701),(-253609701088078229931963884097)⟩⟩,⟨⟨(-663191645980347115204538056048),(-663191645980347115134700015275)⟩,⟨(-250913953101323018054029126546),(-250913953101323017984397671441)⟩⟩,⟨⟨(-662483090176383798659966557762),(-662483090176383798589934871084)⟩,⟨(-248235599511297255527676369987),(-248235599511297255457903471180)⟩⟩] +lemma kernel1_0_r5_9_eq : ∀ k : Fin 16, kernel1_0Expr 5 9 k = kernel1_0_r5_9 k := by decide +kernel +noncomputable def kernel1_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-661767214860227165883956450932),(-661767214860227165813773858326)⟩,⟨(-245575041070876885319900304607),(-245575041070876885250028055484)⟩⟩,⟨⟨(-661044309584447252454314026106),(-661044309584447252383940095039)⟩,⟨(-242932672302390954561300844551),(-242932672302390954491288482870)⟩⟩,⟨⟨(-660314668855133503025590954837),(-660314668855133502955055842997)⟩,⟨(-240308881416037060408599132591),(-240308881416037060338476199069)⟩⟩,⟨⟨(-659578591948942968796477354978),(-659578591948942968725753255258)⟩,⟨(-237704050233649635736860519565),(-237704050233649635666598829806)⟩⟩,⟨⟨(-658836382727229828462652220198),(-658836382727229828391780740959)⟩,⟨(-235118554117878366613015311876),(-235118554117878366542655784943)⟩⟩,⟨⟨(-658088349447435871176395800323),(-658088349447435871105337828227)⟩,⟨(-232552761906826598068569171714),(-232552761906826597998072368346)⟩⟩,⟨⟨(-657334804571923219225349146169),(-657334804571923219154136464628)⟩,⟨(-230007035854192071779253598621),(-230007035854192071708650639783)⟩⟩,⟨⟨(-656576064574431909919611962338),(-656576064574431909848215333961)⟩,⟨(-227481731574944762948169560442),(-227481731574944762877430840513)⟩⟩,⟨⟨(-655812449744345999564951317428),(-655812449744345999493417965664)⟩,⟨(-224977197996568958207615198140),(-224977197996568958136787178666)⟩⟩,⟨⟨(-655044283988952597169121151490),(-655044283988952597097406553469)⟩,⟨(-222493777315889055999770092837),(-222493777315889055928807963587)⟩⟩,⟨⟨(-654271894633878682171878450410),(-654271894633878682100015981184)⟩,⟨(-220031804961490889973317404718),(-220031804961490889902253834868)⟩⟩,⟨⟨(-653495612221890710242203021933),(-653495612221890710170162035531)⟩,⟨(-217591609561742688736723744710),(-217591609561742688665527733123)⟩⟩,⟨⟨(-652715770310241866001294083727),(-652715770310241865929120981926)⟩,⟨(-215173512918412106066357584647),(-215173512918412105995074733879)⟩⟩,⟨⟨(-651932705266751384090679045009),(-651932705266751384018330291229)⟩,⟨(-212777829985868098520228139437),(-212777829985868098448814635946)⟩⟩,⟨⟨(-651146756064799633696599542563),(-651146756064799633624110086044)⟩,⟨(-210404868855848806354561259939),(-210404868855848806283051305709)⟩⟩,⟨⟨(-650358264077421650560344218982),(-650358264077421650487682010348)⟩,⟨(-208054930747769022519976376756),(-208054930747769022448337584088)⟩⟩] +lemma kernel1_0_r5_10_eq : ∀ k : Fin 16, kernel1_0Expr 5 10 k = kernel1_0_r5_10 k := by decide +kernel +noncomputable def kernel1_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-649567572870680509421974217168),(-649567572870680509349192683874)⟩,⟨(-205728310004533326951350985335),(-205728310004533326879635899288)⟩⟩,⟨⟨(-648775027996500364215834359647),(-648775027996500364142883125427)⟩,⟨(-203425294093813532755833385494),(-203425294093813532683991413416)⟩⟩,⟨⟨(-647980976785137149257510516348),(-647980976785137149184426047138)⟩,⟨(-201146163614741750359057501149),(-201146163614741750287124322675)⟩⟩,⟨⟨(-647185768137462838874604215997),(-647185768137462838801353104517)⟩,⟨(-198891192309963138007503266543),(-198891192309963137935445156129)⟩⟩,⟨⟨(-646389752317236812779994542474),(-646389752317236812706627955796)⟩,⟨(-196660647082985284714982514657),(-196660647082985284642849735636)⟩⟩,⟨⟨(-645593280743535277907610458842),(-645593280743535277834080416450)⟩,⟨(-194454788020754176898151544212),(-194454788020754176825895905409)⟩⟩,⟨⟨(-644796705783506862920377892216),(-644796705783506862846722347894)⟩,⟨(-192273868421379844279219924596),(-192273868421379844206878556635)⟩⟩,⟨⟨(-644000380545619438197740719831),(-644000380545619438123924925997)⟩,⟨(-190118134826928075443011492331),(-190118134826928075370549352416)⟩⟩,⟨⟨(-643204658673559931351982070601),(-643204658673559931278063841217)⟩,⟨(-187987827061188049563075941629),(-187987827061188049490549857372)⟩⟩,⟨⟨(-642409894140945416232578772835),(-642409894140945416158503640914)⟩,⟨(-185883178272319358642714520829),(-185883178272319358570069885108)⟩⟩,⟨⟨(-641616441047000062414587879891),(-641616441047000062340395212691)⟩,⟨(-183804414980275704035633069015),(-183804414980275703962908391593)⟩⟩,⟨⟨(-640824653413348653213452151811),(-640824653413348653139105925430)⟩,⟨(-181751757128896551403482491179),(-181751757128896551330641478274)⟩⟩,⟨⟨(-640034884982073324575050218204),(-640034884982073324500606271457)⟩,⟨(-179725418142552228481591272623),(-179725418142552228408688761154)⟩⟩,⟨⟨(-639247489015175956363402420473),(-639247489015175956288808378250)⟩,⟨(-177725604987222358377599209559),(-177725604987222358304582693696)⟩⟩,⟨⟨(-638462818095584273513480734184),(-638462818095584273438777329162)⟩,⟨(-175752518235882145371342537382),(-175752518235882145298251860287)⟩⟩,⟨⟨(-637681223929835199422076195179),(-637681223929835199347226166012)⟩,⟨(-173806352138065877514417354771),(-173806352138065877441215012566)⟩⟩] +lemma kernel1_0_r5_11_eq : ∀ k : Fin 16, kernel1_0Expr 5 11 k = kernel1_0_r5_11 k := by decide +kernel +noncomputable def kernel1_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-636903057152564360229063870539),(-636903057152564360154131687177)⟩,⟨(-171887294693472087353398145549),(-171887294693472087280147505275)⟩⟩,⟨⟨(-636128667132925878919171614533),(-636128667132925878844096418001)⟩,⟨(-169995527729470124860243691615),(-169995527729470124786883860962)⟩⟩,⟨⟨(-635358401783061735224535769626),(-635358401783061735149359556300)⟩,⟨(-168131226982363450586201223263),(-168131226982363450512773279822)⟩⟩,⟨⟨(-634592607368735014041266019996),(-634592607368735013965950384012)⟩,⟨(-166294562182260757022793026059),(-166294562182260756949258349911)⟩⟩,⟨⟨(-633831628322236334472822214780),(-633831628322236334397427475393)⟩,⟨(-164485697141402076412849525209),(-164485697141402076339267342983)⟩⟩,⟨⟨(-633075807057667656725166196204),(-633075807057667656649635739434)⟩,⟨(-162704789845783337487090602886),(-162704789845783337413404258837)⟩⟩,⟨⟨(-632325483788702517947836634757),(-632325483788702517872213662510)⟩,⟨(-160951992549919394889164777263),(-160951992549919394815416527560)⟩⟩,⟨⟨(-631580996348916563773097162168),(-631580996348916563697342176255)⟩,⟨(-159227451874582375907453876133),(-159227451874582375833604038014)⟩⟩,⟨⟨(-630842680014777032709314905478),(-630842680014777032633495895213)⟩,⟨(-157531308907349271481676697241),(-157531308907349271407792072837)⟩⟩,⟨⟨(-630110867331374628567113116892),(-630110867331374628491165926374)⟩,⟨(-155863699305790043670263133504),(-155863699305790043596279622994)⟩⟩,⟨⟨(-629385887940975994464179727875),(-629385887940975994388148648285)⟩,⟨(-154224753403125130657100645938),(-154224753403125130583061570633)⟩⟩,⟨⟨(-628668068414469793239348915854),(-628668068414469793163193467778)⟩,⟨(-152614596316179103220758849294),(-152614596316179103146623574696)⟩⟩,⟨⟨(-627957732085774215666894746724),(-627957732085774215590679474430)⟩,⟨(-151033348055455363121011163394),(-151033348055455363046843058536)⟩⟩,⟨⟨(-627255198889268591836958144250),(-627255198889268591760622425385)⟩,⟨(-149481123637155173312588912472),(-149481123637155173238327406424)⟩⟩,⟨⟨(-626560785200306684318576896177),(-626560785200306684242166030193)⟩,⟨(-147958033196962971001005262223),(-147958033196962970926694662841)⟩⟩,⟨⟨(-625874803678864205827774943561),(-625874803678864205751247547612)⟩,⟨(-146464182105418835571651133809),(-146464182105418835497249932485)⟩⟩] +lemma kernel1_0_r5_12_eq : ∀ k : Fin 16, kernel1_0Expr 5 12 k = kernel1_0_r5_12 k := by decide +kernel +noncomputable def kernel1_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-625197563116368140327535335132),(-625197563116368140250965659697)⟩,⟨(-144999671084698162140695835461),(-144999671084698162066276990790)⟩⟩,⟨⟨(-624529368285750565694977438669),(-624529368285750565618295280271)⟩,⟨(-143564596326618025259332067334),(-143564596326618025184825551608)⟩⟩,⟨⟨(-623870519794764888818617664905),(-623870519794764888741869185830)⟩,⟨(-142159049611689403085652481398),(-142159049611689403011103446582)⟩⟩,⟨⟨(-623221313942597720362397694620),(-623221313942597720285540752096)⟩,⟨(-140783118429034366674031994262),(-140783118429034366599398199901)⟩⟩,⟨⟨(-622582042579805046140895392503),(-622582042579805046063998390579)⟩,⟨(-139436886096987518087116035244),(-139436886096987518012464636774)⟩⟩,⟨⟨(-621952992971596904347929877627),(-621952992971596904270928539398)⟩,⟨(-138120431884201380643749952545),(-138120431884201380569016816499)⟩⟩,⟨⟨(-621334447664490461543447695622),(-621334447664490461466388956034)⟩,⟨(-136833831131076100272018380614),(-136833831131076100197249415242)⟩⟩,⟨⟨(-620726684356347203635253054179),(-620726684356347203558094101770)⟩,⟨(-135577155371334703849038952831),(-135577155371334703774191275864)⟩⟩,⟨⟨(-620129975769805928880838329047),(-620129975769805928803656204101)⟩,⟨(-134350472453566273498186838415),(-134350472453566273423336134259)⟩⟩,⟨⟨(-619544589529119355465785377975),(-619544589529119355388507287332)⟩,⟨(-133153846662560729764122989301),(-133153846662560729689196725831)⟩⟩,⟨⟨(-618970788040398443229597507520),(-618970788040398443152270996822)⟩,⟨(-131987338840260465841029709834),(-131987338840260465766074392656)⟩⟩,⟨⟨(-618408828375264983820367796576),(-618408828375264983742949549271)⟩,⟨(-130851006506155833848582225010),(-130851006506155833773554491306)⟩⟩,⟨⟨(-617858962157909641611812857956),(-617858962157909641534374703453)⟩,⟨(-129744903976953446601486867160),(-129744903976953446526457234282)⟩⟩,⟨⟨(-617321435455549434209948848974),(-617321435455549434132423293808)⟩,⟨(-128669082485348418334006319210),(-128669082485348418258907523014)⟩⟩,⟨⟨(-616796488672275630829054630380),(-616796488672275630751489716664)⟩,⟨(-127623590297734019210370003332),(-127623590297734019135249034987)⟩⟩,⟨⟨(-616284356446280223186378737710),(-616284356446280223108730762778)⟩,⟨(-126608472830684754875649589070),(-126608472830684754800462721896)⟩⟩] +lemma kernel1_0_r5_13_eq : ∀ k : Fin 16, kernel1_0Expr 5 13 k = kernel1_0_r5_13 k := by decide +kernel +noncomputable def kernel1_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-615785267550446490219579581534),(-615785267550446490141931772069)⟩,⟨(-125623772766051597384027778092),(-125623772766051597308856787205)⟩⟩,⟨⟨(-615299444796286737673692227319),(-615299444796286737595965822525)⟩,⟨(-124669530164510981142713662403),(-124669530164510981067480166461)⟩⟩,⟨⟨(-614827104941208048644687402175),(-614827104941208048566930745540)⟩,⟨(-123745782577412230537822345889),(-123745782577412230462573629808)⟩⟩,⟨⟨(-614368458599084833150536304066),(-614368458599084833072705506578)⟩,⟨(-122852565156771298169011981786),(-122852565156771298093704151281)⟩⟩,⟨⟨(-613923710154115114782273664894),(-613923710154115114704443422064)⟩,⟨(-121989910763262057604761362179),(-121989910763262057529467748570)⟩⟩,⟨⟨(-613493057677935840965307344167),(-613493057677935840887407522338)⟩,⟨(-121157850072059905809195648620),(-121157850072059905733846422048)⟩⟩,⟨⟨(-613076692849971050250576185903),(-613076692849971050172655308257)⟩,⟨(-120356411676396081436078265552),(-120356411676396081360720885339)⟩⟩,⟨⟨(-612674800880985474726558598344),(-612674800880985474648572719787)⟩,⟨(-119585622188684889657671692781),(-119585622188684889582262224207)⟩⟩,⟨⟨(-612287560439815096898990771721),(-612287560439815096821024064459)⟩,⟨(-118845506339089935771891093055),(-118845506339089935696512225651)⟩⟩,⟨⟨(-611915143583245316499690146047),(-611915143583245316421663136275)⟩,⟨(-118136087071399502285778744349),(-118136087071399502210351436155)⟩⟩,⟨⟨(-611557715689006711384423470813),(-611557715689006711306384653363)⟩,⟨(-117457385636085351363161735236),(-117457385636085351287733415218)⟩⟩,⟨⟨(-611215435391857895180968262612),(-611215435391857895102873852724)⟩,⟨(-116809421680423490428806119213),(-116809421680423490353333024312)⟩⟩,⟨⟨(-610888454522724679345007764261),(-610888454522724679266934699943)⟩,⟨(-116192213335559797421552521150),(-116192213335559797346110185145)⟩⟩,⟨⟨(-610576918050864634985962491807),(-610576918050864634907838652989)⟩,⟨(-115605777300407857908713934381),(-115605777300407857833230599951)⟩⟩,⟨⟨(-610280964029026215951559994986),(-610280964029026215873433696904)⟩,⟨(-115050128922270913355069345084),(-115050128922270913279592262108)⟩⟩,⟨⟨(-610000723541571844471789866874),(-610000723541571844393617647268)⟩,⟨(-114525282274084452778961156412),(-114525282274084452703446891708)⟩⟩] +lemma kernel1_0_r5_14_eq : ∀ k : Fin 16, kernel1_0Expr 5 14 k = kernel1_0_r5_14 k := by decide +kernel +noncomputable def kernel1_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-609736320655534768956219188078),(-609736320655534768878090110770)⟩,⟨(-114031250228180693451153675387),(-114031250228180693375689738357)⟩⟩,⟨⟨(-609487872374580074691423352235),(-609487872374580074613253326019)⟩,⟨(-113568044526480984988400400703),(-113568044526480984912903219964)⟩⟩,⟨⟨(-609255488595840956143248283980),(-609255488595840956065085201331)⟩,⟨(-113135675847027030086507325273),(-113135675847027030011023732010)⟩⟩,⟨⟨(-609039272069602237895127979644),(-609039272069602237816928954282)⟩,⟨(-112734153866766739316659966618),(-112734153866766739241147105842)⟩⟩,⟨⟨(-608839318361804153116070305286),(-608839318361804153037913752256)⟩,⟨(-112363487320515522096938537512),(-112363487320515522021473393856)⟩⟩,⟨⟨(-608655715819340546674813113279),(-608655715819340546596625730883)⟩,⟨(-112023684056018856536382968915),(-112023684056018856460892642562)⟩⟩,⟨⟨(-608488545538126957068201215734),(-608488545538126956990030314061)⟩,⟨(-111714751085047072848499619462),(-111714751085047072773030365732)⟩⟩,⟨⟨(-608337881333915439376875709093),(-608337881333915439298679150837)⟩,⟨(-111436694630458424118320231557),(-111436694630458424042829942271)⟩⟩,⟨⟨(-608203789715834512350748280403),(-608203789715834512272614581355)⟩,⟨(-111189520169171700175914967318),(-111189520169171700100490602755)⟩⟩,⟨⟨(-608086329862634238050333454221),(-608086329862634237972179382721)⟩,⟨(-110973232470994861118763343482),(-110973232470994861043322202439)⟩⟩,⟨⟨(-607985553601618163547041011739),(-607985553601618163468913037301)⟩,⟨(-110787835633261422681650496771),(-110787835633261422606238004099)⟩⟩,⟨⟨(-607901505390245662118151398319),(-607901505390245662040008402262)⟩,⟨(-110633333111231612351716590144),(-110633333111231612276291648579)⟩⟩,⟨⟨(-607834222300390097035722840919),(-607834222300390096957643875385)⟩,⟨(-110509727744220629132941863600),(-110509727744220629057582083553)⟩⟩,⟨⟨(-607783734005240185147663310709),(-607783734005240185069574778857)⟩,⟨(-110417021777421677555995900986),(-110417021777421677480628104143)⟩⟩,⟨⟨(-607750062768833950507099046121),(-607750062768833950429046385916)⟩,⟨(-110355216879396804352312080940),(-110355216879396804276980673377)⟩⟩,⟨⟨(-607733223438216720720593946261),(-607733223438216720642537263268)⟩,⟨(-110324314155213940701440199080),(-110324314155213940626105295261)⟩⟩] +lemma kernel1_0_r5_15_eq : ∀ k : Fin 16, kernel1_0Expr 5 15 k = kernel1_0_r5_15 k := by decide +kernel +noncomputable def kernel1_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel1_0_r5_0,kernel1_0_r5_1,kernel1_0_r5_2,kernel1_0_r5_3,kernel1_0_r5_4,kernel1_0_r5_5,kernel1_0_r5_6,kernel1_0_r5_7,kernel1_0_r5_8,kernel1_0_r5_9,kernel1_0_r5_10,kernel1_0_r5_11,kernel1_0_r5_12,kernel1_0_r5_13,kernel1_0_r5_14,kernel1_0_r5_15] +lemma kernel1_0_r5_eq (i k : Fin 16) : kernel1_0Expr 5 i k = kernel1_0_r5 i k := by + fin_cases i + · exact kernel1_0_r5_0_eq k + · exact kernel1_0_r5_1_eq k + · exact kernel1_0_r5_2_eq k + · exact kernel1_0_r5_3_eq k + · exact kernel1_0_r5_4_eq k + · exact kernel1_0_r5_5_eq k + · exact kernel1_0_r5_6_eq k + · exact kernel1_0_r5_7_eq k + · exact kernel1_0_r5_8_eq k + · exact kernel1_0_r5_9_eq k + · exact kernel1_0_r5_10_eq k + · exact kernel1_0_r5_11_eq k + · exact kernel1_0_r5_12_eq k + · exact kernel1_0_r5_13_eq k + · exact kernel1_0_r5_14_eq k + · exact kernel1_0_r5_15_eq k +noncomputable def kernel1_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel1_0_r0,kernel1_0_r1,kernel1_0_r2,kernel1_0_r3,kernel1_0_r4,kernel1_0_r5] +lemma kernel1_0_eq (j : Fin 6) (i k : Fin 16) : kernel1_0Expr j i k = kernel1_0 j i k := by + fin_cases j + · exact kernel1_0_r0_eq i k + · exact kernel1_0_r1_eq i k + · exact kernel1_0_r2_eq i k + · exact kernel1_0_r3_eq i k + · exact kernel1_0_r4_eq i k + · exact kernel1_0_r5_eq i k +lemma kernel1_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel1_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(1:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel1_0_eq] + unfold kernel1_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans1_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel1_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans1 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel1_1_r0_0 : Fin 16 → CBox := ![⟨⟨10248226193785290999564899581,10248226193785291001562961587⟩,⟨2837254746515603630021373745,2837254746515603631978337969⟩⟩,⟨⟨10246019563555294230762799057,10246019563555294232760518559⟩,⟨2838181647843899979299985758,2838181647843899981256582321⟩⟩,⟨⟨10241607451996732231769843915,10241607451996732233766875204⟩,⟨2840034364039095426600988067,2840034364039095428556846051⟩⟩,⟨⟨10234992155675051711720656600,10234992155675051713716654055⟩,⟨2842810723604087493187160723,2842810723604087495141909360⟩⟩,⟨⟨10226177116347496311256236145,10226177116347496313250854238⟩,⟨2846507472855036708579486915,2846507472855036710532755536⟩⟩,⟨⟨10215166917261306653049640617,10215166917261306655042534042⟩,⟨2851120280188784149372238474,2851120280188784151323656659⟩⟩,⟨⟨10201967278230146876898623232,10201967278230146878889446841⟩,⟨2856643741761489699042954263,2856643741761489700992151812⟩⟩,⟨⟨10186585049499127542951140413,10186585049499127544939549394⟩,⟨2863071388568874895291736777,2863071388568874897238343879⟩⟩,⟨⟨10169028204411321527917432376,10169028204411321529903082038⟩,⟨2870395694916085482817515111,2870395694916085484761162122⟩⟩,⟨⟨10149305830891152885677148720,10149305830891152887659695055⟩,⟨2878608088262843501632516508,2878608088262843503572834559⟩⟩,⟨⟨10127428121762470338777422986,10127428121762470340756521822⟩,⟨2887698960427241543081879019,2887698960427241545018499149⟩⟩,⟨⟨10103406363921489080966627904,10103406363921489082941936295⟩,⟨2897657680129247291331794881,2897657680129247293264349447⟩⟩,⟨⟨10077252926387089134784583257,10077252926387089136755757591⟩,⟨2908472606852739188800195364,2908472606852739190728316162⟩⟩,⟨⟨10048981247253188149189760772,10048981247253188151156459625⟩,⟨2920131106002688522317734638,2920131106002688524241055761⟩⟩,⟨⟨10018605819570054094359161122,10018605819570054096321041639⟩,⟨2932619565331943868731590206,2932619565331943870649744441⟩⟩,⟨⟨9986142176183482025926832791,9986142176183482027883555320⟩,⟨2945923412609965045948158197,2945923412609965047860781685⟩⟩] +lemma kernel1_1_r0_0_eq : ∀ k : Fin 16, kernel1_1Expr 0 0 k = kernel1_1_r0_0 k := by decide +kernel +noncomputable def kernel1_1_r0_1 : Fin 16 → CBox := ![⟨⟨9951606873562722547089916718,9951606873562722549041138851⟩,⟨2960027134503799797352795707,2960027134503799799259521934⟩⟩,⟨⟨9915017474649911805202765977,9915017474649911807148150611⟩,⟨2974914296639601622389131107,2974914296639601624289599076⟩⟩,⟨⟨9876392530765508268215356342,9876392530765508270154562220⟩,⟨2990567564811055591986850935,2990567564811055593880695599⟩⟩,⟨⟨9835751562605885044001407905,9835751562605885045934100396⟩,⟨3006968727299214693126822780,3006968727299214695013685954⟩⟩,⟨⟨9793115040370753520629480786,9793115040370753522555318845⟩,⟨3024098718266456161386479154,3024098718266456163265996365⟩⟩,⟨⟨9748504363059500503922690628,9748504363059500505841343633⟩,⟨3041937642185549193484500401,3041937642185549195356317884⟩⟩,⟨⟨9701941836976803208943498295,9701941836976803210854626840⟩,⟨3060464799263186063152642586,3060464799263186065016397920⟩⟩,⟨⟨9653450653489041348362665966,9653450653489041350265942708⟩,⟨3079658711815771531584775244,3079658711815771533440118397⟩⟩,⟨⟨9603054866074050612321903719,9603054866074050614216988775⟩,⟨3099497151553793934573189720,3099497151553793936419758220⟩⟩,⟨⟨9550779366707655053199426635,9550779366707655055085998817⟩,⟨3119957167729718665076697529,3119957167729718666914148029⟩⟩,⟨⟨9496649861631175823544961308,9496649861631175825422683334⟩,⟨3141015116103054000258676907,3141015116103054002086650069⟩⟩,⟨⟨9440692846544739464195929713,9440692846544739466064484212⟩,⟨3162646688675043207381969810,3162646688675043209200126653⟩⟩,⟨⟨9382935581271700148091878821,9382935581271700149950927565⟩,⟨3184826944144338266737380701,3184826944144338268545361469⟩⟩,⟨⟨9323406063939847143891274211,9323406063939847145740508102⟩,⟨3207530339034011825952928811,3207530339034011827750403480⟩⟩,⟨⟨9262133004725292000674415794,9262133004725292002513500348⟩,⟨3230730759439367381825279554,3230730759439367383611892735⟩⟩,⟨⟨9199145799205020828589639292,9199145799205020830418269946⟩,⟨3254401553345215174791114259,3254401553345215176566541137⟩⟩] +lemma kernel1_1_r0_1_eq : ∀ k : Fin 16, kernel1_1Expr 0 1 k = kernel1_1_r0_1 k := by decide +kernel +noncomputable def kernel1_1_r0_2 : Fin 16 → CBox := ![⟨⟨9134474501364057335900466136,9134474501364057337718306037⟩,⟨3278515563460594636573097933,3278515563460594638336981396⟩⟩,⟨⟨9068149796303014260020223777,9068149796303014261826980003⟩,⟨3303045160518344960185373977,3303045160518344961937401658⟩⟩,⟨⟨9000202972691517265790669266,9000202972691517267586010876⟩,⟨3327962276986454708098929669,3327962276986454709838751149⟩⟩,⟨⟨8930665895012569514323797157,8930665895012569516107435677⟩,⟨3353238441137760312663750494,3353238441137760314391058659⟩⟩,⟨⟨8859570975642390614028764355,8859570975642390615800365997⟩,⟨3378844811424312547375470713,3378844811424312549089913047⟩⟩,⟨⟨8786951146809614660914945463,8786951146809614662674236052⟩,⟨3404752211102589966210249537,3404752211102589967911534213⟩⟩,⟨⟨8712839832476973067088477534,8712839832476973068835130725⟩,⟨3430931163055709036019463795,3430931163055709037707246647⟩⟩,⟨⟨8637270920187723747399380422,8637270920187723749133127238⟩,⟨3457351924758862040498420599,3457351924758862042172415960⟩⟩,⟨⟨8560278732918124212791217565,8560278732918124214511726474⟩,⟨3483984523334405327509726681,3483984523334405329169586052⟩⟩,⟨⟨8481898000976187749246577588,8481898000976187750953598700⟩,⟨3510798790643321312794251623,3510798790643321314439709589⟩⟩,⟨⟨8402163833985814972487656163,8402163833985814974180869077⟩,⟨3537764398360186743000134188,3537764398360186744630854485⟩⟩,⟨⟨8321111692994163722988296185,8321111692994163724667454960⟩,⟨3564850892979295652025988934,3564850892979295653641711194⟩⟩,⟨⟨8238777362738814805812476043,8238777362738814807477255068⟩,⟨3592027730700206502135590623,3592027730700206503735974342⟩⟩,⟨⟨8155196924109915974450689454,8155196924109915976100864515⟩,⟨3619264312141707165301040751,3619264312141707166885848658⟩⟩,⟨⟨8070406726841048449057641335,8070406726841048450693060822⟩,⟨3646530016834016349514144467,3646530016834016351083362985⟩⟩,⟨⟨7984443362461065907638074850,7984443362461065909258587623⟩,⟨3673794237439963191823803133,3673794237439963193377331824⟩⟩] +lemma kernel1_1_r0_2_eq : ∀ k : Fin 16, kernel1_1Expr 0 2 k = kernel1_1_r0_2 k := by decide +kernel +noncomputable def kernel1_1_r0_3 : Fin 16 → CBox := ![⟨⟨7897343637537612138248619906,7897343637537612139853908052⟩,⟨3701026413656905117379444658,3701026413656905118916954555⟩⟩,⟨⟨7809144547241437285538635043,7809144547241437287128511018⟩,⟨3728196065752254512926793354,3728196065752254514448088028⟩⟩,⟨⟨7719883249259010776288972458,7719883249259010777863136745⟩,⟨3755272827686683823038003483,3755272827686683824542773546⟩⟩,⟨⟨7629597038079278458950329278,7629597038079278460508595875⟩,⟨3782226479780362625720457773,3782226479780362627208509359⟩⟩,⟨⟨7538323319678739084353566313,7538323319678739085895627515⟩,⟨3809026980878945109974740291,3809026980878945111445756725⟩⟩,⟨⟨7446099586627327749633553375,7446099586627327751159252945⟩,⟨3835644499977467955240670438,3835644499977467956694489082⟩⟩,⟨⟨7352963393635897973159850384,7352963393635897974668900142⟩,⟨3862049447261832475199491264,3862049447261832476635816321⟩⟩,⟨⟨7258952333564396170824227920,7258952333564396172316474544⟩,⟨3888212504529126405801588130,3888212504529126407220261101⟩⟩,⟨⟨7164104013908128798922087562,7164104013908128800397230009⟩,⟨3914104654949685072717605917,3914104654949685074118319113⟩⟩,⟨⟨7068456033777839454531832007,7068456033777839455989754073⟩,⟨3939697212135493881393812124,3939697212135493882776445878⟩⟩,⟨⟨6972045961387646697160792900,6972045961387646698601220274⟩,⟨3964961848481288999270533331,3964961848481289000634808330⟩⟩,⟨⟨6874911312063248946621615924,6874911312063248948044430647⟩,⟨3989870622746515481353743355,3989870622746515482699539472⟩⟩,⟨⟨6777089526781185926180522464,6777089526781185927585439187⟩,⟨4014396006848146556090152590,4014396006848146557417180606⟩⟩,⟨⟨6678617951248361875546336730,6678617951248361876933275266⟩,⟨4038510911836248880696943079,4038510911836248882005122553⟩⟩,⟨⟨6579533815529488970560595456,6579533815529488971929297773⟩,⟨4062188713026090771457093690,4062188713026090772746164547⟩⟩,⟨⟨6479874214228604552323676388,6479874214228604553674062257⟩,⟨4085403274262528150359953720,4085403274262528151629836924⟩⟩] +lemma kernel1_1_r0_3_eq : ∀ k : Fin 16, kernel1_1Expr 0 3 k = kernel1_1_r0_3 k := by decide +kernel +noncomputable def kernel1_1_r0_4 : Fin 16 → CBox := ![⟨⟨6379676087229357053279104314,6379676087229357054610897946⟩,⟨4108128971294360640341113986,4108128971294360641591532931⟩⟩,⟨⟨6278976200997346734424277900,6278976200997346735737445967⟩,⟨4130340714238322305390589698,4130340714238322306621514449⟩⟩,⟨⟨6177811130446451988289571978,6177811130446451989583875438⟩,⟨4152013969114352412240474870,4152013969114352413451667627⟩⟩,⟨⟨6076217241369773131137483510,6076217241369773132412881508⟩,⟨4173124778435775777858782889,4173124778435775779050207716⟩⟩,⟨⟨5974230673434586057834844620,5974230673434586059091084448⟩,⟨4193649780840004321534332911,4193649780840004322705739782⟩⟩,⟨⟨5871887323739520253113599749,5871887323739520254350685255⟩,⟨4213566229747346012611308715,4213566229747346013762708730⟩⟩,⟨⟨5769222830931061468833254185,5769222830931061470050967989⟩,⟨4232852011037469257180041273,4232852011037469258311221902⟩⟩,⟨⟨5666272559875430552111143588,5666272559875430553309485224⟩,⟨4251485659735014793136520728,4251485659735014794247490456⟩⟩,⟨⟨5563071586880907750002397093,5563071586880907751181128481⟩,⟨4269446375697768407798125485,4269446375697768408888652543⟩⟩,⟨⟨5459654685464757277417391911,5459654685464757278576566120⟩,⟨4286714038302701469671190561,4286714038302701470741339554⟩⟩,⟨⟨5356056312658060627068215383,5356056312658060628207639105⟩,⟨4303269220127047776403002025,4303269220127047777452588446⟩⟩,⟨⟨5252310595840989300072696230,5252310595840989301192409924⟩,⟨4319093199623410167242788241,4319093199623410168271865749⟩⟩,⟨⟨5148451320100338296931093873,5148451320100338298047627480⟩,⟨4334167972789674550607090857,4334167972789674551634645906⟩⟩,⟨⟨5044511916100500473912610415,5044511916100500475027018320⟩,⟨4348476263836248506540712849,4348476263836248507567998093⟩⟩,⟨⟨4940525448458488085505922351,4940525448458488086617858522⟩,⟨4362001534854832733501943497,4362001534854832734528643804⟩⟩,⟨⟨4836524604613100564666098635,4836524604613100565775463608⟩,⟨4374727994494572866794735496,4374727994494572867820785503⟩⟩] +lemma kernel1_1_r0_4_eq : ∀ k : Fin 16, kernel1_1Expr 0 4 k = kernel1_1_r0_4 k := by decide +kernel +noncomputable def kernel1_1_r0_5 : Fin 16 → CBox := ![⟨⟨4732541684177895637955091188,4732541684177895639061485179⟩,⟨4386640605653023411544513964,4386640605653023412569543764⟩⟩,⟨⟨4628608588767242783850262147,4628608588767242784953631651⟩,⟨4397725092190881787296054888,4397725092190881788320045067⟩⟩,⟨⟨4524756812284422140042243312,4524756812284422141142220334⟩,⟨4407967944680916130882677485,4407967944680916131905289841⟩⟩,⟨⟨4421017431660476358391227770,4421017431660476359487720937⟩,⟨4417356425202913187357837687,4417356425202913188379013639⟩⟩,⟨⟨4317421098032325510438489919,4317421098032325511531084237⟩,⟨4425878571197810257852914776,4425878571197810258872267976⟩⟩,⟨⟨4213998028348513704542485000,4213998028348513705631132439⟩,⟨4433523198395445976288959579,4433523198395445977306474265⟩⟩,⟨⟨4110777997390868176515735589,4110777997390868177600050191⟩,⟨4440279902831567147796327226,4440279902831567148811645630⟩⟩,⟨⟨4007790330200314713442914984,4007790330200314714522817688⟩,⟨4446139061970861778650683523,4446139061970861779663757311⟩⟩,⟨⟨3905063894895104704846248860,3905063894895104705921295028⟩,⟨4451091834953850820206355970,4451091834953850821216767175⟩⟩,⟨⟨3802627095869766130827539922,3802627095869766131897709925⟩,⟨4455130161986462374603237686,4455130161986462375610996604⟩⟩,⟨⟨3700507867363190561314169735,3700507867363190562379064277⟩,⟨4458246762892031776619590024,4458246762892031777624323325⟩⟩,⟨⟨3598733667384407864439171703,3598733667384407865498727978⟩,⟨4460435134846318947536789782,4460435134846318948538462592⟩⟩,⟨⟨3497331471984776876275875995,3497331471984776877329643896⟩,⟨4461689549316910843954595834,4461689549316910844952782365⟩⟩,⟨⟨3396327769865530817410387413,3396327769865530818458359996⟩,⟨4462005048229082075813587798,4462005048229082076808307692⟩⟩,⟨⟨3295748557309857797721943029,3295748557309857798763712446⟩,⟨4461377439380821460200808613,4461377439380821461191677183⟩⟩,⟨⟨3195619333428966383448807881,3195619333428966384484331458⟩,⟨4459803291130297254689871245,4459803291130297255676870161⟩⟩] +lemma kernel1_1_r0_5_eq : ∀ k : Fin 16, kernel1_1Expr 0 5 k = kernel1_1_r0_5 k := by decide +kernel +noncomputable def kernel1_1_r0_6 : Fin 16 → CBox := ![⟨⟨3095965095711880990199351320,3095965095711880991228153937⟩,⟨4457279926379530135355614760,4457279926379530136338290174⟩⟩,⟨⟨2996810335869028932024325545,2996810335869028933046441165⟩,⟨4453805415878471912564811568,4453805415878471913543220015⟩⟩,⟨⟨2898179035960017473265210408,2898179035960017474280227525⟩,⟨4449378570874050964636383854,4449378570874050965610133650⟩⟩,⟨⟨2800094664796352435271834776,2800094664796352436279734226⟩,⟨4443998935129044044426521327,4443998935129044045395613228⟩⟩,⟨⟨2702580174610217119517456928,2702580174610217120517772956⟩,⟨4437666776335870268438410970,4437666776335870269402397073⟩⟩,⟨⟨2605657997980808924034285617,2605657997980808925027066673⟩,⟨4430383076950578672131589252,4430383076950578673090535604⟩⟩,⟨⟨2509350045010118549111447166,2509350045010118550096283010⟩,⟨4422149524472417782677952098,4422149524472417783631464339⟩⟩,⟨⟨2413677700740430712092824241,2413677700740430713069722159⟩,⟨4412968501194436414800778318,4412968501194436415748878557⟩⟩,⟨⟨2318661822806223531703743912,2318661822806223532672223741⟩,⟨4402843073450571634759860247,4402843073450571635702082136⟩⟩,⟨⟨2224322739313544027695565724,2224322739313544028655722034⟩,⟨4391776980384634950507814194,4391776980384634951444264244⟩⟩,⟨⟨2130680246940337460928221436,2130680246940337461879650055⟩,⟨4379774622266513737078695670,4379774622266513738008981192⟩⟩,⟨⟨2037753609251606586267581396,2037753609251606587210318532⟩,⟨4366841048380764221713060735,4366841048380764222637226872⟩⟩,⟨⟨1945561555223671507446973413,1945561555223671508380557754⟩,⟨4352981944512587607499433755,4352981944512587608417028591⟩⟩,⟨⟨1854122277972190040242983337,1854122277972190041167528825⟩,⟨4338203620055954716359836184,4338203620055954717270979208⟩⟩,⟨⟨1763453433678980769222228268,1763453433678980770137341266⟩,⟨4322512994768379512587504138,4322512994768379513491808354⟩⟩,⟨⟨1673572140713064915502479560,1673572140713064916408227059⟩,⟨4305917585196540666384136584,4305917585196540667281671413⟩⟩] +lemma kernel1_1_r0_6_eq : ∀ k : Fin 16, kernel1_1Expr 0 6 k = kernel1_1_r0_6 k := by decide +kernel +noncomputable def kernel1_1_r0_7 : Fin 16 → CBox := ![⟨⟨1584494978941707439696486227,1584494978941707440592396444⟩,⟨4288425490796615569572745561,4288425490796615570463044054⟩⟩,⟨⟨1496237989227591334792926327,1496237989227591335679167976⟩,⟨4270045379772825545083095323,4270045379772825545966324571⟩⟩,⟨⟨1408816673108600793515974828,1408816673108600794392169140⟩,⟨4250786474657296995045363346,4250786474657296995921146054⟩⟩,⟨⟨1322245992657017962105542677,1322245992657017962971788408⟩,⟨4230658537653923471174614368,4230658537653923472043044743⟩⟩,⟨⟨1236540370515253535712412676,1236540370515253536568271359⟩,⟨4209671855768470642729876948,4209671855768470643590516156⟩⟩,⟨⟨1151713690105532843734913487,1151713690105532844580569199⟩,⟨4187837225746702345304286107,4187837225746702346157309268⟩⟩,⟨⟨1067779296011245762050188851,1067779296011245762885281210⟩,⟨4165165938841823720243933948,4165165938841823721088976802⟩⟩,⟨⟨984749994527940325534330821,984749994527940326358990878⟩,⟨4141669765432039232931218941,4141669765432039233768400594⟩⟩,⟨⟨902638054382195952618260800,902638054382195953432049240⟩,⟨4117360939508511346516651454,4117360939508511347345527393⟩⟩,⟨⟨821455207616852484276030496,821455207616852485079184809⟩,⟨4092252143053482002637172332,4092252143053482003457962992⟩⟩,⟨⟨741212650641295624040539022,741212650641295624832720383⟩,⟨4066356490327785912590951058,4066356490327785913403308292⟩⟩,⟨⟨661921045445707769631953546,661921045445707770413324855⟩,⟨4039687512086443990813003680,4039687512086443991617070848⟩⟩,⟨⟨583590520978385656101253678,583590520978385656871414321⟩,⟨4012259139740478972259808875,4012259139740478973055174811⟩⟩,⟨⟨506230674685402763801778549,506230674685402764560981617⟩,⟨3984085689482545153664748421,3984085689482545154451641436⟩⟩,⟨⟨429850574212055228220373349,429850574212055228968303999⟩,⟨3955181846393411992735233562,3955181846393411993513324118⟩⟩,⟨⟨354458759265675230332686470,354458759265675231069538622⟩,⟨3925562648545788594401491528,3925562648545788595170946393⟩⟩] +lemma kernel1_1_r0_7_eq : ∀ k : Fin 16, kernel1_1Expr 0 7 k = kernel1_1_r0_7 k := by decide +kernel +noncomputable def kernel1_1_r0_8 : Fin 16 → CBox := ![⟨⟨280063243639525808989218657,280063243639525809714590078⟩,⟨3895243471121424411308802742,3895243471121424412069204816⟩⟩,⟨⟨206671517397606033974675625,206671517397606034688876650⟩,⟨3864240010556872185126982062,3864240010556872185878608393⟩⟩,⟨⟨134290549220295867214445921,134290549220295867917187670⟩,⟨3832568268732753550367976812,3832568268732753551110518656⟩⟩,⟨⟨62926788910856216235458760,62926788910856216926964268⟩,⟨3800244537220827004111885566,3800244537220827004845531397⟩⟩,⟨⟨(-7413829937127921889611309),(-7413829937127921209694511)⟩,⟨3767285381602623201631629615,3767285381602623202356006833⟩⟩,⟨⟨(-76725887111214258235041548),(-76725887111214257566398530)⟩,⟨3733707625872884756241442129,3733707625872884756956825389⟩⟩,⟨⟨(-145004472790286756585113212),(-145004472790286755928005866)⟩,⟨3699528336940527789064228578,3699528336940527789770331252⟩⟩,⟨⟨(-212245184393228845358060464),(-212245184393228844712238783)⟩,⟨3664764809239331180449807038,3664764809239331181146837622⟩⟩,⟨⟨(-278444123265837159443777429),(-278444123265837158809588275)⟩,⟨3629434549460057513998839414,3629434549460057514686427376⟩⟩,⟨⟨(-343597891205715917548441798),(-343597891205715916925522534)⟩,⟨3593555261415217678512239890,3593555261415217679190699822⟩⟩,⟨⟨(-407703586824892051997472037),(-407703586824892051386056981)⟩,⟨3557144831047209515196562310,3557144831047209515865630849⟩⟩,⟨⟨(-470758801749901451810830451),(-470758801749901451210645564)⟩,⟨3520221311590090193214780890,3520221311590090193874684166⟩⟩,⟨⟨(-532761616659116620361260214),(-532761616659116619772604693)⟩,⟨3482802908894782509428133658,3482802908894782510078544432⟩⟩,⟨⟨(-593710597157115153253267665),(-593710597157115152675776653)⟩,⟨3444907966927067301748055989,3444907966927067302389285458⟩⟩,⟨⟨(-653604789485926183019206048),(-653604789485926182453086553)⟩,⟨3406554953447277828165475579,3406554953447277828797283910⟩⟩,⟨⟨(-712443716073037795792960943),(-712443716073037795237454153)⟩,⟨3367762445880187411632622344,3367762445880187412255566654⟩⟩] +lemma kernel1_1_r0_8_eq : ∀ k : Fin 16, kernel1_1Expr 0 8 k = kernel1_1_r0_8 k := by decide +kernel +noncomputable def kernel1_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-770227370916101892437131706),(-770227370916101891892451030)⟩,⟨3328549117383168933124995150,3328549117383168933738806969⟩⟩,⟨⟨(-826956214804333546031742529),(-826956214804333545497485710)⟩,⟨3288933723120303856037634078,3288933723120303856642661817⟩⟩,⟨⟨(-882631170376669116227956433),(-882631170376669115704312694)⟩,⟨3248935086749729309446153424,3248935086749729310042176931⟩⟩,⟨⟨(-937253617016820751042808914),(-937253617016820750529474677)⟩,⟨3208572087131134214703712721,3208572087131134215290984528⟩⟩,⟨⟨(-990825385585443986763277840),(-990825385585443986260508689)⟩,⟨3167863645259949326752598124,3167863645259949327330833011⟩⟩,⟨⟨(-1043348752989719512642906282),(-1043348752989719512150311407)⟩,⟨3126828711434421148079705116,3126828711434421148649238584⟩⟩,⟨⟨(-1094826436590739382837606623),(-1094826436590739382350819058)⟩,⟨3085486252661415685578503533,3085486252661415686140774984⟩⟩,⟨⟨(-1145261588449181635955417378),(-1145261588449181635473144660)⟩,⟨3043855240306464645148882358,3043855240306464645704465427⟩⟩,⟨⟨(-1194657789409855043996315819),(-1194657789409855043518897828)⟩,⟨3001954637993243546475969648,3001954637993243547024500431⟩⟩,⟨⟨(-1243019043025797197610086311),(-1243019043025797197137187246)⟩,⟨2959803389757358010055813950,2959803389757358010597582832⟩⟩,⟨⟨(-1290349769322714003042927413),(-1290349769322714002574778613)⟩,⟨2917420408459010711104812655,2917420408459010711639563348⟩⟩,⟨⟨(-1336654798404656596237376259),(-1336654798404656595773741421)⟩,⟨2874824564458826777112702685,2874824564458826777640634170⟩⟩,⟨⟨(-1381939363901942368424806002),(-1381939363901942367965985586)⟩,⟨2832034674560829273398748362,2832034674560829273919539430⟩⟩,⟨⟨(-1426209096262439960713967088),(-1426209096262439960259644174)⟩,⟨2789069491226278402774749354,2789069491226278403288682348⟩⟩,⟨⟨(-1469470015887453455934735428),(-1469470015887453455485124263)⟩,⟨2745947692061817656254215738,2745947692061817656761056133⟩⟩,⟨⟨(-1511728526113558325007265755),(-1511728526113558324562127600)⟩,⟨2702687869585106896065129300,2702687869585106896565088500⟩⟩] +lemma kernel1_1_r0_9_eq : ∀ k : Fin 16, kernel1_1Expr 0 9 k = kernel1_1_r0_9 k := by decide +kernel +noncomputable def kernel1_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-1552991406041860739597984838),(-1552991406041860739157629226)⟩,⟨2659308521270865727183590991,2659308521270865727676342641⟩⟩,⟨⟨(-1593265803216272425990456076),(-1593265803216272425554538300)⟩,⟨2615828039880000012074021588,2615828039880000012559886870⟩⟩,⟨⟨(-1632559226152515105176089737),(-1632559226152515104744807161)⟩,⟨2572264704074239496964435320,2572264704074239497443201073⟩⟩,⟨⟨(-1670879536719691553725371668),(-1670879536719691553298485633)⟩,⟨2528636669318474739972129370,2528636669318474740444018008⟩⟩,⟨⟨(-1708234942376384254911850669),(-1708234942376384254489625365)⟩,⟨2484961959072746359254438123,2484961959072746359719171233⟩⟩,⟨⟨(-1744633988263367328235472826),(-1744633988263367327817593939)⟩,⟨2441258456275608557439581095,2441258456275608557897462774⟩⟩,⟨⟨(-1780085549155142777781764086),(-1780085549155142777368412610)⟩,⟨2397543895120361440680191911,2397543895120361441131029345⟩⟩,⟨⟨(-1814598821272637946230988940),(-1814598821272637945821928487)⟩,⟨2353835853125422362215906033,2353835853125422362659931409⟩⟩,⟨⟨(-1848183313959527271784740291),(-1848183313959527271380237699)⟩,⟨2310151743499884920814796061,2310151743499884921251729727⟩⟩,⟨⟨(-1880848841224767898465304866),(-1880848841224767898065029884)⟩,⟨2266508807805094889394662327,2266508807805094889824838833⟩⟩,⟨⟨(-1912605513154065272393835450),(-1912605513154065271997953202)⟩,⟨2222924108912854812169267972,2222924108912854812592513588⟩⟩,⟨⟨(-1943463727193111460727458757),(-1943463727193111460335737269)⟩,⟨2179414524260652883399036204,2179414524260652883815591606⟩⟩,⟨⟨(-1973434159305565454547153038),(-1973434159305565454159820663)⟩,⟨2135996739404096622637326644,2135996739404096623046951954⟩⟩,⟨⟨(-2002527755008871065601023176),(-2002527755008871065217778370)⟩,⟨2092687241866517428966658507,2092687241866517429369674318⟩⟩,⟨⟨(-2030755720291134106695517396),(-2030755720291134106316509859)⟩,⟨2049502315285497993821301895,2049502315285497994217552072⟩⟩,⟨⟨(-2058129512412406267012930222),(-2058129512412406266637934312)⟩,⟨2006458033855860468583222227,2006458033855860468972954695⟩⟩] +lemma kernel1_1_r0_10_eq : ∀ k : Fin 16, kernel1_1Expr 0 10 k = kernel1_1_r0_10 k := by decide +kernel +noncomputable def kernel1_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-2084660830593848369112106226),(-2084660830593848368741356759)⟩,⟨1963570257068438936917269062,1963570257068438937300234228⟩⟩,⟨⟨(-2110361606598370437602396246),(-2110361606598370437235576642)⟩,⟨1920854624743744879250151017,1920854624743744879626702875⟩⟩,⟨⟨(-2135243995206470134690384296),(-2135243995206470134327629279)⟩,⟨1878326552359418714334386506,1878326552359418714704384792⟩⟩,⟨⟨(-2159320364591114539030275465),(-2159320364591114538671367506)⟩,⟨1836001226670143967709181077,1836001226670143968072879626⟩⟩,⟨⟨(-2182603286595632874602028897),(-2182603286595632874247160931)⟩,⟨1793893601618482988073452038,1793893601618482988430642820⟩⟩,⟨⟨(-2205105526918709547176296250),(-2205105526918709546825188168)⟩,⟨1752018394534874281477114625,1752018394534874281828130015⟩⟩,⟨⟨(-2226840035210687626476767597),(-2226840035210687626129539614)⟩,⟨1710390082624811364259594032,1710390082624811364604307793⟩⟩,⟨⟨(-2247819935085512628814990025),(-2247819935085512628471434015)⟩,⟨1669022899741001486716616909,1669022899741001487055287769⟩⟩,⟨⟨(-2268058514052765010720638903),(-2268058514052765010380948354)⟩,⟨1627930833438079622397720554,1627930833438079622730131373⟩⟩,⟨⟨(-2287569213374347078079552739),(-2287569213374347077743442293)⟩,⟨1587127622307228758639860459,1587127622307228758966370142⟩⟩,⟨⟨(-2306365617850505942318562138),(-2306365617850505941986137859)⟩,⟨1546626753587831802660437143,1546626753587831802980931493⟩⟩,⟨⟨(-2324461445539988605380052968),(-2324461445539988605051117326)⟩,⟨1506441461053053408710251386,1506441461053053409024992841⟩⟩,⟨⟨(-2341870537419238113644717727),(-2341870537419238113319428849)⟩,⟨1466584723166021844085261370,1466584723166021844394065118⟩⟩,⟨⟨(-2358606846985650867322555955),(-2358606846985650867000661407)⟩,⟨1427069261503051787737119016,1427069261503051788040325554⟩⟩,⟨⟨(-2374684429810024480227342636),(-2374684429810024479908934751)⟩,⟨1387907539440118870950511694,1387907539440118871248016787⟩⟩,⟨⟨(-2390117433043432923620800023),(-2390117433043432923305692684)⟩,⟨1349111761098566034236129044,1349111761098566034528197963⟩⟩] +lemma kernel1_1_r0_11_eq : ∀ k : Fin 16, kernel1_1Expr 0 11 k = kernel1_1_r0_11 k := by decide +kernel +noncomputable def kernel1_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-2404920084883870919320191441),(-2404920084883870919008546397)⟩,⟨1310693870545790629919326584,1310693870545790630205753561⟩⟩,⟨⟨(-2419106684008112527886783188),(-2419106684008112527578341915)⟩,⟨1272665551246429919269726014,1272665551246429919550883905⟩⟩,⟨⟨(-2432691588974329457723342039),(-2432691588974329457418183370)⟩,⟨1235038225759331500747634084,1235038225759331501023426706⟩⟩,⟨⟨(-2445689207601112644571291942),(-2445689207601112644269241850)⟩,⟨1197823055675364596226426337,1197823055675364596497120666⟩⟩,⟨⟨(-2458113986328635956450833858),(-2458113986328635956152015764)⟩,⟨1161030941790898377947701439,1161030941790898378213126801⟩⟩,⟨⟨(-2469980399567793298952104698),(-2469980399567793298656297880)⟩,⟨1124672524511545031073940768,1124672524511545031334443064⟩⟩,⟨⟨(-2481302939043229756655084873),(-2481302939043229756362355005)⟩,⟨1088758184480538431932871282,1088758184480538432188360252⟩⟩,⟨⟨(-2492096103136273529604173999),(-2492096103136273529314359276)⟩,⟨1053298043425894622052210784,1053298043425894622302954548⟩⟩,⟨⟨(-2502374386233858125246220913),(-2502374386233858124959441549)⟩,⟨1018301965220278137802086923,1018301965220278138047895135⟩⟩,⟨⟨(-2512152268089603357306306927),(-2512152268089603357022344334)⟩,⟨983779557147279201323813317,983779557147279201565057263⟩⟩,⟨⟨(-2521444203203298990473612356),(-2521444203203298990192519285)⟩,⟨949740171367591296669207070,949740171367591296905800735⟩⟩,⟨⟨(-2530264610225106156260765315),(-2530264610225106155982392398)⟩,⟨916192906578367269751173890,916192906578367269983385615⟩⟩,⟨⟨(-2538627861390858750169766001),(-2538627861390858749894202432)⟩,⟨883146609858825341788194317,883146609858825342015858720⟩⟩,⟨⟨(-2546548271994909699563917354),(-2546548271994909699290975579)⟩,⟨850609878694974867109983763,850609878694974867333450244⟩⟩,⟨⟨(-2554040089907025059172150105),(-2554040089907025058901870260)⟩,⟨818591063176135862841877387,818591063176135863061062373⟩⟩,⟨⟨(-2561117485139882138945932513),(-2561117485139882138678177450)⟩,⟨787098268355736864759047368,787098268355736864974218958⟩⟩] +lemma kernel1_1_r0_12_eq : ∀ k : Fin 16, kernel1_1Expr 0 12 k = kernel1_1_r0_12 k := by decide +kernel +noncomputable def kernel1_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-2567794539473776087909235227),(-2567794539473776087644091482)⟩,⟨756139356768693102232261302,756139356768693102443222888⟩⟩,⟨⟨(-2574085236145182338180153378),(-2574085236145182337917435105)⟩,⟨725721951097491921973790886,725721951097491922180924147⟩⟩,⟨⟨(-2580003449605859846319367482),(-2580003449605859846059102500)⟩,⟨695853436978945413755454405,695853436978945413958676925⟩⟩,⟨⟨(-2585562935359211946577948111),(-2585562935359211946320011164)⟩,⟨666540965943411889531211187,666540965943411889730789977⟩⟩,⟨⟨(-2590777319880647646431424792),(-2590777319880647646175871560)⟩,⟨637791458478138825741634972,637791458478138825937402274⟩⟩,⟨⟨(-2595660090628706145826633812),(-2595660090628706145573309421)⟩,⟨609611607206240676761540944,609611607206240676953848649⟩⟩,⟨⟨(-2600224586153721048366378355),(-2600224586153721048115298785)⟩,⟨582007880172696177212781277,582007880172696177401546741⟩⟩,⟨⟨(-2604483986310807960418803238),(-2604483986310807960169854470)⟩,⟨554986524228631933193012362,554986524228631933378501137⟩⟩,⟨⟨(-2608451302583959753623814208),(-2608451302583959753377044617)⟩,⟨528553568505052805110827872,528553568505052805292842463⟩⟩,⟨⟨(-2612139368528027514790223252),(-2612139368528027514545484258)⟩,⟨502714827967085339544644771,502714827967085339723564420⟩⟩,⟨⟨(-2615560830335351949515602669),(-2615560830335351949272898832)⟩,⟨477475907039718827697141246,477475907039718827872882311⟩⟩,⟨⟨(-2618728137533789575276826221),(-2618728137533789575036054200)⟩,⟨452842203295959945839196537,452842203295959946012022519⟩⟩,⟨⟨(-2621653533822850278901509195),(-2621653533822850278662693010)⟩,⟨428818911198261837377306385,428818911198261837547041692⟩⟩,⟨⟨(-2624349048054627575323141150),(-2624349048054627575086156159)⟩,⟨405411025884047369528466135,405411025884047369695464377⟩⟩,⟨⟨(-2626826485366160053763507656),(-2626826485366160053528347728)⟩,⟨382623346986119554417720289,382623346986119554581896112⟩⟩,⟨⟨(-2629097418469811910707154799),(-2629097418469811910473726303)⟩,⟨360460482478740148358932121,360460482478740148520546706⟩⟩] +lemma kernel1_1_r0_13_eq : ∀ k : Fin 16, kernel1_1Expr 0 13 k = kernel1_1_r0_13 k := by decide +kernel +noncomputable def kernel1_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-2631173179108202036169913255),(-2631173179108202035938233601)⟩,⟨338926852540160584936378003,338926852540160585095213329⟩⟩,⟨⟨(-2633064849680144744887225088),(-2633064849680144744657174768)⟩,⟨318026693422407973013513429,318026693422407973169960980⟩⟩,⟨⟨(-2634783255043990846198904963),(-2634783255043990845970467878)⟩,⟨297764061319163178757545637,297764061319163178911518139⟩⟩,⟨⟨(-2636338954504675260455722648),(-2636338954504675260228814030)⟩,⟨278142836222618251062593577,278142836222618251214349328⟩⟩,⟨⟨(-2637742233990686767179058889),(-2637742233990686766953674312)⟩,⟨259166725760266841717061019,259166725760266841866413570⟩⟩,⟨⟨(-2639003098427076679782719025),(-2639003098427076679558760181)⟩,⟨240839269002663972373866582,240839269002663972521170743⟩⟩,⟨⟨(-2640131264310516270244592880),(-2640131264310516270022034629)⟩,⟨223163840233290623355853777,223163840233290623501020278⟩⟩,⟨⟨(-2641136152492297620188368293),(-2641136152492297619967133599)⟩,⟨206143652671774233108499448,206143652671774233251783407⟩⟩,⟨⟨(-2642026881175049277098765626),(-2642026881175049276878841477)⟩,⟨189781762141848324289033918,189781762141848324430212464⟩⟩,⟨⟨(-2642812259128806690261446881),(-2642812259128806690042742087)⟩,⟨174081070675583088649232034,174081070675583088788691174⟩⟩,⟨⟨(-2643500779131937955020674329),(-2643500779131937954803155762)⟩,⟨159044330045583795997885342,159044330045583796135534113⟩⟩,⟨⟨(-2644100611642277991088554472),(-2644100611642277990872151807)⟩,⟨144674145217035222294985775,144674145217035222431075778⟩⟩,⟨⟨(-2644619598703669026640481529),(-2644619598703669026425167051)⟩,⟨130972977711667749477358902,130972977711667749611692592⟩⟩,⟨⟨(-2645065248092942281419640964),(-2645065248092942281205337391)⟩,⟨117943148875934157276136984,117943148875934157409069924⟩⟩,⟨⟨(-2645444727712205186652842639),(-2645444727712205186439510050)⟩,⟨105586843045915138743354350,105586843045915138874794317⟩⟩,⟨⟨(-2645764860231120515838346596),(-2645764860231120515625920181)⟩,⟨93906110601715911621854432,93906110601715911752049339⟩⟩] +lemma kernel1_1_r0_14_eq : ∀ k : Fin 16, kernel1_1Expr 0 14 k = kernel1_1_r0_14 k := by decide +kernel +noncomputable def kernel1_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-2646032117983678617865110964),(-2646032117983678617653556080)⟩,⟨82902870904375604282042894,82902870904375604410748471⟩⟩,⟨⟨(-2646252618123771752615222500),(-2646252618123771752404467568)⟩,⟨72578915108584957512170986,72578915108584957639784728⟩⟩,⟨⟨(-2646432118043680559734320319),(-2646432118043680559524319905)⟩,⟨62935908844795845353577304,62935908844795845480006807⟩⟩,⟨⟨(-2646576011059377194195502174),(-2646576011059377193986195984)⟩,⟨53975394764607677297946346,53975394764607677423435277⟩⟩,⟨⟨(-2646689322366337907730640154),(-2646689322366337907521983949)⟩,⟨45698794943630354282827929,45698794943630354407169848⟩⟩,⟨⟨(-2646776705269340132227784735),(-2646776705269340132019716016)⟩,⟨38107413136350523030367987,38107413136350523153918541⟩⟩,⟨⟨(-2646842437689495737159471699),(-2646842437689495736951941016)⟩,⟨31202436877866777361544862,31202436877866777484212207⟩⟩,⟨⟨(-2646890418951543412926275443),(-2646890418951543412719225807)⟩,⟨24984939427709521873062476,24984939427709521995085946⟩⟩,⟨⟨(-2646924166854189417283809029),(-2646924166854189417077191405)⟩,⟨19455881551321736295630192,19455881551321736416764652⟩⟩,⟨⟨(-2646946815026047570156181912),(-2646946815026047569949938102)⟩,⟨14616113135147116343789115,14616113135147116464425622⟩⟩,⟨⟨(-2646961110569486765275699441),(-2646961110569486765069777383)⟩,⟨10466374631651244621753430,10466374631651244741802144⟩⟩,⟨⟨(-2646969411994447771062098986),(-2646969411994447770856443928)⟩,⟨7007298330988758550929823,7007298330988758670625270⟩⟩,⟨⟨(-2646973687444041116326572553),(-2646973687444041116121132007)⟩,⟨4239409456424099132903016,4239409456424099252034294⟩⟩,⟨⟨(-2646975513213484808427269417),(-2646975513213484808221988850)⟩,⟨2163127081014487491022009,2163127081014487609943643⟩⟩,⟨⟨(-2646976072563684932113710595),(-2646976072563684931908536800)⟩,⟨778764863470406392125312,778764863470406510750706⟩⟩,⟨⟨(-2646976154830504254875701128),(-2646976154830504254670580622)⟩,⟨86531601520163037104794,86531601520163155663432⟩⟩] +lemma kernel1_1_r0_15_eq : ∀ k : Fin 16, kernel1_1Expr 0 15 k = kernel1_1_r0_15 k := by decide +kernel +noncomputable def kernel1_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel1_1_r0_0,kernel1_1_r0_1,kernel1_1_r0_2,kernel1_1_r0_3,kernel1_1_r0_4,kernel1_1_r0_5,kernel1_1_r0_6,kernel1_1_r0_7,kernel1_1_r0_8,kernel1_1_r0_9,kernel1_1_r0_10,kernel1_1_r0_11,kernel1_1_r0_12,kernel1_1_r0_13,kernel1_1_r0_14,kernel1_1_r0_15] +lemma kernel1_1_r0_eq (i k : Fin 16) : kernel1_1Expr 0 i k = kernel1_1_r0 i k := by + fin_cases i + · exact kernel1_1_r0_0_eq k + · exact kernel1_1_r0_1_eq k + · exact kernel1_1_r0_2_eq k + · exact kernel1_1_r0_3_eq k + · exact kernel1_1_r0_4_eq k + · exact kernel1_1_r0_5_eq k + · exact kernel1_1_r0_6_eq k + · exact kernel1_1_r0_7_eq k + · exact kernel1_1_r0_8_eq k + · exact kernel1_1_r0_9_eq k + · exact kernel1_1_r0_10_eq k + · exact kernel1_1_r0_11_eq k + · exact kernel1_1_r0_12_eq k + · exact kernel1_1_r0_13_eq k + · exact kernel1_1_r0_14_eq k + · exact kernel1_1_r0_15_eq k +noncomputable def kernel1_1_r1_0 : Fin 16 → CBox := ![⟨⟨100524692668641916454635821363,100524692668641916477648403613⟩,⟨(-55693760523022391724882083937),(-55693760523022391701885599964)⟩⟩,⟨⟨100508225816817385036518522743,100508225816817385059529795688⟩,⟨(-55685463090241960485237480940),(-55685463090241960462242301415)⟩⟩,⟨⟨100475302395099179593004592767,100475302395099179616013205273⟩,⟨(-55668870247114116737812382547),(-55668870247114116714819853493)⟩⟩,⟨⟨100425942956236942669584232035,100425942956236942692588832549⟩,⟨(-55643986041251154187606052177),(-55643986041251154164617520014)⟩⟩,⟨⟨100360178301589115429957468218,100360178301589115452956704134⟩,⟨(-55610816550922598848567408796),(-55610816550922598825584220969)⟩⟩,⟨⟨100278049447843345729635634998,100278049447843345752628152739⟩,⟨(-55569369893235809617617637131),(-55569369893235809594641142014)⟩⟩,⟨⟨100179607582709736580381484849,100179607582709736603365928589⟩,⟨(-55519656234975766235830144876),(-55519656234975766212861693036)⟩⟩,⟨⟨100064914009643496298425484417,100064914009643496321400497710⟩,⟨(-55461687806046347465195550548),(-55461687806046347442236493121)⟩⟩,⟨⟨99934040081667638176232910486,99934040081667638199197132192⟩,⟨(-55395478915441369145220197029),(-55395478915441369122271889755)⟩⟩,⟨⟨99787067124380427109012916429,99787067124380427131964987084⟩,⟨(-55321045969659877632759558314),(-55321045969659877609823355204)⟩⟩,⟨⟨99624086348246274759744329736,99624086348246274782682880618⟩,⟨(-55238407493466729025707821362),(-55238407493466729002785085552)⟩⟩,⟨⟨99445198750282734496414613422,99445198750282734519338282134⟩,⟨(-55147584152886377632995342457),(-55147584152886377610087430714)⟩⟩,⟨⟨99250515005270132754163423307,99250515005270132777070829279⟩,⟨(-55048598780305096383619218074),(-55048598780305096360727505141)⟩⟩,⟨⟨99040155346624184192112843827,99040155346624184215002623634⟩,⟨(-54941476401544604014446260567),(-54941476401544603991572104045)⟩⟩,⟨⟨98814249437085662744362805475,98814249437085662767233566015⟩,⟨(-54826244264758324282202372358),(-54826244264758324259347159240)⟩⟩,⟨⟨98572936229394827242298514415,98572936229394827265148890268⟩,⟨(-54702931870990294896397410576),(-54702931870990294873562500226)⟩⟩] +lemma kernel1_1_r1_0_eq : ∀ k : Fin 16, kernel1_1Expr 1 0 k = kernel1_1_r1_0 k := by decide +kernel +noncomputable def kernel1_1_r1_1 : Fin 16 → CBox := ![⟨⟨98316363817131815610421313780,98316363817131815633249890524⟩,⟨(-54571571006226120453085357906),(-54571571006226120430272158277)⟩⟩,⟨⟨98044689275917611625493400015,98044689275917611648298817057⟩,⟨(-54432195774755364606696030227),(-54432195774755364583905895634)⟩⟩,⟨⟨97758078495183437770345819425,97758078495183437793126645864⟩,⟨(-54284842633655440307677907563),(-54284842633655440284912262077)⟩⟩,⟨⟨97456706000729520647212141147,97456706000729520669967015171⟩,⟨(-54129550428198419297107119964),(-54129550428198419274367318831)⟩⟩,⟨⟨97140754768307094505559875697,97140754768307094528287332438⟩,⟨(-53966360427974277074547250403),(-53966360427974277051834751170)⟩⟩,⟨⟨96810416028470235367928392581,96810416028470235390627085213⟩,⟨(-53795316363516948753060596278),(-53795316363516948730376738986)⟩⟩,⟨⟨96465889062956633604532059226,96465889062956633627200503336⟩,⟨(-53616464463213223596056567840),(-53616464463213223573402829149)⟩⟩,⟨⟨96107380992868696144320698673,96107380992868696166957547234⟩,⟨(-53429853490268977988720626692),(-53429853490268977966098346507)⟩⟩,⟨⟨95735106558938399301931000193,95735106558938399324534715514⟩,⟨(-53235534779502561799122612342),(-53235534779502561776533319945)⟩⟩,⟨⟨95349287894171066920547563728,95349287894171066943116831614⟩,⟨(-53033562273731332366799436695),(-53033562273731332344244438993)⟩⟩,⟨⟨94950154289174702689281067902,94950154289174702711814333416⟩,⟨(-52823992559514391627814555757),(-52823992559514391605295398809)⟩⟩,⟨⟨94537941950492635692078935637,94537941950492635714574881211⟩,⟨(-52606884902012540036103844371),(-52606884902012540013621838052)⟩⟩,⟨⟨94112893752268019246789936597,94112893752268019269246935107⟩,⟨(-52382301278725327764196503940),(-52382301278725327741753265693)⟩⟩,⟨⟨93675258981579128902694916433,93675258981579128925111702107⟩,⟨(-52150306411864867784472385678),(-52150306411864867762069173477)⟩⟩,⟨⟨93225293077794409419921270498,93225293077794409442296200294⟩,⟨(-51910967799126782233570367703),(-51910967799126782211208814402)⟩⟩,⟨⟨92763257366305795425824217038,92763257366305795448156021109⟩,⟨(-51664355742620285048986620663),(-51664355742620285026667987865)⟩⟩] +lemma kernel1_1_r1_1_eq : ∀ k : Fin 16, kernel1_1Expr 1 1 k = kernel1_1_r1_1 k := by decide +kernel +noncomputable def kernel1_1_r1_2 : Fin 16 → CBox := ![⟨⟨92289418787007948548268105728,92289418787007948570555034661⟩,⟨(-51410543375721959009830817398),(-51410543375721958987556843290)⟩⟩,⟨⟨91804049617899687147058115237,91804049617899687169298986798⟩,⟨(-51149606687621259422576926107),(-51149606687621259400348784738)⟩⟩,⟨⟨91307427194192005082957536101,91307427194192005105150601115⟩,⟨(-50881624545330161793935825760),(-50881624545330161771755254639)⟩⟩,⟨⟨90799833623314654995034193176,90799833623314655017178251162⟩,⟨(-50606678712934655561406560327),(-50606678712934655539274751183)⟩⟩,⟨⟨90281555496220281100332182672,90281555496220281122425355371⟩,⟨(-50324853867871955553847220545),(-50324853867871955531766038778)⟩⟩,⟨⟨89752883595391498619887399294,89752883595391498641928599547⟩,⟨(-50036237614024339203471747217),(-50036237614024339181442271406)⟩⟩,⟨⟨89214112599962104002551081850,89214112599962104024538437068⟩,⟨(-49740920491428399157689915889),(-49740920491428399135714005332)⟩⟩,⟨⟨88665540788368735154167682710,88665540788368735176100085964⟩,⟨(-49438995982407203074288239072),(-49438995982407203052366991513)⟩⟩,⟨⟨88107469738953757605407570128,88107469738953757627282966296⟩,⟨(-49130560513942347012267649052),(-49130560513942346990403104816)⟩⟩,⟨⟨87540204028943905589938797915,87540204028943905611756251513⟩,⟨(-48815713456113144764742598502),(-48815713456113144742935684361)⟩⟩,⟨⟨86964050932232232055080543879,86964050932232232076838042160⟩,⟨(-48494557116441178441054103505),(-48494557116441178419306817169)⟩⟩,⟨⟨86379320116393195640665321540,86379320116393195662361877670⟩,⟨(-48167196729990108322420749192),(-48167196729990108300734067982)⟩⟩,⟨⟨85786323339362214016553265720,85786323339362214038186661012⟩,⟨(-47833740445082962339403574315),(-47833740445082962317779700247)⟩⟩,⟨⟨85185374146211721643501066752,85185374146211721665070515455⟩,⟨(-47494299304512054547902006545),(-47494299304512054526341716472)⟩⟩,⟨⟨84576787566455667766035913400,84576787566455667787539247580⟩,⟨(-47148987222130172198548801993),(-47148987222130172177054246981)⟩⟩,⟨⟨83960879812313460948390215711,83960879812313460969826596603⟩,⟨(-46797920954725674429351815475),(-46797920954725674407923824572)⟩⟩] +lemma kernel1_1_r1_2_eq : ∀ k : Fin 16, kernel1_1Expr 1 2 k = kernel1_1_r1_2 k := by decide +kernel +noncomputable def kernel1_1_r1_3 : Fin 16 → CBox := ![⟨⟨83337967978362595515150980978,83337967978362595536517952517⟩,⟨(-46441220069098611999415879606),(-46441220069098611978056889938)⟩⟩,⟨⟨82708369743006570903095285860,82708369743006570924392300586⟩,⟨(-46079006904269854448527196513),(-46079006904269854427237746920)⟩⟩,⟨⟨82072403072181227620411575441,82072403072181227641636297216⟩,⟨(-45711406528770444321524048642),(-45711406528770444300306456517)⟩⟩,⟨⟨81430385925718266238309776482,81430385925718266259461543612⟩,⟨(-45338546692973931633246603919),(-45338546692973931612101521181)⟩⟩,⟨⟨80782635966779484275073264933,80782635966779484296149439580⟩,⟨(-44960557776450218067713440714),(-44960557776450218046643484345)⟩⟩,⟨⟨80129470274769158431600813916,80129470274769158452601048213⟩,⟨(-44577572730335400731584726203),(-44577572730335400710590235501)⟩⟩,⟨⟨79471205062125017754743556764,79471205062125017775665335451⟩,⟨(-44189727014728189809028404696),(-44189727014728189788111874291)⟩⟩,⟨⟨78808155395380401283019664104,78808155395380401303862531820⟩,⟨(-43797158531139622594039486217),(-43797158531139622573201361801)⟩⟩,⟨⟨78140634920881478978241253527,78140634920881478999002285188⟩,⟨(-43400007550038946968594726563),(-43400007550038946947837909950)⟩⟩,⟨⟨77468955595533847804958904424,77468955595533847825638077330⟩,⟨(-42998416633554639031051188675),(-42998416633554639010375694736)⟩⟩,⟨⟨76793427422942409402458419720,76793427422942409423053031362⟩,⟨(-42592530553405490820538957157),(-42592530553405490799947465926)⟩⟩,⟨⟨76114358195297208821951463964,76114358195297208842461293999⟩,⟨(-42182496204152493740224829278),(-42182496204152493719717551707)⟩⟩,⟨⟨75432053241345885413834576111,75432053241345885434256507430⟩,⟨(-41768462511877790683405115099),(-41768462511877790662985143236)⟩⟩,⟨⟨74746815180780580498175619728,74746815180780580518509880700⟩,⟨(-41350580338412215128510608774),(-41350580338412215108177706777)⟩⟩,⟨⟨74058943685353588476950648087,74058943685353588497194343592⟩,⟨(-40929002381247819767854600589),(-40929002381247819747611639345)⟩⟩,⟨⟨73368735247021758236142923688,73368735247021758256296096295⟩,⟨(-40503883069286263073521939304),(-40503883069286263053368867320)⟩⟩] +lemma kernel1_1_r1_3_eq : ∀ k : Fin 16, kernel1_1Expr 1 3 k = kernel1_1_r1_3 k := by decide +kernel +noncomputable def kernel1_1_r1_4 : Fin 16 → CBox := ![⟨⟨72676482953404682812345191706,72676482953404682832404375182⟩,⟨(-40075378454587913677379954876),(-40075378454587913657320210841)⟩⟩,⟨⟨71982476270826093139407285225,71982476270826093159373139838⟩,⟨(-39643646100299995498995693899),(-39643646100299995479028611428)⟩⟩,⟨⟨71287000835191634930079921749,71287000835191634949949357715⟩,⟨(-39208844964954979249550116706),(-39208844964954979229678759723)⟩⟩,⟨⟨70590338250939397858262722074,70590338250939397878036070409⟩,⟨(-38771135283342678678760129601),(-38771135283342678658984158828)⟩⟩,⟨⟨69892765898282227316222309108,69892765898282227335895938441⟩,⟨(-38330678444171085710913301638),(-38330678444171085691236319554)⟩⟩,⟨⟨69194556748943027755117564478,69194556748943027774692406194⟩,⟨(-37887636864741833245853098511),(-37887636864741833226274168182)⟩⟩,⟨⟨68495979190566011934823060782,68495979190566011954295831009⟩,⟨(-37442173862876266718705587815),(-37442173862876266699227965807)⟩⟩,⟨⟨67797296859968213413246336901,67797296859968213432617678777⟩,⟨(-36994453526337397583339866145),(-36994453526337397563962901916)⟩⟩,⟨⟨67098768485376613343158808684,67098768485376613362424716604⟩,⟨(-36544640580001469184716588306),(-36544640580001469165444256360)⟩⟩,⟨⟨66400647737776991890862746955,66400647737776991910024658148⟩,⟨(-36092900251040457069675966936),(-36092900251040457050506826340)⟩⟩,⟨⟨65703183091481155621144111730,65703183091481155640198552270⟩,⟨(-35639398132383524438387749632),(-35639398132383524419325245790)⟩⟩,⟨⟨65006617693999572541524631378,65006617693999572560472576844⟩,⟨(-35184300044731235805167472902),(-35184300044731235786210623893)⟩⟩,⟨⟨64311189245286724710398198527,64311189245286724729235496896⟩,⟨(-34727771897401178635545730287),(-34727771897401178616698656208)⟩⟩,⟨⟨63617129886406723682196256954,63617129886406723700924646309⟩,⟨(-34269979548287538439346732297),(-34269979548287538420607692259)⟩⟩,⟨⟨62924666097646986366252024512,62924666097646986384867847488⟩,⟨(-33811088663220106344269768855),(-33811088663220106325642390753)⟩⟩,⟨⟨62234018606088098102888155690,62234018606088098121392737609⟩,⟨(-33351264575010162552259182985),(-33351264575010162533742136421)⟩⟩] +lemma kernel1_1_r1_4_eq : ∀ k : Fin 16, kernel1_1Expr 1 4 k = kernel1_1_r1_4 k := by decide +kernel +noncomputable def kernel1_1_r1_5 : Fin 16 → CBox := ![⟨⟨61545402302618455834157849313,61545402302618455852546607260⟩,⟨(-32890672142471671502000483653),(-32890672142471671483598317659)⟩⟩,⟨⟨60859026168362946746787168788,60859026168362946765062451498⟩,⟨(-32429475609706246449511720462),(-32429475609706246431222086037)⟩⟩,⟨⟨60175093210475835648141413492,60175093210475835666299390160⟩,⟨(-31967838465939398153130372415),(-31967838465939398134957070256)⟩⟩,⟨⟨59493800407229265658076738860,59493800407229265676119097244⟩,⟨(-31505923306193684180925003551),(-31505923306193684162866342286)⟩⟩,⟨⟨58815338662310378441522049908,58815338662310378459444139463⟩,⟨(-31043891693081535907325791338),(-31043891693081535889386387723)⟩⟩,⟨⟨58139892768222087604172595307,58139892768222087621977031970⟩,⟨(-30581904019996777394285130187),(-30581904019996777376462369010)⟩⟩,⟨⟨57467641378665045755475708284,57467641378665045773158499331⟩,⟨(-30120119375979185816646032350),(-30120119375979185798943875931)⟩⟩,⟨⟨56798756989761383874940801953,56798756989761383892504007352⟩,⟨(-29658695412520902413426479596),(-29658695412520902395842866009)⟩⟩,⟨⟨56133405929964420559911901879,56133405929964420577350448041⟩,⟨(-29197788212577115262770031316),(-29197788212577115245309999095)⟩⟩,⟨⟨55471748358482785605747984084,55471748358482785623065132244⟩,⟨(-28737552162036233071917796630),(-28737552162036233054578088188)⟩⟩,⟨⟨54813938272032321636055782366,54813938272032321653247392822⟩,⟨(-28278139823896788486477751178),(-28278139823896788469262475888)⟩⟩,⟨⟨54160123519714760760990645112,54160123519714760778059154012⟩,⟨(-27819701815389589052735903809),(-27819701815389589035642625403)⟩⟩,⟨⟨53510445825808559045523285961,53510445825808559062463592054⟩,⟨(-27362386688274215643445058166),(-27362386688274215626478843736)⟩⟩,⟨⟨52865040820244445244041671855,52865040820244445260857301542⟩,⟨(-26906340812528896212775409613),(-26906340812528896195932737698)⟩⟩,⟨⟨52224038076526233756393875125,52224038076526233773080557335⟩,⟨(-26451708263642103862575689248),(-26451708263642103845860801066)⟩⟩,⟨⟨51587561156846293528736181299,51587561156846293545296729428⟩,⟨(-25998630713702991156993209096),(-25998630713702991140403293133)⟩⟩] +lemma kernel1_1_r1_5_eq : ∀ k : Fin 16, kernel1_1Expr 1 5 k = kernel1_1_r1_5 k := by decide +kernel +noncomputable def kernel1_1_r1_6 : Fin 16 → CBox := ![⟨⟨50955727664134779486206136761,50955727664134779502634964799⟩,⟨(-25547247326476028017554446635),(-25547247326476028001095053936)⟩⟩,⟨⟨50328649300772342156034422199,50328649300772342172335797649⟩,⟨(-25097694656633010518324371096),(-25097694656633010501991242692)⟩⟩,⟨⟨49706431933687551749885460807,49706431933687551766054999684⟩,⟨(-24650106553303005899882156925),(-24650106553303005883679647816)⟩⟩,⟨⟨49089175665552718620873725766,49089175665552718636914613831⟩,⟨(-24204614068087849533763964269),(-24204614068087849517688892744)⟩⟩,⟨⟨48476974911785172334252844743,48476974911785172350159599125⟩,⟨(-23761345367677567490893081521),(-23761345367677567474950897591)⟩⟩,⟨⟨47869918483055382367103274060,47869918483055382382880322999⟩,⟨(-23320425651186619300361607116),(-23320425651186619284547892260)⟩⟩,⟨⟨47268089672998566611996281386,47268089672998566627639145956⟩,⟨(-22881977072318195048704036914),(-22881977072318195033023242342)⟩⟩,⟨⟨46671566350822637524101721162,46671566350822637539613952088⟩,⟨(-22446118666450014621297309977),(-22446118666450014605745891311)⟩⟩,⟨⟨46080421058502474294845238253,46080421058502474310220917342⟩,⟨(-22012966282721219640019280856),(-22012966282721219624603123601)⟩⟩,⟨⟨45494721112248573562930841087,45494721112248573578175109371⟩,⟨(-21582632521186074805652482273),(-21582632521186074790366458796)⟩⟩,⟨⟨44914528707937108022947161914,44914528707937108038055465911⟩,⟨(-21155226675086358233294745327),(-21155226675086358218143383065)⟩⟩,⟨⟨44339901030188295549472399184,44339901030188295564448641269⟩,⟨(-20730854678280572070421987581),(-20730854678280572055401392911)⟩⟩,⟨⟨43770890364780731494947006722,43770890364780731509785405812⟩,⟨(-20309619057854495835966237739),(-20309619057854495821082161903)⟩⟩,⟨⟨43207544214090940855312908494,43207544214090940870018746574⟩,⟨(-19891618891924184444853351889),(-19891618891924184430100527748)⟩⟩,⟨⟨42649905415249839250506297425,42649905415249839265074965419⟩,⟨(-19476949772629327804401291399),(-19476949772629327789784304017)⟩⟩,⟨⟨42098012260711023548577977750,42098012260711023563013714517⟩,⟨(-19065703774301984098365752979),(-19065703774301984083880374741)⟩⟩] +lemma kernel1_1_r1_6_eq : ∀ k : Fin 16, kernel1_1Expr 1 6 k = kernel1_1_r1_6 k := by decide +kernel +noncomputable def kernel1_1_r1_7 : Fin 16 → CBox := ![⟨⟨41551898620929813270546918837,41551898620929813284843445134⟩,⟨(-18657969426783117031911688625),(-18657969426783117017564169569)⟩⟩,⟨⟨41011594068856699036560211996,41011594068856699050723594019⟩,⟨(-18253831693847148564563574295),(-18253831693847148550347867192)⟩⟩,⟨⟨40477124005954288449708776628,40477124005954288463734370737⟩,⟨(-17853371956682920575285684996),(-17853371956682920561206411865)⟩⟩,⟨⟨39948509789452935188818115824,39948509789452935202710476470⟩,⟨(-17456668002368076325249717867),(-17456668002368076311302338023)⟩⟩,⟨⟨39425768860566954184833231702,39425768860566954198586371048⟩,⟨(-17063794017262957513387857085),(-17063794017262957499578333108)⟩⟩,⟨⟨38908914873400623570258379374,38908914873400623583878349597⟩,⟨(-16674820585239694237700281829),(-16674820585239694224022581616)⟩⟩,⟨⟨38397957824281010335053565980,38397957824281010348535707021⟩,⟨(-16289814690652269365553181855),(-16289814690652269352011946528)⟩⟩,⟨⟨37892904181262987983505326331,37892904181262987996854486908⟩,⟨(-15908839725943988719121002156),(-15908839725943988705711399299)⟩⟩,⟨⟨37393757013560596864828799386,37393757013560596878038566601⟩,⟨(-15531955503780004060246666121),(-15531955503780004046975084901)⟩⟩,⟨⟨36900516120668086591536950119,36900516120668086604614080872⟩,⟨(-15159218273584333987598980622),(-15159218273584333974458688063)⟩⟩,⟨⟨36413178160943530092084554495,36413178160943530105024392291⟩,⟨(-14790680742353222329505142999),(-14790680742353222316500779595)⟩⟩,⟨⟨35931736779437765304307308577,35931736779437765317114970013⟩,⟨(-14426392099609675162549540099),(-14426392099609675149676008055)⟩⟩,⟨⟨35456182734761558373703988039,35456182734761558386373370322⟩,⟨(-14066398046357633924562972410),(-14066398046357633911826355106)⟩⟩,⟨⟨34986504024794246891514723251,34986504024794246904052537661⟩,⟨(-13710740827888477978335182990),(-13710740827888477965728794238)⟩⟩,⟨⟨34522686011047669163047512413,34522686011047669175449122436⟩,⟨(-13359459270287407288517793663),(-13359459270287407276046257107)⟩⟩,⟨⟨34064711541509872457293085185,34064711541509872469568299746⟩,⟨(-13012588820482733670324447878),(-13012588820482733657978223130)⟩⟩] +lemma kernel1_1_r1_7_eq : ∀ k : Fin 16, kernel1_1Expr 1 7 k = kernel1_1_r1_7 k := by decide +kernel +noncomputable def kernel1_1_r1_8 : Fin 16 → CBox := ![⟨⟨33612561071803877313339485973,33612561071803877325499259156⟩,⟨(-12670161589677203726776899006),(-12670161589677203714546024444)⟩⟩,⟨⟨33166212784507615036161431963,33166212784507615048212837000⟩,⟨(-12332206399997181899992603661),(-12332206399997181887870066640)⟩⟩,⟨⟨32725642706492011547642958535,32725642706492011559580972213⟩,⟨(-11998748834192829348158783601),(-11998748834192829336149628936)⟩⟩,⟨⟨32290824824145024233606267304,32290824824145024245436041356⟩,⟨(-11669811288220312625038843613),(-11669811288220312613137972913)⟩⟩,⟨⟨31861731196360212368788487832,31861731196360212380503462313⟩,⟨(-11345413026535552200744104914),(-11345413026535552188958095418)⟩⟩,⟨⟨31438332065179100813478565168,31438332065179100825085566150⟩,⟨(-11025570239928059506352821312),(-11025570239928059494674904297)⟩⟩,⟨⟨31020595963987147451096924798,31020595963987147462590976397⟩,⟨(-10710296105722995318443460369),(-10710296105722995306878633890)⟩⟩,⟨⟨30608489823173515648625288606,30608489823173515660011733356⟩,⟨(-10399600850179693116045398478),(-10399600850179693104588371579)⟩⟩,⟨⟨30201979073175054206315512786,30201979073175054217587377316⟩,⟨(-10093491812915508182837995214),(-10093491812915508171495758073)⟩⟩,⟨⟨29801027744834871177546234494,29801027744834871188710997580⟩,⟨(-9791973513184954950088401731),(-9791973513184954938853531680)⟩⟩,⟨⟨29405598567015629018660094695,29405598567015629029712846542⟩,⟨(-9495047717845658421720559987),(-9495047717845658410597989166)⟩⟩,⟨⟨29015653061417163316682868655,29015653061417163327629114770⟩,⟨(-9202713510844646486400841106),(-9202713510844646475385113053)⟩⟩,⟨⟨28631151634557214520544213887,28631151634557214531377438190⟩,⟨(-8914967364060923614019601723),(-8914967364060923603117250824)⟩⟩,⟨⟨28252053666882942491897593665,28252053666882942502625037392⟩,⟨(-8631803209343067251538423463),(-8631803209343067240742260145)⟩⟩,⟨⟨27878317598989450260890456431,27878317598989450271507289564⟩,⟨(-8353212511583750014696782263),(-8353212511583750004011658681)⟩⟩,⟨⟨27509901014929761211214380954,27509901014929761221726246721⟩,⟨(-8079184342676586959286605430),(-8079184342676586948706924171)⟩⟩] +lemma kernel1_1_r1_8_eq : ∀ k : Fin 16, kernel1_1Expr 1 8 k = kernel1_1_r1_8 k := by decide +kernel +noncomputable def kernel1_1_r1_9 : Fin 16 → CBox := ![⟨⟨27146760722608560220252985200,27146760722608560230652863743⟩,⟨(-7809705456204511002238501778),(-7809705456204510991771299848)⟩⟩,⟨⟨26788852831259513298793326463,26788852831259513309089180727⟩,⟨(-7544760362712964043498489033),(-7544760362712964033135852413)⟩⟩,⟨⟨26436132826013113283461272296,26436132826013113293648367387⟩,⟨(-7284331405425529647422619189),(-7284331405425529637169304351)⟩⟩,⟨⟨26088555639568754365909213028,26088555639568754375993301049⟩,⟨(-7028398836264198583781945513),(-7028398836264198573632242282)⟩⟩,⟨⟨25746075720991110826212303588,25746075720991110836186989224⟩,⟨(-6776940892041224705804783073),(-6776940892041224695765104859)⟩⟩,⟨⟨25408647101656882227693301430,25408647101656882237566113925⟩,⟨(-6529933870694469574437545780),(-6529933870694469564500406375)⟩⟩,⟨⟨25076223458383567228683534927,25076223458383567238449843580⟩,⟨(-6287352207443224464196688140),(-6287352207443224454366738947)⟩⟩,⟨⟨24748758173777141436956662438,24748758173777141446622303827⟩,⟨(-6049168550746713071434687518),(-6049168550746713061706129444)⟩⟩,⟨⟨24426204393840343313642560998,24426204393840343323200747044⟩,⟨(-5815353837952793268233187370),(-5815353837952793258612825433)⟩⟩,⟨⟨24108515082887719443608681792,24108515082887719453067520947⟩,⟨(-5585877370529768280367050235),(-5585877370529768270846814518)⟩⟩,⟨⟨23795643075817651333158180717,23795643075817651342513157436⟩,⟨(-5360706888779664260030436222),(-5360706888779664250614861848)⟩⟩,⟨⟨23487541127795286362518733900,23487541127795286371775741619⟩,⟨(-5139808645936810853068814350),(-5139808645936810843752040434)⟩⟩,⟨⟨23184161961403632886429209293,23184161961403632895582031421⟩,⟨(-4923147481561053493834106405),(-4923147481561053484622366539)⟩⟩,⟨⟨22885458311323062100490401965,22885458311323062109546733606⟩,⟨(-4710686894140411303482581064),(-4710686894140411294368212199)⟩⟩,⟨⟨22591382966602096517777195935,22591382966602096526732641954⟩,⟨(-4502389112823454196814862450),(-4502389112823454187802277957)⟩⟩,⟨⟨22301888810584666953870995242,22301888810584666962731483063⟩,⟨(-4298215168207089800956506127),(-4298215168207089792039805816)⟩⟩] +lemma kernel1_1_r1_9_eq : ∀ k : Fin 16, kernel1_1Expr 1 9 k = kernel1_1_r1_9 k := by decide +kernel +noncomputable def kernel1_1_r1_10 : Fin 16 → CBox := ![⟨⟨22016928858560997806883970744,22016928858560997815642757719⟩,⟨(-4098124962110808862290566368),(-4098124962110808853476508676)⟩⟩,⟨⟨21736456293210945832209279312,21736456293210945840874739528⟩,⟨(-3902077336273721912895325972),(-3902077336273721904175563262)⟩⟩,⟨⟨21460424497909982828665545276,21460424497909982837233411602⟩,⟨(-3710030139915916175576288825),(-3710030139915916166955104975)⟩⟩,⟨⟨21188787087969090444769932559,21188787087969090453246140404⟩,⟨(-3521940296110757246150311583),(-3521940296110757237621792824)⟩⟩,⟨⟨20921497939880638857468676601,20921497939880638865847229217⟩,⟨(-3337763866919743379429529521),(-3337763866919743370999687998)⟩⟩,⟨⟨20658511218642863861926840561,20658511218642863870215485811⟩,⟨(-3157456117246380726309876154),(-3157456117246380717970983522)⟩⟩,⟨⟨20399781403235852665809959081,20399781403235852674004558710⟩,⟨(-2980971577370276235602671758),(-2980971577370276227358881447)⟩⟩,⟨⟨20145263310322011283119122266,20145263310322011291225600531⟩,⟨(-2808264104127232845079995505),(-2808264104127232836925399100)⟩⟩,⟨⟨19894912116243829829849649126,19894912116243829837861619184⟩,⟨(-2639286940705571797387047662),(-2639286940705571789328046615)⟩⟩,⟨⟨19648683377391400202315482175,19648683377391400210241196446⟩,⟨(-2473992775033193211502250469),(-2473992775033193203530605287)⟩⟩,⟨⟨19406533049011587478946994833,19406533049011587486782447573⟩,⟨(-2312333796734013192062472215),(-2312333796734013184182202181)⟩⟩,⟨⟨19168417502530025717813304888,19168417502530025725564387057⟩,⟨(-2154261752636379493672731969),(-2154261752636379485877956118)⟩⟩,⟨⟨18934293541456214241924284247,18934293541456214249585240959⟩,⟨(-1999728000819864711299928807),(-1999728000819864703596415751)⟩⟩,⟨⟨18704118415940945401490859171,18704118415940945409069395112⟩,⟨(-1848683563190463646151872018),(-1848683563190463638531923324)⟩⟩,⟨⟨18477849836054112294147473729,18477849836054112301639714041⟩,⟨(-1701079176577678224898473983),(-1701079176577678217365976458)⟩⟩,⟨⟨18255445983849637811329200740,18255445983849637818740986997⟩,⟨(-1556865342350258231594416708),(-1556865342350258224143532894)⟩⟩] +lemma kernel1_1_r1_10_eq : ∀ k : Fin 16, kernel1_1Expr 1 10 k = kernel1_1_r1_10 k := by decide +kernel +noncomputable def kernel1_1_r1_11 : Fin 16 → CBox := ![⟨⟨18036865524282847111079357323,18036865524282847118404414142⟩,⟨(-1415992374550478975431829185),(-1415992374550478968068848115)⟩⟩,⟨⟨17822067615044086257041018329,17822067615044086264287650940⟩,⟨(-1278410446549778373692617102),(-1278410446549778366409232557)⟩⟩,⟨⟨17611011915370781960251022702,17611011915370781967415488353⟩,⟨(-1144069636231346917515003823),(-1144069636231346910314968977)⟩⟩,⟨⟨17403658593898452324878435075,17403658593898452331966507299⟩,⟨(-1012919969707866331571693776),(-1012919969707866324449233448)⟩⟩,⟨⟨17199968335609426984688564904,17199968335609426991694738927⟩,⟨(-884911463585028693074446421),(-884911463585028686035077774)⟩⟩,⟨⟨16999902347936227301090671987,16999902347936227308022530644⟩,⟨(-759994165783740084034363661),(-759994165783740077070496893)⟩⟩,⟨⟨16803422366074703167901838746,16803422366074703174755766822⟩,⟨(-638118194936024694606053895),(-638118194936024687721313231)⟩⟩,⟨⟨16610490657560131726611296648,16610490657560131733392988301⟩,⟨(-519233778371600250864972584),(-519233778371600244053656627)⟩⟩,⟨⟨16421070026157563732767950501,16421070026157563739471495376⟩,⟨(-403291288713897631347843150),(-403291288713897624615875234)⟩⟩,⟨⟨16235123815115763716992607015,16235123815115763723626039468⟩,⟨(-290241279105950794418801372),(-290241279105950787758132825)⟩⟩,⟨⟨16052615909832138238014055980,16052615909832138244573887194⟩,⟨(-180034517088092157372645426),(-180034517088092150786772783)⟩⟩,⟨⟨15873510739974089712049505848,15873510739974089718541336486⟩,⟨(-72622017150758068724199664),(-72622017150758062207509706)⟩⟩,⟨⟨15697773281100278309922940375,15697773281100278316341509698⟩,⟨32044928013056096712168261,32044928013056103154403132⟩⟩,⟨⟨15525369055823327537165764159,15525369055823327543518476556⟩,⟨134014717530046356338057207,134014717530046362713260832⟩⟩,⟨⟨15356264134553576171343624090,15356264134553576177627111204⟩,⟨233335413616930234861189081,233335413616930241165986472⟩⟩,⟨⟨15190425135861565573263092677,15190425135861565579482854237⟩,⟨330054714071368926444534743,330054714071368932684443228⟩⟩] +lemma kernel1_1_r1_11_eq : ∀ k : Fin 16, kernel1_1Expr 1 11 k = kernel1_1_r1_11 k := by decide +kernel +noncomputable def kernel1_1_r1_12 : Fin 16 → CBox := ![⟨⟨15027819226495061908052174041,15027819226495061914202368794⟩,⟨424219925955245829770586635,424219925955245835939751299⟩⟩,⟨⟨14868414121084551958220102881,14868414121084551964308735611⟩,⟨515877940441426223830529621,515877940441426229936982496⟩⟩,⟨⟨14712178081569323007649229467,14712178081569323013673050573⟩,⟨605075208794586419928315236,605075208794586425968801025⟩⟩,⟨⟨14559079916374445334303120636,14559079916374445340267518113⟩,⟨691857719456262099398913701,691857719456262105378842653⟩⟩,⟨⟨14409088979367223388343547575,14409088979367223394243490359⟩,⟨776270976203919453595738699,776270976203919459510068037⟩⟩,⟨⟨14262175168619971590712888085,14262175168619971596555564361⟩,⟨858359977353593972574777006,858359977353593978430725602⟩⟩,⟨⟨14118308925004305346396769546,14118308925004305352179040900⟩,⟨938169195975465155226508603,938169195975465161020933057⟩⟩,⟨⟨13977461230640519465149638554,13977461230640519470876778390⟩,⟨1015742561091636007132628645,1015742561091636012870828925⟩⟩,⟨⟨13839603607224056537343446000,13839603607224056543009986494⟩,⟨1091123439825359038003842133,1091123439825359043680336172⟩⟩,⟨⟨13704708114249548434620497055,13704708114249548440234059616⟩,⟨1164354620470990776952860219,1164354620470990782575307295⟩⟩,⟨⟨13572747347151446219941415451,13572747347151446225498970027⟩,⟨1235478296454059937312952228,1235478296454059942878317854⟩⟩,⟨⟨13443694435378838315554974845,13443694435378838321061673908⟩,⟨1304536051150995773561510842,1304536051150995779074977896⟩⟩,⟨⟨13317523040420694497501338714,13317523040420694502952357340⟩,⟨1371568843538278526086907195,1371568843538278531543638173⟩⟩,⟨⟨13194207353796464634433047946,13194207353796464639835342006⟩,⟨1436616994641038948223812475,1436616994641038953630803626⟩⟩,⟨⟨13073722095025706325465863379,13073722095025706330816503941⟩,⟨1499720174751444723415601357,1499720174751444728769919658⟩⟩,⟨⟨12956042509589214774918867222,12956042509589214780222885768⟩,⟨1560917391387564245020224971,1560917391387564250326935767⟩⟩] +lemma kernel1_1_r1_12_eq : ∀ k : Fin 16, kernel1_1Expr 1 12 k = kernel1_1_r1_12 k := by decide +kernel +noncomputable def kernel1_1_r1_13 : Fin 16 → CBox := ![⟨⟨12841144366892981248235654721,12841144366892981253487631077⟩,⟨1620246977963789056175594802,1620246977963789061429261200⟩⟩,⟨⟨12729003958245212991833254631,12729003958245212997040722079⟩,⟨1677746583144321712881630536,1677746583144321718089833768⟩⟩,⟨⟨12619598094855607128141407246,12619598094855607133301535614⟩,⟨1733453160851692595464652830,1733453160851692600624558880⟩⟩,⟨⟨12512904105865083174882122643,12512904105865083179999818583⟩,⟨1787402960902754079312266515,1787402960902754084428818876⟩⟩,⟨⟨12408899836413242781470351350,12408899836413242786540969761⟩,⟨1839631520245110486248458372,1839631520245110491316997870⟩⟩,⟨⟨12307563645749940210076286671,12307563645749940215106550314⟩,⟨1890173654767474543349955991,1890173654767474548377253705⟩⟩,⟨⟨12208874405396512102271882718,12208874405396512107259052676⟩,⟨1939063451657993015962212129,1939063451657993020945525358⟩⟩,⟨⟨12112811497361429164482863119,12112811497361429169431724637⟩,⟨1986334262285153259530197546,1986334262285153264474350963⟩⟩,⟨⟨12019354812414394502745466474,12019354812414394507650891992⟩,⟨2032018695576466316772239832,2032018695576466321672087499⟩⟩,⟨⟨11928484748422222299369349379,11928484748422222304238515431⟩,⟨2076148611870718695176031608,2076148611870718700038805035⟩⟩,⟨⟨11840182208749185156837190880,11840182208749185161667447434⟩,⟨2118755117220192071713480706,2118755117220192076536526077⟩⟩,⟨⟨11754428600723917495992785464,11754428600723917500788795406⟩,⟨2159868558119866011296709846,2159868558119866016084731623⟩⟩,⟨⟨11671205834174404608086669224,11671205834174404612843936291⟩,⟨2199518516641241621934117298,2199518516641241626682603211⟩⟩,⟨⟨11590496320032071014032719207,11590496320032071018757748784⟩,⟨2237733805949052309049185603,2237733805949052313764695598⟩⟩,⟨⟨11512282969005506348082625711,11512282969005506352772850324⟩,⟨2274542466179759974612435627,2274542466179759979292398364⟩⟩,⟨⟨11436549190323930708284567815,11436549190323930712944532820⟩,⟨2309971760661369800679018448,2309971760661369805328022624⟩⟩] +lemma kernel1_1_r1_13_eq : ∀ k : Fin 16, kernel1_1Expr 1 13 k = kernel1_1_r1_13 k := by decide +kernel +noncomputable def kernel1_1_r1_14 : Fin 16 → CBox := ![⟨⟨11363278890550102944580127090,11363278890550102949204649001⟩,⟨2344048172454732952009176843,2344048172454732956622016773⟩⟩,⟨⟨11292456472462013323057132047,11292456472462013327653371502⟩,⟨2376797401197143034416280283,2376797401197143039000178813⟩⟩,⟨⟨11224066834002375048637066932,11224066834002375053202538366⟩,⟨2408244360229667972222892760,2408244360229667976775360348⟩⟩,⟨⟨11158095367294635888342853871,11158095367294635892881984762⟩,⟨2438413173990293241796878633,2438413173990293246322387480⟩⟩,⟨⟨11094527957723970262669538059,11094527957723970267177951295⟩,⟨2467327175655584341788425665,2467327175655584346282580609⟩⟩,⟨⟨11033350983081482323220203930,11033350983081482327704211859⟩,⟨2495008905014205310770184170,2495008905014205315239356774⟩⟩,⟨⟨10974551312769650386250736825,10974551312769650390707929969⟩,⟨2521480106556255426185695269,2521480106556255430627471967⟩⟩,⟨⟨10918116307066871335712587658,10918116307066871340147282180⟩,⟨2546761727763007424214009855,2546761727763007428632752587⟩⟩,⟨⟨10864033816448818957980092731,10864033816448818962387367368⟩,⟨2570873917582247237651653471,2570873917582247242042417437⟩⟩,⟨⟨10812292180964211356019075442,10812292180964211360405753420⟩,⟨2593836025075027000144846656,2593836025075027004514520570⟩⟩,⟨⟨10762880229662488369544038885,10762880229662488373907786603⟩,⟨2615666598220249622176347135,2615666598220249626522593236⟩⟩,⟨⟨10715787280070829078843993240,10715787280070829083189016580⟩,⟨2636383382864104382474524399,2636383382864104386801595070⟩⟩,⟨⟨10671003137717890798644297080,10671003137717890802966306322⟩,⟨2656003321801968534437023749,2656003321801968538740609340⟩⟩,⟨⟨10628518095701623304205456380,10628518095701623308510605457⟩,⟨2674542553980979791689413311,2674542553980979795975730210⟩⟩,⟨⟨10588322934298504231558868167,10588322934298504235844895621⟩,⟨2692016413812068673728584612,2692016413812068677995367196⟩⟩,⟨⟨10550408920611552539091911135,10550408920611552543362918350⟩,⟨2708439430580818052004179284,2708439430580818056255575877⟩⟩] +lemma kernel1_1_r1_14_eq : ∀ k : Fin 16, kernel1_1Expr 1 14 k = kernel1_1_r1_14 k := by decide +kernel +noncomputable def kernel1_1_r1_15 : Fin 16 → CBox := ![⟨⟨10514767808254505517567720303,10514767808254505521818677271⟩,⟨2723825327947089874138207676,2723825327947089878369161262⟩⟩,⟨⟨10481391837069590023805769698,10481391837069590028043540358⟩,⟨2738187023523926033997485303,2738187023523926038214929664⟩⟩,⟨⟨10450273732876379349914556173,10450273732876379354136953591⟩,⟨2751536628526791810977978443,2751536628526791815179722652⟩⟩,⟨⟨10421406707249302409193862593,10421406707249302413404883233⟩,⟨2763885447484786368968905888,2763885447484786373158993453⟩⟩,⟨⟨10394784457321460730964490648,10394784457321460735159904581⟩,⟨2775243978005995662042675125,2775243978005995666216854818⟩⟩,⟨⟨10370401165612510141130529977,10370401165612510145316367824⟩,⟨2785621910589708944993985371,2785621910589708949158352179⟩⟩,⟨⟨10348251499878477018215481637,10348251499878477022389628437⟩,⟨2795028128478761164186559516,2795028128478761168338994717⟩⟩,⟨⟨10328330612981502731109237361,10328330612981502735275590063⟩,⟨2803470707545800061529728270,2803470707545800065674175757⟩⟩,⟨⟨10310634142777643381160514217,10310634142777643385314216434⟩,⟨2810956916207809137434640986,2810956916207809141566217141⟩⟩,⟨⟨10295158212020994401665897203,10295158212020994405813579001⟩,⟨2817493215363745980455261087,2817493215363745984580666361⟩⟩,⟨⟨10281899428282560044930357524,10281899428282560049069979878⟩,⟨2823085258350680192800286633,2823085258350680196917478659⟩⟩,⟨⟨10270854883882445458645285303,10270854883882445462780643889⟩,⟨2827737890914336546385880615,2827737890914336550498701615⟩⟩,⟨⟨10262022155834113082848842654,10262022155834113086975740543⟩,⟨2831455151190467431924628804,2831455151190467436028859915⟩⟩,⟨⟨10255399305799614661716024058,10255399305799614665840405099⟩,⟨2834240269693994462063844863,2834240269693994466165495048⟩⟩,⟨⟨10250984880054884449077473111,10250984880054884453197374629⟩,⟨2836095669313372617799955608,2836095669313372621897059445⟩⟩,⟨⟨10248777909464357390049400478,10248777909464357394168519171⟩,⟨2837022965308141951282622919,2837022965308141955378923038⟩⟩] +lemma kernel1_1_r1_15_eq : ∀ k : Fin 16, kernel1_1Expr 1 15 k = kernel1_1_r1_15 k := by decide +kernel +noncomputable def kernel1_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel1_1_r1_0,kernel1_1_r1_1,kernel1_1_r1_2,kernel1_1_r1_3,kernel1_1_r1_4,kernel1_1_r1_5,kernel1_1_r1_6,kernel1_1_r1_7,kernel1_1_r1_8,kernel1_1_r1_9,kernel1_1_r1_10,kernel1_1_r1_11,kernel1_1_r1_12,kernel1_1_r1_13,kernel1_1_r1_14,kernel1_1_r1_15] +lemma kernel1_1_r1_eq (i k : Fin 16) : kernel1_1Expr 1 i k = kernel1_1_r1 i k := by + fin_cases i + · exact kernel1_1_r1_0_eq k + · exact kernel1_1_r1_1_eq k + · exact kernel1_1_r1_2_eq k + · exact kernel1_1_r1_3_eq k + · exact kernel1_1_r1_4_eq k + · exact kernel1_1_r1_5_eq k + · exact kernel1_1_r1_6_eq k + · exact kernel1_1_r1_7_eq k + · exact kernel1_1_r1_8_eq k + · exact kernel1_1_r1_9_eq k + · exact kernel1_1_r1_10_eq k + · exact kernel1_1_r1_11_eq k + · exact kernel1_1_r1_12_eq k + · exact kernel1_1_r1_13_eq k + · exact kernel1_1_r1_14_eq k + · exact kernel1_1_r1_15_eq k +noncomputable def kernel1_1_r2_0 : Fin 16 → CBox := ![⟨⟨621463624435732509596721978450,621463624435732509692169920288⟩,⟨(-3575016100753866714625045895),(-3575016100753866618784968942)⟩⟩,⟨⟨621404267310534507756852490987,621404267310534507852301105092⟩,⟨(-3609963779179252303104214501),(-3609963779179252207263716729)⟩⟩,⟨⟨621285564935936875339093373877,621285564935936875434543174894⟩,⟨(-3679831042210257732623956165),(-3679831042210257636782773674)⟩⟩,⟨⟨621107541072998416545520294453,621107541072998416640971792603⟩,⟨(-3784561727679303532748445475),(-3784561727679303436906318363)⟩⟩,⟨⟨620870231386925697021482729896,620870231386925697116936427193⟩,⟨(-3924071655999762328101357014),(-3924071655999762232258032945)⟩⟩,⟨⟨620573683475312125317378754713,620573683475312125412835143243⟩,⟨(-4098248706521221763281901955),(-4098248706521221667437137694)⟩⟩,⟨⟨620217956905618706067203833460,620217956905618706162663389584⟩,⟨(-4306952919265669192972408100),(-4306952919265669097125975054)⟩⟩,⟨⟨619803123261750043619980539440,619803123261750043715443727759⟩,⟨(-4550016621983644469566294622),(-4550016621983644373717974718)⟩⟩,⟨⟨619329266199543137780109627911,619329266199543137875576885177⟩,⟨(-4827244582453870442343494451),(-4827244582453870346493095960)⟩⟩,⟨⟨618796481510950854591376023747,618796481510950854686847780694⟩,⟨(-5138414185934137948370492825),(-5138414185934137852517828406)⟩⟩,⟨⟨618204877196666749933379121696,618204877196666750028855760601⟩,⟨(-5483275637655256644868475620),(-5483275637655256549013404427)⟩⟩,⟨⟨617554573546903247013301171497,617554573546903247108783082976⟩,⟨(-5861552190233650007715808115),(-5861552190233649911858178994)⟩⟩,⟨⟨616845703230001095227424574289,616845703230001095322912064038⟩,⟨(-6272940395861638922497427405),(-6272940395861638826637171659)⟩⟩,⟨⟨616078411388514641545001740080,616078411388514641640495159878⟩,⟨(-6717110383117592195713267353),(-6717110383117592099850267975)⟩⟩,⟨⟨615252855742384800287800581618,615252855742384800383300151646⟩,⟨(-7193706158220894864186318860),(-7193706158220894768320587441)⟩⟩,⟨⟨614369206698779786172810773539,614369206698779786268316795573⟩,⟨(-7702345930539069626921516899),(-7702345930539069531052980967)⟩⟩] +lemma kernel1_1_r2_0_eq : ∀ k : Fin 16, kernel1_1Expr 2 0 k = kernel1_1_r2_0 k := by decide +kernel +noncomputable def kernel1_1_r2_1 : Fin 16 → CBox := ![⟨⟨613427647468152751381550638029,613427647468152751477063206907⟩,⟨(-8242622462136358921500871966),(-8242622462136358825629662381)⟩⟩,⟨⟨612428374186035512158547033632,612428374186035512254066421951⟩,⟨(-8814103441134613786393665188),(-8814103441134613690519732538)⟩⟩,⟨⟨611371596040058635186817778505,611371596040058635282343966440⟩,⟨(-9416331878638422371230463038),(-9416331878638422275354046089)⟩⟩,⟨⟨610257535401660349025091472623,610257535401660349120624673581⟩,⟨(-10048826528957030655953240877),(-10048826528957030560074342506)⟩⟩,⟨⟨609086427961920120521493888049,609086427961920120617033895113⟩,⟨(-10711082332835748867204054062),(-10711082332835748771323092441)⟩⟩,⟨⟨607858522870927358544156986063,607858522870927358639704007448⟩,⟨(-11402570883389191026260212360),(-11402570883389190930377188186)⟩⟩,⟨⟨606574082880071644571781096645,606574082880071644667334785462⟩,⟨(-12122740914407857510944958443),(-12122740914407857415060421695)⟩⟩,⟨⟨605233384486618207295109266673,605233384486618207390669761849⟩,⟨(-12871018810688240783752684625),(-12871018810688240687866697076)⟩⟩,⟨⟨603836718079911120530298400964,603836718079911120625865080352⟩,⟨(-13646809140014815814103560500),(-13646809140014815718216938128)⟩⟩,⟨⟨602384388088526972934747928697,602384388088526973030320980882⟩,⟨(-14449495206399976568233643110),(-14449495206399976472346389649)⟩⟩,⟨⟨600876713127683594947889323499,600876713127683595043467978744⟩,⟨(-15278439624165209800095812660),(-15278439624165209704208882295)⟩⟩,⟨⟨599314026146191891798476483138,599314026146191891894060835663⟩,⟨(-16132984912423573060914583664),(-16132984912423572965028065070)⟩⟩,⟨⟨597696674572223977941999018955,597696674572223978037587933932⟩,⟨(-17012454109499885498754864699),(-17012454109499885402870066453)⟩⟩,⟨⟨596025020457157692225919774213,596025020457157692321513454919⟩,⟨(-17916151406800972175500467386),(-17916151406800972079617359903)⟩⟩,⟨⟨594299440616746246243938105358,594299440616746246339535257986⟩,⟨(-18843362801623854242854667124),(-18843362801623854146974707493)⟩⟩,⟨⟨592520326768852269868120041346,592520326768852269963720758096⟩,⟨(-19793356768364981787937390938),(-19793356768364981692060650224)⟩⟩] +lemma kernel1_1_r2_1_eq : ∀ k : Fin 16, kernel1_1Expr 2 1 k = kernel1_1_r2_1 k := by decide +kernel +noncomputable def kernel1_1_r2_2 : Fin 16 → CBox := ![⟨⟨590688085666977914095322434594,590688085666977914190924905122⟩,⟨(-20765384947568501318687180848),(-20765384947568501222815620440)⟩⟩,⟨⟨588803139228816995287110887716,588803139228816995382715438927⟩,⟨(-21758682852226177965037611842),(-21758682852226177869171058525)⟩⟩,⟨⟨586865924659051456509955499313,586865924659051456605560206753⟩,⟨(-22772470590716000158622431225),(-22772470590716000062762949345)⟩⟩,⟨⟨584876894565612717389903787160,584876894565612717485508798068⟩,⟨(-23805953605740732776498127462),(-23805953605740732680645712010)⟩⟩,⟨⟨582836517068628816373190248814,582836517068628816468793010948⟩,⟨(-24858323428601808687308886907),(-24858323428601808591466216544)⟩⟩,⟨⟨580745275901280647303802472809,580745275901280647399403458145⟩,⟨(-25928758448118017654440662473),(-25928758448118017558607397602)⟩⟩,⟨⟨578603670501795080434141263976,578603670501795080529737808077⟩,⟨(-27016424693472528979014276342),(-27016424693472528883193195996)⟩⟩,⟨⟨576412216095809356677928458278,576412216095809356773520832896⟩,⟨(-28120476630245937328154060310),(-28120476630245937232345013028)⟩⟩,⟨⟨574171443768349868848655930204,574171443768349868944240607886⟩,⟨(-29240057968867320820475647136),(-29240057968867320724682259904)⟩⟩,⟨⟨571881900524679305800279929320,571881900524679305895857725872⟩,⟨(-30374302484689821082614798982),(-30374302484689820986836366902)⟩⟩,⟨⟨569544149339279140843058228568,569544149339279140938625628857⟩,⟨(-31522334848872074412501354678),(-31522334848872074316741480613)⟩⟩,⟨⟨567158769192249595440472377026,567158769192249595536029858740⟩,⟨(-32683271469222022236422919260),(-32683271469222022140681223443)⟩⟩,⟨⟨564726355092426498562411018649,564726355092426498657954080628⟩,⟨(-33856221340135291410832540199),(-33856221340135291315113595464)⟩⟩,⟨⟨562247518086533881221908900265,562247518086533881317438677350⟩,⟨(-35040286900736546843079137173),(-35040286900736546747381897539)⟩⟩,⟨⟨559722885253712679026711274636,559722885253712679122223291169⟩,⟨(-36234564900309068905809312705),(-36234564900309068810138313484)⟩⟩,⟨⟨557153099684789541569049145026,557153099684789541664544176855⟩,⟨(-37438147270075386677120245249),(-37438147270075386581474786222)⟩⟩] +lemma kernel1_1_r2_2_eq : ∀ k : Fin 16, kernel1_1Expr 2 2 k = kernel1_1_r2_2 k := by decide +kernel +noncomputable def kernel1_1_r2_3 : Fin 16 → CBox := ![⟨⟨554538820445675438722088250717,554538820445675438817560470015⟩,⟨(-38650122000370197262161353162),(-38650122000370197166547303887)⟩⟩,⟨⟨551880722524311476877018284052,551880722524311476972469485356⟩,⟨(-39869574022226114734395561459),(-39869574022226114638811195592)⟩⟩,⟨⟨549179496760609053104503530712,549179496760609053199928171563⟩,⟨(-41095586092373113884798354747),(-41095586092373113789249245498)⟩⟩,⟨⟨546435849758863136127689027828,546435849758863136223088282890⟩,⟨(-42327239680633958829149984348),(-42327239680633958733635010970)⟩⟩,⟨⟨543650503782151017458531222477,543650503782151017553898101203⟩,⟨(-43563615858680529578488494130),(-43563615858680529483014659384)⟩⟩,⟨⟨540824196628264265270519233232,540824196628264265365856026894⟩,⟨(-44803796189099875634792378411),(-44803796189099875539357438313)⟩⟩,⟨⟨537957681486758772319325190027,537957681486758772414625185687⟩,⟨(-46046863613704128544885441071),(-46046863613704128449496109927)⟩⟩,⟨⟨535051726776746645800792537739,535051726776746645896057418970⟩,⟨(-47291903340005188012833456318),(-47291903340005187917488083836)⟩⟩,⟨⟨532107115965094163363093242210,532107115965094163458314354082⟩,⟨(-48538003724763449942504037013),(-48538003724763449847211258675)⟩⟩,⟨⟨529124647364732031113424721362,529124647364732031208605366484⟩,⟨(-49784257153509858942080018436),(-49784257153509858846836561165)⟩⟩,⟨⟨526105133912827635642637196465,526105133912827635737769395583⟩,⟨(-51029760914932329174191814264),(-51029760914932329079005629199)⟩⟩,⟨⟨523049402928613785918059817428,523049402928613786013145877474⟩,⟨(-52273618069011169843197316364),(-52273618069011169748066110756)⟩⟩,⟨⟨519958295850714489409314739246,519958295850714489504344665344⟩,⟨(-53514938307783655536910816282),(-53514938307783655441844535800)⟩⟩,⟨⟨516832667953855491180405088074,516832667953855491275382895074⟩,⟨(-54752838807615373685888324051),(-54752838807615373590882965567)⟩⟩,⟨⟨513673388044895510391852209054,513673388044895510486768562426⟩,⟨(-55986445071855533851686764519),(-55986445071855533756751605196)⟩⟩,⟨⟨510481338138163215743104600566,510481338138163215837962551803⟩,⟨(-57214891762755103920487232371),(-57214891762755103825619217783)⟩⟩] +lemma kernel1_1_r2_3_eq : ∀ k : Fin 16, kernel1_1Expr 2 3 k = kernel1_1_r2_3 k := by decide +kernel +noncomputable def kernel1_1_r2_4 : Fin 16 → CBox := ![⟨⟨507257413110134864689082250448,507257413110134864783869719285⟩,⟨(-58437323521530508859244502841),(-58437323521530508764455631415)⟩⟩,⟨⟨504002520333538060720235753752,504002520333538060814958250534⟩,⟨(-59652895775461745142122754830),(-59652895775461745047407515558)⟩⟩,⟨⟨500717579291018123954723574629,500717579291018124049370331289⟩,⟨(-60860775530922178860586827670),(-60860775530922178765955902563)⟩⟩,⟨⟨497403521168554983870687157976,497403521168554983965262092298⟩,⟨(-62060142151248052006045377091),(-62060142151248051911494830679)⟩⟩,⟨⟨494061288428870146471956230673,494061288428870146566445886240⟩,⟨(-63250188118368856713381233925),(-63250188118368856618924412625)⟩⟩,⟨⟨490691834365115015353520426722,490691834365115015447931149444⟩,⟨(-64430119777135281407661880960),(-64430119777135281313292424623)⟩⟩,⟨⟨487296122635183507834162947561,487296122635183507928482466448⟩,⟨(-65599158061299408264650954887),(-65599158061299408170381020625)⟩⟩,⟨⟨483875126777043351833725358589,483875126777043351927958582193⟩,⟨(-66756539200122262753994057584),(-66756539200122262659818707082)⟩⟩,⟨⟨480429829705531522729313035330,480429829705531522823444127489⟩,⟨(-67901515404606689679346971687),(-67901515404606689585281899060)⟩⟩,⟨⟨476961223191109826734552120419,476961223191109826828589328135⟩,⟨(-69033355532378854026312783104),(-69033355532378853932349721222)⟩⟩,⟨⟨473470307321126502126798683870,473470307321126502220728177695⟩,⟨(-70151345730269428376391889534),(-70151345730269428282544527301)⟩⟩,⟨⟨469958089944178735183144891843,469958089944178735276972692577⟩,⟨(-71254790053675712091231085004),(-71254790053675711997493362714)⟩⟩,⟨⟨466425586098219017410105438879,466425586098219017503814258365⟩,⟨(-72343011061818502352648340700),(-72343011061818502259037378711)⟩⟩,⟨⟨462873817423095148733784939025,462873817423095148827384067655⟩,⟨(-73415350388042465774007736841),(-73415350388042465680514216802)⟩⟩,⟨⟨459303811558259263276145077543,459303811558259263369619082556⟩,⟨(-74471169284345994787411926471),(-74471169284345994694051115306)⟩⟩,⟨⟨455716601526425367658735064330,455716601526425367752091199655⟩,⟨(-75509849139366019236707850556),(-75509849139366019143472449428)⟩⟩] +lemma kernel1_1_r2_4_eq : ∀ k : Fin 16, kernel1_1Expr 2 4 k = kernel1_1_r2_4 k := by decide +kernel +noncomputable def kernel1_1_r2_5 : Fin 16 → CBox := ![⟨⟨452113225103997386520005945253,452113225103997386613224079467⟩,⟨(-76530791969084915217988174135),(-76530791969084915124898114905)⟩⟩,⟨⟨448494724179130459394052778640,448494724179130459487144718671⟩,⟨(-77533420879570435688412498601),(-77533420879570435595455949196)⟩⟩,⟨⟨444862144098327084418826627934,444862144098327084511775309612⟩,⟨(-78517180501105397117022731830),(-78517180501105397024216566902)⟩⟩,⟨⟨441216533002506519138727025096,441216533002506519231541048127⟩,⟨(-79481537393111600960933122595),(-79481537393111600868268694735)⟩⟩,⟨⟨437558941153520493666149652874,437558941153520493758807635128⟩,⟨(-80425980419322046762065686200),(-80425980419322046669564156792)⟩⟩,⟨⟨433890420252120639111821589268,433890420252120639204336347623⟩,⟨(-81350021092706795426349913481),(-81350021092706795333998437728)⟩⟩,⟨⟨430212022748412963255078892240,430212022748412963347431712185⟩,⟨(-82253193889710748807219893264),(-82253193889710748715036974216)⟩⟩,⟨⟨426524801145862101581369435288,426524801145862101673570372114⟩,⟨(-83135056533415999230198051035),(-83135056533415999138173586175)⟩⟩,⟨⟨422829807299932828228557188451,422829807299932828320581831235⟩,⟨(-83995190245297136719610280157),(-83995190245297136627768430060)⟩⟩,⟨⟨419128091712478329242216537301,419128091712478329334080588272⟩,⟨(-84833199965294841996968116046),(-84833199965294841905293161223)⟩⟩,⟨⟨415420702823003929579737031143,415420702823003929671420125159⟩,⟨(-85648714539991092764392674166),(-85648714539991092672904748253)⟩⟩,⟨⟨411708686297951244292716636137,411708686297951244384230380907⟩,⟨(-86441386878728216205980077736),(-86441386878728216114667529475)⟩⟩,⟨⟨407993084319161021523659710207,407993084319161021614978488431⟩,⟨(-87210894077573673300557233218),(-87210894077573673209445412451)⟩⟩,⟨⟨404274934872683198552914316874,404274934872683198644054989233⟩,⟨(-87956937511092696721611840245),(-87956937511092696630683872321)⟩⟩,⟨⟨400555271039109850601769552959,400555271039109850692710111866⟩,⟨(-88679242891951555707731298797),(-88679242891951555617008941705)⟩⟩,⟨⟨396835120286610734544476214820,396835120286610734635229912618⟩,⟨(-89377560298435116503329609516),(-89377560298435116412799574121)⟩⟩] +lemma kernel1_1_r2_5_eq : ∀ k : Fin 16, kernel1_1Expr 2 5 k = kernel1_1_r2_5 k := by decide +kernel +noncomputable def kernel1_1_r2_6 : Fin 16 → CBox := ![⟨⟨393115503767851986146217965119,393115503767851986236755611591⟩,⟨(-90051664170023330926742821089),(-90051664170023330836434000545)⟩⟩,⟨⟨389397435621976201137226200305,389397435621976201227568287213⟩,⟨(-90701353271232141114010156607),(-90701353271232141023902065904)⟩⟩,⟨⟨385681922282816609944819170047,385681922282816610034942075829⟩,⟨(-91326450623984856681642143621),(-91326450623984856591758138666)⟩⟩,⟨⟨381969961794509347338091100835,381969961794509347428009795762⟩,⟨(-91926803408840161751186226046),(-91926803408840161661511309385)⟩⟩,⟨⟨378262543135655937313431859904,378262543135655937403116475523⟩,⟨(-92502282835462363662538146618),(-92502282835462363573101879587)⟩⟩,⟨⟨374560645553173087624963813829,374560645553173087714435674468⟩,⟨(-93052783982778123611593132680),(-93052783982778123522374203709)⟩⟩,⟨⟨370865237906948756440051780958,370865237906948756529285683463⟩,⟨(-93578225609321534145569006369),(-93578225609321534056592338890)⟩⟩,⟨⟨367177278026402266223757988600,367177278026402266312770690174⟩,⟨(-94078549934325853914947113992),(-94078549934325853826195935875)⟩⟩,⟨⟨363497712080022059104535874256,363497712080022059193293946716⟩,⟨(-94553722390175303772243227244),(-94553722390175303683750633108)⟩⟩,⟨⟨359827473958927586853019688891,359827473958927586941548278167⟩,⟨(-95003731346883901442664154172),(-95003731346883901354405037677)⟩⟩,⟨⟨356167484675471891419087456244,356167484675471891507359830441⟩,⟨(-95428587809320200294876081489),(-95428587809320200206876882774)⟩⟩,⟨⟨352518651777868753605113113646,352518651777868753693147863843⟩,⟨(-95828325087946842198279744936),(-95828325087946842110521872515)⟩⟩,⟨⟨348881868781792973130902476449,348881868781792973218665584180⟩,⟨(-96202998443891882025639534104),(-96202998443891881938156666969)⟩⟩,⟨⟨345258014619864508211256661193,345258014619864508298774214985⟩,⟨(-96552684709214745690337005542),(-96552684709214745603103105194)⟩⟩,⟨⟨341647953109886971433488732362,341647953109886971520732525899⟩,⟨(-96877481883273305681337852746),(-96877481883273305594380823618)⟩⟩,⟨⟨338052532442668484749153367214,338052532442668484836143865967⟩,⟨(-97177508706139766854410402473),(-97177508706139766767709795193)⟩⟩] +lemma kernel1_1_r2_6_eq : ∀ k : Fin 16, kernel1_1Expr 2 6 k = kernel1_1_r2_6 k := by decide +kernel +noncomputable def kernel1_1_r2_7 : Fin 16 → CBox := ![⟨⟨334472584690208281744142251469,334472584690208281830841286157⟩,⟨(-97452904210051728314373216338),(-97452904210051728227966833104)⟩⟩,⟨⟨330908925334985859774365800082,330908925334985859860804065077⟩,⟨(-97703827249920811295085044197),(-97703827249920811208942276446)⟩⟩,⟨⟨327362352821041084960149989296,327362352821041085046297879212⟩,⟨(-97930456013954514385859237628),(-97930456013954514300009380634)⟩⟩,⟨⟨323833648127483602796284437507,323833648127483602882164306715⟩,⟨(-98132987515477382783443988841),(-98132987515477382697864722364)⟩⟩,⟨⟨320323574365018375397694981010,320323574365018375483268870009⟩,⟨(-98311637067065074536407095621),(-98311637067065074451136014470)⟩⟩,⟨⟨316832876396021327311777692103,316832876396021327397076614593⟩,⟨(-98466637738129401995915625672),(-98466637738129401910921810940)⟩⟩,⟨⟨313362280478645113789688955023,313362280478645113874681975932⟩,⟨(-98598239797113860127218178775),(-98598239797113860042532248901)⟩⟩,⟨⟨309912493935380110269650391801,309912493935380110354361767603⟩,⟨(-98706710139477475706517132176),(-98706710139477475622114884072)⟩⟩,⟨⟨306484204846440044089693524861,306484204846440044174081320528⟩,⟨(-98792331702659985151112707327),(-98792331702659985067035687060)⟩⟩,⟨⟨303078081768285435438369859812,303078081768285435522469684455⟩,⟨(-98855402869233348069215037750),(-98855402869233347985427769324)⟩⟩,⟨⟨299694773477541371600271180459,299694773477541371684050859331⟩,⟨(-98896236859453414733904160971),(-98896236859453414650438497666)⟩⟩,⟨⟨296334908740509294150091350247,296334908740509294233577025026⟩,⟨(-98915161114431186682236395865),(-98915161114431186599066269376)⟩⟩,⟨⟨292999096108415619734909387703,292999096108415619818059446168⟩,⟨(-98912516671145550488326661049),(-98912516671145550405493300267)⟩⟩,⟨⟨289687923738483326810545370740,289687923738483326893395775154⟩,⟨(-98888657530518647217441041891),(-98888657530518647134908628227)⟩⟩,⟨⟨286401959240856306233577485350,286401959240856306316094901636⟩,⟨(-98843950019771197500130350545),(-98843950019771197417931893218)⟩⟩,⟨⟨283141749551350472932695570408,283141749551350473014908009025⟩,⟨(-98778772150268179332790163332),(-98778772150268179250897745687)⟩⟩] +lemma kernel1_1_r2_7_eq : ∀ k : Fin 16, kernel1_1Expr 2 7 k = kernel1_1_r2_7 k := by decide +kernel +noncomputable def kernel1_1_r2_8 : Fin 16 → CBox := ![⟨⟨279907820829950545120438572792,279907820829950545202299638909⟩,⟨(-98693512972055308475749567175),(-98693512972055308394209172576)⟩⟩,⟨⟨276700678384917188175141000621,276700678384917188256692204457⟩,⟨(-98588571926273866326267533383),(-98588571926273866245037841403)⟩⟩,⟨⟨273520806622316058626361315466,273520806622316058707568266510⟩,⟨(-98464358196625634411660497811),(-98464358196625634330775572156)⟩⟩,⟨⟨270368669020728329803107220591,270368669020728329883999747991⟩,⟨(-98321290061041115152002482190),(-98321290061041115071432607895)⟩⟩,⟨⟨267244708130851688196814284874,267244708130851688277347478537⟩,⟨(-98159794244682941707242291568),(-98159794244682941627031982620)⟩⟩,⟨⟨264149345599651704724782150035,264149345599651704804996799096⟩,⟨(-97980305275392510913559746042),(-97980305275392510833668406593)⟩⟩,⟨⟨261082982218676046316499180103,261082982218676046396359920663⟩,⟨(-97783264842661526240011186499),(-97783264842661526160473852846)⟩⟩,⟨⟨258045997996098330699296363000,258045997996098330778834802359⟩,⟨(-97569121161181433830160711314),(-97569121161181433750945910484)⟩⟩,⟨⟨255038752252014662250627658812,255038752252014662329794569862⟩,⟨(-97338328339992802605286836498),(-97338328339992802526443375663)⟩⟩,⟨⟨252061583736474131402515559526,252061583736474131481356883884⟩,⟨(-97091345758223674116204751708),(-97091345758223674037686926112)⟩⟩,⟨⟨249114810769684916848917408206,249114810769684916927396914006⟩,⟨(-96828637448370930096191933565),(-96828637448370930018035647831)⟩⟩,⟨⟨246198731403800191341022457131,246198731403800191419173455083⟩,⟨(-96550671488041941286326393768),(-96550671488041941208498490975)⟩⟩,⟨⟨243313623605652880652602246984,243313623605652880730376911790⟩,⟨(-96257919401035320167599307523),(-96257919401035320090147209031)⟩⟩,⟨⟨240459745459775533507787762273,240459745459775533585231473057⟩,⟨(-95950855568599656405162424674),(-95950855568599656328040992119)⟩⟩,⟨⟨237637335391011189577039191216,237637335391011189654114932528⟩,⟨(-95629956651667823558055528636),(-95629956651667823481301451470)⟩⟩,⟨⟨234846612405993234191398494471,234846612405993234268141215055⟩,⟨(-95295701024821967479256392356),(-95295701024821967402834894279)⟩⟩] +lemma kernel1_1_r2_8_eq : ∀ k : Fin 16, kernel1_1Expr 2 8 k = kernel1_1_r2_8 k := by decide +kernel +noncomputable def kernel1_1_r2_9 : Fin 16 → CBox := ![⟨⟨232087776352746842761830140790,232087776352746842838186816603⟩,⟨(-94948568222700780683316231528),(-94948568222700780607279903464)⟩⟩,⟨⟨229361008197641775023991751791,229361008197641775100013839625⟩,⟨(-94589038399516293242461854417),(-94589038399516293166759529484)⟩⟩,⟨⟨226666470318905998712240701196,226666470318905998787890510167⟩,⟨(-94217591802302329781202370858),(-94217591802302329705871416115)⟩⟩,⟨⟨224004306815891913317364290439,224004306815891913392678307238⟩,⟨(-93834708258471153321570626523),(-93834708258471153246574745192)⟩⟩,⟨⟨221374643833271806291500978094,221374643833271806366428863979⟩,⟨(-93440866678208797971725226963),(-93440866678208797897114350156)⟩⟩,⟨⟨218777589899326595609354276280,218777589899326595683945653383⟩,⟨(-93036544572193339425868214685),(-93036544572193339351593004034)⟩⟩,⟨⟨216213236277481873547598136454,216213236277481873621814715413⟩,⟨(-92622217585074017753778863085),(-92622217585074017679877286919)⟩⟩,⟨⟨213681657330237737169874763128,213681657330237737243754489650⟩,⟨(-92198359045102860337025722045),(-92198359045102860263460040875)⟩⟩,⟨⟨211182910894633832651661051849,211182910894633832725148941003⟩,⟨(-91765439530264399318772361180),(-91765439530264399245597127393)⟩⟩,⟨⟨208717038668388406059691144978,208717038668388406132842338142⟩,⟨(-91323926451203378243572848259),(-91323926451203378170733248056)⟩⟩,⟨⟨206284066605849887249681779364,206284066605849887322457490413⟩,⟨(-90874283651205132216318192777),(-90874283651205132143852694731)⟩⟩,⟨⟨203884005322901573266199732692,203884005322901573338639252046⟩,⟨(-90416971023438734878532006676),(-90416971023438734806401541424)⟩⟩,⟨⟨201516850509964253006539420940,201516850509964253078590279766⟩,⟨(-89952444145629157737723506204),(-89952444145629157665980134519)⟩⟩,⟨⟨199182583352248049311060177431,199182583352248049382775827924⟩,⟨(-89481153932281700462519990515),(-89481153932281700391110581088)⟩⟩,⟨⟨196881170956413265368415415208,196881170956413265439756645541⟩,⟨(-89003546304539935498669969233),(-89003546304539935427633420243)⟩⟩,⟨⟨194612566782810521144973513469,194612566782810521215980866897⟩,⟨(-88520061877717470577542727773),(-88520061877717470506838730487)⟩⟩] +lemma kernel1_1_r2_9_eq : ∀ k : Fin 16, kernel1_1Expr 2 9 k = kernel1_1_r2_9 k := by decide +kernel +noncomputable def kernel1_1_r2_10 : Fin 16 → CBox := ![⟨⟨192376711082482859287260837237,192376711082482859357875943829⟩,⟨(-88031135666504064897478545129),(-88031135666504064827165028198)⟩⟩,⟨⟨190173531338126691030971288880,190173531338126691101254338847⟩,⟨(-87537196807808128005100789124),(-87537196807808127935117933510)⟩⟩,⟨⟨188002942708224339709996330889,188002942708224339779907786973⟩,⟨(-87038668301160466078340390960),(-87038668301160466008727424735)⟩⟩,⟨⟨185864848473578417881160752352,185864848473578417950742281109⟩,⟨(-86535966766568392057861529972),(-86535966766568391988577032930)⟩⟩,⟨⟨183759140485497236609114018328,183759140485497236678311389828⟩,⟨(-86029502219675049687625214775),(-86029502219675049618723010969)⟩⟩,⟨⟨181685699614900782736508897883,181685699614900782805378924745⟩,⟨(-85519677864046074959989794666),(-85519677864046074891413422825)⟩⟩,⟨⟨179644396201638401129733227576,179644396201638401198236103735⟩,⟨(-85006889900374581807441835232),(-85006889900374581739230796903)⟩⟩,⟨⟨177635090503332072083162703962,177635090503332072151341127309⟩,⟨(-84491527352365954450458585161),(-84491527352365954382570439261)⟩⟩,⟨⟨175657633143082966997355431025,175657633143082967065150158510⟩,⟨(-83973971909036091191078693781),(-83973971909036091123572250543)⟩⟩,⟨⟨173711865555403685891460744056,173711865555403685958934363830⟩,⟨(-83454597783130600661317832086),(-83454597783130600594130896380)⟩⟩,⟨⟨171797620429764116621938298654,171797620429764116689050824339⟩,⟨(-82933771585348021192488312178),(-82933771585348021125660570934)⟩⟩,⟨⟨169914722151165097244408804069,169914722151165097311203834971⟩,⟨(-82411852214027429452497055612),(-82411852214027429385985175194)⟩⟩,⟨⟨168062987237180900666492708334,168062987237180900732914571587⟩,⟨(-81889190759939831175926340338),(-81889190759939831109785591800)⟩⟩,⟨⟨166242224770938887396516093829,166242224770938887462624489906⟩,⟨(-81366130425803483320085323773),(-81366130425803483254256381841)⟩⟩,⟨⟨164452236829532382926060486130,164452236829532382991815298289⟩,⟨(-80843006460125775462339170745),(-80843006460125775396861857891)⟩⟩,⟨⟨162692818907390828897733476056,162692818907390828963179109714⟩,⟨(-80320146104958484683534300819),(-80320146104958484618364484841)⟩⟩] +lemma kernel1_1_r2_10_eq : ∀ k : Fin 16, kernel1_1Expr 2 10 k = kernel1_1_r2_10 k := by decide +kernel +noncomputable def kernel1_1_r2_11 : Fin 16 → CBox := ![⟨⟨160963760334159432547492014711,160963760334159432612566468449⟩,⟨(-79797868557139092653033371179),(-79797868557139092588232616122)⟩⟩,⟨⟨159264844686668801142155174731,159264844686668801206925153988⟩,⟨(-79276484942578390713769431423),(-79276484942578390649271454984)⟩⟩,⟨⟨157595850194603305056301773500,157595850194603305120727116643⟩,⟨(-78756298303143767828817937074),(-78756298303143767764662612106)⟩⟩,⟨⟨155956550139505076400476716076,155956550139505076464602499948⟩,⟨(-78237603595678341841738152092),(-78237603595678341777880681007)⟩⟩,⟨⟨154346713246778535473997699289,154346713246778535537767096336⟩,⟨(-77720687702688416687305861068),(-77720687702688416623802675069)⟩⟩,⟨⟨152766104070388064777649386325,152766104070388064841124506525⟩,⟨(-77205829454225582950314554255),(-77205829454225582887103936212)⟩⟩,⟨⟨151214483369968844332834611583,151214483369968844395975283228⟩,⟨(-76693299660485078756153028865),(-76693299660485078693274867167)⟩⟩,⟨⟨149691608480097851604786053994,149691608480097851667637939996⟩,⟨(-76183361154638741304628532204),(-76183361154638741242037448109)⟩⟩,⟨⟨148197233671498548074593280365,148197233671498548137094099322⟩,⟨(-75676268845418952362770129814),(-75676268845418952300527978824)⟩⟩,⟨⟨146731110503978760813241434385,146731110503978760875459320123⟩,⟨(-75172269778969357064952835924),(-75172269778969357002991916645)⟩⟩,⟨⟨145292988170926664423033837832,145292988170926664484928682519⟩,⟨(-74671603209478755540000154569),(-74671603209478755478360297191)⟩⟩,⟨⟨143882613835214524336608214974,143882613835214524398226140943⟩,⟨(-74174500678116370451135688514),(-74174500678116370389771058476)⟩⟩,⟨⟨142499732956383929394409758824,142499732956383929455693011503⟩,⟨(-73681186099789618223271974925),(-73681186099789618162239936715)⟩⟩,⟨⟨141144089609009577274724609422,141144089609009577335737273018⟩,⟨(-73191875857249494111660583761),(-73191875857249494050897458357)⟩⟩,⟨⟨139815426792161242839129874054,139815426792161242899831934696⟩,⟨(-72706778902073657048964868263),(-72706778902073656988510397484)⟩⟩,⟨⟨138513486729905323486432817938,138513486729905323546870775439⟩,⟨(-72226096862063204595762191077),(-72226096862063204535570165546)⟩⟩] +lemma kernel1_1_r2_11_eq : ∀ k : Fin 16, kernel1_1Expr 2 11 k = kernel1_1_r2_11 k := by decide +kernel +noncomputable def kernel1_1_r2_12 : Fin 16 → CBox := ![⟨⟨137238011162808288410491657687,137238011162808288470600450712⟩,⟨(-71750024154595896279692001574),(-71750024154595896219827051151)⟩⟩,⟨⟨135988741630424435847313654831,135988741630424435907165144814⟩,⟨(-71278748105486150189851588758),(-71278748105486150130242306607)⟩⟩,⟨⟨134765419744769563873196875990,134765419744769563932751217820⟩,⟨(-70812449072910438272335704754),(-70812449072910438213021669730)⟩⟩,⟨⟨133567787454800470089804885017,133567787454800470149108828206⟩,⟨(-70351300575965676338225078405),(-70351300575965676279159832921)⟩⟩,⟨⟨132395587301937601599715495645,132395587301937601658710559226⟩,⟨(-69895469427437782158716206732),(-69895469427437782099957848376)⟩⟩,⟨⟨131248562666684670821527928982,131248562666684670880279759842⟩,⟨(-69445115870367697069792655318),(-69445115870367697011275950271)⟩⟩,⟨⟨130126458006414630341708875150,130126458006414630400177812833⟩,⟨(-69000393718012772378196354201),(-69000393718012772319960702266)⟩⟩,⟨⟨129029019084406060003184389701,129029019084406060061417367514⟩,⟨(-68561450496812452154703936923),(-68561450496812452096702697518)⟩⟩,⟨⟨127955993190227763903811820356,127955993190227763961744368853⟩,⟨(-68128427591978580931400810516),(-68128427591978580873698036976)⟩⟩,⟨⟨126907129351582209076390010190,126907129351582209134094126014⟩,⟨(-67701460395342372385813984947),(-67701460395342372328338132605)⟩⟩,⟨⟨125882178537730369367495469587,125882178537730369424931741494⟩,⟨(-67280678455102039190505435260),(-67280678455102039133295660427)⟩⟩,⟨⟨124880893854631578083595045161,124880893854631578140810475424⟩,⟨(-66866205627127252766039378430),(-66866205627127252709048971420)⟩⟩,⟨⟨123903030731942154448913621307,123903030731942154505849140345⟩,⟨(-66458160227488924745492383503),(-66458160227488924688780037116)⟩⟩,⟨⟨122948347102025867168612781597,122948347102025867225335258944⟩,⟨(-66056655185895231813992348125),(-66056655185895231757491610456)⟩⟩,⟨⟨122016603571137750816275551268,122016603571137750872745842044⟩,⟨(-65661798199727296769125335629),(-65661798199727296712875102154)⟩⟩,⟨⟨121107563582950416597062566423,121107563582950416653327677964⟩,⟨(-65273691888380448049539882943),(-65273691888380447993493438225)⟩⟩] +lemma kernel1_1_r2_12_eq : ∀ k : Fin 16, kernel1_1Expr 2 12 k = kernel1_1_r2_12 k := by decide +kernel +noncomputable def kernel1_1_r2_13 : Fin 16 → CBox := ![⟨⟨120220993574598819165736942564,120220993574598819221730001032⟩,⟨(-64892433947629466854986820801),(-64892433947629466799210617869)⟩⟩,⟨⟨119356663125425477928407034876,119356663125425477984202982813⟩,⟨(-64518117303748657003963471591),(-64518117303748656948383034266)⟩⟩,⟨⟨118514345098613428232335420637,118514345098613428287895449664⟩,⟨(-64150830267129901921687905320),(-64150830267129901866341798238)⟩⟩,⟨⟨117693815775898719721469934246,117693815775898719776840940222⟩,⟨(-63790656685154072131473575875),(-63790656685154072076315193565)⟩⟩,⟨⟨116894854985558111498801502776,116894854985558111553923953658⟩,⟨(-63437676094083184243258906400),(-63437676094083184188347410386)⟩⟩,⟨⟨116117246223870762904779125625,116117246223870762959720799313⟩,⟨(-63091963869752560006559296572),(-63091963869752559951827328592)⟩⟩,⟨⟨115360776770255211597880677312,115360776770255211652603110182⟩,⟨(-62753591376853865182060116402),(-62753591376853865127545901741)⟩⟩,⟨⟨114625237796284794520221897424,114625237796284794574771823656⟩,⟨(-62422626116611298785764447766),(-62422626116611298731421540765)⟩⟩,⟨⟨113910424468785929847602185818,113910424468785929901913443904⟩,⟨(-62099131872664331937162261921),(-62099131872664331883056416875)⟩⟩,⟨⟨113216136047224366882532802271,113216136047224366936679974687⟩,⟨(-61783168854981242604309035115),(-61783168854981242550366129263)⟩⟩,⟨⟨112542175975584653794651808425,112542175975584653848596841905⟩,⟨(-61474793841638240644876374019),(-61474793841638240591134227783)⟩⟩,⟨⟨111888351968947697762204709905,111888351968947697815994069272⟩,⟨(-61174060318309211472340629905),(-61174060318309211418753064443)⟩⟩,⟨⟨111254476094970425826048027392,111254476094970425879621797694⟩,⟨(-60881018615321013231361360116),(-60881018615321013177987925355)⟩⟩,⟨⟨110640364850470224694742117175,110640364850470224748168735119⟩,⟨(-60595716042138830324735174229),(-60595716042138830271507853468)⟩⟩,⟨⟨110045839233315070486003038267,110045839233315070539244876483⟩,⟨(-60318197019155306148077131227),(-60318197019155306095033324267)⟩⟩,⟨⟨109470724809818081080996292022,109470724809818081134099492511⟩,⟨(-60048503206666042432474836967),(-60048503206666042379568684955)⟩⟩] +lemma kernel1_1_r2_13_eq : ∀ k : Fin 16, kernel1_1Expr 2 13 k = kernel1_1_r2_13 k := by decide +kernel +noncomputable def kernel1_1_r2_14 : Fin 16 → CBox := ![⟨⟨108914851777832659952499860952,108914851777832660005395423019⟩,⟨(-59786673630922555859933146573),(-59786673630922555807233233425)⟩⟩,⟨⟨108378055025741475880843915787,108378055025741475933609460233⟩,⟨(-59532744807161920452788802000),(-59532744807161920400217981020)⟩⟩,⟨⟨107860174187529262059472119550,107860174187529262112070525348⟩,⟨(-59286750859520094049130836858),(-59286750859520093996726006945)⟩⟩,⟨⟨107361053694125844091351848145,107361053694125844143828815732⟩,⟨(-59048723637743327860784859948),(-59048723637743327808500600314)⟩⟩,⟨⟨106880542821201941856027399753,106880542821201941908322725410⟩,⟨(-58818692830619089953721179771),(-58818692830619089901617333788)⟩⟩,⟨⟨106418495733596156875045209775,106418495733596156927227740668⟩,⟨(-58596686076054598111595243255),(-58596686076054598059603382897)⟩⟩,⟨⟨105974771526547175430259687028,105974771526547175482292819296⟩,⟨(-58382729067737357784364281149),(-58382729067737357732520793341)⟩⟩,⟨⟨105549234263900608169694920558,105549234263900608221623868023⟩,⟨(-58176845658318040701781131609),(-58176845658318040650041078492)⟩⟩,⟨⟨105141753013455068216996186092,105141753013455068268753367543⟩,⟨(-57979057959061624331107276589),(-57979057959061624279537837386)⟩⟩,⟨⟨104752201879607079863187820698,104752201879607079914849479828⟩,⟨(-57789386435917947785902804260),(-57789386435917947734428197411)⟩⟩,⟨⟨104380460033449225795742995101,104380460033449225847273126199⟩,⟨(-57607850001967733075834831071),(-57607850001967733024490850699)⟩⟩,⟨⟨104026411740470598564645194720,104026411740470598616088408489⟩,⟨(-57434466106204679632209930849),(-57434466106204679580952237929)⟩⟩,⟨⟨103689946386003136706335089944,103689946386003136757630958365⟩,⟨(-57269250818618473539882371745),(-57269250818618473488771037510)⟩⟩,⟨⟨103370958498551811784534187856,103370958498551811835751762597⟩,⟨(-57112218911547470290487282329),(-57112218911547470239453672720)⟩⟩,⟨⟨103069347771140902775366306866,103069347771140902826470209681⟩,⟨(-56963383937273421239440544020),(-56963383937273421188519830904)⟩⟩,⟨⟨102785019080802760997898379368,102785019080802761048932555962⟩,⟨(-56822758301833930021812422767),(-56822758301833929970960927573)⟩⟩] +lemma kernel1_1_r2_14_eq : ∀ k : Fin 16, kernel1_1Expr 2 14 k = kernel1_1_r2_14 k := by decide +kernel +noncomputable def kernel1_1_r2_15 : Fin 16 → CBox := ![⟨⟨102517882506329543554045960363,102517882506329543604940215115⟩,⟨(-56690353335031357226900098278),(-56690353335031357176187603529)⟩⟩,⟨⟨102267853344402386482930799192,102267853344402386533763900328⟩,⟨(-56566179356619651435073039934),(-56566179356619651384421251831)⟩⟩,⟨⟨102034852124206410203071796277,102034852124206410253809097499⟩,⟨(-56450245738653084514449526597),(-56450245738653084463892890560)⟩⟩,⟨⟨101818804620633808122393429929,101818804620633808173078072388⟩,⟨(-56342560963983121516218394413),(-56342560963983121465714031170)⟩⟩,⟨⟨101619641866171072575345833609,101619641866171072625917280640⟩,⟨(-56243132680891673608398930097),(-56243132680891673558007022172)⟩⟩,⟨⟨101437300161560167762296795619,101437300161560167812824050905⟩,⟨(-56151967753850779605928982659),(-56151967753850779555580941718)⟩⟩,⟨⟨101271721085317173678749363063,101271721085317173729198546758⟩,⟨(-56069072310400351427192294570),(-56069072310400351376921804982)⟩⟩,⟨⟨101122851502185603998693332227,101122851502185604049106713610⟩,⟨(-55994451784137015144248837069),(-55994451784137015094013885898)⟩⟩,⟨⟨100990643570595249761893787764,100990643570595249812202613152⟩,⟨(-55928110953808296322909931271),(-55928110953808296272778870389)⟩⟩,⟨⟨100875054749191024146322734651,100875054749191024196604098887⟩,⟨(-55870053978507450410757207511),(-55870053978507450360653404730)⟩⟩,⟨⟨100776047802489885685827246660,100776047802489885736048152838⟩,⟨(-55820284428965140529617913836),(-55820284428965140479574176359)⟩⟩,⟨⟨100693590805717501604724867437,100693590805717501654926560202⟩,⟨(-55778805314934930832412510820),(-55778805314934930782387844022)⟩⟩,⟨⟨100627657148869882628859727209,100627657148869882678981688385⟩,⟨(-55745619108670208377687437873),(-55745619108670208327742007508)⟩⟩,⟨⟨100578225540038778418471497688,100578225540038778468582416139⟩,⟨(-55720727764490685168713463020),(-55720727764490685118778992620)⟩⟩,⟨⟨100545280008033171029330603880,100545280008033171079398430035⟩,⟨(-55704132734437079587275869563),(-55704132734437079537384224855)⟩⟩,⟨⟨100528809904322744600501862401,100528809904322744650566716046⟩,⟨(-55695834980012948004896424430),(-55695834980012947955007728838)⟩⟩] +lemma kernel1_1_r2_15_eq : ∀ k : Fin 16, kernel1_1Expr 2 15 k = kernel1_1_r2_15 k := by decide +kernel +noncomputable def kernel1_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel1_1_r2_0,kernel1_1_r2_1,kernel1_1_r2_2,kernel1_1_r2_3,kernel1_1_r2_4,kernel1_1_r2_5,kernel1_1_r2_6,kernel1_1_r2_7,kernel1_1_r2_8,kernel1_1_r2_9,kernel1_1_r2_10,kernel1_1_r2_11,kernel1_1_r2_12,kernel1_1_r2_13,kernel1_1_r2_14,kernel1_1_r2_15] +lemma kernel1_1_r2_eq (i k : Fin 16) : kernel1_1Expr 2 i k = kernel1_1_r2 i k := by + fin_cases i + · exact kernel1_1_r2_0_eq k + · exact kernel1_1_r2_1_eq k + · exact kernel1_1_r2_2_eq k + · exact kernel1_1_r2_3_eq k + · exact kernel1_1_r2_4_eq k + · exact kernel1_1_r2_5_eq k + · exact kernel1_1_r2_6_eq k + · exact kernel1_1_r2_7_eq k + · exact kernel1_1_r2_8_eq k + · exact kernel1_1_r2_9_eq k + · exact kernel1_1_r2_10_eq k + · exact kernel1_1_r2_11_eq k + · exact kernel1_1_r2_12_eq k + · exact kernel1_1_r2_13_eq k + · exact kernel1_1_r2_14_eq k + · exact kernel1_1_r2_15_eq k +noncomputable def kernel1_1_r3_0 : Fin 16 → CBox := ![⟨⟨1098844809203212644040321118052,1098844809203212644207489204814⟩,⟨1144681600042920628189450274101,1144681600042920628369021554452⟩⟩,⟨⟨1098860401858280159233287509118,1098860401858280159400461934559⟩,⟨1144556698979235619319482540766,1144556698979235619499059482427⟩⟩,⟨⟨1098891552138619066179747939746,1098891552138619066346934791396⟩,⟨1144306921702933037130314862687,1144306921702933037309902869629⟩⟩,⟨⟨1098938190014331761198824765356,1098938190014331761366030126502⟩,⟨1143932317925714785893523809737,1143932317925714786073128281318⟩⟩,⟨⟨1099000210514797833704507408081,1099000210514797833871737356653⟩,⟨1143432962239015503262085491425,1143432962239015503441711821076⟩⟩,⟨⟨1099077473817715499700826544283,1099077473817715499868087148723⟩,⟨1142808954142560503163874645036,1142808954142560503343528215976⟩⟩,⟨⟨1099169805367773780979337565355,1099169805367773781146634880322⟩,⟨1142060418082276192325428104078,1142060418082276192505114284721⟩⟩,⟨⟨1099276996024912540151357183698,1099276996024912540318697257510⟩,⟨1141187503497410254903689080612,1141187503497410255083413232079⟩⟩,⟨⟨1099398802242116432410181940522,1099398802242116432577570789377⟩,⟨1140190384876683599490749031211,1140190384876683599670516480834⟩⟩,⟨⟨1099534946272677569606008189026,1099534946272677569773451837104⟩,⟨1139069261823261013649210448865,1139069261823261013829026531068⟩⟩,⟨⟨1099685116406850169382563911969,1099685116406850169550068322500⟩,⟨1137824359128292723674288029698,1137824359128292723854158015365⟩⟩,⟨⟨1099848967237808641285509594326,1099848967237808641453080764851⟩,⟨1136455926852744662168867063136,1136455926852744662348796256997⟩⟩,⟨⟨1100026119956808403543954493335,1100026119956808403711598305643⟩,⟨1134964240417201254150253787931,1134964240417201254330247374789⟩⟩,⟨⟨1100216162677436190559377255477,1100216162677436190727099690089⟩,⟨1133349600699290994874663665727,1133349600699290995054726930001⟩⟩,⟨⟨1100418650788823665353110445037,1100418650788823665520917294762⟩,⟨1131612334138352060674143204285,1131612334138352060854281236596⟩⟩,⟨⟨1100633107337684758250705334820,1100633107337684758418602552478⟩,⟨1129752792846922719379516785763,1129752792846922719559734838882⟩⟩] +lemma kernel1_1_r3_0_eq : ∀ k : Fin 16, kernel1_1Expr 3 0 k = kernel1_1_r3_0 k := by decide +kernel +noncomputable def kernel1_1_r3_1 : Fin 16 → CBox := ![⟨⟨1100859023439023279580706530028,1100859023439023279748699761761⟩,⟨1127771354728609441106807190264,1127771354728609441287110201177⟩⟩,⟨⟨1101095858715342968682923459257,1101095858715342968851018670173⟩,⟨1125668423601854405292100695333,1125668423601854405472493925748⟩⟩,⟨⟨1101343041764177214634729248755,1101343041764177214802931961544⟩,⟨1123444429329093608066344119748,1123444429329093608246832376500⟩⟩,⟨⟨1101599970653740188565980826836,1101599970653740188734296977417⟩,⟨1121099827950767047765585961269,1121099827950767047946174472214⟩⟩,⟨⟨1101866013446485038312809645134,1101866013446485038481244520560⟩,⟨1118635101823613558155732357378,1118635101823613558336425684075⟩⟩,⟨⟨1102140508750338090980582489541,1102140508750338091149142089908⟩,⟨1116050759762654821553018379362,1116050759762654821733821811199⟩⟩,⟨⟨1102422766297360667857538574131,1102422766297360668026228032374⟩,⟨1113347337186245980304837566352,1113347337186245980485755502864⟩⟩,⟨⟨1102712067549572121871627697541,1102712067549572122040452978827⟩,⟨1110525396263544128005974397358,1110525396263544128187012087788⟩⟩,⟨⟨1103007666331649046086306053079,1103007666331649046255271920136⟩,⟨1107585526063720854343143225793,1107585526063720854524304686362⟩⟩,⟨⟨1103308789490196261223460729622,1103308789490196261392573310840⟩,⟨1104528342706220992545282689491,1104528342706220992726573332035⟩⟩,⟨⟨1103614637579265162600848153513,1103614637579265162770112053496⟩,⟨1101354489511346828942575258074,1101354489511346829123998932562⟩⟩,⟨⟨1103924385571774287085833940704,1103924385571774287255255221836⟩,⟨1098064637150425332820800554183,1098064637150425333002362600296⟩⟩,⟨⟨1104237183596465546900651443294,1104237183596465547070234195486⟩,⟨1094659483794795504079494580387,1094659483794795504261198317017⟩⟩,⟨⟨1104552157700007470963844918284,1104552157700007471133595475233⟩,⟨1091139755262833768316763797507,1091139755262833768498614837435⟩⟩,⟨⟨1104868410633834000999703203282,1104868410633834001169625481947⟩,⟨1087506205164217525602549704000,1087506205164217525784551184886⟩⟩,⟨⟨1105185022665283917542123384791,1105185022665283917712223631818⟩,⟨1083759615040610531569956383067,1083759615040610531752113824154⟩⟩] +lemma kernel1_1_r3_1_eq : ∀ k : Fin 16, kernel1_1Expr 3 1 k = kernel1_1_r3_1 k := by decide +kernel +noncomputable def kernel1_1_r3_2 : Fin 16 → CBox := ![⟨⟨1105501052412581832495923748934,1105501052412581832666205116936⟩,⟨1079900794501938808114566070306,1079900794501938808296881823214⟩⟩,⟨⟨1105815537703176896103509764361,1105815537703176896273978985928⟩,⟨1075930581357412295745313460094,1075930581357412295927793536944⟩⟩,⟨⟨1106127496454929946775826158216,1106127496454929946946486286957⟩,⟨1071849841740435519386473879721,1071849841740435519569120527125⟩⟩,⟨⟨1106435927579613805882084651464,1106435927579613806052942223513⟩,⟨1067659470226540192067640485386,1067659470226540192250459510436⟩⟩,⟨⟨1106739811908164813712410194983,1106739811908164813883467309620⟩,⟨1063360389943463973161797269913,1063360389943463973344789939783⟩⟩,⟨⟨1107038113137096548780860629306,1107038113137096548952124464366⟩,⟨1058953552672492575017542831482,1058953552672492575200715605924⟩⟩,⟨⟨1107329778795459005682504828959,1107329778795459005853977383205⟩,⟨1054439938940177117870582841137,1054439938940177118053936881720⟩⟩,⟨⟨1107613741231698366032881035236,1107613741231698366204569258197⟩,⟨1049820558099535110048588824236,1049820558099535110232130353864⟩⟩,⟨⟨1107888918619743925689685586035,1107888918619743925861590113131⟩,⟨1045096448399841719114306853380,1045096448399841719298035637472⟩⟩,⟨⟨1108154215983619786468694422282,1108154215983619786640823219376⟩,⟨1040268677044118138132048515316,1040268677044118138315971813157⟩⟩,⟨⟨1108408526239849632769609670781,1108408526239849632941963472979⟩,⟨1035338340233425875913827327934,1035338340233425876097945005401⟩⟩,⟨⟨1108650731256893347596924808381,1108650731256893347769511119644⟩,⟨1030306563197079744749297224057,1030306563197079744933616065892⟩⟩,⟨⟨1108879702930824436838785238649,1108879702930824437011603200638⟩,⟨1025174500207898215028371004598,1025174500207898215212889247351⟩⟩,⟨⟨1109094304276427287492687538989,1109094304276427287665745869507⟩,⟨1019943334581617681844445853115,1019943334581617682029171520667⟩⟩,⟨⟨1109293390532863250554095573174,1109293390532863250727393523671⟩,⟨1014614278659607069678752971287,1014614278659607069863684412712⟩⟩,⟨⟨1109475810283024481778646825891,1109475810283024481952192610730⟩,⟨1009188573774031110012240758571,1009188573774031110197385482280⟩⟩] +lemma kernel1_1_r3_2_eq : ∀ k : Fin 16, kernel1_1Expr 3 2 k = kernel1_1_r3_2 k := by decide +kernel +noncomputable def kernel1_1_r3_3 : Fin 16 → CBox := ![⟨⟨1109640406585664466156778714164,1109640406585664466330569335182⟩,⟨1003667490194624582232937713802,1003667490194624582418291771717⟩⟩,⟨⟨1109786018119364270635783560713,1109786018119364270809829070274⟩,⟨998052327056255825986617322034,998052327056255826172190100541⟩⟩,⟨⟨1109911480337363893448291792873,1109911480337363893622589727052⟩,⟨992344412266475924883285984240,992344412266475925069074083604⟩⟩,⟨⟨1110015626632258689379607130931,1110015626632258689554166585613⟩,⟨986545102392270134992269775161,986545102392270135178281605215⟩⟩,⟨⟨1110097289509531833238556748472,1110097289509531833413372801038⟩,⟨980655782525250390458303626620,980655782525250390644533280276⟩⟩,⟨⟨1110155301768865226089145688823,1110155301768865226264229452961⟩,⟨974677866124552062134089714207,974677866124552062320547663988⟩⟩,⟨⟨1110188497692143240241702210443,1110188497692143240417049264768⟩,⟨968612794836724568114115414978,968612794836724568300796270861⟩⟩,⟨⟨1110195714237036331540047116674,1110195714237036331715667623562⟩,⟨962462038291933927530015172724,962462038291933927716928438259⟩⟩,⟨⟨1110175792235024914986075145240,1110175792235024915161961306850⟩,⟨956227093875825896119077125566,956227093875825896306213970394⟩⟩,⟨⟨1110127577592698097749508456428,1110127577592698097925673342740⟩,⟨949909486476430904058046529479,949909486476430904245419429443⟩⟩,⟨⟨1110049922495136989050468440753,1110049922495136989226905423468⟩,⟨943510768205526608332909110510,943510768205526608520510437344⟩⟩,⟨⟨1109941686610168457316234056107,1109941686610168457492954560465⟩,⟨937032518093910443130363705070,937032518093910443318204260283⟩⟩,⟨⟨1109801738292252480254844969573,1109801738292252480431838787865⟩,⟨930476341760073066571842457595,930476341760073066759910970224⟩⟩,⟨⟨1109628955784744732406542577550,1109628955784744732583824221951⟩,⟨923843871051804019174474167614,923843871051804019362784595427⟩⟩,⟨⟨1109422228419255876853526956045,1109422228419255877031087339126⟩,⟨917136763660303181652172904394,917136763660303181840715131115⟩⟩,⟨⟨1109180457810810272444397926474,1109180457810810272622249943256⟩,⟨910356702706415694239040613622,910356702706415694427826953900⟩⟩] +lemma kernel1_1_r3_3_eq : ∀ k : Fin 16, kernel1_1Expr 3 3 k = kernel1_1_r3_3 k := by decide +kernel +noncomputable def kernel1_1_r3_4 : Fin 16 → CBox := ![⟨⟨1108902559047489573963858107400,1108902559047489574141987701253⟩,⟨903505396298653817976767896980,903505396298653818165783179702⟩⟩,⟨⟨1108587461873231088113254720542,1108587461873231088291679238899⟩,⟨896584577062716715827299744391,896584577062716716016560834208⟩⟩,⟨⟨1108234111862436849682263160018,1108234111862436849860970802456⟩,⟨889596001642268237615688452119,889596001642268237805182494269⟩⟩,⟨⟨1107841471585037294977127937837,1107841471585037295156133283934⟩,⟨882541450170783431317032879809,882541450170783431506773925331⟩⟩,⟨⟨1107408521760643226509541808350,1107408521760643226688828079122⟩,⟨875422725714326591811416576353,875422725714326592001386712491⟩⟩,⟨⟨1106934262400411574819283774489,1106934262400411574998877091940⟩,⟨868241653685177108797479504953,868241653685177108987703019183⟩⟩,⟨⟨1106417713935244357984352259654,1106417713935244358164471783926⟩,⟨861000081226274094117388342206,861000081226274094308037234509⟩⟩,⟨⟨1105857918328936301543843576889,1105857918328936301724506783384⟩,⟨853699876566506655597865924419,853699876566506655788957360710⟩⟩,⟨⟨1105253940174884892300265121062,1105253940174884892481451414821⟩,⟨846342928346933634311776608326,846342928346933634503289000049⟩⟩,⟨⟨1104604867774977275861645991464,1104604867774977276043378838428⟩,⟨838931144918074524066049796999,838931144918074524258006477466⟩⟩,⟨⟨1103909814199271442500303724435,1103909814199271442682565834702⟩,⟨831466453608472029717944818660,831466453608472029910327643513⟩⟩,⟨⟨1103167918325094646826501401790,1103167918325094647009312045923⟩,⟨823950799964786173241206055678,823950799964786173434034147021⟩⟩,⟨⟨1102378345854190036588833552650,1102378345854190036772168583864⟩,⟨816386146963739896967425396778,816386146963739897160673708478⟩⟩,⟨⟨1101540290306553081731148953114,1101540290306553081915033587721⟩,⟨808774474196296611044325201044,808774474196296611238018971323⟩⟩,⟨⟨1100652973989612647824507913759,1100652973989612648008921021243⟩,⟨801117777024510951344434566447,801117777024510951538551898202⟩⟩,⟨⟨1099715648941427492998522781864,1099715648941427493183485667511⟩,⟨793418065711555015099161719391,793418065711555015293723931080⟩⟩] +lemma kernel1_1_r3_4_eq : ∀ k : Fin 16, kernel1_1Expr 3 4 k = kernel1_1_r3_4 k := by decide +kernel +noncomputable def kernel1_1_r3_5 : Fin 16 → CBox := ![⟨⟨1098727597846587622704699684410,1098727597846587622890181841206⟩,⟨785677364525483380835029654751,785677364525483381030005391631⟩⟩,⟨⟨1097688134923531343230594806272,1097688134923531343416625999492⟩,⟨777897710817361149625230879516,777897710817361149820650127267⟩⟩,⟨⟨1096596606782013036704691024180,1096596606782013036891246047142⟩,⟨770081154074439915955744326418,770081154074439916151581200791⟩⟩,⟨⟨1095452393249483653612364383901,1095452393249483653799466816616⟩,⟨762229754949126835574015681980,762229754949126835770293936515⟩⟩,⟨⟨1094254908165175691906773665303,1094254908165175692094389442264⟩,⟨754345584264551649117034088663,754345584264551649313718915825⟩⟩,⟨⟨1093003600140717004795884374291,1093003600140717004984045029061⟩,⟨746430721997595486749285010316,746430721997595486946408306831⟩⟩,⟨⟨1091697953286133143976245983242,1091697953286133144164922004940⟩,⟨738487256240303361664081266623,738487256240303361861612933688⟩⟩,⟨⟨1090337487900136084609235781310,1090337487900136084798453275251⟩,⟨730517282140659299303163716463,730517282140659299501130190383⟩⟩,⟨⟨1088921761123638067060598377750,1088921761123638067250316056223⟩,⟨722522900823758884235475812822,722522900823758884433835116004⟩⟩,⟨⟨1087450367555472893769787164344,1087450367555472893960042016475⟩,⟨714506218294468477530556018157,714506218294468477729345696420⟩⟩,⟨⟨1085922939829353293956148048882,1085922939829353294146906057138⟩,⟨706469344322713304453782509069,706469344322713304652968046988⟩⟩,⟨⟨1084339149151141861431544013634,1084339149151141861622834051307⟩,⟨698414391312587876782384688871,698414391312587876981995443400⟩⟩,⟨⟨1082698705795564519619850990503,1082698705795564519811627876239⟩,⟨690343473156531639043388352811,690343473156531639243378560988⟩⟩,⟨⟨1081001359561549401816040957152,1081001359561549402008343866417⟩,⟨682258704075860158775422534173,682258704075860158975832059466⟩⟩,⟨⟨1079246900185430373411496254230,1079246900185430373604286469604⟩,⟨674162197448987465593311681925,674162197448987465794101398859⟩⟩,⟨⟨1077435157711313076796735834391,1077435157711313076990045251025⟩,⟨666056064628718133835941031494,666056064628718134037143465158⟩⟩] +lemma kernel1_1_r3_5_eq : ∀ k : Fin 16, kernel1_1Expr 3 5 k = kernel1_1_r3_5 k := by decide +kernel +noncomputable def kernel1_1_r3_6 : Fin 16 → CBox := ![⟨⟨1075566002817962250442959010503,1075566002817962250636733556560⟩,⟨657942413750028254323710560287,657942413750028254525271097848⟩⟩,⟨⟨1073639347101632053879668606622,1073639347101632054073954697024⟩,⟨649823348529792412195183253754,649823348529792412397149190305⟩⟩,⟨⟨1071655143314326103849581012781,1071655143314326104044335074408⟩,⟨641700967059949045018984055395,641700967059949045221311499178⟩⟩,⟨⟨1069613385557040769256518888226,1069613385557040769451776071548⟩,⟨633577360595628969157386448750,633577360595628969360111318219⟩⟩,⟨⟨1067514109427613850828768969699,1067514109427613851024471932519⟩,⟨625454612339801309734598566253,625454612339801309937663099306⟩⟩,⟨⟨1065357392122870944956398890523,1065357392122870945152595770053⟩,⟨617334796226017434380359351958,617334796226017434583812666993⟩⟩,⟨⟨1063143352494833411598861704452,1063143352494833411795503921432⟩,⟨609219975700856664387944315009,609219975700856664591737602403⟩⟩,⟨⟨1060872151060824777940964363204,1060872151060824778138090570809⟩,⟨601112202507697418118938265980,601112202507697418323111075393⟩⟩,⟨⟨1058543989967386450251073889365,1058543989967386450448617238529⟩,⟨593013515473453937869084595932,593013515473453938073569701676⟩⟩,⟨⟨1056159112907988607451841783767,1056159112907988607649858460812⟩,⟨584925939299931779289206867611,584925939299931779494061605453⟩⟩,⟨⟨1053717804994597936686878546241,1053717804994597936885314860963⟩,⟨576851483361464727465502413263,576851483361464727670672949574⟩⟩,⟨⟨1051220392583240263740215401920,1051220392583240263939113729508⟩,⟨568792140510501681260839080529,568792140510501681466368804294⟩⟩,⟨⟨1048667243053772944852085984143,1048667243053772945051375965581⟩,⟨560749885892814263003609838511,560749885892814263209428131518⟩⟩,⟨⟨1046058764544158932376812693075,1046058764544158932576552704387⟩,⟨552726675773994420060713234957,552726675773994420266879702297⟩⟩,⟨⟨1043395405639611512381547433083,1043395405639611512581678574997⟩,⟨544724446378906055053077158686,544724446378906055259532842558⟩⟩,⟨⟨1040677655017055642270548831243,1040677655017055642471117428917⟩,⟨536745112745745730358912393972,536745112745745730565704738450⟩⟩] +lemma kernel1_1_r3_6_eq : ∀ k : Fin 16, kernel1_1Expr 3 6 k = kernel1_1_r3_6 k := by decide +kernel +noncomputable def kernel1_1_r3_7 : Fin 16 → CBox := ![⟨⟨1037906041045428393162802619106,1037906041045428393363726842840⟩,⟨528790567596354729354648754660,528790567596354729561695700781⟩⟩,⟨⟨1035081131342417025775591549660,1035081131342417025976940047026⟩,⟨520862680224408222351682346516,520862680224408222559053924415⟩⟩,⟨⟨1032203532288308499833797595940,1032203532288308500035506215737⟩,⟨512963295403086991904078228441,512963295403086992111710311053⟩⟩,⟨⟨1029273888497698535221801507600,1029273888497698535423920714291⟩,⟨505094232313813144393759708936,505094232313813144601703971271⟩⟩,⟨⟨1026292882249881508501398458669,1026292882249881508703844256607⟩,⟨497257283497603508746691679088,497257283497603508954864023615⟩⟩,⟨⟨1023261232878814282615927136161,1023261232878814282818769313790⟩,⟨489454213830563046874247879189,489454213830563047082719514915⟩⟩,⟨⟨1020179696123617334250989292490,1020179696123617334454158400147⟩,⟨481686759525005633922251335042,481686759525005634130952916122⟩⟩,⟨⟨1017049063440645068886770764857,1017049063440645069090321611787⟩,⟨473956627157651081355975895936,473956627157651081564963519807⟩⟩,⟨⟨1013870161278223808096664000121,1013870161278223808300500794068⟩,⟨466265492726305355676607405521,466265492726305355885785211739⟩⟩,⟨⟨1010643850315220411448773412403,1010643850315220411652976858439⟩,⟨458615000736385684948426377220,458615000736385685157876607273⟩⟩,⟨⟨1007371024664666675832992206873,1007371024664666676037487572573⟩,⟨451006763318603750340277066294,451006763318603750549925168180⟩⟩,⟨⟨1004052611043724363287036855829,1004052611043724363491883449965⟩,⟨443442359379068547477071559054,443442359379068547686978192484⟩⟩,⟨⟨1000689567911332776029400539074,1000689567911332776234500346491⟩,⟨435923333783015900087118213255,435923333783015900297185412489⟩⟩,⟨⟨997282884574935063147793161025,997282884574935063353228423820⟩,⟨428451196573314153925100399125,428451196573314154135411954585⟩⟩,⟨⟨993833580267730753781653912873,993833580267730753987344627660⟩,⟨421027422224835419736007217750,421027422224835419946483379344⟩⟩,⟨⟨990342703197950221633073235050,990342703197950221839083376630⟩,⟨413653448935719026850367391676,413653448935719027061073532976⟩⟩] +lemma kernel1_1_r3_7_eq : ∀ k : Fin 16, kernel1_1Expr 3 7 k = kernel1_1_r3_7 k := by decide +kernel +noncomputable def kernel1_1_r3_8 : Fin 16 → CBox := ![⟨⟨986811329571691759251692996154,986811329571691759457910128224⟩,⟨406330677956488759390295482115,406330677956488759601119234521⟩⟩,⟨⟨983240562590903551354445456738,983240562590903551560965750392⟩,⟨399060472957918148712271755919,399060472957918148923310933480⟩⟩,⟨⟨979631531428130968198331389929,979631531428130968405069654473⟩,⟨391844159438468769913853874384,391844159438468770125023608835⟩⟩,⟨⟨975985390179684147057437435302,975985390179684147264462413830⟩,⟨384683024172055325203927746925,384683024172055325415298212581⟩⟩,⟨⟨972303316798911697582697552372,972303316798911697789897096409⟩,⟨377578314696818487181648533958,377578314696818487393107774791⟩⟩,⟨⟨968586512011293472102735356112,968586512011293472310205002329⟩,⟨370531238845512220621816934084,370531238845512220833462095723⟩⟩,⟨⟨964836198213088613452443266350,964836198213088613660092695249⟩,⟨363542964318036807100652031650,363542964318036807312393181791⟩⟩,⟨⟨961053618355294471482430261908,961053618355294471690333114590⟩,⟨356614618296572271628665685447,356614618296572271840577914093⟩⟩,⟨⟨957240034814687418186924436714,957240034814687418394954543525⟩,⟨349747287103689566601902498867,349747287103689566813859854735⟩⟩,⟨⟨953396728253728056109987425715,953396728253728056318254197973⟩,⟨342942015903738920512216552529,342942015903738920724330104210⟩⟩,⟨⟨949524996471120783799883999838,949524996471120784008292125548⟩,⟨336199808447736423340142584465,336199808447736423552317467679⟩⟩,⟨⟨945626153244821146797507136221,945626153244821147006135206582⟩,⟨329521626861891414586675102746,329521626861891414798991360497⟩⟩,⟨⟨941701527169283867034259889631,941701527169283867242981738483⟩,⟨322908391479838780733267514519,322908391479838780945599305804⟩⟩,⟨⟨937752460488739924417033855126,937752460488739924625958953213⟩,⟨316360980718562072980574623352,316360980718562073193033022558⟩⟩,⟨⟨933780307928282591374286750464,933780307928282591583314902927⟩,⟨309880230997915638242749002886,309880230997915638455234318713⟩⟩,⟨⟨929786435524529936361120850644,929786435524529936570335675264⟩,⟨303466936703576928945222525672,303466936703576929157819816773⟩⟩] +lemma kernel1_1_r3_8_eq : ∀ k : Fin 16, kernel1_1Expr 3 8 k = kernel1_1_r3_8 k := by decide +kernel +noncomputable def kernel1_1_r3_9 : Fin 16 → CBox := ![⟨⟨925772219457615070317066497845,925772219457615070526324855976⟩,⟨297121850193184029363090799693,297121850193184029575657267488⟩⟩,⟨⟨921739044886235377492428434156,921739044886235377701856992096⟩,⟨290845681845338413171393155546,290845681845338413384057092661⟩⟩,⟨⟨917688304787468227425279818164,917688304787468227634773694935⟩,⟨284639100151079228925889397240,284639100151079229138546477627⟩⟩,⟨⟨913621398803033298135506334279,913621398803033298345154158360⟩,⟨278502731847363192164429803110,278502731847363192377170071817⟩⟩,⟨⟨909539732093650752889680262278,909539732093650753099342210411⟩,⟨272437162092013633309236593674,272437162092013633521920673740⟩⟩,⟨⟨905444714203110215869489117413,905444714203110216079288966716⟩,⟨266442934679533591193376748682,266442934679533591406129954463⟩⟩,⟨⟨901337757933627907604009362413,901337757933627907813837687358⟩,⟨260520552297111226911805441406,260520552297111227124518948877⟩⟩,⟨⟨897220278234028560533074455106,897220278234028560743024926038⟩,⟨254670476820081427664294764246,254670476820081427877063624017⟩⟩,⟨⟨893093691102244979042936398539,893093691102244979252853003444⟩,⟨248893129646045432429074077837,248893129646045432641742747013⟩⟩,⟨⟨888959412503581485629856380953,888959412503581485839879656680⟩,⟨243188892066790788464967830149,243188892066790788677678363718⟩⟩,⟨⟨884818857306138162177267270307,884818857306138162387283480073⟩,⟨237558105677097077811393215496,237558105677097078024032520256⟩⟩,⟨⟨880673438234740916420077035468,880673438234740916630184819350⟩,⟨232001072819458763907497152581,232001072819458764120165201350⟩⟩,⟨⟨876524564844668148688268512211,876524564844668148898314921043⟩,⟨226518057063705317367207728834,226518057063705317579752127510⟩⟩,⟨⟨872373642516408338789140948015,872373642516408338999264201759⟩,⟨221109283720450593021529574250,221109283720450593234089960973⟩⟩,⟨⟨868222071472624398192509967757,868222071472624398402592195573⟩,⟨215774940387258342559073234197,215774940387258342771532419162⟩⟩,⟨⟨864071245818440323469057496496,864071245818440323679202278961⟩,⟨210515177526368841938662217313,210515177526368842151125056649⟩⟩] +lemma kernel1_1_r3_9_eq : ∀ k : Fin 16, kernel1_1Expr 3 9 k = kernel1_1_r3_9 k := by decide +kernel +noncomputable def kernel1_1_r3_10 : Fin 16 → CBox := ![⟨⟨859922552606103731597516122297,859922552606103731807550204248⟩,⟨205330109072792962068393959457,205330109072792962280687769651⟩⟩,⟨⟨855777370925014447321742655292,855777370925014447531825428610⟩,⟨200219813071544675082715791808,200219813071544675295001341830⟩⟩,⟨⟨851637071018044640141188871364,851637071018044640351198613188⟩,⟨195184332342751015120112285581,195184332342751015332268566824⟩⟩,⟨⟨847503013425010267776402418706,847503013425010267986447501880⟩,⟨190223675173349938118223174500,190223675173349938330359769513⟩⟩,⟨⟨843376548154086968471097561246,843376548154086968681012630019⟩,⟨185337816034061374305057540868,185337816034061374517009745432⟩⟩,⟨⟨839259013881896250243656818479,839259013881896250453594378550⟩,⟨180526696320295052488668475437,180526696320295052700590052230⟩⟩,⟨⟨835151737182920044049137966588,835151737182920044258972628367⟩,⟨175790225115640398065878184891,175790225115640398277644487513⟩⟩,⟨⟨831056031788833610726083037392,831056031788833610935927896494⟩,⟨171128279976568956549533713976,171128279976568956761258974953⟩⟩,⟨⟨826973197878278607020066843225,826973197878278607229738176984⟩,⟨166540707736968349857138245380,166540707736968350068639420139⟩⟩,⟨⟨822904521397530009059547497014,822904521397530009269217280021⟩,⟨162027325331118701160921852560,162027325331118701372372098652⟩⟩,⟨⟨818851273412442743713444450765,818851273412442743922983923592⟩,⟨157587920633717722759745664354,157587920633717722971016990589⟩⟩,⟨⟨814814709491996466037116218337,814814709491996466246642999952⟩,⟨153222253315559196916689712259,153222253315559197127900795913⟩⟩,⟨⟨810796069123690116201032903695,810796069123690116410370026937⟩,⟨148930055713471328839297996379,148930055713471329050272606467⟩⟩,⟨⟨806796575160971857884654566530,806796575160971858093968455091⟩,⟨144711033713126341455948752242,144711033713126341666854378111⟩⟩,⟨⟨802817433302824901959681778959,802817433302824902168840511852⟩,⟨140564867643340631969011717483,140564867643340632179717227717⟩⟩,⟨⟨798859831605565707542766639057,798859831605565707751892228385⟩,⟨136491213180495730487095730790,136491213180495730697724112960⟩⟩] +lemma kernel1_1_r3_10_eq : ∀ k : Fin 16, kernel1_1Expr 3 10 k = kernel1_1_r3_10 k := by decide +kernel +noncomputable def kernel1_1_r3_11 : Fin 16 → CBox := ![⟨⟨794924940026848273274201136494,794924940026848273483093764032⟩,⟨132489702261724093635783420573,132489702261724093846135622113⟩⟩,⟨⟨791013910001806823554800701595,791013910001806823763650900173⟩,⟨128559944005520325808547463745,128559944005520326018814990483⟩⟩,⟨⟨787127874051209288223053551978,787127874051209288431726571914⟩,⟨124701525638457635790389845501,124701525638457636000438755226⟩⟩,⟨⟨783267945421435692361833555627,783267945421435692570455529058⟩,⟨120914013426711088768974358020,120914013426711088978931672500⟩⟩,⟨⟨779435217756039029794545542352,779435217756039030002928806953⟩,⟨117196953611113379580769753443,117196953611113379790448620314⟩⟩,⟨⟨775630764798591494889569047426,775630764798591495097893302275⟩,⟨113549873344495303722083114837,113549873344495303931664089503⟩⟩,⟨⟨771855640126466189290036846610,771855640126466189498164709831⟩,⟨109972281630091705141474749241,109972281630091705350821272034⟩⟩,⟨⟨768110876915153690885723933797,768110876915153691093785498260⟩,⟨106463670259824297264617475001,106463670259824297473860441025⟩⟩,⟨⟨764397487732664250511695309957,764397487732664250719482264011⟩,⟨103023514751305246114008491009,103023514751305246322940435965⟩⟩,⟨⟨760716464363519937138211680541,760716464363519937345925710455⟩,⟨99651275282439629218069200790,99651275282439629426892556693⟩⟩,⟨⟨757068777661796845308066325201,757068777661796845515567751226⟩,⟨96346397622540696803473005620,96346397622540697012048926778⟩⟩,⟨⟨753455377432635560792030045684,753455377432635560999452606482⟩,⟨93108314058909116693194009162,93108314058909116901656948652⟩⟩,⟨⟨749877192341598494454219817958,749877192341598494661366072435⟩,⟨89936444317865934836979493353,89936444317865935045132884070⟩⟩,⟨⟨746335129851215473831988693629,746335129851215474039050812597⟩,⟨86830196479268682693394792085,86830196479268682901431445373⟩⟩,⟨⟨742830076184024151964442840529,742830076184024152171279057048⟩,⟨83788967883580764381980132149,83788967883580764589759124410⟩⟩,⟨⟨739362896311379370015055545179,739362896311379370221803031117⟩,⟨80812146030605815102190279822,80812146030605815309849410296⟩⟩] +lemma kernel1_1_r3_11_eq : ∀ k : Fin 16, kernel1_1Expr 3 11 k = kernel1_1_r3_11 k := by decide +kernel +noncomputable def kernel1_1_r3_12 : Fin 16 → CBox := ![⟨⟨735934433967275602435849517722,735934433967275602642283774259⟩,⟨77899109469040993694475611321,77899109469040993901791305040⟩⟩,⟨⟨732545511686399020928336513753,732545511686399021134678105073⟩,⟨75049228676046014172592774912,75049228676046014379786110135⟩⟩,⟨⟨729196930865600528654397487787,729196930865600528860502928343⟩,⟨72261866926067993762421422666,72261866926067993969349764014⟩⟩,⟨⟨725889471847958323907611149292,725889471847958324113620655787⟩,⟨69536381148205761371800774983,69536381148205761578604881360⟩⟩,⟨⟨722623894028578130541122271400,722623894028578130746829623994⟩,⟨66872122771440996671602083739,66872122771440996878076664662⟩⟩,⟨⟨719400935981261151784721943718,719400935981261151990330742724⟩,⟨64268438557107325815583382618,64268438557107326021932466927⟩⟩,⟨⟨716221315605154029206004229791,716221315605154029411369456399⟩,⟨61724671418012158977512812258,61724671418012159183592236160⟩⟩,⟨⟨713085730290481577914673529138,713085730290481578119938221278⟩,⟨59240161223669495268525805804,59240161223669495474479066984⟩⟩,⟨⟨709994857102451775497739325831,709994857102451775702674159790⟩,⟨56814245591145024744903122660,56814245591145024950501880303⟩⟩,⟨⟨706949352982413353130447620734,706949352982413353335280561865⟩,⟨54446260661057512426002901423,54446260661057512631475420061⟩⟩,⟨⟨703949854965339315563474811221,703949854965339315768059666280⟩,⟨52135541858322547904465014969,52135541858322548109665959220⟩⟩,⟨⟨700996980412704740507148948608,700996980412704740711631162336⟩,⟨49881424637266183836626925786,49881424637266184041702121413⟩⟩,⟨⟨698091327259824211637366216191,698091327259824211841531726299⟩,⟨47683245210776670403142152736,47683245210776670607878514575⟩⟩,⟨⟨695233474276713153738378773522,695233474276713153942441485456⟩,⟨45540341263202329287444000521,45540341263202329492055662876⟩⟩,⟨⟨692423981341538090983107160297,692423981341538091186919913714⟩,⟨43452052646742514105076756935,43452052646742514309417418610⟩⟩,⟨⟨689663389725723364875259817630,689663389725723365078970186599⟩,⟨41417722061116494503286557258,41417722061116494707504098911⟩⟩] +lemma kernel1_1_r3_12_eq : ∀ k : Fin 16, kernel1_1Expr 3 12 k = kernel1_1_r3_12 k := by decide +kernel +noncomputable def kernel1_1_r3_13 : Fin 16 → CBox := ![⟨⟨686952222389786049528971866277,686952222389786049732336182609⟩,⟨39436695716331904159282217277,39436695716331904363134020822⟩⟩,⟨⟨684290984288976609396277128833,684290984288976609599540022300⟩,⟨37508323978410040242294539972,37508323978410040446025320756⟩⟩,⟨⟨681680162687810177489932526102,681680162687810177692946265432⟩,⟨35631961997959731053856659058,35631961997959731257319544478⟩⟩,⟨⟨679120227482582108672927363851,679120227482582108875841169764⟩,⟨33806970321524642771764078614,33806970321524642975108526753⟩⟩,⟨⟨676611631530971600125732435393,676611631530971600328325426354⟩,⟨32032715485660724562051587010,32032715485660724765057734188⟩⟩,⟨⟨674154810987848586703752767280,674154810987848586906247816283⟩,⟨30308570593730948507629531921,30308570593730948710520299643⟩⟩,⟨⟨671750185646411729680729229660,671750185646411729882978220864⟩,⟨28633915875433547215680813238,28633915875433547418308942725⟩⟩,⟨⟨669398159283799040778470900859,669398159283799040980624416161⟩,⟨27008139229107553456760281153,27008139229107553659276527854⟩⟩,⟨⟨667099120010327437591043919174,667099120010327437792855336514⟩,⟨25430636746885574044381494389,25430636746885574246540325967⟩⟩,⟨⟨664853440621533230660476660235,664853440621533230862195513060⟩,⟨23900813222788360879373129207,23900813222788361081423993402⟩⟩,⟨⟨662661478952202117034812857192,662661478952202117236291040528⟩,⟨22418082643878857306042367421,22418082643878857507838013204⟩⟩,⟨⟨660523578231594622145495603962,660523578231594622346884553956⟩,⟨20981868664614984198894564920,20981868664614984400586544421⟩⟩,⟨⟨658440067439091015166245467494,658440067439091015367318454914⟩,⟨19591605064560478880438195369,19591605064560479081800831466⟩⟩,⟨⟨656411261659498448561498616229,656411261659498448762486087162⟩,⟨18246736189631606959110978946,18246736189631607160374610291⟩⟩,⟨⟨654437462437282368536315827532,654437462437282368737069906385⟩,⟨16946717377074532815408900272,16946717377074533016426501177⟩⟩,⟨⟨652518958129004040234192103447,652518958129004040434864739156⟩,⟨15691015364383563249459451176,15691015364383563450383035257⟩⟩] +lemma kernel1_1_r3_13_eq : ∀ k : Fin 16, kernel1_1Expr 3 13 k = kernel1_1_r3_13 k := by decide +kernel +noncomputable def kernel1_1_r3_14 : Fin 16 → CBox := ![⟨⟨650656024253266263180613611987,650656024253266263380943427637⟩,⟨14479108682384379278522830181,14479108682384379479092173604⟩⟩,⟨⟨648848923837489954800997870083,648848923837489955001250632598⟩,⟨13310488032718755528328119561,13310488032718755728808729077⟩⟩,⟨⟨647097907760865192031016008544,647097907760865192231044530588⟩,⟨12184656649978151025978187521,12184656649978151226223720150⟩⟩,⟨⟨645403215092841465305122709366,645403215092841465505078860788⟩,⟨11101130648742958734805397197,11101130648742958934967743240⟩⟩,⟨⟨643765073426543261022568799661,643765073426543261222221122911⟩,⟨10059439355792146360807564354,10059439355792146560656345882⟩⟩,⟨⟨642183699206518596644498025192,642183699206518596844082908180⟩,⟨9059125627754533211001989952,9059125627754533410773359980⟩⟩,⟨⟨640659298050249738968632332011,640659298050249739168003479793⟩,⟨8099746154478055421238532238,8099746154478055620787033942⟩⟩,⟨⟨639192065062876996308731190581,639192065062876996508040047618⟩,⟨7180871748397105439181981379,7180871748397105638659042171⟩⟩,⟨⟨637782185144608148209791319156,637782185144608148408777947864⟩,⟨6302087620180424416774922603,6302087620180424615921773247⟩⟩,⟨⟨636429833290307724297074450598,636429833290307724496004108890⟩,⟨5462993640943113441817968883,5462993640943113640899503332⟩⟩,⟨⟨635135174880781932735326970519,635135174880781932934054719824⟩,⟨4663204591306148680283503911,4663204591306148879155614101⟩⟩,⟨⟨633898365965296537807743653424,633898365965296538006419898487⟩,⟨3902350397585375647968271388,3902350397585375846781315006⟩⟩,⟨⟨632719553534886368027825023282,632719553534886368226214673074⟩,⟨3180076355389359832142455667,3180076355389360030662442029⟩⟩,⟨⟨631598875786036377013493934580,631598875786036377211837639521⟩,⟨2496043340901727037209743648,2496043340901727235676991788⟩⟩,⟨⟨630536462374335258503054817395,630536462374335258701209266996⟩,⟨1849928010118780828024535585,1849928010118781026296557203⟩⟩,⟨⟨629532434657723517010305045014,629532434657723517208419174284⟩,⟨1241422986307281138570844726,1241422986307281336796504866⟩⟩] +lemma kernel1_1_r3_14_eq : ∀ k : Fin 16, kernel1_1Expr 3 14 k = kernel1_1_r3_14 k := by decide +kernel +noncomputable def kernel1_1_r3_15 : Fin 16 → CBox := ![⟨⟨628586905928978602570434418472,628586905928978602768235988537⟩,⟨670237035940353468267025069,670237035940353666175303218⟩⟩,⟨⟨627699981637100220736384694160,627699981637100220934151576953⟩,⟨136095233361618961379464008,136095233361619159247754913⟩⟩,⟨⟨626871759597279219414943015905,626871759597279219612534080554⟩,⟨(-361260885581160209722163462),(-361260885581160012034178347)⟩⟩,⟨⟨626102330189153527093833940761,626102330189153527291395936750⟩,⟨(-822073180701289959029428151),(-822073180701289761375084306)⟩⟩,⟨⟨625391776543074470146927073734,625391776543074470344222632439⟩,⟨(-1246566775216061198401418737),(-1246566775216061001016971555)⟩⟩,⟨⟨624740174714126430454865521575,624740174714126430652137556435⟩,⟨(-1634949933857481071876195550),(-1634949933857480874519126183)⟩⟩,⟨⟨624147593843662221357962542048,624147593843662221555072385986⟩,⟨(-1987413951152897946251611843),(-1987413951152897749059785486)⟩⟩,⟨⟨623614096308135765114535328128,623614096308135765311627088873⟩,⟨(-2304133049690241807915998051),(-2304133049690241610745399778)⟩⟩,⟨⟨623139737855032656006000762217,623139737855032656202805939336⟩,⟨(-2585264288195862508066706775),(-2585264288195862311184623403)⟩⟩,⟨⟨622724567725717999481704364695,622724567725717999678496737146⟩,⟨(-2830947479266776728592801726),(-2830947479266776531725964468)⟩⟩,⟨⟨622368628765039540723274952963,622368628765039540919918907059⟩,⟨(-3041305116613479416568388808),(-3041305116613479219851621403)⟩⟩,⟨⟨622071957517542548901436240330,622071957517542549098072476218⟩,⟨(-3216442311684285450599557481),(-3216442311684285253892252497)⟩⟩,⟨⟨621834584310171221024887202103,621834584310171221221277527297⟩,⟨(-3356446739557390971868641380),(-3356446739557390775407873693)⟩⟩,⟨⟨621656533321349527849949357579,621656533321349528046336802172⟩,⟨(-3461388594002429606627459057),(-3461388594002429410170621974)⟩⟩,⟨⟨621537822636352461354415616676,621537822636352461550668003682⟩,⟨(-3531320551629195069990994516),(-3531320551629194873669487700)⟩⟩,⟨⟨621478464288896577340569550727,621478464288896577536823606938⟩,⟨(-3566277745057356713446247077),(-3566277745057356517123429125)⟩⟩] +lemma kernel1_1_r3_15_eq : ∀ k : Fin 16, kernel1_1Expr 3 15 k = kernel1_1_r3_15 k := by decide +kernel +noncomputable def kernel1_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel1_1_r3_0,kernel1_1_r3_1,kernel1_1_r3_2,kernel1_1_r3_3,kernel1_1_r3_4,kernel1_1_r3_5,kernel1_1_r3_6,kernel1_1_r3_7,kernel1_1_r3_8,kernel1_1_r3_9,kernel1_1_r3_10,kernel1_1_r3_11,kernel1_1_r3_12,kernel1_1_r3_13,kernel1_1_r3_14,kernel1_1_r3_15] +lemma kernel1_1_r3_eq (i k : Fin 16) : kernel1_1Expr 3 i k = kernel1_1_r3 i k := by + fin_cases i + · exact kernel1_1_r3_0_eq k + · exact kernel1_1_r3_1_eq k + · exact kernel1_1_r3_2_eq k + · exact kernel1_1_r3_3_eq k + · exact kernel1_1_r3_4_eq k + · exact kernel1_1_r3_5_eq k + · exact kernel1_1_r3_6_eq k + · exact kernel1_1_r3_7_eq k + · exact kernel1_1_r3_8_eq k + · exact kernel1_1_r3_9_eq k + · exact kernel1_1_r3_10_eq k + · exact kernel1_1_r3_11_eq k + · exact kernel1_1_r3_12_eq k + · exact kernel1_1_r3_13_eq k + · exact kernel1_1_r3_14_eq k + · exact kernel1_1_r3_15_eq k +noncomputable def kernel1_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-22646200740496578540135807507),(-22646200740496578326237307262)⟩,⟨2560453044443873761934428819757,2560453044443873762161563743840⟩⟩,⟨⟨(-22506894611459107320977886742),(-22506894611459107107069407034)⟩,⟨2560391158082394548988942652350,2560391158082394549216089529468⟩⟩,⟨⟨(-22228318419966680135479040707),(-22228318419966679921550841784)⟩,⟨2560267366041276784155333869967,2560267366041276784382504403035⟩⟩,⟨⟨(-21810544297764128214929361745),(-21810544297764128000971704815)⟩,⟨2560081629709265909401234939766,2560081629709265909628440829254⟩⟩,⟨⟨(-21253680438897170176615184148),(-21253680438897169962618333975)⟩,⟨2559833891232126626323640756407,2559833891232126626550893696852⟩⟩,⟨⟨(-20557871095367727597164395292),(-20557871095367727383118620272)⟩,⟨2559524073587780193665291099024,2559524073587780193892602778278⟩⟩,⟨⟨(-19723296571243028908283083356),(-19723296571243028694178660165)⟩,⟨2559152080686423188366577538064,2559152080686423188593959631649⟩⟩,⟨⟨(-18750173215134717165692605734),(-18750173215134716951519810703)⟩,⟨2558717797495572505732825489483,2558717797495572505960289668863⟩⟩,⟨⟨(-17638753410943482939307099791),(-17638753410943482725056232451)⟩,⟨2558221090189967433558412922270,2558221090189967433785970829678⟩⟩,⟨⟨(-16389325566744217159483706127),(-16389325566744216945145049198)⟩,⟨2557661806326245605436331747790,2557661806326245605663995037008⟩⟩,⟨⟨(-15002214101666353822088740097),(-15002214101666353607652626465)⟩,⟨2557039775042295503099336036138,2557039775042295503327116302228⟩⟩,⟨⟨(-13477779430603982599478686854),(-13477779430603982384935404113)⟩,⟨2556354807281173920069750499025,2556354807281173920297659376785⟩⟩,⟨⟨(-11816417946570490221966706191),(-11816417946570490007306643300)⟩,⟨2555606696039462403278710556213,2555606696039462403506759567014⟩⟩,⟨⟨(-10018562000492970579147652523),(-10018562000492970364361089660)⟩,⟨2554795216639922140425376947438,2554795216639922140653577716993⟩⟩,⟨⟨(-8084679878222460428950812085),(-8084679878222460214028195710)⟩,⟨2553920127028292044166518710239,2553920127028292044394882681813⟩⟩,⟨⟨(-6015275774517243965865077887),(-6015275774517243750796686384)⟩,⟨2552981168094059886027338875245,2552981168094059886255877656798⟩⟩] +lemma kernel1_1_r4_0_eq : ∀ k : Fin 16, kernel1_1Expr 4 0 k = kernel1_1_r4_0 k := by decide +kernel +noncomputable def kernel1_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-3810889763738058835749817277),(-3810889763738058620526208528)⟩,⟨2551978064015021240337484479365,2551978064015021240566209377151⟩⟩,⟨⟨(-1472097766976062005100111199),(-1472097766976061789711518818)⟩,⟨2550910522625425699588872908929,2550910522625425699817795555022⟩⟩,⟨⟨1000488484683090339025131685,1000488484683090554588066942⟩,⟨2549778235807494306458870960511,2549778235807494306688002551027⟩⟩,⟨⟨3606221491072695567090816595,3606221491072695782837869318⟩,⟨2548580879906076404496619605027,2548580879906076404725971755309⟩⟩,⟨⟨6344418028366100994088975655,6344418028366101210029315918⟩,⟨2547318116166198130433166875107,2547318116166198130662750557779⟩⟩,⟨⟨9214359199351449154070556525,9214359199351449370214061918⟩,⟨2545989591193238548764696569467,2545989591193238548994523479085⟩⟩,⟨⟨12215290488921368630287792763,12215290488921368846643527083⟩,⟨2544594937435452957471664213967,2544594937435452957701745183168⟩⟩,⟨⟨15346421825153562611428245206,15346421825153562828006097211⟩,⟨2543133773688546167620144849400,2543133773688546167850491553712⟩⟩,⟨⟨18606927646372234215942109844,18606927646372234432750830852⟩,⟨2541605705621981575698216206769,2541605705621981575928839121511⟩⟩,⟨⟨21995946974593573341279944896,21995946974593573558329631355⟩,⟨2540010326326694603890233782258,2540010326326694604121144765839⟩⟩,⟨⟨25512583495771082081680726824,25512583495771082298980026010⟩,⟨2538347216883861579630668940040,2538347216883861579861878324805⟩⟩,⟨⟨29155905647268302639677962047,29155905647268302857236958777⟩,⟨2536615946954357362831091313136,2536615946954357363062610909531⟩⟩,⟨⟨32924946712997501492708214468,32924946712997501710535110171⟩,⟨2534816075388517009894188190995,2534816075388517010126027829994⟩⟩,⟨⟨36818704926673025110519851957,36818704926673025328625050761⟩,⟨2532947150855798492452059319553,2532947150855798492684231105663⟩⟩,⟨⟨40836143583637344928548537782,40836143583637345146940128240⟩,⟨2531008712493924971852169977363,2531008712493924972084683584280⟩⟩,⟨⟨44976191161726222230690225596,44976191161726222449378589022⟩,⟨2529000290577066375689806274206,2529000290577066375922673741911⟩⟩] +lemma kernel1_1_r4_1_eq : ∀ k : Fin 16, kernel1_1Expr 4 1 k = kernel1_1_r4_1 k := by decide +kernel +noncomputable def kernel1_1_r4_2 : Fin 16 → CBox := ![⟨⟨49237741451646917289396223376,49237741451646917508388762969⟩,⟨2526921407202601039882808433448,2526921407202601040116038679832⟩⟩,⟨⟨53619653697349912362648641748,53619653697349912581956275011⟩,⟨2524771576995978980474624464451,2524771576995978980708230044696⟩⟩,⟨⟨58120752746880186434667261165,58120752746880186654297355877⟩,⟨2522550307833188956978058386479,2522550307833188957212048136965⟩⟩,⟨⟨62739829214198643122540880169,62739829214198643342504231220⟩,⟨2520257101580311898973750853958,2520257101580311899208137156890⟩⟩,⟨⟨67475639652467824971477766140,67475639652467825191780871249⟩,⟨2517891454849623507112834038262,2517891454849623507347624777034⟩⟩,⟨⟨72326906739298521321366182027,72326906739298521542020534855⟩,⟨2515452859771688927836269604951,2515452859771688928071477841954⟩⟩,⟨⟨77292319474455267895592010398,77292319474455268116604074725⟩,⟨2512940804782872359156756923126,2512940804782872359392390457331⟩⟩,⟨⟨82370533390519020121064044772,82370533390519020342445166524⟩,⟨2510354775427664295850377218527,2510354775427664296086448908928⟩⟩,⟨⟨87560170777004435933390146582,87560170777004436155145520826⟩,⟨2507694255175208891429813066629,2507694255175208891666329339239⟩⟩,⟨⟨92859820918427205649550919386,92859820918427205871692964569⟩,⟨2504958726249393628327617752289,2504958726249393628564592531922⟩⟩,⟨⟨98268040346813695886023926975,98268040346813696108558003336⟩,⟨2502147670471843175760155748409,2502147670471843175997595579825⟩⟩,⟨⟨103783353109140812322039649942,103783353109140812544977806339⟩,⟨2499260570117139007652298213211,2499260570117139007890216582903⟩⟩,⟨⟨109404251050188414682060146388,109404251050188414905406242202⟩,⟨2496296908779566083569882804121,2496296908779566083808284637714⟩⟩,⟨⟨115129194111279820523938080279,115129194111279820747705443772⟩,⟨2493256172250667698500358391691,2493256172250667698739258453755⟩⟩,⟨⟨120956610645377897809353381137,120956610645377898033546047341⟩,⟨2490137849406869519057373247698,2490137849406869519296776589772⟩⟩,⟨⟨126884897748994957088687730429,126884897748994957313318623161⟩,⟨2486941433106413882581297666142,2486941433106413882821218574744⟩⟩] +lemma kernel1_1_r4_2_eq : ∀ k : Fin 16, kernel1_1Expr 4 2 k = kernel1_1_r4_2 k := by decide +kernel +noncomputable def kernel1_1_r4_3 : Fin 16 → CBox := ![⟨⟨132912421611364101586889588517,132912421611364101811960583569⟩,⟨2483666421094825681741608857763,2483666421094825681982050074961⟩⟩,⟨⟨139037517881307868603435630646,139037517881307868828961561476⟩,⟨2480312316918111632396365316406,2480312316918111632637343061020⟩⟩,⟨⟨145258492052226891550165524739,145258492052226891776148862869⟩,⟨2476878630842875470047744525831,2476878630842875470289262100410⟩⟩,⟨⟨151573619865616923889708192164,151573619865616924116162920572⟩,⟨2473364880782512685239692018499,2473364880782512685481764696056⟩⟩,⟨⟨157981147733506891678777715850,157981147733506891905703926058⟩,⟨2469770593228629837159259026131,2469770593228629837401887565646⟩⟩,⟨⟨164479293180193680160611301683,164479293180193680388025081869⟩,⟨2466095304186815325421829774953,2466095304186815325665031583712⟩⟩,⟨⟨171066245303631114102189737568,171066245303631114330091740771⟩,⟨2462338560115870801758378337938,2462338560115870802002154697027⟩⟩,⟨⟨177740165256811066051984211670,177740165256811066280389683011⟩,⟨2458499918869595216515979677857,2458499918869595216760347053973⟩⟩,⟨⟨184499186749453828716056898449,184499186749453828944963173511⟩,⟨2454578950640196871083999315048,2454578950640196871328955464472⟩⟩,⟨⟨191341416570302827204920890430,191341416570302827434346226565⟩,⟨2450575238902392839120514548415,2450575238902392839366079016861⟩⟩,⟨⟨198264935130295436743854651908,198264935130295436973797612190⟩,⟨2446488381357239780212405847094,2446488381357239780458577605305⟩⟩,⟨⟨205267797026857127154764456412,205267797026857127385241762937⟩,⟨2442317990874725553544597918166,2442317990874725553791394847487⟩⟩,⟨⟨212348031629540395511231435898,212348031629540395742238101260⟩,⟨2438063696434137201085292615041,2438063696434137201332709914948⟩⟩,⟨⟨219503643687202994320129207719,219503643687202994551685170807⟩,⟨2433725144061207864993354360807,2433725144061207865241413204820⟩⟩,⟨⟨226732613956891838917697467555,226732613956891839149798916176⟩,⟨2429301997761033088028227580293,2429301997761033088276924326332⟩⟩,⟨⟨234032899854569712105560680698,234032899854569712338226044922⟩,⟨2424793940445735774465813096142,2424793940445735774715167279370⟩⟩] +lemma kernel1_1_r4_3_eq : ∀ k : Fin 16, kernel1_1Expr 4 3 k = kernel1_1_r4_3 k := by decide +kernel +noncomputable def kernel1_1_r4_4 : Fin 16 → CBox := ![⟨⟨241402436127791507164320752107,241402436127791507397541223128⟩,⟨2420200674855848918179751569048,2420200674855848918429754263944⟩⟩,⟨⟨248839135550405296228603993898,248839135550405296462402629437⟩,⟨2415521924474376089756441221227,2415521924474376090007116728018⟩⟩,⟨⟨256340889639321016776639896003,256340889639321017011010208497⟩,⟨2410757434432481671061362783194,2410757434432481671312704530025⟩⟩,⟨⟨263905569393356075118373987611,263905569393356075353336356869⟩,⟨2405906972405755988332631756695,2405906972405755988584661184428⟩⟩,⟨⟨271531026054132715972506956824,271531026054132716208049841422⟩,⟨2400970329499994877717165511670,2400970329499994877969870702481⟩⟩,⟨⟨279215091888966648495495831026,279215091888966648731644266609⟩,⟨2395947321125428873363781725317,2395947321125428873617188916217⟩⟩,⟨⟨286955580995650201739283240547,286955580995650201976027752383⟩,⟨2390837787858334189844608646936,2390837787858334190098708008052⟩⟩,⟨⟨294750290128996260010054094775,294750290128996260247417266110⟩,⟨2385641596288956028604991700514,2385641596288956028859806844361⟩⟩,⟨⟨302596999548971457771227660160,302596999548971458009193124864⟩,⟨2380358639854674521678965412529,2380358639854674521934479241833⟩⟩,⟨⟨310493473890208654586331830292,310493473890208654824928630063⟩,⟨2374988839657344882699619818142,2374988839657344882955862626495⟩⟩,⟨⟨318437463052649626315623781108,318437463052649626554839134427⟩,⟨2369532145263746111043715378112,2369532145263746111300673742224⟩⟩,⟨⟨326426703113029265662697311465,326426703113029265902556267308⟩,⟨2363988535488076933439441912083,2363988535488076933697141892617⟩⟩,⟨⟨334458917256872452569128468880,334458917256872452809611322427⟩,⟨2358358019155443609899611152053,2358358019155443610158032022759⟩⟩,⟨⟨342531816730634205199432670626,342531816730634205440570933878⟩,⟨2352640635845291816269526840989,2352640635845291816528701352041⟩⟩,⟨⟨350643101813572830554889408192,350643101813572830796666663264⟩,⟨2346836456613744080139647621203,2346836456613744080399558411111⟩⟩,⟨⟨358790462808904638084401502323,358790462808904638326845538577⟩,⟨2340945584693815223583620913097,2340945584693815223844296781592⟩⟩] +lemma kernel1_1_r4_4_eq : ∀ k : Fin 16, kernel1_1Expr 4 4 k = kernel1_1_r4_4 k := by decide +kernel +noncomputable def kernel1_1_r4_5 : Fin 16 → CBox := ![⟨⟨366971581053747440670524242506,366971581053747440913609009429⟩,⟨2334968156172490985243511729121,2334968156172490985504925178596⟩⟩,⟨⟨375184129947318628230234868223,375184129947318628473997288954⟩,⟨2328904340643669482472409334342,2328904340643669482734598649496⟩⟩,⟨⟨383425775996812145447294879098,383425775996812145691714567506⟩,⟨2322754341835981454830285155000,2322754341835981455093228690164⟩⟩,⟨⟨391694179880337324635273491703,391694179880337324880381254267⟩,⟨2316518398214523322774039692604,2316518398214523323037769281230⟩⟩,⟨⟨399986997526261307275674664099,399986997526261307521440917171⟩,⟨2310196783555557015571959927156,2310196783555557015836444240676⟩⟩,⟨⟨408301881208255825115918234388,408301881208255825362382460759⟩,⟨2303789807493252281923361038727,2303789807493252282188640923157⟩⟩,⟨⟨416636480655308497272734034313,416636480655308497519871537771⟩,⟨2297297816037570802872162082269,2297297816037570803138211252515⟩⟩,⟨⟨424988444175918628465856647262,424988444175918628713701542168⟩,⟨2290721192062416882368872687178,2290721192062416882635726321280⟩⟩,⟨⟨433355419795657861471820840635,433355419795657861720336020446⟩,⟨2284060355763206794729464242397,2284060355763206794997083011452⟩⟩,⟨⟨441735056407237041328235730374,441735056407237041577467161037⟩,⟨2277315765083038014046769390958,2277315765083038014315200812376⟩⟩,⟨⟨450125004932182387723094132006,450125004932182387973012472921⟩,⟨2270487916106670527318860785520,2270487916106670527588073588495⟩⟩,⟨⟨458522919493186643888215298277,458522919493186644138858257187⟩,⟨2263577343421565224728158266736,2263577343421565224998191280694⟩⟩,⟨⟨466926458596164373981742167323,466926458596164374233068496053⟩,⟨2256584620445258946180125905358,2256584620445258946450935340550⟩⟩,⟨⟨475333286321005115186578842795,475333286321005115438637579644⟩,⟨2249510359718392116815543808673,2249510359718392117087180296732⟩⟩,⟨⟨483741073519983754097081117480,483741073519983754349862377840⟩,⟨2242355213162742994495022040713,2242355213162742994767454821727⟩⟩,⟨⟨492147499022754387367219669520,492147499022754387620807103814⟩,⟨2235119872303662342715523589333,2235119872303662342988805624530⟩⟩] +lemma kernel1_1_r4_5_eq : ∀ k : Fin 16, kernel1_1Expr 4 5 k = kernel1_1_r4_5 k := by decide +kernel +noncomputable def kernel1_1_r4_6 : Fin 16 → CBox := ![⟨⟨500550250846822141150488764673,500550250846822141404832155364⟩,⟨2227805068456343791279672276933,2227805068456343791553749842136⟩⟩,⟨⟨508947027412357058502489676972,508947027412357058757647367962⟩,⟨2220411572875408207203946530820,2220411572875408207478879432920⟩⟩,⟨⟨517335538760185313109769445860,517335538760185313365702472609⟩,⟨2212940196867325017422442869643,2212940196867325017698189135424⟩⟩,⟨⟨525713507771765764128020290703,525713507771765764384775204158⟩,⟨2205391791865239545104710423195,2205391791865239545381317476563⟩⟩,⟨⟨534078671389934321151724389825,534078671389934321409247060761⟩,⟨2197767249465822979885383311047,2197767249465822980162793315154⟩⟩,⟨⟨542428781839174828562889006587,542428781839174828821240482087⟩,⟨2190067501427810530790503323450,2190067501427810531068778810788⟩⟩,⟨⟨550761607844153290169798985336,550761607844153290428934548207⟩,⟨2182293519631943535791242265756,2182293519631943536070335226888⟩⟩,⟨⟨559074935845232320540476223358,559074935845232320800446938671⟩,⟨2174446316002082745294441427654,2174446316002082745574403917924⟩⟩,⟨⟨567366571209664807804905791552,567366571209664808065646560262⟩,⟨2166526942387312575125313919529,2166526942387312575406076637380⟩⟩,⟨⟨575634339437149979304449616899,575634339437149979566031172027⟩,⟨2158536490404909749468117318654,2158536490404909749749752824083⟩⟩,⟨⟨583876087358421447699352914863,583876087358421447961724459819⟩,⟨2150476091244104332944889124658,2150476091244104333227343053136⟩⟩,⟨⟨592089684325525448103304197568,592089684325525448366521598841⟩,⟨2142346915430616586154042027678,2142346915430616586437371371889⟩⟩,⟨⟨600273023392438419033600510511,600273023392438419297594068844⟩,⟨2134150172552009268889358336983,2134150172552009269173489008688⟩⟩,⟨⟨608424022484666389104961186229,608424022484666389369804950301⟩,⟨2125887110943951854131742058116,2125887110943951854416749993752⟩⟩,⟨⟨616540625556464359989828006183,616540625556464360255464765985⟩,⟨2117559017337550494117207515062,2117559017337550494403031669915⟩⟩,⟨⟨624620803734312071334496266171,624620803734312071600986994898⟩,⟨2109167216467955384069883572597,2109167216467955384356586201112⟩⟩] +lemma kernel1_1_r4_6_eq : ∀ k : Fin 16, kernel1_1Expr 4 6 k = kernel1_1_r4_6 k := by decide +kernel +noncomputable def kernel1_1_r4_7 : Fin 16 → CBox := ![⟨⟨632662556445283236535633957407,632662556445283236802895149193⟩,⟨2100713070644515282954892779878,2100713070644515283242385427852⟩⟩,⟨⟨640663912528948585112438997158,640663912528948585380557152910⟩,⟨2092197979282807254185245201461,2092197979282807254473616719653⟩⟩,⟨⟨648622931331458867323209561184,648622931331458867592120765535⟩,⟨2083623378398928060208390702150,2083623378398928060497573085836⟩⟩,⟨⟨656537703780462392798918202328,656537703780462393068688803658⟩,⟨2074990740066491958454051008054,2074990740066491958744112059123⟩⟩,⟨⟨664406353439522703935730403083,664406353439522704206273320489⟩,⟨2066301571836837775326586395842,2066301571836837775617433992276⟩⟩,⟨⟨672227037540715636540100568891,672227037540715636811504561937⟩,⟨2057557416123005951096872471967,2057557416123005951388597748811⟩⟩,⟨⟨679997947994101297882021826922,679997947994101298154215970199⟩,⟨2048759849548103621664859688891,2048759849548103621957387388960⟩⟩,⟨⟨687717312372785392037587116197,687717312372785392310643429179⟩,⟨2039910482258732602188391206721,2039910482258732602481794993085⟩⟩,⟨⟨695383394872305833304278149322,695383394872305833578094624334⟩,⟨2031010957204211230890798679070,2031010957204211231184970961757⟩⟩,⟨⟨702994497243104692502696032487,702994497243104692777374976078⟩,⟨2022062949382376287133120180122,2022062949382376287428166145266⟩⟩,⟨⟨710548959694872192910104370534,710548959694872193185567597619⟩,⟨2013068165052805484461288974869,2013068165052805484757125878539⟩⟩,⟨⟨718045161771578679925484117349,718045161771578680201809566016⟩,⟨2004028340918354225812351964672,2004028340918354226109059593730⟩⟩,⟨⟨725481523196042191648729390603,725481523196042191925810901778⟩,⟨1994945243275952264454001415348,1994945243275952264751467961622⟩⟩,⟨⟨732856504682913409433372235449,732856504682913409711314948966⟩,⟨1985820667137656512052912471796,1985820667137656512351246015075⟩⟩,⟨⟨740168608718996314059384693616,740168608718996314338102903351⟩,⟨1976656435323005347955492455668,1976656435323005348254602519014⟩⟩,⟨⟨747416380309861753265099027508,747416380309861753544676862097⟩,⟨1967454397523767287055715804970,1967454397523767287355688586225⟩⟩] +lemma kernel1_1_r4_7_eq : ∀ k : Fin 16, kernel1_1Expr 4 7 k = kernel1_1_r4_7 k := by decide +kernel +noncomputable def kernel1_1_r4_8 : Fin 16 → CBox := ![⟨⟨754598407691752271795393575923,754598407691752272075706012238⟩,⟨1958216429342222636028609119529,1958216429342222636329313315708⟩⟩,⟨⟨761713323007819890792261191285,761713323007819891073430897114⟩,⟨1948944431304160690880133832920,1948944431304160691181695707727⟩⟩,⟨⟨768759802947783967507463537334,768759802947783967789397103494⟩,⟨1939640327847816987972943225692,1939640327847816988275264405387⟩⟩,⟨⟨775736569350143730629016741304,775736569350143730911804690041⟩,⟨1930306066290015005170917574603,1930306066290015005474090882675⟩⟩,⟨⟨782642389766129476357742222438,782642389766129476641257817200⟩,⟨1920943615770814413165609543112,1920943615770814413469502043109⟩⟩,⟨⟨789476077984627625001738814748,789476077984627625286105135036⟩,⟨1911554966178003397824098440536,1911554966178003398128836779418⟩⟩,⟨⟨796236494517367770725700736322,796236494517367771010816454620⟩,⟨1902142127052805616140568621053,1902142127052805616446046329599⟩⟩,⟨⟨802922547043714396074412588609,802922547043714396360374867237⟩,⟨1892707126478202920189582084525,1892707126478202920495898870602⟩⟩,⟨⟨809533190814461950651294530812,809533190814461950937957319128⟩,⟨1883252009951303000373587798132,1883252009951303000680590834381⟩⟩,⟨⟨816067429014089387604745978212,816067429014089387892250359918⟩,⟨1873778839241206482405953976280,1873778839241206482713788572115⟩⟩,⟨⟨822524313080988885565311417876,822524313080988885853548029044⟩,⟨1864289691233850689586622155637,1864289691233850689895173647903⟩⟩,⟨⟨828902942985243226386338544919,828902942985243226675411349581⟩,⟨1854786656765327187487670612415,1854786656765327187797045762897⟩⟩,⟨⟨835202467463587015718154277286,835202467463587016007914681873⟩,⟨1845271839445187303740258347522,1845271839445187304050301877183⟩⟩,⟨⟨841422084211248485935771906382,841422084211248486226362358177⟩,⟨1835747354471264010040646059945,1835747354471264010351504658489⟩⟩,⟨⟨847561040030430868176213592835,847561040030430868467516544684⟩,⟨1826215327437549823159871870643,1826215327437549823471422551761⟩⟩,⟨⟨853618630935255118624735679288,853618630935255118916862095129⟩,⟨1816677893136678690711754628116,1816677893136678691024111413846⟩⟩] +lemma kernel1_1_r4_8_eq : ∀ k : Fin 16, kernel1_1Expr 4 8 k = kernel1_1_r4_8 k := by decide +kernel +noncomputable def kernel1_1_r4_9 : Fin 16 → CBox := ![⟨⟨859594202213048988108292296778,859594202213048988401069617068⟩,⟨1807137194358565147672581094264,1807137194358565147985564060052⟩⟩,⟨⟨865487148441930886287052124789,865487148441930886580645542395⟩,⟨1797595380686756341086981749025,1797595380686756341400761142789⟩⟩,⟨⟨871296913464700563989913101494,871296913464700564284196855511⟩,⟨1788054607294051811114348986771,1788054607294051811428793489167⟩⟩,⟨⟨877022990319112170573665637537,877022990319112170868757786145⟩,⟨1778517033738942182791412125489,1778517033738942183106643116227⟩⟩,⟨⟨882664921124668588558947771320,882664921124668588854676889860⟩,⟨1768984822764411169095666475696,1768984822764411169411505430050⟩⟩,⟨⟨888222296926138956494293973426,888222296926138956790823082425⟩,⟨1759460139100635524779272985739,1759460139100635525095887869436⟩⟩,⟨⟨893694757494063815197262970451,893694757494063815494458009897⟩,⟨1749945148273104842952683723775,1749945148273104843269934816118⟩⟩,⟨⟨899081991082574205700988291857,899081991082574205998974570263⟩,⟨1740442015417667381616294740138,1740442015417667381934310938831⟩⟩,⟨⟨904383734144912164746756611648,904383734144912165045338704421⟩,⟨1730952904103989482484444902480,1730952904103989482803023070261⟩⟩,⟨⟨909599771007100263135802909581,909599771007100263435166762878⟩,⟨1721479975168894644681148371131,1721479975168894645000480187779⟩⟩,⟨⟨914729933500266974141166938831,914729933500266974441170241256⟩,⟨1712025385561023994255923616632,1712025385561023994575861027853⟩⟩,⟨⟨919774100552192607152885604978,919774100552192607453660945658⟩,⟨1702591287198232807647595088748,1702591287198232807968274539203⟩⟩,⟨⟨924732197738697163204884461341,924732197738697163506236901554⟩,⟨1693179825839107971405101713186,1693179825839107971726320820179⟩⟩,⟨⟨929604196795546635532951271956,929604196795546635835065387520⟩,⟨1683793139969958867049005993907,1683793139969958867370954990538⟩⟩,⟨⟨934390115091607865976543278357,934390115091607866279268501787⟩,⟨1674433359708599241349085739214,1674433359708599241671608249065⟩⟩,⟨⟨939090015064033957935696714184,939090015064033958239173003229⟩,⟨1665102605726200247589094491557,1665102605726200247912334593972⟩⟩] +lemma kernel1_1_r4_9_eq : ∀ k : Fin 16, kernel1_1Expr 4 9 k = kernel1_1_r4_9 k := by decide +kernel +noncomputable def kernel1_1_r4_10 : Fin 16 → CBox := ![⟨⟨943704003616312325208085123876,943704003616312325512087106705⟩,⟨1655802988188455118119511512499,1655802988188455118443235622353⟩⟩,⟨⟨948232231480055615529007540171,948232231480055615833749295966⟩,⟨1646536605717253954217310290887,1646536605717253954541739121905⟩⟩,⟨⟨952674892541461886306140644499,952674892541461886611463508581⟩,⟨1637305544374023003293862380167,1637305544374023003618831412258⟩⟩,⟨⟨957032223133414432519257930052,957032223133414432825309159596⟩,⟨1628111876665836648430388668474,1628111876665836648756049539952⟩⟩,⟨⟨961304501294233484416311314154,961304501294233484722872160492⟩,⟨1618957660575362278685623521474,1618957660575362279011749764872⟩⟩,⟨⟨965492045994131523764167234982,965492045994131524071444469659⟩,⟨1609844938615648362715574235397,1609844938615648363042378980311⟩⟩,⟨⟨969595216330461137532101191992,969595216330461137839928105972⟩,⟨1600775736910714539239557924508,1600775736910714539566868573768⟩⟩,⟨⟨973614410692879069887604235568,973614410692879070196135421883⟩,⟨1591752064302849495680520650969,1591752064302849496008496434531⟩⟩,⟨⟨977550065899582387793152113021,977550065899582388102139967194⟩,⟨1582775911487467964081120353037,1582775911487467964409505287923⟩⟩,⟨⟨981402656305802390529250467272,981402656305802390838929881020⟩,⟨1573849250176322457053957763045,1573849250176322457382993986766⟩⟩,⟨⟨985172692885769025264444227034,985172692885769025574640683125⟩,⟨1564974032289808534326657867622,1564974032289808534656164959453⟩⟩,⟨⟨988860722289383083382181136958,988860722289383083693056420194⟩,⟨1556152189179044572440170183042,1556152189179044572770314810214⟩⟩,⟨⟨992467325874855317755559886473,992467325874855318066871451770⟩,⟨1547385630878348347820413830364,1547385630878348348150945515574⟩⟩,⟨⟨995993118718590819619572009909,995993118718590819931549175462⟩,⟨1538676245388673379077013848238,1538676245388673379408168941263⟩⟩,⟨⟨999438748603613513300499404348,999438748603613513612959989147⟩,⟨1530025897992508050771432126557,1530025897992508051103022539499⟩⟩,⟨⟨1002804894987839463948448295051,1002804894987839464261561219571⟩,⟨1521436430600680200723741902412,1521436430600680201055941675851⟩⟩] +lemma kernel1_1_r4_10_eq : ∀ k : Fin 16, kernel1_1Expr 4 10 k = kernel1_1_r4_10 k := by decide +kernel +noncomputable def kernel1_1_r4_11 : Fin 16 → CBox := ![⟨⟨1006092267953518851696117284804,1006092267953518852009603998584⟩,⟨1512909661131449238420982341053,1512909661131449238753504157146⟩⟩,⟨⟨1009301607139174957239742178260,1009301607139174957553867427762⟩,⟨1504447382922207114460790156583,1504447382922207114793906865287⟩⟩,⟨⟨1012433680655374348384801317949,1012433680655374348699375609888⟩,⟨1496051364174048720068738811413,1496051364174048720402255025121⟩⟩,⟨⟨1015489283985665681811270981629,1015489283985665682126470108012⟩,⟨1487723347429411699525472887076,1487723347429411699859569740960⟩⟩,⟨⟨1018469238874025173828318591035,1018469238874025174143876649634⟩,⟨1479465049082925342585551795426,1479465049082925342919955296601⟩⟩,⟨⟨1021374392200144889969127452119,1021374392200144890285296222230⟩,⟨1471278158925548321691990679914,1471278158925548322026960268800⟩⟩,⟨⟨1024205614843895604696997271322,1024205614843895605013580145001⟩,⟨1463164339722015680020762132004,1463164339722015680356095327667⟩⟩,⟨⟨1026963800540289144670730317144,1026963800540289144987909839979⟩,⟨1455125226821556787675705061320,1455125226821556788011589965482⟩⟩,⟨⟨1029649864726255913847678176488,1029649864726255914165154665201⟩,⟨1447162427801788087526302236573,1447162427801788087862430349188⟩⟩,⟨⟨1032264743380541774152434619386,1032264743380541774470493233437⟩,⟨1439277522145627467902759460109,1439277522145627468239424561902⟩⟩,⟨⟨1034809391858014695342150894694,1034809391858014695660588337678⟩,⟨1431472060951021140944607971407,1431472060951021141281600927624⟩⟩,⟨⟨1037284783719655671307913013180,1037284783719655671626918232890⟩,⟨1423747566673219082391161516957,1423747566673219082728677027410⟩⟩,⟨⟨1039691909559490411806207554926,1039691909559490412125492036445⟩,⟨1416105532899281505658530468194,1416105532899281505996271812468⟩⟩,⟨⟨1042031775829698347657270900961,1042031775829698347977108450633⟩,⟨1408547424154446599562387379512,1408547424154446599900636600752⟩⟩,⟨⟨1044305403665113627370731316377,1044305403665113627690912235415⟩,⟨1401074675739938949069863532311,1401074675739938949408405134810⟩⟩,⟨⟨1046513827708309131497444280168,1046513827708309131818163695221⟩,⟨1393688693601748770395330534971,1393688693601748770734365580444⟩⟩] +lemma kernel1_1_r4_11_eq : ∀ k : Fin 16, kernel1_1Expr 4 11 k = kernel1_1_r4_11 k := by decide +kernel +noncomputable def kernel1_1_r4_12 : Fin 16 → CBox := ![⟨⟨1048658094936429188963170026536,1048658094936429189284095573495⟩,⟨1386390854229864408304201660177,1386390854229864408643388593849⟩⟩,⟨⟨1050739263490909751562181375785,1050739263490909751883630415631⟩,⟨1379182504587394541420359717136,1379182504587394541760025344350⟩⟩,⟨⟨1052758401511196375887406703417,1052758401511196376209163688548⟩,⟨1372064962068972291486447005571,1372064962068972291826370035523⟩⟩,⟨⟨1054716585973540585785627703312,1054716585973540586107893441383⟩,⟨1365039514487790999607950291962,1365039514487790999948337630016⟩⟩,⟨⟨1056614901535924154535643096488,1056614901535924154858107654956⟩,⟨1358107420090580875174074241253,1358107420090580875514607670819⟩⟩,⟨⟨1058454439390128667439638621724,1058454439390128667762596880668⟩,⟨1351269907599797093822485181255,1351269907599797094163468330304⟩⟩,⟨⟨1060236296121934516708059694418,1060236296121934517031290577622⟩,⟨1344528176282253265849350874423,1344528176282253266190556980806⟩⟩,⟨⟨1061961572580399356412334088968,1061961572580399356736043805126⟩,⟨1337883396043399556010072708620,1337883396043399556351714228014⟩⟩,⟨⟨1063631372757131121308591553476,1063631372757131121632431503413⟩,⟨1331336707546412143841769059263,1331336707546412144183488293682⟩⟩,⟨⟨1065246802676435104829530154353,1065246802676435105153833699311⟩,⟨1324889222355230198513202297179,1324889222355230198855342372873⟩⟩,⟨⟨1066808969297178413480809739024,1066808969297178413805350885999⟩,⟨1318542023100648125962485543715,1318542023100648126304814848755⟩⟩,⟨⟨1068318979427178481383957376902,1068318979427178481708947154455⟩,⟨1312296163668544545026588795403,1312296163668544545369324733414⟩⟩,⟨⟨1069777938650885352816915015915,1069777938650885353142023518748⟩,⟨1306152669409305274100713494983,1306152669409305274443517822041⟩⟩,⟨⟨1071186950271090233776185083337,1071186950271090234101726966169⟩,⟨1300112537367475565689008878108,1300112537367475566032205441347⟩⟩,⟨⟨1072547114265355485509693845571,1072547114265355485835438618234⟩,⟨1294176736530656912833807175196,1294176736530656913177159935159⟩⟩,⟨⟨1073859526257823891100317582869,1073859526257823891426480686854⟩,⟨1288346208096645963406698028356,1288346208096645963750428914436⟩⟩] +lemma kernel1_1_r4_12_eq : ∀ k : Fin 16, kernel1_1Expr 4 12 k = kernel1_1_r4_12 k := by decide +kernel +noncomputable def kernel1_1_r4_13 : Fin 16 → CBox := ![⟨⟨1075125276507027775565644300690,1075125276507027775891846856358⟩,⟨1282621865757797405278506464585,1282621865757797405622227180029⟩⟩,⟨⟨1076345448910281502792330465721,1076345448910281503118935932733⟩,⟨1277004596001579112292927501712,1277004596001579112637011954310⟩⟩,⟨⟨1077521120025204108184843129070,1077521120025204108511617259393⟩,⟨1271495258426276348127671435985,1271495258426276348471879907584⟩⟩,⟨⟨1078653358108882450048000296825,1078653358108882450375162209341⟩,⟨1266094686070792388546917273052,1266094686070792388891475459888⟩⟩,⟨⟨1079743222175149367844456962499,1079743222175149368171658697345⟩,⟨1260803685757485514268680417776,1260803685757485514613231985863⟩⟩,⟨⟨1080791761070416010135784978490,1080791761070416010463359084658⟩,⟨1255623038446976914857397926587,1255623038446976915202284989733⟩⟩,⟨⟨1081800012568462823901029461056,1081800012568462824228738382081⟩,⟨1250553499603860593418408407012,1250553499603860593763388018164⟩⟩,⟨⟨1082769002484559760474976481376,1082769002484559760803042545181⟩,⟨1245595799572244833788178950632,1245595799572244834133480089606⟩⟩,⟨⟨1083699743809253127758475604967,1083699743809253128086507488430⟩,⟨1240750643960055144831518655727,1240750643960055145176740701009⟩⟩,⟨⟨1084593235862124275281115668555,1084593235862124275609489112025⟩,⟨1236018714031030786022187053233,1236018714031030786367716381792⟩⟩,⟨⟨1085450463465794005273980442921,1085450463465794005602455379061⟩,⟨1231400667103350957965560245807,1231400667103350958311151487386⟩⟩,⟨⟨1086272396140416321484189596240,1086272396140416321812990739108⟩,⟨1226897136953832461930843728545,1226897136953832462276728300151⟩⟩,⟨⟨1087059987318875915654917017803,1087059987318875915983680518739⟩,⟨1222508734226648042970468778267,1222508734226648043316274431495⟩⟩,⟨⟨1087814173582875702067714222963,1087814173582875702396788279013⟩,⟨1218236046845523679259979107896,1218236046845523679606063907172⟩⟩,⟨⟨1088535873920073791102636005564,1088535873920073791431778589665⟩,⟨1214079640428383712029125623083,1214079640428383712375242326681⟩⟩,⟨⟨1089225989002403586166219377224,1089225989002403586495656990028⟩,⟨1210040058703424870799169086531,1210040058703424871145550932756⟩⟩] +lemma kernel1_1_r4_13_eq : ∀ k : Fin 16, kernel1_1Expr 4 13 k = kernel1_1_r4_13 k := by decide +kernel +noncomputable def kernel1_1_r4_14 : Fin 16 → CBox := ![⟨⟨1089885400485686232391423810138,1089885400485686232720735201490⟩,⟨1206117823925613881710580970610,1206117823925613882056797024563⟩⟩,⟨⟨1090514970330621472962474022429,1090514970330621473292064521480⟩,⟨1202313437292618395913763751181,1202313437292618396260230610412⟩⟩,⟨⟨1091115540145221107568317585095,1091115540145221107897944156281⟩,⟨1198627379359197383362569114371,1198627379359197383709038626616⟩⟩,⟨⟨1091687930548728720086598351478,1091687930548728720416488277081⟩,⟨1195060110449094847683590700403,1195060110449094848030296894331⟩⟩,⟨⟨1092232940557050167024373618277,1092232940557050167354149859316⟩,⟨1191612071063499672983113997435,1191612071063499673329671418631⟩⟩,⟨⟨1092751346989701507387414270483,1092751346989701507717437778449⟩,⟨1188283682285154556520055738119,1188283682285154556866835433886⟩⟩,⟨⟨1093243903898264616655520088086,1093243903898264616985547389236⟩,⟨1185075346177218255628701078518,1185075346177218255975454555703⟩⟩,⟨⟨1093711342016325665701451507125,1093711342016325666031710018392⟩,⟨1181987446176007727130579301604,1181987446176007727477540716548⟩⟩,⟨⟨1094154368230857958498020112023,1094154368230857958828085185967⟩,⟨1179020347476770107563941482558,1179020347476770107910676722091⟩⟩,⟨⟨1094573665074998304339035895727,1094573665074998304669315713707⟩,⟨1176174397411658818525025401280,1176174397411658818871953875322⟩⟩,⟨⟨1094969890242155140679843329360,1094969890242155141010094978323⟩,⟨1173449925819113330005640211614,1173449925819113330352514094285⟩⟩,⟨⟨1095343676121377006760033309130,1095343676121377007090483262438⟩,⟨1170847245403868223638175555623,1170847245403868223985228026663⟩⟩,⟨⟨1095695629353901676919282330957,1095695629353901677249543284310⟩,⟨1168366652086844116368352263173,1168366652086844116715187591515⟩⟩,⟨⟨1096026330410799272771419077459,1096026330410799273101861509965⟩,⟨1166008425344200683669456966723,1166008425344200684016455884895⟩⟩,⟨⟨1096336333191616958079094928633,1096336333191616958409477192165⟩,⟨1163772828534860411893960945306,1163772828534860412240877000503⟩⟩,⟨⟨1096626164643928348272989531686,1096626164643928348603536352278⟩,⟨1161660109215840765032874508556,1161660109215840765379939081819⟩⟩] +lemma kernel1_1_r4_14_eq : ∀ k : Fin 16, kernel1_1Expr 4 14 k = kernel1_1_r4_14 k := by decide +kernel +noncomputable def kernel1_1_r4_15 : Fin 16 → CBox := ![⟨⟨1096896324403687503477865397369,1096896324403687503808128331318⟩,⟨1159670499444762126933344704546,1159670499444762127280099521778⟩⟩,⟨⟨1097147284456285281421120741232,1097147284456285281751530846808⟩,⟨1157804216068929132304348003891,1157804216068929132651235828958⟩⟩,⟨⟨1097379488818204863189556258093,1097379488818204863519874317280⟩,⟨1156061461000413786675886300960,1156061461000413787022663231689⟩⟩,⟨⟨1097593353239173385653911349485,1097593353239173385984359075841⟩,⟨1154442421476600056430860312813,1154442421476600056777754636915⟩⟩,⟨⟨1097789264924707771721907454027,1097789264924707772052090835761⟩,⟨1152947270305681346329988017832,1152947270305681346676597296451⟩⟩,⟨⟨1097967582278954992666216904045,1097967582278954992996512006153⟩,⟨1151576166096634436299015794193,1151576166096634436645726424454⟩⟩,⟨⟨1098128634667730072237802446303,1098128634667730072567973219922⟩,⟨1150329253473225985958532212696,1150329253473225986305103584089⟩⟩,⟨⟨1098272722201659094136269260084,1098272722201659094466533548362⟩,⟨1149206663271640600164648051107,1149206663271640600511304481039⟩⟩,⟨⟨1098400115539339244407481355747,1098400115539339244737394159168⟩,⟨1148208512721352648917432103908,1148208512721352649263718980012⟩⟩,⟨⟨1098511055710433447953297942456,1098511055710433448283285564978⟩,⟨1147334905608897518885336787952,1147334905608897519231691945816⟩⟩,⟨⟨1098605753958623381124304428759,1098605753958623381454135223242⟩,⟨1146585932424231711355429683327,1146585932424231711701617050469⟩⟩,⟨⟨1098684391604351495976066918403,1098684391604351496305953513002⟩,⟨1145961670489405163634513596393,1145961670489405163980752144123⟩⟩,⟨⟨1098747119927290110295947301314,1098747119927290110625492850372⟩,⟨1145462184069303329967618515229,1145462184069303330313502982924⟩⟩,⟨⟨1098794060068483533497060528120,1098794060068483533826642362429⟩,⟨1145087524464250886993557831440,1145087524464250887339475879268⟩⟩,⟨⟨1098825302952117543278365222070,1098825302952117543607756991672⟩,⟨1144837730084303401684718772518,1144837730084303402030439767516⟩⟩,⟨⟨1098840909226879231738041825676,1098840909226879232067449919414⟩,⟨1144712826505087891376864468238,1144712826505087891722600987796⟩⟩] +lemma kernel1_1_r4_15_eq : ∀ k : Fin 16, kernel1_1Expr 4 15 k = kernel1_1_r4_15 k := by decide +kernel +noncomputable def kernel1_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel1_1_r4_0,kernel1_1_r4_1,kernel1_1_r4_2,kernel1_1_r4_3,kernel1_1_r4_4,kernel1_1_r4_5,kernel1_1_r4_6,kernel1_1_r4_7,kernel1_1_r4_8,kernel1_1_r4_9,kernel1_1_r4_10,kernel1_1_r4_11,kernel1_1_r4_12,kernel1_1_r4_13,kernel1_1_r4_14,kernel1_1_r4_15] +lemma kernel1_1_r4_eq (i k : Fin 16) : kernel1_1Expr 4 i k = kernel1_1_r4 i k := by + fin_cases i + · exact kernel1_1_r4_0_eq k + · exact kernel1_1_r4_1_eq k + · exact kernel1_1_r4_2_eq k + · exact kernel1_1_r4_3_eq k + · exact kernel1_1_r4_4_eq k + · exact kernel1_1_r4_5_eq k + · exact kernel1_1_r4_6_eq k + · exact kernel1_1_r4_7_eq k + · exact kernel1_1_r4_8_eq k + · exact kernel1_1_r4_9_eq k + · exact kernel1_1_r4_10_eq k + · exact kernel1_1_r4_11_eq k + · exact kernel1_1_r4_12_eq k + · exact kernel1_1_r4_13_eq k + · exact kernel1_1_r4_14_eq k + · exact kernel1_1_r4_15_eq k +noncomputable def kernel1_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-1992437474711134874933268209645),(-1992437474711134874722183840291)⟩,⟨2520600101730483779758261289002,2520600101730483779945054404116⟩⟩,⟨⟨(-1992301519487099774311468364987),(-1992301519487099774100373693569)⟩,⟨2520662830305198109792516900462,2520662830305198109979324047293⟩⟩,⟨⟨(-1992029616143496563825259411962),(-1992029616143496563614144316673)⟩,⟨2520788255606551726865293074039,2520788255606551727052128106044⟩⟩,⟨⟨(-1991621778902606774058535162981),(-1991621778902606773847389520732)⟩,⟨2520976313949805952407191438305,2520976313949805952594068209077⟩⟩,⟨⟨(-1991078029131207562174702432967),(-1991078029131207561963516122749)⟩,⟨2521226909836386828230762276696,2521226909836386828417694636056⟩⟩,⟨⟨(-1990398395380558315294837853752),(-1990398395380558315083600753202)⟩,⟨2521539915988141483210990083598,2521539915988141483397991880458⟩⟩,⟨⟨(-1989582913439650743224068156535),(-1989582913439650743012770148464)⟩,⟨2521915173393039053917289363468,2521915173393039054104374438787⟩⟩,⟨⟨(-1988631626401666432294074215845),(-1988631626401666432082705177214)⟩,⟨2522352491362338123438763935836,2522352491362338123625946132953⟩⟩,⟨⟨(-1987544584743571838300799838010),(-1987544584743571838089349660464)⟩,⟨2522851647599247983719927088197,2522851647599247983907220231972⟩⟩,⟨⟨(-1986321846418766711924637473620),(-1986321846418766711713096031117)⟩,⟨2523412388279116268015458157245,2523412388279116268202876085444⟩⟩,⟨⟨(-1984963476962687976814772191412),(-1984963476962687976603129389710)⟩,⟨2524034428141180621829749192752,2524034428141180622017305706673⟩⟩,⟨⟨(-1983469549611257121078644815205),(-1983469549611257120866890519798)⟩,⟨2524717450591927063293518436360,2524717450591927063481227371329⟩⟩,⟨⟨(-1981840145432045219840179111986),(-1981840145432045219628303258172)⟩,⟨2525461107820102507842591705967,2525461107820102508030466822178⟩⟩,⟨⟨(-1980075353468015782664841357173),(-1980075353468015782452833791564)⟩,⟨2526265020923433577953522656976,2526265020923433578141577795279⟩⟩,⟨⟨(-1978175270893691718123205893856),(-1978175270893691717911056580621)⟩,⟨2527128780047108267381457157521,2527128780047108267569706035387⟩⟩,⟨⟨(-1976140003183578832012684042660),(-1976140003183578831800382810539)⟩,⟨2528051944534081261856848355576,2528051944534081262045304816094⟩⟩] +lemma kernel1_1_r5_0_eq : ∀ k : Fin 16, kernel1_1Expr 5 0 k = kernel1_1_r5_0 k := by decide +kernel +noncomputable def kernel1_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-1973969664292664429550253350926),(-1973969664292664429337790230027)⟩,⟨2529034043087267715764899415838,2529034043087267715953577094857⟩⟩,⟨⟨(-1971664376848795779320909216550),(-1971664376848795779108273983797)⟩,⟨2530074573943694028428749283982,2530074573943694028617662058017⟩⟩,⟨⟨(-1969224272356729422439466962540),(-1969224272356729422226649691128)⟩,⟨2531173005060677635978916499084,2531173005060677636168077942592⟩⟩,⟨⟨(-1966649491413628579193581220418),(-1966649491413628578980571659868)⟩,⟨2532328774314111017435582919058,2532328774314111017625006915605⟩⟩,⟨⟨(-1963940183935772222757772346066),(-1963940183935772222544560690429)⟩,⟨2533541289708927988882560870541,2533541289708927989072260854043⟩⟩,⟨⟨(-1961096509396225761237250120422),(-1961096509396225761023826017348)⟩,⟨2534809929601832910129534436255,2534809929601832910319524368528⟩⟩,⟨⟨(-1958118637073209701634490999455),(-1958118637073209701420844699923)⟩,⟨2536134042936375637056373514928,2536134042936375637246666750087⟩⟩,⟨⟨(-1955006746308889169152144768864),(-1955006746308889168938265886956)⟩,⟨2537512949490456903306183744859,2537512949490456903496794253229⟩⟩,⟨⟨(-1951761026778293729896343899013),(-1951761026778293729682222894565)⟩,⟨2538945940136350290947095226100,2538945940136350291138036129557⟩⟩,⟨⟨(-1948381678768063622408127466160),(-1948381678768063622193753768283)⟩,⟨2540432277113328035396913639702,2540432277113328035588199064283⟩⟩,⟨⟨(-1944868913464705251966467480741),(-1944868913464705251751831600078)⟩,⟨2541971194312978590003266659703,2541971194312978590194909648705⟩⟩,⟨⟨(-1941222953252025650283619617656),(-1941222953252025650068710962348)⟩,⟨2543561897577304135389872776632,2543561897577304135581887447542⟩⟩,⟨⟨(-1937444032017402561644383101955),(-1937444032017402561429192488869)⟩,⟨2545203565009686043732846724401,2545203565009686043925245787083⟩⟩,⟨⟨(-1933532395466533894911546553125),(-1933532395466533894696063115291)⟩,⟨2546895347298805684785510518577,2546895347298805684978308330793⟩⟩,⟨⟨(-1929488301446297489919383233017),(-1929488301446297489703597841424)⟩,⟨2548636368055606875572722753437,2548636368055606875765931938231⟩⟩,⟨⟨(-1925312020275339498004937049311),(-1925312020275339497788838820207)⟩,⟨2550425724163384716684372677824,2550425724163384716878007575661⟩⟩] +lemma kernel1_1_r5_1_eq : ∀ k : Fin 16, kernel1_1Expr 5 1 k = kernel1_1_r5_1 k := by decide +kernel +noncomputable def kernel1_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-1921003835081997181797566400816),(-1921003835081997181581146688895)⟩,⟨2552262486141083513113728212740,2552262486141083513307800932533⟩⟩,⟨⟨(-1916564042149149611533973428384),(-1916564042149149611317220906330)⟩,⟨2554145698519883935385976519051,2554145698519883935580501803651⟩⟩,⟨⟨(-1911992951265577587341071017775),(-1911992951265577587123977032365)⟩,⟨2556074380233156526789581527300,2556074380233156526984571455139⟩⟩,⟨⟨(-1907290886083402163003198976634),(-1907290886083402162785752253347)⟩,⟨2558047525019855095082361782674,2558047525019855095277831005877⟩⟩,⟨⟨(-1902458184481159401188302100428),(-1902458184481159400970494608170)⟩,⟨2560064101841419433094024232051,2560064101841419433289984172452⟩⟩,⟨⟨(-1897495198932057468043552719800),(-1897495198932057467825372613355)⟩,⟨2562123055312252183993105845855,2562123055312252184189571679521⟩⟩,⟨⟨(-1892402296876950892178290998594),(-1892402296876950891959730232575)⟩,⟨2564223306143829496276528972536,2564223306143829496473512091988⟩⟩,⟨⟨(-1887179861101555785614657748447),(-1887179861101555785395704546090)⟩,⟨2566363751602499394297096195853,2566363751602499394494611666350⟩⟩,⟨⟨(-1881828290117419069163209679436),(-1881828290117419068943856920447)⟩,⟨2568543265981015516801158173142,2568543265981015516999216424685⟩⟩,⟨⟨(-1876347998546144279292100699355),(-1876347998546144279072335744225)⟩,⟨2570760701083847043881664793067,2570760701083847044080281700087⟩⟩,⟨⟨(-1870739417506366375865222541197),(-1870739417506366375645038102456)⟩,⟨2573014886726298238315439755208,2573014886726298238514625864593⟩⟩,⟨⟨(-1865002995002958138609145877853),(-1865002995002958138388529548319)⟩,⟨2575304631247463067813457466825,2575304631247463068013228375331⟩⟩,⟨⟨(-1859139196317941253808846530599),(-1859139196317941253587792125711)⟩,⟨2577628722037031848680448671825,2577628722037031848880813781248⟩⟩,⟨⟨(-1853148504402566070976604427261),(-1853148504402566070755098512465)⟩,⟨2579985926075957758244043063898,2579985926075957758445018939747⟩⟩,⟨⟨(-1847031420270015271975440107507),(-1847031420270015271753476320072)⟩,⟨2582374990490981403773771734757,2582374990490981403975367901382⟩⟩,⟨⟨(-1840788463388178362605280847212),(-1840788463388178362382846009588)⟩,⟨2584794643123001411207986248829,2584794643123001411410218964989⟩⟩] +lemma kernel1_1_r5_2_eq : ∀ k : Fin 16, kernel1_1Expr 5 2 k = kernel1_1_r5_2 k := by decide +kernel +noncomputable def kernel1_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-1834420172071935989646429627024),(-1834420172071935989423518983249)⟩,⟨2587243593109268210757376668275,2587243593109268210960253806375⟩⟩,⟨⟨(-1827927103874385625806820574502),(-1827927103874385625583419430959)⟩,⟨2589720531479366852474709602835,2589720531479366852678248872181⟩⟩,⟨⟨(-1821309835976433172236857990849),(-1821309835976433172012961091024)⟩,⟨2592224131764942788521756551574,2592224131764942788725966261796⟩⟩,⟨⟨(-1814568965574168524810632396192),(-1814568965574168524586225638903)⟩,⟨2594753050623112116734524131552,2594753050623112116939421347795⟩⟩,⟨⟨(-1807705110263437157981466533973),(-1807705110263437157756546443290)⟩,⟨2597305928473484800081586976790,2597305928473484800287178176638⟩⟩,⟨⟨(-1800718908421014320617071676154),(-1800718908421014320391622477297)⟩,⟨2599881390148715867930951646617,2599881390148715868137255499767⟩⟩,⟨⟨(-1793611019581783533822672809893),(-1793611019581783533596690550610)⟩,⟨2602478045558485578225512830435,2602478045558485578432536222490⟩⟩,⟨⟨(-1786382124811316753438693891238),(-1786382124811316753212163381369)⟩,⟨2605094490366794986604859095710,2605094490366794986812620055308⟩⟩,⟨⟨(-1779032927073249831714745936645),(-1779032927073249831487665730870)⟩,⟨2607729306682448342464292421603,2607729306682448342672795271704⟩⟩,⟨⟨(-1771564151590843805611309832441),(-1771564151590843805383662361259)⟩,⟨2610381063762578227559721916075,2610381063762578227768986989953⟩⟩,⟨⟨(-1763976546202120075133282098367),(-1763976546202120074905064927871)⟩,⟨2613048318729053386102733043883,2613048318729053386312765577077⟩⟩,⟨⟨(-1756270881707955735734145176544),(-1756270881707955735505341848798)⟩,⟨2615729617297592783808911381733,2615729617297592784019730537745⟩⟩,⟨⟨(-1748447952212524215564934903673),(-1748447952212524215335545682997)⟩,⟨2618423494519392595953803279759,2618423494519392596165411532039⟩⟩,⟨⟨(-1740508575455465962272805637308),(-1740508575455465962042811515558)⟩,⟨2621128475535055581470296161293,2621128475535055581682715147412⟩⟩,⟨⟨(-1732453593135174245875326087328),(-1732453593135174245644726379307)⟩,⟨2623843076340594673236780918190,2623843076340594673450013980536⟩⟩,⟨⟨(-1724283871222582214176834751380),(-1724283871222582213945611540944)⟩,⟨2626565804565264627133142453878,2626565804565264627347210074940⟩⟩] +lemma kernel1_1_r5_3_eq : ∀ k : Fin 16, kernel1_1Expr 5 3 k = kernel1_1_r5_3 k := by decide +kernel +noncomputable def kernel1_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-1716000300264839174934827078922),(-1716000300264839174702983512133)⟩,⟨2629295160260957248785146527063,2629295160260957249000048147462⟩⟩,⟨⟨(-1707603795678266703593209677169),(-1707603795678266703360724181137)⟩,⟨2632029636702877083196543097380,2632029636702877083412302777112⟩⟩,⟨⟨(-1699095298029988605242675122838),(-1699095298029988605009549006067)⟩,⟨2634767721201195536110313600974,2634767721201195536326932530840⟩⟩,⟨⟨(-1690475773307633012142005996135),(-1690475773307633011908219682978)⟩,⟨2637507895923362225762527309574,2637507895923362225980027487153⟩⟩,⟨⟨(-1681746213176509990377312412934),(-1681746213176509990142871106112)⟩,⟨2640248638726732969884937784924,2640248638726732970103316425410⟩⟩,⟨⟨(-1672907635223673976858045226163),(-1672907635223673976622925652718)⟩,⟨2642988424001154226911425098612,2642988424001154227130707819409⟩⟩,⟨⟨(-1663961083188287185641399709980),(-1663961083188287185405605431725)⟩,⟨2645725723521124065207113997502,2645725723521124065427299563999⟩⟩,⟨⟨(-1654907627177707824241207900661),(-1654907627177707824004717470250)⟩,⟨2648459007307129863910362223675,2648459007307129864131474356928⟩⟩,⟨⟨(-1645748363868735558635873746845),(-1645748363868735558398696077267)⟩,⟨2651186744495742989053442762512,2651186744495742989275474783627⟩⟩,⟨⟨(-1636484416693456171411985438102),(-1636484416693456171174093957888)⟩,⟨2653907404218030675610006309666,2653907404218030675832986988804⟩⟩,⟨⟨(-1627116936009137780796083975999),(-1627116936009137780557484772848)⟩,⟨2656619456485825317775001874393,2656619456485825317998927263966⟩⟩,⟨⟨(-1617647099251642337755045556399),(-1617647099251642337515715088091)⟩,⟨2659321373085371364992643803097,2659321373085371365217539568511⟩⟩,⟨⟨(-1608076111071828400906471495811),(-1608076111071828400666421256750)⟩,⟨2662011628477850079947247351997,2662011628477850080173104032470⟩⟩,⟨⟨(-1598405203454434410128613158159),(-1598405203454434409887814452882)⟩,⟨2664688700706262577848831430371,2664688700706262578075679774621⟩⟩,⟨⟨(-1588635635818945843298833813978),(-1588635635818945843057295542470)⟩,⟨2667351072308131875743118130767,2667351072308131875970951176112⟩⟩,⟨⟨(-1578768695101964748609627890491),(-1578768695101964748367324182244)⟩,⟨2669997231233465178972262345320,2669997231233465179201107934357⟩⟩] +lemma kernel1_1_r5_4_eq : ∀ k : Fin 16, kernel1_1Expr 5 4 k = kernel1_1_r5_4 k := by decide +kernel +noncomputable def kernel1_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-1568805695820616197706248937347),(-1568805695820616197463196268666)⟩,⟨2672625671767398362815778477855,2672625671767398363045621944755⟩⟩,⟨⟨(-1558747980116543200900539255226),(-1558747980116543200656704473261)⟩,⟨2675234895456925614958154542835,2675234895456925615189030954387⟩⟩,⟨⟨(-1548596917780059561453141264919),(-1548596917780059561208536375263)⟩,⟨2677823412041098533592869484839,2677823412041098533824768553526⟩⟩,⟨⟨(-1538353906254049015911220069621),(-1538353906254049015665816637646)⟩,⟨2680389740384060672039803532002,2680389740384060672272755514666⟩⟩,⟨⟨(-1528020370617218804221234884025),(-1528020370617218803975052194674)⟩,⟨2682932409410265629524248265056,2682932409410265629758235452896⟩⟩,⟨⟨(-1517597763546336527192416257652),(-1517597763546336526945418916816)⟩,⟨2685449959041209355373396525256,2685449959041209355608456084577⟩⟩,⟨⟨(-1507087565257100768097106197909),(-1507087565257100767849309628181)⟩,⟨2687940941132990406704174842545,2687940941132990406940292832589⟩⟩,⟨⟨(-1496491283423318465800005411908),(-1496491283423318465551378361620)⟩,⟨2690403920413995524201210279779,2690403920413995524438419627765⟩⟩,⟨⟨(-1485810453074085412608182576718),(-1485810453074085412358750354256)⟩,⟨2692837475421992113336255661469,2692837475421992113574532367082⟩⟩,⟨⟨(-1475046636468690492560420002904),(-1475046636468690492310141835822)⟩,⟨2695240199439894085778121404013,2695240199439894086017507889666⟩⟩,⟨⟨(-1464201422948989354352634617839),(-1464201422948989354101529657978)⟩,⟨2697610701429453073994497183978,2697610701429453074234975525911⟩⟩,⟨⟨(-1453276428769019104431058444630),(-1453276428769019104179092372540)⟩,⟨2699947606962113327020477109462,2699947606962113327262083161243⟩⟩,⟨⟨(-1442273296901652284530788492170),(-1442273296901652284277990012942)⟩,⟨2702249559146255672476429293605,2702249559146255672719135387403⟩⟩,⟨⟨(-1431193696822115836300449971359),(-1431193696822115836046775606712)⟩,⟨2704515219550043833978456700846,2704515219550043834222307835141⟩⟩,⟨⟨(-1420039324268228923472372529159),(-1420039324268228923217845488044)⟩,⟨2706743269119075168207456324853,2706743269119075168452430247056⟩⟩,⟨⟨(-1408811900977242346799876487478),(-1408811900977242346544459119106)⟩,⟨2708932409088027575341190321409,2708932409088027575587326082411⟩⟩] +lemma kernel1_1_r5_5_eq : ∀ k : Fin 16, kernel1_1Expr 5 5 k = kernel1_1_r5_5 k := by decide +kernel +noncomputable def kernel1_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-1397513174399191813820234429642),(-1397513174399191813563963334450)⟩,⟨2711081361885484982588463279440,2711081361885484982835724990882⟩⟩,⟨⟨(-1386144917386707477221279425962),(-1386144917386707476964104009026)⟩,⟨2713188872031115444352460171253,2713188872031115444600899861530⟩⟩,⟨⟨(-1374708927861252892682987526384),(-1374708927861252892424935376107)⟩,⟨2715253707024368584007012354709,2715253707024368584256603101892⟩⟩,⟨⟨(-1363207028455797827757751023987),(-1363207028455797827498780899869)⟩,⟨2717274658223852859915851610045,2717274658223852860166635930242⟩⟩,⟨⟨(-1351641066133961133624896451573),(-1351641066133961133365048206026)⟩,⟨2719250541716548009170082247252,2719250541716548009422020698118⟩⟩,⟨⟨(-1340012911785692125209415072786),(-1340012911785692124948635673970)⟩,⟨2721180199176004041906661109016,2721180199176004042159808040450⟩⟩,⟨⟨(-1328324459799591553854231366316),(-1328324459799591553592553120795)⟩,⟨2723062498708675360564428053889,2723062498708675360818751517519⟩⟩,⟨⟨(-1316577627612006250085836083907),(-1316577627612006249823213887954)⟩,⟨2724896335687536993665608481417,2724896335687536993921154743971⟩⟩,⟨⟨(-1304774355233064809617066577407),(-1304774355233064809353549300201)⟩,⟨2726680633572129592269053347295,2726680633572129592525773568160⟩⟩,⟨⟨(-1292916604749855239288829512165),(-1292916604749855239024356019155)⟩,⟨2728414344714180766524751592995,2728414344714180766782708181104⟩⟩,⟨⟨(-1281006359806979215031029946259),(-1281006359806979214765637587025)⟩,⟨2730096451147952564871005545905,2730096451147952565130161183359⟩⟩,⟨⟨(-1269045625064751473273906209913),(-1269045625064751473007545758358)⟩,⟨2731725965364468442021480877290,2731725965364468442281885854515⟩⟩,⟨⟨(-1257036425635346801084216697104),(-1257036425635346800816940960262)⟩,⟨2733301931068777944122492720054,2733301931068777944384093919634⟩⟩,⟨⟨(-1244980806497231047661726415471),(-1244980806497231047393471266274)⟩,⟨2734823423919423577785451701513,2734823423919423578048314437882⟩⟩,⟨⟨(-1232880831888246488337518451598),(-1232880831888246488068326623895)⟩,⟨2736289552249281938827898315432,2736289552249281939091979541790⟩⟩,⟨⟨(-1220738584677755668250098752144),(-1220738584677755667979916622073)⟩,⟨2737699457766960168322528868244,2737699457766960168587883190333⟩⟩] +lemma kernel1_1_r5_6_eq : ∀ k : Fin 16, kernel1_1Expr 5 6 k = kernel1_1_r5_6 k := by decide +kernel +noncomputable def kernel1_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-1208556165718281471687694433706),(-1208556165718281471416586334359)⟩,⟨2739052316237939186842041725956,2739052316237939187108604039518⟩⟩,⟨⟨(-1196335693177114538961301817876),(-1196335693177114538689193151860)⟩,⟨2740347338144666938419076800700,2740347338144666938686922921439⟩⟩,⟨⟨(-1184079301848392219057431840956),(-1184079301848392218784371041906)⟩,⟨2741583769324818056417072899052,2741583769324818056686153718283⟩⟩,⟨⟨(-1171789142446185935999825918112),(-1171789142446185935725754712739)⟩,⟨2742760891586950943710672563100,2742760891586950943981047271538⟩⟩,⟨⟨(-1159467380879166092089744011195),(-1159467380879166091814729993959)⟩,⟨2743878023302809235527327740226,2743878023302809235798927617282⟩⟩,⟨⟨(-1147116197507445363933622703716),(-1147116197507445363657589080009)⟩,⟨2744934519975531977883681654432,2744934519975531978156584643838⟩⟩,⟨⟨(-1134737786382232399160530993502),(-1134737786382232398883532231927)⟩,⟨2745929774783055597278043312969,2745929774783055597552193891756⟩⟩,⟨⟨(-1122334354468958424761385707738),(-1122334354468958424483358612072)⟩,⟨2746863219096010844258410846012,2746863219096010844533873083744⟩⟩,⟨⟨(-1109908120854569064004645058241),(-1109908120854569063725669921345)⟩,⟨2747734322969439347329918257199,2747734322969439347606610209871⟩⟩,⟨⟨(-1097461315939702660250552645173),(-1097461315939702659970541156888)⟩,⟨2748542595607677193571600579390,2748542595607677193849611807415⟩⟩,⟨⟨(-1084996180616504555598260346299),(-1084996180616504555317273308721)⟩,⟨2749287585801777034020835996682,2749287585801777034300104248347⟩⟩,⟨⟨(-1072514965432854003831708169139),(-1072514965432854003549677223936)⟩,⟨2749968882338865567588964254239,2749968882338865567869558738710⟩⟩,⟨⟨(-1060019929743806645186396568127),(-1060019929743806644903405930054)⟩,⟨2750586114382859855791112752368,2750586114382859856072947218689⟩⟩,⟨⟨(-1047513340851080670807255505389),(-1047513340851080670523214125617)⟩,⟨2751138951825993727255854386123,2751138951825993727539021105693⟩⟩,⟨⟨(-1034997473131438894492650447804),(-1034997473131438894207625778933)⟩,⟨2751627105610634507800744385548,2751627105610634508085174045441⟩⟩,⟨⟨(-1022474607154841867055840948042),(-1022474607154841866769759209155)⟩,⟨2752050328020900417428277596057,2752050328020900417714044829262⟩⟩] +lemma kernel1_1_r5_7_eq : ∀ k : Fin 16, kernel1_1Expr 5 7 k = kernel1_1_r5_7 k := by decide +kernel +noncomputable def kernel1_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-1009947028793268854721338385227),(-1009947028793268854434300066414)⟩,⟨2752408412943620165258338691380,2752408412943620165545340333860⟩⟩,⟨⟨(-997417028321123899682411422996),(-997417028321123899394310479873)⟩,⟨2752701196098208499278606071405,2752701196098208499566949619832⟩⟩,⟨⟨(-984886899508163232632574349491),(-984886899508163232343485145568)⟩,⟨2752928555235064678864902162748,2752928555235064679154510969153⟩⟩,⟨⟨(-972358938705897960412534278854),(-972358938705897960122377402299)⟩,⟨2753090410302134980243386981526,2753090410302134980534341335240⟩⟩,⟨⟨(-959835443928442155996374297661),(-959835443928442155705252342009)⟩,⟨2753186723579315361473297204216,2753186723579315361765491475952⟩⟩,⟨⟨(-947318713928791184657183245905),(-947318713928791184364989368163)⟩,⟨2753217499780406244325365203508,2753217499780406244618907659607⟩⟩,⟨⟨(-934811047271528263877612015597),(-934811047271528263584427783568)⟩,⟨2753182786122367953160614645177,2753182786122367953455420996194⟩⟩,⟨⟨(-922314741402968832984799861915),(-922314741402968832690539987452)⟩,⟨2753082672361662620554027975921,2753082672361662620850184439165⟩⟩,⟨⟨(-909832091719762262288545705422),(-909832091719762261993329798953)⟩,⟨2752917290797506258565895198697,2752917290797506258863278432035⟩⟩,⟨⟨(-897365390636978724698032410394),(-897365390636978724401738019120)⟩,⟨2752686816241893133592007872056,2752686816241893133890742065233⟩⟩,⟨⟨(-884916926656715652806073287025),(-884916926656715652508789405529)⟩,⟨2752391465956293499936548621850,2752391465956293500236541611087⟩⟩,⟨⟨(-872488983438263082272165836044),(-872488983438263081973801119703)⟩,⟨2752031499554965069054762679762,2752031499554965069356106816316⟩⟩,⟨⟨(-860083838870870312682021373598),(-860083838870870312382698455187)⟩,⟨2751607218874858242544719701237,2751607218874858242847288235522⟩⟩,⟨⟨(-847703764150157678417379934226),(-847703764150157678116974698007)⟩,⟨2751118967812135040641814836996,2751118967812135040945733647502⟩⟩,⟨⟨(-835351022859216796820720029414),(-835351022859216796519329143726)⟩,⟨2750567132125361736133050612781,2750567132125361736438219404625⟩⟩,⟨⟨(-823027870055440435494361351170),(-823027870055440435191887204804)⟩,⟨2749952139205475377097213309305,2749952139205475377403730805211⟩⟩] +lemma kernel1_1_r5_8_eq : ∀ k : Fin 16, kernel1_1Expr 5 8 k = kernel1_1_r5_8 k := by decide +kernel +noncomputable def kernel1_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-810736551364119105391583719311),(-810736551364119105088170328805)⟩,⟨2749274457812664570691148710036,2749274457812664570998865935866⟩⟩,⟨⟨(-798479302079835636070570251414),(-798479302079835635766073620154)⟩,⟨2748534597780345023669436150002,2748534597780345023978499357123⟩⟩,⟨⟨(-786258346276681322892728218728),(-786258346276681322587252845115)⟩,⟨2747733109686450312387178076229,2747733109686450312697478676108⟩⟩,⟨⟨(-774075895928307756127936459988),(-774075895928307755821378341222)⟩,⟨2746870584492298104422388474104,2746870584492298104734031711655⟩⟩,⟨⟨(-761934150038817156191873987244),(-761934150038817155884377263734)⟩,⟨2745947653149331494477419555354,2745947653149331494790256023007⟩⟩,⟨⟨(-749835293785480959211764184568),(-749835293785480958903186136444)⟩,⟨2744964986174074167946025592309,2744964986174074168260200255358⟩⟩,⟨⟨(-737781497674261538676969428405),(-737781497674261538367422587203)⟩,⟨2743923293191676686091529652478,2743923293191676686406925419447⟩⟩,⟨⟨(-725774916709095332263753301513),(-725774916709095331953127093180)⟩,⟨2742823322448469217533507870258,2742823322448469217850236715300⟩⟩,⟨⟨(-713817689575877292426272442545),(-713817689575877292114732881769)⟩,⟨2741665860293973443084387525453,2741665860293973443402277277237⟩⟩,⟨⟨(-701911937842066523652306780918),(-701911937842066523339690822037)⟩,⟨2740451730632863057521148421510,2740451730632863057840364954268⟩⟩,⟨⟨(-690059765172811241142480739254),(-690059765172811240828909040105)⟩,⟨2739181794347398206740078946913,2739181794347398207060496571117⟩⟩,⟨⟨(-678263256564467821949947507347),(-678263256564467821635302849058)⟩,⟨2737856948690894257718524905904,2737856948690894258040262422929⟩⟩,⟨⟨(-666524477596363761140700129171),(-666524477596363760825149423192)⟩,⟨2736478126652819429564854321308,2736478126652819429887738347262⟩⟩,⟨⟨(-654845473701627837067794018206),(-654845473701627836751174762302)⟩,⟨2735046296296148946568431289988,2735046296296148946892627197332⟩⟩,⟨⟨(-643228269457882779917229821919),(-643228269457882779599670934297)⟩,⟨2733562460067635440872795825301,2733562460067635441198169190454⟩⟩,⟨⟨(-631674867898566278506911953271),(-631674867898566278188289447061)⟩,⟨2732027654081686268047209745968,2732027654081686268373886346198⟩⟩] +lemma kernel1_1_r5_9_eq : ∀ k : Fin 16, kernel1_1Expr 5 9 k = kernel1_1_r5_9 k := by decide +kernel +noncomputable def kernel1_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-620187249845615307630249274520),(-620187249845615307310758027012)⟩,⟨2730442947378568141113807675142,2730442947378568141441585064021⟩⟩,⟨⟨(-608767373264216571186540303764),(-608767373264216570865991448012)⟩,⟨2728809441157687978138083526470,2728809441157687978467154276520⟩⟩,⟨⟨(-597417172640292397278831179198),(-597417172640292396957361886996)⟩,⟨2727128267986726039159161528666,2727128267986726039489382492485⟩⟩,⟨⟨(-586138558381356755835020471093),(-586138558381356755512499999227)⟩,⟨2725400590987423247181700276849,2725400590987423247513204216825⟩⟩,⟨⟨(-574933416241340265411047725220),(-574933416241340265087666695930)⟩,⟨2723627602998848995886701451254,2723627602998848996219290031070⟩⟩,⟨⟨(-563803606769946184693423889488),(-563803606769946184368999112320)⟩,⟨2721810525718998697981531140744,2721810525718998698315391177875⟩⟩,⟨⟨(-552750964787061519314725207567),(-552750964787061518989402184227)⟩,⟨2719950608825591780889100608715,2719950608825591781224080157681⟩⟩,⟨⟨(-541777298882708591744311902059),(-541777298882708591417953055985)⟩,⟨2718049129076960752857025281555,2718049129076960753193264189424⟩⟩,⟨⟨(-530884390942982799067980791205),(-530884390942982798740803844472)⟩,⟨2716107389393940308730774806964,2716107389393940309068046538215⟩⟩,⟨⟨(-520073995702381900175055335194),(-520073995702381899846851584384)⟩,⟨2714126717923682190874235657416,2714126717923682191212753430748⟩⟩,⟨⟨(-509347840322891111570125595125),(-509347840322891111241048783763)⟩,⟨2712108467086336641618997053725,2712108467086336641958600221860⟩⟩,⟨⟨(-498707624000146632505527553505),(-498707624000146632175433353284)⟩,⟨2710054012605554758036247139596,2710054012605554758377082569242⟩⟩,⟨⟨(-488155017596958049299377173119),(-488155017596958048968480560511)⟩,⟨2707964752523777871032879832974,2707964752523777871374723573938⟩⟩,⟨⟨(-477691663304427470450070157082),(-477691663304427470118166591685)⟩,⟨2705842106203290206431142281038,2705842106203290206774203374376⟩⟩,⟨⟨(-467319174330860304015652585995),(-467319174330860303682904035587)⟩,⟨2703687513314019537952778951089,2703687513314019538296888072251⟩⟩,⟨⟨(-457039134618619392727764386180),(-457039134618619392394019776110)⟩,⟨2701502432809077307466330287531,2701502432809077307811641334868⟩⟩] +lemma kernel1_1_r5_10_eq : ∀ k : Fin 16, kernel1_1Expr 5 10 k = kernel1_1_r5_10 k := by decide +kernel +noncomputable def kernel1_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-446853098589030856653820742499),(-446853098589030856319329036902)⟩,⟨2699288341889034767554032403638,2699288341889034767900286092221⟩⟩,⟨⟨(-436762590915406544127137053729),(-436762590915406543791661315839)⟩,⟨2697046734955935100895687647593,2697046734955935101243126597596⟩⟩,⟨⟨(-426769106324204545040816273879),(-426769106324204544704526483337)⟩,⟨2694779122558043200098928827190,2694779122558043200447375263330⟩⟩,⟨⟨(-416874109424305861905255158404),(-416874109424305861567993689223)⟩,⟨2692487030326334864695621116509,2692487030326334865045235783482⟩⟩,⟨⟨(-407079034564342147978685581717),(-407079034564342147640691966602)⟩,⟨2690171997903725607699762544421,2690171997903725608050295680924⟩⟩,⟨⟨(-397385285717966492068666630876),(-397385285717966491729714716335)⟩,⟨2687835577868036085187997546189,2687835577868036085539680771709⟩⟩,⟨⟨(-387794236396916638814186950239),(-387794236396916638474454640718)⟩,⟨2685479334649686395819317067714,2685479334649686396171964254045⟩⟩,⟨⟨(-378307229591677862595765882866),(-378307229591677862255089067083)⟩,⟨2683104843445105174039978511843,2683104843445105174393757195864⟩⟩,⟨⟨(-368925577739511042235821547448),(-368925577739511041894472247893)⟩,⟨2680713689126831555880202266881,2680713689126831556234828879151⟩⟩,⟨⟨(-359650562719570390146175320795),(-359650562719570389803896426770)⟩,⟨2678307465151278768433709126472,2678307465151278768789447444533⟩⟩,⟨⟨(-350483435874794849311885642483),(-350483435874794848968862672745)⟩,⟨2675887772465117325713682072688,2675887772465117326070337944870⟩⟩,⟨⟨(-341425418060217458106926882125),(-341425418060217457762989526062)⟩,⟨2673456218411223650431202806770,2673456218411223650788950278859⟩⟩,⟨⟨(-332477699717298067651004409540),(-332477699717298067306416579294)⟩,⟨2671014415635126432561273615574,2671014415635126432919837317141⟩⟩,⟨⟨(-323641440973846748018200110851),(-323641440973846747672714120174)⟩,⟨2668563980992868233657177784305,2668563980992868234016811896645⟩⟩,⟨⟨(-314917771769068104159520040493),(-314917771769068103813328825595)⟩,⟨2666106534461183806081248884821,2666106534461183806441751445222⟩⟩,⟨⟨(-306307792003220603218842032774),(-306307792003220602871769254104)⟩,⟨2663643698050879376689693587604,2663643698050879377051244984657⟩⟩] +lemma kernel1_1_r5_11_eq : ∀ k : Fin 16, kernel1_1Expr 5 11 k = kernel1_1_r5_11 k := by decide +kernel +noncomputable def kernel1_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-297812571711349952335270815405),(-297812571711349951987622519247)⟩,⟨2661177094724278805720194007314,2661177094724278806082475058596⟩⟩,⟨⟨(-289433151260521617374888824378),(-289433151260521617026376700557)⟩,⟨2658708347317583136665585598628,2658708347317583137028892707451⟩⟩,⟨⟨(-281170541569944792454136937079),(-281170541569944792104960877430)⟩,⟨2656239077468969666962040367700,2656239077468969667326164247526⟩⟩,⟨⟨(-273025724353348568554926523378),(-273025724353348568204904588375)⟩,⟨2653770904553235359427303118955,2653770904553235359792430065217⟩⟩,⟨⟨(-264999652382940754556207687721),(-264999652382940754205627441264)⟩,⟨2651305444623767249367012736287,2651305444623767249732842547812⟩⟩,⟨⟨(-257093249774250819862860529603),(-257093249774250819511453361947)⟩,⟨2648844309362599552342772140390,2648844309362599552709580977133⟩⟩,⟨⟨(-249307412291130795244431987917),(-249307412291130794892404479930)⟩,⟨2646389105039293514283139534720,2646389105039293514650711071492⟩⟩,⟨⟨(-241643007670161724829095062994),(-241643007670161724476259914551)⟩,⟨2643941431479351741376485275400,2643941431479351741745011472569⟩⟩,⟨⟨(-234100875963688441191332164423),(-234100875963688440838014715670)⟩,⟨2641502881042853875300619844230,2641502881042853875669761187939⟩⟩,⟨⟨(-226681829900682067425192708503),(-226681829900682067071087989598)⟩,⟨2639075037613975113573390094652,2639075037613975113943460596395⟩⟩,⟨⟨(-219386655264607761724343795966),(-219386655264607761369664521912)⟩,⟨2636659475602023289265536405420,2636659475602023289636313285666⟩⟩,⟨⟨(-212216111287454834561150999002),(-212216111287454834205705032046)⟩,⟨2634257758954604093113509714228,2634257758954604093485190060161⟩⟩,⟨⟨(-205170931059067505779808993538),(-205170931059067505423906413895)⟩,⟨2631871440183497618214534254434,2631871440183497618586794239934⟩⟩,⟨⟨(-198251821950897245112497804193),(-198251821950897244755850081463)⟩,⟨2629502059403802806520413784243,2629502059403802806893550535963⟩⟩,⟨⟨(-191459466053281867633457708298),(-191459466053281867276283293269)⟩,⟨2627151143386879650256971589950,2627151143386879650630756295945⟩⟩,⟨⟨(-184794520625342345031139925661),(-184794520625342344673242211284)⟩,⟨2624820204627592222259120030092,2624820204627592222633754524143⟩⟩] +lemma kernel1_1_r5_12_eq : ∀ k : Fin 16, kernel1_1Expr 5 12 k = kernel1_1_r5_12 k := by decide +kernel +noncomputable def kernel1_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-178257618556575650493151078607),(-178257618556575650134887827817)⟩,⟨2622510740426328848112979398659,2622510740426328848488090251433⟩⟩,⟨⟨(-171849368839210882500108389836),(-171849368839210882141144764751)⟩,⟨2620224231986249059686759724751,2620224231986249060062692268377⟩⟩,⟨⟨(-165570357050386410750016503964),(-165570357050386410390575972018)⟩,⟨2617962143526180452460871229684,2617962143526180452837391374679⟩⟩,⟨⟨(-159421145843197852646109023258),(-159421145843197852285991194582)⟩,⟨2615725921409562274650641671689,2615725921409562275027955286114⟩⟩,⟨⟨(-153402275445660315127219364855),(-153402275445660314766755064105)⟩,⟨2613516993289806569288601956906,2613516993289806569666363459328⟩⟩,⟨⟨(-147514264166623515185323282766),(-147514264166623514824205697970)⟩,⟨2611336767272422033928564904829,2611336767272422034307090695480⟩⟩,⟨⟨(-141757608907675111490657434835),(-141757608907675111129114584635)⟩,⟨2609186631094220517053838026578,2609186631094220517432889229894⟩⟩,⟨⟨(-136132785680065824885640181994),(-136132785680065824523468334333)⟩,⟨2607067951319901293786241073116,2607067951319901294166027131740⟩⟩,⟨⟨(-130640250125689680319808755041),(-130640250125689679957381378376)⟩,⟨2604982072556284011827684847357,2604982072556284012207815797291⟩⟩,⟨⟨(-125280438041153948000234108009),(-125280438041153947637203030147)⟩,⟨2602930316684437524720520050445,2602930316684437525101355385501⟩⟩,⟨⟨(-120053765903976075754851736111),(-120053765903976075391448704580)⟩,⟨2600913982109928783769800432815,2600913982109928784151097353100⟩⟩,⟨⟨(-114960631399949064461001491393),(-114960631399949064097020223682)⟩,⟨2598934343031393589631660950251,2598934343031393590013631647131⟩⟩,⟨⟨(-110001413950722318463707741652),(-110001413950722318099497587457)⟩,⟨2596992648727609353995429932522,2596992648727609354377709406019⟩⟩,⟨⟨(-105176475240651976042542477887),(-105176475240651975677780441025)⟩,⟨2595090122863229132134511673246,2595090122863229132517433407862⟩⟩,⟨⟨(-100486159741983062275283841853),(-100486159741983061910204795942)⟩,⟨2593227962813316096402896955288,2593227962813316096786214860412⟩⟩,⟨⟨(-95930795237435477714884764718),(-95930795237435477349280458299)⟩,⟨2591407339006798363680935652674,2591407339006798364064864058589⟩⟩] +lemma kernel1_1_r5_13_eq : ∀ k : Fin 16, kernel1_1Expr 5 13 k = kernel1_1_r5_13 k := by decide +kernel +noncomputable def kernel1_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-91510693339276809291448529649),(-91510693339276808925724330811)⟩,⟨2589629394288945697718572697739,2589629394288945698102688318726⟩⟩,⟨⟨(-87226150003977191724297148943),(-87226150003977191358075286878)⟩,⟨2587895243302952108196105947536,2587895243302952108580799309636⟩⟩,⟨⟨(-83077446041554924223197575491),(-83077446041554923856715045660)⟩,⟨2586205971890691786653944751633,2586205971890691787038967524095⟩⟩,⟨⟨(-79064847618736223182339321304),(-79064847618736222815386877580)⟩,⟨2584562636512700176202952819716,2584562636512700176588520452340⟩⟩,⟨⟨(-75188606755068330778948890142),(-75188606755068330411891473322)⟩,⟨2582966263687417284655724736529,2582966263687417285041455891759⟩⟩,⟨⟨(-71448961811142165056560375325),(-71448961811142164689061625540)⟩,⟨2581417849449716633352240203570,2581417849449716633738482490882⟩⟩,⟨⟨(-67846137968098751661170874994),(-67846137968098751293469251956)⟩,⟨2579918358828730496983690993287,2579918358828730497370194531683⟩⟩,⟨⟨(-64380347697612782917385956710),(-64380347697612782549271862094)⟩,⟨2578468725344970340046022774949,2578468725344970340433003457355⟩⟩,⟨⟨(-61051791221566767901133194807),(-61051791221566767533018263092)⟩,⟨2577069850526730596661064808456,2577069850526730597048092699789⟩⟩,⟨⟨(-57860656960650328866842192341),(-57860656960650328498344521799)⟩,⟨2575722603445754172323500905297,2575722603445754172710971061343⟩⟩,⟨⟨(-54807121971141225809684160732),(-54807121971141225441042590337)⟩,⟨2574427820272129265249698106034,2574427820272129265637360229543⟩⟩,⟨⟨(-51891352369147613025447520407),(-51891352369147612656453160704)⟩,⟨2573186303848379304542314388949,2573186303848379304930383703431⟩⟩,⟨⟨(-49113503741614810087997186071),(-49113503741614809719027220874)⟩,⟨2571998823282700972221104641889,2571998823282700972609186985113⟩⟩,⟨⟨(-46473721543424465626872440287),(-46473721543424465257580395071)⟩,⟨2570866113561299402839557818460,2570866113561299403228011504117⟩⟩,⟨⟨(-43972141479939366609596234899),(-43972141479939366240220512380)⟩,⟨2569788875179764721337643319534,2569788875179764721726218487430⟩⟩,⟨⟨(-41608889874373259710344452423),(-41608889874373259340677672876)⟩,⟨2568767773793430067217126301611,2568767773793430067606036662485⟩⟩] +lemma kernel1_1_r5_14_eq : ∀ k : Fin 16, kernel1_1Expr 5 14 k = kernel1_1_r5_14 k := by decide +kernel +noncomputable def kernel1_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-39384084019391866119410633384),(-39384084019391865749889443205)⟩,⟨2567803439886648138374163300437,2567803439886648138762952817932⟩⟩,⟨⟨(-37297832512378748502355005208),(-37297832512378748132574567087)⟩,⟨2566896468460921045291431152674,2566896468460921045680518907843⟩⟩,⟨⟨(-35350235573827790673127302496),(-35350235573827790303324314111)⟩,⟨2566047418741816867349172115540,2566047418741816867738310009744⟩⟩,⟨⟨(-33541385348352739241445606167),(-33541385348352738871415441506)⟩,⟨2565256813904605716545218108491,2565256813904605716934617035054⟩⟩,⟨⟨(-31871366187833494659441378263),(-31871366187833494289569341045)⟩,⟨2564525140818548306196979320329,2564525140818548306586236612260⟩⟩,⟨⟨(-30340254916248589826417340461),(-30340254916248589456350867866)⟩,⟨2563852849809770956958470256162,2563852849809770957347950690032⟩⟩,⟨⟨(-28948121075773521134476229644),(-28948121075773520764449448960)⟩,⟨2563240354442662611192577387989,2563240354442662611582035531148⟩⟩,⟨⟨(-27695027153755263457734928090),(-27695027153755263087546821275)⟩,⟨2562688031319731728576128809005,2562688031319731728965771837063⟩⟩,⟨⟨(-26581028790204371340515625336),(-26581028790204370970600948108)⟩,⟨2562196219899863857977421590069,2562196219899863858366795380209⟩⟩,⟨⟨(-25606174965477508239950058551),(-25606174965477507869907810955)⟩,⟨2561765222334924178321084751528,2561765222334924178710604504783⟩⟩,⟨⟨(-24770508167855019153146008285),(-24770508167855018783206398912)⟩,⟨2561395303324653327831552548277,2561395303324653328220976904381⟩⟩,⟨⟨(-24074064540750234784095325188),(-24074064540750234414062265604)⟩,⟨2561086689989809348502560866896,2561086689989809348892091897553⟩⟩,⟨⟨(-23516874009319533325537625251),(-23516874009319532955799990458)⟩,⟨2560839571763513511261743747985,2560839571763513511650975044960⟩⟩,⟨⟨(-23098960386274755095188024676),(-23098960386274754725391618498)⟩,⟨2560654100300763106067215052705,2560654100300763106456513160179⟩⟩,⟨⟨(-22820341456732332034652000599),(-22820341456732331665022092456)⟩,⟨2560530389406079927990114061930,2560530389406079928379242756938⟩⟩,⟨⟨(-22681029041966425146454582361),(-22681029041966424776801022362)⟩,⟨2560468514979269112028169165008,2560468514979269112417324354234⟩⟩] +lemma kernel1_1_r5_15_eq : ∀ k : Fin 16, kernel1_1Expr 5 15 k = kernel1_1_r5_15 k := by decide +kernel +noncomputable def kernel1_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel1_1_r5_0,kernel1_1_r5_1,kernel1_1_r5_2,kernel1_1_r5_3,kernel1_1_r5_4,kernel1_1_r5_5,kernel1_1_r5_6,kernel1_1_r5_7,kernel1_1_r5_8,kernel1_1_r5_9,kernel1_1_r5_10,kernel1_1_r5_11,kernel1_1_r5_12,kernel1_1_r5_13,kernel1_1_r5_14,kernel1_1_r5_15] +lemma kernel1_1_r5_eq (i k : Fin 16) : kernel1_1Expr 5 i k = kernel1_1_r5 i k := by + fin_cases i + · exact kernel1_1_r5_0_eq k + · exact kernel1_1_r5_1_eq k + · exact kernel1_1_r5_2_eq k + · exact kernel1_1_r5_3_eq k + · exact kernel1_1_r5_4_eq k + · exact kernel1_1_r5_5_eq k + · exact kernel1_1_r5_6_eq k + · exact kernel1_1_r5_7_eq k + · exact kernel1_1_r5_8_eq k + · exact kernel1_1_r5_9_eq k + · exact kernel1_1_r5_10_eq k + · exact kernel1_1_r5_11_eq k + · exact kernel1_1_r5_12_eq k + · exact kernel1_1_r5_13_eq k + · exact kernel1_1_r5_14_eq k + · exact kernel1_1_r5_15_eq k +noncomputable def kernel1_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel1_1_r0,kernel1_1_r1,kernel1_1_r2,kernel1_1_r3,kernel1_1_r4,kernel1_1_r5] +lemma kernel1_1_eq (j : Fin 6) (i k : Fin 16) : kernel1_1Expr j i k = kernel1_1 j i k := by + fin_cases j + · exact kernel1_1_r0_eq i k + · exact kernel1_1_r1_eq i k + · exact kernel1_1_r2_eq i k + · exact kernel1_1_r3_eq i k + · exact kernel1_1_r4_eq i k + · exact kernel1_1_r5_eq i k +lemma kernel1_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel1_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(1:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel1_1_eq] + unfold kernel1_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans1_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel3_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans3 j i k) +noncomputable def kernel3_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-64242399215998079944),(-64242399215998079785)⟩,⟨266142600220355177011,266142600220355177174⟩⟩,⟨⟨(-64354997217206057035),(-64354997217206056876)⟩,⟨265950609021076589285,265950609021076589448⟩⟩,⟨⟨(-64579692612548738766),(-64579692612548738607)⟩,⟨265566807527798498819,265566807527798498982⟩⟩,⟨⟨(-64915486205677457732),(-64915486205677457572)⟩,⟨264991558116175587554,264991558116175587718⟩⟩,⟨⟨(-65360884238738603082),(-65360884238738602925)⟩,⟨264225405754038912284,264225405754038912446⟩⟩,⟨⟨(-65913904414487865864),(-65913904414487865706)⟩,⟨263269079663194097013,263269079663194097174⟩⟩,⟨⟨(-66572083889359766398),(-66572083889359766240)⟩,⟨262123495496350076328,262123495496350076489⟩⟩,⟨⟨(-67332489206410065404),(-67332489206410065248)⟩,⟨260789757996381689781,260789757996381689941⟩⟩,⟨⟨(-68191728129442981485),(-68191728129442981329)⟩,⟨259269164097503309515,259269164097503309675⟩⟩,⟨⟨(-69145963332140365384),(-69145963332140365231)⟩,⟨257563206420679137365,257563206420679137524⟩⟩,⟨⟨(-70190927888649211643),(-70190927888649211491)⟩,⟨255673577108786370461,255673577108786370617⟩⟩,⟨⟨(-71321942504880659316),(-71321942504880659164)⟩,⟨253602171940743732506,253602171940743732662⟩⟩,⟨⟨(-72533934422751954280),(-72533934422751954128)⟩,⟨251351094658079055960,251351094658079056116⟩⟩,⟨⟨(-73821457922787204226),(-73821457922787204076)⟩,⟨248922661432289844543,248922661432289844697⟩⟩,⟨⟨(-75178716343908108912),(-75178716343908108763)⟩,⟨246319405396898748460,246319405396898748615⟩⟩,⟨⟨(-76599585532917578660),(-76599585532917578512)⟩,⟨243544081164364463533,243544081164364463686⟩⟩] +lemma kernel3_0_r0_0_eq : ∀ k : Fin 16, kernel3_0Expr 0 0 k = kernel3_0_r0_0 k := by decide +kernel +noncomputable def kernel3_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-78077638630133022923),(-78077638630133022776)⟩,⟨240599669245014281125,240599669245014281275⟩⟩,⟨⟨(-79606172091888146850),(-79606172091888146705)⟩,⟨237489380282947360582,237489380282947360731⟩⟩,⟨⟨(-81178232845218569520),(-81178232845218569376)⟩,⟨234216659022440939211,234216659022440939359⟩⟩,⟨⟨(-82786646465003757406),(-82786646465003757262)⟩,⟨230785187917791291667,230785187917791291815⟩⟩,⟨⟨(-84424046259181833782),(-84424046259181833643)⟩,⟨227198890299746311775,227198890299746311918⟩⟩,⟨⟨(-86082903143410685878),(-86082903143410685738)⟩,⟨223461933012738917277,223461933012738917422⟩⟩,⟨⟨(-87755556182743881065),(-87755556182743880929)⟩,⟨219578728439004663956,219578728439004664097⟩⟩,⟨⟨(-89434243674547970741),(-89434243674547970605)⟩,⟨215553935828350444763,215553935828350444904⟩⟩,⟨⟨(-91111134644032640699),(-91111134644032640566)⟩,⟨211392461855814367061,211392461855814367198⟩⟩,⟨⟨(-92778360621419540095),(-92778360621419539963)⟩,⟨207099460333693437417,207099460333693437552⟩⟩,⟨⟨(-94428047567960760265),(-94428047567960760135)⟩,⟨202680331009382544808,202680331009382544941⟩⟩,⟨⟨(-96052347816753449813),(-96052347816753449687)⟩,⟨198140717386126143067,198140717386126143197⟩⟩,⟨⟨(-97643471893600628675),(-97643471893600628552)⟩,⟨193486503510087792621,193486503510087792748⟩⟩,⟨⟨(-99193720083055404301),(-99193720083055404178)⟩,⟨188723809674041615368,188723809674041615494⟩⟩,⟨⟨(-100695513605269562886),(-100695513605269562766)⟩,⟨183858986995427969782,183858986995427969905⟩⟩,⟨⟨(-102141425270358289672),(-102141425270358289553)⟩,⟨178898610834432927177,178898610834432927300⟩⟩] +lemma kernel3_0_r0_1_eq : ∀ k : Fin 16, kernel3_0Expr 0 1 k = kernel3_0_r0_1 k := by decide +kernel +noncomputable def kernel3_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-103524209478698029916),(-103524209478698029797)⟩,⟨173849473026083055609,173849473026083055729⟩⟩,⟨⟨(-104836831437898567328),(-104836831437898567215)⟩,⟨168718572909025761528,168718572909025761644⟩⟩,⟨⟨(-106072495470134267887),(-106072495470134267775)⟩,⟨163513107142620296361,163513107142620296474⟩⟩,⟨⟨(-107224672287080605725),(-107224672287080605616)⟩,⟨158240458313122542254,158240458313122542366⟩⟩,⟨⟨(-108287125113874390290),(-108287125113874390182)⟩,⟨152908182339033257175,152908182339033257285⟩⟩,⟨⟨(-109253934548289610367),(-109253934548289610263)⟩,⟨147523994695019003671,147523994695019003779⟩⟩,⟨⟨(-110119522046681698769),(-110119522046681698666)⟩,⟨142095755483131581822,142095755483131581926⟩⟩,⟨⟨(-110878671934183581159),(-110878671934183581060)⟩,⟨136631453389269805386,136631453389269805487⟩⟩,⟨⟨(-111526551843115448686),(-111526551843115448589)⟩,⟨131139188571872201831,131139188571872201931⟩⟩,⟨⟨(-112058731490571213672),(-112058731490571213576)⟩,⟨125627154538627535519,125627154538627535616⟩⟩,⟨⟨(-112471199713638638106),(-112471199713638638011)⟩,⟨120103619075470958501,120103619075470958596⟩⟩,⟨⟨(-112760379688663967090),(-112760379688663967002)⟩,⟨114576904300228831732,114576904300228831822⟩⟩,⟨⟨(-112923142269348723302),(-112923142269348723217)⟩,⟨109055365920919865541,109055365920919865628⟩⟩,⟨⟨(-112956817387225832336),(-112956817387225832251)⟩,⟨103547371785853044887,103547371785853044973⟩⟩,⟨⟨(-112859203467160908732),(-112859203467160908647)⟩,⟨98061279819226965135,98061279819226965221⟩⟩,⟨⟨(-112628574819915786031),(-112628574819915785949)⟩,⟨92605415441878572722,92605415441878572804⟩⟩] +lemma kernel3_0_r0_2_eq : ∀ k : Fin 16, kernel3_0Expr 0 2 k = kernel3_0_r0_2 k := by decide +kernel +noncomputable def kernel3_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-112263686983445938313),(-112263686983445938233)⟩,⟨87188048582104876343,87188048582104876423⟩⟩,⟨⟨(-111763779994429610529),(-111763779994429610453)⟩,⟨81817370386047442123,81817370386047442201⟩⟩,⟨⟨(-111128579581490462446),(-111128579581490462373)⟩,⟨76501469740950664839,76501469740950664911⟩⟩,⟨⟨(-110358296281621828326),(-110358296281621828255)⟩,⟨71248309727651200406,71248309727651200478⟩⟩,⟨⟨(-109453622491392460846),(-109453622491392460775)⟩,⟨66065704120904061312,66065704120904061383⟩⟩,⟨⟨(-108415727474553094450),(-108415727474553094383)⟩,⟨60961294057583592176,60961294057583592242⟩⟩,⟨⟨(-107246250357612054948),(-107246250357612054884)⟩,⟨55942524993404186464,55942524993404186528⟩⟩,⟨⟨(-105947291154748106591),(-105947291154748106527)⟩,⟨51016624068581992153,51016624068581992217⟩⟩,⟨⟨(-104521399873021776740),(-104521399873021776680)⟩,⟨46190578001807261625,46190578001807261685⟩⟩,⟨⟨(-102971563758175346027),(-102971563758175345970)⟩,⟨41471111630026093979,41471111630026094035⟩⟩,⟨⟨(-101301192750320596254),(-101301192750320596197)⟩,⟨36864667208855019811,36864667208855019868⟩⟩,⟨⟨(-99514103227448003456),(-99514103227448003403)⟩,⟨32377384584993193086,32377384584993193138⟩⟩,⟨⟨(-97614500122899182647),(-97614500122899182594)⟩,⟨28015082347781739875,28015082347781739927⟩⟩,⟨⟨(-95606957510676375539),(-95606957510676375490)⟩,⟨23783240062120508587,23783240062120508636⟩⟩,⟨⟨(-93496397759671863335),(-93496397759671863286)⟩,⟨19686981679326777227,19686981679326777274⟩⟩,⟨⟨(-91288069364542890487),(-91288069364542890441)⟩,⟨15731060216251019726,15731060216251019771⟩⟩] +lemma kernel3_0_r0_3_eq : ∀ k : Fin 16, kernel3_0Expr 0 3 k = kernel3_0_r0_3 k := by decide +kernel +noncomputable def kernel3_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-88987523566994119821),(-88987523566994119778)⟩,⟨11919843786098758602,11919843786098758646⟩⟩,⟨⟨(-86600589886623844902),(-86600589886623844862)⟩,⟨8257303056996080386,8257303056996080426⟩⟩,⟨⟨(-84133350685210409069),(-84133350685210409031)⟩,⟨4747000206434462252,4747000206434462290⟩⟩,⟨⟨(-81592114892334221969),(-81592114892334221932)⟩,⟨1392079431396231969,1392079431396232004⟩⟩,⟨⟨(-78983391023525787919),(-78983391023525787884)⟩,⟨(-1804740934743973370),(-1804740934743973336)⟩⟩,⟨⟨(-76313859624683467090),(-76313859624683467058)⟩,⟨(-4841174656461021379),(-4841174656461021346)⟩⟩,⟨⟨(-73590345278303449732),(-73590345278303449701)⟩,⟨(-7715372148642344888),(-7715372148642344858)⟩⟩,⟨⟨(-70819788308100865507),(-70819788308100865476)⟩,⟨(-10425923324087231728),(-10425923324087231698)⟩⟩,⟨⟨(-68009216318872413415),(-68009216318872413387)⟩,⟨(-12971858722106265609),(-12971858722106265580)⟩⟩,⟨⟨(-65165715707959838955),(-65165715707959838927)⟩,⟨(-15352648913979233473),(-15352648913979233447)⟩⟩,⟨⟨(-62296403283427542396),(-62296403283427542372)⟩,⟨(-17568202190603602144),(-17568202190603602122)⟩⟩,⟨⟨(-59408398122079120841),(-59408398122079120816)⟩,⟨(-19618860547153704771),(-19618860547153704746)⟩⟩,⟨⟨(-56508793797724163097),(-56508793797724163070)⟩,⟨(-21505393988909323888),(-21505393988909323862)⟩⟩,⟨⟨(-53604631106690302897),(-53604631106690302872)⟩,⟨(-23228993191539541465),(-23228993191539541439)⟩⟩,⟨⟨(-50702871413483109015),(-50702871413483108992)⟩,⟨(-24791260557983988363),(-24791260557983988341)⟩⟩,⟨⟨(-47810370734758883922),(-47810370734758883895)⟩,⟨(-26194199722602139660),(-26194199722602139637)⟩⟩] +lemma kernel3_0_r0_4_eq : ∀ k : Fin 16, kernel3_0Expr 0 4 k = kernel3_0_r0_4 k := by decide +kernel +noncomputable def kernel3_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-44933854674427946416),(-44933854674427946391)⟩,⟨(-27440203561408361345),(-27440203561408361320)⟩⟩,⟨⟨(-42079894316787345498),(-42079894316787345474)⟩,⟨(-28532040774925788869),(-28532040774925788846)⟩⟩,⟨⟨(-39254883178134499206),(-39254883178134499182)⟩,⟨(-29472841117429380425),(-29472841117429380402)⟩⟩,⟨⟨(-36465015310382387964),(-36465015310382387940)⟩,⟨(-30266079353065296792),(-30266079353065296766)⟩⟩,⟨⟨(-33716264642830815710),(-33716264642830815686)⟩,⟨(-30915558025492112043),(-30915558025492112018)⟩⟩,⟨⟨(-31014365640497407789),(-31014365640497407765)⟩,⟨(-31425389133255799871),(-31425389133255799846)⟩⟩,⟨⟨(-28364795349328935233),(-28364795349328935207)⟩,⟨(-31799974808056232509),(-31799974808056232485)⟩⟩,⟨⟨(-25772756890252299292),(-25772756890252299268)⟩,⟨(-32043987097364186012),(-32043987097364185987)⟩⟩,⟨⟨(-23243164455440288937),(-23243164455440288914)⟩,⟨(-32162346956485618788),(-32162346956485618766)⟩⟩,⟨⟨(-20780629851415986191),(-20780629851415986168)⟩,⟨(-32160202558130320092),(-32160202558130320069)⟩⟩,⟨⟨(-18389450624757711182),(-18389450624757711159)⟩,⟨(-32042907029815949359),(-32042907029815949336)⟩⟩,⟨⟨(-16073599797249852590),(-16073599797249852567)⟩,⟨(-31815995731022011689),(-31815995731022011667)⟩⟩,⟨⟨(-13836717228409509437),(-13836717228409509415)⟩,⟨(-31485163182902344736),(-31485163182902344713)⟩⟩,⟨⟨(-11682102614459378649),(-11682102614459378627)⟩,⟨(-31056239763574928844),(-31056239763574928821)⟩⟩,⟨⟨(-9612710124067294589),(-9612710124067294567)⟩,⟨(-30535168281544631697),(-30535168281544631675)⟩⟩,⟨⟨(-7631144662584164699),(-7631144662584164679)⟩,⟨(-29927980538692701304),(-29927980538692701282)⟩⟩] +lemma kernel3_0_r0_5_eq : ∀ k : Fin 16, kernel3_0Expr 0 5 k = kernel3_0_r0_5 k := by decide +kernel +noncomputable def kernel3_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-5739659748134676678),(-5739659748134676656)⟩,⟨(-29240773992505545694),(-29240773992505545672)⟩⟩,⟨⟨(-3940156974796703740),(-3940156974796703718)⟩,⟨(-28479688624837752415),(-28479688624837752393)⟩⟩,⟨⟨(-2234187030290833573),(-2234187030290833551)⟩,⟨(-27650884121537362729),(-27650884121537362707)⟩⟩,⟨⟨(-622952228133047874),(-622952228133047855)⟩,⟨(-26760517463735591211),(-26760517463735591189)⟩⟩,⟨⟨892689492879682018,892689492879682037⟩,⟨(-25814721027552145576),(-25814721027552145557)⟩⟩,⟨⟨2312219155643543281,2312219155643543300⟩,⟨(-24819581284427616940),(-24819581284427616919)⟩⟩,⟨⟨3635449978183848422,3635449978183848441⟩,⟨(-23781118189305196294),(-23781118189305196273)⟩⟩,⟨⟨4862519319282806179,4862519319282806197⟩,⟨(-22705265338486558251),(-22705265338486558232)⟩⟩,⟨⟨5993879407250798754,5993879407250798772⟩,⟨(-21597850973224325439),(-21597850973224325420)⟩⟩,⟨⟨7030286927487600195,7030286927487600211⟩,⟨(-20464579899030773289),(-20464579899030773270)⟩⟩,⟨⟨7972791548630887751,7972791548630887769⟩,⟨(-19311016384325180948),(-19311016384325180929)⟩⟩,⟨⟨8822723470683657584,8822723470683657599⟩,⟨(-18142568095457083888),(-18142568095457083870)⟩⟩,⟨⟨9581680081540904753,9581680081540904771⟩,⟨(-16964471118376664030),(-16964471118376664011)⟩⟩,⟨⟨10251511810794267964,10251511810794267982⟩,⟨(-15781776110323721935),(-15781776110323721916)⟩⟩,⟨⟨10834307271580271541,10834307271580271559⟩,⟨(-14599335617919941102),(-14599335617919941086)⟩⟩,⟨⟨11332377782556127709,11332377782556127724⟩,⟨(-13421792591021704964),(-13421792591021704949)⟩⟩] +lemma kernel3_0_r0_6_eq : ∀ k : Fin 16, kernel3_0Expr 0 6 k = kernel3_0_r0_6 k := by decide +kernel +noncomputable def kernel3_0_r0_7 : Fin 16 → CBox := ![⟨⟨11748241362843291299,11748241362843291314⟩,⟨(-12253570114667874020),(-12253570114667874004)⟩⟩,⟨⟨12084606292983139239,12084606292983139257⟩,⟨(-11098862374482767690),(-11098862374482767675)⟩⟩,⟨⟨12344354334614721214,12344354334614721229⟩,⟨(-9961626864011715201),(-9961626864011715186)⟩⟩,⟨⟨12530523700728143851,12530523700728143866⟩,⟨(-8845577835715769990),(-8845577835715769975)⟩⟩,⟨⟨12646291866988459492,12646291866988459507⟩,⟨(-7754180990772342336),(-7754180990772342321)⟩⟩,⟨⟨12694958312786364440,12694958312786364454⟩,⟨(-6690649396456185590),(-6690649396456185578)⟩⟩,⟨⟨12679927278378550370,12679927278378550384⟩,⟨(-5657940613744536854),(-5657940613744536842)⟩⟩,⟨⟨12604690621759475674,12604690621759475686⟩,⟨(-4658755011932826967),(-4658755011932826953)⟩⟩,⟨⟨12472810855786951522,12472810855786951534⟩,⟨(-3695535241492052702),(-3695535241492052687)⟩⟩,⟨⟨12287904442597368371,12287904442597368383⟩,⟨(-2770466831171588605),(-2770466831171588591)⟩⟩,⟨⟨12053625418525224834,12053625418525224845⟩,⟨(-1885479870474879318),(-1885479870474879307)⟩⟩,⟨⟨11773649418619696752,11773649418619696766⟩,⟨(-1042251734130023778),(-1042251734130023766)⟩⟩,⟨⟨11451658165463090173,11451658165463090185⟩,⟨(-242210801059577566),(-242210801059577555)⟩⟩,⟨⟨11091324482377630244,11091324482377630256⟩,⟨513458883362318834,513458883362318845⟩⟩,⟨⟨10696297886294033618,10696297886294033630⟩,⟨1223812056281521548,1223812056281521559⟩⟩,⟨⟨10270190810583725838,10270190810583725849⟩,⟨1888135854964759393,1888135854964759404⟩⟩] +lemma kernel3_0_r0_7_eq : ∀ k : Fin 16, kernel3_0Expr 0 7 k = kernel3_0_r0_7 k := by decide +kernel +noncomputable def kernel3_0_r0_8 : Fin 16 → CBox := ![⟨⟨9816565503062317995,9816565503062318006⟩,⟨2505942662890868963,2505942662890868974⟩⟩,⟨⟨9338921639190609066,9338921639190609078⟩,⟨3076962246228362770,3076962246228362781⟩⟩,⟨⟨8840684685265895012,8840684685265895023⟩,⟨3601133244206032307,3601133244206032318⟩⟩,⟨⟨8325195041144882017,8325195041144882028⟩,⟨4078594078074003532,4078594078074003544⟩⟩,⟨⟨7795697986803123453,7795697986803123465⟩,⟨4509673344130193749,4509673344130193760⟩⟩,⟨⟨7255334451846498558,7255334451846498566⟩,⟨4894879756660813729,4894879756660813739⟩⟩,⟨⟨6707132621978281987,6707132621978281998⟩,⟨5234891706625131202,5234891706625131210⟩⟩,⟨⟨6154000391419694015,6154000391419694023⟩,⟨5530546501518076597,5530546501518076608⟩⟩,⟨⟨5598718665409620829,5598718665409620837⟩,⟨5782829351085369827,5782829351085369835⟩⟩,⟨⟨5043935512195747097,5043935512195747104⟩,⟨5992862162462459130,5992862162462459138⟩⟩,⟨⟨4492161159397974275,4492161159397974282⟩,⟨6161892206880120026,6161892206880120034⟩⟩,⟨⟨3945763825296974200,3945763825296974207⟩,⟨6291280718346946047,6291280718346946055⟩⟩,⟨⟨3406966371495179993,3406966371495180000⟩,⟨6382491482704306976,6382491482704306984⟩⟩,⟨⟨2877843759531387159,2877843759531387167⟩,⟨6437079473175836495,6437079473175836503⟩⟩,⟨⟨2360321290418142578,2360321290418142586⟩,⟨6456679586025167373,6456679586025167381⟩⟩,⟨⟨1856173602725706259,1856173602725706267⟩,⟨6442995527217130849,6442995527217130856⟩⟩] +lemma kernel3_0_r0_8_eq : ∀ k : Fin 16, kernel3_0Expr 0 8 k = kernel3_0_r0_8 k := by decide +kernel +noncomputable def kernel3_0_r0_9 : Fin 16 → CBox := ![⟨⟨1367024401767801611,1367024401767801619⟩,⟨6397788898074094964,6397788898074094972⟩⟩,⟨⟨894346889660611216,894346889660611223⟩,⟨6322868524855903576,6322868524855903584⟩⟩,⟨⟨439464863533311233,439464863533311237⟩,⟨6220080073994424423,6220080073994424430⟩⟩,⟨⟨3554446969496158,3554446969496165⟩,⟨6091295991407333026,6091295991407333034⟩⟩,⟨⟨(-412353582144343388),(-412353582144343383)⟩,⟨5938405800925467460,5938405800925467464⟩⟩,⟨⟨(-807370905795056716),(-807370905795056711)⟩,⟨5763306793418447511,5763306793418447516⟩⟩,⟨⟨(-1180748261790651925),(-1180748261790651918)⟩,⟨5567895134718207740,5567895134718207745⟩⟩,⟨⟨(-1531871562253115283),(-1531871562253115276)⟩,⟨5354057416942837418,5354057416942837423⟩⟩,⟨⟨(-1860257576173654185),(-1860257576173654177)⟩,⟨5123662674335952447,5123662674335952455⟩⟩,⟨⟨(-2165549218016880686),(-2165549218016880678)⟩,⟨4878554881281035544,4878554881281035552⟩⟩,⟨⟨(-2447510484563766674),(-2447510484563766666)⟩,⟨4620545946745944324,4620545946745944332⟩⟩,⟨⟨(-2706021082131239232),(-2706021082131239224)⟩,⟨4351409216079061975,4351409216079061983⟩⟩,⟨⟨(-2941070786010788026),(-2941070786010788019)⟩,⟨4072873487833016869,4072873487833016876⟩⟩,⟨⟨(-3152753573442270820),(-3152753573442270815)⟩,⟨3786617550150825760,3786617550150825764⟩⟩,⟨⟨(-3341261570696037371),(-3341261570696037364)⟩,⟨3494265238227601017,3494265238227601022⟩⟩,⟨⟨(-3506878853891179145),(-3506878853891179140)⟩,⟨3197381011472023097,3197381011472023101⟩⟩] +lemma kernel3_0_r0_9_eq : ∀ k : Fin 16, kernel3_0Expr 0 9 k = kernel3_0_r0_9 k := by decide +kernel +noncomputable def kernel3_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-3649975142045469801),(-3649975142045469794)⟩,⟨2897466046247539788,2897466046247539796⟩⟩,⟨⟨(-3770999419549251430),(-3770999419549251423)⟩,⟨2595954837484128341,2595954837484128349⟩⟩,⟨⟨(-3870473523797415085),(-3870473523797415078)⟩,⟨2294212300026343119,2294212300026343127⟩⟩,⟨⟨(-3948985732117266354),(-3948985732117266346)⟩,⟨1993531358329658657,1993531358329658665⟩⟩,⟨⟨(-4007184380412147956),(-4007184380412147949)⟩,⟨1695131011040700827,1695131011040700832⟩⟩,⟨⟨(-4045771544117921522),(-4045771544117921514)⟩,⟨1400154855102267374,1400154855102267379⟩⟩,⟨⟨(-4065496810158400224),(-4065496810158400216)⟩,⟨1109670052314074611,1109670052314074618⟩⟩,⟨⟨(-4067151166602970876),(-4067151166602970869)⟩,⟨824666719756548947,824666719756548952⟩⟩,⟨⟨(-4051561034691026818),(-4051561034691026811)⟩,⟨546057724148001644,546057724148001649⟩⟩,⟨⟨(-4019582465809112860),(-4019582465809112853)⟩,⟨274678859054208047,274678859054208055⟩⟩,⟨⟨(-3972095523903012498),(-3972095523903012493)⟩,⟨11289382901586078,11289382901586083⟩⟩,⟨⟨(-3909998871692945937),(-3909998871692945933)⟩,⟨(-243427105042462862),(-243427105042462855)⟩⟩,⟨⟨(-3834204576949489197),(-3834204576949489190)⟩,⟨(-488861474170265147),(-488861474170265140)⟩⟩,⟨⟨(-3745633152993931630),(-3745633152993931626)⟩,⟨(-724477581405079357),(-724477581405079350)⟩⟩,⟨⟨(-3645208845521934344),(-3645208845521934340)⟩,⟨(-949810523609087786),(-949810523609087779)⟩⟩,⟨⟨(-3533855175825070491),(-3533855175825070487)⟩,⟨(-1164464647813913901),(-1164464647813913894)⟩⟩] +lemma kernel3_0_r0_10_eq : ∀ k : Fin 16, kernel3_0Expr 0 10 k = kernel3_0_r0_10 k := by decide +kernel +noncomputable def kernel3_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-3412490748511778455),(-3412490748511778451)⟩,⟨(-1368111343529103532),(-1368111343529103525)⟩⟩,⟨⟨(-3282025329917190545),(-3282025329917190540)⟩,⟨(-1560486641212229153),(-1560486641212229146)⟩⟩,⟨⟨(-3143356201549032370),(-3143356201549032362)⟩,⟨(-1741388640679804608),(-1741388640679804601)⟩⟩,⟨⟨(-2997364791152195907),(-2997364791152195900)⟩,⟨(-1910674792810241778),(-1910674792810241773)⟩⟩,⟨⟨(-2844913582294595269),(-2844913582294595265)⟩,⟨(-2068259057348186913),(-2068259057348186909)⟩⟩,⟨⟨(-2686843301787490538),(-2686843301787490533)⟩,⟨(-2214108958973539472),(-2214108958973539468)⟩⟩,⟨⟨(-2523970382759641871),(-2523970382759641864)⟩,⟨(-2348242563058242939),(-2348242563058242934)⟩⟩,⟨⟨(-2357084699810536237),(-2357084699810536230)⟩,⟨(-2470725391709593651),(-2470725391709593647)⟩⟩,⟨⟨(-2186947571376708892),(-2186947571376708885)⟩,⟨(-2581667299800396803),(-2581667299800396799)⟩⟩,⟨⟨(-2014290023259178683),(-2014290023259178676)⟩,⟨(-2681219329723800423),(-2681219329723800418)⟩⟩,⟨⟨(-1839811306180700611),(-1839811306180700607)⟩,⟨(-2769570562593916931),(-2769570562593916924)⟩⟩,⟨⟨(-1664177659269570902),(-1664177659269570897)⟩,⟨(-2846944982552059186),(-2846944982552059178)⟩⟩,⟨⟨(-1488021310501990061),(-1488021310501990057)⟩,⟨(-2913598369741978993),(-2913598369741978989)⟩⟩,⟨⟨(-1311939704376664642),(-1311939704376664635)⟩,⟨(-2969815236394996359),(-2969815236394996355)⟩⟩,⟨⟨(-1136494946441897795),(-1136494946441897788)⟩,⟨(-3015905819326084942),(-3015905819326084937)⟩⟩,⟨⟨(-962213453744745600),(-962213453744745596)⟩,⟨(-3052203140993169611),(-3052203140993169604)⟩⟩] +lemma kernel3_0_r0_11_eq : ∀ k : Fin 16, kernel3_0Expr 0 11 k = kernel3_0_r0_11 k := by decide +kernel +noncomputable def kernel3_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-789585799821188159),(-789585799821188155)⟩,⟨(-3079060150121994325),(-3079060150121994318)⟩⟩,⟨⟨(-619066742492449176),(-619066742492449172)⟩,⟨(-3096846951755361011),(-3096846951755361007)⟩⟩,⟨⟨(-451075422471895342),(-451075422471895338)⟩,⟨(-3105948135455254880),(-3105948135455254873)⟩⟩,⟨⟨(-285995720615245827),(-285995720615245820)⟩,⟨(-3106760209275773107),(-3106760209275773103)⟩⟩,⟨⟨(-124176761559654345),(-124176761559654341)⟩,⟨(-3099689146039743649),(-3099689146039743642)⟩⟩,⟨⟨34066448510180089,34066448510180097⟩,⟨(-3085148047397796196),(-3085148047397796189)⟩⟩,⟨⟨188452262163383145,188452262163383149⟩,⟨(-3063554930130215856),(-3063554930130215851)⟩⟩,⟨⟨338731521149407950,338731521149407957⟩,⟨(-3035330638173407967),(-3035330638173407963)⟩⟩,⟨⟨484686588806308480,484686588806308484⟩,⟨(-3000896882917917881),(-3000896882917917874)⟩⟩,⟨⟨626130296047713036,626130296047713043⟩,⟨(-2960674413436829702),(-2960674413436829698)⟩⟩,⟨⟨762904812212542249,762904812212542253⟩,⟨(-2915081317464629499),(-2915081317464629495)⟩⟩,⟨⟨894880451700978204,894880451700978211⟩,⟨(-2864531453159362805),(-2864531453159362798)⟩⟩,⟨⟨1021954426917494320,1021954426917494324⟩,⟨(-2809433010946745597),(-2809433010946745593)⟩⟩,⟨⟨1144049557602321023,1144049557602321027⟩,⟨(-2750187204064927199),(-2750187204064927195)⟩⟩,⟨⟨1261112946161867577,1261112946161867581⟩,⟨(-2687187085803521166),(-2687187085803521162)⟩⟩,⟨⟨1373114628111524375,1373114628111524379⟩,⟨(-2620816490860555135),(-2620816490860555130)⟩⟩] +lemma kernel3_0_r0_12_eq : ∀ k : Fin 16, kernel3_0Expr 0 12 k = kernel3_0_r0_12 k := by decide +kernel +noncomputable def kernel3_0_r0_13 : Fin 16 → CBox := ![⟨⟨1480046206225946276,1480046206225946283⟩,⟨(-2551449097725976425),(-2551449097725976421)⟩⟩,⟨⟨1581919476457186833,1581919476457186837⟩,⟨(-2479447608539745406),(-2479447608539745399)⟩⟩,⟨⟨1678765053134522899,1678765053134522903⟩,⟨(-2405163042465464357),(-2405163042465464353)⟩⟩,⟨⟨1770631000405852609,1770631000405852613⟩,⟨(-2328934138265720222),(-2328934138265720218)⟩⟩,⟨⟨1857581476323291455,1857581476323291459⟩,⟨(-2251086861461372918),(-2251086861461372914)⟩⟩,⟨⟨1939695395418893228,1939695395418893232⟩,⟨(-2171934011202149388),(-2171934011202149382)⟩⟩,⟨⟨2017065115063875109,2017065115063875116⟩,⟨(-2091774921768134077),(-2091774921768134073)⟩⟩,⟨⟨2089795150359639743,2089795150359639750⟩,⟨(-2010895253458912145),(-2010895253458912141)⟩⟩,⟨⟨2158000921774289448,2158000921774289452⟩,⟨(-1929566867506890152),(-1929566867506890148)⟩⟩,⟨⟨2221807539216961021,2221807539216961025⟩,⟨(-1848047779571222908),(-1848047779571222904)⟩⟩,⟨⟨2281348625736631811,2281348625736631815⟩,⟨(-1766582186326240006),(-1766582186326240002)⟩⟩,⟨⟨2336765183544235385,2336765183544235392⟩,⟨(-1685400559650636437),(-1685400559650636430)⟩⟩,⟨⟨2388204504588878707,2388204504588878714⟩,⟨(-1604719802948260169),(-1604719802948260165)⟩⟩,⟨⟨2435819127472302675,2435819127472302679⟩,⟨(-1524743464185357375),(-1524743464185357371)⟩⟩,⟨⟨2479765842061844599,2479765842061844603⟩,⟨(-1445662000309878660),(-1445662000309878656)⟩⟩,⟨⟨2520204742762163830,2520204742762163837⟩,⟨(-1367653087823178566),(-1367653087823178559)⟩⟩] +lemma kernel3_0_r0_13_eq : ∀ k : Fin 16, kernel3_0Expr 0 13 k = kernel3_0_r0_13 k := by decide +kernel +noncomputable def kernel3_0_r0_14 : Fin 16 → CBox := ![⟨⟨2557298331030760409,2557298331030760413⟩,⟨(-1290881974400461366),(-1290881974400461360)⟩⟩,⟨⟨2591210667372504636,2591210667372504640⟩,⟨(-1215501866600999637),(-1215501866600999633)⟩⟩,⟨⟨2622106572724442613,2622106572724442620⟩,⟨(-1141654348869907837),(-1141654348869907833)⟩⟩,⟨⟨2650150878844289455,2650150878844289459⟩,⟨(-1069469829207607533),(-1069469829207607526)⟩⟩,⟨⟨2675507727044324052,2675507727044324056⟩,⟨(-999068007068687886),(-999068007068687879)⟩⟩,⟨⟨2698339914366742718,2698339914366742722⟩,⟨(-930558359246369484),(-930558359246369480)⟩⟩,⟨⟨2718808286076645275,2718808286076645279⟩,⟨(-864040639700066153),(-864040639700066149)⟩⟩,⟨⟨2737071173154308331,2737071173154308335⟩,⟨(-799605389489581788),(-799605389489581784)⟩⟩,⟨⟨2753283873298713991,2753283873298713995⟩,⟨(-737334453188386188),(-737334453188386184)⟩⟩,⟨⟨2767598173808806655,2767598173808806659⟩,⟨(-677301498358435447),(-677301498358435443)⟩⟩,⟨⟨2780161914586908576,2780161914586908580⟩,⟨(-619572534878533113),(-619572534878533109)⟩⟩,⟨⟨2791118589409318792,2791118589409318796⟩,⟨(-564206431125810634),(-564206431125810630)⟩⟩,⟨⟨2800606983531463984,2800606983531463988⟩,⟨(-511255424214230161),(-511255424214230157)⟩⟩,⟨⟨2808760845638122810,2808760845638122817⟩,⟨(-460765621693920663),(-460765621693920659)⟩⟩,⟨⟨2815708592112223573,2815708592112223577⟩,⟨(-412777492309637473),(-412777492309637469)⟩⟩,⟨⟨2821573041577502122,2821573041577502126⟩,⟨(-367326343604821778),(-367326343604821774)⟩⟩] +lemma kernel3_0_r0_14_eq : ∀ k : Fin 16, kernel3_0Expr 0 14 k = kernel3_0_r0_14 k := by decide +kernel +noncomputable def kernel3_0_r0_15 : Fin 16 → CBox := ![⟨⟨2826471177669865297,2826471177669865301⟩,⟨(-324442784338909185),(-324442784338909181)⟩⟩,⟨⟨2830513938008583768,2830513938008583772⟩,⟨(-284153169859115026),(-284153169859115022)⟩⟩,⟨⟨2833806027370382806,2833806027370382813⟩,⟨(-246480028733464669),(-246480028733464665)⟩⟩,⟨⟨2836445753116058231,2836445753116058235⟩,⟨(-211442469109027056),(-211442469109027052)⟩⟩,⟨⟨2838524880979375914,2838524880979375918⟩,⟨(-179056563407962444),(-179056563407962440)⟩⟩,⟨⟨2840128509400689936,2840128509400689940⟩,⟨(-149335710114044493),(-149335710114044490)⟩⟩,⟨⟨2841334960671929164,2841334960671929168⟩,⟨(-122290971533810051),(-122290971533810047)⟩⟩,⟨⟨2842215687254370837,2842215687254370841⟩,⟨(-97931386539581525),(-97931386539581521)⟩⟩,⟨⟨2842835191734983680,2842835191734983684⟩,⟨(-76264257416552280),(-76264257416552276)⟩⟩,⟨⟨2843250959000151352,2843250959000151356⟩,⟨(-57295410043272447),(-57295410043272443)⟩⟩,⟨⟨2843513399326376586,2843513399326376590⟩,⟨(-41029426734655503),(-41029426734655499)⟩⟩,⟨⟨2843665801215242951,2843665801215242958⟩,⟨(-27469851169556694),(-27469851169556691)⟩⟩,⟨⟨2843744292933628040,2843744292933628044⟩,⟨(-16619364911635816),(-16619364911635809)⟩⟩,⟨⟨2843777811859099135,2843777811859099138⟩,⟨(-8479935113254782),(-8479935113254778)⟩⟩,⟨⟨2843788080873784254,2843788080873784258⟩,⟨(-3052933068275617),(-3052933068275613)⟩⟩,⟨⟨2843789591197024594,2843789591197024598⟩,⟨(-339223351564978),(-339223351564974)⟩⟩] +lemma kernel3_0_r0_15_eq : ∀ k : Fin 16, kernel3_0Expr 0 15 k = kernel3_0_r0_15 k := by decide +kernel +noncomputable def kernel3_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel3_0_r0_0,kernel3_0_r0_1,kernel3_0_r0_2,kernel3_0_r0_3,kernel3_0_r0_4,kernel3_0_r0_5,kernel3_0_r0_6,kernel3_0_r0_7,kernel3_0_r0_8,kernel3_0_r0_9,kernel3_0_r0_10,kernel3_0_r0_11,kernel3_0_r0_12,kernel3_0_r0_13,kernel3_0_r0_14,kernel3_0_r0_15] +lemma kernel3_0_r0_eq (i k : Fin 16) : kernel3_0Expr 0 i k = kernel3_0_r0 i k := by + fin_cases i + · exact kernel3_0_r0_0_eq k + · exact kernel3_0_r0_1_eq k + · exact kernel3_0_r0_2_eq k + · exact kernel3_0_r0_3_eq k + · exact kernel3_0_r0_4_eq k + · exact kernel3_0_r0_5_eq k + · exact kernel3_0_r0_6_eq k + · exact kernel3_0_r0_7_eq k + · exact kernel3_0_r0_8_eq k + · exact kernel3_0_r0_9_eq k + · exact kernel3_0_r0_10_eq k + · exact kernel3_0_r0_11_eq k + · exact kernel3_0_r0_12_eq k + · exact kernel3_0_r0_13_eq k + · exact kernel3_0_r0_14_eq k + · exact kernel3_0_r0_15_eq k +noncomputable def kernel3_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-494734967394662307364497),(-494734967394662306885483)⟩,⟨(-695138863142160721390161),(-695138863142160720913843)⟩⟩,⟨⟨(-494399587671055171830154),(-494399587671055171351352)⟩,⟨(-694794683166218010226575),(-694794683166218009750467)⟩⟩,⟨⟨(-493729457444539512215286),(-493729457444539511736905)⟩,⟨(-694106869166415060102090),(-694106869166415059626401)⟩⟩,⟨⟨(-492725833261212241574744),(-492725833261212241096996)⟩,⟨(-693076511467267667130810),(-693076511467267666655749)⟩⟩,⟨⟨(-491390595209741127316484),(-491390595209741126839582)⟩,⟨(-691705241613455747054020),(-691705241613455746579799)⟩⟩,⟨⟨(-489726241266517133771086),(-489726241266517133295238)⟩,⟨(-689995227658948848874648),(-689995227658948848401474)⟩⟩,⟨⟨(-487735879791948627311492),(-487735879791948626836906)⟩,⟨(-687949167918440363998421),(-687949167918440363526499)⟩⟩,⟨⟨(-485423220208597312575341),(-485423220208597312102223)⟩,⟨(-685570283208774750561619),(-685570283208774750091155)⟩⟩,⟨⟨(-482792561899238147412696),(-482792561899238146941251)⟩,⟨(-682862307614652206774570),(-682862307614652206305766)⟩⟩,⟨⟨(-479848781370115271414825),(-479848781370115270945254)⟩,⟨(-679829477819285088291221),(-679829477819285087824279)⟩⟩,⟨⟨(-476597317731627108630615),(-476597317731627108163118)⟩,⟨(-676476521046821600482585),(-676476521046821600017702)⟩⟩,⟨⟨(-473044156555371512337102),(-473044156555371511871880)⟩,⟨(-672808641669208483119284),(-672808641669208482656660)⟩⟩,⟨⟨(-469195812172882863809549),(-469195812172882863346793)⟩,⟨(-668831506535701344230369),(-668831506535701343770193)⟩⟩,⟨⟨(-465059308487465876554133),(-465059308487465876094038)⟩,⟨(-664551229088417275953018),(-664551229088417275495483)⟩⟩,⟨⟨(-460642158376245835492263),(-460642158376245835035014)⟩,⟨(-659974352332130397690303),(-659974352332130397235595)⟩⟩,⟨⟨(-455952341764884514810697),(-455952341764884514356481)⟩,⟨(-655107830730910943971878),(-655107830730910943520181)⟩⟩] +lemma kernel3_0_r1_0_eq : ∀ k : Fin 16, kernel3_0Expr 1 0 k = kernel3_0_r1_0 k := by decide +kernel +noncomputable def kernel3_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-450998282462329679058220),(-450998282462329678607216)⟩,⟨(-649959011108179473449387),(-649959011108179473000879)⟩⟩,⟨⟨(-445788823847450847831389),(-445788823847450847383777)⟩,⟨(-644535612630270005276550),(-644535612630270004831409)⟩⟩,⟨⟨(-440333203503444352142711),(-440333203503444351698658)⟩,⟨(-638845705956653052303711),(-638845705956653051862104)⟩⟩,⟨⟨(-434641026899448692329882),(-434641026899448691889561)⟩,⟨(-632897691642548749956745),(-632897691642548749518843)⟩⟩,⟨⟨(-428722240221881590429673),(-428722240221881589993249)⟩,⟨(-626700277881752238812052),(-626700277881752238378019)⟩⟩,⟨⟨(-422587102460580470664604),(-422587102460580470232232)⟩,⟨(-620262457679092370336264),(-620262457679092369906254)⟩⟩,⟨⟨(-416246156856888812155263),(-416246156856888811727101)⟩,⟨(-613593485543048447929044),(-613593485543048447503214)⟩⟩,⟨⟨(-409710201822375214887583),(-409710201822375214463779)⟩,⟨(-606702853789659390457882),(-606702853789659390036378)⟩⟩,⟨⟨(-402990261437896355397082),(-402990261437896354977778)⟩,⟨(-599600268548980171919015),(-599600268548980171501980)⟩⟩,⟨⟨(-396097555643218482183755),(-396097555643218481769092)⟩,⟨(-592295625564979771738028),(-592295625564979771325600)⟩⟩,⟨⟨(-389043470227396853107389),(-389043470227396852697502)⟩,⟨(-584798985878944530694886),(-584798985878944530287199)⟩⟩,⟨⟨(-381839526729583604024203),(-381839526729583603619213)⟩,⟨(-577120551485165206386178),(-577120551485165205983355)⟩⟩,⟨⟨(-374497352358899887061328),(-374497352358899886661366)⟩,⟨(-569270641045962539011822),(-569270641045962538613989)⟩⟩,⟨⟨(-367028650040478463864308),(-367028650040478463469486)⟩,⟨(-561259665750964877524289),(-561259665750964877131559)⟩⟩,⟨⟨(-359445168692771746616484),(-359445168692771746226910)⟩,⟨(-553098105403014991153147),(-553098105403014990765628)⟩⟩,⟨⟨(-351758673838743638195346),(-351758673838743637811126)⟩,⟨(-544796484810176490373984),(-544796484810176489991780)⟩⟩] +lemma kernel3_0_r1_1_eq : ∀ k : Fin 16, kernel3_0Expr 1 1 k = kernel3_0_r1_1 k := by decide +kernel +noncomputable def kernel3_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-343980918650640034424886),(-343980918650640034046120)⟩,⟨(-536365350560060218688042),(-536365350560060218311254)⟩⟩,⟨⟨(-336123615524683496199849),(-336123615524683495826626)⟩,⟨(-527815248249126230287168),(-527815248249126229915881)⟩⟩,⟨⟨(-328198408278285586975355),(-328198408278285586607767)⟩,⟨(-519156700235767709388664),(-519156700235767709022972)⟩⟩,⟨⟨(-320216845058240977423528),(-320216845058240977061646)⟩,⟨(-510400183981880799208916),(-510400183981880798848889)⟩⟩,⟨⟨(-312190352043887808641114),(-312190352043887808285021)⟩,⟨(-501556111043301107927979),(-501556111043301107573699)⟩⟩,⟨⟨(-304130208024417842536908),(-304130208024417842186665)⟩,⟨(-492634806764976608687236),(-492634806764976608338764)⟩⟩,⟨⟨(-296047519924427976846839),(-296047519924427976502513)⟩,⟨(-483646490732081078837183),(-483646490732081078494586)⟩⟩,⟨⟨(-287953199346453416481820),(-287953199346453416143458)⟩,⟨(-474601258023485545539214),(-474601258023485545202538)⟩⟩,⟨⟨(-279857940193644899036115),(-279857940193644898703775)⟩,⟨(-465509061309130651574287),(-465509061309130651243591)⟩⟩,⟨⟨(-271772197429981445739887),(-271772197429981445413604)⟩,⟨(-456379693827913212165091),(-456379693827913211840408)⟩⟩,⟨⟨(-263706167029480346494524),(-263706167029480346174344)⟩,⟨(-447222773277747590284997),(-447222773277747589966374)⟩⟩,⟨⟨(-255669767159812075987989),(-255669767159812075673930)⟩,⟨(-438047726644518031813404),(-438047726644518031500858)⟩⟩,⟨⟨(-247672620639584323514559),(-247672620639584323206660)⟩,⟨(-428863775991731778124142),(-428863775991731777817711)⟩⟩,⟨⟨(-239724038702360977097641),(-239724038702360976795909)⟩,⟨(-419679925227843262126668),(-419679925227843261826360)⟩⟩,⟨⟨(-231833006094263109226438),(-231833006094263108930896)⟩,⟨(-410504947863474105137444),(-410504947863474104843282)⟩⟩,⟨⟨(-224008167525793621840157),(-224008167525793621550800)⟩,⟨(-401347375766127374151721),(-401347375766127373863700)⟩⟩] +lemma kernel3_0_r1_2_eq : ∀ k : Fin 16, kernel3_0Expr 1 2 k = kernel3_0_r1_2 k := by decide +kernel +noncomputable def kernel3_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-216257815492368339076300),(-216257815492368338793146)⟩,⟨(-392215488915511194744817),(-392215488915511194462954)⟩⟩,⟨⟨(-208589879471956158517998),(-208589879471956158241027)⟩,⟨(-383117306158267940765693),(-383117306158267940489970)⟩⟩,⟨⟨(-201011916502260411351429),(-201011916502260411080646)⟩,⟨(-374060576956770371003065),(-374060576956770370733486)⟩⟩,⟨⟨(-193531103134042533305247),(-193531103134042533040620)⟩,⟨(-365052774122712648323856),(-365052774122712648060390)⟩⟩,⟨⟨(-186154228751525699623997),(-186154228751525699365527)⟩,⟨(-356101087522507358951057),(-356101087522507358693705)⟩⟩,⟨⟨(-178887690245346750252544),(-178887690245346750000186)⟩,⟨(-347212418738012425586211),(-347212418738012425334929)⟩⟩,⟨⟨(-171737488018274235901467),(-171737488018274235655207)⟩,⟨(-338393376662864922314259),(-338393376662864922069031)⟩⟩,⟨⟨(-164709223298901521319350),(-164709223298901521079139)⟩,⟨(-329650274011700775047544),(-329650274011700774808322)⟩⟩,⟨⟨(-157808096733777306356538),(-157808096733777306122355)⟩,⟨(-320989124716796502855989),(-320989124716796502622755)⟩⟩,⟨⟨(-151038908223970239637741),(-151038908223970239409523)⟩,⟨(-312415642184185718437532),(-312415642184185718210221)⟩⟩,⟨⟨(-144406057967895853550404),(-144406057967895853328118)⟩,⟨(-303935238379081185180916),(-303935238379081184959496)⟩⟩,⟨⟨(-137913548668376913832363),(-137913548668376913615944)⟩,⟨(-295553023708472962313025),(-295553023708472962097431)⟩⟩,⟨⟨(-131564988858374206487771),(-131564988858374206277180)⟩,⟨(-287273807667072809251340),(-287273807667072809041534)⟩⟩,⟨⟨(-125363597296623196979992),(-125363597296623196775149)⟩,⟨(-279102100211331039893874),(-279102100211331039689778)⟩⟩,⟨⟨(-119312208381549972359942),(-119312208381549972160804)⟩,⟨(-271042113825059237722533),(-271042113825059237524103)⟩⟩,⟨⟨(-113413278529322176960430),(-113413278529322176766912)⟩,⟨(-263097766239243961774245),(-263097766239243961581397)⟩⟩] +lemma kernel3_0_r1_3_eq : ∀ k : Fin 16, kernel3_0Expr 1 3 k = kernel3_0_r1_3 k := by decide +kernel +noncomputable def kernel3_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-107668893459719752158314),(-107668893459719751970365)⟩,⟨(-255272683767924707445564),(-255272683767924707258247)⟩⟩,⟨⟨(-102080776331686432662513),(-102080776331686432480041)⟩,⟨(-247570205221524612529831),(-247570205221524612347954)⟩⟩,⟨⟨(-96650296668944212214860),(-96650296668944212037804)⟩,⟨(-239993386358754306438087),(-239993386358754306261591)⟩⟩,⟨⟨(-91378480014915363732531),(-91378480014915363560796)⟩,⟨(-232545004838146539444837),(-232545004838146539273627)⟩⟩,⟨⟨(-86266018255394089344978),(-86266018255394089178504)⟩,⟨(-225227565630409662052839),(-225227565630409661886855)⟩⟩,⟨⟨(-81313280546934613486050),(-81313280546934613324731)⟩,⟨(-218043306853098877990918),(-218043306853098877830056)⟩⟩,⟨⟨(-76520324788764888980500),(-76520324788764888824267)⟩,⟨(-210994205989582203736840),(-210994205989582203581032)⟩⟩,⟨⟨(-71886909576183806724409),(-71886909576183806573159)⟩,⟨(-204081986454909621645588),(-204081986454909621494731)⟩⟩,⟨⟨(-67412506573842140551664),(-67412506573842140405332)⟩,⟨(-197308124471965192294864),(-197308124471965192148894)⟩⟩,⟨⟨(-63096313248029333819866),(-63096313248029333678334)⟩,⟨(-190673856222178995799418),(-190673856222178995658218)⟩⟩,⟨⟨(-58937265898074364790280),(-58937265898074364653475)⟩,⟨(-184180185236084848028627),(-184180185236084847892124)⟩⟩,⟨⟨(-54934052928202998424446),(-54934052928202998292255)⟩,⟨(-177827889990117092490806),(-177827889990117092358888)⟩⟩,⟨⟨(-51085128302658546946690),(-51085128302658546819043)⟩,⟨(-171617531677231974701235),(-171617531677231974573834)⟩⟩,⟨⟨(-47388725128570902217240),(-47388725128570902094015)⟩,⟨(-165549462120203097775073),(-165549462120203097652068)⟩⟩,⟨⟨(-43842869312930586240287),(-43842869312930586121412)⟩,⟨(-159623831797763618417862),(-159623831797763618299181)⟩⟩,⟨⟨(-40445393242071998658143),(-40445393242071998543493)⟩,⟨(-153840597955138077579311),(-153840597955138077464831)⟩⟩] +lemma kernel3_0_r1_4_eq : ∀ k : Fin 16, kernel3_0Expr 1 4 k = kernel3_0_r1_4 k := by decide +kernel +noncomputable def kernel3_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-37193949434273770447401),(-37193949434273770336907)⟩,⟨(-148199532771912564422845),(-148199532771912564312497)⟩⟩,⟨⟨(-34086024118424899114936),(-34086024118424899008479)⟩,⟨(-142700231561622423500271),(-142700231561622423393937)⟩⟩,⟨⟨(-31118950694163911319768),(-31118950694163911217264)⟩,⟨(-137342120978881757605171),(-137342120978881757502768)⟩⟩,⟨⟨(-28289923031455608790820),(-28289923031455608692154)⟩,⟨(-132124467211329098034593),(-132124467211329097936006)⟩⟩,⟨⟨(-25596008570207230733228),(-25596008570207230638323)⟩,⟨(-127046384135110100127755),(-127046384135110100032909)⟩⟩,⟨⟨(-23034161183224750947988),(-23034161183224750856725)⟩,⟨(-122106841414053024804627),(-122106841414053024713404)⟩⟩,⟨⟨(-20601233768552683102132),(-20601233768552683014433)⟩,⟨(-117304672524108901739303),(-117304672524108901651626)⟩⟩,⟨⟨(-18293990540009977856436),(-18293990540009977772182)⟩,⟨(-112638582686019215320487),(-112638582686019215236236)⟩⟩,⟨⟨(-16109118987513858361466),(-16109118987513858280587)⟩,⟨(-108107156690534042542285),(-108107156690534042461392)⟩⟩,⟨⟨(-14043241481557045902357),(-14043241481557045824734)⟩,⟨(-103708866601827870899950),(-103708866601827870822298)⟩⟩,⟨⟨(-12092926498956926894362),(-12092926498956926819913)⟩,⟨(-99442079326044616444507),(-99442079326044616370014)⟩⟩,⟨⟨(-10254699449713878158191),(-10254699449713878086810)⟩,⟨(-95305064033144115121485),(-95305064033144115050046)⟩⟩,⟨⟨(-8525053087487240190737),(-8525053087487240122349)⟩,⟨(-91295999421416694840248),(-91295999421416694771788)⟩⟩,⟨⟨(-6900457488809355089965),(-6900457488809355024459)⟩,⟨(-87412980815178087924619),(-87412980815178087859031)⟩⟩,⟨⟨(-5377369588699747891578),(-5377369588699747828878)⟩,⟨(-83654027087252226544328),(-83654027087252226481533)⟩⟩,⟨⟨(-3952242262803059976353),(-3952242262803059916355)⟩,⟨(-80017087398893224522850),(-80017087398893224462744)⟩⟩] +lemma kernel3_0_r1_5_eq : ∀ k : Fin 16, kernel3_0Expr 1 5 k = kernel3_0_r1_5 k := by decide +kernel +noncomputable def kernel3_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-2621532948546933522327),(-2621532948546933464962)⟩,⟨(-76500047750789425140548),(-76500047750789425083066)⟩⟩,⟨⟨(-1381711800091948684015),(-1381711800091948629178)⟩,⟨(-73100737339731569510391),(-73100737339731569455426)⟩⟩,⟨⟨(-229269374018232633085),(-229269374018232580703)⟩,⟨(-69816934716414097689875),(-69816934716414097637358)⟩⟩,⟨⟨839276155243172247330,839276155243172297353⟩,⟨(-66646373740673874445345),(-66646373740673874395178)⟩⟩,⟨⟨1827372249276329213119,1827372249276329260853⟩,⟨(-63586749331255084441209),(-63586749331255084393324)⟩⟩,⟨⟨2738425726053579445546,2738425726053579491082⟩,⟨(-60635723007923786867623),(-60635723007923786821929)⟩⟩,⟨⟨3575796942313352997119,3575796942313353040527⟩,⟨(-57790928224442003275769),(-57790928224442003232196)⟩⟩,⟨⟨4342794431849771165629,4342794431849771206999⟩,⟨(-55049975491550768093368),(-55049975491550768051828)⟩⟩,⟨⟨5042669992153773166594,5042669992153773205987⟩,⟨(-52410457289705982342315),(-52410457289705982302748)⟩⟩,⟨⟨5678614210501161542126,5678614210501161579629⟩,⟨(-49869952771861975974529),(-49869952771861975936847)⟩⟩,⟨⟨6253752419361116039667,6253752419361116075344⟩,⟨(-47426032257107284345889),(-47426032257107284310030)⟩⟩,⟨⟨6771141069898086911621,6771141069898086945551⟩,⟨(-45076261516427214442619),(-45076261516427214408503)⟩⟩,⟨⟨7233764511358614109596,7233764511358614141836⟩,⟨(-42818205852300278145037),(-42818205852300278112609)⟩⟩,⟨⟨7644532163270010534942,7644532163270010565571⟩,⟨(-40649433974232467740307),(-40649433974232467709488)⟩⟩,⟨⟨8006276066626948463932,8006276066626948493004⟩,⟨(-38567521672696590006785),(-38567521672696589977521)⟩⟩,⟨⟨8321748799601280516327,8321748799601280543918⟩,⟨(-36570055294275370665151),(-36570055294275370637366)⟩⟩] +lemma kernel3_0_r1_6_eq : ∀ k : Fin 16, kernel3_0Expr 1 6 k = kernel3_0_r1_6 k := by decide +kernel +noncomputable def kernel3_0_r1_7 : Fin 16 → CBox := ![⟨⟨8593621742775978141154,8593621742775978167312⟩,⟨(-34654635021108650992789),(-34654635021108650966437)⟩⟩,⟨⟨8824483678471591722239,8824483678471591747037⟩,⟨(-32818877958018519481706),(-32818877958018519456712)⟩⟩,⟨⟨9016839708398533980045,9016839708398534003530⟩,⟨(-31060421030933376421240),(-31060421030933376397559)⟩⟩,⟨⟨9173110473625918869928,9173110473625918892168⟩,⟨(-29376923700454359581786),(-29376923700454359559350)⟩⟩,⟨⟨9295631660702608461991,9295631660702608483028⟩,⟨(-27766070494606819114539),(-27766070494606819093307)⟩⟩,⟨⟨9386653777693335779355,9386653777693335799253⟩,⟨(-26225573364997083132917),(-26225573364997083112825)⟩⟩,⟨⟨9448342183896982075845,9448342183896982094648⟩,⟨(-24753173870751973627790),(-24753173870751973608795)⟩⟩,⟨⟨9482777357089929643052,9482777357089929660815⟩,⟨(-23346645194756694334252),(-23346645194756694316297)⟩⟩,⟨⟨9491955382279500339524,9491955382279500356284⟩,⟨(-22003793996827005637939),(-22003793996827005620988)⟩⟩,⟨⟨9477788646155454291545,9477788646155454307363⟩,⟨(-20722462108555125583819),(-20722462108555125567812)⟩⟩,⟨⟨9442106721686039458097,9442106721686039473006⟩,⟨(-19500528074656564309687),(-19500528074656564294591)⟩⟩,⟨⟨9386657427613906769565,9386657427613906783616⟩,⟨(-18335908545718044686063),(-18335908545718044671830)⟩⟩,⟨⟨9313108047961199772669,9313108047961199785894⟩,⟨(-17226559527305641664238),(-17226559527305641650830)⟩⟩,⟨⟨9223046697047285834361,9223046697047285846811⟩,⟨(-16170477490438073537087),(-16170477490438073524458)⟩⟩,⟨⟨9117983815952064546740,9117983815952064558444⟩,⟨(-15165700348463422236539),(-15165700348463422224659)⟩⟩,⟨⟨8999353786817886175147,8999353786817886186227⟩,⟨(-14210308305399110734050),(-14210308305399110722800)⟩⟩] +lemma kernel3_0_r1_7_eq : ∀ k : Fin 16, kernel3_0Expr 1 7 k = kernel3_0_r1_7 k := by decide +kernel +noncomputable def kernel3_0_r1_8 : Fin 16 → CBox := ![⟨⟨8868516651869344401060,8868516651869344411832⟩,⟨(-13302424580805335082807),(-13302424580805335071876)⟩⟩,⟨⟨8726759924538279465497,8726759924538279475973⟩,⟨(-12440216016261901944994),(-12440216016261901934369)⟩⟩,⟨⟨8575300480607157618479,8575300480607157628661⟩,⟨(-11621893568508084632771),(-11621893568508084622450)⟩⟩,⟨⟨8415286517823717509351,8415286517823717519248⟩,⟨(-10845712694285172273377),(-10845712694285172263352)⟩⟩,⟨⟨8247799572989756211090,8247799572989756220697⟩,⟨(-10109973631892309118454),(-10109973631892309108727)⟩⟩,⟨⟨8073856586083758651185,8073856586083758660520⟩,⟨(-9413021584428441650148),(-9413021584428441640704)⟩⟩,⟨⟨7894412001537577196816,7894412001537577205873⟩,⟨(-8753246809647128048104),(-8753246809647128038945)⟩⟩,⟨⟨7710359897348597223011,7710359897348597231802⟩,⟨(-8129084621297020712659),(-8129084621297020703774)⟩⟩,⟨⟨7522536133268063757517,7522536133268063766044⟩,⟨(-7539015306759399498837),(-7539015306759399490225)⟩⟩,⟨⟨7331720509861004776521,7331720509861004784792⟩,⟨(-6981563965725594688600),(-6981563965725594680251)⟩⟩,⟨⟨7138638930781202214727,7138638930781202222748⟩,⟨(-6455300274581872908060),(-6455300274581872899968)⟩⟩,⟨⟨6943965561143883476652,6943965561143883484429⟩,⟨(-5958838181087741749318),(-5958838181087741741477)⟩⟩,⟨⟨6748324975407396544367,6748324975407396551897⟩,⟨(-5490835533846034427047),(-5490835533846034419458)⟩⟩,⟨⟨6552294288691456999010,6552294288691457006308⟩,⟨(-5049993650969939576955),(-5049993650969939569605)⟩⟩,⟨⟨6356405265962177864289,6356405265962177871357⟩,⟨(-4635056832253720067661),(-4635056832253720060547)⟩⟩,⟨⟨6161146404001763292751,6161146404001763299596⟩,⟨(-4244811819050597483729),(-4244811819050597476843)⟩⟩] +lemma kernel3_0_r1_8_eq : ∀ k : Fin 16, kernel3_0Expr 1 8 k = kernel3_0_r1_8 k := by decide +kernel +noncomputable def kernel3_0_r1_9 : Fin 16 → CBox := ![⟨⟨5966964981552393714817,5966964981552393721440⟩,⟨(-3878087205953547333264),(-3878087205953547326604)⟩⟩,⟨⟨5774269073478551697351,5774269073478551703763⟩,⟨(-3533752808262938158091),(-3533752808262938151647)⟩⟩,⟨⟨5583429525229093051836,5583429525229093058039⟩,⟨(-3210718989109441913112),(-3210718989109441906881)⟩⟩,⟨⟨5394781884299165793716,5394781884299165799717⟩,⟨(-2907935949981831219270),(-2907935949981831213245)⟩⟩,⟨⟨5208628285792170248553,5208628285792170254355⟩,⟨(-2624392988287550228536),(-2624392988287550222714)⟩⟩,⟨⟨5025239289563017859806,5025239289563017865418⟩,⟨(-2359117725449688611464),(-2359117725449688605835)⟩⟩,⟨⟨4844855666785786460743,4844855666785786466167⟩,⟨(-2111175308917590108222),(-2111175308917590102786)⟩⟩,⟨⟨4667690134131400280391,4667690134131400285634⟩,⟨(-1879667591340173242379),(-1879667591340173237126)⟩⟩,⟨⟨4493929034064200787659,4493929034064200792723⟩,⟨(-1663732290021513490724),(-1663732290021513485652)⟩⟩,⟨⟨4323733960070330279651,4323733960070330284546⟩,⟨(-1462542129647709617409),(-1462542129647709612511)⟩⟩,⟨⟨4157243325915919360190,4157243325915919364917⟩,⟨(-1275303971142901692195),(-1275303971142901687468)⟩⟩,⟨⟨3994573878299423947644,3994573878299423952210⟩,⟨(-1101257929380886305905),(-1101257929380886301340)⟩⟩,⟨⟨3835822152510437209687,3835822152510437214095⟩,⟨(-939676482347438207365),(-939676482347438202960)⟩⟩,⟨⟨3681065870937307255749,3681065870937307260006⟩,⟨(-789863574217538992305),(-789863574217538988053)⟩⟩,⟨⟨3530365284478375906414,3530365284478375910520⟩,⟨(-651153714681562746517),(-651153714681562742416)⟩⟩,⟨⟨3383764457107116705360,3383764457107116709327⟩,⟨(-522911076725392881451),(-522911076725392877492)⟩⟩] +lemma kernel3_0_r1_9_eq : ∀ k : Fin 16, kernel3_0Expr 1 9 k = kernel3_0_r1_9 k := by decide +kernel +noncomputable def kernel3_0_r1_10 : Fin 16 → CBox := ![⟨⟨3241292494020430111047,3241292494020430114871⟩,⟨(-404528594941746950702),(-404528594941746946887)⟩⟩,⟨⟨3102964713962422066651,3102964713962422070341⟩,⟨(-295427066323955134105),(-295427066323955130427)⟩⟩,⟨⟨2968783766463747588733,2968783766463747592293⟩,⟨(-195054255369345577746),(-195054255369345574197)⟩⟩,⟨⟨2838740694869663970792,2838740694869663974226⟩,⟨(-102884005197491520196),(-102884005197491516774)⟩⟩,⟨⟨2712815946148945550657,2712815946148945553968⟩,⟨(-18415356269109514713),(-18415356269109511417)⟩⟩,⟨⟨2590980328581412456674,2590980328581412459869⟩,⟨58828325825414264937,58828325825414268116⟩⟩,⟨⟨2473195918514675533110,2473195918514675536189⟩,⟨129300212152849119519,129300212152849122582⟩⟩,⟨⟨2359416917461458462715,2359416917461458465685⟩,⟨193430860555192235398,193430860555192238352⟩⟩,⟨⟨2249590460878185539173,2249590460878185542035⟩,⟨251629052962595015599,251629052962595018444⟩⟩,⟨⟨2143657380024075753914,2143657380024075756675⟩,⟨304282618869107686361,304282618869107689103⟩⟩,⟨⟨2041552918348410611092,2041552918348410613751⟩,⟨351759244040082563877,351759244040082566518⟩⟩,⟨⟨1943207403892585065752,1943207403892585068317⟩,⟨394407263617360095065,394407263617360097612⟩⟩,⟨⟨1848546879223637451419,1848546879223637453889⟩,⟨432556438881960547237,432556438881960549689⟩⟩,⟨⟨1757493690437800951612,1757493690437800953994⟩,⟨466518717023842863094,466518717023842865457⟩⟩,⟨⟨1669967036786826445067,1669967036786826447362⟩,⟨496588973354312612046,496588973354312614321⟩⟩,⟨⟨1585883482486977846974,1585883482486977849189⟩,⟨523045735478821541343,523045735478821543538⟩⟩] +lemma kernel3_0_r1_10_eq : ∀ k : Fin 16, kernel3_0Expr 1 10 k = kernel3_0_r1_10 k := by decide +kernel +noncomputable def kernel3_0_r1_11 : Fin 16 → CBox := ![⟨⟨1505157432271261525377,1505157432271261527509⟩,⟨546151889026176221294,546151889026176223407⟩⟩,⟨⟨1427701572240166726390,1427701572240166728445⟩,⟨566155364604552146228,566155364604552148265⟩⟩,⟨⟨1353427277555489592894,1353427277555489594873⟩,⟨583289805725196325909,583289805725196327868⟩⟩,⟨⟨1282244988506193636047,1282244988506193637954⟩,⟨597775217501313508759,597775217501313510647⟩⟩,⟨⟨1214064556455207116266,1214064556455207118105⟩,⟨609818595992399240928,609818595992399242748⟩⟩,⟨⟨1148795561152033381914,1148795561152033383687⟩,⟨619614538123249566707,619614538123249568462⟩⟩,⟨⟨1086347600868492196403,1086347600868492198115⟩,⟨627345832162096107378,627345832162096109073⟩⟩,⟨⟨1026630556784234465913,1026630556784234467564⟩,⟨633184028793850651202,633184028793850652837⟩⟩,⟨⟨969554833015273190255,969554833015273191846⟩,⟨637289992872368851815,637289992872368853391⟩⟩,⟨⟨915031573643021273275,915031573643021274811⟩,⟨639814435980040370652,639814435980040372176⟩⟩,⟨⟨862972858063571387572,862972858063571389056⟩,⟨640898429963972749482,640898429963972750955⟩⟩,⟨⟨813291875937522013329,813291875937522014763⟩,⟨640673901655655279714,640673901655655281135⟩⟩,⟨⟨765903082979853357144,765903082979853358527⟩,⟨639264109015370004670,639264109015370006040⟩⟩,⟨⟨720722338787472535362,720722338787472536694⟩,⟨636784098973867830468,636784098973867831791⟩⟩,⟨⟨677667027859344270097,677667027859344271382⟩,⟨633341147272061040231,633341147272061041507⟩⟩,⟨⟨636656164920846727002,636656164920846728245⟩,⟨629035180624815476247,629035180624815477482⟩⟩] +lemma kernel3_0_r1_11_eq : ∀ k : Fin 16, kernel3_0Expr 1 11 k = kernel3_0_r1_11 k := by decide +kernel +noncomputable def kernel3_0_r1_12 : Fin 16 → CBox := ![⟨⟨597610485620368216215,597610485620368217415⟩,⟨623959181557475372349,623959181557475373542⟩⟩,⟨⟨560452523622396999382,560452523622397000540⟩,⟨618199576283642602838,618199576283642603989⟩⟩,⟨⟨525106675077643328787,525106675077643329906⟩,⟨611836606010082838338,611836606010082839450⟩⟩,⟨⟨491499251407242952598,491499251407242953677⟩,⟨604944682069567557684,604944682069567558758⟩⟩,⟨⟨459558521294981182332,459558521294981183376⟩,⟨597592725295107182258,597592725295107183297⟩⟩,⟨⟨429214742738887177176,429214742738887178188⟩,⟨589844490059510671681,589844490059510672689⟩⟩,⟨⟨400400185971605466431,400400185971605467406⟩,⟨581758873412643901264,581758873412643902234⟩⟩,⟨⟨373049148017767946192,373049148017767947137⟩,⟨573390209755274966726,573390209755274967667⟩⟩,⟨⟨347097959616263377000,347097959616263377912⟩,⟨564788551493109508304,564788551493109509213⟩⟩,⟨⟨322484985195918943888,322484985195918944771⟩,⟨555999936117651437635,555999936117651438514⟩⟩,⟨⟨299150616554744075933,299150616554744076786⟩,⟨547066640161989895949,547066640161989896801⟩⟩,⟨⟨277037260855603738005,277037260855603738832⟩,⟨538027420479624942881,538027420479624943707⟩⟩,⟨⟨256089323515039727604,256089323515039728402⟩,⟨528917743293112422508,528917743293112423306⟩⟩,⟨⟨236253186526987409059,236253186526987409835⟩,⟨519770001456739455193,519770001456739455967⟩⟩,⟨⟨217477182729376109273,217477182729376110025⟩,⟨510613720373739351072,510613720373739351823⟩⟩,⟨⟨199711566489080102470,199711566489080103198⟩,⟨501475753003818053756,501475753003818054485⟩⟩] +lemma kernel3_0_r1_12_eq : ∀ k : Fin 16, kernel3_0Expr 1 12 k = kernel3_0_r1_12 k := by decide +kernel +noncomputable def kernel3_0_r1_13 : Fin 16 → CBox := ![⟨⟨182908481249422097568,182908481249422098276⟩,⟨492380464391089298160,492380464391089298866⟩⟩,⟨⟨167021924354433757616,167021924354433758307⟩,⟨483349906135994357193,483349906135994357884⟩⟩,⟨⟨152007709535352948978,152007709535352949651⟩,⟨474403981227502372261,474403981227502372935⟩⟩,⟨⟨137823427417384211717,137823427417384212376⟩,⟨465560599643932519096,465560599643932519755⟩⟩,⟨⟨124428404378561135543,124428404378561136183⟩,⟨456835825122189210974,456835825122189211616⟩⟩,⟨⟨111783660067615916058,111783660067615916684⟩,⟨448244013486131571894,448244013486131572521⟩⟩,⟨⟨99851863864067075160,99851863864067075773⟩,⟨439797942915279739965,439797942915279740581⟩⟩,⟨⟨88597290541262072992,88597290541262073590⟩,⟨431508936525160251883,431508936525160252484⟩⟩,⟨⟨77985775371834874119,77985775371834874705⟩,⟨423386977620373767088,423386977620373767676⟩⟩,⟨⟨67984668894934075156,67984668894934075729⟩,⟨415440817970989609078,415440817970989609654⟩⟩,⟨⟨58562791545617028281,58562791545617028842⟩,⟨407678079452187934215,407678079452187934778⟩⟩,⟨⟨49690388328959402710,49690388328959403260⟩,⟨400105349376232776994,400105349376232777547⟩⟩,⟨⟨41339083704665880653,41339083704665881193⟩,⟨392728269834914937263,392728269834914937804⟩⟩,⟨⟨33481836832252741191,33481836832252741720⟩,⟨385551621359596123476,385551621359596124007⟩⟩,⟨⟨26092897312172285426,26092897312172285944⟩,⟨378579401194954792939,378579401194954793459⟩⟩,⟨⟨19147761544526798542,19147761544526799048⟩,⟨371814896471516089286,371814896471516089796⟩⟩] +lemma kernel3_0_r1_13_eq : ∀ k : Fin 16, kernel3_0Expr 1 13 k = kernel3_0_r1_13 k := by decide +kernel +noncomputable def kernel3_0_r1_14 : Fin 16 → CBox := ![⟨⟨12623129814239738416,12623129814239738914⟩,⟨365260752551076155354,365260752551076155855⟩⟩,⟨⟨6496864199677334868,6496864199677335357⟩,⟨358919036808234639727,358919036808234640218⟩⟩,⟨⟨747947390707775895,747947390707776375⟩,⟨352791298100455050990,352791298100455051472⟩⟩,⟨⟨(-4643557507989417230),(-4643557507989416758)⟩,⟨346878622168404400175,346878622168404400651⟩⟩,⟨⟨(-9696546121931322322),(-9696546121931321859)⟩,⟨341181683197802121340,341181683197802121807⟩⟩,⟨⟨(-14428910842346670611),(-14428910842346670155)⟩,⟨335700791763651677135,335700791763651677595⟩⟩,⟨⟨(-18857577702288677437),(-18857577702288676989)⟩,⟨330435939367552072509,330435939367552072958⟩⟩,⟨⟨(-22998542050651453218),(-22998542050651452776)⟩,⟨325386839768803809237,325386839768803809682⟩⟩,⟨⟨(-26866902987960429171),(-26866902987960428737)⟩,⟨320552967300245405520,320552967300245405958⟩⟩,⟨⟨(-30476896533755810853),(-30476896533755810422)⟩,⟨315933592350191092498,315933592350191092932⟩⟩,⟨⟨(-33841927500754286045),(-33841927500754285621)⟩,⟨311527814182494251586,311527814182494252014⟩⟩,⟨⟨(-36974600055790908878),(-36974600055790908460)⟩,⟨307334591257639219984,307334591257639220407⟩⟩,⟨⟨(-39886746951842214723),(-39886746951842214310)⟩,⟨303352769208869114886,303352769208869115302⟩⟩,⟨⟨(-42589457419244218831),(-42589457419244218422)⟩,⟨299581106618690476787,299581106618690477200⟩⟩,⟨⟨(-45093103707575087263),(-45093103707575086861)⟩,⟨296018298732656409425,296018298732656409830⟩⟩,⟨⟨(-47407366272601040441),(-47407366272601040042)⟩,⟨292662999239116641600,292662999239116642002⟩⟩] +lemma kernel3_0_r1_14_eq : ∀ k : Fin 16, kernel3_0Expr 1 14 k = kernel3_0_r1_14 k := by decide +kernel +noncomputable def kernel3_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-49541257605213574481),(-49541257605213574087)⟩,⟨289513840235632347008,289513840235632347406⟩⟩,⟨⟨(-51503144701443498670),(-51503144701443498281)⟩,⟨286569450494981174412,286569450494981174806⟩⟩,⟨⟨(-53300770174448750524),(-53300770174448750137)⟩,⟨283828472136118151535,283828472136118151926⟩⟩,⟨⟨(-54941272010863665893),(-54941272010863665510)⟩,⟨281289575798104259866,281289575798104260253⟩⟩,⟨⟨(-56431201975091616395),(-56431201975091616015)⟩,⟨278951474407858889540,278951474407858889924⟩⟩,⟨⟨(-57776542666044036701),(-57776542666044036323)⟩,⟨276812935625626538526,276812935625626538910⟩⟩,⟨⟨(-58982723231499330951),(-58982723231499330575)⟩,⟨274872793045262673179,274872793045262673557⟩⟩,⟨⟨(-60054633745696613276),(-60054633745696612903)⟩,⟨273129956219828536181,273129956219828536558⟩⟩,⟨⟨(-60996638256012550774),(-60996638256012550405)⟩,⟨271583419576529126581,271583419576529126954⟩⟩,⟨⟨(-61812586504614837526),(-61812586504614837160)⟩,⟨270232270278721240236,270232270278721240606⟩⟩,⟨⟨(-62505824330862438308),(-62505824330862437942)⟩,⟨269075695086547468190,269075695086547468560⟩⟩,⟨⟨(-63079202759949458540),(-63079202759949458174)⟩,⟨268112986261705051407,268112986261705051777⟩⟩,⟨⟨(-63535085782884494369),(-63535085782884494004)⟩,⟨267343546555922710363,267343546555922710731⟩⟩,⟨⟨(-63875356832378236676),(-63875356832378236310)⟩,⟨266766893316880871719,266766893316880872089⟩⟩,⟨⟨(-64101423958596122173),(-64101423958596121811)⟩,⟨266382661739557652571,266382661739557652937⟩⟩,⟨⟨(-64214223708036716848),(-64214223708036716486)⟩,⟨266190607285300823200,266190607285300823566⟩⟩] +lemma kernel3_0_r1_15_eq : ∀ k : Fin 16, kernel3_0Expr 1 15 k = kernel3_0_r1_15 k := by decide +kernel +noncomputable def kernel3_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel3_0_r1_0,kernel3_0_r1_1,kernel3_0_r1_2,kernel3_0_r1_3,kernel3_0_r1_4,kernel3_0_r1_5,kernel3_0_r1_6,kernel3_0_r1_7,kernel3_0_r1_8,kernel3_0_r1_9,kernel3_0_r1_10,kernel3_0_r1_11,kernel3_0_r1_12,kernel3_0_r1_13,kernel3_0_r1_14,kernel3_0_r1_15] +lemma kernel3_0_r1_eq (i k : Fin 16) : kernel3_0Expr 1 i k = kernel3_0_r1 i k := by + fin_cases i + · exact kernel3_0_r1_0_eq k + · exact kernel3_0_r1_1_eq k + · exact kernel3_0_r1_2_eq k + · exact kernel3_0_r1_3_eq k + · exact kernel3_0_r1_4_eq k + · exact kernel3_0_r1_5_eq k + · exact kernel3_0_r1_6_eq k + · exact kernel3_0_r1_7_eq k + · exact kernel3_0_r1_8_eq k + · exact kernel3_0_r1_9_eq k + · exact kernel3_0_r1_10_eq k + · exact kernel3_0_r1_11_eq k + · exact kernel3_0_r1_12_eq k + · exact kernel3_0_r1_13_eq k + · exact kernel3_0_r1_14_eq k + · exact kernel3_0_r1_15_eq k +noncomputable def kernel3_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-106555412879318640955897171),(-106555412879318640802715127)⟩,⟨(-354958774562073683034563429),(-354958774562073682880266778)⟩⟩,⟨⟨(-106551365842017689300169575),(-106551365842017689147022785)⟩,⟨(-354820727822574804838972550),(-354820727822574804684711425)⟩⟩,⟨⟨(-106543225807432117043732662),(-106543225807432116890656672)⟩,⟨(-354544792985642338398084661),(-354544792985642338243894879)⟩⟩,⟨⟨(-106530901063489716744027614),(-106530901063489716591057926)⟩,⟨(-354131287057155795391901162),(-354131287057155795237818499)⟩⟩,⟨⟨(-106514254560890238774598351),(-106514254560890238621770412)⟩,⟨(-353580684850840651782854985),(-353580684850840651628915160)⟩⟩,⟨⟨(-106493104533076163390372625),(-106493104533076163237721800)⟩,⟨(-352893618155650367749316010),(-352893618155650367595554663)⟩⟩,⟨⟨(-106467225318542189637236860),(-106467225318542189484798420)⟩,⟨(-352070874628099146486901381),(-352070874628099146333354054)⟩⟩,⟨⟨(-106436348381808645217034638),(-106436348381808645064843728)⟩,⟨(-351113396411677974338146390),(-351113396411677974184848501)⟩⟩,⟨⟨(-106400163528498327597350226),(-106400163528498327445441866)⟩,⟨(-350022278486017301199013771),(-350022278486017301046000615)⟩⟩,⟨⟨(-106358320309092362778497972),(-106358320309092362626906999)⟩,⟨(-348798766748988882957021427),(-348798766748988882804328114)⟩⟩,⟨⟨(-106310429605102635918429747),(-106310429605102635767190866)⟩,⟨(-347444255835466380320812744),(-347444255835466380168474252)⟩⟩,⟨⟨(-106256065390590204051225058),(-106256065390590203900372710)⟩,⟨(-345960286676988798872337811),(-345960286676988798720388856)⟩⟩,⟨⟨(-106194766661184697296297759),(-106194766661184697145866275)⟩,⟨(-344348543807092208804563784),(-344348543807092208653038971)⟩⟩,⟨⟨(-106126039522022739455838721),(-106126039522022739305862042)⟩,⟨(-342610852417592775591852039),(-342610852417592775440785587)⟩⟩,⟨⟨(-106049359425327377997687726),(-106049359425327377848199733)⟩,⟨(-340749175171617265865802921),(-340749175171617265715228982)⟩⟩,⟨⟨(-105964173547698713909040901),(-105964173547698713760074965)⟩,⟨(-338765608779685087635436502),(-338765608779685087485388723)⟩⟩] +lemma kernel3_0_r2_0_eq : ∀ k : Fin 16, kernel3_0Expr 2 0 k = kernel3_0_r2_0 k := by decide +kernel +noncomputable def kernel3_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-105869903296581454430997379),(-105869903296581454282586902)⟩,⟨(-336662380345647719309796233),(-336662380345647719160308291)⟩⟩,⟨⟨(-105765946934820835012424888),(-105765946934820834864602534)⟩,⟨(-334441843489786131040573642),(-334441843489786130891678476)⟩⟩,⟨⟨(-105651682311716883114516496),(-105651682311716882967315075)⟩,⟨(-332106474256853471535551368),(-332106474256853471387282062)⟩⟩,⟨⟨(-105526469688540677673718512),(-105526469688540677527169942)⟩,⟨(-329658866817327764206011275),(-329658866817327764058400021)⟩⟩,⟨⟨(-105389654646087173302534702),(-105389654646087173156671240)⟩,⟨(-327101728970606423889757230),(-327101728970606423742836561)⟩⟩,⟨⟨(-105240571061509102959372404),(-105240571061509102814225033)⟩,⟨(-324437877459329782814960426),(-324437877459329782668761596)⟩⟩,⟨⟨(-105078544141406948301750448),(-105078544141406948157350691)⟩,⟨(-321670233104463137123895107),(-321670233104463136978449913)⟩⟩,⟨⟨(-104902893497942172350814399),(-104902893497942172207192329)⟩,⟨(-318801815771194655460422914),(-318801815771194655315761700)⟩⟩,⟨⟨(-104712936254595734114002031),(-104712936254595733971188598)⟩,⟨(-315835739176118324836288132),(-315835739176118324692442120)⟩⟩,⟨⟨(-104507990168111924124684702),(-104507990168111923982708760)⟩,⟨(-312775205546565383732640774),(-312775205546565383589639085)⟩⟩,⟨⟨(-104287376753149029162679961),(-104287376753149029021571554)⟩,⟨(-309623500143322796172602889),(-309623500143322796030475836)⟩⟩,⟨⟨(-104050424396203188040012191),(-104050424396203187899799149)⟩,⟨(-306383985658331601945768108),(-306383985658331601804543784)⟩⟩,⟨⟨(-103796471445479650478176112),(-103796471445479650338887877)⟩,⟨(-303060096499289757681323043),(-303060096499289757541031157)⟩⟩,⟨⟨(-103524869263555788803805813),(-103524869263555788665468731)⟩,⟨(-299655332973391665347817755),(-299655332973391665208484913)⟩⟩,⟨⟨(-103234985229911609976382876),(-103234985229911609839025329)⟩,⟨(-296173255382718270154438579),(-296173255382718270016093421)⟩⟩,⟨⟨(-102926205680694831739876600),(-102926205680694831603523782)⟩,⟨(-292617478044045710455101306),(-292617478044045710317769283)⟩⟩] +lemma kernel3_0_r2_1_eq : ∀ k : Fin 16, kernel3_0Expr 2 1 k = kernel3_0_r2_1 k := by decide +kernel +noncomputable def kernel3_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-102597938773437171867424595),(-102597938773437171732104372)⟩,⟨(-288991663246065354721277586),(-288991663246065354584986817)⟩⟩,⟨⟨(-102249617264844403813286200),(-102249617264844403679021927)⟩,⟨(-285299515157202041278685338),(-285299515157202041143459425)⟩⟩,⟨⟨(-101880701190242715310285779),(-101880701190242715177104012)⟩,⟨(-281544773697378876518847092),(-281544773697378876384712839)⟩⟩,⟨⟨(-101490680433775448987390163),(-101490680433775448855313091)⟩,⟨(-277731208387204548206783441),(-277731208387204548073763274)⟩⟩,⟨⟨(-101079077179004620030481642),(-101079077179004619899535318)⟩,⟨(-273862612188151359555123156),(-273862612188151359423243371)⟩⟩,⟨⟨(-100645448230177657598290395),(-100645448230177657468494908)⟩,⟨(-269942795347347775265665615),(-269942795347347775134946527)⟩⟩,⟨⟨(-100189387195068330813430659),(-100189387195068330684810598)⟩,⟨(-265975579260626997307934376),(-265975579260626997178400805)⟩⟩,⟨⟨(-99710526520988305317396772),(-99710526520988305189970980)⟩,⟨(-261964790367451891294033595),(-261964790367451891165704601)⟩⟩,⟨⟨(-99208539376288542232545832),(-99208539376288542106338603)⟩,⟨(-257914254091275544486251955),(-257914254091275544359152053)⟩⟩,⟨⟨(-98683141370423928856326154),(-98683141370423928731353794)⟩,⟨(-253827788838795092833882543),(-253827788838795092708028242)⟩⟩,⟨⟨(-98134092106436093327275381),(-98134092106436093203560385)⟩,⟨(-249709200071413617188068590),(-249709200071413617063482594)⟩⟩,⟨⟨(-97561196560514143151770250),(-97561196560514143029327816)⟩,⟨(-245562274462040470894653308),(-245562274462040470771351004)⟩⟩,⟨⟨(-96964306284116808267995045),(-96964306284116808146847392)⟩,⟨(-241390774150134148357775518),(-241390774150134148235779324)⟩⟩,⟨⟨(-96343320424977805183133142),(-96343320424977805063292726)⟩,⟨(-237198431107623725252807229),(-237198431107623725132129772)⟩⟩,⟨⟨(-95698186564164750225830226),(-95698186564164750107317341)⟩,⟨(-232988941628035194286783364),(-232988941628035194167445120)⟩⟩,⟨⟨(-95028901367216181961904599),(-95028901367216181844730553)⟩,⟨(-228765960950798100575027584),(-228765960950798100457040018)⟩⟩] +lemma kernel3_0_r2_2_eq : ∀ k : Fin 16, kernel3_0Expr 2 2 k = kernel3_0_r2_2 k := by decide +kernel +noncomputable def kernel3_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-94335511048236740456938757),(-94335511048236740341123953)⟩,⟨(-224533098032316383710568647),(-224533098032316383593952334)⟩⟩,⟨⟨(-93618111646682845936136250),(-93618111646682845821688719)⟩,⟨(-220293910474956119426997983),(-220293910474956119311761086)⟩⟩,⟨⟨(-92876849117415915772363516),(-92876849117415915659301266)⟩,⟨(-216051899624633007746686457),(-216051899624633007632847140)⟩⟩,⟨⟨(-92111919235432919646587776),(-92111919235432919534918043)⟩,⟨(-211810505847175286881792037),(-211810505847175286769357650)⟩⟩,⟨⟨(-91323567317500655636303625),(-91323567317500655526044498)⟩,⟨(-207573103993094795662481898),(-207573103993094795551470672)⟩⟩,⟨⟨(-90512087763716412001954043),(-90512087763716411893109413)⟩,⟨(-203342999059821913009789774),(-203342999059821912900205693)⟩⟩,⟨⟨(-89677823422789681788312443),(-89677823422789681680897981)⟩,⟨(-199123422059851034391276113),(-199123422059851034283134966)⟩⟩,⟨⟨(-88821164785583509000001848),(-88821164785583508894020605)⟩,⟨(-194917526102604270236820893),(-194917526102604270130125808)⟩⟩,⟨⟨(-87942549012166245289657079),(-87942549012166245185125317)⟩,⟨(-190728382697154532757322244),(-190728382697154532652089588)⟩⟩,⟨⟨(-87042458798301575660283740),(-87042458798301575557200602)⟩,⟨(-186558978282257661816358248),(-186558978282257661712587214)⟩⟩,⟨⟨(-86121421087943453011998160),(-86121421087943452910376944)⟩,⟨(-182412210989429444249147006),(-182412210989429444146850973)⟩⟩,⟨⟨(-85180005638900136769381990),(-85180005638900136669221537)⟩,⟨(-178290887644070176983759652),(-178290887644070176882937493)⟩⟩,⟨⟨(-84218823449385199253311658),(-84218823449385199154625788)⟩,⟨(-174197721008889824988915802),(-174197721008889824889581405)⟩⟩,⟨⟨(-83238525053680765379365200),(-83238525053680765282148922)⟩,⟨(-170135327273123965343807478),(-170135327273123965245955857)⟩⟩,⟨⟨(-82239798695597301617819619),(-82239798695597301522083863)⟩,⟨(-166106223790257827258236836),(-166106223790257827161878962)⟩⟩,⟨⟨(-81223368388823189276225746),(-81223368388823189181965190)⟩,⟨(-162112827066196157401480036),(-162112827066196157306610578)⟩⟩] +lemma kernel3_0_r2_3_eq : ∀ k : Fin 16, kernel3_0Expr 2 3 k = kernel3_0_r2_3 k := by decide +kernel +noncomputable def kernel3_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-80189991873614639582692008),(-80189991873614639489918831)⟩,⟨(-158157450999033746632060383),(-158157450999033746538691548)⟩⟩,⟨⟨(-79140458479581089050725617),(-79140458479581088959429993)⟩,⟨(-154242305370798676503336813),(-154242305370798676411458734)⟩⟩,⟨⟨(-78075586904572233603760445),(-78075586904572233513950960)⟩,⟨(-150369494590761130339341028),(-150369494590761130248962295)⟩⟩,⟨⟨(-76996222919869826515446503),(-76996222919869826427113808)⟩,⟨(-146541016689128410804027903),(-146541016689128410715139113)⟩⟩,⟨⟨(-75903237012030112897330645),(-75903237012030112810484352)⟩,⟨(-142758762559185035835728711),(-142758762559185035748339464)⟩⟩,⟨⟨(-74797521971811461153669864),(-74797521971811461068296473)⟩,⟨(-139024515445188822813897806),(-139024515445188822727994522)⟩⟩,⟨⟨(-73679990440656858021991443),(-73679990440656857938097269)⟩,⟨(-135339950672603022988138458),(-135339950672603022903727415)⟩⟩,⟨⟨(-72551572425183249574950190),(-72551572425183249492522068)⟩,⟨(-131706635616534049736965308),(-131706635616534049654033247)⟩⟩,⟨⟨(-71413212790060330259545842),(-71413212790060330178591886)⟩,⟨(-128126029903557258206153597),(-128126029903557258124708585)⟩⟩,⟨⟨(-70265868739541692131248203),(-70265868739541692051750481)⟩,⟨(-124599485841452550806608546),(-124599485841452550726632528)⟩⟩,⟨⟨(-69110507297742912109382242),(-69110507297742912031344890)⟩,⟨(-121128249070740121384255706),(-121128249070740121305752748)⟩⟩,⟨⟨(-67948102797546105169652584),(-67948102797546105093058908)⟩,⟨(-117713459431307058678002118),(-117713459431307058600955391)⟩⟩,⟨⟨(-66779634387750881470932832),(-66779634387750881395788499)⟩,⟨(-114356152036850267580678325),(-114356152036850267505093414)⟩⟩,⟨⟨(-65606083567789919327848128),(-65606083567789919254132175)⟩,⟨(-111057258549332492284434127),(-111057258549332492210289913)⟩⟩,⟨⟨(-64428431758986115893986345),(-64428431758986115821700862)⟩,⟨(-107817608645158179100050726),(-107817608645158179027349197)⟩⟩,⟨⟨(-63247657920950302834121716),(-63247657920950302763246819)⟩,⟨(-104637931664326309619918092),(-104637931664326309548639196)⟩⟩] +lemma kernel3_0_r2_4_eq : ∀ k : Fin 16, kernel3_0Expr 2 4 k = kernel3_0_r2_4 k := by decide +kernel +noncomputable def kernel3_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-62064736221306779543569429),(-62064736221306779474109723)⟩,⟨(-101518858433409737971899985),(-101518858433409737902048221)⟩⟩,⟨⟨(-60880633766491527911548315),(-60880633766491527843478916)⟩,⟨(-98460923252846301530703888),(-98460923252846301462254178)⟩⟩,⟨⟨(-59696308400898154613126835),(-59696308400898154546447948)⟩,⟨(-95464566038707109535988278),(-95464566038707109468940699)⟩⟩,⟨⟨(-58512706581152677683311529),(-58512706581152677618000484)⟩,⟨(-92530134608832755368956333),(-92530134608832755303288018)⟩⟩,⟨⟨(-57330761331783621213224229),(-57330761331783621149283236)⟩,⟨(-89657887102999289617309490),(-89657887102999289553022517)⟩⟩,⟨⟨(-56151390288021937660360090),(-56151390288021937597762300)⟩,⟨(-86847994526592912768452310),(-86847994526592912705519615)⟩⟩,⟨⟨(-54975493830919493976827771),(-54975493830919493915571680)⟩,⟨(-84100543407135516371529184),(-84100543407135516309949113)⟩⟩,⟨⟨(-53803953319418684157115948),(-53803953319418684097176537)⟩,⟨(-81415538552912178758823488),(-81415538552912178698570801)⟩⟩,⟨⟨(-52637629423442588054117825),(-52637629423442587995496516)⟩,⟨(-78792905902906011091415094),(-78792905902906011032491066)⟩⟩,⟨⟨(-51477360561508355250635493),(-51477360561508355193302475)⟩,⟨(-76232495457244610078877306),(-76232495457244610021251889)⟩⟩,⟨⟨(-50323961445799451948140386),(-50323961445799451892092653)⟩,⟨(-73734084277404825875739757),(-73734084277404825819409780)⟩⟩,⟨⟨(-49178221737068273596020665),(-49178221737068273541231314)⟩,⟨(-71297379545507390759310375),(-71297379545507390704248697)⟩⟩,⟨⟨(-48040904811182488797920873),(-48040904811182488744389318)⟩,⟨(-68922021672158754448789067),(-68922021672158754394994941)⟩⟩,⟨⟨(-46912746638579302156208082),(-46912746638579302103903482)⟩,⟨(-66607587442462611909213230),(-66607587442462611856655564)⟩⟩,⟨⟨(-45794454777354418352892088),(-45794454777354418301810160)⟩,⟨(-64353593190026278964476894),(-64353593190026278913151230)⟩⟩,⟨⟨(-44686707480189506812844496),(-44686707480189506762956909)⟩,⟨(-62159497989025288961635030),(-62159497989025288911512793)⟩⟩] +lemma kernel3_0_r2_5_eq : ∀ k : Fin 16, kernel3_0Expr 2 5 k = kernel3_0_r2_5 k := by decide +kernel +noncomputable def kernel3_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-43590152914815878766265648),(-43590152914815878717571620)⟩,⟨(-60024706854661215138835736),(-60024706854661215089915977)⟩⟩,⟨⟨(-42505408497225180739951951),(-42505408497225180692418457)⟩,⟨(-57948573942650497191781453),(-57948573942650497144030887)⟩⟩,⟨⟨(-41433060336372266067401560),(-41433060336372266021023262)⟩,⟨(-55930405738713578033596646),(-55930405738713577987009755)⟩⟩,⟨⟨(-40373662788672907654393795),(-40373662788672907609141409)⟩,⟨(-53969464229391450292233087),(-53969464229391450246780337)⟩⟩,⟨⟨(-39327738120181326532584764),(-39327738120181326488455670)⟩,⟨(-52064970045898204409459736),(-52064970045898204365138336)⟩⟩,⟨⟨(-38295776273941079637910135),(-38295776273941079594871495)⟩,⟨(-50216105573120733645000796),(-50216105573120733601777651)⟩⟩,⟨⟨(-37278234739638904520460702),(-37278234739638904478506347)⟩,⟨(-48422018016297717059534327),(-48422018016297717017403085)⟩⟩,⟨⟨(-36275538522355665111062323),(-36275538522355665070162462)⟩,⟨(-46681822418346678758059635),(-46681822418346678716990261)⟩⟩,⟨⟨(-35288080206902368019294591),(-35288080206902367979446655)⟩,⟨(-44994604621257615969332850),(-44994604621257615929322607)⟩⟩,⟨⟨(-34316220113952892580231748),(-34316220113952892541401819)⟩,⟨(-43359424165431720242270317),(-43359424165431720203285030)⟩⟩,⟨⟨(-33360286543938956424451067),(-33360286543938956386632358)⟩,⟨(-41775317121311437609582460),(-41775317121311437571615169)⟩⟩,⟨⟨(-32420576104457070911937751),(-32420576104457070875100396)⟩,⟨(-40241298848120926251604915),(-40241298848120926214625510)⟩⟩,⟨⟨(-31497354116751776525504143),(-31497354116751776489644260)⟩,⟨(-38756366675011339769432046),(-38756366675011339733436485)⟩⟩,⟨⟨(-30590855096684044956194966),(-30590855096684044921279573)⟩,⟨(-37319502500380835680055136),(-37319502500380835645010189)⟩⟩,⟨⟨(-29701283305467968026631295),(-29701283305467967992653208)⟩,⟨(-35929675305612420054738166),(-35929675305612420020636482)⟩⟩,⟨⟨(-28828813365362128633269548),(-28828813365362128600199193)⟩,⟨(-34585843579941433460463100),(-34585843579941433427274877)⟩⟩] +lemma kernel3_0_r2_6_eq : ∀ k : Fin 16, kernel3_0Expr 2 6 k = kernel3_0_r2_6 k := by decide +kernel +noncomputable def kernel3_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-27973590935433610984991485),(-27973590935433610952825554)⟩,⟨(-33286957653626520031934652),(-33286957653626519999656429)⟩⟩,⟨⟨(-27135733442471555037138509),(-27135733442471555005843593)⟩,⟨(-32031961937051286295803709),(-32031961937051286264401841)⟩⟩,⟨⟨(-26315330862112457700039888),(-26315330862112457669608590)⟩,⟨(-30819797063826669645491667),(-30819797063826669614958602)⟩⟩,⟨⟨(-25512446545249915287702532),(-25512446545249915258105918)⟩,⟨(-29649401936394560239782781),(-29649401936394560210089367)⟩⟩,⟨⟨(-24727118084835925409914580),(-24727118084835925381148220)⟩,⟨(-28519715673049864153866058),(-28519715673049864125007724)⟩⟩,⟨⟨(-23959358218237867342767018),(-23959358218237867314799318)⟩,⟨(-27429679455699521245190289),(-27429679455699521217135223)⟩⟩,⟨⟨(-23209155760393424845670636),(-23209155760393424818494165)⟩,⟨(-26378238278061714600836693),(-26378238278061714573577320)⟩⟩,⟨⟨(-22476476563103507323134127),(-22476476563103507296720875)⟩,⟨(-25364342594375502267084254),(-25364342594375502240592363)⟩⟩,⟨⟨(-21761264495919116877250564),(-21761264495919116851596792)⟩,⟨(-24386949869039395730843297),(-24386949869039395705115022)⟩⟩,⟨⟨(-21063442444210516364615144),(-21063442444210516339689638)⟩,⟨(-23445026027926188846467151),(-23445026027926188821471075)⟩⟩,⟨⟨(-20382913320154369991583641),(-20382913320154369967379082)⟩,⟨(-22537546812429945108591647),(-22537546812429945084320322)⟩⟩,⟨⟨(-19719561082535135680985674),(-19719561082535135657475217)⟩,⟨(-21663499037588970816596193),(-21663499037588970793022590)⟩⟩,⟨⟨(-19073251761429271511598396),(-19073251761429271488777634)⟩,⟨(-20821881755895474034389233),(-20821881755895474011508830)⟩⟩,⟨⟨(-18443834484023174242556617),(-18443834484023174220396469)⟩,⟨(-20011707328648213398802047),(-20011707328648213376585581)⟩⟩,⟨⟨(-17831142498006617525653517),(-17831142498006617504146904)⟩,⟨(-19232002406928691786834117),(-19232002406928691765274393)⟩⟩,⟨⟨(-17234994189181256086889794),(-17234994189181256066011216)⟩,⟨(-18481808824484391974966108),(-18481808824484391954037462)⟩⟩] +lemma kernel3_0_r2_7_eq : ∀ k : Fin 16, kernel3_0Expr 2 7 k = kernel3_0_r2_7 k := by decide +kernel +noncomputable def kernel3_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-16655194090127008267368126),(-16655194090127008247114231)⟩,⟨(-17760184404984351161889671),(-17760184404984351141588653)⟩⟩,⟨⟨(-16091533876976372640503729),(-16091533876976372620846065)⟩,⟨(-17066203686273309329913888),(-17066203686273309310211878)⟩⟩,⟨⟨(-15543793351556583608512601),(-15543793351556583589444435)⟩,⟨(-16398958564391129690646789),(-16398958564391129671536952)⟩⟩,⟨⟨(-15011741406370639934546477),(-15011741406370639916043792)⟩,⟨(-15757558860244662153290270),(-15757558860244662134748445)⟩⟩,⟨⟨(-14495136970099394056275766),(-14495136970099394038334586)⟩,⟨(-15141132811920275714456445),(-15141132811920275696478567)⟩⟩,⟨⟨(-13993729931516889379667577),(-13993729931516889362262024)⟩,⟨(-14548827495707575308763628),(-14548827495707575291323674)⟩⟩,⟨⟨(-13507262039918877649479178),(-13507262039918877632602935)⟩,⟨(-13979809178969065843817479),(-13979809178969065826909045)⟩⟩,⟨⟨(-13035467780368921405061507),(-13035467780368921388692126)⟩,⟨(-13433263608037515088142328),(-13433263608037515071742836)⟩⟩,⟨⟨(-12578075222266754394761910),(-12578075222266754378896381)⟩,⟨(-12908396234353334326961689),(-12908396234353334311068058)⟩⟩,⟨⟨(-12134806839938788329363966),(-12134806839938788313977472)⟩,⟨(-12404432382069321250634837),(-12404432382069321235222121)⟩⟩,⟨⟨(-11705380304140056450811452),(-11705380304140056435898154)⟩,⟨(-11920617360350508207133871),(-11920617360350508192196156)⟩⟩,⟨⟨(-11289509243539798072097838),(-11289509243539798057636905)⟩,⟨(-11456216523583571999595865),(-11456216523583571985112209)⟩⟩,⟨⟨(-10886903975438723661980563),(-10886903975438723647968698)⟩,⟨(-11010515282684248532067069),(-11010515282684248518034113)⟩⟩,⟨⟨(-10497272205134251017895326),(-10497272205134251004310139)⟩,⟨(-10582819070653427277228813),(-10582819070653427263624055)⟩⟩,⟨⟨(-10120319693510244991767511),(-10120319693510244978603675)⟩,⟨(-10172453265484050801085496),(-10172453265484050787903548)⟩⟩,⟨⟨(-9755750892579680520711751),(-9755750892579680507950055)⟩,⟨(-9778763073462584285993016),(-9778763073462584273214570)⟩⟩] +lemma kernel3_0_r2_8_eq : ∀ k : Fin 16, kernel3_0Expr 2 8 k = kernel3_0_r2_8 k := by decide +kernel +noncomputable def kernel3_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-9403269548851911767739368),(-9403269548851911755377613)⟩,⟨(-9401113375841610535746297),(-9401113375841610523369106)⟩⟩,⟨⟨(-9062579274530671971290596),(-9062579274530671959307415)⟩,⟨(-9038888541784993489670510),(-9038888541784993477673109)⟩⟩,⟨⟨(-8733384086674420934603326),(-8733384086674420922993909)⟩,⟨(-8691492210404963505275074),(-8691492210404963493652602)⟩⟩,⟨⟨(-8415388914567136559651407),(-8415388914567136548398148)⟩,⟨(-8358347044622311089249042),(-8358347044622311077983812)⟩⟩,⟨⟨(-8108300075655110607729197),(-8108300075655110596829582)⟩,⟨(-8038894459487503480497241),(-8038894459487503469586698)⟩⟩,⟨⟨(-7811825720503810267677145),(-7811825720503810257112256)⟩,⟨(-7732594327502798594997060),(-7732594327502798584422204)⟩⟩,⟨⟨(-7525676247318511080938046),(-7525676247318511070703600)⟩,⟨(-7438924663384125227410909),(-7438924663384125217167417)⟩⟩,⟨⟨(-7249564686653345303719273),(-7249564686653345293799219)⟩,⟨(-7157381290597390156348564),(-7157381290597390146420313)⟩⟩,⟨⟨(-6983207057005837307701636),(-6983207057005837298094370)⟩,⟨(-6887477491897684053891099),(-6887477491897684044276458)⟩⟩,⟨⟨(-6726322692058146409592935),(-6726322692058146400280660)⟩,⟨(-6628743645992268374292029),(-6628743645992268364973128)⟩⟩,⟨⟨(-6478634540382373173698546),(-6478634540382373164677489)⟩,⟨(-6380726852339870373477427),(-6380726852339870364450462)⟩⟩,⟨⟨(-6239869438475702239151089),(-6239869438475702230406690)⟩,⟨(-6142990545990284146448322),(-6142990545990284137698672)⟩⟩,⟨⟨(-6009758358032172154580290),(-6009758358032172146110804)⟩,⟨(-5915114104260118097148113),(-5915114104260118088674010)⟩⟩,⟨⟨(-5788036628391820060210668),(-5788036628391820052000407)⟩,⟨(-5696692446933244563722160),(-5696692446933244555507859)⟩⟩,⟨⟨(-5574444135135202295999879),(-5574444135135202288045566)⟩,⟨(-5487335631568551667286321),(-5487335631568551659328519)⟩⟩,⟨⟨(-5368725495812209767279019),(-5368725495812209759567495)⟩,⟨(-5286668445393382984505351),(-5286668445393382976790840)⟩⟩] +lemma kernel3_0_r2_9_eq : ∀ k : Fin 16, kernel3_0Expr 2 9 k = kernel3_0_r2_9 k := by decide +kernel +noncomputable def kernel3_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-5170630213809056907743584),(-5170630213809056900274051)⟩,⟨(-5094329995158946306487321),(-5094329995158946299015288)⟩⟩,⟨⟨(-4979912811366708857165891),(-4979912811366708849923542)⟩,⟨(-4909973296234305426912574),(-4909973296234305419668159)⟩⟩,⟨⟨(-4796332942768209196907820),(-4796332942768209189889834)⟩,⟨(-4733264862118624796690604),(-4733264862118624789670969)⟩⟩,⟨⟨(-4619655488711766246498523),(-4619655488711766239693056)⟩,⟨(-4563884295457363049312108),(-4563884295457363042505368)⟩⟩,⟨⟨(-4449650632881432694297882),(-4449650632881432687703884)⟩,⟨(-4401523881557317468125152),(-4401523881557317461530245)⟩⟩,⟨⟨(-4286093921718149213146878),(-4286093921718149206751527)⟩,⟨(-4245888185307981472730171),(-4245888185307981466334234)⟩⟩,⟨⟨(-4128766308381188393908369),(-4128766308381188387709273)⟩,⟨(-4096693652332731534594873),(-4096693652332731528395499)⟩⟩,⟨⟨(-3977454181873992331031915),(-3977454181873992325018448)⟩,⟨(-3953668215113017350669760),(-3953668215113017344656290)⟩⟩,⟨⟨(-3831949382289396201022930),(-3831949382289396195194752)⟩,⟨(-3816550904752068807141275),(-3816550904752068801313364)⟩⟩,⟨⟨(-3692049203107609630748331),(-3692049203107609625093473)⟩,⟨(-3685091468971706998718109),(-3685091468971706993063751)⟩⟩,⟨⟨(-3557556381456412559963810),(-3557556381456412554480272)⟩,⟨(-3559049996866680735548663),(-3559049996866680730065850)⟩⟩,⟨⟨(-3428279077217123237553000),(-3428279077217123232231270)⟩,⟨(-3438196550875547741780136),(-3438196550875547736459327)⟩⟩,⟨⟨(-3304030841832308313454906),(-3304030841832308308294514)⟩,⟨(-3322310806365463147536691),(-3322310806365463142377411)⟩⟩,⟨⟨(-3184630577642208242518780),(-3184630577642208237509341)⟩,⟨(-3211181699170289816108302),(-3211181699170289811100140)⟩⟩,⟨⟨(-3069902488546708701900644),(-3069902488546708697040517)⟩,⟨(-3104607081367151332259285),(-3104607081367151327400591)⟩⟩,⟨⟨(-2959676022758647230811419),(-2959676022758647226092102)⟩,⟨(-3002393385525839724375612),(-3002393385525839719657864)⟩⟩] +lemma kernel3_0_r2_10_eq : ∀ k : Fin 16, kernel3_0Expr 2 10 k = kernel3_0_r2_10 k := by decide +kernel +noncomputable def kernel3_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-2853785808382533992230248),(-2853785808382533987651964)⟩,⟨(-2904355297618283491443731),(-2904355297618283486867150)⟩⟩,⟨⟨(-2752071582520599982532811),(-2752071582520599978085773)⟩,⟨(-2810315438731482991508444),(-2810315438731482987063219)⟩⟩,⟨⟨(-2654378114575662254981441),(-2654378114575662250664321)⟩,⟨(-2720104055686825589188259),(-2720104055686825584873058)⟩⟩,⟨⟨(-2560555124387794630002763),(-2560555124387794625807983)⟩,⟨(-2633558720631389752500205),(-2633558720631389748307432)⟩⟩,⟨⟨(-2470457195809378908059510),(-2470457195809378903987057)⟩,⟨(-2550524039632616354549882),(-2550524039632616350479523)⟩⟩,⟨⟨(-2383943686290935292455365),(-2383943686290935288496872)⟩,⟨(-2470851370276442220270652),(-2470851370276442216314323)⟩⟩,⟨⟨(-2300878633018326121728992),(-2300878633018326117883408)⟩,⟨(-2394398548240526831763739),(-2394398548240526827920386)⟩⟩,⟨⟨(-2221130656110614256021274),(-2221130656110614252281843)⟩,⟨(-2321029622788426560724734),(-2321029622788426556987587)⟩⟩,⟨⟨(-2144572859357142915878850),(-2144572859357142912246066)⟩,⟨(-2250614601107348546092561),(-2250614601107348542462116)⟩⟩,⟨⟨(-2071082728942380647054726),(-2071082728942380643520750)⟩,⟨(-2183029201391314315418769),(-2183029201391314311887171)⟩⟩,⟨⟨(-2000542030577824123406288),(-2000542030577824119970318)⟩,⟨(-2118154614553047521013065),(-2118154614553047517579510)⟩⟩,⟨⟨(-1932836705431841676671946),(-1932836705431841673327958)⟩,⟨(-2055877274431537726757814),(-2055877274431537723416267)⟩⟩,⟨⟨(-1867856765220829675482120),(-1867856765220829672230454)⟩,⟨(-1996088636347891696837262),(-1996088636347891693588066)⟩⟩,⟨⟨(-1805496186798489751361006),(-1805496186798489748194913)⟩,⟨(-1938684963849636056978590),(-1938684963849636053814984)⟩⟩,⟨⟨(-1745652806554455356599395),(-1745652806554455353518288)⟩,⟨(-1883567123472954322394459),(-1883567123472954319315855)⟩⟩,⟨⟨(-1688228214908930309339236),(-1688228214908930306337739)⟩,⟨(-1830640387343304238910680),(-1830640387343304235911694)⟩⟩] +lemma kernel3_0_r2_11_eq : ∀ k : Fin 16, kernel3_0Expr 2 11 k = kernel3_0_r2_11 k := by decide +kernel +noncomputable def kernel3_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-1633127651166470711121488),(-1633127651166470708200452)⟩,⟨(-1779814243427349014588336),(-1779814243427349011669823)⟩⟩,⟨⟨(-1580259898969558283099306),(-1580259898969558280252281)⟩,⟨(-1731002213243033239916431),(-1731002213243033237071929)⟩⟩,⟨⟨(-1529537182571184295063570),(-1529537182571184292290148)⟩,⟨(-1684121676829830347963301),(-1684121676829830345192403)⟩⟩,⟨⟨(-1480875064125289206579691),(-1480875064125289203875083)⟩,⟨(-1639093704777577139716877),(-1639093704777577137014787)⟩⟩,⟨⟨(-1434192342174578688339146),(-1434192342174578685703942)⟩,⟨(-1595842897109790684882195),(-1595842897109790682249507)⟩⟩,⟨⟨(-1389410951496951665060167),(-1389410951496951662488899)⟩,⟨(-1554297228815837109346344),(-1554297228815837106777580)⟩⟩,⟨⟨(-1346455864454515840359829),(-1346455864454515837852246)⟩,⟨(-1514387901825698579923335),(-1514387901825698577418248)⟩⟩,⟨⟨(-1305254993972912390435736),(-1305254993972912387987556)⟩,⟨(-1476049203221277282076125),(-1476049203221277279630426)⟩⟩,⟨⟨(-1265739098263402354389476),(-1265739098263402352001643)⟩,⟨(-1439218369479101337220753),(-1439218369479101334835389)⟩⟩,⟨⟨(-1227841687385858034850771),(-1227841687385858032518081)⟩,⟨(-1403835456540880255438700),(-1403835456540880253108462)⟩⟩,⟨⟨(-1191498931737426349551498),(-1191498931737426347273833)⟩,⟨(-1369843215510524280824756),(-1369843215510524278549527)⟩⟩,⟨⟨(-1156649572539158419453948),(-1156649572539158417227472)⟩,⟨(-1337186973778925163185352),(-1337186973778925160961292)⟩⟩,⟨⟨(-1123234834381299980048736),(-1123234834381299977874217)⟩,⟨(-1305814521380932357802605),(-1305814521380932355630486)⟩⟩,⟨⟨(-1091198339877178411958544),(-1091198339877178409831502)⟩,⟨(-1275676002392489734196414),(-1275676002392489732071748)⟩⟩,⟨⟨(-1060486026465671292709047),(-1060486026465671290629477)⟩,⟨(-1246723811179769181026657),(-1246723811179769178949444)⟩⟩,⟨⟨(-1031046065393064691146007),(-1031046065393064689110463)⟩,⟨(-1218912493316298783047226),(-1218912493316298781014016)⟩⟩] +lemma kernel3_0_r2_12_eq : ∀ k : Fin 16, kernel3_0Expr 2 12 k = kernel3_0_r2_12 k := by decide +kernel +noncomputable def kernel3_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-1002828782896672871900472),(-1002828782896672869910077)⟩,⟨(-1192198650988488244913886),(-1192198650988488242925806)⟩⟩,⟨⟨(-975786583604860397344199),(-975786583604860395394581)⟩,⟨(-1166540852714560472996894),(-1166540852714560471049566)⟩⟩,⟨⟨(-949873876161048605023838),(-949873876161048603115080)⟩,⟨(-1141899547206666848015042),(-1141899547206666846108553)⟩⟩,⟨⟨(-925047001072867136179685),(-925047001072867134308684)⟩,⟨(-1118236981210859316858424),(-1118236981210859314989667)⟩⟩,⟨⟨(-901264160781794039199286),(-901264160781794037366925)⟩,⟨(-1095517121164582847412825),(-1095517121164582845582687)⟩⟩,⟨⟨(-878485351943381969230831),(-878485351943381967433386)⟩,⟨(-1073705578516407948304396),(-1073705578516407946509148)⟩⟩,⟨⟨(-856672299903460831049152),(-856672299903460829286785)⟩,⟨(-1052769538557818674378890),(-1052769538557818672618698)⟩⟩,⟨⟨(-835788395351507336583811),(-835788395351507334853715)⟩,⟨(-1032677692621983355433956),(-1032677692621983353706010)⟩⟩,⟨⟨(-815798633128648722410352),(-815798633128648720713664)⟩,⟨(-1013400173509542281208648),(-1013400173509542279514090)⟩⟩,⟨⟨(-796669553164491605197795),(-796669553164491603530879)⟩,⟨(-994908494006530206428508),(-994908494006530204763697)⟩⟩,⟨⟨(-778369183514108972414671),(-778369183514108970777743)⟩,⟨(-977175488364595472619712),(-977175488364595470984867)⟩⟩,⟨⟨(-760866985464051007242776),(-760866985464051005633289)⟩,⟨(-960175256618667497965178),(-960175256618667496357751)⟩⟩,⟨⟨(-744133800674142329632616),(-744133800674142328051521)⟩,⟨(-943883111622147981514970),(-943883111622147979935914)⟩⟩,⟨⟨(-728141800320063928576310),(-728141800320063927020450)⟩,⟨(-928275528684547776798818),(-928275528684547775244974)⟩⟩,⟨⟨(-712864436200268337442571),(-712864436200268335912218)⟩,⟨(-913330097701251999731902),(-913330097701251998203545)⟩⟩,⟨⟨(-698276393769618390793663),(-698276393769618389286487)⟩,⟨(-899025477669763016894499),(-899025477669763015389296)⟩⟩] +lemma kernel3_0_r2_13_eq : ∀ k : Fin 16, kernel3_0Expr 2 13 k = kernel3_0_r2_13 k := by decide +kernel +noncomputable def kernel3_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-684353547061251274854339),(-684353547061251273371585)⟩,⟨(-885341353491338339620192),(-885341353491338338139394)⟩⟩,⟨⟨(-671072915457529766755656),(-671072915457529765294118)⟩,⟨(-872258394961403192808088),(-872258394961403191348484)⟩⟩,⟨⟨(-658412622270531902234846),(-658412622270531900794829)⟩,⟨(-859758217856471827831965),(-859758217856471826393864)⟩⟩,⟨⟨(-646351855092330282710950),(-646351855092330281290314)⟩,⟨(-847823347029554722486104),(-847823347029554721067363)⟩⟩,⟨⟨(-634870827875305384398212),(-634870827875305382997955)⟩,⟨(-836437181430158798388827),(-836437181430158796990450)⟩⟩,⟨⟨(-623950744702907181018398),(-623950744702907179635774)⟩,⟨(-825583960969003662924401),(-825583960969003661543638)⟩⟩,⟨⟨(-613573765211610786318041),(-613573765211610784953385)⟩,⟨(-815248735151478372762472),(-815248735151478371399660)⟩⟩,⟨⟨(-603722971625290311746523),(-603722971625290310397853)⟩,⟨(-805417333407650714581809),(-805417333407650713234964)⟩⟩,⟨⟨(-594382337363847331679416),(-594382337363847330347946)⟩,⟨(-796076337050315499024135),(-796076337050315497694478)⟩⟩,⟨⟨(-585536697188663795879110),(-585536697188663794562051)⟩,⟨(-787213052796131391152410),(-787213052796131389837147)⟩⟩,⟨⟨(-577171718848292359449594),(-577171718848292358147298)⟩,⟨(-778815487788349349540764),(-778815487788349348240250)⟩⟩,⟨⟨(-569273876188739200164131),(-569273876188739198874752)⟩,⟨(-770872326062982225709886),(-770872326062982224422273)⟩⟩,⟨⟨(-561830423693725560431041),(-561830423693725559155603)⟩,⟨(-763372906403507257454158),(-763372906403507256180475)⟩⟩,⟨⟨(-554829372421425359327841),(-554829372421425358063888)⟩,⟨(-756307201532334161869968),(-756307201532334160607756)⟩⟩,⟨⟨(-548259467305358876129910),(-548259467305358874877807)⟩,⟨(-749665798590314658517881),(-749665798590314657267509)⟩⟩,⟨⟨(-542110165788369013141473),(-542110165788369011899488)⟩,⟨(-743439880858518128597340),(-743439880858518127357073)⟩⟩] +lemma kernel3_0_r2_14_eq : ∀ k : Fin 16, kernel3_0Expr 2 14 k = kernel3_0_r2_14 k := by decide +kernel +noncomputable def kernel3_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-536371617759909960737721),(-536371617759909959507139)⟩,⟨(-737621210679356542417739),(-737621210679356541188866)⟩⟩,⟨⟨(-531034646768231787706693),(-531034646768231786484905)⟩,⟨(-732202113536913736878660),(-732202113536913735658571)⟩⟩,⟨⟨(-526090732480442720990679),(-526090732480442719778052)⟩,⟨(-727175463259023713263313),(-727175463259023712052376)⟩⟩,⟨⟨(-521531994364868359446262),(-521531994364868358241160)⟩,⟨(-722534668306254090362913),(-722534668306254089159491)⟩⟩,⟨⟨(-517351176571598990690681),(-517351176571598989494146)⟩,⟨(-718273659115488524734500),(-718273659115488523539639)⟩⟩,⟨⟨(-513541633988618223797625),(-513541633988618222607381)⟩,⟨(-714386876468270216044241),(-714386876468270214855663)⟩⟩,⟨⟨(-510097319452434424238336),(-510097319452434423054747)⟩,⟨(-710869260856472032888616),(-710869260856472031706687)⟩⟩,⟨⟨(-507012772093687453931666),(-507012772093687452753170)⟩,⟨(-707716242820201856806944),(-707716242820201855630102)⟩⟩,⟨⟨(-504283106799773859947346),(-504283106799773858775196)⟩,⟨(-704923734235139022311093),(-704923734235139021140594)⟩⟩,⟨⟨(-501904004778121138686355),(-501904004778121137518129)⟩,⟨(-702488120528733831817456),(-702488120528733830650874)⟩⟩,⟨⟨(-499871705205343551610962),(-499871705205343550447015)⟩,⟨(-700406253806891671000010),(-700406253806891669837705)⟩⟩,⟨⟨(-498182997949125982314699),(-498182997949125981153526)⟩,⟨(-698675446874910882509466),(-698675446874910881349932)⟩⟩,⟨⟨(-496835217351306546056090),(-496835217351306544898744)⟩,⟨(-697293468138553924120734),(-697293468138553922965026)⟩⟩,⟨⟨(-495826237062261351252991),(-495826237062261350097290)⟩,⟨(-696258537373209097458799),(-696258537373209096304734)⟩⟩,⟨⟨(-495154465918334414384153),(-495154465918334413230441)⟩,⟨(-695569322351149944487536),(-695569322351149943335460)⟩⟩,⟨⟨(-494818844855700851728925),(-494818844855700850575742)⟩,⟨(-695224936318925931216411),(-695224936318925930064863)⟩⟩] +lemma kernel3_0_r2_15_eq : ∀ k : Fin 16, kernel3_0Expr 2 15 k = kernel3_0_r2_15 k := by decide +kernel +noncomputable def kernel3_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel3_0_r2_0,kernel3_0_r2_1,kernel3_0_r2_2,kernel3_0_r2_3,kernel3_0_r2_4,kernel3_0_r2_5,kernel3_0_r2_6,kernel3_0_r2_7,kernel3_0_r2_8,kernel3_0_r2_9,kernel3_0_r2_10,kernel3_0_r2_11,kernel3_0_r2_12,kernel3_0_r2_13,kernel3_0_r2_14,kernel3_0_r2_15] +lemma kernel3_0_r2_eq (i k : Fin 16) : kernel3_0Expr 2 i k = kernel3_0_r2 i k := by + fin_cases i + · exact kernel3_0_r2_0_eq k + · exact kernel3_0_r2_1_eq k + · exact kernel3_0_r2_2_eq k + · exact kernel3_0_r2_3_eq k + · exact kernel3_0_r2_4_eq k + · exact kernel3_0_r2_5_eq k + · exact kernel3_0_r2_6_eq k + · exact kernel3_0_r2_7_eq k + · exact kernel3_0_r2_8_eq k + · exact kernel3_0_r2_9_eq k + · exact kernel3_0_r2_10_eq k + · exact kernel3_0_r2_11_eq k + · exact kernel3_0_r2_12_eq k + · exact kernel3_0_r2_13_eq k + · exact kernel3_0_r2_14_eq k + · exact kernel3_0_r2_15_eq k +noncomputable def kernel3_0_r3_0 : Fin 16 → CBox := ![⟨⟨15213272475003939785865784646,15213272475003939789656748870⟩,⟨(-4099826561034468297688122380),(-4099826561034468294026641617)⟩⟩,⟨⟨15209443674797761410552735871,15209443674797761414343055886⟩,⟨(-4100933294163059756429289179),(-4100933294163059752768450340)⟩⟩,⟨⟨15201788325106429408875213308,15201788325106429412664238446⟩,⟨(-4103144259655370306153517162),(-4103144259655370302493968560)⟩⟩,⟨⟨15190310926636704902589666554,15190310926636704906376746522⟩,⟨(-4106454461061760770929323064),(-4106454461061760767271712584)⟩⟩,⟨⟨15175018228605052684547056730,15175018228605052688331541824⟩,⟨(-4110856416397635702653688253),(-4110856416397635698998663108)⟩⟩,⟨⟨15155919226509985881798044559,15155919226509985885579285800⟩,⟨(-4116340173342172775364690798),(-4116340173342172771712897361)⟩⟩,⟨⟨15133025159136554348510582821,15133025159136554352287932096⟩,⟨(-4122893329454829523299737959),(-4122893329454829519651821603)⟩⟩,⟨⟨15106349504771488021533036392,15106349504771488025305846892⟩,⟨(-4130501057368175823797189592),(-4130501057368175820153794218)⟩⟩,⟨⟨15075907976602384261356980174,15075907976602384265124605967⟩,⟨(-4139146134905351051023223181),(-4139146134905351047384991620)⟩⟩,⟨⟨15041718517269371071113532085,15041718517269371074875329428⟩,⟨(-4148808980060271419292064753),(-4148808980060271415659637434)⟩⟩,⟨⟨15003801292532917483218635045,15003801292532917486973960823⟩,⟨(-4159467690768631351256042888),(-4159467690768631347630059365)⟩⟩,⟨⟨14962178684016928926005766158,14962178684016928929753980640⟩,⟨(-4171098089387768631812658609),(-4171098089387768628193754789)⟩⟩,⟨⟨14916875280981988645921891734,14916875280981988649662354901⟩,⟨(-4183673771793612786691658462),(-4183673771793612783080470240)⟩⟩,⟨⟨14867917871079614762978464775,14867917871079614766710542200⟩,⟨(-4197166160993225981275620329),(-4197166160993225977672777713)⟩⟩,⟨⟨14815335430034723530802758098,14815335430034723534525813718⟩,⟨(-4211544565141892498110218198),(-4211544565141892494516352471)⟩⟩,⟨⟨14759159110200148739153766305,14759159110200148742867171761⟩,⟨(-4226776239844333564647373132),(-4226776239844333561063107548)⟩⟩] +lemma kernel3_0_r3_0_eq : ∀ k : Fin 16, kernel3_0Expr 3 0 k = kernel3_0_r3_0 k := by decide +kernel +noncomputable def kernel3_0_r3_1 : Fin 16 → CBox := ![⟨⟨14699422227924089324630511162,14699422227924089328333633942⟩,⟨(-4242826454610436334283705224),(-4242826454610436330709666772)⟩⟩,⟨⟨14636160249668764923167867542,14636160249668764926860087456⟩,⟨(-4259658563326906868479860119),(-4259658563326906864916663126)⟩⟩,⟨⟨14569410776816373362649083924,14569410776816373366329773735⟩,⟨(-4277234078597505042561274013),(-4277234078597505039009539379)⟩⟩,⟨⟨14499213529096684184099720317,14499213529096684187768268012⟩,⟨(-4295512749796012730440491037),(-4295512749796012726900824078)⟩⟩,⟨⟨14425610326569285495042665135,14425610326569285498698447043⟩,⟨(-4314452644667844034145538145),(-4314452644667844030618555302)⟩⟩,⟨⟨14348645070092643075036529284,14348645070092643078678945058⟩,⟨(-4334010234308246599597867217),(-4334010234308246596084161262)⟩⟩,⟨⟨14268363720211743836859345223,14268363720211743840487778035⟩,⟨(-4354140481337385321006813796),(-4354140481337385317506993388)⟩⟩,⟨⟨14184814274396191472048912547,14184814274396191475662772294⟩,⟨(-4374796931085263295793245509),(-4374796931085263292307892240)⟩⟩,⟨⟨14098046742561209088089012878,14098046742561209091687685418⟩,⟨(-4395931805592439207884144829),(-4395931805592439204413863659)⟩⟩,⟨⟨14008113120805088260399599791,14008113120805088263982511356⟩,⟨(-4417496100225864935980228497),(-4417496100225864932525583734)⟩⟩,⟨⟨13915067363298210176228362987,13915067363298210179794908698⟩,⟨(-4439439682702911676892779561),(-4439439682702911673454365893)⟩⟩,⟨⟨13818965352260854010565714729,13818965352260854014115332543⟩,⟨(-4461711394310796769182010400),(-4461711394310796765760379405)⟩⟩,⟨⟨13719864865969599450470079646,13719864865969599454002166563⟩,⟨(-4484259153103186103580480297),(-4484259153103186100176223700)⟩⟩,⟨⟨13617825544735220983751037592,13617825544735220987265052714⟩,⟨(-4507030058850747711996622759),(-4507030058850747708610270023)⟩⟩,⟨⟨13512908854798555289796460217,13512908854798555293291812116⟩,⟨(-4529970499517889737289312312),(-4529970499517889733921442552)⟩⟩,⟨⟨13405178050094891395960250574,13405178050094891399436411855⟩,⟨(-4553026259033849009375527408),(-4553026259033849006026655561)⟩⟩] +lemma kernel3_0_r3_1_eq : ∀ k : Fin 16, kernel3_0Expr 3 1 k = kernel3_0_r3_1 k := by decide +kernel +noncomputable def kernel3_0_r3_2 : Fin 16 → CBox := ![⟨⟨13294698131841975260942073110,13294698131841975264398451301⟩,⟨(-4576142626122722902779086503),(-4576142626122722899449791606)⟩⟩,⟨⟨13181535805911722688390255554,13181535805911722691826351579⟩,⟨(-4599264503953974438672247050),(-4599264503953974435363014797)⟩⟩,⟨⟨13065759437951181060965581652,13065759437951181064380819181⟩,⟨(-4622336520372405421623101539),(-4622336520372405418334493821)⟩⟩,⟨⟨12947439006224152987605734346,12947439006224152990999627487⟩,⟨(-4645303138464600643235085636),(-4645303138464600639967573961)⟩⟩,⟨⟨12826646052151172864585398106,12826646052151172867957368449⟩,⟨(-4668108767217412775490723217),(-4668108767217412772244870454)⟩⟩,⟨⟨12703453628532187536199679308,12703453628532187539549274712⟩,⟨(-4690697872023196389601692257),(-4690697872023196386377935320)⟩⟩,⟨⟨12577936245443309432323572172,12577936245443309435650233232⟩,⟨(-4713015084786223265653395564),(-4713015084786223262452277392)⟩⟩,⟨⟨12450169813806357329886385763,12450169813806357333189675063⟩,⟨(-4735005313385031199304469421),(-4735005313385031196126411278)⟩⟩,⟨⟨12320231586637546747495225684,12320231586637546750774576324⟩,⟨(-4756613850246384841263065412),(-4756613850246384838108616664)⟩⟩,⟨⟨12188200097989607503229547544,12188200097989607506484565766⟩,⟨(-4777786479788068165146692580),(-4777786479788068162016230160)⟩⟩,⟨⟨12054155099609756885222585955,12054155099609756888452731235⟩,⟨(-4798469584489890742053451174),(-4798469584489890738947497295)⟩⟩,⟨⟨11918177495344308250428826179,11918177495344308253633716465⟩,⟨(-4818610249355079137898340245),(-4818610249355079134817259301)⟩⟩,⟨⟨11780349273329210177670856842,11780349273329210180849943284⟩,⟨(-4838156364527643608106328135),(-4838156364527643605050649709)⟩⟩,⟨⟨11640753436014452661357192313,11640753436014452664510141782⟩,⟨(-4857056725835360042670699594),(-4857056725835360039640738662)⟩⟩,⟨⟨11499473928079005117578825183,11499473928079005120705118250⟩,⟨(-4875261133032686951414304738),(-4875261133032686948410560849)⟩⟩,⟨⟨11356595562301726004890087364,11356595562301726007989403871⟩,⟨(-4892720485523244166462227338),(-4892720485523244163485001830)⟩⟩] +lemma kernel3_0_r3_2_eq : ∀ k : Fin 16, kernel3_0Expr 3 2 k = kernel3_0_r3_2 k := by decide +kernel +noncomputable def kernel3_0_r3_3 : Fin 16 → CBox := ![⟨⟨11212203943462464586093058260,11212203943462464589164861472⟩,⟨(-4909386875347408644217455537),(-4909386875347408641267264394)⟩⟩,⟨⟨11066385390356320041783116405,11066385390356320044827148428⟩,⟨(-4925213677227125748200768546),(-4925213677227125745277850626)⟩⟩,⟨⟨10919226856012689575526738858,10919226856012689578542503741⟩,⟨(-4940155635467181812936009731),(-4940155635467181810040839881)⟩⟩,⟨⟨10770815846219282830473061964,10770815846219282833460307435⟩,⟨(-4954168947519923357632795616),(-4954168947519923354765606543)⟩⟩,⟨⟨10621240336459662306171248302,10621240336459662309129461955⟩,⟨(-4967211344028725336466380392),(-4967211344028725333627662713)⟩⟩,⟨⟨10470588687381046107167214093,10470588687381046110096209054⟩,⟨(-4979242165174388127806450575),(-4979242165174388124996371619)⟩⟩,⟨⟨10318949558917038220880664581,10318949558917038223779970863⟩,⟨(-4990222433158060966013961252),(-4990222433158060963232969088)⟩⟩,⟨⟨10166411823197591145109637855,10166411823197591147979076303⟩,⟨(-5000114920664226140811807681),(-5000114920664226138060061618)⟩⟩,⟨⟨10013064476385815404683513580,10013064476385815407522585931⟩,⟨(-5008884215157709031706101191),(-5008884215157709028984076995)⟩⟩,⟨⟨9858996549588190678037854793,9858996549588190680846462815⟩,⟨(-5016496778879577011408203285),(-5016496778879577008715979725)⟩⟩,⟨⟨9704297018991265509250485622,9704297018991265512028187821⟩,⟨(-5022921004418126197984721277),(-5022921004418126195322717565)⟩⟩,⟨⟨9549054715384019982821052992,9549054715384019985567747565⟩,⟨(-5028127265742897434184536163),(-5028127265742897431552834474)⟩⟩,⟨⟨9393358233230673035012738100,9393358233230673037727957479⟩,⟨(-5032087964601777997295164578),(-5032087964601777994694209854)⟩⟩,⟨⟨9237295839463809895703185120,9237295839463809898386909223⟩,⟨(-5034777572193697563646675656),(-5034777572193697561076468996)⟩⟩,⟨⟨9080955382172254208114525198,9080955382172254210766343546⟩,⟨(-5036172666042178046588270642),(-5036172666042178044049200350)⟩⟩,⟨⟨8924424199362084642625380445,8924424199362084645245271672⟩,⟨(-5036251962008007409028622555),(-5036251962008007406520691110)⟩⟩] +lemma kernel3_0_r3_3_eq : ∀ k : Fin 16, kernel3_0Expr 3 3 k = kernel3_0_r3_3 k := by decide +kernel +noncomputable def kernel3_0_r3_4 : Fin 16 → CBox := ![⟨⟨8767789027972570741773936712,8767789027972570744361447198⟩,⟨(-5034996341392536012191174527),(-5034996341392536009714813098)⟩⟩,⟨⟨8611135913331553368820302242,8611135913331553371375511927⟩,⟨(-5032388873096497524821112406),(-5032388873096497522376223237)⟩⟩,⟨⟨8454550119236900328877516471,8454550119236900331400048267⟩,⟨(-5028414830812790507575180802),(-5028414830812790505162119388)⟩⟩,⟨⟨8298116038852109266985756355,8298116038852109269475671094⟩,⟨(-5023061705245275915852558626),(-5023061705245275913471246496)⟩⟩,⟨⟨8141917106604892660506643912,8141917106604892662963527873⟩,⟨(-5016319211359303318976647738),(-5016319211359303316627477008)⟩⟩,⟨⟨7986035711277651629754333603,7986035711277651632179047691⟩,⟨(-5008179290683327185300724396),(-5008179290683327182982770938)⟩⟩,⟨⟨7830553110478117682760641329,7830553110478117685175900516⟩,⟨(-4998636108694566099550387311),(-4998636108694566097239392243)⟩⟩,⟨⟨7675549346677109036733032926,7675549346677109039138802564⟩,⟨(-4987686047335143848872985933),(-4987686047335143846569003368)⟩⟩,⟨⟨7521103164998308889314460325,7521103164998308891710140028⟩,⟨(-4975327692718483377022800143),(-4975327692718483374726446281)⟩⟩,⟨⟨7367291932942228481453961259,7367291932942228483839608035⟩,⟨(-4961561818098854187331930209),(-4961561818098854185043170749)⟩⟩,⟨⟨7214191562223073021876569608,7214191562223073024251641918⟩,⟨(-4946391362189852729281076123),(-4946391362189852727000471416)⟩⟩,⟨⟨7061876432893092045984726601,7061876432893092048349221774⟩,⟨(-4929821402930176055318383453),(-4929821402930176053045960627)⟩⟩,⟨⟨6910419319924179549918464355,6910419319924179552271753217⟩,⟨(-4911859126807284826354182528),(-4911859126807284824090591194)⟩⟩,⟨⟨6759891322411008703187372805,6759891322411008705529542530⟩,⟨(-4892513793861396879425681029),(-4892513793861396877170861293)⟩⟩,⟨⟨6610361795553859911679285531,6610361795553859914009763128⟩,⟨(-4871796698503662657109876947),(-4871796698503662654864424843)⟩⟩,⟨⟨6461898285572551590558778598,6461898285572551592877598715⟩,⟨(-4849721126293305986847167736),(-4849721126293305984611077372)⟩⟩] +lemma kernel3_0_r3_4_eq : ∀ k : Fin 16, kernel3_0Expr 3 4 k = kernel3_0_r3_4 k := by decide +kernel +noncomputable def kernel3_0_r3_5 : Fin 16 → CBox := ![⟨⟨6314566467695535531211626383,6314566467695535533518099190⟩,⟨(-4826302306828926918564913248),(-4826302306828926916338898596)⟩⟩,⟨⟨6168430087360301610607591310,6168430087360301612901875267⟩,⟨(-4801557362919018514926633841),(-4801557362919018512710567854)⟩⟩,⟨⟨6023550904752781144799532661,6023550904752781147081027556⟩,⟨(-4775505256206009797497048753),(-4775505256206009795291558250)⟩⟩,⟨⟨5879988642804478570035359659,5879988642804478572304142327⟩,⟨(-4748166729426778073115233262),(-4748166729426778070920273721)⟩⟩,⟨⟨5737800938756634099403343840,5737800938756634101658711384⟩,⟨(-4719564245500543814801766132),(-4719564245500543812618067947)⟩⟩,⟨⟨5597043299390864727302157029,5597043299390864729544300458⟩,⟨(-4689721923642341178929189729),(-4689721923642341176756596342)⟩⟩,⟨⟨5457769060015488831108453388,5457769060015488833336749851⟩,⟨(-4658665472706821113097744330),(-4658665472706821110936908067)⟩⟩,⟨⟨5320029347286154035187680436,5320029347286154037402253363⟩,⟨(-4626422121972968987302455332),(-4626422121972968985153287865)⟩⟩,⟨⟨5183873045928504100932450021,5183873045928504103132542915⟩,⟨(-4593020549585385171759948820),(-4593020549585385169623236492)⟩⟩,⟨⟨5049346769419485042819489375,5049346769419485045005375463⟩,⟨(-4558490808872068779372066368),(-4558490808872068777247572981)⟩⟩,⟨⟨4916494834672551353662155890,4916494834672551355833194713⟩,⟨(-4522864252762149161505504721),(-4522864252762149159393902374)⟩⟩,⟨⟨4785359240760539049898905869,4785359240760539052055271035⟩,⟨(-4486173456529717523185399823),(-4486173456529717521086552028)⟩⟩,⟨⟨4655979651698372834176671820,4655979651698372836317605273⟩,⟨(-4448452139091816652819886793),(-4448452139091816650734583414)⟩⟩,⟨⟨4528393383296120071569661644,4528393383296120073695474826⟩,⟨(-4409735083089748336197800417),(-4409735083089748334125768528)⟩⟩,⟨⟨4402635394081244701550801225,4402635394081244703660841164⟩,⟨(-4370058053983157300385236625),(-4370058053983157298327162313)⟩⟩,⟨⟨4278738280277299753478642049,4278738280277299755573135447⟩,⟨(-4329457718385852918479135357),(-4329457718385852916434830299)⟩⟩] +lemma kernel3_0_r3_5_eq : ∀ k : Fin 16, kernel3_0Expr 3 5 k = kernel3_0_r3_5 k := by decide +kernel +noncomputable def kernel3_0_r3_6 : Fin 16 → CBox := ![⟨⟨4156732274814777491601104354,4156732274814777493679238155⟩,⟨(-4287971561871044429955875967),(-4287971561871044427926185976)⟩⟩,⟨⟨4036645250338460401458978668,4036645250338460403521163992⟩,⟨(-4245637806471604690102403264),(-4245637806471604688086956829)⟩⟩,⟨⟨3918502726164432308504149148,3918502726164432310549725839⟩,⟨(-4202495328098157544267279990),(-4202495328098157542266771191)⟩⟩,⟨⟨3802327879128963741674634396,3802327879128963743703884049⟩,⟨(-4158583574094224312659170196),(-4158583574094224310673356358)⟩⟩,⟨⟨3688141558260824597254342162,3688141558260824599266472669⟩,⟨(-4113942481143388331635691308),(-4113942481143388329665397990)⟩⟩,⟨⟨3575962303198243879888971774,3575962303198243881884424079⟩,⟨(-4068612393738468931796719192),(-4068612393738468929841545048)⟩⟩,⟨⟨3465806366261772502489316302,3465806366261772504467428095⟩,⟨(-4022633983417066530842583276),(-4022633983417066528903224736)⟩⟩,⟨⟨3357687738084750343793459031,3357687738084750345754567838⟩,⟨(-3976048168961580380857919431),(-3976048168961580378934077755)⟩⟩,⟨⟨3251618176693970139016069992,3251618176693970140959340589⟩,⟨(-3928896037754944257215580797),(-3928896037754944255308124432)⟩⟩,⟨⟨3147607239924502891254701742,3147607239924502893180675008⟩,⟨(-3881218768475909747121555577),(-3881218768475909745229982938)⟩⟩,⟨⟨3045662321044534171875889992,3045662321044534173783906485⟩,⟨(-3833057555309770723468462348),(-3833057555309770721593466630)⟩⟩,⟨⟨2945788687458486862910779893,2945788687458486864801232887⟩,⟨(-3784453533842006972543562557),(-3784453533842006970684788536)⟩⟩,⟨⟨2847989522349699489514750610,2847989522349699491386835284⟩,⟨(-3735447708793472403320245081),(-3735447708793472401478530358)⟩⟩,⟨⟨2752265969117513058535711762,2752265969117513060389998985⟩,⟨(-3686080883746507894955283725),(-3686080883746507893130095535)⟩⟩,⟨⟨2658617178457812788284853027,2658617178457812790120690692⟩,⟨(-3636393593001765945635585237),(-3636393593001765943827608579)⟩⟩,⟨⟨2567040357930890507745039638,2567040357930890509562875773⟩,⟨(-3586426035695640130268500792),(-3586426035695640128477324425)⟩⟩] +lemma kernel3_0_r3_6_eq : ∀ k : Fin 16, kernel3_0Expr 3 6 k = kernel3_0_r3_6 k := by decide +kernel +noncomputable def kernel3_0_r3_7 : Fin 16 → CBox := ![⟨⟨2477530823855951690800412346,2477530823855951692599395904⟩,⟨(-3536218012298043903202746734),(-3536218012298043901429253274)⟩⟩,⟨⟨2390082055367697563384416264,2390082055367697565165228303⟩,⟨(-3485808863599927861450857875),(-3485808863599927859694403016)⟩⟩,⟨⟨2304685750467173586291989223,2304685750467173588053989274⟩,⟨(-3435237412289409733209037614),(-3435237412289409731470293437)⟩⟩,⟨⟨2221331883896493615434721408,2221331883896493617178410040⟩,⟨(-3384541907204764485136253962),(-3384541907204764483414754987)⟩⟩,⟨⟨2140008766665123589509839546,2140008766665123591234418848⟩,⟨(-3333759970341830089399546925),(-3333759970341830087696121383)⟩⟩,⟨⟨2060703107054135840040405304,2060703107054135841746567568⟩,⟨(-3282928546682674074909694113),(-3282928546682674073223684355)⟩⟩,⟨⟨1983400072924218020856998027,1983400072924218022544117883⟩,⟨(-3232083856901682555334169199),(-3232083856901682553666230594)⟩⟩,⟨⟨1908083355153229084860746420,1908083355153229086529374162⟩,⟨(-3181261352994621424747007147),(-3181261352994621423096622436)⟩⟩,⟨⟨1834735232029725595357507443,1834735232029725597006811097⟩,⟨(-3130495676865721956997492060),(-3130495676865721955365521701)⟩⟩,⟨⟨1763336634430119009490675011,1763336634430119011121446208⟩,⟨(-3079820621897501713489950665),(-3079820621897501711875635557)⟩⟩,⟨⟨1693867211608949786487907045,1693867211608949788099538715⟩,⟨(-3029269097517886293317375987),(-3029269097517886291721351317)⟩⟩,⟨⟨1626305397434156103407712296,1626305397434156105000800516⟩,⟨(-2978873096769285964484387220),(-2978873096769285962906087629)⟩⟩,⟨⟨1560628476902150108500445724,1560628476902150110074215549⟩,⟨(-2928663666874639419961247990),(-2928663666874639418401475101)⟩⟩,⟨⟨1496812652770967350492415935,1496812652770967352047664866⟩,⟨(-2878670882786098391650937479),(-2878670882786098390108923725)⟩⟩,⟨⟨1434833112153697673231414453,1434833112153697674767556011⟩,⟨(-2828923823693022839154045996),(-2828923823693022837630403911)⟩⟩,⟨⟨1374664092918809085820401237,1374664092918809087338072953⟩,⟨(-2779450552457315630059918425),(-2779450552457315628554038698)⟩⟩] +lemma kernel3_0_r3_7_eq : ∀ k : Fin 16, kernel3_0Expr 3 7 k = kernel3_0_r3_7 k := by decide +kernel +noncomputable def kernel3_0_r3_8 : Fin 16 → CBox := ![⟨⟨1316278949748808992390104932,1316278949748808993888488047⟩,⟨(-2730278097935874180731332103),(-2730278097935874179244057978)⟩⟩,⟨⟨1259650219713917450647241829,1259650219713917452127239387⟩,⟨(-2681432440142097905204087804),(-2681432440142097903734543689)⟩⟩,⟨⟨1204749687223021476186140842,1204749687223021477647188999⟩,⟨(-2632938498190985277713845494),(-2632938498190985276262619116)⟩⟩,⟨⟨1151548448220103587496442525,1151548448220103588939215005⟩,⟨(-2584820120965400843877241000),(-2584820120965400842443684258)⟩⟩,⟨⟨1100016973500556898663922357,1100016973500556900087678927⟩,⟨(-2537100080434605827392041252),(-2537100080434605825976916834)⟩⟩,⟨⟨1050125171028277772592328307,1050125171028277773997949464⟩,⟨(-2489800067550138500144300225),(-2489800067550138498746752287)⟩⟩,⟨⟨1001842447141129778567999782,1001842447141129779954945339⟩,⟨(-2442940690638611871822634844),(-2442940690638611870443225232)⟩⟩,⟨⟨955137766539263867752902222,955137766539263869121876884⟩,⟨(-2396541476205973432669366385),(-2396541476205973431307413395)⟩⟩,⟨⟨909979710957823889429456732,909979710957823890779689646⟩,⟨(-2350620872063248884868390021),(-2350620872063248883524684727)⟩⟩,⟨⟨866336536432728803873871637,866336536432728805206326921⟩,⟨(-2305196252679770637370503288),(-2305196252679770636044103623)⟩⟩,⟨⟨824176229075468761049641961,824176229075468762363803939⟩,⟨(-2260283926666371386001714464),(-2260283926666371384693155560)⟩⟩,⟨⟨783466559280147914269628343,783466559280147915566226816⟩,⟨(-2215899146287999976590342242),(-2215899146287999975298914706)⟩⟩,⟨⟨744175134293319648583328813,744175134293319649861665226⟩,⟨(-2172056118902685230853921986),(-2172056118902685229580342532)⟩⟩,⟨⟨706269449084458121756628808,706269449084458123017641285⟩,⟨(-2128768020221725553843594044),(-2128768020221725552586943918)⟩⟩,⟨⟨669716935462163154527274028,669716935462163155770471374⟩,⟨(-2086047009284407889324972682),(-2086047009284407888085760380)⟩⟩,⟨⟨634485009388374425585589305,634485009388374426811720815⟩,⟨(-2043904245039446934063891797),(-2043904245039446932841385931)⟩⟩] +lemma kernel3_0_r3_8_eq : ∀ k : Fin 16, kernel3_0Expr 3 8 k = kernel3_0_r3_8 k := by decide +kernel +noncomputable def kernel3_0_r3_9 : Fin 16 → CBox := ![⟨⟨600541116449947947625443874,600541116449947948833767821⟩,⟨(-2002349904424670632352623656),(-2002349904424670631147582008)⟩⟩,⟨⟨567852775453896811207242814,567852775453896812398782465⟩,⟨(-1961393201836245347554716047),(-1961393201836245346366132274)⟩⟩,⟨⟨536387620119394724523780481,536387620119394725698069067⟩,⟨(-1921042409878916732195248063),(-1921042409878916731023604180)⟩⟩,⟨⟨506113438846262218920442890,506113438846262220078243195⟩,⟨(-1881304881289321820081040533),(-1881304881289321818925589286)⟩⟩,⟨⟨476998212546080590142286857,476998212546080591282944851⟩,⟨(-1842187071925384674973666710),(-1842187071925384673835076292)⟩⟩,⟨⟨449010150528288595862435188,449010150528288596986920431⟩,⟨(-1803694564716121448396975646),(-1803694564716121447274291008)⟩⟩,⟨⟨422117724439594389952325424,422117724439594391060194660⟩,⟨(-1765832094467829449414399014),(-1765832094467829448308076732)⟩⟩,⟨⟨396289700260764787194940384,396289700260764788286964572⟩,⟨(-1728603573424596624656542405),(-1728603573424596623565824826)⟩⟩,⟨⟨371495168370322253972094183,371495168370322255047586637⟩,⟨(-1692012117483319945746243191),(-1692012117483319944671829347)⟩⟩,⟨⟨347703571689875430236689376,347703571689875431296681683⟩,⟨(-1656060072965940461691023261),(-1656060072965940460631893907)⟩⟩,⟨⟨324884731930721790977182236,324884731930721792021253860⟩,⟨(-1620749043854365803334531893),(-1620749043854365802291119101)⟩⟩,⟨⟨303008873965983372118169894,303008873965983373147094473⟩,⟨(-1586079919396534227445446558),(-1586079919396534226416987957)⟩⟩,⟨⟨282046648356862232661728998,282046648356862233674896299⟩,⟨(-1552052901995254393727924635),(-1552052901995254392715041157)⟩⟩,⟨⟨261969152065627163268095339,261969152065627164266482078⟩,⟨(-1518667535294808677577202646),(-1518667535294808676578927907)⟩⟩,⟨⟨242747947391664429382859904,242747947391664430366066857⟩,⟨(-1485922732383811921526409766),(-1485922732383811920543152900)⟩⟩,⟨⟨224355079170342021698132089,224355079170342022666930896⟩,⟨(-1453816804036449510440634117),(-1453816804036449509471632898)⟩⟩] +lemma kernel3_0_r3_9_eq : ∀ k : Fin 16, kernel3_0Expr 3 9 k = kernel3_0_r3_9 k := by decide +kernel +noncomputable def kernel3_0_r3_10 : Fin 16 → CBox := ![⟨⟨206763090277549491024473800,206763090277549491978203949⟩,⟨(-1422347486917956423039096277),(-1422347486917956422085020436)⟩⟩,⟨⟨189945035485585946328183616,189945035485585947267889502⟩,⟨(-1391511971684020980017948099),(-1391511971684020979077761758)⟩⟩,⟨⟨173874493718580551227916358,173874493718580552153218943⟩,⟨(-1361306930907682592522876118),(-1361306930907682591596966767)⟩⟩,⟨⟨158525578757847512424478695,158525578757847513336142907⟩,⟨(-1331728546771221911499595443),(-1331728546771221910587205911)⟩⟩,⟨⟨143872948449506956229120759,143872948449506957126577208⟩,⟨(-1302772538464495238950671745),(-1302772538464495238052379291)⟩⟩,⟨⟨129891812468351178908342496,129891812468351179792554148⟩,⟨(-1274434189235124652073534702),(-1274434189235124651188383283)⟩⟩,⟨⟨116557938693310477090400170,116557938693310477961006449⟩,⟨(-1246708373039903744086258996),(-1246708373039903743214616347)⟩⟩,⟨⟨103847658250982962399861838,103847658250982963257617330⟩,⟨(-1219589580750699946419852803),(-1219589580750699945560970628)⟩⟩,⟨⟨91737869284548089523041767,91737869284548090367339775⟩,⟨(-1193071945872012857110366509),(-1193071945872012856264858231)⟩⟩,⟨⟨80206039505994432865513526,80206039505994433697360712⟩,⟨(-1167149269731169723386987814),(-1167149269731169722553852255)⟩⟩,⟨⟨69230207589969494371910241,69230207589969495190963177⟩,⟨(-1141815046105891166190368049),(-1141815046105891165369954658)⟩⟩,⟨⟨58788983467714484941941443,58788983467714485748940766⟩,⟨(-1117062485257630444130509087),(-1117062485257630443322082236)⟩⟩,⟨⟨48861547579491982494182553,48861547579491983288595179⟩,⟨(-1092884537342667189350349263),(-1092884537342667188554447704)⟩⟩,⟨⟨39427649143661345734095656,39427649143661346516854764⟩,⟨(-1069273915176411860068589819),(-1069273915176411859284284662)⟩⟩,⟨⟨30467603500118208159707869,30467603500118208930485473⟩,⟨(-1046223116329741481405935411),(-1046223116329741480633559676)⟩⟩,⟨⟨21962288585202901556845006,21962288585202902316365218⟩,⟨(-1023724444539432992122714116),(-1023724444539432991361547600)⟩⟩] +lemma kernel3_0_r3_10_eq : ∀ k : Fin 16, kernel3_0Expr 3 10 k = kernel3_0_r3_10 k := by decide +kernel +noncomputable def kernel3_0_r3_11 : Fin 16 → CBox := ![⟨⟨13893140594410948710508722,13893140594410949458185286⟩,⟨(-1001770030417881128449132928),(-1001770030417881127699766734)⟩⟩,⟨⟨6242148888319509413769258,6242148888319510150586428⟩,⟨(-980351851450277720974792048),(-980351851450277720236245095)⟩⟩,⟨⟨(-1008149803910517945268180),(-1008149803910517219624140)⟩,⟨(-959461751270284002097512428),(-959461751270284001370102640)⟩⟩,⟨⟨(-7874677830273658605156355),(-7874677830273657889980420)⟩,⟨(-939091458207943410181838583),(-939091458207943409464863901)⟩⟩,⟨⟨(-14373823659003975580775774),(-14373823659003974876569657)⟩,⟨(-919232603106156726421729620),(-919232603106156725715695784)⟩⟩,⟨⟨(-20521449468492695679829732),(-20521449468492694985701239)⟩,⟨(-899876736404472345739630589),(-899876736404472345043647746)⟩⟩,⟨⟨(-26332899234999136556453875),(-26332899234999135872704129)⟩,⟨(-881015344491231031762042467),(-881015344491231031076415210)⟩⟩,⟨⟨(-31823007270660908190296810),(-31823007270660907516241302)⟩,⟨(-862639865327246371457909342),(-862639865327246370781955332)⟩⟩,⟨⟨(-37006107165919481368523068),(-37006107165919480704705482)⟩,⟨(-844741703346199776329088237),(-844741703346199775663354618)⟩⟩,⟨⟨(-41896041092140667016538488),(-41896041092140666362033213)⟩,⟨(-827312243638783387895887079),(-827312243638783387239449759)⟩⟩,⟨⟨(-46506169421916176935628012),(-46506169421916176290724618)⟩,⟨(-810342865429337362469385457),(-810342865429337361822536872)⟩⟩,⟨⟨(-50849380626272553215069466),(-50849380626272552579105437)⟩,⟨(-793824954855302022309597209),(-793824954855302021671676348)⟩⟩,⟨⟨(-54938101409778165702738284),(-54938101409778165076189042)⟩,⟨(-777749917061243065426355832),(-777749917061243064797840978)⟩⟩,⟨⟨(-58784307046318996548353034),(-58784307046318995930373553)⟩,⟨(-762109187620512681646302499),(-762109187620512681026349585)⟩⟩,⟨⟨(-62399531880101387757279741),(-62399531880101387148149403)⟩,⟨(-746894243298784693706640535),(-746894243298784693095531304)⟩⟩,⟨⟨(-65794879958227176948942439),(-65794879958227176348021252)⟩,⟨(-732096612174751754177318219),(-732096612174751753574413634)⟩⟩] +lemma kernel3_0_r3_11_eq : ∀ k : Fin 16, kernel3_0Expr 3 11 k = kernel3_0_r3_11 k := by decide +kernel +noncomputable def kernel3_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-68981035762966571627698521),(-68981035762966571035522508)⟩,⟨(-717707883134201518603110755),(-717707883134201518008949367)⟩⟩,⟨⟨(-71968275013620125571423631),(-71968275013620124987099442)⟩,⟨(-703719714754501184685865049),(-703719714754501184099553846)⟩⟩,⟨⟨(-74766475509607220039490281),(-74766475509607219463287865)⟩,⟨(-690123843597220659876184833),(-690123843597220659297995706)⟩⟩,⟨⟨(-77385127988138974403047779),(-77385127988138973834350344)⟩,⟨(-676912091927218897582778260),(-676912091927218897012094927)⟩⟩,⟨⟨(-79833346971523482718548686),(-79833346971523482157809884)⟩,⟨(-664076374877010765815324087),(-664076374877010765252602257)⟩⟩,⟨⟨(-82119881580806161098489174),(-82119881580806160544913338)⟩,⟨(-651608707075628422477366428),(-651608707075628421921810458)⟩⟩,⟨⟨(-84253126294063747285283814),(-84253126294063746739132649)⟩,⟨(-639501208761496874235375208),(-639501208761496873687248405)⟩⟩,⟨⟨(-86241131629243540719466350),(-86241131629243540180145940)⟩,⟨(-627746111399063527818176936),(-627746111399063527276885529)⟩⟩,⟨⟨(-88091614732966683729734232),(-88091614732966683197744025)⟩,⟨(-616335762819061440792434476),(-616335762819061440258479771)⟩⟩,⟨⟨(-89811969858192972232992453),(-89811969858192971707505374)⟩,⟨(-605262631902350952219388369),(-605262631902350951691942883)⟩⟩,⟨⟨(-91409278715072572488168201),(-91409278715072571969438273)⟩,⟨(-594519312827279676484259724),(-594519312827279675963578803)⟩⟩,⟨⟨(-92890320680685228722056953),(-92890320680685228209513074)⟩,⟨(-584098528900431652357064943),(-584098528900431651842577344)⟩⟩,⟨⟨(-94261582854688567808275977),(-94261582854688567302354261)⟩,⟨(-573993135990507830700154290),(-573993135990507830192297654)⟩⟩,⟨⟨(-95529269949162786377321460),(-95529269949162785877274163)⟩,⟨(-564196125584897016467088919),(-564196125584897015965114917)⟩⟩,⟨⟨(-96699314002148516937935425),(-96699314002148516444009756)⟩,⟨(-554700627488263676508011208),(-554700627488263676012168147)⟩⟩,⟨⟨(-97777383905527494438227747),(-97777383905527493949874599)⟩,⟨(-545499912182201357085010933),(-545499912182201356594749338)⟩⟩] +lemma kernel3_0_r3_12_eq : ∀ k : Fin 16, kernel3_0Expr 3 12 k = kernel3_0_r3_12 k := by decide +kernel +noncomputable def kernel3_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-98768894738991549824772940),(-98768894738991549342489706)⟩,⟨(-536587392864682334064426255),(-536587392864682333580244983)⟩⟩,⟨⟨(-99679016902884472405337910),(-99679016902884471928330089)⟩,⟨(-527956627187679881610713346),(-527956627187679881131816971)⟩⟩,⟨⟨(-100512685043683679202032747),(-100512685043683678730541015)⟩,⟨(-519601318710953346985293495),(-519601318710953346511923612)⟩⟩,⟨⟨(-101274606766814898099269765),(-101274606766814897632766544)⟩,⟨(-511515318089572026228075349),(-511515318089572025759703835)⟩⟩,⟨⟨(-101969271132363902540874268),(-101969271132363902079781629)⟩,⟨(-503692624012315420379117647),(-503692624012315419916167762)⟩⟩,⟨⟨(-102600956930065597946743785),(-102600956930065597490358180)⟩,⟨(-496127383907628389199140757),(-496127383907628388740907991)⟩⟩,⟨⟨(-103173740730713482277051587),(-103173740730713481825607859)⟩,⟨(-488813894433333383669991893),(-488813894433333383216711860)⟩⟩,⟨⟨(-103691504711842854371228293),(-103691504711842853924219140)⟩,⟨(-481746601765811503706973753),(-481746601765811503258138475)⟩⟩,⟨⟨(-104157944256200415448809170),(-104157944256200415006706074)⟩,⟨(-474920101703862566539207132),(-474920101703862566095289269)⟩⟩,⟨⟨(-104576575322122498765868467),(-104576575322122498327932220)⟩,⟨(-468329139601944458018045663),(-468329139601944457578304809)⟩⟩,⟨⟨(-104950741585505556381573978),(-104950741585505555948033711)⟩,⟨(-461968610146976350585175147),(-461968610146976350149841091)⟩⟩,⟨⟨(-105283621353567290993400043),(-105283621353567290563767920)⟩,⟨(-455833556992371291130039706),(-455833556992371290698623836)⟩⟩,⟨⟨(-105578234251066565128540186),(-105578234251066564703227444)⟩,⟨(-449919172262443383097924685),(-449919172262443382670839217)⟩⟩,⟨⟨(-105837447680076616359045090),(-105837447680076615937386734)⟩,⟨(-444220795939815318782595646),(-444220795939815318359174399)⟩⟩,⟨⟨(-106063983054790856109822311),(-106063983054790855692042198)⟩,⟨(-438733915147935188793103549),(-438733915147935188373570946)⟩⟩,⟨⟨(-106260421813185353997049737),(-106260421813185353582678119)⟩,⟨(-433454163340298961517057999),(-433454163340298961100943445)⟩⟩] +lemma kernel3_0_r3_13_eq : ∀ k : Fin 16, kernel3_0Expr 3 13 k = kernel3_0_r3_13 k := by decide +kernel +noncomputable def kernel3_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-106429211207668744075418789),(-106429211207668743664935540)⟩,⟨(-428377319407468273506816293),(-428377319407468273094600721)⟩⟩,⟨⟨(-106572669877120470717512218),(-106572669877120470310195631)⟩,⟨(-423499306712473528529518203),(-423499306712473528120478497)⟩⟩,⟨⟨(-106692993202953750148100828),(-106692993202953749744169342)⟩,⟨(-418816192064700940461560454),(-418816192064700940055915549)⟩⟩,⟨⟨(-106792258452042074501688117),(-106792258452042074100689222)⟩,⟨(-414324184641880097842453836),(-414324184641880097439750322)⟩⟩,⟨⟨(-106872429709519222489067447),(-106872429709519222091404116)⟩,⟨(-410019634869316759787881418),(-410019634869316759388523124)⟩⟩,⟨⟨(-106935362604604230385467236),(-106935362604604229990506618)⟩,⟨(-405899033265054665011502525),(-405899033265054664614855289)⟩⟩,⟨⟨(-106982808832716251606081762),(-106982808832716251214037221)⟩,⟨(-401959009259200772590623010),(-401959009259200772196900637)⟩⟩,⟨⟨(-107016420477231287088447352),(-107016420477231286698882091)⟩,⟨(-398196329995211060592858924),(-398196329995211060201623683)⟩⟩,⟨⟨(-107037754134294954209580972),(-107037754134294953822951932)⟩,⟨(-394607899120509180405700811),(-394607899120509180017410580)⟩⟩,⟨⟨(-107048274844144285696988337),(-107048274844144285312618590)⟩,⟨(-391190755573398189235741221),(-391190755573398188849717602)⟩⟩,⟨⟨(-107049359832408470145272796),(-107049359832408469763370364)⟩,⟨(-387942072372826450968929130),(-387942072372826450585380540)⟩⟩,⟨⟨(-107042302064854870098501628),(-107042302064854869718644521)⟩,⟨(-384859155417182704942495046),(-384859155417182704560998541)⟩⟩,⟨⟨(-107028313619023937707247260),(-107028313619023937329832675)⟩,⟨(-381939442297922266191485348),(-381939442297922265812438912)⟩⟩,⟨⟨(-107008528876156094071951862),(-107008528876156093696371947)⟩,⟨(-379180501133466273277272217),(-379180501133466272900066623)⟩⟩,⟨⟨(-106984007536756494885373472),(-106984007536756494511830989)⟩,⟨(-376580029428468701305278088),(-376580029428468700930116457)⟩⟩,⟨⟨(-106955737463071066251468230),(-106955737463071065879554639)⟩,⟨(-374135852963211301041864760),(-374135852963211300668337588)⟩⟩] +lemma kernel3_0_r3_14_eq : ∀ k : Fin 16, kernel3_0Expr 3 14 k = kernel3_0_r3_14 k := by decide +kernel +noncomputable def kernel3_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-106924637351660400977986900),(-106924637351660400608171508)⟩,⟨(-371845924717564440604992591),(-371845924717564440233570110)⟩⟩,⟨⟨(-106891559239158144441000015),(-106891559239158144072610314)⟩,⟨(-369708323833641687449955903),(-369708323833641687079964056)⟩⟩,⟨⟨(-106857290844188405087958647),(-106857290844188404721191621)⟩,⟨(-367721254620977496337812071),(-367721254620977495969448167)⟩⟩,⟨⟨(-106822557748293481593037096),(-106822557748293481227496945)⟩,⟨(-365883045607770137127720212),(-365883045607770136760587487)⟩⟩,⟨⟨(-106788025418589740762109835),(-106788025418589740398189884)⟩,⟨(-364192148641455534591112825),(-364192148641455534225605352)⟩⟩,⟨⟨(-106754301074726694029531621),(-106754301074726693666642122)⟩,⟨(-362647138041611491867576401),(-362647138041611491503103034)⟩⟩,⟨⟨(-106721935402573046494423458),(-106721935402573046132755570)⟩,⟨(-361246709807935284974297813),(-361246709807935284611050011)⟩⟩,⟨⟨(-106691424116894528238560968),(-106691424116894527877730375)⟩,⟨(-359989680885790271477804489),(-359989680885790271115396980)⟩⟩,⟨⟨(-106663209375122419329160525),(-106663209375122418969621128)⟩,⟨(-358874988491578346933403618),(-358874988491578346572291174)⟩⟩,⟨⟨(-106637681044139565265917686),(-106637681044139564907024287)⟩,⟨(-357901689499964177567428577),(-357901689499964177206964461)⟩⟩,⟨⟨(-106615177821833030699811426),(-106615177821833030341748651)⟩,⟨(-357068959894753483867947980),(-357068959894753483508317098)⟩⟩,⟨⟨(-106595988214980005314420115),(-106595988214980004956814627)⟩,⟨(-356376094285010574489920511),(-356376094285010574130748579)⟩⟩,⟨⟨(-106580351374846776147645538),(-106580351374846775790888554)⟩,⟨(-355822505487789142993401297),(-355822505487789142635080264)⟩⟩,⟨⟨(-106568457791690108017887772),(-106568457791690107661400912)⟩,⟨(-355407724178644336402331930),(-355407724178644336044282011)⟩⟩,⟨⟨(-106560449849156797083527466),(-106560449849156796727488483)⟩,⟨(-355131398610892566532158705),(-355131398610892566174557914)⟩⟩,⟨⟨(-106556422239381030640596519),(-106556422239381030284642164)⟩,⟨(-354993294404387734050135271),(-354993294404387733692619427)⟩⟩] +lemma kernel3_0_r3_15_eq : ∀ k : Fin 16, kernel3_0Expr 3 15 k = kernel3_0_r3_15 k := by decide +kernel +noncomputable def kernel3_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel3_0_r3_0,kernel3_0_r3_1,kernel3_0_r3_2,kernel3_0_r3_3,kernel3_0_r3_4,kernel3_0_r3_5,kernel3_0_r3_6,kernel3_0_r3_7,kernel3_0_r3_8,kernel3_0_r3_9,kernel3_0_r3_10,kernel3_0_r3_11,kernel3_0_r3_12,kernel3_0_r3_13,kernel3_0_r3_14,kernel3_0_r3_15] +lemma kernel3_0_r3_eq (i k : Fin 16) : kernel3_0Expr 3 i k = kernel3_0_r3 i k := by + fin_cases i + · exact kernel3_0_r3_0_eq k + · exact kernel3_0_r3_1_eq k + · exact kernel3_0_r3_2_eq k + · exact kernel3_0_r3_3_eq k + · exact kernel3_0_r3_4_eq k + · exact kernel3_0_r3_5_eq k + · exact kernel3_0_r3_6_eq k + · exact kernel3_0_r3_7_eq k + · exact kernel3_0_r3_8_eq k + · exact kernel3_0_r3_9_eq k + · exact kernel3_0_r3_10_eq k + · exact kernel3_0_r3_11_eq k + · exact kernel3_0_r3_12_eq k + · exact kernel3_0_r3_13_eq k + · exact kernel3_0_r3_14_eq k + · exact kernel3_0_r3_15_eq k +noncomputable def kernel3_0_r4_0 : Fin 16 → CBox := ![⟨⟨20630981736865079752447615347,20630981736865079787543047678⟩,⟨149589573472872748875892738669,149589573472872748912586577986⟩⟩,⟨⟨20646408966648797303718762125,20646408966648797338812956292⟩,⟨149567359941873571676548625035,149567359941873571713241357681⟩⟩,⟨⟨20677247200757324333646006669,20677247200757324368737665137⟩,⟨149522937175001208749438643850,149522937175001208786129103134⟩⟩,⟨⟨20723464005618872624719100421,20723464005618872659806924266⟩,⟨149456313771243207544166599532,149456313771243207580853616777⟩⟩,⟨⟨20785010774229089347448722657,20785010774229089382531410350⟩,⟨149367502650887464560022355536,149367502650887464596704758564⟩⟩,⟨⟨20861822778142143252488349881,20861822778142143287564596715⟩,⟨149256521081599651907546174969,149256521081599651944222787229⟩⟩,⟨⟨20953819236737215614265375061,20953819236737215649333871470⟩,⟨149123390713042576681688779178,149123390713042576718358417764⟩⟩,⟨⟨21060903403713073207502029464,21060903403713073242561462572⟩,⟨148968137619908896953171782760,148968137619908896989833259684⟩⟩,⟨⟨21182962670751301213933644993,21182962670751301248982692315⟩,⟨148790792353207049062208116415,148790792353207049098860231985⟩⟩,⟨⟨21319868688276498320225556594,21319868688276498355262895311⟩,⟨148591389999609054134775423860,148591389999609054171416975719⟩⟩,⟨⟨21471477503229251999235648688,21471477503229252034259938733⟩,⟨148369970248638142873975067090,148369970248638142910604832938⟩⟩,⟨⟨21637629713754988232884315748,21637629713754988267894222646⟩,⟨148126577467443941725495338259,148126577467443941762112098539⟩⟩,⟨⟨21818150640698797694576553009,21818150640698797729570711600⟩,⟨147861260782883374879329403820,147861260782883374915931904963⟩⟩,⟨⟨22012850515783052648530394625,22012850515783052683507459790⟩,⟨147574074170596528937629509871,147574074170596528974216515057⟩⟩,⟨⟨22221524686331020784981788295,22221524686331020819940367622⟩,⟨147265076550738573320824542643,147265076550738573357394763796⟩⟩,⟨⟨22443953836385731612957011951,22443953836385731647895746450⟩,⟨146934331890001501544586634119,146934331890001501581138812864⟩⟩] +lemma kernel3_0_r4_0_eq : ∀ k : Fin 16, kernel3_0Expr 4 0 k = kernel3_0_r4_0 k := by decide +kernel +noncomputable def kernel3_0_r4_1 : Fin 16 → CBox := ![⟨⟨22679904224059038281964779706,22679904224059038316882234969⟩,⟨146581909309533027283187235603,146581909309533027319720033512⟩⟩,⟨⟨22929127934931126093331088213,22929127934931126128225900085⟩,⟨146207883198334504386572750668,146207883198334504423084895567⟩⟩,⟨⟨23191363151305634859289233839,23191363151305634894159931398⟩,⟨145812333331695310203442908581,145812333331695310239933016226⟩⟩,⟨⟨23466334437110075293477989976,23466334437110075328323193453⟩,⟨145395344994197803733238559964,145395344994197803769705332935⟩⟩,⟨⟨23753753038215322805293912011,23753753038215322840112087210⟩,⟨144957009106804809791308879590,144957009106804809827750859988⟩⟩,⟨⟨24053317197931662021755830386,24053317197931662056545603318⟩,⟨144497422357520651339744489399,144497422357520651376160375192⟩⟩,⟨⟨24364712487422132371703628731,24364712487422132406463420892⟩,⟨144016687335097116391278501158,144016687335097116427666779018⟩⟩,⟨⟨24687612150756793252786661978,24687612150756793287515081802⟩,⟨143514912665237463425762197639,143514912665237463462121536603⟩⟩,⟨⟨25021677464313994695583451070,25021677464313994730278826094⟩,⟨142992213148734697910583538722,142992213148734697946912319275⟩⟩,⟨⟨25366558110216818079467854954,25366558110216818114128821813⟩,⟨142448709900964947818743481485,142448709900964947855040389044⟩⟩,⟨⟨25721892563474557451335235410,25721892563474557485960076880⟩,⟨141884530492142881041264487555,141884530492142881077527845206⟩⟩,⟨⟨26087308492480465581354231049,26087308492480465615941558830⟩,⟨141299809087733792690332921296,141299809087733792726561376686⟩⟩,⟨⟨26462423172498014440175511002,26462423172498014474723482743⟩,⟨140694686588406293051000370836,140694686588406293087192108139⟩⟩,⟨⟨26846843911748645840587722033,26846843911748645875095001871⟩,⟨140069310768900491915281410902,140069310768900491951435117252⟩⟩,⟨⟨27240168489694447245096641162,27240168489694447279561340329⟩,⟨139423836415179243580543832223,139423836415179243616657631514⟩⟩,⟨⟨27641985607089417010922060624,27641985607089417045342814554⟩,⟨138758425459224426890629295542,138758425459224426926701832229⟩⟩] +lemma kernel3_0_r4_1_eq : ∀ k : Fin 16, kernel3_0Expr 4 1 k = kernel3_0_r4_1 k := by decide +kernel +noncomputable def kernel3_0_r4_2 : Fin 16 → CBox := ![⟨⟨28051875347353023505741508090,28051875347353023540116249551⟩,⟨138073247110836420752017757831,138073247110836420788046962154⟩⟩,⟨⟨28469409648799658457396327380,28469409648799658491723792976⟩,⟨137368477985792928222739012615,137368477985792928258723616618⟩⟩,⟨⟨28894152787237385376997582887,28894152787237385411275678898⟩,⟨136644302229723128261999792751,136644302229723128297937685567⟩⟩,⟨⟨29325661868429141482001469641,29325661868429141516228880477⟩,⟨135900911637054816131453196893,135900911637054816167343043471⟩⟩,⟨⟨29763487329889322457655413306,29763487329889322491829829386⟩,⟨135138505764395749535363390738,135138505764395749571202848189⟩⟩,⟨⟨30207173451468523335724014171,30207173451468523369844256611⟩,⟨134357292037715861672154078504,134357292037715861707941934551⟩⟩,⟨⟨30656258874159188752634064935,30656258874159188786697801505⟩,⟨133557485852704343581946857581,133557485852704343617680731559⟩⟩,⟨⟨31110277126535107997448463624,31110277126535108031454458325⟩,⟨132739310667684840827661879957,132739310667684840863340487123⟩⟩,⟨⟨31568757158218143581707345574,31568757158218143615652968453⟩,⟨131902998088483152972762532639,131902998088483153008383177528⟩⟩,⟨⟨32031223879746378209197219662,32031223879746378243081453828⟩,⟨131048787944654862716466934147,131048787944654862752028537530⟩⟩,⟨⟨32497198708199078025170868983,32497198708199078058991111868⟩,⟨130176928356495243846102385148,130176928356495243881602263988⟩⟩,⟨⟨32966200117915576009871918610,32966200117915576043627047995⟩,⟨129287675792270586896666836838,129287675792270586932103790862⟩⟩,⟨⟨33437744195627456275679306028,33437744195627456309366381887⟩,⟨128381295115128716587660034920,128381295115128716623031026267⟩⟩,⟨⟨33911345199306347233924286800,33911345199306347267542449027⟩,⟨127458059619166928142478861865,127458059619166928177782939255⟩⟩,⟨⟨34386516120013289662579025135,34386516120013289696125370037⟩,⟨126518251054157807195798018402,126518251054157807231032165623⟩⟩,⟨⟨34862769246020115967385570446,34862769246020116000859128217⟩,⟨125562159638457381105931975368,125562159638457381141095116021⟩⟩] +lemma kernel3_0_r4_2_eq : ∀ k : Fin 16, kernel3_0Expr 4 2 k = kernel3_0_r4_2 k := by decide +kernel +noncomputable def kernel3_0_r4_3 : Fin 16 → CBox := ![⟨⟨35339616728458641151255540363,35339616728458641184652942896⟩,⟨124590084059645733247833447268,124590084059645733282922082818⟩⟩,⟨⟨35816571147739806002651883395,35816571147739806035972556120⟩,⟨123602331462477545563839302380,123602331462477545598852740027⟩⟩,⟨⟨36293146079972310254544767231,36293146079972310287785477513⟩,⟨122599217423748961742230805913,122599217423748961777165669176⟩⟩,⟨⟨36768856662598808680947719559,36768856662598808714107690719⟩,⟨121581065913717621493754299169,121581065913717621528609677776⟩⟩,⟨⟨37243220158457495867926101310,37243220158457495901001610377⟩,⟨120548209243744637324181847950,120548209243744637358953857661⟩⟩,⟨⟨37715756517467953735104342773,37715756517467953768095043598⟩,⟨119500987999860595043693341139,119500987999860595078381491771⟩⟩,⟨⟨38185988935132555822672789618,38185988935132555855575096306⟩,⟨118439750961992278451781412475,118439750961992278486381944402⟩⟩,⟨⟨38653444407038587520948054557,38653444407038587553761427247⟩,⟨117364855008622662095236746160,117364855008622662129748961208⟩⟩,⟨⟨39117654278541622598060592856,39117654278541622630780787094⟩,⟨116276665006693693227112915721,116276665006693693261532378064⟩⟩,⟨⟨39578154788807661117229492270,39578154788807661149856579030⟩,⟨115175553686599399376740481873,115175553686599399411067096326⟩⟩,⟨⟨40034487608390145999239521818,40034487608390146031769541602⟩,⟨114061901502155810518856518318,114061901502155810553086123885⟩⟩,⟨⟨40486200369518294865663632509,40486200369518294898096326758⟩,⟨112936096475473969131095734360,112936096475473969165227892413⟩⟩,⟨⟨40932847188275265694608368956,40932847188275265726939105062⟩,⟨111798534026702807313268110891,111798534026702807347297970850⟩⟩,⟨⟨41373989177848569651791487001,41373989177848569684020646162⟩,⟨110649616788649783176033146581,110649616788649783209960903578⟩⟩,⟨⟨41809194952040897381665235889,41809194952040897413788469538⟩,⟨109489754406328770468974600761,109489754406328770502795679697⟩⟩,⟨⟨42238041118237175582363552973,42238041118237175614380929336⟩,⟨108319363321526663826853529623,108319363321526663860567800479⟩⟩] +lemma kernel3_0_r4_3_eq : ∀ k : Fin 16, kernel3_0Expr 4 3 k = kernel3_0_r4_3 k := by decide +kernel +noncomputable def kernel3_0_r4_4 : Fin 16 → CBox := ![⟨⟨42660112759033252393155896670,42660112759033252425062148758⟩,⟨107138866542522371683282976565,107138866542522371716884929022⟩⟩,⟨⟨43075003901743150234573322512,43075003901743150266369420864⟩,⟨105948693399134191526042526709,105948693399134191559532930950⟩⟩,⟨⟨43482317975015343886261874639,43482317975015343917943070957⟩,⟨104749279283313866925259730501,104749279283313866958633589950⟩⟩,⟨⟨43881668251804033494672360315,43881668251804033526239094352⟩,⟨103541065375547779745009150960,103541065375547779778266693033⟩⟩,⟨⟨44272678277958893447436053677,44272678277958893478882694933⟩,⟨102324498357367599606153762584,102324498357367599639289093702⟩⟩,⟨⟨44654982285716287826638145788,44654982285716287857966018856⟩,⟨101100030110314160294771099730,101100030110314160327785332065⟩⟩,⟨⟨45028225591396443073527406579,45028225591396443104731358301⟩,⟨99868117401739223025093292760,99868117401739223057981006866⟩⟩,⟨⟨45392064976634542431706423986,45392064976634542462787309024⟩,⟨98629221557869982720658116885,98629221557869982753419945494⟩⟩,⟨⟨45746169052499130679234169053,45746169052499130710185665690⟩,⟨97383808124600539581264404987,97383808124600539613893744891⟩⟩,⟨⟨46090218605878559635777802259,46090218605878559666601958473⟩,⟨96132346516512958855076008031,96132346516512958887574689960⟩⟩,⟨⟨46423906927545424934817822284,46423906927545424965509081043⟩,⟨94875309654667843069690682405,94875309654667843102052869123⟩⟩,⟨⟨46746940121339994529976285611,46746940121339994560535957342⟩,⟨93613173593740411114806471751,93613173593740411147033246935⟩⟩,⟨⟨47059037393946453278816113185,47059037393946453309285106287⟩,⟨92346417139112788179746713379,92346417139112788211854741816⟩⟩,⟨⟨47359931324770321668758237442,47359931324770321699141761467⟩,⟨91075521454566433402600563713,91075521454566433434593495855⟩⟩,⟨⟨47649368115461578404078012760,47649368115461578434369623415⟩,⟨89800969661250245618978768332,89800969661250245650850159131⟩⟩,⟨⟨47927107818665746524322874630,47927107818665746554523864441⟩,⟨88523246428629773460655347886,88523246428629773492406562770⟩⟩] +lemma kernel3_0_r4_4_eq : ∀ k : Fin 16, kernel3_0Expr 4 4 k = kernel3_0_r4_4 k := by decide +kernel +noncomputable def kernel3_0_r4_5 : Fin 16 → CBox := ![⟨⟨48192924545624403796993338969,48192924545624403827095701620⟩,⟨87242837558151000667466884823,87242837558151000699089929901⟩⟩,⟨⟨48446606652287155835035367718,48446606652287155865041929951⟩,⟨85960229560378272565513502227,85960229560378272597011312766⟩⟩,⟨⟨48687956903638963202056998389,48687956903638963231960829437⟩,⟨84675909226389972788299105707,84675909226389972819664796416⟩⟩,⟨⟨48916792615989733418976074750,48916792615989733448778902526⟩,⟨83390363194237454372696878716,83390363194237454403932300425⟩⟩,⟨⟨49132945777017160623175268007,49132945777017160652868759583⟩,⟨82104077511292387079110741605,82104077511292387110207620645⟩⟩,⟨⟨49336263143398799003043296775,49336263143398799032630589499⟩,⟨80817537193325021194318719212,80817537193325021225280348606⟩⟩,⟨⟨49526606315915164812222025173,49526606315915164841695729848⟩,⟨79531225781170812949914879877,79531225781170812980733960126⟩⟩,⟨⟨49703851791952144420175025189,49703851791952144449537347816⟩,⟨78245624895855341959169655365,78245624895855341989848562594⟩⟩,⟨⟨49867890995378006523936077758,49867890995378006553177803629⟩,⟨76961213793057419213244566459,76961213793057419243774185560⟩⟩,⟨⟨50018630283817735283778349355,50018630283817735312903556160⟩,⟨75678468917797686546336919279,75678468917797686576721531892⟩⟩,⟨⟨50155990933395074175080744191,50155990933395074204081619864⟩,⟨74397863460244805646181449883,74397863460244805676413375295⟩⟩,⟨⟨50279909101060451241576896442,50279909101060451270456161686⟩,⟨73119866913533496695821300086,73119866913533496725903472850⟩⟩,⟨⟨50390335764670696324162288952,50390335764670696352910490570⟩,⟨71844944634488193341596016421,71844944634488193371519124801⟩⟩,⟨⟨50487236641034009144967858179,50487236641034009173589440215⟩,⟨70573557408142921546911560692,70573557408142921576680292737⟩⟩,⟨⟨50570592082180842207530955099,50570592082180842236017722224⟩,⟨69306161016942184714225536372,69306161016942184743831866666⟩⟩,⟨⟨50640396950168072287709565189,50640396950168072316064785498⟩,⟨68043205815499156082801854197,68043205815499156112249304343⟩⟩] +lemma kernel3_0_r4_5_eq : ∀ k : Fin 16, kernel3_0Expr 4 5 k = kernel3_0_r4_5 k := by decide +kernel +noncomputable def kernel3_0_r4_6 : Fin 16 → CBox := ![⟨⟨50696660470769897068450394537,50696660470769897096663648915⟩,⟨66785136311776361875340555118,66785136311776361904618881069⟩⟩,⟨⟨50739406066454158399501756743,50739406066454158427578658622⟩,⟨65532390755540315202365184805,65532390755540315231480284738⟩⟩,⟨⟨50768671169087111566651174843,50768671169087111594583191525⟩,⟨64285400734925271714700349113,64285400734925271743643895262⟩⟩,⟨⟨50784507012852883982753095625,50784507012852884010544066969⟩,⟨63044590781922473839718956930,63044590781922473868495077728⟩⟩,⟨⟨50786978407915853020350815278,50786978407915853047990329350⟩,⟨61810377987589991460686784972,61810377987589991489285279329⟩⟩,⟨⟨50776163495394781125065904891,50776163495394781152559834945⟩,⟨60583171627754623107150707447,60583171627754623135577763254⟩⟩,⟨⟨50752153484256641052997318284,50752153484256641080336840701⟩,⟨59363372799951372570265672941,59363372799951372598512702589⟩⟩,⟨⟨50715052370775514219400843808,50715052370775514246590390372⟩,⟨58151374072317849935405300202,58151374072317849963477054127⟩⟩,⟨⟨50664976641237625496571231970,50664976641237625523599526368⟩,⟨56947559145130660729837479199,56947559145130660757722918343⟩⟩,⟨⟨50602054958607369332298946008,50602054958607369359173062973⟩,⟨55752302525638548012098105883,55752302525638548039804649745⟩⟩,⟨⟨50526427833900972540550774794,50526427833900972567261651339⟩,⟨54565969216812853545779245737,54565969216812853573298094198⟩⟩,⟨⟨50438247283044123634928225898,50438247283044123661480895620⟩,⟨53388914420599886950108984294,53388914420599886977445514379⟩⟩,⟨⟨50337676470017380066018638357,50337676470017380092401928188⟩,⟨52221483256222164114487951582,52221483256222164141631254684⟩⟩,⟨⟨50224889337118354428240516224,50224889337118354454461787267⟩,⟨51064010494036332817801516010,51064010494036332844759317466⟩⟩,⟨⟨50100070223192498607441256838,50100070223192498633491256786⟩,⟨49916820305415084832266395511,49916820305415084859029728297⟩⟩,⟨⟨49963413470704680063813954678,49963413470704680089698324070⟩,⟨48780226029078605425536981713,48780226029078605452111849111⟩⟩] +lemma kernel3_0_r4_6_eq : ∀ k : Fin 16, kernel3_0Expr 4 6 k = kernel3_0_r4_6 k := by decide +kernel +noncomputable def kernel3_0_r4_7 : Fin 16 → CBox := ![⟨⟨49815123022541615578165526210,49815123022541615603872143764⟩,⟨47654529954258283247643385832,47654529954258283274017948351⟩⟩,⟨⟨49655412009450543192160000035,49655412009450543217697623802⟩,⟨46540023121031650096847244003,46540023121031650123030643413⟩⟩,⟨⟨49484502329032231119330078137,49484502329032231144689320008⟩,⟨45436985138122998153994481609,45436985138122998179977632973⟩⟩,⟨⟨49302624217216511672192218502,49302624217216511697379319455⟩,⟨44345684018418991549361853874,44345684018418991575151374692⟩⟩,⟨⟨49110015813155967669668103425,49110015813155967694671347125⟩,⟨43266376032403010884114059077,43266376032403010909698533764⟩⟩,⟨⟨48906922718478177717304028496,48906922718478177742132250509⟩,⟨42199305579666105847481394051,42199305579666105872870049510⟩⟩,⟨⟨48693597551839045017538741144,48693597551839045042182466206⟩,⟨41144705078606444863722660257,41144705078606444888906337734⟩⟩,⟨⟨48470299499719202236411717891,48470299499719202260877777557⟩,⟨40102794874383203773087519511,40102794874383203798073435418⟩⟩,⟨⟨48237293864402323063002311611,48237293864402323087278185684⟩,⟨39073783165145088659524754571,39073783165145088684300698691⟩⟩,⟨⟨47994851610068410317617539500,47994851610068410341713393087⟩,⟨38057865946508299871021886451,38057865946508299895598422862⟩⟩,⟨⟨47743248907926811716450532350,47743248907926811740356853588⟩,⟨37055226974213871136826399308,37055226974213871161194341553⟩⟩,⟨⟨47482766681302888418155036006,47482766681302888441879225422⟩,⟨36066037744850112181240355993,36066037744850112205407492508⟩⟩,⟨⟨47213690151578988525354986558,47213690151578988548885001899⟩,⟨35090457494482494016839417516,35090457494482494040794025714⟩⟩,⟨⟨46936308385874727244483576855,46936308385874727267829645548⟩,⟨34128633214990887102888768177,34128633214990887126641471954⟩⟩,⟨⟨46650913847333625685427739800,46650913847333625708580357073⟩,⟨33180699687872732372233450867,33180699687872732395775075484⟩⟩,⟨⟨46357801948862997953833346164,46357801948862997976800457059⟩,⟨32246779535230626423144481328,32246779535230626446483357816⟩⟩] +lemma kernel3_0_r4_7_eq : ∀ k : Fin 16, kernel3_0Expr 4 7 k = kernel3_0_r4_7 k := by decide +kernel +noncomputable def kernel3_0_r4_8 : Fin 16 → CBox := ![⟨⟨46057270611151695817324279698,46057270611151695840092891722⟩,⟨31326983287624061118006820671,31326983287624061141130276962⟩⟩,⟨⟨45749619825766023783268412911,45749619825766023805850274101⟩,⟨30421409468427793597830497651,30421409468427793620750675937⟩⟩,⟨⟨45435151224097933752547019376,45435151224097933774932677413⟩,⟨29530144694303647002007610634,29530144694303647024715389255⟩⟩,⟨⟨45114167652911612647492073250,45114167652911612669689981318⟩,⟨28653263791358558753142899494,28653263791358558775647111091⟩⟩,⟨⟨44786972757204909388181122350,44786972757204909410179115443⟩,⟨27790829926529497608048529519,27790829926529497630337331674⟩⟩,⟨⟨44453870571070835214372224877,44453870571070835236181775512⟩,⟨26942894753705549629882080948,26942894753705549651967328132⟩⟩,⟨⟨44115165117211743955653616375,44115165117211743977265359790⟩,⟨26109498574069104722511685368,26109498574069104744384340430⟩⟩,⟨⟨43771160015724890539638470014,43771160015724890561061332000⟩,⟨25290670510111728140756729126,25290670510111728162426086647⟩⟩,⟨⟨43422158102743013994695007057,43422158102743014015916072662⟩,⟨24486428692756034857164378534,24486428692756034878617840777⟩⟩,⟨⟨43068461059477535059511916874,43068461059477535080543973371⟩,⟨23696780460992748749593286471,23696780460992748770844010844⟩⟩,⟨⟨42710369052175039600625081010,42710369052175039621458887683⟩,⟨22921722573422163633776417415,22921722573422163654815484487⟩⟩,⟨⟨42348180383460079750473400567,42348180383460079771118309439⟩,⟨22161241431071459962979109155,22161241431071459983816225432⟩⟩,⟨⟨41982191155499107775146116162,41982191155499107795590012901⟩,⟨21415313310843790743553217009,21415313310843790764176580216⟩⟩,⟨⟨41612694945381705622976172484,41612694945381705643231580459⟩,⟨20683904608941744556507445212,20683904608941744576929930192⟩⟩,⟨⟨41239982493076327399102289469,41239982493076327419160118042⟩,⟨19966972093596724839116038521,19966972093596724859328866734⟩⟩,⟨⟨40864341402278672563714776515,40864341402278672583584759326⟩,⟨19264463166426945860459807135,19264463166426945880473049332⟩⟩] +lemma kernel3_0_r4_8_eq : ∀ k : Fin 16, kernel3_0Expr 4 8 k = kernel3_0_r4_8 k := by decide +kernel +noncomputable def kernel3_0_r4_9 : Fin 16 → CBox := ![⟨⟨40486055854431692154404452605,40486055854431692174073553198⟩,⟨18576316131740121219926859572,18576316131740121239727780774⟩⟩,⟨⟨40105406336157233659145448205,40105406336157233678627642683⟩,⟨17902460473092485566464458814,17902460473092485586067368145⟩⟩,⟨⟨39722669380300583805682940758,39722669380300583824969316183⟩,⟨17242817136413511502041264092,17242817136413511521437549111⟩⟩,⟨⟨39338117320750800044444410917,39338117320750800063545028755⟩,⟨16597298819005520116986379633,16597298819005520136186419039⟩⟩,⟨⟨38952018061161854010063850352,38952018061161854028966785941⟩,⟨15965810263729286408475675894,15965810263729286427467836336⟩⟩,⟨⟨38564634857662361960494810595,38564634857662361979213409861⟩,⟨15348248557690653738825462370,15348248557690653757623399290⟩⟩,⟨⟨38176226115605160974181552044,38176226115605160992707095191⟩,⟨14744503434749031405259992020,14744503434749031423855272566⟩⟩,⟨⟨37787045200372312643449822329,37787045200372312661792650628⟩,⟨14154457581176386809547289903,14154457581176386827950550778⟩⟩,⟨⟨37397340262216379137676602534,37397340262216379155824055441⟩,⟨13577986943804883204181695186,13577986943804883222380553682⟩⟩,⟨⟨37007354075085114393223848697,37007354075085114411190472249⟩,⟨13014961040012574700897254743,13014961040012574718906543057⟩⟩,⟨⟨36617323889344133687249423241,36617323889344133705026708418⟩,⟨12465243268909466415167842151,12465243268909466432979323156⟩⟩,⟨⟨36227481298280748897313578896,36227481298280748914912090942⟩,⟨11928691223100689183969068452,11928691223100689201593579646⟩⟩,⟨⟨35838052118242058141063852571,35838052118242058158471953994⟩,⟨11405157000419431320322051039,11405157000419431337748218803⟩⟩,⟨⟨35449256282231623755063749334,35449256282231623772295369709⟩,⟨10894487515039517178383423117,10894487515039517195625437750⟩⟩,⟨⟨35061307746761720857644974124,35061307746761720874691821981⟩,⟨10396524807396024011359244323,10396524807396024028409070133⟩⟩,⟨⟨34674414411732241752255379667,34674414411732241769128195548⟩,⟨9911106352361982663716508511,9911106352361982680585134282⟩⟩] +lemma kernel3_0_r4_9_eq : ∀ k : Fin 16, kernel3_0Expr 4 9 k = kernel3_0_r4_9 k := by decide +kernel +noncomputable def kernel3_0_r4_10 : Fin 16 → CBox := ![⟨⟨34288778053082943411442082224,34288778053082943428128229012⟩,⟨9438065365149910391690346919,9438065365149910408365384676⟩⟩,⟨⟨33904594267942863039516493325,33904594267942863056031283443⟩,⟨8977231104428570817521702831,8977231104428570834018699806⟩⟩,⟨⟨33522052431979429667024967162,33522052431979429683360337275⟩,⟨8528429172167841415053664816,8528429172167841431364796675⟩⟩,⟨⟨33141335668630090016958505338,33141335668630090033125315752⟩,⟨8091481809747787683406314680,8091481809747787699542665603⟩⟩,⟨⟨32762620829881159485616577634,32762620829881159501603540393⟩,⟨7666208189891890445120750951,7666208189891890461071266049⟩⟩,⟨⟨32386078488242111994678225174,32386078488242112010499617287⟩,⟨7252424704008744599114604658,7252424704008744614893770355⟩⟩,⟨⟨32011872939548636903681226052,32011872939548636919329210206⟩,⟨6849945244551341664036436316,6849945244551341679636637237⟩⟩,⟨⟨31640162216214511767372584838,31640162216214511782858097236⟩,⟨6458581482028163892696790021,6458581482028163908129161959⟩⟩,⟨⟨31271098110540654819145326803,31271098110540654834456312628⟩,⟨6078143136325656198071015624,6078143136325656213323722186⟩⟩,⟨⟨30904826207679612967217050005,30904826207679612982368841793⟩,⟨5708438242027107803793058990,5708438242027107818881615655⟩⟩,⟨⟨30541485927845186386363408006,30541485927845186401348397487⟩,⟨5349273407438475598118498013,5349273407438475613035501420⟩⟩,⟨⟨30181210577349860646163756558,30181210577349860660992906127⟩,⟨5000454067057126113821047859,5000454067057126128577636174⟩⟩,⟨⟨29824127408047177839972863288,29824127408047177854635260330⟩,⟨4661784727244776965090112613,4661784727244776979675574963⟩⟩,⟨⟨29470357684752090747155127205,29470357684752090761665184843⟩,⟨4333069204890999396658762274,4333069204890999411087670944⟩⟩,⟨⟨29120016760209665699414129525,29120016760209665713764461657⟩,⟨4014110858878423392901566233,4014110858878423407166723325⟩⟩,⟨⟨28773214157181183565415500527,28773214157181183579617057232⟩,⟨3704712814185191907405185973,3704712814185191921517694301⟩⟩] +lemma kernel3_0_r4_10_eq : ∀ k : Fin 16, kernel3_0Expr 4 10 k = kernel3_0_r4_10 k := by decide +kernel +noncomputable def kernel3_0_r4_11 : Fin 16 → CBox := ![⟨⟨28430053657216683544435528252,28430053657216683558476364861⟩,⟨3404678178484172034559516634,3404678178484172048507620436⟩⟩,⟨⟨28090633395684247465706281459,28090633395684247479602042938⟩,⟨3113810251121883792961793040,3113810251121883806761270345⟩⟩,⟨⟨27755045962628776377488689362,27755045962628776391232211196⟩,⟨2831912724382991791267820373,2831912724382991804911678706⟩⟩,⟨⟨27423378509036607261687730060,27423378509036607275289906401⟩,⟨2558789876968466366885424274,2558789876968466380384688531⟩⟩,⟨⟨27095712858086994523214677066,27095712858086994536664972685⟩,⟨2294246759637108650596739514,2294246759637108663941046527⟩⟩,⟨⟨26772125620977175555782537512,26772125620977175569095320204⟩,⟨2038089372981003114618020962,2038089372981003127821851127⟩⟩,⟨⟨26452688316914387905503326591,26452688316914387918671641745⟩,⟨1790124837325571083149166233,1790124837325571096205721561⟩⟩,⟨⟨26137467496875742068748921936,26137467496875742081783578596⟩,⟨1550161554764213839659989741,1550161554764213852580189276⟩⟩,⟨⟨25826524870745212849262736538,25826524870745212862152368433⟩,⟨1318009363356023563082793431,1318009363356023575855431838⟩⟩,⟨⟨25519917437446127215322529132,25519917437446127228082449761⟩,⟨1093479683532678284726832183,1093479683532678297367311659⟩⟩,⟨⟨25217697617697331493695182490,25217697617697331506318642966⟩,⟨876385656777401915054643351,876385656777401927556357080⟩⟩,⟨⟨24919913389031649561954963561,24919913389031649574452653642⟩,⟨666542276654745173620901525,666542276654745185994629913⟩⟩,⟨⟨24626608422726231090919938486,24626608422726231103281679325⟩,⟨463766512284915358006048040,463766512284915370241757695⟩⟩,⟨⟨24337822222305870332044737074,24337822222305870344284713104⟩,⟨267877424370443903918679680,267877424370443916030626447⟩⟩,⟨⟨24053590263292288036063789768,24053590263292288048175445079⟩,⟨78696273896126256269894660,78696273896126268251651125⟩⟩,⟨⟨23773944133884649759601413629,23773944133884649771595297438⟩,⟨(-103953376364601816525602231),(-103953376364601804663414071)⟩⟩] +lemma kernel3_0_r4_11_eq : ∀ k : Fin 16, kernel3_0Expr 4 11 k = kernel3_0_r4_11 k := by decide +kernel +noncomputable def kernel3_0_r4_12 : Fin 16 → CBox := ![⟨⟨23498911676269182550799484331,23498911676269182562664234911⟩,⟨(-280245567392370512222178249),(-280245567392370500490782185)⟩⟩,⟨⟨23228517128268590031794636254,23228517128268590043545669173⟩,⟨(-450351856358773280581580912),(-450351856358773268965512567)⟩⟩,⟨⟨22962781265054996367939165406,22962781265054996379570113862⟩,⟨(-614441235793049122346881927),(-614441235793049110852392165)⟩⟩,⟨⟨22701721540663317758758425207,22701721540663317770279670916⟩,⟨(-772680059305512898421931282),(-772680059305512887038581925)⟩⟩,⟨⟨22445352229055213348732504905,22445352229055213360134194635⟩,⟨(-925231973686933233014672203),(-925231973686933221752193789)⟩⟩,⟨⟨22193684564497055611513921608,22193684564497055622809957132⟩,⟨(-1072257857196143443333497099),(-1072257857196143432177951455)⟩⟩,⟨⟨21946726881028635517909820642,21946726881028635529094009706⟩,⟨(-1213915763842085318254254197),(-1213915763842085307211729117)⟩⟩,⟨⟨21704484750812534874710819306,21704484750812534885793365059⟩,⟨(-1350360873461205631527950549),(-1350360873461205620588201205)⟩⟩,⟨⟨21466961121167214416033699948,21466961121167214427003833936⟩,⟨(-1481745447386626215776984426),(-1481745447386626204950662374)⟩⟩,⟨⟨21234156450099841459429442413,21234156450099841470301973909⟩,⟨(-1608218789501763744350155570),(-1608218789501763733622434284)⟩⟩,⟨⟨21006068840167677779806598458,21006068840167677790575504904⟩,⟨(-1729927212468057082737397011),(-1729927212468057072114205025)⟩⟩,⟨⟨20782694170509432045332215882,20782694170509432056007504360⟩,⟨(-1847014008914138922843515911),(-1847014008914138912314817703)⟩⟩,⟨⟨20564026226900319612571412849,20564026226900319623143512569⟩,⟨(-1959619427372134077179891601),(-1959619427372134066755153950)⟩⟩,⟨⟨20350056829696636257815678432,20350056829696636268298154904⟩,⟨(-2067880652745748099931018946),(-2067880652745748089596668657)⟩⟩,⟨⟨20140775959547414724629558946,20140775959547414735016546764⟩,⟨(-2171931791094394959594789230),(-2171931791094394949356607072)⟩⟩,⟨⟨19936171880762169579997912437,19936171880762169590299217766⟩,⟨(-2271903858517768974539974998),(-2271903858517768964388138129)⟩⟩] +lemma kernel3_0_r4_12_eq : ∀ k : Fin 16, kernel3_0Expr 4 12 k = kernel3_0_r4_12 k := by decide +kernel +noncomputable def kernel3_0_r4_13 : Fin 16 → CBox := ![⟨⟨19736231262234825124322079579,19736231262234825134526896926⟩,⟨(-2367924773925961491775205592),(-2367924773925961481720417459)⟩⟩,⟨⟨19540939295834643806709664809,19540939295834643816832752011⟩,⟨(-2460119355481424060447257217),(-2460119355481424050474770240)⟩⟩,⟨⟨19350279812185311988333692796,19350279812185311998369339169⟩,⟨(-2548609320500754366461035802),(-2548609320500754356576484443)⟩⟩,⟨⟨19164235393763281543258734703,19164235393763281553216533565⟩,⟨(-2633513288606396371231694375),(-2633513288606396361425478959)⟩⟩,⟨⟨18982787485255997519107840349,18982787485255997528978460562⟩,⟨(-2714946787920869666078895424),(-2714946787920869656360257855)⟩⟩,⟨⟨18805916501129753897367552220,18805916501129753907164201703⟩,⟨(-2793022264099043192033578490),(-2793022264099043182389325914)⟩⟩,⟨⟨18633601930365603471635118865,18633601930365603481352229397⟩,⟨(-2867849091997213923638169466),(-2867849091997213914073801332)⟩⟩,⟨⟨18465822438329998053872622612,18465822438329998063519577294⟩,⟨(-2939533589781311293739007306),(-2939533589781311284245143145)⟩⟩,⟨⟨18302555965754647555107993636,18302555965754647564674445756⟩,⟨(-3008179035280393236987350617),(-3008179035280393227574248608)⟩⟩,⟨⟨18143779824807458669862497198,18143779824807458679362604281⟩,⟨(-3073885684395700814370563638),(-3073885684395700805024095960)⟩⟩,⟨⟨17989470792243345294594493815,17989470792243345304022828553⟩,⟨(-3136750791379867455845722855),(-3136750791379867446571254643)⟩⟩,⟨⟨17839605199630194359854980659,17839605199630194369220710367⟩,⟨(-3196868630805408949915580860),(-3196868630805408940703955134)⟩⟩,⟨⟨17694159020651324840581277740,17694159020651324849875263476⟩,⟨(-3254330521046325522200263686),(-3254330521046325513060541403)⟩⟩,⟨⟨17553107955491398061261343280,17553107955491398070496448497⟩,⟨(-3309224849101502919609191278),(-3309224849101502910528541457)⟩⟩,⟨⟨17416427512317929009847479996,17416427512317929019018409243⟩,⟨(-3361637096593581767224998181),(-3361637096593581758208659856)⟩⟩,⟨⟨17284093085875317329949881241,17284093085875317339065591826⟩,⟨(-3411649866782051221661330667),(-3411649866782051212700363407)⟩⟩] +lemma kernel3_0_r4_13_eq : ∀ k : Fin 16, kernel3_0Expr 4 13 k = kernel3_0_r4_13 k := by decide +kernel +noncomputable def kernel3_0_r4_14 : Fin 16 → CBox := ![⟨⟨17156080033212670128173498667,17156080033212670137223424581⟩,⟨(-3459342912434492976588815752),(-3459342912434492967693704282)⟩⟩,⟨⟨17032363746570634801339978184,17032363746570634810338336966⟩,⟨(-3504793164405135116797956116),(-3504793164405135107954530022)⟩⟩,⟨⟨16912919723456007689957884681,16912919723456007698899515327⟩,⟨(-3548074760775153573246827817),(-3548074760775153564460196737)⟩⟩,⟨⟨16797723633936043179748345492,16797723633936043188641991119⟩,⟨(-3589259076414464694566508828),(-3589259076414464685827951939)⟩⟩,⟨⟨16686751385187168245070028929,16686751385187168253906701475⟩,⟨(-3628414752830069692854186338),(-3628414752830069684172621948)⟩⟩,⟨⟨16579979183335220272149041478,16579979183335220280941290958⟩,⟨(-3665607728171325696485213645),(-3665607728171325687848136963)⟩⟩,⟨⟨16477383592626382728327236957,16477383592626382737070028794⟩,⟨(-3700901267267815368936100308),(-3700901267267815360348498882)⟩⟩,⟨⟨16378941591969705683909569462,16378941591969705692611442445⟩,⟨(-3734355991580755304230692088),(-3734355991580755295684053853)⟩⟩,⟨⟨16284630628893478521817960079,16284630628893478530468788482⟩,⟨(-3766029908954111691536674534),(-3766029908954111683041052088)⟩⟩,⟨⟨16194428670958782839976397297,16194428670958782848589794760⟩,⟨(-3795978443056770270418341610),(-3795978443056770261960177886)⟩⟩,⟨⟨16108314254674307233828525289,16108314254674307242399587776⟩,⟨(-3824254462412227771009817114),(-3824254462412227762593972875)⟩⟩,⟨⟨16026266531956965170024927905,16026266531956965178561988432⟩,⟨(-3850908308917326400514812916),(-3850908308917326392132985331)⟩⟩,⟨⟨15948265314183035464184590936,15948265314183035472678769049⟩,⟨(-3875987825756535165353097730),(-3875987825756535157014103194)⟩⟩,⟨⟨15874291113874454948840543361,15874291113874454957304127022⟩,⟨(-3899538384623186657845299831),(-3899538384623186649536904390)⟩⟩,⟨⟨15804325184064547773040556868,15804325184064547781468769193⟩,⟨(-3921602912163901179972317038),(-3921602912163901171699257480)⟩⟩,⟨⟨15738349555386888398181731959,15738349555386888406582708590⟩,⟨(-3942221915567168522832044303),(-3942221915567168514586217778)⟩⟩] +lemma kernel3_0_r4_14_eq : ∀ k : Fin 16, kernel3_0Expr 4 14 k = kernel3_0_r4_14 k := by decide +kernel +noncomputable def kernel3_0_r4_15 : Fin 16 → CBox := ![⟨⟨15676347070930178676654397542,15676347070930178685017727095⟩,⟨(-3961433507221709127056243819),(-3961433507221709118847990822)⟩⟩,⟨⟨15618301418900986263810525602,15618301418900986272149960952⟩,⟨(-3979273428374799395840946576),(-3979273428374799387656580176)⟩⟩,⟨⟨15564197163134954754318959850,15564197163134954762629860517⟩,⟨(-3995775071725220170029061072),(-3995775071725220161873184372)⟩⟩,⟨⟨15514019771495667952437396733,15514019771495667960727696685⟩,⟨(-4010969502889873187308469552),(-4010969502889873179173183120)⟩⟩,⟨⟨15467755642198744038256092001,15467755642198744046516985433⟩,⟨(-4024885480687408899988236836),(-4024885480687408891882286049)⟩⟩,⟨⟨15425392128096962372309380893,15425392128096962380552946049⟩,⟨(-4037549476186422222856638601),(-4037549476186422214768004549)⟩⟩,⟨⟨15386917558960298416468577974,15386917558960298424690309674⟩,⟨(-4048985690469903217814670031),(-4048985690469903209747822739)⟩⟩,⟨⟨15352321261782672690972151002,15352321261782672699179789417⟩,⟨(-4059216071071680635148779923),(-4059216071071680627096014757)⟩⟩,⟨⟨15321593579145019613488180266,15321593579145019621671628102⟩,⟨(-4068260327044571457341196144),(-4068260327044571449312543511)⟩⟩,⟨⟨15294725885661963077255303434,15294725885661963085427873888⟩,⟨(-4076135942623853517571743062),(-4076135942623853509553958190)⟩⟩,⟨⟨15271710602536959154485081064,15271710602536959162642416686⟩,⟨(-4082858189453515780223153136),(-4082858189453515772220560166)⟩⟩,⟨⟨15252541210248243625604593533,15252541210248243633754234195⟩,⟨(-4088440137346517322358191584),(-4088440137346517314363286393)⟩⟩,⟨⟨15237212259385314249963942710,15237212259385314258097126942⟩,⟨(-4092892663554007198887662791),(-4092892663554007190909148308)⟩⟩,⟨⟨15225719379652995779799444412,15225719379652995787928095520⟩,⟨(-4096224460522129331794895823),(-4096224460522129323820910321)⟩⟩,⟨⟨15218059287057390520104618684,15218059287057390528224531946⟩,⟨(-4098442042118665772714010149),(-4098442042118665764748726469)⟩⟩,⟨⟨15214229789285219480150464428,15214229789285219488268981032⟩,⟨(-4099549748315364859805487017),(-4099549748315364851841599227)⟩⟩] +lemma kernel3_0_r4_15_eq : ∀ k : Fin 16, kernel3_0Expr 4 15 k = kernel3_0_r4_15 k := by decide +kernel +noncomputable def kernel3_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel3_0_r4_0,kernel3_0_r4_1,kernel3_0_r4_2,kernel3_0_r4_3,kernel3_0_r4_4,kernel3_0_r4_5,kernel3_0_r4_6,kernel3_0_r4_7,kernel3_0_r4_8,kernel3_0_r4_9,kernel3_0_r4_10,kernel3_0_r4_11,kernel3_0_r4_12,kernel3_0_r4_13,kernel3_0_r4_14,kernel3_0_r4_15] +lemma kernel3_0_r4_eq (i k : Fin 16) : kernel3_0Expr 4 i k = kernel3_0_r4 i k := by + fin_cases i + · exact kernel3_0_r4_0_eq k + · exact kernel3_0_r4_1_eq k + · exact kernel3_0_r4_2_eq k + · exact kernel3_0_r4_3_eq k + · exact kernel3_0_r4_4_eq k + · exact kernel3_0_r4_5_eq k + · exact kernel3_0_r4_6_eq k + · exact kernel3_0_r4_7_eq k + · exact kernel3_0_r4_8_eq k + · exact kernel3_0_r4_9_eq k + · exact kernel3_0_r4_10_eq k + · exact kernel3_0_r4_11_eq k + · exact kernel3_0_r4_12_eq k + · exact kernel3_0_r4_13_eq k + · exact kernel3_0_r4_14_eq k + · exact kernel3_0_r4_15_eq k +noncomputable def kernel3_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-595915062878267073963003187518),(-595915062878267073861518485282)⟩,⟨132021722511247403342665208943,132021722511247403434410513659⟩⟩,⟨⟨(-595852068470548358705602057411),(-595852068470548358604115684620)⟩,⟨132072011877176853815819778458,132072011877176853907566269801⟩⟩,⟨⟨(-595726083781547864128217162558),(-595726083781547864026727593040)⟩,⟨132172552526519761113265319017,132172552526519761205014041712⟩⟩,⟨⟨(-595537117086774590820201620320),(-595537117086774590718707331471)⟩,⟨132323268321249084675003994581,132323268321249084766755991474⟩⟩,⟨⟨(-595285180856029432787808656111),(-595285180856029432686308134091)⟩,⟨132524045121834603847807532291,132524045121834603939563840014⟩⟩,⟨⟨(-594970291821108918650668783961),(-594970291821108918549160522986)⟩,⟨132774730868249576369377727484,132774730868249576461139378002⟩⟩,⟨⟨(-594592471065841858154461243254),(-594592471065841858052943753357)⟩,⟨133075135687969808425659497201,133075135687969808517427510919⟩⟩,⟨⟨(-594151744138257876675083884757),(-594151744138257876573555685035)⟩,⟨133425032030956280311283658802,133425032030956280403059052085⟩⟩,⟨⟨(-593648141184637089412579422924),(-593648141184637089311039060385)⟩,⟨133824154831609698196053883964,133824154831609698287837651269⟩⟩,⟨⟨(-593081697105140785325485341913),(-593081697105140785223931367947)⟩,⟨134272201697682198965241268961,134272201697682199057034406929⟩⟩,⟨⟨(-592452451730674028818734853077),(-592452451730674028717165864767)⟩,⟨134768833126127850564820790012,134768833126127850656624257400⟩⟩,⟨⟨(-591760450020582615262339199167),(-591760450020582615160753784712)⟩,⟨135313672745869495383550877034,135313672745869495475365649469⟩⟩,⟨⟨(-591005742280738905309005884563),(-591005742280738905207402712215)⟩,⟨135906307587454811477945440195,135906307587454811569772423000⟩⟩,⟨⟨(-590188384401523783672256279139),(-590188384401523783570633974765)⟩,⟨136546288379569150588282138474,136546288379569150680122288484⟩⟩,⟨⟨(-589308438115165411759099195536),(-589308438115165411657456506607)⟩,⟨137233129872366690014570449354,137233129872366690106424613566⟩⟩,⟨⟨(-588365971271849641823751184464),(-588365971271849641722086783949)⟩,⟨137966311187574647300947849271,137966311187574647392816959419⟩⟩] +lemma kernel3_0_r5_0_eq : ∀ k : Fin 16, kernel3_0Expr 5 0 k = kernel3_0_r5_0 k := by decide +kernel +noncomputable def kernel3_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-587361058133972004881862469997),(-587361058133972004780175222032)⟩,⟨138745276195317695012936793263,138745276195317695104821603965⟩⟩,⟨⟨(-586293779687857147505587502807),(-586293779687857147403876109428)⟩,⟨139569433917601223542307468377,139569433917601223634208907008⟩⟩,⟨⟨(-585164223972228546040747779698),(-585164223972228545939011211963)⟩,⟨140438158958382682093812421021,140438158958382682185731162314⟩⟩,⟨⟨(-583972486422669343173520866094),(-583972486422669343071757882449)⟩,⟨141350791960149834678530956901,141350791960149834770467899652⟩⟩,⟨⟨(-582718670231274303702148480775),(-582718670231274303600358227666)⟩,⟨142306640086913355791355622851,142306640086913355883311296987⟩⟩,⟨⟨(-581402886720653246514752364917),(-581402886720653246412933607183)⟩,⟨143304977533508720281063993346,143304977533508720373039321212⟩⟩,⟨⟨(-580025255731407950848864440925),(-580025255731407950747016458067)⟩,⟨144345046061088778797044561923,144345046061088778889039973098⟩⟩,⟨⟨(-578585906022167529584280274370),(-578585906022167529482401898872)⟩,⟨145426055558673723651596974383,145426055558673723743613356756⟩⟩,⟨⟨(-577084975681231683145783054311),(-577084975681231683043873823177)⟩,⟨146547184630609314160670852212,146547184630609314252708414532⟩⟩,⟨⟨(-575522612548837166890565514629),(-575522612548837166788624218038)⟩,⟨147707581209767224540950958578,147707581209767224633010665351⟩⟩,⟨⟨(-573898974649030294618043948207),(-573898974649030294516070265045)⟩,⟨148906363196303185267313474987,148906363196303185359395430717⟩⟩,⟨⟨(-572214230630097432603361330815),(-572214230630097432501354143514)⟩,⟨150142619121769199603538278372,150142619121769199695643393438⟩⟩,⟨⟨(-570468560212476283266973600564),(-570468560212476283164932932365)⟩,⟨151415408838355525275588054677,151415408838355525367716131447⟩⟩,⟨⟨(-568662154643043385462687529551),(-568662154643043385360612166007)⟩,⟨152723764233016316846603793521,152723764233016316938755877245⟩⟩,⟨⟨(-566795217154647738713125445071),(-566795217154647738611015565416)⟩,⟨154066689966209832697175646143,154066689966209832789351425168⟩⟩,⟨⟨(-564867963429736859799458828021),(-564867963429736859697313326893)⟩,⟨155443164234959932669089971726,155443164234959932761290424525⟩⟩] +lemma kernel3_0_r5_1_eq : ∀ k : Fin 16, kernel3_0Expr 5 1 k = kernel3_0_r5_1 k := by decide +kernel +noncomputable def kernel3_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-562880622066899968931498005980),(-562880622066899968829317551380)⟩,⟨156852139559920245170103458177,156852139559920245262327832127⟩⟩,⟨⟨(-560833435049133444858603656981),(-560833435049133444756386932271)⟩,⟨158292543596095888422348615765,158292543596095888514598140816⟩⟩,⟨⟨(-558726658212616247665731843761),(-558726658212616247563479634616)⟩,⟨159763279966850017966827081393,159763279966850018059100932241⟩⟩,⟨⟨(-556560561714767746714734462540),(-556560561714767746612445626826)⟩,⟨161263229120793775781784954220,161263229120793775874084232628⟩⟩,⟨⟨(-554335430500347369246831130261),(-554335430500347369144507052413)⟩,⟨162791249211128475592075678418,162791249211128475684399012526⟩⟩,⟨⟨(-552051564764344760260960331480),(-552051564764344760158599575864)⟩,⟨164346176996978120182872492465,164346176996978120275221319543⟩⟩,⟨⟨(-549709280410400771583035825132),(-549709280410400771480639895558)⟩,⟨165926828766218661690121173107,165926828766218661782494049606⟩⟩,⟨⟨(-547308909503493629911452519932),(-547308909503493629809020177688)⟩,⟨167532001279277842648124460547,167532001279277842740522675800⟩⟩,⟨⟨(-544850800715621119389992082287),(-544850800715621119287525657882)⟩,⟨169160472733346057516509695337,169160472733346057608931036372⟩⟩,⟨⟨(-542335319763208599946186620406),(-542335319763208599843684375996)⟩,⟨170811003746404520644394064989,170811003746404520736840361722⟩⟩,⟨⟨(-539762849834974210704556070516),(-539762849834974210602020345033)⟩,⟨172482338360442191890017920126,172482338360442191982486999308⟩⟩,⟨⟨(-537133792008986716877130053353),(-537133792008986716774559437825)⟩,⟨174173205063197475575326776939,174173205063197475667820191741⟩⟩,⟨⟨(-534448565657658183192043845332),(-534448565657658183089441632169)⟩,⟨175882317827724757590500230332,175882317827724757683014914300⟩⟩,⟨⟨(-531707608839423027329064312577),(-531707608839423027226428486180)⟩,⟨177608377169049469873622501873,177608377169049469966160655953⟩⟩,⟨⟨(-528911378675867048546449579187),(-528911378675867048443783433291)⟩,⟨179350071217138666711464660594,179350071217138666804023265989⟩⟩,⟨⟨(-526060351713084760375103350740),(-526060351713084760272405223282)⟩,⟨181106076805377163594404537458,181106076805377163686985494634⟩⟩] +lemma kernel3_0_r5_2_eq : ∀ k : Fin 16, kernel3_0Expr 5 2 k = kernel3_0_r5_2 k := by decide +kernel +noncomputable def kernel3_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-523155024266060797441556886074),(-523155024266060797338831382343)⟩,⟨182875060573702231451382145379,182875060573702231543981189268⟩⟩,⟨⟨(-520195912744891325274688495498),(-520195912744891325171933003061)⟩,⟨184655680085512765952203672979,184655680085512766044823691383⟩⟩,⟨⟨(-517183553961684262812347675510),(-517183553961684262709566562253)⟩,⟨186446584957431876100082899807,186446584957431876192719911079⟩⟩,⟨⟨(-514118505417002728821062982793),(-514118505417002728718254240621)⟩,⟨188246418000965075090667453550,188246418000965075183323797020⟩⟩,⟨⟨(-511001345564744438018948449531),(-511001345564744437916117863100)⟩,⟨190053816375059829243021136522,190053816375059829335691480083⟩⟩,⟨⟨(-507832674054380786452384349617),(-507832674054380786349528865300)⟩,⟨191867412748536250537956666277,191867412748536250630644429634⟩⟩,⟨⟨(-504613111949513058176982454565),(-504613111949513058074107633304)⟩,⟨193685836471323330356437131892,193685836471323330449137251885⟩⟩,⟨⟨(-501343301921739529352252087921),(-501343301921739529249355474543)⟩,⟨195507714753400434035883400255,195507714753400434128598752730⟩⟩,⟨⟨(-498023908418866207384160997019),(-498023908418866207281250059983)⟩,⟨197331673850309937305734688098,197331673850309937398458373692⟩⟩,⟨⟨(-494655617806535480580507732619),(-494655617806535480477578485992)⟩,⟨199156340254074017360842946018,199156340254074017453579398182⟩⟩,⟨⟨(-491239138482391019555085015113),(-491239138482391019452135581913)⟩,⟨200980341888316845063918093889,200980341888316845156682551995⟩⟩,⟨⟨(-487775200961943809643380787577),(-487775200961943809540341196124)⟩,⟨202802309306362892805700619103,202802309306362892898661073511⟩⟩,⟨⟨(-484264557935353140775800882202),(-484264557935353140672679513764)⟩,⟨204620876891052907182690194541,204620876891052907275839443403⟩⟩,⟨⟨(-480707984294387667014854832355),(-480707984294387666911646594255)⟩,⟨206434684054991428696219691020,206434684054991428789563801125⟩⟩,⟨⟨(-477106277128885194191813214611),(-477106277128885194088525981552)⟩,⟨208242376439913702997068096418,208242376439913703090600291586⟩⟩,⟨⟨(-473460255692085575129946676618),(-473460255692085575026576377937)⟩,⟨210042607113835549181394560101,210042607113835549275119825132⟩⟩] +lemma kernel3_0_r5_3_eq : ∀ k : Fin 16, kernel3_0Expr 5 3 k = kernel3_0_r5_3 k := by decide +kernel +noncomputable def kernel3_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-469770761334268894632752015030),(-469770761334268894529309334238)⟩,⟨211834037764627357699182312629,211834037764627357793091020131⟩⟩,⟨⟨(-466038657404190910076724556563),(-466038657404190909973203129368)⟩,⟨213615339888633008466058452224,213615339888633008560157778407⟩⟩,⟨⟨(-462264829117869369985664328750),(-462264829117869369882073705592)⟩,⟨215385195972936250648381964537,215385195972936250742663323356⟩⟩,⟨⟨(-458450183394338246966021881428),(-458450183394338246862357339899)⟩,⟨217142300669861087634268106034,217142300669861087728736976213⟩⟩,⟨⟨(-454595648658051970250751571357),(-454595648658051970147025445576)⟩,⟨218885361962279078138954309095,218885361962279078233599273695⟩⟩,⟨⟨(-450702174607688297213778248912),(-450702174607688297109983537339)⟩,⟨220613102318285306834592226595,220613102318285306929420940062⟩⟩,⟨⟨(-446770731951166386135046269976),(-446770731951166386031194300469)⟩,⟨222324259833796199819618940614,222324259833796199914620899597⟩⟩,⟨⟨(-442802312106765781184862555289),(-442802312106765781080947829111)⟩,⟨224017589361616460472232318733,224017589361616460567413614842⟩⟩,⟨⟨(-438797926870302245695537287230),(-438797926870302245591574813623)⟩,⟨225691863625519272426482118443,225691863625519272521828525720⟩⟩,⟨⟨(-434758608048387525912938005668),(-434758608048387525808919090898)⟩,⟨227345874317883644566247174458,227345874317883644661767865242⟩⟩,⟨⟨(-430685407057872033487748884624),(-430685407057872033383686724892)⟩,⟨228978433179435436908881517048,228978433179435437004563974964⟩⟩,⟨⟨(-426579394491641934565489832966),(-426579394491641934461378023710)⟩,⟨230588373059644277290108056688,230588373059644277385959111681⟩⟩,⟨⟨(-422441659651015055119967395990),(-422441659651015055015822748226)⟩,⟨232174548956337320050906121021,232174548956337320146909596199⟩⟩,⟨⟨(-418273310045053180300434538505),(-418273310045053180196247494579)⟩,⟨233735839033102664161146248567,233735839033102664257312013810⟩⟩,⟨⟨(-414075470857181560136057683357),(-414075470857181560031843387480)⟩,⟨235271145613070285199439177979,235271145613070285295752620608⟩⟩,⟨⟨(-409849284379579551519852381997),(-409849284379579551415603391603)⟩,⟨236779396147676579876307792711,236779396147676579972776610819⟩⟩] +lemma kernel3_0_r5_4_eq : ∀ k : Fin 16, kernel3_0Expr 5 4 k = kernel3_0_r5_4 k := by decide +kernel +noncomputable def kernel3_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-405595909415879140498193482349),(-405595909415879140393929840375)⟩,⟨238259544159040100252553106777,238259544159040100349157753122⟩⟩,⟨⟨(-401316520652780410555853214400),(-401316520652780410451563010751)⟩,⟨239710570154600784437282907634,239710570154600784534035422809⟩⟩,⟨⟨(-397012308001264660924083951352),(-397012308001264660819784341442)⟩,⟨241131482512702978097371166561,241131482512702978194254775995⟩⟩,⟨⟨(-392684475908156641744886425459),(-392684475908156641640568799775)⟩,⟨242521318337833782837228132010,242521318337833782934251530408⟩⟩,⟨⟨(-388334242638857067282723548538),(-388334242638857067178409624730)⟩,⟨243879144284262748990353719547,243879144284262749087495528061⟩⟩,⟨⟨(-383962839532135001302886845553),(-383962839532135001198563843132)⟩,⟨245204057346866626306046806513,245204057346866626403319771824⟩⟩,⟨⟨(-379571510227936687829090677185),(-379571510227936687724777816678)⟩,⟨246495185617963760120529989341,246495185617963760217915120117⟩⟩,⟨⟨(-375161509869232734600120040612),(-375161509869232734495807411410)⟩,⟨247751689009026725477645776447,247751689009026725575152899566⟩⟩,⟨⟨(-370734104278989056439092586758),(-370734104278989056334805424493)⟩,⟨248972759936188868776880327761,248972759936188868874484405776⟩⟩,⟨⟨(-366290569113408464821594838112),(-366290569113408464717317563202)⟩,⟨250157623968510506192256429743,250157623968510506289972829784⟩⟩,⟨⟨(-361832188992649064878657854427),(-361832188992649064774411785621)⟩,⟨251305540438023529542114227104,251305540438023529639921708400⟩⟩,⟨⟨(-357360256610282512605928431603),(-357360256610282512501702231247)⟩,⟨252415803010629001697510094365,252415803010629001795419745386⟩⟩,⟨⟨(-352876071822809518578497894195),(-352876071822809518474318497819)⟩,⟨253487740216980882326203425529,253487740216980882424188352298⟩⟩,⟨⟨(-348380940720601590799004961795),(-348380940720601590694855709814)⟩,⟨254520715942550197417292547846,254520715942550197515369040759⟩⟩,⟨⟨(-343876174681686725319112949246),(-343876174681686725215017280925)⟩,⟨255514129876127628806791304022,255514129876127628904935852585⟩⟩,⟨⟨(-339363089409842422617672832024),(-339363089409842422513617856965)⟩,⟨256467417916088518839688208628,256467417916088518937913294021⟩⟩] +lemma kernel3_0_r5_5_eq : ∀ k : Fin 16, kernel3_0Expr 5 5 k = kernel3_0_r5_5 k := by decide +kernel +noncomputable def kernel3_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-334843003958501881453681512437),(-334843003958501881349698342945)⟩,⟨257380052533812516537394428004,257380052533812516635668845466⟩⟩,⟨⟨(-330317239742018359168684378456),(-330317239742018359064752687554)⟩,⟨258251543093720381902895734399,258251543093720382001239271203⟩⟩,⟨⟨(-325787119535868356005101077422),(-325787119535868355901246423816)⟩,⟨259081436129462651970405831367,259081436129462652068792711827⟩⟩,⟨⟨(-321253966467406358041882347329),(-321253966467406357938090173659)⟩,⟨259869315575868785002241639035,259869315575868785100685858711⟩⟩,⟨⟨(-316719102998812245791154185850),(-316719102998812245687456813913)⟩,⟨260614802956340858918361862441,260614802956340859016830853273⟩⟩,⟨⟨(-312183849903897040723536595229),(-312183849903897040619912879662)⟩,⟨261317557525452720179989484178,261317557525452720278503714160⟩⟩,⟨⟨(-307649525240453328277398790352),(-307649525240453328173876399270)⟩,⟨261977276366593466615144699251,261977276366593466713676142587⟩⟩,⟨⟨(-303117443319853382931038943865),(-303117443319853382827601539998)⟩,⟨262593694444573102483594868806,262593694444573102582159157655⟩⟩,⟨⟨(-298588913675610660160220186364),(-298588913675610660056904350821)⟩,⟨263166584613187921264789762576,263166584613187921363349943232⟩⟩,⟨⟨(-294065240032628855262782344539),(-294065240032628855159562936215)⟩,⟨263695757577823441162368581501,263695757577823441260948968064⟩⟩,⟨⟨(-289547719278867116347576236687),(-289547719278867116244482997661)⟩,⟨264181061813253325964230443576,264181061813253326062800802007⟩⟩,⟨⟨(-285037640441150207350674150812),(-285037640441150207247688869362)⟩,⟨264622383436873452105216702747,264622383436873452203794407436⟩⟩,⟨⟨(-280536283666848428938673961754),(-280536283666848428835834371066)⟩,⟨265019646037690911395329531821,265019646037690911493876336344⟩⟩,⟨⟨(-276044919213143916063435902743),(-276044919213143915960715841349)⟩,⟨265372810461468045959492625129,265372810461468046058033748087⟩⟩,⟨⟨(-271564806445587549644086624515),(-271564806445587549541517867031)⟩,⟨265681874552501374599757293970,265681874552501374698260342363⟩⟩,⟨⟨(-267097192847634168792939608803),(-267097192847634168690501976771)⟩,⟨265946872852594265034111155170,265946872852594265132595350494⟩⟩] +lemma kernel3_0_r5_6_eq : ∀ k : Fin 16, kernel3_0Expr 5 6 k = kernel3_0_r5_6 k := by decide +kernel +noncomputable def kernel3_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-262643313042823085133199341134),(-262643313042823085030935542802)⟩,⟨266167876257860212030471455351,266167876257860212128893466640⟩⟩,⟨⟨(-258204387831246131565069886797),(-258204387831246131462948779116)⟩,⟨266344991634070376670452250663,266344991634070376768842152289⟩⟩,⟨⟨(-253781623241916687236495160350),(-253781623241916687134550481537)⟩,⟨266478361391334408635064242103,266478361391334408733387560046⟩⟩,⟨⟨(-249376209602620384676780728981),(-249376209602620384574990265521)⟩,⟨266568163018977296592615034035,266568163018977296690892919240⟩⟩,⟨⟨(-244989320628791613348787743445),(-244989320628791613247194512883)⟩,⟨266614608581546860738790392723,266614608581546860836979078572⟩⟩,⟨⟨(-240622112532919588400018866602),(-240622112532919588298591275754)⟩,⟨266617944176956310523592682523,266617944176956310621722609438⟩⟩,⟨⟨(-236275723155943768782800090377),(-236275723155943768681573771891)⟩,⟨266578449357833839652543587291,266578449357833839750578279572⟩⟩,⟨⟨(-231951271122050911957715014635),(-231951271122050911856665652439)⟩,⟨266496436517216326227976503905,266496436517216326325939124472⟩⟩,⟨⟨(-227649855018235181588506341946),(-227649855018235181487681811457)⟩,⟨266372250239786662456809456739,266372250239786662554651287740⟩⟩,⟨⟨(-223372552599928629720977230253),(-223372552599928629620340799370)⟩,⟨266206266619913877882199793217,266206266619913877979956322338⟩⟩,⟨⟨(-219120420023952216348698033904),(-219120420023952216248287133167)⟩,⟨265998892547811873653473385322,265998892547811873751106242694⟩⟩,⟨⟨(-214894491109977477572950289812),(-214894491109977477472738462096)⟩,⟨265750564965186093519825500617,265750564965186093617359915555⟩⟩,⟨⟨(-210695776631626188819521995833),(-210695776631626188719557286456)⟩,⟨265461750091787670800916666053,265461750091787670898303647678⟩⟩,⟨⟨(-206525263638270080672749001335),(-206525263638270080572994099590)⟩,⟨265132942624341371111045317948,265132942624341371208320878920⟩⟩,⟨⟨(-202383914808525048825338190826),(-202383914808525048725832232713)⟩,⟨264764664909356871003860702526,264764664909356871100984682958⟩⟩,⟨⟨(-198272667836364560794841013452),(-198272667836364560695555363811)⟩,⟨264357466091372457711827177221,264357466091372457808826926177⟩⟩] +lemma kernel3_0_r5_7_eq : ∀ k : Fin 16, kernel3_0Expr 5 7 k = kernel3_0_r5_7 k := by decide +kernel +noncomputable def kernel3_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-194192434850705311372731735948),(-194192434850705311273720246974)⟩,⟨263911921238216001842987605214,263911921238216001939808254451⟩⟩,⟨⟨(-190144101869244832980185426387),(-190144101869244832881404421352)⟩,⟨263428630444899953027359877849,263428630444899953124043747377⟩⟩,⟨⟨(-186128528287255947859804727634),(-186128528287255947761294925742)⟩,⟨262908217917795060898347015723,262908217917795060994852290021⟩⟩,⟨⟨(-182146546401966882071905029735),(-182146546401966881973635616861)⟩,⟨262351331040751466601968432369,262351331040751466698324597834⟩⟩,⟨⟨(-178198960973078775509284257176),(-178198960973078775411307928955)⟩,⟨261758639424855692977801402922,261758639424855693073954666458⟩⟩,⟨⟨(-174286548819894448831740391132),(-174286548819894448734013990698)⟩,⟨261130833943527848104262767898,261130833943527848200254911940⟩⟩,⟨⟨(-170410058455453859979421562244),(-170410058455453859881987285743)⟩,⟨260468625754675024353712867869,260468625754675024449500539944⟩⟩,⟨⟨(-166570209757992932889853444662),(-166570209757992932792678291099)⟩,⟨259772745311624414641664361487,259772745311624414737279209700⟩⟩,⟨⟨(-162767693679963601937518602153),(-162767693679963601840660596647)⟩,⟨259043941364563084239814819256,259043941364563084335197669352⟩⟩,⟨⟨(-159003171994774218862045699386),(-159003171994774218765455582301)⟩,⟨258282979954210649192708870032,258282979954210649287907587528⟩⟩,⟨⟨(-155277277081331143768009858695),(-155277277081331143671731168002)⟩,⟨257490643399446353528491782645,257490643399446353623461625607⟩⟩,⟨⟨(-151590611746384614319359656262),(-151590611746384614223357235233)⟩,⟨256667729280603253015199329344,256667729280603253109974092604⟩⟩,⟨⟨(-147943749084605079722572708558),(-147943749084605079626903447382)⟩,⟨255815049420129462310399799006,255815049420129462404921389519⟩⟩,⟨⟨(-144337232376240315943946951342),(-144337232376240315848561866757)⟩,⟨254933428862299776961698467265,254933428862299777056014485599⟩⟩,⟨⟨(-140771575022129017693939109061),(-140771575022129017598882963368)⟩,⟨254023704853640526318143302245,254023704853640526412207746704⟩⟩,⟨⟨(-137247260515773396541265835452),(-137247260515773396446501342731)⟩,⟨253086725825706344536843745939,253086725825706344630692546973⟩⟩] +lemma kernel3_0_r5_8_eq : ∀ k : Fin 16, kernel3_0Expr 5 8 k = kernel3_0_r5_8 k := by decide +kernel +noncomputable def kernel3_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-133764742452101801478043554397),(-133764742452101801383633967594)⟩,⟨252123350381819772637106182194,252123350381819772730674853100⟩⟩,⟨⟨(-130324444572482708926752879751),(-130324444572482708832641893395)⟩,⟨251134446289353344128954329175,251134446289353344222297807312⟩⟩,⟨⟨(-126926760845483785646484773825),(-126926760845483785552718227745)⟩,⟨250120889479099189778171232696,250120889479099189871242415174⟩⟩,⟨⟨(-123572055582804283250949008243),(-123572055582804283157487556276)⟩,⟨249083563053233363071081411558,249083563053233363163918310052⟩⟩,⟨⟨(-120260663589745940388519741851),(-120260663589745940295423950799)⟩,⟨248023356303341185635812452040,248023356303341185728353236535⟩⟩,⟨⟨(-116992890349527001151344475677),(-116992890349527001058559716187)⟩,⟨246941163739926098495574664691,246941163739926098587872636298⟩⟩,⟨⟨(-113769012240686048372352004858),(-113769012240686048279925079134)⟩,⟨245837884134777945618111530420,245837884134777945710118611399⟩⟩,⟨⟨(-110589276786767229435364810018),(-110589276786767229343254363403)⟩,⟨244714419577527482866667951307,244714419577527482958424196197⟩⟩,⟨⟨(-107453902937426239874309854861),(-107453902937426239782582198111)⟩,⟨243571674547662376527637339373,243571674547662376619075159654⟩⟩,⟨⟨(-104363081380047234407788849215),(-104363081380047234316382522451)⟩,⟨242410555003226214942450976566,242410555003226215033630551300⟩⟩,⟨⟨(-101316974880914752125127420525),(-101316974880914752034090043553)⟩,⟨241231967487366292960413126936,241231967487366293051285558723⟩⟩,⟨⟨(-98315718654941856064709683185),(-98315718654941855973997989858)⟩,⟨240036818253838334368943453410,240036818253838334459550754757⟩⟩,⟨⟨(-95359420762916068769924598226),(-95359420762916068679602303546)⟩,⟨238826012412517087628665214836,238826012412517087718942387819⟩⟩,⟨⟨(-92448162535188393494241878116),(-92448162535188393404249012195)⟩,⟨237600453095901062841068140881,237600453095901062931073935049⟩⟩,⟨⟨(-89581999020697791982282749003),(-89581999020697791892667637038)⟩,⟨236361040647537772030684990046,236361040647537772120369810075⟩⟩,⟨⟨(-86760959460193978172338361925),(-86760959460193978082894196914)⟩,⟨235108671833232890243227836336,235108671833232890332796543769⟩⟩] +lemma kernel3_0_r5_9_eq : ∀ k : Fin 16, kernel3_0Expr 5 9 k = kernel3_0_r5_9 k := by decide +kernel +noncomputable def kernel3_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-83985047782495304368741702535),(-83985047782495304279522327672)⟩,⟨233844239075842971171221263829,233844239075842971260618659175⟩⟩,⟨⟨(-81254243122595871842123574341),(-81254243122595871753061950039)⟩,⟨232568629714386926540899992706,232568629714386926630191985624⟩⟩,⟨⟨(-78568500360416788813283266451),(-78568500360416788724430172401)⟩,⟨231282725288146610115897620533,231282725288146610205032194237⟩⟩,⟨⟨(-75927750678980710992538362010),(-75927750678980710903848212571)⟩,⟨229987400846361729158163992421,229987400846361729247185616492⟩⟩,⟨⟨(-73331902140776407406730823316),(-73331902140776407318272354007)⟩,⟨228683524284059129602074320010,228683524284059129690913008906⟩⟩,⟨⟨(-70780840281071060155973771862),(-70780840281071060067682989580)⟩,⟨227371955704491453179669068397,227371955704491453268387757005⟩⟩,⟨⟨(-68274428716922283231760591626),(-68274428716922283143689312208)⟩,⟨226053546808595427866408511170,226053546808595427954954171466⟩⟩,⟨⟨(-65812509770639374507207581209),(-65812509770639374419308306554)⟩,⟨224729140311815804671236948421,224729140311815804759656034350⟩⟩,⟨⟨(-63394905106444028499357908249),(-63394905106444028411706395810)⟩,⟨223399569388577365578646065689,223399569388577365666861579793⟩⟩,⟨⟨(-61021416379084558157503876838),(-61021416379084558070028210473)⟩,⟨222065657144624664625583166880,222065657144624664713666059725⟩⟩,⟨⟨(-58691825893164515534922230987),(-58691825893164515447675119337)⟩,⟨220728216117387385102690476857,220728216117387385190586858781⟩⟩,⟨⟨(-56405897271956369251002792344),(-56405897271956369163934936603)⟩,⟨219388047804468551832162346413,219388047804468551919920549722⟩⟩,⟨⟨(-54163376134483488900846827991),(-54163376134483488814030559065)⟩,⟨218045942220293471813950783082,218045942220293471901497271001⟩⟩,⟨⟨(-51963990779668993660156279876),(-51963990779668993573522190868)⟩,⟨216702677480899324558617970301,216702677480899324646021264363⟩⟩,⟨⟨(-49807452876367928371828832668),(-49807452876367928285430423995)⟩,⟨215359019416788912043377298080,215359019416788912130582753088⟩⟩,⟨⟨(-47693458158119613619109306564),(-47693458158119613532895560639)⟩,⟨214015721213717325623739389632,214015721213717325710797138581⟩⟩] +lemma kernel3_0_r5_10_eq : ∀ k : Fin 16, kernel3_0Expr 5 10 k = kernel3_0_r5_10 k := by decide +kernel +noncomputable def kernel3_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-45621687121479749649708221601),(-45621687121479749563760212041)⟩,⟨212673523081227302671241440041,212673523081227302758069214159⟩⟩,⟨⟨(-43591805726816805879902306846),(-43591805726816805794140942137)⟩,⟨211333151948697929312277907248,211333151948697929398954023250⟩⟩,⟨⟨(-41603466100484262456334802892),(-41603466100484262370814227876)⟩,⟨209995321188622188289361586579,209995321188622188375830795199⟩⟩,⟨⟨(-39656307237309249055752313991),(-39656307237309248970419932703)⟩,⟨208660730366781734153812604848,208660730366781734240126702049⟩⟩,⟨⟨(-37749955702368907126046172450),(-37749955702368907040977432047)⟩,⟨207330065018942273835416054160,207330065018942273921498448326⟩⟩,⟨⟨(-35884026331058241445467476109),(-35884026331058241360587983577)⟩,⟨206003996453650101796338416483,206003996453650101882262803196⟩⟩,⟨⟨(-34058122926487180081078881760),(-34058122926487179996443340139)⟩,⟨204683181580669738780596269597,204683181580669738866306884662⟩⟩,⟨⟨(-32271838953279882635208062064),(-32271838953279882550762387886)⟩,⟨203368262764564295620005043098,203368262764564295705555255967⟩⟩,⟨⟨(-30524758226885878904642758173),(-30524758226885878820470128318)⟩,⟨202059867702884163494599719579,202059867702884163579905223014⟩⟩,⟨⟨(-28816455597550237925636268411),(-28816455597550237841653628075)⟩,⟨200758609328395945273686228304,200758609328395945358829495712⟩⟩,⟨⟨(-27146497628128515901793367997),(-27146497628128515818055841039)⟩,⟨199465085734752206074693531084,199465085734752206159618422839⟩⟩,⟨⟨(-25514443264971567218114332486),(-25514443264971567134566501358)⟩,⟨198179880124973643343426309938,198179880124973643428187615510⟩⟩,⟨⟨(-23919844501145284053916115016),(-23919844501145283970636109548)⟩,⟨196903560782088657626869419223,196903560782088657711387935101⟩⟩,⟨⟨(-22362247031290817869752812645),(-22362247031290817786661728825)⟩,⟨195636681061251036748880808727,195636681061251036833234932946⟩⟩,⟨⟨(-20841190897471693952774412198),(-20841190897471693869927713655)⟩,⟨194379779402634532554422882073,194379779402634532638556181661⟩⟩,⟨⟨(-19356211125395325255667548962),(-19356211125395325173008590870)⟩,⟨193133379364383487580836065032,193133379364383487664804641600⟩⟩] +lemma kernel3_0_r5_11_eq : ∀ k : Fin 16, kernel3_0Expr 5 11 k = kernel3_0_r5_11 k := by decide +kernel +noncomputable def kernel3_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-17906838350437634608052421741),(-17906838350437634525669539276)⟩,⟨191897989674881328737354328386,191897989674881328821068775231⟩⟩,⟨⟨(-16492599432940679719197187181),(-16492599432940679637000387403)⟩,⟨190674104303583649433433843374,190674104303583649516983775368⟩⟩,⟨⟨(-15113018062294222274950499004),(-15113018062294222192995444810)⟩,⟨189462202549649707443684571076,189462202549649707527013402886⟩⟩,⟨⟨(-13767615349352974582796011125),(-13767615349352974501025005455)⟩,⟨188262749147595424101185424122,188262749147595424184350392119⟩⟩,⟨⟨(-12455910406781683261753968964),(-12455910406781683180247405697)⟩,⟨187076194389182326714453478381,187076194389182326797373188464⟩⟩,⟨⟨(-11177420916960163202625469910),(-11177420916960163121300475869)⟩,⟨185902974260750270914215007969,185902974260750270996972012449⟩⟩,⟨⟨(-9931663687119775562679496178),(-9931663687119775481591871638)⟩,⟨184743510595197148899721194649,184743510595197148982258817183⟩⟩,⟨⟨(-8718155191421555562967429306),(-8718155191421555482058530179)⟩,⟨183598211237806065055620836286,183598211237806065137997339802⟩⟩,⟨⟨(-7536412099724149611585235042),(-7536412099724149530944000698)⟩,⟨182467470225119570250149037333,182467470225119570332274485407⟩⟩,⟨⟨(-6385951792826832836813773856),(-6385951792826832756347990060)⟩,⟨181351667976061415123782143229,181351667976061415205748549340⟩⟩,⟨⟨(-5266292864009069340407840250),(-5266292864009069260173319077)⟩,⟨180251171494508832846882006979,180251171494508832928632728503⟩⟩,⟨⟨(-4176955606723276119313425706),(-4176955606723276039250752258)⟩,⟨179166334582522512765333357168,179166334582522512846927503332⟩⟩,⟨⟨(-3117462488331591264334020526),(-3117462488331591184525506851)⟩,⟨178097498063447095714694051595,178097498063447095796048380778⟩⟩,⟨⟨(-2087338609810467228676405829),(-2087338609810467149035742461)⟩,⟨177044990014102125644146969393,177044990014102125725347641403⟩⟩,⟨⟨(-1086112151378755986663211614),(-1086112151378755907246160555)⟩,⟨176009126005291845502423841616,176009126005291845583414307766⟩⟩,⟨⟨(-113314804035575885215912098),(-113314804035575805962404951)⟩,⟨174990209349871942279612203638,174990209349871942360452297696⟩⟩] +lemma kernel3_0_r5_12_eq : ∀ k : Fin 16, kernel3_0Expr 5 12 k = kernel3_0_r5_12 k := by decide +kernel +noncomputable def kernel3_0_r5_13 : Fin 16 → CBox := ![⟨⟨831517812976393286764741173,831517812976393365761351957⟩,⟨173988531357622240500186505926,173988531357622240580781930145⟩⟩,⟨⟨1748845748738487632476514059,1748845748738487711314263218⟩,⟨173004371596186329130730727030,173004371596186329211179493350⟩⟩,⟨⟨2639124331184092686181591763,2639124331184092764804899313⟩,⟨172037998157352097974493702285,172037998157352098054739486193⟩⟩,⟨⟨3502803791491362996875939438,3502803791491363075345333476⟩,⟨171089667927961071012693518686,171089667927961071092796679389⟩⟩,⟨⟨4340328902220888174184589315,4340328902220888252416173669⟩,⟨170159626864749171678737760610,170159626864749171758613536440⟩⟩,⟨⟨5152138629055997601733121271,5152138629055997679816071392⟩,⟨169248110272437055856937048192,169248110272437055936674616605⟩⟩,⟨⟨5938665795982240906223871713,5938665795982240984102835210⟩,⟨168355343084404321224776802619,168355343084404321304320106384⟩⟩,⟨⟨6700336763722846506894668715,6700336763722846584630522866⟩,⟨167481540145298666976544681545,167481540145298667055954489429⟩⟩,⟨⟨7437571121228649034986425942,7437571121228649112485782561⟩,⟨166626906494948358652454067867,166626906494948358731636109682⟩⟩,⟨⟨8150781390004086774808852865,8150781390004086852170929670⟩,⟨165791637652964073721003608513,165791637652964073800057216217⟩⟩,⟨⟨8840372741035397257073193182,8840372741035397334242990185⟩,⟨164975919903434292228135984998,164975919903434292307005491147⟩⟩,⟨⟨9506742724073073690782150754,9506742724073073767820700400⟩,⟨164179930579136783422142812706,164179930579136783500889195566⟩⟩,⟨⟨10150281009007974517883219385,10150281009007974594705313273⟩,⟨163403838344707356862001417303,163403838344707356940538657861⟩⟩,⟨⟨10771369139069187178132429731,10771369139069187254829567229⟩,⟨162647803478225831185868618583,162647803478225831264288346799⟩⟩,⟨⟨11370380295561816310921985312,11370380295561816387439571330⟩,⟨161911978150698064683231150656,161911978150698064761478138497⟩⟩,⟨⟨11947679073854274386165683148,11947679073854274462564781787⟩,⟨161196506702931831537127629606,161196506702931831615262935365⟩⟩] +lemma kernel3_0_r5_13_eq : ∀ k : Fin 16, kernel3_0Expr 5 13 k = kernel3_0_r5_13 k := by decide +kernel +noncomputable def kernel3_0_r5_14 : Fin 16 → CBox := ![⟨⟨12503621270317374862715024787,12503621270317374938897515096⟩,⟨160501525919323261900631275541,160501525919323261978555924214⟩⟩,⟨⟨13038553679911537746928789285,13038553679911537822999491209⟩,⟨159827165298089442059139277843,159827165298089442136958341538⟩⟩,⟨⟨13552813904113686062776914425,13552813904113686138681780092⟩,⟨159173547317501545512998783907,159173547317501545590657613820⟩⟩,⟨⟨14046730168871908491847063305,14046730168871908567646971923⟩,⟨158540787697691493093366593994,158540787697691493170926105325⟩⟩,⟨⟨14520621152273655835203055192,14520621152273655910811777045⟩,⟨157928995657623579956271193815,157928995657623580033644390808⟩⟩,⟨⟨14974795821612092983159531682,14974795821612093058670306821⟩,⟨157338274166840722772127817580,157338274166840722849408174034⟩⟩,⟨⟨15409553279535208437467705863,15409553279535208512827076553⟩,⟨156768720191612938492430690572,156768720191612938569564176686⟩⟩,⟨⟨15825182618963353632442927254,15825182618963353707711470022⟩,⟨156220424935133337092954710523,156220424935133337170001974441⟩⟩,⟨⟨16221962786463006916248060555,16221962786463006991328990690⟩,⟨155693474071424268542507252190,155693474071424268619370704134⟩⟩,⟨⟨16600162453767693827589770091,16600162453767693902587134799⟩,⟨155187947972633286245229037821,155187947972633286322013057471⟩⟩,⟨⟨16960039897141107355186476358,16960039897141107430047548362⟩,⟨154703921929415256094003161601,154703921929415256170654475849⟩⟩,⟨⟨17301842884282519795676116031,17301842884282519870460950635⟩,⟨154241466364113236117133191486,154241466364113236193711956128⟩⟩,⟨⟨17625808568480521881745199805,17625808568480521956366795072⟩,⟨153800647036466663854630649013,153800647036466663931049129679⟩⟩,⟨⟨17932163389727925025026123538,17932163389727925099578904328⟩,⟨153381525241590907587297663480,153381525241590907663650595554⟩⟩,⟨⟨18221122982518278687070951035,18221122982518278761502986635⟩,⟨152984157999987357004210856142,152984157999987357080445786217⟩⟩,⟨⟨18492892090052846889275236936,18492892090052846963645917706⟩,⟨152608598239357945459139952895,152608598239357945535316394331⟩⟩] +lemma kernel3_0_r5_14_eq : ∀ k : Fin 16, kernel3_0Expr 5 14 k = kernel3_0_r5_14 k := by decide +kernel +noncomputable def kernel3_0_r5_15 : Fin 16 → CBox := ![⟨⟨18747664484596015614350028735,18747664484596015688558455884⟩,⟨152254894968012309179885113586,152254894968012309255901368999⟩⟩,⟨⟨18985622893726926377460132487,18985622893726926451614720800⟩,⟨151923093439669700973724237034,151923093439669701049689138749⟩⟩,⟨⟨19206938932245610825749600026,19206938932245610899799386448⟩,⟨151613235309471292129103024319,151613235309471292204965107242⟩⟩,⟨⟨19411773039502997383748686381,19411773039502997457752143715⟩,⟨151325358781031623896649568665,151325358781031623972467444171⟩⟩,⟨⟨19600274421935834561600451549,19600274421935834635470128070⟩,⟨151059498744370719141551923034,151059498744370719217237430085⟩⟩,⟨⟨19772581000599787782268346516,19772581000599787856099210504⟩,⟨150815686904580747776738959813,150815686904580747852387426735⟩⟩,⟨⟨19928819363506679067829881297,19928819363506679141572007292⟩,⟨150593951901093170886507216342,150593951901093170962068233186⟩⟩,⟨⟨20069104722585013644195614511,20069104722585013717906407108⟩,⟨150394319417423984525395979425,150394319417423984600927098585⟩⟩,⟨⟨20193540875096536902718743717,20193540875096536976299072151⟩,⟨150216812281286063438375750503,150216812281286063513777071463⟩⟩,⟨⟨20302220169355552018687363375,20302220169355552092243800098⟩,⟨150061450554968687548256848835,150061450554968687623635386657⟩⟩,⟨⟨20395223474612066122921022671,20395223474612066196404865317⟩,⟨149928251615895141785173549062,149928251615895141860480132024⟩⟩,⟨⟨20472620154974484884647518686,20472620154974484958114833721⟩,⟨149817230227279835938630386148,149817230227279836013921230794⟩⟩,⟨⟨20534468047262505719909989338,20534468047262505793273215368⟩,⟨149728398598816720294057571142,149728398598816720369244419748⟩⟩,⟨⟨20580813442696032949580115982,20580813442696033022934092557⟩,⟨149661766437340900638081959960,149661766437340900713260034189⟩⟩,⟨⟨20611691072341318793700012501,20611691072341318866997368908⟩,⟨149617340987415309604188813713,149617340987415309679310285714⟩⟩,⟨⟨20627124096251087067918485270,20627124096251087141213755685⟩,⟨149595127061804097981088109098,149595127061804098056207658952⟩⟩] +lemma kernel3_0_r5_15_eq : ∀ k : Fin 16, kernel3_0Expr 5 15 k = kernel3_0_r5_15 k := by decide +kernel +noncomputable def kernel3_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel3_0_r5_0,kernel3_0_r5_1,kernel3_0_r5_2,kernel3_0_r5_3,kernel3_0_r5_4,kernel3_0_r5_5,kernel3_0_r5_6,kernel3_0_r5_7,kernel3_0_r5_8,kernel3_0_r5_9,kernel3_0_r5_10,kernel3_0_r5_11,kernel3_0_r5_12,kernel3_0_r5_13,kernel3_0_r5_14,kernel3_0_r5_15] +lemma kernel3_0_r5_eq (i k : Fin 16) : kernel3_0Expr 5 i k = kernel3_0_r5 i k := by + fin_cases i + · exact kernel3_0_r5_0_eq k + · exact kernel3_0_r5_1_eq k + · exact kernel3_0_r5_2_eq k + · exact kernel3_0_r5_3_eq k + · exact kernel3_0_r5_4_eq k + · exact kernel3_0_r5_5_eq k + · exact kernel3_0_r5_6_eq k + · exact kernel3_0_r5_7_eq k + · exact kernel3_0_r5_8_eq k + · exact kernel3_0_r5_9_eq k + · exact kernel3_0_r5_10_eq k + · exact kernel3_0_r5_11_eq k + · exact kernel3_0_r5_12_eq k + · exact kernel3_0_r5_13_eq k + · exact kernel3_0_r5_14_eq k + · exact kernel3_0_r5_15_eq k +noncomputable def kernel3_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel3_0_r0,kernel3_0_r1,kernel3_0_r2,kernel3_0_r3,kernel3_0_r4,kernel3_0_r5] +lemma kernel3_0_eq (j : Fin 6) (i k : Fin 16) : kernel3_0Expr j i k = kernel3_0 j i k := by + fin_cases j + · exact kernel3_0_r0_eq i k + · exact kernel3_0_r1_eq i k + · exact kernel3_0_r2_eq i k + · exact kernel3_0_r3_eq i k + · exact kernel3_0_r4_eq i k + · exact kernel3_0_r5_eq i k +lemma kernel3_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel3_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(3:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel3_0_eq] + unfold kernel3_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans3_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel3_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans3 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel3_1_r0_0 : Fin 16 → CBox := ![⟨⟨1481973251781494182561,1481973251781494184391⟩,⟨(-1801474169287118136168),(-1801474169287118134319)⟩⟩,⟨⟨1482083030259508886009,1482083030259508887840⟩,⟨(-1799649244741576276654),(-1799649244741576274805)⟩⟩,⟨⟨1482299775777728028782,1482299775777728030613⟩,⟨(-1796002535879440472313),(-1796002535879440470464)⟩⟩,⟨⟨1482617880975353888061,1482617880975353889903⟩,⟨(-1790540319213110068774),(-1790540319213110066913)⟩⟩,⟨⟨1483028973516491689337,1483028973516491691149⟩,⟨(-1783271999625231623468),(-1783271999625231621634)⟩⟩,⟨⟨1483521962308036872244,1483521962308036874060⟩,⟨(-1774210098443737883533),(-1774210098443737881703)⟩⟩,⟨⟨1484083098744049941773,1484083098744049943589⟩,⟨(-1763370237439985719903),(-1763370237439985718073)⟩⟩,⟨⟨1484696052653980820337,1484696052653980822133⟩,⟨(-1750771118664857030980),(-1750771118664857029165)⟩⟩,⟨⟨1485342002554711314666,1485342002554711316463⟩,⟨(-1736434500019146590598),(-1736434500019146588783)⟩⟩,⟨⟨1485999739731143125097,1485999739731143126867⟩,⟨(-1720385166437804301290),(-1720385166437804299494)⟩⟩,⟨⟨1486645785597374951882,1486645785597374953633⟩,⟨(-1702650896552937912132),(-1702650896552937910363)⟩⟩,⟨⟨1487254521720777323397,1487254521720777325148⟩,⟨(-1683262424688203786316),(-1683262424688203784547)⟩⟩,⟨⟨1487798331824863719814,1487798331824863721565⟩,⟨(-1662253398027578513063),(-1662253398027578511294)⟩⟩,⟨⟨1488247755024129608809,1488247755024129610537⟩,⟨(-1639660328794743778845),(-1639660328794743777099)⟩⟩,⟨⟨1488571649485325673978,1488571649485325675703⟩,⟨(-1615522541275628977745),(-1615522541275628975994)⟩⟩,⟨⟨1488737365655264770934,1488737365655264772643⟩,⟨(-1589882113516203616208),(-1589882113516203614477)⟩⟩] +lemma kernel3_1_r0_0_eq : ∀ k : Fin 16, kernel3_1Expr 0 0 k = kernel3_1_r0_0 k := by decide +kernel +noncomputable def kernel3_1_r0_1 : Fin 16 → CBox := ![⟨⟨1488710928145527637458,1488710928145527639148⟩,⟨(-1562783813530520836960),(-1562783813530520835256)⟩⟩,⟨⟨1488457225319598771663,1488457225319598773335⟩,⟨(-1534275029860372153550),(-1534275029860372151860)⟩⟩,⟨⟨1487940205588273309851,1487940205588273311511⟩,⟨(-1504405696337770094559),(-1504405696337770092881)⟩⟩,⟨⟨1487123079384842384929,1487123079384842386589⟩,⟨(-1473228210914838132715),(-1473228210914838131037)⟩⟩,⟨⟨1485968525762773315971,1485968525762773317574⟩,⟨(-1440797348442523914704),(-1440797348442523913083)⟩⟩,⟨⟨1484438902535506729737,1484438902535506731354⟩,⟨(-1407170167299790194336),(-1407170167299790192696)⟩⟩,⟨⟨1482496458860718702657,1482496458860718704230⟩,⟨(-1372405909798466315647),(-1372405909798466314052)⟩⟩,⟨⟨1480103549160033481153,1480103549160033482725⟩,⟨(-1336565896315611508126),(-1336565896315611506532)⟩⟩,⟨⟨1477222847259779798830,1477222847259779800364⟩,⟨(-1299713413134862625697),(-1299713413134862624145)⟩⟩,⟨⟨1473817559638986556824,1473817559638986558343⟩,⟨(-1261913594010591212865),(-1261913594010591211332)⟩⟩,⟨⟨1469851636677403499232,1469851636677403500729⟩,⟨(-1223233295503522999259),(-1223233295503522997748)⟩⟩,⟨⟨1465289980808867756732,1465289980808867758186⟩,⟨(-1183740966173491936865),(-1183740966173491935392)⟩⟩,⟨⟨1460098650503742553099,1460098650503742554519⟩,⟨(-1143506509753898133396),(-1143506509753898131958)⟩⟩,⟨⟨1454245059028321614368,1454245059028321615785⟩,⟨(-1102601142472877706098),(-1102601142472877704668)⟩⟩,⟨⟨1447698166958880870748,1447698166958880872131⟩,⟨(-1061097244727815042840),(-1061097244727815041444)⟩⟩,⟨⟨1440428667463294908800,1440428667463294910174⟩,⟨(-1019068207362259334231),(-1019068207362259332838)⟩⟩] +lemma kernel3_1_r0_1_eq : ∀ k : Fin 16, kernel3_1Expr 0 1 k = kernel3_1_r0_1 k := by decide +kernel +noncomputable def kernel3_1_r0_2 : Fin 16 → CBox := ![⟨⟨1432409163403615250478,1432409163403615251842⟩,⟨(-976588272837159171176),(-976588272837159169807)⟩⟩,⟨⟨1423614335358496843845,1423614335358496845148⟩,⟨(-933732371631203529215),(-933732371631203527898)⟩⟩,⟨⟨1414021099714595367513,1414021099714595368797⟩,⟨(-890575954247550990825),(-890575954247550989536)⟩⟩,⟨⟨1403608756030751035597,1403608756030751036855⟩,⟨(-847194819245936362771),(-847194819245936361501)⟩⟩,⟨⟨1392359122937608882358,1392359122937608883600⟩,⟨(-803664937759662064733),(-803664937759662063482)⟩⟩,⟨⟨1380256661897961539157,1380256661897961540360⟩,⟨(-760062274995914249189),(-760062274995914247968)⟩⟩,⟨⟨1367288588219176987619,1367288588219176988800⟩,⟨(-716462609254804198035),(-716462609254804196849)⟩⟩,⟨⟨1353444968778209672538,1353444968778209673678⟩,⟨(-672941349037151690921),(-672941349037151689773)⟩⟩,⟨⟨1338718805991490231080,1338718805991490232200⟩,⟨(-629573348842943823989),(-629573348842943822856)⟩⟩,⟨⟨1323106107636033432257,1323106107636033433358⟩,⟨(-586432724291286144875),(-586432724291286143769)⟩⟩,⟨⟨1306605942203969661302,1306605942203969662388⟩,⟨(-543592667218202982243),(-543592667218202981157)⟩⟩,⟨⟨1289220479549956411940,1289220479549956412954⟩,⟨(-501125261430557471512),(-501125261430557470490)⟩⟩,⟨⟨1270955016669119467318,1270955016669119468297⟩,⟨(-459101299812395578122),(-459101299812395577134)⟩⟩,⟨⟨1251817988521860918870,1251817988521860919846⟩,⟨(-417590103493950860357),(-417590103493950859377)⟩⟩,⟨⟨1231820963900603281901,1231820963900603282877⟩,⟨(-376659343803190158602),(-376659343803190157623)⟩⟩,⟨⟨1210978626411867147104,1210978626411867148041⟩,⟨(-336374867724982752740),(-336374867724982751802)⟩⟩] +lemma kernel3_1_r0_2_eq : ∀ k : Fin 16, kernel3_1Expr 0 2 k = kernel3_1_r0_2 k := by decide +kernel +noncomputable def kernel3_1_r0_3 : Fin 16 → CBox := ![⟨⟨1189308740724559321595,1189308740724559322510⟩,⟨(-296800527593621562808),(-296800527593621561893)⟩⟩,⟨⟨1166832104311541151810,1166832104311541152686⟩,⟨(-257998015740437247206),(-257998015740437246321)⟩⟩,⟨⟨1143572484986023946263,1143572484986023947094⟩,⟨(-220026704809585539230),(-220026704809585538404)⟩⟩,⟨⟨1119556544606683459760,1119556544606683460576⟩,⟨(-182943494441754428350),(-182943494441754427530)⟩⟩,⟨⟨1094813749395196269719,1094813749395196270531⟩,⟨(-146802665007568894711),(-146802665007568893899)⟩⟩,⟨⟨1069376267376792779440,1069376267376792780203⟩,⟨(-111655739049942896752),(-111655739049942895994)⟩⟩,⟨⟨1043278853518029334293,1043278853518029335025⟩,⟨(-77551351067654410425),(-77551351067654409693)⟩⟩,⟨⟨1016558723195962212125,1016558723195962212857⟩,⟨(-44535126241148765693),(-44535126241148764962)⟩⟩,⟨⟨989255414688939720277,989255414688939720964⟩,⟨(-12649568666192108133),(-12649568666192107447)⟩⟩,⟨⟨961410641431021907663,961410641431021908312⟩,⟨18066040378282889387,18066040378282890031⟩⟩,⟨⟨933068134819324800388,933068134819324801040⟩,⟨47575733644725580880,47575733644725581531⟩⟩,⟨⟨904273478406131198424,904273478406131199026⟩,⟨75846938176798428544,75846938176798429142⟩⟩,⟨⟨875073934345207189103,875073934345207189706⟩,⟨102850544226751895034,102850544226751895631⟩⟩,⟨⟨845518262994238707293,845518262994238707854⟩,⟨128560962494723608335,128560962494723608894⟩⟩,⟨⟨815656536602514499539,815656536602514500093⟩,⟨152956169408862020463,152956169408862021006⟩⟩,⟨⟨785539948034822963476,785539948034822963999⟩,⟨176017740221732119530,176017740221732120047⟩⟩] +lemma kernel3_1_r0_3_eq : ∀ k : Fin 16, kernel3_1Expr 0 3 k = kernel3_1_r0_3 k := by decide +kernel +noncomputable def kernel3_1_r0_4 : Fin 16 → CBox := ![⟨⟨755220615498926650877,755220615498926651371⟩,⟨197730869756678309816,197730869756678310314⟩⟩,⟨⟨724751384254889975785,724751384254889976242⟩,⟨218084380697308841279,218084380697308841735⟩⟩,⟨⟨694185626289957180629,694185626289957181063⟩,⟨237070719373630697275,237070719373630697708⟩⟩,⟨⟨663577038942637046531,663577038942637046947⟩,⟨254685939059202514959,254685939059202515364⟩⟩,⟨⟨632979443454209696022,632979443454209696418⟩,⟨270929670854583335715,270929670854583336106⟩⟩,⟨⟨602446584415123266297,602446584415123266666⟩,⟨285805082292935939569,285805082292935939942⟩⟩,⟨⟨572031931057820047229,572031931057820047580⟩,⟨299318823863499255633,299318823863499255978⟩⟩,⟨⟨541788481326579234237,541788481326579234588⟩,⟨311480963707386829743,311480963707386830088⟩⟩,⟨⟨511768569629172260435,511768569629172260758⟩,⟨322304910797420373618,322304910797420373945⟩⟩,⟨⟨482023679144709887660,482023679144709887973⟩,⟨331807326969105440368,331807326969105440671⟩⟩,⟨⟨452604259527256885302,452604259527256885570⟩,⟨340008028223052931954,340008028223052932212⟩⟩,⟨⟨423559550805863244179,423559550805863244465⟩,⟨346929875769816789507,346929875769816789793⟩⟩,⟨⟨394937414238895465152,394937414238895465457⟩,⟨352598657335947120674,352598657335947120973⟩⟩,⟨⟨366784170834252325754,366784170834252326042⟩,⟨357042959294764415888,357042959294764416181⟩⟩,⟨⟨339144448197538992016,339144448197538992276⟩,⟨360294030226684415090,360294030226684415345⟩⟩,⟨⟨312061036317888877295,312061036317888877590⟩,⟨362385636551630979677,362385636551630979951⟩⟩] +lemma kernel3_1_r0_4_eq : ∀ k : Fin 16, kernel3_1Expr 0 4 k = kernel3_1_r0_4 k := by decide +kernel +noncomputable def kernel3_1_r0_5 : Fin 16 → CBox := ![⟨⟨285574752846214440272,285574752846214440557⟩,⟨363353910909960078143,363353910909960078428⟩⟩,⟨⟨259724318363596549320,259724318363596549590⟩,⟨363237193998204572834,363237193998204573099⟩⟩,⟨⟨234546242078655186009,234546242078655186279⟩,⟨362075870591689413238,362075870591689413503⟩⟩,⟨⟨210074718332455306437,210074718332455306716⟩,⟨359912200507542840041,359912200507542840331⟩⟩,⟨⟨186341534228166397650,186341534228166397926⟩,⟨356790145278754617723,356790145278754618004⟩⟩,⟨⟨163375988640688492390,163375988640688492666⟩,⟨352755191322651160877,352755191322651161158⟩⟩,⟨⟨141204822799154549298,141204822799154549587⟩,⟨347854170395444271591,347854170395444271869⟩⟩,⟨⟨119852162572987746740,119852162572987747015⟩,⟨342135078128369813568,342135078128369813849⟩⟩,⟨⟨99339472530393769479,99339472530393769737⟩,⟨335646891440399356785,335646891440399357038⟩⟩,⟨⟨79685521777154553713,79685521777154553974⟩,⟨328439385617644756069,328439385617644756330⟩⟩,⟨⟨60906361523701590649,60906361523701590910⟩,⟨320562951840473679603,320562951840473679863⟩⟩,⟨⟨43015314270010571182,43015314270010571440⟩,⟨312068415926130755578,312068415926130755830⟩⟩,⟨⟨26022974441186211857,26022974441186212108⟩,⟨303006859037456952030,303006859037456952287⟩⟩,⟨⟨9937220251990640092,9937220251990640343⟩,⟨293429441087285419956,293429441087285420213⟩⟩,⟨⟨(-5236763473713950355),(-5236763473713950107)⟩,⟨283387227543453707941,283387227543453708189⟩⟩,⟨⟨(-19496451852332446702),(-19496451852332446470)⟩,⟨272931020311318620396,272931020311318620638⟩⟩] +lemma kernel3_1_r0_5_eq : ∀ k : Fin 16, kernel3_1Expr 0 5 k = kernel3_1_r0_5 k := by decide +kernel +noncomputable def kernel3_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-32841936229311106647),(-32841936229311106399)⟩,⟨262111193339417980681,262111193339417980929⟩⟩,⟨⟨(-45275870621756992025),(-45275870621756991777)⟩,⟨250977533559736461542,250977533559736461790⟩⟩,⟨⟨(-56803408769960934962),(-56803408769960934715)⟩,⟨239579087737158011136,239579087737158011384⟩⟩,⟨⟨(-67432132290118999690),(-67432132290118999468)⟩,⟨227964015763394954049,227964015763394954288⟩⟩,⟨⟨(-77171970454261289047),(-77171970454261288833)⟩,⟨216179450889253312151,216179450889253312365⟩⟩,⟨⟨(-86035112153474248124),(-86035112153474247905)⟩,⟨204271367345812842918,204271367345812843149⟩⟩,⟨⟨(-94035910626854606052),(-94035910626854605833)⟩,⟨192284455760261982502,192284455760261982733⟩⟩,⟨⟨(-101190781561196161085),(-101190781561196160881)⟩,⟨180262006726029073847,180262006726029074058⟩⟩,⟨⟨(-107518095185146081462),(-107518095185146081258)⟩,⟨168245802839790128635,168245802839790128846⟩⟩,⟨⟨(-113038062996461165694),(-113038062996461165506)⟩,⟨156276019470207405566,156276019470207405771⟩⟩,⟨⟨(-117772619772056529810),(-117772619772056529606)⟩,⟨144391134475157091648,144391134475157091859⟩⟩,⟨⟨(-121745301517802784117),(-121745301517802783941)⟩,⟨132627847036028522458,132627847036028522652⟩⟩,⟨⟨(-124981120018548805251),(-124981120018548805047)⟩,⟨121021005729705363161,121021005729705363371⟩⟩,⟨⟨(-127506434648703164733),(-127506434648703164530)⟩,⟨109603545911346455045,109603545911346455255⟩⟩,⟨⟨(-129348822099996139311),(-129348822099996139115)⟩,⟨98406436434336184215,98406436434336184398⟩⟩,⟨⟨(-130536944675883312419),(-130536944675883312251)⟩,⟨87458635688025421093,87458635688025421260⟩⟩] +lemma kernel3_1_r0_6_eq : ∀ k : Fin 16, kernel3_1Expr 0 6 k = kernel3_1_r0_6 k := by decide +kernel +noncomputable def kernel3_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-131100417791576444184),(-131100417791576444014)⟩,⟨76787056889375658817,76787056889375658993⟩⟩,⟨⟨(-131069677305049551349),(-131069677305049551156)⟩,⟨66416542521578217867,66416542521578218041⟩⟩,⟨⟨(-130475847287735224369),(-130475847287735224202)⟩,⟨56369847771359328101,56369847771359328268⟩⟩,⟨⟨(-129350608824179023064),(-129350608824179022897)⟩,⟨46667632777196385759,46667632777196385926⟩⟩,⟨⟨(-127726070407851365503),(-127726070407851365337)⟩,⟨37328463463239484034,37328463463239484200⟩⟩,⟨⟨(-125634640475830199957),(-125634640475830199806)⟩,⟨28368820698516438928,28368820698516439066⟩⟩,⟨⟨(-123108902598376349833),(-123108902598376349683)⟩,⟨19803117488141663961,19803117488141664099⟩⟩,⟨⟨(-120181493810746418419),(-120181493810746418281)⟩,⟨11643723872873335810,11643723872873335960⟩⟩,⟨⟨(-116884986544150794131),(-116884986544150793991)⟩,⟨3900999185574288298,3900999185574288457⟩⟩,⟨⟨(-113251774580795843705),(-113251774580795843567)⟩,⟨(-3416668711984207558),(-3416668711984207408)⟩⟩,⟨⟨(-109313963424681409153),(-109313963424681409031)⟩,⟨(-10302817610913471336),(-10302817610913471214)⟩⟩,⟨⟨(-105103265445489610012),(-105103265445489609862)⟩,⟨(-16752858974120639076),(-16752858974120638939)⟩⟩,⟨⟨(-100650900117730325959),(-100650900117730325829)⟩,⟨(-22764020227644990424),(-22764020227644990300)⟩⟩,⟨⟨(-95987499641532001548),(-95987499641532001418)⟩,⟨(-28335281773664894766),(-28335281773664894643)⟩⟩,⟨⟨(-91143020195309342699),(-91143020195309342569)⟩,⟨(-33467309185549693132),(-33467309185549693009)⟩⟩,⟨⟨(-86146659034222853823),(-86146659034222853702)⟩,⟨(-38162381053662091544),(-38162381053662091423)⟩⟩] +lemma kernel3_1_r0_7_eq : ∀ k : Fin 16, kernel3_1Expr 0 7 k = kernel3_1_r0_7 k := by decide +kernel +noncomputable def kernel3_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-81026777612083529449),(-81026777612083529328)⟩,⟨(-42424312956193109842),(-42424312956193109721)⟩⟩,⟨⟨(-75810830868356474891),(-75810830868356474761)⟩,⟨(-46258378032189729361),(-46258378032189729238)⟩⟩,⟨⟨(-70525302786378371009),(-70525302786378370889)⟩,⟨(-49671224634186327037),(-49671224634186326917)⟩⟩,⟨⟨(-65195648294014576816),(-65195648294014576694)⟩,⟨(-52670791535559816490),(-52670791535559816360)⟩⟩,⟨⟨(-59846241543920923679),(-59846241543920923550)⟩,⟨(-55266221162992997708),(-55266221162992997586)⟩⟩,⟨⟨(-54500330577510311253),(-54500330577510311161)⟩,⟨(-57467771317360546941),(-57467771317360546835)⟩⟩,⟨⟨(-49179998344810572420),(-49179998344810572306)⟩,⟨(-59286725837067583934),(-59286725837067583841)⟩⟩,⟨⟨(-43906130021780728031),(-43906130021780727938)⟩,⟨(-60735304646501537578),(-60735304646501537464)⟩⟩,⟨⟨(-38698386537457709229),(-38698386537457709142)⟩,⟨(-61826573618942096201),(-61826573618942096114)⟩⟩,⟨⟨(-33575184195651517887),(-33575184195651517809)⟩,⟨(-62574354668156491048),(-62574354668156490962)⟩⟩,⟨⟨(-28553680249896619190),(-28553680249896619112)⟩,⟨(-62993136466139248490),(-62993136466139248404)⟩⟩,⟨⟨(-23649764266090280078),(-23649764266090280000)⟩,⟨(-63097986166192609847),(-63097986166192609762)⟩⟩,⟨⟨(-18878055084779867565),(-18878055084779867487)⟩,⟨(-62904462490945342731),(-62904462490945342646)⟩⟩,⟨⟨(-14251903174462208231),(-14251903174462208145)⟩,⟨(-62428530524135315753),(-62428530524135315666)⟩⟩,⟨⟨(-9783398148576649054),(-9783398148576648968)⟩,⟨(-61686478523197874052),(-61686478523197873966)⟩⟩,⟨⟨(-5483381202143558356),(-5483381202143558272)⟩,⟨(-60694837047070764431),(-60694837047070764353)⟩⟩] +lemma kernel3_1_r0_8_eq : ∀ k : Fin 16, kernel3_1Expr 0 8 k = kernel3_1_r0_8 k := by decide +kernel +noncomputable def kernel3_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-1361462209242527871),(-1361462209242527785)⟩,⟨(-59470300670309207444),(-59470300670309207357)⟩⟩,⟨⟨2573958790252551105,2573958790252551182⟩,⟨(-58029652530761846453),(-58029652530761846369)⟩⟩,⟨⟨6315665997065535139,6315665997065535187⟩,⟨(-56389691933846945012),(-56389691933846944941)⟩⟩,⟨⟨9857598443262858543,9857598443262858620⟩,⟨(-54567165212041758686),(-54567165212041758602)⟩⟩,⟨⟨13194817065486734516,13194817065486734568⟩,⟨(-52578700013705201927),(-52578700013705201882)⟩⟩,⟨⟨16323468563829020455,16323468563829020509⟩,⟨(-50440743170938039617),(-50440743170938039563)⟩⟩,⟨⟨19240746352670101381,19240746352670101453⟩,⟨(-48169502271982952222),(-48169502271982952165)⟩⟩,⟨⟨21944848911192479831,21944848911192479902⟩,⟨(-45780891039809237146),(-45780891039809237089)⟩⟩,⟨⟨24434935840943892215,24434935840943892300⟩,⟨(-43290478595136502494),(-43290478595136502408)⟩⟩,⟨⟨26711081935844033669,26711081935844033754⟩,⟨(-40713442659343482166),(-40713442659343482081)⟩⟩,⟨⟨28774229566483716086,28774229566483716170⟩,⟨(-38064526730588730352),(-38064526730588730267)⟩⟩,⟨⟨30626139675543056907,30626139675543056992⟩,⟨(-35358001245137443369),(-35358001245137443284)⟩⟩,⟨⟨32269341674749017733,32269341674749017807⟩,⟨(-32607628715432070126),(-32607628715432070052)⟩⟩,⟨⟨33707082526099748824,33707082526099748876⟩,⟨(-29826632816943603039),(-29826632816943602995)⟩⟩,⟨⟨34943275281204930547,34943275281204930618⟩,⟨(-27027671377366103961),(-27027671377366103906)⟩⟩,⟨⟨35982447342631723741,35982447342631723793⟩,⟨(-24222813204330363417),(-24222813204330363373)⟩⟩] +lemma kernel3_1_r0_9_eq : ∀ k : Fin 16, kernel3_1Expr 0 9 k = kernel3_1_r0_9 k := by decide +kernel +noncomputable def kernel3_1_r0_10 : Fin 16 → CBox := ![⟨⟨36829688700211236527,36829688700211236602⟩,⟨(-21423518671565511307),(-21423518671565511224)⟩⟩,⟨⟨37490600383458097375,37490600383458097450⟩,⟨(-18640623968372495537),(-18640623968372495455)⟩⟩,⟨⟨37971243358693861141,37971243358693861215⟩,⟨(-15884328903424058191),(-15884328903424058108)⟩⟩,⟨⟨38278088086251478985,38278088086251479069⟩,⟨(-13164188141296615460),(-13164188141296615376)⟩⟩,⟨⟨38417964939379973594,38417964939379973665⟩,⟨(-10489105738785994644),(-10489105738785994589)⟩⟩,⟨⟨38398015672271304620,38398015672271304700⟩,⟨(-7867332837968539240),(-7867332837968539184)⟩⟩,⟨⟨38225646110098563686,38225646110098563768⟩,⟨(-5306468364140774570),(-5306468364140774496)⟩⟩,⟨⟨37908480219186765417,37908480219186765487⟩,⟨(-2813462569195989662),(-2813462569195989607)⟩⟩,⟨⟨37454315700532003759,37454315700532003830⟩,⟨(-394623254658744131),(-394623254658744077)⟩⟩,⟨⟨36871081234935286749,36871081234935286823⟩,⟨1944375496524443243,1944375496524443325⟩⟩,⟨⟨36166795493113427145,36166795493113427197⟩,⟨4198482254277454007,4198482254277454059⟩⟩,⟨⟨35349528009375860544,35349528009375860589⟩,⟨6363255019396702431,6363255019396702500⟩⟩,⟨⟨34427362002893180647,34427362002893180720⟩,⟨8434846024567974905,8434846024567974978⟩⟩,⟨⟨33408359216305310188,33408359216305310233⟩,⟨10409984738317442590,10409984738317442659⟩⟩,⟨⟨32300526827493905869,32300526827493905914⟩,⟨12285959251417156304,12285959251417156373⟩⟩,⟨⟨31111786476838524996,31111786476838525040⟩,⟨14060596223906298808,14060596223906298876⟩⟩] +lemma kernel3_1_r0_10_eq : ∀ k : Fin 16, kernel3_1Expr 0 10 k = kernel3_1_r0_10 k := by decide +kernel +noncomputable def kernel3_1_r0_11 : Fin 16 → CBox := ![⟨⟨29849945439247167775,29849945439247167819⟩,⟨15732239568627668718,15732239568627668787⟩⟩,⟨⟨28522669957751083506,28522669957751083559⟩,⟨17299728044074163830,17299728044074163899⟩⟩,⟨⟨27137460743527275298,27137460743527275378⟩,⟨18762371925454501237,18762371925454501310⟩⟩,⟨⟨25701630635900101253,25701630635900101322⟩,⟨20119928918284844710,20119928918284844763⟩⟩,⟨⟨24222284405209979372,24222284405209979413⟩,⟨21372579473558380654,21372579473558380696⟩⟩,⟨⟨22706300671450847576,22706300671450847626⟩,⟨22520901657703875515,22520901657703875556⟩⟩,⟨⟨21160315902291366018,21160315902291366087⟩,⟨23565845724182766162,23565845724182766215⟩⟩,⟨⟨19590710445524949648,19590710445524949717⟩,⟨24508708526758073329,24508708526758073373⟩⟩,⟨⟨18003596543152243686,18003596543152243754⟩,⟨25351107907262427781,25351107907262427824⟩⟩,⟨⟨16404808267193059485,16404808267193059554⟩,⟨26094957183160758812,26094957183160758864⟩⟩,⟨⟨14799893310954552827,14799893310954552870⟩,⟨26742439852408293006,26742439852408293074⟩⟩,⟨⟨13194106563845311278,13194106563845311331⟩,⟨27295984625107266793,27295984625107266871⟩⟩,⟨⟨11592405392913334988,11592405392913335029⟩,⟨27758240883324910474,27758240883324910515⟩⟩,⟨⟨9999446550087803494,9999446550087803562⟩,⟨28132054662207199860,28132054662207199902⟩⟩,⟨⟨8419584620604326486,8419584620604326555⟩,⟨28420445237261373091,28420445237261373142⟩⟩,⟨⟨6856871925271851586,6856871925271851628⟩,⟨28626582394436220609,28626582394436220677⟩⟩] +lemma kernel3_1_r0_11_eq : ∀ k : Fin 16, kernel3_1Expr 0 11 k = kernel3_1_r0_11 k := by decide +kernel +noncomputable def kernel3_1_r0_12 : Fin 16 → CBox := ![⟨⟨5315059787074107293,5315059787074107335⟩,⟨28753764451450615132,28753764451450615199⟩⟩,⟨⟨3797601071064074720,3797601071064074761⟩,⟨28805397090752414220,28805397090752414260⟩⟩,⟨⟨2307653905578635957,2307653905578635999⟩,⟨28784973056573211468,28784973056573211536⟩⟩,⟨⟨848086492442151550,848086492442151617⟩,⟨28696052760817505885,28696052760817505927⟩⟩,⟨⟨(-578517085989703314),(-578517085989703272)⟩,⟨28542245835022321395,28542245835022321463⟩⟩,⟨⟨(-1969850154404511094),(-1969850154404511016)⟩,⟨28327193658376264743,28327193658376264813⟩⟩,⟨⟨(-3323875917022119719),(-3323875917022119679)⟩,⟨28054552884823073960,28054552884823074009⟩⟩,⟨⟨(-4638819203694572677),(-4638819203694572610)⟩,⟨27727979985618015757,27727979985618015799⟩⟩,⟨⟨(-5913157576313381593),(-5913157576313381552)⟩,⟨27351116817376710381,27351116817376710448⟩⟩,⟨⟨(-7145611879856709354),(-7145611879856709287)⟩,⟨26927577219672391444,26927577219672391485⟩⟩,⟨⟨(-8335136319718215514),(-8335136319718215474)⟩,⟨26460934640613225155,26460934640613225195⟩⟩,⟨⟨(-9480908143978201347),(-9480908143978201279)⟩,⟨25954710783576903832,25954710783576903900⟩⟩,⟨⟨(-10582317006042530047),(-10582317006042530008)⟩,⟨25412365263402979539,25412365263402979578⟩⟩,⟨⟨(-11638954079621226040),(-11638954079621226000)⟩,⟨24837286255849067444,24837286255849067484⟩⟩,⟨⟨(-12650600994381471369),(-12650600994381471330)⟩,⟨24232782120007058976,24232782120007059015⟩⟩,⟨⟨(-13617218656822712696),(-13617218656822712656)⟩,⟨23602073969649142167,23602073969649142216⟩⟩] +lemma kernel3_1_r0_12_eq : ∀ k : Fin 16, kernel3_1Expr 0 12 k = kernel3_1_r0_12 k := by decide +kernel +noncomputable def kernel3_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-14538936017017374715),(-14538936017017374648)⟩,⟨22948289166127552355,22948289166127552395⟩⟩,⟨⟨(-15416038837870529910),(-15416038837870529870)⟩,⟨22274455702481091935,22274455702481092002⟩⟩,⟨⟨(-16248958519505631152),(-16248958519505631113)⟩,⟨21583497445797973555,21583497445797973595⟩⟩,⟨⟨(-17038261027309335382),(-17038261027309335343)⟩,⟨20878230202638933633,20878230202638933672⟩⟩,⟨⟨(-17784635968093151496),(-17784635968093151456)⟩,⟨20161358570425575582,20161358570425575621⟩⟩,⟨⟨(-18488885854778013528),(-18488885854778013489)⟩,⟨19435473536133724034,19435473536133724091⟩⟩,⟨⟨(-19151915596003023791),(-19151915596003023724)⟩,⟨18703050782386039916,18703050782386039956⟩⟩,⟨⟨(-19774722243122811120),(-19774722243122811054)⟩,⟨17966449660096924592,17966449660096924632⟩⟩,⟨⟨(-20358385023208658573),(-20358385023208658534)⟩,⟨17227912786169512153,17227912786169512192⟩⟩,⟨⟨(-20904055682924369832),(-20904055682924369793)⟩,⟨16489566224362186738,16489566224362186777⟩⟩,⟨⟨(-21412949164524528089),(-21412949164524528050)⟩,⟨15753420207312820314,15753420207312820353⟩⟩,⟨⟨(-21886334631734298254),(-21886334631734298187)⟩,⟨15021370357814590411,15021370357814590478⟩⟩,⟨⟨(-22325526859928394734),(-22325526859928394668)⟩,⟨14295199367759303830,14295199367759303870⟩⟩,⟨⟨(-22731878001842703723),(-22731878001842703684)⟩,⟨13576579093683965750,13576579093683965789⟩⟩,⟨⟨(-23106769737034048743),(-23106769737034048705)⟩,⟨12867073028555245412,12867073028555245451⟩⟩,⟨⟨(-23451605810458839429),(-23451605810458839363)⟩,⟨12168139110285982684,12168139110285982751⟩⟩] +lemma kernel3_1_r0_13_eq : ∀ k : Fin 16, kernel3_1Expr 0 13 k = kernel3_1_r0_13 k := by decide +kernel +noncomputable def kernel3_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-23767804962875414405),(-23767804962875414366)⟩,⟨11481132828479701286,11481132828479701343⟩⟩,⟨⟨(-24056794253291879617),(-24056794253291879579)⟩,⟨10807310592025371250,10807310592025371289⟩⟩,⟨⟨(-24320002771383864619),(-24320002771383864553)⟩,⟨10147833321398002248,10147833321398002287⟩⟩,⟨⟨(-24558855735696288255),(-24558855735696288216)⟩,⟨9503770230844241581,9503770230844241648⟩⟩,⟨⟨(-24774768971520147957),(-24774768971520147918)⟩,⟨8876102767029849175,8876102767029849241⟩⟩,⟨⟨(-24969143760598618488),(-24969143760598618450)⟩,⟨8265728672182323263,8265728672182323301⟩⟩,⟨⟨(-25143362053264447676),(-25143362053264447638)⟩,⟨7673466141262453998,7673466141262454037⟩⟩,⟨⟨(-25298782032239920761),(-25298782032239920723)⟩,⟨7100058044229451841,7100058044229451879⟩⟩,⟨⟨(-25436734016137862159),(-25436734016137862121)⟩,⟨6546176186012700552,6546176186012700590⟩⟩,⟨⟨(-25558516689682850373),(-25558516689682850335)⟩,⟨6012425578357238092,6012425578357238130⟩⟩,⟨⟨(-25665393646820989162),(-25665393646820989124)⟩,⟨5499348699258853581,5499348699258853620⟩⟩,⟨⟨(-25758590232198608529),(-25758590232198608491)⟩,⟨5007429717238286846,5007429717238286884⟩⟩,⟨⟨(-25839290665959092619),(-25839290665959092580)⟩,⟨4537098659213502858,4537098659213502896⟩⟩,⟨⟨(-25908635436426191465),(-25908635436426191399)⟩,⟨4088735502206480837,4088735502206480875⟩⟩,⟨⟨(-25967718945004904473),(-25967718945004904435)⟩,⟨3662674170559490833,3662674170559490872⟩⟩,⟨⟨(-26017587387530315442),(-26017587387530315404)⟩,⟨3259206421729521293,3259206421729521331⟩⟩] +lemma kernel3_1_r0_14_eq : ∀ k : Fin 16, kernel3_1Expr 0 14 k = kernel3_1_r0_14 k := by decide +kernel +noncomputable def kernel3_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-26059236856323432936),(-26059236856323432898)⟩,⟨2878585605073432439,2878585605073432477⟩⟩,⟨⟨(-26093611647363850698),(-26093611647363850660)⟩,⟨2521030279326566788,2521030279326566826⟩⟩,⟨⟨(-26121602757254537158),(-26121602757254537092)⟩,⟨2186727675710908844,2186727675710908882⟩⟩,⟨⟨(-26144046555026927375),(-26144046555026927337)⟩,⟨1875836994783310454,1875836994783310492⟩⟩,⟨⟨(-26161723614307394509),(-26161723614307394471)⟩,⟨1588492526248515538,1588492526248515576⟩⟩,⟨⟨(-26175357691931856677),(-26175357691931856639)⟩,⟨1324806582015287927,1324806582015287956⟩⟩,⟨⟨(-26185614839746567488),(-26185614839746567450)⟩,⟨1084872233767219915,1084872233767219953⟩⟩,⟨⟨(-26193102637063001864),(-26193102637063001826)⟩,⟨868765847253869321,868765847253869359⟩⟩,⟨⟨(-26198369532036285518),(-26198369532036285480)⟩,⟨676549406384540468,676549406384540506⟩⟩,⟨⟨(-26201904281103083397),(-26201904281103083359)⟩,⟨508272621028732397,508272621028732435⟩⟩,⟨⟨(-26204135476539676780),(-26204135476539676742)⟩,⟨363974813197080634,363974813197080672⟩⟩,⟨⟨(-26205431153177705400),(-26205431153177705335)⟩,⟨243686576998115671,243686576998115699⟩⟩,⟨⟨(-26206098466337474789),(-26206098466337474751)⟩,⟨147431208443452597,147431208443452662⟩⟩,⟨⟨(-26206383434100735405),(-26206383434100735376)⟩,⟨75225901811658364,75225901811658402⟩⟩,⟨⟨(-26206470738140471879),(-26206470738140471841)⟩,⟨27082709883949552,27082709883949590⟩⟩,⟨⟨(-26206483578448683839),(-26206483578448683801)⟩,⟨3009265938329690,3009265938329728⟩⟩] +lemma kernel3_1_r0_15_eq : ∀ k : Fin 16, kernel3_1Expr 0 15 k = kernel3_1_r0_15 k := by decide +kernel +noncomputable def kernel3_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel3_1_r0_0,kernel3_1_r0_1,kernel3_1_r0_2,kernel3_1_r0_3,kernel3_1_r0_4,kernel3_1_r0_5,kernel3_1_r0_6,kernel3_1_r0_7,kernel3_1_r0_8,kernel3_1_r0_9,kernel3_1_r0_10,kernel3_1_r0_11,kernel3_1_r0_12,kernel3_1_r0_13,kernel3_1_r0_14,kernel3_1_r0_15] +lemma kernel3_1_r0_eq (i k : Fin 16) : kernel3_1Expr 0 i k = kernel3_1_r0 i k := by + fin_cases i + · exact kernel3_1_r0_0_eq k + · exact kernel3_1_r0_1_eq k + · exact kernel3_1_r0_2_eq k + · exact kernel3_1_r0_3_eq k + · exact kernel3_1_r0_4_eq k + · exact kernel3_1_r0_5_eq k + · exact kernel3_1_r0_6_eq k + · exact kernel3_1_r0_7_eq k + · exact kernel3_1_r0_8_eq k + · exact kernel3_1_r0_9_eq k + · exact kernel3_1_r0_10_eq k + · exact kernel3_1_r0_11_eq k + · exact kernel3_1_r0_12_eq k + · exact kernel3_1_r0_13_eq k + · exact kernel3_1_r0_14_eq k + · exact kernel3_1_r0_15_eq k +noncomputable def kernel3_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-1144205919813765918674440),(-1144205919813765913843723)⟩,⟨5970522256303726286774878,5970522256303726291606062⟩⟩,⟨⟨(-1143966019164407128599230),(-1143966019164407123770572)⟩,⟨5967215628970136942718650,5967215628970136947547773⟩⟩,⟨⟨(-1143486381250861904461229),(-1143486381250861899636669)⟩,⟨5960607959842762772997673,5960607959842762777822696⟩⟩,⟨⟨(-1142767331989789647285749),(-1142767331989789642467343)⟩,⟨5950710403863502362047349,5950710403863502366866216⟩⟩,⟨⟨(-1141809358131305267476111),(-1141809358131305262665934)⟩,⟨5937539653167613064594889,5937539653167613069405522⟩⟩,⟨⟨(-1140613104735175055994978),(-1140613104735175051195055)⟩,⟨5921117888936965638211508,5921117888936965643011882⟩⟩,⟨⟨(-1139179371848840269025608),(-1139179371848840264237957)⟩,⟨5901472717513922126273565,5901472717513922131061661⟩⟩,⟨⟨(-1137509110423586619977112),(-1137509110423586615203747)⟩,⟨5878637091039028629156658,5878637091039028633930462⟩⟩,⟨⟨(-1135603417513489632398119),(-1135603417513489627641027)⟩,⟨5852649212938869835964726,5852649212938869840722248⟩⟩,⟨⟨(-1133463530809578803010502),(-1133463530809578798271655)⟩,⟨5823552428651850455560380,5823552428651850460299648⟩⟩,⟨⟨(-1131090822568890888666362),(-1131090822568890883947702)⟩,⟨5791395102039027177951625,5791395102039027182670697⟩⟩,⟨⟨(-1128486793004644263090729),(-1128486793004644258394221)⟩,⟨5756230477984103832254626,5756230477984103836951536⟩⟩,⟨⟨(-1125653063209589766079794),(-1125653063209589761407298)⟩,⟨5718116531741027375665970,5718116531741027380338856⟩⟩,⟨⟨(-1122591367689614864905528),(-1122591367689614860258948)⟩,⟨5677115805639005555861693,5677115805639005560508652⟩⟩,⟨⟨(-1119303546588842554746709),(-1119303546588842550127864)⟩,⟨5633295233802949484097390,5633295233802949488716601⟩⟩,⟨⟨(-1115791537690729349860257),(-1115791537690729345270969)⟩,⟨5586725955592087117538611,5586725955592087122128250⟩⟩] +lemma kernel3_1_r1_0_eq : ∀ k : Fin 16, kernel3_1Expr 1 0 k = kernel3_1_r1_0 k := by decide +kernel +noncomputable def kernel3_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-1112057368281993370807821),(-1112057368281993366249846)⟩,⟨5537483118500579637839385,5537483118500579642397697⟩⟩,⟨⟨(-1108103146967569989680321),(-1108103146967569985155421)⟩,⟨5485645671301207766355314,5485645671301207770880536⟩⟩,⟨⟨(-1103931055525185724700192),(-1103931055525185720210012)⟩,⟨5431296148246409121941470,5431296148246409126431957⟩⟩,⟨⟨(-1099543340887559044416540),(-1099543340887559039962777)⟩,⟨5374520445169995824286922,5374520445169995828740975⟩⟩,⟨⟨(-1094942307338688383494705),(-1094942307338688379078985)⟩,⟨5315407588357644550186220,5315407588357644554602212⟩⟩,⟨⟨(-1090130309008192727333073),(-1090130309008192722956924)⟩,⟨5254049497074636496826521,5254049497074636501202925⟩⟩,⟨⟨(-1085109742744258851453575),(-1085109742744258847118558)⟩,⟨5190540740655266403665493,5190540740655266408000747⟩⟩,⟨⟨(-1079883041441462072873130),(-1079883041441462068580705)⟩,⟨5124978291069799240605106,5124978291069799244897750⟩⟩,⟨⟨(-1074452667894614134854396),(-1074452667894614130605980)⟩,⟨5057461271891818826492995,5057461271891818830741612⟩⟩,⟨⟨(-1068821109243911497630060),(-1068821109243911493427042)⟩,⟨4988090704591299917684755,4988090704591299921887954⟩⟩,⟨⟨(-1062990872070076944775422),(-1062990872070076940619146)⟩,⟨4916969253076786253204086,4916969253076786257360523⟩⟩,⟨⟨(-1056964478190981511327799),(-1056964478190981507219487)⟩,⟨4844200967403739814358111,4844200967403739818466565⟩⟩,⟨⟨(-1050744461203483232891306),(-1050744461203483228832247)⟩,⟨4769891027555534695663652,4769891027555534699722833⟩⟩,⟨⟨(-1044333363806010526966981),(-1044333363806010522958307)⟩,⟨4694145488188820536564154,4694145488188820540572930⟩⟩,⟨⟨(-1037733735928842020521371),(-1037733735928842016564173)⟩,⟨4617071025216216923947342,4617071025216216927904623⟩⟩,⟨⟨(-1030948133690185575456658),(-1030948133690185571551999)⟩,⟨4538774685076685273452513,4538774685076685277357235⟩⟩] +lemma kernel3_1_r1_1_eq : ∀ k : Fin 16, kernel3_1Expr 1 1 k = kernel3_1_r1_1 k := by decide +kernel +noncomputable def kernel3_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-1023979119187133645971915),(-1023979119187133642120818)⟩,⟨4459363637517643036251196,4459363637517643040102337⟩⟩,⟨⟨(-1016829261121467582820281),(-1016829261121467579023632)⟩,⟨4378944932683140635766517,4378944932683140639563187⟩⟩,⟨⟨(-1009501136251197754840406),(-1009501136251197751099161)⟩,⟨4297625263269436045941990,4297625263269436049683238⟩⟩,⟨⟨(-1001997331649755975405512),(-1001997331649755971720398)⟩,⟨4215510732473313127113116,4215510732473313130798213⟩⟩,⟨⟨(-994320447745996116421944),(-994320447745996112793815)⟩,⟨4132706628419749672005085,4132706628419749675633177⟩⟩,⟨⟨(-986473102109699165020293),(-986473102109699161449788)⟩,⟨4049317205714313792134322,4049317205714313795704771⟩⟩,⟨⟨(-978457933939207319062879),(-978457933939207315550703)⟩,⟨3965445474722227299958808,3965445474722227303470909⟩⟩,⟨⟨(-970277609200209879396544),(-970277609200209875943195)⟩,⟨3881192999130664890345250,3881192999130664893798506⟩⟩,⟨⟨(-961934826357647536945420),(-961934826357647533551522)⟩,⟨3796659702303847182657193,3796659702303847186050981⟩⟩,⟨⟨(-953432322636260260820207),(-953432322636260257486137)⟩,⟨3711943682892127174037945,3711943682892127177371886⟩⟩,⟨⟨(-944772880739539009211560),(-944772880739539005937828)⟩,⟨3627141040106858559667455,3627141040106858562941041⟩⟩,⟨⟨(-935959335951806513817215),(-935959335951806510604035)⟩,⟨3542345709022665888695084,3542345709022665891908101⟩⟩,⟨⟨(-926994583543892523019171),(-926994583543892519866979)⟩,⟨3457649306218103824351274,3457649306218103827503288⟩⟩,⟨⟨(-917881586399420335153727),(-917881586399420332062639)⟩,⟨3373140986014885060923340,3373140986014885064014234⟩⟩,⟨⟨(-908623382776111269595508),(-908623382776111266565807)⟩,⟨3288907307525157032339285,3288907307525157035368778⟩⟩,⟨⟨(-899223094114759671207550),(-899223094114759668239231)⟩,⟨3205032112665992035421646,3205032112665992038389742⟩⟩] +lemma kernel3_1_r1_2_eq : ∀ k : Fin 16, kernel3_1Expr 1 2 k = kernel3_1_r1_2 k := by decide +kernel +noncomputable def kernel3_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-889683932807641548385400),(-889683932807641545478694)⟩,⟨3121596415250589962993397,3121596415250589965899866⟩⟩,⟨⟨(-880009209838094167548227),(-880009209838094164702991)⟩,⟨3038678301216932626891410,3038678301216932629736396⟩⟩,⟨⟨(-870202342203831942460656),(-870202342203831939676992)⟩,⟨2956352840007016231120750,2956352840007016233904152⟩⟩,⟨⟨(-860266860038227034636731),(-860266860038227031914373)⟩,⟨2874692007063552599344398,2874692007063552602066483⟩⟩,⟨⟨(-850206413346254062430477),(-850206413346254059769495)⟩,⟨2793764617366383794860588,2793764617366383797521287⟩⟩,⟨⟨(-840024778275042081494016),(-840024778275042078894013)⟩,⟨2713636269887996097786094,2713636269887996100385805⟩⟩,⟨⟨(-829725862842951016877945),(-829725862842951014338831)⟩,⟨2634369302806628074322668,2634369302806628076861481⟩⟩,⟨⟨(-819313712055744677741070),(-819313712055744675262410)⟩,⟨2556022759276705915639460,2556022759276705918117812⟩⟩,⟨⟨(-808792512343712949051771),(-808792512343712946633430)⟩,⟨2478652363519851036384125,2478652363519851038802149⟩⟩,⟨⟨(-798166595259440951131290),(-798166595259440948772677)⟩,⟨2402310506965614823410222,2402310506965614825768512⟩⟩,⟨⟨(-787440440382267533686036),(-787440440382267531386886)⟩,⟨2327046244139508867959626,2327046244139508870258448⟩⟩,⟨⟨(-776618677382250316777454),(-776618677382250314537165)⟩,⟨2252905297966902063909709,2252905297966902066149667⟩⟩,⟨⟨(-765706087203587582471909),(-765706087203587580290156)⟩,⟨2179930074135015318371337,2179930074135015320552755⟩⟩,⟨⟨(-754707602334864569860503),(-754707602334864567736541)⟩,⟨2108159684131607834050074,2108159684131607836173698⟩⟩,⟨⟨(-743628306141117833794268),(-743628306141117831727721)⟩,⟨2037629976558044679329395,2037629976558044681395603⟩⟩,⟨⟨(-732473431240470626523361),(-732473431240470624513426)⟩,⟨1968373576296273985084077,1968373576296273987093671⟩⟩] +lemma kernel3_1_r1_3_eq : ∀ k : Fin 16, kernel3_1Expr 1 3 k = kernel3_1_r1_3 k := by decide +kernel +noncomputable def kernel3_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-721248356915909537860640),(-721248356915909535906866)⟩,⟨1900419931093816150156718,1900419931093816152110152⟩⟩,⟨⟨(-709958605560573917224868),(-709958605560573915326379)⟩,⟨1833795365118152406097313,1833795365118152407995462⟩⟩,⟨⟨(-698609838162642936160611),(-698609838162642934316862)⟩,⟨1768523139021855277700962,1768523139021855279544374⟩⟩,⟨⟨(-687207848843461280717744),(-687207848843461278927822)⟩,⟨1704623516052372888779234,1704623516052372890568821⟩⟩,⟨⟨(-675758558469877505284022),(-675758558469877503547381)⟩,⟨1642113833735492450746779,1642113833735492452483089⟩⟩,⟨⟨(-664268007368817113669957),(-664268007368817111985578)⟩,⟨1581008580659082217407219,1581008580659082219091270⟩⟩,⟨⟨(-652742347178818036806412),(-652742347178818035173658)⟩,⟨1521319477883650267727219,1521319477883650269359650⟩⟩,⟨⟨(-641187831879566886980134),(-641187831879566885398008)⟩,⟨1463055564508456464860019,1463055564508456466441828⟩⟩,⟨⟨(-629610808046343075420060),(-629610808046343073887965)⟩,⟨1406223286926255055250164,1406223286926255056781949⟩⟩,⟨⟨(-618017704381663141758853),(-618017704381663140275636)⟩,⟨1350826591306105551812460,1350826591306105553295373⟩⟩,⟨⟨(-606415020581283930286858),(-606415020581283928851832)⟩,⟨1296867018851937720476313,1296867018851937721911044⟩⟩,⟨⟨(-594809315596041107362977),(-594809315596041105975038)⟩,⟨1244343803394555865116569,1244343803394555866504221⟩⟩,⟨⟨(-583207195354745666380026),(-583207195354745665038526)⟩,⟨1193253970886376929621848,1193253970886376930963071⟩⟩,⟨⟨(-571615300016518422354371),(-571615300016518421058108)⟩,⟨1143592440381271741287557,1143592440381271742583552⟩⟩,⟨⟨(-560040290823500110428203),(-560040290823500109176494)⟩,⟨1095352126096272537006369,1095352126096272538257820⟩⟩,⟨⟨(-548488836626827650315345),(-548488836626827649106960)⟩,⟨1048524040167475436161006,1048524040167475437369144⟩⟩] +lemma kernel3_1_r1_4_eq : ∀ k : Fin 16, kernel3_1Expr 1 4 k = kernel3_1_r1_4 k := by decide +kernel +noncomputable def kernel3_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-536967600160116348851763),(-536967600160116347686048)⟩,⟨1003097395729056723101173,1003097395729056724266652⟩⟩,⟨⟨(-525483224135439824751759),(-525483224135439823627535)⟩,⟨959059709961790982066258,959059709961790983190258⟩⟩,⟨⟨(-514042317236966117755450),(-514042317236966116671907)⟩,⟨916396906775663914645384,916396906775663915728715⟩⟩,⟨⟨(-502651440087006644113913),(-502651440087006643069905)⟩,⟨875093418809972928641123,875093418809972929684931⟩⟩,⟨⟨(-491317091258285854283193),(-491317091258285853277986)⟩,⟨835132288453568259488593,835132288453568260493613⟩⟩,⟨⟨(-480045693404769318276601),(-480045693404769317309006)⟩,⟨796495267607475249637133,796495267607475250604553⟩⟩,⟨⟨(-468843579581425964117766),(-468843579581425963187029)⟩,⟨759162915931928758371500,759162915931928759302074⟩⟩,⟨⟨(-457716979820879096686955),(-457716979820879095791874)⟩,⟨723114697339723898553682,723114697339723899448615⟩⟩,⟨⟨(-446672008032056244623899),(-446672008032056243763804)⟩,⟨688329074517630400790139,688329074517630401650099⟩⟩,⟨⟨(-435714649282717804075831),(-435714649282717803249530)⟩,⟨654783601277324921950594,654783601277324922776773⟩⟩,⟨⟨(-424850747524168735555327),(-424850747524168734762010)⟩,⟨622455012556767942060108,622455012556767942853318⟩⟩,⟨⟨(-414085993812577494404547),(-414085993812577493643148)⟩,⟨591319311912098549878795,591319311912098550640100⟩⟩,⟨⟨(-403425915077184141603697),(-403425915077184140873475)⟩,⟨561351856358858217071511,561351856358858217801652⟩⟩,⟨⟨(-392875863481317874143083),(-392875863481317873442932)⟩,⟨532527438439608312588379,532527438439608313288462⟩⟩,⟨⟨(-382441006417605758399419),(-382441006417605757728566)⟩,⟨504820365412708243766219,504820365412708244437019⟩⟩,⟨⟨(-372126317174081597655840),(-372126317174081597013228)⟩,⟨478204535474112241730983,478204535474112242373557⟩⟩] +lemma kernel3_1_r1_5_eq : ∀ k : Fin 16, kernel3_1Expr 1 5 k = kernel3_1_r1_5 k := by decide +kernel +noncomputable def kernel3_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-361936566303138204852909),(-361936566303138204237872)⟩,⟨452653510940471228299607,452653510940471228914619⟩⟩,⟨⟨(-351876313720448349663800),(-351876313720448349075253)⟩,⟨428140588337547821288467,428140588337547821877003⟩⟩,⟨⟨(-341949901556148319250055),(-341949901556148318687285)⟩,⟨404638865352930673772834,404638865352930674335605⟩⟩,⟨⟨(-332161447775770642128003),(-332161447775770641589977)⟩,⟨382121304626239468212388,382121304626239468750431⟩⟩,⟨⟨(-322514840583664335006332),(-322514840583664334492346)⟩,⟨360560794363421316578648,360560794363421317092667⟩⟩,⟨⟨(-313013733616985072337255),(-313013733616985071846378)⟩,⟨339930205774336887509299,339930205774336888000224⟩⟩,⟨⟨(-303661541933804556769516),(-303661541933804556301042)⟩,⟨320202447344610280100647,320202447344610280569186⟩⟩,⟨⟨(-294461438794506122517005),(-294461438794506122070018)⟩,⟨301350515963666248329449,301350515963666248776514⟩⟩,⟨⟨(-285416353231427580382976),(-285416353231427579956867)⟩,⟨283347544941002971386368,283347544941002971812569⟩⟩,⟨⟨(-276528968397705088757907),(-276528968397705088351773)⟩,⟨266166848952054231489136,266166848952054231895376⟩⟩,⟨⟨(-267801720682483164574969),(-267801720682483164188169)⟩,⟨249781965963492192189666,249781965963492192576585⟩⟩,⟨⟨(-259236799576102749134720),(-259236799576102748766433)⟩,⟨234166696195525650729166,234166696195525651097584⟩⟩,⟨⟨(-250836148265575607292365),(-250836148265575606942021)⟩,⟨219295138185677018074253,219295138185677018424740⟩⟩,⟨⟨(-242601464937610570429329),(-242601464937610570096107)⟩,⟨205141722024695954361531,205141722024695954694906⟩⟩,⟨⟨(-234534204763683819173129),(-234534204763683818856478)⟩,⟨191681239840712980154955,191681239840712980471771⟩⟩,⟨⟨(-226635582539147494137258),(-226635582539147493836385)⟩,⟨178888873612479347375000,178888873612479347676047⟩⟩] +lemma kernel3_1_r1_6_eq : ∀ k : Fin 16, kernel3_1Expr 1 6 k = kernel3_1_r1_6 k := by decide +kernel +noncomputable def kernel3_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-218906575946151851583972),(-218906575946151851298398)⟩,⟨166740220396608879821537,166740220396608880107294⟩⟩,⟨⟨(-211347929408216978211986),(-211347929408216977940937)⟩,⟨155211315057163941976857,155211315057163942248100⟩⟩,⟨⟨(-203960158502629521730202),(-203960158502629521473204)⟩,⟨144278650588743042070025,144278650588743042327225⟩⟩,⟨⟨(-196743554895454656120953),(-196743554895454655877293)⟩,⟨133919196126464680461740,133919196126464680705610⟩⟩,⟨⟨(-189698191762838319045205),(-189698191762838318814456)⟩,⟨124110412737934449362342,124110412737934449593308⟩⟩,⟨⟨(-182823929661422603480287),(-182823929661422603261775)⟩,⟨114830267093463991444894,114830267093463991663629⟩⟩,⟨⟨(-176120422810099435712151),(-176120422810099435505424)⟩,⟨106057243111515269431520,106057243111515269638474⟩⟩,⟨⟨(-169587125744974295266355),(-169587125744974295070824)⟩,⟨97770351676605600509815,97770351676605600705579⟩⟩,⟨⟨(-163223300309291465786219),(-163223300309291465601507)⟩,⟨89949138526761642508284,89949138526761642693236⟩⟩,⟨⟨(-157028022940172832905683),(-157028022940172832731147)⟩,⟨82573690407087021747820,82573690407087021922602⟩⟩,⟨⟨(-151000192214330372058455),(-151000192214330371893750)⟩,⟨75624639585140896294867,75624639585140896459820⟩⟩,⟨⟨(-145138536615414295680082),(-145138536615414295524683)⟩,⟨69083166822644925811427,69083166822644925967073⟩⟩,⟨⟨(-139441622486339913456487),(-139441622486339913310031)⟩,⟨62931002896574356119537,62931002896574356266248⟩⟩,⟨⟨(-133907862130781775109893),(-133907862130781774971860)⟩,⟨57150428760974612923345,57150428760974613061635⟩⟩,⟨⟨(-128535522029018551706497),(-128535522029018551576579)⟩,⟨51724274438906139521216,51724274438906139651393⟩⟩,⟨⟨(-123322731134441212779945),(-123322731134441212656828)⟩,⟨46635916731784155679207,46635916731784155802578⟩⟩] +lemma kernel3_1_r1_7_eq : ∀ k : Fin 16, kernel3_1Expr 1 7 k = kernel3_1_r1_7 k := by decide +kernel +noncomputable def kernel3_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-118267489218285252113311),(-118267489218285251993561)⟩,⟨41869275831072195694784,41869275831072195814777⟩⟩,⟨⟨(-113367675231500039333900),(-113367675231500039217385)⟩,⟨37408810914832989249179,37408810914832989365926⟩⟩,⟨⟨(-108621055654110126212953),(-108621055654110126099656)⟩,⟨33239514809060390023154,33239514809060390136672⟩⟩,⟨⟨(-104025292803940176601426),(-104025292803940176491257)⟩,⟨29346907791033158519851,29346907791033158630228⟩⟩,⟨⟨(-99577953078153227698387),(-99577953078153227591393)⟩,⟨25717030609165604285302,25717030609165604392494⟩⟩,⟨⟨(-95276515102677863737000),(-95276515102677863633000)⟩,⟨22336436791000149411878,22336436791000149516061⟩⟩,⟨⟨(-91118377766260818300105),(-91118377766260818199152)⟩,⟨19192184308110193206916,19192184308110193308043⟩⟩,⟨⟨(-87100868117565391516901),(-87100868117565391418872)⟩,⟨16271826663774310829953,16271826663774310928146⟩⟩,⟨⟨(-83221249105431437536872),(-83221249105431437441754)⟩,⟨13563403466359584663929,13563403466359584759199⟩⟩,⟨⟨(-79476727144108836405386),(-79476727144108836313085)⟩,⟨11055430548426268802857,11055430548426268895301⟩⟩,⟨⟨(-75864459486963355612799),(-75864459486963355523252)⟩,⟨8736889688650336239639,8736889688650336329317⟩⟩,⟨⟨(-72381561393822442911548),(-72381561393822442824693)⟩,⟨6597217990765904912086,6597217990765904999062⟩⟩,⟨⟨(-69025113078770365650349),(-69025113078770365566215)⟩,⟨4626296970866121936897,4626296970866122021145⟩⟩,⟨⟨(-65792166426809596613094),(-65792166426809596531526)⟩,⟨2814441401577787459921,2814441401577787541592⟩⟩,⟨⟨(-62679751469371592914033),(-62679751469371592835009)⟩,⟨1152387958849801177156,1152387958849801256273⟩⟩,⟨⟨(-59684882610179039998602),(-59684882610179039922041)⟩,⟨(-368716285624549463997),(-368716285624549387352)⟩⟩] +lemma kernel3_1_r1_8_eq : ∀ k : Fin 16, kernel3_1Expr 1 8 k = kernel3_1_r1_8 k := by decide +kernel +noncomputable def kernel3_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-56804564594427904601946),(-56804564594427904527838)⟩,⟨(-1757325485990224880698),(-1757325485990224806512)⟩⟩,⟨⟨(-54035798215666655428830),(-54035798215666655357059)⟩,⟨(-3021506720048951742690),(-3021506720048951670851)⟩⟩,⟨⟨(-51375585756097869532184),(-51375585756097869462727)⟩,⟨(-4168951728065652431987),(-4168951728065652362468)⟩⟩,⟨⟨(-48820936157310922941684),(-48820936157310922874466)⟩,⟨(-5206988659760950359030),(-5206988659760950291757)⟩⟩,⟨⟨(-46368869919670987411013),(-46368869919670987346003)⟩,⟨(-6142593799055982318671),(-6142593799055982253615)⟩⟩,⟨⟨(-44016423729737153038762),(-44016423729737152975859)⟩,⟨(-6982403238423228560476),(-6982403238423228497531)⟩⟩,⟨⟨(-41760654816159775434794),(-41760654816159775373987)⟩,⟨(-7732724476902018097363),(-7732724476902018036524)⟩⟩,⟨⟨(-39598645035513250004135),(-39598645035513249945333)⟩,⟨(-8399547917958359073536),(-8399547917958359014708)⟩⟩,⟨⟨(-37527504690454988147394),(-37527504690454988090579)⟩,⟨(-8988558245404838488966),(-8988558245404838432128)⟩⟩,⟨⟨(-35544376083464514881540),(-35544376083464514826616)⟩,⟨(-9505145657547024664381),(-9505145657547024609445)⟩⟩,⟨⟨(-33646436810208850798572),(-33646436810208850745520)⟩,⟨(-9954416941587976951554),(-9954416941587976898497)⟩⟩,⟨⟨(-31830902797302593226478),(-31830902797302593175213)⟩,⟨(-10341206372102364355436),(-10341206372102364304168)⟩⟩,⟨⟨(-30095031089884627374414),(-30095031089884627324909)⟩,⟨(-10670086419086882369227),(-10670086419086882319724)⟩⟩,⟨⟨(-28436122395019742016240),(-28436122395019741968419)⟩,⟨(-10945378252704986404770),(-10945378252704986356955)⟩⟩,⟨⟨(-26851523387454432074946),(-26851523387454432028802)⟩,⟨(-11171162033372536538945),(-11171162033372536492807)⟩⟩,⟨⟨(-25338628784713915894628),(-25338628784713915850040)⟩,⟨(-11351286977278103008119),(-11351286977278102963546)⟩⟩] +lemma kernel3_1_r1_9_eq : ∀ k : Fin 16, kernel3_1Expr 1 9 k = kernel3_1_r1_9 k := by decide +kernel +noncomputable def kernel3_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-23894883198924155482698),(-23894883198924155439706)⟩,⟨(-11489381188798943911260),(-11489381188798943868284)⟩⟩,⟨⟨(-22517782773080892956099),(-22517782773080892914611)⟩,⟨(-11588861252562737242804),(-11588861252562737201339)⟩⟩,⟨⟨(-21204876609769996806696),(-21204876609769996766651)⟩,⟨(-11652941579117878787020),(-11652941579117878746997)⟩⟩,⟨⟨(-19953768000572451416774),(-19953768000572451378137)⟩,⟨(-11684643499313522773110),(-11684643499313522734498)⟩⟩,⟨⟨(-18762115464565912728703),(-18762115464565912691451)⟩,⟨(-11686804103556627780605),(-11686804103556627743386)⟩⟩,⟨⟨(-17627633604465743608998),(-17627633604465743573040)⟩,⟨(-11662084823109249176089),(-11662084823109249140167)⟩⟩,⟨⟨(-16548093789034723904897),(-16548093789034723870229)⟩,⟨(-11612979751517436189606),(-11612979751517436154975)⟩⟩,⟨⟨(-15521324670435109034535),(-15521324670435109001080)⟩,⟨(-11541823705125647914870),(-11541823705125647881453)⟩⟩,⟨⟨(-14545212545202291204036),(-14545212545202291171789)⟩,⟨(-11450800022429941779626),(-11450800022429941747420)⟩⟩,⟨⟨(-13617701567488882870794),(-13617701567488882839681)⟩,⟨(-11341948102761683775097),(-11341948102761683744032)⟩⟩,⟨⟨(-12736793823164440686420),(-12736793823164440656441)⟩,⟨(-11217170685473573382582),(-11217170685473573352648)⟩⟩,⟨⟨(-11900549273262077465863),(-11900549273262077436933)⟩,⟨(-11078240871423766650658),(-11078240871423766621775)⟩⟩,⟨⟨(-11107085575141604601502),(-11107085575141604573634)⟩,⟨(-10926808889124215231647),(-10926808889124215203826)⟩⟩,⟨⟨(-10354577789592268944250),(-10354577789592268917371)⟩,⟨(-10764408608438403815913),(-10764408608438403789084)⟩⟩,⟨⟨(-9641257981929174519683),(-9641257981929174493781)⟩,⟨(-10592463805183831491879),(-10592463805183831466031)⟩⟩,⟨⟨(-8965414724948597366880),(-8965414724948597341874)⟩,⟨(-10412294180418187164824),(-10412294180418187139872)⟩⟩] +lemma kernel3_1_r1_10_eq : ∀ k : Fin 16, kernel3_1Expr 1 10 k = kernel3_1_r1_10 k := by decide +kernel +noncomputable def kernel3_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-8325392511401000221530),(-8325392511401000197450)⟩,⟨(-10225121138567527040943),(-10225121138567527016916)⟩⟩,⟨⟨(-7719591083418918331231),(-7719591083418918308011)⟩,⟨(-10032073328892148325002),(-10032073328892148301832)⟩⟩,⟨⟨(-7146464686102196404221),(-7146464686102196381862)⟩,⟨(-9834191955083501077862),(-9834191955083501055560)⟩⟩,⟨⟨(-6604521252217376786203),(-6604521252217376764649)⟩,⟨(-9632435858045577172285),(-9632435858045577150785)⟩⟩,⟨⟨(-6092321524713324682514),(-6092321524713324661724)⟩,⟨(-9427686377138899417108),(-9427686377138899396373)⟩⟩,⟨⟨(-5608478123493267604646),(-5608478123493267584593)⟩,⟨(-9220751995356590345026),(-9220751995356590325026)⟩⟩,⟨⟨(-5151654562616048538224),(-5151654562616048518854)⟩,⟨(-9012372774062058442742),(-9012372774062058423422)⟩⟩,⟨⟨(-4720564223828156559460),(-4720564223828156540773)⟩,⟨(-8803224583048571400142),(-8803224583048571381502)⟩⟩,⟨⟨(-4313969292054502351629),(-4313969292054502333613)⟩,⟨(-8593923131784303034000),(-8593923131784303016029)⟩⟩,⟨⟨(-3930679658201335108182),(-3930679658201335090774)⟩,⟨(-8385027807784193193833),(-8385027807784193176461)⟩⟩,⟨⟨(-3569551794350427838929),(-3569551794350427822103)⟩,⟨(-8177045328103935723693),(-8177045328103935706900)⟩⟩,⟨⟨(-3229487606150859281230),(-3229487606150859264976)⟩,⟨(-7970433209983332266008),(-7970433209983332249795)⟩⟩,⟨⟨(-2909433266944457599353),(-2909433266944457583675)⟩,⟨(-7765603066677778789177),(-7765603066677778773539)⟩⟩,⟨⟨(-2608378037894208317557),(-2608378037894208302439)⟩,⟨(-7562923734509381827655),(-7562923734509381812565)⟩⟩,⟨⟨(-2325353078122533938702),(-2325353078122533924115)⟩,⟨(-7362724237144662173714),(-7362724237144662159156)⟩⟩,⟨⟨(-2059430248609099783022),(-2059430248609099768906)⟩,⟨(-7165296593065459836731),(-7165296593065459822640)⟩⟩] +lemma kernel3_1_r1_11_eq : ∀ k : Fin 16, kernel3_1Expr 1 11 k = kernel3_1_r1_11 k := by decide +kernel +noncomputable def kernel3_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-1809720913346375006995),(-1809720913346374993361)⟩,⟨(-6970898472144905461433),(-6970898472144905447822)⟩⟩,⟨⟨(-1575374741006179951850),(-1575374741006179938691)⟩,⟨(-6779755707172505767886),(-6779755707172505754750)⟩⟩,⟨⟨(-1355578510132400815246),(-1355578510132400802530)⟩,⟨(-6592064666092775966800),(-6592064666092775954106)⟩⟩,⟨⟨(-1149554920644393891549),(-1149554920644393879277)⟩,⟨(-6407994490631649622642),(-6407994490631649610386)⟩⟩,⟨⟨(-956561414212706313206),(-956561414212706301330)⟩,⟨(-6227689206885253181963),(-6227689206885253170104)⟩⟩,⟨⟨(-775889005853913074970),(-775889005853913063454)⟩,⟨(-6051269713337634474185),(-6051269713337634462682)⟩⟩,⟨⟨(-606861128884852957143),(-606861128884852946051)⟩,⟨(-5878835651658708220083),(-5878835651658708209007)⟩⟩,⟨⟨(-448832495178522039887),(-448832495178522029131)⟩,⟨(-5710467165511994668691),(-5710467165511994657948)⟩⟩,⟨⟨(-301187972474481792362),(-301187972474481781976)⟩,⟨(-5546226552474590425511),(-5546226552474590415136)⟩⟩,⟨⟨(-163341480315938094777),(-163341480315938084725)⟩,⟨(-5386159814040078053156),(-5386159814040078043118)⟩⟩,⟨⟨(-34734906013680841257),(-34734906013680831533)⟩,⟨(-5230298108539553550554),(-5230298108539553540834)⟩⟩,⟨⟨85162958126168255408,85162958126168264837⟩,⟨(-5078659111677376088851),(-5078659111677376079426)⟩⟩,⟨⟨196857455228216878995,196857455228216888098⟩,⟨(-4931248289237319050712),(-4931248289237319041610)⟩⟩,⟨⟨300829080991259289305,300829080991259298150⟩,⟨(-4788060086372172737810),(-4788060086372172728973)⟩⟩,⟨⟨397534476750204132544,397534476750204141120⟩,⟨(-4649079037746116626698),(-4649079037746116618126)⟩⟩,⟨⟨487407397786694062632,487407397786694070942⟩,⟨(-4514280802654896365322),(-4514280802654896357008)⟩⟩] +lemma kernel3_1_r1_12_eq : ∀ k : Fin 16, kernel3_1Expr 1 12 k = kernel3_1_r1_12 k := by decide +kernel +noncomputable def kernel3_1_r1_13 : Fin 16 → CBox := ![⟨⟨570859656339608924428,570859656339608932499⟩,⟨(-4383633129104517197459),(-4383633129104517189395)⟩⟩,⟨⟨648282038879625561488,648282038879625569373⟩,⟨(-4257096750685268153065),(-4257096750685268145180)⟩⟩,⟨⟨720045197317204597982,720045197317204605666⟩,⟨(-4134626219934846464528),(-4134626219934846456840)⟩⟩,⟨⟨786500513911008871413,786500513911008878934⟩,⟨(-4016170681742546716049),(-4016170681742546708529)⟩⟩,⟨⟨847980939734063918592,847980939734063925904⟩,⟨(-3901674590206264563409),(-3901674590206264556090)⟩⟩,⟨⟨904801806638193303435,904801806638193310584⟩,⟨(-3791078372215755505017),(-3791078372215755497865)⟩⟩,⟨⟨957261612733654584848,957261612733654591857⟩,⟨(-3684319040899466583567),(-3684319040899466576549)⟩⟩,⟨⟨1005642781470725944034,1005642781470725950872⟩,⟨(-3581330761938572634536),(-3581330761938572627688)⟩⟩,⟨⟨1050212394473514254235,1050212394473514260932⟩,⟨(-3482045375620818189703),(-3482045375620818183000)⟩⟩,⟨⟨1091222898333740989874,1091222898333740996427⟩,⟨(-3386392877378582307769),(-3386392877378582301207)⟩⟩,⟨⟨1128912785623982527635,1128912785623982534046⟩,⟨(-3294301859430410492766),(-3294301859430410486348)⟩⟩,⟨⟨1163507250436065702890,1163507250436065709180⟩,⟨(-3205699916023234245436),(-3205699916023234239136)⟩⟩,⟨⟨1195218818791316157150,1195218818791316163318⟩,⟨(-3120514014653739725613),(-3120514014653739719442)⟩⟩,⟨⟨1224247954305391657326,1224247954305391663373⟩,⟨(-3038670835531945316927),(-3038670835531945310874)⟩⟩,⟨⟨1250783639521767132461,1250783639521767138382⟩,⟨(-2960097081438075653700),(-2960097081438075647772)⟩⟩,⟨⟨1275003933354829989382,1275003933354829995174⟩,⟨(-2884719760015329622091),(-2884719760015329616285)⟩⟩] +lemma kernel3_1_r1_13_eq : ∀ k : Fin 16, kernel3_1Expr 1 13 k = kernel3_1_r1_13 k := by decide +kernel +noncomputable def kernel3_1_r1_14 : Fin 16 → CBox := ![⟨⟨1297076505106245218817,1297076505106245224513⟩,⟨(-2812466440436166727022),(-2812466440436166721315)⟩⟩,⟨⟨1317159145537005591842,1317159145537005597432⟩,⟨(-2743265486278298085787),(-2743265486278298080190)⟩⟩,⟨⟨1335400255492631772122,1335400255492631777609⟩,⟨(-2677046266348667810816),(-2677046266348667805322)⟩⟩,⟨⟨1351939312590561992092,1351939312590561997496⟩,⟨(-2613739345099336093486),(-2613739345099336088068)⟩⟩,⟨⟨1366907316487094839568,1366907316487094844869⟩,⟨(-2553276654188302238803),(-2553276654188302233487)⟩⟩,⟨⟨1380427213246537311036,1380427213246537316258⟩,⟨(-2495591646650897577691),(-2495591646650897572454)⟩⟩,⟨⟨1392614299337670822052,1392614299337670827171⟩,⟨(-2440619435063386993959),(-2440619435063386988836)⟩⟩,⟨⟨1403576605782478898626,1403576605782478903684⟩,⟨(-2388296914999786171510),(-2388296914999786166441)⟩⟩,⟨⟨1413415262979471607156,1413415262979471612128⟩,⟨(-2338562875005562958688),(-2338562875005562953702)⟩⟩,⟨⟨1422224846719074351015,1422224846719074355948⟩,⟨(-2291358094237770651313),(-2291358094237770646369)⟩⟩,⟨⟨1430093705901594523472,1430093705901594528329⟩,⟨(-2246625428850176327411),(-2246625428850176322538)⟩⟩,⟨⟨1437104272459401853917,1437104272459401858710⟩,⟨(-2204309888134009842383),(-2204309888134009837571)⟩⟩,⟨⟨1443333353974311529093,1443333353974311533822⟩,⟨(-2164358701359974024563),(-2164358701359974019823)⟩⟩,⟨⟨1448852409468889059027,1448852409468889063714⟩,⟨(-2126721376205024081196),(-2126721376205024076494)⟩⟩,⟨⟨1453727808836639626396,1453727808836639630999⟩,⟨(-2091349749588039683631),(-2091349749588039679016)⟩⟩,⟨⟨1458021076360931229788,1458021076360931234358⟩,⟨(-2058198031681768037148),(-2058198031681768032568)⟩⟩] +lemma kernel3_1_r1_14_eq : ∀ k : Fin 16, kernel3_1Expr 1 14 k = kernel3_1_r1_14 k := by decide +kernel +noncomputable def kernel3_1_r1_15 : Fin 16 → CBox := ![⟨⟨1461789118756151139542,1461789118756151144057⟩,⟨(-2027222843814198288186),(-2027222843814198283655)⟩⟩,⟨⟨1465084438147122020626,1465084438147122025089⟩,⟨(-1998383250920721641857),(-1998383250920721637375)⟩⟩,⟨⟨1467955330384312982506,1467955330384312986942⟩,⟨(-1971640789158919653368),(-1971640789158919648916)⟩⟩,⟨⟨1470446069072969968530,1470446069072969972920⟩,⟨(-1946959489250485160331),(-1946959489250485155925)⟩⟩,⟨⟨1472597075674050549036,1472597075674050553392⟩,⟨(-1924305896069494154558),(-1924305896069494150187)⟩⟩,⟨⟨1474445076013864986846,1474445076013864991187⟩,⟨(-1903649084952888858318),(-1903649084952888853954)⟩⟩,⟨⟨1476023243517676821228,1476023243517676825531⟩,⟨(-1884960675167477343508),(-1884960675167477339198)⟩⟩,⟨⟨1477361329460274714891,1477361329460274719168⟩,⟨(-1868214840927877087870),(-1868214840927877083578)⟩⟩,⟨⟨1478485780503759996357,1478485780503760000588⟩,⟨(-1853388320321501887065),(-1853388320321501882818)⟩⟩,⟨⟨1479419843769563170200,1479419843769563174396⟩,⟨(-1840460422459785825252),(-1840460422459785821040)⟩⟩,⟨⟨1480183659668064938965,1480183659668064943162⟩,⟨(-1829413033139226273614),(-1829413033139226269402)⟩⟩,⟨⟨1480794342685205965402,1480794342685205969599⟩,⟨(-1820230619261381456112),(-1820230619261381451899)⟩⟩,⟨⟨1481266050301173815247,1481266050301173819428⟩,⟨(-1812900232227547979514),(-1812900232227547975321)⟩⟩,⟨⟨1481610040191700916984,1481610040191700921181⟩,⟨(-1807411510491340641311),(-1807411510491340637099)⟩⟩,⟨⟨1481834715837736581652,1481834715837736585803⟩,⟨(-1803756681420671403839),(-1803756681420671399672)⟩⟩,⟨⟨1481945660644309163530,1481945660644309167681⟩,⟨(-1801930562589547151457),(-1801930562589547147290)⟩⟩] +lemma kernel3_1_r1_15_eq : ∀ k : Fin 16, kernel3_1Expr 1 15 k = kernel3_1_r1_15 k := by decide +kernel +noncomputable def kernel3_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel3_1_r1_0,kernel3_1_r1_1,kernel3_1_r1_2,kernel3_1_r1_3,kernel3_1_r1_4,kernel3_1_r1_5,kernel3_1_r1_6,kernel3_1_r1_7,kernel3_1_r1_8,kernel3_1_r1_9,kernel3_1_r1_10,kernel3_1_r1_11,kernel3_1_r1_12,kernel3_1_r1_13,kernel3_1_r1_14,kernel3_1_r1_15] +lemma kernel3_1_r1_eq (i k : Fin 16) : kernel3_1Expr 1 i k = kernel3_1_r1 i k := by + fin_cases i + · exact kernel3_1_r1_0_eq k + · exact kernel3_1_r1_1_eq k + · exact kernel3_1_r1_2_eq k + · exact kernel3_1_r1_3_eq k + · exact kernel3_1_r1_4_eq k + · exact kernel3_1_r1_5_eq k + · exact kernel3_1_r1_6_eq k + · exact kernel3_1_r1_7_eq k + · exact kernel3_1_r1_8_eq k + · exact kernel3_1_r1_9_eq k + · exact kernel3_1_r1_10_eq k + · exact kernel3_1_r1_11_eq k + · exact kernel3_1_r1_12_eq k + · exact kernel3_1_r1_13_eq k + · exact kernel3_1_r1_14_eq k + · exact kernel3_1_r1_15_eq k +noncomputable def kernel3_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-1511678163832360828980017040),(-1511678163832360827751588557)⟩,⟨1548849793322216696934051310,1548849793322216698158138952⟩⟩,⟨⟨(-1510981092322430703611371047),(-1510981092322430702383201775)⟩,⟨1548485829661761671069892469,1548485829661761672293722418⟩⟩,⟨⟨(-1509587866234979288831814565),(-1509587866234979287604166078)⟩,⟨1547758009256895411830083221,1547758009256895413053395425⟩⟩,⟨⟨(-1507500317601341249017859383),(-1507500317601341247790992989)⟩,⟨1546666546502159586556542948,1546666546502159587779077621⟩⟩,⟨⟨(-1504721189889080298237681647),(-1504721189889080297011858314)⟩,⟨1545211764391450793124203681,1545211764391450794345701377⟩⟩,⟨⟨(-1501254132518609818432116877),(-1501254132518609817207597072)⟩,⟨1543394096189201682231607931,1543394096189201683451809701⟩⟩,⟨⟨(-1497103693571909333098266713),(-1497103693571909331875310310)⟩,⟨1541214087639825938535881775,1541214087639825939754529252⟩⟩,⟨⟨(-1492275310710340544249170480),(-1492275310710340543028036568)⟩,⟨1538672399699455041754385022,1538672399699455042971220620⟩⟩,⟨⟨(-1486775300322762354664719804),(-1486775300322762353445666731)⟩,⟨1535769811770174844740889808,1535769811770174845955656682⟩⟩,⟨⟨(-1480610844929302861374677140),(-1480610844929302860157962061)⟩,⟨1532507225413264166387534873,1532507225413264167599977356⟩⟩,⟨⟨(-1473789978870259957071575765),(-1473789978870259955857455095)⟩,⟨1528885668514367241401637345,1528885668514367242611500501⟩⟩,⟨⟨(-1466321572313662980776724743),(-1466321572313662979565453146)⟩,⟨1524906299870117697761582446,1524906299870117698968613086⟩⟩,⟨⟨(-1458215313619027695486197915),(-1458215313619027694278029552)⟩,⟨1520570414162493595762610011,1520570414162493596966555435⟩⟩,⟨⟨(-1449481690098767412590875170),(-1449481690098767411386061518)⟩,⟨1515879447284139848162683449,1515879447284139849363293636⟩⟩,⟨⟨(-1440131967222575790137569496),(-1440131967222575788936361961)⟩,⟨1510834981975063869796506444,1510834981975063870993531417⟩⟩,⟨⟨(-1430178166313862944342851624),(-1430178166313862943145498036)⟩,⟨1505438753728509229872917274,1505438753728509231066110628⟩⟩] +lemma kernel3_1_r2_0_eq : ∀ k : Fin 16, kernel3_1Expr 2 0 k = kernel3_1_r2_0 k := by decide +kernel +noncomputable def kernel3_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-1419633040790997051380106086),(-1419633040790997050186855026)⟩,⟨1499692656921455790639928009,1499692656921455791829042572⟩⟩,⟨⟨(-1408510051009669385486037865),(-1408510051009669384297132546)⟩,⟨1493598751123097349779608494,1493598751123097350964402444⟩⟩,⟨⟨(-1396823337766152343477026527),(-1396823337766152342292711893)⟩,⟨1487159267532821763999044316,1487159267532821765179274084⟩⟩,⟨⟨(-1384587694524547863388746399),(-1384587694524547862209260846)⟩,⟨1480376615497675011447973007,1480376615497675012623401549⟩⟩,⟨⟨(-1371818538434318013291990637),(-1371818538434318012117575914)⟩,⟨1473253389058039167239569517,1473253389058039168409956433⟩⟩,⟨⟨(-1358531880207440530858683859),(-1358531880207440529689572127)⟩,⟨1465792373469302699084080388,1465792373469302700249194818⟩⟩,⟨⟨(-1344744292927429764571574818),(-1344744292927429763408003263)⟩,⟨1457996551646656030506715394,1457996551646656031666321458⟩⟩,⟨⟨(-1330472879865197779132410524),(-1330472879865197777974605388)⟩,⟨1449869110479810428679826840,1449869110479810429833699558⟩⟩,⟨⟨(-1315735241379291309613598434),(-1315735241379291308461793732)⟩,⟨1441413446964416650548579874,1441413446964416651696486492⟩⟩,⟨⟨(-1300549440980417796637476004),(-1300549440980417795491889646)⟩,⟨1432633174097252335709630587,1432633174097252336851354399⟩⟩,⟨⟨(-1284933970642358028313951429),(-1284933970642358027174811670)⟩,⟨1423532126482852977736452146,1423532126482852978871766108⟩⟩,⟨⟨(-1268907715443344241129203693),(-1268907715443344239996721756)⟩,⟨1414114365600177743217788094,1414114365600177744346482129⟩⟩,⟨⟨(-1252489917623751413132030387),(-1252489917623751412006431299)⟩,⟨1404384184679123947659525760,1404384184679123948781376006⟩⟩,⟨⟨(-1235700140147496745344567737),(-1235700140147496744226052410)⟩,⟨1394346113138226366554224715,1394346113138226367669031343⟩⟩,⟨⟨(-1218558229855859176857694665),(-1218558229855859175746481249)⟩,⟨1384004920536691731662516663,1384004920536691732770062619⟩⟩,⟨⟨(-1201084280303508876009060460),(-1201084280303508874905342286)⟩,⟨1373365619996014994401821198,1373365619996014995501914175⟩⟩] +lemma kernel3_1_r2_1_eq : ∀ k : Fin 16, kernel3_1Expr 2 1 k = kernel3_1_r2_1 k := by decide +kernel +noncomputable def kernel3_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-1183298594367368187553896824),(-1183298594367368186457889631)⟩,⟨1362433471048790820248326202,1362433471048790821340751502⟩⟩,⟨⟨(-1165221646719503298438883236),(-1165221646719503297350767251)⟩,⟨1351213981874958291455351974,1351213981874958292539930310⟩⟩,⟨⟨(-1146874046255563407571201439),(-1146874046255563406491183638)⟩,⟨1339712910888584381431086906,1339712910888584382507612274⟩⟩,⟨⟨(-1128276498570335711165739221),(-1128276498570335710093992185)⟩,⟨1327936267641386402868892124,1327936267641386403937192807⟩⟩,⟨⟨(-1109449768571765153217099896),(-1109449768571765152153828402)⟩,⟨1315890313012497930493125002,1315890313012497931552997140⟩⟩,⟨⟨(-1090414643324293668006255303),(-1090414643324293666951616763)⟩,⟨1303581558657477990293128783,1303581558657477991344415736⟩⟩,⟨⟨(-1071191895211601576167195551),(-1071191895211601575121384763)⟩,⟨1291016765693229753982038797,1291016765693229755024546597⟩⟩,⟨⟨(-1051802245507781962666006698),(-1051802245507781961629172827)⟩,⟨1278202942599311689881821346,1278202942599311690915401527⟩⟩,⟨⟨(-1032266328444646458075644810),(-1032266328444646457047982179)⟩,⟨1265147342320069277807823250,1265147342320069278832282254⟩⟩,⟨⟨(-1012604655861248232985086892),(-1012604655861248231966725935)⟩,⟨1251857458556066372083951795,1251857458556066373099159782⟩⟩,⟨⟨(-992837582519816793356327922),(-992837582519816792347450287)⟩,⟨1238341021237428803514713892,1238341021237428804520489888⟩⟩,⟨⟨(-972985272170132193504289026),(-972985272170132192505017979)⟩,⟨1224605991175905032740443700,1224605991175905033736664950⟩⟩,⟨⟨(-953067664441927726182203458),(-953067664441927725192720354)⟩,⟨1210660553896675409263005349,1210660553896675410249491109⟩⟩,⟨⟨(-933104442642205496619316928),(-933104442642205495639724549)⟩,⟨1196513112655178427928176914,1196513112655178428904824799⟩⟩,⟨⟨(-913115002531385374129213603),(-913115002531385373159679546)⟩,⟨1182172280648444805365340380,1182172280648444806331983303⟩⟩,⟨⟨(-893118422148992827261853711),(-893118422148992826302473206)⟩,⟨1167646872434613796450417713,1167646872434613797406960760⟩⟩] +lemma kernel3_1_r2_2_eq : ∀ k : Fin 16, kernel3_1Expr 2 2 k = kernel3_1_r2_2 k := by decide +kernel +noncomputable def kernel3_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-873133432756134620933907371),(-873133432756134619984850850)⟩,⟨1152945894578426739513420073,1152945894578426740459693263⟩⟩,⟨⟨(-853178390958324156116248751),(-853178390958324155177586436)⟩,⟨1138078535544526547693936958,1138078535544526548629870253⟩⟩,⟨⟨(-833271252068312545214564137),(-833271252068312544286448786)⟩,⟨1123054154864315478798056692,1123054154864315479723497682⟩⟩,⟨⟨(-813429544764470796578828715),(-813429544764470795661325750)⟩,⟨1107882271605914430716002054,1107882271605914431630885420⟩⟩,⟨⟨(-793670347095967418245453137),(-793670347095967417338717856)⟩,⟨1092572552180403470887436268,1092572552180403471791606995⟩⟩,⟨⟨(-774010263881510208083598371),(-774010263881510207187670459)⟩,⟨1077134797520984538234606767,1077134797520984539128025153⟩⟩,⟨⟨(-754465405543787948053819522),(-754465405543787947168836234)⟩,⟨1061578929674973586460633573,1061578929674973587343162532⟩⟩,⟨⟨(-735051368416975169940883502),(-735051368416975169066879220)⟩,⟨1045914977851582439308379389,1045914977851582440179984447⟩⟩,⟨⟨(-715783216559770060682462131),(-715783216559770059819580762)⟩,⟨1030153063971273231006120679,1030153063971273231866658043⟩⟩,⟨⟨(-696675465101441730200515378),(-696675465101441729348760669)⟩,⟨1014303387765044908769148800,1014303387765044909618614502⟩⟩,⟨⟨(-677742065143289023226727774),(-677742065143289022386220912)⟩,⟨998376211474327850778121791,998376211474327851616394640⟩⟩,⟨⟨(-658996390232780003699757473),(-658996390232780002870501123)⟩,⟨982381844204206836836549300,982381844204206837663626343⟩⟩,⟨⟨(-640451224422470876441081317),(-640451224422470875623202642)⟩,⟨966330625984453775764039227,966330625984453776579793245⟩⟩,⟨⟨(-622118751920617527111630940),(-622118751920617526305102288)⟩,⟨950232911594320927655288826,950232911594320928459747062⟩⟩,⟨⟨(-604010548335214409039125582),(-604010548335214408244051749)⟩,⟨934099054208215906866228709,934099054208215907659286196⟩⟩,⟨⟨(-586137573508046660760381172),(-586137573508046659976732996)⟩,⟨917939388920246462285826868,917939388920246463067512303⟩⟩] +lemma kernel3_1_r2_3_eq : ∀ k : Fin 16, kernel3_1Expr 2 3 k = kernel3_1_r2_3 k := by decide +kernel +noncomputable def kernel3_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-568510165930244564699237545),(-568510165930244563927131689)⟩,⟨901764216206182784194039347,901764216206182784964235860⟩⟩,⟨⟨(-551138038725807066320986900),(-551138038725807065560357944)⟩,⟨885583785381636703468028439,885583785381636704226800855⟩⟩,⟨⟨(-534030277184635081931332716),(-534030277184635081182268861)⟩,⟨869408278115201392074913818,869408278115201392822173615⟩⟩,⟨⟨(-517195337821807315727823370),(-517195337821807314990264147)⟩,⟨853247792054934732444370558,853247792054934733180177577⟩⟩,⟨⟨(-500641048935162293706723062),(-500641048935162292980766524)⟩,⟨837112324625908982390166026,837112324625908983114421852⟩⟩,⟨⟨(-484374612628740605704655694),(-484374612628740604990207675)⟩,⟨821011757055595159293433280,821011757055595160006231342⟩⟩,⟨⟨(-468402608265310388364959931),(-468402608265310387662092152)⟩,⟨804955838682610935365376019,804955838682610936066644137⟩⟩,⟨⟨(-452730997307065374415256422),(-452730997307065373723878245)⟩,⟨788954171602845733363103947,788954171602845734052931988⟩⟩,⟨⟨(-437365129499665781948957829),(-437365129499665781269157156)⟩,⟨773016195705197740126608453,773016195705197740804908036⟩⟩,⟨⟨(-422309750351104124141245471),(-422309750351104123472892385)⟩,⟨757151174147127862696416194,757151174147127863363316360⟩⟩,⟨⟨(-407569009853435580850646899),(-407569009853435580193796929)⟩,⟨741368179317969829908488478,741368179317969830563933124⟩⟩,⟨⟨(-393146472392229382302016095),(-393146472392229381656550160)⟩,⟨725676079335449609169008316,725676079335449609813115634⟩⟩,⟨⟨(-379045127785685717122854988),(-379045127785685716488842380)⟩,⟨710083525118178183211063332,710083525118178183843763436⟩⟩,⟨⟨(-365267403392732435833808358),(-365267403392732435211094474)⟩,⟨694598938074007703309477867,694598938074007703930924393⟩⟩,⟨⟨(-351815177227076094909395603),(-351815177227076094298020361)⟩,⟨679230498441101220743968614,679230498441101221354120978⟩⟩,⟨⟨(-338689792012139818673923205),(-338689792012139818073741277)⟩,⟨663986134315380497414565042,663986134315380498013567593⟩⟩] +lemma kernel3_1_r2_4_eq : ∀ k : Fin 16, kernel3_1Expr 2 4 k = kernel3_1_r2_4 k := by decide +kernel +noncomputable def kernel3_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-325892070110081476092653131),(-325892070110081475503726387)⟩,⟨648873511394705342635442685,648873511394705343223232896⟩⟩,⟨⟨(-313422329256653468157936389),(-313422329256653467580077327)⟩,⟨633900023466722529213911511,633900023466722529790675823⟩⟩,⟨⟨(-301280399032541940122188688),(-301280399032541939555422447)⟩,⟨619072783663823945604897939,619072783663823946170610478⟩⟩,⟨⟨(-289465638001008663752970066),(-289465638001008663197127822)⟩,⟨604398616505093748896831558,604398616505093749451660110⟩⟩,⟨⟨(-277976951441151636519776563),(-277976951441151635974900947)⟩,⟨589884050741524416605816255,589884050741524417149717464⟩⟩,⟨⟨(-266812809605897369274491492),(-266812809605897368740378025)⟩,⟨575535313017163136276516969,575535313017163136809694226⟩⟩,⟨⟨(-255971266433933967585072665),(-255971266433933967061732668)⟩,⟨561358322355234015617937263,561358322355234016140378464⟩⟩,⟨⟨(-245449978645182926980129342),(-245449978645182926467373575)⟩,⟨547358685474688804929241346,547358685474688805441134663⟩⟩,⟨⟨(-235246225150080982236450729),(-235246225150080981734315764)⟩,⟨533541692939089289412300835,533541692939089289913608944⟩⟩,⟨⟨(-225356926703891824830572465),(-225356926703891824338827741)⟩,⟨519912316136237620133640707,519912316136237620624593056⟩⟩,⟨⟨(-215778665738480091687025898),(-215778665738480091205670185)⟩,⟨506475205083565170528401101,506475205083565171008998120⟩⟩,⟨⟨(-206507706305444499913285151),(-206507706305444499442112183)⟩,⟨493234687050983650129032329,493234687050983650599479208⟩⟩,⟨⟨(-197540014066209933874106621),(-197540014066209933413135994)⟩,⟨480194765989710751194427557,480194765989710751654703932⟩⟩,⟨⟨(-188871276266605181341567194),(-188871276266605180890558198)⟩,⟨467359122752521977660611423,467359122752521978110956903⟩⟩,⟨⟨(-180496921635588401549029398),(-180496921635588401107969707)⟩,⟨454731116087964714280931904,454731116087964714721358018⟩⟩,⟨⟨(-172412140150109987868650158),(-172412140150109987437319897)⟩,⟨442313784388312944218265154,442313784388312944648990727⟩⟩] +lemma kernel3_1_r2_5_eq : ∀ k : Fin 16, kernel3_1Expr 2 5 k = kernel3_1_r2_5 k := by decide +kernel +noncomputable def kernel3_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-164611902610605247478314113),(-164611902610605247056731048)⟩,⟨430109848168452865265079005,430109848168452865686085519⟩⟩,⟨⟨(-157090979974269663454993139),(-157090979974269663042896013)⟩,⟨418121713250481132381657713,418121713250481132793205350⟩⟩,⟨⟨(-149843962396069384131464780),(-149843962396069383728831651)⟩,⟨406351474626577270675366025,406351474626577271077475947⟩⟩,⟨⟨(-142865277930360634665746108),(-142865277930360634272347110)⟩,⟨394800920970687197886443573,394800920970687198279344636⟩⟩,⟨⟨(-136149210849015414029096498),(-136149210849015413644932972)⟩,⟨383471539767731534258205727,383471539767731534641895855⟩⟩,⟨⟨(-129689919535058517495327424),(-129689919535058517120137640)⟩,⟨372364523027434752961547097,372364523027434753336287011⟩⟩,⟨⟨(-123481453913994070816573598),(-123481453913994070450327548)⟩,⟨361480773548462069258283705,361480773548462069624102662⟩⟩,⟨⟨(-117517772388220031705278461),(-117517772388220031347739820)⟩,⟨350820911697351679798516983,350820911697351680155650365⟩⟩,⟨⟨(-111792758243178473051787396),(-111792758243178472702957150)⟩,⟨340385282665740544072128663,340385282665740544420574795⟩⟩,⟨⟨(-106300235497150301296675943),(-106300235497150300956280540)⟩,⟨330173964168600993595741802,330173964168600993935773282⟩⟩,⟨⟨(-101033984169858304257574826),(-101033984169858303925577774)⟩,⟨320186774545630407869547515,320186774545630408201200144⟩⟩,⟨⟨(-95987754948275617053202253),(-95987754948275616729364189)⟩,⟨310423281227563121546592794,310423281227563121870105051⟩⟩,⟨⟨(-91155283231232114875844237),(-91155283231232114560153596)⟩,⟨300882809528997573402221348,300882809528997573717604160⟩⟩,⟨⟨(-86530302537553962744636676),(-86530302537553962436825457)⟩,⟨291564451729346338480174302,291564451729346338787694800⟩⟩,⟨⟨(-82106557265547527107921145),(-82106557265547526807948009)⟩,⟨282467076403714963763448891,282467076403714964063147775⟩⟩,⟨⟨(-77877814794634975070155268),(-77877814794634974777780896)⟩,⟨273589337965889407441938917,273589337965889407734054714⟩⟩] +lemma kernel3_1_r2_6_eq : ∀ k : Fin 16, kernel3_1Expr 2 6 k = kernel3_1_r2_6 k := by decide +kernel +noncomputable def kernel3_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-73837876922853042103050588),(-73837876922853041818267197)⟩,⟨264929686386152497470445927,264929686386152497754985838⟩⟩,⟨⟨(-69980590636727566395209822),(-69980590636727566117742841)⟩,⟨256486377047347590817392094,256486377047347591094629903⟩⟩,⟨⟨(-66299858212724470499055093),(-66299858212724470228859777)⟩,⟨248257480703452322465670913,248257480703452322735650791⟩⟩,⟨⟨(-62789646652044021936489500),(-62789646652044021673329472)⟩,⟨240240893505906252003858987,240240893505906252266816596⟩⟩,⟨⟨(-59443996452961643119480542),(-59443996452961642863336656)⟩,⟨232434347064042191865693534,232434347064042192121647499⟩⟩,⟨⟨(-56257029727218608807969374),(-56257029727218608558580221)⟩,⟨224835418507190557427702642,224835418507190557676913682⟩⟩,⟨⟨(-53222957669124127352961714),(-53222957669124127110280576)⟩,⟨217441540517347511403323162,217441540517347511645837484⟩⟩,⟨⟨(-50336087388042119347782142),(-50336087388042119111578088)⟩,⟨210250011302709148019800311,210250011302709148255848219⟩⟩,⟨⟨(-47590828116798141826760128),(-47590828116798141597018643)⟩,⟨203258004483863601547303429,203258004483863601776898986⟩⟩,⟨⟨(-44981696810252077053597286),(-44981696810252076830057372)⟩,⟨196462578865988942446310592,196462578865988942669714185⟩⟩,⟨⟨(-42503323149839158592875392),(-42503323149839158375489595)⟩,⟨189860688072015348161471924,189860688072015348378730566⟩⟩,⟨⟨(-40150453971285376549911095),(-40150453971285376338456096)⟩,⟨183449190013363820109307037,183449190013363820320643502⟩⟩,⟨⟨(-37917957133953961225789328),(-37917957133953961020243012)⟩,⟨177224856176559462583894754,177224856176559462789330764⟩⟩,⟨⟨(-35800824851379050834902449),(-35800824851379050635019982)⟩,⟨171184380705724192211451945,171184380705724192411231812⟩⟩,⟨⟨(-33794176503493197363417096),(-33794176503493197169151392)⟩,⟨165324389262671268325270515,165324389262671268519440948⟩⟩,⟨⟨(-31893260951860220517691410),(-31893260951860220328828484)⟩,⟨159641447648042250646204297,159641447648042250834978820⟩⟩] +lemma kernel3_1_r2_7_eq : ∀ k : Fin 16, kernel3_1Expr 2 7 k = kernel3_1_r2_7 k := by decide +kernel +noncomputable def kernel3_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-30093458379887958055611421),(-30093458379887957872137065)⟩,⟨154132070168636439515774867,154132070168636439699167356⟩⟩,⟨⟨(-28390281680521201307905187),(-28390281680521201129577312)⟩,⟨148792727737774628352402776,148792727737774628530654874⟩⟩,⟨⟨(-26779377414308645097321962),(-26779377414308644924094824)⟩,⟨143619855697204779234963437,143619855697204779408120568⟩⟩,⟨⟨(-25256526361004629840320359),(-25256526361004629671990691)⟩,⟨138609861350689317987364490,138609861350689318155629537⟩⟩,⟨⟨(-23817643688012861423714657),(-23817643688012861260260953)⟩,⟨133759131201005069651208718,133759131201005069814602902⟩⟩,⟨⟨(-22458778759011587957650997),(-22458778759011587798851710)⟩,⟨129064037883631005726428933,129064037883631005885173437⟩⟩,⟨⟨(-21176114606024627080423177),(-21176114606024626926234603)⟩,⟨124520946791890198811312391,124520946791890198965450653⟩⟩,⟨⟨(-19965967088027152430269130),(-19965967088027152280499659)⟩,⟨120126222389745589673349049,120126222389745589823072356⟩⟩,⟨⟨(-18824783758906423340800737),(-18824783758906423195436131)⟩,⟨115876234209819938663248607,115876234209819938808570973⟩⟩,⟨⟨(-17749142467242958119733848),(-17749142467242957978559547)⟩,⟨111767362535514883086814015,111767362535514883227949696⟩⟩,⟨⟨(-16735749709944351097277714),(-16735749709944350960252695)⟩,⟨107796003767339220393121454,107796003767339220530111256⟩⟩,⟨⟨(-15781438761259367238868616),(-15781438761259367105813609)⟩,⟨103958575474719872827737731,103958575474719872960760663⟩⟩,⟨⟨(-14883167598131421974835239),(-14883167598131421845731846)⟩,⟨100251521135658553875835360,100251521135658554004909635⟩⟩,⟨⟨(-14038016642225283034743613),(-14038016642225282909397003)⟩,⟨96671314567611619510274202,96671314567611619635594406⟩⟩,⟨⟨(-13243186338285895165312471),(-13243186338285895043684741)⟩,⟨93214464053909167367243930,93214464053909167488847794⟩⟩,⟨⟨(-12495994587770532130986728),(-12495994587770532012911194)⟩,⟨89877516170891883965659219,89877516170891884083713215⟩⟩] +lemma kernel3_1_r2_8_eq : ∀ k : Fin 16, kernel3_1Expr 2 8 k = kernel3_1_r2_8 k := by decide +kernel +noncomputable def kernel3_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-11793874055941716723887465),(-11793874055941716609354461)⟩,⟨86657059321730661211080435,86657059321730661325594087⟩⟩,⟨⟨(-11134369369824969214855826),(-11134369369824969103677588)⟩,⟨83549726983605289602006663,83549726983605289713167536⟩⟩,⟨⟨(-10515134223628627817201285),(-10515134223628627709343191)⟩,⟨80552200675555686061189805,80552200675555686169032385⟩⟩,⟨⟨(-9933928407398617279408189),(-9933928407398617174716271)⟩,⟨77661212654883610475971265,77661212654883610580649356⟩⟩,⟨⟨(-9388614773844695870500401),(-9388614773844695768960729)⟩,⟨74873548350476493500376620,74873548350476493601904039⟩⟩,⟨⟨(-8877156157431629451092726),(-8877156157431629352538078)⟩,⟨72186048541849973964241550,72186048541849974062785362⟩⟩,⟨⟨(-8397612258983825085239860),(-8397612258983824989639138)⟩,⟨69595611293064434048422324,69595611293064434144013526⟩⟩,⟨⟨(-7948136508209756681399554),(-7948136508209756588611269)⟩,⟨67099193650965866343828395,67099193650965866436608343⟩⟩,⟨⟨(-7526972915717227081872233),(-7526972915717226991889760)⟩,⟨64693813117435651174643938,64693813117435651264619177⟩⟩,⟨⟨(-7132452925265973187017128),(-7132452925265973099681693)⟩,⟨62376548905510272909925191,62376548905510272997254371⟩⟩,⟨⟨(-6762992276193815032720258),(-6762992276193814948004266)⟩,⟨60144542989353800731978030,60144542989353800816688670⟩⟩,⟨⟨(-6417087885159605399541513),(-6417087885159605317315631)⟩,⟨57995000958136343656366855,57995000958136343738588184⟩⟩,⟨⟨(-6093314755573435940091908),(-6093314755573435860347060)⟩,⟨55925192683893973571683680,55925192683893973651424713⟩⟩,⟨⟨(-5790322922334342942175682),(-5790322922334342864771090)⟩,⟨53932452813423148355025573,53932452813423148432426997⟩⟩,⟨⟨(-5506834438770246413039831),(-5506834438770246337951405)⟩,⟨52014181094198830655885270,52014181094198830730971120⟩⟩,⟨⟨(-5241640411975849586878936),(-5241640411975849513988917)⟩,⟨50167842544203649483371349,50167842544203649556259307⟩⟩] +lemma kernel3_1_r2_9_eq : ∀ k : Fin 16, kernel3_1Expr 2 9 k = kernel3_1_r2_9 k := by decide +kernel +noncomputable def kernel3_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-4993598092073218695142520),(-4993598092073218624449783)⟩,⟨48390967475418923488902769,48390967475418923559593917⟩⟩,⟨⟨(-4761628020277963079004745),(-4761628020277963010375162)⟩,⟨46681151380560438084370776,46681151380560438152999169⟩⟩,⟨⟨(-4544711240042278947164086),(-4544711240042278880576862)⟩,⟨45036054692445755341276286,45036054692445755407862681⟩⟩,⟨⟨(-4341886574965285499872329),(-4341886574965285435220690)⟩,⟨43453402425158662544198886,43453402425158662608850001⟩⟩,⟨⟨(-4152247976611509632113944),(-4152247976611509569393477)⟩,⟨41930983705933159158214111,41930983705933159220934329⟩⟩,⟨⟨(-3974941944860282923184860),(-3974941944860282862278812)⟩,⟨40466651206417057598908386,40466651206417057659814406⟩⟩,⟨⟨(-3809165022922215606482540),(-3809165022922215547373263)⟩,⟨39058320481696622931943513,39058320481696622991052958⟩⟩,⟨⟨(-3654161368703633341966007),(-3654161368703633284557021)⟩,⟨37703969225171361826788122,37703969225171361884197430⟩⟩,⟨⟨(-3509220403775561113029089),(-3509220403775561057321980)⟩,⟨36401636447064615273167053,36401636447064615328874622⟩⟩,⟨⟨(-3373674540810019455018279),(-3373674540810019400903119)⟩,⟨35149421584043393226240019,35149421584043393280355735⟩⟩,⟨⟨(-3246896989982431068418361),(-3246896989982431015880452)⟩,⟨33945483547102146300521932,33945483547102146353060481⟩⟩,⟨⟨(-3128299644504071137046243),(-3128299644504071085998601)⟩,⟨32788039714541984800207840,32788039714541984851256171⟩⟩,⟨⟨(-3017331045141879401912740),(-3017331045141879352355001)⟩,⟨31675364876551163895662663,31675364876551163945221133⟩⟩,⟨⟨(-2913474423303644934110193),(-2913474423303644885946482)⟩,⟨30605790137566241285740570,30605790137566241333905024⟩⟩,⟨⟨(-2816245822013560261765784),(-2816245822013560214984121)⟩,⟨29577701782267817821045247,29577701782267817867827659⟩⟩,⟨⟨(-2725192293875344215820961),(-2725192293875344170343081)⟩,⟨28589540110741684211360423,28589540110741684256839034⟩⟩] +lemma kernel3_1_r2_10_eq : ∀ k : Fin 16, kernel3_1Expr 2 10 k = kernel3_1_r2_10 k := by decide +kernel +noncomputable def kernel3_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-2639890174916428967468781),(-2639890174916428923300400)⟩,⟨27639798248016867596731487,27639798248016867640900580⟩⟩,⟨⟨(-2559943433025936752339650),(-2559943433025936709389634)⟩,⟨26727020932877711503445987,26727020932877711546396674⟩⟩,⟨⟨(-2484982089540151329136299),(-2484982089540151287395083)⟩,⟨25849803290538808882731993,25849803290538808924473836⟩⟩,⟨⟨(-2414660712390719173732567),(-2414660712390719133129920)⟩,⟨25006789593470289361281625,25006789593470289401884839⟩⟩,⟨⟨(-2348656979111691128038308),(-2348656979111691088577144)⟩,⟨24196672014367464504551591,24196672014367464544013264⟩⟩,⟨⟨(-2286670307900534983461170),(-2286670307900534945063223)⟩,⟨23418189374973867974389626,23418189374973868012788009⟩⟩,⟨⟨(-2228420554844222002936358),(-2228420554844221965594210)⟩,⟨22670125894190889638136469,22670125894190889675478981⟩⟩,⟨⟨(-2173646775353241586592604),(-2173646775353241550243239)⟩,⟨21951309938640988654620779,21951309938640988690970425⟩⟩,⟨⟨(-2122106047792777182778810),(-2122106047792777147429635)⟩,⟨21260612778595277689396323,21260612778595277724745702⟩⟩,⟨⟨(-2073572357260160449557071),(-2073572357260160415134181)⟩,⟨20596947351930405408832699,20596947351930405443255705⟩⟩,⟨⟨(-2027835537430019608571556),(-2027835537430019575069498)⟩,⟨19959267038544350039058882,19959267038544350072560970⟩⟩,⟨⟨(-1984700268372198415762086),(-1984700268372198383124317)⟩,⟨19346564447436118495972234,19346564447436118528609939⟩⟩,⟨⟨(-1943985128241530286540380),(-1943985128241530254772431)⟩,⟨18757870218440498066527000,18757870218440498098294799⟩⟩,⟨⟨(-1905521696741936031019378),(-1905521696741936000057324)⟩,⟨18192251840405941111766314,18192251840405941142728124⟩⟩,⟨⟨(-1869153708279145561306830),(-1869153708279145531146932)⟩,⟨17648812487411329842728627,17648812487411329872888192⟩⟩,⟨⟨(-1834736252735741456750398),(-1834736252735741427341888)⟩,⟨17126689874435667748749577,17126689874435667778157659⟩⟩] +lemma kernel3_1_r2_11_eq : ∀ k : Fin 16, kernel3_1Expr 2 11 k = kernel3_1_r2_11 k := by decide +kernel +noncomputable def kernel3_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-1802135021828349417763993),(-1802135021828349389117095)⟩,⟨16625055133723530139082908,16625055133723530167729293⟩⟩,⟨⟨(-1771225599038868312089636),(-1771225599038868284142779)⟩,⟨16143111712928190919598798,16143111712928190947545049⟩⟩,⟨⟨(-1741892791148898640788706),(-1741892791148898613539586)⟩,⟨15680094295963502842534395,15680094295963502869782823⟩⟩,⟨⟨(-1714029999448297553805011),(-1714029999448297527208136)⟩,⟨15235267747354589874275324,15235267747354589900871417⟩⟩,⟨⟨(-1687538628734412017442967),(-1687538628734411991505729)⟩,⟨14807926080745932663298095,14807926080745932689234470⟩⟩,⟨⟨(-1662327532267415846733556),(-1662327532267415821403550)⟩,⟨14397391452103189114682817,14397391452103189140011871⟩⟩,⟨⟨(-1638312490898741961151685),(-1638312490898741936427888)⟩,⟨14003013178031771705923495,14003013178031771730646262⟩⟩,⟨⟨(-1615415724643342508653974),(-1615415724643342484495474)⟩,⟨13624166779530467200592057,13624166779530467224749445⟩⟩,⟨⟨(-1593565435021952331038474),(-1593565435021952307455927)⟩,⟨13260253051401887938154796,13260253051401887961736158⟩⟩,⟨⟨(-1572695376556241782205877),(-1572695376556241759149092)⟩,⟨12910697157452934449969067,12910697157452934473024589⟩⟩,⟨⟨(-1552744455857327934576574),(-1552744455857327912045590)⟩,⟨12574947751537369637834484,12574947751537369660364133⟩⟩,⟨⟨(-1533656356806210375811576),(-1533656356806210353769552)⟩,⟨12252476124418695903212417,12252476124418695925253032⟩⟩,⟨⟨(-1515379190382985840035607),(-1515379190382985818491280)⟩,⟨11942775376364429404230048,11942775376364429425772904⟩⟩,⟨⟨(-1497865167759884815848861),(-1497865167759884794758833)⟩,⟨11645359615322223295066698,11645359615322223316155186⟩⟩,⟨⟨(-1481070295331004384660518),(-1481070295331004364025773)⟩,⟨11359763180473751744493443,11359763180473751765126587⟩⟩,⟨⟨(-1464954090408855747705846),(-1464954090408855727493112)⟩,⟨11085539890913481833743195,11085539890913481853954264⟩⟩] +lemma kernel3_1_r2_12_eq : ∀ k : Fin 16, kernel3_1Expr 2 12 k = kernel3_1_r2_12 k := by decide +kernel +noncomputable def kernel3_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-1449479316374300734923005),(-1449479316374300715144394)⟩,⟨10822262319156091322890893,10822262319156091342667787⟩⟩,⟨⟨(-1434611736121943424912214),(-1434611736121943405525110)⟩,⟨10569521089138005287515618,10569521089138005306900945⟩⟩,⟨⟨(-1420319882697419238423502),(-1420319882697419219429598)⟩,⟨10326924198345001639507702,10326924198345001658499778⟩⟩,⟨⟨(-1406574846076155175182332),(-1406574846076155156551516)⟩,⟨10094096363668762601927667,10094096363668762620556601⟩⟩,⟨⟨(-1393350075084952488982253),(-1393350075084952470724125)⟩,⟨9870678390570325216473441,9870678390570325234729643⟩⟩,⟨⟨(-1380621193518077216164584),(-1380621193518077198242729)⟩,⟨9656326565107319224700108,9656326565107319242619987⟩⟩,⟨⟨(-1368365829548362107293280),(-1368365829548362089710044)⟩,⟨9450712068364397294201489,9450712068364397311782706⟩⟩,⟨⟨(-1356563457581069021348426),(-1356563457581069004076445)⟩,⟨9253520412812094762337052,9253520412812094779606968⟩⟩,⟨⟨(-1345195251743891476525038),(-1345195251743891459576354)⟩,⟨9064450900108250328532886,9064450900108250345479471⟩⟩,⟨⟨(-1334243950250463595657474),(-1334243950250463578996338)⟩,⟨8883216099847834284144811,8883216099847834300803807⟩⟩,⟨⟨(-1323693729917066653125183),(-1323693729917066636754366)⟩,⟨8709541348761338134685321,8709541348761338151053963⟩⟩,⟨⟨(-1313530090152880865099568),(-1313530090152880848994141)⟩,⟨8543164269858562330856762,8543164269858562346959977⟩⟩,⟨⟨(-1303739745783120382523731),(-1303739745783120366693778)⟩,⟨8383834311013492917088811,8383834311013492932916523⟩⟩,⟨⟨(-1294310528101724381859357),(-1294310528101724366273760)⟩,⟨8231312302486790800698269,8231312302486790816281592⟩⟩,⟨⟨(-1285231293585974755118427),(-1285231293585974739780426)⟩,⟨8085370032885048310147635,8085370032885048325483334⟩⟩,⟨⟨(-1276491839739495636978702),(-1276491839739495621865390)⟩,⟨7945789843060227412703337,7945789843060227427814317⟩⟩] +lemma kernel3_1_r2_13_eq : ∀ k : Fin 16, kernel3_1Expr 2 13 k = kernel3_1_r2_13 k := by decide +kernel +noncomputable def kernel3_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-1268082827562591878506870),(-1268082827562591863631236)⟩,⟨7812364237458424145639127,7812364237458424160512409⟩⟩,⟨⟨(-1259995710179837362668913),(-1259995710179837347999184)⟩,⟨7684895512434156943359779,7684895512434156958027129⟩⟩,⟨⟨(-1252222667184268581065540),(-1252222667184268566605221)⟩,⟨7563195401054615426628486,7563195401054615441086405⟩⟩,⟨⟨(-1244756544285516378397636),(-1244756544285516364125607)⟩,⟨7447084733927603616418621,7447084733927603630688225⟩⟩,⟨⟨(-1237590797875764239910990),(-1237590797875764225837707)⟩,⟨7336393115597149748413375,7336393115597149762484219⟩⟩,⟨⟨(-1230719444152602230649002),(-1230719444152602216747197)⟩,⟨7230958616061825322609998,7230958616061825336509343⟩⟩,⟨⟨(-1224137012461700746270927),(-1224137012461700732544338)⟩,⟨7130627476982618865476534,7130627476982618879200647⟩⟩,⟨⟨(-1217838502544807998467030),(-1217838502544807984896035)⟩,⟨7035253832159653530842767,7035253832159653544411266⟩⟩,⟨⟨(-1211819345399930974816999),(-1211819345399930961414192)⟩,⟨6944699441870038410852040,6944699441870038424252342⟩⟩,⟨⟨(-1206075367480743435298919),(-1206075367480743422036496)⟩,⟨6858833440672625005422553,6858833440672625018682455⟩⟩,⟨⟨(-1200602757981328588336934),(-1200602757981328575218761)⟩,⟨6777532098299333485810781,6777532098299333498926421⟩⟩,⟨⟨(-1195398038970360726450179),(-1195398038970360713457928)⟩,⟨6700678593266955594979842,6700678593266955607969545⟩⟩,⟨⟨(-1190458038155811403383160),(-1190458038155811390527468)⟩,⟨6628162798857875911042061,6628162798857875923895199⟩⟩,⟨⟨(-1185779864077283433204207),(-1185779864077283420460556)⟩,⟨6559881081132930272077532,6559881081132930284818615⟩⟩,⟨⟨(-1181360883538181271815664),(-1181360883538181259188022)⟩,⟨6495736108654594425338346,6495736108654594437963414⟩⟩,⟨⟨(-1177198701104169712134363),(-1177198701104169699605484)⟩,⟨6435636673613827550650958,6435636673613827563177252⟩⟩] +lemma kernel3_1_r2_14_eq : ∀ k : Fin 16, kernel3_1Expr 2 14 k = kernel3_1_r2_14 k := by decide +kernel +noncomputable def kernel3_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-1173291140507804003450298),(-1173291140507803991033426)⟩,⟨6379497524069149132344306,6379497524069149144758591⟩⟩,⟨⟨(-1169636227811882340633907),(-1169636227811882328302928)⟩,⟨6327239207021873077110036,6327239207021873089438419⟩⟩,⟨⟨(-1166232176196024065890408),(-1166232176196024053649264)⟩,⟨6278787922066833489997166,6278787922066833502235709⟩⟩,⟨⟨(-1163077372242260812110849),(-1163077372242260799943231)⟩,⟨6234075385373389438204873,6234075385373389450369883⟩⟩,⟨⟨(-1160170363606089107483088),(-1160170363606089095399764)⟩,⟨6193038703766972194628424,6193038703766972206709139⟩⟩,⟨⟨(-1157509847969516555686143),(-1157509847969516543664313)⟩,⟨6155620258696921944603030,6155620258696921956622244⟩⟩,⟨⟨(-1155094663182183485808676),(-1155094663182183473852237)⟩,⟨6121767599891838825401348,6121767599891838837355169⟩⟩,⟨⟨(-1152923778505700818103263),(-1152923778505700806196625)⟩,⟨6091433348519135231093705,6091433348519135242997721⟩⟩,⟨⟨(-1150996286884954730495435),(-1150996286884954718651483)⟩,⟨6064575109680914816355836,6064575109680914828197169⟩⟩,⟨⟨(-1149311398178330525091030),(-1149311398178330513285445)⟩,⟨6041155394093713069901144,6041155394093713081704107⟩⟩,⟨⟨(-1147868433286641988002243),(-1147868433286641976238832)⟩,⟨6021141548815011219599911,6021141548815011231360700⟩⟩,⟨⟨(-1146666819128057792996717),(-1146666819128057781260440)⟩,⟨6004505696894777893617078,6004505696894777905350730⟩⟩,⟨⟨(-1145706084413531638986923),(-1145706084413531627288630)⟩,⟨5991224685845601311225598,5991224685845601322921272⟩⟩,⟨⟨(-1144985856184205665543861),(-1144985856184205653861655)⟩,⟨5981280044840250123952442,5981280044840250135632026⟩⟩,⟨⟨(-1144505857079004472982326),(-1144505857079004461319881)⟩,⟨5974657950560745893960677,5974657950560745905620503⟩⟩,⟨⟨(-1144265903307206465682847),(-1144265903307206454025569)⟩,⟨5971349201638248123274922,5971349201638248134929580⟩⟩] +lemma kernel3_1_r2_15_eq : ∀ k : Fin 16, kernel3_1Expr 2 15 k = kernel3_1_r2_15 k := by decide +kernel +noncomputable def kernel3_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel3_1_r2_0,kernel3_1_r2_1,kernel3_1_r2_2,kernel3_1_r2_3,kernel3_1_r2_4,kernel3_1_r2_5,kernel3_1_r2_6,kernel3_1_r2_7,kernel3_1_r2_8,kernel3_1_r2_9,kernel3_1_r2_10,kernel3_1_r2_11,kernel3_1_r2_12,kernel3_1_r2_13,kernel3_1_r2_14,kernel3_1_r2_15] +lemma kernel3_1_r2_eq (i k : Fin 16) : kernel3_1Expr 2 i k = kernel3_1_r2 i k := by + fin_cases i + · exact kernel3_1_r2_0_eq k + · exact kernel3_1_r2_1_eq k + · exact kernel3_1_r2_2_eq k + · exact kernel3_1_r2_3_eq k + · exact kernel3_1_r2_4_eq k + · exact kernel3_1_r2_5_eq k + · exact kernel3_1_r2_6_eq k + · exact kernel3_1_r2_7_eq k + · exact kernel3_1_r2_8_eq k + · exact kernel3_1_r2_9_eq k + · exact kernel3_1_r2_10_eq k + · exact kernel3_1_r2_11_eq k + · exact kernel3_1_r2_12_eq k + · exact kernel3_1_r2_13_eq k + · exact kernel3_1_r2_14_eq k + · exact kernel3_1_r2_15_eq k +noncomputable def kernel3_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-41994851992362123391959589136),(-41994851992362123369165194824)⟩,⟨(-64072494330235614286065196342),(-64072494330235614262758975855)⟩⟩,⟨⟨(-41995498032745596669846423355),(-41995498032745596647055514878)⟩,⟨(-64053435951407703355280382575),(-64053435951407703331977699716)⟩⟩,⟨⟨(-41996780404909649649378252882),(-41996780404909649626594356180)⟩,⟨(-64015331845494858535525107792),(-64015331845494858512229540695)⟩⟩,⟨⟨(-41998679715088615674267350807),(-41998679715088615651493990326)⟩,⟨(-63958207309589261480785102433),(-63958207309589261457500227850)⟩⟩,⟨⟨(-42001166931183193878893218959),(-42001166931183193856133916721)⟩,⟨(-63882100273322062007201552061),(-63882100273322061983930944511)⟩⟩,⟨⟨(-42004203452876476691398522332),(-42004203452876476668656797483)⟩,⟨(-63787061279591455347497338528),(-63787061279591455324244569911)⟩⟩,⟨⟨(-42007741204883857839499947919),(-42007741204883857816779316298)⟩,⟨(-63673153458761641266461932793),(-63673153458761641243230572004)⟩⟩,⟨⟨(-42011722753133158763980210367),(-42011722753133158741284182173)⟩,⟨(-63540452496243503561279232840),(-63540452496243503538072843504)⟩⟩,⟨⟨(-42016081443620957668698453282),(-42016081443620957646030536119)⟩,⟨(-63389046593346755510111153598),(-63389046593346755486933297190)⟩⟩,⟨⟨(-42020741563641128804106347164),(-42020741563641128781470038367)⟩,⟨(-63219036421272994513549392549),(-63219036421272994490403620722)⟩⟩,⟨⟨(-42025618525032077833449222675),(-42025618525032077810848019320)⟩,⟨(-63030535068099748018412986606),(-63030535068099747995302851338)⟩⟩,⟨⟨(-42030619069040171371717901025),(-42030619069040171349155283328)⟩,⟨(-62823667978587319226678346008),(-62823667978587319203607382945)⟩⟩,⟨⟨(-42035641492348485547059355240),(-42035641492348485524538809610)⟩,⟨(-62598572886623196701805542254),(-62598572886623196678777293973)⟩⟩,⟨⟨(-42040575893772321806166052372),(-42040575893772321783691035566)⟩,⟨(-62355399740103112993742364181),(-62355399740103112970760344134)⟩⟩,⟨⟨(-42045304441076041938490979821),(-42045304441076041916064963862)⟩,⟨(-62094310618033653958530562363),(-62094310618033653935598300197)⟩⟩,⟨⟨(-42049701657319743958885228026),(-42049701657319743936511643060)⟩,⟨(-61815479639628756020910435262),(-61815479639628755998031419262)⟩⟩] +lemma kernel3_1_r3_0_eq : ∀ k : Fin 16, kernel3_1Expr 3 0 k = kernel3_1_r3_0 k := by decide +kernel +noncomputable def kernel3_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-42053634726099223409156615788),(-42053634726099223386838923550)⟩,⟨(-61519092865161599418715810526),(-61519092865161599395893561715)⟩⟩,⟨⟨(-42056963814998629997371227425),(-42056963814998629975112820055)⟩,⟨(-61205348188324419826396833087),(-61205348188324419803634803276)⟩⟩,⟨⟨(-42059542416532328294482296470),(-42059542416532328272286616352)⟩,⟨(-60874455219841718626885263265),(-60874455219841718604186955879)⟩⟩,⟨⟨(-42061217705810796230855269428),(-42061217705810796208725672177)⟩,⟨(-60526635162077344496001898136),(-60526635162077344473370730157)⟩⟩,⟨⟨(-42061830914125040848378423843),(-42061830914125040826318344616)⟩,⟨(-60162120674373027452724380189),(-60162120674373027430163849788)⟩⟩,⟨⟨(-42061217717605073197760763357),(-42061217717605073175773501229)⟩,⟨(-59781155728855242770170764166),(-59781155728855242747684233432)⟩⟩,⟨⟨(-42059208640070560853675514711),(-42059208640070560831764478903)⟩,⟨(-59383995456448827439286617846),(-59383995456448827416877560958)⟩⟩,⟨⟨(-42055629469155965873486613559),(-42055629469155965851655056882)⟩,⟨(-58970905982839616769695530145),(-58970905982839616747367264725)⟩⟩,⟨⟨(-42050301684758377716217691943),(-42050301684758377694469024933)⟩,⟨(-58542164254134552604309259590),(-58542164254134552582065263347)⟩⟩,⟨⟨(-42043042898823964896169046477),(-42043042898823964874506439445)⟩,⟨(-58098057851976265451816185227),(-58098057851976265429659694868)⟩⟩,⟨⟨(-42033667305458596534675473410),(-42033667305458596513102299040)⟩,⟨(-57638884797880066779074652476),(-57638884797880066757009109790)⟩⟩,⟨⟨(-42021986140319826029455323101),(-42021986140319826007974699124)⟩,⟨(-57164953346574608919420459489),(-57164953346574608897449050424)⟩⟩,⟨⟨(-42007808148221183887959246207),(-42007808148221183866574554680)⟩,⟨(-56676581768143170496429988221),(-56676581768143170474556166233)⟩⟩,⟨⟨(-41990940057855694603215808359),(-41990940057855694581930057429)⟩,⟨(-56174098118780584522211299190),(-56174098118780584500438142010)⟩⟩,⟨⟨(-41971187062523811178902951858),(-41971187062523811157719474325)⟩,⟨(-55657840000001211519488368546),(-55657840000001211497819282175)⟩⟩,⟨⟨(-41948353305731646577461006690),(-41948353305731646556382749748)⟩,⟨(-55128154306156025728044654140),(-55128154306156025706482657032)⟩⟩] +lemma kernel3_1_r3_1_eq : ∀ k : Fin 16, kernel3_1Expr 3 1 k = kernel3_1_r3_1 k := by decide +kernel +noncomputable def kernel3_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-41922242370508567630490544591),(-41922242370508567609520871538)⟩,⟨(-54585396960141770756301504541),(-54585396960141770734850035530)⟩⟩,⟨⟨(-41892657771278994529233157380),(-41892657771278994508374863717)⟩,⟨(-54029932637212181530713158053),(-54029932637212181509375084788)⟩⟩,⟨⟨(-41859403447111705089608617831),(-41859403447111705068864991932)⟩,⟨(-53462134476830379332024731698),(-53462134476830379310803419497)⟩⟩,⟨⟨(-41822284255161160611474734391),(-41822284255161160590848515174)⟩,⟨(-52882383782532631165089475459),(-52882383782532631143987736873)⟩⟩,⟨⟨(-41781106463109427620246070269),(-41781106463109427599740585914)⟩,⟨(-52291069709806616822760228486),(-52291069709806616801781470778)⟩⟩,⟨⟨(-41735678239414239997174340000),(-41735678239414239976792145929)⟩,⟨(-51688588942022048262557870430),(-51688588942022048241704723014)⟩⟩,⟨⟨(-41685810140168695850102103688),(-41685810140168695829846437805)⟩,⟨(-51075345354487806515604442266),(-51075345354487806494880223067)⟩⟩,⟨⟨(-41631315591381073155222215125),(-41631315591381073135095568729)⟩,⟨(-50451749666747560617998767831),(-50451749666747560597406043220)⟩⟩,⟨⟨(-41572011365489330605125611362),(-41572011365489330585131298658)⟩,⟨(-49818219083264959932669759050),(-49818219083264959912211925259)⟩⟩,⟨⟨(-41507718050934080175063969675),(-41507718050934080155204238195)⟩,⟨(-49175176922689784805002733338),(-49175176922689784784682112438)⟩⟩,⟨⟨(-41438260513626212044801925086),(-41438260513626212025079954821)⟩,⟨(-48523052235937730615247526492),(-48523052235937730595067380654)⟩⟩,⟨⟨(-41363468349160947891566739367),(-41363468349160947871984734218)⟩,⟨(-47862279413358608223107015453),(-47862279413358608203069623872)⟩⟩,⟨⟨(-41283176324648912649728325747),(-41283176324648912630289549740)⟩,⟨(-47193297781310482957027846444),(-47193297781310482937136556841)⟩⟩,⟨⟨(-41197224809056854756949342931),(-41197224809056854737655724113)⟩,⟨(-46516551188500451018442998099),(-46516551188500450998699812526)⟩⟩,⟨⟨(-41105460190975906989879400025),(-41105460190975906970734050766)⟩,⟨(-45832487582496166543358779159),(-45832487582496166523766893124)⟩⟩,⟨⟨(-41007735282763749243777142258),(-41007735282763749224781940306)⟩,⟨(-45141558576855679328555047994),(-45141558576855679309116413361)⟩⟩] +lemma kernel3_1_r3_2_eq : ∀ k : Fin 16, kernel3_1Expr 3 2 k = kernel3_1_r3_2 k := by decide +kernel +noncomputable def kernel3_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-40903909710038684296162310591),(-40903909710038684277320511032)⟩,⟨(-44444219009366412704956568673),(-44444219009366412685674524979)⟩⟩,⟨⟨(-40793850285538428853231409447),(-40793850285538428834544530567)⟩,⟨(-43740926491926990104175657071),(-43740926491926990085051794192)⟩⟩,⟨⟨(-40677431366394303688298735127),(-40677431366394303669769810011)⟩,⟨(-43032140952647891975005896807),(-43032140952647891956043330549)⟩⟩,⟨⟨(-40554535193912414391849794424),(-40554535193912414373480337945)⟩,⟨(-42318324170788374964309329271),(-42318324170788374945509645881)⟩⟩,⟨⟨(-40425052214997271171380145300),(-40425052214997271153173329899)⟩,⟨(-41599939305187495511494318998),(-41599939305187495492860774199)⟩⟩,⟨⟨(-40288881384400012195507539554),(-40288881384400012177464500147)⟩,⟨(-40877450416886233896388975759),(-40877450416886233877922772521)⟩⟩,⟨⟨(-40145930447022866952922503444),(-40145930447022866935046180539)⟩,⟨(-40151321986675397992456786235),(-40151321986675397974160945818)⟩⟩,⟨⟨(-39996116199563607634851493550),(-39996116199563607617143005675)⟩,⟨(-39422018428339987318061797274),(-39422018428339987299937505237)⟩⟩,⟨⟨(-39839364730838358237456005575),(-39839364730838358219918509062)⟩,⟨(-38690003598404810559017978015),(-38690003598404810541068471786)⟩⟩,⟨⟨(-39675611640178120617664415429),(-39675611640178120600298549042)⟩,⟨(-37955740303218172137151625953),(-37955740303218172119377606590)⟩⟩,⟨⟨(-39504802233353579182609494078),(-39504802233353579165418090997)⟩,⟨(-37219689804240180833985143536),(-37219689804240180816389521391)⟩⟩,⟨⟨(-39326891695543994003582223468),(-39326891695543993986565977115)⟩,⟨(-36482311322429498938738206117),(-36482311322429498921321735681)⟩⟩,⟨⟨(-39141845240929106786325046016),(-39141845240929106769486992748)⟩,⟨(-35744061542646965779848978836),(-35744061542646965762614773074)⟩⟩,⟨⟨(-38949638238547774781970190812),(-38949638238547774765310536529)⟩,⟨(-35005394119016326740259162099),(-35005394119016326723207482533)⟩⟩,⟨⟨(-38750256314133313070790481068),(-38750256314133313054311935625)⟩,⟨(-34266759182201120957716228281),(-34266759182201120940849856728)⟩⟩,⟨⟨(-38543695427703054252185450863),(-38543695427703054235888259504)⟩,⟨(-33528602849572483000223523735),(-33528602849572482983542758985)⟩⟩] +lemma kernel3_1_r3_3_eq : ∀ k : Fin 16, kernel3_1Expr 3 3 k = kernel3_1_r3_3 k := by decide +kernel +noncomputable def kernel3_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-38329961926748205613498211279),(-38329961926748205597385396921)⟩,⟨(-32791366739255064111972863817),(-32791366739255064095480800166)⟩⟩,⟨⟨(-38109072574939467971149275708),(-38109072574939467955220467445)⟩,⟨(-32055487489047359402808876677),(-32055487489047359386505189810)⟩⟩,⟨⟨(-37881054556333840590806102640),(-37881054556333840575063870535)⟩,⟨(-31321396281218335751436045839),(-31321396281218335735323371012)⟩⟩,⟨⟨(-37645945455138329257421927193),(-37645945455138329241866052013)⟩,⟨(-30589518374184304041451639406),(-30589518374184304025529802009)⟩⟩,⟨⟨(-37403793211156650434842306933),(-37403793211156650419475630664)⟩,⟨(-29860272642068397884178945267),(-29860272642068397868450850867)⟩⟩,⟨⟨(-37154656051115229788878059979),(-37154656051115229773695042638)⟩,⟨(-29134071123139755474929117124),(-29134071123139755459389404400)⟩⟩,⟨⟨(-36898602396134571081245160133),(-36898602396134571066093061519)⟩,⟨(-28411318578120515534133254016),(-28411318578120515518633828808)⟩⟩,⟨⟨(-36635710745681162399719263203),(-36635710745681162384598325951)⟩,⟨(-27692412059336014290712180336),(-27692412059336014275253204824)⟩⟩,⟨⟨(-36366069538403230852014931121),(-36366069538403230836929063261)⟩,⟨(-26977740491667108450596264059),(-26977740491667108435181583953)⟩⟩,⟨⟨(-36089776990320594640535731634),(-36089776990320594625484614656)⟩,⟨(-26267684266243367968031502884),(-26267684266243367952660706256)⟩⟩,⟨⟨(-35806940910904335058619098610),(-35806940910904335043606299050)⟩,⟨(-25562614847792019898330175254),(-25562614847792019883006754010)⟩⟩,⟨⟨(-35517678497645765721639774412),(-35517678497645765706665388028)⟩,⟨(-24862894396530037156966207017),(-24862894396530037141690157400)⟩⟩,⟨⟨(-35222116109775962062835904078),(-35222116109775962047904105023)⟩,⟨(-24168875405455728876197596192),(-24168875405455728860973011487)⟩⟩,⟨⟨(-34920389021856686405741042544),(-34920389021856686390851372790)⟩,⟨(-23480900353861696004837411970),(-23480900353861695989663723550)⟩⟩,⟨⟨(-34612641158020665572945298899),(-34612641158020665558101606558)⟩,⟨(-22799301377853178833852786814),(-22799301377853178818733751254)⟩⟩,⟨⟨(-34299024807693620315250018678),(-34299024807693620300452214136)⟩,⟨(-22124399958614772047203191150),(-22124399958614772032138603095)⟩⟩] +lemma kernel3_1_r3_4_eq : ∀ k : Fin 16, kernel3_1Expr 3 4 k = kernel3_1_r3_4 k := by decide +kernel +noncomputable def kernel3_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-33979700323681989971136326737),(-33979700323681989956389059599)⟩,⟨(-21456506629124364754714196581),(-21456506629124364739708609749)⟩⟩,⟨⟨(-33654835803558733902880676043),(-33654835803558733888183076459)⟩,⟨(-20795920699966141438170514325),(-20795920699966141423222932837)⟩⟩,⟨⟨(-33324606755324727917486810471),(-33324606755324727902842981409)⟩,⟨(-20142930004844734364970843746),(-20142930004844734350085264596)⟩⟩,⟨⟨(-32989195748364927057510657500),(-32989195748364927042920287142)⟩,⟨(-19497810666350343319397703090),(-19497810666350343304573685531)⟩⟩,⟨⟨(-32648792050756468405778510924),(-32648792050756468391246414717)⟩,⟨(-18860826882470043018598790061),(-18860826882470043003841039765)⟩⟩,⟨⟨(-32303591254020087065217406921),(-32303591254020087050742549233)⟩,⟨(-18232230734283803831880210191),(-18232230734283803817187554629)⟩⟩,⟨⟨(-31953794886436479984461205729),(-31953794886436479970047914231)⟩,⟨(-17612262015225190732194010136),(-17612262015225190717570659179)⟩⟩,⟨⟨(-31599610016075457954927189140),(-31599610016075457940574894628)⟩,⟨(-17001148082226522679481777922),(-17001148082226522664927023396)⟩⟩,⟨⟨(-31241248844707776241295924656),(-31241248844707776227009874939)⟩,⟨(-16399103729006723033937862181),(-16399103729006723019456832011)⟩⟩,⟨⟨(-30878928293787348105095211176),(-30878928293787348090873871232)⟩,⟨(-15806331081697432179091925492),(-15806331081697432164682938873)⟩⟩,⟨⟨(-30512869583705061516182485334),(-30512869583705061502030373272)⟩,⟨(-15223019516939453806440565221),(-15223019516939453792108013292)⟩⟩,⟨⟨(-30143297807524596030002714689),(-30143297807524596015918972914)⟩,⟨(-14649345602517538748266562898),(-14649345602517538734009442221)⟩⟩,⟨⟨(-29770441500415452703147551918),(-29770441500415452689137516084)⟩,⟨(-14085473060537150756650156299),(-14085473060537150742473674048)⟩⟩,⟨⟨(-29394532205998863941481519790),(-29394532205998863927543436887)⟩,⟨(-13531552753082485016100820650),(-13531552753082485002003073507)⟩⟩,⟨⟨(-29015804040818361662868079519),(-29015804040818361649006622237)⟩,⟨(-12987722690230900561273762227),(-12987722690230900547259289382)⟩⟩,⟨⟨(-28634493258138590821101290377),(-28634493258138590807315285016)⟩,⟨(-12454108060235359003988380323),(-12454108060235358990055858472)⟩⟩] +lemma kernel3_1_r3_5_eq : ∀ k : Fin 16, kernel3_1Expr 3 5 k = kernel3_1_r3_5 k := by decide +kernel +noncomputable def kernel3_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-28250837812263521080204696561),(-28250837812263521066499920580)⟩,⟨(-11930821281623708070180334946),(-11930821281623708056335408079)⟩⟩,⟨⟨(-27865076924548612035752604073),(-27865076924548612022126668398)⟩,⟨(-11417962076901979024709737493),(-11417962076901979010949863669)⟩⟩,⟨⟨(-27477450652260826092155842634),(-27477450652260826078613535943)⟩,⟨(-10915617567488545803785445296),(-10915617567488545790115275733)⟩⟩,⟨⟨(-27088199461415776062542753627),(-27088199461415776049082564932)⟩,⟨(-10423862389447276835773727478),(-10423862389447276822191600772)⟩⟩,⟨⟨(-26697563804692878127512346940),(-26697563804692878114139985100)⟩,⟨(-9942758829530945485674108540),(-9942758829530945472185596481)⟩⟩,⟨⟨(-26305783705497308776985337515),(-26305783705497308763698233234)⟩,⟨(-9472356980991388910997048588),(-9472356980991388897599430511)⟩⟩,⟨⟨(-25913098349202007112361671033),(-25913098349202007099164691348)⟩,⟨(-9012694918560443376491071033),(-9012694918560443363189074952)⟩⟩,⟨⟨(-25519745682564107292157977219),(-25519745682564107279049257026)⟩,⟨(-8563798891955749412347649500),(-8563798891955749399139261834)⟩⟩,⟨⟨(-25125962022268230293142210917),(-25125962022268230280127818032)⟩,⟨(-8125683537218311284934851482),(-8125683537218311271826002419)⟩⟩,⟨⟨(-24731981673504223118422819767),(-24731981673504223105499522735)⟩,⟨(-7698352105144395687127472551),(-7698352105144395674114782570)⟩⟩,⟨⟨(-24338036559439432691536664816),(-24338036559439432678709370413)⟩,⟨(-7281796706033131925078111445),(-7281796706033131912166348957)⟩⟩,⟨⟨(-23944355862395677163695662178),(-23944355862395677150962142144)⟩,⟨(-6875998569933180877551215863),(-6875998569933180864738008514)⟩⟩,⟨⟨(-23551165677488974717154966458),(-23551165677488974704521145670)⟩,⟨(-6480928321537205708269768841),(-6480928321537205695560904856)⟩⟩,⟨⟨(-23158688679436062466205628188),(-23158688679436062453668074518)⟩,⟨(-6096546268841718555987308689),(-6096546268841718543379214091)⟩⟩,⟨⟨(-22767143803176045350243976164),(-22767143803176045337807600402)⟩,⟨(-5722802704662290305897141258),(-5722802704662290293394591102)⟩⟩,⟨⟨(-22376745938898421392595385570),(-22376745938898421380257592552)⟩,⟨(-5359638220070172044634826928),(-5359638220070172032235088469)⟩⟩] +lemma kernel3_1_r3_6_eq : ∀ k : Fin 16, kernel3_1Expr 3 6 k = kernel3_1_r3_6 k := by decide +kernel +noncomputable def kernel3_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-21987705642010503037534140340),(-21987705642010503025301229821)⟩,⟨(-5006984028796144549216299443),(-5006984028796144536925538846)⟩⟩,⟨⟨(-21600228858518163869344922777),(-21600228858518163857212704467)⟩,⟨(-4664762301630924319015396689),(-4664762301630924306829289657)⟩⟩,⟨⟨(-21214516666234155432658804348),(-21214516666234155420632157689)⟩,⟨(-4332886509838729933037225447),(-4332886509838729920960520021)⟩⟩,⟨⟨(-20830765032168228340348231941),(-20830765032168228328424199524)⟩,⟨(-4011261776591650290752515949),(-4011261776591650278782125388)⟩⟩,⟨⟨(-20449164586393220757939893296),(-20449164586393220746124463116)⟩,⟨(-3699785235427236909342743859),(-3699785235427236897484527089)⟩⟩,⟨⟨(-20069900412621406773386280376),(-20069900412621406761675170169)⟩,⟨(-3398346394730227574730892944),(-3398346394730227562980443294)⟩⟩,⟨⟨(-19693151855665982461146268113),(-19693151855665982449544295868)⟩,⟨(-3106827507241441786089931926),(-3106827507241441774451941698)⟩⟩,⟨⟨(-19319092345903856919573446356),(-19319092345903856908077301511)⟩,⟨(-2825103943602595555345351154),(-2825103943602595543816390093)⟩⟩,⟨⟨(-18947889240798149123615094245),(-18947889240798149112231048814)⟩,⟨(-2553044568954973358726686718),(-2553044568954973347312903343)⟩⟩,⟨⟨(-18579703683482199432850549128),(-18579703683482199421573611290)⟩,⟨(-2290512121622461515690395266),(-2290512121622461504386684255)⟩⟩,⟨⟨(-18214690478351706652409906248),(-18214690478351706641244803724)⟩,⟨(-2037363592925268024492348024),(-2037363592925268013303318258)⟩⟩,⟨⟨(-17852997983558005525560472273),(-17852997983558005514503558802)⟩,⟨(-1793450607189592847418029327),(-1793450607189592836339925482)⟩⟩,⟨⟨(-17494768020243700593858385727),(-17494768020243700582915578735)⟩,⟨(-1558619801040420714364797537),(-1558619801040420703403420511)⟩⟩,⟨⟨(-17140135798312052087552265146),(-17140135798312052076718501138)⟩,⟨(-1332713201089324708613842197),(-1332713201089324697764026330)⟩⟩,⟨⟨(-16789229858473835194943735076),(-16789229858473835184223628855)⟩,⟨(-1115568599156521514058841283),(-1115568599156521503325090185)⟩⟩,⟨⟨(-16442172030270018057625901466),(-16442172030270018047015492017)⟩,⟨(-907019924196227071875131751),(-907019924196227061253386609)⟩⟩] +lemma kernel3_1_r3_7_eq : ∀ k : Fin 16, kernel3_1Expr 3 7 k = kernel3_1_r3_7 k := by decide +kernel +noncomputable def kernel3_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-16099077405725663039249004243),(-16099077405725663028754553844)⟩,⟨(-706897610126435151483221812),(-706897610126435140979635144)⟩⟩,⟨⟨(-15760054328250071237960421449),(-15760054328250071227576089231)⟩,⟨(-515028958798384722661105025),(-515028958798384712269746400)⟩⟩,⟨⟨(-15425204396360466705044377916),(-15425204396360466694774644730)⟩,⟨(-331238497376993172554195679),(-331238497376993162279442927)⟩⟩,⟨⟨(-15094622481771542889392113965),(-15094622481771542879232732490)⟩,⟨(-155348329441205226689610027),(-155348329441205216527129581)⟩⟩,⟨⟨(-14768396761361041515296586328),(-14768396761361041505253296918)⟩,⟨12821520847667164365013593,12821520847667174409582668⟩⟩,⟨⟨(-14446608762492259096045629247),(-14446608762492259086112704885)⟩,⟨173452772121171445198839646,173452772121171455131302446⟩⟩,⟨⟨(-14129333421148018014889471419),(-14129333421148018005071245268)⟩,⟨326728557292667028862831630,326728557292667038678949561⟩⟩,⟨⟨(-13816639152307220994042682276),(-13816639152307220984334650019)⟩,⟨472833103687944718603288379,472833103687944728307640475⟩⟩,⟨⟨(-13508587931974637587216253627),(-13508587931974637577624400043)⟩,⟨611951422302622965883249420,611951422302622975469944985⟩⟩,⟨⟨(-13205235390257041616458947700),(-13205235390257041606976902194)⟩,⟨744269006628192632246113293,744269006628192641721588286⟩⟩,⟨⟨(-12906630914864207074137191143),(-12906630914864207064769126918)⟩,⟨869971541445136812739450980,869971541445136822099618296⟩⟩,⟨⟨(-12612817764401540675990314647),(-12612817764401540666731505660)⟩,⟨989244621938095643389575704,989244621938095652639224843⟩⟩,⟨⟨(-12323833190812232312225924573),(-12323833190812232303081860964)⟩,⟨1102273483444766794160864616,1102273483444766803294590768⟩⟩,⟨⟨(-12039708570320677758146228969),(-12039708570320677749110670175)⟩,⟨1209242742107312259395830819,1209242742107312268419929177⟩⟩,⟨⟨(-11760469542225496957386557860),(-11760469542225496948463511447)⟩,⟨1310336146652654780629083949,1310336146652654789539624701⟩⟩,⟨⟨(-11486136154889650744367157654),(-11486136154889650735551710541)⟩,⟨1405736341486357676945625372,1405736341486357685747574312⟩⟩] +lemma kernel3_1_r3_8_eq : ∀ k : Fin 16, kernel3_1Expr 3 8 k = kernel3_1_r3_8 k := by decide +kernel +noncomputable def kernel3_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-11216723018276853666783020989),(-11216723018276853658080991849)⟩,⟨1495624641243945495218965995,1495624641243945503906583301⟩⟩,⟨⟨(-10952239462387586048960748053),(-10952239462387586040365225044)⟩,⟨1580180816903685211154989060,1580180816903685219735229046⟩⟩,⟨⟨(-10692689700954411807512517564),(-10692689700954411799027337614)⟩,⟨1659582893526143724396188770,1659582893526143732865284238⟩⟩,⟨⟨(-10438072999764889733524562528),(-10438072999764889725144664394)⟩,⟨1734006959648391241811415171,1734006959648391250174469993⟩⟩,⟨⟨(-10188383848990998651001235052),(-10188383848990998642731816666)⟩,⟨1803626988324644806804227460,1803626988324644815056113856⟩⟩,⟨⟨(-9943612138916549418981067482),(-9943612138916549410815542220)⟩,⟨1868614669770543290240418434,1868614669770543298387756650⟩⟩,⟨⟨(-9703743338468393223178062450),(-9703743338468393215120098372)⟩,⟨1929139255535204665660671758,1929139255535204673699855890⟩⟩,⟨⟨(-9468758675973216723240461152),(-9468758675973216715284884160)⟩,⟨1985367414093816820497292336,1985367414093816828433529806⟩⟩,⟨⟨(-9238635321579198716946439353),(-9238635321579198709098695383)⟩,⟨2037463097723821423832441532,2037463097723821431660350868⟩⟩,⟨⟨(-9013346570800646928247237787),(-9013346570800646920500224388)⟩,⟨2085587420499821940378995254,2085587420499821948105702022⟩⟩,⟨⟨(-8792862028663793633659622291),(-8792862028663793626016840079)⟩,⟨2129898547216225927583115397,2129898547216225935205174069⟩⟩,⟨⟨(-8577147793953061722397801475),(-8577147793953061714854001464)⟩,⟨2170551593022351409116704494,2170551593022351416639388971⟩⟩,⟨⟨(-8366166643079176168080062809),(-8366166643079176160640137868)⟩,⟨2207698533532309771686448426,2207698533532309779104922574⟩⟩,⟨⟨(-8159878213113349396795406917),(-8159878213113349389452589912)⟩,⟨2241488125151435283799807153,2241488125151435291120854195⟩⟩,⟨⟨(-7958239183555274909028775843),(-7958239183555274901786406554)⟩,⟨2272065835342366011218252782,2272065835342366018438581550⟩⟩,⟨⟨(-7761203456426687288264124325),(-7761203456426687281116912104)⟩,⟨2299573782537085110171944484,2299573782537085117296863030⟩⟩] +lemma kernel3_1_r3_9_eq : ∀ k : Fin 16, kernel3_1Expr 3 9 k = kernel3_1_r3_9 k := by decide +kernel +noncomputable def kernel3_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-7568722334306657857168327066),(-7568722334306657850121540129)⟩,⟨2324150685386288701563604993,2324150685386288708587897818⟩⟩,⟨⟨(-7380744695949467653361297489),(-7380744695949467646407603708)⟩,⟨2345931821024331762635103110,2345931821024331769566109218⟩⟩,⟨⟨(-7197217169150712005214518599),(-7197217169150711998357102057)⟩,⟨2365048992016683786679377667,2365048992016683793513955729⟩⟩,⟨⟨(-7018084300552128143056076618),(-7018084300552128136289639648)⟩,⟨2381630501647261083985159326,2381630501647261090728617827⟩⟩,⟨⟨(-6843288722100389153396522990),(-6843288722100389146725660938)⟩,⟨2395801137195145520704635898,2395801137195145527352425047⟩⟩,⟨⟨(-6672771313899670499374870556),(-6672771313899670492792787416)⟩,⟨2407682160843997088336555487,2407682160843997094895473637⟩⟩,⟨⟨(-6506471363222072041184902600),(-6506471363222072034694636978)⟩,⟨2417391307862861343258432420,2417391307862861349725478490⟩⟩,⟨⟨(-6344326719463878391868810628),(-6344326719463878385465085545)⟩,⟨2425042791693998962833023499,2425042791693998969213479592⟩⟩,⟨⟨(-6186273944859079735527061805),(-6186273944859079729214751243)⟩,⟨2430747315581755700797045163,2430747315581755707086079736⟩⟩,⟨⟨(-6032248460784477028711212595),(-6032248460784477022483129977)⟩,⟨2434612090376275533771158274,2434612090376275539975953174⟩⟩,⟨⟨(-5882184689512989880504333552),(-5882184689512989874363379705)⟩,⟨2436740858146963402033321733,2436740858146963408151009020⟩⟩,⟨⟨(-5736016191293409418776984935),(-5736016191293409412717931974)⟩,⟨2437233921242949866264315626,2437233921242949872300123476⟩⟩,⟨⟨(-5593675796655736092143931501),(-5593675796655736086171100757)⟩,⟨2436188176441319586151661890,2436188176441319592101305648⟩⟩,⟨⟨(-5455095733861364480188168802),(-5455095733861364474294860073)⟩,⟨2433697153828458839033055255,2433697153828458844903227394⟩⟩,⟨⟨(-5320207751436681374248969408),(-5320207751436681368437956992)⟩,⟨2429851060065473635779813011,2429851060065473641567768074⟩⟩,⟨⟨(-5188943235747093813122729883),(-5188943235747093807388856522)⟩,⟨2424736825695148391861885031,2424736825695148397572776534⟩⟩] +lemma kernel3_1_r3_10_eq : ∀ k : Fin 16, kernel3_1Expr 3 10 k = kernel3_1_r3_10 k := by decide +kernel +noncomputable def kernel3_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-5061233323586070965077923116),(-5061233323586070959425909265)⟩,⟨2418438156155274822045632030,2418438156155274827674774695⟩⟩,⟨⟨(-4937009009770444461731982369),(-4937009009770444456154681544)⟩,⟨2411035586171301649971628915,2411035586171301655526155538⟩⟩,⟨⟨(-4816201249748948653316962497),(-4816201249748948647816998323)⟩,⟨2402606537210058830608039316,2402606537210058836085389802⟩⟩,⟨⟨(-4698741057245783565438547060),(-4698741057245783560010667419)⟩,⟨2393225377685717692226317957,2393225377685717697631960463⟩⟩,⟨⟨(-4584559596974842754517596533),(-4584559596974842749165888599)⟩,⟨2382963485619084928061620818,2382963485619084933391485359⟩⟩,⟨⟨(-4473588272473164503876340695),(-4473588272473164498594303651)⟩,⟨2371889313461720024233910234,2371889313461720029494471677⟩⟩,⟨⟨(-4365758809114141337696914632),(-4365758809114141332487106153)⟩,⟨2360068454807141204291049441,2360068454807141209479760390⟩⟩,⟨⟨(-4261003332372067535997468898),(-4261003332372067530854938630)⟩,⟨2347563712722475635676357541,2347563712722475640798148482⟩⟩,⟨⟨(-4159254441419729172137951420),(-4159254441419729167067102877)⟩,⟨2334435169445249657329923433,2334435169445249662380407686⟩⟩,⟨⟨(-4060445278149961873950150399),(-4060445278149961868944170508)⟩,⟨2320740257201541349912376815,2320740257201541354898340086⟩⟩,⟨⟨(-3964509591720437145648785086),(-3964509591720437140710131622)⟩,⟨2306533829913371252718425667,2306533829913371257637418834⟩⟩,⟨⟨(-3871381798728410867654114885),(-3871381798728410862777957160)⟩,⟨2291868235574931094596721140,2291868235574931099453555236⟩⟩,⟨⟨(-3780997039128802439674660925),(-3780997039128802434864876634)⟩,⟨2276793389088992090504609376,2276793389088992095295420227⟩⟩,⟨⟨(-3693291228014797285444337731),(-3693291228014797280694674851)⟩,⟨2261356845366544140347188753,2261356845366544145078203249⟩⟩,⟨⟨(-3608201103385208522578183521),(-3608201103385208517891010258)⟩,⟨2245603872504349109281681616,2245603872504349113950538908⟩⟩,⟨⟨(-3525664270027126728461101255),(-3525664270027126723831714459)⟩,⟨2229577524866602711445147649,2229577524866602716056531662⟩⟩] +lemma kernel3_1_r3_11_eq : ∀ k : Fin 16, kernel3_1Expr 3 11 k = kernel3_1_r3_11 k := by decide +kernel +noncomputable def kernel3_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-3445619239645962595404387042),(-3445619239645962590837127144)⟩,⟨2213318715908251281334446811,2213318715908251285884031332⟩⟩,⟨⟨(-3368005467377879755913257538),(-3368005467377879751401449696)⟩,⟨2196866290588666259684017145,2196866290588666264178450534⟩⟩,⟨⟨(-3292763384821858984873331489),(-3292763384821858980419260225)⟩,⟨2180257097235308296460801149,2180257097235308300897805208⟩⟩,⟨⟨(-3219834429730265829030755791),(-3219834429730265824629854603)⟩,⟨2163526058727685555799178062,2163526058727685560183300685⟩⟩,⟨⟨(-3149161072497847374837228538),(-3149161072497847370493198580)⟩,⟨2146706242882301407444356644,2146706242882301411771907764⟩⟩,⟨⟨(-3080686839589596437666892392),(-3080686839589596433373764280)⟩,⟨2129828931929372654526901637,2129828931929372658803827092⟩⟩,⟨⟨(-3014356334047929012991632676),(-3014356334047929008751616761)⟩,⟨2112923690981861254615835451,2112923690981861258839930424⟩⟩,⟨⟨(-2950115253219159234499167228),(-2950115253219159230307835119)⟩,⟨2096018435406783521448216132,2096018435406783525623891113⟩⟩,⟨⟨(-2887910403838360801729273615),(-2887910403838360797590678519)⟩,⟨2079139497017827207424672782,2079139497017827211547886273⟩⟩,⟨⟨(-2827689714610409781176610270),(-2827689714610409777084495224)⟩,⟨2062311689017007459249398781,2062311689017007463326383614⟩⟩,⟨⟨(-2769402246423345055630642256),(-2769402246423345051587148204)⟩,⟨2045558369621418706416416776,2045558369621418710445036924⟩⟩,⟨⟨(-2712998200328192868459848445),(-2712998200328192864460688575)⟩,⟨2028901504319084729390118159,2028901504319084733374643329⟩⟩,⟨⟨(-2658428923417113302393521026),(-2658428923417113298442252471)⟩,⟨2012361726705469308122698736,2012361726705469312059581331⟩⟩,⟨⟨(-2605646912729170515429677672),(-2605646912729170511520620044)⟩,⟨1995958397859382867715313274,1995958397859382871610212028⟩⟩,⟨⟨(-2554605817310235360146100985),(-2554605817310235356281333120)⟩,⟨1979709664223806211958655371,1979709664223806215809495894⟩⟩,⟨⟨(-2505260438550527657830936412),(-2505260438550527654006310576)⟩,⟨1963632513963552309489187992,1963632513963552313300101730⟩⟩] +lemma kernel3_1_r3_12_eq : ∀ k : Fin 16, kernel3_1Expr 3 12 k = kernel3_1_r3_12 k := by decide +kernel +noncomputable def kernel3_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-2457566728920123635534396747),(-2457566728920123631753946728)⟩,⟨1947742831777704313595414676,1947742831777704317362378602⟩⟩,⟨⟨(-2411481789219418296625132005),(-2411481789219418292882775054)⟩,⟨1932055452150407148937945938,1932055452150407152667020316⟩⟩,⟨⟨(-2366963864458067864859225973),(-2366963864458067861156981592)⟩,⟨1916584211028856990483929071,1916584211028856994173098485⟩⟩,⟨⟨(-2323972338472367624013600104),(-2323972338472367620347459723)⟩,⟨1901341995922234864746304817,1901341995922234868399562382⟩⟩,⟨⟨(-2282467727387367783723711349),(-2282467727387367780097115928)⟩,⟨1886340794419875530440022435,1886340794419875534053935759⟩⟩,⟨⟨(-2242411672026315356647101694),(-2242411672026315353054647651)⟩,⟨1871591741131159759396470187,1871591741131159762976423110⟩⟩,⟨⟨(-2203766929366252958780060015),(-2203766929366252955223713623)⟩,⟨1857105163053476936636939653,1857105163053476940180969711⟩⟩,⟨⟨(-2166497363134824090381682721),(-2166497363134824086857568392)⟩,⟨1842890623378135991641717266,1842890623378135995153685405⟩⟩,⟨⟨(-2130567933639545602987070530),(-2130567933639545599499016201)⟩,⟨1828956963747317075003975088,1828956963747317078480062960⟩⟩,⟨⟨(-2095944686917027155190115645),(-2095944686917027151732407281)⟩,⟨1815312344978065565536280445,1815312344978065568982181860⟩⟩,⟨⟨(-2062594743285858644459170161),(-2062594743285858641033722411)⟩,⟨1801964286271945740888509616,1801964286271945744302313528⟩⟩,⟨⟨(-2030486285383162740613705082),(-2030486285383162737216772368)⟩,⟨1788919702931305832586498235,1788919702931305835971936359⟩⟩,⟨⟨(-1999588545761132370332358872),(-1999588545761132366967292125)⟩,⟨1776184942605171447321790366,1776184942605171450675519745⟩⟩,⟨⟨(-1969871794116252752330739019),(-1969871794116252748992382796)⟩,⟨1763765820089592792788447718,1763765820089592796115605785⟩⟩,⟨⟨(-1941307324220353653613569934),(-1941307324220353650303791344)⟩,⟨1751667650708835139325164320,1751667650708835142623887405⟩⟩,⟨⟨(-1913867440619158124649145460),(-1913867440619158121364321340)⟩,⟨1739895282305133769284542327,1739895282305133772558440461⟩⟩] +lemma kernel3_1_r3_13_eq : ∀ k : Fin 16, kernel3_1Expr 3 13 k = kernel3_1_r3_13 k := by decide +kernel +noncomputable def kernel3_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-1887525445160596221188810112),(-1887525445160596217932833503)⟩,⟨1728453125865846497623835222,1728453125865846500869024874⟩⟩,⟨⟨(-1862255623411842280367143528),(-1862255623411842277134386784)⟩,⟨1717345184817740709056475960,1717345184817740712278565772⟩⟩,⟨⟨(-1838033231020817387503450302),(-1838033231020817384295732473)⟩,⟨1706575083018859558423872347,1706575083018859561621046583⟩⟩,⟨⟨(-1814834480074779051115026870),(-1814834480074779047928843514)⟩,⟨1696146091478935076473479086,1696146091478935079649229729⟩⟩,⟨⟨(-1792636525505601254720488630),(-1792636525505601251559121946)⟩,⟨1686061153839665678002175403,1686061153839665681153227878⟩⟩,⟨⟨(-1771417451588432640001550420),(-1771417451588432636860056643)⟩,⟨1676322910646362924865267428,1676322910646362927996548939⟩⟩,⟨⟨(-1751156258577610517532164811),(-1751156258577610514412318263)⟩,⟨1666933722442507945544046087,1666933722442507948653785523⟩⟩,⟨⟨(-1731832849521004926366040119),(-1731832849521004923264445897)⟩,⟨1657895691718651875833203929,1657895691718651878924784346⟩⟩,⟨⟨(-1713428017291370653608132664),(-1713428017291370650528501195)⟩,⟨1649210683746856892655413793,1649210683746856895725133586⟩⟩,⟨⟨(-1695923431870795963089163909),(-1695923431870795960026183806)⟩,⟨1640880346331514291103584696,1640880346331514294156737968⟩⟩,⟨⟨(-1679301627921954197386106473),(-1679301627921954194341505761)⟩,⟨1632906128506902616390694629,1632906128506902619425556466⟩⟩,⟨⟨(-1663545992677587329439943660),(-1663545992677587326410432472)⟩,⟨1625289298211270698725631740,1625289298211270701745480718⟩⟩,⟨⟨(-1648640754177477399301843562),(-1648640754177477396290655964)⟩,⟨1618030958966555718378647101,1618030958966555721380256577⟩⟩,⟨⟨(-1634570969880090600591082779),(-1634570969880090597593442680)⟩,⟨1611132065592082893265502090,1611132065592082896253632714⟩⟩,⟨⟨(-1621322515674107210529982173),(-1621322515674107207547572518)⟩,⟨1604593438979748354220397647,1604593438979748357193369492⟩⟩,⟨⟨(-1608882075313175862672621035),(-1608882075313175859702248742)⟩,⟨1598415779957267158016321528,1598415779957267160977316872⟩⟩] +lemma kernel3_1_r3_14_eq : ∀ k : Fin 16, kernel3_1Expr 3 14 k = kernel3_1_r3_14 k := by decide +kernel +noncomputable def kernel3_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-1597237130295449795484086710),(-1597237130295449792529560531)⟩,⟨1592599682265080680732625756,1592599682265080683677844878⟩⟩,⟨⟨(-1586375950207772335746476968),(-1586375950207772332802493509)⟩,⟨1587145644671467928931789105,1587145644671467931866518715⟩⟩,⟨⟨(-1576287583552775394161769076),(-1576287583552775391229962573)⟩,⟨1582054082249299310012789480,1582054082249299312935398250⟩⟩,⟨⟨(-1566961849075634329041080527),(-1566961849075634326118351407)⟩,⟨1577325336836714446159721655,1577325336836714449073298792⟩⟩,⟨⟨(-1558389327605781130450677745),(-1558389327605781127540227715)⟩,⟨1572959686702802668233013845,1572959686702802671134364950⟩⟩,⟨⟨(-1550561354427511264834804472),(-1550561354427511261931981636)⟩,⟨1568957355438120510217910024,1568957355438120513111672341⟩⟩,⟨⟨(-1543470012192123307172125655),(-1543470012192123304278515715)⟩,⟨1565318520088599137490826826,1565318520088599140375417456⟩⟩,⟨⟨(-1537108124383000138688078760),(-1537108124383000135800667898)⟩,⟨1562043318550080168241328843,1562043318550080171119751607⟩⟩,⟨⟨(-1531469249343871340140503001),(-1531469249343871337262976656)⟩,⟨1559131856239374481667776665,1559131856239374484536354776⟩⟩,⟨⟨(-1526547674879383691279943063),(-1526547674879383688407199828)⟩,⟨1556584212056368771773497666,1556584212056368774637316760⟩⟩,⟨⟨(-1522338413436045527383739476),(-1522338413436045524517311384)⟩,⟨1554400443650311974600503316,1554400443650311977458034045⟩⟩,⟨⟨(-1518837197870596153409042309),(-1518837197870596150545999353)⟩,⟨1552580592002001212123772042,1552580592002001214977934725⟩⟩,⟨⟨(-1516040477811878553812675101),(-1516040477811878550956201126)⟩,⟨1551124685332157293407261936,1551124685332157296254879998⟩⟩,⟨⟨(-1513945416621357181376960219),(-1513945416621357178522484165)⟩,⟨1550032742344835642070943954,1550032742344835644916574236⟩⟩,⟨⟨(-1512549888956517530892030013),(-1512549888956517528041028053)⟩,⟨1549304774813262165365806963,1549304774813262168207975840⟩⟩,⟨⟨(-1511852478940505332693615768),(-1511852478940505329843236625)⟩,⟨1548940789514017289745111389,1548940789514017292586660711⟩⟩] +lemma kernel3_1_r3_15_eq : ∀ k : Fin 16, kernel3_1Expr 3 15 k = kernel3_1_r3_15 k := by decide +kernel +noncomputable def kernel3_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel3_1_r3_0,kernel3_1_r3_1,kernel3_1_r3_2,kernel3_1_r3_3,kernel3_1_r3_4,kernel3_1_r3_5,kernel3_1_r3_6,kernel3_1_r3_7,kernel3_1_r3_8,kernel3_1_r3_9,kernel3_1_r3_10,kernel3_1_r3_11,kernel3_1_r3_12,kernel3_1_r3_13,kernel3_1_r3_14,kernel3_1_r3_15] +lemma kernel3_1_r3_eq (i k : Fin 16) : kernel3_1Expr 3 i k = kernel3_1_r3 i k := by + fin_cases i + · exact kernel3_1_r3_0_eq k + · exact kernel3_1_r3_1_eq k + · exact kernel3_1_r3_2_eq k + · exact kernel3_1_r3_3_eq k + · exact kernel3_1_r3_4_eq k + · exact kernel3_1_r3_5_eq k + · exact kernel3_1_r3_6_eq k + · exact kernel3_1_r3_7_eq k + · exact kernel3_1_r3_8_eq k + · exact kernel3_1_r3_9_eq k + · exact kernel3_1_r3_10_eq k + · exact kernel3_1_r3_11_eq k + · exact kernel3_1_r3_12_eq k + · exact kernel3_1_r3_13_eq k + · exact kernel3_1_r3_14_eq k + · exact kernel3_1_r3_15_eq k +noncomputable def kernel3_1_r4_0 : Fin 16 → CBox := ![⟨⟨596587783325493458893354376584,596587783325493459069969374308⟩,⟨(-189641354877509848378777015307),(-189641354877509848208954083522)⟩⟩,⟨⟨596490933285898326725737462351,596490933285898326902350094312⟩,⟨(-189696708627395840515377354993),(-189696708627395840345556904519)⟩⟩,⟨⟨596297251963618183044744055244,596297251963618183221351664310⟩,⟨(-189807349581837061553466772635),(-189807349581837061383651572035)⟩⟩,⟨⟨596006776912200887183367049265,596006776912200887359966967271⟩,⟨(-189973144720384707577497406399),(-189973144720384707407690233368)⟩⟩,⟨⟨595619564561146362197101539475,595619564561146362373691079158⟩,⟨(-190193894687862603903801281174),(-190193894687862603734004929616)⟩⟩,⟨⟨595135690334526107199731423319,595135690334526107376307873390⟩,⟨(-190469334004866065761929886785),(-190469334004866065592147170808)⟩⟩,⟨⟨594555248808486372981167036836,594555248808486373157727651623⟩,⟨(-190799131348263800588526208432),(-190799131348263800418759971692)⟩⟩,⟨⟨593878353907074378950708927052,593878353907074379127250931948⟩,⟨(-191182889901561696473362986590),(-191182889901561696303616096054)⟩⟩,⟨⟨593105139135689059338330105358,593105139135689059514850663995⟩,⟨(-191620147774950522321479936708),(-191620147774950522151755314258)⟩⟩,⟨⟨592235757851321445264661290096,592235757851321445441157547371⟩,⟨(-192110378494821739526851866452),(-192110378494821739357152445442)⟩⟩,⟨⟨591270383568615216999891966276,591270383568615217176360963884⟩,⟨(-192652991562496604261926457057),(-192652991562496604092255265088)⟩⟩,⟨⟨590209210300645496823327209041,590209210300645496999765994619⟩,⟨(-193247333081873342893126216234),(-193247333081873342723486266311)⟩⟩,⟨⟨589052452933183895624863170348,589052452933183895801268618538⟩,⟨(-193892686455655237839755538285),(-193892686455655237670150005041)⟩⟩,⟨⟨587800347631090472691878594275,587800347631090472868247652004⟩,⟨(-194588273149778804103124108548),(-194588273149778803933556084829)⟩⟩,⟨⟨586453152275348913359664178153,586453152275348913535993534036⟩,⟨(-195333253525615714881176766483),(-195333253525615714711649589548)⟩⟩,⟨⟨585011146929140166871610057559,585011146929140167047896533758⟩,⟨(-196126727739474606853077996913),(-196126727739474606683594860141)⟩⟩] +lemma kernel3_1_r4_0_eq : ∀ k : Fin 16, kernel3_1Expr 4 0 k = kernel3_1_r4_0 k := by decide +kernel +noncomputable def kernel3_1_r4_1 : Fin 16 → CBox := ![⟨⟨583474634331232308223660568927,583474634331232308399900587748⟩,⟨(-196967736708879233104976950290),(-196967736708879232935541430010)⟩⟩,⟨⟨581843940414850781758057066024,581843940414850781934247359127⟩,⟨(-197855263145047519015148900638),(-197855263145047518845764253935)⟩⟩,⟨⟨580119414850083736714790981341,580119414850083736890927723138⟩,⟨(-198788232650941812897809303601),(-198788232650941812728479324805)⟩⟩,⟨⟨578301431607772158399904102776,578301431607772158575983875378⟩,⟨(-199765514884203923303029568969),(-199765514884203923133757634562)⟩⟩,⟨⟨576390389542734211841792519700,576390389542734212017811110593⟩,⟨(-200785924784229329202683029472),(-200785924784229329033473286700)⟩⟩,⟨⟨574386712994077922228759650469,574386712994077922404713588829⟩,⟨(-201848223862573185380840605285),(-201848223862573185211696451926)⟩⟩,⟨⟨572290852400266287651070062646,572290852400266287826954833590⟩,⟨(-202951121555816388327593082651),(-202951121555816388158518932824)⟩⟩,⟨⟨570103284926514418868295378698,570103284926514419044107336556⟩,⟨(-204093276639953001205617360267),(-204093276639953001036616751331)⟩⟩,⟨⟨567824515102019586080897716161,567824515102019586256631792428⟩,⟨(-205273298705290762258325404541),(-205273298705290762089403263842)⟩⟩,⟨⟨565455075464452375360866034314,565455075464452375536518624999⟩,⟨(-206489749690784240948152251231),(-206489749690784240779312039477)⟩⟩,⟨⟨562995527209070761402009471348,562995527209070761577575187298⟩,⟨(-207741145476645501531643888764),(-207741145476645501362890814183)⟩⟩,⟨⟨560446460839759024305540134443,560446460839759024481015145854⟩,⟨(-209025957533999946218525824805),(-209025957533999946049863534229)⟩⟩,⟨⟨557808496819240302963027663148,557808496819240303138405858097⟩,⟨(-210342614630275421472157777592),(-210342614630275421303592156328)⟩⟩,⟨⟨555082286215665403182117971034,555082286215665403357395666176⟩,⟨(-211689504588930783953503600961),(-211689504588930783785038112165)⟩⟩,⟨⟨552268511342741471318331857335,552268511342741471493502596339⟩,⟨(-213064976102046060378929924874),(-213064976102046060210570755253)⟩⟩,⟨⟨549367886390532498597974485572,549367886390532498773034326800⟩,⟨(-214467340594210242184790331773),(-214467340594210242016541159976)⟩⟩] +lemma kernel3_1_r4_1_eq : ∀ k : Fin 16, kernel3_1Expr 4 1 k = kernel3_1_r4_1 k := by decide +kernel +noncomputable def kernel3_1_r4_2 : Fin 16 → CBox := ![⟨⟨546381158044039519877730632942,546381158044039520052672118788⟩,⟨(-215894874136054796066551723528),(-215894874136054795898419686518)⟩⟩,⟨⟨543309106086651982258325583592,543309106086651982433145145760⟩,⟨(-217345819405691330382706384326),(-217345819405691330214694750391)⟩⟩,⟨⟨540152543985553238417758114569,540152543985553238592448033939⟩,⟨(-218818387696220740510448246088),(-218818387696220740342564369777)⟩⟩,⟨⟨536912319456162606152732710486,536912319456162606327289032156⟩,⟨(-220310760967388788804685824637),(-220310760967388788636933315112)⟩⟩,⟨⟨533589315002704052581996206747,533589315002704052756410009582⟩,⟨(-221821093939369701539547313274),(-221821093939369701371934672874)⟩⟩,⟨⟨530184448432007414738112701070,530184448432007414912380567877⟩,⟨(-223347516226565249633727209040),(-223347516226565249466257472892)⟩⟩,⟨⟨526698673337672245655162329080,526698673337672245829275081846⟩,⟨(-224888134509212203777073605606),(-224888134509212203609755488504)⟩⟩,⟨⟨523132979551756945226955014745,523132979551756945400908813689⟩,⟨(-226441034740496316883407992497),(-226441034740496316716244905712)⟩⟩,⟨⟨519488393561196846680381444093,519488393561196846854165488004⟩,⟨(-228004284386776403216120073752),(-228004284386776403049122296909)⟩⟩,⟨⟨515765978886204410118002423819,515765978886204410291613809203⟩,⟨(-229575934698427985242639472420),(-229575934698427985075809448521)⟩⟩,⟨⟨511966836417962630002109987250,511966836417962630175537889862⟩,⟨(-231154023008722711920560089391),(-231154023008722711753908079848)⟩⟩,⟨⟨508092104712989176727489337504,508092104712989176900730182815⟩,⟨(-232736575058067674653080428492),(-232736575058067674486609499251)⟩⟩,⟨⟨504142960241623623082175245848,504142960241623623255216372255⟩,⟨(-234321607340838230554063665685),(-234321607340838230387785856568)⟩⟩,⟨⟨500120617588173289657194950151,500120617588173289830033927030⟩,⟨(-235907129471949368576439152303),(-235907129471949368410356356882)⟩⟩,⟨⟨496026329600344689384861596557,496026329600344689557485771617⟩,⟨(-237491146570224413328005855975),(-237491146570224413162130065880)⟩⟩,⟨⟨491861387485687144986496083600,491861387485687145158902324411⟩,⟨(-239071661655536352530761060849),(-239071661655536352365094825277)⟩⟩] +lemma kernel3_1_r4_2_eq : ∀ k : Fin 16, kernel3_1Expr 4 2 k = kernel3_1_r4_2 k := by decide +kernel +noncomputable def kernel3_1_r4_3 : Fin 16 → CBox := ![⟨⟨487627120852882752640230173948,487627120852882752812403341858⟩,⟨(-240646678056616701604675335484),(-240646678056616701439233069897)⟩⟩,⟨⟨483324897695832302420323130227,483324897695832302592261895963⟩,⟨(-242214201826349991624728344897),(-242214201826349991459510776076)⟩⟩,⟨⟨478956124318609845739922829213,478956124318609845911612545789⟩,⟨(-243772244161299096295553132133),(-243772244161299096130574153150)⟩⟩,⟨⟨474522245199489099522904394596,474522245199489099694342564278⟩,⟨(-245318823822138111682515056880),(-245318823822138111517776515527)⟩⟩,⟨⟨470024742792382545960966980066,470024742792382546132136321040⟩,⟨(-246851969551605780075825049342),(-246851969551605779911343413814)⟩⟩,⟨⟨465465137264178647660378505145,465465137264178647831278501064⟩,⟨(-248369722486533914201448344092),(-248369722486533914037223466899)⟩⟩,⟨⟨460844986166613745313753923306,460844986166613745484367783855⟩,⟨(-249870138560452332483596323828),(-249870138560452332319644155376)⟩⟩,⟨⟨456165884041472605835219765350,456165884041472606005545840880⟩,⟨(-251351290893224855417319151809),(-251351290893224855253640635410)⟩⟩,⟨⟨451429461958074883056882339618,451429461958074883226900342834⟩,⟨(-252811272164130323209877784982),(-252811272164130323046492305503)⟩⟩,⟨⟨446637386982173553673817081473,446637386982173553843528252540⟩,⟨(-254248196964768750163717599566),(-254248196964768750000623210037)⟩⟩,⟨⟨441791361575565284939711539206,441791361575565285109096816561⟩,⟨(-255660204128145992745348362279),(-255660204128145992582563208144)⟩⟩,⟨⟨436893122925891238836970486209,436893122925891239006029292227⟩,⟨(-257045459030271021233890583705),(-257045459030271021071414492235)⟩⟩,⟨⟨431944442206289556450652184752,431944442206289556619361865802⟩,⟨(-258402155860588376873084030428),(-258402155860588376710938682461)⟩⟩,⟨⟨426947123764747208580789722833,426947123764747208749152748606⟩,⟨(-259728519857564975382802170731),(-259728519857564975220984352561)⟩⟩,⟨⟨421903004243188533981852628571,421903004243188534149847563870⟩,⟨(-261022809505755369522915237977),(-261022809505755369361445404534)⟩⟩,⟨⟨416813951626530083231892867716,416813951626530083399520442903⟩,⟨(-262283318690683170344727589824),(-262283318690683170183604230489)⟩⟩] +lemma kernel3_1_r4_3_eq : ∀ k : Fin 16, kernel3_1Expr 4 3 k = kernel3_1_r4_3 k := by decide +kernel +noncomputable def kernel3_1_r4_4 : Fin 16 → CBox := ![⟨⟨411681864222125792159592942367,411681864222125792326826868909⟩,⟨(-263508378807898785278144349403),(-263508378807898785117392711779)⟩⟩,⟨⟨406508669570222453399138230430,406508669570222453565983627232⟩,⟨(-264696360822605170161273175175),(-264696360822605170000887384899)⟩⟩,⟨⟨401296323286242350416907369207,401296323286242350583340350750⟩,⟨(-265845677276284091224813613916),(-265845677276284091064816526155)⟩⟩,⟨⟨396046807835907162472044411951,396046807835907162638067256130⟩,⟨(-266954784236805600346396877070),(-266954784236805600186785419156)⟩⟩,⟨⟨390762131244414225368750252603,390762131244414225534334377734⟩,⟨(-268022183188563158403596247458),(-268022183188563158244397920190)⟩⟩,⟨⟨385444325741072314225941698003,385444325741072314391093706974⟩,⟨(-269046422859246179001343977120),(-269046422859246178842551413210)⟩⟩,⟨⟨380095446340998664456694932368,380095446340998664621388442356⟩,⟨(-270026100979940754521781556034),(-270026100979940754363420073485)⟩⟩,⟨⟨374717569365671322544105447350,374717569365671322708344524083⟩,⟨(-270959865975337978017213182632),(-270959865975337977859277922708)⟩⟩,⟨⟨369312790904320471439630391394,369312790904320471603382470409⟩,⟨(-271846418580927559947335879065),(-271846418580927559789858286980)⟩⟩,⟨⟨363883225218328456967867530493,363883225218328457131142601658⟩,⟨(-272684513384162291615178022257),(-272684513384162291458147366123)⟩⟩,⟨⟨358431003090990202593440321524,358431003090990202756209490981⟩,⟨(-273472960286696221582709568062),(-273472960286696221426153659268)⟩⟩,⟨⟨352958270125162894631361742718,352958270125162894793631099054⟩,⟨(-274210625884926041756402135887),(-274210625884926041600314111204)⟩⟩,⟨⟨347467184991505608748245785208,347467184991505608910119547737⟩,⟨(-274896434766200940485729174487),(-274896434766200940329923449931)⟩⟩,⟨⟨341959917630175300372333770062,341959917630175300533832458628⟩,⟨(-275529370718210844877997322359),(-275529370718210844722448215781)⟩⟩,⟨⟨336438647409004676830041926418,336438647409004676991133383286⟩,⟨(-276108477849216277307715373623),(-276108477849216277152454973372)⟩⟩,⟨⟨330905561241339302334640826737,330905561241339302495332556397⟩,⟨(-276632861616944685482282144208),(-276632861616944685327303254748)⟩⟩] +lemma kernel3_1_r4_4_eq : ∀ k : Fin 16, kernel3_1Expr 4 4 k = kernel3_1_r4_4 k := by decide +kernel +noncomputable def kernel3_1_r4_5 : Fin 16 → CBox := ![⟨⟨325362851666855270100499656879,325362851666855270260751351354⟩,⟨(-277101689764147725568656954507),(-277101689764147725413999856706)⟩⟩,⟨⟨319812714898814340427041419957,319812714898814340586868441644⟩,⟨(-277514193158991199046950439021),(-277514193158991198892600236238)⟩⟩,⟨⟨314257348841340043789330080767,314257348841340043948697529701⟩,⟨(-277869666538633743395426231038),(-277869666538633743241417944154)⟩⟩,⟨⟨308698951080415363324650697106,308698951080415363483568261235⟩,⟨(-278167469154541494779811435156),(-278167469154541494626135886956)⟩⟩,⟨⟨303139716852409749170527765983,303139716852409749328953164458⟩,⟨(-278407025318283282363413686580),(-278407025318283282210113328177)⟩⟩,⟨⟨297581836994039916042553144787,297581836994039916200503310440⟩,⟨(-278587824846753949339861459041),(-278587824846753949186920010023)⟩⟩,⟨⟨292027495877754706509601733893,292027495877754706667039118738⟩,⟨(-278709423405981563615933115544),(-278709423405981563463388429765)⟩⟩,⟨⟨286478869336608872399867613225,286478869336608872556804310257⟩,⟨(-278771442752886989106426572737),(-278771442752886988954267257843)⟩⟩,⟨⟨280938122582753580212816033800,280938122582753580369204861467⟩,⟨(-278773570874580916391840232339),(-278773570874580916240113810026)⟩⟩,⟨⟨275407408123722467790086546055,275407408123722467945949270941⟩,⟨(-278715562025003352576193070113),(-278715562025003352424878621063)⟩⟩,⟨⟨269888863680730895190340528816,269888863680730895345637090304⟩,⟨(-278597236658933074579797202350),(-278597236658933074428935270398)⟩⟩,⟨⟨264384610113232412803131151240,264384610113232412957876242503⟩,⟨(-278418481263618966960670132564),(-278418481263618966810246900235)⟩⟩,⟨⟨258896749353990229660893975930,258896749353990229815038800275⟩,⟨(-278179248088510785760819940203),(-278179248088510785610884727339)⟩⟩,⟨⟨253427362358922466872873840925,253427362358922467026442036845⟩,⟨(-277879554773792989801202601739),(-277879554773792989651732773321)⟩⟩,⟨⟨247978507075968135329972534082,247978507075968135482921688361⟩,⟨(-277519483878651124247083934539),(-277519483878651124098122554518)⟩⟩,⟨⟨242552216437196042538881704752,242552216437196042691229290779⟩,⟨(-277099182310425083252597479899),(-277099182310425083104128108195)⟩⟩] +lemma kernel3_1_r4_5_eq : ∀ k : Fin 16, kernel3_1Expr 4 5 k = kernel3_1_r4_5 k := by decide +kernel +noncomputable def kernel3_1_r4_6 : Fin 16 → CBox := ![⟨⟨237150496378341219658673330635,237150496378341219810365082903⟩,⟨(-276618860656026668635971196593),(-276618860656026668488048771521)⟩⟩,⟨⟨231775323889903025874402804015,231775323889903026025468444071⟩,⟨(-276078792417219447235495146293),(-276078792417219447088091110570)⟩⟩,⟨⟨226428645103875943121454781719,226428645103875943271849741544⟩,⟨(-275479313151576239498764685050),(-275479313151576239351924413154)⟩⟩,⟨⟨221112373420108380496776346656,221112373420108380646521021959⟩,⟨(-274820819521142899349546947984),(-274820819521142899203251215326)⟩⟩,⟨⟨215828387676196775541523651344,215828387676196775690563363476⟩,⟨(-274103768251045632058170213229),(-274103768251045631912474535165)⟩⟩,⟨⟨210578530364722170001450775940,210578530364722170149816590189⟩,⟨(-273328675000482216043810935484),(-273328675000482215898685523107)⟩⟩,⟨⟨205364605901524560963197209556,205364605901524561110842609788⟩,⟨(-272496113148734434782947999555),(-272496113148734434638440317526)⟩⟩,⟨⟨200188378948587042958722113243,200188378948587043105670542885⟩,⟨(-271606712499029093460738909013),(-271606712499029093316826801256)⟩⟩,⟨⟨195051572794967468261022580267,195051572794967468407214308770⟩,⟨(-270661157903257520866831886709),(-270661157903257520723576048369)⟩⟩,⟨⟨189955867799070512172599541026,189955867799070512318071966581⟩,⟨(-269660187810737794822455340523),(-269660187810737794679819762060)⟩⟩,⟨⟨184902899895398132385331537679,184902899895398132530036436672⟩,⟨(-268604592744369462162540780912),(-268604592744369462020574761449)⟩⟩,⟨⟨179894259168751992941934823376,179894259168751993085898763516⟩,⟨(-267495213707686666628169351036),(-267495213707686666486847703434)⟩⟩,⟨⟨174931488498688059946427597208,174931488498688060089590886510⟩,⟨(-266332940526461799123913928277),(-266332940526461798983297441781)⟩⟩,⟨⟨170016082276841880989185860066,170016082276841881131587421764⟩,⟨(-265118710128647531165942320222),(-265118710128647531025993527604)⟩⟩,⟨⟨165149485199553680711950122470,165149485199553680853540265807⟩,⟨(-263853504766569910406128882082),(-263853504766569910266898660261)⟩⟩,⟨⟨160333091138026020007780098758,160333091138026020148588571866⟩,⟨(-262538350185398655622748394175),(-262538350185398655484208445040)⟩⟩] +lemma kernel3_1_r4_6_eq : ∀ k : Fin 16, kernel3_1Expr 4 6 k = kernel3_1_r4_6 k := by decide +kernel +noncomputable def kernel3_1_r4_7 : Fin 16 → CBox := ![⟨⟨155568242088044083511733411904,155568242088044083651694922894⟩,⟨(-261174313742022500795268056717),(-261174313742022500657484867516)⟩⟩,⟨⟨150856227201080412061097895223,150856227201080412200258847108⟩,⟨(-259762502478547063618284730302),(-259762502478547063481213416277)⟩⟩,⟨⟨146198281898392838426121656844,146198281898392838564431159025⟩,⟨(-258304061154709961072261590200),(-258304061154709960935954321696)⟩⟩,⟨⟨141595587069507289038281093974,141595587069507289175772073565⟩,⟨(-256800170243572521204368999204),(-256800170243572521068794344448)⟩⟩,⟨⟨137049268356256769788219221556,137049268356256769924828010804⟩,⟨(-255252043894899254763775743533),(-255252043894899254628998665932)⟩⟩,⟨⟨132560395523325059561677120365,132560395523325059697450588324⟩,⟨(-253660927870675113379093060287),(-253660927870675113245068226403)⟩⟩,⟨⟨128129981916019197869432819388,128129981916019198004319125356⟩,⟨(-252028097457236385728110147373),(-252028097457236385594890753684)⟩⟩,⟨⟨123758984005769583253702165171,123758984005769583387737399274⟩,⟨(-250354855358503835792095959928),(-250354855358503835659647433192)⟩⟩,⟨⟨119448301023631207600221614864,119448301023631207733337208515⟩,⟨(-248642529574806387053982504087),(-248642529574806386922374778717)⟩⟩,⟨⟨115198774681835044647885608555,115198774681835044780135676436⟩,⟨(-246892471271770375576926293153),(-246892471271770375446106797699)⟩⟩,⟨⟨111011188983215687830991878282,111011188983215687962323898479⟩,⟨(-245106052643723257932910652117),(-245106052643723257802933322738)⟩⟩,⟨⟨106886270118120780698102368799,106886270118120780828555518100⟩,⟨(-243284664776021843336433175213),(-243284664776021843207260350494)⟩⟩,⟨⟨102824686448190375105563970796,102824686448190375235071711339⟩,⟨(-241429715510663850183132719416),(-241429715510663850054832365449)⟩⟩,⟨⟨98827048576180842168305165480,98827048576180842296922055266⟩,⟨(-239542627319478142058548885652),(-239542627319478141931067961947)⟩⟩,⟨⟨94893909500799080536850156777,94893909500799080664523232855⟩,⟨(-237624835189113701609113446454),(-237624835189113701482506371445)⟩⟩,⟨⟨91025764855309222573600994501,91025764855309222700372430148⟩,⟨(-235677784521960623004700221838),(-235677784521960622878926314383)⟩⟩] +lemma kernel3_1_r4_7_eq : ∀ k : Fin 16, kernel3_1Expr 4 7 k = kernel3_1_r4_7 k := by decide +kernel +noncomputable def kernel3_1_r4_8 : Fin 16 → CBox := ![⟨⟨87223053228476509550970692847,87223053228476509676768197245⟩,⟨(-233702929057038559658750374994),(-233702929057038559533883396284)⟩⟩,⟨⟨83486156566222138712381706042,83486156566222138837268267560⟩,⟨(-231701728814779609797403778924),(-231701728814779609673382216102)⟩⟩,⟨⟨79815400652179290272641640917,79815400652179290396564113230⟩,⟨(-229675648069514054064464118352),(-229675648069514053941342597876)⟩⟩,⟨⟨76211055665164796638097400201,76211055665164796761100798930⟩,⟨(-227626153353339208938938517423),(-227626153353339208816673472500)⟩⟩,⟨⟨72673336811413555508871134443,72673336811413555630887152774⟩,⟨(-225554711494914493409867338698),(-225554711494914493288528573091)⟩⟩,⟨⟨69202405029264307883183440459,69202405029264308004273730546⟩,⟨(-223462787696580220955520237400),(-223462787696580220835047511270)⟩⟩,⟨⟨65798367763836252836494535592,65798367763836252956605976536⟩,⟨(-221351843653044248854000787053),(-221351843653044248734448710548)⟩⟩,⟨⟨62461279809096559864541757641,62461279809096559983722057044⟩,⟨(-219223335714720090993266222626),(-219223335714720090874588475680)⟩⟩,⟨⟨59191144214589526825382119993,59191144214589526943558289148⟩,⟨(-217078713098633098369967806476),(-217078713098633098252238892761)⟩⟩,⟨⟨55987913253979229911591602939,55987913253979230028832746172⟩,⟨(-214919416149638520601358898312),(-214919416149638520484511040762)⟩⟩,⟨⟨52851489452449286191758332778,52851489452449286308011578059⟩,⟨(-212746874654517383232743376201),(-212746874654517383116830930876)⟩⟩,⟨⟨49781726669906014785276376174,49781726669906014900591911879⟩,⟨(-210562506211333861081450702524),(-210562506211333860966424791616)⟩⟩,⟨⟨46778431236845006259470927887,46778431236845006373779682591⟩,⟨(-208367714656251915880162708228),(-208367714656251915766093911988)⟩⟩,⟨⟨43841363139666008770791936129,43841363139666008884161792010⟩,⟨(-206163888549820119008821124411),(-206163888549820118895642797691)⟩⟩,⟨⟨40970237252157182320769271431,40970237252157182433147776568⟩,⟨(-203952399724542518917483451498),(-203952399724542518805249512228)⟩⟩,⟨⟨38164724609817179350045732109,38164724609817179461485351386⟩,⟨(-201734601895360856144675923870),(-201734601895360856033335127613)⟩⟩] +lemma kernel3_1_r4_8_eq : ∀ k : Fin 16, kernel3_1Expr 4 8 k = kernel3_1_r4_8 k := by decide +kernel +noncomputable def kernel3_1_r4_9 : Fin 16 → CBox := ![⟨⟨35424453723642153211896122205,35424453723642153322322132942⟩,⟨(-199511829334480087841703145503),(-199511829334480087731331726118)⟩⟩,⟨⟨32749011929974601667574365059,32749011929974601777063020360⟩,⟨(-197285395611775759398580488738),(-197285395611775759289103308885)⟩⟩,⟨⟨30137946772991800882840392048,30137946772991800991339845277⟩,⟨(-195056592401828940667711947252),(-195056592401828940559182290232)⟩⟩,⟨⟨27590767416403313010266223281,27590767416403313117830957199⟩,⟨(-192826688358442899486443806286),(-192826688358442899378808309158)⟩⟩,⟨⟨25106946080929451644831146981,25106946080929451751392193285⟩,⟨(-190596928057306067428782927003),(-190596928057306067322112032430)⟩⟩,⟨⟨22685919504145418218949627050,22685919504145418324580017985⟩,⟨(-188368531007278791624005263405),(-188368531007278791518226951655)⟩⟩,⟨⟨20327090419298794483145438998,20327090419298794587794053748⟩,⟨(-186142690730597467069080016905),(-186142690730597466964246806668)⟩⟩,⟨⟨18029829049740871273043472126,18029829049740871376766580167⟩,⟨(-183920573912109484154277027449),(-183920573912109484050333660483)⟩⟩,⟨⟨15793474615654557824574661119,15793474615654557927298693485⟩,⟨(-181703319617476554959967609702),(-181703319617476554856989117329)⟩⟩,⟨⟨13617336849812963837679982536,13617336849812963939485065844⟩,⟨(-179492038580112917007945627873),(-179492038580112916905852753943)⟩⟩,⟨⟨11500697519162764667458041029,11500697519162764768293916106⟩,⟨(-177287812556459139428082485803),(-177287812556459139326926840705)⟩⟩,⟨⟨9442811949094708979868888490,9442811949094709079793331606⟩,⟨(-175091693749032224434967701974),(-175091693749032224334692406759)⟩⟩,⟨⟨7442910547339645484447753645,7442910547339645583392573167⟩,⟨(-172904704296538821416601721556),(-172904704296538821317276374009)⟩⟩,⟨⟨5500200324511748296183242003,5500200324511748394225437926⟩,⟨(-170727835830191029917347979554),(-170727835830191029818896340099)⟩⟩,⟨⟨3613866408410709153215978762,3613866408410709250306229309⟩,⟨(-168562049095223801862161415373),(-168562049095223801764634104362)⟩⟩,⟨⟨1783073549291024784441364495,1783073549291024880638707204⟩,⟨(-166408273636479664869027946811),(-166408273636479664772366707135)⟩⟩] +lemma kernel3_1_r4_9_eq : ∀ k : Fin 16, kernel3_1Expr 4 9 k = kernel3_1_r4_9 k := by decide +kernel +noncomputable def kernel3_1_r4_10 : Fin 16 → CBox := ![⟨⟨6967613408613355719321847,6967613408613450949475376⟩,⟨(-164267407546800641206383621441),(-164267407546800641110664130817)⟩⟩,⟨⟨(-1715322937737689340481078129),(-1715322937737689246132854812)⟩,⟨(-162140317276849055944578822634),(-162140317276849055849716420193)⟩⟩,⟨⟨(-3384685584940215682501012856),(-3384685584940215589083005679)⟩,⟨(-160027837504868599519865085180),(-160027837504868599425909298210)⟩⟩,⟨⟨(-5002022307946480507547484145),(-5002022307946480414999684655)⟩,⟨(-157930771064794682292921311837),(-157930771064794682199812794825)⟩⟩,⟨⟨(-6568248163487771053093863076),(-6568248163487770961483190268)⟩,⟨(-155849888931028901816753350366),(-155849888931028901724560339125)⟩⟩,⟨⟨(-8084289886784217429784293548),(-8084289886784217339030999990)⟩,⟨(-153785930258106410260882373977),(-153785930258106410169525622042)⟩⟩,⟨⟨(-9551084518512999536769701575),(-9551084518512999446921012098)⟩,⟨(-151739602473407156165676461785),(-151739602473407156075204375385)⟩⟩,⟨⟨(-10969578059099119638682239108),(-10969578059099119549677404947)⟩,⟨(-149711581420992382434179786743),(-149711581420992382344532163764)⟩⟩,⟨⟨(-12340724152059484723956983117),(-12340724152059484635867664509)⟩,⟨(-147702511554586357980145559889),(-147702511554586357891395361587)⟩⟩,⟨⟨(-13665482798001406790921410716),(-13665482798001406703661371964)⟩,⟨(-145713006177670037627846052901),(-145713006177670037539907384750)⟩⟩,⟨⟨(-14944819100746536045675013274),(-14944819100746535959290364064)⟩,⟨(-143743647728608086130091990317),(-143743647728608086043012081816)⟩⟩,⟨⟨(-16179702046921169626959741089),(-16179702046921169541389262476)⟩,⟨(-141794988108693340115690820972),(-141794988108693340029408886693)⟩⟩,⟨⟨(-17371103320224287414329864761),(-17371103320224287329638910579)⟩,⟨(-139867549050963160777883964797),(-139867549050963160692466576559)⟩⟩,⟨⟨(-18519996151455998239478068541),(-18519996151455998155585280154)⟩,⟨(-137961822527620068163885630960),(-137961822527620068079251680852)⟩⟩,⟨⟨(-19627354205261755473137956259),(-19627354205261755390088333303)⟩,⟨(-136078271193874338445014313009),(-136078271193874338361209858777)⟩⟩,⟨⟨(-20694150504422119913110893342),(-20694150504422119830842959015)⟩,⟨(-134217328866018659338435022773),(-134217328866018659255398912396)⟩⟩] +lemma kernel3_1_r4_10_eq : ∀ k : Fin 16, kernel3_1Expr 4 10 k = kernel3_1_r4_10 k := by decide +kernel +noncomputable def kernel3_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-21721356392394386801145734462),(-21721356392394386719731109817)⟩,⟨(-132379401031544226026790131907),(-132379401031544225944595204244)⟩⟩,⟨⟨(-22709940534691405657689932316),(-22709940534691405577039668304)⟩,⟨(-130564865389113551934689157052),(-130564865389113551853246546727)⟩⟩,⟨⟨(-23660867959564735040609794166),(-23660867959564734960767750743)⟩,⟨(-128774072416217480353793106557),(-128774072416217480273147670519)⟩⟩,⟨⟨(-24575099138344192944559825281),(-24575099138344192865464515477)⟩,⟨(-127007345962362114333039951756),(-127007345962362114253130424927)⟩⟩,⟨⟨(-25453589105674165589331472371),(-25453589105674165511046536269)⟩,⟨(-125264983865655321017312992369),(-125264983865655320938204133749)⟩⟩,⟨⟨(-26297286619778975388194922220),(-26297286619778975310638410715)⟩,⟨(-123547258590691789693388956310),(-123547258590691789614998838743)⟩⟩,⟨⟨(-27107133362785409748968628571),(-27107133362785409672183300003)⟩,⟨(-121854417885669998511485117359),(-121854417885669998433857436948)⟩⟩,⟨⟨(-27884063181030377135467166687),(-27884063181030377059391693845)⟩,⟨(-120186685456713534846818164544),(-120186685456713534769891719512)⟩⟩,⟨⟨(-28629001365185761026412420970),(-28629001365185760951115529597)⟩,⟨(-118544261657412675381424361341),(-118544261657412675305268996015)⟩⟩,⟨⟨(-29342863969941036338616245744),(-29342863969941036264010010314)⟩,⟨(-116927324191649618094769839557),(-116927324191649618019297499698)⟩⟩,⟨⟨(-30026557172897221977403771659),(-30026557172897221903529845521)⟩,⟨(-115336028827821922090731703218),(-115336028827821922015984922893)⟩⟩,⟨⟨(-30680976672243368621962647110),(-30680976672243368548760066889)⟩,⟨(-113770510122633205678063399686),(-113770510122633205603981251867)⟩⟩,⟨⟨(-31307007122709100181693347894),(-31307007122709100109224041088)⟩,⟨(-112230882152677633530813285409),(-112230882152677633457458724096)⟩⟩,⟨⟨(-31905521609213795240125726290),(-31905521609213795168307972572)⟩,⟨(-110717239252104848850125423457),(-110717239252104848777416550360)⟩⟩,⟨⟨(-32477381157564843839099777647),(-32477381157564843767974175729)⟩,⟨(-109229656754714439978511978532),(-109229656754714439906490219102)⟩⟩,⟨⟨(-33023434281494056632462586330),(-33023434281494056561962427958)⟩,⟨(-107768191738893442970586853355),(-107768191738893442899189666462)⟩⟩] +lemma kernel3_1_r4_11_eq : ∀ k : Fin 16, kernel3_1Expr 4 11 k = kernel3_1_r4_11 k := by decide +kernel +noncomputable def kernel3_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-33544516565262729072517783218),(-33544516565262729002707765461)⟩,⟨(-106332883773876449819577171938),(-106332883773876449748873263527)⟩⟩,⟨⟨(-34041450281012045107703583962),(-34041450281012045038494571790)⟩,⟨(-104923755665875302679522778077),(-104923755665875302609422476146)⟩⟩,⟨⟨(-34515044039986397058109684754),(-34515044039986396989541534161)⟩,⟨(-103540814202693803480213500498),(-103540814202693803410757216018)⟩⟩,⟨⟨(-34966092476712738222349069233),(-34966092476712738154362240077)⟩,⟨(-102184050895512062389713810116),(-102184050895512062320841699070)⟩⟩,⟨⟨(-35395375965179193948938785723),(-35395375965179193881593906386)⟩,⟨(-100853442716594765609589070702),(-100853442716594765541362471698)⟩⟩,⟨⟨(-35803660366020742462991114630),(-35803660366020742396207544968)⟩,⟨(-99548952831747493087261537801),(-99548952831747493019599308092)⟩⟩,⟨⟨(-36191696803688732423511910399),(-36191696803688732357328529126)⟩,⟨(-98270531326415002687527057150),(-98270531326415002620468580204)⟩⟩,⟨⟨(-36560221472554211654572978502),(-36560221472554211588930945020)⟩,⟨(-97018115924384875196024830256),(-97018115924384875129510930925)⟩⟩,⟨⟨(-36909955470872371490036309959),(-36909955470872371425001862954)⟩,⟨(-95791632698128853843100162237),(-95791632698128853777197796391)⟩⟩,⟨⟨(-37241604661516724764951729850),(-37241604661516724700438367217)⟩,⟨(-94590996769882396385072883600),(-94590996769882396319694963572)⟩⟩,⟨⟨(-37555859558376785228197838044),(-37555859558376785164243470627)⟩,⟨(-93416113002630184831327052595),(-93416113002630184766511948470)⟩⟩,⟨⟨(-37853395237301847273856904364),(-37853395237301847210403515391)⟩,⟨(-92266876680231419612463564443),(-92266876680231419548152900061)⟩⟩,⟨⟨(-38134871270465816420775677418),(-38134871270465816357882473655)⟩,⟨(-91143174175983487597495271745),(-91143174175983487533748875405)⟩⟩,⟨⟨(-38400931683023746875919859600),(-38400931683023746813507339195)⟩,⟨(-90044883608985877435983012240),(-90044883608985877372720827337)⟩⟩,⟨⟨(-38652204930929632743688773259),(-38652204930929632681793937952)⟩,⟨(-88971875487727875935296754355),(-88971875487727875872556201259)⟩⟩,⟨⟨(-38889303898786900983752771554),(-38889303898786900922318480518)⟩,⟨(-87924013340383484315351439085),(-87924013340383484253074997609)⟩⟩] +lemma kernel3_1_r4_12_eq : ∀ k : Fin 16, kernel3_1Expr 4 12 k = kernel3_1_r4_12 k := by decide +kernel +noncomputable def kernel3_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-39112825916607792075736876779),(-39112825916607792014829876807)⟩,⟨(-86901154331355025698520450234),(-86901154331355025636775519884)⟩⟩,⟨⟨(-39323352794365212504550814057),(-39323352794365212444084031887)⟩,⟨(-85903149863662971067233069136),(-85903149863662971005931934224)⟩⟩,⟨⟨(-39521450873230525467094086158),(-39521450873230525407103614768)⟩,⟨(-84929846166833499246999887021),(-84929846166833499186179022708)⟩⟩,⟨⟨(-39707671092402937172119328878),(-39707671092402937112548999894)⟩,⟨(-83981084869987149092042180300),(-83981084869987149031645023718)⟩⟩,⟨⟨(-39882549070450461793068821903),(-39882549070450461733976600656)⟩,⟨(-83056703559881553095865822004),(-83056703559881553035950889704)⟩⟩,⟨⟨(-40046605200098736819126951498),(-40046605200098736760434713088)⟩,⟨(-82156536323708607101258892262),(-82156536323708607041747471630)⟩⟩,⟨⟨(-40200344755422043409689350135),(-40200344755422043351432341263)⟩,⟨(-81280414276491487941583567180),(-81280414276491487882511255030)⟩⟩,⟨⟨(-40344258010410598121643860010),(-40344258010410598063766895917)⟩,⟨(-80428166072969647827340505773),(-80428166072969647768651711440)⟩⟩,⟨⟨(-40478820367909361869812640704),(-40478820367909361812379920480)⟩,⟨(-79599618403900269461924724705),(-79599618403900269403684225694)⟩⟩,⟨⟨(-40604492497946102658712833580),(-40604492497946102601640137013)⟩,⟨(-78794596476742647301271135199),(-78794596476742647243394056311)⟩⟩,⟨⟨(-40721720484490099017665775029),(-40721720484490098960987502195)⟩,⟨(-78012924480727565241684638881),(-78012924480727565184205701764)⟩⟩,⟨⟨(-40830935979707535216845997168),(-40830935979707535160508008377)⟩,⟨(-77254426036346975058666605657),(-77254426036346975001531257024)⟩⟩,⟨⟨(-40932556364805177107523381562),(-40932556364805177051582627646)⟩,⟨(-76518924629330156793539716217),(-76518924629330156736805404400)⟩⟩,⟨⟨(-41026984916580194853214060747),(-41026984916580194797593840950)⟩,⟨(-75806244029201083042963794069),(-75806244029201082986553211827)⟩⟩,⟨⟨(-41114610978820888333810071189),(-41114610978820888278543986328)⟩,⟨(-75116208692537941568741281364),(-75116208692537941512688326196)⟩⟩,⟨⟨(-41195810137730451683005379523),(-41195810137730451628040328899)⟩,⟨(-74448644151079728858812502118),(-74448644151079728803063654806)⟩⟩] +lemma kernel3_1_r4_13_eq : ∀ k : Fin 16, kernel3_1Expr 4 13 k = kernel3_1_r4_13 k := by decide +kernel +noncomputable def kernel3_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-41270944400573671106101617244),(-41270944400573671051503303243)⟩,⟨(-73803377384846550917987788975),(-73803377384846550862609303071)⟩⟩,⟨⟨(-41340362376774477593964273642),(-41340362376774477539647467206)⟩,⟨(-73180237180459801447264667194),(-73180237180459801392170626214)⟩⟩,⟨⟨(-41404399460720473156365817489),(-41404399460720473102363298094)⟩,⟨(-72579054474865781035196891517),(-72579054474865780980420349463)⟩⟩,⟨⟨(-41463378015558822560146518558),(-41463378015558822506406278991)⟩,⟨(-71999662684681627452186476624),(-71999662684681627397675005731)⟩⟩,⟨⟨(-41517607557296166131909164285),(-41517607557296166078487345040)⟩,⟨(-71441898021395703569043968925),(-71441898021395703514854167571)⟩⟩,⟨⟨(-41567384938543383879483585278),(-41567384938543383826304856210)⟩,⟨(-70905599792665895873779420669),(-70905599792665895819835343484)⟩⟩,⟨⟨(-41612994531274054878674300633),(-41612994531274054825770664273)⟩,⟨(-70390610689968675712353387355),(-70390610689968675658687292260)⟩⟩,⟨⟨(-41654708407993243358863925263),(-41654708407993243306184437418)⟩,⟨(-69896777062859332128344813061),(-69896777062859332074905335132)⟩⟩,⟨⟨(-41692786520740745786679927931),(-41692786520740745734287729489)⟩,⟨(-69423949180109566213658303982),(-69423949180109566160509086132)⟩⟩,⟨⟨(-41727476877380099762280552492),(-41727476877380099710093589650)⟩,⟨(-68971981477992710344000583343),(-68971981477992710291058895122)⟩⟩,⟨⟨(-41759015714651440490042085048),(-41759015714651440438091554629)⟩,⟨(-68540732795989270765455502702),(-68540732795989270712752779314)⟩⟩,⟨⟨(-41787627667492655118603926359),(-41787627667492655066839985145)⟩,⟨(-68130066600186358706012857582),(-68130066600186358653498837023)⟩⟩,⟨⟨(-41813525934159196678459032095),(-41813525934159196626937236909)⟩,⟨(-67739851194643943947541599966),(-67739851194643943895272269454)⟩⟩,⟨⟨(-41836912436698350983850300620),(-41836912436698350932496516797)⟩,⟨(-67369959920998806266929105165),(-67369959920998806214829712273)⟩⟩,⟨⟨(-41857977976358680766419940698),(-41857977976358680715264577849)⟩,⟨(-67020271346573644947134949468),(-67020271346573644895236127472)⟩⟩,⟨⟨(-41876902383539786085724219913),(-41876902383539786034718513532)⟩,⟨(-66690669441254105042372432099),(-66690669441254104990625001018)⟩⟩] +lemma kernel3_1_r4_14_eq : ∀ k : Fin 16, kernel3_1Expr 4 14 k = kernel3_1_r4_14 k := by decide +kernel +noncomputable def kernel3_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-41893854661911408631247800996),(-41893854661911408580456726888)⟩,⟨(-66381043743390561180652833512),(-66381043743390561129122267138)⟩⟩,⟨⟨(-41908993126354264895863348542),(-41908993126354264845203633197)⟩,⟨(-66091289514974434744034576553),(-66091289514974434692636906185)⟩⟩,⟨⟨(-41922465534397819182884871067),(-41922465534397819132386078471)⟩,⟨(-65821307886330676879839651808),(-65821307886330676828604651840)⟩⟩,⟨⟨(-41934409210852506424027216530),(-41934409210852506373641715509)⟩,⟨(-65571005990558895733831333419),(-65571005990558895682710962295)⟩⟩,⟨⟨(-41944951165355695563351293708),(-41944951165355695513134227569)⟩,⟨(-65340297087945508382704983580),(-65340297087945508331754797447)⟩⟩,⟨⟨(-41954208202571959618727358090),(-41954208202571959568605605581)⟩,⟨(-65129100680558322020249374995),(-65129100680558321969395636248)⟩⟩,⟨⟨(-41962287024809005083077112731),(-41962287024809005033079398497)⟩,⟨(-64937342617223159805724271539),(-64937342617223159754995903810)⟩⟩,⟨⟨(-41969284326830931256392639043),(-41969284326830931206472444900)⟩,⟨(-64764955189069608149048057783),(-64764955189069608098398138586)⟩⟩,⟨⟨(-41975286882670362871647029506),(-41975286882670362821867448730)⟩,⟨(-64611877215819736735645229375),(-64611877215819736685137324109)⟩⟩,⟨⟨(-41980371624260453507462061866),(-41980371624260453457742297501)⟩,⟨(-64478054122979791889723848088),(-64478054122979791839276480221)⟩⟩,⟨⟨(-41984605711726822045323449852),(-41984605711726821995691310803)⟩,⟨(-64363438010080448501108052115),(-64363438010080448450749219122)⟩⟩,⟨⟨(-41988046595198191638465306670),(-41988046595198191588875454406)⟩,⟨(-64267987710096285288674732661),(-64267987710096285238358699396)⟩⟩,⟨⟨(-41990742068012884370081673899),(-41990742068012884320588995555)⟩,⟨(-64191668840159781293394631787),(-64191668840159781243176689310)⟩⟩,⟨⟨(-41992730311216421066858862826),(-41992730311216421017391050926)⟩,⟨(-64134453843669375994862028642),(-64134453843669375944669256872)⟩⟩,⟨⟨(-41994039929263322414027394352),(-41994039929263322364611312306)⟩,⟨(-64096322023875048348439087088),(-64096322023875048298298528894)⟩⟩,⟨⟨(-41994689976853843915474481078),(-41994689976853843866065986120)⟩,⟨(-64077259569008507698807633360),(-64077259569008507648674758152)⟩⟩] +lemma kernel3_1_r4_15_eq : ∀ k : Fin 16, kernel3_1Expr 4 15 k = kernel3_1_r4_15 k := by decide +kernel +noncomputable def kernel3_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel3_1_r4_0,kernel3_1_r4_1,kernel3_1_r4_2,kernel3_1_r4_3,kernel3_1_r4_4,kernel3_1_r4_5,kernel3_1_r4_6,kernel3_1_r4_7,kernel3_1_r4_8,kernel3_1_r4_9,kernel3_1_r4_10,kernel3_1_r4_11,kernel3_1_r4_12,kernel3_1_r4_13,kernel3_1_r4_14,kernel3_1_r4_15] +lemma kernel3_1_r4_eq (i k : Fin 16) : kernel3_1Expr 4 i k = kernel3_1_r4 i k := by + fin_cases i + · exact kernel3_1_r4_0_eq k + · exact kernel3_1_r4_1_eq k + · exact kernel3_1_r4_2_eq k + · exact kernel3_1_r4_3_eq k + · exact kernel3_1_r4_4_eq k + · exact kernel3_1_r4_5_eq k + · exact kernel3_1_r4_6_eq k + · exact kernel3_1_r4_7_eq k + · exact kernel3_1_r4_8_eq k + · exact kernel3_1_r4_9_eq k + · exact kernel3_1_r4_10_eq k + · exact kernel3_1_r4_11_eq k + · exact kernel3_1_r4_12_eq k + · exact kernel3_1_r4_13_eq k + · exact kernel3_1_r4_14_eq k + · exact kernel3_1_r4_15_eq k +noncomputable def kernel3_1_r5_0 : Fin 16 → CBox := ![⟨⟨588633717332998411869542022274,588633717332998412221767311730⟩,⟨2127076575910146380382873411324,2127076575910146380773493996385⟩⟩,⟨⟨588826441199868954931116029408,588826441199868955283352940636⟩,⟨2126855083569126151023446059755,2126855083569126151414078984415⟩⟩,⟨⟨589211748710133317957816578898,589211748710133318310076189175⟩,⟨2126412097192113678700787052925,2126412097192113679091444098082⟩⟩,⟨⟨589789359500227874817418929080,589789359500227875169712307683⟩,⟨2125747613490501597960429066440,2125747613490501598351121999304⟩⟩,⟨⟨590558853233320177799371440577,590558853233320178151709631809⟩,⟨2124861627784531897522718607572,2124861627784531897913459161757⟩⟩,⟨⟨591519669849631823211784206605,591519669849631823564178235232⟩,⟨2123754134306551613789982560717,2123754134306551614180782438876⟩⟩,⟨⟨592671109900379986405673100751,592671109900379986758133945234⟩,⟨2122425126604474372587108054738,2122425126604474372977978898743⟩⟩,⟨⟨594012334965487798259076285483,594012334965487798611614906281⟩,⟨2120874598044695093979637874753,2120874598044695094370591291682⟩⟩,⟨⟨595542368155248592149489350595,595542368155248592502116621292⟩,⟨2119102542413518346868633414549,2119102542413518347259680903965⟩⟩,⟨⟨597260094696162127723857452002,597260094696162128076584251193⟩,⟨2117108954615974912893731432661,2117108954615974913284884477561⟩⟩,⟨⟨599164262601191850349464367245,599164262601191850702301424348⟩,⟨2114893831470716278671573055125,2114893831470716279062842962041⟩⟩,⟨⟨601253483424720733967239375760,601253483424720734320197480606⟩,⟨2112457172599493210166183251028,2112457172599493210557581361287⟩⟩,⟨⟨603526233102508948088670137129,603526233102508948441759804900⟩,⟨2109798981409542464992380183166,2109798981409542465383917528479⟩⟩,⟨⟨605980852876979162722136244727,605980852876979163075368183048⟩,⟨2106919266167025263406504275405,2106919266167025263798192052053⟩⟩,⟨⟨608615550308174442827376517162,608615550308174443180761005947⟩,⟨2103818041159482566476547742775,2103818041159482566868396676081⟩⟩,⟨⟨611428400370749081088123306871,611428400370749081441670945099⟩,⟨2100495327945095704740101451623,2100495327945095705132122555909⟩⟩] +lemma kernel3_1_r5_0_eq : ∀ k : Fin 16, kernel3_1Expr 5 0 k = kernel3_1_r5_0 k := by decide +kernel +noncomputable def kernel3_1_r5_1 : Fin 16 → CBox := ![⟨⟨614417346637364079798883046197,614417346637364080152603745191⟩,⟨2096951156686366671603746083019,2096951156686366671995949631443⟩⟩,⟨⟨617580202548866036694669183621,617580202548866037048573511067⟩,⟨2093185567565660656875522270589,2093185567565660657267919164961⟩⟩,⟨⟨620914652771630645540160968381,620914652771630645894258512246⟩,⟨2089198612279884366443731218932,2089198612279884366836331317135⟩⟩,⟨⟨624418254642449633808400779982,624418254642449634162701981014⟩,⟨2084990355611407578904256183743,2084990355611407579297070168284⟩⟩,⟨⟨628088439701332484947125426700,628088439701332485301639296648⟩,⟨2080560877072172459087802147892,2080560877072172459480839194447⟩⟩,⟨⟨631922515312581505137095844208,631922515312581505491832894628⟩,⟨2075910272617775617713531954799,2075910272617775618106802719722⟩⟩,⟨⟨635917666374480484012205775967,635917666374480484367174609995⟩,⟨2071038656428152017143546693702,2071038656428152017537059833214⟩⟩,⟨⟨640070957117913172654930564300,640070957117913173010141538230⟩,⟨2065946162751337822312881793687,2065946162751337822706647699155⟩⟩,⟨⟨644379332994197885460716631325,644379332994197885816177471372⟩,⟨2060632947806641435666012200405,2060632947806641436060038522676⟩⟩,⟨⟨648839622652388569193371735668,648839622652388569549093067555⟩,⟨2055099191743408492901837113200,2055099191743408493296134404437⟩⟩,⟨⟨653448540006250536386623167867,653448540006250536742612285985⟩,⟨2049345100651427795096281156841,2049345100651427795490856509685⟩⟩,⟨⟨658202686391070615244666338065,658202686391070615600933630414⟩,⟨2043370908618891279642726220154,2043370908618891280037589822945⟩⟩,⟨⟨663098552810406629548930201272,663098552810406629905481761492⟩,⟨2037176879833692459098560214640,2037176879833692459493717810434⟩⟩,⟨⟨668132522272819816806280214109,668132522272819817163126918131⟩,⟨2030763310723724559061607633303,2030763310723724559457069780627⟩⟩,⟨⟨673300872218565970472658178698,673300872218565970829805640528⟩,⟨2024130532131722142677903308810,2024130532131722143073675131205⟩⟩,⟨⟨678599777036146725146056949762,678599777036146725503515751089⟩,⟨2017278911520078602240240905825,2017278911520078602636332528121⟩⟩] +lemma kernel3_1_r5_1_eq : ∀ k : Fin 16, kernel3_1Expr 5 1 k = kernel3_1_r5_1 k := by decide +kernel +noncomputable def kernel3_1_r5_2 : Fin 16 → CBox := ![⟨⟨684025310668541488397317306010,684025310668541488755091310084⟩,⟨2010208855200966811770839240308,2010208855200966812167253864215⟩⟩,⟨⟨689573449308853079833358532658,689573449308853080191459253597⟩,⟨2002920810586991754250921400175,2002920810586991754647669963364⟩⟩,⟨⟨695240074185006212156241214797,695240074185006212514672183990⟩,⟨1995415268457512349832200682921,1995415268457512350229285908506⟩⟩,⟨⟨701020974433037610551759607437,701020974433037610910531798490⟩,⟨1987692765235685303492114402114,1987692765235685303889546533351⟩⟩,⟨⟨706911850058409911297561139451,706911850058409911656675907067⟩,⟨1979753885271206847830497317996,1979753885271206848228276713821⟩⟩,⟨⟨712908314984668629325752013153,712908314984668629685221582971⟩,⟨1971599263123659062860977026035,1971599263123659063259115060372⟩⟩,⟨⟨719005900188642584859942543007,719005900188642585219767927472⟩,⟨1963229585841306290692313354207,1963229585841306291090809889990⟩⟩,⟨⟨725200056921263404529089966015,725200056921263404889282763674⟩,⟨1954645595230134305985534027412,1954645595230134306384399649499⟩⟩,⟨⟨731486160012949262092606794986,731486160012949262453164954267⟩,⟨1945848090107880625061935603093,1945848090107880625461166900719⟩⟩,⟨⟨737859511262362123848119593946,737859511262362124209056756987⟩,⟨1936837928537768903400079101336,1936837928537768903799688591940⟩⟩,⟨⟨744315342907206665826429930310,744315342907206666187744120144⟩,⟨1927616030036634041495267767454,1927616030036634041895251965964⟩⟩,⟨⟨750848821175593011880415521744,750848821175593012242119241584⟩,⟨1918183377752107642535139669633,1918183377752107642935509779215⟩⟩,⟨⟨757455049916334807365171507306,757455049916334807727259207432⟩,⟨1908541020603526082037017852751,1908541020603526082437766595043⟩⟩,⟨⟨764129074306399221321144483008,764129074306399221683631124477⟩,⟨1898690075381225888240064921682,1898690075381225888641205852424⟩⟩,⟨⟨770865884633566614947386574126,770865884633566615310266694676⟩,⟨1888631728798903608830980357316,1888631728798903609232506136772⟩⟩,⟨⟨777660420152195204210258268858,777660420152195204573545585158⟩,⟨1878367239493740056762182497243,1878367239493740057164105259615⟩⟩] +lemma kernel3_1_r5_2_eq : ∀ k : Fin 16, kernel3_1Expr 5 2 k = kernel3_1_r5_2 k := by decide +kernel +noncomputable def kernel3_1_r5_3 : Fin 16 → CBox := ![⟨⟨784507573009820482076228033980,784507573009820482439912097906⟩,⟨1867897939969021972453355228636,1867897939969021972855662403379⟩⟩,⟨⟨791402192242150876656698798475,791402192242150877020797110795⟩,⟨1857225238474037881818845084038,1857225238474037882221552510458⟩⟩,⟨⟨798339087833850553445536350261,798339087833850553810039452861⟩,⟨1846350620816079421530889851724,1846350620816079421933985821145⟩⟩,⟨⟨805313034842327892206882383799,805313034842327892571805549110⟩,⟨1835275652099444777448219174215,1835275652099444777851717105017⟩⟩,⟨⟨812318777581574471771624610271,812318777581574472136952945967⟩,⟨1824001978386417251122294906048,1824001978386417251526177408674⟩⟩,⟨⟨819351033862924888195587607435,819351033862924888561340538166⟩,⟨1812531328275279422467222850152,1812531328275279422871507426792⟩⟩,⟨⟨826404499289432940713226601028,826404499289432941079390147464⟩,⟨1800865514390521980270612459310,1800865514390521980675282510426⟩⟩,⟨⟨833473851600385189777710946153,833473851600385190144302305563⟩,⟨1789006434780516087658772955654,1789006434780516088063843570583⟩⟩,⟨⟨840553755062299181689862860646,840553755062299182056860659430⟩,⟨1776956074218039152298388423330,1776956074218039152703835335969⟩⟩,⟨⟨847638864902581318224872220264,847638864902581318592299693580⟩,⟨1764716505399176069160610194470,1764716505399176069566454505193⟩⟩,⟨⟨854723831781849012862888726566,854723831781849013230807756996⟩,⟨1752289890036261356858549584984,1752289890036261357264806511483⟩⟩,⟨⟨861803306300754013849802367733,861803306300754014218851955235⟩,⟨1739678479840682047203774629159,1739678479840682047610746835670⟩⟩,⟨⟨868871943536979193234896294882,868871943536979193605054297089⟩,⟨1726884617391526611574083957435,1726884617391526611981744333195⟩⟩,⟨⟨875924407607920311964831972426,875924407607920312336128727142⟩,⟨1713910736886241485430315294284,1713910736886241485838690291590⟩⟩,⟨⟨882955376254407890670347603333,882955376254407891042762547525⟩,⟨1700759364769643720174338840673,1700759364769643720583403253978⟩⟩,⟨⟨889959545440672963354792937850,889959545440672963728352109656⟩,⟨1687433120237835752874317431736,1687433120237835753284093616924⟩⟩] +lemma kernel3_1_r5_3_eq : ∀ k : Fin 16, kernel3_1Expr 5 3 k = kernel3_1_r5_3 k := by decide +kernel +noncomputable def kernel3_1_r5_4 : Fin 16 → CBox := ![⟨⟨896931633965614786906796972252,896931633965614787281468357201⟩,⟨1673934715613776009051047491972,1673934715613776009461498903313⟩⟩,⟨⟨903866388080289141803058974347,903866388080289142178877284699⟩,⟨1660266956591476777511625679636,1660266956591476777922783782713⟩⟩,⟨⟨910758586106403303388342857634,910758586106403303765280075622⟩,⟨1646432742346028220503745563567,1646432742346028220915578191364⟩⟩,⟨⟨917603043050478697484732292731,917603043050478697862816355965⟩,⟨1632435065506884173915258362704,1632435065506884174327790381961⟩⟩,⟨⟨924394615208225279137895310942,924394615208225279517086744605⟩,⟨1618277011992091182718218846911,1618277011992091183131406771198⟩⟩,⟨⟨931128204753563378572264562810,931128204753563378952599938879⟩,⟨1603961760701396603400627040631,1603961760701396603814504807750⟩⟩,⟨⟨937798764306629720181059612845,937798764306629720562502919941⟩,⟨1589492583066434150149533164429,1589492583066434150564061135911⟩⟩,⟨⟨944401301475015099207589775895,944401301475015099590171306433⟩,⟨1574872842456455493105059188987,1574872842456455493520265221684⟩⟩,⟨⟨950930883362402339138085584678,950930883362402339521754201812⟩,⟨1560105993438353929285147722899,1560105993438353929700977160364⟩⟩,⟨⟨957382641038705172581941857201,957382641038705172966740137339⟩,⟨1545195580890010200704971361828,1545195580890010201121464835725⟩⟩,⟨⟨963751773965752088401819693392,963751773965752088787703127234⟩,⟨1530145238966280658229996793270,1530145238966280658647106715845⟩⟩,⟨⟨970033554372514441457542895454,970033554372514441844544616586⟩,⟨1514958689917243560703863516569,1514958689917243561121621238576⟩⟩,⟨⟨976223331573845674110353266408,976223331573845674498413775799⟩,⟨1499639742758619723351450185907,1499639742758619723769793265513⟩⟩,⟨⟨982316536226678765988411479305,982316536226678766377576073902⟩,⟨1484192291794588324664733038084,1484192291794588325083705470208⟩⟩,⟨⟨988308684517622393397933063882,988308684517622393788148271012⟩,⟨1468620314993526756500882832755,1468620314993526756920428637982⟩⟩,⟨⟨994195382275903090469526916762,994195382275903090860829221984⟩,⟨1452927872217514241373111463498,1452927872217514241793266007716⟩⟩] +lemma kernel3_1_r5_4_eq : ∀ k : Fin 16, kernel3_1Expr 5 4 k = kernel3_1_r5_4 k := by decide +kernel +noncomputable def kernel3_1_r5_5 : Fin 16 → CBox := ![⟨⟨999972329005621272179003067775,999972329005621272571318732329⟩,⟨1437119103306751802936802389743,1437119103306751803357489518612⟩⟩,⟨⟨1005635321831323577471422259494,1005635321831323577864805245213⟩,⟨1421198226020365297024076111485,1421198226020365297445349206196⟩⟩,⟨⟨1011180259350942850811266234949,1011180259350942851205653702069⟩,⟨1405169533835372807424691738472,1405169533835372807846486043691⟩⟩,⟨⟨1016603145390220391978811273899,1016603145390220392374243573485⟩,⟨1389037393605911980912602273774,1389037393605911981334957686515⟩⟩,⟨⟨1021900092652803012012104427675,1021900092652803012408499648672⟩,⟨1372806243085136001920547390315,1372806243085136002343380215813⟩⟩,⟨⟨1027067326260300037247325657771,1027067326260300037644740523028⟩,⟨1356480588312498057562223898577,1356480588312498057985590909994⟩⟩,⟨⟨1032101187176692755685153174240,1032101187176692756083515109013⟩,⟨1340065000869452476484316760654,1340065000869452476908144073574⟩⟩,⟨⟨1036998135511610904255972142441,1036998135511610904655325915163⟩,⟨1323564115006905390400347249405,1323564115006905390824679838290⟩⟩,⟨⟨1041754753697127606402735751626,1041754753697127606802983673792⟩,⟨1306982624648047910107858960009,1306982624648047910532597915327⟩⟩,⟨⟨1046367749532875590858865919983,1046367749532875591260075284745⟩,⟨1290325280270499571122034380384,1290325280270499571547247749979⟩⟩,⟨⟨1050833959094453407719374215494,1050833959094453408121462429762⟩,⟨1273596885671978331454129361819,1273596885671978331879733858899⟩⟩,⟨⟨1055150349500270508563208876217,1055150349500270508966225663575⟩,⟨1256802294623994843161879539156,1256802294623994843587925739022⟩⟩,⟨⟨1059314021532174223453306875162,1059314021532174223857145962795⟩,⟨1239946407418342224909564514812,1239946407418342225335945579195⟩⟩,⟨⟨1063322212105409547287601029779,1063322212105409547692333389195⟩,⟨1223034167311417300060844294676,1223034167311417300487632548173⟩⟩,⟨⟨1067172296583683887769971662717,1067172296583683888175504446542⟩,⟨1206070556871664412601663050355,1206070556871664413028765572219⟩⟩,⟨⟨1070861790935343122534925410939,1070861790935343122941313854769⟩,⟨1189060594235677687156025675263,1189060594235677687583499175713⟩⟩] +lemma kernel3_1_r5_5_eq : ∀ k : Fin 16, kernel3_1Expr 5 5 k = kernel3_1_r5_5 k := by decide +kernel +noncomputable def kernel3_1_r5_6 : Fin 16 → CBox := ![⟨⟨1074388353726912008416312291664,1074388353726912008823431258468⟩,⟨1172009329278731175425770653471,1172009329278731175853489996063⟩⟩,⟨⟨1077749787950510676426714251696,1077749787950510676834649019304⟩,⟨1154921839705727968904255094904,1154921839705727969332307575443⟩⟩,⟨⟨1080944042681929077959216615193,1080944042681929078367863947083⟩,⟨1137803227068768322748728275521,1137803227068768323177011203430⟩⟩,⟨⟨1083969214566422219868411534680,1083969214566422220277832709271⟩,⟨1120658612717732424181855860712,1120658612717732424610432580289⟩⟩,⟨⟨1086823549129580191424358587187,1086823549129580191834421601855⟩,⟨1103493133690454979710934014441,1103493133690454980139673196427⟩⟩,⟨⟨1089505441910927653527340550471,1089505441910927653938133431528⟩,⟨1086311938549235653839190577005,1086311938549235654268182780923⟩⟩,⟨⟨1092013439418216896792200291220,1092013439418216897203609323473⟩,⟨1069120183170580971893008606785,1069120183170580972322141275395⟩⟩,⟨⟨1094346239900696006984410656771,1094346239900696007396503708366⟩,⟨1051923026495209047055958646349,1051923026495209047485302265333⟩⟩,⟨⟨1096502693939958293157275222614,1096502693939958293569900686311⟩,⟨1034725626245467897264646162121,1034725626245467897694050369088⟩⟩,⟨⟨1098481804857310090121972317554,1098481804857310090535234179864⟩,⟨1017533134617420719010089092019,1017533134617420719439660972651⟩⟩,⟨⟨1100282728936930464940011761212,1100282728936930465353785854336⟩,⟨1000350693954936869642128998621,1000350693954936870071746142143⟩⟩,⟨⟨1101904775464437330199976746829,1101904775464437330614338020600⟩,⟨983183432413195116631493329402,983183432413195117061233807215⟩⟩,⟨⟨1103347406580819062262912578179,1103347406580819062677702564015⟩,⟨966036459619055634443634689947,966036459619055634873341922999⟩⟩,⟨⟨1104610236952037985132604494052,1104610236952037985547930957208⟩,⟨948914862335789015948180593684,948914862335789016377965868721⟩⟩,⟨⟨1105693033254961035717513625481,1105693033254961036133242009579⟩,⟨931823700139664021731441611159,931823700139664022161172708792⟩⟩,⟨⟨1106595713480622584020543142555,1106595713480622584436755982095⟩,⟨914768001115890782119026600257,914768001115890782548789626248⟩⟩] +lemma kernel3_1_r5_6_eq : ∀ k : Fin 16, kernel3_1Expr 5 6 k = kernel3_1_r5_6 k := by decide +kernel +noncomputable def kernel3_1_r5_7 : Fin 16 → CBox := ![⟨⟨1107318346056173740445271955002,1107318346056173740861787800633⟩,⟨897752757581392617913845552006,897752757581392618343461489253⟩⟩,⟨⟨1107861148787220532121860031185,1107861148787220532538807124302⟩,⟨880782921841837542368509260995,880782921841837542798110321386⟩⟩,⟨⟨1108224487622599057019928798052,1108224487622599057437162387610⟩,⟨863863401990299895812054541337,863863401990299896241498866337⟩⟩,⟨⟨1108408875243978114514991774712,1108408875243978114932602401980⟩,⟨846999057754843554556804245359,846999057754843554986186336496⟩⟩,⟨⟨1108414969483017853754554133698,1108414969483017854172356843352⟩,⟨830194696402220918177656931077,830194696402220918606794872519⟩⟩,⟨⟨1108243571569145674185014774508,1108243571569145674603139460358⟩,⟨813455068704766646761098620042,813455068704766647190126565110⟩⟩,⟨⟨1107895624211336965407270472800,1107895624211336965825562400697⟩,⟨796784864977432186511395965207,796784864977432186940162597800⟩⟩,⟨⟨1107372209517607311419626139423,1107372209517607311838184293751⟩,⟨780188711191756843122144908373,780188711191756843550753496774⟩⟩,⟨⟨1106674546756233552446117602037,1106674546756233552864734181672⟩,⟨763671165173403952310254388175,763671165173403952738500684927⟩⟩,⟨⟨1105803989963022664810964593695,1105803989963022665229791134047⟩,⟨747236712889707029072994773954,747236712889707029501034861222⟩⟩,⟨⟨1104762025399238882192010694452,1104762025399238882610882823502⟩,⟨730889764833471181792616307020,730889764833471182220289721912⟩⟩,⟨⟨1103550268865079967822938555955,1103550268865079968241964030517⟩,⟨714634652509060139658982382501,714634652509060140086401420013⟩⟩,⟨⟨1102170462873862219528648520010,1102170462873862219947616538892⟩,⟨698475625026569600575142736817,698475625026569601002100679273⟩⟩,⟨⟨1100624473692329848936198827214,1100624473692329849355263412055⟩,⟨682416845809643951126757487209,682416845809643951553413062208⟩⟩,⟨⟨1098914288252747065621762751203,1098914288252747066040750238709⟩,⟨666462389422236478053694420640,666462389422236478479878326435⟩⟩,⟨⟨1097042010942659803962105202770,1097042010942659804381132458169⟩,⟨650616238519343765177149246432,650616238519343765602983069075⟩⟩] +lemma kernel3_1_r5_7_eq : ∀ k : Fin 16, kernel3_1Expr 5 7 k = kernel3_1_r5_7 k := by decide +kernel +noncomputable def kernel3_1_r5_8 : Fin 16 → CBox := ![⟨⟨1095009860278427890532607921730,1095009860278427890951436902490⟩,⟨634882280926463876714873124020,634882280926463877140123371025⟩⟩,⟨⟨1092820165468826949014246930568,1092820165468826949433059135746⟩,⟨619264306852236032484342369873,619264306852236032909195362080⟩⟩,⟨⟨1090475362875201916830557568004,1090475362875201917249170537220⟩,⟨603766006238417683796155276353,603766006238417684220433325335⟩⟩,⟨⟨1087977992374820197531363874270,1087977992374820197949903773177⟩,⟨588390966251044134412984717645,588390966251044134836818819682⟩⟩,⟨⟨1085330693634221747101003131080,1085330693634221747519234608907⟩,⟨573142668916297081101879875774,573142668916297081525039669972⟩⟩,⟨⟨1082536202299495401833695929281,1082536202299495402251798579216⟩,⟨558024488904282660192122757194,558024488904282660614792677492⟩⟩,⟨⟨1079597346110525171831973250038,1079597346110525172249756258895⟩,⟨543039691463587788302104793540,543039691463587788724099164669⟩⟩,⟨⟨1076517040946346781026966160422,1076517040946346781444565222873⟩,⟨528191430509146801992132514582,528191430509146802413591899237⟩⟩,⟨⟨1073298286808833228241014851834,1073298286808833228658169152128⟩,⟨513482746865609670319675938002,513482746865609670740344926321⟩⟩,⟨⟨1069944163751988433984593767266,1069944163751988434401509886988⟩,⟨498916566668059422440210002745,498916566668059422860299949483⟩⟩,⟨⟨1066457827764170048043953853187,1066457827764170048460433215390⟩,⟨484495699921580950253700546522,484495699921580950673018332351⟩⟩,⟨⟨1062842506610586210951037533502,1062842506610586211367225425525⟩,⟨470222839220837064493426878297,470222839220837064912122625166⟩⟩,⟨⟨1059101495643416539309572544218,1059101495643416539725210851920⟩,⟨456100558630461648436986826305,456100558630461648854808157909⟩⟩,⟨⟨1055238153586894954925270180834,1055238153586894955340564932137⟩,⟨442131312726735005156915616029,442131312726735005574073227157⟩⟩,⟨⟨1051255898304661377351737937470,1051255898304661377766483322274⟩,⟨428317435800664058193744679142,428317435800664058610038490182⟩⟩,⟨⟨1047158202556640986563590268931,1047158202556640986977941251075⟩,⟨414661141222250951561230355390,414661141222250951976820063381⟩⟩] +lemma kernel3_1_r5_8_eq : ∀ k : Fin 16, kernel3_1Expr 5 8 k = kernel3_1_r5_8 k := by decide +kernel +noncomputable def kernel3_1_r5_9 : Fin 16 → CBox := ![⟨⟨1042948589752644034623265740613,1042948589752644035036933949296⟩,⟨401164520965398792633801186607,401164520965398793048404536223⟩⟩,⟨⟨1038630629709796398156883310072,1038630629709796398570107792997⟩,⟨387829545292573756057864587985,387829545292573756471725036155⟩⟩,⟨⟨1034207934420811629254902671492,1034207934420811629667471063002⟩,⟨374658062598019455910098888345,374658062598019456323010025532⟩⟩,⟨⟨1029684153839999647181136397406,1029684153839999647593213232541⟩,⟨361651799408003302993519398491,361651799408003303405650327873⟩⟩,⟨⟨1025062971693775934905130297860,1025062971693775935316436909830⟩,⟨348812360536266365816797840089,348812360536266366227876213776⟩⟩,⟨⟨1020348101322288729923294727142,1020348101322288730334063740589⟩,⟨336141229392548880861472968534,336141229392548881271735620225⟩⟩,⟨⟨1015543281558620841420592473243,1015543281558620841830605520840⟩,⟨323639768441773802783874443361,323639768441773803193109141685⟩⟩,⟨⟨1010652272651848042111984933314,1010652272651848042521416085026⟩,⟨311309219811191397097246188144,311309219811191397505631347150⟩⟩,⟨⟨1005678852240048169847426006438,1005678852240048170255968868088⟩,⟨299150706042519559394316662720,299150706042519559801552528701⟩⟩,⟨⟨1000626811379154864776041312522,1000626811379154865183960039936⟩,⟨287165230985857950551519282574,287165230985857950957873808696⟩⟩,⟨⟨995499950633338029469244112272,995499950633338029876315037377⟩,⟨275353680831909770429152627726,275353680831909770834408416868⟩⟩,⟨⟨990302076232370428553174176812,990302076232370428959580657961⟩,⟨263716825278813604859949515702,263716825278813605264293993679⟩⟩,⟨⟨985036996301207163940325011103,985036996301207164345770227695⟩,⟨252255318829669770014046814078,252255318829669770417189897388⟩⟩,⟨⟨979708517166762916851525216464,979708517166762917256267936773⟩,⟨240969702216641387291698646268,240969702216641387693902613268⟩⟩,⟨⟨974320439746621702325221532230,974320439746621702729033355684⟩,⟨229860403947320437573155914555,229860403947320437974198728810⟩⟩,⟨⟨968876556024156314392931218568,968876556024156314796721010956⟩,⟨218927741968873596075606670489,218927741968873596476403496394⟩⟩] +lemma kernel3_1_r5_9_eq : ∀ k : Fin 16, kernel3_1Expr 5 9 k = kernel3_1_r5_9 k := by decide +kernel +noncomputable def kernel3_1_r5_10 : Fin 16 → CBox := ![⟨⟨963380645614270540157980672418,963380645614270540561494813672⟩,⟨208171925445322011345243496219,208171925445322011745548019588⟩⟩,⟨⟨957836472423707485320196940911,957836472423707485723729686091⟩,⟨197593056643163579863529450893,197593056643163580263638791979⟩⟩,⟨⟨952247781409592882363466034444,952247781409592882766778662746⟩,⟨187191132920415840171559870522,187191132920415840571241667131⟩⟩,⟨⟨946618295439603945302181848468,946618295439603945705472175110⟩,⟨176966048814042469286804000179,176966048814042469686259400893⟩⟩,⟨⟨940951712256873087260518335079,940951712256873087663465245658⟩,⟨166917598220626555495046490463,166917598220626555893961323505⟩⟩,⟨⟨935251701552452517204074233973,935251701552452517606959559148⟩,⟨157045476665069336047315200575,157045476665069336445973878818⟩⟩,⟨⟨929521902147881256792294601592,929521902147881257194873399528⟩,⟨147349283652023862579556923310,147349283652023862977720876413⟩⟩,⟨⟨923765919290111329970319322975,923765919290111330372799009907⟩,⟨137828525094718975114998786654,137828525094718975512878376380⟩⟩,⟨⟨917987322060765621344217996190,917987322060765621746243475489⟩,⟨128482615815789860133342336425,128482615815789860530589673271⟩⟩,⟨⟨912189640901416998526114037665,912189640901416998928004669840⟩,⟨119310882114707122779156331127,119310882114707123176092692334⟩⟩,⟨⟨906376365256297548833232019496,906376365256297549234737340624⟩,⟨110312564396386453868533341627,110312564396386454264914614949⟩⟩,⟨⟨900550941333568965840027585342,900550941333568966241364232922⟩,⟨101486819855565309627989889847,101486819855565310024035247217⟩⟩,⟨⟨894716769986010981295459834565,894716769986010981696286502288⟩,⟨92832725211551193846234613695,92832725211551194241609822283⟩⟩,⟨⟨888877204711714986428764984273,888877204711714986829391098068⟩,⟨84349279487977745515155204271,84349279487977745910171281924⟩⟩,⟨⟨883035549775105303894014577954,883035549775105304294184666924⟩,⟨76035406832249459368428136143,76035406832249459762835916466⟩⟩,⟨⟨877195058448351602296114882201,877195058448351602696054544178⟩,⟨67889959369413035931569261194,67889959369413036325596448092⟩⟩] +lemma kernel3_1_r5_10_eq : ∀ k : Fin 16, kernel3_1Expr 5 10 k = kernel3_1_r5_10 k := by decide +kernel +noncomputable def kernel3_1_r5_11 : Fin 16 → CBox := ![⟨⟨871358931372983297099167837760,871358931372983297498493631311⟩,⟨59911720085262573282071933057,59911720085262573675342479435⟩⟩,⟨⟨865530315041271023741495143445,865530315041271024140562690189⟩,⟨52099405733566546468132197448,52099405733566546861002505969⟩⟩,⟨⟨859712300396701930127945129200,859712300396701930526494688928⟩,⟨44451669762396217573594267385,44451669762396217965810829650⟩⟩,⟨⟨853907921552645104443525105573,853907921552645104841790689299⟩,⟨36967105254637201018952631403,36967105254637201410751127615⟩⟩,⟨⟨848120154628081376791508669765,848120154628081377189131083155⟩,⟨29644247877877775410370959035,29644247877877775801399301226⟩⟩,⟨⟨842351916699058413336833640355,842351916699058413734148488087⟩,⟨22481578838988567768773284934,22481578838988568159367619710⟩⟩,⟨⟨836606064864327820489084831116,836606064864327820885828565987⟩,⟨15477527838837806230860880328,15477527838837806620763800497⟩⟩,⟨⟨830885395423426212120929025394,830885395423426212517343732621⟩,⟨8630476022723799330149975464,8630476022723799719604794552⟩⟩,⟨⟨825192643165277139860663663250,825192643165277140256352490539⟩,⟨1938758922251000910000897425,1938758922251001298618149673⟩⟩,⟨⟨819530480765215677195050395268,819530480765215677590390919959⟩,⟨(-4599330615472699358487548409),(-4599330615472698970330561794)⟩⟩,⟨⟨813901518288172472207043406142,813901518288172472601768980828⟩,⟨(-10985539515282621090094874991),(-10985539515282620702658771095)⟩⟩,⟨⟨808308302795599389088258636400,808308302795599389482618772463⟩,⟨(-17221651581850581190375276179),(-17221651581850580803409751769)⟩⟩,⟨⟨802753318053574551972391746368,802753318053574552366011539227⟩,⟨(-23309484631660483307109429432),(-23309484631660482920982319319)⟩⟩,⟨⟨797238984339390752798151841708,797238984339390753191391262316⟩,⟨(-29250887652530879700864077399),(-29250887652530879315215922961)⟩⟩,⟨⟨791767658343807815551389226205,791767658343807815943978975823⟩,⟨(-35047737993974898689720341625),(-35047737993974898304814532772)⟩⟩,⟨⟨786341633166036612212181312559,786341633166036612604377876346⟩,⟨(-40701938591511002053319443371),(-40701938591511001668899131690)⟩⟩] +lemma kernel3_1_r5_11_eq : ∀ k : Fin 16, kernel3_1Expr 5 11 k = kernel3_1_r5_11 k := by decide +kernel +noncomputable def kernel3_1_r5_12 : Fin 16 → CBox := ![⟨⟨780963138398419954566092159374,780963138398419954957471172593⟩,⟨(-46215415227859084632381448816),(-46215415227859084248863513401)⟩⟩,⟨⟨775634340297683459250124050613,775634340297683459641099259332⟩,⟨(-51590113833776066801701136344),(-51590113833776066418673305104)⟩⟩,⟨⟨770357342039547586278961477787,770357342039547586669261664827⟩,⟨(-56827997831103957817029176138),(-56827997831103957434756890644)⟩⟩,⟨⟨765134184053420237424816344407,765134184053420237814704177231⟩,⟨(-61931045520421965240608255712),(-61931045520421964858828897998)⟩⟩,⟨⟨759966844433827394052834047554,759966844433827394441921089055⟩,⟨(-66901247515513154659400541877),(-66901247515513154278495560552)⟩⟩,⟨⟨754857239425187070137672102687,754857239425187070526340377865⟩,⟨(-71740604226675966269079958657),(-71740604226675965888668850776)⟩⟩,⟨⟨749807223976489125041992538102,749807223976489125429969276795⟩,⟨(-76451123394732090279347720878),(-76451123394732089899697619018)⟩⟩,⟨⟨744818592362409967901941453418,744818592362409968289495020376⟩,⟨(-81034817677405288307323981015),(-81034817677405287928166965876)⟩⟩,⟨⟨739893078867366614832857248674,739893078867366615219557398091⟩,⟨(-85493702289571195721665053087),(-85493702289571195343424026672)⟩⟩,⟨⟨735032358528998635214685604901,735032358528998635600960255046⟩,⟨(-89829792698706398292528653568),(-89829792698706397914778098605)⟩⟩,⟨⟨730238047937558929710118261689,730238047937558930095693759112⟩,⟨(-94045102376696567878847337972),(-94045102376696567501855414155)⟩⟩,⟨⟨725511706087694690051589659426,725511706087694690436739227711⟩,⟨(-98141640608998562610049535801),(-98141640608998562233543836957)⟩⟩,⟨⟨720854835279107954836171416156,720854835279107955220494976370⟩,⟨(-102121410361990516843408721071),(-102121410361990516467782439880)⟩⟩,⟨⟨716268882062600540452243996315,716268882062600540836143167245⟩,⟨(-105986406209187408126819974797),(-105986406209187407751673943528)⟩⟩,⟨⟨711755238228030425898465883168,711755238228030426281666496495⟩,⟨(-109738612316847708446350421523),(-109738612316847708071953458616)⟩⟩,⟨⟨707315241830735530705737912994,707315241830735531088517471437⟩,⟨(-113380000489349794268112800910),(-113380000489349793894188568922)⟩⟩] +lemma kernel3_1_r5_12_eq : ∀ k : Fin 16, kernel3_1Expr 5 12 k = kernel3_1_r5_12 k := by decide +kernel +noncomputable def kernel3_1_r5_13 : Fin 16 → CBox := ![⟨⟨702950178253015866580155945995,702950178253015866962070274598⟩,⟨(-116912528274575066407839909410),(-116912528274575066034792082231)⟩⟩,⟨⟨698661281297305881664454011042,698661281297305882045963324249⟩,⟨(-120338137129398452115566509829),(-120338137129398451742934744258)⟩⟩,⟨⟨694449734307715065134940408232,694449734307715065515770484498⟩,⟨(-123658750645256337061591151982),(-123658750645256336689645449227)⟩⟩,⟨⟨690316671316666152195648343977,690316671316666152576079809922⟩,⟨(-126876272833637187446984127343),(-126876272833637187075446200680)⟩⟩,⟨⟨686263178213416179554769520499,686263178213416179934392244077⟩,⟨(-129992586471221330058401719344),(-129992586471221329687675996664)⟩⟩,⟨⟨682290293931305805900808447313,682290293931305806280040664961⟩,⟨(-133009551504283693881765253278),(-133009551504283693511437516664)⟩⟩,⟨⟨678399011650646351746541402260,678399011650646352125109329040⟩,⟨(-135929003511866889846820883195),(-135929003511866889477160903125)⟩⟩,⟨⟨674590280014221554815329232996,674590280014221555193516267070⟩,⟨(-138752752227131901123341670371),(-138752752227131900754068554290)⟩⟩,⟨⟨670865004352451714497105422903,670865004352451714874454825253⟩,⟨(-141482580116199938269243078743),(-141482580116199937900807529568)⟩⟩,⟨⟨667224047915341353521027352970,667224047915341353898007031669⟩,⟨(-144120241013711723047148928780),(-144120241013711722679087743682)⟩⟩,⟨⟨663668233108407408075059262014,663668233108407408451396545822⟩,⟨(-146667458814249622699237724156),(-146667458814249622331819755678)⟩⟩,⟨⟨660198342729862930716972558517,660198342729862931092952620950⟩,⟨(-149125926218693664077951193578),(-149125926218693663710893913448)⟩⟩,⟨⟨656815121206411026670791572032,656815121206411027045996017332⟩,⟨(-151497303534514496621570032104),(-151497303534514496255286432037)⟩⟩,⟨⟨653519275825084928829474532932,653519275825084929204335629867⟩,⟨(-153783217528944809468016694009),(-153783217528944809102078894065)⟩⟩,⟨⟨650311477958652448555853287780,650311477958652448930099807003⟩,⟨(-155985260333915488977235848474),(-155985260333915488611911440427)⟩⟩,⟨⟨647192364282186230503971586911,647192364282186230877889803299⟩,⟨(-158104988401593861003457711816),(-158104988401593860638463183711)⟩⟩] +lemma kernel3_1_r5_13_eq : ∀ k : Fin 16, kernel3_1Expr 5 13 k = kernel3_1_r5_13 k := by decide +kernel +noncomputable def kernel3_1_r5_14 : Fin 16 → CBox := ![⟨⟨644162537978485017032719037932,644162537978485017405827393421⟩,⟨(-160143921509318615178233969539),(-160143921509318614814044926693)⟩⟩,⟨⟨641222569930115233106329737891,641222569930115233479126037046⟩,⟨(-162103541812689360550927323206),(-162103541812689360187051180307)⟩⟩,⟨⟨638372999895926393143748449738,638372999895926393515963667135⟩,⟨(-163985292945538104924768648140),(-163985292945538104561470964033)⟩⟩,⟨⟨635614337669977880056046766038,635614337669977880427967145252⟩,⟨(-165790579165485164492971122848),(-165790579165485164129968507938)⟩⟩,⟨⟨632947064220898342823340048649,632947064220898343194540690419⟩,⟨(-167520764543762965738635437008),(-167520764543762965376347631618)⟩⟩,⟨⟨630371632809782107698761721115,630371632809782108069685727820⟩,⟨(-169177172197977758456524927252),(-169177172197977758094513496408)⟩⟩,⟨⟨627888470084809421259247347643,627888470084809421629628176842⟩,⟨(-170761083566471269009599696368),(-170761083566471268648127871227)⟩⟩,⟨⟨625497977150858879168504079581,625497977150858879538627274310⟩,⟨(-172273737722941630864854272208),(-172273737722941630503639434130)⟩⟩,⟨⟨623200530612460897307263637071,623200530612460897676652505462⟩,⟨(-173716330729985372569007968779),(-173716330729985372208521200141)⟩⟩,⟨⟨620996483588520422736072510471,620996483588520423105223530711⟩,⟨(-175090015030229653350301190865),(-175090015030229652990051339668)⟩⟩,⟨⟨618886166697315147948790842209,618886166697315148317440705462⟩,⟨(-176395898873736140029742707516),(-176395898873736139669989916162)⟩⟩,⟨⟨616869889010352186111220965737,616869889010352186479653351569⟩,⟨(-177635045780374738230838372066),(-177635045780374737871301930190)⟩⟩,⟨⟨614947938973741406349019625465,614947938973741406716804714828⟩,⟨(-178808474035886644626469927756),(-178808474035886644267574680200)⟩⟩,⟨⟨613120585295817350868003937228,613120585295817351235592478858⟩,⟨(-179917156220381690942660966850),(-179917156220381690583961026267)⟩⟩,⟨⟨611388077799813809137514112670,611388077799813809504646418726⟩,⟨(-180962018768044518009972783076),(-180962018768044517651724801353)⟩⟩,⟨⟨609750648240465672496387340395,609750648240465672863344417932⟩,⟨(-181943941556857560991913846068),(-181943941556857560633839809167)⟩⟩] +lemma kernel3_1_r5_14_eq : ∀ k : Fin 16, kernel3_1Expr 5 14 k = kernel3_1_r5_14 k := by decide +kernel +noncomputable def kernel3_1_r5_15 : Fin 16 → CBox := ![⟨⟨608208511083481613620317962511,608208511083481613986602009091⟩,⟨(-182863757527185955350251758194),(-182863757527185954992843830524)⟩⟩,⟨⟨606761864246898421238706136061,606761864246898421604836613475⟩,⟨(-183722252328110096743093731305),(-183722252328110096385838113445)⟩⟩,⟨⟨605410889803393476550042772785,605410889803393476915764511350⟩,⟨(-184520163990435516021292869762),(-184520163990435515664441817340)⟩⟩,⟨⟨604155754642695901788089379898,604155754642695902153679374389⟩,⟨(-185258182625356771977942688301),(-185258182625356771621222196981)⟩⟩,⟨⟨602996611093299373372977336789,602996611093299373738002810259⟩,⟨(-185936950147802028877723492424),(-185936950147802028521561492240)⟩⟩,⟨⟨601933597502740513484129069697,601933597502740513849044727140⟩,⟨(-186557060023537683046399250792),(-186557060023537682690346008684)⟩⟩,⟨⟨600966838775766207137535837945,600966838775766207502091428323⟩,⟨(-187119057039167643588628545656),(-187119057039167643232931506743)⟩⟩,⟨⟨600096446869771199503293653106,600096446869771199867761309938⟩,⟨(-187623437094219468290190070848),(-187623437094219467934580068943)⟩⟩,⟨⟨599322521246943982489330464606,599322521246943982853220315374⟩,⟨(-188070647014569319570860012003),(-188070647014569319215821493861)⟩⟩,⟨⟨598645149282614361570996425614,598645149282614361934820090444⟩,⟨(-188461084386519450833936423692),(-188461084386519450478963387696)⟩⟩,⟨⟨598064406629350292777226569573,598064406629350293140739677803⟩,⟨(-188795097410905475645949402543),(-188795097410905475291283514140)⟩⟩,⟨⟨597580357536404692359920299836,597580357536404692723388697582⟩,⟨(-189072984776675827097908143230),(-189072984776675826743286473836)⟩⟩,⟨⟨597193055124165051543979256045,597193055124165051906969274383⟩,⟨(-189294995553452399746701613819),(-189294995553452399392553056161)⟩⟩,⟨⟨596902541613309945389232179973,596902541613309945752198584921⟩,⟨(-189461329102649200228623397759),(-189461329102649199874498187783)⟩⟩,⟨⟨596708848508427023094788793835,596708848508427023457493676435⟩,⟨(-189572135006794734439560370882),(-189572135006794734085693801774)⟩⟩,⟨⟨596611996735896926406326130123,596611996735896926769027992764⟩,⟨(-189627513016773649579600547611),(-189627513016773649225736962218)⟩⟩] +lemma kernel3_1_r5_15_eq : ∀ k : Fin 16, kernel3_1Expr 5 15 k = kernel3_1_r5_15 k := by decide +kernel +noncomputable def kernel3_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel3_1_r5_0,kernel3_1_r5_1,kernel3_1_r5_2,kernel3_1_r5_3,kernel3_1_r5_4,kernel3_1_r5_5,kernel3_1_r5_6,kernel3_1_r5_7,kernel3_1_r5_8,kernel3_1_r5_9,kernel3_1_r5_10,kernel3_1_r5_11,kernel3_1_r5_12,kernel3_1_r5_13,kernel3_1_r5_14,kernel3_1_r5_15] +lemma kernel3_1_r5_eq (i k : Fin 16) : kernel3_1Expr 5 i k = kernel3_1_r5 i k := by + fin_cases i + · exact kernel3_1_r5_0_eq k + · exact kernel3_1_r5_1_eq k + · exact kernel3_1_r5_2_eq k + · exact kernel3_1_r5_3_eq k + · exact kernel3_1_r5_4_eq k + · exact kernel3_1_r5_5_eq k + · exact kernel3_1_r5_6_eq k + · exact kernel3_1_r5_7_eq k + · exact kernel3_1_r5_8_eq k + · exact kernel3_1_r5_9_eq k + · exact kernel3_1_r5_10_eq k + · exact kernel3_1_r5_11_eq k + · exact kernel3_1_r5_12_eq k + · exact kernel3_1_r5_13_eq k + · exact kernel3_1_r5_14_eq k + · exact kernel3_1_r5_15_eq k +noncomputable def kernel3_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel3_1_r0,kernel3_1_r1,kernel3_1_r2,kernel3_1_r3,kernel3_1_r4,kernel3_1_r5] +lemma kernel3_1_eq (j : Fin 6) (i k : Fin 16) : kernel3_1Expr j i k = kernel3_1 j i k := by + fin_cases j + · exact kernel3_1_r0_eq i k + · exact kernel3_1_r1_eq i k + · exact kernel3_1_r2_eq i k + · exact kernel3_1_r3_eq i k + · exact kernel3_1_r4_eq i k + · exact kernel3_1_r5_eq i k +lemma kernel3_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel3_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(3:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel3_1_eq] + unfold kernel3_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans3_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel4_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans4 j i k) +noncomputable def kernel4_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-42690444767545400),(-42690444767545396)⟩,⟨(-120918263664627653),(-120918263664627649)⟩⟩,⟨⟨(-42564937070501263),(-42564937070501258)⟩,⟨(-120855967181480128),(-120855967181480123)⟩⟩,⟨⟨(-42314359358322756),(-42314359358322750)⟩,⟨(-120731259857675276),(-120731259857675270)⟩⟩,⟨⟨(-41939585531534456),(-41939585531534452)⟩,⟨(-120543914889052320),(-120543914889052315)⟩⟩,⟨⟨(-41441922783503727),(-41441922783503723)⟩,⟨(-120293596828748786),(-120293596828748781)⟩⟩,⟨⟨(-40823107213909329),(-40823107213909325)⟩,⟨(-119979867248850543),(-119979867248850538)⟩⟩,⟨⟨(-40085297984230076),(-40085297984230072)⟩,⟨(-119602192207024347),(-119602192207024343)⟩⟩,⟨⟨(-39231070019333689),(-39231070019333684)⟩,⟨(-119159951448522834),(-119159951448522829)⟩⟩,⟨⟨(-38263405260857760),(-38263405260857755)⟩,⟨(-118652449257637644),(-118652449257637640)⟩⟩,⟨⟨(-37185682480063289),(-37185682480063285)⟩,⟨(-118078926857076167),(-118078926857076162)⟩⟩,⟨⟨(-36001665660264946),(-36001665660264941)⟩,⟨(-117438576238983128),(-117438576238983123)⟩⟩,⟨⟨(-34715490961849740),(-34715490961849735)⟩,⟨(-116730555297544916),(-116730555297544912)⟩⟩,⟨⟨(-33331652286326815),(-33331652286326810)⟩,⟨(-115954004120421265),(-115954004120421261)⟩⟩,⟨⟨(-31854985459833068),(-31854985459833063)⟩,⟨(-115108062284755377),(-115108062284755373)⟩⟩,⟨⟨(-30290651061069011),(-30290651061069007)⟩,⟨(-114191886993322085),(-114191886993322081)⟩⟩,⟨⟨(-28644115923760200),(-28644115923760196)⟩,⟨(-113204671877575466),(-113204671877575462)⟩⟩] +lemma kernel4_0_r0_0_eq : ∀ k : Fin 16, kernel4_0Expr 0 0 k = kernel4_0_r0_0 k := by decide +kernel +noncomputable def kernel4_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-26921133349422963),(-26921133349422959)⟩,⟨(-112145666287034034),(-112145666287034030)⟩⟩,⟨⟨(-25127722072437106),(-25127722072437101)⟩,⟨(-111014194878663027),(-111014194878663022)⟩⟩,⟨⟨(-23270144026157946),(-23270144026157942)⟩,⟨(-109809677315737240),(-109809677315737236)⟩⟩,⟨⟨(-21354880965988063),(-21354880965988058)⟩,⟨(-108531647883139653),(-108531647883139648)⟩⟩,⟨⟨(-19388610012915666),(-19388610012915661)⟩,⟨(-107179774825202505),(-107179774825202500)⟩⟩,⟨⟨(-17378178188940611),(-17378178188940607)⟩,⟨(-105753879213046971),(-105753879213046966)⟩⟩,⟨⟨(-15330576023968481),(-15330576023968476)⟩,⟨(-104253953150929216),(-104253953150929211)⟩⟩,⟨⟨(-13252910322066659),(-13252910322066655)⟩,⟨(-102680177135344069),(-102680177135344065)⟩⟩,⟨⟨(-11152376183343771),(-11152376183343766)⟩,⟨(-101032936386548512),(-101032936386548507)⟩⟩,⟨⟨(-9036228386028141),(-9036228386028136)⟩,⟨(-99312835979705753),(-99312835979705748)⟩⟩,⟨⟨(-6911752241469748),(-6911752241469744)⟩,⟨(-97520714611963656),(-97520714611963652)⟩⟩,⟨⟨(-4786234042656492),(-4786234042656488)⟩,⟨(-95657656852400255),(-95657656852400251)⟩⟩,⟨⟨(-2666931234301139),(-2666931234301135)⟩,⟨(-93725003733812281),(-93725003733812277)⟩⟩,⟨⟨(-561042439500230),(-561042439500225)⟩,⟨(-91724361558694347),(-91724361558694342)⟩⟩,⟨⟨1524322515727072,1524322515727077⟩,⟨(-89657608806348710),(-89657608806348706)⟩⟩,⟨⟨3582172433159090,3582172433159095⟩,⟨(-87526901043757885),(-87526901043757880)⟩⟩] +lemma kernel4_0_r0_1_eq : ∀ k : Fin 16, kernel4_0Expr 0 1 k = kernel4_0_r0_1 k := by decide +kernel +noncomputable def kernel4_0_r0_2 : Fin 16 → CBox := ![⟨⟨5605664276799921,5605664276799926⟩,⟨(-85334673759513104),(-85334673759513099)⟩⟩,⟨⟨7588132255742365,7588132255742371⟩,⟨(-83083643057579483),(-83083643057579476)⟩⟩,⟨⟨9523116297531566,9523116297531573⟩,⟨(-80776804165842764),(-80776804165842759)⟩⟩,⟨⟨11404389752582414,11404389752582418⟩,⟨(-78417427733064347),(-78417427733064343)⟩⟩,⟨⟨13225986169912501,13225986169912506⟩,⟨(-76009053906906451),(-76009053906906447)⟩⟩,⟨⟨14982224985444088,14982224985444093⟩,⟨(-73555484204907990),(-73555484204907985)⟩⟩,⟨⟨16667735966450916,16667735966450920⟩,⟨(-71060771209521158),(-71060771209521153)⟩⟩,⟨⟨18277482259411524,18277482259411528⟩,⟨(-68529206137384548),(-68529206137384544)⟩⟩,⟨⟨19806781893597645,19806781893597650⟩,⟨(-65965304351736011),(-65965304351736007)⟩⟩,⟨⟨21251327599175003,21251327599175007⟩,⟨(-63373788905085008),(-63373788905085004)⟩⟩,⟨⟨22607204806409677,22607204806409682⟩,⟨(-60759572216800248),(-60759572216800243)⟩⟩,⟨⟨23870907701723933,23870907701723938⟩,⟨(-58127736006960055),(-58127736006960050)⟩⟩,⟨⟨25039353226782765,25039353226782772⟩,⟨(-55483509623502922),(-55483509623502917)⟩⟩,⟨⟨26109892918451823,26109892918451827⟩,⟨(-52832246914255135),(-52832246914255131)⟩⟩,⟨⟨27080322500268413,27080322500268417⟩,⟨(-50179401808663045),(-50179401808663040)⟩⟩,⟨⟨27948889149914949,27948889149914954⟩,⟨(-47530502785892114),(-47530502785892110)⟩⟩] +lemma kernel4_0_r0_2_eq : ∀ k : Fin 16, kernel4_0Expr 0 2 k = kernel4_0_r0_2 k := by decide +kernel +noncomputable def kernel4_0_r0_3 : Fin 16 → CBox := ![⟨⟨28714296381969081,28714296381969086⟩,⟨(-44891126416259884),(-44891126416259880)⟩⟩,⟨⟨29375706500804851,29375706500804856⟩,⟨(-42266870171645234),(-42266870171645230)⟩⟩,⟨⟨29932740594801154,29932740594801158⟩,⟨(-39663324707478270),(-39663324707478265)⟩⟩,⟨⟨30385476059833791,30385476059833796⟩,⟨(-37086045824095403),(-37086045824095398)⟩⟩,⟨⟨30734441657233581,30734441657233586⟩,⟨(-34540526318592578),(-34540526318592573)⟩⟩,⟨⟨30980610128826760,30980610128826764⟩,⟨(-32032167939793049),(-32032167939793045)⟩⟩,⟨⟨31125388409171852,31125388409171856⟩,⟨(-29566253658550121),(-29566253658550117)⟩⟩,⟨⟨31170605492502785,31170605492502790⟩,⟨(-27147920463333928),(-27147920463333924)⟩⟩,⟨⟨31118498029014303,31118498029014308⟩,⟨(-24782132886926618),(-24782132886926614)⟩⟩,⟨⟨30971693741815982,30971693741815987⟩,⟨(-22473657464113217),(-22473657464113212)⟩⟩,⟨⟨30733192771972689,30733192771972694⟩,⟨(-20227038312564460),(-20227038312564456)⟩⟩,⟨⟨30406347074383046,30406347074383051⟩,⟨(-18046574019738628),(-18046574019738624)⟩⟩,⟨⟨29994838001672499,29994838001672504⟩,⟨(-15936296007674540),(-15936296007674535)⟩⟩,⟨⟨29502652226650484,29502652226650488⟩,⟨(-13899948535115070),(-13899948535115066)⟩⟩,⟨⟨28934056166069349,28934056166069354⟩,⟨(-11940970482612135),(-11940970482612131)⟩⟩,⟨⟨28293569079305375,28293569079305380⟩,⟨(-10062479051255340),(-10062479051255336)⟩⟩] +lemma kernel4_0_r0_3_eq : ∀ k : Fin 16, kernel4_0Expr 0 3 k = kernel4_0_r0_3 k := by decide +kernel +noncomputable def kernel4_0_r0_4 : Fin 16 → CBox := ![⟨⟨27585935025051317,27585935025051322⟩,⟨(-8267255489584382),(-8267255489584378)⟩⟩,⟨⟨26816093867072798,26816093867072802⟩,⟨(-6557732946246616),(-6557732946246611)⟩⟩,⟨⟨25989151526459191,25989151526459196⟩,⟨(-4935986528211189),(-4935986528211184)⟩⟩,⟨⟨25110349682532681,25110349682532685⟩,⟨(-3403725626021573),(-3403725626021568)⟩⟩,⟨⟨24185035127622231,24185035127622236⟩,⟨(-1962288548835409),(-1962288548835404)⟩⟩,⟨⟨23218628982235840,23218628982235844⟩,⟨(-612639493043376),(-612639493043371)⟩⟩,⟨⟨22216595976765557,22216595976765562⟩,⟨644632150742472,644632150742476⟩⟩,⟨⟨21184414003744117,21184414003744121⟩,⟨1809310166407569,1809310166407573⟩⟩,⟨⟨20127544140865999,20127544140866004⟩,⟨2881547589394090,2881547589394095⟩⟩,⟨⟨19051401339533099,19051401339533103⟩,⟨3861860542809193,3861860542809198⟩⟩,⟨⟨17961325966645812,17961325966645816⟩,⟨4751119900720631,4751119900720636⟩⟩,⟨⟨16862556378810383,16862556378810387⟩,⟨5550540863406185,5550540863406189⟩⟩,⟨⟨15760202698163554,15760202698163559⟩,⟨6261670545003684,6261670545003688⟩⟩,⟨⟨14659221947730477,14659221947730482⟩,⟨6886373688605889,6886373688605893⟩⟩,⟨⟨13564394691748276,13564394691748281⟩,⟨7426816637237167,7426816637237171⟩⟩,⟨⟨12480303312833466,12480303312833471⟩,⟨7885449701228090,7885449701228094⟩⟩] +lemma kernel4_0_r0_4_eq : ∀ k : Fin 16, kernel4_0Expr 0 4 k = kernel4_0_r0_4 k := by decide +kernel +noncomputable def kernel4_0_r0_5 : Fin 16 → CBox := ![⟨⟨11411312043384254,11411312043384259⟩,⟨8264988073175958,8264988073175962⟩⟩,⟨⟨10361548853333409,10361548853333414⟩,⟨8568391450865902,8568391450865906⟩⟩,⟨⟨9334889280455486,9334889280455491⟩,⟨8798842536165900,8798842536165904⟩⟩,⟨⟨8334942273039568,8334942273039573⟩,⟨8959724583954817,8959724583954821⟩⟩,⟨⟨7365038098023506,7365038098023511⟩,⟨9054598179565958,9054598179565962⟩⟩,⟨⟨6428218350807602,6428218350807607⟩,⟨9087177426017854,9087177426017858⟩⟩,⟨⟨5527228086083035,5527228086083040⟩,⟨9061305723463407,9061305723463412⟩⟩,⟨⟨4664510072279273,4664510072279278⟩,⟨8980931322838764,8980931322838769⟩⟩,⟨⟨3842201155806673,3842201155806677⟩,⟨8850082833670903,8850082833670907⟩⟩,⟨⟨3062130705291987,3062130705291991⟩,⟨8672844862459197,8672844862459201⟩⟩,⟨⟨2325821090613817,2325821090613822⟩,⟨8453333953046905,8453333953046910⟩⟩,⟨⟨1634490136872848,1634490136872852⟩,⟨8195674994022126,8195674994022131⟩⟩,⟨⟨989055479598080,989055479598085⟩,⟨7903978250525381,7903978250525386⟩⟩,⟨⟨390140734604944,390140734604949⟩,⟨7582317168993966,7582317168993970⟩⟩,⟨⟨(-161916615918204),(-161916615918200)⟩,⟨7234707093452672,7234707093452676⟩⟩,⟨⟨(-667055730227259),(-667055730227254)⟩,⟨6865085021085739,6865085021085744⟩⟩] +lemma kernel4_0_r0_5_eq : ∀ k : Fin 16, kernel4_0Expr 0 5 k = kernel4_0_r0_5 k := by decide +kernel +noncomputable def kernel4_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-1125481425380893),(-1125481425380889)⟩,⟨6477290513121512,6477290513121516⟩⟩,⟨⟨(-1537651834022932),(-1537651834022927)⟩,⟨6075047864660119,6075047864660124⟩⟩,⟨⟨(-1904264833410865),(-1904264833410861)⟩,⟨5661949624110256,5661949624110260⟩⟩,⟨⟨(-2226243386117608),(-2226243386117603)⟩,⟨5241441539510016,5241441539510020⟩⟩,⟨⟨(-2504719936087447),(-2504719936087443)⟩,⟨4816808995325972,4816808995325977⟩⟩,⟨⟨(-2741020006627939),(-2741020006627934)⟩,⟨4391164989490511,4391164989490515⟩⟩,⟨⟨(-2936645148478961),(-2936645148478957)⟩,⟨3967439686583454,3967439686583458⟩⟩,⟨⟨(-3093255386342300),(-3093255386342295)⟩,⟨3548371569320586,3548371569320591⟩⟩,⟨⟨(-3212651311217382),(-3212651311217377)⟩,⟨3136500197003828,3136500197003832⟩⟩,⟨⟨(-3296755963619292),(-3296755963619288)⟩,⟨2734160566434689,2734160566434693⟩⟩,⟨⟨(-3347596649313495),(-3347596649313490)⟩,⟨2343479058105917,2343479058105922⟩⟩,⟨⟨(-3367286824656788),(-3367286824656783)⟩,⟨1966370938369694,1966370938369699⟩⟩,⟨⟨(-3358008183064031),(-3358008183064026)⟩,⟨1604539376828822,1604539376828826⟩⟩,⟨⟨(-3321993067610621),(-3321993067610617)⟩,⟨1259475927495163,1259475927495168⟩⟩,⟨⟨(-3261507327423744),(-3261507327423740)⟩,⟨932462412381298,932462412381302⟩⟩,⟨⟨(-3178833727408749),(-3178833727408745)⟩,⟨624574137201291,624574137201296⟩⟩] +lemma kernel4_0_r0_6_eq : ∀ k : Fin 16, kernel4_0Expr 0 6 k = kernel4_0_r0_6 k := by decide +kernel +noncomputable def kernel4_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-3076256012101960),(-3076256012101956)⟩,⟨336684360806786,336684360806790⟩⟩,⟨⟨(-2956043715142816),(-2956043715142811)⟩,⟨69469932917270,69469932917274⟩⟩,⟨⟨(-2820437796122181),(-2820437796122176)⟩,⟨(-176581991351755),(-176581991351751)⟩⟩,⟨⟨(-2671637176497406),(-2671637176497402)⟩,⟨(-401166256682869),(-401166256682865)⟩⟩,⟨⟨(-2511786235973674),(-2511786235973670)⟩,⟨(-604151132977700),(-604151132977696)⟩⟩,⟨⟨(-2342963320340628),(-2342963320340624)⟩,⟨(-785568964457407),(-785568964457403)⟩⟩,⟨⟨(-2167170301323970),(-2167170301323966)⟩,⟨(-945606147819647),(-945606147819643)⟩⟩,⟨⟨(-1986323218662602),(-1986323218662597)⟩,⟨(-1084592545752251),(-1084592545752246)⟩⟩,⟨⟨(-1802244024445220),(-1802244024445216)⟩,⟨(-1202990442058055),(-1202990442058051)⟩⟩,⟨⟨(-1616653439824798),(-1616653439824794)⟩,⟨(-1301383143670321),(-1301383143670317)⟩⟩,⟨⟨(-1431164924656346),(-1431164924656342)⟩,⟨(-1380463332981993),(-1380463332981989)⟩⟩,⟨⟨(-1247279751447699),(-1247279751447695)⟩,⟨(-1441021271229338),(-1441021271229334)⟩⟩,⟨⟨(-1066383166342776),(-1066383166342772)⟩,⟨(-1483932950221631),(-1483932950221627)⟩⟩,⟨⟨(-889741611731412),(-889741611731408)⟩,⟨(-1510148285559628),(-1510148285559623)⟩⟩,⟨⟨(-718500977551836),(-718500977551832)⟩,⟨(-1520679439706008),(-1520679439706004)⟩⟩,⟨⟨(-553685841464404),(-553685841464400)⟩,⟨(-1516589357934266),(-1516589357934261)⟩⟩] +lemma kernel4_0_r0_7_eq : ∀ k : Fin 16, kernel4_0Expr 0 7 k = kernel4_0_r0_7 k := by decide +kernel +noncomputable def kernel4_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-396199651864374),(-396199651864370)⟩,⟨(-1498980594363858),(-1498980594363853)⟩⟩,⟨⟨(-246825802193752),(-246825802193747)⟩,⟨(-1468984499065863),(-1468984499065858)⟩⟩,⟨⟨(-106229540226973),(-106229540226969)⟩,⟨(-1427750830672399),(-1427750830672395)⟩⟩,⟨⟨25039348047242,25039348047247⟩,⟨(-1376437852121438),(-1376437852121434)⟩⟩,⟨⟨146543143641828,146543143641832⟩,⟨(-1316202960193134),(-1316202960193130)⟩⟩,⟨⟨257952155164087,257952155164091⟩,⟨(-1248193892417845),(-1248193892417841)⟩⟩,⟨⟨359040102929139,359040102929144⟩,⟨(-1173540547831909),(-1173540547831905)⟩⟩,⟨⟨449678995901819,449678995901823⟩,⟨(-1093347450993127),(-1093347450993123)⟩⟩,⟨⟨529833571260995,529833571260999⟩,⟨(-1008686881708640),(-1008686881708635)⟩⟩,⟨⟨599555366219537,599555366219541⟩,⟨(-920592686133903),(-920592686133899)⟩⟩,⟨⟨658976490960072,658976490960076⟩,⟨(-830054778328488),(-830054778328483)⟩⟩,⟨⟨708303170200617,708303170200622⟩,⟨(-738014335053412),(-738014335053407)⟩⟩,⟨⟨747809119028051,747809119028055⟩,⟨(-645359680610614),(-645359680610610)⟩⟩,⟨⟨777828816277522,777828816277526⟩,⟨(-552922852898389),(-552922852898385)⟩⟩,⟨⟨798750735940533,798750735940537⟩,⟨(-461476836620707),(-461476836620703)⟩⟩,⟨⟨811010593904097,811010593904102⟩,⟨(-371733444772367),(-371733444772362)⟩⟩] +lemma kernel4_0_r0_8_eq : ∀ k : Fin 16, kernel4_0Expr 0 8 k = kernel4_0_r0_8 k := by decide +kernel +noncomputable def kernel4_0_r0_9 : Fin 16 → CBox := ![⟨⟨815084663809441,815084663809445⟩,⟨(-284341825147956),(-284341825147952)⟩⟩,⟨⟨811483212023205,811483212023209⟩,⟨(-199887564708062),(-199887564708057)⟩⟩,⟨⟨800744097689147,800744097689151⟩,⟨(-118892361192238),(-118892361192234)⟩⟩,⟨⟨783426579625120,783426579625124⟩,⟨(-41814228401191),(-41814228401186)⟩⟩,⟨⟨760105367499227,760105367499231⟩,⟨30951800918959,30951800918963⟩⟩,⟨⟨731364950309122,731364950309127⟩,⟨99072512673138,99072512673142⟩⟩,⟨⟨697794230746142,697794230746146⟩,⟨162274929127930,162274929127934⟩⟩,⟨⟨659981489595924,659981489595928⟩,⟨220344347467853,220344347467857⟩⟩,⟨⟨618509699950878,618509699950882⟩,⟨273122040590978,273122040590983⟩⟩,⟨⟨573952206725946,573952206725950⟩,⟨320502661783771,320502661783776⟩⟩,⟨⟨526868782813190,526868782813195⟩,⟨362431394768327,362431394768331⟩⟩,⟨⟨477802069214554,477802069214558⟩,⟨398900890100998,398900890101002⟩⟩,⟨⟨427274402684307,427274402684312⟩,⟨429948028047727,429948028047731⟩⟩,⟨⟨375785030817862,375785030817866⟩,⟨455650546897515,455650546897520⟩⟩,⟨⟨323807711162981,323807711162985⟩,⟨476123574232266,476123574232270⟩⟩,⟨⟨271788687820212,271788687820216⟩,⟨491516096980560,491516096980564⟩⟩] +lemma kernel4_0_r0_9_eq : ∀ k : Fin 16, kernel4_0Expr 0 9 k = kernel4_0_r0_9 k := by decide +kernel +noncomputable def kernel4_0_r0_10 : Fin 16 → CBox := ![⟨⟨220145036155390,220145036155394⟩,⟨502007404176745,502007404176749⟩⟩,⟨⟨169263363678584,169263363678588⟩,⟨507803534257644,507803534257648⟩⟩,⟨⟨119498852857252,119498852857256⟩,⟨509133756489362,509133756489366⟩⟩,⟨⟨71174629630489,71174629630493⟩,⟨506247113757355,506247113757360⟩⟩,⟨⟨24581439675976,24581439675980⟩,⟨499409051505529,499409051505534⟩⟩,⟨⟨(-20022386950970),(-20022386950966)⟩,⟨488898155103484,488898155103488⟩⟩,⟨⟨(-62410703341212),(-62410703341208)⟩,⟨475003015384027,475003015384031⟩⟩,⟨⟨(-102389066838077),(-102389066838073)⟩,⟨458019239552087,458019239552091⟩⟩,⟨⟨(-139794035770495),(-139794035770491)⟩,⟨438246622145999,438246622146003⟩⟩,⟨⟨(-174492264234410),(-174492264234406)⟩,⟨415986488256103,415986488256107⟩⟩,⟨⟨(-206379417486992),(-206379417486988)⟩,⟨391539218794310,391539218794314⟩⟩,⟨⟨(-235378930442275),(-235378930442271)⟩,⟨365201965280765,365201965280770⟩⟩,⟨⟨(-261440631478760),(-261440631478756)⟩,⟨337266559386559,337266559386563⟩⟩,⟨⟨(-284539253305993),(-284539253305989)⟩,⟨308017620359178,308017620359182⟩⟩,⟨⟨(-304672852006553),(-304672852006549)⟩,⟨277730861471916,277730861471920⟩⟩,⟨⟨(-321861154590338),(-321861154590334)⟩,⟨246671594790484,246671594790488⟩⟩] +lemma kernel4_0_r0_10_eq : ∀ k : Fin 16, kernel4_0Expr 0 10 k = kernel4_0_r0_10 k := by decide +kernel +noncomputable def kernel4_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-336143854488286),(-336143854488281)⟩,⟨215093431846728,215093431846732⟩⟩,⟨⟨(-347578873391121),(-347578873391117)⟩,⟨183237176257151,183237176257155⟩⟩,⟨⟨(-356240606723868),(-356240606723863)⟩,⟨151329902926454,151329902926458⟩⟩,⟨⟨(-362218168856446),(-362218168856442)⟩,⟨119584217235380,119584217235385⟩⟩,⟨⟨(-365613652902313),(-365613652902309)⟩,⟨88197686528510,88197686528514⟩⟩,⟨⟨(-366540418667237),(-366540418667233)⟩,⟨57352435289178,57352435289182⟩⟩,⟨⟨(-365121420994916),(-365121420994912)⟩,⟨27214894613311,27214894613315⟩⟩,⟨⟨(-361487589430015),(-361487589430011)⟩,⟨(-2064304033417),(-2064304033413)⟩⟩,⟨⟨(-355776268796214),(-355776268796210)⟩,⟨(-30350301274859),(-30350301274855)⟩⟩,⟨⟨(-348129728979833),(-348129728979829)⟩,⟨(-57523859347701),(-57523859347697)⟩⟩,⟨⟨(-338693750929876),(-338693750929872)⟩,⟨(-83481099755230),(-83481099755226)⟩⟩,⟨⟨(-327616294643603),(-327616294643599)⟩,⟨(-108133140215910),(-108133140215905)⟩⟩,⟨⟨(-315046253711894),(-315046253711890)⟩,⟨(-131405642057013),(-131405642057009)⟩⟩,⟨⟨(-301132299858767),(-301132299858763)⟩,⟨(-153238279086493),(-153238279086489)⟩⟩,⟨⟨(-286021819831305),(-286021819831301)⟩,⟨(-173584138765978),(-173584138765974)⟩⟩,⟨⟨(-269859945985108),(-269859945985104)⟩,⟨(-192409066213801),(-192409066213797)⟩⟩] +lemma kernel4_0_r0_11_eq : ∀ k : Fin 16, kernel4_0Expr 0 11 k = kernel4_0_r0_11 k := by decide +kernel +noncomputable def kernel4_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-252788680971221),(-252788680971217)⟩,⟨(-209690961199261),(-209690961199257)⟩⟩,⟨⟨(-234946116065835),(-234946116065831)⟩,⟨(-225419037857590),(-225419037857586)⟩⟩,⟨⟨(-216465741896914),(-216465741896910)⟩,⟨(-239593056368866),(-239593056368862)⟩⟩,⟨⟨(-197475849612937),(-197475849612933)⟩,⟨(-252222535313053),(-252222535313049)⟩⟩,⟨⟨(-178099019908807),(-178099019908803)⟩,⟨(-263325952846013),(-263325952846009)⟩⟩,⟨⟨(-158451696772096),(-158451696772092)⟩,⟨(-272929944247045),(-272929944247041)⟩⟩,⟨⟨(-138643842337827),(-138643842337823)⟩,⟨(-281068502774757),(-281068502774753)⟩⟩,⟨⟨(-118778668840031),(-118778668840027)⟩,⟨(-287782190143231),(-287782190143227)⟩⟩,⟨⟨(-98952443320730),(-98952443320726)⟩,⟨(-293117362301041),(-293117362301037)⟩⟩,⟨⟨(-79254360498796),(-79254360498792)⟩,⟨(-297125415568925),(-297125415568921)⟩⟩,⟨⟨(-59766479008537),(-59766479008533)⟩,⟨(-299862057573083),(-299862057573079)⟩⟩,⟨⟨(-40563716087242),(-40563716087238)⟩,⟨(-301386606806176),(-301386606806172)⟩⟩,⟨⟨(-21713895717774),(-21713895717770)⟩,⟨(-301761324061455),(-301761324061451)⟩⟩,⟨⟨(-3277845212355),(-3277845212351)⟩,⟨(-301050778421230),(-301050778421226)⟩⟩,⟨⟨14690464747673,14690464747677⟩,⟨(-299321249942848),(-299321249942844)⟩⟩,⟨⟨32143741528785,32143741528789⟩,⟨(-296640170676095),(-296640170676091)⟩⟩] +lemma kernel4_0_r0_12_eq : ∀ k : Fin 16, kernel4_0Expr 0 12 k = kernel4_0_r0_12 k := by decide +kernel +noncomputable def kernel4_0_r0_13 : Fin 16 → CBox := ![⟨⟨49041158220049,49041158220053⟩,⟨(-293075605168040),(-293075605168036)⟩⟩,⟨⟨65348112220559,65348112220563⟩,⟨(-288695771166475),(-288695771166471)⟩⟩,⟨⟨81035959218489,81035959218493⟩,⟨(-283568600822741),(-283568600822737)⟩⟩,⟨⟨96081726839284,96081726839288⟩,⟨(-277761342319392),(-277761342319388)⟩⟩,⟨⟨110467812018143,110467812018147⟩,⟨(-271340201508579),(-271340201508575)⟩⟩,⟨⟨124181665912660,124181665912664⟩,⟨(-264370022842795),(-264370022842791)⟩⟩,⟨⟨137215469919307,137215469919311⟩,⟨(-256914008610669),(-256914008610665)⟩⟩,⟨⟨149565806095999,149565806096002⟩,⟨(-249033475255830),(-249033475255826)⟩⟩,⟨⟨161233325025636,161233325025640⟩,⟨(-240787645355574),(-240787645355570)⟩⟩,⟨⟨172222413885803,172222413885807⟩,⟨(-232233473666807),(-232233473666803)⟩⟩,⟨⟨182540867219932,182540867219935⟩,⟨(-223425505508191),(-223425505508187)⟩⟩,⟨⟨192199562638596,192199562638600⟩,⟨(-214415765637578),(-214415765637574)⟩⟩,⟨⟨201212143417923,201212143417927⟩,⟨(-205253675701248),(-205253675701244)⟩⟩,⟨⟨209594709707712,209594709707716⟩,⟨(-195985998274016),(-195985998274012)⟩⟩,⟨⟨217365519816406,217365519816410⟩,⟨(-186656805474957),(-186656805474953)⟩⟩,⟨⟨224544702805145,224544702805149⟩,⟨(-177307470130471),(-177307470130467)⟩⟩] +lemma kernel4_0_r0_13_eq : ∀ k : Fin 16, kernel4_0Expr 0 13 k = kernel4_0_r0_13 k := by decide +kernel +noncomputable def kernel4_0_r0_14 : Fin 16 → CBox := ![⟨⟨231153983399936,231153983399940⟩,⟨(-167976677462335),(-167976677462331)⟩⟩,⟨⟨237216420020388,237216420020392⟩,⟨(-158700455301457),(-158700455301453)⟩⟩,⟨⟨242756156526663,242756156526667⟩,⟨(-149512220866080),(-149512220866076)⟩⟩,⟨⟨247798188103134,247798188103138⟩,⟨(-140442842194385),(-140442842194382)⟩⟩,⟨⟨252368141528956,252368141528960⟩,⟨(-131520712383547),(-131520712383543)⟩⟩,⟨⟨256492069931715,256492069931718⟩,⟨(-122771834859008),(-122771834859004)⟩⟩,⟨⟨260196261981134,260196261981138⟩,⟨(-114219917976773),(-114219917976769)⟩⟩,⟨⟨263507065355022,263507065355026⟩,⟨(-105886477346640),(-105886477346636)⟩⟩,⟨⟨266450724199144,266450724199148⟩,⟨(-97790944353708),(-97790944353704)⟩⟩,⟨⟨269053230206099,269053230206103⟩,⟨(-89950779448004),(-89950779448000)⟩⟩,⟨⟨271340186855127,271340186855131⟩,⟨(-82381588866147),(-82381588866143)⟩⟩,⟨⟨273336686284497,273336686284501⟩,⟨(-75097243543758),(-75097243543754)⟩⟩,⟨⟨275067198210172,275067198210176⟩,⟨(-68109999071251),(-68109999071247)⟩⟩,⟨⟨276555470258264,276555470258268⟩,⟨(-61430615638561),(-61430615638557)⟩⟩,⟨⟨277824439043435,277824439043438⟩,⟨(-55068477004532),(-55068477004528)⟩⟩,⟨⟨278896151300492,278896151300496⟩,⟨(-49031707614273),(-49031707614269)⟩⟩] +lemma kernel4_0_r0_14_eq : ∀ k : Fin 16, kernel4_0Expr 0 14 k = kernel4_0_r0_14 k := by decide +kernel +noncomputable def kernel4_0_r0_15 : Fin 16 → CBox := ![⟨⟨279791694361083,279791694361087⟩,⟨(-43327287071603),(-43327287071599)⟩⟩,⟨⟨280531135260809,280531135260813⟩,⟨(-37961161253550),(-37961161253547)⟩⟩,⟨⟨281133467763838,281133467763841⟩,⟨(-32938349429459),(-32938349429455)⟩⟩,⟨⟨281616566601157,281616566601161⟩,⟨(-28263046817901),(-28263046817897)⟩⟩,⟨⟨281997148234603,281997148234607⟩,⟨(-23938722080764),(-23938722080760)⟩⟩,⟨⟨282290737480793,282290737480797⟩,⟨(-19968209314835),(-19968209314831)⟩⟩,⟨⟨282511639356768,282511639356772⟩,⟨(-16353794157349),(-16353794157345)⟩⟩,⟨⟨282672915541618,282672915541622⟩,⟨(-13097293673261),(-13097293673257)⟩⟩,⟨⟨282786364885269,282786364885272⟩,⟨(-10200129738507),(-10200129738503)⟩⟩,⟨⟨282862507436380,282862507436384⟩,⟨(-7663395675446),(-7663395675442)⟩⟩,⟨⟨282910571505442,282910571505446⟩,⟨(-5487915934412),(-5487915934408)⟩⟩,⟨⟨282938483326127,282938483326131⟩,⟨(-3674298648848),(-3674298648844)⟩⟩,⟨⟨282952858927549,282952858927553⟩,⟨(-2222980921644),(-2222980921640)⟩⟩,⟨⟨282958997881752,282958997881756⟩,⟨(-1134266726807),(-1134266726803)⟩⟩,⟨⟨282960878644046,282960878644050⟩,⟨(-408357334567),(-408357334563)⟩⟩,⟨⟨282961155258750,282961155258754⟩,⟨(-45374189346),(-45374189343)⟩⟩] +lemma kernel4_0_r0_15_eq : ∀ k : Fin 16, kernel4_0Expr 0 15 k = kernel4_0_r0_15 k := by decide +kernel +noncomputable def kernel4_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel4_0_r0_0,kernel4_0_r0_1,kernel4_0_r0_2,kernel4_0_r0_3,kernel4_0_r0_4,kernel4_0_r0_5,kernel4_0_r0_6,kernel4_0_r0_7,kernel4_0_r0_8,kernel4_0_r0_9,kernel4_0_r0_10,kernel4_0_r0_11,kernel4_0_r0_12,kernel4_0_r0_13,kernel4_0_r0_14,kernel4_0_r0_15] +lemma kernel4_0_r0_eq (i k : Fin 16) : kernel4_0Expr 0 i k = kernel4_0_r0 i k := by + fin_cases i + · exact kernel4_0_r0_0_eq k + · exact kernel4_0_r0_1_eq k + · exact kernel4_0_r0_2_eq k + · exact kernel4_0_r0_3_eq k + · exact kernel4_0_r0_4_eq k + · exact kernel4_0_r0_5_eq k + · exact kernel4_0_r0_6_eq k + · exact kernel4_0_r0_7_eq k + · exact kernel4_0_r0_8_eq k + · exact kernel4_0_r0_9_eq k + · exact kernel4_0_r0_10_eq k + · exact kernel4_0_r0_11_eq k + · exact kernel4_0_r0_12_eq k + · exact kernel4_0_r0_13_eq k + · exact kernel4_0_r0_14_eq k + · exact kernel4_0_r0_15_eq k +noncomputable def kernel4_0_r1_0 : Fin 16 → CBox := ![⟨⟨3053744392401084269485,3053744392401084274839⟩,⟨(-5402188128530995443845),(-5402188128530995438469)⟩⟩,⟨⟨3052117847024816337423,3052117847024816342775⟩,⟨(-5397781414640303728529),(-5397781414640303723155)⟩⟩,⟨⟨3048867391954174836805,3048867391954174842151⟩,⟨(-5388978524879516222114),(-5388978524879516216746)⟩⟩,⟨⟨3043998290700685317984,3043998290700685323318⟩,⟨(-5375800493399111374312),(-5375800493399111368955)⟩⟩,⟨⟨3037518418941697681028,3037518418941697686348⟩,⟨(-5358278766932745386788),(-5358278766932745381445)⟩⟩,⟨⟨3029438241126123807014,3029438241126123812317⟩,⟨(-5336455080062294043017),(-5336455080062294037692)⟩⟩,⟨⟨3019770779470478929044,3019770779470478934328⟩,⟨(-5310381289991998166983),(-5310381289991998161677)⟩⟩,⟨⟨3008531575504621726907,3008531575504621732168⟩,⟨(-5280119171753631342772),(-5280119171753631337489)⟩⟩,⟨⟨2995738644363863197508,2995738644363863202742⟩,⟨(-5245740174982497218024),(-5245740174982497212768)⟩⟩,⟨⟨2981412422059720251233,2981412422059720256437⟩,⟨(-5207325143613723354014),(-5207325143613723348788)⟩⟩,⟨⟨2965575705995238563053,2965575705995238568225⟩,⟨(-5164964000048266039739),(-5164964000048266034545)⟩⟩,⟨⟨2948253589022236072604,2948253589022236077738⟩,⟨(-5118755395526878521571),(-5118755395526878516416)⟩⟩,⟨⟨2929473387366786060081,2929473387366786065176⟩,⟨(-5068806328626724382417),(-5068806328626724377300)⟩⟩,⟨⟨2909264562775558693992,2909264562775558699046⟩,⟨(-5015231733958147893494),(-5015231733958147888419)⟩⟩,⟨⟨2887658639259095687508,2887658639259095692517⟩,⟨(-4958154043287272368897),(-4958154043287272363867)⟩⟩,⟨⟨2864689114828560818448,2864689114828560823411⟩,⟨(-4897702721442641578228),(-4897702721442641573244)⟩⟩] +lemma kernel4_0_r1_0_eq : ∀ k : Fin 16, kernel4_0Expr 1 0 k = kernel4_0_r1_0 k := by decide +kernel +noncomputable def kernel4_0_r1_1 : Fin 16 → CBox := ![⟨⟨2840391368639880659245,2840391368639880664155⟩,⟨(-4834013779480238539152),(-4834013779480238534220)⟩⟩,⟨⟨2814802563973391225330,2814802563973391230189⟩,⟨(-4767229267680241625984),(-4767229267680241621104)⟩⟩,⟨⟨2787961547488099093255,2787961547488099098056⟩,⟨(-4697496751030286218253),(-4697496751030286213430)⟩⟩,⟨⟨2759908745197446689396,2759908745197446694143⟩,⟨(-4624968769913415699079),(-4624968769913415694311)⟩⟩,⟨⟨2730686055618072066024,2730686055618072070707⟩,⟨(-4549802288764103020891),(-4549802288764103016187)⟩⟩,⟨⟨2700336740544537802423,2700336740544537807046⟩,⟨(-4472158135482627834200),(-4472158135482627829558)⟩⟩,⟨⟨2668905313901467319697,2668905313901467324255⟩,⟨(-4392200434406777557633),(-4392200434406777553054)⟩⟩,⟨⟨2636437429120094787430,2636437429120094791923⟩,⟨(-4310096035630522906466),(-4310096035630522901953)⟩⟩,⟨⟨2602979765479058657490,2602979765479058661914⟩,⟨(-4226013943432360210082),(-4226013943432360205637)⟩⟩,⟨⟨2568579913839524446672,2568579913839524451026⟩,⟨(-4140124746531911549505),(-4140124746531911545131)⟩⟩,⟨⟨2533286262192606450070,2533286262192606454354⟩,⟨(-4052600052832756128413),(-4052600052832756124110)⟩⟩,⟨⟨2497147881422785059434,2497147881422785063642⟩,⟨(-3963611931233080862193),(-3963611931233080857965)⟩⟩,⟨⟨2460214411674815035735,2460214411674815039871⟩,⟨(-3873332362994446232771),(-3873332362994446228616)⟩⟩,⟨⟨2422535949693729961068,2422535949693729965126⟩,⟨(-3781932705053729252670),(-3781932705053729248593)⟩⟩,⟨⟨2384162937488215895498,2384162937488215899481⟩,⟨(-3689583167545185414184),(-3689583167545185410182)⟩⟩,⟨⟨2345146052647103371413,2345146052647103375317⟩,⟨(-3596452307669703171252),(-3596452307669703167330)⟩⟩] +lemma kernel4_0_r1_1_eq : ∀ k : Fin 16, kernel4_0Expr 1 1 k = kernel4_0_r1_1 k := by decide +kernel +noncomputable def kernel4_0_r1_2 : Fin 16 → CBox := ![⟨⟨2305536100617261837051,2305536100617261840877⟩,⟨(-3502706541907914196236),(-3502706541907914192392)⟩⟩,⟨⟨2265383909229021914580,2265383909229021918326⟩,⟨(-3408509678424133398108),(-3408509678424133394345)⟩⟩,⟨⟨2224740225732639430622,2224740225732639434288⟩,⟨(-3314022471350441542764),(-3314022471350441539081)⟩⟩,⟨⟨2183655616586482884279,2183655616586482887862⟩,⟨(-3219402198475928622465),(-3219402198475928618865)⟩⟩,⟨⟨2142180370214792632551,2142180370214792636053⟩,⟨(-3124802263696544761731),(-3124802263696544758211)⟩⟩,⟨⟨2100364402930231010271,2100364402930231013689⟩,⟨(-3030371825407520234243),(-3030371825407520230808)⟩⟩,⟨⟨2058257168194206822421,2058257168194206825760⟩,⟨(-2936255451844273510548),(-2936255451844273507192)⟩⟩,⟨⟨2015907569366285929808,2015907569366285933065⟩,⟨(-2842592804200464227647),(-2842592804200464224374)⟩⟩,⟨⟨1973363876073043220956,1973363876073043224131⟩,⟨(-2749518348174674869911),(-2749518348174674866720)⟩⟩,⟨⟨1930673644306600797795,1930673644306600800888⟩,⟨(-2657161094421388504815),(-2657161094421388501705)⟩⟩,⟨⟨1887883640343942189343,1887883640343942192353⟩,⟨(-2565644368208687201720),(-2565644368208687198695)⟩⟩,⟨⟨1845039768559980885791,1845039768559980888720⟩,⟨(-2475085608415583921958),(-2475085608415583919013)⟩⟩,⟨⟨1802187003190360133068,1802187003190360135915⟩,⟨(-2385596195837208527536),(-2385596195837208524673)⟩⟩,⟨⟨1759369324084115486911,1759369324084115489678⟩,⟨(-2297281310607209170948),(-2297281310607209168167)⟩⟩,⟨⟨1716629656471667643361,1716629656471667646047⟩,⟨(-2210239818394634541248),(-2210239818394634538547)⟩⟩,⟨⟨1674009814760136922297,1674009814760136924905⟩,⟨(-2124564184888073461726),(-2124564184888073459104)⟩⟩] +lemma kernel4_0_r1_2_eq : ∀ k : Fin 16, kernel4_0Expr 1 2 k = kernel4_0_r1_2 k := by decide +kernel +noncomputable def kernel4_0_r1_3 : Fin 16 → CBox := ![⟨⟨1631550450355670988707,1631550450355670991237⟩,⟨(-2040340417943697381057),(-2040340417943697378514)⟩⟩,⟨⟨1589291003501326094677,1589291003501326097130⟩,⟨(-1957648036646734306722),(-1957648036646734304256)⟩⟩,⟨⟨1547269659108996790891,1547269659108996793268⟩,⟨(-1876560066418358117768),(-1876560066418358115378)⟩⟩,⟨⟨1505523306554894349933,1505523306554894352234⟩,⟨(-1797143059192464688667),(-1797143059192464686354)⟩⟩,⟨⟨1464087503400063867588,1464087503400063869813⟩,⟨(-1719457137589686728322),(-1719457137589686726086)⟩⟩,⟨⟨1422996442990329135372,1422996442990329137523⟩,⟨(-1643556061929535527570),(-1643556061929535525407)⟩⟩,⟨⟨1382282925883781110510,1382282925883781112590⟩,⟨(-1569487318845916481506),(-1569487318845916479414)⟩⟩,⟨⟨1341978335048393635051,1341978335048393637062⟩,⟨(-1497292230206519238415),(-1497292230206519236394)⟩⟩,⟨⟨1302112614767469753506,1302112614767469755445⟩,⟨(-1427006080982715363140),(-1427006080982715361191)⟩⟩,⟨⟨1262714253186303557085,1262714253186303558957⟩,⟨(-1358658264673503222954),(-1358658264673503221073)⟩⟩,⟨⟨1223810268429597007228,1223810268429597009031⟩,⟨(-1292272444854536983450),(-1292272444854536981638)⟩⟩,⟨⟨1185426198215712477446,1185426198215712479182⟩,⟨(-1227866731401103982661),(-1227866731401103980916)⟩⟩,⟨⟨1147586092890687905624,1147586092890687907296⟩,⟨(-1165453869921742358212),(-1165453869921742356531)⟩⟩,⟨⟨1110312511802016222938,1110312511802016224547⟩,⟨(-1105041442936625164291),(-1105041442936625162674)⟩⟩,⟨⟨1073626522929424695645,1073626522929424697192⟩,⟨(-1046632081341428002010),(-1046632081341428000456)⟩⟩,⟨⟨1037547705687221345053,1037547705687221346540⟩,⟨(-990223684712644073946),(-990223684712644072451)⟩⟩] +lemma kernel4_0_r1_3_eq : ∀ k : Fin 16, kernel4_0Expr 1 3 k = kernel4_0_r1_3 k := by decide +kernel +noncomputable def kernel4_0_r1_4 : Fin 16 → CBox := ![⟨⟨1002094156810151609281,1002094156810151610709⟩,⟨(-935809649033670247160),(-935809649033670245725)⟩⟩,⟨⟨967282499232084884334,967282499232084885703⟩,⟨(-883379100451880929734),(-883379100451880928358)⟩⟩,⟨⟨933127893864192972032,933127893864192973345⟩,⟨(-832917133714725209819),(-832917133714725208499)⟩⟩,⟨⟨899644054176565778156,899644054176565779416⟩,⟨(-784405053976996708740),(-784405053976996707474)⟩⟩,⟨⟨866843263484418364103,866843263484418365309⟩,⟨(-737820620721189728786),(-737820620721189727575)⟩⟩,⟨⟨834736394837171442401,834736394837171443556⟩,⟨(-693138292587615676923),(-693138292587615675763)⟩⟩,⟨⟨803332933405737256095,803332933405737257200⟩,⟨(-650329471970054189342),(-650329471970054188232)⟩⟩,⟨⟨772641001260325418139,772641001260325419196⟩,⟨(-609362748295501178423),(-609362748295501177362)⟩⟩,⟨⟨742667384428017225826,742667384428017226834⟩,⟨(-570204138972407544830),(-570204138972407543818)⟩⟩,⟨⟨713417562116267505977,713417562116267506941⟩,⟨(-532817327060048078483),(-532817327060048077515)⟩⟩,⟨⟨684895737985411371868,684895737985411372788⟩,⟨(-497163894781709462449),(-497163894781709461525)⟩⟩,⟨⟨657104873350215478595,657104873350215479471⟩,⟨(-463203552075651632215),(-463203552075651631336)⟩⟩,⟨⟨630046722187559442696,630046722187559443531⟩,⟨(-430894359449717044768),(-430894359449717043929)⟩⟩,⟨⟨603721867824505889855,603721867824505890651⟩,⟨(-400192944477506558811),(-400192944477506558011)⟩⟩,⟨⟨578129761178361760487,578129761178361761244⟩,⟨(-371054711345710056799),(-371054711345710056039)⟩⟩,⟨⟨553268760417894454668,553268760417894455389⟩,⟨(-343434042933010840267),(-343434042933010839543)⟩⟩] +lemma kernel4_0_r1_4_eq : ∀ k : Fin 16, kernel4_0Expr 1 4 k = kernel4_0_r1_4 k := by decide +kernel +noncomputable def kernel4_0_r1_5 : Fin 16 → CBox := ![⟨⟨529136171912689316865,529136171912689317550⟩,⟨(-317284494970547854142),(-317284494970547853455)⟩⟩,⟨⟨505728292335763839245,505728292335763839896⟩,⟨(-292558981901829298691),(-292558981901829298038)⟩⟩,⟨⟨483040451783030709407,483040451783030710024⟩,⟨(-269209954125894019584),(-269209954125894018965)⟩⟩,⟨⟨461067057772065455533,461067057772065456120⟩,⟨(-247189566371100937616),(-247189566371100937027)⟩⟩,⟨⟨439801639981920332609,439801639981920333166⟩,⟨(-226449837007918224392),(-226449837007918223833)⟩⟩,⟨⟨419236895595465367926,419236895595465368453⟩,⟨(-206942798167247904869),(-206942798167247904342)⟩⟩,⟨⟨399364735105956465860,399364735105956466358⟩,⟨(-188620636585960706058),(-188620636585960705559)⟩⟩,⟨⟨380176328450250257706,380176328450250258177⟩,⟨(-171435825153269539822),(-171435825153269539349)⟩⟩,⟨⟨361662151332321519409,361662151332321519855⟩,⟨(-155341245180212589055),(-155341245180212588607)⟩⟩,⟨⟨343812031602501250637,343812031602501251059⟩,⟨(-140290299459756906821),(-140290299459756906398)⟩⟩,⟨⟨326615195560145817741,326615195560145818138⟩,⟨(-126237016226811098007),(-126237016226811097609)⟩⟩,⟨⟨310060314050267927879,310060314050267928256⟩,⟨(-113136144165721488839),(-113136144165721488461)⟩⟩,⟨⟨294135548228000836927,294135548228000837283⟩,⟨(-100943238647618705994),(-100943238647618705638)⟩⟩,⟨⟨278828594868614685079,278828594868614685413⟩,⟨(-89614739411305188061),(-89614739411305187726)⟩⟩,⟨⟨264126731105139414301,264126731105139414617⟩,⟨(-79108039929276923484),(-79108039929276923168)⟩⟩,⟨⟨250016858480448518580,250016858480448518876⟩,⟨(-69381548725024162289),(-69381548725024161992)⟩⟩] +lemma kernel4_0_r1_5_eq : ∀ k : Fin 16, kernel4_0Expr 1 5 k = kernel4_0_r1_5 k := by decide +kernel +noncomputable def kernel4_0_r1_6 : Fin 16 → CBox := ![⟨⟨236485546205893426112,236485546205893426391⟩,⟨(-60394742929044649044),(-60394742929044648765)⟩⟩,⟨⟨223519073524216920148,223519073524216920410⟩,⟨(-52108214379134632770),(-52108214379134632507)⟩⟩,⟨⟨211103471080479262648,211103471080479262895⟩,⟨(-44483708585617757913),(-44483708585617757665)⟩⟩,⟨⟨199224561211062989032,199224561211062989265⟩,⟨(-37484156894362660241),(-37484156894362660008)⟩⟩,⟨⟨187867997067439443358,187867997067439443575⟩,⟨(-31073702189869814168),(-31073702189869813951)⟩⟩,⟨⟨177019300498237686603,177019300498237686808⟩,⟨(-25217718487528420842),(-25217718487528420638)⟩⟩,⟨⟨166663898620208582596,166663898620208582788⟩,⟨(-19882824768512879559),(-19882824768512879367)⟩⟩,⟨⟨156787159015876836329,156787159015876836507⟩,⟨(-15036893412868304997),(-15036893412868304819)⟩⟩,⟨⟨147374423502974311403,147374423502974311571⟩,⟨(-10649053586291276352),(-10649053586291276183)⟩⟩,⟨⟨138411040428101994807,138411040428101994965⟩,⟨(-6689689934112583638),(-6689689934112583479)⟩⟩,⟨⟨129882395444429045493,129882395444429045641⟩,⟨(-3130436932200203293),(-3130436932200203145)⟩⟩,⟨⟨121773940740560098004,121773940740560098142⟩,⟨55830760911205722,55830760911205860⟩⟩,⟨⟨114071222694942572945,114071222694942573075⟩,⟨2895011613230141135,2895011613230141264⟩⟩,⟨⟨106759907937302287953,106759907937302288075⟩,⟨5411793860595989230,5411793860595989351⟩⟩,⟨⟨99825807805548570266,99825807805548570380⟩,⟨7629675160101280891,7629675160101281005⟩⟩,⟨⟨93254901193342347000,93254901193342347104⟩,⟨9570984946018633872,9570984946018633976⟩⟩] +lemma kernel4_0_r1_6_eq : ∀ k : Fin 16, kernel4_0Expr 1 6 k = kernel4_0_r1_6 k := by decide +kernel +noncomputable def kernel4_0_r1_7 : Fin 16 → CBox := ![⟨⟨87033355790038190975,87033355790038191072⟩,⟨11256909189767556257,11256909189767556355⟩⟩,⟨⟨81147547720962959774,81147547720962959865⟩,⟨12707517277335313157,12707517277335313247⟩⟩,⟨⟨75584079601951652548,75584079601951652632⟩,⟨13941790730028590837,13941790730028590921⟩⟩,⟨⟨70329797027700950612,70329797027700950691⟩,⟨14977653507355535145,14977653507355535223⟩⟩,⟨⟨65371803518801565241,65371803518801565315⟩,⟨15832003644105270372,15832003644105270445⟩⟩,⟨⟨60697473957254417235,60697473957254417304⟩,⟨16520745987196340696,16520745987196340764⟩⟩,⟨⟨56294466544848704863,56294466544848704927⟩,⟨17058825811506612277,17058825811506612340⟩⟩,⟨⟨52150733322971380408,52150733322971380465⟩,⟨17460263107582835426,17460263107582835482⟩⟩,⟨⟨48254529296220086710,48254529296220086765⟩,⟨17738187347773901974,17738187347773902029⟩⟩,⟨⟨44594420205601063555,44594420205601063606⟩,⟨17904872550861150824,17904872550861150875⟩⟩,⟨⟨41159289000108866090,41159289000108866138⟩,⟨17971772478602721718,17971772478602721766⟩⟩,⟨⟨37938341058107815229,37938341058107815272⟩,⟨17949555810705119893,17949555810705119935⟩⟩,⟨⟨34921108212170537537,34921108212170537576⟩,⟨17848141157529115309,17848141157529115347⟩⟩,⟨⟨32097451632883908810,32097451632883908846⟩,⟨17676731782280967940,17676731782280967976⟩⟩,⟨⟨29457563628616683732,29457563628616683768⟩,⟨17443849916492378317,17443849916492378352⟩⟩,⟨⟨26991968419367678333,26991968419367678365⟩,⟨17157370564218349025,17157370564218349057⟩⟩] +lemma kernel4_0_r1_7_eq : ∀ k : Fin 16, kernel4_0Expr 1 7 k = kernel4_0_r1_7 k := by decide +kernel +noncomputable def kernel4_0_r1_8 : Fin 16 → CBox := ![⟨⟨24691521943592061670,24691521943592061700⟩,⟨16824554701552014927,16824554701552014958⟩⟩,⟨⟨22547410757351251771,22547410757351251802⟩,⟨16452081788745685010,16452081788745685040⟩⟩,⟨⟨20551150085265664381,20551150085265664411⟩,⟨16046081522419228976,16046081522419229007⟩⟩,⟨⟨18694581082586891958,18694581082586891987⟩,⟨15612164765016734209,15612164765016734237⟩⟩,⟨⟨16969867367265524445,16969867367265524473⟩,⟨15155453597830696491,15155453597830696517⟩⟩,⟨⟨15369490880192244413,15369490880192244440⟩,⟨14680610452544621927,14680610452544621954⟩⟩,⟨⟨13886247130853062058,13886247130853062085⟩,⟨14191866284348275696,14191866284348275723⟩⟩,⟨⟨12513239884484968753,12513239884484968778⟩,⟨13693047757256775240,13693047757256775265⟩⟩,⟨⟨11243875345466406298,11243875345466406322⟩,⟨13187603419320208542,13187603419320208566⟩⟩,⟨⟨10071855890148278866,10071855890148278888⟩,⟨12678628851952112493,12678628851952112515⟩⟩,⟨⟨8991173400646101355,8991173400646101377⟩,⟨12168890783643044935,12168890783643044957⟩⟩,⟨⟨7996102249292279344,7996102249292279364⟩,⟨11660850163871823919,11660850163871823939⟩⟩,⟨⟨7081191981508987334,7081191981508987356⟩,⟨11156684198095827699,11156684198095827721⟩⟩,⟨⟨6241259742825609246,6241259742825609266⟩,⟨10658307349308660999,10658307349308661020⟩⟩,⟨⟨5471382493648497880,5471382493648497898⟩,⟨10167391315815429689,10167391315815429707⟩⟩,⟨⟨4766889053212393753,4766889053212393772⟩,⟨9685383998610844643,9685383998610844661⟩⟩] +lemma kernel4_0_r1_8_eq : ∀ k : Fin 16, kernel4_0Expr 1 8 k = kernel4_0_r1_8 k := by decide +kernel +noncomputable def kernel4_0_r1_9 : Fin 16 → CBox := ![⟨⟨4123352011918861765,4123352011918861784⟩,⟨9213527475072276301,9213527475072276320⟩⟩,⟨⟨3536579549013286828,3536579549013286844⟩,⟨8752874998618244368,8752874998618244385⟩⟩,⟨⟨3002607190283083693,3002607190283083708⟩,⟨8304307046552661280,8304307046552661295⟩⟩,⟨⟨2517689538189588023,2517689538189588041⟩,⟨7868546440536760092,7868546440536760111⟩⟩,⟨⟨2078292004587346168,2078292004587346186⟩,⟨7446172566024471719,7446172566024471736⟩⟩,⟨⟨1681082573948910267,1681082573948910284⟩,⟨7037634718583513098,7037634718583513114⟩⟩,⟨⟨1322923622811428918,1322923622811428932⟩,⟨6643264606323912649,6643264606323912664⟩⟩,⟨⟨1000863819002916855,1000863819002916869⟩,⟨6263288038688188864,6263288038688188879⟩⟩,⟨⟨712130122099678457,712130122099678472⟩,⟨5897835832642617119,5897835832642617134⟩⟩,⟨⟨454119904519531058,454119904519531072⟩,⟨5546953967866232425,5546953967866232440⟩⟩,⟨⟨224393210674827592,224393210674827604⟩,⟨5210613022882166451,5210613022882166465⟩⟩,⟨⟨20665169700469795,20665169700469809⟩,⟨4888716924232764412,4888716924232764425⟩⟩,⟨⟨(-159201424560119554),(-159201424560119542)⟩,⟨4581111040783188259,4581111040783188270⟩⟩,⟨⟨(-317203354379853778),(-317203354379853766)⟩,⟨4287589655064715255,4287589655064715266⟩⟩,⟨⟨(-455204029520689012),(-455204029520689000)⟩,⟨4007902843254789000,4007902843254789011⟩⟩,⟨⟨(-574940340473622236),(-574940340473622224)⟩,⟨3741762794951421780,3741762794951421791⟩⟩] +lemma kernel4_0_r1_9_eq : ∀ k : Fin 16, kernel4_0Expr 1 9 k = kernel4_0_r1_9 k := by decide +kernel +noncomputable def kernel4_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-678029306380471426),(-678029306380471417)⟩,⟨3488849603349357292,3488849603349357302⟩⟩,⟨⟨(-765974511858716331),(-765974511858716319)⟩,⟨3248816555778266386,3248816555778266397⟩⟩,⟨⟨(-840172328268935292),(-840172328268935284)⟩,⟨3021294953832155251,3021294953832155259⟩⟩,⟨⟨(-901917916194399574),(-901917916194399564)⟩,⟨2805898491516307851,2805898491516307861⟩⟩,⟨⟨(-952411007044997011),(-952411007044997003)⟩,⟨2602227218974862057,2602227218974862065⟩⟩,⟨⟨(-992761462754132928),(-992761462754132920)⟩,⟨2409871118449146964,2409871118449146972⟩⟩,⟨⟨(-1023994613509293502),(-1023994613509293494)⟩,⟨2228413318164031799,2228413318164031807⟩⟩,⟨⟨(-1047056374346617583),(-1047056374346617576)⟩,⟨2057432968855844260,2057432968855844268⟩⟩,⟨⟨(-1062818142249488412),(-1062818142249488404)⟩,⟨1896507806649263636,1896507806649263644⟩⟩,⟨⟨(-1072081476123482028),(-1072081476123482019)⟩,⟨1745216424969625263,1745216424969625273⟩⟩,⟨⟨(-1075582562677880759),(-1075582562677880751)⟩,⟨1603140277148244696,1603140277148244704⟩⟩,⟨⟨(-1073996471830454546),(-1073996471830454538)⟩,⟨1469865430347979707,1469865430347979715⟩⟩,⟨⟨(-1067941205770558346),(-1067941205770558338)⟩,⟨1344984090409961457,1344984090409961465⟩⟩,⟨⟨(-1057981546269135385),(-1057981546269135377)⟩,⟨1228095916205307192,1228095916205307200⟩⟩,⟨⟨(-1044632705216380736),(-1044632705216380729)⟩,⟨1118809141072168336,1118809141072168344⟩⟩,⟨⟨(-1028363783702087236),(-1028363783702087228)⟩,⟨1016741517932622788,1016741517932622796⟩⟩] +lemma kernel4_0_r1_10_eq : ∀ k : Fin 16, kernel4_0Expr 1 10 k = kernel4_0_r1_10 k := by decide +kernel +noncomputable def kernel4_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-1009601045233569676),(-1009601045233569668)⟩,⟨921521103719132247,921521103719132255⟩⟩,⟨⟨(-988731008915045187),(-988731008915045181)⟩,⟨832786897799521499,832786897799521506⟩⟩,⟨⟨(-966103368593914762),(-966103368593914754)⟩,⟨750189348175216973,750189348175216981⟩⟩,⟨⟨(-942033744116974738),(-942033744116974731)⟩,⟨673390738341912210,673390738341912216⟩⟩,⟨⟨(-916806270936555146),(-916806270936555138)⟩,⟨602065466846628509,602065466846628517⟩⟩,⟨⟨(-890676034366222451),(-890676034366222443)⟩,⟨535900230751675849,535900230751675857⟩⟩,⟨⟨(-863871354811191346),(-863871354811191341)⟩,⟨474594123425331152,474594123425331157⟩⟩,⟨⟨(-836595930293052666),(-836595930293052661)⟩,⟨417858656321879744,417858656321879748⟩⟩,⟨⟨(-809030842554815526),(-809030842554815521)⟩,⟨365417713690481145,365417713690481151⟩⟩,⟨⟨(-781336432973431227),(-781336432973431221)⟩,⟨317007448463346897,317007448463346903⟩⟩,⟨⟨(-753654054425634316),(-753654054425634311)⟩,⟨272376126918959992,272376126918959999⟩⟩,⟨⟨(-726107705151687980),(-726107705151687976)⟩,⟨231283929095329782,231283929095329786⟩⟩,⟨⟨(-698805550542904042),(-698805550542904034)⟩,⟨193502711341194858,193502711341194866⟩⟩,⟨⟨(-671841338644929959),(-671841338644929953)⟩,⟨158815736839138269,158815736839138276⟩⟩,⟨⟨(-645295715021923181),(-645295715021923176)⟩,⟨127017379413108650,127017379413108656⟩⟩,⟨⟨(-619237442468893256),(-619237442468893249)⟩,⟨97912805443076979,97912805443076985⟩⟩] +lemma kernel4_0_r1_11_eq : ∀ k : Fin 16, kernel4_0Expr 1 11 k = kernel4_0_r1_11 k := by decide +kernel +noncomputable def kernel4_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-593724530892571670),(-593724530892571663)⟩,⟨71317638250632380,71317638250632386⟩⟩,⟨⟨(-568805282506918318),(-568805282506918310)⟩,⟨47057608890280870,47057608890280878⟩⟩,⟨⟨(-544519257309407671),(-544519257309407665)⟩,⟨24968196881039728,24968196881039735⟩⟩,⟨⟨(-520898163620042130),(-520898163620042122)⟩,⟨4894264040545306,4894264040545314⟩⟩,⟨⟨(-497966678277972963),(-497966678277972958)⟩,⟨(-13310315761799278),(-13310315761799273)⟩⟩,⟨⟨(-475743200901906846),(-475743200901906841)⟩,⟨(-29783028436261128),(-29783028436261123)⟩⟩,⟨⟨(-454240546431256651),(-454240546431256646)⟩,⟨(-44653090888196081),(-44653090888196074)⟩⟩,⟨⟨(-433466579976265967),(-433466579976265962)⟩,⟨(-58041819689411940),(-58041819689411933)⟩⟩,⟨⟨(-413424797817996985),(-413424797817996981)⟩,⟨(-70062995527973344),(-70062995527973340)⟩⟩,⟨⟨(-394114858213920011),(-394114858213920007)⟩,⟨(-80823221988615120),(-80823221988615116)⟩⟩,⟨⟨(-375533065482582762),(-375533065482582757)⟩,⟨(-90422277425892545),(-90422277425892541)⟩⟩,⟨⟨(-357672810662082343),(-357672810662082336)⟩,⟨(-98953458883588567),(-98953458883588562)⟩⟩,⟨⟨(-340524971862341383),(-340524971862341379)⟩,⟨(-106503917187834302),(-106503917187834297)⟩⟩,⟨⟨(-324078277260953564),(-324078277260953560)⟩,⟨(-113154982498968098),(-113154982498968094)⟩⟩,⟨⟨(-308319633526990348),(-308319633526990341)⟩,⟨(-118982479749416770),(-118982479749416765)⟩⟩,⟨⟨(-293234422296961407),(-293234422296961402)⟩,⟨(-124057033522853548),(-124057033522853541)⟩⟩] +lemma kernel4_0_r1_12_eq : ∀ k : Fin 16, kernel4_0Expr 1 12 k = kernel4_0_r1_12 k := by decide +kernel +noncomputable def kernel4_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-278806767172344712),(-278806767172344707)⟩,⟨(-128444362044557317),(-128444362044557313)⟩⟩,⟨⟨(-265019773558940610),(-265019773558940604)⟩,⟨(-132205560055215888),(-132205560055215881)⟩⟩,⟨⟨(-251855743524898109),(-251855743524898105)⟩,⟨(-135397370431290782),(-135397370431290778)⟩⟩,⟨⟨(-239296367716704126),(-239296367716704122)⟩,⟨(-138072444495361324),(-138072444495361320)⟩⟩,⟨⟨(-227322896240768725),(-227322896240768719)⟩,⟨(-140279591030417989),(-140279591030417982)⟩⟩,⟨⟨(-215916290292494470),(-215916290292494465)⟩,⟨(-142064014073665343),(-142064014073665338)⟩⟩,⟨⟨(-205057356194864800),(-205057356194864796)⟩,⟨(-143467539618766667),(-143467539618766663)⟩⟩,⟨⟨(-194726863394573672),(-194726863394573667)⟩,⟨(-144528831401318730),(-144528831401318726)⟩⟩,⟨⟨(-184905647855469677),(-184905647855469673)⟩,⟨(-145283595981347862),(-145283595981347857)⟩⟩,⟨⟨(-175574702186501353),(-175574702186501349)⟩,⟨(-145764777369389429),(-145764777369389425)⟩⟩,⟨⟨(-166715253744306936),(-166715253744306930)⟩,⟨(-146002741469834823),(-146002741469834816)⟩⟩,⟨⟨(-158308831858953790),(-158308831858953785)⟩,⟨(-146025450637247869),(-146025450637247864)⟩⟩,⟨⟨(-150337325244949447),(-150337325244949442)⟩,⟨(-145858628658774091),(-145858628658774086)⟩⟩,⟨⟨(-142783030578354437),(-142783030578354432)⟩,⟨(-145525916489063334),(-145525916489063330)⟩⟩,⟨⟨(-135628693144455013),(-135628693144455009)⟩,⟨(-145049019073737342),(-145049019073737338)⟩⟩,⟨⟨(-128857540388822064),(-128857540388822060)⟩,⟨(-144447843603763435),(-144447843603763430)⟩⟩] +lemma kernel4_0_r1_13_eq : ∀ k : Fin 16, kernel4_0Expr 1 13 k = kernel4_0_r1_13 k := by decide +kernel +noncomputable def kernel4_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-122453309137505988),(-122453309137505984)⟩,⟨(-143740629546517550),(-143740629546517546)⟩⟩,⟨⟨(-116400267189408049),(-116400267189408045)⟩,⟨(-142944070800178004),(-142944070800177999)⟩⟩,⟨⟨(-110683229925335913),(-110683229925335908)⟩,⟨(-142073430316700658),(-142073430316700654)⟩⟩,⟨⟨(-105287572523703483),(-105287572523703479)⟩,⟨(-141142647535275328),(-141142647535275323)⟩⟩,⟨⟨(-100199238322082073),(-100199238322082069)⟩,⟨(-140164438963114618),(-140164438963114614)⟩⟩,⟨⟨(-95404743816661655),(-95404743816661650)⟩,⟨(-139150392233919260),(-139150392233919256)⟩⟩,⟨⟨(-90891180747950841),(-90891180747950834)⟩,⟨(-138111053966614507),(-138111053966614502)⟩⟩,⟨⟨(-86646215680548204),(-86646215680548198)⟩,⟨(-137056011738155441),(-137056011738155434)⟩⟩,⟨⟨(-82658087447375749),(-82658087447375745)⟩,⟨(-135993970474530663),(-135993970474530659)⟩⟩,⟨⟨(-78915602794202215),(-78915602794202211)⟩,⟨(-134932823553710724),(-134932823553710719)⟩⟩,⟨⟨(-75408130528428695),(-75408130528428690)⟩,⟨(-133879718903329565),(-133879718903329560)⟩⟩,⟨⟨(-72125594446796201),(-72125594446796197)⟩,⟨(-132841120364478274),(-132841120364478269)⟩⟩,⟨⟨(-69058465289744517),(-69058465289744513)⟩,⟨(-131822864581239374),(-131822864581239370)⟩⟩,⟨⟨(-66197751945449255),(-66197751945449248)⟩,⟨(-130830213663592654),(-130830213663592649)⟩⟩,⟨⟨(-63534992103941391),(-63534992103941387)⟩,⟨(-129867903859162609),(-129867903859162605)⟩⟩,⟨⟨(-61062242541027600),(-61062242541027595)⟩,⟨(-128940190457024690),(-128940190457024685)⟩⟩] +lemma kernel4_0_r1_14_eq : ∀ k : Fin 16, kernel4_0Expr 1 14 k = kernel4_0_r1_14 k := by decide +kernel +noncomputable def kernel4_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-58772069192843984),(-58772069192843980)⟩,⟨(-128050889134503072),(-128050889134503067)⟩⟩,⟨⟨(-56657537164659245),(-56657537164659241)⟩,⟨(-127203413945628016),(-127203413945628011)⟩⟩,⟨⟨(-54712200801870715),(-54712200801870709)⟩,⟨(-126400812137717778),(-126400812137717773)⟩⟩,⟨⟨(-52930093936888401),(-52930093936888396)⟩,⟨(-125645795970442995),(-125645795970442990)⟩⟩,⟨⟨(-51305720412664210),(-51305720412664205)⟩,⟨(-124940771699746722),(-124940771699746718)⟩⟩,⟨⟨(-49834044971886692),(-49834044971886687)⟩,⟨(-124287865877151575),(-124287865877151571)⟩⟩,⟨⟨(-48510484590222331),(-48510484590222326)⟩,⟨(-123688949103300164),(-123688949103300159)⟩⟩,⟨⟨(-47330900322343152),(-47330900322343148)⟩,⟨(-123145657363055457),(-123145657363055452)⟩⟩,⟨⟨(-46291589720742829),(-46291589720742825)⟩,⟨(-122659411058137518),(-122659411058137513)⟩⟩,⟨⟨(-45389279879418923),(-45389279879418918)⟩,⟨(-122231431842091870),(-122231431842091866)⟩⟩,⟨⟨(-44621121147300728),(-44621121147300723)⟩,⟨(-121862757351368290),(-121862757351368285)⟩⟩,⟨⟨(-43984681549747722),(-43984681549747717)⟩,⟨(-121554253915429687),(-121554253915429682)⟩⟩,⟨⟨(-43477941950452593),(-43477941950452588)⟩,⟨(-121306627318098243),(-121306627318098238)⟩⟩,⟨⟨(-43099291980578770),(-43099291980578765)⟩,⟨(-121120431671767076),(-121120431671767072)⟩⟩,⟨⟨(-42847526756870846),(-42847526756870841)⟩,⟨(-120996076455645329),(-120996076455645324)⟩⟩,⟨⟨(-42721844405724923),(-42721844405724918)⟩,⟨(-120933831758845475),(-120933831758845470)⟩⟩] +lemma kernel4_0_r1_15_eq : ∀ k : Fin 16, kernel4_0Expr 1 15 k = kernel4_0_r1_15 k := by decide +kernel +noncomputable def kernel4_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel4_0_r1_0,kernel4_0_r1_1,kernel4_0_r1_2,kernel4_0_r1_3,kernel4_0_r1_4,kernel4_0_r1_5,kernel4_0_r1_6,kernel4_0_r1_7,kernel4_0_r1_8,kernel4_0_r1_9,kernel4_0_r1_10,kernel4_0_r1_11,kernel4_0_r1_12,kernel4_0_r1_13,kernel4_0_r1_14,kernel4_0_r1_15] +lemma kernel4_0_r1_eq (i k : Fin 16) : kernel4_0Expr 1 i k = kernel4_0_r1 i k := by + fin_cases i + · exact kernel4_0_r1_0_eq k + · exact kernel4_0_r1_1_eq k + · exact kernel4_0_r1_2_eq k + · exact kernel4_0_r1_3_eq k + · exact kernel4_0_r1_4_eq k + · exact kernel4_0_r1_5_eq k + · exact kernel4_0_r1_6_eq k + · exact kernel4_0_r1_7_eq k + · exact kernel4_0_r1_8_eq k + · exact kernel4_0_r1_9_eq k + · exact kernel4_0_r1_10_eq k + · exact kernel4_0_r1_11_eq k + · exact kernel4_0_r1_12_eq k + · exact kernel4_0_r1_13_eq k + · exact kernel4_0_r1_14_eq k + · exact kernel4_0_r1_15_eq k +noncomputable def kernel4_0_r2_0 : Fin 16 → CBox := ![⟨⟨16901928990499293589187187,16901928990499293603002001⟩,⟨(-13879651485396182717170862),(-13879651485396182703472729)⟩⟩,⟨⟨16892001059589358652534549,16892001059589358666344611⟩,⟨(-13875029303747502794848273),(-13875029303747502781154813)⟩⟩,⟨⟨16872162301684590739887170,16872162301684590753687700⟩,⟨(-13865787470173187367097076),(-13865787470173187353412988)⟩⟩,⟨⟨16842446877937445847933167,16842446877937445861719400⟩,⟨(-13851931052540819973974807),(-13851931052540819960304777)⟩⟩,⟨⟨16802905913544361327177930,16802905913544361340945108⟩,⟨(-13833467673608319726452409),(-13833467673608319712801117)⟩⟩,⟨⟨16753607358360411784380068,16753607358360411798123456⟩,⟨(-13810407535900461597411197),(-13810407535900461583783302)⟩⟩,⟨⟨16694635801805992434187348,16694635801805992447902226⟩,⟨(-13782763454427767208268312),(-13782763454427767194668453)⟩⟩,⟨⟨16626092242708100649184703,16626092242708100662866383⟩,⟨(-13750550896867035146617083),(-13750550896867035133049874)⟩⟩,⟨⟨16548093814874999770269426,16548093814874999783913246⟩,⟨(-13713788030733568889240351),(-13713788030733568875710377)⟩⟩,⟨⟨16460773469356324512716389,16460773469356324526317727⟩,⟨(-13672495776989859135356227),(-13672495776989859121868038)⟩⟩,⟨⟨16364279614490452008406496,16364279614490452021960764⟩,⟨(-13626697869454796968983032),(-13626697869454796955541142)⟩⟩,⟨⟨16258775714986652607436181,16258775714986652620938839⟩,⟨(-13576420919302108316526042),(-13576420919302108303134920)⟩⟩,⟨⟨16144439851430596055407451,16144439851430596068853997⟩,⟨(-13521694483867239058639105),(-13521694483867239045303183)⟩⟩,⟨⟨16021464241737679379228385,16021464241737679392614381⟩,⟨(-13462551138918966023690110),(-13462551138918966010413760)⟩⟩,⟨⟨15890054726208834128312732,15890054726208834141633778⟩,⟨(-13399026553496091025873738),(-13399026553496091012661291)⟩⟩,⟨⟨15750430217967449334507893,15750430217967449347759675⟩,⟨(-13331159566361164845051212),(-13331159566361164831906920)⟩⟩] +lemma kernel4_0_r2_0_eq : ∀ k : Fin 16, kernel4_0Expr 2 0 k = kernel4_0_r2_0 k := by decide +kernel +noncomputable def kernel4_0_r2_1 : Fin 16 → CBox := ![⟨⟨15602822120673316867269819,15602822120673316880448050⟩,⟨(-13258992263082696090628536),(-13258992263082696077556624)⟩⟩,⟨⟨15447473715519591398954447,15447473715519591412054948⟩,⟨(-13182570052725072185936159),(-13182570052725072172940747)⟩⟩,⟨⟨15284639519621203145366118,15284639519621203158384738⟩,⟨(-13101941743101734786534593),(-13101941743101734773619775)⟩⟩,⟨⟨15114584617997536849065892,15114584617997536861998603⟩,⟨(-13017159613532218660211690),(-13017159613532218647381438)⟩⟩,⟨⟨14937583971438090074938968,14937583971438090087781757⟩,⟨(-12928279484037618881489086),(-12928279484037618868747362)⟩⟩,⟨⟨14753921702616871042107251,14753921702616871054856263⟩,⟨(-12835360779911961108826974),(-12835360779911961096177582)⟩⟩,⟨⟨14563890362889144806471232,14563890362889144819122617⟩,⟨(-12738466590618805692317066),(-12738466590618805679763810)⟩⟩,⟨⟨14367790182262473478171048,14367790182262473490721133⟩,⟨(-12637663721983137466478518),(-12637663721983137454025026)⟩⟩,⟨⟨14165928305082543428592035,14165928305082543441037120⟩,⟨(-12533022740678026171613314),(-12533022740678026159263244)⟩⟩,⟨⟨13958618014012789783601557,13958618014012789795938184⟩,⟨(-12424618010043463471449773),(-12424618010043463459206544)⟩⟩,⟨⟨13746177944915115343388003,13746177944915115355612663⟩,⟨(-12312527716320898448405244),(-12312527716320898436272328)⟩⟩,⟨⟨13528931295256898715741891,13528931295256898727851330⟩,⟨(-12196833884440944697979224),(-12196833884440944685959845)⟩⟩,⟨⟨13307205028676880060359114,13307205028676880072349987⟩,⟨(-12077622382563095675694227),(-12077622382563095663791696)⟩⟩,⟨⟨13081329078339333274182071,13081329078339333286051371⟩,⟨(-11954982914634577848832976),(-11954982914634577837050276)⟩⟩,⟨⟨12851635551692158907717127,12851635551692158919461725⟩,⟨(-11829009000310154746783649),(-11829009000310154735123882)⟩⟩,⟨⟨12618457939220189583262292,12618457939220189594879403⟩,⟨(-11699797941655179229877538),(-11699797941655179218343467)⟩⟩] +lemma kernel4_0_r2_1_eq : ∀ k : Fin 16, kernel4_0Expr 2 1 k = kernel4_0_r2_1 k := by decide +kernel +noncomputable def kernel4_0_r2_2 : Fin 16 → CBox := ![⟨⟨12382130329750166167018248,12382130329750166178504913⟩,⟨(-11567450776139840016751420),(-11567450776139840005345986)⟩⟩,⟨⟨12142986634818646320197167,12142986634818646331550882⟩,⟨(-11432072215522684697929510),(-11432072215522684686655201)⟩⟩,⟨⟨11901359824558726756393801,11901359824558726767611852⟩,⟨(-11293770570315412999743799),(-11293770570315412988603315)⟩⟩,⟨⟨11657581177496127856788453,11657581177496127867868566⟩,⟨(-11152657659617879779255670),(-11152657659617879768251276)⟩⟩,⟨⟨11411979546570187360181893,11411979546570187371121525⟩,⟨(-11008848706211463196625297),(-11008848706211463185759527)⟩⟩,⟨⟨11164880643610973204951282,11164880643610973215748469⟩,⟨(-10862462216899659511144276),(-10862462216899659500419090)⟩⟩,⟨⟨10916606344410439475614330,10916606344410439486266787⟩,⟨(-10713619848186172091514102),(-10713619848186172080931781)⟩⟩,⟨⟨10667474016423748530643963,10667474016423748541149963⟩,⟨(-10562446257482075640183844),(-10562446257482075629746116)⟩⟩,⟨⟨10417795871027049454515870,10417795871027049464873291⟩,⟨(-10409068940134068132325356),(-10409068940134068122034346)⟩⟩,⟨⟨10167878342140666690690934,10167878342140666700898390⟩,⟨(-10253618052664593744776666),(-10253618052664593734633766)⟩⟩,⟨⟨9918021492902385441046832,9918021492902385451102487⟩,⟨(-10096226222710968178226697),(-10096226222710968168233750)⟩⟩,⟨⟨9668518451944935450453933,9668518451944935460356625⟩,⟨(-9937028346243824606066325),(-9937028346243824596224504)⟩⟩,⟨⟨9419654880695523220278161,9419654880695523230026208⟩,⟨(-9776161372734514780597791),(-9776161372734514770908788)⟩⟩,⟨⟨9171708472974029906463342,9171708472974029916055941⟩,⟨(-9613764079025871635338277),(-9613764079025871625802912)⟩⟩,⟨⟨8924948488020994020444158,8924948488020994029879919⟩,⟨(-9449976832740333888309086),(-9449976832740333878928764)⟩⟩,⟨⟨8679635317937476735639717,8679635317937476744918052⟩,⟨(-9284941346133262462908634),(-9284941346133262453683961)⟩⟩] +lemma kernel4_0_r2_2_eq : ∀ k : Fin 16, kernel4_0Expr 2 2 k = kernel4_0_r2_2 k := by decide +kernel +noncomputable def kernel4_0_r2_3 : Fin 16 → CBox := ![⟨⟨8436020090367127131027432,8436020090367127140147077⟩,⟨(-9118800421366806427635380),(-9118800421366806418567638)⟩⟩,⟨⟨8194344307097006231899584,8194344307097006240860337⟩,⟨(-8951697688240420901589032),(-8951697688240420892678449)⟩⟩,⟨⟨7954839519098785582942083,7954839519098785591743003⟩,⟨(-8783777335467677830121772),(-8783777335467677821369311)⟩⟩,⟨⟨7717727038376608720850659,7717727038376608729491723⟩,⟨(-8615183836634981268576859),(-8615183836634981259982568)⟩⟩,⟨⟨7483217686832994510047727,7483217686832994518528115⟩,⟨(-8446061672015904670333391),(-8446061672015904661898117)⟩⟩,⟨⟨7251511582210468507043318,7251511582210468515363382⟩,⟨(-8276555047444877760418964),(-8276555047444877752142383)⟩⟩,⟨⟨7022797961014921993551143,7022797961014922001710372⟩,⟨(-8106807611475701594043447),(-8106807611475701585926099)⟩⟩,⟨⟨6797255038177793352554398,6797255038177793360553318⟩,⟨(-7936962172063767384551079),(-7936962172063767376592467)⟩⟩,⟨⟨6575049903068798610975829,6575049903068798618814001⟩,⟨(-7767160414015871091149329),(-7767160414015871083349925)⟩⟩,⟨⟨6356338451329837815993346,6356338451329837823671693⟩,⟨(-7597542618448192921194047),(-7597542618448192913552961)⟩⟩,⟨⟨6141265351864571960981752,6141265351864571968500172⟩,⟨(-7428247385481456892605062),(-7428247385481456885122428)⟩⟩,⟨⟨5929964048187666992247279,5929964048187666999606811⟩,⟨(-7259411361382673461062277),(-7259411361382673453737091)⟩⟩,⟨⟨5722556793213462989991753,5722556793213462997192359⟩,⟨(-7091168971335433623683096),(-7091168971335433616515430)⟩⟩,⟨⟨5519154716446429998649631,5519154716446430005692720⟩,⟨(-6923652158985761295968579),(-6923652158985761288957059)⟩⟩,⟨⟨5319857922425751363089418,5319857922425751369975263⟩,⟨(-6756990133868393896603520),(-6756990133868393889747908)⟩⟩,⟨⟨5124755619174213496605555,5124755619174213503335667⟩,⟨(-6591309127769453200705048),(-6591309127769453194003871)⟩⟩] +lemma kernel4_0_r2_3_eq : ∀ k : Fin 16, kernel4_0Expr 2 3 k = kernel4_0_r2_3 k := by decide +kernel +noncomputable def kernel4_0_r2_4 : Fin 16 → CBox := ![⟨⟨4933926275307705782837212,4933926275307705789411862⟩,⟨(-6426732161026242013614449),(-6426732161026242007067469)⟩⟩,⟨⟨4747437804376416420171283,4747437804376416426592374⟩,⟨(-6263378819703852888501437),(-6263378819703852882106790)⟩⟩,⟨⟨4565347774932560437557397,4565347774932560443825543⟩,⟨(-6101365044521937172998386),(-6101365044521937166755495)⟩⟩,⟨⟨4387703644752444446599847,4387703644752444452716970⟩,⟨(-5940802932333923412016833),(-5940802932333923405923811)⟩⟩,⟨⟨4214543017583045943488875,4214543017583045949455594⟩,⟨(-5781800550885788381709815),(-5781800550885788375766079)⟩⟩,⟨⟨4045893920735186836228282,4045893920735186842046858⟩,⟨(-5624461767502788442294811),(-5624461767502788436498137)⟩⟩,⟨⟨3881775101806871595790755,3881775101806871601462098⟩,⟨(-5468886092270986160716521),(-5468886092270986155066036)⟩⟩,⟨⟨3722196342791437189292147,3722196342791437194818535⟩,⟨(-5315168536196600132176348),(-5315168536196600126669810)⟩⟩,⟨⟨3567158789805759760193132,3567158789805759765575410⟩,⟨(-5163399484740811835217155),(-5163399484740811829853753)⟩⟩,⟨⟨3416655296663756147951741,3416655296663756153192536⟩,⟨(-5013664587041327997824870),(-5013664587041327992602013)⟩⟩,⟨⟨3270670780519622248286559,3270670780519622253387036⟩,⟨(-4866044661045359120331809),(-4866044661045359115248366)⟩⟩,⟨⟨3129182587813423955476748,3129182587813423960439465⟩,⟨(-4720615614692360834999548),(-4720615614692360830052997)⟩⟩,⟨⟨2992160868768505490173901,2992160868768505494999963⟩,⟨(-4577448383199503387816008),(-4577448383199503383005277)⟩⟩,⟨⟨2859568958715359495727819,2859568958715359500420073⟩,⟨(-4436608882418971881132109),(-4436608882418971876454384)⟩⟩,⟨⟨2731363764549721928805404,2731363764549721933365212⟩,⟨(-4298157978154415099988368),(-4298157978154415095442319)⟩⟩,⟨⟨2607496154673278353468615,2607496154673278357898759⟩,⟨(-4162151471244681563895310),(-4162151471244681559478188)⟩⟩] +lemma kernel4_0_r2_4_eq : ∀ k : Fin 16, kernel4_0Expr 2 4 k = kernel4_0_r2_4 k := by decide +kernel +noncomputable def kernel4_0_r2_5 : Fin 16 → CBox := ![⟨⟨2487911350813024256740708,2487911350813024261042414⟩,⟨(-4028640098146900642038822),(-4028640098146900637749431)⟩⟩,⟨⟨2372549320169504052519033,2372549320169504056695386⟩,⟨(-3897669546678438482073273),(-3897669546678438477908559)⟩⟩,⟨⟨2261345166404325994773834,2261345166404325998826349⟩,⟨(-3769280486508696182458268),(-3769280486508696178416745)⟩⟩,⟨⟨2154229518042953464944461,2154229518042953468876062⟩,⟨(-3643508613927490446222626),(-3643508613927490442301401)⟩⟩,⟨⟨2051128912939227902941139,2051128912939227906753224⟩,⟨(-3520384710357188645026702),(-3520384710357188641224402)⟩⟩,⟨⟨1951966177522791584921125,1951966177522791588616849⟩,⟨(-3399934714021137528387366),(-3399934714021137524700865)⟩⟩,⟨⟨1856660799628946789565389,1856660799628946793146372⟩,⟨(-3282179804131456521312013),(-3282179804131456517739718)⟩⟩,⟨⟨1765129293791904574487892,1765129293791904577957136⟩,⟨(-3167136496915143077624135),(-3167136496915143074163069)⟩⟩,⟨⟨1677285557966234856901331,1677285557966234860260278⟩,⟨(-3054816752758790985122461),(-3054816752758790981771207)⟩⟩,⟨⟨1593041220727028429699091,1593041220727028432950984⟩,⟨(-2945228093719137132680093),(-2945228093719137129435432)⟩⟩,⟨⟨1512305978086229355667291,1512305978086229358813809⟩,⟨(-2838373730619165477836460),(-2838373730619165474696738)⟩⟩,⟨⟨1434987919150215304070789,1434987919150215307114953⟩,⟨(-2734252698927600751959776),(-2734252698927600748921992)⟩⟩,⟨⟨1360993839931434309673595,1360993839931434312616927⟩,⟨(-2632860002603267055946123),(-2632860002603267053008777)⟩⟩,⟨⟨1290229544714211403304089,1290229544714211406149776⟩,⟨(-2534186765074874594377657),(-2534186765074874591537584)⟩⟩,⟨⟨1222600134461205021114125,1222600134461205023863864⟩,⟨(-2438220386521198888950991),(-2438220386521198886206513)⟩⟩,⟨⟨1158010281831936713084221,1158010281831936715740994⟩,⟨(-2344944706616162005121804),(-2344944706616162002469959)⟩⟩] +lemma kernel4_0_r2_5_eq : ∀ k : Fin 16, kernel4_0Expr 2 5 k = kernel4_0_r2_5 k := by decide +kernel +noncomputable def kernel4_0_r2_6 : Fin 16 → CBox := ![⟨⟨1096364492467885025596793,1096364492467885028162075⟩,⟨(-2254340171907812273405452),(-2254340171907812270844781)⟩⟩,⟨⟨1037567352279405340504695,1037567352279405342981658⟩,⟨(-2166384007009395065296698),(-2166384007009395062824048)⟩⟩,⟨⟨981523760547826873143384,981523760547826875533707⟩,⟨(-2081050388794352822258936),(-2081050388794352819872647)⟩⟩,⟨⟨928139148731137595392918,928139148731137597699496⟩,⟨(-1998310622804904663975450),(-1998310622804904661672641)⟩⟩,⟨⟨877319684933386993677275,877319684933386995901602⟩,⟨(-1918133321105531471938767),(-1918133321105531469717958)⟩⟩,⟨⟨828972464066043281237453,828972464066043283382537⟩,⟨(-1840484580837911892033977),(-1840484580837911889892178)⟩⟩,⟨⟨783005683793802858492990,783005683793802860560456⟩,⟨(-1765328162762285897180423),(-1765328162762285895116020)⟩⟩,⟨⟨739328806417571264901864,739328806417571266894486⟩,⟨(-1692625669101523719631946),(-1692625669101523717642180)⟩⟩,⟨⟨697852706903360958072177,697852706903360959991356⟩,⟨(-1622336720038001506990292),(-1622336720038001505073773)⟩⟩,⟨⟨658489807317564230956421,658489807317564232805051⟩,⟨(-1554419128249380789246428),(-1554419128249380787400276)⟩⟩,⟨⟨621154197976378554729919,621154197976378556509551⟩,⟨(-1488829070907207170616654),(-1488829070907207168839328)⟩⟩,⟨⟨585761745660041333223991,585761745660041334937240⟩,⟨(-1425521258601538592131377),(-1425521258601538590420273)⟩⟩,⟨⟨552230189280960260596297,552230189280960262244526⟩,⟨(-1364449100695245494454970),(-1364449100695245492808735)⟩⟩,⟨⟨520479223428825275593229,520479223428825277179115⟩,⟨(-1305564866652863738168027),(-1305564866652863736583994)⟩⟩,⟨⟨490430570245409931583863,490430570245409933108862⟩,⟨(-1248819842930607136539054),(-1248819842930607135015777)⟩⟩,⟨⟨462008040107093488220420,462008040107093489686971⟩,⟨(-1194164485056054427496344),(-1194164485056054426031392)⟩⟩] +lemma kernel4_0_r2_6_eq : ∀ k : Fin 16, kernel4_0Expr 2 6 k = kernel4_0_r2_6 k := by decide +kernel +noncomputable def kernel4_0_r2_7 : Fin 16 → CBox := ![⟨⟨435137581614265754423357,435137581614265755832684⟩,⟨(-1141548564567825432710396),(-1141548564567825431302551)⟩⟩,⟨⟨409747321403843812710029,409747321403843814064657⟩,⟨(-1090921310526980107323211),(-1090921310526980105969958)⟩⟩,⟨⟨385767594314283480986542,385767594314283482287821⟩,⟨(-1042231545352657745326857),(-1042231545352657744026854)⟩⟩,⟨⟨363130964441877577894118,363130964441877579144289⟩,⟨(-995427814774386949399519),(-995427814774386948150530)⟩⟩,⟨⟨341772237632982698597569,341772237632982699797796⟩,⟨(-950458511732325743903872),(-950458511732325742704740)⟩⟩,⟨⟨321628465959304802345978,321628465959304803498535⟩,⟨(-907271994094242129910777),(-907271994094242128759233)⟩⟩,⟨⟨302638944722711080213834,302638944722711081319953⟩,⟨(-865816696094146627871021),(-865816696094146626765839)⟩⟩,⟨⟨284745202532439602016578,284745202532439603078301⟩,⟨(-826041233431989697976681),(-826041233431989696915826)⟩⟩,⟨⟨267890984991273751715454,267890984991273752733807⟩,⟨(-787894502006609661368650),(-787894502006609660351098)⟩⟩,⟨⟨252022232518464141412088,252022232518464142389165⟩,⟨(-751325770285053401997295),(-751325770285053401020960)⟩⟩,⟨⟨237087052826147173099991,237087052826147174036901⟩,⟨(-716284765340406025246158),(-716284765340406024309933)⟩⟩,⟨⟨223035688552957248905323,223035688552957249803907⟩,⟨(-682721752617290252214634),(-682721752617290251316682)⟩⟩,⟨⟨209820480543687424227331,209820480543687425088533⟩,⟨(-650587609509184473827693),(-650587609509184472967075)⟩⟩,⟨⟨197395827247445996219310,197395827247445997044982⟩,⟨(-619833892854631368964208),(-619833892854631368139075)⟩⟩,⟨⟨185718140689003830954899,185718140689003831746034⟩,⟨(-590412900480255527690484),(-590412900480255526899846)⟩⟩,⟨⟨174745799449142225256961,174745799449142226015199⟩,⟨(-562277726937283646342495),(-562277726937283645584716)⟩⟩] +lemma kernel4_0_r2_7_eq : ∀ k : Fin 16, kernel4_0Expr 2 7 k = kernel4_0_r2_7 k := by decide +kernel +noncomputable def kernel4_0_r2_8 : Fin 16 → CBox := ![⟨⟨164439099069998960858094,164439099069998961584240⟩,⟨(-535382313594984721188979),(-535382313594984720463255)⟩⟩,⟨⟨154760200280867167153842,154760200280867167849580⟩,⟨(-509681493269154267923873),(-509681493269154267228523)⟩⟩,⟨⟨145673075418814018246287,145673075418814018912490⟩,⟨(-485131029576502508682302),(-485131029576502508016457)⟩⟩,⟨⟨137143453397029875632505,137143453397029876270626⟩,⟨(-461687651216629520959415),(-461687651216629520321624)⟩⟩,⟨⟨129138763552157747916456,129138763552157748527229⟩,⟨(-439309081392248284595735),(-439309081392248283985265)⟩⟩,⟨⟨121628078680140694790192,121628078680140695375071⟩,⟨(-417954062585525754219419),(-417954062585525753634819)⟩⟩,⟨⟨114582057548501892433927,114582057548501892993677⟩,⟨(-397582376913936197775673),(-397582376913936197216179)⟩⟩,⟨⟨107972887151567183520610,107972887151567184056509⟩,⟨(-378154862292949797205609),(-378154862292949796669946)⟩⟩,⟨⟨101774224954069535822769,101774224954069536335426⟩,⟨(-359633424635307450714950),(-359633424635307450202509)⟩⟩,⟨⟨95961141347943271804039,95961141347943272294754⟩,⟨(-341981046317658049340089),(-341981046317658048849572)⟩⟩,⟨⟨90510062527015587482804,90510062527015587952237⟩,⟨(-325161791145057972340575),(-325161791145057971871324)⟩⟩,⟨⟨85398713964814436496879,85398713964814436946145⟩,⟨(-309140806042356409452677),(-309140806042356409003577)⟩⟩,⟨⟨80606064661904654293280,80606064661904654722917⟩,⟨(-293884319698917160393314),(-293884319698917159963829)⟩⟩,⟨⟨76112272311096656450492,76112272311096656861616⟩,⟨(-279359638389560210464030),(-279359638389560210053045)⟩⟩,⟨⟨71898629511592148436595,71898629511592148829771⟩,⟨(-265535139190145887697275),(-265535139190145887304227)⟩⟩,⟨⟨67947511146677118905970,67947511146677119282161⟩,⟨(-252380260800970114069883),(-252380260800970113693808)⟩⟩] +lemma kernel4_0_r2_8_eq : ∀ k : Fin 16, kernel4_0Expr 2 8 k = kernel4_0_r2_8 k := by decide +kernel +noncomputable def kernel4_0_r2_9 : Fin 16 → CBox := ![⟨⟨64242323023972725194991,64242323023972725554637⟩,⟨(-239865492185187949974212),(-239865492185187949614672)⟩⟩,⟨⟨60767451862529582814175,60767451862529583158257⟩,⟨(-227962359222927940626259),(-227962359222927940282273)⟩⟩,⟨⟨57508216697212434678552,57508216697212435007557⟩,⟨(-216643409574691719347197),(-216643409574691719018279)⟩⟩,⟨⟨54450821757874773207701,54450821757874773522455⟩,⟨(-205882195940137874487938),(-205882195940137874173263)⟩⟩,⟨⟨51582310868764526097210,51582310868764526398102⟩,⟨(-195653257890507826300107),(-195653257890507825999286)⟩⟩,⟨⟨48890523402424090378933,48890523402424090666788⟩,⟨(-185932102444841312628863),(-185932102444841312341073)⟩⟩,⟨⟨46364051812037042088480,46364051812037042363709⟩,⟨(-176695183551822113444603),(-176695183551822113169433)⟩⟩,⟨⟨43992200756711164618570,43992200756711164881879⟩,⟨(-167919880630657919958125),(-167919880630657919694868)⟩⟩,⟨⟨41764947825550219886961,41764947825550220138662⟩,⟨(-159584476315893759465842),(-159584476315893759214188)⟩⟩,⟨⟨39672905858528706925533,39672905858528707166349⟩,⟨(-151668133542542998849590),(-151668133542542998608816)⟩⟩,⟨⟨37707286855115236233633,37707286855115236463902⟩,⟨(-144150872099445457284254),(-144150872099445457054023)⟩⟩,⟨⟨35859867455259107025303,35859867455259107245631⟩,⟨(-137013544770375329644745),(-137013544770375329424450)⟩⟩,⟨⟨34122955971727214820061,34122955971727215030717⟩,⟨(-130237813174164305688530),(-130237813174164305477903)⟩⟩,⟨⟨32489360947819012850603,32489360947819013052188⟩,⟨(-123806123407014535593611),(-123806123407014535392050)⟩⟩,⟨⟨30952361210159282728354,30952361210159282921156⟩,⟨(-117701681582284396119947),(-117701681582284395927167)⟩⟩,⟨⟨29505677382534626689380,29505677382534626873908⟩,⟨(-111908429355365388597885),(-111908429355365388413376)⟩⟩] +lemma kernel4_0_r2_9_eq : ∀ k : Fin 16, kernel4_0Expr 2 9 k = kernel4_0_r2_9 k := by decide +kernel +noncomputable def kernel4_0_r2_10 : Fin 16 → CBox := ![⟨⟨28143444823562240260643,28143444823562240437105⟩,⟨(-106411019513854775774610),(-106411019513854775598164)⟩⟩,⟨⟨26860187948321032008637,26860187948321032177559⟩,⟨(-101194791706085583420604),(-101194791706085583251695)⟩⟩,⟨⟨25650795891898200995123,25650795891898201156741⟩,⟨(-96245748374219456997278),(-96245748374219456835671)⟩⟩,⟨⟨24510499471072202459088,24510499471072202613834⟩,⟨(-91550530951551182842382),(-91550530951551182687645)⟩⟩,⟨⟨23434849399029661607972,23434849399029661756025⟩,⟨(-87096396377425826568776),(-87096396377425826420729)⟩⟩,⟨⟨22419695707064258393008,22419695707064258534805⟩,⟨(-82871193977236793684856),(-82871193977236793543064)⟩⟩,⟨⟨21461168326596084353137,21461168326596084488868⟩,⟨(-78863342749359334244394),(-78863342749359334108665)⟩⟩,⟨⟨20555658784547943246160,20555658784547943376192⟩,⟨(-75061809095580272271677),(-75061809095580272141645)⟩⟩,⟨⟨19699802965089414731131,19699802965089414855600⟩,⟨(-71456085026609988160554),(-71456085026609988036084)⟩⟩,⟨⟨18890464890980603384890,18890464890980603504172⟩,⟨(-68036166869603872900233),(-68036166869603872780949)⟩⟩,⟨⟨18124721478187290606175,18124721478187290720428⟩,⟨(-64792534500272800724180),(-64792534500272800609925)⟩⟩,⟨⟨17399848218071232698977,17399848218071232808508⟩,⟨(-61716131118119285858985),(-61716131118119285749449)⟩⟩,⟨⟨16713305742258768798953,16713305742258768903875⟩,⟨(-58798343579590224237094),(-58798343579590224132167)⟩⟩,⟨⟨16062727226234514948513,16062727226234515049139⟩,⟨(-56030983300479666222835),(-56030983300479666122202)⟩⟩,⟨⟨15445906588773149285358,15445906588773149381814⟩,⟨(-53406267735736170836194),(-53406267735736170739731)⟩⟩,⟨⟨14860787445491167229321,14860787445491167321867⟩,⟨(-50916802441918433961052),(-50916802441918433868497)⟩⟩] +lemma kernel4_0_r2_10_eq : ∀ k : Fin 16, kernel4_0Expr 2 10 k = kernel4_0_r2_10 k := by decide +kernel +noncomputable def kernel4_0_r2_11 : Fin 16 → CBox := ![⟨⟨14305452776053607551189,14305452776053607639909⟩,⟨(-48555563724888930746345),(-48555563724888930657617)⟩⟩,⟨⟨13778115265891254918297,13778115265891255003459⟩,⟨(-46315881872926671820519),(-46315881872926671735346)⟩⟩,⟨⟨13277108284656328539797,13277108284656328621506⟩,⟨(-44191424973264922933765),(-44191424973264922852045)⟩⟩,⟨⟨12800877465055211801498,12800877465055211879971⟩,⟨(-42176183308105752660741),(-42176183308105752582257)⟩⟩,⟨⟨12347972847132769589812,12347972847132769665115⟩,⟨(-40264454324418333127273),(-40264454324418333051958)⟩⟩,⟨⟨11917041554532940894382,11917041554532940966743⟩,⟨(-38450828170279809056869),(-38450828170279808984497)⟩⟩,⟨⟨11506820970714514956542,11506820970714515026042⟩,⟨(-36730173789154146979547),(-36730173789154146910034)⟩⟩,⟨⟨11116132384550387451767,11116132384550387518589⟩,⟨(-35097625562313723345463),(-35097625562313723278628)⟩⟩,⟨⟨10743875076175321651200,10743875076175321715390⟩,⟨(-33548570488578785714971),(-33548570488578785650768)⟩⟩,⟨⟨10389020815364493385462,10389020815364493447214⟩,⟨(-32078635889669893957520),(-32078635889669893895755)⟩⟩,⟨⟨10050608746117003691506,10050608746117003750887⟩,⟨(-30683677628726925477793),(-30683677628726925418398)⟩⟩,⟨⟨9727740632480094661354,9727740632480094718517⟩,⟨(-29359768828934494415990),(-29359768828934494358812)⟩⟩,⟨⟨9419576441976798002531,9419576441976798057516⟩,⟨(-28103189078697383200377),(-28103189078697383145378)⟩⟩,⟨⟨9125330244288710991165,9125330244288711044132⟩,⟨(-26910414109420943255282),(-26910414109420943202300)⟩⟩,⟨⟨8844266404093727871458,8844266404093727922458⟩,⟨(-25778105931660969675301),(-25778105931660969624286)⟩⟩,⟨⟨8575696048163659298472,8575696048163659347634⟩,⟨(-24703103415206336540988),(-24703103415206336491811)⟩⟩] +lemma kernel4_0_r2_11_eq : ∀ k : Fin 16, kernel4_0Expr 2 11 k = kernel4_0_r2_11 k := by decide +kernel +noncomputable def kernel4_0_r2_12 : Fin 16 → CBox := ![⟨⟨8318973787987097766034,8318973787987097813381⟩,⟨(-23682413298537211626153),(-23682413298537211578790)⟩⟩,⟨⟨8073494680297473130003,8073494680297473175678⟩,⟨(-22713201613053942846482),(-22713201613053942800791)⟩⟩,⟨⟨7838691408954266704540,7838691408954266748582⟩,⟨(-21792785507489189005732),(-21792785507489188961674)⟩⟩,⟨⟨7614031672646479863461,7614031672646479905982⟩,⟨(-20918625457991488412440),(-20918625457991488369904)⟩⟩,⟨⟨7399015763861689503332,7399015763861689544351⟩,⟨(-20088317849495616365819),(-20088317849495616324784)⟩⟩,⟨⟨7193174325491671689419,7193174325491671729050⟩,⟨(-19299587914167623089119),(-19299587914167623049472)⟩⟩,⟨⟨6996066272327197527955,6996066272327197566234⟩,⟨(-18550283012924652849763),(-18550283012924652811469)⟩⟩,⟨⟨6807276865530983716629,6807276865530983753642⟩,⟨(-17838366246276232663518),(-17838366246276232626489)⟩⟩,⟨⟨6626415928969883126403,6626415928969883162163⟩,⟨(-17161910381009803865338),(-17161910381009803829561)⟩⟩,⟨⟨6453116197036352922200,6453116197036352956812⟩,⟨(-16519092079544362742675),(-16519092079544362708047)⟩⟩,⟨⟨6287031784296291798185,6287031784296291831668⟩,⟨(-15908186419098062620479),(-15908186419098062586980)⟩⟩,⟨⟨6127836767966849048061,6127836767966849080497⟩,⟨(-15327561688154750811025),(-15327561688154750778573)⟩⟩,⟨⟨5975223874855211272000,5975223874855211303397⟩,⟨(-14775674448067249002470),(-14775674448067248971057)⟩⟩,⟨⟨5828903264979161661358,5828903264979161691803⟩,⟨(-14251064847998633365887),(-14251064847998633335427)⟩⟩,⟨⟨5688601404643917246436,5688601404643917275943⟩,⟨(-13752352181774029753555),(-13752352181774029724032)⟩⟩,⟨⟨5554060022268941543376,5554060022268941572014⟩,⟨(-13278230675591990662100),(-13278230675591990633446)⟩⟩] +lemma kernel4_0_r2_12_eq : ∀ k : Fin 16, kernel4_0Expr 2 12 k = kernel4_0_r2_12 k := by decide +kernel +noncomputable def kernel4_0_r2_13 : Fin 16 → CBox := ![⟨⟨5425035140744674980574,5425035140744675008341⟩,⟨(-12827465495924108752203),(-12827465495924108724419)⟩⟩,⟨⟨5301296180553993296842,5301296180553993323818⟩,⟨(-12398888967312137309634),(-12398888967312137282642)⟩⟩,⟨⟨5182625128318252850924,5182625128318252877121⟩,⟨(-11991396990151750531218),(-11991396990151750505005)⟩⟩,⟨⟨5068815765824548526002,5068815765824548551479⟩,⟨(-11603945648929617463441),(-11603945648929617437949)⟩⟩,⟨⟨4959672954960803036233,4959672954960803060990⟩,⟨(-11235548001754310393209),(-11235548001754310368437)⟩⟩,⟨⟨4855011974329999208131,4855011974329999232230⟩,⟨(-10885271042390529762394),(-10885271042390529738280)⟩⟩,⟨⟨4754657903635692099483,4754657903635692122938⟩,⟨(-10552232826369177535644),(-10552232826369177512174)⟩⟩,⟨⟨4658445052229283865758,4658445052229283888613⟩,⟨(-10235599753102075781950),(-10235599753102075759080)⟩⟩,⟨⟨4566216428486751359489,4566216428486751381744⟩,⟨(-9934583996278872325275),(-9934583996278872303005)⟩⟩,⟨⟨4477823246939874335655,4477823246939874357365⟩,⟨(-9648441075164292452494),(-9648441075164292430769)⟩⟩,⟨⟨4393124470325758361530,4393124470325758382704⟩,⟨(-9376467559745891394225),(-9376467559745891373036)⟩⟩,⟨⟨4311986383939765201071,4311986383939765221751⟩,⟨(-9117998903005447014447),(-9117998903005446993753)⟩⟩,⟨⟨4234282199881984676770,4234282199881984696953⟩,⟨(-8872407393900809859382),(-8872407393900809839184)⟩⟩,⟨⟨4159891688977181809862,4159891688977181829595⟩,⟨(-8639100224949186515763),(-8639100224949186496015)⟩⟩,⟨⟨4088700838323753619678,4088700838323753638967⟩,⟨(-8417517668597335442277),(-8417517668597335422973)⟩⟩,⟨⟨4020601532589600409439,4020601532589600428321⟩,⟨(-8207131356848932460514),(-8207131356848932441618)⟩⟩] +lemma kernel4_0_r2_13_eq : ∀ k : Fin 16, kernel4_0Expr 2 13 k = kernel4_0_r2_13 k := by decide +kernel +noncomputable def kernel4_0_r2_14 : Fin 16 → CBox := ![⟨⟨3955491257322873607795,3955491257322873626264⟩,⟨(-8007442658894405824489),(-8007442658894405806006)⟩⟩,⟨⟨3893272822684172251074,3893272822684172269174⟩,⟨(-7817981151753890701989),(-7817981151753890683875)⟩⟩,⟨⟨3833854106134739437131,3833854106134739454865⟩,⟨(-7638303179199698658179),(-7638303179199698640430)⟩⟩,⟨⟨3777147812733327066253,3777147812733327083653⟩,⟨(-7467990494470968367740),(-7467990494470968350325)⟩⟩,⟨⟨3723071251803374190140,3723071251803374207204⟩,⟨(-7306648982530123387124),(-7306648982530123370046)⟩⟩,⟨⟨3671546128832659171251,3671546128832659188015⟩,⟨(-7153907457838605725074),(-7153907457838605708296)⟩⟩,⟨⟨3622498351560273926904,3622498351560273943371⟩,⟨(-7009416533848300351857),(-7009416533848300335377)⟩⟩,⟨⟨3575857849291224485389,3575857849291224501586⟩,⟨(-6872847560615357811490),(-6872847560615357795279)⟩⟩,⟨⟨3531558404557741935970,3531558404557741951888⟩,⟨(-6743891627145020251872),(-6743891627145020235940)⟩⟩,⟨⟨3489537496319010909362,3489537496319010925042⟩,⟨(-6622258625269836187153),(-6622258625269836171459)⟩⟩,⟨⟨3449736153957973509492,3449736153957973524931⟩,⟨(-6507676372049599258159),(-6507676372049599242705)⟩⟩,⟨⟨3412098821395596807976,3412098821395596823201⟩,⟨(-6399889787859764145841),(-6399889787859764130602)⟩⟩,⟨⟨3376573230699922335094,3376573230699922350098⟩,⟨(-6298660127506284265609),(-6298660127506284250591)⟩⟩,⟨⟨3343110284619738071122,3343110284619738085937⟩,⟨(-6203764261869092302473),(-6203764261869092287645)⟩⟩,⟨⟨3311663947521191580949,3311663947521191595576⟩,⟨(-6114994007734121442653),(-6114994007734121428012)⟩⟩,⟨⟨3282191144250435911143,3282191144250435925605⟩,⟨(-6032155503625160297992),(-6032155503625160283516)⟩⟩] +lemma kernel4_0_r2_14_eq : ∀ k : Fin 16, kernel4_0Expr 2 14 k = kernel4_0_r2_14 k := by decide +kernel +noncomputable def kernel4_0_r2_15 : Fin 16 → CBox := ![⟨⟨3254651666486782601445,3254651666486782615732⟩,⟨(-5955068629592267303304),(-5955068629592267289004)⟩⟩,⟨⟨3229008086189121349644,3229008086189121363787⟩,⟨(-5883566469053260357490),(-5883566469053260343333)⟩⟩,⟨⟨3205225675773825569093,3205225675773825583094⟩,⟨(-5817494810919263613153),(-5817494810919263599140)⟩⟩,⟨⟨3183272334695250216665,3183272334695250230545⟩,⟨(-5756711690364753187243),(-5756711690364753173349)⟩⟩,⟨⟨3163118522130478097696,3163118522130478111444⟩,⟨(-5701086966727312821587),(-5701086966727312807826)⟩⟩,⟨⟨3144737195498402333540,3144737195498402347188⟩,⟨(-5650501937142702441819),(-5650501937142702428158)⟩⟩,⟨⟨3128103754569749816742,3128103754569749830288⟩,⟨(-5604848984637167697783),(-5604848984637167684225)⟩⟩,⟨⟨3113195990949443603812,3113195990949443617276⟩,⟨(-5564031259511484525564),(-5564031259511484512087)⟩⟩,⟨⟨3099994042735949176029,3099994042735949189398⟩,⟨(-5527962392960344070450),(-5527962392960344057068)⟩⟩,⟨⟨3088480354184116907584,3088480354184116920892⟩,⟨(-5496566241976641341876),(-5496566241976641328555)⟩⟩,⟨⟨3078639640218677322704,3078639640218677335948⟩,⟨(-5469776664693334011668),(-5469776664693333998411)⟩⟩,⟨⟨3070458855665114100522,3070458855665114113721⟩,⟨(-5447537325416081077321),(-5447537325416081064108)⟩⟩,⟨⟨3063927169083271537539,3063927169083271550686⟩,⟨(-5429801528698147078618),(-5429801528698147065458)⟩⟩,⟨⟨3059035941106880463759,3059035941106880476879⟩,⟨(-5416532081905355898875),(-5416532081905355885742)⟩⟩,⟨⟨3055778707209335482703,3055778707209335495794⟩,⟨(-5407701185813486188663),(-5407701185813486175558)⟩⟩,⟨⟨3054151164832647732279,3054151164832647745363⟩,⟨(-5403290352873703264766),(-5403290352873703251670)⟩⟩] +lemma kernel4_0_r2_15_eq : ∀ k : Fin 16, kernel4_0Expr 2 15 k = kernel4_0_r2_15 k := by decide +kernel +noncomputable def kernel4_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel4_0_r2_0,kernel4_0_r2_1,kernel4_0_r2_2,kernel4_0_r2_3,kernel4_0_r2_4,kernel4_0_r2_5,kernel4_0_r2_6,kernel4_0_r2_7,kernel4_0_r2_8,kernel4_0_r2_9,kernel4_0_r2_10,kernel4_0_r2_11,kernel4_0_r2_12,kernel4_0_r2_13,kernel4_0_r2_14,kernel4_0_r2_15] +lemma kernel4_0_r2_eq (i k : Fin 16) : kernel4_0Expr 2 i k = kernel4_0_r2 i k := by + fin_cases i + · exact kernel4_0_r2_0_eq k + · exact kernel4_0_r2_1_eq k + · exact kernel4_0_r2_2_eq k + · exact kernel4_0_r2_3_eq k + · exact kernel4_0_r2_4_eq k + · exact kernel4_0_r2_5_eq k + · exact kernel4_0_r2_6_eq k + · exact kernel4_0_r2_7_eq k + · exact kernel4_0_r2_8_eq k + · exact kernel4_0_r2_9_eq k + · exact kernel4_0_r2_10_eq k + · exact kernel4_0_r2_11_eq k + · exact kernel4_0_r2_12_eq k + · exact kernel4_0_r2_13_eq k + · exact kernel4_0_r2_14_eq k + · exact kernel4_0_r2_15_eq k +noncomputable def kernel4_0_r3_0 : Fin 16 → CBox := ![⟨⟨588587586877465449104944584,588587586877465450230446123⟩,⟨3411634799671194340441935452,3411634799671194341591105023⟩⟩,⟨⟨589001739713919351146625644,589001739713919352271819060⟩,⟨3410533699743118367196566366,3410533699743118368345429098⟩⟩,⟨⟨589829028024481526119842991,589829028024481527244418285⟩,⟨3408332307253103787932266161,3408332307253103789080513317⟩⟩,⟨⟨591067419617623304315100824,591067419617623305438748394⟩,⟨3405032236655894630893948083,3405032236655894632041271299⟩⟩,⟨⟨592713872532392671322822136,592713872532392672445233001⟩,⟨3400635908936372162759046246,3400635908936372163905137743⟩⟩,⟨⟨594764342611653395626375146,594764342611653396747241126⟩,⟨3395146550763356535002913872,3395146550763356536147466620⟩⟩,⟨⟨597213793569160315501722867,597213793569160316620736766⟩,⟨3388568193345558547605353018,3388568193345558548748060912⟩⟩,⟨⟨600056209524341874235262028,600056209524341875352117919⟩,⟨3380905670976306684046464258,3380905670976306685187022388⟩⟩,⟨⟨603284609972228744003030498,603284609972228745117423727⟩,⟨3372164619250522465603354445,3372164619250522466741459090⟩⟩,⟨⟨606891067149602044230732024,606891067149602045342359762⟩,⟨3362351472934391232431290416,3362351472934391233566639583⟩⟩,⟨⟨610866725752149874547151616,610866725752149875655712506⟩,⟨3351473463465299353822935813,3351473463465299354955228871⟩⟩,⟨⟨615201824951230405515966354,615201824951230406621161514⟩,⟨3339538616056905428771808754,3339538616056905429900747434⟩⟩,⟨⟨619885722652757498425776625,619885722652757499527308633⟩,⟨3326555746381704116088729990,3326555746381704117214017350⟩⟩,⟨⟨624906921934764797670297442,624906921934764798767872301⟩,⟨3312534456801147586605476101,3312534456801147587726818493⟩⟩,⟨⟨630253099594380639424410634,630253099594380640517735666⟩,⟨3297485132111330752233782946,3297485132111330753350887883⟩⟩,⟨⟨635911136729273273230637977,635911136729273274319424839⟩,⟨3281418934770440592810869699,3281418934770440593923448884⟩⟩] +lemma kernel4_0_r3_0_eq : ∀ k : Fin 16, kernel4_0Expr 3 0 k = kernel4_0_r3_0 k := by decide +kernel +noncomputable def kernel4_0_r3_1 : Fin 16 → CBox := ![⟨⟨641867151273118255330924421,641867151273118256414885568⟩,⟨3264347799572633817069140103,3264347799572633818176905863⟩⟩,⟨⟨648106532399312017129132395,648106532399312018207986297⟩,⟨3246284427731755950035860244,3246284427731755951138530760⟩⟩,⟨⟨654613976702022206894284062,654613976702022207967749349⟩,⟨3227242280337362275788407525,3227242280337362276885700945⟩⟩,⟨⟨661373526058741182273209469,661373526058741183341011918⟩,⟨3207235571144858681042597625,3207235571144858682134239072⟩⟩,⟨⟨668368607073808761927280021,668368607073808762989144397⟩,⟨3186279258661258318617282895,3186279258661258319702996269⟩⟩,⟨⟨675582071997908783803114442,675582071997908784858775361⟩,⟨3164389037488056222604011849,3164389037488056223683530727⟩⟩,⟨⟨682996241014335864945410448,682996241014335865994600285⟩,⟨3141581328883064682947187028,3141581328883064684020242522⟩⟩,⟨⟨690592945778888601164481030,690592945778888602206943242⟩,⟨3117873270503731437876877994,3117873270503731438943212114⟩⟩,⟨⟨698353574096587699255301728,698353574096587700290775478⟩,⟨3093282705295482624279687601,3093282705295482625339037821⟩⟩,⟨⟨706259115615056375020628981,706259115615056376048868832⟩,⟨3067828169489992905907341444,3067828169489992906959460468⟩⟩,⟨⟨714290208411349639812585460,714290208411349640833339773⟩,⟨3041528879679984133680701326,3041528879679984134725335398⟩⟩,⟨⟨722427186346292308971700856,722427186346292309984734276⟩,⟨3014404718939187015906040263,3014404718939187016942951743⟩⟩,⟨⟨730650127057995696489112062,730650127057995697494180311⟩,⟨2986476221958461202690871191,2986476221958461203719813243⟩⟩,⟨⟨738938900464182450294861796,738938900464182451291742791⟩,⟨2957764559171749423592434939,2957764559171749424613182773⟩⟩,⟨⟨747273217641269619804847508,747273217641269620793307607⟩,⟨2928291519848530282209934884,2928291519848530283222251867⟩⟩,⟨⟨755632679946852875456492449,755632679946852876436320833⟩,⟨2898079494132719380794939550,2898079494132719381798611732⟩⟩] +lemma kernel4_0_r3_1_eq : ∀ k : Fin 16, kernel4_0Expr 3 1 k = kernel4_0_r3_1 k := by decide +kernel +noncomputable def kernel4_0_r3_2 : Fin 16 → CBox := ![⟨⟨763996828251310022755431712,763996828251310023726401946⟩,⟨2867151454011534998908253293,2867151454011534999903050807⟩⟩,⟨⟨772345192143708837906601025,772345192143708838868518246⟩,⟨2835530933201676023055711890,2835530933201676024041436342⟩⟩,⟨⟨780657338977071031438396591,780657338977071032391046964⟩,⟨2803242005944237796406866874,2803242005944237797383300587⟩⟩,⟨⟨788912922618317922555040539,788912922618317923498240867⟩,⟨2770309264704095828963849090,2770309264704095829930804931⟩⟩,⟨⟨797091731768910056345414843,797091731768910057278958792⟩,⟨2736757796773995998637491002,2736757796773995999594758380⟩⟩,⟨⟨805173737723297075489974326,805173737723297076413696603⟩,⟨2702613159788279531190159801,2702613159788279532137569129⟩⟩,⟨⟨813139141433818816323075677,813139141433818817236783834⟩,⟨2667901356156016769484399502,2667901356156016770421753707⟩⟩,⟨⟨820968419752645491107698618,820968419752645492011239813⟩,⟨2632648806428299307305015202,2632648806428299308232156787⟩⟩,⟨⟨828642370723714026165514812,828642370723714027058702999⟩,⟨2596882321619518068390318420,2596882321619518069307056339⟩⟩,⟨⟨836142157800407584837472438,836142157800407585720175700⟩,⟨2560629074507606926762704565,2560629074507606927668901952⟩⟩,⟨⟨843449352867932738901940333,843449352867932739773988906⟩,⟨2523916569943428190271856607,2523916569943428191167338398⟩⟩,⟨⟨850545977952968616420369425,850545977952968617281643108⟩,⟨2486772614204687703863423741,2486772614204687704748064488⟩⟩,⟨⟨857414545507187784834809172,857414545507187785685144714⟩,⟨2449225283434962943553478722,2449225283434962944427109557⟩⟩,⟨⟨864038097155670906706868742,864038097155670907546168261⟩,⟨2411302891213576390929728709,2411302891213576391792246292⟩⟩,⟨⟨870400240806045730183651682,870400240806045731011769156⟩,⟨2373033955307117665046563210,2373033955307117665897815678⟩⟩,⟨⟨876485186019363247171324674,876485186019363247988174259⟩,⟨2334447163658380336941973155,2334447163658380337781868985⟩⟩] +lemma kernel4_0_r3_2_eq : ∀ k : Fin 16, kernel4_0Expr 3 2 k = kernel4_0_r3_2 k := by decide +kernel +noncomputable def kernel4_0_r3_3 : Fin 16 → CBox := ![⟨⟨882277777549265467711267621,882277777549265468516707500⟩,⟨2295571339673302276937412765,2295571339673302277765804055⟩⟩,⟨⟨887763526961883925437510735,887763526961883926231480779⟩,⟨2256435406871151418311307382,2256435406871151419128128212⟩⟩,⟨⟨892928642255117583090723650,892928642255117583873102296⟩,⟨2217068352967652206405429781,2217068352967652207210552382⟩⟩,⟨⟨897760055402453252650266449,897760055402453253421003324⟩,⟨2177499193464972788904276953,2177499193464972789697645018⟩⟩,⟨⟨902245447753289202648293330,902245447753289203407271390⟩,⟨2137756934826461237517262649,2137756934826461238298752772⟩⟩,⟨⟨906373273228779797875220346,906373273228779798622415166⟩,⟨2097870537317704005752247337,2097870537317704006521829150⟩⟩,⟨⟨910132779259510665650472276,910132779259510666385787151⟩,⟨2057868877598856022799948591,2057868877598856023557519002⟩⟩,⟨⟨913514025418813321195365551,913514025418813321918785992⟩,⟨2017780711156235446168264038,2017780711156235446913802572⟩⟩,⟨⟨916507899713207282459397107,916507899713207283170827709⟩,⟨1977634634663865006608362615,1977634634663865007341767397⟩⟩,⟨⟨919106132499287007773338301,919106132499287008472793815⟩,⟨1937459048367955813577454302,1937459048367955814298734210⟩⟩,⟨⟨921301308004319850839009020,921301308004319851526417619⟩,⟨1897282118589250207616246988,1897282118589250208325323824⟩⟩,⟨⟨923086873435857950311414775,923086873435857950986797556⟩,⟨1857131740439651669221891804,1857131740439651669918780825⟩⟩,⟨⟨924457145673758964406603505,924457145673758965069890343⟩,⟨1817035500850658130806920646,1817035500850658131491545372⟩⟩,⟨⟨925407315546124503783847664,925407315546124504435087949⟩,⟨1777020642011768896048937178,1777020642011768896721341373⟩⟩,⟨⟨925933449698767132441466851,925933449698767133080613299⟩,⟨1737114025317245850500415278,1737114025317245851160545494⟩⟩,⟨⟨926032490075872648023156716,926032490075872648650264970⟩,⟨1697342095919370424207662463,1697342095919370424855568852⟩⟩] +lemma kernel4_0_r3_3_eq : ∀ k : Fin 16, kernel4_0Expr 3 3 k = kernel4_0_r3_3 k := by decide +kernel +noncomputable def kernel4_0_r3_4 : Fin 16 → CBox := ![⟨⟨925702251037499588362098473,925702251037499588977118335⟩,⟨1657730847985645154379430930,1657730847985645155015057208⟩⟩,⟨⟨924941414147418121291252755,924941414147418121894271765⟩,⟨1618305790756241690310484715,1618305790756241690933913269⟩⟩,⟨⟨923749520672501452698131329,923749520672501453289126015⟩,⟨1579091915496397391293559549,1579091915496397391904761134⟩⟩,⟨⟨922126961842410840772787286,922126961842410841351846084⟩,⟨1540113663436414718691247108,1540113663436414719290305201⟩⟩,⟨⟨920074966925627057562530690,920074966925627058129628456⟩,⟨1501394894789428553479686810,1501394894789428554066570661⟩⟩,⟨⟨917595589184944338585992727,917595589184944339141506823⟩,⟨1462958858934186199526950663,1462958858934186200102021639⟩⟩,⟨⟨914691689782326176055953238,914691689782326176608349722⟩,⟨1424828165846745613111380962,1424828165846745613682729852⟩⟩,⟨⟨911366919709495629980401097,911366919709495630529639932⟩,⟨1387024758861254349681729886,1387024758861254350249324955⟩⟩,⟨⟨907625699826767455197696267,907625699826767455743601928⟩,⟨1349569888835842339408406134,1349569888835842339972079581⟩⟩,⟨⟨903473199098398170815355202,903473199098398171357910828⟩,⟨1312484089795165771074921093,1312484089795165771634665084⟩⟩,⟨⟨898915311118107905857791693,898915311118107906396837797⟩,⟨1275787156116299212342688404,1275787156116299212898351848⟩⟩,⟨⟨893958629023391058396427744,893958629023391058931934445⟩,⟨1239498121319512875103205833,1239498121319512875654768297⟩⟩,⟨⟨888610418901760220015411329,888610418901760220547200560⟩,⟨1203635238520017863368418837,1203635238520017863915711043⟩⟩,⟨⟨882878591796140399222818002,882878591796140399750882835⟩,⟨1168215962591042329951876136,1168215962591042330494901171⟩⟩,⟨⟨876771674420231652022080305,876771674420231652546258513⟩,⟨1133256934082645343120006906,1133256934082645343658611861⟩⟩,⟨⟨870298778697773603907401941,870298778697773604427675865⟩,⟨1098773964934513971447639153,1098773964934513971981816677⟩⟩] +lemma kernel4_0_r3_4_eq : ∀ k : Fin 16, kernel4_0Expr 3 4 k = kernel4_0_r3_4 k := by decide +kernel +noncomputable def kernel4_0_r3_5 : Fin 16 → CBox := ![⟨⟨863469570242263413465674162,863469570242263413981856992⟩,⟨1064782026014654895468493983,1064782026014654895998066816⟩⟩,⟨⟨856294235895790531261209888,856294235895790531773315029⟩,⟨1031295236509418010741898274,1031295236509418011266890590⟩⟩,⟨⟨848783450447250917081891804,848783450447250917589756499⟩,⟨998326855183710040872163002,998326855183710041392422015⟩⟩,⟨⟨840948342651286725341839276,840948342651286725845459862⟩,⟨965889273523605725695500814,965889273523605726211033755⟩⟩,⟨⟨832800460669864170168356442,832800460669864170667549742⟩,⟨933994010766877605817414128,933994010766877606328047920⟩⟩,⟨⟨824351737058454445970118646,824351737058454446464909747⟩,⟨902651710820277794917120303,902651710820277795422891224⟩⟩,⟨⟨815614453418325087287441425,815614453418325087777669185⟩,⟨871872141055751275828381621,871872141055751276329138893⟩⟩,⟨⟨806601204835489622395722956,806601204835489622881399164⟩,⟨841664192971174658799899098,841664192971174659295665719⟩⟩,⟨⟨797324864225412109786613192,797324864225412110267550039⟩,⟨812035884694730879167354208,812035884694730879657952720⟩⟩,⟨⟨787798546700633054446764554,787798546700633054923010546⟩,⟨782994365305682037871639451,782994365305682038357129750⟩⟩,⟨⟨778035574076089705809779465,778035574076089706281177129⟩,⟨754545920938121509440793930,754545920938121509921029062⟩⟩,⟨⟨768049439624064669376267281,768049439624064669842844899⟩,⟨726695982628303315647128693,726695982628303316122148207⟩⟩,⟨⟨757853773187432223594582678,757853773187432224056160538⟩,⟨699449135860390900104557503,699449135860390900574192098⟩⟩,⟨⟨747462306756203959679217591,747462306756203960135857576⟩,⟨672809131759966520036853357,672809131759966520501176220⟩⟩,⟨⟨736888840608328566158898139,736888840608328566610448292⟩,⟨646778899879422375610850394,646778899879422376069720012⟩⟩,⟨⟨726147210111300776592421043,726147210111300777038926777⟩,⟨621360562514439246883374770,621360562514439247336847648⟩⟩] +lemma kernel4_0_r3_5_eq : ∀ k : Fin 16, kernel4_0Expr 3 5 k = kernel4_0_r3_5 k := by decide +kernel +noncomputable def kernel4_0_r3_6 : Fin 16 → CBox := ![⟨⟨715251253276409322185063569,715251253276409322626342045⟩,⟨596555450486169629172988426,596555450486169629620891938⟩⟩,⟨⟨704214779152432240957431220,704214779152432241393571221⟩,⟨572364120319499755737992100,572364120319499756180426080⟩⟩,⟨⟨693051537140300375173103385,693051537140300375603960124⟩,⟨548786372743885754101896641,548786372743885754538726470⟩⟩,⟨⟨681775187304727636576272657,681775187304727637001908825⟩,⟨525821272439758370983974320,525821272439758371415273406⟩⟩,⟨⟨670399271753081731955019989,670399271753081732375266774⟩,⟨503467168950380615082434456,503467168950380615508043877⟩⟩,⟨⟨658937187145874198659119987,658937187145874199074077169⟩,⟨481721718676333176621813044,481721718676333177041843129⟩⟩,⟨⟨647402158397216842270968980,647402158397216842680500264⟩,⟨460581907867500904703761848,460581907867500905118086032⟩⟩,⟨⟨635807213617456180952047640,635807213617456181356232743⟩,⟨440044076525544714286572480,440044076525544714695280656⟩⟩,⟨⟨624165160343991393238854763,624165160343991393637525287⟩,⟨420103943128369260635034460,420103943128369261037967593⟩⟩,⟨⟨612488563100037360873412483,612488563100037361266693718⟩,⟨400756630087037247485586146,400756630087037247882879476⟩⟩,⟨⟨600789722314845022945016804,600789722314845023332782021⟩,⟨381996689844933542550165752,381996689844933542941701705⟩⟩,⟨⟨589080654632668043470884684,589080654632668043853229891⟩,⟨363818131528741172882541018,363818131528741173268425102⟩⟩,⟨⟨577373074631598484896387223,577373074631598485273159972⟩,⟨346214448060949255156032874,346214448060949255536121405⟩⟩,⟨⟨565678377967314448391950412,565678377967314448763285743⟩,⟨329178643644160253118148826,329178643644160253492586034⟩⟩,⟨⟨554007625950817921755889888,554007625950817922121671336⟩,⟨312703261528388810767016849,312703261528388811135694752⟩⟩,⟨⟨542371531563418402957193298,542371531563418403317532090⟩,⟨296780411973832970572778719,296780411973832970935817271⟩⟩] +lemma kernel4_0_r3_6_eq : ∀ k : Fin 16, kernel4_0Expr 3 6 k = kernel4_0_r3_6 k := by decide +kernel +noncomputable def kernel4_0_r3_7 : Fin 16 → CBox := ![⟨⟨530780446906562736088065543,530780446906562736442809119⟩,⟨281401800323235197928549457,281401800323235198285804141⟩⟩,⟨⟨519244352078647830163645113,519244352078647830512953864⟩,⟨266558755099917954396850817,266558755099917954748490418⟩⟩,⟨⟨507772845465702568736708030,507772845465702569080476198⟩,⟨252242256049857723580038450,252242256049857723925964948⟩⟩,⟨⟨496375135427808416348613183,496375135427808416686965742⟩,⟨238442962048732164484023572,238442962048732164824369834⟩⟩,⟨⟨485060033358363179641291971,485060033358363179974095953⟩,⟨225151238797716031305519103,225151238797716031640159468⟩⟩,⟨⟨473835948088795251771160856,473835948088795252098580665⟩,⟨212357186234890230357686931,212357186234890230686793317⟩⟩,⟨⟨462710881607120548382102133,462710881607120548704042794⟩,⟨200050665592441631593355325,200050665592441631916839714⟩⟩,⟨⟨451692426054813215319456191,451692426054813215636054744⟩,⟨188221326033345115796828343,188221326033345116114834807⟩⟩,⟨⟨440787761962843915703763028,440787761962843916014888192⟩,⟨176858630804909457474721313,176858630804909457787125092⟩⟩,⟨⟨430003657684433831965954610,430003657684433832271791143⟩,⟨165951882850410372691572590,165951882850410372998565086⟩⟩,⟨⟨419346469979084091915270292,419346469979084092215733856⟩,⟨155490249824002648513121138,155490249824002648814624183⟩⟩,⟨⟨408822145699772724834856947,408822145699772725130094700⟩,⟨145462788458174029015573924,145462788458174029311740845⟩⟩,⟨⟨398436224532866032661119927,398436224532866032951019143⟩,⟨135858468237152005136064223,135858468237152005426788049⟩⟩,⟨⟨388193842738268023022670105,388193842738268023307416440⟩,⟨126666194333876773878885477,126666194333876774164357635⟩⟩,⟨⟨378099737835628011523903817,378099737835628011803423139⟩,⟨117874829772385867229924126,117874829772385867510075877⟩⟩,⟨⟨368158254181038577392964841,368158254181038577667412412⟩,⟨109473216781695452493562566,109473216781695452768554501⟩⟩] +lemma kernel4_0_r3_7_eq : ∀ k : Fin 16, kernel4_0Expr 3 7 k = kernel4_0_r3_7 k := by decide +kernel +noncomputable def kernel4_0_r3_8 : Fin 16 → CBox := ![⟨⟨358373349377577963588068432,358373349377577963857330276⟩,⟨101450197311488033165345010,101450197311488033435068153⟩⟩,⟨⟨348748601462275365658382946,348748601462275365922663222⟩,⟨93794632684105121178892638,93794632684105121443556094⟩⟩,⟨⟨339287216811595484113680477,339287216811595484372914677⟩,⟨86495422361476332180168823,86495422361476332439712736⟩⟩,⟨⟨329992038707339988643094704,329992038707339988897444053⟩,⟨79541521809674332082892030,79541521809674332337482156⟩⟩,⟨⟨320865556504936685396600117,320865556504936685645970959⟩,⟨72921959447750407320705279,72921959447750407570252256⟩⟩,⟨⟨311909915346419606677449285,311909915346419606922039401⟩,⟨66625852671361700129904844,66625852671361700374610613⟩⟩,⟨⟨303126926360981394203309809,303126926360981394443063519⟩,⟨60642422945433244215152571,60642422945433244454965410⟩⟩,⟨⟨294518077296788817631716139,294518077296788817866798587⟩,⟨54961009963692143639383670,54961009963692143874472516⟩⟩,⟨⟨286084543528777945844830009,286084543528777946075147336⟩,⟨49571084876355267586307897,49571084876355267816582528⟩⟩,⟨⟨277827199388371681611640874,277827199388371681837402563⟩,⟨44462262590534835126253555,44462262590534835351926897⟩⟩,⟨⟨269746629762472950702278985,269746629762472950923437356⟩,⟨39624313151038835384317093,39624313151038835605344788⟩⟩,⟨⟨261843141910665361759292441,261843141910665361976014513⟩,⟨35047172212177413095124304,35047172212177413311676490⟩⟩,⟨⟨254116777451282993949175929,254116777451282994161384620⟩,⟨30720950613935622289882746,30720950613935622501885378⟩⟩,⟨⟨246567324468875430666968397,246567324468875430874864709⟩,⟨26635943078432193502906949,26635943078432193710563830⟩⟩,⟨⟨239194329697576594446410053,239194329697576594649953338⟩,⟨22782636044949427050007166,22782636044949427253280397⟩⟩,⟨⟨231997110736969865320453170,231997110736969865519810492⟩,⟨19151714663988601367939991,19151714663988601566999154⟩⟩] +lemma kernel4_0_r3_8_eq : ∀ k : Fin 16, kernel4_0Expr 3 8 k = kernel4_0_r3_8 k := by decide +kernel +noncomputable def kernel4_0_r3_9 : Fin 16 → CBox := ![⟨⟨224974768259211159015239477,224974768259211159210330124⟩,⟨15734068972777235262763424,15734068972777235457530321⟩⟩,⟨⟨218126198168410236958752164,218126198168410237149786717⟩,⟨12520799276429251763218504,12520799276429251953905939⟩⟩,⟨⟨211450103675563096853843022,211450103675563097040786964⟩,⟨9503220760537801947174052,9503220760537802133749750⟩⟩,⟨⟨204945007254659955031464928,204945007254659955214483614⟩,⟨6672867362365550014117372,6672867362365550196748682⟩⟩,⟨⟨198609262447949780641733359,198609262447949780820763128⟩,⟨4021494928991939901963144,4021494928991940080588446⟩⟩,⟨⟨192441065490709936536096247,192441065490709936711333583⟩,⟨1541083691785638379868901,1541083691785638554686411⟩⟩,⟨⟨186438466728235295278681229,186438466728235295450096769⟩,⟨(-776159912601885662317195),(-776159912601885491335035)⟩⟩,⟨⟨180599381800113062928130372,180599381800113063095886315⟩,⟨(-2937802043872924068546610),(-2937802043872923901236061)⟩⟩,⟨⟨174921602569176086340059262,174921602569176086504088920⟩,⟨(-4951180851017157852579257),(-4951180851017157689005359)⟩⟩,⟨⟨169402807774818095624947855,169402807774818095785451798⟩,⟨(-6823406424886126256353268),(-6823406424886126096314150)⟩⟩,⟨⟨164040573392599442775059621,164040573392599442932012774⟩,⟨(-8561361278582647948320733),(-8561361278582647791840039)⟩⟩,⟨⟨158832382684262601385324165,158832382684262601538884270⟩,⟨(-10171701323814967160440948),(-10171701323814967007359780)⟩⟩,⟨⟨153775635924405018462789056,153775635924405018612902633⟩,⟨(-11660857311477865996674055),(-11660857311477865847044594)⟩⟩,⟨⟨148867659792115750992349651,148867659792115751139202728⟩,⟨(-13035036704963463193918903),(-13035036704963463047554166)⟩⟩,⟨⟨144105716417865429338742197,144105716417865429482313137⟩,⟨(-14300225955063909630611501),(-14300225955063909487532009)⟩⟩,⟨⟨139487012077841064296884448,139487012077841064437325531⟩,⟨(-15462193145797561733931828),(-15462193145797561593984465)⟩⟩] +lemma kernel4_0_r3_9_eq : ∀ k : Fin 16, kernel4_0Expr 3 9 k = kernel4_0_r3_9 k := by decide +kernel +noncomputable def kernel4_0_r3_10 : Fin 16 → CBox := ![⟨⟨135008705529733479042389934,135008705529733479179641236⟩,⟨(-16526490981060273888839189),(-16526490981060273752082849)⟩⟩,⟨⟨130667915985711928844598662,130667915985711928978850016⟩,⟨(-17498460082665011596055662),(-17498460082665011462299864)⟩⟩,⟨⟨126461730719954772646213325,126461730719954772777445826⟩,⟨(-18383232571076923961493418),(-18383232571076923830756211)⟩⟩,⟨⟨122387212309644626841216927,122387212309644626969576532⟩,⟨(-19185735900968322692853078),(-19185735900968322564987931)⟩⟩,⟨⟨118441405509779715666612634,118441405509779715792053153⟩,⟨(-19910696924599862142941432),(-19910696924599862017993750)⟩⟩,⟨⟨114621343763499256612701195,114621343763499256735394229⟩,⟨(-20562646156971986234360128),(-20562646156971986112157886)⟩⟩,⟨⟨110924055350869433817441261,110924055350869433937369948⟩,⟨(-21145922217676048385902863),(-21145922217676048266462280)⟩⟩,⟨⟨107346569180228154333272932,107346569180228154450576360⟩,⟨(-21664676425399361798370438),(-21664676425399361681552061)⟩⟩,⟨⟨103885920227242230620754224,103885920227242230735381193⟩,⟨(-22122877522095070595562691),(-22122877522095070481417111)⟩⟩,⟨⟨100539154627791264492229278,100539154627791264604351208⟩,⟨(-22524316504908774740837064),(-22524316504908774629192639)⟩⟩,⟨⟨97303334431660152482001798,97303334431660152591603337⟩,⟨(-22872611545052299915220052),(-22872611545052299806091660)⟩⟩,⟨⟨94175542024799027171550074,94175542024799027278763016⟩,⟨(-23171212973924281732509981),(-23171212973924281625765627)⟩⟩,⟨⟨91152884228598192946303205,91152884228598193051086291⟩,⟨(-23423408317891147368421036),(-23423408317891147264101532)⟩⟩,⟨⟨88232496085229126125383924,88232496085229126227892288⟩,⟨(-23632327364254863981289771),(-23632327364254863879239897)⟩⟩,⟨⟨85411544338624081970091514,85411544338624082070310825⟩,⟨(-23800947242040146831561948),(-23800947242040146731795694)⟩⟩,⟨⟨82687230621109711907779170,82687230621109712005833753⟩,⟨(-23932097502328775474000666),(-23932097502328775376393634)⟩⟩] +lemma kernel4_0_r3_10_eq : ∀ k : Fin 16, kernel4_0Expr 3 10 k = kernel4_0_r3_10 k := by decide +kernel +noncomputable def kernel4_0_r3_11 : Fin 16 → CBox := ![⟨⟨80056794356077963894975683,80056794356077963990817021⟩,⟨(-24028465183947777682843224),(-24028465183947777587443586)⟩⟩,⟨⟨77517515387374192384430362,77517515387374192478214323⟩,⟨(-24092599851377457044391655),(-24092599851377456951043582)⟩⟩,⟨⟨75066716346311735147451615,75066716346311735239164537⟩,⟨(-24126918592780929092120466),(-24126918592780929000837384)⟩⟩,⟨⟨72701764767388198983761590,72701764767388199073520250⟩,⟨(-24133710967065769446436839),(-24133710967065769357101995)⟩⟩,⟨⟨70420074963885362954934852,70420074963885363042701194⟩,⟨(-24115143889867740402119226),(-24115143889867740314770435)⟩⟩,⟨⟨68219109674586004913671710,68219109674586004999583908⟩,⟨(-24073266449293908885732786),(-24073266449293908800231983)⟩⟩,⟨⟨66096381492841126567876877,66096381492841126651921613⟩,⟨(-24010014643175726956295763),(-24010014643175726872656106)⟩⟩,⟨⟨64049454089174003479734680,64049454089174003562021308⟩,⟨(-23927216030460096956451373),(-23927216030460096874563604)⟩⟩,⟨⟨62075943238517173106293663,62075943238517173186778385⟩,⟨(-23826594290206702801977123),(-23826594290206702721884853)⟩⟩,⟨⟨60173517663048773765583491,60173517663048773844403218⟩,⟨(-23709773682461888704909318),(-23709773682461888626475817)⟩⟩,⟨⟨58339899701429343044631988,58339899701429343121773544⟩,⟨(-23578283406042335642881221),(-23578283406042335566119564)⟩⟩,⟨⟨56572865815042947461180169,56572865815042947536745649⟩,⟨(-23433561848985229880663757),(-23433561848985229805471994)⟩⟩,⟨⟨54870246941620893021697198,54870246941620893095650540⟩,⟨(-23276960728105299390680986),(-23276960728105299317095055)⟩⟩,⟨⟨53229928706375668697066642,53229928706375668769529784⟩,⟨(-23109749114743012287683016),(-23109749114743012215581188)⟩⟩,⟨⟨51649851500500465092019685,51649851500500465162979411⟩,⟨(-22933117344392601979471912),(-22933117344392601908867346)⟩⟩,⟨⟨50128010436598697377426084,50128010436598697446977548⟩,⟨(-22748180808463818747377808),(-22748180808463818678175527)⟩⟩] +lemma kernel4_0_r3_11_eq : ∀ k : Fin 16, kernel4_0Expr 3 11 k = kernel4_0_r3_11 k := by decide +kernel +noncomputable def kernel4_0_r3_12 : Fin 16 → CBox := ![⟨⟨48662455190301392784046030,48662455190301392852145462⟩,⟨(-22555983626957995929795545),(-22555983626957995862039212)⟩⟩,⟨⟨47251289737010861279606733,47251289737010861346377033⟩,⟨(-22357502201327907688076615),(-22357502201327907621643584)⟩⟩,⟨⟨45892671992379368051843118,45892671992379368117270952⟩,⟨(-22153648647242870745672689),(-22153648647242870680576267)⟩⟩,⟨⟨44584813364794013156994238,44584813364794013221168128⟩,⟨(-21945274107396612369126088),(-21945274107396612305277949)⟩⟩,⟨⟨43325978227795972644014286,43325978227795972706899421⟩,⟨(-21733171944876703599143209),(-21733171944876703536578101)⟩⟩,⟨⟨42114483320015773604083758,42114483320015773665787298⟩,⟨(-21518080817962041101920740),(-21518080817962041040531754)⟩⟩,⟨⟨40948697079858303622420997,40948697079858303682929394⟩,⟨(-21300687637530226753771817),(-21300687637530226693572495)⟩⟩,⟨⟨39827038921823570569816866,39827038921823570629212452⟩,⟨(-21081630408541073565948474),(-21081630408541073506856691)⟩⟩,⟨⟨38747978461003449985007725,38747978461003450043250011⟩,⟨(-20861500957317237267011771),(-20861500957317237209067957)⟩⟩,⟨⟨37710034691952248458846236,37710034691952248516041921⟩,⟨(-20640847546569544847695214),(-20640847546569544790792939)⟩⟩,⟨⟨36711775127791187386305065,36711775127791187442440381⟩,⟨(-20420177380314395686191052),(-20420177380314395630344092)⟩⟩,⟨⟨35751814905075043950421597,35751814905075044005573081⟩,⟨(-20199959001005088953304047),(-20199959001005088898436075)⟩⟩,⟨⟨34828815859624210118012831,34828815859624210172146458⟩,⟨(-19980624581349524971648911),(-19980624581349524917793918)⟩⟩,⟨⟨33941485578208250361591439,33941485578208250414801513⟩,⟨(-19762572113414872148128824),(-19762572113414872095192764)⟩⟩,⟨⟨33088576430658436013993347,33088576430658436066265853⟩,⟨(-19546167497726903150779665),(-19546167497726903098776566)⟩⟩,⟨⟨32268884586687373509391180,32268884586687373560797335⟩,⟨(-19331746535159179390799977),(-19331746535159179339658831)⟩⟩] +lemma kernel4_0_r3_12_eq : ∀ k : Fin 16, kernel4_0Expr 3 12 k = kernel4_0_r3_12 k := by decide +kernel +noncomputable def kernel4_0_r3_13 : Fin 16 → CBox := ![⟨⟨31481249021404281003211805,31481249021404281053710580⟩,⟨(-19119616824476467735019382),(-19119616824476467684781174)⟩⟩,⟨⟨30724550513235156727533549,30724550513235156777220999⟩,⟨(-18910059568449039420143079),(-18910059568449039370712023)⟩⟩,⟨⟨29997710637688381849382706,29997710637688381898244621⟩,⟨(-18703331291491121008935158),(-18703331291491120960325484)⟩⟩,⟨⟨29299690760148481726434085,29299690760148481774536775⟩,⟨(-18499665471798990628211919),(-18499665471798990580357522)⟩⟩,⟨⟨28629491030634022709411250,28629491030634022756721222⟩,⟨(-18299274090973243180660298),(-18299274090973243133594643)⟩⟩,⟨⟨27986149383220063452482964,27986149383220063499083727⟩,⟨(-18102349104106740488658074),(-18102349104106740442297902)⟩⟩,⟨⟨27368740542601259146114721,27368740542601259191991872⟩,⟨(-17909063833305820358603350),(-17909063833305820312963083)⟩⟩,⟨⟨26776375040058622275322841,26776375040058622320538257⟩,⟨(-17719574287588514023916268),(-17719574287588513978934227)⟩⟩,⟨⟨26208198240891007693549460,26208198240891007738064224⟩,⟨(-17534020412070812705293876),(-17534020412070812661008939)⟩⟩,⟨⟨25663389385181497259070486,25663389385181497302969201⟩,⟨(-17352527269311375652207945),(-17352527269311375608535763)⟩⟩,⟨⟨25141160643588850889033873,25141160643588850932302014⟩,⟨(-17175206155637374513079158),(-17175206155637374470034275)⟩⟩,⟨⟨24640756189684869397170693,24640756189684869439866115⟩,⟨(-17002155655220258939978858),(-17002155655220258897503609)⟩⟩,⟨⟨24161451290199649519639746,24161451290199649561729335⟩,⟨(-16833462634610889381572462),(-16833462634610889339699936)⟩⟩,⟨⟨23702551414388044242743997,23702551414388044284302537⟩,⟨(-16669203180379445992070751),(-16669203180379445950726394)⟩⟩,⟨⟨23263391363591888974934872,23263391363591889015947746⟩,⟨(-16509443482437466961226273),(-16509443482437466920424720)⟩⟩,⟨⟨22843334421943413235486683,22843334421943413276008164⟩,⟨(-16354240665547924645683985),(-16354240665547924605371147)⟩⟩] +lemma kernel4_0_r3_13_eq : ∀ k : Fin 16, kernel4_0Expr 3 13 k = kernel4_0_r3_13 k := by decide +kernel +noncomputable def kernel4_0_r3_14 : Fin 16 → CBox := ![⟨⟨22441771529035409049867307,22441771529035409089857224⟩,⟨(-16203643571454994175016018),(-16203643571454994135232017)⟩⟩,⟨⟨22058120475272838962441010,22058120475272839001977815⟩,⟨(-16057693493988640063212176),(-16057693493988640023878803)⟩⟩,⟨⟨21691825120518296623499257,21691825120518296662568336⟩,⟨(-15916424869420829627241504),(-15916424869420829588373388)⟩⟩,⟨⟨21342354636549732558457721,21342354636549732597110120⟩,⟨(-15779865924270521865844080),(-15779865924270521827390348)⟩⟩,⟨⟨21009202773762774038008341,21009202773762774076211243⟩,⟨(-15648039282673979210219887),(-15648039282673979172213327)⟩⟩,⟨⟨20691887152471446081944153,20691887152471446119765551⟩,⟨(-15520962535355769646676835),(-15520962535355769609049669)⟩⟩,⟨⟨20389948579089785882860236,20389948579089785920285556⟩,⟨(-15398648772154392569789112),(-15398648772154392532555926)⟩⟩,⟨⟨20102950387412382679700643,20102950387412382716778115⟩,⟨(-15281107079975061791080689),(-15281107079975061754193418)⟩⟩,⟨⟨19830477805153920348253671,19830477805153920384945092⟩,⟨(-15168343007961067772051473),(-15168343007961067735548276)⟩⟩,⟨⟨19572137345856006741977504,19572137345856006778353709⟩,⟨(-15060359001594540634312554),(-15060359001594540598122815)⟩⟩,⟨⟨19327556226223604402545906,19327556226223604438592447⟩,⟨(-14957154807357537871731045),(-14957154807357537835869225)⟩⟩,⟨⟨19096381808912901201420723,19096381808912901237183342⟩,⟨(-14858727849505349680264424),(-14858727849505349644684939)⟩⟩,⟨⟨18878281070757154410997439,18878281070757154446443515⟩,⟨(-14765073580425887652246386),(-14765073580425887616981821)⟩⟩,⟨⟨18672940096386594029652597,18672940096386594064845148⟩,⟨(-14676185805982111765459057),(-14676185805982111730446595)⟩⟩,⟨⟨18480063597172576589333630,18480063597172576624258395⟩,⟨(-14592056987158745633090425),(-14592056987158745598344336)⟩⟩,⟨⟨18299374455404544504282307,18299374455404544538982882⟩,⟨(-14512678519260099032407917),(-14512678519260098997884759)⟩⟩] +lemma kernel4_0_r3_14_eq : ∀ k : Fin 16, kernel4_0Expr 3 14 k = kernel4_0_r3_14 k := by decide +kernel +noncomputable def kernel4_0_r3_15 : Fin 16 → CBox := ![⟨⟨18130613293590683552581080,18130613293590683587017916⟩,⟨(-14438040989832708194220958),(-14438040989832708159960224)⟩⟩,⟨⟨17973538068759207641232423,17973538068759207675474699⟩,⟨(-14368134416414748381617944),(-14368134416414748347550345)⟩⟩,⟨⟨17827923691626671006298716,17827923691626671040333151⟩,⟨(-14302948465143783287517803),(-14302948465143783253656402)⟩⟩,⟨⟨17693561670492358861024350,17693561670492358894892529⟩,⟨(-14242472651185389710557908),(-14242472651185389676861316)⟩⟩,⟨⟨17570259779713393510401010,17570259779713393544070315⟩,⟨(-14186696521877517691628494),(-14186696521877517658129334)⟩⟩,⟨⟨17457841752613478988796803,17457841752613479022326767⟩,⟨(-14135609823419086822229437),(-14135609823419086788868409)⟩⟩,⟨⟨17356146998678967551888265,17356146998678967585265138⟩,⟨(-14089202651866238082887131),(-14089202651866238049678035)⟩⟩,⟨⟨17265030344898948989223765,17265030344898949022487581⟩,⟨(-14047465589135806070662197),(-14047465589135806037565181)⟩⟩,⟨⟨17184361801111130350411594,17184361801111130383524019⟩,⟨(-14010389824652888009955108),(-14010389824652887977008494)⟩⟩,⟨⟨17114026349222188931590051,17114026349222188964615309⟩,⟨(-13977967263217794136055086),(-13977967263217794103194887)⟩⟩,⟨⟨17053923756179852379787457,17053923756179852412712281⟩,⟨(-13950190619607091871607448),(-13950190619607091838846975)⟩⟩,⟨⟨17003968410584000579014223,17003968410584000611877306⟩,⟨(-13927053500363819897173273),(-13927053500363819864474008)⟩⟩,⟨⟨16964089182835414945893272,16964089182835414978662085⟩,⟨(-13908550473173158004623747),(-13908550473173157972018217)⟩⟩,⟨⟨16934229308733247918723197,16934229308733247951455429⟩,⟨(-13894677124161799610719296),(-13894677124161799578150030)⟩⟩,⟨⟨16914346296445679840200426,16914346296445679872883373⟩,⟨(-13885430103401886647079683),(-13885430103401886614559429)⟩⟩,⟨⟨16904411856792407513591181,16904411856792407546262450⟩,⟨(-13880807158843528155654389),(-13880807158843528123145710)⟩⟩] +lemma kernel4_0_r3_15_eq : ∀ k : Fin 16, kernel4_0Expr 3 15 k = kernel4_0_r3_15 k := by decide +kernel +noncomputable def kernel4_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel4_0_r3_0,kernel4_0_r3_1,kernel4_0_r3_2,kernel4_0_r3_3,kernel4_0_r3_4,kernel4_0_r3_5,kernel4_0_r3_6,kernel4_0_r3_7,kernel4_0_r3_8,kernel4_0_r3_9,kernel4_0_r3_10,kernel4_0_r3_11,kernel4_0_r3_12,kernel4_0_r3_13,kernel4_0_r3_14,kernel4_0_r3_15] +lemma kernel4_0_r3_eq (i k : Fin 16) : kernel4_0Expr 3 i k = kernel4_0_r3 i k := by + fin_cases i + · exact kernel4_0_r3_0_eq k + · exact kernel4_0_r3_1_eq k + · exact kernel4_0_r3_2_eq k + · exact kernel4_0_r3_3_eq k + · exact kernel4_0_r3_4_eq k + · exact kernel4_0_r3_5_eq k + · exact kernel4_0_r3_6_eq k + · exact kernel4_0_r3_7_eq k + · exact kernel4_0_r3_8_eq k + · exact kernel4_0_r3_9_eq k + · exact kernel4_0_r3_10_eq k + · exact kernel4_0_r3_11_eq k + · exact kernel4_0_r3_12_eq k + · exact kernel4_0_r3_13_eq k + · exact kernel4_0_r3_14_eq k + · exact kernel4_0_r3_15_eq k +noncomputable def kernel4_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-65877750426736874284134303975),(-65877750426736874256297482887)⟩,⟨(-35141414442978609074799347698),(-35141414442978609046711458897)⟩⟩,⟨⟨(-65871522385232875172729024858),(-65871522385232875144894292415)⟩,⟨(-35124571753997705665527492936),(-35124571753997705637442002195)⟩⟩,⟨⟨(-65859061438648900338820399606),(-65859061438648900310989892791)⟩,⟨(-35090899978912537430905530747),(-35090899978912537402824884169)⟩⟩,⟨⟨(-65840357878178443532570865254),(-65840357878178443504746722594)⟩,⟨(-35040426312900843301223732938),(-35040426312900843273150377497)⟩⟩,⟨⟨(-65815397186429520023731521289),(-65815397186429519995915884059)⟩,⟨(-34973191522281100382606676424),(-34973191522281100354543060834)⟩⟩,⟨⟨(-65784160092277719367233688367),(-65784160092277719339428701245)⟩,⟨(-34889249912748881479919439860),(-34889249912748881451868014893)⟩⟩,⟨⟨(-65746622643790063474411876476),(-65746622643790063446619689096)⟩,⟨(-34788669286982534743420701931),(-34788669286982534715383921645)⟩⟩,⟨⟨(-65702756299037129270284070808),(-65702756299037129242506836698)⟩,⟨(-34671530891582189516733343904),(-34671530891582189488713664238)⟩⟩,⟨⟨(-65652528034565883574806634779),(-65652528034565883547046516620)⟩,⟨(-34537929353297948664609404360),(-34537929353297948636609288078)⟩⟩,⟨⟨(-65595900471261082752227173105),(-65595900471261082724486335397)⟩,⟨(-34387972604495547929900020187),(-34387972604495547901921929209)⟩⟩,⟨⟨(-65532832017278995262921686370),(-65532832017278995235202309251)⟩,⟨(-34221781797800853996310728057),(-34221781797800853968357136964)⟩⟩,⟨⟨(-65463277027693696072248558180),(-65463277027693696044552819103)⟩,⟨(-34039491209858438444807980162),(-34039491209858438416881357542)⟩⟩,⟨⟨(-65387185980453342912920533748),(-65387185980453342885250636887)⟩,⟨(-33841248134134204438150366229),(-33841248134134204410253203788)⟩⟩,⟨⟨(-65304505668201761120187140600),(-65304505668201761092545276009)⟩,⟨(-33627212762687752217622698768),(-33627212762687752189757470154)⟩⟩,⟨⟨(-65215179405479422093277870736),(-65215179405479422065666268732)⟩,⟨(-33397558056836939039112705340),(-33397558056836939011281920249)⟩⟩,⟨⟨(-65119147250777586770537914406),(-65119147250777586742958780573)⟩,⟨(-33152469606635004446642845700),(-33152469606635004418848984544)⟩⟩] +lemma kernel4_0_r4_0_eq : ∀ k : Fin 16, kernel4_0Expr 4 0 k = kernel4_0_r4_0 k := by decide +kernel +noncomputable def kernel4_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-65016346242880086652591696556),(-65016346242880086625047299400)⟩,⟨(-32892145479079772496619965594),(-32892145479079772468865566916)⟩⟩,⟨⟨(-64906710650889018051173102341),(-64906710650889018023665656127)⟩,⟨(-32616796054974882259655882330),(-32616796054974882231943425270)⟩⟩,⟨⟨(-64790172237293617858349738654),(-64790172237293617830881545647)⟩,⟨(-32326643854364803607387657514),(-32326643854364803579719703869)⟩⟩,⟨⟨(-64666660533405858893353510453),(-64666660533405858865926801973)⟩,⟨(-32021923350468626920297444627),(-32021923350468626892676479523)⟩⟩,⟨⟨(-64536103126451937534191498838),(-64536103126451937506808632098)⟩,⟨(-31702880772042325544389802631),(-31702880772042325516818431216)⟩⟩,⟨⟨(-64398425957575913542772137532),(-64398425957575913515435343531)⟩,⟨(-31369773894105423476574741478),(-31369773894105423449055436397)⟩⟩,⟨⟨(-64253553629980389158023403886),(-64253553629980389130735079085)⟩,⟨(-31022871816975794723569049759),(-31022871816975794696104442754)⟩⟩,⟨⟨(-64101409726399368623562145221),(-64101409726399368596324538577)⟩,⟨(-30662454733565703569349376763),(-30662454733565703541941945275)⟩⟩,⟨⟨(-63941917135070406622379918157),(-63941917135070406595195504166)⟩,⟨(-30288813684903186507494351724),(-30288813684903186480146791913)⟩⟩,⟨⟨(-63774998383346919974262731973),(-63774998383346919947133740355)⟩,⟨(-29902250303855487913090136431),(-29902250303855487885804892375)⟩⟩,⟨⟨(-63600575978067185577854823559),(-63600575978067185550783766572)⟩,⟨(-29503076547045494670928799305),(-29503076547045494643708590367)⟩⟩,⟨⟨(-63418572751774161618291022183),(-63418572751774161591280151798)⟩,⟨(-29091614414967962766336998689),(-29091614414967962739184276219)⟩⟩,⟨⟨(-63228912213859929366495709867),(-63228912213859929339547638385)⟩,⟨(-28668195660329774776738587581),(-28668195660329774749656155611)⟩⟩,⟨⟨(-63031518905690338161892898829),(-63031518905690338135009837928)⟩,⟨(-28233161484657485353872222152),(-28233161484657485326862475932)⟩⟩,⟨⟨(-62826318758749422568752602580),(-62826318758749422541937200577)⟩,⟨(-27786862223235966772232951448),(-27786862223235966745298714859)⟩⟩,⟨⟨(-62613239454829421496672360364),(-62613239454829421469926851602)⟩,⟨(-27329657018464013582699269451),(-27329657018464013555842943913)⟩⟩] +lemma kernel4_0_r4_1_eq : ∀ k : Fin 16, kernel4_0Expr 4 1 k = kernel4_0_r4_1 k := by decide +kernel +noncomputable def kernel4_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-62392210787280834244951159240),(-62392210787280834218278329831)⟩,⟨(-26861913481736250062294331820),(-26861913481736250035518862184)⟩⟩,⟨⟨(-62163165022327964221460331175),(-62163165022327964194862334176)⟩,⟨(-26384007343985542850151425612),(-26384007343985542823459114849)⟩⟩,⟨⟨(-61926037259448889611763468075),(-61926037259448889585243105589)⟩,⟨(-25896322095046281037491110155),(-25896322095046281010884901652)⟩⟩,⟨⟨(-61680765789814819071684786779),(-61680765789814819045244249427)⟩,⟨(-25399248612026265111128837892),(-25399248612026265084611054520)⟩⟩,⟨⟨(-61427292451782392107515577862),(-61427292451782392081157828795)⟩,⟨(-24893184776903453771688066334),(-24893184776903453745261794579)⟩⟩,⟨⟨(-61165562982433715251249868802),(-61165562982433715224976986350)⟩,⟨(-24378535083593354419333298058),(-24378535083593354393000730353)⟩⟩,⟨⟨(-60895527364162827582687785039),(-60895527364162827556502739731)⟩,⟨(-23855710234763301415356454313),(-23855710234763301389120666141)⟩⟩,⟨⟨(-60617140165313897390925316260),(-60617140165313897364830223159)⟩,⟨(-23325126728701130571830722729),(-23325126728701130545693924778)⟩⟩,⟨⟨(-60330360873885793806540346600),(-60330360873885793780538392795)⟩,⟨(-22787206436577705671575897852),(-22787206436577705645541363450)⟩⟩,⟨⟨(-60035154223329773851998535167),(-60035154223329773826091655860)⟩,⟨(-22242376170475253096900738694),(-22242376170475253070970479933)⟩⟩,⟨⟨(-59731490509481889691115068886),(-59731490509481889665306413006)⟩,⟨(-21691067242586377203901513226),(-21691067242586377178078746343)⟩⟩,⟨⟨(-59419345897689358008725878245),(-59419345897689357983017449401)⟩,⟨(-21133715016021819249364202901),(-21133715016021819223650989493)⟩⟩,⟨⟨(-59098702719210540098735920145),(-59098702719210540073131104400)⟩,⟨(-20570758447698338343704808469),(-20570758447698338318104582797)⟩⟩,⟨⟨(-58769549755991345285904645703),(-58769549755991345260405229962)⟩,⟨(-20002639623811381126369525303),(-20002639623811381100884113342)⟩⟩,⟨⟨(-58431882512946770552421798417),(-58431882512946770527031115868)⟩,⟨(-19429803288430310537187226290),(-19429803288430310511819990351)⟩⟩,⟨⟨(-58085703476904895080653651096),(-58085703476904895055373553652)⟩,⟨(-18852696365786722621177932540),(-18852696365786722595930744677)⟩⟩] +lemma kernel4_0_r4_2_eq : ∀ k : Fin 16, kernel4_0Expr 4 2 k = kernel4_0_r4_2 k := by decide +kernel +noncomputable def kernel4_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-57731022361401919589566006223),(-57731022361401919564400148418)⟩,⟨(-18271767476858630455809123597),(-18271767476858630430685648303)⟩⟩,⟨⟨(-57367856336550726676796298293),(-57367856336550726651746210537)⟩,⟨(-17687466450884870761701430977),(-17687466450884870736703200155)⟩⟩,⟨⟨(-56996230243241879652455974060),(-56996230243241879627525174228)⟩,⟨(-17100243832474825108699492872),(-17100243832474825083830015564)⟩⟩,⟨⟨(-56616176790974903127765187796),(-56616176790974903102955333809)⟩,⟨(-16510550385008277061795956631),(-16510550385008277037056873665)⟩⟩,⟨⟨(-56227736738659018167183638423),(-56227736738659018142498574698)⟩,⟨(-15918836591048782812698984587),(-15918836591048782788094112733)⟩⟩,⟨⟨(-55830959057766147056951938007),(-55830959057766147032392971428)⟩,⟨(-15325552150521150842991242297),(-15325552150521150818521853363)⟩⟩,⟨⟨(-55425901077264856295155701157),(-55425901077264856270726529186)⟩,⟨(-14731145477429343208498186960),(-14731145477429343184167932625)⟩⟩,⟨⟨(-55012628609811859628228884417),(-55012628609811859603930926498)⟩,⟨(-14136063195915167462677683923),(-14136063195915167438487930722)⟩⟩,⟨⟨(-54591216058727634084148717490),(-54591216058727634059986105597)⟩,⟨(-13540749636480368372398540134),(-13540749636480368348353356072)⟩⟩,⟨⟨(-54161746505334479287890359945),(-54161746505334479263864026743)⟩,⟨(-12945646333215001613551533204),(-12945646333215001589651781206)⟩⟩,⟨⟨(-53724311776288832508586239347),(-53724311776288832484700051329)⟩,⟨(-12351191522893132506251618476),(-12351191522893132482501084053)⟩⟩,⟨⟨(-53279012490594688123250980696),(-53279012490594688099506074416)⟩,⟨(-11757819646812813119496185844),(-11757819646812813095895919016)⟩⟩,⟨⟨(-52825958086041400727106317295),(-52825958086041400703506985802)⟩,⟨(-11165960856270819776945704521),(-11165960856270819753499900227)⟩⟩,⟨⟨(-52365266824866807643091096707),(-52365266824866807619637968152)⟩,⟨(-10576040522573657472373022070),(-10576040522573657449082206545)⟩⟩,⟨⟨(-51897065778505312674334917793),(-51897065778505312651032011623)⟩,⟨(-9988478752494744415668669829),(-9988478752494744392536748793)⟩⟩,⟨⟨(-51421490791340144674563995012),(-51421490791340144651412121029)⟩,⟨(-9403689910093375232959733164),(-9403689910093375209987399158)⟩⟩] +lemma kernel4_0_r4_3_eq : ∀ k : Fin 16, kernel4_0Expr 4 3 k = kernel4_0_r4_3 k := by decide +kernel +noncomputable def kernel4_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-50938686423439251048290077617),(-50938686423439251025293837169)⟩,⟨(-8822082145813932225767111871),(-8822082145813932202958836530)⟩⟩,⟨⟨(-50448805872315010568713887619),(-50448805872315010545873394583)⟩,⟨(-8244056933783788874488126504),(-8244056933783788851843893078)⟩⟩,⟨⟨(-49952010873808949344967526535),(-49952010873808949322286932440)⟩,⟨(-7670008618225358752399412545),(-7670008618225358729923229167)⟩⟩,⟨⟨(-49448471582263711086403997013),(-49448471582263711063883743531)⟩,⟨(-7100323969891729079259548989),(-7100323969891729056951712883)⟩⟩,⟨⟨(-48938366430205456810261523943),(-48938366430205456787906296111)⟩,⟨(-6535381753426237289220644041),(-6535381753426237267085682544)⟩⟩,⟨⟨(-48421881967820435612368414972),(-48421881967820435590177975303)⟩,⟨(-5975552306534170815676178285),(-5975552306534170793713698142)⟩⟩,⟨⟨(-47899212682569460759103536115),(-47899212682569460737082142834)⟩,⟨(-5421197131839478415295291084),(-5421197131839478393509381088)⟩⟩,⟨⟨(-47370560799343226706828865561),(-47370560799343226684976554382)⟩,⟨(-4872668502280973726920321756),(-4872668502280973705310850052)⟩⟩,⟨⟨(-46836136061619595095906428869),(-46836136061619595074228165827)⟩,⟨(-4330309080881000969641890800),(-4330309080881000948213641164)⟩⟩,⟨⟨(-46296155494140944537318543741),(-46296155494140944515813477638)⟩,⟨(-3794451555694946120393264317),(-3794451555694946099145209355)⟩⟩,⟨⟨(-45750843147685205234965423556),(-45750843147685205213637889884)⟩,⟨(-3265418290722356886747235114),(-3265418290722356865683518911)⟩⟩,⟨⟨(-45200429826558073227921069789),(-45200429826558073206770665432)⟩,⟨(-2743520993529838565609270921),(-2743520993529838544729304156)⟩⟩,⟨⟨(-44645152799485912351474878818),(-44645152799485912330471214086)⟩,⟨(-2229060400302392603720271744),(-2229060400302392582993364248)⟩⟩,⟨⟨(-44085255494638802018069170306),(-44085255494638801997208723785)⟩,⟨(-1722325979003547250213196264),(-1722325979003547229635629592)⟩⟩,⟨⟨(-43520987179560878836902739126),(-43520987179560878816190034653)⟩,⟨(-1223595651285596531975259759),(-1223595651285596511551350865)⟩⟩,⟨⟨(-42952602626830360309560007680),(-42952602626830360288994315828)⟩,⟨(-733135533749630507107277833),(-733135533749630486836099326)⟩⟩] +lemma kernel4_0_r4_4_eq : ∀ k : Fin 16, kernel4_0Expr 4 4 k = kernel4_0_r4_4 k := by decide +kernel +noncomputable def kernel4_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-42380361766314247931468683498),(-42380361766314247911055471440)⟩,⟨(-251199699110935777933581120),(-251199699110935757820384149)⟩⟩,⟨⟨(-41804529324922512754920060485),(-41804529324922512734657502776)⟩,⟨221970042221086701639831230,221970042221086721597072932⟩⟩,⟨⟨(-41225374454803406747143032081),(-41225374454803406727035773170)⟩,⟨686144339687943946650216893,686144339687943966447078497⟩⟩,⟨⟨(-40643170350955267114170532483),(-40643170350955267094217417329)⟩,⟨1141106478842080235177851180,1141106478842080254815694505⟩⟩,⟨⟨(-40058193859260649139264180574),(-40058193859260649119470672543)⟩,⟨1586652535964415721177514994,1586652535964415740651103061⟩⟩,⟨⟨(-39470725075975709792634742922),(-39470725075975709772998688131)⟩,⟨2022591510735968858110706936,2022591510735968877422400898⟩⟩,⟨⟨(-38881046939731356776469937337),(-38881046939731356756996068530)⟩,⟨2448745436715646836304079696,2448745436715646855449374562⟩⟩,⟨⟨(-38289444817122677436148070125),(-38289444817122677416834785030)⟩,⟨2864949469433027720311534460,2864949469433027739292243254⟩⟩,⟨⟨(-37696206082979485682962846600),(-37696206082979485663815954881)⟩,⟨3271051951962711741328880752,3271051951962711760139427068⟩⟩,⟨⟨(-37101619696423404815629900420),(-37101619696423404796646514882)⟩,⟨3666914457905365136396365139,3666914457905365155039844015⟩⟩,⟨⟨(-36505975773825687949039604350),(-36505975773825687930224511297)⟩,⟨4052411811759690401612238125,4052411811759690420084094609⟩⟩,⟨⟨(-35909565159784930081017276338),(-35909565159784930062368412302)⟩,⟨4427432086728999858900617050,4427432086728999877203124625⟩⟩,⟨⟨(-35312678997244927748771027266),(-35312678997244927730294116904)⟩,⟨4791876580065609889082599488,4791876580065609907210268027⟩⟩,⟨⟨(-34715608297870191736508630084),(-34715608297870191718200442058)⟩,⟨5145659766115673992331790807,5145659766115674010288056618⟩⟩,⟨⟨(-34118643513790030395669138403),(-34118643513790030377534478134)⟩,⟨5488709227286096254383129820,5488709227286096272163418090⟩⟩,⟨⟨(-33522074111811727867003434802),(-33522074111811727849039769849)⟩,⟨5820965563213575655390875803,5820965563213575672997923822⟩⟩] +lemma kernel4_0_r4_5_eq : ∀ k : Fin 16, kernel4_0Expr 4 5 k = kernel4_0_r4_5 k := by decide +kernel +noncomputable def kernel4_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-32926188151189191846637658810),(-32926188151189191828851082042)⟩,⟨6142382278473390636892180860,6142382278473390654320129010⟩⟩,⟨⟨(-32331271866015605301739452942),(-32331271866015605284125892810)⟩,⟨6452925649222010227207813322,6452925649222010244460929356⟩⟩,⟨⟨(-31737609253287168015017117634),(-31737609253287167997581363477)⟩,⟨6752574569222784964222810814,6752574569222784981296531221⟩⟩,⟨⟨(-31145481667660055466969022766),(-31145481667660055449708074215)⟩,⟨7041320375757605585104113902,7041320375757605602001634689⟩⟩,⟨⟨(-30555167423894368474902257906),(-30555167423894368457821954988)⟩,⟨7319166655979304510134191996,7319166655979304526849899226⟩⟩,⟨⟨(-29966941407947226443574265904),(-29966941407947226426670293768)⟩,⟨7586129034309507029474776530,7586129034309507046013170700⟩⟩,⟨⟨(-29381074697642413757531031900),(-29381074697642413740808131730)⟩,⟨7842234941534417391887454636,7842234941534417408244011975⟩⟩,⟨⟨(-28797834193806280206697013873),(-28797834193806280190151724322)⟩,⟨8087523366296461434498791868,8087523366296461450677156597⟩⟩,⟨⟨(-28217482262719092742382042633),(-28217482262719092726020486095)⟩,⟨8322044589722624895009880337,8322044589722624911004147756⟩⟩,⟨⟨(-27640276390687919684293436268),(-27640276390687919668110493023)⟩,⟨8545859903970560139493520909,8545859903970560155308980383⟩⟩,⟨⟨(-27066468851501593158201983110),(-27066468851501593142202314585)⟩,⟨8759041315510931737610792020,8759041315510931753242987969⟩⟩,⟨⟨(-26496306387480544467976075871),(-26496306387480544452155775946)⟩,⟨8961671233998894922718392343,8961671233998894938171397999⟩⟩,⟨⟨(-25930029904784552639427896734),(-25930029904784552623792778857)⟩,⟨9153842147618926782206697949,9153842147618926797474904043⟩⟩,⟨⟨(-25367874183589908633755518858),(-25367874183589908618300245385)⟩,⟨9335656285815349442992004812,9335656285815349458080902167⟩⟩,⟨⟨(-24810067603694403412523334106),(-24810067603694403397252459633)⟩,⟨9507225270345704602867532571,9507225270345704617772758261⟩⟩,⟨⟨(-24256831886054129198499791963),(-24256831886054129183408987105)⟩,⟨9668669755615582639081306810,9668669755615582653807339187⟩⟩] +lemma kernel4_0_r4_6_eq : ∀ k : Fin 16, kernel4_0Expr 4 6 k = kernel4_0_r4_6 k := by decide +kernel +noncomputable def kernel4_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-23708381850700576072981225150),(-23708381850700576058076622645)⟩,⟨9820119059271516738791362214,9820119059271516753332259710⟩⟩,⟨⟨(-23164925191430149467335467654),(-23164925191430149452610875636)⟩,⟨9961710784043079217228659166,9961710784043079231590745468⟩⟩,⟨⟨(-22626662267601268676423691871),(-22626662267601268661883532561)⟩,⟨10093590431836336362285041411,10093590431836336376464069746⟩⟩,⟨⟨(-22093785913316873038613888968),(-22093785913316873024253440053)⟩,⟨10215911011088319504007654955,10215911011088319518008476730⟩⟩,⟨⟨(-21566481264212700666430282102),(-21566481264212700652255205020)⟩,⟨10328832638396160005964277910,10328832638396160019781404658⟩⟩,⟨⟨(-21044925602014352068620384382),(-21044925602014352054624442288)⟩,⟨10432522135435037499526837544,10432522135435037513166618594⟩⟩,⟨⟨(-20529288216969141651124953027),(-20529288216969141637312416409)⟩,⟨10527152622176143177730134162,10527152622176143191188456805⟩⟩,⟨⟨(-20019730288202303165933246902),(-20019730288202303152297333110)⟩,⟨10612903107409518458921461464,10612903107409518472206799883⟩⟩,⟨⟨(-19516404781991474039579081427),(-19516404781991474026117706735)⟩,⟨10689958077566964361828785681,10689958077566964374950783382⟩⟩,⟨⟨(-19019456367898754487551237954),(-19019456367898754474257734282)⟩,⟨10758507084827313894132818323,10758507084827313907097907521⟩⟩,⟨⟨(-18529021352646228653351093507),(-18529021352646228640229868444)⟩,⟨10818744335470318246525761969,10818744335470318259329351432⟩⟩,⟨⟨(-18045227631568845861545537997),(-18045227631568845848591493265)⟩,⟨10870868279426330686550302031,10870868279426330699197261242⟩⟩,⟨⟨(-17568194657428179578582814072),(-17568194657428179565801663518)⟩,⟨10915081201947005529826198074,10915081201947005542310633817⟩⟩,⟨⟨(-17098033426321988083309775956),(-17098033426321988070694851786)⟩,⟨10951588818297501017459560464,10951588818297501029787904748⟩⟩,⟨⟨(-16634846480377860738420103136),(-16634846480377860725975622772)⟩,⟨10980599872343332827026581880,10980599872343332839194430329⟩⟩,⟨⟨(-16178727926874701329540533632),(-16178727926874701317261108853)⟩,⟨11002325739875227680161487440,11002325739875227692173999335⟩⟩] +lemma kernel4_0_r4_7_eq : ∀ k : Fin 16, kernel4_0Expr 4 7 k = kernel4_0_r4_7 k := by decide +kernel +noncomputable def kernel4_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-15729763473393516414767572950),(-15729763473393516402659223378)⟩,⟨11016980037483241357852345993,11016980037483241369703322198⟩⟩,⟨⟨(-15288030478559069704438081564),(-15288030478559069692493359061)⟩,⟨11024778237757207488356520628,11024778237757207500053173225⟩⟩,⟨⟨(-14853598017896546917221246825),(-14853598017896546905444166067)⟩,⟨11025937291554454550654372582,11025937291554454562192499530⟩⟩,⟨⟨(-14426526964292548792153415581),(-14426526964292548780538343304)⟩,⟨11020675258037856061512528390,11020675258037856072897537073⟩⟩,⟨⟨(-14006870082517577893708318717),(-14006870082517577882260627040)⟩,⟨11009210943147854784756768703,11009210943147854795983106123⟩⟩,⟨⟨(-13594672137237777753054971608),(-13594672137237777741767438358)⟩,⟨10991763547131321249680012154,10991763547131321260754671337⟩⟩,⟨⟨(-13189970013917076212408688084),(-13189970013917076201285120444)⟩,⟨10968552321708167324915298469,10968552321708167335834287102⟩⟩,⟨⟨(-12792792851987119328602658046),(-12792792851987119317637221138)⟩,⟨10939796237413735569346931501,10939796237413735580115864477⟩⟩,⟨⟨(-12403162189641483991418785715),(-12403162189641483980617055215)⟩,⟨10905713661611323042678186500,10905713661611323053291311720⟩⟩,⟨⟨(-12021092119592638274563942309),(-12021092119592638263918098434)⟩,⟨10866522047624971553044662726,10866522047624971563509576940⟩⟩,⟨⟨(-11646589455114976112355664820),(-11646589455114976101869303808)⟩,⟨10822437635398060123621236225,10822437635398060133934162629⟩⟩,⟨⟨(-11279653905684971104914212910),(-11279653905684971094581346116)⟩,⟨10773675164038461761539466512,10773675164038461771706182128⟩⟩,⟨⟨(-10920278261520043736851166378),(-10920278261520043726676781889)⟩,⟨10720447596566263241628467461,10720447596566263251643811547⟩⟩,⟨⟨(-10568448586311074923848094328),(-10568448586311074913824623946)⟩,⟨10662965857135476326935644929,10662965857135476336806973966⟩⟩,⟨⟨(-10224144417439572269660999524),(-10224144417439572259791831856)⟩,⟨10601438580956968450079327736,10601438580956968459803079103⟩⟩,⟨⟨(-9887338972969237876445458328),(-9887338972969237866724495801)⟩,⟨10536071877106180439334128781,10536071877106180448916198820⟩⟩] +lemma kernel4_0_r4_8_eq : ∀ k : Fin 16, kernel4_0Expr 4 8 k = kernel4_0_r4_8 k := by decide +kernel +noncomputable def kernel4_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-9557999364703021312130961762),(-9557999364703021302563492505)⟩,⟨10467069104356240971104325681,10467069104356240980539261996⟩⟩,⟨⟨(-9236086816600581608532750280),(-9236086816600581599110606405)⟩,⟨10394630660134986485340195267,10394630660134986494635964238⟩⟩,⟨⟨(-8921556887857331832559645932),(-8921556887857331823286011938)⟩,⟨10318953782663296970677817788,10318953782663296979831069064⟩⟩,⟨⟨(-8614359699954794230984207525),(-8614359699954794221852924050)⟩,⟨10240232366292198675272016142,10240232366292198684288719857⟩⟩,⟨⟨(-8314440167002740930458600483),(-8314440167002740921474261567)⟩,⟨10158656790017491042621087366,10158656790017491051496492107⟩⟩,⟨⟨(-8021738228706415623593987850),(-8021738228706415614748886617)⟩,⟨10074413759113343490974509586,10074413759113343499716135378⟩⟩,⟨⟨(-7736189085306900621208925275),(-7736189085306900612506051990)⟩,⟨9987686159790484094693912389,9987686159790484103298612531⟩⟩,⟨⟨(-7457723433859281109385827662),(-7457723433859281100819002488)⟩,⟨9898652926750362158582495340,9898652926750362167056273619⟩⟩,⟨⟨(-7186267705231530288456330236),(-7186267705231530280030367883)⟩,⟨9807488923474094646733534493,9807488923474094655071429158⟩⟩,⟨⟨(-6921744301226857906879864851),(-6921744301226857898586641937)⟩,⟨9714364835054176065375738171,9714364835054176073585698900⟩⟩,⟨⟨(-6664071831253490768666044910),(-6664071831253490760508366338)⟩,⟨9619447073347905406561834059,9619447073347905414640909823⟩⟩,⟨⟨(-6413165347988345793110168456),(-6413165347988345785081876059)⟩,⟨9522897694204313961812786219,9522897694204313969766973089⟩⟩,⟨⟨(-6168936581504672146190068906),(-6168936581504672138295379874)⟩,⟨9424874326491105282697382634,9424874326491105290522325569⟩⟩,⟨⟨(-5931294171358336959269363106),(-5931294171358336951500618973)⟩,⟨9325530112624773793217532578,9325530112624773800920732033⟩⟩,⟨⟨(-5700143896152868197716735319),(-5700143896152868190076569105)⟩,⟨9225013660285671707609546741,9225013660285671715188234449⟩⟩,⟨⟨(-5475388900129508954483311317),(-5475388900129508946965621863)⟩,⟨9123469004980355095816928567,9123469004980355103277057936⟩⟩] +lemma kernel4_0_r4_9_eq : ∀ k : Fin 16, kernel4_0Expr 4 9 k = kernel4_0_r4_9 k := by decide +kernel +noncomputable def kernel4_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-5256929916355242751393619123),(-5256929916355242744002976205)⟩,⟨9021035583096059592449228716,9021035583096059599786103483⟩⟩,⟨⟨(-5044665486108885236448942719),(-5044665486108885229177235584)⟩,⟨8917848215076625482881108728,8917848215076625490102695679⟩⟩,⟨⟨(-4838492174092773450861809790),(-4838492174092773443711510648)⟩,⟨8814037098335592971182287678,8814037098335592978285990493⟩⟩,⟨⟨(-4638304779125193230542989180),(-4638304779125193223508089198)⟩,⟨8709727809510495183847074251,8709727809510495190838768422⟩⟩,⟨⟨(-4443996539996346581747449599),(-4443996539996346574831822772)⟩,⟨8605041315652554835781855105,8605041315652554842657549963⟩⟩,⟨⟨(-4255459336198257423924998849),(-4255459336198257417121191986)⟩,⟨8500093993937999051019439314,8500093993937999057786459832⟩⟩,⟨⟨(-4072583883266434840592366646),(-4072583883266434833902706751)⟩,⟨8394997659480997338818606853,8394997659480997345474513052⟩⟩,⟨⟨(-3895259922498252717525316429),(-3895259922498252710943913531)⟩,⟨8289859600823745668198668069,8289859600823745674749230758⟩⟩,⟨⟨(-3723376404839764353878578212),(-3723376404839764347409562973)⟩,⟨8184782622676404778780413256,8184782622676404785221396026⟩⟩,⟨⟨(-3556821668758957717404746268),(-3556821668758957711040395893)⟩,⟨8079865095478388043215039507,8079865095478388049554050999⟩⟩,⟨⟨(-3395483611949185522324772080),(-3395483611949185516067280565)⟩,⟨7975201011352813592934135087,7975201011352813599168879238⟩⟩,⟨⟨(-3239249856731595062726195196),(-3239249856731595056569817528)⟩,⟨7870880046027713365799952514,7870880046027713371936068891⟩⟩,⟨⟨(-3088007909049763440678410496),(-3088007909049763434626722121)⟩,⟨7766987626300751246603715834,7766987626300751252637533100⟩⟩,⟨⟨(-2941645310973349126711116635),(-2941645310973349120756986149)⟩,⟨7663605002628663823352120102,7663605002628663829290669836⟩⟩,⟨⟨(-2800049786650342260988285213),(-2800049786650342255133788543)⟩,⟨7560809326428318575125305744,7560809326428318580966420452⟩⟩,⟨⟨(-2663109381669382233299941948),(-2663109381669382227539497128)⟩,⟨7458673731683102017039182477,7458673731683102022788351734⟩⟩] +lemma kernel4_0_r4_10_eq : ∀ k : Fin 16, kernel4_0Expr 4 10 k = kernel4_0_r4_10 k := by decide +kernel +noncomputable def kernel4_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2530712595814567184004238455),(-2530712595814567178341793139)⟩,⟨7357267420456219839551211261,7357267420456219845204401438⟩⟩,⟨⟨(-2402748509215168178071099414),(-2402748509215168172499202447)⟩,⟨7256655751921327195272922273,7256655751921327200837497672⟩⟩,⟨⟨(-2279106901911649517459526515),(-2279106901911649511980146726)⟩,⟨7156900334530624715558386631,7156900334530624721032296810⟩⟩,⟨⟨(-2159678366877360956755686393),(-2159678366877360951363422479)⟩,⟨7058059120951069656229419812,7058059120951069661617985946⟩⟩,⟨⟨(-2044354416552188630714878687),(-2044354416552188625413053718)⟩,⟨6960186505410577654055781023,6960186505410577659355603118⟩⟩,⟨⟨(-1933027582960316387479321016),(-1933027582960316382261202735)⟩,⟨6863333423107946005476257620,6863333423107946010693993544⟩⟩,⟨⟨(-1825591511499050723487334079),(-1825591511499050718354798103)⟩,⟨6767547451352632821979032824,6767547451352632827112734653⟩⟩,⟨⟨(-1721941048499398812657118778),(-1721941048499398807604953446)⟩,⟨6672872912113398463175723344,6672872912113398468230533973⟩⟩,⟨⟨(-1621972322671763493801796159),(-1621972322671763488833615237)⟩,⟨6579350975668079130028347447,6579350975668079135000584585⟩⟩,⟨⟨(-1525582820561739602644031565),(-1525582820561739597752913037)⟩,⟨6487019765060342767646109292,6487019765060342772542631997⟩⟩,⟨⟨(-1432671456151575257339513317),(-1432671456151575252527249125)⟩,⟨6395914461083102601689345516,6395914461083102606508298132⟩⟩,⟨⟨(-1343138634752416324536513712),(-1343138634752416319798090860)⟩,⟨6306067407522264824038366655,6306067407522264828784703829⟩⟩,⟨⟨(-1256886311341002812235569278),(-1256886311341002807574104025)⟩,⟨6217508216408598437643770478,6217508216408598442314315375⟩⟩,⟨⟨(-1173818043502056337179716435),(-1173818043502056332588913472)⟩,⟨6130263873039674683431811495,6130263873039674688032806700⟩⟩,⟨⟨(-1093839039144215215584692387),(-1093839039144215211066271376)⟩,⟨6044358840547971879209643890,6044358840547971883739313862⟩⟩,⟨⟨(-1016856199163068047476861454),(-1016856199163068043026009961)⟩,⟨5959815163805323532338030620,5959815163805323536801138877⟩⟩] +lemma kernel4_0_r4_11_eq : ∀ k : Fin 16, kernel4_0Expr 4 11 k = kernel4_0_r4_11 k := by decide +kernel +noncomputable def kernel4_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-942778155229640297870505389),(-942778155229640293490761699)⟩,⟨5876652572467851503000191975,5876652572467851507393146273⟩⟩,⟨⟨(-871515302886635861260222910),(-871515302886635856944996756)⟩,⟨5794888582979323721716582380,5794888582979323726045930033⟩⟩,⟨⟨(-802979830137863296854877971),(-802979830137863292605823573)⟩,⟨5714538599364463123425899589,5714538599364463127689937586⟩⟩,⟨⟨(-737085741718622231363644738),(-737085741718622227176152977)⟩,⟨5635616012657070356672635523,5635616012657070360875932526⟩⟩,⟨⟨(-673748879236428459409087995),(-673748879236428455286107902)⟩,⟨5558132298820870427951501205,5558132298820870432091061051⟩⟩,⟨⟨(-612886937372356586764132833),(-612886937372356582699812583)⟩,⟨5482097115033719329902411339,5482097115033719333984050800⟩⟩,⟨⟨(-554419476333517385916939167),(-554419476333517381912877079)⟩,⟨5407518394218181011590227356,5407518394218181015612305659⟩⟩,⟨⟨(-498267930746804508745184051),(-498267930746804504796969654)⟩,⟨5334402437713481382097334267,5334402437713481386064228936⟩⟩,⟨⟨(-444355615183083139538157405),(-444355615183083135649055442)⟩,⟨5262754005995441372235724728,5262754005995441376144128967⟩⟩,⟨⟨(-392607726499492831202963062),(-392607726499492827366945974)⟩,⟨5192576407362165653489935606,5192576407362165657345849862⟩⟩,⟨⟨(-342951343185539139232151500),(-342951343185539135450766738)⟩,⟨5123871584514000812057451368,5123871584514000815859291352⟩⟩,⟨⟨(-295315421896194283175244311),(-295315421896194279444277047)⟩,⟨5056640198966562992973263974,5056640198966562996725218180⟩⟩,⟨⟨(-249630791352355815132199432),(-249630791352355811454467050)⟩,⟨4990881713245459530817344601,4990881713245459534516559125⟩⟩,⟨⟨(-205830143785763249994495730),(-205830143785763246364568643)⟩,⟨4926594470820683858591821891,4926594470820683862243705148⟩⟩,⟨⟨(-163848024101883955181966722),(-163848024101883951601348318)⟩,⟨4863775773747542596788974868,4863775773747542600391991568⟩⟩,⟨⟨(-123620816930388374004041695),(-123620816930388370468704397)⟩,⟨4802421957989375146303304536,4802421957989375149861461686⟩⟩] +lemma kernel4_0_r4_12_eq : ∀ k : Fin 16, kernel4_0Expr 4 12 k = kernel4_0_r4_12 k := by decide +kernel +noncomputable def kernel4_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-85086731728676738629241649),(-85086731728676735142424033)⟩,⟨4742528466405248574029012248,4742528466405248577539038141⟩⟩,⟨⟨(-48185786099529396816764442),(-48185786099529393372752744)⟩,⟨4684089919393255414837186579,4684089919393255418304780387⟩⟩,⟨⟨(-12859787479363933737339878),(-12859787479363930337595997)⟩,⟨4627100183187012478505185354,4627100183187012481928857582⟩⟩,⟨⟨20947686651173828342509713,20947686651173831701832246⟩,⟨4571552435809459877302756710,4571552435809459880686338231⟩⟩,⟨⟨53291309887450875647039933,53291309887450878963226833⟩,⟨4517439230694097926351781901,4517439230694097929692529980⟩⟩,⟨⟨84224029210087231784212749,84224029210087235062309905⟩,⟨4464752557989383418258597951,4464752557989383421561547847⟩⟩,⟨⟨113797088346444818324639645,113797088346444821563221425⟩,⟨4413483903567145445197293955,4413483903567145448460996163⟩⟩,⟨⟨142060052052752292452329035,142060052052752295655072403⟩,⟨4363624305760585000070552139,4363624305760585003298672290⟩⟩,⟨⟨169060831190422799696299171,169060831190422802860153036⟩,⟨4315164409861703610981113509,4315164409861703614170574358⟩⟩,⟨⟨194845708475300594549690565,194845708475300597679910812⟩,⟨4268094520411876700007494113,4268094520411876703163545995⟩⟩,⟨⟨219459364783740257256761302,219459364783740260351957430⟩,⟨4222404651322760399668566637,4222404651322760402789798380⟩⟩,⟨⟨242944905904559704530330394,242944905904559707594018546⟩,⟨4178084573867810013156671356,4178084573867810016246591379⟩⟩,⟨⟨265343889630997862519774554,265343889630997865549318470⟩,⟨4135123862587408466873687632,4135123862587408469929637149⟩⟩,⟨⟨286696353091833791731152524,286696353091833794731266955⟩,⟨4093511939152968655195920467,4093511939152968658222611330⟩⟩,⟨⟨307040840225771784793457284,307040840225771787762783726⟩,⟨4053238114237399471925491247,4053238114237399474921547006⟩⟩,⟨⟨326414429308053525326092391,326414429308053528267998716⟩,⟨4014291627441026688798830695,4014291627441026691767614523⟩⟩] +lemma kernel4_0_r4_13_eq : ∀ k : Fin 16, kernel4_0Expr 4 13 k = kernel4_0_r4_13 k := by decide +kernel +noncomputable def kernel4_0_r4_14 : Fin 16 → CBox := ![⟨⟨344852760443012250424482770,344852760443012253335867184⟩,⟨3976661685323451890378786489,3976661685323451893317174983⟩⟩,⟨⟨362390062940924825662762892,362390062940924828548697348⟩,⟨3940337497592930615053992821,3940337497592930617967059380⟩⟩,⟨⟨379059182502036869949989876,379059182502036872809148816⟩,⟨3905308311505669812428320805,3905308311505669815314724233⟩⟩,⟨⟨394891608135025977343179033,394891608135025980178790985⟩,⟨3871563444527999684578632075,3871563444527999687441598700⟩⟩,⟨⟨409917498741422308554885556,409917498741422311364372683⟩,⟨3839092315314680694226537793,3839092315314680697063471447⟩⟩,⟨⟨424165709301619157528931999,424165709301619160316735924⟩,⟨3807884473056677484789978566,3807884473056677487605323427⟩⟩,⟨⟨437663816602074429591601679,437663816602074432356427649⟩,⟨3777929625251581830605187993,3777929625251581833397635599⟩⟩,⟨⟨450438144447124229343997141,450438144447124232088947768⟩,⟨3749217663949510316415403277,3749217663949510319188056073⟩⟩,⟨⟨462513788302499864489172290,462513788302499867211306032⟩,⟨3721738690526752623779270093,3721738690526752626529168594⟩⟩,⟨⟨473914639321158366514012605,473914639321158369218046547⟩,⟨3695483039038716028823675129,3695483039038716031555542167⟩⟩,⟨⟨484663407705403819792857422,484663407705403822477529517⟩,⟨3670441298202813476028449348,3670441298202813478741010773⟩⟩,⟨⟨494781645362492897842681467,494781645362492900510977729⟩,⟨3646604332060888383541166527,3646604332060888386237409799⟩⟩,⟨⟨504289767813984307883314952,504289767813984310532697800⟩,⟨3623963299369570650744334144,3623963299369570653421706176⟩⟩,⟨⟨513207075322010324705223974,513207075322010327339924734⟩,⟨3602509671765626155859043299,3602509671765626158521781610⟩⟩,⟨⟨521551773198421887782199606,521551773198421890400988684⟩,⟨3582235250751906805584173847,3582235250751906808231038046⟩⟩,⟨⟨529340991265390079702195719,529340991265390082307954768⟩,⟨3563132183547939858873551348,3563132183547939861507425780⟩⟩] +lemma kernel4_0_r4_14_eq : ∀ k : Fin 16, kernel4_0Expr 4 14 k = kernel4_0_r4_14 k := by decide +kernel +noncomputable def kernel4_0_r4_15 : Fin 16 → CBox := ![⟨⟨536590802438539993793280337,536590802438539996382987576⟩,⟨3545192977847523197490224596,3545192977847523200108071334⟩⟩,⟨⟨543316240406052338258342780,543316240406052340836648495⟩,⟨3528410515523926340478567770,3528410515523926343085046173⟩⟩,⟨⟨549531316379398384859634418,549531316379398387425345273⟩,⟨3512778065321443670117920906,3512778065321443672711827899⟩⟩,⟨⟨555249034893480249140430404,555249034893480251696331433⟩,⟨3498289294570114423366275947,3498289294570114425950400149⟩⟩,⟨⟨560481408635936571242006035,560481408635936573785586090⟩,⟨3484938279958420889007150691,3484938279958420891578967191⟩⟩,⟨⟨565239472287249386444360430,565239472287249388979701271⟩,⟨3472719517396708849222446226,3472719517396708851786045159⟩⟩,⟨⟨569533295355057584678359507,569533295355057587204304818⟩,⟨3461627931001949077074678906,3461627931001949079628895028⟩⟩,⟨⟨573371993987752394092545734,573371993987752396611795285⟩,⟨3451658881232281679587870732,3451658881232281682135407995⟩⟩,⟨⟨576763741754007575960997218,576763741754007578470634102⟩,⟨3442808172197561884876157526,3442808172197561887414084390⟩⟩,⟨⟨579715779376388503042480562,579715779376388505546949279⟩,⟨3435072058169861753785425670,3435072058169861756318197031⟩⟩,⟨⟨582234423408597228081870156,582234423408597230580056462⟩,⟨3428447249315582140118278735,3428447249315582142644772030⟩⟩,⟨⟨584325073847252425856674650,584325073847252428351199404⟩,⟨3422930916668497589389969007,3422930916668497591912809576⟩⟩,⟨⟨585992220670381257411105464,585992220670381259899471278⟩,⟨3418520696360698017988575118,3418520696360698020505252677⟩⟩,⟨⟨587239449296022436808068487,587239449296022439294266903⟩,⟨3415214693126008948466254858,3415214693126008950980770281⟩⟩,⟨⟨588069444955513870065562434,588069444955513872548524213⟩,⟨3413011483088070553289711342,3413011483088070555800987473⟩⟩,⟨⟨588483995977172067600863436,588483995977172070083139159⟩,⟨3411910115842838335332345295,3411910115842838337842937226⟩⟩] +lemma kernel4_0_r4_15_eq : ∀ k : Fin 16, kernel4_0Expr 4 15 k = kernel4_0_r4_15 k := by decide +kernel +noncomputable def kernel4_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel4_0_r4_0,kernel4_0_r4_1,kernel4_0_r4_2,kernel4_0_r4_3,kernel4_0_r4_4,kernel4_0_r4_5,kernel4_0_r4_6,kernel4_0_r4_7,kernel4_0_r4_8,kernel4_0_r4_9,kernel4_0_r4_10,kernel4_0_r4_11,kernel4_0_r4_12,kernel4_0_r4_13,kernel4_0_r4_14,kernel4_0_r4_15] +lemma kernel4_0_r4_eq (i k : Fin 16) : kernel4_0Expr 4 i k = kernel4_0_r4 i k := by + fin_cases i + · exact kernel4_0_r4_0_eq k + · exact kernel4_0_r4_1_eq k + · exact kernel4_0_r4_2_eq k + · exact kernel4_0_r4_3_eq k + · exact kernel4_0_r4_4_eq k + · exact kernel4_0_r4_5_eq k + · exact kernel4_0_r4_6_eq k + · exact kernel4_0_r4_7_eq k + · exact kernel4_0_r4_8_eq k + · exact kernel4_0_r4_9_eq k + · exact kernel4_0_r4_10_eq k + · exact kernel4_0_r4_11_eq k + · exact kernel4_0_r4_12_eq k + · exact kernel4_0_r4_13_eq k + · exact kernel4_0_r4_14_eq k + · exact kernel4_0_r4_15_eq k +noncomputable def kernel4_0_r5_0 : Fin 16 → CBox := ![⟨⟨390966252921443989139719646129,390966252921443989262564024560⟩,⟨(-321012903874060098527731647132),(-321012903874060098411166045498)⟩⟩,⟨⟨390878084486174564328384279345,390878084486174564451228185402⟩,⟨(-321029250083840482045028726557),(-321029250083840481928461232676)⟩⟩,⟨⟨390701778279099909372516101141,390701778279099909495358874239⟩,⟨(-321061897155014375436093261659),(-321061897155014375319522171817)⟩⟩,⟨⟨390437395639275052393937161965,390437395639275052516778134363⟩,⟨(-321110754452362803675803234590),(-321110754452362803559226854811)⟩⟩,⟨⟨390085028605506493011085513961,390085028605506493133924002763⟩,⟨(-321175686176884443400552207845),(-321175686176884443283968863167)⟩⟩,⟨⟨389644799952361822149301450718,389644799952361822272136757569⟩,⟨(-321256511550220707080420598543),(-321256511550220706963828634614)⟩⟩,⟨⟨389116863237751450957246730817,389116863237751451080078130589⟩,⟨(-321353005060276517888148256583),(-321353005060276517771546052236)⟩⟩,⟨⟨388501402861714504150686416681,388501402861714504273513165024⟩,⟨(-321464896767796947066854430729),(-321464896767796946950240391756)⟩⟩,⟨⟨387798634135950903440618046457,387798634135950903563439354175⟩,⟨(-321591872673599438774147383107),(-321591872673599438657519969080)⟩⟩,⟨⟨387008803363552936975401255200,387008803363552937098216317516⟩,⟨(-321733575146100582481287048733),(-321733575146100582364644745156)⟩⟩,⟨⟨386132187928302436504445673767,386132187928302436627253615732⟩,⟨(-321889603408715254812694608204),(-321889603408715254696035982140)⟩⟩,⟨⟨385169096392814318388180841139,385169096392814318510980787046⟩,⟨(-322059514086644390523578270526),(-322059514086644390406901902806)⟩⟩,⟨⟨384119868604723937909992333318,384119868604723938032783290646⟩,⟨(-322242821812505610656023761615),(-322242821812505610539328363610)⟩⟩,⟨⟨382984875810034705571879987194,382984875810034705694661003684⟩,⟨(-322438999890198395216358887250),(-322438999890198395099643145851)⟩⟩,⟨⟨381764520772663962421752738393,381764520772663962544522689255⟩,⟨(-322647481016332404970021571684),(-322647481016332404853284362298)⟩⟩,⟨⟨380459237899149448021841918332,380459237899149448144599758303⟩,⟨(-322867658058483906333938866038),(-322867658058483906217179003064)⟩⟩] +lemma kernel4_0_r5_0_eq : ∀ k : Fin 16, kernel4_0Expr 5 0 k = kernel4_0_r5_0 k := by decide +kernel +noncomputable def kernel4_0_r5_1 : Fin 16 → CBox := ![⟨⟨379069493367406053826284262992,379069493367406053949028682689⟩,⟨(-323098884889481016823478568691),(-323098884889481016706695148696)⟩⟩,⟨⟨377595785258353165764002632802,377595785258353165886732513209⟩,⟨(-323340477276853656388277016976),(-323340477276853656271468967738)⟩⟩,⟨⟨376038643689166986377159631258,376038643689166986499873487278⟩,⟨(-323591713826518661422355594431),(-323591713826518661305522229844)⟩⟩,⟨⟨374398630946850006487722149718,374398630946850006610418749579⟩,⟨(-323851836979704501781729887747),(-323851836979704501664870292726)⟩⟩,⟨⟨372676341620751479972503159368,372676341620751480095180750875⟩,⟨(-324120054062053455098228163751),(-324120054062053454981341965385)⟩⟩,⟨⟨370872402732618546591802149931,370872402732618546714459449520⟩,⟨(-324395538383771965534089166262),(-324395538383771965417175550809)⟩⟩,⟨⟨368987473862707743031522984155,368987473862707743154158024110⟩,⟨(-324677430389632284897167928706),(-324677430389632284780226789974)⟩⟩,⟨⟨367022247270441229255701700826,367022247270441229378313063884⟩,⟨(-324964838857560412570997562611),(-324964838857560412454028274497)⟩⟩,⟨⟨364977448008051315025701900499,364977448008051315148287241448⟩,⟨(-325256842144476877908975576272),(-325256842144476877791978465263)⟩⟩,⟨⟨362853834025620969791722554656,362853834025620969914280460935⟩,⟨(-325552489477988116746706403130),(-325552489477988116629680897688)⟩⟩,⟨⟨360652196265897097970979990279,360652196265897098093507885560⟩,⟨(-325850802292457166026425832738),(-325850802292457165909372551001)⟩⟩,⟨⟨358373358747227610293902116067,358373358747227610416398417507⟩,⟨(-326150775607913232173923843709),(-326150775607913232056842447422)⟩⟩,⟨⟨356018178632952858778699901928,356018178632952858901161541996⟩,⟨(-326451379450190486247795793234),(-326451379450190486130687455614)⟩⟩,⟨⟨353587546285566954717860093747,353587546285566954840285559392⟩,⟨(-326751560310617319821437614883),(-326751560310617319704301996408)⟩⟩,⟨⟨351082385303954970362709265197,351082385303954970485095237676⟩,⟨(-327050242643508389173306208511),(-327050242643508389056144803001)⟩⟩,⟨⟨348503652542008137540377334017,348503652542008137662722105184⟩,⟨(-327346330399643221868320406214),(-327346330399643221751133140840)⟩⟩] +lemma kernel4_0_r5_1_eq : ∀ k : Fin 16, kernel4_0Expr 5 1 k = kernel4_0_r5_1 k := by decide +kernel +noncomputable def kernel4_0_r5_2 : Fin 16 → CBox := ![⟨⟨345852338106920988662629038903,345852338106920988784928615232⟩,⟨(-327638708593847110288397623453),(-327638708593847110171186738613)⟩⟩,⟨⟨343129465335482012027356412760,343129465335482012149609298185⟩,⟨(-327926244904722632734603427651),(-327926244904722632617368715954)⟩⟩,⟨⟨340336090746682874073432757497,340336090746682874195634756533⟩,⟨(-328207791304513596166286043105),(-328207791304513596049030024869)⟩⟩,⟨⟨337473303968990641463341129982,337473303968990641585490466728⟩,⟨(-328482185717017666976467234530),(-328482185717017666859190061504)⟩⟩,⟨⟨334542227640652745192753490447,334542227640652745314845159091⟩,⟨(-328748253701399638152979273377),(-328748253701399638035684355589)⟩⟩,⟨⟨331544017281435681051499113572,331544017281435681173531652187⟩,⟨(-329004810159694372104306721798),(-329004810159694371986993982584)⟩⟩,⟨⟨328479861134235632944901888922,328479861134235633066870090709⟩,⟨(-329250661065727165697498579493),(-329250661065727165580171715497)⟩⟩,⟨⟨325350979975042318221661700629,325350979975042318343563796172⟩,⟨(-329484605213119822316384926961),(-329484605213119822199044255536)⟩⟩,⟨⟨322158626889786350372297126324,322158626889786350494126819113⟩,⟨(-329705435979993306182757032160),(-329705435979993306065407425400)⟩⟩,⟨⟨318904087016655239758876034784,318904087016655239880632127474⟩,⟨(-329911943107922723675048814630),(-329911943107922723557690111140)⟩⟩,⟨⟨315588677252523734959237970177,315588677252523735080914111149⟩,⟨(-330102914492647756630666855524),(-330102914492647756513304075563)⟩⟩,⟨⟨312213745922210455174336774152,312213745922210455295931295058⟩,⟨(-330277137983991799212128936794),(-330277137983991799094762482304)⟩⟩,⟨⟨308780672409344568815746333165,308780672409344568937251646738⟩,⟨(-330433403192396161324050253659),(-330433403192396161206686472434)⟩⟩,⟨⟨305290866747703507087827277390,305290866747703507209242421114⟩,⟨(-330570503299432038106245867391),(-330570503299432037988884555063)⟩⟩,⟨⟨301745769171965217579748179811,301745769171965217701065528898⟩,⟨(-330687236869612747776279971375),(-330687236869612747658927612268)⟩⟩,⟨⟨298146849626906096248646837602,298146849626906096369864933324⟩,⟨(-330782409660792249763770768882),(-330782409660792249646427752568)⟩⟩] +lemma kernel4_0_r5_2_eq : ∀ k : Fin 16, kernel4_0Expr 5 2 k = kernel4_0_r5_2 k := by decide +kernel +noncomputable def kernel4_0_r5_3 : Fin 16 → CBox := ![⟨⟨294495607234168302563168579324,294495607234168302684278133610⟩,⟨(-330854836430403410844474186000),(-330854836430403410727148756323)⟩⟩,⟨⟨290793569715817459107736876995,290793569715817459228737564748⟩,⟨(-330903342734761125287119088534),(-330903342734761125169810606956)⟩⟩,⟨⟨287042292774013542152371481035,287042292774013542273254285580⟩,⟨(-330926766718631448349859651588),(-330926766718631448232576195401)⟩⟩,⟨⟨283243359426223843723580868589,283243359426223843844344664097⟩,⟨(-330923960892248598073840746818),(-330923960892248597956582579287)⟩⟩,⟨⟨279398379295516970637862093548,279398379295516970758496094974⟩,⟨(-330893793892947239004354894090),(-330893793892947238887131961597)⟩⟩,⟨⟨275508987855590666133566504672,275508987855590666254070835543⟩,⟨(-330835152228568096250754317194),(-330835152228568096133565742747)⟩⟩,⟨⟨271576845630303502248351659615,271576845630303502368715802904⟩,⟨(-330746941999790863151855827378),(-330746941999790863034711397751)⟩⟩,⟨⟨267603637347600886293035684859,267603637347600886413258982483⟩,⟨(-330628090598549754390200420263),(-330628090598549754273100144399)⟩⟩,⟨⟨263591071047849026906839840737,263591071047849027026909436188⟩,⟨(-330477548379694100731054168461),(-330477548379694100614010275527)⟩⟩,⟨⟨259540877146716173062635736799,259540877146716173182552815189⟩,⟨(-330294290303069250812491112994),(-330294290303069250695501881259)⟩⟩,⟨⟨255454807452868217209866512236,255454807452868217329635553239⟩,⟨(-330077317543211894624619364825),(-330077317543211894507679917677)⟩⟩,⟨⟨251334634140875271916055123630,251334634140875272035803606699⟩,⟨(-329825659063878892200972574654),(-329825659063878892083955908571)⟩⟩,⟨⟨247182148679856705502576837516,247182148679856705622292083059⟩,⟨(-329538373154659902800140090816),(-329538373154659902683058483145)⟩⟩,⟨⟨242999160718523962093021580745,242999160718523962212707337569⟩,⟨(-329214548926961670029109807340),(-329214548926961669911959198130)⟩⟩,⟨⟨238787496927412890374533954741,238787496927412890494178176461⟩,⟨(-328853307766695813752851965451),(-328853307766695813635644110432)⟩⟩,⟨⟨234548999799229848912317872714,234548999799229849031923056197⟩,⟨(-328453804741052477283484942888),(-328453804741052477166217138779)⟩⟩] +lemma kernel4_0_r5_3_eq : ∀ k : Fin 16, kernel4_0Expr 5 3 k = kernel4_0_r5_3 k := by decide +kernel +noncomputable def kernel4_0_r5_4 : Fin 16 → CBox := ![⟨⟨230285526408368121570962409467,230285526408368121690513116818⟩,⟨(-328015229956799224530834591395),(-328015229956799224413522089237)⟩⟩,⟨⟨225998947130782735147424828160,225998947130782735266926342295⟩,⟨(-327536809867608201173153945856),(-327536809867608201055791368797)⟩⟩,⟨⟨221691144325542187949052111636,221691144325542188068490399110⟩,⟨(-327017808527984768653353832434),(-327017808527984768535955139398)⟩⟩,⟨⟨217364010979504434046162664326,217364010979504434165541011922⟩,⟨(-326457528791447568905068382986),(-326457528791447568787630295614)⟩⟩,⟨⟨213019449316691282180757037602,213019449316691282300058076462⟩,⟨(-325855313450693236296382647345),(-325855313450693236178922563953)⟩⟩,⟨⟨208659369374059718900340021138,208659369374059719019569802140⟩,⟨(-325210546317568672082444962602),(-325210546317568671964956950020)⟩⟩,⟨⟨204285687545490111331159356657,204285687545490111450301771208⟩,⟨(-324522653240769841566521185082),(-324522653240769841449021491078)⟩⟩,⟨⟨199900325095929347559055398586,199900325095929347678114682767⟩,⟨(-323791103059288325880777333121),(-323791103059288325763261939812)⟩⟩,⟨⟨195505206647741297558466324760,195505206647741297677421981404⟩,⟨(-323015408489735214091061019238),(-323015408489735213973550664467)⟩⟩,⟨⟨191102258641427096719249533729,191102258641427096838109663067⟩,⟨(-322195126945786186954750553191),(-322195126945786186837237460815)⟩⟩,⟨⟨186693407772983246774454797829,186693407772983246893201146698⟩,⟨(-321329861288111625343640897527),(-321329861288111625226143668351)⟩⟩,⟨⟨182280579410265984408892800889,182280579410265984527530719114⟩,⟨(-320419260503281052925247883191),(-320419260503281052807761587171)⟩⟩,⟨⟨177865695990825386476236323964,177865695990825386594743286380⟩,⟨(-319463020310261947883579813631),(-319463020310261947766127422807)⟩⟩,⟨⟨173450675403761876168800555102,173450675403761876287185714790⟩,⟨(-318460883693268661223856504119),(-318460883693268661106429384446)⟩⟩,⟨⟨169037429358240795194914129039,169037429358240795313157038001⟩,⟨(-317412641359857564287647068073),(-317412641359857564170266215666)⟩⟩,⟨⟨164627861741377158220374106305,164627861741377158338481394176⟩,⟨(-316318132123309296677222833567),(-316318132123309296559882228931)⟩⟩] +lemma kernel4_0_r5_4_eq : ∀ k : Fin 16, kernel4_0Expr 5 4 k = kernel4_0_r5_4 k := by decide +kernel +noncomputable def kernel4_0_r5_5 : Fin 16 → CBox := ![⟨⟨160223866968272271112646026001,160223866968272271230591479525⟩,⟨(-315177243208487756223930070258),(-315177243208487756106656569799)⟩⟩,⟨⟨155827328327046257537862867183,155827328327046257655658478956⟩,⟨(-313989910480517901426652421337),(-313989910480517901309434734483)⟩⟩,⟨⟨151440116321765404536492456813,151440116321765404654115558880⟩,⟨(-312756118595780139572826606075),(-312756118595780139455688138703)⟩⟩,⟨⟨147064087016210335415598012696,147064087016210335533056674512⟩,⟨(-311475901074877646495240487201),(-311475901074877646378173956246)⟩⟩,⟨⟨142701080381470100946251938259,142701080381470101063518177491⟩,⟨(-310149340297393984169308628672),(-310149340297393984052342844916)⟩⟩,⟨⟨138352918650378126872504715647,138352918650378126989591590375⟩,⟨(-308776567418421410683867431221),(-308776567418421410566990204965)⟩⟩,⟨⟨134021404681828374000427320720,134021404681828374117309933960⟩,⟨(-307357762207004858608923670927),(-307357762207004858492160813693)⟩⟩,⟨⟨129708320338023892172283768644,129708320338023892288971792919⟩,⟨(-305893152806812223675101631483),(-305893152806812223558444416638)⟩⟩,⟨⟨125415424877715046539137272902,125415424877715046655598833521⟩,⟨(-304383015419507875082620649663),(-304383015419507874966101951980)⟩⟩,⟨⟨121144453368480959768321172898,121144453368480959884572680659⟩,⟨(-302827673911472680486426798785),(-302827673911472680370031223747)⟩⟩,⟨⟨116897115121095074822436252272,116897115121095074938450601327⟩,⟨(-301227499344679833174071775415),(-301227499344679833057827504562)⟩⟩,⟨⟨112675092148994159726850569697,112675092148994159842639185507⟩,⟨(-299582909432700870176949186285),(-299582909432700870060845880453)⟩⟩,⟨⟨108480037655839541250258167474,108480037655839541365787500589⟩,⟨(-297894367922979967687962869345),(-297894367922979967572035232565)⟩⟩,⟨⟨104313574554119894986987980121,104313574554119895102275750547⟩,⟨(-296162383906676381619363496896),(-296162383906676381503594953651)⟩⟩,⟨⟨100177294017696594971802383608,100177294017696595086819313307⟩,⟨(-294387511057534253758651026505),(-294387511057534253643072074221)⟩⟩,⟨⟨96072754071135530524912664629,96072754071135530639672077135⟩,⟨(-292570346801395417228551026853),(-292570346801395417113149547667)⟩⟩] +lemma kernel4_0_r5_5_eq : ∀ k : Fin 16, kernel4_0Expr 5 5 k = kernel4_0_r5_5 k := by decide +kernel +noncomputable def kernel4_0_r5_6 : Fin 16 → CBox := ![⟨⟨92001478218603559187896229461,92001478218603559302360071920⟩,⟨(-290711531418123802627540344098),(-290711531418123802512355684873)⟩⟩,⟨⟨87964954115033543679850008630,87964954115033543794040332948⟩,⟨(-288811747077859068706477225026),(-288811747077859068591488581722)⟩⟩,⟨⟨83964632282179412401863050401,83964632282179412515748473447⟩,⟨(-286871716813661667926713378171),(-286871716813661667811953477902)⟩⟩,⟨⟨80001924872092114574206497583,80001924872092114687802367638⟩,⟨(-284892203432751228005523519556),(-284892203432751227890978316555)⟩⟩,⟨⟨76078204480448972185265264149,76078204480448972298532564248⟩,⟨(-282874008368674419097254665633),(-282874008368674418982964586572)⟩⟩,⟨⟨72194803012063052460210822001,72194803012063052573172586498⟩,⟨(-280817970476866931530658872389),(-280817970476866931416602214676)⟩⟩,⟨⟨68353010600786117760834756332,68353010600786117873457576406⟩,⟨(-278724964776196377517075089995),(-278724964776196377403286710700)⟩⟩,⟨⟨64554074585898805134524509795,64554074585898805246825877899⟩,⟨(-276595901139188438074384348864),(-276595901139188437960848131334)⟩⟩,⟨⟨60799198546955323476479668758,60799198546955323588416153006⟩,⟨(-274431722933747011288767477175),(-274431722933747011175528364262)⟩⟩,⟨⟨57089541398917537242393730161,57089541398917537353993006281⟩,⟨(-272233405619280111186627028649),(-272233405619280111073658730376)⟩⟩,⟨⟨53426216549275261517646356833,53426216549275261628873100040⟩,⟨(-270001955300236474448058611416),(-270001955300236474335397983940)⟩⟩,⟨⟨49810291118706376829792383254,49810291118706376940666322165⟩,⟨(-267738407240142938520424190256),(-267738407240142938408052929991)⟩⟩,⟨⟨46242785226682457517089224092,46242785226682457627566167463⟩,⟨(-265443824339309371535726412770),(-265443824339309371423690295036)⟩⟩,⟨⟨42724671343273488208036807430,42724671343273488318145610763⟩,⟨(-263119295579436004007589466269),(-263119295579436003895861057660)⟩⟩,⟨⟨39256873708249429778537895555,39256873708249429888241434216⟩,⟨(-260765934438417208149721001354),(-260765934438417208038339019513)⟩⟩,⟨⟨35840267818417414883948998996,35840267818417414993269320545⟩,⟨(-258384877278685898927150408791),(-258384877278685898816094256399)⟩⟩] +lemma kernel4_0_r5_6_eq : ∀ k : Fin 16, kernel4_0Expr 5 6 k = kernel4_0_r5_6 k := by decide +kernel +noncomputable def kernel4_0_r5_7 : Fin 16 → CBox := ![⟨⟨32475679983971742519421279974,32475679983971742628309162852⟩,⟨(-255977281712483631273445642598),(-255977281712483631162766188249)⟩⟩,⟨⟨29163886954470150259514638854,29163886954470150368004598324⟩,⟨(-253544324947473014339220450589),(-253544324947473014228884602665)⟩⟩,⟨⟨25905615614884629216704868188,25905615614884629324758125655⟩,⟨(-251087202116131165313556633852),(-251087202116131165203604804185)⟩⟩,⟨⟨22701542752008873361876750922,22701542752008873469517721628⟩,⟨(-248607124592375527020239448093),(-248607124592375526910648673434)⟩⟩,⟨⟨19552294891337887905806839702,19552294891337888012986634080⟩,⟨(-246105318298876455798377055326),(-246105318298876455689197899995)⟩⟩,⟨⟨16458448204368887881588283251,16458448204368887988341889600⟩,⟨(-243583022008504565894044997187),(-243583022008504565785243888710)⟩⟩,⟨⟨13420528486106963031391211762,13420528486106963137678340615⟩,⟨(-241041485643344946533284004402),(-241041485643344946424902884904)⟩⟩,⟨⟨10439011202394629407382039837,10439011202394629513229514994⟩,⟨(-238481968574685136701956585628),(-238481968574685136593970062614)⟩⟩,⟨⟨7514321606521885784932194838,7514321606521885890286437198⟩,⟨(-235905737927349274570929595574),(-235905737927349274463392946769)⟩⟩,⟨⟨4646834924413288845023149809,4646834924413288949924836343⟩,⟨(-233314066891707292535765896536),(-233314066891707292428639815086)⟩⟩,⟨⟨1836876607531388267678936560,1836876607531388372086436530⟩,⟨(-230708233046635598199319926344),(-230708233046635598092647695155)⟩⟩,⟨⟨(-915277347517859448197680089),(-915277347517859344255132622)⟩,⟨(-228089516696644592778374487198),(-228089516696644592672128261933)⟩⟩,⟨⟨(-3609400013841848537772443204),(-3609400013841848434347827505)⟩,⟨(-225459199226318889977123096569),(-225459199226318889871357542290)⟩⟩,⟨⟨(-6245313084889734013278092882),(-6245313084889733910330187256)⟩,⟨(-222818561475138499882282686648),(-222818561475138499776957903116)⟩⟩,⟨⟨(-8822886362302404448070246943),(-8822886362302404345641863900)⟩,⟨(-220168882135663852943797005623),(-220168882135663852838957438543)⟩⟩,⟨⟨(-11342037182569013499693743396),(-11342037182569013397753245015)⟩,⟨(-217511436177974705639389873098),(-217511436177974705535005213630)⟩⟩] +lemma kernel4_0_r5_7_eq : ∀ k : Fin 16, kernel4_0Expr 5 7 k = kernel4_0_r5_7 k := by decide +kernel +noncomputable def kernel4_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-13802729784204391337411955369),(-13802729784204391236017842892)⟩,⟨(-214847493303153065286076892004),(-214847493303153065182207321269)⟩⟩,⟨⟨(-16204974617284830579163830136),(-16204974617284830478268030130)⟩,⟨(-212178316428493694452123618005),(-212178316428493694348722293112)⟩⟩,⟨⟨(-18548827597296399499551349705),(-18548827597296399399197670779)⟩,⟨(-209505160207012925876074782437),(-209505160207012925773187109290)⟩⟩,⟨⟨(-20834389305359743625958389225),(-20834389305359743526112841511)⟩,⟨(-206829269583707877586625332329),(-206829269583707877484218572735)⟩⟩,⟨⟨(-23061804136997991153572620832),(-23061804136997991054291566218)⟩,⟨(-204151878390894164298148306567),(-204151878390894164196280449805)⟩⟩,⟨⟨(-25231259401709605041598517143),(-25231259401709604942834632828)⟩,⟨(-201474207984821330600864110958),(-201474207984821330499488988550)⟩⟩,⟨⟨(-27342984375695584669259718133),(-27342984375695584571057648062)⟩,⟨(-198797465925631973357655527577),(-198797465925631973256819329995)⟩⟩,⟨⟨(-29397249310170105085806220885),(-29397249310170104988129672448)⟩,⟨(-196122844702593376064563149708),(-196122844702593375964230744212)⟩⟩,⟨⟨(-31394364397755318383120641230),(-31394364397755318286030778442)⟩,⟨(-193451520506389956964482303549),(-193451520506389956864716446819)⟩⟩,⟨⟨(-33334678699524489822879316186),(-33334678699524489726322477438)⟩,⟨(-190784652050121452527606744481),(-190784652050121452428354808626)⟩⟩,⟨⟨(-35218579035312795603197543742),(-35218579035312795507219024817)⟩,⟨(-188123379440506040077986274990),(-188123379440506039979295038661)⟩⟩,⟨⟨(-37046488839961898432030896328),(-37046488839961898336592197468)⟩,⟨(-185468823100640071477570890142),(-185468823100640071379402909971)⟩⟩,⟨⟨(-38818866988202804448604832756),(-38818866988202804353764961196)⟩,⟨(-182822082745517267171592465897),(-182822082745517267074008263423)⟩⟩,⟨⟨(-40536206590911487463331680207),(-40536206590911487369037550906)⟩,⟨(-180184236411360627191842441458),(-180184236411360627094789865928)⟩⟩,⟨⟨(-42199033765493374333693513105),(-42199033765493374239990918008)⟩,⟨(-177556339539670468560766011937),(-177556339539670468464292263981)⟩⟩,⟨⟨(-43807906383166081702933502596),(-43807906383166081609781828497)⟩,⟨(-174939424116742405381400414226),(-174939424116742405285465824461)⟩⟩] +lemma kernel4_0_r5_8_eq : ∀ k : Fin 16, kernel4_0Expr 5 8 k = kernel4_0_r5_8 k := by decide +kernel +noncomputable def kernel4_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-45363412795914874399429730786),(-45363412795914874306893687122)⟩,⟨(-172334497869260247759865994593),(-172334497869260247664536739579)⟩⟩,⟨⟨(-46866170545892305651977433336),(-46866170545892305559996563898)⟩,⟨(-169742543516421196117849702052),(-169742543516421196023066112463)⟩⟩,⟨⟨(-48316825060022554944488964328),(-48316825060022554853109380097)⟩,⟨(-167164518078904822411511728512),(-167164518078904822317321241403)⟩⟩,⟨⟨(-49716048332552285526884912170),(-49716048332552285436064026798)⟩,⟨(-164601352244853617866700243907),(-164601352244853617773061097923)⟩⟩,⟨⟨(-51064537598263612330948679422),(-51064537598263612240747411970)⟩,⟨(-162053949792891789417469047346),(-162053949792891789324443525176)⟩⟩,⟨⟨(-52363013999031240170749901677),(-52363013999031240081109940705)⟩,⟨(-159523187072070926557320176769),(-159523187072070926464850650171)⟩⟩,⟨⟨(-53612221246365263729232567998),(-53612221246365263640200208979)⟩,⟨(-157009912538496538776825159682),(-157009912538496538684959161626)⟩⟩,⟨⟨(-54812924282533799615019670856),(-54812924282533799526550476996)⟩,⟨(-154514946348258661309695748285),(-154514946348258661218389544315)⟩⟩,⟨⟨(-55965907942805852170150745004),(-55965907942805852082310526172)⟩,⟨(-152039080006163100527465940244),(-152039080006163100436786644059)⟩⟩,⟨⟨(-57071975621294923147769553593),(-57071975621294923060493415892)⟩,⟨(-149583076069637772735201536665),(-149583076069637772645084782997)⟩⟩,⟨⟨(-58131947942818202335536151746),(-58131947942818202248870419620)⟩,⟨(-147147667907071288780779139087),(-147147667907071288691272397293)⟩⟩,⟨⟨(-59146661443115078284522762738),(-59146661443115078198421317674)⟩,⟨(-144733559509728733177109076577),(-144733559509728733088166806612)⟩⟩,⟨⟨(-60116967259692555248048091113),(-60116967259692555162573097847)⟩,⟨(-142341425356282734947795741521),(-142341425356282734859481300907)⟩⟩,⟨⟨(-61043729835484335124635976832),(-61043729835484335039724565865)⟩,⟨(-139971910328896655461863718508),(-139971910328896655374114659802)⟩⟩,⟨⟨(-61927825637425211628091580290),(-61927825637425211543789991932)⟩,⟨(-137625629679701225763501966341),(-137625629679701225676365580391)⟩⟩,⟨⟨(-62770141891953425196464055229),(-62770141891953425112488657491)⟩,⟨(-135303169046416424098847575978),(-135303169046416424012096655589)⟩⟩] +lemma kernel4_0_r5_9_eq : ∀ k : Fin 16, kernel4_0Expr 5 9 k = kernel4_0_r5_9 k := by decide +kernel +noncomputable def kernel4_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-63571575339361143521273593643),(-63571575339361143437670569302)⟩,⟨(-133005084515786937293491861756),(-133005084515786937207178536723)⟩⟩,⟨⟨(-64333031008817669409761679352),(-64333031008817669326465263177)⟩,⟨(-130731902733422313277875763689),(-130731902733422313191932811673)⟩⟩,⟨⟨(-65055421015791741547542317743),(-65055421015791741464603969569)⟩,⟨(-128484121058561974643583288681),(-128484121058561974558061402465)⟩⟩,⟨⟨(-65739663383498790508900410065),(-65739663383498790426275897579)⟩,⟨(-126262207762220685606570641852),(-126262207762220685521424270292)⟩⟩,⟨⟨(-66386680889896645417412344951),(-66386680889896645335170271184)⟩,⟨(-124066602267111881267528894272),(-124066602267111881182825960280)⟩⟩,⟨⟨(-66997399941649355069552752529),(-66997399941649354987630798633)⟩,⟨(-121897715427694486513873531650),(-121897715427694486429550307379)⟩⟩,⟨⟨(-67572749476373884167050417429),(-67572749476373884085500008634)⟩,⟨(-119755929848643454714493937689),(-119755929848643454630601068123)⟩⟩,⟨⟨(-68113659894378856034882205482),(-68113659894378855953657402266)⟩,⟨(-117641600240005201292338347775),(-117641600240005201208828590946)⟩⟩,⟨⟨(-68621062020998614154291813480),(-68621062020998614073466774611)⟩,⟨(-115555053807266328367908909584),(-115555053807266328284855758952)⟩⟩,⟨⟨(-69095886100520031781504151139),(-69095886100520031701009237042)⟩,⟨(-113496590674537445328903518529),(-113496590674537445246235924250)⟩⟩,⟨⟨(-69539060822594065701237360751),(-69539060822594065621123812717)⟩,⟨(-111466484339033376197865037170),(-111466484339033376115633456957)⟩⟩,⟨⟨(-69951512381919367509413433266),(-69951512381919367429633764605)⟩,⟨(-109464982155016477482547470845),(-109464982155016477400703143279)⟩⟩,⟨⟨(-70334163571881660191834770260),(-70334163571881660112458522504)⟩,⟨(-107492305845361020113062187542),(-107492305845361020031673960887)⟩⟩,⟨⟨(-70687932912730370377108848414),(-70687932912730370298069298644)⟩,⟨(-105548652038893448619105425276),(-105548652038893448538105228819)⟩⟩,⟨⟨(-71013733814773472529751862056),(-71013733814773472451099972744)⟩,⟨(-103634192831665635945288247696),(-103634192831665635864726265914)⟩⟩,⟨⟨(-71312473776972928624324250679),(-71312473776972928546011117432)⟩,⟨(-101749076370325804278637287497),(-101749076370325804198463378488)⟩⟩] +lemma kernel4_0_r5_10_eq : ∀ k : Fin 16, kernel4_0Expr 5 10 k = kernel4_0_r5_10 k := by decide +kernel +noncomputable def kernel4_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-71585053621226755992810348861),(-71585053621226755914912535729)⟩,⟨(-99893427455764368370547941532),(-99893427455764368290838012035)⟩⟩,⟨⟨(-71832366762529869411939060437),(-71832366762529869334381119053)⟩,⟨(-98067348165229353315702702065),(-98067348165229353236379970232)⟩⟩,⟨⟨(-72055298515114644831668365847),(-72055298515114644754500853470)⟩,⟨(-96270918491128008103760598606),(-96270918491128008024874856802)⟩⟩,⟨⟨(-72254725434583846274034899447),(-72254725434583846197207676961)⟩,⟨(-94504196994757534732390143632),(-94504196994757534653890060535)⟩⟩,⟨⟨(-72431514695963330037219143002),(-72431514695963329960802192077)⟩,⟨(-92767221473238227668181814474),(-92767221473238227590136696973)⟩⟩,⟨⟨(-72586523507519957882913960239),(-72586523507519957806836835257)⟩,⟨(-91060009637956510991893429235),(-91060009637956510914231581519)⟩⟩,⟨⟨(-72720598560111560565482772943),(-72720598560111560489795568511)⟩,⟨(-89382559802863106687419861460),(-89382559802863106610190632833)⟩⟩,⟨⟨(-72834575511760722945433405796),(-72834575511760722870084879462)⟩,⟨(-87734851581012599651721316291),(-87734851581012599574872323557)⟩⟩,⟨⟨(-72929278507072721110177392891),(-72929278507072721035243458676)⟩,⟨(-86116846587774713244250290972),(-86116846587774713167856813862)⟩⟩,⟨⟨(-73005519731050220832534249182),(-73005519731050220757936979083)⟩,⟨(-84528489149194402719047110012),(-84528489149194402643030005657)⟩⟩,⟨⟨(-73064098996793417434181484687),(-73064098996793417359970415783)⟩,⟨(-82969707014027142094239570803),(-82969707014027142018647655639)⟩⟩,⟨⟨(-73105803366514213936082006439),(-73105803366514213862204977887)⟩,⟨(-81440412068027253780213516579),(-81440412068027253704993545276)⟩⟩,⟨⟨(-73131406805236834151158260178),(-73131406805236834077685341991)⟩,⟨(-79940501049120543039858130227),(-79940501049120542965079538910)⟩⟩,⟨⟨(-73141669866504970234023125634),(-73141669866504970160880829793)⟩,⟨(-78469856262147588185193630600),(-78469856262147588110781801393)⟩⟩,⟨⟨(-73137339409367174135169940823),(-73137339409367174062407212473)⟩,⟨(-77028346291920544048039625586),(-77028346291920543974042811694)⟩⟩,⟨⟨(-73119148345867707988326540963),(-73119148345867707915890435617)⟩,⟨(-75615826713393988016200687925),(-75615826713393987942564919701)⟩⟩] +lemma kernel4_0_r5_11_eq : ∀ k : Fin 16, kernel4_0Expr 5 11 k = kernel4_0_r5_11 k := by decide +kernel +noncomputable def kernel4_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-73087815418229443568315760552),(-73087815418229443496284425754)⟩,⟨(-74232140797808928541939832009),(-74232140797808928468742675158)⟩⟩,⟨⟨(-73044045004878605592892141937),(-73044045004878605521182655628)⟩,⟨(-72877120213728366489541405223),(-72877120213728366416698845793)⟩⟩,⟨⟨(-72988526954428134717152492598),(-72988526954428134645813127434)⟩,⟨(-71550585721942518900566508285),(-71550585721942518828126158439)⟩⟩,⟨⟨(-72921936446707138288131499077),(-72921936446707138217108716925)⟩,⟨(-70252347863281760220705208190),(-70252347863281760148612565845)⟩⟩,⟨⟨(-72844933879898223628061019307),(-72844933879898223557424725931)⟩,⟨(-68982207638435294378889891052),(-68982207638435294307214282320)⟩⟩,⟨⟨(-72758164782822382690722546305),(-72758164782822382620396886223)⟩,⟨(-67739957178933338615578486133),(-67739957178933338544243056279)⟩⟩,⟨⟨(-72662259751392421700297884458),(-72662259751392421630330453694)⟩,⟨(-66525380408509982934160901740),(-66525380408509982863212619640)⟩⟩,⟨⟨(-72557834408240599507398599445),(-72557834408240599437735384199)⟩,⟨(-65338253694122704219754184842),(-65338253694122704149138134315)⟩⟩,⟨⟨(-72445489384514040782431571433),(-72445489384514040713148994032)⟩,⟨(-64178346485962588809485690061),(-64178346485962588739277761177)⟩⟩,⟨⟨(-72325810322822504870604406216),(-72325810322822504801618974794)⟩,⟨(-63045421945846489876676708406),(-63045421945846489806792457512)⟩⟩,⟨⟨(-72199367900317092228284110843),(-72199367900317092159642689244)⟩,⟨(-61939237563438465678730058127),(-61939237563438465609215756076)⟩⟩,⟨⟨(-72066717870875326838779324988),(-72066717870875326770427597184)⟩,⟨(-60859545759802771897483891345),(-60859545759802771828284380732)⟩⟩,⟨⟨(-71928401125367629599242377503),(-71928401125367629531249963339)⟩,⟨(-59806094477844287451123576644),(-59806094477844287382307957508)⟩⟩,⟨⟨(-71784943768982355717331441726),(-71784943768982355649620703552)⟩,⟨(-58778627759244420850409006236),(-58778627759244420781898771833)⟩⟩,⟨⟨(-71636857214591167372662732856),(-71636857214591167305279806087)⟩,⟨(-57776886307551166947503126232),(-57776886307551166879343853247)⟩⟩,⟨⟨(-71484638291143408187625719734),(-71484638291143408120516097933)⟩,⟨(-56800608037130966178929490840),(-56800608037130966111065890742)⟩⟩] +lemma kernel4_0_r5_12_eq : ∀ k : Fin 16, kernel4_0Expr 5 12 k = kernel4_0_r5_12 k := by decide +kernel +noncomputable def kernel4_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-71328769366087194219298166942),(-71328769366087194152540110131)⟩,⟨(-55849528607737275167958584237),(-55849528607737275100468446569)⟩⟩,⟨⟨(-71169718480825992677750011936),(-71169718480825992611256352099)⟩,⟨(-54923381944496214297408758148),(-54923381944496214230204088166)⟩⟩,⟨⟨(-71007939498232380132351930101),(-71007939498232380066168020419)⟩,⟨(-54021900743153250199837224383),(-54021900743153250132962850065)⟩⟩,⟨⟨(-70843872261255313281102264196),(-70843872261255313215173578086)⟩,⟨(-53144816960466544512027354318),(-53144816960466544445428023884)⟩⟩,⟨⟨(-70677942761673465646878012232),(-70677942761673465581273819793)⟩,⟨(-52291862289672309675265253381),(-52291862289672309609009776289)⟩⟩,⟨⟨(-70510563318064843164867954790),(-70510563318064843099509366588)⟩,⟨(-51462768620985222171711475581),(-51462768620985222105720214826)⟩⟩,⟨⟨(-70342132762081853475845396217),(-70342132762081853410777004865)⟩,⟨(-50657268487132626258955776758),(-50657268487132626193272832066)⟩⟩,⟨⟨(-70173036632141133892761231407),(-70173036632141133827928578694)⟩,⟨(-49875095493954898265157290107),(-49875095493954898199727531698)⟩⟩,⟨⟨(-70003647373658611034601191779),(-70003647373658610970080837615)⟩,⟨(-49115984736135922024580534109),(-49115984736135921959480102470)⟩⟩,⟨⟨(-69834324544982344540303024544),(-69834324544982344476008132431)⟩,⟨(-48379673198157146777467628468),(-48379673198157146712608981335)⟩⟩,⟨⟨(-69665415028198575877106883959),(-69665415028198575813081241570)⟩,⟨(-47665900140596163584109116915),(-47665900140596163519535579561)⟩⟩,⟨⟨(-69497253244009943452421944452),(-69497253244009943388611314456)⟩,⟨(-46974407471916155393795644828),(-46974407471916155329452358310)⟩⟩,⟨⟨(-69330161369908924301420522470),(-69330161369908924237893847171)⟩,⟨(-46304940105915965890895975173),(-46304940105915965826851475128)⟩⟩,⟨⟨(-69164449560894112967366792337),(-69164449560894112904044348538)⟩,⟨(-45657246305031915362096032129),(-45657246305031915298269954668)⟩⟩,⟨⟨(-69000416172001847538622843867),(-69000416172001847475547630787)⟩,⟨(-45031078009701895580275151449),(-45031078009701895516710061722)⟩⟩,⟨⟨(-68838347981950844382911644471),(-68838347981950844320029729608)⟩,⟨(-44426191154019732398576086075),(-44426191154019732335217475664)⟩⟩] +lemma kernel4_0_r5_13_eq : ∀ k : Fin 16, kernel4_0Expr 5 13 k = kernel4_0_r5_13 k := by decide +kernel +noncomputable def kernel4_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-68678520417222815761665479754),(-68678520417222815699055964910)⟩,⟨(-43842345967923351067906398528),(-43842345967923351004833001632)⟩⟩,⟨⟨(-68521197775927432792064551766),(-68521197775927432729637098517)⟩,⟨(-43279307266173955869394169038),(-43279307266173955806515037752)⟩⟩,⟨⟨(-68366633450825380507330346168),(-68366633450825380445127107151)⟩,⟨(-42736844724395286640813648892),(-42736844724395286578170527536)⟩⟩,⟨⟨(-68215070150908558253934842267),(-68215070150908558191902345714)⟩,⟨(-42214733142452087465994521949),(-42214733142452087403533404088)⟩⟩,⟨⟨(-68066740120961639395866437763),(-68066740120961639334073325577)⟩,⟨(-41712752695455267203649601801),(-41712752695455267141438768370)⟩⟩,⟨⟨(-67921865358554157161578305210),(-67921865358554157099944392512)⟩,⟨(-41230689172687900055684118774),(-41230689172687899993642832571)⟩⟩,⟨⟨(-67780657827936972140864570291),(-67780657827936972079431186134)⟩,⟨(-40768334204751261409322152496),(-40768334204751261347491357274)⟩⟩,⟨⟨(-67643319670341350843858292602),(-67643319670341350782572491870)⟩,⟨(-40325485479233575819557812509),(-40325485479233575757884064863)⟩⟩,⟨⟨(-67510043410202898943215143796),(-67510043410202898882153796375)⟩,⟨(-39901946945206127660406911616),(-39901946945206127598966749627)⟩⟩,⟨⟨(-67381012156856207980524757848),(-67381012156856207919599188496)⟩,⟨(-39497529006851909177446238717),(-39497529006851909116150460991)⟩⟩,⟨⟨(-67256399801269256505495874166),(-67256399801269256444746530592)⟩,⟨(-39112048706531114705627769572),(-39112048706531114644516458510)⟩⟩,⟨⟨(-67136371207409327237558801814),(-67136371207409327176933410897)⟩,⟨(-38745329897585593511221164932),(-38745329897585593450241580600)⟩⟩,⟨⟨(-67021082397854437452598559489),(-67021082397854437392165538786)⟩,⟨(-38397203407180907195843378791),(-38397203407180907135063613421)⟩⟩,⟨⟨(-66910680733286011988987973122),(-66910680733286011928666955850)⟩,⟨(-38067507189479961091201689120),(-38067507189479961030540891057)⟩⟩,⟨⟨(-66805305085519743449835136864),(-66805305085519743389665690540)⟩,⟨(-37756086469436352685544598039),(-37756086469436352625041986361)⟩⟩,⟨⟨(-66705086003752273445880140242),(-66705086003752273385810742175)⟩,⟨(-37462793877488663712659732341),(-37462793877488663652263343902)⟩⟩] +lemma kernel4_0_r5_14_eq : ∀ k : Fin 16, kernel4_0Expr 5 14 k = kernel4_0_r5_14 k := by decide +kernel +noncomputable def kernel4_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-66610145873721487632198651678),(-66610145873721487572308742464)⟩,⟨(-37187489575428975523184928515),(-37187489575428975462973903559)⟩⟩,⟨⟨(-66520599069497845699146301359),(-66520599069497845639344395602)⟩,⟨(-36930041373709968636940697065),(-36930041373709968576823079319)⟩⟩,⟨⟨(-66436552097643269311378203598),(-66436552097643269251702903378)⟩,⟨(-36690324840445135164970323907),(-36690324840445135104984380584)⟩⟩,⟨⟨(-66358103733492694073172008418),(-66358103733492694013572707352)⟩,⟨(-36468223402345944585157948956),(-36468223402345944525252654510)⟩⟩,⟨⟨(-66285345149331467415197243658),(-66285345149331467355742160599)⟩,⟨(-36263628437828315821149239228),(-36263628437828315761392511753)⟩⟩,⟨⟨(-66218360034259357807328055985),(-66218360034259357747936939642)⟩,⟨(-36076439362508517529598509773),(-36076439362508517469909658483)⟩⟩,⟨⟨(-66157224705549050095228860938),(-66157224705549050035939342227)⟩,⟨(-35906563707295698850131604911),(-35906563707295698790547936096)⟩⟩,⟨⟨(-66102008211323658273707999689),(-66102008211323658214470468159)⟩,⟨(-35753917189274698620790571152),(-35753917189274698561262071290)⟩⟩,⟨⟨(-66052772424394014684797351420),(-66052772424394014625689334388)⟩,⟨(-35618423775558645281230800390),(-35618423775558645221834712528)⟩⟩,⟨⟨(-66009572127112320112902041573),(-66009572127112320053834046711)⟩,⟨(-35500015740276194559446167803),(-35500015740276194500092565749)⟩⟩,⟨⟨(-65972455087114191555985079174),(-65972455087114191496993665636)⟩,⟨(-35398633714843108854353489689),(-35398633714843108795078614748)⟩⟩,⟨⟨(-65941462123836254768905943214),(-65941462123836254709942674341)⟩,⟨(-35314226731652311451045835139),(-35314226731652311391800858609)⟩⟩,⟨⟨(-65916627165711230116950199464),(-65916627165711230058083113682)⟩,⟨(-35246752261300599997617024835),(-35246752261300599938469697481)⟩⟩,⟨⟨(-65897977297956987699150300233),(-65897977297956987640299549993)⟩,⟨(-35196176243453925980122090005),(-35196176243453925920992147556)⟩⟩,⟨⟨(-65885532800890337448116144078),(-65885532800890337389317175265)⟩,⟨(-35162473111436588529608393064),(-35162473111436588470530966841)⟩⟩,⟨⟨(-65879307178710409637176739579),(-65879307178710409578382405930)⟩,⟨(-35145625810612899492301745300),(-35145625810612899433229302919)⟩⟩] +lemma kernel4_0_r5_15_eq : ∀ k : Fin 16, kernel4_0Expr 5 15 k = kernel4_0_r5_15 k := by decide +kernel +noncomputable def kernel4_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel4_0_r5_0,kernel4_0_r5_1,kernel4_0_r5_2,kernel4_0_r5_3,kernel4_0_r5_4,kernel4_0_r5_5,kernel4_0_r5_6,kernel4_0_r5_7,kernel4_0_r5_8,kernel4_0_r5_9,kernel4_0_r5_10,kernel4_0_r5_11,kernel4_0_r5_12,kernel4_0_r5_13,kernel4_0_r5_14,kernel4_0_r5_15] +lemma kernel4_0_r5_eq (i k : Fin 16) : kernel4_0Expr 5 i k = kernel4_0_r5 i k := by + fin_cases i + · exact kernel4_0_r5_0_eq k + · exact kernel4_0_r5_1_eq k + · exact kernel4_0_r5_2_eq k + · exact kernel4_0_r5_3_eq k + · exact kernel4_0_r5_4_eq k + · exact kernel4_0_r5_5_eq k + · exact kernel4_0_r5_6_eq k + · exact kernel4_0_r5_7_eq k + · exact kernel4_0_r5_8_eq k + · exact kernel4_0_r5_9_eq k + · exact kernel4_0_r5_10_eq k + · exact kernel4_0_r5_11_eq k + · exact kernel4_0_r5_12_eq k + · exact kernel4_0_r5_13_eq k + · exact kernel4_0_r5_14_eq k + · exact kernel4_0_r5_15_eq k +noncomputable def kernel4_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel4_0_r0,kernel4_0_r1,kernel4_0_r2,kernel4_0_r3,kernel4_0_r4,kernel4_0_r5] +lemma kernel4_0_eq (j : Fin 6) (i k : Fin 16) : kernel4_0Expr j i k = kernel4_0 j i k := by + fin_cases j + · exact kernel4_0_r0_eq i k + · exact kernel4_0_r1_eq i k + · exact kernel4_0_r2_eq i k + · exact kernel4_0_r3_eq i k + · exact kernel4_0_r4_eq i k + · exact kernel4_0_r5_eq i k +lemma kernel4_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel4_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(4:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel4_0_eq] + unfold kernel4_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans4_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel4_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans4 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel4_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-122278518611325989),(-122278518611325942)⟩,⟨1085706275537858256,1085706275537858303⟩⟩,⟨⟨(-122976799491754402),(-122976799491754344)⟩,⟨1084777709770638599,1084777709770638657⟩⟩,⟨⟨(-124369804070677929),(-124369804070677860)⟩,⟨1082921396117578447,1082921396117578517⟩⟩,⟨⟨(-126450435266716116),(-126450435266716066)⟩,⟨1080138977994018067,1080138977994018121⟩⟩,⟨⟨(-129208090590846085),(-129208090590846035)⟩,⟨1076432939539738481,1076432939539738535⟩⟩,⟨⟨(-132628713701237478),(-132628713701237428)⟩,⟨1071806628119224998,1071806628119225052⟩⟩,⟨⟨(-136694862801810586),(-136694862801810539)⟩,⟨1066264283792661957,1066264283792662004⟩⟩,⟨⟨(-141385795592356527),(-141385795592356469)⟩,⟨1059811075311377011,1059811075311377069⟩⟩,⟨⟨(-146677570405453936),(-146677570405453882)⟩,⟨1052453142089108565,1052453142089108615⟩⟩,⟨⟨(-152543163093165970),(-152543163093165919)⟩,⟨1044197641504135729,1044197641504135783⟩⟩,⟨⟨(-158952599154735532),(-158952599154735474)⟩,⟨1035052800798056429,1035052800798056486⟩⟩,⟨⟨(-165873100525381065),(-165873100525381010)⟩,⟨1025027972755811193,1025027972755811243⟩⟩,⟨⟨(-173269246376025033),(-173269246376024979)⟩,⟨1014133694279347835,1014133694279347885⟩⟩,⟨⟨(-181103147204597412),(-181103147204597358)⟩,⟨1002381746904914220,1002381746904914271⟩⟩,⟨⟨(-189334631431718666),(-189334631431718620)⟩,⟨989785218262077662,989785218262077708⟩⟩,⟨⟨(-197921443647390702),(-197921443647390655)⟩,⟨976358563431804227,976358563431804274⟩⟩] +lemma kernel4_1_r0_0_eq : ∀ k : Fin 16, kernel4_1Expr 0 0 k = kernel4_1_r0_0 k := by decide +kernel +noncomputable def kernel4_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-206819453591158041),(-206819453591157995)⟩,⟨962117665131786248,962117665131786294⟩⟩,⟨⟨(-215982874886429325),(-215982874886429267)⟩,⟨947079891640054511,947079891640054569⟩⟩,⟨⟨(-225364492490688147),(-225364492490688100)⟩,⟨931264151363002928,931264151363002975⟩⟩,⟨⟨(-234915897767620354),(-234915897767620296)⟩,⟨914690942961410643,914690942961410701⟩⟩,⟨⟨(-244587730035214638),(-244587730035214580)⟩,⟨897382399967862261,897382399967862318⟩⟩,⟨⟨(-254329923396147105),(-254329923396147055)⟩,⟨879362328861005794,879362328861005848⟩⟩,⟨⟨(-264091957613745655),(-264091957613745597)⟩,⟨860656239606086786,860656239606086844⟩⟩,⟨⟨(-273823111759057602),(-273823111759057555)⟩,⟨841291367726763404,841291367726763451⟩⟩,⟨⟨(-283472719322528406),(-283472719322528348)⟩,⟨821296687039832990,821296687039833048⟩⟩,⟨⟨(-292990423458040775),(-292990423458040717)⟩,⟨800702912261550935,800702912261550993⟩⟩,⟨⟨(-302326431008049098),(-302326431008049052)⟩,⟨779542490780961157,779542490780961203⟩⟩,⟨⟨(-311431763946732956),(-311431763946732909)⟩,⟨757849582991236538,757849582991236584⟩⟩,⟨⟨(-320258506873908974),(-320258506873908927)⟩,⟨735660030673508771,735660030673508818⟩⟩,⟨⟨(-328760049196265685),(-328760049196265627)⟩,⟨713011313038021018,713011313038021076⟩⟩,⟨⟨(-336891320644648577),(-336891320644648523)⟩,⟨689942490143566039,689942490143566090⟩⟩,⟨⟨(-344609018796895536),(-344609018796895478)⟩,⟨666494133536907033,666494133536907090⟩⟩] +lemma kernel4_1_r0_1_eq : ∀ k : Fin 16, kernel4_1Expr 0 1 k = kernel4_1_r0_1 k := by decide +kernel +noncomputable def kernel4_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-351871827305306538),(-351871827305306480)⟩,⟨642708244078001008,642708244078001066⟩⟩,⟨⟨(-358640623566358199),(-358640623566358126)⟩,⟨618628157043097828,618628157043097905⟩⟩,⟨⟨(-364878674617794021),(-364878674617793948)⟩,⟨594298434724886717,594298434724886782⟩⟩,⟨⟨(-370551820104699875),(-370551820104699829)⟩,⟨569764746875506225,569764746875506271⟩⟩,⟨⟨(-375628641221492844),(-375628641221492790)⟩,⟨545073739463129254,545073739463129305⟩⟩,⟨⟨(-380080614610695142),(-380080614610695085)⟩,⟨520272892334694559,520272892334694617⟩⟩,⟨⟨(-383882250281632138),(-383882250281632088)⟩,⟨495410366494925141,495410366494925195⟩⟩,⟨⟨(-387011212702383895),(-387011212702383849)⟩,⟨470534841823838695,470534841823838741⟩⟩,⟨⟨(-389448424315949759),(-389448424315949705)⟩,⟨445695346160349511,445695346160349561⟩⟩,⟨⟨(-391178150836073001),(-391178150836072955)⟩,⟨420941076777194534,420941076777194581⟩⟩,⟨⟨(-392188067788857862),(-392188067788857804)⟩,⟨396321215361265417,396321215361265475⟩⟩,⟨⟨(-392469307882448144),(-392469307882448086)⟩,⟨371884737692567507,371884737692567565⟩⟩,⟨⟨(-392016488907808228),(-392016488907808154)⟩,⟨347680219283622140,347680219283622205⟩⟩,⟨⟨(-390827721998164844),(-390827721998164798)⟩,⟨323755638298456018,323755638298456064⟩⟩,⟨⟨(-388904600201988250),(-388904600201988200)⟩,⟨300158177115772498,300158177115772553⟩⟩,⟨⟨(-386252167453515363),(-386252167453515308)⟩,⟨276934023933983964,276934023933984014⟩⟩] +lemma kernel4_1_r0_2_eq : ∀ k : Fin 16, kernel4_1Expr 0 2 k = kernel4_1_r0_2 k := by decide +kernel +noncomputable def kernel4_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-382878868154712507),(-382878868154712452)⟩,⟨254128175836141334,254128175836141384⟩⟩,⟨⟨(-378796477712169664),(-378796477712169609)⟩,⟨231784244740192303,231784244740192353⟩⟩,⟨⟨(-374020014500633882),(-374020014500633832)⟩,⟨209944267654335194,209944267654335248⟩⟩,⟨⟨(-368567633850630457),(-368567633850630400)⟩,⟨188648522638541212,188648522638541270⟩⟩,⟨⟨(-362460504779802826),(-362460504779802768)⟩,⟨167935351841761551,167935351841761609⟩⟩,⟨⟨(-355722670305157525),(-355722670305157478)⟩,⟨147840992940210502,147840992940210548⟩⟩,⟨⟨(-348380892285288652),(-348380892285288606)⟩,⟨128399420245843584,128399420245843631⟩⟩,⟨⟨(-340464481846879147),(-340464481846879092)⟩,⟨109642196686276881,109642196686276931⟩⟩,⟨⟨(-332005116547388322),(-332005116547388267)⟩,⟨91598337778574745,91598337778574795⟩⟩,⟨⟨(-323036645514951334),(-323036645514951276)⟩,⟨74294188630340212,74294188630340270⟩⟩,⟨⟨(-313594883886331484),(-313594883886331430)⟩,⟨57753314903239427,57753314903239476⟩⟩,⟨⟨(-303717397933547535),(-303717397933547481)⟩,⟨41996408567435628,41996408567435678⟩⟩,⟨⟨(-293443282328915472),(-293443282328915415)⟩,⟨27041209161436281,27041209161436339⟩⟩,⟨⟨(-282812931046156468),(-282812931046156421)⟩,⟨12902441151671327,12902441151671373⟩⟩,⟨⟨(-271867803431498496),(-271867803431498442)⟩,⟨(-408232139118342),(-408232139118292)⟩⟩,⟨⟨(-260650187003016219),(-260650187003016164)⟩,⟨(-12882237694693752),(-12882237694693703)⟩⟩] +lemma kernel4_1_r0_3_eq : ∀ k : Fin 16, kernel4_1Expr 0 3 k = kernel4_1_r0_3 k := by decide +kernel +noncomputable def kernel4_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-249202958548600685),(-249202958548600630)⟩,⟨(-24514104851052323),(-24514104851052274)⟩⟩,⟨⟨(-237569345092836649),(-237569345092836600)⟩,⟨(-35301460149882640),(-35301460149882585)⟩⟩,⟨⟨(-225792686290710742),(-225792686290710684)⟩,⟨(-45245005057732148),(-45245005057732090)⟩⟩,⟨⟨(-213916199781621884),(-213916199781621834)⟩,⟨(-54348476740946511),(-54348476740946457)⟩⟩,⟨⟨(-201982751000868820),(-201982751000868762)⟩,⟨(-62618592216156009),(-62618592216155952)⟩⟩,⟨⟨(-190034628898016361),(-190034628898016311)⟩,⟨(-70064976322266537),(-70064976322266483)⟩⟩,⟨⟨(-178113328952769421),(-178113328952769366)⟩,⟨(-76700074081418253),(-76700074081418203)⟩⟩,⟨⟨(-166259344809785307),(-166259344809785261)⟩,⟨(-82539048132126930),(-82539048132126883)⟩⟩,⟨⟨(-154511969774908232),(-154511969774908175)⟩,⟨(-87599662026805095),(-87599662026805037)⟩⟩,⟨⟨(-142909109327375094),(-142909109327375044)⟩,⟨(-91902150287142460),(-91902150287142405)⟩⟩,⟨⟨(-131487105706461299),(-131487105706461249)⟩,⟨(-95469076203560191),(-95469076203560137)⟩⟩,⟨⟨(-120280575527720518),(-120280575527720471)⟩,⟨(-98325178448389476),(-98325178448389430)⟩⟩,⟨⟨(-109322261274397498),(-109322261274397444)⟩,⟨(-100497207645914518),(-100497207645914468)⟩⟩,⟨⟨(-98642897394779807),(-98642897394779752)⟩,⟨(-102013754105417200),(-102013754105417151)⟩⟩,⟨⟨(-88271091617263833),(-88271091617263779)⟩,⟨(-102905067975436031),(-102905067975435981)⟩⟩,⟨⟨(-78233221972829911),(-78233221972829857)⟩,⟨(-103202873118284007),(-103202873118283958)⟩⟩] +lemma kernel4_1_r0_4_eq : ∀ k : Fin 16, kernel4_1Expr 0 4 k = kernel4_1_r0_4 k := by decide +kernel +noncomputable def kernel4_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-68553349890558806),(-68553349890558752)⟩,⟨(-102940176033255852),(-102940176033255803)⟩⟩,⟨⟨(-59253149606880272),(-59253149606880218)⟩,⟨(-102151071174806352),(-102151071174806303)⟩⟩,⟨⟨(-50351854004529421),(-50351854004529367)⟩,⟨(-100870544018319152),(-100870544018319102)⟩⟩,⟨⟨(-41866216873779087),(-41866216873779033)⟩,⟨(-99134273221051103),(-99134273221051054)⟩⟩,⟨⟨(-33810491467469062),(-33810491467469007)⟩,⟨(-96978433209669503),(-96978433209669453)⟩⟩,⟨⟨(-26196425103681747),(-26196425103681692)⟩,⟨(-94439498498849988),(-94439498498849939)⟩⟩,⟨⟨(-19033269456581235),(-19033269456581178)⟩,⟨(-91554051008114921),(-91554051008114864)⟩⟩,⟨⟨(-12327806067847492),(-12327806067847434)⟩,⟨(-88358591597002547),(-88358591597002490)⟩⟩,⟨⟨(-6084386509135930),(-6084386509135884)⟩,⟨(-84889356982386656),(-84889356982386610)⟩⟩,⟨⟨(-304986530846190),(-304986530846144)⟩,⟨(-81182143137010598),(-81182143137010552)⟩⟩,⟨⟨5010726555126704,5010726555126761⟩,⟨(-77272136195821280),(-77272136195821223)⟩⟩,⟨⟨9865314090454747,9865314090454795⟩,⟨(-73193751817307169),(-73193751817307115)⟩⟩,⟨⟨14263474785869387,14263474785869445⟩,⟨(-68980483861629018),(-68980483861628961)⟩⟩,⟨⟨18211942901452165,18211942901452219⟩,⟨(-64664763156786460),(-64664763156786412)⟩⟩,⟨⟨21719376908450487,21719376908450532⟩,⟨(-60277827029322065),(-60277827029322019)⟩⟩,⟨⟨24796239692088734,24796239692088791⟩,⟨(-55849600178076558),(-55849600178076501)⟩⟩] +lemma kernel4_1_r0_5_eq : ∀ k : Fin 16, kernel4_1Expr 0 5 k = kernel4_1_r0_5 k := by decide +kernel +noncomputable def kernel4_1_r0_6 : Fin 16 → CBox := ![⟨⟨27454671387836703,27454671387836749⟩,⟨(-51408587369232647),(-51408587369232601)⟩⟩,⟨⟨29708355966805165,29708355966805222⟩,⟨(-46981778329273577),(-46981778329273520)⟩⟩,⟨⟨31572382699420216,31572382699420262⟩,⟨(-42594565110479927),(-42594565110479881)⟩⟩,⟨⟨33063103630428914,33063103630428968⟩,⟨(-38270672102114034),(-38270672102113985)⟩⟩,⟨⟨34197988192845408,34197988192845456⟩,⟨(-34032098760384258),(-34032098760384204)⟩⟩,⟨⟨34995476073971657,34995476073971711⟩,⟨(-29899075032496250),(-29899075032496201)⟩⟩,⟨⟨35474829423515843,35474829423515889⟩,⟨(-25890029355385672),(-25890029355385626)⟩⟩,⟨⟨35655985462540171,35655985462540228⟩,⟨(-22021569018843231),(-22021569018843174)⟩⟩,⟨⟨35559410513029249,35559410513029303⟩,⟨(-18308472596378254),(-18308472596378206)⟩⟩,⟨⟨35205956421856561,35205956421856607⟩,⟨(-14763694065953000),(-14763694065952955)⟩⟩,⟨⟨34616720300472743,34616720300472799⟩,⟨(-11398378167214158),(-11398378167214101)⟩⟩,⟨⟨33812908443413592,33812908443413649⟩,⟨(-8221886472541764),(-8221886472541708)⟩⟩,⟨⟨32815705225432873,32815705225432927⟩,⟨(-5241833586539920),(-5241833586539872)⟩⟩,⟨⟨31646147709432922,31646147709432970⟩,⟨(-2464132832848066),(-2464132832848012)⟩⟩,⟨⟨30325006626137316,30325006626137362⟩,⟨106949261387124,106949261387169⟩⟩,⟨⟨28872674312381377,28872674312381425⟩,⟨2468730414184125,2468730414184179⟩⟩] +lemma kernel4_1_r0_6_eq : ∀ k : Fin 16, kernel4_1Expr 0 6 k = kernel4_1_r0_6 k := by decide +kernel +noncomputable def kernel4_1_r0_7 : Fin 16 → CBox := ![⟨⟨27309060118737035,27309060118737080⟩,⟨4620042734998049,4620042734998094⟩⟩,⟨⟨25653493719691036,25653493719691090⟩,⟨6561156359165010,6561156359165058⟩⟩,⟨⟨23924636681486925,23924636681486979⟩,⟨8293697379725751,8293697379725798⟩⟩,⟨⟨22140402564739071,22140402564739116⟩,⟨9820560897090735,9820560897090780⟩⟩,⟨⟨20317885761710730,20317885761710775⟩,⟨11145820011062969,11145820011063014⟩⟩,⟨⟨18473299192375107,18473299192375152⟩,⟨12274631576828681,12274631576828726⟩⟩,⟨⟨16621920909654450,16621920909654495⟩,⟨13213139536951064,13213139536951109⟩⟩,⟨⟨14778049593136811,14778049593136867⟩,⟨13968376625507528,13968376625507584⟩⟩,⟨⟨12954968842615973,12954968842616018⟩,⟨14548165218689236,14548165218689281⟩⟩,⟨⟨11164920118468147,11164920118468192⟩,⟨14961018078865066,14961018078865111⟩⟩,⟨⟨9419084115584791,9419084115584836⟩,⟨15216039706770895,15216039706770940⟩⟩,⟨⟨7727570301686835,7727570301686880⟩,⟨15322828979613696,15322828979613740⟩⟩,⟨⟨6099414299663937,6099414299663982⟩,⟨15291383711997781,15291383711997825⟩⟩,⟨⟨4542582747357561,4542582747357607⟩,⟨15132007732223627,15132007732223680⟩⟩,⟨⟨3063985227136483,3063985227136528⟩,⟨14855221019221045,14855221019221089⟩⟩,⟨⟨1669492821827814,1669492821827860⟩,⟨14471673395708683,14471673395708736⟩⟩] +lemma kernel4_1_r0_7_eq : ∀ k : Fin 16, kernel4_1Expr 0 7 k = kernel4_1_r0_7 k := by decide +kernel +noncomputable def kernel4_1_r0_8 : Fin 16 → CBox := ![⟨⟨363962823151886,363962823151933⟩,⟨13992062221668750,13992062221668803⟩⟩,⟨⟨(-848730906215445),(-848730906215390)⟩,⟨13427054479428715,13427054479428770⟩⟩,⟨⟨(-1965662435485761),(-1965662435485717)⟩,⟨12787213588082933,12787213588082977⟩⟩,⟨⟨(-2984813666406081),(-2984813666406028)⟩,⟨12082931231172647,12082931231172693⟩⟩,⟨⟨(-3905030173809633),(-3905030173809588)⟩,⟨11324364427971896,11324364427971940⟩⟩,⟨⟨(-4725973532364432),(-4725973532364387)⟩,⟨10521378025856422,10521378025856466⟩⟩,⟨⟨(-5448070675211625),(-5448070675211572)⟩,⟨9683492739507615,9683492739507661⟩⟩,⟨⟨(-6072460825029900),(-6072460825029856)⟩,⟨8819838812523965,8819838812524010⟩⟩,⟨⟨(-6600940528618199),(-6600940528618153)⟩,⟨7939115328753296,7939115328753349⟩⟩,⟨⟨(-7035907312661486),(-7035907312661442)⟩,⟨7049555154653455,7049555154653499⟩⟩,⟨⟨(-7380302461253830),(-7380302461253785)⟩,⟨6158895450534231,6158895450534284⟩⟩,⟨⟨(-7637553395340133),(-7637553395340078)⟩,⟨5274353647890075,5274353647890129⟩⟩,⟨⟨(-7811516110857029),(-7811516110856985)⟩,⟨4402608752415008,4402608752415051⟩⟩,⟨⟨(-7906418106372559),(-7906418106372515)⟩,⟨3549787797882958,3549787797883002⟩⟩,⟨⟨(-7926802202809851),(-7926802202809808)⟩,⟨2721457245011441,2721457245011485⟩⟩,⟨⟨(-7877471627769421),(-7877471627769367)⟩,⟨1922619091809604,1922619091809658⟩⟩] +lemma kernel4_1_r0_8_eq : ∀ k : Fin 16, kernel4_1Expr 0 8 k = kernel4_1_r0_8 k := by decide +kernel +noncomputable def kernel4_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-7763436705404672),(-7763436705404628)⟩,⟨1157711437800728,1157711437800772⟩⟩,⟨⟨(-7589863460123157),(-7589863460123112)⟩,⟨430613223932470,430613223932523⟩⟩,⟨⟨(-7362024408937310),(-7362024408937267)⟩,⟨(-255347147065124),(-255347147065080)⟩⟩,⟨⟨(-7085251783416507),(-7085251783416462)⟩,⟨(-897379618685806),(-897379618685753)⟩⟩,⟨⟨(-6764893388226633),(-6764893388226589)⟩,⟨(-1493217035994281),(-1493217035994237)⟩⟩,⟨⟨(-6406271269496311),(-6406271269496259)⟩,⟨(-2041096774149587),(-2041096774149542)⟩⟩,⟨⟨(-6014643333010369),(-6014643333010326)⟩,⟨(-2539739769619422),(-2539739769619379)⟩⟩,⟨⟨(-5595168019774955),(-5595168019774912)⟩,⟨(-2988327284253277),(-2988327284253234)⟩⟩,⟨⟨(-5152872115069801),(-5152872115069757)⟩,⟨(-3386475730177036),(-3386475730176984)⟩⟩,⟨⟨(-4692621736926554),(-4692621736926510)⟩,⟨(-3734209878598745),(-3734209878598693)⟩⟩,⟨⟨(-4219096521246654),(-4219096521246602)⟩,⟨(-4031934768277085),(-4031934768277040)⟩⟩,⟨⟨(-3736766993670017),(-3736766993669974)⟩,⟨(-4280406619813661),(-4280406619813618)⟩⟩,⟨⟨(-3249875092975129),(-3249875092975077)⟩,⟨(-4480703050313339),(-4480703050313294)⟩⟩,⟨⟨(-2762417787352257),(-2762417787352213)⟩,⟨(-4634192869540882),(-4634192869540831)⟩⟩,⟨⟨(-2278133703442550),(-2278133703442508)⟩,⟨(-4742505723720460),(-4742505723720417)⟩⟩,⟨⟨(-1800492668644684),(-1800492668644641)⟩,⟨(-4807501836811983),(-4807501836811940)⟩⟩] +lemma kernel4_1_r0_9_eq : ∀ k : Fin 16, kernel4_1Expr 0 9 k = kernel4_1_r0_9 k := by decide +kernel +noncomputable def kernel4_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-1332688049907498),(-1332688049907456)⟩,⟨(-4831242081683846),(-4831242081683804)⟩⟩,⟨⟨(-877631757074266),(-877631757074224)⟩,⟨(-4815958595316922),(-4815958595316880)⟩⟩,⟨⟨(-437951765822021),(-437951765821979)⟩,⟨(-4764026133239973),(-4764026133239931)⟩⟩,⟨⟨(-15992004332928),(-15992004332884)⟩,⟨(-4677934339025245),(-4677934339025194)⟩⟩,⟨⟨386185560998063,386185560998106⟩,⟨(-4560261085074451),(-4560261085074400)⟩⟩,⟨⟨766796812327418,766796812327460⟩,⟨(-4413647021287285),(-4413647021287243)⟩⟩,⟨⟨1124329515970088,1124329515970130⟩,⟨(-4240771448714294),(-4240771448714252)⟩⟩,⟨⟨1457535686221223,1457535686221265⟩,⟨(-4044329616119424),(-4044329616119382)⟩⟩,⟨⟨1765422457999017,1765422457999059⟩,⟨(-3827011518668512),(-3827011518668470)⟩⟩,⟨⟨2047241648493069,2047241648493111⟩,⟨(-3591482259860461),(-3591482259860419)⟩⟩,⟨⟨2302478186041275,2302478186041317⟩,⟨(-3340364020449805),(-3340364020449764)⟩⟩,⟨⟨2530837581079383,2530837581079426⟩,⟨(-3076219661583082),(-3076219661583032)⟩⟩,⟨⟨2732232609344628,2732232609344669⟩,⟨(-2801537973779365),(-2801537973779323)⟩⟩,⟨⟨2906769371696284,2906769371696326⟩,⟨(-2518720568807315),(-2518720568807274)⟩⟩,⟨⟨3054732888080351,3054732888080392⟩,⟨(-2230070398005080),(-2230070398005039)⟩⟩,⟨⟨3176572375446018,3176572375446060⟩,⟨(-1937781868210907),(-1937781868210865)⟩⟩] +lemma kernel4_1_r0_10_eq : ∀ k : Fin 16, kernel4_1Expr 0 10 k = kernel4_1_r0_10 k := by decide +kernel +noncomputable def kernel4_1_r0_11 : Fin 16 → CBox := ![⟨⟨3272886350953683,3272886350953734⟩,⟨(-1643932515246137),(-1643932515246095)⟩⟩,⟨⟨3344407692729458,3344407692729499⟩,⟨(-1350476184845489),(-1350476184845448)⟩⟩,⟨⟨3391988780848943,3391988780848994⟩,⟨(-1059237662066032),(-1059237662065990)⟩⟩,⟨⟨3416586831296620,3416586831296662⟩,⟨(-771908682519983),(-771908682519933)⟩⟩,⟨⟨3419249525466281,3419249525466322⟩,⟨(-490045252255893),(-490045252255851)⟩⟩,⟨⟨3401101027454662,3401101027454703⟩,⟨(-215066197725336),(-215066197725295)⟩⟩,⟨⟨3363328471059846,3363328471059887⟩,⟨51747137010388,51747137010429⟩⟩,⟨⟨3307168988126397,3307168988126438⟩,⟨309250131906937,309250131906978⟩⟩,⟨⟨3233897339770182,3233897339770223⟩,⟨556433159689010,556433159689051⟩⟩,⟨⟨3144814202149877,3144814202149918⟩,⟨792418971288514,792418971288555⟩⟩,⟨⟨3041235148900048,3041235148900089⟩,⟨1016459287909154,1016459287909195⟩⟩,⟨⟨2924480363169640,2924480363169682⟩,⟨1227930689213338,1227930689213388⟩⟩,⟨⟨2795865103472829,2795865103472870⟩,⟨1426329885928656,1426329885928696⟩⟩,⟨⟨2656690939304650,2656690939304690⟩,⟨1611268463286994,1611268463287034⟩⟩,⟨⟨2508237764741281,2508237764741321⟩,⟨1782467179214197,1782467179214238⟩⟩,⟨⟨2351756591061417,2351756591061458⟩,⟨1939749898150892,1939749898150932⟩⟩] +lemma kernel4_1_r0_11_eq : ∀ k : Fin 16, kernel4_1Expr 0 11 k = kernel4_1_r0_11 k := by decide +kernel +noncomputable def kernel4_1_r0_12 : Fin 16 → CBox := ![⟨⟨2188463112819041,2188463112819081⟩,⟨2083037237880642,2083037237880683⟩⟩,⟨⟨2019532035777375,2019532035777415⟩,⟨2212340002838552,2212340002838592⟩⟩,⟨⟨1846092149694068,1846092149694108⟩,⟨2327752473140675,2327752473140715⟩⟩,⟨⟨1669222124124850,1669222124124890⟩,⟨2429445614080918,2429445614080958⟩⟩,⟨⟨1489947001185815,1489947001185855⟩,⟨2517660266146655,2517660266146695⟩⟩,⟨⟨1309235355572283,1309235355572323⟩,⟨2592700370773569,2592700370773608⟩⟩,⟨⟨1127997089059957,1127997089059997⟩,⟨2654926282144278,2654926282144318⟩⟩,⟨⟨947081824192801,947081824192841⟩,⟨2704748210393250,2704748210393289⟩⟩,⟨⟨767277859868581,767277859868621⟩,⟨2742619836655173,2742619836655212⟩⟩,⟨⟨589311650041780,589311650041820⟩,⟨2769032135535722,2769032135535761⟩⟩,⟨⟨413847765743963,413847765744003⟩,⟨2784507435825845,2784507435825885⟩⟩,⟨⟨241489300044805,241489300044844⟩,⟨2789593745665082,2789593745665122⟩⟩,⟨⟨72778675407735,72778675407775⟩,⟨2784859363912940,2784859363912979⟩⟩,⟨⟨(-91801186900050),(-91801186900010)⟩,⟨2770887795237265,2770887795237305⟩⟩,⟨⟨(-251825375137732),(-251825375137693)⟩,⟨2748272982399433,2748272982399473⟩⟩,⟨⟨(-406925212104840),(-406925212104801)⟩,⟨2717614865423261,2717614865423300⟩⟩] +lemma kernel4_1_r0_12_eq : ∀ k : Fin 16, kernel4_1Expr 0 12 k = kernel4_1_r0_12 k := by decide +kernel +noncomputable def kernel4_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-556786234663674),(-556786234663635)⟩,⟨2679515273794103,2679515273794142⟩⟩,⟨⟨(-701145964237620),(-701145964237581)⟩,⟨2634574154555920,2634574154555959⟩⟩,⟨⟨(-839791503197080),(-839791503197041)⟩,⟨2583386136165523,2583386136165562⟩⟩,⟨⟨(-972556990318120),(-972556990318081)⟩,⟨2526537425225838,2526537425225877⟩⟩,⟨⟨(-1099320946635966),(-1099320946635927)⟩,⟨2464603030757716,2464603030757755⟩⟩,⟨⟨(-1220003541044515),(-1220003541044476)⟩,⟨2398144308476742,2398144308476781⟩⟩,⟨⟨(-1334563802943217),(-1334563802943178)⟩,⟨2327706815616250,2327706815616289⟩⟩,⟨⟨(-1442996807129969),(-1442996807129939)⟩,⟨2253818465170911,2253818465170950⟩⟩,⟨⟨(-1545330854006680),(-1545330854006641)⟩,⟨2176987967019190,2176987967019229⟩⟩,⟨⟨(-1641624666028627),(-1641624666028588)⟩,⟨2097703542206162,2097703542206201⟩⟩,⟨⟨(-1731964619204649),(-1731964619204619)⟩,⟨2016431895720596,2016431895720634⟩⟩,⟨⟨(-1816462026366613),(-1816462026366575)⟩,⟨1933617432365302,1933617432365340⟩⟩,⟨⟨(-1895250486886012),(-1895250486885973)⟩,⟨1849681699787150,1849681699787188⟩⟩,⟨⟨(-1968483315539011),(-1968483315538973)⟩,⟨1765023042385806,1765023042385845⟩⟩,⟨⟨(-2036331061319687),(-2036331061319648)⟩,⟨1680016449643175,1680016449643214⟩⟩,⟨⟨(-2098979125186982),(-2098979125186943)⟩,⟨1595013582394990,1595013582395029⟩⟩] +lemma kernel4_1_r0_13_eq : ∀ k : Fin 16, kernel4_1Expr 0 13 k = kernel4_1_r0_13 k := by decide +kernel +noncomputable def kernel4_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-2156625484010849),(-2156625484010810)⟩,⟨1510342960683957,1510342960683996⟩⟩,⟨⟨(-2209478526363646),(-2209478526363608)⟩,⟨1426310297077199,1426310297077237⟩⟩,⟨⟨(-2257755004292734),(-2257755004292696)⟩,⟨1343198959682817,1343198959682855⟩⟩,⟨⟨(-2301678103806615),(-2301678103806576)⟩,⟨1261270549548275,1261270549548304⟩⟩,⟨⟨(-2341475635520052),(-2341475635520014)⟩,⟨1180765577649242,1180765577649280⟩⟩,⟨⟨(-2377378345726985),(-2377378345726955)⟩,⟨1101904227273448,1101904227273486⟩⟩,⟨⟨(-2409618347108911),(-2409618347108872)⟩,⟨1024887188250918,1024887188250956⟩⟩,⟨⟨(-2438427667336165),(-2438427667336127)⟩,⟨949896550172909,949896550172947⟩⟩,⟨⟨(-2464036912980261),(-2464036912980223)⟩,⟨877096742461509,877096742461547⟩⟩,⟨⟨(-2486674045422475),(-2486674045422437)⟩,⟨806635509892864,806635509892902⟩⟩,⟨⟨(-2506563264815407),(-2506563264815369)⟩,⟨738644912927159,738644912927197⟩⟩,⟨⟨(-2523923997624354),(-2523923997624316)⟩,⟨673242342952141,673242342952179⟩⟩,⟨⟨(-2538969982840642),(-2538969982840604)⟩,⟨610531543291626,610531543291664⟩⟩,⟨⟨(-2551908451615144),(-2551908451615105)⟩,⟨550603627566308,550603627566346⟩⟩,⟨⟨(-2562939394799560),(-2562939394799531)⟩,⟨493538087706804,493538087706842⟩⟩,⟨⟨(-2572254912703332),(-2572254912703294)⟩,⟨439403784610973,439403784611011⟩⟩] +lemma kernel4_1_r0_14_eq : ∀ k : Fin 16, kernel4_1Expr 0 14 k = kernel4_1_r0_14 k := by decide +kernel +noncomputable def kernel4_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-2580038641267969),(-2580038641267931)⟩,⟨388259915099290,388259915099328⟩⟩,⟨⟨(-2586465248822779),(-2586465248822741)⟩,⟨340156949452555,340156949452584⟩⟩,⟨⟨(-2591699997612239),(-2591699997612210)⟩,⟨295137534413303,295137534413341⟩⟩,⟨⟨(-2595898364368933),(-2595898364368895)⟩,⟨253237357090635,253237357090673⟩⟩,⟨⟨(-2599205714343068),(-2599205714343031)⟩,⟨214485965731594,214485965731632⟩⟩,⟨⟨(-2601757023384106),(-2601757023384068)⟩,⟨178907543805308,178907543805346⟩⟩,⟨⟨(-2603676642898346),(-2603676642898308)⟩,⟨146521634291429,146521634291467⟩⟩,⟨⟨(-2605078102772939),(-2605078102772901)⟩,⟨117343811472429,117343811472467⟩⟩,⟨⟨(-2606063947657794),(-2606063947657765)⟩,⟨91386297900042,91386297900080⟩⟩,⟨⟨(-2606725602328788),(-2606725602328750)⟩,⟨68658524541401,68658524541439⟩⟩,⟨⟨(-2607143262213907),(-2607143262213869)⟩,⟨49167632413346,49167632413384⟩⟩,⟨⟨(-2607385805545175),(-2607385805545138)⟩,⟨32918914283574,32918914283612⟩⟩,⟨⟨(-2607510724000703),(-2607510724000666)⟩,⟨19916195261673,19916195261711⟩⟩,⟨⟨(-2607564069120031),(-2607564069119993)⟩,⟨10162151318648,10162151318686⟩⟩,⟨⟨(-2607580412207126),(-2607580412207088)⟩,⟨3658564970123,3658564970161⟩⟩,⟨⟨(-2607582815880307),(-2607582815880269)⟩,⟨406517534062,406517534091⟩⟩] +lemma kernel4_1_r0_15_eq : ∀ k : Fin 16, kernel4_1Expr 0 15 k = kernel4_1_r0_15 k := by decide +kernel +noncomputable def kernel4_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel4_1_r0_0,kernel4_1_r0_1,kernel4_1_r0_2,kernel4_1_r0_3,kernel4_1_r0_4,kernel4_1_r0_5,kernel4_1_r0_6,kernel4_1_r0_7,kernel4_1_r0_8,kernel4_1_r0_9,kernel4_1_r0_10,kernel4_1_r0_11,kernel4_1_r0_12,kernel4_1_r0_13,kernel4_1_r0_14,kernel4_1_r0_15] +lemma kernel4_1_r0_eq (i k : Fin 16) : kernel4_1Expr 0 i k = kernel4_1_r0 i k := by + fin_cases i + · exact kernel4_1_r0_0_eq k + · exact kernel4_1_r0_1_eq k + · exact kernel4_1_r0_2_eq k + · exact kernel4_1_r0_3_eq k + · exact kernel4_1_r0_4_eq k + · exact kernel4_1_r0_5_eq k + · exact kernel4_1_r0_6_eq k + · exact kernel4_1_r0_7_eq k + · exact kernel4_1_r0_8_eq k + · exact kernel4_1_r0_9_eq k + · exact kernel4_1_r0_10_eq k + · exact kernel4_1_r0_11_eq k + · exact kernel4_1_r0_12_eq k + · exact kernel4_1_r0_13_eq k + · exact kernel4_1_r0_14_eq k + · exact kernel4_1_r0_15_eq k +noncomputable def kernel4_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-42857387166105434069635),(-42857387166105434015450)⟩,⟨10870812151617076013813,10870812151617076067991⟩⟩,⟨⟨(-42827076869219377762330),(-42827076869219377708164)⟩,⟨10858628531878087314487,10858628531878087368646⟩⟩,⟨⟨(-42766522439673329576846),(-42766522439673329522739)⟩,⟨10834294203111386881203,10834294203111386935303⟩⟩,⟨⟨(-42675855955167814563497),(-42675855955167814509503)⟩,⟨10797874852850283899257,10797874852850283953244⟩⟩,⟨⟨(-42555274906765699366125),(-42555274906765699312270)⟩,⟨10749468678380767404028,10749468678380767457877⟩⟩,⟨⟨(-42405041452191403976896),(-42405041452191403923213)⟩,⟨10689205987905874213767,10689205987905874267443⟩⟩,⟨⟨(-42225481426673481956123),(-42225481426673481902627)⟩,⟨10617248672053432817785,10617248672053432871274⟩⟩,⟨⟨(-42016983116792190332963),(-42016983116792190279694)⟩,⟨10533789548519445694700,10533789548519445747963⟩⟩,⟨⟨(-41779995804082888899999),(-41779995804082888846996)⟩,⟨10439051583304488649490,10439051583304488702487⟩⟩,⟨⟨(-41515028086385580891318),(-41515028086385580838611)⟩,⟨10333286992643977984139,10333286992643978036840⟩⟩,⟨⟨(-41222645986111713598731),(-41222645986111713546339)⟩,⟨10216776230350976067191,10216776230350976119577⟩⟩,⟨⟨(-40903470855713121373693),(-40903470855713121321682)⟩,⟨10089826865878536318866,10089826865878536370872⟩⟩,⟨⟨(-40558177091676955079025),(-40558177091676955027393)⟩,⟨9952772358963790927713,9952772358963790979339⟩⟩,⟨⟨(-40187489669327527124759),(-40187489669327527073537)⟩,⟨9805970737234642956975,9805970737234643008191⟩⟩,⟨⟨(-39792181511584881270611),(-39792181511584881219833)⟩,⟨9649803183638869895154,9649803183638869945927⟩⟩,⟨⟨(-39373070705605040981800),(-39373070705605040931475)⟩,⟨9484672540991778293165,9484672540991778343484⟩⟩] +lemma kernel4_1_r1_0_eq : ∀ k : Fin 16, kernel4_1Expr 1 0 k = kernel4_1_r1_0 k := by decide +kernel +noncomputable def kernel4_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-38931017581903610531147),(-38931017581903610481341)⟩,⟨9311001741329658814685,9311001741329658864485⟩⟩,⟨⟨(-38466921671138886647377),(-38466921671138886598080)⟩,⟨9129232168099876335010,9129232168099876384301⟩⟩,⟨⟨(-37981718554199973995240),(-37981718554199973946511)⟩,⟨8939821959512514653204,8939821959512514701927⟩⟩,⟨⟨(-37476376621607590641089),(-37476376621607590592898)⟩,⟨8743244261621444114695,8743244261621444162880⟩⟩,⟨⟨(-36951893758489228154267),(-36951893758489228106710)⟩,⟨8539985439893209758175,8539985439893209805726⟩⟩,⟨⟨(-36409293971535942478196),(-36409293971535942431243)⟩,⟨8330543258159326833993,8330543258159326880941⟩⟩,⟨⟨(-35849623974386049582850),(-35849623974386049536530)⟩,⟨8115425033930868972465,8115425033930869018781⟩⟩,⟨⟨(-35273949747813021505855),(-35273949747813021460183)⟩,⟨7895145779083465796429,7895145779083465842096⟩⟩,⟨⟨(-34683353090923414041483),(-34683353090923413996489)⟩,⟨7670226334896191765136,7670226334896191810125⟩⟩,⟨⟨(-34078928179299011310719),(-34078928179299011266424)⟩,⟨7441191510349902369589,7441191510349902413880⟩⟩,⟨⟨(-33461778145649616160417),(-33461778145649616116821)⟩,⟨7208568232460304873053,7208568232460304916646⟩⟩,⟨⟨(-32833011698083833636618),(-32833011698083833593771)⟩,⟨6972883717239750596656,6972883717239750639499⟩⟩,⟨⟨(-32193739790560225938833),(-32193739790560225896705)⟩,⟨6734663669651070966066,6734663669651071008191⟩⟩,⟨⟨(-31545072359456387587172),(-31545072359456387545819)⟩,⟨6494430520638758650268,6494430520638758691618⟩⟩,⟨⟨(-30888115139495343343145),(-30888115139495343302536)⟩,⟨6252701708999752655789,6252701708999752696395⟩⟩,⟨⟨(-30223966571504197344731),(-30223966571504197304912)⟩,⟨6009988015490664159191,6009988015490664199007⟩⟩] +lemma kernel4_1_r1_1_eq : ∀ k : Fin 16, kernel4_1Expr 1 1 k = kernel4_1_r1_1 k := by decide +kernel +noncomputable def kernel4_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-29553714813656516428732),(-29553714813656516389688)⟩,⟨5766791956163406282759,5766791956163406321800⟩⟩,⟨⟨(-28878434866975159712325),(-28878434866975159674082)⟩,⟨5523606241480056393627,5523606241480056431867⟩⟩,⟨⟨(-28199185824954026494569),(-28199185824954026457122)⟩,⟨5280912307283810419282,5280912307283810456726⟩⟩,⟨⟨(-27517008256203472791008),(-27517008256203472754388)⟩,⟨5039178923199719523904,5039178923199719560521⟩⟩,⟨⟨(-26832921728042983485909),(-26832921728042983450091)⟩,⟨4798860883510342274657,4798860883510342310473⟩⟩,⟨⟨(-26147922477964098561509),(-26147922477964098526535)⟩,⟨4560397785001457896489,4560397785001457931462⟩⟩,⟨⟨(-25462981238874496826772),(-25462981238874496792585)⟩,⟨4324212895705638713069,4324212895705638747254⟩⟩,⟨⟨(-24779041223018289397287),(-24779041223018289363924)⟩,⟨4090712117890921185897,4090712117890921219259⟩⟩,⟨⟨(-24097016268455483420171),(-24097016268455483387627)⟩,⟨3860283048052237482830,3860283048052237515373⟩⟩,⟨⟨(-23417789150982463033822),(-23417789150982463002093)⟩,⟨3633294136068874102592,3633294136068874134320⟩⟩,⟨⟨(-22742210063392064823961),(-22742210063392064793073)⟩,⟨3410093945096184997258,3410093945096185028146⟩⟩,⟨⟨(-22071095263012860338485),(-22071095263012860308402)⟩,⟨3191010513168216821701,3191010513168216851783⟩⟩,⟨⟨(-21405225887538610698559),(-21405225887538610669297)⟩,⟨2976350816903821131136,2976350816903821160397⟩⟩,⟨⟨(-20745346938266052530455),(-20745346938266052502005)⟩,⟨2766400337136122285742,2766400337136122314190⟩⟩,⟨⟨(-20092166429007215360876),(-20092166429007215333235)⟩,⟨2561422725727610942489,2561422725727610970131⟩⟩,⟨⟨(-19446354698135818533973),(-19446354698135818507119)⟩,⟨2361659572294182934584,2361659572294182961438⟩⟩] +lemma kernel4_1_r1_2_eq : ∀ k : Fin 16, kernel4_1Expr 1 2 k = kernel4_1_r1_2 k := by decide +kernel +noncomputable def kernel4_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-18808543880469847599335),(-18808543880469847573270)⟩,⟨2167330269044467467499,2167330269044467493564⟩⟩,⟨⟨(-18179327534987487794426),(-18179327534987487769135)⟩,⟨1978631971448871076605,1978631971448871101896⟩⟩,⟨⟨(-17559260423723936955602),(-17559260423723936931076)⟩,⟨1795739651988725295632,1795739651988725320158⟩⟩,⟨⟨(-16948858436604393529157),(-16948858436604393505401)⟩,⟨1618806243802303991785,1618806243802304015542⟩⟩,⟨⟨(-16348598656435306144455),(-16348598656435306121470)⟩,⟨1447962870643508821782,1447962870643508844767⟩⟩,⟨⟨(-15758919557802808044904),(-15758919557802808022661)⟩,⟨1283319159202633458157,1283319159202633480401⟩⟩,⟨⟨(-15180221333214628672131),(-15180221333214628650605)⟩,⟨1124963629508411599827,1124963629508411621354⟩⟩,⟨⟨(-14612866339469642068101),(-14612866339469642047282)⟩,⟨972964158837803457100,972964158837803477920⟩⟩,⟨⟨(-14057179656947050607955),(-14057179656947050587864)⟩,⟨827368514305620997182,827368514305621017275⟩⟩,⟨⟨(-13513449754274023515334),(-13513449754274023495926)⟩,⟨688204949090741966866,688204949090741986275⟩⟩,⟨⟨(-12981929250654994546911),(-12981929250654994528203)⟩,⟨555482857079595843947,555482857079595862657⟩⟩,⟨⟨(-12462835768025961822855),(-12462835768025961804826)⟩,⟨429193480570778362392,429193480570778380423⟩⟩,⟨⟨(-11956352865130860965651),(-11956352865130860948271)⟩,⟨309310665586709428233,309310665586709445615⟩⟩,⟨⟨(-11462631045601922782258),(-11462631045601922765523)⟩,⟨195791659278536325977,195791659278536342713⟩⟩,⟨⟨(-10981788832159128347517),(-10981788832159128331417)⟩,⟨88577943888059460824,88577943888059476925⟩⟩,⟨⟨(-10513913899122456039288),(-10513913899122456023794)⟩,⟨(-12403898255886412603),(-12403898255886397107)⟩⟩] +lemma kernel4_1_r1_3_eq : ∀ k : Fin 16, kernel4_1Expr 1 3 k = kernel4_1_r1_3 k := by decide +kernel +noncomputable def kernel4_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-10059064255551405603839),(-10059064255551405588952)⟩,⟨(-107241294180881842263),(-107241294180881827373)⟩⟩,⟨⟨(-9617269471485963572462),(-9617269471485963558176)⟩,⟨(-196034769547265132446),(-196034769547265118158)⟩⟩,⟨⟨(-9188531939958313156789),(-9188531939958313143074)⟩,⟨(-278897023038145139500),(-278897023038145125784)⟩⟩,⟨⟨(-8772828167671690424266),(-8772828167671690411098)⟩,⟨(-355951991002579608068),(-355951991002579594898)⟩⟩,⟨⟨(-8370110087498313567019),(-8370110087498313554408)⟩,⟨(-427333907323348657127),(-427333907323348644514)⟩⟩,⟨⟨(-7980306386228730730356),(-7980306386228730718267)⟩,⟨(-493186363288245608527),(-493186363288245596436)⟩⟩,⟨⟨(-7603323841306744609737),(-7603323841306744598161)⟩,⟨(-553661372029299918149),(-553661372029299906571)⟩⟩,⟨⟨(-7239048660603842226752),(-7239048660603842215673)⟩,⟨(-608918441860355402237),(-608918441860355391156)⟩⟩,⟨⟨(-6887347819621439283128),(-6887347819621439272552)⟩,⟨(-659123662592515195977),(-659123662592515185400)⟩⟩,⟨⟨(-6548070390855007748864),(-6548070390855007738740)⟩,⟨(-704448808641719543982),(-704448808641719533856)⟩⟩,⟨⟨(-6221048860408195765641),(-6221048860408195755970)⟩,⟨(-745070462465728305526),(-745070462465728295853)⟩⟩,⟨⟨(-5906100427304427155480),(-5906100427304427146267)⟩,⟨(-781169161581596317555),(-781169161581596308340)⟩⟩,⟨⟨(-5603028281305409491254),(-5603028281305409482459)⟩,⟨(-812928572121868362964),(-812928572121868354167)⟩⟩,⟨⟨(-5311622855407891974943),(-5311622855407891966551)⟩,⟨(-840534691590625210283),(-840534691590625201887)⟩⟩,⟨⟨(-5031663049549495522995),(-5031663049549495515010)⟩,⟨(-864175083181539742331),(-864175083181539734345)⟩⟩,⟨⟨(-4762917422409283668872),(-4762917422409283661260)⟩,⟨(-884038143721505125401),(-884038143721505117787)⟩⟩] +lemma kernel4_1_r1_4_eq : ∀ k : Fin 16, kernel4_1Expr 1 4 k = kernel4_1_r1_4 k := by decide +kernel +noncomputable def kernel4_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-4505145348536952580196),(-4505145348536952572961)⟩,⟨(-900312407007308448699),(-900312407007308441463)⟩⟩,⟨⟨(-4258098138384294151231),(-4258098138384294144349)⟩,⟨(-913185884011243855781),(-913185884011243848897)⟩⟩,⟨⟨(-4021520119142333944235),(-4021520119142333937706)⟩,⟨(-922845441146345693940),(-922845441146345687408)⟩⟩,⟨⟨(-3795149674605873115332),(-3795149674605873109114)⟩,⟨(-929476217504778552911),(-929476217504778546691)⟩⟩,⟨⟨(-3578720242592874673286),(-3578720242592874667380)⟩,⟨(-933261081715391249659),(-933261081715391243751)⟩⟩,⟨⟨(-3371961268738224747068),(-3371961268738224741484)⟩,⟨(-934380128809904884082),(-934380128809904878498)⟩⟩,⟨⟨(-3174599115759047810219),(-3174599115759047804933)⟩,⟨(-933010217242872051834),(-933010217242872046546)⟩⟩,⟨⟨(-2986357927551314836099),(-2986357927551314831089)⟩,⟨(-929324545979456958258),(-929324545979456953247)⟩⟩,⟨⟨(-2806960447724474316892),(-2806960447724474312143)⟩,⟨(-923492271348117716311),(-923492271348117711560)⟩⟩,⟨⟨(-2636128792411932118522),(-2636128792411932114029)⟩,⟨(-915678163153129384956),(-915678163153129380462)⟩⟩,⟨⟨(-2473585177410225377148),(-2473585177410225372917)⟩,⟨(-906042299355113638952),(-906042299355113634719)⟩⟩,⟨⟨(-2319052599898628714738),(-2319052599898628710716)⟩,⟨(-894739798456725383525),(-894739798456725379502)⟩⟩,⟨⟨(-2172255475173769477076),(-2172255475173769473279)⟩,⟨(-881920588575624337405),(-881920588575624333607)⟩⟩,⟨⟨(-2032920229000793094828),(-2032920229000793091257)⟩,⟨(-867729212047923548189),(-867729212047923544617)⟩⟩,⟨⟨(-1900775846333988060519),(-1900775846333988057142)⟩,⟨(-852304664282415183143),(-852304664282415179766)⟩⟩,⟨⟨(-1775554377295916323540),(-1775554377295916320369)⟩,⟨(-835780265478859526056),(-835780265478859522884)⟩⟩] +lemma kernel4_1_r1_5_eq : ∀ k : Fin 16, kernel4_1Expr 1 5 k = kernel4_1_r1_5 k := by decide +kernel +noncomputable def kernel4_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-1656991401425437730682),(-1656991401425437727695)⟩,⟨(-818283563732203160213),(-818283563732203157226)⟩⟩,⟨⟨(-1544826451312068952914),(-1544826451312068950102)⟩,⟨(-799936267968378965360),(-799936267968378962546)⟩⟩,⟨⟨(-1438803396827434154906),(-1438803396827434152252)⟩,⟨(-780854209095851537158),(-780854209095851534503)⟩⟩,⟨⟨(-1338670791244746248339),(-1338670791244746245838)⟩,⟨(-761147327709741175778),(-761147327709741173276)⟩⟩,⟨⟨(-1244182180604938273745),(-1244182180604938271413)⟩,⟨(-740919686651549346347),(-740919686651549344015)⟩⟩,⟨⟨(-1155096377743904659262),(-1155096377743904657062)⟩,⟨(-720269506706518444260),(-720269506706518442060)⟩⟩,⟨⟨(-1071177702439990355607),(-1071177702439990353539)⟩,⟨(-699289223711737716888),(-699289223711737714821)⟩⟩,⟨⟨(-992196189175071655974),(-992196189175071654056)⟩,⟨(-678065565350463556840),(-678065565350463554921)⟩⟩,⟨⟨(-917927764026999848976),(-917927764026999847159)⟩,⟨(-656679645920933657291),(-656679645920933655473)⟩⟩,⟨⟨(-848154392226520317264),(-848154392226520315553)⟩,⟨(-635207077390377120115),(-635207077390377118403)⟩⟩,⟨⟨(-782664197918721341126),(-782664197918721339527)⟩,⟨(-613718095076100764615),(-613718095076100763015)⟩⟩,⟨⟨(-721251557668283682046),(-721251557668283680554)⟩,⟨(-592277696334606051240),(-592277696334606049748)⟩⟩,⟨⟨(-663717169239954024878),(-663717169239954023475)⟩,⟨(-570945790685805654333),(-570945790685805652931)⟩⟩,⟨⟨(-609868097171394269143),(-609868097171394267825)⟩,⟨(-549777359851719320639),(-549777359851719319323)⟩⟩,⟨⟨(-559517796635485129492),(-559517796635485128255)⟩,⟨(-528822626246708275536),(-528822626246708274299)⟩⟩,⟨⟨(-512486117063883851915),(-512486117063883850786)⟩,⟨(-508127228518552357777),(-508127228518552356648)⟩⟩] +lemma kernel4_1_r1_6_eq : ∀ k : Fin 16, kernel4_1Expr 1 6 k = kernel4_1_r1_6 k := by decide +kernel +noncomputable def kernel4_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-468599286973724268535),(-468599286973724267475)⟩,⟨(-487732402805708799445),(-487732402805708798384)⟩⟩,⟨⟨(-427689881405348605612),(-427689881405348604626)⟩,⟨(-467675168445173235560),(-467675168445173234576)⟩⟩,⟨⟨(-389596773341392678279),(-389596773341392677364)⟩,⟨(-447988516936785482760),(-447988516936785481845)⟩⟩,⟨⟨(-354165070436899514658),(-354165070436899513801)⟩,⟨(-428701603042917469301),(-428701603042917468446)⟩⟩,⟨⟨(-321246038346872825615),(-321246038346872824812)⟩,⟨(-409839936976622642489),(-409839936976622641687)⟩⟩,⟨⟨(-290697011892234403434),(-290697011892234402685)⟩,⟨(-391425576705932821577),(-391425576705932820828)⟩⟩,⟨⟨(-262381295257923578364),(-262381295257923577668)⟩,⟨(-373477319476521995318),(-373477319476521994623)⟩⟩,⟨⟨(-236168052368249512671),(-236168052368249512051)⟩,⟨(-356010891728924452910),(-356010891728924452292)⟩⟩,⟨⟨(-211932188534928305402),(-211932188534928304799)⟩,⟨(-339039136659449834952),(-339039136659449834349)⟩⟩,⟨⟨(-189554224422829955532),(-189554224422829954972)⟩,⟨(-322572198745478391784),(-322572198745478391225)⟩⟩,⟨⟨(-168920163327622756813),(-168920163327622756285)⟩,⟨(-306617704625588743546),(-306617704625588743019)⟩⟩,⟨⟨(-149921352708507361086),(-149921352708507360618)⟩,⟨(-291180939792654175270),(-291180939792654174803)⟩⟩,⟨⟨(-132454340868328343616),(-132454340868328343191)⟩,⟨(-276265020623370730665),(-276265020623370730242)⟩⟩,⟨⟨(-116420729622763540627),(-116420729622763540230)⟩,⟨(-261871061330420610195),(-261871061330420609798)⟩⟩,⟨⟨(-101727023750224793020),(-101727023750224792628)⟩,⟨(-247998335483436141645),(-247998335483436141254)⟩⟩,⟨⟨(-88284477964741346996),(-88284477964741346642)⟩,⟨(-234644431801958391331),(-234644431801958390978)⟩⟩] +lemma kernel4_1_r1_7_eq : ∀ k : Fin 16, kernel4_1Expr 1 7 k = kernel4_1_r1_7 k := by decide +kernel +noncomputable def kernel4_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-76008942105602686251),(-76008942105602685914)⟩,⟨(-221805403977560734662),(-221805403977560734324)⟩⟩,⟨⟨(-64820705190056048685),(-64820705190056048347)⟩,⟨(-209475914333144482693),(-209475914333144482357)⟩⟩,⟨⟨(-54644338929012820878),(-54644338929012820541)⟩,⟨(-197649371175054404792),(-197649371175054404454)⟩⟩,⟨⟨(-45408541260628413338),(-45408541260628413021)⟩,⟨(-186318059738078131560),(-186318059738078131244)⟩⟩,⟨⟨(-37045980412877625099),(-37045980412877624798)⟩,⟨(-175473266664582036056),(-175473266664582035758)⟩⟩,⟨⟨(-29493139963932943041),(-29493139963932942742)⟩,⟨(-165105397997017595028),(-165105397997017594729)⟩⟩,⟨⟨(-22690165328334189738),(-22690165328334189438)⟩,⟨(-155204090697847664899),(-155204090697847664599)⟩⟩,⟨⟨(-16580712057669326504),(-16580712057669326227)⟩,⟨(-145758317742651424164),(-145758317742651423886)⟩⟩,⟨⟨(-11111796306811207362),(-11111796306811207095)⟩,⟨(-136756486860846181392),(-136756486860846181125)⟩⟩,⟨⟨(-6233647780705972933),(-6233647780705972688)⟩,⟨(-128186533024204306443),(-128186533024204306198)⟩⟩,⟨⟨(-1899565442307830064),(-1899565442307829818)⟩,⟨(-120036004806246871024),(-120036004806246870779)⟩⟩,⟨⟨1934223770484818390,1934223770484818613⟩,⟨(-112292144755775058128),(-112292144755775057905)⟩⟩,⟨⟨5308703002111069266,5308703002111069511⟩,⟨(-104941963945377262044),(-104941963945377261798)⟩⟩,⟨⟨8262200123478033483,8262200123478033711⟩,⟨(-97972310870851926071),(-97972310870851925841)⟩⟩,⟨⟨10830518803331096386,10830518803331096587⟩,⟨(-91369934890246447055),(-91369934890246446854)⟩⟩,⟨⟨13047065873379815392,13047065873379815600⟩,⟨(-85121544401767326522),(-85121544401767326316)⟩⟩] +lemma kernel4_1_r1_8_eq : ∀ k : Fin 16, kernel4_1Expr 1 8 k = kernel4_1_r1_8 k := by decide +kernel +noncomputable def kernel4_1_r1_9 : Fin 16 → CBox := ![⟨⟨14942974878208100488,14942974878208100701⟩,⟨(-79213859968304731044),(-79213859968304730831)⟩⟩,⟨⟨16547225723925899868,16547225723925900052⟩,⟨(-73633662602875200778),(-73633662602875200592)⟩⟩,⟨⟨17886760360896744658,17886760360896744826⟩,⟨(-68367837434058641327),(-68367837434058641159)⟩⟩,⟨⟨18986594455738105688,18986594455738105895⟩,⟨(-63403412973627934674),(-63403412973627934465)⟩⟩,⟨⟨19869925026180160430,19869925026180160627⟩,⟨(-58727596210177346288),(-58727596210177346093)⟩⟩,⟨⟨20558234029327037043,20558234029327037229⟩,⟨(-54327803752782291544),(-54327803752782291360)⟩⟩,⟨⟨21071387909439409877,21071387909439410039⟩,⟨(-50191689247697237332),(-50191689247697237168)⟩⟩,⟨⟨21427733125597296482,21427733125597296644⟩,⟨(-46307167288945638924),(-46307167288945638760)⟩⟩,⟨⟨21644187692557792265,21644187692557792433⟩,⟨(-42662434040496229692),(-42662434040496229523)⟩⟩,⟨⟨21736328779846544980,21736328779846545142⟩,⟨(-39245984783668985731),(-39245984783668985566)⟩⟩,⟨⟨21718476424667462990,21718476424667463135⟩,⟨(-36046628598581549833),(-36046628598581549684)⟩⟩,⟨⟨21603773423636752354,21603773423636752507⟩,⟨(-33053500382937032053),(-33053500382937031902)⟩⟩,⟨⟨21404261476699698922,21404261476699699053⟩,⟨(-30256070405365284292),(-30256070405365284163)⟩⟩,⟨⟨21130953663926698779,21130953663926698911⟩,⟨(-27644151583954401952),(-27644151583954401823)⟩⟩,⟨⟨20793903342263907907,20793903342263908038⟩,⟨(-25207904673633769115),(-25207904673633768986)⟩⟩,⟨⟨20402269554788256436,20402269554788256568⟩,⟨(-22937841538774862800),(-22937841538774862671)⟩⟩] +lemma kernel4_1_r1_9_eq : ∀ k : Fin 16, kernel4_1Expr 1 9 k = kernel4_1_r1_9 k := by decide +kernel +noncomputable def kernel4_1_r1_10 : Fin 16 → CBox := ![⟨⟨19964379049640674336,19964379049640674443⟩,⟨(-20824826679835742361),(-20824826679835742252)⟩⟩,⟨⟨19487785009638699096,19487785009638699227⟩,⟨(-18860077175158274998),(-18860077175158274869)⟩⟩,⟨⟨18979322596652766807,18979322596652766898⟩,⟨(-17035161191196545065),(-17035161191196544974)⟩⟩,⟨⟨18445161417220929081,18445161417220929195⟩,⟨(-15341995206567823881),(-15341995206567823767)⟩⟩,⟨⟨17890855017624759203,17890855017624759294⟩,⟨(-13772840087425778932),(-13772840087425778840)⟩⟩,⟨⟨17321387517803704953,17321387517803705044⟩,⟨(-12320296143805907062),(-12320296143805906971)⟩⟩,⟨⟨16741217494093527167,16741217494093527258⟩,⟨(-10977297288827104718),(-10977297288827104627)⟩⟩,⟨⟨16154319220882544512,16154319220882544596⟩,⟨(-9737104414987706820),(-9737104414987706733)⟩⟩,⟨⟨15564221380931332284,15564221380931332376⟩,⟨(-8593298094301561795),(-8593298094301561704)⟩⟩,⟨⟨14974043353339686480,14974043353339686587⟩,⟨(-7539770701707829599),(-7539770701707829490)⟩⟩,⟨⟨14386529187009653767,14386529187009653858⟩,⟨(-6570718054081230476),(-6570718054081230384)⟩⟩,⟨⟨13804079365983984526,13804079365983984618⟩,⟨(-5680630650287716886),(-5680630650287716795)⟩⟩,⟨⟨13228780471272349077,13228780471272349168⟩,⟨(-4864284591090762473),(-4864284591090762382)⟩⟩,⟨⟨12662432841748033417,12662432841748033509⟩,⟨(-4116732251329189041),(-4116732251329188950)⟩⟩,⟨⟨12106576334438658181,12106576334438658265⟩,⟨(-3433292770669209724),(-3433292770669209637)⟩⟩,⟨⟨11562514282076900775,11562514282076900866⟩,⟨(-2809542423388933727),(-2809542423388933636)⟩⟩] +lemma kernel4_1_r1_10_eq : ∀ k : Fin 16, kernel4_1Expr 1 10 k = kernel4_1_r1_10 k := by decide +kernel +noncomputable def kernel4_1_r1_11 : Fin 16 → CBox := ![⟨⟨11031335743150514157,11031335743150514249⟩,⟨(-2241304922088213745),(-2241304922088213654)⟩⟩,⟨⟨10513936136922525823,10513936136922525896⟩,⟨(-1724641704933407558),(-1724641704933407482)⟩⟩,⟨⟨10011036353007927067,10011036353007927158⟩,⟨(-1255842251046290236),(-1255842251046290145)⟩⟩,⟨⟨9523200422116185285,9523200422116185361⟩,⟨(-831414463928072223),(-831414463928072150)⟩⟩,⟨⟨9050851831521523405,9050851831521523497⟩,⟨(-448075158370688281),(-448075158370688189)⟩⟩,⟨⟨8594288565725402459,8594288565725402550⟩,⟨(-102740682144207665),(-102740682144207573)⟩⟩,⟨⟨8153696949646634307,8153696949646634365⟩,⟨207482300143899338,207482300143899396⟩⟩,⟨⟨7729164368531072611,7729164368531072664⟩,⟨485305837251197855,485305837251197905⟩⟩,⟨⟨7320690935630361661,7320690935630361723⟩,⟨733269515170769044,733269515170769109⟩⟩,⟨⟨6928200175571771953,6928200175571772022⟩,⟨953749057400442872,953749057400442941⟩⟩,⟨⟨6551548788241315464,6551548788241315530⟩,⟨1148964687226188810,1148964687226188882⟩⟩,⟨⟨6190535554941363932,6190535554941363978⟩,⟨1320989240289361562,1320989240289361609⟩⟩,⟨⟨5844909445571867569,5844909445571867660⟩,⟨1471756018141053619,1471756018141053710⟩⟩,⟨⟨5514376982629763926,5514376982629763999⟩,⟨1603066375709587715,1603066375709587791⟩⟩,⟨⟨5198608914931911928,5198608914931911990⟩,⟨1716597037629350851,1716597037629350916⟩⟩,⟨⟨4897246251149458929,4897246251149459005⟩,⟨1813907140211004387,1813907140211004460⟩⟩] +lemma kernel4_1_r1_11_eq : ∀ k : Fin 16, kernel4_1Expr 1 11 k = kernel4_1_r1_11 k := by decide +kernel +noncomputable def kernel4_1_r1_12 : Fin 16 → CBox := ![⟨⟨4609905700501519006,4609905700501519082⟩,⟨1896444997484901069,1896444997484901143⟩⟩,⟨⟨4336184565298056637,4336184565298056729⟩,⟨1965554591231570941,1965554591231571033⟩⟩,⟨⟨4075665127449711112,4075665127449711185⟩,⟨2022481786235566896,2022481786235566972⟩⟩,⟨⟨3827918568578946202,3827918568578946294⟩,⟨2068380273171797076,2068380273171797168⟩⟩,⟨⟨3592508460974618415,3592508460974618473⟩,⟨2104317242566524846,2104317242566524904⟩⟩,⟨⟨3368993864332396480,3368993864332396538⟩,⟨2131278794178049580,2131278794178049638⟩⟩,⟨⟨3156932061017398764,3156932061017398830⟩,⟨2150175086923981300,2150175086923981373⟩⟩,⟨⟨2955880960473342615,2955880960473342680⟩,⟨2161845235151968057,2161845235151968129⟩⟩,⟨⟨2765401201384321759,2765401201384321805⟩,⟨2167061957617377128,2167061957617377174⟩⟩,⟨⟨2585057978270487771,2585057978270487818⟩,⟨2166535986003073443,2166535986003073489⟩⟩,⟨⟨2414422617366454360,2414422617366454413⟩,⟨2160920240201018449,2160920240201018500⟩⟩,⟨⟨2253073924889853351,2253073924889853424⟩,⟨2150813777880500566,2150813777880500632⟩⟩,⟨⟨2100599329155522045,2100599329155522096⟩,⟨2136765526100592645,2136765526100592699⟩⟩,⟨⟨1956595836426394721,1956595836426394768⟩,⟨2119277802891722183,2119277802891722230⟩⟩,⟨⟨1820670818913173025,1820670818913173097⟩,⟨2098809636839463157,2098809636839463222⟩⟩,⟨⟨1692442651938929981,1692442651938930047⟩,⟨2075779892758863659,2075779892758863732⟩⟩] +lemma kernel4_1_r1_12_eq : ∀ k : Fin 16, kernel4_1Expr 1 12 k = kernel4_1_r1_12 k := by decide +kernel +noncomputable def kernel4_1_r1_13 : Fin 16 → CBox := ![⟨⟨1571541215969468040,1571541215969468094⟩,⟨2050570211555484665,2050570211555484715⟩⟩,⟨⟨1457608277972871386,1457608277972871460⟩,⟨2023527772335152428,2023527772335152504⟩⟩,⟨⟨1350297765409534976,1350297765409535023⟩,⟨1994967884753166305,1994967884753166351⟩⟩,⟨⟨1249275945064202557,1249275945064202603⟩,⟨1965176419489957623,1965176419489957669⟩⟩,⟨⟨1154221517911335674,1154221517911335747⟩,⟨1934412084608225870,1934412084608225947⟩⟩,⟨⟨1064825640251558954,1064825640251559012⟩,⟨1902908555390322141,1902908555390322199⟩⟩,⟨⟨980791880467068850,980791880467068896⟩,⟨1870876465077731375,1870876465077731422⟩⟩,⟨⟨901836119914833131,901836119914833185⟩,⟨1838505263740249617,1838505263740249667⟩⟩,⟨⟨827686405705252246,827686405705252297⟩,⟨1805964952293898097,1805964952293898151⟩⟩,⟨⟨758082762397830559,758082762397830605⟩,⟨1773407698466531682,1773407698466531728⟩⟩,⟨⟨692776968981496680,692776968981496753⟩,⟨1740969341280994933,1740969341280995010⟩⟩,⟨⟨631532306892744006,631532306892744064⟩,⟨1708770790389822079,1708770790389822137⟩⟩,⟨⟨574123284257032906,574123284257032964⟩,⟨1676919326354906982,1676919326354907040⟩⟩,⟨⟨520335341015268828,520335341015268882⟩,⟨1645509807722109496,1645509807722109547⟩⟩,⟨⟨469964539115085801,469964539115085847⟩,⟨1614625790496037362,1614625790496037409⟩⟩,⟨⟨422817241503651814,422817241503651864⟩,⟨1584340565375685648,1584340565375685702⟩⟩] +lemma kernel4_1_r1_13_eq : ∀ k : Fin 16, kernel4_1Expr 1 13 k = kernel4_1_r1_13 k := by decide +kernel +noncomputable def kernel4_1_r1_14 : Fin 16 → CBox := ![⟨⟨378709783252376900,378709783252376947⟩,⟨1554718117868486638,1554718117868486684⟩⟩,⟨⟨337468137771951876,337468137771951926⟩,⟨1525814016159723128,1525814016159723182⟩⟩,⟨⟨298927580736366649,298927580736366703⟩,⟨1497676231377134490,1497676231377134540⟩⟩,⟨⟨262932354024837358,262932354024837408⟩,⟨1470345894657709653,1470345894657709707⟩⟩,⟨⟨229335331708895240,229335331708895287⟩,⟨1443857995195797098,1443857995195797145⟩⟩,⟨⟨197997689856328304,197997689856328358⟩,⟨1418242023229335824,1418242023229335874⟩⟩,⟨⟨168788581692391952,168788581692392025⟩,⟨1393522561704685813,1393522561704685879⟩⟩,⟨⟨141584819449976920,141584819449976993⟩,⟨1369719830150572045,1369719830150572122⟩⟩,⟨⟨116270564052595822,116270564052595868⟩,⟨1346850184088331021,1346850184088331067⟩⟩,⟨⟨92737023605567381,92737023605567431⟩,⟨1324926573109157470,1324926573109157524⟩⟩,⟨⟨70882161520169479,70882161520169537⟩,⟨1303958960559515996,1303958960559516054⟩⟩,⟨⟨50610414961413600,50610414961413650⟩,⟨1283954707593365493,1283954707593365547⟩⟩,⟨⟨31832424191164854,31832424191164901⟩,⟨1264918924174347299,1264918924174347345⟩⟩,⟨⟨14464773273365912,14464773273365985⟩,⟨1246854789442558705,1246854789442558770⟩⟩,⟨⟨(-1570257484021735),(-1570257484021688)⟩,⟨1229763843698876560,1229763843698876606⟩⟩,⟨⟨(-16344927056148101),(-16344927056148043)⟩,⟨1213646254104874179,1213646254104874237⟩⟩] +lemma kernel4_1_r1_14_eq : ∀ k : Fin 16, kernel4_1Expr 1 14 k = kernel4_1_r1_14 k := by decide +kernel +noncomputable def kernel4_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-29926256972923712),(-29926256972923662)⟩,⟨1198501056048017209,1198501056048017263⟩⟩,⟨⟨(-42376242170492692),(-42376242170492642)⟩,⟨1184326371979825031,1184326371979825085⟩⟩,⟨⟨(-53752049308760970),(-53752049308760904)⟩,⟨1171119609398814920,1171119609398814982⟩⟩,⟨⟨(-64106202484026476),(-64106202484026418)⟩,⟨1158877639520050303,1158877639520050361⟩⟩,⟨⟨(-73486756301217359),(-73486756301217305)⟩,⟨1147596958048716623,1147596958048716673⟩⟩,⟨⟨(-81937456299058930),(-81937456299058875)⟩,⟨1137273829356058835,1137273829356058885⟩⟩,⟨⟨(-89497886744315609),(-89497886744315551)⟩,⟨1127904415241921436,1127904415241921494⟩⟩,⟨⟨(-96203605828705686),(-96203605828705636)⟩,⟨1119484889358718576,1119484889358718631⟩⟩,⟨⟨(-102086268314734651),(-102086268314734600)⟩,⟨1112011538266596060,1112011538266596114⟩⟩,⟨⟨(-107173735685070213),(-107173735685070159)⟩,⟨1105480849988489381,1105480849988489431⟩⟩,⟨⟨(-111490173854688121),(-111490173854688063)⟩,⟨1099889590836383993,1099889590836384051⟩⟩,⟨⟨(-115056138506316236),(-115056138506316178)⟩,⟨1095234871185996186,1095234871185996244⟩⟩,⟨⟨(-117888648108136423),(-117888648108136365)⟩,⟨1091514200785953242,1091514200785953300⟩⟩,⟨⟨(-120001244668679445),(-120001244668679390)⟩,⟨1088725534099000897,1088725534099000948⟩⟩,⟨⟨(-121404042277759578),(-121404042277759520)⟩,⟨1086867306086439009,1086867306086439067⟩⟩,⟨⟨(-122103763474516572),(-122103763474516514)⟩,⟨1085938458762514228,1085938458762514286⟩⟩] +lemma kernel4_1_r1_15_eq : ∀ k : Fin 16, kernel4_1Expr 1 15 k = kernel4_1_r1_15 k := by decide +kernel +noncomputable def kernel4_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel4_1_r1_0,kernel4_1_r1_1,kernel4_1_r1_2,kernel4_1_r1_3,kernel4_1_r1_4,kernel4_1_r1_5,kernel4_1_r1_6,kernel4_1_r1_7,kernel4_1_r1_8,kernel4_1_r1_9,kernel4_1_r1_10,kernel4_1_r1_11,kernel4_1_r1_12,kernel4_1_r1_13,kernel4_1_r1_14,kernel4_1_r1_15] +lemma kernel4_1_r1_eq (i k : Fin 16) : kernel4_1Expr 1 i k = kernel4_1_r1 i k := by + fin_cases i + · exact kernel4_1_r1_0_eq k + · exact kernel4_1_r1_1_eq k + · exact kernel4_1_r1_2_eq k + · exact kernel4_1_r1_3_eq k + · exact kernel4_1_r1_4_eq k + · exact kernel4_1_r1_5_eq k + · exact kernel4_1_r1_6_eq k + · exact kernel4_1_r1_7_eq k + · exact kernel4_1_r1_8_eq k + · exact kernel4_1_r1_9_eq k + · exact kernel4_1_r1_10_eq k + · exact kernel4_1_r1_11_eq k + · exact kernel4_1_r1_12_eq k + · exact kernel4_1_r1_13_eq k + · exact kernel4_1_r1_14_eq k + · exact kernel4_1_r1_15_eq k +noncomputable def kernel4_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-118733717689751236616078624),(-118733717689751236506630752)⟩,⟨(-47060400123308783708467101),(-47060400123308783598731479)⟩⟩,⟨⟨(-118684513664673680689207995),(-118684513664673680579795447)⟩,⟨(-47021506007238313158460891),(-47021506007238313048760820)⟩⟩,⟨⟨(-118586158476628647534120954),(-118586158476628647424779270)⟩,⟨(-46943799671149651092697049),(-46943799671149650983068302)⟩⟩,⟨⟨(-118438757795350875268878527),(-118438757795350875159643149)⟩,⟨(-46827444648678469189341512),(-46827444648678469079819758)⟩⟩,⟨⟨(-118242469989027699929859027),(-118242469989027699820765358)⟩,⟨(-46672685595130043829274163),(-46672685595130043719895030)⟩⟩,⟨⟨(-117997505960041156838706211),(-117997505960041156729789502)⟩,⟨(-46479847516164093886183752),(-46479847516164093776982710)⟩⟩,⟨⟨(-117704128925033547031957356),(-117704128925033546923252734)⟩,⟨(-46249334744132445717617384),(-46249334744132445608629789)⟩⟩,⟨⟨(-117362654138523889767631019),(-117362654138523889659173421)⟩,⟨(-45981629666121139989401463),(-45981629666121139880662467)⟩⟩,⟨⟨(-116973448559133477868327386),(-116973448559133477760151557)⟩,⟨(-45677291208728403997268456),(-45677291208728403888813024)⟩⟩,⟨⟨(-116536930457325152026367897),(-116536930457325151918508325)⟩,⟨(-45336953085567841210596364),(-45336953085567841102459190)⟩⟩,⟨⟨(-116053568963425681458273880),(-116053568963425681350764813)⟩,⟨(-44961321814418042920901524),(-44961321814418042813117068)⟩⟩,⟨⟨(-115523883554586362860574226),(-115523883554586362753449591)⟩,⟨(-44551174511841510773888068),(-44551174511841510666490458)⟩⟩,⟨⟨(-114948443479245995298466189),(-114948443479245995191759662)⟩,⟨(-44107356473963315503274545),(-44107356473963315396297657)⟩⟩,⟨⟨(-114327867117594884913864753),(-114327867117594884807609575)⟩,⟨(-43630778552929461223571684),(-43630778552929461117048946)⟩⟩,⟨⟨(-113662821276500348727996575),(-113662821276500348622225723)⟩,⟨(-43122414339352780644563128),(-43122414339352780538527713)⟩⟩,⟨⟨(-112954020417344908860563967),(-112954020417344908755309831)⟩,⟨(-42583297161796825211097551),(-42583297161796825105582024)⟩⟩] +lemma kernel4_1_r2_0_eq : ∀ k : Fin 16, kernel4_1Expr 2 0 k = kernel4_1_r2_0 k := by decide +kernel +noncomputable def kernel4_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-112202225815249286167725322),(-112202225815249286063020141)⟩,⟨(-42014516915042288789612930),(-42014516915042288684649705)⟩⟩,⟨⟨(-111408244648204391311736158),(-111408244648204391207611390)⟩,⟨(-41417216729522866422443168),(-41417216729522866318063868)⟩⟩,⟨⟨(-110572929014720422242371478),(-110572929014720422138858441)⟩,⟨(-40792589494905168155557490),(-40792589494905168051793593)⟩⟩,⟨⟨(-109697174878717226816143828),(-109697174878717226713272937)⟩,⟨(-40141874251317680011536455),(-40141874251317679908418531)⟩⟩,⟨⟨(-108781920940528255242772113),(-108781920940528255140573766)⟩,⟨(-39466352462204333776124215),(-39466352462204333673682805)⟩⟩,⟨⟨(-107828147433070344930009221),(-107828147433070344828512634)⟩,⟨(-38767344183186819010876712),(-38767344183186818909141172)⟩⟩,⟨⟨(-106836874842442544967327213),(-106836874842442544866561672)⟩,⟨(-38046204141664423939064878),(-38046204141664423838064620)⟩⟩,⟨⟨(-105809162552458157163990457),(-105809162552458157063983923)⟩,⟨(-37304317742159293919335717),(-37304317742159293819098825)⟩⟩,⟨⟨(-104746107412883774235088188),(-104746107412883774135868943)⟩,⟨(-36543097012627214821963373),(-36543097012627214722518241)⟩⟩,⟨⟨(-103648842231455643819425454),(-103648842231455643721019947)⟩,⟨(-35763976507098343120895614),(-35763976507098343022268797)⟩⟩,⟨⟨(-102518534190065185089272054),(-102518534190065184991707248)⟩,⟨(-34968409180088016054587941),(-34968409180088015956806498)⟩⟩,⟨⟨(-101356383185849650273489592),(-101356383185849650176790536)⟩,⟨(-34157862248224515489944949),(-34157862248224515393034009)⟩⟩,⟨⟨(-100163620098288205518969002),(-100163620098288205423161552)⟩,⟨(-33333813054478397703884047),(-33333813054478397607869551)⟩⟩,⟨⟨(-98941504983785307105563538),(-98941504983785307010670986)⟩,⟨(-32497744950247051274383513),(-32497744950247051179288817)⟩⟩,⟨⟨(-97691325199619151775956767),(-97691325199619151682003472)⟩,⟨(-31651143210349167217979120),(-31651143210349167123828646)⟩⟩,⟨⟨(-96414393459539971356834710),(-96414393459539971263842390)⟩,⟨(-30795490995717809519218985),(-30795490995717809426034506)⟩⟩] +lemma kernel4_1_r2_1_eq : ∀ k : Fin 16, kernel4_1Expr 2 1 k = kernel4_1_r2_1 k := by decide +kernel +noncomputable def kernel4_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-95112045823717644443331768),(-95112045823717644351323666)⟩,⟨(-29932265378249119945443631),(-29932265378249119853248430)⟩⟩,⟨⟨(-93785639626157000132298706),(-93785639626157000041294517)⟩,⟨(-29062933441868085736681649),(-29062933441868085645495456)⟩⟩,⟨⟨(-92436551343118677391095550),(-92436551343118677301116772)⟩,⟨(-28188948473415292906353486),(-28188948473415292816197828)⟩⟩,⟨⟨(-91066174406499797324239190),(-91066174406499797235303907)⟩,⟨(-27311746256441568766742621),(-27311746256441568677635595)⟩⟩,⟨⟨(-89675916966538289396320444),(-89675916966538289308449012)⟩,⟨(-26432741480423600132760591),(-26432741480423600044722567)⟩⟩,⟨⟨(-88267199608603772961326755),(-88267199608603772874534991)⟩,⟨(-25553324277286030437686442),(-25553324277286030350733236)⟩⟩,⟨⟨(-86841453029222755097213786),(-86841453029222755011520199)⟩,⟨(-24674856896437524873398721),(-24674856896437524787548840)⟩⟩,⟨⟨(-85400115676852959100328395),(-85400115676852959015747117)⟩,⟨(-23798670528803470047306019),(-23798670528803469962573578)⟩⟩,⟨⟨(-83944631363267345395697128),(-83944631363267345312245596)⟩,⟨(-22926062289570234908881482),(-22926062289570234825283897)⟩⟩,⟨⟨(-82476446851729468050142517),(-82476446851729467967832333)⟩,⟨(-22058292368549402664561956),(-22058292368549402582110798)⟩⟩,⟨⟨(-80997009428435037637488003),(-80997009428435037556334516)⟩,⟨(-21196581356229454620043515),(-21196581356229454538754099)⟩⟩,⟨⟨(-79507764463956950082150881),(-79507764463956950002164098)⟩,⟨(-20342107752711612850614584),(-20342107752711612770496872)⟩⟩,⟨⟨(-78010152971659838699431084),(-78010152971659838620625323)⟩,⟨(-19496005665830670006552822),(-19496005665830669927621088)⟩⟩,⟨⟨(-76505609170242919586699287),(-76505609170242919509081865)⟩,⟨(-18659362703845537845250163),(-18659362703845537767511662)⟩⟩,⟨⟨(-74995558057724319261756747),(-74995558057724319185339829)⟩,⟨(-17833218067152933340671882),(-17833218067152933264138723)⟩⟩,⟨⟨(-73481413004294294234492280),(-73481413004294294159281624)⟩,⟨(-17018560842536178780810467),(-17018560842536178705488340)⟩⟩] +lemma kernel4_1_r2_2_eq : ∀ k : Fin 16, kernel4_1Expr 2 2 k = kernel4_1_r2_2 k := by decide +kernel +noncomputable def kernel4_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-71964573371537196108688643),(-71964573371537196034695593)⟩,⟨(-16216328502514658114888943),(-16216328502514658040789124)⟩⟩,⟨⟨(-70446422165551464709368142),(-70446422165551464636595527)⟩,⟨(-15427405611413202161876922),(-15427405611413202089002156)⟩⟩,⟨⟨(-68928323731482460975508938),(-68928323731482460903965670)⟩,⟨(-14652622738829710507160272),(-14652622738829710435519393)⟩⟩,⟨⟨(-67411621496924059099478272),(-67411621496924059029165875)⟩,⟨(-13892755580248748138902581),(-13892755580248748068497027)⟩⟩,⟨⟨(-65897635771541450377124137),(-65897635771541450308050730)⟩,⟨(-13148524283633685615332862),(-13148524283633685546170661)⟩⟩,⟨⟨(-64387661610119787033243312),(-64387661610119786965407522)⟩,⟨(-12420592979935069537057692),(-12420592979935069469137377)⟩⟩,⟨⟨(-62882966746051699964404641),(-62882966746051699897812229)⟩,⟨(-11709569514583049714478544),(-11709569514583049647805779)⟩⟩,⟨⟨(-61384789602042311509997611),(-61384789602042311444645919)⟩,⟨(-11016005376191400055334068),(-11016005376191399989906099)⟩⟩,⟨⟨(-59894337384534440741962506),(-59894337384534440677856871)⟩,⟨(-10340395817894284761747692),(-10340395817894284697569750)⟩⟩,⟨⟨(-58412784268040916292483913),(-58412784268040916229618565)⟩,⟨(-9683180165968526386751359),(-9683180165968526323817568)⟩⟩,⟨⟨(-56941269675217251378074119),(-56941269675217251316451757)⟩,⟨(-9044742309667539497706012),(-9044742309667539436018966)⟩⟩,⟨⟨(-55480896658118689073319774),(-55480896658118689012933791)⟩,⟨(-8425411365511814231178442),(-8425411365511814170731423)⟩⟩,⟨⟨(-54032730385663374077222077),(-54032730385663374018074775)⟩,⟨(-7825462508648054476097257),(-7825462508648054416892457)⟩⟩,⟨⟨(-52597796741870996627881236),(-52597796741870996569963054)⟩,⟨(-7245117963307636617554460),(-7245117963307636559582209)⟩⟩,⟨⟨(-51177081038966770206539452),(-51177081038966770149850237)⟩,⟨(-6684548143867433348890063),(-6684548143867433292150095)⟩⟩,⟨⟨(-49771526848937342862974662),(-49771526848937342807504101)⟩,⟨(-6143872937544339987901891),(-6143872937544339932383779)⟩⟩] +lemma kernel4_1_r2_3_eq : ∀ k : Fin 16, kernel4_1Expr 2 3 k = kernel4_1_r2_3 k := by decide +kernel +noncomputable def kernel4_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-48382034956601677802089220),(-48382034956601677747837259)⟩,⟨(-5623163119340752974353928),(-5623163119340752920057508)⟩⟩,⟨⟨(-47009462436719695448529354),(-47009462436719695395482503)⟩,⟨(-5122441889503085636159136),(-5122441889503085583070803)⟩⟩,⟨⟨(-45654621857108284212389678),(-45654621857108284160545138)⟩,⟨(-4641686523460061891819839),(-4641686523460061839936679)⟩⟩,⟨⟨(-44318280609171978718874936),(-44318280609171978668219080)⟩,⟨(-4180830123972492112912436),(-4180830123972492062220715)⟩⟩,⟨⟨(-43001160366688036345464787),(-43001160366688036295994830)⟩,⟨(-3739763465051586593794049),(-3739763465051586544290868)⟩⟩,⟨⟨(-41703936673116690799481329),(-41703936673116690751180866)⟩,⟨(-3318336917088277040174576),(-3318336917088276991843422)⟩⟩,⟨⟨(-40427238657140877305173364),(-40427238657140877258037239)⟩,⟨(-2916362442580775502348114),(-2916362442580775455183717)⟩⟩,⟨⟨(-39171648875579502992872161),(-39171648875579502946883830)⟩,⟨(-2533615651850598916665109),(-2533615651850598870650819)⟩⟩,⟨⟨(-37937703282268083826325627),(-37937703282268083781480491)⟩,⟨(-2169837908197051194446628),(-2169837908197051149577740)⟩⟩,⟨⟨(-36725891320963870187646364),(-36725891320963870143924962)⟩,⟨(-1824738472054855839935139),(-1824738472054855796192090)⟩⟩,⟨⟨(-35536656139812870270357802),(-35536656139812870227752876)⟩,⟨(-1497996673887109605547520),(-1497996673887109562922947)⟩⟩,⟨⟨(-34370394924416707820035105),(-34370394924416707778527746)⟩,⟨(-1189264105763510577066567),(-1189264105763510535541460)⟩⟩,⟨⟨(-33227459346061067703439584),(-33227459346061067663023033)⟩,⟨(-898166821839145856590717),(-898166821839145816158216)⟩⟩,⟨⟨(-32108156121217410160932811),(-32108156121217410121585685)⟩,⟨(-624307538258989954075453),(-624307538258989914714083)⟩⟩,⟨⟨(-31012747678008244185400636),(-31012747678008244147113997)⟩,⟨(-367267823364420992886074),(-367267823364420954586802)⟩⟩,⟨⟨(-29941452924935846976779105),(-29941452924935846939532063)⟩,⟨(-126610269467064720056250),(-126610269467064682798094)⟩⟩] +lemma kernel4_1_r2_4_eq : ∀ k : Fin 16, kernel4_1Expr 2 4 k = kernel4_1_r2_4 k := by decide +kernel +noncomputable def kernel4_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-28894448116816922416315388),(-28894448116816922380100116)⟩,⟨98119362121484614746330,98119362121484650971286⟩⟩,⟨⟨(-27871867812543035423464434),(-27871867812543035388257414)⟩,⟨307390030661788088139626,307390030661788123354985⟩⟩,⟨⟨(-26873805919000166291286455),(-26873805919000166257077377)⟩,⟨501683347537880835447251,501683347537880869663407⟩⟩,⟨⟨(-25900316815231516224749819),(-25900316815231516191516442)⟩,⟨681491556662040095778566,681491556662040129017840⟩⟩,⟨⟨(-24951416550716567458769614),(-24951416550716567426502549)⟩,⟨847315570085390912238466,847315570085390944510325⟩⟩,⟨⟨(-24027084111466852631418138),(-24027084111466852600093089)⟩,⟨999663064630059752094785,999663064630059783423599⟩⟩,⟨⟨(-23127262747505105094783814),(-23127262747505105064389457)⟩,⟨1139046644811027073331752,1139046644811027103728921⟩⟩,⟨⟨(-22251861355199329910854855),(-22251861355199329881368069)⟩,⟨1265982076761262417099184,1265982076761262446587894⟩⟩,⟨⟨(-21400755907866447631504569),(-21400755907866447602915464)⟩,⟨1380986597315935901228781,1380986597315935929818993⟩⟩,⟨⟨(-20573790928040832388784158),(-20573790928040832361067448)⟩,⟨1484577301854159493495766,1484577301854159521212825⟩⟩,⟨⟨(-19770780994820338730546778),(-19770780994820338703690469)⟩,⟨1577269613943351513705939,1577269613943351540561905⟩⟩,⟨⟨(-18991512279755084281143992),(-18991512279755084255124552)⟩,⟨1659575839285306140018762,1659575839285306166037219⟩⟩,⟨⟨(-18235744104830891940803401),(-18235744104830891915610078)⟩,⟨1732003805927568979903676,1732003805927569005095437⟩⟩,⟨⟨(-17503210516218248044474331),(-17503210516218248020082055)⟩,⟨1795055592181748791276410,1795055592181748815666594⟩⟩,⟨⟨(-16793621867607062829966521),(-16793621867607062806362929)⟩,⟨1849226343184692641598081,1849226343184692665199104⟩⟩,⟨⟨(-16106666407125419304162394),(-16106666407125419281324030)⟩,⟨1895003176551541423763199,1895003176551541446598561⟩⟩] +lemma kernel4_1_r2_5_eq : ∀ k : Fin 16, kernel4_1Expr 2 5 k = kernel4_1_r2_5 k := by decide +kernel +noncomputable def kernel4_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-15442011862044713397795275),(-15442011862044713375711570)⟩,⟨1932864177103843582646503,1932864177103843604726819⟩⟩,⟨⟨(-14799307015701847891389049),(-14799307015701847870034774)⟩,⟨1963277480213162110095394,1963277480213162131445933⟩⟩,⟨⟨(-14178183271319073285585280),(-14178183271319073264948014)⟩,⟨1986700442882728521158601,1986700442882728541791831⟩⟩,⟨⟨(-13578256197671225611903604),(-13578256197671225591960336)⟩,⟨2003578901298179766977946,2003578901298179786916907⟩⟩,⟨⟨(-12999127051835999805481986),(-12999127051835999786221763)⟩,⟨2014346513214498253015078,2014346513214498272270763⟩⟩,⟨⟨(-12440384274562997440116668),(-12440384274562997421515378)⟩,⟨2019424183210937684982234,2019424183210937703578786⟩⟩,⟨⟨(-11901604954109075918598890),(-11901604954109075900644315)⟩,⟨2019219568539676799543151,2019219568539676817492820⟩⟩,⟨⟨(-11382356254708497803718630),(-11382356254708497786388526)⟩,⟨2014126663017665938076221,2014126663017665955401278⟩⟩,⟨⟨(-10882196806174068371066390),(-10882196806174068354350374)⟩,⟨2004525456164841338181576,2004525456164841354892432⟩⟩,⟨⟨(-10400678051457449894970776),(-10400678051457449878845408)⟩,⟨1990781664575569234514826,1990781664575569250634945⟩⟩,⟨⟨(-9937345549330822565207514),(-9937345549330822549660982)⟩,⟨1973246532323615351808387,1973246532323615367349605⟩⟩,⟨⟨(-9491740229685787288945517),(-9491740229685787273956651)⟩,⟨1952256697043676118549940,1952256697043676133533445⟩⟩,⟨⟨(-9063399599276745793506475),(-9063399599276745779064992)⟩,⟨1928134118203923503069717,1928134118203923517505816⟩⟩,⟨⟨(-8651858896062940048598647),(-8651858896062940034682685)⟩,⟨1901186063983295573810021,1901186063983295587720589⟩⟩,⟨⟨(-8256652190624009690478765),(-8256652190624009677077108)⟩,⟨1871705153093438211713780,1871705153093438225110054⟩⟩,⟨⟨(-7877313433436597806193671),(-7877313433436597793286390)⟩,⟨1839969447837154146218639,1839969447837154159120559⟩⟩] +lemma kernel4_1_r2_6_eq : ∀ k : Fin 16, kernel4_1Expr 2 6 k = kernel4_1_r2_6 k := by decide +kernel +noncomputable def kernel4_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-7513377447102615914897121),(-7513377447102615902474909)⟩,⟨1806242594671701240134452,1806242594671701252551339⟩⟩,⟨⟨(-7164380862911836586694501),(-7164380862911836574736540)⟩,⟨1770774008544951320089685,1770774008544951332042369⟩⟩,⟨⟨(-6829863001401243617097743),(-6829863001401243605593512)⟩,⟨1733799097293831191574854,1733799097293831203073871⟩⟩,⟨⟨(-6509366696839922376122434),(-6509366696839922365053455)⟩,⟨1695539522436102444102723,1695539522436102455166555⟩⟩,⟨⟨(-6202439065820265331156018),(-6202439065820265320513302)⟩,⟨1656203492746823409934581,1656203492746823420572231⟩⟩,⟨⟨(-5908632220373108305845088),(-5908632220373108295609730)⟩,⟨1615986087088162575141233,1615986087088162585371607⟩⟩,⟨⟨(-5627503926245467802085687),(-5627503926245467792247979)⟩,⟨1575069603053961520360296,1575069603053961530193112⟩⟩,⟨⟨(-5358618207184338327810917),(-5358618207184338318353895)⟩,⟨1533623928096932315676042,1533623928096932325128271⟩⟩,⟨⟨(-5101545896258199295745290),(-5101545896258199286660955)⟩,⟨1491806929924980389962238,1491806929924980399041882⟩⟩,⟨⟨(-4855865135419284127740122),(-4855865135419284119010926)⟩,⟨1449764863082249783540219,1449764863082249792264831⟩⟩,⟨⟨(-4621161824664225242243885),(-4621161824664225233860988)⟩,⟨1407632788768505633921495,1407632788768505642299919⟩⟩,⟨⟨(-4397030022288480206453740),(-4397030022288480198401707)⟩,⟨1365535005095853941474516,1365535005095853949522186⟩⟩,⟨⟨(-4183072297851157424687880),(-4183072297851157416959268)⟩,⟨1323585485133059331639782,1323585485133059339364148⟩⟩,⟨⟨(-3978900039571794297616314),(-3978900039571794290195471)⟩,⟨1281888320243427776210635,1281888320243427783627348⟩⟩,⟨⟨(-3784133717969696172007588),(-3784133717969696164886525)⟩,⟨1240538166381012725045125,1240538166381012732162178⟩⟩,⟨⟨(-3598403107630109332175289),(-3598403107630109325340149)⟩,⟨1199620691170495535593633,1199620691170495542424878⟩⟩] +lemma kernel4_1_r2_7_eq : ∀ k : Fin 16, kernel4_1Expr 2 7 k = kernel4_1_r2_7 k := by decide +kernel +noncomputable def kernel4_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-3421347469040343708411832),(-3421347469040343701856225)⟩,⟨1159213019757281508912766,1159213019757281515464599⟩⟩,⟨⟨(-3252615692483617866163925),(-3252615692483617859873487)⟩,⟨1119384177575023759817258,1119384177575023766104037⟩⟩,⟨⟨(-3091866406009566055823521),(-3091866406009566049791175)⟩,⟨1080195528336909585148822,1080195528336909591177627⟩⟩,⟨⟨(-2938768049518769438802609),(-2938768049518769433015973)⟩,⟨1041701205713679442878180,1041701205713679448661392⟩⟩,⟨⟨(-2792998917005135075816192),(-2792998917005135070269355)⟩,⟨1003948537314650056402815,1003948537314650061946345⟩⟩,⟨⟨(-2654247168995260746687223),(-2654247168995260741367702)⟩,⟨966978459737224929566706,966978459737224934883031⟩⟩,⟨⟨(-2522210817208925963742036),(-2522210817208925958643562)⟩,⟨930825923594832761883290,930825923594832766978682⟩⟩,⟨⟨(-2396597683440386892446796),(-2396597683440386887558397)⟩,⟨895520287572360979793001,895520287572360984678428⟩⟩,⟨⟨(-2277125334627077068844012),(-2277125334627077064160764)⟩,⟨861085700691458639538243,861085700691458644218628⟩⟩,⟨⟨(-2163520996031475723367941),(-2163520996031475718878583)⟩,⟨827541472095164847950134,827541472095164852436733⟩⟩,⟨⟨(-2055521444414140497940516),(-2055521444414140493639600)⟩,⟨794902427781850376772059,794902427781850381070321⟩⟩,⟨⟨(-1952872883022034952883791),(-1952872883022034948761656)⟩,⟨763179253832192389077567,763179253832192393197147⟩⟩,⟨⟨(-1855330800157115843773803),(-1855330800157115839826059)⟩,⟨732378825779658172184363,732378825779658176129652⟩⟩,⟨⟨(-1762659813026456966048858),(-1762659813026456962265767)⟩,⟨702504523874643792429677,702504523874643796210409⟩⟩,⟨⟨(-1674633498507721385505413),(-1674633498507721381882275)⟩,⟨673556534084950378953107,673556534084950382573980⟩⟩,⟨⟨(-1591034212393264196069179),(-1591034212393264192597584)⟩,⟨645532134760694403151186,645532134760694406620605⟩⟩] +lemma kernel4_1_r2_8_eq : ∀ k : Fin 16, kernel4_1Expr 2 8 k = kernel4_1_r2_8 k := by decide +kernel +noncomputable def kernel4_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-1511652898603228839179571),(-1511652898603228835855921)⟩,⟨618425968970101182683739,618425968970101186005304⟩⟩,⟨⟨(-1436288889783327544055286),(-1436288889783327540870943)⟩,⟨592230302584032309084697,592230302584032312267038⟩⟩,⟨⟨(-1364749700627165653992778),(-1364749700627165650943653)⟩,⟨566935268251699111041227,566935268251699114088433⟩⟩,⟨⟨(-1296850815186533253481729),(-1296850815186533250560564)⟩,⟨542529095468003818229289,542529095468003821148614⟩⟩,⟨⟨(-1232415469356555304680422),(-1232415469356555301883983)⟩,⟨518998326984547898298861,518998326984547901093538⟩⟩,⟨⟨(-1171274429646429765756642),(-1171274429646429763077632)⟩,⟨496328021861800350049168,496328021861800352726490⟩⟩,⟨⟨(-1113265769271114958502359),(-1113265769271114955937296)⟩,⟨474501945499497342048900,474501945499497344612349⟩⟩,⟨⟨(-1058234642525133068049934),(-1058234642525133065592560)⟩,⟨453502747016336460523689,453502747016336462979516⟩⟩,⟨⟨(-1006033058326974446372531),(-1006033058326974444020258)⟩,⟨433312124378736009616057,433312124378736011966852⟩⟩,⟨⟨(-956519653751714907998050),(-956519653751714905744420)⟩,⟨413910977702164539645651,413910977702164541897866⟩⟩,⟨⟨(-909559468300653604797223),(-909559468300653602639363)⟩,⟨395279551167626955506823,395279551167626957663331⟩⟩,⟨⟨(-865023719590262721913706),(-865023719590262719846204)⟩,⟨377397564010643427833091,377397564010643429899301⟩⟩,⟨⟨(-822789581078696549829231),(-822789581078696547849825)⟩,⟨360244331050798515832984,360244331050798517811154⟩⟩,⟨⟨(-782739962386686839524372),(-782739962386686837627658)⟩,⟨343798873236990711922833,343798873236990713818365⟩⟩,⟨⟨(-744763292710972167129672),(-744763292710972165313191)⟩,⟨328040018687192610730163,328040018687192612545516⟩⟩,⟨⟨(-708753307772559947168040),(-708753307772559945427215)⟩,⟨312946494702147827180707,312946494702147828920455⟩⟩] +lemma kernel4_1_r2_9_eq : ∀ k : Fin 16, kernel4_1Expr 2 9 k = kernel4_1_r2_9 k := by decide +kernel +noncomputable def kernel4_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-674608840689161763466460),(-674608840689161761799541)⟩,⟨298497011230282706475010,298497011230282708140900⟩⟩,⟨⟨(-642233617111111483534116),(-642233617111111481936339)⟩,⟨284670336256488609490402,284670336256488611087197⟩⟩,⟨⟨(-611536054912983686600012),(-611536054912983685069342)⟩,⟨271445363580612397994932,271445363580612399524664⟩⟩,⟨⟨(-582429068688968825516886),(-582429068688968824049416)⟩,⟨258801173442744344682892,258801173442744346149467⟩⟩,⟨⟨(-554829879258804036031540),(-554829879258804034625742)⟩,⟨246717086441966255379445,246717086441966256784388⟩⟩,⟨⟨(-528659828352660706536617),(-528659828352660705188519)⟩,⟨235172711183356229179443,235172711183356230526726⟩⟩,⟨⟨(-503844198607793287137788),(-503844198607793285845731)⟩,⟨224147986074963789880223,224147986074963791171502⟩⟩,⟨⟨(-480312038976887112756131),(-480312038976887111516777)⟩,⟨213623215682378913591173,213623215682378914829784⟩⟩,⟨⟨(-457995995617824160670517),(-457995995617824159482718)⟩,⟨203579102033614694324456,203579102033614695511548⟩⟩,⟨⟨(-436832148306923483290177),(-436832148306923482150480)⟩,⟨193996771251485147811562,193996771251485148950583⟩⟩,⟨⟨(-416759852392508922147737),(-416759852392508921054767)⟩,⟨184857795874651421068996,184857795874651422161323⟩⟩,⟨⟨(-397721586282806062970249),(-397721586282806061921175)⟩,⟨176144213212181556727528,176144213212181557775986⟩⟩,⟨⟨(-379662804441564164365995),(-379662804441564163359868)⟩,⟨167838540059957084150762,167838540059957085156303⟩⟩,⟨⟨(-362531795846324698555253),(-362531795846324697589172)⟩,⟨159923784090686687184483,159923784090686688150005⟩⟩,⟨⟨(-346279547847801862075112),(-346279547847801861147981)⟩,⟨152383452212762662670033,152383452212762663596630⟩⟩,⟨⟨(-330859615354286663214587),(-330859615354286662323997)⟩,⟨145201556176817070406080,145201556176817071296159⟩⟩] +lemma kernel4_1_r2_10_eq : ∀ k : Fin 16, kernel4_1Expr 2 10 k = kernel4_1_r2_10 k := by decide +kernel +noncomputable def kernel4_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-316227995252219679702060),(-316227995252219678847313)⟩,⟨138362615692686852890560,138362615692686853744823⟩⟩,⟨⟨(-302343005962983857738395),(-302343005962983856916977)⟩,⟨131851659303655132982764,131851659303655133803718⟩⟩,⟨⟨(-289165172026434936511906),(-289165172026434935722905)⟩,⟨125654223249363314030816,125654223249363314819374⟩⟩,⟨⟨(-276657113593602617712178),(-276657113593602616953580)⟩,⟨119756348533739710027046,119756348533739710785222⟩⟩,⟨⟨(-264783440704252643189094),(-264783440704252642460331)⟩,⟨114144576399710385442682,114144576399710386171042⟩⟩,⟨⟨(-253510652219493951362784),(-253510652219493950661734)⟩,⟨108805942398383503095304,108805942398383503795971⟩⟩,⟨⟨(-242807039275245168170101),(-242807039275245167496031)⟩,⟨103727969226858920133567,103727969226858920807270⟩⟩,⟨⟨(-232642593119043937703074),(-232642593119043937054285)⟩,⟨98898658495832200210573,98898658495832200859011⟩⟩,⟨⟨(-222988917190298314729449),(-222988917190298314105556)⟩,⟨94306481575752443252947,94306481575752443876506⟩⟩,⟨⟨(-213819143302553328549582),(-213819143302553327948758)⟩,⟨89940369658466472771655,89940369658466473372160⟩⟩,⟨⟨(-205107851785594111056907),(-205107851785594110478551)⟩,⟨85789703160042944110510,85789703160042944688561⟩⟩,⟨⟨(-196830995445150484298533),(-196830995445150483741207)⟩,⟨81844300579819274463897,81844300579819275020932⟩⟩,⟨⟨(-188965827198532071300224),(-188965827198532070763598)⟩,⟨78094406920648364800732,78094406920648365337081⟩⟩,⟨⟨(-181490831245637887039577),(-181490831245637886522126)⟩,⟨74530681765833798558078,74530681765833799075263⟩⟩,⟨⟨(-174385657636384605956892),(-174385657636384605458168)⟩,⟨71144187099321446091331,71144187099321446589801⟩⟩,⟨⟨(-167631060097622394748805),(-167631060097622394267589)⟩,⟨67926374947349472908172,67926374947349473389146⟩⟩] +lemma kernel4_1_r2_11_eq : ∀ k : Fin 16, kernel4_1Expr 2 11 k = kernel4_1_r2_11 k := by decide +kernel +noncomputable def kernel4_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-161208836984999830637907),(-161208836984999830174008)⟩,⟨64869074911932759463241,64869074911932759926908⟩⟩,⟨⟨(-155101775227947735649295),(-155101775227947735201356)⟩,⟨61964481659255002389798,61964481659255002837516⟩⟩,⟨⟨(-149293597138927595279114),(-149293597138927594846788)⟩,⟨59205142419244133215879,59205142419244133647993⟩⟩,⟨⟨(-143768909961289394161639),(-143768909961289393743866)⟩,⟨56583944546294865361644,56583944546294865779214⟩⟩,⟨⟨(-138513158033465770687729),(-138513158033465770284345)⟩,⟨54094103185256004181172,54094103185256004584363⟩⟩,⟨⟨(-133512577450757547587703),(-133512577450757547197621)⟩,⟨51729149081398858991540,51729149081398859381436⟩⟩,⟨⟨(-128754153109606534446585),(-128754153109606534069486)⟩,⟨49482916568105529286716,49482916568105529663639⟩⟩,⟨⟨(-124225578022974849658756),(-124225578022974849293808)⟩,⟨47349531761440667663969,47349531761440668028746⟩⟩,⟨⟨(-119915214799228743826115),(-119915214799228743473218)⟩,⟨45323400986576214072671,45323400986576214425405⟩⟩,⟨⟨(-115812059180734748246879),(-115812059180734747905030)⟩,⟨43399199457204365644988,43399199457204365986680⟩⟩,⟨⟨(-111905705542195312711769),(-111905705542195312380799)⟩,⟨41571860225578794376709,41571860225578794707530⟩⟩,⟨⟨(-108186314252560813249840),(-108186314252560812928960)⟩,⟨39836563417647351048713,39836563417647351369449⟩⟩,⟨⟨(-104644580808138086508229),(-104644580808138086197381)⟩,⟨38188725764861193196015,38188725764861193506725⟩⟩,⟨⟨(-101271706648257801179368),(-101271706648257800877716)⟩,⟨36623990441646017953644,36623990441646018255165⟩⟩,⟨⟨(-98059371568551293950419),(-98059371568551293657831)⟩,⟨35138217215182077876920,35138217215182078169381⟩⟩,⟨⟨(-94999707650511071463292),(-94999707650511071179108)⟩,⟨33727472912042811639505,33727472912042811923567⟩⟩] +lemma kernel4_1_r2_12_eq : ∀ k : Fin 16, kernel4_1Expr 2 12 k = kernel4_1_r2_12 k := by decide +kernel +noncomputable def kernel4_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-92085274629558759556131),(-92085274629558759280383)⟩,⟨32388022204369865380599,32388022204369865656231⟩⟩,⟨⟨(-89309036627312125726962),(-89309036627312125458880)⟩,⟨31116318716598407529725,31116318716598407797695⟩⟩,⟨⟨(-86664340177122542196297),(-86664340177122541935772)⟩,⟨29908996452275122020257,29908996452275122280674⟩⟩,⟨⟨(-84144893475240770421928),(-84144893475240770168393)⟩,⟨28762861539217062718772,28762861539217062972203⟩⟩,⟨⟨(-81744746793158230230413),(-81744746793158229983875)⟩,⟨27674884290128418605667,27674884290128418852105⟩⟩,⟨⟨(-79458273989759972446318),(-79458273989759972206174)⟩,⟨26642191574810716247817,26642191574810716487865⟩⟩,⟨⟨(-77280155064912308945775),(-77280155064912308711896)⟩,⟨25662059499257394636962,25662059499257394870748⟩⟩,⟨⟨(-75205359698991177112006),(-75205359698991176883966)⟩,⟨24731906386204114652620,24731906386204114880572⟩⟩,⟨⟨(-73229131725636246523651),(-73229131725636246301460)⟩,⟨23849286051100446766637,23849286051100446988742⟩⟩,⟨⟨(-71346974487690560963430),(-71346974487690560746549)⟩,⟨23011881366966279033938,23011881366966279250736⟩⟩,⟨⟨(-69554637028856744070132),(-69554637028856743858481)⟩,⟨22217498111187669771593,22217498111187669983165⟩⟩,⟨⟨(-67848101076069555578791),(-67848101076069555371963)⟩,⟨21464059086982880725085,21464059086982880931836⟩⟩,⟨⟨(-66223568769952353124970),(-66223568769952352922995)⟩,⟨20749598512021563234075,20749598512021563435975⟩⟩,⟨⟨(-64677451102993631471000),(-64677451102993631273421)⟩,⟨20072256666500750956219,20072256666500751153726⟩⟩,⟨⟨(-63206357027251415692097),(-63206357027251415498861)⟩,⟨19430274792863250885352,19430274792863251078518⟩⟩,⟨⟨(-61807083195470267245382),(-61807083195470267056131)⟩,⟨18821990239280596703502,18821990239280596892686⟩⟩] +lemma kernel4_1_r2_13_eq : ∀ k : Fin 16, kernel4_1Expr 2 13 k = kernel4_1_r2_13 k := by decide +kernel +noncomputable def kernel4_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-60476604301480618879597),(-60476604301480618694393)⟩,⟨18245831839007846659084,18245831839007846844223⟩⟩,⟨⟨(-59212063987645850811045),(-59212063987645850629453)⟩,⟨17700315517745589066879,17700315517745589248407⟩⟩,⟨⟨(-58010766288931853904511),(-58010766288931853726502)⟩,⟨17184040121210455298816,17184040121210455476762⟩⟩,⟨⟨(-56870167584899794685479),(-56870167584899794510744)⟩,⟨16695683455214573478096,16695683455214573652771⟩⟩,⟨⟨(-55787869032568474605870),(-55787869032568474434439)⟩,⟨16233998530682486559513,16233998530682486730886⟩⟩,⟨⟨(-54761609454661184439365),(-54761609454661184270877)⟩,⟨15797810006187259371407,15797810006187259539839⟩⟩,⟨⟨(-53789258659246444613377),(-53789258659246444447811)⟩,⟨15386010820762330553626,15386010820762330719136⟩⟩,⟨⟨(-52868811168205654237178),(-52868811168205654074259)⟩,⟨14997559009938988745955,14997559009938988908822⟩⟩,⟨⟨(-51998380333316600044036),(-51998380333316599883862)⟩,⟨14631474698168347052210,14631474698168347212331⟩⟩,⟨⟨(-51176192820033136383217),(-51176192820033136225381)⟩,⟨14286837261008829456087,14286837261008829613872⟩⟩,⟨⟨(-50400583440271242665925),(-50400583440271242510456)⟩,⟨13962782650693214008006,13962782650693214163425⟩⟩,⟨⟨(-49669990316683158676795),(-49669990316683158523436)⟩,⟨13658500878931198708499,13658500878931198861810⟩⟩,⟨⟨(-48982950362017405910553),(-48982950362017405759372)⟩,⟨13373233651052498002733,13373233651052498153866⟩⟩,⟨⟨(-48338095058226185060879),(-48338095058226184911563)⟩,⟨13106272145850085435830,13106272145850085585100⟩⟩,⟨⟨(-47734146520995797006808),(-47734146520995796859339)⟩,⟨12856954935742012599891,12856954935742012747314⟩⟩,⟨⟨(-47169913836343205217677),(-47169913836343205071833)⟩,⟨12624666042132077418265,12624666042132077564064⟩⟩] +lemma kernel4_1_r2_14_eq : ∀ k : Fin 16, kernel4_1Expr 2 14 k = kernel4_1_r2_14 k := by decide +kernel +noncomputable def kernel4_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-46644289656845414077244),(-46644289656845413933133)⟩,⟨12408833121113472308232,12408833121113472452299⟩⟩,⟨⟨(-46156247045950686037260),(-46156247045950685894563)⟩,⟨12208925774924551535002,12208925774924551677655⟩⟩,⟨⟨(-45704836559664399119253),(-45704836559664398977968)⟩,⟨12024453984831290962995,12024453984831291104238⟩⟩,⟨⟨(-45289183555710126308075),(-45289183555710126167972)⟩,⟨11854966661376270881485,11854966661376271021546⟩⟩,⟨⟨(-44908485721040804741327),(-44908485721040804602535)⟩,⟨11700050308198605162794,11700050308198605301545⟩⟩,⟨⟨(-44562010809318095526433),(-44562010809318095388627)⟩,⟨11559327795892781445084,11559327795892781582849⟩⟩,⟨⟨(-44249094580692592054294),(-44249094580692591917501)⟩,⟨11432457242636573319734,11432457242636573456487⟩⟩,⟨⟨(-43969138936905733295197),(-43969138936905733159208)⟩,⟨11319130998578825516807,11319130998578825652756⟩⟩,⟨⟨(-43721610245398379026133),(-43721610245398378891086)⟩,⟨11219074731236859992892,11219074731236860127899⟩⟩,⟨⟨(-43506037846753212699220),(-43506037846753212564774)⟩,⟨11132046609410433992803,11132046609410434127210⟩⟩,⟨⟨(-43322012740420610872712),(-43322012740420610738900)⟩,⟨11057836583374588738317,11057836583374588872089⟩⟩,⟨⟨(-43169186444282465601530),(-43169186444282465468158)⟩,⟨10996265759367399317705,10996265759367399451039⟩⟩,⟨⟨(-43047270024197735396929),(-43047270024197735264079)⟩,⟨10947185866640657891484,10947185866640658024296⟩⟩,⟨⟨(-42956033290249260823155),(-42956033290249260690571)⟩,⟨10910478815592017979065,10910478815592018111611⟩⟩,⟨⟨(-42895304156975608392666),(-42895304156975608260366)⟩,⟨10886056345746255415085,10886056345746255547347⟩⟩,⟨⟨(-42864968165426368081381),(-42864968165426367949159)⟩,⟨10873859762601247756509,10873859762601247888692⟩⟩] +lemma kernel4_1_r2_15_eq : ∀ k : Fin 16, kernel4_1Expr 2 15 k = kernel4_1_r2_15 k := by decide +kernel +noncomputable def kernel4_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel4_1_r2_0,kernel4_1_r2_1,kernel4_1_r2_2,kernel4_1_r2_3,kernel4_1_r2_4,kernel4_1_r2_5,kernel4_1_r2_6,kernel4_1_r2_7,kernel4_1_r2_8,kernel4_1_r2_9,kernel4_1_r2_10,kernel4_1_r2_11,kernel4_1_r2_12,kernel4_1_r2_13,kernel4_1_r2_14,kernel4_1_r2_15] +lemma kernel4_1_r2_eq (i k : Fin 16) : kernel4_1Expr 2 i k = kernel4_1_r2 i k := by + fin_cases i + · exact kernel4_1_r2_0_eq k + · exact kernel4_1_r2_1_eq k + · exact kernel4_1_r2_2_eq k + · exact kernel4_1_r2_3_eq k + · exact kernel4_1_r2_4_eq k + · exact kernel4_1_r2_5_eq k + · exact kernel4_1_r2_6_eq k + · exact kernel4_1_r2_7_eq k + · exact kernel4_1_r2_8_eq k + · exact kernel4_1_r2_9_eq k + · exact kernel4_1_r2_10_eq k + · exact kernel4_1_r2_11_eq k + · exact kernel4_1_r2_12_eq k + · exact kernel4_1_r2_13_eq k + · exact kernel4_1_r2_14_eq k + · exact kernel4_1_r2_15_eq k +noncomputable def kernel4_1_r3_0 : Fin 16 → CBox := ![⟨⟨14869807724386899701178993647,14869807724386899708246708265⟩,⟨(-7889146849799604283794682264),(-7889146849799604276828346733)⟩⟩,⟨⟨14864187435984724137447186247,14864187435984724144513141168⟩,⟨(-7889677486372198338094610757),(-7889677486372198331130025300)⟩⟩,⟨⟨14852951649548993181904980625,14852951649548993188967404204⟩,⟨(-7890734862941527977085163901),(-7890734862941527970124090430)⟩⟩,⟨⟨14836109942491819233268082356,14836109942491819240325204816⟩,⟨(-7892311197945082224694510924),(-7892311197945082217738709432)⟩⟩,⟨⟨14813676672606436005146520075,14813676672606436012196574590⟩,⟨(-7894394847979297391311583445),(-7894394847979297384362810890)⟩⟩,⟨⟨14785670968043471474360554572,14785670968043471481401778074⟩,⟨(-7896970342435999268324789500),(-7896970342435999261384798967)⟩⟩,⟨⟨14752116713889986414444616823,14752116713889986421475250859⟩,⟨(-7900018429531542768634502477),(-7900018429531542761705042302)⟩⟩,⟨⟨14713042535303982986197326735,14713042535303982993215618933⟩,⟨(-7903516133598129403092541551),(-7903516133598129396175353827)⟩⟩,⟨⟨14668481777146131190478284643,14668481777146131197482488451⟩,⟨(-7907436823474700564668314926),(-7907436823474700557765135735)⟩⟩,⟨⟨14618472480040074910049752319,14618472480040074917038130137⟩,⟨(-7911750291803088101528698609),(-7911750291803088094641254870)⟩⟩,⟨⟨14563057352782970381037471677,14563057352782970388008292378⟩,⟨(-7916422845003827174505289862),(-7916422845003827167635301766)⟩⟩,⟨⟨14502283741018980799019938497,14502283741018980805971483403⟩,⟨(-7921417403675274419304690521),(-7921417403675274412453865577)⟩⟩,⟨⟨14436203592080399262773348484,14436203592080399269703904772⟩,⟨(-7926693613129501927132914074),(-7926693613129501920302953624)⟩⟩,⟨⟨14364873415893990987914614104,14364873415893990994822486762⟩,⟨(-7932207963748929931885455608),(-7932207963748929925078042926)⟩⟩,⟨⟨14288354241844121408905176577,14288354241844121415788675024⟩,⟨(-7937913920818894194657743755),(-7937913920818894187874557299)⟩⟩,⟨⟨14206711571479349724743503664,14206711571479349731600960299⟩,⟨(-7943762063463394142037002538),(-7943762063463394135279697526)⟩⟩] +lemma kernel4_1_r3_0_eq : ∀ k : Fin 16, kernel4_1Expr 3 0 k = kernel4_1_r3_0 k := by decide +kernel +noncomputable def kernel4_1_r3_1 : Fin 16 → CBox := ![⟨⟨14120015326945490961294522087,14120015326945490968124270020⟩,⟨(-7949700232284211392861241966),(-7949700232284211386131472468)⟩⟩,⟨⟨14028339795025749588629645674,14028339795025749595430050944⟩,⟨(-7955673685277502160208007093),(-7955673685277502153507393990)⟩⟩,⟨⟨13931763566667462084072092366,13931763566667462090841517287⟩,⟨(-7961625261576927981876689594),(-7961625261576927975206856993)⟩⟩,⟨⟨13830369471875304154463691024,13830369471875304161200537451⟩,⟨(-7967495552548474069634955059),(-7967495552548474062997487273)⟩⟩,⟨⟨13724244509852561465152634195,13724244509852561471855292520⟩,⟨(-7973223079739389751277712871),(-7973223079739389744674205103)⟩⟩,⟨⟨13613479774275262421272246849,13613479774275262427939163459⟩,⟨(-7978744479162246979468337857),(-7978744479162246972900329131)⟩⟩,⟨⟨13498170373588650174635945601,13498170373588650181265547370⟩,⟨(-7983994691375025901240536355),(-7983994691375025894709584582)⟩⟩,⟨⟨13378415346221641313276353698,13378415346221641319867130814⟩,⟨(-7988907156799475170676421522),(-7988907156799475164184021122)⟩⟩,⟨⟨13254317570622583515119772931,13254317570622583521670182874⟩,⟨(-7993414015702831818734312329),(-7993414015702831812281989709)⟩⟩,⟨⟨13125983670028776705745998779,13125983670028776712254589024⟩,⟨(-7997446312252392119818843856),(-7997446312252392113408035412)⟩⟩,⟨⟨12993523911892844758147449262,12993523911892844764612722311⟩,⟨(-8000934202038469968140115000),(-8000934202038469961772301296)⟩⟩,⟨⟨12857052101901110187210664747,12857052101901110193631218424⟩,⟨(-8003807162449029254684530022),(-8003807162449029248361096321)⟩⟩,⟨⟨12716685472532595189317444995,12716685472532595195691814816⟩,⟨(-8005994205268795155390071950),(-8005994205268795149112464924)⟩⟩,⟨⟨12572544566122101288098717018,12572544566122101294425570608⟩,⟨(-8007424090866996280969970845),(-8007424090866996274739505279)⟩⟩,⟨⟨12424753112406949400186796010,12424753112406949406464721916⟩,⟨(-8008025543331121660548405373),(-8008025543331121654366474154)⟩⟩,⟨⟨12273437900554325253505747077,12273437900554325259733469858⟩,⟨(-8007727465899245611346504506),(-8007727465899245605214364777)⟩⟩] +lemma kernel4_1_r3_1_eq : ∀ k : Fin 16, kernel4_1Expr 3 1 k = kernel4_1_r3_1 k := by decide +kernel +noncomputable def kernel4_1_r3_2 : Fin 16 → CBox := ![⟨⟨12118728645684695249623834248,12118728645684695255799973665⟩,⟨(-8006459156040626998803394646),(-8006459156040626992722407244)⟩⟩,⟨⟨11960757849926349403155850651,11960757849926349409279217323⟩,⟨(-8004150519533469285003531256),(-8004150519533469278974866760)⟩⟩,⟨⟨11799660658056696502898202052,11799660658056696508967480516⟩,⟨(-8000732282889970441362861443),(-8000732282889970435387815319)⟩⟩,⟨⟨11635574707807379392373801437,11635574707807379398387861379⟩,⟨(-7996136203482127404731018576),(-7996136203482127398810701740)⟩⟩,⟨⟨11468639974932484712962035393,11468639974932484718919593972⟩,⟨(-7990295276727211755026357273),(-7990295276727211749162031864)⟩⟩,⟨⟨11298998613161973776460908610,11298998613161973782360933726⟩,⟨(-7983143939699418035411618093),(-7983143939699418029604296518)⟩⟩,⟨⟨11126794789185834966032431281,11126794789185834971873712820⟩,⟨(-7974618270543912415505470740),(-7974618270543912409756342016)⟩⟩,⟨⟨10952174512838222743345054240,10952174512838222749126624156⟩,⟨(-7964656183081378043040545805),(-7964656183081378037350557875)⟩⟩,⟨⟨10775285462674868226022023324,10775285462674868231742697160⟩,⟨(-7953197616005156926037044439),(-7953197616005156920407360102)⟩⟩,⟨⟨10596276807161181137981837646,10596276807161181143640764981⟩,⟨(-7940184716089210335920682695),(-7940184716089210330352132264)⟩⟩,⟨⟨10415299021712568760513441084,10415299021712568766109525603⟩,⟨(-7925562014843335331396316321),(-7925562014843335325889974357)⟩⟩,⟨⟨10232503701852427493964799132,10232503701852427499497250374⟩,⟨(-7909276598072349632233306723),(-7909276598072349626789943373)⟩⟩,⟨⟨10048043372776867965246122021,10048043372776867970713870345⟩,⟨(-7891278267818246819092586679),(-7891278267818246813713249491)⟩⟩,⟨⟨9862071295638365399494561451,9862071295638365404896943752⟩,⟨(-7871519696188575179025334080),(-7871519696188575173710666145)⟩⟩,⟨⟨9674741270883033194717485497,9674741270883033200053527016⟩,⟨(-7849956570600443216031634595),(-7849956570600443210782588758)⟩⟩,⟨⟨9486207438997950096919813020,9486207438997950102188913565⟩,⟨(-7826547729997529903255374754),(-7826547729997529898072531254)⟩⟩] +lemma kernel4_1_r3_2_eq : ∀ k : Fin 16, kernel4_1Expr 3 2 k = kernel4_1_r3_2 k := by decide +kernel +noncomputable def kernel4_1_r3_3 : Fin 16 → CBox := ![⟨⟨9296624079045782662647714498,9296624079045782667848912082⟩,⟨(-7801255291627195435119937713),(-7801255291627195430004236497)⟩⟩,⟨⟨9106145405383690177636536904,9106145405383690182769381581⟩,⟨(-7774044767996156168483514253),(-7774044767996156163435385990)⟩⟩,⟨⟨8914925362982037983428283409,8914925362982037988491928464⟩,⟨(-7744885173656103763921320824),(-7744885173656103758941590759)⟩⟩,⟨⟨8723117421775641077311881295,8723117421775641082305926546⟩,⟨(-7713749121505002142641767032),(-7713749121505002137730816336)⟩⟩,⟨⟨8530874370495982402994396942,8530874370495982407918011471⟩,⟨(-7680612908325466704181444476),(-7680612908325466699340082774)⟩⟩,⟨⟨8338348110446975567036403718,8338348110446975571889340941⟩,⟨(-7645456589318489674884313318),(-7645456589318489670112769167)⟩⟩,⟨⟨8145689449699253457485722047,8145689449699253462267268471⟩,⟨(-7608264041428686721691043771),(-7608264041428686716990010242)⟩⟩,⟨⟨7953047898188554473665105016,7953047898188554478375066613⟩,⟨(-7569023015296058707771128070),(-7569023015296058703140781739)⟩⟩,⟨⟨7760571464212448112957673661,7760571464212448117595333469⟩,⟨(-7527725175708837305840592791),(-7527725175708837301281630559)⟩⟩,⟨⟨7568406452826302848960021600,7568406452826302853525362473⟩,⟨(-7484366130472156380008457409),(-7484366130472156375520880358)⟩⟩,⟨⟨7376697266643973689994177188,7376697266643973694486622294⟩,⟨(-7438945447647899215848545690),(-7438945447647899211432911883)⟩⟩,⟨⟨7185586209551108080445746689,7185586209551108084865310408⟩,⟨(-7391466661161946581855597193),(-7391466661161946577511876916)⟩⟩,⟨⟨6995213293839182494140326965,6995213293839182498486433135⟩,⟨(-7341937264816019986549984853),(-7341937264816019982278736179)⟩⟩,⟨⟨6805716051266346334198709620,6805716051266346338471546052⟩,⟨(-7290368694782202971815062421),(-7290368694782202967616083836)⟩⟩,⟨⟨6617229348546835783636019978,6617229348546835787835148189⟩,⟨(-7236776300698853285462255240),(-7236776300698853281335968669)⟩⟩,⟨⟨6429885207764112617911563323,6429885207764112622037204176⟩,⟨(-7181179305526811528517498023),(-7181179305526811524463669918)⟩⟩] +lemma kernel4_1_r3_3_eq : ∀ k : Fin 16, kernel4_1Expr 3 3 k = kernel4_1_r3_3 k := by decide +kernel +noncomputable def kernel4_1_r3_4 : Fin 16 → CBox := ![⟨⟨6243812632193979930812993303,6243812632193979934864680920⟩,⟨(-7123600754364388406044826284),(-7123600754364388402063906758)⟩⟩,⟨⟨6059137438012740322677263319,6059137438012740326655418113⟩,⟨(-7064067452458394902895412909),(-7064067452458394898986970857)⟩⟩,⟨⟨5875982092352018376702268749,5875982092352018380606590154⟩,⟨(-7002609892686291343770685877),(-7002609892686291339935008011)⟩⟩,⟨⟨5694465558146208155444805488,5694465558146208159275714656⟩,⟨(-6939262172821199146250935819),(-6939262172821199142487591370)⟩⟩,⟨⟨5514703146200681757061084518,5514703146200681760818263332⟩,⟨(-6874061902926873956252509623),(-6874061902926873952561803924)⟩⟩,⟨⟨5336806374888974063852790902,5336806374888974067538456500⟩,⟨(-6807050103263616712383755920),(-6807050103263616708763429786)⟩⟩,⟨⟨5160882837865222383707498148,5160882837865222387374078513⟩,⟨(-6738271093118342143503388448),(-6738271093118342139899888388)⟩⟩,⟨⟨4987036080154281315452602710,4987036080154281319099880752⟩,⟨(-6667772371002481600151856349),(-6667772371002481596565433107)⟩⟩,⟨⟨4815365482956258841849731958,4815365482956258845476606000⟩,⟨(-6595604486689926508838071209),(-6595604486689926505269857166)⟩⟩,⟨⟨4645966157474847144832417057,4645966157474847148438817923⟩,⟨(-6521820905593686846308374007),(-6521820905593686842758474828)⟩⟩,⟨⟨4478928848049879822885422329,4478928848049879826470348003⟩,⟨(-6446477866004222679600391188),(-6446477866004222676069842304)⟩⟩,⟨⟨4314339844844175275670774580,4314339844844175279234067616⟩,⟨(-6369634229734393770251562390),(-6369634229734393766740559192)⟩⟩,⟨⟨4152280906303072676429721188,4152280906303072679970252418⟩,⟨(-6291351326735562000516970273),(-6291351326735561997026676855)⟩⟩,⟨⟨3992829191572289381400792528,3992829191572289384918550835⟩,⟨(-6211692794266485905089302826),(-6211692794266485901619770407)⟩⟩,⟨⟨3836057203025991558277366823,3836057203025991561771320878⟩,⟨(-6130724411211190940549934969),(-6130724411211190937102231915)⟩⟩,⟨⟨3682032739022444445281719134,3682032739022444448751783510⟩,⟨(-6048513928153922006418427114),(-6048513928153922002992679938)⟩⟩] +lemma kernel4_1_r3_4_eq : ∀ k : Fin 16, kernel4_1Expr 3 4 k = kernel4_1_r3_4 k := by decide +kernel +noncomputable def kernel4_1_r3_5 : Fin 16 → CBox := ![⟨⟨3530818856969471514042357320,3530818856969471517487332583⟩,⟨(-5965130893828538972844482971),(-5965130893828538969441929068)⟩⟩,⟨⟨3382473846746383616071989847,3382473846746383619491990289⟩,⟨(-5880646478566268882707870084),(-5880646478566268879328437930)⟩⟩,⟨⟨3237051214493223634394784578,3237051214493223637788762234⟩,⟨(-5795133295369562145535236118),(-5795133295369562142180013305)⟩⟩,⟨⟨3094599676742294678547495293,3094599676742294681915447732⟩,⟨(-5708665219240911411199484368),(-5708665219240911407868516436)⟩⟩,⟨⟨2955163164831186398461691608,2955163164831186401802428776⟩,⟨(-5621317205393892864487645082),(-5621317205393892861182162271)⟩⟩,⟨⟨2818780839501069751198060583,2818780839501069754511765026⟩,⟨(-5533165106969407309143009529),(-5533165106969407305862873385)⟩⟩,⟨⟨2685487115549078742691830897,2685487115549078745977450751⟩,⟨(-5444285492873174278311753072),(-5444285492873174275058056659)⟩⟩,⟨⟨2555311696369318267293944769,2555311696369318270551569959⟩,⟨(-5354755466341022696350218642),(-5354755466341022693122916073)⟩⟩,⟨⟨2428279618183605728528010444,2428279618183605731756404348⟩,⟨(-5264652484826496647813848360),(-5264652484826496644614217525)⟩⟩,⟨⟨2304411303730640581517451040,2304411303730640584716942061⟩,⟨(-5174054181790838579781632881),(-5174054181790838576609389873)⟩⟩,⟨⟨2183722625151063484384905140,2183722625151063487554450228⟩,⟨(-5083038190958621872522630270),(-5083038190958621869378859978)⟩⟩,⟨⟨2066224975775970753586025495,2066224975775970756725814043⟩,⟨(-4991681973583289696590742600),(-4991681973583289693475299561)⟩⟩,⟨⟨1951925350498036818325865183,1951925350498036821434697681⟩,⟨(-4900062649245738647587158744),(-4900062649245738644501284042)⟩⟩,⟨⟨1840826434377604107071460230,1840826434377604110149744999⟩,⟨(-4808256830685995869210896189),(-4808256830685995866154225279)⟩⟩,⟨⟨1732926699111052364743742959,1732926699111052367790457600⟩,⟨(-4716340463143119219651185275),(-4716340463143119216624782136)⟩⟩,⟨⟨1628220506965572443090200718,1628220506965572446105639030⟩,⟨(-4624388668651852420924374349),(-4624388668651852417927988076)⟩⟩] +lemma kernel4_1_r3_5_eq : ∀ k : Fin 16, kernel4_1Expr 3 5 k = kernel4_1_r3_5 k := by decide +kernel +noncomputable def kernel4_1_r3_6 : Fin 16 → CBox := ![⟨⟨1526698221763245647982597008,1526698221763245650965521291⟩,⟨(-4532475595716449858342998081),(-4532475595716449855377907311)⟩⟩,⟨⟨1428346326478158556876502931,1428346326478158559827492722⟩,⟨(-4440674274752614358625745904),(-4440674274752614355691413415)⟩⟩,⟨⟨1333147546993241405738022824,1333147546993241408656087507⟩,⟨(-4349056479657837104766513857),(-4349056479657837101863970795)⟩⟩,⟨⟨1241080981548668642442089366,1241080981548668645327629286⟩,⟨(-4257692595838767545467232403),(-4257692595838767542596119481)⟩⟩,⟨⟨1152122235401052112003137290,1152122235401052114854991803⟩,⟨(-4166651494991751694878956570),(-4166651494991751692040474120)⟩⟩,⟨⟨1066243560202325566156713610,1066243560202325568975528421⟩,⟨(-4076000416899540615760664980),(-4076000416899540612954207279)⟩⟩,⟨⟨983413997599184628169303253,983413997599184630954129012⟩,⟨(-3985804858473568992818702724),(-3985804858473568990045257953)⟩⟩,⟨⟨903599526548215752980370216,903599526548215755731713679⟩,⟨(-3896128470237318016065808766),(-3896128470237318013324908736)⟩⟩,⟨⟨826763213838413920786291544,826763213838413923502977988⟩,⟨(-3807032960412287222842785064),(-3807032960412287220135642271)⟩⟩,⟨⟨752865367311630919926640830,752865367311630922609481728⟩,⟨(-3718578006734183675811328821),(-3718578006734183673137168926)⟩⟩,⟨⟨681863691272579913270200414,681863691272579915918295956⟩,⟨(-3630821176093267204964348587),(-3630821176093267202324107987)⟩⟩,⟨⟨613713443583300464735500569,613713443583300467349460831⟩,⟨(-3543817852059535791340376431),(-3543817852059535788733480607)⟩⟩,⟨⟨548367593942401920529666923,548367593942401923108409540⟩,⟨(-3457621170320757919796099167),(-3457621170320757917223665891)⟩⟩,⟨⟨485776982856880882372609919,485776982856880884917007580⟩,⟨(-3372281962029414335735370384),(-3372281962029414333196560789)⟩⟩,⟨⟨425890480823768374028318271,425890480823768376537526892⟩,⟨(-3287848705023547721363284445),(-3287848705023547718858976563)⟩⟩,⟨⟨368655147250211872084621380,368655147250211874559349210⟩,⟨(-3204367482856474310636234746),(-3204367482856474308165752511)⟩⟩] +lemma kernel4_1_r3_6_eq : ∀ k : Fin 16, kernel4_1Expr 3 6 k = kernel4_1_r3_6 k := by decide +kernel +noncomputable def kernel4_1_r3_7 : Fin 16 → CBox := ![⟨⟨314016388653734963346650786,314016388653734965785799746⟩,⟨(-3121881951541415930536473251),(-3121881951541415928100947492)⟩⟩,⟨⟨261918115699232851386148153,261918115699232853790760780⟩,⟨(-3040433313889483868193138619),(-3040433313889483865791556991)⟩⟩,⟨⟨212302898645637587196920700,212302898645637589566213390⟩,⟨(-2960060301293196167616559811),(-2960060301293196165249736935)⟩⟩,⟨⟨165112120792998525681504293,165112120792998528016275732⟩,⟨(-2880799162782935203268637368),(-2880799162782935200935803156)⟩⟩,⟨⟨120286129539841362628669545,120286129539841364927942747⟩,⟨(-2802683661160538926972811185),(-2802683661160538924674972394)⟩⟩,⟨⟨77764384680958936111643205,77764384680958938376486989⟩,⟨(-2725745075992641545118206849),(-2725745075992641542854321170)⟩⟩,⟨⟨37485603597111069424998985,37485603597111071654692752⟩,⟨(-2650012213226500113289989202),(-2650012213226500111060805174)⟩⟩,⟨⟨(-612096989671046951988090),(-612096989671044756564375)⟩,⟨(-2575511421172913158264409645),(-2575511421172913156069072236)⟩⟩,⟨⟨(-36591062998509619948077099),(-36591062998509617787900657)⟩,⟨(-2502266612584494444311257941),(-2502266612584494442150771209)⟩⟩,⟨⟨(-70513968989586349568996021),(-70513968989586347442856914)⟩,⟨(-2430299292543035949076273260),(-2430299292543035946949449933)⟩⟩,⟨⟨(-102443688437231161884054049),(-102443688437231159792608706)⟩,⟨(-2359628591856993810994191832),(-2359628591856993808901713163)⟩⟩,⟨⟨(-132443168507514378599217390),(-132443168507514376541515660)⟩,⟨(-2290271305659262781740022343),(-2290271305659262779680959488)⟩⟩,⟨⟨(-160575309547090263895241244),(-160575309547090261872141554)⟩,⟨(-2222241936886360757996138317),(-2222241936886360755971373416)⟩⟩,⟨⟨(-186902849465408619980698088),(-186902849465408617990981616)⟩,⟨(-2155552744312906762458463432),(-2155552744312906760466796771)⟩⟩,⟨⟨(-211488253167851215680040135),(-211488253167851213724299930)⟩,⟨(-2090213794809814562451392264),(-2090213794809814560493438641)⟩⟩,⟨⟨(-234393607172986219454978100),(-234393607172986217532205557)⟩,⟨(-2026233019490901559844862108),(-2026233019490901557919630731)⟩⟩] +lemma kernel4_1_r3_7_eq : ∀ k : Fin 16, kernel4_1Expr 3 7 k = kernel4_1_r3_7 k := by decide +kernel +noncomputable def kernel4_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-255680519523085771090463611),(-255680519523085769201534302)⟩,⟨(-1963616273410581206568049380),(-1963616273410581204676436753)⟩⟩,⟨⟨(-275410025073432454099111370),(-275410025073432452242672750)⟩,⟨(-1902367398474911145878208538),(-1902367398474911144018877598)⟩⟩,⟨⟨(-293642496222856048249088618),(-293642496222856046425672187)⟩,⟨(-1842488289229444999402367900),(-1842488289229444997575868952)⟩⟩,⟨⟨(-310437559125491629502148578),(-310437559125491627710700148)⟩,⟨(-1783978961190012692802991936),(-1783978961190012691008285327)⟩⟩,⟨⟨(-325854015402025274843197695),(-325854015402025273084456613)⟩,⟨(-1726837621386655704390857734),(-1726837621386655702628700782)⟩⟩,⟨⟨(-339949769347777774687890135),(-339949769347777772960542322)⟩,⟨(-1671060740796387459279917850),(-1671060740796387457549008907)⟩⟩,⟨⟨(-352781760614945073393515727),(-352781760614945071698034595)⟩,⟨(-1616643128347148453268976763),(-1616643128347148451569805293)⟩⟩,⟨⟨(-364405902327233450517093346),(-364405902327233448852391635)⟩,⟨(-1563578006183189891065466358),(-1563578006183189889396956634)⟩⟩,⟨⟨(-374877024567055998403430933),(-374877024567055996770254308)⟩,⟨(-1511857085891054903819549227),(-1511857085891054902182462451)⟩⟩,⟨⟨(-384248823158444459351293712),(-384248823158444457748237655)⟩,⟨(-1461470645395236715555083621),(-1461470645395236713948024636)⟩⟩,⟨⟨(-392573813652918138831515265),(-392573813652918137258998954)⟩,⟨(-1412407606243380865261310835),(-1412407606243380863684712343)⟩⟩,⟨⟨(-399903290410772153097947033),(-399903290410772151554863026)⟩,⟨(-1364655611012465373065710304),(-1364655611012465371518473703)⟩⟩,⟨⟨(-406287290656625160917576789),(-406287290656625159404554729)⟩,⟨(-1318201100579640091991091565),(-1318201100579640090473859500)⟩⟩,⟨⟨(-411774563375618362264380947),(-411774563375618360780067409)⟩,⟨(-1273029391014236533373640195),(-1273029391014236531885066198)⟩⟩,⟨⟨(-416412542905391510415186207),(-416412542905391508959951219)⟩,⟨(-1229124749860775553794482854),(-1229124749860775552334948201)⟩⟩,⟨⟨(-420247327068879077171845443),(-420247327068879075744573141)⟩,⟨(-1186470471596507644732991712),(-1186470471596507643301387009)⟩⟩] +lemma kernel4_1_r3_8_eq : ∀ k : Fin 16, kernel4_1Expr 3 8 k = kernel4_1_r3_8 k := by decide +kernel +noncomputable def kernel4_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-423323659684064499463792209),(-423323659684064498065140096)⟩,⟨(-1145048952061026772544854371),(-1145048952061026771141848253)⟩⟩,⟨⟨(-425684917279089845661038972),(-425684917279089844289574969)⟩,⟨(-1104841761669714287294541834),(-1104841761669714285918706710)⟩⟩,⟨⟨(-427373099834523184496743641),(-427373099834523183152793480)⟩,⟨(-1065829717237108241538101920),(-1065829717237108240189772757)⟩⟩,⟨⟨(-428428825369111471986112400),(-428428825369111470668563387)⟩,⟨(-1027992952250673211557957695),(-1027992952250673210236026241)⟩⟩,⟨⟨(-428891328180962560712965548),(-428891328180962559422353160)⟩,⟨(-991310985449788223692930067),(-991310985449788222397940850)⟩⟩,⟨⟨(-428798460552770757132304386),(-428798460552770755867286802)⟩,⟨(-955762787579001951976327447),(-955762787579001950706941466)⟩⟩,⟨⟨(-428186697727386591637499984),(-428186697727386590398317499)⟩,⟨(-921326846198655989639391415),(-921326846198655988395882936)⟩⟩,⟨⟨(-427091145958689628140386461),(-427091145958689626925854740)⟩,⟨(-887981228449784660144464753),(-887981228449784658925699892)⟩⟩,⟨⟨(-425545553442306360027011693),(-425545553442306358837695421)⟩,⟨(-855703641683704571280412876),(-855703641683704570086959388)⟩⟩,⟨⟨(-423582323931173791538662769),(-423582323931173790373186102)⟩,⟨(-824471491879855182412357142),(-824471491879855181242836069)⟩⟩,⟨⟨(-421232532842231101280192262),(-421232532842231100138816078)⟩,⟨(-794261939788194574672525042),(-794261939788194573527199005)⟩⟩,⟨⟨(-418525945662572871077207059),(-418525945662572869958860129)⟩,⟨(-765051954744749202761996453),(-765051954744749201639791788)⟩⟩,⟨⟨(-415491038466162387390843708),(-415491038466162386295992567)⟩,⟨(-736818366120724751138431153),(-736818366120724750039816386)⟩⟩,⟨⟨(-412155020355626196048224379),(-412155020355626194975585599)⟩,⟨(-709537912376874612758215468),(-709537912376874611681903879)⟩⟩,⟨⟨(-408543857647674626582480625),(-408543857647674625532286152)⟩,⟨(-683187287705565364259407482),(-683187287705565363205632020)⟩⟩,⟨⟨(-404682299625260527339233942),(-404682299625260526310440628)⟩,⟨(-657743186253152320115136302),(-657743186253152319082851048)⟩⟩] +lemma kernel4_1_r3_9_eq : ∀ k : Fin 16, kernel4_1Expr 3 9 k = kernel4_1_r3_9 k := by decide +kernel +noncomputable def kernel4_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-400593905684643397541153605),(-400593905684643396534272638)⟩,⟨(-633182343924865025822810075),(-633182343924865024812527729)⟩⟩,⟨⟨(-396301073711012564521597095),(-396301073711012563535303912)⟩,⟨(-609481577783389249860856753),(-609481577783389248871249032)⟩⟩,⟨⟨(-391825069522186129516042049),(-391825069522186128550544227)⟩,⟨(-586617823060709936191244400),(-586617823060709935222519325)⟩⟩,⟨⟨(-387186057226088494158094301),(-387186057226088493212383422)⟩,⟨(-564568167810544161253495509),(-564568167810544160304641707)⟩⟩,⟨⟨(-382403130344166360994293295),(-382403130344166360068776348)⟩,⟨(-543309885235843829863824863),(-543309885235843828935250098)⟩⟩,⟨⟨(-377494343559580976812196035),(-377494343559580975905669566)⟩,⟨(-522820463732387762040860055),(-522820463732387761131357306)⟩⟩,⟨⟨(-372476744955864895924234081),(-372476744955864895036886009)⟩,⟨(-503077634695418506078888289),(-503077634695418505188645502)⟩⟩,⟨⟨(-367366408618708741286181762),(-367366408618708740417042975)⟩,⟨(-484059398141620342913430360),(-484059398141620342041475414)⟩⟩,⟨⟨(-362178467480603769000679364),(-362178467480603768150190683)⟩,⟨(-465744046203494063121486700),(-465744046203494062268260942)⟩⟩,⟨⟨(-356927146295168431999253612),(-356927146295168431166200358)⟩,⟨(-448110184557376316540113997),(-448110184557376315704399069)⟩⟩,⟨⟨(-351625794635093125829075102),(-351625794635093125013629275)⟩,⟨(-431136751849994063107499914),(-431136751849994062289467559)⟩⟩,⟨⟨(-346286919814711088235179860),(-346286919814711087436415523)⟩,⟨(-414803037191557311703868281),(-414803037191557310902589589)⟩⟩,⟨⟨(-340922219645211935591458967),(-340922219645211934809739422)⟩,⟨(-399088695785997077616270492),(-399088695785997076832108871)⟩⟩,⟨⟨(-335542614937427213150041025),(-335542614937427212384260811)⟩,⟨(-383973762771072943947995531),(-383973762771072943179842104)⟩⟩,⟨⟨(-330158281673907011379787290),(-330158281673907010630106100)⟩,⟨(-369438665342729612762307856),(-369438665342729612010321871)⟩⟩,⟨⟨(-324778682778648275152293360),(-324778682778648274417830595)⟩,⟨(-355464233239299174452893327),(-355464233239299173716191317)⟩⟩] +lemma kernel4_1_r3_10_eq : ∀ k : Fin 16, kernel4_1Expr 3 10 k = kernel4_1_r3_10 k := by decide +kernel +noncomputable def kernel4_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-319412599419306703642518281),(-319412599419306702923688247)⟩,⟨(-342031707661951029572798222),(-342031707661951028851794560)⟩⟩,⟨⟨(-314068161783005527957663689),(-314068161783005527253344042)⟩,⟨(-329122748708210487514725086),(-329122748708210486808294033)⟩⟩,⟨⟨(-308752879272928934595818619),(-308752879272928933906159472)⟩,⟨(-316719441395426352208663575),(-316719441395426351516954685)⟩⟩,⟨⟨(-303473670078740918017607808),(-303473670078740917341775426)⟩,⟨(-304804300350793691582377875),(-304804300350793690904554695)⟩⟩,⟨⟨(-298236890079489708779682501),(-298236890079489708118009058)⟩,⟨(-293360273243956792473889277),(-293360273243956791810283783)⟩⟩,⟨⟨(-293048361043033714710108754),(-293048361043033714061594421)⟩,⟨(-282370743037355090053290649),(-282370743037355089402899976)⟩⟩,⟨⟨(-287913398091149362768828692),(-287913398091149362133616621)⟩,⟨(-271819529128357289922031038),(-271819529128357289284997729)⟩⟩,⟨⟨(-282836836404348600626187227),(-282836836404348600003490596)⟩,⟨(-261690887455881091146719022),(-261690887455881090522253717)⟩⟩,⟨⟨(-277823057145040276313172099),(-277823057145040275703363384)⟩,⟨(-251969509642642327863149939),(-251969509642642327251624954)⟩⟩,⟨⟨(-272876012582013103660290051),(-272876012582013103062369151)⟩,⟨(-242640521242441667751249968),(-242640521242441667151662290)⟩⟩,⟨⟨(-267999250403298026149958602),(-267999250403298025564063505)⟩,⟨(-233689479160002071785312378),(-233689479160002071197799370)⟩⟩,⟨⟨(-263195937208285608770772943),(-263195937208285608196163483)⟩,⟨(-225102368308837930547646739),(-225102368308837929971465901)⟩⟩,⟨⟨(-258468881173532091250728354),(-258468881173532090687715169)⟩,⟨(-216865597570488048439906788),(-216865597570488047875368467)⟩⟩,⟨⟨(-253820553889989648802707719),(-253820553889989648250395504)⟩,⟨(-208965995116199298959134048),(-208965995116199298405340366)⟩⟩,⟨⟨(-249253111372447068514816622),(-249253111372447067973339891)⟩,⟨(-201390803149824583364837018),(-201390803149824582821921879)⟩⟩,⟨⟨(-244768414244772293585105955),(-244768414244772293053769777)⟩,⟨(-194127672128315336563988257),(-194127672128315336031254602)⟩⟩] +lemma kernel4_1_r3_11_eq : ∀ k : Fin 16, kernel4_1Expr 3 11 k = kernel4_1_r3_11 k := by decide +kernel +noncomputable def kernel4_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-240368047107114816798082672),(-240368047107114816277253922)⟩,⟨(-187164654513761748905449866),(-187164654513761748383264397)⟩⟩,⟨⟨(-236053337093561174974136266),(-236053337093561174462904049)⟩,⟨(-180490198108478480635077114),(-180490198108478480122526476)⟩⟩,⟨⟨(-231825371630848903719714372),(-231825371630848903218210644)⟩,⟨(-174093139022164166822601360),(-174093139022164166319816935)⟩⟩,⟨⟨(-227685015410641886087987208),(-227685015410641885595560872)⟩,⟨(-167962694317692544187119755),(-167962694317692543693448523)⟩⟩,⟨⟨(-223632926589562130906438108),(-223632926589562130423384814)⟩,⟨(-162088454379633563232515641),(-162088454379633562748252978)⟩⟩,⟨⟨(-219669572232669044563990407),(-219669572232669044089512545)⟩,⟨(-156460375047165275023049951),(-156460375047165274547396134)⟩⟩,⟨⟨(-215795243017386859679385325),(-215795243017386859213613380)⟩,⟨(-151068769550631435725273056),(-151068769550631435258358039)⟩⟩,⟨⟨(-212010067216013866431609736),(-212010067216013865973933983)⟩,⟨(-145904300288634460084421237),(-145904300288634459625633566)⟩⟩,⟨⟨(-208314023975913357692145854),(-208314023975913357242903546)⟩,⟨(-140957970480236393801772579),(-140957970480236393351449336)⟩⟩,⟨⟨(-204706955917295667485867790),(-204706955917295667044258190)⟩,⟨(-136221115724578832662182357),(-136221115724578832219520829)⟩⟩,⟨⟨(-201188581069163230017449865),(-201188581069163229583602366)⟩,⟨(-131685395498032157375937383),(-131685395498032156941066485)⟩⟩,⟨⟨(-197758504164515989329632921),(-197758504164515988902976989)⟩,⟨(-127342784616850184081816122),(-127342784616850183654163773)⟩⟩,⟨⟨(-194416227316312371755267117),(-194416227316312371336088028)⟩,⟨(-123185564691242648235593015),(-123185564691242647815444278)⟩⟩,⟨⟨(-191161160095960822400828068),(-191161160095960821988415030)⟩,⟨(-119206315594788380755796655),(-119206315594788380342439030)⟩⟩,⟨⟨(-187992629036287794636332038),(-187992629036287794230813877)⟩,⟨(-115397906971199425504293524),(-115397906971199425097855419)⟩⟩,⟨⟨(-184909886580998989885513503),(-184909886580998989486356009)⟩,⟨(-111753489798612851313814608),(-111753489798612850913760435)⟩⟩] +lemma kernel4_1_r3_12_eq : ∀ k : Fin 16, kernel4_1Expr 3 12 k = kernel4_1_r3_12 k := by decide +kernel +noncomputable def kernel4_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-181912119502630197018580105),(-181912119502630196626121339)⟩,⟨(-108266488029834183245700918),(-108266488029834182852368640)⟩⟩,⟨⟨(-178998456810880576870215866),(-178998456810880576483726136)⟩,⟨(-104930590325285207690263392),(-104930590325285207302921708)⟩⟩,⟨⟨(-176167977173042636095624645),(-176167977173042635715232138)⟩,⟨(-101739741893819870943922504),(-101739741893819870562699231)⟩⟩,⟨⟨(-173419715867997036704735774),(-173419715867997036329940140)⟩,⟨(-98688136455065100179878452),(-98688136455065099804272009)⟩⟩,⟨⟨(-170752671294934025301709780),(-170752671294934024932788863)⟩,⟨(-95770208335518216110229057),(-95770208335518215740517154)⟩⟩,⟨⟨(-168165811057603495054333333),(-168165811057603494690650572)⟩,⟨(-92980624709288386550602886),(-92980624709288386186147587)⟩⟩,⟨⟨(-165658077644488988413267207),(-165658077644488988054950400)⟩,⟨(-90314277993105161243187878),(-90314277993105160884116664)⟩⟩,⟨⟨(-163228393724853401924597060),(-163228393724853401571176695)⟩,⟨(-87766278404031105791009885),(-87766278404031105436852151)⟩⟩,⟨⟨(-160875667080121477063571605),(-160875667080121476715366749)⟩,⟨(-85331946687206232639101284),(-85331946687206232290176051)⟩⟩,⟨⟨(-158598795189551686139564930),(-158598795189551685795926407)⟩,⟨(-83006807019917403029032442),(-83006807019917402684689243)⟩⟩,⟨⟨(-156396669488612811043462872),(-156396669488612810704517811)⟩,⟨(-80786580097324049569577844),(-80786580097324049229943537)⟩⟩,⟨⟨(-154268179317922961440675148),(-154268179317922961105982272)⟩,⟨(-78667176404280190427246522),(-78667176404280190091878854)⟩⟩,⟨⟨(-152212215580035228769631549),(-152212215580035228439463359)⟩,⟨(-76644689676869390181318529),(-76644689676869389850489929)⟩⟩,⟨⟨(-150227674120768518791893078),(-150227674120768518465673876)⟩,⟨(-74715390556511584488396788),(-74715390556511584161530453)⟩⟩,⟨⟨(-148313458851187910358580594),(-148313458851187910036436848)⟩,⟨(-72875720438805964259470447),(-72875720438805963936692611)⟩⟩,⟨⟨(-146468484625739392213978885),(-146468484625739391895494663)⟩,⟨(-71122285518639794440209036),(-71122285518639794121102890)⟩⟩] +lemma kernel4_1_r3_13_eq : ∀ k : Fin 16, kernel4_1Expr 3 13 k = kernel4_1_r3_13 k := by decide +kernel +noncomputable def kernel4_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-144691679891441965502489998),(-144691679891441965187992465)⟩,⟨(-69451851032516473573469665),(-69451851032516473258362409)⟩⟩,⟨⟨(-142981989122438505229844887),(-142981989122438504918726486)⟩,⟨(-67861335698534659389928127),(-67861335698534659078211124)⟩⟩,⟨⟨(-141338375053607806765556090),(-141338375053607806457942081)⟩,⟨(-66347806353981231033922941),(-66347806353981230725721260)⟩⟩,⟨⟨(-139759820726345994992297127),(-139759820726345994687794602)⟩,⟨(-64908472790081585704897898),(-64908472790081585399817844)⟩⟩,⟨⟨(-138245331359037783450636581),(-138245331359037783149514030)⟩,⟨(-63540682783078662255991344),(-63540682783078661954301391)⟩⟩,⟨⟨(-136793936054158540990853542),(-136793936054158540692583268)⟩,⟨(-62241917320484574450567018),(-62241917320484574151738553)⟩⟩,⟨⟨(-135404689353378132925014567),(-135404689353378132629720527)⟩,⟨(-61009786021063301819976462),(-61009786021063301524133282)⟩⟩,⟨⟨(-134076672651478222269243649),(-134076672651478221976553171)⟩,⟨(-59842022746857066693777996),(-59842022746857066400546717)⟩⟩,⟨⟨(-132808995479347118627356333),(-132808995479347118337579910)⟩,⟨(-58736481405360429923955215),(-58736481405360429633646383)⟩⟩,⟨⟨(-131600796665781139830405495),(-131600796665781139542990822)⟩,⟨(-57691131939772446754280300),(-57691131939772446466340724)⟩⟩,⟨⟨(-130451245387299427616992749),(-130451245387299427332061990)⟩,⟨(-56704056505116198130863324),(-56704056505116197845415027)⟩⟩,⟨⟨(-129359542114670699840797738),(-129359542114670699557996261)⟩,⟨(-55773445827904493527303141),(-55773445827904493243990841)⟩⟩,⟨⟨(-128324919464355849582284628),(-128324919464355849301878253)⟩,⟨(-54897595746948455622516199),(-54897595746948455341605744)⟩⟩,⟨⟨(-127346642962589804640241695),(-127346642962589804361738241)⟩,⟨(-54074903932850057891721365),(-54074903932850057612719795)⟩⟩,⟨⟨(-126424011729359705298281996),(-126424011729359705021801478)⟩,⟨(-53303866783688593426200546),(-53303866783688593149227758)⟩⟩,⟨⟨(-125556359089084198214639612),(-125556359089084197939843098)⟩,⟨(-52583076494402694528118725),(-52583076494402694252835185)⟩⟩] +lemma kernel4_1_r3_14_eq : ∀ k : Fin 16, kernel4_1Expr 3 14 k = kernel4_1_r3_14 k := by decide +kernel +noncomputable def kernel4_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-124743053114360331692390261),(-124743053114360331419598156)⟩,⟨(-51911218297382171886290440),(-51911218297382171613016654)⟩⟩,⟨⟨(-123983497108719931441183193),(-123983497108719931169851424)⟩,⟨(-51287067871815959033236005),(-51287067871815958761427851)⟩⟩,⟨⟨(-123277130033926110768591998),(-123277130033926110498831138)⟩,⟨(-50709488919392275533541214),(-50709488919392275263309676)⟩⟩,⟨⟨(-122623426886942323236182839),(-122623426886942322967669129)⟩,⟨(-50177430904013285675450736),(-50177430904013285406471384)⟩⟩,⟨⟨(-122021899031320628610139336),(-122021899031320628343138108)⟩,⟨(-49689926953267631661208112),(-49689926953267631393746228)⟩⟩,⟨⟨(-121472094487382082151078185),(-121472094487382081885122704)⟩,⟨(-49246091919498940413853364),(-49246091919498940147441424)⟩⟩,⟨⟨(-120973598185199785257384196),(-120973598185199784992589731)⟩,⟨(-48845120598415492177452795),(-48845120598415491912205876)⟩⟩,⟨⟨(-120526032184043515305903794),(-120526032184043515041958125)⟩,⟨(-48486286103304516563050811),(-48486286103304516298656073)⟩⟩,⟨⟨(-120129055861603303478824930),(-120129055861603303216038611)⟩,⟨(-48168938393042931324789413),(-48168938393042931061557422)⟩⟩,⟨⟨(-119782366075977132084240160),(-119782366075977131822108407)⟩,⟨(-47892502952233704842802009),(-47892502952233704580227186)⟩⟩,⟨⟨(-119485697303084323970817631),(-119485697303084323709451579)⟩,⟨(-47656479621942404506396938),(-47656479621942404244590248)⟩⟩,⟨⟨(-119238821751850413112716209),(-119238821751850412851813806)⟩,⟨(-47460441579660940493536487),(-47460441579660940232195288)⟩⟩,⟨⟨(-119041549459200508530372836),(-119041549459200508270198329)⟩,⟨(-47304034467284124574040697),(-47304034467284124313429214)⟩⟩,⟨⟨(-118893728366595562683485437),(-118893728366595562423585545)⟩,⟨(-47186975666048574729773527),(-47186975666048574469437755)⟩⟩,⟨⟨(-118795244379548680844936020),(-118795244379548680585417248)⟩,⟨(-47109053717551883115090409),(-47109053717551882855136683)⟩⟩,⟨⟨(-118746021411265794792276093),(-118746021411265794532844783)⟩,⟨(-47070127890142033119066310),(-47070127890142032859200403)⟩⟩] +lemma kernel4_1_r3_15_eq : ∀ k : Fin 16, kernel4_1Expr 3 15 k = kernel4_1_r3_15 k := by decide +kernel +noncomputable def kernel4_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel4_1_r3_0,kernel4_1_r3_1,kernel4_1_r3_2,kernel4_1_r3_3,kernel4_1_r3_4,kernel4_1_r3_5,kernel4_1_r3_6,kernel4_1_r3_7,kernel4_1_r3_8,kernel4_1_r3_9,kernel4_1_r3_10,kernel4_1_r3_11,kernel4_1_r3_12,kernel4_1_r3_13,kernel4_1_r3_14,kernel4_1_r3_15] +lemma kernel4_1_r3_eq (i k : Fin 16) : kernel4_1Expr 3 i k = kernel4_1_r3 i k := by + fin_cases i + · exact kernel4_1_r3_0_eq k + · exact kernel4_1_r3_1_eq k + · exact kernel4_1_r3_2_eq k + · exact kernel4_1_r3_3_eq k + · exact kernel4_1_r3_4_eq k + · exact kernel4_1_r3_5_eq k + · exact kernel4_1_r3_6_eq k + · exact kernel4_1_r3_7_eq k + · exact kernel4_1_r3_8_eq k + · exact kernel4_1_r3_9_eq k + · exact kernel4_1_r3_10_eq k + · exact kernel4_1_r3_11_eq k + · exact kernel4_1_r3_12_eq k + · exact kernel4_1_r3_13_eq k + · exact kernel4_1_r3_14_eq k + · exact kernel4_1_r3_15_eq k +noncomputable def kernel4_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-97164823506027632684421767422),(-97164823506027632549463836694)⟩,⟨293880915795172018214656936759,293880915795172018349096798330⟩⟩,⟨⟨(-97098592178729507097582859353),(-97098592178729506962633940722)⟩,⟨293847830777270463025329659928,293847830777270463159761693926⟩⟩,⟨⟨(-96966186419753498582990795234),(-96966186419753498448060133632)⟩,⟨293781643776031904800794540648,293781643776031904935210685027⟩⟩,⟨⟨(-96767719976615520320618513729),(-96767719976615520185715361399)⟩,⟨293682320936031405277451655033,293682320936031405411843837816⟩⟩,⟨⟨(-96503363361230914573991957994),(-96503363361230914439125580247)⟩,⟨293549811662558345575771043651,293549811662558345710131175873⟩⟩,⟨⟨(-96173343718552858776837177714),(-96173343718552858642016856019)⟩,⟨293384048847202181539894734544,293384048847202181674214705845⟩⟩,⟨⟨(-95777944651206169957581489819),(-95777944651206169822816529296)⟩,⟨293184949167757043190623686592,293184949167757043324895356453⟩⟩,⟨⟨(-95317505999933216613503243741),(-95317505999933216478802967963)⟩,⟨292952413461695794672524103816,292952413461695794806739305443⟩⟩,⟨⟨(-94792423579626627223267070400),(-94792423579626627088640846773)⟩,⟨292686327172279108371945682171,292686327172279108506096195838⟩⟩,⟨⟨(-94203148870683974834444930845),(-94203148870683974699902135255)⟩,⟨292386560866181573245514201349,292386560866181573379591788532⟩⟩,⟨⟨(-93550188665383094663469220736),(-93550188665383094529019304173)⟩,⟨292052970821335165423463048555,292052970821335165557459383948⟩⟩,⟨⟨(-92834104668943619968667614938),(-92834104668943619834320015218)⟩,⟨291685399683510874942792720078,291685399683510875076699478778⟩⟩,⟨⟨(-92055513054911148489156236641),(-92055513054911148354920520262)⟩,⟨291283677189982226061447042196,291283677189982226195255756398⟩⟩,⟨⟨(-91215083974475607555636997265),(-91215083974475607421522662545)⟩,⟨290847620958440174338955533338,290847620958440174472657788321⟩⟩,⟨⟨(-90313541019315280744462030450),(-90313541019315280610478769951)⟩,⟨290377037339157740443824287588,290377037339157740577411457645⟩⟩,⟨⟨(-89351660637542980897119501882),(-89351660637542980763276888977)⟩,⟨289871722328235082125423594886,289871722328235082258887156142⟩⟩] +lemma kernel4_1_r4_0_eq : ∀ k : Fin 16, kernel4_1Expr 4 0 k = kernel4_1_r4_0 k := by decide +kernel +noncomputable def kernel4_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-88330271502321367780470431715),(-88330271502321367646778343812)⟩,⟨289331462539591850483968445190,289331462539591850617299550503⟩⟩,⟨⟨(-87250253832710752103765390136),(-87250253832710751970233443256)⟩,⟨288756036233213967947505073032,288756036233213968080695117240⟩⟩,⟨⟨(-86112538666315211845266433960),(-86112538666315211711904669853)⟩,⟨288145214397006751308964767562,288145214397006751442004698105⟩⟩,⟨⟨(-84918107083301753238972743769),(-84918107083301753105790862450)⟩,⟨287498761879455936375475396284,287498761879455936508356480927⟩⟩,⟨⟨(-83667989381382827568804667975),(-83667989381382827435812979113)⟩,⟨286816438570152997968674555558,286816438570152998101387428248⟩⟩,⟨⟨(-82363264201374983634910016707),(-82363264201374983502118221488)⟩,⟨286098000625101560593839665716,286098000625101560726375545907⟩⟩,⟨⟨(-81005057602975977707504990272),(-81005057602975977574923591909)⟩,⟨285343201733588024545477900838,285343201733588024677827179391⟩⟩,⟨⟨(-79594542090439425688600165463),(-79594542090439425556238956051)⟩,⟨284551794423272155361203330287,284551794423272155493357084486⟩⟩,⟨⟨(-78132935587870176920241023272),(-78132935587870176788110889148)⟩,⟨283723531400032668686529637081,283723531400032668818477820884⟩⟩,⟨⟨(-76621500363915088460599868792),(-76621500363915088328710514721)⟩,⟨282858166918989155585348610866,282858166918989155717082334271⟩⟩,⟨⟨(-75061541905682816523053792494),(-75061541905682816391416295200)⟩,⟨281955458183015402327458626299,281955458183015402458967595848⟩⟩,⟨⟨(-73454407741792612062766914338),(-73454407741792611931391093974)⟩,⟨281015166764960629056442573296,281015166764960629187717725146⟩⟩,⟨⟨(-71801486214525863490362547435),(-71801486214525863359259975605)⟩,⟨280037060049704765623998427473,280037060049704765755028912273⟩⟩,⟨⟨(-70104205201135183270574397607),(-70104205201135183139754709090)⟩,⟨279020912692091957708291111078,279020912692091957839067989386⟩⟩,⟨⟨(-68364030784454057172537399457),(-68364030784454057042012353313)⟩,⟨277966508086713403258984392584,277966508086713403389496564181⟩⟩,⟨⟨(-66582465873045293745557967383),(-66582465873045293615337320672)⟩,⟨276873639845446701479865371109,276873639845446701610103709811⟩⟩] +lemma kernel4_1_r4_1_eq : ∀ k : Fin 16, kernel4_1Expr 4 1 k = kernel4_1_r4_1 k := by decide +kernel +noncomputable def kernel4_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-64761048771228513813665318587),(-64761048771228513683761515492)⟩,⟨275742113278604487324467740966,275742113278604487454420394090⟩⟩,⟨⟨(-62901351699435450181282900811),(-62901351699435450051705318908)⟩,⟨274571746875500545505047956060,274571746875500545634706111078⟩⟩,⟨⟨(-61004979265456589535564286930),(-61004979265456589406325467638)⟩,⟨273362373780207157303871745112,273362373780207157433223383730⟩⟩,⟨⟨(-59073566887263343867928641504),(-59073566887263343739038163078)⟩,⟨272113843258253423327105647324,272113843258253423456141687004⟩⟩,⟨⟨(-57108779168216109386839982739),(-57108779168216109258311193815)⟩,⟨270826022150001000250673566344,270826022150001000379381109268⟩⟩,⟨⟨(-55112308225599839130798855692),(-55112308225599839002640809773)⟩,⟨269498796306431344118604434226,269498796306431344246974853255⟩⟩,⟨⟨(-53085871973564665186408299157),(-53085871973564665058634408619)⟩,⟨268132072003087399284814928003,268132072003087399412835189471⟩⟩,⟨⟨(-51031212361689164338856178865),(-51031212361689164211475701069)⟩,⟨266725777327932918733697411707,266725777327932918861358611955⟩⟩,⟨⟨(-48950093570527538301354109874),(-48950093570527538174381546217)⟩,⟨265279863538924429850610376424,265279863538924429977898316338⟩⟩,⟨⟨(-46844300165648713676185514872),(-46844300165648713549629274524)⟩,⟨263794306387134422617648802488,263794306387134422744555355786⟩⟩,⟨⟨(-44715635211824562827335618810),(-44715635211824562701210054459)⟩,⟨262269107401319756710638476754,262269107401319756837149519118⟩⟩,⟨⟨(-42565918349175480404565019796),(-42565918349175480278878907118)⟩,⟨260704295129896649144830455395,260704295129896649270937419093⟩⟩,⟨⟨(-40396983833233769373860854066),(-40396983833233769248629748632)⟩,⟨259099926336362969045521251548,259099926336362969171208730655⟩⟩,⟨⟨(-38210678541038018149431770559),(-38210678541038018024663425628)⟩,⟨257456087144299947949182223922,257456087144299948074442602057⟩⟩,⟨⟨(-36008859945524187631997842424),(-36008859945524187507707603472)⟩,⟨255772894128188791121201721302,255772894128188791246019728065⟩⟩,⟨⟨(-33793394060630755171877001931),(-33793394060630755048072981346)⟩,⟨254050495346392985532399776815,254050495346392985656767361457⟩⟩] +lemma kernel4_1_r4_2_eq : ∀ k : Fin 16, kernel4_1Expr 4 2 k = kernel4_1_r4_2 k := by decide +kernel +noncomputable def kernel4_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-31566153359685247009928283288),(-31566153359685246886627457664)⟩,⟨252289071312784239073813080811,252289071312784239197713261052⟩⟩,⟨⟨(-29329014669787083966018985004),(-29329014669787083843227936182)⟩,⟨250488835903628805454497559703,250488835903628805577923746868⟩⟩,⟨⟨(-27083857045046109864995322220),(-27083857045046109742730417000)⟩,⟨248650037196501257343798773171,248650037196501257466734522251⟩⟩,⟨⟨(-24832559621676705259885255955),(-24832559621676705138153751472)⟩,⟨246772958238154328109950683935,246772958238154328232388655869⟩⟩,⟨⟨(-22576999458083244990178825503),(-22576999458083244868998762766)⟩,⟨244857917738445964623882819261,244857917738445964745804814696⟩⟩,⟨⟨(-20319049363203073079241874371),(-20319049363203072958618838968)⟩,⟨242905270687607887273080023615,242905270687607887394480309665⟩⟩,⟨⟨(-18060575716497383929497966885),(-18060575716497383809449350377)⟩,⟨240915408894333357966409026318,240915408894333358087269982975⟩⟩,⟨⟨(-15803436283097665621094711456),(-15803436283097665501626711870)⟩,⟨238888761442365083910523006284,238888761442365084030838216006⟩⟩,⟨⟨(-13549478027724943704322358319),(-13549478027724943585454593357)⟩,⟨236825795063476757807729148123,236825795063476757927478684543⟩⟩,⟨⟨(-11300534931100244064459706280),(-11300534931100243946196035885)⟩,⟨234727014424963129838925086301,234727014424963129958104811436⟩⟩,⟨⟨(-9058425812656774708714609131),(-9058425812656774591073427355)⟩,⟨232592962329983152450641862610,232592962329983152569233009721⟩⟩,⟨⟨(-6824952163446637859887063188),(-6824952163446637742873303411)⟩,⟨230424219829338018717996851504,230424219829338018835994139192⟩⟩,⟨⟨(-4601895993206784477714982840),(-4601895993206784361349247031)⟩,⟨228221406243510167356219086046,228221406243510167473601462881⟩⟩,⟨⟨(-2391017695609805965196228706),(-2391017695609805849481005269)⟩,⟨225985179094039847576310626323,225985179094039847693075203629⟩⟩,⟨⟨(-194053935774452731331218944),(-194053935774452616285855081)⟩,⟨223716233943571878857682461701,223716233943571878973809384166⟩⟩,⟨⟨1987284435852051649439820580,1987284435852051763811861903⟩,⟨221415304144166019060274315013,221415304144166019175759655118⟩⟩] +lemma kernel4_1_r4_3_eq : ∀ k : Fin 16, kernel4_1Expr 4 3 k = kernel4_1_r4_3 k := by decide +kernel +noncomputable def kernel4_1_r4_4 : Fin 16 → CBox := ![⟨⟨4151314439103251660598531031,4151314439103251774274900495⟩,⟨219083160493729047056636192983,219083160493729047171457017239⟩⟩,⟨⟨6296382985046060169236749896,6296382985046060282217363033⟩,⟨216720610800694417100962407443,216720610800694417215118126198⟩⟩,⟨⟨8420868858130389513474953153,8420868858130389625739583660⟩,⟨214328499357345264281987352099,214328499357345264395457106902⟩⟩,⟨⟨10523184655405095137196370094,10523184655405095248743222639⟩,⟨211907706322447718666919356347,211907706322447718779700785338⟩⟩,⟨⟨12601778678699134764777130576,12601778678699134875583194048⟩,⟨209459147014132980944218099647,209459147014132981056287490038⟩⟩,⟨⟨14655136775710686548125555488,14655136775710686658192336359⟩,⟨206983771114237464888723903055,206983771114237465000082162344⟩⟩,⟨⟨16681784126005174338557610028,16681784126005174447864101378⟩,⟨204482561785579545778573811850,204482561785579545889199190633⟩⟩,⟨⟨18680286967995797112885128250,18680286967995797221431386542⟩,⟨201956534703918080805889876632,201956534703918080915781779589⟩⟩,⟨⟨20649254263067265586092231628,20649254263067265693853568253⟩,⟨199406737006600891646259268442,199406737006600891755392196197⟩⟩,⟨⟨22587339293104956831975011087,22587339293104956938955833833⟩,⟨196834246160169821683977471577,196834246160169821792355163009⟩⟩,⟨⟨24493241187807482626293283448,24493241187807482732471926701⟩,⟨194240168749441803589538024564,194240168749441803697137976824⟩⟩,⟨⟨26365706378290534532284083622,26365706378290534637662620271⟩,⟨191625639190831606206129394759,191625639190831606312952962124⟩⟩,⟨⟨28203529973633553495491286927,28203529973633553600223062073⟩,⟨188991818372920593729314204950,188991818372920593835513506072⟩⟩,⟨⟨30005557057177938774828894017,30005557057177938878932041049⟩,⟨186339892227505962207311513569,186339892227505962312903940341⟩⟩,⟨⟨31770683899555755657821900511,31770683899555755761273969414⟩,⟨183671070234585577308009497272,183671070234585577412971692018⟩⟩,⟨⟨33497859085610750165854334984,33497859085610750268659313521⟩,⟨180986583864943808631879151462,180986583864943808736214343336⟩⟩] +lemma kernel4_1_r4_4_eq : ∀ k : Fin 16, kernel4_1Expr 4 4 k = kernel4_1_r4_4 k := by decide +kernel +noncomputable def kernel4_1_r4_5 : Fin 16 → CBox := ![⟨⟨35186084552568391105802585135,35186084552568391207933108223⟩,⟨178287684964202756834727239955,178287684964202756938407096259⟩⟩,⟨⟨36834416537018029098057010785,36834416537018029199529965634⟩,⟨175575644082390154372702930211,175575644082390154475737822044⟩⟩,⟨⟨38441966428487418997557077953,38441966428487419098357362475⟩,⟨172851748753249184230513734868,172851748753249184332881226082⟩⟩,⟨⟨40007901527617066078589944777,40007901527617066178723386006⟩,⟨170117301727675745227703837825,170117301727675745329409109251⟩⟩,⟨⟨41531445707178339402629353784,41531445707178339502068122505⟩,⟨167373619165814589907616939672,167373619165814590008631300761⟩⟩,⟨⟨43011879974424205513820864394,43011879974424205612575754491⟩,⟨164622028792476619234153403429,164622028792476619334487031269⟩⟩,⟨⟨44448542933513879019058184236,44448542933513879117104895543⟩,⟨161863868020654844248953602406,161863868020654844348581359270⟩⟩,⟨⟨45840831147011724257805773496,45840831147011724355152199377⟩,⟨159100482048015588464188070499,159100482048015588563117216098⟩⟩,⟨⟨47188199395725392699871837146,47188199395725392796487985574⟩,⟨156333221931323942709633782887,156333221931323942807833457629⟩⟩,⟨⟨48490160836417425231721662660,48490160836417425327621882460⟩,⟨153563442643827902879771251865,153563442643827902977255216471⟩⟩,⟨⟨49746287057197336220629455647,49746287057197336315788792213⟩,⟨150792501120673699695501234172,150792501120673699792243706835⟩⟩,⟨⟨50956208030676449404659453796,50956208030676449499087955226⟩,⟨148021754297455322517426109515,148021754297455322613436532104⟩⟩,⟨⟨52119611965244375112232157457,52119611965244375205899852851⟩,⟨145252557147013977959282748302,145252557147013978054530304922⟩⟩,⟨⟨53236245055102889286179580034,53236245055102889379102412707⟩,⟨142486260719598118936051949515,142486260719598119030552025369⟩⟩,⟨⟨54305911129968972725826999994,54305911129968972817979525587⟩,⟨139724210191471721276987215792,139724210191471721370713565196⟩⟩,⟨⟨55328471205632765532800967543,55328471205632765624195452512⟩,⟨136967742927017744348031639284,136967742927017744440995963239⟩⟩] +lemma kernel4_1_r4_5_eq : ∀ k : Fin 16, kernel4_1Expr 4 5 k = kernel4_1_r4_5 k := by decide +kernel +noncomputable def kernel4_1_r4_6 : Fin 16 → CBox := ![⟨⟨56303842936827060911513982850,56303842936827061002118132419⟩,⟨134218186559325341516421711064,134218186559325341608590892176⟩⟩,⟨⟨57231999974131586584929444109,57231999974131586674763376557⟩,⟨131476857094173618830408809988,131476857094173618921802466097⟩⟩,⟨⟨58112971226896598001432511549,58112971226896598090470469564⟩,⟨128745057042231889193142578189,128745057042231889283734190571⟩⟩,⟨⟨58946840034425152654679988907,58946840034425152742936482005⟩,⟨126024073584186826742214643582,126024073584186826832018208519⟩⟩,⟨⟨59733743247900793197142618642,59733743247900793284586231284⟩,⟨123315176773381161563178727648,123315176773381161652162060671⟩⟩,⟨⟨60473870225786214983478188936,60473870225786215070130172536⟩,⟨120619617780407112876804175036,120619617780407112964988076762⟩⟩,⟨⟨61167461745647845720471883594,61167461745647845806306336821⟩,⟨117938627183941256622309269066,117938627183941256709667128821⟩⟩,⟨⟨61814808835580179093724998929,61814808835580179178758674226⟩,⟨115273413311936647594810652589,115273413311936647681358771113⟩⟩,⟨⟨62416251528611287488298558489,62416251528611287572498139855⟩,⟨112625160637103519703410986086,112625160637103519789115326427⟩⟩,⟨⟨62972177543666351904159512252,62972177543666351987550341728⟩,⟨109995028230412585345240719931,109995028230412585430126248265⟩⟩,⟨⟨63483020896848509010043786894,63483020896848509092599994025⟩,⟨107384148276145719047753414167,107384148276145719131793612823⟩⟩,⟨⟨63949260446965107826605065335,63949260446965107908345602051⟩,⟨104793624651798567325586331390,104793624651798567408799769090⟩⟩,⟨⟨64371418379381940277986604202,64371418379381940358879353916⟩,⟨102224531575909350275826188516,102224531575909350358180101266⟩⟩,⟨⟨64750058632427579442731200867,64750058632427579522802580616⟩,⟨99677912326648827891819802080,99677912326648827973340294799⟩⟩,⟨⟨65085785270694118646707431261,65085785270694118725931760558⟩,⟨97154778033759149928341445968,97154778033759150009002260815⟩⟩,⟨⟨65379240809688921290102731310,65379240809688921368501093963⟩,⟨94656106546175178560605416667,94656106546175178640427327325⟩⟩] +lemma kernel4_1_r4_6_eq : ∀ k : Fin 16, kernel4_1Expr 4 6 k = kernel4_1_r4_6 k := by decide +kernel +noncomputable def kernel4_1_r4_7 : Fin 16 → CBox := ![⟨⟨65631104496384111206701325264,65631104496384111284239513261⟩,⟨92182841377401979909692678887,92182841377401979988640891690⟩⟩,⟨⟨65842090550286181783621893291,65842090550286181860330794303⟩,⟨89735890730457655210219133806,89735890730457655288324310124⟩⟩,⟨⟨66012946369707085212495624380,66012946369707085288349906403⟩,⟨87316126603922669823623173012,87316126603922669900859478771⟩⟩,⟨⟨66144450707960368751060688320,66144450707960368826083455421⟩,⟨84924383980366490421768304219,84924383980366490498158608557⟩⟩,⟨⟨66237411824231322022402599930,66237411824231322096561757366⟩,⟨82561460098150810297777886425,82561460098150810373289596349⟩⟩,⟨⟨66292665613878738687942913957,66292665613878738761269599071⟩,⟨80228113807337077294937233329,80228113807337077369601324833⟩⟩,⟨⟨66311073722917908212549561581,66311073722917908285018923003⟩,⟨77925065010155574067680851212,77925065010155574141472049142⟩⟩,⟨⟨66293521651410048823699017832,66293521651410048895351978239⟩,⟨75652994186225054390581062407,75652994186225054463534905772⟩⟩,⟨⟨66240916850442858262257683454,66240916850442858333135264894⟩,⟨73412542002447006489503164357,73412542002447006561635840668⟩⟩,⟨⟨66154186817330556495446294962,66154186817330556565580787158⟩,⟨71204309007238059999752421542,71204309007238060071097240529⟩⟩,⟨⟨66034277193590158284251859206,66034277193590158353616186754⟩,⟨69028855408508907423655489994,69028855408508907494186122124⟩⟩,⟨⟨65882149870164246346260409264,65882149870164246414878506981⟩,⟨66886700934549364028840992536,66886700934549364098582350708⟩⟩,⟨⟨65698781104259786138056548712,65698781104259786205894173850⟩,⟨64778324776737787139457240552,64778324776737787208375808982⟩⟩,⟨⟨65485159652058160671332278866,65485159652058160738421862245⟩,⟨62704165612759912233418063297,62704165612759912301547282796⟩⟩,⟨⟨65242284921424295023298476217,65242284921424295089613729398⟩,⟨60664621708798080817260641325,60664621708798080884574991244⟩⟩,⟨⟨64971165148603224520270940514,64971165148603224585837472879⟩,⟨58660051098937617632953880900,58660051098937617699479943176⟩⟩] +lemma kernel4_1_r4_7_eq : ∀ k : Fin 16, kernel4_1Expr 4 7 k = kernel4_1_r4_7 k := by decide +kernel +noncomputable def kernel4_1_r4_8 : Fin 16 → CBox := ![⟨⟨64672815602741524788286189705,64672815602741524853067831384⟩,⟨56690771839833485139525278181,56690771839833485205227619767⟩⟩,⟨⟨64348256821909495295056599439,64348256821909495359090194488⟩,⟨54757062338487960020130023408,54757062338487960085046492114⟩⟩,⟨⟨63998512884128737188256336261,63998512884128737251516505068⟩,⟨52859161750809531590180978048,52859161750809531654286971892⟩⟩,⟨⟨63624609716729689456264565051,63624609716729689518778410088⟩,⟨50997270448455038486136644899,50997270448455038549460219406⟩⟩,⟨⟨63227573447175709203677887490,63227573447175709265412535428⟩,⟨49171550551301690498322702541,49171550551301690560831738184⟩⟩,⟨⟨62808428798295347221100777652,62808428798295347282092095112⟩,⟨47382126522753447827827140040,47382126522753447889558467942⟩⟩,⟨⟨62368197530663539043667081853,62368197530663539103890676727⟩,⟨45629085824957559017618098445,45629085824957559078548102769⟩⟩,⟨⟨61907896934666473611731553148,61907896934666473671215840048⟩,⟨43912479630892127369847862040,43912479630892127430005878639⟩⟩,⟨⟨61428538374574889436941896088,61428538374574889495652702725⟩,⟨42232323590184547512452922143,42232323590184547571805524508⟩⟩,⟨⟨60931125886737452973893567658,60931125886737453031870325475⟩,⟨40588598645433620935811333771,40588598645433620994398882308⟩⟩,⟨⟨60416654833790659645103392437,60416654833790659702322766983⟩,⟨38981251895735143248711911652,38981251895735143306511836780⟩⟩,⟨⟨59886110616565316183567037354,59886110616565316240058542445⟩,⟨37410197504051709029346579131,37410197504051709086389273441⟩⟩,⟨⟨59340467445153047731778871952,59340467445153047787511434362⟩,⟨35875317645022287808069378088,35875317645022287864324507828⟩⟩,⟨⟨58780687170380336319185200888,58780687170380336374197202348⟩,⟨34376463489775607452097301498,34376463489775607507604120282⟩⟩,⟨⟨58207718176723224022140661438,58207718176723224076409854996⟩,⟨32913456224293297443290293556,32913456224293297498027299152⟩⟩,⟨⟨57622494337483858351083376369,57622494337483858404640169425⟩,⟨31486088097863793509934671546,31486088097863793563933098983⟩⟩] +lemma kernel4_1_r4_8_eq : ∀ k : Fin 16, kernel4_1Expr 4 8 k = kernel4_1_r4_8 k := by decide +kernel +noncomputable def kernel4_1_r4_9 : Fin 16 → CBox := ![⟨⟨57025934032841338303158640261,57025934032841338355970188585⟩,⟨30094123498175830195700938598,30094123498175830248928659566⟩⟩,⟨⟨56418939231184617553992992486,56418939231184617606101373536⟩,⟨28737300049620540299250031943,28737300049620540351749940944⟩⟩,⟨⟨55802394633935275057890330973,55802394633935275109274410335⟩,⟨27415329731403282237850992572,27415329731403282289602672483⟩⟩,⟨⟨55177166883873466688295279179,55177166883873466738986130301⟩,⟨26127900012109826247505305031,26127900012109826298540598978⟩⟩,⟨⟨54544103836791970934744895278,54544103836791970984713482111⟩,⟨24874674997425905488118744983,24874674997425905538409310700⟩⟩,⟨⟨53904033896121533983687989713,53904033896121534032974217036⟩,⟨23655296587773799980333527888,23655296587773800029920017680⟩⟩,⟨⟨53257765409996250318214020259,53257765409996250366797850967⟩,⟨22469385642703959502814268250,22469385642703959551677329019⟩⟩,⟨⟨52606086130060977073895255510,52606086130060977121808224120⟩,⟨21316543148963048425065778814,21316543148963048473237651974⟩⟩,⟨⟨51949762731164212785229961273,51949762731164212832441753371⟩,⟨20196351389251550381761309956,20196351389251550429212342871⟩⟩,⟨⟨51289540390929858370562593077,51289540390929858417115870058⟩,⟨19108375108783524739906002221,19108375108783524786679535884⟩⟩,⟨⟨50626142428060149990103348502,50626142428060150035979156063⟩,⟨18052162676867567034915221956,18052162676867567080992948374⟩⟩,⟨⟨49960269998090084807031243067,49960269998090084852261357986⟩,⟨17027247240840789406275432313,17027247240840789451689769351⟩⟩,⟨⟨49292601845191072415904667480,49292601845191072460462145958⟩,⟨16033147869805996672035314285,16033147869805996716759945824⟩⟩,⟨⟨48623794108508503915655800038,48623794108508503959581108816⟩,⟨15069370685745479978371340816,15069370685745480022447340848⟩⟩,⟨⟨47954480181414551904408146848,47954480181414551947683368240⟩,⟨14135409979712276713497016541,14135409979712276756907072960⟩⟩,⟨⟨47285270621963861456869392817,47285270621963861499526356123⟩,⟨13230749310930653008253453187,13230749310930653051029969253⟩⟩] +lemma kernel4_1_r4_9_eq : ∀ k : Fin 16, kernel4_1Expr 4 9 k = kernel4_1_r4_9 k := by decide +kernel +noncomputable def kernel4_1_r4_10 : Fin 16 → CBox := ![⟨⟨46616753112755878221063729817,46616753112755878263073493760⟩,⟨12354862586771264403944039423,12354862586771264446058666241⟩⟩,⟨⟨45949492468333351205015485266,45949492468333351246421529393⟩,⟨11507215121702265644001107277,11507215121702265685497858249⟩⟩,⟨⟨45284030688181965039539676904,45284030688181965080325082373⟩,⟨10687264673454913512828175688,10687264673454913553690695038⟩⟩,⟨⟨44620887053340976558543582736,44620887053340976598740033582⟩,⟨9894462454780298620532257844,9894462454780298660792736622⟩⟩,⟨⟨43960558264588989610555160293,43960558264588989650137729268⟩,⟨9128254119312137124963490246,9128254119312137164597552826⟩⟩,⟨⟨43303518620132398009810106074,43303518620132398048818954608⟩,⟨8388080720188460848998303212,8388080720188460888046575879⟩⟩,⟨⟨42650220230696321853895996906,42650220230696321892315135584⟩,⟨7673379640222000718959139693,7673379640222000757406152981⟩⟩,⟨⟨42001093269898786817914990533,42001093269898786855775802498⟩,⟨6983585492544529842298527779,6983585492544529880176106369⟩⟩,⟨⟨41356546257778149512092922707,41356546257778149549369046491⟩,⟨6318130990783915760569574023,6318130990783915797851873097⟩⟩,⟨⟨40716966375341027856257445468,40716966375341027892991030435⟩,⟨5676447787963655720939502085,5676447787963655757669063579⟩⟩,⟨⟨40082719808002903278704950824,40082719808002903314880882239⟩,⟨5057967283442796977318162875,5057967283442797013480349197⟩⟩,⟨⟨39454152115805750305349729579,39454152115805750340998930210⟩,⟨4462121397338973292441140131,4462121397338973328067252655⟩⟩,⟨⟨38831588628316130034616747063,38831588628316130069716128474⟩,⟨3888343311998451082689920143,3888343311998451117757344680⟩⟩,⟨⟨38215334862132753679659932572,38215334862132753714248649321⟩,⟨3336068180194241478746228343,3336068180194241513294450439⟩⟩,⟨⟨37605676958964165650185409065,37605676958964165684249145450⟩,⟨2804733799846200888434959126,2804733799846200922450098589⟩⟩,⟨⟨37002882142274488495890451573,37002882142274488529459550752⟩,⟨2293781255165350715056008022,2293781255165350748568727058⟩⟩] +lemma kernel4_1_r4_10_eq : ∀ k : Fin 16, kernel4_1Expr 4 10 k = kernel4_1_r4_10 k := by decide +kernel +noncomputable def kernel4_1_r4_11 : Fin 16 → CBox := ![⟨⟨36407199190537684287338210223,36407199190537684320387475438⟩,⟨1802655524228170020283684345,1802655524228170053269231044⟩⟩,⟨⟨35818858925188085056831620410,35818858925188085089402483264⟩,⟨1330806053085160946103774958,1330806053085160978603842982⟩⟩,⟨⟨35238074711406594258924898534,35238074711406594291003785755⟩,⟨877687296601397253362956639,877687296601397285364368337⟩⟩,⟨⟨34665042969937528852486141365,34665042969937528884102695624⟩,⟨442759226314915931397786692,442759226314915962930448224⟩⟩,⟨⟨34099943698190128384474467266,34099943698190128415607216827⟩,⟨25487805681606898373702936,25487805681606929416544385⟩⟩,⟨⟨33542940998940880140030303357,33542940998940880170716872280⟩,⟨(-374654566847366561390652300),(-374654566847366530799794284)⟩⟩,⟨⟨32994183615017582721904906456,32994183615017582752132386162⟩,⟨(-758188646397657314173885404),(-758188646397657284047561371)⟩⟩,⟨⟨32453805468413088791504841389,32453805468413088821302099589⟩,⟨(-1125627961308904419040897134),(-1125627961308904389350027038)⟩⟩,⟨⟨31921926202345537025446502308,31921926202345537054790423252⟩,⟨(-1477478463191519824189286278),(-1477478463191519794956608881)⟩⟩,⟨⟨31398651724852222405899423688,31398651724852222434829126071⟩,⟨(-1814238206701983375528124701),(-1814238206701983346714369031)⟩⟩,⟨⟨30884074752575695813948398553,30884074752575695842451583305⟩,⟨(-2136397058285214394420942904),(-2136397058285214366038085029)⟩⟩,⟨⟨30378275353472876982970740116,30378275353472877011075422913⟩,⟨(-2444436433087495364651440292),(-2444436433087495336671298725)⟩⟩,⟨⟨29881321487250574065714758911,29881321487250574093400837119⟩,⟨(-2738829059203451089254427010),(-2738829059203451061696766206)⟩⟩,⟨⟨29393269542403510496574545216,29393269542403510523877788735⟩,⟨(-3020038768385606893407842486),(-3020038768385606866236779462)⟩⟩,⟨⟨28914164868803465559590496534,28914164868803465586499146703⟩,⟨(-3288520312314917666713847999),(-3288520312314917639940850579)⟩⟩,⟨⟨28444042304860157640855123707,28444042304860157667396307010⟩,⟨(-3544719203505216876082789922),(-3544719203505216849680607626)⟩⟩] +lemma kernel4_1_r4_11_eq : ∀ k : Fin 16, kernel4_1Expr 4 11 k = kernel4_1_r4_11 k := by decide +kernel +noncomputable def kernel4_1_r4_12 : Fin 16 → CBox := ![⟨⟨27982926698345775955941507519,27982926698345775982092674842⟩,⟨(-3789071579893609490260575067),(-3789071579893609464251433688)⟩⟩,⟨⟨27530833420045354104556455470,27530833420045354130355464739⟩,⟨(-4022004092152242336778640992),(-4022004092152242311124624847)⟩⟩,⟨⟨27087768869464252849599039687,27087768869464252875034628792⟩,⟨(-4243933812744437657297154618),(-4243933812744437632009264349)⟩⟩,⟨⟨26653730971891674985138389254,26653730971891675010236752506⟩,⟨(-4455268165739670658227155626),(-4455268165739670633279110040)⟩⟩,⟨⟨26228709666185186077140446804,26228709666185186101882617254⟩,⟨(-4656404876397103561666412830),(-4656404876397103537076893884)⟩⟩,⟨⟨25812687382705494104662658210,25812687382705494129082397166⟩,⟨(-4847731939526146218345154822),(-4847731939526146194080368043)⟩⟩,⟨⟨25405639510893099991491612804,25405639510893100015578092744⟩,⟨(-5029627605634582614942721155),(-5029627605634582591013259015)⟩⟩,⟨⟨25007534856038739176964006654,25007534856038739200742490310⟩,⟨(-5202460383879967517577642789),(-5202460383879967493958188324)⟩⟩,⟨⟨24618336084857678798200620880,24618336084857678821650304281⟩,⟨(-5366589060848041288655224947),(-5366589060848041265366308043)⟩⟩,⟨⟨24238000159533819812341592340,24238000159533819835497575897⟩,⟨(-5522362734192617370255876583),(-5522362734192617347262408260)⟩⟩,⟨⟨23866478759953098914304633014,23866478759953098937156487830⟩,⟨(-5670120860184551444285493647),(-5670120860184551421597691398)⟩⟩,⟨⟨23503718693896827502224773313,23503718693896827524796821749⟩,⟨(-5810193314232791919677474378),(-5810193314232791897270989976)⟩⟩,⟨⟨23149662295014295238332425786,23149662295014295260606613114⟩,⟨(-5942900463457929810345561493),(-5942900463457929788238207215)⟩⟩,⟨⟨22804247808440169114438546829,22804247808440169136446634151⟩,⟨(-6068553250417908356660621585),(-6068553250417908334820664846)⟩⟩,⟨⟨22467409763965913863790584027,22467409763965913885522493461⟩,⟨(-6187453287106420216970078223),(-6187453287106420195407406427)⟩⟩,⟨⟨22139079336715637064300364630,22139079336715637085779502219⟩,⟨(-6299892958366819922763589038),(-6299892958366819901454794699)⟩⟩] +lemma kernel4_1_r4_12_eq : ∀ k : Fin 16, kernel4_1Expr 4 12 k = kernel4_1_r4_12 k := by decide +kernel +noncomputable def kernel4_1_r4_13 : Fin 16 → CBox := ![⟨⟨21819184695315425008288078146,21819184695315425029493887552⟩,⟨(-6406155533887925247769693809),(-6406155533887925226735091972)⟩⟩,⟨⟨21507651337581396816333926363,21507651337581396837300124505⟩,⟨(-6506515287972693900541583100),(-6506515287972693879747526423)⟩⟩,⟨⟨21204402413785387734181358384,21204402413785387754898196045⟩,⟨(-6601237626296269671146980812),(-6601237626296269650603046522)⟩⟩,⟨⟨20909359037588410533838812434,20909359037588410554329239722⟩,⟨(-6690579218896130826875877880),(-6690579218896130806558245096)⟩⟩,⟨⟨20622440584760877145451866418,20622440584760877165698799500⟩,⟨(-6774788138663887245946397863),(-6774788138663887225871453746)⟩⟩,⟨⟨20343564979835039174913446014,20343564979835039194946740364⟩,⟨(-6854104004635513930525619315),(-6854104004635513910663635420)⟩⟩,⟨⟨20072648970859280508452409602,20072648970859280528262579699⟩,⟨(-6928758129404338071967481918),(-6928758129404338052327843818)⟩⟩,⟨⟨19809608392445828257940618202,19809608392445828277549284952⟩,⟨(-6998973670008784277752920339),(-6998973670008784258314091507)⟩⟩,⟨⟨19554358417323205386544544108,19554358417323205405932333432⟩,⟨(-7064965781674606076871345316),(-7064965781674606057652547362)⟩⟩,⟨⟨19306813796622399293075893708,19306813796622399312274136099⟩,⟨(-7126941773818978208082354924),(-7126941773818978189052403402)⟩⟩,⟨⟨19066889089141338842200710576,19066889089141338861200196809⟩,⟨(-7185101267751288853811599200),(-7185101267751288834979615007)⟩⟩,⟨⟨18834498879845934140267849042,18834498879845934159089375576⟩,⟨(-7239636355532657795287044688),(-7239636355532657776632320405)⟩⟩,⟨⟨18609557987877717397512357027,18609557987877717416139116668⟩,⟨(-7290731759483027663789972982),(-7290731759483027645329187505)⟩⟩,⟨⟨18391981664348109792573778226,18391981664348109811033970608⟩,⟨(-7338564991851051468461228986),(-7338564991851051450166319016)⟩⟩,⟨⟨18181685780207609800418828552,18181685780207609818703494810⟩,⟨(-7383306514187858789532999399),(-7383306514187858771412845286)⟩⟩,⟨⟨17978587004484834992214300609,17978587004484835010343467090⟩,⟨(-7425119895991061592711877730),(-7425119895991061574746545460)⟩⟩] +lemma kernel4_1_r4_13_eq : ∀ k : Fin 16, kernel4_1Expr 4 13 k = kernel4_1_r4_13 k := by decide +kernel +noncomputable def kernel4_1_r4_14 : Fin 16 → CBox := ![⟨⟨17782602973195434019341385423,17782602973195434037295417028⟩,⟨(-7464161972210002200031625711),(-7464161972210002182240613265)⟩⟩,⟨⟨17593652449224500173045287636,17593652449224500190854725833⟩,⟨(-7500582999227201437856170873),(-7500582999227201420209093754)⟩⟩,⟨⟨17411655473488343653037317516,17411655473488343670693453234⟩,⟨(-7534526808954192210587044603),(-7534526808954192193092541714)⟩⟩,⟨⟨17236533507682396457330171177,17236533507682396474852294572⟩,⟨(-7566130960702387211291845062),(-7566130960702387193930720634)⟩⟩,⟨⟨17068209568921710161116933290,17068209568921710178488651050⟩,⟨(-7595526890511300008913688546),(-7595526890511299991702223973)⟩⟩,⟨⟨16906608356579039582280234215,16906608356579039599528349364⟩,⟨(-7622840057637293212286035084),(-7622840057637293195197568155)⟩⟩,⟨⟨16751656371622959239974985590,16751656371622959257091019428⟩,⟨(-7648190087926048378476862857),(-7648190087926048361519809077)⟩⟩,⟨⟨16603282028754907176009298123,16603282028754907193011867465⟩,⟨(-7671690913811127781213252589),(-7671690913811127764369090701)⟩⟩,⟨⟨16461415761639562287531684800,16461415761639562304402174835⟩,⟨(-7693450910699321131530744230),(-7693450910699321114817969372)⟩⟩,⟨⟨16325990121517604388756942439,16325990121517604405523964372⟩,⟨(-7713573029520938662701549281),(-7713573029520938646091706027)⟩⟩,⟨⟨16196939869483745644560305939,16196939869483745661215617342⟩,⟨(-7732154925239827920042702060),(-7732154925239827903543975548)⟩⟩,⟨⟨16074202062706019842554173540,16074202062706019859115757114⟩,⟨(-7749289081133661554701641734),(-7749289081133661538296145173)⟩⟩,⟨⟨15957716134854731345250757263,15957716134854731361702506604⟩,⟨(-7765062928669977682574954367),(-7765062928669977666278693164)⟩⟩,⟨⟨15847423971001254691365533861,15847423971001254707733157157⟩,⟨(-7779558962817566785013080471),(-7779558962817566768800488838)⟩⟩,⟨⟨15743269977238091927151133159,15743269977238091943426617034⟩,⟨(-7792854852646106838391850696),(-7792854852646106822270889615)⟩⟩,⟨⟨15645201145262288093195269321,15645201145262288109396020793⟩,⟨(-7805023547079471542977689241),(-7805023547079471526931047395)⟩⟩] +lemma kernel4_1_r4_14_eq : ∀ k : Fin 16, kernel4_1Expr 4 14 k = kernel4_1_r4_14 k := by decide +kernel +noncomputable def kernel4_1_r4_15 : Fin 16 → CBox := ![⟨⟨15553167112154523158692538291,15553167112154523174799469730⟩,⟨(-7816133375679898130995835200),(-7816133375679898115042485148)⟩⟩,⟨⟨15467120215575985440366873023,15467120215575985456408357332⟩,⟨(-7826248144351226766477445275),(-7826248144351226750589174600)⟩⟩,⟨⟨15387015544594528652560956570,15387015544594528668529227713⟩,⟨(-7835427225859740809836699786),(-7835427225859740794021226299)⟩⟩,⟨⟨15312810986340660883799312056,15312810986340660899711233328⟩,⟨(-7843725645080776114160844304),(-7843725645080776098401399584)⟩⟩,⟨⟨15244467268682644941948811355,15244467268682644957788465014⟩,⟨(-7851194158888259844361647588),(-7851194158888259828674055070)⟩⟩,⟨⟨15181947999098438985933104438,15181947999098439001725403859⟩,⟨(-7857879330612718571739548851),(-7857879330612718556099037536)⟩⟩,⟨⟨15125219699910404990452318781,15125219699910405006189744745⟩,⟨(-7863823599001096627137985029),(-7863823599001096611552029303)⟩⟩,⟨⟨15074251840036688801122168197,15074251840036688816821095556⟩,⟨(-7869065341618985297175622341),(-7869065341618985281627941063)⟩⟩,⟨⟨15029016863400955508086903421,15029016863400955523728907925⟩,⟨(-7873638932642619030104640815),(-7873638932642619014613551110)⟩⟩,⟨⟨14989490214129771654437467946,14989490214129771670049750839⟩,⟨(-7877574794994285066888597252),(-7877574794994285051427054760)⟩⟩,⟨⟨14955650358654383498959591556,14955650358654383514534906798⟩,⟨(-7880899446780657453026805670),(-7880899446780657437602014480)⟩⟩,⟨⟨14927478804820968456405139909,14927478804820968471959399198⟩,⟨(-7883635541999045667539749811),(-7883635541999045652135890294)⟩⟩,⟨⟨14904960118100653588884593274,14904960118100653604401978369⟩,⟨(-7885801905481683284616665911),(-7885801905481683269249465254)⟩⟩,⟨⟨14888081934977717786618950214,14888081934977717802123879254⟩,⟨(-7887413562053014932225615470),(-7887413562053014916870797050)⟩⟩,⟨⟨14876834973581438927008091709,14876834973581438942493604950⟩,⟨(-7888481759879512613596640262),(-7888481759879512598261124189)⟩⟩,⟨⟨14871213041614028583836795717,14871213041614028599318381783⟩,⟨(-7889013987995907928123235306),(-7889013987995907912791623055)⟩⟩] +lemma kernel4_1_r4_15_eq : ∀ k : Fin 16, kernel4_1Expr 4 15 k = kernel4_1_r4_15 k := by decide +kernel +noncomputable def kernel4_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel4_1_r4_0,kernel4_1_r4_1,kernel4_1_r4_2,kernel4_1_r4_3,kernel4_1_r4_4,kernel4_1_r4_5,kernel4_1_r4_6,kernel4_1_r4_7,kernel4_1_r4_8,kernel4_1_r4_9,kernel4_1_r4_10,kernel4_1_r4_11,kernel4_1_r4_12,kernel4_1_r4_13,kernel4_1_r4_14,kernel4_1_r4_15] +lemma kernel4_1_r4_eq (i k : Fin 16) : kernel4_1Expr 4 i k = kernel4_1_r4 i k := by + fin_cases i + · exact kernel4_1_r4_0_eq k + · exact kernel4_1_r4_1_eq k + · exact kernel4_1_r4_2_eq k + · exact kernel4_1_r4_3_eq k + · exact kernel4_1_r4_4_eq k + · exact kernel4_1_r4_5_eq k + · exact kernel4_1_r4_6_eq k + · exact kernel4_1_r4_7_eq k + · exact kernel4_1_r4_8_eq k + · exact kernel4_1_r4_9_eq k + · exact kernel4_1_r4_10_eq k + · exact kernel4_1_r4_11_eq k + · exact kernel4_1_r4_12_eq k + · exact kernel4_1_r4_13_eq k + · exact kernel4_1_r4_14_eq k + · exact kernel4_1_r4_15_eq k +noncomputable def kernel4_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-1232601843430160096405364246912),(-1232601843430160095957451426875)⟩,⟨(-1351511999531431523378318912964),(-1351511999531431522908149996277)⟩⟩,⟨⟨(-1232667065060701561634247709987),(-1232667065060701561186319936350)⟩,⟨(-1351193344886993212008716729576),(-1351193344886993211538542040803)⟩⟩,⟨⟨(-1232797335132006693749839030058),(-1232797335132006693301882073306)⟩,⟨(-1350556133593053582754103318426),(-1350556133593053582283917808914)⟩⟩,⟨⟨(-1232992307482244035917997724421),(-1232992307482244035469997393489)⟩,⟨(-1349600561713502251360359202176),(-1349600561713502250890157852036)⟩⟩,⟨⟨(-1233251463412820506485123319642),(-1233251463412820506037065497985)⟩,⟨(-1348326923528834139799664038123),(-1348326923528834139329441887513)⟩⟩,⟨⟨(-1233574112340928368385467645968),(-1233574112340928367937338298367)⟩,⟨(-1346735611756682975269809413470),(-1346735611756682974799561564548)⟩⟩,⟨⟨(-1233959392668876535343745192848),(-1233959392668876534895530414149)⟩,⟨(-1344827117844103510847809839111),(-1344827117844103510377531500047)⟩⟩,⟨⟨(-1234406272869576590059283832015),(-1234406272869576589610969823979)⟩,⟨(-1342602032330097239427668657665),(-1342602032330097238957355114495)⟩⟩,⟨⟨(-1234913552787393032201381370422),(-1234913552787393031752954545183)⟩,⟨(-1340061045276506858561113791123),(-1340061045276506858090760506760)⟩⟩,⟨⟨(-1235479865153404151722679282165),(-1235479865153404151274126156094)⟩,⟨(-1337204946765039750619833409732),(-1337204946765039750149435912405)⟩⟩,⟨⟨(-1236103677313954118363949175292),(-1236103677313954117915256583279)⟩,⟨(-1334034627457821166435037513541),(-1334034627457821165964591607324)⟩⟩,⟨⟨(-1236783293171207993184913141677),(-1236783293171207992736067977565)⟩,⟨(-1330551079218524532830998133896),(-1330551079218524532360499632834)⟩⟩,⟨⟨(-1237516855334249026711617291487),(-1237516855334249026262606957382)⟩,⟨(-1326755395790780231412018836064),(-1326755395790780230941464011064)⟩⟩,⟨⟨(-1238302347479081460306454520650),(-1238302347479081459857266332188)⟩,⟨(-1322648773530226197373434106890),(-1322648773530226196902819082837)⟩⟩,⟨⟨(-1239137596915721770256281757548),(-1239137596915721769806903763377)⟩,⟨(-1318232512186234635391635022732),(-1318232512186234634920956597702)⟩⟩,⟨⟨(-1240020277360376596387822780608),(-1240020277360376595938242804165)⟩,⟨(-1313508015729029908748644176620),(-1313508015729029908277898853491)⟩⟩] +lemma kernel4_1_r5_0_eq : ∀ k : Fin 16, kernel4_1Expr 5 0 k = kernel4_1_r5_0 k := by decide +kernel +noncomputable def kernel4_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-1240947911910516220924710993800),(-1240947911910516220474917953941)⟩,⟨(-1308476793217604082086779474131),(-1308476793217604081615964783734)⟩⟩,⟨⟨(-1241917876220458187142348956743),(-1241917876220458186692331134330)⟩,⟨(-1303140459703539531032959903466),(-1303140459703539530562072656845)⟩⟩,⟨⟨(-1242927401874876288111503566923),(-1242927401874876287661250740894)⟩,⟨(-1297500737165563304660073844106),(-1297500737165563304189112275527)⟩⟩,⟨⟨(-1243973579957445571310104778526),(-1243973579957445570859605859972)⟩,⟨(-1291559455469386357044372814321),(-1291559455469386356573334197827)⟩⟩,⟨⟨(-1245053364811624096033939686791),(-1245053364811624095583185689068)⟩,⟨(-1285318553347123154604597896386),(-1285318553347123154133481527072)⟩⟩,⟨⟨(-1246163577990356893291102418534),(-1246163577990356892840082673198)⟩,⟨(-1278780079390344302331470659145),(-1278780079390344301860274044508)⟩⟩,⟨⟨(-1247300912391266905006194535619),(-1247300912391266904554901117486)⟩,⟨(-1271946193050587481887646529635),(-1271946193050587481416369833054)⟩⟩,⟨⟨(-1248461936573671662148444111616),(-1248461936573671661696867110446)⟩,⟨(-1264819165640940905129238960388),(-1264819165640940904657880243941)⟩⟩,⟨⟨(-1249643099253533191010323064538),(-1249643099253533190558456263512)⟩,⟨(-1257401381332119383032510052130),(-1257401381332119382561070979247)⟩⟩,⟨⟨(-1250840733972212255636060322100),(-1250840733972212255183894062359)⟩,⟨(-1249695338136276693397139168248),(-1249695338136276692925617828228)⟩⟩,⟨⟨(-1252051063934656746859229208088),(-1252051063934656746406758444854)⟩,⟨(-1241703648871639875997286354436),(-1241703648871639875525685353679)⟩⟩,⟨⟨(-1253270207012408062086561239156),(-1253270207012408061633777260729)⟩,⟨(-1233429042100912037730161395832),(-1233429042100912037258479532488)⟩⟩,⟨⟨(-1254494180906558985983204132178),(-1254494180906558985530104092085)⟩,⟨(-1224874363036270828911935852736),(-1224874363036270828440177689555)⟩⟩,⟨⟨(-1255718908465542235638038029541),(-1255718908465542235184613265043)⟩,⟨(-1216042574403690538506395003746),(-1216042574403690538034559128152)⟩⟩,⟨⟨(-1256940223152370883733231086839),(-1256940223152370883279480053382)⟩,⟨(-1206936757259237298854313400324),(-1206936757259237298382405413543)⟩⟩,⟨⟨(-1258153874655690782739271188343),(-1258153874655690782285186314950)⟩,⟨(-1197560111749929699882376555862),(-1197560111749929699410395865611)⟩⟩] +lemma kernel4_1_r5_1_eq : ∀ k : Fin 16, kernel4_1Expr 5 1 k = kernel4_1_r5_1 k := by decide +kernel +noncomputable def kernel4_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-1259355534638741398749657621566),(-1259355534638741398295240325233)⟩,⟨(-1187915957811721659182218314501),(-1187915957811721658710173210402)⟩⟩,⟨⟨(-1260540802620055694661595401201),(-1260540802620055694206837658925)⟩,⟨(-1178007735797151105514481326474),(-1178007735797151105042370469929)⟩⟩,⟨⟨(-1261705211979462500337061365909),(-1261705211979462499881965761089)⟩,⟨(-1167839007025207291799742424566),(-1167839007025207291327574974538)⟩⟩,⟨⟨(-1262844236082686844219947361343),(-1262844236082686843764507338719)⟩,⟨(-1157413454246001694386201455928),(-1157413454246001693913977240073)⟩⟩,⟨⟨(-1263953294517575717988020576420),(-1263953294517575717532242263907)⟩,⟨(-1146734882012882762947765774441),(-1146734882012882762475497192574)⟩⟩,⟨⟨(-1265027759434709472061323229045),(-1265027759434709471605199271192)⟩,⟨(-1135807216954713491583642484783),(-1135807216954713491111328239077)⟩⟩,⟨⟨(-1266062961984893309556697262176),(-1266062961984893309100235005056)⟩,⟨(-1124634507941133063077232018170),(-1124634507941133062604885399031)⟩⟩,⟨⟨(-1267054198845760017169818434127),(-1267054198845760016713012146453)⟩,⟨(-1113220926133749793587184672883),(-1113220926133749793114805676709)⟩⟩,⟨⟨(-1267996738829455041717942393404),(-1267996738829455041260804111111)⟩,⟨(-1101570764916362332894766528368),(-1101570764916362332422372805025)⟩⟩,⟨⟨(-1268885829563119226721132077427),(-1268885829563119226263654312319)⟩,⟨(-1089688439697479551868475436614),(-1089688439697479551396064870660)⟩⟩,⟨⟨(-1269716704233633935148065802700),(-1269716704233633934690261299974)⟩,⟨(-1077578487578606705505791505149),(-1077578487578606705033382098483)⟩⟩,⟨⟨(-1270484588387848904319504632047),(-1270484588387848903861368209730)⟩,⟨(-1065245566881986161488517562662),(-1065245566881986161016109152600)⟩⟩,⟨⟨(-1271184706779276036626942031554),(-1271184706779276036168491759365)⟩,⟨(-1052694456531725026637350385285),(-1052694456531725026164965941371)⟩⟩,⟨⟨(-1271812290252003478647832671096),(-1271812290252003478189061128269)⟩,⟨(-1039930055282509112453179838078),(-1039930055282509111980816580205)⟩⟩,⟨⟨(-1272362582652364854537035244716),(-1272362582652364854077961197471)⟩,⟨(-1026957380790392509423787530115),(-1026957380790392508951468742592)⟩⟩,⟨⟨(-1272830847758689485665458147866),(-1272830847758689485206076628031)⟩,⟨(-1013781568520464167724448810884),(-1013781568520464167252173790677)⟩⟩] +lemma kernel4_1_r5_2_eq : ∀ k : Fin 16, kernel4_1Expr 5 2 k = kernel4_1_r5_2 k := by decide +kernel +noncomputable def kernel4_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-1273212376219261946507604688775),(-1273212376219261946047941526081)⟩,⟨(-1000407870486526814330332595526),(-1000407870486526813858131312120)⟩⟩,⟨⟨(-1273502492488434481856340379485),(-1273502492488434481396386731960)⟩,⟨(-986841653818278702602656319353),(-986841653818278702130523795612)⟩⟩,⟨⟨(-1273696561750664748666467898758),(-1273696561750664748206249142628)⟩,⟨(-973088399151864442819417645480),(-973088399151864442347382992422)⟩⟩,⟨⟨(-1273789996822095149171065694207),(-1273789996822095148710576673165)⟩,⟨(-959153698840056776642624983012),(-959153698840056776170686518182)⟩⟩,⟨⟨(-1273778265019149782933052926855),(-1273778265019149782472326569355)⟩,⟨(-945043254978745833745408610485),(-945043254978745833273602597116)⟩⟩,⟨⟨(-1273656894983501841928380390995),(-1273656894983501841467407236517)⟩,⟨(-930762877246845266343110572195),(-930762877246845265871430610232)⟩⟩,⟨⟨(-1273421483452659162001055969830),(-1273421483452659161539868556839)⟩,⟨(-916318480557174742172453634487),(-916318480557174741700935176414)⟩⟩,⟨⟨(-1273067701965329657538179021962),(-1273067701965329657076771546926)⟩,⟨(-901716082516344557721444873050),(-901716082516344557250084770473)⟩⟩,⟨⟨(-1272591303490662503825297989609),(-1272591303490662503363712867440)⟩,⟨(-886961800692149505701547798921),(-886961800692149505230390964298)⟩⟩,⟨⟨(-1271988128970416155794578364934),(-1271988128970416155332803170523)⟩,⟨(-872061849687474415113995910521),(-872061849687474414643032151084)⟩⟩,⟨⟨(-1271254113763081522284282563299),(-1271254113763081521822293129004)⟩,⟨(-857022538020221728625152429432),(-857022538020221728154359235594)⟩⟩,⟨⟨(-1270385293978988722303393344184),(-1270385293978988721840687382791)⟩,⟨(-841850264809290770966842382701),(-841850264809290770495716178487)⟩⟩,⟨⟨(-1269377812695449650606690581642),(-1269377812695449650143310309279)⟩,⟨(-826551516267167607724323830869),(-826551516267167607252908437475)⟩⟩,⟨⟨(-1268227926041036830713016219430),(-1268227926041036830248939348763)⟩,⟨(-811132862000222146530003088348),(-811132862000222146058277589536)⟩⟩,⟨⟨(-1266932009138172425552018721336),(-1266932009138172425087285637346)⟩,⟨(-795600951118353882374388033246),(-795600951118353881902393984057)⟩⟩,⟨⟨(-1265486561893300429791918151848),(-1265486561893300429326512063099)⟩,⟨(-779962508156177868960665903214),(-779962508156177868488387469034)⟩⟩] +lemma kernel4_1_r5_3_eq : ∀ k : Fin 16, kernel4_1Expr 5 3 k = kernel4_1_r5_3 k := by decide +kernel +noncomputable def kernel4_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-1263888214624040528350702621796),(-1263888214624040527884678038427)⟩,⟨(-764224328808496489745546243866),(-764224328808496489273038665115)⟩⟩,⟨⟨(-1262133733512874336707079930997),(-1262133733512874336240409603729)⟩,⟨(-748393275483358738553247203314),(-748393275483358738080483774746)⟩⟩,⟨⟨(-1260220025877094119066771402963),(-1260220025877094118599504991449)⟩,⟨(-732476272676565290307456145933),(-732476272676565289834486824044)⟩⟩,⟨⟨(-1258144145244950899051728967229),(-1258144145244950898583847701537)⟩,⟨(-716480302172032899484234660907),(-716480302172032899011040805934)⟩⟩,⟨⟨(-1255903296228173329258145119682),(-1255903296228173328789712665982)⟩,⟨(-700412398072983826974935881916),(-700412398072983826501581009856)⟩⟩,⟨⟨(-1253494839181290867943593106860),(-1253494839181290867474580291018)⟩,⟨(-684279641669473258340864091026),(-684279641669473257867318759507)⟩⟩,⟨⟨(-1250916294638484719254713293033),(-1250916294638484718785179525434)⟩,⟨(-668089156148308210854626856025),(-668089156148308210380949899120)⟩⟩,⟨⟨(-1248165347519007519609694147266),(-1248165347519007519139618056088)⟩,⟨(-651848101151943392422080753309),(-651848101151943391948250122647)⟩⟩,⟨⟨(-1245239851092557682097230491636),(-1245239851092557681626689808623)⟩,⟨(-635563667193461024624803934114),(-635563667193461024150896328817)⟩⟩,⟨⟨(-1242137830696366319066635043142),(-1242137830696366318595593555688)⟩,⟨(-619243069935250926904363035332),(-619243069935250926430341195169)⟩⟩,⟨⟨(-1238857487196153315788612520397),(-1238857487196153315317139789574)⟩,⟨(-602893544339502338744402388813),(-602893544339502338270334436065)⟩⟩,⟨⟨(-1235397200183533878610522084469),(-1235397200183533878138593471570)⟩,⟨(-586522338699098205676799016288),(-586522338699098205202658861639)⟩⟩,⟨⟨(-1231755530902907070265693695508),(-1231755530902907069793396736893)⟩,⟨(-570136708557964169329444120737),(-570136708557964168855317407074)⟩⟩,⟨⟨(-1227931224901332701045480051683),(-1227931224901332700572775438536)⟩,⟨(-553743910530366507742831165052),(-553743910530366507268676790730)⟩⟩,⟨⟨(-1223923214395401583159786855641),(-1223923214395401582686754619103)⟩,⟨(-537351196029074033657051180409),(-537351196029074033182946896710)⟩⟩,⟨⟨(-1219730620349625581162612101395),(-1219730620349625580689223640879)⟩,⟨(-520965804912696784740536039268),(-520965804912696784266451066093)⟩⟩] +lemma kernel4_1_r5_4_eq : ∀ k : Fin 16, kernel4_1Expr 5 4 k = kernel4_1_r5_4 k := by decide +kernel +noncomputable def kernel4_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-1215352754261416998276839806451),(-1215352754261416997803199275948)⟩,⟨(-504594959062887593394552643715),(-504594959062887592920588388089)⟩⟩,⟨⟨(-1210789119648290413531312489767),(-1210789119648290413057370245279)⟩,⟨(-488245855902439728489830502601),(-488245855902439728015934852074)⟩⟩,⟨⟨(-1206039413233502809436718887329),(-1206039413233502808962565642180)⟩,⟨(-471925661865633249572258793963),(-471925661865633249098519373109)⟩⟩,⟨⟨(-1201103525826948284293456856332),(-1201103525826948283819059352676)⟩,⟨(-455641505832473074443219946781),(-455641505832473073969600646407)⟩⟩,⟨⟨(-1195981542898740308991297633249),(-1195981542898740308516769024561)⟩,⟨(-439400472538721686006264339398),(-439400472538721685532874771140)⟩⟩,⟨⟨(-1190673744843545753670016570001),(-1190673744843545753195303944983)⟩,⟨(-423209595973857637226841645215),(-423209595973857636753625796573)⟩⟩,⟨⟨(-1185180606934379074664595953495),(-1185180606934379074189800846333)⟩,⟨(-407075852779286395145120134040),(-407075852779286394672175684060)⟩⟩,⟨⟨(-1179502798965220333608796111479),(-1179502798965220333133879872966)⟩,⟨(-391006155659291541767052322652),(-391006155659291541294337167140)⟩⟩,⟨⟨(-1173641184582485258367174143157),(-1173641184582485257892267667248)⟩,⟨(-375007346817340977721939144555),(-375007346817340977249579852479)⟩⟩,⟨⟨(-1167596820306047419299299312918),(-1167596820306047418824337037870)⟩,⟨(-359086191430453726870001767278),(-359086191430453726397929150578)⟩⟩,⟨⟨(-1161370954241189790717566933416),(-1161370954241189790242661223804)⟩,⟨(-343249371174387511722065808951),(-343249371174387511250387662985)⟩⟩,⟨⟨(-1154965024483543447159575265345),(-1154965024483543446684681374676)⟩,⟨(-327503477812424882881998780165),(-327503477812424882410666377789)⟩⟩,⟨⟨(-1148380657219752810470925835326),(-1148380657219752809996183466061)⟩,⟨(-311855006860515894611403514766),(-311855006860515894140551543478)⟩⟩,⟨⟨(-1141619664527287580658689895948),(-1141619664527287580184029024256)⟩,⟨(-296310351341477812488764507927),(-296310351341477812018318840012)⟩⟩,⟨⟨(-1134684041877499084457971192961),(-1134684041877499083983514943197)⟩,⟨(-280875795640856946331117851040),(-280875795640856945861196388684)⟩⟩,⟨⟨(-1127575965346691072535967702011),(-1127575965346691072061664517972)⟩,⟨(-265557509476924392104064941329),(-265557509476924391634611708391)⟩⟩] +lemma kernel4_1_r5_5_eq : ∀ k : Fin 16, kernel4_1Expr 5 5 k = kernel4_1_r5_5 k := by decide +kernel +noncomputable def kernel4_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-1120297788540639789053857042642),(-1120297788540639788579867150330)⟩,⟨(-250361541997106354277960782649),(-250361541997106353809130300704)⟩⟩,⟨⟨(-1112852039238653223160226185042),(-1112852039238653222686462546523)⟩,⟨(-235293816012941064086548494058),(-235293816012941063618249296424)⟩⟩,⟨⟨(-1105241415763902635248333958363),(-1105241415763902634774930247927)⟩,⟨(-220360122385408514507035649102),(-220360122385408514039395603983)⟩⟩,⟨⟨(-1097468783087388552822995645965),(-1097468783087388552349892836224)⟩,⟨(-205566114572196850735312358174),(-205566114572196850268267671688)⟩⟩,⟨⟨(-1089537168673516299808034676616),(-1089537168673516299335399016783)⟩,⟨(-190917303348150982141470526618),(-190917303348150981675181204681)⟩⟩,⟨⟨(-1081449758075850644153023231662),(-1081449758075850643680764275579)⟩,⟨(-176419051709795658950874370714),(-176419051709795658485245232890)⟩⟩,⟨⟨(-1073209890292193253429709601398),(-1073209890292193252957971296640)⟩,⟨(-162076569974437866975103627353),(-162076569974437866510272306412)⟩⟩,⟨⟨(-1064821052888678325046728341469),(-1064821052888678324575443534411)⟩,⟨(-147894911083933058597784734998),(-147894911083933058133679061703)⟩⟩,⟨⟨(-1056286876903109061182991307305),(-1056286876903109060712346652162)⟩,⟨(-133878966122747715493427664211),(-133878966122747715030227492600)⟩⟩,⟨⟨(-1047611131538258718584527536394),(-1047611131538258718114413827490)⟩,⟨(-120033460059468417216345970153),(-120033460059468416753937247377)⟩⟩,⟨⟨(-1038797718656332994738169207617),(-1038797718656332994268740246190)⟩,⟨(-106362947720396485211462420728),(-106362947720396484749992204793)⟩⟩,⟨⟨(-1029850667086233822990700606765),(-1029850667086233822521880550384)⟩,⟨(-92871810003329020124775092577),(-92871810003329019664162375914)⟩⟩,⟨⟨(-1020774126755676650291781076793),(-1020774126755676649823761810984)⟩,⟨(-79564250339063502092829034659),(-79564250339063501633258526741)⟩⟩,⟨⟨(-1011572362660592482868485540501),(-1011572362660592482401153284655)⟩,⟨(-66444291407575937056985146820),(-66444291407575936598338110066)⟩⟩,⟨⟨(-1002249748684591045328357159424),(-1002249748684591044861875103965)⟩,⟨(-53515772115213765074983703707),(-53515772115213764617416240044)⟩⟩,⟨⟨(-992810761281571070129923500918),(-992810761281571069664206572147)⟩,⟨(-40782344838616448937504336509),(-40782344838616448480926157471)⟩⟩] +lemma kernel4_1_r5_6_eq : ∀ k : Fin 16, kernel4_1Expr 5 6 k = kernel4_1_r5_6 k := by decide +kernel +noncomputable def kernel4_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-983259973034836910768962534143),(-983259973034836910304225818914)⟩,⟨(-28247472940430966127148130571),(-28247472940430965671766712263)⟩⟩,⟨⟨(-973602046106316384025109760325),(-973602046106316383561215892021)⟩,⟨(-15914428561228541343205015935),(-15914428561228540888878164707)⟩⟩,⟨⟨(-963841725589672166806634059971),(-963841725589672166343755010199)⟩,⟨(-3786290691355151957259935305),(-3786290691355151504152274025)⟩⟩,⟨⟨(-953983832781257520655205019783),(-953983832781257520193246068535)⟩,⟨8134056474236059081409961521,8134056474236059533398319823⟩⟩,⟨⟨(-944033258382986061145466594403),(-944033258382986060684643459728)⟩,⟨19843924895814948950718153789,19843924895814949401379277584⟩⟩,⟨⟨(-933994955651264352798693147714),(-933994955651264352338866457280)⟩,⟨31340823761710044672360917895,31340823761710045121838952156⟩⟩,⟨⟨(-923873933506175070660991255928),(-923873933506175070202341147757)⟩,⟨42622460273194473512903098161,42622460273194473961025429863⟩⟩,⟨⟨(-913675249615097262175868333444),(-913675249615097261718290047866)⟩,⟨53686740141169695102948041042,53686740141169695549824455319⟩⟩,⟨⟨(-903404003464908959606407085335),(-903404003464908959150138277331)⟩,⟨64531767795095874013464012878,64531767795095874458864923795⟩⟩,⟨⟨(-893065329436836283505940775679),(-893065329436836283050817727587)⟩,⟨75155846305315112905352820213,75155846305315113349446385355⟩⟩,⟨⟨(-882664389897892647245050570059),(-882664389897892646791260840489)⟩,⟨85557477020604822919432091335,85557477020604823362038370730⟩⟩,⟨⟨(-872206368322692281453289235030),(-872206368322692281000712569248)⟩,⟨95735358923480863220532371323,95735358923480863661804004451⟩⟩,⟨⟨(-861696462459224757214747481073),(-861696462459224756763610534019)⟩,⟨105688387706441401941685061507,105688387706441402381457499266⟩⟩,⟨⟨(-851139877551942358135531843919),(-851139877551942357685668134210)⟩,⟨115415654573000455905501490041,115415654573000456343944355737⟩⟩,⟨⟨(-840541819635241038245439533649),(-840541819635241037797043311957)⟩,⟨124916444768002539811971512058,124916444768002540248897000466⟩⟩,⟨⟨(-829907488910109448623646736011),(-829907488910109448176592439622)⟩,⟨134190235842334653950291002586,134190235842334654385828094601⟩⟩] +lemma kernel4_1_r5_7_eq : ∀ k : Fin 16, kernel4_1Expr 5 7 k = kernel4_1_r5_7 k := by decide +kernel +noncomputable def kernel4_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-819242073216380397673989801542),(-819242073216380397228540186356)⟩,⟨143236695657756902881655788594,143236695657756903315548661940⟩⟩,⟨⟨(-808550741612646532403657240998),(-808550741612646531959615797678)⟩,⟨152055680138156397970807018848,152055680138156398403254828382⟩⟩,⟨⟨(-797838638075498515347524742364),(-797838638075498514905091651323)⟩,⟨160647230774088886822646284013,160647230774088887253455056217⟩⟩,⟨⟨(-787110875329311161086880991144),(-787110875329311160645920203759)⟩,⟨169011571888007013892052385761,169011571888007014321361242583⟩⟩,⟨⟨(-776372528817342629243541017308),(-776372528817342628804307974500)⟩,⟨177149107668081606120127291198,177149107668081606547687330723⟩⟩,⟨⟨(-765628630824425684894791843773),(-765628630824425684457092487128)⟩,⟨185060418979001375439540155737,185060418979001375865547846787⟩⟩,⟨⟨(-754884164761020156750582276061),(-754884164761020156314621960259)⟩,⟨192746259958585545261610144241,192746259958585545685866045569⟩⟩,⟨⟨(-744144059617864049651784636050),(-744144059617864049217416808645)⟩,⟨200207554409461883569913914174,200207554409461883992567271291⟩⟩,⟨⟨(-733413184599909369824643783839),(-733413184599909369392146655122)⟩,⟨207445391995448342745068625233,207445391995448343165847597239⟩⟩,⟨⟨(-722696343947659725026328667531),(-722696343947659724595479655537)⟩,⟨214461024252628989996779741674,214461024252628990415908777250⟩⟩,⟨⟨(-711998271953442340289044453739),(-711998271953442339860053217413)⟩,⟨221255860425433332220869642857,221255860425433332638144656367⟩⟩,⟨⟨(-701323628179549492958640057885),(-701323628179549492531349732535)⟩,⟨227831463138311813002932595957,227831463138311813418512740622⟩⟩,⟨⟨(-690676992884575753472826326519),(-690676992884575753047507470921)⟩,⟨234189543913848654529949053867,234189543913848654943569666965⟩⟩,⟨⟨(-680062862663660071475964016582),(-680062862663660071052395416454)⟩,⟨240331958548365950474670630615,240331958548365950886554494371⟩⟩,⟨⟨(-669485646307717925672129046425),(-669485646307717925250523903581)⟩,⟨246260702356249754541975477894,246260702356249754951914587675⟩⟩,⟨⟨(-658949660886120709763466477357),(-658949660886120709343657811491)⟩,⟨251977905294369769266628739951,251977905294369769674791944840⟩⟩] +lemma kernel4_1_r5_8_eq : ∀ k : Fin 16, kernel4_1Expr 5 8 k = kernel4_1_r5_8 k := by decide +kernel +noncomputable def kernel4_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-648459128056649489200433758859),(-648459128056649488782718965644)⟩,⟨257485826978069184093835180267,257485826978069184499930775250⟩⟩,⟨⟨(-638018170605920441391996927576),(-638018170605920440976121041549)⟩,⟨262786851600270448774977629023,262786851600270449179261536371⟩⟩,⟨⟨(-627630809222851856469013386368),(-627630809222851856055192284306)⟩,⟨267883482765276647371861126036,267883482765276647774122262508⟩⟩,⟨⟨(-617300959507119652135366707903),(-617300959507119651723423711196)⟩,⟨272778338248847147075547394814,272778338248847147475963883496⟩⟩,⟨⟨(-607032429213932015311459828555),(-607032429213932014901677184610)⟩,⟨277474144696090955260312615904,277474144696090955658607325776⟩⟩,⟨⟨(-596828915735846032602181715614),(-596828915735846032194312453063)⟩,⟨281973732268652476319376515105,281973732268652476715797112896⟩⟩,⟨⟨(-586694003821751946903942481229),(-586694003821751946498204463463)⟩,⟨286280029252562987786454628074,286280029252562988180787623558⟩⟩,⟨⟨(-576631163532565835298420542895),(-576631163532565834894627752994)⟩,⟨290396056637998139830721767702,290396056637998140223154201021⟩⟩,⟨⟨(-566643748432600813904666982015),(-566643748432600813503124998896)⟩,⟨294324922682018219393717363878,294324922682018219783948502922⟩⟩,⟨⟨(-556734994015032015833007666256),(-556734994015032015433438614066)⟩,⟨298069817465175007778174132959,298069817465175008166481974276⟩⟩,⟨⟨(-546908016359333137125259062895),(-546908016359333136727882002086)⟩,⟨301634007452648090409714610996,301634007452648090795884037890⟩⟩,⟨⟨(-537165811018043776790827638116),(-537165811018043776395447799234)⟩,⟨305020830070325827897589836108,305020830070325828281816232200⟩⟩,⟨⟨(-527511252129728476108212958185),(-527511252129728475715121049218)⟩,⟨308233688305973324481916134620,308233688305973324863913066547⟩⟩,⟨⟨(-517947091754511541908929433522),(-517947091754511541517854887072)⟩,⟨311276045345333158809365467758,311276045345333159189403365991⟩⟩,⟨⟨(-508475959428117555144334845127),(-508475959428117554755497314271)⟩,⟨314151419252685958750310828212,314151419252685959128173554312⟩⟩,⟨⟨(-499100361929916937633837286691),(-499100361929916937246203969224)⟩,⟨316863377705058744403592917056,316863377705058744780504384428⟩⟩] +lemma kernel4_1_r5_9_eq : ∀ k : Fin 16, kernel4_1Expr 5 9 k = kernel4_1_r5_9 k := by decide +kernel +noncomputable def kernel4_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-489822683260069973880093299934),(-489822683260069973493901825104)⟩,⟨319415532788911012220879481756,319415532788911012596622455096⟩⟩,⟨⟨(-480645184820482036905593425579),(-480645184820482036520548688523)⟩,⟨321811535867753502889739932187,321811535867753503264602905360⟩⟩,⟨⟨(-471570005793928100501780953302),(-471570005793928100118117351885)⟩,⟨324055072528764225996224856544,324055072528764226369970603098⟩⟩,⟨⟨(-462599163715376466287179292462),(-462599163715376465904698529119)⟩,⟨326149857616062361468029387519,326149857616062361840850377112⟩⟩,⟨⟨(-453734555229240402186901293869),(-453734555229240401805916268286)⟩,⟨328099630357884885077646424839,328099630357884885449227363048⟩⟩,⟨⟨(-444977957026012369040628594819),(-444977957026012368660858763765)⟩,⟨329908149594484935656936539927,329908149594484936027551673962⟩⟩,⟨⟨(-436331026951488875509414408240),(-436331026951488875131095471449)⟩,⟨331579189113136809000339995120,331579189113136809369750665407⟩⟩,⟨⟨(-427795305281574804280150290359),(-427795305281574803903075602834)⟩,⟨333116533096191764552494422648,333116533096191764920901563280⟩⟩,⟨⟨(-419372216155464238205709100204),(-419372216155464237830218677685)⟩,⟨334523971687683278220215318703,334523971687683278587276509915⟩⟩,⟨⟨(-411063069159830218074656340970),(-411063069159830217700435334416)⟩,⟨335805296683531648449719927691,335805296683531648815743760923⟩⟩,⟨⟨(-402869061056518213855883799570),(-402869061056518213483168478543)⟩,⟨336964297349947604853071758313,336964297349947605217818915177⟩⟩,⟨⟨(-394791277646127017870621450690),(-394791277646127017499197471932)⟩,⟨338004756374184375700083325378,338004756374184376063762605435⟩⟩,⟨⟨(-386830695759775805173898134400),(-386830695759775804804086227785)⟩,⟨338930445951339087940973593739,338930445951339088303261625883⟩⟩,⟨⟨(-378988185371296697003360338919),(-378988185371296696634857858167)⟩,⟨339745124010458889707018883959,339745124010458890068212418541⟩⟩,⟨⟨(-371264511822057666129042564971),(-371264511822057665762085851847)⟩,⟨340452530582766227326053829423,340452530582766227685913426284⟩⟩,⟨⟨(-363660338150610318011678793172),(-363660338150610317646046326902)⟩,⟨341056384314382637208917081095,341056384314382637567658926149⟩⟩] +lemma kernel4_1_r5_10_eq : ∀ k : Fin 16, kernel4_1Expr 5 10 k = kernel4_1_r5_10 k := by decide +kernel +noncomputable def kernel4_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-356176227519370175449068761531),(-356176227519370175085115250622)⟩,⟨341560379125502517552057749246,341560379125502517909324565157⟩⟩,⟨⟨(-348812645730572726668841068381),(-348812645730572726306222716268)⟩,⟨341968181017548841628987260378,341968181017548841985117065944⟩⟩,⟨⟨(-341569963823805746791872458778),(-341569963823805746430825024482)⟩,⟨342283425029432802509825345981,342283425029432802864579268503⟩⟩,⟨⟨(-334448460747496295326954371278),(-334448460747496294967249932798)⟩,⟨342509712343639997728901213881,342509712343639998082502084581⟩⟩,⟨⟨(-327448326096828305146703532079),(-327448326096828304788668155729)⟩,⟨342650607542477949602351986434,342650607542477949954470990235⟩⟩,⟨⟨(-320569662910682747315425897586),(-320569662910682746958737619687)⟩,⟨342709636014444407333390023452,342709636014444407684343790435⟩⟩,⟨⟨(-313812490520325882335362090851),(-313812490520325881980255741222)⟩,⟨342690281510313801493826883333,342690281510313801843377485427⟩⟩,⟨⟨(-307176747442720964554164617297),(-307176747442720964200406425786)⟩,⟨342595983848191146040525377791,342595983848191146388901764714⟩⟩,⟨⟨(-300662294311503803006699447096),(-300662294311503802654644529539)⟩,⟨342430136766449249249152045050,342430136766449249595996433482⟩⟩,⟨⟨(-294268916838841633146531239085),(-294268916838841632795821837106)⟩,⟨342196085923146860040038042691,342196085923146860385703082378⟩⟩,⟨⟨(-287996328801586643783699373236),(-287996328801586643434568860081)⟩,⟨341897127040222813993109524648,341897127040222814337358784810⟩⟩,⟨⟨(-281844175045339051739697415146),(-281844175045339051391906985088)⟩,⟨341536504190474745490606887652,341536504190474745833674643923⟩⟩,⟨⟨(-275812034500248643925453081121),(-275812034500248643579332217242)⟩,⟨341117408225060809961885405332,341117408225060810303439425608⟩⟩,⟨⟨(-269899423202607039866071525626),(-269899423202607039521281851692)⟩,⟨340642975339009345506341322561,340642975339009345846715309590⟩⟩,⟨⟨(-264105797316514405589601934522),(-264105797316514405246375116157)⟩,⟨340116285771984652353373504194,340116285771984652692332796830⟩⟩,⟨⟨(-258430556150142826941674155019),(-258430556150142826599766946181)⟩,⟨339540362641337163986311098569,339540362641337164324094715113⟩⟩] +lemma kernel4_1_r5_11_eq : ∀ k : Fin 16, kernel4_1Expr 5 11 k = kernel4_1_r5_11 k := by decide +kernel +noncomputable def kernel4_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-252873045161362901982688824299),(-252873045161362901642469824075)⟩,⟨338918170904263236817282298720,338918170904263237153519011372⟩⟩,⟨⟨(-247432558947749238177070223914),(-247432558947749237838155853881)⟩,⟨338252616445713539725777396478,338252616445713540060846362467⟩⟩,⟨⟨(-242108344216233369080883932103),(-242108344216233368743503680104)⟩,⟨337546545288519459878801024891,337546545288519460212469839142⟩⟩,⟨⟨(-236899602727928097778324637209),(-236899602727928097442231682553)⟩,⟨336802742922053875350890614148,336802742922053875683402178384⟩⟩,⟨⟨(-231805494213904426136178506549),(-231805494213904425801704226000)⟩,⟨336023933745605839294720186861,336023933745605839625740448864⟩⟩,⟨⟨(-226825139257960073869387968487),(-226825139257960073536180588138)⟩,⟨335212780622527882373258349549,335212780622527882703135108621⟩⟩,⟨⟨(-221957622142676203707570075681),(-221957622142676203375856792677)⟩,⟨334371884541109427957431018021,334371884541109428285934250715⟩⟩,⟨⟨(-217201993655315465634928010792),(-217201993655315465304458975013)⟩,⟨333503784378039840646114534460,333503784378039840973490480166⟩⟩,⟨⟨(-212557273850369015681396672761),(-212557273850369015352535115920)⟩,⟨332610956760249463888919880907,332610956760249464214802733670⟩⟩,⟨⟨(-208022454765811960587964144172),(-208022454765811960260321244523)⟩,⟨331695816020856180163183889569,331695816020856180487958794375⟩⟩,⟨⟨(-203596503090374983492082269126),(-203596503090374983165882578505)⟩,⟨330760714244898047095295734130,330760714244898047418735412184⟩⟩,⟨⟨(-199278362779384020376647607828),(-199278362779384020051639064374)⟩,⟨329807941400498895338854165498,329807941400498895661207371135⟩⟩,⟨⟨(-195066957616959133793578822703),(-195066957616959133470093754882)⟩,⟨328839725551092863646201375628,328839725551092863967133222197⟩⟩,⟨⟨(-190961193722597569773831632279),(-190961193722597569451507600642)⟩,⟨327858233144325116344732245292,327858233144325116664601884534⟩⟩,⟨⟨(-186959962000393835288273962725),(-186959962000393834967332801006)⟩,⟨326865569373248843491842236816,326865569373248843810425212509⟩⟩,⟨⟨(-183062140529370995447141309493),(-183062140529370995127329286739)⟩,⟨325863778605452475199996672935,325863778605452475517543701504⟩⟩] +lemma kernel4_1_r5_12_eq : ∀ k : Fin 16, kernel4_1Expr 5 12 k = kernel4_1_r5_12 k := by decide +kernel +noncomputable def kernel4_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-179266596893611808442058749559),(-179266596893611808123750108566)⟩,⟨324854844875775229323726818175,324854844875775229639861194421⟩⟩,⟨⟨(-175572190451085386453909612256),(-175572190451085386136695739015)⟩,⟨323840692438303028965756595958,323840692438303029280883939618⟩⟩,⟨⟨(-171977774540264433546330826130),(-171977774540264433230430493019)⟩,⟨322823186373379842381392436065,322823186373379842695291458699⟩⟩,⟨⟨(-168482198623819453969864851978),(-168482198623819453655023488762)⟩,⟨321804133245420981335316437515,321804133245420981648238974179⟩⟩,⟨⟨(-165084310368859377819349579248),(-165084310368859377505899789221)⟩,⟨320785281807374215635961792953,320785281807374215947572817647⟩⟩,⟨⟨(-161782957663362590371219609482),(-161782957663362590058790888026)⟩,⟨319768323747741097283875640878,319768323747741097594543006328⟩⟩,⟨⟨(-158576990568608193005104993810),(-158576990568608192693913070895)⟩,⟨318754894476144021067374656391,318754894476144021376880222311⟩⟩,⟨⟨(-155465263207574323806440639197),(-155465263207574323496230561737)⟩,⟨317746573943503673271733310502,317746573943503673580329556774⟩⟩,⟨⟨(-152446635589418419379901141781),(-152446635589418419071041038533)⟩,⟨316744887492976042721892452349,316744887492976043029208897003⟩⟩,⟨⟨(-149519975370293337241210087531),(-149519975370293336933290665442)⟩,⟨315751306737887509412392739887,315751306737887509718836309616⟩⟩,⟨⟨(-146684159550883246058447768346),(-146684159550883245751681423195)⟩,⟨314767250463000122785713610127,314767250463000123091069601694⟩⟩,⟨⟨(-143938076111164127354190939841),(-143938076111164127048323104754)⟩,⟨313794085545536489701775135004,313794085545536490006295884353⟩⟩,⟨⟨(-141280625583005646004614962231),(-141280625583005645699978253534)⟩,⟨312833127892494186501672905315,312833127892494186805023507780⟩⟩,⟨⟨(-138710722561334095665980398262),(-138710722561334095362198427053)⟩,⟨311885643390882786520882106357,311885643390882786823436855182⟩⟩,⟨⟨(-136227297154670193376524803352),(-136227297154670193073806634528)⟩,⟨310952848867621972520977131881,310952848867621972822524752636⟩⟩,⟨⟨(-133829296375940793995994505951),(-133829296375940793694086412582)⟩,⟨310035913055946324574144593819,310035913055946324874936802751⟩⟩] +lemma kernel4_1_r5_13_eq : ∀ k : Fin 16, kernel4_1Expr 5 13 k = kernel4_1_r5_13 k := by decide +kernel +noncomputable def kernel4_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-131515685474540251408027107645),(-131515685474540251107310929275)⟩,⟨309135957565270803967007262255,309135957565270804266659968987⟩⟩,⟨⟨(-129285449210685321844840651927),(-129285449210685321544888429147)⟩,⟨308254057851580283473008646574,308254057851580283771947978899⟩⟩,⟨⟨(-127137593073167356316359452268),(-127137593073167356017376569259)⟩,⟨307391244185516320122001102893,307391244185516320420019558837⟩⟩,⟨⟨(-125071144441657251926307062692),(-125071144441657251628041436148)⟩,⟨306548502615444370323967499606,306548502615444370621315348528⟩⟩,⟨⟨(-123085153694762428820567613744),(-123085153694762428523351652968)⟩,⟨305726775922894476954865714807,305726775922894477251208378906⟩⟩,⟨⟨(-121178695265071187024805487832),(-121178695265071186728258974549)⟩,⟨304926964567877807947176447395,304926964567877808242892507170⟩⟩,⟨⟨(-119350868642448403430162720842),(-119350868642448403134487402634)⟩,⟨304149927621690016460451059157,304149927621690016755336733161⟩⟩,⟨⟨(-117600799326867891722165459879),(-117600799326867891427111279268)⟩,⟨303396483684919970239196547088,303396483684919970533500250807⟩⟩,⟨⟨(-115927639732081113587158772392),(-115927639732081113293098098594)⟩,⟨302667411788488734619813732217,302667411788488734913160942741⟩⟩,⟨⟨(-114330570041429551677029665215),(-114330570041429551383540885349)⟩,⟨301963452275648587600844916236,301963452275648587893655832019⟩⟩,⟨⟨(-112808799017109192805055995187),(-112808799017109192512336880486)⟩,⟨301285307662975119413558710108,301285307662975119705633601595⟩⟩,⟨⟨(-111361564764190487449507319283),(-111361564764190487157310604287)⟩,⟨300633643478486970647545045955,300633643478486970939129682937⟩⟩,⟨⟨(-109988135450686115833209771862),(-109988135450686115541867689110)⟩,⟨300009089075127363861930089175,300009089075127364152690167384⟩⟩,⟨⟨(-108687809984942170904831924482),(-108687809984942170613962112698)⟩,⟨299412238417939178752286538852,299412238417939179042603129973⟩⟩,⟨⟨(-107459918651606234921982367082),(-107459918651606234631778569482)⟩,⟨298843650843360828152628010758,298843650843360828442305479180⟩⟩,⟨⟨(-106303823707398549930942405590),(-106303823707398549641160599465)⟩,⟨298303851789163551129032431049,298303851789163551418313424105⟩⟩] +lemma kernel4_1_r5_14_eq : ∀ k : Fin 16, kernel4_1Expr 5 14 k = kernel4_1_r5_14 k := by decide +kernel +noncomputable def kernel4_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-105218919937880333681076671213),(-105218919937880333392102427851)⟩,⟨297793333493641911102303579019,297793333493641911390800427038⟩⟩,⟨⟨(-104204635176376540824001488171),(-104204635176376540535398501654)⟩,⟨297312555662758252496909495681,297312555662758252785057409233⟩⟩,⟨⟨(-103260430786169282300930399599),(-103260430786169282012887920807)⟩,⟨296861946104028629532199000375,296861946104028629819806892538⟩⟩,⟨⟨(-102385802107032959193442969480),(-102385802107032958905721090061)⟩,⟨296441901326022294565281108123,296441901326022294852587605593⟩⟩,⟨⟨(-101580278867133203920220338264),(-101580278867133203633150915859)⟩,⟨296052787102429257624010988117,296052787102429257910682230866⟩⟩,⟨⟨(-100843425561259211598287851479),(-100843425561259211311488203073)⟩,⟨295694938999730756709814173535,295694938999730756996231787282⟩⟩,⟨⟨(-100174841796303244519231162290),(-100174841796303244232885970002)⟩,⟨295368662867585779067638495310,295368662867585779353616007461⟩⟩,⟨⟨(-99574162604842256650674171631),(-99574162604842256364548101121)⟩,⟨295074235291123130406903912720,295074235291123130692675443363⟩⟩,⟨⟨(-99041058727614963019161078088),(-99041058727614962733630990047)⟩,⟨294811904004403059167016419510,294811904004403059452203066540⟩⟩,⟨⟨(-98575236865623517576878765722),(-98575236865623517291517195002)⟩,⟨294581888264385215992992258417,294581888264385216278020563544⟩⟩,⟨⟨(-98176439902522506070625793022),(-98176439902522505785612322048)⟩,⟨294384379184810885858898183450,294384379184810886143586808884⟩⟩,⟨⟨(-97844447097889447696759753714),(-97844447097889447411864552072)⟩,⟨294219540029477103397190591231,294219540029477103681768194017⟩⟩,⟨⟨(-97579074251900667942963016414),(-97579074251900667658517341433)⟩,⟨294087506464448592125857798486,294087506464448592409991158937⟩⟩,⟨⟨(-97380173841864489182485613437),(-97380173841864488898108267209)⟩,⟨293988386768820604891259071005,293988386768820605175328443500⟩⟩,⟨⟨(-97247635130990416792491436736),(-97247635130990416508356660608)⟩,⟨293922262003711842862310803499,293922262003711843146140215014⟩⟩,⟨⟨(-97181384249698606056244473050),(-97181384249698605772128574430)⟩,⟨293889186139231856941864187369,293889186139231857225676172056⟩⟩] +lemma kernel4_1_r5_15_eq : ∀ k : Fin 16, kernel4_1Expr 5 15 k = kernel4_1_r5_15 k := by decide +kernel +noncomputable def kernel4_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel4_1_r5_0,kernel4_1_r5_1,kernel4_1_r5_2,kernel4_1_r5_3,kernel4_1_r5_4,kernel4_1_r5_5,kernel4_1_r5_6,kernel4_1_r5_7,kernel4_1_r5_8,kernel4_1_r5_9,kernel4_1_r5_10,kernel4_1_r5_11,kernel4_1_r5_12,kernel4_1_r5_13,kernel4_1_r5_14,kernel4_1_r5_15] +lemma kernel4_1_r5_eq (i k : Fin 16) : kernel4_1Expr 5 i k = kernel4_1_r5 i k := by + fin_cases i + · exact kernel4_1_r5_0_eq k + · exact kernel4_1_r5_1_eq k + · exact kernel4_1_r5_2_eq k + · exact kernel4_1_r5_3_eq k + · exact kernel4_1_r5_4_eq k + · exact kernel4_1_r5_5_eq k + · exact kernel4_1_r5_6_eq k + · exact kernel4_1_r5_7_eq k + · exact kernel4_1_r5_8_eq k + · exact kernel4_1_r5_9_eq k + · exact kernel4_1_r5_10_eq k + · exact kernel4_1_r5_11_eq k + · exact kernel4_1_r5_12_eq k + · exact kernel4_1_r5_13_eq k + · exact kernel4_1_r5_14_eq k + · exact kernel4_1_r5_15_eq k +noncomputable def kernel4_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel4_1_r0,kernel4_1_r1,kernel4_1_r2,kernel4_1_r3,kernel4_1_r4,kernel4_1_r5] +lemma kernel4_1_eq (j : Fin 6) (i k : Fin 16) : kernel4_1Expr j i k = kernel4_1 j i k := by + fin_cases j + · exact kernel4_1_r0_eq i k + · exact kernel4_1_r1_eq i k + · exact kernel4_1_r2_eq i k + · exact kernel4_1_r3_eq i k + · exact kernel4_1_r4_eq i k + · exact kernel4_1_r5_eq i k +lemma kernel4_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel4_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(4:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel4_1_eq] + unfold kernel4_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans4_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel7_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans7 j i k) +noncomputable def kernel7_0_r0_0 : Fin 16 → CBox := ![⟨⟨11579343,11579347⟩,⟨(-6285689),(-6285685)⟩⟩,⟨⟨11571854,11571859⟩,⟨(-6261364),(-6261360)⟩⟩,⟨⟨11556815,11556820⟩,⟨(-6212851),(-6212847)⟩⟩,⟨⟨11534100,11534104⟩,⟨(-6140408),(-6140404)⟩⟩,⟨⟨11503525,11503530⟩,⟨(-6044432),(-6044428)⟩⟩,⟨⟨11464851,11464856⟩,⟨(-5925444),(-5925440)⟩⟩,⟨⟨11417787,11417792⟩,⟨(-5784090),(-5784085)⟩⟩,⟨⟨11362003,11362008⟩,⟨(-5621142),(-5621138)⟩⟩,⟨⟨11297123,11297127⟩,⟨(-5437494),(-5437490)⟩⟩,⟨⟨11222745,11222749⟩,⟨(-5234151),(-5234147)⟩⟩,⟨⟨11138451,11138455⟩,⟨(-5012229),(-5012225)⟩⟩,⟨⟨11043805,11043810⟩,⟨(-4772954),(-4772949)⟩⟩,⟨⟨10938372,10938376⟩,⟨(-4517646),(-4517642)⟩⟩,⟨⟨10821728,10821732⟩,⟨(-4247726),(-4247721)⟩⟩,⟨⟨10693462,10693467⟩,⟨(-3964688),(-3964684)⟩⟩,⟨⟨10553200,10553205⟩,⟨(-3670109),(-3670105)⟩⟩] +lemma kernel7_0_r0_0_eq : ∀ k : Fin 16, kernel7_0Expr 0 0 k = kernel7_0_r0_0 k := by decide +kernel +noncomputable def kernel7_0_r0_1 : Fin 16 → CBox := ![⟨⟨10400607,10400611⟩,⟨(-3365636),(-3365632)⟩⟩,⟨⟨10235396,10235400⟩,⟨(-3052969),(-3052965)⟩⟩,⟨⟨10057343,10057347⟩,⟨(-2733857),(-2733852)⟩⟩,⟨⟨9866298,9866302⟩,⟨(-2410085),(-2410080)⟩⟩,⟨⟨9662182,9662186⟩,⟨(-2083461),(-2083456)⟩⟩,⟨⟨9445006,9445011⟩,⟨(-1755806),(-1755802)⟩⟩,⟨⟨9214880,9214884⟩,⟨(-1428947),(-1428943)⟩⟩,⟨⟨8972005,8972010⟩,⟨(-1104693),(-1104689)⟩⟩,⟨⟨8716688,8716692⟩,⟨(-784824),(-784819)⟩⟩,⟨⟨8449344,8449349⟩,⟨(-471086),(-471082)⟩⟩,⟨⟨8170494,8170498⟩,⟨(-165172),(-165167)⟩⟩,⟨⟨7880767,7880772⟩,⟨131289,131294⟩⟩,⟨⟨7580903,7580908⟩,⟨416755,416759⟩⟩,⟨⟨7271740,7271744⟩,⟨689761,689765⟩⟩,⟨⟨6954216,6954221⟩,⟨948954,948958⟩⟩,⟨⟨6629364,6629369⟩,⟨1193091,1193096⟩⟩] +lemma kernel7_0_r0_1_eq : ∀ k : Fin 16, kernel7_0Expr 0 1 k = kernel7_0_r0_1 k := by decide +kernel +noncomputable def kernel7_0_r0_2 : Fin 16 → CBox := ![⟨⟨6298310,6298314⟩,⟨1421051,1421056⟩⟩,⟨⟨5962243,5962247⟩,⟨1631845,1631849⟩⟩,⟨⟨5622431,5622436⟩,⟨1824631,1824635⟩⟩,⟨⟨5280199,5280203⟩,⟨1998703,1998707⟩⟩,⟨⟨4936907,4936912⟩,⟨2153519,2153523⟩⟩,⟨⟨4593956,4593960⟩,⟨2288683,2288687⟩⟩,⟨⟨4252762,4252767⟩,⟨2403966,2403970⟩⟩,⟨⟨3914745,3914749⟩,⟨2499296,2499300⟩⟩,⟨⟨3581320,3581325⟩,⟨2574750,2574755⟩⟩,⟨⟨3253870,3253874⟩,⟨2630578,2630582⟩⟩,⟨⟨2933747,2933752⟩,⟨2667166,2667170⟩⟩,⟨⟨2622247,2622252⟩,⟨2685053,2685058⟩⟩,⟨⟨2320608,2320612⟩,⟨2684915,2684920⟩⟩,⟨⟨2029976,2029980⟩,⟨2667561,2667566⟩⟩,⟨⟨1751425,1751429⟩,⟨2633910,2633915⟩⟩,⟨⟨1485919,1485924⟩,⟨2584997,2585001⟩⟩] +lemma kernel7_0_r0_2_eq : ∀ k : Fin 16, kernel7_0Expr 0 2 k = kernel7_0_r0_2 k := by decide +kernel +noncomputable def kernel7_0_r0_3 : Fin 16 → CBox := ![⟨⟨1234314,1234319⟩,⟨2521951,2521955⟩⟩,⟨⟨997352,997357⟩,⟨2445981,2445986⟩⟩,⟨⟨775650,775655⟩,⟨2358362,2358367⟩⟩,⟨⟨569699,569703⟩,⟨2260426,2260431⟩⟩,⟨⟨379851,379855⟩,⟨2153541,2153545⟩⟩,⟨⟨206336,206340⟩,⟨2039095,2039100⟩⟩,⟨⟨49244,49248⟩,⟨1918489,1918494⟩⟩,⟨⟨(-91463),(-91459)⟩,⟨1793112,1793116⟩⟩,⟨⟨(-215957),(-215952)⟩,⟨1664333,1664338⟩⟩,⟨⟨(-324525),(-324520)⟩,⟨1533479,1533483⟩⟩,⟨⟨(-417576),(-417572)⟩,⟨1401838,1401843⟩⟩,⟨⟨(-495627),(-495622)⟩,⟨1270631,1270635⟩⟩,⟨⟨(-559296),(-559292)⟩,⟨1141008,1141012⟩⟩,⟨⟨(-609290),(-609286)⟩,⟨1014033,1014038⟩⟩,⟨⟨(-646396),(-646392)⟩,⟨890689,890693⟩⟩,⟨⟨(-671469),(-671464)⟩,⟨771853,771857⟩⟩] +lemma kernel7_0_r0_3_eq : ∀ k : Fin 16, kernel7_0Expr 0 3 k = kernel7_0_r0_3 k := by decide +kernel +noncomputable def kernel7_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-685423),(-685418)⟩,⟨658301,658306⟩⟩,⟨⟨(-689213),(-689209)⟩,⟨550715,550720⟩⟩,⟨⟨(-683825),(-683820)⟩,⟨449651,449656⟩⟩,⟨⟨(-670267),(-670262)⟩,⟨355565,355570⟩⟩,⟨⟨(-649554),(-649549)⟩,⟨268803,268808⟩⟩,⟨⟨(-622689),(-622685)⟩,⟨189603,189607⟩⟩,⟨⟨(-590671),(-590666)⟩,⟨118103,118108⟩⟩,⟨⟨(-554464),(-554459)⟩,⟨54342,54346⟩⟩,⟨⟨(-514996),(-514991)⟩,⟨(-1741),(-1737)⟩⟩,⟨⟨(-473152),(-473148)⟩,⟨(-50281),(-50277)⟩⟩,⟨⟨(-429766),(-429761)⟩,⟨(-91502),(-91497)⟩⟩,⟨⟨(-385610),(-385606)⟩,⟨(-125691),(-125687)⟩⟩,⟨⟨(-341397),(-341393)⟩,⟨(-153201),(-153197)⟩⟩,⟨⟨(-297762),(-297758)⟩,⟨(-174436),(-174431)⟩⟩,⟨⟨(-255274),(-255269)⟩,⟨(-189845),(-189840)⟩⟩,⟨⟨(-214431),(-214427)⟩,⟨(-199904),(-199899)⟩⟩] +lemma kernel7_0_r0_4_eq : ∀ k : Fin 16, kernel7_0Expr 0 4 k = kernel7_0_r0_4 k := by decide +kernel +noncomputable def kernel7_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-175654),(-175650)⟩,⟨(-205123),(-205119)⟩⟩,⟨⟨(-139290),(-139286)⟩,⟨(-206023),(-206019)⟩⟩,⟨⟨(-105614),(-105610)⟩,⟨(-203133),(-203128)⟩⟩,⟨⟨(-74836),(-74832)⟩,⟨(-196977),(-196972)⟩⟩,⟨⟨(-47089),(-47085)⟩,⟨(-188073),(-188069)⟩⟩,⟨⟨(-22456),(-22452)⟩,⟨(-176929),(-176925)⟩⟩,⟨⟨(-957),(-952)⟩,⟨(-164027),(-164023)⟩⟩,⟨⟨17445,17450⟩,⟨(-149822),(-149817)⟩⟩,⟨⟨32828,32832⟩,⟨(-134733),(-134729)⟩⟩,⟨⟨45309,45313⟩,⟨(-119157),(-119152)⟩⟩,⟨⟨55045,55050⟩,⟨(-103442),(-103437)⟩⟩,⟨⟨62220,62225⟩,⟨(-87901),(-87897)⟩⟩,⟨⟨67046,67050⟩,⟨(-72808),(-72804)⟩⟩,⟨⟨69739,69743⟩,⟨(-58394),(-58390)⟩⟩,⟨⟨70538,70542⟩,⟨(-44852),(-44847)⟩⟩,⟨⟨69686,69690⟩,⟨(-32331),(-32327)⟩⟩] +lemma kernel7_0_r0_5_eq : ∀ k : Fin 16, kernel7_0Expr 0 5 k = kernel7_0_r0_5 k := by decide +kernel +noncomputable def kernel7_0_r0_6 : Fin 16 → CBox := ![⟨⟨67423,67427⟩,⟨(-20946),(-20941)⟩⟩,⟨⟨63988,63993⟩,⟨(-10773),(-10768)⟩⟩,⟨⟨59615,59619⟩,⟨(-1859),(-1855)⟩⟩,⟨⟨54523,54528⟩,⟨5780,5784⟩⟩,⟨⟨48921,48926⟩,⟨12155,12159⟩⟩,⟨⟨43003,43007⟩,⟨17306,17310⟩⟩,⟨⟨36937,36941⟩,⟨21288,21292⟩⟩,⟨⟨30880,30884⟩,⟨24175,24180⟩⟩,⟨⟨24970,24974⟩,⟨26051,26056⟩⟩,⟨⟨19313,19318⟩,⟨27016,27021⟩⟩,⟨⟨14012,14016⟩,⟨27176,27180⟩⟩,⟨⟨9134,9139⟩,⟨26631,26635⟩⟩,⟨⟨4740,4745⟩,⟨25499,25503⟩⟩,⟨⟨862,867⟩,⟨23886,23890⟩⟩,⟨⟨(-2475),(-2470)⟩,⟨21894,21898⟩⟩,⟨⟨(-5264),(-5260)⟩,⟨19626,19630⟩⟩] +lemma kernel7_0_r0_6_eq : ∀ k : Fin 16, kernel7_0Expr 0 6 k = kernel7_0_r0_6 k := by decide +kernel +noncomputable def kernel7_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-7517),(-7513)⟩,⟨17173,17177⟩⟩,⟨⟨(-9251),(-9246)⟩,⟨14622,14626⟩⟩,⟨⟨(-10495),(-10491)⟩,⟨12051,12055⟩⟩,⟨⟨(-11281),(-11277)⟩,⟨9525,9529⟩⟩,⟨⟨(-11653),(-11649)⟩,⟨7098,7102⟩⟩,⟨⟨(-11663),(-11659)⟩,⟨4824,4828⟩⟩,⟨⟨(-11353),(-11349)⟩,⟨2737,2742⟩⟩,⟨⟨(-10778),(-10773)⟩,⟨866,871⟩⟩,⟨⟨(-9987),(-9983)⟩,⟨(-771),(-767)⟩⟩,⟨⟨(-9030),(-9025)⟩,⟨(-2161),(-2157)⟩⟩,⟨⟨(-7953),(-7949)⟩,⟨(-3302),(-3297)⟩⟩,⟨⟨(-6803),(-6799)⟩,⟨(-4198),(-4193)⟩⟩,⟨⟨(-5618),(-5614)⟩,⟨(-4852),(-4848)⟩⟩,⟨⟨(-4432),(-4428)⟩,⟨(-5285),(-5281)⟩⟩,⟨⟨(-3280),(-3275)⟩,⟨(-5514),(-5510)⟩⟩,⟨⟨(-2188),(-2184)⟩,⟨(-5554),(-5550)⟩⟩] +lemma kernel7_0_r0_7_eq : ∀ k : Fin 16, kernel7_0Expr 0 7 k = kernel7_0_r0_7 k := by decide +kernel +noncomputable def kernel7_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-1174),(-1170)⟩,⟨(-5434),(-5429)⟩⟩,⟨⟨(-259),(-255)⟩,⟨(-5174),(-5170)⟩⟩,⟨⟨544,548⟩,⟨(-4801),(-4796)⟩⟩,⟨⟨1231,1235⟩,⟨(-4339),(-4335)⟩⟩,⟨⟨1794,1798⟩,⟨(-3810),(-3806)⟩⟩,⟨⟨2239,2243⟩,⟨(-3240),(-3236)⟩⟩,⟨⟨2562,2566⟩,⟨(-2647),(-2643)⟩⟩,⟨⟨2774,2778⟩,⟨(-2048),(-2043)⟩⟩,⟨⟨2879,2884⟩,⟨(-1466),(-1462)⟩⟩,⟨⟨2889,2893⟩,⟨(-912),(-908)⟩⟩,⟨⟨2816,2820⟩,⟨(-395),(-391)⟩⟩,⟨⟨2671,2675⟩,⟨71,75⟩⟩,⟨⟨2466,2470⟩,⟨481,485⟩⟩,⟨⟨2213,2217⟩,⟨832,836⟩⟩,⟨⟨1926,1930⟩,⟨1118,1122⟩⟩,⟨⟨1614,1619⟩,⟨1340,1345⟩⟩] +lemma kernel7_0_r0_8_eq : ∀ k : Fin 16, kernel7_0Expr 0 8 k = kernel7_0_r0_8 k := by decide +kernel +noncomputable def kernel7_0_r0_9 : Fin 16 → CBox := ![⟨⟨1294,1298⟩,⟨1500,1504⟩⟩,⟨⟨969,973⟩,⟨1602,1606⟩⟩,⟨⟨652,656⟩,⟨1643,1648⟩⟩,⟨⟨351,355⟩,⟨1637,1642⟩⟩,⟨⟨69,73⟩,⟨1584,1588⟩⟩,⟨⟨(-185),(-180)⟩,⟨1493,1497⟩⟩,⟨⟨(-407),(-403)⟩,⟨1367,1371⟩⟩,⟨⟨(-595),(-591)⟩,⟨1219,1223⟩⟩,⟨⟨(-750),(-745)⟩,⟨1050,1054⟩⟩,⟨⟨(-868),(-864)⟩,⟨868,872⟩⟩,⟨⟨(-952),(-947)⟩,⟨679,683⟩⟩,⟨⟨(-1002),(-997)⟩,⟨489,494⟩⟩,⟨⟨(-1021),(-1017)⟩,⟨304,309⟩⟩,⟨⟨(-1011),(-1007)⟩,⟨129,133⟩⟩,⟨⟨(-975),(-970)⟩,⟨(-37),(-33)⟩⟩,⟨⟨(-915),(-911)⟩,⟨(-186),(-181)⟩⟩] +lemma kernel7_0_r0_9_eq : ∀ k : Fin 16, kernel7_0Expr 0 9 k = kernel7_0_r0_9 k := by decide +kernel +noncomputable def kernel7_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-838),(-834)⟩,⟨(-315),(-311)⟩⟩,⟨⟨(-744),(-740)⟩,⟨(-428),(-424)⟩⟩,⟨⟨(-639),(-634)⟩,⟨(-520),(-516)⟩⟩,⟨⟨(-527),(-523)⟩,⟨(-592),(-588)⟩⟩,⟨⟨(-410),(-406)⟩,⟨(-643),(-639)⟩⟩,⟨⟨(-293),(-288)⟩,⟨(-672),(-668)⟩⟩,⟨⟨(-174),(-170)⟩,⟨(-684),(-680)⟩⟩,⟨⟨(-64),(-60)⟩,⟨(-677),(-673)⟩⟩,⟨⟨42,46⟩,⟨(-657),(-653)⟩⟩,⟨⟨138,142⟩,⟨(-621),(-617)⟩⟩,⟨⟨223,228⟩,⟨(-572),(-568)⟩⟩,⟨⟨300,304⟩,⟨(-512),(-508)⟩⟩,⟨⟨361,366⟩,⟨(-446),(-442)⟩⟩,⟨⟨411,415⟩,⟨(-373),(-369)⟩⟩,⟨⟨449,453⟩,⟨(-298),(-294)⟩⟩,⟨⟨476,480⟩,⟨(-221),(-217)⟩⟩] +lemma kernel7_0_r0_10_eq : ∀ k : Fin 16, kernel7_0Expr 0 10 k = kernel7_0_r0_10 k := by decide +kernel +noncomputable def kernel7_0_r0_11 : Fin 16 → CBox := ![⟨⟨489,493⟩,⟨(-143),(-139)⟩⟩,⟨⟨490,494⟩,⟨(-66),(-62)⟩⟩,⟨⟨481,485⟩,⟨7,11⟩⟩,⟨⟨463,468⟩,⟨74,78⟩⟩,⟨⟨435,439⟩,⟨137,141⟩⟩,⟨⟨402,406⟩,⟨194,198⟩⟩,⟨⟨361,365⟩,⟨245,249⟩⟩,⟨⟨315,319⟩,⟨287,291⟩⟩,⟨⟨267,271⟩,⟨320,324⟩⟩,⟨⟨213,218⟩,⟨347,351⟩⟩,⟨⟨161,165⟩,⟨366,370⟩⟩,⟨⟨106,110⟩,⟨376,380⟩⟩,⟨⟨54,58⟩,⟨381,385⟩⟩,⟨⟨3,7⟩,⟨378,382⟩⟩,⟨⟨(-47),(-43)⟩,⟨369,373⟩⟩,⟨⟨(-95),(-91)⟩,⟨355,359⟩⟩] +lemma kernel7_0_r0_11_eq : ∀ k : Fin 16, kernel7_0Expr 0 11 k = kernel7_0_r0_11 k := by decide +kernel +noncomputable def kernel7_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-136),(-132)⟩,⟨335,339⟩⟩,⟨⟨(-175),(-171)⟩,⟨310,314⟩⟩,⟨⟨(-210),(-206)⟩,⟨282,286⟩⟩,⟨⟨(-240),(-235)⟩,⟨249,253⟩⟩,⟨⟨(-266),(-262)⟩,⟨216,220⟩⟩,⟨⟨(-287),(-283)⟩,⟨178,182⟩⟩,⟨⟨(-302),(-298)⟩,⟨143,147⟩⟩,⟨⟨(-315),(-311)⟩,⟨106,110⟩⟩,⟨⟨(-321),(-317)⟩,⟨65,69⟩⟩,⟨⟨(-322),(-318)⟩,⟨28,32⟩⟩,⟨⟨(-321),(-317)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-316),(-312)⟩,⟨(-43),(-39)⟩⟩,⟨⟨(-306),(-302)⟩,⟨(-76),(-72)⟩⟩,⟨⟨(-294),(-290)⟩,⟨(-107),(-103)⟩⟩,⟨⟨(-278),(-275)⟩,⟨(-135),(-131)⟩⟩,⟨⟨(-263),(-259)⟩,⟨(-163),(-159)⟩⟩] +lemma kernel7_0_r0_12_eq : ∀ k : Fin 16, kernel7_0Expr 0 12 k = kernel7_0_r0_12 k := by decide +kernel +noncomputable def kernel7_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-242),(-238)⟩,⟨(-188),(-184)⟩⟩,⟨⟨(-222),(-218)⟩,⟨(-210),(-206)⟩⟩,⟨⟨(-198),(-194)⟩,⟨(-229),(-225)⟩⟩,⟨⟨(-175),(-171)⟩,⟨(-245),(-241)⟩⟩,⟨⟨(-149),(-145)⟩,⟨(-259),(-255)⟩⟩,⟨⟨(-126),(-122)⟩,⟨(-270),(-266)⟩⟩,⟨⟨(-100),(-96)⟩,⟨(-277),(-273)⟩⟩,⟨⟨(-74),(-70)⟩,⟨(-285),(-281)⟩⟩,⟨⟨(-49),(-45)⟩,⟨(-287),(-283)⟩⟩,⟨⟨(-26),(-22)⟩,⟨(-290),(-286)⟩⟩,⟨⟨0,4⟩,⟨(-289),(-285)⟩⟩,⟨⟨23,27⟩,⟨(-289),(-285)⟩⟩,⟨⟨45,49⟩,⟨(-285),(-281)⟩⟩,⟨⟨65,69⟩,⟨(-279),(-275)⟩⟩,⟨⟨88,92⟩,⟨(-273),(-269)⟩⟩,⟨⟨105,109⟩,⟨(-264),(-260)⟩⟩] +lemma kernel7_0_r0_13_eq : ∀ k : Fin 16, kernel7_0Expr 0 13 k = kernel7_0_r0_13 k := by decide +kernel +noncomputable def kernel7_0_r0_14 : Fin 16 → CBox := ![⟨⟨125,129⟩,⟨(-255),(-252)⟩⟩,⟨⟨142,146⟩,⟨(-247),(-243)⟩⟩,⟨⟨156,160⟩,⟨(-235),(-231)⟩⟩,⟨⟨170,174⟩,⟨(-224),(-220)⟩⟩,⟨⟨184,188⟩,⟨(-215),(-211)⟩⟩,⟨⟨195,199⟩,⟨(-200),(-197)⟩⟩,⟨⟨206,210⟩,⟨(-189),(-185)⟩⟩,⟨⟨218,222⟩,⟨(-177),(-174)⟩⟩,⟨⟨226,230⟩,⟨(-166),(-162)⟩⟩,⟨⟨235,238⟩,⟨(-155),(-151)⟩⟩,⟨⟨240,244⟩,⟨(-140),(-136)⟩⟩,⟨⟨246,250⟩,⟨(-129),(-125)⟩⟩,⟨⟨251,255⟩,⟨(-117),(-113)⟩⟩,⟨⟨257,261⟩,⟨(-106),(-102)⟩⟩,⟨⟨260,264⟩,⟨(-97),(-94)⟩⟩,⟨⟨265,269⟩,⟨(-86),(-82)⟩⟩] +lemma kernel7_0_r0_14_eq : ∀ k : Fin 16, kernel7_0Expr 0 14 k = kernel7_0_r0_14 k := by decide +kernel +noncomputable def kernel7_0_r0_15 : Fin 16 → CBox := ![⟨⟨268,272⟩,⟨(-77),(-74)⟩⟩,⟨⟨268,272⟩,⟨(-69),(-65)⟩⟩,⟨⟨271,275⟩,⟨(-60),(-56)⟩⟩,⟨⟨274,278⟩,⟨(-52),(-48)⟩⟩,⟨⟨274,278⟩,⟨(-43),(-39)⟩⟩,⟨⟨274,278⟩,⟨(-38),(-34)⟩⟩,⟨⟨277,281⟩,⟨(-29),(-25)⟩⟩,⟨⟨277,281⟩,⟨(-26),(-22)⟩⟩,⟨⟨277,281⟩,⟨(-20),(-17)⟩⟩,⟨⟨277,281⟩,⟨(-15),(-11)⟩⟩,⟨⟨277,281⟩,⟨(-12),(-8)⟩⟩,⟨⟨277,281⟩,⟨(-9),(-5)⟩⟩,⟨⟨277,281⟩,⟨(-6),(-2)⟩⟩,⟨⟨277,281⟩,⟨(-3),1⟩⟩,⟨⟨277,281⟩,⟨(-3),1⟩⟩,⟨⟨277,281⟩,⟨(-3),1⟩⟩] +lemma kernel7_0_r0_15_eq : ∀ k : Fin 16, kernel7_0Expr 0 15 k = kernel7_0_r0_15 k := by decide +kernel +noncomputable def kernel7_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel7_0_r0_0,kernel7_0_r0_1,kernel7_0_r0_2,kernel7_0_r0_3,kernel7_0_r0_4,kernel7_0_r0_5,kernel7_0_r0_6,kernel7_0_r0_7,kernel7_0_r0_8,kernel7_0_r0_9,kernel7_0_r0_10,kernel7_0_r0_11,kernel7_0_r0_12,kernel7_0_r0_13,kernel7_0_r0_14,kernel7_0_r0_15] +lemma kernel7_0_r0_eq (i k : Fin 16) : kernel7_0Expr 0 i k = kernel7_0_r0 i k := by + fin_cases i + · exact kernel7_0_r0_0_eq k + · exact kernel7_0_r0_1_eq k + · exact kernel7_0_r0_2_eq k + · exact kernel7_0_r0_3_eq k + · exact kernel7_0_r0_4_eq k + · exact kernel7_0_r0_5_eq k + · exact kernel7_0_r0_6_eq k + · exact kernel7_0_r0_7_eq k + · exact kernel7_0_r0_8_eq k + · exact kernel7_0_r0_9_eq k + · exact kernel7_0_r0_10_eq k + · exact kernel7_0_r0_11_eq k + · exact kernel7_0_r0_12_eq k + · exact kernel7_0_r0_13_eq k + · exact kernel7_0_r0_14_eq k + · exact kernel7_0_r0_15_eq k +noncomputable def kernel7_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-1665483961583081),(-1665483961583077)⟩,⟨1710657156375845,1710657156375850⟩⟩,⟨⟨(-1663674152662547),(-1663674152662543)⟩,⟨1708024855547670,1708024855547675⟩⟩,⟨⟨(-1660060308503860),(-1660060308503856)⟩,⟨1702771838721445,1702771838721450⟩⟩,⟨⟨(-1654653946141766),(-1654653946141762)⟩,⟨1694921192696772,1694921192696776⟩⟩,⟨⟨(-1647472265527502),(-1647472265527498)⟩,⟨1684507341341254,1684507341341258⟩⟩,⟨⟨(-1638538059433216),(-1638538059433212)⟩,⟨1671575800277508,1671575800277512⟩⟩,⟨⟨(-1627879594360346),(-1627879594360341)⟩,⟨1656182853576756,1656182853576762⟩⟩,⟨⟨(-1615530463326753),(-1615530463326749)⟩,⟨1638395155635457,1638395155635461⟩⟩,⟨⟨(-1601529411609828),(-1601529411609824)⟩,⟨1618289262129675,1618289262129679⟩⟩,⟨⟨(-1585920136714850),(-1585920136714846)⟩,⟨1595951094611548,1595951094611552⟩⟩,⟨⟨(-1568751064017644),(-1568751064017640)⟩,⟨1571475343924791,1571475343924795⟩⟩,⟨⟨(-1550075099696372),(-1550075099696368)⟩,⟨1544964818164850,1544964818164854⟩⟩,⟨⟨(-1529949362717779),(-1529949362717775)⟩,⟨1516529741387567,1516529741387571⟩⟩,⟨⟨(-1508434897777115),(-1508434897777111)⟩,⟨1486287009673064,1486287009673068⟩⟩,⟨⟨(-1485596371206958),(-1485596371206954)⟩,⟨1454359411474750,1454359411474754⟩⟩,⟨⟨(-1461501751967914),(-1461501751967910)⟩,⟨1420874819424195,1420874819424199⟩⟩] +lemma kernel7_0_r1_0_eq : ∀ k : Fin 16, kernel7_0Expr 1 0 k = kernel7_0_r1_0 k := by decide +kernel +noncomputable def kernel7_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-1436221979912409),(-1436221979912405)⟩,⟨1385965360919259,1385965360919263⟩⟩,⟨⟨(-1409830623571801),(-1409830623571797)⟩,⟨1349766574894865,1349766574894870⟩⟩,⟨⟨(-1382403529755926),(-1382403529755922)⟩,⟨1312416562163942,1312416562163946⟩⟩,⟨⟨(-1354018467273698),(-1354018467273694)⟩,⟨1274055136622017,1274055136622021⟩⟩,⟨⟨(-1324754767083085),(-1324754767083081)⟩,⟨1234822984435901,1234822984435905⟩⟩,⟨⟨(-1294692961159761),(-1294692961159757)⟩,⟨1194860838088541,1194860838088546⟩⟩,⟨⟨(-1263914422336000),(-1263914422335996)⟩,⟨1154308671833759,1154308671833763⟩⟩,⟨⟨(-1232501007306407),(-1232501007306403)⟩,⟨1113304924731673,1113304924731678⟩⟩,⟨⟨(-1200534704925184),(-1200534704925180)⟩,⟨1071985756994838,1071985756994842⟩⟩,⟨⟨(-1168097291832461),(-1168097291832457)⟩,⟨1030484344883610,1030484344883615⟩⟩,⟨⟨(-1135269997345756),(-1135269997345752)⟩,⟨988930218854638,988930218854642⟩⟩,⟨⟨(-1102133179438156),(-1102133179438152)⟩,⟨947448649096535,947448649096539⟩⟩,⟨⟨(-1068766013499016),(-1068766013499012)⟩,⟨906160081990194,906160081990198⟩⟩,⟨⟨(-1035246195437053),(-1035246195437048)⟩,⟨865179630415835,865179630415841⟩⟩,⟨⟨(-1001649660541412),(-1001649660541408)⟩,⟨824616620203318,824616620203322⟩⟩,⟨⟨(-968050319365048),(-968050319365044)⟩,⟨784574194394396,784574194394400⟩⟩] +lemma kernel7_0_r1_1_eq : ∀ k : Fin 16, kernel7_0Expr 1 1 k = kernel7_0_r1_1 k := by decide +kernel +noncomputable def kernel7_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-934519811738241),(-934519811738237)⟩,⟨745148976363474,745148976363478⟩⟩,⟨⟨(-901127279859678),(-901127279859674)⟩,⟨706430792234226,706430792234230⟩⟩,⟨⟨(-867939161250045),(-867939161250041)⟩,⟨668502452440523,668502452440527⟩⟩,⟨⟨(-835019002189662),(-835019002189658)⟩,⟨631439591717508,631439591717512⟩⟩,⟨⟨(-802427292099096),(-802427292099092)⟩,⟨595310566278393,595310566278397⟩⟩,⟨⟨(-770221319161082),(-770221319161078)⟩,⟨560176406439509,560176406439514⟩⟩,⟨⟨(-738455047324797),(-738455047324793)⟩,⟨526090822504922,526090822504926⟩⟩,⟨⟨(-707179014680833),(-707179014680828)⟩,⟨493100261315726,493100261315731⟩⟩,⟨⟨(-676440253048189),(-676440253048185)⟩,⟨461244010511037,461244010511041⟩⟩,⟨⟨(-646282228474185),(-646282228474180)⟩,⟨430554347239580,430554347239584⟩⟩,⟨⟨(-616744802215469),(-616744802215465)⟩,⟨401056727803724,401056727803728⟩⟩,⟨⟨(-587864211643857),(-587864211643853)⟩,⟨372770014512534,372770014512538⟩⟩,⟨⟨(-559673070405521),(-559673070405517)⟩,⟨345706735866357,345706735866362⟩⟩,⟨⟨(-532200387056426),(-532200387056422)⟩,⟨319873376091885,319873376091889⟩⟩,⟨⟨(-505471601301431),(-505471601301427)⟩,⟨295270689991800,295270689991804⟩⟩,⟨⟨(-479508636879682),(-479508636879678)⟩,⟨271894039065087,271894039065091⟩⟩] +lemma kernel7_0_r1_2_eq : ∀ k : Fin 16, kernel7_0Expr 1 2 k = kernel7_0_r1_2 k := by decide +kernel +noncomputable def kernel7_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-454329970064737),(-454329970064732)⟩,⟨249733744889955,249733744889959⟩⟩,⟨⟨(-429950712684791),(-429950712684787)⟩,⟨228775455838212,228775455838216⟩⟩,⟨⟨(-406382708516220),(-406382708516216)⟩,⟨209000523304379,209000523304383⟩⟩,⟨⟨(-383634641862570),(-383634641862566)⟩,⟨190386383781035,190386383781039⟩⟩,⟨⟨(-361712157100808),(-361712157100804)⟩,⟨172906943289916,172906943289920⟩⟩,⟨⟨(-340617987956998),(-340617987956993)⟩,⟨156532960882299,156532960882303⟩⟩,⟨⟨(-320352095264316),(-320352095264312)⟩,⟨141232428147576,141232428147580⟩⟩,⟨⟨(-300911811956856),(-300911811956852)⟩,⟨126970941912096,126970941912100⟩⟩,⟨⟨(-282291994062918),(-282291994062914)⟩,⟨113712067566628,113712067566632⟩⟩,⟨⟨(-264485176480572),(-264485176480568)⟩,⟨101417690726772,101417690726777⟩⟩,⟨⟨(-247481732345862),(-247481732345858)⟩,⟨90048355201898,90048355201903⟩⟩,⟨⟨(-231270034839431),(-231270034839426)⟩,⟨79563585521665,79563585521669⟩⟩,⟨⟨(-215836620319863),(-215836620319859)⟩,⟨69922192541022,69922192541027⟩⟩,⟨⟨(-201166351721060),(-201166351721056)⟩,⟨61082560912005,61082560912009⟩⟩,⟨⟨(-187242581205712),(-187242581205708)⟩,⟨53002917470672,53002917470676⟩⟩,⟨⟨(-174047311126637),(-174047311126633)⟩,⟨45641579837679,45641579837683⟩⟩] +lemma kernel7_0_r1_3_eq : ∀ k : Fin 16, kernel7_0Expr 1 3 k = kernel7_0_r1_3 k := by decide +kernel +noncomputable def kernel7_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-161561352411800),(-161561352411796)⟩,⟨38957184769170,38957184769175⟩⟩,⟨⟨(-149764479556256),(-149764479556252)⟩,⟨32908896018860,32908896018864⟩⟩,⟨⟨(-138635581474490),(-138635581474486)⟩,⟨27456591681126,27456591681130⟩⟩,⟨⟨(-128152807538864),(-128152807538860)⟩,⟨22561031177164,22561031177168⟩⟩,⟨⟨(-118293708203289),(-118293708203285)⟩,⟨18184002221084,18184002221088⟩⟩,⟨⟨(-109035369685331),(-109035369685327)⟩,⟨14288448259579,14288448259583⟩⟩,⟨⟨(-100354542253866),(-100354542253862)⟩,⟨10838577017264,10838577017269⟩⟩,⟨⟨(-92227761742539),(-92227761742535)⟩,⟨7799950899742,7799950899746⟩⟩,⟨⟨(-84631463981141),(-84631463981137)⟩,⟨5139560108372,5139560108376⟩⟩,⟨⟨(-77542091906887),(-77542091906882)⟩,⟨2825879404795,2825879404800⟩⟩,⟨⟨(-70936195185117),(-70936195185112)⟩,⟨828909530175,828909530179⟩⟩,⟨⟨(-64790522233517),(-64790522233512)⟩,⟨(-879795665286),(-879795665282)⟩⟩,⟨⟨(-59082104605348),(-59082104605343)⟩,⟨(-2327115291997),(-2327115291993)⟩⟩,⟨⟨(-53788333744847),(-53788333744843)⟩,⟨(-3538359578513),(-3538359578509)⟩⟩,⟨⟨(-48887030181844),(-48887030181839)⟩,⟨(-4537278998563),(-4537278998559)⟩⟩,⟨⟨(-44356505282194),(-44356505282190)⟩,⟨(-5346083253919),(-5346083253915)⟩⟩] +lemma kernel7_0_r1_4_eq : ∀ k : Fin 16, kernel7_0Expr 1 4 k = kernel7_0_r1_4 k := by decide +kernel +noncomputable def kernel7_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-40175615716063),(-40175615716059)⟩,⟨(-5985469015502),(-5985469015497)⟩⟩,⟨⟨(-36323810846862),(-36323810846858)⟩,⟨(-6474655350585),(-6474655350580)⟩⟩,⟨⟨(-32781173280009),(-32781173280005)⟩,⟨(-6831425798179),(-6831425798175)⟩⟩,⟨⟨(-29528452842468),(-29528452842464)⟩,⟨(-7072176096000),(-7072176095996)⟩⟩,⟨⟨(-26547094291223),(-26547094291218)⟩,⟨(-7211966609865),(-7211966609861)⟩⟩,⟨⟨(-23819259071632),(-23819259071628)⟩,⟨(-7264578568866),(-7264578568862)⟩⟩,⟨⟨(-21327841465044),(-21327841465040)⟩,⟨(-7242573265837),(-7242573265833)⟩⟩,⟨⟨(-19056479479249),(-19056479479245)⟩,⟨(-7157353441727),(-7157353441723)⟩⟩,⟨⟨(-16989560845506),(-16989560845502)⟩,⟨(-7019226133488),(-7019226133484)⟩⟩,⟨⟨(-15112224492332),(-15112224492328)⟩,⟨(-6837466326958),(-6837466326954)⟩⟩,⟨⟨(-13410357868890),(-13410357868886)⟩,⟨(-6620380818371),(-6620380818366)⟩⟩,⟨⟨(-11870590490426),(-11870590490421)⟩,⟨(-6375371749721),(-6375371749717)⟩⟩,⟨⟨(-10480284074425),(-10480284074421)⟩,⟨(-6108999343637),(-6108999343632)⟩⟩,⟨⟨(-9227519629903),(-9227519629898)⟩,⟨(-5827043422133),(-5827043422129)⟩⟩,⟨⟨(-8101081853240),(-8101081853236)⟩,⟨(-5534563350165),(-5534563350161)⟩⟩,⟨⟨(-7090441172936),(-7090441172932)⟩,⟨(-5235956098873),(-5235956098869)⟩⟩] +lemma kernel7_0_r1_5_eq : ∀ k : Fin 16, kernel7_0Expr 1 5 k = kernel7_0_r1_5 k := by decide +kernel +noncomputable def kernel7_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-6185733772603),(-6185733772599)⟩,⟨(-4935012174446),(-4935012174442)⟩⟩,⟨⟨(-5377739906893),(-5377739906889)⟩,⟨(-4634969206567),(-4634969206562)⟩⟩,⟨⟨(-4657860809010),(-4657860809006)⟩,⟨(-4338563034895),(-4338563034891)⟩⟩,⟨⟨(-4018094471440),(-4018094471436)⟩,⟨(-4048076173355),(-4048076173351)⟩⟩,⟨⟨(-3451010563521),(-3451010563517)⟩,⟨(-3765383569593),(-3765383569589)⟩⟩,⟨⟨(-2949724731126),(-2949724731122)⟩,⟨(-3491995611198),(-3491995611194)⟩⟩,⟨⟨(-2507872504739),(-2507872504735)⟩,⟨(-3229098360926),(-3229098360922)⟩⟩,⟨⟨(-2119583023366),(-2119583023362)⟩,⟨(-2977591030433),(-2977591030428)⟩⟩,⟨⟨(-1779452762717),(-1779452762713)⟩,⟨(-2738120726013),(-2738120726009)⟩⟩,⟨⟨(-1482519437413),(-1482519437409)⟩,⟨(-2511114520517),(-2511114520513)⟩⟩,⟨⟨(-1224236228732),(-1224236228728)⟩,⟨(-2296808923431),(-2296808923427)⟩⟩,⟨⟨(-1000446471518),(-1000446471513)⟩,⟨(-2095276835867),(-2095276835863)⟩⟩,⟨⟨(-807358916869),(-807358916865)⟩,⟨(-1906452089463),(-1906452089458)⟩⟩,⟨⟨(-641523670722),(-641523670717)⟩,⟨(-1730151677810),(-1730151677806)⟩⟩,⟨⟨(-499808892926),(-499808892922)⟩,⟨(-1566095796433),(-1566095796428)⟩⟩,⟨⟨(-379378326773),(-379378326769)⟩,⟨(-1413925812665),(-1413925812661)⟩⟩] +lemma kernel7_0_r1_6_eq : ∀ k : Fin 16, kernel7_0Expr 1 6 k = kernel7_0_r1_6 k := by decide +kernel +noncomputable def kernel7_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-277669715094),(-277669715090)⟩,⟨(-1273220290155),(-1273220290151)⟩⟩,⟨⟨(-192374146410),(-192374146405)⟩,⟨(-1143509194467),(-1143509194463)⟩⟩,⟨⟨(-121416362741),(-121416362736)⟩,⟨(-1024286406503),(-1024286406498)⟩⟩,⟨⟨(-62936050003),(-62936049999)⟩,⟨(-915020669352),(-915020669348)⟩⟩,⟨⟨(-15270122085),(-15270122081)⟩,⟨(-815165092037),(-815165092033)⟩⟩,⟨⟨23063999042,23063999046⟩,⟨(-724165330408),(-724165330404)⟩⟩,⟨⟨53384112680,53384112684⟩,⟨(-641466561537),(-641466561533)⟩⟩,⟨⟨76857990603,76857990607⟩,⟨(-566519363355),(-566519363351)⟩⟩,⟨⟨94517168477,94517168481⟩,⟨(-498784606102),(-498784606098)⟩⟩,⟨⟨107269801085,107269801090⟩,⟨(-437737456726),(-437737456722)⟩⟩,⟨⟨115912609211,115912609215⟩,⟨(-382870591553),(-382870591549)⟩⟩,⟨⟨121141949717,121141949721⟩,⟨(-333696706577),(-333696706573)⟩⟩,⟨⟨123564043238,123564043243⟩,⟨(-289750408657),(-289750408653)⟩⟩,⟨⟨123704396136,123704396141⟩,⟨(-250589564928),(-250589564923)⟩⟩,⟨⟨122016455100,122016455104⟩,⟨(-215796181604),(-215796181599)⟩⟩,⟨⟨118889533841,118889533846⟩,⟨(-184976877610),(-184976877606)⟩⟩] +lemma kernel7_0_r1_7_eq : ∀ k : Fin 16, kernel7_0Expr 1 7 k = kernel7_0_r1_7 k := by decide +kernel +noncomputable def kernel7_0_r1_8 : Fin 16 → CBox := ![⟨⟨114656052089,114656052093⟩,⟨(-157763012623),(-157763012618)⟩⟩,⟨⟨109598127177,109598127181⟩,⟨(-133810523713),(-133810523709)⟩⟩,⟨⟨103953558512,103953558516⟩,⟨(-112799519404),(-112799519400)⟩⟩,⟨⟨97921244641,97921244645⟩,⟨(-94433674997),(-94433674993)⟩⟩,⟨⟨91666071863,91666071868⟩,⟨(-78439468269),(-78439468265)⟩⟩,⟨⟨85323312401,85323312406⟩,⟨(-64565290215),(-64565290211)⟩⟩,⟨⟨79002568858,79002568862⟩,⟨(-52580461310),(-52580461306)⟩⟩,⟨⟨72791300367,72791300372⟩,⟨(-42274179991),(-42274179986)⟩⟩,⟨⟨66757964298,66757964303⟩,⟨(-33454426460),(-33454426455)⟩⟩,⟨⟨60954805862,60954805867⟩,⟨(-25946841714),(-25946841710)⟩⟩,⟨⟨55420326189,55420326194⟩,⟨(-19593598647),(-19593598643)⟩⟩,⟨⟨50181457838,50181457842⟩,⟨(-14252279513),(-14252279509)⟩⟩,⟨⟨45255474910,45255474915⟩,⟨(-9794771529),(-9794771525)⟩⟩,⟨⟨40651663205,40651663209⟩,⟨(-6106190249),(-6106190244)⟩⟩,⟨⟨36372774200,36372774205⟩,⟨(-3083838419),(-3083838414)⟩⟩,⟨⟨32416284866,32416284871⟩,⟨(-636206362),(-636206357)⟩⟩] +lemma kernel7_0_r1_8_eq : ∀ k : Fin 16, kernel7_0Expr 1 8 k = kernel7_0_r1_8 k := by decide +kernel +noncomputable def kernel7_0_r1_9 : Fin 16 → CBox := ![⟨⟨28775483749,28775483754⟩,⟨1317981673,1317981677⟩⟩,⟨⟨25440402107,25440402111⟩,⟨2850671916,2850671920⟩⟩,⟨⟨22398607429,22398607434⟩,⟨4025334190,4025334194⟩⟩,⟨⟨19635875117,19635875122⟩,⟨4897762615,4897762620⟩⟩,⟨⟨17136752780,17136752785⟩,⟨5516823579,5516823584⟩⟩,⟨⟨14885030227,14885030231⟩,⟨5925151377,5925151382⟩⟩,⟨⟨12864127064,12864127069⟩,⟨6159792443,6159792448⟩⟩,⟨⟨11057408589,11057408593⟩,⟨6252799574,6252799578⟩⟩,⟨⟨9448439590,9448439594⟩,⟨6231777902,6231777907⟩⟩,⟨⟨8021184696,8021184700⟩,⟨6120384679,6120384683⟩⟩,⟨⟨6760162965,6760162969⟩,⟨5938785057,5938785061⟩⟩,⟨⟨5650563519,5650563523⟩,⟨5704066298,5704066302⟩⟩,⟨⟨4678328305,4678328310⟩,⟨5430612867,5430612872⟩⟩,⟨⟨3830207292,3830207297⟩,⟨5130444914,5130444919⟩⟩,⟨⟨3093790771,3093790775⟩,⟨4813522665,4813522669⟩⟩,⟨⟨2457522874,2457522879⟩,⟨4488019221,4488019225⟩⟩] +lemma kernel7_0_r1_9_eq : ∀ k : Fin 16, kernel7_0Expr 1 9 k = kernel7_0_r1_9 k := by decide +kernel +noncomputable def kernel7_0_r1_10 : Fin 16 → CBox := ![⟨⟨1910699832,1910699836⟩,⟨4160564171,4160564176⟩⟩,⟨⟨1443456038,1443456042⟩,⟨3836460409,3836460414⟩⟩,⟨⟨1046740586,1046740590⟩,⟨3519876399,3519876404⟩⟩,⟨⟨712286500,712286505⟩,⟨3214016034,3214016038⟩⟩,⟨⟨432574604,432574608⟩,⟨2921268181,2921268186⟩⟩,⟨⟨200793593,200793597⟩,⟨2643337803,2643337807⟩⟩,⟨⟨10797715,10797719⟩,⟨2381360465,2381360470⟩⟩,⟨⟨(-142936871),(-142936866)⟩,⟨2136001948,2136001952⟩⟩,⟨⟨(-265356143),(-265356139)⟩,⟨1907544462,1907544467⟩⟩,⟨⟨(-360871920),(-360871916)⟩,⟨1695960982,1695960986⟩⟩,⟨⟨(-433404648),(-433404644)⟩,⟨1500978966,1500978970⟩⟩,⟨⟨(-486424827),(-486424822)⟩,⟨1322134698,1322134703⟩⟩,⟨⟨(-522992734),(-522992729)⟩,⟨1158819361,1158819366⟩⟩,⟨⟨(-545796173),(-545796169)⟩,⟨1010317833,1010317837⟩⟩,⟨⟨(-557186115),(-557186111)⟩,⟨875841108,875841112⟩⟩,⟨⟨(-559210126),(-559210121)⟩,⟨754553195,754553199⟩⟩] +lemma kernel7_0_r1_10_eq : ∀ k : Fin 16, kernel7_0Expr 1 10 k = kernel7_0_r1_10 k := by decide +kernel +noncomputable def kernel7_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-553643501),(-553643496)⟩,⟨645593185,645593190⟩⟩,⟨⟨(-542018128),(-542018123)⟩,⟨548093157,548093162⟩⟩,⟨⟨(-525649117),(-525649113)⟩,⟨461192525,461192529⟩⟩,⟨⟨(-505659231),(-505659227)⟩,⟨384049310,384049315⟩⟩,⟨⟨(-483001206),(-483001202)⟩,⟨315848844,315848849⟩⟩,⟨⟨(-458478070),(-458478066)⟩,⟨255810245,255810249⟩⟩,⟨⟨(-432761547),(-432761543)⟩,⟨203191082,203191087⟩⟩,⟨⟨(-406408662),(-406408658)⟩,⟨157290490,157290495⟩⟩,⟨⟨(-379876672),(-379876668)⟩,⟨117451024,117451029⟩⟩,⟨⟨(-353536454),(-353536449)⟩,⟨83059500,83059505⟩⟩,⟨⟨(-327684425),(-327684420)⟩,⟨53546975,53546980⟩⟩,⟨⟨(-302553158),(-302553153)⟩,⟨28388103,28388107⟩⟩,⟨⟨(-278320777),(-278320772)⟩,⟨7099942,7099946⟩⟩,⟨⟨(-255119254),(-255119249)⟩,⟨(-10759596),(-10759592)⟩⟩,⟨⟨(-233041682),(-233041677)⟩,⟨(-25593608),(-25593603)⟩⟩,⟨⟨(-212148677),(-212148673)⟩,⟨(-37768231),(-37768226)⟩⟩] +lemma kernel7_0_r1_11_eq : ∀ k : Fin 16, kernel7_0Expr 1 11 k = kernel7_0_r1_11 k := by decide +kernel +noncomputable def kernel7_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-192473920),(-192473916)⟩,⟨(-47614832),(-47614828)⟩⟩,⟨⟨(-174029005),(-174029000)⟩,⟨(-55432250),(-55432246)⟩⟩,⟨⟨(-156807604),(-156807600)⟩,⟨(-61489053),(-61489048)⟩⟩,⟨⟨(-140789079),(-140789074)⟩,⟨(-66025784),(-66025779)⟩⟩,⟨⟨(-125941531),(-125941527)⟩,⟨(-69257160),(-69257155)⟩⟩,⟨⟨(-112224449),(-112224445)⟩,⟨(-71374197),(-71374193)⟩⟩,⟨⟨(-99590914),(-99590909)⟩,⟨(-72546251),(-72546246)⟩⟩,⟨⟨(-87989453),(-87989449)⟩,⟨(-72922955),(-72922950)⟩⟩,⟨⟨(-77365618),(-77365613)⟩,⟨(-72636042),(-72636037)⟩⟩,⟨⟨(-67663263),(-67663259)⟩,⟨(-71801071),(-71801067)⟩⟩,⟨⟨(-58825596),(-58825591)⟩,⟨(-70519023),(-70519019)⟩⟩,⟨⟨(-50796036),(-50796032)⟩,⟨(-68877781),(-68877776)⟩⟩,⟨⟨(-43518905),(-43518901)⟩,⟨(-66953512),(-66953508)⟩⟩,⟨⟨(-36939945),(-36939941)⟩,⟨(-64811922),(-64811918)⟩⟩,⟨⟨(-31006749),(-31006745)⟩,⟨(-62509417),(-62509412)⟩⟩,⟨⟨(-25669056),(-25669052)⟩,⟨(-60094145),(-60094140)⟩⟩] +lemma kernel7_0_r1_12_eq : ∀ k : Fin 16, kernel7_0Expr 1 12 k = kernel7_0_r1_12 k := by decide +kernel +noncomputable def kernel7_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-20878956),(-20878952)⟩,⟨(-57606970),(-57606965)⟩⟩,⟨⟨(-16591055),(-16591051)⟩,⟨(-55082332),(-55082328)⟩⟩,⟨⟨(-12762542),(-12762537)⟩,⟨(-52549030),(-52549026)⟩⟩,⟨⟨(-9353220),(-9353216)⟩,⟨(-50030931),(-50030926)⟩⟩,⟨⟨(-6325502),(-6325498)⟩,⟨(-47547593),(-47547588)⟩⟩,⟨⟨(-3644369),(-3644365)⟩,⟨(-45114853),(-45114848)⟩⟩,⟨⟨(-1277301),(-1277297)⟩,⟨(-42745304),(-42745300)⟩⟩,⟨⟨805799,805804⟩,⟨(-40448767),(-40448763)⟩⟩,⟨⟨2632724,2632728⟩,⟨(-38232682),(-38232677)⟩⟩,⟨⟨4229050,4229054⟩,⟨(-36102444),(-36102440)⟩⟩,⟨⟨5618267,5618271⟩,⟨(-34061743),(-34061739)⟩⟩,⟨⟨6821891,6821895⟩,⟨(-32112808),(-32112804)⟩⟩,⟨⟨7859590,7859594⟩,⟨(-30256663),(-30256658)⟩⟩,⟨⟨8749302,8749307⟩,⟨(-28493326),(-28493322)⟩⟩,⟨⟨9507361,9507365⟩,⟨(-26821997),(-26821992)⟩⟩,⟨⟨10148595,10148599⟩,⟨(-25241204),(-25241199)⟩⟩] +lemma kernel7_0_r1_13_eq : ∀ k : Fin 16, kernel7_0Expr 1 13 k = kernel7_0_r1_13 k := by decide +kernel +noncomputable def kernel7_0_r1_14 : Fin 16 → CBox := ![⟨⟨10686456,10686461⟩,⟨(-23748951),(-23748947)⟩⟩,⟨⟨11133121,11133125⟩,⟨(-22342829),(-22342825)⟩⟩,⟨⟨11499587,11499591⟩,⟨(-21020113),(-21020108)⟩⟩,⟨⟨11795779,11795783⟩,⟨(-19777850),(-19777846)⟩⟩,⟨⟨12030627,12030632⟩,⟨(-18612928),(-18612923)⟩⟩,⟨⟨12212164,12212168⟩,⟨(-17522142),(-17522138)⟩⟩,⟨⟨12347601,12347606⟩,⟨(-16502245),(-16502241)⟩⟩,⟨⟨12443395,12443399⟩,⟨(-15549981),(-15549976)⟩⟩,⟨⟨12505327,12505332⟩,⟨(-14662123),(-14662119)⟩⟩,⟨⟨12538563,12538567⟩,⟨(-13835516),(-13835511)⟩⟩,⟨⟨12547702,12547707⟩,⟨(-13067082),(-13067078)⟩⟩,⟨⟨12536849,12536854⟩,⟨(-12353839),(-12353835)⟩⟩,⟨⟨12509645,12509650⟩,⟨(-11692930),(-11692925)⟩⟩,⟨⟨12469327,12469331⟩,⟨(-11081620),(-11081616)⟩⟩,⟨⟨12418758,12418763⟩,⟨(-10517307),(-10517303)⟩⟩,⟨⟨12360478,12360482⟩,⟨(-9997536),(-9997532)⟩⟩] +lemma kernel7_0_r1_14_eq : ∀ k : Fin 16, kernel7_0Expr 1 14 k = kernel7_0_r1_14 k := by decide +kernel +noncomputable def kernel7_0_r1_15 : Fin 16 → CBox := ![⟨⟨12296720,12296725⟩,⟨(-9519987),(-9519983)⟩⟩,⟨⟨12229455,12229459⟩,⟨(-9082494),(-9082490)⟩⟩,⟨⟨12160415,12160420⟩,⟨(-8683034),(-8683029)⟩⟩,⟨⟨12091117,12091122⟩,⟨(-8319733),(-8319728)⟩⟩,⟨⟨12022889,12022894⟩,⟨(-7990860),(-7990855)⟩⟩,⟨⟨11956886,11956890⟩,⟨(-7694833),(-7694829)⟩⟩,⟨⟨11894108,11894113⟩,⟨(-7430211),(-7430206)⟩⟩,⟨⟨11835425,11835429⟩,⟨(-7195689),(-7195685)⟩⟩,⟨⟨11781575,11781579⟩,⟨(-6990111),(-6990106)⟩⟩,⟨⟨11733187,11733192⟩,⟨(-6812444),(-6812439)⟩⟩,⟨⟨11690791,11690796⟩,⟨(-6661798),(-6661794)⟩⟩,⟨⟨11654828,11654833⟩,⟨(-6537413),(-6537408)⟩⟩,⟨⟨11625649,11625654⟩,⟨(-6438657),(-6438653)⟩⟩,⟨⟨11603529,11603534⟩,⟨(-6365029),(-6365025)⟩⟩,⟨⟨11588675,11588679⟩,⟨(-6316152),(-6316147)⟩⟩,⟨⟨11581212,11581217⟩,⟨(-6291776),(-6291772)⟩⟩] +lemma kernel7_0_r1_15_eq : ∀ k : Fin 16, kernel7_0Expr 1 15 k = kernel7_0_r1_15 k := by decide +kernel +noncomputable def kernel7_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel7_0_r1_0,kernel7_0_r1_1,kernel7_0_r1_2,kernel7_0_r1_3,kernel7_0_r1_4,kernel7_0_r1_5,kernel7_0_r1_6,kernel7_0_r1_7,kernel7_0_r1_8,kernel7_0_r1_9,kernel7_0_r1_10,kernel7_0_r1_11,kernel7_0_r1_12,kernel7_0_r1_13,kernel7_0_r1_14,kernel7_0_r1_15] +lemma kernel7_0_r1_eq (i k : Fin 16) : kernel7_0Expr 1 i k = kernel7_0_r1 i k := by + fin_cases i + · exact kernel7_0_r1_0_eq k + · exact kernel7_0_r1_1_eq k + · exact kernel7_0_r1_2_eq k + · exact kernel7_0_r1_3_eq k + · exact kernel7_0_r1_4_eq k + · exact kernel7_0_r1_5_eq k + · exact kernel7_0_r1_6_eq k + · exact kernel7_0_r1_7_eq k + · exact kernel7_0_r1_8_eq k + · exact kernel7_0_r1_9_eq k + · exact kernel7_0_r1_10_eq k + · exact kernel7_0_r1_11_eq k + · exact kernel7_0_r1_12_eq k + · exact kernel7_0_r1_13_eq k + · exact kernel7_0_r1_14_eq k + · exact kernel7_0_r1_15_eq k +noncomputable def kernel7_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-4287985663452466440550),(-4287985663452466432583)⟩,⟨1347209119317416996124,1347209119317417004079⟩⟩,⟨⟨(-4284016499989770232983),(-4284016499989770225019)⟩,⟨1346947028427740716236,1346947028427740724186⟩⟩,⟨⟨(-4276088827195128793773),(-4276088827195128785822)⟩,⟨1346420754057757015815,1346420754057757023752⟩⟩,⟨⟨(-4264223908292812807274),(-4264223908292812799338)⟩,⟨1345626134178670416749,1345626134178670424671⟩⟩,⟨⟨(-4248453525767461335422),(-4248453525767461327509)⟩,⟨1344556983391379951607,1344556983391379959506⟩⟩,⟨⟨(-4228819847216283754874),(-4228819847216283746987)⟩,⟨1343205161438223997596,1343205161438224005469⟩⟩,⟨⟨(-4205375247605156441253),(-4205375247605156433400)⟩,⟨1341560663457928453150,1341560663457928460991⟩⟩,⟨⟨(-4178182088880393395898),(-4178182088880393388081)⟩,⟨1339611731061701026279,1339611731061701034082⟩⟩,⟨⟨(-4147312458115853761209),(-4147312458115853753436)⟩,⟨1337344983097294157952,1337344983097294165712⟩⟩,⟨⟨(-4112847865596273093985),(-4112847865596273086259)⟩,⟨1334745564769320882533,1334745564769320890246⟩⟩,⟨⟨(-4074878904450986283349),(-4074878904450986275675)⟩,⟨1331797313600326634805,1331797313600326642465⟩⟩,⟨⟨(-4033504873656293351340),(-4033504873656293343724)⟩,⟨1328482940550091631933,1328482940550091639536⟩⟩,⟨⟨(-3988833366418384620804),(-3988833366418384613251)⟩,⟨1324784224462156219322,1324784224462156226862⟩⟩,⟨⟨(-3940979826130809254480),(-3940979826130809246993)⟩,⟨1320682217878194737078,1320682217878194744551⟩⟩,⟨⟨(-3890067072269809148016),(-3890067072269809140601)⟩,⟨1316157462153939018775,1316157462153939026176⟩⟩,⟨⟨(-3836224798746372065980),(-3836224798746372058640)⟩,⟨1311190209725940074874,1311190209725940082200⟩⟩] +lemma kernel7_0_r2_0_eq : ∀ k : Fin 16, kernel7_0Expr 2 0 k = kernel7_0_r2_0 k := by decide +kernel +noncomputable def kernel7_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3779589047374570400077),(-3779589047374570392819)⟩,⟨1305760651317355980967,1305760651317355988212⟩⟩,⟨⟨(-3720301659240703126621),(-3720301659240703119447)⟩,⟨1299849145833687861698,1299849145833687868860⟩⟩,⟨⟨(-3658509706866086595914),(-3658509706866086588827)⟩,⟨1293436450686193908171,1293436450686193915246⟩⟩,⟨⟨(-3594364910147271608683),(-3594364910147271601689)⟩,⟨1286503950291549549311,1286503950291549556293⟩⟩,⟨⟨(-3528023039130324263657),(-3528023039130324256758)⟩,⟨1279033880530864783646,1279033880530864790532⟩⟩,⟨⟨(-3459643306730026932815),(-3459643306730026926016)⟩,⟨1271009547008816452594,1271009547008816459380⟩⟩,⟨⟨(-3389387754539978669718),(-3389387754539978663021)⟩,⟨1262415535033537211744,1262415535033537218429⟩⟩,⟨⟨(-3317420634895269168791),(-3317420634895269162198)⟩,⟨1253237909338904438293,1253237909338904444874⟩⟩,⟨⟨(-3243907792345464750153),(-3243907792345464743670)⟩,⟨1243464401691634639017,1243464401691634645488⟩⟩,⟨⟨(-3169016047672012857355),(-3169016047672012850983)⟩,⟨1233084584664537449664,1233084584664537456025⟩⟩,⟨⟨(-3092912587540919324037),(-3092912587540919317778)⟩,⟨1222090030012647075062,1222090030012647081309⟩⟩,⟨⟨(-3015764362818902679287),(-3015764362818902673144)⟩,⟨1210474450258784744763,1210474450258784750894⟩⟩,⟨⟨(-2937737498499553982580),(-2937737498499553976554)⟩,⟨1198233822277323948134,1198233822277323954149⟩⟩,⟨⟨(-2858996718085852159737),(-2858996718085852153831)⟩,⟨1185366491857322843162,1185366491857322849057⟩⟩,⟨⟨(-2779704785157377716834),(-2779704785157377711048)⟩,⟨1171873258426457759380,1171873258426457765155⟩⟩,⟨⟨(-2700021964715555639063),(-2700021964715555633400)⟩,⟨1157757439322980930482,1157757439322980936133⟩⟩] +lemma kernel7_0_r2_1_eq : ∀ k : Fin 16, kernel7_0Expr 2 1 k = kernel7_0_r2_1 k := by decide +kernel +noncomputable def kernel7_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-2620105506749210814399),(-2620105506749210808861)⟩,⟨1143024913211847942694,1143024913211847948222⟩⟩,⟨⟨(-2540109154296746726186),(-2540109154296746720773)⟩,⟨1127684142450830313063,1127684142450830318466⟩⟩,⟨⟨(-2460182678101604261383),(-2460182678101604256096)⟩,⟨1111746174420491507394,1111746174420491512672⟩⟩,⟨⟨(-2380471439765690700078),(-2380471439765690694918)⟩,⟨1095224622036066057739,1095224622036066062889⟩⟩,⟨⟨(-2301115985102671548154),(-2301115985102671543122)⟩,⟨1078135623857334774602,1078135623857334779625⟩⟩,⟨⟨(-2222251669180973504691),(-2222251669180973499786)⟩,⟨1060497784402442312248,1060497784402442317144⟩⟩,⟨⟨(-2144008314326726540274),(-2144008314326726535496)⟩,⟨1042332095451303327290,1042332095451303332059⟩⟩,⟨⟨(-2066509902131419726917),(-2066509902131419722269)⟩,⟨1023661839291997994797,1023661839291997999436⟩⟩,⟨⟨(-1989874300279557220829),(-1989874300279557216309)⟩,⟨1004512475017755216749,1004512475017755221260⟩⟩,⟨⟨(-1914213024779913204569),(-1914213024779913200176)⟩,⟨984911509121348528653,984911509121348533037⟩⟩,⟨⟨(-1839631037951952058246),(-1839631037951952053979)⟩,⟨964888351756782973371,964888351756782977630⟩⟩,⟨⟨(-1766226582288456697027),(-1766226582288456692886)⟩,⟨944474160144050755090,944474160144050759224⟩⟩,⟨⟨(-1694091050088228342559),(-1694091050088228338545)⟩,⟨923701670680728718026,923701670680728722033⟩⟩,⟨⟨(-1623308888530680322103),(-1623308888530680318212)⟩,⟨902605021393764977647,902605021393764981530⟩⟩,⟨⟨(-1553957539648983851165),(-1553957539648983847397)⟩,⟨881219566415673634636,881219566415673638398⟩⟩,⟨⟨(-1486107414451795286681),(-1486107414451795283036)⟩,⟨859581684201476306112,859581684201476309750⟩⟩] +lemma kernel7_0_r2_2_eq : ∀ k : Fin 16, kernel7_0Expr 2 2 k = kernel7_0_r2_2 k := by decide +kernel +noncomputable def kernel7_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-1419821900247067482987),(-1419821900247067479461)⟩,⟨837728581216275280825,837728581216275284344⟩⟩,⟨⟨(-1355157400036476716823),(-1355157400036476713416)⟩,⟨815698092818712269434,815698092818712272834⟩⟩,⟨⟨(-1292163402676908547077),(-1292163402676908543789)⟩,⟨793528483043363328413,793528483043363331695⟩⟩,⟨⟨(-1230882582347427874273),(-1230882582347427871099)⟩,⟨771258244946142657259,771258244946142660428⟩⟩,⟨⟨(-1171350925717244904546),(-1171350925717244901487)⟩,⟨748925903122011275210,748925903122011278264⟩⟩,⟨⟨(-1113597885083251865796),(-1113597885083251862849)⟩,⟨726569819934846217536,726569819934846220478⟩⟩,⟨⟨(-1057646555635447086948),(-1057646555635447084109)⟩,⟨704228006916496639408,704228006916496642241⟩⟩,⟨⟨(-1003513874915509460979),(-1003513874915509458249)⟩,⟨681937942697228333264,681937942697228335989⟩⟩,⟨⟨(-951210842458284157397),(-951210842458284154773)⟩,⟨659736398724427205929,659736398724427208549⟩⟩,⟨⟨(-900742757548156265883),(-900742757548156263360)⟩,⟨637659273912158263716,637659273912158266234⟩⟩,⟨⟨(-852109472982210435179),(-852109472982210432758)⟩,⟨615741439242573061474,615741439242573063890⟩⟩,⟨⟨(-805305662709513771561),(-805305662709513769238)⟩,⟨594016593212866233076,594016593212866235394⟩⟩,⟨⟨(-760321101210458989352),(-760321101210458987125)⟩,⟨572517128890146315701,572517128890146317923⟩⟩,⟨⟨(-717140952491346120994),(-717140952491346118861)⟩,⟨551274013202836300541,551274013202836302670⟩⟩,⟨⟨(-675746066596593235155),(-675746066596593233114)⟩,⟨530316678962646135247,530316678962646137284⟩⟩,⟨⟨(-636113281583338591202),(-636113281583338589249)⟩,⟨509672929977296549364,509672929977296551314⟩⟩] +lemma kernel7_0_r2_3_eq : ∀ k : Fin 16, kernel7_0Expr 2 3 k = kernel7_0_r2_3 k := by decide +kernel +noncomputable def kernel7_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-598215728959790413871),(-598215728959790412002)⟩,⟨489368859482479852329,489368859482479854194⟩⟩,⟨⟨(-562023140658445346940),(-562023140658445345156)⟩,⟨469428781993386502657,469428781993386504438⟩⟩,⟨⟨(-527502155697084958771),(-527502155697084957069)⟩,⟨449875178552768897696,449875178552768899395⟩⟩,⟨⟨(-494616624773043123204),(-494616624773043121578)⟩,⟨430728655235101550225,430728655235101551848⟩⟩,⟨⟨(-463327911138323730435),(-463327911138323728886)⟩,⟨412007914655948345497,412007914655948347043⟩⟩,⟨⟨(-433595186213399655054),(-433595186213399653578)⟩,⟨393729740133047339178,393729740133047340651⟩⟩,⟨⟨(-405375718514572808313),(-405375718514572806911)⟩,⟨375908992051616459920,375908992051616461321⟩⟩,⟨⟨(-378625154592242028399),(-378625154592242027062)⟩,⟨358558615901571919313,358558615901571920648⟩⟩,⟨⟨(-353297790803935752188),(-353297790803935750917)⟩,⟨341689661379194240131,341689661379194241399⟩⟩,⟨⟨(-329346834875165668135),(-329346834875165666929)⟩,⟨325311311880591789799,325311311880591791004⟩⟩,⟨⟨(-306724656331727265474),(-306724656331727264328)⟩,⟨309430923659277124968,309430923659277126112⟩⟩,⟨⟨(-285383025017744286687),(-285383025017744285600)⟩,⟨294054073875332402595,294054073875332403680⟩⟩,⟨⟨(-265273337043319672198),(-265273337043319671168)⟩,⟨279184616728914983555,279184616728914984584⟩⟩,⟨⟨(-246346827632982256718),(-246346827632982255742)⟩,⟨264824746846043087970,264824746846043088946⟩⟩,⟨⟨(-228554770470156103188),(-228554770470156102264)⟩,⟨250975069069394949037,250975069069394949960⟩⟩,⟨⟨(-211848663252669290615),(-211848663252669289740)⟩,⟨237634673800845929935,237634673800845930809⟩⟩] +lemma kernel7_0_r2_4_eq : ∀ k : Fin 16, kernel7_0Expr 2 4 k = kernel7_0_r2_4 k := by decide +kernel +noncomputable def kernel7_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-196180399289000618889),(-196180399289000618062)⟩,⟨224801217045162016535,224801217045162017362⟩⟩,⟨⟨(-181502425073778476537),(-181502425073778475755)⟩,⟨212471004315095328657,212471004315095329437⟩⟩,⟨⟨(-167767883883344767530),(-167767883883344766791)⟩,⟨200639077576455294955,200639077576455295693⟩⟩,⟨⟨(-154930745527435059782),(-154930745527435059085)⟩,⟨189299304436874975262,189299304436874975958⟩⟩,⟨⟨(-142945922480768932286),(-142945922480768931629)⟩,⟨178444468813234704016,178444468813234704672⟩⟩,⟨⟨(-131769372698263679889),(-131769372698263679270)⟩,⟨168066362349297861475,168066362349297862093⟩⟩,⟨⟨(-121358189489456143829),(-121358189489456143246)⟩,⟨158155875896295027502,158155875896295028084⟩⟩,⟨⟨(-111670678891417881043),(-111670678891417880494)⟩,⟨148703090414198808100,148703090414198808648⟩⟩,⟨⟨(-102666425034949931043),(-102666425034949930527)⟩,⟨139697366699505322415,139697366699505322930⟩⟩,⟨⟨(-94306344046206247344),(-94306344046206246859)⟩,⟨131127433395739643653,131127433395739644138⟩⟩,⟨⟨(-86552727065263217910),(-86552727065263217452)⟩,⟨122981472794916860739,122981472794916861197⟩⟩,⟨⟨(-79369272994745584323),(-79369272994745583896)⟩,⟨115247203991136485252,115247203991136485679⟩⟩,⟨⟨(-72721111615722715535),(-72721111615722715132)⟩,⟨107911963000724042104,107911963000724042506⟩⟩,⟨⟨(-66574817725048795433),(-66574817725048795056)⟩,⟨100962779516263503754,100962779516263504131⟩⟩,⟨⟨(-60898416958531711202),(-60898416958531710848)⟩,⟨94386450013941129724,94386450013941130077⟩⟩,⟨⟨(-55661383968215860877),(-55661383968215860545)⟩,⟨88169606984351726830,88169606984351727162⟩⟩] +lemma kernel7_0_r2_5_eq : ∀ k : Fin 16, kernel7_0Expr 2 5 k = kernel7_0_r2_5 k := by decide +kernel +noncomputable def kernel7_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-50834633620124742055),(-50834633620124741745)⟩,⟨82298784105864254495,82298784105864254805⟩⟩,⟨⟨(-46390505871526181325),(-46390505871526181035)⟩,⟨76760477226423742816,76760477226423743107⟩⟩,⟨⟨(-42302744974669701284),(-42302744974669701014)⟩,⟨71541201063956530047,71541201063956530317⟩⟩,⟨⟨(-38546473637524635546),(-38546473637524635292)⟩,⟨66627541577078445542,66627541577078445796⟩⟩,⟨⟨(-35098162751844467537),(-35098162751844467300)⟩,⟨62006203996368828898,62006203996368829134⟩⟩,⟨⟨(-31935597275418639072),(-31935597275418638850)⟩,⟨57664056541908785741,57664056541908785962⟩⟩,⟨⟨(-29037838829158819997),(-29037838829158819790)⟩,⟨53588169884982417351,53588169884982417558⟩⟩,⟨⟨(-26385185541198020314),(-26385185541198020121)⟩,⟨49765852440745419870,49765852440745420063⟩⟩,⟨⟨(-23959129639933579705),(-23959129639933579526)⟩,⟨46184681604261346254,46184681604261346432⟩⟩,⟨⟨(-21742313266370581817),(-21742313266370581650)⟩,⟨42832531064617480785,42832531064617480952⟩⟩,⟨⟨(-19718482943644892373),(-19718482943644892216)⟩,⟨39697594350921758500,39697594350921758658⟩⟩,⟨⟨(-17872443108619151350),(-17872443108619151203)⟩,⟨36768404779943873585,36768404779943873732⟩⟩,⟨⟨(-16190009077313082211),(-16190009077313082073)⟩,⟨34033851988120122111,34033851988120122248⟩⟩,⟨⟨(-14657959782980557489),(-14657959782980557362)⟩,⟨31483195240738854708,31483195240738854835⟩⟩,⟨⟨(-13263990593175059182),(-13263990593175059065)⟩,⟨29106073718527485675,29106073718527485792⟩⟩,⟨⟨(-11996666480413263600),(-11996666480413263490)⟩,⟨26892513986754123728,26892513986754123838⟩⟩] +lemma kernel7_0_r2_6_eq : ∀ k : Fin 16, kernel7_0Expr 2 6 k = kernel7_0_r2_6 k := by decide +kernel +noncomputable def kernel7_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-10845375790280162892),(-10845375790280162791)⟩,⟨24832934854529961717,24832934854529961818⟩⟩,⟨⟨(-9800284821211715181),(-9800284821211715085)⟩,⟨22918149832453421403,22918149832453421499⟩⟩,⟨⟨(-8852293401903462396),(-8852293401903462308)⟩,⟨21139367395279042402,21139367395279042490⟩⟩,⟨⟨(-7992991625455891799),(-7992991625455891716)⟩,⟨19488189253129967417,19488189253129967500⟩⟩,⟨⟨(-7214617874080276798),(-7214617874080276721)⟩,⟨17956606830107912122,17956606830107912198⟩⟩,⟨⟨(-6510018244525640690),(-6510018244525640620)⟩,⟨16536996143190084213,16536996143190084283⟩⟩,⟨⟨(-5872607462396309901),(-5872607462396309835)⟩,⟨15222111267233882161,15222111267233882227⟩⟩,⟨⟨(-5296331353235039730),(-5296331353235039670)⟩,⟨14005076563924633735,14005076563924633795⟩⟩,⟨⟨(-4775630919652740493),(-4775630919652740437)⟩,⟨12879377843776882962,12879377843776883018⟩⟩,⟨⟨(-4305408056877575858),(-4305408056877575806)⟩,⟨11838852621002800083,11838852621002800135⟩⟩,⟨⟨(-3880992923842428733),(-3880992923842428684)⟩,⟨10877679611347466312,10877679611347466361⟩⟩,⟨⟨(-3498112973285061140),(-3498112973285061093)⟩,⟨9990367613002987752,9990367613002987798⟩⟩,⟨⟨(-3152863632242379245),(-3152863632242379203)⟩,⟨9171743900581730165,9171743900581730207⟩⟩,⟨⟨(-2841680613711797676),(-2841680613711797638)⟩,⟨8416942251970548754,8416942251970548792⟩⟩,⟨⟨(-2561313831053589896),(-2561313831053589861)⟩,⟨7721390717806835764,7721390717806835800⟩⟩,⟨⟨(-2308802878837035328),(-2308802878837035293)⟩,⟨7080799233404846806,7080799233404846841⟩⟩] +lemma kernel7_0_r2_7_eq : ∀ k : Fin 16, kernel7_0Expr 2 7 k = kernel7_0_r2_7 k := by decide +kernel +noncomputable def kernel7_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-2081454037204461975),(-2081454037204461942)⟩,⟨6491147163295967435,6491147163295967467⟩⟩,⟨⟨(-1876818751352436866),(-1876818751352436837)⟩,⟨5948670859196247391,5948670859196247420⟩⟩,⟨⟨(-1692673533318447437),(-1692673533318447409)⟩,⟨5449851303234182696,5449851303234182724⟩⟩,⟨⟨(-1527001229824336395),(-1527001229824336368)⟩,⟨4991401899706180716,4991401899706180743⟩⟩,⟨⟨(-1377973597375307711),(-1377973597375307687)⟩,⟨4570256470511250883,4570256470511250907⟩⟩,⟨⟨(-1243935124058179122),(-1243935124058179100)⟩,⟨4183557501775895684,4183557501775895706⟩⟩,⟨⟨(-1123388036440045744),(-1123388036440045723)⟩,⟨3828644682032241438,3828644682032241459⟩⟩,⟨⟨(-1014978429557292363),(-1014978429557292343)⟩,⟨3503043765666918508,3503043765666918528⟩⟩,⟨⟨(-917483458127457445),(-917483458127457425)⟩,⟨3204455789218137898,3204455789218137917⟩⟩,⟨⟨(-829799527739587920),(-829799527739587903)⟩,⟨2930746662460978001,2930746662460978017⟩⟩,⟨⟨(-750931425813778649),(-750931425813778633)⟩,⟨2679937151078141775,2679937151078141790⟩⟩,⟨⟨(-679982333503684899),(-679982333503684884)⟩,⟨2450193263053062723,2450193263053062738⟩⟩,⟨⟨(-616144661387934820),(-616144661387934805)⟩,⟨2239817046728274931,2239817046728274946⟩⟩,⟨⟨(-558691653703473364),(-558691653703473349)⟩,⟨2047237804725489904,2047237804725489918⟩⟩,⟨⟨(-506969707966741991),(-506969707966741978)⟩,⟨1871003724603556399,1871003724603556412⟩⟩,⟨⟨(-460391359062828826),(-460391359062828815)⟩,⟨1709773924213346589,1709773924213346600⟩⟩] +lemma kernel7_0_r2_8_eq : ∀ k : Fin 16, kernel7_0Expr 2 8 k = kernel7_0_r2_8 k := by decide +kernel +noncomputable def kernel7_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-418428879218543600),(-418428879218543588)⟩,⟨1562310907170266993,1562310907170267005⟩⟩,⟨⟨(-380608447677471337),(-380608447677471327)⟩,⟨1427473421680378979,1427473421680378989⟩⟩,⟨⟨(-346504846332372505),(-346504846332372495)⟩,⟨1304209714099472499,1304209714099472509⟩⟩,⟨⟨(-315736640015762379),(-315736640015762369)⟩,⟨1191551167050265176,1191551167050265185⟩⟩,⟨⟨(-287961802579802656),(-287961802579802648)⟩,⟨1088606310645858572,1088606310645858581⟩⟩,⟨⟨(-262873752291935248),(-262873752291935242)⟩,⟨994555194342862883,994555194342862890⟩⟩,⟨⟨(-240197762416347679),(-240197762416347671)⟩,⟨908644106151133304,908644106151133312⟩⟩,⟨⟨(-219687715129676609),(-219687715129676602)⟩,⟨830180625335701124,830180625335701130⟩⟩,⟨⟨(-201123169121283270),(-201123169121283260)⟩,⟨758528994338147407,758528994338147417⟩⟩,⟨⟨(-184306713345316722),(-184306713345316715)⟩,⟨693105795398442885,693105795398442892⟩⟩,⟨⟨(-169061581417098928),(-169061581417098921)⟩,⟨633375917254493887,633375917254493894⟩⟩,⟨⟨(-155229503075491775),(-155229503075491768)⟩,⟨578848797316913962,578848797316913969⟩⟩,⟨⟨(-142668770962872981),(-142668770962872974)⟩,⟨529074924843824356,529074924843824363⟩⟩,⟨⟨(-131252502703630157),(-131252502703630150)⟩,⟨483642590859037218,483642590859037225⟩⟩,⟨⟨(-120867079890395954),(-120867079890395947)⟩,⟨442174870852365443,442174870852365450⟩⟩,⟨⟨(-111410747115362185),(-111410747115362178)⟩,⟨404326826659887086,404326826659887093⟩⟩] +lemma kernel7_0_r2_9_eq : ∀ k : Fin 16, kernel7_0Expr 2 9 k = kernel7_0_r2_9 k := by decide +kernel +noncomputable def kernel7_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-102792355613580499),(-102792355613580493)⟩,⟨369782914332866683,369782914332866688⟩⟩,⟨⟨(-94930237418563262),(-94930237418563256)⟩,⟨338254585255990498,338254585255990505⟩⟩,⟨⟨(-87751197170711431),(-87751197170711424)⟩,⟨309478068259033321,309478068259033327⟩⟩,⟨⟨(-81189609869549849),(-81189609869549843)⟩,⟨283212320972541074,283212320972541080⟩⟩,⟨⟨(-75186613925231368),(-75186613925231362)⟩,⟨259237139200093734,259237139200093740⟩⟩,⟨⟨(-69689389847320574),(-69689389847320569)⟩,⟨237351413610654400,237351413610654405⟩⟩,⟨⟨(-64650515813697249),(-64650515813697245)⟩,⟨217371523588730024,217371523588730028⟩⟩,⟨⟨(-60027392193836655),(-60027392193836649)⟩,⟨199129858612685648,199129858612685655⟩⟩,⟨⟨(-55781727863070004),(-55781727863069997)⟩,⟨182473458058417544,182473458058417551⟩⟩,⟨⟨(-51879081842026463),(-51879081842026457)⟩,⟨167262760843218059,167262760843218065⟩⟩,⟨⟨(-48288454432567105),(-48288454432567101)⟩,⟨153370456830174744,153370456830174748⟩⟩,⟨⟨(-44981922602301565),(-44981922602301560)⟩,⟨140680432404497123,140680432404497128⟩⟩,⟨⟨(-41934314898261964),(-41934314898261957)⟩,⟨129086803107897796,129086803107897803⟩⟩,⟨⟨(-39122921650377603),(-39122921650377599)⟩,⟨118493026674139349,118493026674139353⟩⟩,⟨⟨(-36527236660762082),(-36527236660762078)⟩,⟨108811090247040631,108811090247040635⟩⟩,⟨⟨(-34128726969026452),(-34128726969026448)⟩,⟨99960765980890665,99960765980890669⟩⟩] +lemma kernel7_0_r2_10_eq : ∀ k : Fin 16, kernel7_0Expr 2 10 k = kernel7_0_r2_10 k := by decide +kernel +noncomputable def kernel7_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-31910627640214750),(-31910627640214746)⟩,⟨91868929621906674,91868929621906678⟩⟩,⟨⟨(-29857758843676490),(-29857758843676486)⟩,⟨84468937047901597,84468937047901601⟩⟩,⟨⟨(-27956362781206446),(-27956362781206441)⟩,⟨77700054101712282,77700054101712288⟩⟩,⟨⟨(-26193958283864443),(-26193958283864439)⟩,⟨71506935392375405,71506935392375409⟩⟩,⟨⟨(-24559211131617568),(-24559211131617564)⟩,⟨65839148056863897,65839148056863901⟩⟩,⟨⟨(-23041818360720560),(-23041818360720556)⟩,⟨60650736774872887,60650736774872891⟩⟩,⟨⟨(-21632405012785569),(-21632405012785565)⟩,⟨55899826610227832,55899826610227836⟩⟩,⟨⟨(-20322431948837652),(-20322431948837646)⟩,⟨51548260515612472,51548260515612477⟩⟩,⟨⟨(-19104113503192293),(-19104113503192289)⟩,⟨47561268583171139,47561268583171143⟩⟩,⟨⟨(-17970343887456171),(-17970343887456167)⟩,⟨43907166352862422,43907166352862426⟩⟩,⟨⟨(-16914631375927186),(-16914631375927182)⟩,⟨40557079703989984,40557079703989988⟩⟩,⟨⟨(-15931039411602332),(-15931039411602328)⟩,⟨37484694053889208,37484694053889212⟩⟩,⟨⟨(-15014133868212124),(-15014133868212120)⟩,⟨34666025772088967,34666025772088971⟩⟩,⟨⟨(-14158935789388756),(-14158935789388752)⟩,⟨32079213889177549,32079213889177553⟩⟩,⟨⟨(-13360879002332083),(-13360879002332079)⟩,⟨29704330337852961,29704330337852965⟩⟩,⟨⟨(-12615772071150341),(-12615772071150337)⟩,⟨27523207109987475,27523207109987479⟩⟩] +lemma kernel7_0_r2_11_eq : ∀ k : Fin 16, kernel7_0Expr 2 11 k = kernel7_0_r2_11 k := by decide +kernel +noncomputable def kernel7_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-11919764115314667),(-11919764115314663)⟩,⟨25519278848721835,25519278848721839⟩⟩,⟨⟨(-11269314072184399),(-11269314072184395)⟩,⟨23677439519339762,23677439519339766⟩⟩,⟨⟨(-10661163030060535),(-10661163030060529)⟩,⟨21983911917646230,21983911917646236⟩⟩,⟨⟨(-10092309300361857),(-10092309300361853)⟩,⟨20426128880442494,20426128880442498⟩⟩,⟨⟨(-9559985934879724),(-9559985934879720)⟩,⟨18992625160086633,18992625160086637⟩⟩,⟨⟨(-9061640427180319),(-9061640427180315)⟩,⟨17672939014649436,17672939014649440⟩⟩,⟨⟨(-8594916366560147),(-8594916366560143)⟩,⟨16457522647389102,16457522647389106⟩⟩,⟨⟨(-8157636838943710),(-8157636838943706)⟩,⟨15337660704711429,15337660704711433⟩⟩,⟨⟨(-7747789392119635),(-7747789392119631)⟩,⟨14305396110960088,14305396110960092⟩⟩,⟨⟨(-7363512403079859),(-7363512403079855)⟩,⟨13353462581769789,13353462581769794⟩⟩,⟨⟨(-7003082703256216),(-7003082703256212)⟩,⟨12475223215758948,12475223215758952⟩⟩,⟨⟨(-6664904333407350),(-6664904333407346)⟩,⟨11664614617454956,11664614617454960⟩⟩,⟨⟨(-6347498314034283),(-6347498314034279)⟩,⟨10916096052923437,10916096052923442⟩⟩,⟨⟨(-6049493329706455),(-6049493329706451)⟩,⟨10224603183975510,10224603183975514⟩⟩,⟨⟨(-5769617236749448),(-5769617236749444)⟩,⟨9585505967391744,9585505967391749⟩⟩,⟨⟨(-5506689313547155),(-5506689313547151)⟩,⟨8994570342640946,8994570342640950⟩⟩] +lemma kernel7_0_r2_12_eq : ∀ k : Fin 16, kernel7_0Expr 2 12 k = kernel7_0_r2_12 k := by decide +kernel +noncomputable def kernel7_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-5259613181392513),(-5259613181392509)⟩,⟨8447923365376994,8447923365376999⟩⟩,⟨⟨(-5027370331512632),(-5027370331512628)⟩,⟨7942021474836391,7942021474836396⟩⟩,⟨⟨(-4809014200711731),(-4809014200711727)⟩,⟨7473621611381323,7473621611381327⟩⟩,⟨⟨(-4603664744121041),(-4603664744121035)⟩,⟨7039754926067851,7039754926067856⟩⟩,⟨⟨(-4410503458908917),(-4410503458908913)⟩,⟨6637702847477452,6637702847477457⟩⟩,⟨⟨(-4228768817566698),(-4228768817566692)⟩,⟨6264975292327958,6264975292327963⟩⟩,⟨⟨(-4057752073616634),(-4057752073616630)⟩,⟨5919290825756035,5919290825756039⟩⟩,⟨⟨(-3896793406349744),(-3896793406349740)⟩,⟨5598558594802852,5598558594802856⟩⟩,⟨⟨(-3745278374548289),(-3745278374548285)⟩,⟨5300861874688802,5300861874688806⟩⟩,⟨⟨(-3602634652128343),(-3602634652128339)⟩,⟨5024443082071167,5024443082071171⟩⟩,⟨⟨(-3468329021294828),(-3468329021294824)⟩,⟨4767690122767706,4767690122767710⟩⟩,⟨⟨(-3341864601172269),(-3341864601172265)⟩,⟨4529123953516257,4529123953516261⟩⟩,⟨⟨(-3222778291992230),(-3222778291992226)⟩,⟨4307387248332091,4307387248332095⟩⟩,⟨⟨(-3110638416812165),(-3110638416812161)⟩,⟨4101234070019055,4101234070019059⟩⟩,⟨⟨(-3005042544435829),(-3005042544435825)⟩,⟨3909520456476567,3909520456476571⟩⟩,⟨⟨(-2905615478725146),(-2905615478725142)⟩,⟨3731195839704116,3731195839704120⟩⟩] +lemma kernel7_0_r2_13_eq : ∀ k : Fin 16, kernel7_0Expr 2 13 k = kernel7_0_r2_13 k := by decide +kernel +noncomputable def kernel7_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-2812007400857416),(-2812007400857412)⟩,⟨3565295222912505,3565295222912510⟩⟩,⟨⟨(-2723892152307459),(-2723892152307454)⟩,⟨3410932047974851,3410932047974855⟩⟩,⟨⟨(-2640965647437345),(-2640965647437341)⟩,⟨3267291691652229,3267291691652233⟩⟩,⟨⟨(-2562944405570335),(-2562944405570331)⟩,⟨3133625534665730,3133625534665735⟩⟩,⟨⟨(-2489564193322572),(-2489564193322568)⟩,⟨3009245552809750,3009245552809754⟩⟩,⟨⟨(-2420578768776724),(-2420578768776720)⟩,⟨2893519383958109,2893519383958113⟩⟩,⟨⟨(-2355758719815315),(-2355758719815310)⟩,⟨2785865829047537,2785865829047541⟩⟩,⟨⟨(-2294890389596516),(-2294890389596512)⟩,⟨2685750748971325,2685750748971330⟩⟩,⟨⟨(-2237774882758871),(-2237774882758867)⟩,⟨2592683322815178,2592683322815182⟩⟩,⟨⟨(-2184227146490250),(-2184227146490246)⟩,⟨2506212636049573,2506212636049577⟩⟩,⟨⟨(-2134075121096363),(-2134075121096359)⟩,⟨2425924570187995,2425924570187999⟩⟩,⟨⟨(-2087158955160105),(-2087158955160101)⟩,⟨2351438968054850,2351438968054854⟩⟩,⟨⟨(-2043330280799829),(-2043330280799824)⟩,⟨2282407051205117,2282407051205122⟩⟩,⟨⟨(-2002451544916125),(-2002451544916121)⟩,⟨2218509068222172,2218509068222177⟩⟩,⟨⟨(-1964395392666524),(-1964395392666520)⟩,⟨2159452154610790,2159452154610794⟩⟩,⟨⟨(-1929044099729116),(-1929044099729112)⟩,⟨2104968386817670,2104968386817674⟩⟩] +lemma kernel7_0_r2_14_eq : ∀ k : Fin 16, kernel7_0Expr 2 14 k = kernel7_0_r2_14 k := by decide +kernel +noncomputable def kernel7_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-1896289050211958),(-1896289050211954)⟩,⟨2054813014568561,2054813014568565⟩⟩,⟨⟨(-1866030257338337),(-1866030257338333)⟩,⟨2008762857224606,2008762857224610⟩⟩,⟨⟨(-1838175924290377),(-1838175924290373)⟩,⟨1966614851244838,1966614851244842⟩⟩,⟨⟨(-1812642042827581),(-1812642042827577)⟩,⟨1928184737109431,1928184737109435⟩⟩,⟨⟨(-1789352027514298),(-1789352027514294)⟩,⟨1893305875221215,1893305875221219⟩⟩,⟨⟨(-1768236383592783),(-1768236383592779)⟩,⟨1861828181371581,1861828181371585⟩⟩,⟨⟨(-1749232406727742),(-1749232406727738)⟩,⟨1833617173341076,1833617173341080⟩⟩,⟨⟨(-1732283913025761),(-1732283913025757)⟩,⟨1808553121113719,1808553121113723⟩⟩,⟨⟨(-1717340997899835),(-1717340997899831)⟩,⟨1786530294025595,1786530294025599⟩⟩,⟨⟨(-1704359822506742),(-1704359822506738)⟩,⟨1767456298950129,1767456298950133⟩⟩,⟨⟨(-1693302426634234),(-1693302426634230)⟩,⟨1751251504351979,1751251504351983⟩⟩,⟨⟨(-1684136567057050),(-1684136567057046)⟩,⟨1737848545724890,1737848545724894⟩⟩,⟨⟨(-1676835580516464),(-1676835580516460)⟩,⟨1727191908572529,1727191908572534⟩⟩,⟨⟨(-1671378270608491),(-1671378270608487)⟩,⟨1719237585701028,1719237585701033⟩⟩,⟨⟨(-1667748817991736),(-1667748817991732)⟩,⟨1713952806172888,1713952806172892⟩⟩,⟨⟨(-1665936713447996),(-1665936713447991)⟩,⟨1711315833829639,1711315833829644⟩⟩] +lemma kernel7_0_r2_15_eq : ∀ k : Fin 16, kernel7_0Expr 2 15 k = kernel7_0_r2_15 k := by decide +kernel +noncomputable def kernel7_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel7_0_r2_0,kernel7_0_r2_1,kernel7_0_r2_2,kernel7_0_r2_3,kernel7_0_r2_4,kernel7_0_r2_5,kernel7_0_r2_6,kernel7_0_r2_7,kernel7_0_r2_8,kernel7_0_r2_9,kernel7_0_r2_10,kernel7_0_r2_11,kernel7_0_r2_12,kernel7_0_r2_13,kernel7_0_r2_14,kernel7_0_r2_15] +lemma kernel7_0_r2_eq (i k : Fin 16) : kernel7_0Expr 2 i k = kernel7_0_r2 i k := by + fin_cases i + · exact kernel7_0_r2_0_eq k + · exact kernel7_0_r2_1_eq k + · exact kernel7_0_r2_2_eq k + · exact kernel7_0_r2_3_eq k + · exact kernel7_0_r2_4_eq k + · exact kernel7_0_r2_5_eq k + · exact kernel7_0_r2_6_eq k + · exact kernel7_0_r2_7_eq k + · exact kernel7_0_r2_8_eq k + · exact kernel7_0_r2_9_eq k + · exact kernel7_0_r2_10_eq k + · exact kernel7_0_r2_11_eq k + · exact kernel7_0_r2_12_eq k + · exact kernel7_0_r2_13_eq k + · exact kernel7_0_r2_14_eq k + · exact kernel7_0_r2_15_eq k +noncomputable def kernel7_0_r3_0 : Fin 16 → CBox := ![⟨⟨36519586275180393880995074,36519586275180393905746161⟩,⟨3898276721004389822167065,3898276721004389846830798⟩⟩,⟨⟨36501626693304051467873510,36501626693304051492610900⟩,⟨3885477210561458453665569,3885477210561458478315478⟩⟩,⟨⟨36465724967692173161368631,36465724967692173186078600⟩,⟨3859915927934757626696149,3859915927934757651318382⟩⟩,⟨⟨36411915987624745944050031,36411915987624745968718897⟩,⟨3821668214362686876034776,3821668214362686900615525⟩⟩,⟨⟨36340252119134441357983530,36340252119134441382597674⟩,⟨3770846744021244041375731,3770846744021244065901253⟩⟩,⟨⟨36250803242472534112730413,36250803242472534137276296⟩,⟨3707601120255587048909873,3707601120255587073366506⟩⟩,⟨⟨36143656800292559948092837,36143656800292559972557023⟩,⟨3632117339633408965767108,3632117339633408990141296⟩⟩,⟨⟨36018917855056267371826519,36018917855056267396195695⟩,⟨3544617125877903181661163,3544617125877903205939477⟩⟩,⟨⟨35876709153820420493796586,35876709153820420518057576⟩,⟨3445357136241190912534497,3445357136241190936703648⟩⟩,⟨⟨35717171198235244409236279,35717171198235244433376079⟩,⟨3334628043374548914886026,3334628043374548938932901⟩⟩,⟨⟨35540462317279075594287182,35540462317279075618292957⟩,⟨3212753496238024738109101,3212753496238024762020760⟩⟩,⟨⟨35346758739972210626591025,35346758739972210650450148⟩,⟨3080088964067444143548080,3080088964067444167311799⟩⟩,⟨⟨35136254665058951174431735,35136254665058951198131782⟩,⟨2937020467879753547262487,2937020467879753570865748⟩⟩,⟨⟨34909162324423100917949256,34909162324423100941478063⟩,⟨2783963204446421064621396,2783963204446421088051947⟩⟩,⟨⟨34665712036811101745481497,34665712036811101768827122⟩,⟨2621360068097534033816343,2621360068097534057062159⟩⟩,⟨⟨34406152248280742741088548,34406152248280742764239352⟩,⟨2449680076134541956196129,2449680076134541979245498⟩⟩] +lemma kernel7_0_r3_0_eq : ∀ k : Fin 16, kernel7_0Expr 3 0 k = kernel7_0_r3_0 k := by decide +kernel +noncomputable def kernel7_0_r3_1 : Fin 16 → CBox := ![⟨⟨34130749555673776536195442,34130749555673776559140026⟩,⟨2269416704025541114565548,2269416704025541137407002⟩⟩,⟨⟨33839788709329356245540439,33839788709329356268267767⟩,⟨2081086136931802435002184,2081086136931802457624627⟩⟩,⟨⟨33533572591213152359066379,33533572591213152381565659⟩,⟨1885225444466118983200207,1885225444466119005592793⟩⟩,⟨⟨33212422164635167213419590,33212422164635167235680442⟩,⟨1682390685910704484976748,1682390685910704507129051⟩⟩,⟨⟨32876676391768124495454990,32876676391768124517467274⟩,⟨1473154953423030132233922,1473154953423030154135764⟩⟩,⟨⟨32526692115258000032811746,32526692115258000054565805⟩,⟨1258106361030386932945837,1258106361030386954587531⟩⟩,⟨⟨32162843900338539211602448,32162843900338539233088859⟩,⟨1037845987456384761300781,1037845987456384782672883⟩⟩,⟨⟨31785523834021869971968213,31785523834021869993178080⟩,⟨812985781033378657460111,812985781033378678553709⟩⟩,⟨⟨31395141278136597768979398,31395141278136597789904028⟩,⟨584146435132347696745818,584146435132347717552217⟩⟩,⟨⟨30992122573221729767217205,30992122573221729787848533⟩,⟨351955242684527503537100,351955242684527524048236⟩⟩,⟨⟨30576910690557738215370185,30576910690557738235700326⟩,⟨117043938475703763527800,117043938475703783735799⟩⟩,⟨⟨30149964829923016074351355,30149964829923016094373076⟩,⟨(-119953462036776915329718),(-119953462036776895432072)⟩⟩,⟨⟨29711759961002555175011928,29711759961002555194718129⟩,⟨(-358402818603676877326487),(-358402818603676857746263)⟩⟩,⟨⟨29262786306743234781604907,29262786306743234800989266⟩,⟨(-597672007988659477363336),(-597672007988659458106821)⟩⟩,⟨⟨28803548767343706127617279,28803548767343706146673565⟩,⟨(-837133042976083203545949),(-837133042976083184619334)⟩⟩,⟨⟨28334566283983292839723923,28334566283983292858446688⟩,⟨(-1076164159950119888478109),(-1076164159950119869886788)⟩⟩] +lemma kernel7_0_r3_1_eq : ∀ k : Fin 16, kernel7_0Expr 3 1 k = kernel7_0_r3_1 k := by decide +kernel +noncomputable def kernel7_0_r3_2 : Fin 16 → CBox := ![⟨⟨27856371141830157798487890,27856371141830157816871710⟩,⟨(-1314151866545358782358898),(-1314151866545358764108237)⟩⟩,⟨⟨27369508212320565257591739,27369508212320565275632137⟩,⟨(-1550492941042458665745166),(-1550492941042458647839577)⟩⟩,⟨⟨26874534135164567000513731,26874534135164567018206195⟩,⟨(-1784596375397288824460265),(-1784596375397288806904186)⟩⟩,⟨⟨26372016441004892680386636,26372016441004892697727568⟩,⟨(-2015885254048015827222170),(-2015885254048015810019121)⟩⟩,⟨⟨25862532616131147438857556,25862532616131147455843253⟩,⟨(-2243798560941136653135072),(-2243798560941136636288670)⟩⟩,⟨⟨25346669111126461296231477,25346669111126461312859327⟩,⟨(-2467792907553642005048549),(-2467792907553641988561314)⟩⟩,⟨⟨24825020295794305600636104,24825020295794305616903321⟩,⟨(-2687344175063144880925639),(-2687344175063144864800261)⟩⟩,⟨⟨24298187363175105278748451,24298187363175105294653288⟩,⟨(-2901949064229469586143403),(-2901949064229469570381524)⟩⟩,⟨⟨23766777185911385992456698,23766777185911386007997131⟩,⟨(-3111126546998118407741920),(-3111126546998118392345457)⟩⟩,⟨⟨23231401128652436577567436,23231401128652436592742718⟩,⟨(-3314419214316184790111900),(-3314419214316184775081489)⟩⟩,⟨⟨22692673820600891553459959,22692673820600891568268976⟩,⟨(-3511394515162350894037694),(-3511394515162350879374333)⟩⟩,⟨⟨22151211892690454292717055,22151211892690454307159859⟩,⟨(-3701645882332010691332485),(-3701645882332010677036002)⟩⟩,⟨⟨21607632684242589596227246,21607632684242589610303442⟩,⟨(-3884793741083454981658166),(-3884793741083454967728832)⟩⟩,⟨⟨21062552924277043859408926,21062552924277043873119516⟩,⟨(-4060486397338355739286401),(-4060486397338355725723091)⟩⟩,⟨⟨20516587392943392003619757,20516587392943392016965205⟩,⟨(-4228400802736182187236694),(-4228400802736182174038813)⟩⟩,⟨⟨19970347568795645632297382,19970347568795645645279424⟩,⟨(-4388243194464153777814397),(-4388243194464153764980083)⟩⟩] +lemma kernel7_0_r3_2_eq : ∀ k : Fin 16, kernel7_0Expr 3 2 k = kernel7_0_r3_2 k := by decide +kernel +noncomputable def kernel7_0_r3_3 : Fin 16 → CBox := ![⟨⟨19424440267846790244920942,19424440267846790257540656⟩,⟨(-4539749608418189437327256),(-4539749608418189424855298)⟩⟩,⟨⟨18879466280512801267599170,18879466280512801279859203⟩,⟨(-4682686264892198199104124),(-4682686264892198186991745)⟩⟩,⟨⟨18336019012684438667873258,18336019012684438679775516⟩,⟨(-4816849826638999707388604),(-4816849826638999695633764)⟩⟩,⟨⟨17794683137248545485510488,17794683137248545497058218⟩,⟨(-4942067529792097223717862),(-4942067529792097212317183)⟩⟩,⟨⟨17256033262417687255090258,17256033262417687266285904⟩,⟨(-5058197188779324317520984),(-5058197188779324306471889)⟩⟩,⟨⟨16720632623217191734931195,16720632623217191745778810⟩,⟨(-5165127076992898109253212),(-5165127076992898098551520)⟩⟩,⟨⟨16189031802421827497957943,16189031802421827508460697⟩,⟨(-5262775685601496451421822),(-5262775685601496441064232)⟩⟩,⟨⟨15661767487130765629330884,15661767487130765639493334⟩,⟨(-5351091363494540992082073),(-5351091363494540982063903)⟩⟩,⟨⟨15139361267019793215871339,15139361267019793225697055⟩,⟨(-5430051841932904264201543),(-5430051841932904254519094)⟩⟩,⟨⟨14622318480115099132347616,14622318480115099141841885⟩,⟨(-5499663648039879515252224),(-5499663648039879505900090)⟩⟩,⟨⟨14111127111694846634945398,14111127111694846644112447⟩,⟨(-5559961411797726996016880),(-5559961411797726986990712)⟩⟩,⟨⟨13606256751645089957131425,13606256751645089965976885⟩,⟨(-5611007071714902458665467),(-5611007071714902449959519)⟩⟩,⟨⟨13108157615277663060035939,13108157615277663068564346⟩,⟨(-5652888984793871572844453),(-5652888984793871564454076)⟩⟩,⟨⟨12617259632262098097408471,12617259632262098105626046⟩,⟨(-5685720946856164996501099),(-5685720946856164988419963)⟩⟩,⟨⟨12133971607934373582698038,12133971607934373590609842⟩,⟨(-5709641129667267999454431),(-5709641129667267991677368)⟩⟩,⟨⟨11658680460825597047507539,11658680460825597055120024⟩,⟨(-5724810941646615870985808),(-5724810941646615863506271)⟩⟩] +lemma kernel7_0_r3_3_eq : ∀ k : Fin 16, kernel7_0Expr 3 3 k = kernel7_0_r3_3 k := by decide +kernel +noncomputable def kernel7_0_r3_4 : Fin 16 → CBox := ![⟨⟨11191750539807105612863207,11191750539807105620181594⟩,⟨(-5731413819245270931107852),(-5731413819245270923920519)⟩⟩,⟨⟨10733523023778658512902453,10733523023778658519933691⟩,⟨(-5729653956324037707927201),(-5729653956324037701025035)⟩⟩,⟨⟨10284315406337325350078204,10284315406337325356827967⟩,⟨(-5719754979066455650196817),(-5719754979066455643574057)⟩⟩,⟨⟨9844421067360419229944261,9844421067360419236419564⟩,⟨(-5701958574113309918799513),(-5701958574113309912449066)⟩⟩,⟨⟨9414108932920569764921127,9414108932920569771127715⟩,⟨(-5676523077707436428334196),(-5676523077707436422250239)⟩⟩,⟨⟨8993623224429028432032897,8993623224429028437983266⟩,⟨(-5643722033689488509726573),(-5643722033689488503896420)⟩⟩,⟨⟨8583183297378822975568201,8583183297378822981433352⟩,⟨(-5603842728187206528457260),(-5603842728187206522705929)⟩⟩,⟨⟨8182983569536684951525859,8182983569536684957304945⟩,⟨(-5557184708793218577217046),(-5557184708793218571545585)⟩⟩,⟨⟨7793193537915961112430489,7793193537915961118121306⟩,⟨(-5504058295930525467273836),(-5504058295930525461684649)⟩⟩,⟨⟨7413957883356079718822336,7413957883356079724424431⟩,⟨(-5444783093961996045417645),(-5444783093961996039911389)⟩⟩,⟨⟨7045396661041530759005685,7045396661041530764517192⟩,⟨(-5379686509412197072164108),(-5379686509412197066742847)⟩⟩,⟨⟨6687605574818509815003663,6687605574818509820424145⟩,⟨(-5309102283438832163586719),(-5309102283438832158251095)⟩⟩,⟨⟨6340656332713930729885920,6340656332713930735213499⟩,⟨(-5233369045419419292794912),(-5233369045419419287546999)⟩⟩,⟨⟨6004597080632748140627665,6004597080632748145862290⟩,⟨(-5152828894209348513134842),(-5152828894209348507974894)⟩⟩,⟨⟨5679452910808487873422434,5679452910808487878562568⟩,⟨(-5067826013283153936135099),(-5067826013283153931064848)⟩⟩,⟨⟨5365226441211300472021916,5365226441211300477067548⟩,⟨(-4978705325594968401270101),(-4978705325594968396289756)⟩⟩] +lemma kernel7_0_r3_4_eq : ∀ k : Fin 16, kernel7_0Expr 3 4 k = kernel7_0_r3_4 k := by decide +kernel +noncomputable def kernel7_0_r3_5 : Fin 16 → CBox := ![⟨⟨5061898461780146605686880,5061898461780146610636415⟩,⟨(-4885811193590172342796117),(-4885811193590172337907464)⟩⟩,⟨⟨4769428643042966836500954,4769428643042966841354831⟩,⟨(-4789486169371835753173013),(-4789486169371835748375805)⟩⟩,⟨⟨4487756302422600166733374,4487756302422600171490412⟩,⟨(-4690069799576451445671665),(-4690069799576451440967270)⟩⟩,⟨⟨4216801223298147644162761,4216801223298147648823375⟩,⟨(-4587897489047530543255747),(-4587897489047530538643935)⟩⟩,⟨⟨3956464521702408618780876,3956464521702408623343870⟩,⟨(-4483299426916794298185214),(-4483299426916794293667360)⟩⟩,⟨⟨3706629555386553677393690,3706629555386553681859888⟩,⟨(-4376599578214884160902839),(-4376599578214884156478300)⟩⟩,⟨⟨3467162869873574045518382,3467162869873574049886959⟩,⟨(-4268114743640637936368188),(-4268114743640637932037960)⟩⟩,⟨⟨3237915176052131577605006,3237915176052131581876791⟩,⟨(-4158153689623899720908508),(-4158153689623899716671932)⟩⟩,⟨⟨3018722353831740974190759,3018722353831740978364860⟩,⟨(-4047016350325307735962338),(-4047016350325307731820470)⟩⟩,⟨⟨2809406476387920580555251,2809406476387920584632943⟩,⟨(-3934993102731172811958782),(-3934993102731172807910509)⟩⟩,⟨⟨2609776849570900873577109,2609776849570900877557922⟩,⟨(-3822364115525898125213003),(-3822364115525898121258951)⟩⟩,⟨⟨2419631061132228742775571,2419631061132228746660711⟩,⟨(-3709398771961687016544902),(-3709398771961687012684017)⟩⟩,⟨⟨2238756034538419841378435,2238756034538419845167394⟩,⟨(-3596355166498615220267410),(-3596355166498615216500346)⟩⟩,⟨⟨2066929082287706031295768,2066929082287706034990135⟩,⟨(-3483479674560343821813662),(-3483479674560343818138972)⟩⟩,⟨⟨1903918953822689989640960,1903918953822689993240599⟩,⟨(-3371006594344399074183301),(-3371006594344399070601258)⟩⟩,⟨⟨1749486873335947891776800,1749486873335947895283245⟩,⟨(-3259157859243349462395327),(-3259157859243349458904529)⟩⟩] +lemma kernel7_0_r3_5_eq : ∀ k : Fin 16, kernel7_0Expr 3 5 k = kernel7_0_r3_5 k := by decide +kernel +noncomputable def kernel7_0_r3_6 : Fin 16 → CBox := ![⟨⟨1603387562994741763205276,1603387562994741766618275⟩,⟨(-3148142819076385686257115),(-3148142819076385682857941)⟩⟩,⟨⟨1465370247362309705890045,1465370247362309709211552⟩,⟨(-3038158088001474262697951),(-3038158088001474259388567)⟩⟩,⟨⟨1335179635063886922477646,1335179635063886925707826⟩,⟨(-2929387456677824866194334),(-2929387456677824862974694)⟩⟩,⟨⟨1212556874032795514601716,1212556874032795517742376⟩,⟨(-2822001865977993149940640),(-2822001865977993146809049)⟩⟩,⟨⟨1097240476972710334931666,1097240476972710337982898⟩,⟨(-2716159439309336336040437),(-2716159439309336332996911)⟩⟩,⟨⟨988967213983638202107921,988967213983638205071856⟩,⟨(-2612005570396247960662137),(-2612005570396247957704644)⟩⟩,⟨⟨887472969618337351891924,887472969618337354768988⟩,⟨(-2509673063197825522539018),(-2509673063197825519667233)⟩⟩,⟨⟨792493561960002588051732,792493561960002590843940⟩,⟨(-2409282320490290316520604),(-2409282320490290313732603)⟩⟩,⟨⟨703765521638276020138092,703765521638276022845722⟩,⟨(-2310941577529230358447124),(-2310941577529230355742716)⟩⟩,⟨⟨621026829026342313793089,621026829026342316418505⟩,⟨(-2214747177122966229216704),(-2214747177122966226593611)⟩⟩,⟨⟨544017608184484250433746,544017608184484252977583⟩,⟨(-2120783882394197811819396),(-2120783882394197809277059)⟩⟩,⟨⟨472480776432606833693969,472480776432606836158387⟩,⟨(-2029125223481509215257000),(-2029125223481509212793335)⟩⟩,⟨⟨406162648743646005987189,406162648743646008372714⟩,⟨(-1939833874434022496666984),(-1939833874434022494281535)⟩⟩,⟨⟨344813496449398079674921,344813496449398081983970⟩,⟨(-1852962056580053883577951),(-1852962056580053881268368)⟩⟩,⟨⟨288188060038264333126360,288188060038264335359730⟩,⟨(-1768551964702440774309641),(-1768551964702440772075187)⟩⟩,⟨⟨236046016099026754229612,236046016099026756389546⟩,⟨(-1686636212427545071600613),(-1686636212427545069439105)⟩⟩] +lemma kernel7_0_r3_6_eq : ∀ k : Fin 16, kernel7_0Expr 3 6 k = kernel7_0_r3_6 k := by decide +kernel +noncomputable def kernel7_0_r3_7 : Fin 16 → CBox := ![⟨⟨188152398724586140831115,188152398724586142918229⟩,⟨(-1607238293329962935289090),(-1607238293329962933199966)⟩⟩,⟨⟨144277975933343007127403,144277975933343009144215⟩,⟨(-1530373054368764513312095),(-1530373054368764511292889)⟩⟩,⟨⟨104199581892536742349082,104199581892536744296509⟩,⟨(-1456047178401671926123015),(-1456047178401671924172857)⟩⟩,⟨⟨67700405936541558193071,67700405936541560073376⟩,⟨(-1384259672668945529790707),(-1384259672668945527907375)⟩⟩,⟨⟨34570239563218719744921,34570239563218721558881⟩,⟨(-1315002360296858590889585),(-1315002360296858589072346)⟩⟩,⟨⟨4605682762515297643369,4605682762515299393425⟩,⟨(-1248260372039476801420855),(-1248260372039476799667305)⟩⟩,⟨⟨(-22389688816652997803574),(-22389688816652996116432)⟩,⟨(-1184012635655025591673135),(-1184012635655025589982319)⟩⟩,⟨⟨(-46605194222640789697562),(-46605194222640788071102)⟩,⟨(-1122232360497473508075067),(-1122232360497473506444785)⟩⟩,⟨⟨(-68222953328446003183740),(-68222953328446001617169)⟩,⟨(-1062887515093193760543642),(-1062887515093193758973130)⟩⟩,⟨⟨(-87417826883706871423070),(-87417826883706869913966)⟩,⟨(-1005941295664874384617444),(-1005941295664874383104306)⟩⟩,⟨⟨(-104357388568720766340747),(-104357388568720764888089)⟩,⟨(-951352583758505763430028),(-951352583758505761973270)⟩⟩,⟨⟨(-119201927069642129283380),(-119201927069642127885012)⟩,⟨(-899076391322658883865438),(-899076391322658882462925)⟩⟩,⟨⟨(-132104476152927893101646),(-132104476152927891756707)⟩,⟨(-849064291780865532127946),(-849064291780865530778838)⟩⟩,⟨⟨(-143210870692354408220030),(-143210870692354406926247)⟩,⟨(-801264835826327781005024),(-801264835826327779707066)⟩⟩,⟨⟨(-152659826592631042603127),(-152659826592631041359487)⟩,⟨(-755623950852147860319099),(-755623950852147859071294)⟩⟩,⟨⟨(-160583042558806686919750),(-160583042558806685724206)⟩,⟨(-712085323108638417473972),(-712085323108638416274287)⟩⟩] +lemma kernel7_0_r3_7_eq : ∀ k : Fin 16, kernel7_0Expr 3 7 k = kernel7_0_r3_7 k := by decide +kernel +noncomputable def kernel7_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-167105321679269070575684),(-167105321679269069427431)⟩,⟨(-670590761851035600091807),(-670590761851035598939451)⟩⟩,⟨⟨(-172344710821088789906994),(-172344710821088788803843)⟩,⟨(-631080544905213235146099),(-631080544905213234038896)⟩⟩,⟨⟨(-176412655878643127832187),(-176412655878643126773161)⟩,⟨(-593493745235036429887161),(-593493745235036428824142)⟩⟩,⟨⟨(-179414170968732630232008),(-179414170968732629215195)⟩,⟨(-557768538242176765169091),(-557768538242176764148353)⟩⟩,⟨⟨(-181448019726632936610836),(-181448019726632935635411)⟩,⟨(-523842489667043910568284),(-523842489667043909589011)⟩⟩,⟨⟨(-182606906926567777580567),(-182606906926567776644558)⟩,⟨(-491652824087595916134988),(-491652824087595915195212)⟩⟩,⟨⟨(-182977678725824822815650),(-182977678725824821918127)⟩,⟨(-461136674130914017388534),(-461136674130914016487332)⟩⟩,⟨⟨(-182641529913068831674885),(-182641529913068830814092)⟩,⟨(-432231310620418001796901),(-432231310620418000932522)⟩⟩,⟨⟨(-181674216627276010774037),(-181674216627276009949232)⟩,⟨(-404874353979407518675347),(-404874353979407517847052)⟩⟩,⟨⟨(-180146273103102146298472),(-180146273103102145507821)⟩,⟨(-379003967299290046054687),(-379003967299290045260646)⟩⟩,⟨⟨(-178123231090437029041639),(-178123231090437028284280)⟩,⟨(-354559031558530749560281),(-354559031558530748799633)⟩⟩,⟨⟨(-175665840689476170169336),(-175665840689476169443678)⟩,⟨(-331479303546244321773337),(-331479303546244321044492)⟩⟩,⟨⟨(-172830291437004780068127),(-172830291437004779373458)⟩,⟨(-309705557102724628956720),(-309705557102724628258968)⟩⟩,⟨⟨(-169668432573948656976319),(-169668432573948656311015)⟩,⟨(-289179708338415986397134),(-289179708338415985728850)⟩⟩,⟨⟨(-166227991517877981302078),(-166227991517877980665356)⟩,⟨(-269844925533263784051657),(-269844925533263783412060)⟩⟩,⟨⟨(-162552789656396370178422),(-162552789656396369568857)⟩,⟨(-251645724450479535475974),(-251645724450479534863638)⟩⟩] +lemma kernel7_0_r3_8_eq : ∀ k : Fin 16, kernel7_0Expr 3 8 k = kernel7_0_r3_8 k := by decide +kernel +noncomputable def kernel7_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-158682954667620321912047),(-158682954667620321329030)⟩,⟨(-234528049822989522219638),(-234528049822989521633952)⟩⟩,⟨⟨(-154655128661732754417173),(-154655128661732753859213)⟩,⟨(-218439343787708280572637),(-218439343787708280012111)⟩⟩,⟨⟨(-150502671522425239660359),(-150502671522425239126452)⟩,⟨(-203328602052809950382266),(-203328602052809949845992)⟩⟩,⟨⟨(-146255858908538927179919),(-146255858908538926668838)⟩,⟨(-189146418586897201586906),(-189146418586897201073642)⟩⟩,⟨⟨(-141942074454049768610992),(-141942074454049768122200)⟩,⟨(-175845019616931294086653),(-175845019616931293595850)⟩⟩,⟨⟨(-137585995778456216169010),(-137585995778456215701262)⟩,⟨(-163378287714531042496841),(-163378287714531042027241)⟩⟩,⟨⟨(-133209773989411751579487),(-133209773989411751132192)⟩,⟨(-151701776738311851524790),(-151701776738311851075793)⟩⟩,⟨⟨(-128833206424949689747760),(-128833206424949689319839)⟩,⟨(-140772718383848052032508),(-140772718383848051603021)⟩⟩,⟨⟨(-124473902443773934133818),(-124473902443773933724816)⟩,⟨(-130550021073118367588080),(-130550021073118367177640)⟩⟩,⟨⟨(-120147442128784088240264),(-120147442128784087849066)⟩,⟨(-120994261892433962119281),(-120994261892433961726764)⟩⟩,⟨⟨(-115867527821257018247786),(-115867527821257017873872)⟩,⟨(-112067672262329067011676),(-112067672262329066636553)⟩⟩,⟨⟨(-111646128450949132767851),(-111646128450949132410280)⟩,⟨(-103734117995170324140878),(-103734117995170323782199)⟩⟩,⟨⟨(-107493616670878769963125),(-107493616670878769621482)⟩,⟨(-95959074366741984112451),(-95959074366741983769795)⟩⟩,⟨⟨(-103418898844791524892914),(-103418898844791524566248)⟩,⟨(-88709596797192194582986),(-88709596797192194255395)⟩⟩,⟨⟨(-99429537970425377737179),(-99429537970425377425041)⟩,⟨(-81954287704854787079749),(-81954287704854786766765)⟩⟩,⟨⟨(-95531869652822389733362),(-95531869652822389434579)⟩,⟨(-75663260063936194803659),(-75663260063936194504104)⟩⟩] +lemma kernel7_0_r3_9_eq : ∀ k : Fin 16, kernel7_0Expr 3 9 k = kernel7_0_r3_9 k := by decide +kernel +noncomputable def kernel7_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-91731111269244110538493),(-91731111269244110252584)⟩,⟨(-69808098164193990978510),(-69808098164193990691899)⟩⟩,⟨⟨(-88031464490919030254717),(-88031464490919029980891)⟩,⟨(-64361816037818198278264),(-64361816037818198003798)⟩⟩,⟨⟨(-84436211347075154305621),(-84436211347075154043542)⟩,⟨(-59298813986016040707043),(-59298813986016040444383)⟩⟩,⟨⟨(-80947804033691094119006),(-80947804033691093868017)⟩,⟨(-54594833605523709191117),(-54594833605523708939600)⟩⟩,⟨⟨(-77567948683343340520420),(-77567948683343340280270)⟩,⟨(-50226911683625795246396),(-50226911683625795005768)⟩⟩,⟨⟨(-74297683323647729706963),(-74297683323647729476981)⟩,⟨(-46173333299428432561117),(-46173333299428432330702)⟩⟩,⟨⟨(-71137450260302946020931),(-71137450260302945800831)⟩,⟨(-42413584439254510994319),(-42413584439254510773827)⟩⟩,⟨⟨(-68087163126855806625541),(-68087163126855806414754)⟩,⟨(-38928304405233088431228),(-38928304405233088220087)⟩⟩,⟨⟨(-65146268847231854382851),(-65146268847231854181177)⟩,⟨(-35699238268542131329973),(-35699238268542131127980)⟩⟩,⟨⟨(-62313804759015825945928),(-62313804759015825752773)⟩,⟨(-32709189592414614079196),(-32709189592414613885754)⟩⟩,⟨⟨(-59588451145624366634600),(-59588451145624366449720)⟩,⟨(-29941973624993873473078),(-29941973624993873287941)⟩⟩,⟨⟨(-56968579424080344844409),(-56968579424080344667316)⟩,⟨(-27382371138468054631639),(-27382371138468054454316)⟩⟩,⟨⟨(-54452296232258592849452),(-54452296232258592679965)⟩,⟨(-25016083068652255450276),(-25016083068652255280583)⟩⟩,⟨⟨(-52037483655402282131763),(-52037483655402281969388)⟩,⟨(-22829686088332587648983),(-22829686088332587486424)⟩⟩,⟨⟨(-49721835826573321442495),(-49721835826573321287026)⟩,⟨(-20810589228237657638247),(-20810589228237657482615)⟩⟩,⟨⟨(-47502892129655064082132),(-47502892129655063933152)⟩,⟨(-18946991641447114893594),(-18946991641447114744471)⟩⟩] +lemma kernel7_0_r3_10_eq : ∀ k : Fin 16, kernel7_0Expr 3 10 k = kernel7_0_r3_10 k := by decide +kernel +noncomputable def kernel7_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-45378067226716880467151),(-45378067226716880324524)⟩,⟨(-17227841590360924906093),(-17227841590360924763340)⟩⟩,⟨⟨(-43344678124113026312378),(-43344678124113026175667)⟩,⟨(-15642796720005125806962),(-15642796720005125670141)⟩⟩,⟨⟨(-41399968483747501310019),(-41399968483747501179054)⟩,⟨(-14182185667400798498261),(-14182185667400798367200)⟩⟩,⟨⟨(-39541130377606668563782),(-39541130377606668438210)⟩,⟨(-12836971043927388578316),(-12836971043927388452660)⟩⟩,⟨⟨(-37765323675046525512684),(-37765323675046525392370)⟩,⟨(-11598713816018885211500),(-11598713816018885091114)⟩⟩,⟨⟨(-36069693243515992039249),(-36069693243515991923682)⟩,⟨(-10459539099087230011628),(-10459539099087229895999)⟩⟩,⟨⟨(-34451384134486125957064),(-34451384134486125846121)⟩,⟨(-9412103370214243046146),(-9412103370214242935150)⟩⟩,⟨⟨(-32907554917413298514086),(-32907554917413298407483)⟩,⟨(-8449563096831751565002),(-8449563096831751458355)⟩⟩,⟨⟨(-31435389315658797729607),(-31435389315658797627268)⟩,⟨(-7565544771258623846961),(-7565544771258623744586)⟩⟩,⟨⟨(-30032106289476504623963),(-30032106289476504525586)⟩,⟨(-6754116334521590899711),(-6754116334521590801305)⟩⟩,⟨⟨(-28694968702514823798816),(-28694968702514823704295)⟩,⟨(-6009759967292671625585),(-6009759967292671531042)⟩⟩,⟨⟨(-27421290699802260222374),(-27421290699802260131470)⟩,⟨(-5327346220968887654977),(-5327346220968887564057)⟩⟩,⟨⟨(-26208443916934449659084),(-26208443916934449571728)⟩,⟨(-4702109457840020252235),(-4702109457840020164868)⟩⟩,⟨⟨(-25053862632184339120769),(-25053862632184339036714)⟩,⟨(-4129624565879159383324),(-4129624565879159299263)⟩⟩,⟨⟨(-23955047965541097562656),(-23955047965541097481816)⟩,⟨(-3605784910892276591598),(-3605784910892276510755)⟩⟩,⟨⟨(-22909571221266498017349),(-22909571221266497939517)⟩,⟨(-3126781486522664659299),(-3126781486522664581468)⟩⟩] +lemma kernel7_0_r3_11_eq : ∀ k : Fin 16, kernel7_0Expr 3 11 k = kernel7_0_r3_11 k := by decide +kernel +noncomputable def kernel7_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-21915076463454486893888),(-21915076463454486819022)⟩,⟨(-2689083220871787833439),(-2689083220871787758579)⟩⟩,⟨⟨(-20969282407300711376132),(-20969282407300711304010)⟩,⟨(-2289418397220318952273),(-2289418397220318880158)⟩⟩,⟨⟨(-20069983702340365739627),(-20069983702340365670178)⟩,⟨(-1924757145464951139270),(-1924757145464951069832)⟩⟩,⟨⟨(-19215051677797916771056),(-19215051677797916704106)⟩,⟨(-1592294960383694099547),(-1592294960383694032610)⟩⟩,⟨⟨(-18402434614411182631455),(-18402434614411182566968)⟩,⟨(-1289437202663259419575),(-1289437202663259355102)⟩⟩,⟨⟨(-17630157601642388778221),(-17630157601642388716009)⟩,⟨(-1013784538728006344376),(-1013784538728006282180)⟩⟩,⟨⟨(-16896322034065502704587),(-16896322034065502644598)⟩,⟨(-763119275764682515736),(-763119275764682455765)⟩⟩,⟨⟨(-16199104795915755623374),(-16199104795915755565460)⟩,⟨(-535392548907457515229),(-535392548907457457335)⟩⟩,⟨⟨(-15536757178295604596518),(-15536757178295604540655)⟩,⟨(-328712318302734529058),(-328712318302734473217)⟩⟩,⟨⟨(-14907603569341975168360),(-14907603569341975114386)⟩,⟨(-141332134684701411575),(-141332134684701357622)⟩⟩,⟨⟨(-14310039953761900437169),(-14310039953761900385042)⟩,⟨28359366865240734980,28359366865240787085⟩⟩,⟨⟨(-13742532254526261916781),(-13742532254526261866376)⟩,⟨181848284152598631861,181848284152598682244⟩⟩,⟨⟨(-13203614546162247325168),(-13203614546162247276462)⟩,⟨320504614039402299994,320504614039402348676⟩⟩,⟨⟨(-12691887165991944189568),(-12691887165991944142427)⟩,⟨445590804188824582877,445590804188824629993⟩⟩,⟨⟨(-12206014746814489157758),(-12206014746814489112149)⟩,⟨558269725672027969056,558269725672028014641⟩⟩,⟨⟨(-11744724191909567157155),(-11744724191909567112970)⟩,⟨659612100337555735373,659612100337555779532⟩⟩] +lemma kernel7_0_r3_12_eq : ∀ k : Fin 16, kernel7_0Expr 3 12 k = kernel7_0_r3_12 k := by decide +kernel +noncomputable def kernel7_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-11306802610837975181756),(-11306802610837975138991)⟩,⟨750603415435543936107,750603415435543978846⟩⟩,⟨⟨(-10891095232317709991529),(-10891095232317709950061)⟩,⟨832150356571718918998,832150356571718960441⟩⟩,⟨⟨(-10496503308449080480583),(-10496503308449080440383)⟩,⟨905086788649923327664,905086788649923367838⟩⟩,⟨⟨(-10121982022737429399056),(-10121982022737429360037)⟩,⟨970179313055760150693,970179313055760189687⟩⟩,⟨⟨(-9766538412705256840034),(-9766538412705256802186)⟩,⟨1028132427945568675759,1028132427945568713582⟩⟩,⟨⟨(-9429229316385338136571),(-9429229316385338099795)⟩,⟨1079593317140898743576,1079593317140898780326⟩⟩,⟨⟨(-9109159350631718314882),(-9109159350631718279159)⟩,⟨1125156291794427326648,1125156291794427362346⟩⟩,⟨⟨(-8805478927965599920818),(-8805478927965599886069)⟩,⟨1165366907693407198530,1165366907693407233254⟩⟩,⟨⟨(-8517382317577958423808),(-8517382317577958390036)⟩,⟨1200725779804934880108,1200725779804934913855⟩⟩,⟨⟨(-8244105755130553707549),(-8244105755130553674660)⟩,⟨1231692114446486969830,1231692114446487002694⟩⟩,⟨⟨(-7984925605122696631503),(-7984925605122696599482)⟩,⟨1258686978287525473965,1258686978287525505961⟩⟩,⟨⟨(-7739156578814023328599),(-7739156578814023297382)⟩,⟨1282096322255128478908,1282096322255128510100⟩⟩,⟨⟨(-7506150010005479423486),(-7506150010005479393072)⟩,⟨1302273777329638282521,1302273777329638312910⟩⟩,⟨⟨(-7285292190374073638220),(-7285292190374073608533)⟩,⟨1319543238175838062310,1319543238175838091973⟩⟩,⟨⟨(-7076002765524566711686),(-7076002765524566682716)⟩,⟨1334201249561361523751,1334201249561361552698⟩⟩,⟨⟨(-6877733192456435460596),(-6877733192456435432283)⟩,⟨1346519209566742611512,1346519209566742639800⟩⟩] +lemma kernel7_0_r3_13_eq : ∀ k : Fin 16, kernel7_0Expr 3 13 k = kernel7_0_r3_13 k := by decide +kernel +noncomputable def kernel7_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-6689965258740973288012),(-6689965258740973260367)⟩,⟨1356745402690253454755,1356745402690253482376⟩⟩,⟨⟨(-6512209663355482727789),(-6512209663355482700737)⟩,⟨1365106875094727645895,1365106875094727672924⟩⟩,⟨⟨(-6344004658823834820188),(-6344004658823834793723)⟩,⟨1371811163431973811917,1371811163431973838359⟩⟩,⟨⟨(-6184914754060274079705),(-6184914754060274053777)⟩,⟨1377047887912021276858,1377047887912021302764⟩⟩,⟨⟨(-6034529477101684202185),(-6034529477101684176798)⟩,⟨1380990219558027793305,1380990219558027818669⟩⟩,⟨⟨(-5892462196738413711193),(-5892462196738413686288)⟩,⟨1383796230901823166707,1383796230901823191590⟩⟩,⟨⟨(-5758349001911354882607),(-5758349001911354858179)⟩,⟨1385610138728274686161,1385610138728274710566⟩⟩,⟨⟨(-5631847637629762794557),(-5631847637629762770562)⟩,⟨1386563446867384539301,1386563446867384563274⟩⟩,⟨⟨(-5512636496077090286381),(-5512636496077090262829)⟩,⟨1386775996459661344275,1386775996459661367805⟩⟩,⟨⟨(-5400413661507982148776),(-5400413661507982125608)⟩,⟨1386356930581212229046,1386356930581212252192⟩⟩,⟨⟨(-5294896007495869122727),(-5294896007495869099942)⟩,⟨1385405579608527455812,1385405579608527478575⟩⟩,⟨⟨(-5195818345064929781818),(-5195818345064929759374)⟩,⟨1384012273227422537894,1384012273227422560316⟩⟩,⟨⟨(-5102932620230378170830),(-5102932620230378148737)⟩,⟨1382259084544417350729,1382259084544417372800⟩⟩,⟨⟨(-5016007159475133664072),(-5016007159475133642282)⟩,⟨1380220511340339318757,1380220511340339340526⟩⟩,⟨⟨(-4934825961707181456639),(-4934825961707181435149)⟩,⟨1377964099113534470057,1377964099113534491526⟩⟩,⟨⟨(-4859188035268764529962),(-4859188035268764508735)⟩,⟨1375551010192182771058,1375551010192182792264⟩⟩] +lemma kernel7_0_r3_14_eq : ∀ k : Fin 16, kernel7_0Expr 3 14 k = kernel7_0_r3_14 k := by decide +kernel +noncomputable def kernel7_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-4788906778604555772588),(-4788906778604555751638)⟩,⟨1373036542850304854533,1373036542850304875462⟩⟩,⟨⟨(-4723809403239891035532),(-4723809403239891014806)⟩,⟨1370470604038617116964,1370470604038617137670⟩⟩,⟨⟨(-4663736397770889900104),(-4663736397770889879601)⟩,⟨1367898139037983695794,1367898139037983716277⟩⟩,⟨⟨(-4608541031624868960962),(-4608541031624868940648)⟩,⟨1365359521058412557290,1365359521058412577584⟩⟩,⟨⟨(-4558088897410997519195),(-4558088897410997499080)⟩,⟨1362890903538978151865,1362890903538978171960⟩⟩,⟨⟨(-4512257490746898885760),(-4512257490746898865802)⟩,⟨1360524537652398020362,1360524537652398040300⟩⟩,⟨⟨(-4470935826516199132883),(-4470935826516199113083)⟩,⟨1358289057280961913094,1358289057280961932874⟩⟩,⟨⟨(-4434024090584292748558),(-4434024090584292728885)⟩,⟨1356209733506868241884,1356209733506868261537⟩⟩,⟨⟨(-4401433326074332585442),(-4401433326074332565910)⟩,⟨1354308700448563611740,1354308700448563631252⟩⟩,⟨⟨(-4373085153382230548457),(-4373085153382230529025)⟩,⟨1352605154074245182275,1352605154074245201688⟩⟩,⟨⟨(-4348911523187908181144),(-4348911523187908161810)⟩,⟨1351115525433147659778,1351115525433147679093⟩⟩,⟨⟨(-4328854501799849793300),(-4328854501799849774035)⟩,⟨1349853629563505780256,1349853629563505799501⟩⟩,⟨⟨(-4312866088250919925117),(-4312866088250919905933)⟩,⟨1348830791162099366082,1348830791162099385246⟩⟩,⟨⟨(-4300908062645188140774),(-4300908062645188121630)⟩,⟨1348055947933019746095,1348055947933019765219⟩⟩,⟨⟨(-4292951865337969247747),(-4292951865337969228644)⟩,⟨1347535732371736833158,1347535732371736852240⟩⟩,⟨⟨(-4288978506614277744205),(-4288978506614277725116)⟩,⟨1347274532583710415749,1347274532583710434818⟩⟩] +lemma kernel7_0_r3_15_eq : ∀ k : Fin 16, kernel7_0Expr 3 15 k = kernel7_0_r3_15 k := by decide +kernel +noncomputable def kernel7_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel7_0_r3_0,kernel7_0_r3_1,kernel7_0_r3_2,kernel7_0_r3_3,kernel7_0_r3_4,kernel7_0_r3_5,kernel7_0_r3_6,kernel7_0_r3_7,kernel7_0_r3_8,kernel7_0_r3_9,kernel7_0_r3_10,kernel7_0_r3_11,kernel7_0_r3_12,kernel7_0_r3_13,kernel7_0_r3_14,kernel7_0_r3_15] +lemma kernel7_0_r3_eq (i k : Fin 16) : kernel7_0Expr 3 i k = kernel7_0_r3 i k := by + fin_cases i + · exact kernel7_0_r3_0_eq k + · exact kernel7_0_r3_1_eq k + · exact kernel7_0_r3_2_eq k + · exact kernel7_0_r3_3_eq k + · exact kernel7_0_r3_4_eq k + · exact kernel7_0_r3_5_eq k + · exact kernel7_0_r3_6_eq k + · exact kernel7_0_r3_7_eq k + · exact kernel7_0_r3_8_eq k + · exact kernel7_0_r3_9_eq k + · exact kernel7_0_r3_10_eq k + · exact kernel7_0_r3_11_eq k + · exact kernel7_0_r3_12_eq k + · exact kernel7_0_r3_13_eq k + · exact kernel7_0_r3_14_eq k + · exact kernel7_0_r3_15_eq k +noncomputable def kernel7_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-6284982070157762996401298599),(-6284982070157762985755054987)⟩,⟨(-6477783344790653716344569021),(-6477783344790653705606449081)⟩⟩,⟨⟨(-6284729622522116403757140067),(-6284729622522116393113216805)⟩,⟨(-6473956725544804859469717185),(-6473956725544804848733998360)⟩⟩,⟨⟨(-6284221694315846123788941494),(-6284221694315846113149677431)⟩,⟨(-6466307716537700593741553808),(-6466307716537700583010655609)⟩⟩,⟨⟨(-6283452231680806491127826735),(-6283452231680806480495559062)⟩,⟨(-6454844773489161214082801879),(-6454844773489161203359141926)⟩⟩,⟨⟨(-6282412183819428312726869689),(-6282412183819428302103933287)⟩,⟨(-6439580571837507420827172755),(-6439580571837507410113166007)⟩⟩,⟨⟨(-6281089538870746481710786954),(-6281089538870746471099513512)⟩,⟨(-6420531996919673544537046907),(-6420531996919673533835104661)⟩⟩,⟨⟨(-6279469371559454708178183801),(-6279469371559454697580901302)⟩,⟨(-6397720130794923457872952207),(-6397720130794923447185481468)⟩⟩,⟨⟨(-6277533902459401841000584624),(-6277533902459401830419615760)⟩,⟨(-6371170235642048861151954604),(-6371170235642048850481356388)⟩⟩,⟨⟨(-6275262568673977524047341757),(-6275262568673977513485004910)⟩,⟨(-6340911733643778243621001569),(-6340911733643778232969671768)⟩⟩,⟨⟨(-6272632105697324629479914837),(-6272632105697324618938519958)⟩,⟨(-6306978183256879427763726710),(-6306978183256879417134051856)⟩⟩,⟨⟨(-6269616640182356548052589140),(-6269616640182356537534442176)⟩,⟨(-6269407251752267331777137696),(-6269407251752267321171499282)⟩⟩,⟨⟨(-6266187793304245122832680268),(-6266187793304245112340074612)⟩,⟨(-6228240683896492535979277882),(-6228240683896492525400043698)⟩⟩,⟨⟨(-6262314794371477702605186294),(-6262314794371477692140413463)⟩,⟨(-6183524266634438386990455811),(-6183524266634438376439990519)⟩⟩,⟨⟨(-6257964604300859273294829593),(-6257964604300859262860161654)⟩,⟨(-6135307789623038511400552520),(-6135307789623038500881199965)⟩⟩,⟨⟨(-6253102048538059660975291718),(-6253102048538059650573001932)⟩,⟨(-6083645001457476333599972918),(-6083645001457476323114076683)⟩⟩,⟨⟨(-6247689958971580100074763516),(-6247689958971580089707099155)⟩,⟨(-6028593561424765931486809081),(-6028593561424765921036685183)⟩⟩] +lemma kernel7_0_r4_0_eq : ∀ k : Fin 16, kernel7_0Expr 4 0 k = kernel7_0_r4_0 k := by decide +kernel +noncomputable def kernel7_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-6241689324355443623055366003),(-6241689324355443612724582189)⟩,⟨(-5970214986614949671038676466),(-5970214986614949660626647123)⟩⟩,⟨⟨(-6235059448724607106185001520),(-6235059448724607095893313343)⟩,⟨(-5908574594217479953442084868),(-5908574594217479943070430479)⟩⟩,⟨⟨(-6227758117257158308145592797),(-6227758117257158297895230732)⟩,⟨(-5843741438829763776354882905),(-5843741438829763766025897432)⟩⟩,⟨⟨(-6219741769008909056137248438),(-6219741769008909045930394096)⟩,⟨(-5775788244606408892939083352),(-5775788244606408882655009914)⟩⟩,⟨⟨(-6210965675919137000510467351),(-6210965675919136990349330164)⟩,⟨(-5704791332081473287953920152),(-5704791332081473277717027695)⟩⟩,⟨⟨(-6201384127461074731705119327),(-6201384127461074721591835917)⟩,⟨(-5630830539502023950157740256),(-5630830539502023939970222752)⟩⟩,⟨⟨(-6190950620287408228715657469),(-6190950620287408218652405237)⟩,⟨(-5553989138519578822257426563),(-5553989138519578812121516618)⟩⟩,⟨⟨(-6179618052199637764589879026),(-6179618052199637754578752220)⟩,⟨(-5474353744096543123868195132),(-5474353744096543113786039875)⟩⟩,⟨⟨(-6167338919750783567874400510),(-6167338919750783557917554802)⟩,⟨(-5392014218497546891966876137),(-5392014218497546881940681839)⟩⟩,⟨⟨(-6154065518773693936553738529),(-6154065518773693926653206689)⟩,⟨(-5307063569250616440798639691),(-5307063569250616430830487226)⟩⟩,⟨⟨(-6139750147112240754405802047),(-6139750147112240744563697522)⟩,⟨(-5219597840980323235495553930),(-5219597840980323225587602450)⟩⟩,⟨⟨(-6124345308820068724557572094),(-6124345308820068714775877868)⟩,⟨(-5129716001034386988045147267),(-5129716001034386978199422843)⟩⟩,⟨⟨(-6107803919081398143584780711),(-6107803919081398133865587093)⟩,⟨(-5037519818846586186766779982),(-5037519818846586176985413507)⟩⟩,⟨⟨(-6090079509100759612243758715),(-6090079509100759602588970371)⟩,⟨(-4943113739002152536339670590),(-4943113739002152526624604557)⟩⟩,⟨⟨(-6071126430203549603723287056),(-6071126430203549594134941815)⟩,⟨(-4846604747996983243905304318),(-4846604747996983234258611803)⟩⟩,⟨⟨(-6050900056387018197522936365),(-6050900056387018188002880478)⟩,⟨(-4748102234708868081899904529),(-4748102234708868072323464175)⟩⟩] +lemma kernel7_0_r4_1_eq : ∀ k : Fin 16, kernel7_0Expr 4 1 k = kernel7_0_r4_1 k := by decide +kernel +noncomputable def kernel7_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-6029356984561806509782860478),(-6029356984561806500333112899)⟩,⟨(-4647717844627352626409159628),(-4647717844627352616905020152)⟩⟩,⟨⟨(-6006455231727504480204384978),(-6006455231727504470826689978)⟩,⟨(-4545565327918686233779320087),(-4545565327918686224349252554)⟩⟩,⟨⟨(-5982154428331952921281566789),(-5982154428331952911977873931)⟩,⟨(-4441760381433360497094036718),(-4441760381433360487740014805)⟩⟩,⟨⟨(-5956416007073209502379357659),(-5956416007073209493151350123)⟩,⟨(-4336420484795845457404719354),(-4336420484795845448128447360)⟩⟩,⟨⟨(-5929203386415267313273728784),(-5929203386415267304123335799)⟩,⟨(-4229664730749079127435217092),(-4229664730749079118238642660)⟩⟩,⟨⟨(-5900482148103774914462900085),(-5900482148103774905391684158)⟩,⟨(-4121613649959852511970827374),(-4121613649959852502855528355)⟩⟩,⟨⟨(-5870220207986162993421287078),(-5870220207986162984431095967)⟩,⟨(-4012389030525239318748190772),(-4012389030525239309716027558)⟩⟩,⟨⟨(-5838387979461725371823685706),(-5838387979461725362916012866)⟩,⟨(-3902113732454420775423378497),(-3902113732454420766475854125)⟩⟩,⟨⟨(-5804958528911306724867962825),(-5804958528911306716044645743)⟩,⟨(-3790911497434418455909849194),(-3790911497434418447048808039)⟩⟩,⟨⟨(-5769907722483276056259278126),(-5769907722483276047521659133)⟩,⟨(-3678906754222133570452764799),(-3678906754222133561679552995)⟩⟩,⟨⟨(-5733214363642357778959252170),(-5733214363642357770309062655)⟩,⟨(-3566224420038457922871238755),(-3566224420038457914187588829)⟩⟩,⟨⟨(-5694860320920578807446308395),(-5694860320920578798884826400)⟩,⟨(-3452989698372825816456664150),(-3452989698372825807863852275)⟩⟩,⟨⟨(-5654830645344981262368396935),(-5654830645344981253897340970)⟩,⟨(-3339327873638173438269391788),(-3339327873638173429769131991)⟩⟩,⟨⟨(-5613113677054740198530619769),(-5613113677054740190151099544)⟩,⟨(-3225364103146619978944666594),(-3225364103146619970538061111)⟩⟩,⟨⟨(-5569701140660791200924478062),(-5569701140660791192638093789)⟩,⟨(-3111223206905043516787527793),(-3111223206905043508476166815)⟩⟩,⟨⟨(-5524588228943873877002074743),(-5524588228943873868809864937)⟩,⟨(-2997029455756860139431586680),(-2997029455756860131216495834)⟩⟩] +lemma kernel7_0_r4_2_eq : ∀ k : Fin 16, kernel7_0Expr 4 2 k = kernel7_0_r4_2 k := by decide +kernel +noncomputable def kernel7_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-5477773674531877674369369904),(-5477773674531877666272941279)⟩,⟨(-2882906358421499397020854218),(-2882906358421499388903624869)⟩⟩,⟨⟨(-5429259809244363250609431412),(-5429259809244363242609615917)⟩,⟨(-2768976448006084158149084683),(-2768976448006084150130530630)⟩⟩,⟨⟨(-5379052610840937223606076504),(-5379052610840937215704328266)⟩,⟨(-2655361068584459908842447425),(-2655361068584459900924002279)⟩⟩,⟨⟨(-5327161736960576839067454190),(-5327161736960576831264551169)⟩,⟨(-2542180162456781324508403450),(-2542180162456781316690822038)⟩⟩,⟨⟨(-5273600546090815919757740750),(-5273600546090815912055136211)⟩,⟨(-2429552058718170261612680542),(-2429552058718170253897390726)⟩⟩,⟨⟨(-5218386105458683094303102964),(-5218386105458683086701358998)⟩,⟨(-2317593263777342359200384866),(-2317593263777342351587920859)⟩⟩,⟨⟨(-5161539185789184208548096775),(-5161539185789184201048507091)⟩,⟨(-2206418254475409432061618238),(-2206418254475409424553243715)⟩⟩,⟨⟨(-5103084242931688492258688754),(-5103084242931688484861753396)⟩,⟨(-2096139274461170452168162235),(-2096139274461170444764344949)⟩⟩,⟨⟨(-5043049386409548387479816857),(-5043049386409548380186855163)⟩,⟨(-1986866134481993596772015279),(-1986866134481993589474040233)⟩⟩,⟨⟨(-4981466335003383751724812334),(-4981466335003383744536067785)⟩,⟨(-1878706017248774991329079192),(-1878706017248774984137153483)⟩⟩,⟨⟨(-4918370359533413769502689029),(-4918370359533413762419281880)⟩,⟨(-1771763287529367798172495048),(-1771763287529367791087700635)⟩⟩,⟨⟨(-4853800213060740934619070563),(-4853800213060740927641210544)⟩,⟨(-1666139308117262499984805086),(-1666139308117262493007311600)⟩⟩,⟨⟨(-4787798048781294569565397512),(-4787798048781294562694220465)⟩,⟨(-1561932262311143528634332560),(-1561932262311143521765233950)⟩⟩,⟨⟨(-4720409325938939159495341529),(-4720409325938939152730800589)⟩,⟨(-1459236983526250902397658330),(-1459236983526250895636864315)⟩⟩,⟨⟨(-4651682704135758852649381777),(-4651682704135758845992412634)⟩,⟨(-1358144792640264914936837938),(-1358144792640264908285239132)⟩⟩,⟨⟨(-4581669926467460301054505216),(-4581669926467460294505020377)⟩,⟨(-1258743343654758553624984847),(-1258743343654758547082447418)⟩⟩] +lemma kernel7_0_r4_3_eq : ∀ k : Fin 16, kernel7_0Expr 4 3 k = kernel7_0_r4_3 k := by decide +kernel +noncomputable def kernel7_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-4510425691959913032405904079),(-4510425691959913025964894798)⟩,⟨(-1161116478228202310777346005),(-1161116478228202304344813317)⟩⟩,⟨⟨(-4438007517828798213979878105),(-4438007517828798207646953762)⟩,⟨(-1065344089608159981934909234),(-1065344089608159975611941874)⟩⟩,⟨⟨(-4364475592127900500489962702),(-4364475592127900494265866062)⟩,⟨(-971501996458806588864414011),(-971501996458806582651704541)⟩⟩,⟨⟨(-4289892617392502224286139322),(-4289892617392502218170485039)⟩,⟨(-879661827045378843593949391),(-879661827045378837491061595)⟩⟩,⟨⟨(-4214323645922386099124211325),(-4214323645922386093117778207)⟩,⟨(-789890914199805336999608855),(-789890914199805331007269367)⟩⟩,⟨⟨(-4137835907383898422977189868),(-4137835907383898417079308207)⟩,⟨(-702252201451750256724314373),(-702252201451750250841801074)⟩⟩,⟨⟨(-4060498629442162804645288495),(-4060498629442162798856503034)⟩,⟨(-616804160666853681337904812),(-616804160666853675565708848)⟩⟩,⟨⟨(-3982382852162676519239520266),(-3982382852162676513559153706)⟩,⟨(-533600721489295134946776829),(-533600721489295129284167293)⟩⟩,⟨⟨(-3903561236945999631407153530),(-3903561236945999625835830376)⟩,⟨(-452691212839194332540181603),(-452691212839194326987728272)⟩⟩,⟨⟨(-3824107870779914489756530674),(-3824107870779914484293248679)⟩,⟨(-374120316667058824219864306),(-374120316667058818776510721)⟩⟩,⟨⟨(-3744098066610166448937916284),(-3744098066610166443583020780)⟩,⟨(-297928034117771308956936385),(-297928034117771303622972651)⟩⟩,⟨⟨(-3663608160643596103988075877),(-3663608160643596098740610162)⟩,⟨(-224149664205770305533431254),(-224149664205770300307846103)⟩⟩,⟨⟨(-3582715307406064308226364136),(-3582715307406064303073830199)⟩,⟨(-152815795051416895906503194),(-152815795051416890776727727)⟩⟩,⟨⟨(-3501497273382004946862763224),(-3501497273382004941803391974)⟩,⟨(-83952307676365107048944120),(-83952307676365102013154587)⟩⟩,⟨⟨(-3420032230062694354265975654),(-3420032230062694349300286850)⟩,⟨(-17580392303377030695944885),(-17580392303377025754606578)⟩⟩,⟨⟨(-3338398547226404601117397477),(-3338398547226404596244542844)⟩,⟨46283422946238367657251904,46283422946238372505040403⟩⟩] +lemma kernel7_0_r4_4_eq : ∀ k : Fin 16, kernel7_0Expr 4 4 k = kernel7_0_r4_4 k := by decide +kernel +noncomputable def kernel7_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-3256674587265541699291920998),(-3256674587265541694512556820)⟩,⟨107627231116215623234997096,107627231116215627988633506⟩⟩,⟨⟨(-3174938501363716914981192619),(-3174938501363716910294137022)⟩,⟨166443693449692753735340586,166443693449692758396058786⟩⟩,⟨⟨(-3093268028309544162190328347),(-3093268028309544157595942838)⟩,⟨222729974654115076036152140,222729974654115080603643430⟩⟩,⟨⟨(-3011740296713909147555813932),(-3011740296713909143053027200)⟩,⟨276487666705134534397263227,276487666705134538872649783⟩⟩,⟨⟨(-2930431631373652053467966427),(-2930431631373652049057240936)⟩,⟨327722701544983910145871195,327722701544983914528742186⟩⟩,⟨⟨(-2849417364497204849497673138),(-2849417364497204845177649043)⟩,⟨376445253075901296085366694,376445253075901300377131005⟩⟩,⟨⟨(-2768771652476909692356341206),(-2768771652476909688127223463)⟩,⟨422669628892076278015993677,422669628892076282216496129⟩⟩,⟨⟨(-2688567298858720947371196152),(-2688567298858720943231708897)⟩,⟨466414152234032807751635312,466414152234032811862199040⟩⟩,⟨⟨(-2608875584122984988689849906),(-2608875584122984984640352659)⟩,⟨507701034687119851546214939,507701034687119855566528507⟩⟩,⟨⟨(-2529766102850242461561734323),(-2529766102850242457600620898)⟩,⟨546556240180634041142018967,546556240180634045073733352⟩⟩,⟨⟨(-2451306608803767100957378223),(-2451306608803767097084702197)⟩,⟨583009340875854245124107874,583009340875854248967215105⟩⟩,⟨⟨(-2373562868416118104831626662),(-2373562868416118101045930860)⟩,⟨617093365559754157156084888,617093365559754160912084745⟩⟩,⟨⟨(-2296598523120626563451410110),(-2296598523120626559752868661)⟩,⟨648844641186227268251724818,648844641186227271920486602⟩⟩,⟨⟨(-2220474960920757924828822591),(-2220474960920757921215699569)⟩,⟨678302628228185232598597692,678302628228185236181897037⟩⟩,⟨⟨(-2145251197540997270443903659),(-2145251197540997266916110079)⟩,⟨705509750521777405625576838,705509750521777409123543292⟩⟩,⟨⟨(-2070983767452603225609317968),(-2070983767452603222165242070)⟩,⟨730511220298154031895173919,730511220298154035309456397⟩⟩] +lemma kernel7_0_r4_5_eq : ∀ k : Fin 16, kernel7_0Expr 4 5 k = kernel7_0_r4_5 k := by decide +kernel +noncomputable def kernel7_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-1997726625016583777501023795),(-1997726625016583774140763813)⟩,⟨753354859108612384821206884,753354859108612388151745319⟩⟩,⟨⟨(-1925531055934878056148517451),(-1925531055934878052870134580)⟩,⟨774090915355604812328676233,774090915355604815577443286⟩⟩,⟨⟨(-1854445599149295578185110874),(-1854445599149295574988385329)⟩,⟨792771879144957214827416965,792771879144957217994667348⟩⟩,⟨⟨(-1784515979276577917734727201),(-1784515979276577914617922418)⟩,⟨809452295173779112470976371,809452295173779115558477855⟩⟩,⟨⟨(-1715785049617310331320277181),(-1715785049617310328283311603)⟩,⟨824188574364000765545338970,824188574364000768553205399⟩⟩,⟨⟨(-1648292745726617091312712235),(-1648292745726617088353594892)⟩,⟨837038804943332110752690239,837038804943332113682940403⟩⟩,⟨⟨(-1582076049485908098241345617),(-1582076049485908095358811974)⟩,⟨848062563663809594473876493,848062563663809597328700650⟩⟩,⟨⟨(-1517168963567677010013836233),(-1517168963567677007205778155)⟩,⟨857320727833109880038201870,857320727833109882819997294⟩⟩,⟨⟨(-1453602496139739369649384228),(-1453602496139739366915724250)⟩,⟨864875288815614608940477758,864875288815614611649281503⟩⟩,⟨⟨(-1391404655611583488525607416),(-1391404655611583485864290662)⟩,⟨870789167638978281287534017,870789167638978283925357466⟩⟩,⟨⟨(-1330600455183909775041527815),(-1330600455183909772452180898)⟩,⟨875126033317870238223436657,875126033317870240790612299⟩⟩,⟨⟨(-1271211926923159201481495471),(-1271211926923159198962287074)⟩,⟨877950124479836200949376645,877950124479836203447692859⟩⟩,⟨⟨(-1213258145046061679955867972),(-1213258145046061677506574188)⟩,⟨879326074849073631220807118,879326074849073633650447332⟩⟩,⟨⟨(-1156755258065131874218230544),(-1156755258065131871836797408)⟩,⟨879318743112569371544604019,879318743112569373907579394⟩⟩,⟨⟨(-1101716529414742815832727182),(-1101716529414742813518694476)⟩,⟨877993047659748836281278187,877993047659748838578008590⟩⟩,⟨⟨(-1048152386149033250586065747),(-1048152386149033248337566059)⟩,⟨875413806651782769061012806,875413806651782771293323792⟩⟩] +lemma kernel7_0_r4_6_eq : ∀ k : Fin 16, kernel7_0Expr 4 6 k = kernel7_0_r4_6 k := by decide +kernel +noncomputable def kernel7_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-996070475277546391897543395),(-996070475277546389714328108)⟩,⟨871645583840245502102611835,871645583840245504270712588⟩⟩,⟨⟨(-945475727282225863179231297),(-945475727282225861059170175)⟩,⟨866752540517176779938826718,866752540517176782044806182⟩⟩,⟨⟨(-896370426340255955678472792),(-896370426340255953621036517)⟩,⟨860798293940028230556400536,860798293940028232600749129⟩⟩,⟨⟨(-848754286761251764512319147),(-848754286761251762515633784)⟩,⟨853845782535735730040295757,853845782535735732024847525⟩⟩,⟨⟨(-802624535134481549260673616),(-802624535134481547324366939)⟩,⟨845957138148507986686517257,845957138148507988611606731⟩⟩,⟨⟨(-757975997672118078853812908),(-757975997672118076975827299)⟩,⟨837193565556113003629396199,837193565556113005497042168⟩⟩,⟨⟨(-714801192227925868684186861),(-714801192227925866863942109)⟩,⟨827615229439724693607941780,827615229439724695418687754⟩⟩,⟨⟨(-673090424467234988618915772),(-673090424467234986853948008)⟩,⟨817281148953000772292098808,817281148953000774048371260⟩⟩,⟨⟨(-632831887663448291836877856),(-632831887663448290123993788)⟩,⟨806249099997229392008459873,806249099997229393713416029⟩⟩,⟨⟨(-594011765598578396455293141),(-594011765598578394792611781)⟩,⟨794575525271323820756746771,794575525271323822412231802⟩⟩,⟨⟨(-556614338050297946534977949),(-556614338050297944922068077)⟩,⟨782315452128367266561393295,782315452128367268167804542⟩⟩,⟨⟨(-520622088355580940336769992),(-520622088355580938771994394)⟩,⟨769522418234505350672539169,769522418234505352231479882⟩⟩,⟨⟨(-486015812551070092039513542),(-486015812551070090522594335)⟩,⟨756248404991428566601915727,756248404991428568113631557⟩⟩,⟨⟨(-452774729602669245448321496),(-452774729602669243977463674)⟩,⟨742543778650642432118011444,742543778650642433584265058⟩⟩,⟨⟨(-420876592251364506107901598),(-420876592251364504682642396)⟩,⟨728457239016333628544962736,728457239016333629966186189⟩⟩,⟨⟨(-390297798018748176683141822),(-390297798018748175301886052)⟩,⟨714035775604033938845760957,714035775604033940223519012⟩⟩] +lemma kernel7_0_r4_7_eq : ∀ k : Fin 16, kernel7_0Expr 4 7 k = kernel7_0_r4_7 k := by decide +kernel +noncomputable def kernel7_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-361013499933974098938655090),(-361013499933974097601145767)⟩,⟨699324631094570616918527421,699324631094570618253048117⟩⟩,⟨⟨(-332997716563724805526720898),(-332997716563724804231167176)⟩,⟨684367271897064775208200663,684367271897064776501246165⟩⟩,⟨⟨(-306223440948029675569047396),(-306223440948029674314968833)⟩,⟨669205365611073710399884585,669205365611073711651908024⟩⟩,⟨⟨(-280662748067246948000443990),(-280662748067246946786305394)⟩,⟨653878765156426570744025687,653878765156426571956535532⟩⟩,⟨⟨(-256286900489018612282598102),(-256286900489018611108069400)⟩,⟨638425499319915970210818336,638425499319915971384119108⟩⟩,⟨⟨(-233066451868334787829200839),(-233066451868334786692622840)⟩,⟨622881769450804839534570177,622881769450804840670296176⟩⟩,⟨⟨(-210971347998814874518822565),(-210971347998814873419709957)⟩,⟨607281952022095473044322265,607281952022095474142934963⟩⟩,⟨⟨(-189971025138742255169361545),(-189971025138742254106253385)⟩,⟨591658606761678275590878486,591658606761678276653815819⟩⟩,⟨⟨(-170034505361098764696850651),(-170034505361098763669446971)⟩,⟨576042490046808186071988330,576042490046808187099528128⟩⟩,⟨⟨(-151130488702662138098674890),(-151130488702662137105366460)⟩,⟨560462573246810222284065084,560462573246810223277795396⟩⟩,⟨⟨(-133227441912989407564155972),(-133227441912989406604463567)⟩,⟨544946065692442090013389182,544946065692442090973768807⟩⟩,⟨⟨(-116293683629655436880681783),(-116293683629655435953230107)⟩,⟨529518441945879341425490448,529518441945879342353875272⟩⟩,⟨⟨(-100297465831301471853856913),(-100297465831301470958309097)⟩,⟨514203473042764221135883043,514203473042764222032591110⟩⟩,⟨⟨(-85207051444736766447303705),(-85207051444736765582189880)⟩,⟨499023261377090339695924235,499023261377090340562407768⟩⟩,⟨⟨(-70990788006400605671906843),(-70990788006400604836763234)⟩,⟨483998278900790217856785155,483998278900790218693490749⟩⟩,⟨⟨(-57617177301816995790009982),(-57617177301816994983002391)⟩,⟨469147408312652587756454622,469147408312652588565200083⟩⟩] +lemma kernel7_0_r4_8_eq : ∀ k : Fin 16, kernel7_0Expr 4 8 k = kernel7_0_r4_8 k := by decide +kernel +noncomputable def kernel7_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-45054940929155881098858182),(-45054940929155880318592161)⟩,⟨454487986915515810057800259,454487986915515810839963577⟩⟩,⟨⟨(-33273081754560477052562589),(-33273081754560476297729963)⟩,⟨440035852826452378928749228,440035852826452379685624306⟩⟩,⟨⟨(-22240941247429331347375976),(-22240941247429330617634080)⟩,⟨425805393231762716684418296,425805393231762717416333705⟩⟩,⟨⟨(-11928252703284822520372176),(-11928252703284821814627742)⟩,⟨411809594386916871570728801,411809594386916872278764947⟩⟩,⟨⟨(-2305190380159285625110855),(-2305190380159284943147342)⟩,⟨398060093071001061799572529,398060093071001062483933151⟩⟩,⟨⟨6657585408460564068187861,6657585408460564727544222⟩,⟨384567229215622202674963365,384567229215622203336810879⟩⟩,⟨⟨14988887185206118718404018,14988887185206119355478509⟩,⟨371340099439477753274730230,371340099439477753914378528⟩⟩,⟨⟨22716963111357448234027199,22716963111357448849829380⟩,⟨358386611231791688208554792,358386611231791688827003314⟩⟩,⟨⟨29869463613403690777706634,29869463613403691372411761⟩,⟨345713537540433385301810053,345713537540433385899223750⟩⟩,⟨⟨36473411734605004223440282,36473411734605004798160061⟩,⟨333326571533660743588632441,333326571533660744166114284⟩⟩,⟨⟨42555177101692964390108246,42555177101692964945146500⟩,⟨321230381317951424157275324,321230381317951424715120129⟩⟩,⟨⟨48140453387263765194241731,48140453387263765730523147⟩,⟨309428664408200393760001172,309428664408200394299125897⟩⟩,⟨⟨53254239140067672004161364,53254239140067672521876307⟩,⟨297924201760566307730312664,297924201760566308250899604⟩⟩,⟨⟨57920821848250994481007338,57920821848250994981143476⟩,⟨286718911192347249665937683,286718911192347250168967968⟩⟩,⟨⟨62163765094628949609699927,62163765094628950092536721⟩,⟨275813900027367113350739273,275813900027367113836485409⟩⟩,⟨⟨66005898658218928391361289,66005898658218928857739569⟩,⟨265209516819372574509770865,265209516819372574979067986⟩⟩] +lemma kernel7_0_r4_9_eq : ∀ k : Fin 16, kernel7_0Expr 4 9 k = kernel7_0_r4_9 k := by decide +kernel +noncomputable def kernel7_0_r4_10 : Fin 16 → CBox := ![⟨⟨69469311412498492114838802,69469311412498492565772093⟩,⟨254905402019798470020039157,254905402019798470473893682⟩⟩,⟨⟨72575346868121120278089553,72575346868121120714554116⟩,⟨244900537469884191266857198,244900537469884191706240754⟩⟩,⟨⟨75344601206071799622391464,75344601206071800044584101⟩,⟨235193294610449637177556221,235193294610449637602660474⟩⟩,⟨⟨77796923646417418091717376,77796923646417418500345475⟩,⟨225781481315607168401803903,225781481315607168813332312⟩⟩,⟨⟨79951418997844646425104829,79951418997844646820267987⟩,⟨216662387269243237278534731,216662387269243237676582350⟩⟩,⟨⟨81826452234019820535158337,81826452234019820917619926⟩,⟨207832827815203831093515480,207832827815203831478842616⟩⟩,⟨⟨83439654944389373815019717,83439654944389374184956448⟩,⟨199289186223721851252262777,199289186223721851625042418⟩⟩,⟨⟨84807933509303094749621719,84807933509303095107673539⟩,⟨191027454327698591608339258,191027454327698591969208777⟩⟩,⟨⟨85947478852223304516409417,85947478852223304862639302⟩,⟨183043271492968148062025478,183043271492968148411044531⟩⟩,⟨⟨86873777625218770889765199,86873777625218771224887658⟩,⟨175331961896611262631591115,175331961896611262969472412⟩⟩,⟨⟨87601624687871462390548516,87601624687871462714720154⟩,⟨167888570096727683789005254,167888570096727684115902812⟩⟩,⟨⟨88145136744087024377624637,88145136744087024691421351⟩,⟨160707894885812750639893893,160707894885812750956382116⟩⟩,⟨⟨88517767006037675223393779,88517767006037675526971529⟩,⟨153784521428008637106434857,153784521428008637412629394⟩⟩,⟨⟨88732320759522570080457576,88732320759522570374576657⟩,⟨147112851688012159219688392,147112851688012159516286661⟩⟩,⟨⟨88800971710351281330576654,88800971710351281615358232⟩,⟨140687133166322121323897403,140687133166322121611026216⟩⟩,⟨⟨88735278996889080728642603,88735278996889081004587910⟩,⟨134501485961806597919718087,134501485961806598197884895⟩⟩] +lemma kernel7_0_r4_10_eq : ∀ k : Fin 16, kernel7_0Expr 4 10 k = kernel7_0_r4_10 k := by decide +kernel +noncomputable def kernel7_0_r4_11 : Fin 16 → CBox := ![⟨⟨88546204759599021209661148,88546204759599021476789478⟩,⟨128549928188274573979282475,128549928188274574248511665⟩⟩,⟨⟨88244132164229068276605924,88244132164229068535488713⟩,⟨122826399776860407956953759,122826399776860408217822743⟩⟩,⟨⟨87838883781179324931390262,87838883781179325182132920⟩,⟨117324784700589843598216871,117324784700589843850835967⟩⟩,⟨⟨87339740229504360990686973,87339740229504361233738270⟩,⟨112038931661511427143813770,112038931661511427388637116⟩⟩,⟨⟨86755458999921509545119649,86755458999921509780513132⟩,⟨106962673284267933696800723,106962673284267933933866310⟩⟩,⟨⟨86094293377073546890785852,86094293377073547119011953⟩,⟨102089843862971286501004820,102089843862971286730808162⟩⟩,⟨⟨85364011387102343529915464,85364011387102343751064511⟩,⟨97414295710755431772327545,97414295710755431994963191⟩⟩,⟨⟨84571914702300847388186714,84571914702300847602659342⟩,⟨92929914163439822567469116,92929914163439822783342278⟩⟩,⟨⟨83724857440199135577655403,83724857440199135785458067⟩,⟨88630631290367541916347248,88630631290367542125468157⟩⟩,⟨⟨82829264799884187413550475,82829264799884187615140398⟩,⟨84510438366713224663250608,84510438366713224866080826⟩⟩,⟨⟨81891151483633276410891110,81891151483633276606344574⟩,⟨80563397162413729132865538,80563397162413729329484938⟩⟩,⟨⟨80916139857040979891834955,80916139857040980081508628⟩,⟨76783650103385987243578919,76783650103385987434348031⟩⟩,⟨⟨79909477805725907721409171,79909477805725907905317475⟩,⟨73165429360888551829800170,73165429360888552014736643⟩⟩,⟨⟨78876056251403989571197604,78876056251403989749733769⟩,⟨69703064924782702644569689,69703064924782702824070369⟩⟩,⟨⟨77820426294601512640185336,77820426294601512813412677⟩,⟨66390991716081750605080280,66390991716081750779211510⟩⟩,⟨⟨76746815955546248310283322,76746815955546248478518853⟩,⟨63223755793568968075128061,63223755793568968244210084⟩⟩] +lemma kernel7_0_r4_11_eq : ∀ k : Fin 16, kernel7_0Expr 4 11 k = kernel7_0_r4_11 k := by decide +kernel +noncomputable def kernel7_0_r4_12 : Fin 16 → CBox := ![⟨⟨75659146488814174637760079,75659146488814174800990252⟩,⟨60196019708440206371667418,60196019708440206535689371⟩⟩,⟨⟨74561048251119614138991940,74561048251119614297588390⟩,⟨57302567059910722119021549,57302567059910722278358106⟩⟩,⟨⟨73455876105216924754834691,73455876105216924908849047⟩,⟨54538306303540054779362662,54538306303540054934067980⟩⟩,⟨⟨72346724346232652794780886,72346724346232652944494499⟩,⟨51898273862695984421532110,51898273862695984571890221⟩⟩,⟨⟨71236441139870159012686053,71236441139870159158097293⟩,⟨49377636592119567144710881,49377636592119567290722409⟩⟩,⟨⟨70127642464827324343813731,70127642464827324485236862⟩,⟨46971693640987773053758490,46971693640987773195740186⟩⟩,⟨⟨69022725554446329089161540,69022725554446329226637689⟩,⟨44675877761216943848323314,44675877761216943986318403⟩⟩,⟨⟨67923881835077974040560575,67923881835077974174339431⟩,⟨42485756105026556354424040,42485756105026556488684416⟩⟩,⟨⟨66833109360897731886688060,66833109360897732016748040⟩,⟨40397030554004834643990958,40397030554004834774496895⟩⟩,⟨⟨65752224746963573678067982,65752224746963573804703825⟩,⟨38405537620100605386633841,38405537620100605513682125⟩⟩,⟨⟨64682874604164112065115816,64682874604164112188359419⟩,⟨36507247957123256893315001,36507247957123257016939260⟩⟩,⟨⟨63626546481377742646106991,63626546481377742766179973⟩,⟨34698265519477388717550920,34698265519477388837974570⟩⟩,⟨⟨62584579321657641046368721,62584579321657641163256787⟩,⟨32974826403002227773026153,32974826403002227890236439⟩⟩,⟨⟨61558173440582373128030419,61558173440582373241985567⟩,⟨31333297400938529079197277,31333297400938529193447851⟩⟩,⟨⟨60548400036076387668971469,60548400036076387780017511⟩,⟨29770174306216791635434371,29770174306216791746750464⟩⟩,⟨⟨59556210240017792060192964,59556210240017792168526903⟩,⟨28282079989458489460042514,28282079989458489568622585⟩⟩] +lemma kernel7_0_r4_12_eq : ∀ k : Fin 16, kernel7_0Expr 4 12 k = kernel7_0_r4_12 k := by decide +kernel +noncomputable def kernel7_0_r4_13 : Fin 16 → CBox := ![⟨⟨58582443722821612006467948,58582443722821612112055672⟩,⟨26865762280313947882453888,26865762280313947988265083⟩⟩,⟨⟨57627836862924230470183617,57627836862924230573266621⟩,⟨25518091678032855047412638,25518091678032855150697793⟩⟩,⟨⟨56693030493707827629472626,56693030493707827730067792⟩,⟨24236058915481675235884961,24236058915481675336662115⟩⟩,⟨⟨55778577240901200902300980,55778577240901201000583729⟩,⟨23016772399191081692480551,23016772399191081790926300⟩⟩,⟨⟨54884948463883943628396822,54884948463883943724343424⟩,⟨21857455546439834539266971,21857455546439834635358618⟩⟩,⟨⟨54012540814612986674964795,54012540814612986768779373⟩,⟨20755444038862455267206447,20755444038862455361149180⟩⟩,⟨⟨53161682428092080787459195,53161682428092080879152685⟩,⟨19708183010609087327577297,19708183010609087419382998⟩⟩,⟨⟨52332638758423749657162053,52332638758423749746891193⟩,⟨18713224187688962726068502,18713224187688962815894846⟩⟩,⟨⟨51525618074527090612610607,51525618074527090700337298⟩,⟨17768222993795235908997721,17768222993795235996807452⟩⟩,⟨⟨50740776629580724552730899,50740776629580724638650914⟩,⟨16870935636639406514280207,16870935636639406600269950⟩⟩,⟨⟨49978223518165034967884261,49978223518165035052003576⟩,⟨16019216187618478096887114,16019216187618478181063608⟩⟩,⟨⟨49238025234938066119807035,49238025234938066202266200⟩,⟨15211013666497322787227530,15211013666497322869732074⟩⟩,⟨⟨48520209948491187719583833,48520209948491187800352382⟩,⟨14444369141712004996069140,14444369141712005076871958⟩⟩,⟨⟨47824771503799626475840996,47824771503799626555087223⟩,⟨13717412855886297572440178,13717412855886297651710230⟩⟩,⟨⟨47151673166414596292354212,47151673166414596370079943⟩,⟨13028361385202252564538300,13028361385202252642278039⟩⟩,⟨⟨46500851121243047951072304,46500851121243048027404247⟩,⟨12375514840375169848170872,12375514840375169924507595⟩⟩] +lemma kernel7_0_r4_13_eq : ∀ k : Fin 16, kernel7_0Expr 4 13 k = kernel7_0_r4_13 k := by decide +kernel +noncomputable def kernel7_0_r4_14 : Fin 16 → CBox := ![⟨⟨45872217738432666963242860,45872217738432667038135018⟩,⟨11757254116152132644373944,11757254116152132719262220⟩⟩,⟨⟨45265664618527985034609307,45265664618527985108229094⟩,⟨11172038195479763139033991,11172038195479763212641756⟩⟩,⟨⟨44681065428692304309896101,44681065428692304382242018⟩,⟨10618401513769160127412078,10618401513769160199738342⟩⟩,⟨⟨44118278541403200470125369,44118278541403200541312259⟩,⟨10094951388022160449406967,10094951388022160520567039⟩⟩,⟨⟨43577149486629986830916936,43577149486629986900909759⟩,⟨9600365514971070015387551,9600365514971070085346855⟩⟩,⟨⟨43057513228092694963952799,43057513228092695032893820⟩,⟨9133389541821721435503145,9133389541821721504404354⟩⟩,⟨⟨42559196273786571556109493,42559196273786571623994535⟩,⟨8692834712674967879594266,8692834712674967947433617⟩⟩,⟨⟨42082018630536238817137652,42082018630536238884071587⟩,⟨8277575593232321304954185,8277575593232321371836918⟩⟩,⟨⟨41625795611921682519129942,41625795611921682585066566⟩,⟨7886547875965179394241657,7886547875965179460121956⟩⟩,⟨⟨41190339508496030898780201,41190339508496030963861500⟩,⟨7518746267541753516428824,7518746267541753581448989⟩⟩,⟨⟨40775461128794344180503070,40775461128794344244722849⟩,⟨7173222459959219264537138,7173222459959219328691314⟩⟩,⟨⟨40380971219214799431305353,40380971219214799494760100⟩,⟨6849083186518597888353151,6849083186518597951738115⟩⟩,⟨⟨40006681770439970068184451,40006681770439970130836135⟩,⟨6545488363504313955974903,6545488363504314018552949⟩⟩,⟨⟨39652407217657408826414996,39652407217657408888387874⟩,⟨6261649318187179143288938,6261649318187179205184568⟩⟩,⟨⟨39317965541436310113739040,39317965541436310175025439⟩,⟨5996827103556692761734005,5996827103556692822939831⟩⟩,⟨⟨39003179275721345768019404,39003179275721345828708929⟩,⟨5750330900004051701527445,5750330900004051762133300⟩⟩] +lemma kernel7_0_r4_14_eq : ∀ k : Fin 16, kernel7_0Expr 4 14 k = kernel7_0_r4_14 k := by decide +kernel +noncomputable def kernel7_0_r4_15 : Fin 16 → CBox := ![⟨⟨38707876429016373928701385,38707876429016373988743228⟩,⟨5521516504019211864589608,5521516504019211924544967⟩⟩,⟨⟨38431891324450006046261298,38431891324450006105785100⟩,⟨5309784903831889577156160,5309784903831889636590851⟩⟩,⟨⟨38175065364042241071059794,38175065364042241130056976⟩,⟨5114580941815750289145424,5114580941815750348051109⟩⟩,⟨⟨37937247722126675782012621,37937247722126675840567154⟩,⟨4935392063385485129715407,4935392063385485188176242⟩⟩,⟨⟨37718295972526201920427667,37718295972526201978499722⟩,⟨4771747152046372479807853,4771747152046372537784249⟩⟩,⟨⟨37518076653731528798557843,37518076653731528856260230⟩,⟨4623215450203676699731623,4623215450203676757336544⟩⟩,⟨⟨37336465775991156960116654,37336465775991157017440345⟩,⟨4489405565303329450219009,4489405565303329507443637⟩⟩,⟨⟨37173349273888323827042835,37173349273888323884067404⟩,⟨4369964560854313500193152,4369964560854313557117216⟩⟩,⟨⟨37028623407654620951179897,37028623407654621007855459⟩,⟨4264577131875627772004539,4264577131875627828578376⟩⟩,⟨⟨36902195116151052531933769,36902195116151052588379100⟩,⟨4172964864315316264749609,4172964864315316321092117⟩⟩,⟨⟨36793982324134814848629162,36793982324134814904835303⟩,⟨4094885578004507021375959,4094885578004507077478368⟩⟩,⟨⟨36703914206123522222095951,36703914206123522278139101⟩,⟨4030132752734495187898728,4030132752734495243837373⟩⟩,⟨⟨36631931408867437075669714,36631931408867437131509107⟩,⟨3978535037078427171026384,3978535037078427226760703⟩⟩,⟨⟨36577986234143889685445502,36577986234143889741188119⟩,⟨3939955839619953170186487,3939955839619953225823569⟩⟩,⟨⟨36542042783295873232118425,36542042783295873287755828⟩,⟨3914293002298202038296701,3914293002298202093828287⟩⟩,⟨⟨36524077064648119025884511,36524077064648119081490541⟩,⟨3901478555630516539758065,3901478555630516595258127⟩⟩] +lemma kernel7_0_r4_15_eq : ∀ k : Fin 16, kernel7_0Expr 4 15 k = kernel7_0_r4_15 k := by decide +kernel +noncomputable def kernel7_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel7_0_r4_0,kernel7_0_r4_1,kernel7_0_r4_2,kernel7_0_r4_3,kernel7_0_r4_4,kernel7_0_r4_5,kernel7_0_r4_6,kernel7_0_r4_7,kernel7_0_r4_8,kernel7_0_r4_9,kernel7_0_r4_10,kernel7_0_r4_11,kernel7_0_r4_12,kernel7_0_r4_13,kernel7_0_r4_14,kernel7_0_r4_15] +lemma kernel7_0_r4_eq (i k : Fin 16) : kernel7_0Expr 4 i k = kernel7_0_r4 i k := by + fin_cases i + · exact kernel7_0_r4_0_eq k + · exact kernel7_0_r4_1_eq k + · exact kernel7_0_r4_2_eq k + · exact kernel7_0_r4_3_eq k + · exact kernel7_0_r4_4_eq k + · exact kernel7_0_r4_5_eq k + · exact kernel7_0_r4_6_eq k + · exact kernel7_0_r4_7_eq k + · exact kernel7_0_r4_8_eq k + · exact kernel7_0_r4_9_eq k + · exact kernel7_0_r4_10_eq k + · exact kernel7_0_r4_11_eq k + · exact kernel7_0_r4_12_eq k + · exact kernel7_0_r4_13_eq k + · exact kernel7_0_r4_14_eq k + · exact kernel7_0_r4_15_eq k +noncomputable def kernel7_0_r5_0 : Fin 16 → CBox := ![⟨⟨144341563269702510378125252227,144341563269702510570263474196⟩,⟨249213262909881333809190469580,249213262909881334006002937655⟩⟩,⟨⟨144369858883458563675494032051,144369858883458563867623032706⟩,⟨249127662238659365684904322018,249127662238659365881705113940⟩⟩,⟨⟨144426367623892238965469443916,144426367623892239157579666775⟩,⟨248956501009130081178370424667,248956501009130081375147530315⟩⟩,⟨⟨144510924675299736624716392956,144510924675299736816798260064⟩,⟨248699859501173046028657576015,248699859501173046225398967693⟩⟩,⟨⟨144623283210053782983287828362,144623283210053783175331721805⟩,⟨248357858269325708230773423306,248357858269325708427467039207⟩⟩,⟨⟨144763114863145367652664101267,144763114863145367844660358371⟩,⟨247930658303305564171139533410,247930658303305564367773274757⟩⟩,⟨⟨144930010363950536672029928938,144930010363950536863968818068⟩,⟨247418461240145267769662454762,247418461240145267966224163537⟩⟩,⟨⟨145123480324400109410757476447,145123480324400109602629206130⟩,⟨246821509626326479660970671135,246821509626326479857448141182⟩⟩,⟨⟨145342956182520814545003372600,145342956182520814736798042410⟩,⟨246140087227906686597344000653,246140087227906686793724930422⟩⟩,⟨⟨145587791300104486298476316796,145587791300104486490183964754⟩,⟨245374519386249603639258812006,245374519386249603835530854016⟩⟩,⟨⟨145857262213047207790441986986,145857262213047207982052490006⟩,⟨244525173416595652920488202161,244525173416595653116638865175⟩⟩,⟨⟨146150570032682256568473087358,146150570032682256759976279146⟩,⟨243592459046345920218996802530,243592459046345920415013571663⟩⟩,⟨⟨146466841996209068779170830046,146466841996209068970556294396⟩,⟨242576828889582425480984729975,242576828889582425676854861476⟩⟩,⟨⟨146805133164094917207744957259,146805133164094917399002299459⟩,⟨241478778954010976934984521368,241478778954010977130695316555⟩⟩,⟨⟨147164428262096378153425363145,147164428262096378344543834890⟩,⟨240298849176191747342550997665,240298849176191747538089428930⟩⟩,⟨⟨147543643665313790863336807056,147543643665313791054305743611⟩,⟨239037623980618413642156641087,239037623980618413837509791939⟩⟩] +lemma kernel7_0_r5_0_eq : ∀ k : Fin 16, kernel7_0Expr 5 0 k = kernel7_0_r5_0 k := by decide +kernel +noncomputable def kernel7_0_r5_1 : Fin 16 → CBox := ![⟨⟨147941629521453708373111891488,147941629521453708563920109562⟩,⟨237695732857920593350440048730,237695732857920593545594512238⟩⟩,⟨⟨148357172010231791061460858352,148357172010231791252097445565⟩,⟨236273850957197700980987386288,236273850957197701175930058174⟩⟩,⟨⟨148788995735601772422339598924,148788995735601772612792942811⟩,⟨234772699687246492085196790751,234772699687246492279913898142⟩⟩,⟨⟨149235766247245179636486960007,149235766247245179826745823152⟩,⟨233193047321220661619098072662,233193047321220661813576253412⟩⟩,⟨⟨149696092687501652108103238432,149696092687501652298155413129⟩,⟨231535709599060056438029272673,231535709599060056632254228974⟩⟩,⟨⟨150168530559661287478271222443,150168530559661287668105244775⟩,⟨229801550321850422213248525481,229801550321850422407206743413⟩⟩,⟨⟨150651584613278862160504520187,150651584613278862350107671692⟩,⟨227991481932123135652449387404,227991481932123135846126136183⟩⟩,⟨⟨151143711841905515663154536158,151143711841905515852514979008⟩,⟨226106466073979000709784194601,226106466073979000903165667995⟩⟩,⟨⟨151643324588367136682180649240,151643324588367136871284872570⟩,⟨224147514126821759121446221584,224147514126821759314516980723⟩⟩,⟨⟨152148793752450913866719782104,152148793752450914055555810453⟩,⟨222115687706416242339106056830,222115687706416242531852246919⟩⟩,⟨⟨152658452095593071750436244087,152658452095593071938990027188⟩,⟨220012099126943744732446436874,220012099126943744924852171392⟩⟩,⟨⟨153170597636892544032212851903,153170597636892544220471974223⟩,⟨217837911817713802701410108691,217837911817713802893461187997⟩⟩,⟨⟨153683497134508166049561770662,153683497134508166237511200684⟩,⟨215594340688207597207659952573,215594340688207597399339606457⟩⟩,⟨⟨154195389646231899005198980993,154195389646231899192826277601⟩,⟨213282652435174029976622832916,213282652435174030167916938696⟩⟩,⟨⟨154704490162768708664422615058,154704490162768708851712183551⟩,⟨210904165785575419249706035112,210904165785575419440597364186⟩⟩,⟨⟨155208993306996159894935044029,155208993306996160081873968437⟩,⟨208460251669285869540811736860,208460251669285869731285799564⟩⟩] +lemma kernel7_0_r5_1_eq : ∀ k : Fin 16, kernel7_0Expr 5 1 k = kernel7_0_r5_1 k := by decide +kernel +noncomputable def kernel7_0_r5_2 : Fin 16 → CBox := ![⟨⟨155707077092224769996966007599,155707077092224770183537421001⟩,⟨205952333315581724540993645355,205952333315581724731032050451⟩⟩,⟨⟨156196906732234962088665852809,156196906732234962274857065694⟩,⟨203381886267630025756963256273,203381886267630025946551855601⟩⟩,⟨⟨156676638495629401458939077077,156676638495629401644732767461⟩,⟨200750438309377360471677976446,200750438309377360660798040536⟩⟩,⟨⟨157144423596811954889473992153,157144423596811955074856870880⟩,⟨198059569299467553248693179694,198059569299467553437330079748⟩⟩,⟨⟨157598412115687895276568929961,157598412115687895461522213085⟩,⟨195310910907071868324060649628,195310910907071868512194314676⟩⟩,⟨⟨158036756937975720535040900006,158036756937975720719551715501⟩,⟨192506146244799147488507316034,192506146244799147676123660265⟩⟩,⟨⟨158457617707830526198286141011,158457617707830526382335290213⟩,⟨189647009394164878426010087361,189647009394164878613088752251⟩⟩,⟨⟨158859164784303735783972568724,158859164784303735967546565523⟩,⟨186735284819436707323549274457,186735284819436707510075688788⟩⟩,⟨⟨159239583193005623496525674760,159239583193005623679603450715⟩,⟨183772806666038378400253287797,183772806666038378586205352607⟩⟩,⟨⟨159597076564196922809796849875,159597076564196922992365794449⟩,⟨180761457940083369791633469953,180761457940083369976997624759⟩⟩,⟨⟨159929871048415345058807060448,159929871048415345240845987181⟩,⟨177703169566022335444698881782,177703169566022335629453045584⟩⟩,⟨⟨160236219200643447297790157898,160236219200643447479285614006⟩,⟨174599919319823461075428188808,174599919319823461259558094860⟩⟩,⟨⟨160514403823947360163067080546,160514403823947360343995849075⟩,⟨171453730635560475326143453691,171453730635560475509625127130⟩⟩,⟨⟨160762741763462733987317816230,160762741763462734167667574118⟩,⟨168266671283757676601289807165,168266671283757676784110252794⟩⟩,⟨⟨160979587641576141438215781640,160979587641576141617963290174⟩,⟨165040851920333172347364390296,165040851920333172529499753689⟩⟩,⟨⟨161163337525148269803088679296,161163337525148269982220790365⟩,⟨161778424505488695478252547432,161778424505488695659689149694⟩⟩] +lemma kernel7_0_r5_2_eq : ∀ k : Fin 16, kernel7_0Expr 5 2 k = kernel7_0_r5_2 k := by decide +kernel +noncomputable def kernel7_0_r5_3 : Fin 16 → CBox := ![⟨⟨161312432515650642951593284982,161312432515650643130084136235⟩,⟨158481580592414866652875548271,158481580592414866833587052415⟩⟩,⟨⟨161425362253141333478922566028,161425362253141333656760874888⟩,⟨155152549486212511858944219072,155152549486212512038918958217⟩⟩,⟨⟨161500668325088054938441982815,161500668325088055115602448187⟩,⟨151793596273971426522478449904,151793596273971426701690794749⟩⟩,⟨⟨161536947571159941652357548878,161536947571159941828827637862⟩,⟨148407019727495516197533636221,148407019727495516375970813058⟩⟩,⟨⟨161532855275252882888682144262,161532855275252883064433891515⟩,⟨144995150080715176585836717847,144995150080715176763470576778⟩⟩,⟨⟨161487108236187998049338162834,161487108236187998224361124590⟩,⟨141560346684381669462866269939,141560346684381669639686273916⟩⟩,⟨⟨161398487708729095665630373018,161398487708729095839897229707⟩,⟨138104995541191614285118738463,138104995541191614461097530501⟩⟩,⟨⟨161265842206802976389376155139,161265842206802976562875329229⟩,⟨134631506725040008220304655906,134631506725040008395430708673⟩⟩,⟨⟨161088090161076286050376261534,161088090161076286223077018891⟩,⟨131142311688644834491104418729,131142311688644834665347103459⟩⟩,⟨⟨160864222423344202721711704526,160864222423344202893605534132⟩,⟨127639860464322721142142840156,127639860464322721315493842173⟩⟩,⟨⟨160593304610519286220074950277,160593304610519286391169135930⟩,⟨124126618763220660009836388054,124126618763220660182303354400⟩⟩,⟨⟨160274479281372891188857125070,160274479281372891359420509664⟩,⟨120605064978820882160885340538,120605064978820882332738306035⟩⟩,⟨⟨159906967939576031408956358083,159906967939576031578957479675⟩,⟨117077687101032021628023680619,117077687101032021799231571664⟩⟩,⟨⟨159490072857010690743273715308,159490072857010690912706572213⟩,⟨113546979547657125293903965404,113546979547657125464461254196⟩⟩,⟨⟨159023178711775333784253254824,159023178711775333953087504725⟩,⟨110015439920485370258657823628,110015439920485370428534694326⟩⟩,⟨⟨158505754035788626984739601085,158505754035788627152967286777⟩,⟨106485565693687078200139216974,106485565693687078369328318327⟩⟩] +lemma kernel7_0_r5_3_eq : ∀ k : Fin 16, kernel7_0Expr 5 3 k = kernel7_0_r5_3 k := by decide +kernel +noncomputable def kernel7_0_r5_4 : Fin 16 → CBox := ![⟨⟨157937352467401812112914536157,157937352467401812280500351668⟩,⟨102959850842598391275546074024,102959850842598391444012757758⟩⟩,⟨⟨157317613804961277573791777852,157317613804961277740732052418⟩,⟨99440782421360507762450080167,99440782421360507930191412638⟩⟩,⟨⟨156646264857816978917914642333,156646264857816979084176476357⟩,⟨95930837098226483729565522172,95930837098226483896549391542⟩⟩,⟨⟨155923120091847632681869208130,155923120091847632847445954230⟩,⟨92432477657664223723224117552,92432477657664223889444735893⟩⟩,⟨⟨155148082067168054755440725239,155148082067168054920294831843⟩,⟨88948149478665475139486633110,88948149478665475304907358995⟩⟩,⟨⟨154321141666295493050287022990,154321141666295493214416108582⟩,⟨85480276998915619647053723107,85480276998915619811673153767⟩⟩,⟨⟨153442378111678030932735824104,153442378111678031096104632737⟩,⟨82031260174686191243695361011,82031260174686191407479268899⟩⟩,⟨⟨152511958772126698855266111442,152511958772126699017869697632⟩,⟨78603470946479885417797139617,78603470946479885580741668609⟩⟩,⟨⟨151530138758341294133508278867,151530138758341294295305435704⟩,⟨75199249720585080607633515535,75199249720585080769698597726⟩⟩,⟨⟨150497260308375433752777413048,150497260308375433913769090048⟩,⟨71820901876782487340845461065,71820901876782487502033240243⟩⟩,⟨⟨149413751964546320544825107326,149413751964546320704973948811⟩,⟨68470694312489589695813581733,68470694312489589856087945197⟩⟩,⟨⟨148280127543956278859431840704,148280127543956279018734994857⟩,⟨65150852033628376004065432817,65150852033628376163424819081⟩⟩,⟨⟨147096984905453438859900863022,147096984905453439018315477851⟩,⟨61863554802458016534241057363,61863554802458016692643954090⟩⟩,⟨⟨145865004516515098884297439513,145865004516515099041826442124⟩,⟨58610933852526404321637038494,58610933852526404479087750850⟩⟩,⟨⟨144584947824186322996728661357,144584947824186323153332900693⟩,⟨55395068680762828571452247870,55395068680762828727913051574⟩⟩,⟨⟨143257655434845273237419923332,143257655434845273393099019224⟩,⟨52217983926558726825043558095,52217983926558726980515530798⟩⟩] +lemma kernel7_0_r5_4_eq : ∀ k : Fin 16, kernel7_0Expr 5 4 k = kernel7_0_r5_4 k := by decide +kernel +noncomputable def kernel7_0_r5_5 : Fin 16 → CBox := ![⟨⟨141884045108192675506597477550,141884045108192675661304983876⟩,⟨49081646347464924224226932534,49081646347464924378665136256⟩⟩,⟨⟨140465109571472739841830669542,140465109571472739995574146452⟩,⟨45987961900872711161569449203,45987961900872711314982970022⟩⟩,⟨⟨139001914160523906638575643259,139001914160523906791314495253⟩,⟨42938772940743462127195791763,42938772940743462279545610144⟩⟩,⟨⟨137495594294827136097115354406,137495594294827136248852018484⟩,⟨39935855538108415998516288234,39935855538108416149806429496⟩⟩,⟨⟨135947352794264342358856253833,135947352794264342509543805375⟩,⟨36980916933678104006910344106,36980916933678104157095523425⟩⟩,⟨⟨134358457045817335291796056646,134358457045817335441444254720⟩,⟨34075593130481328231889826787,34075593130481328380981439307⟩⟩,⟨⟨132730236028925723417022610115,132730236028925723565589788385⟩,⟨31221446633998374872868477706,31221446633998375020826544923⟩⟩,⟨⟨131064077208678232529227786020,131064077208678232676719516789⟩,⟨28419964346764310076488356339,28419964346764310223320130075⟩⟩,⟨⟨129361423306433533714276605305,129361423306433533860643011104⟩,⟨25672555623897961970629563098,25672555623897962116286900868⟩⟩,⟨⟨127623768957851840799569387574,127623768957851840944825601642⟩,⟨22980550495462932117317368512,22980550495462932261817108166⟩⟩,⟨⟨125852657268665295984088900791,125852657268665296128192589312⟩,⟨20345198060991262258899258253,20345198060991262402200826832⟩⟩,⟨⟨124049676278821768275243000251,124049676278821768418203131686⟩,⟨17767665060900921143002802957,17767665060900921285116899358⟩⟩,⟨⟨122216455345901599149462896426,122216455345901599291230010838⟩,⟨15249034628917922783473612298,15249034628917922924352565670⟩⟩,⟨⟨120354661458928713297632549893,120354661458928713438224403511⟩,⟨12790305228975614862627978898,12790305228975615002291280190⟩⟩,⟨⟨118465995493875261875553289538,118465995493875262014927285109⟩,⟨10392389779410561447732509289,10392389779410561586139356083⟩⟩,⟨⟨116552188422291704754011066242,116552188422291704892179777781⟩,⟨8056114966609651020385921315,8056114966609651157550629065⟩⟩] +lemma kernel7_0_r5_5_eq : ∀ k : Fin 16, kernel7_0Expr 5 5 k = kernel7_0_r5_5 k := by decide +kernel +noncomputable def kernel7_0_r5_6 : Fin 16 → CBox := ![⟨⟨114614997484581327909522219381,114614997484581328046433350417⟩,⟨5782220749589819140300489390,5782220749589819276172569817⟩⟩,⟨⟨112656202339479236115700695367,112656202339479236251378495791⟩,⟨3571360056313362342012235871,3571360056313362476617660931⟩⟩,⟨⟨110677601201290709495524550028,110677601201290709629926570959⟩,⟨1424098671861540906716321682,1424098671861541040014433322⟩⟩,⟨⟨108681006976392563238957323420,108681006976392563372099880187⟩,⟨(-659084682089665128032293408),(-659084682089664996023465617)⟩⟩,⟨⟨106668243410404148856886072644,106668243410404148988718853922⟩,⟨(-2677798077721871288571685754),(-2677798077721871157900667537)⟩⟩,⟨⟨104641141257292475032340370725,104641141257292475162889762740⟩,⟨(-4631735923350979356351677870),(-4631735923350979226990405902)⟩⟩,⟨⟨102601534481489441689885761262,102601534481489441819109849406⟩,⟨(-6520678320079406034456389023),(-6520678320079405906445026746)⟩⟩,⟨⟨100551256503869445416008959995,100551256503869445543927874804⟩,⟨(-8344490236015511823746511637),(-8344490236015511697063276734)⟩⟩,⟨⟨98492136502163932005987664647,98492136502163932132670932399⟩,⟨(-10103120501874987678256249492),(-10103120501874987552829764866)⟩⟩,⟨⟨96425995776077369574115967396,96425995776077369699635666981⟩,⟨(-11796600632381713963630039509),(-11796600632381713839386601474)⟩⟩,⟨⟨94354644187018333034145710294,94354644187018333158457821899⟩,⟨(-13425043478465219786367708526),(-13425043478465219663349667197)⟩⟩,⟨⟨92279876681971868918150712162,92279876681971869041276279354⟩,⟨(-14988641715805681798009146224),(-14988641715805681676193909174)⟩⟩,⟨⟨90203469910617178154419401660,90203469910617178276305597128⟩,⟨(-16487666175802912731309913083),(-16487666175802912610748669836)⟩⟩,⟨⟨88127178944340217808656334879,88127178944340217929335302754⟩,⟨(-17922464025540680161232660248),(-17922464025540680041891788847)⟩⟩,⟨⟨86052734105306544458392203247,86052734105306544577820723047⟩,⟨(-19293456803779833916678598216),(-19293456803779833798599748739)⟩⟩,⟨⟨83981837913248208371358742706,83981837913248208489561531204⟩,⟨(-20601138320441176400631601251),(-20601138320441176283788627264)⟩⟩] +lemma kernel7_0_r5_6_eq : ∀ k : Fin 16, kernel7_0Expr 5 6 k = kernel7_0_r5_6 k := by decide +kernel +noncomputable def kernel7_0_r5_7 : Fin 16 → CBox := ![⟨⟨81916162157082491358166013307,81916162157082491475087796242⟩,⟨(-21846072427430066017346193363),(-21846072427430065901792835562)⟩⟩,⟨⟨79857345097922602230210984561,79857345097922602345891010710⟩,⟨(-23028890669007903080161139187),(-23028890669007902965856808396)⟩⟩,⟨⟨77806988809464031568718547115,77806988809464031683114742942⟩,⟨(-24150289820229641271086333606),(-24150289820229641158071655085)⟩⟩,⟨⟨75766656661138121411806436403,75766656661138121524947102360⟩,⟨(-25211029322240261022505519727),(-25211029322240260910750903318)⟩⟩,⟨⟨73737870948819575538094946897,73737870948819575649928569272⟩,⟨(-26211928623455936854176917461),(-26211928623455936743732477843)⟩⟩,⟨⟨71722110677260203302008871781,71722110677260203412575737173⟩,⟨(-27153864435846871392687404905),(-27153864435846871283511660365)⟩⟩,⟨⟨69720809497800246858677635718,69720809497800246967937104981⟩,⟨(-28037767915688137566620655820),(-28037767915688137458752936785)⟩⟩,⟨⟨67735353804284272342015523192,67735353804284272449999337222⟩,⟨(-28864621778252289532984888674),(-28864621778252289426392319508)⟩⟩,⟨⟨65767080989483866996520548013,65767080989483867103206104824⟩,⟨(-29635457355983130751783415857),(-29635457355983130646446376159)⟩⟩,⟨⟨63817277863707287100152371532,63817277863707287205595694320⟩,⟨(-30351351609714254573730944641),(-30351351609714254469580067926)⟩⟩,⟨⟨61887179236659692067859653452,61887179236659692172020308351⟩,⟨(-31013424102479414704482321317),(-31013424102479414601559044955)⟩⟩,⟨⟨59977966663009542815737756664,59977966663009542918649229286⟩,⟨(-31622833945405274017386713597),(-31622833945405273915658704977)⟩⟩,⟨⟨58090767351519903185137659059,58090767351519903286749563186⟩,⟨(-32180776725081663524720326721),(-32180776725081663424238990622)⟩⟩,⟨⟨56226653237020413617061650191,56226653237020413717420045704⟩,⟨(-32688481421671400721844464681),(-32688481421671400622564936890)⟩⟩,⟨⟨54386640213929129118867131117,54386640213929129217933512309⟩,⟨(-33147207326852396940612888417),(-33147207326852396842574738481)⟩⟩,⟨⟨52571687529485609335304273052,52571687529485609433115136648⟩,⟨(-33558240970480830165366045602),(-33558240970480830068533969728)⟩⟩] +lemma kernel7_0_r5_7_eq : ∀ k : Fin 16, kernel7_0Expr 5 7 k = kernel7_0_r5_7 k := by decide +kernel +noncomputable def kernel7_0_r5_8 : Fin 16 → CBox := ![⟨⟨50782697334329843171658124307,50782697334329843268161143375⟩,⟨(-33922893064627337053892142807),(-33922893064627336958319530183)⟩⟩,⟨⟨49020514387557844463262837746,49020514387557844558510968873⟩,⟨(-34242495473370395885472281033),(-34242495473370395791107400839)⟩⟩,⟨⟨47285925912905954328828687584,47285925912905954422785529410⟩,⟨(-34518398216434371846470478809),(-34518398216434371753350830682)⟩⟩,⟨⟨45579661602263732850517127119,45579661602263732943221867763⟩,⟨(-34751966514436233374434961660),(-34751966514436233282522563420)⟩⟩,⟨⟨43902393762291330894156482888,43902393762291330985562371249⟩,⟨(-34944577883156977609106815144),(-34944577883156977518449509679)⟩⟩,⟨⟨42254737599522720964712150589,42254737599522721054871199553⟩,⟨(-35097619283883660523514068748),(-35097619283883660434061061469)⟩⟩,⟨⟨40637251638972254629617074267,40637251638972254718495081809⟩,⟨(-35212484336478014068710943997),(-35212484336478013980497545308)⟩⟩,⟨⟨39050438270929623683333382405,39050438270929623770971891608⟩,⟨(-35290570601420397627477619315),(-35290570601420397540463480373)⟩⟩,⟨⟨37494744420328152547467164974,37494744420328152633818393706⟩,⟨(-35333276936655754241344545854),(-35333276936655754155578538417)⟩⟩,⟨⟨35970562332803960134880531703,35970562332803960220001975978⟩,⟨(-35342000934633817874572860765),(-35342000934633817789998685221)⟩⟩,⟨⟨34478230471329222615346941963,34478230471329222699206661854⟩,⟨(-35318136444491538926490428396),(-35318136444491538843141121155)⟩⟩,⟨⟨33018034517101672169453753401,33018034517101672252095254032⟩,⟨(-35263071183874036103076578339),(-35263071183874036020909794932)⟩⟩,⟨⟨31590208468204519675616144439,31590208468204519756996854932⟩,⟨(-35178184444433785422317443137),(-35178184444433785341376827852)⟩⟩,⟨⟨30194935829415946976314146227,30194935829415947056490347020⟩,⟨(-35064844894588615831567718404),(-35064844894588615751798138045)⟩⟩,⟨⟨28832350886444756643534472331,28832350886444756722476477370⟩,⟨(-34924408482659728587202080249),(-34924408482659728508634286300)⟩⟩,⟨⟨27502540057798106051685381209,27502540057798106129438265479⟩,⟨(-34758216443053652868793394448),(-34758216443053652791383420480)⟩⟩] +lemma kernel7_0_r5_8_eq : ∀ k : Fin 16, kernel7_0Expr 5 8 k = kernel7_0_r5_8 k := by decide +kernel +noncomputable def kernel7_0_r5_9 : Fin 16 → CBox := ![⟨⟨26205543317447741619694003612,26205543317447741696213446335⟩,⟨(-34567593407698965505629415332),(-34567593407698965429422616205)⟩⟩,⟨⟨24941355681451893346663860170,24941355681451893422011559233⟩,⟨(-34353845624501813420024525506),(-34353845624501813344960290657)⟩⟩,⟨⟨23709928751709956529675135463,23709928751709956603823629273⟩,⟨(-34118259284145751550269485749),(-34118259284145751476376295210)⟩⟩,⟨⟨22511172310075117685113238396,22511172310075117758108745452⟩,⟨(-33862098956132998810049122218),(-33862098956132998737281799009)⟩⟩,⟨⟨21344955956124901514482593915,21344955956124901586286863857⟩,⟨(-33586606134547648680862118948),(-33586606134547648609259898737)⟩⟩,⟨⟨20211110781989849255035777636,20211110781989849325707510566⟩,⟨(-33292997893618247853333963264),(-33292997893618247782839154942)⟩⟩,⟨⟨19109431077764720153753932909,19109431077764720223267796991⟩,⟨(-32982465652768939030726565896),(-32982465652768938961365460161)⟩⟩,⟨⟨18039676061173194222579607912,18039676061173194290982571336⟩,⟨(-32656174050476376100570215841),(-32656174050476376032296807770)⟩⟩,⟨⟨17001571625324438684734284824,17001571625324438751986953409⟩,⟨(-32315259925895042271382893324),(-32315259925895042204237499728)⟩⟩,⟨⟨15994812098586423808924670909,15994812098586423875089570412⟩,⟨(-31960831406877470898079680663),(-31960831406877470832000700465)⟩⟩,⟨⟨15019062010804838350096789452,15019062010804838415150616687⟩,⟨(-31593967102699075764052881457),(-31593967102699075699064507879)⟩⟩,⟨⟨14073957860316136098287148323,14073957860316136162277212710⟩,⟨(-31215715399500588799929150671),(-31215715399500588735984951649)⟩⟩,⟨⟨13159109876436903983659845464,13159109876436904046552016448⟩,⟨(-30827093856185081217583231534),(-30827093856185081154718191097)⟩⟩,⟨⟨12274103772357636676792265045,12274103772357636738645870693⟩,⟨(-30429088698251670124831540285),(-30429088698251670062987163270)⟩⟩,⟨⟨11418502483625398684192216396,11418502483625398744985835355⟩,⟨(-30022654406814610024359867393),(-30022654406814609963558390316)⟩⟩,⟨⟨10591847887665037315974005027,10591847887665037375977750790⟩,⟨(-29608713399844726280161416982),(-29608713399844726220133795408)⟩⟩] +lemma kernel7_0_r5_9_eq : ∀ k : Fin 16, kernel7_0Expr 5 9 k = kernel7_0_r5_9 k := by decide +kernel +noncomputable def kernel7_0_r5_10 : Fin 16 → CBox := ![⟨⟨9793662500060892075263626780,9793662500060892134458778914⟩,⟨(-29188155802480125469836150481),(-29188155802480125410601904087)⟩⟩,⟨⟨9023451143598679506727314313,9023451143598679565169260468⟩,⟨(-28761839303084751613980758006),(-28761839303084751555485224391)⟩⟩,⟨⟨8280702586348815567908445276,8280702586348815625569047008⟩,⟨(-28330589091586466045686154277),(-28330589091586465987958195348)⟩⟩,⟨⟨7564891145356322928317784231,7564891145356322985236580692⟩,⟨(-27895197876500619727107486143),(-27895197876500619670108246000)⟩⟩,⟨⟨6875478252787172761820569898,6875478252787172817958393448⟩,⟨(-27456425976940163932443833603),(-27456425976940163876213169018)⟩⟩,⟨⟨6211913981665012111451017477,6211913981665012166859660695⟩,⟨(-27015001485828716004659370354),(-27015001485828715949146123257)⟩⟩,⟨⟨5573638528614384915772109502,5573638528614384970425047427⟩,⟨(-26571620500468080597434005901),(-26571620500468080542665346861)⟩⟩,⟨⟨4960083651305501769602603735,4960083651305501823539815660⟩,⟨(-26126947416565862418719497965),(-26126947416565862364656042490)⟩⟩,⟨⟨4370674058570167234237361900,4370674058570167287417878013⟩,⟨(-25681615281801260947178196580),(-25681615281801260893861530148)⟩⟩,⟨⟨3804828751427536251840166614,3804828751427536304319500747⟩,⟨(-25236226204997114156281039516),(-25236226204997114103656191987)⟩⟩,⟨⟨3261962313520933065313982711,3261962313520933117067152457⟩,⟨(-24791351816972904837020526348),(-24791351816972904785113049474)⟩⟩,⟨⟨2741486149722106609257340699,2741486149722106660324477609⟩,⟨(-24347533779175860471345749925),(-24347533779175860420116021771)⟩⟩,⟨⟨2242809671906185681624757801,2242809671906185731969725633⟩,⟨(-23905284336224527660686422519),(-23905284336224527610171120135)⟩⟩,⟨⟨1765341431138496065018715245,1765341431138496114693672083⟩,⟨(-23465086908550315829878877053),(-23465086908550315780026303002)⟩⟩,⟨⟨1308490195742661163151997413,1308490195742661212133394065⟩,⟨(-23027396721386490109204363347),(-23027396721386490060038563178)⟩⟩,⟨⟨871665974937467921655764739,871665974937467969983646686⟩,⟨(-22592641466429942088213545985),(-22592641466429942039694903495)⟩⟩] +lemma kernel7_0_r5_10_eq : ∀ k : Fin 16, kernel7_0Expr 5 10 k = kernel7_0_r5_10 k := by decide +kernel +noncomputable def kernel7_0_r5_11 : Fin 16 → CBox := ![⟨⟨454280987937368764296207202,454280987937368811931641860⟩,⟨(-22161221992587763166722795200),(-22161221992587763118890718171)⟩⟩,⟨⟨55750578607821500710008058,55750578607821547709182295⟩,⟨(-21733513022317170457322128959),(-21733513022317170410120808491)⟩⟩,⟨⟨(-324505924048360854503438452),(-324505924048360808162729471)⟩,⟨(-21309863890172676307130753137),(-21309863890172676260582821929)⟩⟩,⟨⟨(-687064399124093211385819526),(-687064399124093165663860381)⟩,⟨(-20890599300287546952572403292),(-20890599300287546906638500846)⟩⟩,⟨⟨(-1032495180149323872327023544),(-1032495180149323827257222416)⟩,⟨(-20476020099636577362456493277),(-20476020099636577317170435024)⟩⟩,⟨⟨(-1361362353779504068497186725),(-1361362353779504024028077944)⟩,⟨(-20066404064053053179045118462),(-20066404064053053134355747540)⟩⟩,⟨⟨(-1674223109932126638275296142),(-1674223109932126594427865442)⟩,⟨(-19662006694103538140109256747),(-19662006694103538096037923649)⟩⟩,⟨⟨(-1971627142345953801491990972),(-1971627142345953758227032314)⟩,⟨(-19263062018058908053290398661),(-19263062018058908009798184609)⟩⟩,⟨⟨(-2254116098422900668224358027),(-2254116098422900625577463119)⟩,⟨(-18869783399337975871377980895),(-18869783399337975828500829774)⟩⟩,⟨⟨(-2522223077109344163998211866),(-2522223077109344121915123420)⟩,⟨(-18482364345940279488328900887),(-18482364345940279446012794927)⟩⟩,⟨⟨(-2776472173481659907473650947),(-2776472173481659865974231312)⟩,⟨(-18100979319526337324939439169),(-18100979319526337283204548244)⟩⟩,⟨⟨(-3017378068619779293522575557),(-3017378068619779252568310527)⟩,⟨(-17725784541946161690808736114),(-17725784541946161649616772690)⟩⟩,⟨⟨(-3245445663282190936999018340),(-3245445663282190896620973081)⟩,⟨(-17356918797159345538418945902),(-17356918797159345497801270605)⟩⟩,⟨⟨(-3461169753835732999609452887),(-3461169753835732959757636571)⟩,⟨(-16994504226631939414451054679),(-16994504226631939374357861612)⟩⟩,⟨⟨(-3665034748843351575939307472),(-3665034748843351536632578484)⟩,⟨(-16638647116435993621742488496),(-16638647116435993582192892455)⟩⟩,⟨⟨(-3857514424672323152033555762),(-3857514424672323113234213718)⟩,⟨(-16289438674416484552917048246),(-16289438674416484513873522048)⟩⟩] +lemma kernel7_0_r5_11_eq : ∀ k : Fin 16, kernel7_0Expr 5 11 k = kernel7_0_r5_11 k := by decide +kernel +noncomputable def kernel7_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-4039071718453820519940190536),(-4039071718453820481682706317)⟩,⟨(-15946955795926850071687811432),(-15946955795926850033185080280)⟩⟩,⟨⟨(-4210158556701686502964422648),(-4210158556701686465195268343)⟩,⟨(-15611261816768050373651183392),(-15611261816768050335635847415)⟩⟩,⟨⟨(-4371215717883398272472822071),(-4371215717883398235209935502)⟩,⟨(-15282407252096518656513404688),(-15282407252096518619003613051)⟩⟩,⟨⟨(-4522672727228975470949353948),(-4522672727228975434155975007)⟩,⟨(-14960430520193187224300751887),(-14960430520193187187259871189)⟩⟩,⟨⟨(-4664947782063518727100605883),(-4664947782063518690805846022)⟩,⟨(-14645358650108631770009326726),(-14645358650108631733466675789)⟩⟩,⟨⟨(-4798447705955668261071996128),(-4798447705955668225227856030)⟩,⟨(-14337207972317976148103584623),(-14337207972317976112011253807)⟩⟩,⟨⟨(-4923567929987051045279584292),(-4923567929987051009903192094)⟩,⟨(-14035984791633291345209199826),(-14035984791633291309584489432)⟩⟩,⟨⟨(-5040692499466247471272993410),(-5040692499466247436328588658)⟩,⟨(-13741686041730596145954519998),(-13741686041730596110761756357)⟩⟩,⟨⟨(-5150194104434467650727129788),(-5150194104434467616246395391)⟩,⟨(-13454299920753053133628210311),(-13454299920753053098899253262)⟩⟩,⟨⟨(-5252434132338503795141648977),(-5252434132338503761074244056)⟩,⟨(-13173806507551419646445348673),(-13173806507551419612129904266)⟩⟩,⟨⟨(-5347762741279148772801330458),(-5347762741279148739163645829)⟩,⟨(-12900178358217162112445726073),(-12900178358217162078560323585)⟩⟩,⟨⟨(-5436518952279683959774086471),(-5436518952279683926531428629)⟩,⟨(-12633381082652810213694824590),(-12633381082652810180204823522)⟩⟩,⟨⟨(-5519030759058797543910522463),(-5519030759058797511090432717)⟩,⟨(-12373373901008082234293945152),(-12373373901008082201227028346)⟩⟩,⟨⟨(-5595615253834968407049160248),(-5595615253834968374605870205)⟩,⟨(-12120110179889051439584764974),(-12120110179889051406895184286)⟩⟩,⟨⟨(-5666578767734528089484746023),(-5666578767734528057429826630)⟩,⟨(-11873537948321168948363599826),(-11873537948321168916065302771)⟩⟩,⟨⟨(-5732217024422899374041348073),(-5732217024422899342334529245)⟩,⟨(-11633600393515359434125914617),(-11633600393515359402182269805)⟩⟩] +lemma kernel7_0_r5_12_eq : ∀ k : Fin 16, kernel7_0Expr 5 12 k = kernel7_0_r5_12 k := by decide +kernel +noncomputable def kernel7_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-5792815305627528634117126905),(-5792815305627528602790039443)⟩,⟨(-11400236336549732634215660237),(-11400236336549732602658148634)⟩⟩,⟨⟨(-5848648627271423626238986880),(-5848648627271423595243165880)⟩,⟨(-11173380688137796761056432533),(-11173380688137796729836319540)⟩⟩,⟨⟨(-5899981924987642204263722259),(-5899981924987642173614768210)⟩,⟨(-10952964884707528229308280899),(-10952964884707528198441000000)⟩⟩,⟨⟨(-5947070247837234193069797995),(-5947070247837234162735634817)⟩,⟨(-10738917305064370315495048652),(-10738917305064370284948289224)⟩⟩,⟨⟨(-5990158959105722660954566943),(-5990158959105722630961926567)⟩,⟨(-10531163667955340028348656167),(-10531163667955339998149006691)⟩⟩,⟨⟨(-6029483943105947004427249598),(-6029483943105946974733016313)⟩,⟨(-10329627410891068119547664946),(-10329627410891068089651768312)⟩⟩,⟨⟨(-6065271816967724105736258239),(-6065271816967724076355447250)⟩,⟨(-10134230050617942397137913359),(-10134230050617942367560631616)⟩⟩,⟨⟨(-6097740146447081225426239053),(-6097740146447081196327784436)⟩,⟨(-9944891525663738196872017012),(-9944891525663738167582069711)⟩⟩,⟨⟨(-6127097664839561189232249082),(-6127097664839561160445747911)⟩,⟨(-9761530521407377476436958313),(-9761530521407377447463816440)⟩⟩,⟨⟨(-6153544494133102419030183919),(-6153544494133102390510079546)⟩,⟨(-9584064778146939976128054034),(-9584064778146939947425935166)⟩⟩,⟨⟨(-6177272367586078180800170536),(-6177272367586078152560934044)⟩,⟨(-9412411382659940173733731974),(-9412411382659940145316967316)⟩⟩,⟨⟨(-6198464852965084394287189121),(-6198464852965084366298763501)⟩,⟨(-9246487043766368394940393773),(-9246487043766368366778730585)⟩⟩,⟨⟨(-6217297575724854699996980613),(-6217297575724854672285054646)⟩,⟨(-9086208352418260270208323137),(-9086208352418260242327331470)⟩⟩,⟨⟨(-6233938441459133669322622836),(-6233938441459133641846062694)⟩,⟨(-8931492026849792235460465407),(-8931492026849792207818809374)⟩⟩,⟨⟨(-6248547856996349000419307842),(-6248547856996348973192099076)⟩,⟨(-8782255143329286974856211473),(-8782255143329286947467749167)⟩⟩,⟨⟨(-6261278949557401894071107590),(-6261278949557401867064157922)⟩,⟨(-8638415353059234189695718603),(-8638415353059234162531179248)⟩⟩] +lemma kernel7_0_r5_13_eq : ∀ k : Fin 16, kernel7_0Expr 5 13 k = kernel7_0_r5_13 k := by decide +kernel +noncomputable def kernel7_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-6272277783434767056631316813),(-6272277783434767029874430681)⟩,⟨(-8499891085772668116542946518),(-8499891085772668089632032505)⟩⟩,⟨⟨(-6281683573692299504661288498),(-6281683573692299478109672129)⟩,⟨(-8366601740574168988063420932),(-8366601740574168961361147941)⟩⟩,⟨⟨(-6289628896423637338881053808),(-6289628896423637312548225690)⟩,⟨(-8238467864571541516081019713),(-8238467864571541489600790068)⟩⟩,⟨⟨(-6296239895143833097668597446),(-6296239895143833071526411854)⟩,⟨(-8115411319840034483697327132),(-8115411319840034457410832140)⟩⟩,⟨⟨(-6301636482923817921428207155),(-6301636482923817895501576666)⟩,⟨(-7997355439254960761810431350),(-7997355439254960735742486062)⟩⟩,⟨⟨(-6305932539910490022799303070),(-6305932539910489997048841154)⟩,⟨(-7884225171720909293201656504),(-7884225171720909267312704766)⟩⟩,⟨⟨(-6309236105906619239135653958),(-6309236105906619213574457208)⟩,⟨(-7775947217316555902978566148),(-7775947217316555877281598439)⟩⟩,⟨⟨(-6311649567714379254269587443),(-6311649567714379228870391238)⟩,⟨(-7672450152863517330570428166),(-7672450152863517305038030546)⟩⟩,⟨⟨(-6313269840974173284275096400),(-6313269840974173259066062927)⟩,⟨(-7573664548415884587649579172),(-7573664548415884562309829070)⟩⟩,⟨⟨(-6314188546256530127094142378),(-6314188546256530102033070886)⟩,⟨(-7479523075154142265179625318),(-7479523075154142239990161636)⟩⟩,⟨⟨(-6314492179189244889787124083),(-6314492179189244864886694545)⟩,⟨(-7389960605153246960624946252),(-7389960605153246935598351516)⟩⟩,⟨⟨(-6314262274424658090753662766),(-6314262274424658065987458203)⟩,⟨(-7304914303479810354435847251),(-7304914303479810329545566919)⟩⟩,⟨⟨(-6313575563273049444216177119),(-6313575563273049419608574373)⟩,⟨(-7224323713057712978423992665),(-7224323713057712953694322494)⟩⟩,⟨⟨(-6312504124847614733273466938),(-6312504124847614708786492818)⟩,⟨(-7148130832725158372385321228),(-7148130832725158347778142859)⟩⟩,⟨⟨(-6311115530584446454072975865),(-6311115530584446429718917248)⟩,⟨(-7076280188889251832708341446),(-7076280188889251808235851562)⟩⟩,⟨⟨(-6309472982017405965803674006),(-6309472982017405941556895791)⟩,⟨(-7008718901166733913735462088),(-7008718901166733889371897825)⟩⟩] +lemma kernel7_0_r5_14_eq : ∀ k : Fin 16, kernel7_0Expr 5 14 k = kernel7_0_r5_14 k := by decide +kernel +noncomputable def kernel7_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-6307635441702814715057458854),(-6307635441702814690946747353)⟩,⟨(-6945396742381589888736252569),(-6945396742381589864510330089)⟩⟩,⟨⟨(-6305657757202565692755014899),(-6305657757202565668738347032)⟩,⟨(-6886266193271959412482136658),(-6886266193271959388351692113)⟩⟩,⟨⟨(-6303590778046627142561640611),(-6303590778046627118650894224)⟩,⟨(-6831282492240146029488843584),(-6831282492240146005465670402)⟩⟩,⟨⟨(-6301481465607044364357437163),(-6301481465607044340527730313)⟩,⟨(-6780403680460628063840566479),(-6780403680460628039899662842)⟩⟩,⟨⟨(-6299372995825509761499745241),(-6299372995825509737775106424)⟩,⟨(-6733590642641848936691852887),(-6733590642641848912857177382)⟩⟩,⟨⟨(-6297304854745435115614745493),(-6297304854745435091958256306)⟩,⟨(-6690807143718258526210470543),(-6690807143718258502444975815)⟩⟩,⟨⟨(-6295312926807293734647113323),(-6295312926807293711070253827)⟩,⟨(-6652019861729624856983413353),(-6652019861729624833298499352)⟩⟩,⟨⟨(-6293429575872874928729095887),(-6293429575872874905207671455)⟩,⟨(-6617198417125069165253723887),(-6617198417125069141625082066)⟩⟩,⟨⟨(-6291683718950081346277948803),(-6291683718950081322838076334)⟩,⟨(-6586315398709624472984195849),(-6586315398709624449437879606)⟩⟩,⟨⟨(-6290100892595073808413160298),(-6290100892595073785013061222)⟩,⟨(-6559346386431401067602623055),(-6559346386431401044096725435)⟩⟩,⟨⟨(-6288703311973001645003701239),(-6288703311973001621654874386)⟩,⟨(-6536269971187680520357709110),(-6536269971187680496903651870)⟩⟩,⟨⟨(-6287509922562322751636160832),(-6287509922562322728315510624)⟩,⟨(-6517067771808468191197672981),(-6517067771808468167772250941)⟩⟩,⟨⟨(-6286536444490890488825095172),(-6286536444490890465556917640)⟩,⟨(-6501724449356224326745017233),(-6501724449356224303372462576)⟩⟩,⟨⟨(-6285795409494638143796811433),(-6285795409494638120545286787)⟩,⟨(-6490227718860674659522350510),(-6490227718860674636166722761)⟩⟩,⟨⟨(-6285296190491900081699546935),(-6285296190491900058475729531)⟩,⟨(-6482568358587779047854962348),(-6482568358587779024527240102)⟩⟩,⟨⟨(-6285045023768246103818696908),(-6285045023768246080600096502)⟩,⟨(-6478740216922115112658772889),(-6478740216922115089336358519)⟩⟩] +lemma kernel7_0_r5_15_eq : ∀ k : Fin 16, kernel7_0Expr 5 15 k = kernel7_0_r5_15 k := by decide +kernel +noncomputable def kernel7_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel7_0_r5_0,kernel7_0_r5_1,kernel7_0_r5_2,kernel7_0_r5_3,kernel7_0_r5_4,kernel7_0_r5_5,kernel7_0_r5_6,kernel7_0_r5_7,kernel7_0_r5_8,kernel7_0_r5_9,kernel7_0_r5_10,kernel7_0_r5_11,kernel7_0_r5_12,kernel7_0_r5_13,kernel7_0_r5_14,kernel7_0_r5_15] +lemma kernel7_0_r5_eq (i k : Fin 16) : kernel7_0Expr 5 i k = kernel7_0_r5 i k := by + fin_cases i + · exact kernel7_0_r5_0_eq k + · exact kernel7_0_r5_1_eq k + · exact kernel7_0_r5_2_eq k + · exact kernel7_0_r5_3_eq k + · exact kernel7_0_r5_4_eq k + · exact kernel7_0_r5_5_eq k + · exact kernel7_0_r5_6_eq k + · exact kernel7_0_r5_7_eq k + · exact kernel7_0_r5_8_eq k + · exact kernel7_0_r5_9_eq k + · exact kernel7_0_r5_10_eq k + · exact kernel7_0_r5_11_eq k + · exact kernel7_0_r5_12_eq k + · exact kernel7_0_r5_13_eq k + · exact kernel7_0_r5_14_eq k + · exact kernel7_0_r5_15_eq k +noncomputable def kernel7_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel7_0_r0,kernel7_0_r1,kernel7_0_r2,kernel7_0_r3,kernel7_0_r4,kernel7_0_r5] +lemma kernel7_0_eq (j : Fin 6) (i k : Fin 16) : kernel7_0Expr j i k = kernel7_0 j i k := by + fin_cases j + · exact kernel7_0_r0_eq i k + · exact kernel7_0_r1_eq i k + · exact kernel7_0_r2_eq i k + · exact kernel7_0_r3_eq i k + · exact kernel7_0_r4_eq i k + · exact kernel7_0_r5_eq i k +lemma kernel7_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel7_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(7:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel7_0_eq] + unfold kernel7_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans7_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel7_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans7 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel7_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-112139385),(-112139339)⟩,⟨5137542,5137588⟩⟩,⟨⟨(-111992610),(-111992556)⟩,⟨4982425,4982475⟩⟩,⟨⟨(-111699105),(-111699050)⟩,⟨4673438,4673488⟩⟩,⟨⟨(-111258900),(-111258853)⟩,⟨4212951,4212998⟩⟩,⟨⟨(-110672140),(-110672085)⟩,⟨3604569,3604619⟩⟩,⟨⟨(-109938976),(-109938922)⟩,⟨2853035,2853085⟩⟩,⟨⟨(-109059672),(-109059614)⟩,⟨1964186,1964244⟩⟩,⟨⟨(-108034662),(-108034608)⟩,⟨944973,945023⟩⟩,⟨⟨(-106864485),(-106864438)⟩,⟨(-196627),(-196580)⟩⟩,⟨⟨(-105549916),(-105549870)⟩,⟨(-1451697),(-1451651)⟩⟩,⟨⟨(-104092003),(-104091956)⟩,⟨(-2810438),(-2810391)⟩⟩,⟨⟨(-102492073),(-102492015)⟩,⟨(-4262181),(-4262123)⟩⟩,⟨⟨(-100751774),(-100751727)⟩,⟨(-5795521),(-5795474)⟩⟩,⟨⟨(-98873249),(-98873199)⟩,⟨(-7398414),(-7398360)⟩⟩,⟨⟨(-96858973),(-96858919)⟩,⟨(-9058253),(-9058203)⟩⟩,⟨⟨(-94711980),(-94711925)⟩,⟨(-10761991),(-10761941)⟩⟩] +lemma kernel7_1_r0_0_eq : ∀ k : Fin 16, kernel7_1Expr 0 0 k = kernel7_1_r0_0 k := by decide +kernel +noncomputable def kernel7_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-92435852),(-92435805)⟩,⟨(-12496178),(-12496132)⟩⟩,⟨⟨(-90034728),(-90034681)⟩,⟨(-14247157),(-14247110)⟩⟩,⟨⟨(-87513357),(-87513306)⟩,⟨(-16001127),(-16001073)⟩⟩,⟨⟨(-84877165),(-84877115)⟩,⟨(-17744264),(-17744210)⟩⟩,⟨⟨(-82132174),(-82132123)⟩,⟨(-19462849),(-19462795)⟩⟩,⟨⟨(-79285113),(-79285058)⟩,⟨(-21143370),(-21143320)⟩⟩,⟨⟨(-76343425),(-76343378)⟩,⟨(-22772628),(-22772582)⟩⟩,⟨⟨(-73315200),(-73315146)⟩,⟨(-24337882),(-24337831)⟩⟩,⟨⟨(-70209134),(-70209084)⟩,⟨(-25826960),(-25826906)⟩⟩,⟨⟨(-67034648),(-67034594)⟩,⟨(-27228322),(-27228272)⟩⟩,⟨⟨(-63801685),(-63801634)⟩,⟨(-28531212),(-28531158)⟩⟩,⟨⟨(-60520804),(-60520746)⟩,⟨(-29725697),(-29725639)⟩⟩,⟨⟨(-57203014),(-57202959)⟩,⟨(-30802877),(-30802826)⟩⟩,⟨⟨(-53859782),(-53859736)⟩,⟨(-31754779),(-31754732)⟩⟩,⟨⟨(-50502935),(-50502881)⟩,⟨(-32574597),(-32574547)⟩⟩,⟨⟨(-47144553),(-47144495)⟩,⟨(-33256656),(-33256598)⟩⟩] +lemma kernel7_1_r0_1_eq : ∀ k : Fin 16, kernel7_1Expr 0 1 k = kernel7_1_r0_1 k := by decide +kernel +noncomputable def kernel7_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-43796993),(-43796943)⟩,⟨(-33796491),(-33796437)⟩⟩,⟨⟨(-40472617),(-40472570)⟩,⟨(-34190849),(-34190803)⟩⟩,⟨⟨(-37183834),(-37183780)⟩,⟨(-34437843),(-34437793)⟩⟩,⟨⟨(-33942974),(-33942927)⟩,⟨(-34536748),(-34536701)⟩⟩,⟨⟨(-30762095),(-30762041)⟩,⟨(-34488202),(-34488151)⟩⟩,⟨⟨(-27652992),(-27652946)⟩,⟨(-34294028),(-34293982)⟩⟩,⟨⟨(-24627046),(-24626992)⟩,⟨(-33957366),(-33957316)⟩⟩,⟨⟨(-21695062),(-21695015)⟩,⟨(-33482493),(-33482447)⟩⟩,⟨⟨(-18867356),(-18867298)⟩,⟨(-32874805),(-32874747)⟩⟩,⟨⟨(-16153346),(-16153300)⟩,⟨(-32140807),(-32140761)⟩⟩,⟨⟨(-13561822),(-13561767)⟩,⟨(-31287976),(-31287926)⟩⟩,⟨⟨(-11100577),(-11100519)⟩,⟨(-30324683),(-30324625)⟩⟩,⟨⟨(-8776538),(-8776488)⟩,⟨(-29260106),(-29260052)⟩⟩,⟨⟨(-6595509),(-6595459)⟩,⟨(-28104132),(-28104078)⟩⟩,⟨⟨(-4562376),(-4562326)⟩,⟨(-26867196),(-26867142)⟩⟩,⟨⟨(-2680830),(-2680776)⟩,⟨(-25560224),(-25560174)⟩⟩] +lemma kernel7_1_r0_2_eq : ∀ k : Fin 16, kernel7_1Expr 0 2 k = kernel7_1_r0_2 k := by decide +kernel +noncomputable def kernel7_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-953426),(-953372)⟩,⟨(-24194491),(-24194441)⟩⟩,⟨⟨618367,618425⟩,⟨(-22781480),(-22781422)⟩⟩,⟨⟨2034234,2034292⟩,⟨(-21332727),(-21332669)⟩⟩,⟨⟨3294987,3295037⟩,⟨(-19859797),(-19859743)⟩⟩,⟨⟨4402567,4402614⟩,⟨(-18374059),(-18374013)⟩⟩,⟨⟨5359903,5359953⟩,⟨(-16886650),(-16886596)⟩⟩,⟨⟨6170997,6171047⟩,⟨(-15408304),(-15408250)⟩⟩,⟨⟨6840761,6840807⟩,⟨(-13949273),(-13949226)⟩⟩,⟨⟨7375026,7375084⟩,⟨(-12519250),(-12519193)⟩⟩,⟨⟨7780362,7780417⟩,⟨(-11127182),(-11127132)⟩⟩,⟨⟨8064102,8064152⟩,⟨(-9781402),(-9781348)⟩⟩,⟨⟨8234140,8234195⟩,⟨(-8489347),(-8489298)⟩⟩,⟨⟨8298946,8298992⟩,⟨(-7257635),(-7257588)⟩⟩,⟨⟨8267316,8267366⟩,⟨(-6091956),(-6091901)⟩⟩,⟨⟨8148417,8148463⟩,⟨(-4997112),(-4997066)⟩⟩,⟨⟨7951562,7951616⟩,⟨(-3976952),(-3976902)⟩⟩] +lemma kernel7_1_r0_3_eq : ∀ k : Fin 16, kernel7_1Expr 0 3 k = kernel7_1_r0_3 k := by decide +kernel +noncomputable def kernel7_1_r0_4 : Fin 16 → CBox := ![⟨⟨7686209,7686267⟩,⟨(-3034351),(-3034293)⟩⟩,⟨⟨7361805,7361855⟩,⟨(-2171355),(-2171300)⟩⟩,⟨⟨6987603,6987660⟩,⟨(-1388995),(-1388938)⟩⟩,⟨⟨6572753,6572810⟩,⟨(-687468),(-687411)⟩⟩,⟨⟨6126080,6126137⟩,⟨(-66139),(-66082)⟩⟩,⟨⟨5655990,5656037⟩,⟨476410,476457⟩⟩,⟨⟨5170524,5170582⟩,⟨942287,942345⟩⟩,⟨⟨4677191,4677245⟩,⟨1334305,1334354⟩⟩,⟨⟨4182888,4182942⟩,⟨1655850,1655899⟩⟩,⟨⟨3693977,3694023⟩,⟨1910761,1910807⟩⟩,⟨⟨3216130,3216187⟩,⟨2103367,2103424⟩⟩,⟨⟨2754412,2754458⟩,⟨2238328,2238374⟩⟩,⟨⟨2313188,2313234⟩,⟨2320552,2320598⟩⟩,⟨⟨1896105,1896155⟩,⟨2355131,2355185⟩⟩,⟨⟨1506161,1506218⟩,⟨2347304,2347361⟩⟩,⟨⟨1145767,1145816⟩,⟨2302284,2302339⟩⟩] +lemma kernel7_1_r0_4_eq : ∀ k : Fin 16, kernel7_1Expr 0 4 k = kernel7_1_r0_4 k := by decide +kernel +noncomputable def kernel7_1_r0_5 : Fin 16 → CBox := ![⟨⟨816598,816645⟩,⟨2225314,2225360⟩⟩,⟨⟨519768,519814⟩,⟨2121478,2121524⟩⟩,⟨⟨255808,255857⟩,⟨1995723,1995777⟩⟩,⟨⟨24774,24823⟩,⟨1852775,1852830⟩⟩,⟨⟨(-173855),(-173809)⟩,⟨1697073,1697119⟩⟩,⟨⟨(-340944),(-340898)⟩,⟨1532814,1532860⟩⟩,⟨⟨(-477778),(-477723)⟩,⟨1363835,1363884⟩⟩,⟨⟨(-585973),(-585916)⟩,⟨1193588,1193645⟩⟩,⟨⟨(-667372),(-667326)⟩,⟨1025153,1025199⟩⟩,⟨⟨(-724068),(-724019)⟩,⟨861273,861327⟩⟩,⟨⟨(-758307),(-758250)⟩,⟨704255,704312⟩⟩,⟨⟨(-772426),(-772372)⟩,⟨556041,556090⟩⟩,⟨⟨(-768887),(-768842)⟩,⟨418172,418218⟩⟩,⟨⟨(-750070),(-750024)⟩,⟨291862,291908⟩⟩,⟨⟨(-718406),(-718358)⟩,⟨177957,178011⟩⟩,⟨⟨(-676244),(-676199)⟩,⟨76981,77027⟩⟩] +lemma kernel7_1_r0_5_eq : ∀ k : Fin 16, kernel7_1Expr 0 5 k = kernel7_1_r0_5 k := by decide +kernel +noncomputable def kernel7_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-625812),(-625763)⟩,⟨(-10856),(-10802)⟩⟩,⟨⟨(-569230),(-569173)⟩,⟨(-85592),(-85535)⟩⟩,⟨⟨(-508470),(-508424)⟩,⟨(-147487),(-147441)⟩⟩,⟨⟨(-445356),(-445302)⟩,⟨(-197041),(-196993)⟩⟩,⟨⟨(-381505),(-381451)⟩,⟨(-234893),(-234845)⟩⟩,⟨⟨(-318364),(-318318)⟩,⟨(-261888),(-261843)⟩⟩,⟨⟨(-257147),(-257101)⟩,⟨(-278923),(-278878)⟩⟩,⟨⟨(-198912),(-198864)⟩,⟨(-287016),(-286962)⟩⟩,⟨⟨(-144549),(-144501)⟩,⟨(-287188),(-287134)⟩⟩,⟨⟨(-94654),(-94598)⟩,⟨(-280536),(-280480)⟩⟩,⟨⟨(-49763),(-49718)⟩,⟨(-268168),(-268123)⟩⟩,⟨⟨(-10190),(-10136)⟩,⟨(-251088),(-251040)⟩⟩,⟨⟨23897,23951⟩,⟨(-230395),(-230347)⟩⟩,⟨⟨52501,52555⟩,⟨(-207031),(-206983)⟩⟩,⟨⟨75674,75728⟩,⟨(-181886),(-181838)⟩⟩,⟨⟨93624,93669⟩,⟨(-155813),(-155768)⟩⟩] +lemma kernel7_1_r0_6_eq : ∀ k : Fin 16, kernel7_1Expr 0 6 k = kernel7_1_r0_6 k := by decide +kernel +noncomputable def kernel7_1_r0_7 : Fin 16 → CBox := ![⟨⟨106659,106704⟩,⟨(-129529),(-129484)⟩⟩,⟨⟨115130,115184⟩,⟨(-103702),(-103654)⟩⟩,⟨⟨119490,119535⟩,⟨(-78890),(-78845)⟩⟩,⟨⟨120130,120175⟩,⟨(-55557),(-55511)⟩⟩,⟨⟨117548,117593⟩,⟨(-34033),(-33988)⟩⟩,⟨⟨112301,112346⟩,⟨(-14643),(-14598)⟩⟩,⟨⟨104810,104857⟩,⟨2426,2479⟩⟩,⟨⟨95588,95644⟩,⟨17077,17133⟩⟩,⟨⟨85106,85151⟩,⟨29284,29329⟩⟩,⟨⟨73771,73825⟩,⟨39024,39071⟩⟩,⟨⟨62002,62049⟩,⟨46395,46448⟩⟩,⟨⟨50154,50201⟩,⟨51546,51599⟩⟩,⟨⟨38542,38586⟩,⟨54585,54629⟩⟩,⟨⟨27401,27446⟩,⟨55746,55791⟩⟩,⟨⟨16979,17032⟩,⟨55254,55300⟩⟩,⟨⟨7485,7530⟩,⟨53291,53335⟩⟩] +lemma kernel7_1_r0_7_eq : ∀ k : Fin 16, kernel7_1Expr 0 7 k = kernel7_1_r0_7 k := by decide +kernel +noncomputable def kernel7_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-1020),(-974)⟩,⟨50125,50178⟩⟩,⟨⟨(-8393),(-8349)⟩,⟨45994,46038⟩⟩,⟨⟨(-14581),(-14534)⟩,⟨41115,41168⟩⟩,⟨⟨(-19600),(-19556)⟩,⟨35732,35776⟩⟩,⟨⟨(-23428),(-23384)⟩,⟨30019,30063⟩⟩,⟨⟨(-26168),(-26124)⟩,⟨24190,24234⟩⟩,⟨⟨(-27821),(-27776)⟩,⟨18405,18449⟩⟩,⟨⟨(-28513),(-28467)⟩,⟨12774,12827⟩⟩,⟨⟨(-28330),(-28277)⟩,⟨7510,7556⟩⟩,⟨⟨(-27368),(-27324)⟩,⟨2661,2705⟩⟩,⟨⟨(-25772),(-25728)⟩,⟨(-1719),(-1675)⟩⟩,⟨⟨(-23653),(-23609)⟩,⟨(-5527),(-5483)⟩⟩,⟨⟨(-21119),(-21075)⟩,⟨(-8744),(-8700)⟩⟩,⟨⟨(-18278),(-18234)⟩,⟨(-11368),(-11324)⟩⟩,⟨⟨(-15259),(-15215)⟩,⟨(-13371),(-13327)⟩⟩,⟨⟨(-12145),(-12091)⟩,⟨(-14789),(-14735)⟩⟩] +lemma kernel7_1_r0_8_eq : ∀ k : Fin 16, kernel7_1Expr 0 8 k = kernel7_1_r0_8 k := by decide +kernel +noncomputable def kernel7_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-9052),(-9008)⟩,⟨(-15637),(-15594)⟩⟩,⟨⟨(-6022),(-5979)⟩,⟨(-15987),(-15943)⟩⟩,⟨⟨(-3164),(-3119)⟩,⟨(-15830),(-15778)⟩⟩,⟨⟨(-523),(-478)⟩,⟨(-15285),(-15232)⟩⟩,⟨⟨1879,1922⟩,⟨(-14354),(-14311)⟩⟩,⟨⟨3967,4019⟩,⟨(-13149),(-13104)⟩⟩,⟨⟨5739,5782⟩,⟨(-11687),(-11644)⟩⟩,⟨⟨7173,7216⟩,⟨(-10090),(-10047)⟩⟩,⟨⟨8279,8331⟩,⟨(-8361),(-8317)⟩⟩,⟨⟨9061,9104⟩,⟨(-6572),(-6529)⟩⟩,⟨⟨9519,9571⟩,⟨(-4775),(-4731)⟩⟩,⟨⟨9688,9742⟩,⟨(-3027),(-2974)⟩⟩,⟨⟨9603,9648⟩,⟨(-1357),(-1305)⟩⟩,⟨⟨9270,9313⟩,⟨192,235⟩⟩,⟨⟨8714,8765⟩,⟨1617,1661⟩⟩,⟨⟨7988,8032⟩,⟨2854,2905⟩⟩] +lemma kernel7_1_r0_9_eq : ∀ k : Fin 16, kernel7_1Expr 0 9 k = kernel7_1_r0_9 k := by decide +kernel +noncomputable def kernel7_1_r0_10 : Fin 16 → CBox := ![⟨⟨7132,7174⟩,⟨3909,3951⟩⟩,⟨⟨6148,6190⟩,⟨4793,4835⟩⟩,⟨⟨5085,5136⟩,⟨5477,5521⟩⟩,⟨⟨4005,4047⟩,⟨5980,6022⟩⟩,⟨⟨2898,2940⟩,⟨6291,6333⟩⟩,⟨⟨1809,1861⟩,⟨6407,6451⟩⟩,⟨⟨741,783⟩,⟨6375,6417⟩⟩,⟨⟨(-234),(-192)⟩,⟨6184,6226⟩⟩,⟨⟨(-1160),(-1118)⟩,⟨5885,5927⟩⟩,⟨⟨(-1979),(-1937)⟩,⟨5456,5497⟩⟩,⟨⟨(-2695),(-2644)⟩,⟨4923,4965⟩⟩,⟨⟨(-3312),(-3270)⟩,⟨4303,4345⟩⟩,⟨⟨(-3798),(-3748)⟩,⟨3647,3689⟩⟩,⟨⟨(-4163),(-4121)⟩,⟨2942,2983⟩⟩,⟨⟨(-4428),(-4387)⟩,⟨2230,2272⟩⟩,⟨⟨(-4595),(-4554)⟩,⟨1513,1554⟩⟩] +lemma kernel7_1_r0_10_eq : ∀ k : Fin 16, kernel7_1Expr 0 10 k = kernel7_1_r0_10 k := by decide +kernel +noncomputable def kernel7_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-4637),(-4595)⟩,⟨800,841⟩⟩,⟨⟨(-4573),(-4532)⟩,⟨107,148⟩⟩,⟨⟨(-4425),(-4384)⟩,⟨(-541),(-500)⟩⟩,⟨⟨(-4212),(-4162)⟩,⟨(-1128),(-1086)⟩⟩,⟨⟨(-3896),(-3855)⟩,⟨(-1670),(-1629)⟩⟩,⟨⟨(-3550),(-3509)⟩,⟨(-2154),(-2113)⟩⟩,⟨⟨(-3138),(-3098)⟩,⟨(-2580),(-2539)⟩⟩,⟨⟨(-2690),(-2649)⟩,⟨(-2920),(-2880)⟩⟩,⟨⟨(-2231),(-2191)⟩,⟨(-3179),(-3139)⟩⟩,⟨⟨(-1733),(-1683)⟩,⟨(-3382),(-3340)⟩⟩,⟨⟨(-1240),(-1200)⟩,⟨(-3513),(-3473)⟩⟩,⟨⟨(-737),(-696)⟩,⟨(-3563),(-3522)⟩⟩,⟨⟨(-264),(-224)⟩,⟨(-3571),(-3530)⟩⟩,⟨⟨194,234⟩,⟨(-3508),(-3468)⟩⟩,⟨⟨639,680⟩,⟨(-3393),(-3353)⟩⟩,⟨⟨1064,1104⟩,⟨(-3236),(-3195)⟩⟩] +lemma kernel7_1_r0_11_eq : ∀ k : Fin 16, kernel7_1Expr 0 11 k = kernel7_1_r0_11 k := by decide +kernel +noncomputable def kernel7_1_r0_12 : Fin 16 → CBox := ![⟨⟨1421,1461⟩,⟨(-3029),(-2989)⟩⟩,⟨⟨1758,1798⟩,⟨(-2779),(-2739)⟩⟩,⟨⟨2058,2098⟩,⟨(-2505),(-2465)⟩⟩,⟨⟨2300,2349⟩,⟨(-2190),(-2149)⟩⟩,⟨⟨2526,2566⟩,⟨(-1876),(-1836)⟩⟩,⟨⟨2695,2735⟩,⟨(-1521),(-1481)⟩⟩,⟨⟨2812,2852⟩,⟨(-1196),(-1157)⟩⟩,⟨⟨2911,2951⟩,⟨(-855),(-815)⟩⟩,⟨⟨2945,2985⟩,⟨(-481),(-441)⟩⟩,⟨⟨2936,2976⟩,⟨(-146),(-106)⟩⟩,⟨⟨2912,2951⟩,⟨161,201⟩⟩,⟨⟨2850,2890⟩,⟨494,534⟩⟩,⟨⟨2745,2785⟩,⟨789,828⟩⟩,⟨⟨2624,2663⟩,⟨1065,1104⟩⟩,⟨⟨2477,2507⟩,⟨1312,1351⟩⟩,⟨⟨2322,2361⟩,⟨1560,1599⟩⟩] +lemma kernel7_1_r0_12_eq : ∀ k : Fin 16, kernel7_1Expr 0 12 k = kernel7_1_r0_12 k := by decide +kernel +noncomputable def kernel7_1_r0_13 : Fin 16 → CBox := ![⟨⟨2122,2161⟩,⟨1778,1818⟩⟩,⟨⟨1933,1973⟩,⟨1971,2010⟩⟩,⟨⟨1709,1749⟩,⟨2135,2174⟩⟩,⟨⟨1496,1535⟩,⟨2272,2311⟩⟩,⟨⟨1256,1295⟩,⟨2391,2430⟩⟩,⟨⟨1045,1084⟩,⟨2484,2523⟩⟩,⟨⟨807,846⟩,⟨2540,2579⟩⟩,⟨⟨569,608⟩,⟨2606,2644⟩⟩,⟨⟨342,381⟩,⟨2617,2656⟩⟩,⟨⟨133,172⟩,⟨2639,2678⟩⟩,⟨⟨(-103),(-64)⟩,⟨2624,2662⟩⟩,⟨⟨(-311),(-273)⟩,⟨2619,2658⟩⟩,⟨⟨(-510),(-471)⟩,⟨2578,2617⟩⟩,⟨⟨(-690),(-651)⟩,⟨2519,2558⟩⟩,⟨⟨(-898),(-859)⟩,⟨2461,2499⟩⟩,⟨⟨(-1050),(-1011)⟩,⟨2376,2415⟩⟩] +lemma kernel7_1_r0_13_eq : ∀ k : Fin 16, kernel7_1Expr 0 13 k = kernel7_1_r0_13 k := by decide +kernel +noncomputable def kernel7_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-1230),(-1192)⟩,⟨2300,2330⟩⟩,⟨⟨(-1383),(-1344)⟩,⟨2216,2255⟩⟩,⟨⟨(-1508),(-1469)⟩,⟨2105,2144⟩⟩,⟨⟨(-1633),(-1595)⟩,⟨2004,2042⟩⟩,⟨⟨(-1759),(-1721)⟩,⟨1920,1959⟩⟩,⟨⟨(-1857),(-1819)⟩,⟨1792,1821⟩⟩,⟨⟨(-1956),(-1917)⟩,⟨1682,1720⟩⟩,⟨⟨(-2063),(-2025)⟩,⟨1581,1610⟩⟩,⟨⟨(-2135),(-2097)⟩,⟨1472,1510⟩⟩,⟨⟨(-2206),(-2177)⟩,⟨1371,1409⟩⟩,⟨⟨(-2259),(-2221)⟩,⟨1234,1272⟩⟩,⟨⟨(-2313),(-2275)⟩,⟨1134,1172⟩⟩,⟨⟨(-2358),(-2319)⟩,⟨1025,1063⟩⟩,⟨⟨(-2412),(-2373)⟩,⟨925,963⟩⟩,⟨⟨(-2438),(-2400)⟩,⟨852,881⟩⟩,⟨⟨(-2483),(-2445)⟩,⟨743,781⟩⟩] +lemma kernel7_1_r0_14_eq : ∀ k : Fin 16, kernel7_1Expr 0 14 k = kernel7_1_r0_14 k := by decide +kernel +noncomputable def kernel7_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-2510),(-2472)⟩,⟨671,700⟩⟩,⟨⟨(-2509),(-2471)⟩,⟨589,627⟩⟩,⟨⟨(-2536),(-2499)⟩,⟨507,545⟩⟩,⟨⟨(-2564),(-2526)⟩,⟨435,473⟩⟩,⟨⟨(-2563),(-2525)⟩,⟨353,391⟩⟩,⟨⟨(-2563),(-2525)⟩,⟨308,346⟩⟩,⟨⟨(-2590),(-2553)⟩,⟨226,264⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨199,237⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨154,182⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨99,137⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨72,110⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨45,83⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨17,55⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨(-10),28⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨(-10),28⟩⟩,⟨⟨(-2590),(-2552)⟩,⟨(-10),28⟩⟩] +lemma kernel7_1_r0_15_eq : ∀ k : Fin 16, kernel7_1Expr 0 15 k = kernel7_1_r0_15 k := by decide +kernel +noncomputable def kernel7_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel7_1_r0_0,kernel7_1_r0_1,kernel7_1_r0_2,kernel7_1_r0_3,kernel7_1_r0_4,kernel7_1_r0_5,kernel7_1_r0_6,kernel7_1_r0_7,kernel7_1_r0_8,kernel7_1_r0_9,kernel7_1_r0_10,kernel7_1_r0_11,kernel7_1_r0_12,kernel7_1_r0_13,kernel7_1_r0_14,kernel7_1_r0_15] +lemma kernel7_1_r0_eq (i k : Fin 16) : kernel7_1Expr 0 i k = kernel7_1_r0 i k := by + fin_cases i + · exact kernel7_1_r0_0_eq k + · exact kernel7_1_r0_1_eq k + · exact kernel7_1_r0_2_eq k + · exact kernel7_1_r0_3_eq k + · exact kernel7_1_r0_4_eq k + · exact kernel7_1_r0_5_eq k + · exact kernel7_1_r0_6_eq k + · exact kernel7_1_r0_7_eq k + · exact kernel7_1_r0_8_eq k + · exact kernel7_1_r0_9_eq k + · exact kernel7_1_r0_10_eq k + · exact kernel7_1_r0_11_eq k + · exact kernel7_1_r0_12_eq k + · exact kernel7_1_r0_13_eq k + · exact kernel7_1_r0_14_eq k + · exact kernel7_1_r0_15_eq k +noncomputable def kernel7_1_r1_0 : Fin 16 → CBox := ![⟨⟨17010261995556374,17010261995556421⟩,⟨154949467809016,154949467809062⟩⟩,⟨⟨16988052104053802,16988052104053849⟩,⟨158205068571110,158205068571157⟩⟩,⟨⟨16943718837715739,16943718837715785⟩,⟨164692345035578,164692345035624⟩⟩,⟨⟨16877434665377044,16877434665377086⟩,⟨174363662740644,174363662740685⟩⟩,⟨⟨16789456884265404,16789456884265445⟩,⟨187148106729575,187148106729616⟩⟩,⟨⟨16680125947335225,16680125947335266⟩,⟨202952118923023,202952118923064⟩⟩,⟨⟨16549863257129114,16549863257129171⟩,⟨221660336860454,221660336860510⟩⟩,⟨⟨16399168446435029,16399168446435070⟩,⟨243136624497904,243136624497945⟩⟩,⟨⟨16228616170610977,16228616170611019⟩,⟨267225283656242,267225283656283⟩⟩,⟨⟨16038852440757195,16038852440757236⟩,⟨293752432773547,293752432773589⟩⟩,⟨⟨15830590530874534,15830590530874575⟩,⟨322527537850479,322527537850520⟩⟩,⟨⟨15604606495716091,15604606495716133⟩,⟨353345078912334,353345078912375⟩⟩,⟨⟨15361734339176316,15361734339176358⟩,⟨385986333964268,385986333964310⟩⟩,⟨⟨15102860875737305,15102860875737346⟩,⟨420221261303382,420221261303423⟩⟩,⟨⟨14828920329677725,14828920329677766⟩,⟨455810460184403,455810460184444⟩⟩,⟨⟨14540888718430526,14540888718430567⟩,⟨492507189225010,492507189225052⟩⟩] +lemma kernel7_1_r1_0_eq : ∀ k : Fin 16, kernel7_1Expr 1 0 k = kernel7_1_r1_0 k := by decide +kernel +noncomputable def kernel7_1_r1_1 : Fin 16 → CBox := ![⟨⟨14239778067635977,14239778067636019⟩,⟨530059421584673,530059421584715⟩⟩,⟨⟨13926630506075954,13926630506076000⟩,⟨568211915861636,568211915861682⟩⟩,⟨⟨13602512288793419,13602512288793461⟩,⟨606708281819533,606708281819575⟩⟩,⟨⟨13268507796310119,13268507796310161⟩,⟨645293020475901,645293020475942⟩⟩,⟨⟨12925713556969819,12925713556969860⟩,⟨683713518745455,683713518745496⟩⟩,⟨⟨12575232338077960,12575232338078006⟩,⟨721721979722150,721721979722196⟩⟩,⟨⟨12218167349708701,12218167349708743⟩,⟨759077270785090,759077270785132⟩⟩,⟨⟨11855616602841685,11855616602841732⟩,⟨795546673009508,795546673009554⟩⟩,⟨⟨11488667460909312,11488667460909353⟩,⟨830907516830259,830907516830301⟩⟩,⟨⟨11118391420924742,11118391420924789⟩,⟨864948690520064,864948690520111⟩⟩,⟨⟨10745839157165201,10745839157165243⟩,⟨897472009782914,897472009782955⟩⟩,⟨⟨10372035856950284,10372035856950325⟩,⟨928293438597013,928293438597054⟩⟩,⟨⟨9997976874432394,9997976874432435⟩,⟨957244153346443,957244153346485⟩⟩,⟨⟨9624623724552087,9624623724552143⟩,⟨984171444227340,984171444227396⟩⟩,⟨⟨9252900435457247,9252900435457289⟩,⟨1008939449877068,1008939449877110⟩⟩,⟨⟨8883690273788248,8883690273788290⟩,⟨1031429723125948,1031429723125990⟩⟩] +lemma kernel7_1_r1_1_eq : ∀ k : Fin 16, kernel7_1Expr 1 1 k = kernel7_1_r1_1 k := by decide +kernel +noncomputable def kernel7_1_r1_2 : Fin 16 → CBox := ![⟨⟨8517832853340815,8517832853340857⟩,⟨1051541627686641,1051541627686683⟩⟩,⟨⟨8156121633776242,8156121633776284⟩,⟨1069192567449840,1069192567449882⟩⟩,⟨⟨7799301812302083,7799301812302124⟩,⟨1084318051826540,1084318051826582⟩⟩,⟨⟨7448068607630124,7448068607630165⟩,⟨1096871602243907,1096871602243949⟩⟩,⟨⟨7103065932071932,7103065932071974⟩,⟨1106824506447081,1106824506447123⟩⟩,⟨⟨6764885444385343,6764885444385389⟩,⟨1114165428666610,1114165428666657⟩⟩,⟨⟨6434065972967457,6434065972967499⟩,⟨1118899884966375,1118899884966417⟩⟩,⟨⟨6111093296222947,6111093296222999⟩,⟨1121049594181011,1121049594181063⟩⟩,⟨⟨5796400264441391,5796400264441433⟩,⟨1120651715776144,1120651715776186⟩⟩,⟨⟨5490367245307184,5490367245307230⟩,⟨1117757986712797,1117757986712844⟩⟩,⟨⟨5193322873251501,5193322873251543⟩,⟨1112433769970577,1112433769970619⟩⟩,⟨⟨4905545081242497,4905545081242539⟩,⟨1104757027777395,1104757027777437⟩⟩,⟨⟨4627262392300500,4627262392300547⟩,⟨1094817232815573,1094817232815620⟩⟩,⟨⟨4358655447015170,4358655447015212⟩,⟨1082714230724918,1082714230724960⟩⟩,⟨⟨4099858742626387,4099858742626429⟩,⟨1068557067113677,1068557067113719⟩⟩,⟨⟨3850962558801643,3850962558801685⟩,⟨1052462792026228,1052462792026270⟩⟩] +lemma kernel7_1_r1_2_eq : ∀ k : Fin 16, kernel7_1Expr 1 2 k = kernel7_1_r1_2 k := by decide +kernel +noncomputable def kernel7_1_r1_3 : Fin 16 → CBox := ![⟨⟨3612015045084589,3612015045084636⟩,⟨1034555254412560,1034555254412607⟩⟩,⟨⟨3383024445090087,3383024445090129⟩,⟨1014963898612964,1014963898613006⟩⟩,⟨⟨3163961432861239,3163961432861281⟩,⟨993822574223653,993822574223696⟩⟩,⟨⟨2954761537365533,2954761537365575⟩,⟨971268369962094,971268369962136⟩⟩,⟨⟨2755327631867836,2755327631867878⟩,⟨947440481317994,947440481318036⟩⟩,⟨⟨2565532465858561,2565532465858609⟩,⟨922479120873428,922479120873475⟩⟩,⟨⟨2385221218310419,2385221218310461⟩,⟨896524479220742,896524479220784⟩⟩,⟨⟨2214214052265822,2214214052265864⟩,⟨869715743411468,869715743411510⟩⟩,⟨⟨2052308652095860,2052308652095902⟩,⟨842190178853957,842190178854000⟩⟩,⟨⟨1899282726198269,1899282726198316⟩,⟨814082279550700,814082279550748⟩⟩,⟨⟨1754896459393399,1754896459393446⟩,⟨785522990547431,785522990547478⟩⟩,⟨⟨1618894900814431,1618894900814478⟩,⟨756639005463780,756639005463828⟩⟩,⟨⟨1491010274648809,1491010274648856⟩,⟨727552141004233,727552141004281⟩⟩,⟨⟨1370964202654948,1370964202654991⟩,⟨698378789417113,698378789417155⟩⟩,⟨⟨1258469828933884,1258469828933926⟩,⟨669229448988657,669229448988700⟩⟩,⟨⟨1153233838962926,1153233838962968⟩,⟨640208331836495,640208331836538⟩⟩] +lemma kernel7_1_r1_3_eq : ∀ k : Fin 16, kernel7_1Expr 1 3 k = kernel7_1_r1_3 k := by decide +kernel +noncomputable def kernel7_1_r1_4 : Fin 16 → CBox := ![⟨⟨1054958366385259,1054958366385306⟩,⟨611413047508626,611413047508674⟩⟩,⟨⟨963342782480734,963342782480777⟩,⟨582934360205994,582934360206036⟩⟩,⟨⟨878085364610323,878085364610366⟩,⟨554856016831697,554856016831739⟩⟩,⟨⟨798884841219096,798884841219138⟩,⟨527254642532255,527254642532298⟩⟩,⟨⟨725441812192712,725441812192754⟩,⟨500199699935025,500199699935067⟩⟩,⟨⟨657460044485339,657460044485382⟩,⟨473753507903471,473753507903514⟩⟩,⟨⟨594647643967386,594647643967434⟩,⟨447971315325385,447971315325433⟩⟩,⟨⟨536718105376051,536718105376094⟩,⟨422901425218018,422901425218060⟩⟩,⟨⟨483391243090655,483391243090698⟩,⟨398585364274319,398585364274362⟩⟩,⟨⟨434394006195770,434394006195823⟩,⟨375058092883385,375058092883439⟩⟩,⟨⟨389461181940420,389461181940469⟩,⟨352348250631057,352348250631104⟩⟩,⟨⟨348335992252321,348335992252370⟩,⟨330478432318050,330478432318098⟩⟩,⟨⟨310770588425501,310770588425549⟩,⟨309465489619760,309465489619808⟩⟩,⟨⟨276526449471007,276526449471049⟩,⟨289320853644728,289320853644771⟩⟩,⟨⟨245374689907730,245374689907778⟩,⟨270050873827151,270050873827199⟩⟩,⟨⟨217096282979477,217096282979520⟩,⟨251657168800881,251657168800924⟩⟩] +lemma kernel7_1_r1_4_eq : ∀ k : Fin 16, kernel7_1Expr 1 4 k = kernel7_1_r1_4 k := by decide +kernel +noncomputable def kernel7_1_r1_5 : Fin 16 → CBox := ![⟨⟨191482205418844,191482205418893⟩,⟨234136985148162,234136985148211⟩⟩,⟨⟨168333509945947,168333509945995⟩,⟨217483560185242,217483560185291⟩⟩,⟨⟨147461331693703,147461331693746⟩,⟨201686485236727,201686485236770⟩⟩,⟨⟨128686834700132,128686834700176⟩,⟨186732066154288,186732066154332⟩⟩,⟨⟨111841104505400,111841104505449⟩,⟨172603678147709,172603678147757⟩⟩,⟨⟨96764992744071,96764992744114⟩,⟨159282112314235,159282112314278⟩⟩,⟨⟨83308919437705,83308919437749⟩,⟨146745911569372,146745911569415⟩⟩,⟨⟨71332638474309,71332638474352⟩,⟨134971693996233,134971693996277⟩⟩,⟨⟨60704971514115,60704971514158⟩,⟨123934461937080,123934461937124⟩⟩,⟨⟨51303515293588,51303515293631⟩,⟨113607895447244,113607895447287⟩⟩,⟨⟨43014327012422,43014327012471⟩,⟨103964629014402,103964629014452⟩⟩,⟨⟨35731592190375,35731592190425⟩,⟨94976510715306,94976510715354⟩⟩,⟨⟨29357279072428,29357279072477⟩,⟨86614843232406,86614843232455⟩⟩,⟨⟨23800783349409,23800783349459⟩,⟨78850606386780,78850606386829⟩⟩,⟨⟨18978566647579,18978566647623⟩,⟨71654661056866,71654661056909⟩⟩,⟨⟨14813791929585,14813791929629⟩,⟨64997934546835,64997934546879⟩⟩] +lemma kernel7_1_r1_5_eq : ∀ k : Fin 16, kernel7_1Expr 1 5 k = kernel7_1_r1_5 k := by decide +kernel +noncomputable def kernel7_1_r1_6 : Fin 16 → CBox := ![⟨⟨11235958643445,11235958643489⟩,⟨58851587641798,58851587641841⟩⟩,⟨⟨8180540156710,8180540156759⟩,⟨53187163740957,53187163741006⟩⟩,⟨⟨5588625724370,5588625724414⟩,⟨47976720592636,47976720592680⟩⟩,⟨⟨3406568960699,3406568960743⟩,⟨43192945269916,43192945269960⟩⟩,⟨⟨1585644519998,1585644520042⟩,⟨38809253120179,38809253120223⟩⟩,⟨⟨81714440362,81714440406⟩,⟨34799871499934,34799871499978⟩⟩,⟨⟨(-1145094632386),(-1145094632342)⟩,⟨31139909166035,31139909166079⟩⟩,⟨⟨(-2130702343604),(-2130702343555)⟩,⟨27805412239654,27805412239704⟩⟩,⟨⟨(-2907372860185),(-2907372860141)⟩,⟨24773407689400,24773407689444⟩⟩,⟨⟨(-3503999829428),(-3503999829384)⟩,⟨22021935296146,22021935296190⟩⟩,⟨⟨(-3946377636218),(-3946377636174)⟩,⟨19530069067976,19530069068020⟩⟩,⟨⟨(-4257458685401),(-4257458685351)⟩,⟨17277929066176,17277929066225⟩⟩,⟨⟨(-4457596576938),(-4457596576889)⟩,⟨15246684589081,15246684589131⟩⟩,⟨⟨(-4564775167925),(-4564775167875)⟩,⟨13418549635698,13418549635747⟩⟩,⟨⟨(-4594823626365),(-4594823626316)⟩,⟨11776771540791,11776771540841⟩⟩,⟨⟨(-4561617679246),(-4561617679202)⟩,⟨10305613636681,10305613636726⟩⟩] +lemma kernel7_1_r1_6_eq : ∀ k : Fin 16, kernel7_1Expr 1 6 k = kernel7_1_r1_6 k := by decide +kernel +noncomputable def kernel7_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-4477267341549),(-4477267341505)⟩,⟨8990332754972,8990332755016⟩⟩,⟨⟨(-4352291484027),(-4352291483977)⟩,⟨7817152337129,7817152337179⟩⟩,⟨⟨(-4195779657898),(-4195779657842)⟩,⟨6773231874469,6773231874525⟩⟩,⟨⟨(-4015541642972),(-4015541642927)⟩,⟨5846633348666,5846633348711⟩⟩,⟨⟨(-3818245225175),(-3818245225130)⟩,⟨5026285293013,5026285293057⟩⟩,⟨⟨(-3609542738595),(-3609542738551)⟩,⟨4301945043618,4301945043663⟩⟩,⟨⟨(-3394186929062),(-3394186929018)⟩,⟨3664159698568,3664159698613⟩⟩,⟨⟨(-3176136709787),(-3176136709743)⟩,⟨3104226253437,3104226253482⟩⟩,⟨⟨(-2958653386500),(-2958653386455)⟩,⟨2614151332173,2614151332217⟩⟩,⟨⟨(-2744387931305),(-2744387931255)⟩,⟨2186610885473,2186610885523⟩⟩,⟨⟨(-2535459879683),(-2535459879639)⟩,⟨1814910183916,1814910183961⟩⟩,⟨⟨(-2333528417055),(-2333528417010)⟩,⟨1492944389593,1492944389637⟩⟩,⟨⟨(-2139856208395),(-2139856208344)⟩,⟨1215159949842,1215159949891⟩⟩,⟨⟨(-1955366509151),(-1955366509095)⟩,⟨976517019228,976517019284⟩⟩,⟨⟨(-1780694076969),(-1780694076919)⟩,⟨772453079814,772453079865⟩⟩,⟨⟨(-1616230383433),(-1616230383382)⟩,⟨598847898483,598847898533⟩⟩] +lemma kernel7_1_r1_7_eq : ∀ k : Fin 16, kernel7_1Expr 1 7 k = kernel7_1_r1_7 k := by decide +kernel +noncomputable def kernel7_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-1462163602780),(-1462163602731)⟩,⟨451989929264,451989929315⟩⟩,⟨⟨(-1318513831059),(-1318513831014)⟩,⟨328544242875,328544242920⟩⟩,⟨⟨(-1185163964997),(-1185163964952)⟩,⟨225522040239,225522040284⟩⟩,⟨⟨(-1061886645100),(-1061886645055)⟩,⟨140251785857,140251785902⟩⟩,⟨⟨(-948367642251),(-948367642199)⟩,⟨70351977516,70351977566⟩⟩,⟨⟨(-844226042714),(-844226042662)⟩,⟨13705551870,13705551920⟩⟩,⟨⟨(-749031561239),(-749031561194)⟩,⟨(-31564089220),(-31564089175)⟩⟩,⟨⟨(-662319288329),(-662319288273)⟩,⟨(-67115458918),(-67115458861)⟩⟩,⟨⟨(-583602153810),(-583602153754)⟩,⟨(-94409810169),(-94409810113)⟩⟩,⟨⟨(-512381367154),(-512381367103)⟩,⟨(-114730451970),(-114730451920)⟩⟩,⟨⟨(-448155071781),(-448155071729)⟩,⟨(-129200610904),(-129200610854)⟩⟩,⟨⟨(-390425431373),(-390425431328)⟩,⟨(-138799897260),(-138799897214)⟩⟩,⟨⟨(-338704345620),(-338704345568)⟩,⟨(-144379439526),(-144379439476)⟩⟩,⟨⟨(-292517974198),(-292517974148)⟩,⟨(-146675753757),(-146675753705)⟩⟩,⟨⟨(-251410231083),(-251410231026)⟩,⟨(-146323416754),(-146323416698)⟩⟩,⟨⟨(-214945394073),(-214945394016)⟩,⟨(-143866612057),(-143866612001)⟩⟩] +lemma kernel7_1_r1_8_eq : ∀ k : Fin 16, kernel7_1Expr 1 8 k = kernel7_1_r1_8 k := by decide +kernel +noncomputable def kernel7_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-182709959654),(-182709959602)⟩,⟨(-139769619182),(-139769619132)⟩⟩,⟨⟨(-154313859044),(-154313858998)⟩,⟨(-134426314638),(-134426314592)⟩⟩,⟨⟨(-129391138584),(-129391138532)⟩,⟨(-128168753207),(-128168753157)⟩⟩,⟨⟨(-107600194941),(-107600194885)⟩,⟨(-121274895692),(-121274895635)⟩⟩,⟨⟨(-88623645534),(-88623645477)⟩,⟨(-113975547463),(-113975547407)⟩⟩,⟨⟨(-72167903617),(-72167903567)⟩,⟨(-106460569723),(-106460569671)⟩⟩,⟨⟨(-57962519380),(-57962519323)⟩,⟨(-98884422794),(-98884422737)⟩⟩,⟨⟨(-45759339400),(-45759339355)⟩,⟨(-91371097754),(-91371097709)⟩⟩,⟨⟨(-35331529876),(-35331529826)⟩,⟨(-84018489938),(-84018489885)⟩⟩,⟨⟨(-26472501994),(-26472501948)⟩,⟨(-76902264653),(-76902264607)⟩⟩,⟨⟨(-18994772675),(-18994772629)⟩,⟨(-70079262442),(-70079262396)⟩⟩,⟨⟨(-12728787618),(-12728787573)⟩,⟨(-63590487881),(-63590487835)⟩⟩,⟨⟨(-7521729829),(-7521729772)⟩,⟨(-57463723402),(-57463723345)⟩⟩,⟨⟨(-3236332202),(-3236332145)⟩,⟨(-51715805935),(-51715805878)⟩⟩,⟨⟨250290646,250290692⟩,⟨(-46354601773),(-46354601727)⟩⟩,⟨⟨3047779197,3047779249⟩,⟨(-41380712174),(-41380712124)⟩⟩] +lemma kernel7_1_r1_9_eq : ∀ k : Fin 16, kernel7_1Expr 1 9 k = kernel7_1_r1_9 k := by decide +kernel +noncomputable def kernel7_1_r1_10 : Fin 16 → CBox := ![⟨⟨5253625264,5253625314⟩,⟨(-36788939087),(-36788939035)⟩⟩,⟨⟨6954220561,6954220611⟩,⟨(-32569538602),(-32569538549)⟩⟩,⟨⟨8225852550,8225852600⟩,⟨(-28709286674),(-28709286622)⟩⟩,⟨⟨9135644134,9135644186⟩,⟨(-25192379397),(-25192379346)⟩⟩,⟨⟨9742435341,9742435391⟩,⟨(-22001188610),(-22001188557)⟩⟩,⟨⟨10097606206,10097606252⟩,⟨(-19116890637),(-19116890591)⟩⟩,⟨⟨10245840793,10245840844⟩,⟨(-16519985005),(-16519984952)⟩⟩,⟨⟨10225833555,10225833608⟩,⟨(-14190717726),(-14190717676)⟩⟩,⟨⟨10070939392,10070939442⟩,⟨(-12109422160),(-12109422107)⟩⟩,⟨⟨9809769485,9809769531⟩,⟨(-10256789446),(-10256789399)⟩⟩,⟨⟨9466735288,9466735334⟩,⟨(-8614078677),(-8614078631)⟩⟩,⟨⟨9062543271,9062543329⟩,⟨(-7163275886),(-7163275829)⟩⟩,⟨⟨8614643360,8614643418⟩,⟨(-5887210030),(-5887209973)⟩⟩,⟨⟨8137633635,8137633681⟩,⟨(-4769633094),(-4769633047)⟩⟩,⟨⟨7643624513,7643624559⟩,⟨(-3795270157),(-3795270111)⟩⟩,⟨⟨7142565498,7142565551⟩,⟨(-2949845029),(-2949844978)⟩⟩] +lemma kernel7_1_r1_10_eq : ∀ k : Fin 16, kernel7_1Expr 1 10 k = kernel7_1_r1_10 k := by decide +kernel +noncomputable def kernel7_1_r1_11 : Fin 16 → CBox := ![⟨⟨6642536897,6642536955⟩,⟨(-2220086026),(-2220085969)⟩⟩,⟨⟨6150009563,6150009620⟩,⟨(-1593715728),(-1593715670)⟩⟩,⟨⟨5670075571,5670075617⟩,⟨(-1059428280),(-1059428234)⟩⟩,⟨⟨5206651982,5206652033⟩,⟨(-606856985),(-606856931)⟩⟩,⟨⟨4762660538,4762660589⟩,⟨(-226534795),(-226534742)⟩⟩,⟨⟨4340185279,4340185325⟩,⟨90150460,90150506⟩⟩,⟨⟨3940610484,3940610534⟩,⟨351004117,351004170⟩⟩,⟨⟨3564740711,3564740761⟩,⟨563074908,563074962⟩⟩,⟨⟨3212904952,3212905003⟩,⟨732705918,732705971⟩⟩,⟨⟨2885046757,2885046814⟩,⟨865585511,865585568⟩⟩,⟨⟨2580801441,2580801499⟩,⟨966797534,966797592⟩⟩,⟨⟨2299562336,2299562390⟩,⟨1040869949,1040869999⟩⟩,⟨⟨2040537019,2040537072⟩,⟨1091821863,1091821914⟩⟩,⟨⟨1802795009,1802795062⟩,⟨1123208283,1123208333⟩⟩,⟨⟨1585307599,1585307657⟩,⟨1138162531,1138162589⟩⟩,⟨⟨1386981430,1386981481⟩,⟨1139436171,1139436225⟩⟩] +lemma kernel7_1_r1_11_eq : ∀ k : Fin 16, kernel7_1Expr 1 11 k = kernel7_1_r1_11 k := by decide +kernel +noncomputable def kernel7_1_r1_12 : Fin 16 → CBox := ![⟨⟨1206685799,1206685845⟩,⟨1129436312,1129436358⟩⟩,⟨⟨1043275381,1043275434⟩,⟨1110260425,1110260476⟩⟩,⟨⟨895608418,895608469⟩,⟨1083728451,1083728505⟩⟩,⟨⟨762561319,762561377⟩,⟨1051412470,1051412528⟩⟩,⟨⟨643039937,643039988⟩,⟨1014663830,1014663884⟩⟩,⟨⟨535988382,535988428⟩,⟨974638081,974638127⟩⟩,⟨⟨440395417,440395475⟩,⟨932317573,932317630⟩⟩,⟨⟨355298928,355298978⟩,⟨888532013,888532067⟩⟩,⟨⟨279789003,279789061⟩,⟨843976958,843977016⟩⟩,⟨⟨213009589,213009635⟩,⟨799230674,799230721⟩⟩,⟨⟨154158964,154159018⟩,⟨754769006,754769056⟩⟩,⟨⟨102489644,102489695⟩,⟨710978895,710978949⟩⟩,⟨⟨57307369,57307415⟩,⟨668170440,668170486⟩⟩,⟨⟨17969608,17969654⟩,⟨626587425,626587472⟩⟩,⟨⟨(-16116207),(-16116156)⟩,⟨586416957,586417011⟩⟩,⟨⟨(-45494855),(-45494804)⟩,⟨547797699,547797753⟩⟩] +lemma kernel7_1_r1_12_eq : ∀ k : Fin 16, kernel7_1Expr 1 12 k = kernel7_1_r1_12 k := by decide +kernel +noncomputable def kernel7_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-70665839),(-70665789)⟩,⟨510827281,510827335⟩⟩,⟨⟨(-92085681),(-92085635)⟩,⟨475568841,475568887⟩⟩,⟨⟨(-110170600),(-110170546)⟩,⟨442056589,442056640⟩⟩,⟨⟨(-125299077),(-125299027)⟩,⟨410300833,410300886⟩⟩,⟨⟨(-137814435),(-137814385)⟩,⟨380292175,380292229⟩⟩,⟨⟨(-148027373),(-148027322)⟩,⟨352005400,352005454⟩⟩,⟨⟨(-156218364),(-156218318)⟩,⟨325402469,325402516⟩⟩,⟨⟨(-162640041),(-162639987)⟩,⟨300435452,300435503⟩⟩,⟨⟨(-167519521),(-167519470)⟩,⟨277048800,277048854⟩⟩,⟨⟨(-171060393),(-171060346)⟩,⟨255181285,255181332⟩⟩,⟨⟨(-173444888),(-173444842)⟩,⟨234767825,234767872⟩⟩,⟨⟨(-174835647),(-174835601)⟩,⟨215740775,215740822⟩⟩,⟨⟨(-175377585),(-175377535)⟩,⟨198031180,198031234⟩⟩,⟨⟨(-175199495),(-175199441)⟩,⟨181569733,181569783⟩⟩,⟨⟨(-174415626),(-174415575)⟩,⟨166287534,166287588⟩⟩,⟨⟨(-173126994),(-173126944)⟩,⟨152116788,152116842⟩⟩] +lemma kernel7_1_r1_13_eq : ∀ k : Fin 16, kernel7_1Expr 1 13 k = kernel7_1_r1_13 k := by decide +kernel +noncomputable def kernel7_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-171422811),(-171422757)⟩,⟨138991299,138991350⟩⟩,⟨⟨(-169381616),(-169381569)⟩,⟨126846863,126846909⟩⟩,⟨⟨(-167072376),(-167072326)⟩,⟨115621569,115621623⟩⟩,⟨⟨(-164555521),(-164555475)⟩,⟨105256052,105256098⟩⟩,⟨⟨(-161883784),(-161883726)⟩,⟨95693578,95693636⟩⟩,⟨⟨(-159103104),(-159103058)⟩,⟨86880273,86880319⟩⟩,⟨⟨(-156253437),(-156253383)⟩,⟨78765035,78765085⟩⟩,⟨⟨(-153369241),(-153369190)⟩,⟨71299639,71299693⟩⟩,⟨⟨(-150480298),(-150480244)⟩,⟨64438646,64438696⟩⟩,⟨⟨(-147612192),(-147612142)⟩,⟨58139463,58139517⟩⟩,⟨⟨(-144786780),(-144786726)⟩,⟨52362246,52362296⟩⟩,⟨⟨(-142022679),(-142022625)⟩,⟨47069694,47069744⟩⟩,⟨⟨(-139335663),(-139335605)⟩,⟨42227188,42227245⟩⟩,⟨⟨(-136739041),(-136738995)⟩,⟨37802551,37802598⟩⟩,⟨⟨(-134243953),(-134243899)⟩,⟨33765931,33765982⟩⟩,⟨⟨(-131859707),(-131859660)⟩,⟨30089823,30089870⟩⟩] +lemma kernel7_1_r1_14_eq : ∀ k : Fin 16, kernel7_1Expr 1 14 k = kernel7_1_r1_14 k := by decide +kernel +noncomputable def kernel7_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-129593955),(-129593900)⟩,⟨26748824,26748874⟩⟩,⟨⟨(-127452970),(-127452923)⟩,⟨23719673,23719719⟩⟩,⟨⟨(-125441890),(-125441832)⟩,⟨20981013,20981071⟩⟩,⟨⟨(-123564798),(-123564740)⟩,⟨18513436,18513494⟩⟩,⟨⟨(-121824969),(-121824911)⟩,⟨16299247,16299305⟩⟩,⟨⟨(-120224960),(-120224914)⟩,⟨14322517,14322564⟩⟩,⟨⟨(-118766757),(-118766699)⟩,⟨12568884,12568942⟩⟩,⟨⟨(-117451854),(-117451808)⟩,⟨11025548,11025594⟩⟩,⟨⟨(-116281388),(-116281338)⟩,⟨9681211,9681265⟩⟩,⟨⟨(-115256136),(-115256078)⟩,⟨8525946,8526004⟩⟩,⟨⟨(-114376666),(-114376612)⟩,⟨7551237,7551287⟩⟩,⟨⟨(-113643405),(-113643347)⟩,⟨6749817,6749875⟩⟩,⟨⟨(-113056584),(-113056529)⟩,⟨6115755,6115805⟩⟩,⟨⟨(-112616363),(-112616309)⟩,⟨5644314,5644365⟩⟩,⟨⟨(-112322860),(-112322810)⟩,⟨5331951,5332006⟩⟩,⟨⟨(-112176086),(-112176032)⟩,⟨5176370,5176421⟩⟩] +lemma kernel7_1_r1_15_eq : ∀ k : Fin 16, kernel7_1Expr 1 15 k = kernel7_1_r1_15 k := by decide +kernel +noncomputable def kernel7_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel7_1_r1_0,kernel7_1_r1_1,kernel7_1_r1_2,kernel7_1_r1_3,kernel7_1_r1_4,kernel7_1_r1_5,kernel7_1_r1_6,kernel7_1_r1_7,kernel7_1_r1_8,kernel7_1_r1_9,kernel7_1_r1_10,kernel7_1_r1_11,kernel7_1_r1_12,kernel7_1_r1_13,kernel7_1_r1_14,kernel7_1_r1_15] +lemma kernel7_1_r1_eq (i k : Fin 16) : kernel7_1Expr 1 i k = kernel7_1_r1 i k := by + fin_cases i + · exact kernel7_1_r1_0_eq k + · exact kernel7_1_r1_1_eq k + · exact kernel7_1_r1_2_eq k + · exact kernel7_1_r1_3_eq k + · exact kernel7_1_r1_4_eq k + · exact kernel7_1_r1_5_eq k + · exact kernel7_1_r1_6_eq k + · exact kernel7_1_r1_7_eq k + · exact kernel7_1_r1_8_eq k + · exact kernel7_1_r1_9_eq k + · exact kernel7_1_r1_10_eq k + · exact kernel7_1_r1_11_eq k + · exact kernel7_1_r1_12_eq k + · exact kernel7_1_r1_13_eq k + · exact kernel7_1_r1_14_eq k + · exact kernel7_1_r1_15_eq k +noncomputable def kernel7_1_r2_0 : Fin 16 → CBox := ![⟨⟨19016940131130085935464,19016940131130085998709⟩,⟨18091643581842376545514,18091643581842376608808⟩⟩,⟨⟨19004942337085729357239,19004942337085729420450⟩,⟨18072061761927832419084,18072061761927832482349⟩⟩,⟨⟨18980963154070008002586,18980963154070008065697⟩,⟨18032957957387540719021,18032957957387540782185⟩⟩,⟨⟨18945035402455551918896,18945035402455551981892⟩,⟨17974451552249972690231,17974451552249972753279⟩⟩,⟨⟨18897208337698773883297,18897208337698773946115⟩,⟨17896720907963397228720,17896720907963397291590⟩⟩,⟨⟨18837547678353941819004,18837547678353941881620⟩,⟨17800002510849372385493,17800002510849372448163⟩⟩,⟨⟨18766135640352482730942,18766135640352482793306⟩,⟨17684589843614353282835,17684589843614353345248⟩⟩,⟨⟨18683070974977245886213,18683070974977245948290⟩,⟨17550831987907304742730,17550831987907304804859⟩⟩,⟨⟨18588469007397217946188,18588469007397218007929⟩,⟨17399131966564770859359,17399131966564770921150⟩⟩,⟨⟨18482461672114470234409,18482461672114470295787⟩,⟨17229944835777091099088,17229944835777091160516⟩⟩,⟨⟨18365197541220366160061,18365197541220366221032⟩,⟨17043775538929039443516,17043775538929039504539⟩⟩,⟨⟨18236841840969835067611,18236841840969835128139⟩,⟨16841176535304283976833,16841176535304284037411⟩⟩,⟨⟨18097576451867418586870,18097576451867418646910⟩,⟨16622745218185491770810,16622745218185491830900⟩⟩,⟨⟨17947599887222332537095,17947599887222332596620⟩,⟨16389121138121076388989,16389121138121076448565⟩⟩,⟨⟨17787127244976321084479,17787127244976321143447⟩,⟨16140983048256681779814,16140983048256681838832⟩⟩,⟨⟨17616390127540750043684,17616390127540750102072⟩,⟨15879045789636507413474,15879045789636507471912⟩⟩] +lemma kernel7_1_r2_0_eq : ∀ k : Fin 16, kernel7_1Expr 2 0 k = kernel7_1_r2_0 k := by decide +kernel +noncomputable def kernel7_1_r2_1 : Fin 16 → CBox := ![⟨⟨17435636524400067837623,17435636524400067895381⟩,⟨15604057035259374665452,15604057035259374723257⟩⟩,⟨⟨17245130652348038933639,17245130652348038990751⟩,⟨15316793912420824176362,15316793912420824233520⟩⟩,⟨⟨17045152748420309650294,17045152748420309706732⟩,⟨15018059523480326692650,15018059523480326749133⟩⟩,⟨⟨16835998810869896696211,16835998810869896751928⟩,⟨14708679385657742841112,14708679385657742896874⟩⟩,⟨⟨16617980283897834504455,16617980283897834559431⟩,⟨14389497810782429996686,14389497810782430051708⟩⟩,⟨⟨16391423682295010623927,16391423682295010678127⟩,⟨14061374246089945080960,14061374246089945135206⟩⟩,⟨⟨16156670152667550742023,16156670152667550795436⟩,⟨13725179597184365452386,13725179597184365505842⟩⟩,⟨⟨15914074968500320937608,15914074968500320990214⟩,⟨13381792554159255956860,13381792554159256009509⟩⟩,⟨⟨15664006956953571077689,15664006956953571129440⟩,⟨13032095941598843047557,13032095941598843099350⟩⟩,⟨⟨15406847855977981292193,15406847855977981343086⟩,⟨12676973112765794349789,12676973112765794400721⟩⟩,⟨⟨15142991601064204392267,15142991601064204442277⟩,⟨12317304407727093420029,12317304407727093470080⟩⟩,⟨⟨14872843541704647043724,14872843541704647092831⟩,⟨11953963694479942779573,11953963694479942828721⟩⟩,⟨⟨14596819588427485668643,14596819588427485716845⟩,⟨11587815011321636306190,11587815011321636354429⟩⟩,⟨⟨14315345292055260767115,14315345292055260814382⟩,⟨11219709327768196584273,11219709327768196631577⟩⟩,⟨⟨14028854857632186745060,14028854857632186791391⟩,⟨10850481440274567937448,10850481440274567983816⟩⟩,⟨⟨13737790096244918131981,13737790096244918177348⟩,⟨10480947017853529875671,10480947017853529921076⟩⟩] +lemma kernel7_1_r2_1_eq : ∀ k : Fin 16, kernel7_1Expr 2 1 k = kernel7_1_r2_1 k := by decide +kernel +noncomputable def kernel7_1_r2_2 : Fin 16 → CBox := ![⟨⟨13442599318720458332994,13442599318720458377395⟩,⟨10111899811441352202807,10111899811441352247241⟩⟩,⟨⟨13143736175912030411378,13143736175912030454802⟩,⟨9744109039526431915532,9744109039526431958990⟩⟩,⟨⟨12841658450969356552168,12841658450969356594613⟩,⟨9378316961154290754345,9378316961154290796820⟩⟩,⟨⟨12536826809624814221779,12536826809624814263226⟩,⟨9015236645960498642684,9015236645960498684162⟩⟩,⟨⟨12229703515102973398511,12229703515102973438960⟩,⟨8655549949374905511666,8655549949374905552145⟩⟩,⟨⟨11920751114770525669828,11920751114770525709282⟩,⟨8299905699598929550769,8299905699598929590252⟩⟩,⟨⟨11610431106079982269355,11610431106079982307814⟩,⟨7948918101395688950853,7948918101395688989340⟩⟩,⟨⟨11299202589718154363339,11299202589718154400777⟩,⟨7603165360163679772680,7603165360163679810146⟩⟩,⟨⟨10987520918144835023379,10987520918144835059812⟩,⟨7263188528201643606629,7263188528201643643090⟩⟩,⟨⟨10675836347894920648060,10675836347894920683496⟩,⟨6929490573528197579571,6929490573528197615033⟩⟩,⟨⟨10364592704116259758204,10364592704116259792654⟩,⟨6602535670107360759345,6602535670107360793819⟩⟩,⟨⟨10054226065824813078213,10054226065824813111675⟩,⟨6282748706862504082459,6282748706862504115943⟩⟩,⟨⟨9745163480278458006224,9745163480278458038685⟩,⟨5970515011448105356892,5970515011448105389375⟩⟩,⟨⟨9437821714702355064128,9437821714702355095614⟩,⟨5666180283401950166579,5666180283401950198089⟩⟩,⟨⟨9132606053344734649807,9132606053344734680333⟩,⟨5370050730030231731676,5370050730030231762220⟩⟩,⟨⟨8829909147505866967037,8829909147505866996585⟩,⟨5082393397193621020832,5082393397193621050401⟩⟩] +lemma kernel7_1_r2_2_eq : ∀ k : Fin 16, kernel7_1Expr 2 2 k = kernel7_1_r2_2 k := by decide +kernel +noncomputable def kernel7_1_r2_3 : Fin 16 → CBox := ![⟨⟨8530109925769473077985,8530109925769473106593⟩,⟨4803436686072071880645,4803436686072071909273⟩⟩,⟨⟨8233572571180484931030,8233572571180484958695⟩,⟨4533371045997103266536,4533371045997103294221⟩⟩,⟨⟨7940645571562274968510,7940645571562274995237⟩,⟨4272349832558646264805,4272349832558646291549⟩⟩,⟨⟨7651660848557398515383,7651660848557398541211⟩,⟨4020490319424168128367,4020490319424168154210⟩⟩,⟨⟨7366932970316296999123,7366932970316297024038⟩,⟨3777874851654390895920,3777874851654390920849⟩⟩,⟨⟨7086758452056574471870,7086758452056574495895⟩,⟨3544552127764981582483,3544552127764981606522⟩⟩,⟨⟨6811415147980040748356,6811415147980040771516⟩,⟨3320538597368344447020,3320538597368344470196⟩⟩,⟨⟨6541161737274619958854,6541161737274619981152⟩,⟨3105819960934110887453,3105819960934110909763⟩⟩,⟨⟨6276237306152484198569,6276237306152484220026⟩,⟨2900352758029919521195,2900352758029919542663⟩⟩,⟨⟨6016861027093414029573,6016861027093414050219⟩,⟨2704066030343271466077,2704066030343271486736⟩⟩,⟨⟨5763231935682307582401,5763231935682307602231⟩,⟨2516863045837194057264,2516863045837194077107⟩⟩,⟨⟨5515528804660606675607,5515528804660606694654⟩,⟨2338623070552673924728,2338623070552673943787⟩⟩,⟨⟨5273910114061470634361,5273910114061470652638⟩,⟨2169203174833892818545,2169203174833892836835⟩⟩,⟨⟨5038514115575632071596,5038514115575632089125⟩,⟨2008440061111912284248,2008440061111912301787⟩⟩,⟨⟨4809458988606282986287,4809458988606283003077⟩,⟨1856151900831529392494,1856151900831529409294⟩⟩,⟨⟨4586843084823694565730,4586843084823694581817⟩,⟨1712140168636820832753,1712140168636820848848⟩⟩] +lemma kernel7_1_r2_3_eq : ∀ k : Fin 16, kernel7_1Expr 2 3 k = kernel7_1_r2_3 k := by decide +kernel +noncomputable def kernel7_1_r2_4 : Fin 16 → CBox := ![⟨⟨4370745257429491629080,4370745257429491644487⟩,⟨1576191462535105416280,1576191462535105431696⟩⟩,⟨⟨4161225270791738170299,4161225270791738185027⟩,⟨1448079299427941544450,1448079299427941559184⟩⟩,⟨⟨3958324285619589326340,3958324285619589340406⟩,⟨1327565876122266903386,1327565876122266917458⟩⟩,⟨⟨3762065414413732212674,3762065414413732226126⟩,⟨1214403786705604504847,1214403786705604518306⟩⟩,⟨⟨3572454341558821017563,3572454341558821030392⟩,⟨1108337687977031781021,1108337687977031793857⟩⟩,⟨⟨3389480002118397266886,3389480002118397279124⟩,⟨1009105905460988196013,1009105905460988208257⟩⟩,⟨⟨3213115313152309497022,3213115313152309508670⟩,⟨916441973384761931464,916441973384761943115⟩⟩,⟨⟨3043317951201512972090,3043317951201512983205⟩,⟨830076102863660604326,830076102863660615446⟩⟩,⟨⟨2880031169474647773871,2880031169474647784444⟩,⟨749736573401776411479,749736573401776422059⟩⟩,⟨⟨2723184648223517011567,2723184648223517021622⟩,⟨675151043672660777280,675151043672660787337⟩⟩,⟨⟨2572695371808369190375,2572695371808369199936⟩,⟨606047778385380724001,606047778385380733566⟩⟩,⟨⟨2428468526025942257918,2428468526025942266998⟩,⟨542156788860155549815,542156788860155558898⟩⟩,⟨⟨2290398409400190106588,2290398409400190115207⟩,⟨483210885727506252002,483210885727506260623⟩⟩,⟨⟨2158369352313622565647,2158369352313622573829⟩,⟨428946642919698244282,428946642919698252464⟩⟩,⟨⟨2032256638081959207109,2032256638081959214860⟩,⟨379105272838031384187,379105272838031391939⟩⟩,⟨⟨1911927420341691105006,1911927420341691112355⟩,⟨333433413249770220787,333433413249770228137⟩⟩] +lemma kernel7_1_r2_4_eq : ∀ k : Fin 16, kernel7_1Expr 2 4 k = kernel7_1_r2_4 k := by decide +kernel +noncomputable def kernel7_1_r2_5 : Fin 16 → CBox := ![⟨⟨1797241631424261636652,1797241631424261643612⟩,⟨291683827090494373205,291683827090494380164⟩⟩,⟨⟨1688052876726828624170,1688052876726828630749⟩,⟨253616016918412313442,253616016918412320025⟩⟩,⟨⟨1584209310452757081137,1584209310452757087368⟩,⟨218996756284488192375,218996756284488198607⟩⟩,⟨⟨1485554488479881574756,1485554488479881580639⟩,⟨187600540744569017907,187600540744569023792⟩⟩,⟨⟨1391928194515973693959,1391928194515973699512⟩,⟨159209961646252962160,159209961646252967714⟩⟩,⟨⟨1303167236113660942399,1303167236113660947637⟩,⟨133616006173856153917,133616006173856159157⟩⟩,⟨⟨1219106207536341085015,1219106207536341089956⟩,⟨110618287429984840322,110618287429984845264⟩⟩,⟨⟨1139578216887713154600,1139578216887713159258⟩,⟨90025208572948401231,90025208572948405891⟩⟩,⟨⟨1064415575335964124539,1064415575335964128923⟩,⟨71654065217127678235,71654065217127682621⟩⟩,⟨⟨993450446675279918622,993450446675279922753⟩,⟨55331090440484008323,55331090440484012453⟩⟩,⟨⟨926515455868406620688,926515455868406624594⟩,⟨40891446832111408492,40891446832111412398⟩⟩,⟨⟨863444255601059589384,863444255601059593031⟩,⟨28179170055904968402,28179170055904972049⟩⟩,⟨⟨804072050249043091424,804072050249043094866⟩,⟨17047068407143303071,17047068407143306514⟩⟩,⟨⟨748236077009383523921,748236077009383527150⟩,⟨7356582800395935182,7356582800395938411⟩⟩,⟨⟨695776044275387874245,695776044275387877276⟩,⟨(-1022388446823482259),(-1022388446823479227)⟩⟩,⟨⟨646534527640518072628,646534527640518075480⟩,⟨(-8211695776203264856),(-8211695776203262005)⟩⟩] +lemma kernel7_1_r2_5_eq : ∀ k : Fin 16, kernel7_1Expr 2 5 k = kernel7_1_r2_5 k := by decide +kernel +noncomputable def kernel7_1_r2_6 : Fin 16 → CBox := ![⟨⟨600357324195927100902,600357324195927103569⟩,⟨(-14325171372375595784),(-14325171372375593118)⟩⟩,⟨⟨557093766040431735108,557093766040431737611⟩,⟨(-19468885002883142355),(-19468885002883139854)⟩⟩,⟨⟨516596994148972626941,516596994148972629270⟩,⟨(-23741418928742482307),(-23741418928742479978)⟩⟩,⟨⟨478724193945962893389,478724193945962895584⟩,⟨(-27234158297036439689),(-27234158297036437495)⟩⟩,⟨⟨443336794103410035529,443336794103410037574⟩,⟨(-30031593637865093525),(-30031593637865091478)⟩⟩,⟨⟨410300630230675172121,410300630230675174040⟩,⟨(-32211632309389582138),(-32211632309389580218)⟩⟩,⟨⟨379486075243845222233,379486075243845224029⟩,⟨(-33845915963459766833),(-33845915963459765037)⟩⟩,⟨⟨350768138298818720778,350768138298818722456⟩,⟨(-35000141337472829099),(-35000141337472827422)⟩⟩,⟨⟨324026534244437642514,324026534244437644067⟩,⟨(-35734381912930943085),(-35734381912930941530)⟩⟩,⟨⟨299145725601609512430,299145725601609513886⟩,⟨(-36103408215152005931),(-36103408215152004475)⟩⟩,⟨⟨276014939102778281868,276014939102778283243⟩,⟨(-36157004759481163518),(-36157004759481162145)⟩⟩,⟨⟨254528158834858397716,254528158834858399002⟩,⟨(-35940281875144574861),(-35940281875144573576)⟩⟩,⟨⟨234584098019470941269,234584098019470942473⟩,⟨(-35493980856822961986),(-35493980856822960782)⟩⟩,⟨⟨216086151438699121890,216086151438699123004⟩,⟨(-34854771104591772234),(-34854771104591771120)⟩⟩,⟨⟨198942330474330131189,198942330474330132217⟩,⟨(-34055538113811032267),(-34055538113811031240)⟩⟩,⟨⟨183065182675395864193,183065182675395865161⟩,⟨(-33125661366819855741),(-33125661366819854773)⟩⟩] +lemma kernel7_1_r2_6_eq : ∀ k : Fin 16, kernel7_1Expr 2 6 k = kernel7_1_r2_6 k := by decide +kernel +noncomputable def kernel7_1_r2_7 : Fin 16 → CBox := ![⟨⟨168371697704475325318,168371697704475326208⟩,⟨(-32091281357091004721),(-32091281357091003831)⟩⟩,⟨⟨154783201439350080001,154783201439350080848⟩,⟨(-30975555143234450915),(-30975555143234450068)⟩⟩,⟨⟨142225239924830970293,142225239924830971070⟩,⟨(-29798899984507435306),(-29798899984507434528)⟩⟩,⟨⟨130627454781450997011,130627454781450997746⟩,⟨(-28579224751075786315),(-28579224751075785580)⟩⟩,⟨⟨119923451584715969995,119923451584715970673⟩,⟨(-27332148931126290064),(-27332148931126289385)⟩⟩,⟨⟨110050662632099770011,110050662632099770632⟩,⟨(-26071209173150153970),(-26071209173150153349)⟩⟩,⟨⟨100950205416243734126,100950205416243734713⟩,⟨(-24808053405531649504),(-24808053405531648917)⟩⟩,⟨⟨92566738023043226935,92566738023043227470⟩,⟨(-23552622667326422723),(-23552622667326422189)⟩⟩,⟨⟨84848312573543231882,84848312573543232381⟩,⟨(-22313320864240385194),(-22313320864240384694)⟩⟩,⟨⟨77746227729772217128,77746227729772217592⟩,⟨(-21097172732842971022),(-21097172732842970558)⟩⟩,⟨⟨71214881187662062287,71214881187662062726⟩,⟨(-19909970354553444223),(-19909970354553443785)⟩⟩,⟨⟨65211622985764467764,65211622985764468180⟩,⟨(-18756408609561833675),(-18756408609561833257)⟩⟩,⟨⟨59696610367207364132,59696610367207364509⟩,⟨(-17640210000259584342),(-17640210000259583964)⟩⟩,⟨⟨54632664844762121583,54632664844762121925⟩,⟨(-16564239304655754566),(-16564239304655754225)⟩⟩,⟨⟨49985132035439883585,49985132035439883905⟩,⟨(-15530608543351665793),(-15530608543351665474)⟩⟩,⟨⟨45721744752037246959,45721744752037247275⟩,⟨(-14540772759651606892),(-14540772759651606576)⟩⟩] +lemma kernel7_1_r2_7_eq : ∀ k : Fin 16, kernel7_1Expr 2 7 k = kernel7_1_r2_7 k := by decide +kernel +noncomputable def kernel7_1_r2_8 : Fin 16 → CBox := ![⟨⟨41812489764756333881,41812489764756334174⟩,⟨(-13595617122003876932),(-13595617122003876637)⟩⟩,⟨⟨38229478576601803857,38229478576601804120⟩,⟨(-12695535861884657965),(-12695535861884657702)⟩⟩,⟨⟨34946822491805556607,34946822491805556861⟩,⟨(-11840503559124928169),(-11840503559124927915)⟩⟩,⟨⟨31940512197082266653,31940512197082266898⟩,⟨(-11030139281178681133),(-11030139281178680888)⟩⟩,⟨⟨29188302021051648410,29188302021051648628⟩,⟨(-10263764073548241023),(-10263764073548240805)⟩⟩,⟨⟨26669598987602466786,26669598987602466987⟩,⟨(-9540452286093371911),(-9540452286093371710)⟩⟩,⟨⟨24365356734201525052,24365356734201525244⟩,⟨(-8859077204791274525),(-8859077204791274333)⟩⟩,⟨⟨22257974326014332409,22257974326014332592⟩,⟨(-8218351441180986965),(-8218351441180986782)⟩⟩,⟨⟨20331199961018774980,20331199961018775158⟩,⟨(-7616862512674161634),(-7616862512674161454)⟩⟩,⟨⟨18570039529850464396,18570039529850464547⟩,⟨(-7053104026559842597),(-7053104026559842445)⟩⟩,⟨⟨16960669966691293461,16960669966691293603⟩,⟨(-6525502859248337579),(-6525502859248337436)⟩⟩,⟨⟨15490357303860126041,15490357303860126180⟩,⟨(-6032442700423449081),(-6032442700423448943)⟩⟩,⟨⟨14147379322636374716,14147379322636374855⟩,⟨(-5572284309599583849),(-5572284309599583710)⟩⟩,⟨⟨12920952675988336139,12920952675988336272⟩,⟨(-5143382810370068243),(-5143382810370068108)⟩⟩,⟨⟨11801164345032034141,11801164345032034261⟩,⟨(-4744102325609791363),(-4744102325609791242)⟩⟩,⟨⟨10778907279958241095,10778907279958241197⟩,⟨(-4372828235250554177),(-4372828235250554075)⟩⟩] +lemma kernel7_1_r2_8_eq : ∀ k : Fin 16, kernel7_1Expr 2 8 k = kernel7_1_r2_8 k := by decide +kernel +noncomputable def kernel7_1_r2_9 : Fin 16 → CBox := ![⟨⟨9845820067585118932,9845820067585119044⟩,⟨(-4027977317141982817),(-4027977317141982705)⟩⟩,⟨⟨8994230461378198607,8994230461378198700⟩,⟨(-3708006011076954069),(-3708006011076953975)⟩⟩,⟨⟨8217102605493612220,8217102605493612313⟩,⟨(-3411417026404580316),(-3411417026404580222)⟩⟩,⟨⟨7507987781920305753,7507987781920305842⟩,⟨(-3136764494858719115),(-3136764494858719025)⟩⟩,⟨⟨6860978508909573527,6860978508909573607⟩,⟨(-2882657852357301639),(-2882657852357301560)⟩⟩,⟨⟨6270665819385211575,6270665819385211637⟩,⟨(-2647764616620193303),(-2647764616620193242)⟩⟩,⟨⟨5732099549737384957,5732099549737385033⟩,⟨(-2430812211536808735),(-2430812211536808660)⟩⟩,⟨⟨5240751472143750741,5240751472143750802⟩,⟨(-2230588974300736450),(-2230588974300736388)⟩⟩,⟨⟨4792481107171714148,4792481107171714242⟩,⟨(-2045944467416064180),(-2045944467416064085)⟩⟩,⟨⟨4383504057748538954,4383504057748539021⟩,⟨(-1875789204757119739),(-1875789204757119672)⟩⟩,⟨⟨4010362710507152189,4010362710507152255⟩,⟨(-1719093888909189502),(-1719093888909189436)⟩⟩,⟨⟨3669899155903452437,3669899155903452503⟩,⟨(-1574888246004307576),(-1574888246004307510)⟩⟩,⟨⟨3359230184246650034,3359230184246650101⟩,⟨(-1442259534159373962),(-1442259534159373895)⟩⟩,⟨⟨3075724220790329929,3075724220790329996⟩,⟨(-1320350792384980600),(-1320350792384980533)⟩⟩,⟨⟨2816980069212383615,2816980069212383682⟩,⟨(-1208358888420278362),(-1208358888420278295)⟩⟩,⟨⟨2580807339091063082,2580807339091063148⟩,⟨(-1105532416317452388),(-1105532416317452321)⟩⟩] +lemma kernel7_1_r2_9_eq : ∀ k : Fin 16, kernel7_1Expr 2 9 k = kernel7_1_r2_9 k := by decide +kernel +noncomputable def kernel7_1_r2_10 : Fin 16 → CBox := ![⟨⟨2365208439296323963,2365208439296324016⟩,⟨(-1011169487702813700),(-1011169487702813647)⟩⟩,⟨⟨2168362025503597365,2168362025503597427⟩,⟨(-924615454433346438),(-924615454433346376)⟩⟩,⟨⟨1988607796252781982,1988607796252782044⟩,⟨(-845260594800876586),(-845260594800876523)⟩⟩,⟨⟨1824432538077861730,1824432538077861788⟩,⟨(-772537790464449062),(-772537790464449004)⟩⟩,⟨⟨1674457326188375184,1674457326188375242⟩,⟨(-705920216869559947),(-705920216869559889)⟩⟩,⟨⟨1537425792965523696,1537425792965523744⟩,⟨(-644919065996479417),(-644919065996479368)⟩⟩,⟨⟨1412193382121176870,1412193382121176909⟩,⟨(-589081316826537550),(-589081316826537511)⟩⟩,⟨⟨1297717511740612892,1297717511740612956⟩,⟨(-537987565884323936),(-537987565884323873)⟩⟩,⟨⟨1193048574577153430,1193048574577153497⟩,⟨(-491249927566705970),(-491249927566705903)⟩⟩,⟨⟨1097321708880454663,1097321708880454722⟩,⟨(-448510011669992467),(-448510011669992408)⟩⟩,⟨⟨1009749277715027950,1009749277715027989⟩,⟨(-409436983540278078),(-409436983540278039)⟩⟩,⟨⟨929613999159440784,929613999159440833⟩,⟨(-373725710567081855),(-373725710567081806)⟩⟩,⟨⟨856262673969950706,856262673969950774⟩,⟨(-341094997287175218),(-341094997287175150)⟩⟩,⟨⟨789100461247519528,789100461247519568⟩,⟨(-311285910136544488),(-311285910136544449)⟩⟩,⟨⟨727585656368472436,727585656368472475⟩,⟨(-284060191858484422),(-284060191858484382)⟩⟩,⟨⟨671224928932179738,671224928932179777⟩,⟨(-259198764721706731),(-259198764721706692)⟩⟩] +lemma kernel7_1_r2_10_eq : ∀ k : Fin 16, kernel7_1Expr 2 10 k = kernel7_1_r2_10 k := by decide +kernel +noncomputable def kernel7_1_r2_11 : Fin 16 → CBox := ![⟨⟨619568981750881204,619568981750881244⟩,⟨(-236500321002921463),(-236500321002921423)⟩⟩,⟨⟨572208594964891843,572208594964891883⟩,⟨(-215779998624373518),(-215779998624373479)⟩⟩,⟨⟨528771022219358983,528771022219359037⟩,⟨(-196868139390873050),(-196868139390872996)⟩⟩,⟨⟨488916708495418707,488916708495418746⟩,⟨(-179609126927230780),(-179609126927230741)⟩⟩,⟨⟨452336301658290203,452336301658290242⟩,⟨(-163860301161575517),(-163860301161575477)⟩⟩,⟨⟨418747932077004033,418747932077004073⟩,⟨(-149490946020149834),(-149490946020149794)⟩⟩,⟨⟨387894736794599692,387894736794599732⟩,⟨(-136381346883582851),(-136381346883582811)⟩⟩,⟨⟨359542606693232123,359542606693232177⟩,⟨(-124421914293317704),(-124421914293317649)⟩⟩,⟨⟨333478136915048505,333478136915048544⟩,⟨(-113512370380975196),(-113512370380975156)⟩⟩,⟨⟨309506762476099068,309506762476099108⟩,⟨(-103560994515173196),(-103560994515173156)⟩⟩,⟨⟨287451062555837919,287451062555837959⟩,⟨(-94483924712856758),(-94483924712856718)⟩⟩,⟨⟨267149218367566085,267149218367566125⟩,⟨(-86204511439567221),(-86204511439567181)⟩⟩,⟨⟨248453610823755011,248453610823755051⟩,⟨(-78652720520107216),(-78652720520107176)⟩⟩,⟨⟨231229545412492644,231229545412492684⟩,⟨(-71764581993269676),(-71764581993269636)⟩⟩,⟨⟨215354092804876686,215354092804876726⟩,⟨(-65481681867846624),(-65481681867846584)⟩⟩,⟨⟨200715034725215188,200715034725215228⟩,⟨(-59750693868735807),(-59750693868735767)⟩⟩] +lemma kernel7_1_r2_11_eq : ∀ k : Fin 16, kernel7_1Expr 2 11 k = kernel7_1_r2_11 k := by decide +kernel +noncomputable def kernel7_1_r2_12 : Fin 16 → CBox := ![⟨⟨187209905543174966,187209905543175006⟩,⟨(-54522948398835463),(-54522948398835423)⟩⟩,⟨⟨174745120895946659,174745120895946699⟩,⟨(-49754036082215468),(-49754036082215428)⟩⟩,⟨⟨163235185425094595,163235185425094654⟩,⟨(-45403443394823924),(-45403443394823865)⟩⟩,⟨⟨152601972422677628,152601972422677668⟩,⟨(-41434218029115042),(-41434218029115002)⟩⟩,⟨⟨142774068829747203,142774068829747244⟩,⟨(-37812661777151088),(-37812661777151047)⟩⟩,⟨⟨133686179622383141,133686179622383181⟩,⟨(-34508048851879427),(-34508048851879386)⟩⟩,⟨⟨125278586160607489,125278586160607530⟩,⟨(-31492367697579048),(-31492367697579008)⟩⟩,⟨⟨117496653568092613,117496653568092653⟩,⟨(-28740084467267068),(-28740084467267027)⟩⟩,⟨⟨110290382659509589,110290382659509629⟩,⟨(-26227926466675439),(-26227926466675399)⟩⟩,⟨⟨103614002341316635,103614002341316681⟩,⟨(-23934683980912989),(-23934683980912944)⟩⟩,⟨⟨97425598784153811,97425598784153852⟩,⟨(-21841029010896423),(-21841029010896382)⟩⟩,⟨⟨91686778003921425,91686778003921465⟩,⟨(-19929349551945462),(-19929349551945422)⟩⟩,⟨⟨86362358796961201,86362358796961246⟩,⟨(-18183598146550646),(-18183598146550601)⟩⟩,⟨⟨81420093255187215,81420093255187256⟩,⟨(-16589153537266258),(-16589153537266218)⟩⟩,⟨⟨76830412341973556,76830412341973601⟩,⟨(-15132694334037904),(-15132694334037859)⟩⟩,⟨⟨72566194241338018,72566194241338059⟩,⟨(-13802083693169536),(-13802083693169496)⟩⟩] +lemma kernel7_1_r2_12_eq : ∀ k : Fin 16, kernel7_1Expr 2 12 k = kernel7_1_r2_12 k := by decide +kernel +noncomputable def kernel7_1_r2_13 : Fin 16 → CBox := ![⟨⟨68602553403527266,68602553403527312⟩,⟨(-12586264082730748),(-12586264082730703)⟩⟩,⟨⟨64916648401394641,64916648401394687⟩,⟨(-11475161281686866),(-11475161281686821)⟩⟩,⟨⟨61487506885692675,61487506885692716⟩,⟨(-10459596827608819),(-10459596827608778)⟩⟩,⟨⟨58295866085162076,58295866085162131⟩,⟨(-9531208190706517),(-9531208190706461)⟩⟩,⟨⟨55324027440527837,55324027440527883⟩,⟨(-8682376010355766),(-8682376010355720)⟩⟩,⟨⟨52555724091533249,52555724091533305⟩,⟨(-7906157784488903),(-7906157784488847)⟩⟩,⟨⟨49976000054156275,49976000054156316⟩,⟨(-7196227452424163),(-7196227452424122)⟩⟩,⟨⟨47571100032257462,47571100032257503⟩,⟨(-6546820358154282),(-6546820358154241)⟩⟩,⟨⟨45328368905106276,45328368905106317⟩,⟨(-5952683124024904),(-5952683124024863)⟩⟩,⟨⟨43236160020433446,43236160020433487⟩,⟨(-5409028004334509),(-5409028004334468)⟩⟩,⟨⟨41283751502690792,41283751502690833⟩,⟨(-4911491324892414),(-4911491324892373)⟩⟩,⟨⟨39461269858822777,39461269858822818⟩,⟨(-4456095648190069),(-4456095648190028)⟩⟩,⟨⟨37759620229750598,37759620229750639⟩,⟨(-4039215334770157),(-4039215334770116)⟩⟩,⟨⟨36170422695566342,36170422695566383⟩,⟨(-3657545199809509),(-3657545199809469)⟩⟩,⟨⟨34685954096696960,34685954096697001⟩,⟨(-3308071990044717),(-3308071990044676)⟩⟩,⟨⟨33299094882542350,33299094882542391⟩,⟨(-2988048430134573),(-2988048430134532)⟩⟩] +lemma kernel7_1_r2_13_eq : ∀ k : Fin 16, kernel7_1Expr 2 13 k = kernel7_1_r2_13 k := by decide +kernel +noncomputable def kernel7_1_r2_14 : Fin 16 → CBox := ![⟨⟨32003280543785797,32003280543785843⟩,⟨(-2694969609531559),(-2694969609531513)⟩⟩,⟨⟨30792457225143774,30792457225143820⟩,⟨(-2426551501077876),(-2426551501077830)⟩⟩,⟨⟨29661041152151011,29661041152151052⟩,⟨(-2180711420990664),(-2180711420990623)⟩⟩,⟨⟨28603881539016756,28603881539016802⟩,⟨(-1955550256790399),(-1955550256790353)⟩⟩,⟨⟨27616226674955067,27616226674955108⟩,⟨(-1749336305178532),(-1749336305178491)⟩⟩,⟨⟨26693692913976307,26693692913976348⟩,⟨(-1560490576002688),(-1560490576002647)⟩⟩,⟨⟨25832236318188071,25832236318188117⟩,⟨(-1387573431366407),(-1387573431366361)⟩⟩,⟨⟨25028126727429869,25028126727429915⟩,⟨(-1229272440746045),(-1229272440745999)⟩⟩,⟨⟨24277924048772291,24277924048772332⟩,⟨(-1084391343762910),(-1084391343762869)⟩⟩,⟨⟨23578456578241719,23578456578241761⟩,⟨(-951840022109681),(-951840022109640)⟩⟩,⟨⟨22926801184265328,22926801184265369⟩,⟨(-830625391125834),(-830625391125793)⟩⟩,⟨⟨22320265197926506,22320265197926547⟩,⟨(-719843129731838),(-719843129731797)⟩⟩,⟨⟨21756369869325245,21756369869325296⟩,⟨(-618670174931925),(-618670174931874)⟩⟩,⟨⟨21232835262283409,21232835262283456⟩,⟨(-526357913945200),(-526357913945154)⟩⟩,⟨⟨20747566471440637,20747566471440678⟩,⟨(-442226013281206),(-442226013281165)⟩⟩,⟨⟨20298641056564237,20298641056564278⟩,⟨(-365656829791295),(-365656829791254)⟩⟩] +lemma kernel7_1_r2_14_eq : ∀ k : Fin 16, kernel7_1Expr 2 14 k = kernel7_1_r2_14 k := by decide +kernel +noncomputable def kernel7_1_r2_15 : Fin 16 → CBox := ![⟨⟨19884297598741874,19884297598741915⟩,⟨(-296090353952468),(-296090353952426)⟩⟩,⟨⟨19502925292133148,19502925292133189⟩,⟨(-233019640417956),(-233019640417915)⟩⟩,⟨⟨19153054493204768,19153054493204809⟩,⟨(-175986685243188),(-175986685243147)⟩⟩,⟨⟨18833348156940375,18833348156940417⟩,⟨(-124578713202522),(-124578713202481)⟩⟩,⟨⟨18542594096468218,18542594096468259⟩,⟨(-78424842288939),(-78424842288898)⟩⟩,⟨⟨18279698008950857,18279698008950898⟩,⟨(-37193095866153),(-37193095866111)⟩⟩,⟨⟨18043677216487144,18043677216487186⟩,⟨(-587736052302),(-587736052260)⟩⟩,⟨⟨17833655076242045,17833655076242086⟩,⟨31653105217255,31653105217296⟩⟩,⟨⟨17648856019091495,17648856019091536⟩,⟨59759518346336,59759518346377⟩⟩,⟨⟨17488601180792400,17488601180792441⟩,⟨83931649889539,83931649889580⟩⟩,⟨⟨17352304594104463,17352304594104504⟩,⟨104341294160202,104341294160243⟩⟩,⟨⟨17239469914437548,17239469914437589⟩,⟨121133256630015,121133256630056⟩⟩,⟨⟨17149687655512610,17149687655512656⟩,⟨134426501097345,134426501097391⟩⟩,⟨⟨17082632915240032,17082632915240079⟩,⟨144315090693047,144315090693093⟩⟩,⟨⟨17038063575566672,17038063575566713⟩,⟨150868930977276,150868930977317⟩⟩,⟨⟨17015818963454287,17015818963454338⟩,⟨154134321640185,154134321640236⟩⟩] +lemma kernel7_1_r2_15_eq : ∀ k : Fin 16, kernel7_1Expr 2 15 k = kernel7_1_r2_15 k := by decide +kernel +noncomputable def kernel7_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel7_1_r2_0,kernel7_1_r2_1,kernel7_1_r2_2,kernel7_1_r2_3,kernel7_1_r2_4,kernel7_1_r2_5,kernel7_1_r2_6,kernel7_1_r2_7,kernel7_1_r2_8,kernel7_1_r2_9,kernel7_1_r2_10,kernel7_1_r2_11,kernel7_1_r2_12,kernel7_1_r2_13,kernel7_1_r2_14,kernel7_1_r2_15] +lemma kernel7_1_r2_eq (i k : Fin 16) : kernel7_1Expr 2 i k = kernel7_1_r2 i k := by + fin_cases i + · exact kernel7_1_r2_0_eq k + · exact kernel7_1_r2_1_eq k + · exact kernel7_1_r2_2_eq k + · exact kernel7_1_r2_3_eq k + · exact kernel7_1_r2_4_eq k + · exact kernel7_1_r2_5_eq k + · exact kernel7_1_r2_6_eq k + · exact kernel7_1_r2_7_eq k + · exact kernel7_1_r2_8_eq k + · exact kernel7_1_r2_9_eq k + · exact kernel7_1_r2_10_eq k + · exact kernel7_1_r2_11_eq k + · exact kernel7_1_r2_12_eq k + · exact kernel7_1_r2_13_eq k + · exact kernel7_1_r2_14_eq k + · exact kernel7_1_r2_15_eq k +noncomputable def kernel7_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-37330524876404484754786607),(-37330524876404484603099858)⟩,⟨(-174627597071802876694329368),(-174627597071802876542049038)⟩⟩,⟨⟨(-37365085239928446882593085),(-37365085239928446730988294)⟩,⟨(-174527019983794100295623776),(-174527019983794100143425038)⟩⟩,⟨⟨(-37434052825637226589493461),(-37434052825637226438052764)⟩,⟨(-174325993014301933473470513),(-174325993014301933321435136)⟩⟩,⟨⟨(-37537121991967093671166950),(-37537121991967093519972238)⟩,⟨(-174024770487883205300246508),(-174024770487883205148456022)⟩⟩,⟨⟨(-37673835876581426057563220),(-37673835876581425906696016)⟩,⟨(-173623733668862155738264928),(-173623733668862155586800500)⟩⟩,⟨⟨(-37843588308614868620893187),(-37843588308614868470434555)⟩,⟨(-173123390490760302934318482),(-173123390490760302783260825)⟩⟩,⟨⟨(-38045626345418403152315589),(-38045626345418403002345994)⟩,⟨(-172524375189656745527030750),(-172524375189656745376459993)⟩⟩,⟨⟨(-38279053422797447876142148),(-38279053422797447726741339)⟩,⟨(-171827447836536220260319585),(-171827447836536220110315148)⟩⟩,⟨⟨(-38542833105059541072496095),(-38542833105059540923743031)⟩,⟨(-171033493762566633260178634),(-171033493762566633110819162)⟩⟩,⟨⟨(-38835793418563585317485611),(-38835793418563585169458249)⟩,⟨(-170143522870210573264206225),(-170143522870210573115569375)⟩⟩,⟨⟨(-39156631749899269283662345),(-39156631749899269136437668)⟩,⟨(-169158668822130538449306711),(-169158668822130538301469181)⟩⟩,⟨⟨(-39503920287333379670878103),(-39503920287333379524531872)⟩,⟨(-168080188099008435120751924),(-168080188099008434973789215)⟩⟩,⟨⟨(-39876111981749495453990702),(-39876111981749495308597514)⟩,⟨(-166909458916678506685644661),(-166909458916678506539631121)⟩⟩,⟨⟨(-40271547000989223954662469),(-40271547000989223810295400)⟩,⟨(-165647979992380275826711432),(-165647979992380275681719915)⟩⟩,⟨⟨(-40688459649286848929356083),(-40688459649286848786086937)⟩,⟨(-164297369149484151920820121),(-164297369149484151776922221)⟩⟩,⟨⟨(-41124985721385093392582186),(-41124985721385093250480977)⟩,⟨(-162859361749735558237993552),(-162859361749735558095259110)⟩⟩] +lemma kernel7_1_r3_0_eq : ∀ k : Fin 16, kernel7_1Expr 3 0 k = kernel7_1_r3_0 k := by decide +kernel +noncomputable def kernel7_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-41579170258937620053616125),(-41579170258937619912751500)⟩,⟨(-161335808941910836215811767),(-161335808941910836074309274)⟩⟩,⟨⟨(-42048975674953711148720183),(-42048975674953711009158647)⟩,⟨(-159728675715785353673865631),(-159728675715785353533661462)⟩⟩,⟨⟨(-42532290210331895090791830),(-42532290210331894952598497)⟩,⟨(-158040038750485180363551133),(-158040038750485180224710298)⟩⟩,⟨⟨(-43026936684971469874511246),(-43026936684971469737748801)⟩,⟨(-156272084046630778701448556),(-156272084046630778564033662)⟩⟩,⟨⟨(-43530681504552944143924774),(-43530681504552944008654536)⟩,⟨(-154427104332185112763438073),(-154427104332185112627510391)⟩⟩,⟨⟨(-44041243882849023011098026),(-44041243882849022877378455)⟩,⟨(-152507496232588444876123811),(-152507496232588444741741778)⟩⟩,⟨⟨(-44556305238375097836823375),(-44556305238375097704711604)⟩,⟨(-150515757196595214474462768),(-150515757196595214341683529)⟩⟩,⟨⟨(-45073518723319916470812574),(-45073518723319916340362623)⟩,⟨(-148454482170220439737633911),(-148454482170220439606511515)⟩⟩,⟨⟨(-45590518842020261719735722),(-45590518842020261591000461)⟩,⟨(-146326360012348044756546045),(-146326360012348044627133437)⟩⟩,⟨⟨(-46104931115764408103668944),(-46104931115764407976697517)⟩,⟨(-144134169646843760566052114),(-144134169646843760438398524)⟩⟩,⟨⟨(-46614381750433442712275642),(-46614381750433442587116204)⟩,⟨(-141880775947441567409013386),(-141880775947441567283167094)⟩⟩,⟨⟨(-47116507263421949906236867),(-47116507263421949782930022)⟩,⟨(-139569125353224318859326968),(-139569125353224318735331158)⟩⟩,⟨⟨(-47608964026423856541648684),(-47608964026423856420234335)⟩,⟨(-137202241214184069871438872),(-137202241214184069749336067)⟩⟩,⟨⟨(-48089437681028179220368711),(-48089437681028179100885685)⟩,⟨(-134783218868112244706871124),(-134783218868112244586700389)⟩⟩,⟨⟨(-48555652384644676254917314),(-48555652384644676137404040)⟩,⟨(-132315220451919432702865587),(-132315220451919432584665602)⟩⟩,⟨⟨(-49005379845071484953324596),(-49005379845071484837814775)⟩,⟨(-129801469452403501475062291),(-129801469452403501358867038)⟩⟩] +lemma kernel7_1_r3_1_eq : ∀ k : Fin 16, kernel7_1Expr 3 1 k = kernel7_1_r3_1 k := by decide +kernel +noncomputable def kernel7_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-49436448103024986259462403),(-49436448103024986145989758)⟩,⟨(-127245245003456122366854211),(-127245245003456122252697703)⟩⟩,⟨⟨(-49846750023174358929295699),(-49846750023174358817888233)⟩,⟨(-124649875938704156264483615),(-124649875938704156152394148)⟩⟩,⟨⟨(-50234251455656198691883756),(-50234251455656198582569831)⟩,⟨(-122018734610605442409046790),(-122018734610605442299053045)⟩⟩,⟨⟨(-50596999031683438644042265),(-50596999031683438536844728)⟩,⟨(-119355230489039677205936021),(-119355230489039677098061160)⟩⟩,⟨⟨(-50933127558701461801509107),(-50933127558701461696451601)⟩,⟨(-116662803554435262674761189),(-116662803554435262569029191)⟩⟩,⟨⟨(-51240866982575167671178960),(-51240866982575167568278487)⟩,⟨(-113944917502433113271180521),(-113944917502433113167608725)⟩⟩,⟨⟨(-51518548886504837579231371),(-51518548886504837478506169)⟩,⟨(-111205052778989357347808953),(-111205052778989357246415945)⟩⟩,⟨⟨(-51764612498755518307853158),(-51764612498755518209315116)⟩,⟨(-108446699466641817719966946),(-108446699466641817620764972)⟩⟩,⟨⟨(-51977610183832500319767624),(-51977610183832500223430511)⟩,⟨(-105673350044391693944353247),(-105673350044391693847356440)⟩⟩,⟨⟨(-52156212394431145912823689),(-52156212394431145818693441)⟩,⟨(-102888492045264198770826444),(-102888492045264198676041093)⟩⟩,⟨⟨(-52299212064318370663577742),(-52299212064318370571662715)⟩,⟨(-100095600637093019087120482),(-100095600637093018994555314)⟩⟩,⟨⟨(-52405528425249822281727066),(-52405528425249822192028452)⟩,⟨(-97298131153407345096113184),(-97298131153407345005769752)⟩⟩,⟨⟨(-52474210234074421577940882),(-52474210234074421490462788)⟩,⟨(-94499511602471948701014027),(-94499511602471948612896815)⟩⟩,⟨⟨(-52504438399308581868029220),(-52504438399308581782767141)⟩,⟨(-91703135183526802345247064),(-91703135183526802259351917)⟩⟩,⟨⟨(-52495527999657336237171687),(-52495527999657336154124575)⟩,⟨(-88912352840080872249911316),(-88912352840080872166237562)⟩⟩,⟨⟨(-52446929690199214819499159),(-52446929690199214738658124)⟩,⟨(-86130465880724441041580665),(-86130465880724440960119757)⟩⟩] +lemma kernel7_1_r3_2_eq : ∀ k : Fin 16, kernel7_1Expr 3 2 k = kernel7_1_r3_2 k := by decide +kernel +noncomputable def kernel7_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-52358230495215813391781547),(-52358230495215813313141905)⟩,⟨(-83360718698326768485456780),(-83360718698326768406204401)⟩⟩,⟨⟨(-52229153989914867714849164),(-52229153989914867638396486)⟩,⟨(-80606291618674053920950779),(-80606291618674053843892834)⟩⟩,⟨⟨(-52059559876546245590188999),(-52059559876546245515913587)⟩,⟨(-77870293909571390994171918),(-77870293909571390919299057)⟩⟩,⟨⟨(-51849442963622374108778967),(-51849442963622374036662775)⟩,⟨(-75155756981178547411196732),(-75155756981178547338491231)⟩⟩,⟨⟨(-51598931560107026731940916),(-51598931560107026661971024)⟩,⟨(-72465627807871824616170125),(-72465627807871824545619396)⟩⟩,⟨⟨(-51308285299508089108895591),(-51308285299508089041049017)⟩,⟨(-69802762601223870616991117),(-69802762601223870548572470)⟩⟩,⟨⟨(-50977892411780265555255129),(-50977892411780265489514506)⟩,⟨(-67169920762773108979422741),(-67169920762773108913119119)⟩⟩,⟨⟨(-50608266463792602879527750),(-50608266463792602815867020)⟩,⟨(-64569759144119429429185912),(-64569759144119429364971525)⟩⟩,⟨⟨(-50200042591823862771138166),(-50200042591823862709537535)⟩,⟨(-62004826640539992375432756),(-62004826640539992313288099)⟩⟩,⟨⟨(-49753973252097761402688840),(-49753973252097761343117714)⟩,⟨(-59477559142777416919040191),(-59477559142777416858934906)⟩⟩,⟨⟨(-49270923517742607845875433),(-49270923517742607788309942)⟩,⟨(-56990274869923111839007499),(-56990274869923111780917970)⟩⟩,⟨⟨(-48751865952739869787404656),(-48751865952739869731812062)⟩,⟨(-54545170104413712223271070),(-54545170104413712167164770)⟩⟩,⟨⟨(-48197875095399056494638757),(-48197875095399056440993293)⟩,⟨(-52144315348092802030000037),(-52144315348092801975851414)⟩⟩,⟨⟨(-47610121585648982196837592),(-47610121585648982145102783)⟩,⟨(-49789651916079160847115911),(-49789651916079160794888669)⟩⟩,⟨⟨(-46989865971956602140607721),(-46989865971956602090754473)⟩,⟨(-47482988982843869262172991),(-47482988982843869211838220)⟩⟩,⟨⟨(-46338452234964654358580476),(-46338452234964654310570854)⟩,⟨(-45226001092450143176704734),(-45226001092450143128224632)⟩⟩] +lemma kernel7_1_r3_3_eq : ∀ k : Fin 16, kernel7_1Expr 3 3 k = kernel7_1_r3_3 k := by decide +kernel +noncomputable def kernel7_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-45657301065970657647382596),(-45657301065970657601186469)⟩,⟨(-43020226142371167051745967),(-43020226142371167005090560)⟩⟩,⟨⟨(-44947902939146763427227133),(-44947902939146763382803344)⟩,⟨(-40867063847692712907355139),(-40867063847692712862483370)⟩⟩,⟨⟨(-44211811016918936246844721),(-44211811016918936204160229)⟩,⟨(-38767774689849846853621674),(-38767774689849846810500609)⟩⟩,⟨⟨(-43450633928183430474347306),(-43450633928183430433360460)⟩,⟨(-36723479351361837555711534),(-36723479351361837514299587)⟩⟩,⟨⟨(-42666028459039127601994108),(-42666028459039127562671348)⟩,⟨(-34735158635337996201148191),(-34735158635337996161411876)⟩⟩,⟨⟨(-41859692195458686035446009),(-41859692195458685997709880)⟩,⟨(-32803653865851090201414967),(-32803653865851090163277225)⟩⟩,⟨⟨(-41033356156814391237017555),(-41033356156814391199755378)⟩,⟨(-30929667762635453422133616),(-30929667762635453384493595)⟩⟩,⟨⟨(-40188777458422860095727775),(-40188777458422860058946766)⟩,⟨(-29113765780984798510454516),(-29113765780984798473318627)⟩⟩,⟨⟨(-39327732040285085029271760),(-39327732040285084992987941)⟩,⟨(-27356377905220214206211625),(-27356377905220214169595102)⟩⟩,⟨⟨(-38452007497985300592316150),(-38452007497985300556534317)⟩,⟨(-25657800881691254791231564),(-25657800881691254755138389)⟩⟩,⟨⟨(-37563396050286173605867605),(-37563396050286173570601711)⟩,⟨(-24018200874980725108102953),(-24018200874980725072546296)⟩⟩,⟨⟨(-36663687676332840230712973),(-36663687676332840195967811)⟩,⟨(-22437616528823855454351308),(-22437616528823855419335152)⟩⟩,⟨⟨(-35754663453569807168611238),(-35754663453569807134400951)⟩,⟨(-20915962411240805923655479),(-20915962411240805889193194)⟩⟩,⟨⟨(-34838089125499491479837232),(-34838089125499491446164193)⟩,⟨(-19453032821532092301614488),(-19453032821532092267707647)⟩⟩,⟨⟨(-33915708926287139651485525),(-33915708926287139618361768)⟩,⟨(-18048505935112205343204061),(-18048505935112205309863932)⟩⟩,⟨⟨(-32989239686962957091772426),(-32989239686962957059200119)⟩,⟨(-16701948260668282376659190),(-16701948260668282343887164)⟩⟩] +lemma kernel7_1_r3_4_eq : ∀ k : Fin 16, kernel7_1Expr 3 4 k = kernel7_1_r3_4 k := by decide +kernel +noncomputable def kernel7_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-32060365245608188433572469),(-32060365245608188401564112)⟩,⟨(-15412819382837238918534799),(-15412819382837238886342626)⟩⟩,⟨⟨(-31130731181457891998368210),(-31130731181457891966923082)⟩,⟨(-14180476962503441562314192),(-14180476962503441530700402)⟩⟩,⟨⟨(-30201939890329902549852989),(-30201939890329902518980961)⟩,⟨(-13004181965935030804075855),(-13004181965935030773049589)⟩⟩,⟨⟨(-29275546016217804681371350),(-29275546016217804651071883)⟩,⟨(-11883104093303657287015758),(-11883104093303657256575757)⟩⟩,⟨⟨(-28353052251286447565969850),(-28353052251286447536252962)⟩,⟨(-10816327376670996220849578),(-10816327376670996191005161)⟩⟩,⟨⟨(-27435905513902197045247482),(-27435905513902197016109987)⟩,⟨(-9802855917275339460047851),(-9802855917275339430795134)⟩⟩,⟨⟨(-26525493511736900300173942),(-26525493511736900271623458)⟩,⟨(-8841619731910331425280765),(-8841619731910331396626700)⟩⟩,⟨⟨(-25623141694423983649752333),(-25623141694423983621785623)⟩,⟨(-7931480678351187500479684),(-7931480678351187472420382)⟩⟩,⟨⟨(-24730110597735986614019048),(-24730110597735986586644205)⟩,⟨(-7071238430145443522173539),(-7071238430145443494716456)⟩⟩,⟨⟨(-23847593578812982050416373),(-23847593578812982023627214)⟩,⟨(-6259636471637722717425679),(-6259636471637722690564013)⟩⟩,⟨⟨(-22976714939617475235362311),(-22976714939617475209164154)⟩,⟨(-5495368084831937073244710),(-5495368084831937046983179)⟩⟩,⟨⟨(-22118528433539017227384702),(-22118528433539017201771785)⟩,⟨(-4777082300599134467875406),(-4777082300599134442207669)⟩⟩,⟨⟨(-21274016147935065130941815),(-21274016147935065105919705)⟩,⟨(-4103389787802980664098189),(-4103389787802980639029249)⟩⟩,⟨⟨(-20444087753386281092394068),(-20444087753386281067954420)⟩,⟨(-3472868655124648528384723),(-3472868655124648503905702)⟩⟩,⟨⟨(-19629580108575659481164978),(-19629580108575659457310877)⟩,⟨(-2884070141710761730992555),(-2884070141710761707106013)⟩⟩,⟨⟨(-18831257207981190201626052),(-18831257207981190178349461)⟩,⟨(-2335524174227324588850736),(-2335524174227324565548142)⟩⟩] +lemma kernel7_1_r3_5_eq : ∀ k : Fin 16, kernel7_1Expr 3 5 k = kernel7_1_r3_5 k := by decide +kernel +noncomputable def kernel7_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-18049810458009149710039443),(-18049810458009149687344191)⟩,⟨(-1825744769463984736187037),(-1825744769463984713471734)⟩⟩,⟨⟨(-17285859265795841203214790),(-17285859265795841181089967)⟩,⟨(-1353235263280818280314603),(-1353235263280818258175234)⟩⟩,⟨⟨(-16539951923674293632024243),(-16539951923674293610470865)⟩,⟨(-916493348408143978530046),(-916493348408143956967179)⟩⟩,⟨⟨(-15812566771242031156783872),(-15812566771242031135791937)⟩,⟨(-514015905382628006167126),(-514015905382627985170346)⟩⟩,⟨⟨(-15104113616077869661029062),(-15104113616077869640600022)⟩,⟨(-144303612714181545042846),(-144303612714181524613197)⟩⟩,⟨⟨(-14414935393439535178538432),(-14414935393439535158660012)⟩,⟨194134675787831287973331,194134675787831307848486⟩⟩,⟨⟨(-13745310044727964582890615),(-13745310044727964563561978)⟩,⟨502777796759087226050202,502777796759087245372075⟩⟩,⟨⟨(-13095452594125236742908315),(-13095452594125236724117874)⟩,⟨783088394491373780483034,783088394491373799263542⟩⟩,⟨⟨(-12465517402596638954636058),(-12465517402596638936383884)⟩,⟨1036509296193432529083683,1036509296193432547323080⟩⟩,⟨⟨(-11855600578387598070842008),(-11855600578387598053114082)⟩,⟨1264460150106907141930918,1264460150106907159643526⟩⟩,⟨⟨(-11265742523236161707623409),(-11265742523236161690417309)⟩,⟨1468334329552144456273797,1468334329552144473462323⟩⟩,⟨⟨(-10695930593753448834664271),(-10695930593753448817967234)⟩,⟨1649496104306799710172832,1649496104306799726850302⟩⟩,⟨⟨(-10146101857789156169980499),(-10146101857789156153790777)⟩,⟨1809278079117646396702458,1809278079117646412870881⟩⟩,⟨⟨(-9616145926087200604224476),(-9616145926087200588527447)⟩,⟨1948978897622046284124709,1948978897622046299798935⟩⟩,⟨⟨(-9105907840137662413745371),(-9105907840137662398537349)⟩,⟨2069861208518409565591505,2069861208518409580775437⟩⟩,⟨⟨(-8615190997834636958387531),(-8615190997834636943654960)⟩,⟨2173149889481707745765570,2173149889481707760472968⟩⟩] +lemma kernel7_1_r3_6_eq : ∀ k : Fin 16, kernel7_1Expr 3 6 k = kernel7_1_r3_6 k := by decide +kernel +noncomputable def kernel7_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-8143760099344307456645858),(-8143760099344307442386206)⟩,⟨2260030523076542391461410,2260030523076542405695001⟩⟩,⟨⟨(-7691344096462187561266307),(-7691344096462187547464020)⟩,⟨2331648117781081240013503,2331648117781081253789012⟩⟩,⟨⟨(-7257639129681610734571676),(-7257639129681610721222073)⟩,⟨2389106066203832652966962,2389106066203832666289236⟩⟩,⟨⟨(-6842311438195737058932803),(-6842311438195737046021924)⟩,⟨2433465331654072191659886,2433465331654072204543018⟩⟩,⟨⟨(-6445000229101306807611065),(-6445000229101306795135112)⟩,⟨2465743853416979452845386,2465743853416979465293327⟩⟩,⟨⟨(-6065320493153026649105459),(-6065320493153026637049138)⟩,⟨2486916160386341412114970,2486916160386341424143127⟩⟩,⟨⟨(-5702865755522092840657495),(-5702865755522092829014981)⟩,⟨2497913182120173663579480,2497913182120173675194459⟩⟩,⟨⟨(-5357210751130620485437779),(-5357210751130620474195047)⟩,⟨2499622245906002903784701,2499622245906002915000683⟩⟩,⟨⟨(-5027914015255842560004042),(-5027914015255842549157024)⟩,⟨2492887248050171405846728,2492887248050171416667808⟩⟩,⟨⟨(-4714520381214618954249529),(-4714520381214618943782846)⟩,⟨2478508987335902472383686,2478508987335902482825250⟩⟩,⟨⟨(-4416563378041432969155364),(-4416563378041432959063286)⟩,⟨2457245648423829431965178,2457245648423829442032981⟩⟩,⟨⟨(-4133567522153704017855405),(-4133567522153704008124261)⟩,⟨2429813422891438574108571,2429813422891438583816282⟩⟩,⟨⟨(-3865050498049676132354439),(-3865050498049676122979501)⟩,⟨2396887255619069019937640,2396887255619069029289998⟩⟩,⟨⟨(-3610525224099856816810483),(-3610525224099856807777149)⟩,⟨2359101704323959791506233,2359101704323959800517833⟩⟩,⟨⟨(-3369501800467240414545475),(-3369501800467240405847854)⟩,⟨2317051900214182808744883,2317051900214182817421615⟩⟩,⟨⟨(-3141489337119378595411095),(-3141489337119378587036033)⟩,⟨2271294597974719090708286,2271294597974719099063292⟩⟩] +lemma kernel7_1_r3_7_eq : ∀ k : Fin 16, kernel7_1Expr 3 7 k = kernel7_1_r3_7 k := by decide +kernel +noncomputable def kernel7_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-2925997660772543856588103),(-2925997660772543848531076)⟩,⟨2222349303601798474089198,2222349303601798482127001⟩⟩,⟨⟨(-2722538900431307977051227),(-2722538900431307969297978)⟩,⟨2170699468962190402585404,2170699468962190410320248⟩⟩,⟨⟨(-2530628951953098209278912),(-2530628951953098201823603)⟩,⟨2116793742364625446492225,2116793742364625453929930⟩⟩,⟨⟨(-2349788822774681063333956),(-2349788822774681056164149)⟩,⟨2061047264884196615339213,2061047264884196622492200⟩⟩,⟨⟨(-2179545858584716761572056),(-2179545858584716754682907)⟩,⟨2003843002670785915361978,2003843002670785922235079⟩⟩,⟨⟨(-2019434854312828979106443),(-2019434854312828972484970)⟩,⟨1945533105992791622183447,1945533105992791628789618⟩⟩,⟨⟨(-1868999052330947965028471),(-1868999052330947958669004)⟩,⟨1886440286311412592506844,1886440286311412598851739⟩⟩,⟨⟨(-1727791031227471213519786),(-1727791031227471207410771)⟩,⟨1826859203242452678467812,1826859203242452684562965⟩⟩,⟨⟨(-1595373488920014893731405),(-1595373488920014887868409)⟩,⟨1767057853836314692580417,1767057853836314698430240⟩⟩,⟨⟨(-1471319924219631994362737),(-1471319924219631988733557)⟩,⟨1707278957187166273901831,1707278957187166279518505⟩⟩,⟨⟨(-1355215221250190067658242),(-1355215221250190062257511)⟩,⟨1647741327964147454753596,1647741327964147460142464⟩⟩,⟨⟨(-1246656141363331581989538),(-1246656141363331576806671)⟩,⟨1588641233036302714043106,1588641233036302719214728⟩⟩,⟨⟨(-1145251727374589685007945),(-1145251727374589680038578)⟩,⟨1530153725934408599699014,1530153725934408604657734⟩⟩,⟨⟨(-1050623625082565230143729),(-1050623625082565225376947)⟩,⟨1472433954453190261423380,1472433954453190266180087⟩⟩,⟨⟨(-962406327123558883380744),(-962406327123558878811609)⟩,⟨1415618437243148724066030,1415618437243148728625645⟩⟩,⟨⟨(-880247344261827467526226),(-880247344261827463145159)⟩,⟨1359826305769341083868346,1359826305769341088240421⟩⟩] +lemma kernel7_1_r3_8_eq : ∀ k : Fin 16, kernel7_1Expr 3 8 k = kernel7_1_r3_8 k := by decide +kernel +noncomputable def kernel7_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-803807309223944644943309),(-803807309223944640746537)⟩,⟨1305160508522362210943477,1305160508522362215131763⟩⟩,⟨⟨(-732760018157914120760214),(-732760018157914116737619)⟩,⟨1251708974852262803395885,1251708974852262807410482⟩⟩,⟨⟨(-666792414737064024715496),(-666792414737064020860888)⟩,⟨1199545736257385622052264,1199545736257385625899603⟩⟩,⟨⟨(-605604521838696513806078),(-605604521838696510111076)⟩,⟨1148732003395661591563857,1148732003395661595252262⟩⟩,⟨⟨(-548909325611293505896182),(-548909325611293502357358)⟩,⟨1099317197494685166814137,1099317197494685170346987⟩⟩,⟨⟨(-496432616605038647671177),(-496432616605038644279963)⟩,⟨1051339935218121048496134,1051339935218121051881946⟩⟩,⟨⟨(-447912792481665889822589),(-447912792481665886575129)⟩,⟨1004828966399228757451724,1004828966399228760694315⟩⟩,⟨⟨(-403100626644230144944542),(-403100626644230141833399)⟩,⟨959804064377360341421042,959804064377360344527800⟩⟩,⟨⟨(-361759006938224701772091),(-361759006938224698794352)⟩,⟨916276868970283263408190,916276868970283266381993⟩⟩,⟨⟨(-323662648375301954879508),(-323662648375301952027439)⟩,⟨874251682384434760061144,874251682384434762909692⟩⟩,⟨⟨(-288597783622283525177346),(-288597783622283522447511)⟩,⟨833726218607265414517415,833726218607265417244109⟩⟩,⟨⟨(-256361834783594362183088),(-256361834783594359568960)⟩,⟨794692307041403078092850,794692307041403080704181⟩⟩,⟨⟨(-226763069786963671041159),(-226763069786963668540040)⟩,⟨757136551330348380039848,757136551330348382538491⟩⟩,⟨⟨(-199620246462259219438895),(-199620246462259217044145)⟩,⟨721040944490820520665105,721040944490820523057673⟩⟩,⟨⟨(-174762247183529538483449),(-174762247183529536192065)⟩,⟨686383441608840051406480,686383441608840053695945⟩⟩,⟨⟨(-152027706726402899279478),(-152027706726402897083152)⟩,⟨653138491476387483616172,653138491476387485810821⟩⟩] +lemma kernel7_1_r3_9_eq : ∀ k : Fin 16, kernel7_1Expr 3 9 k = kernel7_1_r3_9 k := by decide +kernel +noncomputable def kernel7_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-131264635778430574649158),(-131264635778430572544634)⟩,⟨621277528644305862688986,621277528644305864792060⟩⟩,⟨⟨(-112330042330082408634316),(-112330042330082406616014)⟩,⟨590769427446364823679966,590769427446364825697016⟩⟩,⟨⟨(-95089552970048133848013),(-95089552970048131913708)⟩,⟨561580919610447863115707,561580919610447865048947⟩⟩,⟨⟨(-79417035911243539108499),(-79417035911243537253568)⟩,⟨533676977117053657823795,533676977117053659677825⟩⟩,⟨⟨(-65194227384282172363796),(-65194227384282170586613)⟩,⟨507021161994106586853581,507021161994106588630015⟩⟩,⟨⟨(-52310362853815665267462),(-52310362853815663563271)⟩,⟨481575944751828438851487,481575944751828440555065⟩⟩,⟨⟨(-40661814340592668399268),(-40661814340592666766152)⟩,⟨457302993163484985352506,457302993163484986985130⟩⟩,⟨⟨(-30151734968730305281008),(-30151734968730303714941)⟩,⟨434163433088504856050549,434163433088504857616233⟩⟩,⟨⟨(-20689711703804697973641),(-20689711703804696473325)⟩,⟨412118083015047175651328,412118083015047177151360⟩⟩,⟨⟨(-12191427103109908347265),(-12191427103109906908461)⟩,⟨391127663970790588007179,391127663970790589445790⟩⟩,⟨⟨(-4578330764869241769813),(-4578330764869240390875)⟩,⟨371152986414694139797799,371152986414694141176625⟩⟩,⟨⟨2222678961718396948729,2222678961718398271281⟩,⟨352155115679842498048555,352155115679842499371065⟩⟩,⟨⟨8279562559058330738361,8279562559058332005727⟩,⟨334095517489271007267682,334095517489271008535068⟩⟩,⟨⟨13655435875790013183873,13655435875790014399597⟩,⟨316936185013838979032651,316936185013838980248451⟩⟩,⟨⟨18408855369708121665670,18408855369708122831151⟩,⟨300639748884681677192207,300639748884681678357814⟩⟩,⟨⟨22594091903174316611872,22594091903174317730097⟩,⟨285169571513351989529361,285169571513351990647759⟩⟩] +lemma kernel7_1_r3_10_eq : ∀ k : Fin 16, kernel7_1Expr 3 10 k = kernel7_1_r3_10 k := by decide +kernel +noncomputable def kernel7_1_r3_11 : Fin 16 → CBox := ![⟨⟨26261393014647446897149,26261393014647447969019⟩,⟨270489827011221225916548,270489827011221226988627⟩⟩,⟨⟨29457233661221295476272,29457233661221296504944⟩,⟨256565567936735451524778,256565567936735452553696⟩⟩,⟨⟨32224555490543228262270,32224555490543229248912⟩,⟨243362780035342534386663,243362780035342535373578⟩⟩,⟨⟨34602994756604362331158,34602994756604363278323⟩,⟨230848426072873693860865,230848426072873694808326⟩⟩,⟨⟨36629099043066028287950,36629099043066029196545⟩,⟨218990479799377063598459,218990479799377064507371⟩⟩,⟨⟨38336533000450585434078,38336533000450586307866⟩,⟨207757951017295007476545,207757951017295008350668⟩⟩,⟨⟨39756273340112570702625,39756273340112571542446⟩,⟨197120902665830242995670,197120902665830243835838⟩⟩,⟨⟨40916793358853100254210,40916793358853101062121⟩,⟨187050460772683366748327,187050460772683367556599⟩⟩,⟨⟨41844237293775760966331,41844237293775761742826⟩,⟨177518818065341279800840,177518818065341280577705⟩⟩,⟨⟨42562584827926932019389,42562584827926932766681⟩,⟨168499231976980972286422,168499231976980973034092⟩⟩,⟨⟨43093806083827360949367,43093806083827361668183⟩,⟨159966017727011981968065,159966017727011982687266⟩⟩,⟨⟨43458007454581093835675,43458007454581094527762⟩,⟨151894537103460139975972,151894537103460140668450⟩⟩,⟨⟨43673568631223207330545,43673568631223207996363⟩,⟨144261183523905744177334,144261183523905744843546⟩⟩,⟨⟨43757271190702824020009,43757271190702824661374⟩,⟨137043363903609519174009,137043363903609519815769⟩⟩,⟨⟨43724419111737984829651,43724419111737985447164⟩,⟨130219477813839100744462,130219477813839101362367⟩⟩,⟨⟨43588951586050396038472,43588951586050396633649⟩,⟨123768894370270992802622,123768894370270993398191⟩⟩] +lemma kernel7_1_r3_11_eq : ∀ k : Fin 16, kernel7_1Expr 3 11 k = kernel7_1_r3_11 k := by decide +kernel +noncomputable def kernel7_1_r3_12 : Fin 16 → CBox := ![⟨⟨43363548490497538301774,43363548490497538874873⟩,⟨117671927250688904653223,117671927250688905226716⟩⟩,⟨⟨43059728881653902483175,43059728881653903035862⟩,⟨111909808203010128942195,111909808203010129495269⟩⟩,⟨⟨42687942868719051522778,42687942868719052055529⟩,⟨106464659368911038913636,106464659368911039446774⟩⟩,⟨⟨42257657213494879916642,42257657213494880430754⟩,⟨101319464714940090493987,101319464714940091008481⟩⟩,⟨⟨41777434997805503720843,41777434997805504216551⟩,⟨96458040831938820274189,96458040831938820770272⟩⟩,⟨⟨41255009689339371228892,41255009689339371707591⟩,⟨91865007334764981160867,91865007334764981639937⟩⟩,⟨⟨40697353926664809031910,40697353926664809493960⟩,⟨87525757067645702209377,87525757067645702671793⟩⟩,⟨⟨40110743333280053336429,40110743333280053782929⟩,⟨83426426295894533574902,83426426295894534021765⟩⟩,⟨⟨39500815659162763317472,39500815659162763748570⟩,⟨79553865042111773298504,79553865042111773729962⟩⟩,⟨⟨38872625536521975329762,38872625536521975746688⟩,⟨75895607704256537255867,75895607704256537673142⟩⟩,⟨⟨38230695124452226400242,38230695124452226803279⟩,⟨72439844074033509297955,72439844074033509701334⟩⟩,⟨⟨37579060905055746760713,37579060905055747150810⟩,⟨69175390856778118174469,69175390856778118564895⟩⟩,⟨⟨36921316881431516549358,36921316881431516926653⟩,⟨66091663778351977111339,66091663778351977488953⟩⟩,⟨⟨36260654415814578921689,36260654415814579287194⟩,⟨63178650350377607850180,63178650350377608215995⟩⟩,⟨⟨35599898934158852928955,35599898934158853282910⟩,⟨60426883352351165646732,60426883352351166000982⟩⟩,⟨⟨34941543711654823023501,34941543711654823366701⟩,⟨57827415077679701477606,57827415077679701821094⟩⟩] +lemma kernel7_1_r3_12_eq : ∀ k : Fin 16, kernel7_1Expr 3 12 k = kernel7_1_r3_12 k := by decide +kernel +noncomputable def kernel7_1_r3_13 : Fin 16 → CBox := ![⟨⟨34287780942113280205749,34287780942113280538210⟩,⟨55371792380403767663650,55371792380403767996389⟩⟩,⟨⟨33640530282872336146350,33640530282872336469010⟩,⟨53052032550198336148225,53052032550198336471151⟩⟩,⟨⟨33001465055933823977630,33001465055933824290683⟩,⟨50860600035109938565117,50860600035109938878429⟩⟩,⟨⟨32372036275436324670097,32372036275436324974209⟩,⟨48790384024304224371961,48790384024304224676321⟩⟩,⟨⟨31753494661348325948144,31753494661348326243368⟩,⟨46834676896788202014963,46834676896788202310426⟩⟩,⟨⟨31146910789433555944464,31146910789433556231548⟩,⟨44987153536561692860706,44987153536561693148024⟩⟩,⟨⟨30553193518113323224381,30553193518113323503466⟩,⟨43241851509873446782342,43241851509873447061651⟩⟩,⟨⟨29973106823835191888729,29973106823835192160411⟩,⟨41593152096143460985073,41593152096143461256972⟩⟩,⟨⟨29407285167957005631042,29407285167957005895280⟩,⟨40035762160602867750997,40035762160602868015446⟩⟩,⟨⟨28856247509970172408919,28856247509970172666434⟩,⟨38564696853738852715275,38564696853738852972995⟩⟩,⟨⟨28320410074113275741435,28320410074113275992330⟩,⟨37175263120160872150709,37175263120160872401803⟩⟩,⟨⟨27800097969060987244977,27800097969060987489741⟩,⟨35863043997476185876483,35863043997476186121440⟩⟩,⟨⟨27295555753406264750826,27295555753406264989453⟩,⟨34623883684131307608907,34623883684131307847723⟩⟩,⟨⟨26806957033076485074576,26806957033076485307656⟩,⟨33453873353898817278376,33453873353898817511637⟩⟩,⟨⟨26334413170625563736983,26334413170625563964582⟩,⟨32349337693726873549863,32349337693726873777636⟩⟩,⟨⟨25877981180512157724603,25877981180512157947168⟩,⟨31306822140985716210619,31306822140985716433359⟩⟩] +lemma kernel7_1_r3_13_eq : ∀ k : Fin 16, kernel7_1Expr 3 13 k = kernel7_1_r3_13 k := by decide +kernel +noncomputable def kernel7_1_r3_14 : Fin 16 → CBox := ![⟨⟨25437670878995710168542,25437670878995710385990⟩,⟨30323080795708512365461,30323080795708512583077⟩⟩,⟨⟨25013451352143660727383,25013451352143660940296⟩,⟨29395064983203013231706,29395064983203013444780⟩⟩,⟨⟨24605256800630401648512,24605256800630401856921⟩,⟨28519912442378297742071,28519912442378297950638⟩⟩,⟨⟨24212991815506978148810,24212991815506978353106⟩,⟨27694937115262577832952,27694937115262578037401⟩⟩,⟨⟨23836536134915419271393,23836536134915419471527⟩,⟨26917619513461200798630,26917619513461200998914⟩⟩,⟨⟨23475748927798214985011,23475748927798215181449⟩,⟨26185597637698397533972,26185597637698397730556⟩⟩,⟨⟨23130472646997179789652,23130472646997179982417⟩,⟨25496658427083845121254,25496658427083845314164⟩⟩,⟨⟨22800536490732289707876,22800536490732289897318⟩,⟨24848729715329502293990,24848729715329502483573⟩⟩,⟨⟨22485759508285829249201,22485759508285829435229⟩,⟨24239872671798967307010,24239872671798967493176⟩⟩,⟨⟨22185953382776437273732,22185953382776437456807⟩,⟨23668274705987957900150,23668274705987958083360⟩⟩,⟨⟨21900924921177866037985,21900924921177866218107⟩,⟨23132242814799077022787,23132242814799077203043⟩⟩,⟨⟨21630478279205348003721,21630478279205348181218⟩,⟨22630197352776832365282,22630197352776832542911⟩⟩,⟨⟨21374416946345724487454,21374416946345724662241⟩,⟨22160666206301203881137,22160666206301204056053⟩⟩,⟨⟨21132545514133717178907,21132545514133717351363⟩,⟨21722279353592327326327,21722279353592327498909⟩⟩,⟨⟨20904671248764184251107,20904671248764184421247⟩,⟨21313763793248551017996,21313763793248551188260⟩⟩,⟨⟨20690605487267648515091,20690605487267648683203⟩,⟨20933938824919640646814,20933938824919640815048⟩⟩] +lemma kernel7_1_r3_14_eq : ∀ k : Fin 16, kernel7_1Expr 3 14 k = kernel7_1_r3_14 k := by decide +kernel +noncomputable def kernel7_1_r3_15 : Fin 16 → CBox := ![⟨⟨20490164874753053349714,20490164874753053515682⟩,⟨20581711666601522451806,20581711666601522617895⟩⟩,⟨⟨20303172458627312547554,20303172458627312711799⟩,⟨20256073393924711104209,20256073393924711268571⟩⟩,⟨⟨20129458654225966057454,20129458654225966219975⟩,⟨19956095187692204816342,19956095187692204978979⟩⟩,⟨⟨19968862094923789529694,19968862094923789690757⟩,⟨19680924876801512181649,19680924876801512342826⟩⟩,⟨⟨19821230378529632258141,19821230378529632417662⟩,⟨19429783764557529975764,19429783764557530135399⟩⟩,⟨⟨19686420720597604013449,19686420720597604171758⟩,⟨19201963727246646964294,19201963727246647122715⟩⟩,⟨⟨19564300524198932316831,19564300524198932473916⟩,⟨18996824574696580880808,18996824574696581038005⟩⟩,⟨⟨19454747874687689021512,19454747874687689177616⟩,⟨18813791663390336071730,18813791663390336227945⟩⟩,⟨⟨19357651967051821253601,19357651967051821408610⟩,⟨18652353753535920813180,18652353753535920968299⟩⟩,⟨⟨19272913472561535863274,19272913472561536017515⟩,⟨18512061102316018122884,18512061102316018277232⟩⟩,⟨⟨19200444850603408164704,19200444850603408318184⟩,⟨18392523786353865259565,18392523786353865413153⟩⟩,⟨⟨19140170610814228282498,19140170610814228435440⟩,⟨18293410247233604425287,18293410247233604578338⟩⟩,⟨⟨19092027529897431789389,19092027529897431941699⟩,⟨18214446054705964226558,18214446054705964378977⟩⟩,⟨⟨19055964826811084110521,19055964826811084262522⟩,⟨18155412882994137000959,18155412882994137153069⟩⟩,⟨⟨19031944299354099640518,19031944299354099792194⟩,⟨18116147696391098185544,18116147696391098337331⟩⟩,⟨⟨19019940424541148153593,19019940424541148305167⟩,⟨18096542141109460746873,18096542141109460898554⟩⟩] +lemma kernel7_1_r3_15_eq : ∀ k : Fin 16, kernel7_1Expr 3 15 k = kernel7_1_r3_15 k := by decide +kernel +noncomputable def kernel7_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel7_1_r3_0,kernel7_1_r3_1,kernel7_1_r3_2,kernel7_1_r3_3,kernel7_1_r3_4,kernel7_1_r3_5,kernel7_1_r3_6,kernel7_1_r3_7,kernel7_1_r3_8,kernel7_1_r3_9,kernel7_1_r3_10,kernel7_1_r3_11,kernel7_1_r3_12,kernel7_1_r3_13,kernel7_1_r3_14,kernel7_1_r3_15] +lemma kernel7_1_r3_eq (i k : Fin 16) : kernel7_1Expr 3 i k = kernel7_1_r3 i k := by + fin_cases i + · exact kernel7_1_r3_0_eq k + · exact kernel7_1_r3_1_eq k + · exact kernel7_1_r3_2_eq k + · exact kernel7_1_r3_3_eq k + · exact kernel7_1_r3_4_eq k + · exact kernel7_1_r3_5_eq k + · exact kernel7_1_r3_6_eq k + · exact kernel7_1_r3_7_eq k + · exact kernel7_1_r3_8_eq k + · exact kernel7_1_r3_9_eq k + · exact kernel7_1_r3_10_eq k + · exact kernel7_1_r3_11_eq k + · exact kernel7_1_r3_12_eq k + · exact kernel7_1_r3_13_eq k + · exact kernel7_1_r3_14_eq k + · exact kernel7_1_r3_15_eq k +noncomputable def kernel7_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-22037111554713091390538897975),(-22037111554713091339073852619)⟩,⟨30238416893318429345075338482,30238416893318429396227675958⟩⟩,⟨⟨(-22021603909866135594642058781),(-22021603909866135543187572701)⟩,⟨30235243050038521131672789520,30235243050038521182814879991⟩⟩,⟨⟨(-21990607209741746779685067742),(-21990607209741746728251789857)⟩,⟨30228884747272024243449545763,30228884747272024294571052169⟩⟩,⟨⟨(-21944158616632071957429449563),(-21944158616632071906028022466)⟩,⟨30219320800826370039797203802,30219320800826370090887794486⟩⟩,⟨⟨(-21882313831791162545179291731),(-21882313831791162493820349365)⟩,⟨30206519554798144405800887359,30206519554798144456850237923⟩⟩,⟨⟨(-21805147044627346949337446280),(-21805147044627346898031610506)⟩,⟨30190439025569676889631851808,30190439025569676940629648079⟩⟩,⟨⟨(-21712750864650959159560246267),(-21712750864650959108318125204)⟩,⟨30171027093029070977534640148,30171027093029071028470579378⟩⟩,⟨⟨(-21605236235917294715912863846),(-21605236235917294664745045077)⟩,⟨30148221738351313532725909379,30148221738351313583589706590⟩⟩,⟨⟨(-21482732333645260744556394376),(-21482732333645260693473450454)⟩,⟨30121951327515377146740995875,30121951327515377197522377903⟩⟩,⟨⟨(-21345386442636479833052054793),(-21345386442636479782064524241)⟩,⟨30092134939571430200761557160,30092134939571430251450281194⟩⟩,⟨⟨(-21193363817068284250562553418),(-21193363817068284199680962803)⟩,⟨30058682738513794937148481062,30058682738513794987734312153⟩⟩,⟨⟨(-21026847521187754439691099966),(-21026847521187754388925923603)⟩,⟨30021496387459550021491986263,30021496387459550071964737168⟩⟩,⟨⟨(-20846038250393337448787986839),(-20846038250393337398149698891)⟩,⟨29980469503680074967109780656,29980469503680075017459259328⟩⟩,⟨⟨(-20651154132156212910007234334),(-20651154132156212859506225110)⟩,⟨29935488152883801747800208610,29935488152883801798016301451⟩⟩,⟨⟨(-20442430506206000213767767398),(-20442430506206000163414443395)⟩,⟨29886431381003404883536696470,29886431381003404933609267928⟩⟩,⟨⟨(-20220119683385118627061489978),(-20220119683385118576866143893)⟩,⟨29833171781600064806332179659,29833171781600064856251201751⟩⟩] +lemma kernel7_1_r4_0_eq : ∀ k : Fin 16, kernel7_1Expr 4 0 k = kernel7_1_r4_0 k := by decide +kernel +noncomputable def kernel7_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-19984490682563570417567346924),(-19984490682563570367540321228)⟩,⟨29775576096861728328599817927,29775576096861728378355206359⟩⟩,⟨⟨(-19735828945001510394917137889),(-19735828945001510345068595108)⟩,⟨29713505850041920312733541522,29713505850041920362315384892⟩⟩,⟨⟨(-19474436025551031813296519402),(-19474436025551031763636709689)⟩,⟨29646818007061094959978114212,29646818007061095009376406257⟩⟩,⟨⟨(-19200629260101416732713502404),(-19200629260101416683252454807)⟩,⟨29575365664874222161408689940,29575365664874222210613637701⟩⟩,⟨⟨(-18914741408693884690379958549),(-18914741408693884641127851182)⟩,⟨29498998764096757185097543768,29498998764096757234099197293⟩⟩,⟨⟨(-18617120273762777989779109261),(-18617120273762777940745785056)⟩,⟨29417564823276816397467945570,29417564823276816446256681576⟩⟩,⟨⟨(-18308128293000229214123669309),(-18308128293000229165319184267)⟩,⟨29330909692104754142238663711,29330909692104754190804637302⟩⟩,⟨⟨(-17988142106390682178013428784),(-17988142106390682129447455023)⟩,⟨29238878320762880993800738531,29238878320762881042134479559⟩⟩,⟨⟨(-17657552097020126904147625960),(-17657552097020126855830149849)⟩,⟨29141315542538251630699795129,29141315542538251678791510080⟩⟩,⟨⟨(-17316761905332436875795123946),(-17316761905332436827735557175)⟩,⟨29038066866750744472449320673,29038066866750744520289780952⟩⟩,⟨⟨(-16966187916581565859077702837),(-16966187916581565811285865869)⟩,⟨28928979278987507394201267394,28928979278987507441780826020⟩⟩,⟨⟨(-16606258721313303601791235966),(-16606258721313303554276338892)⟩,⟨28813902045583692723710481401,28813902045583692771020091537⟩⟩,⟨⟨(-16237414548803465180841239552),(-16237414548803465133613031719)⟩,⟨28692687519248671174976821624,28692687519248671222006887102⟩⟩,⟨⟨(-15860106673480387926481474291),(-15860106673480387879548828570)⟩,⟨28565191942706997795404097030,28565191942706997842145887461⟩⟩,⟨⟨(-15474796794467954031488046222),(-15474796794467953984860501393)⟩,⟨28431276247204677407405970476,28431276247204677453850079128⟩⟩,⟨⟨(-15081956388500500413361470320),(-15081956388500500367047660226)⟩,⟨28290806842724086929360557186,28290806842724086975498471217⟩⟩] +lemma kernel7_1_r4_1_eq : ∀ k : Fin 16, kernel7_1Expr 4 1 k = kernel7_1_r4_1 k := by decide +kernel +noncomputable def kernel7_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-14682066036582309637674358007),(-14682066036582309591683775856)⟩,⟨28143656396755568231054445716,28143656396755568276876782189⟩⟩,⟨⟨(-14275614724891224290870601605),(-14275614724891224245211433193)⟩,⟨27989704598490480836596732717,27989704598490480882095404765⟩⟩,⟨⟨(-13863099120557561041007448993),(-13863099120557560995688899232)⟩,⟨27828838905329629828944601219,27828838905329629874110491854⟩⟩,⟨⟨(-13445022823085133843752597919),(-13445022823085133798782604151)⟩,⟨27660955268642645582183343370,27660955268642645627008591738⟩⟩,⟨⟨(-13021895592319991884661494982),(-13021895592319991840049213811)⟩,⟨27485958835768223133746553560,27485958835768223178222068322⟩⟩,⟨⟨(-12594232554013554637911653488),(-12594232554013554593664486139)⟩,⟨27303764625312210765858214224,27303764625312210809976647919⟩⟩,⟨⟨(-12162553384169260997498842250),(-12162553384169260953625601773)⟩,⟨27114298172880392667207292833,27114298172880392710959874808⟩⟩,⟨⟨(-11727381473504683947188792863),(-11727381473504683903696595966)⟩,⟨26917496144475401278052189596,26917496144475401321431834143⟩⟩,⟨⟨(-11289243073503309872811594348),(-11289243073503309829709258427)⟩,⟨26713306914892418781512828836,26713306914892418824510738049⟩⟩,⟨⟨(-10848666425670833023679086558),(-10848666425670832980973045490)⟩,⟨26501691108566014947460777855,26501691108566014990070526200⟩⟩,⟨⟨(-10406180875748845622981687443),(-10406180875748845580680297580)⟩,⟨26282622100450381626227119021,26282622100450381668440346930⟩⟩,⟨⟨(-9962315974773178757340792491),(-9962315974773178715450227828)⟩,⟨26056086474657052883947875404,26056086474657052925758394805⟩⟩,⟨⟨(-9517600568993833006707143266),(-9517600568993832965235754776)⟩,⟨25822084438727561691313402295,25822084438727561732712836547⟩⟩,⟨⟨(-9072561880797401388485466250),(-9072561880797401347438661024)⟩,⟨25580630191582923301447068970,25580630191582923342429975017⟩⟩,⟨⟨(-8627724582890114839454375845),(-8627724582890114798839985388)⟩,⟨25331752243366822166142658310,25331752243366822206701157131⟩⟩,⟨⟨(-8183609868109137834737837779),(-8183609868109137794560975972)⟩,⟨25075493685584309970825161310,25075493685584310010954081682⟩⟩] +lemma kernel7_1_r4_2_eq : ∀ k : Fin 16, kernel7_1Expr 4 2 k = kernel7_1_r4_2 k := by decide +kernel +noncomputable def kernel7_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-7740734517330543768919491855),(-7740734517330543729188081778)⟩,⟨24811912410132020837492272614,24811912410132020877183622536⟩⟩,⟨⟨(-7299609968033578344671058103),(-7299609968033578305389257954)⟩,⟨24541081276018628345009861118,24541081276018628384259404685⟩⟩,⟨⟨(-6860741386161491096152594560),(-6860741386161491057327639842)⟩,⟨24263088222784690944543094174,24263088222784690983343506685⟩⟩,⟨⟨(-6424626743988549265912506016),(-6424626743988549227548344948)⟩,⟨23978036329848274390402330412,23978036329848274428749566227⟩⟩,⟨⟨(-5991755906760073127853424399),(-5991755906760073089957349143)⟩,⟨23686043821225855782591575844,23686043821225855820478233914⟩⟩,⟨⟨(-5562609730916742768603105977),(-5562609730916742731178059719)⟩,⟨23387244015305998677004365433,23387244015305998714427386929⟩⟩,⟨⟨(-5137659176745391977449095669),(-5137659176745391940501646819)⟩,⟨23081785219585083284286270661,23081785219585083321238960176⟩⟩,⟨⟨(-4717364438315473638028141934),(-4717364438315473601560982059)⟩,⟨22769830570508872105127098522,22769830570508872141606631426⟩⟩,⟨⟨(-4302174093562886792272024768),(-4302174093562886756291909578)⟩,⟨22451557818799738691432557268,22451557818799738727432033320⟩⟩,⟨⟨(-3892524277370523117591336991),(-3892524277370523082099747124)⟩,⟨22127159060885798555583830161,22127159060885798591101620270⟩⟩,⟨⟨(-3488837880467440195895073248),(-3488837880467440160897842318)⟩,⟨21796840417283740325906007891,21796840417283740360936118643⟩⟩,⟨⟨(-3091523776925820476922583635),(-3091523776925820442421076473)⟩,⟨21460821659020624123405732044,21460821659020624157946635410⟩⟩,⟨⟨(-2700976082976750931512510425),(-2700976082976750897512697504)⟩,⟨21119335783410041134004140767,21119335783410041168049691709⟩⟩,⟨⟨(-2317573449792387164300585802),(-2317573449792387130802613155)⟩,⟨20772628540723556378044986904,20772628540723556411594863996⟩⟩,⟨⟨(-1941678392793382514348138452),(-1941678392793382481357043570)⟩,⟨20420957913518031851109585785,20420957913518031884158564845⟩⟩,⟨⟨(-1573636659936810847850105058),(-1573636659936810815365879666)⟩,⟨20064593550592007707427342541,20064593550592007739975244890⟩⟩] +lemma kernel7_1_r4_3_eq : ∀ k : Fin 16, kernel7_1Expr 4 3 k = kernel7_1_r4_3 k := by decide +kernel +noncomputable def kernel7_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-1213776641321542968685630034),(-1213776641321542936713644933)⟩,⟨19703816157748584236205251408,19703816157748584268246507641⟩⟩,⟨⟨(-862408822315609859018806494),(-862408822315609827557594251)⟩,⟨19338916847737006462677951256,19338916847737006494213833446⟩⟩,⟨⟨(-519825282264066016637679553),(-519825282264065985691430704)⟩,⟨18970196451929254959758936006,18970196451929254990785046652⟩⟩,⟨⟨(-186299240676920764550914759),(-186299240676920734118229460)⟩,⟨18597964796460287796788105180,18597964796460287827305640360⟩⟩,⟨⟨137915347374398057528555214,137915347374398087443253203⟩,⟨18222539945720113459450964678,18222539945720113489455285153⟩⟩,⟨⟨452584145105982572328688511,452584145105982601728176484⟩,⟨17844247416231622655680022604,17844247416231622685173697182⟩⟩,⟨⟨757492735762461979199829576,757492735762462008080801653⟩,⟨17463419364079161623997649269,17463419364079161652977151797⟩⟩,⟨⟨1052446871098823179780628139,1052446871098823208145864445⟩,⟨17080393749168365954509837901,17080393749168365982977735190⟩⟩,⟨⟨1337272665662001207761013518,1337272665662001235606760163⟩,⟨16695513479697055985103495555,16695513479697056013055807957⟩⟩,⟨⟨1611816736148457226836172852,1611816736148457254166803524⟩,⟨16309125540299382084982062205,16309125540299382112422949520⟩⟩,⟨⟨1875946285336979266250272630,1875946285336979293063388055⟩,⟨15921580107390361708957828050,15921580107390361735884664528⟩⟩,⟨⟨2129549130323427803505637292,2129549130323427829805355647⟩,⟨15533229655285037983859904953,15533229655285038010276593114⟩⟩,⟨⟨2372533675014765547178189326,2372533675014765573026763856⟩,⟨15144428056695391097613106283,15144428056695391123581619356⟩⟩,⟨⟨2604828827072086163666283955,2604828827072086189072056483⟩,⟨14755529681218643187227984320,14755529681218643212756450205⟩⟩,⟨⟨2826383859725095443028634860,2826383859725095467988407544⟩,⟨14366888495422626729299506627,14366888495422626754384504005⟩⟩,⟨⟨3037168219112193678301287709,3037168219112193702820278762⟩,⟨13978857168107467048347758546,13978857168107467072993103382⟩⟩] +lemma kernel7_1_r4_4_eq : ∀ k : Fin 16, kernel7_1Expr 4 4 k = kernel7_1_r4_4 k := by decide +kernel +noncomputable def kernel7_1_r4_5 : Fin 16 → CBox := ![⟨⟨3237171278029551737965020124,3237171278029551762039816413⟩,⟨13591786184278113151132430191,13591786184278113175334087107⟩⟩,⟨⟨3426402037197966957219990666,3426402037197966980855870685⟩,⟨13206022971299509411238115767,13206022971299509435001213664⟩⟩,⟨⟨3604888775376450565628694266,3604888775376450588823111825⟩,⟨12821911040625824270067187536,12821911040625824293389017783⟩⟩,⟨⟨3772678649865089179098249791,3772678649865089201855902481⟩,⟨12439789148397648342792350884,12439789148397648365677466171⟩⟩,⟨⟨3929837249145434024378743736,3929837249145434046696531330⟩,⟨12059990478087063821803609381,12059990478087063844248752426⟩⟩,⟨⟨4076448099603250247141804745,4076448099603250269025869924⟩,⟨11682841848240699815441717487,11682841848240699837452895751⟩⟩,⟨⟨4212612128464714057264972276,4212612128464714078713487504⟩,⟨11308662948226158333412532632,11308662948226158354987771445⟩⟩,⟨⟨4338447085251958086981597927,4338447085251958108000265587⟩,⟨10937765604728455204035604780,10937765604728455225180478090⟩⟩,⟨⟨4454086924226195773806657943,4454086924226195794392827232⟩,⟨10570453081571392643797886501,10570453081571392664509603017⟩⟩,⟨⟨4559681150435552612180053946,4559681150435552632341102185⟩,⟨10207019415255172351568522633,10207019415255172371854342880⟩⟩,⟨⟨4655394132119340054878994126,4655394132119340074613805486⟩,⟨9847748788407251797136263922,9847748788407251816994943444⟩⟩,⟨⟨4741404382340073034492688434,4741404382340073053807874878⟩,⟨9492914943139689744032349857,9492914943139689763470391327⟩⟩,⟨⟨4817903812818408525811825224,4817903812818408544705626323⟩,⟨9142780636094324278305389770,9142780636094324297320912399⟩⟩,⟨⟨4885096963033836629154705277,4885096963033836647635161782⟩,⟨8797597136738428238398229202,8797597136738428256999176611⟩⟩,⟨⟨4943200207724969699790430499,4943200207724969717857113854⟩,⟨8457603770249379233628395813,8457603770249379251814231482⟩⟩,⟨⟨4992440945977350152185468443,4992440945977350169845786729⟩,⟨8123027506098775643318736947,8123027506098775661096780426⟩⟩] +lemma kernel7_1_r4_5_eq : ∀ k : Fin 16, kernel7_1Expr 4 5 k = kernel7_1_r4_5 k := by decide +kernel +noncomputable def kernel7_1_r4_6 : Fin 16 → CBox := ![⟨⟨5033056775123655120930471932,5033056775123655138183012817⟩,⟨7794082593215751361227950936,7794082593215751378596690392⟩⟩,⟨⟨5065294652700958433714358608,5065294652700958450568225538⟩,⟨7470970242377418828339109005,7470970242377418845307572467⟩⟩,⟨⟨5089410049712380002221124564,5089410049712380018676537089⟩,⟨7153878356242822307961332815,7153878356242822324529653649⟩⟩,⟨⟨5105666098426191259167234757,5105666098426191275232266572⟩,⟨6842981307216912757250106481,6842981307216912773426291214⟩⟩,⟨⟨5114332737914550425702338410,5114332737914550441376483236⟩,⟨6538439763104233913264337959,6538439763104233929047803368⟩⟩,⟨⟨5115685860486923639883975854,5115685860486923655176644731⟩,⟨6240400560289568457922181647,6240400560289568473322284036⟩⟩,⟨⟨5110006462110425944450624930,5110006462110425959371293518⟩,⟨5948996623966015886601991039,5948996623966015901625162244⟩⟩,⟨⟨5097579799831411197427994728,5097579799831411211987859202⟩,⟨5664346934721083620865451181,5664346934721083635521966338⟩⟩,⟨⟨5078694559120369991742480736,5078694559120370005940744825⟩,⟨5386556540589526043081631167,5386556540589526057370863142⟩⟩,⟨⟨5053642033956366954510852367,5053642033956366968357059509⟩,⟨5115716613488942985870143457,5115716613488942999801820496⟩⟩,⟨⟨5022715322348752365067036280,5022715322348752378561951625⟩,⟨4851904548771547480444011369,4851904548771547494019070134⟩⟩,⟨⟨4986208539863680283180805083,4986208539863680296332846062⟩,⟨4595184106453940747634141196,4595184106453940760861180581⟩⟩,⟨⟨4944416053582083237759584106,4944416053582083250568748810⟩,⟨4345605592527004261960568568,4345605592527004274839756306⟩⟩,⟨⟨4897631738765274151429363572,4897631738765274163905283530⟩,⟨4103206078600848641082460208,4103206078600848653623608271⟩⟩,⟨⟨4846148260345397356246342547,4846148260345397368390283031⟩,⟨3868009658005758505693085199,3868009658005758517897628078⟩⟩,⟨⟨4790256381191695865582673822,4790256381191695877403336522⟩,⟨3640027736349747001327187892,3640027736349747013204002996⟩⟩] +lemma kernel7_1_r4_6_eq : ∀ k : Fin 16, kernel7_1Expr 4 6 k = kernel7_1_r4_6 k := by decide +kernel +noncomputable def kernel7_1_r4_7 : Fin 16 → CBox := ![⟨⟨4730244298931190903003650350,4730244298931190914501209122⟩,⟨3419259354427081627334230195,3419259354427081638883656832⟩⟩,⟨⟨4666397012925087269051600402,4666397012925087280236198935⟩,⟨3205691541280254460155018855,3205691541280254471387373451⟩⟩,⟨⟨4598995722821235568016048945,4598995722821235578889379280⟩,⟨2999299695140526922172938835,2999299695140526933090076585⟩⟩,⟨⟨4528317259919506872184365610,4528317259919506882755274321⟩,⟨2800047989909457287741568531,2800047989909457298352502315⟩⟩,⟨⟨4454633552402160961358005850,4454633552402160971627384541⟩,⟨2607889804795688791878694954,2607889804795688802184474712⟩⟩,⟨⟨4378211125296387211499635833,4378211125296387221477367626⟩,⟨2422768174687606426901309065,2422768174687606436911979043⟩⟩,⟨⟨4299310635852307644863632445,4299310635852307654551756074⟩,⟨2244616258823032224425753104,2244616258823032234143505992⟩⟩,⟨⟨4218186444837955251935767519,4218186444837955261346402801⟩,⟨2073357825311599546386537931,2073357825311599555823648152⟩⟩,⟨⟨4135086224074130991345312274,4135086224074131000494522980⟩,⟨1908907749073415993746206671,1908907749073416002918888999⟩⟩,⟨⟨4050250600357599266153019934,4050250600357599275049932550⟩,⟨1751172520778599029185225923,1751172520778599038102754086⟩⟩,⟨⟨3963912835751743089139361982,3963912835751743097785355583⟩,⟨1600050764405679480784166479,1600050764405679489448061738⟩⟩,⟨⟨3876298544060439429221426595,3876298544060439437624381373⟩,⟨1455433761082077977566569258,1455433761082077985984851237⟩⟩,⟨⟨3787625443144334290952543354,3787625443144334299113049820⟩,⟨1317205976926168655895097448,1317205976926168664068492472⟩⟩,⟨⟨3698103142589622844586061743,3698103142589622852512909254⟩,⟨1185245592677099743339578544,1185245592677099751277007640⟩⟩,⟨⟨3607932966098521071901188586,3607932966098521079596005027⟩,⟨1059425032974742284811023845,1059425032974742292514243809⟩⟩,⟨⟨3517307807838419897047663790,3517307807838419904518223154⟩,⟨939611493237048564524155371,939611493237048572001063919⟩⟩] +lemma kernel7_1_r4_7_eq : ∀ k : Fin 16, kernel7_1Expr 4 7 k = kernel7_1_r4_7 k := by decide +kernel +noncomputable def kernel7_1_r4_8 : Fin 16 → CBox := ![⟨⟨3426412021863726257718281294,3426412021863726264965136562⟩,⟨825667462174852821133996801,825667462174852828385269307⟩⟩,⟨⟨3335421343611020460806465639,3335421343611020467838512461⟩,⟨717451238083848691159017548,717451238083848698193664836⟩⟩,⟨⟨3244502842364714595096682982,3244502842364714601915730029⟩,⟨614817437159226334646573080,614817437159226341466518484⟩⟩,⟨⟨3153814903497119257308275699,3153814903497119263921894917⟩,⟨517617492189336887259229837,517617492189336893872152763⟩⟩,⟨⟨3063507239203870660188350959,3063507239203870666597573658⟩,⟨425700140099863352081396686,425700140099863358488436497⟩⟩,⟨⟨2973720926383113407961785732,2973720926383113414174921931⟩,⟨338911896938414218097360103,338911896938414224306925520⟩⟩,⟨⟨2884588470244675395688011507,2884588470244675401706984623⟩,⟨257097519010333050520759265,257097519010333056534873803⟩⟩,⟨⟨2796233892183636680768349908,2796233892183636686600450044⟩,⟨180100448998969687385529487,180100448998969693211574525⟩⟩,⟨⟨2708772840411040528419621296,2708772840411040534065797832⟩,⟨107763246026849658711944559,107763246026849664350963521⟩⟩,⟨⟨2622312721802813579036362523,2622312721802813584504780267⟩,⟨39927998737304136182111229,39927998737304141642351210⟩⟩,⟨⟨2536952853405983956046995493,2536952853405983961339633378⟩,⟨(-23563279401582898560217878),(-23563279401582893276692179)⟩⟩,⟨⟨2452784632028686102364591008,2452784632028686107488389641⟩,⟨(-82868273248114327770870406),(-82868273248114322657042650)⟩⟩,⟨⟨2369891720336843630173597502,2369891720336843635129792670⟩,⟨(-138144008152104200232188427),(-138144008152104195286742858)⟩⟩,⟨⟨2288350247885405787509988186,2288350247885405792306101669⟩,⟨(-189546511577239855735218201),(-189546511577239850950565808)⟩⟩,⟨⟨2208229025525119003637369671,2208229025525119008275382483⟩,⟨(-237230494511729125854411272),(-237230494511729121228498921)⟩⟩,⟨⟨2129589771646548146046414132,2129589771646548150535924634⟩,⟨(-281349052890035832612937583),(-281349052890035828136104489)⟩⟩] +lemma kernel7_1_r4_8_eq : ∀ k : Fin 16, kernel7_1Expr 4 8 k = kernel7_1_r4_8 k := by decide +kernel +noncomputable def kernel7_1_r4_9 : Fin 16 → CBox := ![⟨⟨2052487348750900086189435701,2052487348750900090537633608⟩,⟨(-322053389144692789641773256),(-322053389144692785306759986)⟩⟩,⟨⟨1976970008871599732053196996,1976970008871599736266852902⟩,⟨(-359492553908209627310700381),(-359492553908209623110683821)⟩⟩,⟨⟨1903079646410963493734518605,1903079646410963497815050239⟩,⟨(-393813207791318828855469537),(-393813207791318824788972740)⟩⟩,⟨⟨1830852057002133082024100500,1830852057002133085977132890⟩,⟨(-425159403075527099121649998),(-425159403075527095183000089)⟩⟩,⟨⟨1760317201057092903763315104,1760317201057092907589595449⟩,⟨(-453672385075404910848879005),(-453672385075404907037273983)⟩⟩,⟨⟨1691499470716514808386315623,1691499470716514812092063542⟩,⟨(-479490412849444853847306212),(-479490412849444850156253372)⟩⟩,⟨⟨1624417958975775352548247451,1624417958975775356134879609⟩,⟨(-502748598867786632009031869),(-502748598867786628437006169)⟩⟩,⟨⟨1559086729823201384850356814,1559086729823201388323116342⟩,⟨(-523578767180729852257346696),(-523578767180729848799087298)⟩⟩,⟨⟨1495515088290859505125703530,1495515088290859508485162419⟩,⟨(-542109329573773306690513914),(-542109329573773303345422988)⟩⟩,⟨⟨1433707849384469053713607849,1433707849384469056965628529⟩,⟨(-558465179142923557601088488),(-558465179142923554363291154)⟩⟩,⟨⟨1373665604926760688556010835,1373665604926760691701922024⟩,⟨(-572767600678155529078164279),(-572767600678155525946311391)⟩⟩,⟨⟨1315384987417318998246902858,1315384987417319001291557176⟩,⟨(-585134197203092701335874187),(-585134197203092698305102049)⟩⟩,⟨⟨1258858930081158033574901325,1258858930081158036519015755⟩,⟨(-595678831985076787124565096),(-595678831985076784194138432)⟩⟩,⟨⟨1204076922347529798340307163,1204076922347529801189131765⟩,⟨(-604511585301655343162373673),(-604511585301655340327035438)⟩⟩,⟨⟨1151025260069332803457134853,1151025260069332806211921413⟩,⟨(-611738725226939449312332246),(-611738725226939446570816624)⟩⟩,⟨⟨1099687289861575942663870489,1099687289861575945329076390⟩,⟨(-617462691684054562444031084),(-617462691684054559791874916)⟩⟩] +lemma kernel7_1_r4_9_eq : ∀ k : Fin 16, kernel7_1Expr 4 9 k = kernel7_1_r4_9 k := by decide +kernel +noncomputable def kernel7_1_r4_10 : Fin 16 → CBox := ![⟨⟨1050043647004298527727634705,1050043647004298530308702036⟩,⟨(-621782092997784943208838350),(-621782092997784940640583940)⟩⟩,⟨⟨1002072486420818599434298249,1002072486420818601936506265⟩,⟨(-624791714174234957196632465),(-624791714174234954706998491)⟩⟩,⟨⟨955749706305879280380211019,955749706305879282804411352⟩,⟨(-626582536131622011930930026),(-626582536131622009519056273)⟩⟩,⟨⟨911049164039920170201602632,911049164039920172551578058⟩,⟨(-627241765107885794788734837),(-627241765107885792450837087)⟩⟩,⟨⟨867942884085083206434444648,867942884085083208710512211⟩,⟨(-626852871476346830904991704),(-626852871476346828640745441)⟩⟩,⟨⟨826401257615467591690974115,826401257615467593897267646⟩,⟨(-625495637209867353343432555),(-625495637209867351148705160)⟩⟩,⟨⟨786393233688405177266935423,786393233688405179404235744⟩,⟨(-623246211246548286713759913),(-623246211246548284587765965)⟩⟩,⟨⟨747886501814995341615993848,747886501814995343687756167⟩,⟨(-620177172025625767519624716),(-620177172025625765458910534)⟩⟩,⟨⟨710847665836705447992733669,710847665836705449999103290⟩,⟨(-616357596480598323903381503),(-616357596480598321907797649)⟩⟩,⟨⟨675242409060425965016205071,675242409060425966961093784⟩,⟨(-611853134797414494513312721),(-611853134797414492578951297)⟩⟩,⟨⟨641035650646911438843195080,641035650646911440727307311⟩,⟨(-606726090268478900653977380),(-606726090268478898780132366)⟩⟩,⟨⟨608191693287007916641597306,608191693287007918468071476⟩,⟨(-601035503597998871254562837),(-601035503597998869438099447)⟩⟩,⟨⟨576674362236455742340062422,576674362236455744109444313⟩,⟨(-594837241040509284381850575),(-594837241040509282622099906)⟩⟩,⟨⟨546447135813377162424265847,546447135813377164140506873⟩,⟨(-588184085782006803960470611),(-588184085782006802253288085)⟩⟩,⟨⟨517473267492844083656492102,517473267492844085320161960⟩,⟨(-581125832001734750087607832),(-581125832001734748432448219)⟩⟩,⟨⟨489715899760223906263991488,489715899760223907877875418⟩,⟨(-573709381082038235997800477),(-573709381082038234391905906)⟩⟩] +lemma kernel7_1_r4_10_eq : ∀ k : Fin 16, kernel7_1Expr 4 10 k = kernel7_1_r4_10 k := by decide +kernel +noncomputable def kernel7_1_r4_11 : Fin 16 → CBox := ![⟨⟨463138169909388185245894787,463138169909388186809980505⟩,⟨(-565978839463621793649432724),(-565978839463621792092837497)⟩⟩,⟨⟨437703307993421984361008961,437703307993421985878507196⟩,⟨(-557975617673769104437430980),(-557975617673769102926950565)⟩⟩,⟨⟨413374727154285893369191608,413374727154285894840602949⟩,⟨(-549738530085422514084213412),(-549738530085422512619368494)⟩⟩,⟨⟨390116106574063413545172725,390116106574063414973009129⟩,⟨(-541303894995280183159971054),(-541303894995280181738272980)⟩⟩,⟨⟨367891467304088637062828064,367891467304088638447179499⟩,⟨(-532705634639078194342468621),(-532705634639078192963846718)⟩⟩,⟨⟨346665241239515295998714706,346665241239515297342351487⟩,⟨(-523975374791826656243110284),(-523975374791826654904816135)⟩⟩,⟨⟨326402333515886803016316644,326402333515886804319670825⟩,⟨(-515142543629821408776772110),(-515142543629821407478391966)⟩⟩,⟨⟨307068178611130856161953289,307068178611130857427283153⟩,⟨(-506234469559630348786757053),(-506234469559630347526052212)⟩⟩,⟨⟨288628790441267692216775359,288628790441267693444028309⟩,⟨(-497276477746844711476695397),(-497276477746844710253734949)⟩⟩,⟨⟨271050806741126155400451033,271050806741126156592230659⟩,⟨(-488291985104094521611170982),(-488291985104094520423369672)⟩⟩,⟨⟨254301528022645061469444140,254301528022645062626116958⟩,⟨(-479302593523571596776377401),(-479302593523571595623384307)⟩⟩,⟨⟨238348951403037094014679368,238348951403037095138269389⟩,⟨(-470328181164014136786736524),(-470328181164014135666543886)⟩⟩,⟨⟨223161799593345437917473871,223161799593345439007989634⟩,⟨(-461386991625728061825172631),(-461386991625728060737786061)⟩⟩,⟨⟨208709545334863961537089087,208709545334863962596781403⟩,⟨(-452495720869707947736401672),(-452495720869707946679585334)⟩⟩,⟨⟨194962431566651296498120431,194962431566651297527293855⟩,⟨(-443669601758242067701990215),(-443669601758242066675452728)⟩⟩,⟨⟨181891487602075093075615304,181891487602075094076080488⟩,⟨(-434922486114519664261055523),(-434922486114519663262999570)⟩⟩] +lemma kernel7_1_r4_11_eq : ∀ k : Fin 16, kernel7_1Expr 4 11 k = kernel7_1_r4_11 k := by decide +kernel +noncomputable def kernel7_1_r4_12 : Fin 16 → CBox := ![⟨⟨169468541586098081220628200,169468541586098082192239960⟩,⟨(-426266924217691890985449176),(-426266924217691890016031870)⟩⟩,⟨⟨157666229497980435833451669,157666229497980436778353946⟩,⟨(-417714241667567593129159227),(-417714241667567592186248842)⟩⟩,⟨⟨146458000956336068233262247,146458000956336069151702733⟩,⟨(-409274613569656121634580513),(-409274613569656120717940391)⟩⟩,⟨⟨135818122075150891839874194,135818122075150892733469856⟩,⟨(-400957136006613949350703122),(-400957136006613948458727122)⟩⟩,⟨⟨125721675610549941404636297,125721675610549942273322930⟩,⟨(-392769894776328831452406457),(-392769894776328830585168848)⟩⟩,⟨⟨116144558628882436268833431,116144558628882437114431949⟩,⟨(-384720031389909309919361717),(-384720031389909309075051324)⟩⟩,⟨⟨107063477917168202115589460,107063477917168202938295560⟩,⟨(-376813806334768293405506324),(-376813806334768292583936645)⟩⟩,⟨⟨98455943347197741810223910,98455943347197742611481150⟩,⟨(-369056659618831436729111135),(-369056659618831435928847289)⟩⟩,⟨⟨90300259394677825049443067,90300259394677825829076621⟩,⟨(-361453268621702013345321168),(-361453268621702012566546439)⟩⟩,⟨⟨82575515004834666375012502,82575515004834667134741971⟩,⟨(-354007603287414925790164264),(-354007603287414925031166720)⟩⟩,⟨⟨75261571985891367594206872,75261571985891368334181660⟩,⟨(-346722978701256932312152924),(-346722978701256931572790789)⟩⟩,⟨⟨68339052101883108219226671,68339052101883108940735337⟩,⟨(-339602105100063516217710905),(-339602105100063515496702474)⟩⟩,⟨⟨61789323026414554568515912,61789323026414555271434414⟩,⟨(-332647135371471936772857380),(-332647135371471936070333758)⟩⟩,⟨⟨55594483309245490895698452,55594483309245491581503313⟩,⟨(-325859710102862663903242164),(-325859710102862663217732791)⟩⟩,⟨⟨49737346498053737517305695,49737346498053738186105234⟩,⟨(-319241000245205901444224190),(-319241000245205900775627048)⟩⟩,⟨⟨44201424548404859676310986,44201424548404860329256863⟩,⟨(-312791747460794638379440880),(-312791747460794637726609655)⟩⟩] +lemma kernel7_1_r4_12_eq : ∀ k : Fin 16, kernel7_1Expr 4 12 k = kernel7_1_r4_12 k := by decide +kernel +noncomputable def kernel7_1_r4_13 : Fin 16 → CBox := ![⟨⟨38970910645886964546232183,38970910645886965183087021⟩,⟨(-306512302226938775611684102),(-306512302226938774974862150)⟩⟩,⟨⟨34030661555572414721847717,34030661555572415344035802⟩,⟨(-300402659770163929353097242),(-300402659770163928730864745)⟩⟩,⟨⟨29366179605468625480303158,29366179605468626087897264⟩,⟨(-294462493907350233325694438),(-294462493907350232717983812)⟩⟩,⟨⟨24963594402435306626162350,24963594402435307220193275⟩,⟨(-288691188871606478774983243),(-288691188871606478180767801)⟩⟩,⟨⟨20809644371189870009271452,20809644371189870589569252⟩,⟨(-283087869201547567396728985),(-283087869201547566816183615)⟩⟩,⟨⟨16891658199507116294986467,16891658199507116862759244⟩,⟨(-277651427773071349083528882),(-277651427773071348515448836)⟩⟩,⟨⟨13197536265551442881338187,13197536265551443436627937⟩,⟨(-272380552052755685251301944),(-272380552052755684695649515)⟩⟩,⟨⟨9715732116464499179284715,9715732116464499723016938⟩,⟨(-267273748651657481692234160),(-267273748651657481148086935)⟩⟩,⟨⟨6435234060870664106114374,6435234060870664638036114⟩,⟨(-262329366257630092259138757),(-262329366257630091726753932)⟩⟩,⟨⟨3345546931856791896894859,3345546931856792418171357⟩,⟨(-257545617023319614934529057),(-257545617023319614412743721)⟩⟩,⟨⟨436674071229126689389684,436674071229127200037076⟩,⟨(-252920596485787935295730064),(-252920596485787934784531604)⟩⟩,⟨⟨(-2300900419554973355900364),(-2300900419554972855048345)⟩,⟨(-248452302092272684227744697),(-248452302092272683726301657)⟩⟩,⟨⟨(-4876229121445561477982657),(-4876229121445560987129457)⟩,⟨(-244138650404961337555911782),(-244138650404961337064431127)⟩⟩,⟨⟨(-7297918397241216091769360),(-7297918397241215609910064)⟩,⟨(-239977493055856278205613737),(-239977493055856277723092174)⟩⟩,⟨⟨(-9574145117205292019322406),(-9574145117205291546462605)⟩,⟨(-235966631520865582805900992),(-235966631520865582332347051)⟩⟩,⟨⟨(-11712672983732371919807950),(-11712672983732371455192829)⟩,⟨(-232103830780194467146704372),(-232103830780194466681364848)⟩⟩] +lemma kernel7_1_r4_13_eq : ∀ k : Fin 16, kernel7_1Expr 4 13 k = kernel7_1_r4_13 k := by decide +kernel +noncomputable def kernel7_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-13720868431715016772899560),(-13720868431715016316824495)⟩,⟨(-228386831929956721370374751),(-228386831929956720913548148)⟩⟩,⟨⟨(-15605716084739376426121235),(-15605716084739375977581399)⟩,⟨(-224813363807694241939618366),(-224813363807694241490300742)⟩⟩,⟨⟨(-17373833750431548363326282),(-17373833750431547922344723)⟩,⟨(-221381153692204301769570861),(-221381153692204301327787703)⟩⟩,⟨⟨(-19031486941196603745278996),(-19031486941196603311168890)⟩,⟨(-218087937135745160174780315),(-218087937135745159739845898)⟩⟩,⟨⟨(-20584602909251049571034410),(-20584602909251049144022310)⟩,⟨(-214931466984336028164378272),(-214931466984336027736521731)⟩⟩,⟨⟨(-22038784187259445430067610),(-22038784187259445009297614)⟩,⟨(-211909521639500734668830709),(-211909521639500734247196673)⟩⟩,⟨⟨(-23399321628059290045039809),(-23399321628059289630549066)⟩,⟨(-209019912612437659801301785),(-209019912612437659385929444)⟩⟩,⟨⟨(-24671206938907462649337574),(-24671206938907462240496662)⟩,⟨(-206260491419242177320365632),(-206260491419242176910626261)⟩⟩,⟨⟨(-25859144707418674476814308),(-25859144707418674073916352)⟩,⟨(-203629155863471215189792050),(-203629155863471214785981143)⟩⟩,⟨⟨(-26967563917903617926953796),(-26967563917903617529141125)⟩,⟨(-201123855750030585428662185),(-201123855750030585029922111)⟩⟩,⟨⟨(-28000628958163633510747960),(-28000628958163633118068273)⟩,⟨(-198742598072091265588535820),(-198742598072091265194916006)⟩⟩,⟨⟨(-28962250117971313726453830),(-28962250117971313338326217)⟩,⟨(-196483451710506553636158722),(-196483451710506553247078640)⟩⟩,⟨⟨(-29856093581473782175818108),(-29856093581473781792484427)⟩,⟨(-194344551683012666989087082),(-194344551683012666604790597)⟩⟩,⟨⟨(-30685590916608333971684285),(-30685590916608333592392528)⟩,⟨(-192324102978354671865174080),(-192324102978354671484909045)⟩⟩,⟨⟨(-31453948065329237220099803),(-31453948065329236844905313)⟩,⟨(-190420384008390494526654558),(-190420384008390494150477804)⟩⟩,⟨⟨(-32164153839019922529715039),(-32164153839019922158076908)⟩,⟨(-188631749709190260277097455),(-188631749709190259904468224)⟩⟩] +lemma kernel7_1_r4_14_eq : ∀ k : Fin 16, kernel7_1Expr 4 14 k = kernel7_1_r4_14 k := by decide +kernel +noncomputable def kernel7_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-32818987923916272202264892),(-32818987923916271834502306)⟩,⟨(-186956634320167668584942858),(-186956634320167668216182304)⟩⟩,⟨⟨(-33421028401703596214404303),(-33421028401703595849730119)⟩,⟨(-185393553868355205912453779),(-185393553868355205546774248)⟩⟩,⟨⟨(-33972658790681067664124411),(-33972658790681067302598465)⟩,⟨(-183941108383065766145160786),(-183941108383065765782623414)⟩⟩,⟨⟨(-34476074613021393376154140),(-34476074613021393017268435)⟩,⟨(-182597983864369174377889697),(-182597983864369174017986472)⟩⟩,⟨⟨(-34933289493698416656102456),(-34933289493698416300108152)⟩,⟨(-181362954027052166000545191),(-181362954027052165643528934)⟩⟩,⟨⟨(-35346140796618892516567399),(-35346140796618892162778946)⟩,⟨(-180234881840023072177429926),(-180234881840023071822614579)⟩⟩,⟨⟨(-35716294803384160030874343),(-35716294803384159679353554)⟩,⟨(-179212720879465903297506491),(-179212720879465902944955033)⟩⟩,⟨⟨(-36045251439929811468251485),(-36045251439929811118516184)⟩,⟨(-178295516512440431083709809),(-178295516512440430732939941)⟩⟩,⟨⟨(-36334348556053321508322221),(-36334348556053321160684793)⟩,⟨(-177482406926062643801446788),(-177482406926062643452772591)⟩⟩,⟨⟨(-36584765762547218617829943),(-36584765762547218271567124)⟩,⟨(-176772624015880689475043905),(-176772624015880689127741372)⟩⟩,⟨⟨(-36797527830314711337358694),(-36797527830314710992531359)⟩,⟨(-176165494145581971598703053),(-176165494145581971252834125)⟩⟩,⟨⟨(-36973507655461395535027008),(-36973507655461395191172964)⟩,⟨(-175660438788724035354310318),(-175660438788724035009412618)⟩⟩,⟨⟨(-37113428793936174254718821),(-37113428793936173912094130)⟩,⟨(-175256975061771696519933748),(-175256975061771696176264847)⟩⟩,⟨⟨(-37217867568841994539573706),(-37217867568841994197526910)⟩,⟨(-174954716156341766316504908),(-174954716156341765973412669)⟩⟩,⟨⟨(-37287254753057412858895565),(-37287254753057412517484055)⟩,⟨(-174753371677200814567622972),(-174753371677200814225165799)⟩⟩,⟨⟨(-37321876829308130558307344),(-37321876829308130217083043)⟩,⟨(-174652747891226670919447249),(-174652747891226670577176873)⟩⟩] +lemma kernel7_1_r4_15_eq : ∀ k : Fin 16, kernel7_1Expr 4 15 k = kernel7_1_r4_15 k := by decide +kernel +noncomputable def kernel7_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel7_1_r4_0,kernel7_1_r4_1,kernel7_1_r4_2,kernel7_1_r4_3,kernel7_1_r4_4,kernel7_1_r4_5,kernel7_1_r4_6,kernel7_1_r4_7,kernel7_1_r4_8,kernel7_1_r4_9,kernel7_1_r4_10,kernel7_1_r4_11,kernel7_1_r4_12,kernel7_1_r4_13,kernel7_1_r4_14,kernel7_1_r4_15] +lemma kernel7_1_r4_eq (i k : Fin 16) : kernel7_1Expr 4 i k = kernel7_1_r4 i k := by + fin_cases i + · exact kernel7_1_r4_0_eq k + · exact kernel7_1_r4_1_eq k + · exact kernel7_1_r4_2_eq k + · exact kernel7_1_r4_3_eq k + · exact kernel7_1_r4_4_eq k + · exact kernel7_1_r4_5_eq k + · exact kernel7_1_r4_6_eq k + · exact kernel7_1_r4_7_eq k + · exact kernel7_1_r4_8_eq k + · exact kernel7_1_r4_9_eq k + · exact kernel7_1_r4_10_eq k + · exact kernel7_1_r4_11_eq k + · exact kernel7_1_r4_12_eq k + · exact kernel7_1_r4_13_eq k + · exact kernel7_1_r4_14_eq k + · exact kernel7_1_r4_15_eq k +noncomputable def kernel7_1_r5_0 : Fin 16 → CBox := ![⟨⟨872812540458296330458200079192,872812540458296331207925851359⟩,⟨(-568018319357351622457460710152),(-568018319357351621724878812743)⟩⟩,⟨⟨872501783823361581384399409924,872501783823361582134093053153⟩,⟨(-568116945458970005662125579741),(-568116945458970004929566237287)⟩⟩,⟨⟨871880408104762570591878982895,871880408104762571341507089446⟩,⟨(-568313895868263941102542784171),(-568313895868263940370029834132)⟩⟩,⟨⟨870948688634357008661849448121,870948688634357009411378532405⟩,⟨(-568608567558473012243546382606),(-568608567558473011511103755436)⟩⟩,⟨⟨869707038981681477808660122011,869707038981681478558056552134⟩,⟨(-569000057391666258284822835153),(-569000057391666257552474630318)⟩⟩,⟨⟨868156011635739924937977373863,868156011635739925687207355163⟩,⟨(-569487163799701498829289067179),(-569487163799701498097059577175)⟩⟩,⟨⟨866296298906885835321399009224,866296298906885836070428493901⟩,⟨(-570068389022676167378562092321),(-570068389022676166646475900530)⟩⟩,⟨⟨864128734042686526289292568180,864128734042686527038087291980⟩,⟨(-570741941902429888638760809497),(-570741941902429887906842761232)⟩⟩,⟨⟨861654292550171826699241036835,861654292550171827447766333283⟩,⟨(-571505741228029869768005245469),(-571505741228029869036280640889)⟩⟩,⟨⟨858874093715410943012396764609,858874093715410943760617747953⟩,⟨(-572357419629528501285458759401),(-572357419629528500553953178738)⟩⟩,⟨⟨855789402309935994863941307413,855789402309935995611822493668⟩,⟨(-573294328015626181465118704353),(-573294328015626180733858393357)⟩⟩,⟨⟨852401630472143912354125298438,852401630472143913101631057862⟩,⟨(-574313540550199253764378343568),(-574313540550199253033389769977)⟩⟩,⟨⟨848712339750465435385659085605,848712339750465436132752853600⟩,⟨(-575411860161961233196325480091),(-575411860161961232465636127996)⟩⟩,⟨⟨844723243293796073455605454605,844723243293796074202250771384⟩,⟨(-576585824580813559264693101519),(-576585824580813558534330442300)⟩⟩,⟨⟨840436208173444211353587021309,840436208173444212099746097889⟩,⟨(-577831712893708549179958641736),(-577831712893708548449951571361)⟩⟩,⟨⟨835853257819671116331220981898,835853257819671117076856374367⟩,⟨(-579145552612090890190020651352),(-579145552612090889460397828508)⟩⟩] +lemma kernel7_1_r5_0_eq : ∀ k : Fin 16, kernel7_1Expr 5 0 k = kernel7_1_r5_0 k := by decide +kernel +noncomputable def kernel7_1_r5_1 : Fin 16 → CBox := ![⟨⟨830976574554781331444398489127,830976574554781332189470794452⟩,⟨(-580523127242204033988315220937),(-580523127242204033259107371928)⟩⟩,⟨⟨825808502203674611763994699210,825808502203674612508465579093⟩,⟨(-581959984348743662849716195301),(-581959984348743662120953106361)⟩⟩,⟨⟨820351548761796812055721582838,820351548761796812799550045345⟩,⟨(-583451444101511719902634856025),(-583451444101511719174349088329)⟩⟩,⟨⟨814608389099531441268987540701,814608389099531442012134059629⟩,⟨(-584992608293871392809450212851),(-584992608293871392081673002136)⟩⟩,⟨⟨808581867681260257511694148186,808581867681260258254115507594⟩,⟨(-586578369820926306215956352551),(-586578369820926305488722757369)⟩⟩,⟨⟨802275001276594389049495808370,802275001276594389791151673243⟩,⟨(-588203422604446756304733446508),(-588203422604446755578075802871)⟩⟩,⟨⟨795690981640640922057655749972,795690981640640922798501003890⟩,⟨(-589862271950643209095084357807),(-589862271950643208369039927686)⟩⟩,⟨⟨788833178139627354211338677206,788833178139627354951331611497⟩,⟨(-591549245325943942944993229261),(-591549245325943942219596040431)⟩⟩,⟨⟨781705140297761186279307902871,781705140297761187018400417389⟩,⟨(-593258503534971470459615589167),(-593258503534971469734906215455)⟩⟩,⟨⟨774310600240857356226742335270,774310600240857356964892252725⟩,⟨(-594984052283933417444472767046),(-594984052283933416720486052789)⟩⟩,⟨⟨766653475012025070432909529877,766653475012025071170066733425⟩,⟨(-596719754111650423231665109553),(-596719754111650422508444003239)⟩⟩,⟨⟨758737868734570407717495370019,758737868734570408453616050122⟩,⟨(-598459340669439274949802740410),(-598459340669439274227384090185)⟩⟩,⟨⟨750568074597244092609656477150,750568074597244093344686795459⟩,⟨(-600196425330057169366465887456),(-600196425330057168644896743553)⟩⟩,⟨⟨742148576637046939550839907880,742148576637046940284736010295⟩,⟨(-601924516104896325596548816288),(-601924516104896324875866472514)⟩⟩,⟨⟨733484051295000181539676305534,733484051295000182272382230916⟩,⟨(-603637028847601098408852602173),(-603637028847601097689106641129)⟩⟩,⟨⟨724579368720595355670670926492,724579368720595356402141043058⟩,⟨(-605327300721266530765730807898),(-605327300721266530046960722463)⟩⟩] +lemma kernel7_1_r5_1_eq : ∀ k : Fin 16, kernel7_1Expr 5 1 k = kernel7_1_r5_1 k := by decide +kernel +noncomputable def kernel7_1_r5_2 : Fin 16 → CBox := ![⟨⟨715439593801059365059148009829,715439593801059365789321492086⟩,⟨(-606988603905372501247249374365),(-606988603905372500529510039309)⟩⟩,⟨⟨706069986892105095749236730408,706069986892105096478068859897⟩,⟨(-608614159517616112530010223625),(-608614159517616111813340669189)⟩⟩,⟨⟨696476004227486428820789527946,696476004227486429548217748850⟩,⟨(-610197151724831833381338212965),(-610197151724831832665795501928)⟩⟩,⟨⟨686663297985438093548562913832,686663297985438094274540230316⟩,⟨(-611730742016239482432864541393),(-611730742016239481718490446710)⟩⟩,⟨⟨676637715990954535529449276470,676637715990954536253907501718⟩,⟨(-613208083611339964628210400956),(-613208083611339963915068087910)⟩⟩,⟨⟨666405301033846326806668603919,666405301033846327529562373292⟩,⟨(-614622335973893451315894871726),(-614622335973893450604024975578)⟩⟩,⟨⟨655972289783605639020786604574,655972289783605639742046123417⟩,⟨(-615966679402570283865476181846),(-615966679402570283154943974944)⟩⟩,⟨⟨645345111283311455402780746344,645345111283311456122358289432⟩,⟨(-617234329668067235923721530862),(-617234329668067235214570512938)⟩⟩,⟨⟨634530385006107529863498431367,634530385006107530581316948263⟩,⟨(-618418552665736917995257307600),(-618418552665736917287560514547)⟩⟩,⟨⟨623534918459188120515083406901,623534918459188121231098553189⟩,⟨(-619512679052092108026065757392),(-619512679052092107319863838602)⟩⟩,⟨⟨612365704321724229370830934939,612365704321724230084965157144⟩,⟨(-620510118832925692292570168540),(-620510118832925691587937198092)⟩⟩,⟨⟨601029917104751958258457734801,601029917104751958970663410486⟩,⟨(-621404375870236701111870542725),(-621404375870236700408850981257)⟩⟩,⟨⟨589534909322719624482946866002,589534909322719625193138500343⟩,⟨(-622189062274679529897539724441),(-622189062274679529196216125874)⟩⟩,⟨⟨577888207168145948420500086575,577888207168145949128634397663⟩,⟨(-622857912649862617970643061608),(-622857912649862617271056102803)⟩⟩,⟨⟨566097505682671916394787114619,566097505682671917100778427124⟩,⟨(-623404798154520205238207982302),(-623404798154520204540440958571)⟩⟩,⟨⟨554170663419687342683291012017,554170663419687343387092788369⟩,⟨(-623823740348371665839187692477),(-623823740348371665143285091640)⟩⟩] +lemma kernel7_1_r5_2_eq : ∀ k : Fin 16, kernel7_1Expr 5 2 k = kernel7_1_r5_2 k := by decide +kernel +noncomputable def kernel7_1_r5_3 : Fin 16 → CBox := ![⟨⟨542115696595672745772715983712,542115696595672746474232224481⟩,⟨(-624108924787372424732773650827),(-624108924787372424038829651175)⟩⟩,⟨⟨529940772729410510625016416634,529940772729410511324207756248⟩,⟨(-624254714334053381592500300075),(-624254714334053380900552792098)⟩⟩,⟨⟨517654203770278600348049179971,517654203770278601044821646517⟩,⟨(-624255662148746523378289364739),(-624255662148746522688431077860)⟩⟩,⟨⟨505264438718937077147305198233,505264438718937077841614466706⟩,⟨(-624106524327707030558823194350),(-624106524327707029871097543586)⟩⟩,⟨⟨492780055745843792477300849071,492780055745843793169042371372⟩,⟨(-623802272154470259589013811829),(-623802272154470258903524674979)⟩⟩,⟨⟨480209753815181869387001229604,480209753815181870076138699430⟩,⟨(-623338103931228623027637308584),(-623338103931228622344420660216)⟩⟩,⟨⟨467562343823938781612622860780,467562343823938782299054025132⟩,⟨(-622709456357581177493234473695),(-622709456357581176812392479302)⟩⟩,⟨⟨454846739268035423800382016413,454846739268035424484066002989⟩,⟨(-621912015424699703526748667756),(-621912015424699702848322434265)⟩⟩,⟨⟨442071946449553830913249405469,442071946449553831594070344026⟩,⟨(-620941726793770668443736143746),(-620941726793770667767842027569)⟩⟩,⟨⟨429247054241244228067081262461,429247054241244228745010096031⟩,⟨(-619794805628513534422988849904),(-619794805628513533749656713351)⟩⟩,⟨⟨416381223426595827608320860829,416381223426595828283390329151⟩,⟨(-618467745852642596359396439842),(-618467745852642595688594990558)⟩⟩,⟨⟨403483675635821107766436945994,403483675635821108439705454302⟩,⟨(-616957328804331426930549533710),(-616957328804331426261224657383)⟩⟩,⟨⟨390563681900120044834924501039,390563681900120045506274947798⟩,⟨(-615260631261054902328618736225),(-615260631261054901660889154887)⟩⟩,⟨⟨377630550848548789043211322891,377630550848548789712626438983⟩,⟨(-613375032809621811030485650090),(-613375032809621810364370530409)⟩⟩,⟨⟨364693616573706511477487987077,364693616573706512144854805821⟩,⟨(-611298222537768625746210546791),(-611298222537768625081825025175)⟩⟩,⟨⟨351762226194264678639992713774,351762226194264679305286160486⟩,⟨(-609028205025358840716413059777),(-609028205025358840053784634753)⟩⟩] +lemma kernel7_1_r5_3_eq : ∀ k : Fin 16, kernel7_1Expr 5 3 k = kernel7_1_r5_3 k := by decide +kernel +noncomputable def kernel7_1_r5_4 : Fin 16 → CBox := ![⟨⟨338845727144085098207683818692,338845727144085098870771064478⟩,⟨(-606563305615018315592939271853),(-606563305615018314932203482911)⟩⟩,⟨⟨325953454219297240985145907055,325953454219297241646018575026⟩,⟨(-603902174943930576366724087808),(-603902174943930575707892241509)⟩⟩,⟨⟨313094716416222406497781150529,313094716416222407156315522016⟩,⟨(-601043792720511544495358742979),(-601043792720511543838557783142)⟩⟩,⟨⟨300278783594433458028202125818,300278783594433458684377898207⟩,⟨(-597987470731774540010824521179),(-597987470731774539356078172822)⟩⟩,⟨⟨287514873000515728361489066568,287514873000515729015163706350⟩,⟨(-594732855069376794713442747732),(-594732855069376794060897279330)⟩⟩,⟨⟨274812135689239394462444717699,274812135689239395113614523656⟩,⟨(-591279927564600621927551463667),(-591279927564600621277214455904)⟩⟩,⟨⟨262179642879858780785559409352,262179642879858781434090439862⟩,⟨(-587629006424857695025522955415),(-587629006424857694377532553629)⟩⟩,⟨⟨249626372286112912032721776983,249626372286112912678599917970⟩,⟨(-583780746066704867812189377508),(-583780746066704867166564022620)⟩⟩,⟨⟨237161194459208075264977329663,237161194459208075908044479642⟩,⟨(-579736136142815348560715420959),(-579736136142815347917617891870)⟩⟩,⟨⟨224792859183611738150201829564,224792859183611738790466925384⟩,⟨(-575496499762850024775473604962),(-575496499762850024134899683044)⟩⟩,⟨⟨212529981965873211110108925889,212529981965873211747428550802⟩,⟨(-571063490910710070286872062526),(-571063490910710069648970247829)⟩⟩,⟨⟨200381030656906020350398598793,200381030656906020984766258783⟩,⟨(-566439091063212978796063198777),(-566439091063212978160845100720)⟩⟩,⟨⟨188354312248216975439544936708,188354312248216976070794654022⟩,⟨(-561625605017808829490197463024),(-561625605017808828857834564415)⟩⟩,⟨⟨176457959882445116290775459080,176457959882445116918923350231⟩,⟨(-556625655939530574116452256195),(-556625655939530573486933876867)⟩⟩,⟨⟨164699920118278732948338937257,164699920118278733573233055982⟩,⟨(-551442179639939879780474931262),(-551442179639939879153958861790)⟩⟩,⟨⟨153087940489349988882723544771,153087940489349989504366417488⟩,⟨(-546078418103376838489615502843),(-546078418103376837866104986238)⟩⟩] +lemma kernel7_1_r5_4_eq : ∀ k : Fin 16, kernel7_1Expr 5 4 k = kernel7_1_r5_4 k := by decide +kernel +noncomputable def kernel7_1_r5_5 : Fin 16 → CBox := ![⟨⟨141629557396064781881913981784,141629557396064782500123695276⟩,⟨(-540537912278335834593543263175),(-540537912278335833973226432964)⟩⟩,⟨⟨130332084368511710913142540374,130332084368511711527952904964⟩,⟨(-534824494154259187978846606173),(-534824494154259187361695650008)⟩⟩,⟨⟨119202600737610680592963313499,119202600737610681204215003136⟩,⟨(-528942278146453051488574078471),(-528942278146453050874754792771)⟩⟩,⟨⟨108247940750511998014347309161,108247940750511998622053172105⟩,⟨(-522895651814174740635184808737),(-522895651814174740024690619677)⟩⟩,⟨⟨97474683164944956730736692243,97474683164944957334711084207⟩,⟨(-516689265939205709074895589394),(-516689265939205708467918917708)⟩⟩,⟨⟨86889141355745930028527164541,86889141355745930628811818953⟩,⟨(-510328023994398517138973463074),(-510328023994398516535478997110)⟩⟩,⟨⟨76497353965175874612949209959,76497353965175875209378689925⟩,⟨(-503817071033758474758078219679),(-503817071033758474158238345728)⟩⟩,⟨⟨66305076126872709305589877904,66305076126872709898188581826⟩,⟨(-497161782037580687577582913543),(-497161782037580686981379853909)⟩⟩,⟨⟨56317771291382950831111502997,56317771291382951419679866072⟩,⟨(-490367749748000990979418967986),(-490367749748000990387059493833)⟩⟩,⟨⟨46540603679187728572110950807,46540603679187729156711378819⟩,⟨(-483440772032025266133776714539),(-483440772032025265545205079637)⟩⟩,⟨⟨36978431384990085685004082179,36978431384990086265466453908⟩,⟨(-476386838810667055311532345026),(-476386838810667054726925944441)⟩⟩,⟨⟨27635800154773234177438403104,27635800154773234753799706879⟩,⟨(-469212118594240067724067030479),(-469212118594240067143395679846)⟩⟩,⟨⟨18516937854783746278600158008,18516937854783746850660311791⟩,⟨(-461922944665112664136487883682),(-461922944665112663559959117739)⟩⟩,⟨⟨9625749649150704483434496731,9625749649150705051265518248⟩,⟨(-454525800950329088642023002930),(-454525800950329088069571564561)⟩⟩,⟨⟨965813900333295381416118969,965813900333295944844678295⟩,⟨(-447027307627431276075703659910),(-447027307627431275507510320513)⟩⟩,⟨⟨(-7459621195992627001966256820),(-7459621195992626442889704582)⟩,⟨(-439434206507570580051396456732),(-439434206507570579487417586586)⟩⟩] +lemma kernel7_1_r5_5_eq : ∀ k : Fin 16, kernel7_1Expr 5 5 k = kernel7_1_r5_5 k := by decide +kernel +noncomputable def kernel7_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-15647640232631323382908919501),(-15647640232631322828398353020)⟩,⟨(-431753346240576732905113501163),(-431753346240576732345570663583)⟩⟩,⟨⟨(-23595662462840483473118999039),(-23595662462840482923077011598)⟩,⟨(-423991667387048706445923871665),(-423991667387048705890726321499)⟩⟩,⟨⟨(-31301442918970078845588293865),(-31301442918970078300189863451)⟩,⟨(-416156187402746805728824032775),(-416156187402746805178154202949)⟩⟩,⟨⟨(-38763072776863295755655881315),(-38763072776863295214815662152)⟩,⟨(-408253985580596202458393550284),(-408253985580596201912190846035)⟩⟩,⟨⟨(-45978978967822035686098610835),(-45978978967822035149981603882)⟩,⟨(-400292187995459107680110121009),(-400292187995459107138584587417)⟩⟩,⟨⟨(-52947923042630539348999109934),(-52947923042630538817501506303)⟩,⟨(-392277952496496809188523324590),(-392277952496496808651576277937)⟩⟩,⟨⟨(-59668999294793685229366071782),(-59668999294793684702664437606)⟩,⟨(-384218453791425775247935043146),(-384218453791425774715748972629)⟩⟩,⟨⟨(-66141632152768420788639921823),(-66141632152768420266656605450)⟩,⟨(-376120868666276864199705311453),(-376120868666276863672207617489)⟩⟩,⟨⟨(-72365572853534847208398925750),(-72365572853534846690852197733)⟩,⟨(-367992361383397267448187078512),(-367992361383397266925102309869)⟩⟩,⟨⟨(-78340895412355280592614887890),(-78340895412355280079212030132)⟩,⟨(-359840069299395992168677138534),(-359840069299395991649717398598)⟩⟩,⟨⟨(-84067991905993154196961732324),(-84067991905993153687888762840)⟩,⟨(-351671088743531222976443767358),(-351671088743531222461800583828)⟩⟩,⟨⟨(-89547567088997399097633419808),(-89547567088997398592808308153)⟩,⟨(-343492461195678436770447869937),(-343492461195678436260043809263)⟩⟩,⟨⟨(-94780632364890998432710491135),(-94780632364890997932357050513)⟩,⟨(-335311159801509171436820257492),(-335311159801509170930884530246)⟩⟩,⟨⟨(-99768499136224435567444383833),(-99768499136224435071435239066)⟩,⟨(-327134076260860148461418689770),(-327134076260860147959828164723)⟩⟩,⟨⟨(-104512771559456122964707128764),(-104512771559456122473227614112)⟩,⟨(-318968008123490040108925163421),(-318968008123490039611870216873)⟩⟩,⟨⟨(-109015338732493728168347238631),(-109015338732493727681301202033)⟩,⟨(-310819646524516248975890536019),(-310819646524516248483279118779)⟩⟩] +lemma kernel7_1_r5_6_eq : ∀ k : Fin 16, kernel7_1Expr 5 6 k = kernel7_1_r5_6 k := by decide +kernel +noncomputable def kernel7_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-113278366344464527893787489693),(-113278366344464527411411759950)⟩,⟨(-302695564389806938895529738304),(-302695564389806938407603608494)⟩⟩,⟨⟨(-117304287818872288055125380697),(-117304287818872287577263857713)⟩,⟨(-294602205139485072325614997532),(-294602205139485071842221739065)⟩⟩,⟨⟨(-121095794982736338779460865680),(-121095794982736338306296671652)⟩,⟨(-286545871915492692544690754832),(-286545871915492692066017996019)⟩⟩,⟨⟨(-124655828295590059001622017672),(-124655828295590058533045003046)⟩,⟨(-278532717356876857201211806303),(-278532717356876856727152954591)⟩⟩,⟨⟨(-127987566673336418839337425579),(-127987566673336418375571496783)⟩,⟨(-270568733944105519258120027636),(-270568733944105518788903322826)⟩⟩,⟨⟨(-131094416942914026422094260542),(-131094416942914025962979531232)⟩,⟨(-262659744931314537486624868813),(-262659744931314537022093578956)⟩⟩,⟨⟨(-133980002964515741085955804433),(-133980002964515740631671844361)⟩,⟨(-254811395882938315390930730857),(-254811395882938314931268348988)⟩⟩,⟨⟨(-136648154458721778982746433939),(-136648154458721778533169413347)⟩,⟨(-247029146828698826818018188353),(-247029146828698826363103865001)⟩⟩,⟨⟨(-139102895576359760452293223498),(-139102895576359760007371564033)⟩,⟨(-239318265048433498000539426007),(-239318265048433497550465510477)⟩⟩,⟨⟨(-141348433249185710475045592947),(-141348433249185710034505861467)⟩,⟨(-231683818495744006804793769696),(-231683818495744006359331494143)⟩⟩,⟨⟨(-143389145359593957003596693273),(-143389145359593956567627391575)⟩,⟨(-224130669866957797669681856555),(-224130669866957797229015623495)⟩⟩,⟨⟨(-145229568767512440779373901380),(-145229568767512440347851747807)⟩,⟨(-216663471319424026143730101974),(-216663471319424025707731736960)⟩⟩,⟨⟨(-146874387232426320279991709478),(-146874387232426319853148380356)⟩,⟨(-209286659840727461578522205440),(-209286659840727461147419229558)⟩⟩,⟨⟨(-148328419268100959905237760182),(-148328419268100959482896784492)⟩,⟨(-202004453268008932506926987713),(-202004453268008932080537850663)⟩⟩,⟨⟨(-149596605967050288233904229770),(-149596605967050287816247849289)⟩,⟨(-194820846954240092847340890944),(-194820846954240092425843456702)⟩⟩,⟨⟨(-150683998831123746887300278201),(-150683998831123746474192388536)⟩,⟨(-187739611076024006981072482201),(-187739611076024006564325614909)⟩⟩] +lemma kernel7_1_r5_7_eq : ∀ k : Fin 16, kernel7_1Expr 5 7 k = kernel7_1_r5_7 k := by decide +kernel +noncomputable def kernel7_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-151595747643770990033045450515),(-151595747643770989624728053162)⟩,⟨(-180764288575291121518579325441),(-180764288575291121106820657122)⟩⟩,⟨⟨(-152337088418595185815850411357),(-152337088418595185412117170067)⟩,⟨(-173898193725141817535120123190),(-173898193725141817128138144392)⟩⟩,⟨⟨(-152913331457730876143929727292),(-152913331457730875744955496631)⟩,⟨(-167144411308060461374315817060),(-167144411308060460972280832501)⟩⟩,⟨⟨(-153329849552389086514114501896),(-153329849552389086119751278924)⟩,⟨(-160505796392799531696981542777),(-160505796392799531299740492208)⟩⟩,⟨⟨(-153592066356609448234905455941),(-153592066356609447845373157738)⟩,⟨(-153984974694413091596146895051),(-153984974694413091203915161717)⟩⟩,⟨⟨(-153705444963855628930133338328),(-153705444963855628545228700389)⟩,⟨(-147584343500212923919875316976),(-147584343500212923532444536169)⟩⟩,⟨⟨(-153675476714595844379344258748),(-153675476714595843999233959896)⟩,⟨(-141306073142833589264983378300),(-141306073142833588882515608021)⟩⟩,⟨⟨(-153507670261434410221998717044),(-153507670261434409846523886374)⟩,⟨(-135152109000129223798399721563),(-135152109000129223420731111025)⟩⟩,⟨⟨(-153207540916713164183150431697),(-153207540916713163812536852095)⟩,⟨(-129124174000288972427913711393),(-129124174000288972055265479800)⟩⟩,⟨⟨(-152780600305793270574155155419),(-152780600305793270208174725515)⟩,⟨(-123223771609352631856687772140),(-123223771609352631488826847688)⟩⟩,⟨⟨(-152232346347468605896205457114),(-152232346347468605535016031660)⟩,⟨(-117452189277235614991296852135),(-117452189277235614628376490183)⟩⟩,⟨⟨(-151568253581161821368883806023),(-151568253581161821012316962108)⟩,⟨(-111810502317434185320327890064),(-111810502317434184962174856550)⟩⟩,⟨⟨(-150793763858723429798924751107),(-150793763858723429447184842764)⟩,⟨(-106299578194778687752359706574),(-106299578194778687399173824498)⟩⟩,⟨⟨(-149914277416802892081070218050),(-149914277416802891733932805636)⟩,⟨(-100920081194934078571123673340),(-100920081194934078222675774355)⟩⟩,⟨⟨(-148935144343898520264278203547),(-148935144343898519921891991285)⟩,⟨(-95672477448812530032674691736),(-95672477448812529689108983493)⟩⟩,⟨⟨(-147861656454329664919381497951),(-147861656454329664581569878604)⟩,⟨(-90557040284660622681826499966),(-90557040284660622342961809690)⟩⟩] +lemma kernel7_1_r5_8_eq : ∀ k : Fin 16, kernel7_1Expr 5 8 k = kernel7_1_r5_8 k := by decide +kernel +noncomputable def kernel7_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-146699039579519413256235729634),(-146699039579519412923211514534)⟩,⟨(-85573855880311311262645945478),(-85573855880311310928690675439)⟩⟩,⟨⟨(-145452446285137842629965854306),(-145452446285137842301479189960)⟩,⟨(-80722829187945468474768998417),(-80722829187945468145468860343)⟩⟩,⟨⟨(-144126949020843309551345291870),(-144126949020843309227535520022)⟩,⟨(-76003690103685765499912595375),(-76003690103685765175402606015)⟩⟩,⟨⟨(-142727533707580429094498626977),(-142727533707580428775182530863)⟩,⟨(-71415999854442754247098408493),(-71415999854442753927191092775)⟩⟩,⟨⟨(-141259093765655962267941216043),(-141259093765655961953305598881)⟩,⟨(-66959157574644559498322291773),(-66959157574644559183200223236)⟩⟩,⟨⟨(-139726424585124921926490688197),(-139726424585124921616296714954)⟩,⟨(-62632407045802375132046432539),(-62632407045802374821466696943)⟩⟩,⟨⟨(-138134218438385439350872813584),(-138134218438385439045250569892)⟩,⟨(-58434843572288363066138704074),(-58434843572288362760227288810)⟩⟩,⟨⟨(-136487059833308354643589006861),(-136487059833308354342350165040)⟩,⟨(-54365420967224574302096230578),(-54365420967224574000660902588)⟩⟩,⟨⟨(-134789421303721579929904634813),(-134789421303721579633241357889)⟩,⟨(-50422958622994820959553434898),(-50422958622994820662782349654)⟩⟩,⟨⟨(-133045659632634921492720667349),(-133045659632634921200375041514)⟩,⟨(-46606148641589426786691115975),(-46606148641589426494322676896)⟩⟩,⟨⟨(-131260012502232524336313984924),(-131260012502232524048407010000)⟩,⟨(-42913563000768652359384371902),(-42913563000768652071535749011)⟩⟩,⟨⟨(-129436595563381107803714661764),(-129436595563381107520054525661)⟩,⟨(-39343660732877344384629735221),(-39343660732877344101105594443)⟩⟩,⟨⟨(-127579399916205780396522713662),(-127579399916205780117278379074)⟩,⟨(-35894795094053895347232637768),(-35894795094053895068198208827)⟩⟩,⟨⟨(-125692289992173946587893439482),(-125692289992173946312818752245)⟩,⟨(-32565220702543754543133299701),(-32565220702543754268339150063)⟩⟩,⟨⟨(-123779001827103551904185996210),(-123779001827103551633393284862)⟩,⟨(-29353100625844322493982852781),(-29353100625844322223537777969)⟩⟩,⟨⟨(-121843141713575984564662435559),(-121843141713575984296967787452)⟩,⟨(-26256513397466936639082378347),(-26256513397466936371798381767)⟩⟩] +lemma kernel7_1_r5_9_eq : ∀ k : Fin 16, kernel7_1Expr 5 9 k = kernel7_1_r5_9 k := by decide +kernel +noncomputable def kernel7_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-119888185220387134513393707439),(-119888185220387134248894828001)⟩,⟨(-23273459945195740886841472279),(-23273459945195740622812727011)⟩⟩,⟨⟨(-117917476565912637937139593765),(-117917476565912637675602589687)⟩,⟨(-20401870413845566047160413584),(-20401870413845565786150235763)⟩⟩,⟨⟨(-115934228331594926296343244332),(-115934228331594926037907197311)⟩,⟨(-17639610866664729569865710955),(-17639610866664729312010009311)⟩⟩,⟨⟨(-113941521501179582844833285754),(-113941521501179582589334221486)⟩,⟨(-14984489850687281366104169862),(-14984489850687281111236292836)⟩⟩,⟨⟨(-111942305810835453852436065375),(-111942305810835453600062634021)⟩,⟨(-12434264812506293597739268858),(-12434264812506293346044770719)⟩⟩,⟨⟨(-109939400394885301440437790110),(-109939400394885301190970283248)⟩,⟨(-9986648352109188067577706177),(-9986648352109187818834475493)⟩⟩,⟨⟨(-107935494711549454452373475038),(-107935494711549454205943773457)⟩,⟨(-7639314303581969821328080791),(-7639314303581969575665141317)⟩⟩,⟨⟨(-105933149732861479559449646574),(-105933149732861479315890213340)⟩,⟨(-5389903632646050624811412482),(-5389903632646050382058939029)⟩⟩,⟨⟨(-103934799382749589078375643695),(-103934799382749588837883542235)⟩,⟨(-3236030142133888186063523736),(-3236030142133887946415758023)⟩⟩,⟨⟨(-101942752207187257363460758557),(-101942752207187257125797606305)⟩,⟨(-1175285977633066479785158463),(-1175285977633066243001737472)⟩⟩,⟨⟨(-99959193260298001866474010691),(-99959193260298001631764648383)⟩,⟨794753073371814203108560830,794753073371814436905341190⟩⟩,⟨⟨(-97986186190348935949239041549),(-97986186190348935717313607299)⟩,⟨2676522494458128699335927040,2676522494458128930317844218⟩⟩,⟨⟨(-96025675509681761012573922060),(-96025675509681760783607789015)⟩,⟨4472464169883427427296550419,4472464169883427655290731673⟩⟩,⟨⟨(-94079489032804417372736755305),(-94079489032804417146504737899)⟩,⟨6185021734415781884232736930,6185021734415782109465999197⟩⟩,⟨⟨(-92149340467097611103004924907),(-92149340467097610879625187463)⟩,⟨7816636145961809162323798439,7816636145961809384680221291⟩⟩,⟨⟨(-90236832140873737614067722635),(-90236832140873737393369135529)⟩,⟨9369741482651137094831321408,9369741482651137314483600258⟩⟩] +lemma kernel7_1_r5_10_eq : ∀ k : Fin 16, kernel7_1Expr 5 10 k = kernel7_1_r5_10 k := by decide +kernel +noncomputable def kernel7_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-88343457853857128603137644204),(-88343457853857128385308397402)⟩,⟨10846760965152196668215583290,10846760965152196884977789156⟩⟩,⟨⟨(-86470605835529820570507757645),(-86470605835529820355302386892)⟩,⟨12250103204155152479355347979,12250103204155152693474186344⟩⟩,⟨⟨(-84619561797201939202787453506),(-84619561797201938990314566209)⟩,⟨13582158672165050029896935687,13582158672165050241277725302⟩⟩,⟨⟨(-82791512064116095845747787380),(-82791512064116095635835679457)⟩,⟨14845296398003069130095944887,14845296398003069338913123394⟩⟩,⟨⟨(-80987546774376728933334319139),(-80987546774376728726146082790)⟩,⟨16041860881716990884543425589,16041860881716991090635279273⟩⟩,⟨⟨(-79208663132003994572179707143),(-79208663132003994367489585157)⟩,⟨17174169226954157781736571695,17174169226954157985329312688⟩⟩,⟨⟨(-77455768701943608909012694935),(-77455768701943608706926707944)⟩,⟨18244508487251575105501847619,18244508487251575306490597563⟩⟩,⟨⟨(-75729684735415074849203143193),(-75729684735415074649550820234)⟩,⟨19255133222148323480822285811,19255133222148323679377995110⟩⟩,⟨⟨(-74031149514547220975397983059),(-74031149514547220778352412041)⟩,⟨20208263258524814496946960328,20208263258524814692897727430⟩⟩,⟨⟨(-72360821705828319932911149548),(-72360821705828319738231854822)⟩,⟨21106081652121061565456810797,21106081652121061759043344258⟩⟩,⟨⟨(-70719283712484774254246009335),(-70719283712484774062033501537)⟩,⟨21950732843781263200063915865,21950732843781263391186636744⟩⟩,⟨⟨(-69107045016494166669906645736),(-69107045016494166479992043176)⟩,⟨22744321004613601142255071696,22744321004613601331083165847⟩⟩,⟨⟨(-67524545501532255871972070428),(-67524545501532255684507503830)⟩,⟨23488908563941045121184804163,23488908563941045307567092888⟩⟩,⟨⟨(-65972158748746331084082640530),(-65972158748746330898845449965)⟩,⟨24186514913649761695338396573,24186514913649761879497648969⟩⟩,⟨⟨(-64450195297836486176783745332),(-64450195297836485993869436753)⟩,⟨24839115282314926774570238134,24839115282314926956411695932⟩⟩,⟨⟨(-62958905866509300078831204276),(-62958905866509299898073129214)⟩,⟨25448639772297687633751417859,25448639772297687813441885671⟩⟩] +lemma kernel7_1_r5_11_eq : ∀ k : Fin 16, kernel7_1Expr 5 11 k = kernel7_1_r5_11 k := by decide +kernel +noncomputable def kernel7_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-61498484521942777968332898686),(-61498484521942777789898872973)⟩,⟨26016972552859944559408802077,26016972552859944736781284398⟩⟩,⟨⟨(-60069071798465080722595709826),(-60069071798465080546244932744)⟩,⟨26545951202233663691012949559,26545951202233663866308181022⟩⟩,⟨⟨(-58670757756200611703712830909),(-58670757756200611529536159501)⟩,⟨27037366191506652989384446490,27037366191506653162512158895⟩⟩,⟨⟨(-57303584975973701474610713416),(-57303584975973701302444413227)⟩,⟨27492960503145134421981560890,27492960503145134593105522453⟩⟩,⟨⟨(-55967551486280888539080826018),(-55967551486280888369067662690)⟩,⟨27914429376962985664161437005,27914429376962985833139509616⟩⟩,⟨⟨(-54662613618646284302183150243),(-54662613618646284134106348710)⟩,⟨28303420176366133989666417983,28303420176366134156715246901⟩⟩,⟨⟨(-53388688788159564975467269936),(-53388688788159564809413538983)⟩,⟨28661532367746180187088877989,28661532367746180352122208268⟩⟩,⟨⟨(-52145658196461763034242643313),(-52145658196461762870051546450)⟩,⟨28990317605967827958848693117,28990317605967828122026895459⟩⟩,⟨⟨(-50933369454889419077026073170),(-50933369454889418914852255417)⟩,⟨29291279918988023738569513245,29291279918988023899738473910⟩⟩,⟨⟨(-49751639125912149079823341406),(-49751639125912148919437545529)⟩,⟨29565875984758826856164741218,29565875984758827015553470467⟩⟩,⟨⟨(-48600255181401785893656777939),(-48600255181401785735141897223)⟩,⟨29815515493698919035382930192,29815515493698919192908875036⟩⟩,⟨⟨(-47478979376652618932351980665),(-47478979376652618775551304544)⟩,⟨30041561590168358221073770383,30041561590168358376893496629⟩⟩,⟨⟨(-46387549539431672514655555602),(-46387549539431672359704176867)⟩,⟨30245331386545770531947085752,30245331386545770685925893818⟩⟩,⟨⟨(-45325681773675350912449174785),(-45325681773675350759137813129)⟩,⟨30428096543684801901066291375,30428096543684802053413179930⟩⟩,⟨⟨(-44293072577764176444848929671),(-44293072577764176293246684959)⟩,⟨30591083911715530830021997938,30591083911715530980675800783⟩⟩,⟨⟨(-43289400877600906127458913554),(-43289400877600905977396329422)⟩,⟨30735476225354961201468694255,30735476225354961350610914965⟩⟩] +lemma kernel7_1_r5_12_eq : ∀ k : Fin 16, kernel7_1Expr 5 12 k = kernel7_1_r5_12 k := by decide +kernel +noncomputable def kernel7_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-42314329974989283583358300189),(-42314329974989283434988418000)⟩,⟨30862412848097031968396035693,30862412848097032115873045166⟩⟩,⟨⟨(-41367509412061408889020896853),(-41367509412061408742119330901)⟩,⟨30972990559865242291792839567,30972990559865242437827780299⟩⟩,⟨⟨(-40448576752731614710648589117),(-40448576752731614565292761472)⟩,⟨31068264382928523676582377206,31068264382928523821097135421⟩⟩,⟨⟨(-39557159282364320584715879775),(-39557159282364320440758159395)⟩,⟨31149248441102008081379226713,31149248441102008224520377422⟩⟩,⟨⟨(-38692875627033160803162339979),(-38692875627033160660732691224)⟩,⟨31216916847477543421220316516,31216916847477543562857317143⟩⟩,⟨⟨(-37855337293919363043812670407),(-37855337293919362902710918160)⟩,⟨31272204616152983888660342405,31272204616152984028992272945⟩⟩,⟨⟨(-37044150134549559928734481831),(-37044150134549559789035135955)⟩,⟨31316008593653308757196795643,31316008593653308896148508148⟩⟩,⟨⟨(-36258915732707648872704658235),(-36258915732707648734264079741)⟩,⟨31349188405959464013819724440,31349188405959464151533901243⟩⟩,⟨⟨(-35499232718972713566482936782),(-35499232718972713429444679658)⟩,⟨31372567417281527087908642224,31372567417281527224241219638⟩⟩,⟨⟨(-34764698013936144739164246991),(-34764698013936144603315674066)⟩,⟨31386933696930501899298632868,31386933696930502034461232979⟩⟩,⟨⟨(-34054908002236728063686180026),(-34054908002236727929099082344)⟩,⟨31393040990856978387883487121,31393040990856978521803732736⟩⟩,⟨⟨(-33369459639623394723757871764),(-33369459639623394590292688409)⟩,⟨31391609694634337348134541654,31391609694634337480951129482⟩⟩,⟨⟨(-32707951495312352798896391401),(-32707951495312352666678150011)⟩,⟨31383327824868525763661705987,31383327824868525895249118532⟩⟩,⟨⟨(-32069984731949233551226898280),(-32069984731949233420063114587)⟩,⟨31368851986215123209698546639,31368851986215123340248373333⟩⟩,⟨⟨(-31455164025518489992617118512),(-31455164025518489862577145826)⟩,⟨31348808331376991829183495726,31348808331376991958625846083⟩⟩,⟨⟨(-30863098427562361236109041145),(-30863098427562361107057277822)⟩,⟨31323793511641845379412301395,31323793511641845507881996968⟩⟩] +lemma kernel7_1_r5_13_eq : ∀ k : Fin 16, kernel7_1Expr 5 13 k = kernel7_1_r5_13 k := by decide +kernel +noncomputable def kernel7_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-30293402172081037842416046440),(-30293402172081037714497120043)⟩,⟨31294375615698246956540171787,31294375615698247083892161242⟩⟩,⟨⟨(-29745695429484987169084543268),(-29745695429484987042087832684)⟩,⟨31261095094640572293684361547,31261095094640572420128431286⟩⟩,⟨⟨(-29219605009960460629774049069),(-29219605009960460503766562519)⟩,⟨31224465671238136538458023234,31224465671238136663926672693⟩⟩,⟨⟨(-28714765018590721574285929137),(-28714765018590721449136024939)⟩,⟨31184975231700812500032328933,31184975231700812624656495011⟩⟩,⟨⟨(-28230817464549193323088870679),(-28230817464549193198917873178)⟩,⟨31143086698322954139164724078,31143086698322954262822670024⟩⟩,⟨⟨(-27767412826647195202348487542),(-27767412826647195078970895495)⟩,⟨31099238881529214805036692832,31099238881529214927913188065⟩⟩,⟨⟨(-27324210577478845290135040915),(-27324210577478845167615740764)⟩,⟨31053847309979893817620469608,31053847309979893939650175466⟩⟩,⟨⟨(-26900879668359667368264845636),(-26900879668359667246475928724)⟩,⟨31007305037519776522696675089,31007305037519776644006861240⟩⟩,⟨⟨(-26497098977204020830576350138),(-26497098977204020709654669975)⟩,⟨30959983425873108340616701451,30959983425873108461070151128⟩⟩,⟨⟨(-26112557721430219071245206188),(-26112557721430218950991277649)⟩,⟨30912232902098453075406092663,30912232902098453195201608393⟩⟩,⟨⟨(-25746955837921625141363284195),(-25746955837921625021839905870)⟩,⟨30864383689920851335177044257,30864383689920851454251410041⟩⟩,⟨⟨(-25400004332007591944545716495),(-25400004332007591825628633501)⟩,⟨30816746514155065782005074602,30816746514155065900481962678⟩⟩,⟨⟨(-25071425597360294336560561585),(-25071425597360294218368525343)⟩,⟨30769613277522950713279556018,30769613277522950831039863402⟩⟩,⟨⟨(-24760953708632696520892766096),(-24760953708632696403246046643)⟩,⟨30723257709250311255816523794,30723257709250311373039370509⟩⟩,⟨⟨(-24468334688589492655029000129),(-24468334688589492537988431455)⟩,⟨30677935984904239302870584636,30677935984904239419494748567⟩⟩,⟨⟨(-24193326751407203026289761567),(-24193326751407202909734505717)⟩,⟨30633887317001063895079003265,30633887317001064011224786437⟩⟩] +lemma kernel7_1_r5_14_eq : ∀ k : Fin 16, kernel7_1Expr 5 14 k = kernel7_1_r5_14 k := by decide +kernel +noncomputable def kernel7_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-23935700523742023455016043618),(-23935700523742023339085979821)⟩,⟨30591334515977983147824595790,30591334515977983263351808797⟩⟩,⟨⟨(-23695239245084803091006552414),(-23695239245084802975502179949)⟩,⟨30550484521178416542758045338,30550484521178416657865605844⟩⟩,⟨⟨(-23471738948841928170258828554),(-23471738948841928055238951387)⟩,⟨30511528901552405499068336361,30511528901552405613697075773⟩⟩,⟨⟨(-23265008625499151751220162395),(-23265008625499151636567295263)⟩,⟨30474644325819281524259361106,30474644325819281638526266121⟩⟩,⟨⟨(-23074870369142740697571691061),(-23074870369142740583402900759)⟩,⟨30439993001880608190481066828,30439993001880608304268760886⟩⟩,⟨⟨(-22901159508528894876460998753),(-22901159508528894762600964773)⟩,⟨30407723085307385901465320106,30407723085307386014948594178⟩⟩,⟨⟨(-22743724723808389535712167837),(-22743724723808389422217730661)⟩,⟨30377969056756992898306267634,30377969056756993011427934286⟩⟩,⟨⟨(-22602428149928937587786109418),(-22602428149928937474542891532)⟩,⟨30350852068202632833208215572,30350852068202632946082181757⟩⟩,⟨⟨(-22477145467652980562960726035),(-22477145467652980450095829397)⟩,⟨30326480257881482918060004265,30326480257881483030558882252⟩⟩,⟨⟨(-22367765983043592376496370788),(-22367765983043592263810957919)⟩,⟨30304949033887604425329757234,30304949033887604537651863799⟩⟩,⟨⟨(-22274192696185997905770779782),(-22274192696185997793321732619)⟩,⟨30286341326352308749638438572,30286341326352308861726557332⟩⟩,⟨⟨(-22196342359826931478001865302),(-22196342359826931365679951265)⟩,⟨30270727808168388534960885038,30270727808168388646923797804⟩⟩,⟨⟨(-22134145528528736697405205890),(-22134145528528736585328751920)⟩,⟨30258167084225746970419023170,30258167084225747082138116233⟩⟩,⟨⟨(-22087546598849773415690180927),(-22087546598849773303688815292)⟩,⟨30248705849134812484695296574,30248705849134812596340452688⟩⟩,⟨⟨(-22056503840977373304337411128),(-22056503840977373192465859345)⟩,⟨30242379013421034517893169333,30242379013421034629409334279⟩⟩,⟨⟨(-22040989422154285756973347519),(-22040989422154285645125225282)⟩,⟨30239209798179042900761843192,30239209798179043012254960588⟩⟩] +lemma kernel7_1_r5_15_eq : ∀ k : Fin 16, kernel7_1Expr 5 15 k = kernel7_1_r5_15 k := by decide +kernel +noncomputable def kernel7_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel7_1_r5_0,kernel7_1_r5_1,kernel7_1_r5_2,kernel7_1_r5_3,kernel7_1_r5_4,kernel7_1_r5_5,kernel7_1_r5_6,kernel7_1_r5_7,kernel7_1_r5_8,kernel7_1_r5_9,kernel7_1_r5_10,kernel7_1_r5_11,kernel7_1_r5_12,kernel7_1_r5_13,kernel7_1_r5_14,kernel7_1_r5_15] +lemma kernel7_1_r5_eq (i k : Fin 16) : kernel7_1Expr 5 i k = kernel7_1_r5 i k := by + fin_cases i + · exact kernel7_1_r5_0_eq k + · exact kernel7_1_r5_1_eq k + · exact kernel7_1_r5_2_eq k + · exact kernel7_1_r5_3_eq k + · exact kernel7_1_r5_4_eq k + · exact kernel7_1_r5_5_eq k + · exact kernel7_1_r5_6_eq k + · exact kernel7_1_r5_7_eq k + · exact kernel7_1_r5_8_eq k + · exact kernel7_1_r5_9_eq k + · exact kernel7_1_r5_10_eq k + · exact kernel7_1_r5_11_eq k + · exact kernel7_1_r5_12_eq k + · exact kernel7_1_r5_13_eq k + · exact kernel7_1_r5_14_eq k + · exact kernel7_1_r5_15_eq k +noncomputable def kernel7_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel7_1_r0,kernel7_1_r1,kernel7_1_r2,kernel7_1_r3,kernel7_1_r4,kernel7_1_r5] +lemma kernel7_1_eq (j : Fin 6) (i k : Fin 16) : kernel7_1Expr j i k = kernel7_1 j i k := by + fin_cases j + · exact kernel7_1_r0_eq i k + · exact kernel7_1_r1_eq i k + · exact kernel7_1_r2_eq i k + · exact kernel7_1_r3_eq i k + · exact kernel7_1_r4_eq i k + · exact kernel7_1_r5_eq i k +lemma kernel7_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel7_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(7:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel7_1_eq] + unfold kernel7_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans7_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel9_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans9 j i k) +noncomputable def kernel9_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩] +lemma kernel9_0_r0_0_eq : ∀ k : Fin 16, kernel9_0Expr 0 0 k = kernel9_0_r0_0 k := by decide +kernel +noncomputable def kernel9_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩] +lemma kernel9_0_r0_1_eq : ∀ k : Fin 16, kernel9_0Expr 0 1 k = kernel9_0_r0_1 k := by decide +kernel +noncomputable def kernel9_0_r0_2 : Fin 16 → CBox := ![⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩] +lemma kernel9_0_r0_2_eq : ∀ k : Fin 16, kernel9_0Expr 0 2 k = kernel9_0_r0_2 k := by decide +kernel +noncomputable def kernel9_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩] +lemma kernel9_0_r0_3_eq : ∀ k : Fin 16, kernel9_0Expr 0 3 k = kernel9_0_r0_3 k := by decide +kernel +noncomputable def kernel9_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩] +lemma kernel9_0_r0_4_eq : ∀ k : Fin 16, kernel9_0Expr 0 4 k = kernel9_0_r0_4 k := by decide +kernel +noncomputable def kernel9_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨(-3),1⟩,⟨(-4),0⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-3),1⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩] +lemma kernel9_0_r0_5_eq : ∀ k : Fin 16, kernel9_0Expr 0 5 k = kernel9_0_r0_5 k := by decide +kernel +noncomputable def kernel9_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-1),3⟩,⟨0,4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩,⟨⟨(-4),0⟩,⟨(-1),3⟩⟩] +lemma kernel9_0_r0_6_eq : ∀ k : Fin 16, kernel9_0Expr 0 6 k = kernel9_0_r0_6 k := by decide +kernel +noncomputable def kernel9_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩] +lemma kernel9_0_r0_7_eq : ∀ k : Fin 16, kernel9_0Expr 0 7 k = kernel9_0_r0_7 k := by decide +kernel +noncomputable def kernel9_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩] +lemma kernel9_0_r0_8_eq : ∀ k : Fin 16, kernel9_0Expr 0 8 k = kernel9_0_r0_8 k := by decide +kernel +noncomputable def kernel9_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩] +lemma kernel9_0_r0_9_eq : ∀ k : Fin 16, kernel9_0Expr 0 9 k = kernel9_0_r0_9 k := by decide +kernel +noncomputable def kernel9_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-4),1⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩] +lemma kernel9_0_r0_10_eq : ∀ k : Fin 16, kernel9_0Expr 0 10 k = kernel9_0_r0_10 k := by decide +kernel +noncomputable def kernel9_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-3),4⟩,⟨(-4),1⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩] +lemma kernel9_0_r0_11_eq : ∀ k : Fin 16, kernel9_0Expr 0 11 k = kernel9_0_r0_11 k := by decide +kernel +noncomputable def kernel9_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-1),4⟩,⟨(-3),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-4),3⟩,⟨(-1),4⟩⟩,⟨⟨(-3),3⟩,⟨(-1),3⟩⟩,⟨⟨(-3),3⟩,⟨(-1),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩] +lemma kernel9_0_r0_12_eq : ∀ k : Fin 16, kernel9_0Expr 0 12 k = kernel9_0_r0_12 k := by decide +kernel +noncomputable def kernel9_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩] +lemma kernel9_0_r0_13_eq : ∀ k : Fin 16, kernel9_0Expr 0 13 k = kernel9_0_r0_13 k := by decide +kernel +noncomputable def kernel9_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩] +lemma kernel9_0_r0_14_eq : ∀ k : Fin 16, kernel9_0Expr 0 14 k = kernel9_0_r0_14 k := by decide +kernel +noncomputable def kernel9_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩,⟨⟨(-3),3⟩,⟨(-3),1⟩⟩] +lemma kernel9_0_r0_15_eq : ∀ k : Fin 16, kernel9_0Expr 0 15 k = kernel9_0_r0_15 k := by decide +kernel +noncomputable def kernel9_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel9_0_r0_0,kernel9_0_r0_1,kernel9_0_r0_2,kernel9_0_r0_3,kernel9_0_r0_4,kernel9_0_r0_5,kernel9_0_r0_6,kernel9_0_r0_7,kernel9_0_r0_8,kernel9_0_r0_9,kernel9_0_r0_10,kernel9_0_r0_11,kernel9_0_r0_12,kernel9_0_r0_13,kernel9_0_r0_14,kernel9_0_r0_15] +lemma kernel9_0_r0_eq (i k : Fin 16) : kernel9_0Expr 0 i k = kernel9_0_r0 i k := by + fin_cases i + · exact kernel9_0_r0_0_eq k + · exact kernel9_0_r0_1_eq k + · exact kernel9_0_r0_2_eq k + · exact kernel9_0_r0_3_eq k + · exact kernel9_0_r0_4_eq k + · exact kernel9_0_r0_5_eq k + · exact kernel9_0_r0_6_eq k + · exact kernel9_0_r0_7_eq k + · exact kernel9_0_r0_8_eq k + · exact kernel9_0_r0_9_eq k + · exact kernel9_0_r0_10_eq k + · exact kernel9_0_r0_11_eq k + · exact kernel9_0_r0_12_eq k + · exact kernel9_0_r0_13_eq k + · exact kernel9_0_r0_14_eq k + · exact kernel9_0_r0_15_eq k +noncomputable def kernel9_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-13048004027),(-13048004023)⟩,⟨(-125619339703),(-125619339699)⟩⟩,⟨⟨(-12988680448),(-12988680444)⟩,⟨(-125409690433),(-125409690429)⟩⟩,⟨⟨(-12870501401),(-12870501397)⟩,⟨(-124991426449),(-124991426445)⟩⟩,⟨⟨(-12694397891),(-12694397887)⟩,⟨(-124366608397),(-124366608393)⟩⟩,⟨⟨(-12461753490),(-12461753486)⟩,⟨(-123538306202),(-123538306198)⟩⟩,⟨⟨(-12174389020),(-12174389016)⟩,⟨(-122510574080),(-122510574076)⟩⟩,⟨⟨(-11834542452),(-11834542448)⟩,⟨(-121288417655),(-121288417651)⟩⟩,⟨⟨(-11444844367),(-11444844363)⟩,⟨(-119877753591),(-119877753586)⟩⟩,⟨⟨(-11008289245),(-11008289241)⟩,⟨(-118285362147),(-118285362143)⟩⟩,⟨⟨(-10528203068),(-10528203064)⟩,⟨(-116518833228),(-116518833224)⟩⟩,⟨⟨(-10008207610),(-10008207606)⟩,⟨(-114586506503),(-114586506499)⟩⟩,⟨⟨(-9452181983),(-9452181979)⟩,⟨(-112497406280),(-112497406276)⟩⟩,⟨⟨(-8864221916),(-8864221912)⟩,⟨(-110261171821),(-110261171817)⟩⟩,⟨⟨(-8248597322),(-8248597318)⟩,⟨(-107887983865),(-107887983861)⟩⟩,⟨⟨(-7609708765),(-7609708761)⟩,⟨(-105388488154),(-105388488149)⟩⟩,⟨⟨(-6952043321),(-6952043317)⟩,⟨(-102773716714),(-102773716710)⟩⟩] +lemma kernel9_0_r1_0_eq : ∀ k : Fin 16, kernel9_0Expr 1 0 k = kernel9_0_r1_0 k := by decide +kernel +noncomputable def kernel9_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-6280130476),(-6280130471)⟩,⟨(-100055007775),(-100055007771)⟩⟩,⟨⟨(-5598498559),(-5598498555)⟩,⟨(-97243925060),(-97243925056)⟩⟩,⟨⟨(-4911632295),(-4911632291)⟩,⟨(-94352177288),(-94352177284)⟩⟩,⟨⟨(-4223931921),(-4223931916)⟩,⟨(-91391538647),(-91391538643)⟩⟩,⟨⟨(-3539674410),(-3539674406)⟩,⟨(-88373770977),(-88373770972)⟩⟩,⟨⟨(-2862977158),(-2862977154)⟩,⟨(-85310548358),(-85310548354)⟩⟩,⟨⟨(-2197764567),(-2197764563)⟩,⟨(-82213384759),(-82213384755)⟩⟩,⟨⟨(-1547737799),(-1547737795)⟩,⟨(-79093565340),(-79093565336)⟩⟩,⟨⟨(-916348046),(-916348041)⟩,⟨(-75962081958),(-75962081954)⟩⟩,⟨⟨(-306773430),(-306773426)⟩,⟨(-72829573301),(-72829573297)⟩⟩,⟨⟨278100220,278100225⟩,⟨(-69706270119),(-69706270115)⟩⟩,⟨⟨835694685,835694689⟩,⟨(-66601945812),(-66601945808)⟩⟩,⟨⟨1363750707,1363750711⟩,⟨(-63525872670),(-63525872666)⟩⟩,⟨⟨1860335386,1860335391⟩,⟨(-60486783943),(-60486783939)⟩⟩,⟨⟨2323845746,2323845750⟩,⟨(-57492841830),(-57492841826)⟩⟩,⟨⟨2753008524,2753008528⟩,⟨(-54551611454),(-54551611450)⟩⟩] +lemma kernel9_0_r1_1_eq : ∀ k : Fin 16, kernel9_0Expr 1 1 k = kernel9_0_r1_1 k := by decide +kernel +noncomputable def kernel9_0_r1_2 : Fin 16 → CBox := ![⟨⟨3146876427,3146876431⟩,⟨(-51670040783),(-51670040779)⟩⟩,⟨⟨3504821040,3504821045⟩,⟨(-48854446371),(-48854446367)⟩⟩,⟨⟨3826522627,3826522631⟩,⟨(-46110504847),(-46110504843)⟩⟩,⟨⟨4111957130,4111957134⟩,⟨(-43443249847),(-43443249843)⟩⟩,⟨⟨4361380662,4361380666⟩,⟨(-40857074217),(-40857074213)⟩⟩,⟨⟨4575311818,4575311822⟩,⟨(-38355737111),(-38355737107)⟩⟩,⟨⟨4754512138,4754512142⟩,⟨(-35942375723),(-35942375719)⟩⟩,⟨⟨4899965096,4899965101⟩,⟨(-33619521208),(-33619521204)⟩⟩,⟨⟨5012853903,5012853907⟩,⟨(-31389118462),(-31389118458)⟩⟩,⟨⟨5094538515,5094538520⟩,⟨(-29252549303),(-29252549299)⟩⟩,⟨⟨5146532180,5146532184⟩,⟨(-27210658651),(-27210658647)⟩⟩,⟨⟨5170477774,5170477778⟩,⟨(-25263783275),(-25263783271)⟩⟩,⟨⟨5168124325,5168124329⟩,⟨(-23411782666),(-23411782661)⟩⟩,⟨⟨5141303927,5141303931⟩,⟨(-21654071620),(-21654071616)⟩⟩,⟨⟨5091909312,5091909317⟩,⟨(-19989654112),(-19989654108)⟩⟩,⟨⟨5021872342,5021872347⟩,⟨(-18417158052),(-18417158048)⟩⟩] +lemma kernel9_0_r1_2_eq : ∀ k : Fin 16, kernel9_0Expr 1 2 k = kernel9_0_r1_2 k := by decide +kernel +noncomputable def kernel9_0_r1_3 : Fin 16 → CBox := ![⟨⟨4933143580,4933143584⟩,⟨(-16934870551),(-16934870547)⟩⟩,⟨⟨4827673131,4827673135⟩,⟨(-15540773321),(-15540773316)⟩⟩,⟨⟨4707392900,4707392904⟩,⟨(-14232577885),(-14232577881)⟩⟩,⟨⟨4574200344,4574200348⟩,⟨(-13007760276),(-13007760272)⟩⟩,⟨⟨4429943850,4429943854⟩,⟨(-11863594948),(-11863594944)⟩⟩,⟨⟨4276409735,4276409739⟩,⟨(-10797187641),(-10797187637)⟩⟩,⟨⟨4115310967,4115310971⟩,⟨(-9805506980),(-9805506976)⟩⟩,⟨⟨3948277531,3948277535⟩,⟨(-8885414627),(-8885414623)⟩⟩,⟨⟨3776848474,3776848478⟩,⟨(-8033693809),(-8033693805)⟩⟩,⟨⟨3602465574,3602465578⟩,⟨(-7247076089),(-7247076084)⟩⟩,⟨⟨3426468562,3426468566⟩,⟨(-6522266322),(-6522266317)⟩⟩,⟨⟨3250091831,3250091836⟩,⟨(-5855965649),(-5855965645)⟩⟩,⟨⟨3074462537,3074462541⟩,⟨(-5244892563),(-5244892559)⟩⟩,⟨⟨2900600002,2900600006⟩,⟨(-4685801949),(-4685801945)⟩⟩,⟨⟨2729416299,2729416303⟩,⟨(-4175502168),(-4175502164)⟩⟩,⟨⟨2561717900,2561717904⟩,⟨(-3710870165),(-3710870161)⟩⟩] +lemma kernel9_0_r1_3_eq : ∀ k : Fin 16, kernel9_0Expr 1 3 k = kernel9_0_r1_3 k := by decide +kernel +noncomputable def kernel9_0_r1_4 : Fin 16 → CBox := ![⟨⟨2398208297,2398208301⟩,⟨(-3288864636),(-3288864632)⟩⟩,⟨⟨2239491428,2239491432⟩,⟨(-2906537364),(-2906537360)⟩⟩,⟨⟨2086075841,2086075845⟩,⟨(-2561042721),(-2561042717)⟩⟩,⟨⟨1938379436,1938379441⟩,⟨(-2249645486),(-2249645482)⟩⟩,⟨⟨1796734691,1796734696⟩,⟨(-1969727029),(-1969727025)⟩⟩,⟨⟨1661394259,1661394263⟩,⟨(-1718789994),(-1718789990)⟩⟩,⟨⟨1532536824,1532536828⟩,⟨(-1494461560),(-1494461556)⟩⟩,⟨⟨1410273144,1410273148⟩,⟨(-1294495407),(-1294495403)⟩⟩,⟨⟨1294652156,1294652160⟩,⟨(-1116772515),(-1116772511)⟩⟩,⟨⟨1185667094,1185667098⟩,⟨(-959300869),(-959300865)⟩⟩,⟨⟨1083261529,1083261533⟩,⟨(-820214240),(-820214236)⟩⟩,⟨⟨987335274,987335278⟩,⟨(-697770094),(-697770090)⟩⟩,⟨⟨897750104,897750109⟩,⟨(-590346800),(-590346796)⟩⟩,⟨⟨814335236,814335240⟩,⟨(-496440183),(-496440179)⟩⟩,⟨⟨736892524,736892529⟩,⟨(-414659569),(-414659565)⟩⟩,⟨⟨665201372,665201376⟩,⟨(-343723397),(-343723393)⟩⟩] +lemma kernel9_0_r1_4_eq : ∀ k : Fin 16, kernel9_0Expr 1 4 k = kernel9_0_r1_4 k := by decide +kernel +noncomputable def kernel9_0_r1_5 : Fin 16 → CBox := ![⟨⟨599023292,599023296⟩,⟨(-282454468),(-282454464)⟩⟩,⟨⟨538106142,538106147⟩,⟨(-229774968),(-229774964)⟩⟩,⟨⟨482187998,482188002⟩,⟨(-184701265),(-184701261)⟩⟩,⟨⟨431000666,431000670⟩,⟨(-146338632),(-146338628)⟩⟩,⟨⟨384272848,384272852⟩,⟨(-113875882),(-113875877)⟩⟩,⟨⟨341732948,341732953⟩,⟨(-86580025),(-86580021)⟩⟩,⟨⟨303111550,303111555⟩,⟨(-63790966),(-63790961)⟩⟩,⟨⟨268143553,268143557⟩,⟨(-44916305),(-44916301)⟩⟩,⟨⟨236570006,236570010⟩,⟨(-29426257),(-29426253)⟩⟩,⟨⟨208139639,208139643⟩,⟨(-16848736),(-16848732)⟩⟩,⟨⟨182610134,182610139⟩,⟨(-6764627),(-6764623)⟩⟩,⟨⟨159749128,159749132⟩,⟨1196745,1196749⟩⟩,⟨⟨139334977,139334981⟩,⟨7361911,7361915⟩⟩,⟨⟨121157329,121157333⟩,⟨12017348,12017353⟩⟩,⟨⟨105017497,105017502⟩,⟨15413304,15413309⟩⟩,⟨⟨90728649,90728653⟩,⟨17767393,17767397⟩⟩] +lemma kernel9_0_r1_5_eq : ∀ k : Fin 16, kernel9_0Expr 1 5 k = kernel9_0_r1_5 k := by decide +kernel +noncomputable def kernel9_0_r1_6 : Fin 16 → CBox := ![⟨⟨78115861,78115866⟩,⟨19267950,19267954⟩⟩,⟨⟨67016055,67016059⟩,⟨20077145,20077149⟩⟩,⟨⟨57277789,57277793⟩,⟨20333852,20333856⟩⟩,⟨⟨48760986,48760991⟩,⟨20156299,20156303⟩⟩,⟨⟨41336574,41336578⟩,⟨19644492,19644497⟩⟩,⟨⟨34886062,34886067⟩,⟨18882419,18882423⟩⟩,⟨⟨29301067,29301072⟩,⟨17940060,17940065⟩⟩,⟨⟨24482810,24482814⟩,⟨16875205,16875209⟩⟩,⟨⟨20341580,20341585⟩,⟨15735086,15735090⟩⟩,⟨⟨16796202,16796206⟩,⟨14557834,14557838⟩⟩,⟨⟨13773455,13773459⟩,⟨13373795,13373800⟩⟩,⟨⟨11207542,11207546⟩,⟨12206690,12206695⟩⟩,⟨⟨9039539,9039543⟩,⟨11074639,11074643⟩⟩,⟨⟨7216854,7216858⟩,⟨9991054,9991059⟩⟩,⟨⟨5692715,5692719⟩,⟨8965452,8965456⟩⟩,⟨⟨4425669,4425673⟩,⟨8004126,8004130⟩⟩] +lemma kernel9_0_r1_6_eq : ∀ k : Fin 16, kernel9_0Expr 1 6 k = kernel9_0_r1_6 k := by decide +kernel +noncomputable def kernel9_0_r1_7 : Fin 16 → CBox := ![⟨⟨3379112,3379117⟩,⟨7110744,7110749⟩⟩,⟨⟨2520843,2520848⟩,⟨6286873,6286877⟩⟩,⟨⟨1822624,1822628⟩,⟨5532404,5532408⟩⟩,⟨⟨1259799,1259803⟩,⟨4845937,4845941⟩⟩,⟨⟨810916,810921⟩,⟨4225091,4225096⟩⟩,⟨⟨457391,457395⟩,⟨3666772,3666776⟩⟩,⟨⟨183185,183189⟩,⟨3167386,3167390⟩⟩,⟨⟨(-25483),(-25479)⟩,⟨2723025,2723029⟩⟩,⟨⟨(-180397),(-180393)⟩,⟨2329615,2329620⟩⟩,⟨⟨(-291591),(-291586)⟩,⟨1983017,1983021⟩⟩,⟨⟨(-367563),(-367558)⟩,⟨1679141,1679145⟩⟩,⟨⟨(-415468),(-415464)⟩,⟨1413996,1414001⟩⟩,⟨⟨(-441306),(-441302)⟩,⟨1183762,1183766⟩⟩,⟨⟨(-450066),(-450062)⟩,⟨984806,984810⟩⟩,⟨⟨(-445870),(-445865)⟩,⟨813727,813731⟩⟩,⟨⟨(-432103),(-432099)⟩,⟨667364,667369⟩⟩] +lemma kernel9_0_r1_7_eq : ∀ k : Fin 16, kernel9_0Expr 1 7 k = kernel9_0_r1_7 k := by decide +kernel +noncomputable def kernel9_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-411516),(-411512)⟩,⟨542797,542802⟩⟩,⟨⟨(-386323),(-386319)⟩,⟨437357,437361⟩⟩,⟨⟨(-358289),(-358284)⟩,⟨348617,348622⟩⟩,⟨⟨(-328794),(-328790)⟩,⟨274386,274390⟩⟩,⟨⟨(-298913),(-298909)⟩,⟨212697,212701⟩⟩,⟨⟨(-269451),(-269446)⟩,⟨161793,161798⟩⟩,⟨⟨(-241002),(-240997)⟩,⟨120114,120118⟩⟩,⟨⟨(-213985),(-213980)⟩,⟨86289,86294⟩⟩,⟨⟨(-188681),(-188677)⟩,⟨59104,59109⟩⟩,⟨⟨(-165262),(-165258)⟩,⟨37508,37512⟩⟩,⟨⟨(-143807),(-143803)⟩,⟨20579,20583⟩⟩,⟨⟨(-124330),(-124326)⟩,⟨7529,7533⟩⟩,⟨⟨(-106799),(-106794)⟩,⟨(-2329),(-2324)⟩⟩,⟨⟨(-91135),(-91131)⟩,⟨(-9577),(-9573)⟩⟩,⟨⟨(-77247),(-77242)⟩,⟨(-14709),(-14705)⟩⟩,⟨⟨(-65010),(-65005)⟩,⟨(-18148),(-18144)⟩⟩] +lemma kernel9_0_r1_8_eq : ∀ k : Fin 16, kernel9_0Expr 1 8 k = kernel9_0_r1_8 k := by decide +kernel +noncomputable def kernel9_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-54306),(-54302)⟩,⟨(-20246),(-20241)⟩⟩,⟨⟨(-45001),(-44997)⟩,⟨(-21295),(-21290)⟩⟩,⟨⟨(-36962),(-36957)⟩,⟨(-21541),(-21536)⟩⟩,⟨⟨(-30064),(-30060)⟩,⟨(-21185),(-21180)⟩⟩,⟨⟨(-24182),(-24178)⟩,⟨(-20392),(-20388)⟩⟩,⟨⟨(-19203),(-19198)⟩,⟨(-19292),(-19287)⟩⟩,⟨⟨(-15015),(-15011)⟩,⟨(-17991),(-17987)⟩⟩,⟨⟨(-11522),(-11517)⟩,⟨(-16575),(-16571)⟩⟩,⟨⟨(-8628),(-8623)⟩,⟨(-15107),(-15103)⟩⟩,⟨⟨(-6256),(-6251)⟩,⟨(-13638),(-13633)⟩⟩,⟨⟨(-4328),(-4323)⟩,⟨(-12202),(-12198)⟩⟩,⟨⟨(-2780),(-2775)⟩,⟨(-10829),(-10824)⟩⟩,⟨⟨(-1551),(-1547)⟩,⟨(-9533),(-9529)⟩⟩,⟨⟨(-594),(-589)⟩,⟨(-8332),(-8327)⟩⟩,⟨⟨141,146⟩,⟨(-7225),(-7221)⟩⟩,⟨⟨689,693⟩,⟨(-6219),(-6215)⟩⟩] +lemma kernel9_0_r1_9_eq : ∀ k : Fin 16, kernel9_0Expr 1 9 k = kernel9_0_r1_9 k := by decide +kernel +noncomputable def kernel9_0_r1_10 : Fin 16 → CBox := ![⟨⟨1085,1089⟩,⟨(-5313),(-5308)⟩⟩,⟨⟨1355,1359⟩,⟨(-4502),(-4498)⟩⟩,⟨⟨1529,1533⟩,⟨(-3785),(-3781)⟩⟩,⟨⟨1624,1629⟩,⟨(-3151),(-3147)⟩⟩,⟨⟨1656,1660⟩,⟨(-2598),(-2594)⟩⟩,⟨⟨1643,1647⟩,⟨(-2118),(-2114)⟩⟩,⟨⟨1593,1597⟩,⟨(-1707),(-1702)⟩⟩,⟨⟨1521,1525⟩,⟨(-1353),(-1349)⟩⟩,⟨⟨1430,1435⟩,⟨(-1055),(-1050)⟩⟩,⟨⟨1328,1332⟩,⟨(-803),(-798)⟩⟩,⟨⟨1221,1225⟩,⟨(-590),(-586)⟩⟩,⟨⟨1109,1114⟩,⟨(-417),(-412)⟩⟩,⟨⟨1002,1007⟩,⟨(-273),(-268)⟩⟩,⟨⟨897,901⟩,⟨(-159),(-154)⟩⟩,⟨⟨796,801⟩,⟨(-65),(-61)⟩⟩,⟨⟨702,707⟩,⟨6,11⟩⟩] +lemma kernel9_0_r1_10_eq : ∀ k : Fin 16, kernel9_0Expr 1 10 k = kernel9_0_r1_10 k := by decide +kernel +noncomputable def kernel9_0_r1_11 : Fin 16 → CBox := ![⟨⟨614,618⟩,⟨61,66⟩⟩,⟨⟨535,539⟩,⟨103,108⟩⟩,⟨⟨459,464⟩,⟨134,138⟩⟩,⟨⟨394,398⟩,⟨155,159⟩⟩,⟨⟨333,338⟩,⟨167,171⟩⟩,⟨⟨281,285⟩,⟨175,179⟩⟩,⟨⟨234,238⟩,⟨177,181⟩⟩,⟨⟨191,196⟩,⟨176,180⟩⟩,⟨⟨155,159⟩,⟨169,173⟩⟩,⟨⟨124,128⟩,⟨162,166⟩⟩,⟨⟨96,101⟩,⟨154,159⟩⟩,⟨⟨72,76⟩,⟨145,149⟩⟩,⟨⟨55,59⟩,⟨134,138⟩⟩,⟨⟨36,41⟩,⟨125,129⟩⟩,⟨⟨22,27⟩,⟨112,116⟩⟩,⟨⟨9,14⟩,⟨103,107⟩⟩] +lemma kernel9_0_r1_11_eq : ∀ k : Fin 16, kernel9_0Expr 1 11 k = kernel9_0_r1_11 k := by decide +kernel +noncomputable def kernel9_0_r1_12 : Fin 16 → CBox := ![⟨⟨0,5⟩,⟨93,97⟩⟩,⟨⟨(-7),(-2)⟩,⟨84,88⟩⟩,⟨⟨(-12),(-7)⟩,⟨76,80⟩⟩,⟨⟨(-18),(-13)⟩,⟨64,69⟩⟩,⟨⟨(-20),(-16)⟩,⟨57,62⟩⟩,⟨⟨(-23),(-18)⟩,⟨50,55⟩⟩,⟨⟨(-25),(-21)⟩,⟨43,48⟩⟩,⟨⟨(-25),(-21)⟩,⟨38,42⟩⟩,⟨⟨(-28),(-23)⟩,⟨31,35⟩⟩,⟨⟨(-26),(-22)⟩,⟨28,33⟩⟩,⟨⟨(-27),(-22)⟩,⟨23,27⟩⟩,⟨⟨(-28),(-23)⟩,⟨19,24⟩⟩,⟨⟨(-26),(-21)⟩,⟨14,19⟩⟩,⟨⟨(-25),(-20)⟩,⟨12,17⟩⟩,⟨⟨(-24),(-19)⟩,⟨10,14⟩⟩,⟨⟨(-22),(-18)⟩,⟨7,12⟩⟩] +lemma kernel9_0_r1_12_eq : ∀ k : Fin 16, kernel9_0Expr 1 12 k = kernel9_0_r1_12 k := by decide +kernel +noncomputable def kernel9_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-21),(-17)⟩,⟨5,9⟩⟩,⟨⟨(-20),(-16)⟩,⟨3,7⟩⟩,⟨⟨(-19),(-15)⟩,⟨0,5⟩⟩,⟨⟨(-19),(-15)⟩,⟨0,5⟩⟩,⟨⟨(-18),(-14)⟩,⟨(-2),2⟩⟩,⟨⟨(-16),(-11)⟩,⟨(-1),3⟩⟩,⟨⟨(-15),(-10)⟩,⟨(-3),1⟩⟩,⟨⟨(-15),(-10)⟩,⟨(-3),1⟩⟩,⟨⟨(-14),(-9)⟩,⟨(-6),(-1)⟩⟩,⟨⟨(-11),(-7)⟩,⟨(-5),0⟩⟩,⟨⟨(-11),(-7)⟩,⟨(-5),0⟩⟩,⟨⟨(-11),(-7)⟩,⟨(-5),0⟩⟩,⟨⟨(-10),(-6)⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-10),(-6)⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-6),(-2)⟩⟩] +lemma kernel9_0_r1_13_eq : ∀ k : Fin 16, kernel9_0Expr 1 13 k = kernel9_0_r1_13 k := by decide +kernel +noncomputable def kernel9_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-8),(-3)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-5),(-1)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-1)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-1)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),0⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-4),0⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-4),0⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-4),0⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-4),0⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-4),0⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-4),0⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩] +lemma kernel9_0_r1_14_eq : ∀ k : Fin 16, kernel9_0Expr 1 14 k = kernel9_0_r1_14 k := by decide +kernel +noncomputable def kernel9_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-2),3⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-3),3⟩,⟨(-6),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩,⟨⟨(-3),2⟩,⟨(-4),0⟩⟩] +lemma kernel9_0_r1_15_eq : ∀ k : Fin 16, kernel9_0Expr 1 15 k = kernel9_0_r1_15 k := by decide +kernel +noncomputable def kernel9_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel9_0_r1_0,kernel9_0_r1_1,kernel9_0_r1_2,kernel9_0_r1_3,kernel9_0_r1_4,kernel9_0_r1_5,kernel9_0_r1_6,kernel9_0_r1_7,kernel9_0_r1_8,kernel9_0_r1_9,kernel9_0_r1_10,kernel9_0_r1_11,kernel9_0_r1_12,kernel9_0_r1_13,kernel9_0_r1_14,kernel9_0_r1_15] +lemma kernel9_0_r1_eq (i k : Fin 16) : kernel9_0Expr 1 i k = kernel9_0_r1 i k := by + fin_cases i + · exact kernel9_0_r1_0_eq k + · exact kernel9_0_r1_1_eq k + · exact kernel9_0_r1_2_eq k + · exact kernel9_0_r1_3_eq k + · exact kernel9_0_r1_4_eq k + · exact kernel9_0_r1_5_eq k + · exact kernel9_0_r1_6_eq k + · exact kernel9_0_r1_7_eq k + · exact kernel9_0_r1_8_eq k + · exact kernel9_0_r1_9_eq k + · exact kernel9_0_r1_10_eq k + · exact kernel9_0_r1_11_eq k + · exact kernel9_0_r1_12_eq k + · exact kernel9_0_r1_13_eq k + · exact kernel9_0_r1_14_eq k + · exact kernel9_0_r1_15_eq k +noncomputable def kernel9_0_r2_0 : Fin 16 → CBox := ![⟨⟨7152797450720816332,7152797450720816387⟩,⟨(-13922650675169100638),(-13922650675169100584)⟩⟩,⟨⟨7141165753834207571,7141165753834207623⟩,⟨(-13909094999107601583),(-13909094999107601531)⟩⟩,⟨⟨7117953543820327124,7117953543820327177⟩,⟨(-13882019451457062987),(-13882019451457062933)⟩⟩,⟨⟨7083262838551730453,7083262838551730507⟩,⟨(-13841495516380977190),(-13841495516380977137)⟩⟩,⟨⟨7037245793862117084,7037245793862117139⟩,⟨(-13787630108356382529),(-13787630108356382474)⟩⟩,⟨⟨6980103667134775606,6980103667134775659⟩,⟨(-13720565198579367275),(-13720565198579367221)⟩⟩,⟨⟨6912085449917039758,6912085449917039812⟩,⟨(-13640477317742682115),(-13640477317742682062)⟩⟩,⟨⟨6833486181785334820,6833486181785334872⟩,⟨(-13547576936008591319),(-13547576936008591266)⟩⟩,⟨⟨6744644960493119517,6744644960493119571⟩,⟨(-13442107721264877859),(-13442107721264877806)⟩⟩,⟨⟨6645942666080540546,6645942666080540598⟩,⟨(-13324345677053349040),(-13324345677053348987)⟩⟩,⟨⟨6537799419081999646,6537799419081999699⟩,⟨(-13194598161902991886),(-13194598161902991834)⟩⟩,⟨⟨6420671795210444137,6420671795210444188⟩,⟨(-13053202792187513309),(-13053202792187513258)⟩⟩,⟨⟨6295049820901965373,6295049820901965424⟩,⟨(-12900526231061331606),(-12900526231061331555)⟩⟩,⟨⟨6161453775851012267,6161453775851012319⟩,⟨(-12736962866509578933),(-12736962866509578881)⟩⟩,⟨⟨6020430830138074346,6020430830138074396⟩,⟨(-12562933382075136659),(-12562933382075136609)⟩⟩,⟨⟨5872551544734225441,5872551544734225489⟩,⟨(-12378883224396334593),(-12378883224396334544)⟩⟩] +lemma kernel9_0_r2_0_eq : ∀ k : Fin 16, kernel9_0Expr 2 0 k = kernel9_0_r2_0 k := by decide +kernel +noncomputable def kernel9_0_r2_1 : Fin 16 → CBox := ![⟨⟨5718406265050055372,5718406265050055421⟩,⟨(-12185280972298268062),(-12185280972298268013)⟩⟩,⟨⟨5558601437773423243,5558601437773423292⟩,⟨(-11982616612822738350),(-11982616612822738302)⟩⟩,⟨⟨5393755881507940037,5393755881507940084⟩,⟨(-11771399730249161908),(-11771399730249161861)⟩⟩,⟨⟨5224497041682577098,5224497041682577145⟩,⟨(-11552157614842661072),(-11552157614842661025)⟩⟩,⟨⟨5051457259856370862,5051457259856370906⟩,⟨(-11325433298756029894),(-11325433298756029849)⟩⟩,⟨⟨4875270086898472953,4875270086898472998⟩,⟨(-11091783527198493638),(-11091783527198493593)⟩⟩,⟨⟨4696566668593829828,4696566668593829873⟩,⟨(-10851776673654547773),(-10851776673654547728)⟩⟩,⟨⟨4515972231022884757,4515972231022884801⟩,⟨(-10605990608578581458),(-10605990608578581415)⟩⟩,⟨⟨4334102691607254799,4334102691607254841⟩,⟨(-10355010531593140425),(-10355010531593140383)⟩⟩,⟨⟨4151561420022535729,4151561420022535770⟩,⟨(-10099426777768280682),(-10099426777768280641)⟩⟩,⟨⟨3968936171276947060,3968936171276947099⟩,⟨(-9839832609044530727),(-9839832609044530687)⟩⟩,⟨⟨3786796211165377060,3786796211165377098⟩,⟨(-9576822002271113064),(-9576822002271113026)⟩⟩,⟨⟨3605689652059320531,3605689652059320571⟩,⟨(-9310987445653705330),(-9310987445653705290)⟩⟩,⟨⟨3426141014612514532,3426141014612514570⟩,⟨(-9042917755632651076),(-9042917755632651039)⟩⟩,⟨⟨3248649028479175197,3248649028479175233⟩,⟨(-8773195926334961510),(-8773195926334961474)⟩⟩,⟨⟨3073684682586740719,3073684682586740753⟩,⟨(-8502397023754976150),(-8502397023754976115)⟩⟩] +lemma kernel9_0_r2_1_eq : ∀ k : Fin 16, kernel9_0Expr 2 1 k = kernel9_0_r2_1 k := by decide +kernel +noncomputable def kernel9_0_r2_2 : Fin 16 → CBox := ![⟨⟨2901689532908356632,2901689532908356669⟩,⟨(-8231086136714127360),(-8231086136714127323)⟩⟩,⟨⟨2733074273072326409,2733074273072326444⟩,⟨(-7959816396426627713),(-7959816396426627678)⟩⟩,⟨⟨2568217570556220399,2568217570556220431⟩,⟨(-7689127076153707388),(-7689127076153707356)⟩⟩,⟨⟨2407465168671229731,2407465168671229763⟩,⟨(-7419541781964854589),(-7419541781964854557)⟩⟩,⟨⟨2251129252075351025,2251129252075351056⟩,⟨(-7151566745042904684),(-7151566745042904653)⟩⟩,⟨⟨2099488071188169699,2099488071188169731⟩,⟨(-6885689225275275317),(-6885689225275275285)⟩⟩,⟨⟨1952785818639527071,1952785818639527101⟩,⟨(-6622376035072529040),(-6622376035072529011)⟩⟩,⟨⟨1811232748791151786,1811232748791151813⟩,⟨(-6362072191455918581),(-6362072191455918554)⟩⟩,⟨⟨1675005529443893969,1675005529443893996⟩,⟨(-6105199703467436276),(-6105199703467436249)⟩⟩,⟨⟨1544247813100339039,1544247813100339064⟩,⟨(-5852156500890433092),(-5852156500890433067)⟩⟩,⟨⟨1419071013607286106,1419071013607286132⟩,⟨(-5603315509138662484),(-5603315509138662458)⟩⟩,⟨⟨1299555272665893796,1299555272665893820⟩,⟨(-5359023873990273316),(-5359023873990273292)⟩⟩,⟨⟨1185750599577245060,1185750599577245084⟩,⟨(-5119602338625282585),(-5119602338625282560)⟩⟩,⟨⟨1077678166692639377,1077678166692639400⟩,⟨(-4885344774185432182),(-4885344774185432159)⟩⟩,⟨⟨975331742363041142,975331742363041164⟩,⟨(-4656517863829413962),(-4656517863829413941)⟩⟩,⟨⟨878679242729799174,878679242729799196⟩,⟨(-4433360939019617230),(-4433360939019617208)⟩⟩] +lemma kernel9_0_r2_2_eq : ∀ k : Fin 16, kernel9_0Expr 2 2 k = kernel9_0_r2_2 k := by decide +kernel +noncomputable def kernel9_0_r2_3 : Fin 16 → CBox := ![⟨⟨787664383465163165,787664383465163186⟩,⟨(-4216085965563977754),(-4216085965563977734)⟩⟩,⟨⟨702208412549726502,702208412549726521⟩,⟨(-4004877675762879235),(-4004877675762879216)⟩⟩,⟨⟨622211905355686187,622211905355686206⟩,⟨(-3799893841890353475),(-3799893841890353456)⟩⟩,⟨⟨547556603678412296,547556603678412315⟩,⟨(-3601265685184081201),(-3601265685184081181)⟩⟩,⟨⟨478107280910911648,478107280910911666⟩,⟨(-3409098413541806324),(-3409098413541806306)⟩⟩,⟨⟨413713616271242649,413713616271242666⟩,⟨(-3223471880233317751),(-3223471880233317734)⟩⟩,⟨⟨354212061855209267,354212061855209283⟩,⟨(-3044441355146231620),(-3044441355146231604)⟩⟩,⟨⟨299427687277982069,299427687277982085⟩,⟨(-2872038399397944218),(-2872038399397944202)⟩⟩,⟨⟨249175987770053789,249175987770053803⟩,⟨(-2706271833571169894),(-2706271833571169880)⟩⟩,⟨⟨203264642785976275,203264642785976291⟩,⟨(-2547128789370552691),(-2547128789370552676)⟩⟩,⟨⟨161495213449240964,161495213449240978⟩,⟨(-2394575834155322996),(-2394575834155322982)⟩⟩,⟨⟨123664768474103335,123664768474103347⟩,⟨(-2248560157578506709),(-2248560157578506696)⟩⟩,⟨⟨89567429556093674,89567429556093687⟩,⟨(-2109010809455740466),(-2109010809455740453)⟩⟩,⟨⟨58995828588978352,58995828588978364⟩,⟨(-1975839977993641609),(-1975839977993641598)⟩⟩,⟨⟨31742470429451463,31742470429451475⟩,⟨(-1848944297624748273),(-1848944297624748262)⟩⟩,⟨⟨7600996275311948,7600996275311959⟩,⟨(-1728206175917710180),(-1728206175917710168)⟩⟩] +lemma kernel9_0_r2_3_eq : ∀ k : Fin 16, kernel9_0Expr 2 3 k = kernel9_0_r2_3 k := by decide +kernel +noncomputable def kernel9_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-13632655966978624),(-13632655966978614)⟩,⟨(-1613495129350850566),(-1613495129350850555)⟩⟩,⟨⟨(-32159196687556052),(-32159196687556041)⟩,⟨(-1504669118146517427),(-1504669118146517416)⟩⟩,⟨⟨(-48175036112133804),(-48175036112133795)⟩,⟨(-1401575870853962063),(-1401575870853962054)⟩⟩,⟨⟨(-61871442405681745),(-61871442405681735)⟩,⟨(-1304054189930249475),(-1304054189930249465)⟩⟩,⟨⟨(-73433805322312521),(-73433805322312511)⟩,⟨(-1211935230191790853),(-1211935230191790842)⟩⟩,⟨⟨(-83041003421247617),(-83041003421247606)⟩,⟨(-1125043742682998985),(-1125043742682998975)⟩⟩,⟨⟨(-90864872000597262),(-90864872000597253)⟩,⟨(-1043199277222626643),(-1043199277222626634)⟩⟩,⟨⟨(-97069768130037373),(-97069768130037365)⟩,⟨(-966217337631875331),(-966217337631875323)⟩⟩,⟨⟨(-101812228492662800),(-101812228492662793)⟩,⟨(-893910484410840575),(-893910484410840569)⟩⟩,⟨⟨(-105240715176150161),(-105240715176150152)⟩,⟨(-826089380401093975),(-826089380401093966)⟩⟩,⟨⟨(-107495444083234088),(-107495444083234081)⟩,⟨(-762563775742457708),(-762563775742457701)⟩⟩,⟨⟨(-108708290259409715),(-108708290259409709)⟩,⟨(-703143429192157942),(-703143429192157936)⟩⟩,⟨⟨(-109002764158535717),(-109002764158535711)⟩,⟨(-647638963616098846),(-647638963616098840)⟩⟩,⟨⟨(-108494052680372951),(-108494052680372943)⟩,⟨(-595862654177312606),(-595862654177312598)⟩⟩,⟨⟨(-107289118712880108),(-107289118712880102)⟩,⟨(-547629148428900374),(-547629148428900368)⟩⟩,⟨⟨(-105486852890358276),(-105486852890358268)⟩,⟨(-502756118162076260),(-502756118162076252)⟩⟩] +lemma kernel9_0_r2_4_eq : ∀ k : Fin 16, kernel9_0Expr 2 4 k = kernel9_0_r2_4 k := by decide +kernel +noncomputable def kernel9_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-103178271329733938),(-103178271329733932)⟩,⟨(-461064843459288099),(-461064843459288093)⟩⟩,⟨⟨(-100446753224374034),(-100446753224374028)⟩,⟨(-422380729953789510),(-422380729953789504)⟩⟩,⟨⟨(-97368312350499080),(-97368312350499073)⟩,⟨(-386533760797395316),(-386533760797395310)⟩⟩,⟨⟨(-94011896767986366),(-94011896767986361)⟩,⟨(-353358885285307366),(-353358885285307361)⟩⟩,⟨⟨(-90439711267574233),(-90439711267574228)⟩,⟨(-322696346479577755),(-322696346479577750)⟩⟩,⟨⟨(-86707557422705344),(-86707557422705338)⟩,⟨(-294391950510548874),(-294391950510548868)⟩⟩,⟨⟨(-82865186439181067),(-82865186439181062)⟩,⟨(-268297280518823466),(-268297280518823461)⟩⟩,⟨⟨(-78956660352420606),(-78956660352420601)⟩,⟨(-244269858430035051),(-244269858430035045)⟩⟩,⟨⟨(-75020717493770985),(-75020717493770979)⟩,⟨(-222173257932611813),(-222173257932611807)⟩⟩,⟨⟨(-71091138527773852),(-71091138527773848)⟩,⟨(-201877172157117798),(-201877172157117794)⟩⟩,⟨⟨(-67197109745826180),(-67197109745826174)⟩,⟨(-183257439637354679),(-183257439637354673)⟩⟩,⟨⟨(-63363580683067917),(-63363580683067913)⟩,⟨(-166196032171351761),(-166196032171351757)⟩⟩,⟨⟨(-59611613499942105),(-59611613499942101)⟩,⟨(-150581008198109757),(-150581008198109753)⟩⟩,⟨⟨(-55958721933627513),(-55958721933627509)⟩,⟨(-136306435267175775),(-136306435267175771)⟩⟩,⟨⟨(-52419197973945510),(-52419197973945505)⟩,⟨(-123272285106648179),(-123272285106648174)⟩⟩,⟨⟨(-49004424750469915),(-49004424750469911)⟩,⟨(-111384304694957466),(-111384304694957462)⟩⟩] +lemma kernel9_0_r2_5_eq : ∀ k : Fin 16, kernel9_0Expr 2 5 k = kernel9_0_r2_5 k := by decide +kernel +noncomputable def kernel9_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-45723174430058106),(-45723174430058100)⟩,⟨(-100553866616674848),(-100553866616674842)⟩⟩,⟨⟨(-42581890215046554),(-42581890215046549)⟩,⟨(-90697801836548906),(-90697801836548901)⟩⟩,⟨⟨(-39584951800593622),(-39584951800593618)⟩,⟨(-81738217862747049),(-81738217862747045)⟩⟩,⟨⟨(-36734923894257353),(-36734923894257349)⟩,⟨(-73602305093518582),(-73602305093518578)⟩⟩,⟨⟨(-34032787621448877),(-34032787621448872)⟩,⟨(-66222133954648485),(-66222133954648480)⟩⟩,⟨⟨(-31478154836875281),(-31478154836875276)⟩,⟨(-59534445241362896),(-59534445241362891)⟩⟩,⟨⟨(-29069465534797402),(-29069465534797398)⟩,⟨(-53480435880759817),(-53480435880759813)⟩⟩,⟨⟨(-26804168700496221),(-26804168700496217)⟩,⟨(-48005542132088057),(-48005542132088053)⟩⟩,⟨⟨(-24678887072640539),(-24678887072640535)⟩,⟨(-43059222044722326),(-43059222044722322)⟩⟩,⟨⟨(-22689566392363471),(-22689566392363467)⟩,⟨(-38594738799638038),(-38594738799638034)⟩⟩,⟨⟨(-20831609801040251),(-20831609801040247)⟩,⟨(-34568946371446095),(-34568946371446091)⟩⟩,⟨⟨(-19099998116397721),(-19099998116397717)⟩,⟨(-30942078766196179),(-30942078766196175)⟩⟩,⟨⟨(-17489396767150669),(-17489396767150666)⟩,⟨(-27677543916514315),(-27677543916514312)⟩⟩,⟨⟨(-15994250201382424),(-15994250201382420)⟩,⟨(-24741723151264500),(-24741723151264496)⟩⟩,⟨⟨(-14608864604922962),(-14608864604922956)⟩,⟨(-22103777002626330),(-22103777002626325)⟩⟩,⟨⟨(-13327479774581320),(-13327479774581316)⟩,⟨(-19735457969844233),(-19735457969844229)⟩⟩] +lemma kernel9_0_r2_6_eq : ∀ k : Fin 16, kernel9_0Expr 2 6 k = kernel9_0_r2_6 k := by decide +kernel +noncomputable def kernel9_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-12144330988788289),(-12144330988788285)⟩,⟨(-17610930726302050),(-17610930726302046)⟩⟩,⟨⟨(-11053701706481324),(-11053701706481321)⟩,⟨(-15706600135192886),(-15706600135192882)⟩⟩,⟨⟨(-10049967905334474),(-10049967905334470)⟩,⟨(-14000947328902676),(-14000947328902673)⟩⟩,⟨⟨(-9127634844041946),(-9127634844041943)⟩,⟨(-12474374008172458),(-12474374008172455)⟩⟩,⟨⟨(-8281367001557826),(-8281367001557823)⟩,⟨(-11109055028887421),(-11109055028887417)⟩⟩,⟨⟨(-7506011910133592),(-7506011910133588)⟩,⟨(-9888799266591092),(-9888799266591088)⟩⟩,⟨⟨(-6796618559736782),(-6796618559736778)⟩,⟨(-8798918681082783),(-8798918681082779)⟩⟩,⟨⟨(-6148451009932878),(-6148451009932874)⟩,⟨(-7826105445198462),(-7826105445198459)⟩⟩,⟨⟨(-5556997802419253),(-5556997802419250)⟩,⟨(-6958316952518363),(-6958316952518359)⟩⟩,⟨⟨(-5017977723864695),(-5017977723864692)⟩,⟨(-6184668477670854),(-6184668477670850)⟩⟩,⟨⟨(-4527342425180828),(-4527342425180824)⟩,⟨(-5495333229469274),(-5495333229469270)⟩⟩,⟨⟨(-4081276360388960),(-4081276360388956)⟩,⟨(-4881449510673632),(-4881449510673628)⟩⟩,⟨⟨(-3676194466313940),(-3676194466313936)⟩,⟨(-4335034678059171),(-4335034678059167)⟩⟩,⟨⟨(-3308737963818360),(-3308737963818356)⟩,⟨(-3848905582054910),(-3848905582054906)⟩⟩,⟨⟨(-2975768622492103),(-2975768622492099)⟩,⟨(-3416605155860920),(-3416605155860916)⟩⟩,⟨⟨(-2674361793869346),(-2674361793869342)⟩,⟨(-3032334819060357),(-3032334819060353)⟩⟩] +lemma kernel9_0_r2_7_eq : ∀ k : Fin 16, kernel9_0Expr 2 7 k = kernel9_0_r2_7 k := by decide +kernel +noncomputable def kernel9_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-2401798483530302),(-2401798483530298)⟩,⟨(-2690892359737639),(-2690892359737635)⟩⟩,⟨⟨(-2155556699974283),(-2155556699974279)⟩,⟨(-2387614961456528),(-2387614961456524)⟩⟩,⟨⟨(-1933302287991211),(-1933302287991207)⟩,⟨(-2118327046636800),(-2118327046636796)⟩⟩,⟨⟨(-1732879426434141),(-1732879426434138)⟩,⟨(-1879292615428265),(-1879292615428261)⟩⟩,⟨⟨(-1552300944793569),(-1552300944793565)⟩,⟨(-1667171768688227),(-1667171768688223)⟩⟩,⟨⟨(-1389738589752204),(-1389738589752200)⟩,⟨(-1478981114733612),(-1478981114733608)⟩⟩,⟨⟨(-1243513351888448),(-1243513351888442)⟩,⟨(-1312057771811558),(-1312057771811553)⟩⟩,⟨⟨(-1112085943810112),(-1112085943810108)⟩,⟨(-1164026691399477),(-1164026691399473)⟩⟩,⟨⟨(-994047504133619),(-994047504133616)⟩,⟨(-1032771041230846),(-1032771041230842)⟩⟩,⟨⟨(-888110586762947),(-888110586762943)⟩,⟨(-916405401104372),(-916405401104368)⟩⟩,⟨⟨(-793100481745024),(-793100481745020)⟩,⟨(-813251538862466),(-813251538862462)⟩⟩,⟨⟨(-707946902456290),(-707946902456286)⟩,⟨(-721816548240883),(-721816548240880)⟩⟩,⟨⟨(-631676063880387),(-631676063880383)⟩,⟨(-640773144444280),(-640773144444276)⟩⟩,⟨⟨(-563403168140355),(-563403168140351)⟩,⟨(-568941927166804),(-568941927166800)⟩⟩,⟨⟨(-502325306123907),(-502325306123903)⟩,⟨(-505275434250833),(-505275434250829)⟩⟩,⟨⟨(-447714777864997),(-447714777864993)⟩,⟨(-448843822179472),(-448843822179468)⟩⟩] +lemma kernel9_0_r2_8_eq : ∀ k : Fin 16, kernel9_0Expr 2 8 k = kernel9_0_r2_8 k := by decide +kernel +noncomputable def kernel9_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-398912829200899),(-398912829200895)⟩,⟨(-398822022067056),(-398822022067052)⟩⟩,⟨⟨(-355323798000030),(-355323798000026)⟩,⟨(-354478231700704),(-354478231700700)⟩⟩,⟨⟨(-316409659846267),(-316409659846263)⟩,⟨(-315163615463406),(-315163615463402)⟩⟩,⟨⟨(-281684960372587),(-281684960372583)⟩,⟨(-280303094615941),(-280303094615937)⟩⟩,⟨⟨(-250712119369419),(-250712119369415)⟩,⟨(-249387120422738),(-249387120422734)⟩⟩,⟨⟨(-223097090267555),(-223097090267551)⟩,⟨(-221964331975868),(-221964331975864)⟩⟩,⟨⟨(-198485357535629),(-198485357535626)⟩,⟨(-197635009309682),(-197635009309678)⟩⟩,⟨⟨(-176558253868726),(-176558253868722)⟩,⟨(-176045240520071),(-176045240520067)⟩⟩,⟨⟨(-157029578715406),(-157029578715402)⟩,⟨(-156881729125752),(-156881729125748)⟩⟩,⟨⟨(-139642499639663),(-139642499639660)⟩,⟨(-139867174856975),(-139867174856971)⟩⟩,⟨⟨(-124166718192571),(-124166718192567)⟩,⟨(-124756167455008),(-124756167455004)⟩⟩,⟨⟨(-110395882331801),(-110395882331797)⟩,⟨(-111331538941215),(-111331538941212)⟩⟩,⟨⟨(-98145227937877),(-98145227937873)⟩,⟨(-99401125196125),(-99401125196121)⟩⟩,⟨⟨(-87249432600334),(-87249432600330)⟩,⟨(-88794892606210),(-88794892606206)⟩⟩,⟨⟨(-77560665556389),(-77560665556385)⟩,⟨(-79362390018662),(-79362390018658)⟩⟩,⟨⟨(-68946818434634),(-68946818434630)⟩,⟨(-70970490321942),(-70970490321938)⟩⟩] +lemma kernel9_0_r2_9_eq : ∀ k : Fin 16, kernel9_0Expr 2 9 k = kernel9_0_r2_9 k := by decide +kernel +noncomputable def kernel9_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-61289902265723),(-61289902265719)⟩,⟨(-63501389670890),(-63501389670886)⟩⟩,⟨⟨(-54484597053595),(-54484597053591)⟩,⟨(-56850835728148),(-56850835728144)⟩⟩,⟨⟨(-48436941039881),(-48436941039877)⟩,⟨(-50926559325315),(-50926559325311)⟩⟩,⟨⟨(-43063147628705),(-43063147628701)⟩,⟨(-45646886683721),(-45646886683717)⟩⟩,⟨⟨(-38288538759726),(-38288538759722)⟩,⟨(-40939511800345),(-40939511800341)⟩⟩,⟨⟨(-34046584316104),(-34046584316100)⟩,⟨(-36740410822678),(-36740410822674)⟩⟩,⟨⟨(-30278037925343),(-30278037925339)⟩,⟨(-32992882228613),(-32992882228609)⟩⟩,⟨⟨(-26930160250192),(-26930160250188)⟩,⟨(-29646698414724),(-29646698414720)⟩⟩,⟨⟨(-23956021570881),(-23956021570877)⟩,⟨(-26657355896728),(-26657355896724)⟩⟩,⟨⟨(-21313876126787),(-21313876126783)⟩,⟨(-23985412757960),(-23985412757956)⟩⟩,⟨⟨(-18966601314034),(-18966601314030)⟩,⟨(-21595903260694),(-21595903260690)⟩⟩,⟨⟨(-16881195425059),(-16881195425055)⟩,⟨(-19457820676805),(-19457820676801)⟩⟩,⟨⟨(-15028328166939),(-15028328166935)⟩,⟨(-17543660411621),(-17543660411617)⟩⟩,⟨⟨(-13381938708035),(-13381938708031)⟩,⟨(-15829016400911),(-15829016400907)⟩⟩,⟨⟨(-11918876478030),(-11918876478026)⟩,⟨(-14292224566861),(-14292224566857)⟩⟩,⟨⟨(-10618580386342),(-10618580386338)⟩,⟨(-12914047835171),(-12914047835167)⟩⟩] +lemma kernel9_0_r2_10_eq : ∀ k : Fin 16, kernel9_0Expr 2 10 k = kernel9_0_r2_10 k := by decide +kernel +noncomputable def kernel9_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-9462792529400),(-9462792529396)⟩,⟨(-11677397851384),(-11677397851380)⟩⟩,⟨⟨(-8435302830260),(-8435302830256)⟩,⟨(-10567089098882),(-10567089098878)⟩⟩,⟨⟨(-7521721396098),(-7521721396094)⟩,⟨(-9569621621219),(-9569621621215)⟩⟩,⟨⟨(-6709275692298),(-6709275692294)⟩,⟨(-8672988994682),(-8672988994678)⟩⟩,⟨⟨(-5986629917741),(-5986629917737)⟩,⟨(-7866508589355),(-7866508589351)⟩⟩,⟨⟨(-5343724226476),(-5343724226472)⟩,⟨(-7140671504116),(-7140671504112)⟩⟩,⟨⟨(-4771631678023),(-4771631678018)⟩,⟨(-6487009868074),(-6487009868070)⟩⟩,⟨⟨(-4262431013781),(-4262431013777)⟩,⟨(-5897979472227),(-5897979472223)⟩⟩,⟨⟨(-3809093552079),(-3809093552075)⟩,⟨(-5366855934966),(-5366855934962)⟩⟩,⟨⟨(-3405382671044),(-3405382671040)⟩,⟨(-4887642816620),(-4887642816616)⟩⟩,⟨⟨(-3045764507962),(-3045764507958)⟩,⟨(-4454990285255),(-4454990285251)⟩⟩,⟨⟨(-2725328647897),(-2725328647893)⟩,⟨(-4064123100733),(-4064123100729)⟩⟩,⟨⟨(-2439717704023),(-2439717704019)⟩,⟨(-3710776829605),(-3710776829601)⟩⟩,⟨⟨(-2185064809002),(-2185064808998)⟩,⟨(-3391141331667),(-3391141331663)⟩⟩,⟨⟨(-1957938141778),(-1957938141774)⟩,⟨(-3101810672188),(-3101810672184)⟩⟩,⟨⟨(-1755291708402),(-1755291708398)⟩,⟨(-2839738713566),(-2839738713562)⟩⟩] +lemma kernel9_0_r2_11_eq : ∀ k : Fin 16, kernel9_0Expr 2 11 k = kernel9_0_r2_11 k := by decide +kernel +noncomputable def kernel9_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-1574421680221),(-1574421680217)⟩,⟨(-2602199728069),(-2602199728065)⟩⟩,⟨⟨(-1412927668501),(-1412927668496)⟩,⟨(-2386753450872),(-2386753450868)⟩⟩,⟨⟨(-1268678382542),(-1268678382538)⟩,⟨(-2191214060845),(-2191214060841)⟩⟩,⟨⟨(-1139781179003),(-1139781178998)⟩,⟨(-2013622636818),(-2013622636814)⟩⟩,⟨⟨(-1024555064514),(-1024555064510)⟩,⟨(-1852222690056),(-1852222690052)⟩⟩,⟨⟨(-921506762124),(-921506762120)⟩,⟨(-1705438420442),(-1705438420438)⟩⟩,⟨⟨(-829309495396),(-829309495391)⟩,⟨(-1571855385121),(-1571855385117)⟩⟩,⟨⟨(-746784182566),(-746784182562)⟩,⟨(-1450203304613),(-1450203304609)⟩⟩,⟨⟨(-672882767613),(-672882767609)⟩,⟨(-1339340763521),(-1339340763517)⟩⟩,⟨⟨(-606673445684),(-606673445680)⟩,⟨(-1238241591103),(-1238241591099)⟩⟩,⟨⟨(-547327567603),(-547327567598)⟩,⟨(-1145982731936),(-1145982731932)⟩⟩,⟨⟨(-494108032505),(-494108032501)⟩,⟨(-1061733438842),(-1061733438838)⟩⟩,⟨⟨(-446358999153),(-446358999149)⟩,⟨(-984745639628),(-984745639624)⟩⟩,⟨⟨(-403496765701),(-403496765697)⟩,⟨(-914345346227),(-914345346223)⟩⟩,⟨⟨(-365001684749),(-365001684745)⟩,⟨(-849924990017),(-849924990013)⟩⟩,⟨⟨(-330410995574),(-330410995570)⟩,⟨(-790936580300),(-790936580296)⟩⟩] +lemma kernel9_0_r2_12_eq : ∀ k : Fin 16, kernel9_0Expr 2 12 k = kernel9_0_r2_12 k := by decide +kernel +noncomputable def kernel9_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-299312468971),(-299312468967)⟩,⟨(-736885594763),(-736885594759)⟩⟩,⟨⟨(-271338771943),(-271338771939)⟩,⟨(-687325521067),(-687325521063)⟩⟩,⟨⟨(-246162470153),(-246162470149)⟩,⟨(-641852977947),(-641852977943)⟩⟩,⟨⟨(-223491595367),(-223491595363)⟩,⟨(-600103352256),(-600103352252)⟩⟩,⟨⟨(-203065713436),(-203065713432)⟩,⟨(-561746895596),(-561746895592)⟩⟩,⟨⟨(-184652435789),(-184652435785)⟩,⟨(-526485230504),(-526485230500)⟩⟩,⟨⟨(-168044323853),(-168044323849)⟩,⟨(-494048221776),(-494048221772)⟩⟩,⟨⟨(-153056141669),(-153056141665)⟩,⟨(-464191173465),(-464191173461)⟩⟩,⟨⟨(-139522417102),(-139522417098)⟩,⟨(-436692316512),(-436692316508)⟩⟩,⟨⟨(-127295276490),(-127295276486)⟩,⟨(-411350555824),(-411350555820)⟩⟩,⟨⟨(-116242521735),(-116242521731)⟩,⟨(-387983449091),(-387983449087)⟩⟩,⟨⟨(-106245922282),(-106245922278)⟩,⟨(-366425392701),(-366425392697)⟩⟩,⟨⟨(-97199697630),(-97199697626)⟩,⟨(-346525992764),(-346525992760)⟩⟩,⟨⟨(-89009168817),(-89009168813)⟩,⟨(-328148601750),(-328148601746)⟩⟩,⟨⟨(-81589559777),(-81589559773)⟩,⟨(-311169003297),(-311169003293)⟩⟩,⟨⟨(-74864931630),(-74864931626)⟩,⟨(-295474229698),(-295474229694)⟩⟩] +lemma kernel9_0_r2_13_eq : ∀ k : Fin 16, kernel9_0Expr 2 13 k = kernel9_0_r2_13 k := by decide +kernel +noncomputable def kernel9_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-68767234957),(-68767234953)⟩,⟨(-280961498224),(-280961498220)⟩⟩,⟨⟨(-63235466756),(-63235466752)⟩,⟨(-267537253959),(-267537253955)⟩⟩,⟨⟨(-58214920342),(-58214920338)⟩,⟨(-255116308144),(-255116308139)⟩⟩,⟨⟨(-53656517781),(-53656517777)⟩,⟨(-243621062185),(-243621062181)⟩⟩,⟨⟨(-49516215622),(-49516215618)⟩,⟨(-232980808601),(-232980808597)⟩⟩,⟨⟨(-45754475750),(-45754475746)⟩,⟨(-223131101040),(-223131101035)⟩⟩,⟨⟨(-42335794131),(-42335794127)⟩,⟨(-214013186362),(-214013186358)⟩⟩,⟨⟨(-39228281022),(-39228281017)⟩,⟨(-205573492597),(-205573492593)⟩⟩,⟨⟨(-36403286941),(-36403286937)⟩,⟨(-197763167097),(-197763167093)⟩⟩,⟨⟨(-33835069382),(-33835069378)⟩,⟨(-190537659944),(-190537659940)⟩⟩,⟨⟨(-31500495782),(-31500495777)⟩,⟨(-183856348143),(-183856348139)⟩⟩,⟨⟨(-29378778795),(-29378778791)⟩,⟨(-177682196555),(-177682196551)⟩⟩,⟨⟨(-27451240334),(-27451240330)⟩,⟨(-171981452042),(-171981452037)⟩⟩,⟨⟨(-25701101314),(-25701101310)⟩,⟨(-166723367586),(-166723367582)⟩⟩,⟨⟨(-24113294276),(-24113294272)⟩,⟨(-161879953545),(-161879953541)⟩⟩,⟨⟨(-22674296506),(-22674296502)⟩,⟨(-157425753469),(-157425753465)⟩⟩] +lemma kernel9_0_r2_14_eq : ∀ k : Fin 16, kernel9_0Expr 2 14 k = kernel9_0_r2_14 k := by decide +kernel +noncomputable def kernel9_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-21371981436),(-21371981432)⟩,⟨(-153337642185),(-153337642181)⟩⟩,⟨⟨(-20195486456),(-20195486452)⟩,⟨(-149594644118),(-149594644114)⟩⟩,⟨⟨(-19135095392),(-19135095388)⟩,⟨(-146177770011),(-146177770007)⟩⟩,⟨⟨(-18182134187),(-18182134183)⟩,⟨(-143069870416),(-143069870412)⟩⟩,⟨⟨(-17328878455),(-17328878451)⟩,⟨(-140255504499),(-140255504495)⟩⟩,⟨⟨(-16568471713),(-16568471709)⟩,⟨(-137720822887),(-137720822883)⟩⟩,⟨⟨(-15894853318),(-15894853314)⟩,⟨(-135453463382),(-135453463378)⟩⟩,⟨⟨(-15302695145),(-15302695141)⟩,⟨(-133442458555),(-133442458551)⟩⟩,⟨⟨(-14787346277),(-14787346273)⟩,⟨(-131678154319),(-131678154315)⟩⟩,⟨⟨(-14344784977),(-14344784972)⟩,⟨(-130152138693),(-130152138689)⟩⟩,⟨⟨(-13971577374),(-13971577370)⟩,⟨(-128857180079),(-128857180075)⟩⟩,⟨⟨(-13664842369),(-13664842365)⟩,⟨(-127787174483),(-127787174479)⟩⟩,⟨⟨(-13422222280),(-13422222276)⟩,⟨(-126937101146),(-126937101142)⟩⟩,⟨⟨(-13241858926),(-13241858922)⟩,⟨(-126302986205),(-126302986201)⟩⟩,⟨⟨(-13122374831),(-13122374827)⟩,⟨(-125881874005),(-125881874001)⟩⟩,⟨⟨(-13062859313),(-13062859309)⟩,⟨(-125671805834),(-125671805830)⟩⟩] +lemma kernel9_0_r2_15_eq : ∀ k : Fin 16, kernel9_0Expr 2 15 k = kernel9_0_r2_15 k := by decide +kernel +noncomputable def kernel9_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel9_0_r2_0,kernel9_0_r2_1,kernel9_0_r2_2,kernel9_0_r2_3,kernel9_0_r2_4,kernel9_0_r2_5,kernel9_0_r2_6,kernel9_0_r2_7,kernel9_0_r2_8,kernel9_0_r2_9,kernel9_0_r2_10,kernel9_0_r2_11,kernel9_0_r2_12,kernel9_0_r2_13,kernel9_0_r2_14,kernel9_0_r2_15] +lemma kernel9_0_r2_eq (i k : Fin 16) : kernel9_0Expr 2 i k = kernel9_0_r2 i k := by + fin_cases i + · exact kernel9_0_r2_0_eq k + · exact kernel9_0_r2_1_eq k + · exact kernel9_0_r2_2_eq k + · exact kernel9_0_r2_3_eq k + · exact kernel9_0_r2_4_eq k + · exact kernel9_0_r2_5_eq k + · exact kernel9_0_r2_6_eq k + · exact kernel9_0_r2_7_eq k + · exact kernel9_0_r2_8_eq k + · exact kernel9_0_r2_9_eq k + · exact kernel9_0_r2_10_eq k + · exact kernel9_0_r2_11_eq k + · exact kernel9_0_r2_12_eq k + · exact kernel9_0_r2_13_eq k + · exact kernel9_0_r2_14_eq k + · exact kernel9_0_r2_15_eq k +noncomputable def kernel9_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-1698576138186381279623359),(-1698576138186381277917088)⟩,⟨(-508970586332864949624740),(-508970586332864947917184)⟩⟩,⟨⟨(-1697618379785206277478990),(-1697618379785206275773979)⟩,⟨(-507986881897591742315429),(-507986881897591740609145)⟩⟩,⟨⟨(-1695703711405502863073716),(-1695703711405502861371228)⟩,⟨(-506022665475397803417880),(-506022665475397801714142)⟩⟩,⟨⟨(-1692833833402056941876913),(-1692833833402056940178203)⟩,⟨(-503084308749253537567213),(-503084308749253535867288)⟩⟩,⟨⟨(-1689011305022987359352140),(-1689011305022987357658456)⟩,⟨(-499181336266804319445887),(-499181336266804317751035)⟩⟩,⟨⟨(-1684239554707679800136060),(-1684239554707679798448641)⟩,⟨(-494326386029115593741410),(-494326386029115592052881)⟩⟩,⟨⟨(-1678522893550571553310851),(-1678522893550571551630921)⟩,⟨(-488535157210059347243958),(-488535157210059345562987)⟩⟩,⟨⟨(-1671866531705813897986272),(-1671866531705813896315041)⟩,⟨(-481826345234877184640086),(-481826345234877182967896)⟩⟩,⟨⟨(-1664276597456186962027722),(-1664276597456186960366382)⟩,⟨(-474221564502395342918718),(-474221564502395341256510)⟩⟩,⟨⟨(-1655760158620985228048354),(-1655760158620985226398077)⟩,⟨(-465745259090491360594765),(-465745259090491358943721)⟩⟩,⟨⟨(-1646325245932464431777629),(-1646325245932464430139565)⟩,⟨(-456424601838538517012202),(-456424601838538515373482)⟩⟩,⟨⟨(-1635980877969341869749543),(-1635980877969341868124815)⟩,⟨(-446289382253490891272930),(-446289382253490889647666)⟩⟩,⟨⟨(-1624737087199231954500985),(-1624737087199231952890690)⟩,⟨(-435371883737817094855029),(-435371883737817093244328)⟩⟩,⟨⟨(-1612604946650192780617494),(-1612604946650192779022702)⟩,⟨(-423706750687431944987923),(-423706750687431943392862)⟩⟩,⟨⟨(-1599596596705124442156387),(-1599596596705124440578136)⟩,⟨(-411330846055889470252618),(-411330846055889468674243)⟩⟩,⟨⟨(-1585725271491910322639724),(-1585725271491910321079016)⟩,⟨(-398283100027154303077548),(-398283100027154301516868)⟩⟩] +lemma kernel9_0_r3_0_eq : ∀ k : Fin 16, kernel9_0Expr 3 0 k = kernel9_0_r3_0 k := by decide +kernel +noncomputable def kernel9_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-1571005324327187089582810),(-1571005324327187088040618)⟩,⟨(-384604350483018841000379),(-384604350483018839458373)⟩⟩,⟨⟨(-1555452251662667340537238),(-1555452251662667339014492)⟩,⟨(-370337175992429366410818),(-370337175992429364888423)⟩⟩,⟨⟨(-1539082714980159196209131),(-1539082714980159194706730)⟩,⟨(-355525722088367723618739),(-355525722088367722116860)⟩⟩,⟨⟨(-1521914560084904977789088),(-1521914560084904976307883)⟩,⟨(-340215521633243608548209),(-340215521633243607067700)⟩⟩,⟨⟨(-1503966833256607499711682),(-1503966833256607498252493)⟩,⟨(-324453310105721213316121),(-324453310105721211857806)⟩⟩,⟨⟨(-1485259793733473603882806),(-1485259793733473602446401)⟩,⟨(-308286836670268580849431),(-308286836670268579414082)⟩⟩,⟨⟨(-1465814922026661619914166),(-1465814922026661618501280)⟩,⟨(-291764671915217874719827),(-291764671915217873308181)⟩⟩,⟨⟨(-1445654923590489512426314),(-1445654923590489511037626)⟩,⟨(-274936013165506172670439),(-274936013165506171283177)⟩⟩,⟨⟨(-1424803727407397751667236),(-1424803727407397750303394)⟩,⟨(-257850488292286295078705),(-257850488292286293716475)⟩⟩,⟨⟨(-1403286479085658718833687),(-1403286479085658717495279)⟩,⟨(-240557958953026963006769),(-240557958953026961670160)⟩⟩,⟨⟨(-1381129528111817802822800),(-1381129528111817801510379)⟩,⟨(-223108324202350983655534),(-223108324202350982345101)⟩⟩,⟨⟨(-1358360408948420389630488),(-1358360408948420388344549)⟩,⟨(-205551325415501255861183),(-205551325415501254577417)⟩⟩,⟨⟨(-1335007815720252788230244),(-1335007815720252786971251)⟩,⟨(-187936353462815536272880),(-187936353462815535016245)⟩⟩,⟨⟨(-1311101570288586352057447),(-1311101570288586350825797)⟩,⟨(-170312259064800625822493),(-170312259064800624593384)⟩⟩,⟨⟨(-1286672583572203758041186),(-1286672583572203756837248)⟩,⟨(-152727167243227303197794),(-152727167243227301996575)⟩⟩,⟨⟨(-1261752810035709831959813),(-1261752810035709830783890)⟩,⟨(-135228296764058650008911),(-135228296764058648835883)⟩⟩] +lemma kernel9_0_r3_1_eq : ∀ k : Fin 16, kernel9_0Expr 3 1 k = kernel9_0_r3_1 k := by decide +kernel +noncomputable def kernel9_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-1236375195329161865716502),(-1236375195329161864568873)⟩,⟨(-117861785442956566994599),(-117861785442956565850036)⟩⟩,⟨⟨(-1210573617127748091409109),(-1210573617127748090289977)⟩,⟨(-100672522153607720299273),(-100672522153607719183373)⟩⟩,⟨⟨(-1184382819285433319824182),(-1184382819285433318733733)⟩,⟨(-83703986343239928769137),(-83703986343239927682082)⟩⟩,⟨⟨(-1157838339481503683375892),(-1157838339481503682314237)⟩,⟨(-66998095818579586627196),(-66998095818579585569090)⟩⟩,⟨⟨(-1130976430603101691791835),(-1130976430603101690759073)⟩,⟨(-50595063519295298707174),(-50595063519295297678111)⟩⟩,⟨⟨(-1103833976169477331668538),(-1103833976169477330664690)⟩,⟨(-34533263944897058376048),(-34533263944897057376039)⟩⟩,⟨⟨(-1076448400164132233994084),(-1076448400164132233019159)⟩,⟨(-18849109845378009313897),(-18849109845378008342947)⟩⟩,⟨⟨(-1048857571698663478309327),(-1048857571698663477363257)⟩,⟨(-3576939725909873667330),(-3576939725909872725362)⟩⟩,⟨⟨(-1021099704986310068914317),(-1021099704986310067997036)⟩,⟨11251083348006260646487,11251083348006261559546⟩⟩,⟨⟨(-993213255153391354354238),(-993213255153391353465592)⟩,⟨25605061225969225859088,25605061225969226743400⟩⟩,⟨⟨(-965236810462466351002156),(-965236810462466350141996)⟩,⟨39457438080238969777728,39457438080238970633451⟩⟩,⟨⟨(-937208981561646844942998),(-937208981561646844111097)⟩,⟨52783065470089328681470,52783065470089329508841⟩⟩,⟨⟨(-909168288409628888393295),(-909168288409628887589436)⟩,⟨65559254862788069248811,65559254862788070048054⟩⟩,⟨⟨(-881153045555288488579585),(-881153045555288487803464)⟩,⟨77765817487730099161175,77765817487730099932605⟩⟩,⟨⟨(-853201246473802045096918),(-853201246473802044348249)⟩,⟨89385091477874526581528,89385091477874527325439⟩⟩,⟨⟨(-825350447677950890113891),(-825350447677950889392306)⟩,⟨100401956330596045589166,100401956330596046305935⟩⟩] +lemma kernel9_0_r3_2_eq : ∀ k : Fin 16, kernel9_0Expr 3 2 k = kernel9_0_r3_2 k := by decide +kernel +noncomputable def kernel9_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-797637653333371940503832),(-797637653333371939808992)⟩,⟨110803834797742521537844,110803834797742522227820⟩⟩,⟨⟨(-770099201109914351355466),(-770099201109914350686941)⟩,⟨120580682391472799682641,120580682391472800346262⟩⟩,⟨⟨(-742770649997919427759312),(-742770649997919427116701)⟩,⟨129724964767710071806008,129724964767710072443685⟩⟩,⟨⟨(-715686670808195510791987),(-715686670808195510174813)⟩,⟨138231623322171130982475,138231623322171131594695⟩⟩,⟨⟨(-688880940057821600908345),(-688880940057821600316169)⟩,⟨146098029404318084845292,146098029404318085432501⟩⟩,⟨⟨(-662386037920865152267867),(-662386037920865151700161)⟩,⟨153323927621644079782002,153323927621644080344739⟩⟩,⟨⟨(-636233350893892092099733),(-636233350893892091556013)⟩,⟨159911368769892513433802,159911368769892513972559⟩⟩,⟨⟨(-610452979791098197277534),(-610452979791098196757239)⟩,⟨165864632983597523235790,165864632983597523751135⟩⟩,⟨⟨(-585073653643380241123737),(-585073653643380240626358)⟩,⟨171190143755239127225372,171190143755239127717823⟩⟩,⟨⟨(-560122650030130069028304),(-560122650030130068553246)⟩,⟨175896373519891388012719,175896373519891388482880⟩⟩,⟨⟨(-535625722322464311032149),(-535625722322464310578866)⟩,⟨179993741545119007461705,179993741545119007910128⟩⟩,⟨⟨(-511607034262532125372727),(-511607034262532124940608)⟩,⟨183494504902714659321982,183494504902714659749287⟩⟩,⟨⟨(-488089102246047867539157),(-488089102246047867127649)⟩,⟨186412643329393145060342,186412643329393145467089⟩⟩,⟨⟨(-465092745614881801346325),(-465092745614881800954790)⟩,⟨188763738807558600727316,188763738807558601114147⟩⟩,⟨⟨(-442637045204041556694057),(-442637045204041556321922)⟩,⟨190564850714591939132151,190564850714591939499647⟩⟩,⟨⟨(-420739310323338617919744),(-420739310323338617566374)⟩,⟨191834387399688560879320,191834387399688561228122⟩⟩] +lemma kernel9_0_r3_3_eq : ∀ k : Fin 16, kernel9_0Expr 3 3 k = kernel9_0_r3_3 k := by decide +kernel +noncomputable def kernel9_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-399415054289115384839032),(-399415054289115384503854)⟩,⟨192591975051099632528752,192591975051099632859439⟩⟩,⟨⟨(-378677978556268071304670),(-378677978556268070987037)⟩,⟨192858324713749823193349,192858324713749823506573⟩⟩,⟨⟨(-358539965436090874967135),(-358539965436090874666466)⟩,⟨192655098307742694681400,192655098307742694977746⟩⟩,⟨⟨(-339011079321824916469324),(-339011079321824916184982)⟩,⟨192004774482409031478482,192004774482409031758592⟩⟩,⟨⟨(-320099576281836877172052),(-320099576281836876903470)⟩,⟨190930515118552443563318,190930515118552443827762⟩⟩,⟨⟨(-301811921820663489823741),(-301811921820663489569988)⟩,⟨189456033263708446341303,189456033263708446591022⟩⟩,⟨⟨(-284152816551289857687821),(-284152816551289857439039)⟩,⟨187605463251920361963581,187605463251920362208602⟩⟩,⟨⟨(-267125229468491151679015),(-267125229468491151435244)⟩,⟨185403233721160016464277,185403233721160016704550⟩⟩,⟨⟨(-250730438463320702993107),(-250730438463320702754443)⟩,⟨182873944198539930792180,182873944198539931027595⟩⟩,⟨⟨(-234968077673283335148878),(-234968077673283334915337)⟩,⟨180042245876371596478203,180042245876371596708733⟩⟩,⟨⟨(-219836191221745862012155),(-219836191221745861783813)⟩,⟨176932727151448700862529,176932727151448701088088⟩⟩,⟨⟨(-205331292864003266508710),(-205331292864003266285576)⟩,⟨173569804446227510948303,173569804446227511168871⟩⟩,⟨⟨(-191448431026374530556477),(-191448431026374530338614)⟩,⟨169977618774410312880251,169977618774410313095751⟩⟩,⟨⟨(-178181258698919502145926),(-178181258698919501933321)⟩,⟨166179938455394681492517,166179938455394681702953⟩⟩,⟨⟨(-165522107621957858932939),(-165522107621957858725634)⟩,⟨162200068322718803608936,162200068322718803814256⟩⟩,⟨⟨(-153462066191580989190731),(-153462066191580988988705)⟩,⟨158060765711596064639655,158060765711596064839868⟩⟩] +lemma kernel9_0_r3_4_eq : ∀ k : Fin 16, kernel9_0Expr 3 4 k = kernel9_0_r3_4 k := by decide +kernel +noncomputable def kernel9_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-141991060499763971208425),(-141991060499763971011716)⟩,⟨153784163450466404141557,153784163450466404336617⟩⟩,⟨⟨(-131097937920434919375643),(-131097937920434919184204)⟩,⟨149391700021757635885386,149391700021757636075329⟩⟩,⟨⟨(-120770552653813200894372),(-120770552653813200708216)⟩,⟨144904056998285269101448,144904056998285269286252⟩⟩,⟨⟨(-110995852647303483123115),(-110995852647303482942192)⟩,⟨140341103804435099347023,140341103804435099526730⟩⟩,⟨⟨(-101759967321996939186714),(-101759967321996939011032)⟩,⟨135721849795947004544510,135721849795947004719101⟩⟩,⟨⟨(-93048295549107035139430),(-93048295549107034968917)⟩,⟨131064403599191734889357,131064403599191735058897⟩⟩,⟨⟨(-84845593340138047460160),(-84845593340138047294806)⟩,⟨126385939600704510364404,126385939600704510528895⟩⟩,⟨⟨(-77136060737898129342582),(-77136060737898129182309)⟩,⟨121702671430764854580126,121702671430764854739637⟩⟩,⟨⟨(-69903427422244688879902),(-69903427422244688724695)⟩,⟨117029832241299041804455,117029832241299041958994⟩⟩,⟨⟨(-63131036574284197683088),(-63131036574284197532850)⟩,⟨112381661538588488331741,112381661538588488481399⟩⟩,⟨⟨(-56801926575220137289700),(-56801926575220137144397)⟩,⟨107771398295402802831657,107771398295402802976459⟩⟩,⟨⟨(-50898910150719006768382),(-50898910150719006627919)⟩,⟨103211280035397724506090,103211280035397724646127⟩⟩,⟨⟨(-45404650608106923797760),(-45404650608106923662100)⟩,⟨98712547555033020409303,98712547555033020544604⟩⟩,⟨⟨(-40301734851480124686583),(-40301734851480124555611)⟩,⟨94285454924931155884514,94285454924931156015189⟩⟩,⟨⟨(-35572742898478774984388),(-35572742898478774858056)⟩,⟨89939284393523640131636,89939284393523640257728⟩⟩,⟨⟨(-31200313661612586419334),(-31200313661612586297525)⟩,⟨85682365800981775515517,85682365800981775637137⟩⟩] +lemma kernel9_0_r3_5_eq : ∀ k : Fin 16, kernel9_0Expr 3 5 k = kernel9_0_r3_5 k := by decide +kernel +noncomputable def kernel9_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-27167206796231624177658),(-27167206796231624060324)⟩,⟨81522100100722039127309,81522100100722039244499⟩⟩,⟨⟨(-23456360456118667089524),(-23456360456118666976537)⟩,⟨77464986579093028174700,77464986579093028287586⟩⟩,⟨⟨(-20050944835876105946742),(-20050944835876105838038)⟩,⟨73516653361033379301396,73516653361033379410036⟩⟩,⟨⟨(-16934411416452757038654),(-16934411416452756934109)⟩,⟨69681890790347713121789,69681890790347713226303⟩⟩,⟨⟨(-14090537865995600039749),(-14090537865995599939299)⟩,⟨65964687277560687841208,65964687277560687941658⟩⟩,⟨⟨(-11503468582441369786763),(-11503468582441369690278)⟩,⟨62368267215832949146559,62368267215832949243070⟩⟩,⟨⟨(-9157750896639448406101),(-9157750896639448313504)⟩,⟨58895130575891787897332,58895130575891787989977⟩⟩,⟨⟨(-7038366985111324336387),(-7038366985111324247552)⟩,⟨55547093804062046019585,55547093804062046108488⟩⟩,⟨⟨(-5130761569628719969482),(-5130761569628719884340)⟩,⟨52325331662985698739992,52325331662985698825220⟩⟩,⟨⟨(-3420865506493152974539),(-3420865506493152892954)⟩,⟨49230419672190363473406,49230419672190363555092⟩⟩,⟨⟨(-1895115391619714687768),(-1895115391619714609661)⟩,⟨46262376825002944584216,46262376825002944662436⟩⟩,⟨⟨(-540469328196626311466),(-540469328196626236710)⟩,⟨43420708279100256134607,43420708279100256209487⟩⟩,⟨⟨655580978228294888431,655580978228294959912⟩,⟨40704447739943308919705,40704447739943308991318⟩⟩,⟨⟨1705001616899707953045,1705001616899708021380⟩,⟨38112199279162923401481,38112199279162923469954⟩⟩,⟨⟨2619211168001399718772,2619211168001399784044⟩,⟨35642178353368806409822,35642178353368806475236⟩⟩,⟨⟨3409078494169132163663,3409078494169132225992⟩,⟨33292251812572753544826,33292251812572753607303⟩⟩] +lemma kernel9_0_r3_6_eq : ∀ k : Fin 16, kernel9_0Expr 3 6 k = kernel9_0_r3_6 k := by decide +kernel +noncomputable def kernel9_0_r3_7 : Fin 16 → CBox := ![⟨⟨4084923415808370289432,4084923415808370348894⟩,⟨31059976711195303459858,31059976711195303519470⟩⟩,⟨⟨4656520053078766148429,4656520053078766205147⟩,⟨28942637758227611057639,28942637758227611114509⟩⟩,⟨⟨5133102614072051160586,5133102614072051214643⟩,⟨26937283266329328739555,26937283266329328793763⟩⟩,⟨⟨5523373407485422414906,5523373407485422466416⟩,⟨25040759482262112639094,25040759482262112690756⟩⟩,⟨⟨5835512858834080307913,5835512858834080356948⟩,⟨23249743202911535197289,23249743202911535246474⟩⟩,⟨⟨6077191311798956197398,6077191311798956244074⟩,⟨21560772602084058966268,21560772602084059013093⟩⟩,⟨⟨6255582400505442466204,6255582400505442510597⟩,⟨19970276213148724261943,19970276213148724306482⟩⟩,⟨⟨6377377784207221849388,6377377784207221891604⟩,⟨18474600031315672153426,18474600031315672195784⟩⟩,⟨⟨6448803042834238512273,6448803042834238552378⟩,⟨17070032716817445659227,17070032716817445699472⟩⟩,⟨⟨6475634539982983776464,6475634539982983814566⟩,⟨15752828896416945890418,15752828896416945928655⟩⟩,⟨⟨6463217069009644442510,6463217069009644478679⟩,⟨14519230575460720540376,14519230575460720576676⟩⟩,⟨⟨6416482107764844593573,6416482107764844627903⟩,⟨13365486686099596919268,13365486686099596953726⟩⟩,⟨⟨6339966518020527024389,6339966518020527056944⟩,⟨12287870809299874868082,12287870809299874900759⟩⟩,⟨⟨6237831536629593326623,6237831536629593357496⟩,⟨11282697118872988371323,11282697118872988402314⟩⟩,⟨⟨6113881916779995327837,6113881916779995357090⟩,⟨10346334604980158089325,10346334604980158118691⟩⟩,⟨⟨5971585089218999755436,5971585089218999783154⟩,⟨9475219642454776539243,9475219642454776567070⟩⟩] +lemma kernel9_0_r3_7_eq : ∀ k : Fin 16, kernel9_0Expr 3 7 k = kernel9_0_r3_7 k := by decide +kernel +noncomputable def kernel9_0_r3_8 : Fin 16 → CBox := ![⟨⟨5814090224902372605246,5814090224902372631485⟩,⟨8665866975874443551545,8665866975874443577887⟩⟩,⟨⟨5644247092050034768582,5644247092050034793434⟩,⟨7914879198662109355675,7914879198662109380623⟩⟩,⟨⟨5464624611958311693533,5464624611958311717059⟩,⟨7218954807665554505244,7218954807665554528855⟩⟩,⟨⟨5277529029034686503120,5277529029034686525394⟩,⟨6574894917727205911673,6574894917727205934024⟩⟩,⟨⟨5085021621300965146085,5085021621300965167149⟩,⟨5979608722788210499929,5979608722788210521062⟩⟩,⟨⟨4888935887983439588993,4888935887983439608918⟩,⟨5430117791151864941715,5430117791151864961703⟩⟩,⟨⟨4690894160713699464269,4690894160713699483102⟩,⟨4923559282744628233762,4923559282744628252650⟩⟩,⟨⟨4492323594251790533307,4492323594251790551109⟩,⟨4457188175642056785438,4457188175642056803291⟩⟩,⟨⟨4294471501475467765444,4294471501475467782273⟩,⟨4028378587856317129019,4028378587856317145892⟩⟩,⟨⟨4098420005626221049319,4098420005626221065248⟩,⟨3634624278494812573131,3634624278494812589099⟩⟩,⟨⟨3905099990444667090856,3905099990444667105922⟩,⟨3273538409977492329196,3273538409977492344297⟩⟩,⟨⟨3715304335853436731170,3715304335853436745421⟩,⟨2942852650122596971195,2942852650122596985477⟩⟩,⟨⟨3529700433251270150617,3529700433251270164084⟩,⟨2640415689652664102288,2640415689652664115782⟩⟩,⟨⟨3348841980271118100900,3348841980271118113632⟩,⟨2364191247106461899776,2364191247106461912532⟩⟩,⟨⟨3173180060037339352250,3173180060037339364276⟩,⟨2112255629335722281296,2112255629335722293343⟩⟩,⟨⟨3003073514547756962566,3003073514547756973929⟩,⟨1882794911781040044704,1882794911781040056084⟩⟩] +lemma kernel9_0_r3_8_eq : ∀ k : Fin 16, kernel9_0Expr 3 8 k = kernel9_0_r3_8 k := by decide +kernel +noncomputable def kernel9_0_r3_9 : Fin 16 → CBox := ![⟨⟨2838798625825264843751,2838798625825264854474⟩,⟨1674101798617110146479,1674101798617110157218⟩⟩,⟨⟨2680558121954692513803,2680558121954692523929⟩,⟨1484572218686542959082,1484572218686542969222⟩⟩,⟨⟨2528489528070808532498,2528489528070808542069⟩,⟨1312701708951632207126,1312701708951632216708⟩⟩,⟨⟨2382672884822297389503,2382672884822297398553⟩,⟨1157081633027313621346,1157081633027313630405⟩⟩,⟨⟨2243137858835824613571,2243137858835824622121⟩,⟨1016395278253730753404,1016395278253730761962⟩⟩,⟨⟨2109870271276782007033,2109870271276782015113⟩,⟨889413870755958275273,889413870755958283360⟩⟩,⟨⟨1982818071782636825424,1982818071782636833056⟩,⟨774992544049395759564,774992544049395767202⟩⟩,⟨⟨1861896785864950365774,1861896785864950372983⟩,⟨672066293005463752943,672066293005463760156⟩⟩,⟨⟨1746994464370899256242,1746994464370899263045⟩,⟨579645941412545342067,579645941412545348874⟩⟩,⟨⟨1637976163797822065179,1637976163797822071602⟩,⟨496814147966647110734,496814147966647117159⟩⟩,⟨⟨1534687986197368491091,1534687986197368497153⟩,⟨422721472316320680628,422721472316320686692⟩⟩,⟨⟨1436960707120561096913,1436960707120561102637⟩,⟨356582519774910335576,356582519774910341301⟩⟩,⟨⟨1344613019571440974783,1344613019571440980181⟩,⟨297672180505016063671,297672180505016069069⟩⟩,⟨⟨1257454421283362386308,1257454421283362391401⟩,⟨245321976377269267047,245321976377269272141⟩⟩,⟨⟨1175287771835141505409,1175287771835141510214⟩,⟨198916526307753214697,198916526307753219502⟩⟩,⟨⟨1097911545209073122148,1097911545209073126687⟩,⟨157890138683171610190,157890138683171614727⟩⟩] +lemma kernel9_0_r3_9_eq : ∀ k : Fin 16, kernel9_0Expr 3 9 k = kernel9_0_r3_9 k := by decide +kernel +noncomputable def kernel9_0_r3_10 : Fin 16 → CBox := ![⟨⟨1025121802382370201311,1025121802382370205598⟩,⟨121723537485849969905,121723537485849974191⟩⟩,⟨⟨956713907459025383791,956713907459025387841⟩,⟨89940726925966669356,89940726925966673405⟩⟩,⟨⟨892484009709713411827,892484009709713415651⟩,⟨62105997768888615650,62105997768888619473⟩⟩,⟨⟨832230312710542832373,832230312710542835986⟩,⟨37821077102929054670,37821077102929058282⟩⟩,⟨⟨775754150572780291489,775754150572780294900⟩,⟨16722422018243975438,16722422018243978848⟩⟩,⟨⟨722860890048888901445,722860890048888904668⟩,⟨(-1521343448665468798),(-1521343448665465576)⟩⟩,⟨⟨673360676097416760788,673360676097416763832⟩,⟨(-17211849718284841097),(-17211849718284838055)⟩⟩,⟨⟨627069037300897477840,627069037300897480716⟩,⟨(-30623263862506420795),(-30623263862506417920)⟩⟩,⟨⟨583807366365912735629,583807366365912738343⟩,⟨(-42004435735443694605),(-42004435735443691892)⟩⟩,⟨⟨543403289800326770686,543403289800326773253⟩,⟨(-51580911770526898239),(-51580911770526895674)⟩⟩,⟨⟨505690939765627012972,505690939765627015395⟩,⟨(-59556820651005309498),(-59556820651005307077)⟩⟩,⟨⟨470511140047278437553,470511140047278439845⟩,⟨(-66116635440759030852),(-66116635440759028561)⟩⟩,⟨⟨437711517076905487082,437711517076905489245⟩,⟨(-71426817054185697766),(-71426817054185695606)⟩⟩,⟨⟨407146545979845508684,407146545979845510729⟩,⟨(-75637344157028833324),(-75637344157028831281)⟩⟩,⟨⟨378677540712173492926,378677540712173494858⟩,⟨(-78883134733062733831),(-78883134733062731901)⟩⟩,⟨⟨352172596493893639216,352172596493893641041⟩,⟨(-81285364632770284745),(-81285364632770282921)⟩⟩] +lemma kernel9_0_r3_10_eq : ∀ k : Fin 16, kernel9_0Expr 3 10 k = kernel9_0_r3_10 k := by decide +kernel +noncomputable def kernel9_0_r3_11 : Fin 16 → CBox := ![⟨⟨327506491940151676679,327506491940151678404⟩,⟨(-82952688447263729263),(-82952688447263727540)⟩⟩,⟨⟨304560557539965718009,304560557539965719641⟩,⟨(-83982368030899339096),(-83982368030899337466)⟩⟩,⟨⟨283222516431511219451,283222516431511220994⟩,⟨(-84461313935989749148),(-84461313935989747606)⟩⟩,⟨⟨263386302773401336838,263386302773401338298⟩,⟨(-84467044928856946102),(-84467044928856944644)⟩⟩,⟨⟨244951862411290607168,244951862411290608548⟩,⟨(-84068570633806081380),(-84068570633806080001)⟩⟩,⟨⟨227824939986816761250,227824939986816762560⟩,⟨(-83327202205536447320),(-83327202205536446012)⟩⟩,⟨⟨211916856129469244756,211916856129469245998⟩,⟨(-82297295765648604938),(-82297295765648603698)⟩⟩,⟨⟨197144277909342590715,197144277909342591892⟩,⟨(-81026933159390259339),(-81026933159390258164)⟩⟩,⟨⟨183428985307678218402,183428985307678219517⟩,⟨(-79558544398292789627),(-79558544398292788513)⟩⟩,⟨⟨170697636080313999495,170697636080314000553⟩,⟨(-77929475956145680070),(-77929475956145679013)⟩⟩,⟨⟨158881531044293691483,158881531044293692487⟩,⟨(-76172508882700070523),(-76172508882700069520)⟩⟩,⟨⟨147916381507569634825,147916381507569635779⟩,⟨(-74316330494077637654),(-74316330494077636701)⟩⟩,⟨⟨137742080283606313072,137742080283606313977⟩,⟨(-72385963193237049612),(-72385963193237048708)⟩⟩,⟨⟨128302477484440224185,128302477484440225045⟩,⟨(-70403153769852687727),(-70403153769852686868)⟩⟩,⟨⟨119545162065109641834,119545162065109642651⟩,⟨(-68386726328137244979),(-68386726328137244162)⟩⟩,⟨⟨111421249897144655472,111421249897144656247⟩,⟨(-66352901794778459335),(-66352901794778458561)⟩⟩] +lemma kernel9_0_r3_11_eq : ∀ k : Fin 16, kernel9_0Expr 3 11 k = kernel9_0_r3_11 k := by decide +kernel +noncomputable def kernel9_0_r3_12 : Fin 16 → CBox := ![⟨⟨103885178976896104883,103885178976896105621⟩,⟨(-64315586768312698566),(-64315586768312697829)⟩⟩,⟨⟨96894512223868380534,96894512223868381237⟩,⟨(-62286634286765705899),(-62286634286765705198)⟩⟩,⟨⟨90409748192993265243,90409748192993265912⟩,⟨(-60276078912907258197),(-60276078912907257530)⟩⟩,⟨⟨84394139911133524228,84394139911133524865⟩,⟨(-58292348366479644948),(-58292348366479644312)⟩⟩,⟨⟨78813521950337817012,78813521950337817619⟩,⟨(-56342453770612070763),(-56342453770612070156)⟩⟩,⟨⟨73636145766894311962,73636145766894312540⟩,⟨(-54432160425539927974),(-54432160425539927396)⟩⟩,⟨⟨68832523264569964000,68832523264569964552⟩,⟨(-52566140876815624524),(-52566140876815623973)⟩⟩,⟨⟨64375278481204247185,64375278481204247711⟩,⟨(-50748111907439039663),(-50748111907439039137)⟩⟩,⟨⟨60239007248783773815,60239007248783774317⟩,⟨(-48980956953684421871),(-48980956953684421370)⟩⟩,⟨⟨56400144637092949146,56400144637092949627⟩,⟨(-47266835322724353070),(-47266835322724352590)⟩⟩,⟨⟨52836839958948593626,52836839958948594085⟩,⟨(-45607279476263731908),(-45607279476263731449)⟩⟩,⟨⟨49528839089909553358,49528839089909553798⟩,⟨(-44003281538067239419),(-44003281538067238980)⟩⟩,⟨⟨46457373836320402679,46457373836320403099⟩,⟨(-42455370084227605028),(-42455370084227604609)⟩⟩,⟨⟨43605058071799525962,43605058071799526365⟩,⟨(-40963678182988037056),(-40963678182988036653)⟩⟩,⟨⟨40955790353092517703,40955790353092518088⟩,⟨(-39528003565590108840),(-39528003565590108455)⟩⟩,⟨⟨38494662720931397868,38494662720931398237⟩,⟨(-38147861730644945008),(-38147861730644944638)⟩⟩] +lemma kernel9_0_r3_12_eq : ∀ k : Fin 16, kernel9_0Expr 3 12 k = kernel9_0_r3_12 k := by decide +kernel +noncomputable def kernel9_0_r3_13 : Fin 16 → CBox := ![⟨⟨36207875389585944610,36207875389585944963⟩,⟨(-36822532711589881971),(-36822532711589881617)⟩⟩,⟨⟨34082657029645668519,34082657029645668859⟩,⟨(-35551102169560997401),(-35551102169560997062)⟩⟩,⟨⟨32107190351767651027,32107190351767651354⟩,⟨(-34332497412150944116),(-34332497412150943790)⟩⟩,⟨⟨30270542704257826835,30270542704257827149⟩,⟨(-33165518881702336615),(-33165518881702336301)⟩⟩,⟨⟨28562601404061048546,28562601404061048849⟩,⟨(-32048867604687135341),(-32048867604687135038)⟩⟩,⟨⟨26974013528702392086,26974013528702392376⟩,⟨(-30981169046028456486),(-30981169046028456196)⟩⟩,⟨⟨25496129905672721165,25496129905672721446⟩,⟨(-29960993768629876349),(-29960993768629876069)⟩⟩,⟨⟨24120953045445865097,24120953045445865367⟩,⟨(-28986875258597232276),(-28986875258597232006)⟩⟩,⟨⟨22841088774545868052,22841088774545868312⟩,⟨(-28057325240390488458),(-28057325240390488199)⟩⟩,⟨⟨21649701335672931187,21649701335672931438⟩,⟨(-27170846773163136684),(-27170846773163136433)⟩⟩,⟨⟨20540471732694376632,20540471732694376875⟩,⟨(-26325945389582304157),(-26325945389582303914)⟩⟩,⟨⟨19507559109184028511,19507559109184028747⟩,⟨(-25521138511236655056),(-25521138511236654821)⟩⟩,⟨⟨18545564960042343376,18545564960042343604⟩,⟨(-24754963350107666993),(-24754963350107666766)⟩⟩,⟨⟨17649499986461237083,17649499986461237303⟩,⟨(-24025983483293117638),(-24025983483293117418)⟩⟩,⟨⟨16814753415038754955,16814753415038755168⟩,⟨(-23332794268033357758),(-23332794268033357545)⟩⟩,⟨⟨16037064612140538161,16037064612140538368⟩,⟨(-22674027245918087597),(-22674027245918087390)⟩⟩] +lemma kernel9_0_r3_13_eq : ∀ k : Fin 16, kernel9_0Expr 3 13 k = kernel9_0_r3_13 k := by decide +kernel +noncomputable def kernel9_0_r3_14 : Fin 16 → CBox := ![⟨⟨15312496834600787519,15312496834600787721⟩,⟨(-22048353668773552136),(-22048353668773551934)⟩⟩,⟨⟨14637412967519146833,14637412967519147029⟩,⟨(-21454487263989233547),(-21454487263989233352)⟩⟩,⟨⟨14008453109214892698,14008453109214892887⟩,⟨(-20891186343792858268),(-20891186343792858078)⟩⟩,⟨⟨13422513872327237706,13422513872327237890⟩,⟨(-20357255351087599893),(-20357255351087599708)⟩⟩,⟨⟨12876729278588421882,12876729278588422063⟩,⟨(-19851545923801042764),(-19851545923801042583)⟩⟩,⟨⟨12368453132938328373,12368453132938328549⟩,⟨(-19372957550147020613),(-19372957550147020438)⟩⟩,⟨⟨11895242770394202572,11895242770394202744⟩,⟨(-18920437878663458957),(-18920437878663458785)⟩⟩,⟨⟨11454844076439309918,11454844076439310085⟩,⟨(-18492982739265190917),(-18492982739265190750)⟩⟩,⟨⟨11045177688656006773,11045177688656006936⟩,⟨(-18089635924751929535),(-18089635924751929372)⟩⟩,⟨⟨10664326293910417856,10664326293910418017⟩,⟨(-17709488776157331625),(-17709488776157331465)⟩⟩,⟨⟨10310522941608602034,10310522941608602193⟩,⟨(-17351679609941622754),(-17351679609941622596)⟩⟩,⟨⟨9982140299400367695,9982140299400367850⟩,⟨(-17015393020250368712),(-17015393020250368558)⟩⟩,⟨⟨9677680783220726815,9677680783220726966⟩,⟨(-16699859085224531834),(-16699859085224531684)⟩⟩,⟨⟨9395767498745307848,9395767498745307996⟩,⟨(-16404352502596379420),(-16404352502596379272)⟩⟩,⟨⟨9135135936210546522,9135135936210546668⟩,⟨(-16128191676491689647),(-16128191676491689501)⟩⟩,⟨⟨8894626365128273296,8894626365128273439⟩,⟨(-15870737774435312084),(-15870737774435311941)⟩⟩] +lemma kernel9_0_r3_14_eq : ∀ k : Fin 16, kernel9_0Expr 3 14 k = kernel9_0_r3_14 k := by decide +kernel +noncomputable def kernel9_0_r3_15 : Fin 16 → CBox := ![⟨⟨8673176879723816735,8673176879723816876⟩,⟨(-15631393770983083251),(-15631393770983083111)⟩⟩,⟨⟨8469817049963443879,8469817049963444019⟩,⟨(-15409603492140910644),(-15409603492140910504)⟩⟩,⟨⟨8283662136827328997,8283662136827329133⟩,⟨(-15204850672747651039),(-15204850672747650904)⟩⟩,⟨⟨8113907834044606140,8113907834044606274⟩,⟨(-15016658037261615997),(-15016658037261615863)⟩⟩,⟨⟨7959825501853519348,7959825501853519482⟩,⟨(-14844586412873497109),(-14844586412873496974)⟩⟩,⟨⟨7820757861498049163,7820757861498049296⟩,⟨(-14688233882546253906),(-14688233882546253773)⟩⟩,⟨⟨7696115122138144676,7696115122138144806⟩,⟨(-14547234984432504128),(-14547234984432503997)⟩⟩,⟨⟨7585371514648942698,7585371514648942829⟩,⟨(-14421259963121829652),(-14421259963121829521)⟩⟩,⟨⟨7488062209429847123,7488062209429847251⟩,⟨(-14310014077305740033),(-14310014077305739904)⟩⟩,⟨⟨7403780597851425320,7403780597851425448⟩,⟨(-14213236967700135419),(-14213236967700135291)⟩⟩,⟨⟨7332175919350728562,7332175919350728689⟩,⟨(-14130702088418840113),(-14130702088418839986)⟩⟩,⟨⟨7272951218457467928,7272951218457468056⟩,⟨(-14062216204433356397),(-14062216204433356270)⟩⟩,⟨⟨7225861618207738079,7225861618207738205⟩,⟨(-14007618957270824787),(-14007618957270824661)⟩⟩,⟨⟨7190712898491620232,7190712898491620358⟩,⟨(-13966782500682712747),(-13966782500682712621)⟩⟩,⟨⟨7167360369898665408,7167360369898665534⟩,⟨(-13939611207650311963),(-13939611207650311837)⟩⟩,⟨⟨7155708035583356763,7155708035583356888⟩,⟨(-13926041449769768245),(-13926041449769768119)⟩⟩] +lemma kernel9_0_r3_15_eq : ∀ k : Fin 16, kernel9_0Expr 3 15 k = kernel9_0_r3_15 k := by decide +kernel +noncomputable def kernel9_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel9_0_r3_0,kernel9_0_r3_1,kernel9_0_r3_2,kernel9_0_r3_3,kernel9_0_r3_4,kernel9_0_r3_5,kernel9_0_r3_6,kernel9_0_r3_7,kernel9_0_r3_8,kernel9_0_r3_9,kernel9_0_r3_10,kernel9_0_r3_11,kernel9_0_r3_12,kernel9_0_r3_13,kernel9_0_r3_14,kernel9_0_r3_15] +lemma kernel9_0_r3_eq (i k : Fin 16) : kernel9_0Expr 3 i k = kernel9_0_r3 i k := by + fin_cases i + · exact kernel9_0_r3_0_eq k + · exact kernel9_0_r3_1_eq k + · exact kernel9_0_r3_2_eq k + · exact kernel9_0_r3_3_eq k + · exact kernel9_0_r3_4_eq k + · exact kernel9_0_r3_5_eq k + · exact kernel9_0_r3_6_eq k + · exact kernel9_0_r3_7_eq k + · exact kernel9_0_r3_8_eq k + · exact kernel9_0_r3_9_eq k + · exact kernel9_0_r3_10_eq k + · exact kernel9_0_r3_11_eq k + · exact kernel9_0_r3_12_eq k + · exact kernel9_0_r3_13_eq k + · exact kernel9_0_r3_14_eq k + · exact kernel9_0_r3_15_eq k +noncomputable def kernel9_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-1026552639308199404247184817),(-1026552639308199398930604658)⟩,⟨1953266301671890502780096284,1953266301671890508089566715⟩⟩,⟨⟨(-1025434069845763680413382248),(-1025434069845763675098557803)⟩,⟨1952807812734958948621732568,1952807812734958953929467785⟩⟩,⟨⟨(-1023198926417165376528828677),(-1023198926417165371217524020)⟩,⟨1951890226049967390553822377,1951890226049967395858078760⟩⟩,⟨⟨(-1019851196502841840415389187),(-1019851196502841835109365692)⟩,⟨1950512329192042952919189554,1950512329192042958218226085⟩⟩,⟨⟨(-1015396852540801515212008050),(-1015396852540801509913023122)⟩,⟨1948672316489954178243592829,1948672316489954183535672316⟩⟩,⟨⟨(-1009843841380908141926111375),(-1009843841380908136635917089)⟩,⟨1946367804508849481918085470,1946367804508849487201475858⟩⟩,⟨⟨(-1003202070213363160522806233),(-1003202070213363155243148137)⟩,⟨1943595852566662267572334697,1943595852566662272845310218⟩⟩,⟨⟨(-995483388962997709262872774),(-995483388962997703995488184)⟩,⟨1940352988175805082461393329,1940352988175805087722236161⟩⟩,⟨⟨(-986701569139712143625768828),(-986701569139712138372386399)⟩,⟨1936635237275542982971270278,1936635237275542988218270931⟩⟩,⟨⟨(-976872279134663799870385338),(-976872279134663794632722100)⟩,⟨1932438159094777348736193746,1932438159094777353967653980⟩⟩,⟨⟨(-966013055951697364766499960),(-966013055951697359546262629)⟩,⟨1927756885459998782743811956,1927756885459998787958043420⟩⟩,⟨⟨(-954143273364124463150389364),(-954143273364124457949269188)⟩,⟨1922586164338993539248308825,1922586164338993544443638176⟩⟩,⟨⟨(-941284106488369954503271702),(-941284106488369949322948915)⟩,⟨1916920407387622981999128062,1916920407387622987173892464⟩⟩,⟨⟨(-927458492768283254579499342),(-927458492768283249421633532)⟩,⟨1910753741244749236371385569,1910753741244749241523942288⟩⟩,⟨⟨(-912691089367125517735790268),(-912691089367125512602029816)⟩,⟨1904080062299259977290555734,1904080062299259982419272657⟩⟩,⟨⟨(-897008226968439122855517696),(-897008226968439117747485418)⟩,⟨1896893094633256518277237896,1896893094633256523380507854⟩⟩] +lemma kernel9_0_r4_0_eq : ∀ k : Fin 16, kernel9_0Expr 4 0 k = kernel9_0_r4_0 k := by decide +kernel +noncomputable def kernel9_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-880437859992224929792787749),(-880437859992224924712096879)⟩,⟨1889186450826914770575582556,1889186450826914775651807304⟩⟩,⟨⟨(-863009513239123862936722551),(-863009513239123857884952203)⟩,⟨1880953695293407920790530764,1880953695293407925838145484⟩⟩,⟨⟨(-844754224982638982459864614),(-844754224982638977438586431)⟩,⟨1872188409796688997955473204,1872188409796689002972919826⟩⟩,⟨⟨(-825704486537846153305574226),(-825704486537846148316319868)⟩,⟨1862884260790962975430006192,1862884260790962980415765872⟩⟩,⟨⟨(-805894178344516621714262419),(-805894178344516616758560631)⟩,⟨1853035068208419161814137186,1853035068208419166766693214⟩⟩,⟨⟨(-785358502613091041015631604),(-785358502613091036094957974)⟩,⟨1842634875311327630396831387,1842634875311327635314719395⟩⟩,⟨⟨(-764133912593466332215324136),(-764133912593466327331156198)⟩,⟨1831678019216004706480397111,1831678019216004711362149956⟩⟩,⟨⟨(-742258038539035638722057329),(-742258038539035633875813152)⟩,⟨1820159201689491940291502164,1820159201689491945135711310⟩⟩,⟨⟨(-719769610451795958218656548),(-719769610451795953411764739)⟩,⟨1808073559815133201526868746,1808073559815133206332114238⟩⟩,⟨⟨(-696708377708533517010082823),(-696708377708533512243892053)⟩,⟨1795416736120630307908551366,1795416736120630312673492295⟩⟩,⟨⟨(-673115025683027003009540194),(-673115025683026998285417639)⟩,⟨1782184947761655124206143606,1782184947761655128929419648⟩⟩,⟨⟨(-649031089494775039903705027),(-649031089494775035222933380)⟩,⟨1768375054355732241200664709,1768375054355732245880999101⟩⟩,⟨⟨(-624498865030847310206587655),(-624498865030847305570479558)⟩,⟨1753984624064908112096363770,1753984624064908116732448868⟩⟩,⟨⟨(-599561317403958737396694734),(-599561317403958732806451041)⟩,⟨1739011997531706224950165293,1739011997531706229540804300⟩⟩,⟨⟨(-574261987026643906422060155),(-574261987026643901878922788)⟩,⟨1723456349281038634543718182,1723456349281038639087672287⟩⟩,⟨⟨(-548644893498326804555345491),(-548644893498326800060441321)⟩,⟨1707317746211095274219665534,1707317746211095278715810037⟩⟩] +lemma kernel9_0_r4_1_eq : ∀ k : Fin 16, kernel9_0Expr 4 1 k = kernel9_0_r4_1 k := by decide +kernel +noncomputable def kernel9_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-522754437518994057880715594),(-522754437518994053435230003)⟩,⟨1690597202808744903383760307,1690597202808744907830911036⟩⟩,⟨⟨(-496635301059937079937780700),(-496635301059937075542744289)⟩,⟨1673296732739623527795732355,1673296732739623532192858989⟩⟩,⟨⟨(-470332346038474095808325494),(-470332346038474091464841571)⟩,⟨1655419396479812708473231246,1655419396479812712819229804⟩⟩,⟨⟨(-443890511759537594850662149),(-443890511759537590559683391)⟩,⟨1636969344674762951077875427,1636969344674762955371791639⟩⟩,⟨⟨(-417354711402355165016545350),(-417354711402355160779114804)⟩,⟨1617951856931824291450845510,1617951856931824295691633800⟩⟩,⟨⟨(-390769727845000173190396883),(-390769727845000169007360359)⟩,⟨1598373375775321470542705645,1598373375775321474729516783⟩⟩,⟨⟨(-364180109133182767267470087),(-364180109133182763139780816)⟩,⟨1578241535517455202334868887,1578241535517455206466745309⟩⟩,⟨⟨(-337630063912133242275352527),(-337630063912133238203773255)⟩,⟨1557565185824310869851765569,1557565185824310873927939342⟩⟩,⟨⟨(-311163357151645255437948733),(-311163357151645251423375147)⟩,⟨1536354409783785096290778546,1536354409783785100310347908⟩⟩,⟨⟨(-284823206504147878142728351),(-284823206504147874185801926)⟩,⟨1514620536311159652048260922,1514620536311159656010577529⟩⟩,⟨⟨(-258652179643922668177337941),(-258652179643922664278852446)⟩,⟨1492376146758209281868224153,1492376146758209285772486521⟩⟩,⟨⟨(-232692092942143465283539770),(-232692092942143461444055806)⟩,⟨1469635075622961723002409212,1469635075622961726848048284⟩⟩,⟨⟨(-206983911837171594031352783),(-206983911837171590251604632)⟩,⟨1446412405289359928668483852,1446412405289359932454756080⟩⟩,⟨⟨(-181567653262378683327840434),(-181567653262378679607264431)⟩,⟨1422724454758923772692653644,1422724454758923776420109385⟩⟩,⟨⟨(-156482290494597771148260254),(-156482290494597767486751688)⟩,⟨1398588762369877778966120401,1398588762369877782634851247⟩⟩,⟨⟨(-131765660785039716403817408),(-131765660785039712801742979)⟩,⟨1374024062532901391612687278,1374024062532901395222315379⟩⟩] +lemma kernel9_0_r4_2_eq : ∀ k : Fin 16, kernel9_0Expr 4 2 k = kernel9_0_r4_2 k := by decide +kernel +noncomputable def kernel9_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-107454376131090869418758127),(-107454376131090865876714371)⟩,⟨1349050256546461190347180019,1349050256546461193897096998⟩⟩,⟨⟨(-83583737541780887272805598),(-83583737541780883791022327)⟩,⟨1323688377588387398709890366,1323688377588387402199854097⟩⟩,⟨⟨(-60187653141845579503688355),(-60187653141845576082647514)⟩,⟨1297960550013743609002796282,1297960550013743612432311873⟩⟩,⟨⟨(-37298560449196152484192849),(-37298560449196149124056859)⟩,⟨1271889943121890476715796965,1271889943121890480084688650⟩⟩,⟨⟨(-14947353148249530216910199),(-14947353148249526918114100)⟩,⟨1245500719587742556996713083,1245500719587742560304531907⟩⟩,⟨⟨6836687332999779239270543,6836687332999782476701036⟩,⟨1218817978783345258693344423,1218817978783345261940050481⟩⟩,⟨⟨28025955151032356778309612,28025955151032359954053665⟩,⟨1191867695245842104635581697,1191867695245842107820839466⟩⟩,⟨⟨48594578007701366923921789,48594578007701370038021033⟩,⟨1164676652576452177921027358,1164676652576452181044863580⟩⟩,⟨⟨68518469492572944422562418,68518469492572947474729162⟩,⟨1137272373082031726025297423,1137272373082031729087409076⟩⟩,⟨⟨87775375578105899785656855,87775375578105902776081175⟩,⟨1109683043495958968849504071,1109683043495958971850065856⟩⟩,⟨⟨106344915063664681638034707,106344915063664684566555254⟩,⟨1081937437138274225280576850,1081937437138274228219411664⟩⟩,⟨⟨124208613790617164656183075,124208613790617167523040418⟩,⟨1054064832896057699550023172,1054064832896057702427355856⟩⟩,⟨⟨141349932478530895386620190,141349932478530898191686959⟩,⟨1026094931423777620762740689,1026094931423777623578427832⟩⟩,⟨⟨157754288061576734103939103,157754288061576736847597125⟩,⟨998057768979650236851518452,998057768979650239605926020⟩⟩,⟨⟨173409068434492013902717464,173409068434492016584960032⟩,⟨969983629327795572295097401,969983629327795574988202575⟩⟩,⟨⟨188303640548648351287035228,188303640548648353908291999⟩,⟨941902954147042147830869811,941902954147042150463086384⟩⟩] +lemma kernel9_0_r4_3_eq : ∀ k : Fin 16, kernel9_0Expr 4 3 k = kernel9_0_r4_3 k := by decide +kernel +noncomputable def kernel9_0_r4_4 : Fin 16 → CBox := ![⟨⟨202429351830703002080802421,202429351830703004641080172⟩,⟨913846252395542623644303870,913846252395542626215622550⟩⟩,⟨⟨215779524928768824817775886,215779524928768827317656167⟩,⟨885844009085843486218376954,885844009085843488729363646⟩⟩,⟨⟨228349445823790801154835394,228349445823790803594458037⟩,⟨857926593927659540104871501,857926593927659542555650248⟩⟩,⟨⟨240136345376635630182919801,240136345376635632562889097⟩,⟨830124170295313990757471436,830124170295313993148631195⟩⟩,⟨⟨251139374414050855353311292,251139374414050857673783486⟩,⟨802466604973615477763763194,802466604973615480095444784⟩⟩,⟨⟨261359572488895868482955700,261359572488895870744669918⟩,⟨774983379129875206328189676,774983379129875208601117422⟩⟩,⟨⟨270799830481654586021737003,270799830481654588224968436⟩,⟨747703500950863522454282495,747703500950863524668716739⟩⟩,⟨⟨279464847240977469615750388,279464847240977471761259402⟩,⟨720655420371831409311397030,720655420371831411468083935⟩⟩,⟨⟨287361080490643143532851806,287361080490643145620907780⟩,⟨693866946310365890283451431,693866946310365892382646149⟩⟩,⟨⟨294496692258658979043198089,294496692258658981074701717⟩,⟨667365166800917931091490590,667365166800917933134080429⟩⟩,⟨⟨300881489111027138200347115,300881489111027140175694991⟩,⟨641176372406466293800975009,641176372406466295787343177⟩⟩,⟨⟨306526857497790792886706081,306526857497790794806792621⟩,⟨615325983262109437591279475,615325983262109439522307819⟩⟩,⟨⟨311445694542161170683531269,311445694542161172554142866⟩,⟨589838480081576629473922713,589838480081576631354923107⟩⟩,⟨⟨315652334624641610153492317,315652334624641611975758194⟩,⟨564737339431902239403671734,564737339431902241235755883⟩⟩,⟨⟨319162472132958696403019168,319162472132958698177186685⟩,⟨540044973554012120230932375,540044973554012122014361815⟩⟩,⟨⟨321993080765149872510891981,321993080765149874237714615⟩,⟨515782674977939667480553326,515782674977939669216096381⟩⟩] +lemma kernel9_0_r4_4_eq : ∀ k : Fin 16, kernel9_0Expr 4 4 k = kernel9_0_r4_4 k := by decide +kernel +noncomputable def kernel9_0_r4_5 : Fin 16 → CBox := ![⟨⟨324162329787228332138763834,324162329787228333818458586⟩,⟨491970566151044641582059764,491970566151044643269948140⟩⟩,⟨⟨325689497658356763980524343,325689497658356765613973143⟩,⟨468627554266182483817484214,468627554266182485458615247⟩⟩,⟨⟨326594883445340371303908042,326594883445340372891448503⟩,⟨445771291444505254821294180,445771291444505256416020685⟩⟩,⟨⟨326899716454447339460781485,326899716454447341003260575⟩,⟨423418140394712084428734953,423418140394712085977919605⟩⟩,⟨⟨326626064512054846246039777,326626064512054847743773675⟩,⟨401583145637354541137237089,401583145637354542641211549⟩⟩,⟨⟨325796741326396698872426459,325796741326396700326365106⟩,⟨380280010349488524809474126,380280010349488526269204297⟩⟩,⟨⟨324435213360773169536502298,324435213360773170947060812⟩,⟨359521078851795332117563783,359521078851795333533480475⟩⟩,⟨⟨322565506644015244484931883,322565506644015245853030244⟩,⟨339317324727512640490912678,339317324727512641863951876⟩⟩,⟨⟨320212113936836633868731683,320212113936836635194741889⟩,⟨319678344530357348868216076,319678344530357350198765475⟩⟩,⟨⟨317399902663040759932394386,317399902663040761217344077⟩,⟨300612357007314292381970559,300612357007314293671073798⟩⟩,⟨⟨314154024002479734467693564,314154024002479735712061250⟩,⟨282126207731925346769755242,282126207731925348017906483⟩⟩,⟨⟨310499823528309998869767129,310499823528310000074524299⟩,⟨264225379014747755947368981,264225379014747757155555496⟩⟩,⟨⟨306462753754594178368724900,306462753754594179534314606⟩,⟨246914004930150183124231680,246914004930150184292911947⟩⟩,⟨⟨302068288941816017097985958,302068288941816018225461080⟩,⟨230194891272756090620234379,230194891272756091750476794⟩⟩,⟨⟨297341842487574434026296327,297341842487574435116183744⟩,⟨214069540232785848152491183,214069540232785849244837764⟩⟩,⟨⟨292308687207785592599151459,292308687207785593652452677⟩,⟨198538179557432666152789777,198538179557432667208257126⟩⟩] +lemma kernel9_0_r4_5_eq : ∀ k : Fin 16, kernel9_0Expr 4 5 k = kernel9_0_r4_5 k := by decide +kernel +noncomputable def kernel9_0_r4_6 : Fin 16 → CBox := ![⟨⟨286993878790340725477366498,286993878790340726494549148⟩,⟨183599795945355222837059301,183599795945355223856129748⟩⟩,⟨⟨281422182678543125495843894,281422182678543126477997137⟩,⟨169252172403484047543819288,169252172403484048527596621⟩⟩,⟨⟨275618004615987497037395664,275618004615987497985079519⟩,⟨155491929279701288200283277,155491929279701289149341733⟩⟩,⟨⟨269605325058060441978272017,269605325058060442892497116⟩,⟨142314568671625632715198341,142314568671625633630562575⟩⟩,⟨⟨263407637628146223227499004,263407637628146224108778278⟩,⟨129714521900756206166826753,129714521900756207049023322⟩⟩,⟨⟨257047891769131340154391232,257047891769131341003792752⟩,⟨117685199732620782048987591,117685199732620782899097954⟩⟩,⟨⟨250548439713127312031029985,250548439713127312849893788⟩,⟨106219045017333707857461279,106219045017333708676839035⟩⟩,⟨⟨243930987864682096238059619,243930987864682097027607815⟩,⟨95307587421076673733969459,95307587421076674523849553⟩⟩,⟨⟨237216552665329835344834999,237216552665329836105520194⟩,⟨84941499917430716650604052,84941499917430717411451319⟩⟩,⟨⟨230425420980331792325704083,230425420980331793058528860⟩,⟨75110656708152160703123756,75110656708152161435952642⟩⟩,⟨⟨223577115022074995904849937,223577115022074996610338561⟩,⟨65804192245822756625539576,65804192245822757330885830⟩⟩,⟨⟨216690361798995300771967668,216690361798995301451038702⟩,⟨57010561035723225511069035,57010561035723226189862287⟩⟩,⟨⟨209783067054242351763621304,209783067054242352416746308⟩,⟨48717597901173120958254505,48717597901173121610977028⟩⟩,⟨⟨202872293634756268371538751,202872293634756268999675001⟩,⟨40912578405328515446857374,40912578405328516074476697⟩⟩,⟨⟨195974244209116511640899838,195974244209116512244568284⟩,⟨33582279132900892063234707,33582279132900892666281687⟩⟩,⟨⟨189104248231574124239883100,189104248231574124819967391⟩,⟨26713037547314103282026167,26713037547314103861393881⟩⟩] +lemma kernel9_0_r4_6_eq : ∀ k : Fin 16, kernel9_0Expr 4 6 k = kernel9_0_r4_6 k := by decide +kernel +noncomputable def kernel9_0_r4_7 : Fin 16 → CBox := ![⟨⟨182276753030195439986473851,182276753030195440543425445⟩,⟨20290811152301273516386478,20290811152301274072535510⟩⟩,⟨⟨175505318879118391253155018,175505318879118391787902138⟩,⟨14301235701703327719975568,14301235701703328253842722⟩⟩,⟨⟨168802617898625220939431562,168802617898625221452481556⟩,⟨8729682217103738428550644,8729682217103738940651573⟩⟩,⟨⟨162180436612124716243825950,162180436612124716736015897⟩,⟨3561312589755191380891539,3561312589755191872071102⟩⟩,⟨⟨155649681976253552717895054,155649681976253553189676745⟩,⟨(-1218866439143259893165825),(-1218866439143259422448306)⟩⟩,⟨⟨149220390689174286470711740,149220390689174286922942867⟩,⟨(-5625951107541666021520697),(-5625951107541665570400570)⟩⟩,⟨⟨142901741572775475298438574,142901741572775475731604213⟩,⟨(-9675090440061259905905901),(-9675090440061259473891354)⟩⟩,⟨⟨136702070816860619198226576,136702070816860619613336195⟩,⟨(-13381438184038589616468730),(-13381438184038589202543934)⟩⟩,⟨⟨130628889867525817144203760,130628889867525817542712658⟩,⟨(-16760107005096055681578290),(-16760107005096055284281216)⟩⟩,⟨⟨124688905737736250409957152,124688905737736250792578601⟩,⟨(-19826125054170467040294542),(-19826125054170466658906575)⟩⟩,⟨⟨118888043515571047632761606,118888043515571047999861148⟩,⟨(-22594394999020716318028433),(-22594394999020715952178836)⟩⟩,⟨⟨113231470844655230420640060,113231470844655230772853247⟩,⟨(-25079655594623116952365115),(-25079655594623116601413660)⟩⟩,⟨⟨107723624151866097375806885,107723624151866097713450964⟩,⟨(-27296445848675034183183682),(-27296445848675033846808569)⟩⟩,⟨⟨102368236399409914203295620,102368236399409914527021930⟩,⟨(-29259071820781050730952258),(-29259071820781050408498160)⟩⟩,⟨⟨97168366141725206164051461,97168366141725206474204568⟩,⟨(-30981576076897449629754776),(-30981576076897449320873233)⟩⟩,⟨⟨92126427672286340850003487,92126427672286341147169508⟩,⟨(-32477709804355730594246514),(-32477709804355730298348007)⟩⟩] +lemma kernel9_0_r4_7_eq : ∀ k : Fin 16, kernel9_0Expr 4 7 k = kernel9_0_r4_7 k := by decide +kernel +noncomputable def kernel9_0_r4_8 : Fin 16 → CBox := ![⟨⟨87244222051154721393773210,87244222051154721678238307⟩,⟨(-33760907577358352660521748),(-33760907577358352377316766)⟩⟩,⟨⟨82522968810949547410375170,82522968810949547682748096⟩,⟨(-34844264748312538461337238),(-34844264748312538190214236)⟩⟩,⟨⟨77963338146677232972153250,77963338146677233232753778⟩,⟨(-35740517426801798051247525),(-35740517426801797791883963)⟩⟩,⟨⟨73565483403457619929178002,73565483403457620178539998⟩,⟨(-36462024995439280153100524),(-36462024995439279904960224)⟩⟩,⟨⟨69329073685504610060498082,69329073685504610298896294⟩,⟨(-37020755100340181363948726),(-37020755100340181126754637)⟩⟩,⟨⟨65253326419647487206893496,65253326419647487434938964⟩,⟨(-37428271043519158437862160),(-37428271043519158210937697)⟩⟩,⟨⟨61337039717106990354159386,61337039717106990572143604⟩,⟨(-37695721495179166694213824),(-37695721495179166477266815)⟩⟩,⟨⟨57578624388059336786836024,57578624388059336995233600⟩,⟨(-37833832435616283291845102),(-37833832435616283084405273)⟩⟩,⟨⟨53976135474627206906000013,53976135474627207105047521⟩,⟨(-37852901229317036969692543),(-37852901229317036771527324)⟩⟩,⟨⟨50527303179228442251200830,50527303179228442441384530⟩,⟨(-37762792727757622683557291),(-37762792727757622494184537)⟩⟩,⟨⟨47229563076594773354506907,47229563076594773536085395⟩,⟨(-37572937292406775547860969),(-37572937292406775367025884)⟩⟩,⟨⟨44080085509153450646067948,44080085509153450819464349⟩,⟨(-37292330625456965540724374),(-37292330625456965368007650)⟩⟩,⟨⟨41075804076759164495101249,41075804076759164660535006⟩,⟨(-36929535292825975216958727),(-36929535292825975052144455)⟩⟩,⟨⟨38213443142893307548687296,38213443142893307706582819⟩,⟨(-36492683821940719354074432),(-36492683821940719196741772)⟩⟩,⟨⟨35489544290340225980321340,35489544290340226130909408⟩,⟨(-35989483255689902135138367),(-35989483255689901985059846)⟩⟩,⟨⟨32900491669940221682965688,32900491669940221826709228⟩,⟨(-35427221043659796329239217),(-35427221043659796185955201)⟩⟩] +lemma kernel9_0_r4_8_eq : ∀ k : Fin 16, kernel9_0Expr 4 8 k = kernel9_0_r4_8 k := by decide +kernel +noncomputable def kernel9_0_r4_9 : Fin 16 → CBox := ![⟨⟨30442536196248284676264119,30442536196248284813525533⟩,⟨(-34812772152292350174609044),(-34812772152292350037760199)⟩⟩,⟨⟨28111818553744494351394092,28111818553744494482531206⟩,⟨(-34152607276868314610335582),(-34152607276868314479567110)⟩⟩,⟨⟨25904390986602427184099183,25904390986602427309293576⟩,⟨(-33452802040159284420068300),(-33452802040159284295201427)⟩⟩,⟨⟨23816237853888424628016826,23816237853888424747574764⟩,⟨(-32719047065149156601131276),(-32719047065149156481862484)⟩⟩,⟨⟨21843294940406720220233087,21843294940406720334305311⟩,⟨(-31956658812334464088223239),(-31956658812334463974404336)⟩⟩,⟨⟨19981467521199339846366326,19981467521199339955260135⟩,⟨(-31170591075711173161295928),(-31170591075711173052622125)⟩⟩,⟨⟨18226647184937881206119719,18226647184937881309994894⟩,⟨(-30365447035580168837236921),(-30365447035580168733550763)⟩⟩,⟨⟨16574727428095314139485151,16574727428095314238609117⟩,⟨(-29545491770693180527654360),(-29545491770693180428690677)⟩⟩,⟨⟨15021618037854099029955759,15021618037854099124455478⟩,⟨(-28714665136955265143450311),(-28714665136955265049084237)⟩⟩,⟨⟨13563258287191800487404217,13563258287191800577552105⟩,⟨(-27876594924841118357957331),(-27876594924841118267918484)⟩⟩,⟨⟨12195628970491502360998092,12195628970491502446933173⟩,⟨(-27034610212814777831254448),(-27034610212814777745405693)⟩⟩,⟨⟨10914763312360724523894706,10914763312360724605848433⟩,⟨(-26191754839312801588128626),(-26191754839312801506240318)⟩⟩,⟨⟨9716756786122270126242468,9716756786122270204328636⟩,⟨(-25350800921209854190725594),(-25350800921209854112685627)⟩⟩,⟨⟨8597775881680166532128863,8597775881680166606578258⟩,⟨(-24514262352086160785864842),(-24514262352086160711444036)⟩⟩,⟨⟨7554065865183431768075350,7554065865183431839007638⟩,⟨(-23684408219015261386600104),(-23684408219015261315680299)⟩⟩,⟨⟨6581957575132339646047948,6581957575132339713661859⟩,⟨(-22863276081948225410812797),(-22863276081948225343196678)⟩⟩] +lemma kernel9_0_r4_9_eq : ∀ k : Fin 16, kernel9_0Expr 4 9 k = kernel9_0_r4_9 k := by decide +kernel +noncomputable def kernel9_0_r4_10 : Fin 16 → CBox := ![⟨⟨5677873301320984507411924,5677873301320984571912443⟩,⟨(-22052685065050901200266264),(-22052685065050901135750217)⟩⟩,⟨⟨4838331794312926927850818,4838331794312926989443365⟩,⟨(-21254248714521463033055919),(-21254248714521462971435766)⟩⟩,⟨⟨4059952454031647553224372,4059952454031647612000697⟩,⟨(-20469387582447711912030715),(-20469387582447711853215873)⟩⟩,⟨⟨3339458746543621194313772,3339458746543621250433950⟩,⟨(-19699341501132121203964843),(-19699341501132121147796317)⟩⟩,⟨⟨2673680898248918863232058,2673680898248918916768919⟩,⟨(-18945181516995853080253960),(-18945181516995853026659947)⟩⟩,⟨⟨2059557916502582530804897,2059557916502582581918761⟩,⟨(-18207821457652682085175125),(-18207821457652682033996234)⟩⟩,⟨⟨1494138985199874615622535,1494138985199874664391329⟩,⟨(-17488029110005006428717407),(-17488029110005006379876601)⟩⟩,⟨⟨974584283099923567141636,974584283099923613701866⟩,⟨(-16786436991245091964843152),(-16786436991245091918204730)⟩⟩,⟨⟨498165271664817843212789,498165271664817887622734⟩,⟨(-16103552698436518979281199),(-16103552698436518934787659)⟩⟩,⟨⟨62264497983672693615826,62264497983672736015172⟩,⟨(-15439768825897395405245826),(-15439768825897395362758161)⟩⟩,⟨⟨(-335625043038481669605340),(-335625043038481629150998)⟩,⟨(-14795372442904737586566112),(-14795372442904737546019391)⟩⟩,⟨⟨(-697900944592144333799303),(-697900944592144295174263)⟩,⟨(-14170554127287338722588822),(-14170554127287338683867921)⟩⟩,⟨⟨(-1026852781015014770232197),(-1026852781015014733360344)⟩,⟨(-13565416553273434036853560),(-13565416553273433999882950)⟩⟩,⟨⟨(-1324663818804025668950227),(-1324663818804025633675053)⟩,⟨(-12979982634512457057685486),(-12979982634512457022309162)⟩⟩,⟨⟨(-1593413008270817055791927),(-1593413008270817022064188)⟩,⟨(-12414203225501815940116081),(-12414203225501815906285276)⟩⟩,⟨⟨(-1835077220448094841708770),(-1835077220448094809435888)⟩,⟨(-11867964386726072632037594),(-11867964386726072599660131)⟩⟩] +lemma kernel9_0_r4_10_eq : ∀ k : Fin 16, kernel9_0Expr 4 10 k = kernel9_0_r4_10 k := by decide +kernel +noncomputable def kernel9_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2051533695820371824805936),(-2051533695820371793953848)⟩,⟨(-11341094220664664675911562),(-11341094220664664644953789)⟩⟩,⟨⟨(-2244562673442190936108393),(-2244562673442190906580614)⟩,⟨(-10833369287453970163607026),(-10833369287453970133972779)⟩⟩,⟨⟨(-2415850171003525736735218),(-2415850171003525708490849)⟩,⟨(-10344520610409609848744374),(-10344520610409609820393089)⟩⟩,⟨⟨(-2566990888390670017346957),(-2566990888390669990307776)⟩,⟨(-9874239282835685331605951),(-9874239282835685304459675)⟩⟩,⟨⟨(-2699491209258152383185170),(-2699491209258152357321092)⟩,⟨(-9422181688580028721091192),(-9422181688580028695120120)⟩⟩,⟨⟨(-2814772277061148518778164),(-2814772277061148494009981)⟩,⟨(-8987974349649772182981147),(-8987974349649772158106282)⟩⟩,⟨⟨(-2914173123888090298818345),(-2914173123888090275105259)⟩,⟨(-8571218414891200235901491),(-8571218414891200212082263)⟩⟩,⟨⟨(-2998953832270676907033909),(-2998953832270676884276081)⟩,⟨(-8171493804273636016331999),(-8171493804273635993468760)⟩⟩,⟨⟨(-3070298711925615194834090),(-3070298711925615173012299)⟩,⟨(-7788363023710774946746094),(-7788363023710774924819811)⟩⟩,⟨⟨(-3129319475092765270976669),(-3129319475092765250024992)⟩,⟨(-7421374665616075151211584),(-7421374665616075130156450)⟩⟩,⟨⟨(-3177058395772749909307141),(-3177058395772749889200888)⟩,⟨(-7070066610533027979302877),(-7070066610533027959094344)⟩⟩,⟨⟨(-3214491439729425469151739),(-3214491439729425449838083)⟩,⟨(-6733968945217589767230735),(-6733968945217589747816065)⟩⟩,⟨⟨(-3242531353605862585470549),(-3242531353605862566932827)⟩,⟨(-6412606612489652589278262),(-6412606612489652570640912)⟩⟩,⟨⟨(-3262030702904549806635717),(-3262030702904549788819561)⟩,⟨(-6105501808023671129094481),(-6105501808023671111180137)⟩⟩,⟨⟨(-3273784849902179127201321),(-3273784849902179110086688)⟩,⟨(-5812176139025507430340233),(-5812176139025507413128937)⟩⟩,⟨⟨(-3278534863806145589429046),(-3278534863806145572966892)⟩,⟨(-5532152559452785985214245),(-5532152559452785968658963)⟩⟩] +lemma kernel9_0_r4_11_eq : ∀ k : Fin 16, kernel9_0Expr 4 11 k = kernel9_0_r4_11 k := by decide +kernel +noncomputable def kernel9_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-3276970356614038730964274),(-3276970356614038715139422)⟩,⟨(-5264957096088636401161300),(-5264957096088636385248729)⟩⟩,⟨⟨(-3269732239209785457069368),(-3269732239209785441834394)⟩,⟨(-5010120379382172348235748),(-5010120379382172332918149)⟩⟩,⟨⟨(-3257415393222128161263730),(-3257415393222128146603141)⟩,⟨(-4767178992531395938035359),(-4767178992531395923296983)⟩⟩,⟨⟨(-3240571255084664262926001),(-3240571255084664248802816)⟩,⟨(-4535676651812850296510810),(-4535676651812850282314401)⟩⟩,⟨⟨(-3219710309574009619915636),(-3219710309574009606320483)⟩,⟨(-4315165230664134350980425),(-4315165230664134337316382)⟩⟩,⟨⟨(-3195304490866389455042883),(-3195304490866389441937076)⟩,⟨(-4105205639506651571738404),(-4105205639506651558567788)⟩⟩,⟨⟨(-3167789489845991769162365),(-3167789489845991756533493)⟩,⟨(-3905368572762450620968468),(-3905368572762450608278653)⟩⟩,⟨⟨(-3137566967023842961030534),(-3137566967023842948847323)⟩,⟨(-3715235133975958912998767),(-3715235133975958900758256)⟩⟩,⟨⟨(-3105006670987052980852780),(-3105006670987052969109426)⟩,⟨(-3534397349403521295286156),(-3534397349403521283488959)⟩⟩,⟨⟨(-3070448462798416167260960),(-3070448462798416155923229)⟩,⟨(-3362458579885149329825895),(-3362458579885149318437569)⟩⟩,⟨⟨(-3034204247209008410474337),(-3034204247209008399532365)⟩,⟨(-3199033840267500509805640),(-3199033840267500498816147)⟩⟩,⟨⟨(-2996559811935093580811379),(-2996559811935093570238691)⟩,⟨(-3043750035108128218436922),(-3043750035108128207819607)⟩⟩,⟨⟨(-2957776576588847891345958),(-2957776576588847881137487)⟩,⟨(-2896246118861333160041997),(-2896246118861333149791640)⟩⟩,⟨⟨(-2918093253143609066530983),(-2918093253143609056658522)⟩,⟨(-2756173188227966269491482),(-2756173188227966259579708)⟩⟩,⟨⟨(-2877727420061984109657890),(-2877727420061984100113674)⟩,⟨(-2623194513847369530620484),(-2623194513847369521039391)⟩⟩,⟨⟨(-2836877012422556037046289),(-2836877012422556027807850)⟩,⟨(-2496985518021036458227748),(-2496985518021036448954718)⟩⟩] +lemma kernel9_0_r4_12_eq : ∀ k : Fin 16, kernel9_0Expr 4 12 k = kernel9_0_r4_12 k := by decide +kernel +noncomputable def kernel9_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-2795721730551372733399614),(-2795721730551372724464718)⟩,⟨(-2377233704685950894755205),(-2377233704685950885787887)⟩⟩,⟨⟨(-2754424369801026418530506),(-2754424369801026409873649)⟩,⟨(-2263638547402051464183577),(-2263638547402051455496328)⟩⟩,⟨⟨(-2713132074225963341336462),(-2713132074225963332951595)⟩,⟨(-2155911340683733321278406),(-2155911340683733312865066)⟩⟩,⟨⟨(-2671977516980590238598459),(-2671977516980590230466455)⟩,⟨(-2053775019590361405489395),(-2053775019590361397330720)⟩⟩,⟨⟨(-2631080010319515923202167),(-2631080010319515915320817)⟩,⟨(-1956963952095836123037457),(-1956963952095836115131142)⟩⟩,⟨⟨(-2590546548109485904133160),(-2590546548109485896481590)⟩,⟨(-1865223708382535585750292),(-1865223708382535578075352)⟩⟩,⟨⟨(-2550472783772688284777556),(-2550472783772688277351110)⟩,⟨(-1778310810850499173959819),(-1778310810850499166511512)⟩⟩,⟨⟨(-2510943946573432112033331),(-2510943946573432104815653)⟩,⟨(-1695992468298405692738735),(-1695992468298405685500609)⟩⟩,⟨⟨(-2472035699136875261973378),(-2472035699136875254964149)⟩,⟨(-1618046297418495270922449),(-1618046297418495263894108)⟩⟩,⟨⟨(-2433814939051508208545974),(-2433814939051508201726193)⟩,⟨(-1544260034452734305774747),(-1544260034452734298937105)⟩⟩,⟨⟨(-2396340547358335434812750),(-2396340547358335428178892)⟩,⟨(-1474431239581778419812163),(-1474431239581778413161624)⟩⟩,⟨⟨(-2359664086670846552604148),(-2359664086670846546142151)⟩,⟨(-1408366996361120799653458),(-1408366996361120793175885)⟩⟩,⟨⟨(-2323830451602503385240018),(-2323830451602503378949521)⟩,⟨(-1345883608279627993089411),(-1345883608279627986784381)⟩⟩,⟨⟨(-2288878474104021570473494),(-2288878474104021564338666)⟩,⟨(-1286806294293815225212043),(-1286806294293815219063657)⟩⟩,⟨⟨(-2254841486232500652659323),(-2254841486232500646677542)⟩,⟨(-1230968884986010783717897),(-1230968884986010777723478)⟩⟩,⟨⟨(-2221747842789636852598226),(-2221747842789636846757316)⟩,⟨(-1178213520805286157255156),(-1178213520805286151402469)⟩⟩] +lemma kernel9_0_r4_13_eq : ∀ k : Fin 16, kernel9_0Expr 4 13 k = kernel9_0_r4_13 k := by decide +kernel +noncomputable def kernel9_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-2189621406177902358150154),(-2189621406177902352451404)⟩,⟨(-1128390353675946967331859),(-1128390353675946961622143)⟩⟩,⟨⟨(-2158481995732648053195659),(-2158481995732648047624092)⟩,⟨(-1081357253098738790853336),(-1081357253098738785271560)⟩⟩,⟨⟨(-2128345803695432964253908),(-2128345803695432958807621)⟩,⟨(-1036979517723966545287200),(-1036979517723966539831417)⟩⟩,⟨⟨(-2099225779900255662018162),(-2099225779900255656686524)⟩,⟨(-995129593242702864667045),(-995129593242702859326577)⟩⟩,⟨⟨(-2071131987150421670770136),(-2071131987150421665553956)⟩,⟨(-955686797321423954044642),(-955686797321423948820258)⟩⟩,⟨⟨(-2044071929170103244598841),(-2044071929170103239485690)⟩,⟨(-918537052196027157939119),(-918537052196027152818349)⟩⟩,⟨⟨(-2018050852921731932844921),(-2018050852921731927833460)⟩,⟨(-883572625442535608974401),(-883572625442535603955868)⟩⟩,⟨⟨(-1993072026988636161868855),(-1993072026988636156949713)⟩,⟨(-850691879353184201593524),(-850691879353184196667821)⟩⟩,⟨⟨(-1969136997632155160235654),(-1969136997632155155410740)⟩,⟨(-819799029267332527112495),(-819799029267332522281500)⟩⟩,⟨⟨(-1946245824044125686901400),(-1946245824044125682158807)⟩,⟨(-790803911136113639007322),(-790803911136113634259094)⟩⟩,⟨⟨(-1924397294229392446821890),(-1924397294229392442160710)⟩,⟨(-763621758537278129668925),(-763621758537278125002528)⟩⟩,⟨⟨(-1903589122869029641901449),(-1903589122869029637313329)⟩,⟨(-738172989301733932113073),(-738172989301733927520123)⟩⟩,⟨⟨(-1883818132433427007630154),(-1883818132433427003116616)⟩,⟨(-714383001865244631089875),(-714383001865244626571867)⟩⟩,⟨⟨(-1865080418735394958651228),(-1865080418735394954202056)⟩,⟨(-692181981417092595091440),(-692181981417092590638133)⟩⟩,⟨⟨(-1847371502037049147298918),(-1847371502037049142913533)⟩,⟨(-671504715881726335489991),(-671504715881726331100782)⟩⟩,⟨⟨(-1830686464750480756217447),(-1830686464750480751888301)⟩,⟨(-652290421739011089801513),(-652290421739011085468830)⟩⟩] +lemma kernel9_0_r4_14_eq : ∀ k : Fin 16, kernel9_0Expr 4 14 k = kernel9_0_r4_14 k := by decide +kernel +noncomputable def kernel9_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-1815020076701111608242328),(-1815020076701111603972019)⟩,⟨(-634482579663232733881479),(-634482579663232729607898)⟩⟩,⟨⟨(-1800366908854152884097796),(-1800366908854152879876021)⟩,⟨(-618028779940040239697768),(-618028779940040235472966)⟩⟩,⟨⟨(-1786721436338689914875387),(-1786721436338689910701795)⟩,⟨(-602880577603650155288345),(-602880577603650151111949)⟩⟩,⟨⟨(-1774078131540539781919369),(-1774078131540539777787045)⟩,⟨(-588993357223502839329495),(-588993357223502835194572)⟩⟩,⟨⟨(-1762431547974092044452319),(-1762431547974092040363192)⟩,⟨(-576326207259803902330605),(-576326207259803898239065)⟩⟩,⟨⟨(-1751776395584748952421739),(-1751776395584748948366934)⟩,⟨(-564841803900678396335139),(-564841803900678392278089)⟩⟩,⟨⟨(-1742107608077219561935163),(-1742107608077219557914478)⟩,⟨(-554506304289704829516668),(-554506304289704825493887)⟩⟩,⟨⟨(-1733420402810670117204581),(-1733420402810670113211575)⟩,⟨(-545289249051096970357523),(-545289249051096966362555)⟩⟩,⟨⟨(-1725710333749458693622389),(-1725710333749458689659777)⟩,⟨(-537163474020499001372760),(-537163474020498997408306)⟩⟩,⟨⟨(-1718973337907744607578290),(-1718973337907744603636928)⟩,⟨(-530105031092007255061295),(-530105031092007251118192)⟩⟩,⟨⟨(-1713205775677514377611779),(-1713205775677514373691538)⟩,⟨(-524093118096399441093699),(-524093118096399437171805)⟩⟩,⟨⟨(-1708404465382351792266002),(-1708404465382351788360780)⟩,⟨(-519110017631424956695148),(-519110017631424952788344)⟩⟩,⟨⟨(-1704566712353440464226202),(-1704566712353440460338126)⟩,⟨(-515141044772186143464426),(-515141044772186139574824)⟩⟩,⟨⟨(-1701690332779659410247012),(-1701690332779659406367854)⟩,⟨(-512174503597930871004320),(-512174503597930867123679)⟩⟩,⟨⟨(-1699773672540048463678926),(-1699773672540048459808560)⟩,⟨(-510201652480802811391540),(-510201652480802807519718)⟩⟩,⟨⟨(-1698815621184210640485210),(-1698815621184210636617749)⟩,⟨(-509216678092087492281275),(-509216678092087488412374)⟩⟩] +lemma kernel9_0_r4_15_eq : ∀ k : Fin 16, kernel9_0Expr 4 15 k = kernel9_0_r4_15 k := by decide +kernel +noncomputable def kernel9_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel9_0_r4_0,kernel9_0_r4_1,kernel9_0_r4_2,kernel9_0_r4_3,kernel9_0_r4_4,kernel9_0_r4_5,kernel9_0_r4_6,kernel9_0_r4_7,kernel9_0_r4_8,kernel9_0_r4_9,kernel9_0_r4_10,kernel9_0_r4_11,kernel9_0_r4_12,kernel9_0_r4_13,kernel9_0_r4_14,kernel9_0_r4_15] +lemma kernel9_0_r4_eq (i k : Fin 16) : kernel9_0Expr 4 i k = kernel9_0_r4 i k := by + fin_cases i + · exact kernel9_0_r4_0_eq k + · exact kernel9_0_r4_1_eq k + · exact kernel9_0_r4_2_eq k + · exact kernel9_0_r4_3_eq k + · exact kernel9_0_r4_4_eq k + · exact kernel9_0_r4_5_eq k + · exact kernel9_0_r4_6_eq k + · exact kernel9_0_r4_7_eq k + · exact kernel9_0_r4_8_eq k + · exact kernel9_0_r4_9_eq k + · exact kernel9_0_r4_10_eq k + · exact kernel9_0_r4_11_eq k + · exact kernel9_0_r4_12_eq k + · exact kernel9_0_r4_13_eq k + · exact kernel9_0_r4_14_eq k + · exact kernel9_0_r4_15_eq k +noncomputable def kernel9_0_r5_0 : Fin 16 → CBox := ![⟨⟨196696671260708029259951316924,196696671260708029514284054305⟩,⟨21116227037097889550583252122,21116227037097889803302946091⟩⟩,⟨⟨196649796961461289165484413474,196649796961461289419792751495⟩,⟨21051587993439335983716738218,21051587993439336236410964914⟩⟩,⟨⟨196556030591538992709257795054,196556030591538992963516893971⟩,⟨20922411275779853406425579943,20922411275779853659068434678⟩⟩,⟨⟨196415336799668611206484954824,196415336799668611460669952817⟩,⟨20728899488319733757876703128,20728899488319734010442264487⟩⟩,⟨⟨196227663037126331928075378626,196227663037126332182161370586⟩,⟨20471356199445617983224338464,20471356199445618235686649756⟩⟩,⟨⟨195992940129383372715391008683,195992940129383372969353043127⟩,⟨20150185535882880798871671227,20150185535882881051204740035⟩⟩,⟨⟨195711083034681329227125773908,195711083034681329480938824313⟩,⟨19765891640988975685020446695,19765891640988975937198218852⟩⟩,⟨⟨195381991786446658420490433974,195381991786446658674129414258⟩,⟨19319077996710725465456763933,19319077996710725717453141571⟩⟩,⟨⟨195005552615697868722091367897,195005552615697868975531070979⟩,⟨18810446608630557843384878379,18810446608630558095173661090⟩⟩,⟨⟨194581639248853111322234875694,194581639248853111575450039757⟩,⟨18240797053442654328617505949,18240797053442654580172459515⟩⟩,⟨⟨194110114375612807729581790672,194110114375612807982546971352⟩,⟨17611025388132474011693339655,17611025388132474262988070803⟩⟩,⟨⟨193590831280873879041840906839,193590831280873879294530636789⟩,⟨16922122920084579979619804504,16922122920084580230627922781⟩⟩,⟨⟨193023635633931249020416939391,193023635633931249272805459399⟩,⟨16175174837316447094492435460,16175174837316447345187286912⟩⟩,⟨⟨192408367427540776273693460886,192408367427540776525755082201⟩,⟨15371358698032120606661614656,15371358698032120857016646205⟩⟩,⟨⟨191744863058757843431894342009,191744863058757843683602955878⟩,⟨14511942778711207639497422503,14511942778711207889485694088⟩⟩,⟨⟨191032957542829716444498644720,191032957542829716695828303285⟩,⟨13598284279997510310915982977,13598284279997510560510750207⟩⟩] +lemma kernel9_0_r5_0_eq : ∀ k : Fin 16, kernel9_0Expr 5 0 k = kernel9_0_r5_0 k := by decide +kernel +noncomputable def kernel9_0_r5_1 : Fin 16 → CBox := ![⟨⟨190272486850809715943142901835,190272486850809716194067029443⟩,⟨12631827389729237362869375387,12631827389729237612043303538⟩⟩,⟨⟨189463290360979449499956525961,189463290360979449750448963749⟩,⟨11614101202560528249451838487,11614101202560528498178048335⟩⟩,⟨⟨188605213413614071668652750438,188605213413614071918686483389⟩,⟨10546717495763124271525669037,10546717495763124519776466815⟩⟩,⟨⟨187698109958106993478195982015,187698109958106993727744558473⟩,⟨9431368360968314911089958716,9431368360968315158838256411⟩⟩,⟨⟨186741845280986865339816743860,186741845280986865588852512982⟩,⟨8269823691813407245724466423,8269823691813407492942022340⟩⟩,⟨⟨185736298802913194801403707712,185736298802913195049900076400⟩,⟨7063928527694279757574620807,7063928527694280004234296427⟩⟩,⟨⟨184681366932329788372263290272,184681366932329788620192106534⟩,⟨5815600254096182756473356346,5815600254096183002546503300⟩⟩,⟨⟨183576965963089436842587106606,183576965963089437089921465808⟩,⟨4526825660278649446575660379,4526825660278649692034925935⟩⟩,⟨⟨182423035003040953678131719087,182423035003040953924842625239⟩,⟨3199657855426712560630489889,3199657855426712805446482295⟩⟩,⟨⟨181219538920292816688003027993,181219538920292816934063599883⟩,⟨1836213044748821171739011130,1836213044748821415884503549⟩⟩,⟨⟨179966471293638164340486538665,179966471293638164585867295471⟩,⟨438667167400870554529037099,438667167400870797974258246⟩⟩,⟨⟨178663857353445575353032293443,178663857353445575597706008535⟩,⟨(-990747601455744937066474702),(-990747601455744694348989802)⟩⟩,⟨⟨177311756899190619561478153708,177311756899190619805414315656⟩,⟨(-2449746481697797061958194315),(-2449746481697796819999137726)⟩⟩,⟨⟨175910267179726190709386854410,175910267179726190952558461311⟩,⟨(-3935995849139057229913013279),(-3935995849139056988739514896)⟩⟩,⟨⟨174459525722366557974884426626,174459525722366558217260514020⟩,⟨(-5447117122531702756830838014),(-5447117122531702516473930525)⟩⟩,⟨⟨172959713096892185969925022423,172959713096892186211478257920⟩,⟨(-6980690772390354530253626900),(-6980690772390354290740657316)⟩⟩] +lemma kernel9_0_r5_1_eq : ∀ k : Fin 16, kernel9_0Expr 5 1 k = kernel9_0_r5_1 k := by decide +kernel +noncomputable def kernel9_0_r5_2 : Fin 16 → CBox := ![⟨⟨171411055600670782320364102715,171411055600670782561062183933⟩,⟨(-8534260446812872928383564903),(-8534260446812872689746788534)⟩⟩,⟨⟨169813827851235657588247077033,169813827851235657828063284815⟩,⟨(-10105337208910480398280903005),(-10105337208910480160546939582)⟩⟩,⟨⟨168168355272866037927406084382,168168355272866038166307875434⟩,⟨(-11691403879885785306314944345),(-11691403879885785069516174773)⟩⟩,⟨⟨166475016463975948150523632614,166475016463975948388483862656⟩,⟨(-13289919481214259075651365503),(-13289919481214258839814719182)⟩⟩,⟨⟨164734245432438936139123079023,164734245432438936376107703612⟩,⟨(-14898323768796270786558706219),(-14898323768796270551717948716)⟩⟩,⟨⟨162946533686355241047641915841,162946533686355241283624715796⟩,⟨(-16514041851356690707540286981),(-16514041851356690473721309025)⟩⟩,⟨⟨161112432168205754108723878805,161112432168205754343670700745⟩,⟨(-18134488884781271777195234825),(-18134488884781271544431796875)⟩⟩,⟨⟨159232553020832740258901721027,159232553020832740492785976056⟩,⟨(-19757074833497571955317073211),(-19757074833497571723635322589)⟩⟩,⟨⟨157307571174239949820265863432,157307571174239950053051466875⟩,⟨(-21379209289437262207196186261),(-21379209289437261976631701005)⟩⟩,⟨⟨155338225742813321129251090323,155338225742813321360913035212⟩,⟨(-22998306338560524827944461588),(-22998306338560524598521698678)⟩⟩,⟨⟨153325321223226518645358560162,153325321223226518875861120204⟩,⟨(-24611789464386185208927529126),(-24611789464386184980681600075)⟩⟩,⟨⟨151269728484011314019977532945,151269728484011314249295117417⟩,⟨(-26217096477457557992909564042),(-26217096477457557765865402790)⟩⟩,⟨⟨149172385538539228817471346997,149172385538539229045566197958⟩,⟨(-27811684459188036884686260331),(-27811684459188036658880903633)⟩⟩,⟨⟨147034298093975525472512207081,147034298093975525699360706790⟩,⟨(-29393034708076485775048033520),(-29393034708076485550504343060)⟩⟩,⟨⟨144856539869626845624836112691,144856539869626845850401075027⟩,⟨(-30958657675864693350334176647),(-30958657675864693127088519024)⟩⟩,⟨⟨142640252679006522273741223879,142640252679006522497998552164⟩,⟨(-32506097880831623977265556041),(-32506097880831623755341175812)⟩⟩] +lemma kernel9_0_r5_2_eq : ∀ k : Fin 16, kernel9_0Expr 5 2 k = kernel9_0_r5_2 k := by decide +kernel +noncomputable def kernel9_0_r5_3 : Fin 16 → CBox := ![⟨⟨140386646270883491457200778142,140386646270883491680110619353⟩,⟨(-34032938785085885555429056693),(-34032938785085885334864891610)⟩⟩,⟨⟨138096997925558152380674446370,138096997925558152602215671152⟩,⟨(-35536807622432519942168432099),(-35536807622432519722984673900)⟩⟩,⟨⟨135772651803617529182021418347,135772651803617529402155574704⟩,⟨(-37015380163156479390988512538),(-37015380163156479173222613969)⟩⟩,⟨⟨133415018045458447992659643097,133415018045458448211364668134⟩,⟨(-38466385401886323543133657186),(-38466385401886323326806661259)⟩⟩,⟨⟨131025571620926668620879281145,131025571620926668838114129296⟩,⟨(-39887610154580829711639145740),(-39887610154580829496791018032)⟩⟩,⟨⟨128605850929497262240112598106,128605850929497262455858507269⟩,⟨(-41276903550621132046486595974),(-41276903550621131833135009770)⟩⟩,⟨⟨126157456152512039409743774647,126157456152512039623961294969⟩,⟨(-42632181405994145527195616641),(-42632181405994145315378874796)⟩⟩,⟨⟨123682047360088338042427653840,123682047360088338255097319924⟩,⟨(-43951430463621490047015963913),(-43951430463621489836752378445)⟩⟩,⟨⟨121181342376414633132785169464,121181342376414633343864136987⟩,⟨(-45232712487023633392967239643),(-45232712487023633184298444043)⟩⟩,⟨⟨118657114408246735390918745982,118657114408246735600392106307⟩,⟨(-46474168193712846194269855072),(-46474168193712845987209556198)⟩⟩,⟨⟨116111189442508192980729190700,116111189442508193188605248464⟩,⟨(-47674021014981714540614829606),(-47674021014981714335144407635)⟩⟩,⟨⟨113545443419974203105677277615,113545443419974203312308115247⟩,⟨(-48830580669096858312948504732),(-48830580669096858108646308290)⟩⟩,⟨⟨110961799193074131739102531101,110961799193074131944443418368⟩,⟨(-49942246535320175898908485313),(-49942246535320175695819286318)⟩⟩,⟨⟨108362223276877869840448850472,108362223276877870044486605962⟩,⟨(-51007510816661937337175623492),(-51007510816661937135312749379)⟩⟩,⟨⟨105748722403329985918232919488,105748722403329986120924972681⟩,⟨(-52024961479820466312811724555),(-52024961479820466112217921649)⟩⟩,⟨⟨103123339889757292835986273990,103123339889757293037317698044⟩,⟨(-52993284961380600358399488208),(-52993284961380600159089956507)⟩⟩] +lemma kernel9_0_r5_3_eq : ∀ k : Fin 16, kernel9_0Expr 5 3 k = kernel9_0_r5_3 k := by decide +kernel +noncomputable def kernel9_0_r5_4 : Fin 16 → CBox := ![⟨⟨100488151833594457794338229306,100488151833594457994261290855⟩,⟨(-53911268630025735925213537311),(-53911268630025735727236310843)⟩⟩,⟨⟨97845263146143216126069882824,97845263146143216324575549890⟩,⟨(-54777802995263715576183487367),(-54777802995263715379548005675)⟩⟩,⟨⟨95196803438998350664822291860,95196803438998350861866645489⟩,⟨(-55591883653972296914059914423),(-55591883653972296718810529906)⟩⟩,⟨⟨92544922777532838455148969655,92544922777532838650720095248⟩,⟨(-56352612966932199480622732260),(-56352612966932199286771888964)⟩⟩,⟨⟨89891787316530674683653966341,89891787316530674877703345812⟩,⟨(-57059201458431057430598617455),(-57059201458431057238195388245)⟩⟩,⟨⟨87239574833684386982033622972,87239574833684387174555214902⟩,⟨(-57710968932985889216832048889),(-57710968932985889025883132134)⟩⟩,⟨⟨84590470177231013340698786208,84590470177231013531647827354⟩,⟨(-58307345304240405741384456998),(-58307345304240405551935296246)⟩⟩,⟨⟨81946660644481565112916481242,81946660644481565302284649114⟩,⟨(-58847871132141713779422807631),(-58847871132141713591482497152)⟩⟩,⟨⟨79310331308401367060799186677,79310331308401367248535775188⟩,⟨(-59332197865583482662278818097),(-59332197865583482475898856618)⟩⟩,⟨⟨76683660309719226579195677869,76683660309719226765300147299⟩,⟨(-59760087788813864516531735858),(-59760087788813864331713553305)⟩⟩,⟨⟨74068814132279663001566107150,74068814132279663185993399098⟩,⟨(-60131413671040547077729328754),(-60131413671040546894518892307)⟩⟩,⟨⟨71467942879502440442320455912,71467942879502440625066376928⟩,⟨(-60446158119816186748399455912),(-60446158119816186566801951515)⟩⟩,⟨⟨68883175569875917146088043759,68883175569875917327102320059⟩,⟨(-60704412639948830741608255768),(-60704412639948830561674967525)⟩⟩,⟨⟨66316615469384300023306891027,66316615469384300202592913499⟩,⟨(-60906376400847345651277933955),(-60906376400847345473006567279)⟩⟩,⟨⟨63770335478653364497555107110,63770335478653364675068094847⟩,⟨(-61052354716374767711186243351),(-61052354716374767534622690891)⟩⟩,⟨⟨61246373592394707069808284287,61246373592394707245548642850⟩,⟨(-61142757242436253397445393744),(-61142757242436253222590434558)⟩⟩] +lemma kernel9_0_r5_4_eq : ∀ k : Fin 16, kernel9_0Expr 5 4 k = kernel9_0_r5_4 k := by decide +kernel +noncomputable def kernel9_0_r5_5 : Fin 16 → CBox := ![⟨⟨58746728448435837842756415522,58746728448435838016672279686⟩,⟨(-61178095898666295752525883732),(-61178095898666295579432580839)⟩⟩,⟨⟨56273354983243647732789277175,56273354983243647904891024799⟩,⟨(-61158982521695470190609447610),(-61158982521695470019268695431)⟩⟩,⟨⟨53828160210383811033717832278,53828160210383811203961543239⟩,⟨(-61086126258563651391332268563),(-61086126258563651221789270253)⟩⟩,⟨⟨51412999137810867777620847411,51412999137810867946011901550⟩,⟨(-60960330709897996461800360360),(-60960330709897996294051078347)⟩⟩,⟨⟨49029670839255968375973178244,49029670839255968542461856447⟩,⟨(-60782490833483792007427345955),(-60782490833483791841522852160)⟩⟩,⟨⟨46679914694274972724847910513,46679914694274972889448712765⟩,⟨(-60553589619818511703319589655),(-60553589619818511539246793504)⟩⟩,⟨⟨44365406810742695379416551793,44365406810742695542086975112⟩,⟨(-60274694552148394577618228413),(-60274694552148394415421050650)⟩⟩,⟨⟨42087756642733971661526218764,42087756642733971822276899852⟩,⟨(-59946953864337115617679592451),(-59946953864337115457348857429)⟩⟩,⟨⟨39848503815823728217055099076,39848503815823728375835831248⟩,⟨(-59571592610702619640829914620),(-59571592610702619482417297433)⟩⟩,⟨⟨37649115170871632097832830830,37649115170871632254753725304⟩,⟨(-59149908562676263338116331591),(-59149908562676263181513798247)⟩⟩,⟨⟨35490982036337800324279848262,35490982036337800479318935571⟩,⟨(-58683267947783828739444665693),(-58683267947783828584675813907)⟩⟩,⟨⟨33375417738110452039033479484,33375417738110452192204293881⟩,⟨(-58173101047016969988347526591),(-58173101047016969835400338907)⟩⟩,⟨⟨31303655354720549960208389733,31303655354720550111461334852⟩,⟨(-57620897667152965809334849975),(-57620897667152965658260444558)⟩⟩,⟨⟨29276845724678931314877735370,29276845724678931464236602259⟩,⟨(-57028202504987525097518315035),(-57028202504987524948294440913)⟩⟩,⟨⟨27296055711504900329328344100,27296055711504900476752148016⟩,⟨(-56396610420767627740869980473),(-56396610420767627593539165777)⟩⟩,⟨⟨25362266730828630352403563396,25362266730828630497911128302⟩,⟨(-55727761638347331422822159818),(-55727761638347331277367131726)⟩⟩] +lemma kernel9_0_r5_5_eq : ∀ k : Fin 16, kernel9_0Expr 5 5 k = kernel9_0_r5_5 k := by decide +kernel +noncomputable def kernel9_0_r5_6 : Fin 16 → CBox := ![⟨⟨23476373542749995279694335570,23476373542749995423235545243⟩,⟨(-55023336889738063520629953367),(-55023336889738063377102382818)⟩⟩,⟨⟨21639183311430663147472809005,21639183311430663289079622510⟩,⟨(-54285052521785650056891495262),(-54285052521785649915260975941)⟩⟩,⟨⟨19851414932691488423644159609,19851414932691488563278123706⟩,⟨(-53514655582679297372189144991),(-53514655582679297232495685243)⟩⟩,⟨⟨18113698629190433594379624008,18113698629190433732064827758⟩,⟨(-52713918905883602690819069697),(-52713918905883602553040125257)⟩⟩,⟨⟨16426575811574334990690916897,16426575811574335126381877106⟩,⟨(-51884636208884665535237905269),(-51884636208884665399420507273)⟩⟩,⟨⟨14790499202837551898781113325,14790499202837552032513077905⟩,⟨(-51028617223857302375251276545),(-51028617223857302241361702987)⟩⟩,⟨⟨13205833221988452108739410111,13205833221988452240476832929⟩,⟨(-50147682876994575875163881935),(-50147682876994575743239207470)⟩⟩,⟨⟨11672854622027095188846719123,11672854622027095318618814140⟩,⟨(-49243660532796205278786146890),(-49243660532796205148798658135)⟩⟩,⟨⟨10191753376180389982896200136,10191753376180390110776621060⟩,⟨(-48318379319092292175713588962),(-48318379319092292047591134804)⟩⟩,⟨⟨8762633805330105150886636345,8762633805330105276955079498⟩,⟨(-47373665547987012071075444269),(-47373665547987011944739790344)⟩⟩,⟨⟨7385515938609709046440348507,7385515938609709170660043201⟩,⟨(-46411338247247759595519054209),(-46411338247247759471008438987)⟩⟩,⟨⟨6060337098243008273854913405,6060337098243008396255643216⟩,⟨(-45433204815943367239282160212),(-45433204815943367116568223341)⟩⟩,⟨⟨4786953698855403816656979964,4786953698855403937194316618⟩,⟨(-44441056817355478973689387577),(-44441056817355478852817986908)⟩⟩,⟨⟨3565143250711283150863769165,3565143250711283269579160597⟩,⟨(-43436665921355305374274830662),(-43436665921355305255205887857)⟩⟩,⟨⟨2394606555622118534592280655,2394606555622118651452084537⟩,⟨(-42421780007559445639518546860),(-42421780007559445522287080968)⟩⟩,⟨⟨1274970083632237397490892101,1274970083632237512529461308⟩,⟨(-41398119439659093487216143705),(-41398119439659093371789119058)⟩⟩] +lemma kernel9_0_r5_6_eq : ∀ k : Fin 16, kernel9_0Expr 5 6 k = kernel9_0_r5_6 k := by decide +kernel +noncomputable def kernel9_0_r5_7 : Fin 16 → CBox := ![⟨⟨205788518025436681393734345,205788518025436794566713775⟩,⟨(-40367373520362789817378449290),(-40367373520362789703801549578)⟩⟩,⟨⟨(-813452544292440421714006782),(-813452544292440310357560900)⟩,⟨(-39331197135410120843635335787),(-39331197135410120731860753909)⟩⟩,⟨⟨(-1783333750390770583369538266),(-1783333750390770473859944050)⟩,⟨(-38291207594108647141542958057),(-38291207594108647031602273940)⟩⟩,⟨⟨(-2704499020580012001495990327),(-2704499020580011893794721270)⟩,⟨(-37248981672825184627378825922),(-37248981672825184519234702481)⟩⟩,⟨⟨(-3577652463289577965991609765),(-3577652463289577860137001609)⟩,⟨(-36206052866831629456258815836),(-36206052866831629349950792535)⟩⟩,⟨⟨(-4403555189677742055338947623),(-4403555189677741951280669844)⟩,⟨(-35163908854871053309737149370),(-35163908854871053205216008955)⟩⟩,⟨⟨(-5183022042192880072710775425),(-5183022042192879970475738373)⟩,⟨(-34123989179777917225706386415),(-34123989179777917123000168664)⟩⟩,⟨⟨(-5916918251328565915438440148),(-5916918251328565814984413060)⟩,⟨(-33087683147462936179397402037),(-33087683147462936078464922737)⟩⟩,⟨⟨(-6606156034763904179891453401),(-6606156034763904081188680611)⟩,⟨(-32056327945564157662638970351),(-32056327945564157563451584087)⟩⟩,⟨⟨(-7251691152957186485250827174),(-7251691152957186388222241761)⟩,⟨(-31031206982076750050834762125),(-31031206982076749953316374251)⟩⟩,⟨⟨(-7854519435068117280822939095),(-7854519435068117185495320633)⟩,⟨(-30013548443310118259919971254),(-30013548443310118164098342071)⟩⟩,⟨⟨(-8415673288824485054435864291),(-8415673288824484960766969240)⟩,⟨(-29004524069587262238923889628),(-29004524069587262144757665826)⟩⟩,⟨⟨(-8936218207626640979846143176),(-8936218207626640887871116487)⟩,⟨(-28005248146202424516725658444),(-28005248146202424424250900623)⟩⟩,⟨⟨(-9417249287801206364341345061),(-9417249287801206274006302179)⟩,⟨(-27016776706293334972762067336),(-27016776706293334881925696562)⟩⟩,⟨⟨(-9859887768478075536375201210),(-9859887768478075447703652550)⟩,⟨(-26040106941467672111295162751),(-26040106941467672022121522919)⟩⟩,⟨⟨(-10265277606076281716636725702),(-10265277606076281629583667414)⟩,⟨(-25076176815253238244210602245),(-25076176815253238156655427254)⟩⟩] +lemma kernel9_0_r5_7_eq : ∀ k : Fin 16, kernel9_0Expr 5 7 k = kernel9_0_r5_7 k := by decide +kernel +noncomputable def kernel9_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-10634582094849136779946084162),(-10634582094849136694540619404)⟩,⟨(-24125864873720893576181196503),(-24125864873720893490277872730)⟩⟩,⟨⟨(-10968980544361905220369833063),(-10968980544361905136513761812)⟩,⟨(-23189990246961186881086544667),(-23189990246961186796759422684)⟩⟩,⟨⟨(-11269665024160927630314851606),(-11269665024160927548030882928)⟩,⟨(-22269312834482099606015249965),(-22269312834482099523286331914)⟩⟩,⟨⟨(-11537837185246464467077779219),(-11537837185246464386321069343)⟩,⟨(-21364533667038189340835583044),(-21364533667038189259659257014)⟩⟩,⟨⟨(-11774705167287536759179673124),(-11774705167287536679981356142)⟩,⟨(-20476295436902043535652519493),(-20476295436902043456059211364)⟩⟩,⟨⟨(-11981480599820662361840471624),(-11981480599820662284144468606)⟩,⟨(-19605183188148267385617334030),(-19605183188148267307550186896)⟩⟩,⟨⟨(-12159375704960567523398062005),(-12159375704960567447223857056)⟩,⟨(-18751725158138737021397439016),(-18751725158138736944875217598)⟩⟩,⟨⟨(-12309600508424577724086687494),(-12309600508424577649387627415)⟩,⟨(-17916393761075641353874954204),(-17916393761075641278850239610)⟩⟩,⟨⟨(-12433360164938248594807070763),(-12433360164938248521613729152)⟩,⟨(-17099606704225602639135559600),(-17099606704225602565638216193)⟩⟩,⟨⟨(-12531852403352549666298325809),(-12531852403352549594550472415)⟩,⟨(-16301728227213212208373436173),(-16301728227213212136342468348)⟩⟩,⟨⟨(-12606265096067065384177988788),(-12606265096067065313892067881)⟩,⟨(-15523070454634584174453226677),(-15523070454634584103904368075)⟩⟩,⟨⟨(-12657773956623547966143085718),(-12657773956623547897271229373)⟩,⟨(-14763894852149613722144856444),(-14763894852149613653029496328)⟩⟩,⟨⟨(-12687540368613852546616717787),(-12687540368613852479183812204)⟩,⟨(-14024413776173806332535210737),(-14024413776173806264877541047)⟩⟩,⟨⟨(-12696709348339679808824886714),(-12696709348339679742772591694)⟩,⟨(-13304792107304805356487448087),(-13304792107304805290228398116)⟩⟩,⟨⟨(-12686407642972264172462272354),(-12686407642972264107804246738)⟩,⟨(-12605148957682807147831194670),(-12605148957682807082983739018)⟩⟩,⟨⟨(-12657741965291525076367562332),(-12657741965291525013055292263)⟩,⟨(-11925559442595397305771459663),(-11925559442595397242286381042)⟩⟩] +lemma kernel9_0_r5_8_eq : ∀ k : Fin 16, kernel9_0Expr 5 8 k = kernel9_0_r5_8 k := by decide +kernel +noncomputable def kernel9_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-12611797365439308877620380654),(-12611797365439308815679132952)⟩,⟨(-11266056506793241820409526648),(-11266056506793241758311431296)⟩⟩,⟨⟨(-12549635739502957906637871280),(-12549635739502957846005842825)⟩,⟨(-10626632796180617683346937998),(-10626632796180617622573338401)⟩⟩,⟨⟨(-12472294474156016554997522985),(-12472294474156016495685860145)⟩,⟨(-10007242565780914572669433938),(-10007242565780914513230832429)⟩⟩,⟨⟨(-12380785226024579065433857423),(-12380785226024579007393967066)⟩,⟨(-9407803615148809285630217866),(-9407803615148809227477369726)⟩⟩,⟨⟨(-12276092833922446825173797781),(-12276092833922446768425166615)⟩,⟨(-8828199242704544847676698954),(-8828199242704544790828473417)⟩⟩,⟨⟨(-12159174361607431718451543460),(-12159174361607431662936037774)⟩,⟨(-8268280210798313165557842738),(-8268280210798313109955481020)⟩⟩,⟨⟨(-12030958268256047361191842816),(-12030958268256047306918412777)⟩,⟨(-7727866713670787514037414900),(-7727866713670787459689273358)⟩⟩,⟨⟨(-11892343703435401992207008285),(-11892343703435401939127482562)⟩,⟨(-7206750340856017105047613860),(-7206750340856017051904929937)⟩⟩,⟨⟨(-11744199922969982787938773616),(-11744199922969982736072869760)⟩,⟨(-6704696028971838432833627268),(-6704696028971838380915553984)⟩⟩,⟨⟨(-11587365821757555958448288827),(-11587365821757555907736208401)⟩,⟨(-6221443995257379079123488185),(-6221443995257379028369666147)⟩⟩,⟨⟨(-11422649579282683782859382205),(-11422649579282683733308185353)⟩,⟨(-5756711646643897949536172187),(-5756711646643897899953124407)⟩⟩,⟨⟨(-11250828413308204978507340479),(-11250828413308204930069750328)⟩,⟨(-5310195458580977815651729460),(-5310195458580977767191653100)⟩⟩,⟨⟨(-11072648436994022287294837154),(-11072648436994022239986033342)⟩,⟨(-4881572818281924448562796932),(-4881572818281924401240364257)⟩⟩,⟨⟨(-10888824614498048563251789411),(-10888824614498048517015939458)⟩,⟨(-4470503827497218134795679674),(-4470503827497218088554565383)⟩⟩,⟨⟨(-10700040809955328686058890229),(-10700040809955328640901482783)⟩,⟨(-4076633060370233355006216808),(-4076633060370233309851432343)⟩⟩,⟨⟨(-10506949924607137170196203442),(-10506949924607137125884868892)⟩,⟨(-3699591272372568215742739585),(-3699591272372568171441323202)⟩⟩] +lemma kernel9_0_r5_9_eq : ∀ k : Fin 16, kernel9_0Expr 5 9 k = kernel9_0_r5_9 k := by decide +kernel +noncomputable def kernel9_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-10310174116761036002850465386),(-10310174116761035959389408662)⟩,⟨(-3338997056754747226046424450),(-3338997056754747182602125428)⟩⟩,⟨⟨(-10110305099204096422418618418),(-10110305099204096379759658982)⟩,⟨(-2994458445379491733775486652),(-2994458445379491691139707851)⟩⟩,⟨⟨(-9907904508663240386240426092),(-9907904508663240344397135735)⟩,⟨(-2665574451227083574157519802),(-2665574451227083532343424353)⟩⟩,⟨⟨(-9703504341907325875355982936),(-9703504341907325834292331305)⟩,⟨(-2351936550273655533566840056),(-2351936550273655492538012040)⟩⟩,⟨⟨(-9497607453113472566681245134),(-9497607453113472526418525125)⟩,⟨(-2053130100841791213596572170),(-2053130100841791173373923228)⟩⟩,⟨⟨(-9290688107173411180375452523),(-9290688107173411140869105377)⟩,⟨(-1768735698907060344953629482),(-1768735698907060305492248378)⟩⟩,⟨⟨(-9083192583692492294656610643),(-9083192583692492255918597203)⟩,⟨(-1498330468212696404319273845),(-1498330468212696365630770744)⟩⟩,⟨⟨(-8875539826532518338616666363),(-8875539826532518300611410332)⟩,⟨(-1241489284396372037073016639),(-1241489284396371999121491469)⟩⟩,⟨⟨(-8668122133867850684031717741),(-8668122133867850646781182583)⟩,⟨(-997785932666959294380805488),(-997785932666959257187895410)⟩⟩,⟨⟨(-8461305883860368129216819988),(-8461305883860368092674833711)⟩,⟨(-766794198884471114895088492),(-766794198884471078414330314)⟩⟩,⟨⟨(-8255432291210895374193291487),(-8255432291210895338370413234)⟩,⟨(-548088894192437241935165302),(-548088894192437206176822167)⟩⟩,⟨⟨(-8050818190010781891366030925),(-8050818190010781856227431131)⟩,⟨(-341246813628308918433216607),(-341246813628308883362192555)⟩⟩,⟨⟨(-7847756838495527024883490330),(-7847756838495526990447280985)⟩,⟨(-145847629393809222881962567),(-145847629393809188516095925)⟩⟩,⟨⟨(-7646518741490894554455502903),(-7646518741490894520678985180)⟩,⟨38525280296701772900865069,38525280296701806604509541⟩⟩,⟨⟨(-7447352486539072379896898110),(-7447352486539072346789446448)⟩,⟨212284065655805033311537758,212284065655805066343831390⟩⟩,⟨⟨(-7250485589896407480200899550),(-7250485589896407447728657036)⟩,⟨375835701720585209464248317,375835701720585241859262414⟩⟩] +lemma kernel9_0_r5_10_eq : ∀ k : Fin 16, kernel9_0Expr 5 10 k = kernel9_0_r5_10 k := by decide +kernel +noncomputable def kernel9_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-7056125348803452060665806606),(-7056125348803452028848405063)⟩,⟨529581345202113286797153921,529581345202113318535484574⟩⟩,⟨⟨(-6864459696640942101927173939),(-6864459696640942070720333382)⟩,⟨673915750124131303133554815,673915750124131334259667344⟩⟩,⟨⟨(-6675658057800427527249036551),(-6675658057800427496661130631)⟩,⟨809226740450561452322930413,809226740450561482828651817⟩⟩,⟨⟨(-6489872199314206651420985182),(-6489872199314206621419331097)⟩,⟨935894737782245655955570230,935894737782245685873751607⟩⟩,⟨⟨(-6307237076504702380787068165),(-6307237076504702351387355563)⟩,⟨1054292342101918779547713910,1054292342101918808862850179⟩⟩,⟨⟨(-6127871670127265473864391074),(-6127871670127265445026680574)⟩,⟨1164783963462129182061075042,1164783963462129210813248719⟩⟩,⟨⟨(-5951879812691510063831277795),(-5951879812691510035563128761)⟩,⟨1267725502442884884259815483,1267725502442884912441628161⟩⟩,⟨⟨(-5779351001853685643345577834),(-5779351001853685615615611287)⟩,⟨1363464077153413524794580227,1363464077153413552437539147⟩⟩,⟨⟨(-5610361198975372727750828993),(-5610361198975372700575957100)⟩,⟨1452337794514730811254020518,1452337794514730838341362924⟩⟩,⟨⟨(-5444973611141158265036974408),(-5444973611141158238376625770)⟩,⟨1534675563535836084906438729,1534675563535836111478840302⟩⟩,⟨⟨(-5283239455119198601056286108),(-5283239455119198574917353633)⟩,⟨1610796948285393710442433122,1610796948285393736493127650⟩⟩,⟨⟨(-5125198701933102421085110795),(-5125198701933102395437628316)⟩,⟨1681012058261800378364883624,1681012058261800403923931437⟩⟩,⟨⟨(-4970880800890843601438761621),(-4970880800890843576296660037)⟩,⟨1745621473876660150870854802,1745621473876660175924441716⟩⟩,⟨⟨(-4820305382086011025103670657),(-4820305382086011000430256636)⟩,⟨1804916204788971348911578582,1804916204788971373496472012⟩⟩,⟨⟨(-4673482936548268717765462894),(-4673482936548268693567105717)⟩,⟨1859177678858859931493769865,1859177678858859955603698188⟩⟩,⟨⟨(-4530415473373163440936113547),(-4530415473373163417184308586)⟩,⟨1908677759529574140676493556,1908677759529574164340027053⟩⟩] +lemma kernel9_0_r5_11_eq : ∀ k : Fin 16, kernel9_0Expr 5 11 k = kernel9_0_r5_11 k := by decide +kernel +noncomputable def kernel9_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-4391097153306180695724862410),(-4391097153306180672435568390)⟩,⟨1953678789493805017643780444,1953678789493805040845052840⟩⟩,⟨⟨(-4255514898392086104530749173),(-4255514898392086081666009613)⟩,⟨1994433658554360655819194847,1994433658554360678596459144⟩⟩,⟨⟨(-4123648977428034262440962544),(-4123648977428034240004226675)⟩,⟨2031185893648970200433067897,2031185893648970222785962859⟩⟩,⟨⟨(-3995473567077678119145250844),(-3995473567077678097109657222)⟩,⟨2064169769073729380849728893,2064169769073729402804974968⟩⟩,⟨⟨(-3870957288613620309026340262),(-3870957288613620287404723724)⟩,⟨2093610435008659847794833969,2093610435008659869339487702⟩⟩,⟨⟨(-3750063720357114950999302573),(-3750063720357114929758494100)⟩,⟨2119724062521313656173151641,2119724062521313677340242860⟩⟩,⟨⟨(-3632751885977100489102791373),(-3632751885977100468248553694)⟩,⟨2142718003299624544620310568,2142718003299624565403968248⟩⟩,⟨⟨(-3518976718895607301310946066),(-3518976718895607280817870778)⟩,⟨2162790962442642146119039994,2162790962442642166544545571⟩⟩,⟨⟨(-3408689503123559410337965439),(-3408689503123559390220389543)⟩,⟨2180133182716778178289978702,2180133182716778198342897957⟩⟩,⟨⟨(-3301838290920229595155995210),(-3301838290920229575380364718)⟩,⟨2194926638765181210697717592,2194926638765181230411478622⟩⟩,⟨⟨(-3198368297731389538286441754),(-3198368297731389518858250875)⟩,⟨2207345239838317189329268942,2207345239838317208698280041⟩⟩,⟨⟨(-3098222274915821222401258621),(-3098222274915821203296530850)⟩,⟨2217555039694286989909431981,2217555039694287008957556618⟩⟩,⟨⟨(-3001340860817640288206099355),(-3001340860817640269436787857)⟩,⟨2225714452397422000981934416,2225714452397422019697131156⟩⟩,⟨⟨(-2907662910783158167926745157),(-2907662910783158149462893124)⟩,⟨2231974472822867162021671595,2231974472822867180433786953⟩⟩,⟨⟨(-2817125806756119625210021784),(-2817125806756119607053075660)⟩,⟨2236478900752831028098605033,2236478900752831046206104126⟩⟩,⟨⟨(-2729665747114445088223755958),(-2729665747114445070344980283)⟩,⟨2239364567526636098511327770,2239364567526636116342843731⟩⟩] +lemma kernel9_0_r5_12_eq : ∀ k : Fin 16, kernel9_0Expr 5 12 k = kernel9_0_r5_12 k := by decide +kernel +noncomputable def kernel9_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-2645218017435436122430675356),(-2645218017435436104844572778)⟩,⟨2240761564281359032108496595,2240761564281359049649449833⟩⟩,⟨⟨(-2563717242895122053997921627),(-2563717242895122036674040532)⟩,⟨2240793470892464532125278925,2240793470892464549406023008⟩⟩,⟨⟨(-2485097623021389296666623481),(-2485097623021389279610554098)⟩,⟨2239577584794197870662280209,2239577584794197887677148371⟩⟩,⟨⟨(-2409293149530091903138029101),(-2409293149530091886328866957)⟩,⟨2237225148927430906181753326,2237225148927430922951562917⟩⟩,⟨⟨(-2336237807978836114901018277),(-2336237807978836098350579621)⟩,⟨2233841578128007271573421940,2233841578128007288086287920⟩⟩,⟨⟨(-2265865763974899581393983264),(-2265865763974899565075542431)⟩,⟨2229526683331285082378297966,2229526683331285098660861656⟩⟩,⟨⟨(-2198111534672114725016084272),(-2198111534672114708935071852)⟩,⟨2224374893028437675279117525,2224374893028437691325881251⟩⟩,⟨⟨(-2132910146286832256228515472),(-2132910146286832240365164742)⟩,⟨2218475471467076950078175502,2218475471467076965908830229⟩⟩,⟨⟨(-2070197278355590291912839240),(-2070197278355590276280583313)⟩,⟨2211912733142865103409411818,2211912733142865119010465022⟩⟩,⟨⟨(-2009909395447139537600797378),(-2009909395447139522172233786)⟩,⟨2204766253179955058984725294,2204766253179955074383505496⟩⟩,⟨⟨(-1951983867029294857896711966),(-1951983867029294842677131144)⟩,⟨2197111073246342883559494311,2197111073246342898750652565⟩⟩,⟨⟨(-1896359076176963649928745001),(-1896359076176963634899451563)⟩,⟨2189017902695539259748774025,2189017902695539274750940132⟩⟩,⟨⟨(-1842974517791892751715403101),(-1842974517791892736887769413)⟩,⟨2180553314668399380355205867,2180553314668399395156955038⟩⟩,⟨⟨(-1791770886987414510305706328),(-1791770886987414495655322614)⟩,⟨2171779936928532803025831178,2171779936928532817651509954⟩⟩,⟨⟨(-1742690158272980640382794099),(-1742690158272980625914834967)⟩,⟨2162756637241500244541938095,2162756637241500258986320972⟩⟩,⟨⟨(-1695675656153756322786090611),(-1695675656153756308482842269)⟩,⟨2153538703142056828568680948,2153538703142056842849425066⟩⟩] +lemma kernel9_0_r5_13_eq : ∀ k : Fin 16, kernel9_0Expr 5 13 k = kernel9_0_r5_13 k := by decide +kernel +noncomputable def kernel9_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-1650672117740198555597125170),(-1650672117740198541472192251)⟩,⟨2144178015965093724988126242,2144178015965093739091582092⟩⟩,⟨⟨(-1607625747941539421111119138),(-1607625747941539407138671741)⟩,⟨2134723219044742795466779204,2134723219044742809418721339⟩⟩,⟨⟨(-1566484267795599673963428778),(-1566484267795599660148526273)⟩,⟨2125219880012428422498318091,2125219880012428436293642876⟩⟩,⟨⟨(-1527196956465519891039968091),(-1527196956465519877365804746)⟩,⟨2115710647148568834111018999,2115710647148568847766483239⟩⟩,⟨⟨(-1489714687411950737713706565),(-1489714687411950724191355042)⟩,⟨2106235399764241571101607634,2106235399764241584606098945⟩⟩,⟨⟨(-1453989959227112918244213078),(-1453989959227112904851160317)⟩,⟨2096831392608532810950240089,2096831392608532824326224355⟩⟩,⟨⟨(-1419976921595030627090247343),(-1419976921595030613831449429)⟩,⟨2087533394314588571591868447,2087533394314588584834350994⟩⟩,⟨⟨(-1387631396820257183358582216),(-1387631396820257170218044472)⟩,⟨2078373819912678998005388693,2078373819912679011130321814⟩⟩,⟨⟨(-1356910897345633778753167957),(-1356910897345633765743689929)⟩,⟨2069382857451976978808505182,2069382857451976991803054995⟩⟩,⟨⟨(-1327774639658126625109756778),(-1327774639658126612207755904)⟩,⟨2060588588784340920476714932,2060588588784340933364422615⟩⟩,⟨⟨(-1300183554960638505849343587),(-1300183554960638493059662925)⟩,⟨2052017104573279381160815240,2052017104573279393936803894⟩⟩,⟨⟨(-1274100296966942192827758166),(-1274100296966942180135137166)⟩,⟨2043692613599561748241960327,2043692613599561760921453550⟩⟩,⟨⟨(-1249489247156580461592044388),(-1249489247156580449007366719)⟩,⟨2035637546441721661063030872,2035637546441721673635114363⟩⟩,⟨⟨(-1226316517806756886648542997),(-1226316517806756874150740080)⟩,⟨2027872653615073585207645206,2027872653615073597693351689⟩⟩,⟨⟨(-1204549953098931439020515740),(-1204549953098931426614315931)⟩,⟨2020417098256920406239629341,2020417098256920418634200489⟩⟩,⟨⟨(-1184159128579055776154692157),(-1184159128579055763825477724)⟩,⟨2013288543448460852373128458,2013288543448460864691149433⟩⟩] +lemma kernel9_0_r5_14_eq : ∀ k : Fin 16, kernel9_0Expr 5 14 k = kernel9_0_r5_14 k := by decide +kernel +noncomputable def kernel9_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-1165115349232148603252687027),(-1165115349232148591013619814)⟩,⟨2006503234265596663622490001,2006503234265596675850772011⟩⟩,⟨⟨(-1147391646414228684035524049),(-1147391646414228671863734810)⟩,⟨2000076074651474197175462990,2000076074651474209336843071⟩⟩,⟨⟨(-1130962773867493073833692831),(-1130962773867493061733773262)⟩,⟨1994020699203253814179929565,1994020699203253826269789090⟩⟩,⟨⟨(-1115805203028046517720655931),(-1115805203028046505678562144)⟩,⟨1988349539964359814661613829,1988349539964359826693967521⟩⟩,⟨⟨(-1101897117819445233436759854),(-1101897117819445221463261347)⟩,⟨1983073888311397418554889306,1983073888311397430518942863⟩⟩,⟨⟨(-1089218409109800420486993924),(-1089218409109800408562024995)⟩,⟨1978203952022101557378894991,1978203952022101569294685365⟩⟩,⟨⟨(-1077750668995175560669089726),(-1077750668995175548797096319)⟩,⟨1973748907607172019958925970,1973748907607172031821982545⟩⟩,⟨⟨(-1067477185057484885430670761),(-1067477185057484873598097091)⟩,⟨1969716947984714602314581781,1969716947984714614138433655⟩⟩,⟨⟨(-1058382934731032862897397089),(-1058382934731032851116129397)⟩,⟨1966115325571309128812650451,1966115325571309140585388646⟩⟩,⟨⟨(-1050454579898197741981010616),(-1050454579898197730228714056)⟩,⟨1962950390858520428796867190,1962950390858520440540799680⟩⟩,⟨⟨(-1043680461821524909324800788),(-1043680461821524897605960802)⟩,⟨1960227626538012743438454438,1960227626538012755149072614⟩⟩,⟨⟨(-1038050596506624501368689991),(-1038050596506624489670386551)⟩,⟨1957951677232374241285810746,1957951677232374252976009556⟩⟩,⟨⟨(-1033556670577726700148865018),(-1033556670577726688482030399)⟩,⟨1956126374882356657623234657,1956126374882356669282059938⟩⟩,⟨⟨(-1030192037735499941880560505),(-1030192037735499930225901740)⟩,⟨1954754759834533757439183069,1954754759834533769085902396⟩⟩,⟨⟨(-1027951715854742835306786949),(-1027951715854742823668587573)⟩,⟨1953839097666427707264208897,1953839097666427718894516352⟩⟩,⟨⟨(-1026832384767779570344883817),(-1026832384767779558710572049)⟩,⟨1953380891778989257823904788,1953380891778989269450347849⟩⟩] +lemma kernel9_0_r5_15_eq : ∀ k : Fin 16, kernel9_0Expr 5 15 k = kernel9_0_r5_15 k := by decide +kernel +noncomputable def kernel9_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel9_0_r5_0,kernel9_0_r5_1,kernel9_0_r5_2,kernel9_0_r5_3,kernel9_0_r5_4,kernel9_0_r5_5,kernel9_0_r5_6,kernel9_0_r5_7,kernel9_0_r5_8,kernel9_0_r5_9,kernel9_0_r5_10,kernel9_0_r5_11,kernel9_0_r5_12,kernel9_0_r5_13,kernel9_0_r5_14,kernel9_0_r5_15] +lemma kernel9_0_r5_eq (i k : Fin 16) : kernel9_0Expr 5 i k = kernel9_0_r5 i k := by + fin_cases i + · exact kernel9_0_r5_0_eq k + · exact kernel9_0_r5_1_eq k + · exact kernel9_0_r5_2_eq k + · exact kernel9_0_r5_3_eq k + · exact kernel9_0_r5_4_eq k + · exact kernel9_0_r5_5_eq k + · exact kernel9_0_r5_6_eq k + · exact kernel9_0_r5_7_eq k + · exact kernel9_0_r5_8_eq k + · exact kernel9_0_r5_9_eq k + · exact kernel9_0_r5_10_eq k + · exact kernel9_0_r5_11_eq k + · exact kernel9_0_r5_12_eq k + · exact kernel9_0_r5_13_eq k + · exact kernel9_0_r5_14_eq k + · exact kernel9_0_r5_15_eq k +noncomputable def kernel9_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel9_0_r0,kernel9_0_r1,kernel9_0_r2,kernel9_0_r3,kernel9_0_r4,kernel9_0_r5] +lemma kernel9_0_eq (j : Fin 6) (i k : Fin 16) : kernel9_0Expr j i k = kernel9_0 j i k := by + fin_cases j + · exact kernel9_0_r0_eq i k + · exact kernel9_0_r1_eq i k + · exact kernel9_0_r2_eq i k + · exact kernel9_0_r3_eq i k + · exact kernel9_0_r4_eq i k + · exact kernel9_0_r5_eq i k +lemma kernel9_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel9_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(9:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel9_0_eq] + unfold kernel9_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans9_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel9_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans9 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel9_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩] +lemma kernel9_1_r0_0_eq : ∀ k : Fin 16, kernel9_1Expr 0 0 k = kernel9_1_r0_0 k := by decide +kernel +noncomputable def kernel9_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-31),24⟩,⟨(-8),42⟩⟩,⟨⟨(-42),8⟩,⟨(-31),24⟩⟩,⟨⟨(-42),8⟩,⟨(-31),24⟩⟩,⟨⟨(-42),8⟩,⟨(-31),24⟩⟩,⟨⟨(-42),8⟩,⟨(-31),24⟩⟩,⟨⟨(-42),8⟩,⟨(-31),24⟩⟩,⟨⟨(-42),8⟩,⟨(-31),24⟩⟩,⟨⟨(-42),8⟩,⟨(-31),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩] +lemma kernel9_1_r0_1_eq : ∀ k : Fin 16, kernel9_1Expr 0 1 k = kernel9_1_r0_1 k := by decide +kernel +noncomputable def kernel9_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-23),24⟩⟩,⟨⟨(-42),4⟩,⟨(-22),24⟩⟩,⟨⟨(-42),4⟩,⟨(-22),24⟩⟩,⟨⟨(-42),4⟩,⟨(-22),24⟩⟩,⟨⟨(-42),4⟩,⟨(-22),24⟩⟩,⟨⟨(-42),4⟩,⟨(-22),24⟩⟩,⟨⟨(-42),4⟩,⟨(-22),24⟩⟩] +lemma kernel9_1_r0_2_eq : ∀ k : Fin 16, kernel9_1Expr 0 2 k = kernel9_1_r0_2 k := by decide +kernel +noncomputable def kernel9_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-24),22⟩,⟨(-43),4⟩⟩,⟨⟨(-25),22⟩,⟨(-43),4⟩⟩,⟨⟨(-25),22⟩,⟨(-43),4⟩⟩,⟨⟨(-25),22⟩,⟨(-43),4⟩⟩,⟨⟨(-4),43⟩,⟨(-25),22⟩⟩] +lemma kernel9_1_r0_3_eq : ∀ k : Fin 16, kernel9_1Expr 0 3 k = kernel9_1_r0_3 k := by decide +kernel +noncomputable def kernel9_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),43⟩,⟨(-25),22⟩⟩,⟨⟨(-4),43⟩,⟨(-25),22⟩⟩,⟨⟨(-4),43⟩,⟨(-25),22⟩⟩,⟨⟨(-4),43⟩,⟨(-25),22⟩⟩,⟨⟨(-4),43⟩,⟨(-25),22⟩⟩,⟨⟨(-4),43⟩,⟨(-25),22⟩⟩,⟨⟨(-4),43⟩,⟨(-25),21⟩⟩,⟨⟨(-4),43⟩,⟨(-25),21⟩⟩,⟨⟨(-4),43⟩,⟨(-25),21⟩⟩,⟨⟨(-4),43⟩,⟨(-25),21⟩⟩,⟨⟨(-4),43⟩,⟨(-25),21⟩⟩,⟨⟨(-4),43⟩,⟨(-25),21⟩⟩,⟨⟨(-21),25⟩,⟨(-4),43⟩⟩,⟨⟨(-21),25⟩,⟨(-4),43⟩⟩,⟨⟨(-21),25⟩,⟨(-4),43⟩⟩,⟨⟨(-21),25⟩,⟨(-4),43⟩⟩] +lemma kernel9_1_r0_4_eq : ∀ k : Fin 16, kernel9_1Expr 0 4 k = kernel9_1_r0_4 k := by decide +kernel +noncomputable def kernel9_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-21),25⟩,⟨(-4),43⟩⟩,⟨⟨(-21),25⟩,⟨(-4),43⟩⟩,⟨⟨(-21),25⟩,⟨(-4),43⟩⟩,⟨⟨(-21),25⟩,⟨(-4),43⟩⟩,⟨⟨(-21),25⟩,⟨(-3),43⟩⟩,⟨⟨(-21),25⟩,⟨(-3),43⟩⟩,⟨⟨(-43),3⟩,⟨(-21),25⟩⟩,⟨⟨(-43),3⟩,⟨(-21),25⟩⟩,⟨⟨(-43),3⟩,⟨(-21),25⟩⟩,⟨⟨(-43),3⟩,⟨(-20),26⟩⟩,⟨⟨(-43),3⟩,⟨(-20),26⟩⟩,⟨⟨(-43),3⟩,⟨(-20),26⟩⟩,⟨⟨(-43),3⟩,⟨(-20),26⟩⟩,⟨⟨(-43),3⟩,⟨(-20),26⟩⟩,⟨⟨(-43),3⟩,⟨(-20),26⟩⟩,⟨⟨(-43),20⟩,⟨(-45),29⟩⟩] +lemma kernel9_1_r0_5_eq : ∀ k : Fin 16, kernel9_1Expr 0 5 k = kernel9_1_r0_5 k := by decide +kernel +noncomputable def kernel9_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-43),20⟩,⟨(-45),29⟩⟩,⟨⟨(-26),20⟩,⟨(-42),3⟩⟩,⟨⟨(-26),20⟩,⟨(-42),3⟩⟩,⟨⟨(-26),20⟩,⟨(-42),3⟩⟩,⟨⟨(-26),20⟩,⟨(-42),3⟩⟩,⟨⟨(-26),20⟩,⟨(-42),3⟩⟩,⟨⟨(-26),20⟩,⟨(-42),3⟩⟩,⟨⟨(-29),45⟩,⟨(-42),20⟩⟩,⟨⟨(-29),45⟩,⟨(-42),19⟩⟩,⟨⟨(-3),42⟩,⟨(-26),19⟩⟩,⟨⟨(-3),42⟩,⟨(-26),19⟩⟩,⟨⟨(-3),42⟩,⟨(-26),19⟩⟩,⟨⟨(-3),42⟩,⟨(-26),19⟩⟩,⟨⟨(-3),42⟩,⟨(-26),19⟩⟩,⟨⟨(-3),42⟩,⟨(-26),19⟩⟩,⟨⟨(-3),42⟩,⟨(-26),19⟩⟩] +lemma kernel9_1_r0_6_eq : ∀ k : Fin 16, kernel9_1Expr 0 6 k = kernel9_1_r0_6 k := by decide +kernel +noncomputable def kernel9_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-19),42⟩,⟨(-29),45⟩⟩,⟨⟨(-19),42⟩,⟨(-29),45⟩⟩,⟨⟨(-19),42⟩,⟨(-29),45⟩⟩,⟨⟨(-19),42⟩,⟨(-29),45⟩⟩,⟨⟨(-45),29⟩,⟨(-19),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-44),29⟩,⟨(-18),42⟩⟩,⟨⟨(-42),18⟩,⟨(-44),29⟩⟩,⟨⟨(-42),18⟩,⟨(-44),29⟩⟩,⟨⟨(-42),18⟩,⟨(-44),29⟩⟩] +lemma kernel9_1_r0_7_eq : ∀ k : Fin 16, kernel9_1Expr 0 7 k = kernel9_1_r0_7 k := by decide +kernel +noncomputable def kernel9_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-42),18⟩,⟨(-44),29⟩⟩,⟨⟨(-42),18⟩,⟨(-44),29⟩⟩,⟨⟨(-42),17⟩,⟨(-44),29⟩⟩,⟨⟨(-42),17⟩,⟨(-44),29⟩⟩,⟨⟨(-42),17⟩,⟨(-44),29⟩⟩,⟨⟨(-29),44⟩,⟨(-42),17⟩⟩,⟨⟨(-29),44⟩,⟨(-42),17⟩⟩,⟨⟨(-29),44⟩,⟨(-42),17⟩⟩,⟨⟨(-29),44⟩,⟨(-42),17⟩⟩,⟨⟨(-29),43⟩,⟨(-42),17⟩⟩,⟨⟨(-29),43⟩,⟨(-42),17⟩⟩,⟨⟨(-29),43⟩,⟨(-42),17⟩⟩,⟨⟨(-29),43⟩,⟨(-41),17⟩⟩,⟨⟨(-29),43⟩,⟨(-41),16⟩⟩,⟨⟨(-16),41⟩,⟨(-29),43⟩⟩,⟨⟨(-16),41⟩,⟨(-29),43⟩⟩] +lemma kernel9_1_r0_8_eq : ∀ k : Fin 16, kernel9_1Expr 0 8 k = kernel9_1_r0_8 k := by decide +kernel +noncomputable def kernel9_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-16),41⟩,⟨(-29),43⟩⟩,⟨⟨(-16),41⟩,⟨(-29),43⟩⟩,⟨⟨(-16),41⟩,⟨(-29),43⟩⟩,⟨⟨(-16),41⟩,⟨(-29),43⟩⟩,⟨⟨(-16),41⟩,⟨(-29),43⟩⟩,⟨⟨(-16),41⟩,⟨(-29),43⟩⟩,⟨⟨(-41),16⟩,⟨(-43),29⟩⟩,⟨⟨(-41),16⟩,⟨(-43),29⟩⟩,⟨⟨(-41),16⟩,⟨(-42),29⟩⟩,⟨⟨(-41),15⟩,⟨(-42),29⟩⟩,⟨⟨(-41),15⟩,⟨(-42),29⟩⟩,⟨⟨(-41),15⟩,⟨(-42),29⟩⟩,⟨⟨(-41),15⟩,⟨(-42),29⟩⟩,⟨⟨(-41),15⟩,⟨(-42),29⟩⟩,⟨⟨(-29),42⟩,⟨(-41),15⟩⟩,⟨⟨(-29),42⟩,⟨(-41),15⟩⟩] +lemma kernel9_1_r0_9_eq : ∀ k : Fin 16, kernel9_1Expr 0 9 k = kernel9_1_r0_9 k := by decide +kernel +noncomputable def kernel9_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-29),42⟩,⟨(-41),15⟩⟩,⟨⟨(-29),42⟩,⟨(-41),15⟩⟩,⟨⟨(-29),42⟩,⟨(-41),15⟩⟩,⟨⟨(-29),42⟩,⟨(-40),15⟩⟩,⟨⟨(-29),42⟩,⟨(-40),14⟩⟩,⟨⟨(-29),42⟩,⟨(-40),14⟩⟩,⟨⟨(-14),40⟩,⟨(-29),42⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-14),40⟩,⟨(-29),41⟩⟩,⟨⟨(-41),29⟩,⟨(-14),40⟩⟩] +lemma kernel9_1_r0_10_eq : ∀ k : Fin 16, kernel9_1Expr 0 10 k = kernel9_1_r0_10 k := by decide +kernel +noncomputable def kernel9_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),29⟩,⟨(-13),40⟩⟩,⟨⟨(-41),29⟩,⟨(-13),40⟩⟩,⟨⟨(-41),29⟩,⟨(-13),40⟩⟩,⟨⟨(-41),29⟩,⟨(-13),40⟩⟩,⟨⟨(-41),29⟩,⟨(-13),40⟩⟩,⟨⟨(-40),29⟩,⟨(-13),40⟩⟩,⟨⟨(-40),29⟩,⟨(-13),40⟩⟩,⟨⟨(-40),29⟩,⟨(-13),40⟩⟩,⟨⟨(-39),13⟩,⟨(-40),29⟩⟩,⟨⟨(-39),13⟩,⟨(-40),29⟩⟩,⟨⟨(-39),13⟩,⟨(-40),29⟩⟩,⟨⟨(-39),13⟩,⟨(-40),29⟩⟩,⟨⟨(-39),12⟩,⟨(-40),29⟩⟩,⟨⟨(-39),12⟩,⟨(-40),29⟩⟩,⟨⟨(-39),12⟩,⟨(-40),29⟩⟩,⟨⟨(-39),12⟩,⟨(-40),29⟩⟩] +lemma kernel9_1_r0_11_eq : ∀ k : Fin 16, kernel9_1Expr 0 11 k = kernel9_1_r0_11 k := by decide +kernel +noncomputable def kernel9_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-39),12⟩,⟨(-40),29⟩⟩,⟨⟨(-39),12⟩,⟨(-40),29⟩⟩,⟨⟨(-39),12⟩,⟨(-40),29⟩⟩,⟨⟨(-29),40⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),12⟩⟩,⟨⟨(-29),39⟩,⟨(-39),11⟩⟩,⟨⟨(-29),29⟩,⟨(-29),11⟩⟩,⟨⟨(-29),29⟩,⟨(-29),11⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩] +lemma kernel9_1_r0_12_eq : ∀ k : Fin 16, kernel9_1Expr 0 12 k = kernel9_1_r0_12 k := by decide +kernel +noncomputable def kernel9_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-11),29⟩,⟨(-28),29⟩⟩,⟨⟨(-10),29⟩,⟨(-28),29⟩⟩,⟨⟨(-10),29⟩,⟨(-28),29⟩⟩,⟨⟨(-10),29⟩,⟨(-28),29⟩⟩,⟨⟨(-10),29⟩,⟨(-28),29⟩⟩,⟨⟨(-10),29⟩,⟨(-28),29⟩⟩,⟨⟨(-29),28⟩,⟨(-10),29⟩⟩,⟨⟨(-29),28⟩,⟨(-10),29⟩⟩,⟨⟨(-29),28⟩,⟨(-10),29⟩⟩] +lemma kernel9_1_r0_13_eq : ∀ k : Fin 16, kernel9_1Expr 0 13 k = kernel9_1_r0_13 k := by decide +kernel +noncomputable def kernel9_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),28⟩,⟨(-10),29⟩⟩,⟨⟨(-29),28⟩,⟨(-10),29⟩⟩,⟨⟨(-29),28⟩,⟨(-10),29⟩⟩,⟨⟨(-29),28⟩,⟨(-10),29⟩⟩,⟨⟨(-29),28⟩,⟨(-10),29⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩] +lemma kernel9_1_r0_14_eq : ∀ k : Fin 16, kernel9_1Expr 0 14 k = kernel9_1_r0_14 k := by decide +kernel +noncomputable def kernel9_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩,⟨⟨(-28),28⟩,⟨(-10),28⟩⟩] +lemma kernel9_1_r0_15_eq : ∀ k : Fin 16, kernel9_1Expr 0 15 k = kernel9_1_r0_15 k := by decide +kernel +noncomputable def kernel9_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel9_1_r0_0,kernel9_1_r0_1,kernel9_1_r0_2,kernel9_1_r0_3,kernel9_1_r0_4,kernel9_1_r0_5,kernel9_1_r0_6,kernel9_1_r0_7,kernel9_1_r0_8,kernel9_1_r0_9,kernel9_1_r0_10,kernel9_1_r0_11,kernel9_1_r0_12,kernel9_1_r0_13,kernel9_1_r0_14,kernel9_1_r0_15] +lemma kernel9_1_r0_eq (i k : Fin 16) : kernel9_1Expr 0 i k = kernel9_1_r0 i k := by + fin_cases i + · exact kernel9_1_r0_0_eq k + · exact kernel9_1_r0_1_eq k + · exact kernel9_1_r0_2_eq k + · exact kernel9_1_r0_3_eq k + · exact kernel9_1_r0_4_eq k + · exact kernel9_1_r0_5_eq k + · exact kernel9_1_r0_6_eq k + · exact kernel9_1_r0_7_eq k + · exact kernel9_1_r0_8_eq k + · exact kernel9_1_r0_9_eq k + · exact kernel9_1_r0_10_eq k + · exact kernel9_1_r0_11_eq k + · exact kernel9_1_r0_12_eq k + · exact kernel9_1_r0_13_eq k + · exact kernel9_1_r0_14_eq k + · exact kernel9_1_r0_15_eq k +noncomputable def kernel9_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-582715382134),(-582715382092)⟩,⟨685694638356,685694638398⟩⟩,⟨⟨(-581920878471),(-581920878429)⟩,⟨684380354329,684380354370⟩⟩,⟨⟨(-580335003778),(-580335003737)⟩,⟨681759061792,681759061833⟩⟩,⟨⟨(-577964003583),(-577964003542)⟩,⟨677845245999,677845246040⟩⟩,⟨⟨(-574817196953),(-574817196912)⟩,⟨672660471478,672660471519⟩⟩,⟨⟨(-570906917881),(-570906917839)⟩,⟨666233188253,666233188294⟩⟩,⟨⟨(-566248437939),(-566248437897)⟩,⟨658598477082,658598477123⟩⟩,⟨⟨(-560859870751),(-560859870704)⟩,⟨649797737342,649797737389⟩⟩,⟨⟨(-554762059225),(-554762059184)⟩,⟨639878320785,639878320826⟩⟩,⟨⟨(-547978446298),(-547978446257)⟩,⟨628893116155,628893116197⟩⟩,⟨⟨(-540534930491),(-540534930450)⟩,⟨616900089338,616900089379⟩⟩,⟨⟨(-532459707257),(-532459707216)⟩,⟨603961784900,603961784942⟩⟩,⟨⟨(-523783097508),(-523783097466)⟩,⟨590144794674,590144794716⟩⟩,⟨⟨(-514537364796),(-514537364755)⟩,⟨575519199674,575519199715⟩⟩,⟨⟨(-504756522458),(-504756522411)⟩,⟨560157992107,560157992153⟩⟩,⟨⟨(-494476132396),(-494476132355)⟩,⟨544136483452,544136483493⟩⟩] +lemma kernel9_1_r1_0_eq : ∀ k : Fin 16, kernel9_1Expr 1 0 k = kernel9_1_r1_0 k := by decide +kernel +noncomputable def kernel9_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-483733097128),(-483733097081)⟩,⟨527531705834,527531705880⟩⟩,⟨⟨(-472565446572),(-472565446531)⟩,⟨510421812783,510421812824⟩⟩,⟨⟨(-461012121361),(-461012121319)⟩,⟨492885485965,492885486006⟩⟩,⟨⟨(-449112754387),(-449112754341)⟩,⟨475001353902,475001353948⟩⟩,⟨⟨(-436907452012),(-436907451965)⟩,⟨456847428695,456847428741⟩⟩,⟨⟨(-424436576891),(-424436576849)⟩,⟨438500565815,438500565857⟩⟩,⟨⟨(-411740533622),(-411740533580)⟩,⟨420035952265,420035952307⟩⟩,⟨⟨(-398859559156),(-398859559115)⟩,⟨401526627267,401526627308⟩⟩,⟨⟨(-385833519045),(-385833518999)⟩,⟨383043039764,383043039811⟩⟩,⟨⟨(-372701711162),(-372701711120)⟩,⟨364652645412,364652645454⟩⟩,⟨⟨(-359502678179),(-359502678133)⟩,⟨346419546419,346419546466⟩⟩,⟨⟨(-346274029753),(-346274029712)⟩,⟨328404175858,328404175899⟩⟩,⟨⟨(-333052275839),(-333052275798)⟩,⟨310663027914,310663027955⟩⟩,⟨⟨(-319872671744),(-319872671698)⟩,⟨293248435192,293248435239⟩⟩,⟨⟨(-306769076053),(-306769076011)⟩,⟨276208392767,276208392809⟩⟩,⟨⟨(-293773821887),(-293773821845)⟩,⟨259586429117,259586429158⟩⟩] +lemma kernel9_1_r1_1_eq : ∀ k : Fin 16, kernel9_1Expr 1 1 k = kernel9_1_r1_1 k := by decide +kernel +noncomputable def kernel9_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-280917602220),(-280917602178)⟩,⟨243421522731,243421522772⟩⟩,⟨⟨(-268229369520),(-268229369473)⟩,⟨227748062787,227748062834⟩⟩,⟨⟨(-255736250228),(-255736250186)⟩,⟨212595852590,212595852631⟩⟩,⟨⟨(-243463473986),(-243463473944)⟩,⟨197990152711,197990152753⟩⟩,⟨⟨(-231434317829),(-231434317787)⟩,⟨183951761843,183951761885⟩⟩,⟨⟨(-219670065018),(-219670064977)⟩,⟨170497131833,170497131875⟩⟩,⟨⟨(-208189978550),(-208189978508)⟩,⟨157638514209,157638514251⟩⟩,⟨⟨(-197011288777),(-197011288730)⟩,⟨145384134231,145384134278⟩⟩,⟨⟨(-186149194686),(-186149194644)⟩,⟨133738389592,133738389634⟩⟩,⟨⟨(-175616878381),(-175616878334)⟩,⟨122702069580,122702069627⟩⟩,⟨⟨(-165425532036),(-165425531994)⟩,⟨112272591409,112272591451⟩⟩,⟨⟨(-155584396488),(-155584396446)⟩,⟨102444250176,102444250218⟩⟩,⟨⟨(-146100810838),(-146100810791)⟩,⟨93208478685,93208478732⟩⟩,⟨⟨(-136980272035),(-136980271993)⟩,⟨84554114006,84554114048⟩⟩,⟨⟨(-128226503475),(-128226503428)⟩,⟨76467667463,76467667510⟩⟩,⟨⟨(-119841531780),(-119841531733)⟩,⟨68933594998,68933595046⟩⟩] +lemma kernel9_1_r1_2_eq : ∀ k : Fin 16, kernel9_1Expr 1 2 k = kernel9_1_r1_2 k := by decide +kernel +noncomputable def kernel9_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-111825770672),(-111825770630)⟩,⟨61934565097,61934565139⟩⟩,⟨⟨(-104178110897),(-104178110850)⟩,⟨55451721723,55451721770⟩⟩,⟨⟨(-96896015272),(-96896015230)⟩,⟨49464939961,49464940003⟩⟩,⟨⟨(-89975617684),(-89975617642)⟩,⟨43953072292,43953072334⟩⟩,⟨⟨(-83411825248),(-83411825206)⟩,⟨38894183716,38894183759⟩⟩,⟨⟨(-77198422363),(-77198422321)⟩,⟨34265774310,34265774352⟩⟩,⟨⟨(-71328176084),(-71328176041)⟩,⟨30044987724,30044987766⟩⟩,⟨⟨(-65792941562),(-65792941520)⟩,⟨26208805088,26208805130⟩⟩,⟨⟨(-60583766907),(-60583766865)⟩,⟨22734223252,22734223295⟩⟩,⟨⟨(-55690996580),(-55690996533)⟩,⟨19598416955,19598417003⟩⟩,⟨⟨(-51104372752),(-51104372705)⟩,⟨16778884990,16778885038⟩⟩,⟨⟨(-46813133633),(-46813133585)⟩,⟨14253579847,14253579894⟩⟩,⟨⟨(-42806108519),(-42806108477)⟩,⟨12001021543,12001021586⟩⟩,⟨⟨(-39071808803),(-39071808761)⟩,⟨10000395441,10000395483⟩⟩,⟨⟨(-35598514585),(-35598514542)⟩,⟨8231635059,8231635101⟩⟩,⟨⟨(-32374356459),(-32374356417)⟩,⟨6675490210,6675490253⟩⟩] +lemma kernel9_1_r1_3_eq : ∀ k : Fin 16, kernel9_1Expr 1 3 k = kernel9_1_r1_3 k := by decide +kernel +noncomputable def kernel9_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-29387392170),(-29387392127)⟩,⟨5313581094,5313581136⟩⟩,⟨⟨(-26625677932),(-26625677890)⟩,⟨4128439658,4128439701⟩⟩,⟨⟨(-24077334159),(-24077334116)⟩,⟨3103538478,3103538520⟩⟩,⟨⟨(-21730605581),(-21730605533)⟩,⟨2223308645,2223308692⟩⟩,⟨⟨(-19573915579),(-19573915531)⟩,⟨1473147349,1473147397⟩⟩,⟨⟨(-17595914948),(-17595914906)⟩,⟨839416268,839416311⟩⟩,⟨⟨(-15785524889),(-15785524847)⟩,⟨309431709,309431752⟩⟩,⟨⟨(-14131974547),(-14131974504)⟩,⟨(-128552524),(-128552482)⟩⟩,⟨⟨(-12624833206),(-12624833163)⟩,⟨(-485368415),(-485368372)⟩⟩,⟨⟨(-11254037216),(-11254037173)⟩,⟨(-770962521),(-770962478)⟩⟩,⟨⟨(-10009912092),(-10009912049)⟩,⟨(-994429032),(-994428989)⟩⟩,⟨⟨(-8883189761),(-8883189718)⟩,⟨(-1164046589),(-1164046546)⟩⟩,⟨⟨(-7865021585),(-7865021537)⟩,⟨(-1287317783),(-1287317736)⟩⟩,⟨⟨(-6946987077),(-6946987034)⟩,⟨(-1371010839),(-1371010796)⟩⟩,⟨⟨(-6121098917),(-6121098869)⟩,⟨(-1421202628),(-1421202580)⟩⟩,⟨⟨(-5379804465),(-5379804422)⟩,⟨(-1443322488),(-1443322445)⟩⟩] +lemma kernel9_1_r1_4_eq : ∀ k : Fin 16, kernel9_1Expr 1 4 k = kernel9_1_r1_4 k := by decide +kernel +noncomputable def kernel9_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-4715984008),(-4715983965)⟩,⟨(-1442196412),(-1442196369)⟩⟩,⟨⟨(-4122946323),(-4122946274)⟩,⟨(-1422090824),(-1422090776)⟩⟩,⟨⟨(-3594421494),(-3594421451)⟩,⟨(-1386755913),(-1386755869)⟩⟩,⟨⟨(-3124551745),(-3124551702)⟩,⟨(-1339467767),(-1339467724)⟩⟩,⟨⟨(-2707880138),(-2707880090)⟩,⟨(-1283069344),(-1283069295)⟩⟩,⟨⟨(-2339337778),(-2339337729)⟩,⟨(-1220009761),(-1220009713)⟩⟩,⟨⟨(-2014229630),(-2014229576)⟩,⟨(-1152381969),(-1152381915)⟩⟩,⟨⟨(-1728219263),(-1728219219)⟩,⟨(-1081958289),(-1081958246)⟩⟩,⟨⟨(-1477312745),(-1477312702)⟩,⟨(-1010224168),(-1010224125)⟩⟩,⟨⟨(-1257841863),(-1257841820)⟩,⟨(-938409589),(-938409546)⟩⟩,⟨⟨(-1066447086),(-1066447037)⟩,⟨(-867518531),(-867518483)⟩⟩,⟨⟨(-900060140),(-900060097)⟩,⟨(-798356160),(-798356116)⟩⟩,⟨⟨(-755886674),(-755886630)⟩,⟨(-731553860),(-731553816)⟩⟩,⟨⟨(-631388903),(-631388855)⟩,⟨(-667592315),(-667592265)⟩⟩,⟨⟨(-524268677),(-524268623)⟩,⟨(-606822404),(-606822349)⟩⟩,⟨⟨(-432450689),(-432450646)⟩,⟨(-549484124),(-549484080)⟩⟩] +lemma kernel9_1_r1_5_eq : ∀ k : Fin 16, kernel9_1Expr 1 5 k = kernel9_1_r1_5 k := by decide +kernel +noncomputable def kernel9_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-354066305),(-354066256)⟩,⟨(-495723767),(-495723718)⟩⟩,⟨⟨(-287437863),(-287437819)⟩,⟨(-445609219),(-445609175)⟩⟩,⟨⟨(-231063584),(-231063540)⟩,⟨(-399143561),(-399143517)⟩⟩,⟨⟨(-183603132),(-183603083)⟩,⟨(-356277156),(-356277107)⟩⟩,⟨⟨(-143863885),(-143863837)⟩,⟨(-316918269),(-316918219)⟩⟩,⟨⟨(-110788009),(-110787960)⟩,⟨(-280942298),(-280942249)⟩⟩,⟨⟨(-83440097),(-83440043)⟩,⟨(-248199798),(-248199743)⟩⟩,⟨⟨(-60995730),(-60995686)⟩,⟨(-218523363),(-218523319)⟩⟩,⟨⟨(-42730714),(-42730664)⟩,⟨(-191733556),(-191733507)⟩⟩,⟨⟨(-28011148),(-28011103)⟩,⟨(-167643773),(-167643729)⟩⟩,⟨⟨(-16284024),(-16283975)⟩,⟨(-146064380),(-146064330)⟩⟩,⟨⟨(-7068750),(-7068701)⟩,⟨(-126806135),(-126806085)⟩⟩,⟨⟨50716,50760⟩,⟨(-109682936),(-109682892)⟩⟩,⟨⟨5433071,5433120⟩,⟨(-94513908),(-94513858)⟩⟩,⟨⟨9386327,9386372⟩,⟨(-81125170),(-81125126)⟩⟩,⟨⟨12173738,12173782⟩,⟨(-69351050),(-69351006)⟩⟩] +lemma kernel9_1_r1_6_eq : ∀ k : Fin 16, kernel9_1Expr 1 6 k = kernel9_1_r1_6 k := by decide +kernel +noncomputable def kernel9_1_r1_7 : Fin 16 → CBox := ![⟨⟨14019196,14019251⟩,⟨(-59034951),(-59034896)⟩⟩,⟨⟨15112183,15112234⟩,⟨(-50029982),(-50029932)⟩⟩,⟨⟨15612171,15612215⟩,⟨(-42199186),(-42199142)⟩⟩,⟨⟨15652520,15652565⟩,⟨(-35415728),(-35415683)⟩⟩,⟨⟨15344057,15344112⟩,⟨(-29562757),(-29562702)⟩⟩,⟨⟨14778184,14778228⟩,⟨(-24533210),(-24533166)⟩⟩,⟨⟨14029621,14029665⟩,⟨(-20229520),(-20229476)⟩⟩,⟨⟨13158921,13158966⟩,⟨(-16563147),(-16563102)⟩⟩,⟨⟨12214586,12214635⟩,⟨(-13454203),(-13454152)⟩⟩,⟨⟨11234907,11234958⟩,⟨(-10830782),(-10830732)⟩⟩,⟨⟨10249721,10249772⟩,⟨(-8628616),(-8628566)⟩⟩,⟨⟨9281682,9281731⟩,⟨(-6790393),(-6790343)⟩⟩,⟨⟨8347659,8347703⟩,⟨(-5265274),(-5265229)⟩⟩,⟨⟨7459639,7459683⟩,⟨(-4008308),(-4008263)⟩⟩,⟨⟨6625718,6625769⟩,⟨(-2979983),(-2979933)⟩⟩,⟨⟨5850913,5850962⟩,⟨(-2145653),(-2145602)⟩⟩] +lemma kernel9_1_r1_7_eq : ∀ k : Fin 16, kernel9_1Expr 1 7 k = kernel9_1_r1_7 k := by decide +kernel +noncomputable def kernel9_1_r1_8 : Fin 16 → CBox := ![⟨⟨5137675,5137725⟩,⟨(-1475070),(-1475019)⟩⟩,⟨⟨4486556,4486601⟩,⟨(-941973),(-941928)⟩⟩,⟨⟨3896625,3896681⟩,⟨(-523648),(-523592)⟩⟩,⟨⟨3365838,3365883⟩,⟨(-200511),(-200466)⟩⟩,⟨⟨2891386,2891431⟩,⟨44211,44256⟩⟩,⟨⟨2469875,2469931⟩,⟨224824,224880⟩⟩,⟨⟨2097605,2097657⟩,⟨353516,353566⟩⟩,⟨⟨1770706,1770762⟩,⟨440482,440539⟩⟩,⟨⟨1485235,1485285⟩,⟨494402,494453⟩⟩,⟨⟨1237343,1237389⟩,⟨522441,522486⟩⟩,⟨⟨1023244,1023289⟩,⟨530571,530617⟩⟩,⟨⟨839376,839422⟩,⟨523672,523717⟩⟩,⟨⟨682368,682424⟩,⟨505792,505848⟩⟩,⟨⟨549068,549114⟩,⟨480172,480217⟩⟩,⟨⟨436623,436675⟩,⟨449397,449447⟩⟩,⟨⟨342335,342387⟩,⟨415526,415576⟩⟩] +lemma kernel9_1_r1_8_eq : ∀ k : Fin 16, kernel9_1Expr 1 8 k = kernel9_1_r1_8 k := by decide +kernel +noncomputable def kernel9_1_r1_9 : Fin 16 → CBox := ![⟨⟨263865,263915⟩,⟨380191,380243⟩⟩,⟨⟨199032,199082⟩,⟨344596,344648⟩⟩,⟨⟨145886,145942⟩,⟨309660,309717⟩⟩,⟨⟨102750,102801⟩,⟨276083,276135⟩⟩,⟨⟨68075,68120⟩,⟨244322,244368⟩⟩,⟨⟨40560,40617⟩,⟨214663,214720⟩⟩,⟨⟨19042,19088⟩,⟨187304,187350⟩⟩,⟨⟨2501,2553⟩,⟨162320,162370⟩⟩,⟨⟨(-9937),(-9884)⟩,⟨139696,139746⟩⟩,⟨⟨(-18993),(-18936)⟩,⟨119398,119455⟩⟩,⟨⟨(-25318),(-25266)⟩,⟨101314,101364⟩⟩,⟨⟨(-29454),(-29397)⟩,⟨85321,85378⟩⟩,⟨⟨(-31847),(-31801)⟩,⟨71268,71314⟩⟩,⟨⟨(-32897),(-32840)⟩,⟨59023,59080⟩⟩,⟨⟨(-32904),(-32852)⟩,⟨48394,48444⟩⟩,⟨⟨(-32123),(-32077)⟩,⟨39253,39299⟩⟩] +lemma kernel9_1_r1_9_eq : ∀ k : Fin 16, kernel9_1Expr 1 9 k = kernel9_1_r1_9 k := by decide +kernel +noncomputable def kernel9_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-30789),(-30738)⟩,⟨31430,31483⟩⟩,⟨⟨(-29041),(-28995)⟩,⟨24802,24848⟩⟩,⟨⟨(-27071),(-27025)⟩,⟨19211,19257⟩⟩,⟨⟨(-24948),(-24895)⟩,⟨14511,14562⟩⟩,⟨⟨(-22746),(-22700)⟩,⟨10634,10680⟩⟩,⟨⟨(-20570),(-20524)⟩,⟨7435,7481⟩⟩,⟨⟨(-18446),(-18395)⟩,⟨4852,4905⟩⟩,⟨⟨(-16423),(-16377)⟩,⟨2759,2805⟩⟩,⟨⟨(-14521),(-14464)⟩,⟨1106,1163⟩⟩,⟨⟨(-12731),(-12680)⟩,⟨(-175),(-122)⟩⟩,⟨⟨(-11081),(-11035)⟩,⟨(-1169),(-1123)⟩⟩,⟨⟨(-9576),(-9519)⟩,⟨(-1889),(-1832)⟩⟩,⟨⟨(-8224),(-8166)⟩,⟨(-2423),(-2366)⟩⟩,⟨⟨(-7005),(-6955)⟩,⟨(-2758),(-2705)⟩⟩,⟨⟨(-5914),(-5860)⟩,⟨(-2976),(-2925)⟩⟩,⟨⟨(-4961),(-4903)⟩,⟨(-3076),(-3018)⟩⟩] +lemma kernel9_1_r1_10_eq : ∀ k : Fin 16, kernel9_1Expr 1 10 k = kernel9_1_r1_10 k := by decide +kernel +noncomputable def kernel9_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-4109),(-4059)⟩,⟨(-3081),(-3027)⟩⟩,⟨⟨(-3382),(-3332)⟩,⟨(-3039),(-2986)⟩⟩,⟨⟨(-2728),(-2675)⟩,⟨(-2932),(-2882)⟩⟩,⟨⟨(-2179),(-2133)⟩,⟨(-2802),(-2755)⟩⟩,⟨⟨(-1708),(-1655)⟩,⟨(-2634),(-2583)⟩⟩,⟨⟨(-1303),(-1257)⟩,⟨(-2468),(-2422)⟩⟩,⟨⟨(-964),(-918)⟩,⟨(-2286),(-2240)⟩⟩,⟨⟨(-673),(-619)⟩,⟨(-2105),(-2054)⟩⟩,⟨⟨(-441),(-394)⟩,⟨(-1901),(-1855)⟩⟩,⟨⟨(-250),(-204)⟩,⟨(-1723),(-1677)⟩⟩,⟨⟨(-92),(-35)⟩,⟨(-1562),(-1505)⟩⟩,⟨⟨48,95⟩,⟨(-1388),(-1342)⟩⟩,⟨⟨123,170⟩,⟨(-1240),(-1194)⟩⟩,⟨⟨215,268⟩,⟨(-1102),(-1052)⟩⟩,⟨⟨262,315⟩,⟨(-952),(-902)⟩⟩,⟨⟨318,371⟩,⟨(-835),(-784)⟩⟩] +lemma kernel9_1_r1_11_eq : ∀ k : Fin 16, kernel9_1Expr 1 11 k = kernel9_1_r1_11 k := by decide +kernel +noncomputable def kernel9_1_r1_12 : Fin 16 → CBox := ![⟨⟨341,395⟩,⟨(-727),(-676)⟩⟩,⟨⟨355,409⟩,⟨(-634),(-583)⟩⟩,⟨⟨358,412⟩,⟨(-556),(-506)⟩⟩,⟨⟨353,411⟩,⟨(-452),(-395)⟩⟩,⟨⟨346,397⟩,⟨(-390),(-336)⟩⟩,⟨⟨333,390⟩,⟨(-331),(-274)⟩⟩,⟨⟨326,377⟩,⟨(-269),(-215)⟩⟩,⟨⟨306,352⟩,⟨(-225),(-179)⟩⟩,⟨⟨293,347⟩,⟨(-166),(-116)⟩⟩,⟨⟨273,324⟩,⟨(-156),(-102)⟩⟩,⟨⟨253,307⟩,⟨(-112),(-62)⟩⟩,⟨⟨245,303⟩,⟨(-87),(-29)⟩⟩,⟨⟨210,268⟩,⟨(-58),0⟩⟩,⟨⟨195,253⟩,⟨(-48),10⟩⟩,⟨⟨180,234⟩,⟨(-30),21⟩⟩,⟨⟨161,211⟩,⟨(-19),35⟩⟩] +lemma kernel9_1_r1_12_eq : ∀ k : Fin 16, kernel9_1Expr 1 12 k = kernel9_1_r1_12 k := by decide +kernel +noncomputable def kernel9_1_r1_13 : Fin 16 → CBox := ![⟨⟨146,192⟩,⟨(-1),46⟩⟩,⟨⟨131,177⟩,⟨10,56⟩⟩,⟨⟨111,162⟩,⟨21,75⟩⟩,⟨⟨112,162⟩,⟨21,75⟩⟩,⟨⟨96,143⟩,⟨39,86⟩⟩,⟨⟨78,132⟩,⟨20,70⟩⟩,⟨⟨63,117⟩,⟨31,81⟩⟩,⟨⟨63,117⟩,⟨31,81⟩⟩,⟨⟨44,102⟩,⟨42,100⟩⟩,⟨⟨33,83⟩,⟨27,81⟩⟩,⟨⟨33,83⟩,⟨26,80⟩⟩,⟨⟨33,83⟩,⟨26,80⟩⟩,⟨⟨18,64⟩,⟨45,92⟩⟩,⟨⟨18,64⟩,⟨45,92⟩⟩,⟨⟨(-1),53⟩,⟨26,76⟩⟩,⟨⟨(-1),53⟩,⟨26,76⟩⟩] +lemma kernel9_1_r1_13_eq : ∀ k : Fin 16, kernel9_1Expr 1 13 k = kernel9_1_r1_13 k := by decide +kernel +noncomputable def kernel9_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-1),53⟩,⟨26,76⟩⟩,⟨⟨(-1),53⟩,⟨26,76⟩⟩,⟨⟨(-1),54⟩,⟨26,76⟩⟩,⟨⟨(-1),54⟩,⟨26,76⟩⟩,⟨⟨(-12),35⟩,⟨11,57⟩⟩,⟨⟨(-12),35⟩,⟨11,57⟩⟩,⟨⟨(-12),35⟩,⟨11,57⟩⟩,⟨⟨(-27),20⟩,⟨22,69⟩⟩,⟨⟨(-27),20⟩,⟨22,69⟩⟩,⟨⟨(-27),20⟩,⟨22,69⟩⟩,⟨⟨(-27),20⟩,⟨22,69⟩⟩,⟨⟨(-27),20⟩,⟨22,69⟩⟩,⟨⟨(-27),20⟩,⟨22,69⟩⟩,⟨⟨(-27),20⟩,⟨22,69⟩⟩,⟨⟨(-46),8⟩,⟨4,54⟩⟩,⟨⟨(-46),8⟩,⟨4,54⟩⟩] +lemma kernel9_1_r1_14_eq : ∀ k : Fin 16, kernel9_1Expr 1 14 k = kernel9_1_r1_14 k := by decide +kernel +noncomputable def kernel9_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),8⟩,⟨4,54⟩⟩,⟨⟨(-46),8⟩,⟨4,54⟩⟩,⟨⟨(-46),8⟩,⟨4,54⟩⟩,⟨⟨(-46),8⟩,⟨4,54⟩⟩,⟨⟨(-46),8⟩,⟨4,54⟩⟩,⟨⟨(-46),8⟩,⟨4,54⟩⟩,⟨⟨(-46),23⟩,⟨(-12),58⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩,⟨⟨(-31),23⟩,⟨(-8),42⟩⟩] +lemma kernel9_1_r1_15_eq : ∀ k : Fin 16, kernel9_1Expr 1 15 k = kernel9_1_r1_15 k := by decide +kernel +noncomputable def kernel9_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel9_1_r1_0,kernel9_1_r1_1,kernel9_1_r1_2,kernel9_1_r1_3,kernel9_1_r1_4,kernel9_1_r1_5,kernel9_1_r1_6,kernel9_1_r1_7,kernel9_1_r1_8,kernel9_1_r1_9,kernel9_1_r1_10,kernel9_1_r1_11,kernel9_1_r1_12,kernel9_1_r1_13,kernel9_1_r1_14,kernel9_1_r1_15] +lemma kernel9_1_r1_eq (i k : Fin 16) : kernel9_1Expr 1 i k = kernel9_1_r1 i k := by + fin_cases i + · exact kernel9_1_r1_0_eq k + · exact kernel9_1_r1_1_eq k + · exact kernel9_1_r1_2_eq k + · exact kernel9_1_r1_3_eq k + · exact kernel9_1_r1_4_eq k + · exact kernel9_1_r1_5_eq k + · exact kernel9_1_r1_6_eq k + · exact kernel9_1_r1_7_eq k + · exact kernel9_1_r1_8_eq k + · exact kernel9_1_r1_9_eq k + · exact kernel9_1_r1_10_eq k + · exact kernel9_1_r1_11_eq k + · exact kernel9_1_r1_12_eq k + · exact kernel9_1_r1_13_eq k + · exact kernel9_1_r1_14_eq k + · exact kernel9_1_r1_15_eq k +noncomputable def kernel9_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-91363296663000916078),(-91363296663000915645)⟩,⟨2862622870710908193,2862622870710908628⟩⟩,⟨⟨(-91262417392219656541),(-91262417392219656127)⟩,⟨2885217167132481948,2885217167132482362⟩⟩,⟨⟨(-91060975415486092078),(-91060975415486091650)⟩,⟨2930237428651668790,2930237428651669215⟩⟩,⟨⟨(-90759602349504981408),(-90759602349504980983)⟩,⟨2997348470222797643,2997348470222798070⟩⟩,⟨⟨(-90359241845420508789),(-90359241845420508351)⟩,⟨3086051192632519341,3086051192632519779⟩⟩,⟨⟨(-89861145083801683603),(-89861145083801683176)⟩,⟨3195686952897534270,3195686952897534695⟩⟩,⟨⟨(-89266864807319521191),(-89266864807319520766)⟩,⟨3325443319323356073,3325443319323356500⟩⟩,⟨⟨(-88578247924644858510),(-88578247924644858091)⟩,⟨3474361150534865013,3474361150534865430⟩⟩,⟨⟨(-87797426727211153591),(-87797426727211153165)⟩,⟨3641342924027937806,3641342924027938233⟩⟩,⟨⟨(-86926808768420100663),(-86926808768420100243)⟩,⟨3825162226942018801,3825162226942019218⟩⟩,⟨⟨(-85969065462579054186),(-85969065462579053768)⟩,⟨4024474309970544678,4024474309970545097⟩⟩,⟨⟨(-84927119468306015387),(-84927119468306014980)⟩,⟨4237827594749502465,4237827594749502872⟩⟩,⟨⟨(-83804130928276434707),(-83804130928276434300)⟩,⟨4463676015817473761,4463676015817474168⟩⟩,⟨⟨(-82603482643970787530),(-82603482643970787115)⟩,⟨4700392070428591217,4700392070428591631⟩⟩,⟨⟨(-81328764270465806030),(-81328764270465805631)⟩,⟨4946280443208728482,4946280443208728881⟩⟩,⟨⟨(-79983755622247308279),(-79983755622247307890)⟩,⟨5199592067940229008,5199592067940229394⟩⟩] +lemma kernel9_1_r2_0_eq : ∀ k : Fin 16, kernel9_1Expr 2 0 k = kernel9_1_r2_0 k := by decide +kernel +noncomputable def kernel9_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-78572409186460034217),(-78572409186460033826)⟩,⟨5458538485685474580,5458538485685474972⟩⟩,⟨⟨(-77098831944900995967),(-77098831944900995580)⟩,⟨5721306357036700693,5721306357036701082⟩⟩,⟨⟨(-75567266610359420366),(-75567266610359419991)⟩,⟨5986071986508807269,5986071986508807644⟩⟩,⟨⟨(-73982072386561644139),(-73982072386561643764)⟩,⟨6251015718951796841,6251015718951797216⟩⟩,⟨⟨(-72347705363948796469),(-72347705363948796112)⟩,⟨6514336071306871491,6514336071306871846⟩⟩,⟨⟨(-70668698665757383971),(-70668698665757383611)⟩,⟨6774263468001564378,6774263468001564738⟩⟩,⟨⟨(-68949642460350656447),(-68949642460350656087)⟩,⟨7029073454691543098,7029073454691543458⟩⟩,⟨⟨(-67195163956429553077),(-67195163956429552729)⟩,⟨7277099272808780248,7277099272808780597⟩⟩,⟨⟨(-65409907497609693807),(-65409907497609693471)⟩,⟨7516743686350054269,7516743686350054605⟩⟩,⟨⟨(-63598514871865662840),(-63598514871865662511)⟩,⟨7746489962404018208,7746489962404018537⟩⟩,⟨⟨(-61765605949503695023),(-61765605949503694705)⟩,⟨7964911917924595608,7964911917924595924⟩⟩,⟨⟨(-59915759760625089865),(-59915759760625089560)⟩,⟨8170682957058136162,8170682957058136467⟩⟩,⟨⟨(-58053496119490415558),(-58053496119490415237)⟩,⟨8362584035758516181,8362584035758516502⟩⟩,⟨⟨(-56183257898803366566),(-56183257898803366266)⟩,⟨8539510503309597692,8539510503309597994⟩⟩,⟨⟨(-54309394051727226075),(-54309394051727225786)⟩,⟨8700477783546539795,8700477783546540085⟩⟩,⟨⟨(-52436143473460303894),(-52436143473460303615)⟩,⟨8844625871854256786,8844625871854257063⟩⟩] +lemma kernel9_1_r2_1_eq : ∀ k : Fin 16, kernel9_1Expr 2 1 k = kernel9_1_r2_1 k := by decide +kernel +noncomputable def kernel9_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-50567619787473319263),(-50567619787473318965)⟩,⟨8971222637252695389,8971222637252695687⟩⟩,⟨⟨(-48707797134104899274),(-48707797134104898992)⟩,⟨9079665931888830554,9079665931888830836⟩⟩,⟨⟨(-46860497031183783753),(-46860497031183783495)⟩,⟨9169484522885359880,9169484522885360138⟩⟩,⟨⟨(-45029376367769179548),(-45029376367769179290)⟩,⟨9240337873595931709,9240337873595931968⟩⟩,⟨⟨(-43217916583053059200),(-43217916583053058950)⟩,⟨9292014812747206176,9292014812747206426⟩⟩,⟨⟨(-41429414073036040627),(-41429414073036040369)⟩,⟨9324431140582674837,9324431140582675095⟩⟩,⟨⟨(-39666971857863663803),(-39666971857863663565)⟩,⟨9337626230849780688,9337626230849780928⟩⟩,⟨⟨(-37933492532788899776),(-37933492532788899558)⟩,⟨9331758696193900593,9331758696193900811⟩⟩,⟨⟨(-36231672515709428347),(-36231672515709428129)⟩,⟨9307101192160211215,9307101192160211433⟩⟩,⟨⟨(-34563997594216396136),(-34563997594216395933)⟩,⟨9264034441494758214,9264034441494758416⟩⟩,⟨⟨(-32932739765187299320),(-32932739765187299109)⟩,⟨9203040565734411077,9203040565734411288⟩⟩,⟨⟨(-31339955350260620878),(-31339955350260620683)⟩,⟨9124695815155018188,9124695815155018383⟩⟩,⟨⟨(-29787484361142717911),(-29787484361142717711)⟩,⟨9029662790999030612,9029662790999030810⟩⟩,⟨⟨(-28276951079713100546),(-28276951079713100358)⟩,⟨8918682255536626792,8918682255536626980⟩⟩,⟨⟨(-26809765809402258696),(-26809765809402258522)⟩,⟨8792564625953173625,8792564625953173801⟩⟩,⟨⟨(-25387127746399535205),(-25387127746399535025)⟩,⟨8652181247341747581,8652181247341747760⟩⟩] +lemma kernel9_1_r2_2_eq : ∀ k : Fin 16, kernel9_1Expr 2 2 k = kernel9_1_r2_2 k := by decide +kernel +noncomputable def kernel9_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-24010028911982354786),(-24010028911982354620)⟩,⟨8498455538268098698,8498455538268098867⟩⟩,⟨⟨(-22679259080708652475),(-22679259080708652320)⟩,⟨8332354099535838734,8332354099535838890⟩⟩,⟨⟨(-21395411633438069343),(-21395411633438069187)⟩,⟨8154877872992479687,8154877872992479843⟩⟩,⟨⟨(-20158890259190336485),(-20158890259190336324)⟩,⟨7967053432573009726,7967053432573009885⟩⟩,⟨⟨(-18969916425746113208),(-18969916425746113061)⟩,⟨7769924484376018832,7769924484376018980⟩⟩,⟨⟨(-17828537535669809800),(-17828537535669809660)⟩,⟨7564543646513446086,7564543646513446225⟩⟩,⟨⟨(-16734635682097439497),(-16734635682097439365)⟩,⟨7351964572878817311,7351964572878817443⟩⟩,⟨⟨(-15687936917185583525),(-15687936917185583393)⟩,⟨7133234477953020386,7133234477953020518⟩⟩,⟨⟨(-14688020945549061121),(-14688020945549061005)⟩,⟨6909387112424652091,6909387112424652207⟩⟩,⟨⟨(-13734331155302911668),(-13734331155302911541)⟩,⟨6681436231856183930,6681436231856184059⟩⟩,⟨⟨(-12826184900436535424),(-12826184900436535309)⟩,⟨6450369592987346489,6450369592987346605⟩⟩,⟨⟨(-11962783950142454947),(-11962783950142454842)⟩,⟨6217143504638650801,6217143504638650903⟩⟩,⟨⟨(-11143225023348626538),(-11143225023348626430)⟩,⟨5982677952660571441,5982677952660571549⟩⟩,⟨⟨(-10366510330003363255),(-10366510330003363161)⟩,⟨5747852311060345024,5747852311060345121⟩⟩,⟨⟨(-9631558044570990061),(-9631558044570989966)⟩,⟨5513501644413269625,5513501644413269722⟩⟩,⟨⟨(-8937212641644229529),(-8937212641644229432)⟩,⟨5280413600004543694,5280413600004543789⟩⟩] +lemma kernel9_1_r2_3_eq : ∀ k : Fin 16, kernel9_1Expr 2 3 k = kernel9_1_r2_3 k := by decide +kernel +noncomputable def kernel9_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-8282255028491775801),(-8282255028491775712)⟩,⟨5049325881917126089,5049325881917126175⟩⟩,⟨⟨(-7665412414659438592),(-7665412414659438501)⟩,⟨4820924293536757555,4820924293536757647⟩⟩,⟨⟨(-7085367864351900011),(-7085367864351899936)⟩,⟨4595841329732645725,4595841329732645800⟩⟩,⟨⟨(-6540769483160413032),(-6540769483160412948)⟩,⟨4374655295326332103,4374655295326332187⟩⟩,⟨⟨(-6030239196691380965),(-6030239196691380876)⟩,⟨4157889922406439750,4157889922406439837⟩⟩,⟨⟨(-5552381084715324318),(-5552381084715324231)⟩,⟨3946014455597663843,3946014455597663932⟩⟩,⟨⟨(-5105789240521867878),(-5105789240521867803)⟩,⟨3739444171553077860,3739444171553077936⟩⟩,⟨⟨(-4689055131164584577),(-4689055131164584510)⟩,⟨3538541296704945902,3538541296704945969⟩⟩,⟨⟨(-4300774440145068873),(-4300774440145068819)⟩,⟨3343616285667608743,3343616285667608799⟩⟩,⟨⟨(-3939553379759183130),(-3939553379759183054)⟩,⟨3154929421615773661,3154929421615773737⟩⟩,⟨⟨(-3604014465756748787),(-3604014465756748727)⟩,⟨2972692699434961108,2972692699434961168⟩⟩,⟨⟨(-3292801752102229137),(-3292801752102229086)⟩,⟨2797071952424292518,2797071952424292569⟩⟩,⟨⟨(-3004585528428134245),(-3004585528428134194)⟩,⟨2628189183786636850,2628189183786636902⟩⟩,⟨⟨(-2738066487211890654),(-2738066487211890586)⟩,⟨2466125065024784390,2466125065024784458⟩⟩,⟨⟨(-2491979371754678017),(-2491979371754677965)⟩,⟨2310921564629213511,2310921564629213562⟩⟩,⟨⟨(-2265096119678100047),(-2265096119678099979)⟩,⟨2162584672045551353,2162584672045551422⟩⟩] +lemma kernel9_1_r2_4_eq : ∀ k : Fin 16, kernel9_1Expr 2 4 k = kernel9_1_r2_4 k := by decide +kernel +noncomputable def kernel9_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-2056228519869138229),(-2056228519869138177)⟩,⟨2021087183799290497,2021087183799290549⟩⟩,⟨⟨(-1864230403589719013),(-1864230403589718962)⟩,⟨1886371520782754562,1886371520782754613⟩⟩,⟨⟨(-1687999392824592471),(-1687999392824592416)⟩,⟨1758352548026325034,1758352548026325091⟩⟩,⟨⟨(-1526478230875918443),(-1526478230875918400)⟩,⟨1636920370735458428,1636920370735458472⟩⟩,⟨⟨(-1378655721735972838),(-1378655721735972795)⟩,⟨1521943082931901293,1521943082931901336⟩⟩,⟨⟨(-1243567305896304001),(-1243567305896303949)⟩,⟨1413269447649114735,1413269447649114786⟩⟩,⟨⟨(-1120295301002069529),(-1120295301002069486)⟩,⟨1310731490258592787,1310731490258592831⟩⟩,⟨⟨(-1007968836157134956),(-1007968836157134907)⟩,⟨1214146989109191755,1214146989109191802⟩⟩,⟨⟨(-905763508754556978),(-905763508754556926)⟩,⟨1123321850213104891,1123321850213104943⟩⟩,⟨⟨(-812900792476196107),(-812900792476196072)⟩,⟨1038052355180871048,1038052355180871083⟩⟩,⟨⟨(-728647224603850204),(-728647224603850152)⟩,⟨958127273968885303,958127273968885355⟩⟩,⟨⟨(-652313400042894583),(-652313400042894548)⟩,⟨883329836235338687,883329836235338723⟩⟩,⟨⟨(-583252798508814926),(-583252798508814891)⟩,⟨813439557187328639,813439557187328674⟩⟩,⟨⟨(-520860470198020368),(-520860470198020332)⟩,⟨748233915729846897,748233915729846932⟩⟩,⟨⟨(-464571603987205046),(-464571603987205003)⟩,⟨687489884486905653,687489884486905697⟩⟩,⟨⟨(-413860000809639648),(-413860000809639613)⟩,⟨630985312850091357,630985312850091392⟩⟩] +lemma kernel9_1_r2_5_eq : ∀ k : Fin 16, kernel9_1Expr 2 5 k = kernel9_1_r2_5 k := by decide +kernel +noncomputable def kernel9_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-368236473370204701),(-368236473370204648)⟩,⟨578500165617402879,578500165617402931⟩⟩,⟨⟨(-327247191810237323),(-327247191810237279)⟩,⟨529817621015311361,529817621015311405⟩⟩,⟨⟨(-290471993343059665),(-290471993343059630)⟩,⟨484725032952144601,484725032952144636⟩⟩,⟨⟨(-257522672274096927),(-257522672274096892)⟩,⟨443014763236007760,443014763236007795⟩⟩,⟨⟨(-228041265216356361),(-228041265216356317)⟩,⟨404484890212317925,404484890212317970⟩⟩,⟨⟨(-201698344731085729),(-201698344731085685)⟩,⟨368939800843106872,368939800843106917⟩⟩,⟨⟨(-178191333080765184),(-178191333080765148)⟩,⟨336190673672303784,336190673672303820⟩⟩,⟨⟨(-157242846291062480),(-157242846291062444)⟩,⟨306055860409034268,306055860409034304⟩⟩,⟨⟨(-138599077291630379),(-138599077291630343)⟩,⟨278361174026076279,278361174026076315⟩⟩,⟨⟨(-122028225552139559),(-122028225552139523)⟩,⟨252940091324968725,252940091324968760⟩⟩,⟨⟨(-107318979357164102),(-107318979357164067)⟩,⟨229633877875059187,229633877875059223⟩⟩,⟨⟨(-94279055676994197),(-94279055676994161)⟩,⟨208291643103182160,208291643103182196⟩⟩,⟨⟨(-82733801494878210),(-82733801494878183)⟩,⟨188770333105655831,188770333105655859⟩⟩,⟨⟨(-72524859446704499),(-72524859446704463)⟩,⟨170934668486485060,170934668486485096⟩⟩,⟨⟨(-63508899717359354),(-63508899717359306)⟩,⟨154657034206162746,154657034206162796⟩⟩,⟨⟨(-55556419318281055),(-55556419318281019)⟩,⟨139817328064752417,139817328064752453⟩⟩] +lemma kernel9_1_r2_6_eq : ∀ k : Fin 16, kernel9_1Expr 2 6 k = kernel9_1_r2_6 k := by decide +kernel +noncomputable def kernel9_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-48550609141272764),(-48550609141272727)⟩,⟨126302774050781132,126302774050781169⟩⟩,⟨⟨(-42386288541676806),(-42386288541676773)⟩,⟨114007706372865305,114007706372865336⟩⟩,⟨⟨(-36968906645979748),(-36968906645979717)⟩,⟨102833329562105838,102833329562105871⟩⟩,⟨⟨(-32213609100589143),(-32213609100589116)⟩,⟨92687459597449977,92687459597450005⟩⟩,⟨⟨(-28044368575173141),(-28044368575173108)⟩,⟨83484250569902501,83484250569902532⟩⟩,⟨⟨(-24393177000484242),(-24393177000484205)⟩,⟨75143910970315100,75143910970315136⟩⟩,⟨⟨(-21199297251652118),(-21199297251652082)⟩,⟨67592413264306162,67592413264306198⟩⟩,⟨⟨(-18408571778047151),(-18408571778047120)⟩,⟨60761200010699773,60761200010699806⟩⟩,⟨⟨(-15972785524465642),(-15972785524465609)⟩,⟨54586889390010959,54586889390010990⟩⟩,⟨⟨(-13849080380099333),(-13849080380099300)⟩,⟨49010982639547024,49010982639547056⟩⟩,⟨⟨(-11999418326177384),(-11999418326177347)⟩,⟨43979575543602383,43979575543602420⟩⟩,⟨⟨(-10390090425142494),(-10390090425142458)⟩,⟨39443075802381463,39443075802381500⟩⟩,⟨⟨(-8991268798812397),(-8991268798812360)⟩,⟨35355927802554736,35355927802554773⟩⟩,⟨⟨(-7776598775523477),(-7776598775523440)⟩,⟨31676346036140598,31676346036140635⟩⟩,⟨⟨(-6722828442395793),(-6722828442395756)⟩,⟨28366058162716534,28366058162716571⟩⟩,⟨⟨(-5809472914560273),(-5809472914560236)⟩,⟨25390058482458003,25390058482458040⟩⟩] +lemma kernel9_1_r2_7_eq : ∀ k : Fin 16, kernel9_1Expr 2 7 k = kernel9_1_r2_7 k := by decide +kernel +noncomputable def kernel9_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-5018510724745961),(-5018510724745924)⟩,⟨22716372383558806,22716372383558843⟩⟩,⟨⟨(-4334109840669904),(-4334109840669867)⟩,⟨20315832146339341,20315832146339378⟩⟩,⟨⟨(-3742380931175658),(-3742380931175621)⟩,⟨18161864326753593,18161864326753630⟩⟩,⟨⟨(-3231155622328125),(-3231155622328091)⟩,⟨16230288802866063,16230288802866095⟩⟩,⟨⟨(-2789787609312519),(-2789787609312482)⟩,⟨14499129447892705,14499129447892743⟩⟩,⟨⟨(-2408974616926892),(-2408974616926854)⟩,⟨12948436291218989,12948436291219026⟩⟩,⟨⟨(-2080599328914424),(-2080599328914374)⟩,⟨11560118943020899,11560118943020951⟩⟩,⟨⟨(-1797587532834287),(-1797587532834249)⟩,⟨10317790987310020,10317790987310057⟩⟩,⟨⟨(-1553781851348579),(-1553781851348546)⟩,⟨9206624990999833,9206624990999865⟩⟩,⟨⟨(-1343829551665964),(-1343829551665927)⟩,⟨8213217731579467,8213217731579505⟩⟩,⟨⟨(-1163083041594701),(-1163083041594663)⟩,⟨7325465211862484,7325465211862521⟩⟩,⟨⟨(-1007511772569089),(-1007511772569057)⟩,⟨6532447005788192,6532447005788226⟩⟩,⟨⟨(-873624376638431),(-873624376638394)⟩,⟨5824319463201238,5824319463201276⟩⟩,⟨⟨(-758399965406858),(-758399965406820)⟩,⟨5192217292802011,5192217292802048⟩⟩,⟨⟨(-659227614072206),(-659227614072168)⟩,⟨4628163040008995,4628163040009032⟩⟩,⟨⟨(-573853142925484),(-573853142925446)⟩,⟨4124983979350883,4124983979350920⟩⟩] +lemma kernel9_1_r2_8_eq : ∀ k : Fin 16, kernel9_1Expr 2 8 k = kernel9_1_r2_8 k := by decide +kernel +noncomputable def kernel9_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-500332391927737),(-500332391927699)⟩,⟨3676235948336253,3676235948336291⟩⟩,⟨⟨(-436990261339500),(-436990261339462)⟩,⟨3276133660744448,3276133660744486⟩⟩,⟨⟨(-382384862967243),(-382384862967205)⟩,⟨2919487051231259,2919487051231297⟩⟩,⟨⟨(-335276192586414),(-335276192586376)⟩,⟨2601643219415425,2601643219415463⟩⟩,⟨⟨(-294598794719466),(-294598794719428)⟩,⟨2318433559647441,2318433559647479⟩⟩,⟨⟨(-259437946434590),(-259437946434552)⟩,⟨2066125681970176,2066125681970214⟩⟩,⟨⟨(-229008937454359),(-229008937454325)⟩,⟨1841379749937172,1841379749937204⟩⟩,⟨⟨(-202639069904165),(-202639069904127)⟩,⟨1641208881592612,1641208881592650⟩⟩,⟨⟨(-179752042776750),(-179752042776712)⟩,⟨1462943280726823,1462943280726861⟩⟩,⟨⟨(-159854423932327),(-159854423932293)⟩,⟨1304197786241572,1304197786241605⟩⟩,⟨⟨(-142523946481865),(-142523946481826)⟩,⟨1162842547875465,1162842547875504⟩⟩,⟨⟨(-127399396998918),(-127399396998885)⟩,⟨1036976556474365,1036976556474399⟩⟩,⟨⟨(-114171890445345),(-114171890445307)⟩,⟨924903776306796,924903776306835⟩⟩,⟨⟨(-102577351244158),(-102577351244119)⟩,⟨825111645510980,825111645511018⟩⟩,⟨⟨(-92390041839189),(-92390041839150)⟩,⟨736251728536726,736251728536764⟩⟩,⟨⟨(-83416999585052),(-83416999585014)⟩,⟨657122321357381,657122321357420⟩⟩] +lemma kernel9_1_r2_9_eq : ∀ k : Fin 16, kernel9_1Expr 2 9 k = kernel9_1_r2_9 k := by decide +kernel +noncomputable def kernel9_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-75493260135030),(-75493260134991)⟩,⟨586652826234694,586652826234733⟩⟩,⟨⟨(-68477760849538),(-68477760849499)⟩,⟨523889727906543,523889727906582⟩⟩,⟨⟨(-62249831326873),(-62249831326835)⟩,⟨467984017227330,467984017227369⟩⟩,⟨⟨(-56706190142687),(-56706190142648)⟩,⟨418179921531121,418179921531160⟩⟩,⟨⟨(-51758377438780),(-51758377438741)⟩,⟨373804813325698,373804813325736⟩⟩,⟨⟨(-47330562279605),(-47330562279566)⟩,⟨334260180386247,334260180386286⟩⟩,⟨⟨(-43357671832322),(-43357671832283)⟩,⟨299013550930084,299013550930123⟩⟩,⟨⟨(-39783796553082),(-39783796553043)⟩,⟨267591277356270,267591277356309⟩⟩,⟨⟨(-36560831788355),(-36560831788316)⟩,⟨239572091061753,239572091061792⟩⟩,⟨⟨(-33647321633845),(-33647321633806)⟩,⟨214581349142842,214581349142882⟩⟩,⟨⟨(-31007475623116),(-31007475623077)⟩,⟨192285901396153,192285901396192⟩⟩,⟨⟨(-28610332931078),(-28610332931039)⟩,⟨172389512992123,172389512992162⟩⟩,⟨⟨(-26429052345436),(-26429052345396)⟩,⟨154628784546290,154628784546329⟩⟩,⟨⟨(-24440309350931),(-24440309350892)⟩,⟨138769517103163,138769517103202⟩⟩,⟨⟨(-22623784345302),(-22623784345263)⟩,⟨124603474812587,124603474812627⟩⟩,⟨⟨(-20961728314618),(-20961728314578)⟩,⟨111945502860588,111945502860628⟩⟩] +lemma kernel9_1_r2_10_eq : ∀ k : Fin 16, kernel9_1Expr 2 10 k = kernel9_1_r2_10 k := by decide +kernel +noncomputable def kernel9_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-19438594286384),(-19438594286344)⟩,⟨100630962551290,100630962551329⟩⟩,⟨⟨(-18040724592451),(-18040724592412)⟩,⟨90513449361081,90513449361121⟩⟩,⟨⟨(-16756085446716),(-16756085446676)⟩,⟨81462763332957,81462763332997⟩⟩,⟨⟨(-15574041606361),(-15574041606322)⟩,⟨73363104381554,73363104381594⟩⟩,⟨⟨(-14485164968808),(-14485164968769)⟩,⟨66111467966028,66111467966067⟩⟩,⟨⟨(-13481071883325),(-13481071883285)⟩,⟨59616219187211,59616219187250⟩⟩,⟨⟨(-12554284748469),(-12554284748425)⟩,⟨53795825703940,53795825703985⟩⟩,⟨⟨(-11698114141941),(-11698114141901)⟩,⟨48577731963634,48577731963674⟩⟩,⟨⟨(-10906558306207),(-10906558306168)⟩,⟨43897359127656,43897359127696⟩⟩,⟨⟨(-10174217302187),(-10174217302148)⟩,⟨39697216762463,39697216762503⟩⟩,⟨⟨(-9496219561184),(-9496219561144)⟩,⟨35926113881767,35926113881807⟩⟩,⟨⟨(-8868158917561),(-8868158917521)⟩,⟨32538458280549,32538458280589⟩⟩,⟨⟨(-8286040505392),(-8286040505352)⟩,⟨29493634313672,29493634313712⟩⟩,⟨⟨(-7746234155486),(-7746234155446)⟩,⟨26755450355181,26755450355221⟩⟩,⟨⟨(-7245434143983),(-7245434143943)⟩,⟨24291648141866,24291648141906⟩⟩,⟨⟨(-6780624325348),(-6780624325308)⟩,⟨22073467067476,22073467067516⟩⟩] +lemma kernel9_1_r2_11_eq : ∀ k : Fin 16, kernel9_1Expr 2 11 k = kernel9_1_r2_11 k := by decide +kernel +noncomputable def kernel9_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-6349047834960),(-6349047834920)⟩,⟨20075257264187,20075257264227⟩⟩,⟨⟨(-5948180676168),(-5948180676123)⟩,⟨18274135993740,18274135993786⟩⟩,⟨⟨(-5575708614511),(-5575708614471)⟩,⟨16649682482084,16649682482124⟩⟩,⟨⟨(-5229506894050),(-5229506894005)⟩,⟨15183666875191,15183666875236⟩⟩,⟨⟨(-4907622366680),(-4907622366639)⟩,⟨13859809478431,13859809478472⟩⟩,⟨⟨(-4608257690389),(-4608257690349)⟩,⟨12663566871970,12663566872010⟩⟩,⟨⟨(-4329757306321),(-4329757306276)⟩,⟨11581941878297,11581941878342⟩⟩,⟨⟨(-4070594949877),(-4070594949837)⟩,⟨10603314697605,10603314697645⟩⟩,⟨⟨(-3829362489384),(-3829362489343)⟩,⟨9717292829877,9717292829918⟩⟩,⟨⟨(-3604759917283),(-3604759917243)⟩,⟨8914577670624,8914577670664⟩⟩,⟨⟨(-3395586346135),(-3395586346090)⟩,⟨8186845905674,8186845905719⟩⟩,⟨⟨(-3200731883487),(-3200731883446)⟩,⟨7526644042596,7526644042636⟩⟩,⟨⟨(-3019170279045),(-3019170279005)⟩,⟨6927294603631,6927294603671⟩⟩,⟨⟨(-2849952252579),(-2849952252539)⟩,⟨6382812671880,6382812671920⟩⟩,⟨⟨(-2692199424841),(-2692199424801)⟩,⟨5887831630735,5887831630775⟩⟩,⟨⟨(-2545098784470),(-2545098784429)⟩,⟨5437537066959,5437537067000⟩⟩] +lemma kernel9_1_r2_12_eq : ∀ k : Fin 16, kernel9_1Expr 2 12 k = kernel9_1_r2_12 k := by decide +kernel +noncomputable def kernel9_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-2407897633102),(-2407897633062)⟩,⟨5027607924986,5027607925026⟩⟩,⟨⟨(-2279898958955),(-2279898958914)⟩,⟨4654164102294,4654164102335⟩⟩,⟨⟨(-2160457195541),(-2160457195500)⟩,⟨4313719767984,4313719768025⟩⟩,⟨⟨(-2048974327731),(-2048974327691)⟩,⟨4003141767113,4003141767153⟩⟩,⟨⟨(-1944896312269),(-1944896312228)⟩,⟨3719612545489,3719612545530⟩⟩,⟨⟨(-1847709783454),(-1847709783413)⟩,⟨3460597093515,3460597093556⟩⟩,⟨⟨(-1756939018591),(-1756939018550)⟩,⟨3223813463751,3223813463792⟩⟩,⟨⟨(-1672143140259),(-1672143140218)⟩,⟨3007206467244,3007206467285⟩⟩,⟨⟨(-1592913535102),(-1592913535061)⟩,⟨2808924198191,2808924198232⟩⟩,⟨⟨(-1518871471199),(-1518871471158)⟩,⟨2627297075236,2627297075277⟩⟩,⟨⟨(-1449665897406),(-1449665897365)⟩,⟨2460819123423,2460819123463⟩⟩,⟨⟨(-1384971410277),(-1384971410236)⟩,⟨2308131251221,2308131251261⟩⟩,⟨⟨(-1324486375029),(-1324486374988)⟩,⟨2168006304445,2168006304486⟩⟩,⟨⟨(-1267931188668),(-1267931188627)⟩,⟨2039335703686,2039335703727⟩⟩,⟨⟨(-1215046674103),(-1215046674062)⟩,⟨1921117492982,1921117493023⟩⟩,⟨⟨(-1165592595456),(-1165592595415)⟩,⟨1812445646779,1812445646820⟩⟩] +lemma kernel9_1_r2_13_eq : ∀ k : Fin 16, kernel9_1Expr 2 13 k = kernel9_1_r2_13 k := by decide +kernel +noncomputable def kernel9_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-1119346285147),(-1119346285106)⟩,⟨1712500499321,1712500499362⟩⟩,⟨⟨(-1076101374579),(-1076101374538)⟩,⟨1620540175456,1620540175497⟩⟩,⟨⟨(-1035666620633),(-1035666620587)⟩,⟨1535892915437,1535892915482⟩⟩,⟨⟨(-997864820733),(-997864820692)⟩,⟨1457950198010,1457950198051⟩⟩,⟨⟨(-962531810237),(-962531810196)⟩,⟨1386160576770,1386160576811⟩⟩,⟨⟨(-929515535960),(-929515535914)⟩,⟨1320024154006,1320024154052⟩⟩,⟨⟨(-898675200179),(-898675200138)⟩,⟨1259087624551,1259087624592⟩⟩,⟨⟨(-869880470379),(-869880470333)⟩,⟨1202939829894,1202939829940⟩⟩,⟨⟨(-843010749578),(-843010749537)⟩,⟨1151207768755,1151207768796⟩⟩,⟨⟨(-817954503189),(-817954503148)⟩,⟨1103553016704,1103553016745⟩⟩,⟨⟨(-794608638306),(-794608638260)⟩,⟨1059668512587,1059668512634⟩⟩,⟨⟨(-772877931557),(-772877931516)⟩,⟨1019275673696,1019275673737⟩⟩,⟨⟨(-752674502470),(-752674502423)⟩,⟨982121806122,982121806168⟩⟩,⟨⟨(-733917328652),(-733917328611)⟩,⟨947977780584,947977780625⟩⟩,⟨⟨(-716531800480),(-716531800439)⟩,⟨916635946544,916635946585⟩⟩,⟨⟨(-700449312146),(-700449312105)⟩,⟨887908261360,887908261401⟩⟩] +lemma kernel9_1_r2_14_eq : ∀ k : Fin 16, kernel9_1Expr 2 14 k = kernel9_1_r2_14 k := by decide +kernel +noncomputable def kernel9_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-685606886872),(-685606886831)⟩,⟨861624612823,861624612864⟩⟩,⟨⟨(-671946833870),(-671946833829)⟩,⟨837631316670,837631316712⟩⟩,⟨⟨(-659416435163),(-659416435122)⟩,⟨815789771974,815789772015⟩⟩,⟨⟨(-647967660216),(-647967660175)⟩,⟨795975259725,795975259767⟩⟩,⟨⟨(-637556906649),(-637556906608)⟩,⟨778075871360,778075871402⟩⟩,⟨⟨(-628144765705),(-628144765664)⟩,⟨761991555461,761991555502⟩⟩,⟨⟨(-619695810625),(-619695810583)⟩,⟨747633272439,747633272480⟩⟩,⟨⟨(-612178407103),(-612178407062)⟩,⟨734922247885,734922247927⟩⟩,⟨⟨(-605564544336),(-605564544295)⟩,⟨723789316838,723789316880⟩⟩,⟨⟨(-599829685832),(-599829685786)⟩,⟨714174351725,714174351771⟩⟩,⟨⟨(-594952638933),(-594952638892)⟩,⟨706025768076,706025768117⟩⟩,⟨⟨(-590915442393),(-590915442352)⟩,⟨699300102856,699300102897⟩⟩,⟨⟨(-587703271222),(-587703271180)⟩,⟨693961660714,693961660755⟩⟩,⟨⟨(-585304358308),(-585304358267)⟩,⟨689982224778,689982224819⟩⟩,⟨⟨(-583709932181),(-583709932139)⟩,⟨687340828738,687340828780⟩⟩,⟨⟨(-582914170813),(-582914170771)⟩,⟨686023587995,686023588036⟩⟩] +lemma kernel9_1_r2_15_eq : ∀ k : Fin 16, kernel9_1Expr 2 15 k = kernel9_1_r2_15 k := by decide +kernel +noncomputable def kernel9_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel9_1_r2_0,kernel9_1_r2_1,kernel9_1_r2_2,kernel9_1_r2_3,kernel9_1_r2_4,kernel9_1_r2_5,kernel9_1_r2_6,kernel9_1_r2_7,kernel9_1_r2_8,kernel9_1_r2_9,kernel9_1_r2_10,kernel9_1_r2_11,kernel9_1_r2_12,kernel9_1_r2_13,kernel9_1_r2_14,kernel9_1_r2_15] +lemma kernel9_1_r2_eq (i k : Fin 16) : kernel9_1Expr 2 i k = kernel9_1_r2 i k := by + fin_cases i + · exact kernel9_1_r2_0_eq k + · exact kernel9_1_r2_1_eq k + · exact kernel9_1_r2_2_eq k + · exact kernel9_1_r2_3_eq k + · exact kernel9_1_r2_4_eq k + · exact kernel9_1_r2_5_eq k + · exact kernel9_1_r2_6_eq k + · exact kernel9_1_r2_7_eq k + · exact kernel9_1_r2_8_eq k + · exact kernel9_1_r2_9_eq k + · exact kernel9_1_r2_10_eq k + · exact kernel9_1_r2_11_eq k + · exact kernel9_1_r2_12_eq k + · exact kernel9_1_r2_13_eq k + · exact kernel9_1_r2_14_eq k + · exact kernel9_1_r2_15_eq k +noncomputable def kernel9_1_r3_0 : Fin 16 → CBox := ![⟨⟨222523396999429976623637,222523396999429987113840⟩,⟨8618688843826204876342722,8618688843826204886840692⟩⟩,⟨⟨225726233078432168495430,225726233078432178978031⟩,⟨8612881791367317860815428,8612881791367317871305834⟩⟩,⟨⟨232118240194126829777245,232118240194126840244627⟩,⟨8601275743854712357639679,8601275743854712368114940⟩⟩,⟨⟨241672153592454507750987,241672153592454518195575⟩,⟨8583886816618728898961527,8583886816618728909414106⟩⟩,⟨⟨254347239139354252681618,254347239139354263095878⟩,⟨8560739183749698283929912,8560739183749698294352314⟩⟩,⟨⟨270089487996294736539798,270089487996294746916252⟩,⟨8531865078839933890627976,8531865078839933901012758⟩⟩,⟨⟨288831874656829022795426,288831874656829033126685⟩,⟨8497304795028248743532370,8497304795028248753872177⟩⟩,⟨⟨310494677040087812987373,310494677040087823266119⟩,⟨8457106683553430508614443,8457106683553430518901999⟩⟩,⟨⟨334985857021185592482546,334985857021185602701584⟩,⟨8411327149844840319057644,8411327149844840329285782⟩⟩,⟨⟨362201499469328294195125,362201499469328304347370⟩,⟨8360030646013127129471084,8360030646013127139632750⟩⟩,⟨⟨392026307563361636273367,392026307563361646351864⟩,⟨8303289658454267439754103,8303289658454267449842374⟩⟩,⟨⟨424334151862980749473579,424334151862980759471533⟩,⟨8241184689147880764474221,8241184689147880774482330⟩⟩,⟨⟨458988670333240466483869,458988670333240476394634⟩,⟨8173804229117970821750194,8173804229117970831671526⟩⟩,⟨⟨495843916251777475592380,495843916251777485409478⟩,⟨8101244722432622088434022,8101244722432622098262119⟩⟩,⟨⟨534745050673701787503188,534745050673701797220325⟩,⟨8023610519050226249037722,8023610519050226258766313⟩⟩,⟨⟨575529075889857181841963,575529075889857191453059⟩,⟨7941013814774754483512596,7941013814774754493135623⟩⟩] +lemma kernel9_1_r3_0_eq : ∀ k : Fin 16, kernel9_1Expr 3 0 k = kernel9_1_r3_0 k := by decide +kernel +noncomputable def kernel9_1_r3_1 : Fin 16 → CBox := ![⟨⟨618025606091503349315346,618025606091503358814492⟩,⟨7853574576562391588088841,7853574576562391597600412⟩⟩,⟨⟨662057671249836031472007,662057671249836040853544⟩,⟨7761420451427186714543982,7761420451427186723938459⟩⟩,⟨⟨707442550033510154504052,707442550033510163762504⟩,⟨7664686657224641272589624,7664686657224641281861545⟩⟩,⟨⟨753992627422802775897385,753992627422802785027573⟩,⟨7563515853649436701453461,7563515853649436710597656⟩⟩,⟨⟨801516272536536329735021,801516272536536338731939⟩,⟨7458057991866590227594044,7458057991866590236605515⟩⟩,⟨⟨849818732068603649563926,849818732068603658422875⟩,⟨7348470141303699059374099,7348470141303699068248158⟩⟩,⟨⟨898703034636041880317392,898703034636041889033875⟩,⟨7234916292264775910418819,7234916292264775919150969⟩⟩,⟨⟨947970901271146089283033,947970901271146097852882⟩,⟨7117567133182379975134405,7117567133182379983720483⟩⟩,⟨⟨997423657247038428670132,997423657247038437089366⟩,⟨6996599801502910981256191,6996599801502910989692212⟩⟩,⟨⟨1046863140410231683440872,1046863140410231691705865⟩,⟨6872197607398390555551836,6872197607398390563834172⟩⟩,⟨⟨1096092601205720348914062,1096092601205720357021383⟩,⟨6744549729714878828960794,6744549729714878837086017⟩⟩,⟨⟨1144917589620512013179332,1144917589620512021125924⟩,⟨6613850883800700934890363,6613850883800700942855398⟩⟩,⟨⟨1193146824340615799217993,1193146824340615807000960⟩,⟨6480300961104507574943652,6480300961104507582745596⟩⟩,⟨⟨1240593039514482422530550,1240593039514482430147404⟩,⟨6344104640691294265147679,6344104640691294272784035⟩⟩,⟨⟨1287073804642688642067870,1287073804642688649516298⟩,⟨6205470973091118841424020,6205470973091118848892453⟩⟩,⟨⟨1332412313269009539789550,1332412313269009547067621⟩,⟨6064612937167514785965279,6064612937167514793263846⟩⟩] +lemma kernel9_1_r3_1_eq : ∀ k : Fin 16, kernel9_1Expr 3 1 k = kernel9_1_r3_1 k := by decide +kernel +noncomputable def kernel9_1_r3_2 : Fin 16 → CBox := ![⟨⟨1376438136331432775557969,1376438136331432782663904⟩,⟨5921746970967523697099632,5921746970967523704226531⟩⟩,⟨⟨1418987936242415329378170,1418987936242415336310646⟩,⟨5777092477789817847447332,5777092477789817854401221⟩⟩,⟨⟨1459906138004803670792196,1459906138004803677549981⟩,⟨5630871308978471023061839,5630871308978471029841465⟩⟩,⟨⟨1499045553932131508532617,1499045553932131515114948⟩,⟨5483307225214479435580438,5483307225214479442185010⟩⟩,⟨⟨1536267958828034689642515,1536267958828034696048681⟩,⟨5334625338332085932262835,5334625338332085938691620⟩⟩,⟨⟨1571444612787603955838705,1571444612787603962068494⟩,⟨5185051535929342116899977,5185051535929342123152726⟩⟩,⟨⟨1604456729111727293918673,1604456729111727299971910⟩,⟨5034811891269282631956140,5034811891269282638032659⟩⟩,⟨⟨1635195885171729097821799,1635195885171729103698803⟩,⟨4884132061176852939989649,4884132061176852945890222⟩⟩,⟨⟨1663564374423561201613183,1663564374423561207314601⟩,⟨4733236674824770076504843,4733236674824770082229852⟩⟩,⟨⟨1689475498145918422459107,1689475498145918427985874⟩,⟨4582348716466454815207033,4582348716466454820757316⟩⟩,⟨⟨1712853795862244605682622,1712853795862244611035526⟩,⟨4431688905313939143776430,4431688905313939149152747⟩⟩,⟨⟨1733635213799821089807748,1733635213799821094988060⟩,⟨4281475075871373546506603,4281475075871373551710198⟩⟩,⟨⟨1751767211137020391096340,1751767211137020396105249⟩,⟨4131921562118870185406829,4131921562118870190438873⟩⟩,⟨⟨1767208804189298984901569,1767208804189298989740819⟩,⟨3983238588995664637249197,3983238588995664642111405⟩⟩,⟨⟨1779930549082461856967962,1779930549082461861639168⟩,⟨3835631674655029774910887,3835631674655029779604851⟩⟩,⟨⟨1789914463854989037568323,1789914463854989042073612⟩,⟨3689301046955438905149616,3689301046955438909677443⟩⟩] +lemma kernel9_1_r3_2_eq : ∀ k : Fin 16, kernel9_1Expr 3 2 k = kernel9_1_r3_2 k := by decide +kernel +noncomputable def kernel9_1_r3_3 : Fin 16 → CBox := ![⟨⟨1797153891316597776840242,1797153891316597781181560⟩,⟨3544441077612907746168431,3544441077612907750532040⟩⟩,⟨⟨1801653304364580283285211,1801653304364580287465063⟩,⟨3401239737368355724960164,3401239737368355729162044⟩⟩,⟨⟨1803428055819726837549781,1803428055819726841570500⟩,⟨3259878075421679580725584,3259878075421679584768041⟩⟩,⟨⟨1802504075186836516222892,1802504075186836520087284⟩,⟨3120529726251839378365046,3120529726251839382250864⟩⟩,⟨⟨1798917515068083489467088,1798917515068083493177707⟩,⟨2983360446780773230478757,2983360446780773234210475⟩⟩,⟨⟨1792714350258161381032694,1792714350258161384592674⟩,⟨2848527686649865477929647,2848527686649865481510374⟩⟩,⟨⟨1783949932825683138627924,1783949932825683142040108⟩,⟨2716180194162788676449366,2716180194162788679881929⟩⟩,⟨⟨1772688506733506590250127,1772688506733506593517842⟩,⟨2586457660209908010755498,2586457660209908014043211⟩⟩,⟨⟨1759002685769476583657539,1759002685769476586783794⟩,⟨2459490402229429018096744,2459490402229429021242598⟩⟩,⟨⟨1742972898746790861517827,1742972898746790864506179⟩,⟨2335399089981674499460186,2335399089981674502467720⟩⟩,⟨⟨1724686806088374722047113,1724686806088374724900799⟩,⟨2214294514618088977190497,2214294514618088980062938⟩⟩,⟨⟨1704238692031171468213059,1704238692031171470935746⟩,⟨2096277402218755652545135,2096277402218755655286134⟩⟩,⟨⟨1681728836773334301231298,1681728836773334303826281⟩,⟨1981438272654473712050505,1981438272654473714663345⟩⟩,⟨⟨1657262872939493405961541,1657262872939493408432647⟩,⟨1869857344304982739835995,1869857344304982742324500⟩⟩,⟨⟨1630951130756467973638293,1630951130756467975988960⟩,⟨1761604484836993950771546,1761604484836993953139143⟩⟩,⟨⟨1602907976314242282667669,1602907976314242284901728⟩,⟨1656739207917571504146202,1656739207917571506396712⟩⟩] +lemma kernel9_1_r3_3_eq : ∀ k : Fin 16, kernel9_1Expr 3 3 k = kernel9_1_r3_3 k := by decide +kernel +noncomputable def kernel9_1_r3_4 : Fin 16 → CBox := ![⟨⟨1573251147235317064964163,1573251147235317067085058⟩,⟨1555310715413356450051961,1555310715413356452188821⟩⟩,⟨⟨1542101089990607958022366,1542101089990607960034014⟩,⟨1457357984307335311446794,1457357984307335313473916⟩⟩,⟨⟨1509580302983142205908936,1509580302983142207814838⟩,⟨1362909897255420268955833,1362909897255420270876717⟩⟩,⟨⟨1475812689373461917907075,1475812689373461919711104⟩,⟨1271985415407987990184020,1271985415407987992002533⟩⟩,⟨⟨1440922923444724953677504,1440922923444724955383082⟩,⟨1184593791839508588831099,1184593791839508590550667⟩⟩,⟨⟨1405035834103116101232188,1405035834103116102845113⟩,⟨1100734823665071948088693,1100734823665071949715094⟩⟩,⟨⟨1368275808882693536072615,1368275808882693537656739⟩,⟨1020399140678341368568560,1020399140678341370165148⟩⟩,⟨⟨1330766221575759539978117,1330766221575759541533081⟩,⟨943568528123333088812427,943568528123333090378883⟩⟩,⟨⟨1292628886342998062771177,1292628886342998064296238⟩,⟨870216281014255012307560,870216281014255013843194⟩⟩,⟨⟨1253983540874845864282813,1253983540874845865777756⟩,⟨800307587244963013187304,800307587244963014691945⟩⟩,⟨⟨1214947360879847111345258,1214947360879847112809482⟩,⟨733799936583622746024135,733799936583622747497224⟩⟩,⟨⟨1175634507870142949095535,1175634507870142950528865⟩,⟨670643552529794295682282,670643552529794297123687⟩⟩,⟨⟨1136155711901861499617306,1136155711901861501019202⟩,⟨610781843920957984409103,610781843920957985818336⟩⟩,⟨⟨1096617890612091318901978,1096617890612091320272413⟩,⟨554151873113720019123325,554151873113720020500397⟩⟩,⟨⟨1057123805577395460863978,1057123805577395462202562⟩,⟨500684837531504404962937,500684837531504406307497⟩⟩,⟨⟨1017771756704433530948908,1017771756704433532255652⟩,⟨450306561365069133873239,450306561365069135185341⟩⟩] +lemma kernel9_1_r3_4_eq : ∀ k : Fin 16, kernel9_1Expr 3 4 k = kernel9_1_r3_4 k := by decide +kernel +noncomputable def kernel9_1_r3_5 : Fin 16 → CBox := ![⟨⟨978655315054078513177491,978655315054078514452034⟩,⟨402937994233997305683552,402937994233997306962871⟩⟩,⟨⟨939863094199179149396168,939863094199179150638692⟩,⟨358495713665441575784016,358495713665441577030774⟩⟩,⟨⟨901478559925396452779031,901478559925396453989333⟩,⟨316892428319613414269822,316892428319613415483851⟩⟩,⟨⟨863579877806711841877572,863579877806711843055865⟩,⟨278037478988336112605433,278037478988336113786978⟩⟩,⟨⟨826239797924427230604821,826239797924427231750924⟩,⟨241837334511735167733892,241837334511735168882812⟩⟩,⟨⟨789525575752683506081324,789525575752683507195598⟩,⟨208196079896945701891062,208196079896945703007746⟩⟩,⟨⟨753498928006393463743741,753498928006393464826135⟩,⟨177015894079538307263077,177015894079538308347505⟩⟩,⟨⟨718216022040438015374590,718216022040438016425495⟩,⟨148197514941037101430777,148197514941037102483373⟩⟩,⟨⟨683727497203161282161088,683727497203161283180490⟩,⟨121640689382163485471264,121640689382163486492042⟩⟩,⟨⟨650078516383499261795875,650078516383499262784306⟩,⟨97244606448955799104971,97244606448955800094485⟩⟩,⟨⟨617308845850093306617409,617308845850093307574971⟩,⟨74908311715322668361897,74908311715322669320283⟩⟩,⟨⟨585452961362809128208072,585452961362809129135296⟩,⟨54531101338514976685010,54531101338514977612814⟩⟩,⟨⟨554540178442276952944137,554540178442276953841149⟩,⟨36012894421100868282528,36012894421100869179905⟩⟩,⟨⟨524594804611208345762140,524594804611208346629600⟩,⟨19254582532004952628111,19254582532004953495740⟩⟩,⟨⟨495636311371909686067931,495636311371909686906055⟩,⟨4158355457810113959288,4158355457810114797405⟩⟩,⟨⟨467679523656956597838819,467679523656956598648279⟩,⟨(-9371997528296548273479),(-9371997528296547464182)⟩⟩] +lemma kernel9_1_r3_5_eq : ∀ k : Fin 16, kernel9_1Expr 3 5 k = kernel9_1_r3_5 k := by decide +kernel +noncomputable def kernel9_1_r3_6 : Fin 16 → CBox := ![⟨⟨440734824483566749562037,440734824483566750343046⟩,⟨(-21430811380813937065314),(-21430811380813936284602)⟩⟩,⟨⟨414808372555772904763404,414808372555772905516729⟩,⟨(-32110294274888533535626),(-32110294274888532782723)⟩⟩,⟨⟨389902330590851622376789,389902330590851623102753⟩,⟨(-41500301975919936024718),(-41500301975919935299281)⟩⟩,⟨⟨366015102196261158697798,366015102196261159397136⟩,⟨(-49688137495820334117531),(-49688137495820333418810)⟩⟩,⟨⟨343141575189121910100022,343141575189121910773080⟩,⟨(-56758375768810558107348),(-56758375768810557434990)⟩⟩,⟨⟨321273369330476542730025,321273369330476543377576⟩,⟨(-62792712914489335670641),(-62792712914489335023855)⟩⟩,⟨⟨300399086539566560858189,300399086539566561480661⟩,⟨(-67869839503700149756795),(-67869839503700149135140)⟩⟩,⟨⟨280504561757482341530163,280504561757482342128322⟩,⟨(-72065337104199121068574),(-72065337104199120471277)⟩⟩,⟨⟨261573112743085628082008,261573112743085628656240⟩,⟨(-75451597258861533541994),(-75451597258861532968660)⟩⟩,⟨⟨243585787205366392875229,243585787205366393426370⟩,⟨(-78097761939528208352806),(-78097761939528207802590)⟩⟩,⟨⟨226521605803698229332869,226521605803698229861372⟩,⟨(-80069684424776761485787),(-80069684424776760958227)⟩⟩,⟨⟨210357799679154907978541,210357799679154908485194⟩,⟨(-81429909469922765129559),(-81429909469922764623862)⟩⟩,⟨⟨195070041314558562083124,195070041314558562568378⟩,⟨(-82237671572263282376974),(-82237671572263281892663)⟩⟩,⟨⟨180632667656732410470619,180632667656732410935284⟩,⟨(-82548910083668819610006),(-82548910083668819146252)⟩⟩,⟨⟨167018894570099276557113,167018894570099277001681⟩,⟨(-82416299885668763671815),(-82416299885668763228123)⟩⟩,⟨⟨154201021824970635652220,154201021824970636077456⟩,⟨(-81889296318594197106968),(-81889296318594196682582)⟩⟩] +lemma kernel9_1_r3_6_eq : ∀ k : Fin 16, kernel9_1Expr 3 6 k = kernel9_1_r3_6 k := by decide +kernel +noncomputable def kernel9_1_r3_7 : Fin 16 → CBox := ![⟨⟨142150627955386413973809,142150627955386414380153⟩,⟨(-81014193045465159165891),(-81014193045465158760362)⟩⟩,⟨⟨130838754449085518580784,130838754449085518969018⟩,⟨(-79834191532367337543923),(-79834191532367337156473)⟩⟩,⟨⟨120236078855124272918202,120236078855124273288823⟩,⟨(-78389480839207977460158),(-78389480839207977090283)⟩⟩,⟨⟨110313076511952227415731,110313076511952227769477⟩,⟨(-76717326437062248240580),(-76717326437062247887552)⟩⟩,⟨⟨101040170709665967387878,101040170709665967725174⟩,⟨(-74852166799862430586253),(-74852166799862430249638)⟩⟩,⟨⟨92387871204081196918371,92387871204081197239969⟩,⟨(-72825716557954499968825),(-72825716557954499647878)⟩⟩,⟨⟨84326901096705163916518,84326901096705164222882⟩,⟨(-70667075048044291802329),(-70667075048044291496581)⟩⟩,⟨⟨76828312183289567925436,76828312183289568217244⟩,⟨(-68402839147269292146075),(-68402839147269291854847)⟩⟩,⟨⟨69863588954148328987807,69863588954148329265481⟩,⟨(-66057219337562269693458),(-66057219337562269416338)⟩⟩,⟨⟨63404741501694551915018,63404741501694552179244⟩,⟨(-63652158009140313907362),(-63652158009140313643656)⟩⟩,⟨⟨57424387654648904393964,57424387654648904645190⟩,⟨(-61207449077909428486772),(-61207449077909428236036)⟩⟩,⟨⟨51895824714154427116775,51895824714154427355617⟩,⟨(-58740858059913053059841),(-58740858059913052821463)⟩⟩,⟨⟨46793091214743757238953,46793091214743757465803⟩,⟨(-56268241815813365735580),(-56268241815813365509163)⟩⟩,⟨⟨42091019172964393542876,42091019172964393758352⟩,⟨(-53803667248972352087789),(-53803667248972351872720)⟩⟩,⟨⟨37765277318764473510706,37765277318764473715199⟩,⟨(-51359528311250867948219),(-51359528311250867744106)⟩⟩,⟨⟨33792405829822655017219,33792405829822655211294⟩,⟨(-48946660740487805132879),(-48946660740487804939163)⟩⟩] +lemma kernel9_1_r3_7_eq : ∀ k : Fin 16, kernel9_1Expr 3 7 k = kernel9_1_r3_7 k := by decide +kernel +noncomputable def kernel9_1_r3_8 : Fin 16 → CBox := ![⟨⟨30149843107267363909207,30149843107267364093212⟩,⟨(-46574454022144400195088),(-46574454022144400011414)⟩⟩,⟨⟨26815945143109090007048,26815945143109090181591⟩,⟨(-44250960134255645656192),(-44250960134255645481952)⟩⟩,⟨⟨23769998035671779317794,23769998035671779483252⟩,⟨(-41982998699145716546837),(-41982998699145716381642)⟩⟩,⟨⟨20992224209845288114037,20992224209845288270917⟩,⟨(-39776258226930053319392),(-39776258226930053162746)⟩⟩,⟨⟨18463782894594275533027,18463782894594275681597⟩,⟨(-37635393194303377207555),(-37635393194303377059190)⟩⟩,⟨⟨16166765401360559907144,16166765401360560047887⟩,⟨(-35564116757225883554422),(-35564116757225883413861)⟩⟩,⟨⟨14084185734296487978948,14084185734296488112162⟩,⟨(-33565288947657103576445),(-33565288947657103443387)⟩⟩,⟨⟨12199967047170547656541,12199967047170547782653⟩,⟨(-31641000252295537154399),(-31641000252295537028426)⟩⟩,⟨⟨10498924442785662372553,10498924442785662491936⟩,⟨(-29792650515264542697166),(-29792650515264542577899)⟩⟩,⟨⟨8966744589320940608440,8966744589320940721600⟩,⟨(-28021023146794631274013),(-28021023146794631160953)⟩⟩,⟨⟨7589962604603809753271,7589962604603809860456⟩,⟨(-26326354656189376021193),(-26326354656189375914093)⟩⟩,⟨⟨6355936634371775730254,6355936634371775831787⟩,⟨(-24708399559768694650088),(-24708399559768694548627)⟩⟩,⟨⟨5252820524494733597498,5252820524494733693581⟩,⟨(-23166490743138572585195),(-23166490743138572489171)⟩⟩,⟨⟨4269534960273786746196,4269534960273786837168⟩,⟨(-21699595382152077565602),(-21699595382152077474680)⟩⟩,⟨⟨3395737418654150841290,3395737418654150927340⟩,⟨(-20306366548442205164714),(-20306366548442205078703)⟩⟩,⟨⟨2621791251799490662015,2621791251799490743432⟩,⟨(-18985190643585253661107),(-18985190643585253579718)⟩⟩] +lemma kernel9_1_r3_8_eq : ∀ k : Fin 16, kernel9_1Expr 3 8 k = kernel9_1_r3_8 k := by decide +kernel +noncomputable def kernel9_1_r3_9 : Fin 16 → CBox := ![⟨⟨1938734193252455016708,1938734193252455093656⟩,⟨(-17734230820975343435288),(-17734230820975343358364)⟩⟩,⟨⟨1338246551098720746592,1338246551098720819361⟩,⟨(-16551466566552192144561),(-16551466566552192071810)⟩⟩,⟨⟨812619326375497298952,812619326375497367826⟩,⟨(-15434729618831759887881),(-15434729618831759819016)⟩⟩,⟨⟨354722469605483658381,354722469605483723597⟩,⟨(-14381736415456282983382),(-14381736415456282918169)⟩⟩,⟨⟨(-42026536050474026771),(-42026536050473965067)⟩,⟨(-13390117257923553848828),(-13390117257923553787125)⟩⟩,⟨⟨(-383693599816541975260),(-383693599816541916864)⟩,⟨(-12457442388492745009738),(-12457442388492744951340)⟩⟩,⟨⟨(-675858313381832176875),(-675858313381832121637)⟩,⟨(-11581245173711246047300),(-11581245173711245992057)⟩⟩,⟨⟨(-923643483726431752847),(-923643483726431700600)⟩,⟨(-10759042587775132949691),(-10759042587775132897434)⟩⟩,⟨⟨(-1131743805859075518597),(-1131743805859075469218)⟩,⟨(-9988353186229878170353),(-9988353186229878120965)⟩⟩,⟨⟨(-1304453590742706731307),(-1304453590742706684626)⟩,⟨(-9266712756534510423788),(-9266712756534510377093)⟩⟩,⟨⟨(-1445693480414596128317),(-1445693480414596084194)⟩,⟨(-8591687826938947428756),(-8591687826938947384620)⟩⟩,⟨⟨(-1559036097659697903556),(-1559036097659697861836)⟩,⟨(-7960887209137383864668),(-7960887209137383822932)⟩⟩,⟨⟨(-1647730591585956284183),(-1647730591585956244786)⟩,⟨(-7371971743425754482383),(-7371971743425754442968)⟩⟩,⟨⟨(-1714726053107406337730),(-1714726053107406300500)⟩,⟨(-6822662407761766690643),(-6822662407761766653398)⟩⟩,⟨⟨(-1762693785704944296994),(-1762693785704944261823)⟩,⟨(-6310746944342839691344),(-6310746944342839656156)⟩⟩,⟨⟨(-1794048426954326330690),(-1794048426954326297427)⟩,⟨(-5834085149209057011622),(-5834085149209056978338)⟩⟩] +lemma kernel9_1_r3_9_eq : ∀ k : Fin 16, kernel9_1Expr 3 9 k = kernel9_1_r3_9 k := by decide +kernel +noncomputable def kernel9_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-1810967925242296154266),(-1810967925242296122801)⟩,⟨(-5390612962061055798601),(-5390612962061055767118)⟩⟩,⟨⟨(-1815412383896432058772),(-1815412383896432029005)⟩,⟨(-4978345485060511848918),(-4978345485060511819132)⟩⟩,⟨⟨(-1809141791698273286672),(-1809141791698273258525)⟩,⟨(-4595379050945485193518),(-4595379050945485165354)⟩⟩,⟨⟨(-1793732664501388399797),(-1793732664501388373166)⟩,⟨(-4239892452424836056517),(-4239892452424836029869)⟩⟩,⟨⟨(-1770593627506878115885),(-1770593627506878090708)⟩,⟨(-3910147436584722616935),(-3910147436584722591742)⟩⟩,⟨⟨(-1740979971729642469984),(-1740979971729642446161)⟩,⟨(-3604488560005019425153),(-3604488560005019401315)⟩⟩,⟨⟨(-1706007221390630298346),(-1706007221390630275819)⟩,⟨(-3321342492493826946040),(-3321342492493826923496)⟩⟩,⟨⟨(-1666663751463235012302),(-1666663751463234990984)⟩,⟨(-3059216849844561339077),(-3059216849844561317745)⟩⟩,⟨⟨(-1623822496454295944391),(-1623822496454295924245)⟩,⟨(-2816698628834624656648),(-2816698628834624636489)⟩⟩,⟨⟨(-1578251792777818808730),(-1578251792777818789654)⟩,⟨(-2592452310842015057395),(-2592452310842015038305)⟩⟩,⟨⟨(-1530625397845808956831),(-1530625397845808938800)⟩,⟨(-2385217693974276868766),(-2385217693974276850722)⟩⟩,⟨⟨(-1481531729315678318387),(-1481531729315678301303)⟩,⟨(-2193807507494634779801),(-2193807507494634762707)⟩⟩,⟨⟨(-1431482367854322819899),(-1431482367854322803764)⟩,⟨(-2017104856599313617815),(-2017104856599313601666)⟩⟩,⟨⟨(-1380919866358380644019),(-1380919866358380628740)⟩,⟨(-1854060540249475952623),(-1854060540249475937332)⟩⟩,⟨⟨(-1330224907857888247450),(-1330224907857888232996)⟩,⟨(-1703690279788362160393),(-1703690279788362145928)⟩⟩,⟨⟨(-1279722853372314935294),(-1279722853372314921617)⟩,⟨(-1565071891473024654244),(-1565071891473024640560)⟩⟩] +lemma kernel9_1_r3_10_eq : ∀ k : Fin 16, kernel9_1Expr 3 10 k = kernel9_1_r3_10 k := by decide +kernel +noncomputable def kernel9_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-1229689719825789417261),(-1229689719825789404322)⟩,⟨(-1437342431811486121727),(-1437342431811486108778)⟩⟩,⟨⟨(-1180357626800537283058),(-1180357626800537270801)⟩,⟨(-1319695340708756842313),(-1319695340708756830046)⟩⟩,⟨⟨(-1131919749448809264425),(-1131919749448809252817)⟩,⟨(-1211377603875487630182),(-1211377603875487618567)⟩⟩,⟨⟨(-1084534813325076243357),(-1084534813325076232363)⟩,⟨(-1111686952726145120055),(-1111686952726145109053)⟩⟩,⟨⟨(-1038331165269820635260),(-1038331165269820624851)⟩,⟨(-1019969117073358153790),(-1019969117073358143376)⟩⟩,⟨⟨(-993410452798496347190),(-993410452798496337302)⟩,⟨(-935615143294577350955),(-935615143294577341059)⟩⟩,⟨⟨(-949850942745782897514),(-949850942745782888128)⟩,⟨(-858058788288995366325),(-858058788288995356932)⟩⟩,⟨⟨(-907710508204928350595),(-907710508204928341690)⟩,⟨(-786773997439141654609),(-786773997439141645696)⟩⟩,⟨⟨(-867029311100947129927),(-867029311100947121476)⟩,⟨(-721272472925039737956),(-721272472925039729500)⟩⟩,⟨⟨(-827832206058482656942),(-827832206058482648914)⟩,⟨(-661101337091838239309),(-661101337091838231276)⟩⟩,⟨⟨(-790130889581816056740),(-790130889581816049112)⟩,⟨(-605840894127299327772),(-605840894127299320140)⟩⟩,⟨⟨(-753925816965338987664),(-753925816965338980408)⟩,⟨(-555102492046844066591),(-555102492046844059330)⟩⟩,⟨⟨(-719207907805525441404),(-719207907805525434512)⟩,⟨(-508526485895011249216),(-508526485895011242321)⟩⟩,⟨⟨(-685960059496111118912),(-685960059496111112355)⟩,⟨(-465780302137871202810),(-465780302137871196250)⟩⟩,⟨⟨(-654158486661437064293),(-654158486661437058053)⟩,⟨(-426556603426588064887),(-426556603426588058645)⟩⟩,⟨⟨(-623773903122062698907),(-623773903122062692985)⟩,⟨(-390571552244180507550),(-390571552244180501625)⟩⟩] +lemma kernel9_1_r3_11_eq : ∀ k : Fin 16, kernel9_1Expr 3 11 k = kernel9_1_r3_11 k := by decide +kernel +noncomputable def kernel9_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-594772561693995174437),(-594772561693995168792)⟩,⟨(-357563171392655752820),(-357563171392655747172)⟩⟩,⟨⟨(-567117165899424303867),(-567117165899424298489)⟩,⟨(-327289798823989966604),(-327289798823989961221)⟩⟩,⟨⟨(-540767666513053272324),(-540767666513053267201)⟩,⟨(-299528633954647837676),(-299528633954647832547)⟩⟩,⟨⟨(-515681954783609157329),(-515681954783609152441)⟩,⟨(-274074372319058322594),(-274074372319058317703)⟩⟩,⟨⟨(-491816463153929051717),(-491816463153929047049)⟩,⟨(-250737925203093185267),(-250737925203093180599)⟩⟩,⟨⟨(-469126683353666946735),(-469126683353666942285)⟩,⟨(-229345220745325262303),(-229345220745325257853)⟩⟩,⟨⟨(-447567610854261300945),(-447567610854261296696)⟩,⟨(-209736082893634231247),(-209736082893634226995)⟩⟩,⟨⟨(-427094123854122971024),(-427094123854122966966)⟩,⟨(-191763184550269871251),(-191763184550269867194)⟩⟩,⟨⟨(-407661304200573544474),(-407661304200573540603)⟩,⟨(-175291071223161181999),(-175291071223161178125)⟩⟩,⟨⟨(-389224706951222230753),(-389224706951222227040)⟩,⟨(-160195251519113879358),(-160195251519113875642)⟩⟩,⟨⟨(-371740584628421227269),(-371740584628421223718)⟩,⟨(-146361350860222648633),(-146361350860222645082)⟩⟩,⟨⟨(-355166071623309147119),(-355166071623309143716)⟩,⟨(-133684324873565246565),(-133684324873565243160)⟩⟩,⟨⟨(-339459333657824940238),(-339459333657824936987)⟩,⟨(-122067728991802355188),(-122067728991802351935)⟩⟩,⟨⟨(-324579686711033255216),(-324579686711033252089)⟩,⟨(-111423040904930801555),(-111423040904930798428)⟩⟩,⟨⟨(-310487689357256521939),(-310487689357256518949)⟩,⟨(-101669032617831086942),(-101669032617831083952)⟩⟩,⟨⟨(-297145212045022193016),(-297145212045022190143)⟩,⟨(-92731188991529442628),(-92731188991529439757)⟩⟩] +lemma kernel9_1_r3_12_eq : ∀ k : Fin 16, kernel9_1Expr 3 12 k = kernel9_1_r3_12 k := by decide +kernel +noncomputable def kernel9_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-284515486464941945592),(-284515486464941942840)⟩,⟨(-84541169775752991565),(-84541169775752988816)⟩⟩,⟨⟨(-272563137808669340438),(-272563137808669337795)⟩,⟨(-77036312274229004183),(-77036312274229001538)⟩⟩,⟨⟨(-261254202407462019330),(-261254202407462016786)⟩,⟨(-70159171920409328863),(-70159171920409326317)⟩⟩,⟨⟨(-250556132955144468385),(-250556132955144465935)⟩,⟨(-63857098178310038030),(-63857098178310035581)⟩⟩,⟨⟨(-240437793264086751842),(-240437793264086749476)⟩,⟨(-58081843319613783346),(-58081843319613780980)⟩⟩,⟨⟨(-230869444271965372691),(-230869444271965370426)⟩,⟨(-52789201762979312981),(-52789201762979310715)⟩⟩,⟨⟨(-221822722809461579643),(-221822722809461577450)⟩,⟨(-47938677793726453765),(-47938677793726451571)⟩⟩,⟨⟨(-213270614452712631506),(-213270614452712629393)⟩,⟨(-43493179610976325801),(-43493179610976323689)⟩⟩,⟨⟨(-205187421617419981089),(-205187421617419979058)⟩,⟨(-39418737774338613162),(-39418737774338611129)⟩⟩,⟨⟨(-197548727902314736350),(-197548727902314734382)⟩,⟨(-35684246242896350813),(-35684246242896348846)⟩⟩,⟨⟨(-190331359556584119237),(-190331359556584117331)⟩,⟨(-32261224315205449993),(-32261224315205448087)⟩⟩,⟨⟨(-183513344827387440050),(-183513344827387438203)⟩,⟨(-29123597890062388373),(-29123597890062386523)⟩⟩,⟨⟨(-177073871838361778870),(-177073871838361777085)⟩,⟨(-26247498573746020114),(-26247498573746018326)⟩⟩,⟨⟨(-170993245556767624096),(-170993245556767622367)⟩,⟨(-23611079260228040990),(-23611079260228039261)⟩⟩,⟨⟨(-165252844324485519037),(-165252844324485517362)⟩,⟨(-21194344906452484433),(-21194344906452482758)⟩⟩,⟨⟨(-159835076355374121485),(-159835076355374119856)⟩,⟨(-18978997315240338705),(-18978997315240337076)⟩⟩] +lemma kernel9_1_r3_13_eq : ∀ k : Fin 16, kernel9_1Expr 3 13 k = kernel9_1_r3_13 k := by decide +kernel +noncomputable def kernel9_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-154723336537555748165),(-154723336537555746574)⟩,⟨(-16948292823756061461),(-16948292823756059870)⟩⟩,⟨⟨(-149901963823109656143),(-149901963823109654603)⟩,⟨(-15086911875888162075),(-15086911875888160533)⟩⟩,⟨⟨(-145356199438607180905),(-145356199438607179410)⟩,⟨(-13380839532483633208),(-13380839532483631715)⟩⟩,⟨⟨(-141072146107171197760),(-141072146107171196303)⟩,⟨(-11817256044295134993),(-11817256044295133539)⟩⟩,⟨⟨(-137036728435608395636),(-137036728435608394208)⟩,⟨(-10384436678926370316),(-10384436678926368888)⟩⟩,⟨⟨(-133237654588033120376),(-133237654588033118992)⟩,⟨(-9071660055183083213),(-9071660055183081826)⟩⟩,⟨⟨(-129663379339721176221),(-129663379339721174862)⟩,⟨(-7869124296250944542),(-7869124296250943183)⟩⟩,⟨⟨(-126303068581200033926),(-126303068581200032606)⟩,⟨(-6767870367228736252),(-6767870367228734932)⟩⟩,⟨⟨(-123146565322347028950),(-123146565322347027660)⟩,⟨(-5759712012949560061),(-5759712012949558772)⟩⟩,⟨⟨(-120184357229123447500),(-120184357229123446232)⟩,⟨(-4837171758928239208),(-4837171758928237937)⟩⟩,⟨⟨(-117407545711155583945),(-117407545711155582692)⟩,⟨(-3993422481881858768),(-3993422481881857512)⟩⟩,⟨⟨(-114807816566357552407),(-114807816566357551185)⟩,⟨(-3222234096781437275),(-3222234096781436051)⟩⟩,⟨⟨(-112377412178883060136),(-112377412178883058945)⟩,⟨(-2517924945000503061),(-2517924945000501868)⟩⟩,⟨⟨(-110109105258634124769),(-110109105258634123597)⟩,⟨(-1875317503019916459),(-1875317503019915286)⟩⟩,⟨⟨(-107996174104111960429),(-107996174104111959272)⟩,⟨(-1289698063510575054),(-1289698063510573897)⟩⟩,⟨⟨(-106032379365362872708),(-106032379365362871574)⟩,⟨(-756780070622986093),(-756780070622984959)⟩⟩] +lemma kernel9_1_r3_14_eq : ∀ k : Fin 16, kernel9_1Expr 3 14 k = kernel9_1_r3_14 k := by decide +kernel +noncomputable def kernel9_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-104211942279967191542),(-104211942279967190428)⟩,⟨(-272670819134465018),(-272670819134463902)⟩⟩,⟨⟨(-102529524352280230401),(-102529524352280229291)⟩,⟨166158747096836890,166158747096838001⟩⟩,⟨⟨(-100980208444318080077),(-100980208444318079003)⟩,⟨562901377991709750,562901377991710827⟩⟩,⟨⟨(-99559481245661769036),(-99559481245661767972)⟩,⟨920438219834322174,920438219834323238⟩⟩,⟨⟨(-98263217089420182917),(-98263217089420181848)⟩,⟨1241361075361897765,1241361075361898832⟩⟩,⟨⟨(-97087663081547936523),(-97087663081547935466)⟩,⟨1527992399955373872,1527992399955374928⟩⟩,⟨⟨(-96029425511574027365),(-96029425511574026327)⟩,⟨1782403194659874287,1782403194659875322⟩⟩,⟨⟨(-95085457513986213945),(-95085457513986212904)⟩,⟨2006428940093566187,2006428940093567228⟩⟩,⟨⟨(-94253047951069814129),(-94253047951069813107)⟩,⟨2201683699714471085,2201683699714472105⟩⟩,⟨⟨(-93529811489861565843),(-93529811489861564825)⟩,⟨2369572506297173595,2369572506297174612⟩⟩,⟨⟨(-92913679848000261866),(-92913679848000260857)⟩,⟨2511302131720331563,2511302131720332573⟩⟩,⟨⟨(-92402894185593431569),(-92402894185593430557)⟩,⟨2627890327181311091,2627890327181312105⟩⟩,⟨⟨(-91995998622736339390),(-91995998622736338388)⟩,⟨2720173608640256173,2720173608640257175⟩⟩,⟨⟨(-91691834864983742691),(-91691834864983741689)⟩,⟨2788813650560329936,2788813650560330938⟩⟩,⟨⟨(-91489537921858002753),(-91489537921858001751)⟩,⟨2834302339764922972,2834302339764923974⟩⟩,⟨⟨(-91388532906354464622),(-91388532906354463622)⟩,⟨2856965530390348772,2856965530390349769⟩⟩] +lemma kernel9_1_r3_15_eq : ∀ k : Fin 16, kernel9_1Expr 3 15 k = kernel9_1_r3_15 k := by decide +kernel +noncomputable def kernel9_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel9_1_r3_0,kernel9_1_r3_1,kernel9_1_r3_2,kernel9_1_r3_3,kernel9_1_r3_4,kernel9_1_r3_5,kernel9_1_r3_6,kernel9_1_r3_7,kernel9_1_r3_8,kernel9_1_r3_9,kernel9_1_r3_10,kernel9_1_r3_11,kernel9_1_r3_12,kernel9_1_r3_13,kernel9_1_r3_14,kernel9_1_r3_15] +lemma kernel9_1_r3_eq (i k : Fin 16) : kernel9_1Expr 3 i k = kernel9_1_r3 i k := by + fin_cases i + · exact kernel9_1_r3_0_eq k + · exact kernel9_1_r3_1_eq k + · exact kernel9_1_r3_2_eq k + · exact kernel9_1_r3_3_eq k + · exact kernel9_1_r3_4_eq k + · exact kernel9_1_r3_5_eq k + · exact kernel9_1_r3_6_eq k + · exact kernel9_1_r3_7_eq k + · exact kernel9_1_r3_8_eq k + · exact kernel9_1_r3_9_eq k + · exact kernel9_1_r3_10_eq k + · exact kernel9_1_r3_11_eq k + · exact kernel9_1_r3_12_eq k + · exact kernel9_1_r3_13_eq k + · exact kernel9_1_r3_14_eq k + · exact kernel9_1_r3_15_eq k +noncomputable def kernel9_1_r4_0 : Fin 16 → CBox := ![⟨⟨8702692834422801934766092683,8702692834422801960229104676⟩,⟨2818069353417490721954370739,2818069353417490747431447244⟩⟩,⟨⟨8700156318581122976429056424,8700156318581123001884196648⟩,⟨2813768299972164556983818890,2813768299972164582452946488⟩⟩,⟨⟨8695081765862688031225961764,8695081765862688056665317218⟩,⟨2805174647994470033899395599,2805174647994470059352584347⟩⟩,⟨⟨8687466154111601509543783532,8687466154111601534959451836⟩,⟨2792305290954375892856612904,2792305290954375918285883862⟩⟩,⟨⟨8677304999766920050115618993,8677304999766920075499713326⟩,⟨2775185528165029052133211770,2775185528165029077530602123⟩⟩,⟨⟨8664592417154936394008184567,8664592417154936419352839042⟩,⟨2753849015707594821119269050,2753849015707594846476837673⟩⟩,⟨⟨8649321197021709477358980951,8649321197021709502656355213⟩,⟨2728337700990695692810386578,2728337700990695718120218820⟩⟩,⟨⟨8631482903859782811173323230,8631482903859782836415609506⟩,⟨2698701740941032410566010055,2698701740941032435820224970⟩⟩,⟨⟨8611067991475207784723287991,8611067991475207809902712051⟩,⟨2664999403824128489298635525,2664999403824128514489387005⟩⟩,⟨⟨8588065936135614988302022505,8588065936135615013410856773⟩,⟨2627296954698585391544961760,2627296954698585416664451824⟩⟩,⟨⟨8562465386537637562919900003,8562465386537637587950456167⟩,⟨2585668524514135835788105137,2585668524514135860828576734⟩⟩,⟨⟨8534254329732963822016209769,8534254329732963846960862487⟩,⟨2540195962873475275141208377,2540195962873475300094969232⟩⟩,⟨⟨8503420272057154013814831055,8503420272057154038665995517⟩,⟨2490968674490642693552947357,2490968674490642718412347722⟩⟩,⟨⟨8469950434014563080583063933,8469950434014563105333241106⟩,⟨2438083439394882206866533611,2438083439394882231624011642⟩⟩,⟨⟨8433831957986724090567068251,8433831957986724115208798558⟩,⟨2381644216948678091640558164,2381644216948678116288593785⟩⟩,⟨⟨8395052127550812032555691546,8395052127550812057081622883⟩,⟨2321761933772207018408567361,2321761933772207042939750393⟩⟩] +lemma kernel9_1_r4_0_eq : ∀ k : Fin 16, kernel9_1Expr 4 0 k = kernel9_1_r4_0 k := by decide +kernel +noncomputable def kernel9_1_r4_1 : Fin 16 → CBox := ![⟨⟨8353598597119759362261842845,8353598597119759386664652863⟩,⟨2258554255693936440633039014,2258554255693936465039991632⟩⟩,⟨⟨8309459630546653750328981347,8309459630546653774601494481⟩,⟨2192145343878613562894019297,2192145343878613587169513154⟩⟩,⟨⟨8262624347273619652156816328,8262624347273619676291874853⟩,⟨2122665595319481527608279562,2122665595319481551745107017⟩⟩,⟨⟨8213082974549855140464760527,8213082974549855164455380054⟩,⟨2050251367921223353099788091,2050251367921223377090917773⟩⟩,⟨⟨8160827104195229809768139667,8160827104195229833607330085⟩,⟨1975044690443811917368494112,1975044690443811941206892032⟩⟩,⟨⟨8105849952345191154727493130,8105849952345191178408499581⟩,⟨1897192957625024592729093716,1897192957625024616407964282⟩⟩,⟨⟨8048146620579992398989293083,8048146620579992422505330098⟩,⟨1816848610850698889068638019,1816848610850698912581158330⟩⟩,⟨⟨7987714356816732345789112931,7987714356816732369133659437⟩,⟨1734168804796641980419094033,1734168804796642003758708887⟩⟩,⟨⟨7924552814326643881989615116,7924552814326643905156076611⟩,⟨1649315060524190752239697482,1649315060524190775399781772⟩⟩,⟨⟨7858664307232704230033683135,7858664307232704253015827159⟩,⟨1562452905572426900385574557,1562452905572426923359868609⟩⟩,⟨⟨7790054060844151408339401797,7790054060844151431130882857⟩,⟨1473751501653610690496205151,1473751501653610713278339914⟩⟩,⟨⟨7718730455195021794573233523,7718730455195021817168089335⟩,⟨1383383260624086752323629509,1383383260624086774907622646⟩⟩,⟨⟨7644705260173474181678865286,7644705260173474204070964178⟩,⟨1291523449470270486551056578,1291523449470270508930760141⟩⟩,⟨⟨7567993860657491368226169562,7567993860657491390409894399⟩,⟨1198349785117837593119687858,1198349785117837615289471948⟩⟩,⟨⟨7488615470110557750293202488,7488615470110557772262712115⟩,⟨1104042019941367506572912263,1104042019941367528526926821⟩⟩,⟨⟨7406593331138056338215147887,7406593331138056359965131337⟩,⟨1008781518920856337234850437,1008781518920856358967779095⟩⟩] +lemma kernel9_1_r4_1_eq : ∀ k : Fin 16, kernel9_1Expr 4 1 k = kernel9_1_r4_1 k := by decide +kernel +noncomputable def kernel9_1_r4_2 : Fin 16 → CBox := ![⟨⟨7321954901561313858008063492,7321954901561313879532900481⟩,⟨912750829460109725412674092,912750829460109746918895121⟩⟩,⟨⟨7234732024631295995006133225,7234732024631296016300926035⟩,⟨816133244949420646058224796,816133244949420667332842403⟩⟩,⟨⟨7144961082077707873109120265,7144961082077707894168592498⟩,⟨719112363220483326762365161,719112363220483347800108840⟩⟩,⟨⟨7052683128771421444197954457,7052683128771421465017532740⟩,⟨621871641104531395513259368,621871641104531416309564965⟩⟩,⟨⟨6957944007868407170768212136,6957944007868407191342858068⟩,⟨524593946364549252376138306,524593946364549272925980592⟩⟩,⟨⟨6860794445401309169464887719,6860794445401309189790492820⟩,⟨427461108328423664012651628,427461108328423684311938379⟩⟩,⟨⟨6761290123390029333580427200,6761290123390029353652334773⟩,⟨330653468601417551703856141,330653468601417571747950833⟩⟩,⟨⟨6659491730654677584720112967,6659491730654677604534564830⟩,⟨234349433282713017512159926,234349433282713037297327490⟩⟩,⟨⟨6555464990632446483339845971,6555464990632446502892411020⟩,⟨138725028151358985005397665,138725028151359004527234004⟩⟩,⟨⟨6449280665623768349953807375,6449280665623768369241264618⟩,⟨43953458321170323078553930,43953458321170342333867580⟩⟩,⟨⟨6341014537021848790101277263,6341014537021848809119638341⟩,⟨(-49795326108606715210786153),(-49795326108606696225950226)⟩⟩,⟨⟨6230747361212629565022904396,6230747361212629583769290901⟩,⟨(-142355056860250226212616417),(-142355056860250207501100956)⟩⟩,⟨⟨6118564800968657617265031710,6118564800968657635735692890⟩,⟨(-233563565183680147794937145),(-233563565183680129360453505)⟩⟩,⟨⟨6004557332299425363303051661,6004557332299425381500529111⟩,⟨(-323263188899810167287801206),(-323263188899810149127755191)⟩⟩,⟨⟨5888820126861662471592572586,5888820126861662489517158167⟩,⟨(-411301167224487934758839051),(-411301167224487916872885794)⟩⟩,⟨⟨5771452910174931554952815375,5771452910174931572602493258⟩,⟨(-497530021830714763373940410),(-497530021830714745764049790)⟩⟩] +lemma kernel9_1_r4_2_eq : ∀ k : Fin 16, kernel9_1Expr 4 2 k = kernel9_1_r4_2 k := by decide +kernel +noncomputable def kernel9_1_r4_3 : Fin 16 → CBox := ![⟨⟨5652559796029813447105000890,5652559796029813464476607723⟩,⟨(-581807922630468156643422315),(-581807922630468139312708268)⟩⟩,⟨⟨5532249097617045720743555446,5532249097617045737835699903⟩,⟨(-663999036790543982595254450),(-663999036790543965545058081)⟩⟩,⟨⟨5410633116045270939176550031,5410633116045270955986583734⟩,⟨(-743973859539480374249615549),(-743973859539480357482531692)⟩⟩,⟨⟨5287827907051622270737126276,5287827907051622287263945769⟩,⟨(-821609525374833945109257168),(-821609525374833928626335119)⟩⟩,⟨⟨5163953026842287635474879738,5163953026842287651716022747⟩,⟨(-896790098341780878637515901),(-896790098341780862441160598)⟩⟩,⟨⟨5039131258128521787063458161,5039131258128521803018492197⟩,⟨(-969406840125058316205087930),(-969406840125058300295514154)⟩⟩,⟨⟨4913488317546406867199400915,4913488317546406882866468669⟩,⟨(-1039358454776409163137349650),(-1039358454776409147516015444)⟩⟩,⟨⟨4787152545765107966624789295,4787152545765107982003711948⟩,⟨(-1106551308988626491723729705),(-1106551308988626476390765631)⟩⟩,⟨⟨4660254581697574666769849411,4660254581697574681858807999⟩,⟨(-1170899626924610220221283391),(-1170899626924610205178457953)⟩⟩,⟨⟨4532927022328785427518165571,4532927022328785442317679131⟩,⟨(-1232325658715066105005285075),(-1232325658715066090252030677)⟩⟩,⟨⟨4405304069768949135907127017,4405304069768949150415964664⟩,⟨(-1290759821851034709627412406),(-1290759821851034695164909343)⟩⟩,⟨⟨4277521167221851782063658714,4277521167221851796282559351⟩,⟨(-1346140814816700816435659666),(-1346140814816700802263120265)⟩⟩,⟨⟨4149714625631112391294676944,4149714625631112405222545663⟩,⟨(-1398415702433196459111892367),(-1398415702433196445230360965)⟩⟩,⟨⟨4022021242828905712275192704,4022021242828905725913441178⟩,⟨(-1447539972514603078002607979),(-1447539972514603064410624940)⟩⟩,⟨⟨3894577917062209064859467729,3894577917062209078207570703⟩,⟨(-1493477563572250797942427483),(-1493477563572250784640468481)⟩⟩,⟨⟨3767521256810406808463989217,3767521256810406821523574027⟩,⟨(-1536200863441823543322611895),(-1536200863441823530309002548)⟩⟩] +lemma kernel9_1_r4_3_eq : ∀ k : Fin 16, kernel9_1Expr 4 3 k = kernel9_1_r4_3 k := by decide +kernel +noncomputable def kernel9_1_r4_4 : Fin 16 → CBox := ![⟨⟨3640987188834793048821133658,3640987188834793061591717373⟩,⟨(-1575690678848780432952875594),(-1575690678848780420228050283)⟩⟩,⟨⟨3515110566414896037947444659,3515110566414896050431391388⟩,⟨(-1611936176070232051392919342),(-1611936176070232038954468841)⟩⟩,⟨⟨3390024779728443987586723777,3390024779728443999784192221⟩,⟨(-1644934792994671185822064530),(-1644934792994671173669783708)⟩⟩,⟨⟨3265861370321135320433990904,3265861370321135332347445671⟩,⟨(-1674692123023837672466746212),(-1674692123023837660598127157)⟩⟩,⟨⟨3142749651589198009806908871,3142749651589198021436573951⟩,⟨(-1701221771402471306230643169),(-1701221771402471294645417508)⟩⟩,⟨⟨3020816337162152451505960096,3020816337162152462854963721⟩,⟨(-1724545184700748894616541690),(-1724545184700748883311540685)⟩⟩,⟨⟨2900185179025458614024155492,2900185179025458625093303871⟩,⟨(-1744691454309792964322688047),(-1744691454309792953297064055)⟩⟩,⟨⟨2780976617163156834095066769,2780976617163156844887590251⟩,⟨(-1761697094941779347554181886),(-1761697094941779336804666716)⟩⟩,⟨⟨2663307442429623834953128467,2663307442429623845469795621⟩,⟨(-1775605799251884910432913045),(-1775605799251884899958699456)⟩⟩,⟨⟨2547290474277675104575858318,2547290474277675114820602389⟩,⟨(-1786468169818667450052864532),(-1786468169818667439849985025)⟩⟩,⟨⟨2433034254878054007665398968,2433034254878054017639623094⟩,⟨(-1794341429831565150817243823),(-1794341429831565140884260279)⟩⟩,⟨⟨2320642761063542969743690949,2320642761063542979451301500⟩,⟨(-1799289113938204973505345685),(-1799289113938204963838320669)⟩⟩,⟨⟨2210215135420276821078682813,2210215135420276830546268757⟩,⟨(-1801380740799342319425817797),(-1801380740799342309996583013)⟩⟩,⟨⟨2101845437730168438361029775,2101845437730168447593726370⟩,⟨(-1800691468984812601417014120),(-1800691468984812592220388083)⟩⟩,⟨⟨1995622417842571842942734022,1995622417842571851941368427⟩,⟨(-1797301737919230207930583145),(-1797301737919230198965798042)⟩⟩,⟨⟨1891629310921363737540283300,1891629310921363746308239165⟩,⟨(-1791296895650776104760895546),(-1791296895650776096024630149)⟩⟩] +lemma kernel9_1_r4_4_eq : ∀ k : Fin 16, kernel9_1Expr 4 4 k = kernel9_1_r4_4 k := by decide +kernel +noncomputable def kernel9_1_r4_5 : Fin 16 → CBox := ![⟨⟨1789943655876524483586116020,1789943655876524492124064856⟩,⟨(-1782766815269814767754845349),(-1782766815269814759246489531)⟩⟩,⟨⟨1690637137648085591698346341,1690637137648085600010327565⟩,⟨(-1771805501845909963666447283),(-1771805501845909955382026201)⟩⟩,⟨⟨1593775453866053705964012220,1593775453866053714051309393⟩,⟨(-1758510691781799179047308952),(-1758510691781799170985602418)⟩⟩,⟨⟨1499418206263710703619887182,1499418206263710711486371740⟩,⟨(-1742983446500869223477247029),(-1742983446500869215634449157)⟩⟩,⟨⟨1407618817074624879195102443,1407618817074624886841951769⟩,⟨(-1725327742390582063717396553),(-1725327742390582056092394378)⟩⟩,⟨⟨1318424470496887174497706192,1318424470496887181929326021⟩,⟨(-1705650058918162444077000964),(-1705650058918162436665455154)⟩⟩,⟨⟨1231876079162595869545744321,1231876079162595876763821365⟩,⟨(-1684058966816809660323974171),(-1684058966816809653124263203)⟩⟩,⟨⟨1148008275407518813597146866,1148008275407518820605948014⟩,⟨(-1660664718210965838467969074),(-1660664718210965831475892409)⟩⟩,⟨⟨1066849426996199140610153896,1066849426996199147411152599⟩,⟨(-1635578840508088906777491250),(-1635578840508088899991640579)⟩⟩,⟨⟨988421676822533383844894718,988421676822533390442923250⟩,⟨(-1608913735832358963476743087),(-1608913735832358956892352221)⟩⟩,⟨⟨912741005975985938397633249,912741005975985944794719915⟩,⟨(-1580782287713298276012713248),(-1580782287713298269627818709)⟩⟩,⟨⟨839817319439999637962004007,839817319439999644162711673⟩,⟨(-1551297476669996051989177363),(-1551297476669996045799281291)⟩⟩,⟨⟨769654553572642660836444707,769654553572642666842630705⟩,⟨(-1520572006250163429334993513),(-1520572006250163423338302431)⟩⟩,⟨⟨702250804410849142937951248,702250804410849148754615615⟩,⟨(-1488717940993334492402226324),(-1488717940993334486593803843)⟩⟩,⟨⟨637598475739438993223082917,637598475739438998852527713⟩,⟨(-1455846357689969077905283011),(-1455846357689969072282889590)⟩⟩,⟨⟨575684445775032677275734339,575684445775032682722716673⟩,⟨(-1422067011203848861986017536),(-1422067011203848856544957829)⟩⟩] +lemma kernel9_1_r4_5_eq : ∀ k : Fin 16, kernel9_1Expr 4 5 k = kernel9_1_r4_5 k := by decide +kernel +noncomputable def kernel9_1_r4_6 : Fin 16 → CBox := ![⟨⟨516490251233513041144996770,516490251233513046411527224⟩,⟨(-1387488016014879786538488915),(-1387488016014879781276813071)⟩⟩,⟨⟨459992287478241852631932864,459992287478241857723243530⟩,⟨(-1352215544524146180579826155),(-1352215544524146175492361607)⟩⟩,⟨⟨406162023385133972480962004,406162023385133977399557899⟩,⟨(-1316353543043755358957927008),(-1316353543043755354042227287)⟩⟩,⟨⟨354966229510153027551865875,354966229510153032302597224⟩,⟨(-1280003466271632499718527854),(-1280003466271632494969799690)⟩⟩,⟨⟨306367218104950702252733637,306367218104950706837878452⟩,⟨(-1243264030926947284266680349),(-1243264030926947279682701870)⟩⟩,⟨⟨260323093497265016364273427,260323093497265020789005000⟩,⟨(-1206230989096246448046716041),(-1206230989096246443622367997)⟩⟩,⟨⟨216788011334266771503957512,216788011334266775774883327⟩,⟨(-1168996921714588435630317360),(-1168996921714588431359047490)⟩⟩,⟨⟨175712445179153712225956684,175712445179153716349093026⟩,⟨(-1131651052480965415432016065),(-1131651052480965411307859654)⟩⟩,⟨⟨137043458953708769618399430,137043458953708773595761154⟩,⟨(-1094279082383962396986887577),(-1094279082383962393007880096)⟩⟩,⟨⟨100724983731950179835872047,100724983731950183672357920⟩,⟨(-1056963044892814340353006882),(-1056963044892814336514296977)⟩⟩,⟨⟨66698097412018753628808638,66698097412018757326826698⟩,⟨(-1019781181751606624831530965),(-1019781181751606621130757606)⟩⟩,⟨⟨34901305824611642537967150,34901305824611646102002072⟩,⟨(-982807839201097433220363713),(-982807839201097429653086389)⟩⟩,⟨⟨5270823876058560724094258,5270823876058564156296211⟩,⟨(-946113384344240578446981387),(-946113384344240575011093850)⟩⟩,⟨⟨(-22259144628036162208510799),(-22259144628036158903428604)⟩,⟨(-909764141268609560627493526),(-909764141268609557318323084)⟩⟩,⟨⟨(-47756129777426251135249092),(-47756129777426247954857006)⟩,⟨(-873822346442156698167116115),(-873822346442156694982273498)⟩⟩,⟨⟨(-71289122207001652015905421),(-71289122207001648955851503)⟩,⟨(-838346122808602921191663568),(-838346122808602918126834001)⟩⟩] +lemma kernel9_1_r4_6_eq : ∀ k : Fin 16, kernel9_1Expr 4 6 k = kernel9_1_r4_6 k := by decide +kernel +noncomputable def kernel9_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-92928304770589387044076878),(-92928304770589384102278560)⟩,⟨(-803389471925688787556524197),(-803389471925688784609662444)⟩⟩,⟨⟨(-112744790334373813146731460),(-112744790334373810318575685)⟩,⟨(-769002283413894781144509275),(-769002283413894778311035626)⟩⟩,⟨⟨(-130810366707721544346191070),(-130810366707721541629279207)⟩,⟨(-735230360915352019696259971),(-735230360915352016973809459)⟩⟩,⟨⟨(-147197249647620872109724735),(-147197249647620869499899520)⟩,⟨(-702115463702729741185716914),(-702115463702729738570162469)⟩⟩,⟨⟨(-161977844788376444277106943),(-161977844788376441772194336)⟩,⟨(-669695363026044170017832592),(-669695363026044167507067681)⟩⟩,⟨⟨(-175224519261403363233249912),(-175224519261403360828825274)⟩,⟨(-638003912241651044177825327),(-638003912241651041767549143)⟩⟩,⟨⟨(-187009383681695451395697120),(-187009383681695449089451484)⟩,⟨(-607071129732155480349167724),(-607071129732155478037088645)⟩⟩,⟨⟨(-197404085088536706909048723),(-197404085088536704695863074)⟩,⟨(-576923293598522906047655860),(-576923293598522903828669661)⟩⟩,⟨⟨(-206479611338994873900166231),(-206479611338994871772513196)⟩,⟨(-547583047086162596380835727),(-547583047086162594247432492)⟩⟩,⟨⟨(-214306107364363129156335741),(-214306107364363127110634423)⟩,⟨(-519069513694978232639773755),(-519069513694978230588383886)⟩⟩,⟨⟨(-220952703612646035615439683),(-220952703612646033649960636)⟩,⟨(-491398420919077926170290719),(-491398420919077924199196938)⟩⟩,⟨⟨(-226487356915024713404952152),(-226487356915024711516508566)⟩,⟨(-464582231564697128714403390),(-464582231564697126820428353)⟩⟩,⟨⟨(-230976703931544871522475974),(-230976703931544869709581352)⟩,⟨(-438630281604552625899310527),(-438630281604552624080977951)⟩⟩,⟨⟨(-234485927251563454334790519),(-234485927251563452594151974)⟩,⟨(-413548923542913850283306161),(-413548923542913848537330402)⟩⟩,⟨⟨(-237078634148228291905794775),(-237078634148228290235761981)⟩,⟨(-389341674287712909457313958),(-389341674287712907782052684)⟩⟩,⟨⟨(-238816747913860943008425057),(-238816747913860941406035189)⟩,⟨(-366009366553551127919398389),(-366009366553551126311894450)⟩⟩] +lemma kernel9_1_r4_7_eq : ∀ k : Fin 16, kernel9_1Expr 4 7 k = kernel9_1_r4_7 k := by decide +kernel +noncomputable def kernel9_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-239760411634922678664221923),(-239760411634922677128124154)⟩,⟨(-343550302852007861868092898),(-343550302852007860327001912)⟩⟩,⟨⟨(-239967904201569480450955335),(-239967904201569478978043952)⟩,⟨(-321960411162709250820398878),(-321960411162709249342618915)⟩⟩,⟨⟨(-239495568287891525595366065),(-239495568287891524184091851)⟩,⟨(-301233401419650663700168451),(-301233401419650662284154848)⟩⟩,⟨⟨(-238397749984979173505609332),(-238397749984979172153251994)⟩,⟨(-281360921991760601612249020),(-281360921991760600255284107)⟩⟩,⟨⟨(-236726749720101027397980607),(-236726749720101026103220042)⟩,⟨(-262332715384118330289335878),(-262332715384118328990102824)⟩⟩,⟨⟨(-234532784051608633152747653),(-234532784051608631912144888)⟩,⟨(-244136772436069123570768212),(-244136772436069122326038084)⟩⟩,⟨⟨(-231863957890735561584246399),(-231863957890735560396377882)⟩,⟨(-226759484344205093968609152),(-226759484344205092776956265)⟩⟩,⟨⟨(-228766246668227550340270765),(-228766246668227549202724647)⟩,⟨(-210185791891294795901344703),(-210185791891294794760338463)⟩⟩,⟨⟨(-225283487935672190092958405),(-225283487935672189004615924)⟩,⟨(-194399331316267029484491272),(-194399331316267028392995748)⟩⟩,⟨⟨(-221457381868397152780105207),(-221457381868397151738470249)⟩,⟨(-179382576314820388168484753),(-179382576314820387123986116)⟩⟩,⟨⟨(-217327500118743066726002009),(-217327500118743065729818159)⟩,⟨(-165116975714701040570303869),(-165116975714701039571529441)⟩⟩,⟨⟨(-212931302455224370388802421),(-212931302455224369435900035)⟩,⟨(-151583086423754840892179203),(-151583086423754839936943019)⟩⟩,⟨⟨(-208304160614371707346350272),(-208304160614371706435672519)⟩,⟨(-138760701302133109678221335),(-138760701302133108765451461)⟩⟩,⟨⟨(-203479388787678720591340801),(-203479388787678719720692195)⟩,⟨(-126628971662162306686158236),(-126628971662162305813644019)⟩⟩,⟨⟨(-198488280165807564121324515),(-198488280165807563289570151)⟩,⟨(-115166524150056717893505920),(-115166524150056717060098368)⟩⟩,⟨⟨(-193360148965775073166565440),(-193360148965775072371277600)⟩,⟨(-104351571812573946253987788),(-104351571812573945457245289)⟩⟩] +lemma kernel9_1_r4_8_eq : ∀ k : Fin 16, kernel9_1Expr 4 8 k = kernel9_1_r4_8 k := by decide +kernel +noncomputable def kernel9_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-188122377373964030076461448),(-188122377373964029315758887)⟩,⟨(-94162019198633080733294893),(-94162019198633079971323156)⟩⟩,⟨⟨(-182800466848188470781808484),(-182800466848188470053824610)⟩,⟨(-84575561390616620432103198),(-84575561390616619703022947)⟩⟩,⟨⟨(-177418093235387660466130603),(-177418093235387659769970870)⟩,⟨(-75569776902375075337539574),(-75569776902375074640444365)⟩⟩,⟨⟨(-171997165177524845713413462),(-171997165177524845047482635)⟩,⟨(-67122214420696434178553046),(-67122214420696433511836185)⟩⟩,⟨⟨(-166557885296617479360919227),(-166557885296617478724482655)⟩,⟨(-59210473404072539120361934),(-59210473404072538483277939)⟩⟩,⟨⟨(-161118813670220351315906791),(-161118813670220350707349460)⟩,⟨(-51812278586903204106735539),(-51812278586903203497659043)⟩⟩,⟨⟨(-155696933130821494172427183),(-155696933130821493590952410)⟩,⟨(-44905548468768826597549723),(-44905548468768826015674219)⟩⟩,⟨⟨(-150307715946199469616876079),(-150307715946199469061078412)⟩,⟨(-38468457897043616362407790),(-38468457897043615806318567)⟩⟩,⟨⟨(-144965191462545613152695012),(-144965191462545612621951239)⟩,⟨(-32479494876911119761499081),(-32479494876911119230564033)⟩⟩,⟨⟨(-139682014317803291574885477),(-139682014317803291067749758)⟩,⟨(-26917511765802602289769930),(-26917511765802601782534996)⟩⟩,⟨⟨(-134469532858958554618272206),(-134469532858958554134043344)⟩,⟨(-21761771029450586840025114),(-21761771029450586355781152)⟩⟩,⟨⟨(-129337857423687622098229454),(-129337857423687621635680273)⟩,⟨(-16991985754198188575279705),(-16991985754198188112792250)⟩⟩,⟨⟨(-124295928173597057835703956),(-124295928173597057394266288)⟩,⟨(-12588355125011653741800662),(-12588355125011653300494411)⟩⟩,⟨⟨(-119351582193069529487166339),(-119351582193069529065606008)⟩,⟨(-8531595090906369879165093),(-8531595090906369457799510)⟩⟩,⟨⟨(-114511619594256382811535115),(-114511619594256382409241918)⟩,⟨(-4802964449326905066198813),(-4802964449326904664157401)⟩⟩,⟨⟨(-109781868394860317104098770),(-109781868394860316720009845)⟩,⟨(-1384286588542199535010397),(-1384286588542199151224708)⟩⟩] +lemma kernel9_1_r4_9_eq : ∀ k : Fin 16, kernel9_1Expr 4 9 k = kernel9_1_r4_9 k := by decide +kernel +noncomputable def kernel9_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-105167247960867709554801792),(-105167247960867709187814510)⟩,⟨1742032867539872233088931,1742032867539872599727282⟩⟩,⟨⟨(-100671830831179116898415307),(-100671830831179116547417745)⟩,⟨4592992264429090188051757,4592992264429090538659452⟩⟩,⟨⟨(-96298902765024567449341777),(-96298902765024567113864815)⟩,⟨7184983722858635499719091,7184983722858635834770104⟩⟩,⟨⟨(-92051020876031350832100203),(-92051020876031350511281587)⟩,⟨9533786296549522461620290,9533786296549522781981021⟩⟩,⟨⟨(-87930069738747042133988655),(-87930069738747041827460939)⟩,⟨11654562235068163272329731,11654562235068163578371940⟩⟩,⟨⟨(-83937315374236773241542236),(-83937315374236772948434380)⟩,⟨13561856108278861125438840,13561856108278861418037016⟩⟩,⟨⟨(-80073457041014234084976716),(-80073457041014233804886125)⟩,⟨15269596553552928592520139,15269596553552928872080550⟩⟩,⟨⟨(-76338676775988287761467171),(-76338676775988287493652307)⟩,⟨16791100412701114775458697,16791100412701115042725861⟩⟩,⟨⟨(-72732686647283019611599635),(-72732686647283019355765382)⟩,⟨18139079032402192419554162,18139079032402192674826465⟩⟩,⟨⟨(-69254773696702997383469507),(-69254773696702997138849825)⟩,⟨19325646509568585189525347,19325646509568585433571206⟩⟩,⟨⟨(-65903842564263839056873837),(-65903842564263838823120743)⟩,⟨20362329671485947391652536,20362329671485947624835362⟩⟩,⟨⟨(-62678455800598008977665498),(-62678455800598008754144701)⟩,⟨21260079589559986966101454,21260079589559987189058686⟩⟩,⟨⟨(-59576871885193967193118454),(-59576871885193966979423057)⟩,⟨22029284434979699479141709,22029284434979699692281480⟩⟩,⟨⟨(-56597080979358923217053540),(-56597080979358923012308897)⟩,⟨22679783494447995762925661,22679783494447995967123185⟩⟩,⟨⟨(-53736838452544647770404610),(-53736838452544647574353689)⟩,⟨23220882174232544950347446,23220882174232545145860621⟩⟩,⟨⟨(-50993696229281809247568933),(-50993696229281809059701417)⟩,⟨23661367831053496205616326,23661367831053496392955843⟩⟩] +lemma kernel9_1_r4_10_eq : ∀ k : Fin 16, kernel9_1Expr 4 10 k = kernel9_1_r4_10 k := by decide +kernel +noncomputable def kernel9_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-48365032011476443318079858),(-48365032011476443138223391)⟩,⟨24009526278660597886214936,24009526278660598065553903⟩⟩,⟨⟨(-45848076437282377024546552),(-45848076437282376852164016)⟩,⟨24273158829278191704916684,24273158829278191876792342⟩⟩,⟨⟨(-43439938243229371026060946),(-43439938243229370860936952)⟩,⟨24459599739338747567105022,24459599739338747731733248⟩⟩,⟨⟨(-41137627500814931640576002),(-41137627500814931482275932)⟩,⟨24575733939018064812376578,24575733939018064970192081⟩⟩,⟨⟨(-38938077002416752934460852),(-38938077002416752782829539)⟩,⟨24628014934969769311830611,24628014934969769462988942⟩⟩,⟨⟨(-36838161874212472334281303),(-36838161874212472188875002)⟩,⟨24622482785282536843207544,24622482785282536988152383⟩⟩,⟨⟨(-34834717495864397170376573),(-34834717495864397030974826)⟩,⟨24564782055007009445851152,24564782055007009584803180⟩⟩,⟨⟨(-32924555808099648749149279),(-32924555808099648615184418)⟩,⟨24460179669583926282717718,24460179669583926416244576⟩⟩,⟨⟨(-31104480090050817871744692),(-31104480090050817743119753)⟩,⟨24313582592120319567771668,24313582592120319695970482⟩⟩,⟨⟨(-29371298288377765337796512),(-29371298288377765214139056)⟩,⟨24129555258682558666637864,24129555258682558789880833⟩⟩,⟨⟨(-27721834979825232764457180),(-27721834979825232645636072)⟩,⟨23912336713585047198299372,23912336713585047316717653⟩⟩,⟨⟨(-26152942048039252831604863),(-26152942048039252717322243)⟩,⟨23665857394038201331674514,23665857394038201445565730⟩⟩,⟨⟨(-24661508154221654905563671),(-24661508154221654795733970)⟩,⟨23393755520470466434036246,23393755520470466543485972⟩⟩,⟨⟨(-23244467079597580043930025),(-23244467079597579938244170)⟩,⟨23099393055352423156714851,23099393055352423262031846⟩⟩,⟨⟨(-21898805015754610683827875),(-21898805015754610582178688)⟩,⟨22785871199426276123529776,22785871199426276224821126⟩⟩,⟨⟨(-20621566876729925430455210),(-20621566876729925332572079)⟩,⟨22456045399884492447742921,22456045399884492545285193⟩⟩] +lemma kernel9_1_r4_11_eq : ∀ k : Fin 16, kernel9_1Expr 4 11 k = kernel9_1_r4_11 k := by decide +kernel +noncomputable def kernel9_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-19409861704317015937052973),(-19409861704317015842864307)⟩,⟨22112539850253436978989289,22112539850253437072859693⟩⟩,⟨⟨(-18260867235476254572695524),(-18260867235476254481927989)⟩,⟨21757761466530604291252389,21757761466530604381722858⟩⟩,⟨⟨(-17171833698001343430084680),(-17171833698001343342653833)⟩,⟨21393913328508858331073020,21393913328508858418226877⟩⟩,⟨⟨(-16140086897750831703320422),(-16140086897750831619013554)⟩,⟨21023007579211302451375700,21023007579211302535424445⟩⟩,⟨⟨(-15163030657831970430221353),(-15163030657831970348989484)⟩,⟨20646877778970980883368621,20646877778970980964360234⟩⟩,⟨⟨(-14238148667151830631058973),(-14238148667151830552678071)⟩,⟨20267190713936832015364833,20267190713936832093522240⟩⟩,⟨⟨(-13363005792753705301559760),(-13363005792753705225961858)⟩,⟨19885457661688467242857300,19885457661688467318247536⟩⟩,⟨⟨(-12535248907358515100839729),(-12535248907358515027843879)⟩,⟨19503045119215481752095250,19503045119215481824898297⟩⟩,⟨⟨(-11752607280551822427958210),(-11752607280551822357535183)⟩,⟨19121185000780669821999051,19121185000780669892243328⟩⟩,⟨⟨(-11012892579115242431443905),(-11012892579115242363394102)⟩,⟨18740984315159561507480241,18740984315159561575364451⟩⟩,⟨⟨(-10313998519112298421684273),(-10313998519112298355953483)⟩,⟨18363434333450058168807535,18363434333450058234385136⟩⟩,⟨⟨(-9653900209516678421435308),(-9653900209516678357869481)⟩,⟨17989419260094479433008174,17989419260094479496432451⟩⟩,⟨⟨(-9030653224426924941554876),(-9030653224426924880127970)⟩,⟨17619724420970669576820931,17619724420970669638117259⟩⟩,⟨⟨(-8442392438255431771880029),(-8442392438255431712426828)⟩,⟨17255043983407208354425553,17255043983407208413758447⟩⟩,⟨⟨(-7887330655719059205492838),(-7887330655719059147970571)⟩,⟨16895988223778014317540069,16895988223778014374951703⟩⟩,⟨⟨(-7363757065999915628355791),(-7363757065999915572632988)⟩,⟨16543090358950930547893101,16543090358950930603514326⟩⟩] +lemma kernel9_1_r4_12_eq : ∀ k : Fin 16, kernel9_1Expr 4 12 k = kernel9_1_r4_12 k := by decide +kernel +noncomputable def kernel9_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-6870035548092606966959943),(-6870035548092606913026661)⟩,⟨16196812958319807214488559,16196812958319807268328797⟩⟩,⟨⟨(-6404602852111897944916746),(-6404602852111897892622631)⟩,⟨15857553953455995090533156,15857553953455995142742201⟩⟩,⟨⟨(-5965966679204420017088458),(-5965966679204419966400137)⟩,⟨15525652262588132813933960,15525652262588132864544706⟩⟩,⟨⟨(-5552703680690876349569699),(-5552703680690876300374687)⟩,⟨15201393047172948179855974,15201393047172948228980428⟩⟩,⟨⟨(-5163457395161249871762914),(-5163457395161249824050655)⟩,⟨14885012617767983157288603,14885012617767983204936898⟩⟩,⟨⟨(-4796936140454087816217757),(-4796936140454087769864715)⟩,⟨14576703006272347030718619,14576703006272347077013858⟩⟩,⟨⟨(-4451910875770552555921818),(-4451910875770552510902313)⟩,⟨14276616221375622384328334,14276616221375622429295818⟩⟩,⟨⟨(-4127213047602499649948556),(-4127213047602499606165917)⟩,⟨13984868203758886312373469,13984868203758886356109495⟩⟩,⟨⟨(-3821732431688739457654697),(-3821732431688739415109210)⟩,⟨13701542497235639022439303,13701542497235639064943240⟩⟩,⟨⟨(-3534414981851780412489946),(-3534414981851780371068549)⟩,⟨13426693651613629178266155,13426693651613629219650744⟩⟩,⟨⟨(-3264260695305295428759770),(-3264260695305295388443049)⟩,⟨13160350372609728241747393,13160350372609728282031742⟩⟩,⟨⟨(-3010321502856560905701135),(-3010321502856560866405599)⟩,⟨12902518433666982724502178,12902518433666982763769492⟩⟩,⟨⟨(-2771699191354228179715314),(-2771699191354228141440534)⟩,⟨12653183364012891292042758,12653183364012891330293186⟩⟩,⟨⟨(-2547543364745873333750040),(-2547543364745873296401479)⟩,⟨12412312926767252852681082,12412312926767252890008917⟩⟩,⟨⟨(-2337049449207596023364984),(-2337049449207595986928271)⟩,⟨12179859400362398456113011,12179859400362398492532383⟩⟩,⟨⟨(-2139456746985202435274237),(-2139456746985202399676769)⟩,⟨11955761675983422642649193,11955761675983422678232490⟩⟩] +lemma kernel9_1_r4_13_eq : ∀ k : Fin 16, kernel9_1Expr 4 13 k = kernel9_1_r4_13 k := by decide +kernel +noncomputable def kernel9_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-1954046542838893141964454),(-1954046542838893107215483)⟩,⟨11739947183175756231825003,11739947183175756266562742⟩⟩,⟨⟨(-1780140266306582556804467),(-1780140266306582522814098)⟩,⟨11532333655206115395491433,11532333655206115429473329⟩⟩,⟨⟨(-1617097712390751723095473),(-1617097712390751689853362)⟩,⟨11332830745204056489816419,11332830745204056523052623⟩⟩,⟨⟨(-1464315322725906231854431),(-1464315322725906199296932)⟩,⟨11141341503558126301099942,11141341503558126333653938⟩⟩,⟨⟨(-1321224528794202360790665),(-1321224528794202328923834)⟩,⟨10957763726495550900999943,10957763726495550932865487⟩⟩,⟨⟨(-1187290158321662727701299),(-1187290158321662696450341)⟩,⟨10781991185239779525897235,10781991185239779557148995⟩⟩,⟨⟨(-1062008905602808545512036),(-1062008905602808514869766)⟩,⟨10613914744617850936786467,10613914744617850967431464⟩⟩,⟨⟨(-944907866163817000673262),(-944907866163816970583376)⟩,⟨10453423379481000462892653,10453423379481000492987073⟩⟩,⟨⟨(-835543135879954109037931),(-835543135879954079513005)⟩,⟨10300405096808392464066295,10300405096808392493597407⟩⟩,⟨⟨(-733498474408683853900000),(-733498474408683824868081)⟩,⟨10154747770886284379705076,10154747770886284408744743⟩⟩,⟨⟨(-638384032582329533926881),(-638384032582329505383223)⟩,⟨10016339898493994243047364,10016339898493994271600204⟩⟩,⟨⟨(-549835143220449265183630),(-549835143220449237077874)⟩,⟨9885071280584218674213025,9885071280584218702329305⟩⟩,⟨⟨(-467511174669341357873902),(-467511174669341330216089)⟩,⟨9760833636518797674714326,9760833636518797702383872⟩⟩,⟨⟨(-391094446251643266864502),(-391094446251643239592773)⟩,⟨9643521156512032495944626,9643521156512032523229240⟩⟩,⟨⟨(-320289204710323541784517),(-320289204710323514895978)⟩,⟨9533030997542062090887974,9533030997542062117790440⟩⟩,⟨⟨(-254820660656146721460593),(-254820660656146694909613)⟩,⟨9429263727616381802243714,9429263727616381828809598⟩⟩] +lemma kernel9_1_r4_14_eq : ∀ k : Fin 16, kernel9_1Expr 4 14 k = kernel9_1_r4_14 k := by decide +kernel +noncomputable def kernel9_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-194434083973732343397288),(-194434083973732317200392)⟩,⟨9332123722920012816528900,9332123722920012842741560⟩⟩,⟨⟨(-138893957106600535531135),(-138893957106600509625729)⟩,⟨9241519522033664215493863,9241519522033664241415860⟩⟩,⟨⟨(-87983185124214703793233),(-87983185124214678177700)⟩,⟨9157364141083940964526072,9157364141083940990158925⟩⟩,⟨⟨(-41502361472253965535570),(-41502361472253940168015)⟩,⟨9079575353377631548857267,9079575353377631574242829⟩⟩,⟨⟨730911680434915253916,730911680434940361155⟩,⟨9008075936776681222228977,9008075936776681247354811⟩⟩,⟨⟨38882649560027271946158,38882649560027296847069⟩,⟨8942793891788886559281979,8942793891788886584202043⟩⟩,⟨⟨73103058396996736562846,73103058396996761258213⟩,⟨8883662633080851428801617,8883662633080851453516612⟩⟩,⟨⟨103527057506653019747838,103527057506653044276753⟩,⟨8830621156863500438194875,8830621156863500462743861⟩⟩,⟨⟨130274750766605045849106,130274750766605070194448⟩,⟨8783614186355596694489192,8783614186355596718854963⟩⟩,⟨⟨153451848354617281923469,153451848354617306140990⟩,⟨8742592297296372291580116,8742592297296372315818399⟩⟩,⟨⟨173150039541417300238064,173150039541417324328135⟩,⟨8707512025253645915039179,8707512025253645939150282⟩⟩,⟨⟨189447317258281392691812,189447317258281416691526⟩,⟨8678335956257748130305748,8678335956257748154326727⟩⟩,⟨⟨202408255079494633073706,202408255079494656969601⟩,⟨8655032802083262914452730,8655032802083262938370039⟩⟩,⟨⟨212084237175812159416557,212084237175812183258792⟩,⟨8637577461299074361472998,8637577461299074385336789⟩⟩,⟨⟨218513641707545375422547,218513641707545399211520⟩,⟨8625951067011522282918929,8625951067011522306729528⟩⟩,⟨⟨221721978035519633477326,221721978035519657248818⟩,⟨8620141022034655241465674,8620141022034655265258844⟩⟩] +lemma kernel9_1_r4_15_eq : ∀ k : Fin 16, kernel9_1Expr 4 15 k = kernel9_1_r4_15 k := by decide +kernel +noncomputable def kernel9_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel9_1_r4_0,kernel9_1_r4_1,kernel9_1_r4_2,kernel9_1_r4_3,kernel9_1_r4_4,kernel9_1_r4_5,kernel9_1_r4_6,kernel9_1_r4_7,kernel9_1_r4_8,kernel9_1_r4_9,kernel9_1_r4_10,kernel9_1_r4_11,kernel9_1_r4_12,kernel9_1_r4_13,kernel9_1_r4_14,kernel9_1_r4_15] +lemma kernel9_1_r4_eq (i k : Fin 16) : kernel9_1Expr 4 i k = kernel9_1_r4 i k := by + fin_cases i + · exact kernel9_1_r4_0_eq k + · exact kernel9_1_r4_1_eq k + · exact kernel9_1_r4_2_eq k + · exact kernel9_1_r4_3_eq k + · exact kernel9_1_r4_4_eq k + · exact kernel9_1_r4_5_eq k + · exact kernel9_1_r4_6_eq k + · exact kernel9_1_r4_7_eq k + · exact kernel9_1_r4_8_eq k + · exact kernel9_1_r4_9_eq k + · exact kernel9_1_r4_10_eq k + · exact kernel9_1_r4_11_eq k + · exact kernel9_1_r4_12_eq k + · exact kernel9_1_r4_13_eq k + · exact kernel9_1_r4_14_eq k + · exact kernel9_1_r4_15_eq k +noncomputable def kernel9_1_r5_0 : Fin 16 → CBox := ![⟨⟨39316170166940284392367939185,39316170166940285353064567339⟩,⟨(-714242755756632242577151762365),(-714242755756632241609020043226)⟩⟩,⟨⟨39086103424882564070272292836,39086103424882565030887924182⟩,⟨(-714068464621550693639040970059),(-714068464621550692670986289723)⟩⟩,⟨⟨38626335684344632565599850201,38626335684344633526051814207⟩,⟨(-713719815120121773922315080279),(-713719815120121772954416164841)⟩⟩,⟨⟨37937597969163169880536716112,37937597969163170840742256963⟩,⟨(-713196673499302213548084623078),(-713196673499302212580420304679)⟩⟩,⟨⟨37020985656166587361345402649,37020985656166588321221597825⟩,⟨(-712498840900466753244678287349),(-712498840900466752277327595945)⟩⟩,⟨⟨35877957082708010247616122987,35877957082708011207079870615⟩,⟨(-711626055476754868575454433943),(-711626055476754867608496620185)⟩⟩,⟨⟨34510331687150517559596907857,34510331687150518518564816809⟩,⟨(-710577995203251946172684858636),(-710577995203251945206199514065)⟩⟩,⟨⟨32920287679891643367023905473,32920287679891644325412352983⟩,⟨(-709354281368947454290712740583),(-709354281368947453324779749897)⟩⟩,⟨⟨31110359241992782877314488202,31110359241992783835039385071⟩,⟨(-707954482736699224465131368158),(-707954482736699223499831154301)⟩⟩,⟨⟨29083433248011582089893760579,29083433248011583046870801477⟩,⟨(-706378120354753692561525230776),(-706378120354753691596938513881)⟩⟩,⟨⟨26842745509231587638446937779,26842745509231588594591113647⟩,⟨(-704624673000733858586439715635),(-704624673000733857622648011126)⟩⟩,⟨⟨24391876533152933117229262808,24391876533152934072455465509⟩,⟨(-702693583236416933837091724184),(-702693583236416932874176746310)⟩⟩,⟨⟨21734746794859684331597362465,21734746794859685285819360049⟩,⟨(-700584264049089374934287895109),(-700584264049089373972332592839)⟩⟩,⟨⟨18875611515722143412023323965,18875611515722144365155136111⟩,⟨(-698296106052795591939555819300),(-698296106052795590978643007078)⟩⟩,⟨⟨15819054944833782682503545089,15819054944833783634457574525⟩,⟨(-695828485220395511078022847057),(-695828485220395510118237085832)⟩⟩,⟨⟨12569984138629722408448610793,12569984138629723359137850211⟩,⟨(-693180771115022933690239447369),(-693180771115022932731664841628)⟩⟩] +lemma kernel9_1_r5_0_eq : ∀ k : Fin 16, kernel9_1Expr 5 0 k = kernel9_1_r5_0 k := by decide +kernel +noncomputable def kernel9_1_r5_1 : Fin 16 → CBox := ![⟨⟨9133622234293219983772695463,9133622234293220933107722401⟩,⟨(-690352335587298932307201615408),(-690352335587298931349924832572)⟩⟩,⟨⟨5515501212834144266307104309,5515501212834145214200053423⟩,⟨(-687342561902510131775652792929),(-687342561902510130819759090741)⟩⟩,⟨⟨1721454148123663732192080739,1721454148123664678551792838⟩,⟨(-684150854259918493495818536636),(-684150854259918492541396631694)⟩⟩,⟨⟨(-2242393061303716632470456207),(-2242393061303715687733032864)⟩,⟨(-680776647664435077170346218899),(-680776647664435076217482881297)⟩⟩,⟨⟨(-6369630480213111464870473552),(-6369630480213110521849003239)⟩,⟨(-677219418109073165239628818083),(-677219418109073164288415612287)⟩⟩,⟨⟨(-10653573446141415046092396665),(-10653573446141414104876561260)⟩,⟨(-673478693024904086478736442811),(-673478693024904085529261121110)⟩⟩,⟨⟨(-15087272401202156137782685707),(-15087272401202155198468164848)⟩,⟨(-669554061953680039024533304113),(-669554061953680038076889813963)⟩⟩,⟨⟨(-19663523245993285830769096603),(-19663523245993284893446874030)⟩,⟨(-665445187396870110684120116398),(-665445187396870109738397889614)⟩⟩,⟨⟨(-24374878214193468155003153428),(-24374878214193467219772259847)⟩,⟨(-661151815793586355327678861557),(-661151815793586354383975589935)⟩⟩,⟨⟨(-29213657265118554350589167111),(-29213657265118553417540637651)⟩,⟨(-656673788578763901011374409098),(-656673788578763900069779971817)⟩⟩,⟨⟨(-34171959990070097259888589389),(-34171959990070096329123466802)⟩,⟨(-652011053272010144257731640887),(-652011053272010143318346151442)⟩⟩,⟨⟨(-39241678026746381480602385598),(-39241678026746380552189750716)⟩,⟨(-647163674546760392030311248321),(-647163674546760391093225083062)⟩⟩,⟨⟨(-44414507974308979561901186133),(-44414507974308978635935013536)⟩,⟨(-642131845228777818486533880263),(-642131845228777817551851009709)⟩⟩,⟨⟨(-49681964799910850443791395241),(-49681964799910849520362754836)⟩,⟨(-636915897172620921769844817894),(-636915897172620920837656707263)⟩⟩,⟨⟨(-55035395725603097532095484161),(-55035395725603096611310763757)⟩,⟨(-631516311964477992975227925526),(-631516311964477992045641564109)⟩⟩,⟨⟨(-60465994582555369367149493953),(-60465994582555368449101358185)⟩,⟨(-625933731399741158663638061027),(-625933731399741157736746858066)⟩⟩] +lemma kernel9_1_r5_1_eq : ∀ k : Fin 16, kernel9_1Expr 5 1 k = kernel9_1_r5_1 k := by decide +kernel +noncomputable def kernel9_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-65964816617459199440799979947),(-65964816617459198525600309080)⟩,⟨(-620168967683867495419759030226),(-620168967683867494495675826578)⟩⟩,⟨⟨(-71522793733845003466693841674),(-71522793733845002554433329025)⟩,⟨(-614223013305456090618557870778),(-614223013305456089697374447753)⟩⟩,⟨⟨(-77130750148843573185762011566),(-77130750148843572276553881337)⟩,⟨(-608097050531061606693933205233),(-608097050531061605775764097635)⟩⟩,⟨⟨(-82779418443674193879594802872),(-82779418443674192973531800804)⟩,⟨(-601792460472070017407929256151),(-601792460472070016492868648332)⟩⟩,⟨⟨(-88459455983857252948266045913),(-88459455983857252045467632929)⟩,⟨(-595310831674983030839284257629),(-595310831674983029927453278154)⟩⟩,⟨⟨(-94161461682843432066263646793),(-94161461682843431166819494332)⟩,⟨(-588653968187695724766062115121),(-588653968187695723857552208205)⟩⟩,⟨⟨(-99875993080438990828678745999),(-99875993080438989932709267518)⟩,⟨(-581823897055807587372908893356),(-581823897055807586467842478537)⟩⟩,⟨⟨(-105593583705102550311199921640),(-105593583705102549418796735205)⟩,⟨(-574822875204679975616279020968),(-574822875204679974714749825286)⟩⟩,⟨⟨(-111304760686908965482999255776),(-111304760686908964594290801647)⟩,⟨(-567653395664841421822169993901),(-567653395664841420924308806339)⟩⟩,⟨⟨(-117000062585736534849638894412),(-117000062585736533964711289108)⟩,⟨(-560318193100443585177324081643),(-560318193100443584283219435538)⟩⟩,⟨⟨(-122670057397051435014041601796),(-122670057397051434133022565847)⟩,⟨(-552820248602781167134266008147),(-552820248602781166244048282510)⟩⟩,⟨⟨(-128305360695554582546691317340),(-128305360695554581669669851546)⟩,⟨(-545162793713403819733742619128),(-545162793713403818847503541432)⟩⟩,⟨⟨(-133896653874937893350733018489),(-133896653874937892477845409042)⟩,⟨(-537349313644060798299530253643),(-537349313644060797417409079880)⟩⟩,⟨⟨(-139434702440085873835920703844),(-139434702440085872967249039400)⟩,⟨(-529383549663622441560712873016),(-529383549663622440682794688618)⟩⟩,⟨⟨(-144910374306271227250896809106),(-144910374306271226386575963386)⟩,⟨(-521269500625207858221217124456),(-521269500625207857347640042592)⟩⟩,⟨⟨(-150314658058246003398273215000),(-150314658058246002538387877041)⟩,⟨(-513011423610005568743144743200),(-513011423610005567873996717288)⟩⟩] +lemma kernel9_1_r5_2_eq : ∀ k : Fin 16, kernel9_1Expr 5 2 k = kernel9_1_r5_2 k := by decide +kernel +noncomputable def kernel9_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-155638681120638669020956305785),(-155638681120638668165652536798)⟩,⟨(-504613833667692163356364961665),(-504613833667692162491795563493)⟩⟩,⟨⟨(-160873727789747709194692917445),(-160873727789747708344044740837)⟩,⟨(-496081502636920935082347575434),(-496081502636920934222434308073)⟩⟩,⟨⟨(-166011257075688712214725393357),(-166011257075688711368874380627)⟩,⟨(-487419457033054372449420741619),(-487419457033054371594308899665)⟩⟩,⟨⟨(-171042920302918286961278290070),(-171042920302918286120302942641)⟩,⟨(-478632974994136628512732807590),(-478632974994136627662504590322)⟩⟩,⟨⟨(-175960578416437654566866514562),(-175960578416437653730919481429)⟩,⟨(-469727582280028780535913680214),(-469727582280028779690725673624)⟩⟩,⟨⟨(-180756318940483363765027703243),(-180756318940483362934175602172)⟩,⟨(-460709047323643957139470399209),(-460709047323643956299393074245)⟩⟩,⟨⟨(-185422472536253179930001507824),(-185422472536253179104391864329)⟩,⟨(-451583375337303342964551383012),(-451583375337303342129736352623)⟩⟩,⟨⟨(-189951629105201418578975130795),(-189951629105201417758678265359)⟩,⟨(-442356801481368866979657261378),(-442356801481368866150178853095)⟩⟩,⟨⟨(-194336653384678105628186243719),(-194336653384678104813364055275)⟩,⟨(-433035783106474406606431453266),(-433035783106474405782455807484)⟩⟩,⟨⟨(-198570699983187165306752529332),(-198570699983187164497458623281)⟩,⟨(-423626991084854237355120727398),(-423626991084854236536705537247)⟩⟩,⟨⟨(-202647227803305634776789688099),(-202647227803305633972954218890)⟩,⟨(-414137300250434251351683271923),(-414137300250434250538794032208)⟩⟩,⟨⟨(-206560013801342330468931388840),(-206560013801342329668923401685)⟩,⟨(-404573778971486683881043052914),(-404573778971486683072286996815)⟩⟩,⟨⟨(-210303166034122399014827302384),(-210303166034122398218820198205)⟩,⟨(-394943677883730878174159731590),(-394943677883730877369710063730)⟩⟩,⟨⟨(-213871135944863976581039294202),(-213871135944863975789083943976)⟩,⟨(-385254417815768899797196878153),(-385254417815768898997103795401)⟩⟩,⟨⟨(-217258729841963155672541623735),(-217258729841963154884804804555)⟩,⟨(-375513576942653399648704756585),(-375513576942653398853134295047)⟩⟩,⟨⟨(-220461119526620185706436108130),(-220461119526620184922977138709)⟩,⟨(-365728877207173883445503936809),(-365728877207173882654514237745)⟩⟩] +lemma kernel9_1_r5_3_eq : ∀ k : Fin 16, kernel9_1Expr 5 3 k = kernel9_1_r5_3 k := by decide +kernel +noncomputable def kernel9_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-223473852027618026084624508990),(-223473852027618025305632306784)⟩,⟨(-355908170052094539258127727240),(-355908170052094538471906470632)⟩⟩,⟨⟨(-226292858404196880659066035299),(-226292858404196879884578427552)⟩,⟨(-346059421510060420017780198680),(-346059421510060419236363489548)⟩⟩,⟨⟨(-228914461580846170139289785399),(-228914461580846169369482594441)⟩,⟨(-336190696701188001449992732428),(-336190696701188000673554614370)⟩⟩,⟨⟨(-231335383180947714044629996145),(-231335383180947713279553993981)⟩,⟨(-326310143791450531053010191486),(-326310143791450530281599233512)⟩⟩,⟨⟨(-233552749329538074197948954468),(-233552749329538073437800014857)⟩,⟨(-316425977467838567694153931360),(-316425977467838566927963742547)⟩⟩,⟨⟨(-235564095398999696576405614270),(-235564095398999695821212996568)⟩,⟨(-306546461988903079907936311896),(-306546461988903079146993434556)⟩⟩,⟨⟨(-237367369675223645903239291179),(-237367369675223645153185975025)⟩,⟨(-296679893871654949882247293173),(-296679893871654949126731931078)⟩⟩,⟨⟨(-238960935925693738291648541366),(-238960935925693737546774375340)⟩,⟨(-286834584277884522069662339573),(-286834584277884521319611170196)⟩⟩,⟨⟨(-240343574855003631913774192988),(-240343574855003631174287627202)⟩,⟨(-277018841164763160266709431915),(-277018841164763159522327677241)⟩⟩,⟨⟨(-241514484437514445776848877753),(-241514484437514445042760538097)⟩,⟨(-267240951266082404861346490082),(-267240951266082404122641128961)⟩⟩,⟨⟨(-242473279121169000146727109705),(-242473279121168999418224977665)⟩,⟨(-257509161971663696548124388677),(-257509161971663695815279700754)⟩⟩,⟨⟨(-243219987900876950557547890078),(-243219987900876949834658581104)⟩,⟨(-247831663173322985121142002603),(-247831663173322984394180552489)⟩⟩,⟨⟨(-243755051264349095012954692217),(-243755051264349094295888846346)⟩,⟨(-238216569146291991757135023011),(-238216569146291991036263336077)⟩⟩,⟨⟨(-244079317017764337674916824124),(-244079317017764336963672392456)⟩,⟨(-228671900535175537939068385726),(-228671900535175537224279948588)⟩⟩,⟨⟨(-244194035003173920195891698135),(-244194035003173919490659318982)⟩,⟨(-219205566513358343757694616748),(-219205566513358343049175539934)⟩⟩,⟨⟨(-244100850724058850506550715465),(-244100850724058849807341624477)⟩,⟨(-209825347184263295100739714247),(-209825347184263294398496419405)⟩⟩] +lemma kernel9_1_r5_4_eq : ∀ k : Fin 16, kernel9_1Expr 5 4 k = kernel9_1_r5_4 k := by decide +kernel +noncomputable def kernel9_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-243801797899931957050716206817),(-243801797899931956357751213124)⟩,⟨(-200538876292006802015048331677),(-200538876292006801319296745102)⟩⟩,⟨⟨(-243299289975289573792260520020),(-243299289975289573105512381453)⟩,⟨(-191353624307798122239267132823),(-191353624307798121549974853688)⟩⟩,⟨⟨(-242596110612543520542724712470),(-242596110612543519862384237893)⟩,⟨(-182276881956893202040606750610),(-182276881956893201357959359356)⟩⟩,⟨⟨(-241695403202776084246073805892),(-241695403202776083572134983874)⟩,⟨(-173315744249046676120233078107),(-173315744249046675444219126560)⟩⟩,⟨⟨(-240600659432233921152602070767),(-240600659432233920485280753159)⟩,⟨(-164477095073217317302078862450),(-164477095073217316632908681129)⟩⟩,⟨⟨(-239315706946386662639288591571),(-239315706946386661978543348985)⟩,⟨(-155767592414783703008690928534),(-155767592414783702346317392802)⟩⟩,⟨⟨(-237844696157098867184495387639),(-237844696157098866530514724336)⟩,⟨(-147193654250731496968537553296),(-147193654250731496313143383978)⟩⟩,⟨⟨(-236192086241977223203750306792),(-236192086241977222556509380004)⟩,⟨(-138761445175196841057910543313),(-138761445175196840409464996402)⟩⟩,⟨⟨(-234362630388237211803898341797),(-234362630388237211163618376723)⟩,⟨(-130476863804409110727500540748),(-130476863804409110086218835768)⟩⟩,⟨⟨(-232361360336464827492654413180),(-232361360336464826858911863775)⟩,⟨(-122345531006489681285068115172),(-122345531006489680650518685048)⟩⟩,⟨⟨(-230193570282411032014427600333),(-230193570282411031387330565869)⟩,⟨(-114372778997752003949457277306),(-114372778997752003321741646674)⟩⟩,⟨⟨(-227864800197432693001474424392),(-227864800197432692380987101698)⟩,⟨(-106563641343134330775281021193),(-106563641343134330154357263996)⟩⟩,⟨⟨(-225380818630368987286618189625),(-225380818630368986672961291811)⟩,⟨(-98922843894203340386352506531),(-98922843894203339772435086846)⟩⟩,⟨⟨(-222747605055503740779385619665),(-222747605055503740172482571480)⟩,⟨(-91454796693819372720788590141),(-91454796693819372113794737369)⟩⟩,⟨⟨(-219971331832801108095595322348),(-219971331832801107495633246086)⟩,⟨(-84163586872077660448657049732),(-84163586872077659848767556977)⟩⟩,⟨⟨(-217058345847805690563998795690),(-217058345847805689970921948069)⟩,⟨(-77052972553561349490617149801),(-77052972553561348897770029858)⟩⟩] +lemma kernel9_1_r5_5_eq : ∀ k : Fin 16, kernel9_1Expr 5 5 k = kernel9_1_r5_5 k := by decide +kernel +noncomputable def kernel9_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-214015149899462193989194260764),(-214015149899462193403228346568)⟩,⟨(-70126377791288361263651155224),(-70126377791288360678065708526)⟩⟩,⟨⟨(-210848383904629849539783028399),(-210848383904629848960819347822)⟩,⟨(-63386888538032823047800549122),(-63386888538032822469361857265)⟩⟩,⟨⟨(-207564805988241174437802979375),(-207564805988241173866020816229)⟩,⟨(-56837249660980662265783772988),(-56837249660980661694664731089)⟩⟩,⟨⟨(-204171273527883658334649721878),(-204171273527883657769972910805)⟩,⟨(-50479863000965825398490896716),(-50479863000965824834609140451)⟩⟩,⟨⟨(-200674724221069356251844169357),(-200674724221069355694481956668)⟩,⟨(-44316786472856054031123035973),(-44316786472856053474681424161)⟩⟩,⟨⟨(-197082157242606158511053279108),(-197082157242606157960884113019)⟩,⟨(-38349734199042447236916415903),(-38349734199042446687787306118)⟩⟩,⟨⟨(-193400614558302934166750327300),(-193400614558302933623943656505)⟩,⟨(-32580077663461784863976051961),(-32580077663461784322322601310)⟩⟩,⟨⟨(-189637162459738218108553488153),(-189637162459738217573012694008)⟩,⟨(-27008847869170614003478439106),(-27008847869170613469198029373)⟩⟩,⟨⟨(-185798873383010130890809521459),(-185798873383010130362255132098)⟩,⟨(-21636738478220266181218502372),(-21636738478220265654025435785)⟩⟩,⟨⟨(-181892808072277269329838662579),(-181892808072277268807964637759)⟩,⟨(-16464109908475972920939404608),(-16464109908475972400521840568)⟩⟩,⟨⟨(-177925998146511741172471666593),(-177925998146511740657452455920)⟩,⟨(-11490994358103452743297639775),(-11490994358103452229823974426)⟩⟩,⟨⟨(-173905429125233435374899491051),(-173905429125233434866634542010)⟩,⟨(-6717101724733640364067894340),(-6717101724733639857431910190)⟩⟩,⟨⟨(-169838023966097713226833297307),(-169838023966097712725529641891)⟩,⟨(-2141826382829879110722998608),(-2141826382829878611125795052)⟩⟩,⟨⟨(-165730627164087106008019899782),(-165730627164087105513528630977)⟩,⟨2235745220460594393712179488,2235745220460594886424916082⟩⟩,⟨⟨(-161589989458732714305989669477),(-161589989458732713818473749100)⟩,⟨6416826193672040804033584059,6416826193672041289704581835⟩⟩,⟨⟨(-157422753192285318840441279423),(-157422753192285318359781042638)⟩,⟨10402920099013478166327985811,10402920099013478645082123952⟩⟩] +lemma kernel9_1_r5_6_eq : ∀ k : Fin 16, kernel9_1Expr 5 6 k = kernel9_1_r5_6 k := by decide +kernel +noncomputable def kernel9_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-153235438358093138540706084978),(-153235438358093138067109801327)⟩,⟨14195811167825829773407562874,14195811167825830245042113362⟩⟩,⟨⟨(-149034429374646834388830688893),(-149034429374646833922113089686)⟩,⟨17797553883469667316029158736,17797553883469667780757827706⟩⟩,⟨⟨(-144825962616847408862882720701),(-144825962616847408403193087075)⟩,⟨21210461983439222808766484777,21210461983439223266449948658⟩⟩,⟨⟨(-140616114732064072921524874744),(-140616114732064072468725642758)⟩,⟨24437096934020362012612637704,24437096934020362463391954558⟩⟩,⟨⟨(-136410791764502062478206868873),(-136410791764502062032482410739)⟩,⟨27480255932022231242321568682,27480255932022231686016178848⟩⟩,⟨⟨(-132215719107319842577588639971),(-132215719107319842138751470198)⟩,⟨30342959489013410644930162933,30342959489013411081730720906⟩⟩,⟨⟨(-128036432297845949415757974120),(-128036432297845948983944824655)⟩,⟨33028438654084855668042821700,33028438654084856097816077207⟩⟩,⟨⟨(-123878268667172263751121740544),(-123878268667172263326178489426)⟩,⟨35540121931446983353499817888,35540121931446983776402846795⟩⟩,⟨⟨(-119746359851366548559022646141),(-119746359851366548140847829785)⟩,⟨37881621949152267226996051258,37881621949152267643133732866⟩⟩,⟨⟨(-115645625167575602984846136843),(-115645625167575602573137325372)⟩,⟨40056721934924874604683589331,40056721934924875014360995585⟩⟩,⟨⟨(-111580765854403428131136463271),(-111580765854403427726029131577)⟩,⟨42069362054484271693763573096,42069362054484272096848130668⟩⟩,⟨⟨(-107556260172167325046641334709),(-107556260172167324647978902896)⟩,⟨43923625666881110870543231103,43923625666881111267193908535⟩⟩,⟨⟨(-103576359354978585902031680571),(-103576359354978585509985297190)⟩,⟨45623725550233471669645957747,45623725550233472059694281470⟩⟩,⟨⟨(-99645084403081785841214185964),(-99645084403081785455577208997)⟩,⟨47173990149873484242712256217,47173990149873484626366933191⟩⟩,⟨⟨(-95766223700534573710072216910),(-95766223700534573330966474361)⟩,⟨48578849899303671851010636488,48578849899303672228152183477⟩⟩,⟨⟨(-91943331440133689075750444074),(-91943331440133688703006122524)⟩,⟨49842823662535325902436935464,49842823662535326273237022815⟩⟩] +lemma kernel9_1_r5_7_eq : ∀ k : Fin 16, kernel9_1Expr 5 7 k = kernel9_1_r5_7 k := by decide +kernel +noncomputable def kernel9_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-88179726834506474067316334245),(-88179726834506473701092683393)⟩,⟨50970505344355203272906292502,50970505344355203637219819975⟩⟩,⟨⟨(-84478494089502493341357138013),(-84478494089502492981340687485)⟩,⟨51966550712859991786372180293,51966550712859992144589045131⟩⟩,⟨⟨(-80842483113447389105356999401),(-80842483113447388751660332463)⟩,⟨52835664476229193102534565155,52835664476229193454539214089⟩⟩,⟨⟨(-77274310933469390610240590127),(-77274310933469390262687198553)⟩,⟨53582587653195711791207281795,53582587653195712137172927583⟩⟩,⟨⟨(-73776363787984810671383377306),(-73776363787984810330122177431)⟩,⟨54212085274039260994090429779,54212085274039261333865185845⟩⟩,⟨⟨(-70350799862537472000533070320),(-70350799862537471665338727007)⟩,⟨54728934446190638943822323630,54728934446190639277628192487⟩⟩,⟨⟨(-66999552634531642031808167811),(-66999552634531641702779685156)⟩,⟨55137912815714971936866289092,55137912815714972264601238915⟩⟩,⟨⟨(-63724334790980329514925083235),(-63724334790980329191876815575)⟩,⟨55443787453059013871277091592,55443787453059014193123508918⟩⟩,⟨⟨(-60526642682210652522841729913),(-60526642682210652205920615379)⟩,⟨55651304188521128221132707996,55651304188521128536940670527⟩⟩,⟨⟨(-57407761273523757467961049208),(-57407761273523757156922172555)⟩,⟨55765177419951834690354381430,55765177419951835000365553607⟩⟩,⟨⟨(-54368769556095242935464464349),(-54368769556095242630393777181)⟩,⟨55790080412236418029590997735,55790080412236418333716431014⟩⟩,⟨⟨(-51410546377918551298700352073),(-51410546377918550999405439403)⟩,⟨55730636105167044590156340928,55730636105167044888585311502⟩⟩,⟨⟨(-48533776655332296280284310265),(-48533776655332295986887737346)⟩,⟨55591408443397310053503679650,55591408443397310346110689553⟩⟩,⟨⟨(-45738957925625686335738666132),(-45738957925625686048001815962)⟩,⟨55376894239303467267161006635,55376894239303467554181597485⟩⟩,⟨⟨(-43026407201375607657122300290),(-43026407201375607375118924233)⟩,⟨55091515576769104657754461335,55091515576769104939111989647⟩⟩,⟨⟨(-40396268087525019448540299624),(-40396268087525019172073526532)⟩,⟨54739612761178063626637711108,54739612761178063902526096839⟩⟩] +lemma kernel9_1_r5_8_eq : ∀ k : Fin 16, kernel9_1Expr 5 8 k = kernel9_1_r5_8 k := by decide +kernel +noncomputable def kernel9_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-37848518122754623822473235610),(-37848518122754623551667361905)⟩,⟨54325437818257083636726988979,54325437818257083907019132337⟩⟩,⟨⟨(-35382976307417021824746484776),(-35382976307417021559345859773)⟩,⟨53853148541867063803462522665,53853148541867064068411219866⟩⟩,⟨⟨(-32999310781182778357585940261),(-32999310781182778097653077558)⟩,⟨53326803088410736902081736935,53326803088410737161621745565⟩⟩,⟨⟨(-30697046614578440981382725653),(-30697046614578440726718656923)⟩,⟨52750355113214533064503343551,52750355113214533318830918559⟩⟩,⟨⟨(-28475573679764587331430057458),(-28475573679764587082133704860)⟩,⟨52127649442061775800847014614,52127649442061776049860604187⟩⟩,⟨⟨(-26334154567194077622503916348),(-26334154567194077378333606494)⟩,⟨51462418269010148348127857648,51462418269010148592066551366⟩⟩,⟨⟨(-24271932516193311960666810556),(-24271932516193311721675008078)⟩,⟨50758277869724381043876543966,50758277869724381282685354488⟩⟩,⟨⟨(-22287939329008785305166940866),(-22287939329008785071154710595)⟩,⟨50018725817799884501044693939,50018725817799884734920114353⟩⟩,⟨⟨(-20381103239443952146339694998),(-20381103239443951917406747790)⟩,⟨49247138689947915068517269825,49247138689947915297357170238⟩⟩,⟨⟨(-18550256708863826154622886890),(-18550256708863825930518145055)⟩,⟨48446770244459951299400166518,48446770244459951523453334054⟩⟩,⟨⟨(-16794144124053524255835653242),(-16794144124053524036602713726)⟩,⟨47620750056069285473606815869,47620750056069285692827365022⟩⟩,⟨⟨(-15111429373169096988883096882),(-15111429373169096774325114665)⟩,⟨46772082589181305249628607518,46772082589181305464211230762⟩⟩,⟨⟨(-13500703277801828520584876633),(-13500703277801828310781153585)⟩,⟨45903646690449437178017414454,45903646690449437387880627997⟩⟩,⟨⟨(-11960490860978561055630342650),(-11960490860978560850345215314)⟩,⟨45018195480829156224324029037,45018195480829156429701506046⟩⟩,⟨⟨(-10489258432728848095936320813),(-10489258432728847895205794794)⟩,⟨44118356626544841898424533975,44118356626544842099278229042⟩⟩,⟨⟨(-9085420476653805307866452229),(-9085420476653805110667914353)⟩,⟨43206632967849760281585179365,43206632967849760478935393368⟩⟩] +lemma kernel9_1_r5_9_eq : ∀ k : Fin 16, kernel9_1Expr 5 9 k = kernel9_1_r5_9 k := by decide +kernel +noncomputable def kernel9_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-7747346322720982114552512011),(-7747346322720981920913705055)⟩,⟨42285403484043495359262129243,42285403484043495553079148442⟩⟩,⟨⟨(-6473366593274679599251447333),(-6473366593274679408966462649)⟩,⟨41356924572928487828185114212,41356924572928488018673192465⟩⟩,⟨⟨(-5261779410982866426906392762),(-5261779410982866240044462760)⟩,⟨40423331622732110865426814789,40423331622732111052514959568⟩⟩,⟨⟨(-4110856359131914362142106072),(-4110856359131914178550827884)⟩,⟨39486640854486545751729755880,39486640854486545935568825155⟩⟩,⟨⟨(-3018848186321272100693575134),(-3018848186321271920476748194)⟩,⟨38548751412938799876252479172,38548751412938800056737006178⟩⟩,⟨⟨(-1983990249195179067128081329),(-1983990249195178890094558005)⟩,⟨37611447684250356007767331582,37611447684250356185087084694⟩⟩,⟨⟨(-1004507688371627196540046849),(-1004507688371627022751768993)⟩,⟨36676401819032687995156262813,36676401819032688169247783116⟩⟩,⟨⟨(-78620334184822696771259306),(-78620334184822526076669331)⟩,⟨35745176439643544072552451004,35745176439643544243566020027⟩⟩,⟨⟨795452659758036965742698704,795452659758037133236701135⟩,⟨34819227511131662386929933499,34819227511131662554757206308⟩⟩,⟨⟨1619488455895438822504856968,1619488455895438986998075490⟩,⟨33899907355756547649660596189,33899907355756547814500271455⟩⟩,⟨⟨2395256444364113989424651707,2395256444364114150861625768⟩,⟨32988467791617196318015480055,32988467791617196479810810130⟩⟩,⟨⟨3124514425292881460469556527,3124514425292881618999697540⟩,⟨32086063376591353832892466084,32086063376591353991791834331⟩⟩,⟨⟨3809005058976000480767430389,3809005058976000636301225019⟩,⟨31193754739507270398076889254,31193754739507270553989564012⟩⟩,⟨⟨4450452580177838467596081664,4450452580177838620320868060⟩,⟨30312511981235397721156941223,30312511981235397874267987747⟩⟩,⟨⟨5050559771917298274169642383,5050559771917298424041790697⟩,⟨29443218129190647557390951586,29443218129190647707650731284⟩⟩,⟨⟨5611005193259865866917639699,5611005193259866014082983523⟩,⟨28586672629569568155119496274,28586672629569568302673365728⟩⟩] +lemma kernel9_1_r5_10_eq : ∀ k : Fin 16, kernel9_1Expr 5 10 k = kernel9_1_r5_10 k := by decide +kernel +noncomputable def kernel9_1_r5_11 : Fin 16 → CBox := ![⟨⟨6133440654906535072197592949,6133440654906535216559396029⟩,⟨27743594862504222663659562678,27743594862504222808410084515⟩⟩,⟨⟨6619488935710951915293473721,6619488935710952057045530962⟩,⟨26914627666189123270013228590,26914627666189123412153848271⟩⟩,⟨⟨7070741732677166940579992464,7070741732677167079676919913⟩,⟨26100340856923075408743506519,26100340856923075548228269345⟩⟩,⟨⟨7488757836488261304251088119,7488757836488261440834656804⟩,⟨25301234732898369112576029161,25301234732898369249546369981⟩⟩,⟨⟨7875061524188339036631580085,7875061524188339170623176371⟩,⟨24517743550459950421115349289,24517743550459950555492118303⟩⟩,⟨⟨8231141160284161360721872044,8231141160284161492296995443⟩,⟨23750238962441938445936213572,23750238962441938577894673560⟩⟩,⟨⟨8558447997244980346447116295,8558447997244980475564481785⟩,⟨22999033409063448548295683846,22999033409063448677794116632⟩⟩,⟨⟨8858395166156625007272024025,8858395166156625134068688303⟩,⟨22264383452725870924498741374,22264383452725871051673984518⟩⟩,⟨⟨9132356848125136202697127223,9132356848125136327089092916⟩,⟨21546493048895676184889959397,21546493048895676309657597529⟩⟩,⟨⟨9381667616922626083910988791,9381667616922626206078043894⟩,⟨20845516746077020043403391935,20845516746077020165943090393⟩⟩,⟨⟨9607621943319835187369713779,9607621943319835307274037595⟩,⟨20161562808673842715118232290,20161562808673842835391852526⟩⟩,⟨⟨9811473851552286054669096682,9811473851552286172442455999⟩,⟨19494696257309141314983676757,19494696257309141433122861337⟩⟩,⟨⟨9994436718416158641948288689,9994436718416158757520636029⟩,⟨18844941821907352473814499568,18844941821907352589748900057⟩⟩,⟨⟨10157683205582204596270951942,10157683205582204709805595141⟩,⟨18212286803552402122622331287,18212286803552402236515205011⟩⟩,⟨⟨10302345315847360666651964497,10302345315847360778113913014⟩,⟨17596683841807397089831673607,17596683841807397201647806888⟩⟩,⟨⟨10429514564210449088623777979,10429514564210449198139193798⟩,⟨16998053584820921741425045229,16998053584820921851290550959⟩⟩] +lemma kernel9_1_r5_11_eq : ∀ k : Fin 16, kernel9_1Expr 5 11 k = kernel9_1_r5_11 k := by decide +kernel +noncomputable def kernel9_1_r5_12 : Fin 16 → CBox := ![⟨⟨10540242254856768326816521879,10540242254856768434306244443⟩,⟨16416287260148553058278509522,16416287260148553166114001953⟩⟩,⟨⟨10635539855362876178467606781,10635539855362876284103041763⟩,⟨15851249144785908500710425213,15851249144785908606686484077⟩⟩,⟨⟨10716379459683954070150079543,10716379459683954173922299838⟩,⟨15302778933440960548710683765,15302778933440960652807997381⟩⟩,⟨⟨10783694331758447589381084198,10783694331758447691409008182⟩,⟨14770694004568415671818083633,14770694004568415774156204039⟩⟩,⟨⟨10838379521854974800827128409,10838379521854974901045659034⟩,⟨14254791584147826508962616287,14254791584147826609476907424⟩⟩,⟨⟨10881292548091702696991031125,10881292548091702795548929261⟩,⟨13754850807610163057697814329,13754850807610163156537663860⟩⟩,⟨⟨10913254135875595526470709613,10913254135875595623335993568⟩,⟨13270634680705385598780516568,13270634680705385695914408132⟩⟩,⟨⟨10935049008335386392534782885,10935049008335386487820720693⟩,⟨12801891940456887153258903856,12801891940456887248800669704⟩⟩,⟨⟨10947426721155237634780489029,10947426721155237728415344960⟩,⟨12348358817668408794888636573,12348358817668408888766955463⟩⟩,⟨⟨10951102535553434127998931013,10951102535553434220134451371⟩,⟨11909760702736213717100197143,11909760702736213809467375470⟩⟩,⟨⟨10946758323489872268305031191,10946758323489872358910968052⟩,⟨11485813716775087452490001911,11485813716775087543316211964⟩⟩,⟨⟨10935043499525519081377067014,10935043499525519170561017270⟩,⟨11076226190292360893997424845,11076226190292360983390760024⟩⟩,⟨⟨10916575974094549796185230350,10916575974094549883886931556⟩,⟨10680700051840958210634270305,10680700051840958298534848162⟩⟩,⟨⟨10891943123283831131749777969,10891943123283831218105270317⟩,⟨10298932129251844941592137104,10298932129251845028136480721⟩⟩,⟨⟨10861702770543274034863379685,10861702770543274119861829213⟩,⟨9930615366189631760990710564,9930615366189631846168366986⟩⟩,⟨⟨10826384176072971333112997767,10826384176072971416885276937⟩,⟨9575439956893949169119396308,9575439956893949253061679467⟩⟩] +lemma kernel9_1_r5_12_eq : ∀ k : Fin 16, kernel9_1Expr 5 12 k = kernel9_1_r5_12 k := by decide +kernel +noncomputable def kernel9_1_r5_13 : Fin 16 → CBox := ![⟨⟨10786489029947759892800781012,10786489029947759975275045301⟩,⟨9233094402065040199493571465,9233094402065040282128971208⟩⟩,⟨⟨10742492445345853714155622601,10742492445345853795471283399⟩,⟨8903266488926322332197369234,8903266488926322413665719478⟩⟩,⟨⟨10694843948544580558719543744,10694843948544580638846812422⟩,⟨8585644198550942929922457837,8585644198550943010194302420⟩⟩,⟨⟨10643968462632255630616576890,10643968462632255709650428030⟩,⟨8279916543575077846241176203,8279916543575077925411862776⟩⟩,⟨⟨10590267282160208086773369600,10590267282160208164654844436⟩,⟨7985774339439361015437931923,7985774339439361093448803358⟩⟩,⟨⟨10534119036222429326832086091,10534119036222429403683936573⟩,⟨7702910912302813828505603083,7702910912302813905479768424⟩⟩,⟨⟨10475880637701840574265721958,10475880637701840650059251336⟩,⟨7431022746762359369258980861,7431022746762359445168036136⟩⟩,⟨⟨10415888216661492196973372561,10415888216661492271798896701⟩,⟨7169810076486806907397572149,7169810076486806982332152881⟩⟩,⟨⟨10354458036085917785252191110,10354458036085917859043341305⟩,⟨6918977420838376449063112136,6918977420838376522957114117⟩⟩,⟨⟨10291887388392271453547682257,10291887388392271526431163210⟩,⟨6678234070508648596035966734,6678234070508648669016400668⟩⟩,⟨⟨10228455471332758326502253680,10228455471332758398450334262⟩,⟨6447294525140461949430159374,6447294525140462021469550864⟩⟩,⟨⟨10164424242099280835272266394,10164424242099280906370818578⟩,⟨6225878885843870083338533687,6225878885843870154523026918⟩⟩,⟨⟨10100039248618288721373940181,10100039248618288791566544210⟩,⟨6013713205443882805701703014,6013713205443882875975113618⟩⟩,⟨⟨10035530437188718810987349813,10035530437188718880387224042⟩,⟨5810529799221359551808199606,5810529799221359621284002242⟩⟩,⟨⟨9971112935768873758951415365,9971112935768873827531644119⟩,⟨5616067518827040570520228766,5616067518827040639171732430⟩⟩,⟨⟨9906987812359394125550285236,9906987812359394193392628110⟩,⟨5430071991963174766595469273,5430071991963174834504664401⟩⟩] +lemma kernel9_1_r5_13_eq : ∀ k : Fin 16, kernel9_1Expr 5 13 k = kernel9_1_r5_13 k := by decide +kernel +noncomputable def kernel9_1_r5_14 : Fin 16 → CBox := ![⟨⟨9843342808059441005347499857,9843342808059441072385109689⟩,⟨5252295830338349098067851580,5252295830338349165168097783⟩⟩,⟨⟨9780353044492175177021905019,9780353044492175243375320713⟩,⟨5082498808309698122701212294,5082498808309698189113265059⟩⟩,⟨⟨9718181705403968512939256752,9718181705403968578582341773⟩,⟨4920448014533366941685498616,4920448014533367007383418105⟩⟩,⟨⟨9656980692339910938407031818,9656980692339911003417696246⟩,⟨4765917978849549515227799113,4765917978849549580289690713⟩⟩,⟨⟨9596891254386495138144117403,9596891254386495202467697189⟩,⟨4618690776533201742370237710,4618690776533201806741621223⟩⟩,⟨⟨9538044592051297358991710430,9538044592051297422733480634⟩,⟨4478556111946152781674771533,4478556111946152845461102557⟩⟩,⟨⟨9480562435419460218250396862,9480562435419460281384910513⟩,⟨4345311383531272290601639002,4345311383531272353777643284⟩⟩,⟨⟨9424557596788261113149101640,9424557596788261175750800393⟩,⟨4218761731995006702752813775,4218761731995006765393098371⟩⟩,⟨⟨9370134498034457626415837720,9370134498034457688421948122⟩,⟨4098720073431335526719060451,4098720073431335588761015983⟩⟩,⟨⟨9317389673014877505306679088,9317389673014877566827992630⟩,⟨3985007119048332583722068451,3985007119048332645276637500⟩⟩,⟨⟨9266412245339299336201023758,9266412245339299397212798971⟩,⟨3877451383068315738520066769,3877451383068315799562660457⟩⟩,⟨⟨9217284381886478326755629134,9217284381886478387329132550⟩,⟨3775889180284258131070576839,3775889180284258191672602443⟩⟩,⟨⟨9170081722459628507513147032,9170081722459628567594849856⟩,⟨3680164614668900334670090119,3680164614668900394778165765⟩⟩,⟨⟨9124873785997186832205604438,9124873785997186891894650406⟩,⟨3590129560348994911987016778,3590129560348994971700413815⟩⟩,⟨⟨9081724353768653204471586800,9081724353768653263743918810⟩,⟨3505643636175446199199738806,3505643636175446258494536265⟩⟩,⟨⟨9040691829994107820010505191,9040691829994107878934582646⟩,⟨3426574175040859921494002391,3426574175040859980438780669⟩⟩] +lemma kernel9_1_r5_14_eq : ∀ k : Fin 16, kernel9_1Expr 5 14 k = kernel9_1_r5_14 k := by decide +kernel +noncomputable def kernel9_1_r5_15 : Fin 16 → CBox := ![⟨⟨9001829580330024313392313995,9001829580330024371903794723⟩,⟨3352796189019240341740404686,3352796189019240400270956759⟩⟩,⟨⟨8965186248663580801095955510,8965186248663580859302869365⟩,⟨3284192331328290044967656935,3284192331328290103192119925⟩⟩,⟨⟨8930806052653163238844310628,8930806052653163296723362879⟩,⟨3220652856042976442901524894,3220652856042976500796727173⟩⟩,⟨⟨8898729058444483997370404102,8898729058444484054987514612⟩,⟨3162075576419703308149312191,3162075576419703365781279421⟩⟩,⟨⟨8868991434980015856135751462,8868991434980015913438087952⟩,⟨3108365822623517215722640526,3108365822623517273038663629⟩⟩,⟨⟨8841625688304565683201295116,8841625688304565740283687482⟩,⟨3059436399586220103585838869,3059436399586220160680842390⟩⟩,⟨⟨8816660876252066507670617961,8816660876252066564510551318⟩,⟨3015207545660964866283731578,3015207545660964923135313963⟩⟩,⟨⟨8794122803878321116089251916,8794122803878321172750458860⟩,⟨2975606892678779438456889515,2975606892678779495128878230⟩⟩,⟨⟨8774034199981740929076186583,8774034199981740985500528231⟩,⟨2940569427954380204953822158,2940569427954380261388195988⟩⟩,⟨⟨8756414875029334171745302020,8756414875029334228038625717⟩,⟨2910037458732468810343033225,2910037458732468866645722485⟩⟩,⟨⟨8741281860778538675903150985,8741281860778538732042811524⟩,⟨2883960579511317041107626625,2883960579511317097256092774⟩⟩,⟨⟨8728649531857187289814704008,8728649531857187345861486794⟩,⟨2862295642627681734465453014,2862295642627681790520569411⟩⟩,⟨⟨8718529709534147827184462640,8718529709534147883084836270⟩,⟨2845006732435796049593900452,2845006732435796105502246940⟩⟩,⟨⟨8710931747882195474891754754,8710931747882195530737081015⟩,⟨2832065143363187605133306563,2832065143363187660986324119⟩⟩,⟨⟨8705862602502646094621821433,8705862602502646150390453044⟩,⟨2823449362077204044168852300,2823449362077204099944996632⟩⟩,⟨⟨8703326881948389232808399988,8703326881948389288559498787⟩,⟨2819145053948203084764517934,2819145053948203140523035720⟩⟩] +lemma kernel9_1_r5_15_eq : ∀ k : Fin 16, kernel9_1Expr 5 15 k = kernel9_1_r5_15 k := by decide +kernel +noncomputable def kernel9_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel9_1_r5_0,kernel9_1_r5_1,kernel9_1_r5_2,kernel9_1_r5_3,kernel9_1_r5_4,kernel9_1_r5_5,kernel9_1_r5_6,kernel9_1_r5_7,kernel9_1_r5_8,kernel9_1_r5_9,kernel9_1_r5_10,kernel9_1_r5_11,kernel9_1_r5_12,kernel9_1_r5_13,kernel9_1_r5_14,kernel9_1_r5_15] +lemma kernel9_1_r5_eq (i k : Fin 16) : kernel9_1Expr 5 i k = kernel9_1_r5 i k := by + fin_cases i + · exact kernel9_1_r5_0_eq k + · exact kernel9_1_r5_1_eq k + · exact kernel9_1_r5_2_eq k + · exact kernel9_1_r5_3_eq k + · exact kernel9_1_r5_4_eq k + · exact kernel9_1_r5_5_eq k + · exact kernel9_1_r5_6_eq k + · exact kernel9_1_r5_7_eq k + · exact kernel9_1_r5_8_eq k + · exact kernel9_1_r5_9_eq k + · exact kernel9_1_r5_10_eq k + · exact kernel9_1_r5_11_eq k + · exact kernel9_1_r5_12_eq k + · exact kernel9_1_r5_13_eq k + · exact kernel9_1_r5_14_eq k + · exact kernel9_1_r5_15_eq k +noncomputable def kernel9_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel9_1_r0,kernel9_1_r1,kernel9_1_r2,kernel9_1_r3,kernel9_1_r4,kernel9_1_r5] +lemma kernel9_1_eq (j : Fin 6) (i k : Fin 16) : kernel9_1Expr j i k = kernel9_1 j i k := by + fin_cases j + · exact kernel9_1_r0_eq i k + · exact kernel9_1_r1_eq i k + · exact kernel9_1_r2_eq i k + · exact kernel9_1_r3_eq i k + · exact kernel9_1_r4_eq i k + · exact kernel9_1_r5_eq i k +lemma kernel9_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel9_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(9:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel9_1_eq] + unfold kernel9_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans9_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues100.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues100.lean new file mode 100644 index 0000000000000000000000000000000000000000..7833ad9d33efd0c53cc5d64e203369b57f11aac6 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues100.lean @@ -0,0 +1,3941 @@ +import OAI.Analysis.PlanarPacking.Grid +import OAI.Analysis.PlanarPacking.Certificate.TransformedPowers100 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid IntegerAlpha IntegerCompact +noncomputable def kernel91_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans91 j i k) +noncomputable def kernel91_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_0_eq : ∀ k : Fin 16, kernel91_0Expr 0 0 k = kernel91_0_r0_0 k := by decide +kernel +noncomputable def kernel91_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_1_eq : ∀ k : Fin 16, kernel91_0Expr 0 1 k = kernel91_0_r0_1 k := by decide +kernel +noncomputable def kernel91_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_2_eq : ∀ k : Fin 16, kernel91_0Expr 0 2 k = kernel91_0_r0_2 k := by decide +kernel +noncomputable def kernel91_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_3_eq : ∀ k : Fin 16, kernel91_0Expr 0 3 k = kernel91_0_r0_3 k := by decide +kernel +noncomputable def kernel91_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_4_eq : ∀ k : Fin 16, kernel91_0Expr 0 4 k = kernel91_0_r0_4 k := by decide +kernel +noncomputable def kernel91_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_5_eq : ∀ k : Fin 16, kernel91_0Expr 0 5 k = kernel91_0_r0_5 k := by decide +kernel +noncomputable def kernel91_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_6_eq : ∀ k : Fin 16, kernel91_0Expr 0 6 k = kernel91_0_r0_6 k := by decide +kernel +noncomputable def kernel91_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_7_eq : ∀ k : Fin 16, kernel91_0Expr 0 7 k = kernel91_0_r0_7 k := by decide +kernel +noncomputable def kernel91_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_8_eq : ∀ k : Fin 16, kernel91_0Expr 0 8 k = kernel91_0_r0_8 k := by decide +kernel +noncomputable def kernel91_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_9_eq : ∀ k : Fin 16, kernel91_0Expr 0 9 k = kernel91_0_r0_9 k := by decide +kernel +noncomputable def kernel91_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_10_eq : ∀ k : Fin 16, kernel91_0Expr 0 10 k = kernel91_0_r0_10 k := by decide +kernel +noncomputable def kernel91_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r0_11_eq : ∀ k : Fin 16, kernel91_0Expr 0 11 k = kernel91_0_r0_11 k := by decide +kernel +noncomputable def kernel91_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r0_12_eq : ∀ k : Fin 16, kernel91_0Expr 0 12 k = kernel91_0_r0_12 k := by decide +kernel +noncomputable def kernel91_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r0_13_eq : ∀ k : Fin 16, kernel91_0Expr 0 13 k = kernel91_0_r0_13 k := by decide +kernel +noncomputable def kernel91_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r0_14_eq : ∀ k : Fin 16, kernel91_0Expr 0 14 k = kernel91_0_r0_14 k := by decide +kernel +noncomputable def kernel91_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r0_15_eq : ∀ k : Fin 16, kernel91_0Expr 0 15 k = kernel91_0_r0_15 k := by decide +kernel +noncomputable def kernel91_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel91_0_r0_0,kernel91_0_r0_1,kernel91_0_r0_2,kernel91_0_r0_3,kernel91_0_r0_4,kernel91_0_r0_5,kernel91_0_r0_6,kernel91_0_r0_7,kernel91_0_r0_8,kernel91_0_r0_9,kernel91_0_r0_10,kernel91_0_r0_11,kernel91_0_r0_12,kernel91_0_r0_13,kernel91_0_r0_14,kernel91_0_r0_15] +lemma kernel91_0_r0_eq (i k : Fin 16) : kernel91_0Expr 0 i k = kernel91_0_r0 i k := by + fin_cases i + · exact kernel91_0_r0_0_eq k + · exact kernel91_0_r0_1_eq k + · exact kernel91_0_r0_2_eq k + · exact kernel91_0_r0_3_eq k + · exact kernel91_0_r0_4_eq k + · exact kernel91_0_r0_5_eq k + · exact kernel91_0_r0_6_eq k + · exact kernel91_0_r0_7_eq k + · exact kernel91_0_r0_8_eq k + · exact kernel91_0_r0_9_eq k + · exact kernel91_0_r0_10_eq k + · exact kernel91_0_r0_11_eq k + · exact kernel91_0_r0_12_eq k + · exact kernel91_0_r0_13_eq k + · exact kernel91_0_r0_14_eq k + · exact kernel91_0_r0_15_eq k +noncomputable def kernel91_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_0_eq : ∀ k : Fin 16, kernel91_0Expr 1 0 k = kernel91_0_r1_0 k := by decide +kernel +noncomputable def kernel91_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_1_eq : ∀ k : Fin 16, kernel91_0Expr 1 1 k = kernel91_0_r1_1 k := by decide +kernel +noncomputable def kernel91_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_2_eq : ∀ k : Fin 16, kernel91_0Expr 1 2 k = kernel91_0_r1_2 k := by decide +kernel +noncomputable def kernel91_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_3_eq : ∀ k : Fin 16, kernel91_0Expr 1 3 k = kernel91_0_r1_3 k := by decide +kernel +noncomputable def kernel91_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_4_eq : ∀ k : Fin 16, kernel91_0Expr 1 4 k = kernel91_0_r1_4 k := by decide +kernel +noncomputable def kernel91_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_5_eq : ∀ k : Fin 16, kernel91_0Expr 1 5 k = kernel91_0_r1_5 k := by decide +kernel +noncomputable def kernel91_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_6_eq : ∀ k : Fin 16, kernel91_0Expr 1 6 k = kernel91_0_r1_6 k := by decide +kernel +noncomputable def kernel91_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_7_eq : ∀ k : Fin 16, kernel91_0Expr 1 7 k = kernel91_0_r1_7 k := by decide +kernel +noncomputable def kernel91_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_8_eq : ∀ k : Fin 16, kernel91_0Expr 1 8 k = kernel91_0_r1_8 k := by decide +kernel +noncomputable def kernel91_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_9_eq : ∀ k : Fin 16, kernel91_0Expr 1 9 k = kernel91_0_r1_9 k := by decide +kernel +noncomputable def kernel91_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_10_eq : ∀ k : Fin 16, kernel91_0Expr 1 10 k = kernel91_0_r1_10 k := by decide +kernel +noncomputable def kernel91_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_11_eq : ∀ k : Fin 16, kernel91_0Expr 1 11 k = kernel91_0_r1_11 k := by decide +kernel +noncomputable def kernel91_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_12_eq : ∀ k : Fin 16, kernel91_0Expr 1 12 k = kernel91_0_r1_12 k := by decide +kernel +noncomputable def kernel91_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_13_eq : ∀ k : Fin 16, kernel91_0Expr 1 13 k = kernel91_0_r1_13 k := by decide +kernel +noncomputable def kernel91_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_14_eq : ∀ k : Fin 16, kernel91_0Expr 1 14 k = kernel91_0_r1_14 k := by decide +kernel +noncomputable def kernel91_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r1_15_eq : ∀ k : Fin 16, kernel91_0Expr 1 15 k = kernel91_0_r1_15 k := by decide +kernel +noncomputable def kernel91_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel91_0_r1_0,kernel91_0_r1_1,kernel91_0_r1_2,kernel91_0_r1_3,kernel91_0_r1_4,kernel91_0_r1_5,kernel91_0_r1_6,kernel91_0_r1_7,kernel91_0_r1_8,kernel91_0_r1_9,kernel91_0_r1_10,kernel91_0_r1_11,kernel91_0_r1_12,kernel91_0_r1_13,kernel91_0_r1_14,kernel91_0_r1_15] +lemma kernel91_0_r1_eq (i k : Fin 16) : kernel91_0Expr 1 i k = kernel91_0_r1 i k := by + fin_cases i + · exact kernel91_0_r1_0_eq k + · exact kernel91_0_r1_1_eq k + · exact kernel91_0_r1_2_eq k + · exact kernel91_0_r1_3_eq k + · exact kernel91_0_r1_4_eq k + · exact kernel91_0_r1_5_eq k + · exact kernel91_0_r1_6_eq k + · exact kernel91_0_r1_7_eq k + · exact kernel91_0_r1_8_eq k + · exact kernel91_0_r1_9_eq k + · exact kernel91_0_r1_10_eq k + · exact kernel91_0_r1_11_eq k + · exact kernel91_0_r1_12_eq k + · exact kernel91_0_r1_13_eq k + · exact kernel91_0_r1_14_eq k + · exact kernel91_0_r1_15_eq k +noncomputable def kernel91_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_0_eq : ∀ k : Fin 16, kernel91_0Expr 2 0 k = kernel91_0_r2_0 k := by decide +kernel +noncomputable def kernel91_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_1_eq : ∀ k : Fin 16, kernel91_0Expr 2 1 k = kernel91_0_r2_1 k := by decide +kernel +noncomputable def kernel91_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_2_eq : ∀ k : Fin 16, kernel91_0Expr 2 2 k = kernel91_0_r2_2 k := by decide +kernel +noncomputable def kernel91_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_3_eq : ∀ k : Fin 16, kernel91_0Expr 2 3 k = kernel91_0_r2_3 k := by decide +kernel +noncomputable def kernel91_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_4_eq : ∀ k : Fin 16, kernel91_0Expr 2 4 k = kernel91_0_r2_4 k := by decide +kernel +noncomputable def kernel91_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_5_eq : ∀ k : Fin 16, kernel91_0Expr 2 5 k = kernel91_0_r2_5 k := by decide +kernel +noncomputable def kernel91_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_6_eq : ∀ k : Fin 16, kernel91_0Expr 2 6 k = kernel91_0_r2_6 k := by decide +kernel +noncomputable def kernel91_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_7_eq : ∀ k : Fin 16, kernel91_0Expr 2 7 k = kernel91_0_r2_7 k := by decide +kernel +noncomputable def kernel91_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_8_eq : ∀ k : Fin 16, kernel91_0Expr 2 8 k = kernel91_0_r2_8 k := by decide +kernel +noncomputable def kernel91_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_9_eq : ∀ k : Fin 16, kernel91_0Expr 2 9 k = kernel91_0_r2_9 k := by decide +kernel +noncomputable def kernel91_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r2_10_eq : ∀ k : Fin 16, kernel91_0Expr 2 10 k = kernel91_0_r2_10 k := by decide +kernel +noncomputable def kernel91_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r2_11_eq : ∀ k : Fin 16, kernel91_0Expr 2 11 k = kernel91_0_r2_11 k := by decide +kernel +noncomputable def kernel91_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r2_12_eq : ∀ k : Fin 16, kernel91_0Expr 2 12 k = kernel91_0_r2_12 k := by decide +kernel +noncomputable def kernel91_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r2_13_eq : ∀ k : Fin 16, kernel91_0Expr 2 13 k = kernel91_0_r2_13 k := by decide +kernel +noncomputable def kernel91_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r2_14_eq : ∀ k : Fin 16, kernel91_0Expr 2 14 k = kernel91_0_r2_14 k := by decide +kernel +noncomputable def kernel91_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel91_0_r2_15_eq : ∀ k : Fin 16, kernel91_0Expr 2 15 k = kernel91_0_r2_15 k := by decide +kernel +noncomputable def kernel91_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel91_0_r2_0,kernel91_0_r2_1,kernel91_0_r2_2,kernel91_0_r2_3,kernel91_0_r2_4,kernel91_0_r2_5,kernel91_0_r2_6,kernel91_0_r2_7,kernel91_0_r2_8,kernel91_0_r2_9,kernel91_0_r2_10,kernel91_0_r2_11,kernel91_0_r2_12,kernel91_0_r2_13,kernel91_0_r2_14,kernel91_0_r2_15] +lemma kernel91_0_r2_eq (i k : Fin 16) : kernel91_0Expr 2 i k = kernel91_0_r2 i k := by + fin_cases i + · exact kernel91_0_r2_0_eq k + · exact kernel91_0_r2_1_eq k + · exact kernel91_0_r2_2_eq k + · exact kernel91_0_r2_3_eq k + · exact kernel91_0_r2_4_eq k + · exact kernel91_0_r2_5_eq k + · exact kernel91_0_r2_6_eq k + · exact kernel91_0_r2_7_eq k + · exact kernel91_0_r2_8_eq k + · exact kernel91_0_r2_9_eq k + · exact kernel91_0_r2_10_eq k + · exact kernel91_0_r2_11_eq k + · exact kernel91_0_r2_12_eq k + · exact kernel91_0_r2_13_eq k + · exact kernel91_0_r2_14_eq k + · exact kernel91_0_r2_15_eq k +noncomputable def kernel91_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_0_eq : ∀ k : Fin 16, kernel91_0Expr 3 0 k = kernel91_0_r3_0 k := by decide +kernel +noncomputable def kernel91_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_1_eq : ∀ k : Fin 16, kernel91_0Expr 3 1 k = kernel91_0_r3_1 k := by decide +kernel +noncomputable def kernel91_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_2_eq : ∀ k : Fin 16, kernel91_0Expr 3 2 k = kernel91_0_r3_2 k := by decide +kernel +noncomputable def kernel91_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_3_eq : ∀ k : Fin 16, kernel91_0Expr 3 3 k = kernel91_0_r3_3 k := by decide +kernel +noncomputable def kernel91_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_4_eq : ∀ k : Fin 16, kernel91_0Expr 3 4 k = kernel91_0_r3_4 k := by decide +kernel +noncomputable def kernel91_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_5_eq : ∀ k : Fin 16, kernel91_0Expr 3 5 k = kernel91_0_r3_5 k := by decide +kernel +noncomputable def kernel91_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_6_eq : ∀ k : Fin 16, kernel91_0Expr 3 6 k = kernel91_0_r3_6 k := by decide +kernel +noncomputable def kernel91_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_7_eq : ∀ k : Fin 16, kernel91_0Expr 3 7 k = kernel91_0_r3_7 k := by decide +kernel +noncomputable def kernel91_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_8_eq : ∀ k : Fin 16, kernel91_0Expr 3 8 k = kernel91_0_r3_8 k := by decide +kernel +noncomputable def kernel91_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_9_eq : ∀ k : Fin 16, kernel91_0Expr 3 9 k = kernel91_0_r3_9 k := by decide +kernel +noncomputable def kernel91_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_10_eq : ∀ k : Fin 16, kernel91_0Expr 3 10 k = kernel91_0_r3_10 k := by decide +kernel +noncomputable def kernel91_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_11_eq : ∀ k : Fin 16, kernel91_0Expr 3 11 k = kernel91_0_r3_11 k := by decide +kernel +noncomputable def kernel91_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_12_eq : ∀ k : Fin 16, kernel91_0Expr 3 12 k = kernel91_0_r3_12 k := by decide +kernel +noncomputable def kernel91_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_13_eq : ∀ k : Fin 16, kernel91_0Expr 3 13 k = kernel91_0_r3_13 k := by decide +kernel +noncomputable def kernel91_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_14_eq : ∀ k : Fin 16, kernel91_0Expr 3 14 k = kernel91_0_r3_14 k := by decide +kernel +noncomputable def kernel91_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r3_15_eq : ∀ k : Fin 16, kernel91_0Expr 3 15 k = kernel91_0_r3_15 k := by decide +kernel +noncomputable def kernel91_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel91_0_r3_0,kernel91_0_r3_1,kernel91_0_r3_2,kernel91_0_r3_3,kernel91_0_r3_4,kernel91_0_r3_5,kernel91_0_r3_6,kernel91_0_r3_7,kernel91_0_r3_8,kernel91_0_r3_9,kernel91_0_r3_10,kernel91_0_r3_11,kernel91_0_r3_12,kernel91_0_r3_13,kernel91_0_r3_14,kernel91_0_r3_15] +lemma kernel91_0_r3_eq (i k : Fin 16) : kernel91_0Expr 3 i k = kernel91_0_r3 i k := by + fin_cases i + · exact kernel91_0_r3_0_eq k + · exact kernel91_0_r3_1_eq k + · exact kernel91_0_r3_2_eq k + · exact kernel91_0_r3_3_eq k + · exact kernel91_0_r3_4_eq k + · exact kernel91_0_r3_5_eq k + · exact kernel91_0_r3_6_eq k + · exact kernel91_0_r3_7_eq k + · exact kernel91_0_r3_8_eq k + · exact kernel91_0_r3_9_eq k + · exact kernel91_0_r3_10_eq k + · exact kernel91_0_r3_11_eq k + · exact kernel91_0_r3_12_eq k + · exact kernel91_0_r3_13_eq k + · exact kernel91_0_r3_14_eq k + · exact kernel91_0_r3_15_eq k +noncomputable def kernel91_0_r4_0 : Fin 16 → CBox := ![⟨⟨179,185⟩,⟨10,16⟩⟩,⟨⟨178,184⟩,⟨9,15⟩⟩,⟨⟨177,183⟩,⟨7,13⟩⟩,⟨⟨175,181⟩,⟨5,11⟩⟩,⟨⟨171,179⟩,⟨2,10⟩⟩,⟨⟨168,174⟩,⟨0,6⟩⟩,⟨⟨164,170⟩,⟨(-3),3⟩⟩,⟨⟨159,165⟩,⟨(-8),(-2)⟩⟩,⟨⟨153,159⟩,⟨(-12),(-6)⟩⟩,⟨⟨146,153⟩,⟨(-17),(-10)⟩⟩,⟨⟨139,147⟩,⟨(-21),(-13)⟩⟩,⟨⟨131,138⟩,⟨(-25),(-18)⟩⟩,⟨⟨124,130⟩,⟨(-30),(-24)⟩⟩,⟨⟨116,122⟩,⟨(-33),(-27)⟩⟩,⟨⟨107,113⟩,⟨(-37),(-31)⟩⟩,⟨⟨99,105⟩,⟨(-40),(-34)⟩⟩] +lemma kernel91_0_r4_0_eq : ∀ k : Fin 16, kernel91_0Expr 4 0 k = kernel91_0_r4_0 k := by decide +kernel +noncomputable def kernel91_0_r4_1 : Fin 16 → CBox := ![⟨⟨90,96⟩,⟨(-43),(-37)⟩⟩,⟨⟨81,87⟩,⟨(-46),(-40)⟩⟩,⟨⟨71,78⟩,⟨(-47),(-40)⟩⟩,⟨⟨63,69⟩,⟨(-48),(-42)⟩⟩,⟨⟨55,61⟩,⟨(-48),(-42)⟩⟩,⟨⟨47,53⟩,⟨(-47),(-41)⟩⟩,⟨⟨39,45⟩,⟨(-48),(-41)⟩⟩,⟨⟨32,38⟩,⟨(-45),(-39)⟩⟩,⟨⟨24,31⟩,⟨(-44),(-37)⟩⟩,⟨⟨18,24⟩,⟨(-42),(-36)⟩⟩,⟨⟨13,20⟩,⟨(-40),(-34)⟩⟩,⟨⟨8,14⟩,⟨(-37),(-31)⟩⟩,⟨⟨4,10⟩,⟨(-34),(-27)⟩⟩,⟨⟨1,7⟩,⟨(-31),(-25)⟩⟩,⟨⟨(-3),3⟩,⟨(-27),(-21)⟩⟩,⟨⟨(-6),2⟩,⟨(-25),(-18)⟩⟩] +lemma kernel91_0_r4_1_eq : ∀ k : Fin 16, kernel91_0Expr 4 1 k = kernel91_0_r4_1 k := by decide +kernel +noncomputable def kernel91_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-7),(-1)⟩,⟨(-21),(-15)⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-18),(-12)⟩⟩,⟨⟨(-9),(-3)⟩,⟨(-16),(-10)⟩⟩,⟨⟨(-9),(-3)⟩,⟨(-14),(-7)⟩⟩,⟨⟨(-9),(-3)⟩,⟨(-11),(-5)⟩⟩,⟨⟨(-9),(-3)⟩,⟨(-9),(-3)⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-7),(-1)⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-6),0⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-6),0⟩⟩,⟨⟨(-7),(-1)⟩,⟨(-4),2⟩⟩,⟨⟨(-7),(-1)⟩,⟨(-3),3⟩⟩,⟨⟨(-5),0⟩,⟨(-3),2⟩⟩,⟨⟨(-6),0⟩,⟨(-2),4⟩⟩,⟨⟨(-5),1⟩,⟨(-3),3⟩⟩,⟨⟨(-3),1⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),4⟩⟩] +lemma kernel91_0_r4_2_eq : ∀ k : Fin 16, kernel91_0Expr 4 2 k = kernel91_0_r4_2 k := by decide +kernel +noncomputable def kernel91_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r4_3_eq : ∀ k : Fin 16, kernel91_0Expr 4 3 k = kernel91_0_r4_3 k := by decide +kernel +noncomputable def kernel91_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_4_eq : ∀ k : Fin 16, kernel91_0Expr 4 4 k = kernel91_0_r4_4 k := by decide +kernel +noncomputable def kernel91_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_5_eq : ∀ k : Fin 16, kernel91_0Expr 4 5 k = kernel91_0_r4_5 k := by decide +kernel +noncomputable def kernel91_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_6_eq : ∀ k : Fin 16, kernel91_0Expr 4 6 k = kernel91_0_r4_6 k := by decide +kernel +noncomputable def kernel91_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_7_eq : ∀ k : Fin 16, kernel91_0Expr 4 7 k = kernel91_0_r4_7 k := by decide +kernel +noncomputable def kernel91_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_8_eq : ∀ k : Fin 16, kernel91_0Expr 4 8 k = kernel91_0_r4_8 k := by decide +kernel +noncomputable def kernel91_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_9_eq : ∀ k : Fin 16, kernel91_0Expr 4 9 k = kernel91_0_r4_9 k := by decide +kernel +noncomputable def kernel91_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_10_eq : ∀ k : Fin 16, kernel91_0Expr 4 10 k = kernel91_0_r4_10 k := by decide +kernel +noncomputable def kernel91_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel91_0_r4_11_eq : ∀ k : Fin 16, kernel91_0Expr 4 11 k = kernel91_0_r4_11 k := by decide +kernel +noncomputable def kernel91_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r4_12_eq : ∀ k : Fin 16, kernel91_0Expr 4 12 k = kernel91_0_r4_12 k := by decide +kernel +noncomputable def kernel91_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r4_13_eq : ∀ k : Fin 16, kernel91_0Expr 4 13 k = kernel91_0_r4_13 k := by decide +kernel +noncomputable def kernel91_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r4_14_eq : ∀ k : Fin 16, kernel91_0Expr 4 14 k = kernel91_0_r4_14 k := by decide +kernel +noncomputable def kernel91_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel91_0_r4_15_eq : ∀ k : Fin 16, kernel91_0Expr 4 15 k = kernel91_0_r4_15 k := by decide +kernel +noncomputable def kernel91_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel91_0_r4_0,kernel91_0_r4_1,kernel91_0_r4_2,kernel91_0_r4_3,kernel91_0_r4_4,kernel91_0_r4_5,kernel91_0_r4_6,kernel91_0_r4_7,kernel91_0_r4_8,kernel91_0_r4_9,kernel91_0_r4_10,kernel91_0_r4_11,kernel91_0_r4_12,kernel91_0_r4_13,kernel91_0_r4_14,kernel91_0_r4_15] +lemma kernel91_0_r4_eq (i k : Fin 16) : kernel91_0Expr 4 i k = kernel91_0_r4 i k := by + fin_cases i + · exact kernel91_0_r4_0_eq k + · exact kernel91_0_r4_1_eq k + · exact kernel91_0_r4_2_eq k + · exact kernel91_0_r4_3_eq k + · exact kernel91_0_r4_4_eq k + · exact kernel91_0_r4_5_eq k + · exact kernel91_0_r4_6_eq k + · exact kernel91_0_r4_7_eq k + · exact kernel91_0_r4_8_eq k + · exact kernel91_0_r4_9_eq k + · exact kernel91_0_r4_10_eq k + · exact kernel91_0_r4_11_eq k + · exact kernel91_0_r4_12_eq k + · exact kernel91_0_r4_13_eq k + · exact kernel91_0_r4_14_eq k + · exact kernel91_0_r4_15_eq k +noncomputable def kernel91_0_r5_0 : Fin 16 → CBox := ![⟨⟨31412847423939226590134,31412849299110346763910⟩,⟨(-25811102306061606347882),(-25811100430890486174611)⟩⟩,⟨⟨31246862592542479988084,31246864464364090582850⟩,⟨(-25831637585948193081537),(-25831635714126582487271)⟩⟩,⟨⟨30916134387139114170419,30916136252275793554984⟩,⟨(-25871045479608475393063),(-25871043614471796008989)⟩⟩,⟨⟨30423152619440707780151,30423154474591576124150⟩,⟨(-25926043231449510474697),(-25926041376298642131177)⟩⟩,⟨⟨29771668217003044294451,29771670058918610208602⟩,⟨(-25991812424361607927328),(-25991810582446042013638)⟩⟩,⟨⟨28966709831548581409491,28966711657047301762429⟩,⟨(-26062123799832124883741),(-26062121974333404531243)⟩⟩,⟨⟨28014601383440731707251,28014603189424824967917⟩,⟨(-26129500261760591106865),(-26129498455776497846615)⟩⟩,⟨⟨26922976874506171524401,26922978657977071571703⟩,⟨(-26185415087665751613553),(-26185413304194851566637)⟩⟩,⟨⟨25700788219265337689820,25700789977337783058811⟩,⟨(-26220521586284741409585),(-26220519828212296040951)⟩⟩,⟨⟨24358301471626107460830,24358303201542233635935⟩,⟨(-26224909646964963499566),(-26224907917048837324784)⟩⟩,⟨⟨22907076687775209398910,22907078386916918218663⟩,⟨(-26188383838481319316151),(-26188382139339610496684)⟩⟩,⟨⟨21359926785879772095386,21359928451923367578311⟩,⟨(-26100756954824944041735),(-26100755288781348559058)⟩⟩,⟨⟨19730851150192114114661,19730852780836975021248⟩,⟨(-25952152200935403202396),(-25952150570290542296017)⟩⟩,⟨⟨18034940379106693838870,18034941972222308330674⟩,⟨(-25733306598375839956631),(-25733305005260225464996)⟩⟩,⟨⟨16288249486063610074372,16288251039694042505835⟩,⟨(-25435867703860010582321),(-25435866150229578150987)⟩⟩,⟨⟨14507638000401282817747,14507639512775283326437⟩,⟨(-25052675417594296282638),(-25052673905220295774036)⟩⟩] +lemma kernel91_0_r5_0_eq : ∀ k : Fin 16, kernel91_0Expr 5 0 k = kernel91_0_r5_0 k := by decide +kernel +noncomputable def kernel91_0_r5_1 : Fin 16 → CBox := ![⟨⟨12710576750474186993170,12710578220005249930376⟩,⟨(-24578020549530941521735),(-24578019079999878584577)⟩⟩,⟨⟨10914922593848482648483,10914924019144871882980⟩,⟨(-24007871948491313088046),(-24007870523194923853559)⟩⟩,⟨⟨9138663931261143719055,9138665311120542539546⟩,⟨(-23340064411362898394766),(-23340063031503499574249)⟩⟩,⟨⟨7399641434230216022559,7399642767648873819082⟩,⟨(-22574440298464365033662),(-22574438965045707237078)⟩⟩,⟨⟨5715249956252651507194,5715251242415300396469⟩,⟨(-21712938795452224655567),(-21712937509289575766197)⟩⟩,⟨⟨4102129005667651330406,4102130243957798949785⟩,⟨(-20759628076543898371687),(-20759626838253750752185)⟩⟩,⟨⟨2575850356046265367624,2575851546029009986832⟩,⟨(-19720677216413490780546),(-19720676026430746161189)⟩⟩,⟨⟨1150612282196524719980,1150613423633388922664⟩,⟨(-18604266530506397816500),(-18604265389069533613644)⟩⟩,⟨⟨(-161049529741386201266),(-161048436918802019669)⟩,⟨(-17420437039717473778286),(-17420435946894889596497)⟩⟩,⟨⟨(-1348524195732568781256),(-1348523151413239304426)⟩,⟨(-16180881884590861210724),(-16180880840271531733686)⟩⟩,⟨⟨(-2403351058029075383432),(-2403350061946575466495)⟩,⟨(-14898684671324760613777),(-14898683675242260696620)⟩⟩,⟨⟨(-3319399158411306164934),(-3319398210131341935600)⟩,⟨(-13588011823156304278477),(-13588010874876340048915)⟩⟩,⟨⟨(-4092992805508911912468),(-4092991904460767724336)⟩,⟨(-12263767935990310328744),(-12263767034942166140378)⟩⟩,⟨⟨(-4722976914474459777478),(-4722976059906501544571)⟩,⟨(-10941224797467217327645),(-10941223942899259094514)⟩⟩,⟨⟨(-5210717802177620275826),(-5210716993188752190470)⟩,⟨(-9635636029589598601719),(-9635635220600730516177)⟩⟩,⟨⟨(-5560037421088733292187),(-5560036656715076180372)⟩,⟨(-8361850175504910480242),(-8361849411131253368277)⟩⟩] +lemma kernel91_0_r5_1_eq : ∀ k : Fin 16, kernel91_0Expr 5 1 k = kernel91_0_r5_1 k := by decide +kernel +noncomputable def kernel91_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-5777081511642655461216),(-5777080790828286897722)⟩,⟨(-7133935406018968853721),(-7133934685204600290110)⟩⟩,⟨⟨(-5870124732283336199015),(-5870124053857251835470)⟩,⟨(-5964828829170209065966),(-5964828150744124702334)⟩⟩,⟨⟨(-5849318364930995666871),(-5849317727652647396644)⟩,⟨(-4866022632233355001910),(-4866021994955006731626)⟩⟩,⟨⟨(-5726388562803777136543),(-5726387965343828316687)⟩,⟨(-3847297983457866906906),(-3847297385997918087016)⟩⟩,⟨⟨(-5514295182852090857693),(-5514294623830878417730)⟩,⟨(-2916515814721239415709),(-2916515255700026975733)⟩⟩,⟨⟨(-5226862914190949884688),(-5226862392132413750781)⟩,⟨(-2079471370176520266695),(-2079470848117984132792)⟩⟩,⟨⟨(-4878397581124813280431),(-4878397094562306218078)⟩,⟨(-1339816838247353730583),(-1339816351684846668249)⟩⟩,⟨⟨(-4483301096253841929612),(-4483300643672195684464)⟩,⟨(-699053607040037499302),(-699053154458391254184)⟩⟩,⟨⟨(-4055698524119002088956),(-4055698104000494135228)⟩,⟨(-156592830104925399181),(-156592409986417445493)⟩⟩,⟨⟨(-3609090084527966826311),(-3609089695309637420949)⟩,⟨290119794743341007957,290120183961670413273⟩⟩,⟨⟨(-3156039703158527113871),(-3156039343305898791063)⟩,⟨645421706885711636956,645422066738339959714⟩⟩,⟨⟨(-2707909968744616919868),(-2707909636712026608942)⟩,⟨915202532755558407151,915202864788148718024⟩⟩,⟨⟨(-2274651171465181199474),(-2274650865734541164522)⟩,⟨1106635194336234802515,1106635500066874837422⟩⟩,⟨⟨(-1864649594791390055508),(-1864649313849514673412)⟩,⟨1227881006731421604884,1227881287673296986947⟩⟩,⟨⟨(-1484637546510118356715),(-1484637288886858473027)⟩,⟨1287781338386255840859,1287781596009515724523⟩⟩,⟨⟨(-1139664889670992095418),(-1139664653914501336719)⟩,⟨1295548430496552235955,1295548666253042994640⟩⟩] +lemma kernel91_0_r5_2_eq : ∀ k : Fin 16, kernel91_0Expr 5 2 k = kernel91_0_r5_2 k := by decide +kernel +noncomputable def kernel91_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-833129214699542847525),(-833128999413101286525)⟩,⟨1260467390000994598472,1260467605287436159465⟩⟩,⟨⟨(-566859417122769552701),(-566859220933028565652)⟩,⟨1191620231146476006581,1191620427336216993629⟩⟩,⟨⟨(-341245429267147104788),(-341245250863778450010)⟩,⟨1097641225088875277399,1097641403492243932180⟩⟩,⟨⟨(-155405294472707793347),(-155405132580841219365)⟩,⟨986510830070874541819,986510991962741115808⟩⟩,⟨⟨(-7379732249671278765),(-7379585661443188406)⟩,⟨865393241593252716973,865393388181480807340⟩⟩,⟨⟨105656145345667614542,105656277799890091125⟩,⟨740520255556782940258,740520388011005416851⟩⟩,⟨⟨187174246098209232956,187174365518512461330⟩,⟨617121813486247209278,617121932906550437663⟩⟩,⟨⟨241077745966552369029,241077853408192755730⟩,⟨499401423665187820940,499401531106828207650⟩⟩,⟨⟨271496860464898523219,271496956913496598323⟩,⟨390552737438286374690,390552833886884449801⟩⟩,⟨⟨282603446151652834121,282603532549253103643⟩,⟨292811994019327531264,292812080416927800790⟩⟩,⟨⟨278450104669583917904,278450181912827298933⟩,⟨207539892588431929635,207539969831675310666⟩⟩,⟨⟨262837684815870479457,262837753883423999993⟩,⟨135325738820009664562,135325807887563185099⟩⟩,⟨⟨239213273324386191332,239213334942380140845⟩,⟨76106447917839035854,76106509535832985366⟩⟩,⟨⟨210599036266658027299,210599091122705660261⟩,⟨29293140028301581505,29293194884349214465⟩⟩,⟨⟨179550717156224314768,179550765881844681194⟩,⟨(-6101408406685772954),(-6101359681065406529)⟩⟩,⟨⟨148143282403991084126,148143325591898243153⟩,⟨(-31340366596364847901),(-31340323408457688876)⟩⟩] +lemma kernel91_0_r5_3_eq : ∀ k : Fin 16, kernel91_0Expr 5 3 k = kernel91_0_r5_3 k := by decide +kernel +noncomputable def kernel91_0_r5_4 : Fin 16 → CBox := ![⟨⟨117980185983921814725,117980224175086108896⟩,⟨(-47850363015936947841),(-47850324824772653672)⟩⟩,⟨⟨90222027176917381953,90222060877770977823⟩,⟨(-57122584588000175985),(-57122550887146580117)⟩⟩,⟨⟨65630003025879813798,65630032695706472715⟩,⟨(-60629902476628512170),(-60629872806801853253)⟩⟩,⟨⟨44619492356598029549,44619518421323335957⟩,⟨(-59761264899324635897),(-59761238834599329490)⟩⟩,⟨⟨27319315735362954147,27319338579226552405⟩,⟨(-55773497099972559301),(-55773474256108961043)⟩⟩,⟨⟨13632646015463246400,13632665993736742143⟩,⟨(-49759702904506352698),(-49759682926232856955)⟩⟩,⟨⟨3296140016914387507,3296157448119842099⟩,⟨(-42632707459981990518),(-42632690028776535924)⟩⟩,⟨⟨(-4065437886371383029),(-4065422710329783972)⟩,⟨(-35121436425475507424),(-35121421249433908367)⟩⟩,⟨⟨(-8891084127864240278),(-8891070946617146652)⟩,⟨(-27777795256004919817),(-27777782074757826191)⟩⟩,⟨⟨(-11643163961796548579),(-11643152537560096821)⟩,⟨(-20991481462219969169),(-20991470037983517410)⟩⟩,⟨⟨(-12775325071047208367),(-12775315192807761586)⟩,⟨(-15010208629189336006),(-15010198750949889224)⟩⟩,⟨⟨(-12708690331313392356),(-12708681808195149645)⟩,⟨(-9963011434931996844),(-9963002911813754132)⟩⟩,⟨⟨(-11815823177852533545),(-11815815841861118767)⟩,⟨(-5884598564188804800),(-5884591228197390021)⟩⟩,⟨⟨(-10411602882439562103),(-10411596581093680079)⟩,⟨(-2739086962413457544),(-2739080661067575520)⟩⟩,⟨⟨(-8749915630438741203),(-8749910230627620834)⟩,⟨(-441849363450822514),(-441843963639702145)⟩⟩,⟨⟨(-7024952721788599960),(-7024948104552880639)⟩,⟨1121395000583110532,1121399617818829852⟩⟩] +lemma kernel91_0_r5_4_eq : ∀ k : Fin 16, kernel91_0Expr 5 4 k = kernel91_0_r5_4 k := by decide +kernel +noncomputable def kernel91_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-5375894466702292570),(-5375890528402177594)⟩,⟨2078746003522763544,2078749941822878520⟩⟩,⟨⟨(-3893828143255022134),(-3893824790946650305)⟩,⟨2559720477477620590,2559723829785992419⟩⟩,⟨⟨(-2629878934825277712),(-2629876087510737209)⟩,⟨2686194474642683595,2686197321957224097⟩⟩,⟨⟨(-1603702327031216293),(-1603699913864747403)⟩,⟨2566403817701533024,2566406230868001914⟩⟩,⟨⟨(-811674616140192043),(-811672576025746644)⟩,⟨2291583937685659707,2291585977800105106⟩⟩,⟨⟨(-234307532086831544),(-234305810928884139)⟩,⟨1934757470735509501,1934759191893456906⟩⟩,⟨⟨157410415276451793,157411863767035246⟩,⟨1551157516595474510,1551158965086057963⟩⟩,⟨⟨396889261494069814,396890477903484553⟩,⟨1179795284368945600,1179796500778360339⟩⟩,⟨⟨518047610321862268,518048629252078845⟩,⟨845731767166103470,845732786096320047⟩⟩,⟨⟨552581007393017976,552581859665463511⟩,⟨562682979189719869,562683831462165404⟩⟩,⟨⟨528248428882347555,528249140095032747⟩,⟨335667232766247999,335667943978933191⟩⟩,⟨⟨468000384672383459,468000976918830623⟩,⟨163482581803201693,163483174049648857⟩⟩,⟨⟨389759221181251707,389759713116002544⟩,⟨40876618537892788,40877110472643625⟩⟩,⟨⟨306667483658386608,306667891446018349⟩,⟨(-39665079559920389),(-39664671772288649)⟩⟩,⟨⟨227638406806986728,227638744003285010⟩,⟨(-86533777429756451),(-86533440233458169)⟩⟩,⟨⟨158068740866659153,158069019165316208⟩,⟨(-107998971567683782),(-107998693269026727)⟩⟩] +lemma kernel91_0_r5_5_eq : ∀ k : Fin 16, kernel91_0Expr 5 5 k = kernel91_0_r5_5 k := by decide +kernel +noncomputable def kernel91_0_r5_6 : Fin 16 → CBox := ![⟨⟨100603882677510877,100604111788035750⟩,⟨(-111553604782422152),(-111553375671897279)⟩⟩,⟨⟨55875188163038544,55875376409734776⟩,⟨(-103545552484587991),(-103545364237891759)⟩⟩,⟨⟨23156877965137326,23157032260401674⟩,⟨(-89032218296402756),(-89032064001138407)⟩⟩,⟨⟨913475961261331,913602174273874⟩,⟨(-71796475233241395),(-71796349020228853)⟩⟩,⟨⟨(-12772567301455355),(-12772464319979860)⟩,⟨(-54468390892286580),(-54468287910811085)⟩⟩,⟨⟨(-19889689152193212),(-19889605288023019)⟩,⟨(-38706208657910864),(-38706124793740671)⟩⟩,⟨⟨(-22290022516369459),(-22289954388151988)⟩,⟨(-25400264812717598),(-25400196684500127)⟩⟩,⟨⟨(-21568704478559852),(-21568649241950853)⟩,⟨(-14873643407311041),(-14873588170702043)⟩⟩,⟨⟨(-19010351574615686),(-19010306842964012)⟩,⟨(-7062526578181087),(-7062481846529413)⟩⟩,⟨⟨(-15583881101751893),(-15583844926847535)⟩,⟨(-1666870832934693),(-1666834658030334)⟩⟩,⟨⟨(-11968918865648769),(-11968889681503075)⟩,⟨1731995013558414,1732024197704108⟩⟩,⟨⟨(-8599947818769575),(-8599924318635116)⟩,⟨3585990223195350,3586013723329809⟩⟩,⟨⟨(-5717565031213513),(-5717546154898135)⟩,⟨4323533774079234,4323552650394612⟩⟩,⟨⟨(-3419323495130357),(-3419308359334742)⟩,⟨4316393662971507,4316408798767122⟩⟩,⟨⟨(-1705378126044856),(-1705366018285070)⟩,⟨3864640061241573,3864652169001359⟩⟩,⟨⟨(-516393718983913),(-516384050117214)⟩,⟨3194440776286845,3194450445153543⟩⟩] +lemma kernel91_0_r5_6_eq : ∀ k : Fin 16, kernel91_0Expr 5 6 k = kernel91_0_r5_6 k := by decide +kernel +noncomputable def kernel91_0_r5_7 : Fin 16 → CBox := ![⟨⟨237137890902683,237145593145207⟩,⟨2464101025686502,2464108727929026⟩⟩,⟨⟨653857415185844,653863541361048⟩,⟨1774627775852106,1774633902027310⟩⟩,⟨⟨827748268460971,827753130710204⟩,⟨1182029346798816,1182034209048049⟩⟩,⟨⟨840222564353466,840226416948333⟩,⟨709431255983046,709435108577913⟩⟩,⟨⟨756628050137604,756631095564925⟩,⟨357833281841710,357836327269032⟩⟩,⟨⟨625819685013825,625822088713140⟩,⟨114920029360085,114922433059400⟩⟩,⟨⟨481641452761771,481643345679785⟩,⟨(-38235009326512),(-38233116408498)⟩⟩,⟨⟨345409805971889,345411294314695⟩,⟨(-122449400765089),(-122447912422282)⟩⟩,⟨⟨228737828974043,228738997397017⟩,⟨(-157411252796050),(-157410084373076)⟩⟩,⟨⟨136261765016504,136262681276796⟩,⟨(-160004223451802),(-160003307191510)⟩⟩,⟨⟨68014863472232,68015580427767⟩,⟨(-143619213818810),(-143618496863274)⟩⟩,⟨⟨21332815928797,21333376131175⟩,⟨(-118129617511506),(-118129057309128)⟩⟩,⟨⟨(-7727734778973),(-7727298033575)⟩,⟨(-90263739461300),(-90263302715903)⟩⟩,⟨⟨(-23415312976235),(-23414972878664)⟩,⟨(-64171447798620),(-64171107701049)⟩⟩,⟨⟨(-29680061206002),(-29679796915677)⟩,⟨(-42042657452923),(-42042393162597)⟩⟩,⟨⟨(-29855281006348),(-29855075889422)⟩,⟨(-24687344915816),(-24687139798890)⟩⟩] +lemma kernel91_0_r5_7_eq : ∀ k : Fin 16, kernel91_0Expr 5 7 k = kernel91_0_r5_7 k := by decide +kernel +noncomputable def kernel91_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-26541772929668),(-26541614071361)⟩,⟨(-12027975233389),(-12027816375082)⟩⟩,⟨⟨(-21623683062738),(-21623560092993)⟩,⟨(-3485244947088),(-3485121977344)⟩⟩,⟨⟨(-16359120434855),(-16359025433260)⟩,⟨1742013696991,1742108698585⟩⟩,⟨⟨(-11503849791122),(-11503776478759)⟩,⟨4490238836310,4490312148673⟩⟩,⟨⟨(-7439963706783),(-7439907245625)⟩,⟨5519890534261,5519946995420⟩⟩,⟨⟨(-4292635163544),(-4292591719836)⟩,⟨5460453905001,5460497348709⟩⟩,⟨⟨(-2026534914995),(-2026501540560)⟩,⟨4794145522915,4794178897349⟩⟩,⟨⟨(-519410949946),(-519385332443)⟩,⟨3863704963747,3863730581251⟩⟩,⟨⟨385954304254,385973929494⟩,⟨2893055067655,2893074692895⟩⟩,⟨⟨848185547725,848200572174⟩,⟨2012890196652,2012905221101⟩⟩,⟨⟨1008154009873,1008165494781⟩,⟨1286071259270,1286082744177⟩⟩,⟨⟨980237942953,980246715652⟩,⟨729927733195,729936505894⟩⟩,⟨⟨850511982872,850518672115⟩,⟨334181858399,334188547644⟩⟩,⟨⟨679063420237,679068518734⟩,⟨74283749776,74288848273⟩⟩,⟨⟨504359859907,504363739944⟩,⟨(-79417492495),(-79413612459)⟩⟩,⟨⟨348252308701,348255260027⟩,⟨(-155931503504),(-155928552178)⟩⟩] +lemma kernel91_0_r5_8_eq : ∀ k : Fin 16, kernel91_0Expr 5 8 k = kernel91_0_r5_8 k := by decide +kernel +noncomputable def kernel91_0_r5_9 : Fin 16 → CBox := ![⟨⟨220740522564,220742763737⟩,⟨(-180490302210),(-180488061036)⟩⟩,⟨⟨124038285973,124039987513⟩,⟨(-173244292937),(-173242591396)⟩⟩,⟨⟨55763232241,55764522324⟩,⟨(-149137631876),(-149136341794)⟩⟩,⟨⟨11257935027,11258912832⟩,⟨(-118456388859),(-118455411055)⟩⟩,⟨⟨(-14849720675),(-14848980634)⟩,⟨(-87685953675),(-87685213634)⟩⟩,⟨⟨(-27695386036),(-27694825971)⟩,⟨(-60438020701),(-60437460635)⟩⟩,⟨⟨(-31678834655),(-31678411302)⟩,⟨(-38305493544),(-38305070192)⟩⟩,⟨⟨(-30274572712),(-30274252731)⟩,⟨(-21575357273),(-21575037291)⟩⟩,⟨⟨(-26036648583),(-26036407054)⟩,⟨(-9777825774),(-9777584245)⟩⟩,⟨⟨(-20710238097),(-20710055740)⟩,⟨(-2079462704),(-2079280348)⟩⟩,⟨⟨(-15388870856),(-15388733312)⟩,⟨2456717135,2456854679⟩⟩,⟨⟨(-10678098478),(-10677994720)⟩,⟨4715484347,4715588106⟩⟩,⟨⟨(-6843236595),(-6843158406)⟩,⟨5449644544,5449722733⟩⟩,⟨⟨(-3930790282),(-3930731335)⟩,⟨5251596309,5251655256⟩⟩,⟨⟨(-1861006195),(-1860961789)⟩,⟨4556477145,4556521551⟩⟩,⟨⟨(-493605499),(-493571866)⟩,⟨3662292601,3662326235⟩⟩] +lemma kernel91_0_r5_9_eq : ∀ k : Fin 16, kernel91_0Expr 5 9 k = kernel91_0_r5_9 k := by decide +kernel +noncomputable def kernel91_0_r5_10 : Fin 16 → CBox := ![⟨⟨328973586,328999051⟩,⟨2756994142,2757019607⟩⟩,⟨⟨755768433,755787731⟩,⟨1946178811,1946198108⟩⟩,⟨⟨914080732,914095344⟩,⟨1277876398,1277891010⟩⟩,⟨⟨904718040,904729115⟩,⟨762835484,762846559⟩⟩,⟨⟨802423921,802432308⟩,⟨389974022,389982409⟩⟩,⟨⟨659100874,659107233⟩,⟨137382338,137388697⟩⟩,⟨⟨508189763,508194584⟩,⟨(-20385947),(-20381126)⟩⟩,⟨⟨369176991,369180648⟩,⟨(-107898527),(-107894869)⟩⟩,⟨⟨251653466,251656238⟩,⟨(-146511928),(-146509156)⟩⟩,⟨⟨158663323,158665430⟩,⟨(-153447290),(-153445184)⟩⟩,⟨⟨89281971,89283572⟩,⟨(-141743083),(-141741483)⟩⟩,⟨⟨40479413,40480632⟩,⟨(-120693966),(-120692747)⟩⟩,⟨⟨8381534,8382464⟩,⟨(-96506660),(-96505730)⟩⟩,⟨⟨(-10940316),(-10939607)⟩,⟨(-73001381),(-73000672)⟩⟩,⟨⟨(-21026723),(-21026181)⟩,⟨(-52260044),(-52259503)⟩⟩,⟨⟨(-24827227),(-24826811)⟩,⟨(-35173412),(-35172996)⟩⟩] +lemma kernel91_0_r5_10_eq : ∀ k : Fin 16, kernel91_0Expr 5 10 k = kernel91_0_r5_10 k := by decide +kernel +noncomputable def kernel91_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-24651409),(-24651091)⟩,⟨(-21872420),(-21872102)⟩⟩,⟨⟨(-22210080),(-22209834)⟩,⟨(-12048638),(-12048392)⟩⟩,⟨⟨(-18701595),(-18701405)⟩,⟨(-5178821),(-5178631)⟩⟩,⟨⟨(-14913739),(-14913592)⟩,⟨(-672414),(-672267)⟩⟩,⟨⟨(-11323279),(-11323165)⟩,⟨2039259,2039373⟩⟩,⟨⟨(-8183653),(-8183563)⟩,⟨3455507,3455597⟩⟩,⟨⟨(-5596846),(-5596776)⟩,⟨3986835,3986905⟩⟩,⟨⟨(-3569004),(-3568948)⟩,⟨3953083,3953138⟩⟩,⟨⟨(-2051249),(-2051205)⟩,⟨3591495,3591539⟩⟩,⟨⟨(-968088),(-968051)⟩,⟨3069486,3069523⟩⟩,⟨⟨(-236028),(-235998)⟩,⟨2498707,2498738⟩⟩,⟨⟨225143,225170⟩,⟨1948421,1948448⟩⟩,⟨⟨486306,486328⟩,⟨1457154,1457175⟩⟩,⟨⟨606466,606484⟩,⟨1042227,1042244⟩⟩,⟨⟨632437,632453⟩,⟨707175,707191⟩⟩,⟨⟨599797,599811⟩,⟨447249,447263⟩⟩] +lemma kernel91_0_r5_11_eq : ∀ k : Fin 16, kernel91_0Expr 5 11 k = kernel91_0_r5_11 k := by decide +kernel +noncomputable def kernel91_0_r5_12 : Fin 16 → CBox := ![⟨⟨534472,534484⟩,⟨253322,253335⟩⟩,⟨⟨454516,454527⟩,⟨114516,114527⟩⟩,⟨⟨371850,371861⟩,⟨19869,19880⟩⟩,⟨⟨293795,293804⟩,⟨(-40700),(-40691)⟩⟩,⟨⟨224363,224373⟩,⟨(-75916),(-75906)⟩⟩,⟨⟨165295,165304⟩,⟨(-92986),(-92977)⟩⟩,⟨⟨116845,116854⟩,⟨(-97637),(-97629)⟩⟩,⟨⟨78373,78380⟩,⟨(-94267),(-94259)⟩⟩,⟨⟨48749,48756⟩,⟨(-86136),(-86128)⟩⟩,⟨⟨26651,26658⟩,⟨(-75574),(-75567)⟩⟩,⟨⟨10730,10739⟩,⟨(-64182),(-64173)⟩⟩,⟨⟨(-268),(-261)⟩,⟨(-52995),(-52987)⟩⟩,⟨⟨(-7456),(-7448)⟩,⟨(-42644),(-42637)⟩⟩,⟨⟨(-11775),(-11768)⟩,⟨(-33459),(-33452)⟩⟩,⟨⟨(-14001),(-13994)⟩,⟨(-25570),(-25563)⟩⟩,⟨⟨(-14752),(-14744)⟩,⟨(-18977),(-18969)⟩⟩] +lemma kernel91_0_r5_12_eq : ∀ k : Fin 16, kernel91_0Expr 5 12 k = kernel91_0_r5_12 k := by decide +kernel +noncomputable def kernel91_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-14504),(-14498)⟩,⟨(-13595),(-13589)⟩⟩,⟨⟨(-13625),(-13617)⟩,⟨(-9299),(-9291)⟩⟩,⟨⟨(-12380),(-12372)⟩,⟨(-5945),(-5938)⟩⟩,⟨⟨(-10960),(-10953)⟩,⟨(-3382),(-3374)⟩⟩,⟨⟨(-9498),(-9491)⟩,⟨(-1473),(-1466)⟩⟩,⟨⟨(-8082),(-8075)⟩,⟨(-91),(-84)⟩⟩,⟨⟨(-6763),(-6756)⟩,⟨872,879⟩⟩,⟨⟨(-5572),(-5565)⟩,⟨1510,1518⟩⟩,⟨⟨(-4522),(-4514)⟩,⟨1902,1909⟩⟩,⟨⟨(-3611),(-3604)⟩,⟨2109,2117⟩⟩,⟨⟨(-2835),(-2829)⟩,⟨2184,2190⟩⟩,⟨⟨(-2184),(-2176)⟩,⟨2162,2169⟩⟩,⟨⟨(-1644),(-1636)⟩,⟨2076,2084⟩⟩,⟨⟨(-1200),(-1192)⟩,⟨1951,1959⟩⟩,⟨⟨(-840),(-834)⟩,⟨1803,1809⟩⟩,⟨⟨(-552),(-545)⟩,⟨1642,1649⟩⟩] +lemma kernel91_0_r5_13_eq : ∀ k : Fin 16, kernel91_0Expr 5 13 k = kernel91_0_r5_13 k := by decide +kernel +noncomputable def kernel91_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-324),(-318)⟩,⟨1481,1487⟩⟩,⟨⟨(-145),(-139)⟩,⟨1322,1328⟩⟩,⟨⟨(-9),(-3)⟩,⟨1172,1178⟩⟩,⟨⟨94,101⟩,⟨1032,1040⟩⟩,⟨⟨171,178⟩,⟨905,911⟩⟩,⟨⟨227,233⟩,⟨789,795⟩⟩,⟨⟨266,272⟩,⟨686,692⟩⟩,⟨⟨291,297⟩,⟨594,600⟩⟩,⟨⟨306,312⟩,⟨511,517⟩⟩,⟨⟨313,319⟩,⟨440,446⟩⟩,⟨⟨315,321⟩,⟨377,383⟩⟩,⟨⟨312,318⟩,⟨322,328⟩⟩,⟨⟨306,312⟩,⟨275,281⟩⟩,⟨⟨298,305⟩,⟨233,240⟩⟩,⟨⟨289,295⟩,⟨198,204⟩⟩,⟨⟨279,285⟩,⟨168,174⟩⟩] +lemma kernel91_0_r5_14_eq : ∀ k : Fin 16, kernel91_0Expr 5 14 k = kernel91_0_r5_14 k := by decide +kernel +noncomputable def kernel91_0_r5_15 : Fin 16 → CBox := ![⟨⟨269,275⟩,⟨141,147⟩⟩,⟨⟨258,264⟩,⟨119,125⟩⟩,⟨⟨248,255⟩,⟨100,106⟩⟩,⟨⟨238,246⟩,⟨82,90⟩⟩,⟨⟨229,237⟩,⟨69,76⟩⟩,⟨⟨221,227⟩,⟨58,64⟩⟩,⟨⟨214,220⟩,⟨47,53⟩⟩,⟨⟨206,213⟩,⟨38,45⟩⟩,⟨⟨200,207⟩,⟨31,38⟩⟩,⟨⟨196,202⟩,⟨26,32⟩⟩,⟨⟨191,197⟩,⟨21,27⟩⟩,⟨⟨186,193⟩,⟨16,24⟩⟩,⟨⟨183,191⟩,⟨13,21⟩⟩,⟨⟨182,188⟩,⟨11,17⟩⟩,⟨⟨180,186⟩,⟨11,17⟩⟩,⟨⟨180,186⟩,⟨10,16⟩⟩] +lemma kernel91_0_r5_15_eq : ∀ k : Fin 16, kernel91_0Expr 5 15 k = kernel91_0_r5_15 k := by decide +kernel +noncomputable def kernel91_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel91_0_r5_0,kernel91_0_r5_1,kernel91_0_r5_2,kernel91_0_r5_3,kernel91_0_r5_4,kernel91_0_r5_5,kernel91_0_r5_6,kernel91_0_r5_7,kernel91_0_r5_8,kernel91_0_r5_9,kernel91_0_r5_10,kernel91_0_r5_11,kernel91_0_r5_12,kernel91_0_r5_13,kernel91_0_r5_14,kernel91_0_r5_15] +lemma kernel91_0_r5_eq (i k : Fin 16) : kernel91_0Expr 5 i k = kernel91_0_r5 i k := by + fin_cases i + · exact kernel91_0_r5_0_eq k + · exact kernel91_0_r5_1_eq k + · exact kernel91_0_r5_2_eq k + · exact kernel91_0_r5_3_eq k + · exact kernel91_0_r5_4_eq k + · exact kernel91_0_r5_5_eq k + · exact kernel91_0_r5_6_eq k + · exact kernel91_0_r5_7_eq k + · exact kernel91_0_r5_8_eq k + · exact kernel91_0_r5_9_eq k + · exact kernel91_0_r5_10_eq k + · exact kernel91_0_r5_11_eq k + · exact kernel91_0_r5_12_eq k + · exact kernel91_0_r5_13_eq k + · exact kernel91_0_r5_14_eq k + · exact kernel91_0_r5_15_eq k +noncomputable def kernel91_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel91_0_r0,kernel91_0_r1,kernel91_0_r2,kernel91_0_r3,kernel91_0_r4,kernel91_0_r5] +lemma kernel91_0_eq (j : Fin 6) (i k : Fin 16) : kernel91_0Expr j i k = kernel91_0 j i k := by + fin_cases j + · exact kernel91_0_r0_eq i k + · exact kernel91_0_r1_eq i k + · exact kernel91_0_r2_eq i k + · exact kernel91_0_r3_eq i k + · exact kernel91_0_r4_eq i k + · exact kernel91_0_r5_eq i k +lemma kernel91_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel91_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(91:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel91_0_eq] + unfold kernel91_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans91_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel91_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans91 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel91_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r0_0_eq : ∀ k : Fin 16, kernel91_1Expr 0 0 k = kernel91_1_r0_0 k := by decide +kernel +noncomputable def kernel91_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r0_1_eq : ∀ k : Fin 16, kernel91_1Expr 0 1 k = kernel91_1_r0_1 k := by decide +kernel +noncomputable def kernel91_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r0_2_eq : ∀ k : Fin 16, kernel91_1Expr 0 2 k = kernel91_1_r0_2 k := by decide +kernel +noncomputable def kernel91_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r0_3_eq : ∀ k : Fin 16, kernel91_1Expr 0 3 k = kernel91_1_r0_3 k := by decide +kernel +noncomputable def kernel91_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r0_4_eq : ∀ k : Fin 16, kernel91_1Expr 0 4 k = kernel91_1_r0_4 k := by decide +kernel +noncomputable def kernel91_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel91_1_r0_5_eq : ∀ k : Fin 16, kernel91_1Expr 0 5 k = kernel91_1_r0_5 k := by decide +kernel +noncomputable def kernel91_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel91_1_r0_6_eq : ∀ k : Fin 16, kernel91_1Expr 0 6 k = kernel91_1_r0_6 k := by decide +kernel +noncomputable def kernel91_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel91_1_r0_7_eq : ∀ k : Fin 16, kernel91_1Expr 0 7 k = kernel91_1_r0_7 k := by decide +kernel +noncomputable def kernel91_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel91_1_r0_8_eq : ∀ k : Fin 16, kernel91_1Expr 0 8 k = kernel91_1_r0_8 k := by decide +kernel +noncomputable def kernel91_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel91_1_r0_9_eq : ∀ k : Fin 16, kernel91_1Expr 0 9 k = kernel91_1_r0_9 k := by decide +kernel +noncomputable def kernel91_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel91_1_r0_10_eq : ∀ k : Fin 16, kernel91_1Expr 0 10 k = kernel91_1_r0_10 k := by decide +kernel +noncomputable def kernel91_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel91_1_r0_11_eq : ∀ k : Fin 16, kernel91_1Expr 0 11 k = kernel91_1_r0_11 k := by decide +kernel +noncomputable def kernel91_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel91_1_r0_12_eq : ∀ k : Fin 16, kernel91_1Expr 0 12 k = kernel91_1_r0_12 k := by decide +kernel +noncomputable def kernel91_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel91_1_r0_13_eq : ∀ k : Fin 16, kernel91_1Expr 0 13 k = kernel91_1_r0_13 k := by decide +kernel +noncomputable def kernel91_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel91_1_r0_14_eq : ∀ k : Fin 16, kernel91_1Expr 0 14 k = kernel91_1_r0_14 k := by decide +kernel +noncomputable def kernel91_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel91_1_r0_15_eq : ∀ k : Fin 16, kernel91_1Expr 0 15 k = kernel91_1_r0_15 k := by decide +kernel +noncomputable def kernel91_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel91_1_r0_0,kernel91_1_r0_1,kernel91_1_r0_2,kernel91_1_r0_3,kernel91_1_r0_4,kernel91_1_r0_5,kernel91_1_r0_6,kernel91_1_r0_7,kernel91_1_r0_8,kernel91_1_r0_9,kernel91_1_r0_10,kernel91_1_r0_11,kernel91_1_r0_12,kernel91_1_r0_13,kernel91_1_r0_14,kernel91_1_r0_15] +lemma kernel91_1_r0_eq (i k : Fin 16) : kernel91_1Expr 0 i k = kernel91_1_r0 i k := by + fin_cases i + · exact kernel91_1_r0_0_eq k + · exact kernel91_1_r0_1_eq k + · exact kernel91_1_r0_2_eq k + · exact kernel91_1_r0_3_eq k + · exact kernel91_1_r0_4_eq k + · exact kernel91_1_r0_5_eq k + · exact kernel91_1_r0_6_eq k + · exact kernel91_1_r0_7_eq k + · exact kernel91_1_r0_8_eq k + · exact kernel91_1_r0_9_eq k + · exact kernel91_1_r0_10_eq k + · exact kernel91_1_r0_11_eq k + · exact kernel91_1_r0_12_eq k + · exact kernel91_1_r0_13_eq k + · exact kernel91_1_r0_14_eq k + · exact kernel91_1_r0_15_eq k +noncomputable def kernel91_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel91_1_r1_0_eq : ∀ k : Fin 16, kernel91_1Expr 1 0 k = kernel91_1_r1_0 k := by decide +kernel +noncomputable def kernel91_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel91_1_r1_1_eq : ∀ k : Fin 16, kernel91_1Expr 1 1 k = kernel91_1_r1_1 k := by decide +kernel +noncomputable def kernel91_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel91_1_r1_2_eq : ∀ k : Fin 16, kernel91_1Expr 1 2 k = kernel91_1_r1_2 k := by decide +kernel +noncomputable def kernel91_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel91_1_r1_3_eq : ∀ k : Fin 16, kernel91_1Expr 1 3 k = kernel91_1_r1_3 k := by decide +kernel +noncomputable def kernel91_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel91_1_r1_4_eq : ∀ k : Fin 16, kernel91_1Expr 1 4 k = kernel91_1_r1_4 k := by decide +kernel +noncomputable def kernel91_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel91_1_r1_5_eq : ∀ k : Fin 16, kernel91_1Expr 1 5 k = kernel91_1_r1_5 k := by decide +kernel +noncomputable def kernel91_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel91_1_r1_6_eq : ∀ k : Fin 16, kernel91_1Expr 1 6 k = kernel91_1_r1_6 k := by decide +kernel +noncomputable def kernel91_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel91_1_r1_7_eq : ∀ k : Fin 16, kernel91_1Expr 1 7 k = kernel91_1_r1_7 k := by decide +kernel +noncomputable def kernel91_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel91_1_r1_8_eq : ∀ k : Fin 16, kernel91_1Expr 1 8 k = kernel91_1_r1_8 k := by decide +kernel +noncomputable def kernel91_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel91_1_r1_9_eq : ∀ k : Fin 16, kernel91_1Expr 1 9 k = kernel91_1_r1_9 k := by decide +kernel +noncomputable def kernel91_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r1_10_eq : ∀ k : Fin 16, kernel91_1Expr 1 10 k = kernel91_1_r1_10 k := by decide +kernel +noncomputable def kernel91_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r1_11_eq : ∀ k : Fin 16, kernel91_1Expr 1 11 k = kernel91_1_r1_11 k := by decide +kernel +noncomputable def kernel91_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r1_12_eq : ∀ k : Fin 16, kernel91_1Expr 1 12 k = kernel91_1_r1_12 k := by decide +kernel +noncomputable def kernel91_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r1_13_eq : ∀ k : Fin 16, kernel91_1Expr 1 13 k = kernel91_1_r1_13 k := by decide +kernel +noncomputable def kernel91_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r1_14_eq : ∀ k : Fin 16, kernel91_1Expr 1 14 k = kernel91_1_r1_14 k := by decide +kernel +noncomputable def kernel91_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel91_1_r1_15_eq : ∀ k : Fin 16, kernel91_1Expr 1 15 k = kernel91_1_r1_15 k := by decide +kernel +noncomputable def kernel91_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel91_1_r1_0,kernel91_1_r1_1,kernel91_1_r1_2,kernel91_1_r1_3,kernel91_1_r1_4,kernel91_1_r1_5,kernel91_1_r1_6,kernel91_1_r1_7,kernel91_1_r1_8,kernel91_1_r1_9,kernel91_1_r1_10,kernel91_1_r1_11,kernel91_1_r1_12,kernel91_1_r1_13,kernel91_1_r1_14,kernel91_1_r1_15] +lemma kernel91_1_r1_eq (i k : Fin 16) : kernel91_1Expr 1 i k = kernel91_1_r1 i k := by + fin_cases i + · exact kernel91_1_r1_0_eq k + · exact kernel91_1_r1_1_eq k + · exact kernel91_1_r1_2_eq k + · exact kernel91_1_r1_3_eq k + · exact kernel91_1_r1_4_eq k + · exact kernel91_1_r1_5_eq k + · exact kernel91_1_r1_6_eq k + · exact kernel91_1_r1_7_eq k + · exact kernel91_1_r1_8_eq k + · exact kernel91_1_r1_9_eq k + · exact kernel91_1_r1_10_eq k + · exact kernel91_1_r1_11_eq k + · exact kernel91_1_r1_12_eq k + · exact kernel91_1_r1_13_eq k + · exact kernel91_1_r1_14_eq k + · exact kernel91_1_r1_15_eq k +noncomputable def kernel91_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel91_1_r2_0_eq : ∀ k : Fin 16, kernel91_1Expr 2 0 k = kernel91_1_r2_0 k := by decide +kernel +noncomputable def kernel91_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel91_1_r2_1_eq : ∀ k : Fin 16, kernel91_1Expr 2 1 k = kernel91_1_r2_1 k := by decide +kernel +noncomputable def kernel91_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel91_1_r2_2_eq : ∀ k : Fin 16, kernel91_1Expr 2 2 k = kernel91_1_r2_2 k := by decide +kernel +noncomputable def kernel91_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel91_1_r2_3_eq : ∀ k : Fin 16, kernel91_1Expr 2 3 k = kernel91_1_r2_3 k := by decide +kernel +noncomputable def kernel91_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel91_1_r2_4_eq : ∀ k : Fin 16, kernel91_1Expr 2 4 k = kernel91_1_r2_4 k := by decide +kernel +noncomputable def kernel91_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel91_1_r2_5_eq : ∀ k : Fin 16, kernel91_1Expr 2 5 k = kernel91_1_r2_5 k := by decide +kernel +noncomputable def kernel91_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel91_1_r2_6_eq : ∀ k : Fin 16, kernel91_1Expr 2 6 k = kernel91_1_r2_6 k := by decide +kernel +noncomputable def kernel91_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel91_1_r2_7_eq : ∀ k : Fin 16, kernel91_1Expr 2 7 k = kernel91_1_r2_7 k := by decide +kernel +noncomputable def kernel91_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel91_1_r2_8_eq : ∀ k : Fin 16, kernel91_1Expr 2 8 k = kernel91_1_r2_8 k := by decide +kernel +noncomputable def kernel91_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel91_1_r2_9_eq : ∀ k : Fin 16, kernel91_1Expr 2 9 k = kernel91_1_r2_9 k := by decide +kernel +noncomputable def kernel91_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel91_1_r2_10_eq : ∀ k : Fin 16, kernel91_1Expr 2 10 k = kernel91_1_r2_10 k := by decide +kernel +noncomputable def kernel91_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel91_1_r2_11_eq : ∀ k : Fin 16, kernel91_1Expr 2 11 k = kernel91_1_r2_11 k := by decide +kernel +noncomputable def kernel91_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel91_1_r2_12_eq : ∀ k : Fin 16, kernel91_1Expr 2 12 k = kernel91_1_r2_12 k := by decide +kernel +noncomputable def kernel91_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel91_1_r2_13_eq : ∀ k : Fin 16, kernel91_1Expr 2 13 k = kernel91_1_r2_13 k := by decide +kernel +noncomputable def kernel91_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel91_1_r2_14_eq : ∀ k : Fin 16, kernel91_1Expr 2 14 k = kernel91_1_r2_14 k := by decide +kernel +noncomputable def kernel91_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel91_1_r2_15_eq : ∀ k : Fin 16, kernel91_1Expr 2 15 k = kernel91_1_r2_15 k := by decide +kernel +noncomputable def kernel91_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel91_1_r2_0,kernel91_1_r2_1,kernel91_1_r2_2,kernel91_1_r2_3,kernel91_1_r2_4,kernel91_1_r2_5,kernel91_1_r2_6,kernel91_1_r2_7,kernel91_1_r2_8,kernel91_1_r2_9,kernel91_1_r2_10,kernel91_1_r2_11,kernel91_1_r2_12,kernel91_1_r2_13,kernel91_1_r2_14,kernel91_1_r2_15] +lemma kernel91_1_r2_eq (i k : Fin 16) : kernel91_1Expr 2 i k = kernel91_1_r2 i k := by + fin_cases i + · exact kernel91_1_r2_0_eq k + · exact kernel91_1_r2_1_eq k + · exact kernel91_1_r2_2_eq k + · exact kernel91_1_r2_3_eq k + · exact kernel91_1_r2_4_eq k + · exact kernel91_1_r2_5_eq k + · exact kernel91_1_r2_6_eq k + · exact kernel91_1_r2_7_eq k + · exact kernel91_1_r2_8_eq k + · exact kernel91_1_r2_9_eq k + · exact kernel91_1_r2_10_eq k + · exact kernel91_1_r2_11_eq k + · exact kernel91_1_r2_12_eq k + · exact kernel91_1_r2_13_eq k + · exact kernel91_1_r2_14_eq k + · exact kernel91_1_r2_15_eq k +noncomputable def kernel91_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel91_1_r3_0_eq : ∀ k : Fin 16, kernel91_1Expr 3 0 k = kernel91_1_r3_0 k := by decide +kernel +noncomputable def kernel91_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel91_1_r3_1_eq : ∀ k : Fin 16, kernel91_1Expr 3 1 k = kernel91_1_r3_1 k := by decide +kernel +noncomputable def kernel91_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel91_1_r3_2_eq : ∀ k : Fin 16, kernel91_1Expr 3 2 k = kernel91_1_r3_2 k := by decide +kernel +noncomputable def kernel91_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel91_1_r3_3_eq : ∀ k : Fin 16, kernel91_1Expr 3 3 k = kernel91_1_r3_3 k := by decide +kernel +noncomputable def kernel91_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel91_1_r3_4_eq : ∀ k : Fin 16, kernel91_1Expr 3 4 k = kernel91_1_r3_4 k := by decide +kernel +noncomputable def kernel91_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel91_1_r3_5_eq : ∀ k : Fin 16, kernel91_1Expr 3 5 k = kernel91_1_r3_5 k := by decide +kernel +noncomputable def kernel91_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel91_1_r3_6_eq : ∀ k : Fin 16, kernel91_1Expr 3 6 k = kernel91_1_r3_6 k := by decide +kernel +noncomputable def kernel91_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel91_1_r3_7_eq : ∀ k : Fin 16, kernel91_1Expr 3 7 k = kernel91_1_r3_7 k := by decide +kernel +noncomputable def kernel91_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel91_1_r3_8_eq : ∀ k : Fin 16, kernel91_1Expr 3 8 k = kernel91_1_r3_8 k := by decide +kernel +noncomputable def kernel91_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel91_1_r3_9_eq : ∀ k : Fin 16, kernel91_1Expr 3 9 k = kernel91_1_r3_9 k := by decide +kernel +noncomputable def kernel91_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel91_1_r3_10_eq : ∀ k : Fin 16, kernel91_1Expr 3 10 k = kernel91_1_r3_10 k := by decide +kernel +noncomputable def kernel91_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel91_1_r3_11_eq : ∀ k : Fin 16, kernel91_1Expr 3 11 k = kernel91_1_r3_11 k := by decide +kernel +noncomputable def kernel91_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel91_1_r3_12_eq : ∀ k : Fin 16, kernel91_1Expr 3 12 k = kernel91_1_r3_12 k := by decide +kernel +noncomputable def kernel91_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel91_1_r3_13_eq : ∀ k : Fin 16, kernel91_1Expr 3 13 k = kernel91_1_r3_13 k := by decide +kernel +noncomputable def kernel91_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel91_1_r3_14_eq : ∀ k : Fin 16, kernel91_1Expr 3 14 k = kernel91_1_r3_14 k := by decide +kernel +noncomputable def kernel91_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel91_1_r3_15_eq : ∀ k : Fin 16, kernel91_1Expr 3 15 k = kernel91_1_r3_15 k := by decide +kernel +noncomputable def kernel91_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel91_1_r3_0,kernel91_1_r3_1,kernel91_1_r3_2,kernel91_1_r3_3,kernel91_1_r3_4,kernel91_1_r3_5,kernel91_1_r3_6,kernel91_1_r3_7,kernel91_1_r3_8,kernel91_1_r3_9,kernel91_1_r3_10,kernel91_1_r3_11,kernel91_1_r3_12,kernel91_1_r3_13,kernel91_1_r3_14,kernel91_1_r3_15] +lemma kernel91_1_r3_eq (i k : Fin 16) : kernel91_1Expr 3 i k = kernel91_1_r3 i k := by + fin_cases i + · exact kernel91_1_r3_0_eq k + · exact kernel91_1_r3_1_eq k + · exact kernel91_1_r3_2_eq k + · exact kernel91_1_r3_3_eq k + · exact kernel91_1_r3_4_eq k + · exact kernel91_1_r3_5_eq k + · exact kernel91_1_r3_6_eq k + · exact kernel91_1_r3_7_eq k + · exact kernel91_1_r3_8_eq k + · exact kernel91_1_r3_9_eq k + · exact kernel91_1_r3_10_eq k + · exact kernel91_1_r3_11_eq k + · exact kernel91_1_r3_12_eq k + · exact kernel91_1_r3_13_eq k + · exact kernel91_1_r3_14_eq k + · exact kernel91_1_r3_15_eq k +noncomputable def kernel91_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-90),(-60)⟩,⟨(-768),(-738)⟩⟩,⟨⟨(-93),(-64)⟩,⟨(-763),(-733)⟩⟩,⟨⟨(-101),(-71)⟩,⟨(-757),(-728)⟩⟩,⟨⟨(-108),(-78)⟩,⟨(-748),(-718)⟩⟩,⟨⟨(-118),(-79)⟩,⟨(-739),(-700)⟩⟩,⟨⟨(-123),(-93)⟩,⟨(-716),(-686)⟩⟩,⟨⟨(-133),(-103)⟩,⟨(-697),(-668)⟩⟩,⟨⟨(-150),(-120)⟩,⟨(-673),(-644)⟩⟩,⟨⟨(-162),(-132)⟩,⟨(-646),(-616)⟩⟩,⟨⟨(-178),(-144)⟩,⟨(-619),(-584)⟩⟩,⟨⟨(-190),(-151)⟩,⟨(-592),(-553)⟩⟩,⟨⟨(-200),(-166)⟩,⟨(-552),(-517)⟩⟩,⟨⟨(-215),(-185)⟩,⟨(-515),(-485)⟩⟩,⟨⟨(-222),(-192)⟩,⟨(-480),(-450)⟩⟩,⟨⟨(-232),(-202)⟩,⟨(-441),(-411)⟩⟩,⟨⟨(-239),(-209)⟩,⟨(-406),(-376)⟩⟩] +lemma kernel91_1_r4_0_eq : ∀ k : Fin 16, kernel91_1Expr 4 0 k = kernel91_1_r4_0 k := by decide +kernel +noncomputable def kernel91_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-245),(-215)⟩,⟨(-367),(-337)⟩⟩,⟨⟨(-251),(-221)⟩,⟨(-328),(-298)⟩⟩,⟨⟨(-248),(-214)⟩,⟨(-291),(-257)⟩⟩,⟨⟨(-246),(-216)⟩,⟨(-253),(-223)⟩⟩,⟨⟨(-241),(-211)⟩,⟨(-220),(-190)⟩⟩,⟨⟨(-231),(-201)⟩,⟨(-188),(-158)⟩⟩,⟨⟨(-229),(-195)⟩,⟨(-155),(-125)⟩⟩,⟨⟨(-212),(-182)⟩,⟨(-128),(-98)⟩⟩,⟨⟨(-203),(-168)⟩,⟨(-101),(-66)⟩⟩,⟨⟨(-190),(-160)⟩,⟨(-73),(-43)⟩⟩,⟨⟨(-179),(-148)⟩,⟨(-58),(-24)⟩⟩,⟨⟨(-162),(-132)⟩,⟨(-36),(-6)⟩⟩,⟨⟨(-147),(-113)⟩,⟨(-22),9⟩⟩,⟨⟨(-133),(-103)⟩,⟨(-11),19⟩⟩,⟨⟨(-113),(-83)⟩,⟨2,32⟩⟩,⟨⟨(-105),(-69)⟩,⟨4,43⟩⟩] +lemma kernel91_1_r4_1_eq : ∀ k : Fin 16, kernel91_1Expr 4 1 k = kernel91_1_r4_1 k := by decide +kernel +noncomputable def kernel91_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-86),(-56)⟩,⟨15,45⟩⟩,⟨⟨(-73),(-43)⟩,⟨16,47⟩⟩,⟨⟨(-64),(-34)⟩,⟨19,49⟩⟩,⟨⟨(-56),(-22)⟩,⟨17,48⟩⟩,⟨⟨(-44),(-13)⟩,⟨16,46⟩⟩,⟨⟨(-35),(-5)⟩,⟨14,44⟩⟩,⟨⟨(-28),2⟩,⟨8,39⟩⟩,⟨⟨(-24),6⟩,⟨8,38⟩⟩,⟨⟨(-24),6⟩,⟨8,38⟩⟩,⟨⟨(-16),14⟩,⟨2,32⟩⟩,⟨⟨(-12),18⟩,⟨1,32⟩⟩,⟨⟨(-13),12⟩,⟨(-2),23⟩⟩,⟨⟨(-9),21⟩,⟨(-4),27⟩⟩,⟨⟨(-14),17⟩,⟨(-7),23⟩⟩,⟨⟨(-10),15⟩,⟨(-7),14⟩⟩,⟨⟨(-10),19⟩,⟨(-12),14⟩⟩] +lemma kernel91_1_r4_2_eq : ∀ k : Fin 16, kernel91_1Expr 4 2 k = kernel91_1_r4_2 k := by decide +kernel +noncomputable def kernel91_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-10),19⟩,⟨(-12),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-15),11⟩⟩,⟨⟨(-19),11⟩,⟨(-15),16⟩⟩,⟨⟨(-19),11⟩,⟨(-15),16⟩⟩,⟨⟨(-19),11⟩,⟨(-15),16⟩⟩,⟨⟨(-15),11⟩,⟨(-10),15⟩⟩,⟨⟨(-15),11⟩,⟨(-10),15⟩⟩,⟨⟨(-15),16⟩,⟨(-11),20⟩⟩] +lemma kernel91_1_r4_3_eq : ∀ k : Fin 16, kernel91_1Expr 4 3 k = kernel91_1_r4_3 k := by decide +kernel +noncomputable def kernel91_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel91_1_r4_4_eq : ∀ k : Fin 16, kernel91_1Expr 4 4 k = kernel91_1_r4_4 k := by decide +kernel +noncomputable def kernel91_1_r4_5 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel91_1_r4_5_eq : ∀ k : Fin 16, kernel91_1Expr 4 5 k = kernel91_1_r4_5 k := by decide +kernel +noncomputable def kernel91_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel91_1_r4_6_eq : ∀ k : Fin 16, kernel91_1Expr 4 6 k = kernel91_1_r4_6 k := by decide +kernel +noncomputable def kernel91_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel91_1_r4_7_eq : ∀ k : Fin 16, kernel91_1Expr 4 7 k = kernel91_1_r4_7 k := by decide +kernel +noncomputable def kernel91_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel91_1_r4_8_eq : ∀ k : Fin 16, kernel91_1Expr 4 8 k = kernel91_1_r4_8 k := by decide +kernel +noncomputable def kernel91_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel91_1_r4_9_eq : ∀ k : Fin 16, kernel91_1Expr 4 9 k = kernel91_1_r4_9 k := by decide +kernel +noncomputable def kernel91_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel91_1_r4_10_eq : ∀ k : Fin 16, kernel91_1Expr 4 10 k = kernel91_1_r4_10 k := by decide +kernel +noncomputable def kernel91_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel91_1_r4_11_eq : ∀ k : Fin 16, kernel91_1Expr 4 11 k = kernel91_1_r4_11 k := by decide +kernel +noncomputable def kernel91_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel91_1_r4_12_eq : ∀ k : Fin 16, kernel91_1Expr 4 12 k = kernel91_1_r4_12 k := by decide +kernel +noncomputable def kernel91_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel91_1_r4_13_eq : ∀ k : Fin 16, kernel91_1Expr 4 13 k = kernel91_1_r4_13 k := by decide +kernel +noncomputable def kernel91_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel91_1_r4_14_eq : ∀ k : Fin 16, kernel91_1Expr 4 14 k = kernel91_1_r4_14 k := by decide +kernel +noncomputable def kernel91_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel91_1_r4_15_eq : ∀ k : Fin 16, kernel91_1Expr 4 15 k = kernel91_1_r4_15 k := by decide +kernel +noncomputable def kernel91_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel91_1_r4_0,kernel91_1_r4_1,kernel91_1_r4_2,kernel91_1_r4_3,kernel91_1_r4_4,kernel91_1_r4_5,kernel91_1_r4_6,kernel91_1_r4_7,kernel91_1_r4_8,kernel91_1_r4_9,kernel91_1_r4_10,kernel91_1_r4_11,kernel91_1_r4_12,kernel91_1_r4_13,kernel91_1_r4_14,kernel91_1_r4_15] +lemma kernel91_1_r4_eq (i k : Fin 16) : kernel91_1Expr 4 i k = kernel91_1_r4 i k := by + fin_cases i + · exact kernel91_1_r4_0_eq k + · exact kernel91_1_r4_1_eq k + · exact kernel91_1_r4_2_eq k + · exact kernel91_1_r4_3_eq k + · exact kernel91_1_r4_4_eq k + · exact kernel91_1_r4_5_eq k + · exact kernel91_1_r4_6_eq k + · exact kernel91_1_r4_7_eq k + · exact kernel91_1_r4_8_eq k + · exact kernel91_1_r4_9_eq k + · exact kernel91_1_r4_10_eq k + · exact kernel91_1_r4_11_eq k + · exact kernel91_1_r4_12_eq k + · exact kernel91_1_r4_13_eq k + · exact kernel91_1_r4_14_eq k + · exact kernel91_1_r4_15_eq k +noncomputable def kernel91_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-99103287183048466575857),(-99103280059634536447702)⟩,⟨(-108586007887730499721803),(-108586000764316569591857)⟩⟩,⟨⟨(-99148096768721969405318),(-99148089657912255481901)⟩,⟨(-107982993648391173600764),(-107982986537581459675576)⟩⟩,⟨⟨(-99231917840428791338502),(-99231910754775287477202)⟩,⟨(-106781724001903771889474),(-106781716916250268026438)⟩⟩,⟨⟨(-99343309016202615983983),(-99343301968128672243580)⟩,⟨(-104991734916147644627242),(-104991727868073700885150)⟩⟩,⟨⟨(-99465492498288589072010),(-99465485500026159910268)⟩,⟨(-102627372478451007573180),(-102627365480188578409819)⟩⟩,⟨⟨(-99576807428031620878225),(-99576800491559553313376)⟩,⟨(-99707833483782728142081),(-99707826547310660575694)⟩⟩,⟨⟨(-99651301332260953613301),(-99651294469246046332664)⟩,⟨(-96257203435206771295841),(-96257196572191864013759)⟩⟩,⟨⟨(-99659448379393678992849),(-99659441601133027683760)⟩,⟨(-92304479140753070960045),(-92304472362492419649626)⟩⟩,⟨⟨(-99568980241305672474162),(-99568973558674107343052)⟩,⟨(-87883561101582748371385),(-87883554418951183239058)⟩⟩,⟨⟨(-99345812430893206943315),(-99345805854290612915906)⟩,⟨(-83033199653774843171213),(-83033193077172249142718)⟩⟩,⟨⟨(-98955046112290950199938),(-98955039651596018720209)⟩,⟨(-77796878447912853508436),(-77796871987217922027763)⟩⟩,⟨⟨(-98362022642750509870561),(-98362016306733320009597)⟩,⟨(-72222619395306192410666),(-72222613059289002548904)⟩⟩,⟨⟨(-97533405604375247770729),(-97533399401729441490260)⟩,⟨(-66362694708674963386101),(-66362688506029157104988)⟩⟩,⟨⟨(-96438262951429223608695),(-96438256890213405344784)⟩,⟨(-60273234121238604959672),(-60273228060022786695267)⟩⟩,⟨⟨(-95049120256869408905865),(-95049114344490415942032)⟩,⟨(-54013718719671926089249),(-54013712807292933125075)⟩⟩,⟨⟨(-93342955052010066687854),(-93342949295184628246848)⟩,⟨(-47646357001589244543786),(-47646351244763806102595)⟩⟩] +lemma kernel91_1_r5_0_eq : ∀ k : Fin 16, kernel91_1Expr 5 0 k = kernel91_1_r5_0 k := by decide +kernel +noncomputable def kernel91_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-91302102040778650251193),(-91302096445533151371769)⟩,⟨(-41235343617265556529320),(-41235338022020057649862)⟩⟩,⟨⟨(-88915039669216412396524),(-88915034240848578079877)⟩,⟨(-34846006608510114186590),(-34846001180142279870053)⟩⟩,⟨⟨(-86177030241574923563330),(-86177024984673902058138)⟩,⟨(-28543854596248461397497),(-28543849339347439892550)⟩⟩,⟨⟨(-83090588564971669425566),(-83090583483382775777184)⟩,⟨(-22393541044813294606534),(-22393535963224400958528)⟩⟩,⟨⟨(-79665757997115545772031),(-79665753093978134321478)⟩,⟨(-16457768172459855823039),(-16457763269322444372987)⟩⟩,⟨⟨(-75920177736843117173199),(-75920173014550688264805)⟩,⟨(-10796158000973643322850),(-10796153278681214415061)⟩⟩,⟨⟨(-71878931145175698977427),(-71878926605440639056638)⟩,⟨(-5464122158418279690566),(-5464117618683219770476)⟩⟩,⟨⟨(-67574171666254623360847),(-67574167310050747510862)⟩,⟨(-511765102445125101322),(-511760746241249252119)⟩⟩,⟨⟨(-63044530320586748264540),(-63044526148248837666741)⟩,⟨4017142819448597647248,4017146991786508244198⟩⟩,⟨⟨(-58334316503188559343992),(-58334312514375650378636)⟩,⟨8086085797621899324370,8086089786434808288850⟩⟩,⟨⟨(-53492531621926144079963),(-53492527815712154012697)⟩,⟨11666581160228060361273,11666584966442050427647⟩⟩,⟨⟨(-48571722613310020125318),(-48571718988134952764957)⟩,⟨14738783856241576924772,14738787481416644284238⟩⟩,⟨⟨(-43626709210130249247201),(-43626705763919156081069)⟩,⟨17291889196235997821036,17291892642447090986275⟩⟩,⟨⟨(-38713224651147824494293),(-38713221381139351068647)⟩,⟨19324312403584925508799,19324315673593398933608⟩⟩,⟨⟨(-33886513980314881066134),(-33886510883180086534773)⟩,⟨20843631014471285097676,20843634111606079628351⟩⟩,⟨⟨(-29199936896415222691380),(-29199933968588114589391)⟩,⟨21866284662710737224258,21866287590537845325701⟩⟩] +lemma kernel91_1_r5_1_eq : ∀ k : Fin 16, kernel91_1Expr 5 1 k = kernel91_1_r5_1 k := by decide +kernel +noncomputable def kernel91_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-24703623058836050682375),(-24703620296400583968458)⟩,⟨22417035932919860224386,22417038695355326937887⟩⟩,⟨⟨(-20443226693843417633925),(-20443224092444006124790)⟩,⟨22528205342462365098713,22528207943861776607548⟩⟩,⟨⟨(-16458824241401556810717),(-16458821796416384412931)⟩,⟨22238702661403322936834,22238705106388495334436⟩⟩,⟨⟨(-12783993701282806800120),(-12783991407748881864945)⟩,⟨21592885237219272444578,21592887530753197379658⟩⟩,⟨⟨(-9445107455693700563251),(-9445105308453307611935)⟩,⟨20639281309872415576456,20639283457112808527757⟩⟩,⟨⟨(-6460861949189582493446),(-6460859942712236009980)⟩,⟨19429222076504066993583,19429224082981413477099⟩⟩,⟨⟨(-3842058066622915165890),(-3842056195410834087950)⟩,⟨18015430164653741618897,18015432035865822696942⟩⟩,⟨⟨(-1591635821709245345241),(-1591634080073942220828)⟩,⟨16450613954023948370847,16450615695659251495406⟩⟩,⟨⟨295043453785537913558,295045071547292388692⟩,⟨14786116728542471652685,14786118346304226128000⟩⟩,⟨⟨1829684316447481716935,1829685816218724695575⟩,⟨13070666929588105826414,13070668429359348805250⟩⟩,⟨⟨3030339953690942745000,3030341341251306270532⟩,⟨11349270946879635325358,11349272334439998851090⟩⟩,⟨⟨3920524525610609149350,3920525806789658779211⟩,⟨9662283161836106617334,9662284443015156247397⟩⟩,⟨⟨4528195375340920681883,4528196555869178088116⟩,⟨8044679707679628550832,8044680888207885957233⟩⟩,⟨⟨4884649553859754521327,4884650639456571078871⟩,⟨6525553065307270840382,6525554150904087398046⟩⟩,⟨⟨5023381069086639287345,5023382065313232074985⟩,⟨5127834681986876948318,5127835678213469736042⟩⟩,⟨⟨4978944954217553960935,4978945866572773310415⟩,⟨3868242809375612901547,3868243721730832251073⟩⟩] +lemma kernel91_1_r5_2_eq : ∀ k : Fin 16, kernel91_1Expr 5 2 k = kernel91_1_r5_2 k := by decide +kernel +noncomputable def kernel91_1_r5_3 : Fin 16 → CBox := ![⟨⟨4785871731352552255578,4785872565130584690522⟩,⟨2757443242178536453087,2757444075956568888050⟩⟩,⟨⟨4477671317215639714752,4477672077628944295601⟩,⟨1800402088598152183985,1800402849011456764830⟩⟩,⟨⟨4085959192237345294896,4085959884263068623201⟩,⟨996902548699410093350,996903240725133421636⟩⟩,⟨⟨3639730129720448787970,3639730758207124309615⟩,⟨342192245741522667447,342192874228198189058⟩⟩,⟨⟨3164796427243431006033,3164796996788413797889⟩,⟨(-172275827167903312643),(-172275257622920520825)⟩⟩,⟨⟨2683398890475347965897,2683399405536290422135⟩,⟨(-558047124800048024613),(-558046609739105568417)⟩⟩,⟨⟨2213990289761109552552,2213990754534001401318⟩,⟨(-828851938780085025219),(-828851474007193176496)⟩⟩,⟨⟨1771183100723491738337,1771183519238409491997⟩,⟨(-999809730019307648057),(-999809311504389894431)⟩⟩,⟨⟨1365846455694999980129,1365846831719164484094⟩,⟨(-1086682730739923265318),(-1086682354715758761378)⟩⟩,⟨⟨1005331684434614367848,1005332021573476416555⟩,⟨(-1105204825572267819734),(-1105204488433405771040)⟩⟩,⟨⟨693801826872255601722,693802128562080521601⟩,⟨(-1070505524582330912011),(-1070505222892505992138)⟩⟩,⟨⟨432638157728402151464,432638427734100205111⟩,⟨(-996642188817827978036),(-996641918812129924390)⟩⟩,⟨⟨220896070413856513016,220896311521356748067⟩,⟨(-896246975420086301617),(-896246734312586066560)⟩⟩,⟨⟨55783507658788926163,55783722509870939244⟩,⟨(-780288632050003822516),(-780288417198921809425)⟩⟩,⟨⟨(-66862679443756033846),(-66862488420705634368)⟩,⟨(-657943605514560764591),(-657943414491510365108)⟩⟩,⟨⟨(-152123800492608144472),(-152123631015374006281)⟩,⟨(-536566221646469813835),(-536566052169235675636)⟩⟩] +lemma kernel91_1_r5_3_eq : ∀ k : Fin 16, kernel91_1Expr 5 3 k = kernel91_1_r5_3 k := by decide +kernel +noncomputable def kernel91_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-205587136610025797136),(-205586986593777205465)⟩,⟨(-421744099025476980657),(-421743949009228388979)⟩⟩,⟨⟨(-232987320423867254424),(-232987187914121082961)⟩,⟨(-317422577487967139359),(-317422444978220967888)⟩⟩,⟨⟨(-239909498203035482636),(-239909381425659411983)⟩,⟨(-226080769421818443227),(-226080652644442372574)⟩⟩,⟨⟨(-231558040362872663492),(-231557937670345481681)⟩,⟨(-148941802445317850650),(-148941699752790668836)⟩⟩,⟨⟨(-212590534193134975282),(-212590444097785433674)⟩,⟨(-86200772158869754510),(-86200682063520212902)⟩⟩,⟨⟨(-187013367926134243234),(-187013289050479770673)⟩,⟨(-37255675007120335613),(-37255596131465863052)⟩⟩,⟨⟨(-158132523958106745112),(-158132455065968577354)⟩,⟨(-928923512080638778),(-928854619942471027)⟩⟩,⟨⟨(-128551304439463366451),(-128551244396388910659)⟩,⟨24330268114894453478,24330328157968909270⟩⟩,⟨⟨(-100205613426554934838),(-100205561219646985943)⟩,⟨40269523127990017372,40269575334897966266⟩⟩,⟨⟨(-74427063997944994281),(-74427018700831137424)⟩,⟨48687110826469272060,48687156123583128914⟩⟩,⟨⟨(-52024469049624117596),(-52024429839381594747)⟩,⟨51317551009097200850,51317590219339723696⟩⟩,⟨⟨(-33375086176326963630),(-33375052307526883105)⟩,⟨49748477756655879201,49748511625455959723⟩⟩,⟨⟨(-18518177536300065882),(-18518148352217341017)⟩,⟨45366498861004559391,45366528045087284252⟩⟩,⟨⟨(-7244870677453645561),(-7244845581076151712)⟩,⟨39328531733612865657,39328556829990359506⟩⟩,⟨⟨820171649976091953,820193180334295187⟩,⟨32554310811833863868,32554332342192067103⟩⟩,⟨⟨6148265019768577131,6148283450989743179⟩,⟨25735409370047457112,25735427801268623164⟩⟩] +lemma kernel91_1_r5_4_eq : ∀ k : Fin 16, kernel91_1Expr 5 4 k = kernel91_1_r5_4 k := by decide +kernel +noncomputable def kernel91_1_r5_5 : Fin 16 → CBox := ![⟨⟨9249012815167598918,9249028554437724503⟩,⟨19356141006450382666,19356156745720508251⟩⟩,⟨⟨10625834387356321166,10625847800412019865⟩,⟨13722026649433303541,13722040062489002240⟩⟩,⟨⟨10744178338560318322,10744189744508495372⟩,⟨8992049318188725358,8992060724136902411⟩⟩,⟨⟨10011182195792976020,10011191874103124994⟩,⟨5211588202678508276,5211597880988657250⟩⟩,⟨⟨8765081762837655738,8765089954784755216⟩,⟨2343650514681543713,2343658706628643191⟩⟩,⟨⟨7272440705104639322,7272447624651670451⟩,⟨296739322692153404,296746242239184533⟩⟩,⟨⟨5731229620589398499,5731235451022908241⟩,⟨(-1051641887587926402),(-1051636057154416660)⟩⟩,⟨⟨4277892701278669326,4277897603546118797⟩,⟨(-1836277128812224115),(-1836272226544774644)⟩⟩,⟨⟨2996755786426243846,2996759897899567088⟩,⟨(-2190290002361710425),(-2190285890888387184)⟩⟩,⟨⟨1930410121327666518,1930413564596747256⟩,⟨(-2235593873753693818),(-2235590430484613080)⟩⟩,⟨⟨1090014454029193701,1090017330997547437⟩,⟨(-2077151834507186203),(-2077148957538832467)⟩⟩,⟨⟨464763506343996105,464765905092119501⟩,⟨(-1800339588955221783),(-1800337190207098388)⟩⟩,⟨⟨30050618219680660,30052613205068611⟩,⟨(-1470671898858652725),(-1470669903873264773)⟩⟩,⟨⟨(-245908876981021327),(-245907221136107028)⟩,⟨(-1135186950432380195),(-1135185294587465893)⟩⟩,⟨⟨(-397037110200769241),(-397035739239831757)⟩,⟨(-824862513113467061),(-824861142152529577)⟩⟩,⟨⟨(-455840584352162834),(-455839451395581313)⟩,⟨(-557544305237584586),(-557543172281003064)⟩⟩] +lemma kernel91_1_r5_5_eq : ∀ k : Fin 16, kernel91_1Expr 5 5 k = kernel91_1_r5_5 k := by decide +kernel +noncomputable def kernel91_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-451158283947033848),(-451157350025929487)⟩,⟨(-340984372519659215),(-340983438598554855)⟩⟩,⟨⟨(-406975958599531938),(-406975190250508197)⟩,⟨(-175702863894457878),(-175702095545434137)⟩⟩,⟨⟨(-342056836310519567),(-342056205712263049)⟩,⟨(-57491201992800695),(-57490571394544181)⟩⟩,⟨⟨(-270149751595703936),(-270149235088760838)⟩,⟨20537297039288000,20537813546231100⟩⟩,⟨⟨(-200563385136097696),(-200562963142565868)⟩,⟨66374457070300810,66374879063832638⟩⟩,⟨⟨(-138932549944725691),(-138932205832185432)⟩,⟨87997560271899089,87997904384439348⟩⟩,⟨⟨(-88043051576792923),(-88042771658644555)⟩,⟨92646931956554068,92647211874702436⟩⟩,⟨⟨(-48620990344268279),(-48620763089206904)⟩,⟨86428227221653894,86428454476715273⟩⟩,⟨⟨(-20027321490391975),(-20027137206884665)⟩,⟨74162179561403835,74162363844911145⟩⟩,⟨⟨(-827287775080165),(-827138541597113)⟩,⟨59408415119321759,59408564352804809⟩⟩,⟨⟨10773677727621357,10773798285473286⟩,⟨44599216893598214,44599337451450143⟩⟩,⟨⟨16620626330495367,16620723540439562⟩,⟨31231211116982892,31231308326927087⟩⟩,⟨⟨18409920977932416,18409999167986320⟩,⟨20075788533462891,20075866723516794⟩⟩,⟨⟨17579133754173130,17579196536225289⟩,⟨11381200276142474,11381263058194634⟩⟩,⟨⟨15263913944955752,15263964236150174⟩,⟨5049766826699584,5049817117894007⟩⟩,⟨⟨12301202611460588,12301242827886995⟩,⟨782046974867362,782087191293772⟩⟩] +lemma kernel91_1_r5_6_eq : ∀ k : Fin 16, kernel91_1Expr 5 6 k = kernel91_1_r5_6 k := by decide +kernel +noncomputable def kernel91_1_r5_7 : Fin 16 → CBox := ![⟨⟨9261138432786859,9261170513691322⟩,⟨(-1813964266195437),(-1813932185290973)⟩⟩,⟨⟨6493646165116927,6493671716946961⟩,⟨(-3146358091467359),(-3146332539637325)⟩⟩,⟨⟨4179424389142461,4179444697489598⟩,⟨(-3590858130083946),(-3590837821736809)⟩⟩,⟨⟨2378449304844248,2378465418606890⟩,⟨(-3464614320480938),(-3464598206718296)⟩⟩,⟨⟨1071959800769171,1071972556328958⟩,⟨(-3016372427900851),(-3016359672341068)⟩⟩,⟨⟨196093137954041,196103219807931⟩,⟨(-2427689632281403),(-2427679550427513)⟩⟩,⟨⟨(-333090649291182),(-333082698647984)⟩,⟨(-1820757061530286),(-1820749110887088)⟩⟩,⟨⟨(-602453737196377),(-602447477045994)⟩,⟨(-1269408169740680),(-1269401909590301)⟩⟩,⟨⟨(-691208776732612),(-691203855269247)⟩,⟨(-810882537792247),(-810877616328882)⟩⟩,⟨⟨(-665445342001587),(-665441477207485)⟩,⟨(-456783833948524),(-456779969154422)⟩⟩,⟨⟨(-576305993933143),(-576302965528488)⟩,⟨(-202371176682592),(-202368148277940)⟩⟩,⟨⟨(-460541931204244),(-460539561568536)⟩,⟨(-33844170333346),(-33841800697638)⟩⟩,⟨⟨(-342424683846079),(-342422833808263)⟩,⟨66364232379580,66366082417399⟩⟩,⟨⟨(-236251661529898),(-236250218843242)⟩,⟨116059945466220,116061388152876⟩⟩,⟨⟨(-148924917844182),(-148923795137108)⟩,⟨131194553123463,131195675830533⟩⟩,⟨⟨(-82285396143070),(-82284523565994)⟩,⟨124850672479926,124851545057002⟩⟩] +lemma kernel91_1_r5_7_eq : ∀ k : Fin 16, kernel91_1Expr 5 7 k = kernel91_1_r5_7 k := by decide +kernel +noncomputable def kernel91_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-35041735697202),(-35041058945052)⟩,⟨106974338260415,106975015012565⟩⟩,⟨⟨(-4244275327601),(-4243750718752)⟩,⟨84574652718144,84575177326997⟩⟩,⟨⟨13673339816392,13673745685489⟩,⟨62173307908253,62173713777354⟩⟩,⟨⟨22222623610449,22222937263913⟩,⟨42348133547143,42348447200607⟩⟩,⟨⟨24480085537223,24480327439731⟩,⟨26268902904157,26269144806662⟩⟩,⟨⟨22919142313872,22919328709200⟩,⟨14167035437405,14167221832733⟩⟩,⟨⟨19383623063605,19383766460369⟩,⟨5712967659755,5713111056522⟩⟩,⟨⟨15145685055134,15145795279906⟩,⟨296721405242,296831630010⟩⟩,⟨⟨11005345937501,11005430499238⟩,⟨(-2779637813542),(-2779553251806)⟩⟩,⟨⟨7402167087420,7402231917037⟩,⟨(-4182361428688),(-4182296599071)⟩⟩,⟨⟨4520775980866,4520825607835⟩,⟨(-4481891434894),(-4481841807921)⟩⟩,⟨⟨2380485209970,2380523171013⟩,⟨(-4127824802242),(-4127786841200)⟩⟩,⟨⟨905333883988,905362870491⟩,⟨(-3448993092389),(-3448964105894)⟩⟩,⟨⟨(-25220084608),(-25197960090)⟩,⟨(-2667740529581),(-2667718405063)⟩⟩,⟨⟨(-542529808916),(-542512948070)⟩,⟨(-1920525234942),(-1920508374093)⟩⟩,⟨⟨(-768525686830),(-768512843679)⟩,⟨(-1279637999633),(-1279625156482)⟩⟩] +lemma kernel91_1_r5_8_eq : ∀ k : Fin 16, kernel91_1Expr 5 8 k = kernel91_1_r5_8 k := by decide +kernel +noncomputable def kernel91_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-805493353045),(-805483586531)⟩,⟨(-772968131222),(-772958364711)⟩⟩,⟨⟨(-732683549755),(-732676124442)⟩,⟨(-400321871994),(-400314446684)⟩⟩,⟨⟨(-607150320546),(-607144682914)⟩,⟨(-145866497837),(-145860860201)⟩⟩,⟨⟨(-466851982463),(-466847703517)⟩,⟨13074534953,13078813903⟩⟩,⟨⟨(-334644075533),(-334640832550)⟩,⟨100311623395,100314866378⟩⟩,⟨⟨(-222292251893),(-222289794184)⟩,⟨137478894536,137481352242⟩⟩,⟨⟨(-134016898838),(-134015038492)⟩,⟨142453780107,142455640455⟩⟩,⟨⟨(-69354439963),(-69353031919)⟩,⟨128925600125,128927008165⟩⟩,⟨⟨(-25298108284),(-25297044002)⟩,⟨106652679467,106653743749⟩⟩,⟨⟨2215706570,2216511212⟩,⟨82069972529,82070777174⟩⟩,⟨⟨17360282710,17360890448⟩,⟨59018054234,59018661972⟩⟩,⟨⟨23882050164,23882509247⟩,⟨39452278358,39452737437⟩⟩,⟨⟨24854521933,24854868350⟩,⟨24056607729,24056954146⟩⟩,⟨⟨22621567288,22621828807⟩,⟨12731949869,12732211387⟩⟩,⟨⟨18851701577,18851898849⟩,⟨4957450928,4957648200⟩⟩,⟨⟨14647041700,14647191317⟩,⟨39097514,39247129⟩⟩] +lemma kernel91_1_r5_9_eq : ∀ k : Fin 16, kernel91_1Expr 5 9 k = kernel91_1_r5_9 k := by decide +kernel +noncomputable def kernel91_1_r5_10 : Fin 16 → CBox := ![⟨⟨10669459204,10669572634⟩,⟨(-2733018746),(-2732905316)⟩⟩,⟨⟨7261315491,7261401561⟩,⟨(-3996173889),(-3996087816)⟩⟩,⟨⟨4549037776,4549103036⟩,⟨(-4274642619),(-4274577359)⟩⟩,⟨⟨2525134975,2525184503⟩,⟨(-3970505865),(-3970456337)⟩⟩,⟨⟨1108801914,1108839471⟩,⟨(-3372643956),(-3372606400)⟩⟩,⟨⟨187719477,187747990⟩,⟨(-2674664096),(-2674635584)⟩⟩,⟨⟨(-355308801),(-355287157)⟩,⟨(-1995650772),(-1995629127)⟩⟩,⟨⟨(-627116247),(-627099803)⟩,⟨(-1400069204),(-1400052764)⟩⟩,⟨⟨(-716937367),(-716924890)⟩,⟨(-914915077),(-914902599)⟩⟩,⟨⟨(-694393202),(-694383710)⟩,⟨(-543390164),(-543380668)⟩⟩,⟨⟨(-610571310),(-610564089)⟩,⟨(-275113051),(-275105826)⟩⟩,⟨⟨(-500682598),(-500677090)⟩,⟨(-93270421),(-93264913)⟩⟩,⟨⟨(-387284184),(-387279976)⟩,⟨20718561,20722769⟩⟩,⟨⟨(-283452078),(-283448866)⟩,⟨84427051,84430264⟩⟩,⟨⟨(-195572408),(-195569953)⟩,⟨112993406,112995864⟩⟩,⟨⟨(-125613560),(-125611671)⟩,⟨118593759,118595648⟩⟩] +lemma kernel91_1_r5_10_eq : ∀ k : Fin 16, kernel91_1Expr 5 10 k = kernel91_1_r5_10 k := by decide +kernel +noncomputable def kernel91_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-72862281),(-72860835)⟩,⟨110467891,110469337⟩⟩,⟨⟨(-35174718),(-35173598)⟩,⟨95247040,95248161⟩⟩,⟨⟨(-9823856),(-9822989)⟩,⟨77412696,77413563⟩⟩,⟨⟨5967042,5967714⟩,⟨59778035,59778706⟩⟩,⟨⟨14721668,14722190⟩,⟨43930438,43930959⟩⟩,⟨⟨18567696,18568109⟩,⟨30605380,30605792⟩⟩,⟨⟨19197320,19197641⟩,⟨19982931,19983252⟩⟩,⟨⟨17889346,17889599⟩,⟨11910290,11910547⟩⟩,⟨⟨15563146,15563349⟩,⟨6060262,6060464⟩⟩,⟨⟨12844825,12844996⟩,⟨2037685,2037856⟩⟩,⟨⟨10133408,10133551⟩,⟨(-553785),(-553646)⟩⟩,⟨⟨7660373,7660498⟩,⟨(-2073951),(-2073825)⟩⟩,⟨⟨5539516,5539614⟩,⟨(-2828155),(-2828054)⟩⟩,⟨⟨3806451,3806531⟩,⟨(-3062420),(-3062336)⟩⟩,⟨⟨2448470,2448544⟩,⟨(-2966213),(-2966138)⟩⟩,⟨⟨1426039,1426105⟩,⟨(-2679313),(-2679247)⟩⟩] +lemma kernel91_1_r5_11_eq : ∀ k : Fin 16, kernel91_1Expr 5 11 k = kernel91_1_r5_11 k := by decide +kernel +noncomputable def kernel91_1_r5_12 : Fin 16 → CBox := ![⟨⟨687562,687622⟩,⟨(-2300354),(-2300297)⟩⟩,⟨⟨178908,178960⟩,⟨(-1895416),(-1895364)⟩⟩,⟨⟨(-150874),(-150822)⟩,⟨(-1505927),(-1505875)⟩⟩,⟨⟨(-346553),(-346510)⟩,⟨(-1155347),(-1155304)⟩⟩,⟨⟨(-445541),(-445494)⟩,⟨(-854672),(-854625)⟩⟩,⟨⟨(-477833),(-477790)⟩,⟨(-606608),(-606565)⟩⟩,⟨⟨(-466606),(-466568)⟩,⟨(-408785),(-408743)⟩⟩,⟨⟨(-429172),(-429134)⟩,⟨(-255991),(-255956)⟩⟩,⟨⟨(-377974),(-377937)⟩,⟨(-141738),(-141704)⟩⟩,⟨⟨(-321600),(-321566)⟩,⟨(-59293),(-59259)⟩⟩,⟨⟨(-265685),(-265642)⟩,⟨(-2263),(-2220)⟩⟩,⟨⟨(-213637),(-213599)⟩,⟨35061,35095⟩⟩,⟨⟨(-167326),(-167291)⟩,⟨57522,57560⟩⟩,⟨⟨(-127505),(-127471)⟩,⟨69138,69172⟩⟩,⟨⟨(-94226),(-94192)⟩,⟨73109,73142⟩⟩,⟨⟨(-67107),(-67068)⟩,⟨71929,71968⟩⟩] +lemma kernel91_1_r5_12_eq : ∀ k : Fin 16, kernel91_1Expr 5 12 k = kernel91_1_r5_12 k := by decide +kernel +noncomputable def kernel91_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-45508),(-45479)⟩,⟨67488,67517⟩⟩,⟨⟨(-28700),(-28662)⟩,⟨61163,61202⟩⟩,⟨⟨(-15933),(-15899)⟩,⟨53965,54003⟩⟩,⟨⟨(-6477),(-6439)⟩,⟨46563,46598⟩⟩,⟨⟨304,338⟩,⟨39406,39440⟩⟩,⟨⟨4981,5015⟩,⟨32771,32805⟩⟩,⟨⟨8023,8057⟩,⟨26798,26832⟩⟩,⟨⟨9830,9868⟩,⟨21551,21586⟩⟩,⟨⟨10730,10764⟩,⟨17033,17071⟩⟩,⟨⟨10971,11009⟩,⟨13204,13239⟩⟩,⟨⟨10764,10793⟩,⟨10011,10041⟩⟩,⟨⟨10242,10277⟩,⟨7374,7412⟩⟩,⟨⟨9535,9574⟩,⟨5238,5277⟩⟩,⟨⟨8732,8771⟩,⟨3517,3556⟩⟩,⟨⟨7892,7922⟩,⟨2162,2192⟩⟩,⟨⟨7045,7079⟩,⟨1095,1129⟩⟩] +lemma kernel91_1_r5_13_eq : ∀ k : Fin 16, kernel91_1Expr 5 13 k = kernel91_1_r5_13 k := by decide +kernel +noncomputable def kernel91_1_r5_14 : Fin 16 → CBox := ![⟨⟨6239,6268⟩,⟨280,310⟩⟩,⟨⟨5472,5501⟩,⟨(-341),(-312)⟩⟩,⟨⟨4770,4800⟩,⟨(-794),(-764)⟩⟩,⟨⟨4130,4169⟩,⟨(-1124),(-1089)⟩⟩,⟨⟨3561,3592⟩,⟨(-1350),(-1317)⟩⟩,⟨⟨3052,3082⟩,⟨(-1496),(-1466)⟩⟩,⟨⟨2606,2636⟩,⟨(-1585),(-1555)⟩⟩,⟨⟨2214,2244⟩,⟨(-1624),(-1595)⟩⟩,⟨⟨1866,1896⟩,⟨(-1629),(-1600)⟩⟩,⟨⟨1572,1602⟩,⟨(-1609),(-1580)⟩⟩,⟨⟨1314,1343⟩,⟨(-1575),(-1545)⟩⟩,⟨⟨1092,1121⟩,⟨(-1525),(-1495)⟩⟩,⟨⟨904,934⟩,⟨(-1468),(-1439)⟩⟩,⟨⟨738,772⟩,⟨(-1412),(-1377)⟩⟩,⟨⟨602,631⟩,⟨(-1346),(-1316)⟩⟩,⟨⟨486,516⟩,⟨(-1285),(-1255)⟩⟩] +lemma kernel91_1_r5_14_eq : ∀ k : Fin 16, kernel91_1Expr 5 14 k = kernel91_1_r5_14 k := by decide +kernel +noncomputable def kernel91_1_r5_15 : Fin 16 → CBox := ![⟨⟨383,412⟩,⟨(-1225),(-1196)⟩⟩,⟨⟨301,330⟩,⟨(-1165),(-1136)⟩⟩,⟨⟨229,260⟩,⟨(-1116),(-1082)⟩⟩,⟨⟨162,201⟩,⟨(-1068),(-1029)⟩⟩,⟨⟨115,150⟩,⟨(-1021),(-983)⟩⟩,⟨⟨77,107⟩,⟨(-972),(-943)⟩⟩,⟨⟨37,67⟩,⟨(-936),(-906)⟩⟩,⟨⟨5,40⟩,⟨(-902),(-867)⟩⟩,⟨⟨(-19),15⟩,⟨(-873),(-838)⟩⟩,⟨⟨(-36),(-7)⟩,⟨(-848),(-818)⟩⟩,⟨⟨(-53),(-24)⟩,⟨(-824),(-794)⟩⟩,⟨⟨(-71),(-32)⟩,⟨(-806),(-771)⟩⟩,⟨⟨(-82),(-43)⟩,⟨(-796),(-756)⟩⟩,⟨⟨(-88),(-58)⟩,⟨(-780),(-751)⟩⟩,⟨⟨(-87),(-57)⟩,⟨(-772),(-743)⟩⟩,⟨⟨(-91),(-61)⟩,⟨(-772),(-742)⟩⟩] +lemma kernel91_1_r5_15_eq : ∀ k : Fin 16, kernel91_1Expr 5 15 k = kernel91_1_r5_15 k := by decide +kernel +noncomputable def kernel91_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel91_1_r5_0,kernel91_1_r5_1,kernel91_1_r5_2,kernel91_1_r5_3,kernel91_1_r5_4,kernel91_1_r5_5,kernel91_1_r5_6,kernel91_1_r5_7,kernel91_1_r5_8,kernel91_1_r5_9,kernel91_1_r5_10,kernel91_1_r5_11,kernel91_1_r5_12,kernel91_1_r5_13,kernel91_1_r5_14,kernel91_1_r5_15] +lemma kernel91_1_r5_eq (i k : Fin 16) : kernel91_1Expr 5 i k = kernel91_1_r5 i k := by + fin_cases i + · exact kernel91_1_r5_0_eq k + · exact kernel91_1_r5_1_eq k + · exact kernel91_1_r5_2_eq k + · exact kernel91_1_r5_3_eq k + · exact kernel91_1_r5_4_eq k + · exact kernel91_1_r5_5_eq k + · exact kernel91_1_r5_6_eq k + · exact kernel91_1_r5_7_eq k + · exact kernel91_1_r5_8_eq k + · exact kernel91_1_r5_9_eq k + · exact kernel91_1_r5_10_eq k + · exact kernel91_1_r5_11_eq k + · exact kernel91_1_r5_12_eq k + · exact kernel91_1_r5_13_eq k + · exact kernel91_1_r5_14_eq k + · exact kernel91_1_r5_15_eq k +noncomputable def kernel91_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel91_1_r0,kernel91_1_r1,kernel91_1_r2,kernel91_1_r3,kernel91_1_r4,kernel91_1_r5] +lemma kernel91_1_eq (j : Fin 6) (i k : Fin 16) : kernel91_1Expr j i k = kernel91_1 j i k := by + fin_cases j + · exact kernel91_1_r0_eq i k + · exact kernel91_1_r1_eq i k + · exact kernel91_1_r2_eq i k + · exact kernel91_1_r3_eq i k + · exact kernel91_1_r4_eq i k + · exact kernel91_1_r5_eq i k +lemma kernel91_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel91_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(91:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel91_1_eq] + unfold kernel91_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans91_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel93_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans93 j i k) +noncomputable def kernel93_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_0_eq : ∀ k : Fin 16, kernel93_0Expr 0 0 k = kernel93_0_r0_0 k := by decide +kernel +noncomputable def kernel93_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_1_eq : ∀ k : Fin 16, kernel93_0Expr 0 1 k = kernel93_0_r0_1 k := by decide +kernel +noncomputable def kernel93_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_2_eq : ∀ k : Fin 16, kernel93_0Expr 0 2 k = kernel93_0_r0_2 k := by decide +kernel +noncomputable def kernel93_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_3_eq : ∀ k : Fin 16, kernel93_0Expr 0 3 k = kernel93_0_r0_3 k := by decide +kernel +noncomputable def kernel93_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_4_eq : ∀ k : Fin 16, kernel93_0Expr 0 4 k = kernel93_0_r0_4 k := by decide +kernel +noncomputable def kernel93_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_5_eq : ∀ k : Fin 16, kernel93_0Expr 0 5 k = kernel93_0_r0_5 k := by decide +kernel +noncomputable def kernel93_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_6_eq : ∀ k : Fin 16, kernel93_0Expr 0 6 k = kernel93_0_r0_6 k := by decide +kernel +noncomputable def kernel93_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_7_eq : ∀ k : Fin 16, kernel93_0Expr 0 7 k = kernel93_0_r0_7 k := by decide +kernel +noncomputable def kernel93_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_8_eq : ∀ k : Fin 16, kernel93_0Expr 0 8 k = kernel93_0_r0_8 k := by decide +kernel +noncomputable def kernel93_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_9_eq : ∀ k : Fin 16, kernel93_0Expr 0 9 k = kernel93_0_r0_9 k := by decide +kernel +noncomputable def kernel93_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_10_eq : ∀ k : Fin 16, kernel93_0Expr 0 10 k = kernel93_0_r0_10 k := by decide +kernel +noncomputable def kernel93_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r0_11_eq : ∀ k : Fin 16, kernel93_0Expr 0 11 k = kernel93_0_r0_11 k := by decide +kernel +noncomputable def kernel93_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r0_12_eq : ∀ k : Fin 16, kernel93_0Expr 0 12 k = kernel93_0_r0_12 k := by decide +kernel +noncomputable def kernel93_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r0_13_eq : ∀ k : Fin 16, kernel93_0Expr 0 13 k = kernel93_0_r0_13 k := by decide +kernel +noncomputable def kernel93_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r0_14_eq : ∀ k : Fin 16, kernel93_0Expr 0 14 k = kernel93_0_r0_14 k := by decide +kernel +noncomputable def kernel93_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r0_15_eq : ∀ k : Fin 16, kernel93_0Expr 0 15 k = kernel93_0_r0_15 k := by decide +kernel +noncomputable def kernel93_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel93_0_r0_0,kernel93_0_r0_1,kernel93_0_r0_2,kernel93_0_r0_3,kernel93_0_r0_4,kernel93_0_r0_5,kernel93_0_r0_6,kernel93_0_r0_7,kernel93_0_r0_8,kernel93_0_r0_9,kernel93_0_r0_10,kernel93_0_r0_11,kernel93_0_r0_12,kernel93_0_r0_13,kernel93_0_r0_14,kernel93_0_r0_15] +lemma kernel93_0_r0_eq (i k : Fin 16) : kernel93_0Expr 0 i k = kernel93_0_r0 i k := by + fin_cases i + · exact kernel93_0_r0_0_eq k + · exact kernel93_0_r0_1_eq k + · exact kernel93_0_r0_2_eq k + · exact kernel93_0_r0_3_eq k + · exact kernel93_0_r0_4_eq k + · exact kernel93_0_r0_5_eq k + · exact kernel93_0_r0_6_eq k + · exact kernel93_0_r0_7_eq k + · exact kernel93_0_r0_8_eq k + · exact kernel93_0_r0_9_eq k + · exact kernel93_0_r0_10_eq k + · exact kernel93_0_r0_11_eq k + · exact kernel93_0_r0_12_eq k + · exact kernel93_0_r0_13_eq k + · exact kernel93_0_r0_14_eq k + · exact kernel93_0_r0_15_eq k +noncomputable def kernel93_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_0_eq : ∀ k : Fin 16, kernel93_0Expr 1 0 k = kernel93_0_r1_0 k := by decide +kernel +noncomputable def kernel93_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_1_eq : ∀ k : Fin 16, kernel93_0Expr 1 1 k = kernel93_0_r1_1 k := by decide +kernel +noncomputable def kernel93_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_2_eq : ∀ k : Fin 16, kernel93_0Expr 1 2 k = kernel93_0_r1_2 k := by decide +kernel +noncomputable def kernel93_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_3_eq : ∀ k : Fin 16, kernel93_0Expr 1 3 k = kernel93_0_r1_3 k := by decide +kernel +noncomputable def kernel93_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_4_eq : ∀ k : Fin 16, kernel93_0Expr 1 4 k = kernel93_0_r1_4 k := by decide +kernel +noncomputable def kernel93_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_5_eq : ∀ k : Fin 16, kernel93_0Expr 1 5 k = kernel93_0_r1_5 k := by decide +kernel +noncomputable def kernel93_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_6_eq : ∀ k : Fin 16, kernel93_0Expr 1 6 k = kernel93_0_r1_6 k := by decide +kernel +noncomputable def kernel93_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_7_eq : ∀ k : Fin 16, kernel93_0Expr 1 7 k = kernel93_0_r1_7 k := by decide +kernel +noncomputable def kernel93_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_8_eq : ∀ k : Fin 16, kernel93_0Expr 1 8 k = kernel93_0_r1_8 k := by decide +kernel +noncomputable def kernel93_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_9_eq : ∀ k : Fin 16, kernel93_0Expr 1 9 k = kernel93_0_r1_9 k := by decide +kernel +noncomputable def kernel93_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_10_eq : ∀ k : Fin 16, kernel93_0Expr 1 10 k = kernel93_0_r1_10 k := by decide +kernel +noncomputable def kernel93_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_11_eq : ∀ k : Fin 16, kernel93_0Expr 1 11 k = kernel93_0_r1_11 k := by decide +kernel +noncomputable def kernel93_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_12_eq : ∀ k : Fin 16, kernel93_0Expr 1 12 k = kernel93_0_r1_12 k := by decide +kernel +noncomputable def kernel93_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_13_eq : ∀ k : Fin 16, kernel93_0Expr 1 13 k = kernel93_0_r1_13 k := by decide +kernel +noncomputable def kernel93_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_14_eq : ∀ k : Fin 16, kernel93_0Expr 1 14 k = kernel93_0_r1_14 k := by decide +kernel +noncomputable def kernel93_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r1_15_eq : ∀ k : Fin 16, kernel93_0Expr 1 15 k = kernel93_0_r1_15 k := by decide +kernel +noncomputable def kernel93_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel93_0_r1_0,kernel93_0_r1_1,kernel93_0_r1_2,kernel93_0_r1_3,kernel93_0_r1_4,kernel93_0_r1_5,kernel93_0_r1_6,kernel93_0_r1_7,kernel93_0_r1_8,kernel93_0_r1_9,kernel93_0_r1_10,kernel93_0_r1_11,kernel93_0_r1_12,kernel93_0_r1_13,kernel93_0_r1_14,kernel93_0_r1_15] +lemma kernel93_0_r1_eq (i k : Fin 16) : kernel93_0Expr 1 i k = kernel93_0_r1 i k := by + fin_cases i + · exact kernel93_0_r1_0_eq k + · exact kernel93_0_r1_1_eq k + · exact kernel93_0_r1_2_eq k + · exact kernel93_0_r1_3_eq k + · exact kernel93_0_r1_4_eq k + · exact kernel93_0_r1_5_eq k + · exact kernel93_0_r1_6_eq k + · exact kernel93_0_r1_7_eq k + · exact kernel93_0_r1_8_eq k + · exact kernel93_0_r1_9_eq k + · exact kernel93_0_r1_10_eq k + · exact kernel93_0_r1_11_eq k + · exact kernel93_0_r1_12_eq k + · exact kernel93_0_r1_13_eq k + · exact kernel93_0_r1_14_eq k + · exact kernel93_0_r1_15_eq k +noncomputable def kernel93_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_0_eq : ∀ k : Fin 16, kernel93_0Expr 2 0 k = kernel93_0_r2_0 k := by decide +kernel +noncomputable def kernel93_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_1_eq : ∀ k : Fin 16, kernel93_0Expr 2 1 k = kernel93_0_r2_1 k := by decide +kernel +noncomputable def kernel93_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_2_eq : ∀ k : Fin 16, kernel93_0Expr 2 2 k = kernel93_0_r2_2 k := by decide +kernel +noncomputable def kernel93_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_3_eq : ∀ k : Fin 16, kernel93_0Expr 2 3 k = kernel93_0_r2_3 k := by decide +kernel +noncomputable def kernel93_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_4_eq : ∀ k : Fin 16, kernel93_0Expr 2 4 k = kernel93_0_r2_4 k := by decide +kernel +noncomputable def kernel93_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_5_eq : ∀ k : Fin 16, kernel93_0Expr 2 5 k = kernel93_0_r2_5 k := by decide +kernel +noncomputable def kernel93_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_6_eq : ∀ k : Fin 16, kernel93_0Expr 2 6 k = kernel93_0_r2_6 k := by decide +kernel +noncomputable def kernel93_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_7_eq : ∀ k : Fin 16, kernel93_0Expr 2 7 k = kernel93_0_r2_7 k := by decide +kernel +noncomputable def kernel93_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_8_eq : ∀ k : Fin 16, kernel93_0Expr 2 8 k = kernel93_0_r2_8 k := by decide +kernel +noncomputable def kernel93_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_9_eq : ∀ k : Fin 16, kernel93_0Expr 2 9 k = kernel93_0_r2_9 k := by decide +kernel +noncomputable def kernel93_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r2_10_eq : ∀ k : Fin 16, kernel93_0Expr 2 10 k = kernel93_0_r2_10 k := by decide +kernel +noncomputable def kernel93_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r2_11_eq : ∀ k : Fin 16, kernel93_0Expr 2 11 k = kernel93_0_r2_11 k := by decide +kernel +noncomputable def kernel93_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r2_12_eq : ∀ k : Fin 16, kernel93_0Expr 2 12 k = kernel93_0_r2_12 k := by decide +kernel +noncomputable def kernel93_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r2_13_eq : ∀ k : Fin 16, kernel93_0Expr 2 13 k = kernel93_0_r2_13 k := by decide +kernel +noncomputable def kernel93_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r2_14_eq : ∀ k : Fin 16, kernel93_0Expr 2 14 k = kernel93_0_r2_14 k := by decide +kernel +noncomputable def kernel93_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel93_0_r2_15_eq : ∀ k : Fin 16, kernel93_0Expr 2 15 k = kernel93_0_r2_15 k := by decide +kernel +noncomputable def kernel93_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel93_0_r2_0,kernel93_0_r2_1,kernel93_0_r2_2,kernel93_0_r2_3,kernel93_0_r2_4,kernel93_0_r2_5,kernel93_0_r2_6,kernel93_0_r2_7,kernel93_0_r2_8,kernel93_0_r2_9,kernel93_0_r2_10,kernel93_0_r2_11,kernel93_0_r2_12,kernel93_0_r2_13,kernel93_0_r2_14,kernel93_0_r2_15] +lemma kernel93_0_r2_eq (i k : Fin 16) : kernel93_0Expr 2 i k = kernel93_0_r2 i k := by + fin_cases i + · exact kernel93_0_r2_0_eq k + · exact kernel93_0_r2_1_eq k + · exact kernel93_0_r2_2_eq k + · exact kernel93_0_r2_3_eq k + · exact kernel93_0_r2_4_eq k + · exact kernel93_0_r2_5_eq k + · exact kernel93_0_r2_6_eq k + · exact kernel93_0_r2_7_eq k + · exact kernel93_0_r2_8_eq k + · exact kernel93_0_r2_9_eq k + · exact kernel93_0_r2_10_eq k + · exact kernel93_0_r2_11_eq k + · exact kernel93_0_r2_12_eq k + · exact kernel93_0_r2_13_eq k + · exact kernel93_0_r2_14_eq k + · exact kernel93_0_r2_15_eq k +noncomputable def kernel93_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_0_eq : ∀ k : Fin 16, kernel93_0Expr 3 0 k = kernel93_0_r3_0 k := by decide +kernel +noncomputable def kernel93_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_1_eq : ∀ k : Fin 16, kernel93_0Expr 3 1 k = kernel93_0_r3_1 k := by decide +kernel +noncomputable def kernel93_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_2_eq : ∀ k : Fin 16, kernel93_0Expr 3 2 k = kernel93_0_r3_2 k := by decide +kernel +noncomputable def kernel93_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_3_eq : ∀ k : Fin 16, kernel93_0Expr 3 3 k = kernel93_0_r3_3 k := by decide +kernel +noncomputable def kernel93_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_4_eq : ∀ k : Fin 16, kernel93_0Expr 3 4 k = kernel93_0_r3_4 k := by decide +kernel +noncomputable def kernel93_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_5_eq : ∀ k : Fin 16, kernel93_0Expr 3 5 k = kernel93_0_r3_5 k := by decide +kernel +noncomputable def kernel93_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_6_eq : ∀ k : Fin 16, kernel93_0Expr 3 6 k = kernel93_0_r3_6 k := by decide +kernel +noncomputable def kernel93_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_7_eq : ∀ k : Fin 16, kernel93_0Expr 3 7 k = kernel93_0_r3_7 k := by decide +kernel +noncomputable def kernel93_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_8_eq : ∀ k : Fin 16, kernel93_0Expr 3 8 k = kernel93_0_r3_8 k := by decide +kernel +noncomputable def kernel93_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_9_eq : ∀ k : Fin 16, kernel93_0Expr 3 9 k = kernel93_0_r3_9 k := by decide +kernel +noncomputable def kernel93_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_10_eq : ∀ k : Fin 16, kernel93_0Expr 3 10 k = kernel93_0_r3_10 k := by decide +kernel +noncomputable def kernel93_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_11_eq : ∀ k : Fin 16, kernel93_0Expr 3 11 k = kernel93_0_r3_11 k := by decide +kernel +noncomputable def kernel93_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_12_eq : ∀ k : Fin 16, kernel93_0Expr 3 12 k = kernel93_0_r3_12 k := by decide +kernel +noncomputable def kernel93_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_13_eq : ∀ k : Fin 16, kernel93_0Expr 3 13 k = kernel93_0_r3_13 k := by decide +kernel +noncomputable def kernel93_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_14_eq : ∀ k : Fin 16, kernel93_0Expr 3 14 k = kernel93_0_r3_14 k := by decide +kernel +noncomputable def kernel93_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r3_15_eq : ∀ k : Fin 16, kernel93_0Expr 3 15 k = kernel93_0_r3_15 k := by decide +kernel +noncomputable def kernel93_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel93_0_r3_0,kernel93_0_r3_1,kernel93_0_r3_2,kernel93_0_r3_3,kernel93_0_r3_4,kernel93_0_r3_5,kernel93_0_r3_6,kernel93_0_r3_7,kernel93_0_r3_8,kernel93_0_r3_9,kernel93_0_r3_10,kernel93_0_r3_11,kernel93_0_r3_12,kernel93_0_r3_13,kernel93_0_r3_14,kernel93_0_r3_15] +lemma kernel93_0_r3_eq (i k : Fin 16) : kernel93_0Expr 3 i k = kernel93_0_r3 i k := by + fin_cases i + · exact kernel93_0_r3_0_eq k + · exact kernel93_0_r3_1_eq k + · exact kernel93_0_r3_2_eq k + · exact kernel93_0_r3_3_eq k + · exact kernel93_0_r3_4_eq k + · exact kernel93_0_r3_5_eq k + · exact kernel93_0_r3_6_eq k + · exact kernel93_0_r3_7_eq k + · exact kernel93_0_r3_8_eq k + · exact kernel93_0_r3_9_eq k + · exact kernel93_0_r3_10_eq k + · exact kernel93_0_r3_11_eq k + · exact kernel93_0_r3_12_eq k + · exact kernel93_0_r3_13_eq k + · exact kernel93_0_r3_14_eq k + · exact kernel93_0_r3_15_eq k +noncomputable def kernel93_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-13),(-7)⟩,⟨(-46),(-40)⟩⟩,⟨⟨(-13),(-7)⟩,⟨(-46),(-40)⟩⟩,⟨⟨(-14),(-8)⟩,⟨(-45),(-39)⟩⟩,⟨⟨(-14),(-8)⟩,⟨(-45),(-39)⟩⟩,⟨⟨(-15),(-9)⟩,⟨(-45),(-38)⟩⟩,⟨⟨(-16),(-10)⟩,⟨(-43),(-37)⟩⟩,⟨⟨(-16),(-10)⟩,⟨(-42),(-36)⟩⟩,⟨⟨(-16),(-10)⟩,⟨(-40),(-34)⟩⟩,⟨⟨(-17),(-11)⟩,⟨(-39),(-33)⟩⟩,⟨⟨(-18),(-11)⟩,⟨(-37),(-31)⟩⟩,⟨⟨(-19),(-11)⟩,⟨(-35),(-28)⟩⟩,⟨⟨(-19),(-12)⟩,⟨(-33),(-26)⟩⟩,⟨⟨(-20),(-14)⟩,⟨(-30),(-24)⟩⟩,⟨⟨(-19),(-13)⟩,⟨(-28),(-22)⟩⟩,⟨⟨(-19),(-13)⟩,⟨(-25),(-19)⟩⟩,⟨⟨(-19),(-13)⟩,⟨(-24),(-18)⟩⟩] +lemma kernel93_0_r4_0_eq : ∀ k : Fin 16, kernel93_0Expr 4 0 k = kernel93_0_r4_0 k := by decide +kernel +noncomputable def kernel93_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-19),(-13)⟩,⟨(-21),(-15)⟩⟩,⟨⟨(-19),(-13)⟩,⟨(-18),(-12)⟩⟩,⟨⟨(-19),(-13)⟩,⟨(-17),(-11)⟩⟩,⟨⟨(-19),(-13)⟩,⟨(-14),(-8)⟩⟩,⟨⟨(-18),(-12)⟩,⟨(-13),(-7)⟩⟩,⟨⟨(-17),(-11)⟩,⟨(-11),(-5)⟩⟩,⟨⟨(-16),(-10)⟩,⟨(-9),(-3)⟩⟩,⟨⟨(-16),(-10)⟩,⟨(-7),(-1)⟩⟩,⟨⟨(-15),(-7)⟩,⟨(-7),1⟩⟩,⟨⟨(-14),(-8)⟩,⟨(-4),2⟩⟩,⟨⟨(-12),(-6)⟩,⟨(-3),3⟩⟩,⟨⟨(-12),(-6)⟩,⟨(-2),4⟩⟩,⟨⟨(-10),(-4)⟩,⟨(-2),4⟩⟩,⟨⟨(-10),(-4)⟩,⟨(-2),4⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-1),5⟩⟩,⟨⟨(-8),(-1)⟩,⟨(-2),6⟩⟩] +lemma kernel93_0_r4_1_eq : ∀ k : Fin 16, kernel93_0Expr 4 1 k = kernel93_0_r4_1 k := by decide +kernel +noncomputable def kernel93_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-7),(-1)⟩,⟨(-1),6⟩⟩,⟨⟨(-7),(-1)⟩,⟨(-1),6⟩⟩,⟨⟨(-6),0⟩,⟨(-1),5⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-4),2⟩,⟨0,6⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-1),5⟩⟩,⟨⟨(-3),3⟩,⟨(-1),5⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩] +lemma kernel93_0_r4_2_eq : ∀ k : Fin 16, kernel93_0Expr 4 2 k = kernel93_0_r4_2 k := by decide +kernel +noncomputable def kernel93_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r4_3_eq : ∀ k : Fin 16, kernel93_0Expr 4 3 k = kernel93_0_r4_3 k := by decide +kernel +noncomputable def kernel93_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_4_eq : ∀ k : Fin 16, kernel93_0Expr 4 4 k = kernel93_0_r4_4 k := by decide +kernel +noncomputable def kernel93_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_5_eq : ∀ k : Fin 16, kernel93_0Expr 4 5 k = kernel93_0_r4_5 k := by decide +kernel +noncomputable def kernel93_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_6_eq : ∀ k : Fin 16, kernel93_0Expr 4 6 k = kernel93_0_r4_6 k := by decide +kernel +noncomputable def kernel93_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_7_eq : ∀ k : Fin 16, kernel93_0Expr 4 7 k = kernel93_0_r4_7 k := by decide +kernel +noncomputable def kernel93_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_8_eq : ∀ k : Fin 16, kernel93_0Expr 4 8 k = kernel93_0_r4_8 k := by decide +kernel +noncomputable def kernel93_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_9_eq : ∀ k : Fin 16, kernel93_0Expr 4 9 k = kernel93_0_r4_9 k := by decide +kernel +noncomputable def kernel93_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_10_eq : ∀ k : Fin 16, kernel93_0Expr 4 10 k = kernel93_0_r4_10 k := by decide +kernel +noncomputable def kernel93_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel93_0_r4_11_eq : ∀ k : Fin 16, kernel93_0Expr 4 11 k = kernel93_0_r4_11 k := by decide +kernel +noncomputable def kernel93_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r4_12_eq : ∀ k : Fin 16, kernel93_0Expr 4 12 k = kernel93_0_r4_12 k := by decide +kernel +noncomputable def kernel93_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r4_13_eq : ∀ k : Fin 16, kernel93_0Expr 4 13 k = kernel93_0_r4_13 k := by decide +kernel +noncomputable def kernel93_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r4_14_eq : ∀ k : Fin 16, kernel93_0Expr 4 14 k = kernel93_0_r4_14 k := by decide +kernel +noncomputable def kernel93_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel93_0_r4_15_eq : ∀ k : Fin 16, kernel93_0Expr 4 15 k = kernel93_0_r4_15 k := by decide +kernel +noncomputable def kernel93_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel93_0_r4_0,kernel93_0_r4_1,kernel93_0_r4_2,kernel93_0_r4_3,kernel93_0_r4_4,kernel93_0_r4_5,kernel93_0_r4_6,kernel93_0_r4_7,kernel93_0_r4_8,kernel93_0_r4_9,kernel93_0_r4_10,kernel93_0_r4_11,kernel93_0_r4_12,kernel93_0_r4_13,kernel93_0_r4_14,kernel93_0_r4_15] +lemma kernel93_0_r4_eq (i k : Fin 16) : kernel93_0Expr 4 i k = kernel93_0_r4 i k := by + fin_cases i + · exact kernel93_0_r4_0_eq k + · exact kernel93_0_r4_1_eq k + · exact kernel93_0_r4_2_eq k + · exact kernel93_0_r4_3_eq k + · exact kernel93_0_r4_4_eq k + · exact kernel93_0_r4_5_eq k + · exact kernel93_0_r4_6_eq k + · exact kernel93_0_r4_7_eq k + · exact kernel93_0_r4_8_eq k + · exact kernel93_0_r4_9_eq k + · exact kernel93_0_r4_10_eq k + · exact kernel93_0_r4_11_eq k + · exact kernel93_0_r4_12_eq k + · exact kernel93_0_r4_13_eq k + · exact kernel93_0_r4_14_eq k + · exact kernel93_0_r4_15_eq k +noncomputable def kernel93_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-1560227472549237447540),(-1560225145142215543932)⟩,⟨(-27883915556693787140637),(-27883913229286765236687)⟩⟩,⟨⟨(-1640680429351648199642),(-1640678106197311070187)⟩,⟨(-27798403445113678129367),(-27798401121959340999569)⟩⟩,⟨⟨(-1800097985378058703652),(-1800095670710585630847)⟩,⟨(-27627393461555043613812),(-27627391146887570540663)⟩⟩,⟨⟨(-2035525619031935259009),(-2035523317040606010788)⟩,⟨(-27370936591894661536222),(-27370934289903332287653)⟩⟩,⟨⟨(-2342587050142390688995),(-2342584764949694705461)⟩,⟨(-27029164637326126229988),(-27029162352133430246103)⟩⟩,⟨⟨(-2715550867474985870912),(-2715548603115126083638)⟩,⟨(-26602353982243798975504),(-26602351717883939187873)⟩⟩,⟨⟨(-3147419329069934980798),(-3147417089468308569762)⟩,⟨(-26091006328364283754813),(-26091004088762657343415)⟩⟩,⟨⟨(-3630039154130460865748),(-3630036943083648254872)⟩,⟨(-25495942868738728321358),(-25495940657691915710115)⟩⟩,⟨⟨(-4154233904059138894311),(-4154231725216657723597)⟩,⟨(-24818407681930548868172),(-24818405503088067697086)⟩⟩,⟨⟨(-4709957229827409668567),(-4709955086673547469230)⟩,⟨(-24060175558220063209328),(-24060173415066201009615)⟩⟩,⟨⟨(-5286465840254207028167),(-5286463736092080705611)⟩,⟨(-23223659049823694593289),(-23223656945661568270350)⟩⟩,⟨⟨(-5872510526207527582811),(-5872508463967143708389)⟩,⟨(-22312009287656727371060),(-22312007225416343496251)⟩⟩,⟨⟨(-6456542972038053367517),(-6456540954611911967760)⟩,⟨(-21329205046352801315908),(-21329203028926659915758)⟩⟩,⟨⟨(-7026935421998419427663),(-7026933452059050076134)⟩,⟨(-20280124684465723746554),(-20280122714526354394631)⟩⟩,⟨⟨(-7572209570635758343926),(-7572207650629980344338)⟩,⟨(-19170595942678285392221),(-19170594022672507392238)⟩⟩,⟨⟨(-8081270354493994411966),(-8081268486630311270766)⟩,⟨(-18007419158411761221019),(-18007417290548078079456)⟩⟩] +lemma kernel93_0_r5_0_eq : ∀ k : Fin 16, kernel93_0Expr 5 0 k = kernel93_0_r5_0 k := by decide +kernel +noncomputable def kernel93_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-8543639674346131547456),(-8543637860594660908827)⟩,⟨(-16798360240473321007844),(-16798358426721850368886)⟩⟩,⟨⟨(-8949684519540998932001),(-8949682761621203827075)⟩,⟨(-15552110730702398348561),(-15552108972782603243343)⟩⟩,⟨⟨(-9290833543193646158044),(-9290831842581155747151)⟩,⟨(-14278213436292534793700),(-14278211735680044382550)⟩⟩,⟨⟨(-9559775892307069329048),(-9559774250222720370599)⟩,⟨(-12986953412995588050248),(-12986951770911239091578)⟩⟩,⟨⟨(-9750636068528389495280),(-9750634485951072916797)⟩,⟨(-11689215471929601921650),(-11689213889352285342981)⟩⟩,⟨⟨(-9859118813964214242389),(-9859117291618718687335)⟩,⟨(-10396310819129234042822),(-10396309296783738487616)⟩⟩,⟨⟨(-9882618502077780889441),(-9882617040456540292723)⟩,⟨(-9119776857402198665997),(-9119775395780958069159)⟩⟩,⟨⟨(-9820288273883812304986),(-9820286873229364311231)⟩,⟨(-7871155520436001223164),(-7871154119781553229320)⟩⟩,⟨⟨(-9673065186685741132653),(-9673063847023850879784)⟩,⟨(-6661756702495721097108),(-6661755362833830844178)⟩⟩,⟨⟨(-9443648914127183342580),(-9443647635256189421854)⟩,⟨(-5502414328996324853118),(-5502413050125330932356)⟩⟩,⟨⟨(-9136433012923384167890),(-9136431794444516950077)⟩,⟨(-4403243323110104775392),(-4403242104631237557568)⟩⟩,⟨⟨(-8757389400241833474952),(-8757388241544868121999)⟩,⟨(-3373406111124528156797),(-3373404952427562803855)⟩⟩,⟨⟨(-8313908398677223151406),(-8313907298979899161133)⟩,⟨(-2420897335491231188847),(-2420896235793907198603)⟩⟩,⟨⟨(-7814598426643605763152),(-7814597384938325833896)⟩,⟨(-1552355087813570992274),(-1552354046108291063065)⟩⟩,⟨⟨(-7269051056184771572641),(-7269050071278180872969)⟩,⟨(-772906229754707355319),(-772905244848116655707)⟩⟩,⟨⟨(-6687578643086289938069),(-6687577713705841783982)⟩,⟨(-86052255562327371525),(-86051326181879217508)⟩⟩] +lemma kernel93_0_r5_1_eq : ∀ k : Fin 16, kernel93_0Expr 5 1 k = kernel93_0_r5_1 k := by decide +kernel +noncomputable def kernel93_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-6080932972336041791216),(-6080932097095155593326)⟩,⟨506399297984966910460,506400173225853108271⟩⟩,⟨⟨(-5460014281184643722947),(-5460013458555685314651)⟩,⟨1004354612598007511256,1004355435226965919468⟩⟩,⟨⟨(-4835580562140075291483),(-4835579790510618671808)⟩,⟨1409403163435608620322,1409403935065065239910⟩⟩,⟨⟨(-4217967165561782799455),(-4217966443212199493135)⟩,⟨1724737786915982852284,1724738509265566158516⟩⟩,⟨⟨(-3616826394394471416503),(-3616825719545395954430)⟩,⟨1955027968284232819994,1955028643133308281998⟩⟩,⟨⟨(-3040896015415446527214),(-3040895386173036313805)⟩,⟨2106251031020214306164,2106251660262624519519⟩⟩,⟨⟨(-2497804428249571024629),(-2497803842734007136551)⟩,⟨2185487671672469897962,2185488257188033786000⟩⟩,⟨⟨(-1993918688626553967914),(-1993918144902819895342)⟩,⟨2200689755750686563153,2200690299474420635700⟩⟩,⟨⟨(-1534239747298288872808),(-1534239243432147883175)⟩,⟨2160429395085557587617,2160429898951698577234⟩⟩,⟨⟨(-1122347234896051295318),(-1122346768903431865172)⟩,⟨2073639001462060655740,2073639467454680085881⟩⟩,⟨⟨(-760393997771633507961),(-760393567707586756678)⟩,⟨1949352220972725835156,1949352651036772586442⟩⟩,⟨⟨(-449148483667137456006),(-449148087578747384798)⟩,⟨1796455385904586777388,1796455781992976848605⟩⟩,⟨⟨(-188081097480508113356),(-188080733453615298554)⟩,⟨1623458395270302767713,1623458759297195582527⟩⟩,⟨⟨24511098331857423323,24511432199378668106⟩,⟨1438292793234662110995,1438293127102183355795⟩⟩,⟨⟨191348389541880920959,191348695094473774451⟩,⟨1248143326403702664568,1248143631956295518078⟩⟩,⟨⟨315989206912657727892,315989485966307231667⟩,⟨1059317512462067332480,1059317791515716836273⟩⟩] +lemma kernel93_0_r5_2_eq : ∀ k : Fin 16, kernel93_0Expr 5 2 k = kernel93_0_r5_2 k := by decide +kernel +noncomputable def kernel93_0_r5_3 : Fin 16 → CBox := ![⟨⟨402636397025421909656,402636651323887460378⟩,⟨877155846920415086101,877156101218880636840⟩⟩,⟨⟨455937792995498425591,455938024247850168622⟩,⟨705983319590122749289,705983550842474492332⟩⟩,⟨⟨480789608179991131477,480789818013787265185⟩,⟨549101018187137720435,549101228020933854152⟩⟩,⟨⟨482150461955834215761,482150651949703044462⟩,⟨408814864106639599192,408815054100508427899⟩⟩,⟨⟨464872781532395647389,464872953179070318247⟩,⟨286497044868637265714,286497216515311936575⟩⟩,⟨⟨433556984169039605673,433557138909310368912⟩,⟨182674547510113651351,182674702250384414590⟩⟩,⟨⟨392432322318963491425,392432461505232321302⟩,⟨97138405408080504148,97138544594349334023⟩⟩,⟨⟨345266666540669299773,345266791466111484780⟩,⟨29066868367604744194,29066993293046929198⟩⟩,⟨⟨295305905944715293287,295306017814685168660⟩,⟨(-22844310088578717213),(-22844198218608841844)⟩⟩,⟨⟨245242152963719921267,245242252926389734335⟩,⟨(-60250931835368080822),(-60250831872698267757)⟩⟩,⟨⟨197208627395910087770,197208716540377751387⟩,⟨(-85034569446007990624),(-85034480301540327012)⟩⟩,⟨⟨152798024067872290841,152798103571106148766⟩,⟨(-99186847301038563291),(-99186767797804705368)⟩⟩,⟨⟨113100381345634181460,113100452087113891798⟩,⟨(-104707625132692069726),(-104707554391212359390)⟩⟩,⟨⟨78755980928041140498,78756043737628067065⟩,⟨(-103519757070789441788),(-103519694261202515222)⟩⟩,⟨⟨50018626570459877819,50018682208594017737⟩,⟨(-97401918355421074397),(-97401862717286934481)⟩⟩,⟨⟨26824742899176422149,26824792077073773456⟩,⟨(-87939872572365158222),(-87939823394467806916)⟩⟩] +lemma kernel93_0_r5_3_eq : ∀ k : Fin 16, kernel93_0Expr 5 3 k = kernel93_0_r5_3 k := by decide +kernel +noncomputable def kernel93_0_r5_4 : Fin 16 → CBox := ![⟨⟨8864074391155128334,8864117756431503085⟩,⟨(-76495549656812814614),(-76495506291536439863)⟩⟩,⟨⟨(-4351703531962008944),(-4351665375306756902)⟩,⟨(-64192469461066500444),(-64192431304411248401)⟩⟩,⟨⟨(-13425479393923213102),(-13425445899439559516)⟩,⟨(-51915406818857144825),(-51915373324373491238)⟩⟩,⟨⟨(-19018576255581749044),(-19018546918361034593)⟩,⟨(-40321766724396773578),(-40321737387176059127)⟩⟩,⟨⟨(-21803497491025871184),(-21803471856722238222)⟩,⟨(-29861920414021561866),(-29861894779717928903)⟩⟩,⟨⟨(-22426307000760911123),(-22426284650909497122)⟩,⟨(-20805729866652592982),(-20805707516801178982)⟩⟩,⟨⟨(-21478735037868058779),(-21478715598266493325)⟩,⟨(-13272632539573827266),(-13272613099972261811)⟩⟩,⟨⟨(-19479537138150987684),(-19479520267175555372)⟩,⟨(-7262936093654403837),(-7262919222678971525)⟩⟩,⟨⟨(-16864194135072814119),(-16864179528834041744)⟩,⟨(-2688345456939302647),(-2688330850700530272)⟩⟩,⟨⟨(-13981734818592753964),(-13981722200674158416)⟩,⟨599827299257496412,599839917176091960⟩⟩,⟨⟨(-11097287165031255700),(-11097276290835720130)⟩,⟨2785873719575569808,2785884593771105377⟩⟩,⟨⟨(-8398908613426625870),(-8398899262566976378)⟩,⟨4068992146973208069,4069001497832857560⟩⟩,⟨⟨(-6007292768616003556),(-6007284747669085875)⟩,⟨4646964365909904788,4646972386856822469⟩⟩,⟨⟨(-3987077468668100144),(-3987070602849874902)⟩,⟨4704155588411410446,4704162454229635688⟩⟩,⟨⟨(-2358663300338957660),(-2358657437498894114)⟩,⟨4403527593160985771,4403533456001049318⟩⟩,⟨⟨(-1109668883065309748),(-1109663887779352143)⟩,⟨3882169775016106326,3882174770302063931⟩⟩] +lemma kernel93_0_r5_4_eq : ∀ k : Fin 16, kernel93_0Expr 5 4 k = kernel93_0_r5_4 k := by decide +kernel +noncomputable def kernel93_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-205377700667397555),(-205373455309800175)⟩,⟨3249740866782505880,3249745112140103259⟩⟩,⟨⟨402247273084402882,402250873519005686⟩,⟨2589167882600022442,2589171483034625246⟩⟩,⟨⟨767204811545535795,767207858249425078⟩,⟨1958957933383371191,1958960980087260474⟩⟩,⟨⟨943807111575180274,943809684009352054⟩,⟨1396530254433942276,1396532826868114056⟩⟩,⟨⟨982663902351643655,982666068818616363⟩,⟨922056936360026885,922059102826999593⟩⟩,⟨⟨928126272609856553,928128093304899107⟩,⟨542398736344042021,542400557039084575⟩⟩,⟨⟨816958934006459897,816960460269944764⟩,⟨254825834443650871,254827360707135738⟩⟩,⟨⟨677982965398654155,677984242041480903⟩,⟨50313330248075892,50314606890902640⟩⟩,⟨⟨532430602314202400,532431667409229052⟩,⟨(-83709055081060024),(-83707989986033371)⟩⟩,⟨⟨394772819392443588,394773706661147528⟩,⟨(-161198596674892978),(-161197709406189038)⟩⟩,⟨⟨273812842555885641,273813579929474898⟩,⟨(-195919764937126484),(-195919027563537226)⟩⟩,⟨⟨173878295457898328,173878906935477989⟩,⟨(-200389045501565199),(-200388434023985539)⟩⟩,⟨⟨95986406947846515,95986912719220676⟩,⟨(-185264986088371921),(-185264480316997759)⟩⟩,⟨⟨38896581198033752,38896998670852556⟩,⟨(-159092270619291674),(-159091853146472870)⟩⟩,⟨⟨(-71859772323),271858942256⟩,⟨(-128307634581583120),(-128307290862868540)⟩⟩,⟨⟨(-23975603207865090),(-23975320761098868)⟩,⟨(-97422344426627302),(-97422061979861080)⟩⟩] +lemma kernel93_0_r5_5_eq : ∀ k : Fin 16, kernel93_0Expr 5 5 k = kernel93_0_r5_5 k := by decide +kernel +noncomputable def kernel93_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-36443699835030374),(-36443468333096056)⟩,⟨(-69307923324333090),(-69307691822398771)⟩⟩,⟨⟨(-40605633628768468),(-40605444263601343)⟩,⟨(-45526347847219636),(-45526158482052512)⟩⟩,⟨⟨(-39238313706360701),(-39238159192432360)⟩,⟨(-26661039376239290),(-26660884862310950)⟩⟩,⟨⟨(-34594935820252009),(-34594810002844335)⟩,⟨(-12619156025583365),(-12619030208175692)⟩⟩,⟨⟨(-28388494618709824),(-28388392431477031)⟩,⟨(-2887972370379050),(-2887870183146256)⟩⟩,⟨⟨(-21830927637239856),(-21830844805955961)⟩,⟨3261990731147926,3262073562431820⟩⟩,⟨⟨(-15704808408639850),(-15704741434834058)⟩,⟨6627102054997459,6627169028803251⟩⟩,⟨⟨(-10449402505367022),(-10449348461712717)⟩,⟨7969125854082823,7969179897737127⟩⟩,⟨⟨(-6247847146453662),(-6247803590026683)⟩,⟨7954384449468991,7954428005895971⟩⟩,⟨⟨(-3106734757098307),(-3106699702553745)⟩,⟨7124720840236004,7124755894780565⟩⟩,⟨⟨(-923184186710990),(-923156044143957)⟩,⟨5891492966765641,5891521109332675⟩⟩,⟨⟨462554732152189,462577282184997⟩,⟨4544731184957021,4544753734989829⟩⟩,⟨⟨1228799928076605,1228817951390505⟩,⟨3270940609503933,3270958632817833⟩⟩,⟨⟨1546920992390466,1546935371895082⟩,⟨2174543718565648,2174558098070263⟩⟩,⟨⟨1566369386892005,1566380831595653⟩,⟨1299430227826353,1299441672530001⟩⟩,⟨⟨1407779088580531,1407788181418215⟩,⟨648377271010767,648386363848451⟩⟩] +lemma kernel93_0_r5_6_eq : ∀ k : Fin 16, kernel93_0Expr 5 6 k = kernel93_0_r5_6 k := by decide +kernel +noncomputable def kernel93_0_r5_7 : Fin 16 → CBox := ![⟨⟨1161762337255751,1161769543440405⟩,⟨199155117974080,199162324158733⟩⟩,⟨⟨891331856696007,891337558645494⟩,⟨(-83079038901664),(-83073336952177)⟩⟩,⟨⟨636288333174464,636292835102617⟩,⟨(-236959487105492),(-236954985177340)⟩⟩,⟨⟨418340541672546,418344090001952⟩,⟨(-299201034203841),(-299197485874435)⟩⟩,⟨⟨246122811048774,246125601087014⟩,⟨(-301385046015742),(-301382255977502)⟩⟩,⟨⟨119609706322518,119611896683526⟩,⟨(-268599926674064),(-268597736313055)⟩⟩,⟨⟨33688443892323,33690159522076⟩,⟨(-219344541810709),(-219342826180956)⟩⟩,⟨⟨(-19164504702309),(-19163163069240)⟩,⟨(-166198562058735),(-166197220425666)⟩⟩,⟨⟨(-47036614369162),(-47035566871750)⟩,⟨(-116876171728596),(-116875124231184)⟩⟩,⟨⟨(-57430891967069),(-57430075051515)⟩,⟨(-75390276531754),(-75389459616199)⟩⟩,⟨⟨(-56659368043915),(-56658732362423)⟩,⟨(-43151617584796),(-43150981903304)⟩⟩,⟨⟨(-49624429375774),(-49623935445963)⟩,⟨(-19905484409404),(-19904990479592)⟩⟩,⟨⟨(-39852714529732),(-39852331611742)⟩,⟨(-4466643247322),(-4466260329333)⟩⟩,⟨⟨(-29672881917480),(-29672585418912)⟩,⟨4747813599617,4748110098184⟩⟩,⟨⟨(-20456777679613),(-20456548578723)⟩,⟨9364719383695,9364948484584⟩⟩,⟨⟨(-12869512554350),(-12869335763992)⟩,⟨10846051788778,10846228579137⟩⟩] +lemma kernel93_0_r5_7_eq : ∀ k : Fin 16, kernel93_0Expr 5 7 k = kernel93_0_r5_7 k := by decide +kernel +noncomputable def kernel93_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-7095580642605),(-7095444509414)⟩,⟨10388364797530,10388500930721⟩⟩,⟨⟨(-3024692655422),(-3024587885850)⟩,⟨8896411835511,8896516605082⟩⟩,⟨⟨(-392581763060),(-392501292555)⟩,⟨7002528828035,7002609298540⟩⟩,⟨⟨1120642689958,1120704425955⟩,⟨5109948830044,5110010566041⟩⟩,⟨⟨1828078713696,1828125980179⟩,⟨3444644247481,3444691513964⟩⟩,⟨⟨2001530150207,2001566304499⟩,⟨2105839699007,2105875853299⟩⟩,⟨⟨1856991384102,1857018993948⟩,⟨1109718217894,1109745827739⟩⟩,⟨⟨1553194594751,1553215661227⟩,⟨424015811167,424036877643⟩⟩,⟨⟨1197708404444,1197724446629⟩,⟨(-6705121881),(-6689079697)⟩⟩,⟨⟨856549942755,856562150325⟩,⟨(-244093061881),(-244080854311)⟩⟩,⟨⟨564602266309,564611541643⟩,⟨(-345773508269),(-345764232935)⟩⟩,⟨⟨335213190025,335220232029⟩,⟨(-360132156255),(-360125114250)⟩⟩,⟨⟨168163736580,168169073506⟩,⟨(-324539251564),(-324533914638)⟩⟩,⟨⟨55751423734,55755466679⟩,⟨(-265710060571),(-265706017626)⟩⟩,⟨⟨(-12921846993),(-12918789086)⟩,⟨(-201209263714),(-201206205807)⟩⟩,⟨⟨(-49185873681),(-49183561994)⟩,⟨(-141405266504),(-141402954817)⟩⟩] +lemma kernel93_0_r5_8_eq : ∀ k : Fin 16, kernel93_0Expr 5 8 k = kernel93_0_r5_8 k := by decide +kernel +noncomputable def kernel93_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-63222823608),(-63221078978)⟩,⟨(-91432884144),(-91431139514)⟩⟩,⟨⟨(-63337577710),(-63336261339)⟩,⟨(-52918512275),(-52917195905)⟩⟩,⟨⟨(-55786947352),(-55785955484)⟩,⟨(-25361130709),(-25360138840)⟩⟩,⟨⟨(-44937780006),(-44937032899)⟩,⟨(-7153039223),(-7152292115)⟩⟩,⟨⟨(-33586284118),(-33585722197)⟩,⟨3723761939,3724323860⟩⟩,⟨⟨(-23326309400),(-23325886790)⟩,⟨9265394677,9265817287⟩⟩,⟨⟨(-14898846550),(-14898529096)⟩,⟨11212208789,11212526242⟩⟩,⟨⟨(-8487984542),(-8487746103)⟩,⟨10952327367,10952565806⟩⟩,⟨⟨(-3950978353),(-3950799502)⟩,⟨9512226733,9512405583⟩⟩,⟨⟨(-983904899),(-983770712)⟩,⟨7595969844,7596104030⟩⟩,⟨⟨768264377,768364955⟩,⟨5646107900,5646208477⟩⟩,⟨⟨1645440334,1645515728⟩,⟨3908855599,3908930993⟩⟩,⟨⟨1938207795,1938264253⟩,⟨2493553786,2493610243⟩⟩,⟨⟨1875222914,1875265211⟩,⟨1421705227,1421747524⟩⟩,⟨⟨1623889078,1623920741⟩,⟨664323105,664354768⟩⟩,⟨⟨1298152188,1298176019⟩,⟨168357535,168381366⟩⟩] +lemma kernel93_0_r5_9_eq : ∀ k : Fin 16, kernel93_0Expr 5 9 k = kernel93_0_r5_9 k := by decide +kernel +noncomputable def kernel93_0_r5_10 : Fin 16 → CBox := ![⟨⟨969201785,969219715⟩,⟨(-126032390),(-126014460)⟩⟩,⟨⟨676439162,676452665⟩,⟨(-275275766),(-275262264)⟩⟩,⟨⟨437255412,437265573⟩,⟨(-327256550),(-327246390)⟩⟩,⟨⟨254977965,254985619⟩,⟨(-319547894),(-319540240)⟩⟩,⟨⟨124864786,124870546⟩,⟨(-279682259),(-279676498)⟩⟩,⟨⟨38319531,38323872⟩,⟨(-226490503),(-226486161)⟩⟩,⟨⟨(-14361869),(-14358598)⟩,⟨(-171858294),(-171855022)⟩⟩,⟨⟨(-42367657),(-42365190)⟩,⟨(-122498242),(-122495776)⟩⟩,⟨⟨(-53547573),(-53545715)⟩,⟨(-81519409),(-81517550)⟩⟩,⟨⟨(-54121082),(-54119678)⟩,⟨(-49701109),(-49699706)⟩⟩,⟨⟨(-48707306),(-48706245)⟩,⟨(-26456352),(-26455290)⟩⟩,⟨⟨(-40525653),(-40524848)⟩,⟨(-10514162),(-10513357)⟩⟩,⟨⟨(-31665425),(-31664814)⟩,⟨(-369941),(-369330)⟩⟩,⟨⟨(-23361518),(-23361055)⟩,⟨5442137,5442600⟩⟩,⟨⟨(-16241585),(-16241233)⟩,⟨8204705,8205057⟩⟩,⟨⟨(-10529349),(-10529078)⟩,⟨8958766,8959037⟩⟩] +lemma kernel93_0_r5_10_eq : ∀ k : Fin 16, kernel93_0Expr 5 10 k = kernel93_0_r5_10 k := by decide +kernel +noncomputable def kernel93_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-6200924),(-6200717)⟩,⟨8498632,8498838⟩⟩,⟨⟨(-3097901),(-3097743)⟩,⟨7396412,7396571⟩⟩,⟨⟨(-1004181),(-1004058)⟩,⟨6039852,6039976⟩⟩,⟨⟨305516,305612⟩,⟨4673201,4673296⟩⟩,⟨⟨1037937,1038012⟩,⟨3435196,3435271⟩⟩,⟨⟨1368020,1368079⟩,⟨2391308,2391368⟩⟩,⟨⟨1434923,1434969⟩,⟨1559315,1559361⟩⟩,⟨⟨1343586,1343624⟩,⟨928469,928507⟩⟩,⟨⟨1169174,1169204⟩,⟨473096,473126⟩⟩,⟨⟨962594,962619⟩,⟨161673,161698⟩⟩,⟨⟨756061,756083⟩,⟨(-37512),(-37490)⟩⟩,⟨⟨568079,568098⟩,⟨(-153187),(-153167)⟩⟩,⟨⟨407597,407612⟩,⟨(-209621),(-209605)⟩⟩,⟨⟨277278,277292⟩,⟨(-226245),(-226231)⟩⟩,⟨⟨175958,175970⟩,⟨(-217907),(-217895)⟩⟩,⟨⟨100390,100400⟩,⟨(-195454),(-195444)⟩⟩] +lemma kernel93_0_r5_11_eq : ∀ k : Fin 16, kernel93_0Expr 5 11 k = kernel93_0_r5_11 k := by decide +kernel +noncomputable def kernel93_0_r5_12 : Fin 16 → CBox := ![⟨⟨46429,46438⟩,⟨(-166451),(-166442)⟩⟩,⟨⟨9793,9802⟩,⟨(-135892),(-135883)⟩⟩,⟨⟨(-13506),(-13497)⟩,⟨(-106846),(-106836)⟩⟩,⟨⟨(-26927),(-26917)⟩,⟨(-80993),(-80984)⟩⟩,⟨⟨(-33329),(-33320)⟩,⟨(-59071),(-59062)⟩⟩,⟨⟨(-34977),(-34968)⟩,⟨(-41198),(-41189)⟩⟩,⟨⟨(-33596),(-33589)⟩,⟨(-27126),(-27118)⟩⟩,⟨⟨(-30460),(-30452)⟩,⟨(-16410),(-16403)⟩⟩,⟨⟨(-26463),(-26456)⟩,⟨(-8527),(-8519)⟩⟩,⟨⟨(-22212),(-22204)⟩,⟨(-2947),(-2940)⟩⟩,⟨⟨(-18093),(-18085)⟩,⟨817,826⟩⟩,⟨⟨(-14330),(-14322)⟩,⟨3197,3205⟩⟩,⟨⟨(-11039),(-11031)⟩,⟨4552,4560⟩⟩,⟨⟨(-8253),(-8245)⟩,⟨5173,5180⟩⟩,⟨⟨(-5959),(-5952)⟩,⟨5290,5298⟩⟩,⟨⟨(-4122),(-4114)⟩,⟨5079,5087⟩⟩] +lemma kernel93_0_r5_12_eq : ∀ k : Fin 16, kernel93_0Expr 5 12 k = kernel93_0_r5_12 k := by decide +kernel +noncomputable def kernel93_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-2683),(-2676)⟩,⟨4672,4678⟩⟩,⟨⟨(-1584),(-1576)⟩,⟨4158,4166⟩⟩,⟨⟨(-767),(-759)⟩,⟨3608,3615⟩⟩,⟨⟨(-177),(-169)⟩,⟨3062,3070⟩⟩,⟨⟨233,239⟩,⟨2550,2555⟩⟩,⟨⟨503,509⟩,⟨2083,2090⟩⟩,⟨⟨667,675⟩,⟨1672,1679⟩⟩,⟨⟨754,760⟩,⟨1317,1324⟩⟩,⟨⟨783,791⟩,⟨1017,1025⟩⟩,⟨⟨776,782⟩,⟨767,773⟩⟩,⟨⟨741,747⟩,⟨562,568⟩⟩,⟨⟨689,697⟩,⟨395,402⟩⟩,⟨⟨629,637⟩,⟨262,270⟩⟩,⟨⟨567,573⟩,⟨159,165⟩⟩,⟨⟨504,510⟩,⟨78,84⟩⟩,⟨⟨442,449⟩,⟨16,24⟩⟩] +lemma kernel93_0_r5_13_eq : ∀ k : Fin 16, kernel93_0Expr 5 13 k = kernel93_0_r5_13 k := by decide +kernel +noncomputable def kernel93_0_r5_14 : Fin 16 → CBox := ![⟨⟨384,390⟩,⟨(-29),(-23)⟩⟩,⟨⟨332,339⟩,⟨(-63),(-56)⟩⟩,⟨⟨285,291⟩,⟨(-86),(-79)⟩⟩,⟨⟨242,249⟩,⟨(-102),(-94)⟩⟩,⟨⟨205,211⟩,⟨(-111),(-105)⟩⟩,⟨⟨172,178⟩,⟨(-116),(-110)⟩⟩,⟨⟨144,150⟩,⟨(-118),(-112)⟩⟩,⟨⟨120,126⟩,⟨(-117),(-111)⟩⟩,⟨⟨97,104⟩,⟨(-115),(-108)⟩⟩,⟨⟨80,86⟩,⟨(-111),(-105)⟩⟩,⟨⟨64,70⟩,⟨(-107),(-101)⟩⟩,⟨⟨51,57⟩,⟨(-102),(-96)⟩⟩,⟨⟨40,47⟩,⟨(-98),(-90)⟩⟩,⟨⟨31,37⟩,⟨(-93),(-86)⟩⟩,⟨⟨23,29⟩,⟨(-86),(-81)⟩⟩,⟨⟨16,22⟩,⟨(-82),(-76)⟩⟩] +lemma kernel93_0_r5_14_eq : ∀ k : Fin 16, kernel93_0Expr 5 14 k = kernel93_0_r5_14 k := by decide +kernel +noncomputable def kernel93_0_r5_15 : Fin 16 → CBox := ![⟨⟨10,16⟩,⟨(-78),(-72)⟩⟩,⟨⟨6,13⟩,⟨(-73),(-67)⟩⟩,⟨⟨2,8⟩,⟨(-70),(-64)⟩⟩,⟨⟨(-1),5⟩,⟨(-67),(-60)⟩⟩,⟨⟨(-3),3⟩,⟨(-63),(-57)⟩⟩,⟨⟨(-6),0⟩,⟨(-59),(-53)⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-58),(-52)⟩⟩,⟨⟨(-10),(-3)⟩,⟨(-56),(-49)⟩⟩,⟨⟨(-11),(-5)⟩,⟨(-53),(-47)⟩⟩,⟨⟨(-11),(-5)⟩,⟨(-51),(-45)⟩⟩,⟨⟨(-13),(-7)⟩,⟨(-50),(-44)⟩⟩,⟨⟨(-13),(-6)⟩,⟨(-49),(-43)⟩⟩,⟨⟨(-14),(-7)⟩,⟨(-49),(-41)⟩⟩,⟨⟨(-14),(-8)⟩,⟨(-47),(-41)⟩⟩,⟨⟨(-14),(-8)⟩,⟨(-47),(-41)⟩⟩,⟨⟨(-15),(-7)⟩,⟨(-47),(-39)⟩⟩] +lemma kernel93_0_r5_15_eq : ∀ k : Fin 16, kernel93_0Expr 5 15 k = kernel93_0_r5_15 k := by decide +kernel +noncomputable def kernel93_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel93_0_r5_0,kernel93_0_r5_1,kernel93_0_r5_2,kernel93_0_r5_3,kernel93_0_r5_4,kernel93_0_r5_5,kernel93_0_r5_6,kernel93_0_r5_7,kernel93_0_r5_8,kernel93_0_r5_9,kernel93_0_r5_10,kernel93_0_r5_11,kernel93_0_r5_12,kernel93_0_r5_13,kernel93_0_r5_14,kernel93_0_r5_15] +lemma kernel93_0_r5_eq (i k : Fin 16) : kernel93_0Expr 5 i k = kernel93_0_r5 i k := by + fin_cases i + · exact kernel93_0_r5_0_eq k + · exact kernel93_0_r5_1_eq k + · exact kernel93_0_r5_2_eq k + · exact kernel93_0_r5_3_eq k + · exact kernel93_0_r5_4_eq k + · exact kernel93_0_r5_5_eq k + · exact kernel93_0_r5_6_eq k + · exact kernel93_0_r5_7_eq k + · exact kernel93_0_r5_8_eq k + · exact kernel93_0_r5_9_eq k + · exact kernel93_0_r5_10_eq k + · exact kernel93_0_r5_11_eq k + · exact kernel93_0_r5_12_eq k + · exact kernel93_0_r5_13_eq k + · exact kernel93_0_r5_14_eq k + · exact kernel93_0_r5_15_eq k +noncomputable def kernel93_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel93_0_r0,kernel93_0_r1,kernel93_0_r2,kernel93_0_r3,kernel93_0_r4,kernel93_0_r5] +lemma kernel93_0_eq (j : Fin 6) (i k : Fin 16) : kernel93_0Expr j i k = kernel93_0 j i k := by + fin_cases j + · exact kernel93_0_r0_eq i k + · exact kernel93_0_r1_eq i k + · exact kernel93_0_r2_eq i k + · exact kernel93_0_r3_eq i k + · exact kernel93_0_r4_eq i k + · exact kernel93_0_r5_eq i k +lemma kernel93_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel93_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(93:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel93_0_eq] + unfold kernel93_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans93_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel93_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans93 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel93_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r0_0_eq : ∀ k : Fin 16, kernel93_1Expr 0 0 k = kernel93_1_r0_0 k := by decide +kernel +noncomputable def kernel93_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r0_1_eq : ∀ k : Fin 16, kernel93_1Expr 0 1 k = kernel93_1_r0_1 k := by decide +kernel +noncomputable def kernel93_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r0_2_eq : ∀ k : Fin 16, kernel93_1Expr 0 2 k = kernel93_1_r0_2 k := by decide +kernel +noncomputable def kernel93_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r0_3_eq : ∀ k : Fin 16, kernel93_1Expr 0 3 k = kernel93_1_r0_3 k := by decide +kernel +noncomputable def kernel93_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r0_4_eq : ∀ k : Fin 16, kernel93_1Expr 0 4 k = kernel93_1_r0_4 k := by decide +kernel +noncomputable def kernel93_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel93_1_r0_5_eq : ∀ k : Fin 16, kernel93_1Expr 0 5 k = kernel93_1_r0_5 k := by decide +kernel +noncomputable def kernel93_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel93_1_r0_6_eq : ∀ k : Fin 16, kernel93_1Expr 0 6 k = kernel93_1_r0_6 k := by decide +kernel +noncomputable def kernel93_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel93_1_r0_7_eq : ∀ k : Fin 16, kernel93_1Expr 0 7 k = kernel93_1_r0_7 k := by decide +kernel +noncomputable def kernel93_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel93_1_r0_8_eq : ∀ k : Fin 16, kernel93_1Expr 0 8 k = kernel93_1_r0_8 k := by decide +kernel +noncomputable def kernel93_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel93_1_r0_9_eq : ∀ k : Fin 16, kernel93_1Expr 0 9 k = kernel93_1_r0_9 k := by decide +kernel +noncomputable def kernel93_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel93_1_r0_10_eq : ∀ k : Fin 16, kernel93_1Expr 0 10 k = kernel93_1_r0_10 k := by decide +kernel +noncomputable def kernel93_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel93_1_r0_11_eq : ∀ k : Fin 16, kernel93_1Expr 0 11 k = kernel93_1_r0_11 k := by decide +kernel +noncomputable def kernel93_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel93_1_r0_12_eq : ∀ k : Fin 16, kernel93_1Expr 0 12 k = kernel93_1_r0_12 k := by decide +kernel +noncomputable def kernel93_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel93_1_r0_13_eq : ∀ k : Fin 16, kernel93_1Expr 0 13 k = kernel93_1_r0_13 k := by decide +kernel +noncomputable def kernel93_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel93_1_r0_14_eq : ∀ k : Fin 16, kernel93_1Expr 0 14 k = kernel93_1_r0_14 k := by decide +kernel +noncomputable def kernel93_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel93_1_r0_15_eq : ∀ k : Fin 16, kernel93_1Expr 0 15 k = kernel93_1_r0_15 k := by decide +kernel +noncomputable def kernel93_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel93_1_r0_0,kernel93_1_r0_1,kernel93_1_r0_2,kernel93_1_r0_3,kernel93_1_r0_4,kernel93_1_r0_5,kernel93_1_r0_6,kernel93_1_r0_7,kernel93_1_r0_8,kernel93_1_r0_9,kernel93_1_r0_10,kernel93_1_r0_11,kernel93_1_r0_12,kernel93_1_r0_13,kernel93_1_r0_14,kernel93_1_r0_15] +lemma kernel93_1_r0_eq (i k : Fin 16) : kernel93_1Expr 0 i k = kernel93_1_r0 i k := by + fin_cases i + · exact kernel93_1_r0_0_eq k + · exact kernel93_1_r0_1_eq k + · exact kernel93_1_r0_2_eq k + · exact kernel93_1_r0_3_eq k + · exact kernel93_1_r0_4_eq k + · exact kernel93_1_r0_5_eq k + · exact kernel93_1_r0_6_eq k + · exact kernel93_1_r0_7_eq k + · exact kernel93_1_r0_8_eq k + · exact kernel93_1_r0_9_eq k + · exact kernel93_1_r0_10_eq k + · exact kernel93_1_r0_11_eq k + · exact kernel93_1_r0_12_eq k + · exact kernel93_1_r0_13_eq k + · exact kernel93_1_r0_14_eq k + · exact kernel93_1_r0_15_eq k +noncomputable def kernel93_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel93_1_r1_0_eq : ∀ k : Fin 16, kernel93_1Expr 1 0 k = kernel93_1_r1_0 k := by decide +kernel +noncomputable def kernel93_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel93_1_r1_1_eq : ∀ k : Fin 16, kernel93_1Expr 1 1 k = kernel93_1_r1_1 k := by decide +kernel +noncomputable def kernel93_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel93_1_r1_2_eq : ∀ k : Fin 16, kernel93_1Expr 1 2 k = kernel93_1_r1_2 k := by decide +kernel +noncomputable def kernel93_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel93_1_r1_3_eq : ∀ k : Fin 16, kernel93_1Expr 1 3 k = kernel93_1_r1_3 k := by decide +kernel +noncomputable def kernel93_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel93_1_r1_4_eq : ∀ k : Fin 16, kernel93_1Expr 1 4 k = kernel93_1_r1_4 k := by decide +kernel +noncomputable def kernel93_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel93_1_r1_5_eq : ∀ k : Fin 16, kernel93_1Expr 1 5 k = kernel93_1_r1_5 k := by decide +kernel +noncomputable def kernel93_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel93_1_r1_6_eq : ∀ k : Fin 16, kernel93_1Expr 1 6 k = kernel93_1_r1_6 k := by decide +kernel +noncomputable def kernel93_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel93_1_r1_7_eq : ∀ k : Fin 16, kernel93_1Expr 1 7 k = kernel93_1_r1_7 k := by decide +kernel +noncomputable def kernel93_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel93_1_r1_8_eq : ∀ k : Fin 16, kernel93_1Expr 1 8 k = kernel93_1_r1_8 k := by decide +kernel +noncomputable def kernel93_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel93_1_r1_9_eq : ∀ k : Fin 16, kernel93_1Expr 1 9 k = kernel93_1_r1_9 k := by decide +kernel +noncomputable def kernel93_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r1_10_eq : ∀ k : Fin 16, kernel93_1Expr 1 10 k = kernel93_1_r1_10 k := by decide +kernel +noncomputable def kernel93_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r1_11_eq : ∀ k : Fin 16, kernel93_1Expr 1 11 k = kernel93_1_r1_11 k := by decide +kernel +noncomputable def kernel93_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r1_12_eq : ∀ k : Fin 16, kernel93_1Expr 1 12 k = kernel93_1_r1_12 k := by decide +kernel +noncomputable def kernel93_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r1_13_eq : ∀ k : Fin 16, kernel93_1Expr 1 13 k = kernel93_1_r1_13 k := by decide +kernel +noncomputable def kernel93_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r1_14_eq : ∀ k : Fin 16, kernel93_1Expr 1 14 k = kernel93_1_r1_14 k := by decide +kernel +noncomputable def kernel93_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel93_1_r1_15_eq : ∀ k : Fin 16, kernel93_1Expr 1 15 k = kernel93_1_r1_15 k := by decide +kernel +noncomputable def kernel93_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel93_1_r1_0,kernel93_1_r1_1,kernel93_1_r1_2,kernel93_1_r1_3,kernel93_1_r1_4,kernel93_1_r1_5,kernel93_1_r1_6,kernel93_1_r1_7,kernel93_1_r1_8,kernel93_1_r1_9,kernel93_1_r1_10,kernel93_1_r1_11,kernel93_1_r1_12,kernel93_1_r1_13,kernel93_1_r1_14,kernel93_1_r1_15] +lemma kernel93_1_r1_eq (i k : Fin 16) : kernel93_1Expr 1 i k = kernel93_1_r1 i k := by + fin_cases i + · exact kernel93_1_r1_0_eq k + · exact kernel93_1_r1_1_eq k + · exact kernel93_1_r1_2_eq k + · exact kernel93_1_r1_3_eq k + · exact kernel93_1_r1_4_eq k + · exact kernel93_1_r1_5_eq k + · exact kernel93_1_r1_6_eq k + · exact kernel93_1_r1_7_eq k + · exact kernel93_1_r1_8_eq k + · exact kernel93_1_r1_9_eq k + · exact kernel93_1_r1_10_eq k + · exact kernel93_1_r1_11_eq k + · exact kernel93_1_r1_12_eq k + · exact kernel93_1_r1_13_eq k + · exact kernel93_1_r1_14_eq k + · exact kernel93_1_r1_15_eq k +noncomputable def kernel93_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel93_1_r2_0_eq : ∀ k : Fin 16, kernel93_1Expr 2 0 k = kernel93_1_r2_0 k := by decide +kernel +noncomputable def kernel93_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel93_1_r2_1_eq : ∀ k : Fin 16, kernel93_1Expr 2 1 k = kernel93_1_r2_1 k := by decide +kernel +noncomputable def kernel93_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel93_1_r2_2_eq : ∀ k : Fin 16, kernel93_1Expr 2 2 k = kernel93_1_r2_2 k := by decide +kernel +noncomputable def kernel93_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel93_1_r2_3_eq : ∀ k : Fin 16, kernel93_1Expr 2 3 k = kernel93_1_r2_3 k := by decide +kernel +noncomputable def kernel93_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel93_1_r2_4_eq : ∀ k : Fin 16, kernel93_1Expr 2 4 k = kernel93_1_r2_4 k := by decide +kernel +noncomputable def kernel93_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel93_1_r2_5_eq : ∀ k : Fin 16, kernel93_1Expr 2 5 k = kernel93_1_r2_5 k := by decide +kernel +noncomputable def kernel93_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel93_1_r2_6_eq : ∀ k : Fin 16, kernel93_1Expr 2 6 k = kernel93_1_r2_6 k := by decide +kernel +noncomputable def kernel93_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel93_1_r2_7_eq : ∀ k : Fin 16, kernel93_1Expr 2 7 k = kernel93_1_r2_7 k := by decide +kernel +noncomputable def kernel93_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel93_1_r2_8_eq : ∀ k : Fin 16, kernel93_1Expr 2 8 k = kernel93_1_r2_8 k := by decide +kernel +noncomputable def kernel93_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel93_1_r2_9_eq : ∀ k : Fin 16, kernel93_1Expr 2 9 k = kernel93_1_r2_9 k := by decide +kernel +noncomputable def kernel93_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel93_1_r2_10_eq : ∀ k : Fin 16, kernel93_1Expr 2 10 k = kernel93_1_r2_10 k := by decide +kernel +noncomputable def kernel93_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel93_1_r2_11_eq : ∀ k : Fin 16, kernel93_1Expr 2 11 k = kernel93_1_r2_11 k := by decide +kernel +noncomputable def kernel93_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel93_1_r2_12_eq : ∀ k : Fin 16, kernel93_1Expr 2 12 k = kernel93_1_r2_12 k := by decide +kernel +noncomputable def kernel93_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel93_1_r2_13_eq : ∀ k : Fin 16, kernel93_1Expr 2 13 k = kernel93_1_r2_13 k := by decide +kernel +noncomputable def kernel93_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel93_1_r2_14_eq : ∀ k : Fin 16, kernel93_1Expr 2 14 k = kernel93_1_r2_14 k := by decide +kernel +noncomputable def kernel93_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel93_1_r2_15_eq : ∀ k : Fin 16, kernel93_1Expr 2 15 k = kernel93_1_r2_15 k := by decide +kernel +noncomputable def kernel93_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel93_1_r2_0,kernel93_1_r2_1,kernel93_1_r2_2,kernel93_1_r2_3,kernel93_1_r2_4,kernel93_1_r2_5,kernel93_1_r2_6,kernel93_1_r2_7,kernel93_1_r2_8,kernel93_1_r2_9,kernel93_1_r2_10,kernel93_1_r2_11,kernel93_1_r2_12,kernel93_1_r2_13,kernel93_1_r2_14,kernel93_1_r2_15] +lemma kernel93_1_r2_eq (i k : Fin 16) : kernel93_1Expr 2 i k = kernel93_1_r2 i k := by + fin_cases i + · exact kernel93_1_r2_0_eq k + · exact kernel93_1_r2_1_eq k + · exact kernel93_1_r2_2_eq k + · exact kernel93_1_r2_3_eq k + · exact kernel93_1_r2_4_eq k + · exact kernel93_1_r2_5_eq k + · exact kernel93_1_r2_6_eq k + · exact kernel93_1_r2_7_eq k + · exact kernel93_1_r2_8_eq k + · exact kernel93_1_r2_9_eq k + · exact kernel93_1_r2_10_eq k + · exact kernel93_1_r2_11_eq k + · exact kernel93_1_r2_12_eq k + · exact kernel93_1_r2_13_eq k + · exact kernel93_1_r2_14_eq k + · exact kernel93_1_r2_15_eq k +noncomputable def kernel93_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel93_1_r3_0_eq : ∀ k : Fin 16, kernel93_1Expr 3 0 k = kernel93_1_r3_0 k := by decide +kernel +noncomputable def kernel93_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel93_1_r3_1_eq : ∀ k : Fin 16, kernel93_1Expr 3 1 k = kernel93_1_r3_1 k := by decide +kernel +noncomputable def kernel93_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel93_1_r3_2_eq : ∀ k : Fin 16, kernel93_1Expr 3 2 k = kernel93_1_r3_2 k := by decide +kernel +noncomputable def kernel93_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel93_1_r3_3_eq : ∀ k : Fin 16, kernel93_1Expr 3 3 k = kernel93_1_r3_3 k := by decide +kernel +noncomputable def kernel93_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel93_1_r3_4_eq : ∀ k : Fin 16, kernel93_1Expr 3 4 k = kernel93_1_r3_4 k := by decide +kernel +noncomputable def kernel93_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel93_1_r3_5_eq : ∀ k : Fin 16, kernel93_1Expr 3 5 k = kernel93_1_r3_5 k := by decide +kernel +noncomputable def kernel93_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel93_1_r3_6_eq : ∀ k : Fin 16, kernel93_1Expr 3 6 k = kernel93_1_r3_6 k := by decide +kernel +noncomputable def kernel93_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel93_1_r3_7_eq : ∀ k : Fin 16, kernel93_1Expr 3 7 k = kernel93_1_r3_7 k := by decide +kernel +noncomputable def kernel93_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel93_1_r3_8_eq : ∀ k : Fin 16, kernel93_1Expr 3 8 k = kernel93_1_r3_8 k := by decide +kernel +noncomputable def kernel93_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel93_1_r3_9_eq : ∀ k : Fin 16, kernel93_1Expr 3 9 k = kernel93_1_r3_9 k := by decide +kernel +noncomputable def kernel93_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel93_1_r3_10_eq : ∀ k : Fin 16, kernel93_1Expr 3 10 k = kernel93_1_r3_10 k := by decide +kernel +noncomputable def kernel93_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel93_1_r3_11_eq : ∀ k : Fin 16, kernel93_1Expr 3 11 k = kernel93_1_r3_11 k := by decide +kernel +noncomputable def kernel93_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel93_1_r3_12_eq : ∀ k : Fin 16, kernel93_1Expr 3 12 k = kernel93_1_r3_12 k := by decide +kernel +noncomputable def kernel93_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel93_1_r3_13_eq : ∀ k : Fin 16, kernel93_1Expr 3 13 k = kernel93_1_r3_13 k := by decide +kernel +noncomputable def kernel93_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel93_1_r3_14_eq : ∀ k : Fin 16, kernel93_1Expr 3 14 k = kernel93_1_r3_14 k := by decide +kernel +noncomputable def kernel93_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel93_1_r3_15_eq : ∀ k : Fin 16, kernel93_1Expr 3 15 k = kernel93_1_r3_15 k := by decide +kernel +noncomputable def kernel93_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel93_1_r3_0,kernel93_1_r3_1,kernel93_1_r3_2,kernel93_1_r3_3,kernel93_1_r3_4,kernel93_1_r3_5,kernel93_1_r3_6,kernel93_1_r3_7,kernel93_1_r3_8,kernel93_1_r3_9,kernel93_1_r3_10,kernel93_1_r3_11,kernel93_1_r3_12,kernel93_1_r3_13,kernel93_1_r3_14,kernel93_1_r3_15] +lemma kernel93_1_r3_eq (i k : Fin 16) : kernel93_1Expr 3 i k = kernel93_1_r3 i k := by + fin_cases i + · exact kernel93_1_r3_0_eq k + · exact kernel93_1_r3_1_eq k + · exact kernel93_1_r3_2_eq k + · exact kernel93_1_r3_3_eq k + · exact kernel93_1_r3_4_eq k + · exact kernel93_1_r3_5_eq k + · exact kernel93_1_r3_6_eq k + · exact kernel93_1_r3_7_eq k + · exact kernel93_1_r3_8_eq k + · exact kernel93_1_r3_9_eq k + · exact kernel93_1_r3_10_eq k + · exact kernel93_1_r3_11_eq k + · exact kernel93_1_r3_12_eq k + · exact kernel93_1_r3_13_eq k + · exact kernel93_1_r3_14_eq k + · exact kernel93_1_r3_15_eq k +noncomputable def kernel93_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-183),(-154)⟩,⟨56,86⟩⟩,⟨⟨(-183),(-154)⟩,⟨56,86⟩⟩,⟨⟨(-179),(-149)⟩,⟨60,89⟩⟩,⟨⟨(-179),(-149)⟩,⟨60,89⟩⟩,⟨⟨(-178),(-144)⟩,⟨63,94⟩⟩,⟨⟨(-169),(-139)⟩,⟨66,96⟩⟩,⟨⟨(-165),(-135)⟩,⟨66,96⟩⟩,⟨⟨(-157),(-127)⟩,⟨64,94⟩⟩,⟨⟨(-152),(-122)⟩,⟨68,98⟩⟩,⟨⟨(-144),(-113)⟩,⟨66,100⟩⟩,⟨⟨(-136),(-101)⟩,⟨64,103⟩⟩,⟨⟨(-127),(-92)⟩,⟨67,102⟩⟩,⟨⟨(-113),(-83)⟩,⟨74,104⟩⟩,⟨⟨(-106),(-76)⟩,⟨68,98⟩⟩,⟨⟨(-94),(-64)⟩,⟨66,96⟩⟩,⟨⟨(-89),(-60)⟩,⟨65,95⟩⟩] +lemma kernel93_1_r4_0_eq : ∀ k : Fin 16, kernel93_1Expr 4 0 k = kernel93_1_r4_0 k := by decide +kernel +noncomputable def kernel93_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-77),(-47)⟩,⟨63,93⟩⟩,⟨⟨(-65),(-35)⟩,⟨61,91⟩⟩,⟨⟨(-61),(-31)⟩,⟨61,90⟩⟩,⟨⟨(-49),(-19)⟩,⟨58,88⟩⟩,⟨⟨(-45),(-15)⟩,⟨54,83⟩⟩,⟨⟨(-38),(-8)⟩,⟨48,78⟩⟩,⟨⟨(-30),0⟩,⟨43,72⟩⟩,⟨⟨(-22),8⟩,⟨41,71⟩⟩,⟨⟨(-24),15⟩,⟨27,67⟩⟩,⟨⟨(-11),19⟩,⟨31,61⟩⟩,⟨⟨(-8),21⟩,⟨22,52⟩⟩,⟨⟨(-4),26⟩,⟨21,51⟩⟩,⟨⟨(-6),24⟩,⟨13,43⟩⟩,⟨⟨(-6),24⟩,⟨13,43⟩⟩,⟨⟨(-3),27⟩,⟨4,34⟩⟩,⟨⟨(-8),31⟩,⟨(-1),35⟩⟩] +lemma kernel93_1_r4_1_eq : ∀ k : Fin 16, kernel93_1Expr 4 1 k = kernel93_1_r4_1 k := by decide +kernel +noncomputable def kernel93_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-4),30⟩,⟨(-1),30⟩⟩,⟨⟨(-4),30⟩,⟨(-1),30⟩⟩,⟨⟨(-5),25⟩,⟨(-4),26⟩⟩,⟨⟨(-10),20⟩,⟨(-12),18⟩⟩,⟨⟨(-10),20⟩,⟨(-12),18⟩⟩,⟨⟨(-2),28⟩,⟨(-13),17⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-7),23⟩,⟨(-17),14⟩⟩,⟨⟨(-7),23⟩,⟨(-17),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-14),11⟩⟩,⟨⟨(-15),10⟩,⟨(-14),11⟩⟩] +lemma kernel93_1_r4_2_eq : ∀ k : Fin 16, kernel93_1Expr 4 2 k = kernel93_1_r4_2 k := by decide +kernel +noncomputable def kernel93_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-15),10⟩,⟨(-14),11⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-10),15⟩,⟨(-11),15⟩⟩,⟨⟨(-11),19⟩,⟨(-16),15⟩⟩,⟨⟨(-11),19⟩,⟨(-16),15⟩⟩,⟨⟨(-11),19⟩,⟨(-16),15⟩⟩,⟨⟨(-11),15⟩,⟨(-15),10⟩⟩,⟨⟨(-11),15⟩,⟨(-15),10⟩⟩,⟨⟨(-16),15⟩,⟨(-20),11⟩⟩] +lemma kernel93_1_r4_3_eq : ∀ k : Fin 16, kernel93_1Expr 4 3 k = kernel93_1_r4_3 k := by decide +kernel +noncomputable def kernel93_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel93_1_r4_4_eq : ∀ k : Fin 16, kernel93_1Expr 4 4 k = kernel93_1_r4_4 k := by decide +kernel +noncomputable def kernel93_1_r4_5 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel93_1_r4_5_eq : ∀ k : Fin 16, kernel93_1Expr 4 5 k = kernel93_1_r4_5 k := by decide +kernel +noncomputable def kernel93_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel93_1_r4_6_eq : ∀ k : Fin 16, kernel93_1Expr 4 6 k = kernel93_1_r4_6 k := by decide +kernel +noncomputable def kernel93_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel93_1_r4_7_eq : ∀ k : Fin 16, kernel93_1Expr 4 7 k = kernel93_1_r4_7 k := by decide +kernel +noncomputable def kernel93_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel93_1_r4_8_eq : ∀ k : Fin 16, kernel93_1Expr 4 8 k = kernel93_1_r4_8 k := by decide +kernel +noncomputable def kernel93_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel93_1_r4_9_eq : ∀ k : Fin 16, kernel93_1Expr 4 9 k = kernel93_1_r4_9 k := by decide +kernel +noncomputable def kernel93_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel93_1_r4_10_eq : ∀ k : Fin 16, kernel93_1Expr 4 10 k = kernel93_1_r4_10 k := by decide +kernel +noncomputable def kernel93_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel93_1_r4_11_eq : ∀ k : Fin 16, kernel93_1Expr 4 11 k = kernel93_1_r4_11 k := by decide +kernel +noncomputable def kernel93_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel93_1_r4_12_eq : ∀ k : Fin 16, kernel93_1Expr 4 12 k = kernel93_1_r4_12 k := by decide +kernel +noncomputable def kernel93_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel93_1_r4_13_eq : ∀ k : Fin 16, kernel93_1Expr 4 13 k = kernel93_1_r4_13 k := by decide +kernel +noncomputable def kernel93_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel93_1_r4_14_eq : ∀ k : Fin 16, kernel93_1Expr 4 14 k = kernel93_1_r4_14 k := by decide +kernel +noncomputable def kernel93_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel93_1_r4_15_eq : ∀ k : Fin 16, kernel93_1Expr 4 15 k = kernel93_1_r4_15 k := by decide +kernel +noncomputable def kernel93_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel93_1_r4_0,kernel93_1_r4_1,kernel93_1_r4_2,kernel93_1_r4_3,kernel93_1_r4_4,kernel93_1_r4_5,kernel93_1_r4_6,kernel93_1_r4_7,kernel93_1_r4_8,kernel93_1_r4_9,kernel93_1_r4_10,kernel93_1_r4_11,kernel93_1_r4_12,kernel93_1_r4_13,kernel93_1_r4_14,kernel93_1_r4_15] +lemma kernel93_1_r4_eq (i k : Fin 16) : kernel93_1Expr 4 i k = kernel93_1_r4 i k := by + fin_cases i + · exact kernel93_1_r4_0_eq k + · exact kernel93_1_r4_1_eq k + · exact kernel93_1_r4_2_eq k + · exact kernel93_1_r4_3_eq k + · exact kernel93_1_r4_4_eq k + · exact kernel93_1_r4_5_eq k + · exact kernel93_1_r4_6_eq k + · exact kernel93_1_r4_7_eq k + · exact kernel93_1_r4_8_eq k + · exact kernel93_1_r4_9_eq k + · exact kernel93_1_r4_10_eq k + · exact kernel93_1_r4_11_eq k + · exact kernel93_1_r4_12_eq k + · exact kernel93_1_r4_13_eq k + · exact kernel93_1_r4_14_eq k + · exact kernel93_1_r4_15_eq k +noncomputable def kernel93_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-100396684710577995461097),(-100396675869206974678600)⟩,⟨10869984869459496566792,10869993710830517347831⟩⟩,⟨⟨(-100073651606616467936726),(-100073642781251735578070)⟩,⟨11145368339125603294022,11145377164490335651219⟩⟩,⟨⟨(-99427884418850326924704),(-99427875625429516461546)⟩,⟨11690763051486128915493,11690771844906939377192⟩⟩,⟨⟨(-98460059004237654322028),(-98460050258531101151076)⟩,⟨12495508201120714864439,12495516946827268033923⟩⟩,⟨⟨(-97171380277214481949250),(-97171371594743643626486)⟩,⟨13543821630297370640303,13543830312768208961597⟩⟩,⟨⟨(-95563802103341288348158),(-95563793499298599510454)⟩,⟨14815050398513743841562,14815059002556432677783⟩⟩,⟨⟨(-93640305004386813258602),(-93640296493559167659855)⟩,⟨16284004119722666525616,16284012630550312122873⟩⟩,⟨⟨(-91405218964754402747871),(-91405210561448462779655)⟩,⟨17921369897851563291026,17921378301157503257747⟩⟩,⟨⟨(-88864576155185705595798),(-88864567873159797915416)⟩,⟨19694206789421000964573,19694215071446908643456⟩⟩,⟨⟨(-86026476380674227280544),(-86026468233070400551438)⟩,⟨21566516478565516701149,21566524626169343428756⟩⟩,⟨⟨(-82901446601222188257041),(-82901438600506583440956)⟩,⟨23499885257341203235626,23499893258056808050204⟩⟩,⟨⟨(-79502775045079497722509),(-79502767202313223608110)⟩,⟨25454190484062624057333,25454198326828898170227⟩⟩,⟨⟨(-75846800298603130138097),(-75846792624718953739100)⟩,⟨27388362498815073060082,27388370172699249457571⟩⟩,⟨⟨(-71953136375540542140694),(-71953128880649676767789)⟩,⟨29261190579858206095335,29261198074749071466746⟩⟩,⟨⟨(-67844816153636915445497),(-67844808847007493639550)⟩,⟨31032159054309388220711,31032166360938810025179⟩⟩,⟨⟨(-63548337747053390084673),(-63548330637062631824527)⟩,⟨32662297239563156322111,32662304349553914580906⟩⟩] +lemma kernel93_1_r5_0_eq : ∀ k : Fin 16, kernel93_1Expr 5 0 k = kernel93_1_r5_0 k := by decide +kernel +noncomputable def kernel93_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-59093601316820655100350),(-59093594410954553913895)⟩,⟨34115024656058436865208,34115031561924538050446⟩⟩,⟨⟨(-54513727461202659755576),(-54513720766009054317052)⟩,⟨35356971066841602669530,35356977762035208106982⟩⟩,⟨⟨(-49844752577983434317937),(-49844746099097581405457)⟩,⟨36358749528558123068883,36358756007443975980429⟩⟩,⟨⟨(-45125201324065766030538),(-45125195066168037277668)⟩,⟨37095659932950515454192,37095666190848244206268⟩⟩,⟨⟨(-40395541350404625544769),(-40395535317268727740367)⟩,⟨37548300611747366750041,37548306644883264553785⟩⟩,⟨⟨(-35697530669292961000832),(-35697524863738728284824)⟩,⟨37703066573870309159421,37703072379424541874903⟩⟩,⟨⟨(-31073473096252411859525),(-31073467520227700354428)⟩,⟨37552514908636798264328,37552520484661509769022⟩⟩,⟨⟨(-26565401966738984736594),(-26565396621251620143493)⟩,⟨37095580838661364784636,37095586184148729377454⟩⟩,⟨⟨(-22214216516163807067373),(-22214211401406688216087)⟩,⟨36337631808154208512670,36337636922911327363780⟩⟩,⟨⟨(-18058798699056120556060),(-18058793814365216666659)⟩,⟨35290351752169696040880,35290356636860599930202⟩⟩,⟨⟨(-14135140594013698426757),(-14135135937982384362502)⟩,⟨33971453163869280814070,33971457819900594878339⟩⟩,⟨⟨(-10475513719612748728767),(-10475509290035505855961)⟩,⟨32404220555041692992469,32404224984618935865373⟩⟩,⟨⟨(-7107711439216039169363),(-7107707233237544564141)⟩,⟨30616895144091339108631,30616899350069833714019⟩⟩,⟨⟨(-4054394091092830237941),(-4054390105002479713234)⟩,⟨28641916818586613477274,28641920804676964002212⟩⟩,⟨⟨(-1332563538111438961705),(-1332559767492841158673)⟩,⟨26515045304304410842342,26515049074923008645652⟩⟩,⟨⟨1046810436353848973374,1046813996216547704072⟩,⟨24274387715489899672705,24274391275352598403717⟩⟩] +lemma kernel93_1_r5_1_eq : ∀ k : Fin 16, kernel93_1Expr 5 1 k = kernel93_1_r5_1 k := by decide +kernel +noncomputable def kernel93_1_r5_2 : Fin 16 → CBox := ![⟨⟨3078994909540283529084,3078998263797040048701⟩,⟨21959363968865719049832,21959367323122475569782⟩⟩,⟨⟨4765519214324507000635,4765522368664438226585⟩,⟨19609644653299174074458,19609647807639105300745⟩⟩,⟨⟨6114017477596394302038,6114020438033674402569⟩,⟨17264097642759050013230,17264100603196330114097⟩⟩,⟨⟨7137892272589286572765,7137895045550517276217⟩,⟨14959779879367216398277,14959782652328447102059⟩⟩,⟨⟨7855810780355879591743,7855813372499364904395⟩,⟨12731009271394266187506,12731011863537751500413⟩⟩,⟨⟨8291051880871408564346,8291054299298757515729⟩,⟨10608548566930588067023,10608550985357937018601⟩⟩,⟨⟨8470728855610398823158,8470731107374110378724⟩,⟨8618928496052768291755,8618930747816479847462⟩⟩,⟨⟨8424917537357864563802,8424919629728287147190⟩,⟨6783931617309841121014,6783933709680263704486⟩⟩,⟨⟨8185723515076447574023,8185725455327488258574⟩,⟨5120251446253846260019,5120253386504886944618⟩⟩,⟨⟨7786324172646532980100,7786325968251408858981⟩,⟨3639333917840962823546,3639335713445838702434⟩⟩,⟨⟨7260021798691083525539,7260023456980555609787⟩,⟨2347400437325193878637,2347402095614665962861⟩⟩,⟨⟨6639342718971521036754,6639344247315912428392⟩,⟨1245644105046775007923,1245645633391166399515⟩⟩,⟨⟨5955214458387108726207,5955215864016696178115⟩,⟨330583569902963544743,330584975532550996594⟩⟩,⟨⟨5236248503367511891538,5236249793476071615524⟩,⟨(-405447260904509013185),(-405445970795949289274)⟩⟩,⟨⟨4508150575249676830104,4508151756818525207134⟩,⟨(-973700427064563185008),(-973699245495714808052)⟩⟩,⟨⟨3793273766291546451841,3793274846202656360163⟩,⟨(-1388336339207280123439),(-1388335259296170215188)⟩⟩] +lemma kernel93_1_r5_2_eq : ∀ k : Fin 16, kernel93_1Expr 5 2 k = kernel93_1_r5_2 k := by decide +kernel +noncomputable def kernel93_1_r5_3 : Fin 16 → CBox := ![⟨⟨3110322816312265461016,3110323801179090890186⟩,⟨(-1665699634217298530128),(-1665698649350473101023)⟩⟩,⟨⟨2474210617527025643996,2474211513839769094872⟩,⟨(-1823580909163201139602),(-1823580012850457688769)⟩⟩,⟨⟨1896061132099765668417,1896061946043950932915⟩,⟨(-1880495385450888534802),(-1880494571506703270335)⟩⟩,⟨⟨1383346656866955706510,1383347394449500874554⟩,⟨(-1855006677152515083002),(-1855005939569969914978)⟩⟩,⟨⟨940142095311302792572,940142762216849337738⟩,⟨(-1765119701621530344784),(-1765119034715983799626)⟩⟩,⟨⟨567474838991539858146,567475440713917635353⟩,⟨(-1627761677278071716230),(-1627761075555693939021)⟩⟩,⟨⟨263746183835715421765,263746725535936580843⟩,⟨(-1458364439359587184533),(-1458363897659366025445)⟩⟩,⟨⟨25198973338521831174,25199459957685250641⟩,⟨(-1270555335985433170091),(-1270554849366269750610)⟩⟩,⟨⟨(-153593651437294990376),(-153593215289825820221)⟩,⟨(-1075958097493246883732),(-1075957661345777713560)⟩⟩,⟨⟨(-279242023623956934693),(-279241633551771561574)⟩,⟨(-884099635410621791785),(-884099245338436418653)⟩⟩,⟨⟨(-359077261401508836026),(-359076913228935225331)⟩,⟨(-702414000521734724279),(-702413652349161113565)⟩⟩,⟨⟨(-400729652918320397776),(-400729342116430637081)⟩,⟨(-536330931726519597390),(-536330620924629836688)⟩⟩,⟨⟨(-411761573411529144237),(-411761296604378462520)⟩,⟨(-389433694172814864333),(-389433417365664182608)⟩⟩,⟨⟨(-399364028234862744218),(-399363782232675305195)⟩,⟨(-263669307813610203415),(-263669061811422764389)⟩⟩,⟨⟨(-370121532387603009076),(-370121314264857274562)⟩,⟨(-159593768534344580023),(-159593550411598845504)⟩⟩,⟨⟨(-329845925199388410676),(-329845732216338939395)⟩,⟨(-76635402910398882486),(-76635209927349411202)⟩⟩] +lemma kernel93_1_r5_3_eq : ∀ k : Fin 16, kernel93_1Expr 5 3 k = kernel93_1_r5_3 k := by decide +kernel +noncomputable def kernel93_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-283476074896564975149),(-283475904556220523425)⟩,⟨(-13360905538724816777),(-13360735198380365054)⟩⟩,⟨⟨(-235037431797026051492),(-235037281767333544827)⟩,⟨32269289508614591421,32269439538307098082⟩⟩,⟨⟨(-187653140898258323746),(-187653009067426992221)⟩,⟨62667072890284762929,62667204721116094450⟩⟩,⟨⟨(-143596971222386110025),(-143596855636539712597)⟩,⟨80412092538177946550,80412208124024343978⟩⟩,⟨⟨(-104377644010729140171),(-104377542909987747037)⟩,⟨88081604881930690196,88081705982672083326⟩⟩,⟨⟨(-70844181687924453116),(-70844093449110522604)⟩,⟨88117053379329684593,88117141618143615109⟩⟩,⟨⟨(-43302547787797130205),(-43302470958015021215)⟩,⟨82727237294482886150,82727314124264995137⟩⟩,⟨⟨(-21634974119595222192),(-21634907370619383387)⟩,⟨73825895047910393593,73825961796886232398⟩⟩,⟨⟨(-5414827576432053307),(-5414769725565769365)⟩,⟨62999965000822571880,63000022851688855821⟩⟩,⟨⟨5988491265302350411,5988541295367613205⟩,⟨51503726440070500846,51503776470135763641⟩⟩,⟨⟨13318441434531210085,13318484598077354884⟩,⟨40273452586966730640,40273495750512875443⟩⟩,⟨⟨17356240182897133962,17356277340940356050⟩,⟨29957078954543746189,29957116112586968280⟩⟩,⟨⟨18862539653334441926,18862571562311039931⟩,⟨20953635646892462514,20953667555869060519⟩⟩,⟨⟨18535448892323438610,18535476236825583202⟩,⟨13457725834952829816,13457753179454974408⟩⟩,⟨⟨16983537142105701481,16983560518672741073⟩,⟨7505064759376078891,7505088135943118479⟩⟩,⟨⟨14711807675510664484,14711827615844203667⟩,⟨3015934717439910659,3015954657773449842⟩⟩] +lemma kernel93_1_r5_4_eq : ∀ k : Fin 16, kernel93_1Expr 5 4 k = kernel93_1_r5_4 k := by decide +kernel +noncomputable def kernel93_1_r5_5 : Fin 16 → CBox := ![⟨⟨12118258499752271540,12118275466166220230⟩,⟨(-165718073573918971),(-165701107159970278)⟩⟩,⟨⟨9498516773547900504,9498531179391429924⟩,⟨(-2238986941813081862),(-2238972535969552442)⟩⟩,⟨⟨7056106316958054522,7056118521632381037⟩,⟨(-3419208035587456927),(-3419195830913130412)⟩⟩,⟨⟨4916132976547727530,4916143293621196463⟩,⟨(-3917743970558072973),(-3917733653484604039)⟩⟩,⟨⟨3140500959579693808,3140509658887163159⟩,⟨(-3927950659319813825),(-3927941960012344475)⟩⟩,⟨⟨1743156811384068235,1743164131098679721⟩,⟨(-3616596983304692539),(-3616589663590081053)⟩⟩,⟨⟨704255261728269937,704261405211609436⟩,⟨(-3119809512943709791),(-3119803369460370293)⟩⟩,⟨⟨(-17480736017751447),(-17475591002842539)⟩,⟨(-2542535533595669213),(-2542530388580760305)⟩⟩,⟨⟨(-474598775220594132),(-474594477468189152)⟩,⟨(-1960534277806048463),(-1960529980053643487)⟩⟩,⟨⟨(-723071572340960020),(-723067987683365387)⟩,⟨(-1423993657656474217),(-1423990072998879584)⟩⟩,⟨⟨(-816673561747042731),(-816670578953673961)⟩,⟨(-962003007178072946),(-962000024384704180)⟩⟩,⟨⟨(-803340136761118198),(-803337660122037065)⟩,⟨(-587269143552971487),(-587266666913890351)⟩⟩,⟨⟨(-723184080271852038),(-723182029173613134)⟩,⟨(-300624477291127598),(-300622426192888698)⟩⟩,⟨⟨(-607808293129226407),(-607806597957058176)⟩,⟨(-95027762793380867),(-95026067621212635)⟩⟩,⟨⟨(-480558051398282369),(-480556653918732410)⟩,⟨41109608621646769,41111006101196726⟩⟩,⟨⟨(-357388415149207144),(-357387265305632235)⟩,⟨121331581640398528,121332731483973437⟩⟩] +lemma kernel93_1_r5_5_eq : ∀ k : Fin 16, kernel93_1Expr 5 5 k = kernel93_1_r5_5 k := by decide +kernel +noncomputable def kernel93_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-248072257327089714),(-248071313657905242)⟩,⟨159259217050648756,159260160719833224⟩⟩,⟨⟨(-157532443582340274),(-157531670668157966)⟩,⟨167351570831569559,167352343745751870⟩⟩,⟨⟨(-87140499501567992),(-87139868009640938)⟩,⟨156199832228333050,156200463720260107⟩⟩,⟨⟨(-35878329286059538),(-35877814398067272)⟩,⟨134236655609784590,134237170497776859⟩⟩,⟨⟨(-1305750520326613),(-1305331781411996)⟩,⟨107744696715543332,107745115454457946⟩⟩,⟨⟨19686861677916527,19687201552304458⟩,⟨81060133407751799,81060473282139734⟩⟩,⟨⟨30334989131664665,30335264306686152⟩,⟨56884346881710620,56884622056732107⟩⟩,⟨⟨33642322918740187,33642545265734303⟩,⟨36636570422403275,36636792769397394⟩⟩,⟨⟨32176548714762084,32176728156629964⟩,⟨20799655066914346,20799834508782223⟩⟩,⟨⟨27982884747917077,27983029359544237⟩,⟨9228421750159472,9228566361786635⟩⟩,⟨⟨22580991593238657,22581107848395307⟩,⟨1404394711306291,1404510966462938⟩⟩,⟨⟨17015030824479654,17015124104262146⟩,⟨(-3368339683840148),(-3368246404057657)⟩⟩,⟨⟨11932299147653711,11932373804378667⟩,⟨(-5823756130870621),(-5823681474145665)⟩⟩,⟨⟨7671941677699768,7672001322718222⟩,⟨(-6643882219936932),(-6643822574918474)⟩⟩,⟨⟨4351005518846387,4351053055948745⟩,⟨(-6408708063271816),(-6408660526169458)⟩⟩,⟨⟨1940063440405888,1940101260912569⟩,⟨(-5576015840605505),(-5575978020098824)⟩⟩] +lemma kernel93_1_r5_6_eq : ∀ k : Fin 16, kernel93_1Expr 5 6 k = kernel93_1_r5_6 k := by decide +kernel +noncomputable def kernel93_1_r5_7 : Fin 16 → CBox := ![⟨⟨324595284818670,324625299573553⟩,⟨(-4481796159552966),(-4481766144798081)⟩⟩,⟨⟨(-648785703548102),(-648761921132598)⟩,⟨(-3353297906446877),(-3353274124031373)⟩⟩,⟨⟨(-1140249961578059),(-1140231158198117)⟩,⟨(-2328451333376465),(-2328432529996520)⟩⟩,⟨⟨(-1296699363476216),(-1296684522326342)⟩,⟨(-1477121945039782),(-1477107103889909)⟩⟩,⟨⟨(-1241167842888351),(-1241156157007910)⟩,⟨(-821204009855292),(-821192323974851)⟩⟩,⟨⟨(-1069083231328174),(-1069074044280725)⟩,⟨(-351845212428156),(-351836025380711)⟩⟩,⟨⟨(-849068265733252),(-849061059737047)⟩,⟨(-43070063974842),(-43062857978637)⟩⟩,⟨⟨(-626376511262820),(-626370868191391)⟩,⟨138250254238938,138255897310367⟩⟩,⟨⟨(-427522608384732),(-427518196266644)⟩,⟨225712144996805,225716557114892⟩⟩,⟨⟨(-265107681043745),(-265104235286632)⟩,⟨249392012412031,249395458169141⟩⟩,⟨⟨(-142219299280726),(-142216614175872)⟩,⟨233904827337105,233907512441959⟩⟩,⟨⟨(-56083459837480),(-56081370532319)⟩,⟨197889821452377,197891910757535⟩⟩,⟨⟨(-861495880603),(-859873853754)⟩,⟨154393969957528,154395591984380⟩⟩,⟨⟨30374027627974,30375285368584⟩,⟨111737625120517,111738882861130⟩⟩,⟨⟨44370233906467,44371207128578⟩,⟨74561989044266,74562962266380⟩⟩,⟨⟨46983011461690,46983763536214⟩,⟨44861047701326,44861799775847⟩⟩] +lemma kernel93_1_r5_7_eq : ∀ k : Fin 16, kernel93_1Expr 5 7 k = kernel93_1_r5_7 k := by decide +kernel +noncomputable def kernel93_1_r5_8 : Fin 16 → CBox := ![⟨⟨42872489022698,42873068963599⟩,⟨22884310378998,22884890319899⟩⟩,⟨⟨35468976163184,35469423127147⟩,⟨7859178572418,7859625536385⟩⟩,⟨⟨27098674052916,27099017841791⟩,⟨(-1475585237569),(-1475241448694)⟩⟩,⟨⟨19186223394282,19186487520393⟩,⟨(-6507934609588),(-6507670483477)⟩⟩,⟨⟨12477153272437,12477355781224⟩,⟨(-8531789999924),(-8531587491137)⟩⟩,⟨⟨7245126530698,7245281650771⟩,⟨(-8633182237642),(-8633027117570)⟩⟩,⟨⟨3465697045561,3465815674163⟩,⟨(-7650842884147),(-7650724255542)⟩⟩,⟨⟨950162957261,950253600265⟩,⟨(-6183762159544),(-6183671516540)⟩⟩,⟨⟨(-559314584741),(-559245461768)⟩,⟨(-4624397159987),(-4624328037010)⟩⟩,⟨⟨(-1327968911859),(-1327916236909)⟩,⟨(-3202324408437),(-3202271733487)⟩⟩,⟨⟨(-1592967347383),(-1592927268112)⟩,⟨(-2028460591695),(-2028420512423)⟩⟩,⟨⟨(-1547022746520),(-1546992274501)⟩,⟨(-1134211048938),(-1134180576922)⟩⟩,⟨⟨(-1334684059376),(-1334660932876)⟩,⟨(-502992741883),(-502969615383)⟩⟩,⟨⟨(-1056162247183),(-1056144703147)⟩,⟨(-93636105401),(-93618561366)⟩⟩,⟨⟨(-774884621244),(-774871332992)⟩,⟨143612128937,143625417189⟩⟩,⟨⟨(-526192664233),(-526182604570)⟩,⟨257168482333,257178541996⟩⟩] +lemma kernel93_1_r5_8_eq : ∀ k : Fin 16, kernel93_1Expr 5 8 k = kernel93_1_r5_8 k := by decide +kernel +noncomputable def kernel93_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-325602082023),(-325594479331)⟩,⟨288789504643,288797107335⟩⟩,⟨⟨(-175801085011),(-175795340535)⟩,⟨271450776448,271456520928⟩⟩,⟨⟨(-72086554891),(-72082220444)⟩,⟨229257621324,229261955768⟩⟩,⟨⟨(-6266272614),(-6263003212)⟩,⟨178487441692,178490711090⟩⟩,⟨⟨30766490237,30768952669⟩,⟨129126179511,129128641943⟩⟩,⟨⟨47506941664,47508796182⟩,⟨86486108216,86487962734⟩⟩,⟨⟨51077247464,51078642455⟩,⟨52667926174,52669321169⟩⟩,⟨⟨46978261153,46979310377⟩,⟨27756434090,27757483313⟩⟩,⟨⟨39152886059,39153674151⟩,⟨10722399485,10723187580⟩⟩,⟨⟨30211904870,30212496963⟩,⟨52233863,52825959⟩⟩,⟨⟨21720583902,21721028302⟩,⟨(-5848755269),(-5848310865)⟩⟩,⟨⟨14483009023,14483342605⟩,⟨(-8426387541),(-8426053959)⟩⟩,⟨⟨8790117698,8790367832⟩,⟨(-8870378783),(-8870128645)⟩⟩,⟨⟨4617422459,4617610110⟩,⟨(-8087117522),(-8086929871)⟩⟩,⟨⟨1771074051,1771214713⟩,⟨(-6719287590),(-6719146927)⟩⟩,⟨⟨(-12066780),(-11960769)⟩,⟨(-5188537488),(-5188431477)⟩⟩] +lemma kernel93_1_r5_9_eq : ∀ k : Fin 16, kernel93_1Expr 5 9 k = kernel93_1_r5_9 k := by decide +kernel +noncomputable def kernel93_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-1001575673),(-1001495806)⟩,⟨(-3745436414),(-3745356548)⟩⟩,⟨⟨(-1438485384),(-1438425161)⟩,⟨(-2517288008),(-2517227781)⟩⟩,⟨⟨(-1519680574),(-1519635197)⟩,⟨(-1548956644),(-1548911264)⟩⟩,⟨⟨(-1394692650),(-1394658421)⟩,⟨(-834951129),(-834916900)⟩⟩,⟨⟨(-1169602129),(-1169576332)⟩,⟨(-342886969),(-342861176)⟩⟩,⟨⟨(-914322403),(-914302935)⟩,⟨(-29448656),(-29429191)⟩⟩,⟨⟨(-670840141),(-670825452)⟩,⟨149629424,149644111⟩⟩,⟨⟨(-460988489),(-460977402)⟩,⟨234016267,234027357⟩⟩,⟨⟨(-293041002),(-293032634)⟩,⟨256301030,256309395⟩⟩,⟨⟨(-166884747),(-166878422)⟩,⟨241464166,241470493⟩⟩,⟨⟨(-77812769),(-77807976)⟩,⟨207470371,207475160⟩⟩,⟨⟨(-19122772),(-19119134)⟩,⟨166400040,166403678⟩⟩,⟨⟨16235292,16238057⟩,⟨125740770,125743535⟩⟩,⟨⟨34719019,34721117⟩,⟨89615664,89617762⟩⟩,⟨⟨41746118,41747716⟩,⟨59835541,59837138⟩⟩,⟨⟨41566008,41567240⟩,⟨36734711,36735943⟩⟩] +lemma kernel93_1_r5_10_eq : ∀ k : Fin 16, kernel93_1Expr 5 10 k = kernel93_1_r5_10 k := by decide +kernel +noncomputable def kernel93_1_r5_11 : Fin 16 → CBox := ![⟨⟨37319612,37320550⟩,⟨19793762,19794703⟩⟩,⟨⟨31194686,31195410⟩,⟨8075813,8076534⟩⟩,⟨⟨24615861,24616427⟩,⟨512212,512774⟩⟩,⟨⟨18432299,18432734⟩,⟨(-3925886),(-3925448)⟩⟩,⟨⟨13083257,13083600⟩,⟨(-6137203),(-6136859)⟩⟩,⟨⟨8733403,8733678⟩,⟨(-6854433),(-6854162)⟩⟩,⟨⟨5376750,5376962⟩,⟨(-6641958),(-6641746)⟩⟩,⟨⟨2912194,2912369⟩,⟨(-5912284),(-5912109)⟩⟩,⟨⟨1195365,1195504⟩,⟨(-4950975),(-4950836)⟩⟩,⟨⟨71868,71984⟩,⟨(-3943608),(-3943492)⟩⟩,⟨⟨(-603130),(-603028)⟩,⟨(-3001001),(-3000899)⟩⟩,⟨⟨(-954933),(-954841)⟩,⟨(-2180837),(-2180748)⟩⟩,⟨⟨(-1085692),(-1085618)⟩,⟨(-1505093),(-1505022)⟩⟩,⟨⟨(-1074687),(-1074621)⟩,⟨(-973332),(-973267)⟩⟩,⟨⟨(-980696),(-980639)⟩,⟨(-572348),(-572292)⟩⟩,⟨⟨(-845299),(-845252)⟩,⟨(-282876),(-282829)⟩⟩] +lemma kernel93_1_r5_11_eq : ∀ k : Fin 16, kernel93_1Expr 5 11 k = kernel93_1_r5_11 k := by decide +kernel +noncomputable def kernel93_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-696417),(-696374)⟩,⟨(-83921),(-83879)⟩⟩,⟨⟨(-551583),(-551541)⟩,⟨44599,44641⟩⟩,⟨⟨(-420779),(-420732)⟩,⟨120485,120528⟩⟩,⟨⟨(-308717),(-308673)⟩,⟨158609,158656⟩⟩,⟨⟨(-216672),(-216629)⟩,⟨170902,170945⟩⟩,⟨⟨(-143778),(-143735)⟩,⟨166524,166567⟩⟩,⟨⟨(-88009),(-87971)⟩,⟨152277,152311⟩⟩,⟨⟨(-46816),(-46782)⟩,⟨132998,133036⟩⟩,⟨⟨(-17555),(-17518)⟩,⟨111992,112026⟩⟩,⟨⟨2271,2305⟩,⟨91369,91407⟩⟩,⟨⟨14861,14903⟩,⟨72400,72439⟩⟩,⟨⟨22090,22128⟩,⟨55723,55762⟩⟩,⟨⟨25477,25516⟩,⟨41587,41625⟩⟩,⟨⟨26217,26251⟩,⟨29946,29984⟩⟩,⟨⟨25230,25268⟩,⟨20609,20644⟩⟩,⟨⟨23203,23242⟩,⟨13317,13356⟩⟩] +lemma kernel93_1_r5_12_eq : ∀ k : Fin 16, kernel93_1Expr 5 12 k = kernel93_1_r5_12 k := by decide +kernel +noncomputable def kernel93_1_r5_13 : Fin 16 → CBox := ![⟨⟨20636,20666⟩,⟨7766,7800⟩⟩,⟨⟨17850,17889⟩,⟨3647,3686⟩⟩,⟨⟨15098,15133⟩,⟨697,735⟩⟩,⟨⟨12507,12545⟩,⟨(-1339),(-1300)⟩⟩,⟨⟨10169,10194⟩,⟨(-2656),(-2628)⟩⟩,⟨⟨8101,8135⟩,⟨(-3447),(-3417)⟩⟩,⟨⟨6328,6362⟩,⟨(-3852),(-3814)⟩⟩,⟨⟨4833,4866⟩,⟨(-3964),(-3934)⟩⟩,⟨⟨3596,3635⟩,⟨(-3894),(-3855)⟩⟩,⟨⟨2588,2617⟩,⟨(-3691),(-3662)⟩⟩,⟨⟨1779,1808⟩,⟨(-3414),(-3384)⟩⟩,⟨⟨1134,1169⟩,⟨(-3101),(-3063)⟩⟩,⟨⟨634,673⟩,⟨(-2770),(-2731)⟩⟩,⟨⟨258,287⟩,⟨(-2440),(-2411)⟩⟩,⟨⟨(-29),0⟩,⟨(-2130),(-2101)⟩⟩,⟨⟨(-241),(-202)⟩,⟨(-1842),(-1807)⟩⟩] +lemma kernel93_1_r5_13_eq : ∀ k : Fin 16, kernel93_1Expr 5 13 k = kernel93_1_r5_13 k := by decide +kernel +noncomputable def kernel93_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-384),(-355)⟩,⟨(-1571),(-1541)⟩⟩,⟨⟨(-488),(-454)⟩,⟨(-1341),(-1307)⟩⟩,⟨⟨(-549),(-516)⟩,⟨(-1130),(-1100)⟩⟩,⟨⟨(-586),(-548)⟩,⟨(-949),(-915)⟩⟩,⟨⟨(-597),(-568)⟩,⟨(-787),(-758)⟩⟩,⟨⟨(-595),(-566)⟩,⟨(-650),(-620)⟩⟩,⟨⟨(-584),(-555)⟩,⟨(-534),(-505)⟩⟩,⟨⟨(-564),(-535)⟩,⟨(-437),(-408)⟩⟩,⟨⟨(-541),(-507)⟩,⟨(-350),(-315)⟩⟩,⟨⟨(-512),(-483)⟩,⟨(-278),(-249)⟩⟩,⟨⟨(-485),(-456)⟩,⟨(-216),(-186)⟩⟩,⟨⟨(-456),(-426)⟩,⟨(-166),(-137)⟩⟩,⟨⟨(-433),(-394)⟩,⟨(-130),(-94)⟩⟩,⟨⟨(-406),(-372)⟩,⟨(-92),(-61)⟩⟩,⟨⟨(-372),(-346)⟩,⟨(-62),(-33)⟩⟩,⟨⟨(-350),(-321)⟩,⟨(-37),(-8)⟩⟩] +lemma kernel93_1_r5_14_eq : ∀ k : Fin 16, kernel93_1Expr 5 14 k = kernel93_1_r5_14 k := by decide +kernel +noncomputable def kernel93_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-330),(-300)⟩,⟨(-15),14⟩⟩,⟨⟨(-308),(-277)⟩,⟨(-7),27⟩⟩,⟨⟨(-292),(-262)⟩,⟨12,41⟩⟩,⟨⟨(-278),(-244)⟩,⟨21,52⟩⟩,⟨⟨(-260),(-230)⟩,⟨27,57⟩⟩,⟨⟨(-241),(-212)⟩,⟨37,66⟩⟩,⟨⟨(-236),(-206)⟩,⟨44,74⟩⟩,⟨⟨(-227),(-193)⟩,⟨46,81⟩⟩,⟨⟨(-213),(-184)⟩,⟨53,83⟩⟩,⟨⟨(-205),(-176)⟩,⟨52,81⟩⟩,⟨⟨(-200),(-170)⟩,⟨59,89⟩⟩,⟨⟨(-196),(-166)⟩,⟨54,88⟩⟩,⟨⟨(-196),(-157)⟩,⟨57,92⟩⟩,⟨⟨(-187),(-157)⟩,⟨61,91⟩⟩,⟨⟨(-187),(-157)⟩,⟨61,91⟩⟩,⟨⟨(-188),(-148)⟩,⟨56,95⟩⟩] +lemma kernel93_1_r5_15_eq : ∀ k : Fin 16, kernel93_1Expr 5 15 k = kernel93_1_r5_15 k := by decide +kernel +noncomputable def kernel93_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel93_1_r5_0,kernel93_1_r5_1,kernel93_1_r5_2,kernel93_1_r5_3,kernel93_1_r5_4,kernel93_1_r5_5,kernel93_1_r5_6,kernel93_1_r5_7,kernel93_1_r5_8,kernel93_1_r5_9,kernel93_1_r5_10,kernel93_1_r5_11,kernel93_1_r5_12,kernel93_1_r5_13,kernel93_1_r5_14,kernel93_1_r5_15] +lemma kernel93_1_r5_eq (i k : Fin 16) : kernel93_1Expr 5 i k = kernel93_1_r5 i k := by + fin_cases i + · exact kernel93_1_r5_0_eq k + · exact kernel93_1_r5_1_eq k + · exact kernel93_1_r5_2_eq k + · exact kernel93_1_r5_3_eq k + · exact kernel93_1_r5_4_eq k + · exact kernel93_1_r5_5_eq k + · exact kernel93_1_r5_6_eq k + · exact kernel93_1_r5_7_eq k + · exact kernel93_1_r5_8_eq k + · exact kernel93_1_r5_9_eq k + · exact kernel93_1_r5_10_eq k + · exact kernel93_1_r5_11_eq k + · exact kernel93_1_r5_12_eq k + · exact kernel93_1_r5_13_eq k + · exact kernel93_1_r5_14_eq k + · exact kernel93_1_r5_15_eq k +noncomputable def kernel93_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel93_1_r0,kernel93_1_r1,kernel93_1_r2,kernel93_1_r3,kernel93_1_r4,kernel93_1_r5] +lemma kernel93_1_eq (j : Fin 6) (i k : Fin 16) : kernel93_1Expr j i k = kernel93_1 j i k := by + fin_cases j + · exact kernel93_1_r0_eq i k + · exact kernel93_1_r1_eq i k + · exact kernel93_1_r2_eq i k + · exact kernel93_1_r3_eq i k + · exact kernel93_1_r4_eq i k + · exact kernel93_1_r5_eq i k +lemma kernel93_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel93_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(93:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel93_1_eq] + unfold kernel93_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans93_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel96_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans96 j i k) +noncomputable def kernel96_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_0_eq : ∀ k : Fin 16, kernel96_0Expr 0 0 k = kernel96_0_r0_0 k := by decide +kernel +noncomputable def kernel96_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_1_eq : ∀ k : Fin 16, kernel96_0Expr 0 1 k = kernel96_0_r0_1 k := by decide +kernel +noncomputable def kernel96_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_2_eq : ∀ k : Fin 16, kernel96_0Expr 0 2 k = kernel96_0_r0_2 k := by decide +kernel +noncomputable def kernel96_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_3_eq : ∀ k : Fin 16, kernel96_0Expr 0 3 k = kernel96_0_r0_3 k := by decide +kernel +noncomputable def kernel96_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_4_eq : ∀ k : Fin 16, kernel96_0Expr 0 4 k = kernel96_0_r0_4 k := by decide +kernel +noncomputable def kernel96_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_5_eq : ∀ k : Fin 16, kernel96_0Expr 0 5 k = kernel96_0_r0_5 k := by decide +kernel +noncomputable def kernel96_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_6_eq : ∀ k : Fin 16, kernel96_0Expr 0 6 k = kernel96_0_r0_6 k := by decide +kernel +noncomputable def kernel96_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_7_eq : ∀ k : Fin 16, kernel96_0Expr 0 7 k = kernel96_0_r0_7 k := by decide +kernel +noncomputable def kernel96_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_8_eq : ∀ k : Fin 16, kernel96_0Expr 0 8 k = kernel96_0_r0_8 k := by decide +kernel +noncomputable def kernel96_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_9_eq : ∀ k : Fin 16, kernel96_0Expr 0 9 k = kernel96_0_r0_9 k := by decide +kernel +noncomputable def kernel96_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_10_eq : ∀ k : Fin 16, kernel96_0Expr 0 10 k = kernel96_0_r0_10 k := by decide +kernel +noncomputable def kernel96_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r0_11_eq : ∀ k : Fin 16, kernel96_0Expr 0 11 k = kernel96_0_r0_11 k := by decide +kernel +noncomputable def kernel96_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r0_12_eq : ∀ k : Fin 16, kernel96_0Expr 0 12 k = kernel96_0_r0_12 k := by decide +kernel +noncomputable def kernel96_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r0_13_eq : ∀ k : Fin 16, kernel96_0Expr 0 13 k = kernel96_0_r0_13 k := by decide +kernel +noncomputable def kernel96_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r0_14_eq : ∀ k : Fin 16, kernel96_0Expr 0 14 k = kernel96_0_r0_14 k := by decide +kernel +noncomputable def kernel96_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r0_15_eq : ∀ k : Fin 16, kernel96_0Expr 0 15 k = kernel96_0_r0_15 k := by decide +kernel +noncomputable def kernel96_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel96_0_r0_0,kernel96_0_r0_1,kernel96_0_r0_2,kernel96_0_r0_3,kernel96_0_r0_4,kernel96_0_r0_5,kernel96_0_r0_6,kernel96_0_r0_7,kernel96_0_r0_8,kernel96_0_r0_9,kernel96_0_r0_10,kernel96_0_r0_11,kernel96_0_r0_12,kernel96_0_r0_13,kernel96_0_r0_14,kernel96_0_r0_15] +lemma kernel96_0_r0_eq (i k : Fin 16) : kernel96_0Expr 0 i k = kernel96_0_r0 i k := by + fin_cases i + · exact kernel96_0_r0_0_eq k + · exact kernel96_0_r0_1_eq k + · exact kernel96_0_r0_2_eq k + · exact kernel96_0_r0_3_eq k + · exact kernel96_0_r0_4_eq k + · exact kernel96_0_r0_5_eq k + · exact kernel96_0_r0_6_eq k + · exact kernel96_0_r0_7_eq k + · exact kernel96_0_r0_8_eq k + · exact kernel96_0_r0_9_eq k + · exact kernel96_0_r0_10_eq k + · exact kernel96_0_r0_11_eq k + · exact kernel96_0_r0_12_eq k + · exact kernel96_0_r0_13_eq k + · exact kernel96_0_r0_14_eq k + · exact kernel96_0_r0_15_eq k +noncomputable def kernel96_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_0_eq : ∀ k : Fin 16, kernel96_0Expr 1 0 k = kernel96_0_r1_0 k := by decide +kernel +noncomputable def kernel96_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_1_eq : ∀ k : Fin 16, kernel96_0Expr 1 1 k = kernel96_0_r1_1 k := by decide +kernel +noncomputable def kernel96_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_2_eq : ∀ k : Fin 16, kernel96_0Expr 1 2 k = kernel96_0_r1_2 k := by decide +kernel +noncomputable def kernel96_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_3_eq : ∀ k : Fin 16, kernel96_0Expr 1 3 k = kernel96_0_r1_3 k := by decide +kernel +noncomputable def kernel96_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_4_eq : ∀ k : Fin 16, kernel96_0Expr 1 4 k = kernel96_0_r1_4 k := by decide +kernel +noncomputable def kernel96_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_5_eq : ∀ k : Fin 16, kernel96_0Expr 1 5 k = kernel96_0_r1_5 k := by decide +kernel +noncomputable def kernel96_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_6_eq : ∀ k : Fin 16, kernel96_0Expr 1 6 k = kernel96_0_r1_6 k := by decide +kernel +noncomputable def kernel96_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_7_eq : ∀ k : Fin 16, kernel96_0Expr 1 7 k = kernel96_0_r1_7 k := by decide +kernel +noncomputable def kernel96_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_8_eq : ∀ k : Fin 16, kernel96_0Expr 1 8 k = kernel96_0_r1_8 k := by decide +kernel +noncomputable def kernel96_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_9_eq : ∀ k : Fin 16, kernel96_0Expr 1 9 k = kernel96_0_r1_9 k := by decide +kernel +noncomputable def kernel96_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_10_eq : ∀ k : Fin 16, kernel96_0Expr 1 10 k = kernel96_0_r1_10 k := by decide +kernel +noncomputable def kernel96_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_11_eq : ∀ k : Fin 16, kernel96_0Expr 1 11 k = kernel96_0_r1_11 k := by decide +kernel +noncomputable def kernel96_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_12_eq : ∀ k : Fin 16, kernel96_0Expr 1 12 k = kernel96_0_r1_12 k := by decide +kernel +noncomputable def kernel96_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_13_eq : ∀ k : Fin 16, kernel96_0Expr 1 13 k = kernel96_0_r1_13 k := by decide +kernel +noncomputable def kernel96_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_14_eq : ∀ k : Fin 16, kernel96_0Expr 1 14 k = kernel96_0_r1_14 k := by decide +kernel +noncomputable def kernel96_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r1_15_eq : ∀ k : Fin 16, kernel96_0Expr 1 15 k = kernel96_0_r1_15 k := by decide +kernel +noncomputable def kernel96_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel96_0_r1_0,kernel96_0_r1_1,kernel96_0_r1_2,kernel96_0_r1_3,kernel96_0_r1_4,kernel96_0_r1_5,kernel96_0_r1_6,kernel96_0_r1_7,kernel96_0_r1_8,kernel96_0_r1_9,kernel96_0_r1_10,kernel96_0_r1_11,kernel96_0_r1_12,kernel96_0_r1_13,kernel96_0_r1_14,kernel96_0_r1_15] +lemma kernel96_0_r1_eq (i k : Fin 16) : kernel96_0Expr 1 i k = kernel96_0_r1 i k := by + fin_cases i + · exact kernel96_0_r1_0_eq k + · exact kernel96_0_r1_1_eq k + · exact kernel96_0_r1_2_eq k + · exact kernel96_0_r1_3_eq k + · exact kernel96_0_r1_4_eq k + · exact kernel96_0_r1_5_eq k + · exact kernel96_0_r1_6_eq k + · exact kernel96_0_r1_7_eq k + · exact kernel96_0_r1_8_eq k + · exact kernel96_0_r1_9_eq k + · exact kernel96_0_r1_10_eq k + · exact kernel96_0_r1_11_eq k + · exact kernel96_0_r1_12_eq k + · exact kernel96_0_r1_13_eq k + · exact kernel96_0_r1_14_eq k + · exact kernel96_0_r1_15_eq k +noncomputable def kernel96_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_0_eq : ∀ k : Fin 16, kernel96_0Expr 2 0 k = kernel96_0_r2_0 k := by decide +kernel +noncomputable def kernel96_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_1_eq : ∀ k : Fin 16, kernel96_0Expr 2 1 k = kernel96_0_r2_1 k := by decide +kernel +noncomputable def kernel96_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_2_eq : ∀ k : Fin 16, kernel96_0Expr 2 2 k = kernel96_0_r2_2 k := by decide +kernel +noncomputable def kernel96_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_3_eq : ∀ k : Fin 16, kernel96_0Expr 2 3 k = kernel96_0_r2_3 k := by decide +kernel +noncomputable def kernel96_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_4_eq : ∀ k : Fin 16, kernel96_0Expr 2 4 k = kernel96_0_r2_4 k := by decide +kernel +noncomputable def kernel96_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_5_eq : ∀ k : Fin 16, kernel96_0Expr 2 5 k = kernel96_0_r2_5 k := by decide +kernel +noncomputable def kernel96_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_6_eq : ∀ k : Fin 16, kernel96_0Expr 2 6 k = kernel96_0_r2_6 k := by decide +kernel +noncomputable def kernel96_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_7_eq : ∀ k : Fin 16, kernel96_0Expr 2 7 k = kernel96_0_r2_7 k := by decide +kernel +noncomputable def kernel96_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_8_eq : ∀ k : Fin 16, kernel96_0Expr 2 8 k = kernel96_0_r2_8 k := by decide +kernel +noncomputable def kernel96_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_9_eq : ∀ k : Fin 16, kernel96_0Expr 2 9 k = kernel96_0_r2_9 k := by decide +kernel +noncomputable def kernel96_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r2_10_eq : ∀ k : Fin 16, kernel96_0Expr 2 10 k = kernel96_0_r2_10 k := by decide +kernel +noncomputable def kernel96_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r2_11_eq : ∀ k : Fin 16, kernel96_0Expr 2 11 k = kernel96_0_r2_11 k := by decide +kernel +noncomputable def kernel96_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r2_12_eq : ∀ k : Fin 16, kernel96_0Expr 2 12 k = kernel96_0_r2_12 k := by decide +kernel +noncomputable def kernel96_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r2_13_eq : ∀ k : Fin 16, kernel96_0Expr 2 13 k = kernel96_0_r2_13 k := by decide +kernel +noncomputable def kernel96_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r2_14_eq : ∀ k : Fin 16, kernel96_0Expr 2 14 k = kernel96_0_r2_14 k := by decide +kernel +noncomputable def kernel96_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel96_0_r2_15_eq : ∀ k : Fin 16, kernel96_0Expr 2 15 k = kernel96_0_r2_15 k := by decide +kernel +noncomputable def kernel96_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel96_0_r2_0,kernel96_0_r2_1,kernel96_0_r2_2,kernel96_0_r2_3,kernel96_0_r2_4,kernel96_0_r2_5,kernel96_0_r2_6,kernel96_0_r2_7,kernel96_0_r2_8,kernel96_0_r2_9,kernel96_0_r2_10,kernel96_0_r2_11,kernel96_0_r2_12,kernel96_0_r2_13,kernel96_0_r2_14,kernel96_0_r2_15] +lemma kernel96_0_r2_eq (i k : Fin 16) : kernel96_0Expr 2 i k = kernel96_0_r2 i k := by + fin_cases i + · exact kernel96_0_r2_0_eq k + · exact kernel96_0_r2_1_eq k + · exact kernel96_0_r2_2_eq k + · exact kernel96_0_r2_3_eq k + · exact kernel96_0_r2_4_eq k + · exact kernel96_0_r2_5_eq k + · exact kernel96_0_r2_6_eq k + · exact kernel96_0_r2_7_eq k + · exact kernel96_0_r2_8_eq k + · exact kernel96_0_r2_9_eq k + · exact kernel96_0_r2_10_eq k + · exact kernel96_0_r2_11_eq k + · exact kernel96_0_r2_12_eq k + · exact kernel96_0_r2_13_eq k + · exact kernel96_0_r2_14_eq k + · exact kernel96_0_r2_15_eq k +noncomputable def kernel96_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_0_eq : ∀ k : Fin 16, kernel96_0Expr 3 0 k = kernel96_0_r3_0 k := by decide +kernel +noncomputable def kernel96_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_1_eq : ∀ k : Fin 16, kernel96_0Expr 3 1 k = kernel96_0_r3_1 k := by decide +kernel +noncomputable def kernel96_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_2_eq : ∀ k : Fin 16, kernel96_0Expr 3 2 k = kernel96_0_r3_2 k := by decide +kernel +noncomputable def kernel96_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_3_eq : ∀ k : Fin 16, kernel96_0Expr 3 3 k = kernel96_0_r3_3 k := by decide +kernel +noncomputable def kernel96_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_4_eq : ∀ k : Fin 16, kernel96_0Expr 3 4 k = kernel96_0_r3_4 k := by decide +kernel +noncomputable def kernel96_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_5_eq : ∀ k : Fin 16, kernel96_0Expr 3 5 k = kernel96_0_r3_5 k := by decide +kernel +noncomputable def kernel96_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_6_eq : ∀ k : Fin 16, kernel96_0Expr 3 6 k = kernel96_0_r3_6 k := by decide +kernel +noncomputable def kernel96_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_7_eq : ∀ k : Fin 16, kernel96_0Expr 3 7 k = kernel96_0_r3_7 k := by decide +kernel +noncomputable def kernel96_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_8_eq : ∀ k : Fin 16, kernel96_0Expr 3 8 k = kernel96_0_r3_8 k := by decide +kernel +noncomputable def kernel96_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_9_eq : ∀ k : Fin 16, kernel96_0Expr 3 9 k = kernel96_0_r3_9 k := by decide +kernel +noncomputable def kernel96_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_10_eq : ∀ k : Fin 16, kernel96_0Expr 3 10 k = kernel96_0_r3_10 k := by decide +kernel +noncomputable def kernel96_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_11_eq : ∀ k : Fin 16, kernel96_0Expr 3 11 k = kernel96_0_r3_11 k := by decide +kernel +noncomputable def kernel96_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_12_eq : ∀ k : Fin 16, kernel96_0Expr 3 12 k = kernel96_0_r3_12 k := by decide +kernel +noncomputable def kernel96_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_13_eq : ∀ k : Fin 16, kernel96_0Expr 3 13 k = kernel96_0_r3_13 k := by decide +kernel +noncomputable def kernel96_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_14_eq : ∀ k : Fin 16, kernel96_0Expr 3 14 k = kernel96_0_r3_14 k := by decide +kernel +noncomputable def kernel96_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r3_15_eq : ∀ k : Fin 16, kernel96_0Expr 3 15 k = kernel96_0_r3_15 k := by decide +kernel +noncomputable def kernel96_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel96_0_r3_0,kernel96_0_r3_1,kernel96_0_r3_2,kernel96_0_r3_3,kernel96_0_r3_4,kernel96_0_r3_5,kernel96_0_r3_6,kernel96_0_r3_7,kernel96_0_r3_8,kernel96_0_r3_9,kernel96_0_r3_10,kernel96_0_r3_11,kernel96_0_r3_12,kernel96_0_r3_13,kernel96_0_r3_14,kernel96_0_r3_15] +lemma kernel96_0_r3_eq (i k : Fin 16) : kernel96_0Expr 3 i k = kernel96_0_r3 i k := by + fin_cases i + · exact kernel96_0_r3_0_eq k + · exact kernel96_0_r3_1_eq k + · exact kernel96_0_r3_2_eq k + · exact kernel96_0_r3_3_eq k + · exact kernel96_0_r3_4_eq k + · exact kernel96_0_r3_5_eq k + · exact kernel96_0_r3_6_eq k + · exact kernel96_0_r3_7_eq k + · exact kernel96_0_r3_8_eq k + · exact kernel96_0_r3_9_eq k + · exact kernel96_0_r3_10_eq k + · exact kernel96_0_r3_11_eq k + · exact kernel96_0_r3_12_eq k + · exact kernel96_0_r3_13_eq k + · exact kernel96_0_r3_14_eq k + · exact kernel96_0_r3_15_eq k +noncomputable def kernel96_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-3),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),3⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),3⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),3⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-3),3⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-4),3⟩,⟨(-8),(-1)⟩⟩,⟨⟨(-4),3⟩,⟨(-8),0⟩⟩,⟨⟨(-4),2⟩,⟨(-7),0⟩⟩,⟨⟨(-4),2⟩,⟨(-6),0⟩⟩,⟨⟨(-4),2⟩,⟨(-6),0⟩⟩,⟨⟨(-4),2⟩,⟨(-6),0⟩⟩,⟨⟨(-4),2⟩,⟨(-6),0⟩⟩] +lemma kernel96_0_r4_0_eq : ∀ k : Fin 16, kernel96_0Expr 4 0 k = kernel96_0_r4_0 k := by decide +kernel +noncomputable def kernel96_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-5),2⟩,⟨(-6),0⟩⟩,⟨⟨(-5),2⟩,⟨(-6),0⟩⟩,⟨⟨(-5),3⟩,⟨(-6),2⟩⟩,⟨⟨(-4),2⟩,⟨(-4),2⟩⟩,⟨⟨(-4),2⟩,⟨(-4),2⟩⟩,⟨⟨(-4),2⟩,⟨(-4),2⟩⟩,⟨⟨(-4),2⟩,⟨(-4),2⟩⟩,⟨⟨(-4),2⟩,⟨(-4),2⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-3),4⟩⟩] +lemma kernel96_0_r4_1_eq : ∀ k : Fin 16, kernel96_0Expr 4 1 k = kernel96_0_r4_1 k := by decide +kernel +noncomputable def kernel96_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩] +lemma kernel96_0_r4_2_eq : ∀ k : Fin 16, kernel96_0Expr 4 2 k = kernel96_0_r4_2 k := by decide +kernel +noncomputable def kernel96_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩] +lemma kernel96_0_r4_3_eq : ∀ k : Fin 16, kernel96_0Expr 4 3 k = kernel96_0_r4_3 k := by decide +kernel +noncomputable def kernel96_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_4_eq : ∀ k : Fin 16, kernel96_0Expr 4 4 k = kernel96_0_r4_4 k := by decide +kernel +noncomputable def kernel96_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_5_eq : ∀ k : Fin 16, kernel96_0Expr 4 5 k = kernel96_0_r4_5 k := by decide +kernel +noncomputable def kernel96_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_6_eq : ∀ k : Fin 16, kernel96_0Expr 4 6 k = kernel96_0_r4_6 k := by decide +kernel +noncomputable def kernel96_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_7_eq : ∀ k : Fin 16, kernel96_0Expr 4 7 k = kernel96_0_r4_7 k := by decide +kernel +noncomputable def kernel96_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_8_eq : ∀ k : Fin 16, kernel96_0Expr 4 8 k = kernel96_0_r4_8 k := by decide +kernel +noncomputable def kernel96_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_9_eq : ∀ k : Fin 16, kernel96_0Expr 4 9 k = kernel96_0_r4_9 k := by decide +kernel +noncomputable def kernel96_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_10_eq : ∀ k : Fin 16, kernel96_0Expr 4 10 k = kernel96_0_r4_10 k := by decide +kernel +noncomputable def kernel96_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel96_0_r4_11_eq : ∀ k : Fin 16, kernel96_0Expr 4 11 k = kernel96_0_r4_11 k := by decide +kernel +noncomputable def kernel96_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r4_12_eq : ∀ k : Fin 16, kernel96_0Expr 4 12 k = kernel96_0_r4_12 k := by decide +kernel +noncomputable def kernel96_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r4_13_eq : ∀ k : Fin 16, kernel96_0Expr 4 13 k = kernel96_0_r4_13 k := by decide +kernel +noncomputable def kernel96_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r4_14_eq : ∀ k : Fin 16, kernel96_0Expr 4 14 k = kernel96_0_r4_14 k := by decide +kernel +noncomputable def kernel96_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel96_0_r4_15_eq : ∀ k : Fin 16, kernel96_0Expr 4 15 k = kernel96_0_r4_15 k := by decide +kernel +noncomputable def kernel96_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel96_0_r4_0,kernel96_0_r4_1,kernel96_0_r4_2,kernel96_0_r4_3,kernel96_0_r4_4,kernel96_0_r4_5,kernel96_0_r4_6,kernel96_0_r4_7,kernel96_0_r4_8,kernel96_0_r4_9,kernel96_0_r4_10,kernel96_0_r4_11,kernel96_0_r4_12,kernel96_0_r4_13,kernel96_0_r4_14,kernel96_0_r4_15] +lemma kernel96_0_r4_eq (i k : Fin 16) : kernel96_0Expr 4 i k = kernel96_0_r4 i k := by + fin_cases i + · exact kernel96_0_r4_0_eq k + · exact kernel96_0_r4_1_eq k + · exact kernel96_0_r4_2_eq k + · exact kernel96_0_r4_3_eq k + · exact kernel96_0_r4_4_eq k + · exact kernel96_0_r4_5_eq k + · exact kernel96_0_r4_6_eq k + · exact kernel96_0_r4_7_eq k + · exact kernel96_0_r4_8_eq k + · exact kernel96_0_r4_9_eq k + · exact kernel96_0_r4_10_eq k + · exact kernel96_0_r4_11_eq k + · exact kernel96_0_r4_12_eq k + · exact kernel96_0_r4_13_eq k + · exact kernel96_0_r4_14_eq k + · exact kernel96_0_r4_15_eq k +noncomputable def kernel96_0_r5_0 : Fin 16 → CBox := ![⟨⟨15809164829017763256679,15809168047265644948437⟩,⟨1691473136654225509131,1691476354902107200760⟩⟩,⟨⟨15767215532999092552955,15767218745168721488716⟩,⟨1636692581020325585611,1636695793189954521242⟩⟩,⟨⟨15683179604122004297370,15683182804162892486971⟩,⟨1528023658146821340272,1528026858187709529740⟩⟩,⟨⟨15556798511479537492718,15556801693407606586430⟩,⟨1367239315563732661950,1367242497491801755527⟩⟩,⟨⟨15387724216043611231199,15387727373973553304542⟩,⟨1156970291213754551173,1156973449143696624377⟩⟩,⟨⟨15175565214155701463061,15175568342332709266854⟩,⟨900670404915760384084,900673533092768187736⟩⟩,⟨⟨14919945194390021562467,14919948287220057179957⟩,⟨602569858603080506768,602572951433116124111⟩⟩,⟨⟨14620572046743352224831,14620575098822577007178⟩,⟨267616298530859597390,267619350610084379586⟩⟩,⟨⟨14277314502632261531744,14277317508773869131465⟩,⟨(-98596533745571790419),(-98593527603964190855)⟩⟩,⟨⟨13890283295175235673312,13890286250435995869758⟩,⟨(-489912583182715085284),(-489909627921954889001)⟩⟩,⟨⟨13459913426896452750322,13459916326599982812286⟩,⟨(-899709483735226429008),(-899706584031696367214)⟩⟩,⟨⟨12987043930972142020930,12987046770974337724844⟩,⟨(-1321006255429280085458),(-1321003415427084381717)⟩⟩,⟨⟨12472991427193046773017,12472994203420413263403⟩,⟨(-1746581782216150093261),(-1746579005988783603053)⟩⟩,⟨⟨11919613813396641512401,11919616522098513042010⟩,⟨(-2169102712233037770974),(-2169100003531166241547)⟩⟩,⟨⟨11329360612990315697419,11329363250747167112287⟩,⟨(-2581258933107592330387),(-2581256295350740915705)⟩⟩,⟨⟨10705306816015925602970,10705309379756882092501⟩,⟨(-2975904274201982657847),(-2975901710461026168505)⟩⟩] +lemma kernel96_0_r5_0_eq : ∀ k : Fin 16, kernel96_0Expr 5 0 k = kernel96_0_r5_0 k := by decide +kernel +noncomputable def kernel96_0_r5_1 : Fin 16 → CBox := ![⟨⟨10051167511937818006602,10051169998940697078385⟩,⟨(-3346199596790541887078),(-3346197109787662815487)⟩⟩,⟨⟨9371291207851771091209,9371293615759629008069⟩,⟨(-3685754986717351712984),(-3685752578809493796318)⟩⟩,⟨⟨8670630445065302139152,8670632771876563817445⟩,⟨(-3988767393283807627891),(-3988765066472545949772)⟩⟩,⟨⟨7954689150434716052159,7954691394517442869365⟩,⟨(-4250149795075495554371),(-4250147550992768737319)⟩⟩,⟨⟨7229447060644528851739,7229449220717893199289⟩,⟨(-4465647846881475741331),(-4465645686808111393914)⟩⟩,⟨⟨6501262504650279836317,6501264579800018943277⟩,⟨(-4631939996557357064939),(-4631937921407617958092)⟩⟩,⟨⟨5776755783858072729339,5776757773505470450872⟩,⟨(-4746717273850307893397),(-4746715284202910171958)⟩⟩,⟨⟨5062676308109803507996,5062678212034074014401⟩,⟨(-4808739354604639905611),(-4808737450680369399280)⟩⟩,⟨⟨4365757483877377676444,4365759302168906149817⟩,⟨(-4817864092056788819710),(-4817862273765260346392)⟩⟩,⟨⟨3692564063419449013947,3692565796492496993819⟩,⟨(-4775048471395749089210),(-4775046738322701109378)⟩⟩,⟨⟨3049337208457718924366,3049338857007394730685⟩,⟨(-4682319860798346628989),(-4682318212248670822697)⟩⟩,⟨⟨2441842860992095544104,2441844426011807060231⟩,⟨(-4542717469214778359696),(-4542715904195066843581)⟩⟩,⟨⟨1875229118878820587387,1875230601604898148398⟩,⟨(-4360205034100026762087),(-4360203551373949201076)⟩⟩,⟨⟨1353898164848668164051,1353899566830081202731⟩,⟨(-4139556900985347938008),(-4139555499003934899317)⟩⟩,⟨⟨881397889470906771837,881399212513392718503⟩,⟨(-3886220763624036649838),(-3886219440581550703152)⟩⟩,⟨⟨460337687029362639808,460338933050077159375⟩,⟨(-3606161351195631910231),(-3606160105174917390636)⟩⟩] +lemma kernel96_0_r5_1_eq : ∀ k : Fin 16, kernel96_0Expr 5 1 k = kernel96_0_r5_1 k := by decide +kernel +noncomputable def kernel96_0_r5_2 : Fin 16 → CBox := ![⟨⟨92332011172703205059,92333182245358314737⟩,⟨(-3305690219149871210733),(-3305689048077216101022)⟩⟩,⟨⟨(-222025809822402407151),(-222024711433395232629)⟩,⟨(-2991287470280345779133),(-2991286371891338604573)⟩⟩,⟨⟨(-483158232831700783501),(-483157204748528703490)⟩,⟨(-2669421659591320170157),(-2669420631508148090104)⟩⟩,⟨⟨(-692466691538075442812),(-692465731241521276400)⟩,⟨(-2346374287495255329121),(-2346373327198701162666)⟩⟩,⟨⟨(-852264719978191963502),(-852263824872721363635)⟩,⟨(-2028075142921389190547),(-2028074247815918590639)⟩⟩,⟨⟨(-965683703446656099471),(-965682870789607455254)⟩,⟨(-1719954320969470153967),(-1719953488312421509718)⟩⟩,⟨⟨(-1036555128793089184635),(-1036554355866676169672)⟩,⟨(-1426816022892864208120),(-1426815249966451193132)⟩⟩,⟨⟨(-1069274201635519035084),(-1069273485656460001342)⟩,⟨(-1152738284252364996218),(-1152737568273305962458)⟩⟩,⟨⟨(-1068650454361179038902),(-1068649792555915453733)⟩,⟨(-901001615019634790623),(-901000953214371205443)⟩⟩,⟨⟨(-1039751447297059177074),(-1039750836836417031061)⟩,⟨(-674048237160389207455),(-674047626699747061436)⟩⟩,⟨⟨(-987745836809355842657),(-987745274926444139167)⟩,⟨(-473472237105977974061),(-473471675223066270569)⟩⟩,⟨⟨(-917751943169824137521),(-917751427099113369030)⟩,⟨(-300039589641541923871),(-300039073570831155382)⟩⟩,⟨⟨(-834697505887066325793),(-834697032926182887335)⟩,⟨(-153735727590147477011),(-153735254629264038558)⟩⟩,⟨⟨(-743195596402608720394),(-743195163878105272408)⟩,⟨(-33837200060349449420),(-33836767535846001441)⟩⟩,⟨⟨(-647440710583910383268),(-647440315910992530782)⟩,⟨60996961699402561679,60997356372320414157⟩⟩,⟨⟨(-551127946848978304196),(-551127587493906232708)⟩,⟨132619219504007017954,132619578859079089433⟩⟩] +lemma kernel96_0_r5_2_eq : ∀ k : Fin 16, kernel96_0Expr 5 2 k = kernel96_0_r5_2 k := by decide +kernel +noncomputable def kernel96_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-457396956330627312230),(-457396629867354651669)⟩,⟨183278276710489784783,183278603173762445334⟩⟩,⟨⟨(-368801103371317032910),(-368800807433167184513)⟩,⟨215500118489494436018,215500414427644284409⟩⟩,⟨⟨(-287301068566388301043),(-287300800906052727953)⟩,⟨231970660128025105884,231970927788360678970⟩⟩,⟨⟨(-214281031274163736964),(-214280789721728495807)⟩,⟨235424852016916555641,235425093569351796795⟩⟩,⟨⟨(-150584639885966676850),(-150584422395691564511)⟩,⟨228546399182955573598,228546616673230685935⟩⟩,⟨⟨(-96567262209637069075),(-96567066816336205008)⟩,⟨213881390329216064216,213881585722516928283⟩⟩,⟨⟨(-52160532216526068356),(-52160357081211106383)⟩,⟨193768158821950114122,193768333957265076095⟩⟩,⟨⟨(-16944986342470375311),(-16944829714870565716)⟩,⟨170284678998349095135,170284835625948904732⟩⟩,⟨⟨9773394078266348725,9773533824439474797⟩,⟨145213800525649921908,145213940271823047981⟩⟩,⟨⟨28886667277814707398,28886791684035435968⟩,⟨120025698130470004929,120025822536690733502⟩⟩,⟨⟨41411933322044229507,41412043843154212420⟩,⟨95876114134766848479,95876224655876831394⟩⟩,⟨⟨48424753981574769171,48424852167870647987⟩,⟨73618332776221390045,73618430962517268863⟩⟩,⟨⟨51001201582101920395,51001288603091291106⟩,⟨53826373194579484423,53826460215568855134⟩⟩,⟨⟨50170011219372719018,50170088172818769169⟩,⟨36826627866018709124,36826704819464759275⟩⟩,⟨⟨46875581971012020782,46875649859373561956⟩,⟨22735106875314145957,22735174763675687131⟩⟩,⟨⟨41951888706266013541,41951948462284320823⟩,⟨11497550174222952416,11497609930241259697⟩⟩] +lemma kernel96_0_r5_3_eq : ∀ k : Fin 16, kernel96_0Expr 5 3 k = kernel96_0_r5_3 k := by decide +kernel +noncomputable def kernel96_0_r5_4 : Fin 16 → CBox := ![⟨⟨36106771248613845752,36106823718599897000⟩,⟨2929920496298280305,2929972966284331552⟩⟩,⟨⟨29915584705931284321,29915630674861162105⟩,⟨(-3242849230194108583),(-3242803261264230799)⟩⟩,⟨⟨23822841719219728411,23822881894665510149⟩,⟨(-7351544017418602293),(-7351503841972820555)⟩⟩,⟨⟨18150258649696628378,18150293681919254126⟩,⟨(-9752008397916653625),(-9751973365694027878)⟩⟩,⟨⟨13109529249260308237,13109559721155990026⟩,⟨(-10799886254322995405),(-10799855782427313617)⟩⟩,⟨⟨8818177362966654483,8818203808337969332⟩,⟨(-10831061307582373826),(-10831034862211058977)⟩⟩,⟨⟨5316965665412035269,5316988559706573056⟩,⟨(-10147713026987437963),(-10147690132692900175)⟩⟩,⟨⟨2587536211241786085,2587555986070026664⟩,⟨(-9009587463805420043),(-9009567688977179464)⟩⟩,⟨⟨569205768796017485,569222806506643100⟩,⟨(-7629848615299050442),(-7629831577588424828)⟩⟩,⟨⟨(-825890785269071418),(-825876138948748796)⟩,⟨(-6174725884762168296),(-6174711238441845673)⟩⟩,⟨⟨(-1699844524115241257),(-1699831964581373767)⟩,⟨(-4766102337776507800),(-4766089778242640309)⟩⟩,⟨⟨(-2158486570516958913),(-2158475824906913785)⟩,⟨(-3486187670141519180),(-3486176924531474052)⟩⟩,⟨⟨(-2303434191937161191),(-2303425021798896325)⟩,⟨(-2383475872812921741),(-2383466702674656876)⟩⟩,⟨⟨(-2226552079986408428),(-2226544271249789822)⟩,⟨(-1479285865533173605),(-1479278056796554999)⟩⟩,⟨⟨(-2006579380593885614),(-2006572747711996759)⟩,⟨(-774308339306403754),(-774301706424514900)⟩⟩,⟨⟨(-1707586912470001155),(-1707581291285804988)⟩,⟨(-254719459453594660),(-254713838269398493)⟩⟩] +lemma kernel96_0_r5_4_eq : ∀ k : Fin 16, kernel96_0Expr 5 4 k = kernel96_0_r5_4 k := by decide +kernel +noncomputable def kernel96_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-1378885748896864067),(-1378880997487136651)⟩,⟨102440846153545493,102445597563272908⟩⟩,⟨⟨(-1056002082641138514),(-1055998075161034488)⟩,⟨324801408829103463,324805416309207490⟩⟩,⟨⟨(-762356214768832340),(-762352842497982342)⟩,⟨441169194575457958,441172566846307955⟩⟩,⟨⟨(-511327390891279862),(-511324559631288864)⟩,⟨478993915622462790,478996746882453788⟩⟩,⟨⟨(-308442756945744817),(-308440386126819889)⟩,⟨462702032977117814,462704403796042741⟩⟩,⟨⟨(-153490618690235958),(-153488637793052710)⟩,⟨412772833954784673,412774814851967922⟩⟩,⟨⟨(-42419277457430921),(-42417626635344095)⟩,⟨345408310104245804,345409960926332630⟩⟩,⟨⟨31061606622825689,31062979254019100⟩,⟨272644633081523131,272646005712716542⟩⟩,⟨⟨74213031351010839,74214169644442193⟩,⟨202762159897544774,202763298190976130⟩⟩,⟨⟨94330914846656791,94331857322519427⟩,⟨140868919109645623,140869861585508260⟩⟩,⟨⟨98114938212330456,98115716642580755⟩,⟨89555645622720607,89556424052970906⟩⟩,⟨⟨91297607950909841,91298249452369015⟩,⟨49545301524527087,49545943025986262⟩⟩,⟨⟨78481061278075106,78481588537509338⟩,⟨20284109714854177,20284636974288409⟩⟩,⟨⟨63127843260395868,63128275694001285⟩,⟨442556004728859,442988438334276⟩⟩,⟨⟨47655609463218649,47655963202875299⟩,⟨(-11687475342523419),(-11687121602866769)⟩⟩,⟨⟨33592643827553508,33592932612699517⟩,⟨(-17899770352315241),(-17899481567169232)⟩⟩] +lemma kernel96_0_r5_5_eq : ∀ k : Fin 16, kernel96_0Expr 5 5 k = kernel96_0_r5_5 k := by decide +kernel +noncomputable def kernel96_0_r5_6 : Fin 16 → CBox := ![⟨⟨21759680322322315,21759915458254081⟩,⟨(-19876046804493844),(-19875811668562078)⟩⟩,⟨⟨12452493045113543,12452684100459489⟩,⟨(-19068802419616344),(-19068611364270398)⟩⟩,⟨⟨5608153214896503,5608308057402004⟩,⟨(-16647654676363106),(-16647499833857605)⟩⟩,⟨⟨945123616597229,945248842921370⟩,⟨(-13491970593273689),(-13491845366949548)⟩⟩,⟨⟨(-1926832347262536),(-1926731339923105)⟩,⟨(-10214112189991105),(-10214011182651674)⟩⟩,⟨⟨(-3426695959950070),(-3426614654192381)⟩,⟨(-7200125708300919),(-7200044402543230)⟩⟩,⟨⟨(-3949159280419200),(-3949094001657571)⟩,⟨(-4657620066068512),(-4657554787306883)⟩⟩,⟨⟨(-3833926131025639),(-3833873828669389)⟩,⟨(-2663498197944428),(-2663445895588178)⟩⟩,⟨⟨(-3352192811256637),(-3352150960027763)⟩,⟨(-1206834688950850),(-1206792837721976)⟩⟩,⟨⟨(-2705295077027224),(-2705261638300262)⟩,⟨(-224373860305052),(-224340421578091)⟩⟩,⟨⟨(-2031102397143177),(-2031075747659699)⟩,⟨372212701827128,372239351310605⟩⟩,⟨⟨(-1414571866092150),(-1414550669676635)⟩,⟨677011279037993,677032475453508⟩⟩,⟨⟨(-899774489248459),(-899757673709972)⟩,⟨777485081960655,777501897499143⟩⟩,⟨⟨(-501558616350621),(-501545301020768)⟩,⟨747670814300649,747684129630502⟩⟩,⟨⟨(-215746446600388),(-215735929023773)⟩,⟨645519230770089,645529748346704⟩⟩,⟨⟨(-27336919401948),(-27328626906584)⟩,⟨513049387933637,513057680429001⟩⟩] +lemma kernel96_0_r5_6_eq : ∀ k : Fin 16, kernel96_0Expr 5 6 k = kernel96_0_r5_6 k := by decide +kernel +noncomputable def kernel96_0_r5_7 : Fin 16 → CBox := ![⟨⟨83394415257808,83400936610402⟩,⟨378193765717610,378200287070204⟩⟩,⟨⟨136736275337082,136741395388168⟩,⟨257461829981902,257466950032988⟩⟩,⟨⟨151010862327482,151014873215849⟩,⟨158800142934462,158804153822828⟩⟩,⟨⟨141300915894429,141304052282644⟩,⟨84249810134928,84252946523144⟩⟩,⟨⟨119069973046513,119072419590506⟩,⟨32183018448095,32185464992088⟩⟩,⟨⟨92355670431831,92357575756718⟩,⟨(-964910700237),(-963005375349)⟩⟩,⟨⟨66279276543196,66280756882317⟩,⟨(-19460356256142),(-19458875917021)⟩⟩,⟨⟨43682171519305,43683319752051⟩,⟨(-27471468665532),(-27470320432785)⟩⟩,⟨⟨25762405995005,25763295159814⟩,⟨(-28616450564182),(-28615561399373)⟩⟩,⟨⟨12636464691612,12637152416302⟩,⟨(-25768025858969),(-25767338134279)⟩⟩,⟨⟨3791070005531,3791600719581⟩,⟨(-21029868444903),(-21029337730854)⟩⟩,⟨⟨(-1582505944557),(-1582097017660)⟩,⟨(-15815336494130),(-15814927567234)⟩⟩,⟨⟨(-4361967877068),(-4361653520948)⟩,⟨(-10975717554020),(-10975403197901)⟩⟩,⟨⟨(-5356802137819),(-5356560785652)⟩,⟨(-6941414015619),(-6941172663451)⟩⟩,⟨⟨(-5238825853509),(-5238640950047)⟩,⟨(-3853370112244),(-3853185208782)⟩⟩,⟨⟨(-4519842997259),(-4519701533824)⟩,⟨(-1672871901042),(-1672730437608)⟩⟩] +lemma kernel96_0_r5_7_eq : ∀ k : Fin 16, kernel96_0Expr 5 7 k = kernel96_0_r5_7 k := by decide +kernel +noncomputable def kernel96_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-3558802534415),(-3558694541524)⟩,⟨(-265563330454),(-265455337562)⟩⟩,⟨⟨(-2584772722692),(-2584690329653)⟩,⟨539515375714,539597768753⟩⟩,⟨⟨(-1725983283693),(-1725920550777)⟩,⟨912315580606,912378313523⟩⟩,⟨⟨(-1038655334293),(-1038607627486)⟩,⟨1000910456780,1000958163587⟩⟩,⟨⟨(-532096355619),(-532060151450)⟩,⟨922627582729,922663786898⟩⟩,⟨⟨(-188548058159),(-188520610243)⟩,⟨763004691542,763032139457⟩⟩,⟨⟨22399235020,22420009926⟩,⟨579236204316,579256979221⟩⟩,⟨⟨134240011104,134255721045⟩,⟨405676606346,405692316287⟩⟩,⟨⟨177891196170,177903052118⟩,⟨259782197525,259794053474⟩⟩,⟨⟨178910109392,178919050170⟩,⟨147535391396,147544332174⟩⟩,⟨⟨156656085441,156662817266⟩,⟨67888557558,67895289382⟩⟩,⟨⟨124627884299,124632948852⟩,⟨16097610713,16102675265⟩⟩,⟨⟨91402180613,91405983932⟩,⟨(-13982669389),(-13978866071)⟩⟩,⟨⟨61779441361,61782296200⟩,⟨(-28467721252),(-28464866413)⟩⟩,⟨⟨37894612230,37896751701⟩,⟨(-32669140693),(-32667001222)⟩⟩,⟨⟨20164533493,20166135991⟩,⟨(-30778644994),(-30777042496)⟩⟩] +lemma kernel96_0_r5_8_eq : ∀ k : Fin 16, kernel96_0Expr 5 8 k = kernel96_0_r5_8 k := by decide +kernel +noncomputable def kernel96_0_r5_9 : Fin 16 → CBox := ![⟨⟨8023586220,8024784464⟩,⟨(-25841889262),(-25840691017)⟩⟩,⟨⟨448801173,449696914⟩,⟨(-19892843587),(-19891947845)⟩⟩,⟨⟨(-3697333213),(-3696664546)⟩,⟨(-14157529752),(-14156861085)⟩⟩,⟨⟨(-5467220873),(-5466721894)⟩,⟨(-9268667793),(-9268168815)⟩⟩,⟨⟨(-5731725278),(-5731353481)⟩,⟨(-5458196674),(-5457824877)⟩⟩,⟨⟨(-5151881458),(-5151604449)⟩,⟨(-2712768239),(-2712491230)⟩⟩,⟨⟨(-4190916539),(-4190710403)⟩,⟨(-889045291),(-888839155)⟩⟩,⟨⟨(-3146334418),(-3146181041)⟩,⟨207612439,207765816⟩⟩,⟨⟨(-2188564163),(-2188450196)⟩,⟨774348234,774462200⟩⟩,⟨⟨(-1398084212),(-1397999509)⟩,⟨984362756,984447459⟩⟩,⟨⟨(-796894732),(-796831841)⟩,⟨975863643,975926535⟩⟩,⟨⟨(-372878243),(-372831542)⟩,⟨850672006,850718707⟩⟩,⟨⟨(-97200611),(-97165969)⟩,⟨678161801,678196443⟩⟩,⟨⟨64253815,64279526⟩,⟨501529599,501555310⟩⟩,⟨⟨144104928,144123993⟩,⟨344493710,344512776⟩⟩,⟨⟨170053419,170067634⟩,⟨217355746,217369961⟩⟩] +lemma kernel96_0_r5_9_eq : ∀ k : Fin 16, kernel96_0Expr 5 9 k = kernel96_0_r5_9 k := by decide +kernel +noncomputable def kernel96_0_r5_10 : Fin 16 → CBox := ![⟨⟨163682551,163693146⟩,⟨121942116,121952710⟩⟩,⟨⟨140596111,140604015⟩,⟨55314310,55322214⟩⟩,⟨⟨111248962,111254855⟩,⟨12349840,12355733⟩⟩,⟨⟨82038985,82043385⟩,⟨(-12606728),(-12602329)⟩⟩,⟨⟨56398781,56402063⟩,⟨(-24796665),(-24793384)⟩⟩,⟨⟨35748614,35751065⟩,⟨(-28593930),(-28591480)⟩⟩,⟨⟨20255241,20257071⟩,⟨(-27371455),(-27369625)⟩⟩,⟨⟨9392120,9393488⟩,⟨(-23553881),(-23552513)⟩⟩,⟨⟨2323934,2324956⟩,⟨(-18762609),(-18761587)⟩⟩,⟨⟨(-1850145),(-1849380)⟩,⟨(-13991820),(-13991055)⟩⟩,⟨⟨(-3958462),(-3957887)⟩,⟨(-9779038),(-9778463)⟩⟩,⟨⟨(-4691835),(-4691403)⟩,⟨(-6351739),(-6351307)⟩⟩,⟨⟨(-4585332),(-4585005)⟩,⟨(-3743214),(-3742887)⟩⟩,⟨⟨(-4027140),(-4026894)⟩,⟨(-1877898),(-1877651)⟩⟩,⟨⟨(-3280808),(-3280620)⟩,⟨(-630102),(-629914)⟩⟩,⟨⟨(-2511899),(-2511755)⟩,⟨138532,138675⟩⟩] +lemma kernel96_0_r5_10_eq : ∀ k : Fin 16, kernel96_0Expr 5 10 k = kernel96_0_r5_10 k := by decide +kernel +noncomputable def kernel96_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-1813829),(-1813720)⟩,⟨557402,557512⟩⟩,⟨⟨(-1230172),(-1230088)⟩,⟨736348,736434⟩⟩,⟨⟨(-772435),(-772369)⟩,⟨762191,762257⟩⟩,⟨⟨(-433339),(-433286)⟩,⟨699500,699553⟩⟩,⟨⟨(-196130),(-196089)⟩,⟨593547,593588⟩⟩,⟨⟨(-40700),(-40669)⟩,⟨474067,474098⟩⟩,⟨⟨52730,52757⟩,⟨359037,359063⟩⟩,⟨⟨101634,101656⟩,⟨258036,258058⟩⟩,⟨⟨120363,120381⟩,⟨174992,175011⟩⟩,⟨⟨120027,120044⟩,⟨110293,110311⟩⟩,⟨⟨108796,108811⟩,⟨62324,62339⟩⟩,⟨⟨92358,92372⟩,⟨28518,28532⟩⟩,⟨⟨74448,74460⟩,⟨6046,6058⟩⟩,⟨⟨57327,57338⟩,⟨(-7793),(-7783)⟩⟩,⟨⟨42215,42224⟩,⟨(-15358),(-15349)⟩⟩,⟨⟨29619,29629⟩,⟨(-18586),(-18576)⟩⟩] +lemma kernel96_0_r5_11_eq : ∀ k : Fin 16, kernel96_0Expr 5 11 k = kernel96_0_r5_11 k := by decide +kernel +noncomputable def kernel96_0_r5_12 : Fin 16 → CBox := ![⟨⟨19603,19610⟩,⟨(-18984),(-18976)⟩⟩,⟨⟨11964,11973⟩,⟨(-17684),(-17675)⟩⟩,⟨⟨6380,6388⟩,⟨(-15487),(-15480)⟩⟩,⟨⟨2477,2486⟩,⟨(-12941),(-12932)⟩⟩,⟨⟨(-102),(-94)⟩,⟨(-10395),(-10386)⟩⟩,⟨⟨(-1683),(-1675)⟩,⟨(-8049),(-8040)⟩⟩,⟨⟨(-2539),(-2532)⟩,⟨(-6009),(-6002)⟩⟩,⟨⟨(-2892),(-2884)⟩,⟨(-4311),(-4304)⟩⟩,⟨⟨(-2911),(-2904)⟩,⟨(-2949),(-2941)⟩⟩,⟨⟨(-2726),(-2718)⟩,⟨(-1891),(-1883)⟩⟩,⟨⟨(-2427),(-2420)⟩,⟨(-1096),(-1088)⟩⟩,⟨⟨(-2080),(-2073)⟩,⟨(-520),(-512)⟩⟩,⟨⟨(-1728),(-1722)⟩,⟨(-117),(-111)⟩⟩,⟨⟨(-1396),(-1389)⟩,⟨148,155⟩⟩,⟨⟨(-1098),(-1091)⟩,⟨311,318⟩⟩,⟨⟨(-841),(-834)⟩,⟨399,406⟩⟩] +lemma kernel96_0_r5_12_eq : ∀ k : Fin 16, kernel96_0Expr 5 12 k = kernel96_0_r5_12 k := by decide +kernel +noncomputable def kernel96_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-626),(-618)⟩,⟨434,442⟩⟩,⟨⟨(-449),(-441)⟩,⟨434,442⟩⟩,⟨⟨(-309),(-301)⟩,⟨411,418⟩⟩,⟨⟨(-199),(-193)⟩,⟨375,382⟩⟩,⟨⟨(-116),(-110)⟩,⟨331,338⟩⟩,⟨⟨(-54),(-47)⟩,⟨285,293⟩⟩,⟨⟨(-10),(-3)⟩,⟨243,249⟩⟩,⟨⟨21,28⟩,⟨201,208⟩⟩,⟨⟨40,48⟩,⟨164,172⟩⟩,⟨⟨54,60⟩,⟨132,138⟩⟩,⟨⟨60,67⟩,⟨104,111⟩⟩,⟨⟨62,68⟩,⟨81,87⟩⟩,⟨⟨61,69⟩,⟨60,68⟩⟩,⟨⟨59,65⟩,⟨44,51⟩⟩,⟨⟨55,61⟩,⟨31,37⟩⟩,⟨⟨50,56⟩,⟨21,26⟩⟩] +lemma kernel96_0_r5_13_eq : ∀ k : Fin 16, kernel96_0Expr 5 13 k = kernel96_0_r5_13 k := by decide +kernel +noncomputable def kernel96_0_r5_14 : Fin 16 → CBox := ![⟨⟨45,51⟩,⟨12,18⟩⟩,⟨⟨40,46⟩,⟨5,12⟩⟩,⟨⟨35,43⟩,⟨0,7⟩⟩,⟨⟨31,38⟩,⟨(-4),3⟩⟩,⟨⟨26,33⟩,⟨(-7),(-1)⟩⟩,⟨⟨22,28⟩,⟨(-9),(-3)⟩⟩,⟨⟨19,25⟩,⟨(-10),(-4)⟩⟩,⟨⟨16,23⟩,⟨(-12),(-4)⟩⟩,⟨⟨14,20⟩,⟨(-12),(-6)⟩⟩,⟨⟨11,18⟩,⟨(-14),(-6)⟩⟩,⟨⟨10,16⟩,⟨(-13),(-7)⟩⟩,⟨⟨7,13⟩,⟨(-13),(-7)⟩⟩,⟨⟨6,12⟩,⟨(-12),(-6)⟩⟩,⟨⟨4,12⟩,⟨(-13),(-6)⟩⟩,⟨⟨3,10⟩,⟨(-12),(-5)⟩⟩,⟨⟨2,8⟩,⟨(-12),(-6)⟩⟩] +lemma kernel96_0_r5_14_eq : ∀ k : Fin 16, kernel96_0Expr 5 14 k = kernel96_0_r5_14 k := by decide +kernel +noncomputable def kernel96_0_r5_15 : Fin 16 → CBox := ![⟨⟨2,8⟩,⟨(-12),(-6)⟩⟩,⟨⟨1,7⟩,⟨(-11),(-5)⟩⟩,⟨⟨0,7⟩,⟨(-11),(-3)⟩⟩,⟨⟨0,6⟩,⟨(-10),(-4)⟩⟩,⟨⟨(-1),5⟩,⟨(-10),(-4)⟩⟩,⟨⟨(-1),5⟩,⟨(-10),(-4)⟩⟩,⟨⟨(-1),5⟩,⟨(-10),(-4)⟩⟩,⟨⟨(-3),5⟩,⟨(-10),(-2)⟩⟩,⟨⟨(-2),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-2),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-2),4⟩,⟨(-8),(-2)⟩⟩,⟨⟨(-4),4⟩,⟨(-9),(-2)⟩⟩,⟨⟨(-4),4⟩,⟨(-9),(-2)⟩⟩,⟨⟨(-4),4⟩,⟨(-9),(-2)⟩⟩,⟨⟨(-4),4⟩,⟨(-9),(-2)⟩⟩,⟨⟨(-4),4⟩,⟨(-9),(-2)⟩⟩] +lemma kernel96_0_r5_15_eq : ∀ k : Fin 16, kernel96_0Expr 5 15 k = kernel96_0_r5_15 k := by decide +kernel +noncomputable def kernel96_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel96_0_r5_0,kernel96_0_r5_1,kernel96_0_r5_2,kernel96_0_r5_3,kernel96_0_r5_4,kernel96_0_r5_5,kernel96_0_r5_6,kernel96_0_r5_7,kernel96_0_r5_8,kernel96_0_r5_9,kernel96_0_r5_10,kernel96_0_r5_11,kernel96_0_r5_12,kernel96_0_r5_13,kernel96_0_r5_14,kernel96_0_r5_15] +lemma kernel96_0_r5_eq (i k : Fin 16) : kernel96_0Expr 5 i k = kernel96_0_r5 i k := by + fin_cases i + · exact kernel96_0_r5_0_eq k + · exact kernel96_0_r5_1_eq k + · exact kernel96_0_r5_2_eq k + · exact kernel96_0_r5_3_eq k + · exact kernel96_0_r5_4_eq k + · exact kernel96_0_r5_5_eq k + · exact kernel96_0_r5_6_eq k + · exact kernel96_0_r5_7_eq k + · exact kernel96_0_r5_8_eq k + · exact kernel96_0_r5_9_eq k + · exact kernel96_0_r5_10_eq k + · exact kernel96_0_r5_11_eq k + · exact kernel96_0_r5_12_eq k + · exact kernel96_0_r5_13_eq k + · exact kernel96_0_r5_14_eq k + · exact kernel96_0_r5_15_eq k +noncomputable def kernel96_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel96_0_r0,kernel96_0_r1,kernel96_0_r2,kernel96_0_r3,kernel96_0_r4,kernel96_0_r5] +lemma kernel96_0_eq (j : Fin 6) (i k : Fin 16) : kernel96_0Expr j i k = kernel96_0 j i k := by + fin_cases j + · exact kernel96_0_r0_eq i k + · exact kernel96_0_r1_eq i k + · exact kernel96_0_r2_eq i k + · exact kernel96_0_r3_eq i k + · exact kernel96_0_r4_eq i k + · exact kernel96_0_r5_eq i k +lemma kernel96_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel96_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(96:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel96_0_eq] + unfold kernel96_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans96_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel96_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans96 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel96_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r0_0_eq : ∀ k : Fin 16, kernel96_1Expr 0 0 k = kernel96_1_r0_0 k := by decide +kernel +noncomputable def kernel96_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r0_1_eq : ∀ k : Fin 16, kernel96_1Expr 0 1 k = kernel96_1_r0_1 k := by decide +kernel +noncomputable def kernel96_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r0_2_eq : ∀ k : Fin 16, kernel96_1Expr 0 2 k = kernel96_1_r0_2 k := by decide +kernel +noncomputable def kernel96_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r0_3_eq : ∀ k : Fin 16, kernel96_1Expr 0 3 k = kernel96_1_r0_3 k := by decide +kernel +noncomputable def kernel96_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r0_4_eq : ∀ k : Fin 16, kernel96_1Expr 0 4 k = kernel96_1_r0_4 k := by decide +kernel +noncomputable def kernel96_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel96_1_r0_5_eq : ∀ k : Fin 16, kernel96_1Expr 0 5 k = kernel96_1_r0_5 k := by decide +kernel +noncomputable def kernel96_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel96_1_r0_6_eq : ∀ k : Fin 16, kernel96_1Expr 0 6 k = kernel96_1_r0_6 k := by decide +kernel +noncomputable def kernel96_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel96_1_r0_7_eq : ∀ k : Fin 16, kernel96_1Expr 0 7 k = kernel96_1_r0_7 k := by decide +kernel +noncomputable def kernel96_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel96_1_r0_8_eq : ∀ k : Fin 16, kernel96_1Expr 0 8 k = kernel96_1_r0_8 k := by decide +kernel +noncomputable def kernel96_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel96_1_r0_9_eq : ∀ k : Fin 16, kernel96_1Expr 0 9 k = kernel96_1_r0_9 k := by decide +kernel +noncomputable def kernel96_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel96_1_r0_10_eq : ∀ k : Fin 16, kernel96_1Expr 0 10 k = kernel96_1_r0_10 k := by decide +kernel +noncomputable def kernel96_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel96_1_r0_11_eq : ∀ k : Fin 16, kernel96_1Expr 0 11 k = kernel96_1_r0_11 k := by decide +kernel +noncomputable def kernel96_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel96_1_r0_12_eq : ∀ k : Fin 16, kernel96_1Expr 0 12 k = kernel96_1_r0_12 k := by decide +kernel +noncomputable def kernel96_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel96_1_r0_13_eq : ∀ k : Fin 16, kernel96_1Expr 0 13 k = kernel96_1_r0_13 k := by decide +kernel +noncomputable def kernel96_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel96_1_r0_14_eq : ∀ k : Fin 16, kernel96_1Expr 0 14 k = kernel96_1_r0_14 k := by decide +kernel +noncomputable def kernel96_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel96_1_r0_15_eq : ∀ k : Fin 16, kernel96_1Expr 0 15 k = kernel96_1_r0_15 k := by decide +kernel +noncomputable def kernel96_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel96_1_r0_0,kernel96_1_r0_1,kernel96_1_r0_2,kernel96_1_r0_3,kernel96_1_r0_4,kernel96_1_r0_5,kernel96_1_r0_6,kernel96_1_r0_7,kernel96_1_r0_8,kernel96_1_r0_9,kernel96_1_r0_10,kernel96_1_r0_11,kernel96_1_r0_12,kernel96_1_r0_13,kernel96_1_r0_14,kernel96_1_r0_15] +lemma kernel96_1_r0_eq (i k : Fin 16) : kernel96_1Expr 0 i k = kernel96_1_r0 i k := by + fin_cases i + · exact kernel96_1_r0_0_eq k + · exact kernel96_1_r0_1_eq k + · exact kernel96_1_r0_2_eq k + · exact kernel96_1_r0_3_eq k + · exact kernel96_1_r0_4_eq k + · exact kernel96_1_r0_5_eq k + · exact kernel96_1_r0_6_eq k + · exact kernel96_1_r0_7_eq k + · exact kernel96_1_r0_8_eq k + · exact kernel96_1_r0_9_eq k + · exact kernel96_1_r0_10_eq k + · exact kernel96_1_r0_11_eq k + · exact kernel96_1_r0_12_eq k + · exact kernel96_1_r0_13_eq k + · exact kernel96_1_r0_14_eq k + · exact kernel96_1_r0_15_eq k +noncomputable def kernel96_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel96_1_r1_0_eq : ∀ k : Fin 16, kernel96_1Expr 1 0 k = kernel96_1_r1_0 k := by decide +kernel +noncomputable def kernel96_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel96_1_r1_1_eq : ∀ k : Fin 16, kernel96_1Expr 1 1 k = kernel96_1_r1_1 k := by decide +kernel +noncomputable def kernel96_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel96_1_r1_2_eq : ∀ k : Fin 16, kernel96_1Expr 1 2 k = kernel96_1_r1_2 k := by decide +kernel +noncomputable def kernel96_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel96_1_r1_3_eq : ∀ k : Fin 16, kernel96_1Expr 1 3 k = kernel96_1_r1_3 k := by decide +kernel +noncomputable def kernel96_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel96_1_r1_4_eq : ∀ k : Fin 16, kernel96_1Expr 1 4 k = kernel96_1_r1_4 k := by decide +kernel +noncomputable def kernel96_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel96_1_r1_5_eq : ∀ k : Fin 16, kernel96_1Expr 1 5 k = kernel96_1_r1_5 k := by decide +kernel +noncomputable def kernel96_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel96_1_r1_6_eq : ∀ k : Fin 16, kernel96_1Expr 1 6 k = kernel96_1_r1_6 k := by decide +kernel +noncomputable def kernel96_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel96_1_r1_7_eq : ∀ k : Fin 16, kernel96_1Expr 1 7 k = kernel96_1_r1_7 k := by decide +kernel +noncomputable def kernel96_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel96_1_r1_8_eq : ∀ k : Fin 16, kernel96_1Expr 1 8 k = kernel96_1_r1_8 k := by decide +kernel +noncomputable def kernel96_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel96_1_r1_9_eq : ∀ k : Fin 16, kernel96_1Expr 1 9 k = kernel96_1_r1_9 k := by decide +kernel +noncomputable def kernel96_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r1_10_eq : ∀ k : Fin 16, kernel96_1Expr 1 10 k = kernel96_1_r1_10 k := by decide +kernel +noncomputable def kernel96_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r1_11_eq : ∀ k : Fin 16, kernel96_1Expr 1 11 k = kernel96_1_r1_11 k := by decide +kernel +noncomputable def kernel96_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r1_12_eq : ∀ k : Fin 16, kernel96_1Expr 1 12 k = kernel96_1_r1_12 k := by decide +kernel +noncomputable def kernel96_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r1_13_eq : ∀ k : Fin 16, kernel96_1Expr 1 13 k = kernel96_1_r1_13 k := by decide +kernel +noncomputable def kernel96_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r1_14_eq : ∀ k : Fin 16, kernel96_1Expr 1 14 k = kernel96_1_r1_14 k := by decide +kernel +noncomputable def kernel96_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel96_1_r1_15_eq : ∀ k : Fin 16, kernel96_1Expr 1 15 k = kernel96_1_r1_15 k := by decide +kernel +noncomputable def kernel96_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel96_1_r1_0,kernel96_1_r1_1,kernel96_1_r1_2,kernel96_1_r1_3,kernel96_1_r1_4,kernel96_1_r1_5,kernel96_1_r1_6,kernel96_1_r1_7,kernel96_1_r1_8,kernel96_1_r1_9,kernel96_1_r1_10,kernel96_1_r1_11,kernel96_1_r1_12,kernel96_1_r1_13,kernel96_1_r1_14,kernel96_1_r1_15] +lemma kernel96_1_r1_eq (i k : Fin 16) : kernel96_1Expr 1 i k = kernel96_1_r1 i k := by + fin_cases i + · exact kernel96_1_r1_0_eq k + · exact kernel96_1_r1_1_eq k + · exact kernel96_1_r1_2_eq k + · exact kernel96_1_r1_3_eq k + · exact kernel96_1_r1_4_eq k + · exact kernel96_1_r1_5_eq k + · exact kernel96_1_r1_6_eq k + · exact kernel96_1_r1_7_eq k + · exact kernel96_1_r1_8_eq k + · exact kernel96_1_r1_9_eq k + · exact kernel96_1_r1_10_eq k + · exact kernel96_1_r1_11_eq k + · exact kernel96_1_r1_12_eq k + · exact kernel96_1_r1_13_eq k + · exact kernel96_1_r1_14_eq k + · exact kernel96_1_r1_15_eq k +noncomputable def kernel96_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel96_1_r2_0_eq : ∀ k : Fin 16, kernel96_1Expr 2 0 k = kernel96_1_r2_0 k := by decide +kernel +noncomputable def kernel96_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel96_1_r2_1_eq : ∀ k : Fin 16, kernel96_1Expr 2 1 k = kernel96_1_r2_1 k := by decide +kernel +noncomputable def kernel96_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel96_1_r2_2_eq : ∀ k : Fin 16, kernel96_1Expr 2 2 k = kernel96_1_r2_2 k := by decide +kernel +noncomputable def kernel96_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel96_1_r2_3_eq : ∀ k : Fin 16, kernel96_1Expr 2 3 k = kernel96_1_r2_3 k := by decide +kernel +noncomputable def kernel96_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel96_1_r2_4_eq : ∀ k : Fin 16, kernel96_1Expr 2 4 k = kernel96_1_r2_4 k := by decide +kernel +noncomputable def kernel96_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel96_1_r2_5_eq : ∀ k : Fin 16, kernel96_1Expr 2 5 k = kernel96_1_r2_5 k := by decide +kernel +noncomputable def kernel96_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel96_1_r2_6_eq : ∀ k : Fin 16, kernel96_1Expr 2 6 k = kernel96_1_r2_6 k := by decide +kernel +noncomputable def kernel96_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel96_1_r2_7_eq : ∀ k : Fin 16, kernel96_1Expr 2 7 k = kernel96_1_r2_7 k := by decide +kernel +noncomputable def kernel96_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel96_1_r2_8_eq : ∀ k : Fin 16, kernel96_1Expr 2 8 k = kernel96_1_r2_8 k := by decide +kernel +noncomputable def kernel96_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel96_1_r2_9_eq : ∀ k : Fin 16, kernel96_1Expr 2 9 k = kernel96_1_r2_9 k := by decide +kernel +noncomputable def kernel96_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel96_1_r2_10_eq : ∀ k : Fin 16, kernel96_1Expr 2 10 k = kernel96_1_r2_10 k := by decide +kernel +noncomputable def kernel96_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel96_1_r2_11_eq : ∀ k : Fin 16, kernel96_1Expr 2 11 k = kernel96_1_r2_11 k := by decide +kernel +noncomputable def kernel96_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel96_1_r2_12_eq : ∀ k : Fin 16, kernel96_1Expr 2 12 k = kernel96_1_r2_12 k := by decide +kernel +noncomputable def kernel96_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel96_1_r2_13_eq : ∀ k : Fin 16, kernel96_1Expr 2 13 k = kernel96_1_r2_13 k := by decide +kernel +noncomputable def kernel96_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel96_1_r2_14_eq : ∀ k : Fin 16, kernel96_1Expr 2 14 k = kernel96_1_r2_14 k := by decide +kernel +noncomputable def kernel96_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel96_1_r2_15_eq : ∀ k : Fin 16, kernel96_1Expr 2 15 k = kernel96_1_r2_15 k := by decide +kernel +noncomputable def kernel96_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel96_1_r2_0,kernel96_1_r2_1,kernel96_1_r2_2,kernel96_1_r2_3,kernel96_1_r2_4,kernel96_1_r2_5,kernel96_1_r2_6,kernel96_1_r2_7,kernel96_1_r2_8,kernel96_1_r2_9,kernel96_1_r2_10,kernel96_1_r2_11,kernel96_1_r2_12,kernel96_1_r2_13,kernel96_1_r2_14,kernel96_1_r2_15] +lemma kernel96_1_r2_eq (i k : Fin 16) : kernel96_1Expr 2 i k = kernel96_1_r2 i k := by + fin_cases i + · exact kernel96_1_r2_0_eq k + · exact kernel96_1_r2_1_eq k + · exact kernel96_1_r2_2_eq k + · exact kernel96_1_r2_3_eq k + · exact kernel96_1_r2_4_eq k + · exact kernel96_1_r2_5_eq k + · exact kernel96_1_r2_6_eq k + · exact kernel96_1_r2_7_eq k + · exact kernel96_1_r2_8_eq k + · exact kernel96_1_r2_9_eq k + · exact kernel96_1_r2_10_eq k + · exact kernel96_1_r2_11_eq k + · exact kernel96_1_r2_12_eq k + · exact kernel96_1_r2_13_eq k + · exact kernel96_1_r2_14_eq k + · exact kernel96_1_r2_15_eq k +noncomputable def kernel96_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel96_1_r3_0_eq : ∀ k : Fin 16, kernel96_1Expr 3 0 k = kernel96_1_r3_0 k := by decide +kernel +noncomputable def kernel96_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel96_1_r3_1_eq : ∀ k : Fin 16, kernel96_1Expr 3 1 k = kernel96_1_r3_1 k := by decide +kernel +noncomputable def kernel96_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel96_1_r3_2_eq : ∀ k : Fin 16, kernel96_1Expr 3 2 k = kernel96_1_r3_2 k := by decide +kernel +noncomputable def kernel96_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel96_1_r3_3_eq : ∀ k : Fin 16, kernel96_1Expr 3 3 k = kernel96_1_r3_3 k := by decide +kernel +noncomputable def kernel96_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel96_1_r3_4_eq : ∀ k : Fin 16, kernel96_1Expr 3 4 k = kernel96_1_r3_4 k := by decide +kernel +noncomputable def kernel96_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel96_1_r3_5_eq : ∀ k : Fin 16, kernel96_1Expr 3 5 k = kernel96_1_r3_5 k := by decide +kernel +noncomputable def kernel96_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel96_1_r3_6_eq : ∀ k : Fin 16, kernel96_1Expr 3 6 k = kernel96_1_r3_6 k := by decide +kernel +noncomputable def kernel96_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel96_1_r3_7_eq : ∀ k : Fin 16, kernel96_1Expr 3 7 k = kernel96_1_r3_7 k := by decide +kernel +noncomputable def kernel96_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel96_1_r3_8_eq : ∀ k : Fin 16, kernel96_1Expr 3 8 k = kernel96_1_r3_8 k := by decide +kernel +noncomputable def kernel96_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel96_1_r3_9_eq : ∀ k : Fin 16, kernel96_1Expr 3 9 k = kernel96_1_r3_9 k := by decide +kernel +noncomputable def kernel96_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel96_1_r3_10_eq : ∀ k : Fin 16, kernel96_1Expr 3 10 k = kernel96_1_r3_10 k := by decide +kernel +noncomputable def kernel96_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel96_1_r3_11_eq : ∀ k : Fin 16, kernel96_1Expr 3 11 k = kernel96_1_r3_11 k := by decide +kernel +noncomputable def kernel96_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel96_1_r3_12_eq : ∀ k : Fin 16, kernel96_1Expr 3 12 k = kernel96_1_r3_12 k := by decide +kernel +noncomputable def kernel96_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel96_1_r3_13_eq : ∀ k : Fin 16, kernel96_1Expr 3 13 k = kernel96_1_r3_13 k := by decide +kernel +noncomputable def kernel96_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel96_1_r3_14_eq : ∀ k : Fin 16, kernel96_1Expr 3 14 k = kernel96_1_r3_14 k := by decide +kernel +noncomputable def kernel96_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel96_1_r3_15_eq : ∀ k : Fin 16, kernel96_1Expr 3 15 k = kernel96_1_r3_15 k := by decide +kernel +noncomputable def kernel96_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel96_1_r3_0,kernel96_1_r3_1,kernel96_1_r3_2,kernel96_1_r3_3,kernel96_1_r3_4,kernel96_1_r3_5,kernel96_1_r3_6,kernel96_1_r3_7,kernel96_1_r3_8,kernel96_1_r3_9,kernel96_1_r3_10,kernel96_1_r3_11,kernel96_1_r3_12,kernel96_1_r3_13,kernel96_1_r3_14,kernel96_1_r3_15] +lemma kernel96_1_r3_eq (i k : Fin 16) : kernel96_1Expr 3 i k = kernel96_1_r3 i k := by + fin_cases i + · exact kernel96_1_r3_0_eq k + · exact kernel96_1_r3_1_eq k + · exact kernel96_1_r3_2_eq k + · exact kernel96_1_r3_3_eq k + · exact kernel96_1_r3_4_eq k + · exact kernel96_1_r3_5_eq k + · exact kernel96_1_r3_6_eq k + · exact kernel96_1_r3_7_eq k + · exact kernel96_1_r3_8_eq k + · exact kernel96_1_r3_9_eq k + · exact kernel96_1_r3_10_eq k + · exact kernel96_1_r3_11_eq k + · exact kernel96_1_r3_12_eq k + · exact kernel96_1_r3_13_eq k + · exact kernel96_1_r3_14_eq k + · exact kernel96_1_r3_15_eq k +noncomputable def kernel96_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-36),(-6)⟩,⟨(-15),18⟩⟩,⟨⟨(-36),(-6)⟩,⟨(-15),18⟩⟩,⟨⟨(-36),(-6)⟩,⟨(-15),18⟩⟩,⟨⟨(-36),(-6)⟩,⟨(-15),18⟩⟩,⟨⟨(-36),(-6)⟩,⟨(-15),18⟩⟩,⟨⟨(-35),(-6)⟩,⟨(-11),18⟩⟩,⟨⟨(-35),(-6)⟩,⟨(-11),18⟩⟩,⟨⟨(-35),(-6)⟩,⟨(-11),18⟩⟩,⟨⟨(-35),(-6)⟩,⟨(-11),18⟩⟩,⟨⟨(-35),(-1)⟩,⟨(-12),22⟩⟩,⟨⟨(-35),3⟩,⟨(-13),23⟩⟩,⟨⟨(-31),3⟩,⟨(-9),22⟩⟩,⟨⟨(-26),3⟩,⟨(-9),21⟩⟩,⟨⟨(-26),3⟩,⟨(-9),21⟩⟩,⟨⟨(-26),3⟩,⟨(-9),21⟩⟩,⟨⟨(-26),3⟩,⟨(-9),21⟩⟩] +lemma kernel96_1_r4_0_eq : ∀ k : Fin 16, kernel96_1Expr 4 0 k = kernel96_1_r4_0 k := by decide +kernel +noncomputable def kernel96_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-26),4⟩,⟨(-9),25⟩⟩,⟨⟨(-26),4⟩,⟨(-9),25⟩⟩,⟨⟨(-27),12⟩,⟨(-14),25⟩⟩,⟨⟨(-18),12⟩,⟨(-10),20⟩⟩,⟨⟨(-18),12⟩,⟨(-10),20⟩⟩,⟨⟨(-18),12⟩,⟨(-10),20⟩⟩,⟨⟨(-18),12⟩,⟨(-10),20⟩⟩,⟨⟨(-18),12⟩,⟨(-10),20⟩⟩,⟨⟨(-18),16⟩,⟨(-11),20⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-15),20⟩,⟨(-16),19⟩⟩] +lemma kernel96_1_r4_1_eq : ∀ k : Fin 16, kernel96_1Expr 4 1 k = kernel96_1_r4_1 k := by decide +kernel +noncomputable def kernel96_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-14),11⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩] +lemma kernel96_1_r4_2_eq : ∀ k : Fin 16, kernel96_1Expr 4 2 k = kernel96_1_r4_2 k := by decide +kernel +noncomputable def kernel96_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-10),15⟩,⟨(-11),14⟩⟩,⟨⟨(-10),15⟩,⟨(-11),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),15⟩,⟨(-15),10⟩⟩,⟨⟨(-16),15⟩,⟨(-19),11⟩⟩,⟨⟨(-16),15⟩,⟨(-19),11⟩⟩,⟨⟨(-16),15⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-15),11⟩⟩,⟨⟨(-15),10⟩,⟨(-15),11⟩⟩,⟨⟨(-20),11⟩,⟨(-15),16⟩⟩] +lemma kernel96_1_r4_3_eq : ∀ k : Fin 16, kernel96_1Expr 4 3 k = kernel96_1_r4_3 k := by decide +kernel +noncomputable def kernel96_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel96_1_r4_4_eq : ∀ k : Fin 16, kernel96_1Expr 4 4 k = kernel96_1_r4_4 k := by decide +kernel +noncomputable def kernel96_1_r4_5 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel96_1_r4_5_eq : ∀ k : Fin 16, kernel96_1Expr 4 5 k = kernel96_1_r4_5 k := by decide +kernel +noncomputable def kernel96_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel96_1_r4_6_eq : ∀ k : Fin 16, kernel96_1Expr 4 6 k = kernel96_1_r4_6 k := by decide +kernel +noncomputable def kernel96_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel96_1_r4_7_eq : ∀ k : Fin 16, kernel96_1Expr 4 7 k = kernel96_1_r4_7 k := by decide +kernel +noncomputable def kernel96_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel96_1_r4_8_eq : ∀ k : Fin 16, kernel96_1Expr 4 8 k = kernel96_1_r4_8 k := by decide +kernel +noncomputable def kernel96_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel96_1_r4_9_eq : ∀ k : Fin 16, kernel96_1Expr 4 9 k = kernel96_1_r4_9 k := by decide +kernel +noncomputable def kernel96_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel96_1_r4_10_eq : ∀ k : Fin 16, kernel96_1Expr 4 10 k = kernel96_1_r4_10 k := by decide +kernel +noncomputable def kernel96_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel96_1_r4_11_eq : ∀ k : Fin 16, kernel96_1Expr 4 11 k = kernel96_1_r4_11 k := by decide +kernel +noncomputable def kernel96_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel96_1_r4_12_eq : ∀ k : Fin 16, kernel96_1Expr 4 12 k = kernel96_1_r4_12 k := by decide +kernel +noncomputable def kernel96_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel96_1_r4_13_eq : ∀ k : Fin 16, kernel96_1Expr 4 13 k = kernel96_1_r4_13 k := by decide +kernel +noncomputable def kernel96_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel96_1_r4_14_eq : ∀ k : Fin 16, kernel96_1Expr 4 14 k = kernel96_1_r4_14 k := by decide +kernel +noncomputable def kernel96_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel96_1_r4_15_eq : ∀ k : Fin 16, kernel96_1Expr 4 15 k = kernel96_1_r4_15 k := by decide +kernel +noncomputable def kernel96_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel96_1_r4_0,kernel96_1_r4_1,kernel96_1_r4_2,kernel96_1_r4_3,kernel96_1_r4_4,kernel96_1_r4_5,kernel96_1_r4_6,kernel96_1_r4_7,kernel96_1_r4_8,kernel96_1_r4_9,kernel96_1_r4_10,kernel96_1_r4_11,kernel96_1_r4_12,kernel96_1_r4_13,kernel96_1_r4_14,kernel96_1_r4_15] +lemma kernel96_1_r4_eq (i k : Fin 16) : kernel96_1Expr 4 i k = kernel96_1_r4 i k := by + fin_cases i + · exact kernel96_1_r4_0_eq k + · exact kernel96_1_r4_1_eq k + · exact kernel96_1_r4_2_eq k + · exact kernel96_1_r4_3_eq k + · exact kernel96_1_r4_4_eq k + · exact kernel96_1_r4_5_eq k + · exact kernel96_1_r4_6_eq k + · exact kernel96_1_r4_7_eq k + · exact kernel96_1_r4_8_eq k + · exact kernel96_1_r4_9_eq k + · exact kernel96_1_r4_10_eq k + · exact kernel96_1_r4_11_eq k + · exact kernel96_1_r4_12_eq k + · exact kernel96_1_r4_13_eq k + · exact kernel96_1_r4_14_eq k + · exact kernel96_1_r4_15_eq k +noncomputable def kernel96_1_r5_0 : Fin 16 → CBox := ![⟨⟨3139358208480960819461,3139370433984833195669⟩,⟨(-57405003113686798674927),(-57404990888182926298123)⟩⟩,⟨⟨2948982027429427015868,2948994230048988050022⟩,⟨(-57243804938681642312566),(-57243792736062081277812)⟩⟩,⟨⟨2571474377433370643963,2571486534387433327296⟩,⟨(-56921061672522934130698),(-56921049515568871446755)⟩⟩,⟨⟨2013280880106400208083,2013292968861388991413⟩,⟨(-56436135984282432315518),(-56436123895527443531572)⟩⟩,⟨⟨1283960151290894476771,1283972149681524598746⟩,⟨(-55788210949537999785784),(-55788198951147369663178)⟩⟩,⟨⟨396051223532286511154,396063109879943242208⟩,⟨(-54976450880707712761465),(-54976438994360056029772)⟩⟩,⟨⟨(-635104345373216134908),(-635092592147526418268)⟩,⟨(-54000205830442218126123),(-54000194077216528408823)⟩⟩,⟨⟨(-1791586236205043342414),(-1791574636470776036021)⟩,⟨(-52859251565216036242066),(-52859239965481768935000)⟩⟩,⟨⟨(-3053165228244602132398),(-3053153801561447454165)⟩,⟨(-51554055152535203593025),(-51554043725852048914101)⟩⟩,⟨⟨(-4397618772268719843920),(-4397607537287273367957)⟩,⟨(-50086054920439365514353),(-50086043685457919037686)⟩⟩,⟨⟨(-5801091002364800112168),(-5801079976739449252389)⟩,⟨(-48457942487677981262274),(-48457931462052630401776)⟩⟩,⟨⟨(-7238494745030911550834),(-7238483944411539998531)⟩,⟨(-46673933881034662434068),(-46673923080415290881045)⟩⟩,⟨⟨(-8683951666027458252208),(-8683941105815701003528)⟩,⟨(-44740016497859979674238),(-44740005937648222424832)⟩⟩,⟨⟨(-10111265090146372169033),(-10111254784537362170462)⟩,⟨(-42664158891134356531382),(-42664148585525346532081)⟩⟩,⟨⟨(-11494418281407499749718),(-11494408243358636067266)⟩,⟨(-40456471055751605131313),(-40456461017702741448127)⟩⟩,⟨⟨(-12808089201706800376305),(-12808079442871253794005)⟩,⟨(-38129304125589848308730),(-38129294366754301725698)⟩⟩] +lemma kernel96_1_r5_0_eq : ∀ k : Fin 16, kernel96_1Expr 5 0 k = kernel96_1_r5_0 k := by decide +kernel +noncomputable def kernel96_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-14028171051628445791326),(-14028161582354868809495)⟩,⟨(-35697280122615330486609),(-35697270653341753504046)⟩⟩,⟨⟨(-15132286363272807029217),(-15132277192541959298051)⟩,⟨(-33177244620395649454755),(-33177235449664801722863)⟩⟩,⟨⟨(-16100281172777166004063),(-16100272308238859550128)⟩,⟨(-30588137842151800284964),(-30588128977613493830382)⟩⟩,⟨⟨(-16914684963625232748345),(-16914676411543113344797)⟩,⟨(-27950782735714495179808),(-27950774183632375775693)⟩⟩,⟨⟨(-17561121741502870571810),(-17561113506823894817885)⟩,⟨(-25287591854482079465670),(-25287583619803103711259)⟩⟩,⟨⟨(-18028657862944658933393),(-18028649949238876267116)⟩,⟨(-22622198304259671917091),(-22622190390553889250406)⟩⟩,⟨⟨(-18310073150615628591929),(-18310065560192919391127)⟩,⟨(-19979019447224138654376),(-19979011856801429453241)⟩⟩,⟨⟨(-18402043417671085302035),(-18402036151494088034249)⟩,⟨(-17382765332273968180689),(-17382758066096970912647)⟩⟩,⟨⟨(-18305224781254664232594),(-18305217839115302747904)⟩,⟨(-14857906779835468624082),(-14857899837696107139208)⟩⟩,⟨⟨(-18024233026062248943822),(-18024226406531277106442)⟩,⟨(-12428120529720895085580),(-12428113910189923248076)⟩⟩,⟨⟨(-17567514691372709561143),(-17567508391961927927627)⟩,⟨(-10115730707817589610950),(-10115724408406807977359)⟩⟩,⟨⟨(-16947110375933294540440),(-16947104393026714071819)⟩,⟨(-7941166953882395137268),(-7941160970975814668629)⟩⟩,⟨⟨(-16178314819788334111127),(-16178309148851559450675)⟩,⟨(-5922459773934466656218),(-5922454102997691995793)⟩⟩,⟨⟨(-15279242445954532179123),(-15279237081265795545001)⟩,⟨(-4074792978449804022486),(-4074787613761067388433)⟩⟩,⟨⟨(-14270311016812623966600),(-14270305951673807451518)⟩,⟨(-2410131420887260309651),(-2410126355748443794671)⟩⟩,⟨⟨(-13173659672932613818577),(-13173654900223361892278)⟩,⟨(-936939699747393172951),(-936934927038141246783)⟩⟩] +lemma kernel96_1_r5_1_eq : ∀ k : Fin 16, kernel96_1Expr 5 1 k = kernel96_1_r5_1 k := by decide +kernel +noncomputable def kernel96_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-12012520665014361407698),(-12012516177017482238438)⟩,⟨339995886575044597144,340000374571923766254⟩⟩,⟨⟨(-10810566376257985944200),(-10810562164526475720550)⟩,⟨1419633902272796876203,1419638114004307099693⟩⟩,⟨⟨(-9591254612732047743764),(-9591250668383210928617)⟩,⟨2304629182678617841935,2304633127027454656913⟩⟩,⟨⟨(-8377195500563993024980),(-8377191814170069332802)⟩,⟨3001170259362100180257,3001173945756023872270⟩⟩,⟨⟨(-7189562614318343116054),(-7189559176154317041341)⟩,⟨3518708853677621671253,3518712291841647745812⟩⟩,⟨⟨(-6047569180058692440199),(-6047565979828469471622)⟩,⟨3869592151184398515012,3869595351414621483472⟩⟩,⟨⟨(-4968027409665141474924),(-4968024437160641384904)⟩,⟨4068612764157431828130,4068615736661931918060⟩⟩,⟨⟨(-3965005366180449159669),(-3965002610933046052153)⟩,⟨4132494779047886434925,4132497534295289542379⟩⟩,⟨⟨(-3049591404507430963331),(-3049588856075919213659)⟩,⟨4079336886265060372796,4079339434696572122432⟩⟩,⟨⟨(-2229771417738993843066),(-2229769065456876349445)⟩,⟨3928035142156568485749,3928037494438685979354⟩⟩,⟨⟨(-1510419092273942278745),(-1510416925702418663823)⟩,⟨3697708344134381243170,3697710510705904858091⟩⟩,⟨⟨(-893394418501667572860),(-893392427194181325428)⟩,⟨3407148279179666565492,3407150270487152812938⟩⟩,⟨⟨(-377741078044078993301),(-377739251783919124636)⟩,⟨3074315293102337880743,3074317119362497749433⟩⟩,⟨⟨40030707081270973860,40032378413547045892⟩,⟨2715896828359365254978,2715898499691641327041⟩⟩,⟨⟨365592519886071169107,365594046082333087668⟩,⟨2346942975030664271026,2346944501226926189620⟩⟩,⟨⟨606396224236805004932,606397614906790586392⟩,⟨1980588886525560937870,1980590277195546519366⟩⟩] +lemma kernel96_1_r5_2_eq : ∀ k : Fin 16, kernel96_1Expr 5 2 k = kernel96_1_r5_2 k := by decide +kernel +noncomputable def kernel96_1_r5_3 : Fin 16 → CBox := ![⟨⟨771242730026407737112,771243994378696564670⟩,⟨1627869388280284994832,1627870652632573822428⟩⟩,⟨⟨869841335201931374864,869842482230850142894⟩,⟨1297626516059087957608,1297627663088006725660⟩⟩,⟨⟨912379008267042345125,912380046520068215300⟩,⟨996506330865799082830,996507369118824953020⟩⟩,⟨⟨909117092966998243566,909118030707047830836⟩,⟨729037406711693728123,729038344451743315403⟩⟩,⟨⟨870030239916636629844,870031084940119142288⟩,⟨497780087735825635581,497780932759308148030⟩⟩,⟨⟨804499091657265243919,804499851462847964887⟩,⟨303533111866296509379,303533871671879230347⟩⟩,⟨⟨721064602069484135685,721065283680103094258⟩,⟨145582602282838721573,145583283893457680144⟩⟩,⟨⟨627248091656644028248,627248701764483189408⟩,⟨21977763737749363060,21978373845588524211⟩⟩,⟨⟨529437465540773798107,529438010369200971667⟩,⟨(-70182134297276759741),(-70181589468849586185)⟩⟩,⟨⟨432836656984281273667,432837142439566575205⟩,⟨(-134463841810191197618),(-134463356354905896091)⟩⟩,⟨⟨341472486479364954790,341472918142936566081⟩,⟨(-174831878494138818543),(-174831446830567207260)⟩⟩,⟨⟨258250870587372308393,258251254426932373005⟩,⟨(-195406273766314916866),(-195405889926754852260)⟩⟩,⟨⟨185052760737900321798,185053101245792096798⟩,⟨(-200254007365279545533),(-200253666857387770533)⟩⟩,⟨⟨122859352504288714710,122859653902801038009⟩,⟨(-193219117415725610953),(-193218816017213287654)⟩⟩,⟨⟨71895980743093030828,71896246891411116759⟩,⟨(-177793727566249796492),(-177793461417931710560)⟩⟩,⟨⟨31784602544008307333,31784837037536056634⟩,⟨(-157029755296667063308),(-157029520803139314003)⟩⟩] +lemma kernel96_1_r5_3_eq : ∀ k : Fin 16, kernel96_1Expr 5 3 k = kernel96_1_r5_3 k := by decide +kernel +noncomputable def kernel96_1_r5_4 : Fin 16 → CBox := ![⟨⟨1695792633307337638,1695998737274486582⟩,⟨(-133488903159129998749),(-133488697055162849802)⟩⟩,⟨⟨(-19507411102978439236),(-19507230355888085841)⟩,⟨(-109226815298652708780),(-109226634551562355385)⟩⟩,⟨⟨(-33139805024893489014),(-33139646898484636198)⟩,⟨(-85806050073021061339),(-85805891946612208522)⟩⟩,⟨⟨(-40582672429319744944),(-40582534405709983385)⟩,⟨(-64331792924841052083),(-64331654901231290521)⟩⟩,⟨⟨(-43193240741095017653),(-43193120561070266697)⟩,⟨(-45503986284530323650),(-45503866104505572691)⟩⟩,⟨⟨(-42235762014676742003),(-42235657606456948983)⟩,⟨(-29679733959898268584),(-29679629551678475564)⟩⟩,⟨⟨(-38833623763611977933),(-38833533280087665221)⟩,⟨(-16940367744838697325),(-16940277261314384616)⟩⟩,⟨⟨(-33940765642491786968),(-33940687404601053105)⟩,⟨(-7158355461963391701),(-7158277224072657839)⟩⟩,⟨⟨(-28329855448595308078),(-28329787967409046010)⟩,⟨(-60185110351009180),(-60117629164747108)⟩⟩,⟨⟨(-22594170588051079415),(-22594112515370070112)⟩,⟨4717611826089836054,4717669898770845353⟩⟩,⟨⟨(-17159917447992095488),(-17159867594739238908)⟩,⟨7581117993063234137,7581167846316090713⟩⟩,⟨⟨(-12305764247044889758),(-12305721546602634023)⟩,⟨8941250703599099828,8941293404041355563⟩⟩,⟨⟨(-8186611350494049095),(-8186574869797904725)⟩,⟨9185620090649997312,9185656571346141687⟩⟩,⟨⟨(-4859020847114819209),(-4858989747250504567)⟩,⟨8659454238762577745,8659485338626892387⟩⟩,⟨⟨(-2306215838061708332),(-2306189391150917679)⟩,⟨7654552289065004846,7654578735975795503⟩⟩,⟨⟨(-461086461750160676),(-461064022937106119)⟩,⟨6404932340209047358,6404954779022101916⟩⟩] +lemma kernel96_1_r5_4_eq : ∀ k : Fin 16, kernel96_1Expr 5 4 k = kernel96_1_r5_4 k := by decide +kernel +noncomputable def kernel96_1_r5_5 : Fin 16 → CBox := ![⟨⟨773842842119413707,773861830951903324⟩,⟨5087706892109741376,5087725880942230996⟩⟩,⟨⟨1510057517119169419,1510073551608806007⟩,⟨3827719588374887778,3827735622864524363⟩⟩,⟨⟨1860479081089230500,1860492589939765593⟩,⟨2704583904637753870,2704597413488288967⟩⟩,⟨⟨1930526413631182069,1930537768758421949⟩,⟨1760944830684243605,1760956185811483485⟩⟩,⟨⟨1812437480184568977,1812447000054034753⟩,⟨1011008106736595468,1011017626606061248⟩⟩,⟨⟨1582334906569420524,1582342870342439721⟩,⟨448620444357183132,448628408130202326⟩⟩,⟨⟨1299453229398550547,1299459874252527235⟩,⟨54416167812753595,54422812666730283⟩⟩,⟨⟨1006942523355529676,1006948055214407168⟩,⟨(-198245991893101632),(-198240460034224141)⟩⟩,⟨⟨733707055527610571,733711648642036761⟩,⟨(-338658167136436862),(-338653574022010679)⟩⟩,⟨⟨496812712828775951,496816520529018005⟩,⟨(-395418568366810592),(-395414760666568541)⟩⟩,⟨⟨304088963749078202,304092112623166543⟩,⟨(-394240300001875712),(-394237151127787370)⟩⟩,⟨⟨156647653861430879,156650252104828910⟩,⟨(-356730547353676880),(-356727949110278852)⟩⟩,⟨⟨51132783874420176,51134922115040833⟩,⟨(-299931729138736858),(-299929590898116202)⟩⟩,⟨⟨(-18404135926678725),(-18402380005383991)⟩,⟨(-236416203717468164),(-236414447796173430)⟩⟩,⟨⟨(-59043104885130808),(-59041666662784427)⟩,⟨(-174743978051274375),(-174742539828927994)⟩⟩,⟨⟨(-77939998355829909),(-77938822708648285)⟩,⟨(-120121944140597641),(-120120768493416017)⟩⟩] +lemma kernel96_1_r5_5_eq : ∀ k : Fin 16, kernel96_1Expr 5 5 k = kernel96_1_r5_5 k := by decide +kernel +noncomputable def kernel96_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-81634187937212375),(-81633229454797866)⟩,⟨(-75137505174821613),(-75136546692407104)⟩⟩,⟨⟨(-75658428614013026),(-75657648801185091)⟩,⟨(-40474441301437018),(-40473661488609084)⟩⟩,⟨⟨(-64382664050093484),(-64382031215285392)⟩,⟨(-15551067933421370),(-15550435098613277)⟩⟩,⟨⟨(-51024729052963031),(-51024216583887342)⟩,⟨951909373320683,952421842396372⟩⟩,⟨⟨(-37768059496611108),(-37767645592618160)⟩,⟨10685008516342999,10685422420335947⟩⟩,⟨⟨(-25936961022447902),(-25936627407618688)⟩,⟨15340821224573546,15341154839402759⟩⟩,⟨⟨(-16191649782877458),(-16191381572277486)⟩,⟨16468052808430760,16468321019030732⟩⟩,⟨⟨(-8716649085227457),(-8716433902300857)⟩,⟨15369576861164650,15369792044091250⟩⟩,⟨⟨(-3386173467966085),(-3386001051098978)⟩,⟨13063853872008180,13064026288875287⟩⟩,⟨⟨101684520778658,101822466622101⟩,⟨10290146112248267,10290284058091713⟩⟩,⟨⟨2124023323376373,2124133410699699⟩,⟨7540632130746173,7540742218069502⟩⟩,⟨⟨3063357751202547,3063445431652756⟩,⟨5105963181800927,5106050862251136⟩⟩,⟨⟨3264453205394209,3264522859234721⟩,⟨3124391239013172,3124460892853681⟩⟩,⟨⟨3012133230746207,3012188461654090⟩,⟨1627908551449491,1627963782357374⟩⟩,⟨⟨2524329768203382,2524373454360008⟩,⟨581626755581294,581670441737919⟩⟩,⟨⟨1955192531593964,1955227023178133⟩,⟨(-85221321277053),(-85186829692884)⟩⟩] +lemma kernel96_1_r5_6_eq : ∀ k : Fin 16, kernel96_1Expr 5 6 k = kernel96_1_r5_6 k := by decide +kernel +noncomputable def kernel96_1_r5_7 : Fin 16 → CBox := ![⟨⟨1403974183602047,1404001345936768⟩,⟨(-456749205863559),(-456722043528837)⟩⟩,⟨⟨926432068682179,926453424041886⟩,⟨(-615486819007146),(-615465463647439)⟩⟩,⟨⟨546479480507868,546496232942671⟩,⟨(-633685978965356),(-633669226530550)⟩⟩,⟨⟨266680860565020,266693978740434⟩,⟨(-569337815834261),(-569324697658850)⟩⟩,⟨⟨76870913258470,76881160437231⟩,⟨(-465451928436810),(-465441681258048)⟩⟩,⟨⟨(-39323508626294),(-39315517107964)⟩,⟨(-351355538984243),(-351347547465917)⟩⟩,⟨⟨(-99951665765920),(-99945448038541)⟩,⟨(-245038109486067),(-245031891758688)⟩⟩,⟨⟨(-121904512480648),(-121899682874434)⟩,⟨(-155840122803888),(-155835293197677)⟩⟩,⟨⟨(-119406734585108),(-119402989372860)⟩,⟨(-87029744607656),(-87025999395409)⟩⟩,⟨⟨(-103461038199868),(-103458137370977)⟩,⟨(-38010920391310),(-38008019562420)⟩⟩,⟨⟨(-81912284651487),(-81910042926838)⟩,⟨(-6055418156532),(-6053176431879)⟩⟩,⟨⟨(-59863197398020),(-59861467652105)⟩,⟨12447625412788,12449355158707⟩⟩,⟨⟨(-40243091142018),(-40241759540788)⟩,⟨21170770695910,21172102297143⟩⟩,⟨⟨(-24395884589113),(-24394860778354)⟩,⟨23373045230438,23374069041194⟩⟩,⟨⟨(-12607651169488),(-12606865698343)⟩,⟨21680599588882,21681385060027⟩⟩,⟨⟨(-4535132922992),(-4534531130872)⟩,⟨18040277890303,18040879682426⟩⟩] +lemma kernel96_1_r5_7_eq : ∀ k : Fin 16, kernel96_1Expr 5 7 k = kernel96_1_r5_7 k := by decide +kernel +noncomputable def kernel96_1_r5_8 : Fin 16 → CBox := ![⟨⟨474803139415,475263199850⟩,⟨13777282189923,13777742250355⟩⟩,⟨⟨3167039388307,3167390890359⟩,⟨9704720707735,9705072209787⟩⟩,⟨⟨4244455762565,4244723772303⟩,⟨6248863771623,6249131781358⟩⟩,⟨⟨4298400363818,4298604468619⟩,⟨3567600561458,3567804666259⟩⟩,⟨⟨3783943964500,3784099077846⟩,⟨1650220472881,1650375586227⟩⟩,⟨⟨3023316557485,3023434322828⟩,⟨394166995123,394284760469⟩⟩,⟨⟨2224637092908,2224726354472⟩,⟨(-340767513609),(-340678252042)⟩⟩,⟨⟨1506772828833,1506840424204⟩,⟨(-697682641517),(-697615046147)⟩⟩,⟨⟨924431965449,924483050665⟩,⟨(-803023573301),(-802972488088)⟩⟩,⟨⟨490176131407,490214710341⟩,⟨(-757952142841),(-757913563907)⟩⟩,⟨⟨191910094496,191939183110⟩,⟨(-636848902101),(-636819813483)⟩⟩,⟨⟨5631953474,5653868701⟩,⟨(-489933325733),(-489911410503)⟩⟩,⟨⟨(-96062958177),(-96046477259)⟩,⟨(-347806938620),(-347790457699)⟩⟩,⟨⟨(-138903477054),(-138891088709)⟩,⟨(-226462648399),(-226450260054)⟩⟩,⟨⟨(-144393592342),(-144384295188)⟩,⟨(-131899837497),(-131890540344)⟩⟩,⟨⟨(-128973669886),(-128966696368)⟩,⟨(-63925713888),(-63918740370)⟩⟩] +lemma kernel96_1_r5_8_eq : ∀ k : Fin 16, kernel96_1Expr 5 8 k = kernel96_1_r5_8 k := by decide +kernel +noncomputable def kernel96_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-104221178317),(-104215956644)⟩,⟨(-19019697992),(-19014476322)⟩⟩,⟨⟨(-77589835616),(-77585926709)⟩,⟨7683709320,7687618224⟩⟩,⟨⟨(-53344197850),(-53341275789)⟩,⟨21148227736,21151149798⟩⟩,⟨⟨(-33478145696),(-33475962129)⟩,⟨25749872807,25752056377⟩⟩,⟨⟨(-18504792691),(-18503163414)⟩,⟨24983396277,24985025554⟩⟩,⟨⟨(-8073989178),(-8072773593)⟩,⟨21418553721,21419769306⟩⟩,⟨⟨(-1416394165),(-1415488336)⟩,⟨16796574369,16797480197⟩⟩,⟨⟨2363620167,2364295085⟩,⟨12189380277,12190055196⟩⟩,⟨⟨4114429724,4114931909⟩,⟨8171720242,8172222431⟩⟩,⟨⟨4550226819,4550600570⟩,⟨4977772498,4978146248⟩⟩,⟨⟨4221789691,4222067580⟩,⟨2629034282,2629312167⟩⟩,⟨⟨3521910311,3522116941⟩,⟨1030206760,1030413389⟩⟩,⟨⟨2708636842,2708790325⟩,⟨35522682,35676165⟩⟩,⟨⟨1935006885,1935120953⟩,⟨(-509311838),(-509197771)⟩⟩,⟨⟨1278393107,1278477807⟩,⟨(-743611649),(-743526953)⟩⟩,⟨⟨765847978,765911212⟩,⟨(-781071915),(-781008680)⟩⟩] +lemma kernel96_1_r5_9_eq : ∀ k : Fin 16, kernel96_1Expr 5 9 k = kernel96_1_r5_9 k := by decide +kernel +noncomputable def kernel96_1_r5_10 : Fin 16 → CBox := ![⟨⟨394051498,394098689⟩,⟨(-707349523),(-707302329)⟩⟩,⟨⟨143818307,143853561⟩,⟨(-582334529),(-582299274)⟩⟩,⟨⟨(-10148377),(-10122057)⟩,⟨(-444623720),(-444597401)⟩⟩,⟨⟨(-93279083),(-93259410)⟩,⟨(-316594729),(-316575052)⟩⟩,⟨⟨(-127929550),(-127914856)⟩,⟨(-209152372),(-209137675)⟩⟩,⟨⟨(-132052070),(-132041084)⟩,⟨(-125698593),(-125687603)⟩⟩,⟨⟨(-119033986),(-119025769)⟩,⟨(-65187218),(-65179002)⟩⟩,⟨⟨(-98177239),(-98171088)⟩,⟨(-24307740),(-24301590)⟩⟩,⟨⟨(-75458408),(-75453807)⟩,⟨1068061,1072662⟩⟩,⟨⟨(-54343270),(-54339821)⟩,⟨15011860,15015309⟩⟩,⟨⟨(-36528995),(-36526399)⟩,⟨21077811,21080406⟩⟩,⟨⟨(-22556227),(-22554274)⟩,⟨22118256,22120209⟩⟩,⟨⟨(-12276668),(-12275188)⟩,⟨20269553,20271034⟩⟩,⟨⟨(-5186466),(-5185347)⟩,⟨17030220,17031335⟩⟩,⟨⟨(-647664),(-646810)⟩,⟨13378727,13379580⟩⟩,⟨⟨1976896,1977546⟩,⟨9898345,9898999⟩⟩] +lemma kernel96_1_r5_10_eq : ∀ k : Fin 16, kernel96_1Expr 5 10 k = kernel96_1_r5_10 k := by decide +kernel +noncomputable def kernel96_1_r5_11 : Fin 16 → CBox := ![⟨⟨3251000,3251500⟩,⟨6890686,6891183⟩⟩,⟨⟨3634495,3634886⟩,⟨4469706,4470090⟩⟩,⟨⟨3478759,3479061⟩,⟨2634150,2634452⟩⟩,⟨⟨3036678,3036921⟩,⟨1319917,1320160⟩⟩,⟨⟨2479281,2479469⟩,⟨435559,435747⟩⟩,⟨⟨1913931,1914073⟩,⟨(-115376),(-115234)⟩⟩,⟨⟨1401327,1401448⟩,⟨(-421674),(-421550)⟩⟩,⟨⟨969956,970058⟩,⟨(-558310),(-558208)⟩⟩,⟨⟨627470,627557⟩,⟨(-584748),(-584663)⟩⟩,⟨⟨369176,369259⟩,⟨(-545569),(-545489)⟩⟩,⟨⟨184013,184083⟩,⟨(-472480),(-472410)⟩⟩,⟨⟨58494,58560⟩,⟨(-386772),(-386706)⟩⟩,⟨⟨(-20823),(-20767)⟩,⟨(-301759),(-301703)⟩⟩,⟨⟨(-66043),(-65995)⟩,⟨(-224950),(-224899)⟩⟩,⟨⟨(-87312),(-87269)⟩,⟨(-159867),(-159824)⟩⟩,⟨⟨(-92684),(-92637)⟩,⟨(-107435),(-107388)⟩⟩] +lemma kernel96_1_r5_11_eq : ∀ k : Fin 16, kernel96_1Expr 5 11 k = kernel96_1_r5_11 k := by decide +kernel +noncomputable def kernel96_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-88234),(-88197)⟩,⟨(-67006),(-66972)⟩⟩,⟨⟨(-78388),(-78346)⟩,⟨(-37146),(-37103)⟩⟩,⟨⟨(-66167),(-66133)⟩,⟨(-16055),(-16018)⟩⟩,⟨⟨(-53554),(-53511)⟩,⟨(-1936),(-1893)⟩⟩,⟨⟨(-41737),(-41695)⟩,⟨6872,6911⟩⟩,⟨⟨(-31328),(-31286)⟩,⟨11785,11824⟩⟩,⟨⟨(-22590),(-22556)⟩,⟨13973,14006⟩⟩,⟨⟨(-15535),(-15501)⟩,⟨14335,14373⟩⟩,⟨⟨(-10037),(-10000)⟩,⟨13566,13601⟩⟩,⟨⟨(-5890),(-5852)⟩,⟨12155,12193⟩⟩,⟨⟨(-2872),(-2835)⟩,⟨10454,10488⟩⟩,⟨⟨(-768),(-730)⟩,⟨8691,8726⟩⟩,⟨⟨636,665⟩,⟨7021,7051⟩⟩,⟨⟨1495,1529⟩,⟨5508,5542⟩⟩,⟨⟨1963,1997⟩,⟨4201,4235⟩⟩,⟨⟨2155,2188⟩,⟨3106,3140⟩⟩] +lemma kernel96_1_r5_12_eq : ∀ k : Fin 16, kernel96_1Expr 5 12 k = kernel96_1_r5_12 k := by decide +kernel +noncomputable def kernel96_1_r5_13 : Fin 16 → CBox := ![⟨⟨2158,2196⟩,⟨2210,2248⟩⟩,⟨⟨2044,2082⟩,⟨1494,1533⟩⟩,⟨⟨1860,1895⟩,⟨943,981⟩⟩,⟨⟨1645,1678⟩,⟨529,559⟩⟩,⟨⟨1413,1446⟩,⟨222,252⟩⟩,⟨⟨1185,1223⟩,⟨(-4),30⟩⟩,⟨⟨986,1016⟩,⟨(-154),(-120)⟩⟩,⟨⟨796,830⟩,⟨(-253),(-219)⟩⟩,⟨⟨633,671⟩,⟨(-310),(-271)⟩⟩,⟨⟨495,524⟩,⟨(-336),(-307)⟩⟩,⟨⟨377,411⟩,⟨(-347),(-313)⟩⟩,⟨⟨283,312⟩,⟨(-335),(-306)⟩⟩,⟨⟨197,236⟩,⟨(-327),(-288)⟩⟩,⟨⟨134,168⟩,⟨(-299),(-269)⟩⟩,⟨⟨84,114⟩,⟨(-273),(-244)⟩⟩,⟨⟨47,72⟩,⟨(-246),(-217)⟩⟩] +lemma kernel96_1_r5_13_eq : ∀ k : Fin 16, kernel96_1Expr 5 13 k = kernel96_1_r5_13 k := by decide +kernel +noncomputable def kernel96_1_r5_14 : Fin 16 → CBox := ![⟨⟨14,43⟩,⟨(-220),(-191)⟩⟩,⟨⟨(-12),22⟩,⟨(-196),(-166)⟩⟩,⟨⟨(-30),5⟩,⟨(-180),(-142)⟩⟩,⟨⟨(-43),(-9)⟩,⟨(-157),(-123)⟩⟩,⟨⟨(-52),(-21)⟩,⟨(-134),(-101)⟩⟩,⟨⟨(-56),(-27)⟩,⟨(-112),(-83)⟩⟩,⟨⟨(-58),(-29)⟩,⟨(-100),(-70)⟩⟩,⟨⟨(-65),(-27)⟩,⟨(-91),(-56)⟩⟩,⟨⟨(-63),(-34)⟩,⟨(-78),(-48)⟩⟩,⟨⟨(-70),(-32)⟩,⟨(-70),(-35)⟩⟩,⟨⟨(-65),(-35)⟩,⟨(-61),(-31)⟩⟩,⟨⟨(-63),(-33)⟩,⟨(-49),(-19)⟩⟩,⟨⟨(-58),(-28)⟩,⟨(-45),(-16)⟩⟩,⟨⟨(-62),(-27)⟩,⟨(-45),(-7)⟩⟩,⟨⟨(-56),(-22)⟩,⟨(-38),(-3)⟩⟩,⟨⟨(-55),(-25)⟩,⟨(-29),1⟩⟩] +lemma kernel96_1_r5_14_eq : ∀ k : Fin 16, kernel96_1Expr 5 14 k = kernel96_1_r5_14 k := by decide +kernel +noncomputable def kernel96_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-55),(-25)⟩,⟨(-29),1⟩⟩,⟨⟨(-50),(-21)⟩,⟨(-26),4⟩⟩,⟨⟨(-50),(-12)⟩,⟨(-27),8⟩⟩,⟨⟨(-46),(-16)⟩,⟨(-22),8⟩⟩,⟨⟨(-45),(-15)⟩,⟨(-18),12⟩⟩,⟨⟨(-45),(-15)⟩,⟨(-18),12⟩⟩,⟨⟨(-45),(-15)⟩,⟨(-18),12⟩⟩,⟨⟨(-45),(-6)⟩,⟨(-20),20⟩⟩,⟨⟨(-36),(-6)⟩,⟨(-15),14⟩⟩,⟨⟨(-36),(-6)⟩,⟨(-15),14⟩⟩,⟨⟨(-36),(-6)⟩,⟨(-15),14⟩⟩,⟨⟨(-40),(-5)⟩,⟨(-15),23⟩⟩,⟨⟨(-40),(-5)⟩,⟨(-15),23⟩⟩,⟨⟨(-40),(-5)⟩,⟨(-15),23⟩⟩,⟨⟨(-40),(-5)⟩,⟨(-15),23⟩⟩,⟨⟨(-40),(-5)⟩,⟨(-15),23⟩⟩] +lemma kernel96_1_r5_15_eq : ∀ k : Fin 16, kernel96_1Expr 5 15 k = kernel96_1_r5_15 k := by decide +kernel +noncomputable def kernel96_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel96_1_r5_0,kernel96_1_r5_1,kernel96_1_r5_2,kernel96_1_r5_3,kernel96_1_r5_4,kernel96_1_r5_5,kernel96_1_r5_6,kernel96_1_r5_7,kernel96_1_r5_8,kernel96_1_r5_9,kernel96_1_r5_10,kernel96_1_r5_11,kernel96_1_r5_12,kernel96_1_r5_13,kernel96_1_r5_14,kernel96_1_r5_15] +lemma kernel96_1_r5_eq (i k : Fin 16) : kernel96_1Expr 5 i k = kernel96_1_r5 i k := by + fin_cases i + · exact kernel96_1_r5_0_eq k + · exact kernel96_1_r5_1_eq k + · exact kernel96_1_r5_2_eq k + · exact kernel96_1_r5_3_eq k + · exact kernel96_1_r5_4_eq k + · exact kernel96_1_r5_5_eq k + · exact kernel96_1_r5_6_eq k + · exact kernel96_1_r5_7_eq k + · exact kernel96_1_r5_8_eq k + · exact kernel96_1_r5_9_eq k + · exact kernel96_1_r5_10_eq k + · exact kernel96_1_r5_11_eq k + · exact kernel96_1_r5_12_eq k + · exact kernel96_1_r5_13_eq k + · exact kernel96_1_r5_14_eq k + · exact kernel96_1_r5_15_eq k +noncomputable def kernel96_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel96_1_r0,kernel96_1_r1,kernel96_1_r2,kernel96_1_r3,kernel96_1_r4,kernel96_1_r5] +lemma kernel96_1_eq (j : Fin 6) (i k : Fin 16) : kernel96_1Expr j i k = kernel96_1 j i k := by + fin_cases j + · exact kernel96_1_r0_eq i k + · exact kernel96_1_r1_eq i k + · exact kernel96_1_r2_eq i k + · exact kernel96_1_r3_eq i k + · exact kernel96_1_r4_eq i k + · exact kernel96_1_r5_eq i k +lemma kernel96_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel96_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(96:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel96_1_eq] + unfold kernel96_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans96_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel97_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans97 j i k) +noncomputable def kernel97_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_0_eq : ∀ k : Fin 16, kernel97_0Expr 0 0 k = kernel97_0_r0_0 k := by decide +kernel +noncomputable def kernel97_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_1_eq : ∀ k : Fin 16, kernel97_0Expr 0 1 k = kernel97_0_r0_1 k := by decide +kernel +noncomputable def kernel97_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_2_eq : ∀ k : Fin 16, kernel97_0Expr 0 2 k = kernel97_0_r0_2 k := by decide +kernel +noncomputable def kernel97_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_3_eq : ∀ k : Fin 16, kernel97_0Expr 0 3 k = kernel97_0_r0_3 k := by decide +kernel +noncomputable def kernel97_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_4_eq : ∀ k : Fin 16, kernel97_0Expr 0 4 k = kernel97_0_r0_4 k := by decide +kernel +noncomputable def kernel97_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_5_eq : ∀ k : Fin 16, kernel97_0Expr 0 5 k = kernel97_0_r0_5 k := by decide +kernel +noncomputable def kernel97_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_6_eq : ∀ k : Fin 16, kernel97_0Expr 0 6 k = kernel97_0_r0_6 k := by decide +kernel +noncomputable def kernel97_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_7_eq : ∀ k : Fin 16, kernel97_0Expr 0 7 k = kernel97_0_r0_7 k := by decide +kernel +noncomputable def kernel97_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_8_eq : ∀ k : Fin 16, kernel97_0Expr 0 8 k = kernel97_0_r0_8 k := by decide +kernel +noncomputable def kernel97_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_9_eq : ∀ k : Fin 16, kernel97_0Expr 0 9 k = kernel97_0_r0_9 k := by decide +kernel +noncomputable def kernel97_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_10_eq : ∀ k : Fin 16, kernel97_0Expr 0 10 k = kernel97_0_r0_10 k := by decide +kernel +noncomputable def kernel97_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r0_11_eq : ∀ k : Fin 16, kernel97_0Expr 0 11 k = kernel97_0_r0_11 k := by decide +kernel +noncomputable def kernel97_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r0_12_eq : ∀ k : Fin 16, kernel97_0Expr 0 12 k = kernel97_0_r0_12 k := by decide +kernel +noncomputable def kernel97_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r0_13_eq : ∀ k : Fin 16, kernel97_0Expr 0 13 k = kernel97_0_r0_13 k := by decide +kernel +noncomputable def kernel97_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r0_14_eq : ∀ k : Fin 16, kernel97_0Expr 0 14 k = kernel97_0_r0_14 k := by decide +kernel +noncomputable def kernel97_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r0_15_eq : ∀ k : Fin 16, kernel97_0Expr 0 15 k = kernel97_0_r0_15 k := by decide +kernel +noncomputable def kernel97_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel97_0_r0_0,kernel97_0_r0_1,kernel97_0_r0_2,kernel97_0_r0_3,kernel97_0_r0_4,kernel97_0_r0_5,kernel97_0_r0_6,kernel97_0_r0_7,kernel97_0_r0_8,kernel97_0_r0_9,kernel97_0_r0_10,kernel97_0_r0_11,kernel97_0_r0_12,kernel97_0_r0_13,kernel97_0_r0_14,kernel97_0_r0_15] +lemma kernel97_0_r0_eq (i k : Fin 16) : kernel97_0Expr 0 i k = kernel97_0_r0 i k := by + fin_cases i + · exact kernel97_0_r0_0_eq k + · exact kernel97_0_r0_1_eq k + · exact kernel97_0_r0_2_eq k + · exact kernel97_0_r0_3_eq k + · exact kernel97_0_r0_4_eq k + · exact kernel97_0_r0_5_eq k + · exact kernel97_0_r0_6_eq k + · exact kernel97_0_r0_7_eq k + · exact kernel97_0_r0_8_eq k + · exact kernel97_0_r0_9_eq k + · exact kernel97_0_r0_10_eq k + · exact kernel97_0_r0_11_eq k + · exact kernel97_0_r0_12_eq k + · exact kernel97_0_r0_13_eq k + · exact kernel97_0_r0_14_eq k + · exact kernel97_0_r0_15_eq k +noncomputable def kernel97_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_0_eq : ∀ k : Fin 16, kernel97_0Expr 1 0 k = kernel97_0_r1_0 k := by decide +kernel +noncomputable def kernel97_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_1_eq : ∀ k : Fin 16, kernel97_0Expr 1 1 k = kernel97_0_r1_1 k := by decide +kernel +noncomputable def kernel97_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_2_eq : ∀ k : Fin 16, kernel97_0Expr 1 2 k = kernel97_0_r1_2 k := by decide +kernel +noncomputable def kernel97_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_3_eq : ∀ k : Fin 16, kernel97_0Expr 1 3 k = kernel97_0_r1_3 k := by decide +kernel +noncomputable def kernel97_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_4_eq : ∀ k : Fin 16, kernel97_0Expr 1 4 k = kernel97_0_r1_4 k := by decide +kernel +noncomputable def kernel97_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_5_eq : ∀ k : Fin 16, kernel97_0Expr 1 5 k = kernel97_0_r1_5 k := by decide +kernel +noncomputable def kernel97_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_6_eq : ∀ k : Fin 16, kernel97_0Expr 1 6 k = kernel97_0_r1_6 k := by decide +kernel +noncomputable def kernel97_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_7_eq : ∀ k : Fin 16, kernel97_0Expr 1 7 k = kernel97_0_r1_7 k := by decide +kernel +noncomputable def kernel97_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_8_eq : ∀ k : Fin 16, kernel97_0Expr 1 8 k = kernel97_0_r1_8 k := by decide +kernel +noncomputable def kernel97_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_9_eq : ∀ k : Fin 16, kernel97_0Expr 1 9 k = kernel97_0_r1_9 k := by decide +kernel +noncomputable def kernel97_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_10_eq : ∀ k : Fin 16, kernel97_0Expr 1 10 k = kernel97_0_r1_10 k := by decide +kernel +noncomputable def kernel97_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_11_eq : ∀ k : Fin 16, kernel97_0Expr 1 11 k = kernel97_0_r1_11 k := by decide +kernel +noncomputable def kernel97_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_12_eq : ∀ k : Fin 16, kernel97_0Expr 1 12 k = kernel97_0_r1_12 k := by decide +kernel +noncomputable def kernel97_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_13_eq : ∀ k : Fin 16, kernel97_0Expr 1 13 k = kernel97_0_r1_13 k := by decide +kernel +noncomputable def kernel97_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_14_eq : ∀ k : Fin 16, kernel97_0Expr 1 14 k = kernel97_0_r1_14 k := by decide +kernel +noncomputable def kernel97_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r1_15_eq : ∀ k : Fin 16, kernel97_0Expr 1 15 k = kernel97_0_r1_15 k := by decide +kernel +noncomputable def kernel97_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel97_0_r1_0,kernel97_0_r1_1,kernel97_0_r1_2,kernel97_0_r1_3,kernel97_0_r1_4,kernel97_0_r1_5,kernel97_0_r1_6,kernel97_0_r1_7,kernel97_0_r1_8,kernel97_0_r1_9,kernel97_0_r1_10,kernel97_0_r1_11,kernel97_0_r1_12,kernel97_0_r1_13,kernel97_0_r1_14,kernel97_0_r1_15] +lemma kernel97_0_r1_eq (i k : Fin 16) : kernel97_0Expr 1 i k = kernel97_0_r1 i k := by + fin_cases i + · exact kernel97_0_r1_0_eq k + · exact kernel97_0_r1_1_eq k + · exact kernel97_0_r1_2_eq k + · exact kernel97_0_r1_3_eq k + · exact kernel97_0_r1_4_eq k + · exact kernel97_0_r1_5_eq k + · exact kernel97_0_r1_6_eq k + · exact kernel97_0_r1_7_eq k + · exact kernel97_0_r1_8_eq k + · exact kernel97_0_r1_9_eq k + · exact kernel97_0_r1_10_eq k + · exact kernel97_0_r1_11_eq k + · exact kernel97_0_r1_12_eq k + · exact kernel97_0_r1_13_eq k + · exact kernel97_0_r1_14_eq k + · exact kernel97_0_r1_15_eq k +noncomputable def kernel97_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_0_eq : ∀ k : Fin 16, kernel97_0Expr 2 0 k = kernel97_0_r2_0 k := by decide +kernel +noncomputable def kernel97_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_1_eq : ∀ k : Fin 16, kernel97_0Expr 2 1 k = kernel97_0_r2_1 k := by decide +kernel +noncomputable def kernel97_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_2_eq : ∀ k : Fin 16, kernel97_0Expr 2 2 k = kernel97_0_r2_2 k := by decide +kernel +noncomputable def kernel97_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_3_eq : ∀ k : Fin 16, kernel97_0Expr 2 3 k = kernel97_0_r2_3 k := by decide +kernel +noncomputable def kernel97_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_4_eq : ∀ k : Fin 16, kernel97_0Expr 2 4 k = kernel97_0_r2_4 k := by decide +kernel +noncomputable def kernel97_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_5_eq : ∀ k : Fin 16, kernel97_0Expr 2 5 k = kernel97_0_r2_5 k := by decide +kernel +noncomputable def kernel97_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_6_eq : ∀ k : Fin 16, kernel97_0Expr 2 6 k = kernel97_0_r2_6 k := by decide +kernel +noncomputable def kernel97_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_7_eq : ∀ k : Fin 16, kernel97_0Expr 2 7 k = kernel97_0_r2_7 k := by decide +kernel +noncomputable def kernel97_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_8_eq : ∀ k : Fin 16, kernel97_0Expr 2 8 k = kernel97_0_r2_8 k := by decide +kernel +noncomputable def kernel97_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_9_eq : ∀ k : Fin 16, kernel97_0Expr 2 9 k = kernel97_0_r2_9 k := by decide +kernel +noncomputable def kernel97_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r2_10_eq : ∀ k : Fin 16, kernel97_0Expr 2 10 k = kernel97_0_r2_10 k := by decide +kernel +noncomputable def kernel97_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r2_11_eq : ∀ k : Fin 16, kernel97_0Expr 2 11 k = kernel97_0_r2_11 k := by decide +kernel +noncomputable def kernel97_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r2_12_eq : ∀ k : Fin 16, kernel97_0Expr 2 12 k = kernel97_0_r2_12 k := by decide +kernel +noncomputable def kernel97_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r2_13_eq : ∀ k : Fin 16, kernel97_0Expr 2 13 k = kernel97_0_r2_13 k := by decide +kernel +noncomputable def kernel97_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r2_14_eq : ∀ k : Fin 16, kernel97_0Expr 2 14 k = kernel97_0_r2_14 k := by decide +kernel +noncomputable def kernel97_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel97_0_r2_15_eq : ∀ k : Fin 16, kernel97_0Expr 2 15 k = kernel97_0_r2_15 k := by decide +kernel +noncomputable def kernel97_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel97_0_r2_0,kernel97_0_r2_1,kernel97_0_r2_2,kernel97_0_r2_3,kernel97_0_r2_4,kernel97_0_r2_5,kernel97_0_r2_6,kernel97_0_r2_7,kernel97_0_r2_8,kernel97_0_r2_9,kernel97_0_r2_10,kernel97_0_r2_11,kernel97_0_r2_12,kernel97_0_r2_13,kernel97_0_r2_14,kernel97_0_r2_15] +lemma kernel97_0_r2_eq (i k : Fin 16) : kernel97_0Expr 2 i k = kernel97_0_r2 i k := by + fin_cases i + · exact kernel97_0_r2_0_eq k + · exact kernel97_0_r2_1_eq k + · exact kernel97_0_r2_2_eq k + · exact kernel97_0_r2_3_eq k + · exact kernel97_0_r2_4_eq k + · exact kernel97_0_r2_5_eq k + · exact kernel97_0_r2_6_eq k + · exact kernel97_0_r2_7_eq k + · exact kernel97_0_r2_8_eq k + · exact kernel97_0_r2_9_eq k + · exact kernel97_0_r2_10_eq k + · exact kernel97_0_r2_11_eq k + · exact kernel97_0_r2_12_eq k + · exact kernel97_0_r2_13_eq k + · exact kernel97_0_r2_14_eq k + · exact kernel97_0_r2_15_eq k +noncomputable def kernel97_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_0_eq : ∀ k : Fin 16, kernel97_0Expr 3 0 k = kernel97_0_r3_0 k := by decide +kernel +noncomputable def kernel97_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_1_eq : ∀ k : Fin 16, kernel97_0Expr 3 1 k = kernel97_0_r3_1 k := by decide +kernel +noncomputable def kernel97_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_2_eq : ∀ k : Fin 16, kernel97_0Expr 3 2 k = kernel97_0_r3_2 k := by decide +kernel +noncomputable def kernel97_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_3_eq : ∀ k : Fin 16, kernel97_0Expr 3 3 k = kernel97_0_r3_3 k := by decide +kernel +noncomputable def kernel97_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_4_eq : ∀ k : Fin 16, kernel97_0Expr 3 4 k = kernel97_0_r3_4 k := by decide +kernel +noncomputable def kernel97_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_5_eq : ∀ k : Fin 16, kernel97_0Expr 3 5 k = kernel97_0_r3_5 k := by decide +kernel +noncomputable def kernel97_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_6_eq : ∀ k : Fin 16, kernel97_0Expr 3 6 k = kernel97_0_r3_6 k := by decide +kernel +noncomputable def kernel97_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_7_eq : ∀ k : Fin 16, kernel97_0Expr 3 7 k = kernel97_0_r3_7 k := by decide +kernel +noncomputable def kernel97_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_8_eq : ∀ k : Fin 16, kernel97_0Expr 3 8 k = kernel97_0_r3_8 k := by decide +kernel +noncomputable def kernel97_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_9_eq : ∀ k : Fin 16, kernel97_0Expr 3 9 k = kernel97_0_r3_9 k := by decide +kernel +noncomputable def kernel97_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_10_eq : ∀ k : Fin 16, kernel97_0Expr 3 10 k = kernel97_0_r3_10 k := by decide +kernel +noncomputable def kernel97_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_11_eq : ∀ k : Fin 16, kernel97_0Expr 3 11 k = kernel97_0_r3_11 k := by decide +kernel +noncomputable def kernel97_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_12_eq : ∀ k : Fin 16, kernel97_0Expr 3 12 k = kernel97_0_r3_12 k := by decide +kernel +noncomputable def kernel97_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_13_eq : ∀ k : Fin 16, kernel97_0Expr 3 13 k = kernel97_0_r3_13 k := by decide +kernel +noncomputable def kernel97_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_14_eq : ∀ k : Fin 16, kernel97_0Expr 3 14 k = kernel97_0_r3_14 k := by decide +kernel +noncomputable def kernel97_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r3_15_eq : ∀ k : Fin 16, kernel97_0Expr 3 15 k = kernel97_0_r3_15 k := by decide +kernel +noncomputable def kernel97_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel97_0_r3_0,kernel97_0_r3_1,kernel97_0_r3_2,kernel97_0_r3_3,kernel97_0_r3_4,kernel97_0_r3_5,kernel97_0_r3_6,kernel97_0_r3_7,kernel97_0_r3_8,kernel97_0_r3_9,kernel97_0_r3_10,kernel97_0_r3_11,kernel97_0_r3_12,kernel97_0_r3_13,kernel97_0_r3_14,kernel97_0_r3_15] +lemma kernel97_0_r3_eq (i k : Fin 16) : kernel97_0Expr 3 i k = kernel97_0_r3 i k := by + fin_cases i + · exact kernel97_0_r3_0_eq k + · exact kernel97_0_r3_1_eq k + · exact kernel97_0_r3_2_eq k + · exact kernel97_0_r3_3_eq k + · exact kernel97_0_r3_4_eq k + · exact kernel97_0_r3_5_eq k + · exact kernel97_0_r3_6_eq k + · exact kernel97_0_r3_7_eq k + · exact kernel97_0_r3_8_eq k + · exact kernel97_0_r3_9_eq k + · exact kernel97_0_r3_10_eq k + · exact kernel97_0_r3_11_eq k + · exact kernel97_0_r3_12_eq k + · exact kernel97_0_r3_13_eq k + · exact kernel97_0_r3_14_eq k + · exact kernel97_0_r3_15_eq k +noncomputable def kernel97_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),4⟩⟩,⟨⟨(-2),6⟩,⟨(-2),4⟩⟩,⟨⟨(-2),6⟩,⟨(-2),4⟩⟩,⟨⟨(-2),6⟩,⟨(-2),4⟩⟩,⟨⟨(-2),6⟩,⟨(-2),4⟩⟩,⟨⟨(-2),6⟩,⟨(-3),4⟩⟩,⟨⟨(-2),6⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r4_0_eq : ∀ k : Fin 16, kernel97_0Expr 4 0 k = kernel97_0_r4_0 k := by decide +kernel +noncomputable def kernel97_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-2),5⟩,⟨(-3),3⟩⟩,⟨⟨(-2),5⟩,⟨(-3),3⟩⟩,⟨⟨(-2),5⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩] +lemma kernel97_0_r4_1_eq : ∀ k : Fin 16, kernel97_0Expr 4 1 k = kernel97_0_r4_1 k := by decide +kernel +noncomputable def kernel97_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩] +lemma kernel97_0_r4_2_eq : ∀ k : Fin 16, kernel97_0Expr 4 2 k = kernel97_0_r4_2 k := by decide +kernel +noncomputable def kernel97_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r4_3_eq : ∀ k : Fin 16, kernel97_0Expr 4 3 k = kernel97_0_r4_3 k := by decide +kernel +noncomputable def kernel97_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_4_eq : ∀ k : Fin 16, kernel97_0Expr 4 4 k = kernel97_0_r4_4 k := by decide +kernel +noncomputable def kernel97_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_5_eq : ∀ k : Fin 16, kernel97_0Expr 4 5 k = kernel97_0_r4_5 k := by decide +kernel +noncomputable def kernel97_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_6_eq : ∀ k : Fin 16, kernel97_0Expr 4 6 k = kernel97_0_r4_6 k := by decide +kernel +noncomputable def kernel97_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_7_eq : ∀ k : Fin 16, kernel97_0Expr 4 7 k = kernel97_0_r4_7 k := by decide +kernel +noncomputable def kernel97_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_8_eq : ∀ k : Fin 16, kernel97_0Expr 4 8 k = kernel97_0_r4_8 k := by decide +kernel +noncomputable def kernel97_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_9_eq : ∀ k : Fin 16, kernel97_0Expr 4 9 k = kernel97_0_r4_9 k := by decide +kernel +noncomputable def kernel97_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_10_eq : ∀ k : Fin 16, kernel97_0Expr 4 10 k = kernel97_0_r4_10 k := by decide +kernel +noncomputable def kernel97_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel97_0_r4_11_eq : ∀ k : Fin 16, kernel97_0Expr 4 11 k = kernel97_0_r4_11 k := by decide +kernel +noncomputable def kernel97_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r4_12_eq : ∀ k : Fin 16, kernel97_0Expr 4 12 k = kernel97_0_r4_12 k := by decide +kernel +noncomputable def kernel97_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r4_13_eq : ∀ k : Fin 16, kernel97_0Expr 4 13 k = kernel97_0_r4_13 k := by decide +kernel +noncomputable def kernel97_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r4_14_eq : ∀ k : Fin 16, kernel97_0Expr 4 14 k = kernel97_0_r4_14 k := by decide +kernel +noncomputable def kernel97_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel97_0_r4_15_eq : ∀ k : Fin 16, kernel97_0Expr 4 15 k = kernel97_0_r4_15 k := by decide +kernel +noncomputable def kernel97_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel97_0_r4_0,kernel97_0_r4_1,kernel97_0_r4_2,kernel97_0_r4_3,kernel97_0_r4_4,kernel97_0_r4_5,kernel97_0_r4_6,kernel97_0_r4_7,kernel97_0_r4_8,kernel97_0_r4_9,kernel97_0_r4_10,kernel97_0_r4_11,kernel97_0_r4_12,kernel97_0_r4_13,kernel97_0_r4_14,kernel97_0_r4_15] +lemma kernel97_0_r4_eq (i k : Fin 16) : kernel97_0Expr 4 i k = kernel97_0_r4 i k := by + fin_cases i + · exact kernel97_0_r4_0_eq k + · exact kernel97_0_r4_1_eq k + · exact kernel97_0_r4_2_eq k + · exact kernel97_0_r4_3_eq k + · exact kernel97_0_r4_4_eq k + · exact kernel97_0_r4_5_eq k + · exact kernel97_0_r4_6_eq k + · exact kernel97_0_r4_7_eq k + · exact kernel97_0_r4_8_eq k + · exact kernel97_0_r4_9_eq k + · exact kernel97_0_r4_10_eq k + · exact kernel97_0_r4_11_eq k + · exact kernel97_0_r4_12_eq k + · exact kernel97_0_r4_13_eq k + · exact kernel97_0_r4_14_eq k + · exact kernel97_0_r4_15_eq k +noncomputable def kernel97_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-12319418668147798797319),(-12319415082767652181119)⟩,⟨4677185310407818174849,4677188895787964790799⟩⟩,⟨⟨(-12267335253469931148825),(-12267331674934888061412)⟩,⟨4702203242142766568107,4702206820677809655269⟩⟩,⟨⟨(-12163406329964276890337),(-12163402765087682631023)⟩,⟨4751513344747736375049,4751516909624330634113⟩⟩,⟨⟨(-12008115594665340711113),(-12008112050184913661025)⟩,⟨4823679051718630377999,4823682596199057427839⟩⟩,⟨⟨(-11802207801647172037332),(-11802204284188158165011)⟩,⟨4916582752011447260923,4916586269470461133002⟩⟩,⟨⟨(-11546710417333850719266),(-11546706933372913493869)⟩,⟨5027470047999308736243,5027473531960245961405⟩⟩,⟨⟨(-11242960224655598413679),(-11242956780486380018614)⟩,⟨5153008022124612172179,5153011466293830567017⟩⟩,⟨⟨(-10892633040307077874925),(-10892629642006747539352)⟩,⟨5289356818086927222833,5289360216387257558189⟩⟩,⟨⟨(-10497774385285598516142),(-10497771038684354617610)⟩,⟨5432253605093907988738,5432256951695151887066⟩⟩,⟨⟨(-10060828711136778062182),(-10060825421787742225651)⟩,⟨5577107724064969776674,5577111013414005613014⟩⟩,⟨⟨(-9584664646225154609704),(-9584661419377986379050)⟩,⟨5719105515723963512983,5719108742571131743459⟩⟩,⟨⟨(-9072593698821357378573),(-9072590539126533738821)⟩,⟨5853323009323755579379,5853326169018579218967⟩⟩,⟨⟨(-8528379943349208926039),(-8528376855371476850791)⟩,⟨5974844319858480214641,5974847407836212289740⟩⟩,⟨⟨(-7956238430275172501350),(-7956235418212593919741)⟩,⟨6078883272591572099730,6078886284654150681206⟩⟩,⟨⟨(-7360820390528843847092),(-7360817458203406577261)⟩,⟨6160905472696914893516,6160908405022352163231⟩⟩,⟨⟨(-6747183755515282613212),(-6747180906353376134200)⟩,⟨6216747776375702278067,6216750625537608756979⟩⟩] +lemma kernel97_0_r5_0_eq : ∀ k : Fin 16, kernel97_0Expr 5 0 k = kernel97_0_r5_0 k := by decide +kernel +noncomputable def kernel97_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-6120748064826646007654),(-6120745301859050273781)⟩,⟨6242731927656072945032,6242734690623668678821⟩⟩,⟨⟨(-5487233472492696046280),(-5487230798336319996762)⟩,⟨6235769020297751419379,6235771694454127468828⟩⟩,⟨⟨(-4852584265115455015537),(-4852581681984515017819)⟩,⟨6193451448282621066917,6193454031413561064581⟩⟩,⟨⟨(-4222878044173258531286),(-4222875553863732071266)⟩,⟨6114129137650382351779,6114131627959908811760⟩⟩,⟨⟨(-3604222467652104214629),(-3604220071562673810616)⟩,⟨5996967119171033667320,5996969515260464071308⟩⟩,⟨⟨(-3002642158121460927919),(-3002639857236822386470)⟩,⟨5841981910554869019619,5841984211439507561057⟩⟩,⟨⟨(-2423959027978218555262),(-2423956822904012626508)⟩,⟨5650054727012720343214,5650056932086926271969⟩⟩,⟨⟨(-1873669811746389436702),(-1873667702684980086280)⟩,⟨5422920218935339414221,5422922327996748764656⟩⟩,⟨⟨(-1356824994897328679461),(-1356822981700275194155)⟩,⟨5163130226872789006259,5163132240069842491588⟩⟩,⟨⟨(-877913559607599302512),(-877911641762272111242)⟩,⟨4873992918399624759244,4873994836244951950544⟩⟩,⟨⟨(-440758005882365826062),(-440756182560316384875)⟩,⟨4559488594681797673847,4559490418003847115071⟩⟩,⟨⟨(-48423937928515960565),(-48422207966931345161)⟩,⟨4224164384165498931366,4224166114127083546814⟩⟩,⟨⟨296851874957671541100,296853512993933371924⟩,⟨3873010932287038292852,3873012570323300123725⟩⟩,⟨⟨593711638399500692955,593713186294104151609⟩,⟨3511325001058705369854,3511326548953308828561⟩⟩,⟨⟨841702320583691776411,841703780406146495285⟩,⟨3144562565985395696739,3144564025807850415668⟩⟩,⟨⟨1041275460327041080105,1041276834271486062663⟩,⟨2778187496351403970762,2778188870295848953377⟩⟩] +lemma kernel97_0_r5_1_eq : ∀ k : Fin 16, kernel97_0Expr 5 1 k = kernel97_0_r5_1 k := by decide +kernel +noncomputable def kernel97_0_r5_2 : Fin 16 → CBox := ![⟨⟨1193760409505037763683,1193761699939406172987⟩,⟨2417521194755970555882,2417522485190338965234⟩⟩,⟨⟨1301311530364217333220,1301312739867094590841⟩,⟨2067598627601463632397,2067599837104340890056⟩⟩,⟨⟨1366830983366161720398,1366832114640844496260⟩,⟨1733035985769868967313,1733037117044551743204⟩⟩,⟨⟨1393869806980359727381,1393870862884967629124⟩,⟨1417914775307254345760,1417915831211862247524⟩⟩,⟨⟨1386510949258859306656,1386511932734021281343⟩,⟨1125686466645004689062,1125687450120166663762⟩⟩,⟨⟨1349238706610243481183,1349239620756226320436⟩,⟨859100955200427910366,859101869346410749625⟩⟩,⟨⟨1286799613605070263099,1286800461492213913977⟩,⟨620161049786368069386,620161897673511720266⟩⟩,⟨⟨1204060171330545398294,1204060956098023085831⟩,⟨410104058190118006041,410104842957595693575⟩⟩,⟨⟨1105866882558645263932,1105867607331463808909⟩,⟨229410344954299850196,229411069727118395167⟩⟩,⟨⟨996913870128859212111,996914538088997834520⟩,⟨77837555281926369423,77838223242064991823⟩⟩,⟨⟨881622904316028265772,881623518572941966468⟩,⟨(-45521901198431589565),(-45521286941517888880)⟩⟩,⟨⟨764039978489593215751,764040542146601644763⟩,⟨(-142163475618467467014),(-142162911961459038015)⟩⟩,⟨⟨647751693340570900267,647752209427042911462⟩,⟨(-214077353225988262922),(-214076837139516251739)⟩⟩,⟨⟨535823687542186214205,535824159050727202642⟩,⟨(-263644255428736949995),(-263643783920195961569)⟩⟩,⟨⟨430762249741555110590,430762679562700849159⟩,⟨(-293525135303590375313),(-293524705482444636752)⟩⟩,⟨⟨334499125620035474714,334499516583165669144⟩,⟨(-306549751359352756236),(-306549360396222561811)⟩⟩] +lemma kernel97_0_r5_2_eq : ∀ k : Fin 16, kernel97_0Expr 5 2 k = kernel97_0_r5_2 k := by decide +kernel +noncomputable def kernel97_0_r5_3 : Fin 16 → CBox := ![⟨⟨248398460468988882369,248398815280629796603⟩,⟨(-305608865585318537748),(-305608510773677623517)⟩⟩,⟨⟨173283850359236747040,173284171655656702693⟩,⟨(-293554339108153709512),(-293554017811733753861)⟩⟩,⟨⟨109482666471474920721,109482956753545087017⟩,⟨(-273110727531363872275),(-273110437249293705980)⟩⟩,⟨⟨56884205196401587327,56884466875297186547⟩,⟨(-246801158221848379594),(-246800896542952780373)⟩⟩,⟨⟨15007828304127041090,15008063650761488009⟩,⟨(-216889357344668470297),(-216889121998034023375)⟩⟩,⟨⟨(-16922899034140456470),(-16922687841664336082)⟩,⟨(-185338746178310187359),(-185338534985834066969)⟩⟩,⟨⟨(-39903993168421098744),(-39903804093973879819)⟩,⟨(-153788600713381805141),(-153788411638934586214)⟩⟩,⟨⟨(-55076402753272935076),(-55076233861915900033)⟩,⟨(-123546420699492381480),(-123546251808135346435)⟩⟩,⟨⟨(-63656114537705548275),(-63655964033469132136)⟩,⟨(-95594927631073969966),(-95594777126837553824)⟩⟩,⟨⟨(-66871616463453808812),(-66871482646795468487)⟩,⟨(-70611541079999199990),(-70611407263340859664)⟩⟩,⟨⟨(-65910646207307482067),(-65910527476837935587)⟩,⟨(-48997789144390428846),(-48997670413920882364)⟩⟩,⟨⟨(-61877442202295609768),(-61877336859161018496)⟩,⟨(-30915900678936213598),(-30915795335801622326)⟩⟩,⟨⟨(-55761011876621275371),(-55760918635538345102)⟩,⟨(-16329797533816954347),(-16329704292734024078)⟩⟩,⟨⟨(-48414284500533515172),(-48414202157135544282)⟩,⟨(-5047841161780630309),(-5047758818382659419)⟩⟩,⟨⟨(-40543451570958588096),(-40543379026721585550)⟩,⟨3235043419560152007,3235115963797154552⟩⟩,⟨⟨(-32706350715977140625),(-32706286950509337186)⟩,⟨8897865768338356774,8897929533806160213⟩⟩] +lemma kernel97_0_r5_3_eq : ∀ k : Fin 16, kernel97_0Expr 5 3 k = kernel97_0_r5_3 k := by decide +kernel +noncomputable def kernel97_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-25318426654044982033),(-25318370742620284434)⟩,⟨12358247624771293348,12358303536195990947⟩⟩,⟨⟨(-18664613982370841918),(-18664565068831136406)⟩,⟨14042362984830826678,14042411898370532189⟩⟩,⟨⟨(-12915424396388016105),(-12915381709957181815)⟩,⟨14360753644735303246,14360796331166137536⟩⟩,⟨⟨(-8145572860809373599),(-8145535694400524572)⟩,⟨13690196817162841257,13690233983571690284⟩⟩,⟨⟨(-4353622927707554200),(-4353590648307390007)⟩,⟨12361423138046715482,12361455417446879675⟩⟩,⟨⟨(-1481347827845005672),(-1481319856843780784)⟩,⟨10652179096543894975,10652207067545119864⟩⟩,⟨⟨568234760110781196,568258937379337066⟩,⟨8784907095622916564,8784931272891472435⟩⟩,⟨⟨1914914578959602969,1914935428839726757⟩,⟨6928180081979340363,6928200931859464152⟩⟩,⟨⟨2687908350847448211,2687926285880652511⟩,⟨5200971665000810923,5200989600034015223⟩⟩,⟨⟨3015269711517060035,3015285104004118559⟩,⟨3678856587637339940,3678871980124398464⟩⟩,⟨⟨3016089314935388377,3016102492413873147⟩,⟨2401307282055274784,2401320459533759554⟩⟩,⟨⟨2795306315847818848,2795317571161124226⟩,⟨1379364357748563550,1379375613061868928⟩⟩,⟨⟨2440822694443170180,2440832283133602261⟩,⟨603096759811882440,603106348502314521⟩⟩,⟨⟨2022530530727975406,2022538681716203558⟩,⟨48415889050830675,48424040039058827⟩⟩,⟨⟨1592825748967587918,1592832660383092415⟩,⟨(-317045481853892932),(-317038570438388436)⟩⟩,⟨⟨1188183279256987374,1188189126039920108⟩,⟨(-529144617640532068),(-529138770857599334)⟩⟩] +lemma kernel97_0_r5_4_eq : ∀ k : Fin 16, kernel97_0Expr 5 4 k = kernel97_0_r5_4 k := by decide +kernel +noncomputable def kernel97_0_r5_5 : Fin 16 → CBox := ![⟨⟨831400040253851689,831404973414032581⟩,⟨(-623571199047879064),(-623566265887698172)⟩⟩,⟨⟨534164567939794510,534168721082532938⟩,⟨(-633270866321176609),(-633266713178438181)⟩⟩,⟨⟨299676988887759601,299680477236121582⟩,⟨(-586835026129851141),(-586831537781489161)⟩⟩,⟨⟨125112425703604212,125115348901691629⟩,⟨(-507701554940112551),(-507698631742025135)⟩⟩,⟨⟨3788485636899469,3790928770160004⟩,⟨(-413992445852362388),(-413990002719101852)⟩⟩,⟨⟨(-73041707540997640),(-73039670169735305)⟩,⟨(-318813998867196848),(-318811961495934513)⟩⟩,⟨⟨(-114798536591926877),(-114796842030994269)⟩,⟨(-230858362671120346),(-230856668110187738)⟩⟩,⟨⟨(-130575142754336728),(-130573736549192399)⟩,⟨(-155167638250328423),(-155166232045184094)⟩⟩,⟨⟨(-128487373196029940),(-128486209401832933)⟩,⟨(-93949115228263782),(-93947951434066774)⟩⟩,⟨⟨(-115318150806952685),(-115317189175644790)⟩,⟨(-47359017601799637),(-47358055970491742)⟩⟩,⟨⟨(-96392631865074518),(-96391839247410521)⟩,⟨(-14199548271143170),(-14198755653479174)⟩⟩,⟨⟨(-75620634262340539),(-75619982428827259)⟩,⟨7501853314478979,7502505147992259⟩⟩,⟨⟨(-55648273234111617),(-55647738610998339)⟩,⟨20042485339528021,20043019962641300⟩⟩,⟨⟨(-38069586663663159),(-38069149124920892)⟩,⟨25720265946464914,25720703485207182⟩⟩,⟨⟨(-23659375099108027),(-23659017954629522)⟩,⟨26622227751171197,26622584895649701⟩⟩,⟨⟨(-12599144987324134),(-12598854057932280)⟩,⟨24506606878206865,24506897807598718⟩⟩] +lemma kernel97_0_r5_5_eq : ∀ k : Fin 16, kernel97_0Expr 5 5 k = kernel97_0_r5_5 k := by decide +kernel +noncomputable def kernel97_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-4677882739181063),(-4677646379284169)⟩,⟨20757298485769828,20757534845666722⟩⟩,⟨⟨542233087097929,542424709182566⟩,⟨16389872412137394,16390064034222031⟩⟩,⟨⟨3598491058827073,3598646011013495⟩,⟨12090556319198372,12090711271384793⟩⟩,⟨⟨5037243557183493,5037368587097519⟩,⟨8272819238985334,8272944268899360⟩⟩,⟨⟨5355976302785241,5356076919862136⟩,⟨5139806349062463,5139906966139358⟩⟩,⟨⟨4971799881430409,4971880684948676⟩,⟨2744404875804919,2744485679323186⟩⟩,⟨⟨4209857086858808,4209921810193235⟩,⟨1041852263732719,1041916987067146⟩⟩,⟨⟨3305480933114258,3305532667596089⟩,⟨(-67649174225847),(-67597439744017)⟩⟩,⟨⟨2414777282876055,2414818580671681⟩,⟨(-706928583644387),(-706887285848760)⟩⟩,⟨⟨1629386425516779,1629419342361885⟩,⟨(-999767623356272),(-999734706511167)⟩⟩,⟨⟨992307933496549,992334103100984⟩,⟨(-1057290378254008),(-1057264208649572)⟩⟩,⟨⟨512718349697939,512739113211215⟩,⟨(-971024379079485),(-971003615566209)⟩⟩,⟨⟨178592741361106,178609172568991⟩,⟨(-810805481360160),(-810789050152275)⟩⟩,⟨⟨(-33375886167995),(-33362907764731)⟩,⟨(-625874204771986),(-625861226368722)⟩⟩,⟨⟨(-150581338144369),(-150571112608841)⟩,⟨(-447797303558545),(-447787078023016)⟩⟩,⟨⟨(-199750546829264),(-199742505142172)⟩,⟨(-294175271461249),(-294167229774157)⟩⟩] +lemma kernel97_0_r5_6_eq : ∀ k : Fin 16, kernel97_0Expr 5 6 k = kernel97_0_r5_6 k := by decide +kernel +noncomputable def kernel97_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-204189980708638),(-204183672852489)⟩,⟨(-172412908940335),(-172406601084186)⟩⟩,⟨⟨(-182541344911374),(-182536405317192)⟩,⟨(-83105712171457),(-83100772577274)⟩⟩,⟨⟨(-148579877707154),(-148576018294237)⟩,⟨(-22813971849431),(-22810112436513)⟩⟩,⟨⟨(-111655926903229),(-111652916912847)⟩,⟨13843656355561,13846666345943⟩⟩,⟨⟨(-77466670220729),(-77464328506002)⟩,⟨32740440382277,32742782097004⟩⟩,⟨⟨(-48932974673734),(-48931155865881)⟩,⟨39339631093474,39341449901327⟩⟩,⟨⟨(-27035399081058),(-27033989769221)⟩,⟨38219578789159,38220988100995⟩⟩,⟨⟨(-11527764292379),(-11526674119635)⟩,⟨32904440816950,32905530989694⟩⟩,⟨⟨(-1494676127081),(-1493834230585)⟩,⟨25892879241760,25893721138256⟩⟩,⟨⟨4248128241552,4248777613863⟩,⟨18798082301631,18798731673942⟩⟩,⟨⟨6892437145797,6892936874457⟩,⟨12535177821655,12535677550314⟩⟩,⟨⟨7487870566010,7488254543551⟩,⟨7513147389536,7513531367076⟩⟩,⟨⟨6874432140536,6874726488228⟩,⟨3805872736058,3806167083750⟩⟩,⟨⟨5670283585511,5670508937159⟩,⟨1290239091390,1290464443038⟩⟩,⟨⟨4292428596831,4292600751101⟩,⟨(-251572953324),(-251400799054)⟩⟩,⟨⟨2993462771225,2993594103884⟩,⟨(-1062811931923),(-1062680599265)⟩⟩] +lemma kernel97_0_r5_7_eq : ∀ k : Fin 16, kernel97_0Expr 5 7 k = kernel97_0_r5_7 k := by decide +kernel +noncomputable def kernel97_0_r5_8 : Fin 16 → CBox := ![⟨⟨1902794864577,1902894835158⟩,⟨(-1370183257110),(-1370083286528)⟩⟩,⟨⟨1065196525136,1065272576844⟩,⟨(-1362516281389),(-1362440229682)⟩⟩,⟨⟨472981113263,473038849489⟩,⟨(-1183698332791),(-1183640596564)⟩⟩,⟨⟨90533599578,90577378087⟩,⟨(-934479257815),(-934435479305)⟩⟩,⟨⟨(-128549835302),(-128516709963)⟩,⟨(-678985703362),(-678952578022)⟩⟩,⟨⟨(-230623057290),(-230598017777)⟩,⟨(-453015993680),(-452990954166)⟩⟩,⟨⟨(-256033859174),(-256014963426)⟩,⟨(-272252884224),(-272233988476)⟩⟩,⟨⟨(-236632491725),(-236618245423)⟩,⟨(-139370224141),(-139355977839)⟩⟩,⟨⟨(-195509942684),(-195499223528)⟩,⟨(-49609340212),(-49598621055)⟩⟩,⟨⟨(-147994209017),(-147986149840)⟩,⟨5209735526,5217794704⟩⟩,⟨⟨(-103205119430),(-103199069730)⟩,⟨34057262968,34063312669⟩⟩,⟨⟨(-65710770574),(-65706233011)⟩,⟨45160544561,45165082124⟩⟩,⟨⟨(-37021967443),(-37018570253)⟩,⟨45269732379,45273129570⟩⟩,⟨⟨(-16802198711),(-16799656512)⟩,⟨39454279769,39456821969⟩⟩,⟨⟨(-3763964850),(-3762065518)⟩,⟨31213892432,31215791764⟩⟩,⟨⟨3722818365,3724236618⟩,⟨22744914494,22746332748⟩⟩] +lemma kernel97_0_r5_8_eq : ∀ k : Fin 16, kernel97_0Expr 5 8 k = kernel97_0_r5_8 k := by decide +kernel +noncomputable def kernel97_0_r5_9 : Fin 16 → CBox := ![⟨⟨7258268473,7259325680⟩,⟨15255412844,15256470052⟩⟩,⟨⟨8216323579,8217111442⟩,⟨9264767883,9265555746⟩⟩,⟨⟨7669340568,7669926881⟩,⟨4855245853,4855832165⟩⟩,⟨⟨6387511250,6387947412⟩,⟨1864429762,1864865924⟩⟩,⟨⟨4878439391,4878763370⟩,⟨20440734,20764713⟩⟩,⟨⟨3442935669,3443176296⟩,⟨(-971390211),(-971149583)⟩⟩,⟨⟨2232067565,2232246067⟩,⟨(-1379276009),(-1379097506)⟩⟩,⟨⟨1297302239,1297434640⟩,⟨(-1422220641),(-1422088241)⟩⟩,⟨⟨630320289,630418360⟩,⟨(-1264388548),(-1264290477)⟩⟩,⟨⟨192055942,192128603⟩,⟨(-1019326503),(-1019253843)⟩⟩,⟨⟨(-67831030),(-67777249)⟩,⟨(-758857460),(-758803679)⟩⟩,⟨⟨(-199137463),(-199097654)⟩,⟨(-523276729),(-523236920)⟩⟩,⟨⟨(-244916630),(-244887193)⟩,⟨(-330890080),(-330860643)⟩⟩,⟨⟨(-239071215),(-239049435)⟩,⟨(-185945260),(-185923479)⟩⟩,⟨⟨(-206269778),(-206253677)⟩,⟨(-84668545),(-84652445)⟩⟩,⟨⟨(-163102900),(-163090932)⟩,⟨(-19506390),(-19494423)⟩⟩] +lemma kernel97_0_r5_9_eq : ∀ k : Fin 16, kernel97_0Expr 5 9 k = kernel97_0_r5_9 k := by decide +kernel +noncomputable def kernel97_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-119742380),(-119733489)⟩,⟨18137822,18146712⟩⟩,⟨⟨(-81649528),(-81642914)⟩,⟨36319169,36325783⟩⟩,⟨⟨(-51086224),(-51081309)⟩,⟨41781803,41786718⟩⟩,⟨⟨(-28325699),(-28322041)⟩,⟨39719491,39723149⟩⟩,⟨⟨(-12547928),(-12545208)⟩,⟨33846881,33849601⟩⟩,⟨⟨(-2453153),(-2451128)⟩,⟨26625386,26627411⟩⟩,⟨⟨3352226,3353735⟩,⟨19541632,19543141⟩⟩,⟨⟨6139198,6140324⟩,⟨13377947,13379072⟩⟩,⟨⟨6956698,6957537⟩,⟨8444160,8444999⟩⟩,⟨⟨6606511,6607137⟩,⟨4759593,4760219⟩⟩,⟨⟨5660612,5661082⟩,⟨2185755,2186226⟩⟩,⟨⟨4498709,4499062⟩,⟨516351,516704⟩⟩,⟨⟨3351789,3352055⟩,⟨(-466532),(-466265)⟩⟩,⟨⟨2343418,2343619⟩,⟨(-961065),(-960864)⟩⟩,⟨⟨1524758,1524910⟩,⟨(-1131366),(-1131214)⟩⟩,⟨⟨901951,902068⟩,⟨(-1103936),(-1103820)⟩⟩] +lemma kernel97_0_r5_10_eq : ∀ k : Fin 16, kernel97_0Expr 5 10 k = kernel97_0_r5_10 k := by decide +kernel +noncomputable def kernel97_0_r5_11 : Fin 16 → CBox := ![⟨⟨456130,456218⟩,⟨(-970249),(-970161)⟩⟩,⟨⟨157079,157149⟩,⟨(-792281),(-792212)⟩⟩,⟨⟨(-28100),(-28045)⟩,⟨(-608935),(-608880)⟩⟩,⟨⟨(-130035),(-129991)⟩,⟨(-442181),(-442137)⟩⟩,⟨⟨(-174676),(-174642)⟩,⟨(-302311),(-302278)⟩⟩,⟨⟨(-182537),(-182510)⟩,⟨(-192114),(-192087)⟩⟩,⟨⟨(-168904),(-168881)⟩,⟨(-109962),(-109939)⟩⟩,⟨⟨(-144527),(-144508)⟩,⟨(-51997),(-51978)⟩⟩,⟨⟨(-116518),(-116502)⟩,⟨(-13546),(-13530)⟩⟩,⟨⟨(-89222),(-89206)⟩,⟨10006,10022⟩⟩,⟨⟨(-64997),(-64984)⟩,⟨22766,22779⟩⟩,⟨⟨(-44864),(-44852)⟩,⟨28119,28132⟩⟩,⟨⟨(-28992),(-28980)⟩,⟨28712,28723⟩⟩,⟨⟨(-17060),(-17049)⟩,⟨26502,26513⟩⟩,⟨⟨(-8505),(-8496)⟩,⟨22876,22885⟩⟩,⟨⟨(-2688),(-2679)⟩,⟨18754,18764⟩⟩] +lemma kernel97_0_r5_11_eq : ∀ k : Fin 16, kernel97_0Expr 5 11 k = kernel97_0_r5_11 k := by decide +kernel +noncomputable def kernel97_0_r5_12 : Fin 16 → CBox := ![⟨⟨1013,1021⟩,⟨14711,14718⟩⟩,⟨⟨3151,3160⟩,⟨11065,11074⟩⟩,⟨⟨4186,4193⟩,⟨7968,7976⟩⟩,⟨⟨4480,4489⟩,⟨5457,5466⟩⟩,⟨⟨4311,4319⟩,⟨3502,3510⟩⟩,⟨⟨3879,3887⟩,⟨2036,2045⟩⟩,⟨⟨3324,3331⟩,⟨983,991⟩⟩,⟨⟨2738,2746⟩,⟨258,265⟩⟩,⟨⟨2179,2187⟩,⟨(-213),(-205)⟩⟩,⟨⟨1678,1685⟩,⟨(-493),(-485)⟩⟩,⟨⟨1248,1255⟩,⟨(-636),(-628)⟩⟩,⟨⟨893,900⟩,⟨(-685),(-678)⟩⟩,⟨⟨611,617⟩,⟨(-672),(-666)⟩⟩,⟨⟨390,397⟩,⟨(-623),(-616)⟩⟩,⟨⟨224,232⟩,⟨(-554),(-546)⟩⟩,⟨⟨104,110⟩,⟨(-476),(-469)⟩⟩] +lemma kernel97_0_r5_12_eq : ∀ k : Fin 16, kernel97_0Expr 5 12 k = kernel97_0_r5_12 k := by decide +kernel +noncomputable def kernel97_0_r5_13 : Fin 16 → CBox := ![⟨⟨18,25⟩,⟨(-400),(-392)⟩⟩,⟨⟨(-39),(-32)⟩,⟨(-327),(-319)⟩⟩,⟨⟨(-75),(-67)⟩,⟨(-261),(-253)⟩⟩,⟨⟨(-94),(-88)⟩,⟨(-203),(-198)⟩⟩,⟨⟨(-104),(-97)⟩,⟨(-156),(-149)⟩⟩,⟨⟨(-106),(-98)⟩,⟨(-115),(-108)⟩⟩,⟨⟨(-102),(-95)⟩,⟨(-83),(-77)⟩⟩,⟨⟨(-95),(-87)⟩,⟨(-58),(-50)⟩⟩,⟨⟨(-86),(-79)⟩,⟨(-39),(-31)⟩⟩,⟨⟨(-76),(-70)⟩,⟨(-22),(-17)⟩⟩,⟨⟨(-66),(-60)⟩,⟨(-11),(-5)⟩⟩,⟨⟨(-57),(-51)⟩,⟨(-3),3⟩⟩,⟨⟨(-50),(-42)⟩,⟨3,11⟩⟩,⟨⟨(-41),(-35)⟩,⟨8,14⟩⟩,⟨⟨(-35),(-29)⟩,⟨10,16⟩⟩,⟨⟨(-29),(-23)⟩,⟨11,17⟩⟩] +lemma kernel97_0_r5_13_eq : ∀ k : Fin 16, kernel97_0Expr 5 13 k = kernel97_0_r5_13 k := by decide +kernel +noncomputable def kernel97_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-24),(-18)⟩,⟨12,18⟩⟩,⟨⟨(-20),(-13)⟩,⟨11,19⟩⟩,⟨⟨(-17),(-10)⟩,⟨11,19⟩⟩,⟨⟨(-14),(-6)⟩,⟨10,17⟩⟩,⟨⟨(-11),(-4)⟩,⟨9,17⟩⟩,⟨⟨(-9),(-2)⟩,⟨8,15⟩⟩,⟨⟨(-7),(-1)⟩,⟨8,14⟩⟩,⟨⟨(-6),0⟩,⟨7,13⟩⟩,⟨⟨(-5),1⟩,⟨7,13⟩⟩,⟨⟨(-4),4⟩,⟨5,12⟩⟩,⟨⟨(-3),3⟩,⟨5,11⟩⟩,⟨⟨(-2),4⟩,⟨4,10⟩⟩,⟨⟨(-2),4⟩,⟨3,9⟩⟩,⟨⟨(-2),5⟩,⟨2,10⟩⟩,⟨⟨(-2),5⟩,⟨1,8⟩⟩,⟨⟨(-2),4⟩,⟨1,7⟩⟩] +lemma kernel97_0_r5_14_eq : ∀ k : Fin 16, kernel97_0Expr 5 14 k = kernel97_0_r5_14 k := by decide +kernel +noncomputable def kernel97_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨1,7⟩⟩,⟨⟨(-1),5⟩,⟨1,7⟩⟩,⟨⟨(-2),5⟩,⟨0,7⟩⟩,⟨⟨(-1),5⟩,⟨1,7⟩⟩,⟨⟨(-1),5⟩,⟨0,6⟩⟩,⟨⟨(-1),5⟩,⟨0,6⟩⟩,⟨⟨(-1),5⟩,⟨0,6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),5⟩,⟨(-2),6⟩⟩,⟨⟨(-2),5⟩,⟨(-2),6⟩⟩,⟨⟨(-2),5⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩,⟨⟨(-2),6⟩,⟨(-2),6⟩⟩] +lemma kernel97_0_r5_15_eq : ∀ k : Fin 16, kernel97_0Expr 5 15 k = kernel97_0_r5_15 k := by decide +kernel +noncomputable def kernel97_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel97_0_r5_0,kernel97_0_r5_1,kernel97_0_r5_2,kernel97_0_r5_3,kernel97_0_r5_4,kernel97_0_r5_5,kernel97_0_r5_6,kernel97_0_r5_7,kernel97_0_r5_8,kernel97_0_r5_9,kernel97_0_r5_10,kernel97_0_r5_11,kernel97_0_r5_12,kernel97_0_r5_13,kernel97_0_r5_14,kernel97_0_r5_15] +lemma kernel97_0_r5_eq (i k : Fin 16) : kernel97_0Expr 5 i k = kernel97_0_r5 i k := by + fin_cases i + · exact kernel97_0_r5_0_eq k + · exact kernel97_0_r5_1_eq k + · exact kernel97_0_r5_2_eq k + · exact kernel97_0_r5_3_eq k + · exact kernel97_0_r5_4_eq k + · exact kernel97_0_r5_5_eq k + · exact kernel97_0_r5_6_eq k + · exact kernel97_0_r5_7_eq k + · exact kernel97_0_r5_8_eq k + · exact kernel97_0_r5_9_eq k + · exact kernel97_0_r5_10_eq k + · exact kernel97_0_r5_11_eq k + · exact kernel97_0_r5_12_eq k + · exact kernel97_0_r5_13_eq k + · exact kernel97_0_r5_14_eq k + · exact kernel97_0_r5_15_eq k +noncomputable def kernel97_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel97_0_r0,kernel97_0_r1,kernel97_0_r2,kernel97_0_r3,kernel97_0_r4,kernel97_0_r5] +lemma kernel97_0_eq (j : Fin 6) (i k : Fin 16) : kernel97_0Expr j i k = kernel97_0 j i k := by + fin_cases j + · exact kernel97_0_r0_eq i k + · exact kernel97_0_r1_eq i k + · exact kernel97_0_r2_eq i k + · exact kernel97_0_r3_eq i k + · exact kernel97_0_r4_eq i k + · exact kernel97_0_r5_eq i k +lemma kernel97_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel97_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(97:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel97_0_eq] + unfold kernel97_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans97_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel97_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans97 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel97_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r0_0_eq : ∀ k : Fin 16, kernel97_1Expr 0 0 k = kernel97_1_r0_0 k := by decide +kernel +noncomputable def kernel97_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r0_1_eq : ∀ k : Fin 16, kernel97_1Expr 0 1 k = kernel97_1_r0_1 k := by decide +kernel +noncomputable def kernel97_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r0_2_eq : ∀ k : Fin 16, kernel97_1Expr 0 2 k = kernel97_1_r0_2 k := by decide +kernel +noncomputable def kernel97_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r0_3_eq : ∀ k : Fin 16, kernel97_1Expr 0 3 k = kernel97_1_r0_3 k := by decide +kernel +noncomputable def kernel97_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r0_4_eq : ∀ k : Fin 16, kernel97_1Expr 0 4 k = kernel97_1_r0_4 k := by decide +kernel +noncomputable def kernel97_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel97_1_r0_5_eq : ∀ k : Fin 16, kernel97_1Expr 0 5 k = kernel97_1_r0_5 k := by decide +kernel +noncomputable def kernel97_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel97_1_r0_6_eq : ∀ k : Fin 16, kernel97_1Expr 0 6 k = kernel97_1_r0_6 k := by decide +kernel +noncomputable def kernel97_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel97_1_r0_7_eq : ∀ k : Fin 16, kernel97_1Expr 0 7 k = kernel97_1_r0_7 k := by decide +kernel +noncomputable def kernel97_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel97_1_r0_8_eq : ∀ k : Fin 16, kernel97_1Expr 0 8 k = kernel97_1_r0_8 k := by decide +kernel +noncomputable def kernel97_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel97_1_r0_9_eq : ∀ k : Fin 16, kernel97_1Expr 0 9 k = kernel97_1_r0_9 k := by decide +kernel +noncomputable def kernel97_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel97_1_r0_10_eq : ∀ k : Fin 16, kernel97_1Expr 0 10 k = kernel97_1_r0_10 k := by decide +kernel +noncomputable def kernel97_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel97_1_r0_11_eq : ∀ k : Fin 16, kernel97_1Expr 0 11 k = kernel97_1_r0_11 k := by decide +kernel +noncomputable def kernel97_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel97_1_r0_12_eq : ∀ k : Fin 16, kernel97_1Expr 0 12 k = kernel97_1_r0_12 k := by decide +kernel +noncomputable def kernel97_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel97_1_r0_13_eq : ∀ k : Fin 16, kernel97_1Expr 0 13 k = kernel97_1_r0_13 k := by decide +kernel +noncomputable def kernel97_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel97_1_r0_14_eq : ∀ k : Fin 16, kernel97_1Expr 0 14 k = kernel97_1_r0_14 k := by decide +kernel +noncomputable def kernel97_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel97_1_r0_15_eq : ∀ k : Fin 16, kernel97_1Expr 0 15 k = kernel97_1_r0_15 k := by decide +kernel +noncomputable def kernel97_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel97_1_r0_0,kernel97_1_r0_1,kernel97_1_r0_2,kernel97_1_r0_3,kernel97_1_r0_4,kernel97_1_r0_5,kernel97_1_r0_6,kernel97_1_r0_7,kernel97_1_r0_8,kernel97_1_r0_9,kernel97_1_r0_10,kernel97_1_r0_11,kernel97_1_r0_12,kernel97_1_r0_13,kernel97_1_r0_14,kernel97_1_r0_15] +lemma kernel97_1_r0_eq (i k : Fin 16) : kernel97_1Expr 0 i k = kernel97_1_r0 i k := by + fin_cases i + · exact kernel97_1_r0_0_eq k + · exact kernel97_1_r0_1_eq k + · exact kernel97_1_r0_2_eq k + · exact kernel97_1_r0_3_eq k + · exact kernel97_1_r0_4_eq k + · exact kernel97_1_r0_5_eq k + · exact kernel97_1_r0_6_eq k + · exact kernel97_1_r0_7_eq k + · exact kernel97_1_r0_8_eq k + · exact kernel97_1_r0_9_eq k + · exact kernel97_1_r0_10_eq k + · exact kernel97_1_r0_11_eq k + · exact kernel97_1_r0_12_eq k + · exact kernel97_1_r0_13_eq k + · exact kernel97_1_r0_14_eq k + · exact kernel97_1_r0_15_eq k +noncomputable def kernel97_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel97_1_r1_0_eq : ∀ k : Fin 16, kernel97_1Expr 1 0 k = kernel97_1_r1_0 k := by decide +kernel +noncomputable def kernel97_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel97_1_r1_1_eq : ∀ k : Fin 16, kernel97_1Expr 1 1 k = kernel97_1_r1_1 k := by decide +kernel +noncomputable def kernel97_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel97_1_r1_2_eq : ∀ k : Fin 16, kernel97_1Expr 1 2 k = kernel97_1_r1_2 k := by decide +kernel +noncomputable def kernel97_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel97_1_r1_3_eq : ∀ k : Fin 16, kernel97_1Expr 1 3 k = kernel97_1_r1_3 k := by decide +kernel +noncomputable def kernel97_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel97_1_r1_4_eq : ∀ k : Fin 16, kernel97_1Expr 1 4 k = kernel97_1_r1_4 k := by decide +kernel +noncomputable def kernel97_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel97_1_r1_5_eq : ∀ k : Fin 16, kernel97_1Expr 1 5 k = kernel97_1_r1_5 k := by decide +kernel +noncomputable def kernel97_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel97_1_r1_6_eq : ∀ k : Fin 16, kernel97_1Expr 1 6 k = kernel97_1_r1_6 k := by decide +kernel +noncomputable def kernel97_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel97_1_r1_7_eq : ∀ k : Fin 16, kernel97_1Expr 1 7 k = kernel97_1_r1_7 k := by decide +kernel +noncomputable def kernel97_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel97_1_r1_8_eq : ∀ k : Fin 16, kernel97_1Expr 1 8 k = kernel97_1_r1_8 k := by decide +kernel +noncomputable def kernel97_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel97_1_r1_9_eq : ∀ k : Fin 16, kernel97_1Expr 1 9 k = kernel97_1_r1_9 k := by decide +kernel +noncomputable def kernel97_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r1_10_eq : ∀ k : Fin 16, kernel97_1Expr 1 10 k = kernel97_1_r1_10 k := by decide +kernel +noncomputable def kernel97_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r1_11_eq : ∀ k : Fin 16, kernel97_1Expr 1 11 k = kernel97_1_r1_11 k := by decide +kernel +noncomputable def kernel97_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r1_12_eq : ∀ k : Fin 16, kernel97_1Expr 1 12 k = kernel97_1_r1_12 k := by decide +kernel +noncomputable def kernel97_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r1_13_eq : ∀ k : Fin 16, kernel97_1Expr 1 13 k = kernel97_1_r1_13 k := by decide +kernel +noncomputable def kernel97_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r1_14_eq : ∀ k : Fin 16, kernel97_1Expr 1 14 k = kernel97_1_r1_14 k := by decide +kernel +noncomputable def kernel97_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel97_1_r1_15_eq : ∀ k : Fin 16, kernel97_1Expr 1 15 k = kernel97_1_r1_15 k := by decide +kernel +noncomputable def kernel97_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel97_1_r1_0,kernel97_1_r1_1,kernel97_1_r1_2,kernel97_1_r1_3,kernel97_1_r1_4,kernel97_1_r1_5,kernel97_1_r1_6,kernel97_1_r1_7,kernel97_1_r1_8,kernel97_1_r1_9,kernel97_1_r1_10,kernel97_1_r1_11,kernel97_1_r1_12,kernel97_1_r1_13,kernel97_1_r1_14,kernel97_1_r1_15] +lemma kernel97_1_r1_eq (i k : Fin 16) : kernel97_1Expr 1 i k = kernel97_1_r1 i k := by + fin_cases i + · exact kernel97_1_r1_0_eq k + · exact kernel97_1_r1_1_eq k + · exact kernel97_1_r1_2_eq k + · exact kernel97_1_r1_3_eq k + · exact kernel97_1_r1_4_eq k + · exact kernel97_1_r1_5_eq k + · exact kernel97_1_r1_6_eq k + · exact kernel97_1_r1_7_eq k + · exact kernel97_1_r1_8_eq k + · exact kernel97_1_r1_9_eq k + · exact kernel97_1_r1_10_eq k + · exact kernel97_1_r1_11_eq k + · exact kernel97_1_r1_12_eq k + · exact kernel97_1_r1_13_eq k + · exact kernel97_1_r1_14_eq k + · exact kernel97_1_r1_15_eq k +noncomputable def kernel97_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel97_1_r2_0_eq : ∀ k : Fin 16, kernel97_1Expr 2 0 k = kernel97_1_r2_0 k := by decide +kernel +noncomputable def kernel97_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel97_1_r2_1_eq : ∀ k : Fin 16, kernel97_1Expr 2 1 k = kernel97_1_r2_1 k := by decide +kernel +noncomputable def kernel97_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel97_1_r2_2_eq : ∀ k : Fin 16, kernel97_1Expr 2 2 k = kernel97_1_r2_2 k := by decide +kernel +noncomputable def kernel97_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel97_1_r2_3_eq : ∀ k : Fin 16, kernel97_1Expr 2 3 k = kernel97_1_r2_3 k := by decide +kernel +noncomputable def kernel97_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel97_1_r2_4_eq : ∀ k : Fin 16, kernel97_1Expr 2 4 k = kernel97_1_r2_4 k := by decide +kernel +noncomputable def kernel97_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel97_1_r2_5_eq : ∀ k : Fin 16, kernel97_1Expr 2 5 k = kernel97_1_r2_5 k := by decide +kernel +noncomputable def kernel97_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel97_1_r2_6_eq : ∀ k : Fin 16, kernel97_1Expr 2 6 k = kernel97_1_r2_6 k := by decide +kernel +noncomputable def kernel97_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel97_1_r2_7_eq : ∀ k : Fin 16, kernel97_1Expr 2 7 k = kernel97_1_r2_7 k := by decide +kernel +noncomputable def kernel97_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel97_1_r2_8_eq : ∀ k : Fin 16, kernel97_1Expr 2 8 k = kernel97_1_r2_8 k := by decide +kernel +noncomputable def kernel97_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel97_1_r2_9_eq : ∀ k : Fin 16, kernel97_1Expr 2 9 k = kernel97_1_r2_9 k := by decide +kernel +noncomputable def kernel97_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel97_1_r2_10_eq : ∀ k : Fin 16, kernel97_1Expr 2 10 k = kernel97_1_r2_10 k := by decide +kernel +noncomputable def kernel97_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel97_1_r2_11_eq : ∀ k : Fin 16, kernel97_1Expr 2 11 k = kernel97_1_r2_11 k := by decide +kernel +noncomputable def kernel97_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel97_1_r2_12_eq : ∀ k : Fin 16, kernel97_1Expr 2 12 k = kernel97_1_r2_12 k := by decide +kernel +noncomputable def kernel97_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel97_1_r2_13_eq : ∀ k : Fin 16, kernel97_1Expr 2 13 k = kernel97_1_r2_13 k := by decide +kernel +noncomputable def kernel97_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel97_1_r2_14_eq : ∀ k : Fin 16, kernel97_1Expr 2 14 k = kernel97_1_r2_14 k := by decide +kernel +noncomputable def kernel97_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel97_1_r2_15_eq : ∀ k : Fin 16, kernel97_1Expr 2 15 k = kernel97_1_r2_15 k := by decide +kernel +noncomputable def kernel97_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel97_1_r2_0,kernel97_1_r2_1,kernel97_1_r2_2,kernel97_1_r2_3,kernel97_1_r2_4,kernel97_1_r2_5,kernel97_1_r2_6,kernel97_1_r2_7,kernel97_1_r2_8,kernel97_1_r2_9,kernel97_1_r2_10,kernel97_1_r2_11,kernel97_1_r2_12,kernel97_1_r2_13,kernel97_1_r2_14,kernel97_1_r2_15] +lemma kernel97_1_r2_eq (i k : Fin 16) : kernel97_1Expr 2 i k = kernel97_1_r2 i k := by + fin_cases i + · exact kernel97_1_r2_0_eq k + · exact kernel97_1_r2_1_eq k + · exact kernel97_1_r2_2_eq k + · exact kernel97_1_r2_3_eq k + · exact kernel97_1_r2_4_eq k + · exact kernel97_1_r2_5_eq k + · exact kernel97_1_r2_6_eq k + · exact kernel97_1_r2_7_eq k + · exact kernel97_1_r2_8_eq k + · exact kernel97_1_r2_9_eq k + · exact kernel97_1_r2_10_eq k + · exact kernel97_1_r2_11_eq k + · exact kernel97_1_r2_12_eq k + · exact kernel97_1_r2_13_eq k + · exact kernel97_1_r2_14_eq k + · exact kernel97_1_r2_15_eq k +noncomputable def kernel97_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel97_1_r3_0_eq : ∀ k : Fin 16, kernel97_1Expr 3 0 k = kernel97_1_r3_0 k := by decide +kernel +noncomputable def kernel97_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel97_1_r3_1_eq : ∀ k : Fin 16, kernel97_1Expr 3 1 k = kernel97_1_r3_1 k := by decide +kernel +noncomputable def kernel97_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel97_1_r3_2_eq : ∀ k : Fin 16, kernel97_1Expr 3 2 k = kernel97_1_r3_2 k := by decide +kernel +noncomputable def kernel97_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel97_1_r3_3_eq : ∀ k : Fin 16, kernel97_1Expr 3 3 k = kernel97_1_r3_3 k := by decide +kernel +noncomputable def kernel97_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel97_1_r3_4_eq : ∀ k : Fin 16, kernel97_1Expr 3 4 k = kernel97_1_r3_4 k := by decide +kernel +noncomputable def kernel97_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel97_1_r3_5_eq : ∀ k : Fin 16, kernel97_1Expr 3 5 k = kernel97_1_r3_5 k := by decide +kernel +noncomputable def kernel97_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel97_1_r3_6_eq : ∀ k : Fin 16, kernel97_1Expr 3 6 k = kernel97_1_r3_6 k := by decide +kernel +noncomputable def kernel97_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel97_1_r3_7_eq : ∀ k : Fin 16, kernel97_1Expr 3 7 k = kernel97_1_r3_7 k := by decide +kernel +noncomputable def kernel97_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel97_1_r3_8_eq : ∀ k : Fin 16, kernel97_1Expr 3 8 k = kernel97_1_r3_8 k := by decide +kernel +noncomputable def kernel97_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel97_1_r3_9_eq : ∀ k : Fin 16, kernel97_1Expr 3 9 k = kernel97_1_r3_9 k := by decide +kernel +noncomputable def kernel97_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel97_1_r3_10_eq : ∀ k : Fin 16, kernel97_1Expr 3 10 k = kernel97_1_r3_10 k := by decide +kernel +noncomputable def kernel97_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel97_1_r3_11_eq : ∀ k : Fin 16, kernel97_1Expr 3 11 k = kernel97_1_r3_11 k := by decide +kernel +noncomputable def kernel97_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel97_1_r3_12_eq : ∀ k : Fin 16, kernel97_1Expr 3 12 k = kernel97_1_r3_12 k := by decide +kernel +noncomputable def kernel97_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel97_1_r3_13_eq : ∀ k : Fin 16, kernel97_1Expr 3 13 k = kernel97_1_r3_13 k := by decide +kernel +noncomputable def kernel97_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel97_1_r3_14_eq : ∀ k : Fin 16, kernel97_1Expr 3 14 k = kernel97_1_r3_14 k := by decide +kernel +noncomputable def kernel97_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel97_1_r3_15_eq : ∀ k : Fin 16, kernel97_1Expr 3 15 k = kernel97_1_r3_15 k := by decide +kernel +noncomputable def kernel97_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel97_1_r3_0,kernel97_1_r3_1,kernel97_1_r3_2,kernel97_1_r3_3,kernel97_1_r3_4,kernel97_1_r3_5,kernel97_1_r3_6,kernel97_1_r3_7,kernel97_1_r3_8,kernel97_1_r3_9,kernel97_1_r3_10,kernel97_1_r3_11,kernel97_1_r3_12,kernel97_1_r3_13,kernel97_1_r3_14,kernel97_1_r3_15] +lemma kernel97_1_r3_eq (i k : Fin 16) : kernel97_1Expr 3 i k = kernel97_1_r3 i k := by + fin_cases i + · exact kernel97_1_r3_0_eq k + · exact kernel97_1_r3_1_eq k + · exact kernel97_1_r3_2_eq k + · exact kernel97_1_r3_3_eq k + · exact kernel97_1_r3_4_eq k + · exact kernel97_1_r3_5_eq k + · exact kernel97_1_r3_6_eq k + · exact kernel97_1_r3_7_eq k + · exact kernel97_1_r3_8_eq k + · exact kernel97_1_r3_9_eq k + · exact kernel97_1_r3_10_eq k + · exact kernel97_1_r3_11_eq k + · exact kernel97_1_r3_12_eq k + · exact kernel97_1_r3_13_eq k + · exact kernel97_1_r3_14_eq k + · exact kernel97_1_r3_15_eq k +noncomputable def kernel97_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),18⟩,⟨(-28),10⟩⟩,⟨⟨(-13),18⟩,⟨(-28),10⟩⟩,⟨⟨(-13),18⟩,⟨(-28),10⟩⟩,⟨⟨(-13),18⟩,⟨(-28),10⟩⟩,⟨⟨(-13),18⟩,⟨(-28),10⟩⟩,⟨⟨(-17),18⟩,⟨(-28),11⟩⟩,⟨⟨(-17),18⟩,⟨(-28),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩] +lemma kernel97_1_r4_0_eq : ∀ k : Fin 16, kernel97_1Expr 4 0 k = kernel97_1_r4_0 k := by decide +kernel +noncomputable def kernel97_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-16),14⟩,⟨(-23),11⟩⟩,⟨⟨(-16),14⟩,⟨(-23),11⟩⟩,⟨⟨(-16),14⟩,⟨(-23),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩] +lemma kernel97_1_r4_1_eq : ∀ k : Fin 16, kernel97_1Expr 4 1 k = kernel97_1_r4_1 k := by decide +kernel +noncomputable def kernel97_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-10),15⟩,⟨(-11),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-14),11⟩⟩,⟨⟨(-15),10⟩,⟨(-14),11⟩⟩] +lemma kernel97_1_r4_2_eq : ∀ k : Fin 16, kernel97_1Expr 4 2 k = kernel97_1_r4_2 k := by decide +kernel +noncomputable def kernel97_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-15),10⟩,⟨(-14),11⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-10),15⟩,⟨(-11),15⟩⟩,⟨⟨(-11),19⟩,⟨(-16),15⟩⟩,⟨⟨(-11),19⟩,⟨(-16),15⟩⟩,⟨⟨(-11),19⟩,⟨(-16),15⟩⟩,⟨⟨(-11),15⟩,⟨(-15),10⟩⟩,⟨⟨(-11),15⟩,⟨(-15),10⟩⟩,⟨⟨(-16),15⟩,⟨(-20),11⟩⟩] +lemma kernel97_1_r4_3_eq : ∀ k : Fin 16, kernel97_1Expr 4 3 k = kernel97_1_r4_3 k := by decide +kernel +noncomputable def kernel97_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel97_1_r4_4_eq : ∀ k : Fin 16, kernel97_1Expr 4 4 k = kernel97_1_r4_4 k := by decide +kernel +noncomputable def kernel97_1_r4_5 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel97_1_r4_5_eq : ∀ k : Fin 16, kernel97_1Expr 4 5 k = kernel97_1_r4_5 k := by decide +kernel +noncomputable def kernel97_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel97_1_r4_6_eq : ∀ k : Fin 16, kernel97_1Expr 4 6 k = kernel97_1_r4_6 k := by decide +kernel +noncomputable def kernel97_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel97_1_r4_7_eq : ∀ k : Fin 16, kernel97_1Expr 4 7 k = kernel97_1_r4_7 k := by decide +kernel +noncomputable def kernel97_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel97_1_r4_8_eq : ∀ k : Fin 16, kernel97_1Expr 4 8 k = kernel97_1_r4_8 k := by decide +kernel +noncomputable def kernel97_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel97_1_r4_9_eq : ∀ k : Fin 16, kernel97_1Expr 4 9 k = kernel97_1_r4_9 k := by decide +kernel +noncomputable def kernel97_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel97_1_r4_10_eq : ∀ k : Fin 16, kernel97_1Expr 4 10 k = kernel97_1_r4_10 k := by decide +kernel +noncomputable def kernel97_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel97_1_r4_11_eq : ∀ k : Fin 16, kernel97_1Expr 4 11 k = kernel97_1_r4_11 k := by decide +kernel +noncomputable def kernel97_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel97_1_r4_12_eq : ∀ k : Fin 16, kernel97_1Expr 4 12 k = kernel97_1_r4_12 k := by decide +kernel +noncomputable def kernel97_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel97_1_r4_13_eq : ∀ k : Fin 16, kernel97_1Expr 4 13 k = kernel97_1_r4_13 k := by decide +kernel +noncomputable def kernel97_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel97_1_r4_14_eq : ∀ k : Fin 16, kernel97_1Expr 4 14 k = kernel97_1_r4_14 k := by decide +kernel +noncomputable def kernel97_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel97_1_r4_15_eq : ∀ k : Fin 16, kernel97_1Expr 4 15 k = kernel97_1_r4_15 k := by decide +kernel +noncomputable def kernel97_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel97_1_r4_0,kernel97_1_r4_1,kernel97_1_r4_2,kernel97_1_r4_3,kernel97_1_r4_4,kernel97_1_r4_5,kernel97_1_r4_6,kernel97_1_r4_7,kernel97_1_r4_8,kernel97_1_r4_9,kernel97_1_r4_10,kernel97_1_r4_11,kernel97_1_r4_12,kernel97_1_r4_13,kernel97_1_r4_14,kernel97_1_r4_15] +lemma kernel97_1_r4_eq (i k : Fin 16) : kernel97_1Expr 4 i k = kernel97_1_r4 i k := by + fin_cases i + · exact kernel97_1_r4_0_eq k + · exact kernel97_1_r4_1_eq k + · exact kernel97_1_r4_2_eq k + · exact kernel97_1_r4_3_eq k + · exact kernel97_1_r4_4_eq k + · exact kernel97_1_r4_5_eq k + · exact kernel97_1_r4_6_eq k + · exact kernel97_1_r4_7_eq k + · exact kernel97_1_r4_8_eq k + · exact kernel97_1_r4_9_eq k + · exact kernel97_1_r4_10_eq k + · exact kernel97_1_r4_11_eq k + · exact kernel97_1_r4_12_eq k + · exact kernel97_1_r4_13_eq k + · exact kernel97_1_r4_14_eq k + · exact kernel97_1_r4_15_eq k +noncomputable def kernel97_1_r5_0 : Fin 16 → CBox := ![⟨⟨19202763147096133757251,19202776767264771405498⟩,⟨43607509460304854845920,43607523080473492495107⟩⟩,⟨⟨19283861273283246772102,19283874867677927320531⟩,⟨43414992507886354847746,43415006102281035397116⟩⟩,⟨⟨19443476525231829507713,19443490068196594580632⟩,⟨43030939079333422413579,43030952622298187487435⟩⟩,⟨⟨19676502145353375637913,19676515611514305337944⟩,⟨42457336252660797371721,42457349718821727072679⟩⟩,⟨⟨19975415491905059240206,19975428856307705289370⟩,⟨41697228157660633111404,41697241522063279161471⟩⟩,⟨⟨20330441280003674741396,20330454518247808312598⟩,⟨40754787216964047221063,40754800455208180793141⟩⟩,⟨⟨20729766215370858139799,20729779303739010025541⟩,⟨39635401047361117544508,39635414135729269431094⟩⟩,⟨⟨21159802242503081041809,21159815158085505086821⟩,⟨38345768493490741453531,38345781409073165499348⟩⟩,⟨⟨21605494722607362490669,21605507443415977229853⟩,⟨36893997129894089864691,36894009850702704604629⟩⟩,⟨⟨22050670845456476156249,22050683350537545939922⟩,⟨35289693747606580094508,35289706252687649878884⟩⟩,⟨⟨22478422476045685234418,22478434745578612496808⟩,⟨33544038885823546881958,33544051155356474145000⟩⟩,⟨⟨22871516468667935698928,22871528485088617352290⟩,⟨31669836415232568540356,31669848431653250194315⟩⟩,⟨⟨23212824294451793349772,23212836040499377920574⟩,⟨29681529557562981978668,29681541303610566550009⟩⟩,⟨⟨23485761665206825320744,23485773124991150342071⟩,⟨27595175532866631035029,27595186992650956056831⟩⟩,⟨⟨23674727792536078031815,23674738951572972484756⟩,⟨25428372285334775106325,25428383444371669559676⟩⟩,⟨⟨23765533036169092994321,23765543881454542187563⟩,⟨23200132390419129528824,23200143235704578722414⟩⟩] +lemma kernel97_1_r5_0_eq : ∀ k : Fin 16, kernel97_1Expr 5 0 k = kernel97_1_r5_0 k := by decide +kernel +noncomputable def kernel97_1_r5_1 : Fin 16 → CBox := ![⟨⟨23745803076732622161871,23745813596742980214155⟩,⟨20930701275209574594440,20930711795219932647011⟩⟩,⟨⟨23605347458323772344157,23605357643085738573177⟩,⟨18641319211147743815427,18641329395909710044674⟩⟩,⟨⟨23336480460337065112911,23336490301385862375986⟩,⟨16353929083470537986921,16353938924519335250166⟩⟩,⟨⟨22934282831622432700028,22934292322062031255411⟩,⟨14090834600717952634823,14090844091157551190319⟩⟩,⟨⟨22396793993373796264784,22396803127798386762364⟩,⟨11874316263579623210590,11874325398004213708229⟩⟩,⟨⟨21725125903593237382013,21725134678152357684519⟩,⟨9726214934828391079594,9726223709387511382106⟩⟩,⟨⟨20923491864986415667417,20923500277253507475932⟩,⟨7667495109336496157308,7667503521603587965784⟩⟩,⟨⟨19999146104538483803124,19999154153605211846764⟩,⟨5717801840969723822876,5717809890036451866433⟩⟩,⟨⟨18962232885516124253261,18962240571794308236204⟩,⟨3895026621841055083463,3895034308119239066285⟩⟩,⟨⟨17825547123624240973378,17825554448899166536759⟩,⟨2214898220439338716767,2214905545714264280001⟩⟩,⟨⟨16604211841340487786536,16604218808588575729346⟩,⟨690614492366426680153,690621459614514622791⟩⟩,⟨⟨15315281151476092124932,15315287764938192565113⟩,⟨(-667469571262554378493),(-667462957800453938509)⟩⟩,⟨⟨13977280650412314150822,13977286915359168477508⟩,⟨(-1852083803427709325168),(-1852077538480854998689)⟩⟩,⟨⟨12609699947750153129730,12609705870776426832881⟩,⟨(-2859203320203074273219),(-2859197397176800570282)⟩⟩,⟨⟨11232454401721777422281,11232459990509332741280⟩,⟨(-3688118871784463694350),(-3688113282996908375565)⟩⟩,⟨⟨9865334813308760402297,9865340076012090923953⟩,⟨(-4341411925038649954086),(-4341406662335319432645)⟩⟩] +lemma kernel97_1_r5_1_eq : ∀ k : Fin 16, kernel97_1Expr 5 1 k = kernel97_1_r5_1 k := by decide +kernel +noncomputable def kernel97_1_r5_2 : Fin 16 → CBox := ![⟨⟨8527464739289885809466,8527469684726356317214⟩,⟨(-4824833151076451886371),(-4824828205639981378801)⟩⟩,⟨⟨7236785129833263961420,7236789767626747488757⟩,⟨(-5147087028562452389371),(-5147082390768968862172)⟩⟩,⟨⟨6009585134857529295058,6009589475111411767953⟩,⟨(-5319529312922084745034),(-5319524972668202272243)⟩⟩,⟨⟨4860096168080390933673,4860100221495259162926⟩,⟨(-5355787945237619752520),(-5355783891822751523339)⟩⟩,⟨⟨3800163731265974355412,3800167508864294889860⟩,⟨(-5271321370372733020557),(-5271317592774412486151)⟩⟩,⟨⟨2839008190942716350166,2839011704367129499415⟩,⟨(-5082931013446732452018),(-5082927500022319302784)⟩⟩,⟨⟨1983081831799982006559,1983085092586918035147⟩,⟨(-4808246656609704598024),(-4808243395822768569435)⟩⟩,⟨⟨1236025272284620664854,1236028292245229372902⟩,⟨(-4465204552086151447554),(-4465201532125542739487)⟩⟩,⟨⟨598721953813856601575,598724744716243254925⟩,⟨(-4071538220130283740247),(-4071535429227897086867)⟩⟩,⟨⟨69445126757385810664,69447700601759719046⟩,⟨(-3644301013114662555000),(-3644298439270288646577)⟩⟩,⟨⟨(-355912199107096157856),(-355909830585986710455)⟩,⟨(-3199437711894587957789),(-3199435343373478510341)⟩⟩,⟨⟨(-683537291125228083897),(-683535116201526467325)⟩,⟨(-2751419773381859267075),(-2751417598458157650451)⟩⟩,⟨⟨(-921343356995922227764),(-921341364213440875162)⟩,⟨(-2312955512321629977777),(-2312953519539148625129)⟩⟩,⟨⟨(-1078578303935308767901),(-1078576481963520544414)⟩,⟨(-1894782682543677982121),(-1894780860571889758593)⟩⟩,⟨⟨(-1165414939195156309679),(-1165413277081045493128)⟩,⟨(-1505546837993858381965),(-1505545175879747565384)⟩⟩,⟨⟨(-1192540862985019471456),(-1192539349994852124613)⟩,⟨(-1151764747290330000159),(-1151763234300162653299)⟩⟩] +lemma kernel97_1_r5_2_eq : ∀ k : Fin 16, kernel97_1Expr 5 2 k = kernel97_1_r5_2 k := by decide +kernel +noncomputable def kernel97_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-1170765268504073322137),(-1170763894362024703331)⟩,⟨(-837868235194283200598),(-837866861052234581782)⟩⟩,⟨⟨(-1110657985066403957087),(-1110656739751173816701)⟩,⟨(-566320352728331336322),(-566319107413101195931)⟩⟩,⟨⟨(-1022233515949011330186),(-1022232389946396633026)⟩,⟨(-337792911068071777025),(-337791785065457079863)⟩⟩,⟨⟨(-914689721940066091565),(-914688706066306465945)⟩,⟨(-151392297668313740825),(-151391281794554115210)⟩⟩,⟨⟨(-796207385821128403149),(-796206471419633737700)⟩,⟨(-4919204566737292437),(-4918290165242627001)⟩⟩,⟨⟨(-673813387533322680795),(-673812566291132312299)⟩,⟨104852526591761252875,104853347833951621363⟩⟩,⟨⟨(-553306831321697778638),(-553306095461251665156)⟩,⟨181892335642355485505,181893071502801598978⟩⟩,⟨⟨(-439244394332552862736),(-439243736453986001537)⟩,⟨230637887822825560269,230638545701392421460⟩⟩,⟨⟨(-334978566022670494472),(-334977979251780277763)⟩,⟨255739988165122259374,255740574936012476073⟩⟩,⟨⟨(-242740444094670574539),(-242739921918177532168)⟩,⟨261836673366649883624,261837195543142925992⟩⟩,⟨⟨(-163757411525379590642),(-163756947798417823404)⟩,⟨253363147822763552269,253363611549725319501⟩⟩,⟨⟨(-98395367213521528867),(-98394955395741100058)⟩,⟨234401577581817442000,234401989399597870809⟩⟩,⟨⟨(-46315187205394721900),(-46314822358651367248)⟩,⟨208572171300050532329,208572536146793886982⟩⟩,⟨⟨(-6633700597473695352),(-6633378088490382280)⟩,⟨178964600904374939692,178964923413358252764⟩⟩,⟨⟨21919454658740789194,21919739059869741829⟩,⟨148106798686247220783,148107083087376173422⟩⟩,⟨⟨40856264523426871522,40856514750766600263⟩,⟨117966565049876553538,117966815277216282278⟩⟩] +lemma kernel97_1_r5_3_eq : ∀ k : Fin 16, kernel97_1Expr 5 3 k = kernel97_1_r5_3 k := by decide +kernel +noncomputable def kernel97_1_r5_4 : Fin 16 → CBox := ![⟨⟨51801545080805280341,51801764702865554373⟩,⟨89980313436381559747,89980533058441833778⟩⟩,⟨⟨56384625108653732760,56384817433774290527⟩,⟨65102659043854638716,65102851368975196487⟩⟩,⟨⟨56153462592316194192,56153630601703102815⟩,⟨43870409065248434073,43870577074635342696⟩⟩,⟨⟨52511549916924188386,52511696349023744822⟩,⟨26474776654216289656,26474923086315846092⟩⟩,⟨⟨46676589918013619070,46676717226768912468⟩,⟨12836245072551554158,12836372381306847556⟩⟩,⟨⟨39658837622553315875,39658948054069249222⟩,⟨2677359867494092618,2677470299010025961⟩⟩,⟨⟨32256231545966524285,32256327100099610995⟩,⟨(-4410267472682153565),(-4410171918549066859)⟩⟩,⟨⟨25062983803533899788,25063066294801236903⟩,⟨(-8907395507615490046),(-8907313016348152935)⟩⟩,⟨⟨18488140571671896180,18488211606879787095⟩,⟨(-11318635275527597205),(-11318564240319706290)⟩⟩,⟨⟨12780722299786644981,12780783331019828430⟩,⟨(-12134632588655279268),(-12134571557422095819)⟩⟩,⟨⟨8058355939402104753,8058408245496729315⟩,⟨(-11804790143870821125),(-11804737837776196563)⟩⟩,⟨⟨4336759529548777520,4336804255427889837⟩,⟨(-10719728630339045904),(-10719683904459933587)⟩⟩,⟨⟨1557974681341491550,1558012827124245495⟩,⟨(-9202229910541755034),(-9202191764759001089)⟩⟩,⟨⟨(-384191324952036243),(-384158862001842512)⟩,⟨(-7505131706736859805),(-7505099243786666074)⟩⟩,⟨⟨(-1622501376560655629),(-1622473819068701536)⟩,⟨(-5814534622979156685),(-5814507065487202588)⟩⟩,⟨⟨(-2298892459296604961),(-2298869119931691843)⟩,⟨(-4256713569361100767),(-4256690229996187649)⟩⟩] +lemma kernel97_1_r5_4_eq : ∀ k : Fin 16, kernel97_1Expr 5 4 k = kernel97_1_r5_4 k := by decide +kernel +noncomputable def kernel97_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-2551418631681318276),(-2551398916489892263)⟩,⟨(-2907264125969578649),(-2907244410778152637)⟩⟩,⟨⟨(-2505278057711290138),(-2505261440405035347)⟩,⟨(-1801227115082382064),(-1801210497776127273)⟩⟩,⟨⟨(-2267439801136707407),(-2267425827295716441)⟩,⟨(-943188404313820410),(-943174430472829441)⟩⟩,⟨⟨(-1924249350125597989),(-1924237626268963302)⟩,⟨(-316617368890486807),(-316605645033852117)⟩⟩,⟨⟨(-1541336230334781918),(-1541326420091796569)⟩,⟨108037516813571526,108047327056556871⟩⟩,⟨⟨(-1165157763956019396),(-1165149573141056218)⟩,⟨366750835700800721,366759026515763898⟩⟩,⟨⟨(-825572710182242737),(-825565889271593650)⟩,⟨496888001232529382,496894822143178469⟩⟩,⟨⟨(-538930239326292673),(-538924572160597640)⟩,⟨533664093349713349,533669760515408382⟩⟩,⟨⟨(-311267566754873690),(-311262870742608183)⟩,⟨507921719857278577,507926415869544080⟩⟩,⟨⟨(-141320645193755517),(-141316760103527748)⟩,⟨444999412328396728,445003297418624497⟩⟩,⟨⟨(-23156255868253033),(-23153049603821300)⟩,⟨364440570814126548,364443777078558285⟩⟩,⟨⟨51676040432835290,51678680523669493⟩,⟨280298547107626494,280301187198460697⟩⟩,⟨⟨92501411699418039,92503579802600906⟩,⟨201818280902080676,201820449005263539⟩⟩,⟨⟨108362759864130155,108364536515123962⟩,⟨134311190230770567,134312966881764370⟩⟩,⟨⟨107290289325414326,107291741390966533⟩,⟨80081403215707983,80082855281260194⟩⟩,⟨⟨95919702214390781,95920886590818414⟩,⟨39302619630147583,39303804006575219⟩⟩] +lemma kernel97_1_r5_5_eq : ∀ k : Fin 16, kernel97_1Expr 5 5 k = kernel97_1_r5_5 k := by decide +kernel +noncomputable def kernel97_1_r5_6 : Fin 16 → CBox := ![⟨⟨79375068834497138,79376032306149329⟩,⟨10782303980141751,10783267451793942⟩⟩,⟨⟨61335952691894601,61336734817927116⟩,⟨(-7418795398480134),(-7418013272447619)⟩⟩,⟨⟨44218228327017521,44218861610086921⟩,⟨(-17519601440925136),(-17518968157855733)⟩⟩,⟨⟨29411268737859313,29411780403157436⟩,⟨(-21694919677951682),(-21694408012653559)⟩⟩,⟨⟨17528502255310467,17528914560100596⟩,⟨(-21875157460156309),(-21874745155366180)⟩⟩,⟨⟨8641990651054797,8642322205088764⟩,⟨(-19644712775437577),(-19644381221403610)⟩⟩,⟨⟨2483571465999016,2483837394517354⟩,⟨(-16213243209622946),(-16212977281104609)⟩⟩,⟨⟨(-1395368363248459),(-1395155516677013)⟩,⟨(-12435954232138371),(-12435741385566922)⟩⟩,⟨⟨(-3506406240363812),(-3506236103506855)⟩,⟨(-8862682752292555),(-8862512615435602)⟩⟩,⟨⟨(-4345165792741103),(-4345029999833473)⟩,⟨(-5799960604979662),(-5799824812072029)⟩⟩,⟨⟨(-4344636239861796),(-4344528134888305)⟩,⟨(-3374701283099749),(-3374593178126262)⟩⟩,⟨⟨(-3853380657333866),(-3853294767613942)⟩,⟨(-1592186503006096),(-1592100613286172)⟩⟩,⟨⟨(-3131405324418812),(-3131337262564340)⟩,⟨(-384365377021182),(-384297315166710)⟩⟩,⟨⟨(-2357305140118840),(-2357251306755111)⟩,⟨352984670744004,353038504107733⟩⟩,⟨⟨(-1641512397083234),(-1641469923958193)⟩,⟨733935255101899,733977728226937⟩⟩,⟨⟨(-1041796422472336),(-1041762974093408)⟩,⟨865557038844495,865590487223423⟩⟩] +lemma kernel97_1_r5_6_eq : ∀ k : Fin 16, kernel97_1Expr 5 6 k = kernel97_1_r5_6 k := by decide +kernel +noncomputable def kernel97_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-578403421949300),(-578377148856775)⟩,⟨838663679940409,838689953032935⟩⟩,⟨⟨(-247284153459361),(-247263550772236)⟩,⟨724159519452775,724180122139896⟩⟩,⟨⟨(-30681151324509),(-30665031563154)⟩,⟨573154796953613,573170916714965⟩⟩,⟨⟨95065179429196,95077768936332⟩,⟨419312447900134,419325037407270⟩⟩,⟨⟨154258696161717,154268504270414⟩,⟨282248558729713,282258366838411⟩⟩,⟨⟨168704710318949,168712338958236⟩,⟨171160236142477,171167864781764⟩⟩,⟨⟨156178610753034,156184530151275⟩,⟨88162642562016,88168561960261⟩⟩,⟨⟨130018485038497,130023070437297⟩,⟨31062047916381,31066633315181⟩⟩,⟨⟨99421476273904,99425022389355⟩,⟨(-4529524712188),(-4525978596736)⟩⟩,⟨⟨70113199558914,70115938617127⟩,⟨(-23715186282193),(-23712447223980)⟩⟩,⟨⟨45152147051058,45154257894091⟩,⟨(-31379952076028),(-31377841232992)⟩⟩,⟨⟨25714136326488,25715760537534⟩,⟨(-31685266014880),(-31683641803830)⟩⟩,⟨⟨11769422021013,11770668867264⟩,⟨(-27870721442316),(-27869474596065)⟩⟩,⟨⟨2615141672643,2616097609537⟩,⟨(-22255768447781),(-22254812510887)⟩⟩,⟨⟨(-2740512735674),(-2739781423182)⟩,⟨(-16355080363232),(-16354349050740)⟩⟩,⟨⟨(-5326088890291),(-5325530194970)⟩,⟨(-11044052809144),(-11043494113819)⟩⟩] +lemma kernel97_1_r5_7_eq : ∀ k : Fin 16, kernel97_1Expr 5 7 k = kernel97_1_r5_7 k := by decide +kernel +noncomputable def kernel97_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-6060847257194),(-6060421372595)⟩,⟨(-6731920503237),(-6731494618642)⟩⟩,⟨⟨(-5686941783438),(-5686617334535)⟩,⟨(-3517381888294),(-3517057439388)⟩⟩,⟨⟨(-4754091735424),(-4753845072717)⟩,⟨(-1314711276311),(-1314464613608)⟩⟩,⟨⟨(-3635584138230),(-3635396839925)⟩,⟨52672937022,52860235323⟩⟩,⟨⟨(-2559709382499),(-2559567460105)⟩,⟨788746661519,788888583910⟩⟩,⟨⟨(-1645751165863),(-1645643733772)⟩,⟨1086298853472,1086406285560⟩⟩,⟨⟨(-937866671610),(-937785484043)⟩,⟨1107114938705,1107196126272⟩⟩,⟨⟨(-433422505004),(-433361207253)⟩,⟨975094813177,975156110929⟩⟩,⟨⟨(-104598290656),(-104552103678)⟩,⟨777394855290,777441042264⟩⟩,⟨⟨86521751753,86556526633⟩,⟨569832259470,569867034347⟩⟩,⟨⟨178398064686,178424205805⟩,⟨383921460055,383947601170⟩⟩,⟨⟨204765024014,204784658864⟩,⟨233881804838,233901439688⟩⟩,⟨⟨192387003306,192401724353⟩,⟨122710218631,122724939675⟩⟩,⟨⟨160756677571,160767709244⟩,⟨46946130788,46957162457⟩⟩,⟨⟨122887807631,122896061251⟩,⟨98469383,106723003⟩⟩,⟨⟨86596191360,86602363111⟩,⟨(-25104796164),(-25098624416)⟩⟩] +lemma kernel97_1_r5_8_eq : ∀ k : Fin 16, kernel97_1Expr 5 8 k = kernel97_1_r5_8 k := by decide +kernel +noncomputable def kernel97_1_r5_9 : Fin 16 → CBox := ![⟨⟨55875222820,55879829886⟩,⟨(-35401058305),(-35396451242)⟩⟩,⟨⟨32140281076,32143719213⟩,⟨(-36355630050),(-36352191913)⟩⟩,⟨⟨15237583295,15240145467⟩,⟨(-32173919389),(-32171357213)⟩⟩,⟨⟨4192558931,4194467610⟩,⟨(-25780220541),(-25778311862)⟩⟩,⟨⟨(-2280846077),(-2279426347)⟩,⟨(-19029064777),(-19027645047)⟩⟩,⟨⟨(-5466572758),(-5465516822)⟩,⟨(-12959530283),(-12958474350)⟩⟩,⟨⟨(-6479148537),(-6478364137)⟩,⟨(-8038737625),(-8037953229)⟩⟩,⟨⟨(-6196737091),(-6196154479)⟩,⟨(-4367249720),(-4366667105)⟩⟩,⟨⟨(-5256579583),(-5256147439)⟩,⟨(-1836884408),(-1836452264)⟩⟩,⟨⟨(-4084275730),(-4083955119)⟩,⟨(-242255812),(-241935197)⟩⟩,⟨⟨(-2937180274),(-2936942642)⟩,⟨647085660,647323292⟩⟩,⟨⟨(-1949559095),(-1949382959)⟩,⟨1044995556,1045171692⟩⟩,⟨⟨(-1172707022),(-1172576600)⟩,⟨1128768347,1128898769⟩⟩,⟨⟨(-607100812),(-607004180)⟩,⟨1033307353,1033403981⟩⟩,⟨⟨(-226094375),(-226022850)⟩,⟨853555434,853626962⟩⟩,⟨⟨7978026,8031261⟩,⟨650979175,651032414⟩⟩] +lemma kernel97_1_r5_9_eq : ∀ k : Fin 16, kernel97_1Expr 5 9 k = kernel97_1_r5_9 k := by decide +kernel +noncomputable def kernel97_1_r5_10 : Fin 16 → CBox := ![⟨⟨133829792,133869392⟩,⟨461349507,461389111⟩⟩,⟨⟨185795127,185824628⟩,⟨302188331,302217831⟩⟩,⟨⟨191514798,191536750⟩,⟨179069210,179091162⟩⟩,⟨⟨171566648,171583008⟩,⟨90492116,90508476⟩⟩,⟨⟨140172167,140184347⟩,⟨31373711,31385891⟩⟩,⟨⟨106379940,106389020⟩,⟨(-4644773),(-4635693)⟩⟩,⟨⟨75349091,75355867⟩,⟨(-23810843),(-23804067)⟩⟩,⟨⟨49521042,49526101⟩,⟨(-31538416),(-31533354)⟩⟩,⟨⟨29582850,29586628⟩,⟨(-32128565),(-32124788)⟩⟩,⟨⟨15198235,15201058⟩,⟨(-28759896),(-28757074)⟩⟩,⟨⟨5523367,5525493⟩,⟨(-23622666),(-23620543)⟩⟩,⟨⟨(-455894),(-454298)⟩,⟨(-18112016),(-18110420)⟩⟩,⟨⟨(-3723489),(-3722280)⟩,⟨(-13028471),(-13027266)⟩⟩,⟨⟨(-5129798),(-5128886)⟩,⟨(-8757227),(-8756316)⟩⟩,⟨⟨(-5352692),(-5352002)⟩,⟨(-5414160),(-5413470)⟩⟩,⟨⟨(-4897374),(-4896846)⟩,⟨(-2956219),(-2955687)⟩⟩] +lemma kernel97_1_r5_10_eq : ∀ k : Fin 16, kernel97_1Expr 5 10 k = kernel97_1_r5_10 k := by decide +kernel +noncomputable def kernel97_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-4116910),(-4116509)⟩,⟨(-1259439),(-1259038)⟩⟩,⟨⟨(-3241244),(-3240928)⟩,⟨(-170401),(-170082)⟩⟩,⟨⟨(-2407200),(-2406948)⟩,⟨462789,463041⟩⟩,⟨⟨(-1685488),(-1685286)⟩,⟨773931,774133⟩⟩,⟨⟨(-1102859),(-1102707)⟩,⟨871964,872120⟩⟩,⟨⟨(-659130),(-659006)⟩,⟨840117,840242⟩⟩,⟨⟨(-339352),(-339245)⟩,⟨738408,738514⟩⟩,⟨⟨(-122158),(-122070)⟩,⟨607571,607659⟩⟩,⟨⟨15073,15147⟩,⟨473366,473440⟩⟩,⟨⟨93206,93280⟩,⟨350536,350610⟩⟩,⟨⟨129983,130044⟩,⟨246210,246270⟩⟩,⟨⟨139510,139570⟩,⟨162523,162580⟩⟩,⟨⟨132471,132523⟩,⟨98649,98705⟩⟩,⟨⟨116513,116565⟩,⟨52189,52240⟩⟩,⟨⟨96867,96909⟩,⟨20090,20133⟩⟩,⟨⟨76846,76893⟩,⟨(-753),(-710)⟩⟩] +lemma kernel97_1_r5_11_eq : ∀ k : Fin 16, kernel97_1Expr 5 11 k = kernel97_1_r5_11 k := by decide +kernel +noncomputable def kernel97_1_r5_12 : Fin 16 → CBox := ![⟨⟨58396,58430⟩,⟨(-13152),(-13115)⟩⟩,⟨⟨42467,42509⟩,⟨(-19528),(-19485)⟩⟩,⟨⟨29402,29440⟩,⟨(-21790),(-21756)⟩⟩,⟨⟨19133,19176⟩,⟨(-21445),(-21402)⟩⟩,⟨⟨11379,11417⟩,⟨(-19561),(-19523)⟩⟩,⟨⟨5750,5792⟩,⟨(-16921),(-16882)⟩⟩,⟨⟨1857,1894⟩,⟨(-14031),(-13997)⟩⟩,⟨⟨(-699),(-664)⟩,⟨(-11226),(-11188)⟩⟩,⟨⟨(-2247),(-2209)⟩,⟨(-8681),(-8643)⟩⟩,⟨⟨(-3061),(-3024)⟩,⟨(-6483),(-6449)⟩⟩,⟨⟨(-3368),(-3330)⟩,⟨(-4660),(-4625)⟩⟩,⟨⟨(-3342),(-3308)⟩,⟨(-3196),(-3163)⟩⟩,⟨⟨(-3110),(-3081)⟩,⟨(-2062),(-2033)⟩⟩,⟨⟨(-2773),(-2739)⟩,⟨(-1206),(-1172)⟩⟩,⟨⟨(-2389),(-2351)⟩,⟨(-584),(-545)⟩⟩,⟨⟨(-1996),(-1963)⟩,⟨(-140),(-110)⟩⟩] +lemma kernel97_1_r5_12_eq : ∀ k : Fin 16, kernel97_1Expr 5 12 k = kernel97_1_r5_12 k := by decide +kernel +noncomputable def kernel97_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-1634),(-1596)⟩,⟨154,189⟩⟩,⟨⟨(-1302),(-1264)⟩,⟨338,372⟩⟩,⟨⟨(-1013),(-974)⟩,⟨437,475⟩⟩,⟨⟨(-764),(-739)⟩,⟨486,515⟩⟩,⟨⟨(-568),(-534)⟩,⟨491,525⟩⟩,⟨⟨(-401),(-367)⟩,⟨468,506⟩⟩,⟨⟨(-274),(-244)⟩,⟨436,469⟩⟩,⟨⟨(-178),(-139)⟩,⟨386,424⟩⟩,⟨⟨(-106),(-68)⟩,⟨341,375⟩⟩,⟨⟨(-43),(-18)⟩,⟨295,324⟩⟩,⟨⟨(-5),25⟩,⟨246,276⟩⟩,⟨⟨22,51⟩,⟨205,234⟩⟩,⟨⟨40,79⟩,⟨163,202⟩⟩,⟨⟨56,85⟩,⟨132,162⟩⟩,⟨⟨60,89⟩,⟨107,136⟩⟩,⟨⟨60,89⟩,⟨81,111⟩⟩] +lemma kernel97_1_r5_13_eq : ∀ k : Fin 16, kernel97_1Expr 5 13 k = kernel97_1_r5_13 k := by decide +kernel +noncomputable def kernel97_1_r5_14 : Fin 16 → CBox := ![⟨⟨61,90⟩,⟨60,90⟩⟩,⟨⟨53,91⟩,⟨39,74⟩⟩,⟨⟨51,89⟩,⟨27,62⟩⟩,⟨⟨44,79⟩,⟨12,51⟩⟩,⟨⟨39,77⟩,⟨4,39⟩⟩,⟨⟨33,68⟩,⟨(-3),32⟩⟩,⟨⟨33,62⟩,⟨(-6),23⟩⟩,⟨⟨28,58⟩,⟨(-9),20⟩⟩,⟨⟨27,57⟩,⟨(-14),16⟩⟩,⟨⟨17,52⟩,⟨(-25),13⟩⟩,⟨⟨18,47⟩,⟨(-20),9⟩⟩,⟨⟨13,43⟩,⟨(-24),6⟩⟩,⟨⟨9,39⟩,⟨(-23),7⟩⟩,⟨⟨4,43⟩,⟨(-28),7⟩⟩,⟨⟨0,35⟩,⟨(-26),8⟩⟩,⟨⟨1,30⟩,⟨(-22),8⟩⟩] +lemma kernel97_1_r5_14_eq : ∀ k : Fin 16, kernel97_1Expr 5 14 k = kernel97_1_r5_14 k := by decide +kernel +noncomputable def kernel97_1_r5_15 : Fin 16 → CBox := ![⟨⟨1,30⟩,⟨(-22),8⟩⟩,⟨⟨0,30⟩,⟨(-26),4⟩⟩,⟨⟨(-4),30⟩,⟨(-26),9⟩⟩,⟨⟨0,30⟩,⟨(-26),4⟩⟩,⟨⟨(-4),26⟩,⟨(-25),5⟩⟩,⟨⟨(-4),26⟩,⟨(-25),5⟩⟩,⟨⟨(-4),26⟩,⟨(-25),5⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-12),26⟩,⟨(-25),10⟩⟩,⟨⟨(-12),26⟩,⟨(-25),10⟩⟩,⟨⟨(-12),26⟩,⟨(-25),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩,⟨⟨(-13),26⟩,⟨(-29),10⟩⟩] +lemma kernel97_1_r5_15_eq : ∀ k : Fin 16, kernel97_1Expr 5 15 k = kernel97_1_r5_15 k := by decide +kernel +noncomputable def kernel97_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel97_1_r5_0,kernel97_1_r5_1,kernel97_1_r5_2,kernel97_1_r5_3,kernel97_1_r5_4,kernel97_1_r5_5,kernel97_1_r5_6,kernel97_1_r5_7,kernel97_1_r5_8,kernel97_1_r5_9,kernel97_1_r5_10,kernel97_1_r5_11,kernel97_1_r5_12,kernel97_1_r5_13,kernel97_1_r5_14,kernel97_1_r5_15] +lemma kernel97_1_r5_eq (i k : Fin 16) : kernel97_1Expr 5 i k = kernel97_1_r5 i k := by + fin_cases i + · exact kernel97_1_r5_0_eq k + · exact kernel97_1_r5_1_eq k + · exact kernel97_1_r5_2_eq k + · exact kernel97_1_r5_3_eq k + · exact kernel97_1_r5_4_eq k + · exact kernel97_1_r5_5_eq k + · exact kernel97_1_r5_6_eq k + · exact kernel97_1_r5_7_eq k + · exact kernel97_1_r5_8_eq k + · exact kernel97_1_r5_9_eq k + · exact kernel97_1_r5_10_eq k + · exact kernel97_1_r5_11_eq k + · exact kernel97_1_r5_12_eq k + · exact kernel97_1_r5_13_eq k + · exact kernel97_1_r5_14_eq k + · exact kernel97_1_r5_15_eq k +noncomputable def kernel97_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel97_1_r0,kernel97_1_r1,kernel97_1_r2,kernel97_1_r3,kernel97_1_r4,kernel97_1_r5] +lemma kernel97_1_eq (j : Fin 6) (i k : Fin 16) : kernel97_1Expr j i k = kernel97_1 j i k := by + fin_cases j + · exact kernel97_1_r0_eq i k + · exact kernel97_1_r1_eq i k + · exact kernel97_1_r2_eq i k + · exact kernel97_1_r3_eq i k + · exact kernel97_1_r4_eq i k + · exact kernel97_1_r5_eq i k +lemma kernel97_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel97_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(97:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel97_1_eq] + unfold kernel97_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans97_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel99_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans99 j i k) +noncomputable def kernel99_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_0_eq : ∀ k : Fin 16, kernel99_0Expr 0 0 k = kernel99_0_r0_0 k := by decide +kernel +noncomputable def kernel99_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_1_eq : ∀ k : Fin 16, kernel99_0Expr 0 1 k = kernel99_0_r0_1 k := by decide +kernel +noncomputable def kernel99_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_2_eq : ∀ k : Fin 16, kernel99_0Expr 0 2 k = kernel99_0_r0_2 k := by decide +kernel +noncomputable def kernel99_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_3_eq : ∀ k : Fin 16, kernel99_0Expr 0 3 k = kernel99_0_r0_3 k := by decide +kernel +noncomputable def kernel99_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_4_eq : ∀ k : Fin 16, kernel99_0Expr 0 4 k = kernel99_0_r0_4 k := by decide +kernel +noncomputable def kernel99_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_5_eq : ∀ k : Fin 16, kernel99_0Expr 0 5 k = kernel99_0_r0_5 k := by decide +kernel +noncomputable def kernel99_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_6_eq : ∀ k : Fin 16, kernel99_0Expr 0 6 k = kernel99_0_r0_6 k := by decide +kernel +noncomputable def kernel99_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_7_eq : ∀ k : Fin 16, kernel99_0Expr 0 7 k = kernel99_0_r0_7 k := by decide +kernel +noncomputable def kernel99_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_8_eq : ∀ k : Fin 16, kernel99_0Expr 0 8 k = kernel99_0_r0_8 k := by decide +kernel +noncomputable def kernel99_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_9_eq : ∀ k : Fin 16, kernel99_0Expr 0 9 k = kernel99_0_r0_9 k := by decide +kernel +noncomputable def kernel99_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_10_eq : ∀ k : Fin 16, kernel99_0Expr 0 10 k = kernel99_0_r0_10 k := by decide +kernel +noncomputable def kernel99_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r0_11_eq : ∀ k : Fin 16, kernel99_0Expr 0 11 k = kernel99_0_r0_11 k := by decide +kernel +noncomputable def kernel99_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r0_12_eq : ∀ k : Fin 16, kernel99_0Expr 0 12 k = kernel99_0_r0_12 k := by decide +kernel +noncomputable def kernel99_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r0_13_eq : ∀ k : Fin 16, kernel99_0Expr 0 13 k = kernel99_0_r0_13 k := by decide +kernel +noncomputable def kernel99_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r0_14_eq : ∀ k : Fin 16, kernel99_0Expr 0 14 k = kernel99_0_r0_14 k := by decide +kernel +noncomputable def kernel99_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r0_15_eq : ∀ k : Fin 16, kernel99_0Expr 0 15 k = kernel99_0_r0_15 k := by decide +kernel +noncomputable def kernel99_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel99_0_r0_0,kernel99_0_r0_1,kernel99_0_r0_2,kernel99_0_r0_3,kernel99_0_r0_4,kernel99_0_r0_5,kernel99_0_r0_6,kernel99_0_r0_7,kernel99_0_r0_8,kernel99_0_r0_9,kernel99_0_r0_10,kernel99_0_r0_11,kernel99_0_r0_12,kernel99_0_r0_13,kernel99_0_r0_14,kernel99_0_r0_15] +lemma kernel99_0_r0_eq (i k : Fin 16) : kernel99_0Expr 0 i k = kernel99_0_r0 i k := by + fin_cases i + · exact kernel99_0_r0_0_eq k + · exact kernel99_0_r0_1_eq k + · exact kernel99_0_r0_2_eq k + · exact kernel99_0_r0_3_eq k + · exact kernel99_0_r0_4_eq k + · exact kernel99_0_r0_5_eq k + · exact kernel99_0_r0_6_eq k + · exact kernel99_0_r0_7_eq k + · exact kernel99_0_r0_8_eq k + · exact kernel99_0_r0_9_eq k + · exact kernel99_0_r0_10_eq k + · exact kernel99_0_r0_11_eq k + · exact kernel99_0_r0_12_eq k + · exact kernel99_0_r0_13_eq k + · exact kernel99_0_r0_14_eq k + · exact kernel99_0_r0_15_eq k +noncomputable def kernel99_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_0_eq : ∀ k : Fin 16, kernel99_0Expr 1 0 k = kernel99_0_r1_0 k := by decide +kernel +noncomputable def kernel99_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_1_eq : ∀ k : Fin 16, kernel99_0Expr 1 1 k = kernel99_0_r1_1 k := by decide +kernel +noncomputable def kernel99_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_2_eq : ∀ k : Fin 16, kernel99_0Expr 1 2 k = kernel99_0_r1_2 k := by decide +kernel +noncomputable def kernel99_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_3_eq : ∀ k : Fin 16, kernel99_0Expr 1 3 k = kernel99_0_r1_3 k := by decide +kernel +noncomputable def kernel99_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_4_eq : ∀ k : Fin 16, kernel99_0Expr 1 4 k = kernel99_0_r1_4 k := by decide +kernel +noncomputable def kernel99_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_5_eq : ∀ k : Fin 16, kernel99_0Expr 1 5 k = kernel99_0_r1_5 k := by decide +kernel +noncomputable def kernel99_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_6_eq : ∀ k : Fin 16, kernel99_0Expr 1 6 k = kernel99_0_r1_6 k := by decide +kernel +noncomputable def kernel99_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_7_eq : ∀ k : Fin 16, kernel99_0Expr 1 7 k = kernel99_0_r1_7 k := by decide +kernel +noncomputable def kernel99_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_8_eq : ∀ k : Fin 16, kernel99_0Expr 1 8 k = kernel99_0_r1_8 k := by decide +kernel +noncomputable def kernel99_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_9_eq : ∀ k : Fin 16, kernel99_0Expr 1 9 k = kernel99_0_r1_9 k := by decide +kernel +noncomputable def kernel99_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_10_eq : ∀ k : Fin 16, kernel99_0Expr 1 10 k = kernel99_0_r1_10 k := by decide +kernel +noncomputable def kernel99_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_11_eq : ∀ k : Fin 16, kernel99_0Expr 1 11 k = kernel99_0_r1_11 k := by decide +kernel +noncomputable def kernel99_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_12_eq : ∀ k : Fin 16, kernel99_0Expr 1 12 k = kernel99_0_r1_12 k := by decide +kernel +noncomputable def kernel99_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_13_eq : ∀ k : Fin 16, kernel99_0Expr 1 13 k = kernel99_0_r1_13 k := by decide +kernel +noncomputable def kernel99_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_14_eq : ∀ k : Fin 16, kernel99_0Expr 1 14 k = kernel99_0_r1_14 k := by decide +kernel +noncomputable def kernel99_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r1_15_eq : ∀ k : Fin 16, kernel99_0Expr 1 15 k = kernel99_0_r1_15 k := by decide +kernel +noncomputable def kernel99_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel99_0_r1_0,kernel99_0_r1_1,kernel99_0_r1_2,kernel99_0_r1_3,kernel99_0_r1_4,kernel99_0_r1_5,kernel99_0_r1_6,kernel99_0_r1_7,kernel99_0_r1_8,kernel99_0_r1_9,kernel99_0_r1_10,kernel99_0_r1_11,kernel99_0_r1_12,kernel99_0_r1_13,kernel99_0_r1_14,kernel99_0_r1_15] +lemma kernel99_0_r1_eq (i k : Fin 16) : kernel99_0Expr 1 i k = kernel99_0_r1 i k := by + fin_cases i + · exact kernel99_0_r1_0_eq k + · exact kernel99_0_r1_1_eq k + · exact kernel99_0_r1_2_eq k + · exact kernel99_0_r1_3_eq k + · exact kernel99_0_r1_4_eq k + · exact kernel99_0_r1_5_eq k + · exact kernel99_0_r1_6_eq k + · exact kernel99_0_r1_7_eq k + · exact kernel99_0_r1_8_eq k + · exact kernel99_0_r1_9_eq k + · exact kernel99_0_r1_10_eq k + · exact kernel99_0_r1_11_eq k + · exact kernel99_0_r1_12_eq k + · exact kernel99_0_r1_13_eq k + · exact kernel99_0_r1_14_eq k + · exact kernel99_0_r1_15_eq k +noncomputable def kernel99_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_0_eq : ∀ k : Fin 16, kernel99_0Expr 2 0 k = kernel99_0_r2_0 k := by decide +kernel +noncomputable def kernel99_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_1_eq : ∀ k : Fin 16, kernel99_0Expr 2 1 k = kernel99_0_r2_1 k := by decide +kernel +noncomputable def kernel99_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_2_eq : ∀ k : Fin 16, kernel99_0Expr 2 2 k = kernel99_0_r2_2 k := by decide +kernel +noncomputable def kernel99_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_3_eq : ∀ k : Fin 16, kernel99_0Expr 2 3 k = kernel99_0_r2_3 k := by decide +kernel +noncomputable def kernel99_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_4_eq : ∀ k : Fin 16, kernel99_0Expr 2 4 k = kernel99_0_r2_4 k := by decide +kernel +noncomputable def kernel99_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_5_eq : ∀ k : Fin 16, kernel99_0Expr 2 5 k = kernel99_0_r2_5 k := by decide +kernel +noncomputable def kernel99_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_6_eq : ∀ k : Fin 16, kernel99_0Expr 2 6 k = kernel99_0_r2_6 k := by decide +kernel +noncomputable def kernel99_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_7_eq : ∀ k : Fin 16, kernel99_0Expr 2 7 k = kernel99_0_r2_7 k := by decide +kernel +noncomputable def kernel99_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_8_eq : ∀ k : Fin 16, kernel99_0Expr 2 8 k = kernel99_0_r2_8 k := by decide +kernel +noncomputable def kernel99_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_9_eq : ∀ k : Fin 16, kernel99_0Expr 2 9 k = kernel99_0_r2_9 k := by decide +kernel +noncomputable def kernel99_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r2_10_eq : ∀ k : Fin 16, kernel99_0Expr 2 10 k = kernel99_0_r2_10 k := by decide +kernel +noncomputable def kernel99_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r2_11_eq : ∀ k : Fin 16, kernel99_0Expr 2 11 k = kernel99_0_r2_11 k := by decide +kernel +noncomputable def kernel99_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r2_12_eq : ∀ k : Fin 16, kernel99_0Expr 2 12 k = kernel99_0_r2_12 k := by decide +kernel +noncomputable def kernel99_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r2_13_eq : ∀ k : Fin 16, kernel99_0Expr 2 13 k = kernel99_0_r2_13 k := by decide +kernel +noncomputable def kernel99_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r2_14_eq : ∀ k : Fin 16, kernel99_0Expr 2 14 k = kernel99_0_r2_14 k := by decide +kernel +noncomputable def kernel99_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel99_0_r2_15_eq : ∀ k : Fin 16, kernel99_0Expr 2 15 k = kernel99_0_r2_15 k := by decide +kernel +noncomputable def kernel99_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel99_0_r2_0,kernel99_0_r2_1,kernel99_0_r2_2,kernel99_0_r2_3,kernel99_0_r2_4,kernel99_0_r2_5,kernel99_0_r2_6,kernel99_0_r2_7,kernel99_0_r2_8,kernel99_0_r2_9,kernel99_0_r2_10,kernel99_0_r2_11,kernel99_0_r2_12,kernel99_0_r2_13,kernel99_0_r2_14,kernel99_0_r2_15] +lemma kernel99_0_r2_eq (i k : Fin 16) : kernel99_0Expr 2 i k = kernel99_0_r2 i k := by + fin_cases i + · exact kernel99_0_r2_0_eq k + · exact kernel99_0_r2_1_eq k + · exact kernel99_0_r2_2_eq k + · exact kernel99_0_r2_3_eq k + · exact kernel99_0_r2_4_eq k + · exact kernel99_0_r2_5_eq k + · exact kernel99_0_r2_6_eq k + · exact kernel99_0_r2_7_eq k + · exact kernel99_0_r2_8_eq k + · exact kernel99_0_r2_9_eq k + · exact kernel99_0_r2_10_eq k + · exact kernel99_0_r2_11_eq k + · exact kernel99_0_r2_12_eq k + · exact kernel99_0_r2_13_eq k + · exact kernel99_0_r2_14_eq k + · exact kernel99_0_r2_15_eq k +noncomputable def kernel99_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_0_eq : ∀ k : Fin 16, kernel99_0Expr 3 0 k = kernel99_0_r3_0 k := by decide +kernel +noncomputable def kernel99_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_1_eq : ∀ k : Fin 16, kernel99_0Expr 3 1 k = kernel99_0_r3_1 k := by decide +kernel +noncomputable def kernel99_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_2_eq : ∀ k : Fin 16, kernel99_0Expr 3 2 k = kernel99_0_r3_2 k := by decide +kernel +noncomputable def kernel99_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_3_eq : ∀ k : Fin 16, kernel99_0Expr 3 3 k = kernel99_0_r3_3 k := by decide +kernel +noncomputable def kernel99_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_4_eq : ∀ k : Fin 16, kernel99_0Expr 3 4 k = kernel99_0_r3_4 k := by decide +kernel +noncomputable def kernel99_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_5_eq : ∀ k : Fin 16, kernel99_0Expr 3 5 k = kernel99_0_r3_5 k := by decide +kernel +noncomputable def kernel99_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_6_eq : ∀ k : Fin 16, kernel99_0Expr 3 6 k = kernel99_0_r3_6 k := by decide +kernel +noncomputable def kernel99_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_7_eq : ∀ k : Fin 16, kernel99_0Expr 3 7 k = kernel99_0_r3_7 k := by decide +kernel +noncomputable def kernel99_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_8_eq : ∀ k : Fin 16, kernel99_0Expr 3 8 k = kernel99_0_r3_8 k := by decide +kernel +noncomputable def kernel99_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_9_eq : ∀ k : Fin 16, kernel99_0Expr 3 9 k = kernel99_0_r3_9 k := by decide +kernel +noncomputable def kernel99_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_10_eq : ∀ k : Fin 16, kernel99_0Expr 3 10 k = kernel99_0_r3_10 k := by decide +kernel +noncomputable def kernel99_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_11_eq : ∀ k : Fin 16, kernel99_0Expr 3 11 k = kernel99_0_r3_11 k := by decide +kernel +noncomputable def kernel99_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_12_eq : ∀ k : Fin 16, kernel99_0Expr 3 12 k = kernel99_0_r3_12 k := by decide +kernel +noncomputable def kernel99_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_13_eq : ∀ k : Fin 16, kernel99_0Expr 3 13 k = kernel99_0_r3_13 k := by decide +kernel +noncomputable def kernel99_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_14_eq : ∀ k : Fin 16, kernel99_0Expr 3 14 k = kernel99_0_r3_14 k := by decide +kernel +noncomputable def kernel99_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r3_15_eq : ∀ k : Fin 16, kernel99_0Expr 3 15 k = kernel99_0_r3_15 k := by decide +kernel +noncomputable def kernel99_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel99_0_r3_0,kernel99_0_r3_1,kernel99_0_r3_2,kernel99_0_r3_3,kernel99_0_r3_4,kernel99_0_r3_5,kernel99_0_r3_6,kernel99_0_r3_7,kernel99_0_r3_8,kernel99_0_r3_9,kernel99_0_r3_10,kernel99_0_r3_11,kernel99_0_r3_12,kernel99_0_r3_13,kernel99_0_r3_14,kernel99_0_r3_15] +lemma kernel99_0_r3_eq (i k : Fin 16) : kernel99_0Expr 3 i k = kernel99_0_r3 i k := by + fin_cases i + · exact kernel99_0_r3_0_eq k + · exact kernel99_0_r3_1_eq k + · exact kernel99_0_r3_2_eq k + · exact kernel99_0_r3_3_eq k + · exact kernel99_0_r3_4_eq k + · exact kernel99_0_r3_5_eq k + · exact kernel99_0_r3_6_eq k + · exact kernel99_0_r3_7_eq k + · exact kernel99_0_r3_8_eq k + · exact kernel99_0_r3_9_eq k + · exact kernel99_0_r3_10_eq k + · exact kernel99_0_r3_11_eq k + · exact kernel99_0_r3_12_eq k + · exact kernel99_0_r3_13_eq k + · exact kernel99_0_r3_14_eq k + · exact kernel99_0_r3_15_eq k +noncomputable def kernel99_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r4_0_eq : ∀ k : Fin 16, kernel99_0Expr 4 0 k = kernel99_0_r4_0 k := by decide +kernel +noncomputable def kernel99_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-3),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),4⟩,⟨(-3),4⟩⟩] +lemma kernel99_0_r4_1_eq : ∀ k : Fin 16, kernel99_0Expr 4 1 k = kernel99_0_r4_1 k := by decide +kernel +noncomputable def kernel99_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩] +lemma kernel99_0_r4_2_eq : ∀ k : Fin 16, kernel99_0Expr 4 2 k = kernel99_0_r4_2 k := by decide +kernel +noncomputable def kernel99_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r4_3_eq : ∀ k : Fin 16, kernel99_0Expr 4 3 k = kernel99_0_r4_3 k := by decide +kernel +noncomputable def kernel99_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_4_eq : ∀ k : Fin 16, kernel99_0Expr 4 4 k = kernel99_0_r4_4 k := by decide +kernel +noncomputable def kernel99_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_5_eq : ∀ k : Fin 16, kernel99_0Expr 4 5 k = kernel99_0_r4_5 k := by decide +kernel +noncomputable def kernel99_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_6_eq : ∀ k : Fin 16, kernel99_0Expr 4 6 k = kernel99_0_r4_6 k := by decide +kernel +noncomputable def kernel99_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_7_eq : ∀ k : Fin 16, kernel99_0Expr 4 7 k = kernel99_0_r4_7 k := by decide +kernel +noncomputable def kernel99_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_8_eq : ∀ k : Fin 16, kernel99_0Expr 4 8 k = kernel99_0_r4_8 k := by decide +kernel +noncomputable def kernel99_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_9_eq : ∀ k : Fin 16, kernel99_0Expr 4 9 k = kernel99_0_r4_9 k := by decide +kernel +noncomputable def kernel99_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_10_eq : ∀ k : Fin 16, kernel99_0Expr 4 10 k = kernel99_0_r4_10 k := by decide +kernel +noncomputable def kernel99_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel99_0_r4_11_eq : ∀ k : Fin 16, kernel99_0Expr 4 11 k = kernel99_0_r4_11 k := by decide +kernel +noncomputable def kernel99_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r4_12_eq : ∀ k : Fin 16, kernel99_0Expr 4 12 k = kernel99_0_r4_12 k := by decide +kernel +noncomputable def kernel99_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r4_13_eq : ∀ k : Fin 16, kernel99_0Expr 4 13 k = kernel99_0_r4_13 k := by decide +kernel +noncomputable def kernel99_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r4_14_eq : ∀ k : Fin 16, kernel99_0Expr 4 14 k = kernel99_0_r4_14 k := by decide +kernel +noncomputable def kernel99_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel99_0_r4_15_eq : ∀ k : Fin 16, kernel99_0Expr 4 15 k = kernel99_0_r4_15 k := by decide +kernel +noncomputable def kernel99_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel99_0_r4_0,kernel99_0_r4_1,kernel99_0_r4_2,kernel99_0_r4_3,kernel99_0_r4_4,kernel99_0_r4_5,kernel99_0_r4_6,kernel99_0_r4_7,kernel99_0_r4_8,kernel99_0_r4_9,kernel99_0_r4_10,kernel99_0_r4_11,kernel99_0_r4_12,kernel99_0_r4_13,kernel99_0_r4_14,kernel99_0_r4_15] +lemma kernel99_0_r4_eq (i k : Fin 16) : kernel99_0Expr 4 i k = kernel99_0_r4 i k := by + fin_cases i + · exact kernel99_0_r4_0_eq k + · exact kernel99_0_r4_1_eq k + · exact kernel99_0_r4_2_eq k + · exact kernel99_0_r4_3_eq k + · exact kernel99_0_r4_4_eq k + · exact kernel99_0_r4_5_eq k + · exact kernel99_0_r4_6_eq k + · exact kernel99_0_r4_7_eq k + · exact kernel99_0_r4_8_eq k + · exact kernel99_0_r4_9_eq k + · exact kernel99_0_r4_10_eq k + · exact kernel99_0_r4_11_eq k + · exact kernel99_0_r4_12_eq k + · exact kernel99_0_r4_13_eq k + · exact kernel99_0_r4_14_eq k + · exact kernel99_0_r4_15_eq k +noncomputable def kernel99_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-2406267939879980928966),(-2406263489812016650846)⟩,⟨8725972691889849072739,8725977141957813350893⟩⟩,⟨⟨(-2370548733977827035411),(-2370544292588135379273)⟩,⟨8706867313120935609175,8706871754510627265349⟩⟩,⟨⟨(-2299629831802005213049),(-2299625407727357252197)⟩,⟨8668487252013757168083,8668491676088405128971⟩⟩,⟨⟨(-2194544842785263639886),(-2194540444564424038089)⟩,⟨8610504993544574672807,8610509391765414274643⟩⟩,⟨⟨(-2056830524228949974269),(-2056826160254946133425)⟩,⟨8532456626447018653062,8532460990421022493947⟩⟩,⟨⟨(-1888510037337820322658),(-1888505715811208793956)⟩,⟨8433773650173131151376,8433777971699742680122⟩⟩,⟨⟨(-1692070072065625378367),(-1692065800949942835111)⟩,⟨8313823693752606340791,8313827964868288884095⟩⟩,⟨⟨(-1470431453185827942364),(-1470427240164402428408)⟩,⟨8171958739490106784046,8171962952511532298054⟩⟩,⟨⟨(-1226912842507566656766),(-1226908694944150285952)⟩,⟨8007569146787296848472,8007573294350713219342⟩⟩,⟨⟨(-965187212931363253384),(-965183137831430022043)⟩,⟨7820141512202966091565,7820145587302899322967⟩⟩,⟨⟨(-689230893014938599991),(-689226896991791398308)⟩,⟨7609318190729744119063,7609322186752891320811⟩⟩,⟨⟨(-403265166245251191032),(-403261255152958232345)⟩,⟨7374956149847814737333,7374960060940107696091⟩⟩,⟨⟨(-111690652011475481783),(-111686831579970069170)⟩,⟨7117182743346856210394,7117186563778361623081⟩⟩,⟨⟨180985008047604905444,180988732561132060286⟩,⟨6836445980586978485675,6836449705100505640595⟩⟩,⟨⟨470225305543833674859,470228929366890307546⟩,⟨6533556945821366906647,6533560569644423539418⟩⟩,⟨⟨751547652628710581887,751551171497754025908⟩,⟨6209722185369466487354,6209725704238509931461⟩⟩] +lemma kernel99_0_r5_0_eq : ∀ k : Fin 16, kernel99_0Expr 5 0 k = kernel99_0_r5_0 k := by decide +kernel +noncomputable def kernel99_0_r5_1 : Fin 16 → CBox := ![⟨⟨1020609233882541699736,1020612644042875480634⟩,⟨5866564139733461063795,5866567549893794844783⟩⟩,⟨⟨1273294015204933240487,1273297313432911763950⟩,⟨5506128047326888517712,5506131345554867041267⟩⟩,⟨⟨1505798702650665041926,1505801886239329713316⟩,⟨5130874182508841832390,5130877366097506503873⟩⟩,⟨⟨1714715207819078598527,1714718274596548337853⟩,⟨4743654802369435444223,4743657869146905183642⟩⟩,⟨⟨1897107025059700544026,1897109973362377755175⟩,⟨4347675749528458346884,4347678697831135558121⟩⟩,⟨⟨2050576877506410486855,2050579706198354784347⟩,⟨3946443271592420757313,3946446100284365054882⟩⟩,⟨⟨2173323058914256348639,2173325767342854199748⟩,⟨3543697248227275850784,3543699956655873701958⟩⟩,⟨⟨2264182094676292475786,2264184682700507166617⟩,⟨3143332635538111087948,3143335223562325778834⟩⟩,⟨⟨2322655671531234982050,2322658139455497493601⟩,⟨2749311515491979188199,2749313983416241699794⟩⟩,⟨⟨2348920235232562763765,2348922583821438351064⟩,⟨2365568643625568998908,2365570992214444586240⟩⟩,⟨⟨2343818217313620021296,2343820447730664352902⟩,⟨1995913792781975279072,1995916023199019610702⟩⟩,⟨⟨2308830504279139738364,2308832618107664945061⟩,⟨1643934466024384652639,1643936579852909859351⟩⟩,⟨⟨2246030478886355494285,2246032478051555880371⟩,⟨1312902677579366266666,1312904676744566652760⟩⟩,⟨⟨2158020708879628269223,2158022595739491971854⟩,⟨1005689460053906338487,1005691346913770041120⟩⟩,⟨⟨2047854097613298577953,2047855874879727850406⟩,⟨724690543823203726590,724692321089632999037⟩⟩,⟨⟨1918942001706720754441,1918943672247158844494⟩,⟨471766270672227405943,471767941212665495986⟩⟩] +lemma kernel99_0_r5_1_eq : ∀ k : Fin 16, kernel99_0Expr 5 1 k = kernel99_0_r5_1 k := by decide +kernel +noncomputable def kernel99_0_r5_2 : Fin 16 → CBox := ![⟨⟨1774952425242265542862,1774953992137945545875⟩,⟨248198262101110111207,248199828996790114207⟩⟩,⟨⟨1619701881252058074004,1619703347840850931597⟩,⟨54664684915832555645,54666151504625413222⟩⟩,⟨⟨1457044836660175396552,1457046206430341175718⟩,⟨(-108764827694164382913),(-108763457923998603766)⟩⟩,⟨⟨1290764803951682784906,1290766080576593015907⟩,⟨(-242614392925477242998),(-242613116300567012017)⟩⟩,⟨⟨1124471098036140940242,1124472285285012770093⟩,⟨(-347967900693496995735),(-347966713444625165905)⟩⟩,⟨⟨961505035436401232623,961506137265758891000⟩,⟨(-426417361336123540541),(-426416259506765882183)⟩⟩,⟨⟨804858926119845464745,804859946443260898880⟩,⟨(-479995879156352556041),(-479994858832937121922)⟩⟩,⟨⟨657110613376778456097,657111556182804478082⟩,⟨(-511098220631963697789),(-511097277825937675816)⟩⟩,⟨⟨520375588897926216183,520376458149045270842⟩,⟨(-522392460524554481241),(-522391591273435426589)⟩⟩,⟨⟨396277883799801483229,396278683516749929752⟩,⟨(-516726524955928658360),(-516725725238980211841)⟩⟩,⟨⟨285940062144903468268,285940796250460185348⟩,⟨(-497033585142429139929),(-497032851036872422852)⟩⟩,⟨⟨189991767124352526055,189992439522193990627⟩,⟨(-466240186507346165051),(-466239514109504700479)⟩⟩,⟨⟨108595444484778431644,108596058977832868305⟩,⟨(-427180728375546555190),(-427180113882492118526)⟩⟩,⟨⟨41487135732334295913,41487696066701009396⟩,⟨(-382521461713322367764),(-382520901378955654277)⟩⟩,⟨⟨(-11970362100475061604),(-11969852313565281213)⟩,⟨(-334696573319589753332),(-334696063532679972938)⟩⟩,⟨⟨(-52725104700139648134),(-52724641935835891075)⟩,⟨(-285858215906832267423),(-285857753142528510358)⟩⟩] +lemma kernel99_0_r5_2_eq : ∀ k : Fin 16, kernel99_0Expr 5 2 k = kernel99_0_r5_2 k := by decide +kernel +noncomputable def kernel99_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-81967756690598308646),(-81967337583592824311)⟩,⟨(-237841567568877576267),(-237841148461872091928)⟩⟩,⟨⟨(-101060930055762001217),(-101060551337933293483)⟩,⟨(-192145211256502529775),(-192144832538673822037)⟩⟩,⟨⟨(-111469405524265832318),(-111469064101403742752)⟩,⟨(-149926360645496397474),(-149926019222634307905)⟩⟩,⟨⟨(-114694235752910941770),(-114693928650480054738)⟩,⟨(-112009769105213930716),(-112009462002783043683)⟩⟩,⟨⟨(-112213284105405292824),(-112213008527565762059)⟩,⟨(-78908578377234895912),(-78908302799395365146)⟩⟩,⟨⟨(-105430202124868606509),(-105429955398261277715)⟩,⟨(-50854923222436486848),(-50854676495829158055)⟩⟩,⟨⟨(-95633230893474098287),(-95633010524189076955)⟩,⟨(-27837823128101322318),(-27837602758816300986)⟩⟩,⟨⟨(-83964570602014572974),(-83964374227244205681)⟩,⟨(-9645770101414686157),(-9645573726644318865)⟩⟩,⟨⟨(-71400438175277361601),(-71400263606597981988)⟩,⟨4088544333739442109,4088718902418821720⟩⟩,⟨⟨(-58741363487534964660),(-58741208660660243254)⟩,⟨13843743148528470332,13843897975403191736⟩⟩,⟨⟨(-46611789513823230287),(-46611652490000305602)⟩,⟨20167605029244015973,20167742053066940657⟩⟩,⟨⟨(-35467664451014468266),(-35467543191183508056)⟩,⟨23638935864388988252,23639057124219948462⟩⟩,⟨⟨(-25610455418729000441),(-25610348371878665047)⟩,⟨24834736373194240398,24834843420044575792⟩⟩,⟨⟨(-17205881538891062883),(-17205787256582441486)⟩,⟨24303470110537678985,24303564392846300383⟩⟩,⟨⟨(-10305645605894912080),(-10305562770089865948)⟩,⟨22544789913490060500,22544872749295106633⟩⟩,⟨⟨(-4870535771021742703),(-4870463161538290580)⟩,⟨19995667371136408738,19995739980619860861⟩⟩] +lemma kernel99_0_r5_3_eq : ∀ k : Fin 16, kernel99_0Expr 5 3 k = kernel99_0_r5_3 k := by decide +kernel +noncomputable def kernel99_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-793443468347729097),(-793379982082533268)⟩,⟨17022520410138239970,17022583896403435800⟩⟩,⟨⟨2078916245651155052,2078971626357355586⟩,⟨13918658449602122441,13918713830308322976⟩⟩,⟨⟨3926517439084011657,3926565628107029733⟩,⟨10906173017610264834,10906221206633282910⟩⟩,⟨⟨4939411075035891645,4939452907785968596⟩,⟨8141294218329724329,8141336051079801279⟩⟩,⟨⟨5304343723115609792,5304379945532248712⟩,⟨5722205561246821184,5722241783663460104⟩⟩,⟨⟨5194702317810430063,5194733609189107514⟩,⟨3698350438600999057,3698381729979676508⟩⟩,⟨⟨4763658957172271541,4763685920107731822⟩,⟨2080359814129111882,2080386777064572164⟩⟩,⟨⟨4140216581988471773,4140239760484197360⟩,⟨849866104066214844,849889282561940432⟩⟩,⟨⟨3427735574220431691,3427755448165249790⟩,⟨(-31372910699725333),(-31353036754907234)⟩⟩,⟨⟨2704451717532859010,2704468718331950275⟩,⟨(-613449803432807819),(-613432802633716555)⟩⟩,⟨⟨2025473551825607135,2025488057900144110⟩,⟨(-951631282568137095),(-951616776493600120)⟩⟩,⟨⟨1425764312797362285,1425776661195217688⟩,⟨(-1101133460378594427),(-1101121111980739025)⟩⟩,⟨⟨923661710760780401,923672194739375419⟩,⟨(-1113330372866770888),(-1113319888888175869)⟩⟩,⟨⟨524557779357585895,524566660508466728⟩,⟨(-1033283724486874640),(-1033274843335993806)⟩⟩,⟨⟨224441683804891152,224449187868054163⟩,⟨(-898416915107241555),(-898409411044078544)⟩⟩,⟨⟨13091955337540826,13098280843635052⟩,⟨(-738119326818708602),(-738113001312614375)⟩⟩] +lemma kernel99_0_r5_4_eq : ∀ k : Fin 16, kernel99_0Expr 5 4 k = kernel99_0_r5_4 k := by decide +kernel +noncomputable def kernel99_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-123215684645955821),(-123210366862028334)⟩,⟨(-574054146295866647),(-574048828511939160)⟩⟩,⟨⟨(-199548386767486098),(-199543926223536303)⟩,⟨(-420950371904709024),(-420945911360759228)⟩⟩,⟨⟨(-230709757499264942),(-230706024871776678)⟩,⟨(-287681754241696814),(-287678021614208549)⟩⟩,⟨⟨(-230149016328158431),(-230145900200552692)⟩,⟨(-178467150999504905),(-178464034871899167)⟩⟩,⟨⟨(-209318386772817258),(-209315792326446462)⟩,⟨(-94063175856069531),(-94060581409698735)⟩⟩,⟨⟨(-177395126173822134),(-177392970978383639)⟩,⟨(-32857062206509853),(-32854907011071358)⟩⟩,⟨⟨(-141279433488812214),(-141277647942876422)⟩,⟨8197905970739611,8199691516675403⟩⟩,⟨⟨(-105783002003461377),(-105781526166717028)⟩,⟨32832361506232480,32833837342976829⟩⟩,⟨⟨(-73932563104179793),(-73931346581800622)⟩,⟨44900540572874276,44901757095253447⟩⟩,⟨⟨(-47325998155549231),(-47324997037457599)⟩,⟨47996739039190688,47997740157282321⟩⟩,⟨⟨(-26493283708894669),(-26492461935965167)⟩,⟨45224476758409448,45225298531338950⟩⟩,⟨⟨(-11229032301983261),(-11228359302455868)⟩,⟨39088551564471525,39089224563998918⟩⟩,⟨⟨(-876419009565617),(-875869349135652)⟩,⟨31478790881814645,31479340542244610⟩⟩,⟨⟨5446854396324915,5447302326859962⟩,⟨23716119507022460,23716567437557507⟩⟩,⟨⟨8681592498475977,8681956551230103⟩,⟨16635484457639341,16635848510393467⟩⟩,⟨⟨9714381021804869,9714676287570063⟩,⟨10685189889093578,10685485154858771⟩⟩] +lemma kernel99_0_r5_5_eq : ∀ k : Fin 16, kernel99_0Expr 5 5 k = kernel99_0_r5_5 k := by decide +kernel +noncomputable def kernel99_0_r5_6 : Fin 16 → CBox := ![⟨⟨9310865174967062,9311104001940884⟩,⟨6027511608072097,6027750435045918⟩⟩,⟨⟨8085215576848237,8085408337458694⟩,⟨2630469960557661,2630662721168117⟩⟩,⟨⟨6495854349367478,6496009521148868⟩,⟨344971313585095,345126485366485⟩⟩,⟨⟨4858398318938210,4858522956955698⟩,⟨(-1035031749725522),(-1034907111708034)⟩⟩,⟨⟨3368254257896264,3368354098965838⟩,⟨(-1729201942314054),(-1729102101244479)⟩⟩,⟨⟨2127022733939428,2127102542266941⟩,⟨(-1942511327397640),(-1942431519070128)⟩⟩,⟨⟨1168582661743956,1168646288361398⟩,⟨(-1849293506120216),(-1849229879502774)⟩⟩,⟨⟨482261158299623,482311775462814⟩,⟨(-1586680539260320),(-1586629922097129)⟩⟩,⟨⟨31750891261313,31791104049178⟩,⟨(-1254564600476675),(-1254524387688810)⟩⟩,⟨⟨(-230618495632500),(-230586598243023)⟩,⟨(-919597499901984),(-919565602512508)⟩⟩,⟨⟨(-354004988050535),(-353979752436144)⟩,⟨(-621241686063934),(-621216450449543)⟩⟩,⟨⟨(-382944778713913),(-382924854661716)⟩,⟨(-378415911898232),(-378395987846035)⟩⟩,⟨⟨(-354207932664181),(-354192243965855)⟩,⟨(-195769682330862),(-195753993632535)⟩⟩,⟨⟨(-295799485249535),(-295787155338747)⟩,⟨(-69033653737121),(-69021323826332)⟩⟩,⟨⟨(-227365045489659),(-227355379934194)⟩,⟨10789257130889,10798922686353⟩⟩,⟨⟨(-161391959905888),(-161384397307527)⟩,⟨54404301676697,54411864275057⟩⟩] +lemma kernel99_0_r5_6_eq : ∀ k : Fin 16, kernel99_0Expr 5 6 k = kernel99_0_r5_6 k := by decide +kernel +noncomputable def kernel99_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-104746784357212),(-104740882754394)⟩,⟨72250978418016,72256880020834⟩⟩,⟨⟨(-60234002796245),(-60229405259351)⟩,⟨73378599280373,73383196817267⟩⟩,⟨⟨(-27984732155332),(-27981158747463)⟩,⟨64955286820295,64958860228165⟩⟩,⟨⟨(-6581430318581),(-6578658047487)⟩,⟨52207326476400,52210098747494⟩⟩,⟨⟨6105954829058,6108100167936⟩,⟨38617601716624,38619747055502⟩⟩,⟨⟨12352422079555,12354079460651⟩,⟨26251088897070,26252746278166⟩⟩,⟨⟨14234915280462,14236192597970⟩,⟨16114610347668,16115887665176⟩⟩,⟨⟨13460879716674,13461862428318⟩,⟨8492418436827,8493401148471⟩⟩,⟨⟨11316572888696,11317327653384⟩,⟨3226588855187,3227343619875⟩⟩,⟨⟨8690350046901,8690929011577⟩,⟨(-68957527698),(-68378563022)⟩⟩,⟨⟨6135800297005,6136243376450⟩,⟨(-1859002465979),(-1858559386534)⟩⟩,⟨⟨3949577370194,3949915922765⟩,⟨(-2593043400650),(-2592704848079)⟩⟩,⟨⟨2247697773001,2247955843326⟩,⟨(-2654576865990),(-2654318795664)⟩⟩,⟨⟨1031256637299,1031453099864⟩,⟨(-2341229382622),(-2341032920057)⟩⟩,⟨⟨237784967175,237934199640⟩,⟨(-1864751813769),(-1864602581304)⟩⟩,⟨⟨(-222044748129),(-221931552458)⟩,⟨(-1362128050468),(-1362014854797)⟩⟩] +lemma kernel99_0_r5_7_eq : ∀ k : Fin 16, kernel99_0Expr 5 7 k = kernel99_0_r5_7 k := by decide +kernel +noncomputable def kernel99_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-440634517440),(-440548847923)⟩,⟨(-911438446449),(-911352776931)⟩⟩,⟨⟨(-499953180690),(-499888385037)⟩,⟨(-548299115365),(-548234319712)⟩⟩,⟨⟨(-465484966227),(-465436061118)⟩,⟨(-280467311436),(-280418406326)⟩⟩,⟨⟨(-385088640605),(-385051774926)⟩,⟨(-99514691071),(-99477825391)⟩⟩,⟨⟨(-290707461735),(-290679730842)⟩,⟨10654839776,10682570669⟩⟩,⟨⟨(-201415582904),(-201394744766)⟩,⟨68146965628,68167803765⟩⟩,⟨⟨(-126788856274),(-126773224286)⟩,⟨89735807853,89751439840⟩⟩,⟨⟨(-70001884608),(-69990169203)⟩,⟨89232004945,89243720349⟩⟩,⟨⟨(-30360632178),(-30351870059)⟩,⟨76998672407,77007434526⟩⟩,⟨⟨(-5188338912),(-5181790718)⟩,⟨60154445009,60160993203⟩⟩,⟨⟨8892771174,8897656979⟩,⟨43120499657,43125385463⟩⟩,⟨⟨15178930133,15182572518⟩,⟨28278864108,28282506493⟩⟩,⟨⟨16476908921,16479619327⟩,⟨16601253660,16603964065⟩⟩,⟨⟨14952511163,14954527048⟩,⟨8176522786,8178538670⟩⟩,⟨⟨12136957227,12138454116⟩,⟨2611988435,2613485324⟩⟩,⟨⟨9016679226,9017790104⟩,⟨(-687415229),(-686304351)⟩⟩] +lemma kernel99_0_r5_8_eq : ∀ k : Fin 16, kernel99_0Expr 5 8 k = kernel99_0_r5_8 k := by decide +kernel +noncomputable def kernel99_0_r5_9 : Fin 16 → CBox := ![⟨⟨6155293279,6156116259⟩,⟨(-2343234910),(-2342411930)⟩⟩,⟨⟨3815966140,3816575659⟩,⟨(-2906596832),(-2905987313)⟩⟩,⟨⟨2067226137,2067676920⟩,⟨(-2816503365),(-2816052582)⟩⟩,⟨⟨865481392,865814651⟩,⟨(-2393096143),(-2392762884)⟩⟩,⟨⟨113900081,114146084⟩,⟨(-1850327691),(-1850081689)⟩⟩,⟨⟨(-299275655),(-299094081)⟩,⟨(-1317142238),(-1316960664)⟩⟩,⟨⟨(-478513877),(-478380023)⟩,⟨(-860230271),(-860096417)⟩⟩,⟨⟨(-510301242),(-510202581)⟩,⟨(-504489445),(-504390785)⟩⟩,⟨⟨(-459973739),(-459901116)⟩,⟨(-249470677),(-249398054)⟩⟩,⟨⟨(-372931553),(-372878083)⟩,⟨(-81462591),(-81409121)⟩⟩,⟨⟨(-277985104),(-277945775)⟩,⟨18367210,18406539⟩⟩,⟨⟨(-191359963),(-191331035)⟩,⟨69009422,69038350⟩⟩,⟨⟨(-120498689),(-120477432)⟩,⟨86991936,87013194⟩⟩,⟨⟨(-67238164),(-67222534)⟩,⟨85340056,85355685⟩⟩,⟨⟨(-30227855),(-30216372)⟩,⟨73504428,73515910⟩⟩,⟨⟨(-6623542),(-6615061)⟩,⟨57803682,57812164⟩⟩] +lemma kernel99_0_r5_9_eq : ∀ k : Fin 16, kernel99_0Expr 5 9 k = kernel99_0_r5_9 k := by decide +kernel +noncomputable def kernel99_0_r5_10 : Fin 16 → CBox := ![⟨⟨6826766,6833028⟩,⟨42075794,42082056⟩⟩,⟨⟨13160269,13164898⟩,⟨28349920,28354550⟩⟩,⟨⟨14902500,14905921⟩,⟨17438620,17442040⟩⟩,⟨⟨13979871,13982402⟩,⟨9408850,9411381⟩⟩,⟨⟨11753069,11754939⟩,⟨3926846,3928716⟩⟩,⟨⟨9108917,9110301⟩,⟨491221,492605⟩⟩,⟨⟨6570497,6571523⟩,⟨(-1423055),(-1422029)⟩⟩,⟨⟨4402203,4402964⟩,⟨(-2286205),(-2285444)⟩⟩,⟨⟨2698298,2698862⟩,⟨(-2479638),(-2479073)⟩⟩,⟨⟨1451292,1451711⟩,⟨(-2289585),(-2289166)⟩⟩,⟨⟨600848,601161⟩,⟨(-1915948),(-1915636)⟩⟩,⟨⟨66205,66441⟩,⟨(-1487959),(-1487723)⟩⟩,⟨⟨(-234196),(-234019)⟩,⟨(-1081357),(-1081180)⟩⟩,⟨⟨(-372290),(-372157)⟩,⟨(-734163),(-734029)⟩⟩,⟨⟨(-406100),(-405999)⟩,⟨(-459700),(-459599)⟩⟩,⟨⟨(-379199),(-379121)⟩,⟨(-256522),(-256443)⟩⟩] +lemma kernel99_0_r5_10_eq : ∀ k : Fin 16, kernel99_0Expr 5 10 k = kernel99_0_r5_10 k := by decide +kernel +noncomputable def kernel99_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-322210),(-322152)⟩,⟨(-115486),(-115427)⟩⟩,⟨⟨(-255187),(-255139)⟩,⟨(-24427),(-24380)⟩⟩,⟨⟨(-190144),(-190108)⟩,⟨29004,29040⟩⟩,⟨⟨(-133387),(-133357)⟩,⟨55797,55827⟩⟩,⟨⟨(-87411),(-87386)⟩,⟨64946,64970⟩⟩,⟨⟨(-52376),(-52356)⟩,⟨63328,63347⟩⟩,⟨⟨(-27162),(-27145)⟩,⟨55893,55911⟩⟩,⟨⟨(-10084),(-10070)⟩,⟨45999,46014⟩⟩,⟨⟨664,678⟩,⟨35755,35769⟩⟩,⟨⟨6753,6765⟩,⟨26367,26379⟩⟩,⟨⟨9600,9611⟩,⟨18411,18421⟩⟩,⟨⟨10327,10338⟩,⟨12056,12067⟩⟩,⟨⟨9780,9791⟩,⟨7237,7248⟩⟩,⟨⟨8558,8567⟩,⟨3761,3770⟩⟩,⟨⟨7067,7074⟩,⟨1385,1392⟩⟩,⟨⟨5558,5568⟩,⟨(-139),(-129)⟩⟩] +lemma kernel99_0_r5_11_eq : ∀ k : Fin 16, kernel99_0Expr 5 11 k = kernel99_0_r5_11 k := by decide +kernel +noncomputable def kernel99_0_r5_12 : Fin 16 → CBox := ![⟨⟨4182,4191⟩,⟨(-1026),(-1018)⟩⟩,⟨⟨3005,3013⟩,⟨(-1467),(-1459)⟩⟩,⟨⟨2049,2057⟩,⟨(-1607),(-1599)⟩⟩,⟨⟨1306,1314⟩,⟨(-1560),(-1551)⟩⟩,⟨⟨752,760⟩,⟨(-1405),(-1397)⟩⟩,⟨⟨357,364⟩,⟨(-1200),(-1193)⟩⟩,⟨⟨87,95⟩,⟨(-984),(-977)⟩⟩,⟨⟨(-85),(-77)⟩,⟨(-777),(-769)⟩⟩,⟨⟨(-185),(-178)⟩,⟨(-592),(-585)⟩⟩,⟨⟨(-234),(-227)⟩,⟨(-436),(-429)⟩⟩,⟨⟨(-249),(-241)⟩,⟨(-308),(-301)⟩⟩,⟨⟨(-240),(-234)⟩,⟨(-206),(-199)⟩⟩,⟨⟨(-219),(-213)⟩,⟨(-129),(-123)⟩⟩,⟨⟨(-194),(-186)⟩,⟨(-72),(-65)⟩⟩,⟨⟨(-164),(-156)⟩,⟨(-32),(-24)⟩⟩,⟨⟨(-136),(-128)⟩,⟨(-3),5⟩⟩] +lemma kernel99_0_r5_12_eq : ∀ k : Fin 16, kernel99_0Expr 5 12 k = kernel99_0_r5_12 k := by decide +kernel +noncomputable def kernel99_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-110),(-102)⟩,⟨15,22⟩⟩,⟨⟨(-87),(-79)⟩,⟨26,33⟩⟩,⟨⟨(-66),(-59)⟩,⟨31,39⟩⟩,⟨⟨(-50),(-43)⟩,⟨33,41⟩⟩,⟨⟨(-36),(-30)⟩,⟨33,40⟩⟩,⟨⟨(-26),(-18)⟩,⟨30,38⟩⟩,⟨⟨(-17),(-11)⟩,⟨27,33⟩⟩,⟨⟨(-12),(-4)⟩,⟨23,31⟩⟩,⟨⟨(-6),1⟩,⟨19,27⟩⟩,⟨⟨(-3),3⟩,⟨17,23⟩⟩,⟨⟨0,6⟩,⟨13,19⟩⟩,⟨⟨1,7⟩,⟨11,17⟩⟩,⟨⟨2,7⟩,⟨8,14⟩⟩,⟨⟨2,9⟩,⟨5,12⟩⟩,⟨⟨2,9⟩,⟨4,11⟩⟩,⟨⟨2,9⟩,⟨2,8⟩⟩] +lemma kernel99_0_r5_13_eq : ∀ k : Fin 16, kernel99_0Expr 5 13 k = kernel99_0_r5_13 k := by decide +kernel +noncomputable def kernel99_0_r5_14 : Fin 16 → CBox := ![⟨⟨2,8⟩,⟨1,7⟩⟩,⟨⟨1,8⟩,⟨0,7⟩⟩,⟨⟨1,9⟩,⟨(-2),6⟩⟩,⟨⟨1,7⟩,⟨(-2),4⟩⟩,⟨⟨1,7⟩,⟨(-3),4⟩⟩,⟨⟨0,7⟩,⟨(-3),4⟩⟩,⟨⟨0,7⟩,⟨(-3),4⟩⟩,⟨⟨(-1),7⟩,⟨(-4),4⟩⟩,⟨⟨(-1),5⟩,⟨(-3),3⟩⟩,⟨⟨(-1),5⟩,⟨(-3),3⟩⟩,⟨⟨(-1),5⟩,⟨(-3),3⟩⟩,⟨⟨(-1),5⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),5⟩,⟨(-4),3⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel99_0_r5_14_eq : ∀ k : Fin 16, kernel99_0Expr 5 14 k = kernel99_0_r5_14 k := by decide +kernel +noncomputable def kernel99_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),5⟩,⟨(-4),3⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩] +lemma kernel99_0_r5_15_eq : ∀ k : Fin 16, kernel99_0Expr 5 15 k = kernel99_0_r5_15 k := by decide +kernel +noncomputable def kernel99_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel99_0_r5_0,kernel99_0_r5_1,kernel99_0_r5_2,kernel99_0_r5_3,kernel99_0_r5_4,kernel99_0_r5_5,kernel99_0_r5_6,kernel99_0_r5_7,kernel99_0_r5_8,kernel99_0_r5_9,kernel99_0_r5_10,kernel99_0_r5_11,kernel99_0_r5_12,kernel99_0_r5_13,kernel99_0_r5_14,kernel99_0_r5_15] +lemma kernel99_0_r5_eq (i k : Fin 16) : kernel99_0Expr 5 i k = kernel99_0_r5 i k := by + fin_cases i + · exact kernel99_0_r5_0_eq k + · exact kernel99_0_r5_1_eq k + · exact kernel99_0_r5_2_eq k + · exact kernel99_0_r5_3_eq k + · exact kernel99_0_r5_4_eq k + · exact kernel99_0_r5_5_eq k + · exact kernel99_0_r5_6_eq k + · exact kernel99_0_r5_7_eq k + · exact kernel99_0_r5_8_eq k + · exact kernel99_0_r5_9_eq k + · exact kernel99_0_r5_10_eq k + · exact kernel99_0_r5_11_eq k + · exact kernel99_0_r5_12_eq k + · exact kernel99_0_r5_13_eq k + · exact kernel99_0_r5_14_eq k + · exact kernel99_0_r5_15_eq k +noncomputable def kernel99_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel99_0_r0,kernel99_0_r1,kernel99_0_r2,kernel99_0_r3,kernel99_0_r4,kernel99_0_r5] +lemma kernel99_0_eq (j : Fin 6) (i k : Fin 16) : kernel99_0Expr j i k = kernel99_0 j i k := by + fin_cases j + · exact kernel99_0_r0_eq i k + · exact kernel99_0_r1_eq i k + · exact kernel99_0_r2_eq i k + · exact kernel99_0_r3_eq i k + · exact kernel99_0_r4_eq i k + · exact kernel99_0_r5_eq i k +lemma kernel99_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel99_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(99:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel99_0_eq] + unfold kernel99_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans99_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel99_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans99 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel99_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r0_0_eq : ∀ k : Fin 16, kernel99_1Expr 0 0 k = kernel99_1_r0_0 k := by decide +kernel +noncomputable def kernel99_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r0_1_eq : ∀ k : Fin 16, kernel99_1Expr 0 1 k = kernel99_1_r0_1 k := by decide +kernel +noncomputable def kernel99_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r0_2_eq : ∀ k : Fin 16, kernel99_1Expr 0 2 k = kernel99_1_r0_2 k := by decide +kernel +noncomputable def kernel99_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r0_3_eq : ∀ k : Fin 16, kernel99_1Expr 0 3 k = kernel99_1_r0_3 k := by decide +kernel +noncomputable def kernel99_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r0_4_eq : ∀ k : Fin 16, kernel99_1Expr 0 4 k = kernel99_1_r0_4 k := by decide +kernel +noncomputable def kernel99_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel99_1_r0_5_eq : ∀ k : Fin 16, kernel99_1Expr 0 5 k = kernel99_1_r0_5 k := by decide +kernel +noncomputable def kernel99_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel99_1_r0_6_eq : ∀ k : Fin 16, kernel99_1Expr 0 6 k = kernel99_1_r0_6 k := by decide +kernel +noncomputable def kernel99_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel99_1_r0_7_eq : ∀ k : Fin 16, kernel99_1Expr 0 7 k = kernel99_1_r0_7 k := by decide +kernel +noncomputable def kernel99_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel99_1_r0_8_eq : ∀ k : Fin 16, kernel99_1Expr 0 8 k = kernel99_1_r0_8 k := by decide +kernel +noncomputable def kernel99_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel99_1_r0_9_eq : ∀ k : Fin 16, kernel99_1Expr 0 9 k = kernel99_1_r0_9 k := by decide +kernel +noncomputable def kernel99_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel99_1_r0_10_eq : ∀ k : Fin 16, kernel99_1Expr 0 10 k = kernel99_1_r0_10 k := by decide +kernel +noncomputable def kernel99_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel99_1_r0_11_eq : ∀ k : Fin 16, kernel99_1Expr 0 11 k = kernel99_1_r0_11 k := by decide +kernel +noncomputable def kernel99_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel99_1_r0_12_eq : ∀ k : Fin 16, kernel99_1Expr 0 12 k = kernel99_1_r0_12 k := by decide +kernel +noncomputable def kernel99_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel99_1_r0_13_eq : ∀ k : Fin 16, kernel99_1Expr 0 13 k = kernel99_1_r0_13 k := by decide +kernel +noncomputable def kernel99_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel99_1_r0_14_eq : ∀ k : Fin 16, kernel99_1Expr 0 14 k = kernel99_1_r0_14 k := by decide +kernel +noncomputable def kernel99_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel99_1_r0_15_eq : ∀ k : Fin 16, kernel99_1Expr 0 15 k = kernel99_1_r0_15 k := by decide +kernel +noncomputable def kernel99_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel99_1_r0_0,kernel99_1_r0_1,kernel99_1_r0_2,kernel99_1_r0_3,kernel99_1_r0_4,kernel99_1_r0_5,kernel99_1_r0_6,kernel99_1_r0_7,kernel99_1_r0_8,kernel99_1_r0_9,kernel99_1_r0_10,kernel99_1_r0_11,kernel99_1_r0_12,kernel99_1_r0_13,kernel99_1_r0_14,kernel99_1_r0_15] +lemma kernel99_1_r0_eq (i k : Fin 16) : kernel99_1Expr 0 i k = kernel99_1_r0 i k := by + fin_cases i + · exact kernel99_1_r0_0_eq k + · exact kernel99_1_r0_1_eq k + · exact kernel99_1_r0_2_eq k + · exact kernel99_1_r0_3_eq k + · exact kernel99_1_r0_4_eq k + · exact kernel99_1_r0_5_eq k + · exact kernel99_1_r0_6_eq k + · exact kernel99_1_r0_7_eq k + · exact kernel99_1_r0_8_eq k + · exact kernel99_1_r0_9_eq k + · exact kernel99_1_r0_10_eq k + · exact kernel99_1_r0_11_eq k + · exact kernel99_1_r0_12_eq k + · exact kernel99_1_r0_13_eq k + · exact kernel99_1_r0_14_eq k + · exact kernel99_1_r0_15_eq k +noncomputable def kernel99_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel99_1_r1_0_eq : ∀ k : Fin 16, kernel99_1Expr 1 0 k = kernel99_1_r1_0 k := by decide +kernel +noncomputable def kernel99_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel99_1_r1_1_eq : ∀ k : Fin 16, kernel99_1Expr 1 1 k = kernel99_1_r1_1 k := by decide +kernel +noncomputable def kernel99_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel99_1_r1_2_eq : ∀ k : Fin 16, kernel99_1Expr 1 2 k = kernel99_1_r1_2 k := by decide +kernel +noncomputable def kernel99_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel99_1_r1_3_eq : ∀ k : Fin 16, kernel99_1Expr 1 3 k = kernel99_1_r1_3 k := by decide +kernel +noncomputable def kernel99_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel99_1_r1_4_eq : ∀ k : Fin 16, kernel99_1Expr 1 4 k = kernel99_1_r1_4 k := by decide +kernel +noncomputable def kernel99_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel99_1_r1_5_eq : ∀ k : Fin 16, kernel99_1Expr 1 5 k = kernel99_1_r1_5 k := by decide +kernel +noncomputable def kernel99_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel99_1_r1_6_eq : ∀ k : Fin 16, kernel99_1Expr 1 6 k = kernel99_1_r1_6 k := by decide +kernel +noncomputable def kernel99_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel99_1_r1_7_eq : ∀ k : Fin 16, kernel99_1Expr 1 7 k = kernel99_1_r1_7 k := by decide +kernel +noncomputable def kernel99_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel99_1_r1_8_eq : ∀ k : Fin 16, kernel99_1Expr 1 8 k = kernel99_1_r1_8 k := by decide +kernel +noncomputable def kernel99_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel99_1_r1_9_eq : ∀ k : Fin 16, kernel99_1Expr 1 9 k = kernel99_1_r1_9 k := by decide +kernel +noncomputable def kernel99_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r1_10_eq : ∀ k : Fin 16, kernel99_1Expr 1 10 k = kernel99_1_r1_10 k := by decide +kernel +noncomputable def kernel99_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r1_11_eq : ∀ k : Fin 16, kernel99_1Expr 1 11 k = kernel99_1_r1_11 k := by decide +kernel +noncomputable def kernel99_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r1_12_eq : ∀ k : Fin 16, kernel99_1Expr 1 12 k = kernel99_1_r1_12 k := by decide +kernel +noncomputable def kernel99_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r1_13_eq : ∀ k : Fin 16, kernel99_1Expr 1 13 k = kernel99_1_r1_13 k := by decide +kernel +noncomputable def kernel99_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r1_14_eq : ∀ k : Fin 16, kernel99_1Expr 1 14 k = kernel99_1_r1_14 k := by decide +kernel +noncomputable def kernel99_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel99_1_r1_15_eq : ∀ k : Fin 16, kernel99_1Expr 1 15 k = kernel99_1_r1_15 k := by decide +kernel +noncomputable def kernel99_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel99_1_r1_0,kernel99_1_r1_1,kernel99_1_r1_2,kernel99_1_r1_3,kernel99_1_r1_4,kernel99_1_r1_5,kernel99_1_r1_6,kernel99_1_r1_7,kernel99_1_r1_8,kernel99_1_r1_9,kernel99_1_r1_10,kernel99_1_r1_11,kernel99_1_r1_12,kernel99_1_r1_13,kernel99_1_r1_14,kernel99_1_r1_15] +lemma kernel99_1_r1_eq (i k : Fin 16) : kernel99_1Expr 1 i k = kernel99_1_r1 i k := by + fin_cases i + · exact kernel99_1_r1_0_eq k + · exact kernel99_1_r1_1_eq k + · exact kernel99_1_r1_2_eq k + · exact kernel99_1_r1_3_eq k + · exact kernel99_1_r1_4_eq k + · exact kernel99_1_r1_5_eq k + · exact kernel99_1_r1_6_eq k + · exact kernel99_1_r1_7_eq k + · exact kernel99_1_r1_8_eq k + · exact kernel99_1_r1_9_eq k + · exact kernel99_1_r1_10_eq k + · exact kernel99_1_r1_11_eq k + · exact kernel99_1_r1_12_eq k + · exact kernel99_1_r1_13_eq k + · exact kernel99_1_r1_14_eq k + · exact kernel99_1_r1_15_eq k +noncomputable def kernel99_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel99_1_r2_0_eq : ∀ k : Fin 16, kernel99_1Expr 2 0 k = kernel99_1_r2_0 k := by decide +kernel +noncomputable def kernel99_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel99_1_r2_1_eq : ∀ k : Fin 16, kernel99_1Expr 2 1 k = kernel99_1_r2_1 k := by decide +kernel +noncomputable def kernel99_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel99_1_r2_2_eq : ∀ k : Fin 16, kernel99_1Expr 2 2 k = kernel99_1_r2_2 k := by decide +kernel +noncomputable def kernel99_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel99_1_r2_3_eq : ∀ k : Fin 16, kernel99_1Expr 2 3 k = kernel99_1_r2_3 k := by decide +kernel +noncomputable def kernel99_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel99_1_r2_4_eq : ∀ k : Fin 16, kernel99_1Expr 2 4 k = kernel99_1_r2_4 k := by decide +kernel +noncomputable def kernel99_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel99_1_r2_5_eq : ∀ k : Fin 16, kernel99_1Expr 2 5 k = kernel99_1_r2_5 k := by decide +kernel +noncomputable def kernel99_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel99_1_r2_6_eq : ∀ k : Fin 16, kernel99_1Expr 2 6 k = kernel99_1_r2_6 k := by decide +kernel +noncomputable def kernel99_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel99_1_r2_7_eq : ∀ k : Fin 16, kernel99_1Expr 2 7 k = kernel99_1_r2_7 k := by decide +kernel +noncomputable def kernel99_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel99_1_r2_8_eq : ∀ k : Fin 16, kernel99_1Expr 2 8 k = kernel99_1_r2_8 k := by decide +kernel +noncomputable def kernel99_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel99_1_r2_9_eq : ∀ k : Fin 16, kernel99_1Expr 2 9 k = kernel99_1_r2_9 k := by decide +kernel +noncomputable def kernel99_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel99_1_r2_10_eq : ∀ k : Fin 16, kernel99_1Expr 2 10 k = kernel99_1_r2_10 k := by decide +kernel +noncomputable def kernel99_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel99_1_r2_11_eq : ∀ k : Fin 16, kernel99_1Expr 2 11 k = kernel99_1_r2_11 k := by decide +kernel +noncomputable def kernel99_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel99_1_r2_12_eq : ∀ k : Fin 16, kernel99_1Expr 2 12 k = kernel99_1_r2_12 k := by decide +kernel +noncomputable def kernel99_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel99_1_r2_13_eq : ∀ k : Fin 16, kernel99_1Expr 2 13 k = kernel99_1_r2_13 k := by decide +kernel +noncomputable def kernel99_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel99_1_r2_14_eq : ∀ k : Fin 16, kernel99_1Expr 2 14 k = kernel99_1_r2_14 k := by decide +kernel +noncomputable def kernel99_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel99_1_r2_15_eq : ∀ k : Fin 16, kernel99_1Expr 2 15 k = kernel99_1_r2_15 k := by decide +kernel +noncomputable def kernel99_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel99_1_r2_0,kernel99_1_r2_1,kernel99_1_r2_2,kernel99_1_r2_3,kernel99_1_r2_4,kernel99_1_r2_5,kernel99_1_r2_6,kernel99_1_r2_7,kernel99_1_r2_8,kernel99_1_r2_9,kernel99_1_r2_10,kernel99_1_r2_11,kernel99_1_r2_12,kernel99_1_r2_13,kernel99_1_r2_14,kernel99_1_r2_15] +lemma kernel99_1_r2_eq (i k : Fin 16) : kernel99_1Expr 2 i k = kernel99_1_r2 i k := by + fin_cases i + · exact kernel99_1_r2_0_eq k + · exact kernel99_1_r2_1_eq k + · exact kernel99_1_r2_2_eq k + · exact kernel99_1_r2_3_eq k + · exact kernel99_1_r2_4_eq k + · exact kernel99_1_r2_5_eq k + · exact kernel99_1_r2_6_eq k + · exact kernel99_1_r2_7_eq k + · exact kernel99_1_r2_8_eq k + · exact kernel99_1_r2_9_eq k + · exact kernel99_1_r2_10_eq k + · exact kernel99_1_r2_11_eq k + · exact kernel99_1_r2_12_eq k + · exact kernel99_1_r2_13_eq k + · exact kernel99_1_r2_14_eq k + · exact kernel99_1_r2_15_eq k +noncomputable def kernel99_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel99_1_r3_0_eq : ∀ k : Fin 16, kernel99_1Expr 3 0 k = kernel99_1_r3_0 k := by decide +kernel +noncomputable def kernel99_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel99_1_r3_1_eq : ∀ k : Fin 16, kernel99_1Expr 3 1 k = kernel99_1_r3_1 k := by decide +kernel +noncomputable def kernel99_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel99_1_r3_2_eq : ∀ k : Fin 16, kernel99_1Expr 3 2 k = kernel99_1_r3_2 k := by decide +kernel +noncomputable def kernel99_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel99_1_r3_3_eq : ∀ k : Fin 16, kernel99_1Expr 3 3 k = kernel99_1_r3_3 k := by decide +kernel +noncomputable def kernel99_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel99_1_r3_4_eq : ∀ k : Fin 16, kernel99_1Expr 3 4 k = kernel99_1_r3_4 k := by decide +kernel +noncomputable def kernel99_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel99_1_r3_5_eq : ∀ k : Fin 16, kernel99_1Expr 3 5 k = kernel99_1_r3_5 k := by decide +kernel +noncomputable def kernel99_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel99_1_r3_6_eq : ∀ k : Fin 16, kernel99_1Expr 3 6 k = kernel99_1_r3_6 k := by decide +kernel +noncomputable def kernel99_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel99_1_r3_7_eq : ∀ k : Fin 16, kernel99_1Expr 3 7 k = kernel99_1_r3_7 k := by decide +kernel +noncomputable def kernel99_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel99_1_r3_8_eq : ∀ k : Fin 16, kernel99_1Expr 3 8 k = kernel99_1_r3_8 k := by decide +kernel +noncomputable def kernel99_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel99_1_r3_9_eq : ∀ k : Fin 16, kernel99_1Expr 3 9 k = kernel99_1_r3_9 k := by decide +kernel +noncomputable def kernel99_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel99_1_r3_10_eq : ∀ k : Fin 16, kernel99_1Expr 3 10 k = kernel99_1_r3_10 k := by decide +kernel +noncomputable def kernel99_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel99_1_r3_11_eq : ∀ k : Fin 16, kernel99_1Expr 3 11 k = kernel99_1_r3_11 k := by decide +kernel +noncomputable def kernel99_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel99_1_r3_12_eq : ∀ k : Fin 16, kernel99_1Expr 3 12 k = kernel99_1_r3_12 k := by decide +kernel +noncomputable def kernel99_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel99_1_r3_13_eq : ∀ k : Fin 16, kernel99_1Expr 3 13 k = kernel99_1_r3_13 k := by decide +kernel +noncomputable def kernel99_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel99_1_r3_14_eq : ∀ k : Fin 16, kernel99_1Expr 3 14 k = kernel99_1_r3_14 k := by decide +kernel +noncomputable def kernel99_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel99_1_r3_15_eq : ∀ k : Fin 16, kernel99_1Expr 3 15 k = kernel99_1_r3_15 k := by decide +kernel +noncomputable def kernel99_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel99_1_r3_0,kernel99_1_r3_1,kernel99_1_r3_2,kernel99_1_r3_3,kernel99_1_r3_4,kernel99_1_r3_5,kernel99_1_r3_6,kernel99_1_r3_7,kernel99_1_r3_8,kernel99_1_r3_9,kernel99_1_r3_10,kernel99_1_r3_11,kernel99_1_r3_12,kernel99_1_r3_13,kernel99_1_r3_14,kernel99_1_r3_15] +lemma kernel99_1_r3_eq (i k : Fin 16) : kernel99_1Expr 3 i k = kernel99_1_r3 i k := by + fin_cases i + · exact kernel99_1_r3_0_eq k + · exact kernel99_1_r3_1_eq k + · exact kernel99_1_r3_2_eq k + · exact kernel99_1_r3_3_eq k + · exact kernel99_1_r3_4_eq k + · exact kernel99_1_r3_5_eq k + · exact kernel99_1_r3_6_eq k + · exact kernel99_1_r3_7_eq k + · exact kernel99_1_r3_8_eq k + · exact kernel99_1_r3_9_eq k + · exact kernel99_1_r3_10_eq k + · exact kernel99_1_r3_11_eq k + · exact kernel99_1_r3_12_eq k + · exact kernel99_1_r3_13_eq k + · exact kernel99_1_r3_14_eq k + · exact kernel99_1_r3_15_eq k +noncomputable def kernel99_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩] +lemma kernel99_1_r4_0_eq : ∀ k : Fin 16, kernel99_1Expr 4 0 k = kernel99_1_r4_0 k := by decide +kernel +noncomputable def kernel99_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-15),20⟩,⟨(-16),19⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-16),19⟩,⟨(-20),15⟩⟩] +lemma kernel99_1_r4_1_eq : ∀ k : Fin 16, kernel99_1Expr 4 1 k = kernel99_1_r4_1 k := by decide +kernel +noncomputable def kernel99_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-14),11⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-10),15⟩,⟨(-11),14⟩⟩,⟨⟨(-10),15⟩,⟨(-11),14⟩⟩] +lemma kernel99_1_r4_2_eq : ∀ k : Fin 16, kernel99_1Expr 4 2 k = kernel99_1_r4_2 k := by decide +kernel +noncomputable def kernel99_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-10),15⟩,⟨(-11),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-15),11⟩⟩,⟨⟨(-19),11⟩,⟨(-15),16⟩⟩,⟨⟨(-19),11⟩,⟨(-15),16⟩⟩,⟨⟨(-19),11⟩,⟨(-15),16⟩⟩,⟨⟨(-15),11⟩,⟨(-10),15⟩⟩,⟨⟨(-15),11⟩,⟨(-10),15⟩⟩,⟨⟨(-15),16⟩,⟨(-11),20⟩⟩] +lemma kernel99_1_r4_3_eq : ∀ k : Fin 16, kernel99_1Expr 4 3 k = kernel99_1_r4_3 k := by decide +kernel +noncomputable def kernel99_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel99_1_r4_4_eq : ∀ k : Fin 16, kernel99_1Expr 4 4 k = kernel99_1_r4_4 k := by decide +kernel +noncomputable def kernel99_1_r4_5 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel99_1_r4_5_eq : ∀ k : Fin 16, kernel99_1Expr 4 5 k = kernel99_1_r4_5 k := by decide +kernel +noncomputable def kernel99_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel99_1_r4_6_eq : ∀ k : Fin 16, kernel99_1Expr 4 6 k = kernel99_1_r4_6 k := by decide +kernel +noncomputable def kernel99_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel99_1_r4_7_eq : ∀ k : Fin 16, kernel99_1Expr 4 7 k = kernel99_1_r4_7 k := by decide +kernel +noncomputable def kernel99_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel99_1_r4_8_eq : ∀ k : Fin 16, kernel99_1Expr 4 8 k = kernel99_1_r4_8 k := by decide +kernel +noncomputable def kernel99_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel99_1_r4_9_eq : ∀ k : Fin 16, kernel99_1Expr 4 9 k = kernel99_1_r4_9 k := by decide +kernel +noncomputable def kernel99_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel99_1_r4_10_eq : ∀ k : Fin 16, kernel99_1Expr 4 10 k = kernel99_1_r4_10 k := by decide +kernel +noncomputable def kernel99_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel99_1_r4_11_eq : ∀ k : Fin 16, kernel99_1Expr 4 11 k = kernel99_1_r4_11 k := by decide +kernel +noncomputable def kernel99_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel99_1_r4_12_eq : ∀ k : Fin 16, kernel99_1Expr 4 12 k = kernel99_1_r4_12 k := by decide +kernel +noncomputable def kernel99_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel99_1_r4_13_eq : ∀ k : Fin 16, kernel99_1Expr 4 13 k = kernel99_1_r4_13 k := by decide +kernel +noncomputable def kernel99_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel99_1_r4_14_eq : ∀ k : Fin 16, kernel99_1Expr 4 14 k = kernel99_1_r4_14 k := by decide +kernel +noncomputable def kernel99_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel99_1_r4_15_eq : ∀ k : Fin 16, kernel99_1Expr 4 15 k = kernel99_1_r4_15 k := by decide +kernel +noncomputable def kernel99_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel99_1_r4_0,kernel99_1_r4_1,kernel99_1_r4_2,kernel99_1_r4_3,kernel99_1_r4_4,kernel99_1_r4_5,kernel99_1_r4_6,kernel99_1_r4_7,kernel99_1_r4_8,kernel99_1_r4_9,kernel99_1_r4_10,kernel99_1_r4_11,kernel99_1_r4_12,kernel99_1_r4_13,kernel99_1_r4_14,kernel99_1_r4_15] +lemma kernel99_1_r4_eq (i k : Fin 16) : kernel99_1Expr 4 i k = kernel99_1_r4 i k := by + fin_cases i + · exact kernel99_1_r4_0_eq k + · exact kernel99_1_r4_1_eq k + · exact kernel99_1_r4_2_eq k + · exact kernel99_1_r4_3_eq k + · exact kernel99_1_r4_4_eq k + · exact kernel99_1_r4_5_eq k + · exact kernel99_1_r4_6_eq k + · exact kernel99_1_r4_7_eq k + · exact kernel99_1_r4_8_eq k + · exact kernel99_1_r4_9_eq k + · exact kernel99_1_r4_10_eq k + · exact kernel99_1_r4_11_eq k + · exact kernel99_1_r4_12_eq k + · exact kernel99_1_r4_13_eq k + · exact kernel99_1_r4_14_eq k + · exact kernel99_1_r4_15_eq k +noncomputable def kernel99_1_r5_0 : Fin 16 → CBox := ![⟨⟨31961591963532651455106,31961608868483770702964⟩,⟨7050549903283139731956,7050566808234258979628⟩⟩,⟨⟨31886254420446525267233,31886271292715113255055⟩,⟨6924960035199868653027,6924976907468456640658⟩⟩,⟨⟨31735055062716951930927,31735071869774781611422⟩,⟨6675684679433287696788,6675701486491117377090⟩⟩,⟨⟨31506984548730405847287,31507001258414899643406⟩,⟨6306511312167408781325,6306528021851902577241⟩⟩,⟨⟨31200625517721147849301,31200642098413486896340⟩,⟨5823067513129529977613,5823084093821869024441⟩⟩,⟨⟨30814264812039837599924,30814281232839422886651⟩,⟨5232755471296704944160,5232771892096290230666⟩⟩,⟨⟨30346036920676618445666,30346053151567416102977⟩,⟨4544662923730921044328,4544679154621718701403⟩⟩,⟨⟨29794093504404830830649,29794109516416773908056⟩,⟨3769449336598724571424,3769465348610667648580⟩⟩,⟨⟨29156792787217084483836,29156808552573215078273⟩,⟨2919206191228123993489,2919221956584254587661⟩⟩,⟨⟨28432901670161133645639,28432917162422513433126⟩,⟨2007290496938748917411,2007305989200128704615⟩⟩,⟨⟨27621802677409853095667,27621817871602520603017⟩,⟨1048131129383643729901,1048146323576311236953⟩⟩,⟨⟨26723697315477189008071,26723712189486528564871⟩,⟨57008286740843498780,57023160750183055261⟩⟩,⟨⟨25739797154992994405874,25739811687147740876486⟩,⟨(-950192744015461625414),(-950178211860715155132)⟩⟩,⟨⟨24672493944422553356700,24672508114819290904135⟩,⟨(-1957251260646705849359),(-1957237090249968302263)⟩⟩,⟨⟨23525500398327378423386,23525514188875546769347⟩,⟨(-2947900802535248267750),(-2947887011987079922142)⟩⟩,⟨⟨22303953943107658482435,22303967337621725127388⟩,⟨(-3906134082024314792734),(-3906120687510248148136)⟩⟩] +lemma kernel99_1_r5_0_eq : ∀ k : Fin 16, kernel99_1Expr 5 0 k = kernel99_1_r5_0 k := by decide +kernel +noncomputable def kernel99_1_r5_1 : Fin 16 → CBox := ![⟨⟨21014476693017750419841,21014489677217090791472⟩,⟨(-4816517216517039401334),(-4816504232317699030064)⟩⟩,⟨⟨19665186243683103249181,19665198805277171747215⟩,⟨(-5664506105834201272071),(-5664493544240132774399)⟩⟩,⟨⟨18265653492795267867051,18265665621429908228653⟩,⟨(-6436756775786371262246),(-6436744647151730901003)⟩⟩,⟨⟨16826805586132993490941,16826817273461829334763⟩,⟨(-7121420726634535552951),(-7121409039305699709481)⟩⟩,⟨⟨15360774185592099750496,15360785425176120789048⟩,⟨(-7708415857898464890149),(-7708404618314443851925)⟩⟩,⟨⟨13880691487532773164012,13880702274916148497596⟩,⟨(-8189663455912439528513),(-8189652668529064195214)⟩⟩,⟨⟨12400438696829375003617,12400449029372698469683⟩,⟨(-8559282074463928631501),(-8559271741920605165674)⟩⟩,⟨⟨10934353879658359120718,10934363756648903580647⟩,⟨(-8813729943528279986699),(-8813720066537735526967)⟩⟩,⟨⟨9496908170344833583510,9496917592747069780311⟩,⟨(-8951888807689503471848),(-8951879385287267275202)⟩⟩,⟨⟨8102361079195496559903,8102370049709936320477⟩,⟨(-8975083806165544553499),(-8975074835651104793038)⟩⟩,⟨⟨6764407037583246475132,6764415560416002321468⟩,⟨(-8887036105201281141399),(-8887027582368525295142)⟩⟩,⟨⟨5495826223883395969248,5495834304828639265757⟩,⟨(-8693747408019877295557),(-8693739327074633999092)⟩⟩,⟨⟨4308153068101845832902,4308160714247432035658⟩,⟨(-8403318089539488402378),(-8403310443393902199639)⟩⟩,⟨⟨3211375577874349594285,3211382797952850116521⟩,⟨(-8025703414292912959392),(-8025696194214412437150)⟩⟩,⟨⟨2213677749470721460957,2213684553561499963530⟩,⟨(-7572414952187761869970),(-7572408148096983367362)⟩⟩,⟨⟨1321235830416522397051,1321242229189601914683⟩,⟨(-7056176770724326440372),(-7056170371951246922690)⟩⟩] +lemma kernel99_1_r5_1_eq : ∀ k : Fin 16, kernel99_1Expr 5 1 k = kernel99_1_r5_1 k := by decide +kernel +noncomputable def kernel99_1_r5_2 : Fin 16 → CBox := ![⟨⟨538077140444802406928,538083145386418244083⟩,⟨(-6490548105674302952547),(-6490542100732687115332)⟩⟩,⟨⟨(-133992381164659261946),(-133986757584860964279)⟩,⟨(-5889525864374481377479),(-5889520240794683079739)⟩⟩,⟨⟨(-695388639777940160595),(-695383384511141888029)⟩,⟨(-5267141391642747022340),(-5267136136375948749694)⟩⟩,⟨⟨(-1148677724864301766249),(-1148672824146610454202)⟩,⟨(-4637066342492101336144),(-4637061441774410024017)⟩⟩,⟨⟨(-1498435170618439981755),(-1498430610310749774776)⟩,⟨(-4012242211728741039228),(-4012237651421050832169)⟩⟩,⟨⟨(-1751042257318049818588),(-1751038022552227955180)⟩,⟨(-3404547070188677694843),(-3404542835422855831363)⟩⟩,⟨⟨(-1914428259459400875354),(-1914424335520597833931)⟩,⟨(-2824511380240664640588),(-2824507456301861599107)⟩⟩,⟨⟨(-1997769899959397522930),(-1997766271831141458015)⟩,⟨(-2281092500607186292582),(-2281088872478930227625)⟩⟩,⟨⟨(-2011161040938253025650),(-2011157693689348684744)⟩,⟨(-1781514745656059128000),(-1781511398407154787070)⟩⟩,⟨⟨(-1965266747021816903617),(-1965263665480195687438)⟩,⟨(-1331178803478180679826),(-1331175721936559463634)⟩⟩,⟨⟨(-1870976219349229741755),(-1870973388702201006333)⟩,⟨(-933641094609030051888),(-933638263962001316458)⟩⟩,⟨⟨(-1739068716257326619823),(-1739066121746869998165)⟩,⟨(-590660465265584100295),(-590657870755127478641)⟩⟩,⟨⟨(-1579905467187877650047),(-1579903094424667984480)⟩,⟨(-302306622056690028663),(-302304249293480363109)⟩⟩,⟨⟨(-1403158838436686014977),(-1403156673230079186819)⟩,⟨(-67122108890321794087),(-67119943683714965947)⟩⟩,⟨⟨(-1217587726410154292038),(-1217585755069226428659)⟩,⟨117672469089709982923,117674440430637846289⟩⟩,⟨⟨(-1030865492529087937054),(-1030863701675200934055)⟩,⟨255941738833768073270,255943529687655076245⟩⟩] +lemma kernel99_1_r5_2_eq : ∀ k : Fin 16, kernel99_1Expr 5 2 k = kernel99_1_r5_2 k := by decide +kernel +noncomputable def kernel99_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-849463873546998061476),(-849462250396873610070)⟩,⟨352379919786701397603,352381542936825848994⟩⟩,⟨⟨(-678593386766142659665),(-678591918890838974234)⟩,⟨412248875749928240856,412250343625231926272⟩⟩,⟨⟨(-522197967538478565768),(-522196643161002512893)⟩,⟨441121880492514254388,441123204869990307254⟩⟩,⟨⟨(-382999093103018326012),(-382997900888795849350)⟩,⟨444643901941691932563,444645094155914409222⟩⟩,⟨⟨(-262582586556298598678),(-262581515842927422603)⟩,⟨428317491277538869236,428318561990910045308⟩⟩,⟨⟨(-161519763825512940562),(-161518804405446719165)⟩,⟨397321269550826192629,397322228970892414031⟩⟩,⟨⟨(-79513635497776926427),(-79512777840685919614)⟩,⟨356365694329640416852,356366551986731423666⟩⟩,⟨⟨(-15560527667503145966),(-15559762733436862611)⟩,⟨309588411758119438612,309589176692185721972⟩⟩,⟨⟨31882290259979998553,31882970850917786558⟩,⟨260489212953962087989,260489893544899876001⟩⟩,⟨⟨64731642621169129927,64732246783277745143⟩,⟨211902545410095940318,211903149572204555541⟩⟩,⟨⟨85123662220100545737,85124197395623200599⟩,⟨166003795177289243712,166004330352811898578⟩⟩,⟨⟨95275224693031711717,95275698733932762934⟩,⟨124344225959154225419,124344700000055276636⟩⟩,⟨⟨97365993429399311598,97366412297279261571⟩,⟨87908587576429729499,87909006444309679472⟩⟩,⟨⟨93443743422889601235,93444112692220806704⟩,⟨57188980146241038011,57189349415572243477⟩⟩,⟨⟨85353986608550232138,85354311356558430144⟩,⟨32268588557793021948,32268913305801219950⟩⟩,⟨⟨74693411430592852650,74693696363464972548⟩,⟨12909290752084078432,12909575684956198329⟩⟩] +lemma kernel99_1_r5_3_eq : ∀ k : Fin 16, kernel99_1Expr 5 3 k = kernel99_1_r5_3 k := by decide +kernel +noncomputable def kernel99_1_r5_4 : Fin 16 → CBox := ![⟨⟨62785390272464242391,62785639648766792779⟩,⟨(-1362144191939840524),(-1361894815637290139)⟩⟩,⟨⟨50674831738235567362,50675049491869034051⟩,⟨(-11173623656432270860),(-11173405902798804175)⟩⟩,⟨⟨39138995086950393652,39139184753972319710⟩,⟨(-17236358879838500715),(-17236169212816574656)⟩⟩,⟨⟨28710537333483878417,28710702150521996637⟩,⟨(-20284745477502149464),(-20284580660464031240)⟩⟩,⟨⟨19709009979489339706,19709152839355153915⟩,⟨(-21028627641553055907),(-21028484781687241698)⟩⟩,⟨⟨12277218345249367605,12277341885853267066⟩,⟨(-20118121101254076166),(-20117997560650176705)⟩⟩,⟨⟨6419251300775021675,6419357864505222476⟩,⟨(-18120368236124961087),(-18120261672394760289)⟩⟩,⟨⟨2037520687551582200,2037612391843214559⟩,⟨(-15506983318342120858),(-15506891614050488503)⟩⟩,⟨⟨(-1033240799763281651),(-1033162085116607467)⟩,⟨(-12650526323656616878),(-12650447609009942694)⟩⟩,⟨⟨(-2996445611429626748),(-2996378203236935151)⟩,⟨(-9828116986199921378),(-9828049578007229777)⟩⟩,⟨⟨(-4069402299977652241),(-4069344720213189798)⟩,⟨(-7230246445050726473),(-7230188865286264031)⟩⟩,⟨⟨(-4464638423178640667),(-4464589353647235654)⟩,⟨(-4972934745934709998),(-4972885676403304981)⟩⟩,⟨⟨(-4376640286969522952),(-4376598579546312731)⟩,⟨(-3111582689215130374),(-3111540981791920156)⟩⟩,⟨⟨(-3973519569803675126),(-3973484198833844528)⟩,⟨(-1655140440080190238),(-1655105069110359644)⟩⟩,⟨⟨(-3392891286700287298),(-3392861366178202762)⟩,⟨(-579526456251080425),(-579496535728995889)⟩⟩,⟨⟨(-2741125963438964776),(-2741100713092459389)⟩,⟨160451870760043209,160477121106548592⟩⟩] +lemma kernel99_1_r5_4_eq : ∀ k : Fin 16, kernel99_1Expr 5 4 k = kernel99_1_r5_4 k := by decide +kernel +noncomputable def kernel99_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-2095107144172499307),(-2095085891846556463)⟩,⟨621126443311884766,621147695637827610⟩⟩,⟨⟨(-1505666566486823389),(-1505648719225232575)⟩,⟨862135776807384798,862153624068975608⟩⟩,⟨⟨(-1001962942568298107),(-1001947990178918649)⟩,⟨940711259847047704,940726212236427159⟩⟩,⟨⟨(-596197063242017288),(-596184565617083031)⟩,⟨907906205770880470,907918703395814729⟩⟩,⟨⟨(-288197344612955778),(-288186926782000301)⟩,⟨806489722452423733,806500140283379209⟩⟩,⟨⟨(-69551196803576663),(-69542532301739150)⟩,⟨670174371992795304,670183036494632816⟩⟩,⟨⟨72913066982701052,72920254124251125⟩,⟨523834572072317634,523841759213867708⟩⟩,⟨⟨154379153602247823,154385101391162388⟩,⟨384391946445871183,384397894234785747⟩⟩,⟨⟨190029771331058870,190034680106191568⟩,⟨262084690372570203,262089599147702901⟩⟩,⟨⟨193705277454573815,193709322075503596⟩,⟨161890980739171993,161895025360101772⟩⟩,⟨⟨177133298476255142,177136622678369866⟩,⟨84933814948662554,84937139150777279⟩⟩,⟨⟨149610294586335030,149613020404887611⟩,⟨29749968463339546,29752694281892127⟩⟩,⟨⟨118013800435372121,118016029520681199⟩,⟨(-6645117759221502),(-6642888673912424)⟩⟩,⟨⟨87033276317680891,87035095165141398⟩,⟨(-27924579604293583),(-27922760756833076)⟩⟩,⟨⟨59524072272153410,59525552425131462⟩,⟨(-37847283011647728),(-37845802858669676)⟩⟩,⟨⟨36909102305561031,36910304335407360⟩,⟨(-39862174078939567),(-39860972049093234)⟩⟩] +lemma kernel99_1_r5_5_eq : ∀ k : Fin 16, kernel99_1Expr 5 5 k = kernel99_1_r5_5 k := by decide +kernel +noncomputable def kernel99_1_r5_6 : Fin 16 → CBox := ![⟨⟨19573557331927451,19574530860102403⟩,⟨(-36885261804403849),(-36884288276228893)⟩⟩,⟨⟨7217134817958482,7217921591005893⟩,⟨(-31209959947828988),(-31209173174781573)⟩⟩,⟨⟨(-855458512274857),(-854824331730054)⟩,⟨(-24512096899618484),(-24511462719073681)⟩⟩,⟨⟨(-5512274972258232),(-5511764910735178)⟩,⟨(-17915070746421236),(-17914560684898182)⟩⟩,⟨⟨(-7637640270777077),(-7637231145879916)⟩,⟨(-12086770108249935),(-12086360983352777)⟩⟩,⟨⟨(-8033187192189114),(-8032859721634635)⟩,⟨(-7346765493999386),(-7346438023444904)⟩⟩,⟨⟨(-7365277332491871),(-7365015910050445)⟩,⟨(-3768937931214600),(-3768676508773173)⟩⟩,⟨⟨(-6146939546778117),(-6146731297091246)⟩,⟨(-1270563101199913),(-1270354851513042)⟩⟩,⟨⟨(-4743199447057832),(-4743033780168523)⟩,⟨316430432885206,316596099774515⟩⟩,⟨⟨(-3390323148716827),(-3390191561401914)⟩,⟨1192842463213942,1192974050528859⟩⟩,⟨⟨(-2221552577511605),(-2221448330791657)⟩,⟨1556740587943022,1556844834662969⟩⟩,⟨⟨(-1294007760782757),(-1293925343552098)⟩,⟨1582381298354906,1582463715585564⟩⟩,⟨⟨(-613330633028148),(-613265646819595)⟩,⟨1410221661644664,1410286647853213⟩⟩,⟨⟨(-154210886791149),(-154159743321591)⟩,⟨1144768395343262,1144819538812817⟩⟩,⟨⟨123886200222678,123926347395866⟩,⟨857397125657871,857437272831063⟩⟩,⟨⟨265662242718857,265693698388885⟩,⟨591833306283407,591864761953438⟩⟩] +lemma kernel99_1_r5_6_eq : ∀ k : Fin 16, kernel99_1Expr 5 6 k = kernel99_1_r5_6 k := by decide +kernel +noncomputable def kernel99_1_r5_7 : Fin 16 → CBox := ![⟨⟨312989308537413,313013889528676⟩,⟨370592747063898,370617328055161⟩⟩,⟨⟨301139306789426,301158482780542⟩,⟨201244583354123,201263759345240⟩⟩,⟨⟨257363594623955,257378519816805⟩,⟨81835502484397,81850427677244⟩⟩,⟨⟨201024184069522,201035779298174⟩,⟨5178673390879,5190268619532⟩⟩,⟨⟨144618788200172,144627773802332⟩,⟨(-38034147119467),(-38025161517307)⟩⟩,⟨⟨95204045743606,95210997309448⟩,⟨(-57181511323165),(-57174559757324)⟩⟩,⟨⟨55877519920210,55882884915250⟩,⟨(-60526167006632),(-60520802011592)⟩⟩,⟨⟨27112523737363,27116657141742⟩,⟨(-54674240901255),(-54670107496877)⟩⟩,⟨⟨7843839485876,7847018597245⟩,⟨(-44472627805649),(-44469448694280)⟩⟩,⟨⟨(-3724139993263),(-3721697915084)⟩,⟨(-33170452377843),(-33168010299664)⟩⟩,⟨⟨(-9568770301681),(-9566898743702)⟩,⟨(-22711180506373),(-22709308948393)⟩⟩,⟨⟨(-11517165818988),(-11515733753911)⟩,⟨(-14062323227139),(-14060891162062)⟩⟩,⟨⟨(-11079002791416),(-11077909614784)⟩,⟨(-7524687023119),(-7523593846490)⟩⟩,⟨⟨(-9393661978325),(-9392828588306)⟩,⟨(-2990687458587),(-2989854068568)⟩⟩,⟨⟨(-7248441213204),(-7247807272693)⟩,⟨(-140897497049),(-140263556538)⟩⟩,⟨⟨(-5134249693569),(-5133768153846)⟩,⟨1419345267352,1419826807075⟩⟩] +lemma kernel99_1_r5_7_eq : ∀ k : Fin 16, kernel99_1Expr 5 7 k = kernel99_1_r5_7 k := by decide +kernel +noncomputable def kernel99_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-3315004415476),(-3314639454829)⟩,⟨2074512183836,2074877144479⟩⟩,⟨⟨(-1895610950233),(-1895334521480)⟩,⟨2153061549304,2153337978057⟩⟩,⟨⟨(-880252901166),(-880043967063)⟩,⟨1909581332652,1909790266751⟩⟩,⟨⟨(-217658321006),(-217500597973)⟩,⟨1524733524900,1524891247929⟩⟩,⟨⟨166793708917,166912519312⟩,⟨1115014854628,1115133665023⟩⟩,⟨⟨350453310689,350542716765⟩,⟨746610829042,746700235121⟩⟩,⟨⟨401817831995,401884996471⟩,⟨449645534002,449712698481⟩⟩,⟨⟨375431723177,375482131201⟩,⟨230740540485,230790948513⟩⟩,⟨⟨310999578070,311037332513⟩,⟨82968182647,83005937090⟩⟩,⟨⟨234905036914,234933291988⟩,⟨(-6950240006),(-6921984932)⟩⟩,⟨⟨162827202107,162848313967⟩,⟨(-53909578953),(-53888467097)⟩⟩,⟨⟨102594957664,102610718918⟩,⟨(-71657521698),(-71641760444)⟩⟩,⟨⟨56782045175,56793790174⟩,⟨(-71468096820),(-71456351818)⟩⟩,⟨⟨24809564746,24818312513⟩,⟨(-61767779302),(-61759031531)⟩⟩,⟨⟨4497853984,4504358773⟩,⟨(-48323080497),(-48316575709)⟩⟩,⟨⟨(-6888198145),(-6883363988)⟩,⟨(-34702896496),(-34698062338)⟩⟩] +lemma kernel99_1_r5_8_eq : ∀ k : Fin 16, kernel99_1Expr 5 8 k = kernel99_1_r5_8 k := by decide +kernel +noncomputable def kernel99_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-12007116705),(-12003530349)⟩,⟨(-22824162563),(-22820576207)⟩⟩,⟨⟨(-13115544201),(-13112884335)⟩,⟨(-13467181153),(-13464521287)⟩⟩,⟨⟨(-11950557027),(-11948587114)⟩,⟨(-6704125791),(-6702155878)⟩⟩,⟨⟨(-9738315217),(-9736856850)⟩,⟨(-2222705558),(-2221247191)⟩⟩,⟨⟨(-7268411758),(-7267333735)⟩,⟨450160856,451238882⟩⟩,⟨⟨(-4992764774),(-4991967981)⟩,⟨1808246155,1809042948⟩⟩,⟨⟨(-3123871614),(-3123283416)⟩,⟨2289291376,2289879574⟩⟩,⟨⟨(-1719242841),(-1718808698)⟩,⟨2242218060,2242652206⟩⟩,⟨⟨(-746964546),(-746644537)⟩,⟨1921976226,1922296235⟩⟩,⟨⟨(-132350421),(-132114485)⟩,⟨1499623653,1499859589⟩⟩,⟨⟨211733178,211906954⟩,⟨1079025923,1079199699⟩⟩,⟨⟨367254626,367382619⟩,⟨714740557,714868550⟩⟩,⟨⟨402475562,402569746⟩,⟨428079347,428173528⟩⟩,⟨⟨369322989,369392328⟩,⟨220023662,220093004⟩⟩,⟨⟨304213796,304264805⟩,⟨80735414,80786427⟩⟩,⟨⟨230571308,230609040⟩,⟨(-4005024),(-3967295)⟩⟩] +lemma kernel99_1_r5_9_eq : ∀ k : Fin 16, kernel99_1Expr 5 9 k = kernel99_1_r5_9 k := by decide +kernel +noncomputable def kernel99_1_r5_10 : Fin 16 → CBox := ![⟨⟨161885704,161913597⟩,⟨(-48838283),(-48810389)⟩⟩,⟨⟨104643346,104663997⟩,⟨(-66695812),(-66675164)⟩⟩,⟨⟨60794010,60809285⟩,⟨(-67911200),(-67895921)⟩⟩,⟨⟨29644617,29655936⟩,⟨(-60099419),(-60088099)⟩⟩,⟨⟨9200638,9209013⟩,⟨(-48452548),(-48444173)⟩⟩,⟨⟨(-2960011),(-2953805)⟩,⟨(-36213515),(-36207309)⟩⟩,⟨⟨(-9172746),(-9168139)⟩,⟨(-25179531),(-25174924)⟩⟩,⟨⟨(-11428019),(-11424597)⟩,⟨(-16154554),(-16151132)⟩⟩,⟨⟨(-11280456),(-11277913)⟩,⟨(-9315404),(-9312864)⟩⟩,⟨⟨(-9857413),(-9855523)⟩,⟨(-4484918),(-4483028)⟩⟩,⟨⟨(-7918174),(-7916764)⟩,⟨(-1320798),(-1319385)⟩⟩,⟨⟨(-5932048),(-5930981)⟩,⟨563986,565054⟩⟩,⟨⟨(-4156185),(-4155383)⟩,⟨1532185,1532987⟩⟩,⟨⟨(-2703300),(-2702693)⟩,⟨1888918,1889522⟩⟩,⟨⟨(-1595439),(-1594980)⟩,⟨1871342,1871801⟩⟩,⟨⟨(-803616),(-803257)⟩,⟨1651586,1651941⟩⟩] +lemma kernel99_1_r5_10_eq : ∀ k : Fin 16, kernel99_1Expr 5 10 k = kernel99_1_r5_10 k := by decide +kernel +noncomputable def kernel99_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-275098),(-274829)⟩,⟨1346356,1346621⟩⟩,⟨⟨49261,49476⟩,⟨1028730,1028949⟩⟩,⟨⟨225074,225239⟩,⟨739822,739987⟩⟩,⟨⟨299493,299631⟩,⟨498689,498826⟩⟩,⟨⟨309689,309800⟩,⟨310352,310467⟩⟩,⟨⟨283139,283227⟩,⟨171663,171755⟩⟩,⟨⟨238949,239031⟩,⟨75406,75485⟩⟩,⟨⟨189571,189641⟩,⟨13002,13068⟩⟩,⟨⟨142409,142475⟩,⟨(-23948),(-23883)⟩⟩,⟨⟨101340,101397⟩,⟨(-42774),(-42718)⟩⟩,⟨⟨67863,67910⟩,⟨(-49473),(-49422)⟩⟩,⟨⟨42014,42065⟩,⟨(-48629),(-48577)⟩⟩,⟨⟨23052,23103⟩,⟨(-43581),(-43529)⟩⟩,⟨⟨9861,9904⟩,⟨(-36607),(-36564)⟩⟩,⟨⟨1235,1268⟩,⟨(-29202),(-29168)⟩⟩,⟨⟨(-3969),(-3922)⟩,⟨(-22250),(-22202)⟩⟩] +lemma kernel99_1_r5_11_eq : ∀ k : Fin 16, kernel99_1Expr 5 11 k = kernel99_1_r5_11 k := by decide +kernel +noncomputable def kernel99_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-6696),(-6657)⟩,⟨(-16190),(-16148)⟩⟩,⟨⟨(-7751),(-7713)⟩,⟨(-11195),(-11157)⟩⟩,⟨⟨(-7731),(-7693)⟩,⟨(-7271),(-7233)⟩⟩,⟨⟨(-7088),(-7046)⟩,⟨(-4315),(-4276)⟩⟩,⟨⟨(-6125),(-6087)⟩,⟨(-2183),(-2144)⟩⟩,⟨⟨(-5056),(-5023)⟩,⟨(-716),(-682)⟩⟩,⟨⟨(-4021),(-3987)⟩,⟨233,270⟩⟩,⟨⟨(-3081),(-3042)⟩,⟨796,834⟩⟩,⟨⟨(-2272),(-2239)⟩,⟨1088,1122⟩⟩,⟨⟨(-1613),(-1580)⟩,⟨1188,1222⟩⟩,⟨⟨(-1088),(-1054)⟩,⟨1164,1202⟩⟩,⟨⟨(-681),(-648)⟩,⟨1071,1101⟩⟩,⟨⟨(-384),(-355)⟩,⟨938,968⟩⟩,⟨⟨(-171),(-137)⟩,⟨793,830⟩⟩,⟨⟨(-29),10⟩,⟨645,684⟩⟩,⟨⟨71,109⟩,⟨514,552⟩⟩] +lemma kernel99_1_r5_12_eq : ∀ k : Fin 16, kernel99_1Expr 5 12 k = kernel99_1_r5_12 k := by decide +kernel +noncomputable def kernel99_1_r5_13 : Fin 16 → CBox := ![⟨⟨127,161⟩,⟨398,435⟩⟩,⟨⟨156,191⟩,⟨297,335⟩⟩,⟨⟨164,202⟩,⟨213,247⟩⟩,⟨⟨161,199⟩,⟨147,181⟩⟩,⟨⟨153,186⟩,⟨95,124⟩⟩,⟨⟨133,172⟩,⟨47,86⟩⟩,⟨⟨116,146⟩,⟨22,51⟩⟩,⟨⟨95,134⟩,⟨(-5),34⟩⟩,⟨⟨76,114⟩,⟨(-23),12⟩⟩,⟨⟨66,96⟩,⟨(-28),1⟩⟩,⟨⟨48,78⟩,⟨(-38),(-8)⟩⟩,⟨⟨39,69⟩,⟨(-40),(-11)⟩⟩,⟨⟨27,56⟩,⟨(-38),(-13)⟩⟩,⟨⟨14,48⟩,⟨(-45),(-11)⟩⟩,⟨⟨10,44⟩,⟨(-45),(-10)⟩⟩,⟨⟨2,32⟩,⟨(-43),(-9)⟩⟩] +lemma kernel99_1_r5_13_eq : ∀ k : Fin 16, kernel99_1Expr 5 13 k = kernel99_1_r5_13 k := by decide +kernel +noncomputable def kernel99_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-2),28⟩,⟨(-38),(-8)⟩⟩,⟨⟨(-6),28⟩,⟨(-38),(-4)⟩⟩,⟨⟨(-15),24⟩,⟨(-41),(-2)⟩⟩,⟨⟨(-13),16⟩,⟨(-32),(-2)⟩⟩,⟨⟨(-18),16⟩,⟨(-32),(-2)⟩⟩,⟨⟨(-18),17⟩,⟨(-32),3⟩⟩,⟨⟨(-18),17⟩,⟨(-32),3⟩⟩,⟨⟨(-22),17⟩,⟨(-32),7⟩⟩,⟨⟨(-16),13⟩,⟨(-23),7⟩⟩,⟨⟨(-16),13⟩,⟨(-23),7⟩⟩,⟨⟨(-16),13⟩,⟨(-23),7⟩⟩,⟨⟨(-16),13⟩,⟨(-23),7⟩⟩,⟨⟨(-20),10⟩,⟨(-18),11⟩⟩,⟨⟨(-20),14⟩,⟨(-23),11⟩⟩,⟨⟨(-20),10⟩,⟨(-18),11⟩⟩,⟨⟨(-20),10⟩,⟨(-18),11⟩⟩] +lemma kernel99_1_r5_14_eq : ∀ k : Fin 16, kernel99_1Expr 5 14 k = kernel99_1_r5_14 k := by decide +kernel +noncomputable def kernel99_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-20),10⟩,⟨(-18),11⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-20),15⟩,⟨(-23),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩] +lemma kernel99_1_r5_15_eq : ∀ k : Fin 16, kernel99_1Expr 5 15 k = kernel99_1_r5_15 k := by decide +kernel +noncomputable def kernel99_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel99_1_r5_0,kernel99_1_r5_1,kernel99_1_r5_2,kernel99_1_r5_3,kernel99_1_r5_4,kernel99_1_r5_5,kernel99_1_r5_6,kernel99_1_r5_7,kernel99_1_r5_8,kernel99_1_r5_9,kernel99_1_r5_10,kernel99_1_r5_11,kernel99_1_r5_12,kernel99_1_r5_13,kernel99_1_r5_14,kernel99_1_r5_15] +lemma kernel99_1_r5_eq (i k : Fin 16) : kernel99_1Expr 5 i k = kernel99_1_r5 i k := by + fin_cases i + · exact kernel99_1_r5_0_eq k + · exact kernel99_1_r5_1_eq k + · exact kernel99_1_r5_2_eq k + · exact kernel99_1_r5_3_eq k + · exact kernel99_1_r5_4_eq k + · exact kernel99_1_r5_5_eq k + · exact kernel99_1_r5_6_eq k + · exact kernel99_1_r5_7_eq k + · exact kernel99_1_r5_8_eq k + · exact kernel99_1_r5_9_eq k + · exact kernel99_1_r5_10_eq k + · exact kernel99_1_r5_11_eq k + · exact kernel99_1_r5_12_eq k + · exact kernel99_1_r5_13_eq k + · exact kernel99_1_r5_14_eq k + · exact kernel99_1_r5_15_eq k +noncomputable def kernel99_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel99_1_r0,kernel99_1_r1,kernel99_1_r2,kernel99_1_r3,kernel99_1_r4,kernel99_1_r5] +lemma kernel99_1_eq (j : Fin 6) (i k : Fin 16) : kernel99_1Expr j i k = kernel99_1 j i k := by + fin_cases j + · exact kernel99_1_r0_eq i k + · exact kernel99_1_r1_eq i k + · exact kernel99_1_r2_eq i k + · exact kernel99_1_r3_eq i k + · exact kernel99_1_r4_eq i k + · exact kernel99_1_r5_eq i k +lemma kernel99_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel99_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(99:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel99_1_eq] + unfold kernel99_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans99_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel100_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans100 j i k) +noncomputable def kernel100_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_0_eq : ∀ k : Fin 16, kernel100_0Expr 0 0 k = kernel100_0_r0_0 k := by decide +kernel +noncomputable def kernel100_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_1_eq : ∀ k : Fin 16, kernel100_0Expr 0 1 k = kernel100_0_r0_1 k := by decide +kernel +noncomputable def kernel100_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_2_eq : ∀ k : Fin 16, kernel100_0Expr 0 2 k = kernel100_0_r0_2 k := by decide +kernel +noncomputable def kernel100_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_3_eq : ∀ k : Fin 16, kernel100_0Expr 0 3 k = kernel100_0_r0_3 k := by decide +kernel +noncomputable def kernel100_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_4_eq : ∀ k : Fin 16, kernel100_0Expr 0 4 k = kernel100_0_r0_4 k := by decide +kernel +noncomputable def kernel100_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_5_eq : ∀ k : Fin 16, kernel100_0Expr 0 5 k = kernel100_0_r0_5 k := by decide +kernel +noncomputable def kernel100_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_6_eq : ∀ k : Fin 16, kernel100_0Expr 0 6 k = kernel100_0_r0_6 k := by decide +kernel +noncomputable def kernel100_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_7_eq : ∀ k : Fin 16, kernel100_0Expr 0 7 k = kernel100_0_r0_7 k := by decide +kernel +noncomputable def kernel100_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_8_eq : ∀ k : Fin 16, kernel100_0Expr 0 8 k = kernel100_0_r0_8 k := by decide +kernel +noncomputable def kernel100_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_9_eq : ∀ k : Fin 16, kernel100_0Expr 0 9 k = kernel100_0_r0_9 k := by decide +kernel +noncomputable def kernel100_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_10_eq : ∀ k : Fin 16, kernel100_0Expr 0 10 k = kernel100_0_r0_10 k := by decide +kernel +noncomputable def kernel100_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r0_11_eq : ∀ k : Fin 16, kernel100_0Expr 0 11 k = kernel100_0_r0_11 k := by decide +kernel +noncomputable def kernel100_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r0_12_eq : ∀ k : Fin 16, kernel100_0Expr 0 12 k = kernel100_0_r0_12 k := by decide +kernel +noncomputable def kernel100_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r0_13_eq : ∀ k : Fin 16, kernel100_0Expr 0 13 k = kernel100_0_r0_13 k := by decide +kernel +noncomputable def kernel100_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r0_14_eq : ∀ k : Fin 16, kernel100_0Expr 0 14 k = kernel100_0_r0_14 k := by decide +kernel +noncomputable def kernel100_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r0_15_eq : ∀ k : Fin 16, kernel100_0Expr 0 15 k = kernel100_0_r0_15 k := by decide +kernel +noncomputable def kernel100_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel100_0_r0_0,kernel100_0_r0_1,kernel100_0_r0_2,kernel100_0_r0_3,kernel100_0_r0_4,kernel100_0_r0_5,kernel100_0_r0_6,kernel100_0_r0_7,kernel100_0_r0_8,kernel100_0_r0_9,kernel100_0_r0_10,kernel100_0_r0_11,kernel100_0_r0_12,kernel100_0_r0_13,kernel100_0_r0_14,kernel100_0_r0_15] +lemma kernel100_0_r0_eq (i k : Fin 16) : kernel100_0Expr 0 i k = kernel100_0_r0 i k := by + fin_cases i + · exact kernel100_0_r0_0_eq k + · exact kernel100_0_r0_1_eq k + · exact kernel100_0_r0_2_eq k + · exact kernel100_0_r0_3_eq k + · exact kernel100_0_r0_4_eq k + · exact kernel100_0_r0_5_eq k + · exact kernel100_0_r0_6_eq k + · exact kernel100_0_r0_7_eq k + · exact kernel100_0_r0_8_eq k + · exact kernel100_0_r0_9_eq k + · exact kernel100_0_r0_10_eq k + · exact kernel100_0_r0_11_eq k + · exact kernel100_0_r0_12_eq k + · exact kernel100_0_r0_13_eq k + · exact kernel100_0_r0_14_eq k + · exact kernel100_0_r0_15_eq k +noncomputable def kernel100_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_0_eq : ∀ k : Fin 16, kernel100_0Expr 1 0 k = kernel100_0_r1_0 k := by decide +kernel +noncomputable def kernel100_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_1_eq : ∀ k : Fin 16, kernel100_0Expr 1 1 k = kernel100_0_r1_1 k := by decide +kernel +noncomputable def kernel100_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_2_eq : ∀ k : Fin 16, kernel100_0Expr 1 2 k = kernel100_0_r1_2 k := by decide +kernel +noncomputable def kernel100_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_3_eq : ∀ k : Fin 16, kernel100_0Expr 1 3 k = kernel100_0_r1_3 k := by decide +kernel +noncomputable def kernel100_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_4_eq : ∀ k : Fin 16, kernel100_0Expr 1 4 k = kernel100_0_r1_4 k := by decide +kernel +noncomputable def kernel100_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_5_eq : ∀ k : Fin 16, kernel100_0Expr 1 5 k = kernel100_0_r1_5 k := by decide +kernel +noncomputable def kernel100_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_6_eq : ∀ k : Fin 16, kernel100_0Expr 1 6 k = kernel100_0_r1_6 k := by decide +kernel +noncomputable def kernel100_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_7_eq : ∀ k : Fin 16, kernel100_0Expr 1 7 k = kernel100_0_r1_7 k := by decide +kernel +noncomputable def kernel100_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_8_eq : ∀ k : Fin 16, kernel100_0Expr 1 8 k = kernel100_0_r1_8 k := by decide +kernel +noncomputable def kernel100_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_9_eq : ∀ k : Fin 16, kernel100_0Expr 1 9 k = kernel100_0_r1_9 k := by decide +kernel +noncomputable def kernel100_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_10_eq : ∀ k : Fin 16, kernel100_0Expr 1 10 k = kernel100_0_r1_10 k := by decide +kernel +noncomputable def kernel100_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_11_eq : ∀ k : Fin 16, kernel100_0Expr 1 11 k = kernel100_0_r1_11 k := by decide +kernel +noncomputable def kernel100_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_12_eq : ∀ k : Fin 16, kernel100_0Expr 1 12 k = kernel100_0_r1_12 k := by decide +kernel +noncomputable def kernel100_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_13_eq : ∀ k : Fin 16, kernel100_0Expr 1 13 k = kernel100_0_r1_13 k := by decide +kernel +noncomputable def kernel100_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_14_eq : ∀ k : Fin 16, kernel100_0Expr 1 14 k = kernel100_0_r1_14 k := by decide +kernel +noncomputable def kernel100_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r1_15_eq : ∀ k : Fin 16, kernel100_0Expr 1 15 k = kernel100_0_r1_15 k := by decide +kernel +noncomputable def kernel100_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel100_0_r1_0,kernel100_0_r1_1,kernel100_0_r1_2,kernel100_0_r1_3,kernel100_0_r1_4,kernel100_0_r1_5,kernel100_0_r1_6,kernel100_0_r1_7,kernel100_0_r1_8,kernel100_0_r1_9,kernel100_0_r1_10,kernel100_0_r1_11,kernel100_0_r1_12,kernel100_0_r1_13,kernel100_0_r1_14,kernel100_0_r1_15] +lemma kernel100_0_r1_eq (i k : Fin 16) : kernel100_0Expr 1 i k = kernel100_0_r1 i k := by + fin_cases i + · exact kernel100_0_r1_0_eq k + · exact kernel100_0_r1_1_eq k + · exact kernel100_0_r1_2_eq k + · exact kernel100_0_r1_3_eq k + · exact kernel100_0_r1_4_eq k + · exact kernel100_0_r1_5_eq k + · exact kernel100_0_r1_6_eq k + · exact kernel100_0_r1_7_eq k + · exact kernel100_0_r1_8_eq k + · exact kernel100_0_r1_9_eq k + · exact kernel100_0_r1_10_eq k + · exact kernel100_0_r1_11_eq k + · exact kernel100_0_r1_12_eq k + · exact kernel100_0_r1_13_eq k + · exact kernel100_0_r1_14_eq k + · exact kernel100_0_r1_15_eq k +noncomputable def kernel100_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_0_eq : ∀ k : Fin 16, kernel100_0Expr 2 0 k = kernel100_0_r2_0 k := by decide +kernel +noncomputable def kernel100_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_1_eq : ∀ k : Fin 16, kernel100_0Expr 2 1 k = kernel100_0_r2_1 k := by decide +kernel +noncomputable def kernel100_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_2_eq : ∀ k : Fin 16, kernel100_0Expr 2 2 k = kernel100_0_r2_2 k := by decide +kernel +noncomputable def kernel100_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_3_eq : ∀ k : Fin 16, kernel100_0Expr 2 3 k = kernel100_0_r2_3 k := by decide +kernel +noncomputable def kernel100_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_4_eq : ∀ k : Fin 16, kernel100_0Expr 2 4 k = kernel100_0_r2_4 k := by decide +kernel +noncomputable def kernel100_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_5_eq : ∀ k : Fin 16, kernel100_0Expr 2 5 k = kernel100_0_r2_5 k := by decide +kernel +noncomputable def kernel100_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_6_eq : ∀ k : Fin 16, kernel100_0Expr 2 6 k = kernel100_0_r2_6 k := by decide +kernel +noncomputable def kernel100_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_7_eq : ∀ k : Fin 16, kernel100_0Expr 2 7 k = kernel100_0_r2_7 k := by decide +kernel +noncomputable def kernel100_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_8_eq : ∀ k : Fin 16, kernel100_0Expr 2 8 k = kernel100_0_r2_8 k := by decide +kernel +noncomputable def kernel100_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_9_eq : ∀ k : Fin 16, kernel100_0Expr 2 9 k = kernel100_0_r2_9 k := by decide +kernel +noncomputable def kernel100_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r2_10_eq : ∀ k : Fin 16, kernel100_0Expr 2 10 k = kernel100_0_r2_10 k := by decide +kernel +noncomputable def kernel100_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r2_11_eq : ∀ k : Fin 16, kernel100_0Expr 2 11 k = kernel100_0_r2_11 k := by decide +kernel +noncomputable def kernel100_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r2_12_eq : ∀ k : Fin 16, kernel100_0Expr 2 12 k = kernel100_0_r2_12 k := by decide +kernel +noncomputable def kernel100_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r2_13_eq : ∀ k : Fin 16, kernel100_0Expr 2 13 k = kernel100_0_r2_13 k := by decide +kernel +noncomputable def kernel100_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r2_14_eq : ∀ k : Fin 16, kernel100_0Expr 2 14 k = kernel100_0_r2_14 k := by decide +kernel +noncomputable def kernel100_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel100_0_r2_15_eq : ∀ k : Fin 16, kernel100_0Expr 2 15 k = kernel100_0_r2_15 k := by decide +kernel +noncomputable def kernel100_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel100_0_r2_0,kernel100_0_r2_1,kernel100_0_r2_2,kernel100_0_r2_3,kernel100_0_r2_4,kernel100_0_r2_5,kernel100_0_r2_6,kernel100_0_r2_7,kernel100_0_r2_8,kernel100_0_r2_9,kernel100_0_r2_10,kernel100_0_r2_11,kernel100_0_r2_12,kernel100_0_r2_13,kernel100_0_r2_14,kernel100_0_r2_15] +lemma kernel100_0_r2_eq (i k : Fin 16) : kernel100_0Expr 2 i k = kernel100_0_r2 i k := by + fin_cases i + · exact kernel100_0_r2_0_eq k + · exact kernel100_0_r2_1_eq k + · exact kernel100_0_r2_2_eq k + · exact kernel100_0_r2_3_eq k + · exact kernel100_0_r2_4_eq k + · exact kernel100_0_r2_5_eq k + · exact kernel100_0_r2_6_eq k + · exact kernel100_0_r2_7_eq k + · exact kernel100_0_r2_8_eq k + · exact kernel100_0_r2_9_eq k + · exact kernel100_0_r2_10_eq k + · exact kernel100_0_r2_11_eq k + · exact kernel100_0_r2_12_eq k + · exact kernel100_0_r2_13_eq k + · exact kernel100_0_r2_14_eq k + · exact kernel100_0_r2_15_eq k +noncomputable def kernel100_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_0_eq : ∀ k : Fin 16, kernel100_0Expr 3 0 k = kernel100_0_r3_0 k := by decide +kernel +noncomputable def kernel100_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_1_eq : ∀ k : Fin 16, kernel100_0Expr 3 1 k = kernel100_0_r3_1 k := by decide +kernel +noncomputable def kernel100_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_2_eq : ∀ k : Fin 16, kernel100_0Expr 3 2 k = kernel100_0_r3_2 k := by decide +kernel +noncomputable def kernel100_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_3_eq : ∀ k : Fin 16, kernel100_0Expr 3 3 k = kernel100_0_r3_3 k := by decide +kernel +noncomputable def kernel100_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_4_eq : ∀ k : Fin 16, kernel100_0Expr 3 4 k = kernel100_0_r3_4 k := by decide +kernel +noncomputable def kernel100_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_5_eq : ∀ k : Fin 16, kernel100_0Expr 3 5 k = kernel100_0_r3_5 k := by decide +kernel +noncomputable def kernel100_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_6_eq : ∀ k : Fin 16, kernel100_0Expr 3 6 k = kernel100_0_r3_6 k := by decide +kernel +noncomputable def kernel100_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_7_eq : ∀ k : Fin 16, kernel100_0Expr 3 7 k = kernel100_0_r3_7 k := by decide +kernel +noncomputable def kernel100_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_8_eq : ∀ k : Fin 16, kernel100_0Expr 3 8 k = kernel100_0_r3_8 k := by decide +kernel +noncomputable def kernel100_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_9_eq : ∀ k : Fin 16, kernel100_0Expr 3 9 k = kernel100_0_r3_9 k := by decide +kernel +noncomputable def kernel100_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_10_eq : ∀ k : Fin 16, kernel100_0Expr 3 10 k = kernel100_0_r3_10 k := by decide +kernel +noncomputable def kernel100_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_11_eq : ∀ k : Fin 16, kernel100_0Expr 3 11 k = kernel100_0_r3_11 k := by decide +kernel +noncomputable def kernel100_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_12_eq : ∀ k : Fin 16, kernel100_0Expr 3 12 k = kernel100_0_r3_12 k := by decide +kernel +noncomputable def kernel100_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_13_eq : ∀ k : Fin 16, kernel100_0Expr 3 13 k = kernel100_0_r3_13 k := by decide +kernel +noncomputable def kernel100_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_14_eq : ∀ k : Fin 16, kernel100_0Expr 3 14 k = kernel100_0_r3_14 k := by decide +kernel +noncomputable def kernel100_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r3_15_eq : ∀ k : Fin 16, kernel100_0Expr 3 15 k = kernel100_0_r3_15 k := by decide +kernel +noncomputable def kernel100_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel100_0_r3_0,kernel100_0_r3_1,kernel100_0_r3_2,kernel100_0_r3_3,kernel100_0_r3_4,kernel100_0_r3_5,kernel100_0_r3_6,kernel100_0_r3_7,kernel100_0_r3_8,kernel100_0_r3_9,kernel100_0_r3_10,kernel100_0_r3_11,kernel100_0_r3_12,kernel100_0_r3_13,kernel100_0_r3_14,kernel100_0_r3_15] +lemma kernel100_0_r3_eq (i k : Fin 16) : kernel100_0Expr 3 i k = kernel100_0_r3 i k := by + fin_cases i + · exact kernel100_0_r3_0_eq k + · exact kernel100_0_r3_1_eq k + · exact kernel100_0_r3_2_eq k + · exact kernel100_0_r3_3_eq k + · exact kernel100_0_r3_4_eq k + · exact kernel100_0_r3_5_eq k + · exact kernel100_0_r3_6_eq k + · exact kernel100_0_r3_7_eq k + · exact kernel100_0_r3_8_eq k + · exact kernel100_0_r3_9_eq k + · exact kernel100_0_r3_10_eq k + · exact kernel100_0_r3_11_eq k + · exact kernel100_0_r3_12_eq k + · exact kernel100_0_r3_13_eq k + · exact kernel100_0_r3_14_eq k + · exact kernel100_0_r3_15_eq k +noncomputable def kernel100_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩] +lemma kernel100_0_r4_0_eq : ∀ k : Fin 16, kernel100_0Expr 4 0 k = kernel100_0_r4_0 k := by decide +kernel +noncomputable def kernel100_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-4),3⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),3⟩,⟨(-3),4⟩⟩] +lemma kernel100_0_r4_1_eq : ∀ k : Fin 16, kernel100_0Expr 4 1 k = kernel100_0_r4_1 k := by decide +kernel +noncomputable def kernel100_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩] +lemma kernel100_0_r4_2_eq : ∀ k : Fin 16, kernel100_0Expr 4 2 k = kernel100_0_r4_2 k := by decide +kernel +noncomputable def kernel100_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-4),2⟩,⟨(-3),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-2),3⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-4),2⟩⟩] +lemma kernel100_0_r4_3_eq : ∀ k : Fin 16, kernel100_0Expr 4 3 k = kernel100_0_r4_3 k := by decide +kernel +noncomputable def kernel100_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_4_eq : ∀ k : Fin 16, kernel100_0Expr 4 4 k = kernel100_0_r4_4 k := by decide +kernel +noncomputable def kernel100_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_5_eq : ∀ k : Fin 16, kernel100_0Expr 4 5 k = kernel100_0_r4_5 k := by decide +kernel +noncomputable def kernel100_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_6_eq : ∀ k : Fin 16, kernel100_0Expr 4 6 k = kernel100_0_r4_6 k := by decide +kernel +noncomputable def kernel100_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_7_eq : ∀ k : Fin 16, kernel100_0Expr 4 7 k = kernel100_0_r4_7 k := by decide +kernel +noncomputable def kernel100_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_8_eq : ∀ k : Fin 16, kernel100_0Expr 4 8 k = kernel100_0_r4_8 k := by decide +kernel +noncomputable def kernel100_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_9_eq : ∀ k : Fin 16, kernel100_0Expr 4 9 k = kernel100_0_r4_9 k := by decide +kernel +noncomputable def kernel100_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_10_eq : ∀ k : Fin 16, kernel100_0Expr 4 10 k = kernel100_0_r4_10 k := by decide +kernel +noncomputable def kernel100_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩] +lemma kernel100_0_r4_11_eq : ∀ k : Fin 16, kernel100_0Expr 4 11 k = kernel100_0_r4_11 k := by decide +kernel +noncomputable def kernel100_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-2),2⟩,⟨(-2),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r4_12_eq : ∀ k : Fin 16, kernel100_0Expr 4 12 k = kernel100_0_r4_12 k := by decide +kernel +noncomputable def kernel100_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r4_13_eq : ∀ k : Fin 16, kernel100_0Expr 4 13 k = kernel100_0_r4_13 k := by decide +kernel +noncomputable def kernel100_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r4_14_eq : ∀ k : Fin 16, kernel100_0Expr 4 14 k = kernel100_0_r4_14 k := by decide +kernel +noncomputable def kernel100_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel100_0_r4_15_eq : ∀ k : Fin 16, kernel100_0Expr 4 15 k = kernel100_0_r4_15 k := by decide +kernel +noncomputable def kernel100_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel100_0_r4_0,kernel100_0_r4_1,kernel100_0_r4_2,kernel100_0_r4_3,kernel100_0_r4_4,kernel100_0_r4_5,kernel100_0_r4_6,kernel100_0_r4_7,kernel100_0_r4_8,kernel100_0_r4_9,kernel100_0_r4_10,kernel100_0_r4_11,kernel100_0_r4_12,kernel100_0_r4_13,kernel100_0_r4_14,kernel100_0_r4_15] +lemma kernel100_0_r4_eq (i k : Fin 16) : kernel100_0Expr 4 i k = kernel100_0_r4 i k := by + fin_cases i + · exact kernel100_0_r4_0_eq k + · exact kernel100_0_r4_1_eq k + · exact kernel100_0_r4_2_eq k + · exact kernel100_0_r4_3_eq k + · exact kernel100_0_r4_4_eq k + · exact kernel100_0_r4_5_eq k + · exact kernel100_0_r4_6_eq k + · exact kernel100_0_r4_7_eq k + · exact kernel100_0_r4_8_eq k + · exact kernel100_0_r4_9_eq k + · exact kernel100_0_r4_10_eq k + · exact kernel100_0_r4_11_eq k + · exact kernel100_0_r4_12_eq k + · exact kernel100_0_r4_13_eq k + · exact kernel100_0_r4_14_eq k + · exact kernel100_0_r4_15_eq k +noncomputable def kernel100_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-1493113106365264703383),(-1493108148641087836258)⟩,⟨(-7351934609514263181862),(-7351929651790086314620)⟩⟩,⟨⟨(-1512544454000777987929),(-1512539506046439454567)⟩,⟨(-7324142051522593522705),(-7324137103568254989226)⟩⟩,⟨⟨(-1550950635192130064076),(-1550945706730052601916)⟩,⟨(-7268628014510332985668),(-7268623086048255523390)⟩⟩,⟨⟨(-1607427027475316143547),(-1607422128116392466886)⟩,⟨(-7185541013705023148239),(-7185536114346099471460)⟩⟩,⟨⟨(-1680637669108171031178),(-1680632808297457150838)⟩,⟨(-7075119379699476438812),(-7075114518888762558353)⟩⟩,⟨⟨(-1768840298395049705755),(-1768835485358617884514)⟩,⟨(-6937708999511335920864),(-6937704186474904099504)⟩⟩,⟨⟨(-1869919502407997948661),(-1869914746102286800151)⟩,⟨(-6773785457149679067036),(-6773780700843967918407)⟩⟩,⟨⟨(-1981427723427456533853),(-1981423032490214216644)⟩,⟨(-6583979341329121857065),(-6583974650391879539735)⟩⟩,⟨⟨(-2100633752703773885685),(-2100629135409347939908)⟩,⟨(-6369103261055593368890),(-6369098643761167422991)⟩⟩,⟨⟨(-2224578192463528964493),(-2224573656678999608688)⟩,⟨(-6130178935721336976347),(-6130174399936807620421)⟩⟩,⟨⟨(-2350135189202649565892),(-2350130742349430590199)⟩,⟨(-5868462614009245377746),(-5868458167156026401930)⟩⟩,⟨⟨(-2474079538302611414083),(-2474075186947499248294)⟩,⟨(-5585467033214883598628),(-5585462681859771432726)⟩⟩,⟨⟨(-2593158037361233519092),(-2593153787922748029976)⟩,⟨(-5282978162007187788048),(-5282973912568702298829)⟩⟩,⟨⟨(-2704163738535886568242),(-2704159596895960639974)⟩,⟨(-4963065084156429967002),(-4963060942516504038639)⟩⟩,⟨⟨(-2804011520863427841983),(-2804007492353929921899)⟩,⟨(-4628081569063671961058),(-4628077540554174040888)⟩⟩,⟨⟨(-2889813199467268447416),(-2889809288842988295190)⟩,⟨(-4280658147845244382467),(-4280654237220964230166)⟩⟩] +lemma kernel100_0_r5_0_eq : ∀ k : Fin 16, kernel100_0Expr 5 0 k = kernel100_0_r5_0 k := by decide +kernel +noncomputable def kernel100_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-2958950215261326175161),(-2958946426700171790806)⟩,⟨(-3923683855217890730928),(-3923680066656736346507)⟩⟩,⟨⟨(-3009141827672536039414),(-3009138164751071069552)⟩,⟨(-3560277203319377770953),(-3560273540397912801035)⟩⟩,⟨⟨(-3038506677629793796446),(-3038503143339533396476)⟩,⟨(-3193746408734502915263),(-3193742874444242515246)⟩⟩,⟨⟨(-3045615612666052064773),(-3045612209393500140356)⟩,⟨(-2827539381868700004314),(-2827535978596148079860)⟩⟩,⟨⟨(-3029533780331404451538),(-3029530509888372702383)⟩,⟨(-2465184487486646291031),(-2465181217043614541847)⟩⟩,⟨⟨(-2989850207095771766650),(-2989847070698566714405)⟩,⟨(-2110223574297879015644),(-2110220437900673963378)⟩⟩,⟨⟨(-2926693388041860719471),(-2926690386361238032043)⟩,⟨(-1766139224552091624035),(-1766136222871468936594)⟩⟩,⟨⟨(-2840731814254557395375),(-2840728947385279965030)⟩,⟨(-1436278567451705807044),(-1436275700582428376694)⟩⟩,⟨⟨(-2733158848334380410488),(-2733156115869439717207)⟩,⟨(-1123776307686272752757),(-1123773575221332059478)⟩⟩,⟨⟨(-2605661908513533190674),(-2605659309528911169852)⟩,⟨(-831479822153123651836),(-831477223168501631022)⟩⟩,⟨⟨(-2460376514844974152712),(-2460374047968400117950)⟩,⟨(-561879254992969759841),(-561876788116395725092)⟩⟩,⟨⟨(-2299826361423195175260),(-2299824024812277010414)⟩,⟨(-317045482819102755570),(-317043146208184590742)⟩⟩,⟨⟨(-2126851174807993477241),(-2126848966237481916983)⟩,⟨(-98578621640653025781),(-98576413070141465544)⟩⟩,⟨⟨(-1944524670196592969235),(-1944522586959131084693)⟩,⟨92430591750633025383,92432674988094909902⟩⟩,⟨⟨(-1756065389709929120114),(-1756063428704542650219)⟩,⟨255424679698270853085,255426640703657322954⟩⟩,⟨⟨(-1564743573939410504407),(-1564741731891579126646)⟩,⟨390387278440341357799,390389120488172735533⟩⟩] +lemma kernel100_0_r5_1_eq : ∀ k : Fin 16, kernel100_0Expr 5 1 k = kernel100_0_r5_1 k := by decide +kernel +noncomputable def kernel100_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-1373787451650568443598),(-1373785725048868399167)⟩,⟨497834344065799938068,497836070667499982472⟩⟩,⟨⟨(-1186292414392289480751),(-1186290799442255268381)⟩,⟨578788801589019700480,578790416539053912827⟩⟩,⟨⟨(-1005136463205013714557),(-1005134955947282190275)⟩,⟨634739459043983609162,634740966301715133425⟩⟩,⟨⟨(-832905070588062500851),(-832903666861141450792)⟩,⟨667585714763679326962,667587118490600377007⟩⟩,⟨⟨(-671828199914815680309),(-671826895454263400855)⟩,⟨679570229502900136424,679571533963452415868⟩⟩,⟨⟨(-523731686113617067730),(-523730476452469398659)⟩,⟨673202276939477657810,673203486600625326876⟩⟩,⟨⟨(-390004529787748761074),(-390003410510296541615)⟩,⟨651174896909545696171,651176016186997915628⟩⟩,⟨⟨(-271582929450547234741),(-271581896063470260219)⟩,⟨616279227608563780224,616280260995640754744⟩⟩,⟨⟨(-168951108642384376038),(-168950156686245242801)⟩,⟨571319474680345597972,571320426636484731211⟩⟩,⟨⟨(-82158233997715466717),(-82157358955154385049)⟩,⟨519031876612716356756,519032751655277438427⟩⟩,⟨⟨(-10850004943600675660),(-10849202410894648988)⟩,⟨462010757820678325084,462011560353384351760⟩⟩,⟨⟨45687130124581051797,45687864523468424526⟩,⟨402644335751579948993,402645070150467321727⟩⟩,⟨⟨88471681883607901421,88472352407458064299⟩,⟨343062396520262380246,343063067044112543130⟩⟩,⟨⟨118765657826356440273,118766268664442163941⟩,⟨285097305547790778524,285097916385876502198⟩⟩,⟨⟨138009025599604068522,138009580786402383946⟩,⟨230259118652496301190,230259673839294616618⟩⟩,⟨⟨147753214960523953637,147753718428527608563⟩,⟨179724844941886266737,179725348409889921666⟩⟩] +lemma kernel100_0_r5_2_eq : ∀ k : Fin 16, kernel100_0Expr 5 2 k = kernel100_0_r5_2 k := by decide +kernel +noncomputable def kernel100_0_r5_3 : Fin 16 → CBox := ![⟨⟨149596622582788856490,149597078082861261761⟩,⟨134341230440756882827,134341685940829288099⟩⟩,⟨⟨145124782646269514956,145125193815571612394⟩,⟨94639817717900242957,94640228887202340395⟩⟩,⟨⟨135857439432560442572,135857809711313165708⟩,⟨60862527414189329252,60862897692942052388⟩⟩,⟨⟨123204235907352221000,123204568597953622403⟩,⟨32995625581544509776,32995958272145911179⟩⟩,⟨⟨108430153690542419031,108430451893839224916⟩,⟨10809704156252337854,10810002359549143739⟩⟩,⟨⟨92631241421236005992,92631508097743829563⟩,⟨(-6096786160141869657),(-6096519483634046087)⟩⟩,⟨⟨76720590317996323206,76720828226614345132⟩,⟨(-18252853553164140223),(-18252615644546118298)⟩⟩,⟨⟨61423989902419481957,61424201653103876627⟩,⟨(-26271348867752712373),(-26271137117068317704)⟩⟩,⟨⟨47284253663305550618,47284441670785143635⟩,⟨(-30808334274514067908),(-30808146267034474892)⟩⟩,⟨⟨34672862749363526251,34673029287779974875⟩,⟨(-32526978978002082065),(-32526812439585633442)⟩⟩,⟨⟨23807349409156320010,23807496610924718974⟩,⟨(-32067097063711866261),(-32066949861943467296)⟩⟩,⟨⟨14772732473616143944,14772862572125095966⟩,⟨(-30020998585096477859),(-30020868486587525837)⟩⟩,⟨⟨7545321651923514741,7545436350277575351⟩,⟨(-26915892141972498771),(-26915777443618438161)⟩⟩,⟨⟨2017308778058013504,2017409664061940689⟩,⟨(-23202686462828748482),(-23202585576824821297)⟩⟩,⟨⟨(-1979247202745704243),(-1979158685949347054)⟩,⟨(-19250702304417214781),(-19250613787620857592)⟩⟩,⟨⟨(-4650192185371227268),(-4650114704009341974)⟩,⟨(-15347550266285718496),(-15347472784923833202)⟩⟩] +lemma kernel100_0_r5_3_eq : ∀ k : Fin 16, kernel100_0Expr 5 3 k = kernel100_0_r5_3 k := by decide +kernel +noncomputable def kernel100_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-6219673874914372470),(-6219606224667003214)⟩,⟨(-11703252566326831964),(-11703184916079462708)⟩⟩,⟨⟨(-6913738467650150368),(-6913679539448452807)⟩,⟨(-8457594055458495667),(-8457535127256798107)⟩⟩,⟨⟨(-6947416631877343810),(-6947365431016768215)⟩,⟨(-5689672148802863095),(-5689620947942287500)⟩⟩,⟨⟨(-6515330668891821003),(-6515286287662880754)⟩,⟨(-3428667832518577037),(-3428623451289636788)⟩⟩,⟨⟨(-5785637168880350422),(-5785598797855002610)⟩,⟨(-1664965904851030438),(-1664927533825682626)⟩⟩,⟨⟨(-4896951508286222877),(-4896918411712123199)⟩,⟨(-360897170850827189),(-360864074276727511)⟩⟩,⟨⟨(-3957785214495856864),(-3957756740583694956)⟩,⟨539458493697719768,539486967609881676⟩⟩,⟨⟨(-3047964378943014948),(-3047939940356168637)⟩,⟨1101796219061389300,1101820657648235611⟩⟩,⟨⟨(-2221481777721639253),(-2221460857078716891)⟩,⟨1394659391258444462,1394680311901366825⟩⟩,⟨⟨(-1510260220893276478),(-1510242353976929397)⟩,⟨1484135395057799779,1484153261974146861⟩⟩,⟨⟨(-928360210314381509),(-928344990523016141)⟩,⟨1430123676385404750,1430138896176770118⟩⟩,⟨⟨(-476241641082438105),(-476228706955283079)⟩,⟨1284031528962937046,1284044463090092072⟩⟩,⟨⟨(-144776898803010928),(-144765936304699495)⟩,⟨1087689197256670688,1087700159754982121⟩⟩,⟨⟨81197227548371144,81206497954048502⟩,⟨873240954550402759,873250224956080119⟩⟩,⟨⟨219916430531289190,219924249711452597⟩,⟨663759582637409919,663767401817573326⟩⟩,⟨⟨290367486056234514,290374065428086062⟩,⟨474343094338342162,474349673710193710⟩⟩] +lemma kernel100_0_r5_4_eq : ∀ k : Fin 16, kernel100_0Expr 5 4 k = kernel100_0_r5_4 k := by decide +kernel +noncomputable def kernel100_0_r5_5 : Fin 16 → CBox := ![⟨⟨310600780520661605,310606301719932275⟩,⟨313479359254184689,313484880453455359⟩⟩,⟨⟨296623619302680732,296628241977088003⟩,⟨184500722068928848,184505344743336119⟩⟩,⟨⟨261791347438693103,261795208547590858⟩,⟨86991776322963574,86995637431861329⟩⟩,⟨⟨216597561809850679,216600779125917095⟩,⟨18054640961377396,18057858277443813⟩⟩,⟨⟨168760952643938190,168763626225692798⟩,⟨(-26625882512344792),(-26623208930590185)⟩⟩,⟨⟨123511797425072617,123514014063719104⟩,⟨(-51942432732649872),(-51940216094003385)⟩⟩,⟨⟨83993074062680607,83994906916996235⟩,⟨(-62749978799461267),(-62748145945145639)⟩⟩,⟨⟨51706816122124741,51708328057182065⟩,⟨(-63456514364539753),(-63455002429482429)⟩⟩,⟨⟨26953417381456644,26954661157135577⟩,⟨(-57788956475645572),(-57787712699966639)⟩⟩,⟨⟨9228184957351556,9229206422768316⟩,⟨(-48698027475215482),(-48697006009798721)⟩⟩,⟨⟨(-2445731431112069),(-2444894680819455)⟩,⟨(-38365057756277459),(-38364221005984846)⟩⟩,⟨⟨(-9256706379090233),(-9256022540199297)⟩,⟨(-28276351641654308),(-28275667802763372)⟩⟩,⟨⟨(-12415692781831482),(-12415135444871277)⟩,⟨(-19335689773391120),(-19335132436430915)⟩⟩,⟨⟨(-13032025004193635),(-13031571785571233)⟩,⟨(-11991638937711167),(-11991185719088766)⟩⟩,⟨⟨(-12043321428514728),(-12042953871672920)⟩,⟨(-6362653927109958),(-6362286370268151)⟩⟩,⟨⟨(-10187315906386046),(-10187018448256048)⟩,⟨(-2348852147680885),(-2348554689550886)⟩⟩] +lemma kernel100_0_r5_5_eq : ∀ k : Fin 16, kernel100_0Expr 5 5 k = kernel100_0_r5_5 k := by decide +kernel +noncomputable def kernel100_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-8003566622054340),(-8003326551902220)⟩,⟨275627465933919,275867536086039⟩⟩,⟨⟨(-5854235844658364),(-5854042512250792)⟩,⟨1791801778713646,1791995111121219⟩⟩,⟨⟨(-3955011128401989),(-3954855846706442)⟩,⟨2485832164334479,2485987446030028⟩⟩,⟨⟨(-2409368177670554),(-2409243735140456)⟩,⟨2617282624058315,2617407066588413⟩⟩,⟨⟨(-1241452776406816),(-1241353321093656)⟩,⟨2402168728082923,2402268183396083⟩⟩,⟨⟨(-424698060450455),(-424618745112484)⟩,⟨2007056668619556,2007135983957527⟩⟩,⟨⟨95219063955725,95282149203306⟩,⟨1550687986683053,1550751071930634⟩⟩,⟨⟨383372189500118,383422257085924⟩,⟨1110109736533765,1110159804119571⟩⟩,⟨⟨504082166906472,504121847927542⟩,⟨728932451511362,728972132532433⟩⟩,⟨⟨514044821274057,514076220837501⟩,⟨425999802311399,426031201874843⟩⟩,⟨⟨459044619266312,459069400461297⟩,⟨203358076438533,203382857633518⟩⟩,⟨⟨373214072292315,373233589428220⟩,⟨52914943873897,52934461009801⟩⟩,⟨⟨279916428055585,279931758178010⟩,⟨(-38442156236908),(-38426826114483)⟩⟩,⟨⟨193505036556440,193517054475349⟩,⟨(-85235555528250),(-85223537609341)⟩⟩,⟨⟨121406014361254,121415411533664⟩,⟨(-101103641041200),(-101094243868790)⟩⟩,⟨⟨66152245948889,66159579814866⟩,⟨(-97557319816516),(-97549985950540)⟩⟩] +lemma kernel100_0_r5_6_eq : ∀ k : Fin 16, kernel100_0Expr 5 6 k = kernel100_0_r5_6 k := by decide +kernel +noncomputable def kernel100_0_r5_7 : Fin 16 → CBox := ![⟨⟨27150706441287,27156414837067⟩,⟨(-83504434536732),(-83498726140953)⟩⟩,⟨⟨2083739840997,2088175337073⟩,⟨(-65283426709882),(-65278991213806)⟩⟩,⟨⟨(-12071529621664),(-12068091167329)⟩,⟨(-46991944927663),(-46988506473328)⟩⟩,⟨⟨(-18369545344010),(-18366884796669)⟩,⟨(-30948330177783),(-30945669630442)⟩⟩,⟨⟨(-19505473050112),(-19503419634492)⟩,⟨(-18174398833814),(-18172345418194)⟩⟩,⟨⟨(-17635933956389),(-17634351833691)⟩,⟨(-8831522340555),(-8829940217857)⟩⟩,⟨⟨(-14343801635618),(-14342585604334)⟩,⟨(-2575999146866),(-2574783115582)⟩⟩,⟨⟨(-10690071276796),(-10689138255636)⟩,⟨1176052649339,1176985670500⟩⟩,⟨⟨(-7308987862212),(-7308273221081)⟩,⟨3068692203094,3069406844225⟩⟩,⟨⟨(-4515798254602),(-4515251577080)⟩,⟨3697166217888,3697712895410⟩⟩,⟨⟨(-2407966627010),(-2407549416466)⟩,⟨3553016327841,3553433538385⟩⟩,⟨⟨(-949756334427),(-949438437548)⟩,⟨3006742529424,3007060426302⟩⟩,⟨⟨(-36567526048),(-36325881620)⟩,⟨2313817644613,2314059289042⟩⟩,⟨⟨460396480958,460579918974⟩,⟨1632999055136,1633182493153⟩⟩,⟨⟨666262395342,666401338149⟩,⟨1049117551123,1049256493930⟩⟩,⟨⟨687610830798,687715920064⟩,⟨595366492671,595471581937⟩⟩] +lemma kernel100_0_r5_7_eq : ∀ k : Fin 16, kernel100_0Expr 5 7 k = kernel100_0_r5_7 k := by decide +kernel +noncomputable def kernel100_0_r5_8 : Fin 16 → CBox := ![⟨⟨606758039949,606837345461⟩,⟨272377648033,272456953545⟩⟩,⟨⟨481849478068,481909286762⟩,⟨62995071630,63054880324⟩⟩,⟨⟨350138737040,350183746847⟩,⟨(-57283999002),(-57238989195)⟩⟩,⟨⟨232573607542,232607437610⟩,⟨(-113641360914),(-113607530845)⟩⟩,⟨⟨138480749544,138506122182⟩,⟨(-128227523615),(-128202150978)⟩⟩,⟨⟨69671528571,69690538277⟩,⟨(-118563592855),(-118544583148)⟩⟩,⟨⟨23677436413,23691654436⟩,⟨(-97306588763),(-97292370739)⟩⟩,⟨⟨(-3925955751),(-3915331829)⟩,⟨(-72785124369),(-72774500447)⟩⟩,⟨⟨(-18004188182),(-17996266208)⟩,⟨(-49877806528),(-49869884553)⟩⟩,⟨⟨(-22992229364),(-22986326851)⟩,⟨(-30955992908),(-30950090396)⟩⟩,⟨⟨(-22487751614),(-22483360878)⟩,⟨(-16731583595),(-16727192860)⟩⟩,⟨⟨(-19149482995),(-19146219616)⟩,⟨(-6937281124),(-6934017745)⟩⟩,⟨⟨(-14772526552),(-14770105570)⟩,⟨(-823414312),(-820993330)⟩⟩,⟨⟨(-10447598663),(-10445803542)⟩,⟨2511698521,2513493641⟩⟩,⟨⟨(-6742791622),(-6741462747)⟩,⟨3925706601,3927035476⟩⟩,⟨⟨(-3872065324),(-3871082168)⟩,⟨4134643978,4135627135⟩⟩] +lemma kernel100_0_r5_8_eq : ∀ k : Fin 16, kernel100_0Expr 5 8 k = kernel100_0_r5_8 k := by decide +kernel +noncomputable def kernel100_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-1833267759),(-1832541647)⟩,⟨3681053593,3681779705⟩⟩,⟨⟨(-510850687),(-510314574)⟩,⟨2941251198,2941787311⟩⟩,⟨⟨254354002,254749267⟩,⟨2152221667,2152616931⟩⟩,⟨⟨622419900,622711206⟩,⟨1445089525,1445380831⟩⟩,⟨⟨731794680,732009043⟩,⟨877376752,877591115⟩⟩,⟨⟨690496553,690654281⟩,⟨460118245,460275972⟩⟩,⟨⟨575730838,575846749⟩,⟨178501364,178617276⟩⟩,⟨⟨437961056,438046223⟩,⟨6236704,6321872⟩⟩,⟨⟨306739484,306801978⟩,⟨(-85348050),(-85285555)⟩⟩,⟨⟨196641473,196687341⟩,⟨(-122234990),(-122189122)⟩⟩,⟨⟨112428023,112461655⟩,⟨(-125443099),(-125409468)⟩⟩,⟨⟨53088012,53112672⟩,⟨(-110529202),(-110504541)⟩⟩,⟨⟨14736953,14755018⟩,⟨(-88079902),(-88061837)⟩⟩,⟨⟨(-7480417),(-7467175)⟩,⟨(-64650256),(-64637014)⟩⟩,⟨⟨(-18267666),(-18257968)⟩,⟨(-43804171),(-43794473)⟩⟩,⟨⟨(-21613966),(-21606826)⟩,⟨(-27064039),(-27056899)⟩⟩] +lemma kernel100_0_r5_9_eq : ∀ k : Fin 16, kernel100_0Expr 5 9 k = kernel100_0_r5_9 k := by decide +kernel +noncomputable def kernel100_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-20598838),(-20593582)⟩,⟨(-14682271),(-14677015)⟩⟩,⟨⟨(-17414336),(-17410463)⟩,⟨(-6214818),(-6210945)⟩⟩,⟨⟨(-13496560),(-13493706)⟩,⟨(-913355),(-910502)⟩⟩,⟨⟨(-9695950),(-9693844)⟩,⟨2029862,2031968⟩⟩,⟨⟨(-6444399),(-6442848)⟩,⟨3346760,3348310⟩⟩,⟨⟨(-3898119),(-3896974)⟩,⟨3633247,3634392⟩⟩,⟨⟨(-2048601),(-2047754)⟩,⟨3336031,3336877⟩⟩,⟨⟨(-802194),(-801569)⟩,⟨2765497,2766122⟩⟩,⟨⟨(-32743),(-32279)⟩,⟨2120374,2120838⟩⟩,⟨⟨386732,387077⟩,⟨1515234,1515578⟩⟩,⟨⟨567396,567653⟩,⟨1005773,1006029⟩⟩,⟨⟨597976,598168⟩,⟨609651,609843⟩⟩,⟨⟨544187,544332⟩,⟨322260,322405⟩⟩,⟨⟨451370,451480⟩,⟨127832,127941⟩⟩,⟨⟨348471,348555⟩,⟨6653,6737⟩⟩,⟨⟨252187,252252⟩,⟨(-60641),(-60576)⟩⟩] +lemma kernel100_0_r5_10_eq : ∀ k : Fin 16, kernel100_0Expr 5 10 k = kernel100_0_r5_10 k := by decide +kernel +noncomputable def kernel100_0_r5_11 : Fin 16 → CBox := ![⟨⟨170682,170731⟩,⟨(-90858),(-90809)⟩⟩,⟨⟨106591,106630⟩,⟨(-97416),(-97377)⟩⟩,⟨⟨59300,59330⟩,⟨(-90308),(-90279)⟩⟩,⟨⟨26526,26551⟩,⟨(-76518),(-76493)⟩⟩,⟨⟨5372,5393⟩,⟨(-60588),(-60567)⟩⟩,⟨⟨(-7056),(-7039)⟩,⟨(-45229),(-45212)⟩⟩,⟨⟨(-13310),(-13295)⟩,⟨(-31853),(-31837)⟩⟩,⟨⟨(-15470),(-15456)⟩,⟨(-21009),(-20997)⟩⟩,⟨⟨(-15121),(-15108)⟩,⟨(-12723),(-12711)⟩⟩,⟨⟨(-13407),(-13395)⟩,⟨(-6729),(-6717)⟩⟩,⟨⟨(-11105),(-11094)⟩,⟨(-2637),(-2626)⟩⟩,⟨⟨(-8704),(-8693)⟩,⟨(-30),(-20)⟩⟩,⟨⟨(-6488),(-6478)⟩,⟨1476,1487⟩⟩,⟨⟨(-4593),(-4584)⟩,⟨2211,2220⟩⟩,⟨⟨(-3067),(-3059)⟩,⟨2435,2443⟩⟩,⟨⟨(-1897),(-1888)⟩,⟨2344,2353⟩⟩] +lemma kernel100_0_r5_11_eq : ∀ k : Fin 16, kernel100_0Expr 5 11 k = kernel100_0_r5_11 k := by decide +kernel +noncomputable def kernel100_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-1040),(-1031)⟩,⟨2082,2091⟩⟩,⟨⟨(-442),(-434)⟩,⟨1746,1753⟩⟩,⟨⟨(-50),(-42)⟩,⟨1396,1404⟩⟩,⟨⟨188,197⟩,⟨1070,1078⟩⟩,⟨⟨316,323⟩,⟨786,793⟩⟩,⟨⟨367,375⟩,⟨551,559⟩⟩,⟨⟨370,377⟩,⟨365,373⟩⟩,⟨⟨341,349⟩,⟨223,231⟩⟩,⟨⟨299,306⟩,⟨118,126⟩⟩,⟨⟨250,257⟩,⟨46,53⟩⟩,⟨⟨203,210⟩,⟨(-3),4⟩⟩,⟨⟨157,165⟩,⟨(-33),(-27)⟩⟩,⟨⟨119,125⟩,⟨(-50),(-45)⟩⟩,⟨⟨86,93⟩,⟨(-59),(-52)⟩⟩,⟨⟨60,67⟩,⟨(-60),(-52)⟩⟩,⟨⟨39,46⟩,⟨(-58),(-50)⟩⟩] +lemma kernel100_0_r5_12_eq : ∀ k : Fin 16, kernel100_0Expr 5 12 k = kernel100_0_r5_12 k := by decide +kernel +noncomputable def kernel100_0_r5_13 : Fin 16 → CBox := ![⟨⟨23,30⟩,⟨(-53),(-46)⟩⟩,⟨⟨11,19⟩,⟨(-48),(-40)⟩⟩,⟨⟨2,10⟩,⟨(-41),(-33)⟩⟩,⟨⟨(-4),3⟩,⟨(-35),(-28)⟩⟩,⟨⟨(-7),(-1)⟩,⟨(-28),(-22)⟩⟩,⟨⟨(-11),(-3)⟩,⟨(-24),(-16)⟩⟩,⟨⟨(-11),(-5)⟩,⟨(-18),(-12)⟩⟩,⟨⟨(-12),(-4)⟩,⟨(-15),(-7)⟩⟩,⟨⟨(-12),(-4)⟩,⟨(-12),(-5)⟩⟩,⟨⟨(-11),(-5)⟩,⟨(-10),(-4)⟩⟩,⟨⟨(-11),(-4)⟩,⟨(-7),(-1)⟩⟩,⟨⟨(-10),(-4)⟩,⟨(-6),0⟩⟩,⟨⟨(-9),(-3)⟩,⟨(-5),1⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-4),3⟩⟩,⟨⟨(-8),(-2)⟩,⟨(-3),3⟩⟩,⟨⟨(-8),0⟩,⟨(-3),4⟩⟩] +lemma kernel100_0_r5_13_eq : ∀ k : Fin 16, kernel100_0Expr 5 13 k = kernel100_0_r5_13 k := by decide +kernel +noncomputable def kernel100_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-6),0⟩,⟨(-2),4⟩⟩,⟨⟨(-6),2⟩,⟨(-3),5⟩⟩,⟨⟨(-6),2⟩,⟨(-3),5⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-4),2⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-3),3⟩,⟨(-2),4⟩⟩] +lemma kernel100_0_r5_14_eq : ∀ k : Fin 16, kernel100_0Expr 5 14 k = kernel100_0_r5_14 k := by decide +kernel +noncomputable def kernel100_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-2),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-2),4⟩,⟨(-3),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩,⟨⟨(-3),4⟩,⟨(-4),3⟩⟩] +lemma kernel100_0_r5_15_eq : ∀ k : Fin 16, kernel100_0Expr 5 15 k = kernel100_0_r5_15 k := by decide +kernel +noncomputable def kernel100_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel100_0_r5_0,kernel100_0_r5_1,kernel100_0_r5_2,kernel100_0_r5_3,kernel100_0_r5_4,kernel100_0_r5_5,kernel100_0_r5_6,kernel100_0_r5_7,kernel100_0_r5_8,kernel100_0_r5_9,kernel100_0_r5_10,kernel100_0_r5_11,kernel100_0_r5_12,kernel100_0_r5_13,kernel100_0_r5_14,kernel100_0_r5_15] +lemma kernel100_0_r5_eq (i k : Fin 16) : kernel100_0Expr 5 i k = kernel100_0_r5 i k := by + fin_cases i + · exact kernel100_0_r5_0_eq k + · exact kernel100_0_r5_1_eq k + · exact kernel100_0_r5_2_eq k + · exact kernel100_0_r5_3_eq k + · exact kernel100_0_r5_4_eq k + · exact kernel100_0_r5_5_eq k + · exact kernel100_0_r5_6_eq k + · exact kernel100_0_r5_7_eq k + · exact kernel100_0_r5_8_eq k + · exact kernel100_0_r5_9_eq k + · exact kernel100_0_r5_10_eq k + · exact kernel100_0_r5_11_eq k + · exact kernel100_0_r5_12_eq k + · exact kernel100_0_r5_13_eq k + · exact kernel100_0_r5_14_eq k + · exact kernel100_0_r5_15_eq k +noncomputable def kernel100_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel100_0_r0,kernel100_0_r1,kernel100_0_r2,kernel100_0_r3,kernel100_0_r4,kernel100_0_r5] +lemma kernel100_0_eq (j : Fin 6) (i k : Fin 16) : kernel100_0Expr j i k = kernel100_0 j i k := by + fin_cases j + · exact kernel100_0_r0_eq i k + · exact kernel100_0_r1_eq i k + · exact kernel100_0_r2_eq i k + · exact kernel100_0_r3_eq i k + · exact kernel100_0_r4_eq i k + · exact kernel100_0_r5_eq i k +lemma kernel100_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel100_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(100:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel100_0_eq] + unfold kernel100_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans100_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel100_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans100 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel100_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r0_0_eq : ∀ k : Fin 16, kernel100_1Expr 0 0 k = kernel100_1_r0_0 k := by decide +kernel +noncomputable def kernel100_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r0_1_eq : ∀ k : Fin 16, kernel100_1Expr 0 1 k = kernel100_1_r0_1 k := by decide +kernel +noncomputable def kernel100_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r0_2_eq : ∀ k : Fin 16, kernel100_1Expr 0 2 k = kernel100_1_r0_2 k := by decide +kernel +noncomputable def kernel100_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r0_3_eq : ∀ k : Fin 16, kernel100_1Expr 0 3 k = kernel100_1_r0_3 k := by decide +kernel +noncomputable def kernel100_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r0_4_eq : ∀ k : Fin 16, kernel100_1Expr 0 4 k = kernel100_1_r0_4 k := by decide +kernel +noncomputable def kernel100_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel100_1_r0_5_eq : ∀ k : Fin 16, kernel100_1Expr 0 5 k = kernel100_1_r0_5 k := by decide +kernel +noncomputable def kernel100_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel100_1_r0_6_eq : ∀ k : Fin 16, kernel100_1Expr 0 6 k = kernel100_1_r0_6 k := by decide +kernel +noncomputable def kernel100_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel100_1_r0_7_eq : ∀ k : Fin 16, kernel100_1Expr 0 7 k = kernel100_1_r0_7 k := by decide +kernel +noncomputable def kernel100_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel100_1_r0_8_eq : ∀ k : Fin 16, kernel100_1Expr 0 8 k = kernel100_1_r0_8 k := by decide +kernel +noncomputable def kernel100_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel100_1_r0_9_eq : ∀ k : Fin 16, kernel100_1Expr 0 9 k = kernel100_1_r0_9 k := by decide +kernel +noncomputable def kernel100_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel100_1_r0_10_eq : ∀ k : Fin 16, kernel100_1Expr 0 10 k = kernel100_1_r0_10 k := by decide +kernel +noncomputable def kernel100_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel100_1_r0_11_eq : ∀ k : Fin 16, kernel100_1Expr 0 11 k = kernel100_1_r0_11 k := by decide +kernel +noncomputable def kernel100_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel100_1_r0_12_eq : ∀ k : Fin 16, kernel100_1Expr 0 12 k = kernel100_1_r0_12 k := by decide +kernel +noncomputable def kernel100_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel100_1_r0_13_eq : ∀ k : Fin 16, kernel100_1Expr 0 13 k = kernel100_1_r0_13 k := by decide +kernel +noncomputable def kernel100_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel100_1_r0_14_eq : ∀ k : Fin 16, kernel100_1Expr 0 14 k = kernel100_1_r0_14 k := by decide +kernel +noncomputable def kernel100_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel100_1_r0_15_eq : ∀ k : Fin 16, kernel100_1Expr 0 15 k = kernel100_1_r0_15 k := by decide +kernel +noncomputable def kernel100_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel100_1_r0_0,kernel100_1_r0_1,kernel100_1_r0_2,kernel100_1_r0_3,kernel100_1_r0_4,kernel100_1_r0_5,kernel100_1_r0_6,kernel100_1_r0_7,kernel100_1_r0_8,kernel100_1_r0_9,kernel100_1_r0_10,kernel100_1_r0_11,kernel100_1_r0_12,kernel100_1_r0_13,kernel100_1_r0_14,kernel100_1_r0_15] +lemma kernel100_1_r0_eq (i k : Fin 16) : kernel100_1Expr 0 i k = kernel100_1_r0 i k := by + fin_cases i + · exact kernel100_1_r0_0_eq k + · exact kernel100_1_r0_1_eq k + · exact kernel100_1_r0_2_eq k + · exact kernel100_1_r0_3_eq k + · exact kernel100_1_r0_4_eq k + · exact kernel100_1_r0_5_eq k + · exact kernel100_1_r0_6_eq k + · exact kernel100_1_r0_7_eq k + · exact kernel100_1_r0_8_eq k + · exact kernel100_1_r0_9_eq k + · exact kernel100_1_r0_10_eq k + · exact kernel100_1_r0_11_eq k + · exact kernel100_1_r0_12_eq k + · exact kernel100_1_r0_13_eq k + · exact kernel100_1_r0_14_eq k + · exact kernel100_1_r0_15_eq k +noncomputable def kernel100_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel100_1_r1_0_eq : ∀ k : Fin 16, kernel100_1Expr 1 0 k = kernel100_1_r1_0 k := by decide +kernel +noncomputable def kernel100_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel100_1_r1_1_eq : ∀ k : Fin 16, kernel100_1Expr 1 1 k = kernel100_1_r1_1 k := by decide +kernel +noncomputable def kernel100_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel100_1_r1_2_eq : ∀ k : Fin 16, kernel100_1Expr 1 2 k = kernel100_1_r1_2 k := by decide +kernel +noncomputable def kernel100_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel100_1_r1_3_eq : ∀ k : Fin 16, kernel100_1Expr 1 3 k = kernel100_1_r1_3 k := by decide +kernel +noncomputable def kernel100_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel100_1_r1_4_eq : ∀ k : Fin 16, kernel100_1Expr 1 4 k = kernel100_1_r1_4 k := by decide +kernel +noncomputable def kernel100_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel100_1_r1_5_eq : ∀ k : Fin 16, kernel100_1Expr 1 5 k = kernel100_1_r1_5 k := by decide +kernel +noncomputable def kernel100_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel100_1_r1_6_eq : ∀ k : Fin 16, kernel100_1Expr 1 6 k = kernel100_1_r1_6 k := by decide +kernel +noncomputable def kernel100_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel100_1_r1_7_eq : ∀ k : Fin 16, kernel100_1Expr 1 7 k = kernel100_1_r1_7 k := by decide +kernel +noncomputable def kernel100_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel100_1_r1_8_eq : ∀ k : Fin 16, kernel100_1Expr 1 8 k = kernel100_1_r1_8 k := by decide +kernel +noncomputable def kernel100_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel100_1_r1_9_eq : ∀ k : Fin 16, kernel100_1Expr 1 9 k = kernel100_1_r1_9 k := by decide +kernel +noncomputable def kernel100_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r1_10_eq : ∀ k : Fin 16, kernel100_1Expr 1 10 k = kernel100_1_r1_10 k := by decide +kernel +noncomputable def kernel100_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r1_11_eq : ∀ k : Fin 16, kernel100_1Expr 1 11 k = kernel100_1_r1_11 k := by decide +kernel +noncomputable def kernel100_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r1_12_eq : ∀ k : Fin 16, kernel100_1Expr 1 12 k = kernel100_1_r1_12 k := by decide +kernel +noncomputable def kernel100_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r1_13_eq : ∀ k : Fin 16, kernel100_1Expr 1 13 k = kernel100_1_r1_13 k := by decide +kernel +noncomputable def kernel100_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r1_14_eq : ∀ k : Fin 16, kernel100_1Expr 1 14 k = kernel100_1_r1_14 k := by decide +kernel +noncomputable def kernel100_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel100_1_r1_15_eq : ∀ k : Fin 16, kernel100_1Expr 1 15 k = kernel100_1_r1_15 k := by decide +kernel +noncomputable def kernel100_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel100_1_r1_0,kernel100_1_r1_1,kernel100_1_r1_2,kernel100_1_r1_3,kernel100_1_r1_4,kernel100_1_r1_5,kernel100_1_r1_6,kernel100_1_r1_7,kernel100_1_r1_8,kernel100_1_r1_9,kernel100_1_r1_10,kernel100_1_r1_11,kernel100_1_r1_12,kernel100_1_r1_13,kernel100_1_r1_14,kernel100_1_r1_15] +lemma kernel100_1_r1_eq (i k : Fin 16) : kernel100_1Expr 1 i k = kernel100_1_r1 i k := by + fin_cases i + · exact kernel100_1_r1_0_eq k + · exact kernel100_1_r1_1_eq k + · exact kernel100_1_r1_2_eq k + · exact kernel100_1_r1_3_eq k + · exact kernel100_1_r1_4_eq k + · exact kernel100_1_r1_5_eq k + · exact kernel100_1_r1_6_eq k + · exact kernel100_1_r1_7_eq k + · exact kernel100_1_r1_8_eq k + · exact kernel100_1_r1_9_eq k + · exact kernel100_1_r1_10_eq k + · exact kernel100_1_r1_11_eq k + · exact kernel100_1_r1_12_eq k + · exact kernel100_1_r1_13_eq k + · exact kernel100_1_r1_14_eq k + · exact kernel100_1_r1_15_eq k +noncomputable def kernel100_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel100_1_r2_0_eq : ∀ k : Fin 16, kernel100_1Expr 2 0 k = kernel100_1_r2_0 k := by decide +kernel +noncomputable def kernel100_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel100_1_r2_1_eq : ∀ k : Fin 16, kernel100_1Expr 2 1 k = kernel100_1_r2_1 k := by decide +kernel +noncomputable def kernel100_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel100_1_r2_2_eq : ∀ k : Fin 16, kernel100_1Expr 2 2 k = kernel100_1_r2_2 k := by decide +kernel +noncomputable def kernel100_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel100_1_r2_3_eq : ∀ k : Fin 16, kernel100_1Expr 2 3 k = kernel100_1_r2_3 k := by decide +kernel +noncomputable def kernel100_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel100_1_r2_4_eq : ∀ k : Fin 16, kernel100_1Expr 2 4 k = kernel100_1_r2_4 k := by decide +kernel +noncomputable def kernel100_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel100_1_r2_5_eq : ∀ k : Fin 16, kernel100_1Expr 2 5 k = kernel100_1_r2_5 k := by decide +kernel +noncomputable def kernel100_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel100_1_r2_6_eq : ∀ k : Fin 16, kernel100_1Expr 2 6 k = kernel100_1_r2_6 k := by decide +kernel +noncomputable def kernel100_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel100_1_r2_7_eq : ∀ k : Fin 16, kernel100_1Expr 2 7 k = kernel100_1_r2_7 k := by decide +kernel +noncomputable def kernel100_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel100_1_r2_8_eq : ∀ k : Fin 16, kernel100_1Expr 2 8 k = kernel100_1_r2_8 k := by decide +kernel +noncomputable def kernel100_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel100_1_r2_9_eq : ∀ k : Fin 16, kernel100_1Expr 2 9 k = kernel100_1_r2_9 k := by decide +kernel +noncomputable def kernel100_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel100_1_r2_10_eq : ∀ k : Fin 16, kernel100_1Expr 2 10 k = kernel100_1_r2_10 k := by decide +kernel +noncomputable def kernel100_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel100_1_r2_11_eq : ∀ k : Fin 16, kernel100_1Expr 2 11 k = kernel100_1_r2_11 k := by decide +kernel +noncomputable def kernel100_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel100_1_r2_12_eq : ∀ k : Fin 16, kernel100_1Expr 2 12 k = kernel100_1_r2_12 k := by decide +kernel +noncomputable def kernel100_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel100_1_r2_13_eq : ∀ k : Fin 16, kernel100_1Expr 2 13 k = kernel100_1_r2_13 k := by decide +kernel +noncomputable def kernel100_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel100_1_r2_14_eq : ∀ k : Fin 16, kernel100_1Expr 2 14 k = kernel100_1_r2_14 k := by decide +kernel +noncomputable def kernel100_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel100_1_r2_15_eq : ∀ k : Fin 16, kernel100_1Expr 2 15 k = kernel100_1_r2_15 k := by decide +kernel +noncomputable def kernel100_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel100_1_r2_0,kernel100_1_r2_1,kernel100_1_r2_2,kernel100_1_r2_3,kernel100_1_r2_4,kernel100_1_r2_5,kernel100_1_r2_6,kernel100_1_r2_7,kernel100_1_r2_8,kernel100_1_r2_9,kernel100_1_r2_10,kernel100_1_r2_11,kernel100_1_r2_12,kernel100_1_r2_13,kernel100_1_r2_14,kernel100_1_r2_15] +lemma kernel100_1_r2_eq (i k : Fin 16) : kernel100_1Expr 2 i k = kernel100_1_r2 i k := by + fin_cases i + · exact kernel100_1_r2_0_eq k + · exact kernel100_1_r2_1_eq k + · exact kernel100_1_r2_2_eq k + · exact kernel100_1_r2_3_eq k + · exact kernel100_1_r2_4_eq k + · exact kernel100_1_r2_5_eq k + · exact kernel100_1_r2_6_eq k + · exact kernel100_1_r2_7_eq k + · exact kernel100_1_r2_8_eq k + · exact kernel100_1_r2_9_eq k + · exact kernel100_1_r2_10_eq k + · exact kernel100_1_r2_11_eq k + · exact kernel100_1_r2_12_eq k + · exact kernel100_1_r2_13_eq k + · exact kernel100_1_r2_14_eq k + · exact kernel100_1_r2_15_eq k +noncomputable def kernel100_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel100_1_r3_0_eq : ∀ k : Fin 16, kernel100_1Expr 3 0 k = kernel100_1_r3_0 k := by decide +kernel +noncomputable def kernel100_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel100_1_r3_1_eq : ∀ k : Fin 16, kernel100_1Expr 3 1 k = kernel100_1_r3_1 k := by decide +kernel +noncomputable def kernel100_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel100_1_r3_2_eq : ∀ k : Fin 16, kernel100_1Expr 3 2 k = kernel100_1_r3_2 k := by decide +kernel +noncomputable def kernel100_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel100_1_r3_3_eq : ∀ k : Fin 16, kernel100_1Expr 3 3 k = kernel100_1_r3_3 k := by decide +kernel +noncomputable def kernel100_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel100_1_r3_4_eq : ∀ k : Fin 16, kernel100_1Expr 3 4 k = kernel100_1_r3_4 k := by decide +kernel +noncomputable def kernel100_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩] +lemma kernel100_1_r3_5_eq : ∀ k : Fin 16, kernel100_1Expr 3 5 k = kernel100_1_r3_5 k := by decide +kernel +noncomputable def kernel100_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-20),20⟩,⟨(-20),20⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel100_1_r3_6_eq : ∀ k : Fin 16, kernel100_1Expr 3 6 k = kernel100_1_r3_6 k := by decide +kernel +noncomputable def kernel100_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩] +lemma kernel100_1_r3_7_eq : ∀ k : Fin 16, kernel100_1Expr 3 7 k = kernel100_1_r3_7 k := by decide +kernel +noncomputable def kernel100_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-21),21⟩,⟨(-21),21⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel100_1_r3_8_eq : ∀ k : Fin 16, kernel100_1Expr 3 8 k = kernel100_1_r3_8 k := by decide +kernel +noncomputable def kernel100_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩,⟨⟨(-22),22⟩,⟨(-22),22⟩⟩] +lemma kernel100_1_r3_9_eq : ∀ k : Fin 16, kernel100_1Expr 3 9 k = kernel100_1_r3_9 k := by decide +kernel +noncomputable def kernel100_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel100_1_r3_10_eq : ∀ k : Fin 16, kernel100_1Expr 3 10 k = kernel100_1_r3_10 k := by decide +kernel +noncomputable def kernel100_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩] +lemma kernel100_1_r3_11_eq : ∀ k : Fin 16, kernel100_1Expr 3 11 k = kernel100_1_r3_11 k := by decide +kernel +noncomputable def kernel100_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel100_1_r3_12_eq : ∀ k : Fin 16, kernel100_1Expr 3 12 k = kernel100_1_r3_12 k := by decide +kernel +noncomputable def kernel100_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel100_1_r3_13_eq : ∀ k : Fin 16, kernel100_1Expr 3 13 k = kernel100_1_r3_13 k := by decide +kernel +noncomputable def kernel100_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel100_1_r3_14_eq : ∀ k : Fin 16, kernel100_1Expr 3 14 k = kernel100_1_r3_14 k := by decide +kernel +noncomputable def kernel100_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel100_1_r3_15_eq : ∀ k : Fin 16, kernel100_1Expr 3 15 k = kernel100_1_r3_15 k := by decide +kernel +noncomputable def kernel100_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel100_1_r3_0,kernel100_1_r3_1,kernel100_1_r3_2,kernel100_1_r3_3,kernel100_1_r3_4,kernel100_1_r3_5,kernel100_1_r3_6,kernel100_1_r3_7,kernel100_1_r3_8,kernel100_1_r3_9,kernel100_1_r3_10,kernel100_1_r3_11,kernel100_1_r3_12,kernel100_1_r3_13,kernel100_1_r3_14,kernel100_1_r3_15] +lemma kernel100_1_r3_eq (i k : Fin 16) : kernel100_1Expr 3 i k = kernel100_1_r3 i k := by + fin_cases i + · exact kernel100_1_r3_0_eq k + · exact kernel100_1_r3_1_eq k + · exact kernel100_1_r3_2_eq k + · exact kernel100_1_r3_3_eq k + · exact kernel100_1_r3_4_eq k + · exact kernel100_1_r3_5_eq k + · exact kernel100_1_r3_6_eq k + · exact kernel100_1_r3_7_eq k + · exact kernel100_1_r3_8_eq k + · exact kernel100_1_r3_9_eq k + · exact kernel100_1_r3_10_eq k + · exact kernel100_1_r3_11_eq k + · exact kernel100_1_r3_12_eq k + · exact kernel100_1_r3_13_eq k + · exact kernel100_1_r3_14_eq k + · exact kernel100_1_r3_15_eq k +noncomputable def kernel100_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩] +lemma kernel100_1_r4_0_eq : ∀ k : Fin 16, kernel100_1Expr 4 0 k = kernel100_1_r4_0 k := by decide +kernel +noncomputable def kernel100_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),16⟩,⟨(-15),20⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-15),20⟩,⟨(-16),19⟩⟩] +lemma kernel100_1_r4_1_eq : ∀ k : Fin 16, kernel100_1Expr 4 1 k = kernel100_1_r4_1 k := by decide +kernel +noncomputable def kernel100_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),14⟩,⟨(-15),10⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-14),11⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-19),11⟩,⟨(-14),16⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),11⟩,⟨(-10),15⟩⟩] +lemma kernel100_1_r4_2_eq : ∀ k : Fin 16, kernel100_1Expr 4 2 k = kernel100_1_r4_2 k := by decide +kernel +noncomputable def kernel100_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-14),11⟩,⟨(-10),15⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-14),16⟩,⟨(-11),19⟩⟩,⟨⟨(-10),15⟩,⟨(-11),14⟩⟩,⟨⟨(-10),15⟩,⟨(-11),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),15⟩,⟨(-15),10⟩⟩,⟨⟨(-16),15⟩,⟨(-19),11⟩⟩,⟨⟨(-16),15⟩,⟨(-19),11⟩⟩,⟨⟨(-16),15⟩,⟨(-19),11⟩⟩,⟨⟨(-15),10⟩,⟨(-15),11⟩⟩,⟨⟨(-15),10⟩,⟨(-15),11⟩⟩,⟨⟨(-20),11⟩,⟨(-15),16⟩⟩] +lemma kernel100_1_r4_3_eq : ∀ k : Fin 16, kernel100_1Expr 4 3 k = kernel100_1_r4_3 k := by decide +kernel +noncomputable def kernel100_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-10),10⟩,⟨(-10),10⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel100_1_r4_4_eq : ∀ k : Fin 16, kernel100_1Expr 4 4 k = kernel100_1_r4_4 k := by decide +kernel +noncomputable def kernel100_1_r4_5 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel100_1_r4_5_eq : ∀ k : Fin 16, kernel100_1Expr 4 5 k = kernel100_1_r4_5 k := by decide +kernel +noncomputable def kernel100_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel100_1_r4_6_eq : ∀ k : Fin 16, kernel100_1Expr 4 6 k = kernel100_1_r4_6 k := by decide +kernel +noncomputable def kernel100_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩] +lemma kernel100_1_r4_7_eq : ∀ k : Fin 16, kernel100_1Expr 4 7 k = kernel100_1_r4_7 k := by decide +kernel +noncomputable def kernel100_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-11),11⟩,⟨(-11),11⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel100_1_r4_8_eq : ∀ k : Fin 16, kernel100_1Expr 4 8 k = kernel100_1_r4_8 k := by decide +kernel +noncomputable def kernel100_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel100_1_r4_9_eq : ∀ k : Fin 16, kernel100_1Expr 4 9 k = kernel100_1_r4_9 k := by decide +kernel +noncomputable def kernel100_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel100_1_r4_10_eq : ∀ k : Fin 16, kernel100_1Expr 4 10 k = kernel100_1_r4_10 k := by decide +kernel +noncomputable def kernel100_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩] +lemma kernel100_1_r4_11_eq : ∀ k : Fin 16, kernel100_1Expr 4 11 k = kernel100_1_r4_11 k := by decide +kernel +noncomputable def kernel100_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-12),12⟩,⟨(-12),12⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel100_1_r4_12_eq : ∀ k : Fin 16, kernel100_1Expr 4 12 k = kernel100_1_r4_12 k := by decide +kernel +noncomputable def kernel100_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel100_1_r4_13_eq : ∀ k : Fin 16, kernel100_1Expr 4 13 k = kernel100_1_r4_13 k := by decide +kernel +noncomputable def kernel100_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel100_1_r4_14_eq : ∀ k : Fin 16, kernel100_1Expr 4 14 k = kernel100_1_r4_14 k := by decide +kernel +noncomputable def kernel100_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩,⟨⟨(-19),19⟩,⟨(-19),19⟩⟩] +lemma kernel100_1_r4_15_eq : ∀ k : Fin 16, kernel100_1Expr 4 15 k = kernel100_1_r4_15 k := by decide +kernel +noncomputable def kernel100_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel100_1_r4_0,kernel100_1_r4_1,kernel100_1_r4_2,kernel100_1_r4_3,kernel100_1_r4_4,kernel100_1_r4_5,kernel100_1_r4_6,kernel100_1_r4_7,kernel100_1_r4_8,kernel100_1_r4_9,kernel100_1_r4_10,kernel100_1_r4_11,kernel100_1_r4_12,kernel100_1_r4_13,kernel100_1_r4_14,kernel100_1_r4_15] +lemma kernel100_1_r4_eq (i k : Fin 16) : kernel100_1Expr 4 i k = kernel100_1_r4 i k := by + fin_cases i + · exact kernel100_1_r4_0_eq k + · exact kernel100_1_r4_1_eq k + · exact kernel100_1_r4_2_eq k + · exact kernel100_1_r4_3_eq k + · exact kernel100_1_r4_4_eq k + · exact kernel100_1_r4_5_eq k + · exact kernel100_1_r4_6_eq k + · exact kernel100_1_r4_7_eq k + · exact kernel100_1_r4_8_eq k + · exact kernel100_1_r4_9_eq k + · exact kernel100_1_r4_10_eq k + · exact kernel100_1_r4_11_eq k + · exact kernel100_1_r4_12_eq k + · exact kernel100_1_r4_13_eq k + · exact kernel100_1_r4_14_eq k + · exact kernel100_1_r4_15_eq k +noncomputable def kernel100_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-26267685708908765304632),(-26267666875469468327805)⟩,⟨6772183738954858158622,6772202572394155134985⟩⟩,⟨⟨(-26163870251593389325337),(-26163851454950816467520)⟩,⟨6837410686018531895722,6837429482661104753076⟩⟩,⟨⟨(-25956572638593759849332),(-25956553915368285913367)⟩,⟨6966227997965337853550,6966246721190811789050⟩⟩,⟨⟨(-25646481101823374520070),(-25646462488219187260887)⟩,⟨7155393868529264560826,7155412482133451819544⟩⟩,⟨⟨(-25234680855661735244926),(-25234662387264147573616)⟩,⟨7400123781302621950946,7400142249700209621790⟩⟩,⟨⟨(-24722714203553142703514),(-24722695915130150518453)⟩,⟨7694183744968319387669,7694202033391311572267⟩⟩,⟨⟨(-24112655247071541772399),(-24112637172384659969752)⟩,⟨8030013526054046784419,8030031600740928586606⟩⟩,⟨⟨(-23407194783842154183468),(-23407176955463049976187)⟩,⟨8398878786676977364826,8398896615056081571643⟩⟩,⟨⟨(-22609730178244472306274),(-22609712627387818126438)⟩,⟨8791050571387671330925,8791068122244325510296⟩⟩,⟨⟨(-21724454381399680386773),(-21724437137758875863709)⟩,⟨9196010022972253184548,9196027266613057707156⟩⟩,⟨⟨(-20756437896747306839785),(-20756420988350612351766)⟩,⟨9602675546057253033214,9602692454453947520773⟩⟩,⟨⟨(-19711697362660694201777),(-19711680814317742897713)⟩,⟨9999648893843114345875,9999665442186065649519⟩⟩,⟨⟨(-18597244568991978246815),(-18597228404980774474105)⟩,⟨10375475859220823483660,10375492023232027255989⟩⟩,⟨⟨(-17421110172376051329835),(-17421094414967609507783)⟩,⟨10718916423708455986074,10718932181116897807776⟩⟩,⟨⟨(-16192337088372212926170),(-16192321757779794506926)⟩,⟨11019218441192892714682,11019233771785311133612⟩⟩,⟨⟨(-14920939556675580560484),(-14920924670951990632518)⟩,⟨11266388211829856677817,11266403097553446605511⟩⟩] +lemma kernel100_1_r5_0_eq : ∀ k : Fin 16, kernel100_1Expr 5 0 k = kernel100_1_r5_0 k := by decide +kernel +noncomputable def kernel100_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-13617825136636224295944),(-13617810711674220478634)⟩,⟨11451450730692886477102,11451465155654890294176⟩⟩,⟨⟨(-12294678377874779360687),(-12294664427313190729260)⟩,⟨11566692012869540759705,11566705963431129390934⟩⟩,⟨⟨(-10963806567617115996724),(-10963793102901728274483)⟩,⟨11605875762321533870376,11605889227036921592454⟩⟩,⟨⟨(-9637949720955233245407),(-9637936751261205943820)⟩,⟨11564426810150237591773,11564439779844264893236⟩⟩,⟨⟨(-8330058775173445018857),(-8330046307518910941542)⟩,⟨11439574235859325506710,11439586703513859583932⟩⟩,⟨⟨(-7053047692507870930157),(-7053035731672355974443)⟩,⟨11230447920070599966521,11230459880906114922174⟩⟩,⟨⟨(-5819526774840062770856),(-5819515323552367118341)⟩,⟨10938123462727206361093,10938134914014902013576⟩⟩,⟨⟨(-4641525861542201176719),(-4641514920361440716070)⟩,⟨10565611914215818003955,10565622855396578464603⟩⟩,⟨⟨(-3530217127988644236189),(-3530206695584312137396)⟩,⟨10117792570265447361428,10117803002669779460245⟩⟩,⟨⟨(-2495647855453156242644),(-2495637928543715899251)⟩,⟨9601289107044761883773,9601299033954202227213⟩⟩,⟨⟨(-1546493736999435118369),(-1546484310611431473232)⟩,⟨9024291502826538398900,9024300929214542044103⟩⟩,⟨⟨(-689842983760775309343),(-689834051141757533409)⟩,⟨8396328401839858980748,8396337334458876756766⟩⟩,⟨⟨68979319327615354986,68987766379247467475⟩,⟨7727996718965808410209,7728005166017440522794⟩⟩,⟨⟨726538471459755535538,726546442978096340830⟩,⟨7030657238499089090270,7030665210017429895661⟩⟩,⟨⟨1281362664668242249866,1281370172185656020868⟩,⟨6316106618446557776607,6316114125963971547715⟩⟩,⟨⟨1733956536978869512308,1733963592687193508212⟩,⟨5596237460056518260439,5596244515764842256449⟩⟩] +lemma kernel100_1_r5_1_eq : ∀ k : Fin 16, kernel100_1Expr 5 1 k = kernel100_1_r5_1 k := by decide +kernel +noncomputable def kernel100_1_r5_2 : Fin 16 → CBox := ![⟨⟨2086754011624457690460,2086760628620429338028⟩,⟨4882698858415653032183,4882705475411624679854⟩⟩,⟨⟨2344011283008267289019,2344017475473689011794⟩,⟨4186570048934811323966,4186576241400233046827⟩⟩,⟨⟨2511643458820420032906,2511649241572673520247⟩,⟨3518059365623634571940,3518065148375888059350⟩⟩,⟨⟨2597010906965214158552,2597016295603098810415⟩,⟨2886239733655721956238,2886245122293606608151⟩⟩,⟨⟨2608663644408752539888,2608668654934876656714⟩,⟨2298830366809563689414,2298835377335687806274⟩⟩,⟨⟨2556054002959511008304,2556058652165532412381⟩,⟨1762032292373690542422,1762036941579711946515⟩⟩,⟨⟨2449229210912504471610,2449233515406706699249⟩,⟨1280422893432024405179,1280427197926226632821⟩⟩,⟨⟨2298516341577167301073,2298520318281547567946⟩,⟨856911957020606877572,856915933724987144447⟩⟩,⟨⟨2114212265067490284246,2114215930790862788748⟩,⟨492758910004136162462,492762575727508666953⟩⟩,⟨⟨1906290766659193278922,1906294138452272751333⟩,⟨187648150378250392943,187651522171329865339⟩⟩,⟨⟨1684137909224559067470,1684141003720710188296⟩,⟨(-60183185846323083860),(-60180091350171963052)⟩⟩,⟨⟨1456325069289610843430,1456327903036947791509⟩,⟨(-253772914433158871350),(-253770080685821923292)⟩⟩,⟨⟨1230426982246463525854,1230429571363315836480⟩,⟨(-397226601015827507417),(-397224011898975196815)⟩⟩,⟨⟨1012889707125352496296,1012892067485054630069⟩,⟨(-495486326788221971955),(-495483966428519838204)⟩⟩,⟨⟨808950826388702857177,808952973290549748669⟩,⟨(-554086867460920992809),(-554084720559074101332)⟩⟩,⟨⟨622611578074367765016,622613526447705999845⟩,⟨(-578910690252498881813),(-578908741879160646995)⟩⟩] +lemma kernel100_1_r5_2_eq : ∀ k : Fin 16, kernel100_1Expr 5 2 k = kernel100_1_r5_2 k := by decide +kernel +noncomputable def kernel100_1_r5_3 : Fin 16 → CBox := ![⟨⟨456658140156207167205,456659904252224502493⟩,⟨(-575952520776867790569),(-575950756680850455284)⟩⟩,⟨⟨312727083511739894212,312728677165955334299⟩,⟨(-551103038005463384413),(-551101444351247944326)⟩⟩,⟨⟨191408207856874449551,191409644166197633728⟩,⟨(-509959608549733295265),(-509958172240410111087)⟩⟩,⟨⟨92376654074729577991,92377945625778292969⟩,⟨(-457670001651234046850),(-457668710100185331871)⟩⟩,⟨⟨14545408011937694996,14546566632884003716⟩,⟨(-398812862212573957101),(-398811703591627648380)⟩⟩,⟨⟨(-43770919445713109902),(-43769882448546222169)⟩,⟨(-337316513070477761366),(-337315476073310873629)⟩⟩,⟨⟨(-84689848293531257606),(-84688922374961260959)⟩,⟨(-276415539593098497803),(-276414613674528501152)⟩⟩,⟨⟨(-110600362676194172711),(-110599537848688330973)⟩,⟨(-218642711256187722800),(-218641886428681881058)⟩⟩,⟨⟨(-124014701610154218724),(-124013968625363922403)⟩,⟨(-165852209526171506575),(-165851476541381210250)⟩⟩,⟨⟨(-127438048207248842386),(-127437398344613378819)⟩,⟨(-119268938541608630499),(-119268288678973166929)⟩⟩,⟨⟨(-123259951203392365780),(-123259376275750900563)⟩,⟨(-79557928087651333125),(-79557353160009867911)⟩⟩,⟨⟨(-113669661315911702021),(-113669152721978157175)⟩,⟨(-46907510660067464090),(-46907002066133919245)⟩⟩,⟨⟨(-100595971925514700890),(-100595523117761379875)⟩,⟨(-21120034108816903250),(-21119585301063582236)⟩⟩,⟨⟨(-85670732089391546597),(-85670336955800283125)⟩,⟨(-1704326002937516564),(-1703930869346253093)⟩⟩,⟨⟨(-70213991159148173914),(-70213644139483271078)⟩,⟨12035148575823010976,12035495595487913811⟩⟩,⟨⟨(-55237833160504817447),(-55237529109492083070)⟩,⟨20916536634531673399,20916840685544407775⟩⟩] +lemma kernel100_1_r5_3_eq : ∀ k : Fin 16, kernel100_1Expr 5 3 k = kernel100_1_r5_3 k := by decide +kernel +noncomputable def kernel100_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-41465351269972854086),(-41465085537400564225)⟩,⟨25809293481341290793,25809559213913580654⟩⟩,⟨⟨(-29360920253376530885),(-29360688551202368692)⟩,⟨27575263464031884618,27575495166206046815⟩⟩,⟨⟨(-19167915629200520674),(-19167714107896762727)⟩,⟨27023030062212545756,27023231583516303704⟩⟩,⟨⟨(-10950266427509443088),(-10950091569708114627)⟩,⟨24875476044858759623,24875650902660088084⟩⟩,⟨⟨(-4634657535581528357),(-4634506201682772079)⟩,⟨21749710684822021325,21749862018720777602⟩⟩,⟨⟨(-50761215257842629),(-50630547613140100)⟩,⟨18147924251850449215,18148054919495151745⟩⟩,⟨⟨3032487969513711709,3032600504971798331⟩,⟨14457334167943124094,14457446703401210717⟩⟩,⟨⟨4875909242275016449,4876005932039605560⟩,⟨10957184465398996859,10957281155163585970⟩⟩,⟨⟨5745100294952830402,5745183155252126940⟩,⟨7830733545941718987,7830816406241015522⟩⟩,⟨⟨5891642112411630221,5891712954760478848⟩,⟨5180283350759868196,5180354193108716820⟩⟩,⟨⟨5540208363140468047,5540268775900636323⟩,⟨3043532155063642917,3043592567823811193⟩⟩,⟨⟨4880968077336256830,4881019474413518341⟩,⟨1409833979515244590,1409885376592506101⟩⟩,⟨⟨4066450188832141576,4066493799905206291⟩,⟨235284887016958106,235328498090022820⟩⟩,⟨⟨3211925927585557104,3211962848840913651⟩,⟨(-544103487819913465),(-544066566564556924)⟩⟩,⟨⟨2398347015956080232,2398378192926166970⟩,⟨(-1001565341277176946),(-1001534164307090209)⟩⟩,⟨⟨1676934349705351126,1676960613440863292⟩,⟨(-1211224630364376361),(-1211198366628864195)⟩⟩] +lemma kernel100_1_r5_4_eq : ∀ k : Fin 16, kernel100_1Expr 5 4 k = kernel100_1_r5_4 k := by decide +kernel +noncomputable def kernel100_1_r5_5 : Fin 16 → CBox := ![⟨⟨1074623288935421641,1074645354203227872⟩,⟨(-1242148422829327907),(-1242126357561521676)⟩⟩,⟨⟨599715941415220242,599734437383497721⟩,⟨(-1154575588673528986),(-1154557092705251507)⟩⟩,⟨⟨247249460800830988,247264927868963887⟩,⟨(-997983755093307072),(-997968288025174174)⟩⟩,⟨⟨3745714869242638,3758618323330653⟩,⟨(-810607395997246173),(-810594492543158162)⟩⟩,⟨⟨(-148850026016288431),(-148839290422337188)⟩,⟨(-620013546925206965),(-620002811331255719)⟩⟩,⟨⟨(-230114001871586797),(-230105090350486418)⟩,⟨(-444368854172918973),(-444359942651818594)⟩⟩,⟨⟨(-258951939785877496),(-258944562219642417)⟩,⟨(-294081403676568467),(-294074026110333389)⟩⟩,⟨⟨(-252184081837005841),(-252177988567809282)⟩,⟨(-173563125271021817),(-173557032001825257)⟩⟩,⟨⟨(-223781486076898941),(-223776467332297168)⟩,⟨(-82924630145601961),(-82919611401000188)⟩⟩,⟨⟨(-184610417754872309),(-184606290928638512)⟩,⟨(-19477573403036288),(-19473446576802494)⟩⟩,⟨⟨(-142541728905086395),(-142538344117157342)⟩,⟨21024927969398253,21028312757327309⟩⟩,⟨⟨(-102794919330059001),(-102792149609338527)⟩,⟨43434192540954028,43436962261674502⟩⟩,⟨⟨(-68407061385719134),(-68404801169115444)⟩,⟨52529083088866788,52531343305470478⟩⟩,⟨⟨(-40741006505693743),(-40739166185653221)⟩,⟨52584832090381638,52586672410422163⟩⟩,⟨⟨(-19971760201325871),(-19970265801550459)⟩,⟨47143692562046348,47145186961821763⟩⟩,⟨⟨(-5512343195067176),(-5511132240082069)⟩,⟨38939146895112368,38940357850097471⟩⟩] +lemma kernel100_1_r5_5_eq : ∀ k : Fin 16, kernel100_1Expr 5 5 k = kernel100_1_r5_5 k := by decide +kernel +noncomputable def kernel100_1_r5_6 : Fin 16 → CBox := ![⟨⟨3640723918194166,3641702513925271⟩,⟨29927057919893677,29928036515624782⟩⟩,⟨⟨8647589947355207,8648379054253705⟩,⟨21382716931544105,21383506038442599⟩⟩,⟨⟨10645948175698315,10646582805457663⟩,⟨14030490439741809,14031125069501150⟩⟩,⟨⟨10641359237432243,10641868498953837⟩,⟨8181176328473705,8181685589995299⟩⟩,⟨⟨9452752766343189,9453160310502541⟩,⟨3860228221526376,3860635765685729⟩⟩,⟨⟨7698305501319122,7698630949032585⟩,⟨916970036836570,917295484550033⟩⟩,⟨⟨5808078089344538,5808337287461673⟩,⟨(-889526329742788),(-889267131625653)⟩⟩,⟨⟨4051968353701083,4052174342310661⟩,⟨(-1828199020951728),(-1827993032342150)⟩⟩,⟨⟨2574147213369764,2574310689509431⟩,⟨(-2155065887307820),(-2154902411168156)⟩⟩,⟨⟨1427745024204136,1427874557821491⟩,⟨(-2089861256944849),(-2089731723327494)⟩⟩,⟨⟨605879917131008,605982286673256⟩,⟨(-1805996989676300),(-1805894620134051)⟩⟩,⟨⟨67010270692305,67091004685355⟩,⟨(-1429754594413678),(-1429673860420625)⟩⟩,⟨⟨(-245999650584356),(-245936149679929)⟩,⟨(-1045160764467776),(-1045097263563348)⟩⟩,⟨⟨(-392768840385922),(-392718991033367)⟩,⟨(-701735482295498),(-701685632942944)⟩⟩,⟨⟨(-427363587794037),(-427324555385644)⟩,⟨(-423073441917027),(-423034409508634)⟩⟩,⟨⟨(-394221255103238),(-394190750816591)⟩,⟨(-214928449877000),(-214897945590350)⟩⟩] +lemma kernel100_1_r5_6_eq : ∀ k : Fin 16, kernel100_1Expr 5 6 k = kernel100_1_r5_6 k := by decide +kernel +noncomputable def kernel100_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-326901969256944),(-326878192999697)⟩,⟨(-72056329514005),(-72032553256754)⟩⟩,⟨⟨(-248658920209997),(-248640420079316)⟩,⟨16484059966513,16502560097194⟩⟩,⟨⟨(-174009935918706),(-173995574391580)⟩,⟨63568806305718,63583167832845⟩⟩,⟨⟨(-110706141773522),(-110695013837720)⟩,⟨81600217813583,81611345749385⟩⟩,⟨⟨(-61692946563408),(-61684345975399)⟩,⟨81178958184362,81187558772371⟩⟩,⟨⟨(-26826637557666),(-26820001648682)⟩,⟨70565504837366,70572140746349⟩⟩,⟨⟨(-4238015087450),(-4232907507098)⟩,⟨55663856944414,55668964524766⟩⟩,⟨⟨8676417060751,8680341460930⟩,⟨40307459026936,40311383427112⟩⟩,⟨⟨14600689062360,14603699171048⟩,⟨26682327956711,26685338065399⟩⟩,⟨⟨15920442453389,15922748344064⟩,⟨15774961932726,15777267823402⟩⟩,⟨⟨14548207586530,14549969874832⟩,⟨7777395340686,7779157628988⟩⟩,⟨⟨11886487641418,11887832333665⟩,⟨2416177631975,2417522324225⟩⟩,⟨⟨8873218729907,8874242327029⟩,⟨(-803857093753),(-802833496634)⟩⟩,⟨⟨6067541159887,6068319300051⟩,⟨(-2435231047126),(-2434452906967)⟩⟩,⟨⟨3746924462097,3747514692072⟩,⟨(-2989269822127),(-2988679592152)⟩⟩,⟨⟨1997870696307,1998317751001⟩,⟨(-2887124364448),(-2886677309754)⟩⟩] +lemma kernel100_1_r5_7_eq : ∀ k : Fin 16, kernel100_1Expr 5 7 k = kernel100_1_r5_7 k := by decide +kernel +noncomputable def kernel100_1_r5_8 : Fin 16 → CBox := ![⟨⟨791099078755,791436928106⟩,⟨(-2444752695640),(-2444414846290)⟩⟩,⟨⟨38180594220,38435747798⟩,⟨(-1878672290395),(-1878417136817)⟩⟩,⟨⟨(-369590168149),(-369397875694)⟩,⟨(-1322387914885),(-1322195622430)⟩⟩,⟨⟨(-537283624637),(-537138888908)⟩,⟨(-846486187485),(-846341451759)⟩⟩,⟨⟨(-553825439502),(-553716732832)⟩,⟨(-478033376130),(-477924669456)⟩⟩,⟨⟨(-487398772189),(-487317210998)⟩,⟨(-216975649638),(-216894088450)⟩⟩,⟨⟨(-385772856727),(-385711767493)⟩,⟨(-48684703463),(-48623614232)⟩⟩,⟨⟨(-279259529648),(-279213817958)⟩,⟨47293416446,47339128136⟩⟩,⟨⟨(-184686881465),(-184652747056)⟩,⟨91737765742,91771900147⟩⟩,⟨⟨(-109377583520),(-109352114525)⟩,⟨102756780453,102782249451⟩⟩,⟨⟨(-54582936414),(-54563963785)⟩,⟨94551610051,94570582683⟩⟩,⟨⟨(-18152184293),(-18138063066)⟩,⟨77293190428,77307311655⟩⟩,⟨⟨3576144970,3586635812⟩,⟨57612439789,57622930630⟩⟩,⟨⟨14559811438,14567601219⟩,⟨39349790368,39357580151⟩⟩,⟨⟨18367428227,18373202905⟩,⟨24338997969,24344772647⟩⟩,⟨⟨17869250882,17873529241⟩,⟨13100210997,13104489353⟩⟩] +lemma kernel100_1_r5_8_eq : ∀ k : Fin 16, kernel100_1Expr 5 8 k = kernel100_1_r5_8 k := by decide +kernel +noncomputable def kernel100_1_r5_9 : Fin 16 → CBox := ![⟨⟨15170535341,15173699569⟩,⟨5388576060,5391740288⟩⟩,⟨⟨11682489275,11684828807⟩,⟨589941733,592281264⟩⟩,⟨⟨8256032709,8257760006⟩,⟨(-2019324347),(-2017597047)⟩⟩,⟨⟨5329977490,5331252269⟩,⟨(-3120429842),(-3119155064)⟩⟩,⟨⟨3066128292,3067067667⟩,⟨(-3278222940),(-3277283565)⟩⟩,⟨⟨1458633846,1459325993⟩,⟨(-2918556877),(-2917864727)⟩⟩,⟨⟨414572160,415081515⟩,⟨(-2335712392),(-2335203041)⟩⟩,⟨⟨(-191788985),(-191414213)⟩,⟨(-1714534630),(-1714159861)⟩⟩,⟨⟨(-486065963),(-485790582)⟩,⟨(-1157170950),(-1156895573)⟩⟩,⟨⟨(-576573088),(-576370696)⟩,⟨(-708487631),(-708285239)⟩⟩,⟨⟨(-547739652),(-547591052)⟩,⟨(-377253266),(-377104663)⟩⟩,⟨⟨(-459971646),(-459862533)⟩,⟨(-152170628),(-152061519)⟩⟩,⟨⟨(-352886349),(-352806311)⟩,⟨(-12997003),(-12916965)⟩⟩,⟨⟨(-249854036),(-249795287)⟩,⟨62431849,62490598⟩⟩,⟨⟨(-162589495),(-162546412)⟩,⟨94280244,94323328⟩⟩,⟨⟨(-95135944),(-95104182)⟩,⟨98943576,98975339⟩⟩] +lemma kernel100_1_r5_9_eq : ∀ k : Fin 16, kernel100_1Expr 5 9 k = kernel100_1_r5_9 k := by decide +kernel +noncomputable def kernel100_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-46983553),(-46960141)⟩,⟨88641465,88664878⟩⟩,⟨⟨(-15311535),(-15294260)⟩,⟨71772473,71789748⟩⟩,⟨⟨3532538,3545281⟩,⟨53616130,53628877⟩⟩,⟨⟨13150503,13159922⟩,⟨37118733,37128152⟩⟩,⟨⟨16641166,16648108⟩,⟨23615711,23622656⟩⟩,⟨⟨16431843,16436977⟩,⟨13423101,13428236⟩⟩,⟨⟨14280097,14283897⟩,⟨6281365,6285168⟩⟩,⟨⟨11363260,11366071⟩,⟨1662914,1665725⟩⟩,⟨⟨8401557,8403646⟩,⟨(-1032275),(-1030186)⟩⟩,⟨⟨5782331,5783883⟩,⟨(-2365030),(-2363475)⟩⟩,⟨⟨3668199,3669355⟩,⟨(-2803822),(-2802661)⟩⟩,⟨⟨2082760,2083629⟩,⟨(-2708957),(-2708088)⟩⟩,⟨⟨973287,973944⟩,⟨(-2338227),(-2337571)⟩⟩,⟨⟨253368,253863⟩,⟨(-1862954),(-1862456)⟩⟩,⟨⟨(-170530),(-170148)⟩,⟨(-1387438),(-1387056)⟩⟩,⟨⟨(-384150),(-383854)⟩,⟨(-967582),(-967286)⟩⟩] +lemma kernel100_1_r5_10_eq : ∀ k : Fin 16, kernel100_1Expr 5 10 k = kernel100_1_r5_10 k := by decide +kernel +noncomputable def kernel100_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-458608),(-458384)⟩,⟨(-626759),(-626535)⟩⟩,⟨⟨(-448634),(-448455)⟩,⟨(-368210),(-368031)⟩⟩,⟨⟨(-393618),(-393484)⟩,⟨(-184046),(-183909)⟩⟩,⟨⟨(-320098),(-319983)⟩,⟨(-61392),(-61276)⟩⟩,⟨⟨(-244562),(-244465)⟩,⟨13792,13889⟩⟩,⟨⟨(-176210),(-176131)⟩,⟨54530,54609⟩⟩,⟨⟨(-119256),(-119183)⟩,⟨71766,71836⟩⟩,⟨⟨(-74730),(-74673)⟩,⟨74107,74171⟩⟩,⟨⟨(-41848),(-41791)⟩,⟨67892,67952⟩⟩,⟨⟨(-18902),(-18846)⟩,⟨57540,57596⟩⟩,⟨⟨(-3897),(-3845)⟩,⟨45937,45988⟩⟩,⟨⟨5113,5160⟩,⟨34794,34845⟩⟩,⟨⟨9826,9877⟩,⟨25034,25082⟩⟩,⟨⟨11640,11683⟩,⟨17013,17056⟩⟩,⟨⟨11625,11663⟩,⟨10769,10807⟩⟩,⟨⟨10556,10598⟩,⟨6129,6172⟩⟩] +lemma kernel100_1_r5_11_eq : ∀ k : Fin 16, kernel100_1Expr 5 11 k = kernel100_1_r5_11 k := by decide +kernel +noncomputable def kernel100_1_r5_12 : Fin 16 → CBox := ![⟨⟨8987,9030⟩,⟨2850,2892⟩⟩,⟨⟨7277,7311⟩,⟨659,696⟩⟩,⟨⟨5633,5671⟩,⟨(-703),(-665)⟩⟩,⟨⟨4177,4215⟩,⟨(-1464),(-1421)⟩⟩,⟨⟨2958,2991⟩,⟨(-1795),(-1762)⟩⟩,⟨⟨1981,2019⟩,⟨(-1860),(-1822)⟩⟩,⟨⟨1231,1269⟩,⟨(-1753),(-1719)⟩⟩,⟨⟨677,715⟩,⟨(-1552),(-1514)⟩⟩,⟨⟨281,318⟩,⟨(-1313),(-1279)⟩⟩,⟨⟨21,55⟩,⟨(-1070),(-1036)⟩⟩,⟨⟨(-147),(-113)⟩,⟨(-850),(-816)⟩⟩,⟨⟨(-240),(-209)⟩,⟨(-649),(-612)⟩⟩,⟨⟨(-283),(-258)⟩,⟨(-476),(-448)⟩⟩,⟨⟨(-299),(-265)⟩,⟨(-342),(-309)⟩⟩,⟨⟨(-286),(-248)⟩,⟨(-237),(-203)⟩⟩,⟨⟨(-265),(-227)⟩,⟨(-154),(-119)⟩⟩] +lemma kernel100_1_r5_12_eq : ∀ k : Fin 16, kernel100_1Expr 5 12 k = kernel100_1_r5_12 k := by decide +kernel +noncomputable def kernel100_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-234),(-201)⟩,⟨(-92),(-58)⟩⟩,⟨⟨(-207),(-169)⟩,⟨(-51),(-13)⟩⟩,⟨⟨(-173),(-134)⟩,⟨(-19),19⟩⟩,⟨⟨(-144),(-110)⟩,⟨6,40⟩⟩,⟨⟨(-113),(-84)⟩,⟨18,47⟩⟩,⟨⟨(-96),(-57)⟩,⟨22,61⟩⟩,⟨⟨(-70),(-41)⟩,⟨28,57⟩⟩,⟨⟨(-59),(-20)⟩,⟨20,59⟩⟩,⟨⟨(-46),(-12)⟩,⟨19,57⟩⟩,⟨⟨(-38),(-8)⟩,⟨22,52⟩⟩,⟨⟨(-26),4⟩,⟨16,50⟩⟩,⟨⟨(-22),7⟩,⟨16,45⟩⟩,⟨⟨(-19),11⟩,⟨11,40⟩⟩,⟨⟨(-15),18⟩,⟨6,36⟩⟩,⟨⟨(-11),18⟩,⟨6,35⟩⟩,⟨⟨(-13),22⟩,⟨(-3),35⟩⟩] +lemma kernel100_1_r5_13_eq : ∀ k : Fin 16, kernel100_1Expr 5 13 k = kernel100_1_r5_13 k := by decide +kernel +noncomputable def kernel100_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-9),21⟩,⟨(-3),26⟩⟩,⟨⟨(-14),25⟩,⟨(-12),27⟩⟩,⟨⟨(-14),25⟩,⟨(-12),27⟩⟩,⟨⟨(-10),20⟩,⟨(-11),18⟩⟩,⟨⟨(-10),20⟩,⟨(-11),18⟩⟩,⟨⟨(-10),20⟩,⟨(-11),18⟩⟩,⟨⟨(-10),20⟩,⟨(-11),18⟩⟩,⟨⟨(-11),20⟩,⟨(-15),18⟩⟩,⟨⟨(-11),19⟩,⟨(-15),14⟩⟩,⟨⟨(-11),19⟩,⟨(-15),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-11),19⟩,⟨(-16),14⟩⟩] +lemma kernel100_1_r5_14_eq : ∀ k : Fin 16, kernel100_1Expr 5 14 k = kernel100_1_r5_14 k := by decide +kernel +noncomputable def kernel100_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-11),19⟩,⟨(-16),14⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),19⟩,⟨(-20),15⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-16),14⟩,⟨(-19),11⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩,⟨⟨(-20),15⟩,⟨(-19),16⟩⟩] +lemma kernel100_1_r5_15_eq : ∀ k : Fin 16, kernel100_1Expr 5 15 k = kernel100_1_r5_15 k := by decide +kernel +noncomputable def kernel100_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel100_1_r5_0,kernel100_1_r5_1,kernel100_1_r5_2,kernel100_1_r5_3,kernel100_1_r5_4,kernel100_1_r5_5,kernel100_1_r5_6,kernel100_1_r5_7,kernel100_1_r5_8,kernel100_1_r5_9,kernel100_1_r5_10,kernel100_1_r5_11,kernel100_1_r5_12,kernel100_1_r5_13,kernel100_1_r5_14,kernel100_1_r5_15] +lemma kernel100_1_r5_eq (i k : Fin 16) : kernel100_1Expr 5 i k = kernel100_1_r5 i k := by + fin_cases i + · exact kernel100_1_r5_0_eq k + · exact kernel100_1_r5_1_eq k + · exact kernel100_1_r5_2_eq k + · exact kernel100_1_r5_3_eq k + · exact kernel100_1_r5_4_eq k + · exact kernel100_1_r5_5_eq k + · exact kernel100_1_r5_6_eq k + · exact kernel100_1_r5_7_eq k + · exact kernel100_1_r5_8_eq k + · exact kernel100_1_r5_9_eq k + · exact kernel100_1_r5_10_eq k + · exact kernel100_1_r5_11_eq k + · exact kernel100_1_r5_12_eq k + · exact kernel100_1_r5_13_eq k + · exact kernel100_1_r5_14_eq k + · exact kernel100_1_r5_15_eq k +noncomputable def kernel100_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel100_1_r0,kernel100_1_r1,kernel100_1_r2,kernel100_1_r3,kernel100_1_r4,kernel100_1_r5] +lemma kernel100_1_eq (j : Fin 6) (i k : Fin 16) : kernel100_1Expr j i k = kernel100_1 j i k := by + fin_cases j + · exact kernel100_1_r0_eq i k + · exact kernel100_1_r1_eq i k + · exact kernel100_1_r2_eq i k + · exact kernel100_1_r3_eq i k + · exact kernel100_1_r4_eq i k + · exact kernel100_1_r5_eq i k +lemma kernel100_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel100_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(100:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel100_1_eq] + unfold kernel100_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans100_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues20.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues20.lean new file mode 100644 index 0000000000000000000000000000000000000000..50f4cb9dc5f48750b9cd8596667dd92133518ccf --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues20.lean @@ -0,0 +1,3287 @@ +import OAI.Analysis.PlanarPacking.Grid +import OAI.Analysis.PlanarPacking.Certificate.TransformedPowers20 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid IntegerAlpha IntegerCompact +noncomputable def kernel12_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans12 j i k) +noncomputable def kernel12_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_0_eq : ∀ k : Fin 16, kernel12_0Expr 0 0 k = kernel12_0_r0_0 k := by decide +kernel +noncomputable def kernel12_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_1_eq : ∀ k : Fin 16, kernel12_0Expr 0 1 k = kernel12_0_r0_1 k := by decide +kernel +noncomputable def kernel12_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_2_eq : ∀ k : Fin 16, kernel12_0Expr 0 2 k = kernel12_0_r0_2 k := by decide +kernel +noncomputable def kernel12_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_3_eq : ∀ k : Fin 16, kernel12_0Expr 0 3 k = kernel12_0_r0_3 k := by decide +kernel +noncomputable def kernel12_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_4_eq : ∀ k : Fin 16, kernel12_0Expr 0 4 k = kernel12_0_r0_4 k := by decide +kernel +noncomputable def kernel12_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_5_eq : ∀ k : Fin 16, kernel12_0Expr 0 5 k = kernel12_0_r0_5 k := by decide +kernel +noncomputable def kernel12_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_6_eq : ∀ k : Fin 16, kernel12_0Expr 0 6 k = kernel12_0_r0_6 k := by decide +kernel +noncomputable def kernel12_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_7_eq : ∀ k : Fin 16, kernel12_0Expr 0 7 k = kernel12_0_r0_7 k := by decide +kernel +noncomputable def kernel12_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_8_eq : ∀ k : Fin 16, kernel12_0Expr 0 8 k = kernel12_0_r0_8 k := by decide +kernel +noncomputable def kernel12_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_9_eq : ∀ k : Fin 16, kernel12_0Expr 0 9 k = kernel12_0_r0_9 k := by decide +kernel +noncomputable def kernel12_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_10_eq : ∀ k : Fin 16, kernel12_0Expr 0 10 k = kernel12_0_r0_10 k := by decide +kernel +noncomputable def kernel12_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r0_11_eq : ∀ k : Fin 16, kernel12_0Expr 0 11 k = kernel12_0_r0_11 k := by decide +kernel +noncomputable def kernel12_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel12_0_r0_12_eq : ∀ k : Fin 16, kernel12_0Expr 0 12 k = kernel12_0_r0_12 k := by decide +kernel +noncomputable def kernel12_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel12_0_r0_13_eq : ∀ k : Fin 16, kernel12_0Expr 0 13 k = kernel12_0_r0_13 k := by decide +kernel +noncomputable def kernel12_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel12_0_r0_14_eq : ∀ k : Fin 16, kernel12_0Expr 0 14 k = kernel12_0_r0_14 k := by decide +kernel +noncomputable def kernel12_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel12_0_r0_15_eq : ∀ k : Fin 16, kernel12_0Expr 0 15 k = kernel12_0_r0_15 k := by decide +kernel +noncomputable def kernel12_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel12_0_r0_0,kernel12_0_r0_1,kernel12_0_r0_2,kernel12_0_r0_3,kernel12_0_r0_4,kernel12_0_r0_5,kernel12_0_r0_6,kernel12_0_r0_7,kernel12_0_r0_8,kernel12_0_r0_9,kernel12_0_r0_10,kernel12_0_r0_11,kernel12_0_r0_12,kernel12_0_r0_13,kernel12_0_r0_14,kernel12_0_r0_15] +lemma kernel12_0_r0_eq (i k : Fin 16) : kernel12_0Expr 0 i k = kernel12_0_r0 i k := by + fin_cases i + · exact kernel12_0_r0_0_eq k + · exact kernel12_0_r0_1_eq k + · exact kernel12_0_r0_2_eq k + · exact kernel12_0_r0_3_eq k + · exact kernel12_0_r0_4_eq k + · exact kernel12_0_r0_5_eq k + · exact kernel12_0_r0_6_eq k + · exact kernel12_0_r0_7_eq k + · exact kernel12_0_r0_8_eq k + · exact kernel12_0_r0_9_eq k + · exact kernel12_0_r0_10_eq k + · exact kernel12_0_r0_11_eq k + · exact kernel12_0_r0_12_eq k + · exact kernel12_0_r0_13_eq k + · exact kernel12_0_r0_14_eq k + · exact kernel12_0_r0_15_eq k +noncomputable def kernel12_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-7456),(-7452)⟩,⟨48013,48017⟩⟩,⟨⟨(-7459),(-7455)⟩,⟨47900,47905⟩⟩,⟨⟨(-7464),(-7460)⟩,⟨47678,47682⟩⟩,⟨⟨(-7470),(-7466)⟩,⟨47344,47348⟩⟩,⟨⟨(-7476),(-7472)⟩,⟨46904,46908⟩⟩,⟨⟨(-7486),(-7482)⟩,⟨46360,46364⟩⟩,⟨⟨(-7495),(-7491)⟩,⟨45713,45717⟩⟩,⟨⟨(-7503),(-7499)⟩,⟨44972,44976⟩⟩,⟨⟨(-7512),(-7507)⟩,⟨44138,44142⟩⟩,⟨⟨(-7516),(-7512)⟩,⟨43218,43223⟩⟩,⟨⟨(-7519),(-7515)⟩,⟨42217,42221⟩⟩,⟨⟨(-7518),(-7514)⟩,⟨41143,41147⟩⟩,⟨⟨(-7511),(-7507)⟩,⟨40003,40007⟩⟩,⟨⟨(-7498),(-7494)⟩,⟨38801,38806⟩⟩,⟨⟨(-7478),(-7474)⟩,⟨37546,37550⟩⟩,⟨⟨(-7453),(-7449)⟩,⟨36245,36249⟩⟩] +lemma kernel12_0_r1_0_eq : ∀ k : Fin 16, kernel12_0Expr 1 0 k = kernel12_0_r1_0 k := by decide +kernel +noncomputable def kernel12_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-7417),(-7413)⟩,⟨34907,34912⟩⟩,⟨⟨(-7372),(-7367)⟩,⟨33537,33541⟩⟩,⟨⟨(-7318),(-7313)⟩,⟨32145,32150⟩⟩,⟨⟨(-7253),(-7247)⟩,⟨30735,30741⟩⟩,⟨⟨(-7176),(-7172)⟩,⟨29319,29323⟩⟩,⟨⟨(-7088),(-7084)⟩,⟨27897,27901⟩⟩,⟨⟨(-6990),(-6985)⟩,⟨26482,26487⟩⟩,⟨⟨(-6880),(-6875)⟩,⟨25077,25081⟩⟩,⟨⟨(-6758),(-6754)⟩,⟨23687,23691⟩⟩,⟨⟨(-6625),(-6621)⟩,⟨22321,22325⟩⟩,⟨⟨(-6481),(-6477)⟩,⟨20981,20985⟩⟩,⟨⟨(-6329),(-6323)⟩,⟨19669,19675⟩⟩,⟨⟨(-6164),(-6160)⟩,⟨18397,18401⟩⟩,⟨⟨(-5990),(-5986)⟩,⟨17163,17167⟩⟩,⟨⟨(-5808),(-5804)⟩,⟨15969,15973⟩⟩,⟨⟨(-5621),(-5616)⟩,⟨14820,14824⟩⟩] +lemma kernel12_0_r1_1_eq : ∀ k : Fin 16, kernel12_0Expr 1 1 k = kernel12_0_r1_1 k := by decide +kernel +noncomputable def kernel12_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-5426),(-5422)⟩,⟨13720,13724⟩⟩,⟨⟨(-5223),(-5219)⟩,⟨12667,12671⟩⟩,⟨⟨(-5019),(-5015)⟩,⟨11664,11668⟩⟩,⟨⟨(-4809),(-4805)⟩,⟨10712,10716⟩⟩,⟨⟨(-4597),(-4593)⟩,⟨9812,9816⟩⟩,⟨⟨(-4384),(-4380)⟩,⟨8962,8967⟩⟩,⟨⟨(-4170),(-4166)⟩,⟨8162,8167⟩⟩,⟨⟨(-3956),(-3952)⟩,⟨7414,7418⟩⟩,⟨⟨(-3744),(-3739)⟩,⟨6716,6720⟩⟩,⟨⟨(-3533),(-3529)⟩,⟨6064,6069⟩⟩,⟨⟨(-3328),(-3324)⟩,⟨5461,5465⟩⟩,⟨⟨(-3126),(-3122)⟩,⟨4903,4907⟩⟩,⟨⟨(-2928),(-2924)⟩,⟨4387,4392⟩⟩,⟨⟨(-2734),(-2730)⟩,⟨3915,3919⟩⟩,⟨⟨(-2549),(-2544)⟩,⟨3481,3485⟩⟩,⟨⟨(-2369),(-2365)⟩,⟨3085,3089⟩⟩] +lemma kernel12_0_r1_2_eq : ∀ k : Fin 16, kernel12_0Expr 1 2 k = kernel12_0_r1_2 k := by decide +kernel +noncomputable def kernel12_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-2195),(-2191)⟩,⟨2725,2729⟩⟩,⟨⟨(-2029),(-2025)⟩,⟨2401,2405⟩⟩,⟨⟨(-1871),(-1867)⟩,⟨2105,2109⟩⟩,⟨⟨(-1721),(-1717)⟩,⟨1840,1844⟩⟩,⟨⟨(-1578),(-1574)⟩,⟨1601,1605⟩⟩,⟨⟨(-1443),(-1439)⟩,⟨1389,1394⟩⟩,⟨⟨(-1316),(-1312)⟩,⟨1198,1202⟩⟩,⟨⟨(-1199),(-1195)⟩,⟨1029,1033⟩⟩,⟨⟨(-1086),(-1082)⟩,⟨880,884⟩⟩,⟨⟨(-982),(-978)⟩,⟨750,754⟩⟩,⟨⟨(-888),(-884)⟩,⟨634,639⟩⟩,⟨⟨(-797),(-793)⟩,⟨534,538⟩⟩,⟨⟨(-716),(-712)⟩,⟨445,450⟩⟩,⟨⟨(-641),(-637)⟩,⟨372,376⟩⟩,⟨⟨(-571),(-567)⟩,⟨306,310⟩⟩,⟨⟨(-509),(-505)⟩,⟨248,253⟩⟩] +lemma kernel12_0_r1_3_eq : ∀ k : Fin 16, kernel12_0Expr 1 3 k = kernel12_0_r1_3 k := by decide +kernel +noncomputable def kernel12_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-452),(-448)⟩,⟨201,205⟩⟩,⟨⟨(-398),(-394)⟩,⟨162,166⟩⟩,⟨⟨(-351),(-347)⟩,⟨127,131⟩⟩,⟨⟨(-309),(-305)⟩,⟨99,103⟩⟩,⟨⟨(-271),(-267)⟩,⟨76,81⟩⟩,⟨⟨(-238),(-234)⟩,⟨56,60⟩⟩,⟨⟨(-208),(-204)⟩,⟨39,43⟩⟩,⟨⟨(-181),(-176)⟩,⟨26,30⟩⟩,⟨⟨(-156),(-152)⟩,⟨16,20⟩⟩,⟨⟨(-136),(-131)⟩,⟨8,13⟩⟩,⟨⟨(-115),(-111)⟩,⟨1,5⟩⟩,⟨⟨(-100),(-96)⟩,⟨(-5),0⟩⟩,⟨⟨(-86),(-81)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-73),(-68)⟩,⟨(-10),(-6)⟩⟩,⟨⟨(-63),(-59)⟩,⟨(-11),(-7)⟩⟩,⟨⟨(-53),(-49)⟩,⟨(-13),(-9)⟩⟩] +lemma kernel12_0_r1_4_eq : ∀ k : Fin 16, kernel12_0Expr 1 4 k = kernel12_0_r1_4 k := by decide +kernel +noncomputable def kernel12_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-45),(-41)⟩,⟨(-12),(-8)⟩⟩,⟨⟨(-39),(-34)⟩,⟨(-13),(-9)⟩⟩,⟨⟨(-30),(-26)⟩,⟨(-13),(-9)⟩⟩,⟨⟨(-27),(-23)⟩,⟨(-13),(-9)⟩⟩,⟨⟨(-22),(-18)⟩,⟨(-12),(-8)⟩⟩,⟨⟨(-17),(-13)⟩,⟨(-11),(-7)⟩⟩,⟨⟨(-15),(-11)⟩,⟨(-10),(-6)⟩⟩,⟨⟨(-13),(-9)⟩,⟨(-9),(-4)⟩⟩,⟨⟨(-10),(-6)⟩,⟨(-9),(-5)⟩⟩,⟨⟨(-8),(-4)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-8),(-4)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-6),(-2)⟩,⟨(-7),(-2)⟩⟩,⟨⟨(-6),(-2)⟩,⟨(-7),(-2)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩] +lemma kernel12_0_r1_5_eq : ∀ k : Fin 16, kernel12_0Expr 1 5 k = kernel12_0_r1_5 k := by decide +kernel +noncomputable def kernel12_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩,⟨⟨0,4⟩,⟨(-2),2⟩⟩] +lemma kernel12_0_r1_6_eq : ∀ k : Fin 16, kernel12_0Expr 1 6 k = kernel12_0_r1_6 k := by decide +kernel +noncomputable def kernel12_0_r1_7 : Fin 16 → CBox := ![⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨0,4⟩,⟨(-3),2⟩⟩,⟨⟨(-2),3⟩,⟨0,4⟩⟩] +lemma kernel12_0_r1_7_eq : ∀ k : Fin 16, kernel12_0Expr 1 7 k = kernel12_0_r1_7 k := by decide +kernel +noncomputable def kernel12_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),3⟩,⟨(-2),4⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩] +lemma kernel12_0_r1_8_eq : ∀ k : Fin 16, kernel12_0Expr 1 8 k = kernel12_0_r1_8 k := by decide +kernel +noncomputable def kernel12_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r1_9_eq : ∀ k : Fin 16, kernel12_0Expr 1 9 k = kernel12_0_r1_9 k := by decide +kernel +noncomputable def kernel12_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-3),4⟩,⟨(-4),2⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r1_10_eq : ∀ k : Fin 16, kernel12_0Expr 1 10 k = kernel12_0_r1_10 k := by decide +kernel +noncomputable def kernel12_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r1_11_eq : ∀ k : Fin 16, kernel12_0Expr 1 11 k = kernel12_0_r1_11 k := by decide +kernel +noncomputable def kernel12_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r1_12_eq : ∀ k : Fin 16, kernel12_0Expr 1 12 k = kernel12_0_r1_12 k := by decide +kernel +noncomputable def kernel12_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r1_13_eq : ∀ k : Fin 16, kernel12_0Expr 1 13 k = kernel12_0_r1_13 k := by decide +kernel +noncomputable def kernel12_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r1_14_eq : ∀ k : Fin 16, kernel12_0Expr 1 14 k = kernel12_0_r1_14 k := by decide +kernel +noncomputable def kernel12_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel12_0_r1_15_eq : ∀ k : Fin 16, kernel12_0Expr 1 15 k = kernel12_0_r1_15 k := by decide +kernel +noncomputable def kernel12_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel12_0_r1_0,kernel12_0_r1_1,kernel12_0_r1_2,kernel12_0_r1_3,kernel12_0_r1_4,kernel12_0_r1_5,kernel12_0_r1_6,kernel12_0_r1_7,kernel12_0_r1_8,kernel12_0_r1_9,kernel12_0_r1_10,kernel12_0_r1_11,kernel12_0_r1_12,kernel12_0_r1_13,kernel12_0_r1_14,kernel12_0_r1_15] +lemma kernel12_0_r1_eq (i k : Fin 16) : kernel12_0Expr 1 i k = kernel12_0_r1 i k := by + fin_cases i + · exact kernel12_0_r1_0_eq k + · exact kernel12_0_r1_1_eq k + · exact kernel12_0_r1_2_eq k + · exact kernel12_0_r1_3_eq k + · exact kernel12_0_r1_4_eq k + · exact kernel12_0_r1_5_eq k + · exact kernel12_0_r1_6_eq k + · exact kernel12_0_r1_7_eq k + · exact kernel12_0_r1_8_eq k + · exact kernel12_0_r1_9_eq k + · exact kernel12_0_r1_10_eq k + · exact kernel12_0_r1_11_eq k + · exact kernel12_0_r1_12_eq k + · exact kernel12_0_r1_13_eq k + · exact kernel12_0_r1_14_eq k + · exact kernel12_0_r1_15_eq k +noncomputable def kernel12_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-2432977198416696),(-2432977198416693)⟩,⟨2104349443230819,2104349443230822⟩⟩,⟨⟨(-2428629595128951),(-2428629595128948)⟩,⟨2102075268768640,2102075268768643⟩⟩,⟨⟨(-2419956548925550),(-2419956548925547)⟩,⟨2097532303557245,2097532303557248⟩⟩,⟨⟨(-2407002201311577),(-2407002201311573)⟩,⟨2090731318175405,2090731318175409⟩⟩,⟨⟨(-2389832318366185),(-2389832318366181)⟩,⟨2081688475809712,2081688475809715⟩⟩,⟨⟨(-2368533760677786),(-2368533760677783)⟩,⟨2070425339474009,2070425339474013⟩⟩,⟨⟨(-2343213785433251),(-2343213785433248)⟩,⟨2056968879077171,2056968879077175⟩⟩,⟨⟨(-2313999188094751),(-2313999188094747)⟩,⟨2041351476238039,2041351476238043⟩⟩,⟨⟨(-2281035292776701),(-2281035292776696)⟩,⟨2023610924332679,2023610924332684⟩⟩,⟨⟨(-2244484801998262),(-2244484801998258)⟩,⟨2003790420915659,2003790420915663⟩⟩,⟨⟨(-2204526517914209),(-2204526517914205)⟩,⟨1981938549393895,1981938549393899⟩⟩,⟨⟨(-2161353948401120),(-2161353948401116)⟩,⟨1958109246656610,1958109246656614⟩⟩,⟨⟨(-2115173812481314),(-2115173812481310)⟩,⟨1932361753283986,1932361753283990⟩⟩,⟨⟨(-2066204460490457),(-2066204460490453)⟩,⟨1904760542973398,1904760542973402⟩⟩,⟨⟨(-2014674225125811),(-2014674225125808)⟩,⟨1875375227936831,1875375227936835⟩⟩,⟨⟨(-1960819720042733),(-1960819720042730)⟩,⟨1844280437234459,1844280437234462⟩⟩] +lemma kernel12_0_r2_0_eq : ∀ k : Fin 16, kernel12_0Expr 2 0 k = kernel12_0_r2_0 k := by decide +kernel +noncomputable def kernel12_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-1904884102992182),(-1904884102992179)⟩,⟨1811555665313640,1811555665313644⟩⟩,⟨⟨(-1847115320609585),(-1847115320609582)⟩,⟨1777285088413454,1777285088413458⟩⟩,⟨⟨(-1787764351875906),(-1787764351875901)⟩,⟨1741557346963871,1741557346963876⟩⟩,⟨⟨(-1727083466979125),(-1727083466979122)⟩,⟨1704465292645632,1704465292645636⟩⟩,⟨⟨(-1665324517814762),(-1665324517814758)⟩,⟨1666105699369634,1666105699369637⟩⟩,⟨⟨(-1602737275686886),(-1602737275686881)⟩,⟨1626578938070015,1626578938070020⟩⟩,⟨⟨(-1539567830917982),(-1539567830917978)⟩,⟨1585988615868606,1585988615868609⟩⟩,⟨⟨(-1476057068061277),(-1476057068061273)⟩,⟨1544441180845156,1544441180845159⟩⟩,⟨⟨(-1412439229248914),(-1412439229248909)⟩,⟨1502045494322265,1502045494322270⟩⟩,⟨⟨(-1348940576921995),(-1348940576921991)⟩,⟨1458912373231151,1458912373231154⟩⟩,⟨⟨(-1285778165793711),(-1285778165793708)⟩,⟨1415154105749384,1415154105749387⟩⟩,⟨⟨(-1223158732415606),(-1223158732415601)⟩,⟨1370883943980659,1370883943980664⟩⟩,⟨⟨(-1161277709171534),(-1161277709171531)⟩,⟨1326215577966587,1326215577966590⟩⟩,⟨⟨(-1100318367936490),(-1100318367936487)⟩,⟨1281262595769984,1281262595769987⟩⟩,⟨⟨(-1040451097030990),(-1040451097030986)⟩,⟨1236137934738622,1236137934738626⟩⟩,⟨⟨(-981832813498709),(-981832813498706)⟩,⟨1190953329339663,1190953329339666⟩⟩] +lemma kernel12_0_r2_1_eq : ∀ k : Fin 16, kernel12_0Expr 2 1 k = kernel12_0_r2_1 k := by decide +kernel +noncomputable def kernel12_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-924606511157434),(-924606511157431)⟩,⟨1145818761142560,1145818761142563⟩⟩,⟨⟨(-868900943342344),(-868900943342341)⟩,⟨1100841916618216,1100841916618220⟩⟩,⟨⟨(-814830437796041),(-814830437796037)⟩,⟨1056127658413071,1056127658413075⟩⟩,⟨⟨(-762494839779881),(-762494839779876)⟩,⟨1011777515649407,1011777515649412⟩⟩,⟨⟨(-711979578202648),(-711979578202644)⟩,⟨967889198600180,967889198600184⟩⟩,⟨⟨(-663355848399896),(-663355848399890)⟩,⟨924556142792942,924556142792948⟩⟩,⟨⟨(-616680904162613),(-616680904162610)⟩,⟨881867087219735,881867087219739⟩⟩,⟨⟨(-571998450717227),(-571998450717224)⟩,⟨839905690876202,839905690876205⟩⟩,⟨⟨(-529339129607479),(-529339129607476)⟩,⟨798750191333818,798750191333822⟩⟩,⟨⟨(-488721085827519),(-488721085827515)⟩,⟨758473108474503,758473108474507⟩⟩,⟨⟨(-450150607106677),(-450150607106674)⟩,⟨719140995899118,719140995899122⟩⟩,⟨⟨(-413622824949741),(-413622824949737)⟩,⟨680814241872686,680814241872689⟩⟩,⟨⟨(-379122466889425),(-379122466889421)⟩,⟨643546921002291,643546921002295⟩⟩,⟨⟨(-346624649405270),(-346624649405267)⟩,⟨607386697171329,607386697171333⟩⟩,⟨⟨(-316095701098260),(-316095701098255)⟩,⟨572374777588198,572374777588203⟩⟩,⟨⟨(-287494005974209),(-287494005974206)⟩,⟨538545917160945,538545917160949⟩⟩] +lemma kernel12_0_r2_2_eq : ∀ k : Fin 16, kernel12_0Expr 2 2 k = kernel12_0_r2_2 k := by decide +kernel +noncomputable def kernel12_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-260770857070871),(-260770857070867)⟩,⟨505928471792334,505928471792338⟩⟩,⟨⟨(-235871311151508),(-235871311151504)⟩,⟨474544498612779,474544498612783⟩⟩,⟨⟨(-212735035768732),(-212735035768729)⟩,⟨444409900640170,444409900640174⟩⟩,⟨⟨(-191297140662272),(-191297140662268)⟩,⟨415534612883476,415534612883479⟩⟩,⟨⟨(-171488986178953),(-171488986178949)⟩,⟨387922826497171,387922826497174⟩⟩,⟨⟨(-153238962177630),(-153238962177627)⟩,⟨361573247250641,361573247250645⟩⟩,⟨⟨(-136473231691395),(-136473231691392)⟩,⟨336479384303776,336479384303780⟩⟩,⟨⟨(-121116434449933),(-121116434449928)⟩,⟨312629865078628,312629865078632⟩⟩,⟨⟨(-107092346202302),(-107092346202299)⟩,⟨290008771887160,290008771887163⟩⟩,⟨⟨(-94324490611840),(-94324490611836)⟩,⟨268595995915665,268595995915669⟩⟩,⟨⟨(-82736701308102),(-82736701308098)⟩,⟨248367604174550,248367604174554⟩⟩,⟨⟨(-72253632464851),(-72253632464847)⟩,⟨229296215094165,229296215094168⟩⟩,⟨⟨(-62801217018264),(-62801217018260)⟩,⟨211351378578540,211351378578544⟩⟩,⟨⟨(-54307072337567),(-54307072337563)⟩,⟨194499956513321,194499956513325⟩⟩,⟨⟨(-46700853804041),(-46700853804037)⟩,⟨178706499955870,178706499955874⟩⟩,⟨⟨(-39914557338422),(-39914557338417)⟩,⟨163933619507451,163933619507456⟩⟩] +lemma kernel12_0_r2_3_eq : ∀ k : Fin 16, kernel12_0Expr 2 3 k = kernel12_0_r2_3 k := by decide +kernel +noncomputable def kernel12_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-33882772437016),(-33882772437012)⟩,⟨150142345672465,150142345672469⟩⟩,⟨⟨(-28542887730682),(-28542887730679)⟩,⟨137292476340643,137292476340646⟩⟩,⟨⟨(-23835251466893),(-23835251466889)⟩,⟨125342908877674,125342908877677⟩⟩,⟨⟨(-19703289633385),(-19703289633382)⟩,⟨114251954670752,114251954670756⟩⟩,⟨⟨(-16093584693408),(-16093584693404)⟩,⟨103977634341206,103977634341210⟩⟩,⟨⟨(-12955918089671),(-12955918089667)⟩,⟨94477952200416,94477952200420⟩⟩,⟨⟨(-10243279799588),(-10243279799584)⟩,⟨85711148881676,85711148881680⟩⟩,⟨⟨(-7911848292461),(-7911848292458)⟩,⟨77635931424300,77635931424303⟩⟩,⟨⟨(-5920944254034),(-5920944254031)⟩,⟨70211680412492,70211680412496⟩⟩,⟨⟨(-4232961410661),(-4232961410657)⟩,⟨63398634076564,63398634076567⟩⟩,⟨⟨(-2813277709237),(-2813277709233)⟩,⟨57158049544510,57158049544513⟩⟩,⟨⟨(-1630149995801),(-1630149995798)⟩,⟨51452341685643,51452341685647⟩⟩,⟨⟨(-654595190818),(-654595190814)⟩,⟨46245200213056,46245200213059⟩⟩,⟨⟨139739211689,139739211693⟩,⟨41501685906987,41501685906990⟩⟩,⟨⟨776712685398,776712685402⟩,⟨37188306986563,37188306986567⟩⟩,⟨⟨1277834824190,1277834824194⟩,⟨33273076792799,33273076792803⟩⟩] +lemma kernel12_0_r2_4_eq : ∀ k : Fin 16, kernel12_0Expr 2 4 k = kernel12_0_r2_4 k := by decide +kernel +noncomputable def kernel12_0_r2_5 : Fin 16 → CBox := ![⟨⟨1662411893751,1662411893755⟩,⟨29725554052020,29725554052023⟩⟩,⟨⟨1947694792775,1947694792779⟩,⟨26516867067195,26516867067199⟩⟩,⟨⟨2149026658617,2149026658621⟩,⟨23619723236463,23619723236467⟩⟩,⟨⟨2279988574300,2279988574304⟩,⟨21008405325473,21008405325476⟩⟩,⟨⟨2352542050580,2352542050584⟩,⟨18658755925012,18658755925016⟩⟩,⟨⟨2377167165278,2377167165283⟩,⟨16548151510096,16548151510101⟩⟩,⟨⟨2362995440257,2362995440261⟩,⟨14655467483784,14655467483787⟩⟩,⟨⟨2317936722167,2317936722171⟩,⟨12961035540673,12961035540676⟩⟩,⟨⟨2248799505314,2248799505317⟩,⟨11446594624134,11446594624138⟩⟩,⟨⟨2161404292396,2161404292400⟩,⟨10095236679885,10095236679888⟩⟩,⟨⟨2060689731163,2060689731167⟩,⟨8891348329136,8891348329139⟩⟩,⟨⟨1950811391804,1950811391809⟩,⟨7820549499293,7820549499298⟩⟩,⟨⟨1835233161192,1835233161196⟩,⟨6869629960992,6869629960996⟩⟩,⟨⟨1716811326354,1716811326358⟩,⟨6026484629268,6026484629272⟩⟩,⟨⟨1597871501240,1597871501244⟩,⟨5280048395161,5280048395165⟩⟩,⟨⟨1480278618692,1480278618696⟩,⟨4620231163814,4620231163818⟩⟩] +lemma kernel12_0_r2_5_eq : ∀ k : Fin 16, kernel12_0Expr 2 5 k = kernel12_0_r2_5 k := by decide +kernel +noncomputable def kernel12_0_r2_6 : Fin 16 → CBox := ![⟨⟨1365500264470,1365500264474⟩,⟨4037853687212,4037853687216⟩⟩,⟨⟨1254663673104,1254663673107⟩,⟨3524584695230,3524584695233⟩⟩,⟨⟨1148606737377,1148606737380⟩,⟨3072879748491,3072879748495⟩⟩,⟨⟨1047923405464,1047923405468⟩,⟨2675922161321,2675922161325⟩⟩,⟨⟨953003853194,953003853198⟩,⟨2327566273183,2327566273187⟩⟩,⟨⟨864069824811,864069824815⟩,⟨2022283283099,2022283283102⟩⟩,⟨⟨781205534865,781205534870⟩,⟨1755109803315,1755109803321⟩⟩,⟨⟨704384517688,704384517692⟩,⟨1521599236508,1521599236512⟩⟩,⟨⟨633492800078,633492800082⟩,⟨1317776034567,1317776034571⟩⟩,⟨⟨568348758360,568348758364⟩,⟨1140092856781,1140092856784⟩⟩,⟨⟨508720003665,508720003670⟩,⟨985390610336,985390610341⟩⟩,⟨⟨454337619809,454337619813⟩,⟨850861326618,850861326622⟩⟩,⟨⟨404908057283,404908057287⟩,⟨734013802227,734013802231⟩⟩,⟨⟨360122965026,360122965030⟩,⟨632641913620,632641913624⟩⟩,⟨⟨319667219527,319667219531⟩,⟨544795498470,544795498474⟩⟩,⟨⟨283225388624,283225388627⟩,⟨468753684826,468753684830⟩⟩] +lemma kernel12_0_r2_6_eq : ∀ k : Fin 16, kernel12_0Expr 2 6 k = kernel12_0_r2_6 k := by decide +kernel +noncomputable def kernel12_0_r2_7 : Fin 16 → CBox := ![⟨⟨250486845673,250486845677⟩,⟨403000540469,403000540473⟩⟩,⟨⟨221149728570,221149728574⟩,⟨346202909185,346202909189⟩⟩,⟨⟨194923918060,194923918064⟩,⟨297190297568,297190297571⟩⟩,⟨⟨171533190529,171533190533⟩,⟨254936675141,254936675145⟩⟩,⟨⟨150716682554,150716682558⟩,⟨218544051515,218544051519⟩⟩,⟨⟨132229787878,132229787881⟩,⟨187227696969,187227696973⟩⟩,⟨⟨115844591950,115844591954⟩,⟨160302876615,160302876619⟩⟩,⟨⟨101349935263,101349935267⟩,⟨137172973192,137172973196⟩⟩,⟨⟨88551183820,88551183824⟩,⟨117318879141,117318879145⟩⟩,⟨⟨77269773647,77269773651⟩,⟨100289544769,100289544773⟩⟩,⟨⟨67342585946,67342585950⟩,⟨85693575908,85693575912⟩⟩,⟨⟨58621200307,58621200310⟩,⟨73191781150,73191781154⟩⟩,⟨⟨50971065433,50971065437⟩,⟨62490575698,62490575701⟩⟩,⟨⟨44270619695,44270619699⟩,⟨53336155584,53336155588⟩⟩,⟨⟨38410387712,38410387716⟩,⟨45509362780,45509362783⟩⟩,⟨⟨33292073917,33292073921⟩,⟨38821168174,38821168178⟩⟩] +lemma kernel12_0_r2_7_eq : ∀ k : Fin 16, kernel12_0Expr 2 7 k = kernel12_0_r2_7 k := by decide +kernel +noncomputable def kernel12_0_r2_8 : Fin 16 → CBox := ![⟨⟨28827669484,28827669487⟩,⟨33108705701,33108705705⟩⟩,⟨⟨24938585152,24938585157⟩,⟨28231796787,28231796792⟩⟩,⟨⟨21554819299,21554819303⟩,⟨24069909983,24069909987⟩⟩,⟨⟨18614167835,18614167839⟩,⟨20519505905,20519505909⟩⟩,⟨⟨16061480352,16061480356⟩,⟨17491722551,17491722554⟩⟩,⟨⟨13847965071,13847965075⟩,⟨14910360621,14910360625⟩⟩,⟨⟨11930543739,11930543743⟩,⟨12710132732,12710132736⟩⟩,⟨⟨10271256416,10271256419⟩,⟨10835144241,10835144245⟩⟩,⟨⟨8836715250,8836715254⟩,⟨9237576960,9237576963⟩⟩,⟨⟨7597605633,7597605637⟩,⟨7876550284,7876550288⟩⟩,⟨⟨6528232616,6528232620⟩,⟨6717137144,6717137148⟩⟩,⟨⟨5606110202,5606110205⟩,⟨5729514815,5729514819⟩⟩,⟨⟨4811590813,4811590817⟩,⟨4888233054,4888233058⟩⟩,⟨⟨4127532191,4127532195⟩,⟨4171584061,4171584065⟩⟩,⟨⟨3538998904,3538998908⟩,⟨3561060749,3561060753⟩⟩,⟨⟨3032995673,3032995677⟩,⟨3040891424,3040891428⟩⟩] +lemma kernel12_0_r2_8_eq : ∀ k : Fin 16, kernel12_0Expr 2 8 k = kernel12_0_r2_8 k := by decide +kernel +noncomputable def kernel12_0_r2_9 : Fin 16 → CBox := ![⟨⟨2598229816,2598229820⟩,⟨2597640526,2597640530⟩⟩,⟨⟨2224900170,2224900174⟩,⟨2219866389,2219866393⟩⟩,⟨⟨1904510011,1904510014⟩,⟨1897828119,1897828123⟩⟩,⟨⟨1629701653,1629701657⟩,⟨1623234812,1623234816⟩⟩,⟨⟨1394110521,1394110525⟩,⟨1389031121,1389031125⟩⟩,⟨⟨1192236675,1192236679⟩,⟨1189214074,1189214078⟩⟩,⟨⟨1019331928,1019331932⟩,⟨1018676699,1018676703⟩⟩,⟨⟨871300871,871300875⟩,⟨873074607,873074611⟩⟩,⟨⟨744614194,744614198⟩,⟨748712257,748712261⟩⟩,⟨⟨636232967,636232971⟩,⟨642446019,642446023⟩⟩,⟨⟨543542568,543542572⟩,⟨551601643,551601647⟩⟩,⟨⟨464295103,464295107⟩,⟨473903979,473903983⟩⟩,⟨⟨396559343,396559347⟩,⟨407417194,407417198⟩⟩,⟨⟨338677211,338677215⟩,⟨350493907,350493911⟩⟩,⟨⟨289226052,289226056⟩,⟨301731936,301731939⟩⟩,⟨⟨246985918,246985924⟩,⟨259937547,259937552⟩⟩] +lemma kernel12_0_r2_9_eq : ∀ k : Fin 16, kernel12_0Expr 2 9 k = kernel12_0_r2_9 k := by decide +kernel +noncomputable def kernel12_0_r2_10 : Fin 16 → CBox := ![⟨⟨210911276,210911280⟩,⟨224094200,224094204⟩⟩,⟨⟨180106528,180106532⟩,⟨193336000,193336004⟩⟩,⟨⟨153804891,153804895⟩,⟨166925135,166925139⟩⟩,⟨⟨131350161,131350165⟩,⟨144232726,144232729⟩⟩,⟨⟨112181006,112181010⟩,⟨124722522,124722526⟩⟩,⟨⟨95817431,95817435⟩,⟨107937099,107937103⟩⟩,⟨⟨81849141,81849145⟩,⟨93486088,93486092⟩⟩,⟨⟨69925539,69925543⟩,⟨81036208,81036212⟩⟩,⟨⟨59747123,59747127⟩,⟨70302781,70302785⟩⟩,⟨⟨51058110,51058114⟩,⟨61042520,61042524⟩⟩,⟨⟨43640105,43640111⟩,⟨53047414,53047420⟩⟩,⟨⟨37306684,37306688⟩,⟨46139517,46139521⟩⟩,⟨⟨31898732,31898736⟩,⟨40166510,40166514⟩⟩,⟨⟨27280470,27280474⟩,⟨34997954,34997958⟩⟩,⟨⟨23336051,23336055⟩,⟨30522064,30522068⟩⟩,⟨⟨19966638,19966642⟩,⟨26643006,26643010⟩⟩] +lemma kernel12_0_r2_10_eq : ∀ k : Fin 16, kernel12_0Expr 2 10 k = kernel12_0_r2_10 k := by decide +kernel +noncomputable def kernel12_0_r2_11 : Fin 16 → CBox := ![⟨⟨17087922,17087926⟩,⟨23278550,23278554⟩⟩,⟨⟨14627981,14627985⟩,⟨20358111,20358115⟩⟩,⟨⟨12525471,12525475⟩,⟨17821059,17821063⟩⟩,⟨⟨10728067,10728071⟩,⟨15615271,15615275⟩⟩,⟨⟨9191140,9191144⟩,⟨13695928,13695932⟩⟩,⟨⟨7876620,7876624⟩,⟨12024448,12024452⟩⟩,⟨⟨6752032,6752036⟩,⟨10567608,10567612⟩⟩,⟨⟨5789672,5789676⟩,⟨9296775,9296779⟩⟩,⟨⟨4965906,4965910⟩,⟨8187253,8187257⟩⟩,⟨⟨4260569,4260573⟩,⟨7217738,7217742⟩⟩,⟨⟨3656452,3656456⟩,⟨6369827,6369831⟩⟩,⟨⟨3138866,3138871⟩,⟨5627617,5627623⟩⟩,⟨⟨2695275,2695279⟩,⟨4977360,4977364⟩⟩,⟨⟨2314973,2314977⟩,⟨4407155,4407159⟩⟩,⟨⟨1988825,1988829⟩,⟨3906696,3906700⟩⟩,⟨⟨1709022,1709026⟩,⟨3467053,3467057⟩⟩] +lemma kernel12_0_r2_11_eq : ∀ k : Fin 16, kernel12_0Expr 2 11 k = kernel12_0_r2_11 k := by decide +kernel +noncomputable def kernel12_0_r2_12 : Fin 16 → CBox := ![⟨⟨1468893,1468897⟩,⟨3080483,3080487⟩⟩,⟨⟨1262742,1262746⟩,⟨2740263,2740267⟩⟩,⟨⟨1085698,1085702⟩,⟨2440558,2440562⟩⟩,⟨⟨933596,933600⟩,⟨2176292,2176296⟩⟩,⟨⟨802877,802881⟩,⟨1943058,1943062⟩⟩,⟨⟨690494,690499⟩,⟨1737011,1737015⟩⟩,⟨⟨593840,593844⟩,⟨1554806,1554810⟩⟩,⟨⟨510686,510690⟩,⟨1393529,1393533⟩⟩,⟨⟨439121,439125⟩,⟨1250637,1250641⟩⟩,⟨⟨377507,377511⟩,⟨1123907,1123911⟩⟩,⟨⟨324444,324448⟩,⟨1011400,1011404⟩⟩,⟨⟨278729,278733⟩,⟨911419,911423⟩⟩,⟨⟨239334,239338⟩,⟨822483,822487⟩⟩,⟨⟨205373,205378⟩,⟨743286,743290⟩⟩,⟨⟨176092,176096⟩,⟨672694,672699⟩⟩,⟨⟨150833,150838⟩,⟨609708,609712⟩⟩] +lemma kernel12_0_r2_12_eq : ∀ k : Fin 16, kernel12_0Expr 2 12 k = kernel12_0_r2_12 k := by decide +kernel +noncomputable def kernel12_0_r2_13 : Fin 16 → CBox := ![⟨⟨129043,129047⟩,⟨553447,553452⟩⟩,⟨⟨110239,110243⟩,⟨503144,503148⟩⟩,⟨⟨94009,94013⟩,⟨458121,458125⟩⟩,⟨⟨80000,80004⟩,⟨417782,417786⟩⟩,⟨⟨67903,67907⟩,⟨381603,381607⟩⟩,⟨⟨57457,57461⟩,⟨349121,349125⟩⟩,⟨⟨48438,48442⟩,⟨319930,319934⟩⟩,⟨⟨40647,40651⟩,⟨293667,293671⟩⟩,⟨⟨33922,33926⟩,⟨270014,270019⟩⟩,⟨⟨28112,28116⟩,⟨248693,248698⟩⟩,⟨⟨23096,23100⟩,⟨229454,229458⟩⟩,⟨⟨18765,18769⟩,⟨212075,212079⟩⟩,⟨⟨15029,15033⟩,⟨196363,196368⟩⟩,⟨⟨11805,11809⟩,⟨182143,182148⟩⟩,⟨⟨9024,9028⟩,⟨169264,169268⟩⟩,⟨⟨6626,6630⟩,⟨157587,157591⟩⟩] +lemma kernel12_0_r2_13_eq : ∀ k : Fin 16, kernel12_0Expr 2 13 k = kernel12_0_r2_13 k := by decide +kernel +noncomputable def kernel12_0_r2_14 : Fin 16 → CBox := ![⟨⟨4560,4565⟩,⟨146991,146995⟩⟩,⟨⟨2783,2787⟩,⟨137368,137372⟩⟩,⟨⟨1252,1256⟩,⟨128621,128625⟩⟩,⟨⟨(-64),(-59)⟩,⟨120668,120673⟩⟩,⟨⟨(-1192),(-1188)⟩,⟨113430,113434⟩⟩,⟨⟨(-2162),(-2158)⟩,⟨106836,106840⟩⟩,⟨⟨(-2991),(-2987)⟩,⟨100830,100834⟩⟩,⟨⟨(-3701),(-3697)⟩,⟨95355,95359⟩⟩,⟨⟨(-4309),(-4305)⟩,⟨90363,90367⟩⟩,⟨⟨(-4825),(-4821)⟩,⟨85810,85814⟩⟩,⟨⟨(-5265),(-5261)⟩,⟨81656,81660⟩⟩,⟨⟨(-5638),(-5634)⟩,⟨77867,77871⟩⟩,⟨⟨(-5953),(-5949)⟩,⟨74414,74418⟩⟩,⟨⟨(-6220),(-6216)⟩,⟨71266,71270⟩⟩,⟨⟨(-6445),(-6440)⟩,⟨68400,68404⟩⟩,⟨⟨(-6635),(-6630)⟩,⟨65791,65797⟩⟩] +lemma kernel12_0_r2_14_eq : ∀ k : Fin 16, kernel12_0Expr 2 14 k = kernel12_0_r2_14 k := by decide +kernel +noncomputable def kernel12_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-6790),(-6786)⟩,⟨63423,63427⟩⟩,⟨⟨(-6923),(-6918)⟩,⟨61275,61279⟩⟩,⟨⟨(-7030),(-7025)⟩,⟨59332,59336⟩⟩,⟨⟨(-7120),(-7116)⟩,⟨57579,57583⟩⟩,⟨⟨(-7194),(-7190)⟩,⟨56004,56009⟩⟩,⟨⟨(-7253),(-7249)⟩,⟨54598,54602⟩⟩,⟨⟨(-7303),(-7299)⟩,⟨53346,53350⟩⟩,⟨⟨(-7340),(-7336)⟩,⟨52243,52247⟩⟩,⟨⟨(-7372),(-7368)⟩,⟨51280,51284⟩⟩,⟨⟨(-7398),(-7394)⟩,⟨50452,50456⟩⟩,⟨⟨(-7416),(-7412)⟩,⟨49751,49755⟩⟩,⟨⟨(-7430),(-7426)⟩,⟨49175,49179⟩⟩,⟨⟨(-7442),(-7438)⟩,⟨48719,48723⟩⟩,⟨⟨(-7448),(-7444)⟩,⟨48379,48383⟩⟩,⟨⟨(-7453),(-7449)⟩,⟨48153,48157⟩⟩,⟨⟨(-7457),(-7453)⟩,⟨48041,48045⟩⟩] +lemma kernel12_0_r2_15_eq : ∀ k : Fin 16, kernel12_0Expr 2 15 k = kernel12_0_r2_15 k := by decide +kernel +noncomputable def kernel12_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel12_0_r2_0,kernel12_0_r2_1,kernel12_0_r2_2,kernel12_0_r2_3,kernel12_0_r2_4,kernel12_0_r2_5,kernel12_0_r2_6,kernel12_0_r2_7,kernel12_0_r2_8,kernel12_0_r2_9,kernel12_0_r2_10,kernel12_0_r2_11,kernel12_0_r2_12,kernel12_0_r2_13,kernel12_0_r2_14,kernel12_0_r2_15] +lemma kernel12_0_r2_eq (i k : Fin 16) : kernel12_0Expr 2 i k = kernel12_0_r2 i k := by + fin_cases i + · exact kernel12_0_r2_0_eq k + · exact kernel12_0_r2_1_eq k + · exact kernel12_0_r2_2_eq k + · exact kernel12_0_r2_3_eq k + · exact kernel12_0_r2_4_eq k + · exact kernel12_0_r2_5_eq k + · exact kernel12_0_r2_6_eq k + · exact kernel12_0_r2_7_eq k + · exact kernel12_0_r2_8_eq k + · exact kernel12_0_r2_9_eq k + · exact kernel12_0_r2_10_eq k + · exact kernel12_0_r2_11_eq k + · exact kernel12_0_r2_12_eq k + · exact kernel12_0_r2_13_eq k + · exact kernel12_0_r2_14_eq k + · exact kernel12_0_r2_15_eq k +noncomputable def kernel12_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-10124295648347683059616),(-10124295648347683031415)⟩,⟨15854028366635499886968,15854028366635499915069⟩⟩,⟨⟨(-10107205133207755377569),(-10107205133207755349394)⟩,⟨15844704748321173982325,15844704748321174010400⟩⟩,⟨⟨(-10073086153275817190266),(-10073086153275817162150)⟩,⟨15826057069218827672674,15826057069218827700691⟩⟩,⟨⟨(-10022062515936913307474),(-10022062515936913279444)⟩,⟨15798084611745678753712,15798084611745678781645⟩⟩,⟨⟨(-9954319200333263541810),(-9954319200333263513893)⟩,⟨15760786715675282155448,15760786715675282183267⟩⟩,⟨⟨(-9870101482798102845227),(-9870101482798102817452)⟩,⟨15714163271203118704415,15714163271203118732094⟩⟩,⟨⟨(-9769713777026834598836),(-9769713777026834571230)⟩,⟨15658215365928377087144,15658215365928377114655⟩⟩,⟨⟨(-9653518194348012443189),(-9653518194348012415780)⟩,⟨15592946076964222345705,15592946076964222373021⟩⟩,⟨⟨(-9521932830792792930121),(-9521932830792792902933)⟩,⟨15518361397389837108164,15518361397389837135260⟩⟩,⟨⟨(-9375429788992823988505),(-9375429788992823961567)⟩,⟨15434471284387225352678,15434471284387225379527⟩⟩,⟨⟨(-9214532944260353005663),(-9214532944260352978999)⟩,⟨15341290814686726318669,15341290814686726345246⟩⟩,⟨⟨(-9039815465517084871019),(-9039815465517084844653)⟩,⟨15238841431398244097858,15238841431398244124139⟩⟩,⟨⟨(-8851897103035476970730),(-8851897103035476944685)⟩,⟨15127152264949261093532,15127152264949261119495⟩⟩,⟨⟨(-8651441256232204400653),(-8651441256232204374952)⟩,⟨15006261509702508796703,15006261509702508822324⟩⟩,⟨⟨(-8439151836001916976076),(-8439151836001916950741)⟩,⟨14876217836900083469443,14876217836900083494703⟩⟩,⟨⟨(-8215769937292571627593),(-8215769937292571602644)⟩,⟨14737081823888630381764,14737081823888630406639⟩⟩] +lemma kernel12_0_r3_0_eq : ∀ k : Fin 16, kernel12_0Expr 3 0 k = kernel12_0_r3_0 k := by decide +kernel +noncomputable def kernel12_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-7982070338793008419767),(-7982070338793008395223)⟩,⟨14588927379131081939782,14588927379131081964255⟩⟩,⟨⟨(-7738857847719581643886),(-7738857847719581619767)⟩,⟨14431843142310588589262,14431843142310588613315⟩⟩,⟨⟨(-7486963508741283037494),(-7486963508741283013816)⟩,⟨14265933838885057324114,14265933838885057347729⟩⟩,⟨⟨(-7227240697060944669401),(-7227240697060944646180)⟩,⟨14091321568756439630353,14091321568756439653513⟩⟩,⟨⟨(-6960561116562304291679),(-6960561116562304268931)⟩,⟨13908147009274882963562,13908147009274882986253⟩⟩,⟨⟨(-6687810724727137292640),(-6687810724727137270378)⟩,⟨13716570513598339671246,13716570513598339693456⟩⟩,⟨⟨(-6409885606711355509286),(-6409885606711355487525)⟩,⟨13516773086464483626405,13516773086464483648117⟩⟩,⟨⟨(-6127687821532084441804),(-6127687821532084420554)⟩,⟨13308957220692168917984,13308957220692168939190⟩⟩,⟨⟨(-5842121243747726928991),(-5842121243747726908260)⟩,⟨13093347579199722658093,13093347579199722678782⟩⟩,⟨⟨(-5554087424298950009975),(-5554087424298949989773)⟩,⟨12870191508989985341056,12870191508989985361220⟩⟩,⟨⟨(-5264481494310267397491),(-5264481494310267377825)⟩,⟨12639759375387616866906,12639759375387616886538⟩⟩,⟨⟨(-4974188135620385340360),(-4974188135620385321238)⟩,⟨12402344706800943916225,12402344706800943935317⟩⟩,⟨⟨(-4684077641607007973159),(-4684077641607007954584)⟩,⟨12158264142394707723192,12158264142394707741741⟩⟩,⟨⟨(-4395002091492184231243),(-4395002091492184213220)⟩,⟨11907857177275940564878,11907857177275940582878⟩⟩,⟨⟨(-4107791660753111146888),(-4107791660753111129420)⟩,⟨11651485702085913400330,11651485702085913417778⟩⟩,⟨⟨(-3823251089518131566684),(-3823251089518131549772)⟩,⟨11389533336228649468553,11389533336228649485449⟩⟩] +lemma kernel12_0_r3_1_eq : ∀ k : Fin 16, kernel12_0Expr 3 1 k = kernel12_0_r3_1 k := by decide +kernel +noncomputable def kernel12_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-3542156329898139008210),(-3542156329898138991854)⟩,⟨11122404556322172913874,11122404556322172930217⟩⟩,⟨⟨(-3265251392091637318231),(-3265251392091637302429)⟩,⟨10850523623803402719645,10850523623803402735438⟩⟩,⟨⟨(-2993245407811549452039),(-2993245407811549436791)⟩,⟨10574333317922398688363,10574333317922398703606⟩⟩,⟨⟨(-2726809928120177924977),(-2726809928120177910280)⟩,⟨10294293482597936397640,10294293482597936412335⟩⟩,⟨⟨(-2466576471134551886822),(-2466576471134551872670)⟩,⟨10010879397746367226112,10010879397746367240263⟩⟩,⟨⟨(-2213134333289198858523),(-2213134333289198844912)⟩,⟨9724579987712839967391,9724579987712839981005⟩⟩,⟨⟨(-1967028675930910657951),(-1967028675930910644876)⟩,⟨9435895881303219693459,9435895881303219706540⟩⟩,⟨⟨(-1728758896986285227302),(-1728758896986285214756)⟩,⟨9145337339613350060365,9145337339613350072919⟩⟩,⟨⟨(-1498777295305706382453),(-1498777295305706370429)⟩,⟨8853422069358821201452,8853422069358821213487⟩⟩,⟨⟨(-1277488033066794022730),(-1277488033066794011219)⟩,⟨8560672940704818834431,8560672940704818845956⟩⟩,⟨⟨(-1065246399337636152571),(-1065246399337636141564)⟩,⟨8267615629666433466049,8267615629666433477072⟩⟩,⟨⟨(-862358375578041981616),(-862358375578041971102)⟩,⟨7974776205982516669284,7974776205982516679815⟩⟩,⟨⟨(-669080501519392436154),(-669080501519392426123)⟩,⟨7682678687951501308353,7682678687951501318403⟩⟩,⟨⟨(-485620037534861332880),(-485620037534861323323)⟩,⟨7391842586049605230593,7391842586049605240171⟩⟩,⟨⟨(-312135417316630584542),(-312135417316630575446)⟩,⟨7102780457227980458901,7102780457227980468019⟩⟩,⟨⟨(-148736982440000906919),(-148736982440000898272)⟩,⟨6815995491606566143551,6815995491606566152221⟩⟩] +lemma kernel12_0_r3_2_eq : ∀ k : Fin 16, kernel12_0Expr 3 2 k = kernel12_0_r3_2 k := by decide +kernel +noncomputable def kernel12_0_r3_3 : Fin 16 → CBox := ![⟨⟨4512011759606081297,4512011759606089507⟩,⟨6531979152852991806532,6531979152852991814766⟩⟩,⟨⟨147594131618213557040,147594131618213564826⟩,⟨6251208892862545550572,6251208892862545558384⟩⟩,⟨⟨280536256423367468148,280536256423367475521⟩,⟨5974145960450880239877,5974145960450880247277⟩⟩,⟨⟨403407841851129173360,403407841851129180332⟩,⟨5701233322648734975105,5701233322648734982106⟩⟩,⟨⟨516318973467546176518,516318973467546183106⟩,⟨5432893715864276324122,5432893715864276330739⟩⟩,⟨⟨619418229614846774829,619418229614846781046⟩,⟨5169527842673043574725,5169527842673043580971⟩⟩,⟨⟨712890374213981182188,712890374213981188044⟩,⟨4911512728329490369639,4911512728329490375526⟩⟩,⟨⟨796953901012959931300,796953901012959936812⟩,⟨4659200249291231755249,4659200249291231760792⟩⟩,⟨⟨871858451585248609885,871858451585248615065⟩,⟨4412915844132346773784,4412915844132346778995⟩⟩,⟨⟨937882129927707551319,937882129927707556182⟩,⟨4172957415221613038305,4172957415221613043198⟩⟩,⟨⟨995328736819663051992,995328736819663056549⟩,⟨3939594427482261683153,3939594427482261687741⟩⟩,⟨⟨1044524947183158639293,1044524947183158643558⟩,⟨3713067208458965960441,3713067208458965964737⟩⟩,⟨⟨1085817453531796869912,1085817453531796873899⟩,⟨3493586451822455642898,3493586451822455646915⟩⟩,⟨⟨1119570098217361725133,1119570098217361728856⟩,⟨3281332924369031153164,3281332924369031156916⟩⟩,⟨⟨1146161016588000072397,1146161016588000075866⟩,⟨3076457374547100646558,3076457374547100650057⟩⟩,⟨⟨1165979812370247556592,1165979812370247559822⟩,⟨2879080638590189515283,2879080638590189518541⟩⟩] +lemma kernel12_0_r3_3_eq : ∀ k : Fin 16, kernel12_0Expr 3 3 k = kernel12_0_r3_3 k := by decide +kernel +noncomputable def kernel12_0_r3_4 : Fin 16 → CBox := ![⟨⟨1179424785593239005976,1179424785593239008978⟩,⟨2689293938478585085380,2689293938478585088411⟩⟩,⟨⟨1186900232202956464813,1186900232202956467598⟩,⟨2507159364210879401760,2507159364210879404574⟩⟩,⟨⟨1188813833185257557321,1188813833185257559902⟩,⟨2332710531260976082284,2332710531260976084891⟩⟩,⟨⟨1185574149548316364830,1185574149548316367218⟩,⟨2165953402642034622303,2165953402642034624717⟩⟩,⟨⟨1177588237929000662473,1177588237929000664678⟩,⟨2006867263710138044672,2006867263710138046903⟩⟩,⟨⟨1165259399905641451671,1165259399905641453708⟩,⟨1855405836728249686505,1855405836728249688568⟩⟩,⟨⟨1148985076344344020064,1148985076344344022047⟩,⟨1711498521283507164870,1711498521283507166876⟩⟩,⟨⟨1129154896300490556430,1129154896300490558359⟩,⟨1575051745913454698723,1575051745913454700672⟩⟩,⟨⟨1106148888164410447008,1106148888164410448881⟩,⟨1445950415751950988466,1445950415751950990358⟩⟩,⟨⟨1080335858902990568467,1080335858902990570285⟩,⟨1324059440652921719332,1324059440652921721166⟩⟩,⟨⟨1052071945429206996293,1052071945429206998055⟩,⟨1209225328086869953309,1209225328086869955085⟩⟩,⟨⟨1021699340350114751007,1021699340350114752712⟩,⟨1101277825125578752338,1101277825125578754057⟩⟩,⟨⟨989545192620375676917,989545192620375678567⟩,⟨1000031594026833339399,1000031594026833341060⟩⟩,⟨⟨955920681981036809385,955920681981036810978⟩,⟨905287906293196155045,905287906293196156649⟩⟩,⟨⟨921120264508335255415,921120264508335256954⟩,⟨816836340594918608478,816836340594918610026⟩⟩,⟨⟨885421085149206390075,885421085149206391558⟩,⟨734456470603356138850,734456470603356140341⟩⟩] +lemma kernel12_0_r3_4_eq : ∀ k : Fin 16, kernel12_0Expr 3 4 k = kernel12_0_r3_4 k := by decide +kernel +noncomputable def kernel12_0_r3_5 : Fin 16 → CBox := ![⟨⟨849082551791239064327,849082551791239065755⟩,⟨657919529562796528486,657919529562796529921⟩⟩,⟨⟨812346064215207446385,812346064215207447759⟩,⟨586990039319377987851,586990039319377989231⟩⟩,⟨⟨775434890215932181138,775434890215932182458⟩,⟨521427392508960267726,521427392508960269052⟩⟩,⟨⟨738554180257748432841,738554180257748434109⟩,⟨460987377664148899970,460987377664148901242⟩⟩,⟨⟨701891111257716517791,701891111257716519009⟩,⟨405423638116715333590,405423638116715334812⟩⟩,⟨⟨665615149464157339043,665615149464157340209⟩,⟨354489056728067067211,354489056728067068379⟩⟩,⟨⟨629878421919299369387,629878421919299370503⟩,⟨307937059660237244985,307937059660237246104⟩⟩,⟨⟨594816185659992334289,594816185659992335357⟩,⟨265522833586735669720,265522833586735670789⟩⟩,⟨⟨560547383614965619251,560547383614965620270⟩,⟨227004451921025125481,227004451921025126502⟩⟩,⟨⟨527175276094733530711,527175276094733531685⟩,⟨192143906795884796848,192143906795884797823⟩⟩,⟨⟨494788136833267686682,494788136833267687611⟩,⟨160708044646223252720,160708044646223253650⟩⟩,⟨⟨463460002720011672424,463460002720011673309⟩,⟨132469404319069954430,132469404319069955314⟩⟩,⟨⟨433251466646710380654,433251466646710381495⟩,⟨107206957647010563292,107206957647010564133⟩⟩,⟨⟨404210503275052967661,404210503275052968462⟩,⟨84706753366256043171,84706753366256043972⟩⟩,⟨⟨376373317996870554628,376373317996870555389⟩,⟨64762466130424721355,64762466130424722116⟩⟩,⟨⟨349765209896788777212,349765209896788777935⟩,⟨47175853160116895157,47175853160116895879⟩⟩] +lemma kernel12_0_r3_5_eq : ∀ k : Fin 16, kernel12_0Expr 3 5 k = kernel12_0_r3_5 k := by decide +kernel +noncomputable def kernel12_0_r3_6 : Fin 16 → CBox := ![⟨⟨324401440125834365924,324401440125834366610⟩,⟨31757121772176192653,31757121772176193338⟩⟩,⟨⟨300288097741576531710,300288097741576532359⟩,⟨18325211648379313770,18325211648379314417⟩⟩,⟨⟨277422955754192626042,277422955754192626657⟩,⟨6707996229846441205,6707996229846441819⟩⟩,⟨⟨255796310826997000490,255796310826997001071⟩,⟨(-3257591939243528865),(-3257591939243528285)⟩⟩,⟨⟨235391800803593602497,235391800803593603046⟩,⟨(-11725506745712119533),(-11725506745712118985)⟩⟩,⟨⟨216187194961684716150,216187194961684716668⟩,⟨(-18840599482459382684),(-18840599482459382167)⟩⟩,⟨⟨198155152616223496419,198155152616223496908⟩,⟨(-24738689645997790696),(-24738689645997790208)⟩⟩,⟨⟨181263946403411795046,181263946403411795508⟩,⟨(-29546689833735196210),(-29546689833735195749)⟩⟩,⟨⟨165478147264300560869,165478147264300561304⟩,⟨(-33382778986711101316),(-33382778986711100882)⟩⟩,⟨⟨150759268805684404008,150759268805684404418⟩,⟨(-36356618258740249734),(-36356618258740249325)⟩⟩,⟨⟨137066369340809805520,137066369340809805904⟩,⟨(-38569603888825029116),(-38569603888825028733)⟩⟩,⟨⟨124356610498337868887,124356610498337869248⟩,⟨(-40115151603753496598),(-40115151603753496238)⟩⟩,⟨⟨112585771831191276783,112585771831191277122⟩,⟨(-41079007275295223660),(-41079007275295223322)⟩⟩,⟨⟨101708721354492271245,101708721354492271563⟩,⟨(-41539578794559743565),(-41539578794559743248)⟩⟩,⟨⟨91679842391791719840,91679842391791720138⟩,⟨(-41568284398147622714),(-41568284398147622417)⟩⟩,⟨⟨82453417510080616623,82453417510080616904⟩,⟨(-41229912980098341489),(-41229912980098341209)⟩⟩] +lemma kernel12_0_r3_6_eq : ∀ k : Fin 16, kernel12_0Expr 3 6 k = kernel12_0_r3_6 k := by decide +kernel +noncomputable def kernel12_0_r3_7 : Fin 16 → CBox := ![⟨⟨73983970676338647054,73983970676338647318⟩,⟨(-40582992243950103759),(-40582992243950103496)⟩⟩,⟨⟨66226569072005651622,66226569072005651868⟩,⟨(-39680160884412126726),(-39680160884412126481)⟩⟩,⟨⟨59137086257803103287,59137086257803103516⟩,⟨(-38568541332523085357),(-38568541332523085128)⟩⟩,⟨⟨52672428591392896664,52672428591392896879⟩,⟨(-37290109946471655005),(-37290109946471654790)⟩⟩,⟨⟨46790726966533872368,46790726966533872567⟩,⟨(-35882061877696499373),(-35882061877696499174)⟩⟩,⟨⟨41451496067180140511,41451496067180140698⟩,⟨(-34377168184170303380),(-34377168184170303194)⟩⟩,⟨⟨36615763416180184996,36615763416180185172⟩,⟨(-32804123096125788856),(-32804123096125788681)⟩⟩,⟨⟨32246170548948237932,32246170548948238096⟩,⟨(-31187879660641066303),(-31187879660641066139)⟩⟩,⟨⟨28307048660927618599,28307048660927618752⟩,⟨(-29549972297723545030),(-29549972297723544878)⟩⟩,⟨⟨24764471067190632004,24764471067190632148⟩,⟨(-27908825089576808171),(-27908825089576808027)⟩⟩,⟨⟨21586284776501836550,21586284776501836683⟩,⟨(-26280044894849393409),(-26280044894849393276)⟩⟩,⟨⟨18742123423974191910,18742123423974192034⟩,⟨(-24676698629553952175),(-24676698629553952051)⟩⟩,⟨⟨16203403729366049551,16203403729366049666⟩,⟨(-23109574285144398856),(-23109574285144398741)⟩⟩,⟨⟨13943307555284844906,13943307555284845015⟩,⟨(-21587425461476374379),(-21587425461476374271)⟩⟩,⟨⟨11936751534116025882,11936751534116025982⟩,⟨(-20117199377938495078),(-20117199377938494978)⟩⟩,⟨⟨10160346117240152298,10160346117240152393⟩,⟨(-18704248490131892117),(-18704248490131892022)⟩⟩] +lemma kernel12_0_r3_7_eq : ∀ k : Fin 16, kernel12_0Expr 3 7 k = kernel12_0_r3_7 k := by decide +kernel +noncomputable def kernel12_0_r3_8 : Fin 16 → CBox := ![⟨⟨8592345777692300709,8592345777692300797⟩,⟨(-17352525982574329512),(-17352525982574329424)⟩⟩,⟨⟨7212591970291854032,7212591970291854116⟩,⟨(-16064765530730769987),(-16064765530730769904)⟩⟩,⟨⟨6002450323632803229,6002450323632803305⟩,⟨(-14842645829140380020),(-14842645829140379943)⟩⟩,⟨⟨4944743408143472074,4944743408143472147⟩,⟨(-13686940467595944860),(-13686940467595944788)⟩⟩,⟨⟨4023680295430657025,4023680295430657092⟩,⟨(-12597653805434187874),(-12597653805434187806)⟩⟩,⟨⟨3224783997811916493,3224783997811916556⟩,⟨(-11574143546302772265),(-11574143546302772202)⟩⟩,⟨⟨2534817754577835172,2534817754577835231⟩,⟨(-10615230753628403904),(-10615230753628403846)⟩⟩,⟨⟨1941711014161123434,1941711014161123488⟩,⟨(-9719298071797219555),(-9719298071797219501)⟩⟩,⟨⟨1434485849861968462,1434485849861968512⟩,⟨(-8884376931155349777),(-8884376931155349727)⟩⟩,⟨⟨1003184441736723286,1003184441736723334⟩,⟨(-8108224517709085101),(-8108224517709085052)⟩⟩,⟨⟨638798159169866654,638798159169866698⟩,⟨(-7388391282179607734),(-7388391282179607690)⟩⟩,⟨⟨333198687826148301,333198687826148344⟩,⟨(-6722279749124477307),(-6722279749124477264)⟩⟩,⟨⟨79071561285750604,79071561285750643⟩,⟨(-6107195366390452600),(-6107195366390452562)⟩⟩,⟨⟨(-130147618262119144),(-130147618262119108)⟩,⟨(-5540390109349086147),(-5540390109349086111)⟩⟩,⟨⟨(-300334054424976200),(-300334054424976166)⟩,⟨(-5019099524245606957),(-5019099524245606923)⟩⟩,⟨⟨(-436731571575048221),(-436731571575048191)⟩,⟨(-4540573861534171767),(-4540573861534171736)⟩⟩] +lemma kernel12_0_r3_8_eq : ∀ k : Fin 16, kernel12_0Expr 3 8 k = kernel12_0_r3_8 k := by decide +kernel +noncomputable def kernel12_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-544007270163702602),(-544007270163702573)⟩,⟨(-4102103914160557667),(-4102103914160557638)⟩⟩,⟨⟨(-626302969811395877),(-626302969811395850)⟩,⟨(-3701042138178480960),(-3701042138178480933)⟩⟩,⟨⟨(-687283428927611167),(-687283428927611143)⟩,⟨(-3334819594550118962),(-3334819594550118938)⟩⟩,⟨⟨(-730181365014858481),(-730181365014858458)⟩,⟨(-3000959212099826623),(-3000959212099826600)⟩⟩,⟨⟨(-757839329703819733),(-757839329703819711)⟩,⟨(-2697085832893075021),(-2697085832893074999)⟩⟩,⟨⟨(-772748517387568513),(-772748517387568493)⟩,⟨(-2420933463250942895),(-2420933463250942875)⟩⟩,⟨⟨(-777084606512282820),(-777084606512282800)⟩,⟨(-2170350116559680891),(-2170350116559680871)⟩⟩,⟨⟨(-772740748579457461),(-772740748579457443)⟩,⟨(-1943300598300957428),(-1943300598300957410)⟩⟩,⟨⟨(-761357832151918075),(-761357832151918058)⟩,⟨(-1737867549553579819),(-1737867549553579802)⟩⟩,⟨⟨(-744352158051296742),(-744352158051296725)⟩,⟨(-1552251032786102444),(-1552251032786102427)⟩⟩,⟨⟨(-722940667888804587),(-722940667888804572)⟩,⟨(-1384766913204281931),(-1384766913204281916)⟩⟩,⟨⟨(-698163871463895247),(-698163871463895232)⟩,⟨(-1233844260324421899),(-1233844260324421884)⟩⟩,⟨⟨(-670906619753018081),(-670906619753018068)⟩,⟨(-1098021967859765909),(-1098021967859765896)⟩⟩,⟨⟨(-641916869524143378),(-641916869524143365)⟩,⟨(-975944765444186278),(-975944765444186265)⟩⟩,⟨⟨(-611822583356864437),(-611822583356864424)⟩,⟨(-866358773158099351),(-866358773158099338)⟩⟩,⟨⟨(-581146905300692988),(-581146905300692977)⟩,⟨(-768106729224012170),(-768106729224012158)⟩⟩] +lemma kernel12_0_r3_9_eq : ∀ k : Fin 16, kernel12_0Expr 3 9 k = kernel12_0_r3_9 k := by decide +kernel +noncomputable def kernel12_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-550321747817075458),(-550321747817075448)⟩,⟨(-680123002541656725),(-680123002541656714)⟩⟩,⟨⟨(-519699920248936720),(-519699920248936710)⟩,⟨(-601428484857783746),(-601428484857783735)⟩⟩,⟨⟨(-489565923045180150),(-489565923045180140)⟩,⟨(-531125442223762753),(-531125442223762743)⟩⟩,⟨⟨(-460145525512341984),(-460145525512341975)⟩,⟨(-468392391886768035),(-468392391886768026)⟩⟩,⟨⟨(-431614238124481767),(-431614238124481757)⟩,⟨(-412479058783224643),(-412479058783224634)⟩⟩,⟨⟨(-404104783527006451),(-404104783527006442)⟩,⟨(-362701455248667678),(-362701455248667670)⟩⟩,⟨⟨(-377713663432326896),(-377713663432326888)⟩,⟨(-318437118317326200),(-318437118317326191)⟩⟩,⟨⟨(-352506911718762772),(-352506911718762764)⟩,⟨(-279120530949256629),(-279120530949256620)⟩⟩,⟨⟨(-328525117286212039),(-328525117286212031)⟩,⟨(-244238746586474184),(-244238746586474175)⟩⟩,⟨⟨(-305787793655229389),(-305787793655229381)⟩,⟨(-213327230499306041),(-213327230499306033)⟩⟩,⟨⟨(-284297165969539666),(-284297165969539658)⟩,⟨(-185965926341394328),(-185965926341394320)⟩⟩,⟨⟨(-264041440013191961),(-264041440013191954)⟩,⟨(-161775552092643112),(-161775552092643105)⟩⟩,⟨⟨(-244997612109861454),(-244997612109861447)⟩,⟨(-140414126045633298),(-140414126045633291)⟩⟩,⟨⟨(-227133873351702899),(-227133873351702893)⟩,⟨(-121573720600132895),(-121573720600132890)⟩⟩,⟨⟨(-210411656519546911),(-210411656519546904)⟩,⟨(-104977439295812235),(-104977439295812228)⟩⟩,⟨⟨(-194787369309593421),(-194787369309593415)⟩,⟨(-90376610664692574),(-90376610664692568)⟩⟩] +lemma kernel12_0_r3_10_eq : ∀ k : Fin 16, kernel12_0Expr 3 10 k = kernel12_0_r3_10 k := by decide +kernel +noncomputable def kernel12_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-180213853073236255),(-180213853073236249)⟩,⟨(-77548191057776453),(-77548191057776448)⟩⟩,⟨⟨(-166641602201003215),(-166641602201003209)⟩,⟨(-66292367536165415),(-66292367536165409)⟩⟩,⟨⟨(-154019775530043917),(-154019775530043912)⟩,⟨(-56430351162871645),(-56430351162871639)⟩⟩,⟨⟨(-142297027715600176),(-142297027715600173)⟩,⟨(-47802350539995624),(-47802350539995621)⟩⟩,⟨⟨(-131422185366804975),(-131422185366804969)⟩,⟨(-40265715164613924),(-40265715164613918)⟩⟩,⟨⟨(-121344789890803799),(-121344789890803795)⟩,⟨(-33693238088042191),(-33693238088042187)⟩⟩,⟨⟨(-112015526400375035),(-112015526400375030)⟩,⟨(-27971607424014473),(-27971607424014469)⟩⟩,⟨⟨(-103386555702134084),(-103386555702134080)⟩,⟨(-22999996432776295),(-22999996432776290)⟩⟩,⟨⟨(-95411764277974246),(-95411764277974242)⟩,⟨(-18688782184925555),(-18688782184925551)⟩⟩,⟨⟨(-88046945284597767),(-88046945284597762)⟩,⟨(-14958383159287176),(-14958383159287172)⟩⟩,⟨⟨(-81249921908068389),(-81249921908068384)⟩,⟨(-11738206534515516),(-11738206534515512)⟩⟩,⟨⟨(-74980622905979862),(-74980622905979856)⟩,⟨(-8965696378614577),(-8965696378614571)⟩⟩,⟨⟨(-69201118833398912),(-69201118833398907)⟩,⟨(-6585474410773088),(-6585474410773083)⟩⟩,⟨⟨(-63875626265239304),(-63875626265239298)⟩,⟨(-4548565494663744),(-4548565494663738)⟩⟩,⟨⟨(-58970486282983571),(-58970486282983565)⟩,⟨(-2811700512436782),(-2811700512436776)⟩⟩,⟨⟨(-54454122574364166),(-54454122574364162)⟩,⟨(-1336689756539684),(-1336689756539681)⟩⟩] +lemma kernel12_0_r3_11_eq : ∀ k : Fin 16, kernel12_0Expr 3 11 k = kernel12_0_r3_11 k := by decide +kernel +noncomputable def kernel12_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-50296983688292568),(-50296983688292562)⟩,⟨(-89860456196046),(-89860456196040)⟩⟩,⟨⟨(-46471473282412920),(-46471473282412915)⟩,⟨958447477857205,958447477857210⟩⟩,⟨⟨(-42951871586462336),(-42951871586462331)⟩,⟨1834332956574802,1834332956574807⟩⟩,⟨⟨(-39714250771308277),(-39714250771308273)⟩,⟨2560737499006710,2560737499006714⟩⟩,⟨⟨(-36736386452101394),(-36736386452101390)⟩,⟨3157805927362939,3157805927362942⟩⟩,⟨⟨(-33997667156223142),(-33997667156223138)⟩,⟨3643208208788510,3643208208788513⟩⟩,⟨⟨(-31479003245171960),(-31479003245171957)⟩,⟨4032426317540356,4032426317540359⟩⟩,⟨⟨(-29162736487483540),(-29162736487483535)⟩,⟨4339009650182401,4339009650182405⟩⟩,⟨⟨(-27032551231151368),(-27032551231151364)⟩,⟨4574802208480410,4574802208480413⟩⟩,⟨⟨(-25073387913356437),(-25073387913356434)⟩,⟨4750144469453297,4750144469453301⟩⟩,⟨⟨(-23271359467757193),(-23271359467757189)⟩,⟨4874052588865379,4874052588865382⟩⟩,⟨⟨(-21613671040789193),(-21613671040789189)⟩,⟨4954377332496282,4954377332496286⟩⟩,⟨⟨(-20088543304519056),(-20088543304519053)⟩,⟨4997944897848833,4997944897848837⟩⟩,⟨⟨(-18685139551171201),(-18685139551171198)⟩,⟨5010681576511602,5010681576511605⟩⟩,⟨⟨(-17393496670481303),(-17393496670481300)⟩,⟨4997724013089468,4997724013089471⟩⟩,⟨⟨(-16204460042871971),(-16204460042871966)⟩,⟨4963516639333361,4963516639333366⟩⟩] +lemma kernel12_0_r3_12_eq : ∀ k : Fin 16, kernel12_0Expr 3 12 k = kernel12_0_r3_12 k := by decide +kernel +noncomputable def kernel12_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-15109622326764774),(-15109622326764768)⟩,⟨4911897700714679,4911897700714685⟩⟩,⟨⟨(-14101266075101670),(-14101266075101667)⟩,⟨4846175146087646,4846175146087650⟩⟩,⟨⟨(-13172310082572973),(-13172310082572970)⟩,⟨4769193518176709,4769193518176713⟩⟩,⟨⟨(-12316259339596087),(-12316259339596083)⟩,⟨4683392862363736,4683392862363741⟩⟩,⟨⟨(-11527158450423922),(-11527158450423918)⟩,⟨4590860562622594,4590860562622598⟩⟩,⟨⟨(-10799548359731957),(-10799548359731953)⟩,⟨4493376915496784,4493376915496787⟩⟩,⟨⟨(-10128426223647582),(-10128426223647578)⟩,⟨4392455164831276,4392455164831279⟩⟩,⟨⟨(-9509208256595926),(-9509208256595922)⟩,⟨4289376640699360,4289376640699365⟩⟩,⟨⟨(-8937695383818523),(-8937695383818518)⟩,⟨4185221574811008,4185221574811013⟩⟩,⟨⟨(-8410041530359730),(-8410041530359727)⟩,⟨4080896100907815,4080896100907818⟩⟩,⟨⟨(-7922724380189830),(-7922724380189827)⟩,⟨3977155891552144,3977155891552147⟩⟩,⟨⟨(-7472518443505225),(-7472518443505222)⟩,⟨3874626831667920,3874626831667923⟩⟩,⟨⟨(-7056470275747826),(-7056470275747822)⟩,⟨3773823083601928,3773823083601931⟩⟩,⟨⟨(-6671875698212127),(-6671875698212122)⟩,⟨3675162857809432,3675162857809437⟩⟩,⟨⟨(-6316258877006771),(-6316258877006767)⟩,⟨3578982167034656,3578982167034661⟩⟩,⟨⟨(-5987353124400268),(-5987353124400264)⟩,⟨3485546809605675,3485546809605679⟩⟩] +lemma kernel12_0_r3_13_eq : ∀ k : Fin 16, kernel12_0Expr 3 13 k = kernel12_0_r3_13 k := by decide +kernel +noncomputable def kernel12_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-5683083294038938),(-5683083294038935)⟩,⟨3395062798786115,3395062798786118⟩⟩,⟨⟨(-5401549649043436),(-5401549649043433)⟩,⟨3307685429651051,3307685429651055⟩⟩,⟨⟨(-5141013089460006),(-5141013089460003)⟩,⟨3223527152345172,3223527152345176⟩⟩,⟨⟨(-4899881632879339),(-4899881632879335)⟩,⟨3142664400533245,3142664400533249⟩⟩,⟨⟨(-4676698049174692),(-4676698049174689)⟩,⟨3065143506091187,3065143506091191⟩⟩,⟨⟨(-4470128557203010),(-4470128557203006)⟩,⟨2990985815362969,2990985815362974⟩⟩,⟨⟨(-4278952497923394),(-4278952497923390)⟩,⟨2920192108401231,2920192108401235⟩⟩,⟨⟨(-4102052904692592),(-4102052904692587)⟩,⟨2852746410317653,2852746410317658⟩⟩,⟨⟨(-3938407897482831),(-3938407897482826)⟩,⟨2788619273013180,2788619273013185⟩⟩,⟨⟨(-3787082833425986),(-3787082833425981)⟩,⟨2727770595977201,2727770595977206⟩⟩,⟨⟨(-3647223151418986),(-3647223151418981)⟩,⟨2670152046394797,2670152046394802⟩⟩,⟨⟨(-3518047853531864),(-3518047853531860)⟩,⟨2615709131353605,2615709131353609⟩⟩,⟨⟨(-3398843570649535),(-3398843570649530)⟩,⟨2564382968381730,2564382968381734⟩⟩,⟨⟨(-3288959164161247),(-3288959164161243)⟩,⟨2516111794773235,2516111794773239⟩⟩,⟨⟨(-3187800819600198),(-3187800819600194)⟩,⟨2470832251076753,2470832251076756⟩⟩,⟨⟨(-3094827591943662),(-3094827591943658)⟩,⟨2428480469654482,2428480469654486⟩⟩] +lemma kernel12_0_r3_14_eq : ∀ k : Fin 16, kernel12_0Expr 3 14 k = kernel12_0_r3_14 k := by decide +kernel +noncomputable def kernel12_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3009547365826245),(-3009547365826242)⟩,⟨2388992995291147,2388992995291151⟩⟩,⟨⟨(-2931513197210949),(-2931513197210944)⟩,⟨2352307561381070,2352307561381075⟩⟩,⟨⟨(-2860320006120548),(-2860320006120544)⟩,⟨2318363742189474,2318363742189478⟩⟩,⟨⟨(-2795601592871383),(-2795601592871379)⟩,⟨2287103499020709,2287103499020713⟩⟩,⟨⟨(-2737027952888823),(-2737027952888818)⟩,⟨2258471635786393,2258471635786398⟩⟩,⟨⟨(-2684302867634165),(-2684302867634162)⟩,⟨2232416177410464,2232416177410467⟩⟩,⟨⟨(-2637161751451862),(-2637161751451859)⟩,⟨2208888682700492,2208888682700495⟩⟩,⟨⟨(-2595369736268502),(-2595369736268499)⟩,⟨2187844501723545,2187844501723549⟩⟩,⟨⟨(-2558719978055656),(-2558719978055652)⟩,⟨2169242986322596,2169242986322599⟩⟩,⟨⟨(-2527032170821122),(-2527032170821118)⟩,⟨2153047661170658,2153047661170661⟩⟩,⟨⟨(-2500151255631062),(-2500151255631057)⟩,⟨2139226361662284,2139226361662289⟩⟩,⟨⟨(-2477946313801857),(-2477946313801853)⟩,⟨2127751343965646,2127751343965650⟩⟩,⟨⟨(-2460309634947775),(-2460309634947770)⟩,⟨2118599371685016,2118599371685021⟩⟩,⟨⟨(-2447155952040952),(-2447155952040948)⟩,⟨2111751782796875,2111751782796878⟩⟩,⟨⟨(-2438421837045342),(-2438421837045339)⟩,⟨2107194539807888,2107194539807891⟩⟩,⟨⟨(-2434065252037748),(-2434065252037745)⟩,⟨2104918265426243,2104918265426247⟩⟩] +lemma kernel12_0_r3_15_eq : ∀ k : Fin 16, kernel12_0Expr 3 15 k = kernel12_0_r3_15 k := by decide +kernel +noncomputable def kernel12_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel12_0_r3_0,kernel12_0_r3_1,kernel12_0_r3_2,kernel12_0_r3_3,kernel12_0_r3_4,kernel12_0_r3_5,kernel12_0_r3_6,kernel12_0_r3_7,kernel12_0_r3_8,kernel12_0_r3_9,kernel12_0_r3_10,kernel12_0_r3_11,kernel12_0_r3_12,kernel12_0_r3_13,kernel12_0_r3_14,kernel12_0_r3_15] +lemma kernel12_0_r3_eq (i k : Fin 16) : kernel12_0Expr 3 i k = kernel12_0_r3 i k := by + fin_cases i + · exact kernel12_0_r3_0_eq k + · exact kernel12_0_r3_1_eq k + · exact kernel12_0_r3_2_eq k + · exact kernel12_0_r3_3_eq k + · exact kernel12_0_r3_4_eq k + · exact kernel12_0_r3_5_eq k + · exact kernel12_0_r3_6_eq k + · exact kernel12_0_r3_7_eq k + · exact kernel12_0_r3_8_eq k + · exact kernel12_0_r3_9_eq k + · exact kernel12_0_r3_10_eq k + · exact kernel12_0_r3_11_eq k + · exact kernel12_0_r3_12_eq k + · exact kernel12_0_r3_13_eq k + · exact kernel12_0_r3_14_eq k + · exact kernel12_0_r3_15_eq k +noncomputable def kernel12_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-190294465751390749344999308),(-190294465751390747550373643)⟩,⟨186917050175515676878891785,186917050175515678670836243⟩⟩,⟨⟨(-190099826104370494156492128),(-190099826104370492362738349)⟩,⟨186900618830887801756639586,186900618830887803547716245⟩⟩,⟨⟨(-189710914599268081195696568),(-189710914599268079403688751)⟩,⟨186867505401626774958562917,186867505401626776747901782⟩⟩,⟨⟨(-189128466305762734981424021),(-189128466305762733192034022)⟩,⟨186817210081345947810057327,186817210081345949596790605⟩⟩,⟨⟨(-188353582554187013836974832),(-188353582554187012051071194)⟩,⟨186748987335307874549143207,186748987335307876332406380⟩⟩,⟨⟨(-187387729396225519384301391),(-187387729396225517602748247)⟩,⟨186661850884463717030686808,186661850884463718809619735⟩⟩,⟨⟨(-186232735535577980285123515),(-186232735535577978508779535)⟩,⟨186554580307996401201305429,186554580307996402975053378⟩⟩,⟨⟨(-184890789714457446020262334),(-184890789714457444249979513)⟩,⟨186425729227865551273230421,186425729227865553040945278⟩⟩,⟨⟨(-183364437538740397215945715),(-183364437538740395452568614)⟩,⟨186273635030002968683233071,186273635030002970444074088⟩⟩,⟨⟨(-181656577721843017090494398),(-181656577721843015334858512)⟩,⟨186096430068143504656475667,186096430068143506409611080⟩⟩,⟨⟨(-179770457725021466441350989),(-179770457725021464694282598)⟩,⟨185892054287835765158594465,185892054287835766903201639⟩⟩,⟨⟨(-177709668769834570900540077),(-177709668769834569162853921)⟩,⟨185658269199998846822792360,185658269199998848558060106⟩⟩,⟨⟨(-175478140197011105448197803),(-175478140197011103720698003)⟩,⟨185392673125514384584858800,185392673125514386309986441⟩⟩,⟨⟨(-173080133144971975232886802),(-173080133144971973516363060)⟩,⟨185092717624807200104103220,185092717624807201818304383⟩⟩,⟨⟨(-170520233520805553414222012),(-170520233520805551709452252)⟩,⟨184755725019212750617910507,184755725019212752320410480⟩⟩,⟨⟨(-167803344236611680473505311),(-167803344236611678781250332)⟩,⟨184378906904195617627212400,184378906904195619317253462⟩⟩] +lemma kernel12_0_r4_0_eq : ∀ k : Fin 16, kernel12_0Expr 4 0 k = kernel12_0_r4_0 k := by decide +kernel +noncomputable def kernel12_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-164934676684839308922311199),(-164934676684839307243319524)⟩,⟨183959383548210756742948561,183959383548210758419785134⟩⟩,⟨⟨(-161919741427560616662620595),(-161919741427560614997619805)⟩,⟨183494204065228343954925769,183494204065228345617833071⟩⟩,⟨⟨(-158764338076559618046880478),(-158764338076559616396585622)⟩,⟨182980367243713612752571251,182980367243713614400836882⟩⟩,⟨⟨(-155474544343667540412076014),(-155474544343667538777178381)⟩,⟨182414842910204221186454584,182414842910204222819389747⟩⟩,⟨⟨(-152056704243944678005206650),(-152056704243944676386385630)⟩,⟨181794593701597548046229366,181794593701597549663157004⟩⟩,⟨⟨(-148517415438075681791731606),(-148517415438075680189637720)⟩,⟨181116597116885637228386483,181116597116885638828658235⟩⟩,⟨⟨(-144863515704691307886191461),(-144863515704691306301464148)⟩,⟨180377867716391238736741141,180377867716391240319719561⟩⟩,⟨⟨(-141102068538226034010746784),(-141102068538226032443993916)⟩,⟨179575479334597250279978048,179575479334597251845057075⟩⟩,⟨⟨(-137240347873331807310855029),(-137240347873331805762675489)⟩,⟨178706587171453867160906051,178706587171453868707488437⟩⟩,⟨⟨(-133285821942750523952642607),(-133285821942750522423596558)⟩,⟨177768449626619748970288517,177768449626619750497815547⟩⟩,⟨⟨(-129246136281851859881618017),(-129246136281851858372258610)⟩,⟨176758449741468696925045146,176758449741468698432964931⟩⟩,⟨⟨(-125129095899712546333602489),(-125129095899712544844442368)⟩,⟨175674116114890741262139796,175674116114890742749940765⟩⟩,⟨⟨(-120942646643585932079880342),(-120942646643585930611428271)⟩,⟨174513143160950564092153988,174513143160950565559328262⟩⟩,⟨⟨(-116694855790819108869024833),(-116694855790819107421740138)⟩,⟨173273410579346125282916261,173273410579346126729005203⟩⟩,⟨⟨(-112393891909646622870060627),(-112393891909646621444401885)⟩,⟨171953001913339963691237008,171953001913339965115782542⟩⟩,⟨⟨(-108048004037748382890212176),(-108048004037748381486587525)⟩,⟨170550222074412698489767893,170550222074412699892362187⟩⟩] +lemma kernel12_0_r4_1_eq : ∀ k : Fin 16, kernel12_0Expr 4 1 k = kernel12_0_r4_1 k := by decide +kernel +noncomputable def kernel12_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-103665500234924993681199321),(-103665500234924992300021239)⟩,⟨169063613718304209244026779,169063613718304210624257474⟩⟩,⟨⟨(-99254725573634047991003655),(-99254725573634046632621903)⟩,⟨167491972363347632031133099,167491972363347633388650360⟩⟩,⟨⟨(-94824039638361895532948729),(-94824039638361894197721583)⟩,⟨165834360149042564933304037,165834360149042566267749327⟩⟩,⟨⟨(-90381793611792300789135150),(-90381793611792299477359919)⟩,⟨164090118140627518904893256,164090118140627520215968819⟩⟩,⟨⟨(-85936307032391612529235419),(-85936307032391611241223074)⟩,⟨162258877093961246624676708,162258877093961247912070947⟩⟩,⟨⟨(-81495844314276145192715692),(-81495844314276143928702520)⟩,⟨160340566604264440369715824,160340566604264441633191642⟩⟩,⟨⟨(-77068591125980082555438299),(-77068591125980081315679339)⟩,⟨158335422572156507434219286,158335422572156508673520668⟩⟩,⟨⟨(-72662630729923120448398245),(-72662630729923119233076805)⟩,⟨156243992930888734418910952,156243992930888735633853439⟩⟩,⟨⟨(-68285920388912096406226694),(-68285920388912095215552281)⟩,⟨154067141589660328688409492,154067141589660329878782262⟩⟩,⟨⟨(-63946267949830852060024063),(-63946267949830850894116402)⟩,⟨151806050559336257285736460,151806050559336258451418317⟩⟩,⟨⟨(-59651308717714308229275232),(-59651308717714307088285983)⟩,⟨149462220238688089103391504,149462220238688090244229165⟩⟩,⟨⟨(-55408482735609767541173670),(-55408482735609766425172367)⟩,⟨147037467851368222096789255,147037467851368223212711419⟩⟩,⟨⟨(-51225012586951964189538539),(-51225012586951963098632673)⟩,⟨144533924036116032618122253,144533924036116033709019521⟩⟩,⟨⟨(-47107881837577868262292028),(-47107881837577867196211880)⟩,⟨141954027605089461060000919,141954027605089462126140984⟩⟩,⟨⟨(-43063814233951237629862889),(-43063814233951236588461834)⟩,⟨139300518497621727677669719,139300518497621728719197056⟩⟩,⟨⟨(-39099253772633475344990092),(-39099253772633474328239281)⟩,⟨136576428969022033682637131,136576428969022034699578315⟩⟩] +lemma kernel12_0_r4_2_eq : ∀ k : Fin 16, kernel12_0Expr 4 2 k = kernel12_0_r4_2 k := by decide +kernel +noncomputable def kernel12_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-35220345753514606557208165),(-35220345753514605565132500)⟩,⟨133785073066171349484154454,133785073066171350476482211⟩⟩,⟨⟨(-31432918925804630070805757),(-31432918925804629103315108)⟩,⟨130930034453509136786104492,130930034453509137753906482⟩⟩,⟨⟨(-27742468831290235797847497),(-27742468831290234854911695)⟩,⟨128015152664463843916864032,128015152664463844860167865⟩⟩,⟨⟨(-24154142443904745441494572),(-24154142443904744522983997)⟩,⟨125044507864350402996407828,125044507864350403915340496⟩⟩,⟨⟨(-20672724198270669630278886),(-20672724198270668736128978)⟩,⟨122022404221145372027517581,122022404221145372922140938⟩⟩,⟨⟨(-17302623492595572867918018),(-17302623492595571997942524)⟩,⟨118953351990261999608759331,118953351990262000479256876⟩⟩,⟨⟨(-14047863743184357586568530),(-14047863743184356740652229)⟩,⟨115842048428395182339140342,115842048428395183185624486⟩⟩,⟨⟨(-10912073058935828839808477),(-10912073058935828017548110)⟩,⟨112693357659607567275928372,112693357659607568098798950⟩⟩,⟨⟨(-7898476594588991350017538),(-7898476594588990551222700)⟩,⟨109512289624007162463220766,109512289624007163262665159⟩⟩,⟨⟨(-5009890631254098173880318),(-5009890631254097398283533)⟩,⟨106303978245555658849246433,106303978245555659625529267⟩⟩,⟨⟨(-2248718421991988349895769),(-2248718421991987597314853)⟩,⟨103073658960685687680893783,103073658960685688434194375⟩⟩,⟨⟨383052171013374003187678,383052171013374733045608⟩,⟨99826645753444241734491691,99826645753444242465100067⟩⟩,⟨⟨2883849232710177659840006,2883849232710178367179305⟩,⟨96568307845778337318199714,96568307845778338026317371⟩⟩,⟨⟨5252515541691438783272827,5252515541691439468432872⟩,⟨93304046193308201716737743,93304046193308202402701234⟩⟩,⟨⟨7488305515737493133108270,7488305515737493796335136⟩,⟨90039269937474482981268491,90039269937474483645321080⟩⟩,⟨⟨9590880377127054188850266,9590880377127054830503280⟩,⟨86779372964292318882881868,86779372964292319525380122⟩⟩] +lemma kernel12_0_r4_3_eq : ∀ k : Fin 16, kernel12_0Expr 4 3 k = kernel12_0_r4_3 k := by decide +kernel +noncomputable def kernel12_0_r4_4 : Fin 16 → CBox := ![⟨⟨11560301570333426724443702,11560301570333427344781671⟩,⟨83529710718101381544076174,83529710718101382165276164⟩⟩,⟨⟨13397022476399973160185196,13397022476399973759610764⟩,⟨80295577415683803974656267,80295577415683804574957978⟩⟩,⟨⟨15101878479655688133868902,15101878479655688712680228⟩,⟨77082183801959446982766498,77082183801959447562465466⟩⟩,⟨⟨16676075453380061475756689,16676075453380062034365343⟩,⟨73894635583199992234783141,73894635583199992794288402⟩⟩,⟨⟨18121176741452624750892072,18121176741452625289605279⟩,⟨70737912667380654566391363,70737912667380655106007653⟩⟩,⟨⟨19439088722828243696121361,19439088722828244215384046⟩,⟨67616849333972281657277559,67616849333972282177447425⟩⟩,⟨⟨20632045054772308409131330,20632045054772308909281243⟩,⟨64536115447238575852279462,64536115447238576353338329⟩⟩,⟨⟨21702589699085955417956297,21702589699085955899442427⟩,⟨61500198818023616053262290,61500198818023616535656939⟩⟩,⟨⟨22653558842974299844637837,22653558842974300307797746⟩,⟨58513388809182528033317351,58513388809182528497383197⟩⟩,⟨⟨23488061832693720127313587,23488061832693720572625241⟩,⟨55579761269319063370183574,55579761269319063816396575⟩⟩,⟨⟨24209461243601039783843178,24209461243601040211671265⟩,⟨52703164868450180830011438,52703164868450181258734335⟩⟩,⟨⟨24821352214672305554739486,24821352214672305965555616⟩,⟨49887208897726649374165180,49887208897726649785867773⟩⟩,⟨⟨25327541178927378987655280,25327541178927379383069149⟩,⟨47135252583511128500184567,47135252583511128896425407⟩⟩,⟨⟨25732024123465993853498151,25732024123465994233998513⟩,⟨44450395954064512308702663,44450395954064512689969331⟩⟩,⟨⟨26038964513980381499031230,26038964513980381864910690⟩,⟨41835472284932080766727123,41835472284932081133314476⟩⟩,⟨⟨26252671018660011802573504,26252671018660012154228272⟩,⟨39293042136967543009688353,39293042136967543361994898⟩⟩] +lemma kernel12_0_r4_4_eq : ∀ k : Fin 16, kernel12_0Expr 4 4 k = kernel12_0_r4_4 k := by decide +kernel +noncomputable def kernel12_0_r4_5 : Fin 16 → CBox := ![⟨⟨26377575165358192681754065,26377575165358193019468147⟩,⟨36825388988898252009283036,36825388988898252347595061⟩⟩,⟨⟨26418209063772478014295689,26418209063772478338485608⟩,⟨34434516454528810364035171,34434516454528810688771518⟩⟩,⟨⟨26379183321236410124805561,26379183321236410435775511⟩,⟨32122147063209048698920944,32122147063209049010388099⟩⟩,⟨⟨26265165276574969603012169,26265165276574969901163963⟩,⟨29889722571156820599397957,29889722571156820898000037⟩⟩,⟨⟨26080857671395982135529150,26080857671395982421157607⟩,⟨27738405760720805229336870,27738405760720805515370964⟩⟩,⟨⟨25830977872239453747674426,25830977872239454021192700⟩,⟨25669083674780824103868828,25669083674780824377750363⟩⟩,⟨⟨25520237750259329405183971,25520237750259329666899112⟩,⟨23682372224292146385118485,23682372224292146647156738⟩⟩,⟨⟨25153324317647589819623385,25153324317647590069932754⟩,⟨21778622098555983887346349,21778622098555984137940896⟩⟩,⟨⟨24734881211915067102878102,24734881211915067342073274⟩,⟨19957925900201340079600216,19957925900201340319044794⟩⟩,⟨⟨24269491110507933150254622,24269491110507933378741894⟩,⟨18220126420143910062075699,18220126420143910290778743⟩⟩,⟨⟨23761659149158282495783326,23761659149158282713864735⟩,⟨16564825961985646060087765,16564825961985646278353393⟩⟩,⟨⟨23215797407938895006638121,23215797407938895214697778⟩,⟨14991396620462972721483808,14991396620462972929698171⟩⟩,⟨⟨22636210519314719073989773,22636210519314719272314085⟩,⟨13498991414660692454139073,13498991414660692652590558⟩⟩,⟨⟨22027082442655544657646750,22027082442655544846621426⟩,⟨12086556173789821712347286,12086556173789821901423537⟩⟩,⟨⟨21392464439793323827735259,21392464439793324007665824⟩,⟨10752842071377824535789837,10752842071377824715798258⟩⟩,⟨⟨20736264276368997406171916,20736264276368997577520408⟩,⟨9496418702725591493869018,9496418702725591665273529⟩⟩] +lemma kernel12_0_r4_5_eq : ∀ k : Fin 16, kernel12_0Expr 4 5 k = kernel12_0_r4_5 k := by decide +kernel +noncomputable def kernel12_0_r4_6 : Fin 16 → CBox := ![⟨⟨20062236664009541789767965,20062236664009541952795144⟩,⟨8315687600423889621278654,8315687600423889784341756⟩⟩,⟨⟨19373974948893985851458238,19373974948893986006519748⟩,⟨7208896083560499774261682,7208896083560499929340690⟩⟩,⟨⟨18674904043089855024728739,18674904043089855172089223⟩,⟨6174151337946934364471353,6174151337946934511832517⟩⟩,⟨⟨17968274586245312706630805,17968274586245312846619737⟩,⟨5209434627201784807846268,5209434627201784947820599⟩⟩,⟨⟨17257158316876849950477602,17257158316876850083341221⟩,⟨4312615537790745851151145,4312615537790745983986350⟩⟩,⟨⟨16544444624660009855346250,16544444624660009981409342⟩,⟨3481466165079541105668661,3481466165079541231690925⟩⟩,⟨⟨15832838247865750291062847,15832838247865750410676748⟩,⟨2713675152038602034083293,2713675152038602153645277⟩⟩,⟨⟨15124858073433852133682130,15124858073433852247174724⟩,⟨2006861497376626188145638,2006861497376626301576484⟩⟩,⟨⟨14422836991175011258524041,14422836991175011366106385⟩,⟨1358588055500185390230184,1358588055500185497742141⟩⟩,⟨⟨13728922748274070022351715,13728922748274070124307881⟩,⟨766374656722436753227717,766374656722436855105975⟩⟩,⟨⟨13045079745648824081948904,13045079745648824178489362⟩,⟨227710782498712000741050,227710782498712097197134⟩⟩,⟨⟨12373091713814090544222645,12373091713814090635606765⟩,⟨(-259932262926766123172102),(-259932262926766031877838)⟩⟩,⟨⟨11714565202713104003781379,11714565202713104090214843⟩,⟨(-699089736296819123623876),(-699089736296819037284799)⟩⟩,⟨⟨11070933817503753369219518,11070933817503753450994938⟩,⟨(-1092292439490741517493931),(-1092292439490741435816497)⟩⟩,⟨⟨10443463130514108176259134,10443463130514108253560361⟩,⟨(-1442056342086163985583852),(-1442056342086163908383423)⟩⟩,⟨⟨9833256198491514776882405,9833256198491514849934954⟩,⟨(-1750872873500147731946117),(-1750872873500147658996463)⟩⟩] +lemma kernel12_0_r4_6_eq : ∀ k : Fin 16, kernel12_0Expr 4 6 k = kernel12_0_r4_6 k := by decide +kernel +noncomputable def kernel12_0_r4_7 : Fin 16 → CBox := ![⟨⟨9241259613837224410244479,9241259613837224479213435⟩,⟨(-2021199909108693834055574),(-2021199909108693765190938)⟩⟩,⟨⟨8668270018713171863792680,8668270018713171928897718⟩,⟨(-2255453468141015114381487),(-2255453468141015049381595)⟩⟩,⟨⟨8114941011693121906691824,8114941011693121968095149⟩,⟨(-2456000134762083268586673),(-2456000134762083207288759)⟩⟩,⟨⟨7581790377966454191418314,7581790377966454249317047⟩,⟨(-2625150207643933812398991),(-2625150207643933754605437)⟩⟩,⟨⟨7069207575945153442049631,7069207575945153496589946⟩,⟨(-2765151577527060285577753),(-2765151577527060231141925)⟩⟩,⟨⟨6577461415425910824508249,6577461415425910875879006⟩,⟨(-2878184326826088460366323),(-2878184326826088409098964)⟩⟩,⟨⟨6106707865170175453285018,6106707865170175501627078⟩,⟨(-2966356040270856093936802),(-2966356040270856045696683)⟩⟩,⟨⟨5656997930834550251410459,5656997930834550296918740⟩,⟨(-3031697810920997350858836),(-3031697810920997305449381)⟩⟩,⟨⟨5228285547560314414173305,5228285547560314457084198⟩,⟨(-3076160921669052979349103),(-3076160921669052936527690)⟩⟩,⟨⟨4820435435162143100450282,4820435435162143140911537⟩,⟨(-3101614178567979458039905),(-3101614178567979417659370)⟩⟩,⟨⟨4433230867690844352783796,4433230867690844390901865⟩,⟨(-3109841868991964112999695),(-3109841868991964074954139)⟩⟩,⟨⟨4066381313132787888912025,4066381313132787924818148⟩,⟨(-3102542314767451551338024),(-3102542314767451515496753)⟩⟩,⟨⟨3719529903100927241415707,3719529903100927275204663⟩,⟨(-3081326987991882302824072),(-3081326987991882269092824)⟩⟩,⟨⟨3392260696522288308193354,3392260696522288339990355⟩,⟨(-3047720155283686249595023),(-3047720155283686217849090)⟩⟩,⟨⟨3084105705490415272728447,3084105705490415302624565⟩,⟨(-3003159014667032947874524),(-3003159014667032918023312)⟩⟩,⟨⟨2794551655587321081421866,2794551655587321109528484⟩,⟨(-2948994288173250461668106),(-2948994288173250433600695)⟩⟩] +lemma kernel12_0_r4_7_eq : ∀ k : Fin 16, kernel12_0Expr 4 7 k = kernel12_0_r4_7 k := by decide +kernel +noncomputable def kernel12_0_r4_8 : Fin 16 → CBox := ![⟨⟨2523046457049965115758138,2523046457049965142154713⟩,⟨(-2886491232518736955391235),(-2886491232518736929028602)⟩⟩,⟨⟨2269005367126580368282033,2269005367126580393075266⟩,⟨(-2816831029874654112833367),(-2816831029874654088069231)⟩⟩,⟨⟨2031816827807298466687464,2031816827807298489954167⟩,⟨(-2741112520752235031575569),(-2741112520752235008333514)⟩⟩,⟨⟨1810847966794185241256416,1810847966794185263089854⟩,⟨(-2660354241362646201584985),(-2660354241362646179772121)⟩⟩,⟨⟨1605449753074478969474643,1605449753074478989942276⟩,⟨(-2575496728443928795850622),(-2575496728443928775399843)⟩⟩,⟨⟨1414961801757760301721889,1414961801757760320933080⟩,⟨(-2487405055450413094586587),(-2487405055450413075388874)⟩⟩,⟨⟨1238716825916935639698139,1238716825916935657715976⟩,⟨(-2396871565142283237651292),(-2396871565142283219643871)⟩⟩,⟨⟨1076044736021863846928152,1076044736021863863827431⟩,⟨(-2304618764964540624055267),(-2304618764964540607163638)⟩⟩,⟨⟨926276390164264134793439,926276390164264150627111⟩,⟨(-2211302353135472033598690),(-2211302353135472017770175)⟩⟩,⟨⟨788747000637588874957830,788747000637588889796755⟩,⟨(-2117514345045350215832279),(-2117514345045350200996279)⟩⟩,⟨⟨662799204553318862108294,662799204553318876003051⟩,⟨(-2023786271367753602091725),(-2023786271367753588197901)⟩⟩,⟨⟨547785808046015343159716,547785808046015356171593⟩,⟨(-1930592421180938337222641),(-1930592421180938324209929)⟩⟩,⟨⟨443072215246457228937790,443072215246457241110613⟩,⟨(-1838353105358800742251118),(-1838353105358800730075898)⟩⟩,⟨⟨348038554590696337548331,348038554590696348939339⟩,⟨(-1747437917495327903125248),(-1747437917495327891730474)⟩⟩,⟨⟨262081516190380373125069,262081516190380383775417⟩,⟨(-1658168971649937517803985),(-1658168971649937507148678)⟩⟩,⟨⟨184615914925559521648427,184615914925559531617322⟩,⟨(-1570824098222467820685357),(-1570824098222467810710475)⟩⟩] +lemma kernel12_0_r4_8_eq : ∀ k : Fin 16, kernel12_0Expr 4 8 k = kernel12_0_r4_8 k := by decide +kernel +noncomputable def kernel12_0_r4_9 : Fin 16 → CBox := ![⟨⟨115075994646305344679178,115075994646305354019583⟩,⟨(-1485639981266424587439428),(-1485639981266424578092163)⟩⟩,⟨⟨52916489396017160960498,52916489396017169715818⟩,⟨(-1402815222510033767593220),(-1402815222510033758830303)⟩⟩,⟨⟨(-2386542089514986055395),(-2386542089514977855118)⟩,⟨(-1322513319261301715927140),(-1322513319261301707718652)⟩⟩,⟨⟨(-51335092183392731578352),(-51335092183392723896053)⟩,⟨(-1244865545212274280173095),(-1244865545212274272482083)⟩⟩,⟨⟨(-94408774032352965079368),(-94408774032352957889330)⟩,⟨(-1169973724917615869215278),(-1169973724917615862016129)⟩⟩,⟨⟨(-132064568777112264948836),(-132064568777112258216478)⟩,⟨(-1097912894394035142385628),(-1097912894394035135643851)⟩⟩,⟨⟨(-164736734276549209515215),(-164736734276549203216380)⟩,⟨(-1028733841862359482050820),(-1028733841862359475742343)⟩⟩,⟨⟨(-192836859652280085828561),(-192836859652280079933513)⟩,⟨(-962465524127370854807906),(-962465524127370848903065)⟩⟩,⟨⟨(-216754050436123949212062),(-216754050436123943697614)⟩,⟨(-899117355457693118550488),(-899117355457693113026167)⟩⟩,⟨⟨(-236855229652317849177654),(-236855229652317844013133)⟩,⟨(-838681367086449443780400),(-838681367086449438605986)⟩⟩,⟨⟨(-253485540785465175387821),(-253485540785465170554626)⟩,⟨(-781134236601900495160531),(-781134236601900490317476)⟩⟩,⟨⟨(-266968839261051326649167),(-266968839261051322124226)⟩,⟨(-726439187535939416114948),(-726439187535939411580223)⟩⟩,⟨⟨(-277608259785641271064926),(-277608259785641266832532)⟩,⟨(-674547760388432454453831),(-674547760388432450211769)⟩⟩,⟨⟨(-285686847647081665665354),(-285686847647081661704081)⟩,⟨(-625401457149256853926425),(-625401457149256849955632)⟩⟩,⟨⟨(-291468242850515927672274),(-291468242850515923967438)⟩,⟨(-578933262100696995807797),(-578933262100696992093618)⟩⟩,⟨⟨(-295197406754021153296726),(-295197406754021149830095)⟩,⟨(-535069042304574194835527),(-535069042304574191359756)⟩⟩] +lemma kernel12_0_r4_9_eq : ∀ k : Fin 16, kernel12_0Expr 4 9 k = kernel12_0_r4_9 k := by decide +kernel +noncomputable def kernel12_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-297101381659336087443819),(-297101381659336084196853)⟩,⟨(-493728831705697510408619),(-493728831705697507153306)⟩⟩,⟨⟨(-297390074600528927694084),(-297390074600528924649737)⟩,⟨(-454828003221036509078886),(-454828003221036506026995)⟩⟩,⟨⟨(-296257057349520497896915),(-296257057349520495044505)⟩,⟨(-418278333537932092639289),(-418278333537932089780079)⟩⟩,⟨⟨(-293880375415991454044352),(-293880375415991451370302)⟩,⟨(-383988965620466062058199),(-383988965620466059378038)⟩⟩,⟨⟨(-290423359555085433455944),(-290423359555085430951347)⟩,⟨(-351867274126779751366188),(-351867274126779748856118)⟩⟩,⟨⟨(-286035434005026785489258),(-286035434005026783141473)⟩,⟨(-321819639077739455690698),(-321819639077739453338029)⟩⟩,⟨⟨(-280852916354643019903669),(-280852916354643017704327)⟩,⟨(-293752133194978990609647),(-293752133194978988405963)⟩⟩,⟨⟨(-274999804584900543573701),(-274999804584900541512130)⟩,⟨(-267571128350037102145832),(-267571128350037100080420)⟩⟩,⟨⟨(-268588547436699509621663),(-268588547436699507691056)⟩,⟨(-243183826541957507827241),(-243183826541957505893252)⟩⟩,⟨⟨(-261720794827737221237744),(-261720794827737219428038)⟩,⟨(-220498720754063651103250),(-220498720754063649290585)⟩⟩,⟨⟨(-254488125573226876216700),(-254488125573226874521385)⟩,⟨(-199425990937167978060191),(-199425990937167976362302)⟩⟩,⟨⟨(-246972750158160038258530),(-246972750158160036669268)⟩,⟨(-179877840231475771132056),(-179877840231475769540571)⟩⟩,⟨⟨(-239248186762604223112339),(-239248186762604221622848)⟩,⟨(-161768776377855358530808),(-161768776377855357039418)⟩⟩,⟨⟨(-231379909156619470339711),(-231379909156619468940824)⟩,⟨(-145015843085616298808135),(-145015843085616297407642)⟩⟩,⟨⟨(-223425965458504603936608),(-223425965458504602623575)⟩,⟨(-129538805922782849397247),(-129538805922782848082874)⟩⟩,⟨⟨(-215437567090294690977796),(-215437567090294689744379)⟩,⟨(-115260297080051322722580),(-115260297080051321488065)⟩⟩] +lemma kernel12_0_r4_10_eq : ∀ k : Fin 16, kernel12_0Expr 4 10 k = kernel12_0_r4_10 k := by decide +kernel +noncomputable def kernel12_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-207459647569030894288460),(-207459647569030893130890)⟩,⟨(-102105923134813914723444),(-102105923134813913564995)⟩⟩,⟨⟨(-199531391042826135341384),(-199531391042826134253717)⟩,⟨(-90004339710113388338492),(-90004339710113387250145)⟩⟩,⟨⟨(-191686730718833798745080),(-191686730718833797723647)⟩,⟨(-78887296688120590428061),(-78887296688120589406124)⟩⟩,⟨⟨(-183954817537696650923283),(-183954817537696649963220)⟩,⟨(-68689657401329467351069),(-68689657401329466390663)⟩⟩,⟨⟨(-176360459627802781761144),(-176360459627802780859478)⟩,⟨(-59349394989454134793261),(-59349394989454133891395)⟩⟩,⟨⟨(-168924533224654441679419),(-168924533224654440831602)⟩,⟨(-50807568877998594613372),(-50807568877998593765484)⟩⟩,⟨⟨(-161664365867840702947640),(-161664365867840702150635)⟩,⟨(-43008284107373639883498),(-43008284107373639086536)⟩⟩,⟨⟨(-154594092792473471094201),(-154594092792473470343239)⟩,⟨(-35898636020709430110291),(-35898636020709429359475)⟩⟩,⟨⟨(-147724987515454563698021),(-147724987515454562991032)⟩,⟨(-29428642605357110375839),(-29428642605357109669086)⟩⟩,⟨⟨(-141065767681504673221206),(-141065767681504672554708)⟩,⟨(-23551166578457760043425),(-23551166578457759377241)⟩⟩,⟨⟨(-134622877281361423892043),(-134622877281361423263991)⟩,⟨(-18221829111638621704419),(-18221829111638621076751)⟩⟩,⟨⟨(-128400746386731557822861),(-128400746386731557230424)⟩,⟨(-13398916904438942505567),(-13398916904438941913574)⟩⟩,⟨⟨(-122402029565168767466466),(-122402029565168766908028)⟩,⟨(-9043284140861363752288),(-9043284140861363194346)⟩⟩,⟨⟨(-116627824144661915815018),(-116627824144661915287901)⟩,⟨(-5118250698725503239200),(-5118250698725502712623)⟩⟩,⟨⟨(-111077869493881284449835),(-111077869493881283952477)⟩,⟨(-1589497827367614222867),(-1589497827367613726088)⟩⟩,⟨⟨(-105750728471166814715537),(-105750728471166814245382)⟩,⟨1575037634335704902913,1575037634335705372456⟩⟩] +lemma kernel12_0_r4_11_eq : ∀ k : Fin 16, kernel12_0Expr 4 11 k = kernel12_0_r4_11 k := by decide +kernel +noncomputable def kernel12_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-100643952174774368413356),(-100643952174774367968925)⟩,⟨4405269560763208197114,4405269560763208640907⟩⟩,⟨⟨(-95754229099843983804949),(-95754229099843983384161)⟩,⟨6929068547194193898155,6929068547194194318281⟩⟩,⟨⟨(-91077519775136559225180),(-91077519775136558826912)⟩,⟨9172366919267773174245,9172366919267773571835⟩⟩,⟨⟨(-86609177915821210648984),(-86609177915821210271574)⟩,⟨11159262144545640823991,11159262144545641200710⟩⟩,⟨⟨(-82344059088406522638200),(-82344059088406522280785)⟩,⟨12912118140573196859263,12912118140573197215976⟩⟩,⟨⟨(-78276617841123298913133),(-78276617841123298574120)⟩,⟨14451664059146945684437,14451664059146946022740⟩⟩,⟨⟨(-74400994208423052423644),(-74400994208423052102177)⟩,⟨15797090203470929632889,15797090203470929953642⟩⟩,⟨⟨(-70711090452409371310699),(-70711090452409371005114)⟩,⟨16966140803993930567536,16966140803993930872405⟩⟩,⟨⟨(-67200638857542609024991),(-67200638857542608734638)⟩,⟨17975203440445293723231,17975203440445294012868⟩⟩,⟨⟨(-63863261348351550275867),(-63863261348351549999500)⟩,⟨18839394952417380628181,18839394952417380903835⟩⟩,⟨⟨(-60692521653578918025403),(-60692521653578917762406)⟩,⟨19572643729261840794163,19572643729261841056450⟩⟩,⟨⟨(-57681970694546934079357),(-57681970694546933828743)⟩,⟨20187768312553293884188,20187768312553294134097⟩⟩,⟨⟨(-54825185830862085743838),(-54825185830862085505158)⟩,⟨20696552281394896961955,20696552281394897199936⟩⟩,⟨⟨(-52115804553138811980381),(-52115804553138811752668)⟩,⟨21109815422848584396835,21109815422848584623856⟩⟩,⟨⟨(-49547553170415688239305),(-49547553170415688021840)⟩,⟨21437481217204429650567,21437481217204429867348⟩⟩,⟨⟨(-47114270999527093379872),(-47114270999527093171865)⟩,⟨21688640691075359286462,21688640691075359493795⟩⟩] +lemma kernel12_0_r4_12_eq : ∀ k : Fin 16, kernel12_0Expr 4 12 k = kernel12_0_r4_12 k := by decide +kernel +noncomputable def kernel12_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-44809930525001738274402),(-44809930525001738075574)⟩,⟨21871612710811393278002,21871612710811393476165⟩⟩,⟨⟨(-42628653961175917414892),(-42628653961175917224462)⟩,⟨21994000804845903201314,21994000804845903391088⟩⟩,⟨⟨(-40564726613192798328326),(-40564726613192798145962)⟩,⟨22062746616666763188625,22062746616666763370344⟩⟩,⟨⟨(-38612607400442041609666),(-38612607400442041434765)⟩,⟨22084180100476565006241,22084180100476565180508⟩⟩,⟨⟨(-36766936874786355193526),(-36766936874786355025856)⟩,⟨22064066579574266098901,22064066579574266265957⟩⟩,⟨⟨(-35022543036613597549424),(-35022543036613597388356)⟩,⟨22007650793339113477670,22007650793339113638158⟩⟩,⟨⟨(-33374445224318703249065),(-33374445224318703094352)⟩,⟨21919698062687666627135,21919698062687666781301⟩⟩,⟨⟨(-31817856327219283207527),(-31817856327219283058688)⟩,⟨21804532706245958150776,21804532706245958299099⟩⟩,⟨⟨(-30348183548091325921990),(-30348183548091325778887)⟩,⟨21666073840450298275223,21666073840450298417838⟩⟩,⟨⟨(-28961027919417095196128),(-28961027919417095058248)⟩,⟨21507868696561151901510,21507868696561152038929⟩⟩,⟨⟨(-27652182756999188213001),(-27652182756999188080159)⟩,⟨21333123586325266260149,21333123586325266392556⟩⟩,⟨⟨(-26417631215740644178384),(-26417631215740644050189)⟩,⟨21144732645914382185049,21144732645914382312831⟩⟩,⟨⟨(-25253543095045128115098),(-25253543095045127991443)⟩,⟨20945304484950283099471,20945304484950283222736⟩⟩,⟨⟨(-24156271025375336079514),(-24156271025375335959993)⟩,⟨20737186864025856566135,20737186864025856685287⟩⟩,⟨⟨(-23122346152942440461726),(-23122346152942440346199)⟩,⟨20522489520265962676980,20522489520265962792156⟩⟩,⟨⟨(-22148473426204951530349),(-22148473426204951418496)⟩,⟨20303105256242465880569,20303105256242465992089⟩⟩] +lemma kernel12_0_r4_13_eq : ∀ k : Fin 16, kernel12_0Expr 4 13 k = kernel12_0_r4_13 k := by decide +kernel +noncomputable def kernel12_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-21231526575752753459772),(-21231526575752753351542)⟩,⟨20080729403054638097931,20080729403054638205846⟩⟩,⟨⟨(-20368542868163520133638),(-20368542868163520028673)⟩,⟨19856877763687753052250,19856877763687753156916⟩⟩,⟨⟨(-19556717704468340805740),(-19556717704468340703932)⟩,⟨19632903137937147202472,19632903137937147303995⟩⟩,⟨⟨(-18793399124877633822187),(-18793399124877633723276)⟩,⟨19410010525290954697813,19410010525290954796453⟩⟩,⟨⟨(-18076082273326438348837),(-18076082273326438252777)⟩,⟨19189271097252207514698,19189271097252207610501⟩⟩,⟨⟨(-17402403868132059477113),(-17402403868132059383616)⟩,⟨18971635025692384459972,18971635025692384553223⟩⟩,⟨⟨(-16770136718552080056652),(-16770136718552079965643)⟩,⟨18757943248999220146338,18757943248999220237113⟩⟩,⟨⟨(-16177184321225523910597),(-16177184321225523821855)⟩,⟨18548938253040876061284,18548938253040876149803⟩⟩,⟨⟨(-15621575565316418668953),(-15621575565316418582466)⟩,⟨18345273939340141961993,18345273939340142048266⟩⟩,⟨⟨(-15101459570602527274881),(-15101459570602527190388)⟩,⟨18147524648354998878368,18147524648354998962657⟩⟩,⟨⟨(-14615100678711353123658),(-14615100678711353041104)⟩,⟨17956193401410143521115,17956193401410143603474⟩⟩,⟨⟨(-14160873614152778319575),(-14160873614152778238771)⟩,⟨17771719420628669757160,17771719420628669837776⟩⟩,⟨⟨(-13737258828688241519234),(-13737258828688241440171)⟩,⟨17594484982181440528169,17594484982181440607052⟩⟩,⟨⟨(-13342838039868747384896),(-13342838039868747307359)⟩,⟨17424821654308304171175,17424821654308304248539⟩⟩,⟨⟨(-12976289972229826036904),(-12976289972229825960850)⟩,⟨17263015967872271323693,17263015967872271399581⟩⟩,⟨⟨(-12636386307615356467847),(-12636386307615356393113)⟩,⟨17109314563684999871177,17109314563684999945749⟩⟩] +lemma kernel12_0_r4_14_eq : ∀ k : Fin 16, kernel12_0Expr 4 14 k = kernel12_0_r4_14 k := by decide +kernel +noncomputable def kernel12_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-12321987849381246816835),(-12321987849381246743438)⟩,⟨16963928857487545139470,16963928857487545212712⟩⟩,⟨⟨(-12032040903774279009875),(-12032040903774278937608)⟩,⟨16827039260280890441688,16827039260280890513805⟩⟩,⟨⟨(-11765573880563413639326),(-11765573880563413568155)⟩,⟨16698798988671555079448,16698798988671555150471⟩⟩,⟨⟨(-11521694113995282146045),(-11521694113995282075828)⟩,⟨16579337497022781125862,16579337497022781195937⟩⟩,⟨⟨(-11299584904329411826981),(-11299584904329411757728)⟩,⟨16468763560474735861542,16468763560474735930658⟩⟩,⟨⟨(-11098502779560899993346),(-11098502779560899924881)⟩,⟨16367168035310417185579,16367168035310417253910⟩⟩,⟨⟨(-10917774976439609533075),(-10917774976439609465372)⟩,⟨16274626320689513705497,16274626320689513773069⟩⟩,⟨⟨(-10756797139528049655954),(-10756797139528049588884)⟩,⟨16191200543441884224469,16191200543441884291410⟩⟩,⟨⟨(-10615031236789054244881),(-10615031236789054178468)⟩,⟨16116941485396755137599,16116941485396755203886⟩⟩,⟨⟨(-10492003690044725951023),(-10492003690044725885093)⟩,⟨16051890270614083468188,16051890270614083533993⟩⟩,⟨⟨(-10387303718586716810457),(-10387303718586716744989)⟩,⟨15996079827871485363737,15996079827871485429082⟩⟩,⟨⟨(-10300581894232761352153),(-10300581894232761287025)⟩,⟨15949536141834222143337,15949536141834222208344⟩⟩,⟨⟨(-10231548906204487376077),(-10231548906204487311308)⟩,⟨15912279304487401201654,15912279304487401266304⟩⟩,⟨⟨(-10179974534336824388381),(-10179974534336824323813)⟩,⟨15884324376629150831259,15884324376629150895708⟩⟩,⟨⟨(-10145686829310509893494),(-10145686829310509829108)⟩,⟨15865682067501387518735,15865682067501387583003⟩⟩,⟨⟨(-10128571498817619142035),(-10128571498817619077716)⟩,⟨15856359238961209525763,15856359238961209589964⟩⟩] +lemma kernel12_0_r4_15_eq : ∀ k : Fin 16, kernel12_0Expr 4 15 k = kernel12_0_r4_15 k := by decide +kernel +noncomputable def kernel12_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel12_0_r4_0,kernel12_0_r4_1,kernel12_0_r4_2,kernel12_0_r4_3,kernel12_0_r4_4,kernel12_0_r4_5,kernel12_0_r4_6,kernel12_0_r4_7,kernel12_0_r4_8,kernel12_0_r4_9,kernel12_0_r4_10,kernel12_0_r4_11,kernel12_0_r4_12,kernel12_0_r4_13,kernel12_0_r4_14,kernel12_0_r4_15] +lemma kernel12_0_r4_eq (i k : Fin 16) : kernel12_0Expr 4 i k = kernel12_0_r4 i k := by + fin_cases i + · exact kernel12_0_r4_0_eq k + · exact kernel12_0_r4_1_eq k + · exact kernel12_0_r4_2_eq k + · exact kernel12_0_r4_3_eq k + · exact kernel12_0_r4_4_eq k + · exact kernel12_0_r4_5_eq k + · exact kernel12_0_r4_6_eq k + · exact kernel12_0_r4_7_eq k + · exact kernel12_0_r4_8_eq k + · exact kernel12_0_r4_9_eq k + · exact kernel12_0_r4_10_eq k + · exact kernel12_0_r4_11_eq k + · exact kernel12_0_r4_12_eq k + · exact kernel12_0_r4_13_eq k + · exact kernel12_0_r4_14_eq k + · exact kernel12_0_r4_15_eq k +noncomputable def kernel12_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-29978499370549516765501760861),(-29978499370549516404607879356)⟩,⟨108561501191990023578819717872,108561501191990023940149755042⟩⟩,⟨⟨(-29924375983749255632484844284),(-29924375983749255271650588581)⟩,⟨108533889944428534400770568936,108533889944428534762042014925⟩⟩,⟨⟨(-29816226680224208391951909915),(-29816226680224208031237525513)⟩,⟨108478633943083853442327505706,108478633943083853803481146762⟩⟩,⟨⟨(-29654246266627666470568951451),(-29654246266627666110034684313)⟩,⟨108395666449480284764681708618,108395666449480285125658324971⟩⟩,⟨⟨(-29438726618777705243117733740),(-29438726618777704882823845076)⟩,⟨108284888039576573996410654000,108284888039576574357151002308⟩⟩,⟨⟨(-29170056279500085963564014882),(-29170056279500085603570769709)⟩,⟨108146167420684574402112104447,108146167420684574762556926499⟩⟩,⟨⟨(-28848719920500847991484105950),(-28848719920500847631851798413)⟩,⟨107979342514891100409413420086,107979342514891100769503414760⟩⟩,⟨⟨(-28475297666664799179526650624),(-28475297666664798820315565573)⟩,⟨107784221804029857758020993634,107784221804029858117696852637⟩⟩,⟨⟨(-28050464280824990544826001396),(-28050464280824990186096486614)⟩,⟨107560585930038321317678828300,107560585930038321676881161285⟩⟩,⟨⟨(-27574988206729778505654231958),(-27574988206729778147466586326)⟩,⟨107308189543340089328495766013,107308189543340089687165209825⟩⟩,⟨⟨(-27049730467654186623517552957),(-27049730467654186265932062946)⟩,⟨107026763390720274863153597091,107026763390720275221230776371⟩⟩,⟨⟨(-26475643417866622222520461521),(-26475643417866621865569143745)⟩,⟨106716016633013681665185783671,106716016633013682022639495940⟩⟩,⟨⟨(-25853769343975867558514611773),(-25853769343975867202255598467)⟩,⟨106375639381806720935333604493,106375639381806721292106567269⟩⟩,⟨⟨(-25185238913051533197541548204),(-25185238913051532842032722915)⟩,⟨106005305443268220247226728400,106005305443268220603261876570⟩⟩,⟨⟨(-24471269464338268384088298357),(-24471269464338268029387985866)⟩,⟨105604675256175512629599737582,105604675256175512984839531090⟩⟩,⟨⟨(-23713163141373915720021258420),(-23713163141373915366187377831)⟩,⟨105173399010194623191745176068,105173399010194623546132444781⟩⟩] +lemma kernel12_0_r5_0_eq : ∀ k : Fin 16, kernel12_0Expr 5 0 k = kernel12_0_r5_0 k := by decide +kernel +noncomputable def kernel12_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-22912304861377893335034312966),(-22912304861377892982125492752)⟩,⟨104711119929511230661479642719,104711119929511231014956469074⟩⟩,⟨⟨(-22070160118901240073570893011),(-22070160118901239721644961530)⟩,⟨104217477705996689017970754997,104217477705996689370479981756⟩⟩,⟨⟨(-21188272620926223283502342964),(-21188272620926222932618133093)⟩,⟨103692112065235133468168929987,103692112065235133819652353345⟩⟩,⟨⟨(-20268261750872812127445285172),(-20268261750872811777660591555)⟩,⟨103134666447937998425410032515,103134666447937998775810443439⟩⟩,⟨⟨(-19311819859312635842415096468),(-19311819859312635493789173272)⟩,⟨102544791788535605150853313078,102544791788535605500111997344⟩⟩,⟨⟨(-18320709379608574326999178878),(-18320709379608573979589508301)⟩,⟨101922150372066300367107116806,101922150372066300715167085569⟩⟩,⟨⟨(-17296759767189472882636688600),(-17296759767189472536502687665)⟩,⟨101266419749886388194868368097,101266419749886388541670648856⟩⟩,⟨⟨(-16241864261733532677693549450),(-16241864261733532332892564827)⟩,⟨100577296694203184911736220805,100577296694203185257223862086⟩⟩,⟨⟨(-15157976472168887960733158315),(-15157976472168887617325185556)⟩,⟨99854501170993237844524898692,99854501170993238188638248554⟩⟩,⟨⟨(-14047106785103207254500299485),(-14047106785103206912542006010)⟩,⟨99097780310512256320342121871,99097780310512256663024805189⟩⟩,⟨⟨(-12911318598062600701828595268),(-12911318598062600361379972761)⟩,⟨98306912354336604660573924784,98306912354336605001766188367⟩⟩,⟨⟨(-11752724379749724255449279841),(-11752724379749723916566768585)⟩,⟨97481710557702092338418929989,97481710557702092678064519059⟩⟩,⟨⟨(-10573481560417094846445596379),(-10573481560417094509189875470)⟩,⟨96622027025827793731413358905,96622027025827794069451724315⟩⟩,⟨⟨(-9375788256388946374169062166),(-9375788256388946038595466952)⟩,⟨95727756462933962884827546045,95727756462933963221203428721⟩⟩,⟨⟨(-8161878833747493157132907265),(-8161878833747492823301910906)⟩,⟨94798839812786647189654970406,94798839812786647524307916727⟩⟩,⟨⟨(-6934019317220637179391200943),(-6934019317220636847357740880)⟩,⟨93835267769829815506258046848,93835267769829815839133084764⟩⟩] +lemma kernel12_0_r5_1_eq : ∀ k : Fin 16, kernel12_0Expr 5 1 k = kernel12_0_r5_1 k := by decide +kernel +noncomputable def kernel12_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-5694502651360790394703299263),(-5694502651360790064528795061)⟩,⟨92837084140300718099856466476,92837084140300718430892084331⟩⟩,⟨⟨(-4445643822180879900108741615),(-4445643822180879571846334204)⟩,⟨91804389033167306696555438096,91804389033167307025698349587⟩⟩,⟨⟨(-3189774848505571818017485901),(-3189774848505571491727923338)⟩,⟨90737341861278837577524382709,90737341861278837904713636838⟩⟩,⟨⟨(-1929239653394667697447988541),(-1929239653394667373183989071)⟩,⟨89636164133782645041407641233,89636164133782645366590264210⟩⟩,⟨⟨(-666388827092502874706519901),(-666388827092502552529817558)⟩,⟨88501142021631263187256723703,88501142021631263510370668768⟩⟩,⟨⟨596425705957287662383134870,596425705957287982422199594⟩,⟨87332628678883679610133028441,87332628678883679931127592191⟩⟩,⟨⟨1856856102427605160644221448,1856856102427605478484945756⟩,⟨86131046303490912718663904234,86131046303490913037477964787⟩⟩,⟨⟨3112564083116190116206484178,3112564083116190431799188809⟩,⟨84896887922346972100603006882,84896887922346972417186417633⟩⟩,⟨⟨4361226468014485634180770497,4361226468014485947463376684⟩,⟨83630718886578491870467954453,83630718886578492184758114408⟩⟩,⟨⟨5600540746861481775098039890,5600540746861482086024292254⟩,⟨82333178064336051877522694251,82333178064336052189472781828⟩⟩,⟨⟨6828230667723068651728767129,6828230667723068960238438940⟩,⟨81004978719732770049882819987,81004978719732770359431989416⟩⟩,⟨⟨8042051825322817857962860106,8042051825322818164010223346⟩,⟨79646909068045723328303927352,79646909068045723635405790423⟩⟩,⟨⟨9239797230114029512545990150,9239797230114029816069517330⟩,⟨78259832498846913638948708505,78259832498846913943541027076⟩⟩,⟨⟨10419302838434213873528806532,10419302838434214174486853430⟩,⟨76844687460355846131270425517,76844687460355846433310809402⟩⟩,⟨⟨11578453023530368089966591359,11578453023530368388299946226⟩,⟨75402486999997583681264293942,75402486999997583980692737922⟩⟩,⟨⟨12715185966794376134838196927,12715185966794376430506040385⟩,⟨73934317957899913527108125742,73934317957899913823882985487⟩⟩] +lemma kernel12_0_r5_2_eq : ∀ k : Fin 16, kernel12_0Expr 5 2 k = kernel12_0_r5_2 k := by decide +kernel +noncomputable def kernel12_0_r5_3 : Fin 16 → CBox := ![⟨⟨13827498948209903309454289846,13827498948209903602395474727⟩,⟨72441339811861848887558202974,72441339811861849181617461743⟩⟩,⟨⟨14913453514791877031398699427,14913453514791877321577931783⟩,⟨70924783174163285934014863627,70924783174163286225322334295⟩⟩,⟨⟨15971180505702866022765166269,15971180505702866310124886937⟩,⟨69385947942451848177478830218,69385947942451848465976019518⟩⟩,⟨⟨16998884912762361279187598209,16998884912762361563692868357⟩,⟨67826201108826848985951094013,67826201108826849271602109390⟩⟩,⟨⟨17994850555229174139439305610,17994850555229174421030946639⟩,⟨66246974233130499325364522058,66246974233130499608109194115⟩⟩,⟨⟨18957444548036966192001484862,18957444548036966470650594228⟩,⟨64649760588341206869348977558,64649760588341207149157402333⟩⟩,⟨⟨19885121543100341830397845532,19885121543100342106049224872⟩,⟨63036111987830976652333280113,63036111987830976929149224940⟩⟩,⟨⟨20776427723884912191699893778,20776427723884912464325425360⟩,⟨61407635306086241546235446229,61407635306086241820029753009⟩⟩,⟨⟨21630004534149102809953415674,21630004534149103079495448704⟩,⟨59765988706286513957671361329,59765988706286514228385309700⟩⟩,⟨⟨22444592122616901342243165447,22444592122616901608681286748⟩,⟨58112877589875630825859044284,58112877589875631093471156340⟩⟩,⟨⟨23219032486326734422014832209,23219032486326734685372724185⟩,⟨56450050284933720083897550843,56450050284933720348424545524⟩⟩,⟨⟨23952272296518559101457848807,23952272296518559362288258713⟩,⟨54779293491752197848084299418,54779293491752198110033838547⟩⟩,⟨⟨24643365392164220779343545699,24643365392164221037584121301⟩,⟨53102427505517261466073421175,53102427505517261725383462863⟩⟩,⟨⟨25291474927609179462074241589,25291474927609179717703755975⟩,⟨51421301237408033058517168767,51421301237408033315166870084⟩⟩,⟨⟨25895875162269727882151874358,25895875162269728135112450087⟩,⟨49737787056702807911460613750,49737787056702808165392518874⟩⟩,⟨⟨26455952881910620414849163198,26455952881910620665118814023⟩,⟨48053775477650473121561821020,48053775477650473372754433887⟩⟩] +lemma kernel12_0_r5_3_eq : ∀ k : Fin 16, kernel12_0Expr 5 3 k = kernel12_0_r5_3 k := by decide +kernel +noncomputable def kernel12_0_r5_4 : Fin 16 → CBox := ![⟨⟨26971208442704367470806738025,26971208442704367718322907700⟩,⟨46371169715894513931271825268,46371169715894514179663115434⟩⟩,⟨⟨27441256431035119168326847642,27441256431035119413076532196⟩,⟨44691880140125376239376198374,44691880140125376484953758391⟩⟩,⟨⟨27865825933845957124867495571,27865825933845957366794827130⟩,⟨43017818645375484764839290864,43017818645375485007547882821⟩⟩,⟨⟨28244760416226609446310366434,28244760416226609685400289971⟩,⟨41350892974953119083517748701,41350892974953119323343010782⟩⟩,⟨⟨28578017204886452636903681373,28578017204886452873096629802⟩,⟨39693001018430907255855460647,39693001018430907492738550652⟩⟩,⟨⟨28865666578141894425391267569,28865666578141894658681106547⟩,⟨38046025113357354779212469387,38046025113357355013148040703⟩⟩,⟨⟨29107890465054060882886161944,29107890465054061113220007691⟩,⟨36411826378442255449289434575,36411826378442255680225419976⟩⟩,⟨⟨29304980758367962723667283834,29304980758367962951037829087⟩,⟨34792239105876976377189253506,34792239105876976605119217312⟩⟩,⟨⟨29457337247913541176853695242,29457337247913541401202976344⟩,⟨33189065240187733141331197752,33189065240187733366198073698⟩⟩,⟨⟨29565465183117601931635196911,29565465183117602152967067048⟩,⟨31604068970584676810691011047,31604068970584677032499603255⟩⟩,⟨⟨29629972475229033239359177670,29629972475229033457624674270⟩,⟨30038971463163863688554889926,30038971463163863907257209177⟩⟩,⟨⟨29651566551763389803525735262,29651566551763390018725947476⟩,⟨28495445758546291285131864411,28495445758546291500730017458⟩⟩,⟨⟨29631050877512681846024570990,29631050877512682058106561483⟩,⟨26975111859602827348685138094,26975111859602827561127224970⟩⟩,⟨⟨29569321158228201908518193999,29569321158228202117493791869⟩,⟨25479532032822021290303384310,25479532032822021499602311915⟩⟩,⟨⟨29467361244755133625633017838,29467361244755133831458033271⟩,⟨24010206345636739957762756763,24010206345636740163875429190⟩⟩,⟨⟨29326238756964846983134296537,29326238756964847185818655248⟩,⟨22568568460643813472379900472,22568568460643813675317368798⟩⟩] +lemma kernel12_0_r5_4_eq : ∀ k : Fin 16, kernel12_0Expr 5 4 k = kernel12_0_r5_4 k := by decide +kernel +noncomputable def kernel12_0_r5_5 : Fin 16 → CBox := ![⟨⟨29147100448282292428226077055,29147100448282292627719628643⟩,⟨21155981706138077657016715971,21155981706138077856729968017⟩⟩,⟨⟨28931167332930744699929586994,28931167332930744896269361865⟩,⟨19773735440749110673498688575,19773735440749110870026012207⟩⟩,⟨⟨28679729599204290780627192249,28679729599204290973825418406⟩,⟨18423041728227334151531261490,18423041728227334344886398264⟩⟩,⟨⟨28394141333120968554197469387,28394141333120968744270923384⟩,⟨17105032336588632644490889542,17105032336588632834691789605⟩⟩,⟨⟨28075815077698583940302755409,28075815077698584127206166441⟩,⟨15820756073906677187856439215,15820756073906677374859011445⟩⟩,⟨⟨27726216253824457493505754526,27726216253824457677267784625⟩,⟨14571176471053826202693330747,14571176471053826386527427711⟩⟩,⟨⟨27346857469254485976679829997,27346857469254486157265508158⟩,⟨13357169819649470821631951473,13357169819649471002263795188⟩⟩,⟨⟨26939292742672126036258981608,26939292742672126213693958743⟩,⟨12179523571394054429284360573,12179523571394054606740798035⟩⟩,⟨⟨26505111669961794613684602725,26505111669961794787927478684⟩,⟨11038935102863065339360211688,11038935102863065513601038677⟩⟩,⟨⟨26045933559902738034441456151,26045933559902738205625203289⟩,⟨9936010847723549844152189401,9936010847723550015311565323⟩⟩,⟨⟨25563401566369085401007057342,25563401566369085569121432660⟩,⟨8871265796231587032518598556,8871265796231587200587468225⟩⟩,⟨⟨25059176843831434013399275922,25059176843831434178474539865⟩,⟨7845123359788025984735688331,7845123359788026149745490349⟩⟩,⟨⟨24534932752498180721623933333,24534932752498180883622416694⟩,⟨6857915596286642250070070601,6857915596286642411984308339⟩⟩,⟨⟨23992349138815546412573373167,23992349138815546571537762080⟩,⟨5909883789998332174170535931,5909883789998332333033049386⟩⟩,⟨⟨23433106716269791452686310807,23433106716269791608590272355⟩,⟨5001179377811083378001955786,5001179377811083533787557755⟩⟩,⟨⟨22858881570510691594518616784,22858881570510691747400578739⟩,⟨4131865211801608969075449399,4131865211801609121823689710⟩⟩] +lemma kernel12_0_r5_5_eq : ∀ k : Fin 16, kernel12_0Expr 5 5 k = kernel12_0_r5_5 k := by decide +kernel +noncomputable def kernel12_0_r5_6 : Fin 16 → CBox := ![⟨⟨22271339811750317714057054271,22271339811750317863883060903⟩,⟨3301917146363284099428449559,3301917146363284249106485276⟩⟩,⟨⟨21672132396195009316453518723,21672132396195009463276979462⟩,⟨2511225936468040069282075269,2511225936468040215944396054⟩⟩,⟨⟨21062890136951612496480524699,21062890136951612640281635366⟩,⟨1759599432107809679000214632,1759599432107809822628085407⟩⟩,⟨⟨20445218923422912370976879157,20445218923422912511801629970⟩,⟨1046765052553539012462515845,1046765052553539153102961089⟩⟩,⟨⟨19820695166683839170528628387,19820695166683839308351835882⟩,⟨372372522795075279074821422,372372522795075416703679722⟩⟩,⟨⟨19190861486722221427811597933,19190861486722221562691572754⟩,⟨(-264003146609436281836484102),(-264003146609436147159923127)⟩⟩,⟨⟨18557222655748870151798394503,18557222655748870283721801542⟩,⟨(-862858456034788631714850056),(-862858456034788500002955791)⟩⟩,⟨⟨17921241810045259636029725691,17921241810045259765049312595⟩,⟨(-1424758010239044889517787530),(-1424758010239044760716890497)⟩⟩,⟨⟨17284336941036928646828925797,17284336941036928773080350398⟩,⟨(-1950330930046081376801507669),(-1950330930046081250775000038)⟩⟩,⟨⟨16647877674470980400113017620,16647877674470980523709067784⟩,⟨(-2440267104072577332577670114),(-2440267104072577209211898176)⟩⟩,⟨⟨16013182344750712605313470813,16013182344750712726238013408⟩,⟨(-2895313302684750700826262319),(-2895313302684750580136520824)⟩⟩,⟨⟨15381515369653311623670607084,15381515369653311741973438461⟩,⟨(-3316269176587943487499373935),(-3316269176587943369435078425)⟩⟩,⟨⟨14754084928841271756999381166,14754084928841271872658496931⟩,⟨(-3703983162516787810822272203),(-3703983162516787695404651724)⟩⟩,⟨⟨14132040947787926619143003880,14132040947787926732220023052⟩,⟨(-4059348318408458138708186873),(-4059348318408458025874904872)⟩⟩,⟨⟨13516473386984864165195276208,13516473386984864275679980351⟩,⟨(-4383298110210940864044133841),(-4383298110210940753804703541)⟩⟩,⟨⟨12908410834596077214551917547,12908410834596077322499349187⟩,⟨(-4676802172107945540218267382),(-4676802172107945432516995307)⟩⟩] +lemma kernel12_0_r5_6_eq : ∀ k : Fin 16, kernel12_0Expr 5 6 k = kernel12_0_r5_6 k := by decide +kernel +noncomputable def kernel12_0_r5_7 : Fin 16 → CBox := ![⟨⟨12308819399081792598120488252,12308819399081792703511691594⟩,⟨(-4940862061438690979681684484),(-4940862061438690874536885769)⟩⟩,⟨⟨11718601896744529246852049534,11718601896744529349759843220⟩,⟨(-5176507028961915585556284544),(-5176507028961915482889530646)⟩⟩,⟨⟨11138597327660674649734885941,11138597327660674750162523339⟩,⟨(-5384789824367523398186720893),(-5384789824367523297983419690)⟩⟩,⟨⟨10569580632061400319235049125,10569580632061400417241004597⟩,⟨(-5566782556085468474014745176),(-5566782556085468376216987227)⟩⟩,⟨⟨10012262717924709331327206737,10012262717924709426899814488⟩,⟨(-5723572623489620124503657476),(-5723572623489620029123657234)⟩⟩,⟨⟨9467290749342417612088057070,9467290749342417705296542697⟩,⟨(-5856258738554785261747161052),(-5856258738554785168716269279)⟩⟩,⟨⟨8935248684137425439649746431,8935248684137425530493705851⟩,⟨(-5965947052908548218659106209),(-5965947052908548127978285723)⟩⟩,⟨⟨8416658048232143188396561745,8416658048232143276937628471⟩,⟨(-6053747405037176483841991059),(-6053747405037176395450184132)⟩⟩,⟨⟨7911978933411692472256922590,7911978933411692558543285689⟩,⟨(-6120769701167769110049521249),(-6120769701167769023899096434)⟩⟩,⟨⟨7421611204387703114161796988,7421611204387703198283767779⟩,⟨(-6168120442068399727233338278),(-6168120442068399643234558886)⟩⟩,⟨⟨6945895900451273081943882315,6945895900451273163901533987⟩,⟨(-6196899406695495546704521860),(-6196899406695495464857870220)⟩⟩,⟨⟨6485116816506998525728585486,6485116816506998605581805327⟩,⟨(-6208196502284220430646056674),(-6208196502284220350892208120)⟩⟩,⟨⟨6039502247902938700687397210,6039502247902938778429861400⟩,⟨(-6203088789134072383933768625),(-6203088789134072306279591480)⟩⟩,⟨⟨5609226883212006114074931435,5609226883212006189776044592⟩,⟨(-6182637686998803606366874449),(-6182637686998803530743514088)⟩⟩,⟨⟨5194413828975697689906599144,5194413828975697763570415230⟩,⟨(-6147886368657239133958089139),(-6147886368657239060362023187)⟩⟩,⟨⟨4795136750387585189025918027,4795136750387585260713692036⟩,⟨(-6099857344929218425089951210),(-6099857344929218353460454744)⟩⟩] +lemma kernel12_0_r5_7_eq : ∀ k : Fin 16, kernel12_0Expr 5 7 k = kernel12_0_r5_7 k := by decide +kernel +noncomputable def kernel12_0_r5_8 : Fin 16 → CBox := ![⟨⟨4411422111967054638256360441,4411422111967054707968398677⟩,⟨(-6039550244117748457076611829),(-6039550244117748387413890645)⟩⟩,⟨⟨4043251502448207479177450584,4043251502448207547020268452⟩,⟨(-5967939787612935906262153228),(-5967939787612935838460199966)⟩⟩,⟨⟨3690564028378762877595006730,3690564028378762943573698897⟩,⟨(-5885973962193069758094531003),(-5885973962193069692148743027)⟩⟩,⟨⟨3353258761282836316292663958,3353258761282836380466650599⟩,⟨(-5794572388410332360113720101),(-5794572388410332295965160629)⟩⟩,⟨⟨3031197223682757304953021725,3031197223682757367320928716⟩,⟨(-5694624883359239430308163856),(-5694624883359239367958674401)⟩⟩,⟨⟨2724205899791395840944368762,2724205899791395901573723555⟩,⟨(-5586990215100471857333361466),(-5586990215100471796715870974)⟩⟩,⟨⟨2432078757270270314320382541,2432078757270270373233663082⟩,⟨(-5472495045055884914432464117),(-5472495045055884855525012934)⟩⟩,⟨⟨2154579767092281260049817585,2154579767092281317311386187⟩,⟨(-5351933053805975800992565290),(-5351933053805975743731244966)⟩⟩,⟨⟨1891445409243406545611106220,1891445409243406601219086890⟩,⟨(-5226064244911965164783611387),(-5226064244911965109170703554)⟩⟩,⟨⟨1642387152737213887034017000,1642387152737213941055739662⟩,⟨(-5095614420653116095758642037),(-5095614420653116041727206121)⟩⟩,⟨⟨1407093899191741294778681422,1407093899191741347222915104⟩,⟨(-4961274822917414919203740184),(-4961274822917414866745383759)⟩⟩,⟨⟨1185234380022418573509062557,1185234380022418624432623450⟩,⟨(-4823701931910964800312693778),(-4823701931910964749370959847)⟩⟩,⟨⟨976459498129682469876097149,976459498129682519281369124⟩,⟨(-4683517414858374627578347893),(-4683517414858374578151200569)⟩⟩,⟨⟨780404605798441453295880655,780404605798441501246373500⟩,⟨(-4541308216452365757628991826),(-4541308216452365709653249451)⟩⟩,⟨⟨596691711371534514405609679,596691711371534560911683445⟩,⟨(-4397626782474440667926352839),(-4397626782474440621391973369)⟩⟩,⟨⟨424931608104107017163152911,424931608104107062279898178⟩,⟨(-4252991407747849923226679659),(-4252991407747849878078870916)⟩⟩] +lemma kernel12_0_r5_8_eq : ∀ k : Fin 16, kernel12_0Expr 5 8 k = kernel12_0_r5_8 k := by decide +kernel +noncomputable def kernel12_0_r5_9 : Fin 16 → CBox := ![⟨⟨264725919444088572666990406,264725919444088616396209096⟩,⟨(-4107886699396814956381468830),(-4107886699396814912618719130)⟩⟩,⟨⟨115669055809820959316525002,115669055809821001721638630⟩,⟨(-3962764146269094202653028159),(-3962764146269094160212183520)⟩⟩,⟨⟨(-22649921256078614089213299),(-22649921256078572996804114)⟩,⟨(-3818042785329177574127748882),(-3818042785329177532997669246)⟩⟩,⟨⟨(-150645530892269957208909064),(-150645530892269917376445213)⟩,⟨(-3674109955842952835339037751),(-3674109955842952795467203967)⟩⟩,⟨⟨(-268734203261270470206163307),(-268734203261270431628391423)⟩,⟨(-3531322132247593444306978182),(-3531322132247593405688371189)⟩⟩,⟨⟨(-377332710279806442071955573),(-377332710279806404690780943)⟩,⟨(-3390005826728406771614622702),(-3390005826728406734191358975)⟩⟩,⟨⟨(-476856697895407870413709983),(-476856697895407834217196068)⟩,⟨(-3250458552702995878970957098),(-3250458552702995842731306885)⟩⟩,⟨⟨(-567719320412968883105487726),(-567719320412968848043667602)⟩,⟨(-3112949840637728983003381919),(-3112949840637728947897564446)⟩⟩,⟨⟨(-650329976760177120349804406),(-650329976760177086418366172)⟩,⟨(-2977722297887492705247417123),(-2977722297887492671271304119)⟩⟩,⟨⟨(-725093148007746211549690753),(-725093148007746178692223294)⟩,⟨(-2844992704552305072862825632),(-2844992704552305039960165696)⟩⟩,⟨⟨(-792407334930703082833474790),(-792407334930703051037929806)⟩,⟨(-2714953137678868275203266548),(-2714953137678868243362169763)⟩⟩,⟨⟨(-852664093911562619862149094),(-852664093911562589081705147)⟩,⟨(-2587772116496888783737414905),(-2587772116496888752911198303)⟩⟩,⟨⟨(-906247169045604245442118096),(-906247169045604215670472271)⟩,⟨(-2463595761764416165629798219),(-2463595761764416135812296959)⟩⟩,⟨⟨(-953531717912773667652282716),(-953531717912773638838424314)⟩,⟨(-2342548962699113823109110258),(-2342548962699113794249429300)⟩⟩,⟨⟨(-994883628129709288494283441),(-994883628129709260626410538)⟩,⟨(-2224736545388998909129014002),(-2224736545388998881215467769)⟩⟩,⟨⟨(-1030658921488422970755502002),(-1030658921488422943663555831)⟩,⟨(-2110244437002689009607604419),(-2110244437002688982472875197)⟩⟩] +lemma kernel12_0_r5_9_eq : ∀ k : Fin 16, kernel12_0Expr 5 9 k = kernel12_0_r5_9 k := by decide +kernel +noncomputable def kernel12_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-1061203242224312591881511841),(-1061203242224312565555218691)⟩,⟨(-1999140820551698636898215030),(-1999140820551698610532216294)⟩⟩,⟨⟨(-1086851425734222324929971316),(-1086851425734222299328836919)⟩,⟨(-1891477275392202850593483923),(-1891477275392202824955580003)⟩⟩,⟨⟨(-1107927143883711966442677942),(-1107927143883711941564029870)⟩,⟨(-1787289899087543358204029216),(-1787289899087543333291418733)⟩⟩,⟨⟨(-1124742622899841107120105806),(-1124742622899841082931706698)⟩,⟨(-1686600406682472978366091121),(-1686600406682472954146403066)⟩⟩,⟨⟨(-1137598429739718893895803507),(-1137598429739718870399737190)⟩,⟨(-1589417203862868683666267682),(-1589417203862868660141463121)⟩⟩,⟨⟨(-1146783322753758550179932931),(-1146783322753758527339698543)⟩,⟨(-1495736430887820818754929627),(-1495736430887820795888379341)⟩⟩,⟨⟨(-1152574162423823794987774273),(-1152574162423823772800236278)⟩,⟨(-1405542974582335706885613076),(-1405542974582335684674063508)⟩⟩,⟨⟨(-1155235877947981335464908328),(-1155235877947981313899677388)⟩,⟨(-1318811446066358872785754418),(-1318811446066358851198696114)⟩⟩,⟨⟨(-1155021485463031456350721459),(-1155021485463031435410587051)⟩,⟨(-1235507122267699845820232983),(-1235507122267699824860344781)⟩⟩,⟨⟨(-1152172153740988595291330291),(-1152172153740988574940647732)⟩,⟨(-1155586849621249159522542553),(-1155586849621249139154065984)⟩⟩,⟨⟨(-1146917313263821667763629707),(-1146917313263821647999038118)⟩,⟨(-1078999908693416250365860680),(-1078999908693416230585329950)⟩⟩,⟨⟨(-1139474804669643975117689167),(-1139474804669643955910795854)⟩,⟨(-1005688838788025842156573375),(-1005688838788025822935490788)⟩⟩,⟨⟨(-1130051062670798494915057227),(-1130051062670798476266914124)⟩,⟨(-935590221887270124176758993),(-935590221887270105516079032)⟩⟩,⟨⟨(-1118841331667598647997351674),(-1118841331667598629876016723)⟩,⟨(-868635425558228778554354154),(-868635425558228760422036917)⟩⟩,⟨⟨(-1106029909418605473699740248),(-1106029909418605456101826791)⟩,⟨(-804751304711652354415996742),(-804751304711652336808564628)⟩⟩,⟨⟨(-1091790415277078419364939998),(-1091790415277078402264120666)⟩,⟨(-743860862335064274634726100),(-743860862335064257525762188)⟩⟩] +lemma kernel12_0_r5_10_eq : ∀ k : Fin 16, kernel12_0Expr 5 10 k = kernel12_0_r5_10 k := by decide +kernel +noncomputable def kernel12_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-1076286079661551000595651658),(-1076286079661550983994236001)⟩,⟨(-685883869536858412126219260),(-685883869536858395517949524)⟩⟩,⟨⟨(-1059670051594380883614942056),(-1059670051594380867481832936)⟩,⟨(-630737445432199598847908783),(-630737445432199582709153642)⟩⟩,⟨⟨(-1042085721313745742043734632),(-1042085721313745726375665958)⟩,⟨(-578336597575565304409157181),(-578336597575565288736573449)⟩⟩,⟨⟨(-1023667055140160350575053607),(-1023667055140160335347787235)⟩,⟨(-528594723799217903433533847),(-528594723799217888202808737)⟩⟩,⟨⟨(-1004538939956560054980020089),(-1004538939956560040194308271)⟩,⟨(-481424076452400133219639318),(-481424076452400118431454721)⟩⟩,⟨⟨(-984817534839841933366718797),(-984817534839841918995330255)⟩,⟨(-436736190153329093942641957),(-436736190153329079569698877)⟩⟩,⟨⟨(-964610627560117867546909464),(-964610627560117853586813842)⟩,⟨(-394442274265934467679079490),(-394442274265934453718283535)⟩⟩,⟨⟨(-944017993840583092721918880),(-944017993840583079150927449)⟩,⟨(-354453571396618195823199372),(-354453571396618182252300931)⟩⟩,⟨⟨(-923131757444737656444772959),(-923131757444737643264727592)⟩,⟨(-316681683274030944686144791),(-316681683274030931506927664)⟩⟩,⟨⟨(-902036749327740717798162283),(-902036749327740704983016967)⟩,⟨(-281038865427929021726458889),(-281038865427929008912822594)⟩⟩,⟨⟨(-880810864254075595098076336),(-880810864254075582644401763)⟩,⟨(-247438292122583812561924904),(-247438292122583800110385082)⟩⟩,⟨⟨(-859525413443722261035308845),(-859525413443722248920244671)⟩,⟨(-215794293026968885454538242),(-215794293026968873342175282)⟩⟩,⟨⟨(-838245471963052428757946673),(-838245471963052416982598660)⟩,⟨(-186022563119056615239471637),(-186022563119056603467345257)⟩⟩,⟨⟨(-817030219724167210589592391),(-817030219724167199131372289)⟩,⟨(-158040347326020444430906926),(-158040347326020432976386924)⟩⟩,⟨⟨(-795933275096977080580209182),(-795933275096977069436950613)⟩,⟨(-131766601396951213745440827),(-131766601396951202606319949)⟩⟩,⟨⟨(-775003020271662335125016531),(-775003020271662324278567305)⟩,⟨(-107122130490825980119882498),(-107122130490825969277971390)⟩⟩] +lemma kernel12_0_r5_11_eq : ∀ k : Fin 16, kernel12_0Expr 5 11 k = kernel12_0_r5_11 k := by decide +kernel +noncomputable def kernel12_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-754282917635021729432808776),(-754282917635021718885632294)⟩,⟨(-84029706940857681293334683),(-84029706940857670751059966)⟩⟩,⟨⟨(-733811816542471342283700627),(-733811816542471332013615547)⟩,⟨(-62414168627913316552233644),(-62414168627913306287381862)⟩⟩,⟨⟨(-713624249978023389793075829),(-713624249978023379794358793)⟩,⟨(-42202499361288889876648076),(-42202499361288879883463874)⟩⟩,⟨⟨(-693750720697451588586643671),(-693750720697451578843123677)⟩,⟨(-23323892625601794686128035),(-23323892625601784948412052)⟩⟩,⟨⟨(-674217976545092245542848829),(-674217976545092236056181067)⟩,⟨(-5709800008691893343827931),(-5709800008691883863206658)⟩⟩,⟨⟨(-655049274722448786621485676),(-655049274722448777373154730)⟩,⟨10706034422049004227163867,10706034422049013469229979⟩⟩,⟨⟨(-636264634867119369449418313),(-636264634867119360438191350)⟩,⟨25987552577881605110826360,25987552577881614115594931⟩⟩,⟨⟨(-617881080873750828617228063),(-617881080873750819828458850)⟩,⟨40196372477069836694945384,40196372477069845477083730⟩⟩,⟨⟨(-599912871454970534215063033),(-599912871454970525651396417)⟩,⟨53391788933314745320618236,53391788933314753877503769⟩⟩,⟨⟨(-582371719499822912096471089),(-582371719499822903740161547)⟩,⟨65630783749663946826264954,65630783749663955175660548⟩⟩,⟨⟨(-565267000340425154875989190),(-565267000340425146726107641)⟩,⟨76968044419379776736939640,76968044419379784879793153⟩⟩,⟨⟨(-548605949084661476441623099),(-548605949084661468484925587)⟩,⟨87455990391527730037612180,87455990391527737987182752⟩⟩,⟨⟨(-532393847214075571098423344),(-532393847214075563336854137)⟩,⟨97144806015111393160401527,97144806015111400914761653⟩⟩,⟨⟨(-516634198682024931237367545),(-516634198682024923655543172)⟩,⟨106082479331073988273069723,106082479331073995847615035⟩⟩,⟨⟨(-501328895777962436546839967),(-501328895777962429142596456)⟩,⟨114314845936095745770427472,114314845936095753167335880⟩⟩,⟨⟨(-486478375049746629395682408),(-486478375049746622154651157)⟩,⟨121885637195567132238999116,121885637195567139472649715⟩⟩] +lemma kernel12_0_r5_12_eq : ∀ k : Fin 16, kernel12_0Expr 5 12 k = kernel12_0_r5_12 k := by decide +kernel +noncomputable def kernel12_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-472081763597488082552817484),(-472081763597488075478297487)⟩,⟨128836532135175472901322992,128836532135175479968429486⟩⟩,⟨⟨(-458137016069947512284149623),(-458137016069947505361333583)⟩,⟨135207212391007820282260853,135207212391007827197638288⟩⟩,⟨⟨(-444641042708238162654046663),(-444641042708238155882784260)⟩,⟨141035419646780855476748453,141035419646780862240557253⟩⟩,⟨⟨(-431589828791868888082242010),(-431589828791868881451891476)⟩,⟨146357015033625264698372401,146357015033625271321261156⟩⟩,⟨⟨(-418978545849303958555395062),(-418978545849303952068396177)⟩,⟨151206040012672347980815558,151206040012672354460353610⟩⟩,⟨⟨(-406801654999508374105044733),(-406801654999508367748718452)⟩,⟨155614778303435928844251676,155614778303435935193122777⟩⟩,⟨⟨(-395053002792678474663884520),(-395053002792678468438289121)⟩,⟨159613818461598302015467748,159613818461598308233620742⟩⟩,⟨⟨(-383725909917798608065082943),(-383725909917798601960542338)⟩,⟨163232116748262025551538061,163232116748262031648653032⟩⟩,⟨⟨(-372813253142073269301329830),(-372813253142073263321098447)⟩,⟨166497059969006315147715229,166497059969006321120544464⟩⟩,⟨⟨(-362307540842903608835999793),(-362307540842903602967683716)⟩,⟨169434527995191383146063772,169434527995191389007003226⟩⟩,⟨⟨(-352200982487135842739250184),(-352200982487135836982954997)⟩,⟨172068955711905244544828474,172068955711905250293936522⟩⟩,⟨⟨(-342485552405020221974614837),(-342485552405020216321463395)⟩,⟨174423394166777502691004971,174423394166777508337231871⟩⟩,⟨⟨(-333153048197881206752156148),(-333153048197881201204791388)⟩,⟨176519570721637062571996435,176519570721637068112689051⟩⟩,⟨⟨(-324195144109095904105579192),(-324195144109095898653237453)⟩,⟨178377948034718930470683808,178377948034718935916592511⟩⟩,⟨⟨(-315603439677777664601643665),(-315603439677777659244736224)⟩,⟨180017781724890678464064855,180017781724890683814768296⟩⟩,⟨⟨(-307369503983719801542789889),(-307369503983719796273262821)⟩,⟨181457176591239838726329931,181457176591239843989870211⟩⟩] +lemma kernel12_0_r5_13_eq : ∀ k : Fin 16, kernel12_0Expr 5 13 k = kernel12_0_r5_13 k := by decide +kernel +noncomputable def kernel12_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-299484915780811734654700518),(-299484915780811729476156917)⟩,⟨182713141281412778304058230,182713141281412783476823607⟩⟩,⟨⟨(-291941299804424255920280113),(-291941299804424250821832290)⟩,⟨183801641320400860843850498,183801641320400865936716873⟩⟩,⟨⟨(-284730359526287152206403950),(-284730359526287147188591510)⟩,⟨184737650428111223531497168,184737650428111228543916191⟩⟩,⟨⟨(-277843906618254080546173253),(-277843906618254075601599216)⟩,⟨185535200069119499973846291,185535200069119504913204675⟩⟩,⟨⟨(-271273887374157882700997441),(-271273887374157877832449667)⟩,⟨186207427191563544727658636,186207427191563549591160859⟩⟩,⟨⟨(-265012406326785122499837597),(-265012406326785117697988100)⟩,⟨186766620124284137447001864,186766620124284142243965843⟩⟩,⟨⟨(-259051747284912033606747791),(-259051747284912028872241971)⟩,⟨187224262612133781771427671,187224262612133786501200418⟩⟩,⟨⟨(-253384392003406264101404817),(-253384392003406259427408043)⟩,⟨187591075978940022915238997,187591075978940027584646220⟩⟩,⟨⟨(-248003036687661922725518248),(-248003036687661918115528171)⟩,⟨187877059416005572662998964,187877059416005577268536515⟩⟩,⟨⟨(-242900606522143379621213721),(-242900606522143375065802441)⟩,⟨188091528401332325978431399,188091528401332330529518248⟩⟩,⟨⟨(-238070268401602372544363282),(-238070268401602368044254387)⟩,⟨188243151261046087850918369,188243151261046092346824325⟩⟩,⟨⟨(-233505442032632561450793084),(-233505442032632556999633993)⟩,⟨188339983889846849624570140,188339983889846854071639987⟩⟩,⟨⟨(-229199809562658710511396382),(-229199809562658706112080907)⟩,⟨188389502651786220671117970,188389502651786225066452128⟩⟩,⟨⟨(-225147323883241278048801711),(-225147323883241273693026142)⟩,⟨188398635486346531119773676,188398635486346535471668119⟩⟩,⟨⟨(-221342215744723183974984796),(-221342215744723179663528126)⟩,⟨188373791247729390605638186,188373791247729394913308122⟩⟩,⟨⟨(-217778999809760931474915611),(-217778999809760927201827397)⟩,⟨188320887307516074247594294,188320887307516078516983289⟩⟩] +lemma kernel12_0_r5_14_eq : ∀ k : Fin 16, kernel12_0Expr 5 14 k = kernel12_0_r5_14 k := by decide +kernel +noncomputable def kernel12_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-214452479764169795109903906),(-214452479764169790878929669)⟩,⟨188245375452495678000979878,188245375452495682228337483⟩⟩,⟨⟨(-211357752594771286975533753),(-211357752594771282777925263)⟩,⟨188152266110523919375502754,188152266110523923569570157⟩⟩,⟨⟨(-208490212135555947702272184),(-208490212135555943538836245)⟩,⟨188046150937826882562477845,188046150937826886722443080⟩⟩,⟨⟨(-205845551975457971948304341),(-205845551975457967813425878)⟩,⟨187931223801247854814427406,187931223801247858945899381⟩⟩,⟨⟨(-203419767813369830695076268),(-203419767813369826591717548)⟩,⟨187811300188596508844072841,187811300188596512944084756⟩⟩,⟨⟨(-201209159338692052648696784),(-201209159338692048569221037)⟩,⟨187689835079539896395861824,187689835079539900472044193⟩⟩,⟨⟨(-199210331708700719639542183),(-199210331708700715584762194)⟩,⟨187569939308413010642129265,187569939308413014693664611⟩⟩,⟨⟨(-197420196687306219204000959),(-197420196687306215168568271)⟩,⟨187454394448959307842435475,187454394448959311874666613⟩⟩,⟨⟨(-195835973503352982423851924),(-195835973503352978411055881)⟩,⟨187345666249372247467860579,187345666249372251477494073⟩⟩,⟨⟨(-194455189480451535629004504),(-194455189480451531630452841)⟩,⟨187245916644128913512382060,187245916644128917507804207⟩⟩,⟨⟨(-193275680484420241393050900),(-193275680484420237409633799)⟩,⟨187157014367015199024147184,187157014367015203004463438⟩⟩,⟨⟨(-192295591228722616723287978),(-192295591228722612749962339)⟩,⟨187080544187465916598679855,187080544187465920568928033⟩⟩,⟨⟨(-191513375472794256231707951),(-191513375472794252271571994)⟩,⟨187017814789907742681323627,187017814789907746638401607⟩⟩,⟨⟨(-190927796142837600561736967),(-190927796142837596607592916)⟩,⟨186969865313221666645643016,186969865313221670596743033⟩⟩,⟨⟨(-190537925399498925177935864),(-190537925399498921230624473)⟩,⟨186937470564756702668888786,186937470564756706613165881⟩⟩,⟨⟨(-190343144671805348253896973),(-190343144671805344308522441)⟩,⟨186921144920548891868028135,186921144920548895810372997⟩⟩] +lemma kernel12_0_r5_15_eq : ∀ k : Fin 16, kernel12_0Expr 5 15 k = kernel12_0_r5_15 k := by decide +kernel +noncomputable def kernel12_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel12_0_r5_0,kernel12_0_r5_1,kernel12_0_r5_2,kernel12_0_r5_3,kernel12_0_r5_4,kernel12_0_r5_5,kernel12_0_r5_6,kernel12_0_r5_7,kernel12_0_r5_8,kernel12_0_r5_9,kernel12_0_r5_10,kernel12_0_r5_11,kernel12_0_r5_12,kernel12_0_r5_13,kernel12_0_r5_14,kernel12_0_r5_15] +lemma kernel12_0_r5_eq (i k : Fin 16) : kernel12_0Expr 5 i k = kernel12_0_r5 i k := by + fin_cases i + · exact kernel12_0_r5_0_eq k + · exact kernel12_0_r5_1_eq k + · exact kernel12_0_r5_2_eq k + · exact kernel12_0_r5_3_eq k + · exact kernel12_0_r5_4_eq k + · exact kernel12_0_r5_5_eq k + · exact kernel12_0_r5_6_eq k + · exact kernel12_0_r5_7_eq k + · exact kernel12_0_r5_8_eq k + · exact kernel12_0_r5_9_eq k + · exact kernel12_0_r5_10_eq k + · exact kernel12_0_r5_11_eq k + · exact kernel12_0_r5_12_eq k + · exact kernel12_0_r5_13_eq k + · exact kernel12_0_r5_14_eq k + · exact kernel12_0_r5_15_eq k +noncomputable def kernel12_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel12_0_r0,kernel12_0_r1,kernel12_0_r2,kernel12_0_r3,kernel12_0_r4,kernel12_0_r5] +lemma kernel12_0_eq (j : Fin 6) (i k : Fin 16) : kernel12_0Expr j i k = kernel12_0 j i k := by + fin_cases j + · exact kernel12_0_r0_eq i k + · exact kernel12_0_r1_eq i k + · exact kernel12_0_r2_eq i k + · exact kernel12_0_r3_eq i k + · exact kernel12_0_r4_eq i k + · exact kernel12_0_r5_eq i k +lemma kernel12_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel12_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(12:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel12_0_eq] + unfold kernel12_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans12_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel12_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans12 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel12_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r0_0_eq : ∀ k : Fin 16, kernel12_1Expr 0 0 k = kernel12_1_r0_0 k := by decide +kernel +noncomputable def kernel12_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r0_1_eq : ∀ k : Fin 16, kernel12_1Expr 0 1 k = kernel12_1_r0_1 k := by decide +kernel +noncomputable def kernel12_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r0_2_eq : ∀ k : Fin 16, kernel12_1Expr 0 2 k = kernel12_1_r0_2 k := by decide +kernel +noncomputable def kernel12_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r0_3_eq : ∀ k : Fin 16, kernel12_1Expr 0 3 k = kernel12_1_r0_3 k := by decide +kernel +noncomputable def kernel12_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r0_4_eq : ∀ k : Fin 16, kernel12_1Expr 0 4 k = kernel12_1_r0_4 k := by decide +kernel +noncomputable def kernel12_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel12_1_r0_5_eq : ∀ k : Fin 16, kernel12_1Expr 0 5 k = kernel12_1_r0_5 k := by decide +kernel +noncomputable def kernel12_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel12_1_r0_6_eq : ∀ k : Fin 16, kernel12_1Expr 0 6 k = kernel12_1_r0_6 k := by decide +kernel +noncomputable def kernel12_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel12_1_r0_7_eq : ∀ k : Fin 16, kernel12_1Expr 0 7 k = kernel12_1_r0_7 k := by decide +kernel +noncomputable def kernel12_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel12_1_r0_8_eq : ∀ k : Fin 16, kernel12_1Expr 0 8 k = kernel12_1_r0_8 k := by decide +kernel +noncomputable def kernel12_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel12_1_r0_9_eq : ∀ k : Fin 16, kernel12_1Expr 0 9 k = kernel12_1_r0_9 k := by decide +kernel +noncomputable def kernel12_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel12_1_r0_10_eq : ∀ k : Fin 16, kernel12_1Expr 0 10 k = kernel12_1_r0_10 k := by decide +kernel +noncomputable def kernel12_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel12_1_r0_11_eq : ∀ k : Fin 16, kernel12_1Expr 0 11 k = kernel12_1_r0_11 k := by decide +kernel +noncomputable def kernel12_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel12_1_r0_12_eq : ∀ k : Fin 16, kernel12_1Expr 0 12 k = kernel12_1_r0_12 k := by decide +kernel +noncomputable def kernel12_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel12_1_r0_13_eq : ∀ k : Fin 16, kernel12_1Expr 0 13 k = kernel12_1_r0_13 k := by decide +kernel +noncomputable def kernel12_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel12_1_r0_14_eq : ∀ k : Fin 16, kernel12_1Expr 0 14 k = kernel12_1_r0_14 k := by decide +kernel +noncomputable def kernel12_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel12_1_r0_15_eq : ∀ k : Fin 16, kernel12_1Expr 0 15 k = kernel12_1_r0_15 k := by decide +kernel +noncomputable def kernel12_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel12_1_r0_0,kernel12_1_r0_1,kernel12_1_r0_2,kernel12_1_r0_3,kernel12_1_r0_4,kernel12_1_r0_5,kernel12_1_r0_6,kernel12_1_r0_7,kernel12_1_r0_8,kernel12_1_r0_9,kernel12_1_r0_10,kernel12_1_r0_11,kernel12_1_r0_12,kernel12_1_r0_13,kernel12_1_r0_14,kernel12_1_r0_15] +lemma kernel12_1_r0_eq (i k : Fin 16) : kernel12_1Expr 0 i k = kernel12_1_r0 i k := by + fin_cases i + · exact kernel12_1_r0_0_eq k + · exact kernel12_1_r0_1_eq k + · exact kernel12_1_r0_2_eq k + · exact kernel12_1_r0_3_eq k + · exact kernel12_1_r0_4_eq k + · exact kernel12_1_r0_5_eq k + · exact kernel12_1_r0_6_eq k + · exact kernel12_1_r0_7_eq k + · exact kernel12_1_r0_8_eq k + · exact kernel12_1_r0_9_eq k + · exact kernel12_1_r0_10_eq k + · exact kernel12_1_r0_11_eq k + · exact kernel12_1_r0_12_eq k + · exact kernel12_1_r0_13_eq k + · exact kernel12_1_r0_14_eq k + · exact kernel12_1_r0_15_eq k +noncomputable def kernel12_1_r1_0 : Fin 16 → CBox := ![⟨⟨283964,284005⟩,⟨(-198037),(-197995)⟩⟩,⟨⟨283397,283443⟩,⟨(-197479),(-197433)⟩⟩,⟨⟨282277,282319⟩,⟨(-196374),(-196333)⟩⟩,⟨⟨280586,280627⟩,⟨(-194726),(-194685)⟩⟩,⟨⟨278349,278390⟩,⟨(-192565),(-192524)⟩⟩,⟨⟨275596,275637⟩,⟨(-189880),(-189839)⟩⟩,⟨⟨272307,272348⟩,⟨(-186700),(-186659)⟩⟩,⟨⟨268530,268571⟩,⟨(-183069),(-183028)⟩⟩,⟨⟨264274,264320⟩,⟨(-178987),(-178940)⟩⟩,⟨⟨259561,259607⟩,⟨(-174507),(-174460)⟩⟩,⟨⟨254421,254462⟩,⟨(-169632),(-169591)⟩⟩,⟨⟨248887,248928⟩,⟨(-164427),(-164386)⟩⟩,⟨⟨242984,243025⟩,⟨(-158931),(-158889)⟩⟩,⟨⟨236733,236780⟩,⟨(-153166),(-153120)⟩⟩,⟨⟨230176,230217⟩,⟨(-147167),(-147126)⟩⟩,⟨⟨223359,223400⟩,⟨(-140971),(-140930)⟩⟩] +lemma kernel12_1_r1_0_eq : ∀ k : Fin 16, kernel12_1Expr 1 0 k = kernel12_1_r1_0 k := by decide +kernel +noncomputable def kernel12_1_r1_1 : Fin 16 → CBox := ![⟨⟨216298,216345⟩,⟨(-134654),(-134607)⟩⟩,⟨⟨209025,209071⟩,⟨(-128218),(-128171)⟩⟩,⟨⟨201600,201651⟩,⟨(-121721),(-121669)⟩⟩,⟨⟨194025,194086⟩,⟨(-115193),(-115131)⟩⟩,⟨⟨186376,186417⟩,⟨(-108662),(-108621)⟩⟩,⟨⟨178633,178674⟩,⟨(-102173),(-102132)⟩⟩,⟨⟨170873,170925⟩,⟨(-95774),(-95723)⟩⟩,⟨⟨163112,163158⟩,⟨(-89465),(-89418)⟩⟩,⟨⟨155375,155416⟩,⟨(-83284),(-83242)⟩⟩,⟨⟨147702,147744⟩,⟨(-77275),(-77234)⟩⟩,⟨⟨140111,140152⟩,⟨(-71444),(-71403)⟩⟩,⟨⟨132614,132676⟩,⟨(-65805),(-65743)⟩⟩,⟨⟨125280,125321⟩,⟨(-60382),(-60340)⟩⟩,⟨⟨118086,118128⟩,⟨(-55205),(-55164)⟩⟩,⟨⟨111060,111101⟩,⟨(-50259),(-50218)⟩⟩,⟨⟨104235,104281⟩,⟨(-45559),(-45512)⟩⟩] +lemma kernel12_1_r1_1_eq : ∀ k : Fin 16, kernel12_1Expr 1 1 k = kernel12_1_r1_1 k := by decide +kernel +noncomputable def kernel12_1_r1_2 : Fin 16 → CBox := ![⟨⟨97632,97674⟩,⟨(-41125),(-41083)⟩⟩,⟨⟨91226,91267⟩,⟨(-36962),(-36920)⟩⟩,⟨⟨85071,85113⟩,⟨(-33044),(-33002)⟩⟩,⟨⟨79149,79190⟩,⟨(-29404),(-29362)⟩⟩,⟨⟨73483,73524⟩,⟨(-26025),(-25983)⟩⟩,⟨⟨68068,68115⟩,⟨(-22898),(-22851)⟩⟩,⟨⟨62904,62951⟩,⟨(-20014),(-19967)⟩⟩,⟨⟨58006,58048⟩,⟨(-17377),(-17336)⟩⟩,⟨⟨53369,53416⟩,⟨(-14985),(-14938)⟩⟩,⟨⟨48981,49028⟩,⟨(-12806),(-12759)⟩⟩,⟨⟨44870,44911⟩,⟨(-10832),(-10790)⟩⟩,⟨⟨41002,41044⟩,⟨(-9068),(-9026)⟩⟩,⟨⟨37369,37416⟩,⟨(-7494),(-7447)⟩⟩,⟨⟨33980,34022⟩,⟨(-6107),(-6065)⟩⟩,⟨⟨30825,30872⟩,⟨(-4870),(-4823)⟩⟩,⟨⟨27899,27941⟩,⟨(-3786),(-3744)⟩⟩] +lemma kernel12_1_r1_2_eq : ∀ k : Fin 16, kernel12_1Expr 1 2 k = kernel12_1_r1_2 k := by decide +kernel +noncomputable def kernel12_1_r1_3 : Fin 16 → CBox := ![⟨⟨25181,25223⟩,⟨(-2855),(-2813)⟩⟩,⟨⟨22686,22728⟩,⟨(-2061),(-2019)⟩⟩,⟨⟨20375,20417⟩,⟨(-1365),(-1323)⟩⟩,⟨⟨18261,18303⟩,⟨(-783),(-741)⟩⟩,⟨⟨16314,16356⟩,⟨(-295),(-253)⟩⟩,⟨⟨14545,14592⟩,⟨93,140⟩⟩,⟨⟨12923,12965⟩,⟨428,470⟩⟩,⟨⟨11463,11505⟩,⟨698,740⟩⟩,⟨⟨10125,10167⟩,⟨888,930⟩⟩,⟨⟨8929,8971⟩,⟨1027,1069⟩⟩,⟨⟨7855,7903⟩,⟨1142,1189⟩⟩,⟨⟨6877,6919⟩,⟨1201,1243⟩⟩,⟨⟨6006,6053⟩,⟨1245,1293⟩⟩,⟨⟨5247,5289⟩,⟨1248,1290⟩⟩,⟨⟨4548,4591⟩,⟨1236,1278⟩⟩,⟨⟨3931,3979⟩,⟨1218,1266⟩⟩] +lemma kernel12_1_r1_3_eq : ∀ k : Fin 16, kernel12_1Expr 1 3 k = kernel12_1_r1_3 k := by decide +kernel +noncomputable def kernel12_1_r1_4 : Fin 16 → CBox := ![⟨⟨3396,3438⟩,⟨1180,1223⟩⟩,⟨⟨2916,2958⟩,⟨1111,1153⟩⟩,⟨⟨2492,2535⟩,⟨1056,1099⟩⟩,⟨⟨2130,2172⟩,⟨991,1033⟩⟩,⟨⟨1813,1861⟩,⟨914,962⟩⟩,⟨⟨1538,1581⟩,⟨859,901⟩⟩,⟨⟨1294,1337⟩,⟨797,840⟩⟩,⟨⟨1080,1128⟩,⟨725,773⟩⟩,⟨⟨902,945⟩,⟨657,700⟩⟩,⟨⟨750,803⟩,⟨589,642⟩⟩,⟨⟨607,650⟩,⟨531,574⟩⟩,⟨⟨497,545⟩,⟨482,530⟩⟩,⟨⟨401,450⟩,⟨428,476⟩⟩,⟨⟨321,370⟩,⟨374,422⟩⟩,⟨⟨268,311⟩,⟨334,377⟩⟩,⟨⟨204,247⟩,⟨295,338⟩⟩] +lemma kernel12_1_r1_4_eq : ∀ k : Fin 16, kernel12_1Expr 1 4 k = kernel12_1_r1_4 k := by decide +kernel +noncomputable def kernel12_1_r1_5 : Fin 16 → CBox := ![⟨⟨165,208⟩,⟨249,292⟩⟩,⟨⟨122,171⟩,⟨219,267⟩⟩,⟨⟨79,122⟩,⟨179,222⟩⟩,⟨⟨62,106⟩,⟨164,208⟩⟩,⟨⟨40,83⟩,⟨134,177⟩⟩,⟨⟨17,61⟩,⟨103,147⟩⟩,⟨⟨11,55⟩,⟨88,131⟩⟩,⟨⟨5,54⟩,⟨67,116⟩⟩,⟨⟨(-11),32⟩,⟨57,101⟩⟩,⟨⟨(-18),26⟩,⟨42,85⟩⟩,⟨⟨(-18),26⟩,⟨42,85⟩⟩,⟨⟨(-24),25⟩,⟨21,70⟩⟩,⟨⟨(-24),25⟩,⟨21,70⟩⟩,⟨⟨(-25),18⟩,⟨5,49⟩⟩,⟨⟨(-25),18⟩,⟨5,49⟩⟩,⟨⟨(-25),18⟩,⟨5,49⟩⟩] +lemma kernel12_1_r1_5_eq : ∀ k : Fin 16, kernel12_1Expr 1 5 k = kernel12_1_r1_5 k := by decide +kernel +noncomputable def kernel12_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-32),12⟩,⟨(-10),34⟩⟩,⟨⟨(-34),10⟩,⟨(-32),12⟩⟩,⟨⟨(-34),10⟩,⟨(-32),12⟩⟩] +lemma kernel12_1_r1_6_eq : ∀ k : Fin 16, kernel12_1Expr 1 6 k = kernel12_1_r1_6 k := by decide +kernel +noncomputable def kernel12_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-39),10⟩,⟨(-32),19⟩⟩,⟨⟨(-40),10⟩,⟨(-32),19⟩⟩,⟨⟨(-40),10⟩,⟨(-32),19⟩⟩,⟨⟨(-40),10⟩,⟨(-32),19⟩⟩,⟨⟨(-40),10⟩,⟨(-32),19⟩⟩,⟨⟨(-19),32⟩,⟨(-40),10⟩⟩] +lemma kernel12_1_r1_7_eq : ∀ k : Fin 16, kernel12_1Expr 1 7 k = kernel12_1_r1_7 k := by decide +kernel +noncomputable def kernel12_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-29),44⟩,⟨(-40),32⟩⟩,⟨⟨(-29),44⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-29),45⟩,⟨(-40),32⟩⟩,⟨⟨(-32),40⟩,⟨(-29),45⟩⟩] +lemma kernel12_1_r1_8_eq : ∀ k : Fin 16, kernel12_1Expr 1 8 k = kernel12_1_r1_8 k := by decide +kernel +noncomputable def kernel12_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-32),40⟩,⟨(-29),45⟩⟩,⟨⟨(-32),40⟩,⟨(-29),45⟩⟩,⟨⟨(-32),40⟩,⟨(-29),45⟩⟩,⟨⟨(-32),41⟩,⟨(-29),45⟩⟩,⟨⟨(-32),41⟩,⟨(-29),45⟩⟩,⟨⟨(-32),41⟩,⟨(-29),45⟩⟩,⟨⟨(-32),41⟩,⟨(-29),45⟩⟩,⟨⟨(-32),41⟩,⟨(-30),45⟩⟩,⟨⟨(-32),41⟩,⟨(-30),45⟩⟩,⟨⟨(-32),41⟩,⟨(-30),45⟩⟩,⟨⟨(-32),41⟩,⟨(-30),45⟩⟩,⟨⟨(-32),41⟩,⟨(-30),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel12_1_r1_9_eq : ∀ k : Fin 16, kernel12_1Expr 1 9 k = kernel12_1_r1_9 k := by decide +kernel +noncomputable def kernel12_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),30⟩,⟨(-32),41⟩⟩,⟨⟨(-45),30⟩,⟨(-32),41⟩⟩,⟨⟨(-45),30⟩,⟨(-32),41⟩⟩,⟨⟨(-45),30⟩,⟨(-32),41⟩⟩,⟨⟨(-45),30⟩,⟨(-32),41⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r1_10_eq : ∀ k : Fin 16, kernel12_1Expr 1 10 k = kernel12_1_r1_10 k := by decide +kernel +noncomputable def kernel12_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r1_11_eq : ∀ k : Fin 16, kernel12_1Expr 1 11 k = kernel12_1_r1_11 k := by decide +kernel +noncomputable def kernel12_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r1_12_eq : ∀ k : Fin 16, kernel12_1Expr 1 12 k = kernel12_1_r1_12 k := by decide +kernel +noncomputable def kernel12_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r1_13_eq : ∀ k : Fin 16, kernel12_1Expr 1 13 k = kernel12_1_r1_13 k := by decide +kernel +noncomputable def kernel12_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r1_14_eq : ∀ k : Fin 16, kernel12_1Expr 1 14 k = kernel12_1_r1_14 k := by decide +kernel +noncomputable def kernel12_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel12_1_r1_15_eq : ∀ k : Fin 16, kernel12_1Expr 1 15 k = kernel12_1_r1_15 k := by decide +kernel +noncomputable def kernel12_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel12_1_r1_0,kernel12_1_r1_1,kernel12_1_r1_2,kernel12_1_r1_3,kernel12_1_r1_4,kernel12_1_r1_5,kernel12_1_r1_6,kernel12_1_r1_7,kernel12_1_r1_8,kernel12_1_r1_9,kernel12_1_r1_10,kernel12_1_r1_11,kernel12_1_r1_12,kernel12_1_r1_13,kernel12_1_r1_14,kernel12_1_r1_15] +lemma kernel12_1_r1_eq (i k : Fin 16) : kernel12_1Expr 1 i k = kernel12_1_r1 i k := by + fin_cases i + · exact kernel12_1_r1_0_eq k + · exact kernel12_1_r1_1_eq k + · exact kernel12_1_r1_2_eq k + · exact kernel12_1_r1_3_eq k + · exact kernel12_1_r1_4_eq k + · exact kernel12_1_r1_5_eq k + · exact kernel12_1_r1_6_eq k + · exact kernel12_1_r1_7_eq k + · exact kernel12_1_r1_8_eq k + · exact kernel12_1_r1_9_eq k + · exact kernel12_1_r1_10_eq k + · exact kernel12_1_r1_11_eq k + · exact kernel12_1_r1_12_eq k + · exact kernel12_1_r1_13_eq k + · exact kernel12_1_r1_14_eq k + · exact kernel12_1_r1_15_eq k +noncomputable def kernel12_1_r2_0 : Fin 16 → CBox := ![⟨⟨17634948300453372,17634948300453397⟩,⟨6473023532994005,6473023532994029⟩⟩,⟨⟨17611390390456645,17611390390456670⟩,⟨6457056064519501,6457056064519526⟩⟩,⟨⟨17564361112151355,17564361112151380⟩,⟨6425220050532680,6425220050532705⟩⟩,⟨⟨17494033102192159,17494033102192191⟩,⟨6377712412189612,6377712412189645⟩⟩,⟨⟨17400664200674260,17400664200674287⟩,⟨6314826230536785,6314826230536815⟩⟩,⟨⟨17284596118658310,17284596118658340⟩,⟨6236948016974767,6236948016974795⟩⟩,⟨⟨17146252670578533,17146252670578563⟩,⟨6144554125536782,6144554125536810⟩⟩,⟨⟨16986137579400069,16986137579400102⟩,⟨6038206350295198,6038206350295231⟩⟩,⟨⟨16804831864494504,16804831864494545⟩,⟨5918546760846571,5918546760846611⟩⟩,⟨⟨16602990824383857,16602990824383889⟩,⟨5786291837699202,5786291837699235⟩⟩,⟨⟨16381340628766321,16381340628766354⟩,⟨5642225977370094,5642225977370127⟩⟩,⟨⟨16140674536579063,16140674536579096⟩,⟨5487194443981582,5487194443981615⟩⟩,⟨⟨15881848759265920,15881848759265953⟩,⟨5322095850036569,5322095850036602⟩⟩,⟨⟨15605777990884993,15605777990885026⟩,⟨5147874253770033,5147874253770066⟩⟩,⟨⟨15313430629191654,15313430629191684⟩,⟨4965510963964671,4965510963964699⟩⟩,⟨⟨15005823714337373,15005823714337398⟩,⟨4776016145343439,4776016145343464⟩⟩] +lemma kernel12_1_r2_0_eq : ∀ k : Fin 16, kernel12_1Expr 2 0 k = kernel12_1_r2_0 k := by decide +kernel +noncomputable def kernel12_1_r2_1 : Fin 16 → CBox := ![⟨⟨14684017614300913,14684017614300943⟩,⟨4580420318593394,4580420318593421⟩⟩,⟨⟨14349110488576974,14349110488577004⟩,⟨4379765848737015,4379765848737042⟩⟩,⟨⟨14002232563944369,14002232563944410⟩,⟨4175098513971388,4175098513971429⟩⟩,⟨⟨13644540258277559,13644540258277589⟩,⟨3967459244286098,3967459244286126⟩⟩,⟨⟨13277210190301860,13277210190301888⟩,⟨3757876115207345,3757876115207375⟩⟩,⟨⟨12901433114878617,12901433114878658⟩,⟨3547356676979189,3547356676979229⟩⟩,⟨⟨12518407824792618,12518407824792646⟩,⟨3336880693475153,3336880693475183⟩⟩,⟨⟨12129335061058459,12129335061058487⟩,⟨3127393358245929,3127393358245959⟩⟩,⟨⟨11735411474422674,11735411474422715⟩,⟨2919799047470699,2919799047470740⟩⟩,⟨⟨11337823680980295,11337823680980323⟩,⟨2714955661320948,2714955661320978⟩⟩,⟨⟨10937742454618555,10937742454618580⟩,⟨2513669596505582,2513669596505607⟩⟩,⟨⟨10536317098325751,10536317098325792⟩,⟨2316691383686353,2316691383686393⟩⟩,⟨⟨10134670035246025,10134670035246050⟩,⟨2124712014177920,2124712014177945⟩⟩,⟨⟨9733891658716966,9733891658716991⟩,⟨1938359971022355,1938359971022380⟩⟩,⟨⟨9335035478402878,9335035478402911⟩,⟨1758198970295518,1758198970295551⟩⟩,⟨⟨8939113597044706,8939113597044731⟩,⟨1584726409497980,1584726409498005⟩⟩] +lemma kernel12_1_r2_1_eq : ∀ k : Fin 16, kernel12_1Expr 2 1 k = kernel12_1_r2_1 k := by decide +kernel +noncomputable def kernel12_1_r2_2 : Fin 16 → CBox := ![⟨⟨8547092549314740,8547092549314765⟩,⟨1418372511236426,1418372511236451⟩⟩,⟨⟨8159889530822856,8159889530822886⟩,⟨1259500142231158,1259500142231186⟩⟩,⟨⟨7778369041512893,7778369041512926⟩,⟨1108405280099592,1108405280099626⟩⟩,⟨⟨7403339963564219,7403339963564260⟩,⟨965318093459468,965318093459509⟩⟩,⟨⟨7035553089530495,7035553089530528⟩,⟨830404594748888,830404594748921⟩⟩,⟨⟨6675699111868118,6675699111868168⟩,⟨703768819838253,703768819838302⟩⟩,⟨⟨6324407080298578,6324407080298608⟩,⟨585455484060421,585455484060449⟩⟩,⟨⟨5982243328680056,5982243328680081⟩,⟨475453060741976,475453060742001⟩⟩,⟨⟨5649710868308551,5649710868308582⟩,⟨373697225696914,373697225696942⟩⟩,⟨⟨5327249239895357,5327249239895390⟩,⟨280074609442068,280074609442101⟩⟩,⟨⟨5015234811948776,5015234811948806⟩,⟨194426798097550,194426798097578⟩⟩,⟨⟨4713981508988208,4713981508988236⟩,⟨116554524012505,116554524012535⟩⟩,⟨⟨4423741949001080,4423741949001113⟩,⟨46221988063732,46221988063765⟩⟩,⟨⟨4144708965874322,4144708965874353⟩,⟨(-16838742745082),(-16838742745053)⟩⟩,⟨⟨3877017489240629,3877017489240670⟩,⟨(-72923316368561),(-72923316368520)⟩⟩,⟨⟨3620746751319730,3620746751319760⟩,⟨(-122350706456822),(-122350706456793)⟩⟩] +lemma kernel12_1_r2_2_eq : ∀ k : Fin 16, kernel12_1Expr 2 2 k = kernel12_1_r2_2 k := by decide +kernel +noncomputable def kernel12_1_r2_3 : Fin 16 → CBox := ![⟨⟨3375922787937144,3375922787937177⟩,⟨(-165458900146118),(-165458900146084)⟩⟩,⟨⟨3142521198994184,3142521198994217⟩,⟨(-202600706278007),(-202600706277974)⟩⟩,⟨⟨2920470132257193,2920470132257223⟩,⟨(-234139723026247),(-234139723026219)⟩⟩,⟨⟨2709653453437697,2709653453437726⟩,⟨(-260446499236991),(-260446499236960)⟩⟩,⟨⟨2509914065144881,2509914065144909⟩,⟨(-281894918928496),(-281894918928465)⟩⟩,⟨⟨2321057337395576,2321057337395606⟩,⟨(-298858833440576),(-298858833440547)⟩⟩,⟨⟨2142854612944151,2142854612944181⟩,⟨(-311708960757061),(-311708960757033)⟩⟩,⟨⟨1975046751718342,1975046751718378⟩,⟨(-320810066626495),(-320810066626456)⟩⟩,⟨⟨1817347680080914,1817347680080940⟩,⟨(-326518437351371),(-326518437351346)⟩⟩,⟨⟨1669447912442559,1669447912442593⟩,⟨(-329179649570789),(-329179649570755)⟩⟩,⟨⟨1531018014882503,1531018014882537⟩,⟨(-329126638082397),(-329126638082364)⟩⟩,⟨⟨1401711982841000,1401711982841029⟩,⟨(-326678058788265),(-326678058788234)⟩⟩,⟨⟨1281170507582941,1281170507582975⟩,⟨(-322136940243687),(-322136940243653)⟩⟩,⟨⟨1169024108939519,1169024108939553⟩,⟨(-315789614069674),(-315789614069641)⟩⟩,⟨⟨1064896114764751,1064896114764785⟩,⟨(-307904911680766),(-307904911680732)⟩⟩,⟨⟨968405470543241,968405470543283⟩,⟨(-298733612391501),(-298733612391459)⟩⟩] +lemma kernel12_1_r2_3_eq : ∀ k : Fin 16, kernel12_1Expr 2 3 k = kernel12_1_r2_3 k := by decide +kernel +noncomputable def kernel12_1_r2_4 : Fin 16 → CBox := ![⟨⟨879169365604970,879169365605004⟩,⟨(-288508126001810),(-288508126001776)⟩⟩,⟨⟨796805665395345,796805665395371⟩,⟨(-277442391419909),(-277442391419884)⟩⟩,⟨⟨720935142170985,720935142171014⟩,⟨(-265731971749186),(-265731971749155)⟩⟩,⟨⟨651183499303676,651183499303707⟩,⟨(-253554325526072),(-253554325526043)⟩⟩,⟨⟨587183187041801,587183187041835⟩,⟨(-241069233425571),(-241069233425537)⟩⟩,⟨⟨528575010071633,528575010071667⟩,⟨(-228419359721374),(-228419359721340)⟩⟩,⟨⟨475009529513668,475009529513702⟩,⟨(-215730928068879),(-215730928068844)⟩⟩,⟨⟨426148264064184,426148264064210⟩,⟨(-203114491734928),(-203114491734903)⟩⟩,⟨⟨381664696833646,381664696833677⟩,⟨(-190665779194627),(-190665779194597)⟩⟩,⟨⟨341245096034798,341245096034827⟩,⟨(-178466597014030),(-178466597013999)⟩⟩,⟨⟨304589159027435,304589159027464⟩,⟨(-166585773102547),(-166585773102516)⟩⟩,⟨⟨271410490337278,271410490337309⟩,⟨(-155080124712772),(-155080124712743)⟩⟩,⟨⟨241436925136350,241436925136379⟩,⟨(-143995436954886),(-143995436954855)⟩⟩,⟨⟨214410710310309,214410710310338⟩,⟨(-133367439042770),(-133367439042738)⟩⟩,⟨⟨190088555656847,190088555656881⟩,⟨(-123222766970817),(-123222766970783)⟩⟩,⟨⟨168241567972413,168241567972447⟩,⟨(-113579902804131),(-113579902804096)⟩⟩] +lemma kernel12_1_r2_4_eq : ∀ k : Fin 16, kernel12_1Expr 2 4 k = kernel12_1_r2_4 k := by decide +kernel +noncomputable def kernel12_1_r2_5 : Fin 16 → CBox := ![⟨⟨148655080808623,148655080808652⟩,⟨(-104450082227145),(-104450082227114)⟩⟩,⟨⟨131128392534047,131128392534081⟩,⟨(-95838163413395),(-95838163413360)⟩⟩,⟨⟨115474425039282,115474425039317⟩,⟨(-87743451634722),(-87743451634687)⟩⟩,⟨⟨101519314995496,101519314995525⟩,⟨(-80160475305651),(-80160475305620)⟩⟩,⟨⟨89101949037274,89101949037309⟩,⟨(-73079710346322),(-73079710346287)⟩⟩,⟨⟨78073453610838,78073453610881⟩,⟨(-66488250835636),(-66488250835593)⟩⟩,⟨⟨68296649527549,68296649527578⟩,⟨(-60370424910307),(-60370424910276)⟩⟩,⟨⟨59645480508282,59645480508312⟩,⟨(-54708355739923),(-54708355739892)⟩⟩,⟨⟨52004424215008,52004424215039⟩,⟨(-49482468174096),(-49482468174066)⟩⟩,⟨⟨45267893456386,45267893456416⟩,⟨(-44671942314663),(-44671942314631)⟩⟩,⟨⟨39339634440400,39339634440430⟩,⟨(-40255115817592),(-40255115817560)⟩⟩,⟨⟨34132128140700,34132128140743⟩,⟨(-36209837180615),(-36209837180572)⟩⟩,⟨⟨29566000055911,29566000055946⟩,⟨(-32513772627836),(-32513772627801)⟩⟩,⟨⟨25569442882886,25569442882921⟩,⟨(-29144669471144),(-29144669471109)⟩⟩,⟨⟨22077655902434,22077655902469⟩,⟨(-26080579014519),(-26080579014484)⟩⟩,⟨⟨19032304196588,19032304196624⟩,⟨(-23300042182336),(-23300042182301)⟩⟩] +lemma kernel12_1_r2_5_eq : ∀ k : Fin 16, kernel12_1Expr 2 5 k = kernel12_1_r2_5 k := by decide +kernel +noncomputable def kernel12_1_r2_6 : Fin 16 → CBox := ![⟨⟨16381000184345,16381000184380⟩,⟨(-20782241102345),(-20782241102309)⟩⟩,⟨⟨14076809381311,14076809381338⟩,⟨(-18507119867769),(-18507119867742)⟩⟩,⟨⟨12077781760072,12077781760104⟩,⟨(-16455477648760),(-16455477648730)⟩⟩,⟨⟨10346509613018,10346509613053⟩,⟨(-14609037228925),(-14609037228890)⟩⟩,⟨⟨8849712397123,8849712397158⟩,⟨(-12950491915222),(-12950491915186)⟩⟩,⟨⟨7557848671448,7557848671478⟩,⟨(-11463533617092),(-11463533617060)⟩⟩,⟨⟨6444754918630,6444754918679⟩,⟨(-10132864717781),(-10132864717733)⟩⟩,⟨⟨5487310771299,5487310771335⟩,⟨(-8944196175636),(-8944196175600)⟩⟩,⟨⟨4665129938348,4665129938384⟩,⟨(-7884234098983),(-7884234098947)⟩⟩,⟨⟨3960275943447,3960275943477⟩,⟨(-6940656840073),(-6940656840041)⟩⟩,⟨⟨3357001642382,3357001642426⟩,⟨(-6102084456496),(-6102084456451)⟩⟩,⟨⟨2841511376771,2841511376807⟩,⟨(-5358042193540),(-5358042193504)⟩⟩,⟨⟨2401744542850,2401744542886⟩,⟨(-4698919453808),(-4698919453772)⟩⟩,⟨⟨2027179303802,2027179303838⟩,⟨(-4115925539515),(-4115925539479)⟩⟩,⟨⟨1708655147165,1708655147201⟩,⟨(-3601043284131),(-3601043284095)⟩⟩,⟨⟨1438212983861,1438212983894⟩,⟨(-3146981530718),(-3146981530687)⟩⟩] +lemma kernel12_1_r2_6_eq : ∀ k : Fin 16, kernel12_1Expr 2 6 k = kernel12_1_r2_6 k := by decide +kernel +noncomputable def kernel12_1_r2_7 : Fin 16 → CBox := ![⟨⟨1208951496977,1208951497013⟩,⟨(-2747127268181),(-2747127268145)⟩⟩,⟨⟨1014898475822,1014898475858⟩,⟨(-2395498101710),(-2395498101674)⟩⟩,⟨⟨850895908697,850895908728⟩,⟨(-2086695613025),(-2086695612992)⟩⟩,⟨⟨712497656811,712497656848⟩,⟨(-1815860056094),(-1815860056058)⟩⟩,⟨⟨595878586356,595878586393⟩,⟨(-1578626737008),(-1578626736972)⟩⟩,⟨⟨497754096513,497754096546⟩,⟨(-1371084342054),(-1371084342022)⟩⟩,⟨⟨415309045171,415309045208⟩,⟨(-1189735402561),(-1189735402524)⟩⟩,⟨⟨346135139656,346135139692⟩,⟨(-1031459022102),(-1031459022065)⟩⟩,⟨⟨288175926407,288175926444⟩,⟨(-893475936632),(-893475936596)⟩⟩,⟨⟨239678579423,239678579460⟩,⟨(-773315932579),(-773315932543)⟩⟩,⟨⟨199151752108,199151752145⟩,⟨(-668787610410),(-668787610373)⟩⟩,⟨⟨165328819630,165328819663⟩,⟨(-577950449906),(-577950449874)⟩⟩,⟨⟨137135899145,137135899176⟩,⟨(-499089110049),(-499089110016)⟩⟩,⟨⟨113664092204,113664092241⟩,⟨(-430689876688),(-430689876651)⟩⟩,⟨⟨94145447685,94145447717⟩,⟨(-371419157779),(-371419157746)⟩⟩,⟨⟨77932193719,77932193756⟩,⟨(-320103916150),(-320103916113)⟩⟩] +lemma kernel12_1_r2_7_eq : ∀ k : Fin 16, kernel12_1Expr 2 7 k = kernel12_1_r2_7 k := by decide +kernel +noncomputable def kernel12_1_r2_8 : Fin 16 → CBox := ![⟨⟨64478834320,64478834353⟩,⟨(-275713923375),(-275713923343)⟩⟩,⟨⟨53326749320,53326749366⟩,⟨(-237345715060),(-237345715014)⟩⟩,⟨⟨44090976342,44090976379⟩,⟨(-204208127107),(-204208127070)⟩⟩,⟨⟨36448889692,36448889729⟩,⟨(-175609293760),(-175609293723)⟩⟩,⟨⟨30130524358,30130524390⟩,⟨(-150944990634),(-150944990600)⟩⟩,⟨⟨24910322960,24910322998⟩,⟨(-129688210318),(-129688210280)⟩⟩,⟨⟨20600110793,20600110830⟩,⟨(-111379862844),(-111379862807)⟩⟩,⟨⟨17043128087,17043128120⟩,⟨(-95620498858),(-95620498826)⟩⟩,⟨⟨14108970253,14108970285⟩,⟨(-82062959403),(-82062959370)⟩⟩,⟨⟨11689306422,11689306460⟩,⟨(-70405862497),(-70405862460)⟩⟩,⟨⟨9694263399,9694263436⟩,⟨(-60387842897),(-60387842859)⟩⟩,⟨⟨8049377145,8049377178⟩,⟨(-51782468016),(-51782467984)⟩⟩,⟨⟨6693027743,6693027781⟩,⟨(-44393758980),(-44393758942)⟩⟩,⟨⟨5574284831,5574284869⟩,⟨(-38052251759),(-38052251721)⟩⟩,⟨⟨4651101152,4651101190⟩,⟨(-32611539428),(-32611539390)⟩⟩,⟨⟨3888800594,3888800631⟩,⟨(-27945241534),(-27945241496)⟩⟩] +lemma kernel12_1_r2_8_eq : ∀ k : Fin 16, kernel12_1Expr 2 8 k = kernel12_1_r2_8 k := by decide +kernel +noncomputable def kernel12_1_r2_9 : Fin 16 → CBox := ![⟨⟨3258814841,3258814878⟩,⟨(-23944352250),(-23944352213)⟩⟩,⟨⟨2737629643,2737629681⟩,⟨(-20514923347),(-20514923309)⟩⟩,⟨⟨2305907209,2305907243⟩,⟨(-17576042529),(-17576042496)⟩⟩,⟨⟨1947756638,1947756676⟩,⟨(-15058072290),(-15058072252)⟩⟩,⟨⟨1650128244,1650128282⟩,⟨(-12901117331),(-12901117293)⟩⟩,⟨⟨1402311550,1402311589⟩,⟨(-11053692864),(-11053692826)⟩⟩,⟨⟨1195519921,1195519959⟩,⟨(-9471568720),(-9471568682)⟩⟩,⟨⟨1022547154,1022547192⟩,⟨(-8116767354),(-8116767316)⟩⟩,⟨⟨877484329,877484367⟩,⟨(-6956695996),(-6956695958)⟩⟩,⟨⟨755486227,755486265⟩,⟨(-5963395978),(-5963395939)⟩⟩,⟨⟨652579268,652579306⟩,⟨(-5112894067),(-5112894029)⟩⟩,⟨⟨565503592,565503631⟩,⟨(-4384642226),(-4384642187)⟩⟩,⟨⟨491583422,491583460⟩,⟨(-3761034551),(-3761034512)⟩⟩,⟨⟨428620764,428620803⟩,⟨(-3226990771),(-3226990733)⟩⟩,⟨⟨374808260,374808294⟩,⟨(-2769597660),(-2769597626)⟩⟩,⟨⟨328658034,328658086⟩,⟨(-2377800463),(-2377800409)⟩⟩] +lemma kernel12_1_r2_9_eq : ∀ k : Fin 16, kernel12_1Expr 2 9 k = kernel12_1_r2_9 k := by decide +kernel +noncomputable def kernel12_1_r2_10 : Fin 16 → CBox := ![⟨⟨288943382,288943420⟩,⟨(-2042137440),(-2042137401)⟩⟩,⟨⟨254651156,254651195⟩,⟨(-1754511970),(-1754511931)⟩⟩,⟨⟨224942931,224942970⟩,⟨(-1507996582),(-1507996543)⟩⟩,⟨⟨199123361,199123395⟩,⟨(-1296664979),(-1296664944)⟩⟩,⟨⟨176614190,176614229⟩,⟨(-1115447780),(-1115447741)⟩⟩,⟨⟨156933349,156933387⟩,⟨(-960008955),(-960008916)⟩⟩,⟨⟨139677638,139677677⟩,⟨(-826639851),(-826639812)⟩⟩,⟨⟨124508781,124508820⟩,⟨(-712168511),(-712168472)⟩⟩,⟨⟨111142012,111142051⟩,⟨(-613881924),(-613881885)⟩⟩,⟨⟨99336724,99336763⟩,⟨(-529459509),(-529459470)⟩⟩,⟨⟨88888915,88888974⟩,⟨(-456916264),(-456916206)⟩⟩,⟨⟨79624968,79625007⟩,⟨(-394554018),(-394553979)⟩⟩,⟨⟨71396478,71396517⟩,⟨(-340919879),(-340919840)⟩⟩,⟨⟨64076253,64076293⟩,⟨(-294770570),(-294770530)⟩⟩,⟨⟨57554725,57554765⟩,⟨(-255042011),(-255041972)⟩⟩,⟨⟨51737310,51737350⟩,⟨(-220823362),(-220823323)⟩⟩] +lemma kernel12_1_r2_10_eq : ∀ k : Fin 16, kernel12_1Expr 2 10 k = kernel12_1_r2_10 k := by decide +kernel +noncomputable def kernel12_1_r2_11 : Fin 16 → CBox := ![⟨⟨46541923,46541962⟩,⟨(-191334733),(-191334693)⟩⟩,⟨⟨41897208,41897248⟩,⟨(-165908211),(-165908171)⟩⟩,⟨⟨37740887,37740926⟩,⟨(-143971667),(-143971627)⟩⟩,⟨⟨34018396,34018436⟩,⟨(-125034811),(-125034771)⟩⟩,⟨⟨30681891,30681931⟩,⟨(-108677458),(-108677418)⟩⟩,⟨⟨27689228,27689268⟩,⟨(-94539287),(-94539247)⟩⟩,⟨⟨25003253,25003293⟩,⟨(-82311264),(-82311224)⟩⟩,⟨⟨22591113,22591153⟩,⟨(-71728222),(-71728182)⟩⟩,⟨⟨20423678,20423717⟩,⟨(-62562546),(-62562506)⟩⟩,⟨⟨18475136,18475176⟩,⟨(-54618821),(-54618781)⟩⟩,⟨⟨16722524,16722564⟩,⟨(-47729139),(-47729099)⟩⟩,⟨⟨15145406,15145461⟩,⟨(-41749200),(-41749146)⟩⟩,⟨⟨13725601,13725641⟩,⟨(-36554907),(-36554867)⟩⟩,⟨⟨12446858,12446898⟩,⟨(-32039550),(-32039510)⟩⟩,⟨⟨11294651,11294691⟩,⟨(-28111272),(-28111232)⟩⟩,⟨⟨10256033,10256073⟩,⟨(-24690957),(-24690917)⟩⟩] +lemma kernel12_1_r2_11_eq : ∀ k : Fin 16, kernel12_1Expr 2 11 k = kernel12_1_r2_11 k := by decide +kernel +noncomputable def kernel12_1_r2_12 : Fin 16 → CBox := ![⟨⟨9319430,9319470⟩,⟨(-21710448),(-21710408)⟩⟩,⟨⟨8474448,8474488⟩,⟨(-19110999),(-19110959)⟩⟩,⟨⟨7711813,7711853⟩,⟨(-16841944),(-16841904)⟩⟩,⟨⟨7023192,7023232⟩,⟨(-14859535),(-14859495)⟩⟩,⟨⟨6401148,6401188⟩,⟨(-13126044),(-13126004)⟩⟩,⟨⟨5838971,5839016⟩,⟨(-11608823),(-11608778)⟩⟩,⟨⟨5330680,5330721⟩,⟨(-10279647),(-10279607)⟩⟩,⟨⟨4870884,4870924⟩,⟨(-9114148),(-9114107)⟩⟩,⟨⟨4454764,4454805⟩,⟨(-8091194),(-8091153)⟩⟩,⟨⟨4077985,4078025⟩,⟨(-7192467),(-7192426)⟩⟩,⟨⟨3736649,3736690⟩,⟨(-6402119),(-6402079)⟩⟩,⟨⟨3427266,3427306⟩,⟨(-5706382),(-5706341)⟩⟩,⟨⟨3146701,3146742⟩,⟨(-5093340),(-5093300)⟩⟩,⟨⟨2892108,2892153⟩,⟨(-4552584),(-4552538)⟩⟩,⟨⟨2660969,2661014⟩,⟨(-4075132),(-4075087)⟩⟩,⟨⟨2451020,2451065⟩,⟨(-3653111),(-3653065)⟩⟩] +lemma kernel12_1_r2_12_eq : ∀ k : Fin 16, kernel12_1Expr 2 12 k = kernel12_1_r2_12 k := by decide +kernel +noncomputable def kernel12_1_r2_13 : Fin 16 → CBox := ![⟨⟨2260180,2260225⟩,⟨(-3279701),(-3279655)⟩⟩,⟨⟨2086621,2086661⟩,⟨(-2948952),(-2948911)⟩⟩,⟨⟨1928682,1928723⟩,⟨(-2655686),(-2655645)⟩⟩,⟨⟨1784860,1784901⟩,⟨(-2395383),(-2395342)⟩⟩,⟨⟨1653833,1653873⟩,⟨(-2164073),(-2164033)⟩⟩,⟨⟨1534379,1534420⟩,⟨(-1958311),(-1958270)⟩⟩,⟨⟨1425408,1425449⟩,⟨(-1775094),(-1775053)⟩⟩,⟨⟨1325943,1325984⟩,⟨(-1611743),(-1611702)⟩⟩,⟨⟨1235072,1235118⟩,⟨(-1465976),(-1465930)⟩⟩,⟨⟨1152042,1152088⟩,⟨(-1335735),(-1335690)⟩⟩,⟨⟨1076111,1076152⟩,⟨(-1219253),(-1219212)⟩⟩,⟨⟨1006627,1006668⟩,⟨(-1114957),(-1114916)⟩⟩,⟨⟨943004,943050⟩,⟨(-1021499),(-1021453)⟩⟩,⟨⟨884715,884762⟩,⟨(-937636),(-937590)⟩⟩,⟨⟨831298,831339⟩,⟨(-862317),(-862276)⟩⟩,⟨⟨782308,782349⟩,⟨(-794601),(-794560)⟩⟩] +lemma kernel12_1_r2_13_eq : ∀ k : Fin 16, kernel12_1Expr 2 13 k = kernel12_1_r2_13 k := by decide +kernel +noncomputable def kernel12_1_r2_14 : Fin 16 → CBox := ![⟨⟨737350,737396⟩,⟨(-733666),(-733620)⟩⟩,⟨⟨696078,696119⟩,⟨(-678776),(-678735)⟩⟩,⟨⟨658175,658217⟩,⟨(-629275),(-629234)⟩⟩,⟨⟨623362,623413⟩,⟨(-584628),(-584577)⟩⟩,⟨⟨591367,591408⟩,⟨(-544298),(-544257)⟩⟩,⟨⟨561951,561993⟩,⟨(-507831),(-507790)⟩⟩,⟨⟨534908,534949⟩,⟨(-474868),(-474827)⟩⟩,⟨⟨510044,510085⟩,⟨(-445030),(-444989)⟩⟩,⟨⟨487193,487234⟩,⟨(-418005),(-417964)⟩⟩,⟨⟨466173,466214⟩,⟨(-393536),(-393494)⟩⟩,⟨⟨446852,446893⟩,⟨(-371352),(-371311)⟩⟩,⟨⟨429097,429138⟩,⟨(-351249),(-351208)⟩⟩,⟨⟨412800,412842⟩,⟨(-333045),(-333003)⟩⟩,⟨⟨397850,397891⟩,⟨(-316541),(-316499)⟩⟩,⟨⟨384149,384195⟩,⟨(-301604),(-301557)⟩⟩,⟨⟨371612,371669⟩,⟨(-288079),(-288023)⟩⟩] +lemma kernel12_1_r2_14_eq : ∀ k : Fin 16, kernel12_1Expr 2 14 k = kernel12_1_r2_14 k := by decide +kernel +noncomputable def kernel12_1_r2_15 : Fin 16 → CBox := ![⟨⟨360156,360197⟩,⟨(-275863),(-275821)⟩⟩,⟨⟨349720,349766⟩,⟨(-264833),(-264786)⟩⟩,⟨⟨340221,340267⟩,⟨(-254914),(-254868)⟩⟩,⟨⟨331626,331667⟩,⟨(-245990),(-245949)⟩⟩,⟨⟨323867,323913⟩,⟨(-238013),(-237966)⟩⟩,⟨⟨316907,316948⟩,⟨(-230916),(-230874)⟩⟩,⟨⟨310697,310739⟩,⟨(-224611),(-224570)⟩⟩,⟨⟨305193,305234⟩,⟨(-219091),(-219049)⟩⟩,⟨⟨300387,300428⟩,⟨(-214271),(-214230)⟩⟩,⟨⟨296247,296288⟩,⟨(-210134),(-210093)⟩⟩,⟨⟨292723,292764⟩,⟨(-206651),(-206610)⟩⟩,⟨⟨289824,289865⟩,⟨(-203793),(-203752)⟩⟩,⟨⟨287533,287574⟩,⟨(-201525),(-201484)⟩⟩,⟨⟨285810,285852⟩,⟨(-199849),(-199808)⟩⟩,⟨⟨284671,284712⟩,⟨(-198730),(-198688)⟩⟩,⟨⟨284113,284154⟩,⟨(-198167),(-198126)⟩⟩] +lemma kernel12_1_r2_15_eq : ∀ k : Fin 16, kernel12_1Expr 2 15 k = kernel12_1_r2_15 k := by decide +kernel +noncomputable def kernel12_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel12_1_r2_0,kernel12_1_r2_1,kernel12_1_r2_2,kernel12_1_r2_3,kernel12_1_r2_4,kernel12_1_r2_5,kernel12_1_r2_6,kernel12_1_r2_7,kernel12_1_r2_8,kernel12_1_r2_9,kernel12_1_r2_10,kernel12_1_r2_11,kernel12_1_r2_12,kernel12_1_r2_13,kernel12_1_r2_14,kernel12_1_r2_15] +lemma kernel12_1_r2_eq (i k : Fin 16) : kernel12_1Expr 2 i k = kernel12_1_r2 i k := by + fin_cases i + · exact kernel12_1_r2_0_eq k + · exact kernel12_1_r2_1_eq k + · exact kernel12_1_r2_2_eq k + · exact kernel12_1_r2_3_eq k + · exact kernel12_1_r2_4_eq k + · exact kernel12_1_r2_5_eq k + · exact kernel12_1_r2_6_eq k + · exact kernel12_1_r2_7_eq k + · exact kernel12_1_r2_8_eq k + · exact kernel12_1_r2_9_eq k + · exact kernel12_1_r2_10_eq k + · exact kernel12_1_r2_11_eq k + · exact kernel12_1_r2_12_eq k + · exact kernel12_1_r2_13_eq k + · exact kernel12_1_r2_14_eq k + · exact kernel12_1_r2_15_eq k +noncomputable def kernel12_1_r3_0 : Fin 16 → CBox := ![⟨⟨88587534774363805297904,88587534774363805470749⟩,⟨22749531989252646549793,22749531989252646722891⟩⟩,⟨⟨88519985386583337402992,88519985386583337575680⟩,⟨22683900358726310958219,22683900358726311131161⟩⟩,⟨⟨88384968315677393517051,88384968315677393689388⟩,⟨22552924527749784115673,22552924527749784288260⟩⟩,⟨⟨88182647372461327365883,88182647372461327537711⟩,⟨22357177787502585677114,22357177787502585849185⟩⟩,⟨⟨87913269268045525791823,87913269268045525962965⟩,⟨22097516161228063389684,22097516161228063561072⟩⟩,⟨⟨87577164782971585721933,87577164782971585892228⟩,⟨21775073732907649213585,21775073732907649384121⟩⟩,⟨⟨87174750285217597832816,87174750285217598002097⟩,⟨21391256460240809357707,21391256460240809527225⟩⟩,⟨⟨86706529562802339733573,86706529562802339901675⟩,⟨20947734507237780590492,20947734507237780758824⟩⟩,⟨⟨86173095929062258566186,86173095929062258732960⟩,⟨20446433140317084842055,20446433140317085009056⟩⟩,⟨⟨85575134551610073843851,85575134551610074009131⟩,⟨19889522240218476914803,19889522240218477080299⟩⟩,⟨⟨84913424949611187374044,84913424949611187537681⟩,⟨19279404490256432023139,19279404490256432186984⟩⟩,⟨⟨84188843598426597217029,84188843598426597378877⟩,⟨18618702309409293599225,18618702309409293761274⟩⟩,⟨⟨83402366575951424444775,83402366575951424604698⟩,⟨17910243606422180893646,17910243606422181053762⟩⟩,⟨⟨82555072181198112908035,82555072181198113065891⟩,⟨17157046438452727017239,17157046438452727175280⟩⟩,⟨⟨81648143452892397826570,81648143452892397982239⟩,⟨16362302664760438749921,16362302664760438905758⟩⟩,⟨⟨80682870514114864230456,80682870514114864383798⟩,⟨15529360692483656052876,15529360692483656206381⟩⟩] +lemma kernel12_1_r3_0_eq : ∀ k : Fin 16, kernel12_1Expr 3 0 k = kernel12_1_r3_0 k := by decide +kernel +noncomputable def kernel12_1_r3_1 : Fin 16 → CBox := ![⟨⟨79660652668364301900796,79660652668364302051704⟩,⟨14661707417611766584473,14661707417611766735535⟩⟩,⟨⟨78583000172859911337838,78583000172859911486199⟩,⟨13762949469792301614199,13762949469792301762698⟩⟩,⟨⟨77451535616441994905562,77451535616441995051271⟩,⟨12836793874559970690283,12836793874559970836119⟩⟩,⟨⟨76267994832064631372646,76267994832064631515599⟩,⟨11887028250884804965661,11887028250884805108734⟩⟩,⟨⟨75034227277573817412961,75034227277573817553069⟩,⟨10917500665557439411733,10917500665557439551948⟩⟩,⟨⟨73752195823190977723268,73752195823190977860457⟩,⟨9932099268810954485409,9932099268810954622688⟩⟩,⟨⟨72423975889820764694653,72423975889820764828820⟩,⟨8934731837673054277813,8934731837673054412060⟩⟩,⟨⟨71051753888906288276427,71051753888906288407520⟩,⟨7929305354805756131708,7929305354805756262864⟩⟩,⟨⟨69637824921984129477013,69637824921984129604968⟩,⟨6919705750982932993251,6919705750982933121263⟩⟩,⟨⟨68184589706253628995739,68184589706253629120503⟩,⟨5909777938845379433831,5909777938845379558639⟩⟩,⟨⟨66694550701267198617379,66694550701267198738908⟩,⟨4903306264131626711967,4903306264131626833527⟩⟩,⟨⟨65170307421158516292447,65170307421158516410690⟩,⟨3903995498191194492200,3903995498191194610460⟩⟩,⟨⟨63614550926533157590844,63614550926533157705781⟩,⟨2915452492234530335055,2915452492234530449997⟩⟩,⟨⟨62030057500124760082564,62030057500124760194158⟩,⟨1941168609459055156469,1941168609459055268057⟩⟩,⟨⟨60419681520437724030187,60419681520437724138418⟩,⟨984503045922000558370,984503045922000666585⟩⟩,⟨⟨58786347557720248873413,58786347557720248978277⟩,⟨48667144827136108223,48667144827136213058⟩⟩] +lemma kernel12_1_r3_1_eq : ∀ k : Fin 16, kernel12_1Expr 3 1 k = kernel12_1_r3_1 k := by decide +kernel +noncomputable def kernel12_1_r3_2 : Fin 16 → CBox := ![⟨⟨57133041726603579699464,57133041726603579800954⟩,⟨(-863290198215968472435),(-863290198215968370983)⟩⟩,⟨⟨55462802339469834886469,55462802339469834984600⟩,⟨(-1748495949373652365226),(-1748495949373652267145)⟩⟩,⟨⟨53778709913939510849438,53778709913939510944208⟩,⟨(-2604265089407806374821),(-2604265089407806280115)⟩⟩,⟨⟨52083876596673074753124,52083876596673074844543⟩,⟨(-3428111433861698341209),(-3428111433861698249863)⟩⟩,⟨⟨50381435073837734140267,50381435073837734228360⟩,⟨(-4217757059545132355508),(-4217757059545132267490)⟩⟩,⟨⟨48674527045987479468253,48674527045987479553057⟩,⟨(-4971140287046197789710),(-4971140287046197704994)⟩⟩,⟨⟨46966291351638672132595,46966291351638672214131⟩,⟨(-5686422180286302220321),(-5686422180286302138881)⟩⟩,⟨⟨45259851829403065070614,45259851829403065148920⟩,⟨(-6361991535817559956333),(-6361991535817559878129)⟩⟩,⟨⟨43558305013086288856536,43558305013086288931656⟩,⟨(-6996468346527122332653),(-6996468346527122257644)⟩⟩,⟨⟨41864707757607647904145,41864707757607647976131⟩,⟨(-7588705736545757405320),(-7588705736545757333454)⟩⟩,⟨⟨40182064895896737521516,40182064895896737590417⟩,⟨(-8137790376337289168347),(-8137790376337289099572)⟩⟩,⟨⟨38513317028039945284875,38513317028039945350750⟩,⟨(-8643041399047625164949),(-8643041399047625099201)⟩⟩,⟨⟨36861328543867765901823,36861328543867765964737⟩,⟨(-9104007851091791767794),(-9104007851091791705013)⟩⟩,⟨⟨35228875978891157305415,35228875978891157365419⟩,⟨(-9520464721529666056542),(-9520464721529665996675)⟩⟩,⟨⟨33618636801027750618553,33618636801027750675721⟩,⟨(-9892407605902977039188),(-9892407605902976982160)⟩⟩,⟨⟨32033178721938962307189,32033178721938962361592⟩,⟨(-10220046070758495357422),(-10220046070758495303161)⟩⟩] +lemma kernel12_1_r3_2_eq : ∀ k : Fin 16, kernel12_1Expr 3 2 k = kernel12_1_r3_2 k := by decide +kernel +noncomputable def kernel12_1_r3_3 : Fin 16 → CBox := ![⟨⟨30474949622075334775023,30474949622075334826732⟩,⟨(-10503795794951565958863),(-10503795794951565907297)⟩⟩,⟨⟨28946268172763431002827,28946268172763431051926⟩,⟨(-10744269572903976523253),(-10744269572903976474299)⟩⟩,⟨⟨27449315231941312495603,27449315231941312542154⟩,⟨(-10942267273183219643604),(-10942267273183219597198)⟩⟩,⟨⟨25986126082552111242717,25986126082552111286795⟩,⟨(-11098764852989536257868),(-11098764852989536213937)⟩⟩,⟨⟨24558583574239207078286,24558583574239207119983⟩,⟨(-11214902535307527559964),(-11214902535307527518409)⟩⟩,⟨⟨23168412219964843032990,23168412219964843072386⟩,⟨(-11291972260538346985705),(-11291972260538346946446)⟩⟩,⟨⟨21817173289617747864950,21817173289617747902114⟩,⟨(-11331404528328216430816),(-11331404528328216393793)⟩⟩,⟨⟨20506260932711981725340,20506260932711981760365⟩,⟨(-11334754748015625872472),(-11334754748015625837583)⟩⟩,⟨⟨19236899352040684598935,19236899352040684631894⟩,⟨(-11303689217614664425174),(-11303689217614664392349)⟩⟩,⟨⟨18010141039768959327632,18010141039768959358610⟩,⟨(-11239970851532582143535),(-11239970851532582112684)⟩⟩,⟨⟨16826866077064327967514,16826866077064327996588⟩,⟨(-11145444776298508563047),(-11145444776298508534100)⟩⟩,⟨⟨15687782488103866609880,15687782488103866637130⟩,⟨(-11022023911485166394085),(-11022023911485166366958)⟩⟩,⟨⟨14593427629293286418863,14593427629293286444370⟩,⟨(-10871674649779147077922),(-10871674649779147052533)⟩⟩,⟨⟨13544170584908235669392,13544170584908235693241⟩,⟨(-10696402745854689513551),(-10696402745854689489814)⟩⟩,⟨⟨12540215531237806718597,12540215531237806740859⟩,⟨(-10498239518400907121603),(-10498239518400907099455)⟩⟩,⟨⟨11581606022781358542470,11581606022781358563222⟩,⟨(-10279228463425018953367),(-10279228463425018932719)⟩⟩] +lemma kernel12_1_r3_3_eq : ∀ k : Fin 16, kernel12_1Expr 3 3 k = kernel12_1_r3_3 k := by decide +kernel +noncomputable def kernel12_1_r3_4 : Fin 16 → CBox := ![⟨⟨10668230146218408925504,10668230146218408944828⟩,⟨(-10041412369896983626258),(-10041412369896983607039)⟩⟩,⟨⟨9799826480821721711502,9799826480821721729461⟩,⟨(-9786821021015776576742),(-9786821021015776558887)⟩⟩,⟨⟨8975990797787086888383,8975990797787086905041⟩,⟨(-9517459555973656496295),(-9517459555973656479728)⟩⟩,⟨⟨8196183425667187576507,8196183425667187591948⟩,⟨(-9235297558187156723933),(-9235297558187156708582)⟩⟩,⟨⟨7459737204764576458397,7459737204764576472681⟩,⟨(-8942258926671176769946),(-8942258926671176755749)⟩⟩,⟨⟨6765865949988727578963,6765865949988727592184⟩,⟨(-8640212577676500804564),(-8640212577676500791429)⟩⟩,⟨⟨6113673339328288139195,6113673339328288152069⟩,⟨(-8330964014012647933275),(-8330964014012647920477)⟩⟩,⟨⟨5502162143731439377356,5502162143731439389882⟩,⟨(-8016247789756915891160),(-8016247789756915878699)⟩⟩,⟨⟨4930243713810038841953,4930243713810038854127⟩,⟨(-7697720888423259674184),(-7697720888423259662072)⟩⟩,⟨⟨4396747639358912131957,4396747639358912143776⟩,⟨(-7376957023242735728469),(-7376957023242735716702)⟩⟩,⟨⟨3900431499169711274042,3900431499169711285502⟩,⟨(-7055441859095643850265),(-7055441859095643838849)⟩⟩,⟨⟨3439990620967099215611,3439990620967099226715⟩,⟨(-6734569146931358105700),(-6734569146931358094638)⟩⟩,⟨⟨3014067774441327504148,3014067774441327514895⟩,⟨(-6415637753303238361050),(-6415637753303238350337)⟩⟩,⟨⟨2621262724224298032186,2621262724224298042576⟩,⟨(-6099849560010962045085),(-6099849560010962034728)⟩⟩,⟨⟨2260141574177220380531,2260141574177220390572⟩,⟨(-5788308201848227868931),(-5788308201848227858915)⟩⟩,⟨⟨1929245839442328657385,1929245839442328667070⟩,⟨(-5482018604155682352244),(-5482018604155682342582)⟩⟩] +lemma kernel12_1_r3_4_eq : ∀ k : Fin 16, kernel12_1Expr 3 4 k = kernel12_1_r3_4 k := by decide +kernel +noncomputable def kernel12_1_r3_5 : Fin 16 → CBox := ![⟨⟨1627101188269762178144,1627101188269762187477⟩,⟨(-5181887276320847143765),(-5181887276320847134450)⟩⟩,⟨⟨1352225801571799954316,1352225801571799963304⟩,⟨(-4888723312580464943834),(-4888723312580464934861)⟩⟩,⟨⟨1103138304387088880555,1103138304387088889201⟩,⟨(-4603240047485697855584),(-4603240047485697846952)⟩⟩,⟨⟨878365229864515852305,878365229864515860613⟩,⟨(-4326057310194882623858),(-4326057310194882615559)⟩⟩,⟨⟨676447982908860283450,676447982908860291441⟩,⟨(-4057704219358590264582),(-4057704219358590256599)⟩⟩,⟨⟨495949277180306354803,495949277180306362454⟩,⟨(-3798622458743307378285),(-3798622458743307370636)⟩⟩,⟨⟨335459025623568498503,335459025623568505840⟩,⟨(-3549169972878895094159),(-3549169972878895086826)⟩⟩,⟨⟨193599671041451734970,193599671041451741992⟩,⟨(-3309625021877703373372),(-3309625021877703366348)⟩⟩,⟨⟨69030949350126401083,69030949350126407797⟩,⟨(-3080190535118304566452),(-3080190535118304559739)⟩⟩,⟨⟨(-39545916005639950958),(-39545916005639944537)⟩,⟨(-2860998704665690288206),(-2860998704665690281783)⟩⟩,⟨⟨(-133384584496726059692),(-133384584496726053559)⟩,⟨(-2652115761057971285068),(-2652115761057971278934)⟩⟩,⟨⟨(-213690524718073038238),(-213690524718073032397)⟩,⟨(-2453546876367925246129),(-2453546876367925240281)⟩⟩,⟨⟨(-281618482579296217434),(-281618482579296211871)⟩,⟨(-2265241142183413915462),(-2265241142183413909895)⟩⟩,⟨⟨(-338270473468775169207),(-338270473468775163901)⟩,⟨(-2087096573278652006010),(-2087096573278652000700)⟩⟩,⟨⟨(-384694276639002478321),(-384694276639002473273)⟩,⟨(-1918965091202275830158),(-1918965091202275825106)⟩⟩,⟨⟨(-421882406815628682543),(-421882406815628677746)⟩,⟨(-1760657445721757661124),(-1760657445721757656320)⟩⟩] +lemma kernel12_1_r3_5_eq : ∀ k : Fin 16, kernel12_1Expr 3 5 k = kernel12_1_r3_5 k := by decide +kernel +noncomputable def kernel12_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-450771535292304179022),(-450771535292304174464)⟩,⟨(-1611948035971514503017),(-1611948035971514498452)⟩⟩,⟨⟨(-472242330537297789158),(-472242330537297784844)⟩,⟨(-1472579597190533677435),(-1472579597190533673112)⟩⟩,⟨⟨(-487119686598072702090),(-487119686598072697992)⟩,⟨(-1342267723043698830759),(-1342267723043698826655)⟩⟩,⟨⟨(-496173306332150667418),(-496173306332150663542)⟩,⟨(-1220705197641964634736),(-1220705197641964630854)⟩⟩,⟨⟨(-500118605696533308050),(-500118605696533304382)⟩,⟨(-1107566115456949443213),(-1107566115456949439539)⟩⟩,⟨⟨(-499617904968467854725),(-499617904968467851258)⟩,⟨(-1002509771316902792025),(-1002509771316902788553)⟩⟩,⟨⟨(-495281872817965088360),(-495281872817965085083)⟩,⟨(-905184306529929200123),(-905184306529929196840)⟩⟩,⟨⟨(-487671189574241653349),(-487671189574241650248)⟩,⟨(-815230100868727046586),(-815230100868727043480)⟩⟩,⟨⟨(-477298396788520208009),(-477298396788520205085)⟩,⟨(-732282903636364452106),(-732282903636364449177)⟩⟩,⟨⟨(-464629901256819161989),(-464629901256819159229)⟩,⟨(-655976700287777024634),(-655976700287777021870)⟩⟩,⟨⟨(-450088102989773251105),(-450088102989773248516)⟩,⟨(-585946314085292374603),(-585946314085292372010)⟩⟩,⟨⟨(-434053618162961966341),(-434053618162961963904)⟩,⟨(-521829745002534482181),(-521829745002534479740)⟩⟩,⟨⟨(-416867569811696755648),(-416867569811696753356)⟩,⟨(-463270250548709961628),(-463270250548709959332)⟩⟩,⟨⟨(-398833920910535815601),(-398833920910535813448)⟩,⟨(-409918175358618760726),(-409918175358618758569)⟩⟩,⟨⟨(-380221826463089021234),(-380221826463089019214)⟩,⟨(-361432538281429023115),(-361432538281429021091)⟩⟩,⟨⟨(-361267983286865279185),(-361267983286865277277)⟩,⟨(-317482387306157196705),(-317482387306157194794)⟩⟩] +lemma kernel12_1_r3_6_eq : ∀ k : Fin 16, kernel12_1Expr 3 6 k = kernel12_1_r3_6 k := by decide +kernel +noncomputable def kernel12_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-342178958278098923180),(-342178958278098921385)⟩,⟨(-277747933990500821527),(-277747933990500819728)⟩⟩,⟨⟨(-323133478052264611289),(-323133478052264609614)⟩,⟨(-241921480122082596006),(-241921480122082594328)⟩⟩,⟨⟨(-304284664949685133586),(-304284664949685132019)⟩,⟨(-209708150150010185159),(-209708150150010183592)⟩⟩,⟨⟨(-285762206447500849711),(-285762206447500848238)⟩,⟨(-180826443495023445838),(-180826443495023444365)⟩⟩,⟨⟨(-267674447007570937738),(-267674447007570936372)⟩,⟨(-155008621195364377227),(-155008621195364375861)⟩⟩,⟨⟨(-250110393295947810890),(-250110393295947809609)⟩,⟨(-132000941491273620864),(-132000941491273619581)⟩⟩,⟨⟨(-233141625517791137684),(-233141625517791136477)⟩,⟨(-111563758913098117598),(-111563758913098116389)⟩⟩,⟨⟨(-216824109309338126140),(-216824109309338125009)⟩,⟨(-93471501236386124251),(-93471501236386123120)⟩⟩,⟨⟨(-201199904206070780468),(-201199904206070779416)⟩,⟨(-77512538322261829431),(-77512538322261828376)⟩⟩,⟨⟨(-186298766156496859481),(-186298766156496858485)⟩,⟨(-63488956392900430903),(-63488956392900429906)⟩⟩,⟨⟨(-172139642869517345408),(-172139642869517344486)⟩,⟨(-51216250719726051159),(-51216250719726050237)⟩⟩,⟨⟨(-158732061968063002240),(-158732061968063001379)⟩,⟨(-40522949044999233725),(-40522949044999232864)⟩⟩,⟨⟨(-146077412972542523281),(-146077412972542522481)⟩,⟨(-31250177333805597493),(-31250177333805596693)⟩⟩,⟨⟨(-134170125056539258277),(-134170125056539257523)⟩,⟨(-23251178680066062926),(-23251178680066062169)⟩⟩,⟨⟨(-122998743307653699502),(-122998743307653698805)⟩,⟨(-16390795382788816815),(-16390795382788816117)⟩⟩,⟨⟨(-112546906893350262732),(-112546906893350262068)⟩,⟨(-10544923381759114129),(-10544923381759113465)⟩⟩] +lemma kernel12_1_r3_7_eq : ∀ k : Fin 16, kernel12_1Expr 3 7 k = kernel12_1_r3_7 k := by decide +kernel +noncomputable def kernel12_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-102794233081230404210),(-102794233081230403594)⟩,⟨(-5599947408188875389),(-5599947408188874773)⟩⟩,⟨⟨(-93717111502355090803),(-93717111502355090219)⟩,⟨(-1452164377048654561),(-1452164377048653974)⟩⟩,⟨⟨(-85289413382827641930),(-85289413382827641391)⟩,⟨1992798266052247961,1992798266052248496⟩⟩,⟨⟨(-77483120711080597860),(-77483120711080597352)⟩,⟨4820563320857198548,4820563320857199059⟩⟩,⟨⟨(-70268880464763106665),(-70268880464763106188)⟩,⟨7108578568228732164,7108578568228732638⟩⟩,⟨⟨(-63616489100519528058),(-63616489100519527613)⟩,⟨8926681025384861626,8926681025384862071⟩⟩,⟨⟨(-57495312520998679366),(-57495312520998678954)⟩,⟨10337646961771056944,10337646961771057359⟩⟩,⟨⟨(-51874646684707245751),(-51874646684707245369)⟩,⟨11397724553434131897,11397724553434132280⟩⟩,⟨⟨(-46724023924133969341),(-46724023924133968987)⟩,⟨12157146643323224445,12157146643323224800⟩⟩,⟨⟨(-42013469893883880500),(-42013469893883880154)⟩,⟨12660621615967486435,12660621615967486779⟩⟩,⟨⟨(-37713715890904076134),(-37713715890904075821)⟩,⟨12947800886948534733,12947800886948535047⟩⟩,⟨⟨(-33796371080293891531),(-33796371080293891224)⟩,⟨13053721950741395245,13053721950741395551⟩⟩,⟨⟨(-30234058929177978476),(-30234058929177978202)⟩,⟨13009226325742745515,13009226325742745792⟩⟩,⟨⟨(-27000521903622899337),(-27000521903622899079)⟩,⟨12841352084097972069,12841352084097972326⟩⟩,⟨⟨(-24070698224959954617),(-24070698224959954373)⟩,⟨12573700958194868598,12573700958194868842⟩⟩,⟨⟨(-21420774216920635932),(-21420774216920635711)⟩,⟨12226780277692704711,12226780277692704929⟩⟩] +lemma kernel12_1_r3_8_eq : ∀ k : Fin 16, kernel12_1Expr 3 8 k = kernel12_1_r3_8 k := by decide +kernel +noncomputable def kernel12_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-19028215507902678014),(-19028215507902677805)⟩,⟨11818320213260848893,11818320213260849102⟩⟩,⟨⟨(-16871780087110892451),(-16871780087110892257)⟩,⟨11363566988571264829,11363566988571265023⟩⟩,⟨⟨(-14931515952367728747),(-14931515952367728574)⟩,⟨10875552873413252766,10875552873413252940⟩⟩,⟨⟨(-13188745833665598106),(-13188745833665597939)⟩,⟨10365343891031985607,10365343891031985773⟩⟩,⟨⟨(-11626041232163111378),(-11626041232163111218)⟩,⟨9842266264900693298,9842266264900693457⟩⟩,⟨⟨(-10227187780998428372),(-10227187780998428226)⟩,⟨9314112697049217744,9314112697049217889⟩⟩,⟨⟨(-8977143713292341452),(-8977143713292341306)⟩,⟨8787329614642164476,8787329614642164622⟩⟩,⟨⟨(-7861993014967923037),(-7861993014967922906)⟩,⟨8267186546472075260,8267186546472075391⟩⟩,⟨⟨(-6868894646127490754),(-6868894646127490630)⟩,⟨7757928799016039228,7757928799016039352⟩⟩,⟨⟨(-5986029035023777002),(-5986029035023776877)⟩,⟨7262914595152313398,7262914595152313522⟩⟩,⟨⟨(-5202542883218408998),(-5202542883218408888)⟩,⟨6784737819832270600,6784737819832270710⟩⟩,⟨⟨(-4508493169206503328),(-4508493169206503218)⟩,⟨6325337488059650661,6325337488059650771⟩⟩,⟨⟨(-3894791100296306749),(-3894791100296306653)⟩,⟨5886095013368051204,5886095013368051300⟩⟩,⟨⟨(-3353146638419542707),(-3353146638419542611)⟩,⟨5467920311349326174,5467920311349326270⟩⟩,⟨⟨(-2876014114249910056),(-2876014114249909959)⟩,⟨5071327724228827334,5071327724228827430⟩⟩,⟨⟨(-2456539344875163644),(-2456539344875163558)⟩,⟨4696502700390167954,4696502700390168038⟩⟩] +lemma kernel12_1_r3_9_eq : ∀ k : Fin 16, kernel12_1Expr 3 9 k = kernel12_1_r3_9 k := by decide +kernel +noncomputable def kernel12_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-2088508582589819817),(-2088508582589819738)⟩,⟨4343360108334587183,4343360108334587260⟩⟩,⟨⟨(-1766299545395417799),(-1766299545395417720)⟩,⟨4011595008869182129,4011595008869182206⟩⟩,⟨⟨(-1484834712733516310),(-1484834712733516235)⟩,⟨3700726653254340808,3700726653254340883⟩⟩,⟨⟨(-1239537012044425215),(-1239537012044425148)⟩,⟨3410136419363547516,3410136419363547583⟩⟩,⟨⟨(-1026287972157663800),(-1026287972157663731)⟩,⟨3139100343249438459,3139100343249438531⟩⟩,⟨⟨(-841388377509296589),(-841388377509296527)⟩,⟨2886816850382491733,2886816850382491798⟩⟩,⟨⟨(-681521422001945357),(-681521422001945292)⟩,⟨2652430239641436445,2652430239641436508⟩⟩,⟨⟨(-543718332262106439),(-543718332262106374)⟩,⟨2435050424201635992,2435050424201636055⟩⟩,⟨⟨(-425326406429830809),(-425326406429830743)⟩,⟨2233769387020530695,2233769387020530758⟩⟩,⟨⟨(-323979395801836512),(-323979395801836452)⟩,⟨2047674764816348643,2047674764816348704⟩⟩,⟨⟨(-237570142047815116),(-237570142047815056)⟩,⟨1875860933373701089,1875860933373701149⟩⟩,⟨⟨(-164225371782674830),(-164225371782674777)⟩,⟨1717437928729957163,1717437928729957217⟩⟩,⟨⟨(-102282542501303910),(-102282542501303856)⟩,⟨1571538503297132291,1571538503297132345⟩⟩,⟨⟨(-50268628808313709),(-50268628808313669)⟩,⟨1437323583215988030,1437323583215988074⟩⟩,⟨⟨(-6880735087903517),(-6880735087903464)⟩,⟨1313986363152566787,1313986363152566840⟩⟩,⟨⟨29031580114684851,29031580114684897⟩,⟨1200755247239059400,1200755247239059445⟩⟩] +lemma kernel12_1_r3_10_eq : ∀ k : Fin 16, kernel12_1Expr 3 10 k = kernel12_1_r3_10 k := by decide +kernel +noncomputable def kernel12_1_r3_11 : Fin 16 → CBox := ![⟨⟨58482382021716025,58482382021716066⟩,⟨1096895819819003168,1096895819819003211⟩⟩,⟨⟨82363951890686354,82363951890686400⟩,⟨1001712006956160127,1001712006956160173⟩⟩,⟨⟨101460002632156498,101460002632156542⟩,⟨914546569172610755,914546569172610796⟩⟩,⟨⟨116457622971318770,116457622971318793⟩,⟨834781047454559222,834781047454559245⟩⟩,⟨⟨127958050927034270,127958050927034316⟩,⟨761835268061425794,761835268061425840⟩⟩,⟨⟨136486372528407382,136486372528407414⟩,⟨695166496952281120,695166496952281152⟩⟩,⟨⟨142500236545256800,142500236545256834⟩,⟨634268321562851514,634268321562851550⟩⟩,⟨⟨146397670696256574,146397670696256610⟩,⟨578669326089170544,578669326089170577⟩⟩,⟨⟨148524079418037578,148524079418037609⟩,⟨527931616228425146,527931616228425177⟩⟩,⟨⟨149178497913237058,149178497913237092⟩,⟨481649240367573791,481649240367573827⟩⟩,⟨⟨148619171912654331,148619171912654364⟩,⟨439446546376499265,439446546376499301⟩⟩,⟨⟨147068527439803741,147068527439803787⟩,⟨400976506342556826,400976506342556873⟩⟩,⟨⟨144717589896755991,144717589896756030⟩,⟨365919035672569826,365919035672569866⟩⟩,⟨⟨141729907029406995,141729907029407041⟩,⟨333979327889325510,333979327889325557⟩⟩,⟨⟨138245025800576948,138245025800576995⟩,⟨304886222072657341,304886222072657387⟩⟩,⟨⟨134381568915529527,134381568915529554⟩,⟨278390616157857373,278390616157857402⟩⟩] +lemma kernel12_1_r3_11_eq : ∀ k : Fin 16, kernel12_1Expr 3 11 k = kernel12_1_r3_11 k := by decide +kernel +noncomputable def kernel12_1_r3_12 : Fin 16 → CBox := ![⟨⟨130239952715277034,130239952715277081⟩,⟨254263936131179077,254263936131179124⟩⟩,⟨⟨125904784381896214,125904784381896253⟩,⟨232296668485155257,232296668485155296⟩⟩,⟨⟨121446972886295310,121446972886295350⟩,⟨212296961053466583,212296961053466622⟩⟩,⟨⟨116925584848330096,116925584848330127⟩,⟨194089295480394548,194089295480394579⟩⟩,⟨⟨112389473465073215,112389473465073241⟩,⟨177513233043459014,177513233043459043⟩⟩,⟨⟨107878705886560038,107878705886560065⟩,⟨162422234294998318,162422234294998347⟩⟩,⟨⟨103425811869101621,103425811869101645⟩,⟨148682551979451193,148682551979451218⟩⟩,⟨⟨99056874202838812,99056874202838846⟩,⟨136172195882728342,136172195882728379⟩⟩,⟨⟨94792479280481142,94792479280481169⟩,⟨124779967647238219,124779967647238248⟩⟩,⟨⟨90648544235617096,90648544235617125⟩,⟨114404563113540655,114404563113540682⟩⟩,⟨⟨86637035318959364,86637035318959391⟩,⟨104953739403331042,104953739403331071⟩⟩,⟨⟨82766590586839496,82766590586839528⟩,⟨96343543717659034,96343543717659066⟩⟩,⟨⟨79043058535875077,79043058535875106⟩,⟨88497600670862713,88497600670862740⟩⟩,⟨⟨75469963019055305,75469963019055329⟩,⟨81346454899006423,81346454899006447⟩⟩,⟨⟨72048903610050919,72048903610050944⟩,⟨74826965658188604,74826965658188629⟩⟩,⟨⟨68779899533412528,68779899533412568⟩,⟨68881750151405278,68881750151405318⟩⟩] +lemma kernel12_1_r3_12_eq : ∀ k : Fin 16, kernel12_1Expr 3 12 k = kernel12_1_r3_12 k := by decide +kernel +noncomputable def kernel12_1_r3_13 : Fin 16 → CBox := ![⟨⟨65661684338124547,65661684338124594⟩,⟨63458672382892787,63458672382892835⟩⟩,⟨⟨62691957650988413,62691957650988442⟩,⟨58510374427703481,58510374427703508⟩⟩,⟨⟨59867599595407985,59867599595408014⟩,⟨53993847114675211,53993847114675238⟩⟩,⟨⟨57184852791858033,57184852791858070⟩,⟨49870037247066929,49870037247066964⟩⟩,⟨⟨54639476260771736,54639476260771768⟩,⟨46103488622064865,46103488622064897⟩⟩,⟨⟨52226875019530676,52226875019530703⟩,⟨42662014254093127,42662014254093157⟩⟩,⟨⟨49942208696007262,49942208696007289⟩,⟨39516397354099435,39516397354099464⟩⟩,⟨⟨47780482065582451,47780482065582489⟩,⟨36640118765074460,36640118765074495⟩⟩,⟨⟨45736620051156577,45736620051156617⟩,⟨34009108700883265,34009108700883305⟩⟩,⟨⟨43805529401303479,43805529401303503⟩,⟨31601520779377993,31601520779378017⟩⟩,⟨⟨41982148975770152,41982148975770177⟩,⟨29397526480443620,29397526480443645⟩⟩,⟨⟨40261490315813597,40261490315813621⟩,⟨27379128294151340,27379128294151364⟩⟩,⟨⟨38638669955615443,38638669955615470⟩,⟨25529989952868949,25529989952868979⟩⟩,⟨⟨37108934736817309,37108934736817349⟩,⟨23835282263544607,23835282263544647⟩⟩,⟨⟨35667681218013510,35667681218013548⟩,⟨22281543172155924,22281543172155959⟩⟩,⟨⟨34310470122072880,34310470122072913⟩,⟨20856550801370706,20856550801370739⟩⟩] +lemma kernel12_1_r3_13_eq : ∀ k : Fin 16, kernel12_1Expr 3 13 k = kernel12_1_r3_13 k := by decide +kernel +noncomputable def kernel12_1_r3_14 : Fin 16 → CBox := ![⟨⟨33033036633977666,33033036633977691⟩,⟨19549208304782963,19549208304782988⟩⟩,⟨⟨31831297248262750,31831297248262780⟩,⟨18349439476749623,18349439476749650⟩⟩,⟨⟨30701353766149678,30701353766149708⟩,⟨17248094146013312,17248094146013340⟩⟩,⟨⟨29639494956347758,29639494956347790⟩,⟨16236862464162210,16236862464162243⟩⟩,⟨⟨28642196318683909,28642196318683938⟩,⟨15308197276802096,15308197276802123⟩⟩,⟨⟨27706118324842305,27706118324842343⟩,⟨14455243836374538,14455243836374573⟩⟩,⟨⟨26828103454321186,26828103454321219⟩,⟨13671776181149315,13671776181149347⟩⟩,⟨⟨26005172295163423,26005172295163463⟩,⟨12952139565355280,12952139565355321⟩⟩,⟨⟨25234518937133486,25234518937133526⟩,⟨12291198381008184,12291198381008224⟩⟩,⟨⟨24513505848949965,24513505848950005⟩,⟨11684289063055581,11684289063055622⟩⟩,⟨⟨23839658400197240,23839658400197281⟩,⟨11127177516299715,11127177516299756⟩⟩,⟨⟨23210659161976094,23210659161976126⟩,⟨10616020645475386,10616020645475419⟩⟩,⟨⟨22624342097635739,22624342097635775⟩,⟨10147331609144052,10147331609144090⟩⟩,⟨⟨22078686735553896,22078686735553929⟩,⟨9717948453993817,9717948453993849⟩⟩,⟨⟨21571812399454257,21571812399454284⟩,⟨9325005818973162,9325005818973192⟩⟩,⟨⟨21101972557784277,21101972557784309⟩,⟨8965909428685994,8965909428686026⟩⟩] +lemma kernel12_1_r3_14_eq : ∀ k : Fin 16, kernel12_1Expr 3 14 k = kernel12_1_r3_14 k := by decide +kernel +noncomputable def kernel12_1_r3_15 : Fin 16 → CBox := ![⟨⟨20667549341882110,20667549341882139⟩,⟨8638313122873156,8638313122873184⟩⟩,⟨⟨20267048272743235,20267048272743276⟩,⟨8340098193825519,8340098193825559⟩⟩,⟨⟨19899093227897604,19899093227897636⟩,⟨8069354826425058,8069354826425091⟩⟩,⟨⟨19562421673001034,19562421673001067⟩,⟨7824365456389097,7824365456389130⟩⟩,⟨⟨19255880177035528,19255880177035568⟩,⟨7603589881383494,7603589881383535⟩⟩,⟨⟨18978420225330672,18978420225330697⟩,⟨7405651977142444,7405651977142469⟩⟩,⟨⟨18729094340816075,18729094340816100⟩,⟨7229327886746921,7229327886746946⟩⟩,⟨⟨18507052520862595,18507052520862625⟩,⟨7073535565918449,7073535565918477⟩⟩,⟨⟨18311538994658216,18311538994658244⟩,⟨6937325580718289,6937325580718319⟩⟩,⟨⟨18141889304194694,18141889304194722⟩,⟨6819873066534616,6819873066534646⟩⟩,⟨⟨17997527710530170,17997527710530210⟩,⟨6720470768811901,6720470768811942⟩⟩,⟨⟨17877964925967473,17877964925967506⟩,⟨6638523096741568,6638523096741601⟩⟩,⟨⟨17782796172083363,17782796172083403⟩,⟨6573541131196794,6573541131196835⟩⟩,⟨⟨17711699563105946,17711699563105973⟩,⟨6525138537659078,6525138537659107⟩⟩,⟨⟨17664434813914092,17664434813914117⟩,⟨6493028343842821,6493028343842845⟩⟩,⟨⟨17640842271883199,17640842271883229⟩,⟨6477020550270694,6477020550270721⟩⟩] +lemma kernel12_1_r3_15_eq : ∀ k : Fin 16, kernel12_1Expr 3 15 k = kernel12_1_r3_15 k := by decide +kernel +noncomputable def kernel12_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel12_1_r3_0,kernel12_1_r3_1,kernel12_1_r3_2,kernel12_1_r3_3,kernel12_1_r3_4,kernel12_1_r3_5,kernel12_1_r3_6,kernel12_1_r3_7,kernel12_1_r3_8,kernel12_1_r3_9,kernel12_1_r3_10,kernel12_1_r3_11,kernel12_1_r3_12,kernel12_1_r3_13,kernel12_1_r3_14,kernel12_1_r3_15] +lemma kernel12_1_r3_eq (i k : Fin 16) : kernel12_1Expr 3 i k = kernel12_1_r3 i k := by + fin_cases i + · exact kernel12_1_r3_0_eq k + · exact kernel12_1_r3_1_eq k + · exact kernel12_1_r3_2_eq k + · exact kernel12_1_r3_3_eq k + · exact kernel12_1_r3_4_eq k + · exact kernel12_1_r3_5_eq k + · exact kernel12_1_r3_6_eq k + · exact kernel12_1_r3_7_eq k + · exact kernel12_1_r3_8_eq k + · exact kernel12_1_r3_9_eq k + · exact kernel12_1_r3_10_eq k + · exact kernel12_1_r3_11_eq k + · exact kernel12_1_r3_12_eq k + · exact kernel12_1_r3_13_eq k + · exact kernel12_1_r3_14_eq k + · exact kernel12_1_r3_15_eq k +noncomputable def kernel12_1_r4_0 : Fin 16 → CBox := ![⟨⟨897638876315765913980701453,897638876315765922568165640⟩,⟨645762400932491284656990442,645762400932491293253556111⟩⟩,⟨⟨897450979946112692115664845,897450979946112700699124419⟩,⟨644977155810047234442574032,644977155810047243035119328⟩⟩,⟨⟨897074360750845385771916215,897074360750845394347355576⟩,⟨643408304117950567719633619,643408304117950576304127210⟩⟩,⟨⟨896507372425370980352374633,896507372425370988915787804⟩,⟨641059120112377063874736760,641059120112377072447157010⟩⟩,⟨⟨895747561992009684026089237,895747561992009692573484557⟩,⟨637934508042519549248806077,637934508042519557805145811⟩⟩,⟨⟨894791689465702940523408334,894791689465702949050813272⟩,⟨634040993556408760388951756,634040993556408768925223066⟩⟩,⟨⟨893635753893228519656753414,893635753893228528160219072⟩,⟨629386712189278600768897622,629386712189278609281136446⟩⟩,⟨⟨892275025611177013594910578,892275025611177022070517038⟩,⟨623981394890792267798826437,623981394890792276283097923⟩⟩,⟨⟨890704084530537194133668356,890704084530537202577527836⟩,⟨617836350538395855418505830,617836350538395863870907531⟩⟩,⟨⟨888916864219186877639517752,888916864219186886047781938⟩,⟨610964445376232283734798699,610964445376232292151467965⟩⟩,⟨⟨886906701518065113243472965,886906701518065121612333292⟩,⟨603380079312643098996297368,603380079312643107373411637⟩⟩,⟨⟨884666391392485625382189943,884666391392485633707888304⟩,⟨595099159004504715226108880,595099159004504723559896428⟩⟩,⟨⟨882188246687116368777548364,882188246687116377056372245⟩,⟨586139067653666091269442747,586139067653666099556177868⟩⟩,⟨⟨879464162421772249627403208,879464162421772257855703510⟩,⟨576518631439732642855103612,576518631439732651091124469⟩⟩,⟨⟨876485684235524122149623853,876485684235524130323801845⟩,⟨566258082514509241031454836,566258082514509249213150434⟩⟩,⟨⟨873244080558893186677819933,873244080558893194794352506⟩,⟨555379018486681325460631229,555379018486681333584466722⟩⟩] +lemma kernel12_1_r4_0_eq : ∀ k : Fin 16, kernel12_1Expr 4 0 k = kernel12_1_r4_0 k := by decide +kernel +noncomputable def kernel12_1_r4_1 : Fin 16 → CBox := ![⟨⟨869730418068250714636528196,869730418068250722691944257⟩,⟨543904358330858724421982025,543904358330858732484475116⟩⟩,⟨⟨865935639953151181220677661,865935639953151189211599390⟩,⟨531858294662984970427756847,531858294662984978425519092⟩⟩,⟨⟨861850646506361592021596883,861850646506361599944699037⟩,⟨519266242334349829278208804,519266242334349837207904932⟩⟩,⟨⟨857466377527975558676198933,857466377527975566528262498⟩,⟨506154783309028510513401191,506154783309028518371802784⟩⟩,⟨⟨852773896019375889726681424,852773896019375897504536355⟩,⟨492551607804471111267026577,492551607804471119050954822⟩⟩,⟨⟨847764472630084763861484027,847764472630084771562090566⟩,⟨478485451692112937430372804,478485451692112945136779857⟩⟩,⟨⟨842429670310857138252535038,842429670310857145872897995⟩,⟨463986030174172336148782127,463986030174172343774665381⟩⟩,⟨⟨836761428619860830534854600,836761428619860838072121685⟩,⟨449083967774119050639712930,449083967774119058182213393⟩⟩,⟨⟨830752147125562429471658707,830752147125562436923011725⟩,⟨433810724701474674319115664,433810724701474681775409145⟩⟩,⟨⟨824394767350103421994629021,824394767350103429357426879⟩,⟨418198519676460704326736557,418198519676460711694176701⟩⟩,⟨⟨817682852700590131027670729,817682852700590138299296604⟩,⟨402280249326324898774546696,402280249326324906050512160⟩⟩,⟨⟨810610665842899596260067109,810610665842899603438089793⟩,⟨386089404292713532156718242,386089404292713539338774041⟩⟩,⟨⟨803173242983365725168802213,803173242983365732250799460⟩,⟨369659982217952657789081558,369659982217952664874802422⟩⟩,⟨⟨795366464538077339663345768,795366464538077346647124038⟩,⟨353026397807271467595522678,353026397807271474582712805⟩⟩,⟨⟨787187121687488975768838630,787187121687488982652198146⟩,⟨336223390193542708768665172,336223390193542715655123276⟩⟩,⟨⟨778632978335587095936336061,778632978335587102717310766⟩,⟨319285927860710830788436382,319285927860710837572195656⟩⟩] +lemma kernel12_1_r4_1_eq : ∀ k : Fin 16, kernel12_1Expr 4 1 k = kernel12_1_r4_1 k := by decide +kernel +noncomputable def kernel12_1_r4_2 : Fin 16 → CBox := ![⟨⟨769702828017911797169804381,769702828017911803846397354⟩,⟨302249111411397808113616618,302249111411397814792680144⟩⟩,⟨⟨760396545331221445769567818,760396545331221452340075533⟩,⟨285148074492880337311032057,285148074492880343883697053⟩⟩,⟨⟨750715131489389591668377198,750715131489389598131045145⟩,⟨268017883223376134852783283,268017883223376141317296733⟩⟩,⟨⟨740660753645094399788096886,740660753645094406141455985⟩,⟨250893434487015850787804516,250893434487015857142699551⟩⟩,⟨⟨730236777654824518355544574,730236777654824524598049949⟩,⟨233809353490667802770045506,233809353490667809013780183⟩⟩,⟨⟨719447794005475126664025938,719447794005475132794485220⟩,⟨216799890998589158219963812,216799890998589164351349390⟩⟩,⟨⟨708299636664107142440293165,708299636664107148457413772⟩,⟨199898820681373964357183623,199898820681373970374931823⟩⟩,⟨⟨696799394658025242229441065,696799394658025248132269406⟩,⟨183139337033545022450180017,183139337033545028353342209⟩⟩,⟨⟨684955416239902432139697795,684955416239902437927144089⟩,⟨166553954329101386325369067,166553954329101392112861099⟩⟩,⟨⟨672777305541919942553777135,672777305541919948225179264⟩,⟨150174407096117403219655408,150174407096117408890821362⟩⟩,⟨⟨660275911673456331783812774,660275911673456337338344906⟩,⟨134031552599850439196077887,134031552599850444750098757⟩⟩,⟨⟨647463310268381984420420889,647463310268381989857648744⟩,⟨118155275828540586394668492,118155275828540591831117346⟩⟩,⟨⟨634352777540108579598242434,634352777540108584917538951⟩,⟨102574397476997979457642840,102574397476997984775900549⟩⟩,⟨⟨620958756954805423496831858,620958756954805428699402089⟩,⟨87316585420029470420114074,87316585420029475621394031⟩⟩,⟨⟨607296818685211065558206264,607296818685211070644650542⟩,⟨72408270160652928120110921,72408270160652933205022325⟩⟩,⟨⟨593383612058815859288026014,593383612058815864258364409⟩,⟨57874564726822136770735101,57874564726822141739307301⟩⟩] +lemma kernel12_1_r4_2_eq : ∀ k : Fin 16, kernel12_1Expr 4 2 k = kernel12_1_r4_2 k := by decide +kernel +noncomputable def kernel12_1_r4_3 : Fin 16 → CBox := ![⟨⟨579236811264440894168338388,579236811264440899022321803⟩,⟨43739189475018922259945642,43739189475018927111939262⟩⟩,⟨⟨564875054629962406180945422,564875054629962410918881064⟩,⟨30024402239586724104402972,30024402239586728840135230⟩⟩,⟨⟨550317877830703801556527365,550317877830703806178423284⟩,⟨16750934243151350234757623,16750934243151354854246984⟩⟩,⟨⟨535585641432423845763509514,535585641432423850269855511⟩,⟨3937932156015329989135437,3937932156015334492882306⟩⟩,⟨⟨520699453214466667084590106,520699453214466671475551975⟩,⟨(-8397093338817743092824195),(-8397093338817738704643054)⟩⟩,⟨⟨505681085757122165613996024,505681085757122169890332110⟩,⟨(-20238312153129054062427480),(-20238312153129049789042680)⟩⟩,⟨⟨490552889812211805320323669,490552889812211809482439390⟩,⟨(-31571612289737160464763052),(-31571612289737156305757841)⟩⟩,⟨⟨475337704007029067431755423,475337704007029071481466735⟩,⟨(-42384629984922856625305997),(-42384629984922852578851112)⟩⟩,⟨⟨460058761458721626975637544,460058761458721630913713513⟩,⟨(-52666772298288117001040810),(-52666772298288113066355115)⟩⟩,⟨⟨444739593898734222221676489,444739593898734226049264112⟩,⟨(-62409231997514455056827200),(-62409231997514451232752367)⟩⟩,⟨⟨429403933924806580295132090,429403933924806584012955563⟩,⟨(-71604994633645430111528886),(-71604994633645426397329219)⟩⟩,⟨⟨414075616011050986110075219,414075616011050989719405256⟩,⟨(-80248837752214712095508607),(-80248837752214708489892898)⟩⟩,⟨⟨398778476914675289242640794,398778476914675292744319988⟩,⟨(-88337322236333739693688864),(-88337322236333736195752149)⟩⟩,⟨⟨383536256120872631265227283,383536256120872634660750946⟩,⟨(-95868775829282331623812768),(-95868775829282328232051384)⟩⟩,⟨⟨368372496965221186834389392,368372496965221190124790436⟩,⟨(-102843268935739600730591607),(-102843268935739597443964278)⟩⟩,⟨⟨353310449065628164473039408,353310449065628167659911492⟩,⟨(-109262582852071727796722045),(-109262582852071724613627126)⟩⟩] +lemma kernel12_1_r4_3_eq : ∀ k : Fin 16, kernel12_1Expr 4 3 k = kernel12_1_r4_3 k := by decide +kernel +noncomputable def kernel12_1_r4_4 : Fin 16 → CBox := ![⟨⟨338372972683465434255766078,338372972683465437340204355⟩,⟨(-115130170626576247289021661),(-115130170626576244208356027)⟩⟩,⟨⟨323582445616183483959872209,323582445616183486943686453⟩,⟨(-120451110799791897727695405),(-120451110799791894747641798)⟩⟩,⟨⟨308960673201510192360095635,308960673201510195244577422⟩,⟨(-125232054322450600938782001),(-125232054322450598058041418)⟩⟩,⟨⟨294528801986544325158852651,294528801986544327945859159⟩,⟨(-129481164993920532650798395),(-129481164993920529867506703)⟩⟩,⟨⟨280307237583890934185333857,280307237583890936876204203⟩,⟨(-133208053806633716656502775),(-133208053806633713969313995)⟩⟩,⟨⟨266315567201751757531476448,266315567201751760128238491⟩,⟨(-136423707621600932582023155),(-136423707621600929988903122)⟩⟩,⟨⟨252572487295914534996050439,252572487295914537500199653⟩,⟨(-139140412636314350095890559),(-139140412636314347595337606)⟩⟩,⟨⟨239095736749254972265730640,239095736749254974679321286⟩,⟨(-141371673138782691978381359),(-141371673138782689568335567)⟩⟩,⟨⟨225902035939081723873224064,225902035939081726197756005⟩,⟨(-143132126069832644410026013),(-143132126069832642088982002)⟩⟩,⟨⟨213007032004855163930280700,213007032004855166167960642⟩,⟨(-144437451939884333197444350),(-144437451939884330963190507)⟩⟩,⟨⟨200425250578955977135616214,200425250578955979288086795⟩,⟨(-145304282665954620327358570),(-145304282665954618178247491)⟩⟩,⟨⟨188170054191749695386584330,188170054191749697456029191⟩,⟨(-145750106909494892430113970),(-145750106909494890363957804)⟩⟩,⟨⟨176253607509681510728234248,176253607509681512722362005⟩,⟨(-145793173505715425922212641),(-145793173505715423931133224)⟩⟩,⟨⟨164686849512042898175384591,164686849512042900096491616⟩,⟨(-145452393580223421912684934),(-145452393580223419994383938)⟩⟩,⟨⟨153479472658880459428554845,153479472658880461277968067⟩,⟨(-144747241949095632953112141),(-144747241949095631106272098)⟩⟩,⟨⟨142639909049766601074432434,142639909049766602854004926⟩,⟨(-143697658393960365211027038),(-143697658393960363433804525)⟩⟩] +lemma kernel12_1_r4_4_eq : ∀ k : Fin 16, kernel12_1Expr 4 4 k = kernel12_1_r4_4 k := by decide +kernel +noncomputable def kernel12_1_r4_5 : Fin 16 → CBox := ![⟨⟨132175323521310063835563436,132175323521310065546585127⟩,⟨(-142323949394369913893217003),(-142323949394369912184331635)⟩⟩,⟨⟨122091613580825429057734676,122091613580825430702169502⟩,⟨(-140646690885845241785273410),(-140646690885845240142770951)⟩⟩,⟨⟨112393416024957319027783753,112393416024957320607031123⟩,⟨(-138686632593659567389106724),(-138686632593659565811597319)⟩⟩,⟨⟨103084120045694065712247067,103084120045694067228205461⟩,⟨(-136464604469930948513700671),(-136464604469930946999295429)⟩⟩,⟨⟨94165886582503669584389039,94165886582503671038418111⟩,⟨(-134001425735191925413511491),(-134001425735191923960860191)⟩⟩,⟨⟨85639673638643725714178064,85639673638643727108243357⟩,⟨(-131317816995610553889927041),(-131317816995610552497073557)⟩⟩,⟨⟨77505267242360037018959538,77505267242360038354491399⟩,⟨(-128434315873798918387407678),(-128434315873798917052930886)⟩⟩,⟨⟨69761317699977610699404161,69761317699977611978297817⟩,⟨(-125371196555038506454450833),(-125371196555038505176464644)⟩⟩,⟨⟨62405380758040151561380256,62405380758040152784995918⟩,⟨(-122148393612176563104821486),(-122148393612176561881974617)⟩⟩,⟨⟨55433963265861305888200793,55433963265861307058489621⟩,⟨(-118785430431822320336540720),(-118785430431822319166890788)⟩⟩,⟨⟨48842572908256472439425165,48842572908256473557810159⟩,⟨(-115301352522228730093057813),(-115301352522228728975190383)⟩⟩,⟨⟨42625771560923396878566815,42625771560923397946896366⟩,⟨(-111714665939823821441316619),(-111714665939823820373391640)⟩⟩,⟨⟨36777231807980068855040143,36777231807980069874666556⟩,⟨(-108043281027198307209528478),(-108043281027198306190201773)⟩⟩,⟨⟨31289796152548940143951902,31289796152548941116742580⟩,⟨(-104304461610901925515737767),(-104304461610901924543149800)⟩⟩,⟨⟨26155538446949886506495122,26155538446949887433910588⟩,⟨(-100514779763081448984596663),(-100514779763081448057294583)⟩⟩,⟨⟨21365827068938543571930020,21365827068938544456243198⟩,⟨(-96690076187226472166913407),(-96690076187226471282631861)⟩⟩] +lemma kernel12_1_r4_5_eq : ∀ k : Fin 16, kernel12_1Expr 4 5 k = kernel12_1_r4_5 k := by decide +kernel +noncomputable def kernel12_1_r4_6 : Fin 16 → CBox := ![⟨⟨16911389374367066227474891,16911389374367067069926779⟩,⟨(-92845426245475368951119728),(-92845426245475368108624822)⟩⟩,⟨⟨12782376964476730069998753,12782376964476730872325233⟩,⟨(-88995111603451474206989203),(-88995111603451473404551781)⟩⟩,⟨⟨8968431317545448489102133,8968431317545449252573752⟩,⟨(-85152597428800853666067552),(-85152597428800852902423592)⟩⟩,⟨⟨5458749349564808965856065,5458749349564809692083994⟩,⟨(-81330515041810778576886363),(-81330515041810777850430854)⟩⟩,⟨⟨2242148486738459142413556,2242148486738459832582291⟩,⟨(-77540649880992576566070452),(-77540649880992575875624846)⟩⟩,⟨⟨(-692869146420111227812327),(-692869146420110572105557)⟩,⟨(-73793934613569369701731565),(-73793934613569369045704192)⟩⟩,⟨⟨(-3358053796073956006755091),(-3358053796073955383768988)⟩,⟨(-70100447190637041669606351),(-70100447190637041046261250)⟩⟩,⟨⟨(-5765346752058601632195131),(-5765346752058601040304065)⟩,⟨(-66469413619546185227932869),(-66469413619546184635649384)⟩⟩,⟨⟨(-7926820944178259839993806),(-7926820944178259278176363)⟩,⟨(-62909215201925447316962534),(-62909215201925446754724041)⟩⟩,⟨⟨(-9854623751931738309531830),(-9854623751931737776380930)⟩,⟨(-59427399964835142236561925),(-59427399964835141702965709)⟩⟩,⟨⟨(-11560922287461124928157385),(-11560922287461124422646255)⟩,⟨(-56030697994867916076815094),(-56030697994867915570838586)⟩⟩,⟨⟨(-13057851380354241544013258),(-13057851380354241064844642)⟩,⟨(-52725040370626234291647988),(-52725040370626233812005309)⟩⟩,⟨⟨(-14357464461286778992610071),(-14357464461286778538766755)⟩,⟨(-49515581377893365853750185),(-49515581377893365399433176)⟩⟩,⟨⟨(-15471687509694274501941875),(-15471687509694274071953879)⟩,⟨(-46406723683929126650410234),(-46406723683929126219951211)⟩⟩,⟨⟨(-16412276199036052745894940),(-16412276199036052338859914)⟩,⟨(-43402146142584747944981360),(-43402146142584747537479883)⟩⟩,⟨⟨(-17190776342054123926828571),(-17190776342054123541620755)⟩,⟨(-40504833900233192937154814),(-40504833900233192551486730)⟩⟩] +lemma kernel12_1_r4_6_eq : ∀ k : Fin 16, kernel12_1Expr 4 6 k = kernel12_1_r4_6 k := by decide +kernel +noncomputable def kernel12_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-17818487708021001382522553),(-17818487708021001018331053)⟩,⟨(-37717110473714669146987467),(-37717110473714668782343433)⟩⟩,⟨⟨(-18306431254570198143346147),(-18306431254570197799067890)⟩,⟨(-35040671475439866364844805),(-35040671475439866020122982)⟩⟩,⟨⟨(-18665319788546043289691537),(-18665319788546042964523580)⟩,⟨(-32476619667291946283136165),(-32476619667291945957534803)⟩⟩,⟨⟨(-18905532043603615917741537),(-18905532043603615610692298)⟩,⟨(-30025501033820667860818966),(-30025501033820667553347427)⟩⟩,⟨⟨(-19037090137215991302282821),(-19037090137215991012627511)⟩,⟨(-27687341576211588759483880),(-27687341576211588469418265)⟩⟩,⟨⟨(-19069640346457632951858187),(-19069640346457632678641713)⟩,⟨(-25461684541411986463792629),(-25461684541411986190178489)⟩⟩,⟨⟨(-19012437120554365886320704),(-19012437120554365628839932)⟩,⟨(-23347627815366946625001699),(-23347627815366946367136512)⟩⟩,⟨⟨(-18874330228818445493098415),(-18874330228818445250352708)⟩,⟨(-21343861225323245376354959),(-21343861225323245133242943)⟩⟩,⟨⟨(-18663754925290553641806577),(-18663754925290553412549273)⟩,⟨(-19448703513352996196185472),(-19448703513352995966599947)⟩⟩,⟨⟨(-18388724996230914790506046),(-18388724996230914573989212)⟩,⟨(-17660138761392875871652417),(-17660138761392875654842923)⟩⟩,⟨⟨(-18056828543555093304296366),(-18056828543555093099990213)⟩,⟨(-15975852066951803561831017),(-15975852066951803357265398)⟩⟩,⟨⟨(-17675226346387925424258429),(-17675226346387925231497449)⟩,⟨(-14393264287980922607134897),(-14393264287980922414145309)⟩⟩,⟨⟨(-17250652634080161599650599),(-17250652634080161417962431)⟩,⟨(-12909565695004665473548913),(-12909565695004665291660796)⟩⟩,⟨⟨(-16789418097244485143377082),(-16789418097244484972123008)⟩,⟨(-11521748388272025724655189),(-11521748388272025553227683)⟩⟩,⟨⟨(-16297414958549406690186153),(-16297414958549406528908783)⟩,⟨(-10226637357207588459040518),(-10226637357207588297614206)⟩⟩,⟨⟨(-15780123922073053368584402),(-15780123922073053216714281)⟩,⟨(-9020920078641767880517866),(-9020920078641767728521341)⟩⟩] +lemma kernel12_1_r4_7_eq : ∀ k : Fin 16, kernel12_1Expr 4 7 k = kernel12_1_r4_7 k := by decide +kernel +noncomputable def kernel12_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-15242622818861401496643123),(-15242622818861401353780982)⟩,⟨(-7901174569014371249091930),(-7901174569014371106124092)⟩⟩,⟨⟨(-14689596766842009484150373),(-14689596766842009349747182)⟩,⟨(-6863895823827182713063494),(-6863895823827182578573553)⟩⟩,⟨⟨(-14125349665289674792353958),(-14125349665289674666020442)⟩,⟨(-5905520594939315480296962),(-5905520594939315353893982)⟩⟩,⟨⟨(-13553816847491707126419800),(-13553816847491707007675205)⟩,⟨(-5022450472740982616849232),(-5022450472740982498050898)⟩⟩,⟨⟨(-12978578719979072922920012),(-12978578719979072811421894)⟩,⟨(-4211073255712319891520545),(-4211073255712319779982933)⟩⟩,⟨⟨(-12402875222533375795018082),(-12402875222533375690193633)⟩,⟨(-3467782604296894893844451),(-3467782604296894788993343)⟩⟩,⟨⟨(-11829620950004803130334211),(-11829620950004803031860751)⟩,⟨(-2788995989334801946176324),(-2788995989334801847687734)⟩⟩,⟨⟨(-11261420784639425085235639),(-11261420784639424992724753)⟩,⟨(-2171170957464735246804016),(-2171170957464735154288318)⟩⟩,⟨⟨(-10700585895974259218450940),(-10700585895974259131632081)⟩,⟨(-1610819746891059945768250),(-1610819746891059858953763)⟩⟩,⟨⟨(-10149149974277597149793925),(-10149149974277597068296822)⟩,⟨(-1104522296708586640892800),(-1104522296708586559408201)⟩⟩,⟨⟨(-9608885572857505788154880),(-9608885572857505711718987)⟩,⟨(-648937701586386628436499),(-648937701586386552020254)⟩⟩,⟨⟨(-9081320444206641811252074),(-9081320444206641739556522)⟩,⟨(-240814171047257862200038),(-240814171047257790530379)⟩⟩,⟨⟨(-8567753764777257720701985),(-8567753764777257653520656)⟩,⟨123002441132366383275271,123002441132366450425307⟩⟩,⟨⟨(-8069272153075305565721606),(-8069272153075305502753110)⟩,⟨445561466699625817419887,445561466699625880352451⟩⟩,⟨⟨(-7586765395624371380251949),(-7586765395624371321282411)⟩,⟨729801537064473455572218,729801537064473514501899⟩⟩,⟨⟨(-7120941805085538639798496),(-7120941805085538584512938)⟩,⟨978545903885041562926906,978545903885041618169328⟩⟩] +lemma kernel12_1_r4_8_eq : ∀ k : Fin 16, kernel12_1Expr 4 8 k = kernel12_1_r4_8 k := by decide +kernel +noncomputable def kernel12_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-6672343144344475453484748),(-6672343144344475401601358)⟩,⟨1194498886034707686900316,1194498886034707738737914⟩⟩,⟨⟨(-6241359059618083752251483),(-6241359059618083703540098)⟩,⟨1380243361625636812056514,1380243361625636860719969⟩⟩,⟨⟨(-5828240974525703088576892),(-5828240974525703042880573)⟩,⟨1538239223322088733254715,1538239223322088778901541⟩⟩,⟨⟨(-5433115405559530552628757),(-5433115405559530509749964)⟩,⟨1670822715483540179514200,1670822715483540222343974⟩⟩,⟨⟨(-5055996667430419271067382),(-5055996667430419230871723)⟩,⟨1780206572660060757352229,1780206572660060797499566⟩⟩,⟨⟨(-4696798944322451791456753),(-4696798944322451753759542)⟩,⟨1868480880547247317709085,1868480880547247355358825⟩⟩,⟨⟨(-4355347710135215141056016),(-4355347710135215105730059)⟩,⟨1937614582622605683253250,1937614582622605718532750⟩⟩,⟨⟨(-4031390487307262846645299),(-4031390487307262813531431)⟩,⟨1989457558258047433775614,1989457558258047466844149⟩⟩,⟨⟨(-3724606939786178584701657),(-3724606939786178553676760)⟩,⟨2025743201064591123259744,2025743201064591154240559⟩⟩,⟨⟨(-3434618301135308037010472),(-3434618301135308007908670)⟩,⟨2048091429508484979786030,2048091429508485008845082⟩⟩,⟨⟨(-3160996143646324251427383),(-3160996143646324224149999)⟩,⟨2058012065379023388060596,2058012065379023415296637⟩⟩,⟨⟨(-2903270498667777431882506),(-2903270498667777406305115)⟩,⟨2056908519427140173823442,2056908519427140199360934⟩⟩,⟨⟨(-2660937342175142401470405),(-2660937342175142377509605)⟩,⟨2046081727374217194762693,2046081727374217218685083⟩⟩,⟨⟨(-2433465462914490857345755),(-2433465462914490834885337)⟩,⟨2026734283460464263400898,2026734283460464285824405⟩⟩,⟨⟨(-2220302733270387073630740),(-2220302733270387052592152)⟩,⟨1999974722714134653352287,1999974722714134674355476⟩⟩,⟨⟨(-2020881805362637625989433),(-2020881805362637606273597)⟩,⟨1966821907133685712679153,1966821907133685732361107⟩⟩] +lemma kernel12_1_r4_9_eq : ∀ k : Fin 16, kernel12_1Expr 4 9 k = kernel12_1_r4_9 k := by decide +kernel +noncomputable def kernel12_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-1834625256792308954524672),(-1834625256792308936032842)⟩,⟨1928209474946276218290663,1928209474946276236751962⟩⟩,⟨⟨(-1660950211963064186056624),(-1660950211963064168695482)⟩,⟨1884990316003736557030822,1884990316003736574364743⟩⟩,⟨⟨(-1499272466028838597200291),(-1499272466028838580912051)⟩,⟨1837941040171821862784087,1837941040171821879048160⟩⟩,⟨⟨(-1349010139293521969502398),(-1349010139293521954212496)⟩,⟨1787766409234937989794022,1787766409234938005062570⟩⟩,⟨⟨(-1209586890343415937824102),(-1209586890343415923484343)⟩,⟨1735103706355526158619555,1735103706355526172940551⟩⟩,⟨⟨(-1080434716359564861638020),(-1080434716359564848178619)⟩,⟨1680527020477740184099408,1680527020477740197542425⟩⟩,⟨⟨(-960996368965044717368730),(-960996368965044704744079)⟩,⟨1624551426235475126024473,1624551426235475138634918⟩⟩,⟨⟨(-850727413641688001210205),(-850727413641687989361293)⟩,⟨1567637042905163862646232,1567637042905163874482936⟩⟩,⟨⟨(-749097960230329387307025),(-749097960230329376196783)⟩,⟨1510192958727162756152672,1510192958727162767252527⟩⟩,⟨⟨(-655594091336106902041916),(-655594091336106891614394)⟩,⟨1452581009501989811233688,1452581009501989821652489⟩⟩,⟨⟨(-569719014621913276030993),(-569719014621913266250454)⟩,⟨1395119402747738905778022,1395119402747738915551345⟩⟩,⟨⟨(-490993964013517159808908),(-490993964013517150628925)⟩,⟨1338086180883555802915362,1338086180883555812089492⟩⟩,⟨⟨(-418958873782296842798753),(-418958873782296834184607)⟩,⟨1281722518884031427910603,1281722518884031436520141⟩⟩,⟨⟨(-353172848337383436057469),(-353172848337383427957579)⟩,⟨1226235853635398461079010,1226235853635398469175409⟩⟩,⟨⟨(-293214449367984346815714),(-293214449367984339203878)⟩,⟨1171802843822645687007220,1171802843822645694616570⟩⟩,⟨⟨(-238681820746676228160866),(-238681820746676221002145)⟩,⟨1118572160594461109839681,1118572160594461116996822⟩⟩] +lemma kernel12_1_r4_10_eq : ∀ k : Fin 16, kernel12_1Expr 4 10 k = kernel12_1_r4_10 k := by decide +kernel +noncomputable def kernel12_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-189192670351687862538907),(-189192670351687855812554)⟩,⟨1066667110498647684958431,1066667110498647691684010⟩⟩,⟨⟨(-144384126705077845201639),(-144384126705077838874181)⟩,⟨1016188093263471221684326,1016188093263471228011736⟩⟩,⟨⟨(-103912487067008203939469),(-103912487067008197990524)⟩,⟨967214897930021834810833,967214897930021840760365⟩⟩,⟨⟨(-67452872385162697152219),(-67452872385162691554382)⟩,⟨919808841627214330839586,919808841627214336438579⟩⟩,⟨⟨(-34698803282352547668015),(-34698803282352542404793)⟩,⟨874014755934862398390545,874014755934862403655422⟩⟩,⟨⟨(-5361710082628321539682),(-5361710082628316585321)⟩,⟨829862826311759563327752,829862826311759568284209⟩⟩,⟨⟨20829611266457104275081,20829611266457108937604⟩,⟨787370290485260056918974,787370290485260061583974⟩⟩,⟨⟨44129586614914216069626,44129586614914220467530⟩,⟨746543002016686735347011,746543002016686739747729⟩⟩,⟨⟨64776484661436353166176,64776484661436357310974⟩,⟨707376865482955382884821,707376865482955387032717⟩⟩,⟨⟨82993062915400624532337,82993062915400628443877⟩,⟨669859149858712433413712,669859149858712437328589⟩⟩,⟨⟨98987230789237758923038,98987230789237762612781⟩,⟨633969686754251504778995,633969686754251508472282⟩⟩,⟨⟨112952722922439854352366,112952722922439857836457⟩,⟨599681960171264734127484,599681960171264737615289⟩⟩,⟨⟨125069776662707873639878,125069776662707876927359⟩,⟨566964094389366827086418,566964094389366830377750⟩⟩,⟨⟨135505808396426415774332,135505808396426418880547⟩,⟨535779746499052031826931,535779746499052034937106⟩⟩,⟨⟨144416084130374894881406,144416084130374897815154⟩,⟨506088909958518498030701,506088909958518500968497⟩⟩,⟨⟨151944380380421886878902,151944380380421889654992⟩,⟨477848635379286376601970,477848635379286379382111⟩⟩] +lemma kernel12_1_r4_11_eq : ∀ k : Fin 16, kernel12_1Expr 4 11 k = kernel12_1_r4_11 k := by decide +kernel +noncomputable def kernel12_1_r4_12 : Fin 16 → CBox := ![⟨⟨158223632022400900309895,158223632022400902936805⟩,⟨451013674544864827189859,451013674544864829820744⟩⟩,⟨⟨163376564307273298422797,163376564307273300912488⟩,⟨425537053443467896774672,425537053443467899268268⟩⟩,⟨⟨167516306739166409785876,167516306739166412144701⟩,⟨401370579854990861066082,401370579854990863428725⟩⟩,⟨⟨170746986963266155975009,170746986963266158212525⟩,⟨378465290778676455170794,378465290778676457412041⟩⟩,⟨⟨173164303213337724071183,173164303213337726192231⟩,⟨356771844725172988256822,356771844725172990381515⟩⟩,⟨⟨174856074228449011778967,174856074228449013792756⟩,⟨336240863628594992098189,336240863628594994115535⟩⟩,⟨⟨175902765867950105199013,175902765867950107110400⟩,⟨316823228863881947602406,316823228863881949517257⟩⟩,⟨⟨176377993935616002925896,176377993935616004744567⟩,⟨298470335584938311634621,298470335584938313456664⟩⟩,⟨⟨176349002970781711329877,176349002970781713059499⟩,⟨281134309332070087196161,281134309332070088929062⟩⟩,⟨⟨175877120978947226068235,175877120978947227716058⟩,⟨264768188595095233630770,264768188595095235281778⟩⟩,⟨⟨175018190259305345695396,175018190259305347264914⟩,⟨249326076762856287864649,249326076762856289437261⟩⟩,⟨⟨173822974644470551508389,173822974644470553005338⟩,⟨234763266642064769403068,234763266642064770903021⟩⟩,⟨⟨172337543600791427240985,172337543600791428667895⟩,⟨221036340489549653713660,221036340489549655143485⟩⟩,⟨⟨170603633748335119530593,170603633748335120893111⟩,⟨208103248272915302195880,208103248272915303561226⟩⟩,⟨⟨168658988450147296728757,168658988450147298031060⟩,⟨195923366655970191821207,195923366655970193126252⟩⟩,⟨⟨166537676192799707829018,166537676192799709075727⟩,⟨184457540997507399904970,184457540997507401154334⟩⟩] +lemma kernel12_1_r4_12_eq : ∀ k : Fin 16, kernel12_1Expr 4 12 k = kernel12_1_r4_12 k := by decide +kernel +noncomputable def kernel12_1_r4_13 : Fin 16 → CBox := ![⟨⟨164270388536497886519982,164270388536497887712648⟩,⟨173668112455373561896153,173668112455373563091393⟩⟩,⟨⟨161884718454963098559467,161884718454963099702676⟩,⟨163518932102380937580482,163518932102380938726188⟩⟩,⟨⟨159405419914625469406404,159405419914625470502058⟩,⟨153975363786497077660756,153975363786497078758827⟩⟩,⟨⟨156854649560941602466202,156854649560941603517838⟩,⟨145004277304780626380755,145004277304780627434731⟩⟩,⟨⟨154252191388326731708833,154252191388326732717798⟩,⟨136574033308521850358767,136574033308521851369971⟩⟩,⟨⟨151615665270593511132138,151615665270593512102207⟩,⟨128654461215719510308435,128654461215719511280600⟩⟩,⟨⟨148960720222124451407397,148960720222124452339979⟩,⟨121216831276047847852429,121216831276047848786970⟩⟩,⟨⟨146301213247367936460788,146301213247367937358708⟩,⟨114233821812456706217534,114233821812456707117284⟩⟩,⟨⟨143649374618627079573255,143649374618627080437264⟩,⟨107679482552085138839779,107679482552085139705502⟩⟩,⟨⟨141015960400393957234623,141015960400393958067758⟩,⟨101529194856808242287894,101529194856808243122632⟩⟩,⟨⟨138410393013461851294753,138410393013461852098070⟩,⟨95759629570014002521546,95759629570014003326360⟩⟩,⟨⟨135840890604429479518458,135840890604429480294254⟩,⟨90348703110646518823996,90348703110646519601196⟩⟩,⟨⟨133314585956616112003284,133314585956616112752159⟩,⟨85275532367674664125930,85275532367674664876118⟩⟩,⟨⟨130837635647381354640330,130837635647381355364692⟩,⟨80520388877472942742555,80520388877472943468144⟩⟩,⟨⟨128415320124864810516798,128415320124864811217438⟩,⟨76064652702661868562901,76064652702661869264693⟩⟩,⟨⟨126052135344641475823172,126052135344641476501992⟩,⟨71890766373286296553163,71890766373286297233063⟩⟩] +lemma kernel12_1_r4_13_eq : ∀ k : Fin 16, kernel12_1Expr 4 13 k = kernel12_1_r4_13 k := by decide +kernel +noncomputable def kernel12_1_r4_14 : Fin 16 → CBox := ![⟨⟨123751876574083033498942,123751876574083034156213⟩,⟨67982189199362480961802,67982189199362481620081⟩⟩,⟨⟨121517714939624821600228,121517714939624822238083⟩,⟨64323352217364400943477,64323352217364401582276⟩⟩,⟨⟨119352267259917165952686,119352267259917166571738⟩,⟨60899613991730750120685,60899613991730750740625⟩⟩,⟨⟨117257659676199160919041,117257659676199161520842⟩,⟨57697217455558510726578,57697217455558511329211⟩⟩,⟨⟨115235585560345769911863,115235585560345770496664⟩,⟨54703247941929741070959,54703247941929741656537⟩⟩,⟨⟨113287358151044163975084,113287358151044164544599⟩,⟨51905592528438188037126,51905592528438188607374⟩⟩,⟨⟨111413958339561254312804,111413958339561254867469⟩,⟨49292900792105576650392,49292900792105577205743⟩⟩,⟨⟨109616077998653606157068,109616077998653606698203⟩,⟨46854547049688841139763,46854547049688841681541⟩⟩,⟨⟨107894159221402325894586,107894159221402326422233⟩,⟨44580594139084803566565,44580594139084804094819⟩⟩,⟨⟨106248429811167859762162,106248429811167860277899⟩,⟨42461758780863895259916,42461758780863895776220⟩⟩,⟨⟨104678935339474225419201,104678935339474225923339⟩,⟨40489378544655295572258,40489378544655296076929⟩⟩,⟨⟨103185568065455308521470,103185568065455309015136⟩,⟨38655380432927337081012,38655380432927337575184⟩⟩,⟨⟨101768092988521003453230,101768092988521003936467⟩,⟨36952251084442606323707,36952251084442606807420⟩⟩,⟨⟨100426171285110870982178,100426171285110871456280⟩,⟨35373008591117838076140,35373008591117838550691⟩⟩,⟨⟨99159381360771303603436,99159381360771304068652⟩,⟨33911175915002133921239,33911175915002134386876⟩⟩,⟨⟨97967237730285137550279,97967237730285138007578⟩,⟨32560755886436681602324,32560755886436682060028⟩⟩] +lemma kernel12_1_r4_14_eq : ∀ k : Fin 16, kernel12_1Expr 4 14 k = kernel12_1_r4_14 k := by decide +kernel +noncomputable def kernel12_1_r4_15 : Fin 16 → CBox := ![⟨⟨96849207921160334788483,96849207921160335237761⟩,⟨31316207760023298837700,31316207760023299287357⟩⟩,⟨⟨95804727579401982382709,95804727579401982825212⟩,⟨30172425301669959831620,30172425301669960274484⟩⟩,⟨⟨94833213941100760450303,94833213941100760886214⟩,⟨29124716377574131318375,29124716377574131754637⟩⟩,⟨⟨93934077818919582723482,93934077818919583153678⟩,⟨28168784014436430614206,28168784014436431044732⟩⟩,⟨⟨93106734238994475179616,93106734238994475604020⟩,⟨27300708899366135884317,27300708899366136309033⟩⟩,⟨⟨92350611851030519582420,92350611851030520002093⟩,⟨26516933287754995762993,26516933287754996182966⟩⟩,⟨⟨91665161222412407239325,91665161222412407654415⟩,⟨25814246287774569796436,25814246287774570211816⟩⟩,⟨⟨91049862115904783940964,91049862115904784352250⟩,⟨25189770491021531845605,25189770491021532257172⟩⟩,⟨⟨90504229839932834536624,90504229839932834943954⟩,⟨24640949920129327979901,24640949920129328387500⟩⟩,⟨⟨90027820750451198564055,90027820750451198968478⟩,⟨24165539265824679785556,24165539265824680190245⟩⟩,⟨⟨89620236973972306817742,89620236973972307219384⟩,⟨23761594387881362446055,23761594387881362847956⟩⟩,⟨⟨89281130412376946541559,89281130412376946941161⟩,⟨23427464056664791766811,23427464056664792166664⟩⟩,⟨⟨89010206081614143738999,89010206081614144136436⟩,⟨23161782914427522817947,23161782914427523215628⟩⟩,⟨⟨88807224828258669023823,88807224828258669420048⟩,⟨22963465638170432256743,22963465638170432653212⟩⟩,⟨⟨88672005460077545619953,88672005460077546015079⟩,⟨22831702288693500585037,22831702288693500980405⟩⟩,⟨⟨88604426319207304201636,88604426319207304596358⟩,⟨22765954833393260330876,22765954833393260725840⟩⟩] +lemma kernel12_1_r4_15_eq : ∀ k : Fin 16, kernel12_1Expr 4 15 k = kernel12_1_r4_15 k := by decide +kernel +noncomputable def kernel12_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel12_1_r4_0,kernel12_1_r4_1,kernel12_1_r4_2,kernel12_1_r4_3,kernel12_1_r4_4,kernel12_1_r4_5,kernel12_1_r4_6,kernel12_1_r4_7,kernel12_1_r4_8,kernel12_1_r4_9,kernel12_1_r4_10,kernel12_1_r4_11,kernel12_1_r4_12,kernel12_1_r4_13,kernel12_1_r4_14,kernel12_1_r4_15] +lemma kernel12_1_r4_eq (i k : Fin 16) : kernel12_1Expr 4 i k = kernel12_1_r4 i k := by + fin_cases i + · exact kernel12_1_r4_0_eq k + · exact kernel12_1_r4_1_eq k + · exact kernel12_1_r4_2_eq k + · exact kernel12_1_r4_3_eq k + · exact kernel12_1_r4_4_eq k + · exact kernel12_1_r4_5_eq k + · exact kernel12_1_r4_6_eq k + · exact kernel12_1_r4_7_eq k + · exact kernel12_1_r4_8_eq k + · exact kernel12_1_r4_9_eq k + · exact kernel12_1_r4_10_eq k + · exact kernel12_1_r4_11_eq k + · exact kernel12_1_r4_12_eq k + · exact kernel12_1_r4_13_eq k + · exact kernel12_1_r4_14_eq k + · exact kernel12_1_r4_15_eq k +noncomputable def kernel12_1_r5_0 : Fin 16 → CBox := ![⟨⟨397648133410064807836512261670,397648133410064809210319346792⟩,⟨87867883485631234098354358170,87867883485631235469812082107⟩⟩,⟨⟨397542762063045170261110217468,397542762063045171634717422122⟩,⟨87675217013320227761027669220,87675217013320229132281633813⟩⟩,⟨⟨397331900652330502200793438660,397331900652330503573998490583⟩,⟨87290236951687636502334438543,87290236951687637873178504793⟩⟩,⟨⟨397015312740969009530899102754,397015312740969010903499657009⟩,⟨86713648599080319476249503362,86713648599080320846477481248⟩⟩,⟨⟨396592646160081094834056481887,396592646160081096205850029199⟩,⟨85946508732272898724079493542,85946508732272900093485061168⟩⟩,⟨⟨396063435980269997809034420803,396063435980269999179818295679⟩,⟨84990224196933993048710506235,84990224196933994417087228620⟩⟩,⟨⟨395427108452791222595485292461,395427108452791223965056541657⟩,⟨83846550020591110697428345854,83846550020591112064569554027⟩⟩,⟨⟨394682985902795712807313063401,394682985902795714175468556887⟩,⟨82517587041680398580453228854,82517587041680399946152141237⟩⟩,⟨⟨393830292552625491021968905559,393830292552625492388505026840⟩,⟨81005779046849087460859443058,81005779046849088824908866226⟩⟩,⟨⟨392868161248861678387824905067,392868161248861679752537941831⟩,⟨79313909407381464249233395888,79313909407381465611426125157⟩⟩,⟨⟨391795641062615683159910612653,391795641062615684522596581835⟩,⟨77445097204465779785683829303,77445097204465781145812485203⟩⟩,⟨⟨390611705728427501621798685214,390611705728427502982360511058⟩,⟨75402792832030802550269268878,75402792832030803908233723738⟩⟩,⟨⟨389315262883103533124659678030,389315262883103534482900860147⟩,⟨73190773065076627173874286656,73190773065076628529474880486⟩⟩,⟨⟨387905164061903538227917084135,387905164061903539583641662670⟩,⟨70813135580823279306949550991,70813135580823280659987286049⟩⟩,⟨⟨386380215405686290466738248998,386380215405686291819748145025⟩,⟨68274292919619469860386984627,68274292919619471210660876208⟩⟩,⟨⟨384739189028960477393705187010,384739189028960478743803395775⟩,⟨65578965872407640535864878165,65578965872407641883175154483⟩⟩] +lemma kernel12_1_r5_0_eq : ∀ k : Fin 16, kernel12_1Expr 5 0 k = kernel12_1_r5_0 k := by decide +kernel +noncomputable def kernel12_1_r5_1 : Fin 16 → CBox := ![⟨⟨382980834995276339036623218000,382980834995276340383609529118⟩,⟨62732176281643417481246656969,62732176281643418825390490122⟩⟩,⟨⟨381103893843049666296448392608,381103893843049667640125110519⟩,⟨59739239242928934209104843553,59739239242928935549882074294⟩⟩,⟨⟨379107109601748784761141392410,379107109601748786101306427049⟩,⟨56605754695249231925307352517,56605754695249233262513592655⟩⟩,⟨⟨376989243235413026061774030161,376989243235413027398228654449⟩,⟨53337598388605864843303942731,53337598388605866176738334784⟩⟩,⟨⟨374749086447724213786508056763,374749086447724215119047350279⟩,⟨49940912219026334834852353625,49940912219026336164308027220⟩⟩,⟨⟨372385475780337323731185285003,372385475780337325059610432791⟩,⟨46422093922394006326515677958,46422093922394007651792046867⟩⟩,⟨⟨369897306933909264285154759063,369897306933909265609258876976⟩,⟨42787786120290135516930586060,42787786120290136837819188465⟩⟩,⟨⟨367283549239262179235523983451,367283549239262180555107379592⟩,⟨39044864713064431512642757790,39044864713064432828942512905⟩⟩,⟨⟨364543260204396163433735818434,364543260204396164748587941781⟩,⟨35200426617647370809975135980,35200426617647372121474309529⟩⟩,⟨⟨361675600061641865983142372335,361675600061641867293064621634⟩,⟨31261776850177883863423967788,31261776850177885169922969557⟩⟩,⟨⟨358679846238131750673429366652,358679846238131751978209639613⟩,⟨27236414956332945437874044659,27236414956332946739159998907⟩⟩,⟨⟨355555407671984791173609144175,355555407671984792473048101034⟩,⟨23132020795297315564063262614,23132020795297316859936256431⟩⟩,⟨⟨352301838896157315494689126933,352301838896157316788570364663⟩,⟨18956439686585881898547536390,18956439686585883188790817697⟩⟩,⟨⟨348918853811825831737653906986,348918853811825833025780609422⟩,⟨14717666932408890930075698839,14717666932408892214492302060⟩⟩,⟨⟨345406339073448065912358444673,345406339073448067194513229918⟩,⟨10423831731930504308151807160,10423831731930505586524431399⟩⟩,⟨⟨341764367008306884091488533851,341764367008306885367474317277⟩,⟨6083180507589893600848630443,6083180507589894872980473004⟩⟩] +lemma kernel12_1_r5_1_eq : ∀ k : Fin 16, kernel12_1Expr 5 1 k = kernel12_1_r5_1 k := by decide +kernel +noncomputable def kernel12_1_r5_2 : Fin 16 → CBox := ![⟨⟨337993207994387487448487493724,337993207994387488718081405438⟩,⟨1704059667605567596584061103,1704059667605568862252770042⟩⟩,⟨⟨334093342221878773614361432194,334093342221878774877371400421⟩,⟨(-2705102167160208471612608965),(-2705102167160207212598395266)⟩⟩,⟨⟨330065470765430661338675448949,330065470765430662594879238870⟩,⟨(-7135812439669139069310259384),(-7135812439669137817171826956)⟩⟩,⟨⟨325910525896544004584618075848,325910525896544005833823293409⟩,⟨(-11579533400025049454869866164),(-11579533400025048209798470569)⟩⟩,⟨⟨321629680568119749949075013315,321629680568119751191053616686⟩,⟨(-16027701274976939086306936996),(-16027701274976937848529241435)⟩⟩,⟨⟨317224357006248077223480500924,317224357006248078458048186585⟩,⟨(-20471745818782272329698788758),(-20471745818782271099384051701)⟩⟩,⟨⟨312696234347772707338792575291,312696234347772708565724300005⟩,⟨(-24903110196506906664120515664),(-24903110196506905441476884769)⟩⟩,⟨⟨308047255266013976634883560417,308047255266013977853994593161⟩,⟨(-29313271146835653204080815333),(-29313271146835651989291055117)⟩⟩,⟨⟨303279631531267474088237491348,303279631531267475299294278350⟩,⟨(-33693759367598398546669788384),(-33693759367598397339965298549)⟩⟩,⟨⟨298395848457300943296539691936,298395848457300944499368582661⟩,⟨(-38036180063517988655920636950),(-38036180063517987457472821042)⟩⟩,⟨⟨293398668190035734207817137111,293398668190035735402189526029⟩,⟨(-42332233592194557413845794262),(-42332233592194556223880829414)⟩⟩,⟨⟨288291131799902327342727326621,288291131799902328528469464983⟩,⟨(-46573736141093098728994547981),(-46573736141093097547683668769)⟩⟩,⟨⟨283076560144981315549011944097,283076560144981316725887967301⟩,⟨(-50752640365332476313949886162),(-50752640365332475141526269035)⟩⟩,⟨⟨277758553477957695013840616296,277758553477957696181690390486⟩,⟨(-54861055913419268749287541204),(-54861055913419267585908575777)⟩⟩,⟨⟨272340989776100425110906794608,272340989776100426269501151413⟩,⟨(-58891269765761935653478746531),(-58891269765761934499370692262)⟩⟩,⟨⟨266828021779901137827571685494,266828021779901138976751524785⟩,⟨(-62835766308871050919483036968),(-62835766308871049774802038703)⟩⟩] +lemma kernel12_1_r5_2_eq : ∀ k : Fin 16, kernel12_1Expr 5 2 k = kernel12_1_r5_2 k := by decide +kernel +noncomputable def kernel12_1_r5_3 : Fin 16 → CBox := ![⟨⟨261224072732633030297927080974,261224072732633031437453455126⟩,⟨(-66687247066628947528237310135),(-66687247066628946393219203716)⟩⟩,⟨⟨255533830819888166132422844633,255533830819888167262155898823⟩,⟨(-70438650008923777639098526985),(-70438650008923776513880047262)⟩⟩,⟨⟨249762242315081016004046006795,249762242315081017123758429811⟩,⟨(-74083168357312677617068081043),(-74083168357312676501873274692)⟩⟩,⟨⟨243914503443928232125626365874,243914503443928233235177554566⟩,⟨(-77614268807227353772396600296),(-77614268807227352667362804453)⟩⟩,⟨⟨237996050987987534772328667795,237996050987987535871482737591⟩,⟨(-81025709086580553567074822597),(-81025709086580552472434524761)⟩⟩,⟨⟨232012551654418634626214043089,232012551654418635714851739913⟩,⟨(-84311554771487555273860777028),(-84311554771487554189729872427)⟩⟩,⟨⟨225969890246171346268309643277,225969890246171347346208316888⟩,⟨(-87466195281193176618560972372),(-87466195281193175545158635297)⟩⟩,⟨⟨219874156673764395168447054550,219874156673764396235488457582⟩,⟨(-90484358976198032521356559174),(-90484358976198031458797607494)⟩⟩,⟨⟨213731631856646067018967171133,213731631856646068074916854902⟩,⟨(-93361127286009840063040201681),(-93361127286009839011555549491)⟩⟩,⟨⟨207548772568777602481240877551,207548772568777603526008631521⟩,⟨(-96091947795904131239858726957),(-96091947795904130199535142986)⟩⟩,⟨⟨201332195289504922679670079453,201332195289504923713315401191⟩,⟨(-98672646225557029960727442177),(-98672646225557028931481778261)⟩⟩,⟨⟨195088659126937115568301431466,195088659126937116592812003485⟩,⟨(-101099437236399544345723969515),(-101099437236399543325414384898)⟩⟩,⟨⟨188825047886885181911143850870,188825047886885182926272185976⟩,⟨(-103368934009022395012093417123),(-103368934009022394000968720727)⟩⟩,⟨⟨182548351365887139069224635301,182548351365887140074883516793⟩,⟨(-105478156536912560078193057173),(-105478156536912559076342110469)⟩⟩,⟨⟨176265645951912684830396589985,176265645951912685826354424321⟩,⟨(-107424538588202894587971961663),(-107424538588202893595628129534)⟩⟩,⟨⟨169984074620961290730193088771,169984074620961291716358313244⟩,⟨(-109205933292935530742025364666),(-109205933292935529759282276154)⟩⟩] +lemma kernel12_1_r5_3_eq : ∀ k : Fin 16, kernel12_1Expr 5 3 k = kernel12_1_r5_3 k := by decide +kernel +noncomputable def kernel12_1_r5_4 : Fin 16 → CBox := ![⟨⟨163710826421903379361390365862,163710826421903380337511327957⟩,⟨(-110820617319545330244450823384),(-110820617319545329271562318288)⟩⟩,⟨⟨157453115545529592508668304810,157453115545529593474687337059⟩,⟨(-112267293610824581917873108795),(-112267293610824580954899347889)⟩⟩,⟨⟨151218160076835803062885629549,151218160076835804018575708769⟩,⟨(-113545092656493902740337335648),(-113545092656493901787507950023)⟩⟩,⟨⟨145013160532052827542907483904,145013160532052828488201538388⟩,⟨(-114653572286633031981610916337),(-114653572286633031038995852880)⟩⟩,⟨⟨138845278283805093551050503923,138845278283805094485705220813⟩,⟨(-115592715977571997941465527875),(-115592715977571997009311087132)⟩⟩,⟨⟨132721613979031419076353368121,132721613979031420000335503400⟩,⟨(-116362929669358413777867219729),(-116362929669358412856209897599)⟩⟩,⟨⟨126649186054907724284578888796,126649186054907725197669836670⟩,⟨(-116965037101548591769877269498),(-116965037101548590858939028285)⟩⟩,⟨⟨120634909457964852125712409450,120634909457964853027873011029⟩,⟨(-117400273681765096126030309676),(-117400273681765095225853890486)⟩⟩,⟨⟨114685574670888615436675648000,114685574670888616327665479393⟩,⟨(-117670278909166258450953872788),(-117670278909166257561783380066)⟩⟩,⟨⟨108807827150122714420239735420,108807827150122715300062548102⟩,⟨(-117777087382628148018374511502),(-117777087382628147140210089423)⟩⟩,⟨⟨103008147275372478950821252258,103008147275372479819270651392⟩,⟨(-117723118430990226720856013543),(-117723118430990225853908041807)⟩⟩,⟨⟨97292830909437929544308789963,97292830909437930401376383775⟩,⟨(-117511164410106258125063391966),(-117511164410106257269344419072)⟩⟩,⟨⟨91667970663503101540658641321,91667970663503102386120567463⟩,⟨(-117144377718616458392774933337),(-117144377718616457548513064036)⟩⟩,⟨⟨86139437959094800097411457897,86139437959094800931300855356⟩,⟨(-116626256591261015206050368580),(-116626256591261014373216854462)⟩⟩,⟨⟨80712865973422876155280135843,80712865973422876977406375617⟩,⟨(-115960629735136279740517559087),(-115960629735136278919307496113)⟩⟩,⟨⟨75393633549755563917494209767,75393633549755564727881787973⟩,⟨(-115151639880502660479818030812),(-115151639880502659670211498089)⟩⟩] +lemma kernel12_1_r5_4_eq : ∀ k : Fin 16, kernel12_1Expr 5 4 k = kernel12_1_r5_4 k := by decide +kernel +noncomputable def kernel12_1_r5_5 : Fin 16 → CBox := ![⟨⟨70186850148901911470528470891,70186850148901912268961353351⟩,⟨(-114203726323539692816736405436),(-114203726323539692018954084507)⟩⟩,⟨⟨65097341911807798771871600632,65097341911807799558481946542⟩,⟨(-113121606543764240498553527286),(-113121606543764239712468298620)⟩⟩,⟨⟨60129638896765505766102832537,60129638896765506540924304751⟩,⟨(-111910256983641197978855881407),(-111910256983641197204440030836)⟩⟩,⟨⟨55287963547836046616530142690,55287963547836047379613164442⟩,⟨(-110574893082185285954946751197),(-110574893082185285192154618449)⟩⟩,⟨⟨50576220443838646466921485179,50576220443838647218067003307⟩,⟨(-109120948658044799992479553348),(-109120948658044799241515013522)⟩⟩,⟨⟨45997987369725832993080700414,45997987369725833732385913036⟩,⟨(-107554054740645400921629582280),(-107554054740645400182400255092)⟩⟩,⟨⟨41556507744391109423178313286,41556507744391110150484129963⟩,⟨(-105880017950431106555915686595),(-105880017950431105828585531218)⟩⟩,⟨⟨37254684431006468115320150908,37254684431006468830710905996⟩,⟨(-104104798531052634525230978786),(-104104798531052633809720496257)⟩⟩,⟨⟨33095074947917908851056689087,33095074947917909554345971656⟩,⟨(-102234488137507608925129707287),(-102234488137507608221630194651)⟩⟩,⟨⟨29079888089998335858372824054,29079888089998336550077698891⟩,⟨(-100275287484725833310970521517),(-100275287484725832618969698414)⟩⟩,⟨⟨25210981962228743405191660870,25210981962228744085251326084⟩,⟨(-98233483960914372849057354269),(-98233483960914372168620865341)⟩⟩,⟨⟨21489863419210258774706365531,21489863419210259443223512872⟩,⟨(-96115429309135683032332566194),(-96115429309135682363362463190)⟩⟩,⟨⟨17917688896360415481567769033,17917688896360416138369533255⟩,⟨(-93927517479097108549526025095),(-93927517479097107892199959258)⟩⟩,⟨⟨14495266610774681957194871760,14495266610774682602433682637⟩,⟨(-91676162748996820344900403535),(-91676162748996819699070572653)⟩⟩,⟨⟨11223060102194627083459839617,11223060102194627717007642863⟩,⟨(-89367778214519997312463276561),(-89367778214519996678262400776)⟩⟩,⟨⟨8101193077270662426667913766,8101193077270663048659440473⟩,⟨(-87008754738735181635416673321),(-87008754738735181012714519282)⟩⟩] +lemma kernel12_1_r5_5_eq : ∀ k : Fin 16, kernel12_1Expr 5 5 k = kernel12_1_r5_5 k := by decide +kernel +noncomputable def kernel12_1_r5_6 : Fin 16 → CBox := ![⟨⟨5129455513390720440198979317,5129455513390721050473993822⟩,⟨(-84605440452734421744719648627),(-84605440452734421133680994509)⟩⟩,⟨⟨2307310971813875220650703392,2307310971813875819404567428⟩,⟨(-82164120892426715574442011281),(-82164120892426714974875801720)⟩⟩,⟨⟨(-366094936256552213456378551),(-366094936256551626327174607)⟩,⟨(-79690999851971143779644266945),(-79690999851971143191658360693)⟩⟩,⟨⟨(-2891924992662859518890376311),(-2891924992662858943220883387)⟩,⟨(-77192181028966415334737024681),(-77192181028966414758170596971)⟩⟩,⟨⟨(-5271639791482615734535220942),(-5271639791482615170451878636)⟩,⟨(-74673650530743090774023916013),(-74673650530743090209007573141)⟩⟩,⟨⟨(-7506986206156162685561994349),(-7506986206156162132841130691)⟩,⟨(-72141260304982066085575313480),(-72141260304982065531896553889)⟩⟩,⟨⟨(-9599984980332596736866493607),(-9599984980332596195575912132)⟩,⟨(-69600712551458876888074646916),(-69600712551458876345814535245)⟩⟩,⟨⟨(-11552917521678291947363923323),(-11552917521678291417312068899)⟩,⟨(-67057545165040710995001169486),(-67057545165040710463970909856)⟩⟩,⟨⟨(-13368311980761063448518104500),(-13368311980761062929171274613)⟩,⟨(-64517118253195676661029037571),(-64517118253195676140697871486)⟩⟩,⟨⟨(-15048928699387743640835717790),(-15048928699387743131752882961)⟩,⟨(-61984601764266598748729171351),(-61984601764266598238658595959)⟩⟩,⟨⟨(-16597745114428567805007929323),(-16597745114428567306279212324)⟩,⟨(-59464964255669366637189585682),(-59464964255669366137472240339)⟩⟩,⟨⟨(-18017940204208893537782877998),(-18017940204208893049226391982)⟩,⟨(-56962962824053298079458421938),(-56962962824053297589914674928)⟩⟩,⟨⟨(-19312878564993101580513947866),(-19312878564993101102244789196)⟩,⟨(-54483134212361962827812670201),(-54483134212361962348559901715)⟩⟩,⟨⟨(-20486094204937720189257446264),(-20486094204937719721044649740)⟩,⟨(-52029787101709971798639119919),(-52029787101709971329448352957)⟩⟩,⟨⟨(-21541274142166338914448857033),(-21541274142166338456359188828)⟩,⟨(-49606995589095144861707121979),(-49606995589095144402647135915)⟩⟩,⟨⟨(-22482241892337720831199826004),(-22482241892337720383029189044)⟩,⟨(-47218593845244761183609060515),(-47218593845244760734477518532)⟩⟩] +lemma kernel12_1_r5_6_eq : ∀ k : Fin 16, kernel12_1Expr 5 6 k = kernel12_1_r5_6 k := by decide +kernel +noncomputable def kernel12_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-23312940929264916146148240168),(-23312940929264915708000184962)⟩,⟨(-44868171940395171433332364629),(-44868171940395170994234602165)⟩⟩,⟨⟨(-24037418199825267135406901638),(-24037418199825266706983803370)⟩,⟨(-42559072819568799444116301277),(-42559072819568799014773413079)⟩⟩,⟨⟨(-24659807771610664574897306583),(-24659807771610664156169350731)⟩,⟨(-40294390402981022559744226533),(-40294390402981022140164778645)⟩⟩,⟨⟨(-25184314688539114746534882200),(-25184314688539114337286556360)⟩,⟨(-38076968781617495544300638487),(-38076968781617495134266706987)⟩⟩,⟨⟨(-25615199106020189054681531560),(-25615199106020188654990338725)⟩,⟨(-35909402472802187215317501067),(-35909402472802186814904275719)⟩⟩,⟨⟨(-25956760773278146717020399881),(-25956760773278146326624983625)⟩,⟨(-33794037695755661766225218614),(-33794037695755661375168892023)⟩⟩,⟨⟨(-26213323926129196124579595377),(-26213323926129195743510080108)⟩,⟨(-31732974622745653005508643018),(-31732974622745652623836985679)⟩⟩,⟨⟨(-26389222648926650029613708165),(-26389222648926649657639467941)⟩,⟨(-29728070557477108364233444959),(-29728070557477107991713396368)⟩⟩,⟨⟨(-26488786759573742982050649328),(-26488786759573742618996823461)⟩,⟨(-27780943988871591045463143556),(-27780943988871590681917498128)⟩⟩,⟨⟨(-26516328266503226124702905630),(-26516328266503225770216226327)⟩,⟨(-25892979465356801131541724617),(-25892979465356800776614793585)⟩⟩,⟨⟨(-26476128441380202472725978714),(-26476128441380202126832937516)⟩,⟨(-24065333232232237730852637789),(-24065333232232237384568578876)⟩⟩,⟨⟨(-26372425546044312838153236773),(-26372425546044312500627410423)⟩,⟨(-22298939572598639373059168711),(-22298939572598639035189198749)⟩⟩,⟨⟨(-26209403246912845958811601663),(-26209403246912845629706154212)⟩,⟨(-20594517790734640439569015730),(-20594517790734640110164012470)⟩⟩,⟨⟨(-25991179744759975624369054953),(-25991179744759975303416071809)⟩,⟨(-18952579775667934463800304487),(-18952579775667934142590055798)⟩⟩,⟨⟨(-25721797642509942891442418684),(-25721797642509942578650521991)⟩,⟨(-17373438082010247901544225146),(-17373438082010247588535124500)⟩⟩,⟨⟨(-25405214568472562144075109051),(-25405214568472561839209542185)⟩,⟨(-15857214464892185214959025182),(-15857214464892184909914108931)⟩⟩] +lemma kernel12_1_r5_7_eq : ∀ k : Fin 16, kernel12_1Expr 5 7 k = kernel12_1_r5_7 k := by decide +kernel +noncomputable def kernel12_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-25045294567344734662973011768),(-25045294567344734366057726127)⟩,⟨(-14403848806028835647389810569),(-14403848806028835350330880910)⟩⟩,⟨⟨(-24645800266336076243797445757),(-24645800266336075954403248769)⟩,⟨(-13013108368550294665204433617),(-13013108368550294375700192869)⟩⟩,⟨⟨(-24210385818982026316164971814),(-24210385818982026034294188909)⟩,⟨(-11684597319220652096360976953),(-11684597319220651814411691394)⟩⟩,⟨⟨(-23742590624612780573265740303),(-23742590624612780298688154997)⟩,⟨(-10417766458019905777620422799),(-10417766458019905502993878256)⟩⟩,⟨⟨(-23245833817076955805710947678),(-23245833817076955538455869099)⟩,⟨(-9211923096749049342732697580),(-9211923096749049075456244175)⟩⟩,⟨⟨(-22723409512197821694492116090),(-22723409512197821434293178320)⟩,⟨(-8066241030310977934444605677),(-8066241030310977674250002726)⟩⟩,⟨⟨(-22178482799586799609068910934),(-22178482799586799355852501298)⟩,⟨(-6979770546589270486052253851),(-6979770546589270232863781528)⟩⟩,⟨⟨(-21614086460870086714649735596),(-21614086460870086468161347515)⟩,⟨(-5951448423362791739085251832),(-5951448423362791492646561024)⟩⟩,⟨⟨(-21033118393112839702451388764),(-21033118393112839462720737229)⟩,⟨(-4980107863425234423952706999),(-4980107863425234184291805971)⟩⟩,⟨⟨(-20438339713261273741417787854),(-20438339713261273508175876427)⟩,⟨(-4064488321993716540130417679),(-4064488321993716306976722730)⟩⟩,⟨⟨(-19832373516773093001972124604),(-19832373516773092775201881299)⟩,⟨(-3203245183557901723961323214),(-3203245183557901497296185620)⟩⟩,⟨⟨(-19217704261274624272822612599),(-19217704261274624052298792119)⟩,⟨(-2394959248509679964537618418),(-2394959248509679744134329156)⟩⟩,⟨⟨(-18596677744069711889900444262),(-18596677744069711675632731441)⟩,⟨(-1638145993172686391182693559),(-1638145993172686177049475018)⟩⟩,⟨⟨(-17971501640628915826042977962),(-17971501640628915617775615476)⟩,⟨(-931264570191159888543953508),(-931264570191159680423724842)⟩⟩,⟨⟨(-17344246569803296672348074474),(-17344246569803296470055195868)⟩,⟨(-272726519610257815760763144),(-272726519610257613626328642)⟩⟩,⟨⟨(-16716847650428114871521981315),(-16716847650428114674982752168)⟩,⟨339095835642337576777051670,339095835642337773147729019⟩⟩] +lemma kernel12_1_r5_8_eq : ∀ k : Fin 16, kernel12_1Expr 5 8 k = kernel12_1_r5_8 k := by decide +kernel +noncomputable def kernel12_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-16091106513198944060478556136),(-16091106513198943869703440352)⟩,⟨905861332806652465738194512,905861332806652656335872629⟩⟩,⟨⟨(-15468693731204824185130391495),(-15468693731204823999860743198)⟩,⟨1429252270493414944208839165,1429252270493415129293225083⟩⟩,⟨⟨(-14851151632277203441521352450),(-14851151632277203261724608589)⟩,⟨1910967084415686107384578219,1910967084415686286990069119⟩⟩,⟨⟨(-14239897456345031649301470836),(-14239897456345031474763109837)⟩,⟨2352713410867580018015757672,2352713410867580192361324072⟩⟩,⟨⟨(-13636226821259643419428283721),(-13636226821259643250141912013)⟩,⟨2756201548117185351922524055,2756201548117185521015243390⟩⟩,⟨⟨(-13041317461051090199859178403),(-13041317461051090035586246226)⟩,⟨3123138322951988089273644311,3123138322951988253352607949⟩⟩,⟨⟨(-12456233201282567858757064824),(-12456233201282567699460861697)⟩,⟨3455221366823179878971611992,3455221366823180038074108988⟩⟩,⟨⟨(-11881928137063125215795585614),(-11881928137063125061271683808)⟩,⟨3754133803392523770430858566,3754133803392523924761783467⟩⟩,⟨⟨(-11319250980342091331366917497),(-11319250980342091181611222382)⟩,⟨4021539346802186007408793985,4021539346802186156972746360⟩⟩,⟨⟨(-10768949544322572355611049125),(-10768949544322572210389304336)⟩,⟨4259077807672358744206902536,4259077807672358889238511611⟩⟩,⟨⟨(-10231675334176868677764371009),(-10231675334176868537037377767)⟩,⟨4468361001689859269926886645,4468361001689859410465762337⟩⟩,⟨⟨(-9707988214704838013767892074),(-9707988214704837877342223546)⟩,⟨4650969053687570101648612216,4650969053687570237888495394⟩⟩,⟨⟨(-9198361127128497706860195282),(-9198361127128497574721151806)⟩,⟨4808447088332149752466398033,4808447088332149884422335608⟩⟩,⟨⟨(-8703184828844420627910379090),(-8703184828844420499844612835)⟩,⟨4942302296936759742722241006,4942302296936759870607819125⟩⟩,⟨⟨(-8222772631642254677989941060),(-8222772631642254553957423042)⟩,⟨5054001368495889082429655452,5054001368495889206285174512⟩⟩,⟨⟨(-7757365115626248546968439373),(-7757365115626248426235173555)⟩,⟨5144968271798508185030817086,5144968271798508305599477852⟩⟩] +lemma kernel12_1_r5_9_eq : ∀ k : Fin 16, kernel12_1Expr 5 9 k = kernel12_1_r5_9 k := by decide +kernel +noncomputable def kernel12_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-7307134797831104756848199424),(-7307134797831104639378920180)⟩,⟨5216582374410197347752954415,5216582374410197465070540729⟩⟩,⟨⟨(-6872190736288848250880575829),(-6872190736288848136503651516)⟩,⟨5270176883419801493141887826,5270176883419801607379407361⟩⟩,⟨⟨(-6452583052065744340914227291),(-6452583052065744229626317552)⟩,⟨5307037592115711841785423273,5307037592115711952945657423⟩⟩,⟨⟨(-6048307353534735661625177785),(-6048307353534735553290586928)⟩,⟨5328401916184269279064228670,5328401916184269387282289068⟩⟩,⟨⟨(-5659309048867609015571829867),(-5659309048867608910208054215)⟩,⟨5335458202600415132244880068,5335458202600415237502739449⟩⟩,⟨⟨(-5285487534411494126719469754),(-5285487534411494024170927943)⟩,⟨5329345294100296902106886580,5329345294100297004559568023⟩⟩,⟨⟨(-4926700248246823530999144929),(-4926700248246823431259477262)⟩,⟨5311152331978235561569125173,5311152331978235661222478168⟩⟩,⟨⟨(-4582766579800173565664137295),(-4582766579800173468604336275)⟩,⟨5281918779927021477476948003,5281918779927021574459461195⟩⟩,⟨⟨(-4253471627898217081403723598),(-4253471627898216987043650694)⟩,⟨5242634651731369629449235197,5242634651731369723740568732⟩⟩,⟨⟨(-3938569801092211532896433324),(-3938569801092211441082684804)⟩,⟨5194240925819784337838099315,5194240925819784429591168502⟩⟩,⟨⟨(-3637788255450957407920579591),(-3637788255450957318644867962)⟩,⟨5137630129970228940258304295,5137630129970229029480943934⟩⟩,⟨⟨(-3350830166309960001884054525),(-3350830166309959915024871108)⟩,⟨5073647079840051671092312644,5073647079840051757905583008⟩⟩,⟨⟨(-3077377831672565166715999250),(-3077377831672565082284587756)⟩,⟨5003089755440875265591094644,5003089755440875349983330644⟩⟩,⟨⟨(-2817095606082999859254000131),(-2817095606082999777112103451)⟩,⟨4926710300195090464960625736,4926710300195090547069670080⟩⟩,⟨⟨(-2569632664830285042533977685),(-2569632664830284962672325947)⟩,⟨4845216127782936991668379654,4845216127782937071503110306⟩⟩,⟨⟨(-2334625599295463701814415055),(-2334625599295463624119464860)⟩,⟨4759271122608965846344161642,4759271122608965924017744130⟩⟩] +lemma kernel12_1_r5_10_eq : ∀ k : Fin 16, kernel12_1Expr 5 10 k = kernel12_1_r5_10 k := by decide +kernel +noncomputable def kernel12_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-2111700845122804538064429573),(-2111700845122804462552401452)⟩,⟨4669496920375386533489969543,4669496920375386608985820920⟩⟩,⟨⟨(-1900476945679581017799850380),(-1900476945679580944334889417)⟩,⟨4576474255939266977604710221,4576474255939267051058341958⟩⟩,⟨⟨(-1700566653970270727993491690),(-1700566653970270656566067706)⟩,⟨4480744366343087286085065542,4480744366343087357505675849⟩⟩,⟨⟨(-1511578876791693909349658673),(-1511578876791693839854463671)⟩,⟨4382810437636555360214961100,4382810437636555429707547156⟩⟩,⟨⟨(-1333120465458305012693024287),(-1333120465458304945138505445)⟩,⟨4283139084845188092442608880,4283139084845188159998418336⟩⟩,⟨⟨(-1164797857894563156116434203),(-1164797857894563090383037502)⟩,⟨4182161855181787799492372511,4182161855181787865230681629⟩⟩,⟨⟨(-1006218577287371802787744341),(-1006218577287371738866273440)⟩,⟨4080276745334974742030419747,4080276745334974805960149205⟩⟩,⟨⟨(-856992592819607855926184974),(-856992592819607793719549489)⟩,⟨3977849724399283809195012422,3977849724399283871413002949⟩⟩,⟨⟨(-716733548269587676037445463),(-716733548269587615558461130)⟩,⟨3875216254729439330981313339,3875216254729439391474495814⟩⟩,⟨⟨(-585059864464937966139120353),(-585059864464937907272486873)⟩,⟨3772682803703252263674327634,3772682803703252322557784287⟩⟩,⟨⟨(-461595721726860780321894333),(-461595721726860723055891990)⟩,⟨3670528340059614380357877416,3670528340059614437643093512⟩⟩,⟨⟨(-345971928536376129463542119),(-345971928536376073696883893)⟩,⟨3569005809137263226251126587,3569005809137263282039157258⟩⟩,⟨⟨(-237826682701985359505245304),(-237826682701985305246775494)⟩,⟨3468343581973800779629302115,3468343581973800833911100945⟩⟩,⟨⟨(-136806231312497160539165076),(-136806231312497107688401622)⟩,⟨3368746873830758951957387838,3368746873830759004833272259⟩⟩,⟨⟨(-42565435723614611635277395),(-42565435723614560185697787)⟩,⟨3270399128287631701102587214,3270399128287631752578902752⟩⟩,⟨⟨45231752243671042500639681,45231752243671092629521323⟩,⟨3173463363594449611836406455,3173463363594449661993492417⟩⟩] +lemma kernel12_1_r5_11_eq : ∀ k : Fin 16, kernel12_1Expr 5 11 k = kernel12_1_r5_11 k := by decide +kernel +noncomputable def kernel12_1_r5_12 : Fin 16 → CBox := ![⟨⟨126911896816876688826911129,126911896816876737620462340⟩,⟨3078083478487740774259535664,3078083478487740823082595945⟩⟩,⟨⟨202791761551760229108262053,202791761551760276666008968⟩,⟨2984385515158024642163347375,2984385515158024689751787696⟩⟩,⟨⟨273178063585567503572746398,273178063585567549918234988⟩,⟨2892478877508057495652577310,2892478877508057542029804702⟩⟩,⟨⟨338367293245829662045158496,338367293245829707250535251⟩,⟨2802457503259905247813175133,2802457503259905293051227669⟩⟩,⟨⟨398645593588566653822587881,398645593588566697877425355⟩,⟨2714400988855830535131794644,2714400988855830579220116973⟩⟩,⟨⟨454288694645859502535822480,454288694645859545524034756⟩,⟨2628375666453439542639719047,2628375666453439585661722116⟩⟩,⟨⟨505561897380278001846069411,505561897380278043771093362⟩,⟨2544435632640229727692210488,2544435632640229769651043244⟩⟩,⟨⟨552720102569926469537565726,552720102569926510465094679⟩,⟨2462623728787472406890888843,2462623728787472447852205754⟩⟩,⟨⟨596007880080440699822699753,596007880080440739738007193⟩,⟨2382972473229258513696609232,2382972473229258553645621279⟩⟩,⟨⟨635659574216883511916440461,635659574216883550899972795⟩,⟨2305504945690656618738416460,2305504945690656657755546184⟩⟩,⟨⟨671899441087097831160177086,671899441087097869214065873⟩,⟨2230235624600502240923088782,2230235624600502279010420531⟩⟩,⟨⟨704941814146838597784859189,704941814146838634968861261⟩,⟨2157171178110655944815952896,2157171178110655982033220825⟩⟩,⟨⟨734991294334265864405914634,734991294334265900708891138⟩,⟨2086311209805991250548380218,2086311209805991286884401842⟩⟩,⟨⟨762242961435676503462349432,762242961435676538954332742⟩,⟨2017648960229297717268723078,2017648960229297752793519201⟩⟩,⟨⟨786882603554395760056891861,786882603554395794746147612⟩,⟨1951171965464128364717635805,1951171965464128399439439922⟩⟩,⟨⟨809086961779427899191180179,809086961779427933143290628⟩,⟨1886862674117810742559770194,1886862674117810776544154011⟩⟩] +lemma kernel12_1_r5_12_eq : ∀ k : Fin 16, kernel12_1Expr 5 12 k = kernel12_1_r5_12 k := by decide +kernel +noncomputable def kernel12_1_r5_13 : Fin 16 → CBox := ![⟨⟨829023987368824153590973002,829023987368824186788744197⟩,⟨1824699024127799421860424674,1824699024127799455090162570⟩⟩,⟨⟨846853108973964236880941318,846853108973964269392260775⟩,⟨1764654980878679944710956704,1764654980878679977253936285⟩⟩,⟨⟨862725507634404260723951924,862725507634404292547958151⟩,⟨1706701038165819206547896776,1706701038165819238403235889⟩⟩,⟨⟨876784397468089296002658873,876784397468089327187898769⟩,⟨1650804683576238420287931304,1650804683576238451504175158⟩⟩,⟨⟨889165310168153897681549851,889165310168153928215085332⟩,⟨1596930829879063104896875598,1596930829879063135461066207⟩⟩,⟨⟨899996381594939735616613128,899996381594939765556774198⟩,⟨1545042214028132018985941047,1545042214028132048956414112⟩⟩,⟨⟨909398638920047202631957610,909398638920047231977139029⟩,⟨1495099765379221931554512566,1495099765379221960929650738⟩⟩,⟨⟨917486286938098872031801750,917486286938098900826373272⟩,⟨1447062944715008242191843921,1447062944715008271016021559⟩⟩,⟨⟨924366992311398978885312255,924366992311399007112675189⟩,⟨1400890055653412855497783776,1400890055653412883754388817⟩⟩,⟨⟨930142164652868210625542121,930142164652868238343061375⟩,⟨1356538529990407958619273443,1356538529990407986365682527⟩⟩,⟨⟨934907233483623274585464798,934907233483623301792160811⟩,⟨1313965188497601308426983295,1313965188497601335661672011⟩⟩,⟨⟨938751920223516691205673569,938751920223516717942748518⟩,⟨1273126478658914966922512563,1273126478658914993686450766⟩⟩,⟨⟨941760504486061472350728126,941760504486061498604569941⟩,⟨1233978690790210774093341158,1233978690790210800372960116⟩⟩,⟨⟨944012084053684634277084081,944012084053684660097618950⟩,⟨1196478153941574553465000856,1196478153941574579310287012⟩⟩,⟨⟨945580828005462401911111314,945580828005462427295384341⟩,⟨1160581412934847356118743088,1160581412934847381526784903⟩⟩,⟨⟨946536222557694473821036460,946536222557694498806277632⟩,⟨1126245387839525722260019858,1126245387839525747268100115⟩⟩] +lemma kernel12_1_r5_13_eq : ∀ k : Fin 16, kernel12_1Expr 5 13 k = kernel12_1_r5_13 k := by decide +kernel +noncomputable def kernel12_1_r5_14 : Fin 16 → CBox := ![⟨⟨946943309258201588031879117,946943309258201612600058448⟩,⟨1093427517138925208202467985,1093427517138925232792593311⟩⟩,⟨⟨946862915248422171638501395,946862915248422195840416930⟩,⟨1062085885786037211951122153,1062085885786037236174143455⟩⟩,⟨⟨946351875373593272906717538,946351875373593296738956298⟩,⟨1032179339295279502736989051,1032179339295279526589530931⟩⟩,⟨⟨945463245980888132515856659,945463245980888156012761175⟩,⟨1003667584962765638462928857,1003667584962765661979379139⟩⟩,⟨⟨944246510298710461251102563,944246510298710484398628110⟩,⟨976511281254168955083947645,976511281254168978250294253⟩⟩,⟨⟨942747775337776193559659726,942747775337776216401431727⟩,⟨950672116346058638411046038,950672116346058661270958790⟩⟩,⟨⟨941009960296506380281861400,941009960296506402814087514⟩,⟨926112876754021296874824655,926112876754021319424543768⟩⟩,⟨⟨939072976489963431188944862,939072976489963453443482283⟩,⟨902797506929194186646465308,902797506929194208917886860⟩⟩,⟨⟨936973898853432734871820624,936973898853432756831334395⟩,⟨880691160654231368552580627,880691160654231390528397379⟩⟩,⟨⟨934747129099118750395033583,934747129099118772103817946⟩,⟨859760245020372761196389649,859760245020372782920934675⟩⟩,⟨⟨932424550627613876366003389,932424550627613897819993751⟩,⟨839972457719327767925753941,839972457719327789394990946⟩⟩,⟨⟨930035675315122382144224153,930035675315122403373133861⟩,⟨821296818337230282844074890,821296818337230304087750777⟩⟩,⟨⟨927607782313179889115873274,927607782313179910105319249⟩,⟨803703694293054250488391585,803703694293054271492147988⟩⟩,⟨⟨925166049010086925316097174,925166049010086946105168714⟩,⟨787164822020658221872343828,787164822020658242675303154⟩⟩,⟨⟨922733674312744264158924745,922733674312744284743372362⟩,⟨771653323952091292071267358,771653323952091312669204939⟩⟩,⟨⟨920331994414294859598856415,920331994414294880006595161⟩,⟨757143721819959452734811510,757143721819959473155671641⟩⟩] +lemma kernel12_1_r5_14_eq : ∀ k : Fin 16, kernel12_1Expr 5 14 k = kernel12_1_r5_14 k := by decide +kernel +noncomputable def kernel12_1_r5_15 : Fin 16 → CBox := ![⟨⟨917980591217184336045927756,917980591217184356258560689⟩,⟨743611946758521060742324303,743611946758521080967731266⟩⟩,⟨⟨915697393583176737229112806,915697393583176757287974600⟩,⟨731035346646737277412829894,731035346646737297484148041⟩⟩,⟨⟨913498771581717778625094292,913498771581717798525863990⟩,⟨719392691101718345679500207,719392691101718365592430650⟩⟩,⟨⟨911399623906023326330580292,911399623906023346099662581⟩,⟨708664174497837329070180523,708664174497837348851153870⟩⟩,⟨⟨909413458622571767418009700,909413458622571787040794629⟩,⟨698831417355176320943009106,698831417355176340577434959⟩⟩,⟨⟨907552467414467750582377887,907552467414467770094977864⟩,⟨689877466410863372250603199,689877466410863391774619996⟩⟩,⟨⟨905827593472581347947251863,905827593472581367345362406⟩,⟨681786793658180292225946291,681786793658180311635269586⟩⟩,⟨⟨904248593180599022952929714,904248593180599042261746410⟩,⟨674545294610993545424179864,674545294610993564744028727⟩⟩,⟨⟨902824091731287719208920111,902824091731287738412296814⟩,⟨668140286024997894823583915,668140286024997914037829932⟩⟩,⟨⟨901561632801497311198628199,901561632801497330336357132⟩,⟨662560503282375002314103307,662560503282375021462563173⟩⟩,⟨⟨900467722402826339612069296,900467722402826358679506463⟩,⟨657796097622662066602362218,657796097622662085680410563⟩⟩,⟨⟨899547867013559313401373617,899547867013559332422295709⟩,⟨653838633379800018454494417,653838633379800037485929777⟩⟩,⟨⟨898806606085550827252491992,898806606085550846211687789⟩,⟨650681085363384798221328907,650681085363384817190956981⟩⟩,⟨⟨898247539007275098941218978,898247539007275117872797889⟩,⟨648317836500974076011455074,648317836500974094953407914⟩⟩,⟨⟨897873346591365790056918990,897873346591365808956489412⟩,⟨646744675837798474296140073,646744675837798493206044000⟩⟩,⟨⟨897685807141721251809047753,897685807141721270699700513⟩,⟨645958796970282135408080194,645958796970282154309047099⟩⟩] +lemma kernel12_1_r5_15_eq : ∀ k : Fin 16, kernel12_1Expr 5 15 k = kernel12_1_r5_15 k := by decide +kernel +noncomputable def kernel12_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel12_1_r5_0,kernel12_1_r5_1,kernel12_1_r5_2,kernel12_1_r5_3,kernel12_1_r5_4,kernel12_1_r5_5,kernel12_1_r5_6,kernel12_1_r5_7,kernel12_1_r5_8,kernel12_1_r5_9,kernel12_1_r5_10,kernel12_1_r5_11,kernel12_1_r5_12,kernel12_1_r5_13,kernel12_1_r5_14,kernel12_1_r5_15] +lemma kernel12_1_r5_eq (i k : Fin 16) : kernel12_1Expr 5 i k = kernel12_1_r5 i k := by + fin_cases i + · exact kernel12_1_r5_0_eq k + · exact kernel12_1_r5_1_eq k + · exact kernel12_1_r5_2_eq k + · exact kernel12_1_r5_3_eq k + · exact kernel12_1_r5_4_eq k + · exact kernel12_1_r5_5_eq k + · exact kernel12_1_r5_6_eq k + · exact kernel12_1_r5_7_eq k + · exact kernel12_1_r5_8_eq k + · exact kernel12_1_r5_9_eq k + · exact kernel12_1_r5_10_eq k + · exact kernel12_1_r5_11_eq k + · exact kernel12_1_r5_12_eq k + · exact kernel12_1_r5_13_eq k + · exact kernel12_1_r5_14_eq k + · exact kernel12_1_r5_15_eq k +noncomputable def kernel12_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel12_1_r0,kernel12_1_r1,kernel12_1_r2,kernel12_1_r3,kernel12_1_r4,kernel12_1_r5] +lemma kernel12_1_eq (j : Fin 6) (i k : Fin 16) : kernel12_1Expr j i k = kernel12_1 j i k := by + fin_cases j + · exact kernel12_1_r0_eq i k + · exact kernel12_1_r1_eq i k + · exact kernel12_1_r2_eq i k + · exact kernel12_1_r3_eq i k + · exact kernel12_1_r4_eq i k + · exact kernel12_1_r5_eq i k +lemma kernel12_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel12_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(12:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel12_1_eq] + unfold kernel12_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans12_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel13_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans13 j i k) +noncomputable def kernel13_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_0_eq : ∀ k : Fin 16, kernel13_0Expr 0 0 k = kernel13_0_r0_0 k := by decide +kernel +noncomputable def kernel13_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_1_eq : ∀ k : Fin 16, kernel13_0Expr 0 1 k = kernel13_0_r0_1 k := by decide +kernel +noncomputable def kernel13_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_2_eq : ∀ k : Fin 16, kernel13_0Expr 0 2 k = kernel13_0_r0_2 k := by decide +kernel +noncomputable def kernel13_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_3_eq : ∀ k : Fin 16, kernel13_0Expr 0 3 k = kernel13_0_r0_3 k := by decide +kernel +noncomputable def kernel13_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_4_eq : ∀ k : Fin 16, kernel13_0Expr 0 4 k = kernel13_0_r0_4 k := by decide +kernel +noncomputable def kernel13_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_5_eq : ∀ k : Fin 16, kernel13_0Expr 0 5 k = kernel13_0_r0_5 k := by decide +kernel +noncomputable def kernel13_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_6_eq : ∀ k : Fin 16, kernel13_0Expr 0 6 k = kernel13_0_r0_6 k := by decide +kernel +noncomputable def kernel13_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_7_eq : ∀ k : Fin 16, kernel13_0Expr 0 7 k = kernel13_0_r0_7 k := by decide +kernel +noncomputable def kernel13_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_8_eq : ∀ k : Fin 16, kernel13_0Expr 0 8 k = kernel13_0_r0_8 k := by decide +kernel +noncomputable def kernel13_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_9_eq : ∀ k : Fin 16, kernel13_0Expr 0 9 k = kernel13_0_r0_9 k := by decide +kernel +noncomputable def kernel13_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_10_eq : ∀ k : Fin 16, kernel13_0Expr 0 10 k = kernel13_0_r0_10 k := by decide +kernel +noncomputable def kernel13_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r0_11_eq : ∀ k : Fin 16, kernel13_0Expr 0 11 k = kernel13_0_r0_11 k := by decide +kernel +noncomputable def kernel13_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel13_0_r0_12_eq : ∀ k : Fin 16, kernel13_0Expr 0 12 k = kernel13_0_r0_12 k := by decide +kernel +noncomputable def kernel13_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel13_0_r0_13_eq : ∀ k : Fin 16, kernel13_0Expr 0 13 k = kernel13_0_r0_13 k := by decide +kernel +noncomputable def kernel13_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel13_0_r0_14_eq : ∀ k : Fin 16, kernel13_0Expr 0 14 k = kernel13_0_r0_14 k := by decide +kernel +noncomputable def kernel13_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel13_0_r0_15_eq : ∀ k : Fin 16, kernel13_0Expr 0 15 k = kernel13_0_r0_15 k := by decide +kernel +noncomputable def kernel13_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel13_0_r0_0,kernel13_0_r0_1,kernel13_0_r0_2,kernel13_0_r0_3,kernel13_0_r0_4,kernel13_0_r0_5,kernel13_0_r0_6,kernel13_0_r0_7,kernel13_0_r0_8,kernel13_0_r0_9,kernel13_0_r0_10,kernel13_0_r0_11,kernel13_0_r0_12,kernel13_0_r0_13,kernel13_0_r0_14,kernel13_0_r0_15] +lemma kernel13_0_r0_eq (i k : Fin 16) : kernel13_0Expr 0 i k = kernel13_0_r0 i k := by + fin_cases i + · exact kernel13_0_r0_0_eq k + · exact kernel13_0_r0_1_eq k + · exact kernel13_0_r0_2_eq k + · exact kernel13_0_r0_3_eq k + · exact kernel13_0_r0_4_eq k + · exact kernel13_0_r0_5_eq k + · exact kernel13_0_r0_6_eq k + · exact kernel13_0_r0_7_eq k + · exact kernel13_0_r0_8_eq k + · exact kernel13_0_r0_9_eq k + · exact kernel13_0_r0_10_eq k + · exact kernel13_0_r0_11_eq k + · exact kernel13_0_r0_12_eq k + · exact kernel13_0_r0_13_eq k + · exact kernel13_0_r0_14_eq k + · exact kernel13_0_r0_15_eq k +noncomputable def kernel13_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-341),(-337)⟩,⟨98,102⟩⟩,⟨⟨(-340),(-335)⟩,⟨96,100⟩⟩,⟨⟨(-340),(-335)⟩,⟨96,100⟩⟩,⟨⟨(-338),(-334)⟩,⟨95,99⟩⟩,⟨⟨(-334),(-329)⟩,⟨93,97⟩⟩,⟨⟨(-329),(-325)⟩,⟨91,95⟩⟩,⟨⟨(-325),(-320)⟩,⟨89,93⟩⟩,⟨⟨(-320),(-316)⟩,⟨87,91⟩⟩,⟨⟨(-314),(-310)⟩,⟨83,87⟩⟩,⟨⟨(-306),(-302)⟩,⟨81,85⟩⟩,⟨⟨(-301),(-296)⟩,⟨77,82⟩⟩,⟨⟨(-291),(-287)⟩,⟨73,78⟩⟩,⟨⟨(-286),(-281)⟩,⟨70,74⟩⟩,⟨⟨(-276),(-272)⟩,⟨66,70⟩⟩,⟨⟨(-267),(-263)⟩,⟨62,66⟩⟩,⟨⟨(-258),(-254)⟩,⟨58,62⟩⟩] +lemma kernel13_0_r1_0_eq : ∀ k : Fin 16, kernel13_0Expr 1 0 k = kernel13_0_r1_0 k := by decide +kernel +noncomputable def kernel13_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-249),(-245)⟩,⟨54,58⟩⟩,⟨⟨(-240),(-236)⟩,⟨50,54⟩⟩,⟨⟨(-228),(-224)⟩,⟨46,50⟩⟩,⟨⟨(-219),(-215)⟩,⟨42,46⟩⟩,⟨⟨(-210),(-206)⟩,⟨38,42⟩⟩,⟨⟨(-198),(-194)⟩,⟨34,38⟩⟩,⟨⟨(-189),(-185)⟩,⟨30,34⟩⟩,⟨⟨(-180),(-176)⟩,⟨26,30⟩⟩,⟨⟨(-169),(-165)⟩,⟨24,28⟩⟩,⟨⟨(-160),(-156)⟩,⟨20,24⟩⟩,⟨⟨(-151),(-147)⟩,⟨16,20⟩⟩,⟨⟨(-141),(-137)⟩,⟨15,19⟩⟩,⟨⟨(-132),(-128)⟩,⟨11,15⟩⟩,⟨⟨(-125),(-121)⟩,⟨8,13⟩⟩,⟨⟨(-114),(-110)⟩,⟨6,10⟩⟩,⟨⟨(-106),(-102)⟩,⟨4,8⟩⟩] +lemma kernel13_0_r1_1_eq : ∀ k : Fin 16, kernel13_0Expr 1 1 k = kernel13_0_r1_1 k := by decide +kernel +noncomputable def kernel13_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-99),(-95)⟩,⟨1,5⟩⟩,⟨⟨(-92),(-88)⟩,⟨1,5⟩⟩,⟨⟨(-85),(-81)⟩,⟨(-2),3⟩⟩,⟨⟨(-78),(-74)⟩,⟨(-2),2⟩⟩,⟨⟨(-71),(-67)⟩,⟨(-5),0⟩⟩,⟨⟨(-65),(-60)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-61),(-56)⟩,⟨(-7),(-1)⟩⟩,⟨⟨(-55),(-51)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-49),(-45)⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-46),(-42)⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-41),(-37)⟩,⟨(-9),(-5)⟩⟩,⟨⟨(-36),(-32)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-33),(-29)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-30),(-26)⟩,⟨(-9),(-4)⟩⟩,⟨⟨(-27),(-23)⟩,⟨(-9),(-5)⟩⟩,⟨⟨(-25),(-21)⟩,⟨(-8),(-3)⟩⟩] +lemma kernel13_0_r1_2_eq : ∀ k : Fin 16, kernel13_0Expr 1 2 k = kernel13_0_r1_2 k := by decide +kernel +noncomputable def kernel13_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-22),(-18)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-19),(-15)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-17),(-13)⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-16),(-12)⟩,⟨(-9),(-4)⟩⟩,⟨⟨(-14),(-10)⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-12),(-8)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-11),(-7)⟩,⟨(-8),(-3)⟩⟩,⟨⟨(-9),(-5)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-9),(-5)⟩,⟨(-6),(-2)⟩⟩,⟨⟨(-7),(-3)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-7),(-3)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-7),(-3)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-1)⟩,⟨(-3),1⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩] +lemma kernel13_0_r1_3_eq : ∀ k : Fin 16, kernel13_0Expr 1 3 k = kernel13_0_r1_3 k := by decide +kernel +noncomputable def kernel13_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩] +lemma kernel13_0_r1_4_eq : ∀ k : Fin 16, kernel13_0Expr 1 4 k = kernel13_0_r1_4 k := by decide +kernel +noncomputable def kernel13_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel13_0_r1_5_eq : ∀ k : Fin 16, kernel13_0Expr 1 5 k = kernel13_0_r1_5 k := by decide +kernel +noncomputable def kernel13_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-2),4⟩⟩,⟨⟨(-2),4⟩,⟨(-2),4⟩⟩] +lemma kernel13_0_r1_6_eq : ∀ k : Fin 16, kernel13_0Expr 1 6 k = kernel13_0_r1_6 k := by decide +kernel +noncomputable def kernel13_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-2),4⟩,⟨(-3),4⟩⟩,⟨⟨(-4),2⟩,⟨(-4),3⟩⟩] +lemma kernel13_0_r1_7_eq : ∀ k : Fin 16, kernel13_0Expr 1 7 k = kernel13_0_r1_7 k := by decide +kernel +noncomputable def kernel13_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_8_eq : ∀ k : Fin 16, kernel13_0Expr 1 8 k = kernel13_0_r1_8 k := by decide +kernel +noncomputable def kernel13_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_9_eq : ∀ k : Fin 16, kernel13_0Expr 1 9 k = kernel13_0_r1_9 k := by decide +kernel +noncomputable def kernel13_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_10_eq : ∀ k : Fin 16, kernel13_0Expr 1 10 k = kernel13_0_r1_10 k := by decide +kernel +noncomputable def kernel13_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_11_eq : ∀ k : Fin 16, kernel13_0Expr 1 11 k = kernel13_0_r1_11 k := by decide +kernel +noncomputable def kernel13_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_12_eq : ∀ k : Fin 16, kernel13_0Expr 1 12 k = kernel13_0_r1_12 k := by decide +kernel +noncomputable def kernel13_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_13_eq : ∀ k : Fin 16, kernel13_0Expr 1 13 k = kernel13_0_r1_13 k := by decide +kernel +noncomputable def kernel13_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_14_eq : ∀ k : Fin 16, kernel13_0Expr 1 14 k = kernel13_0_r1_14 k := by decide +kernel +noncomputable def kernel13_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel13_0_r1_15_eq : ∀ k : Fin 16, kernel13_0Expr 1 15 k = kernel13_0_r1_15 k := by decide +kernel +noncomputable def kernel13_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel13_0_r1_0,kernel13_0_r1_1,kernel13_0_r1_2,kernel13_0_r1_3,kernel13_0_r1_4,kernel13_0_r1_5,kernel13_0_r1_6,kernel13_0_r1_7,kernel13_0_r1_8,kernel13_0_r1_9,kernel13_0_r1_10,kernel13_0_r1_11,kernel13_0_r1_12,kernel13_0_r1_13,kernel13_0_r1_14,kernel13_0_r1_15] +lemma kernel13_0_r1_eq (i k : Fin 16) : kernel13_0Expr 1 i k = kernel13_0_r1 i k := by + fin_cases i + · exact kernel13_0_r1_0_eq k + · exact kernel13_0_r1_1_eq k + · exact kernel13_0_r1_2_eq k + · exact kernel13_0_r1_3_eq k + · exact kernel13_0_r1_4_eq k + · exact kernel13_0_r1_5_eq k + · exact kernel13_0_r1_6_eq k + · exact kernel13_0_r1_7_eq k + · exact kernel13_0_r1_8_eq k + · exact kernel13_0_r1_9_eq k + · exact kernel13_0_r1_10_eq k + · exact kernel13_0_r1_11_eq k + · exact kernel13_0_r1_12_eq k + · exact kernel13_0_r1_13_eq k + · exact kernel13_0_r1_14_eq k + · exact kernel13_0_r1_15_eq k +noncomputable def kernel13_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-169945928673996),(-169945928673992)⟩,⟨(-84581736573971),(-84581736573967)⟩⟩,⟨⟨(-169704310138434),(-169704310138431)⟩,⟨(-84381439493918),(-84381439493914)⟩⟩,⟨⟨(-169222012007710),(-169222012007706)⟩,⟨(-83982114952906),(-83982114952903)⟩⟩,⟨⟨(-168500907139634),(-168500907139631)⟩,⟨(-83386289742737),(-83386289742733)⟩⟩,⟨⟨(-167543792282724),(-167543792282721)⟩,⟨(-82597723095756),(-82597723095753)⟩⟩,⟨⟨(-166354373084583),(-166354373084579)⟩,⟨(-81621369985648),(-81621369985645)⟩⟩,⟨⟨(-164937244194655),(-164937244194651)⟩,⟨(-80463332933051),(-80463332933048)⟩⟩,⟨⟨(-163297864542098),(-163297864542094)⟩,⟨(-79130802933652),(-79130802933648)⟩⟩,⟨⟨(-161442527892389),(-161442527892385)⟩,⟨(-77631990262657),(-77631990262653)⟩⟩,⟨⟨(-159378328810711),(-159378328810707)⟩,⟨(-75976046034053),(-75976046034049)⟩⟩,⟨⟨(-157113124186328),(-157113124186324)⟩,⟨(-74172975504145),(-74172975504141)⟩⟩,⟨⟨(-154655490499904),(-154655490499900)⟩,⟨(-72233544204659),(-72233544204656)⟩⟩,⟨⟨(-152014677045094),(-152014677045091)⟩,⟨(-70169178070127),(-70169178070124)⟩⟩,⟨⟨(-149200555346509),(-149200555346506)⟩,⟨(-67991858785929),(-67991858785926)⟩⟩,⟨⟨(-146223565047854),(-146223565047850)⟩,⟨(-65714015626809),(-65714015626805)⟩⟩,⟨⟨(-143094656576480),(-143094656576476)⟩,⟨(-63348415080209),(-63348415080205)⟩⟩] +lemma kernel13_0_r2_0_eq : ∀ k : Fin 16, kernel13_0Expr 2 0 k = kernel13_0_r2_0 k := by decide +kernel +noncomputable def kernel13_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-139825230923020),(-139825230923016)⟩,⟨(-60908049554388),(-60908049554384)⟩⟩,⟨⟨(-136427076906724),(-136427076906720)⟩,⟨(-58406026458116),(-58406026458113)⟩⟩,⟨⟨(-132912306327895),(-132912306327892)⟩,⟨(-55855458907395),(-55855458907392)⟩⟩,⟨⟨(-129293287437723),(-129293287437720)⟩,⟨(-53269359265761),(-53269359265757)⟩⟩,⟨⟨(-125582577181998),(-125582577181993)⟩,⟨(-50660536659591),(-50660536659586)⟩⟩,⟨⟨(-121792852698163),(-121792852698160)⟩,⟨(-48041499529703),(-48041499529699)⟩⟩,⟨⟨(-117936842563894),(-117936842563890)⟩,⟨(-45424364186909),(-45424364186905)⟩⟩,⟨⟨(-114027258309494),(-114027258309489)⟩,⟨(-42820770234093),(-42820770234088)⟩⟩,⟨⟨(-110076726715076),(-110076726715072)⟩,⟨(-40241803602523),(-40241803602519)⟩⟩,⟨⟨(-106097723416372),(-106097723416369)⟩,⟨(-37697927827708),(-37697927827705)⟩⟩,⟨⟨(-102102508339537),(-102102508339533)⟩,⟨(-35198924062239),(-35198924062235)⟩⟩,⟨⟨(-98103063475376),(-98103063475373)⟩,⟨(-32753840192015),(-32753840192012)⟩⟩,⟨⟨(-94111033486700),(-94111033486697)⟩,⟨(-30370949290097),(-30370949290094)⟩⟩,⟨⟨(-90137669619131),(-90137669619128)⟩,⟨(-28057717511462),(-28057717511458)⟩⟩,⟨⟨(-86193777355691),(-86193777355687)⟩,⟨(-25820781404101),(-25820781404097)⟩⟩,⟨⟨(-82289668219269),(-82289668219265)⟩,⟨(-23665934489241),(-23665934489237)⟩⟩] +lemma kernel13_0_r2_1_eq : ∀ k : Fin 16, kernel13_0Expr 2 1 k = kernel13_0_r2_1 k := by decide +kernel +noncomputable def kernel13_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-78435116084982),(-78435116084978)⟩,⟨(-21598122847761),(-21598122847758)⟩⟩,⟨⟨(-74639318316975),(-74639318316971)⟩,⟨(-19621449342698),(-19621449342694)⟩⟩,⟨⟨(-70910861992350),(-70910861992346)⟩,⟨(-17739186010554),(-17739186010551)⟩⟩,⟨⟨(-67257695419024),(-67257695419019)⟩,⟨(-15953794068136),(-15953794068131)⟩⟩,⟨⟨(-63687105095707),(-63687105095704)⟩,⟨(-14266950907672),(-14266950907668)⟩⟩,⟨⟨(-60205698201526),(-60205698201523)⟩,⟨(-12679583391861),(-12679583391857)⟩⟩,⟨⟨(-56819390641206),(-56819390641202)⟩,⟨(-11191906712539),(-11191906712536)⟩⟩,⟨⟨(-53533400610241),(-53533400610238)⟩,⟨(-9803468042143),(-9803468042139)⟩⟩,⟨⟨(-50352247584007),(-50352247584003)⟩,⟨(-8513194185865),(-8513194185862)⟩⟩,⟨⟨(-47279756576408),(-47279756576404)⟩,⟨(-7319442434206),(-7319442434202)⟩⟩,⟨⟨(-44319067458365),(-44319067458362)⟩,⟨(-6220053819765),(-6220053819762)⟩⟩,⟨⟨(-41472649074961),(-41472649074957)⟩,⟨(-5212407998129),(-5212407998125)⟩⟩,⟨⟨(-38742317853365),(-38742317853362)⟩,⟨(-4293478999399),(-4293478999395)⟩⟩,⟨⟨(-36129260552253),(-36129260552249)⟩,⟨(-3459891133425),(-3459891133421)⟩⟩,⟨⟨(-33634060768030),(-33634060768026)⟩,⟨(-2707974376871),(-2707974376867)⟩⟩,⟨⟨(-31256728784097),(-31256728784093)⟩,⟨(-2033818622589),(-2033818622585)⟩⟩] +lemma kernel13_0_r2_2_eq : ∀ k : Fin 16, kernel13_0Expr 2 2 k = kernel13_0_r2_2 k := by decide +kernel +noncomputable def kernel13_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-28996734326961),(-28996734326957)⟩,⟨(-1433326230097),(-1433326230093)⟩⟩,⟨⟨(-26853041777480),(-26853041777475)⟩,⟨(-902262378889),(-902262378884)⟩⟩,⟨⟨(-24824147376787),(-24824147376783)⟩,⟨(-436302792412),(-436302792408)⟩⟩,⟨⟨(-22908117964508),(-22908117964504)⟩,⟨(-31078468623),(-31078468620)⟩⟩,⟨⟨(-21102630791400),(-21102630791396)⟩,⟨317782878333,317782878337⟩⟩,⟨⟨(-19405013959361),(-19405013959356)⟩,⟨614618892747,614618892752⟩⟩,⟨⟨(-17812287058106),(-17812287058102)⟩,⟨863698329362,863698329366⟩⟩,⟨⟨(-16321201589518),(-16321201589514)⟩,⟨1069190580247,1069190580251⟩⟩,⟨⟨(-14928280796857),(-14928280796853)⟩,⟨1235139014058,1235139014061⟩⟩,⟨⟨(-13629858546065),(-13629858546062)⟩,⟨1365438109484,1365438109487⟩⟩,⟨⟨(-12422116939771),(-12422116939768)⟩,⟨1463814314046,1463814314050⟩⟩,⟨⟨(-11301122380251),(-11301122380247)⟩,⟨1533810514081,1533810514085⟩⟩,⟨⟨(-10262859835144),(-10262859835141)⟩,⟨1578773962257,1578773962260⟩⟩,⟨⟨(-9303265098157),(-9303265098153)⟩,⟨1601847475310,1601847475314⟩⟩,⟨⟨(-8418254875777),(-8418254875773)⟩,⟨1605963687135,1605963687138⟩⟩,⟨⟨(-7603754569464),(-7603754569459)⟩,⟨1593842120595,1593842120600⟩⟩] +lemma kernel13_0_r2_3_eq : ∀ k : Fin 16, kernel13_0Expr 2 3 k = kernel13_0_r2_3 k := by decide +kernel +noncomputable def kernel13_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-6855723660255),(-6855723660251)⟩,⟨1567988825615,1567988825618⟩⟩,⟨⟨(-6170178638711),(-6170178638707)⟩,⟨1530698320552,1530698320556⟩⟩,⟨⟨(-5543213457116),(-5543213457112)⟩,⟨1484057568733,1484057568736⟩⟩,⟨⟨(-4971017512505),(-4971017512501)⟩,⟨1429951721353,1429951721356⟩⟩,⟨⟨(-4449891197983),(-4449891197980)⟩,⟨1370071361867,1370071361870⟩⟩,⟨⟨(-3976259085751),(-3976259085747)⟩,⟨1305920994388,1305920994392⟩⟩,⟨⟨(-3546680828079),(-3546680828074)⟩,⟨1238828529510,1238828529515⟩⟩,⟨⟨(-3157859882071),(-3157859882068)⟩,⟨1169955534448,1169955534452⟩⟩,⟨⟨(-2806650180311),(-2806650180307)⟩,⟨1100308030126,1100308030130⟩⟩,⟨⟨(-2490060882581),(-2490060882577)⟩,⟨1030747635239,1030747635242⟩⟩,⟨⟨(-2205259353771),(-2205259353768)⟩,⟨962002875896,962002875900⟩⟩,⟨⟨(-1949572519916),(-1949572519913)⟩,⟨894680498777,894680498780⟩⟩,⟨⟨(-1720486758438),(-1720486758433)⟩,⟨829276645326,829276645331⟩⟩,⟨⟨(-1515646480058),(-1515646480054)⟩,⟨766187764076,766187764080⟩⟩,⟨⟨(-1332851558928),(-1332851558924)⟩,⟨705721157235,705721157238⟩⟩,⟨⟨(-1170053764489),(-1170053764486)⟩,⟨648105076162,648105076166⟩⟩] +lemma kernel13_0_r2_4_eq : ∀ k : Fin 16, kernel13_0Expr 2 4 k = kernel13_0_r2_4 k := by decide +kernel +noncomputable def kernel13_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-1025352343650),(-1025352343646)⟩,⟨593498297765,593498297769⟩⟩,⟨⟨(-896988895503),(-896988895499)⟩,⟨541999130161,541999130165⟩⟩,⟨⟨(-783341672983),(-783341672979)⟩,⟨493653811050,493653811053⟩⟩,⟨⟨(-682919437208),(-682919437204)⟩,⟨448464275809,448464275813⟩⟩,⟨⟨(-594354980714),(-594354980711)⟩,⟨406395284600,406395284604⟩⟩,⟨⟨(-516398425794),(-516398425790)⟩,⟨367380908448,367380908451⟩⟩,⟨⟨(-447910393878),(-447910393874)⟩,⟨331330383545,331330383549⟩⟩,⟨⟨(-387855131500),(-387855131496)⟩,⟨298133350828,298133350831⟩⟩,⟨⟨(-335293668075),(-335293668071)⟩,⟨267664504348,267664504352⟩⟩,⟨⟨(-289377070764),(-289377070760)⟩,⟨239787677096,239787677099⟩⟩,⟨⟨(-249339851904),(-249339851900)⟩,⟨214359396842,214359396846⟩⟩,⟨⟨(-214493575423),(-214493575419)⟩,⟨191231947498,191231947502⟩⟩,⟨⟨(-184220699960),(-184220699956)⟩,⟨170255973178,170255973182⟩⟩,⟨⟨(-157968688491),(-157968688487)⟩,⟨151282663286,151282663290⟩⟩,⟨⟨(-135244406886),(-135244406882)⟩,⟨134165557013,134165557016⟩⟩,⟨⟨(-115608827293),(-115608827290)⟩,⟨118762005209,118762005212⟩⟩] +lemma kernel13_0_r2_5_eq : ∀ k : Fin 16, kernel13_0Expr 2 5 k = kernel13_0_r2_5 k := by decide +kernel +noncomputable def kernel13_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-98672046259),(-98672046256)⟩,⟨104934326630,104934326634⟩⟩,⟨⟨(-84088622371),(-84088622368)⟩,⟨92550694032,92550694036⟩⟩,⟨⟨(-71553233626),(-71553233622)⟩,⟨81485783864,81485783868⟩⟩,⟨⟨(-60796650918),(-60796650915)⟩,⟨71621221194,71621221198⟩⟩,⟨⟨(-51582020776),(-51582020773)⟩,⟨62845849295,62845849299⟩⟩,⟨⟨(-43701447823),(-43701447819)⟩,⟨55055850950,55055850954⟩⟩,⟨⟨(-36972865330),(-36972865327)⟩,⟨48154746152,48154746156⟩⟩,⟨⟨(-31237180580),(-31237180577)⟩,⟨42053288439,42053288443⟩⟩,⟨⟨(-26355680577),(-26355680574)⟩,⟨36669279767,36669279770⟩⟩,⟨⟨(-22207682801),(-22207682797)⟩,⟨31927321554,31927321558⟩⟩,⟨⟨(-18688415296),(-18688415291)⟩,⟨27758517309,27758517314⟩⟩,⟨⟨(-15707110126),(-15707110122)⟩,⟨24100140280,24100140284⟩⟩,⟨⟨(-13185294375),(-13185294371)⟩,⟨20895277572,20895277576⟩⟩,⟨⟨(-11055263102),(-11055263098)⟩,⟨18092460508,18092460512⟩⟩,⟨⟨(-9258719112),(-9258719109)⟩,⟨15645289344,15645289348⟩⟩,⟨⟨(-7745565012),(-7745565009)⟩,⟨13512059064,13512059068⟩⟩] +lemma kernel13_0_r2_6_eq : ∀ k : Fin 16, kernel13_0Expr 2 6 k = kernel13_0_r2_6 k := by decide +kernel +noncomputable def kernel13_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-6472833649),(-6472833645)⟩,⟨11655391643,11655391647⟩⟩,⟨⟨(-5403743832),(-5403743828)⟩,⟨10041879067,10041879071⟩⟩,⟨⟨(-4506868993),(-4506868988)⟩,⟨8641740398,8641740403⟩⟩,⟨⟨(-3755407302),(-3755407298)⟩,⟨7428495280,7428495284⟩⟩,⟨⟨(-3126542596),(-3126542592)⟩,⟨6378655592,6378655595⟩⟩,⟨⟨(-2600886259),(-2600886255)⟩,⟨5471436314,5471436318⟩⟩,⟨⟨(-2161991095),(-2161991091)⟩,⟨4688486118,4688486121⟩⟩,⟨⟨(-1795928949),(-1795928946)⟩,⟨4013637827,4013637830⟩⟩,⟨⟨(-1490924627),(-1490924623)⟩,⟨3432678503,3432678507⟩⟩,⟨⟨(-1237039381),(-1237039377)⟩,⟨2933138674,2933138677⟩⟩,⟨⟨(-1025897892),(-1025897888)⟩,⟨2504099972,2504099976⟩⟩,⟨⟨(-850453313),(-850453309)⟩,⟨2136020350,2136020354⟩⟩,⟨⟨(-704785539),(-704785535)⟩,⟨1820575879,1820575883⟩⟩,⟨⟨(-583928358),(-583928354)⟩,⟨1550518107,1550518111⟩⟩,⟨⟨(-483721703),(-483721699)⟩,⟨1319545906,1319545910⟩⟩,⟨⟨(-400685609),(-400685605)⟩,⟨1122190707,1122190711⟩⟩] +lemma kernel13_0_r2_7_eq : ∀ k : Fin 16, kernel13_0Expr 2 7 k = kernel13_0_r2_7 k := by decide +kernel +noncomputable def kernel13_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-331912900),(-331912896)⟩,⟨953714066,953714070⟩⟩,⟨⟨(-274978032),(-274978028)⟩,⟨810016494,810016498⟩⟩,⟨⟨(-227859791),(-227859787)⟩,⟨687556558,687556562⟩⟩,⟨⟨(-188875872),(-188875868)⟩,⟨583279306,583279310⟩⟩,⟨⟨(-156627619),(-156627615)⟩,⟨494553056,494553060⟩⟩,⟨⟨(-129953438),(-129953434)⟩,⟨419113765,419113769⟩⟩,⟨⟨(-107889575),(-107889571)⟩,⟨355016167,355016171⟩⟩,⟨⟨(-89637169),(-89637165)⟩,⟨300590933,300590937⟩⟩,⟨⟨(-74534616),(-74534612)⟩,⟨254407227,254407231⟩⟩,⟨⟨(-62034413),(-62034409)⟩,⟨215240015,215240019⟩⟩,⟨⟨(-51683816),(-51683812)⟩,⟨182041609,182041613⟩⟩,⟨⟨(-43108678),(-43108674)⟩,⟨153916923,153916927⟩⟩,⟨⟨(-35999975),(-35999971)⟩,⟨130102012,130102015⟩⟩,⟨⟨(-30102597),(-30102593)⟩,⟨109945461,109945465⟩⟩,⟨⟨(-25206017),(-25206013)⟩,⟨92892340,92892344⟩⟩,⟨⟨(-21136564),(-21136560)⟩,⟨78470294,78470298⟩⟩] +lemma kernel13_0_r2_8_eq : ∀ k : Fin 16, kernel13_0Expr 2 8 k = kernel13_0_r2_8 k := by decide +kernel +noncomputable def kernel13_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-17750987),(-17750983)⟩,⟨66277609,66277613⟩⟩,⟨⟨(-14931148),(-14931144)⟩,⟨55972898,55972901⟩⟩,⟨⟨(-12579614),(-12579610)⟩,⟨47266261,47266265⟩⟩,⟨⟨(-10616021),(-10616017)⟩,⟨39911695,39911698⟩⟩,⟨⟨(-8974074),(-8974070)⟩,⟨33700582,33700585⟩⟩,⟨⟨(-7599063),(-7599059)⟩,⟨28456115,28456118⟩⟩,⟨⟨(-6445819),(-6445815)⟩,⟨24028538,24028542⟩⟩,⟨⟨(-5477031),(-5477027)⟩,⟨20291071,20291075⟩⟩,⟨⟨(-4661859),(-4661854)⟩,⟨17136448,17136453⟩⟩,⟨⟨(-3974792),(-3974788)⟩,⟨14473945,14473949⟩⟩,⟨⟨(-3394707),(-3394703)⟩,⟨12226869,12226873⟩⟩,⟨⟨(-2904101),(-2904097)⟩,⟨10330411,10330415⟩⟩,⟨⟨(-2488446),(-2488442)⟩,⟨8729829,8729833⟩⟩,⟨⟨(-2135683),(-2135679)⟩,⟨7378893,7378897⟩⟩,⟨⟨(-1835777),(-1835773)⟩,⟨6238573,6238577⟩⟩,⟨⟨(-1580370),(-1580366)⟩,⟨5275935,5275939⟩⟩] +lemma kernel13_0_r2_9_eq : ∀ k : Fin 16, kernel13_0Expr 2 9 k = kernel13_0_r2_9 k := by decide +kernel +noncomputable def kernel13_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-1362491),(-1362488)⟩,⟨4463182,4463185⟩⟩,⟨⟨(-1176318),(-1176314)⟩,⟨3776869,3776873⟩⟩,⟨⟨(-1016980),(-1016976)⟩,⟨3197219,3197223⟩⟩,⟨⟨(-880391),(-880387)⟩,⟨2707549,2707553⟩⟩,⟨⟨(-763123),(-763119)⟩,⟨2293796,2293800⟩⟩,⟨⟨(-662292),(-662288)⟩,⟨1944100,1944104⟩⟩,⟨⟨(-575472),(-575467)⟩,⟨1648455,1648460⟩⟩,⟨⟨(-500608),(-500604)⟩,⟨1398435,1398439⟩⟩,⟨⟨(-435970),(-435965)⟩,⟨1186922,1186928⟩⟩,⟨⟨(-380089),(-380085)⟩,⟨1007928,1007932⟩⟩,⟨⟨(-331716),(-331712)⟩,⟨856392,856396⟩⟩,⟨⟨(-289796),(-289792)⟩,⟨728051,728055⟩⟩,⟨⟨(-253423),(-253419)⟩,⟨619309,619313⟩⟩,⟨⟨(-221832),(-221828)⟩,⟨527131,527135⟩⟩,⟨⟨(-194364),(-194360)⟩,⟨448958,448962⟩⟩,⟨⟨(-170455),(-170451)⟩,⟨382631,382635⟩⟩] +lemma kernel13_0_r2_10_eq : ∀ k : Fin 16, kernel13_0Expr 2 10 k = kernel13_0_r2_10 k := by decide +kernel +noncomputable def kernel13_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-149625),(-149621)⟩,⟨326322,326326⟩⟩,⟨⟨(-131459),(-131455)⟩,⟨278497,278501⟩⟩,⟨⟨(-115604),(-115600)⟩,⟨237852,237856⟩⟩,⟨⟨(-101752),(-101748)⟩,⟨203291,203295⟩⟩,⟨⟨(-89640),(-89636)⟩,⟨173886,173890⟩⟩,⟨⟨(-79039),(-79035)⟩,⟨148851,148855⟩⟩,⟨⟨(-69757),(-69753)⟩,⟨127524,127528⟩⟩,⟨⟨(-61618),(-61614)⟩,⟨109344,109348⟩⟩,⟨⟨(-54479),(-54475)⟩,⟨93837,93841⟩⟩,⟨⟨(-48212),(-48208)⟩,⟨80598,80602⟩⟩,⟨⟨(-42705),(-42701)⟩,⟨69290,69295⟩⟩,⟨⟨(-37861),(-37857)⟩,⟨59623,59627⟩⟩,⟨⟨(-33599),(-33595)⟩,⟨51355,51359⟩⟩,⟨⟨(-29846),(-29842)⟩,⟨44275,44279⟩⟩,⟨⟨(-26540),(-26536)⟩,⟨38209,38213⟩⟩,⟨⟨(-23622),(-23618)⟩,⟨33006,33010⟩⟩] +lemma kernel13_0_r2_11_eq : ∀ k : Fin 16, kernel13_0Expr 2 11 k = kernel13_0_r2_11 k := by decide +kernel +noncomputable def kernel13_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-21047),(-21043)⟩,⟨28543,28547⟩⟩,⟨⟨(-18772),(-18768)⟩,⟨24708,24712⟩⟩,⟨⟨(-16762),(-16758)⟩,⟨21412,21416⟩⟩,⟨⟨(-14982),(-14978)⟩,⟨18576,18580⟩⟩,⟨⟨(-13406),(-13402)⟩,⟨16133,16137⟩⟩,⟨⟨(-12010),(-12006)⟩,⟨14028,14032⟩⟩,⟨⟨(-10770),(-10766)⟩,⟨12213,12217⟩⟩,⟨⟨(-9671),(-9667)⟩,⟨10645,10649⟩⟩,⟨⟨(-8694),(-8690)⟩,⟨9289,9293⟩⟩,⟨⟨(-7826),(-7822)⟩,⟨8116,8120⟩⟩,⟨⟨(-7053),(-7049)⟩,⟨7101,7105⟩⟩,⟨⟨(-6365),(-6361)⟩,⟨6218,6222⟩⟩,⟨⟨(-5751),(-5747)⟩,⟨5453,5458⟩⟩,⟨⟨(-5204),(-5200)⟩,⟨4790,4794⟩⟩,⟨⟨(-4715),(-4711)⟩,⟨4213,4217⟩⟩,⟨⟨(-4278),(-4274)⟩,⟨3710,3715⟩⟩] +lemma kernel13_0_r2_12_eq : ∀ k : Fin 16, kernel13_0Expr 2 12 k = kernel13_0_r2_12 k := by decide +kernel +noncomputable def kernel13_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-3888),(-3882)⟩,⟨3271,3277⟩⟩,⟨⟨(-3537),(-3532)⟩,⟨2890,2894⟩⟩,⟨⟨(-3222),(-3218)⟩,⟨2558,2562⟩⟩,⟨⟨(-2940),(-2936)⟩,⟨2265,2269⟩⟩,⟨⟨(-2688),(-2684)⟩,⟨2010,2014⟩⟩,⟨⟨(-2461),(-2456)⟩,⟨1785,1790⟩⟩,⟨⟨(-2255),(-2251)⟩,⟨1590,1594⟩⟩,⟨⟨(-2073),(-2069)⟩,⟨1417,1421⟩⟩,⟨⟨(-1907),(-1903)⟩,⟨1265,1269⟩⟩,⟨⟨(-1756),(-1752)⟩,⟨1131,1135⟩⟩,⟨⟨(-1622),(-1616)⟩,⟨1013,1019⟩⟩,⟨⟨(-1498),(-1494)⟩,⟨910,914⟩⟩,⟨⟨(-1387),(-1383)⟩,⟨818,823⟩⟩,⟨⟨(-1288),(-1284)⟩,⟨737,741⟩⟩,⟨⟨(-1198),(-1194)⟩,⟨665,669⟩⟩,⟨⟨(-1114),(-1110)⟩,⟨602,606⟩⟩] +lemma kernel13_0_r2_13_eq : ∀ k : Fin 16, kernel13_0Expr 2 13 k = kernel13_0_r2_13 k := by decide +kernel +noncomputable def kernel13_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-1039),(-1035)⟩,⟨545,549⟩⟩,⟨⟨(-973),(-969)⟩,⟨495,499⟩⟩,⟨⟨(-912),(-908)⟩,⟨450,454⟩⟩,⟨⟨(-854),(-850)⟩,⟨410,414⟩⟩,⟨⟨(-804),(-800)⟩,⟨375,379⟩⟩,⟨⟨(-757),(-753)⟩,⟨343,348⟩⟩,⟨⟨(-716),(-712)⟩,⟨315,319⟩⟩,⟨⟨(-676),(-672)⟩,⟨289,293⟩⟩,⟨⟨(-640),(-636)⟩,⟨267,272⟩⟩,⟨⟨(-609),(-605)⟩,⟨248,252⟩⟩,⟨⟨(-580),(-575)⟩,⟨230,234⟩⟩,⟨⟨(-553),(-549)⟩,⟨212,216⟩⟩,⟨⟨(-528),(-523)⟩,⟨199,203⟩⟩,⟨⟨(-505),(-501)⟩,⟨187,191⟩⟩,⟨⟨(-486),(-482)⟩,⟨174,178⟩⟩,⟨⟨(-468),(-464)⟩,⟨163,167⟩⟩] +lemma kernel13_0_r2_14_eq : ∀ k : Fin 16, kernel13_0Expr 2 14 k = kernel13_0_r2_14 k := by decide +kernel +noncomputable def kernel13_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-450),(-446)⟩,⟨156,160⟩⟩,⟨⟨(-435),(-431)⟩,⟨145,149⟩⟩,⟨⟨(-422),(-418)⟩,⟨139,143⟩⟩,⟨⟨(-410),(-406)⟩,⟨132,136⟩⟩,⟨⟨(-398),(-394)⟩,⟨125,129⟩⟩,⟨⟨(-389),(-385)⟩,⟨121,125⟩⟩,⟨⟨(-379),(-374)⟩,⟨115,119⟩⟩,⟨⟨(-371),(-367)⟩,⟨113,117⟩⟩,⟨⟨(-365),(-359)⟩,⟨108,114⟩⟩,⟨⟨(-359),(-355)⟩,⟨106,110⟩⟩,⟨⟨(-353),(-349)⟩,⟨102,106⟩⟩,⟨⟨(-350),(-346)⟩,⟨102,106⟩⟩,⟨⟨(-345),(-341)⟩,⟨100,104⟩⟩,⟨⟨(-344),(-340)⟩,⟨98,102⟩⟩,⟨⟨(-343),(-339)⟩,⟨97,101⟩⟩,⟨⟨(-343),(-339)⟩,⟨97,101⟩⟩] +lemma kernel13_0_r2_15_eq : ∀ k : Fin 16, kernel13_0Expr 2 15 k = kernel13_0_r2_15 k := by decide +kernel +noncomputable def kernel13_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel13_0_r2_0,kernel13_0_r2_1,kernel13_0_r2_2,kernel13_0_r2_3,kernel13_0_r2_4,kernel13_0_r2_5,kernel13_0_r2_6,kernel13_0_r2_7,kernel13_0_r2_8,kernel13_0_r2_9,kernel13_0_r2_10,kernel13_0_r2_11,kernel13_0_r2_12,kernel13_0_r2_13,kernel13_0_r2_14,kernel13_0_r2_15] +lemma kernel13_0_r2_eq (i k : Fin 16) : kernel13_0Expr 2 i k = kernel13_0_r2 i k := by + fin_cases i + · exact kernel13_0_r2_0_eq k + · exact kernel13_0_r2_1_eq k + · exact kernel13_0_r2_2_eq k + · exact kernel13_0_r2_3_eq k + · exact kernel13_0_r2_4_eq k + · exact kernel13_0_r2_5_eq k + · exact kernel13_0_r2_6_eq k + · exact kernel13_0_r2_7_eq k + · exact kernel13_0_r2_8_eq k + · exact kernel13_0_r2_9_eq k + · exact kernel13_0_r2_10_eq k + · exact kernel13_0_r2_11_eq k + · exact kernel13_0_r2_12_eq k + · exact kernel13_0_r2_13_eq k + · exact kernel13_0_r2_14_eq k + · exact kernel13_0_r2_15_eq k +noncomputable def kernel13_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3263463349984183550491),(-3263463349984183543464)⟩,⟨(-2536505465480095907713),(-2536505465480095900658)⟩⟩,⟨⟨(-3261623248834578356374),(-3261623248834578349354)⟩,⟨(-2532249387463624004354),(-2532249387463623997306)⟩⟩,⟨⟨(-3257941496167644028697),(-3257941496167644021693)⟩,⟨(-2523753142667261657558),(-2523753142667261650526)⟩⟩,⟨⟨(-3252415044811171098794),(-3252415044811171091813)⟩,⟨(-2511048476386591451079),(-2511048476386591444071)⟩⟩,⟨⟨(-3245039457204047186001),(-3245039457204047179050)⟩,⟨(-2494182813963783552762),(-2494182813963783545784)⟩⟩,⟨⟨(-3235809063251066685557),(-3235809063251066678644)⟩,⟨(-2473219030626464797729),(-2473219030626464790789)⟩⟩,⟨⟨(-3224717167518871511844),(-3224717167518871504978)⟩,⟨(-2448235146208530816848),(-2448235146208530809956)⟩⟩,⟨⟨(-3211756303015568701722),(-3211756303015568694909)⟩,⟨(-2419323946129703809168),(-2419323946129703802328)⟩⟩,⟨⟨(-3196918528170917726830),(-3196918528170917720076)⟩,⟨(-2386592530358605417854),(-2386592530358605411074)⟩⟩,⟨⟨(-3180195763049731570252),(-3180195763049731563564)⟩,⟨(-2350161792433881525946),(-2350161792433881519233)⟩⟩,⟨⟨(-3161580160295514249187),(-3161580160295514242574)⟩,⟨(-2310165830969158194373),(-2310165830969158187736)⟩⟩,⟨⟨(-3141064505821025228500),(-3141064505821025221967)⟩,⟨(-2266751296419656917754),(-2266751296419656911196)⟩⟩,⟨⟨(-3118642643843437499818),(-3118642643843437493371)⟩,⟨(-2220076676240108920454),(-2220076676240108913983)⟩⟩,⟨⟨(-3094309920509343386624),(-3094309920509343380269)⟩,⟨(-2170311521913740995097),(-2170311521913740988720)⟩⟩,⟨⟨(-3068063640073577849986),(-3068063640073577843728)⟩,⟨(-2117635621678709912112),(-2117635621678709905832)⟩⟩,⟨⟨(-3039903527389345647079),(-3039903527389345640924)⟩,⟨(-2062238123119182173327),(-2062238123119182167151)⟩⟩] +lemma kernel13_0_r3_0_eq : ∀ k : Fin 16, kernel13_0Expr 3 0 k = kernel13_0_r3_0 k := by decide +kernel +noncomputable def kernel13_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-3009832190338232024085),(-3009832190338232018038)⟩,⟨(-2004316610120640444533),(-2004316610120640438465)⟩⟩,⟨⟨(-2977855575779183983183),(-2977855575779183977249)⟩,⟨(-1944076139009928390855),(-1944076139009928384901)⟩⟩,⟨⟨(-2943983412626337373846),(-2943983412626337368029)⟩,⟨(-1881728239006671404802),(-1881728239006671398967)⟩⟩,⟨⟨(-2908229635776509594041),(-2908229635776509588347)⟩,⟨(-1817489882400398393782),(-1817489882400398388070)⟩⟩,⟨⟨(-2870612784797153351539),(-2870612784797153345970)⟩,⟨(-1751582430133081847781),(-1751582430133081842196)⟩⟩,⟨⟨(-2831156371552450660119),(-2831156371552450654678)⟩,⟨(-1684230558705896622803),(-1684230558705896617347)⟩⟩,⟨⟨(-2789889211285912408809),(-2789889211285912403501)⟩,⟨(-1615661174537679871591),(-1615661174537679866269)⟩⟩,⟨⟨(-2746845712088277381752),(-2746845712088277376578)⟩,⟨(-1546102322076766911475),(-1546102322076766906287)⟩⟩,⟨⟨(-2702066118154702027169),(-2702066118154702022133)⟩,⟨(-1475782092103584105634),(-1475782092103584100585)⟩⟩,⟨⟨(-2655596702769365479006),(-2655596702769365474110)⟩,⟨(-1404927536754786651708),(-1404927536754786646800)⟩⟩,⟨⟨(-2607489907542057005437),(-2607489907542057000680)⟩,⟨(-1333763597847298263187),(-1333763597847298258419)⟩⟩,⟨⟨(-2557804425052724109125),(-2557804425052724104510)⟩,⟨(-1262512055079169068929),(-1262512055079169064304)⟩⟩,⟨⟨(-2506605222728372918770),(-2506605222728372914298)⟩,⟨(-1191390500630999842644),(-1191390500630999838164)⟩⟩,⟨⟨(-2453963506473637648150),(-2453963506473637643821)⟩,⟨(-1120611346584604145085),(-1120611346584604140749)⟩⟩,⟨⟨(-2399956623292867137479),(-2399956623292867133296)⟩,⟨(-1050380871413027017013),(-1050380871413027012822)⟩⟩,⟨⟨(-2344667902868510880306),(-2344667902868510876266)⟩,⟨(-980898311577120583160),(-980898311577120579114)⟩⟩] +lemma kernel13_0_r3_1_eq : ∀ k : Fin 16, kernel13_0Expr 3 1 k = kernel13_0_r3_1 k := by decide +kernel +noncomputable def kernel13_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-2288186438788548304503),(-2288186438788548300607)⟩,⟨(-912355003988439240688),(-912355003988439236786)⟩⟩,⟨⟨(-2230606810835272876108),(-2230606810835272872354)⟩,⟨(-844933584766884011527),(-844933584766884007768)⟩⟩,⟨⟨(-2172028750449583637431),(-2172028750449583633819)⟩,⟨(-778807249335728697158),(-778807249335728693542)⟩⟩,⟨⟨(-2112556752159937809630),(-2112556752159937806157)⟩,⟨(-714139078458653476174),(-714139078458653472699)⟩⟩,⟨⟨(-2052299634404517077835),(-2052299634404517074503)⟩,⟨(-651081434336269643054),(-651081434336269639719)⟩⟩,⟨⟨(-1991370053770674315934),(-1991370053770674312738)⟩,⟨(-589775430347221826446),(-589775430347221823248)⟩⟩,⟨⟨(-1929883977219675517751),(-1929883977219675514691)⟩,⟨(-530350477445952164182),(-530350477445952161121)⟩⟩,⟨⟨(-1867960117350168457143),(-1867960117350168454218)⟩,⟨(-472923909620977988843),(-472923909620977985918)⟩⟩,⟨⟨(-1805719336174550942096),(-1805719336174550939301)⟩,⟨(-417600690180102432703),(-417600690180102429909)⟩⟩,⟨⟨(-1743284023233247307776),(-1743284023233247305110)⟩,⟨(-364473199968957821886),(-364473199968957819221)⟩⟩,⟨⟨(-1680777454148595350751),(-1680777454148595348211)⟩,⟨(-313621107953775177186),(-313621107953775174648)⟩⟩,⟨⟨(-1618323135919418404055),(-1618323135919418401638)⟩,⟨(-265111323915765642450),(-265111323915765640035)⟩⟩,⟨⟨(-1556044145377335515985),(-1556044145377335513687)⟩,⟨(-218998032320750545537),(-218998032320750543243)⟩⟩,⟨⟨(-1494062467265509506991),(-1494062467265509504810)⟩,⟨(-175322805751598743392),(-175322805751598741214)⟩⟩,⟨⟨(-1432498338360058779355),(-1432498338360058777288)⟩,⟨(-134114795630563878400),(-134114795630563876336)⟩⟩,⟨⟨(-1371469603935116147581),(-1371469603935116145625)⟩,⟨(-95390997321601630860),(-95390997321601628907)⟩⟩] +lemma kernel13_0_r3_2_eq : ∀ k : Fin 16, kernel13_0Expr 3 2 k = kernel13_0_r3_2 k := by decide +kernel +noncomputable def kernel13_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-1311091092676974466981),(-1311091092676974465131)⟩,⟨(-59156586096801929584),(-59156586096801927738)⟩⟩,⟨⟨(-1251474015884454228214),(-1251474015884454226466)⟩,⟨(-25405319883454171945),(-25405319883454170202)⟩⟩,⟨⟨(-1192725396456112624682),(-1192725396456112623035)⟩,⟨5879995814238269837,5879995814238271479⟩⟩,⟨⟨(-1134947532765668899043),(-1134947532765668897492)⟩,⟨34726985895964911969,34726985895964913515⟩⟩,⟨⟨(-1078237502071367276608),(-1078237502071367275150)⟩,⟨61173132040170312643,61173132040170314096⟩⟩,⟨⟨(-1022686707599987597446),(-1022686707599987596076)⟩,⟨85265153317318929417,85265153317318930782⟩⟩,⟨⟨(-968380472899507757162),(-968380472899507755878)⟩,⟨107058347173308571902,107058347173308573181⟩⟩,⟨⟨(-915397686474167399901),(-915397686474167398697)⟩,⟨126615897133820264652,126615897133820265851⟩⟩,⟨⟨(-863810499110372749484),(-863810499110372748358)⟩,⟨144008153729106140837,144008153729106141957⟩⟩,⟨⟨(-813684075680219289608),(-813684075680219288557)⟩,⟨159311895216129877407,159311895216129878451⟩⟩,⟨⟨(-765076402580158970537),(-765076402580158969557)⟩,⟨172609574681122891255,172609574681122892229⟩⟩,⟨⟨(-718038151334192752423),(-718038151334192751509)⟩,⟨183988560041542903255,183988560041542904162⟩⟩,⟨⟨(-672612598272405094654),(-672612598272405093806)⟩,⟨193540373334135189817,193540373334135190660⟩⟩,⟨⟨(-628835599594806644433),(-628835599594806643644)⟩,⟨201359935478250667533,201359935478250668316⟩⟩,⟨⟨(-586735620554978319074),(-586735620554978318344)⟩,⟨207544822444593861587,207544822444593862312⟩⟩,⟨⟨(-546333816954996156223),(-546333816954996155547)⟩,⟨212194538443783992257,212194538443783992927⟩⟩] +lemma kernel13_0_r3_3_eq : ∀ k : Fin 16, kernel13_0Expr 3 3 k = kernel13_0_r3_3 k := by decide +kernel +noncomputable def kernel13_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-507644166638961946680),(-507644166638961946056)⟩,⟨215409811381854022128,215409811381854022747⟩⟩,⟨⟨(-470673648212802329343),(-470673648212802328767)⟩,⟨217291915417040911855,217291915417040912425⟩⟩,⟨⟨(-435422463807623306589),(-435422463807623306059)⟩,⟨217942025000398106009,217942025000398106535⟩⟩,⟨⟨(-401884302346720972159),(-401884302346720971671)⟩,⟨217460604298743143768,217460604298743144251⟩⟩,⟨⟨(-370046639475327536657),(-370046639475327536210)⟩,⟨215946835389366505652,215946835389366506094⟩⟩,⟨⟨(-339891070069342528265),(-339891070069342527854)⟩,⟨213498088089050328815,213498088089050329221⟩⟩,⟨⟨(-311393669055742146907),(-311393669055742146507)⟩,⟨210209433742584639726,210209433742584640122⟩⟩,⟨⟨(-284525376153222364330),(-284525376153222363943)⟩,⟨206173204755341894393,206173204755341894776⟩⟩,⟨⟨(-259252400076159906919),(-259252400076159906546)⟩,⟨201478601117592138530,201478601117592138901⟩⟩,⟨⟨(-235536637736562230381),(-235536637736562230020)⟩,⟨196211344641815161697,196211344641815162055⟩⟩,⟨⟨(-213336104024922092768),(-213336104024922092418)⟩,⟨190453381124588942396,190453381124588942743⟩⟩,⟨⟨(-192605367848672548140),(-192605367848672547803)⟩,⟨184282630157506857147,184282630157506857481⟩⟩,⟨⟨(-173295990252494040163),(-173295990252494039839)⟩,⟨177772781852230926696,177772781852230927018⟩⟩,⟨⟨(-155356960633749170348),(-155356960633749170036)⟩,⟨170993139317824138476,170993139317824138786⟩⟩,⟨⟨(-138735127294054282894),(-138735127294054282594)⟩,⟨164008505337840739253,164008505337840739552⟩⟩,⟨⟨(-123375618829331730199),(-123375618829331729911)⟩,⟨156879111343494297816,156879111343494298102⟩⟩] +lemma kernel13_0_r3_4_eq : ∀ k : Fin 16, kernel13_0Expr 3 4 k = kernel13_0_r3_4 k := by decide +kernel +noncomputable def kernel13_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-109222253150266212087),(-109222253150266211811)⟩,⟨149660586470040494996,149660586470040495270⟩⟩,⟨⟨(-96217931237410659869),(-96217931237410659603)⟩,⟨142403964218036972297,142403964218036972562⟩⟩,⟨⟨(-84305013064703125191),(-84305013064703124938)⟩,⟨135155724020377029704,135155724020377029957⟩⟩,⟨⟨(-73425673466366288818),(-73425673466366288574)⟩,⟨127957864840228249954,127957864840228250196⟩⟩,⟨⟨(-63522236069704021909),(-63522236069704021676)⟩,⟨120848007793854626573,120848007793854626806⟩⟩,⟨⟨(-54537483765043592912),(-54537483765043592691)⟩,⟨113859524704740855080,113859524704740855300⟩⟩,⟨⟨(-46414944529149793052),(-46414944529149792840)⟩,⟨107021689449867968363,107021689449867968574⟩⟩,⟨⟨(-39099151755367814115),(-39099151755367813915)⟩,⟨100359848953286943198,100359848953286943398⟩⟩,⟨⟨(-32535878568455047114),(-32535878568455046923)⟩,⟨93895610713722549137,93895610713722549328⟩⟩,⟨⟨(-26672345910911047354),(-26672345910911047173)⟩,⟨87647043818850138469,87647043818850138650⟩⟩,⟨⟨(-21457404477467314402),(-21457404477467314229)⟩,⟨81628890495848407020,81628890495848407193⟩⟩,⟨⟨(-16841690842617052218),(-16841690842617052054)⟩,⟨75852785372329351733,75852785372329351897⟩⟩,⟨⟨(-12777758370527621201),(-12777758370527621048)⟩,⟨70327479770107349836,70327479770107349989⟩⟩,⟨⟨(-9220183715777768435),(-9220183715777768289)⟩,⟨65059068522725725383,65059068522725725530⟩⟩,⟨⟨(-6125649915995882590),(-6125649915995882451)⟩,⟨60051216992421893860,60051216992421893999⟩⟩,⟨⟨(-3453007243029226465),(-3453007243029226334)⟩,⟨55305386159533355471,55305386159533355602⟩⟩] +lemma kernel13_0_r3_5_eq : ∀ k : Fin 16, kernel13_0Expr 3 5 k = kernel13_0_r3_5 k := by decide +kernel +noncomputable def kernel13_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-1163313117592907665),(-1163313117592907540)⟩,⟨50821053863579207969,50821053863579208093⟩⟩,⟨⟨780147496294981332,780147496294981448⟩,⟨46595930486901639944,46595930486901640060⟩⟩,⟨⟨2411859715725140077,2411859715725140187⟩,⟨42626167585524662520,42626167585524662631⟩⟩,⟨⟨3764092821013691555,3764092821013691659⟩,⟨38906558184727069855,38906558184727069960⟩⟩,⟨⟨4866929198577384288,4866929198577384386⟩,⟨35430727665946977566,35430727665946977665⟩⟩,⟨⟨5748306534218106781,5748306534218106872⟩,⟨32191314374543719006,32191314374543719098⟩⟩,⟨⟨6434071653688858199,6434071653688858286⟩,⟨29180139272457227578,29180139272457227664⟩⟩,⟨⟨6948044433322901190,6948044433322901272⟩,⟨26388364144063113219,26388364144063113301⟩⟩,⟨⟨7312090246056749368,7312090246056749443⟩,⟨23806638035984123322,23806638035984123398⟩⟩,⟨⟨7546199465249117089,7546199465249117159⟩,⟨21425231771065811468,21425231771065811538⟩⟩,⟨⟨7668572618149164339,7668572618149164406⟩,⟨19234160522247003856,19234160522247003923⟩⟩,⟨⟨7695709860568064123,7695709860568064187⟩,⟨17223294563042031251,17223294563042031314⟩⟩,⟨⟨7642503532175226101,7642503532175226160⟩,⟨15382458427468744129,15382458427468744188⟩⟩,⟨⟨7522332645869537302,7522332645869537356⟩,⟨13701518813428848679,13701518813428848733⟩⟩,⟨⟨7347158262966060720,7347158262966060771⟩,⟨12170461649933602777,12170461649933602828⟩⟩,⟨⟨7127618806715062621,7127618806715062669⟩,⟨10779458820534652058,10779458820534652106⟩⟩] +lemma kernel13_0_r3_6_eq : ∀ k : Fin 16, kernel13_0Expr 3 6 k = kernel13_0_r3_6 k := by decide +kernel +noncomputable def kernel13_0_r3_7 : Fin 16 → CBox := ![⟨⟨6873124468301531190,6873124468301531236⟩,⟨9518925093413572967,9518925093413573013⟩⟩,⟨⟨6591949960484083725,6591949960484083767⟩,⟨8379565853504114270,8379565853504114313⟩⟩,⟨⟨6291324973111634618,6291324973111634657⟩,⟨7352416264592855415,7352416264592855454⟩⟩,⟨⟨5977521780763124120,5977521780763124157⟩,⟨6428872510489653453,6428872510489653490⟩⟩,⟨⟨5655939544719181969,5655939544719182003⟩,⟨5600715775073380786,5600715775073380821⟩⟩,⟨⟨5331184938592296240,5331184938592296272⟩,⟨4860129622342996962,4860129622342996995⟩⟩,⟨⟨5007148808574565293,5007148808574565323⟩,⟨4199711430605538674,4199711430605538704⟩⟩,⟨⟨4687078654925810640,4687078654925810668⟩,⟨3612478520681748504,3612478520681748532⟩⟩,⟨⟨4373646790682244174,4373646790682244200⟩,⟨3091869597563003257,3091869597563003283⟩⟩,⟨⟨4069014096414523043,4069014096414523069⟩,⟨2631742099335745901,2631742099335745927⟩⟩,⟨⟨3774889346124028451,3774889346124028474⟩,⟨2226366017383559202,2226366017383559224⟩⟩,⟨⟨3492584129067173415,3492584129067173436⟩,⟨1870414718808927944,1870414718808927966⟩⟩,⟨⟨3223063435564929366,3223063435564929386⟩,⟨1558953266549159379,1558953266549159399⟩⟩,⟨⟨2966992011896119020,2966992011896119039⟩,⟨1287424695585764239,1287424695585764259⟩⟩,⟨⟨2724776620464444425,2724776620464444444⟩,⟨1051634665680605870,1051634665680605890⟩⟩,⟨⟨2496604366902174310,2496604366902174327⟩,⟨847734872854373899,847734872854373916⟩⟩] +lemma kernel13_0_r3_7_eq : ∀ k : Fin 16, kernel13_0Expr 3 7 k = kernel13_0_r3_7 k := by decide +kernel +noncomputable def kernel13_0_r3_8 : Fin 16 → CBox := ![⟨⟨2282477276002229358,2282477276002229375⟩,⟨672205563914001343,672205563914001360⟩⟩,⟨⟨2082243313760535588,2082243313760535603⟩,⟨521837461218318313,521837461218318328⟩⟩,⟨⟨1895624063787765741,1895624063787765756⟩,⟨393713368952607973,393713368952607988⟩⟩,⟨⟨1722239273350341142,1722239273350341154⟩,⟨285189697797352107,285189697797352120⟩⟩,⟨⟨1561628487763118041,1561628487763118055⟩,⟨193878112290422194,193878112290422208⟩⟩,⟨⟨1413269992213188514,1413269992213188526⟩,⟨117627474597720383,117627474597720394⟩⟩,⟨⟨1276597277766265807,1276597277766265818⟩,⟨54506229968873597,54506229968873608⟩⟩,⟨⟨1151013243697362739,1151013243697362752⟩,⟨2785352953385139,2785352953385151⟩⟩,⟨⟨1035902341777371585,1035902341777371595⟩,⟨(-39078050466892533),(-39078050466892523)⟩⟩,⟨⟨930640860093178651,930640860093178662⟩,⟨(-72456411307557271),(-72456411307557261)⟩⟩,⟨⟨834605534710182198,834605534710182207⟩,⟨(-98566582433519406),(-98566582433519397)⟩⟩,⟨⟨747180667302692304,747180667302692314⟩,⟨(-118483902882127802),(-118483902882127791)⟩⟩,⟨⟨667763916050120010,667763916050120018⟩,⟨(-133155419790180362),(-133155419790180354)⟩⟩,⟨⟨595770915865690301,595770915865690309⟩,⟨(-143412259139989466),(-143412259139989458)⟩⟩,⟨⟨530638872600772910,530638872600772918⟩,⟨(-149981147741192739),(-149981147741192731)⟩⟩,⟨⟨471829264434390196,471829264434390203⟩,⟨(-153495098315855278),(-153495098315855271)⟩⟩] +lemma kernel13_0_r3_8_eq : ∀ k : Fin 16, kernel13_0Expr 3 8 k = kernel13_0_r3_8 k := by decide +kernel +noncomputable def kernel13_0_r3_9 : Fin 16 → CBox := ![⟨⟨418829772369317897,418829772369317902⟩,⟨(-154503277391741078),(-154503277391741072)⟩⟩,⟨⟨371155550743008675,371155550743008682⟩,⟨(-153480082073046407),(-153480082073046399)⟩⟩,⟨⟨328349938028982500,328349938028982506⟩,⟨(-150833456790598919),(-150833456790598913)⟩⟩,⟨⟨289984698036008790,289984698036008796⟩,⟨(-146912484973917887),(-146912484973917881)⟩⟩,⟨⟨255659871972085004,255659871972085009⟩,⟨(-142014293371140092),(-142014293371140086)⟩⟩,⟨⟨225003312773771475,225003312773771480⟩,⟨(-136390308599698499),(-136390308599698494)⟩⟩,⟨⟨197669964638964520,197669964638964525⟩,⟨(-130251906564094666),(-130251906564094660)⟩⟩,⟨⟨173340942859008784,173340942859008789⟩,⟨(-123775495742721652),(-123775495742721647)⟩⟩,⟨⟨151722461828677723,151722461828677728⟩,⟨(-117107075130695016),(-117107075130695010)⟩⟩,⟨⟨132544652514522221,132544652514522227⟩,⟨(-110366306928489961),(-110366306928489955)⟩⟩,⟨⟨115560304669675611,115560304669675615⟩,⟨(-103650142976368754),(-103650142976368750)⟩⟩,⟨⟨100543563676004113,100543563676004118⟩,⟨(-97036042532682870),(-97036042532682866)⟩⟩,⟨⟨87288607046859008,87288607046859013⟩,⟨(-90584817351947365),(-90584817351947361)⟩⟩,⟨⟨75608321306024779,75608321306024784⟩,⟨(-84343138199435978),(-84343138199435974)⟩⟩,⟨⟨65332996138362474,65332996138362478⟩,⟨(-78345734998182882),(-78345734998182877)⟩⟩,⟨⟨56309049350907615,56309049350907619⟩,⟨(-72617320789345434),(-72617320789345430)⟩⟩] +lemma kernel13_0_r3_9_eq : ∀ k : Fin 16, kernel13_0Expr 3 9 k = kernel13_0_r3_9 k := by decide +kernel +noncomputable def kernel13_0_r3_10 : Fin 16 → CBox := ![⟨⟨48397793254636810,48397793254636813⟩,⟨(-67174267638449434),(-67174267638449431)⟩⟩,⟨⟨41474250541386295,41474250541386298⟩,⟨(-62026060572155478),(-62026060572155475)⟩⟩,⟨⟨35426025552495562,35426025552495566⟩,⟨(-57176553610966108),(-57176553610966104)⟩⟩,⟨⟨30152234981546396,30152234981546401⟩,⟨(-52625049995497397),(-52625049995497392)⟩⟩,⟨⟨25562500490230953,25562500490230957⟩,⟨(-48367226805542715),(-48367226805542711)⟩⟩,⟨⟨21576004412642575,21576004412642579⟩,⟨(-44395922355913300),(-44395922355913295)⟩⟩,⟨⟨18120608649662486,18120608649662491⟩,⟨(-40701803031008328),(-40701803031008323)⟩⟩,⟨⟨15132035984077003,15132035984077007⟩,⟨(-37273924598111550),(-37273924598111545)⟩⟩,⟨⟨12553112353095491,12553112353095496⟩,⟨(-34100201521669436),(-34100201521669431)⟩⟩,⟨⟨10333068074606862,10333068074606866⟩,⟨(-31167796389115790),(-31167796389115786)⟩⟩,⟨⟨8426895615430975,8426895615430979⟩,⟨(-28463440253099534),(-28463440253099531)⟩⟩,⟨⟨6794761194630995,6794761194630999⟩,⟨(-25973693493618886),(-25973693493618881)⟩⟩,⟨⟨5401467315247665,5401467315247669⟩,⟨(-23685155703696109),(-23685155703696105)⟩⟩,⟨⟨4215963198056264,4215963198056267⟩,⟨(-21584632100005560),(-21584632100005557)⟩⟩,⟨⟨3210900037353476,3210900037353480⟩,⟨(-19659263050732334),(-19659263050732330)⟩⟩,⟨⟨2362227999223679,2362227999223684⟩,⟨(-17896622491811887),(-17896622491811883)⟩⟩] +lemma kernel13_0_r3_10_eq : ∀ k : Fin 16, kernel13_0Expr 3 10 k = kernel13_0_r3_10 k := by decide +kernel +noncomputable def kernel13_0_r3_11 : Fin 16 → CBox := ![⟨⟨1648831926608278,1648831926608282⟩,⟨(-16284790264166969),(-16284790264166966)⟩⟩,⟨⟨1052202793606545,1052202793606549⟩,⟨(-14812402743013681),(-14812402743013676)⟩⟩,⟨⟨556142055849539,556142055849544⟩,⟨(-13468685540086879),(-13468685540086874)⟩⟩,⟨⟨146496167744710,146496167744714⟩,⟨(-12243471535108342),(-12243471535108338)⟩⟩,⟨⟨(-189081324838650),(-189081324838645)⟩,⟨(-11127207028480858),(-11127207028480854)⟩⟩,⟨⟨(-461342561083843),(-461342561083839)⟩,⟨(-10110948397713246),(-10110948397713243)⟩⟩,⟨⟨(-679635303756058),(-679635303756054)⟩,⟨(-9186351280372356),(-9186351280372353)⟩⟩,⟨⟨(-852072178957557),(-852072178957553)⟩,⟨(-8345653991591878),(-8345653991591875)⟩⟩,⟨⟨(-985681203567476),(-985681203567473)⟩,⟨(-7581656609808048),(-7581656609808045)⟩⟩,⟨⟨(-1086539437008297),(-1086539437008294)⟩,⟨(-6887696926206211),(-6887696926206208)⟩⟩,⟨⟨(-1159891448715884),(-1159891448715880)⟩,⟨(-6257624247427073),(-6257624247427069)⟩⟩,⟨⟨(-1210254153192184),(-1210254153192181)⟩,⟨(-5685771863784175),(-5685771863784172)⟩⟩,⟨⟨(-1241509431667521),(-1241509431667517)⟩,⟨(-5166928843275295),(-5166928843275292)⟩⟩,⟨⟨(-1256985833788063),(-1256985833788060)⟩,⟨(-4696311682015705),(-4696311682015702)⟩⟩,⟨⟨(-1259530534734643),(-1259530534734638)⟩,⟨(-4269536231648082),(-4269536231648078)⟩⟩,⟨⟨(-1251572612940447),(-1251572612940443)⟩,⟨(-3882590231327380),(-3882590231327375)⟩⟩] +lemma kernel13_0_r3_11_eq : ∀ k : Fin 16, kernel13_0Expr 3 11 k = kernel13_0_r3_11 k := by decide +kernel +noncomputable def kernel13_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-1235178611121695),(-1235178611121692)⟩,⟨(-3531806693825865),(-3531806693825861)⟩⟩,⟨⟨(-1212101248558429),(-1212101248558425)⟩,⟨(-3213838330174680),(-3213838330174677)⟩⟩,⟨⟨(-1183822065257697),(-1183822065257694)⟩,⟨(-2925633143292042),(-2925633143292038)⟩⟩,⟨⟨(-1151588698522477),(-1151588698522474)⟩,⟨(-2664411276682276),(-2664411276682272)⟩⟩,⟨⟨(-1116447419207205),(-1116447419207201)⟩,⟨(-2427643168145109),(-2427643168145106)⟩⟩,⟨⟨(-1079271488199647),(-1079271488199643)⟩,⟨(-2213029029297429),(-2213029029297425)⟩⟩,⟨⟨(-1040785833040870),(-1040785833040866)⟩,⟨(-2018479648517474),(-2018479648517470)⟩⟩,⟨⟨(-1001588489680291),(-1001588489680288)⟩,⟨(-1842098496746231),(-1842098496746228)⟩⟩,⟨⟨(-962169204758919),(-962169204758916)⟩,⟨(-1682165101616521),(-1682165101616518)⟩⟩,⟨⟨(-922925549122288),(-922925549122285)⟩,⟨(-1537119644928795),(-1537119644928791)⟩⟩,⟨⟨(-884176853096822),(-884176853096819)⟩,⟨(-1405548730951984),(-1405548730951981)⟩⟩,⟨⟨(-846176238044649),(-846176238044645)⟩,⟨(-1286172267881106),(-1286172267881102)⟩⟩,⟨⟨(-809120986484211),(-809120986484207)⟩,⟨(-1177831401588611),(-1177831401588607)⟩⟩,⟨⟨(-773161464288658),(-773161464288655)⟩,⟨(-1079477439187755),(-1079477439187751)⟩⟩,⟨⟨(-738408782831947),(-738408782831942)⟩,⟨(-990161699564686),(-990161699564681)⟩⟩,⟨⟨(-704941366146456),(-704941366146453)⟩,⟨(-909026228662984),(-909026228662980)⟩⟩] +lemma kernel13_0_r3_12_eq : ∀ k : Fin 16, kernel13_0Expr 3 12 k = kernel13_0_r3_12 k := by decide +kernel +noncomputable def kernel13_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-672810567908822),(-672810567908818)⟩,⟨(-835295318695008),(-835295318695005)⟩⟩,⟨⟨(-642045465127044),(-642045465127041)⟩,⟨(-768267772420645),(-768267772420641)⟩⟩,⟨⟨(-612656939526708),(-612656939526704)⟩,⟨(-707309856020900),(-707309856020897)⟩⟩,⟨⟨(-584641143611414),(-584641143611411)⟩,⟨(-651848886773272),(-651848886773268)⟩⟩,⟨⟨(-557982436006022),(-557982436006017)⟩,⟨(-601367404603940),(-601367404603935)⟩⟩,⟨⟨(-532655859801751),(-532655859801747)⟩,⟨(-555397879564497),(-555397879564493)⟩⟩,⟨⟨(-508629228047591),(-508629228047588)⟩,⟨(-513517910291056),(-513517910291052)⟩⟩,⟨⟨(-485864872126078),(-485864872126075)⟩,⟨(-475345871498262),(-475345871498259)⟩⟩,⟨⟨(-464321101381274),(-464321101381270)⟩,⟨(-440536971499146),(-440536971499142)⟩⟩,⟨⟨(-443953415913855),(-443953415913852)⟩,⟨(-408779683592796),(-408779683592793)⟩⟩,⟨⟨(-424715508816074),(-424715508816069)⟩,⟨(-379792517902909),(-379792517902905)⟩⟩,⟨⟨(-406560089192709),(-406560089192705)⟩,⟨(-353321102865093),(-353321102865089)⟩⟩,⟨⟨(-389439553017944),(-389439553017940)⟩,⟨(-329135548039189),(-329135548039185)⟩⟩,⟨⟨(-373306525136441),(-373306525136438)⟩,⟨(-307028062258274),(-307028062258271)⟩⟩,⟨⟨(-358114292462621),(-358114292462617)⟩,⟨(-286810803316322),(-286810803316318)⟩⟩,⟨⟨(-343817145605167),(-343817145605164)⟩,⟨(-268313937441461),(-268313937441457)⟩⟩] +lemma kernel13_0_r3_13_eq : ∀ k : Fin 16, kernel13_0Expr 3 13 k = kernel13_0_r3_13 k := by decide +kernel +noncomputable def kernel13_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-330370643691495),(-330370643691491)⟩,⟨(-251383888704174),(-251383888704171)⟩⟩,⟨⟨(-317731815042076),(-317731815042073)⟩,⟨(-235881760273245),(-235881760273242)⟩⟩,⟨⟨(-305859304506145),(-305859304506142)⟩,⟨(-221681911062344),(-221681911062340)⟩⟩,⟨⟨(-294713476681690),(-294713476681687)⟩,⟨(-208670672812535),(-208670672812531)⟩⟩,⟨⟨(-284256482871882),(-284256482871877)⟩,⟨(-196745194037687),(-196745194037682)⟩⟩,⟨⟨(-274452298448809),(-274452298448806)⟩,⟨(-185812398527434),(-185812398527431)⟩⟩,⟨⟨(-265266736279116),(-265266736279111)⟩,⟨(-175788047263301),(-175788047263297)⟩⟩,⟨⟨(-256667440992818),(-256667440992812)⟩,⟨(-166595893664812),(-166595893664806)⟩⟩,⟨⟨(-248623868127657),(-248623868127653)⟩,⟨(-158166923051143),(-158166923051140)⟩⟩,⟨⟨(-241107251539836),(-241107251539832)⟩,⟨(-150438668086695),(-150438668086692)⟩⟩,⟨⟨(-234090561923690),(-234090561923687)⟩,⟨(-143354592782655),(-143354592782651)⟩⟩,⟨⟨(-227548458815001),(-227548458814998)⟩,⟨(-136863538357540),(-136863538357536)⟩⟩,⟨⟨(-221457238054284),(-221457238054280)⟩,⟨(-130919224923578),(-130919224923574)⟩⟩,⟨⟨(-215794776347909),(-215794776347906)⟩,⟨(-125479803568621),(-125479803568618)⟩⟩,⟨⟨(-210540474278102),(-210540474278098)⟩,⟨(-120507453950077),(-120507453950073)⟩⟩,⟨⟨(-205675198870350),(-205675198870347)⟩,⟨(-115968023013306),(-115968023013302)⟩⟩] +lemma kernel13_0_r3_14_eq : ∀ k : Fin 16, kernel13_0Expr 3 14 k = kernel13_0_r3_14 k := by decide +kernel +noncomputable def kernel13_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-201181226622414),(-201181226622409)⟩,⟨(-111830700896487),(-111830700896482)⟩⟩,⟨⟨(-197042187727504),(-197042187727501)⟩,⟨(-108067730491606),(-108067730491603)⟩⟩,⟨⟨(-193243012080597),(-193243012080594)⟩,⟨(-104654147500737),(-104654147500734)⟩⟩,⟨⟨(-189769877537148),(-189769877537145)⟩,⟨(-101567548162099),(-101567548162095)⟩⟩,⟨⟨(-186610160794397),(-186610160794393)⟩,⟨(-98787882124618),(-98787882124614)⟩⟩,⟨⟨(-183752391183672),(-183752391183669)⟩,⟨(-96297268226330),(-96297268226326)⟩⟩,⟨⟨(-181186207595279),(-181186207595276)⟩,⟨(-94079831183519),(-94079831183516)⟩⟩,⟨⟨(-178902318703340),(-178902318703337)⟩,⟨(-92121557426981),(-92121557426978)⟩⟩,⟨⟨(-176892466614348),(-176892466614345)⟩,⟨(-90410168531418),(-90410168531414)⟩⟩,⟨⟨(-175149394028714),(-175149394028710)⟩,⟨(-88935010876180),(-88935010876176)⟩⟩,⟨⟨(-173666814977575),(-173666814977571)⟩,⟨(-87686960352383),(-87686960352379)⟩⟩,⟨⟨(-172439389176583),(-172439389176579)⟩,⟨(-86658341094834),(-86658341094831)⟩⟩,⟨⟨(-171462700022944),(-171462700022940)⟩,⟨(-85842857368962),(-85842857368958)⟩⟩,⟨⟨(-170733236251075),(-170733236251071)⟩,⟨(-85235537884912),(-85235537884908)⟩⟩,⟨⟨(-170248377254636),(-170248377254633)⟩,⟨(-84832691944483),(-84832691944480)⟩⟩,⟨⟨(-170006382078062),(-170006382078058)⟩,⟨(-84631876953483),(-84631876953480)⟩⟩] +lemma kernel13_0_r3_15_eq : ∀ k : Fin 16, kernel13_0Expr 3 15 k = kernel13_0_r3_15 k := by decide +kernel +noncomputable def kernel13_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel13_0_r3_0,kernel13_0_r3_1,kernel13_0_r3_2,kernel13_0_r3_3,kernel13_0_r3_4,kernel13_0_r3_5,kernel13_0_r3_6,kernel13_0_r3_7,kernel13_0_r3_8,kernel13_0_r3_9,kernel13_0_r3_10,kernel13_0_r3_11,kernel13_0_r3_12,kernel13_0_r3_13,kernel13_0_r3_14,kernel13_0_r3_15] +lemma kernel13_0_r3_eq (i k : Fin 16) : kernel13_0Expr 3 i k = kernel13_0_r3 i k := by + fin_cases i + · exact kernel13_0_r3_0_eq k + · exact kernel13_0_r3_1_eq k + · exact kernel13_0_r3_2_eq k + · exact kernel13_0_r3_3_eq k + · exact kernel13_0_r3_4_eq k + · exact kernel13_0_r3_5_eq k + · exact kernel13_0_r3_6_eq k + · exact kernel13_0_r3_7_eq k + · exact kernel13_0_r3_8_eq k + · exact kernel13_0_r3_9_eq k + · exact kernel13_0_r3_10_eq k + · exact kernel13_0_r3_11_eq k + · exact kernel13_0_r3_12_eq k + · exact kernel13_0_r3_13_eq k + · exact kernel13_0_r3_14_eq k + · exact kernel13_0_r3_15_eq k +noncomputable def kernel13_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-19625358663382794520514565),(-19625358663382793277771024)⟩,⟨(-130420796130806579575312444),(-130420796130806578331140197)⟩⟩,⟨⟨(-19679323124825350059294789),(-19679323124825348817222154)⟩,⟨(-130331086332289778889382337),(-130331086332289777645880556)⟩⟩,⟨⟨(-19787009570068013362910732),(-19787009570068012122181226)⟩,⟨(-130151754489681991488954456),(-130151754489681990246794928)⟩⟩,⟨⟨(-19947934077467723405810641),(-19947934077467722167094542)⟩,⟨(-129882976465698362215547740),(-129882976465698360975400318)⟩⟩,⟨⟨(-20161373345086386211070669),(-20161373345086384975035352)⟩,⟨(-129525016933437074876785921),(-129525016933437073639317567)⟩⟩,⟨⟨(-20426367777298143247710570),(-20426367777298142015019544)⟩,⟨(-129078230415490149433510303),(-129078230415490148199384133)⟩⟩,⟨⟨(-20741725583540926969016273),(-20741725583540925740328258)⟩,⟨(-128543062643385163111959954),(-128543062643385161881834310)⟩⟩,⟨⟨(-21106027874843456214893552),(-21106027874843454990861442)⟩,⟨(-127920052215357774810198130),(-127920052215357773584725561)⟩⟩,⟨⟨(-21517634740127677744124033),(-21517634740127676525394183)⟩,⟨(-127209832525351325640772874),(-127209832525351324420599417)⟩⟩,⟨⟨(-21974692280633694644105151),(-21974692280633693431316059)⟩,⟨(-126413133931296238486848427),(-126413133931296237272612295)⟩⟩,⟨⟨(-22475140577139117783368573),(-22475140577139116577150598)⟩,⟨(-125530786126186242446178159),(-125530786126186241238509464)⟩⟩,⟨⟨(-23016722560949300860539994),(-23016722560949299661513569)⟩,⟨(-124563720671286116168927078),(-124563720671286114968446047)⟩⟩,⟨⟨(-23596993755923181056428527),(-23596993755923179865204630)⟩,⟨(-123512973647019538249693180),(-123512973647019537057010630)⟩⟩,⟨⟨(-24213332855078103910802269),(-24213332855078102727979635)⟩,⟨(-122379688373735603204738174),(-122379688373735602020452721)⟩⟩,⟨⟨(-24862953091595434341899289),(-24862953091595433168066073)⟩,⟨(-121165118151675097880017799),(-121165118151675096704717533)⟩⟩,⟨⟨(-25542914360339143700767014),(-25542914360339142536496959)⟩,⟨(-119870628967085526816213118),(-119870628967085525650471767)⟩⟩] +lemma kernel13_0_r4_0_eq : ∀ k : Fin 16, kernel13_0Expr 4 0 k = kernel13_0_r4_0 k := by decide +kernel +noncomputable def kernel13_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-26250136042316999387296271),(-26250136042316998233151909)⟩,⟨(-118497702109595895949499190),(-118497702109595894793879325)⟩⟩,⟨⟨(-26981410480876442335736572),(-26981410480876441192263121)⟩,⟨(-117047936644682854353892132),(-117047936644682853208939065)⟩⟩,⟨⟨(-27733417054855527426765483),(-27733417054855526294496520)⟩,⟨(-115523051684358783040345624),(-115523051684358781906593083)⟩⟩,⟨⟨(-28502736790426954045492533),(-28502736790426952924942149)⟩,⟨(-113924888399104763558151875),(-113924888399104762436114158)⟩⟩,⟨⟨(-29285867450006311360018552),(-29285867450006310251689407)⟩,⟨(-112255411714566905037250959),(-112255411714566903927430996)⟩⟩,⟨⟨(-30079239033372610551415322),(-30079239033372609455786898)⟩,⟨(-110516711637637794215263086),(-110516711637637793118140685)⟩⟩,⟨⟨(-30879229623100416628743235),(-30879229623100415546283957)⟩,⟨(-108711004158254919984768535),(-108711004158254918900812507)⟩⟩,⟨⟨(-31682181503560567055783305),(-31682181503560565986936432)⟩,⟨(-106840631675558268711507043),(-106840631675558267641161091)⟩⟩,⟨⟨(-32484417480144025468205880),(-32484417480144024413404894)⟩,⟨(-104908062899947656618553475),(-104908062899947655562251585)⟩⟩,⟨⟨(-33282257323035195746882758),(-33282257323035194706530990)⟩,⟨(-102915892186048801671574366),(-102915892186048800629720429)⟩⟩,⟨⟨(-34072034257841747471878850),(-34072034257841746446371103)⟩,⟨(-100866838255611966017226991),(-100866838255611964990216428)⟩⟩,⟨⟨(-34850111423712306453680028),(-34850111423712305443379695)⟩,⟨(-98763742273898898998600394),(-98763742273898897986797267)⟩⟩,⟨⟨(-35612898218275231540175235),(-35612898218275230545439237)⟩,⟨(-96609565248127931515123009),(-96609565248127930518884963)⟩⟩,⟨⟨(-36356866447843923335826511),(-36356866447843922356974303)⟩,⟨(-94407384722003220402491526),(-94407384722003219422138791)⟩⟩,⟨⟨(-37078566200887720469807391),(-37078566200887719507154053)⟩,⟨(-92160390746207016393721790),(-92160390746207015429570267)⟩⟩,⟨⟨(-37774641362791128483507212),(-37774641362791127537329761)⟩,⟨(-89871881110933326708324033),(-89871881110933325760651604)⟩⟩] +lemma kernel13_0_r4_1_eq : ∀ k : Fin 16, kernel13_0Expr 4 1 k = kernel13_0_r4_1 k := by decide +kernel +noncomputable def kernel13_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-38441844690443688329818445),(-38441844690443687400392953)⟩,⟨(-87545255833032917317850023),(-87545255833032916386933670)⟩⟩,⟨⟨(-39077052366240566382660364),(-39077052366240565470216679)⟩,⟨(-85184010897064685562838002),(-85184010897064684648908517)⟩⟩,⟨⟨(-39677277952648295446651759),(-39677277952648294551421645)⟩,⟨(-82791731256444929079372809),(-82791731256444928182662938)⟩⟩,⟨⟨(-40239685670614899923299362),(-40239685670614899045396619)⟩,⟨(-80372083107888840920917728),(-80372083107888840041580036)⟩⟩,⟨⟨(-40761602927787851320380959),(-40761602927787850459976027)⟩,⟨(-77928805459380164104514369),(-77928805459380163242731609)⟩⟩,⟨⟨(-41240532025750542556477964),(-41240532025750541713711235)⟩,⟨(-75465701018916063277276946),(-75465701018916062433189584)⟩⟩,⟨⟨(-41674160979296182852390652),(-41674160979296182027411674)⟩,⟨(-72986626438184551417420636),(-72986626438184550591178196)⟩⟩,⟨⟨(-42060373385119185002365057),(-42060373385119184195272131)⟩,⟨(-70495481952070511433198007),(-70495481952070510624898661)⟩⟩,⟨⟨(-42397257282204067830999361),(-42397257282204067041904977)⟩,⟨(-67996200461383121047075419),(-67996200461383120256831431)⟩⟩,⟨⟨(-42683112951610166079783349),(-42683112951610165308737093)⟩,⟨(-65492736112383116628630947),(-65492736112383115856491575)⟩⟩,⟨⟨(-42916459609260236806861889),(-42916459609260236053931469)⟩,⟨(-62989052432495537644055274),(-62989052432495536890087804)⟩⟩,⟨⟨(-43096040951709302717055403),(-43096040951709301982251143)⟩,⟨(-60489110086957808825949635),(-60489110086957808090163869)⟩⟩,⟨⟨(-43220829521657561000240799),(-43220829521657560283595202)⟩,⟨(-57996854326013158729807008),(-57996854326013158012234844)⟩⟩,⟨⟨(-43290029867132777762297711),(-43290029867132777063593630)⟩,⟨(-55516202196558600883666770),(-55516202196558600184090353)⟩⟩,⟨⟨(-43303080475752554197250869),(-43303080475752553516350304)⟩,⟨(-53051029595843148582853384),(-53051029595843147901133928)⟩⟩,⟨⟨(-43259654473229277635834270),(-43259654473229276972673595)⟩,⟨(-50605158247839388107492978),(-50605158247839387443565981)⟩⟩] +lemma kernel13_0_r4_2_eq : ∀ k : Fin 16, kernel13_0Expr 4 2 k = kernel13_0_r4_2 k := by decide +kernel +noncomputable def kernel13_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-43159659083239857208757821),(-43159659083239856563306128)⟩,⟨(-48182342685240088095362052),(-48182342685240087449195654)⟩⟩,⟨⟨(-43003233853883780437699062),(-43003233853883779809848075)⟩,⟨(-45786257321628142138856650),(-45786257321628141510341537)⟩⟩,⟨⟨(-42790747664128450919451928),(-42790747664128450309130263)⟩,⟨(-43420483699207178967616159),(-43420483699207178356679844)⟩⟩,⟨⟨(-42522794531819286470156554),(-42522794531819285877226242)⟩,⟨(-41088497997543793966518388),(-41088497997543793373021725)⟩⟩,⟨⟨(-42200188252940833928667271),(-42200188252940833353030567)⟩,⟨(-38793658888050874291454403),(-38793658888050873715298409)⟩⟩,⟨⟨(-41823955909780240839395749),(-41823955909780240280874603)⟩,⟨(-36539195817433622723240055),(-36539195817433622164245373)⟩⟩,⟨⟨(-41395330293391623798143136),(-41395330293391623256603680)⟩,⟨(-34328197801032890347051943),(-34328197801032889805083352)⟩⟩,⟨⟨(-40915741293215653455783381),(-40915741293215652930906899)⟩,⟨(-32163602803950143885085250),(-32163602803950143359822541)⟩⟩,⟨⟨(-40386806313801070444405626),(-40386806313801069936008294)⟩,⟨(-30048187784049169411425316),(-30048187784049168902683192)⟩⟩,⟨⟨(-39810319785234368393865363),(-39810319785234367901712894)⟩,⟨(-27984559466434129403086253),(-27984559466434128910628930)⟩⟩,⟨⟨(-39188241840044421915370459),(-39188241840044421439281876)⟩,⟨(-25975145913842562266513706),(-25975145913842561790158684)⟩⟩,⟨⟨(-38522686234948541028591585),(-38522686234948540568314883)⟩,⟨(-24022188951613698816359078),(-24022188951613698355852791)⟩⟩,⟨⟨(-37815907600788521468171061),(-37815907600788521023509487)⟩,⟨(-22127737499552558330665219),(-22127737499552557885809334)⟩⟩,⟨⟨(-37070288108318811937730793),(-37070288108318811508402012)⟩,⟨(-20293641856170695987206724),(-20293641856170695557717301)⟩⟩,⟨⟨(-36288323641109580555636477),(-36288323641109580141416428)⟩,⟨(-18521548973513052619722488),(-18521548973513052205373850)⟩⟩,⟨⟨(-35472609569678077129515952),(-35472609569678076730109492)⟩,⟨(-16812898753150004224637822),(-16812898753150003825133199)⟩⟩] +lemma kernel13_0_r4_3_eq : ∀ k : Fin 16, kernel13_0Expr 4 3 k = kernel13_0_r4_3 k := by decide +kernel +noncomputable def kernel13_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-34625826223032838950952854),(-34625826223032838566127452)⟩,⟨(-15168921386001511800020267),(-15168921386001511415125495)⟩⟩,⟨⟨(-33750724155085742046271493),(-33750724155085741675705325)⟩,⟨(-13590635750546593608601994),(-13590635750546593237993619)⟩⟩,⟨⟨(-32850109303843943457598024),(-32850109303843943101034296)⟩,⟨(-12078848875738846026995792),(-12078848875738845670415396)⟩⟩,⟨⟨(-31926828140933422621546867),(-31926828140933422278659216)⟩,⟨(-10634156466681385824677685),(-10634156466681385481797290)⟩⟩,⟨⟨(-30983752907832989885993712),(-30983752907832989556520450)⟩,⟨(-9256944482896602776876334),(-9256944482896602447432654)⟩⟩,⟨⟨(-30023767033226001026848765),(-30023767033226000710444563)⟩,⟨(-7947391750940953779201357),(-7947391750940953462847484)⟩⟩,⟨⟨(-29049750823129010807400143),(-29049750823129010503785969)⟩,⟨(-6705473585244355880336095),(-6705473585244355576791440)⟩⟩,⟨⟨(-28064567511963072307592486),(-28064567511963072016422672)⟩,⟨(-5530966383476398345753994),(-5530966383476398054671361)⟩⟩,⟨⟨(-27071049758533269407043280),(-27071049758533269128040690)⟩,⟨(-4423453155532671571328397),(-4423453155532671292429153)⟩⟩,⟨⟨(-26071986666021872298980024),(-26071986666021872031784089)⟩,⟨(-3382329938464391655762498),(-3382329938464391388684618)⟩⟩,⟨⟨(-25070111399633743875328196),(-25070111399633743619647820)⟩,⟨(-2406813043408031115224024),(-2406813043408030859674986)⟩⟩,⟨⟨(-24068089469519126124123016),(-24068089469519125879604627)⟩,⟨(-1495947074867383044263569),(-1495947074867382799888424)⟩⟩,⟨⟨(-23068507740104072252719361),(-23068507740104072018326445)⟩,⟨(-648613657609927320165346),(-648613657609927085926045)⟩⟩,⟨⟨(-22073864220052634113396191),(-22073864220052633888773842)⟩,⟨136459197993504893557765,136459197993505118017408⟩⟩,⟨⟨(-21086558679841332910560281),(-21086558679841332695471924)⟩,⟨860687165096047715453926,860687165096047930371711⟩⟩,⟨⟨(-20108884136422144812273049),(-20108884136422144606422549)⟩,⟨1525619179897557043028508,1525619179897557248701740⟩⟩] +lemma kernel13_0_r4_4_eq : ∀ k : Fin 16, kernel13_0Expr 4 4 k = kernel13_0_r4_4 k := by decide +kernel +noncomputable def kernel13_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-19143019236763792249276986),(-19143019236763792052435426)⟩,⟨2132926609769500555624007,2132926609769500752282726⟩⟩,⟨⟨(-18191021564271975186426629),(-18191021564271974998289328)⟩,⟨2684392089716884853404997,2684392089716885041354943⟩⟩,⟨⟨(-17254821884276589337530929),(-17254821884276589157860235)⟩,⟨3181898107688992601949587,3181898107688992781429428⟩⟩,⟨⟨(-16336219337016112072630259),(-16336219337016111901133760)⟩,⟨3627415419283552320559840,3627415419283552491862940⟩⟩,⟨⟨(-15436877578922250277501162),(-15436877578922250113949879)⟩,⟨4022991371693508255479120,4022991371693508418835362⟩⟩,⟨⟨(-14558321865584685650028290),(-14558321865584685494127214)⟩,⟨4370738215345548175354222,4370738215345548331059453⟩⟩,⟨⟨(-13701937062625498123732872),(-13701937062625497975249601)⟩,⟨4672821479606306752807031,4672821479606306901094446⟩⟩,⟨⟨(-12868966563900109533952614),(-12868966563900109392605358)⟩,⟨4931448486224028793254057,4931448486224028934406169⟩⟩,⟨⟨(-12060512090025502881019983),(-12060512090025502746588833)⟩,⟨5148857070875154284900795,5148857070875154419138200⟩⟩,⟨⟨(-11277534334270173211617004),(-11277534334270173083819463)⟩,⟨5327304579347125626690407,5327304579347125754296216⟩⟩,⟨⟨(-10520854417370363620392587),(-10520854417370363499003351)⟩,⟨5469057200565926727210055,5469057200565926848413573⟩⟩,⟨⟨(-9791156107903294327204425),(-9791156107903294211947963)⟩,⟨5576379693928681096940190,5576379693928681212027312⟩⟩,⟨⟨(-9088988760482699580797309),(-9088988760482699471465780)⟩,⟨5651525563290456285937051,5651525563290456395114793⟩⟩,⟨⟨(-8414770920269971156800153),(-8414770920269971053132922)⟩,⟨5696727724544906764414059,5696727724544906867942224⟩⟩,⟨⟨(-7768794539132927405604308),(-7768794539132927307387193)⟩,⟨5714189708096567796689008,5714189708096567894780966⟩⟩,⟨⟨(-7151229746243489662713309),(-7151229746243489569649385)⟩,⟨5706077431714999132239083,5706077431714999225190941⟩⟩] +lemma kernel13_0_r4_5_eq : ∀ k : Fin 16, kernel13_0Expr 4 5 k = kernel13_0_r4_5 k := by decide +kernel +noncomputable def kernel13_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-6562130113987726553326594),(-6562130113987726465230638)⟩,⟨5674511573353688477292244,5674511573353688565288446⟩⟩,⟨⟨(-6001438358761981168369325),(-6001438358761981085006745)⟩,⟨5621560567574552034115091,5621560567574552117389457⟩⟩,⟨⟨(-5468992415535387094996238),(-5468992415535387016183682)⟩,⟨5549234243304885111973721,5549234243304885190708861⟩⟩,⟨⟨(-4964531824953769488854795),(-4964531824953769414376180)⟩,⟨5459478114827837633589254,5459478114827837708000522⟩⟩,⟨⟨(-4487704372218459453049874),(-4487704372218459382735593)⟩,⟨5354168332226610657424092,5354168332226610727680393⟩⟩,⟨⟨(-4038072917966192276356142),(-4038072917966192209996914)⟩,⟨5235107292019263566188255,5235107292019263632498186⟩⟩,⟨⟨(-3615122362868408650164254),(-3615122362868408587539812)⟩,⟨5104019903483423378998997,5104019903483423441582173⟩⟩,⟨⟨(-3218266689621103763648544),(-3218266689621103704553133)⟩,⟨4962550501221466055597399,4962550501221466114658941⟩⟩,⟨⟨(-2846856028367498322083195),(-2846856028367498266373950)⟩,⟨4812260389894752773436240,4812260389894752829118410⟩⟩,⟨⟨(-2500183694340021132526489),(-2500183694340021080024444)⟩,⟨4654626002792547498857777,4654626002792547551338961⟩⟩,⟨⟨(-2177493149578046239472184),(-2177493149578046190038309)⟩,⟨4491037652023886683408811,4491037652023886732827487⟩⟩,⟨⟨(-1877984843924747513103233),(-1877984843924747466575156)⟩,⟨4322798844649690832739780,4322798844649690879257795⟩⟩,⟨⟨(-1600822894080822988426046),(-1600822894080822944670703)⟩,⟨4151126136022789491242141,4151126136022789534992056⟩⟩,⟨⟨(-1345141563245150475888438),(-1345141563245150434730653)⟩,⟨3977149488984574354425651,3977149488984574395582155⟩⟩,⟨⟨(-1110051507753703720155264),(-1110051507753703681476555)⟩,⟨3801913105382479552767991,3801913105382479591449125⟩⟩,⟨⟨(-894645761090511767063705),(-894645761090511730726286)⟩,⟨3626376694620916029604706,3626376694620916065947840⟩⟩] +lemma kernel13_0_r4_6_eq : ∀ k : Fin 16, kernel13_0Expr 4 6 k = kernel13_0_r4_6 k := by decide +kernel +noncomputable def kernel13_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-698005429642050520844267),(-698005429642050486742104)⟩,⟨3451417142633187389614671,3451417142633187423725448⟩⟩,⟨⟨(-519205078555419818778638),(-519205078555419786780150)⟩,⟨3277830543752202051331119,3277830543752202083340756⟩⟩,⟨⟨(-357317789999862940435264),(-357317789999862910438802)⟩,⟨3106334557448175797141515,3106334557448175827151322⟩⟩,⟨⟨(-211419879982561261314558),(-211419879982561233202823)⟩,⟨2937571051772927341731811,2937571051772927369858771⟩⟩,⟨⟨(-80595263598479896017089),(-80595263598479869699046)⟩,⟨2772108995580448095388074,2772108995580448121722929⟩⟩,⟨⟨36060537830747808851165,36060537830747833485829⟩,⟨2610447562157009885969372,2610447562157009910622169⟩⟩,⟨⟨139436750879642207798724,139436750879642230835825⟩,⟨2453019407763688755293212,2453019407763688778349516⟩⟩,⟨⟨230404065364245796023129,230404065364245817574495⟩,⟨2300194089740553050671276,2300194089740553072242687⟩⟩,⟨⟨309811707904803375603750,309811707904803395804527⟩,⟨2152281590214306735180400,2152281590214306755401839⟩⟩,⟨⟨378484867973804675168418,378484867973804694102333⟩,⟨2009535913058487091064289,2009535913058487110019299⟩⟩,⟨⟨437222468221742233767852,437222468221742251498167⟩,⟨1872158723545622057720229,1872158723545622075471906⟩⟩,⟨⟨486795268656154129640430,486795268656154146241010⟩,⟨1740303002072365141494629,1740303002072365158116688⟩⟩,⟨⟨527944292295954005486868,527944292295954021013701⟩,⟨1614076685400336665903778,1614076685400336681452072⟩⟩,⟨⟨561379558233605971516095,561379558233605986038310⟩,⟨1493546271006854147042551,1493546271006854161586094⟩⟩,⟨⟨587779106610125766781944,587779106610125780352093⟩,⟨1378740362351762577189355,1378740362351762590780592⟩⟩,⟨⟨607788298837032167115912,607788298837032179794972⟩,⟨1269653135111485052713876,1269653135111485065413696⟩⟩] +lemma kernel13_0_r4_7_eq : ∀ k : Fin 16, kernel13_0Expr 4 7 k = kernel13_0_r4_7 k := by decide +kernel +noncomputable def kernel13_0_r4_8 : Fin 16 → CBox := ![⟨⟨622019375477473199963488,622019375477473211797156⟩,⟨1166247706683238522492735,1166247706683238534346752⟩⟩,⟨⟨631051253515739453535208,631051253515739464584100⟩,⟨1068459393497061957783802,1068459393497061968850942⟩⟩,⟨⟨635429544288181745586925,635429544288181755893677⟩,⟨976198842868940725563724,976198842868940735886760⟩⟩,⟨⟨635666773105418740390117,635666773105418750003987⟩,⟨889355028265148726957712,889355028265148736586046⟩⟩,⟨⟨632242781550527945412839,632242781550527954371017⟩,⟨807798098908526113731496,807798098908526122702454⟩⟩,⟨⟨625605293574475368407351,625605293574475376764636⟩,⟨731382076626651378651819,731382076626651387020331⟩⟩,⟨⟨616170626811405830756709,616170626811405838547089⟩,⟨659947394706970486283478,659947394706970494083656⟩⟩,⟨⟨604324530985158812245844,604324530985158819507851⟩,⟨593323275274431831697311,593323275274431838967806⟩⟩,⟨⟨590423135856852307708965,590423135856852314471184⟩,⟨531329943334803857598160,531329943334803864367666⟩⟩,⟨⟨574793991853982213536328,574793991853982219834535⟩,⟨473780677125534512378454,473780677125534518682853⟩⟩,⟨⟨557737187306868910817439,557737187306868916678269⟩,⟨420483695781702886118046,420483695781702891984071⟩⟩,⟨⟨539526527081557822136062,539526527081557827590246⟩,⟨371243886555180027073313,371243886555180032531789⟩⟩,⟨⟨520410758323195368138973,520410758323195373209461⟩,⟨325864374920191617968443,325864374920191623042405⟩⟩,⟨⟨500614829994992630115411,500614829994992634830362⟩,⟨284147941859302873853433,284147941859302878571123⟩⟩,⟨⟨480341173900607128118133,480341173900607132498624⟩,⟨245898293453112572060489,245898293453112576443058⟩⟩,⟨⟨459770995898585105730501,459770995898585109804604⟩,⟨210921188598608649631852,210921188598608653707442⟩⟩] +lemma kernel13_0_r4_8_eq : ∀ k : Fin 16, kernel13_0Expr 4 8 k = kernel13_0_r4_8 k := by decide +kernel +noncomputable def kernel13_0_r4_9 : Fin 16 → CBox := ![⟨⟨439065567043972209104145,439065567043972212896861⟩,⟨179025431260263184129530,179025431260263187923209⟩⟩,⟨⟨418367505413026448889454,418367505413026452421642⟩,⟨150023734120519965680637,150023734120519969213323⟩⟩,⟨⟨397802040372040996475056,397802040372040999761866⟩,⟨123733460849104763956937,123733460849104767243836⟩⟩,⟨⟨377478252031685880694351,377478252031685883753487⟩,⟨99977254460917483922425,99977254460917486981290⟩⟩,⟨⟨357490279576274949996290,357490279576274952840673⟩,⟨78583559387942174678122,78583559387942177521922⟩⟩,⟨⟨337918493066391686020965,337918493066391688666788⟩,⟨59387044959730525610860,59387044959730528255830⟩⟩,⟨⟨318830624177929155822345,318830624177929158281460⟩,⟨42228937977837571250958,42228937977837573708990⟩⟩,⟨⟨300282852156462539191014,300282852156462541477239⟩,⟨26957271990417814777764,26957271990417817062711⟩⟩,⟨⟨282320842029648428323592,282320842029648430447967⟩,⟨13427060732260769931794,13427060732260772054728⟩⟩,⟨⟨264980732829662388142888,264980732829662390119134⟩,⟨1500403000925958258556,1500403000925960233227⟩⟩,⟨⟨248290074231058998899684,248290074231059000736711⟩,⟨(-8953474000853364821422),(-8953474000853362986076)⟩⟩,⟨⟨232268710606188401130041,232268710606188402838298⟩,⟨(-18058226105196386103810),(-18058226105196384397319)⟩⟩,⟨⟨216929612040479441500325,216929612040479443087319⟩,⟨(-25930451960362964075194),(-25930451960362962490029)⟩⟩,⟨⟨202279652334197267455283,202279652334197268930519⟩,⟨(-32679795046854660017241),(-32679795046854658543879)⟩⟩,⟨⟨188320334446962886473494,188320334446962887843821⟩,⟨(-38409082174969911305853),(-38409082174969909937429)⟩⟩,⟨⟨175048464218128902323899,175048464218128903597347⟩,⟨(-43214493076197476073791),(-43214493076197474802262)⟩⟩] +lemma kernel13_0_r4_9_eq : ∀ k : Fin 16, kernel13_0Expr 4 9 k = kernel13_0_r4_9 k := by decide +kernel +noncomputable def kernel13_0_r4_10 : Fin 16 → CBox := ![⟨⟨162456773522191741434785,162456773522191742619988⟩,⟨(-47185756074016747529835),(-47185756074016746346552)⟩⟩,⟨⟨150534494296271529527207,150534494296271530631479⟩,⟨(-50406365195605524890638),(-50406365195605523788276)⟩⟩,⟨⟨139267885109054428182167,139267885109054429210327⟩,⟨(-52953814460456605571080),(-52953814460456604544810)⟩⟩,⟨⟨128640712130413843430200,128640712130413844388026⟩,⟨(-54899845451302869152155),(-54899845451302868196192)⟩⟩,⟨⟨118634686511288175761191,118634686511288176652698⟩,⟨(-56310704633868527079600),(-56310704633868526189922)⟩⟩,⟨⟨109229860297456785496795,109229860297456786327250⟩,⟨(-57247407242098339118620),(-57247407242098338289956)⟩⟩,⟨⟨100404983081817482406948,100404983081817483180070⟩,⟨(-57766004882414136154581),(-57766004882414135383170)⟩⟩,⟨⟨92137821650810815272220,92137821650810815992528⟩,⟨(-57917854332380343267278),(-57917854332380342548509)⟩⟩,⟨⟨84405444904890876770909,84405444904890877441386⟩,⟨(-57749885314493608194720),(-57749885314493607525625)⟩⟩,⟨⟨77184476333457923905866,77184476333457924530569⟩,⟨(-57304865313576129813432),(-57304865313576129189969)⟩⟩,⟨⟨70451316304382415999105,70451316304382416580799⟩,⟨(-56621659775709506022043),(-56621659775709505441453)⟩⟩,⟨⟨64182336389966948787962,64182336389966949329992⟩,⟨(-55735486277356560048796),(-55735486277356559507748)⟩⟩,⟨⟨58354047897564258430454,58354047897564258935404⟩,⟨(-54678161485109826367269),(-54678161485109825863188)⟩⟩,⟨⟨52943246706583084653475,52943246706583085124855⟩,⟨(-53478339939438857363365),(-53478339939438856892751)⟩⟩,⟨⟨47927136436581650815578,47927136436581651255368⟩,⟨(-52161743890149408832271),(-52161743890149408393152)⟩⟩,⟨⟨43283431885702696852062,43283431885702697262709⟩,⟨(-50751383587454788442125),(-50751383587454788032064)⟩⟩] +lemma kernel13_0_r4_10_eq : ∀ k : Fin 16, kernel13_0Expr 4 10 k = kernel13_0_r4_10 k := by decide +kernel +noncomputable def kernel13_0_r4_11 : Fin 16 → CBox := ![⟨⟨38990444586792988142000,38990444586792988525090⟩,⟨(-49267767591177701786260),(-49267767591177701403677)⟩⟩,⟨⟨35027152231939515310456,35027152231939515668264⟩,⟨(-47729102802353484415915),(-47729102802353484058543)⟩⟩,⟨⟨31373253616429196096356,31373253616429196430375⟩,⟨(-46151484047191048846697),(-46151484047191048513050)⟩⟩,⟨⟨28009210651707980152271,28009210651707980464359⟩,⟨(-44549073153836834044155),(-44549073153836833732379)⟩⟩,⟨⟨24916278895018636196987,24916278895018636488358⟩,⟨(-42934267558602017487590),(-42934267558602017196479)⟩⟩,⟨⟨22076527942112380603160,22076527942112380875513⟩,⟨(-41317858561210304306243),(-41317858561210304034102)⟩⟩,⟨⟨19472852929683416947358,19472852929683417201882⟩,⟨(-39709179419176156240944),(-39709179419176155986589)⟩⟩,⟨⟨17088978296749951126405,17088978296749951364809⟩,⟨(-38116243530607909979804),(-38116243530607909741529)⟩⟩,⟨⟨14909454859750163605606,14909454859750163828730⟩,⟨(-36545873003514263930011),(-36545873003514263706982)⟩⟩,⟨⟨12919651165164663874257,12919651165164664083371⟩,⟨(-35003817949023918531985),(-35003817949023918322936)⟩⟩,⟨⟨11105739996434404020550,11105739996434404216451⟩,⟨(-33494866866726302736012),(-33494866866726302540147)⟩⟩,⟨⟨9454680829130409487434,9454680829130409671154⟩,⟨(-32022948513490515299763),(-32022948513490515116055)⟩⟩,⟨⟨7954198949974223895595,7954198949974224067770⟩,⟨(-30591225663463093315256),(-30591225663463093143071)⟩⟩,⟨⟨6592761881550748385197,6592761881550748546779⟩,⟨(-29202181177280998767357),(-29202181177280998605746)⟩⟩,⟨⟨5359553685472865670457,5359553685472865822044⟩,⟨(-27857696803614007018313),(-27857696803614006866681)⟩⟩,⟨⟨4244447652363392078566,4244447652363392221040⟩,⟨(-26559125136669943674555),(-26559125136669943532020)⟩⟩] +lemma kernel13_0_r4_11_eq : ∀ k : Fin 16, kernel13_0Expr 4 11 k = kernel13_0_r4_11 k := by decide +kernel +noncomputable def kernel13_0_r4_12 : Fin 16 → CBox := ![⟨⟨3237977827275538770681,3237977827275538904591⟩,⟨(-25307355149905104433234),(-25307355149905104299250)⟩⟩,⟨⟨2331309763994846083501,2331309763994846209566⟩,⟨(-24102871719477349943683),(-24102871719477349817532)⟩⟩,⟨⟨1516210850933234809829,1516210850933234928476⟩,⟨(-22945809541506411911616),(-22945809541506411792875)⟩⟩,⟨⟨785020504889080811200,785020504889080923002⟩,⟨(-21836001835460543087396),(-21836001835460542975491)⟩⟩,⟨⟨130620486631890689517,130620486631890794806⟩,⟨(-20773024212418063987870),(-20773024212418063882471)⟩⟩,⟨⟨(-453594446116214747711),(-453594446116214648396)⟩,⟨(-19756234071957427695690),(-19756234071957427596260)⟩⟩,⟨⟨(-973745367393169263849),(-973745367393169170191)⟩,⟨(-18784805875366766903369),(-18784805875366766809590)⟩⟩,⟨⟨(-1435497343649369933073),(-1435497343649369844528)⟩,⟨(-17857762626048405053472),(-17857762626048404964803)⟩⟩,⟨⟨(-1844086804451243330970),(-1844086804451243247298)⟩,⟨(-16974003870701308973496),(-16974003870701308889697)⟩⟩,⟨⟨(-2204348026145922538429),(-2204348026145922459217)⟩,⟨(-16132330517334361982634),(-16132330517334361903292)⟩⟩,⟨⟨(-2520738653348670888597),(-2520738653348670813620)⟩,⟨(-15331466748601462147894),(-15331466748601462072786)⟩⟩,⟨⟨(-2797364202436518378273),(-2797364202436518307206)⟩,⟨(-14570079291530770481151),(-14570079291530770409951)⟩⟩,⟨⟨(-3038001508135150272090),(-3038001508135150204763)⟩,⟨(-13846794287591792866383),(-13846794287591792798922)⟩⟩,⟨⟨(-3246121088976005491051),(-3246121088976005427151)⟩,⟨(-13160211990326746947182),(-13160211990326746883148)⟩⟩,⟨⟨(-3424908420073155745052),(-3424908420073155684342)⟩,⟨(-12508919501565290422824),(-12508919501565290361980)⟩⟩,⟨⟨(-3577284112511991170738),(-3577284112511991112965)⟩,⟨(-11891501741622138454804),(-11891501741622138396897)⟩⟩] +lemma kernel13_0_r4_12_eq : ∀ k : Fin 16, kernel13_0Expr 4 12 k = kernel13_0_r4_12 k := by decide +kernel +noncomputable def kernel13_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-3705923007831285935548),(-3705923007831285880604)⟩,⟨(-11306550833905171174925),(-11306550833905171119848)⟩⟩,⟨⟨(-3813272203783756466200),(-3813272203783756413839)⟩,⟨(-10752674070081119654335),(-10752674070081119601842)⟩⟩,⟨⟨(-3901568033934043653511),(-3901568033934043603615)⟩,⟨(-10228500608386629307527),(-10228500608386629257500)⟩⟩,⟨⟨(-3972852028842739823471),(-3972852028842739775848)⟩,⟨(-9732687044852130481074),(-9732687044852130433323)⟩⟩,⟨⟨(-4028985890725594580330),(-4028985890725594534879)⟩,⟨(-9263921985131801039691),(-9263921985131800994113)⟩⟩,⟨⟨(-4071665516692864962098),(-4071665516692864918600)⟩,⟨(-8820929733303466551498),(-8820929733303466507874)⟩⟩,⟨⟨(-4102434108079237266436),(-4102434108079237224809)⟩,⟨(-8402473203408633143740),(-8402473203408633101989)⟩⟩,⟨⟨(-4122694405074327382417),(-4122694405074327342515)⟩,⟨(-8007356149629954216581),(-8007356149629954176557)⟩⟩,⟨⟨(-4133720086952541707159),(-4133720086952541668931)⟩,⟨(-7634424801831296880802),(-7634424801831296842453)⟩⟩,⟨⟨(-4136666378765183364935),(-4136666378765183328229)⟩,⟨(-7282568984690254698233),(-7282568984690254661408)⟩⟩,⟨⟨(-4132579905474797419180),(-4132579905474797383934)⟩,⟨(-6950722790807465002872),(-6950722790807464967510)⟩⟩,⟨⟨(-4122407834251604268491),(-4122407834251604234582)⟩,⟨(-6637864870952194667465),(-6637864870952194633447)⟩⟩,⟨⟨(-4107006345076797762724),(-4107006345076797730112)⟩,⟨(-6343018397968555758859),(-6343018397968555726143)⟩⟩,⟨⟨(-4087148468962919623249),(-4087148468962919591816)⟩,⟨(-6065250754789627900708),(-6065250754789627869178)⟩⟩,⟨⟨(-4063531332056530733954),(-4063531332056530703659)⟩,⟨(-5803672991455456764166),(-5803672991455456733777)⟩⟩,⟨⟨(-4036782842676187957116),(-4036782842676187927865)⟩,⟨(-5557439090973088492203),(-5557439090973088462863)⟩⟩] +lemma kernel13_0_r4_13_eq : ∀ k : Fin 16, kernel13_0Expr 4 13 k = kernel13_0_r4_13 k := by decide +kernel +noncomputable def kernel13_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-4007467856997139025802),(-4007467856997138997574)⟩,⟨(-5325745079260526482064),(-5325745079260526453751)⟩⟩,⟨⟨(-3976093857656109111884),(-3976093857656109084576)⟩,⟨(-5107828010250409676823),(-5107828010250409649435)⟩⟩,⟨⟨(-3943116178043567652857),(-3943116178043567626438)⟩,⟨(-4902964853462808867426),(-4902964853462808840931)⟩⟩,⟨⟨(-3908942803501411831438),(-3908942803501411805832)⟩,⟨(-4710471307960354192013),(-4710471307960354166335)⟩⟩,⟨⟨(-3873938779071945885498),(-3873938779071945860690)⟩,⟨(-4529700563544657864044),(-4529700563544657839166)⟩⟩,⟨⟨(-3838430251866993597577),(-3838430251866993573484)⟩,⟨(-4360042027313682096712),(-4360042027313682072554)⟩⟩,⟨⟨(-3802708174558682127926),(-3802708174558682104527)⟩,⟨(-4200920031249683424285),(-4200920031249683400822)⟩⟩,⟨⟨(-3767031694948035268991),(-3767031694948035246222)⟩,⟨(-4051792534322405742206),(-4051792534322405719377)⟩⟩,⟨⟨(-3731631255053895443177),(-3731631255053895421031)⟩,⟨(-3912149830649485621424),(-3912149830649485599220)⟩⟩,⟨⟨(-3696711421690735937018),(-3696711421690735915427)⟩,⟨(-3781513273534191923586),(-3781513273534191901939)⟩⟩,⟨⟨(-3662453469075752421837),(-3662453469075752400780)⟩,⟨(-3659434023679676124994),(-3659434023679676103883)⟩⟩,⟨⟨(-3629017732627829626399),(-3629017732627829605825)⟩,⟨(-3545491828540271373086),(-3545491828540271352461)⟩⟩,⟨⟨(-3596545751796831144313),(-3596545751796831124219)⟩,⟨(-3439293838596801305423),(-3439293838596801285279)⟩⟩,⟨⟨(-3565162218493278285001),(-3565162218493278265324)⟩,⟨(-3340473465318392679524),(-3340473465318392659800)⟩⟩,⟨⟨(-3534976746477005671263),(-3534976746477005651994)⟩,⟨(-3248689284683217045631),(-3248689284683217026315)⟩⟩,⟨⟨(-3506085475909107829009),(-3506085475909107810102)⟩,⟨(-3163623989361384012424),(-3163623989361383993473)⟩⟩] +lemma kernel13_0_r4_14_eq : ∀ k : Fin 16, kernel13_0Expr 4 14 k = kernel13_0_r4_14 k := by decide +kernel +noncomputable def kernel13_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-3478572526174014726212),(-3478572526174014707667)⟩,⟨(-3084983392002456834432),(-3084983392002456815845)⟩⟩,⟨⟨(-3452511309036852581360),(-3452511309036852563125)⟩,⟨(-3012495481506396472883),(-3012495481506396454607)⟩⟩,⟨⟨(-3427965713213861354844),(-3427965713213861336909)⟩,⟨(-2945909533679784842976),(-2945909533679784825000)⟩⟩,⟨⟨(-3404991170498645644750),(-3404991170498645627075)⟩,⟨(-2884995277279472778958),(-2884995277279472761244)⟩⟩,⟨⟨(-3383635612702191320417),(-3383635612702191303003)⟩,⟨(-2829542116114737890245),(-2829542116114737872792)⟩⟩,⟨⟨(-3363940327827377565364),(-3363940327827377548165)⟩,⟨(-2779358407608805282322),(-2779358407608805265085)⟩⟩,⟨⟨(-3345940723106431071921),(-3345940723106431054929)⟩,⟨(-2734270798004088976912),(-2734270798004088959883)⟩⟩,⟨⟨(-3329667001779517305823),(-3329667001779517289002)⟩,⟨(-2694123614226326875378),(-2694123614226326858521)⟩⟩,⟨⟨(-3315144759781426957176),(-3315144759781426940530)⟩,⟨(-2658778312295085155436),(-2658778312295085138754)⟩⟩,⟨⟨(-3302395507827982827850),(-3302395507827982811337)⟩,⟨(-2628112982076624530547),(-2628112982076624513999)⟩⟩,⟨⟨(-3291437123751183847457),(-3291437123751183831068)⟩,⟨(-2602021908115068796087),(-2602021908115068779664)⟩⟩,⟨⟨(-3282284239318991725440),(-3282284239318991709143)⟩,⟨(-2580415186244853140378),(-2580415186244853124046)⟩⟩,⟨⟨(-3274948565188794315830),(-3274948565188794299628)⟩,⟨(-2563218395677602289482),(-2563218395677602273247)⟩⟩,⟨⟨(-3269439157079672455426),(-3269439157079672439279)⟩,⟨(-2550372326266283293482),(-2550372326266283277302)⟩⟩,⟨⟨(-3265762625704369409234),(-3265762625704369393135)⟩,⟨(-2541832760675374500705),(-2541832760675374484572)⟩⟩,⟨⟨(-3263923292474027261037),(-3263923292474027244957)⟩,⟨(-2537570311224818912203),(-2537570311224818896090)⟩⟩] +lemma kernel13_0_r4_15_eq : ∀ k : Fin 16, kernel13_0Expr 4 15 k = kernel13_0_r4_15 k := by decide +kernel +noncomputable def kernel13_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel13_0_r4_0,kernel13_0_r4_1,kernel13_0_r4_2,kernel13_0_r4_3,kernel13_0_r4_4,kernel13_0_r4_5,kernel13_0_r4_6,kernel13_0_r4_7,kernel13_0_r4_8,kernel13_0_r4_9,kernel13_0_r4_10,kernel13_0_r4_11,kernel13_0_r4_12,kernel13_0_r4_13,kernel13_0_r4_14,kernel13_0_r4_15] +lemma kernel13_0_r4_eq (i k : Fin 16) : kernel13_0Expr 4 i k = kernel13_0_r4 i k := by + fin_cases i + · exact kernel13_0_r4_0_eq k + · exact kernel13_0_r4_1_eq k + · exact kernel13_0_r4_2_eq k + · exact kernel13_0_r4_3_eq k + · exact kernel13_0_r4_4_eq k + · exact kernel13_0_r4_5_eq k + · exact kernel13_0_r4_6_eq k + · exact kernel13_0_r4_7_eq k + · exact kernel13_0_r4_8_eq k + · exact kernel13_0_r4_9_eq k + · exact kernel13_0_r4_10_eq k + · exact kernel13_0_r4_11_eq k + · exact kernel13_0_r4_12_eq k + · exact kernel13_0_r4_13_eq k + · exact kernel13_0_r4_14_eq k + · exact kernel13_0_r4_15_eq k +noncomputable def kernel13_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-18545253852132509064897751173),(-18545253852132508661374422541)⟩,⟨(-91482407851786923637544601092),(-91482407851786923232568541710)⟩⟩,⟨⟨(-18577326370502974860144477654),(-18577326370502974456696521825)⟩,⟨(-91438239013758973790642692792),(-91438239013758973385741703409)⟩⟩,⟨⟨(-18641372370644784853720851451),(-18641372370644784450424329589)⟩,⟨(-91349915239884268645802848338),(-91349915239884268241052689829)⟩⟩,⟨⟨(-18737194033204531785754255034),(-18737194033204531382685213245)⟩,⟨(-91217464526630457499287076354),(-91217464526630457094763499075)⟩⟩,⟨⟨(-18864495263550354446779529388),(-18864495263550354044014007508)⟩,⟨(-91040929347502999923913735369),(-91040929347502999519692490190)⟩⟩,⟨⟨(-19022882452445746902187049604),(-19022882452445746499801060497)⟩,⟨(-90820367223531663768731692549),(-90820367223531663364888512382)⟩⟩,⟨⟨(-19211865489258542896466005987),(-19211865489258542494535556134)⟩,⟨(-90555851477144166155391610125),(-90555851477144165752002232702)⟩⟩,⟨⟨(-19430859026796754481927354111),(-19430859026796754080528392568)⟩,⟨(-90247472163663992153767902299),(-90247472163663991750908021264)⟩⟩,⟨⟨(-19679183996596769787955122822),(-19679183996596769387163614403)⟩,⟨(-89895337173283841521804978955),(-89895337173283841119550319178)⟩⟩,⟨⟨(-19956069373197938554111546704),(-19956069373197938154003338487)⟩,⟨(-89499573495017198704131072150),(-89499573495017198302557258225)⟩⟩,⟨⟨(-20260654185616487609098211412),(-20260654185616487209749067073)⟩,⟨(-89060328632825373503374656599),(-89060328632825373102557249344)⟩⟩,⟨⟨(-20591989773877104200337308608),(-20591989773877103801791486118)⟩,⟨(-88577772162863110724143086374),(-88577772162863110324126187569)⟩⟩,⟨⟨(-20949042288068953894112322277),(-20949042288068953496443042164)⟩,⟨(-88052097419589501051356830072),(-88052097419589500652213503840)⟩⟩,⟨⟨(-21330695426961425709750217000),(-21330695426961425313030329431)⟩,⟨(-87483523297359297980955850835),(-87483523297359297582758815651)⟩⟩,⟨⟨(-21735753412741147518970977430),(-21735753412741147123273727912)⟩,⟨(-86872296153049558934495000258),(-86872296153049558537317396568)⟩⟩,⟨⟨(-22162944197914025415467658349),(-22162944197914025020865730338)⟩,⟨(-86218691794294304557201411732),(-86218691794294304161115845751)⟩⟩] +lemma kernel13_0_r5_0_eq : ∀ k : Fin 16, kernel13_0Expr 5 0 k = kernel13_0_r5_0 k := by decide +kernel +noncomputable def kernel13_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-22610922899853116224400515480),(-22610922899853115830967271845)⟩,⟨(-85523017537001940420556119888),(-85523017537001940025635906952)⟩⟩,⟨⟨(-23078275457864609932316393712),(-23078275457864609540124177598)⟩,⟨(-84785614315022579473819168048),(-84785614315022579080136634168)⟩⟩,⟨⟨(-23563522506990356889062137305),(-23563522506990356498184284983)⟩,⟨(-84006858824120934085228242947),(-84006858824120933692856739611)⟩⟩,⟨⟨(-24065123462067233959345103751),(-24065123462067233569853649524)⟩,⟨(-83187165681800591504526685322),(-83187165681800591113538294620)⟩⟩,⟨⟨(-24581480804822962256266572114),(-24581480804822961868235034925)⟩,⟨(-82326989584022370304850498042),(-82326989584022369915318821272)⟩⟩,⟨⟨(-25110944566007278985134689458),(-25110944566007278598634450026)⟩,⟨(-81426827439467806652216678548),(-81426827439467806264213212804)⟩⟩,⟨⟨(-25651816993739893867119872348),(-25651816993739893482224309313)⟩,⟨(-80487220461722928312672142158),(-80487220461722927926270418721)⟩⟩,⟨⟨(-26202357398406439619443179822),(-26202357398406439236223185214)⟩,⟨(-79508756199601148234215932174),(-79508756199601147849487030816)⟩⟩,⟨⟨(-26760787163555399712143041528),(-26760787163555399330672283253)⟩,⟨(-78492070485790626985297042493),(-78492070485790626602314856385)⟩⟩,⟨⟨(-27325294911348215659399123860),(-27325294911348215279747364630)⟩,⟨(-77437849284103518858062445323),(-77437849284103518476896997627)⟩⟩,⟨⟨(-27894041810197566084533591943),(-27894041810197565706774103959)⟩,⟨(-76346830415824215125658032466),(-76346830415824214746382894018)⟩⟩,⟨⟨(-28465167011301931659714682044),(-28465167011301931283916570389)⟩,⟨(-75219805146002450819643070842),(-75219805146002450442327680480)⟩⟩,⟨⟨(-29036793199855362286979074089),(-29036793199855361913215950067)⟩,⟨(-74057619611015662448796802204),(-74057619611015662073515143355)⟩⟩,⟨⟨(-29607032245787726243182357503),(-29607032245787725871503460895)⟩,⟨(-72861176069333239421808575013),(-72861176069333239048621178750)⟩⟩,⟨⟨(-30173990937980995427396807447),(-30173990937980995057830407191)⟩,⟨(-71631433958152481899465653174),(-71631433958152481528427934114)⟩⟩,⟨⟨(-30735776785020055586184278744),(-30735776785020055218796416479)⟩,⟨(-70369410739440522711210292175),(-70369410739440522342389039593)⟩⟩] +lemma kernel13_0_r5_1_eq : ∀ k : Fin 16, kernel13_0Expr 5 1 k = kernel13_0_r5_1 k := by decide +kernel +noncomputable def kernel13_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-31290503864681197326558440018),(-31290503864681196961422245585)⟩,⟨(-69076182519905701287819176171),(-69076182519905700921288222268)⟩⟩,⟨⟨(-31836298703547154509123910032),(-31836298703547154146303196635)⟩,⟨(-67752884430532529159783348607),(-67752884430532528795607156060)⟩⟩,⟨⟨(-32371306167373774263872641574),(-32371306167373773903439534750)⟩,⟨(-66400710752542201847014965130),(-66400710752542201485266261489)⟩⟩,⟨⟨(-32893695342129648486818726013),(-32893695342129648128836307716)⟩,⟨(-65020914777980427480523943575),(-65020914777980427121266357768)⟩⟩,⟨⟨(-33401665384995792037535325978),(-33401665384995791682076519308)⟩,⟨(-63614808394580083788449432390),(-63614808394580083431756385160)⟩⟩,⟨⟨(-33893451324057059762558584494),(-33893451324057059409683540987)⟩,⟨(-62183761386090899247645456870),(-62183761386090898893577539098)⟩⟩,⟨⟨(-34367329784949551716747687661),(-34367329784949551366527858037)⟩,⟨(-60729200440904100796611717434),(-60729200440904100445240768277)⟩⟩,⟨⟨(-34821624622357514974047736060),(-34821624622357514626542211147)⟩,⟨(-59252607863518021173383774692),(-59252607863518020824769213740)⟩⟩,⟨⟨(-35254712433987510580218608250),(-35254712433987510235499985773)⟩,⟨(-57755519985181406206866777831),(-57755519985181405861081479577)⟩⟩,⟨⟨(-35665027934494618907580409908),(-35665027934494618565703633655)⟩,⟨(-56239525271904187842217017637),(-56239525271904187499316140199)⟩⟩,⟨⟨(-36051069166802291374063951425),(-36051069166802291035099165128)⟩,⟨(-54706262129929610737511294845),(-54706262129929610397565143469)⟩⟩,⟨⟨(-36411402528350449778353859623),(-36411402528350449442355024918)⟩,⟨(-53157416410704931572738698634),(-53157416410704931235801333924)⟩⟩,⟨⟨(-36744667590031063479007786595),(-36744667590031063146046021701)⟩,⟨(-51594718619357924587826942125),(-51594718619357924253969527989)⟩⟩,⟨⟨(-37049581685931235740250887074),(-37049581685931235410375220530)⟩,⟨(-50019940832670035656250408730),(-50019940832670035325521955177)⟩⟩,⟨⟨(-37324944252504316995976634503),(-37324944252504316669255143254)⟩,⟨(-48434893334520664638834552124),(-48434893334520664311303064335)⟩⟩,⟨⟨(-37569640896432149785983647132),(-37569640896432149462463978840)⟩,⟨(-46841420978746772944770798450),(-46841420978746772620483789111)⟩⟩] +lemma kernel13_0_r5_2_eq : ∀ k : Fin 16, kernel13_0Expr 5 2 k = kernel13_0_r5_2 k := by decide +kernel +noncomputable def kernel13_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-37782647171227489082616872007),(-37782647171227488762368678213)⟩,⟨(-45241399291303580067545432768),(-45241399291303579746572365824)⟩⟩,⟨⟨(-37963032043554964264603959404),(-37963032043554963947668319604)⟩,⟨(-43636730325511127327153183551),(-43636730325511127009534886947)⟩⟩,⟨⟨(-38109961031320421934284869618),(-38109961031320421620726925545)⟩,⟨(-42029338286013490786281406893),(-42029338286013490472082719189)⟩⟩,⟨⟨(-38222698996789580964997166129),(-38222698996789580654857062687)⟩,⟨(-40421164938848024726735144217),(-40421164938848024415995845819)⟩⟩,⟨⟨(-38300612579343792878023173801),(-38300612579343792571367185267)⟩,⟨(-38814164826707008739021701643),(-38814164826707008431807651960)⟩⟩,⟨⟨(-38343172253958156246221212663),(-38343172253958155943082315506)⟩,⟨(-37210300310059570649751409793),(-37210300310059570346095109994)⟩⟩,⟨⟨(-38349954003088788215032546500),(-38349954003088787915472011491)⟩,⟨(-35611536456274328485165748420),(-35611536456274328185127945549)⟩⟩,⟨⟨(-38320640591373915532919403109),(-38320640591373915236968739879)⟩,⟨(-34019835800229981585725532760),(-34019835800229981289337156029)⟩⟩,⟨⟨(-38255022434378554061346577416),(-38255022434378553769068999269)⟩,⟨(-32437153001109937615406103385),(-32437153001109937322729739579)⟩⟩,⟨⟨(-38152998054534627766187232878),(-38152998054534627477605242002)⟩,⟨(-30865429421136679238894641295),(-30865429421136678949952111610)⟩⟩,⟨⟨(-38014574119436013572216822426),(-38014574119436013287308510842)⟩,⟨(-29306587652901602518443547960),(-29306587652901602233212167604)⟩⟩,⟨⟨(-37839865059728692811614161572),(-37839865059728692529809097480)⟩,⟨(-27762526022677227293926836815),(-27762526022677227011835005505)⟩⟩,⟨⟨(-37629092265976468273202913362),(-37629092265976467994568177865)⟩,⟨(-26235113097652905023841748610),(-26235113097652904744955744154)⟩⟩,⟨⟨(-37382582866068216953382783890),(-37382582866068216677940729694)⟩,⟨(-24726182225405639200413322968),(-24726182225405638924754649947)⟩⟩,⟨⟨(-37100768086948282025227198323),(-37100768086948281753039266175)⟩,⟨(-23237526134098977129354834518),(-23237526134098976856984049413)⟩⟩,⟨⟨(-36784181206681621290389285274),(-36784181206681621021477920195)⟩,⟨(-21770891621891181927071724426),(-21770891621891181658010348956)⟩⟩] +lemma kernel13_0_r5_3_eq : ∀ k : Fin 16, kernel13_0Expr 5 3 k = kernel13_0_r5_3 k := by decide +kernel +noncomputable def kernel13_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-36433455105093487683564316034),(-36433455105093487417995130570)⟩,⟨(-20327974363826632775871274836),(-20327974363826632510183965754)⟩⟩,⟨⟨(-36049319423433137158372647292),(-36049319423433136896157698501)⟩,⟨(-18910413864080796886986125326),(-18910413864080796624683950063)⟩⟩,⟨⟨(-35632597345685563544382543494),(-35632597345685563285579413921)⟩,⟨(-17519788580829958666161317327),(-17519788580829958407300840475)⟩⟩,⟨⟨(-35184202016277736992628896675),(-35184202016277736737251104164)⟩,⟨(-16157611250224617277111323558),(-16157611250224617021705017656)⟩⟩,⟨⟨(-34705132610979588731512432272),(-34705132610979588479620624224)⟩,⟨(-14825324434964163597644428501),(-14825324434964163345751871244)⟩⟩,⟨⟨(-34196470079768649230822129976),(-34196470079768648982419550259)⟩,⟨(-13524296321805855240993682011),(-13524296321805854992617026777)⟩⟩,⟨⟨(-33659372582294876515739883442),(-33659372582294876270879172921)⟩,⟨(-12255816791000573646230840771),(-12255816791000573401421617982)⟩⟩,⟨⟨(-33095070638333494201076416694),(-33095070638333493959761338322)⟩,⟨(-11021093779140291367102797646),(-11021093779140291125863645582)⟩⟩,⟨⟨(-32504862017234062981534752505),(-32504862017234062743822436943)⟩,⟨(-9821249955238031275970205774),(-9821249955238031038357114458)⟩⟩,⟨⟨(-31890106391849936832169960100),(-31890106391849936598051594618)⟩,⟨(-8657319728052224003068867735),(-8657319728052223769071877338)⟩⟩,⟨⟨(-31252219783751187896211299303),(-31252219783751187665733595703)⟩,⟨(-7530246600726963075684901162),(-7530246600726962845349564900)⟩⟩,⟨⟨(-30592668827674720176325169097),(-30592668827674719949481546277)⟩,⟨(-6440880886762142060907492297),(-6440880886762141834226070090)⟩⟩,⟨⟨(-29912964884137671528054038949),(-29912964884137671304894509528)⟩,⟨(-5389977799168358526068192912),(-5389977799168358303089530887)⟩⟩,⟨⟨(-29214658029925819921629564809),(-29214658029925819702135533929)⟩,⟨(-4378195922417272613842000578),(-4378195922417272394546345339)⟩⟩,⟨⟨(-28499330956760609313252358704),(-28499330956760609097463773117)⟩,⟨(-3406096074486113272528573376),(-3406096074486113056954709814)⟩⟩,⟨⟨(-27768592808841272802888071992),(-27768592808841272590787698467)⟩,⟨(-2474140563933185430581525483),(-2474140563933185218711071875)⟩⟩] +lemma kernel13_0_r5_4_eq : ∀ k : Fin 16, kernel13_0Expr 5 4 k = kernel13_0_r5_4 k := by decide +kernel +noncomputable def kernel13_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-27024072990148735643783658038),(-27024072990148735435416823902)⟩,⟨(-1582692844547983817973861415),(-1582692844547983609850996443)⟩⟩,⟨⟨(-26267414972383654699357190155),(-26267414972383654494677769502)⟩,⟨(-732017567713610180202578279),(-732017567713609975780029233)⟩⟩,⟨⟨(-25500270134191996518051761496),(-25500270134191996317039537864)⟩,⟨77718969780503679138054867,77718969780503879881701723⟩⟩,⟨⟨(-24724291661909661248498261673),(-24724291661909661051127867910)⟩,⟨846447987112220941218990897,846447987112221138310192457⟩⟩,⟨⟨(-23941128541436287902555736335),(-23941128541436287708865986834)⟩,⟨1574196996954357288493064470,1574196996954357481894089506⟩⟩,⟨⟨(-23152419670032738490877304143),(-23152419670032738300829927682)⟩,⟨2261088208393288271651265504,2261088208393288461401433552⟩⟩,⟨⟨(-22359788115833763263794349086),(-22359788115833763077416717147)⟩,⟨2907336566665281130790840815,2907336566665281316863819198⟩⟩,⟨⟨(-21564835551685537172652670280),(-21564835551685536989909157269)⟩,⟨3513247443230993171800488521,3513247443230993354232904338⟩⟩,⟨⟨(-20769136888567215825689944932),(-20769136888567215646613806691)⟩,⟨4079213991690169817085919255,4079213991690169995845507001⟩⟩,⟨⟨(-19974235132347919523059106825),(-19974235132347919347504620618)⟩,⟨4605714186893283293670827204,4605714186893283468904252497⟩⟩,⟨⟨(-19181636485978475420350426812),(-19181636485978475248318707745)⟩,⟨5093307566321091927955055169,5093307566321092099662133411⟩⟩,⟨⟨(-18392805717434884655391803360),(-18392805717434884486842076263)⟩,⟨5542631694364632915107031604,5542631694364633083329422424⟩⟩,⟨⟨(-17609161811832937950552471726),(-17609161811832937785513209643)⟩,⟨5954398371536211655094490711,5954398371536211819804590642⟩⟩,⟨⟨(-16832073924136679058620982699),(-16832073924136678897038346352)⟩,⟨6329389611867298277110113306,6329389611867298438362577113⟩⟩,⟨⟨(-16062857646804239644260677042),(-16062857646804239486150969196)⟩,⟨6668453412794301720427308203,6668453412794301878206632613⟩⟩,⟨⟨(-15302771604570229084627558042),(-15302771604570228929927836498)⟩,⟨6972499342692073484468774413,6972499342692073638857049199⟩⟩] +lemma kernel13_0_r5_5_eq : ∀ k : Fin 16, kernel13_0Expr 5 5 k = kernel13_0_r5_5 k := by decide +kernel +noncomputable def kernel13_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-14553014386372026882335546396),(-14553014386372026731067787137)⟩,⟨7242493971883542531002602988,7242493971883542681980584576⟩⟩,⟨⟨(-13814721822205864450902202946),(-13814721822205864303002147259)⟩,⟨7479456173429702832890228449,7479456173429702980521520386⟩⟩,⟨⟨(-13088964610465389339098239716),(-13088964610465389194575440031)⟩,⟨7684452320286628203015462210,7684452320286628347289860713⟩⟩,⟨⟨(-12376746299088214369878080664),(-12376746299088214228675631940)⟩,⟨7858591405506379939772537868,7858591405506380080746269165⟩⟩,⟨⟨(-11679001621632171424943944879),(-11679001621632171287076319163)⟩,⟨8003020112059412038689246692,8003020112059412176347165104⟩⟩,⟨⟨(-10996595187239519651807790142),(-10996595187239519517205594802)⟩,⟨8118917858571828102780479827,8118917858571828237191279174⟩⟩,⟨⟨(-10330320521340445000797359601),(-10330320521340444869462804684)⟩,⟨8207491846807644820142254543,8207491846807644951303033736⟩⟩,⟨⟨(-9680899451912264772673328574),(-9680899451912264644542573412)⟩,⟨8269972136091601115525119143,8269972136091601243499011985⟩⟩,⟨⟨(-9048981834162298401190704712),(-9048981834162298276118611615)⟩,⟨8307606769070939599653531581,8307606769070939724584984892⟩⟩,⟨⟨(-8435145604653787011147987068),(-8435145604653786889012233119)⟩,⟨8321656972265168233503555246,8321656972265168355514182496⟩⟩,⟨⟨(-7839897154157751823752075149),(-7839897154157751704557918014)⟩,⟨8313392453762417660647618737,8313392453762417779731462436⟩⟩,⟨⟨(-7263672006900200120852451024),(-7263672006900200004539919431)⟩,⟨8284086819201978995646773152,8284086819201979111863100069⟩⟩,⟨⟨(-6706835792393173881430130483),(-6706835792393173768009915871)⟩,⟨8235013125848129562816469599,8235013125848129676153896437⟩⟩,⟨⟨(-6169685494697915079227151198),(-6169685494697914968627692725)⟩,⟨8167439593124324410078192107,8167439593124324520607586611⟩⟩,⟨⟨(-5652450962775539432692594918),(-5652450962775539324912762265)⟩,⟨8082625486453688744171255909,8082625486453688851893069486⟩⟩,⟨⟨(-5155296664540206610246195805),(-5155296664540206505221026823)⟩,⟨7981817189656315417973027077,7981817189656315522951548192⟩⟩] +lemma kernel13_0_r5_6_eq : ∀ k : Fin 16, kernel13_0Expr 5 6 k = kernel13_0_r5_6 k := by decide +kernel +noncomputable def kernel13_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-4678323666345470803570041346),(-4678323666345470701306687511)⟩,⟨7866244479501202235987284174,7866244479501202338214702409⟩⟩,⟨⟨(-4221571818908400324160890829),(-4221571818908400224572383619)⟩,⟨7737117014315873162975476369,7737117014315873262538060358⟩⟩,⟨⟨(-3785022130108788148619964982),(-3785022130108788051681167444)⟩,⟨7595621046834845016469081104,7595621046834845113391226999⟩⟩,⟨⟨(-3368599304691506122848422235),(-3368599304691506028492288434)⟩,⟨7442916369733919675862835107,7442916369733919770210978351⟩⟩,⟨⟨(-2972174430646555864031126085),(-2972174430646555772258317797)⟩,⟨7280133500565215301870287271,7280133500565215393643170929⟩⟩,⟨⟨(-2595567791940082087356685649),(-2595567791940081998090071135)⟩,⟨7108371111091800466958865096,7108371111091800556233042453⟩⟩,⟨⟨(-2238551787315733136494619303),(-2238551787315733049724032091)⟩,⟨6928693704334028951005378913,6928693704334029037790453691⟩⟩,⟨⟨(-1900853935073315850827370566),(-1900853935073315766483330539)⟩,⟨6742129540994709200998862390,6742129540994709285363771355⟩⟩,⟨⟨(-1582159944053678946432210932),(-1582159944053678864458616758)⟩,⟨6549668815338752630255970989,6549668815338752712256287203⟩⟩,⟨⟨(-1282116831507206432546756576),(-1282116831507206352847607641)⟩,⟨6352262079075666354321862487,6352262079075666434053081212⟩⟩,⟨⟨(-1000336069089416385596497480),(-1000336069089416308161656008)⟩,⟨6150818910339918582762386478,6150818910339918660234155035⟩⟩,⟨⟨(-736396738901438618664069689),(-736396738901438543426838132)⟩,⟨5946206823493472212212740108,5946206823493472287491289271⟩⟩,⟨⟨(-489848682265501644539309614),(-489848682265501571495647415)⟩,⟨5739250414194206447702201107,5739250414194206520791118720⟩⟩,⟨⟨(-260215624785451393059419988),(-260215624785451322134061653)⟩,⟨5530730732989937954732060461,5530730732989938025706186029⟩⟩,⟨⟨(-46998262178876281923579893),(-46998262178876213102853346)⟩,⟨5321384879615564277210307148,5321384879615564346082900137⟩⟩,⟨⟨150322707630456939297969134,150322707630457006081183874⟩,⟨5111905809194574141236561038,5111905809194574208074354989⟩⟩] +lemma kernel13_0_r5_7_eq : ∀ k : Fin 16, kernel13_0Expr 5 7 k = kernel13_0_r5_7 k := by decide +kernel +noncomputable def kernel13_0_r5_8 : Fin 16 → CBox := ![⟨⟨332283619614612992624856156,332283619614613057380551767⟩,⟨4902942340678742220404844447,4902942340678742285217457387⟩⟩,⟨⟨499434956292888817061202382,499434956292888879897873076⟩,⟨4695099357103062520054789452,4695099357103062582950370652⟩⟩,⟨⟨652338553155462649707003452,652338553155462710638719854⟩,⟨4488938186587593901344274144,4488938186587593962336559913⟩⟩,⟨⟨791564904928532721489701052,791564904928532780580692191⟩,⟨4284977152483564259209022860,4284977152483564318361934965⟩⟩,⟨⟨917690581585447790148362276,917690581585447847406540482⟩,⟨4083692280636483762047932455,4083692280636483819369085631⟩⟩,⟨⟨1031295761842443612561193252,1031295761842443668057747087⟩,⟨3885518151421899211111936778,3885518151421899266672251524⟩⟩,⟨⟨1132961890720025933949093719,1132961890720025987713441137⟩,⟨3690848883996667896344486755,3690848883996667950173116502⟩⟩,⟨⟨1223269466610665984903293901,1223269466610666037002987891⟩,⟨3500039240096343751352876162,3500039240096343803517139657⟩⟩,⟨⟨1302795962178544893660638695,1302795962178544944102613173⟩,⟨3313405834692852393466043525,3313405834692852443972649219⟩⟩,⟨⟨1372113882335157943748268640,1372113882335157992602244111⟩,⟨3131228440900868618275801222,3131228440900868667194273606⟩⟩,⟨⟨1431788961492502071638040594,1431788961492502118928128781⟩,⟨2953751376680453636684931671,2953751376680453684034776077⟩⟩,⟨⟨1482378501299400897779420416,1482378501299400943565062992⟩,⟨2781184961121371187477499135,2781184961121371233318072348⟩⟩,⟨⟨1524429849121580044687324638,1524429849121580088978158112⟩,⟨2613707028404539009292029640,2613707028404539053633178295⟩⟩,⟨⟨1558479016636920909158387324,1558479016636920952018817869⟩,⟨2451464487911475345157718624,2451464487911475388064067332⟩⟩,⟨⟨1585049437087643949461482930,1585049437087643990908032362⟩,⟨2294574919386377311532563744,2294574919386377353020841555⟩⟩,⟨⟨1604650858963984090136661945,1604650858963984130225625336⟩,⟨2143128192540526777472815130,2143128192540526817599527909⟩⟩] +lemma kernel13_0_r5_8_eq : ∀ k : Fin 16, kernel13_0Expr 5 8 k = kernel13_0_r5_8 k := by decide +kernel +noncomputable def kernel13_0_r5_9 : Fin 16 → CBox := ![⟨⟨1617778373191450390705363472,1617778373191450429445384449⟩,⟨1997188101017945004500015794,1997188101017945043274007019⟩⟩,⟨⟨1624911570257512038630865558,1624911570257512076085107716⟩,⟨1856794001207545549522926698,1856794001207545587007563763⟩⟩,⟨⟨1626513823144329789658594854,1626513823144329825843906547⟩,⟨1721962446983520484459890332,1721962446983520520672214568⟩⟩,⟨⟨1623031691432104488034150517,1623031691432104523003671479⟩,⟨1592688812075573621561992632,1592688812075573656555336522⟩⟩,⟨⟨1614894441502274115429945446,1614894441502274149194825327⟩,⟨1468948892407359316270092358,1468948892407359350055788567⟩⟩,⟨⟨1602513677400119451429532077,1602513677400119484047049585⟩,⟨1350700481388856916902422347,1350700481388856949537932030⟩⟩,⟨⟨1586283076610776382420657018,1586283076610776413907486761⟩,⟨1237884911800499883596789119,1237884911800499915098959982⟩⟩,⟨⟨1566578224759171385850201446,1566578224759171416255944266⟩,⟨1130428558558142910804376466,1130428558558142941222979399⟩⟩,⟨⟨1543756543060551020978443200,1543756543060551050312849970⟩,⟨1028244297293244989710084532,1028244297293245019055031951⟩⟩,⟨⟨1518157302221259879489202586,1518157302221259907806919893⟩,⟨931232914317246602346097915,931232914317246630672194608⟩⟩,⟨⟨1490101716416120419969904868,1490101716416120447287034193⟩,⟨839284464158738008502496906,839284464158738035825994581⟩⟩,⟨⟨1459893110945814709789267696,1459893110945814736151611545⟩,⟨752279571462814169430091618,752279571462814195796937996⟩⟩,⟨⟨1427817157201493429553513648,1427817157201493454971932073⟩,⟨670090674620605162804657251,670090674620605188225850705⟩⟩,⟨⟨1394142168630722314034830787,1394142168630722338558184933⟩,⟨592583209050427250102774533,592583209050427274627308943⟩⟩,⟨⟨1359119451504999552278510261,1359119451504999575922014862⟩,⟨519616728577835443570186451,519616728577835467213403038⟩⟩,⟨⟨1322983704430562863813325643,1322983704430562886726831482⟩,⟨451045963858028173428337485,451045963858028196340232336⟩⟩] +lemma kernel13_0_r5_9_eq : ∀ k : Fin 16, kernel13_0Expr 5 9 k = kernel13_0_r5_9 k := by decide +kernel +noncomputable def kernel13_0_r5_10 : Fin 16 → CBox := ![⟨⟨1285953460717162612073535021,1285953460717162634270042557⟩,⟨386721817248937604292316436,386721817248937626486005754⟩⟩,⟨⟨1248231567920045028753722707,1248231567920045050271430245⟩,⟨326492293975721390072501911,326492293975721411586289875⟩⟩,⟨⟨1210005699094768296518036820,1210005699094768317363153696⟩,⟨270203369826425728792542686,270203369826425749632739998⟩⟩,⟨⟨1171448890548960619736703450,1171448890548960639940103094⟩,⟨217699795983851320882021598,217699795983851341079596356⟩⟩,⟨⟨1132720101136144987929966738,1132720101136145007493703445⟩,⟨168825841929997188468761213,168825841929997208025858681⟩⟩,⟨⟨1093964788410871391952248281,1093964788410871410910408345⟩,⟨123425977657067479581582227,123425977657067498532372297⟩⟩,⟨⟨1055315497248356219510014166,1055315497248356237868796637⟩,⟨81345496683371855681574328,81345496683371874032336573⟩⟩,⟨⟨1016892456822561630875424520,1016892456822561648663476881⟩,⟨42431081604253932612211932,42431081604253950391667537⟩⟩,⟨⟨978804182131288913204193298,978804182131288930422644141⟩,⟨6531314108393204460970244,6531314108393221670319309⟩⟩,⟨⟨941148076552756564815130677,941148076552756581496627210⟩,⟨(-26502868440410719768539954),(-26502868440410703096586495)⟩⟩,⟨⟨904011032212854366901064584,904011032212854383051593386⟩,⟨(-56817767615233394189297011),(-56817767615233378048690479)⟩⟩,⟨⟨867470025233602199462242372,867470025233602215108148972⟩,⟨(-84556567378113036744540528),(-84556567378113021108879926)⟩⟩,⟨⟨831592703219316591625110366,831592703219316606768601579⟩,⟨(-109859023931706713310259903),(-109859023931706698177284027)⟩⟩,⟨⟨796437962615844060471082823,796437962615844075141079046⟩,⟨(-132861199467613042363627158),(-132861199467613027704368651)⟩⟩,⟨⟨762056513848425171814945838,762056513848425186017066243⟩,⟨(-153695237268819309444628281),(-153695237268819295253421578)⟩⟩,⟨⟨728491432403990267388143211,728491432403990281146433071⟩,⟨(-172489175605069608912343408),(-172489175605069595165103095)⟩⟩] +lemma kernel13_0_r5_10_eq : ∀ k : Fin 16, kernel13_0Expr 5 10 k = kernel13_0_r5_10 k := by decide +kernel +noncomputable def kernel13_0_r5_11 : Fin 16 → CBox := ![⟨⟨695778694272849236271619126,695778694272849249586939203⟩,⟨(-189366797860487935749021168),(-189366797860487922444846184)⟩⟩,⟨⟨663947694401915906971447157,663947694401915919871385926⟩,⟨(-204447516350745024839956640),(-204447516350745011951225676)⟩⟩,⟨⟨633021747036084788068837638,633021747036084800558546755⟩,⟨(-217846287320665614529882170),(-217846287320665602051410160)⟩⟩,⟨⟨603018567035614754211677378,603018567035614766312946880⟩,⟨(-229673554660701081067108669),(-229673554660701068977077906)⟩⟩,⟨⟨573950731454998130916740773,573950731454998142631360067⟩,⟨(-240035219940454027302064752),(-240035219940454015598657349)⟩⟩,⟨⟨545826120852585581064926911,545826120852585592416794519⟩,⟨(-249032636427806799899372311),(-249032636427806788558667883)⟩⟩,⟨⟨518648339970119134774328319,518648339970119145768531342⟩,⟨(-256762624841612873522465442),(-256762624841612862538779839)⟩⟩,⟨⟨492417117577347077359563827,492417117577347088015781294⟩,⟨(-263317508672872137665570201),(-263317508672872127019154373)⟩⟩,⟨⟨467128685419218961624943900,467128685419218971943773241⟩,⟨(-268785167002424305294548536),(-268785167002424294984837223)⟩⟩,⟨⟨442776136332051666545647541,442776136332051676549469858⟩,⟨(-273249102841142388998575234),(-273249102841142379003222361)⟩⟩,⟨⟨419349761710871462811472432,419349761710871472504858690⟩,⟨(-276788525120165069171698146),(-276788525120165059486163837)⟩⟩,⟨⟨396837368613301658456943980,396837368613301667859513706⟩,⟨(-279478442562740888402153388),(-279478442562740879006850842)⟩⟩,⟨⟨375224576876373761678211882,375224576876373770790864436⟩,⟨(-281389767774731175694046852),(-281389767774731166588105282)⟩⟩,⟨⟨354495096702038023312837119,354495096702038032154761326⟩,⟨(-282589429996789594859367762),(-282589429996789586023628565)⟩⟩,⟨⟨334630987235524464607695737,334630987235524473182191914⟩,⟨(-283140495066854901274493001),(-283140495066854892705682807)⟩⟩,⟨⟨315612896718677768790909412,315612896718677777113523853⟩,⟨(-283102291246102197606491957),(-283102291246102189289092002)⟩⟩] +lemma kernel13_0_r5_11_eq : ∀ k : Fin 16, kernel13_0Expr 5 11 k = kernel13_0_r5_11 k := by decide +kernel +noncomputable def kernel13_0_r5_12 : Fin 16 → CBox := ![⟨⟨297420284848601148579410630,297420284848601156649772607⟩,⟨(-282530539664228019745946499),(-282530539664228011680352069)⟩⟩,⟨⟨280031628011052169148777013,280031628011052176985333608⟩,⟨(-281477488240313006322671984),(-281477488240312998490461714)⟩⟩,⟨⟨263424608088700734330397896,263424608088700741938894652⟩,⟨(-279992048033011674868168958),(-279992048033011667263620269)⟩⟩,⟨⟨247576285567248898660993633,247576285567248906055076836⟩,⟨(-278119931068038598251232196),(-278119931068038590860721922)⟩⟩,⟨⟨232463257678180218333095714,232463257678180225512797151⟩,⟨(-275903788781503815360169655),(-275903788781503808183686871)⟩⟩,⟨⟨218061802326197482940836514,218061802326197489921418905⟩,⟨(-273383350304315697938963042),(-273383350304315690961266284)⟩⟩,⟨⟨204348008552849821124252140,204348008552849827907833390⟩,⟨(-270595559895398143071102136),(-270595559895398136290092722)⟩⟩,⟨⟨191297894286050789814182002,191297894286050796412936585⟩,⟨(-267574712909700560815700032),(-267574712909700554219222543)⟩⟩,⟨⟨178887512118731787100237082,178887512118731793513282293⟩,⟨(-264352589760806573325943158),(-264352589760806566914897616)⟩⟩,⟨⟨167093043849317147723307802,167093043849317153965003116⟩,⟨(-260958587407311699146022753),(-260958587407311692906067056)⟩⟩,⟨⟨155890884502577195901593934,155890884502577201973646354⟩,⟨(-257419847957025850509115416),(-257419847957025844438558387)⟩⟩,⟨⟨145257716532211817560112650,145257716532211823473368833⟩,⟨(-253761384043485927181319404),(-253761384043485921269329831)⟩⟩,⟨⟨135170574886707042847364062,135170574886707048601317057⟩,⟨(-250006200685293634506908830),(-250006200685293628754007885)⟩⟩,⟨⟨125606903598026127636723322,125606903598026133243686411⟩,⟨(-246175413390509728889297049),(-246175413390509723283185344)⟩⟩,⟨⟨116544604528948039474314360,116544604528948044936740965⟩,⟨(-242288362315849197140595445),(-242288362315849191678832409)⟩⟩,⟨⟨107962078889721469986901434,107962078889721475316206514⟩,⟨(-238362722333864606821163147),(-238362722333864601492346138)⟩⟩] +lemma kernel13_0_r5_12_eq : ∀ k : Fin 16, kernel13_0Expr 5 12 k = kernel13_0_r5_12 k := by decide +kernel +noncomputable def kernel13_0_r5_13 : Fin 16 → CBox := ![⟨⟨99838262108501344521716774,99838262108501349716256696⟩,⟨(-234414608900826732110770030),(-234414608900826726916554194)⟩⟩,⟨⟨92152652613086243807301931,92152652613086248878710391⟩,⟨(-230458679653776363487378547),(-230458679653776358416141153)⟩⟩,⟨⟨84885335054058194220132829,84885335054058199169237768⟩,⟨(-226508231697403688562369604),(-226508231697403683613293014)⟩⟩,⟨⟨78016998471791054467835611,78016998471791059303108656⟩,⟨(-222575294570194593250323583),(-222575294570194588414945848)⟩⟩,⟨⟨71528949882162734628777070,71528949882162739349102399⟩,⟨(-218670718904854947426886265),(-218670718904854942706332429)⟩⟩,⟨⟨65403123728375971571605840,65403123728375976186852494⟩,⟨(-214804260820575806638102078),(-214804260820575802022511601)⟩⟩,⟨⟨59622087619233786088586455,59622087619233790599319246⟩,⟨(-210984662104426927009710063),(-210984662104426922498526305)⟩⟩,⟨⟨54169044747677196452726258,54169044747677200866542387⟩,⟨(-207219726256254716672401492),(-207219726256254712258034739)⟩⟩,⟨⟨49027833357500651424503361,49027833357500655739610975⟩,⟨(-203516390486103013309082097),(-203516390486103008993331545)⟩⟩,⟨⟨44182923601021185861660116,44182923601021190087546807⟩,⟨(-199880793765556408316914550),(-199880793765556404090299070)⟩⟩,⟨⟨39619412106178097237184241,39619412106178101374563507⟩,⟨(-196318341044706834388057094),(-196318341044706830249870933)⟩⟩,⟨⟨35323014548151529841941898,35323014548151533897814107⟩,⟨(-192833763754839502302882507),(-192833763754839498246131586)⟩⟩,⟨⟨31280056498165725150277318,31280056498165729123193435⟩,⟨(-189431176723592032512047203),(-189431176723592028538186194)⟩⟩,⟨⟨27477462800726760454505173,27477462800726764352608502⟩,⟨(-186114131634421479794418685),(-186114131634421475895309018)⟩⟩,⟨⟨23902745710163598313075255,23902745710163602136480176⟩,⟨(-182885667165870798756546589),(-182885667165870794932078766)⟩⟩,⟨⟨20543991998012138395516655,20543991998012142150367117⟩,⟨(-179748355948503906446227616),(-179748355948503902690261854)⟩⟩] +lemma kernel13_0_r5_13_eq : ∀ k : Fin 16, kernel13_0Expr 5 13 k = kernel13_0_r5_13 k := by decide +kernel +noncomputable def kernel13_0_r5_14 : Fin 16 → CBox := ![⟨⟨17389849224511606413010815,17389849224511610097116174⟩,⟨(-176704348478613259306345283),(-176704348478613255621076689)⟩⟩,⟨⟨14429511350269120973797010,14429511350269124595271595⟩,⟨(-173755414128023683318469253),(-173755414128023679695786915)⟩⟩,⟨⟨11652703847982059126981541,11652703847982062685786054⟩,⟨(-170902979388640474626001692),(-170902979388640471065948679)⟩⟩,⟨⟨9049668458972684104376233,9049668458972687606091104⟩,⟨(-168148163488929465838035989),(-168148163488929462335034930)⟩⟩,⟨⟨6611147725163554151177777,6611147725163557594145700⟩,⟨(-165491811517374444010599303),(-165491811517374440566310952)⟩⟩,⟨⟨4328369413978910261614697,4328369413978913652743391⟩,⟨(-162934525185227481600013891),(-162934525185227478207532993)⟩⟩,⟨⟨2193030941466042753566173,2193030941466046092690521⟩,⟨(-160476691357636963679880352),(-160476691357636960339374918)⟩⟩,⟨⟨197283887657898841858788,197283887657902134082677⟩,⟨(-158118508478585292592588010),(-158118508478585289298956354)⟩⟩,⟨⟨(-1666281312192230438174898),(-1666281312192227195046603)⟩,⟨(-155860011011065025393357608),(-155860011011065022148797600)⟩⟩,⟨⟨(-3404650426419238628802356),(-3404650426419235427871108)⟩,⟨(-153701092009633153848276240),(-153701092009633150645890979)⟩⟩,⟨⟨(-5024400170454441738987838),(-5024400170454438580514947)⟩,⟨(-151641523937966324864402687),(-151641523937966321704455702)⟩⟩,⟨⟨(-6531712577666501077931614),(-6531712577666497957216047)⟩,⟨(-149680977839346685498799562),(-149680977839346682376591359)⟩⟩,⟨⟨(-7932388947420422977111481),(-7932388947420419895953193)⟩,⟨(-147819040963184460639156841),(-147819040963184457556489483)⟩⟩,⟨⟨(-9231863326809110243667009),(-9231863326809107196022370)⟩,⟨(-146055232945769517365010970),(-146055232945769514315841933)⟩⟩,⟨⟨(-10435215488438186660090522),(-10435215488438183646292221)⟩,⟨(-144389020638475030945815430),(-144389020638475027930479104)⟩⟩,⟨⟨(-11547183371968229174497571),(-11547183371968226190176498)⟩,⟨(-142819831671642107506683762),(-142819831671642104520812081)⟩⟩] +lemma kernel13_0_r5_14_eq : ∀ k : Fin 16, kernel13_0Expr 5 14 k = kernel13_0_r5_14 k := by decide +kernel +noncomputable def kernel13_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-12572174961878413396144086),(-12572174961878410443718438)⟩,⟨(-141347066837380523511121959),(-141347066837380520557134865)⟩⟩,⟨⟨(-13514279578150310671632070),(-13514279578150307744797373)⟩,⟨(-139970111369549163981853623),(-139970111369549161053447242)⟩⟩,⟨⟨(-14377278560317546608950354),(-14377278560317543708083795)⟩,⟨(-138688345194248025607236226),(-138688345194248022704789065)⟩⟩,⟨⟨(-15164655328622489201287042),(-15164655328622486322291909)⟩,⟨(-137501152219276055968587568),(-137501152219276053088003598)⟩⟩,⟨⟨(-15879604808900122850474175),(-15879604808900119995238972)⟩,⟨(-136407928726196697827288224),(-136407928726196694970457312)⟩⟩,⟨⟨(-16525042210305577280365761),(-16525042210305574443399676)⟩,⟨(-135408090923913971993092492),(-135408090923913969154524185)⟩⟩,⟨⟨(-17103611147147941379716119),(-17103611147147938561418879)⟩,⟨(-134501081718001810972921811),(-134501081718001808153016884)⟩⟩,⟨⟨(-17617691097920257603706594),(-17617691097920254800194565)⟩,⟨(-133686376745451326978372883),(-133686376745451324173248139)⟩⟩,⟨⟨(-18069404196153971045631298),(-18069404196153968259033974)⟩,⟨(-132963489720005812034624451),(-132963489720005809246410588)⟩⟩,⟨⟨(-18460621349004399577811602),(-18460621349004396802139989)⟩,⟨(-132331977128840674898539571),(-132331977128840672121247683)⟩⟩,⟨⟨(-18792967680519643679023168),(-18792967680519640914743035)⟩,⟨(-131791442317012680404328206),(-131791442317012677638424934)⟩⟩,⟨⟨(-19067827297385327142057954),(-19067827297385324385515267)⟩,⟨(-131341538991845744787564971),(-131341538991845742029396575)⟩⟩,⟨⟨(-19286347375597205170366611),(-19286347375597202423564096)⟩,⟨(-130981974175233825683355152),(-130981974175233822934925377)⟩⟩,⟨⟨(-19449441567017629519388801),(-19449441567017626777181144)⟩,⟨(-130712510627718671875899817),(-130712510627718669132063393)⟩⟩,⟨⟨(-19557792725143935202654698),(-19557792725143932465479713)⟩,⟨(-130532968764133946387081928),(-130532968764133943648277445)⟩⟩,⟨⟨(-19611854949680108891262868),(-19611854949680106155576892)⟩,⟨(-130443228076589281697046665),(-130443228076589278959730690)⟩⟩] +lemma kernel13_0_r5_15_eq : ∀ k : Fin 16, kernel13_0Expr 5 15 k = kernel13_0_r5_15 k := by decide +kernel +noncomputable def kernel13_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel13_0_r5_0,kernel13_0_r5_1,kernel13_0_r5_2,kernel13_0_r5_3,kernel13_0_r5_4,kernel13_0_r5_5,kernel13_0_r5_6,kernel13_0_r5_7,kernel13_0_r5_8,kernel13_0_r5_9,kernel13_0_r5_10,kernel13_0_r5_11,kernel13_0_r5_12,kernel13_0_r5_13,kernel13_0_r5_14,kernel13_0_r5_15] +lemma kernel13_0_r5_eq (i k : Fin 16) : kernel13_0Expr 5 i k = kernel13_0_r5 i k := by + fin_cases i + · exact kernel13_0_r5_0_eq k + · exact kernel13_0_r5_1_eq k + · exact kernel13_0_r5_2_eq k + · exact kernel13_0_r5_3_eq k + · exact kernel13_0_r5_4_eq k + · exact kernel13_0_r5_5_eq k + · exact kernel13_0_r5_6_eq k + · exact kernel13_0_r5_7_eq k + · exact kernel13_0_r5_8_eq k + · exact kernel13_0_r5_9_eq k + · exact kernel13_0_r5_10_eq k + · exact kernel13_0_r5_11_eq k + · exact kernel13_0_r5_12_eq k + · exact kernel13_0_r5_13_eq k + · exact kernel13_0_r5_14_eq k + · exact kernel13_0_r5_15_eq k +noncomputable def kernel13_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel13_0_r0,kernel13_0_r1,kernel13_0_r2,kernel13_0_r3,kernel13_0_r4,kernel13_0_r5] +lemma kernel13_0_eq (j : Fin 6) (i k : Fin 16) : kernel13_0Expr j i k = kernel13_0 j i k := by + fin_cases j + · exact kernel13_0_r0_eq i k + · exact kernel13_0_r1_eq i k + · exact kernel13_0_r2_eq i k + · exact kernel13_0_r3_eq i k + · exact kernel13_0_r4_eq i k + · exact kernel13_0_r5_eq i k +lemma kernel13_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel13_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(13:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel13_0_eq] + unfold kernel13_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans13_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel13_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans13 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel13_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r0_0_eq : ∀ k : Fin 16, kernel13_1Expr 0 0 k = kernel13_1_r0_0 k := by decide +kernel +noncomputable def kernel13_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r0_1_eq : ∀ k : Fin 16, kernel13_1Expr 0 1 k = kernel13_1_r0_1 k := by decide +kernel +noncomputable def kernel13_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r0_2_eq : ∀ k : Fin 16, kernel13_1Expr 0 2 k = kernel13_1_r0_2 k := by decide +kernel +noncomputable def kernel13_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r0_3_eq : ∀ k : Fin 16, kernel13_1Expr 0 3 k = kernel13_1_r0_3 k := by decide +kernel +noncomputable def kernel13_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r0_4_eq : ∀ k : Fin 16, kernel13_1Expr 0 4 k = kernel13_1_r0_4 k := by decide +kernel +noncomputable def kernel13_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel13_1_r0_5_eq : ∀ k : Fin 16, kernel13_1Expr 0 5 k = kernel13_1_r0_5 k := by decide +kernel +noncomputable def kernel13_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel13_1_r0_6_eq : ∀ k : Fin 16, kernel13_1Expr 0 6 k = kernel13_1_r0_6 k := by decide +kernel +noncomputable def kernel13_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel13_1_r0_7_eq : ∀ k : Fin 16, kernel13_1Expr 0 7 k = kernel13_1_r0_7 k := by decide +kernel +noncomputable def kernel13_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel13_1_r0_8_eq : ∀ k : Fin 16, kernel13_1Expr 0 8 k = kernel13_1_r0_8 k := by decide +kernel +noncomputable def kernel13_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel13_1_r0_9_eq : ∀ k : Fin 16, kernel13_1Expr 0 9 k = kernel13_1_r0_9 k := by decide +kernel +noncomputable def kernel13_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel13_1_r0_10_eq : ∀ k : Fin 16, kernel13_1Expr 0 10 k = kernel13_1_r0_10 k := by decide +kernel +noncomputable def kernel13_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel13_1_r0_11_eq : ∀ k : Fin 16, kernel13_1Expr 0 11 k = kernel13_1_r0_11 k := by decide +kernel +noncomputable def kernel13_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel13_1_r0_12_eq : ∀ k : Fin 16, kernel13_1Expr 0 12 k = kernel13_1_r0_12 k := by decide +kernel +noncomputable def kernel13_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel13_1_r0_13_eq : ∀ k : Fin 16, kernel13_1Expr 0 13 k = kernel13_1_r0_13 k := by decide +kernel +noncomputable def kernel13_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel13_1_r0_14_eq : ∀ k : Fin 16, kernel13_1Expr 0 14 k = kernel13_1_r0_14 k := by decide +kernel +noncomputable def kernel13_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel13_1_r0_15_eq : ∀ k : Fin 16, kernel13_1Expr 0 15 k = kernel13_1_r0_15 k := by decide +kernel +noncomputable def kernel13_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel13_1_r0_0,kernel13_1_r0_1,kernel13_1_r0_2,kernel13_1_r0_3,kernel13_1_r0_4,kernel13_1_r0_5,kernel13_1_r0_6,kernel13_1_r0_7,kernel13_1_r0_8,kernel13_1_r0_9,kernel13_1_r0_10,kernel13_1_r0_11,kernel13_1_r0_12,kernel13_1_r0_13,kernel13_1_r0_14,kernel13_1_r0_15] +lemma kernel13_1_r0_eq (i k : Fin 16) : kernel13_1Expr 0 i k = kernel13_1_r0 i k := by + fin_cases i + · exact kernel13_1_r0_0_eq k + · exact kernel13_1_r0_1_eq k + · exact kernel13_1_r0_2_eq k + · exact kernel13_1_r0_3_eq k + · exact kernel13_1_r0_4_eq k + · exact kernel13_1_r0_5_eq k + · exact kernel13_1_r0_6_eq k + · exact kernel13_1_r0_7_eq k + · exact kernel13_1_r0_8_eq k + · exact kernel13_1_r0_9_eq k + · exact kernel13_1_r0_10_eq k + · exact kernel13_1_r0_11_eq k + · exact kernel13_1_r0_12_eq k + · exact kernel13_1_r0_13_eq k + · exact kernel13_1_r0_14_eq k + · exact kernel13_1_r0_15_eq k +noncomputable def kernel13_1_r1_0 : Fin 16 → CBox := ![⟨⟨2163,2205⟩,⟨1233,1274⟩⟩,⟨⟨2143,2190⟩,⟨1232,1279⟩⟩,⟨⟨2143,2190⟩,⟨1232,1279⟩⟩,⟨⟨2134,2175⟩,⟨1232,1273⟩⟩,⟨⟨2099,2145⟩,⟨1216,1262⟩⟩,⟨⟨2069,2111⟩,⟨1205,1246⟩⟩,⟨⟨2035,2081⟩,⟨1189,1236⟩⟩,⟨⟨2005,2046⟩,⟨1178,1219⟩⟩,⟨⟨1955,1997⟩,⟨1167,1208⟩⟩,⟨⟨1906,1947⟩,⟨1135,1176⟩⟩,⟨⟨1856,1908⟩,⟨1119,1170⟩⟩,⟨⟨1792,1838⟩,⟨1092,1138⟩⟩,⟨⟨1748,1794⟩,⟨1080,1127⟩⟩,⟨⟨1683,1724⟩,⟨1054,1095⟩⟩,⟨⟨1619,1660⟩,⟨1027,1068⟩⟩,⟨⟨1554,1596⟩,⟨1000,1041⟩⟩] +lemma kernel13_1_r1_0_eq : ∀ k : Fin 16, kernel13_1Expr 1 0 k = kernel13_1_r1_0 k := by decide +kernel +noncomputable def kernel13_1_r1_1 : Fin 16 → CBox := ![⟨⟨1490,1531⟩,⟨973,1014⟩⟩,⟨⟨1426,1467⟩,⟨946,988⟩⟩,⟨⟨1346,1388⟩,⟨904,945⟩⟩,⟨⟨1282,1323⟩,⟨877,919⟩⟩,⟨⟨1217,1259⟩,⟨850,892⟩⟩,⟨⟨1138,1179⟩,⟨808,850⟩⟩,⟨⟨1073,1115⟩,⟨782,823⟩⟩,⟨⟨1009,1050⟩,⟨755,796⟩⟩,⟨⟨945,986⟩,⟨708,750⟩⟩,⟨⟨880,921⟩,⟨681,723⟩⟩,⟨⟨815,857⟩,⟨655,696⟩⟩,⟨⟨761,802⟩,⟨608,650⟩⟩,⟨⟨696,738⟩,⟨582,623⟩⟩,⟨⟨646,693⟩,⟨556,602⟩⟩,⟨⟨582,623⟩,⟨514,556⟩⟩,⟨⟨532,573⟩,⟨483,524⟩⟩] +lemma kernel13_1_r1_1_eq : ∀ k : Fin 16, kernel13_1Expr 1 1 k = kernel13_1_r1_1 k := by decide +kernel +noncomputable def kernel13_1_r1_2 : Fin 16 → CBox := ![⟨⟨482,523⟩,⟨462,503⟩⟩,⟨⟨447,489⟩,⟨426,467⟩⟩,⟨⟨397,444⟩,⟨400,446⟩⟩,⟨⟨362,404⟩,⟨369,410⟩⟩,⟨⟨312,359⟩,⟨343,390⟩⟩,⟨⟨277,324⟩,⟨312,359⟩⟩,⟨⟨247,304⟩,⟨291,348⟩⟩,⟨⟨227,269⟩,⟨271,313⟩⟩,⟨⟨192,234⟩,⟨245,287⟩⟩,⟨⟨177,219⟩,⟨230,272⟩⟩,⟨⟨142,184⟩,⟨214,256⟩⟩,⟨⟨122,164⟩,⟨184,225⟩⟩,⟨⟨107,149⟩,⟨168,210⟩⟩,⟨⟨87,134⟩,⟨153,200⟩⟩,⟨⟨71,113⟩,⟨143,185⟩⟩,⟨⟨66,114⟩,⟨122,169⟩⟩] +lemma kernel13_1_r1_2_eq : ∀ k : Fin 16, kernel13_1Expr 1 2 k = kernel13_1_r1_2 k := by decide +kernel +noncomputable def kernel13_1_r1_3 : Fin 16 → CBox := ![⟨⟨51,93⟩,⟨112,154⟩⟩,⟨⟨36,78⟩,⟨97,139⟩⟩,⟨⟨31,73⟩,⟨81,123⟩⟩,⟨⟨16,63⟩,⟨81,129⟩⟩,⟨⟨16,58⟩,⟨66,108⟩⟩,⟨⟨10,53⟩,⟨51,93⟩⟩,⟨⟨(-5),42⟩,⟨51,98⟩⟩,⟨⟨(-5),37⟩,⟨35,78⟩⟩,⟨⟨(-5),37⟩,⟨35,78⟩⟩,⟨⟨(-10),32⟩,⟨20,62⟩⟩,⟨⟨(-10),32⟩,⟨20,62⟩⟩,⟨⟨(-10),32⟩,⟨20,62⟩⟩,⟨⟨(-10),32⟩,⟨(-1),42⟩⟩,⟨⟨(-26),17⟩,⟨5,47⟩⟩,⟨⟨(-26),17⟩,⟨5,47⟩⟩,⟨⟨(-26),17⟩,⟨5,47⟩⟩] +lemma kernel13_1_r1_3_eq : ∀ k : Fin 16, kernel13_1Expr 1 3 k = kernel13_1_r1_3 k := by decide +kernel +noncomputable def kernel13_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-26),17⟩,⟨5,47⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-31),11⟩,⟨(-11),32⟩⟩,⟨⟨(-32),11⟩,⟨(-11),32⟩⟩,⟨⟨(-32),11⟩,⟨(-11),32⟩⟩,⟨⟨(-32),11⟩,⟨(-11),32⟩⟩,⟨⟨(-32),11⟩,⟨(-11),33⟩⟩] +lemma kernel13_1_r1_4_eq : ∀ k : Fin 16, kernel13_1Expr 1 4 k = kernel13_1_r1_4 k := by decide +kernel +noncomputable def kernel13_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-32),12⟩,⟨(-11),33⟩⟩,⟨⟨(-32),12⟩,⟨(-11),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-32),12⟩,⟨(-10),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩] +lemma kernel13_1_r1_5_eq : ∀ k : Fin 16, kernel13_1Expr 1 5 k = kernel13_1_r1_5 k := by decide +kernel +noncomputable def kernel13_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),33⟩⟩,⟨⟨(-43),22⟩,⟨(-32),34⟩⟩,⟨⟨(-43),22⟩,⟨(-32),34⟩⟩,⟨⟨(-43),22⟩,⟨(-32),34⟩⟩,⟨⟨(-43),22⟩,⟨(-32),34⟩⟩,⟨⟨(-43),22⟩,⟨(-32),34⟩⟩,⟨⟨(-44),22⟩,⟨(-32),34⟩⟩,⟨⟨(-44),22⟩,⟨(-32),34⟩⟩,⟨⟨(-44),22⟩,⟨(-32),34⟩⟩,⟨⟨(-44),22⟩,⟨(-32),34⟩⟩,⟨⟨(-44),22⟩,⟨(-32),34⟩⟩,⟨⟨(-44),22⟩,⟨(-32),34⟩⟩,⟨⟨(-34),32⟩,⟨(-44),22⟩⟩,⟨⟨(-34),32⟩,⟨(-44),22⟩⟩] +lemma kernel13_1_r1_6_eq : ∀ k : Fin 16, kernel13_1Expr 1 6 k = kernel13_1_r1_6 k := by decide +kernel +noncomputable def kernel13_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),28⟩⟩,⟨⟨(-39),32⟩,⟨(-44),29⟩⟩,⟨⟨(-39),32⟩,⟨(-44),29⟩⟩,⟨⟨(-40),32⟩,⟨(-44),29⟩⟩,⟨⟨(-40),32⟩,⟨(-44),29⟩⟩,⟨⟨(-40),32⟩,⟨(-44),29⟩⟩,⟨⟨(-40),32⟩,⟨(-44),29⟩⟩,⟨⟨(-32),40⟩,⟨(-29),44⟩⟩] +lemma kernel13_1_r1_7_eq : ∀ k : Fin 16, kernel13_1Expr 1 7 k = kernel13_1_r1_7 k := by decide +kernel +noncomputable def kernel13_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel13_1_r1_8_eq : ∀ k : Fin 16, kernel13_1Expr 1 8 k = kernel13_1_r1_8 k := by decide +kernel +noncomputable def kernel13_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel13_1_r1_9_eq : ∀ k : Fin 16, kernel13_1Expr 1 9 k = kernel13_1_r1_9 k := by decide +kernel +noncomputable def kernel13_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r1_10_eq : ∀ k : Fin 16, kernel13_1Expr 1 10 k = kernel13_1_r1_10 k := by decide +kernel +noncomputable def kernel13_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r1_11_eq : ∀ k : Fin 16, kernel13_1Expr 1 11 k = kernel13_1_r1_11 k := by decide +kernel +noncomputable def kernel13_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r1_12_eq : ∀ k : Fin 16, kernel13_1Expr 1 12 k = kernel13_1_r1_12 k := by decide +kernel +noncomputable def kernel13_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r1_13_eq : ∀ k : Fin 16, kernel13_1Expr 1 13 k = kernel13_1_r1_13 k := by decide +kernel +noncomputable def kernel13_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r1_14_eq : ∀ k : Fin 16, kernel13_1Expr 1 14 k = kernel13_1_r1_14 k := by decide +kernel +noncomputable def kernel13_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel13_1_r1_15_eq : ∀ k : Fin 16, kernel13_1Expr 1 15 k = kernel13_1_r1_15 k := by decide +kernel +noncomputable def kernel13_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel13_1_r1_0,kernel13_1_r1_1,kernel13_1_r1_2,kernel13_1_r1_3,kernel13_1_r1_4,kernel13_1_r1_5,kernel13_1_r1_6,kernel13_1_r1_7,kernel13_1_r1_8,kernel13_1_r1_9,kernel13_1_r1_10,kernel13_1_r1_11,kernel13_1_r1_12,kernel13_1_r1_13,kernel13_1_r1_14,kernel13_1_r1_15] +lemma kernel13_1_r1_eq (i k : Fin 16) : kernel13_1Expr 1 i k = kernel13_1_r1 i k := by + fin_cases i + · exact kernel13_1_r1_0_eq k + · exact kernel13_1_r1_1_eq k + · exact kernel13_1_r1_2_eq k + · exact kernel13_1_r1_3_eq k + · exact kernel13_1_r1_4_eq k + · exact kernel13_1_r1_5_eq k + · exact kernel13_1_r1_6_eq k + · exact kernel13_1_r1_7_eq k + · exact kernel13_1_r1_8_eq k + · exact kernel13_1_r1_9_eq k + · exact kernel13_1_r1_10_eq k + · exact kernel13_1_r1_11_eq k + · exact kernel13_1_r1_12_eq k + · exact kernel13_1_r1_13_eq k + · exact kernel13_1_r1_14_eq k + · exact kernel13_1_r1_15_eq k +noncomputable def kernel13_1_r2_0 : Fin 16 → CBox := ![⟨⟨48879962723072,48879962723105⟩,⟨1107498693938743,1107498693938776⟩⟩,⟨⟨49238209166339,49238209166369⟩,⟨1105712927464739,1105712927464767⟩⟩,⟨⟨49950726423335,49950726423363⟩,⟨1102149591066718,1102149591066748⟩⟩,⟨⟨51009613809435,51009613809465⟩,⟨1096825019785560,1096825019785588⟩⟩,⟨⟨52403145960711,52403145960736⟩,⟨1089763571539238,1089763571539263⟩⟩,⟨⟨54115921478333,54115921478361⟩,⟨1080997454958581,1080997454958611⟩⟩,⟨⟨56129057577004,56129057577032⟩,⟨1070566502169103,1070566502169133⟩⟩,⟨⟨58420427781012,58420427781045⟩,⟨1058517888494624,1058517888494657⟩⟩,⟨⟨60964939072140,60964939072172⟩,⟨1044905801521655,1044905801521688⟩⟩,⟨⟨63734844318018,63734844318050⟩,⟨1029791062405530,1029791062405563⟩⟩,⟨⟨66700085307205,66700085307238⟩,⟨1013240702717421,1013240702717454⟩⟩,⟨⟨69828661296944,69828661296972⟩,⟨995327500519704,995327500519734⟩⟩,⟨⟨73087017647223,73087017647248⟩,⟨976129479713572,976129479713597⟩⟩,⟨⟨76440448876993,76440448877018⟩,⟨955729377022348,955729377022373⟩⟩,⟨⟨79853510336287,79853510336320⟩,⟨934214081253148,934214081253181⟩⟩,⟨⟨83290432644715,83290432644748⟩,⟨911674049715482,911674049715515⟩⟩] +lemma kernel13_1_r2_0_eq : ∀ k : Fin 16, kernel13_1Expr 2 0 k = kernel13_1_r2_0 k := by decide +kernel +noncomputable def kernel13_1_r2_1 : Fin 16 → CBox := ![⟨⟨86715533100566,86715533100599⟩,⟨888202706864152,888202706864184⟩⟩,⟨⟨90093618413798,90093618413826⟩,⟨863895830373359,863895830373389⟩⟩,⟨⟨93390373355598,93390373355623⟩,⟨838850929936488,838850929936513⟩⟩,⟨⟨96572730242187,96572730242217⟩,⟨813166624120110,813166624120138⟩⟩,⟨⟨99609214572236,99609214572277⟩,⟨786942020579537,786942020579578⟩⟩,⟨⟨102470262608166,102470262608196⟩,⟨760276104867410,760276104867438⟩⟩,⟨⟨105128507221256,105128507221289⟩,⟨733267142934214,733267142934247⟩⟩,⟨⟨107559028898035,107559028898076⟩,⟨706012102234357,706012102234398⟩⟩,⟨⟨109739569419151,109739569419184⟩,⟨678606096111089,678606096111122⟩⟩,⟨⟨111650706360703,111650706360728⟩,⟨651141855844567,651141855844592⟩⟩,⟨⟨113275987218781,113275987218814⟩,⟨623709234409735,623709234409768⟩⟩,⟨⟨114602022608998,114602022609023⟩,⟨596394745610255,596394745610280⟩⟩,⟨⟨115618538632612,115618538632637⟩,⟨569281141834827,569281141834852⟩⟩,⟨⟨116318389118055,116318389118085⟩,⟨542447033229963,542447033229991⟩⟩,⟨⟨116697529030634,116697529030667⟩,⟨515966550601895,515966550601928⟩⟩,⟨⟨116754950885123,116754950885156⟩,⟨489909053859085,489909053859118⟩⟩] +lemma kernel13_1_r2_1_eq : ∀ k : Fin 16, kernel13_1Expr 2 1 k = kernel13_1_r2_1 k := by decide +kernel +noncomputable def kernel13_1_r2_2 : Fin 16 → CBox := ![⟨⟨116492586486853,116492586486881⟩,⟨464338887290621,464338887290652⟩⟩,⟨⟨115915176760167,115915176760200⟩,⟨439315182451944,439315182451977⟩⟩,⟨⟨115030112793282,115030112793310⟩,⟨414891708906484,414891708906514⟩⟩,⟨⟨113847251530480,113847251530522⟩,⟨391116772554916,391116772554957⟩⟩,⟨⟨112378709775149,112378709775179⟩,⟨368033160782294,368033160782322⟩⟩,⟨⟨110638640327347,110638640327377⟩,⟨345678133172041,345678133172069⟩⟩,⟨⟨108642994169284,108642994169312⟩,⟨324083456083277,324083456083307⟩⟩,⟨⟨106409272631457,106409272631487⟩,⟨303275478968060,303275478968088⟩⟩,⟨⟨103956273425523,103956273425551⟩,⟨283275249924985,283275249925016⟩⟩,⟨⟨101303834320145,101303834320178⟩,⟨264098667648787,264098667648821⟩⟩,⟨⟨98472578069448,98472578069473⟩,⟨245756666646183,245756666646208⟩⟩,⟨⟨95483661984894,95483661984927⟩,⟨228255432349250,228255432349284⟩⟩,⟨⟨92358535278833,92358535278863⟩,⟨211596642571290,211596642571318⟩⟩,⟨⟨89118707007180,89118707007213⟩,⟨195777731616458,195777731616492⟩⟩,⟨⟨85785527108986,85785527109019⟩,⟨180792173275788,180792173275821⟩⟩,⟨⟨82379982688302,82379982688335⟩,⟨166629778914831,166629778914864⟩⟩] +lemma kernel13_1_r2_2_eq : ∀ k : Fin 16, kernel13_1Expr 2 2 k = kernel13_1_r2_2 k := by decide +kernel +noncomputable def kernel13_1_r2_3 : Fin 16 → CBox := ![⟨⟨78922511317687,78922511317720⟩,⟨153277006882984,153277006883017⟩⟩,⟨⟨75432832769830,75432832769871⟩,⟨140717279547670,140717279547712⟩⟩,⟨⟨71929800211879,71929800211913⟩,⟨128931304374995,128931304375029⟩⟩,⟨⟨68431271532315,68431271532344⟩,⟨117897395638494,117897395638525⟩⟩,⟨⟨64954001119468,64954001119501⟩,⟨107591793534778,107591793534811⟩⟩,⟨⟨61513552079338,61513552079380⟩,⟨97988977714015,97988977714057⟩⟩,⟨⟨58124228572626,58124228572660⟩,⟨89061972489083,89061972489117⟩⟩,⟨⟨54799027671243,54799027671277⟩,⟨80782641264950,80782641264984⟩⟩,⟨⟨51549609886523,51549609886552⟩,⟨73121968023307,73121968023338⟩⟩,⟨⟨48386287305412,48386287305438⟩,⟨66050324000760,66050324000786⟩⟩,⟨⟨45318028091179,45318028091209⟩,⟨59537718008327,59537718008355⟩⟩,⟨⟨42352475959503,42352475959537⟩,⟨53554029148086,53554029148120⟩⟩,⟨⟨39495983131263,39495983131288⟩,⟨48069220986647,48069220986672⟩⟩,⟨⟨36753655187339,36753655187373⟩,⟨43053536539301,43053536539334⟩⟩,⟨⟨34129406208423,34129406208451⟩,⟨38477673699605,38477673699636⟩⟩,⟨⟨31626022570163,31626022570205⟩,⟨34312941012957,34312941012999⟩⟩] +lemma kernel13_1_r2_3_eq : ∀ k : Fin 16, kernel13_1Expr 2 3 k = kernel13_1_r2_3 k := by decide +kernel +noncomputable def kernel13_1_r2_4 : Fin 16 → CBox := ![⟨⟨29245233781269,29245233781298⟩,⟨30531393937301,30531393937332⟩⟩,⟨⟨26987788793011,26987788793045⟩,⟨27105951955978,27105951956012⟩⟩,⟨⟨24853536273904,24853536273933⟩,⟨24010497106497,24010497106528⟩⟩,⟨⟨22841507425779,22841507425808⟩,⟨21219954662133,21219954662164⟩⟩,⟨⟨20950000017693,20950000017719⟩,⟨18710356851156,18710356851182⟩⟩,⟨⟨19176662424845,19176662424879⟩,⟨16458890620343,16458890620377⟩⟩,⟨⟨17518576581186,17518576581228⟩,⟨14443930546134,14443930546177⟩⟩,⟨⟨15972338880877,15972338880908⟩,⟨12645058068561,12645058068590⟩⟩,⟨⟨14534138193667,14534138193701⟩,⟨11043068271343,11043068271378⟩⟩,⟨⟨13199830289599,13199830289628⟩,⟨9619965458339,9619965458370⟩⟩,⟨⟨11965008096345,11965008096376⟩,⟨8358948782053,8358948782082⟩⟩,⟨⟨10825067336442,10825067336468⟩,⟨7244389168000,7244389168026⟩⟩,⟨⟨9775267209472,9775267209514⟩,⟨6261798750023,6261798750066⟩⟩,⟨⟨8810785894534,8810785894568⟩,⟨5397793988991,5397793989026⟩⟩,⟨⟨7926770749405,7926770749435⟩,⟨4640053592486,4640053592517⟩⟩,⟨⟨7118383175344,7118383175376⟩,⟨3977272289211,3977272289240⟩⟩] +lemma kernel13_1_r2_4_eq : ∀ k : Fin 16, kernel13_1Expr 2 4 k = kernel13_1_r2_4 k := by decide +kernel +noncomputable def kernel13_1_r2_5 : Fin 16 → CBox := ![⟨⟨6380838197439,6380838197473⟩,⟨3399111439037,3399111439072⟩⟩,⟨⟨5709438882017,5709438882051⟩,⟨2896147382970,2896147383005⟩⟩,⟨⟨5099605773098,5099605773128⟩,⟨2459818354997,2459818355029⟩⟩,⟨⟨4546901580056,4546901580091⟩,⟨2082370695376,2082370695410⟩⟩,⟨⟨4047051389069,4047051389101⟩,⟨1756805020755,1756805020784⟩⟩,⟨⟨3595958701373,3595958701402⟩,⟨1476822924002,1476822924033⟩⟩,⟨⟨3189717623533,3189717623568⟩,⟨1236774696532,1236774696566⟩⟩,⟨⟨2824621548316,2824621548345⟩,⟨1031608488507,1031608488538⟩⟩,⟨⟨2497168671359,2497168671394⟩,⟨856821249287,856821249322⟩⟩,⟨⟨2204064688947,2204064688977⟩,⟨708411722773,708411722805⟩⟩,⟨⟨1942223015904,1942223015939⟩,⟨582835708518,582835708553⟩⟩,⟨⟨1708762853216,1708762853251⟩,⟨476963742651,476963742687⟩⟩,⟨⟨1501005419464,1501005419500⟩,⟨388041300731,388041300766⟩⟩,⟨⟨1316468643988,1316468644023⟩,⟨313651578717,313651578752⟩⟩,⟨⟨1152860598940,1152860598970⟩,⟨251680867979,251680868011⟩⟩,⟨⟨1008071926505,1008071926531⟩,⟨200286505982,200286506009⟩⟩] +lemma kernel13_1_r2_5_eq : ∀ k : Fin 16, kernel13_1Expr 2 5 k = kernel13_1_r2_5 k := by decide +kernel +noncomputable def kernel13_1_r2_6 : Fin 16 → CBox := ![⟨⟨880167494988,880167495019⟩,⟨157867354412,157867354443⟩⟩,⟨⟨767377494458,767377494490⟩,⟨123036732898,123036732928⟩⟩,⟨⟨668088159799,668088159834⟩,⟨94597716184,94597716219⟩⟩,⟨⟨580832286437,580832286469⟩,⟨71520687958,71520687988⟩⟩,⟨⟨504279682230,504279682262⟩,⟨52923032588,52923032618⟩⟩,⟨⟨437227678333,437227678368⟩,⟨38050838472,38050838507⟩⟩,⟨⟨378591802345,378591802377⟩,⟨26262481545,26262481576⟩⟩,⟨⟨327396698774,327396698807⟩,⟨17013955406,17013955436⟩⟩,⟨⟨282767365485,282767365512⟩,⟨9845814726,9845814753⟩⟩,⟨⟨243920759498,243920759533⟩,⟨4371600055,4371600091⟩⟩,⟨⟨210157812158,210157812203⟩,⟨267616488,267616532⟩⟩,⟨⟨180855881706,180855881742⟩,⟨(-2736057567),(-2736057531)⟩⟩,⟨⟨155461660689,155461660725⟩,⟨(-4863448700),(-4863448664)⟩⟩,⟨⟨133484547014,133484547050⟩,⟨(-6299565037),(-6299565001)⟩⟩,⟨⟨114490479274,114490479307⟩,⟨(-7196375346),(-7196375316)⟩⟩,⟨⟨98096231158,98096231190⟩,⟨(-7677987574),(-7677987543)⟩⟩] +lemma kernel13_1_r2_6_eq : ∀ k : Fin 16, kernel13_1Expr 2 6 k = kernel13_1_r2_6 k := by decide +kernel +noncomputable def kernel13_1_r2_7 : Fin 16 → CBox := ![⟨⟨83964154052,83964154089⟩,⟨(-7845116492),(-7845116455)⟩⟩,⟨⟨71797353102,71797353138⟩,⟨(-7778922853),(-7778922817)⟩⟩,⟨⟨61335278571,61335278616⟩,⟨(-7544299406),(-7544299360)⟩⟩,⟨⟨52349712018,52349712054⟩,⟨(-7192671797),(-7192671761)⟩⟩,⟨⟨44641125159,44641125191⟩,⟨(-6764376272),(-6764376239)⟩⟩,⟨⟨38035388243,38035388279⟩,⟨(-6290669453),(-6290669416)⟩⟩,⟨⟨32380804110,32380804142⟩,⟨(-5795419554),(-5795419521)⟩⟩,⟨⟨27545444276,27545444304⟩,⟨(-5296523228),(-5296523200)⟩⟩,⟨⟨23414763471,23414763508⟩,⟨(-4807086785),(-4807086748)⟩⟩,⟨⟨19889469925,19889469956⟩,⟨(-4336406068),(-4336406035)⟩⟩,⟨⟨16883629086,16883629123⟩,⟨(-3890775119),(-3890775082)⟩⟩,⟨⟨14322980006,14322980042⟩,⟨(-3474149661),(-3474149624)⟩⟩,⟨⟨12143444281,12143444318⟩,⟨(-3088688220),(-3088688183)⟩⟩,⟨⟨10289808862,10289808899⟩,⟨(-2735190609),(-2735190573)⟩⟩,⟨⟨8714565397,8714565434⟩,⟨(-2413450583),(-2413450546)⟩⟩,⟨⟨7376889780,7376889817⟩,⟨(-2122537172),(-2122537135)⟩⟩] +lemma kernel13_1_r2_7_eq : ∀ k : Fin 16, kernel13_1Expr 2 7 k = kernel13_1_r2_7 k := by decide +kernel +noncomputable def kernel13_1_r2_8 : Fin 16 → CBox := ![⟨⟨6241747038,6241747075⟩,⟨(-1861017181),(-1861017144)⟩⟩,⟨⟨5279107880,5279107917⟩,⟨(-1627129118),(-1627129081)⟩⟩,⟨⟨4463264408,4463264445⟩,⟨(-1418917606),(-1418917569)⟩⟩,⟨⟨3772233762,3772233799⟩,⟨(-1234335727),(-1234335690)⟩⟩,⟨⟨3187239154,3187239191⟩,⟨(-1071321328),(-1071321291)⟩⟩,⟨⟨2692259413,2692259450⟩,⟨(-927852675),(-927852638)⟩⟩,⟨⟨2273638554,2273638591⟩,⟨(-801987757),(-801987719)⟩⟩,⟨⟨1919747922,1919747959⟩,⟨(-691890584),(-691890547)⟩⟩,⟨⟨1620694483,1620694520⟩,⟨(-595847572),(-595847534)⟩⟩,⟨⟨1368069161,1368069199⟩,⟨(-512276274),(-512276237)⟩⟩,⟨⟨1154730326,1154730364⟩,⟨(-439728333),(-439728295)⟩⟩,⟨⟨974617570,974617607⟩,⟨(-376888239),(-376888202)⟩⟩,⟨⟨822591900,822591932⟩,⟨(-322569109),(-322569076)⟩⟩,⟨⟨694298662,694298700⟩,⟨(-275706278),(-275706241)⟩⟩,⟨⟨586050399,586050437⟩,⟨(-235349769),(-235349731)⟩⟩,⟨⟨494726469,494726507⟩,⟨(-200655719),(-200655681)⟩⟩] +lemma kernel13_1_r2_8_eq : ∀ k : Fin 16, kernel13_1Expr 2 8 k = kernel13_1_r2_8 k := by decide +kernel +noncomputable def kernel13_1_r2_9 : Fin 16 → CBox := ![⟨⟨417687518,417687556⟩,⟨(-170877810),(-170877772)⟩⟩,⟨⟨352702394,352702427⟩,⟨(-145358378),(-145358344)⟩⟩,⟨⟨297885953,297885991⟩,⟨(-123519958),(-123519920)⟩⟩,⟨⟨251646133,251646166⟩,⟨(-104857085),(-104857051)⟩⟩,⟨⟨212638948,212638980⟩,⟨(-88928618),(-88928584)⟩⟩,⟨⟨179730218,179730251⟩,⟨(-75350574),(-75350540)⟩⟩,⟨⟨151963154,151963192⟩,⟨(-63789590),(-63789552)⟩⟩,⟨⟨128530819,128530857⟩,⟨(-53956882),(-53956844)⟩⟩,⟨⟨108752869,108752917⟩,⟨(-45602886),(-45602839)⟩⟩,⟨⟨92055778,92055816⟩,⟨(-38512274),(-38512235)⟩⟩,⟨⟨77956137,77956176⟩,⟨(-32499727),(-32499688)⟩⟩,⟨⟨66046589,66046627⟩,⟨(-27405929),(-27405890)⟩⟩,⟨⟨55983864,55983902⟩,⟨(-23094248),(-23094210)⟩⟩,⟨⟨47478745,47478784⟩,⟨(-19447584),(-19447546)⟩⟩,⟨⟨40287511,40287550⟩,⟨(-16365789),(-16365751)⟩⟩,⟨⟨34204840,34204879⟩,⟨(-13763348),(-13763309)⟩⟩] +lemma kernel13_1_r2_9_eq : ∀ k : Fin 16, kernel13_1Expr 2 9 k = kernel13_1_r2_9 k := by decide +kernel +noncomputable def kernel13_1_r2_10 : Fin 16 → CBox := ![⟨⟨29057688,29057717⟩,⟨(-11567269),(-11567240)⟩⟩,⟨⟨24700249,24700287⟩,⟨(-9715414),(-9715375)⟩⟩,⟨⟨21009659,21009697⟩,⟨(-8154843),(-8154804)⟩⟩,⟨⟨17882305,17882344⟩,⟨(-6840591),(-6840552)⟩⟩,⟨⟨15230880,15230919⟩,⟨(-5734478),(-5734439)⟩⟩,⟨⟨12981751,12981790⟩,⟨(-4804113),(-4804074)⟩⟩,⟨⟨11072796,11072844⟩,⟨(-4022008),(-4021960)⟩⟩,⟨⟨9451646,9451685⟩,⟨(-3364936),(-3364897)⟩⟩,⟨⟨8074044,8074098⟩,⟨(-2813214),(-2813161)⟩⟩,⟨⟨6902721,6902760⟩,⟨(-2350195),(-2350156)⟩⟩,⟨⟨5906103,5906143⟩,⟨(-1961864),(-1961825)⟩⟩,⟨⟨5057595,5057634⟩,⟨(-1636329),(-1636290)⟩⟩,⟨⟨4334678,4334718⟩,⟨(-1363610),(-1363571)⟩⟩,⟨⟨3718344,3718383⟩,⟨(-1135244),(-1135205)⟩⟩,⟨⟨3192498,3192537⟩,⟨(-944138),(-944098)⟩⟩,⟨⟨2743525,2743564⟩,⟨(-784321),(-784282)⟩⟩] +lemma kernel13_1_r2_10_eq : ∀ k : Fin 16, kernel13_1Expr 2 10 k = kernel13_1_r2_10 k := by decide +kernel +noncomputable def kernel13_1_r2_11 : Fin 16 → CBox := ![⟨⟨2359882,2359921⟩,⟨(-650728),(-650689)⟩⟩,⟨⟨2031827,2031867⟩,⟨(-539154),(-539114)⟩⟩,⟨⟨1751079,1751119⟩,⟨(-446007),(-445968)⟩⟩,⟨⟨1510623,1510663⟩,⟨(-368316),(-368276)⟩⟩,⟨⟨1304511,1304550⟩,⟨(-303563),(-303524)⟩⟩,⟨⟨1127674,1127714⟩,⟨(-249641),(-249601)⟩⟩,⟨⟨975849,975889⟩,⟨(-204760),(-204721)⟩⟩,⟨⟨845362,845402⟩,⟨(-167468),(-167429)⟩⟩,⟨⟨733134,733173⟩,⟨(-136502),(-136462)⟩⟩,⟨⟨636506,636546⟩,⟨(-110806),(-110766)⟩⟩,⟨⟨553245,553290⟩,⟨(-89533),(-89489)⟩⟩,⟨⟨481421,481461⟩,⟨(-71937),(-71897)⟩⟩,⟨⟨419427,419467⟩,⟨(-57416),(-57377)⟩⟩,⟨⟨365849,365889⟩,⟨(-45440),(-45400)⟩⟩,⟨⟨319513,319553⟩,⟨(-35581),(-35541)⟩⟩,⟨⟨279377,279417⟩,⟨(-27494),(-27454)⟩⟩] +lemma kernel13_1_r2_11_eq : ∀ k : Fin 16, kernel13_1Expr 2 11 k = kernel13_1_r2_11 k := by decide +kernel +noncomputable def kernel13_1_r2_12 : Fin 16 → CBox := ![⟨⟨244605,244645⟩,⟨(-20883),(-20843)⟩⟩,⟨⟨214428,214468⟩,⟨(-15484),(-15443)⟩⟩,⟨⟨188229,188269⟩,⟨(-11092),(-11052)⟩⟩,⟨⟨165444,165484⟩,⟨(-7545),(-7505)⟩⟩,⟨⟨145611,145651⟩,⟨(-4685),(-4644)⟩⟩,⟨⟨128338,128378⟩,⟨(-2395),(-2355)⟩⟩,⟨⟨113270,113310⟩,⟨(-591),(-551)⟩⟩,⟨⟨100118,100159⟩,⟨840,880⟩⟩,⟨⟨88616,88656⟩,⟨1953,1993⟩⟩,⟨⟨78554,78595⟩,⟨2810,2850⟩⟩,⟨⟨69742,69782⟩,⟨3447,3488⟩⟩,⟨⟨61999,62040⟩,⟨3931,3971⟩⟩,⟨⟨55204,55250⟩,⟨4259,4304⟩⟩,⟨⟨49243,49284⟩,⟨4482,4523⟩⟩,⟨⟨43992,44032⟩,⟨4610,4651⟩⟩,⟨⟨39361,39407⟩,⟨4667,4712⟩⟩] +lemma kernel13_1_r2_12_eq : ∀ k : Fin 16, kernel13_1Expr 2 12 k = kernel13_1_r2_12 k := by decide +kernel +noncomputable def kernel13_1_r2_13 : Fin 16 → CBox := ![⟨⟨35268,35328⟩,⟨4664,4725⟩⟩,⟨⟨31667,31713⟩,⟨4629,4675⟩⟩,⟨⟨28486,28527⟩,⟨4546,4586⟩⟩,⟨⟨25654,25695⟩,⟨4450,4491⟩⟩,⟨⟨23157,23197⟩,⟨4335,4376⟩⟩,⟨⟨20925,20976⟩,⟨4201,4252⟩⟩,⟨⟨18955,18996⟩,⟨4058,4099⟩⟩,⟨⟨17206,17247⟩,⟨3927,3968⟩⟩,⟨⟨15640,15681⟩,⟨3782,3823⟩⟩,⟨⟨14236,14277⟩,⟨3631,3672⟩⟩,⟨⟨12984,13045⟩,⟨3474,3535⟩⟩,⟨⟨11876,11917⟩,⟨3339,3380⟩⟩,⟨⟨10876,10922⟩,⟨3195,3240⟩⟩,⟨⟨9989,10029⟩,⟨3071,3112⟩⟩,⟨⟨9190,9231⟩,⟨2947,2988⟩⟩,⟨⟨8466,8507⟩,⟨2811,2852⟩⟩] +lemma kernel13_1_r2_13_eq : ∀ k : Fin 16, kernel13_1Expr 2 13 k = kernel13_1_r2_13 k := by decide +kernel +noncomputable def kernel13_1_r2_14 : Fin 16 → CBox := ![⟨⟨7815,7856⟩,⟨2695,2736⟩⟩,⟨⟨7243,7284⟩,⟨2591,2632⟩⟩,⟨⟨6720,6761⟩,⟨2491,2532⟩⟩,⟨⟨6237,6278⟩,⟨2382,2423⟩⟩,⟨⟨5817,5859⟩,⟨2291,2332⟩⟩,⟨⟨5428,5474⟩,⟨2196,2242⟩⟩,⟨⟨5087,5128⟩,⟨2123,2164⟩⟩,⟨⟨4761,4802⟩,⟨2041,2082⟩⟩,⟨⟨4475,4522⟩,⟨1956,2002⟩⟩,⟨⟨4229,4270⟩,⟨1892,1933⟩⟩,⟨⟨3992,4038⟩,⟨1823,1870⟩⟩,⟨⟨3774,3815⟩,⟨1776,1817⟩⟩,⟨⟨3582,3628⟩,⟨1704,1751⟩⟩,⟨⟨3414,3455⟩,⟨1648,1690⟩⟩,⟨⟨3256,3297⟩,⟨1613,1654⟩⟩,⟨⟨3112,3153⟩,⟨1573,1615⟩⟩] +lemma kernel13_1_r2_14_eq : ∀ k : Fin 16, kernel13_1Expr 2 14 k = kernel13_1_r2_14 k := by decide +kernel +noncomputable def kernel13_1_r2_15 : Fin 16 → CBox := ![⟨⟨2989,3031⟩,⟨1514,1555⟩⟩,⟨⟨2860,2901⟩,⟨1490,1531⟩⟩,⟨⟨2767,2808⟩,⟨1452,1493⟩⟩,⟨⟨2673,2714⟩,⟨1424,1465⟩⟩,⟨⟨2578,2620⟩,⟨1396,1437⟩⟩,⟨⟨2514,2556⟩,⟨1369,1410⟩⟩,⟨⟨2430,2476⟩,⟨1341,1388⟩⟩,⟨⟨2386,2427⟩,⟨1315,1356⟩⟩,⟨⟨2321,2383⟩,⟨1288,1349⟩⟩,⟨⟨2292,2333⟩,⟨1287,1328⟩⟩,⟨⟨2242,2283⟩,⟨1275,1317⟩⟩,⟨⟨2228,2269⟩,⟨1260,1301⟩⟩,⟨⟨2193,2234⟩,⟨1244,1285⟩⟩,⟨⟨2178,2219⟩,⟨1248,1290⟩⟩,⟨⟨2168,2209⟩,⟨1248,1289⟩⟩,⟨⟨2168,2209⟩,⟨1248,1289⟩⟩] +lemma kernel13_1_r2_15_eq : ∀ k : Fin 16, kernel13_1Expr 2 15 k = kernel13_1_r2_15 k := by decide +kernel +noncomputable def kernel13_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel13_1_r2_0,kernel13_1_r2_1,kernel13_1_r2_2,kernel13_1_r2_3,kernel13_1_r2_4,kernel13_1_r2_5,kernel13_1_r2_6,kernel13_1_r2_7,kernel13_1_r2_8,kernel13_1_r2_9,kernel13_1_r2_10,kernel13_1_r2_11,kernel13_1_r2_12,kernel13_1_r2_13,kernel13_1_r2_14,kernel13_1_r2_15] +lemma kernel13_1_r2_eq (i k : Fin 16) : kernel13_1Expr 2 i k = kernel13_1_r2 i k := by + fin_cases i + · exact kernel13_1_r2_0_eq k + · exact kernel13_1_r2_1_eq k + · exact kernel13_1_r2_2_eq k + · exact kernel13_1_r2_3_eq k + · exact kernel13_1_r2_4_eq k + · exact kernel13_1_r2_5_eq k + · exact kernel13_1_r2_6_eq k + · exact kernel13_1_r2_7_eq k + · exact kernel13_1_r2_8_eq k + · exact kernel13_1_r2_9_eq k + · exact kernel13_1_r2_10_eq k + · exact kernel13_1_r2_11_eq k + · exact kernel13_1_r2_12_eq k + · exact kernel13_1_r2_13_eq k + · exact kernel13_1_r2_14_eq k + · exact kernel13_1_r2_15_eq k +noncomputable def kernel13_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-6773299261861954290571),(-6773299261861954247275)⟩,⟨18920916380271181718342,18920916380271181761559⟩⟩,⟨⟨(-6756277976964554691184),(-6756277976964554647929)⟩,⟨18906293411153766997948,18906293411153767041123⟩⟩,⟨⟨(-6722311064427234769956),(-6722311064427234726798)⟩,⟨18877061984189013792309,18877061984189013835388⟩⟩,⟨⟨(-6671549412887056462334),(-6671549412887056419319)⟩,⟨18833251270142328743138,18833251270142328786076⟩⟩,⟨⟨(-6604218293054989129326),(-6604218293054989086493)⟩,⟨18774905392853087082414,18774905392853087125171⟩⟩,⟨⟨(-6520616089875640320071),(-6520616089875640277467)⟩,⟨18702083862463765671684,18702083862463765714211⟩⟩,⟨⟨(-6421112623474335392800),(-6421112623474335350485)⟩,⟨18614862139846836549249,18614862139846836591491⟩⟩,⟨⟨(-6306147068620278194371),(-6306147068620278152371)⟩,⟨18513332321147286519511,18513332321147286561434⟩⟩,⟨⟨(-6176225484811097764364),(-6176225484811097722725)⟩,⟨18397603928887381604998,18397603928887381646565⟩⟩,⟨⟨(-6031917971421445621768),(-6031917971421445580533)⟩,⟨18267804793802852608630,18267804793802852649796⟩⟩,⟨⟨(-5873855464646575096652),(-5873855464646575055874)⟩,⟨18124082009529160541429,18124082009529160582140⟩⟩,⟨⟨(-5702726195200145616023),(-5702726195200145575724)⟩,⟨17966602940463055105122,17966602940463055145351⟩⟩,⟨⟨(-5519271827881942923793),(-5519271827881942884019)⟩,⟨17795556261615027488437,17795556261615027528146⟩⟩,⟨⟨(-5324283306202818317054),(-5324283306202818277846)⟩,⟨17611153008065484397427,17611153008065484436576⟩⟩,⟨⟨(-5118596427226914513226),(-5118596427226914474604)⟩,⟨17413627610760450478536,17413627610760450517099⟩⟩,⟨⟨(-4903087173650184674945),(-4903087173650184636951)⟩,⟨17203238894845889998283,17203238894845890036221⟩⟩] +lemma kernel13_1_r3_0_eq : ∀ k : Fin 16, kernel13_1Expr 3 0 k = kernel13_1_r3_0 k := by decide +kernel +noncomputable def kernel13_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-4678666831863499826264),(-4678666831863499788924)⟩,⟨16980271016553277946918,16980271016553277984203⟩⟩,⟨⟨(-4446276926331773796036),(-4446276926331773759385)⟩,⟨16745034314818028766100,16745034314818028802700⟩⟩,⟨⟨(-4206884002040540405019),(-4206884002040540369085)⟩,⟨16497866054337109442606,16497866054337109478494⟩⟩,⟨⟨(-3961474288001104856067),(-3961474288001104820880)⟩,⟨16239131037647993645699,16239131037647993680842⟩⟩,⟨⟨(-3711048275847642989047),(-3711048275847642954627)⟩,⟨15969222065028510417666,15969222065028510452049⟩⟩,⟨⟨(-3456615248387714484700),(-3456615248387714451061)⟩,⟨15688560222561726867679,15688560222561726901284⟩⟩,⟨⟨(-3199187793565604414100),(-3199187793565604381272)⟩,⟨15397594980562717675965,15397594980562717708762⟩⟩,⟨⟨(-2939776339650828620965),(-2939776339650828588950)⟩,⟨15096804086701385871398,15096804086701385903381⟩⟩,⟨⟨(-2679383747558622930780),(-2679383747558622899608)⟩,⟨14786693240549695209113,14786693240549695240257⟩⟩,⟨⟨(-2418999996033721037028),(-2418999996033721006712)⟩,⟨14467795538901201739671,14467795538901201769963⟩⟩,⟨⟨(-2159596994973858361349),(-2159596994973858331882)⟩,⟨14140670684020646197420,14140670684020646226865⟩⟩,⟨⟨(-1902123561428423030725),(-1902123561428423002127)⟩,⟨13805903949943636439509,13805903949943636468090⟩⟩,⟨⟨(-1647500591776590093291),(-1647500591776590065572)⟩,⟨13464104905020702874251,13464104905020702901958⟩⟩,⟨⟨(-1396616462267360443404),(-1396616462267360416561)⟩,⟨13115905892043946905348,13115905892043946932184⟩⟩,⟨⟨(-1150322688493819809609),(-1150322688493819783651)⟩,⟨12761960270464521276770,12761960270464521302717⟩⟩,⟨⟨(-909429872481860260792),(-909429872481860235714)⟩,⟨12402940428361006809684,12402940428361006834757⟩⟩] +lemma kernel13_1_r3_1_eq : ∀ k : Fin 16, kernel13_1Expr 3 1 k = kernel13_1_r3_1 k := by decide +kernel +noncomputable def kernel13_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-674703963909507221661),(-674703963909507197462)⟩,⟨12039535574908079474524,12039535574908079498719⟩⟩,⟨⟨(-446862859550589473683),(-446862859550589450356)⟩,⟨11672449327078020076466,11672449327078020099792⟩⟩,⟨⟨(-226573362373274995728),(-226573362373274973273)⟩,⟨11302397107142214887153,11302397107142214909610⟩⟩,⟨⟨(-14448518841169657300),(-14448518841169635704)⟩,⟨10930103370185367169634,10930103370185367191238⟩⟩,⟨⟨188954650113011033482,188954650113011054220⟩,⟨10556298683263777326898,10556298683263777347641⟩⟩,⟨⟨383137012215653620099,383137012215653639999⟩,⟨10181716679995988230918,10181716679995988250827⟩⟩,⟨⟨567658772236925701606,567658772236925720668⟩,⟨9807090916238259986855,9807090916238260005930⟩⟩,⟨⟨742140500268497368068,742140500268497386298⟩,⟨9433151654041851511060,9433151654041851529305⟩⟩,⟨⟨906263738078684061661,906263738078684079088⟩,⟨9060622602291683594456,9060622602291683611901⟩⟩,⟨⟨1059771185305180153138,1059771185305180169774⟩,⟨8690217643269363140790,8690217643269363157443⟩⟩,⟨⟨1202466470810255643586,1202466470810255659443⟩,⟨8322637574855753775539,8322637574855753791416⟩⟩,⟨⟨1334213518037149928573,1334213518037149943673⟩,⟨7958566898182746039753,7958566898182746054873⟩⟩,⟨⟨1454935516629576416759,1454935516629576431116⟩,⟨7598670680259653246985,7598670680259653261369⟩⟩,⟨⟨1564613515869436795915,1564613515869436809556⟩,⟨7243591520441378456825,7243591520441378470489⟩⟩,⟨⟨1663284658612865727778,1663284658612865740716⟩,⟨6893946648583330521736,6893946648583330534697⟩⟩,⟨⟨1751040077325174064243,1751040077325174076496⟩,⟨6550325181357537052639,6550325181357537064914⟩⟩] +lemma kernel13_1_r3_2_eq : ∀ k : Fin 16, kernel13_1Expr 3 2 k = kernel13_1_r3_2 k := by decide +kernel +noncomputable def kernel13_1_r3_3 : Fin 16 → CBox := ![⟨⟨1828022476497068688500,1828022476497068700093⟩,⟨6213285561506133294481,6213285561506133306100⟩⟩,⟨⟨1894423428136547702893,1894423428136547713851⟩,⟨5883353202807777128063,5883353202807777139049⟩⟩,⟨⟨1950480409145378183442,1950480409145378193774⟩,⟨5561018361259259966518,5561018361259259976878⟩⟩,⟨⟨1996473611182232008988,1996473611182232018726⟩,⟨5246734250462189961941,5246734250462189971706⟩⟩,⟨⟨2032722555066851767994,2032722555066851777156⟩,⟨4940915416489923637996,4940915416489923647185⟩⟩,⟨⟨2059582542876138209975,2059582542876138218592⟩,⟨4643936384632370570871,4643936384632370579513⟩⟩,⟨⟨2077440981613764912580,2077440981613764920662⟩,⟨4356130587417338582568,4356130587417338590675⟩⟩,⟨⟨2086713612694849546670,2086713612694849554256⟩,⟨4077789580229469158356,4077789580229469165965⟩⟩,⟨⟨2087840681476479685831,2087840681476479692927⟩,⟨3809162547734871607736,3809162547734871614858⟩⟩,⟨⟨2081283080688747785781,2081283080688747792404⟩,⟨3550456101214517810201,3550456101214517816854⟩⟩,⟨⟨2067518500889643109113,2067518500889643115298⟩,⟨3301834363854704300557,3301834363854704306767⟩⟩,⟨⟨2047037619995740480207,2047037619995740485976⟩,⟨3063419338079322308936,3063419338079322314732⟩⟩,⟨⟨2020340362548718248424,2020340362548718253790⟩,⟨2835291546175053485054,2835291546175053490441⟩⟩,⟨⟨1987932257689117356272,1987932257689117361264⟩,⟨2617490932792944753507,2617490932792944758522⟩⟩,⟨⟨1950320922850966926524,1950320922850966931151⟩,⟨2410018015440848777338,2410018015440848781984⟩⟩,⟨⟨1908012697994769414282,1908012697994769418565⟩,⟨2212835266839939000803,2212835266839939005108⟩⟩] +lemma kernel13_1_r3_3_eq : ∀ k : Fin 16, kernel13_1Expr 3 3 k = kernel13_1_r3_3 k := by decide +kernel +noncomputable def kernel13_1_r3_4 : Fin 16 → CBox := ![⟨⟨1861509452795413999079,1861509452795414003040⟩,⟨2025868711029771633111,2025868711029771637091⟩⟩,⟨⟨1811305586631577751518,1811305586631577755172⟩,⟨1849009713390569871936,1849009713390569875612⟩⟩,⟨⟨1757885238521331248911,1757885238521331252285⟩,⟨1682116943324268585705,1682116943324268589093⟩⟩,⟨⟨1701719721353157322121,1701719721353157325226⟩,⟨1525018487208286625639,1525018487208286628761⟩⟩,⟨⟨1643265191910874171687,1643265191910874174533⟩,⟨1377514088414034417111,1377514088414034419973⟩⟩,⟨⟨1582960565323147807442,1582960565323147810060⟩,⟨1239377490667044053824,1239377490667044056458⟩⟩,⟨⟨1521225679720567366862,1521225679720567369417⟩,⟨1110358860813865849118,1110358860813865851686⟩⟩,⟨⟨1458459714091317099027,1458459714091317101501⟩,⟨990187267144567149193,990187267144567151680⟩⟩,⟨⟨1395039859623952514628,1395039859623952517024⟩,⟨878573189786658086238,878573189786658088641⟩⟩,⟨⟨1331320242243805939505,1331320242243805941823⟩,⟨775211040320571559486,775211040320571561812⟩⟩,⟨⟨1267631091616310720666,1267631091616310722915⟩,⟨679781668649021290119,679781668649021292378⟩⟩,⟨⟨1204278149630966559954,1204278149630966562122⟩,⟨591954836260252581460,591954836260252583637⟩⟩,⟨⟨1141542309315134263303,1141542309315134265394⟩,⟨511391636333499509742,511391636333499511838⟩⟩,⟨⟨1079679473274944157550,1079679473274944159566⟩,⟨437746842617017360346,437746842617017362367⟩⟩,⟨⟨1018920619135029531598,1018920619135029533543⟩,⟨370671170636586074337,370671170636586076285⟩⟩,⟨⟨959472058059303661303,959472058059303663167⟩,⟨309813436536201452180,309813436536201454050⟩⟩] +lemma kernel13_1_r3_4_eq : ∀ k : Fin 16, kernel13_1Expr 3 4 k = kernel13_1_r3_4 k := by decide +kernel +noncomputable def kernel13_1_r3_5 : Fin 16 → CBox := ![⟨⟨901515871287401241905,901515871287401243694⟩,⟨254822600683245203010,254822600683245204804⟩⟩,⟨⟨845210508717671568266,845210508717671569997⟩,⟨205349685058362405324,205349685058362407057⟩⟩,⟨⟨790691532906018673655,790691532906018675307⟩,⟨161049555366822083458,161049555366822085110⟩⟩,⟨⟨738072491425231105659,738072491425231107246⟩,⟨121582560725627495696,121582560725627497288⟩⟩,⟨⟨687445900333316271217,687445900333316272743⟩,⟨86616025672907085894,86616025672907087419⟩⟩,⟨⟨638884321520434049285,638884321520434050730⟩,⟨55825591088839413838,55825591088839415285⟩⟩,⟨⟨592441516928438917989,592441516928438919377⟩,⟨28896402388390832089,28896402388390833479⟩⟩,⟨⟨548153663048735594289,548153663048735595604⟩,⟨5524145025727720382,5524145025727721697⟩⟩,⟨⟨506040609685289038894,506040609685289040152⟩,⟨(-14584071078840162495),(-14584071078840161237)⟩⟩,⟨⟨466107167700980161585,466107167700980162778⟩,⟨(-31708975130537492305),(-31708975130537491112)⟩⟩,⟨⟨428344411326858198875,428344411326858200017⟩,⟨(-46118542698199209107),(-46118542698199207965)⟩⟩,⟨⟨392730981584421526463,392730981584421527548⟩,⟨(-58067541056554260753),(-58067541056554259669)⟩⟩,⟨⟨359234378429873108116,359234378429873109130⟩,⟨(-67797206069979073562),(-67797206069979072550)⟩⟩,⟨⟨327812230355519704191,327812230355519705164⟩,⟨(-75535043187167483746),(-75535043187167482776)⟩⟩,⟨⟨298413531356787289176,298413531356787290099⟩,⟨(-81494744401829962714),(-81494744401829961791)⟩⟩,⟨⟨270979836374180640701,270979836374180641573⟩,⟨(-85876212472033347290),(-85876212472033346419)⟩⟩] +lemma kernel13_1_r3_5_eq : ∀ k : Fin 16, kernel13_1Expr 3 5 k = kernel13_1_r3_5 k := by decide +kernel +noncomputable def kernel13_1_r3_6 : Fin 16 → CBox := ![⟨⟨245446407529461266921,245446407529461267749⟩,⟨(-88865683276278391013),(-88865683276278390182)⟩⟩,⟨⟨221743304677188080889,221743304677188081663⟩,⟨(-90635936912073704200),(-90635936912073703427)⟩⟩,⟨⟨199796414970875245575,199796414970875246314⟩,⟨(-91346588005067744893),(-91346588005067744157)⟩⟩,⟨⟨179528417283315713312,179528417283315714013⟩,⟨(-91144445684752003722),(-91144445684752003025)⟩⟩,⟨⟨160859678410775030384,160859678410775031046⟩,⟨(-90163933786162317104),(-90163933786162316445)⟩⟩,⟨⟨143709079020254209850,143709079020254210466⟩,⟨(-88527562044771208823),(-88527562044771208210)⟩⟩,⟨⟨127994768259154012036,127994768259154012617⟩,⟨(-86346439352112167571),(-86346439352112166988)⟩⟩,⟨⟨113634846830562557777,113634846830562558329⟩,⟨(-83720820520431263328),(-83720820520431262776)⟩⟩,⟨⟨100547979139924287204,100547979139924287715⟩,⟨(-80740678453482231349),(-80740678453482230842)⟩⟩,⟨⟨88653935836624045421,88653935836624045894⟩,⟨(-77486294125186287395),(-77486294125186286922)⟩⟩,⟨⟨77874068705235283318,77874068705235283771⟩,⟨(-74028857316246647803),(-74028857316246647349)⟩⟩,⟨⟨68131720405525174510,68131720405525174939⟩,⟨(-70431071639359818792),(-70431071639359818360)⟩⟩,⟨⟨59352572018826484116,59352572018826484516⟩,⟨(-66747757985416794955),(-66747757985416794554)⟩⟩,⟨⟨51464931733329814751,51464931733329815118⟩,⟨(-63026451135778511992),(-63026451135778511625)⟩⟩,⟨⟨44399968295527866880,44399968295527867227⟩,⟨(-59307984899911969550),(-59307984899911969202)⟩⟩,⟨⟨38091893073657474025,38091893073657474353⟩,⟨(-55627061744865374679),(-55627061744865374352)⟩⟩] +lemma kernel13_1_r3_6_eq : ∀ k : Fin 16, kernel13_1Expr 3 6 k = kernel13_1_r3_6 k := by decide +kernel +noncomputable def kernel13_1_r3_7 : Fin 16 → CBox := ![⟨⟨32478094726471323688,32478094726471324002⟩,⟨(-52012803475683854143),(-52012803475683853828)⟩⟩,⟨⟨27499230552541441495,27499230552541441787⟩,⟨(-48489280097356441759),(-48489280097356441469)⟩⟩,⟨⟨23099278617486185417,23099278617486185685⟩,⟨(-45076014533677511720),(-45076014533677511453)⟩⟩,⟨⟨19225554725235992728,19225554725235992982⟩,⟨(-41788461391931379398),(-41788461391931379144)⟩⟩,⟨⟨15828698221068953224,15828698221068953463⟩,⟨(-38638458440962084005),(-38638458440962083769)⟩⟩,⟨⟨12862630495035172738,12862630495035172964⟩,⟨(-35634649911288400090),(-35634649911288399868)⟩⟩,⟨⟨10284489900839722052,10284489900839722260⟩,⟨(-32782881127651180570),(-32782881127651180363)⟩⟩,⟨⟨8054546623373453014,8054546623373453208⟩,⟨(-30086564345722666301),(-30086564345722666107)⟩⟩,⟨⟨6136100823707500062,6136100823707500242⟩,⟨(-27547015985381268091),(-27547015985381267910)⟩⟩,⟨⟨4495367169004026756,4495367169004026936⟩,⟨(-25163765733327729188),(-25163765733327729007)⟩⟩,⟨⟨3101348621556725218,3101348621556725373⟩,⟨(-22934838228826808463),(-22934838228826808304)⟩⟩,⟨⟨1925702120744128244,1925702120744128396⟩,⟨(-20857008249427719181),(-20857008249427719032)⟩⟩,⟨⟨942598548284017304,942598548284017444⟩,⟨(-18926030480477564851),(-18926030480477564711)⟩⟩,⟨⟨128579124571875530,128579124571875668⟩,⟨(-17136845085252495368),(-17136845085252495233)⟩⟩,⟨⟨(-537589854654357664),(-537589854654357526)⟩,⟨(-15483760393999398180),(-15483760393999398044)⟩⟩,⟨⟨(-1075062263756199998),(-1075062263756199878)⟩,⟨(-13960614102694056214),(-13960614102694056094)⟩⟩] +lemma kernel13_1_r3_7_eq : ∀ k : Fin 16, kernel13_1Expr 3 7 k = kernel13_1_r3_7 k := by decide +kernel +noncomputable def kernel13_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-1501055919647045466),(-1501055919647045347)⟩,⟨(-12560914418580770613),(-12560914418580770494)⟩⟩,⟨⟨(-1830993637529090424),(-1830993637529090318)⟩,⟨(-11277962612318272260),(-11277962612318272154)⟩⟩,⟨⟨(-2078640524979348055),(-2078640524979347949)⟩,⟨(-10104958438572983937),(-10104958438572983831)⟩⟩,⟨⟨(-2256236654569388883),(-2256236654569388793)⟩,⟨(-9035089870883589164),(-9035089870883589076)⟩⟩,⟨⟨(-2374624425917163703),(-2374624425917163604)⟩,⟨(-8061608565195856897),(-8061608565195856797)⟩⟩,⟨⟨(-2443370083960948178),(-2443370083960948097)⟩,⟨(-7177892422141741543),(-7177892422141741459)⟩⟩,⟨⟨(-2470879001183309104),(-2470879001183309026)⟩,⟨(-6377496563276290506),(-6377496563276290427)⟩⟩,⟨⟨(-2464504457612623108),(-2464504457612623020)⟩,⟨(-5654193973290590333),(-5654193973290590243)⟩⟩,⟨⟨(-2430649764017992524),(-2430649764017992453)⟩,⟨(-5002006990711717297),(-5002006990711717225)⟩⟩,⟨⟨(-2374863671293672025),(-2374863671293671951)⟩,⟨(-4415230755617312642),(-4415230755617312565)⟩⟩,⟨⟨(-2301929093247686693),(-2301929093247686628)⟩,⟨(-3888449646077516119),(-3888449646077516054)⟩⟩,⟨⟨(-2215945241624392705),(-2215945241624392628)⟩,⟨(-3416547656843480683),(-3416547656843480609)⟩⟩,⟨⟨(-2120403332043578189),(-2120403332043578131)⟩,⟨(-2994713595494098516),(-2994713595494098458)⟩⟩,⟨⟨(-2018256068527512565),(-2018256068527512507)⟩,⟨(-2618441893913287765),(-2618441893913287707)⟩⟩,⟨⟨(-1911981153343850044),(-1911981153343849986)⟩,⟨(-2283529757508077005),(-2283529757508076947)⟩⟩,⟨⟨(-1803639098961188671),(-1803639098961188620)⟩,⟨(-1986071301738622482),(-1986071301738622431)⟩⟩] +lemma kernel13_1_r3_8_eq : ∀ k : Fin 16, kernel13_1Expr 3 8 k = kernel13_1_r3_8 k := by decide +kernel +noncomputable def kernel13_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-1694925640935353901),(-1694925640935353859)⟩,⟨(-1722449255909926072),(-1722449255909926033)⟩⟩,⟨⟨(-1587219065438372489),(-1587219065438372433)⟩,⟨(-1489324748227872417),(-1489324748227872364)⟩⟩,⟨⟨(-1481622773796824597),(-1481622773796824553)⟩,⟨(-1283625624180924998),(-1283625624180924953)⟩⟩,⟨⟨(-1379003409668064529),(-1379003409668064485)⟩,⟨(-1102533692593876096),(-1102533692593876052)⟩⟩,⟨⟨(-1280024873148411405),(-1280024873148411363)⟩,⟨(-943471240334237389),(-943471240334237349)⟩⟩,⟨⟨(-1185178540918523958),(-1185178540918523921)⟩,⟨(-804087107673533577),(-804087107673533540)⟩⟩,⟨⟨(-1094810003170794213),(-1094810003170794171)⟩,⟨(-682242571681451339),(-682242571681451300)⟩⟩,⟨⟨(-1009142617154043996),(-1009142617154043959)⟩,⟨(-575997244667157287),(-575997244667157250)⟩⟩,⟨⟨(-928298164273122057),(-928298164273122015)⟩,⟨(-483595158437021937),(-483595158437021898)⟩⟩,⟨⟨(-852314883295545955),(-852314883295545911)⟩,⟨(-403451172830788950),(-403451172830788905)⟩⟩,⟨⟨(-781163136785409501),(-781163136785409470)⟩,⟨(-334137818418889324),(-334137818418889294)⟩⟩,⟨⟨(-714758951791018730),(-714758951791018697)⟩,⟨(-274372658161002254),(-274372658161002219)⟩⟩,⟨⟨(-652975659388116742),(-652975659388116710)⟩,⟨(-223006230995159319),(-223006230995159284)⟩⟩,⟨⟨(-595653841205942145),(-595653841205942112)⟩,⟨(-179010621495201108),(-179010621495201073)⟩⟩,⟨⟨(-542609774773200897),(-542609774773200861)⟩,⟨(-141468683647595277),(-141468683647595245)⟩⟩,⟨⟨(-493642553607399022),(-493642553607398992)⟩,⟨(-109563933204248331),(-109563933204248300)⟩⟩] +lemma kernel13_1_r3_9_eq : ∀ k : Fin 16, kernel13_1Expr 3 9 k = kernel13_1_r3_9 k := by decide +kernel +noncomputable def kernel13_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-448540042587643977),(-448540042587643954)⟩,⟨(-82571111719784006),(-82571111719783983)⟩⟩,⟨⟨(-407083814417458517),(-407083814417458494)⟩,⟨(-59847416042635921),(-59847416042635898)⟩⟩,⟨⟨(-369053198989530812),(-369053198989530781)⟩,⟨(-40824379473339529),(-40824379473339499)⟩⟩,⟨⟨(-334228564271306089),(-334228564271306051)⟩,⟨(-25000384817738046),(-25000384817738008)⟩⟩,⟨⟨(-302393934978667681),(-302393934978667651)⟩,⟨(-11933784948739707),(-11933784948739676)⟩⟩,⟨⟨(-273339043814901229),(-273339043814901194)⟩,⟨(-1236603063959501),(-1236603063959468)⟩⟩,⟨⟨(-246860899427533411),(-246860899427533373)⟩,⟨7431217580565645,7431217580565683⟩⟩,⟨⟨(-222764945466797702),(-222764945466797666)⟩,⟨14367046221792844,14367046221792877⟩⟩,⟨⟨(-200865876195759579),(-200865876195759541)⟩,⟨19830312001538242,19830312001538280⟩⟩,⟨⟨(-180988165974240539),(-180988165974240508)⟩,⟨24046799024953123,24046799024953153⟩⟩,⟨⟨(-162966362580711090),(-162966362580711064)⟩,⟨27212521569542903,27212521569542931⟩⟩,⟨⟨(-146645187707547574),(-146645187707547538)⟩,⟨29497211270503995,29497211270504028⟩⟩,⟨⟨(-131879482021447712),(-131879482021447681)⟩,⟨31047447119017103,31047447119017134⟩⟩,⟨⟨(-118534026876376244),(-118534026876376221)⟩,⟨31989457883678406,31989457883678429⟩⟩,⟨⟨(-106483270054291138),(-106483270054291107)⟩,⟨32431625164768138,32431625164768169⟩⟩,⟨⟨(-95610978742241990),(-95610978742241956)⟩,⟨32466713770422988,32466713770423024⟩⟩] +lemma kernel13_1_r3_10_eq : ∀ k : Fin 16, kernel13_1Expr 3 10 k = kernel13_1_r3_10 k := by decide +kernel +noncomputable def kernel13_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-85809839287167747),(-85809839287167721)⟩,⟨32173854508365009,32173854508365038⟩⟩,⟨⟨(-76981020057142145),(-76981020057142108)⟩,⟨31620302854408222,31620302854408256⟩⟩,⟨⟨(-69033710937024465),(-69033710937024427)⟩,⟨30862995320521788,30862995320521827⟩⟩,⟨⟨(-61884650556716791),(-61884650556716760)⟩,⟨29949923725833350,29949923725833381⟩⟩,⟨⟨(-55457650253130580),(-55457650253130547)⟩,⟨28921345993469111,28921345993469148⟩⟩,⟨⟨(-49683121966675877),(-49683121966675851)⟩,⟨27810850569906855,27810850569906883⟩⟩,⟨⟨(-44497615736357049),(-44497615736357022)⟩,⟨26646290103057789,26646290103057818⟩⟩,⟨⟨(-39843371153760027),(-39843371153760000)⟩,⟨25450598628798439,25450598628798467⟩⟩,⟨⟨(-35667886037307742),(-35667886037307718)⟩,⟨24242505208581769,24242505208581793⟩⟩,⟨⟨(-31923504668620603),(-31923504668620579)⟩,⟨23037155736200898,23037155736200921⟩⟩,⟨⟨(-28567027169550015),(-28567027169549983)⟩,⟨21846653490998770,21846653490998802⟩⟩,⟨⟨(-25559340970661453),(-25559340970661429)⟩,⟨20680527957520405,20680527957520429⟩⟩,⟨⟨(-22865074811004293),(-22865074811004267)⟩,⟨19546140456279340,19546140456279369⟩⟩,⟨⟨(-20452275298322255),(-20452275298322231)⟩,⟨18449034234498875,18449034234498898⟩⟩,⟨⟨(-18292105733712256),(-18292105733712222)⟩,⟨17393235846218241,17393235846218277⟩⟩,⟨⟨(-16358566652139790),(-16358566652139753)⟩,⟨16381513904334060,16381513904334094⟩⟩] +lemma kernel13_1_r3_11_eq : ∀ k : Fin 16, kernel13_1Expr 3 11 k = kernel13_1_r3_11 k := by decide +kernel +noncomputable def kernel13_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-14628237338757236),(-14628237338757207)⟩,⟨15415600608934833,15415600608934859⟩⟩,⟨⟨(-13080037440672591),(-13080037440672564)⟩,⟨14496380842425195,14496380842425224⟩⟩,⟨⟨(-11695007696005787),(-11695007696005758)⟩,⟨13624053068065623,13624053068065650⟩⟩,⟨⟨(-10456108739235999),(-10456108739235970)⟩,⟨12798265770304370,12798265770304397⟩⟩,⟨⟨(-9348036907519680),(-9348036907519654)⟩,⟨12018232728341162,12018232728341191⟩⟩,⟨⟨(-8357055961302611),(-8357055961302579)⟩,⟨11282830014545075,11282830014545107⟩⟩,⟨⟨(-7470843639439892),(-7470843639439860)⟩,⟨10590677252621686,10590677252621717⟩⟩,⟨⟨(-6678351990175643),(-6678351990175619)⟩,⟨9940205352943786,9940205352943810⟩⟩,⟨⟨(-5969680451352513),(-5969680451352488)⟩,⟨9329712660598445,9329712660598469⟩⟩,⟨⟨(-5335960693306490),(-5335960693306461)⟩,⟨8757411202054808,8757411202054835⟩⟩,⟨⟨(-4769252283718354),(-4769252283718330)⟩,⟨8221464495748939,8221464495748963⟩⟩,⟨⟨(-4262448283318378),(-4262448283318346)⟩,⟨7720018197374111,7720018197374143⟩⟩,⟨⟨(-3809189933208778),(-3809189933208746)⟩,⟨7251224679544952,7251224679544984⟩⟩,⟨⟨(-3403789647417315),(-3403789647417286)⟩,⟨6813262495285805,6813262495285832⟩⟩,⟨⟨(-3041161577120660),(-3041161577120620)⟩,⟨6404351543203948,6404351543203987⟩⟩,⟨⟨(-2716759064992057),(-2716759064992028)⟩,⟨6022764637180841,6022764637180868⟩⟩] +lemma kernel13_1_r3_12_eq : ∀ k : Fin 16, kernel13_1Expr 3 12 k = kernel13_1_r3_12 k := by decide +kernel +noncomputable def kernel13_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-2426518358733624),(-2426518358733597)⟩,⟨5666836083074106,5666836083074136⟩⟩,⟨⟨(-2166808001597956),(-2166808001597927)⟩,⟨5334967777577808,5334967777577835⟩⟩,⟨⟨(-1934383364266871),(-1934383364266844)⟩,⟨5025633268514224,5025633268514253⟩⟩,⟨⟨(-1726345826617522),(-1726345826617493)⟩,⟨4737380150059135,4737380150059162⟩⟩,⟨⟨(-1540106159534977),(-1540106159534937)⟩,⟨4468831109510644,4468831109510684⟩⟩,⟨⟨(-1373351695960955),(-1373351695960923)⟩,⟨4218683893106533,4218683893106565⟩⟩,⟨⟨(-1224016916790112),(-1224016916790082)⟩,⟨3985710416104203,3985710416104230⟩⟩,⟨⟨(-1090257111069294),(-1090257111069269)⟩,⟨3768755205998668,3768755205998693⟩⟩,⟨⟨(-970424801286927),(-970424801286895)⟩,⟨3566733336601546,3566733336601578⟩⟩,⟨⟨(-863048653446556),(-863048653446531)⟩,⟨3378627984063945,3378627984063969⟩⟩,⟨⟨(-766814618208267),(-766814618208232)⟩,⟨3203487713201850,3203487713201887⟩⟩,⟨⟨(-680549073770446),(-680549073770414)⟩,⟨3040423583151310,3040423583151343⟩⟩,⟨⟨(-603203763480185),(-603203763480152)⟩,⟨2888606144981926,2888606144981958⟩⟩,⟨⟨(-533842341529967),(-533842341529943)⟩,⟨2747262390029021,2747262390029045⟩⟩,⟨⟨(-471628358654448),(-471628358654416)⟩,⟨2615672696014951,2615672696014984⟩⟩,⟨⟨(-415814536610147),(-415814536610118)⟩,⟨2493167808211307,2493167808211334⟩⟩] +lemma kernel13_1_r3_13_eq : ∀ k : Fin 16, kernel13_1Expr 3 13 k = kernel13_1_r3_13 k := by decide +kernel +noncomputable def kernel13_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-365733195530965),(-365733195530937)⟩,⟨2379125884679654,2379125884679683⟩⟩,⟨⟨(-320787712123006),(-320787712122981)⟩,⟨2272969627785849,2272969627785874⟩⟩,⟨⟨(-280444899211544),(-280444899211515)⟩,⟨2174163518511118,2174163518511145⟩⟩,⟨⟨(-244228208488884),(-244228208488855)⟩,⟨2082211165407477,2082211165407505⟩⟩,⟨⟨(-211711668540826),(-211711668540786)⟩,⟨1996652776215423,1996652776215463⟩⟩,⟨⟨(-182514479447020),(-182514479446995)⟩,⟨1917062757047944,1917062757047969⟩⟩,⟨⟨(-156296193548663),(-156296193548628)⟩,⟨1843047441535795,1843047441535833⟩⟩,⟨⟨(-132752419439290),(-132752419439242)⟩,⟨1774242950328451,1774242950328499⟩⟩,⟨⟨(-111610992940420),(-111610992940392)⟩,⟨1710313179770977,1710313179771007⟩⟩,⟨⟨(-92628564843589),(-92628564843562)⟩,⟨1650947917359821,1650947917359850⟩⟩,⟨⟨(-75587560601340),(-75587560601310)⟩,⟨1595861080659926,1595861080659954⟩⟩,⟨⟨(-60293471993035),(-60293471993006)⟩,⟨1544789075690319,1544789075690347⟩⟩,⟨⟨(-46572445130352),(-46572445130319)⟩,⟨1497489270313613,1497489270313646⟩⟩,⟨⟨(-34269133055316),(-34269133055291)⟩,⟨1453738577858770,1453738577858795⟩⟩,⟨⟨(-23244784664393),(-23244784664361)⟩,⟨1413332146036174,1413332146036206⟩⟩,⟨⟨(-13375544808978),(-13375544808948)⟩,⟨1376082146143570,1376082146143597⟩⟩] +lemma kernel13_1_r3_14_eq : ∀ k : Fin 16, kernel13_1Expr 3 14 k = kernel13_1_r3_14 k := by decide +kernel +noncomputable def kernel13_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-4550943212829),(-4550943212789)⟩,⟨1341816657588094,1341816657588135⟩⟩,⟨⟨3327447654899,3327447654924⟩,⟨1310378642847714,1310378642847739⟩⟩,⟨⟨10347203374891,10347203374915⟩,⟨1281625008146610,1281625008146635⟩⟩,⟨⟨16586102660005,16586102660035⟩,⟨1255425745314671,1255425745314699⟩⟩,⟨⟨22113060545839,22113060545872⟩,⟨1231663150527737,1231663150527770⟩⟩,⟨⟨26988951896249,26988951896279⟩,⟨1210231115877169,1210231115877196⟩⟩,⟨⟨31267335979751,31267335979776⟩,⟨1191034489985779,1191034489985803⟩⟩,⟨⟨34995091565419,34995091565443⟩,⟨1173988504168798,1173988504168822⟩⟩,⟨⟨38212970806635,38212970806665⟩,⟨1159018260927123,1159018260927151⟩⟩,⟨⟨40956079112134,40956079112166⟩,⟨1146058281854516,1146058281854549⟩⟩,⟨⟨43254287231679,43254287231712⟩,⟨1135052112336386,1135052112336418⟩⟩,⟨⟨45132580895975,45132580896002⟩,⟨1125951980715039,1125951980715068⟩⟩,⟨⟨46611352534698,46611352534731⟩,⟨1118718509892002,1118718509892034⟩⟩,⟨⟨47706638842091,47706638842124⟩,⟨1113320479633588,1113320479633621⟩⟩,⟨⟨48430307256377,48430307256401⟩,⟨1109734638138116,1109734638138140⟩⟩,⟨⟨48790193757322,48790193757350⟩,⟨1107945561715043,1107945561715073⟩⟩] +lemma kernel13_1_r3_15_eq : ∀ k : Fin 16, kernel13_1Expr 3 15 k = kernel13_1_r3_15 k := by decide +kernel +noncomputable def kernel13_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel13_1_r3_0,kernel13_1_r3_1,kernel13_1_r3_2,kernel13_1_r3_3,kernel13_1_r3_4,kernel13_1_r3_5,kernel13_1_r3_6,kernel13_1_r3_7,kernel13_1_r3_8,kernel13_1_r3_9,kernel13_1_r3_10,kernel13_1_r3_11,kernel13_1_r3_12,kernel13_1_r3_13,kernel13_1_r3_14,kernel13_1_r3_15] +lemma kernel13_1_r3_eq (i k : Fin 16) : kernel13_1Expr 3 i k = kernel13_1_r3 i k := by + fin_cases i + · exact kernel13_1_r3_0_eq k + · exact kernel13_1_r3_1_eq k + · exact kernel13_1_r3_2_eq k + · exact kernel13_1_r3_3_eq k + · exact kernel13_1_r3_4_eq k + · exact kernel13_1_r3_5_eq k + · exact kernel13_1_r3_6_eq k + · exact kernel13_1_r3_7_eq k + · exact kernel13_1_r3_8_eq k + · exact kernel13_1_r3_9_eq k + · exact kernel13_1_r3_10_eq k + · exact kernel13_1_r3_11_eq k + · exact kernel13_1_r3_12_eq k + · exact kernel13_1_r3_13_eq k + · exact kernel13_1_r3_14_eq k + · exact kernel13_1_r3_15_eq k +noncomputable def kernel13_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-518985832410273876557694019),(-518985832410273870597858090)⟩,⟨172032300626377851278842926,172032300626377857232656020⟩⟩,⟨⟨(-518585403797444646142162345),(-518585403797444640185431408)⟩,⟨172196591591257639547428282,172196591591257645498136379⟩⟩,⟨⟨(-517785039083965130376970354),(-517785039083965124426456083)⟩,⟨172524230942152921291346371,172524230942152927235837801⟩⟩,⟨⟨(-516585724245016516074392895),(-516585724245016510133198408)⟩,⟨173013337916060543880199528,173013337916060549815371212⟩⟩,⟨⟨(-514988940598861155762856631),(-514988940598861149834072257)⟩,⟨173661102338357500304949311,173661102338357506227710989⟩⟩,⟨⟨(-512996667573262774634925979),(-512996667573262768721625028)⟩,⟨174463797739243921655236622,174463797739243927562515108⟩⟩,⟨⟨(-510611386294427248626663739),(-510611386294427242731898407)⟩,⟨175416798763292575369062808,175416798763292581257806070⟩⟩,⟨⟨(-507836083914393135646609198),(-507836083914393129773406007)⟩,⟨176514602804327841111145658,176514602804327846978327427⟩⟩,⟨⟨(-504674258573418223677403839),(-504674258573418217828760535)⟩,⟨177750855780888826970397516,177750855780888832813020375⟩⟩,⟨⟨(-501129924875596872682126151),(-501129924875596866861005726)⟩,⟨179118381950562718984129707,179118381950562724799231076⟩⟩,⟨⟨(-497207619738898796569666807),(-497207619738898790778996492)⟩,⟨180609217644520968104328181,180609217644520973888981349⟩⟩,⟨⟨(-492912408465229151283660178),(-492912408465229145526323184)⟩,⟨182214648786675769482540282,182214648786675775233862664⟩⟩,⟨⟨(-488249890862146850534836638),(-488249890862146844813674724)⟩,⟨183925252045029585044417427,183925252045029590759568013⟩⟩,⟨⟨(-483226207235704359064111993),(-483226207235704353381912364)⟩,⟨185730939446057912664926564,185730939446057918341119004⟩⟩,⟨⟨(-477848044063634714831779715),(-477848044063634709191283312)⟩,⟨187621006266396999699027448,187621006266397005333521804⟩⟩,⟨⟨(-472122639149941140106175295),(-472122639149941134510058639)⟩,⟨189584181999766161655912963,189584181999766167246033845⟩⟩] +lemma kernel13_1_r4_0_eq : ∀ k : Fin 16, kernel13_1Expr 4 0 k = kernel13_1_r4_0 k := by decide +kernel +noncomputable def kernel13_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-466057786055954926836243716),(-466057786055954921287134528)⟩,⟨191608684181011914643418497,191608684181011920186539458⟩⟩,⟨⟨(-459661837599213335679238965),(-459661837599213330179687081)⟩,⟨193682274833501991783051133,193682274833501997276623749⟩⟩,⟨⟨(-452943708210146268130689810),(-452943708210146262683194640)⟩,⟨195792319290915521300967299,195792319290915526742493722⟩⟩,⟨⟨(-445912874937602856623735130),(-445912874937602851230708146)⟩,⟨197925847129874988077993365,197925847129874993465063821⟩⟩,⟨⟨(-438579376897729492611451827),(-438579376897729487275255467)⟩,⟨200069614935958850595551784,200069614935958855925805699⟩⟩,⟨⟨(-430953812966639233580962453),(-430953812966639228303853766)⟩,⟨202210170612541579672447643,202210170612541584943629965⟩⟩,⟨⟨(-423047337525675850097727507),(-423047337525675844881916581)⟩,⟨204333918929757898340299439,204333918929757903550202228⟩⟩,⟨⟨(-414871654078837184885500272),(-414871654078837179733082456)⟩,⟨206427187999812900010076931,206427187999812905156607120⟩⟩,⟨⟨(-406439006575021258612641075),(-406439006575021253525671139)⟩,⟨208476296354995923728441691,208476296354995928809546941⟩⟩,⟨⟨(-397762168283109938684978450),(-397762168283109933665372531)⟩,⟨210467620296241825989205176,210467620296241831002971905⟩⟩,⟨⟨(-388854428085400417163895575),(-388854428085400412213535378)⟩,⟨212387661173056728583170877,212387661173056733527720074⟩⟩,⟨⟨(-379729574074402200274288819),(-379729574074402195394911341)⟩,⟨214223112250222326691576041,214223112250222331565173507⟩⟩,⟨⟨(-370401874359381950929775212),(-370401874359381946123092996)⟩,⟨215960924813044860562495292,215960924813044865363431408⟩⟩,⟨⟨(-360886055012083559361486267),(-360886055012083554629037855)⟩,⟨217588373161146631681881705,217588373161146636408620954⟩⟩,⟨⟨(-351197275105578646526078848),(-351197275105578641869388404)⟩,⟨219093118141025212869315780,219093118141025217520337118⟩⟩,⟨⟨(-341351098825996311388653761),(-341351098825996306809068339)⟩,⟨220463268869932675928940363,220463268869932680502899931⟩⟩] +lemma kernel13_1_r4_1_eq : ∀ k : Fin 16, kernel13_1Expr 4 1 k = kernel13_1_r4_1 k := by decide +kernel +noncomputable def kernel13_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-331363464663705523844591336),(-331363464663705519343460129)⟩,⟨221687442308145067592827002,221687442308145072088378896⟩⟩,⟨⟨(-321250651718128472605119301),(-321250651718128468183574608)⟩,⟨222754820343476048732897849,222754820343476053148913094⟩⟩,⟨⟨(-311029243178484001822503130),(-311029243178483997481693056)⟩,⟨223655204060995251436967485,223655204060995255772301371⟩⟩,⟨⟨(-300716087071121252186253676),(-300716087071121247926916643)⟩,⟨224379064882378883242707193,224379064882378887496752126⟩⟩,⟨⟨(-290328254392420230765561076),(-290328254392420226588606962)⟩,⟨224917592273163253833387144,224917592273163258005274714⟩⟩,⟨⟨(-279882994774217748524333926),(-279882994774217744430482629)⟩,⟨225262737732383987944439739,225262737732383992033450130⟩⟩,⟨⟨(-269397689856070426441798839),(-269397689856070422431820168)⟩,⟨225407254797633160530467012,225407254797633164535830108⟩⟩,⟨⟨(-258889804565097775684856262),(-258889804565097771759276670)⟩,⟨225344734819396581323652501,225344734819396585244841111⟩⟩,⟨⟨(-248376836529367453885402037),(-248376836529367450044822102)⟩,⟨225069638281561133053624960,225069638281561136890037388⟩⟩,⟨⟨(-237876263874507965622363894),(-237876263874507961867083510)⟩,⟨224577321470098308364124754,224577321470098312115459570⟩⟩,⟨⟨(-227405491675187422909003407),(-227405491675187419239415397)⟩,⟨223864058318999519201650304,223864058318999522867512777⟩⟩,⟨⟨(-216981797353019757606840620),(-216981797353019754023063143)⟩,⟨222927057291400149409080336,222927057291400152989349997⟩⟩,⟨⟨(-206622275330107612209044911),(-206622275330107608711308592)⟩,⟨221764473184296413351153313,221764473184296416845596896⟩⟩,⟨⟨(-196343781262579194527073364),(-196343781262579191114395474)⟩,⟨220375413777121719597691158,220375413777121723007288341⟩⟩,⟨⟨(-186162876190922379343493489),(-186162876190922376015279402)⟩,⟨218759941277474947232279675,218759941277474950557621724⟩⟩,⟨⟨(-176095770953486362296675383),(-176095770953486359052696218)⟩,⟨216919068551228960420828785,216919068551228963662140860⟩⟩] +lemma kernel13_1_r4_2_eq : ∀ k : Fin 16, kernel13_1Expr 4 2 k = kernel13_1_r4_2 k := by decide +kernel +noncomputable def kernel13_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-166158271216060269441104831),(-166158271216060266281295055)⟩,⟨214854750158822847523387270,214854750158822850680730888⟩⟩,⟨⟨(-156365723473830634237776003),(-156365723473830631161695001)⟩,⟨212569868254469325264507717,212569868254469328338319133⟩⟩,⟨⟨(-146732962382179190706929362),(-146732962382179187714319976)⟩,⟨210068213439990494943648348,210068213439990497934180106⟩⟩,⟨⟨(-137274259769656547868307039),(-137274259769656544958588696)⟩,⟨207354460699722325839530929,207354460699722328747358700⟩⟩,⟨⟨(-128003275680038749359865746),(-128003275680038746532657492)⟩,⟨204434140577086608739333140,204434140577086611564832734⟩⟩,⟨⟨(-118933011780661261601178356),(-118933011780661258855707387)⟩,⟨201313605786702123712739130,201313605786702126456677945⟩⟩,⟨⟨(-110075767461283790076863269),(-110075767461283787412575578)⟩,⟨197999993487979339335782382,197999993487979341998708832⟩⟩,⟨⟨(-101443098931661093778904368),(-101443098931661091194338099)⟩,⟨194501183476705386001839383,194501183476705388585209243⟩⟩,⟨⟨(-93045781606907105265831707),(-93045781606907102760189036)⟩,⟨190825752579877836749701511,190825752579877839254306562⟩⟩,⟨⟨(-84893776047804475477466471),(-84893776047804473049701969)⟩,⟨186982925565699596790104654,186982925565699599216984194⟩⟩,⟨⟨(-76996197698624837928778786),(-76996197698624835578110522)⟩,⟨182982522904932440891651284,182982522904932443241581003⟩⟩,⟨⟨(-69361290638013764484560439),(-69361290638013762209856601)⟩,⟨178834905741473461775575388,178834905741473464049680731⟩⟩,⟨⟨(-61996405529314774266934375),(-61996405529314772067336293)⟩,⟨174550918448840882024428186,174550918448840884223561371⟩⟩,⟨⟨(-54907981925641343885116451),(-54907981925641341759342421)⟩,⟨170141829165034464314689987,170141829165034466440126201⟩⟩,⟨⟨(-48101535052360230577414833),(-48101535052360228524471134)⟩,⟨165619268710802281333047837,165619268710802283385774226⟩⟩,⟨⟨(-41581647155748704838049705),(-41581647155748702856590030)⟩,⟨160995168305563569175084493,160995168305563571156440782⟩⟩] +lemma kernel13_1_r4_3_eq : ∀ k : Fin 16, kernel13_1Expr 4 3 k = kernel13_1_r4_3 k := by decide +kernel +noncomputable def kernel13_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-35351963471773375605831231),(-35351963471773373694818934)⟩,⟨156281696501005132062214012,156281696501005133973230223⟩⟩,⟨⟨(-29415192833561713867347492),(-29415192833561712025301746)⟩,⟨151491195754620963414647469,151491195754620965256797866⟩⟩,⟨⟨(-23773112900559054491713276),(-23773112900559052717474941)⟩,⟨146636119064173594205855973,146636119064173595980293131⟩⟩,⟨⟨(-18426579956946667874843151),(-18426579956946666166905564)⟩,⟨141728967079231592751030948,141728967079231594459255052⟩⟩,⟨⟨(-13375543192001821386917187),(-13375543192001819744093970)⟩,⟨136782226097629445976740065,136782226097629447619931047⟩⟩,⟨⟨(-8619063341063982006219639),(-8619063341063980426905559)⟩,⟨131808307342990641498561811,131808307342990643078318602⟩⟩,⟨⟨(-4155335532977415337478707),(-4155335532977413820397038)⟩,⟨126819487904476232532735563,126819487904476234050328639⟩⟩,⟨⟨18283841360332517666191,18283841360333974127426⟩,⟨121827853701829410234201407,121827853701829411691236668⟩⟩,⟨⟨3905246454090791029252399,3905246454090792426365004⟩,⟨116845244817775470884724924,116845244817775472282468177⟩⟩,⟨⟨7509777801097366070448485,7509777801097367409904723⟩,⟨111883203516131465721560499,111883203516131467061698249⟩⟩,⟨⟨10836839665095213580832068,10836839665095214863979081⟩,⟨106952925237834955236023530,106952925237834956519897241⟩⟩,⟨⟨13892089570042819857508128,13892089570042821086009655⟩,⟨102065212838796434007202712,102065212838796435236470698⟩⟩,⟨⟨16681837535117918395170855,16681837535117919574131966⟩,⟨97230434303316952528728006,97230434303316953708489362⟩⟩,⟨⟨19213000452791831654172344,19213000452791832785284077⟩,⟨92458484135111224301314888,92458484135111225433252156⟩⟩,⟨⟨21493054428681006144580820,21493054428681007228956493⟩,⟨87758748595071143913894761,87758748595071144999101291⟩⟩,⟨⟨23529985430759764583898769,23529985430759765622933577⟩,⟨83140074921139050282700423,83140074921139051322568230⟩⟩] +lemma kernel13_1_r4_4_eq : ∀ k : Fin 16, kernel13_1Expr 4 4 k = kernel13_1_r4_4 k := by decide +kernel +noncomputable def kernel13_1_r4_5 : Fin 16 → CBox := ![⟨⟨25332238602129853387655948,25332238602129854382408623⟩,⟨78610744631383584999848816,78610744631383585995433560⟩⟩,⟨⟨26908666594844547063876655,26908666594844548015791866⟩,⟨74178450976933972127887396,74178450976933973080630977⟩⟩,⟨⟨28268477282300514295226153,28268477282300515205412637⟩,⟨69850280577177951547840264,69850280577177952458848744⟩⟩,⟨⟨29421181204499451539007226,29421181204499452408854404⟩,⟨65632699235903706899429668,65632699235903707770090065⟩⟩,⟨⟨30376539094139866437050906,30376539094139867267629660⟩,⟨61531541904194365057754360,61531541904194365889135268⟩⟩,⟨⟨31144509822157849009249373,31144509822157849801969403⟩,⟨57552006724176643601164895,57552006724176644394674007⟩⟩,⟨⟨31735199089156708289321714,31735199089156709045277853⟩,⟨53698653057475173941190007,53698653057475174697920250⟩⟩,⟨⟨32158809174340785456993545,32158809174340786177535661⟩,⟨49975403373700337171268424,49975403373700337892568036⟩⟩,⟨⟨32425590036316637391182684,32425590036316638077348645⟩,⟨46385548847743784092217815,46385548847743784779123106⟩⟩,⟨⟨32545792040686049792978008,32545792040686050446128876⟩,⟨42931758490287553969305796,42931758490287554623176555⟩⟩,⟨⟨32529620567990175346540386,32529620567990175967763101⟩,⟨39616091613934862182785962,39616091613934862804696509⟩⟩,⟨⟨32387192732548131235898419,32387192732548131826568133⟩,⟨36440013417896192882024478,36440013417896193473316149⟩⟩,⟨⟨32128496418353763900908003,32128496418353764462009461⟩,⟨33404413457333161376615650,33404413457333161938276679⟩⟩,⟨⟨31763351812745622870285625,31763351812745623403078525⟩,⟨30509626749360763123367798,30509626749360763656661401⟩⟩,⟨⟨31301375592345590273522627,31301375592345590779031957⟩,⟨27755457256388217654889803,27755457256388218160844383⟩⟩,⟨⟨30751947889068734969155926,30751947889068735448837149⟩,⟨25141203478958146764829765,25141203478958147244904210⟩⟩] +lemma kernel13_1_r4_5_eq : ∀ k : Fin 16, kernel13_1Expr 4 5 k = kernel13_1_r4_5 k := by decide +kernel +noncomputable def kernel13_1_r4_6 : Fin 16 → CBox := ![⟨⟨30124182137134155121330259,30124182137134155576067485⟩,⟨22665685884508975840338078,22665685884508976295419763⟩⟩,⟨⟨29426897875239251667861902,29426897875239252098797906⟩,⟨20327275895490308560732843,20327275895490308991967770⟩⟩,⟨⟨28668596551672080739827458,28668596551672081147844011⟩,⟨18123926159929749321422415,18123926159929749729695451⟩⟩,⟨⟨27857440354387691080930897,27857440354387691467082960⟩,⟨16053201829778458316142124,16053201829778458702511261⟩⟩,⟨⟨27001234063206834918644668,27001234063206835283749929⟩,⟨14112312577022260217941673,14112312577022260583227515⟩⟩,⟨⟨26107409897531478883068243,26107409897531479228154044⟩,⟨12298145084483066605851288,12298145084483066951084002⟩⟩,⟨⟨25183015310511513739106172,25183015310511514065261226⟩,⟨10607295757279285075495318,10607295757279285401766318⟩⟩,⟨⟨24234703659617675031883084,24234703659617675340124926⟩,⟨9036103411874268669871429,9036103411874268978200853⟩⟩,⟨⟨23268727664228665654390128,23268727664228665945411946⟩,⟨7580681712315281295719855,7580681712315281586803378⟩⟩,⟨⟨22290935543251656943823897,22290935543251657218510686⟩,⟨6236951137437795476095101,6236951137437795750820084⟩⟩,⟨⟨21306769710064203137302163,21306769710064203396333375⟩,⟨5000670278259620785782880,5000670278259621044831038⟩⟩,⟨⟨20321267888265132974932854,20321267888265133219113358⟩,⟨3867466281290559205892819,3867466281290559450071150⟩⟩,⟨⟨19339066499899003099973728,19339066499899003329957779⟩,⟨2832864270809047139690959,2832864270809047369655770⟩⟩,⟨⟨18364406167994507586273535,18364406167994507802939854⟩,⟨1892315601082492334325221,1892315601082492550957181⟩⟩,⟨⟨17401139167428596823361547,17401139167428597027293954⟩,⟨1041224807812361467036772,1041224807812361670921493⟩⟩,⟨⟨16452738652268482251539864,16452738652268482443426681⟩,⟨274975146555448318598873,274975146555448510426342⟩⟩] +lemma kernel13_1_r4_6_eq : ∀ k : Fin 16, kernel13_1Expr 4 6 k = kernel13_1_r4_6 k := by decide +kernel +noncomputable def kernel13_1_r4_7 : Fin 16 → CBox := ![⟨⟨15522309483805020800621607,15522309483805020980986327⟩,⟨(-411047375694223327462289),(-411047375694223147166998)⟩⟩,⟨⟨14612600481405118955487581,14612600481405119124991348⟩,⟨(-1021431551374294900751015),(-1021431551374294731325319)⟩⟩,⟨⟨13726017917991791477133017,13726017917991791636281216⟩,⟨(-1560720163487905810153638),(-1560720163487905651090791)⟩⟩,⟨⟨12864640083306589963343709,12864640083306590112727151⟩,⟨(-2033390857588843755168607),(-2033390857588843605876559)⟩⟩,⟨⟨12030232741004970980362722,12030232741004971120435207⟩,⟨(-2443838718692450312811023),(-2443838718692450172834803)⟩⟩,⟨⟨11224265309954249022546921,11224265309954249153867460⟩,⟨(-2796360561519516263872426),(-2796360561519516132650900)⟩⟩,⟨⟨10447927605710610169278567,10447927605710610292278371⟩,⟨(-3095140927768870799887222),(-3095140927768870676986123)⟩⟩,⟨⟨9702146984904187893682051,9702146984904188008932455⟩,⟨(-3344239770451126913560024),(-3344239770451126798407501)⟩⟩,⟨⟨8987605743013039271990153,8987605743013039380189765⟩,⟨(-3547581792775341798563236),(-3547581792775341690460142)⟩⟩,⟨⟨8304758624609490358674956,8304758624609490460250280⟩,⟨(-3708947397718289678599743),(-3708947397718289577119192)⟩⟩,⟨⟨7653850314467172481286663,7653850314467172576556358⟩,⟨(-3831965194261048614882050),(-3831965194261048519705036)⟩⟩,⟨⟨7034932787777465855289331,7034932787777465944630581⟩,⟨(-3920105997371105016719449),(-3920105997371104927468505)⟩⟩,⟨⟨6447882407996999604933304,6447882407996999688628821⟩,⟨(-3976678251145508464783235),(-3976678251145508381175389)⟩⟩,⟨⟨5892416671395613308337168,5892416671395613386741912⟩,⟨(-4004824798102047570954293),(-4004824798102047492634401)⟩⟩,⟨⟨5368110508065762046241370,5368110508065762119622438⟩,⟨(-4007520912387401337464879),(-4007520912387401264165669)⟩⟩,⟨⟨4874412059866679817215461,4874412059866679885886838⟩,⟨(-3987573510627653602399328),(-3987573510627653533806702)⟩⟩] +lemma kernel13_1_r4_7_eq : ∀ k : Fin 16, kernel13_1Expr 4 7 k = kernel13_1_r4_7 k := by decide +kernel +noncomputable def kernel13_1_r4_8 : Fin 16 → CBox := ![⟨⟨4410657866395600596884909,4410657866395600661079278⟩,⟨(-3947621451230210002448132),(-3947621451230209938329297)⟩⟩,⟨⟨3976087400499646350177098,3976087400499646410202159⟩,⟨(-3890136831100117178493656),(-3890136831100117118535524)⟩⟩,⟨⟨3569856904971695828811890,3569856904971695884887060⟩,⟨(-3817427187892947128529540),(-3817427187892947072513298)⟩⟩,⟨⟨3191052491828530290253017,3191052491828530342634801⟩,⟨(-3731638516018963106541020),(-3731638516018963054210784)⟩⟩,⟨⟨2838702474877741650995057,2838702474877741699875344⟩,⟨(-3634759005562176215311286),(-3634759005562176166475748)⟩⟩,⟨⟨2511788915080314860277320,2511788915080314905944974⟩,⟨(-3528623415002271562111343),(-3528623415002271516482203)⟩⟩,⟨⟨2209258366458480562139660,2209258366458480604771108⟩,⟨(-3414917991043922839789550),(-3414917991043922797190907)⟩⟩,⟨⟨1930031817944130677433956,1930031817944130717231314⟩,⟨(-3295185851882263194040560),(-3295185851882263154270805)⟩⟩,⟨⟨1673013833582895172566855,1673013833582895209678595⟩,⟨(-3170832753780821302241785),(-3170832753780821265152909)⟩⟩,⟨⟨1437100899883826271849339,1437100899883826306464109⟩,⟨(-3043133164825788926708653),(-3043133164825788892112452)⟩⟩,⟨⟨1221188994824692906603302,1221188994824692938860324⟩,⟨(-2913236574066911301243081),(-2913236574066911269000747)⟩⟩,⟨⟨1024180398086869040705204,1024180398086869070766901⟩,⟨(-2782173968882432953625556),(-2782173968882432923575059)⟩⟩,⟨⟨844989766508224688166189,844989766508224716152779⟩,⟨(-2650864418238983894296561),(-2650864418238983866318040)⟩⟩,⟨⟨682549502520832053128465,682549502520832079189505⟩,⟨(-2520121704487024660455260),(-2520121704487024634399500)⟩⟩,⟨⟨535814446502410932266024,535814446502410956512545⟩,⟨(-2390660951373337591306799),(-2390660951373337567063077)⟩⟩,⟨⟨403765926541350968505889,403765926541350991088184⟩,⟨(-2263105201004185865070915),(-2263105201004185842489226)⟩⟩] +lemma kernel13_1_r4_8_eq : ∀ k : Fin 16, kernel13_1Expr 4 8 k = kernel13_1_r4_8 k := by decide +kernel +noncomputable def kernel13_1_r4_9 : Fin 16 → CBox := ![⟨⟨285415201124490841196283,285415201124490862248278⟩,⟨(-2137991897501846803570853),(-2137991897501846782517547)⟩⟩,⟨⟨179806331737950718628660,179806331737950738261868⟩,⟨(-2015779240014676795195119),(-2015779240014676775558921)⟩⟩,⟨⟨86018523360475577710904,86018523360475596005568⟩,⟨(-1896852372523901840705475),(-1896852372523901822406373)⟩⟩,⟨⟨3167971364395720325859,3167971364395737376804⟩,⟨(-1781529382501960326054566),(-1781529382501960308997931)⟩⟩,⟨⟨(-69590746538651333599822),(-69590746538651317724032)⟩,⟨(-1670067084886157791464984),(-1670067084886157775582448)⟩⟩,⟨⟨(-133063694920966954289116),(-133063694920966939501330)⟩,⟨(-1562666572011859138311370),(-1562666572011859123515946)⟩⟩,⟨⟨(-188016984027628510018020),(-188016984027628496254994)⟩,⟨(-1459478514080972348413629),(-1459478514080972334642236)⟩⟩,⟨⟨(-235176515001917530731327),(-235176515001917517918521)⟩,⟨(-1360608198408617755728203),(-1360608198408617742906435)⟩⟩,⟨⟨(-275228031144502502407609),(-275228031144502490485750)⟩,⟨(-1266120299082871817075154),(-1266120299082871805143868)⟩⟩,⟨⟨(-308817440743054733733273),(-308817440743054722627751)⟩,⟨(-1176043371782907683231242),(-1176043371782907672115936)⟩⟩,⟨⟨(-336551378525028278108840),(-336551378525028267771342)⟩,⟨(-1090374071327271025020295),(-1090374071327271014673085)⟩⟩,⟨⟨(-358997974444030995900716),(-358997974444030986274500)⟩,⟨(-1009081092067539371470109),(-1009081092067539361834342)⟩⟩,⟨⟨(-376687800276817641156828),(-376687800276817632201577)⟩,⟨(-932108833507492118859298),(-932108833507492109894698)⟩⟩,⟨⟨(-390114966353051861223400),(-390114966353051852887319)⟩,⟨(-859380795521204010292958),(-859380795521204001947757)⟩⟩,⟨⟨(-399738342635686079070962),(-399738342635686071317068)⟩,⟨(-790802709274570416217642),(-790802709274570408454884)⟩⟩,⟨⟨(-405982880290719478273767),(-405982880290719471058217)⟩,⟨(-726265411435061360187067),(-726265411435061352962922)⟩⟩] +lemma kernel13_1_r4_9_eq : ∀ k : Fin 16, kernel13_1Expr 4 9 k = kernel13_1_r4_9 k := by decide +kernel +noncomputable def kernel13_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-409241011808422079930293),(-409241011808422073205605)⟩,⟨(-665647470496976545041391),(-665647470496976538308403)⟩⟩,⟨⟨(-409874109643643630048338),(-409874109643643623774335)⟩,⟨(-608817575068389773593209),(-608817575068389767311210)⟩⟩,⟨⟨(-408213985212884577017801),(-408213985212884571168339)⟩,⟨(-555636694776515655018668),(-555636694776515649161526)⟩⟩,⟨⟨(-404564411905184745051270),(-404564411905184739594623)⟩,⟨(-505960025066223290046333),(-505960025066223284582322)⟩⟩,⟨⟨(-399202657519745021910782),(-399202657519745016825153)⟩,⟨(-459638727608035888382914),(-459638727608035883290241)⟩⟩,⟨⟨(-392381013224950997773881),(-392381013224950993030217)⟩,⟨(-416521478313475923380152),(-416521478313475918629757)⟩⟩,⟨⟨(-384328307732642613536215),(-384328307732642609114032)⟩,⟨(-376455835093215955755628),(-376455835093215951327147)⟩⟩,⟨⟨(-375251396891564456537398),(-375251396891564452411305)⟩,⟨(-339289437503047575504809),(-339289437503047571373127)⟩⟩,⟨⟨(-365336620320239910216844),(-365336620320239906370637)⟩,⟨(-304871050319591798657583),(-304871050319591794806435)⟩⟩,⟨⟨(-354751218018986696518662),(-354751218018986692929883)⟩,⟨(-273051462886748415863584),(-273051462886748412270449)⟩⟩,⟨⟨(-343644701121858740121734),(-343644701121858736775227)⟩,⟨(-243684255789210268358042),(-243684255789210265007731)⟩⟩,⟨⟨(-332150172071701233888627),(-332150172071701230765857)⟩,⟨(-216626446054240886954451),(-216626446054240883828372)⟩⟩,⟨⟨(-320385590526135536602268),(-320385590526135533688992)⟩,⟨(-191739021669753063464939),(-191739021669753060548808)⟩⟩,⟨⟨(-308454982231035524208594),(-308454982231035521485153)⟩,⟨(-168887375747042152860572),(-168887375747042150134687)⟩⟩,⟨⟨(-296449588933647977950738),(-296449588933647975406237)⟩,⟨(-147941650160892418535485),(-147941650160892415988918)⟩⟩,⟨⟨(-284448958153377698966147),(-284448958153377696586945)⟩,⟨(-128776997977808886590472),(-128776997977808884209539)⟩⟩] +lemma kernel13_1_r4_10_eq : ∀ k : Fin 16, kernel13_1Expr 4 10 k = kernel13_1_r4_10 k := by decide +kernel +noncomputable def kernel13_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-272521972288401153586446),(-272521972288401151363822)⟩,⟨(-111273773443506242218785),(-111273773443506239994739)⟩⟩,⟨⟨(-260727817115131290166371),(-260727817115131288087568)⟩,⟨(-95317657751255637149503),(-95317657751255635069554)⟩⟩,⟨⟨(-249116890239900861966499),(-249116890239900860023254)⟩,⟨(-80799728260091982529709),(-80799728260091980585563)⟩⟩,⟨⟨(-237731650493058973499588),(-237731650493058971681459)⟩,⟨(-67616478282192587356891),(-67616478282192585538089)⟩⟩,⟨⟨(-226607409620117210683250),(-226607409620117208983528)⟩,⟨(-55669794017101544528369),(-55669794017101542828170)⟩⟩,⟨⟨(-215773067927822628331724),(-215773067927822626740817)⟩,⟨(-44866894681263975965345),(-44866894681263974374141)⟩⟩,⟨⟨(-205251795790242587894836),(-205251795790242586406102)⟩,⟨(-35120241368195003187007),(-35120241368195001698133)⟩⟩,⟨⟨(-195061663116210104568504),(-195061663116210103172217)⟩,⟨(-26347419680513342141141),(-26347419680513340744860)⟩⟩,⟨⟨(-185216219029757288385048),(-185216219029757287076553)⟩,⟨(-18471000702376187440339),(-18471000702376186131971)⟩⟩,⟨⟨(-175725024124245610201415),(-175725024124245608973501)⟩,⟨(-11418384431358563243961),(-11418384431358562016281)⟩⟩,⟨⟨(-166594137723365445884044),(-166594137723365444732239)⟩,⟨(-5121629363821044073116),(-5121629363821042921644)⟩⟩,⟨⟨(-157826562622370735429152),(-157826562622370734347600)⟩,⟨482728471849665503831,482728471849666584969⟩⟩,⟨⟨(-149422649794931676321341),(-149422649794931675306482)⟩,⟨5453864113612622729677,5453864113612623744050⟩⟩,⟨⟨(-141380465538656549848141),(-141380465538656548894540)⟩,⟨9846857323218138672358,9846857323218139625411⟩⟩,⟨⟨(-133696123499205698300580),(-133696123499205697404872)⟩,⟨13712889052462768109908,13712889052462769005019⟩⟩,⟨⟨(-126364083962270901955986),(-126364083962270901113099)⟩,⟨17099438765008956025154,17099438765008956867396⟩⟩] +lemma kernel13_1_r4_11_eq : ∀ k : Fin 16, kernel13_1Expr 4 11 k = kernel13_1_r4_11 k := by decide +kernel +noncomputable def kernel13_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-119377422737519270718563),(-119377422737519269925392)⟩,⟨20050480932944621290034,20050480932944622082523⟩⟩,⟨⟨(-112728071881626680142753),(-112728071881626679395162)⟩,⟨22606679275907805963186,22606679275907806710062⟩⟩,⟨⟨(-106407034421210519254692),(-106407034421210518550275)⟩,⟨24805577536447486974141,24805577536447487677823⟩⟩,⟨⟨(-100404575143017872044880),(-100404575143017871380333)⟩,⟨26681785789406067932390,26681785789406068596180⟩⟩,⟨⟨(-94710389420091591417132),(-94710389420091590790585)⟩,⟨28267161466641939014076,28267161466641939639852⟩⟩,⟨⟨(-89313751940549976896222),(-89313751940549976304555)⟩,⟨29590984442564416547824,29590984442564417138730⟩⟩,⟨⟨(-84203647101585471253215),(-84203647101585470694614)⟩,⟨30680125671961588875188,30680125671961589433039⟩⟩,⟨⟨(-79368882726620804129696),(-79368882726620803601009)⟩,⟨31559209000708919161809,31559209000708919689765⟩⟩,⟨⟨(-74798188659376603131390),(-74798188659376602631253)⟩,⟨32250765883392974312140,32250765883392974811563⟩⟩,⟨⟨(-70480301685849542414634),(-70480301685849541940643)⟩,⟨32775382840891947198398,32775382840891947671690⟩⟩,⟨⟨(-66404038134664159662626),(-66404038134664159213503)⟩,⟨33151841576714378927050,33151841576714379375493⟩⟩,⟨⟨(-62558355408591530016030),(-62558355408591529589882)⟩,⟨33397251744562120731186,33397251744562121156670⟩⟩,⟨⟨(-58932403605742740632296),(-58932403605742740228157)⟩,⟨33527176422258988952326,33527176422258989355817⟩⟩,⟨⟨(-55515568298448668650149),(-55515568298448668266195)⟩,⟨33555750399926459619580,33555750399926460002904⟩⟩,⟨⟨(-52297505451432442356979),(-52297505451432441991831)⟩,⟨33495791434089539449622,33495791434089539814158⟩⟩,⟨⟨(-49268169378780325668708),(-49268169378780325320885)⟩,⟨33358904655198031578591,33358904655198031925817⟩⟩] +lemma kernel13_1_r4_12_eq : ∀ k : Fin 16, kernel13_1Expr 4 12 k = kernel13_1_r4_12 k := by decide +kernel +noncomputable def kernel13_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-46417834561555865291047),(-46417834561555864959941)⟩,⟨33155580344728583016274,33155580344728583346801⟩⟩,⟨⟨(-43737112074748931276515),(-43737112074748930960680)⟩,⟨32895285320407785069331,32895285320407785384605⟩⟩,⟨⟨(-41216961303616180009133),(-41216961303616179707889)⟩,⟨32586548184921939963679,32586548184921940264377⟩⟩,⟨⟨(-38848697565314276182053),(-38848697565314275894281)⟩,⟨32237038705450753422023,32237038705450753709271⟩⟩,⟨⟨(-36623996191973218364931),(-36623996191973218090040)⟩,⟨31853641599117688251890,31853641599117688526272⟩⟩,⟨⟨(-34534893575892404869744),(-34534893575892404606437)⟩,⟨31442525003570258043649,31442525003570258306460⟩⟩,⟨⟨(-32573785626228065255937),(-32573785626228065003745)⟩,⟨31009203912916509843787,31009203912916510095499⟩⟩,⟨⟨(-30733424039217917992915),(-30733424039217917750976)⟩,⟨30558598857625486223246,30558598857625486464719⟩⟩,⟨⟨(-29006910740482206669596),(-29006910740482206437617)⟩,⟨30095090103177369130664,30095090103177369362189⟩⟩,⟨⟨(-27387690818063168152067),(-27387690818063167929151)⟩,⟨29622567636605726214888,29622567636605726437364⟩⟩,⟨⟨(-25869544228423678899849),(-25869544228423678685641)⟩,⟨29144477202949925176154,29144477202949925389939⟩⟩,⟨⟨(-24446576524422464838530),(-24446576524422464632318)⟩,⟨28663862645331216100725,28663862645331216306542⟩⟩,⟨⟨(-23113208824118814299901),(-23113208824118814101448)⟩,⟨28183404793145839439805,28183404793145839637885⟩⟩,⟨⟨(-21864167211936374341304),(-21864167211936374149916)⟩,⟨27705457132964165835332,27705457132964166026375⟩⟩,⟨⟨(-20694471739038693904106),(-20694471739038693719527)⟩,⟨27232078486337285073907,27232078486337285258155⟩⟩,⟨⟨(-19599425167548857892273),(-19599425167548857713954)⟩,⟨26765062908014966703021,26765062908014966881029⟩⟩] +lemma kernel13_1_r4_13_eq : ∀ k : Fin 16, kernel13_1Expr 4 13 k = kernel13_1_r4_13 k := by decide +kernel +noncomputable def kernel13_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-18574601583298079570719),(-18574601583298079398537)⟩,⟨26305967007219831043185,26305967007219831215072⟩⟩,⟨⟨(-17615834983936824442117),(-17615834983936824275461)⟩,⟨25856134883727680779060,25856134883727680945442⟩⟩,⟨⟨(-16719207933318114605384),(-16719207933318114444069)⟩,⟨25416720859678834148154,25416720859678834309211⟩⟩,⟨⟨(-15881040358905679830772),(-15881040358905679674344)⟩,⟨24988710177377532345494,24988710177377532501680⟩⟩,⟨⟨(-15097878556417883107000),(-15097878556417882955367)⟩,⟨24572937822897626232381,24572937822897626383782⟩⟩,⟨⟨(-14366484454849076865508),(-14366484454849076718184)⟩,⟨24170105625160205661526,24170105625160205808636⟩⟩,⟨⟨(-13683825185279436714212),(-13683825185279436571058)⟩,⟨23780797770327622285664,23780797770327622428610⟩⟩,⟨⟨(-13047062988367480617192),(-13047062988367480477837)⟩,⟨23405494861902621665326,23405494861902621804488⟩⟩,⟨⟨(-12453545488000282053102),(-12453545488000281917500)⟩,⟨23044586647855759112178,23044586647855759247595⟩⟩,⟨⟨(-11900796352147228501103),(-11900796352147228368845)⟩,⟨22698383527445498337225,22698383527445498469307⟩⟩,⟨⟨(-11386506356424711697172),(-11386506356424711568134)⟩,⟨22367126942152970583906,22367126942152970712775⟩⟩,⟨⟨(-10908524861139929075890),(-10908524861139928949771)⟩,⟨22050998747330946687962,22050998747330946813924⟩⟩,⟨⟨(-10464851708558142121373),(-10464851708558141998148)⟩,⟨21750129653762767642457,21750129653762767765530⟩⟩,⟨⟨(-10053629543752553194708),(-10053629543752553074007)⟩,⟨21464606821336213798150,21464606821336213918710⟩⟩,⟨⟨(-9673136559579460512636),(-9673136559579460394393)⟩,⟨21194480680450516598263,21194480680450516716367⟩⟩,⟨⟨(-9321779664009908830125),(-9321779664009908714075)⟩,⟨20939771050580036911049,20939771050580037026970⟩⟩] +lemma kernel13_1_r4_14_eq : ∀ k : Fin 16, kernel13_1Expr 4 14 k = kernel13_1_r4_14 k := by decide +kernel +noncomputable def kernel13_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-8998088066184979781213),(-8998088066184979667356)⟩,⟨20700472619601370263562,20700472619601370377297⟩⟩,⟨⟨(-8700707276092990657842),(-8700707276092990545858)⟩,⟨20476559842035802392763,20476559842035802504629⟩⟩,⟨⟨(-8428393511646141713494),(-8428393511646141603320)⟩,⟨20267991309248741723309,20267991309248741833366⟩⟩,⟨⟨(-8180008506119243599645),(-8180008506119243491047)⟩,⟨20074713639863564491637,20074713639863564600125⟩⟩,⟨⟨(-7954514708366087773025),(-7954514708366087666004)⟩,⟨19896664934170037284184,19896664934170037391096⟩⟩,⟨⟨(-7750970867915793538614),(-7750970867915793432895)⟩,⟨19733777832117439274687,19733777832117439380301⟩⟩,⟨⟨(-7568527996941706136848),(-7568527996941706032384)⟩,⟨19585982210559698153580,19585982210559698257942⟩⟩,⟨⟨(-7406425701162058038755),(-7406425701162057935327)⟩,⟨19453207551744146213316,19453207551744146316646⟩⟩,⟨⟨(-7263988871950546873535),(-7263988871950546771167)⟩,⟨19335385011586753106302,19335385011586753208573⟩⟩,⟨⟨(-7140624732284813096206),(-7140624732284812994645)⟩,⟨19232449213034845497979,19232449213034845599446⟩⟩,⟨⟨(-7035820229622496694732),(-7035820229622496593926)⟩,⟨19144339786763489133857,19144339786763489234573⟩⟩,⟨⟨(-6949139769351216235558),(-6949139769351216135302)⟩,⟨19071002678564204937026,19071002678564205037188⟩⟩,⟨⟨(-6880223283095414079350),(-6880223283095413979680)⟩,⟨19012391240045077675517,19012391240045077775101⟩⟩,⟨⟨(-6828784626866142381918),(-6828784626866142282580)⟩,⟨18968467116650406588569,18968467116650406687821⟩⟩,⟨⟨(-6794610304797513737024),(-6794610304797513637972)⟩,⟨18939200944506906092845,18939200944506906191807⟩⟩,⟨⟨(-6777558515014871064021),(-6777558515014870965088)⟩,⟨18924572865193391512029,18924572865193391610875⟩⟩] +lemma kernel13_1_r4_15_eq : ∀ k : Fin 16, kernel13_1Expr 4 15 k = kernel13_1_r4_15 k := by decide +kernel +noncomputable def kernel13_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel13_1_r4_0,kernel13_1_r4_1,kernel13_1_r4_2,kernel13_1_r4_3,kernel13_1_r4_4,kernel13_1_r4_5,kernel13_1_r4_6,kernel13_1_r4_7,kernel13_1_r4_8,kernel13_1_r4_9,kernel13_1_r4_10,kernel13_1_r4_11,kernel13_1_r4_12,kernel13_1_r4_13,kernel13_1_r4_14,kernel13_1_r4_15] +lemma kernel13_1_r4_eq (i k : Fin 16) : kernel13_1Expr 4 i k = kernel13_1_r4 i k := by + fin_cases i + · exact kernel13_1_r4_0_eq k + · exact kernel13_1_r4_1_eq k + · exact kernel13_1_r4_2_eq k + · exact kernel13_1_r4_3_eq k + · exact kernel13_1_r4_4_eq k + · exact kernel13_1_r4_5_eq k + · exact kernel13_1_r4_6_eq k + · exact kernel13_1_r4_7_eq k + · exact kernel13_1_r4_8_eq k + · exact kernel13_1_r4_9_eq k + · exact kernel13_1_r4_10_eq k + · exact kernel13_1_r4_11_eq k + · exact kernel13_1_r4_12_eq k + · exact kernel13_1_r4_13_eq k + · exact kernel13_1_r4_14_eq k + · exact kernel13_1_r4_15_eq k +noncomputable def kernel13_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-326863355124022074555876616891),(-326863355124022073016660736811)⟩,⟨84145786575818843651446303716,84145786575818845184894349750⟩⟩,⟨⟨(-326700257627887326027749131689),(-326700257627887324488792988710)⟩,⟨84256774876088516762447513703,84256774876088518295635570511⟩⟩,⟨⟨(-326374116436532058337372519735),(-326374116436532056798938507918)⟩,⟨84478394252528722985537284454,84478394252528724518202714408⟩⟩,⟨⟨(-325885039854349348433281161285),(-325885039854349346895631696649)⟩,⟨84809931166896127576413657810,84809931166896129108293814942⟩⟩,⟨⟨(-325233192089050298244646088178),(-325233192089050296708043681634)⟩,⟨85250317586091945602120331427,85250317586091947132952495226⟩⟩,⟨⟨(-324418795338223377192167089753),(-324418795338223375656874307890)⟩,⟨85798133709521672189204206906,85798133709521673718725628199⟩⟩,⟨⟨(-323442132546846620446401903193),(-323442132546846618912681485799)⟩,⟨86451611602580529276465269499,86451611602580530804413059482⟩⟩,⟨⟨(-322303550814849515665336993163),(-322303550814849514133451698202)⟩,⟨87208639733576359100990377164,87208639733576360627101668723⟩⟩,⟨⟨(-321003465428788157176613522298),(-321003465428788155646826443109)⟩,⟨88066768410579150842187390899,88066768410579152366199027830⟩⟩,⟨⟨(-319542364486792015430875512868),(-319542364486792013903449608861)⟩,⟨89023216113766304559541802837,89023216113766306081190814854⟩⟩,⟨⟨(-317920814081188708087894883558),(-317920814081188706563093149883)⟩,⟨90074876717798359911340799598,90074876717798361430364239348⟩⟩,⟨⟨(-316139463998639492593512110923),(-316139463998639491071478206368)⟩,⟨91218327597595956606613052262,91218327597595958122867458684⟩⟩,⟨⟨(-314199053893247573523473112409),(-314199053893247572004461134378)⟩,⟨92449838609581641550046354499,92449838609581643063277816901⟩⟩,⟨⟨(-312100419883958128155380559929),(-312100419883958126639643647360)⟩,⟨93765381938988070998835822009,93765381938988072508791460784⟩⟩,⟨⟨(-309844501523677171593425372839),(-309844501523677170081218657322)⟩,⟨95160642802207523403318326939,95160642802207524909743348986⟩⟩,⟨⟨(-307432349083919464869054633250),(-307432349083919463360631628018)⟩,⟨96631030991359031119211296192,96631030991359032621852607880⟩⟩] +lemma kernel13_1_r5_0_eq : ∀ k : Fin 16, kernel13_1Expr 5 0 k = kernel13_1_r5_0 k := by decide +kernel +noncomputable def kernel13_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-304865131095476458524592312325),(-304865131095476457020209676207)⟩,⟨98171693246273842831099194362,98171693246273844329700644578⟩⟩,⟨⟨(-302144142082595878614881085293),(-302144142082595877114792182376)⟩,⟨99777526436944856252629869188,99777526436944857746938689079⟩⟩,⟨⟨(-299270810425506274124245447364),(-299270810425506272628708051954)⟩,⟨101443191537151262900003675013,101443191537151264389762781123⟩⟩,⟨⟨(-296246706283822948311730767139),(-296246706283822946820998346725)⟩,⟨103163128367458798786041849627,103163128367458800270998558102⟩⟩,⟨⟨(-293073549511455364270110797196),(-293073549511455362784443171862)⟩,⟨104931571083114359848120392852,104931571083114361328015769094⟩⟩,⟨⟨(-289753217492118246975555152845),(-289753217492118245495204705760)⟩,⟨106742564379509806838991664395,106742564379509808313574305750⟩⟩,⟨⟨(-286287752823445667441285995821),(-286287752823445665966513487083)⟩,⟨108589980384894874566770302942,108589980384894876035780536169⟩⟩,⟨⟨(-282679370777034256772975483923),(-282679370777034255304032961324)⟩,⟨110467536206887355853767131091,110467536206887357316954091906⟩⟩,⟨⟨(-278930466461511454869317357320),(-278930466461511453406468282458)⟩,⟨112368812096077064268212607071,112368812096077065725314126971⟩⟩,⟨⟨(-275043621615948499256623422961),(-275043621615948497800117174652)⟩,⟨114287270186668101126788223048,114287270186668102577556310173⟩⟩,⟨⟨(-271021610961624729718872312979),(-271021610961624728268972550374)⟩,⟨116216273770673863168440544158,116216273770673864612613037081⟩⟩,⟨⟨(-266867408041306450696196414909),(-266867408041306449253151753567)⟩,⟨118149107058695687411906190769,118149107058695688849236063577⟩⟩,⟨⟨(-262584190476834311641145420816),(-262584190476834310205222634885)⟩,⟨120078995376805993363614728868,120078995376805994793836907569⟩⟩,⟨⟨(-258175344577919554519476321690),(-258175344577919553090889324131)⟩,⟨121999125745549306423833159790,121999125745549307846772785964⟩⟩,⟨⟨(-253644469237630362259512340083),(-253644469237630360838453008389)⟩,⟨123902667783600568024530872310,123902667783600569440089386639⟩⟩,⟨⟨(-248995379053100807462344904742),(-248995379053100806049054727534)⟩,⟨125782794875212229311634482150,125782794875212230719573298893⟩⟩] +lemma kernel13_1_r5_1_eq : ∀ k : Fin 16, kernel13_1Expr 5 1 k = kernel13_1_r5_1 k := by decide +kernel +noncomputable def kernel13_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-244232106613509361714331482428),(-244232106613509360309079818653)⟩,⟨127632705537273717507286735701,127632705537273718907339221618⟩⟩,⟨⟨(-239358903901341212649420016475),(-239358903901341211252441212064)⟩,⟨129445644918633950783508152549,129445644918633952175442470271⟩⟩,⟨⟨(-234380242757355100801247593141),(-234380242757355099412808620797)⟩,⟨131214926361335393526040262610,131214926361335394909591762665⟩⟩,⟨⟨(-229300814364504034980533858294),(-229300814364504033600867723316)⟩,⟨132933952950612825731899732904,132933952950612827106837508329⟩⟩,⟨⟨(-224125527711289683452342603755),(-224125527711289682081720886315)⟩,⟨134596238977957728419767552659,134596238977957729785821929224⟩⟩,⟨⟨(-218859507000638667891673493220),(-218859507000638666530319472562)⟩,⟨136195431239275813896323473964,136195431239275815253272839431⟩⟩,⟨⟨(-213508087976348209812563837166),(-213508087976348208460745043467)⟩,⟨137725330088205897133040933611,137725330088205898480619226478⟩⟩,⟨⟨(-208076813145428044836405244327),(-208076813145428043494342463693)⟩,⟨139179910163057052334139701401,139179910163057053672127360939⟩⟩,⟨⟨(-202571425881231406383616154870),(-202571425881231405051583017257)⟩,⟨140553340704590370740140663248,140553340704590372068265082435⟩⟩,⟨⟨(-196997863399083207344700390598),(-196997863399083206022903355127)⟩,⟨141840005381052284764729613447,141840005381052286082785100896⟩⟩,⟨⟨(-191362248603138330128350499655),(-191362248603138328817055477202)⟩,⟨143034521536486721644568397894,143034521536486722952289604775⟩⟩,⟨⟨(-185670880810394368478201780688),(-185670880810394367177613126146)⟩,⟨144131758778439006141985161401,144131758778439007439168040986⟩⟩,⟨⟨(-179930225365095852329024484800),(-179930225365095851039413674478)⟩,⟨145126856821738124412253896757,145126856821738125698627072867⟩⟩,⟨⟨(-174146902164153202934667466190),(-174146902164153201656221537624)⟩,⟨146015242506124985410201609779,146015242506124986685577884434⟩⟩,⟨⟨(-168327673121609650043373159909),(-168327673121609648776353682967)⟩,⟨146792645907098256104958352709,146792645907098257369075787290⟩⟩,⟨⟨(-162479428607571636189126663039),(-162479428607571634933717090037)⟩,⟨147455115461487772052624622042,147455115461487773305299140860⟩⟩] +lemma kernel13_1_r5_2_eq : ∀ k : Fin 16, kernel13_1Expr 5 2 k = kernel13_1_r5_2 k := by decide +kernel +noncomputable def kernel13_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-156609172904320039998989120730),(-156609172904320038755459022334)⟩,⟨147999032031945719328655068773,147999032031945720569616270844⟩⟩,⟨⟨(-150724008729487135405848662493),(-150724008729487134174357845101)⟩,⟨148421121837770508438554420206,148421121837770509667641412183⟩⟩,⟨⟨(-144831120883163313740874791404),(-144831120883163312521677276254)⟩,⟨148718468183245555988882730253,148718468183245557205840199955⟩⟩,⟨⟨(-138937759082533906544661222707),(-138937759082533905337914980953)⟩,⟨148888521918978220143534439255,148888521918978221348202880661⟩⟩,⟨⟨(-133051220054086029417736111817),(-133051220054086028223701538144)⟩,⟨148929110576551080642745726700,148929110576551081834863009244⟩⟩,⟨⟨(-127178828959515169456883958673),(-127178828959515168275692992506)⟩,⟨148838446122131747297100412756,148838446122131748476532623272⟩⟩,⟨⟨(-121327920237149579246115887569),(-121327920237149578078011453106)⟩,⟨148615131280506501580809266490,148615131280506502747311312041⟩⟩,⟨⟨(-115505817945947606700241932555),(-115505817945947605545352056257)⟩,⟨148258164387280392788386473865,148258164387280393941827938388⟩⟩,⟨⟨(-109719815703861438580414914120),(-109719815703861437438992108762)⟩,⟨147766942733690079736471094015,147766942733690080876596886347⟩⟩,⟨⟨(-103977156316555785233595163491),(-103977156316555784105734151191)⟩,⟨147141264375569129624798508560,147141264375569130751511120885⟩⟩,⟨⟨(-98285011196080549857047949211),(-98285011196080548742670625103)⟩,⟨146381328385447507081097059433,146381328385447508194471450999⟩⟩,⟨⟨(-92650459672085084075344236610),(-92650459672085082972227110512)⟩,⟨145487733534512173591812739579,145487733534512174694067896953⟩⟩,⟨⟨(-87080468300495064589458742491),(-87080468300495063497868712647)⟩,⟨144461475399154668483846765236,144461475399154669574712503548⟩⟩,⟨⟨(-81581870276222834251128727665),(-81581870276222833171158600907)⟩,⟨143303941895031257593228899711,143303941895031258672608964366⟩⟩,⟨⟨(-76161345057424785172451940384),(-76161345057424784104348527701)⟩,⟨142016907249905535421297584384,142016907249905536488941557896⟩⟩,⟨⟨(-70825398309036960076436910329),(-70825398309036959020295087747)⟩,⟨140602524434973355472856027930,140602524434973356528665290656⟩⟩] +lemma kernel13_1_r5_3_eq : ∀ k : Fin 16, kernel13_1Expr 5 3 k = kernel13_1_r5_3 k := by decide +kernel +noncomputable def kernel13_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-65580342272800132112321840129),(-65580342272800131068406841355)⟩,⟨139063316082824535353084217269,139063316082824536396789642317⟩⟩,⟨⟨(-60432276669721740375621291962),(-60432276669721739343988942901)⟩,⟨137402163928612162614551505986,137402163928612163646093268445⟩⟩,⟨⟨(-55387070238913871480404642147),(-55387070238913870461290652317)⟩,⟨135622296819314643068164042907,135622296819314644087302297527⟩⟩,⟨⟨(-50450343013999896202194686966),(-50450343013999895195662293234)⟩,⟨133727277344123517082822117516,133727277344123518089489410063⟩⟩,⟨⟨(-45627449434809619391042176090),(-45627449434809618397341228892)⟩,⟨131720987146907274251976225793,131720987146907275245918362530⟩⟩,⟨⟨(-40923462387902426554853151799),(-40923462387902425574008077845)⟩,⟨129607610989324427380715661931,129607610989324428361903829468⟩⟩,⟨⟨(-36343158264594716939734001479),(-36343158264594715971965086740)⟩,⟨127391619640425855480020698552,127391619640425856448230111756⟩⟩,⟨⟨(-31891003119652837912255516783),(-31891003119652836957590831433)⟩,⟨125077751675436806506882722192,125077751675436807462080792250⟩⟩,⟨⟨(-27571140007682653816989812939),(-27571140007682652875669452137)⟩,⟨122670994272785524442232767530,122670994272785525384174777025⟩⟩,⟨⟨(-23387377567544345896431493133),(-23387377567544344968435343474)⟩,⟨120176563104294046217097749385,120176563104294047145799217966⟩⟩,⟨⟨(-19343179917893951407590779383),(-19343179917893950493119627251)⟩,⟨117599881418716953041579758493,117599881418716953956835215710⟩⟩,⟨⟨(-15441657919254376887306556010),(-15441657919254375986350588617)⟩,⟨114946558423459796717397374712,114946558423459797619211995316⟩⟩,⟨⟨(-11685561849905547531373784228),(-11685561849905546644148866059)⟩,⟨112222367073289493269059622272,112222367073289494157212824174⟩⟩,⟨⟨(-8077275534417383819181043326),(-8077275534417382945631048471)⟩,⟨109433221378128488579620418446,109433221378128489454163706785⟩⟩,⟨⟨(-4618811954895296312126859648),(-4618811954895295452429460868)⟩,⟨106585153344573038980010744679,106585153344573039840761758441⟩⟩,⟨⟨(-1311810366033600623909260266),(-1311810366033599778015034802)⟩,⟨103684289667569736159368138155,103684289667569737006371723023⟩⟩] +lemma kernel13_1_r5_4_eq : ∀ k : Fin 16, kernel13_1Expr 5 4 k = kernel13_1_r5_4 k := by decide +kernel +noncomputable def kernel13_1_r5_5 : Fin 16 → CBox := ![⟨⟨1842465074052342340402546465,1842465074052343172292607578⟩,⟨100736828289706093326730264604,100736828289706094159780789609⟩⟩,⟨⟨4843125154447802341835356831,4843125154447803159884991043⟩,⟨97749014945809908603268915982,97749014945809909422525579466⟩⟩,⟨⟨7689653949956359622083377231,7689653949956360426355001162⟩,⟨94727119810004355989090643244,94727119810004356794609086828⟩⟩,⟨⟨10381905663099081306501806321,10381905663099082097095709099⟩,⟨91677414361034344042566189407,91677414361034344834424529382⟩⟩,⟨⟨12920099994185527797444464560,12920099994185528574181857281⟩,⟨88606148579574552032309758531,88606148579574552810325757406⟩⟩,⟨⟨15304816072842399847760653167,15304816072842400610771425015⟩,⟨85519528588367463682537162264,85519528588367464446837486389⟩⟩,⟨⟨17536984992902773420905475317,17536984992902774170055213088⟩,⟨82423694842444124082736307223,82423694842444124833183300599⟩⟩,⟨⟨19617881000731287968489681225,19617881000731288703896793458⟩,⟨79324700972381176327811057642,79324700972381177064520096542⟩⟩,⟨⟨21549111394825230545792149429,21549111394825231267296994878⟩,⟨76228493378581108372417419506,76228493378581109095225818559⟩⟩,⟨⟨23332605201828940865405115469,23332605201828941573569984948⟩,⟨73140891668970503680466736015,73140891668970504389933998528⟩⟩,⟨⟨24970600700874546606334836941,24970600700874547301129616311⟩,⟨70067570026340794109412407235,70067570026340794805505625973⟩⟩,⟨⟨26465631874365895235585057188,26465631874365895917148649011⟩,⟨67014039584859836641594550237,67014039584859837324450060016⟩⟩,⟨⟨27820513868910297358833642137,27820513868910298027024133659⟩,⟨63985631888117241542694718084,63985631888117242212168048320⟩⟩,⟨⟨29038327555035815364158957961,29038327555035816019167606704⟩,⟨60987483493492237113607636394,60987483493492237769887743384⟩⟩,⟨⟨30122403278578002560024965970,30122403278578003201758082794⟩,⟨58024521779713615022301981965,58024521779713615665292891943⟩⟩,⟨⟨31076303900153384667699494578,31076303900153385296454099438⟩,⟨55101452006283134396054152255,55101452006283135025987810580⟩⟩] +lemma kernel13_1_r5_5_eq : ∀ k : Fin 16, kernel13_1Expr 5 5 k = kernel13_1_r5_5 k := by decide +kernel +noncomputable def kernel13_1_r5_6 : Fin 16 → CBox := ![⟨⟨31903807221938422207155400321,31903807221938422822821401559⟩,⟨52222745665024690619522908889,52222745665024691236280338512⟩⟩,⟨⟨32608887903029853170588455542,32608887903029853773394329472⟩,⟨49392630155470741768598475817,49392630155470742372410922275⟩⟩,⟨⟨33195698965969704884866604903,33195698965969705474739682018⟩,⟨46615079807174541087566620712,46615079807174541678364140374⟩⟩,⟨⟨33668552997577231320538322113,33668552997577231897677275678⟩,⟨43893808263410998084815338946,43893808263410998662799456184⟩⟩,⟨⟨34031903147048660339492377956,34031903147048660903803830178⟩,⟨41232262232168882134186116464,41232262232168882699266264424⟩⟩,⟨⟨34290324023378566731916827424,34290324023378567283650862626⟩,⟨38633616601909363071844893816,38633616601909363624274080836⟩⟩,⟨⟨34448492592544877740592926660,34448492592544878279706114417⟩,⟨36100770911335050964740745733,36100770911335051504478420106⟩⟩,⟨⟨34511169172609926480188652510,34511169172609927006908897404⟩,⟨33636347154441361235197657257,33636347154441361762474668362⟩⟩,⟨⟨34483178621955181474624397826,34483178621955181989515175488⟩,⟨31242688894466339423673430241,31242688894466339939056131707⟩⟩,⟨⟨34369391812325080538697929399,34369391812325081042230691684⟩,⟨28921861653070192890685625082,28921861653070193394648414774⟩⟩,⟨⟨34174707474248282840429962664,34174707474248283332550784840⟩,⟨26675654534211396639986219416,26675654534211397132478077488⟩⟩,⟨⟨33904034497779312467766933439,33904034497779312948691360162⟩,⟨24505583035787196497812659138,24505583035787196979052044458⟩⟩,⟨⟨33562274766410316223466563678,33562274766410316693118088525⟩,⟨22412892996212230536990419549,22412892996212231006903695513⟩⟩,⟨⟨33154306596494850289220071080,33154306596494850747862973014⟩,⟨20398565617753924761260681375,20398565617753925220114983413⟩⟩,⟨⟨32684968848659021642709332315,32684968848659022090316230476⟩,⟨18463323503655660219179684858,18463323503655660666950442953⟩⟩,⟨⟨32159045771507515994166353955,32159045771507516430975201853⟩,⟨16607637641880948429857959598,16607637641880948866785896547⟩⟩] +lemma kernel13_1_r5_6_eq : ∀ k : Fin 16, kernel13_1Expr 5 6 k = kernel13_1_r5_6 k := by decide +kernel +noncomputable def kernel13_1_r5_7 : Fin 16 → CBox := ![⟨⟨31581252631521787563458403219,31581252631521787989407589827⟩,⟨14831735264720527694536291293,14831735264720528120562525285⟩⟩,⟨⟨30956222176454249727571300079,30956222176454250142991348503⟩,⟨13135608510529976468650384761,13135608510529976884108269580⟩⟩,⟨⟨30288491972804893629881621201,30288491972804894034845799501⟩,⟨11519023811512795027407688786,11519023811512795432373477384⟩⟩,⟨⟨29582492651183900024895551350,29582492651183900419653185010⟩,⟨9981531929731810215598164786,9981531929731810610323683233⟩⟩,⟨⟨28842537086572769976333712051,28842537086572770360851440228⟩,⟨8522478562413484383778384961,8522478562413484768232739923⟩⟩,⟨⟨28072810533752756524155011888,28072810533752756898725694617⟩,⟨7141015437093171420858958643,7141015437093171795337367148⟩⟩,⟨⟨27277361731526100823968177946,27277361731526101188604518459⟩,⟨5836111817217405809809517967,5836111817217406174327009528⟩⟩,⟨⟨26460094982863160810027132913,26460094982863161164991442101⟩,⟨4606566339450055690280834617,4606566339450056045101930053⟩⟩,⟨⟨25624763211814177452552649820,25624763211814177798051887188⟩,⟨3451019105096398323226854276,3451019105096398668560701149⟩⟩,⟨⟨24774961991971805157923839462,24774961991971805494334267575⟩,⟨2367963949732746084577721462,2367963949732746420802622847⟩⟩,⟨⟨23914124535499418363366017422,23914124535499418690702721328⟩,⟨1355760817275552614988977342,1355760817275552942122040703⟩⟩,⟨⟨23045517626286243030513244338,23045517626286243349030735646⟩,⟨412648167306353561080230906,412648167306353879377850722⟩⟩,⟨⟨22172238475684860754075557308,22172238475684861063763944307⟩,⟨(-463244652551672963584945577),(-463244652551672654130790582)⟩⟩,⟨⟨21297212474556423156244985607,21297212474556423457396629860⟩,⟨(-1273885134074432502159045777),(-1273885134074432201254290272)⟩⟩,⟨⟨20423191811016250997639419130,20423191811016251290286219696⟩,⟨(-2021325496915283951546755271),(-2021325496915283659157803895)⟩⟩,⟨⟨19552754919355024319826471415,19552754919355024604228879644⟩,⟨(-2707690795423268023110601766),(-2707690795423267738970856152)⟩⟩] +lemma kernel13_1_r5_7_eq : ∀ k : Fin 16, kernel13_1Expr 5 7 k = kernel13_1_r5_7 k := by decide +kernel +noncomputable def kernel13_1_r5_8 : Fin 16 → CBox := ![⟨⟨18688306722121556594804427458,18688306722121556870979895776⟩,⟨(-3335167296959846094897004793),(-3335167296959845818986458866)⟩⟩,⟨⟨17832079624300728110811776200,17832079624300728379197973500⟩,⟨(-3905991180548035488671081552),(-3905991180548035220551115371)⟩⟩,⟨⟨16986135215908671646862641773,16986135215908671907495663354⟩,⟨(-4422437600225675091927680760),(-4422437600225674831561234969)⟩⟩,⟨⟨16152366637156658299861342670,16152366637156658552992201017⟩,⟨(-4886810152917999901180021746),(-4886810152917999648315254467)⟩⟩,⟨⟨15332501558601188815691396823,15332501558601189061330861989⟩,⟨(-5301430786035496673005078606),(-5301430786035496427630382533)⟩⟩,⟨⟨14528105727392624559221740529,14528105727392624797652322282⟩,⟨(-5668630175381310665240019079),(-5668630175381310427072193960)⟩⟩,⟨⟨13740587029846834020753093514,13740587029846834252078993030⟩,⟨(-5990738599356503557801687959),(-5990738599356503326735816857)⟩⟩,⟨⟨12971200020079096630943823241,12971200020079096855433967721⟩,⟨(-6270077330917234300892434071),(-6270077330917234076659006122)⟩⟩,⟨⟨12221050864339294166572112795,12221050864339294384235365831⟩,⟨(-6508950564298986209746376633),(-6508950564298985992335942314)⟩⟩,⟨⟨11491102650952051256922696652,11491102650952051468039102330⟩,⟨(-6709637889210151757151101484),(-6709637889210151546283163158)⟩⟩,⟨⟨10782181016372547715152845773,10782181016372547919789459832⟩,⟨(-6874387321038616686807880598),(-6874387321038616482399827352)⟩⟩,⟨⟨10094980038793923040201918854,10094980038793923238596593083⟩,⟨(-7005408891635483639748208158),(-7005408891635483441562104384)⟩⟩,⟨⟨9430068351959706819227083536,9430068351959707011403977821⟩,⟨(-7104868801461702343950100130),(-7104868801461702151962688131)⟩⟩,⟨⟨8787895433317541099141261358,8787895433317541285362445364⟩,⟨(-7174884130324974291629054944),(-7174884130324974105579210743)⟩⟩,⟨⟨8168798022370783150118189119,8168798022370783330438697890⟩,⟨(-7217518100611596349878055939),(-7217518100611596169711632969)⟩⟩,⟨⟨7573006627014061427031222996,7573006627014061601679509921⟩,⟨(-7234775883843523429061360210),(-7234775883843523254550811191)⟩⟩] +lemma kernel13_1_r5_8_eq : ∀ k : Fin 16, kernel13_1Expr 5 8 k = kernel13_1_r5_8 k := by decide +kernel +noncomputable def kernel13_1_r5_9 : Fin 16 → CBox := ![⟨⟨7000652077748995767326731873,7000652077748995936324507914⟩,⟨(-7228600938574449792678776578),(-7228600938574449623803245393)⟩⟩,⟨⟨6451772091938697898608468567,6451772091938698062215583543⟩,⟨(-7200871865086767517834726286),(-7200871865086767354335234835)⟩⟩,⟨⟨5926317812646355594402813153,5926317812646355752677767981⟩,⟨(-7153399760067663215905486074),(-7153399760067663057724357333)⟩⟩,⟨⟨5424160289086850137154250346,5424160289086850290314698939⟩,⟨(-7087926052428475129351674400),(-7087926052428474976272074273)⟩⟩,⟨⟨4945096868274535271870915027,4945096868274535419951385055⟩,⟨(-7006120799685340396475645803),(-7006120799685340248463827427)⟩⟩,⟨⟨4488857470049695412976192077,4488857470049695556213886316⟩,⟨(-6909581422837359263181297090),(-6909581422837359120000829158)⟩⟩,⟨⟨4055110720286769184412312312,4055110720286769322866971818⟩,⟨(-6799831856455081405567304216),(-6799831856455081267159182226)⟩⟩,⟨⟨3643469919706584127772591880,3643469919706584261649175725⟩,⟨(-6678322089719226958757488354),(-6678322089719226824917469179)⟩⟩,⟨⟨3253498828311586656225152497,3253498828311586785553859059⟩,⟨(-6546428073417608220258559226),(-6546428073417608090957132790)⟩⟩,⟨⟨2884717248018032039324144709,2884717248018032164333491314⟩,⟨(-6405451967406121718921845820),(-6405451967406121593931155680)⟩⟩,⟨⟨2536606388554739887302019881,2536606388554740008051146234⟩,⟨(-6256622702755045997962435053),(-6256622702755045877223978886)⟩⟩,⟨⟨2208614004118543698221877695,2208614004118543814901649442⟩,⟨(-6101096832721245239027704931),(-6101096832721245122351222040)⟩⟩,⟨⟨1900159290608023433793069976,1900159290608023546440324975⟩,⟨(-5939959646795919961761446269),(-5939959646795919849110686939)⟩⟩,⟨⟨1610637535487400096902622092,1610637535487400205723014669⟩,⟨(-5774226522361288941013288528),(-5774226522361288832183146279)⟩⟩,⟨⟨1339424514451304735417579012,1339424514451304840468136027⟩,⟨(-5604844488932604728665291205),(-5604844488932604623599274371)⟩⟩,⟨⟨1085880631060011527492726944,1085880631060011629429778570⟩,⟨(-5432693980548510067422012790),(-5432693980548509965464371718)⟩⟩] +lemma kernel13_1_r5_9_eq : ∀ k : Fin 16, kernel13_1Expr 5 9 k = kernel13_1_r5_9 k := by decide +kernel +noncomputable def kernel13_1_r5_10 : Fin 16 → CBox := ![⟨⟨849354797386880279218202747,849354797386880378091054515⟩,⟨(-5258590752587161059937516334),(-5258590752587160961039437345)⟩⟩,⟨⟨629188055460089307600242532,629188055460089403570826356⟩,⟨(-5083287940112082966403715156),(-5083287940112082870403697447)⟩⟩,⟨⟨424716940885743121547123005,424716940885743214635162035⟩,⟨(-4907478235774925397581861569),(-4907478235774925304460611383)⟩⟩,⟨⟨235276591507092848383493837,235276591507092938719128525⟩,⟨(-4731796166307053007903235152),(-4731796166307052917530997622)⟩⟩,⟨⟨60203605284286967625285445,60203605284287055210144321⟩,⟨(-4556820447703642322755705062),(-4556820447703642235131239266)⟩⟩,⟨⟨(-101161347228562814874258458),(-101161347228562729894879118)⟩,⟨(-4383076400328646861697359018),(-4383076400328646776675703533)⟩⟩,⟨⟨(-249471149375326794434156443),(-249471149375326712039564312)⟩,⟨(-4211038406333318446847540191),(-4211038406333318364408342803)⟩⟩,⟨⟨(-385370096500839531532379319),(-385370096500839451600855510)⟩,⟨(-4041132392972370363683875839),(-4041132392972370283705712584)⟩⟩,⟨⟨(-509491977511406243609678585),(-509491977511406166142861564)⟩,⟨(-3873738326608596743627492081),(-3873738326608596666112306789)⟩⟩,⟨⟨(-622458371067896949648947055),(-622458371067896874505213095)⟩,⟨(-3709192703407948250986619636),(-3709192703407948175793986677)⟩⟩,⟨⟨(-724877147033835983886590416),(-724877147033835911045054112)⟩,⟨(-3547791023932732744078198242),(-3547791023932732671187636583)⟩⟩,⟨⟨(-817341163361070729859193152),(-817341163361070659207163386)⟩,⟨(-3389790240031706553595098848),(-3389790240031706482894049650)⟩⟩,⟨⟨(-900427148262200097035797983),(-900427148262200028569310042)⟩,⟨(-3235411163594220501554063485),(-3235411163594220433038709617)⟩⟩,⟨⟨(-974694757285177968431489800),(-974694757285177902025534298)⟩,⟨(-3084840827874082652287872502),(-3084840827874082585833307444)⟩⟩,⟨⟨(-1040685794764326927035993168),(-1040685794764326862670718006)⟩,⟨(-2938234793191106932010308784),(-2938234793191106867596798742)⟩⟩,⟨⟨(-1098923589066174201780466561),(-1098923589066174139352247223)⟩,⟨(-2795719389879033605253360005),(-2795719389879033542777365689)⟩⟩] +lemma kernel13_1_r5_10_eq : ∀ k : Fin 16, kernel13_1Expr 5 10 k = kernel13_1_r5_10 k := by decide +kernel +noncomputable def kernel13_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-1149912511070737197355660778),(-1149912511070737136865840581)⟩,⟨(-2657393892363095904092219054),(-2657393892363095843555185021)⟩⟩,⟨⟨(-1194137625421813523708566002),(-1194137625421813465036810462)⟩,⟨(-2523332619215254154303093363),(-2523332619215254095584745559)⟩⟩,⟨⟨(-1232064464236207052206110340),(-1232064464236206995333843366)⟩,⟨(-2393586954947095955739474141),(-2393586954947095898821312928)⟩⟩,⟨⟨(-1264138913174512635368087911),(-1264138913174512580200723037)⟩,⟨(-2268187290157418046264557030),(-2268187290157417991052044891)⟩⟩,⟨⟨(-1290787200038138878872197438),(-1290787200038138825406118546)⟩,⟨(-2147144877452060911288225548),(-2147144877452060857777809031)⟩⟩,⟨⟨(-1312415976361957255870725689),(-1312415976361957204001168368)⟩,⟨(-2030453601296796291496236606),(-2030453601296796239583182199)⟩⟩,⟨⟨(-1329412482812890961663508072),(-1329412482812890911369125843)⟩,⟨(-1918091660649688790746863709),(-1918091660649688740411821826)⟩⟩,⟨⟨(-1342144789575774885467563305),(-1342144789575774836662107989)⟩,⟨(-1810023163847612441077017062),(-1810023163847612392233938549)⟩⟩,⟨⟨(-1350962103303146340430636255),(-1350962103303146293115487768)⟩,⟨(-1706199635793221450149714874),(-1706199635793221402799838975)⟩⟩,⟨⟨(-1356195132619844604147240121),(-1356195132619844558223670669)⟩,⟨(-1606561438004790656177243807),(-1606561438004790610221686498)⟩⟩,⟨⟨(-1358156504601363755930057196),(-1358156504601363711380856036)⟩,⟨(-1511039102553460454439201806),(-1511039102553460409860616321)⟩⟩,⟨⟨(-1357141225082163626836291062),(-1357141225082163583574865810)⟩,⟨(-1419554581322362250683561729),(-1419554581322362207395211902)⟩⟩,⟨⟨(-1353427176092336554877608453),(-1353427176092336512903302336)⟩,⟨(-1332022412381947357574432843),(-1332022412381947315575537000)⟩⟩,⟨⟨(-1347275644164284646657989859),(-1347275644164284605885716702)⟩,⟨(-1248350805587895342216481365),(-1248350805587895301421820701)⟩⟩,⟨⟨(-1338931873691903850492164071),(-1338931873691903810909896335)⟩,⟨(-1168442649774710346953073200),(-1168442649774710307350502471)⟩⟩,⟨⟨(-1328625639960098993462340971),(-1328625639960098955001349580)⟩,⟨(-1092196444142129912909040593),(-1092196444142129874429710846)⟩⟩] +lemma kernel13_1_r5_11_eq : ∀ k : Fin 16, kernel13_1Expr 5 11 k = kernel13_1_r5_11 k := by decide +kernel +noncomputable def kernel13_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-1316571836889539940164505127),(-1316571836889539902829465156)⟩,⟨(-1019507156615466681609106749),(-1019507156615466644257585631)⟩⟩,⟨⟨(-1302971074958041781237251528),(-1302971074958041744945627340)⟩,⟨(-950267012107732287241880310),(-950267012107732250935521139)⟩⟩,⟨⟨(-1288010285163780825806265881),(-1288010285163780790534130937)⟩,⟨(-884366213723632787590264114),(-884366213723632752305040230)⟩⟩,⟨⟨(-1271863325285035632488803258),(-1271863325285035598175437302)⟩,⟨(-821693600026050023497010326),(-821693600026049989172102185)⟩⟩,⟨⟨(-1254691585064864826794127997),(-1254691585064864793441852175)⟩,⟨(-762137241537177494888911200),(-762137241537177461526548636)⟩⟩,⟨⟨(-1236644587305981325326790527),(-1236644587305981292867048106)⟩,⟨(-705584979671754623596829621),(-705584979671754591128365640)⟩⟩,⟨⟨(-1217860582200199119036912118),(-1217860582200199087462107436)⟩,⟨(-651924911301459905340040319),(-651924911301459873757795553)⟩⟩,⟨⟨(-1198467132537599055258936411),(-1198467132537599024514547764)⟩,⟨(-601045822130013562311859067),(-601045822130013531561231203)⟩⟩,⟨⟨(-1178581687742589677735869426),(-1178581687742589647828090191)⟩,⟨(-552837572020334155549335150),(-552837572020334125636441393)⟩⟩,⟨⟨(-1158312144967133067492211808),(-1158312144967133038356051931)⟩,⟨(-507191435360508517282115105),(-507191435360508488141893220)⟩⟩,⟨⟨(-1137757395735547291589372806),(-1137757395735547263218754916)⟩,⟨(-464000399486566007816551080),(-464000399486565979442854802)⟩⟩,⟨⟨(-1117007856880628442138887637),(-1117007856880628414484934710)⟩,⟨(-423159424099164154892433757),(-423159424099164127236321838)⟩⟩,⟨⟨(-1096145984737637210502656870),(-1096145984737637183569479376)⟩,⟨(-384565664520228460373921049),(-384565664520228433439441285)⟩⟩,⟨⟨(-1075246771771368736460429825),(-1075246771771368710192047742)⟩,⟨(-348118661536144934976094019),(-348118661536144908707209872)⟩⟩,⟨⟨(-1054378225002574073754578496),(-1054378225002574048141074547)⟩,⟨(-313720500467944378465988118),(-313720500467944352852726336)⟩⟩,⟨⟨(-1033601825774017162154665208),(-1033601825774017137144007870)⟩,⟨(-281275941997572096949198455),(-281275941997572071939477321)⟩⟩] +lemma kernel13_1_r5_12_eq : ∀ k : Fin 16, kernel13_1Expr 5 12 k = kernel13_1_r5_12 k := by decide +kernel +noncomputable def kernel13_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-1012972970554093510966044805),(-1012972970554093486567380570)⟩,⟨(-250692527164201989085665209),(-250692527164201964688579843)⟩⟩,⟨⟨(-992541392617923058183579162),(-992541392617923034343632071)⟩,⟨(-221880658826895943940092261),(-221880658826895920102323692)⟩⟩,⟨⟨(-972351564572920225101136242),(-972351564572920201817312836)⟩,⟨(-194753661770868292409893563),(-194753661770868269128803376)⟩⟩,⟨⟨(-952443081808830565184572680),(-952443081808830542418258070)⟩,⟨(-169227823515209236548807411),(-169227823515209213785742243)⟩⟩,⟨⟨(-932851027051917435175160371),(-932851027051917412932800129)⟩,⟨(-145222417761053286861652279),(-145222417761053264623016455)⟩⟩,⟨⟨(-913606316290206198792376110),(-913606316290206177028607434)⟩,⟨(-122659712301641141820108839),(-122659712301641120060507208)⟩⟩,⟨⟨(-894736026412271928107627255),(-894736026412271906820867928)⟩,⟨(-101464963100204586213991367),(-101464963100204564931805943)⟩⟩,⟨⟨(-876263704966808041706117942),(-876263704966808020861550961)⟩,⟨(-81566396128694878937844738),(-81566396128694858098229674)⟩⟩,⟨⟨(-858209662504944171281650868),(-858209662504944150888730768)⟩,⟨(-62895178450575968827687819),(-62895178450575948440064117)⟩⟩,⟨⟨(-840591248012780198679393956),(-840591248012780178694236099)⟩,⟨(-45385379924630868668360176),(-45385379924630848688820140)⟩⟩,⟨⟨(-823423107978635539744374278),(-823423107978635520164507566)⟩,⟨(-28973926804321383725821265),(-28973926804321364151861071)⟩⟩,⟨⟨(-806717429668817370486252171),(-806717429668817351279409711)⟩,⟨(-13600548408966092247041712),(-13600548408966073046371407)⟩⟩,⟨⟨(-790484169207997691922917451),(-790484169207997673096779845)⟩,⟨792282050937383772750145,792282050937402592476037⟩⟩,⟨⟨(-774731265076233600292623277),(-774731265076233581809391689)⟩,⟨14259411501376689794931455,14259411501376708271527697⟩⟩,⟨⟨(-759464837644910248486451919),(-759464837644910230346326526)⟩,⟨26853074977488055776628894,26853074977488073909917057⟩⟩,⟨⟨(-744689375379038510720932513),(-744689375379038492895478124)⟩,⟨38622966713490177353685732,38622966713490195172115558⟩⟩] +lemma kernel13_1_r5_13_eq : ∀ k : Fin 16, kernel13_1Expr 5 13 k = kernel13_1_r5_13 k := by decide +kernel +noncomputable def kernel13_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-730407908333969604078694686),(-730407908333969586578991790)⟩,⟨49616313597790801970611018,49616313597790819463123534⟩⟩,⟨⟨(-716622169571230374068134692),(-716622169571230356856300613)⟩,⟨59877950312199847295741498,59877950312199864500229146⟩⟩,⟨⟨(-703332745111332310017047666),(-703332745111332293093886350)⟩,⟨69450395540676331898752514,69450395540676348814428325⟩⟩,⟨⟨(-690539213031524876350675322),(-690539213031524859690246465)⟩,⟨78373928695078815964723696,78373928695078832617537786⟩⟩,⟨⟨(-678240272303973883151647804),(-678240272303973866762401707)⟩,⟨86686666663090056683865749,86686666663090073065384567⟩⟩,⟨⟨(-666433861955137927336850053),(-666433861955137911186455507)⟩,⟨94424640136974431387985221,94424640136974447530546095⟩⟩,⟨⟨(-655117271110546145676138082),(-655117271110546129765896049)⟩,⟨101621869131244806462732540,101621869131244822365047724⟩⟩,⟨⟨(-644287240471071803353689784),(-644287240471071787659780840)⟩,⟨108310437342819405766470416,108310437342819421452365514⟩⟩,⟨⟨(-633940055747440576844702868),(-633940055747440561378042286)⟩,⟨114520565049003558923495670,114520565049003574382138096⟩⟩,⟨⟨(-624071633559372050313264911),(-624071633559372035041417351)⟩,⟨120280680276807381502056246,120280680276807396765886765⟩⟩,⟨⟨(-614677600284662029046435408),(-614677600284662013971080731)⟩,⟨125617488011884314148257188,125617488011884329215601393⟩⟩,⟨⟨(-605753364321879298297683807),(-605753364321879283396806982)⟩,⟨130556037246925372084843288,130556037246925386977715232⟩⟩,⟨⟨(-597294182208355951537824431),(-597294182208355936820418469)⟩,⟨135119785697849057679192833,135119785697849072388605935⟩⟩,⟨⟨(-589295219012954536289776803),(-589295219012954521727368948)⟩,⟨139330662041765591256385381,139330662041765605810808999⟩⟩,⟨⟨(-581751603400835385270843021),(-581751603400835370865390267)⟩,⟨143209125553642893224261045,143209125553642907621742108⟩⟩,⟨⟨(-574658477745240761068223890),(-574658477745240746799203955)⟩,⟨146774223039034069477769765,146774223039034083738828490⟩⟩] +lemma kernel13_1_r5_14_eq : ∀ k : Fin 16, kernel13_1Expr 5 14 k = kernel13_1_r5_14 k := by decide +kernel +noncomputable def kernel13_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-568011043639257281614282973),(-568011043639257267493597742)⟩,⟨150043642978311615303986958,150043642978311629416727262⟩⟩,⟨⟨(-561804603138695720906096705),(-561804603138695706903935925)⟩,⟨153033766813757204991079089,153033766813757218985306250⟩⟩,⟨⟨(-556034596045703084012848796),(-556034596045703070131333615)⟩,⟨155759717324737737307934827,155759717324737751181530509⟩⟩,⟨⟨(-550696633521546768011889957),(-550696633521546754231730649)⟩,⟨158235404048212745275905658,158235404048212759048156783⟩⟩,⟨⟨(-545786528296222393117392432),(-545786528296222379447923710)⟩,⟨160473565712114107818227797,160473565712114121479803834⟩⟩,⟨⟨(-541300321722161322859150739),(-541300321722161309274385287)⟩,⟨162485809657859097044952650,162485809657859110621836045⟩⟩,⟨⟨(-537234307899365983759512839),(-537234307899365970261644358)⟩,⟨164282648235539124090465970,164282648235539137580465049⟩⟩,⟨⟨(-533585055079786121936684257),(-533585055079786108507392969)⟩,⟨165873532161300210316635752,165873532161300223738067022⟩⟩,⟨⟨(-530349424539663665494338358),(-530349424539663652144089148)⟩,⟨167266880831222589843658534,167266880831222603186061198⟩⟩,⟨⟨(-527524587089906713676950902),(-527524587089906700377324552)⟩,⟨168470109589735803196214498,168470109589735816488001969⟩⟩,⟨⟨(-525108037376286288812587232),(-525108037376286275566069648)⟩,⟨169489653953386786631109326,169489653953386799869797212⟩⟩,⟨⟨(-523097606103358767100796470),(-523097606103358753890135357)⟩,⟨170330990792721488843499013,170330990792721502046336113⟩⟩,⟨⟨(-521491470298472974898598758),(-521491470298472961733636220)⟩,⟨170998656476250603025619001,170998656476250616182766393⟩⟩,⟨⟨(-520288161714989874835715996),(-520288161714989861692046351)⟩,⟨171496261981048095810754174,171496261981048108946612134⟩⟩,⟨⟨(-519486573456886764273712613),(-519486573456886751153675742)⟩,⟨171826504974574670570236888,171826504974574683682466757⟩⟩,⟨⟨(-519085964890195917352097139),(-519085964890195904238954927)⟩,⟨171991178871921232459462394,171991178871921245564798725⟩⟩] +lemma kernel13_1_r5_15_eq : ∀ k : Fin 16, kernel13_1Expr 5 15 k = kernel13_1_r5_15 k := by decide +kernel +noncomputable def kernel13_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel13_1_r5_0,kernel13_1_r5_1,kernel13_1_r5_2,kernel13_1_r5_3,kernel13_1_r5_4,kernel13_1_r5_5,kernel13_1_r5_6,kernel13_1_r5_7,kernel13_1_r5_8,kernel13_1_r5_9,kernel13_1_r5_10,kernel13_1_r5_11,kernel13_1_r5_12,kernel13_1_r5_13,kernel13_1_r5_14,kernel13_1_r5_15] +lemma kernel13_1_r5_eq (i k : Fin 16) : kernel13_1Expr 5 i k = kernel13_1_r5 i k := by + fin_cases i + · exact kernel13_1_r5_0_eq k + · exact kernel13_1_r5_1_eq k + · exact kernel13_1_r5_2_eq k + · exact kernel13_1_r5_3_eq k + · exact kernel13_1_r5_4_eq k + · exact kernel13_1_r5_5_eq k + · exact kernel13_1_r5_6_eq k + · exact kernel13_1_r5_7_eq k + · exact kernel13_1_r5_8_eq k + · exact kernel13_1_r5_9_eq k + · exact kernel13_1_r5_10_eq k + · exact kernel13_1_r5_11_eq k + · exact kernel13_1_r5_12_eq k + · exact kernel13_1_r5_13_eq k + · exact kernel13_1_r5_14_eq k + · exact kernel13_1_r5_15_eq k +noncomputable def kernel13_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel13_1_r0,kernel13_1_r1,kernel13_1_r2,kernel13_1_r3,kernel13_1_r4,kernel13_1_r5] +lemma kernel13_1_eq (j : Fin 6) (i k : Fin 16) : kernel13_1Expr j i k = kernel13_1 j i k := by + fin_cases j + · exact kernel13_1_r0_eq i k + · exact kernel13_1_r1_eq i k + · exact kernel13_1_r2_eq i k + · exact kernel13_1_r3_eq i k + · exact kernel13_1_r4_eq i k + · exact kernel13_1_r5_eq i k +lemma kernel13_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel13_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(13:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel13_1_eq] + unfold kernel13_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans13_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel15_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans15 j i k) +noncomputable def kernel15_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_0_eq : ∀ k : Fin 16, kernel15_0Expr 0 0 k = kernel15_0_r0_0 k := by decide +kernel +noncomputable def kernel15_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_1_eq : ∀ k : Fin 16, kernel15_0Expr 0 1 k = kernel15_0_r0_1 k := by decide +kernel +noncomputable def kernel15_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_2_eq : ∀ k : Fin 16, kernel15_0Expr 0 2 k = kernel15_0_r0_2 k := by decide +kernel +noncomputable def kernel15_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_3_eq : ∀ k : Fin 16, kernel15_0Expr 0 3 k = kernel15_0_r0_3 k := by decide +kernel +noncomputable def kernel15_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_4_eq : ∀ k : Fin 16, kernel15_0Expr 0 4 k = kernel15_0_r0_4 k := by decide +kernel +noncomputable def kernel15_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_5_eq : ∀ k : Fin 16, kernel15_0Expr 0 5 k = kernel15_0_r0_5 k := by decide +kernel +noncomputable def kernel15_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_6_eq : ∀ k : Fin 16, kernel15_0Expr 0 6 k = kernel15_0_r0_6 k := by decide +kernel +noncomputable def kernel15_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_7_eq : ∀ k : Fin 16, kernel15_0Expr 0 7 k = kernel15_0_r0_7 k := by decide +kernel +noncomputable def kernel15_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_8_eq : ∀ k : Fin 16, kernel15_0Expr 0 8 k = kernel15_0_r0_8 k := by decide +kernel +noncomputable def kernel15_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_9_eq : ∀ k : Fin 16, kernel15_0Expr 0 9 k = kernel15_0_r0_9 k := by decide +kernel +noncomputable def kernel15_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_10_eq : ∀ k : Fin 16, kernel15_0Expr 0 10 k = kernel15_0_r0_10 k := by decide +kernel +noncomputable def kernel15_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r0_11_eq : ∀ k : Fin 16, kernel15_0Expr 0 11 k = kernel15_0_r0_11 k := by decide +kernel +noncomputable def kernel15_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel15_0_r0_12_eq : ∀ k : Fin 16, kernel15_0Expr 0 12 k = kernel15_0_r0_12 k := by decide +kernel +noncomputable def kernel15_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel15_0_r0_13_eq : ∀ k : Fin 16, kernel15_0Expr 0 13 k = kernel15_0_r0_13 k := by decide +kernel +noncomputable def kernel15_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel15_0_r0_14_eq : ∀ k : Fin 16, kernel15_0Expr 0 14 k = kernel15_0_r0_14 k := by decide +kernel +noncomputable def kernel15_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel15_0_r0_15_eq : ∀ k : Fin 16, kernel15_0Expr 0 15 k = kernel15_0_r0_15 k := by decide +kernel +noncomputable def kernel15_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel15_0_r0_0,kernel15_0_r0_1,kernel15_0_r0_2,kernel15_0_r0_3,kernel15_0_r0_4,kernel15_0_r0_5,kernel15_0_r0_6,kernel15_0_r0_7,kernel15_0_r0_8,kernel15_0_r0_9,kernel15_0_r0_10,kernel15_0_r0_11,kernel15_0_r0_12,kernel15_0_r0_13,kernel15_0_r0_14,kernel15_0_r0_15] +lemma kernel15_0_r0_eq (i k : Fin 16) : kernel15_0Expr 0 i k = kernel15_0_r0 i k := by + fin_cases i + · exact kernel15_0_r0_0_eq k + · exact kernel15_0_r0_1_eq k + · exact kernel15_0_r0_2_eq k + · exact kernel15_0_r0_3_eq k + · exact kernel15_0_r0_4_eq k + · exact kernel15_0_r0_5_eq k + · exact kernel15_0_r0_6_eq k + · exact kernel15_0_r0_7_eq k + · exact kernel15_0_r0_8_eq k + · exact kernel15_0_r0_9_eq k + · exact kernel15_0_r0_10_eq k + · exact kernel15_0_r0_11_eq k + · exact kernel15_0_r0_12_eq k + · exact kernel15_0_r0_13_eq k + · exact kernel15_0_r0_14_eq k + · exact kernel15_0_r0_15_eq k +noncomputable def kernel15_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel15_0_r1_0_eq : ∀ k : Fin 16, kernel15_0Expr 1 0 k = kernel15_0_r1_0 k := by decide +kernel +noncomputable def kernel15_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel15_0_r1_1_eq : ∀ k : Fin 16, kernel15_0Expr 1 1 k = kernel15_0_r1_1 k := by decide +kernel +noncomputable def kernel15_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel15_0_r1_2_eq : ∀ k : Fin 16, kernel15_0Expr 1 2 k = kernel15_0_r1_2 k := by decide +kernel +noncomputable def kernel15_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_3_eq : ∀ k : Fin 16, kernel15_0Expr 1 3 k = kernel15_0_r1_3 k := by decide +kernel +noncomputable def kernel15_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_4_eq : ∀ k : Fin 16, kernel15_0Expr 1 4 k = kernel15_0_r1_4 k := by decide +kernel +noncomputable def kernel15_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_5_eq : ∀ k : Fin 16, kernel15_0Expr 1 5 k = kernel15_0_r1_5 k := by decide +kernel +noncomputable def kernel15_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_6_eq : ∀ k : Fin 16, kernel15_0Expr 1 6 k = kernel15_0_r1_6 k := by decide +kernel +noncomputable def kernel15_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_7_eq : ∀ k : Fin 16, kernel15_0Expr 1 7 k = kernel15_0_r1_7 k := by decide +kernel +noncomputable def kernel15_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_8_eq : ∀ k : Fin 16, kernel15_0Expr 1 8 k = kernel15_0_r1_8 k := by decide +kernel +noncomputable def kernel15_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_9_eq : ∀ k : Fin 16, kernel15_0Expr 1 9 k = kernel15_0_r1_9 k := by decide +kernel +noncomputable def kernel15_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_10_eq : ∀ k : Fin 16, kernel15_0Expr 1 10 k = kernel15_0_r1_10 k := by decide +kernel +noncomputable def kernel15_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_11_eq : ∀ k : Fin 16, kernel15_0Expr 1 11 k = kernel15_0_r1_11 k := by decide +kernel +noncomputable def kernel15_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_12_eq : ∀ k : Fin 16, kernel15_0Expr 1 12 k = kernel15_0_r1_12 k := by decide +kernel +noncomputable def kernel15_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_13_eq : ∀ k : Fin 16, kernel15_0Expr 1 13 k = kernel15_0_r1_13 k := by decide +kernel +noncomputable def kernel15_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_14_eq : ∀ k : Fin 16, kernel15_0Expr 1 14 k = kernel15_0_r1_14 k := by decide +kernel +noncomputable def kernel15_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel15_0_r1_15_eq : ∀ k : Fin 16, kernel15_0Expr 1 15 k = kernel15_0_r1_15 k := by decide +kernel +noncomputable def kernel15_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel15_0_r1_0,kernel15_0_r1_1,kernel15_0_r1_2,kernel15_0_r1_3,kernel15_0_r1_4,kernel15_0_r1_5,kernel15_0_r1_6,kernel15_0_r1_7,kernel15_0_r1_8,kernel15_0_r1_9,kernel15_0_r1_10,kernel15_0_r1_11,kernel15_0_r1_12,kernel15_0_r1_13,kernel15_0_r1_14,kernel15_0_r1_15] +lemma kernel15_0_r1_eq (i k : Fin 16) : kernel15_0Expr 1 i k = kernel15_0_r1 i k := by + fin_cases i + · exact kernel15_0_r1_0_eq k + · exact kernel15_0_r1_1_eq k + · exact kernel15_0_r1_2_eq k + · exact kernel15_0_r1_3_eq k + · exact kernel15_0_r1_4_eq k + · exact kernel15_0_r1_5_eq k + · exact kernel15_0_r1_6_eq k + · exact kernel15_0_r1_7_eq k + · exact kernel15_0_r1_8_eq k + · exact kernel15_0_r1_9_eq k + · exact kernel15_0_r1_10_eq k + · exact kernel15_0_r1_11_eq k + · exact kernel15_0_r1_12_eq k + · exact kernel15_0_r1_13_eq k + · exact kernel15_0_r1_14_eq k + · exact kernel15_0_r1_15_eq k +noncomputable def kernel15_0_r2_0 : Fin 16 → CBox := ![⟨⟨625416754697,625416754700⟩,⟨(-214211213760),(-214211213757)⟩⟩,⟨⟨624160990561,624160990565⟩,⟨(-214084080679),(-214084080675)⟩⟩,⟨⟨621656711112,621656711115⟩,⟨(-213828806832),(-213828806828)⟩⟩,⟨⟨617918347738,617918347742⟩,⟨(-213443403858),(-213443403854)⟩⟩,⟨⟨612967382662,612967382665⟩,⟨(-212924956123),(-212924956119)⟩⟩,⟨⟨606832153316,606832153319⟩,⟨(-212269699349),(-212269699345)⟩⟩,⟨⟨599547595144,599547595149⟩,⟨(-211473122753),(-211473122748)⟩⟩,⟨⟨591154925904,591154925908⟩,⟨(-210530092430),(-210530092427)⟩⟩,⟨⟨581701275173,581701275177⟩,⟨(-209434993285),(-209434993282)⟩⟩,⟨⟨571239263486,571239263490⟩,⟨(-208181886418),(-208181886415)⟩⟩,⟨⟨559826535997,559826536001⟩,⟨(-206764678527),(-206764678524)⟩⟩,⟨⟨547525256147,547525256151⟩,⟨(-205177299667),(-205177299663)⟩⟩,⟨⟨534401565211,534401565216⟩,⟨(-203413885524),(-203413885519)⟩⟩,⟨⟨520525013958,520525013962⟩,⟨(-201468960310),(-201468960307)⟩⟩,⟨⟨505967972897,505967972901⟩,⟨(-199337616394),(-199337616391)⟩⟩,⟨⟨490805027800,490805027804⟩,⟨(-197015686848),(-197015686845)⟩⟩] +lemma kernel15_0_r2_0_eq : ∀ k : Fin 16, kernel15_0Expr 2 0 k = kernel15_0_r2_0 k := by decide +kernel +noncomputable def kernel15_0_r2_1 : Fin 16 → CBox := ![⟨⟨475112367246,475112367250⟩,⟨(-194499907354),(-194499907350)⟩⟩,⟨⟨458967168916,458967168920⟩,⟨(-191788064091),(-191788064088)⟩⟩,⟨⟨442446991298,442446991301⟩,⟨(-188879124613),(-188879124609)⟩⟩,⟨⟨425629177258,425629177261⟩,⟨(-185773349095),(-185773349092)⟩⟩,⟨⟨408590275641,408590275644⟩,⟨(-182472379779),(-182472379775)⟩⟩,⟨⟨391405486759,391405486763⟩,⟨(-178979306935),(-178979306932)⟩⟩,⟨⟨374148137151,374148137155⟩,⟨(-175298710153),(-175298710150)⟩⟩,⟨⟨356889188521,356889188524⟩,⟨(-171436674324),(-171436674321)⟩⟩,⟨⟨339696785227,339696785230⟩,⟨(-167400780193),(-167400780189)⟩⟩,⟨⟨322635844070,322635844074⟩,⟨(-163200069860),(-163200069856)⟩⟩,⟨⟨305767689477,305767689480⟩,⟨(-158844988150),(-158844988147)⟩⟩,⟨⟨289149736560,289149736563⟩,⟨(-154347301195),(-154347301191)⟩⟩,⟨⟨272835223784,272835223789⟩,⟨(-149719994008),(-149719994003)⟩⟩,⟨⟨256872996329,256872996332⟩,⟨(-144977149214),(-144977149211)⟩⟩,⟨⟨241307340515,241307340518⟩,⟨(-140133809396),(-140133809392)⟩⟩,⟨⟨226177869033,226177869037⟩,⟨(-135205825768),(-135205825765)⟩⟩] +lemma kernel15_0_r2_1_eq : ∀ k : Fin 16, kernel15_0Expr 2 1 k = kernel15_0_r2_1 k := by decide +kernel +noncomputable def kernel15_0_r2_2 : Fin 16 → CBox := ![⟨⟨211519456014,211519456018⟩,⟨(-130209696103),(-130209696100)⟩⟩,⟨⟨197362220424,197362220427⟩,⟨(-125162394905),(-125162394901)⟩⟩,⟨⟨183731555681,183731555685⟩,⟨(-120081198938),(-120081198934)⟩⟩,⟨⟨170648202889,170648202893⟩,⟨(-114983511128),(-114983511124)⟩⟩,⟨⟨158128364613,158128364617⟩,⟨(-109886685839),(-109886685835)⟩⟩,⟨⟨146183855772,146183855776⟩,⟨(-104807858352),(-104807858349)⟩⟩,⟨⟨134822287880,134822287883⟩,⟨(-99763781199),(-99763781196)⟩⟩,⟨⟨124047282617,124047282621⟩,⟨(-94770669758),(-94770669755)⟩⟩,⟨⟨113858710582,113858710585⟩,⟨(-89844059242),(-89844059238)⟩⟩,⟨⟨104252950911,104252950915⟩,⟨(-84998674922),(-84998674919)⟩⟩,⟨⟨95223167472,95223167476⟩,⟨(-80248317085),(-80248317081)⟩⟩,⟨⟨86759597350,86759597355⟩,⟨(-75605761861),(-75605761856)⟩⟩,⟨⟨78849847469,78849847473⟩,⟨(-71082678787),(-71082678784)⟩⟩,⟨⟨71479195293,71479195297⟩,⟨(-66689565534),(-66689565530)⟩⟩,⟨⟨64630889861,64630889866⟩,⟨(-62435699959),(-62435699954)⟩⟩,⟨⟨58286449538,58286449541⟩,⟨(-58329109298),(-58329109295)⟩⟩] +lemma kernel15_0_r2_2_eq : ∀ k : Fin 16, kernel15_0Expr 2 2 k = kernel15_0_r2_2 k := by decide +kernel +noncomputable def kernel15_0_r2_3 : Fin 16 → CBox := ![⟨⟨52425953291,52425953295⟩,⟨(-54376556059),(-54376556056)⟩⟩,⟨⟨47028322513,47028322517⟩,⟨(-50583539835),(-50583539831)⟩⟩,⟨⟨42071590844,42071590847⟩,⟨(-46954314114),(-46954314110)⟩⟩,⟨⟨37533159750,37533159754⟩,⟨(-43491916913),(-43491916909)⟩⟩,⟨⟨33390038041,33390038044⟩,⟨(-40198213903),(-40198213899)⟩⟩,⟨⟨29619063815,29619063819⟩,⟨(-37073952573),(-37073952570)⟩⟩,⟨⟨26197107763,26197107768⟩,⟨(-34118825932),(-34118825927)⟩⟩,⟨⟨23101257050,23101257054⟩,⟨(-31331544119),(-31331544115)⟩⟩,⟨⟨20308979366,20308979369⟩,⟨(-28709912356),(-28709912353)⟩⟩,⟨⟨17798267049,17798267052⟩,⟨(-26250913645),(-26250913641)⟩⟩,⟨⟨15547761457,15547761460⟩,⟨(-23950794668),(-23950794665)⟩⟩,⟨⟨13536858039,13536858042⟩,⟨(-21805153448),(-21805153444)⟩⟩,⟨⟨11745792771,11745792775⟩,⟨(-19809027366),(-19809027362)⟩⟩,⟨⟨10155710838,10155710844⟩,⟨(-17956980299),(-17956980294)⟩⟩,⟨⟨8748718589,8748718593⟩,⟨(-16243187729),(-16243187725)⟩⟩,⟨⟨7507919910,7507919913⟩,⟨(-14661518831),(-14661518827)⟩⟩] +lemma kernel15_0_r2_3_eq : ∀ k : Fin 16, kernel15_0Expr 2 3 k = kernel15_0_r2_3 k := by decide +kernel +noncomputable def kernel15_0_r2_4 : Fin 16 → CBox := ![⟨⟨6417438314,6417438318⟩,⟨(-13205614682),(-13205614679)⟩⟩,⟨⟨5462426028,5462426032⟩,⟨(-11868961870),(-11868961866)⟩⟩,⟨⟨4629061484,4629061488⟩,⟨(-10644960935),(-10644960931)⟩⟩,⟨⟨3904536568,3904536571⟩,⟨(-9526989225),(-9526989221)⟩⟩,⟨⟨3277034997,3277035000⟩,⟨(-8508457854),(-8508457850)⟩⟩,⟨⟨2735703172,2735703175⟩,⟨(-7582862586),(-7582862582)⟩⟩,⟨⟨2270614766,2270614769⟩,⟨(-6743828622),(-6743828618)⟩⟩,⟨⟨1872730289,1872730293⟩,⟨(-5985149289),(-5985149285)⟩⟩,⟨⟨1533852763,1533852766⟩,⟨(-5300818820),(-5300818816)⟩⟩,⟨⟨1246580537,1246580540⟩,⟨(-4685059397),(-4685059394)⟩⟩,⟨⟨1004258238,1004258242⟩,⟨(-4132342779),(-4132342775)⟩⟩,⟨⟨800926696,800926700⟩,⟨(-3637406820),(-3637406817)⟩⟩,⟨⟨631272605,631272608⟩,⟨(-3195267281),(-3195267277)⟩⟩,⟨⟨490578588,490578592⟩,⟨(-2801225310),(-2801225306)⟩⟩,⟨⟨374674238,374674242⟩,⟨(-2450871050),(-2450871046)⟩⟩,⟨⟨279888604,279888608⟩,⟨(-2140083772),(-2140083769)⟩⟩] +lemma kernel15_0_r2_4_eq : ∀ k : Fin 16, kernel15_0Expr 2 4 k = kernel15_0_r2_4 k := by decide +kernel +noncomputable def kernel15_0_r2_5 : Fin 16 → CBox := ![⟨⟨203004497,203004500⟩,⟨(-1865028987),(-1865028983)⟩⟩,⟨⟨141214935,141214939⟩,⟨(-1622152940),(-1622152936)⟩⟩,⟨⟨92081956,92081959⟩,⟨(-1408174916),(-1408174912)⟩⟩,⟨⟨53497938,53497942⟩,⟨(-1220077723),(-1220077719)⟩⟩,⟨⟨23649561,23649565⟩,⟨(-1055096729),(-1055096725)⟩⟩,⟨⟨984408,984412⟩,⟨(-910707779),(-910707776)⟩⟩,⟨⟨(-15819746),(-15819742)⟩,⟨(-784614312),(-784614309)⟩⟩,⟨⟨(-27883026),(-27883022)⟩,⟨(-674733935),(-674733931)⟩⟩,⟨⟨(-36149000),(-36148995)⟩,⟨(-579184708),(-579184703)⟩⟩,⟨⟨(-41407753),(-41407748)⟩,⟨(-496271365),(-496271360)⟩⟩,⟨⟨(-44316643),(-44316639)⟩,⟨(-424471626),(-424471623)⟩⟩,⟨⟨(-45418828),(-45418824)⟩,⟨(-362422788),(-362422784)⟩⟩,⟨⟨(-45159751),(-45159748)⟩,⟨(-308908682),(-308908678)⟩⟩,⟨⟨(-43901695),(-43901692)⟩,⟨(-262847156),(-262847152)⟩⟩,⟨⟨(-41936593),(-41936589)⟩,⟨(-223278091),(-223278087)⟩⟩,⟨⟨(-39497212),(-39497208)⟩,⟨(-189352076),(-189352073)⟩⟩] +lemma kernel15_0_r2_5_eq : ∀ k : Fin 16, kernel15_0Expr 2 5 k = kernel15_0_r2_5 k := by decide +kernel +noncomputable def kernel15_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-36766892),(-36766887)⟩,⟨(-160319748),(-160319743)⟩⟩,⟨⟨(-33887951),(-33887947)⟩,⟨(-135521800),(-135521796)⟩⟩,⟨⟨(-30968922),(-30968919)⟩,⟨(-114379738),(-114379734)⟩⟩,⟨⟨(-28090739),(-28090735)⟩,⟨(-96387297),(-96387293)⟩⟩,⟨⟨(-25311972),(-25311967)⟩,⟨(-81102573),(-81102568)⟩⟩,⟨⟨(-22673274),(-22673270)⟩,⟨(-68140820),(-68140816)⟩⟩,⟨⟨(-20201094),(-20201090)⟩,⟨(-57167884),(-57167880)⟩⟩,⟨⟨(-17910769),(-17910765)⟩,⟨(-47894261),(-47894257)⟩⟩,⟨⟨(-15809089),(-15809085)⟩,⟨(-40069728),(-40069725)⟩⟩,⟨⟨(-13896396),(-13896393)⟩,⟨(-33478518),(-33478514)⟩⟩,⟨⟨(-12168286),(-12168282)⟩,⟨(-27935003),(-27934999)⟩⟩,⟨⟨(-10616989),(-10616984)⟩,⟨(-23279847),(-23279842)⟩⟩,⟨⟨(-9232459),(-9232455)⟩,⟨(-19376570),(-19376566)⟩⟩,⟨⟨(-8003236),(-8003232)⟩,⟨(-16108538),(-16108534)⟩⟩,⟨⟨(-6917115),(-6917111)⟩,⟨(-13376276),(-13376272)⟩⟩,⟨⟨(-5961655),(-5961652)⟩,⟨(-11095119),(-11095115)⟩⟩] +lemma kernel15_0_r2_6_eq : ∀ k : Fin 16, kernel15_0Expr 2 6 k = kernel15_0_r2_6 k := by decide +kernel +noncomputable def kernel15_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-5124547),(-5124543)⟩,⟨(-9193153),(-9193150)⟩⟩,⟨⟨(-4393897),(-4393893)⟩,⟨(-7609418),(-7609414)⟩⟩,⟨⟨(-3758408),(-3758405)⟩,⟨(-6292334),(-6292330)⟩⟩,⟨⟨(-3207509),(-3207505)⟩,⟨(-5198342),(-5198338)⟩⟩,⟨⟨(-2731417),(-2731413)⟩,⟨(-4290721),(-4290718)⟩⟩,⟨⟨(-2321173),(-2321169)⟩,⟨(-3538574),(-3538570)⟩⟩,⟨⟨(-1968641),(-1968637)⟩,⟨(-2915944),(-2915940)⟩⟩,⟨⟨(-1666493),(-1666489)⟩,⟨(-2401064),(-2401060)⟩⟩,⟨⟨(-1408168),(-1408164)⟩,⟨(-1975706),(-1975702)⟩⟩,⟨⟨(-1187827),(-1187823)⟩,⟨(-1624641),(-1624637)⟩⟩,⟨⟨(-1000304),(-1000300)⟩,⟨(-1335148),(-1335144)⟩⟩,⟨⟨(-841049),(-841045)⟩,⟨(-1096631),(-1096627)⟩⟩,⟨⟨(-706078),(-706073)⟩,⟨(-900270),(-900265)⟩⟩,⟨⟨(-591905),(-591901)⟩,⟨(-738734),(-738730)⟩⟩,⟨⟨(-495504),(-495500)⟩,⟨(-605939),(-605935)⟩⟩,⟨⟨(-414252),(-414249)⟩,⟨(-496840),(-496836)⟩⟩] +lemma kernel15_0_r2_7_eq : ∀ k : Fin 16, kernel15_0Expr 2 7 k = kernel15_0_r2_7 k := by decide +kernel +noncomputable def kernel15_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-345885),(-345881)⟩,⟨(-407262),(-407258)⟩⟩,⟨⟨(-288452),(-288446)⟩,⟨(-333753),(-333747)⟩⟩,⟨⟨(-240272),(-240269)⟩,⟨(-273457),(-273454)⟩⟩,⟨⟨(-199922),(-199918)⟩,⟨(-224022),(-224018)⟩⟩,⟨⟨(-166172),(-166168)⟩,⟨(-183507),(-183503)⟩⟩,⟨⟨(-137979),(-137975)⟩,⟨(-150312),(-150308)⟩⟩,⟨⟨(-114460),(-114456)⟩,⟨(-123122),(-123118)⟩⟩,⟨⟨(-94865),(-94861)⟩,⟨(-100857),(-100853)⟩⟩,⟨⟨(-78556),(-78552)⟩,⟨(-82626),(-82622)⟩⟩,⟨⟨(-64998),(-64994)⟩,⟨(-67700),(-67696)⟩⟩,⟨⟨(-53737),(-53733)⟩,⟨(-55482),(-55479)⟩⟩,⟨⟨(-44396),(-44392)⟩,⟨(-45480),(-45476)⟩⟩,⟨⟨(-36654),(-36650)⟩,⟨(-37293),(-37289)⟩⟩,⟨⟨(-30239),(-30235)⟩,⟨(-30589),(-30585)⟩⟩,⟨⟨(-24935),(-24931)⟩,⟨(-25099),(-25095)⟩⟩,⟨⟨(-20549),(-20545)⟩,⟨(-20603),(-20599)⟩⟩] +lemma kernel15_0_r2_8_eq : ∀ k : Fin 16, kernel15_0Expr 2 8 k = kernel15_0_r2_8 k := by decide +kernel +noncomputable def kernel15_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-16924),(-16920)⟩,⟨(-16921),(-16917)⟩⟩,⟨⟨(-13934),(-13930)⟩,⟨(-13903),(-13899)⟩⟩,⟨⟨(-11466),(-11462)⟩,⟨(-11431),(-11427)⟩⟩,⟨⟨(-9431),(-9427)⟩,⟨(-9403),(-9399)⟩⟩,⟨⟨(-7755),(-7750)⟩,⟨(-7740),(-7734)⟩⟩,⟨⟨(-6374),(-6370)⟩,⟨(-6373),(-6369)⟩⟩,⟨⟨(-5237),(-5233)⟩,⟨(-5252),(-5248)⟩⟩,⟨⟨(-4303),(-4299)⟩,⟨(-4332),(-4328)⟩⟩,⟨⟨(-3533),(-3529)⟩,⟨(-3576),(-3572)⟩⟩,⟨⟨(-2901),(-2897)⟩,⟨(-2953),(-2949)⟩⟩,⟨⟨(-2380),(-2376)⟩,⟨(-2441),(-2437)⟩⟩,⟨⟨(-1956),(-1952)⟩,⟨(-2019),(-2015)⟩⟩,⟨⟨(-1605),(-1601)⟩,⟨(-1671),(-1668)⟩⟩,⟨⟨(-1317),(-1313)⟩,⟨(-1386),(-1382)⟩⟩,⟨⟨(-1081),(-1077)⟩,⟨(-1149),(-1145)⟩⟩,⟨⟨(-886),(-882)⟩,⟨(-953),(-949)⟩⟩] +lemma kernel15_0_r2_9_eq : ∀ k : Fin 16, kernel15_0Expr 2 9 k = kernel15_0_r2_9 k := by decide +kernel +noncomputable def kernel15_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-727),(-723)⟩,⟨(-793),(-789)⟩⟩,⟨⟨(-597),(-593)⟩,⟨(-660),(-656)⟩⟩,⟨⟨(-491),(-487)⟩,⟨(-549),(-545)⟩⟩,⟨⟨(-403),(-399)⟩,⟨(-458),(-454)⟩⟩,⟨⟨(-329),(-326)⟩,⟨(-381),(-377)⟩⟩,⟨⟨(-271),(-267)⟩,⟨(-319),(-315)⟩⟩,⟨⟨(-223),(-219)⟩,⟨(-267),(-263)⟩⟩,⟨⟨(-183),(-180)⟩,⟨(-224),(-220)⟩⟩,⟨⟨(-150),(-146)⟩,⟨(-186),(-182)⟩⟩,⟨⟨(-124),(-119)⟩,⟨(-157),(-152)⟩⟩,⟨⟨(-101),(-97)⟩,⟨(-131),(-127)⟩⟩,⟨⟨(-83),(-79)⟩,⟨(-111),(-107)⟩⟩,⟨⟨(-71),(-67)⟩,⟨(-94),(-90)⟩⟩,⟨⟨(-59),(-55)⟩,⟨(-79),(-75)⟩⟩,⟨⟨(-48),(-44)⟩,⟨(-66),(-62)⟩⟩,⟨⟨(-40),(-35)⟩,⟨(-58),(-52)⟩⟩] +lemma kernel15_0_r2_10_eq : ∀ k : Fin 16, kernel15_0Expr 2 10 k = kernel15_0_r2_10 k := by decide +kernel +noncomputable def kernel15_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-32),(-28)⟩,⟨(-49),(-45)⟩⟩,⟨⟨(-28),(-24)⟩,⟨(-42),(-38)⟩⟩,⟨⟨(-23),(-19)⟩,⟨(-34),(-30)⟩⟩,⟨⟨(-18),(-14)⟩,⟨(-30),(-26)⟩⟩,⟨⟨(-17),(-13)⟩,⟨(-25),(-21)⟩⟩,⟨⟨(-13),(-9)⟩,⟨(-23),(-19)⟩⟩,⟨⟨(-12),(-8)⟩,⟨(-18),(-14)⟩⟩,⟨⟨(-10),(-6)⟩,⟨(-17),(-13)⟩⟩,⟨⟨(-9),(-5)⟩,⟨(-15),(-11)⟩⟩,⟨⟨(-7),(-3)⟩,⟨(-14),(-10)⟩⟩,⟨⟨(-7),(-3)⟩,⟨(-11),(-7)⟩⟩,⟨⟨(-5),(-1)⟩,⟨(-9),(-5)⟩⟩,⟨⟨(-5),(-1)⟩,⟨(-9),(-5)⟩⟩,⟨⟨(-4),0⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-4),0⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩] +lemma kernel15_0_r2_11_eq : ∀ k : Fin 16, kernel15_0Expr 2 11 k = kernel15_0_r2_11 k := by decide +kernel +noncomputable def kernel15_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),0⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩] +lemma kernel15_0_r2_12_eq : ∀ k : Fin 16, kernel15_0Expr 2 12 k = kernel15_0_r2_12 k := by decide +kernel +noncomputable def kernel15_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩] +lemma kernel15_0_r2_13_eq : ∀ k : Fin 16, kernel15_0Expr 2 13 k = kernel15_0_r2_13 k := by decide +kernel +noncomputable def kernel15_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel15_0_r2_14_eq : ∀ k : Fin 16, kernel15_0Expr 2 14 k = kernel15_0_r2_14 k := by decide +kernel +noncomputable def kernel15_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel15_0_r2_15_eq : ∀ k : Fin 16, kernel15_0Expr 2 15 k = kernel15_0_r2_15 k := by decide +kernel +noncomputable def kernel15_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel15_0_r2_0,kernel15_0_r2_1,kernel15_0_r2_2,kernel15_0_r2_3,kernel15_0_r2_4,kernel15_0_r2_5,kernel15_0_r2_6,kernel15_0_r2_7,kernel15_0_r2_8,kernel15_0_r2_9,kernel15_0_r2_10,kernel15_0_r2_11,kernel15_0_r2_12,kernel15_0_r2_13,kernel15_0_r2_14,kernel15_0_r2_15] +lemma kernel15_0_r2_eq (i k : Fin 16) : kernel15_0Expr 2 i k = kernel15_0_r2 i k := by + fin_cases i + · exact kernel15_0_r2_0_eq k + · exact kernel15_0_r2_1_eq k + · exact kernel15_0_r2_2_eq k + · exact kernel15_0_r2_3_eq k + · exact kernel15_0_r2_4_eq k + · exact kernel15_0_r2_5_eq k + · exact kernel15_0_r2_6_eq k + · exact kernel15_0_r2_7_eq k + · exact kernel15_0_r2_8_eq k + · exact kernel15_0_r2_9_eq k + · exact kernel15_0_r2_10_eq k + · exact kernel15_0_r2_11_eq k + · exact kernel15_0_r2_12_eq k + · exact kernel15_0_r2_13_eq k + · exact kernel15_0_r2_14_eq k + · exact kernel15_0_r2_15_eq k +noncomputable def kernel15_0_r3_0 : Fin 16 → CBox := ![⟨⟨132377123308597789374,132377123308597789807⟩,⟨149328412799679888565,149328412799679889000⟩⟩,⟨⟨132319445952157461854,132319445952157462287⟩,⟨149076389948813712114,149076389948813712549⟩⟩,⟨⟨132203809599464761850,132203809599464762282⟩,⟨148573330845315355221,148573330845315355655⟩⟩,⟨⟨132029655860680332174,132029655860680332604⟩,⟨147821203789378378602,147821203789378379033⟩⟩,⟨⟨131796159311462199104,131796159311462199533⟩,⟨146822949008683158528,146822949008683158958⟩⟩,⟨⟨131502241906953956886,131502241906953957312⟩,⟨145582464042077676707,145582464042077677134⟩⟩,⟨⟨131146591905344925233,131146591905344925657⟩,⟨144104584336429674776,144104584336429675201⟩⟩,⟨⟨130727687052897113314,130727687052897113732⟩,⟨142395059130896954919,142395059130896955340⟩⟩,⟨⟨130243821726278162086,130243821726278162501⟩,⟨140460522722801147464,140460522722801147882⟩⟩,⟨⟨129693137675861179391,129693137675861179801⟩,⟨138308461230051174616,138308461230051175026⟩⟩,⟨⟨129073657966024996010,129073657966024996415⟩,⟨135947174986718137830,135947174986718138237⟩⟩,⟨⟨128383323666030975503,128383323666030975902⟩,⟨133385736730939425554,133385736730939425955⟩⟩,⟨⟨127620032808321929984,127620032808321930377⟩,⟨130633945767801779260,130633945767801779654⟩⟩,⟨⟨126781681100572050993,126781681100572051380⟩,⟨127702278314142423213,127702278314142423602⟩⟩,⟨⟨125866203853924710667,125866203853924711047⟩,⟨124601834257180367424,124601834257180367806⟩⟩,⟨⟨124871618572915667401,124871618572915667774⟩,⟨121344280584357443529,121344280584357443903⟩⟩] +lemma kernel15_0_r3_0_eq : ∀ k : Fin 16, kernel15_0Expr 3 0 k = kernel15_0_r3_0 k := by decide +kernel +noncomputable def kernel15_0_r3_1 : Fin 16 → CBox := ![⟨⟨123796067642833056946,123796067642833057312⟩,⟨117941791767487452616,117941791767487452983⟩⟩,⟨⟨122637860547861021868,122637860547861022225⟩,⟨114406987409988106070,114406987409988106429⟩⟩,⟨⟨121395515058344175305,121395515058344175655⟩,⟨110752867491264129975,110752867491264130325⟩⟩,⟨⟨120067796837851233109,120067796837851233450⟩,⟨106992745566840715746,106992745566840716088⟩⟩,⟨⟨118653756940265787392,118653756940265787723⟩,⟨103140180306201363347,103140180306201363679⟩⟩,⟨⟨117152766693650209646,117152766693650209971⟩,⟨99208905772025736521,99208905772025736846⟩⟩,⟨⟨115564549500778844545,115564549500778844859⟩,⟨95212760864199344074,95212760864199344389⟩⟩,⟨⟨113889209125589799347,113889209125589799652⟩,⟨91165618369121148044,91165618369121148351⟩⟩,⟨⟨112127254079843132830,112127254079843133126⟩,⟨87081314069017460008,87081314069017460305⟩⟩,⟨⟨110279617774397006613,110279617774397006900⟩,⟨82973576376748158281,82973576376748158568⟩⟩,⟨⟨108347674154047143818,108347674154047144096⟩,⟨78855956968560512906,78855956968560513184⟩⟩,⟨⟨106333248593077032908,106333248593077033175⟩,⟨74741762890042583871,74741762890042584139⟩⟩,⟨⟨104238623889738447438,104238623889738447697⟩,⟨70643990608838199085,70643990608838199344⟩⟩,⟨⟨102066541260980247618,102066541260980247866⟩,⟨66575262481254605900,66575262481254606149⟩⟩,⟨⟨99820196302990848943,99820196302990849183⟩,⟨62547766088536073751,62547766088536073991⟩⟩,⟨⟨97503229947618360667,97503229947618360897⟩,⟨58573196882181781975,58573196882181782206⟩⟩] +lemma kernel15_0_r3_1_eq : ∀ k : Fin 16, kernel15_0Expr 3 1 k = kernel15_0_r3_1 k := by decide +kernel +noncomputable def kernel15_0_r3_2 : Fin 16 → CBox := ![⟨⟨95119714508577299324,95119714508577299545⟩,⟨54662704556225649438,54662704556225649660⟩⟩,⟨⟨92674134973643884504,92674134973643884716⟩,⟨50826843537926605485,50826843537926605697⟩⟩,⟨⟨90171365758906054764,90171365758906054967⟩,⟨47075527956985739416,47075527956985739619⟩⟩,⟨⟨87616643197727255858,87616643197727256052⟩,⟨43417991417446263253,43417991417446263447⟩⟩,⟨⟨85015534089611102726,85015534089611102909⟩,⟨39862751856165263569,39862751856165263754⟩⟩,⟨⟨82373900681885215143,82373900681885215319⟩,⟨36417581727578976774,36417581727578976950⟩⟩,⟨⟨79697862499398751196,79697862499398751364⟩,⟨33089483706900916236,33089483706900916404⟩⟩,⟨⟨76993755473676229441,76993755473676229600⟩,⟨29884672053451587403,29884672053451587562⟩⟩,⟨⟨74268088852711615308,74268088852711615460⟩,⟨26808559723139796987,26808559723139797140⟩⟩,⟨⟨71527500395445626054,71527500395445626197⟩,⟨23865751264871486344,23865751264871486486⟩⟩,⟨⟨68778710370679235851,68778710370679235987⟩,⟨21060041480566482639,21060041480566482775⟩⟩,⟨⟨66028474888584527431,66028474888584527561⟩,⟨18394419773258815971,18394419773258816101⟩⟩,⟨⟨63283539094043482237,63283539094043482358⟩,⟨15871080053199383916,15871080053199384038⟩⟩,⟨⟨60550590744855530988,60550590744855531101⟩,⟨13491436018728649859,13491436018728649972⟩⟩,⟨⟨57836214684599729621,57836214684599729729⟩,⟨11256141577686211690,11256141577686211798⟩⟩,⟨⟨55146848699921873878,55146848699921873980⟩,⟨9165116126990438207,9165116126990438309⟩⟩] +lemma kernel15_0_r3_2_eq : ∀ k : Fin 16, kernel15_0Expr 3 2 k = kernel15_0_r3_2 k := by decide +kernel +noncomputable def kernel15_0_r3_3 : Fin 16 → CBox := ![⟨⟨52488741225649854011,52488741225649854106⟩,⟨7217574363430756912,7217574363430757007⟩⟩,⟨⟨49867911328927784706,49867911328927784796⟩,⟨5412060258289377346,5412060258289377436⟩⟩,⟨⟨47290111366093438128,47290111366093438212⟩,⟨3746484792704188733,3746484792704188817⟩⟩,⟨⟨44760792663972223572,44760792663972223650⟩,⟨2218167020179877660,2218167020179877737⟩⟩,⟨⟨42285074531355092753,42285074531355092826⟩,⟨823877997744296460,823877997744296532⟩⟩,⟨⟨39867716857446926917,39867716857446926985⟩,⟨(-440112891766335386),(-440112891766335318)⟩⟩,⟨⟨37513096502830120024,37513096502830120088⟩,⟨(-1577989716722487371),(-1577989716722487308)⟩⟩,⟨⟨35225187635818372466,35225187635818372524⟩,⟨(-2594340370154300546),(-2594340370154300488)⟩⟩,⟨⟨33007546113815273517,33007546113815273573⟩,⟨(-3494106037283337214),(-3494106037283337159)⟩⟩,⟨⟨30863297956267055805,30863297956267055855⟩,⟨(-4282530249171412091),(-4282530249171412041)⟩⟩,⟨⟨28795131903809157348,28795131903809157394⟩,⟨(-4965108003014276713),(-4965108003014276667)⟩⟩,⟨⟨26805296008012513855,26805296008012513897⟩,⟨(-5547535412480007593),(-5547535412480007550)⟩⟩,⟨⟨24895598148446012344,24895598148446012384⟩,⟨(-6035660329123391203),(-6035660329123391163)⟩⟩,⟨⟨23067410329230590877,23067410329230590914⟩,⟨(-6435434348752750187),(-6435434348752750150)⟩⟩,⟨⟨21321676566438607675,21321676566438607711⟩,⟨(-6752866585206525697),(-6752866585206525661)⟩⟩,⟨⟨19658924141077883410,19658924141077883441⟩,⟨(-6993979558892073393),(-6993979558892073362)⟩⟩] +lemma kernel15_0_r3_3_eq : ∀ k : Fin 16, kernel15_0Expr 3 3 k = kernel15_0_r3_3 k := by decide +kernel +noncomputable def kernel15_0_r3_4 : Fin 16 → CBox := ![⟨⟨18079277960393478523,18079277960393478552⟩,⟨(-7164767509271606572),(-7164767509271606543)⟩⟩,⟨⟨16582477743129330248,16582477743129330274⟩,⟨(-7271157399904941196),(-7271157399904941170)⟩⟩,⟨⟨15167897722428766873,15167897722428766898⟩,⟨(-7318972842349447017),(-7318972842349446992)⟩⟩,⟨⟨13834568543334560251,13834568543334560273⟩,⟨(-7313901121854034223),(-7313901121854034200)⟩⟩,⟨⟨12581201020398520766,12581201020398520787⟩,⟨(-7261463464038883124),(-7261463464038883103)⟩⟩,⟨⟨11406211414660035559,11406211414660035579⟩,⟨(-7166988638279668916),(-7166988638279668897)⟩⟩,⟨⟨10307747888049236912,10307747888049236931⟩,⟨(-7035589950937507316),(-7035589950937507297)⟩⟩,⟨⟨9283717796881592113,9283717796881592131⟩,⟨(-6872145640476201844),(-6872145640476201826)⟩⟩,⟨⟨8331815494233585095,8331815494233585112⟩,⟨(-6681282647419120469),(-6681282647419120451)⟩⟩,⟨⟨7449550323258831186,7449550323258831202⟩,⟨(-6467363695493991378),(-6467363695493991362)⟩⟩,⟨⟨6634274499503393333,6634274499503393349⟩,⟨(-6234477586605980443),(-6234477586605980427)⟩⟩,⟨⟨5883210599549642038,5883210599549642054⟩,⟨(-5986432581809907957),(-5986432581809907941)⟩⟩,⟨⟨5193478395370355304,5193478395370355319⟩,⟨(-5726752713492070309),(-5726752713492070295)⟩⟩,⟨⟨4562120798099659295,4562120798099659310⟩,⟨(-5458676850718501919),(-5458676850718501904)⟩⟩,⟨⟨3986128701006497298,3986128701006497313⟩,⟨(-5185160320284399758),(-5185160320284399743)⟩⟩,⟨⟨3462464538772404550,3462464538772404564⟩,⟨(-4908878870462340578),(-4908878870462340564)⟩⟩] +lemma kernel15_0_r3_4_eq : ∀ k : Fin 16, kernel15_0Expr 3 4 k = kernel15_0_r3_4 k := by decide +kernel +noncomputable def kernel15_0_r3_5 : Fin 16 → CBox := ![⟨⟨2988084408222185560,2988084408222185573⟩,⟨(-4632234752780117648),(-4632234752780117635)⟩⟩,⟨⟨2559958623947193956,2559958623947193968⟩,⟨(-4357364689283797595),(-4357364689283797581)⟩⟩,⟨⟨2175090610337662536,2175090610337662548⟩,⟨(-4086149488520583609),(-4086149488520583598)⟩⟩,⟨⟨1830534058978992364,1830534058978992376⟩,⟨(-3820225072719469522),(-3820225072719469510)⟩⟩,⟨⟨1523408306783605197,1523408306783605209⟩,⟨(-3560994681120164649),(-3560994681120164638)⟩⟩,⟨⟨1250911915286390911,1250911915286390923⟩,⟨(-3309642019828948249),(-3309642019828948237)⟩⟩,⟨⟨1010334454937699070,1010334454937699079⟩,⟨(-3067145136660182806),(-3067145136660182797)⟩⟩,⟨⟨799066519743301145,799066519743301154⟩,⟨(-2834290809827833859),(-2834290809827833849)⟩⟩,⟨⟨614608017037026267,614608017037026278⟩,⟨(-2611689251741366241),(-2611689251741366231)⟩⟩,⟨⟨454574794390983676,454574794390983685⟩,⟨(-2399788943186371609),(-2399788943186371600)⟩⟩,⟨⟨316703680582146868,316703680582146878⟩,⟨(-2198891428483597561),(-2198891428483597551)⟩⟩,⟨⟨198856030101638735,198856030101638743⟩,⟨(-2009165918478446160),(-2009165918478446151)⟩⟩,⟨⟨99019870917647634,99019870917647642⟩,⟨(-1830663565086559789),(-1830663565086559781)⟩⟩,⟨⟨15310763128378364,15310763128378373⟩,⟨(-1663331288297415094),(-1663331288297415086)⟩⟩,⟨⟨(-54028518152090867),(-54028518152090858)⟩,⟨(-1507025053726455385),(-1507025053726455376)⟩⟩,⟨⟨(-110629358733029008),(-110629358733029000)⟩,⟨(-1361522515742317718),(-1361522515742317710)⟩⟩] +lemma kernel15_0_r3_5_eq : ∀ k : Fin 16, kernel15_0Expr 3 5 k = kernel15_0_r3_5 k := by decide +kernel +noncomputable def kernel15_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-155999621539186964),(-155999621539186957)⟩,⟨(-1226534957642582920),(-1226534957642582912)⟩⟩,⟨⟨(-191526784662633568),(-191526784662633560)⟩,⟨(-1101718476102881918),(-1101718476102881911)⟩⟩,⟨⟨(-218481784692705409),(-218481784692705402)⟩,⟨(-986684372005209431),(-986684372005209424)⟩⟩,⟨⟨(-238023451998783826),(-238023451998783821)⟩,⟨(-881008723618778268),(-881008723618778263)⟩⟩,⟨⟨(-251203429146728312),(-251203429146728306)⟩,⟨(-784241130849002951),(-784241130849002946)⟩⟩,⟨⟨(-258971469188424260),(-258971469188424254)⟩,⟨(-695912630806054495),(-695912630806054488)⟩⟩,⟨⟨(-262181016979333613),(-262181016979333606)⟩,⟨(-615542795221734834),(-615542795221734827)⟩⟩,⟨⟨(-261594983760654070),(-261594983760654064)⟩,⟨(-542646029237123104),(-542646029237123099)⟩⟩,⟨⟨(-257891632808504838),(-257891632808504832)⟩,⟨(-476737098793266818),(-476737098793266813)⟩⟩,⟨⟨(-251670501831230131),(-251670501831230125)⟩,⟨(-417335920305032971),(-417335920305032965)⟩⟩,⟨⟨(-243458295829295006),(-243458295829295001)⟩,⟨(-363971651525402254),(-363971651525402248)⟩⟩,⟨⟨(-233714692176899019),(-233714692176899013)⟩,⟨(-316186126571796823),(-316186126571796818)⟩⟩,⟨⟨(-222838007612757347),(-222838007612757342)⟩,⟨(-273536681058875071),(-273536681058875066)⟩⟩,⟨⟨(-211170684528430186),(-211170684528430181)⟩,⟨(-235598415245700308),(-235598415245700303)⟩⟩,⟨⟨(-199004561321838983),(-199004561321838977)⟩,⟨(-201965944149299815),(-201965944149299810)⟩⟩,⟨⟨(-186585898563571692),(-186585898563571686)⟩,⟨(-172254683796659467),(-172254683796659462)⟩⟩] +lemma kernel15_0_r3_6_eq : ∀ k : Fin 16, kernel15_0Expr 3 6 k = kernel15_0_r3_6 k := by decide +kernel +noncomputable def kernel15_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-174120139242826985),(-174120139242826982)⟩,⟨(-146101722281266468),(-146101722281266465)⟩⟩,⟨⟨(-161776387372408440),(-161776387372408437)⟩,⟨(-123166323157162798),(-123166323157162795)⟩⟩,⟨⟨(-149691594706551624),(-149691594706551620)⟩,⟨(-103130107040511290),(-103130107040511286)⟩⟩,⟨⟨(-137974450243346536),(-137974450243346530)⟩,⟨(-85696955190278613),(-85696955190278607)⟩⟩,⟨⟨(-126708971538897605),(-126708971538897601)⟩,⟨(-70592676395721444),(-70592676395721440)⟩⟩,⟨⟨(-115957800657537852),(-115957800657537847)⟩,⟨(-57564475793230913),(-57564475793230907)⟩⟩,⟨⟨(-105765210834939163),(-105765210834939159)⟩,⟨(-46380261346553511),(-46380261346553507)⟩⟩,⟨⟨(-96159832660107727),(-96159832660107721)⟩,⟨(-36827820723133120),(-36827820723133114)⟩⟩,⟨⟨(-87157110815585733),(-87157110815585728)⟩,⟨(-28713898248431063),(-28713898248431058)⟩⟩,⟨⟨(-78761504185187984),(-78761504185187979)⟩,⟨(-21863198574961014),(-21863198574961009)⟩⟩,⟨⟨(-70968443481414724),(-70968443481414719)⟩,⟨(-16117340711054559),(-16117340711054554)⟩⟩,⟨⟨(-63766061498880553),(-63766061498880547)⟩,⟨(-11333783156089345),(-11333783156089339)⟩⟩,⟨⟨(-57136711705636797),(-57136711705636794)⟩,⟨(-7384738116800352),(-7384738116800349)⟩⟩,⟨⟨(-51058291181510825),(-51058291181510820)⟩,⟨(-4156090159193589),(-4156090159193584)⟩⟩,⟨⟨(-45505383941494549),(-45505383941494546)⟩,⟨(-1546332201920637),(-1546332201920634)⟩⟩,⟨⟨(-40450240481620775),(-40450240481620772)⟩,⟨534470506670252,534470506670256⟩⟩] +lemma kernel15_0_r3_7_eq : ∀ k : Fin 16, kernel15_0Expr 3 7 k = kernel15_0_r3_7 k := by decide +kernel +noncomputable def kernel15_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-35863608991805546),(-35863608991805541)⟩,⟨2165679855894540,2165679855894546⟩⟩,⟨⟨(-31715433129784439),(-31715433129784436)⟩,⟨3417041085872216,3417041085872219⟩⟩,⟨⟨(-27975430575001490),(-27975430575001486)⟩,⟨4349590724406882,4349590724406886⟩⟩,⟨⟨(-24613565810843231),(-24613565810843228)⟩,⟨5016512709188339,5016512709188342⟩⟩,⟨⟨(-21600429744770958),(-21600429744770955)⟩,⟨5463940454108193,5463940454108196⟩⟩,⟨⟨(-18907537892550650),(-18907537892550646)⟩,⟨5731703738047000,5731703738047004⟩⟩,⟨⟨(-16507557945812526),(-16507557945812522)⟩,⟨5854020246940769,5854020246940772⟩⟩,⟨⟨(-14374476629598085),(-14374476629598081)⟩,⟨5860132397035169,5860132397035173⟩⟩,⟨⟨(-12483714853602164),(-12483714853602160)⟩,⟨5774890721586867,5774890721586871⟩⟩,⟨⟨(-10812199280099065),(-10812199280099061)⟩,⟨5619285627927063,5619285627927067⟩⟩,⟨⟨(-9338397583225583),(-9338397583225579)⟩,⟨5410929739947019,5410929739947022⟩⟩,⟨⟨(-8042323866317033),(-8042323866317030)⟩,⟨5164493345741106,5164493345741109⟩⟩,⟨⟨(-6905519942277046),(-6905519942277042)⟩,⟨4892095684022948,4892095684022953⟩⟩,⟨⟨(-5911017470637317),(-5911017470637314)⟩,⟨4603654938139407,4603654938139410⟩⟩,⟨⟨(-5043285286589500),(-5043285286589496)⟩,⟨4307199874482434,4307199874482437⟩⟩,⟨⟨(-4288165653055637),(-4288165653055633)⟩,⟨4009146073489074,4009146073489077⟩⟩] +lemma kernel15_0_r3_8_eq : ∀ k : Fin 16, kernel15_0Expr 3 8 k = kernel15_0_r3_8 k := by decide +kernel +noncomputable def kernel15_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3632802616870283),(-3632802616870280)⟩,⟨3714539666017574,3714539666017578⟩⟩,⟨⟨(-3065565153493130),(-3065565153493127)⟩,⟨3427271414591370,3427271414591373⟩⟩,⟨⟨(-2575967339706388),(-2575967339706385)⟩,⟨3150263875804305,3150263875804309⟩⟩,⟨⟨(-2154587398226812),(-2154587398226809)⟩,⟨2885634254172099,2885634254172103⟩⟩,⟨⟨(-1792987109376703),(-1792987109376700)⟩,⟨2634835415115504,2634835415115507⟩⟩,⟨⟨(-1483632779890411),(-1483632779890408)⟩,⟨2398777370952892,2398777370952895⟩⟩,⟨⟨(-1219818694355504),(-1219818694355500)⟩,⟨2177931393360992,2177931393360995⟩⟩,⟨⟨(-995593747366546),(-995593747366543)⟩,⟨1972418742598551,1972418742598554⟩⟩,⟨⟨(-805691760844101),(-805691760844098)⟩,⟨1782085841075906,1782085841075909⟩⟩,⟨⟨(-645465827824542),(-645465827824539)⟩,⟨1606567559184839,1606567559184842⟩⟩,⟨⟨(-510826888136751),(-510826888136747)⟩,⟨1445340126726650,1445340126726653⟩⟩,⟨⟨(-398186629667367),(-398186629667364)⟩,⟨1297765035362386,1297765035362390⟩⟩,⟨⟨(-304404718465570),(-304404718465567)⟩,⟨1163125157409849,1163125157409852⟩⟩,⟨⟨(-226740289031816),(-226740289031813)⟩,⟨1040654174820040,1040654174820044⟩⟩,⟨⟨(-162807570259609),(-162807570259605)⟩,⟨929560289767768,929560289767772⟩⟩,⟨⟨(-110535480355733),(-110535480355729)⟩,⟨829045075218503,829045075218508⟩⟩] +lemma kernel15_0_r3_9_eq : ∀ k : Fin 16, kernel15_0Expr 3 9 k = kernel15_0_r3_9 k := by decide +kernel +noncomputable def kernel15_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-68130993567605),(-68130993567601)⟩,⟨738318220107277,738318220107282⟩⟩,⟨⟨(-34046060823451),(-34046060823448)⟩,⟨656608829237060,656608829237063⟩⟩,⟨⟨(-6947853773612),(-6947853773608)⟩,⟨583173852392449,583173852392452⟩⟩,⟨⟨14307904263587,14307904263590⟩,⟨517304140087049,517304140087053⟩⟩,⟨⟨30700757589979,30700757589983⟩,⟨458328554363296,458328554363299⟩⟩,⟨⟨43066721206023,43066721206026⟩,⟨405616501635214,405616501635218⟩⟩,⟨⟨52117094391638,52117094391641⟩,⟨358579200170625,358579200170628⟩⟩,⟨⟨58455102214400,58455102214405⟩,⟨316669946898339,316669946898343⟩⟩,⟨⟨62590571350874,62590571350877⟩,⟨279383606245967,279383606245971⟩⟩,⟨⟨64952834391372,64952834391375⟩,⟨246255507122681,246255507122685⟩⟩,⟨⟨65902043880935,65902043880939⟩,⟨216859902434269,216859902434273⟩⟩,⟨⟨65739064114578,65739064114582⟩,⟨190808118154651,190808118154654⟩⟩,⟨⟨64714095460614,64714095460618⟩,⟨167746495506852,167746495506855⟩⟩,⟨⟨63034172972815,63034172972819⟩,⟨147354209786515,147354209786520⟩⟩,⟨⟨60869668453864,60869668453867⟩,⟨129341032384739,129341032384743⟩⟩,⟨⟨58359913084980,58359913084984⟩,⟨113445088260089,113445088260092⟩⟩] +lemma kernel15_0_r3_10_eq : ∀ k : Fin 16, kernel15_0Expr 3 10 k = kernel15_0_r3_10 k := by decide +kernel +noncomputable def kernel15_0_r3_11 : Fin 16 → CBox := ![⟨⟨55618046334716,55618046334720⟩,⟨99430649131567,99430649131570⟩⟩,⟨⟨52735186166185,52735186166189⟩,⟨87085992706572,87085992706576⟩⟩,⟨⟨49784005611255,49784005611258⟩,⟨76221350044100,76221350044103⟩⟩,⟨⟨46821791585732,46821791585735⟩,⟨66666956436034,66666956436037⟩⟩,⟨⟨43893053377453,43893053377456⟩,⟨58271215749366,58271215749369⟩⟩,⟨⟨41031740532204,41031740532207⟩,⟨50898983815869,50898983815873⟩⟩,⟨⟨38263122863443,38263122863446⟩,⟨44429973013514,44429973013518⟩⟩,⟨⟨35605378986592,35605378986595⟩,⟨38757277507526,38757277507530⟩⟩,⟨⟨33070934088056,33070934088061⟩,⟨33786016580113,33786016580117⟩⟩,⟨⟨30667582540996,30667582540999⟩,⟨29432091965476,29432091965479⟩⟩,⟨⟨28399426430505,28399426430509⟩,⟨25621054025760,25621054025764⟩⟩,⟨⟨26267657006515,26267657006518⟩,⟨22287070872818,22287070872821⟩⟩,⟨⟨24271202499865,24271202499868⟩,⟨19371994091167,19371994091171⟩⟩,⟨⟨22407262573925,22407262573930⟩,⟨16824514491353,16824514491358⟩⟩,⟨⟨20671746900547,20671746900550⟩,⟨14599401271149,14599401271153⟩⟩,⟨⟨19059632907214,19059632907217⟩,⟨12656818044419,12656818044422⟩⟩] +lemma kernel15_0_r3_11_eq : ∀ k : Fin 16, kernel15_0Expr 3 11 k = kernel15_0_r3_11 k := by decide +kernel +noncomputable def kernel15_0_r3_12 : Fin 16 → CBox := ![⟨⟨17565255606528,17565255606531⟩,⟨10961709380328,10961709380332⟩⟩,⟨⟨16182540556590,16182540556594⟩,⟨9483251751517,9483251751520⟩⟩,⟨⟨14905189381310,14905189381315⟩,⟨8194363096587,8194363096592⟩⟩,⟨⟨13726825875029,13726825875033⟩,⟨7071265541796,7071265541799⟩⟩,⟨⟨12641109501395,12641109501398⟩,⟨6093096184909,6093096184913⟩⟩,⟨⟨11641822048723,11641822048727⟩,⟨5241561209587,5241561209591⟩⟩,⟨⟨10722932303041,10722932303044⟩,⟨4500628962735,4500628962739⟩⟩,⟨⟨9878642826950,9878642826953⟩,⟨3856257983540,3856257983544⟩⟩,⟨⟨9103422270969,9103422270973⟩,⟨3296156316443,3296156316446⟩⟩,⟨⟨8392026079679,8392026079682⟩,⟨2809568767910,2809568767914⟩⟩,⟨⟨7739507974506,7739507974510⟩,⟨2387089076098,2387089076102⟩⟩,⟨⟨7141224187458,7141224187461⟩,⟨2020494252094,2020494252098⟩⟩,⟨⟨6592832074961,6592832074964⟩,⟨1702598620753,1702598620756⟩⟩,⟨⟨6090284449889,6090284449893⟩,⟨1427125338038,1427125338042⟩⟩,⟨⟨5629820724839,5629820724843⟩,⟨1188593390631,1188593390635⟩⟩,⟨⟨5207955754240,5207955754243⟩,⟨982218292903,982218292907⟩⟩] +lemma kernel15_0_r3_12_eq : ∀ k : Fin 16, kernel15_0Expr 3 12 k = kernel15_0_r3_12 k := by decide +kernel +noncomputable def kernel15_0_r3_13 : Fin 16 → CBox := ![⟨⟨4821467091156,4821467091159⟩,⟨803824887204,803824887208⟩⟩,⟨⟨4467381231493,4467381231497⟩,⟨649770826521,649770826524⟩⟩,⟨⟨4142959299573,4142959299577⟩,⟨516879475251,516879475255⟩⟩,⟨⟨3845682530855,3845682530860⟩,⟨402381105121,402381105126⟩⟩,⟨⟨3573237826789,3573237826793⟩,⟨303861390275,303861390280⟩⟩,⟨⟨3323503590578,3323503590582⟩,⟨219216319576,219216319579⟩⟩,⟨⟨3094535998733,3094535998737⟩,⟨146612746065,146612746069⟩⟩,⟨⟨2884555819643,2884555819646⟩,⟨84453884630,84453884633⟩⟩,⟨⟨2691935855265,2691935855269⟩,⟨31349150018,31349150022⟩⟩,⟨⟨2515189054081,2515189054084⟩,⟨(-13912200487),(-13912200484)⟩⟩,⟨⟨2352957321295,2352957321298⟩,⟨(-52384091330),(-52384091326)⟩⟩,⟨⟨2204001035062,2204001035066⟩,⟨(-84983734697),(-84983734693)⟩⟩,⟨⟨2067189264166,2067189264170⟩,⟨(-112509182818),(-112509182813)⟩⟩,⟨⟨1941490672589,1941490672593⟩,⟨(-135654646602),(-135654646598)⟩⟩,⟨⟨1825965088995,1825965088998⟩,⟨(-155023861481),(-155023861477)⟩⟩,⟨⟨1719755713874,1719755713879⟩,⟨(-171141746642),(-171141746637)⟩⟩] +lemma kernel15_0_r3_13_eq : ∀ k : Fin 16, kernel15_0Expr 3 13 k = kernel15_0_r3_13 k := by decide +kernel +noncomputable def kernel15_0_r3_14 : Fin 16 → CBox := ![⟨⟨1622081933581,1622081933584⟩,⟨(-184464573423),(-184464573420)⟩⟩,⟨⟨1532232708198,1532232708202⟩,⟨(-195388831769),(-195388831766)⟩⟩,⟨⟨1449560499155,1449560499160⟩,⟨(-204258960078),(-204258960073)⟩⟩,⟨⟨1373475702134,1373475702138⟩,⟨(-211374083058),(-211374083054)⟩⟩,⟨⟨1303441551116,1303441551120⟩,⟨(-216993884030),(-216993884027)⟩⟩,⟨⟨1238969460345,1238969460348⟩,⟨(-221343722152),(-221343722148)⟩⟩,⟨⟨1179614771990,1179614771994⟩,⟨(-224619091068),(-224619091064)⟩⟩,⟨⟨1124972878842,1124972878845⟩,⟨(-226989503276),(-226989503272)⟩⟩,⟨⟨1074675692820,1074675692824⟩,⟨(-228601873747),(-228601873743)⟩⟩,⟨⟨1028388431866,1028388431870⟩,⟨(-229583466965),(-229583466962)⟩⟩,⟨⟨985806699405,985806699409⟩,⟨(-230044463395),(-230044463391)⟩⟩,⟨⟨946653832365,946653832369⟩,⟨(-230080194159),(-230080194156)⟩⟩,⟨⟨910678495447,910678495451⟩,⟨(-229773086488),(-229773086484)⟩⟩,⟨⟨877652500954,877652500959⟩,⟨(-229194357010),(-229194357005)⟩⟩,⟨⟨847368835177,847368835180⟩,⟨(-228405485184),(-228405485181)⟩⟩,⟨⟨819639873818,819639873821⟩,⟨(-227459494988),(-227459494985)⟩⟩] +lemma kernel15_0_r3_14_eq : ∀ k : Fin 16, kernel15_0Expr 3 14 k = kernel15_0_r3_14 k := by decide +kernel +noncomputable def kernel15_0_r3_15 : Fin 16 → CBox := ![⟨⟨794295770453,794295770457⟩,⟨(-226402069339),(-226402069336)⟩⟩,⟨⟨771183003362,771183003365⟩,⟨(-225272518546),(-225272518543)⟩⟩,⟨⟨750163067425,750163067429⟩,⟨(-224104621292),(-224104621287)⟩⟩,⟨⟨731111298980,731111298983⟩,⟨(-222927354225),(-222927354221)⟩⟩,⟨⟨713915822689,713915822695⟩,⟨(-221765524137),(-221765524131)⟩⟩,⟨⟨698476610555,698476610559⟩,⟨(-220640314758),(-220640314755)⟩⟩,⟨⟨684704644190,684704644194⟩,⟨(-219569758725),(-219569758721)⟩⟩,⟨⟨672521172456,672521172460⟩,⟨(-218569143641),(-218569143638)⟩⟩,⟨⟨661857057381,661857057384⟩,⟨(-217651360106),(-217651360103)⟩⟩,⟨⟨652652202134,652652202137⟩,⟨(-216827198283),(-216827198280)⟩⟩,⟨⟨644855055616,644855055619⟩,⟨(-216105598758),(-216105598754)⟩⟩,⟨⟨638422188873,638422188876⟩,⟨(-215493862426),(-215493862422)⟩⟩,⟨⟨633317939326,633317939330⟩,⟨(-214997823471),(-214997823467)⟩⟩,⟨⟨629514119368,629514119371⟩,⟨(-214621988732),(-214621988728)⟩⟩,⟨⟨626989786533,626989786537⟩,⟨(-214369646117),(-214369646114)⟩⟩,⟨⟨625731073038,625731073041⟩,⟨(-214242944141),(-214242944137)⟩⟩] +lemma kernel15_0_r3_15_eq : ∀ k : Fin 16, kernel15_0Expr 3 15 k = kernel15_0_r3_15 k := by decide +kernel +noncomputable def kernel15_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel15_0_r3_0,kernel15_0_r3_1,kernel15_0_r3_2,kernel15_0_r3_3,kernel15_0_r3_4,kernel15_0_r3_5,kernel15_0_r3_6,kernel15_0_r3_7,kernel15_0_r3_8,kernel15_0_r3_9,kernel15_0_r3_10,kernel15_0_r3_11,kernel15_0_r3_12,kernel15_0_r3_13,kernel15_0_r3_14,kernel15_0_r3_15] +lemma kernel15_0_r3_eq (i k : Fin 16) : kernel15_0Expr 3 i k = kernel15_0_r3 i k := by + fin_cases i + · exact kernel15_0_r3_0_eq k + · exact kernel15_0_r3_1_eq k + · exact kernel15_0_r3_2_eq k + · exact kernel15_0_r3_3_eq k + · exact kernel15_0_r3_4_eq k + · exact kernel15_0_r3_5_eq k + · exact kernel15_0_r3_6_eq k + · exact kernel15_0_r3_7_eq k + · exact kernel15_0_r3_8_eq k + · exact kernel15_0_r3_9_eq k + · exact kernel15_0_r3_10_eq k + · exact kernel15_0_r3_11_eq k + · exact kernel15_0_r3_12_eq k + · exact kernel15_0_r3_13_eq k + · exact kernel15_0_r3_14_eq k + · exact kernel15_0_r3_15_eq k +noncomputable def kernel15_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-28806462313170779949520262),(-28806462313170779353331177)⟩,⟨14487195034904179365683888,14487195034904179961358980⟩⟩,⟨⟨(-28777634024140955570156974),(-28777634024140954974353408)⟩,⟨14493727251492272038027274,14493727251492272633317527⟩⟩,⟨⟨(-28720029224375432957922408),(-28720029224375432362890292)⟩,⟨14506725915262572246922822,14506725915262572841442981⟩⟩,⟨⟨(-28633751474267971064705543),(-28633751474267970470829434)⟩,⟨14526059893474936313852808,14526059893474936907218992⟩⟩,⟨⟨(-28518956122136081872975016),(-28518956122136081280637413)⟩,⟨14551533500003113442826419,14551533500003114034656797⟩⟩,⟨⟨(-28375850308515373958354478),(-28375850308515373367935146)⟩,⟨14582887704774746661037888,14582887704774747250953358⟩⟩,⟨⟨(-28204692963664756424720101),(-28204692963664755836595416)⟩,⟨14619801736140163226555749,14619801736140163814180591⟩⟩,⟨⟨(-28005794791387287076540841),(-28005794791387286491083082)⟩,⟨14661895067445620240907815,14661895067445620825870395⟩⟩,⟨⟨(-27779518230734514717654128),(-27779518230734514135230929)⟩,⟨14708729776948811492649033,14708729776948812074582346⟩⟩,⟨⟨(-27526277385746897823946620),(-27526277385746897244920142)⟩,⟨14759813268106792837794261,14759813268106793416336770⟩⟩,⟨⟨(-27246537912110725365558155),(-27246537912110724790284759)⟩,⟨14814601335196430538268148,14814601335196431113064096⟩⟩,⟨⟨(-26940816848502822009051327),(-26940816848502821437880534)⟩,⟨14872501557203071502152500,14872501557203072072852955⟩⟩,⟨⟨(-26609682379466318204412192),(-26609682379466317637686728)⟩,⟨14932877000943152701588606,14932877000943153267851415⟩⟩,⟨⟨(-26253753515930045011374856),(-26253753515930044449429151)⟩,⟨14995050212480445819584612,14995050212480446381075896⟩⟩,⟨⟨(-25873699678964621879935819),(-25873699678964621323096647)⟩,⟨15058307474063879949809253,15058307474063880506202774⟩⟩,⟨⟨(-25470240172071615125624933),(-25470240172071614574209427)⟩,⟨15121903302068462841462785,15121903302068463392441918⟩⟩] +lemma kernel15_0_r4_0_eq : ∀ k : Fin 16, kernel15_0Expr 4 0 k = kernel15_0_r4_0 k := by decide +kernel +noncomputable def kernel15_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-25044143527237286832864418),(-25044143527237286287181457)⟩,⟨15185065159771505091156752,15185065159771505636413107⟩⟩,⟨⟨(-24596226710155775328756960),(-24596226710155774789104141)⟩,⟨15246998357256558894368027,15246998357256559433604467⟩⟩,⟨⟨(-24127354170441592034599046),(-24127354170441591501265254)⟩,⟨15306891109320173703503308,15306891109320174236431390⟩⟩,⟨⟨(-23638436723308730266476330),(-23638436723308729739737922)⟩,⟨15363919720975123022952455,15363919720975123549296232⟩⟩,⟨⟨(-23130430250091140291590817),(-23130430250091139771715323)⟩,⟨15417253869011812829175989,15417253869011813348668316⟩⟩,⟨⟨(-22604334206111512411274115),(-22604334206111511898514629)⟩,⟨15466061947110875465700059,15466061947110875978088196⟩⟩,⟨⟨(-22061189925763902109704674),(-22061189925763901604305477)⟩,⟨15509516441208107480058758,15509516441208107985098751⟩⟩,⟨⟨(-21502078716249428300481164),(-21502078716249427802671057)⟩,⟨15546799301211224087176347,15546799301211224584639691⟩⟩,⟨⟨(-20928119733178864063244542),(-20928119733178863573243985)⟩,⟨15577107274769116279409191,15577107274769116769075692⟩⟩,⟨⟨(-20340467633214390494245454),(-20340467633214390012257049)⟩,⟨15599657168610344744978596,15599657168610345226645884⟩⟩,⟨⟨(-19740310001045388718862898),(-19740310001045388245081419)⟩,⟨15613691003009366800480363,15613691003009367273953867⟩⟩,⟨⟨(-19128864550257681753375851),(-19128864550257681287977641)⟩,⟨15618481025216035047418732,15618481025216035512522280⟩⟩,⟨⟨(-18507376100037579947517695),(-18507376100037579490672184)⟩,⟨15613334548204229164803263,15613334548204229621367560⟩⟩,⟨⟨(-17877113332124838733460662),(-17877113332124838285316121)⟩,⟨15597598581865270497585707,15597598581865270945462587⟩⟩,⟨⟨(-17239365334963820757840322),(-17239365334963820318539107)⟩,⟨15570664224795158162506993,15570664224795158601554172⟩⟩,⟨⟨(-16595437944569894316297461),(-16595437944569893885960630)⟩,⟨15531970786103521826608124,15531970786103522256704584⟩⟩] +lemma kernel15_0_r4_1_eq : ∀ k : Fin 16, kernel15_0Expr 4 1 k = kernel15_0_r4_1 k := by decide +kernel +noncomputable def kernel15_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-15946649894197370885843742),(-15946649894197370464588046)⟩,⟨15481009608205911507801130,15481009608205911928830123⟩⟩,⟨⟨(-15294328787434266780206226),(-15294328787434266368123612)⟩,⟨15417327563346405561059861,15417327563346405972929416⟩⟩,⟨⟨(-14639806911825635008810367),(-14639806911825634605989879)⟩,⟨15340530198628509180851009,15340530198628509583472023⟩⟩,⟨⟨(-13984416912508907057139259),(-13984416912508906663613544)⟩,⟨15250284506600058312350750,15250284506600058705690464⟩⟩,⟨⟨(-13329487347599762699101798),(-13329487347599762314925043)⟩,⟨15146321300930523453561649,15146321300930523837565752⟩⟩,⟨⟨(-12676338149164479619049512),(-12676338149164479244258847)⟩,⟨15028437179421956024364004,15028437179421956398995214⟩⟩,⟨⟨(-12026276015524714507297486),(-12026276015524714141930686)⟩,⟨14896496059490141315782143,14896496059490141681002505⟩⟩,⟨⟨(-11380589762335103078066875),(-11380589762335102722135640)⟩,⟨14750430274319768528576025,14750430274319768884373631⟩⟩,⟨⟨(-10740545661326874876368570),(-10740545661326874529887639)⟩,⟨14590241221113322636310954,14590241221113322982670831⟩⟩,⟨⟨(-10107382796798255596574438),(-10107382796798255259527785)⟩,⟨14415999556192109710552944,14415999556192110047490857⟩⟩,⟨⟨(-9482308470833999130135914),(-9482308470833998802512503)⟩,⟨14227844935141174125570324,14227844935141174453097024⟩⟩,⟨⟨(-8866493688834346629480892),(-8866493688834346311241852)⟩,⟨14025985299687608482299486,14025985299687608800453533⟩⟩,⟨⟨(-8261068757213917435264762),(-8261068757213917126378170)⟩,⟨13810695716531889706311836,13810695716531890015124824⟩⟩,⟨⟨(-7667119025083102028271704),(-7667119025083101728596343)⟩,⟨13582316776880981585184341,13582316776880981884797135⟩⟩,⟨⟨(-7085680801342011970910396),(-7085680801342011680337585)⟩,⟨13341252568925585282858273,13341252568925585573379181⟩⟩,⟨⟨(-6517737477897631408222758),(-6517737477897631126673477)⟩,⟨13087968238927049409582497,13087968238927049691090153⟩⟩] +lemma kernel15_0_r4_2_eq : ∀ k : Fin 16, kernel15_0Expr 4 2 k = kernel15_0_r4_2 k := by decide +kernel +noncomputable def kernel15_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-5964215888660429926941619),(-5964215888660429654348718)⟩,⟨12822987159896861245422184,12822987159896861517983336⟩⟩,⟨⟨(-5425982932593547204293730),(-5425982932593546940555416)⟩,⟨12546887730028420152646830,12546887730028420416362852⟩⟩,⟨⟨(-4903842487386237105145356),(-4903842487386236850173715)⟩,⟨12260299826042803417580456,12260299826042803672538832⟩⟩,⟨⟨(-4398532638318265266738680),(-4398532638318265020416373)⟩,⟨11963900939404581397396333,11963900939404581643713964⟩⟩,⟨⟨(-3910723244592170621816639),(-3910723244592170384041739)⟩,⟨11658412025919250120948015,11658412025919250358726379⟩⟩,⟨⟨(-3441013862858391458762089),(-3441013862858391229398225)⟩,⟨11344593101511532131774977,11344593101511532361149990⟩⟩,⟨⟨(-2989932044870510749790885),(-2989932044870510528718946)⟩,⟨11023238618977276234093200,11023238618977276455183514⟩⟩,⟨⟨(-2557932023213896078684007),(-2557932023213895865709081)⟩,⟨10695172662177620220102185,10695172662177620433102251⟩⟩,⟨⟨(-2145393795883342770130906),(-2145393795883342565112695)⟩,⟨10361243995482529720679183,10361243995482529925728835⟩⟩,⟨⟨(-1752622617179046862165217),(-1752622617179046664942558)⟩,⟨10022321007255591096159387,10022321007255591293419323⟩⟩,⟨⟨(-1379848898982474066251756),(-1379848898982473876684689)⟩,⟨9679286586790837245398290,9679286586790837435008012⟩⟩,⟨⟨(-1027228523003155123678176),(-1027228523003154941598223)⟩,⟨9333032974357490112907827,9333032974357490295035353⟩⟩,⟨⟨(-694843561093869700683750),(-694843561093869525923021)⟩,⟨8984456623876293940412692,8984456623876294115225394⟩⟩,⟨⟨(-382703397255314139201361),(-382703397255313971575935)⟩,⟨8634453117242585995935006,8634453117242586163616348⟩⟩,⟨⟨(-90746241532347798079316),(-90746241532347637433977)⟩,⟨8283912168431954053218443,8283912168431954213923212⟩⟩,⟨⟨181158977318189590127803,181158977318189743975409⟩,⟨7933712754284325971898932,7933712754284326125809061⟩⟩] +lemma kernel15_0_r4_3_eq : ∀ k : Fin 16, kernel15_0Expr 4 3 k = kernel15_0_r4_3 k := by decide +kernel +noncomputable def kernel15_0_r4_4 : Fin 16 → CBox := ![⟨⟨433210356694959444892236,433210356694959592099547⟩,⟨7584718407276102916817485,7584718407276103064090001⟩⟩,⟨⟨665670421876787754914486,665670421876787895672410⟩,⟨7237772703676201765697168,7237772703676201906522583⟩⟩,⟨⟨878863206735198270734546,878863206735198405208118⟩,⟨6893694978263334974846941,6893694978263335109389905⟩⟩,⟨⟨1073171038136475638696316,1073171038136475767075812⟩,⟨6553276294284950849550525,6553276294284950978000944⟩⟩,⟨⟨1249031051039611634338771,1249031051039611756788880⟩,⟨6217275694592750351616679,6217275694592750474138886⟩⟩,⟨⟨1406931463310026260756360,1406931463310026377471636⟩,⟨5886416756928286505210338,5886416756928286621998550⟩⟩,⟨⟨1547407640970374415840634,1547407640970374526989495⟩,⟨5561384473190011595900842,5561384473190011707123155⟩⟩,⟨⟨1671037985982269349185891,1671037985982269454959674⟩,⟨5242822469227416673699543,5242822469227416779546991⟩⟩,⟨⟨1778439679683994647002940,1778439679683994747566253⟩,⟨4931330578317211251789877,4931330578317211352426777⟩⟩,⟨⟨1870264315691393715571150,1870264315691393811117038⟩,⟨4627462778020328713683408,4627462778020328809302538⟩⟩,⟨⟨1947193456398884160417402,1947193456398884251111967⟩,⟨4331725496636772993582715,4331725496636773084349926⟩⟩,⟨⟨2009934147196313303776092,2009934147196313389805747⟩,⟨4044576292007590351935905,4044576292007590438037378⟩⟩,⟨⟨2059214422151049335929845,2059214422151049417725088⟩,⟨3766422901998436881072355,3766422901998436962933420⟩⟩,⟨⟨2095778834203573883520885,2095778834203573961259678⟩,⟨3497622662674896452564524,3497622662674896530363095⟩⟩,⟨⟨2120384041903362228906723,2120384041903362302723331⟩,⟨3238482286981651841422828,3238482286981651915293468⟩⟩,⟨⟨2133794483388360858366338,2133794483388360928413859⟩,⟨2989257993699302337907963,2989257993699302408004072⟩⟩] +lemma kernel15_0_r4_4_eq : ∀ k : Fin 16, kernel15_0Expr 4 4 k = kernel15_0_r4_4 k := by decide +kernel +noncomputable def kernel15_0_r4_5 : Fin 16 → CBox := ![⟨⟨2136778166707817935267842,2136778166707818001674603⟩,⟨2750155973604810838001944,2750155973604810904452146⟩⟩,⟨⟨2130102603729693077984794,2130102603729693140902999⟩,⟨2521333177131901793778283,2521333177131901856735076⟩⟩,⟨⟨2114530912788227568330272,2114530912788227627887646⟩,⟨2302898405440431189244900,2302898405440431248836300⟩⟩,⟨⟨2090818112944649091333793,2090818112944649147674412⟩,⟨2094913684679316503920635,2094913684679316560291006⟩⟩,⟨⟨2059707630286377423909453,2059707630286377477154504⟩,⟨1897395901382640277450425,1897395901382640330721232⟩⟩,⟨⟨2021928034110750943282368,2021928034110750993572699⟩,⟨1710318675385562584697821,1710318675385562635010188⟩⟩,⟨⟨1978190018162256023409620,1978190018162256070863736⟩,⟨1533614445394104108287215,1533614445394104155759914⟩⟩,⟨⟨1929183639351831253652024,1929183639351831298402315⟩,⟨1367176741394965525190257,1367176741394965569955936⟩⟩,⟨⟨1875575823617120994826630,1875575823617121036983793⟩,⟨1210862617448526202470690,1210862617448526244640298⟩⟩,⟨⟨1818008145816931861220268,1818008145816931900912735⟩,⟨1064495218066255009696044,1064495218066255049398256⟩⟩,⟨⟨1757094887823782214211818,1757094887823782251549973⟩,⟨927866451325431495397011,927866451325431532742447⟩⟩,⟨⟨1693421376315898265291702,1693421376315898300402982⟩,⟨800739742108238050157387,800739742108238085273714⟩⟩,⟨⟨1627542599202870247713762,1627542599202870280696705⟩,⟨682852839354605570732770,682852839354605603718738⟩⟩,⟨⟨1559982097173663578181525,1559982097173663609148749⟩,⟨573920651971405685108714,573920651971405716077142⟩⟩,⟨⟨1491231124555369961808173,1491231124555369990856320⟩,⟨473638089024837996439586,473638089024838025487311⟩⟩,⟨⟨1421748071536689519381903,1421748071536689546629949⟩,⟨381682881036132559859104,381682881036132587105282⟩⟩] +lemma kernel15_0_r4_5_eq : ∀ k : Fin 16, kernel15_0Expr 4 5 k = kernel15_0_r4_5 k := by decide +kernel +noncomputable def kernel15_0_r4_6 : Fin 16 → CBox := ![⟨⟨1351958137859299520729575,1351958137859299546261683⟩,⟨297718360579170991404866,297718360579171016933830⟩⟩,⟨⟨1282253246327435969006699,1282253246327435992919631⟩,⟨221396181917163255947098,221396181917163279855775⟩⟩,⟨⟨1212992182942371707338775,1212992182942371729712701⟩,⟨152358961088009037147058,152358961088009059515766⟩⟩,⟨⟨1144500949141915262834870,1144500949141915283757582⟩,⟨90242819627820609531856,90242819627820630448527⟩⟩,⟨⟨1077073310520226864904969,1077073310520226884449432⟩,⟨34679816982587495903441,34679816982587515441173⟩⟩,⟨⟨1010971525521639779586237,1010971525521639797834857⟩,⟨(-14699741427283878013503),(-14699741427283859772182)⟩⟩,⟨⟨946427236942247149137808,946427236942247166177969⟩,⟨(-58265131581560096517926),(-58265131581560079485516)⟩⟩,⟨⟨883642508630376874794028,883642508630376890704314⟩,⟨(-96383182818866319401800),(-96383182818866303499612)⟩⟩,⟨⟨822790989544701946663793,822790989544701961502775⟩,⟨(-129416401597036279839019),(-129416401597036265008390)⟩⟩,⟨⟨764019187297200154566998,764019187297200168401526⟩,⟨(-157721252386769935922380),(-157721252386769922096377)⟩⟩,⟨⟨707447833465941653388211,707447833465941666273151⟩,⟨(-181646599205800621181331),(-181646599205800608305010)⟩⟩,⟨⟨653173323296368705189661,653173323296368717184692⟩,⟨(-201532309555821314795886),(-201532309555821302809505)⟩⟩,⟨⟨601269212904432403944974,601269212904432415100849⟩,⟨(-217708020874807740040850),(-217708020874807728893595)⟩⟩,⟨⟨551787757734539963753987,551787757734539974130878⟩,⟨(-230492068076698589963309),(-230492068076698579594956)⟩⟩,⟨⟨504761476792708854573074,504761476792708864215545⟩,⟨(-240190569329926837803401),(-240190569329926828169339)⟩⟩,⟨⟨460204728052985726170254,460204728052985735126800⟩,⟨(-247096665934980187241855),(-247096665934980178293357)⟩⟩] +lemma kernel15_0_r4_6_eq : ∀ k : Fin 16, kernel15_0Expr 4 6 k = kernel15_0_r4_6 k := by decide +kernel +noncomputable def kernel15_0_r4_7 : Fin 16 → CBox := ![⟨⟨418115281405131088645782,418115281405131096956291⟩,⟨(-251489911005624799424601),(-251489911005624791121218)⟩⟩,⟨⟨378475876555838834911701,378475876555838842620634⟩,⟨(-253635800643013780896611),(-253635800643013773193951)⟩⟩,⟨⟨341255754396643618171380,341255754396643625314919⟩,⟨(-253785440418806013037418),(-253785440418806005899365)⟩⟩,⟨⟨306412151491950532575682,306412151491950539192809⟩,⟨(-252175339252771116954775),(-252175339252771110342409)⟩⟩,⟨⟨273891748503792546357241,273891748503792552479807⟩,⟨(-249027322180368792913188),(-249027322180368786794718)⟩⟩,⟨⟨243632064540376709492106,243632064540376715155605⟩,⟨(-244548553052932128774164),(-244548553052932123114154)⟩⟩,⟨⟨215562790578682506430094,215562790578682511663495⟩,⟨(-238931657892252390281912),(-238931657892252385051449)⟩⟩,⟨⟨189607056253989272364494,189607056253989277201821⟩,⟨(-232354939426078556945223),(-232354939426078552110332)⟩⟩,⟨⟨165682625419206513620955,165682625419206518100298⟩,⟨(-224982673253653914281695),(-224982673253653909804336)⟩⟩,⟨⟨143703016943617551567941,143703016943617555715208⟩,⟨(-216965476122288397585229),(-216965476122288393439539)⟩⟩,⟨⟨123578548234911579357315,123578548234911583193266⟩,⟨(-208440736927716009264512),(-208440736927716005429774)⟩⟩,⟨⟨105217299922413630984273,105217299922413634531384⟩,⟨(-199533101272651860389861),(-199533101272651856843640)⟩⟩,⟨⟨88526001026916811753804,88526001026916815030148⟩,⟨(-190355000719210669681088),(-190355000719210666405345)⟩⟩,⟨⟨73410834758588881547942,73410834758588884573846⟩,⟨(-181007218241156260011664),(-181007218241156256986109)⟩⟩,⟨⟨59778165825552069724752,59778165825552072516544⟩,⟨(-171579481810780578818042),(-171579481810780576026378)⟩⟩,⟨⟨47535190799714448321555,47535190799714450896825⟩,⟨(-162151078532161673764339),(-162151078532161671189004)⟩⟩] +lemma kernel15_0_r4_7_eq : ∀ k : Fin 16, kernel15_0Expr 4 7 k = kernel15_0_r4_7 k := by decide +kernel +noncomputable def kernel15_0_r4_8 : Fin 16 → CBox := ![⟨⟨36590513672282670508756,36590513672282672881516⟩,⟨(-152791482247504764238178),(-152791482247504761865188)⟩⟩,⟨⟨26854649239260122365465,26854649239260124552903⟩,⟨(-143560988086516691718283),(-143560988086516689530475)⟩⟩,⟨⟨18240457388309311757915,18240457388309313772522⟩,⟨(-134511347991101800805058),(-134511347991101798789964)⟩⟩,⟨⟨10663511714725948760087,10663511714725950615266⟩,⟨(-125686401820498295585647),(-125686401820498293729881)⟩⟩,⟨⟨4042406178827461158161,4042406178827462864620⟩,⟨(-117122699217372258612903),(-117122699217372256905778)⟩⟩,⟨⟨(-1700996266625239845893),(-1700996266625238274478)⟩,⟨(-108850107986151476131710),(-108850107986151474559563)⟩⟩,⟨⟨(-6641368998139608150837),(-6641368998139606705053)⟩,⟨(-100892405294574981431822),(-100892405294574979985257)⟩⟩,⟨⟨(-10849776818806146111196),(-10849776818806144781080)⟩,⟨(-93267848552401880763071),(-93267848552401879432137)⟩⟩,⟨⟨(-14393576619583158991769),(-14393576619583157769356)⟩,⟨(-85989723342598759543890),(-85989723342598758320634)⟩⟩,⟨⟨(-17336359404261563133292),(-17336359404261562009147)⟩,⟨(-79066866276024798730176),(-79066866276024797605174)⟩⟩,⟨⟨(-19737929533325456255432),(-19737929533325455222625)⟩,⟨(-72504161107336303717323),(-72504161107336302683653)⟩⟩,⟨⟨(-21654317136271396898761),(-21654317136271395949850)⟩,⟨(-66303006884949374475609),(-66303006884949373525838)⟩⟩,⟨⟨(-23137819769859247710804),(-23137819769859246839923)⟩,⟨(-60461757309537385132216),(-60461757309537384260482)⟩⟩,⟨⟨(-24237069556076829454518),(-24237069556076828655084)⟩,⟨(-54976130842454486270920),(-54976130842454485470647)⟩⟩,⟨⟨(-24997122213325412133353),(-24997122213325411400186)⟩,⟨(-49839591437021274246361),(-49839591437021273512372)⟩⟩,⟨⟨(-25459564592721961899148),(-25459564592721961226024)⟩,⟨(-45043700061680680986542),(-45043700061680680312642)⟩⟩] +lemma kernel15_0_r4_8_eq : ∀ k : Fin 16, kernel15_0Expr 4 8 k = kernel15_0_r4_8 k := by decide +kernel +noncomputable def kernel15_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-25662637543992761362107),(-25662637543992760743472)⟩,⟨(-40578437445012436364348),(-40578437445012435745033)⟩⟩,⟨⟨(-25641371158039024017743),(-25641371158039023448978)⟩,⟨(-36432498699289979846175),(-36432498699289979276816)⟩⟩,⟨⟨(-25427729662063677711815),(-25427729662063677189359)⟩,⟨(-32593560672847110111685),(-32593560672847109588713)⟩⟩,⟨⟨(-25050763474690196332046),(-25050763474690195852045)⟩,⟨(-29048523043472706333940),(-29048523043472705853494)⟩⟩,⟨⟨(-24536766159675063326093),(-24536766159675062885555)⟩,⟨(-25783724297100410439799),(-25783724297100409998879)⟩⟩,⟨⟨(-23909434244879166409313),(-23909434244879166004837)⟩,⟨(-22785133840131860523197),(-22785133840131860118398)⟩⟩,⟨⟨(-23190028095749005647798),(-23190028095749005276748)⟩,⟨(-20038521571897153302716),(-20038521571897152931396)⟩⟩,⟨⟨(-22397532247650995414438),(-22397532247650995073969)⟩,⟨(-17529606298182123616895),(-17529606298182123276202)⟩⟩,⟨⟨(-21548813807329008088083),(-21548813807329007775854)⟩,⟨(-15244184399660093805288),(-15244184399660093492877)⟩⟩,⟨⟨(-20658777729169770676721),(-20658777729169770390074)⟩,⟨(-13168240182692270927336),(-13168240182692270640545)⟩⟩,⟨⟨(-19740517955821075680448),(-19740517955821075417499)⟩,⟨(-11288039336522825783118),(-11288039336522825520056)⟩⟩,⟨⟨(-18805463584254804041846),(-18805463584254803800554)⟩,⟨(-9590206902559459262630),(-9590206902559459021255)⟩⟩,⟨⟨(-17863519377099471539667),(-17863519377099471318468)⟩,⟨(-8061791130290902222065),(-8061791130290902000808)⟩⟩,⟨⟨(-16923200084717231897511),(-16923200084717231694613)⟩,⟨(-6690314552446660428809),(-6690314552446660225876)⟩⟩,⟨⟨(-15991758176006858261459),(-15991758176006858075493)⟩,⟨(-5463813561136380316625),(-5463813561136380130643)⟩⟩,⟨⟨(-15075304695397290968081),(-15075304695397290797562)⟩,⟨(-4370867708676220216566),(-4370867708676220046048)⟩⟩] +lemma kernel15_0_r4_9_eq : ∀ k : Fin 16, kernel15_0Expr 4 9 k = kernel15_0_r4_9 k := by decide +kernel +noncomputable def kernel15_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-14178923070231954140033),(-14178923070231953983457)⟩,⟨(-3400619893242882990656),(-3400619893242882834095)⟩⟩,⟨⟨(-13306775787139793249575),(-13306775787139793105650)⟩,⟨(-2542788521877517190159),(-2542788521877517046260)⟩⟩,⟨⟨(-12462203938560688487814),(-12462203938560688355611)⟩,⟨(-1787672673033359629566),(-1787672673033359497401)⟩⟩,⟨⟨(-11647819711942722410640),(-11647819711942722289141)⟩,⟨(-1126151209021181123935),(-1126151209021181002481)⟩⟩,⟨⟨(-10865591954924949052441),(-10865591954924948940880)⟩,⟨(-549676716412336585716),(-549676716412336474208)⟩⟩,⟨⟨(-10116925000777531838189),(-10116925000777531735674)⟩,⟨(-50265080630144854100),(-50265080630144751643)⟩⟩,⟨⟨(-9402730980237803866600),(-9402730980237803772435)⟩,⟨379518569615730974324,379518569615731068426⟩⟩,⟨⟨(-8723495879418142682659),(-8723495879418142596048)⟩,⟨746576881057340317086,746576881057340403630⟩⟩,⟨⟨(-8079339629434397883807),(-8079339629434397804219)⟩,⟨1057299656962645817160,1057299656962645896680⟩⟩,⟨⟨(-7470070532568184875918),(-7470070532568184802709)⟩,⟨1317585063098544885757,1317585063098544958896⟩⟩,⟨⟨(-6895234342870680014679),(-6895234342870679947381)⟩,⟨1532862181126961546791,1532862181126961614018⟩⟩,⟨⟨(-6354158326851516723916),(-6354158326851516662007)⟩,⟨1708114488574374363350,1708114488574374425187⟩⟩,⟨⟨(-5845990632953386356322),(-5845990632953386299362)⟩,⟨1847903897438407351141,1847903897438407408029⟩⟩,⟨⟨(-5369735297532942958416),(-5369735297532942905874)⟩,⟨1956395032669506895165,1956395032669506947637⟩⟩,⟨⟨(-4924283210652456738323),(-4924283210652456689880)⟩,⟨2037379477157616210271,2037379477157616258645⟩⟩,⟨⟨(-4508439357691647820086),(-4508439357691647775385)⟩,⟨2094299751483206171386,2094299751483206216020⟩⟩] +lemma kernel15_0_r4_10_eq : ∀ k : Fin 16, kernel15_0Expr 4 10 k = kernel15_0_r4_10 k := by decide +kernel +noncomputable def kernel15_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-4120946643127544819091),(-4120946643127544777877)⟩,⟨2130272834624598914555,2130272834624598955702⟩⟩,⟨⟨(-3760506591268799827314),(-3760506591268799789269)⟩,⟨2148113066152624985997,2148113066152625023979⟩⟩,⟨⟨(-3425797205691110781596),(-3425797205691110746486)⟩,⟨2150354301323400054804,2150354301323400089856⟩⟩,⟨⟨(-3115488254979326031068),(-3115488254979325998637)⟩,⟨2139271218058721449957,2139271218058721482336⟩⟩,⟨⟨(-2828254237473564585508),(-2828254237473564555573)⟩,⟨2116899699257926476115,2116899699257926506005⟩⟩,⟨⟨(-2562785262334345531702),(-2562785262334345504037)⟩,⟨2085056235404750227172,2085056235404750254798⟩⟩,⟨⟨(-2317796068639497246694),(-2317796068639497221130)⟩,⟨2045356311215915501211,2045356311215915526740⟩⟩,⟨⟨(-2092033388621335963713),(-2092033388621335940037)⟩,⟨1999231756327388595948,1999231756327388619594⟩⟩,⟨⟨(-1884281845730324215768),(-1884281845730324193857)⟩,⟨1947947053932822273032,1947947053932822294915⟩⟩,⟨⟨(-1693368563124162994348),(-1693368563124162974041)⟩,⟨1892614613077979366422,1892614613077979386706⟩⟩,⟨⟨(-1518166643553779356315),(-1518166643553779337500)⟩,⟨1834209020171647543001,1834209020171647561795⟩⟩,⟨⟨(-1357597667549156150924),(-1357597667549156133473)⟩,⟨1773580293387941616409,1773580293387941633841⟩⟩,⟨⟨(-1210633343374787208297),(-1210633343374787192121)⟩,⟨1711466170189051773482,1711466170189051789642⟩⟩,⟨⟨(-1076296429482867774885),(-1076296429482867759869)⟩,⟨1648503463364219258826,1648503463364219273829⟩⟩,⟨⟨(-953661038180530416945),(-953661038180530403012)⟩,⟨1585238524922597258699,1585238524922597272621⟩⟩,⟨⟨(-841852417968485188704),(-841852417968485175749)⟩,⟨1522136860046504280807,1522136860046504293754⟩⟩] +lemma kernel15_0_r4_11_eq : ∀ k : Fin 16, kernel15_0Expr 4 11 k = kernel15_0_r4_11 k := by decide +kernel +noncomputable def kernel15_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-740046301512073411121),(-740046301512073399073)⟩,⟨1459591935248125486048,1459591935248125498089⟩⟩,⟨⟨(-647467896470556485244),(-647467896470556474024)⟩,⟨1397933226006488110475,1397933226006488121690⟩⟩,⟨⟨(-563390587425657077350),(-563390587425657066902)⟩,⟨1337433549610929714781,1337433549610929725225⟩⟩,⟨⟨(-487134408897521418299),(-487134408897521408556)⟩,⟨1278315728809795342811,1278315728809795352550⟩⟩,⟨⟨(-418064341890817249812),(-418064341890817240734)⟩,⟨1220758631255698135701,1220758631255698144778⟩⟩,⟨⟨(-355588479546281796341),(-355588479546281787866)⟩,⟨1164902628738213496729,1164902628738213505203⟩⟩,⟨⟨(-299156101250764094295),(-299156101250764086384)⟩,⟨1110854518878623725696,1110854518878623733607⟩⟩,⟨⟨(-248255688946204208206),(-248255688946204200804)⟩,⟨1058691950397551204111,1058691950397551211513⟩⟩,⟨⟨(-202412914337963510207),(-202412914337963503282)⟩,⟨1008467391314870408941,1008467391314870415867⟩⟩,⟨⟨(-161188621197511832087),(-161188621197511825599)⟩,⟨960211677554246073464,960211677554246079954⟩⟩,⟨⟨(-124176822945530778724),(-124176822945530772643)⟩,⟨913937177446926840807,913937177446926846891⟩⟩,⟨⟨(-91002732151189400183),(-91002732151189394476)⟩,⟨869640605599421352899,869640605599421358608⟩⟩,⟨⟨(-61320835454655475961),(-61320835454655470609)⟩,⟨827305517539868097037,827305517539868102392⟩⟩,⟨⟨(-34813024676931584395),(-34813024676931579363)⟩,⟨786904514515422548941,786904514515422553976⟩⟩,⟨⟨(-11186792489378963058),(-11186792489378958323)⟩,⟨748401185800198922440,748401185800198927178⟩⟩,⟨⟨9826501058027315604,9826501058027320067⟩,⟨711751813908357929726,711751813908357934192⟩⟩] +lemma kernel15_0_r4_12_eq : ∀ k : Fin 16, kernel15_0Expr 4 12 k = kernel15_0_r4_12 k := by decide +kernel +noncomputable def kernel15_0_r4_13 : Fin 16 → CBox := ![⟨⟨28473286636643202643,28473286636643206848⟩,⟨676906866204229361767,676906866204229365976⟩⟩,⟨⟨44979365382047257201,44979365382047261171⟩,⟨643812294572030422676,643812294572030426650⟩⟩,⟨⟨59551408591535563027,59551408591535566776⟩,⟨612410663060075800823,612410663060075804576⟩⟩,⟨⟨72378376779187038673,72378376779187042217⟩,⟨582642121754210887071,582642121754210890620⟩⟩,⟨⟨83632858400548362131,83632858400548365484⟩,⟨554445243566279084141,554445243566279087499⟩⟩,⟨⟨93472329307316020371,93472329307316023552⟩,⟨527757739147730373790,527757739147730376976⟩⟩,⟨⟨102040334599602896808,102040334599602899825⟩,⟨502517063756482176163,502517063756482179185⟩⟩,⟨⟨109467595027337901461,109467595027337904329⟩,⟨478660928616122472968,478660928616122475840⟩⟩,⟨⟨115873040469247519712,115873040469247522437⟩,⟨456127728108771608262,456127728108771610991⟩⟩,⟨⟨121364773302306863169,121364773302306865764⟩,⟨434856893033871540992,434856893033871543592⟩⟩,⟨⟨126040964679632512902,126040964679632515374⟩,⟨414789179141709461332,414789179141709463808⟩⟩,⟨⟨129990686872236833708,129990686872236836068⟩,⟨395866899208999947266,395866899208999949631⟩⟩,⟨⟨133294684910300407499,133294684910300409753⟩,⟨378034106060403769925,378034106060403772184⟩⟩,⟨⟨136026090791883235299,136026090791883237456⟩,⟨361236733150285162081,361236733150285164242⟩⟩,⟨⟨138251083519432555156,138251083519432557222⟩,⟨345422698599005516329,345422698599005518400⟩⟩,⟨⟨140029498184205344268,140029498184205346250⟩,⟨330541977923270792517,330541977923270794503⟩⟩] +lemma kernel15_0_r4_13_eq : ∀ k : Fin 16, kernel15_0Expr 4 13 k = kernel15_0_r4_13 k := by decide +kernel +noncomputable def kernel15_0_r4_14 : Fin 16 → CBox := ![⟨⟨141415387252051258124,141415387252051260023⟩,⟨316546650106155853158,316546650106155855062⟩⟩,⟨⟨142457537116322333233,142457537116322335060⟩,⟨303390921115150292536,303390921115150294368⟩⟩,⟨⟨143199942879677054709,143199942879677056468⟩,⟨291031128491743119988,291031128491743121751⟩⟩,⟨⟨143682244210254742709,143682244210254744404⟩,⟨279425730199663902411,279425730199663904111⟩⟩,⟨⟨143940124992547433377,143940124992547435011⟩,⟨268535280527066364029,268535280527066365667⟩⟩,⟨⟨144005679362201221015,144005679362201222594⟩,⟨258322395487000289845,258322395487000291428⟩⟩,⟨⟨143907746579383223571,143907746579383225098⟩,⟨248751709846986921252,248751709846986922783⟩⟩,⟨⟨143672217059289985112,143672217059289986591⟩,⟨239789827639111891494,239789827639111892978⟩⟩,⟨⟨143322311742524642860,143322311742524644292⟩,⟨231405267753703340048,231405267753703341484⟩⟩,⟨⟨142878836853795738747,142878836853795740137⟩,⟨223568405999501452332,223568405999501453726⟩⟩,⟨⟨142360415965779043079,142360415965779044431⟩,⟨216251414818581831165,216251414818581832521⟩⟩,⟨⟨141783701156887556264,141783701156887557580⟩,⟨209428201672698645120,209428201672698646439⟩⟩,⟨⟨141163564927762665316,141163564927762666596⟩,⟨203074346966884899844,203074346966884901127⟩⟩,⟨⟨140513274422005504858,140513274422005506109⟩,⟨197167042243989684137,197167042243989685391⟩⟩,⟨⟨139844649382337586885,139844649382337588105⟩,⟨191685029268423040024,191685029268423041248⟩⟩,⟨⟨139168205164213644924,139168205164213646118⟩,⟨186608540516959882408,186608540516959883605⟩⟩] +lemma kernel15_0_r4_14_eq : ∀ k : Fin 16, kernel15_0Expr 4 14 k = kernel15_0_r4_14 k := by decide +kernel +noncomputable def kernel15_0_r4_15 : Fin 16 → CBox := ![⟨⟨138493282025001579135,138493282025001580305⟩,⟨181919241507421507972,181919241507421509144⟩⟩,⟨⟨137828161808200330578,137828161808200331724⟩,⟨177600175320947699249,177600175320947700399⟩⟩,⟨⟨137180173048719332187,137180173048719333310⟩,⟨173635709609069879254,173635709609069880380⟩⟩,⟨⟨136555785436865810845,136555785436865811950⟩,⟨170011486321696514858,170011486321696515965⟩⟩,⟨⟨135960694495202898593,135960694495202899679⟩,⟨166714374345341261541,166714374345341262630⟩⟩,⟨⟨135399897243637429455,135399897243637430525⟩,⟨163732425201482941578,163732425201482942651⟩⟩,⟨⟨134877759553725697278,134877759553725698335⟩,⟨161054831921961482322,161054831921961483382⟩⟩,⟨⟨134398075822978476453,134398075822978477496⟩,⟨158671891190990170522,158671891190990171568⟩⟩,⟨⟨133964121533614995158,133964121533614996188⟩,⟨156574968820986034874,156574968820986035906⟩⟩,⟨⟨133578699197457295024,133578699197457296046⟩,⟨154756468611342202556,154756468611342203580⟩⟩,⟨⟨133244178129159560943,133244178129159561956⟩,⟨153209804624907796660,153209804624907797676⟩⟩,⟨⟨132962528433412689543,132962528433412690550⟩,⟨151929376905778050882,151929376905778051892⟩⟩,⟨⟨132735349537829157483,132735349537829158484⟩,⟨150910550653555305640,150910550653555306642⟩⟩,⟨⟨132563893551570962816,132563893551570963812⟩,⟨150149638863089238754,150149638863089239752⟩⟩,⟨⟨132449083680106408467,132449083680106409460⟩,⟨149643888434448089962,149643888434448090957⟩⟩,⟨⟨132391527878441600162,132391527878441601154⟩,⟨149391469755149113403,149391469755149114397⟩⟩] +lemma kernel15_0_r4_15_eq : ∀ k : Fin 16, kernel15_0Expr 4 15 k = kernel15_0_r4_15 k := by decide +kernel +noncomputable def kernel15_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel15_0_r4_0,kernel15_0_r4_1,kernel15_0_r4_2,kernel15_0_r4_3,kernel15_0_r4_4,kernel15_0_r4_5,kernel15_0_r4_6,kernel15_0_r4_7,kernel15_0_r4_8,kernel15_0_r4_9,kernel15_0_r4_10,kernel15_0_r4_11,kernel15_0_r4_12,kernel15_0_r4_13,kernel15_0_r4_14,kernel15_0_r4_15] +lemma kernel15_0_r4_eq (i k : Fin 16) : kernel15_0Expr 4 i k = kernel15_0_r4 i k := by + fin_cases i + · exact kernel15_0_r4_0_eq k + · exact kernel15_0_r4_1_eq k + · exact kernel15_0_r4_2_eq k + · exact kernel15_0_r4_3_eq k + · exact kernel15_0_r4_4_eq k + · exact kernel15_0_r4_5_eq k + · exact kernel15_0_r4_6_eq k + · exact kernel15_0_r4_7_eq k + · exact kernel15_0_r4_8_eq k + · exact kernel15_0_r4_9_eq k + · exact kernel15_0_r4_10_eq k + · exact kernel15_0_r4_11_eq k + · exact kernel15_0_r4_12_eq k + · exact kernel15_0_r4_13_eq k + · exact kernel15_0_r4_14_eq k + · exact kernel15_0_r4_15_eq k +noncomputable def kernel15_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-58230053441289619839793702052),(-58230053441289619334305173042)⟩,⟨(-26840427586361322967306800147),(-26840427586361322461783897655)⟩⟩,⟨⟨(-58216705938728392591054739263),(-58216705938728392085680278111)⟩,⟨(-26799233119103443215908482517),(-26799233119103442710500522102)⟩⟩,⟨⟨(-58189968007889687803192556610),(-58189968007889687298047077159)⟩,⟨(-26716924536105362296693336396),(-26716924536105361791516103647)⟩⟩,⟨⟨(-58149754114622673649957200202),(-58149754114622673145155564139)⟩,⟨(-26593662445368317388459939819),(-26593662445368316883629163242)⟩⟩,⟨⟨(-58095936749364544062047218043),(-58095936749364543557704229146)⟩,⟨(-26429687520490682317457390632),(-26429687520490681813088733450)⟩⟩,⟨⟨(-58028347372826322712539950664),(-58028347372826322208770312009)⟩,⟨(-26225320212304497655916385321),(-26225320212304497152125400247)⟩⟩,⟨⟨(-57946777669734595037847978166),(-57946777669734594534766300948)⟩,⟨(-25980960360626782447966554110),(-25980960360626781944868689763)⟩⟩,⟨⟨(-57850981104503718080964160446),(-57850981104503717578684882953)⟩,⟨(-25697086702968501762890768361),(-25697086702968501260601285866)⟩⟩,⟨⟨(-57740674771210220694382711104),(-57740674771210220193020173058)⟩,⟨(-25374256276340620048919880747),(-25374256276340619547553925727)⟩⟩,⟨⟨(-57615541528757792575396885307),(-57615541528757792075065143329)⟩,⟨(-25013103707649398024509182539),(-25013103707649397524181598287)⟩⟩,⟨⟨(-57475232410661865442879533822),(-57475232410661864943692388615)⟩,⟨(-24614340387592177828185268680),(-24614340387592177329010621098)⟩⟩,⟨⟨(-57319369297451957817888211513),(-57319369297451957319920305897)⟩,⟨(-24178753522459970699411886306),(-24178753522459970201465563045)⟩⟩,⟨⟨(-57147547838292605278549030844),(-57147547838292604781910697317)⟩,⟨(-23707205057833185293201350902),(-23707205057833184796594400373)⟩⟩,⟨⟨(-56959340607065043160068919664),(-56959340607065042664869829335)⟩,⟨(-23200630467830048191373525286),(-23200630467830047696216306612)⟩⟩,⟨⟨(-56754300476837365806211228202),(-56754300476837365312561328826)⟩,⟨(-22660037403341089081476145793),(-22660037403341088587879264817)⟩⟩,⟨⟨(-56531964195386481120430373570),(-56531964195386480628438676215)⟩,⟨(-22086504192564014669526825023),(-22086504192564014177599919078)⟩⟩] +lemma kernel15_0_r5_0_eq : ∀ k : Fin 16, kernel15_0Expr 5 0 k = kernel15_0_r5_0 k := by decide +kernel +noncomputable def kernel15_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-56291856143226939426236817091),(-56291856143226938936012925651)⟩,⟨(-21481178187146933995231513655),(-21481178187146933505084779198)⟩⟩,⟨⟨(-56033492254456057710558131684),(-56033492254456057222210105845)⟩,⟨(-20845273947358745838006676400),(-20845273947358745349748730277)⟩⟩,⟨⟨(-55756384079648364507117406455),(-55756384079648364020754249560)⟩,⟨(-20180071259936983830595190464),(-20180071259936983344335556047)⟩⟩,⟨⟨(-55460042969032168004244012660),(-55460042969032167519972794940)⟩,⟨(-19486912982617814965688033770),(-19486912982617814481534262722)⟩⟩,⟨⟨(-55143984353264099260975096349),(-55143984353264098778904400196)⟩,⟨(-18767202709831284367017470672),(-18767202709831283885078586648)⟩⟩,⟨⟨(-54807732098291038086563884658),(-54807732098291037606799281976)⟩,⟨(-18022402254647140273662070232),(-18022402254647139794044045054)⟩⟩,⟨⟨(-54450822910060199899212594611),(-54450822910060199421861761953)⟩,⟨(-17254028942781239511017950651),(-17254028942781239033828818017)⟩⟩,⟨⟨(-54072810764214660942973467844),(-54072810764214660468140601476)⟩,⟨(-16463652715316920434631337807),(-16463652715316919959975607493)⟩⟩,⟨⟨(-53673271335400466525903733615),(-53673271335400466053696049300)⟩,⟨(-15652893037755835630185578470),(-15652893037755835158170734826)⟩⟩,⟨⟨(-53251806400419784067381016290),(-53251806400419783597900455907)⟩,⟨(-14823415614083261746964887971),(-14823415614083261277693096117)⟩⟩,⟨⟨(-52808048189199161701328172555),(-52808048189199161234680553797)⟩,⟨(-13976928905707264176348646508),(-13976928905707263709925900822)⟩⟩,⟨⟨(-52341663657409319726213527967),(-52341663657409319262499036435)⟩,⟨(-13115180456401442508491812121),(-13115180456401442045018428302)⟩⟩,⟨⟨(-51852358654579075085439635042),(-51852358654579074624763504220)⟩,⟨(-12239953025738243812054241799),(-12239953025738243351635535758)⟩⟩,⟨⟨(-51339881961696466486998009945),(-51339881961696466029443203443)⟩,⟨(-11353060534933749804425498797),(-11353060534933749347144436097)⟩⟩,⟨⟨(-50804029172589742279770239320),(-50804029172589741825405270201)⟩,⟨(-10456343830524046341760408590),(-10456343830524045887685407979)⟩⟩,⟨⟨(-50244646393833666682526335197),(-50244646393833666231445509343)⟩,⟨(-9551666272845348415182264982),(-9551666272845347964407572141)⟩⟩] +lemma kernel15_0_r5_1_eq : ∀ k : Fin 16, kernel15_0Expr 5 1 k = kernel15_0_r5_1 k := by decide +kernel +noncomputable def kernel15_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-49661633738535800177042377797),(-49661633738535799729348026527)⟩,⟨(-8640909157881599682705515886),(-8640909157881599235333353971)⟩⟩,⟨⟨(-49054948590125260212149868544),(-49054948590125259767932206118)⟩,⟨(-7725966982660049438778771020),(-7725966982660048994899200086)⟩⟩,⟨⟨(-48424608613194152400406161068),(-48424608613194151959764861321)⟩,⟨(-6808742566002337901345418833),(-6808742566002337461057911140)⟩⟩,⟨⟨(-47770694489529414988353662363),(-47770694489529414551376601546)⟩,⟨(-5891142038060270628814082507),(-5891142038060270192206267823)⟩⟩,⟨⟨(-47093352358719045957316637917),(-47093352358719045524102940096)⟩,⟨(-4975069713665618106686366408),(-4975069713665617673857076057)⟩⟩,⟨⟨(-46392795944119087685939988883),(-46392795944119087256572423505)⟩,⟨(-4062422866085469839909688045),(-4062422866085469410941356042)⟩⟩,⟨⟨(-45669308346522473739777175705),(-45669308346522473314351461624)⟩,⟨(-3155086419282238989040394782),(-3155086419282238564028360006)⟩⟩,⟨⟨(-44923243489572634444709394986),(-44923243489572634023305402455)⟩,⟨(-2254927578213652708242625856),(-2254927578213652287266338243)⟩⟩,⟨⟨(-44155027202806911714584812178),(-44155027202806911297297947006)⟩,⟨(-1363790418056405273359624974),(-1363790418056404856514027614)⟩⟩,⟨⟨(-43365157930189192296510829550),(-43365157930189191883414244472)⟩,⟨(-483490454481330364009480532),(-483490454481329951367226800)⟩⟩,⟨⟨(-42554207054088118812792053545),(-42554207054088118403976401422)⟩,⟨384190781767819728600716221,384190781767820136949512458⟩⟩,⟨⟨(-41722818826865726925524705920),(-41722818826865726521060200233)⟩,⟨1237511141750743988184721375,1237511141750744392170418929⟩⟩,⟨⟨(-40871709904548927653577087015),(-40871709904548927253553687261)⟩,⟨2074773201581078936975830484,2074773201581079336509078621⟩⟩,⟨⟨(-40001668479449099084892521104),(-40001668479449098689372678537)⟩,⟨2894329526292829822072844565,2894329526292830217091829123⟩⟩,⟨⟨(-39113553011058086714020277345),(-39113553011058086323088364761)⟩,⟨3694587828062189288665517467,3694587828062189679086535551⟩⟩,⟨⟨(-38208290557065865818951156238),(-38208290557065865432666100093)⟩,⟨4474015992207312647509293239,4474015992207313033274112365⟩⟩] +lemma kernel15_0_r5_2_eq : ∀ k : Fin 16, kernel15_0Expr 5 2 k = kernel15_0_r5_2 k := by decide +kernel +noncomputable def kernel15_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-37286874708898646447694492747),(-37286874708898646066140541258)⟩,⟨5231146944266520531235429354,5231146944266520912260524294⟩⟩,⟨⟨(-36350363138748008022209199150),(-36350363138748007645435509281)⟩,⟨5964583331535699097599042287,5964583331535699473835996810⟩⟩,⟨⟨(-35399874767632640417336342332),(-35399874767632640045419735195)⟩,⟨6673001992734217893777377195,6673001992734218265150135611⟩⟩,⟨⟨(-34436586566584704871593856857),(-34436586566584704504580435525)⟩,⟨7355158189969455280386908329,7355158189969455646850146135⟩⟩,⟨⟨(-33461730005562509403541799238),(-33461730005562509041507618627)⟩,⟨8009889577884999881418968402,8009889577885000242897429461⟩⟩,⟨⟨(-32476587167139641358545435807),(-32476587167139641001526128058)⟩,⟨8636119885806715209763289203,8636119885806715566222146241⟩⟩,⟨⟨(-31482486544387359396181230336),(-31482486544387359044244807738)⟩,⟨9232862289841930727111732882,9232862289841931078483793992⟩⟩,⟨⟨(-30480798544631495441421566370),(-30480798544631495094599957954)⟩,⟨9799222453235725359601890493,9799222453235725705856048190⟩⟩,⟨⟨(-29472930722907277115563689079),(-29472930722907276773925016783)⟩,⟨10334401214838109560831138192,10334401214838109901900103173⟩⟩,⟨⟨(-28460322770935841232554866974),(-28460322770935840896118503128)⟩,⟨10837696907278255435850210441,10837696907278255771715436225⟩⟩,⟨⟨(-27444441289286042082268351177),(-27444441289286041750999434661)⟩,⟨11308507288366031723101578185,11308507288366032053802328962⟩⟩,⟨⟨(-26426774372046740014854565421),(-26426774372046739688070025087)⟩,⟨11746331071334191008797025181,11746331071334191335043762173⟩⟩,⟨⟨(-25408826034801577697567177116),(-25408826034801577375339947047)⟩,⟨12150769041781898621139714066,12150769041781898942859142360⟩⟩,⟨⟨(-24392110517955226190249582163),(-24392110517955225872599718985)⟩,⟨12521524751565317988829764548,12521524751565318306001416999⟩⟩,⟨⟨(-23378146498493739978525979178),(-23378146498493739665517777811)⟩,⟨12858404782385410297369901862,12858404782385410609929041145⟩⟩,⟨⟨(-22368451244060326736968580977),(-22368451244060326428620353380)⟩,⟨13161318574427166306468850179,13161318574427166614396676376⟩⟩] +lemma kernel15_0_r5_3_eq : ∀ k : Fin 16, kernel15_0Expr 5 3 k = kernel15_0_r5_3 k := by decide +kernel +noncomputable def kernel15_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-21364534743781804693789230572),(-21364534743781804390167916365)⟩,⟨13430277818087013299634276944,13430277818087013602863332931⟩⟩,⟨⟨(-20367893850582688851326963133),(-20367893850582688552437077714)⟩,⟨13665395409563830979454911944,13665395409563831277980120364⟩⟩,⟨⟨(-19380006469767852940765078669),(-19380006469767852646662239656)⟩,⟨13866883973860641554728074588,13866883973860641848493229066⟩⟩,⟨⟨(-18402325828438029670618995692),(-18402325828438029381307592543)⟩,⟨14035053961524697238021545516,14035053961524697527021629080⟩⟩,⟨⟨(-17436274859824423472673677762),(-17436274859824423188210666201)⟩,⟨14170311328219019491076216133,14170311328219019775253621422⟩⟩,⟨⟨(-16483240735891265764507963085),(-16483240735891265484884280533)⟩,⟨14273154808943915080750118445,14273154808943915360113220522⟩⟩,⟨⟨(-15544569580562574115731307146),(-15544569580562573840992763375)⟩,⟨14344172801388156372954080059,14344172801388156647456360926⟩⟩,⟨⟨(-14621561394688489880435709391),(-14621561394688489610572135032)⟩,⟨14384039875462273757601440149,14384039875462274027252331201⟩⟩,⟨⟨(-13715465222386606962458072857),(-13715465222386606697518225161)⟩,⟨14393512928527296151590235989,14393512928527296416340224785⟩⟩,⟨⟨(-12827474586686279678014915093),(-12827474586686279417972877025)⟩,⟨14373427008158708450897578293,14373427008158708710771800755⟩⟩,⟨⟨(-11958723220482894450070425601),(-11958723220482894194961330846)⟩,⟨14324690826455935138539371187,14324690826455935393501899164⟩⟩,⟨⟨(-11110281116690538918016607948),(-11110281116690538667815512777)⟩,⟨14248281991902261419667685944,14248281991902261669742649522⟩⟩,⟨⟨(-10283150919183426841927273554),(-10283150919183426596671004366)⟩,⟨14145241986580345974240320268,14145241986580346219390069526⟩⟩,⟨⟨(-9478264673658676297274293886),(-9478264673658676056897933927)⟩,⟨14016670918137780670776752942,14016670918137780911065196486⟩⟩,⟨⟨(-8696480954957042519287257518),(-8696480954957042283803117191)⟩,⟨13863722077260964086357831422,13863722077260964321771738236⟩⟩,⟨⟨(-7938582384666814163592262238),(-7938582384666813932962548290)⟩,⟨13687596332541534046811525295,13687596332541534277387850214⟩⟩] +lemma kernel15_0_r5_4_eq : ∀ k : Fin 16, kernel15_0Expr 5 4 k = kernel15_0_r5_4 k := by decide +kernel +noncomputable def kernel15_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-7205273550033277655692657875),(-7205273550033277429947094941)⟩,⟨13489536395497756600451010821,13489536395497756826159188575⟩⟩,⟨⟨(-6497179332326812196136751597),(-6497179332326811975205095870)⟩,⟨13270820989136069682520956943,13270820989136069903430389299⟩⟩,⟨⟨(-5814843649912290109794762565),(-5814843649912289893634907706)⟩,⟨13032758953800459770266684645,13032758953800459986418640060⟩⟩,⟨⟨(-5158728618336856211504598470),(-5158728618336856000068178101)⟩,⟨12776683324157152228620692169,12776683324157152440062698243⟩⟩,⟨⟨(-4529214126838235421924613874),(-4529214126838235215231621562)⟩,⟨12503945410999501577777745517,12503945410999501784488974693⟩⟩,⟨⟨(-3926597827797132369282035641),(-3926597827797132167269286386)⟩,⟨12215908921135887619025936485,12215908921135887821068748636⟩⟩,⟨⟨(-3351095532840193361545460781),(-3351095532840193164219317398)⟩,⟨11913944147947358936151247881,11913944147947359133518463158⟩⟩,⟨⟨(-2802842006568768634912349857),(-2802842006568768442211685636)⟩,⟨11599422264279737683330266207,11599422264279737876082207874⟩⟩,⟨⟨(-2281892146266660229217314191),(-2281892146266660041153382497)⟩,⟨11273709748177346731485925427,11273709748177346919610547291⟩⟩,⟨⟨(-1788222533449186141378020167),(-1788222533449185957774171566)⟩,⟨10938162970585165507560996757,10938162970585165691234174516⟩⟩,⟨⟨(-1321733340776716986538889623),(-1321733340776716807372523402)⟩,⟨10594122972557913794500770384,10594122972557913973744344293⟩⟩,⟨⟨(-882250575687080006075094960),(-882250575687079831279369620)⟩,⟨10242910457735094707250387439,10242910457735094882130460916⟩⟩,⟨⟨(-469528640119668780931289508),(-469528640119668610511034960)⟩,⟨9885821023888925067882367915,9885821023888925238393388157⟩⟩,⟨⟨(-83253183924430746117171375),(-83253183924430579991522171)⟩,⟨9524120655247377390836303060,9524120655247377557058439899⟩⟩,⟨⟨276955772016430936141209795,276955772016431097980954914⟩,⟨9159041495058551200159295938,9159041495058551362100571976⟩⟩,⟨⟨611540468267122699241242700,611540468267122856900499230⟩,⟨8791777915517589263259195984,8791777915517589421024344481⟩⟩] +lemma kernel15_0_r5_5_eq : ∀ k : Fin 16, kernel15_0Expr 5 5 k = kernel15_0_r5_5 k := by decide +kernel +noncomputable def kernel15_0_r5_6 : Fin 16 → CBox := ![⟨⟨921001821339221109968972955,921001821339221263453261657⟩,⟨8423482899746405952313139038,8423482899746406105907046593⟩⟩,⟨⟨1205895647508457226831475792,1205895647508457376231638349⟩,⟨8055264748023120894757137194,8055264748023121044270051108⟩⟩,⟨⟨1466828723872530014613221752,1466828723872530159945290502⟩,⟨7688184117926009740703458495,7688184117926009886150835255⟩⟩,⟨⟨1704454714966709712328721463,1704454714966709853675968231⟩,⟨7323251405509639962643598173,7323251405509640104108167280⟩⟩,⟨⟨1919469993407665219492930555,1919469993407665356866984487⟩,⟨6961424472091958171782520711,6961424472091958309275388012⟩⟩,⟨⟨2112609382956339136738890881,2112609382956339270235366860⟩,⟨6603606718723144967472602298,6603606718723145101088896280⟩⟩,⟨⟨2284641852084656456886391999,2284641852084656586529491285⟩,⟨6250645507951921270761112375,6250645507951921400524566970⟩⟩,⟨⟨2436366185607372956025512199,2436366185607373081904907764⟩,⟨5903330930123473869356506356,5903330930123473995356362902⟩⟩,⟨⟨2568606661210407850568526757,2568606661210407972864326666⟩,⟨5562394909154784418222587768,5562394909154784540631433493⟩⟩,⟨⟨2682208756783325071207954026,2682208756783325190067855231⟩,⟨5228510640555942059944692265,5228510640555942178908074747⟩⟩,⟨⟨2778034913360601315493600037,2778034913360601430936078128⟩,⟨4902292352416404937505682529,4902292352416405053042455688⟩⟩,⟨⟨2856960377209722248876850238,2856960377209722360983829702⟩,⟨4584295378167781182296344863,4584295378167781294488822856⟩⟩,⟨⟨2919869143190939486755487139,2919869143190939595540467870⟩,⟨4275016528182261941761778524,4275016528182262050623846259⟩⟩,⟨⟨2967650019971614230868612413,2967650019971614336424256215⟩,⟨3974894745679110832602920141,3974894745679110938227633428⟩⟩,⟨⟨3001192836026104522941221597,3001192836026104625292473711⟩,⟨3684312030999304497477498396,3684312030999304599890189871⟩⟩,⟨⟨3021384803609244541621614978,3021384803609244640854153802⟩,⟨3403594617077158105379043604,3403594617077158204665782584⟩⟩] +lemma kernel15_0_r5_6_eq : ∀ k : Fin 16, kernel15_0Expr 5 6 k = kernel15_0_r5_6 k := by decide +kernel +noncomputable def kernel15_0_r5_7 : Fin 16 → CBox := ![⟨⟨3029107056076991469016454130,3029107056076991565147410414⟩,⟨3133014377892103385957565990,3133014377892103482135866132⟩⟩,⟨⟨3025231372061176766875712424,3025231372061176860010723695⟩,⟨2872790450826196128084776675,2872790450826196221260659153⟩⟩,⟨⟨3010617098105694270872036749,3010617098105694361058047890⟩,⟨2623091053183876615165453643,2623091053183876705386236806⟩⟩,⟨⟨2986108279457677304287083565,2986108279457677391609966875⟩,⟨2384035472648501572564596332,2384035472648501659916524773⟩⟩,⟨⟨2952531006797442333295225025,2952531006797442417777702501⟩,⟨2155696211151862202223756820,2155696211151862286729914849⟩⟩,⟨⟨2910690984802596723306744248,2910690984802596805043133913⟩,⟨1938101261513204287947959615,1938101261513204369703022272⟩⟩,⟨⟨2861371326591153715401347523,2861371326591153794423991256⟩,⟨1731236496256458808010135207,1731236496256458887046790591⟩⟩,⟨⟨2805330576291093729516837192,2805330576291093805911946151⟩,⟨1535048148230285913752707739,1535048148230285990157504944⟩⟩,⟨⟨2743300960253649106675483297,2743300960253649180525012126⟩,⟨1349445363025624574494270525,1349445363025624648349541968⟩⟩,⟨⟨2675986865777421260466821352,2675986865777421331881497237⟩,⟨1174302803699066587978519037,1174302803699066659395321451⟩⟩,⟨⟨2604063544651592173623713373,2604063544651592242633348279⟩,⟨1009463288955901847117489879,1009463288955901916125935290⟩⟩,⟨⟨2528176037368805890955977144,2528176037368805957640599382⟩,⟨854740446711677948961364871,854740446711678015641770027⟩⟩,⟨⟨2448938312510080850297519145,2448938312510080914681077657⟩,⟨709921365822529339365317747,709921365822529403741909146⟩⟩,⟨⟨2366932614572132316504852459,2366932614572132378673885218⟩,⟨574769229738868351298001610,574769229738868413457581702⟩⟩,⟨⟨2282709012396949143998948164,2282709012396949203985313240⟩,⟨449025916880539442792452842,449025916880539502767133432⟩⟩,⟨⟨2196785139378065460869960934,2196785139378065518751815430⟩,⟨332414553640373800318545554,332414553640373858186723833⟩⟩] +lemma kernel15_0_r5_7_eq : ∀ k : Fin 16, kernel15_0Expr 5 7 k = kernel15_0_r5_7 k := by decide +kernel +noncomputable def kernel15_0_r5_8 : Fin 16 → CBox := ![⟨⟨2109646115759890403087967213,2109646115759890458893326309⟩,⟨224642007083471028004478781,224642007083471083794399937⟩⟩,⟨⟨2021744642616467487357352690,2021744642616467541198516262⟩,⟨125401305607930088043307830,125401305607930141867486785⟩⟩,⟨⟨1933501256493524642865941716,1933501256493524694773416638⟩,⟨34373977055973285249433506,34373977055973337138582583⟩⟩,⟨⟨1845304733220760302571700399,1845304733220760352618390102⟩,⟨(-48767705000226536784601729),(-48767705000226486757388065)⟩⟩,⟨⟨1757512629046918335867610210,1757512629046918384078131691⟩,⟨(-124358574838260858487829380),(-124358574838260810297751984)⟩⟩,⟨⟨1670451947014181741410283447,1670451947014181787862202574⟩,⟨(-192738534846814485594338306),(-192738534846814439163664416)⟩⟩,⟨⟨1584419916365639546331577756,1584419916365639591066654009⟩,⟨(-254250628082324382158152422),(-254250628082324337444963825)⟩⟩,⟨⟨1499684872764079456884819493,1499684872764079499976036756⟩,⟨(-309239227563814021009435189),(-309239227563813977940603435)⟩⟩,⟨⟨1416487227185426459863322556,1416487227185426501332917121⟩,⟨(-358048345618102686648931364),(-358048345618102645202082679)⟩⟩,⟨⟨1335040511528473466564216562,1335040511528473506485684321⟩,⟨(-401020065504930807483074574),(-401020065504930767584590628)⟩⟩,⟨⟨1255532489246338382366809986,1255532489246338420776755698⟩,⟨(-438493096523636630345586064),(-438493096523636591958743657)⟩⟩,⟨⟨1178126319646173242406005810,1178126319646173279368165059⟩,⟨(-470801452835619770022027163),(-470801452835619733082987992)⟩⟩,⟨⟨1102961764913639819276644448,1102961764913639854814131806⟩,⟨(-498273255334677076882696511),(-498273255334677041367896270)⟩⟩,⟨⟨1030156429389013662574810877,1030156429389013696755207786⟩,⟨(-521229655064144152466953898),(-521229655064144118307191782)⟩⟩,⟨⟨959807021143919658451247613,959807021143919691301927771⟩,⟨(-539983875918400374436654420),(-539983875918400341604659724)⟩⟩,⟨⟨891990626473144860166242097,891990626473144891745686254⟩,⟨(-554840373678541758207334112),(-554840373678541726644730843)⟩⟩] +lemma kernel15_0_r5_8_eq : ∀ k : Fin 16, kernel15_0Expr 5 8 k = kernel15_0_r5_8 k := by decide +kernel +noncomputable def kernel15_0_r5_9 : Fin 16 → CBox := ![⟨⟨826765988516391400112281814,826765988516391430440840157⟩,⟨(-566094107818851698249386040),(-566094107818851667935923830)⟩⟩,⟨⟨764174781852144564764286264,764174781852144593904615385⟩,⟨(-574029921982227271175093991),(-574029921982227242048217741)⟩⟩,⟨⟨704242875552281257007784981,704242875552281284985797521⟩,⟨(-578922028558296290158223179),(-578922028558296262192116650)⟩⟩,⟨⟨646981577844260944558516325,646981577844260971427769415⟩,⟨(-581033592406226115625445088),(-581033592406226088766647138)⟩⟩,⟨⟨592388856190794534687034893,592388856190794560468229346⟩,⟨(-580616408443177486607562058),(-580616408443177460835463118)⟩⟩,⟨⟨540450527258331985034732877,540450527258332009783411386⟩,⟨(-577910667566425136478679023),(-577910667566425111737826920)⟩⟩,⟨⟨491141411899623631044469794,491141411899623654784701903⟩,⟨(-573144805189286638120303682),(-573144805189286614386714718)⟩⟩,⟨⟨444426450916617221792559322,444426450916617244572836625⟩,⟨(-566535426544685791769402525),(-566535426544685768994669024)⟩⟩,⟨⟨400261777993240952408769584,400261777993240974247164322⟩,⟨(-558287302841593256217872336),(-558287302841593234384001608)⟩⟩,⟨⟨358595746788953888438531675,358595746788953909386182470⟩,⟨(-548593432344625383149467860),(-548593432344625362205398723)⟩⟩,⟨⟨319369909759654519992984830,319369909759654540071873493⟩,⟨(-537635160481425954607138494),(-537635160481425934530962407)⟩⟩,⟨⟨282519946819528655661691907,282519946819528674915248248⟩,⟨(-525582353161647678266530588),(-525582353161647659014888150)⟩⟩,⟨⟨247976542473146883449587749,247976542473146901895185618⟩,⟨(-512593617610855353415402218),(-512593617610855334970986280)⟩⟩,⟨⟨215666210529582561559536309,215666210529582579241783244⟩,⟨(-498816565177934529613882614),(-498816565177934511932149247)⟩⟩,⟨⟨185512065958018895295732479,185512065958018912234391421⟩,⟨(-484388110761084774920422558),(-484388110761084757981669019)⟩⟩,⟨⟨157434543856237132525895192,157434543856237148838213910⟩,⟨(-469434803710762552222218021),(-469434803710762535909263754)⟩⟩] +lemma kernel15_0_r5_9_eq : ∀ k : Fin 16, kernel15_0Expr 5 9 k = kernel15_0_r5_9 k := by decide +kernel +noncomputable def kernel15_0_r5_10 : Fin 16 → CBox := ![⟨⟨131352065878968597736090710,131352065878968613438593019⟩,⟨(-454073185303695831522257782),(-454073185303695815818633042)⟩⟩,⟨⟨107181654812210451417618737,107181654812210466544134096⟩,⟨(-438410168136162495040898227),(-438410168136162479912822855)⟩⟩,⟨⟨84839498282489518437553651,84839498282489532998999772⟩,⟨(-422543433053141779076275591),(-422543433053141764512878592)⟩⟩,⟨⟨64241462857294843277216299,64241462857294857301531645⟩,⟨(-406561839508966512982058284),(-406561839508966498955444519)⟩⟩,⟨⟨45303560025377639145388618,45303560025377652640168867⟩,⟨(-390545845541218924787767861),(-390545845541218911290382779)⟩⟩,⟨⟨27942365744493457558179844,27942365744493470552936197⟩,⟨(-374567933829577050826874876),(-374567933829577037829244835)⟩⟩,⟨⟨12075395410820556657137359,12075395410820569161884391⟩,⟨(-358693040602154425242904152),(-358693040602154412735050250)⟩⟩,⟨⟨(-2378563759693555870659090),(-2378563759693543830814184)⟩,⟨(-342978984440881508942155382),(-342978984440881496899002828)⟩⟩,⟨⟨(-15499160840697788750654378),(-15499160840697777169540812)⟩,⟨(-327476892322231879476380081),(-327476892322231867891789022)⟩⟩,⟨⟨(-27364227618107130412713851),(-27364227618107119263124283)⟩,⟨(-312231620507957496025764334),(-312231620507957484872554822)⟩⟩,⟨⟨(-38049561093739194529443097),(-38049561093739183802350785)⟩,⟨(-297282168170598735912724347),(-297282168170598725181895853)⟩⟩,⟨⟨(-47628739805774218014470060),(-47628739805774207687509715)⟩,⟨(-282662081898778260043345466),(-282662081898778249712555907)⟩⟩,⟨⟨(-56172971691184420294543399),(-56172971691184410361569369)⟩,⟨(-268399849476334061111358761),(-268399849476334051174484781)⟩⟩,⟨⟨(-63750971223632282844494654),(-63750971223632273281995035)⟩,⟨(-254519281566104666076523514),(-254519281566104656510072302)⟩⟩,⟨⟨(-70428863585742361808019247),(-70428863585742352607988548)⟩,⟨(-241039880152790767561078666),(-241039880152790758357063174)⟩⟩,⟨⟨(-76270113675133468015735537),(-76270113675133459158399670)⟩,⟨(-227977192809144014277274240),(-227977192809144005415936145)⟩⟩] +lemma kernel15_0_r5_10_eq : ∀ k : Fin 16, kernel15_0Expr 5 10 k = kernel15_0_r5_10 k := by decide +kernel +noncomputable def kernel15_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-81335477797239500624339124),(-81335477797239492105104496)⟩,⟨(-215343152045339899464452645),(-215343152045339890941213788)⟩⟩,⟨⟨(-85682975962901341760676733),(-85682975962901333557983747)⟩,⟨(-203146399182528667308830813),(-203146399182528659102144009)⟩⟩,⟨⟨(-89367882783216413361894809),(-89367882783216405468671949)⟩,⟨(-191392592358146169342487540),(-191392592358146161445334187)⟩⟩,⟨⟨(-92442735036518351690100644),(-92442735036518344088553800)⟩,⟨(-180084698422677798586506997),(-180084698422677790981341006)⟩⟩,⟨⟨(-94957354071060504882779847),(-94957354071060497568385351)⟩,⟨(-169223268625409773015490751),(-169223268625409765697772474)⟩⟩,⟨⟨(-96958881300535352857432464),(-96958881300535345811986498)⟩,⟨(-158806698110597524129062164),(-158806698110597517080571065)⟩⟩,⟨⟨(-98491825146631162047896773),(-98491825146631155264421418)⟩,⟨(-148831469355856282186336364),(-148831469355856275400079094)⟩⟩,⟨⟨(-99598117882174965306283058),(-99598117882174958769565108)⟩,⟨(-139292379781944908451945258),(-139292379781944901912693176)⟩⟩,⟨⟨(-100317180928919650546930250),(-100317180928919644253781112)⟩,⟨(-130182753848051550770929788),(-130182753848051544475480331)⟩⟩,⟨⟨(-100685997264698622678036860),(-100685997264698616612086186)⟩,⟨(-121494640019835712757535068),(-121494640019835706689503513)⟩⟩,⟨⟨(-100739189694601828225290952),(-100739189694601822381187623)⟩,⟨(-113218993059515491591515612),(-113218993059515485745537792)⟩⟩,⟨⟨(-100509103839237934398449464),(-100509103839237928761897649)⟩,⟨(-105345842138921256956917881),(-105345842138921251318684958)⟩⟩,⟨⟨(-100025894789359426814928315),(-100025894789359421383027590)⟩,⟨(-97864445318397510781880376),(-97864445318397505348480040)⟩⟩,⟨⟨(-99317616469560026235446710),(-99317616469560020994485585)⟩,⟨(-90763430967462018045928652),(-90763430967462012803637487)⟩⟩,⟨⟨(-98410312843920761607545987),(-98410312843920756553410158)⟩,⟨(-84030926727964822689729422),(-84030926727964817634422224)⟩⟩,⟨⟨(-97328110182983951663161586),(-97328110182983946784614065)⟩,⟨(-77654676637861196373156167),(-77654676637861191493585252)⟩⟩] +lemma kernel15_0_r5_11_eq : ∀ k : Fin 16, kernel15_0Expr 5 11 k = kernel15_0_r5_11 k := by decide +kernel +noncomputable def kernel15_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-96093309693956727551802968),(-96093309693956722847075510)⟩,⟨(-71622147044339220278649530),(-71622147044339215573036851)⟩⟩,⟨⟨(-94726479894346445135477697),(-94726479894346440591907596)⟩,⟨(-65920621939621582409744443),(-65920621939621577865417606)⟩⟩,⟨⟨(-93246548183137114780103219),(-93246548183137110392571560)⟩,⟨(-60537288351964075206628081),(-60537288351964070818459287)⟩⟩,⟨⟨(-91670891133018880463762776),(-91670891133018876222684703)⟩,⟨(-55459312418842748754700235),(-55459312418842744513096047)⟩⟩,⟨⟨(-90015423092027561274283068),(-90015423092027557178000398)⟩,⟨(-50673906759667828381891362),(-50673906759667824285185661)⟩⟩,⟨⟨(-88294682743233885072443157),(-88294682743233881110671944)⟩,⟨(-46168389752160609004497027),(-46168389752160605042398223)⟩⟩,⟨⟨(-86521917326881384825249625),(-86521917326881380995295603)⟩,⟨(-41930237300318295797367231),(-41930237300318291967173965)⟩⟩,⟨⟨(-84709164280684804005738463),(-84709164280684800299296894)⟩,⟨(-37947127663172236497755787),(-37947127663172232791156592)⟩⟩,⟨⟨(-82867330100976293302091014),(-82867330100976289718289393)⟩,⟨(-34206979892780099800408327),(-34206979892780096216524409)⟩⟩,⟨⟨(-81006266270160742674416630),(-81006266270160739203916249)⟩,⟨(-30697986407507055397494632),(-30697986407507051926981365)⟩⟩,⟨⟨(-79134842134672565773542874),(-79134842134672562414153971)⟩,⟨(-27408640203031932423336538),(-27408640203031929063998611)⟩⟩,⟨⟨(-77261014652490192220807362),(-77261014652490188965340360)⟩,⟨(-24327757179011775783714192),(-24327757179011772528356862)⟩⟩,⟨⟨(-75391894960451171908646180),(-75391894960451168756245870)⟩,⟨(-21444494034266473436210941),(-21444494034266470283974103)⟩⟩,⟨⟨(-73533811739319890317112687),(-73533811739319887259945029)⟩,⟨(-18748362157984047215352864),(-18748362157984044158398002)⟩⟩,⟨⟨(-71692371378997831378142476),(-71692371378997828413736571)⟩,⟨(-16229237919043788113545219),(-16229237919043785149396752)⟩⟩,⟨⟨(-69872514967643197580792799),(-69872514967643194701812501)⟩,⟨(-13877369730324570840239722),(-13877369730324567961556985)⟩⟩] +lemma kernel15_0_r5_12_eq : ∀ k : Fin 16, kernel15_0Expr 5 12 k = kernel15_0_r5_12 k := by decide +kernel +noncomputable def kernel15_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-68078572146993678481586985),(-68078572146993675688014645)⟩,⟨(-11683382239996053232517313),(-11683382239996050439278981)⟩⟩,⟨⟨(-66314311892073223018034464),(-66314311892073220302744228)⟩,⟨(-9638277977440401980918220),(-9638277977440399265995216)⟩⟩,⟨⟨(-64582990286917630875457472),(-64582990286917628237187452)⟩,⟨(-7733436757755716558397131),(-7733436757755713920524413)⟩⟩,⟨⟨(-62887395379176622840291164),(-62887395379176620273741527)⟩,⟨(-5960613125860160099274575),(-5960613125860157533149523)⟩⟩,⟨⟨(-61229889205637557504546761),(-61229889205637555009562105)⟩,⟨(-4311932099137330055585940),(-4311932099137327561050390)⟩⟩,⟨⟨(-59612447088056570003000544),(-59612447088056567573647490)⟩,⟨(-2779883446408617657360536),(-2779883446408615228478779)⟩⟩,⟨⟨(-58036694304356818570292274),(-58036694304356816205597426)⟩,⟨(-1357314720839741526217844),(-1357314720839739162014142)⟩⟩,⟨⟨(-56503940244432018082750444),(-56503940244432015778084014)⟩,⟨(-37423245223181753161165),(-37423245223179449003733)⟩⟩,⟨⟨(-55015210162638384308394373),(-55015210162638382064073985)⟩,⟨1186252770051122886244372,1186252770051125130039978⟩⟩,⟨⟨(-53571274640721641001643225),(-53571274640721638812141490)⟩,⟨2319843813106961199280970,2319843813106963388243744⟩⟩,⟨⟨(-52172676875550077166951887),(-52172676875550075031343924)⟩,⟨3369159213580631837669315,3369159213580633972725843⟩⟩,⟨⟨(-50819757905742055447595241),(-50819757905742053361736654)⟩,⟨4339697710310775121179324,4339697710310777206475377⟩⟩,⟨⟨(-49512679890209253553587220),(-49512679890209251517716289)⟩,⟨5236658325499595496993266,5236658325499597532292069⟩⟩,⟨⟨(-48251447549897941428123806),(-48251447549897939437581413)⟩,⟨6064951440105422203947496,6064951440105424193909251⟩⟩,⟨⟨(-47035927881702957392414935),(-47035927881702955446684647)⟩,⟨6829209977237911327447303,6829209977237913272589668⟩⟩,⟨⟨(-45865868250746785705615074),(-45865868250746783801131756)⟩,⟨7533800611403742502457003,7533800611403744406346032⟩⟩] +lemma kernel15_0_r5_13_eq : ∀ k : Fin 16, kernel15_0Expr 5 13 k = kernel15_0_r5_13 k := by decide +kernel +noncomputable def kernel15_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-44740912964044495301312128),(-44740912964044493438767603)⟩,⟨8182834931629329210080447,8182834931629331072025430⟩⟩,⟨⟨(-43660618425091119162653177),(-43660618425091117337542459)⟩,⟨8780180495807395452507879,8780180495807397277014453⟩⟩,⟨⟨(-42624466965180216775252073),(-42624466965180214987216748)⟩,⟨9329471722117707925193529,9329471722117709712620969⟩⟩,⟨⟨(-41631879443352240295736098),(-41631879443352238541610066)⟩,⟨9834120571101443987220876,9834120571101445740735854⟩⟩,⟨⟨(-40682226702833245912988378),(-40682226702833244193255804)⟩,⟨10297326978966913064651265,10297326978966914783770390⟩⟩,⟨⟨(-39774839967706209745936339),(-39774839967706208056814409)⟩,⟨10722089009015058856489953,10722089009015060544996408⟩⟩,⟨⟨(-38909020259400372029256733),(-38909020259400370370514246)⟩,⟨11111212693739482723212830,11111212693739484381338407⟩⟩,⟨⟨(-38084046908424652674122342),(-38084046908424651042923162)⟩,⟨11467321545220114000055254,11467321545220115630636403⟩⟩,⟨⟨(-37299185232640073799946034),(-37299185232640072197089727)⟩,⟨11792865715933613856575896,11792865715933615458813614⟩⟩,⟨⟨(-36553693449289357093848795),(-36553693449289355515648349)⟩,⟨12090130796087421878967494,12090130796087423456548922⟩⟩,⟨⟨(-35846828884001170165049131),(-35846828884001168611371926)⟩,⟨12361246237086908300936582,12361246237086909853994730⟩⟩,⟨⟨(-35177853536079680176933109),(-35177853536079678645215190)⟩,⟨12608193393803675735289221,12608193393803677266388169⟩⟩,⟨⟨(-34546039055591387012588126),(-34546039055591385503471930)⟩,⟨12832813180963269448408656,12832813180963270956906345⟩⟩,⟨⟨(-33950671184081710831395149),(-33950671184081709341687757)⟩,⟨13036813341246240890695212,13036813341246242379784551⟩⟩,⟨⟨(-33391053707201699270023309),(-33391053707201697799666773)⟩,⟨13221775324629681505339591,13221775324629682975078770⟩⟩,⟨⟨(-32866511964106149490511705),(-32866511964106148037161479)⟩,⟨13389160780117174963123157,13389160780117176415856720⟩⟩] +lemma kernel15_0_r5_14_eq : ∀ k : Fin 16, kernel15_0Expr 5 14 k = kernel15_0_r5_14 k := by decide +kernel +noncomputable def kernel15_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-32376395955201801414796761),(-32376395955201799979425338)⟩,⟨13540317662341935302328672,13540317662341936737084405⟩⟩,⟨⟨(-31920083086679448317018665),(-31920083086679446896361686)⟩,⟨13676485956607212241679823,13676485956607213661721940⟩⟩,⟨⟨(-31496980587256474810124710),(-31496980587256473404176006)⟩,⟨13798803026774574685954895,13798803026774576091289702⟩⟩,⟨⟨(-31106527629684585203729173),(-31106527629684583810319465)⟩,⟨13908308591047417103172498,13908308591047418495969185⟩⟩,⟨⟨(-30748197186838111391881133),(-30748197186838110011746897)⟩,⟨14005949331145290205022602,14005949331145291584544861⟩⟩,⟨⟨(-30421497649586923369978693),(-30421497649586922000292346)⟩,⟨14092583140644160640737809,14092583140644162009813029⟩⟩,⟨⟨(-30125974231169252840082757),(-30125974231169251480870846)⟩,⟨14168983018386664549191774,14168983018386665907793475⟩⟩,⟨⟨(-29861210180407482734569462),(-29861210180407481383796151)⟩,⟨14235840612861621411916610,14235840612861622762080478⟩⟩,⟨⟨(-29626827823847237196270671),(-29626827823847235854802150)⟩,⟨14293769423328970467895145,14293769423328971808757751⟩⟩,⟨⟨(-29422489454739407766841012),(-29422489454739406431636838)⟩,⟨14343307663239099008224204,14343307663239100342827965⟩⟩,⟨⟨(-29247898084718045905812547),(-29247898084718044576946211)⟩,⟨14384920791177331797731327,14384920791177333126002037⟩⟩,⟨⟨(-29102798072045893007956776),(-29102798072045891683522892)⟩,⟨14419003714167190727462007,14419003714167192051304158⟩⟩,⟨⟨(-28986975638394913603304654),(-28986975638394912284119541)⟩,⟨14445882667701029612261230,14445882667701030930857882⟩⟩,⟨⟨(-28900259284292470138609250),(-28900259284292468822056411)⟩,⟨14465816776344088592985701,14465816776344089908952400⟩⟩,⟨⟨(-28842520111585425363136434),(-28842520111585424049283331)⟩,⟨14478999298187460090534831,14478999298187461403803430⟩⟩,⟨⟨(-28813672059544997259270196),(-28813672059544995946273335)⟩,⟨14485558555815857563380238,14485558555815858875793366⟩⟩] +lemma kernel15_0_r5_15_eq : ∀ k : Fin 16, kernel15_0Expr 5 15 k = kernel15_0_r5_15 k := by decide +kernel +noncomputable def kernel15_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel15_0_r5_0,kernel15_0_r5_1,kernel15_0_r5_2,kernel15_0_r5_3,kernel15_0_r5_4,kernel15_0_r5_5,kernel15_0_r5_6,kernel15_0_r5_7,kernel15_0_r5_8,kernel15_0_r5_9,kernel15_0_r5_10,kernel15_0_r5_11,kernel15_0_r5_12,kernel15_0_r5_13,kernel15_0_r5_14,kernel15_0_r5_15] +lemma kernel15_0_r5_eq (i k : Fin 16) : kernel15_0Expr 5 i k = kernel15_0_r5 i k := by + fin_cases i + · exact kernel15_0_r5_0_eq k + · exact kernel15_0_r5_1_eq k + · exact kernel15_0_r5_2_eq k + · exact kernel15_0_r5_3_eq k + · exact kernel15_0_r5_4_eq k + · exact kernel15_0_r5_5_eq k + · exact kernel15_0_r5_6_eq k + · exact kernel15_0_r5_7_eq k + · exact kernel15_0_r5_8_eq k + · exact kernel15_0_r5_9_eq k + · exact kernel15_0_r5_10_eq k + · exact kernel15_0_r5_11_eq k + · exact kernel15_0_r5_12_eq k + · exact kernel15_0_r5_13_eq k + · exact kernel15_0_r5_14_eq k + · exact kernel15_0_r5_15_eq k +noncomputable def kernel15_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel15_0_r0,kernel15_0_r1,kernel15_0_r2,kernel15_0_r3,kernel15_0_r4,kernel15_0_r5] +lemma kernel15_0_eq (j : Fin 6) (i k : Fin 16) : kernel15_0Expr j i k = kernel15_0 j i k := by + fin_cases j + · exact kernel15_0_r0_eq i k + · exact kernel15_0_r1_eq i k + · exact kernel15_0_r2_eq i k + · exact kernel15_0_r3_eq i k + · exact kernel15_0_r4_eq i k + · exact kernel15_0_r5_eq i k +lemma kernel15_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel15_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(15:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel15_0_eq] + unfold kernel15_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans15_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel15_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans15 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel15_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r0_0_eq : ∀ k : Fin 16, kernel15_1Expr 0 0 k = kernel15_1_r0_0 k := by decide +kernel +noncomputable def kernel15_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r0_1_eq : ∀ k : Fin 16, kernel15_1Expr 0 1 k = kernel15_1_r0_1 k := by decide +kernel +noncomputable def kernel15_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r0_2_eq : ∀ k : Fin 16, kernel15_1Expr 0 2 k = kernel15_1_r0_2 k := by decide +kernel +noncomputable def kernel15_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r0_3_eq : ∀ k : Fin 16, kernel15_1Expr 0 3 k = kernel15_1_r0_3 k := by decide +kernel +noncomputable def kernel15_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r0_4_eq : ∀ k : Fin 16, kernel15_1Expr 0 4 k = kernel15_1_r0_4 k := by decide +kernel +noncomputable def kernel15_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel15_1_r0_5_eq : ∀ k : Fin 16, kernel15_1Expr 0 5 k = kernel15_1_r0_5 k := by decide +kernel +noncomputable def kernel15_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel15_1_r0_6_eq : ∀ k : Fin 16, kernel15_1Expr 0 6 k = kernel15_1_r0_6 k := by decide +kernel +noncomputable def kernel15_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel15_1_r0_7_eq : ∀ k : Fin 16, kernel15_1Expr 0 7 k = kernel15_1_r0_7 k := by decide +kernel +noncomputable def kernel15_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel15_1_r0_8_eq : ∀ k : Fin 16, kernel15_1Expr 0 8 k = kernel15_1_r0_8 k := by decide +kernel +noncomputable def kernel15_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel15_1_r0_9_eq : ∀ k : Fin 16, kernel15_1Expr 0 9 k = kernel15_1_r0_9 k := by decide +kernel +noncomputable def kernel15_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel15_1_r0_10_eq : ∀ k : Fin 16, kernel15_1Expr 0 10 k = kernel15_1_r0_10 k := by decide +kernel +noncomputable def kernel15_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel15_1_r0_11_eq : ∀ k : Fin 16, kernel15_1Expr 0 11 k = kernel15_1_r0_11 k := by decide +kernel +noncomputable def kernel15_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel15_1_r0_12_eq : ∀ k : Fin 16, kernel15_1Expr 0 12 k = kernel15_1_r0_12 k := by decide +kernel +noncomputable def kernel15_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel15_1_r0_13_eq : ∀ k : Fin 16, kernel15_1Expr 0 13 k = kernel15_1_r0_13 k := by decide +kernel +noncomputable def kernel15_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel15_1_r0_14_eq : ∀ k : Fin 16, kernel15_1Expr 0 14 k = kernel15_1_r0_14 k := by decide +kernel +noncomputable def kernel15_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel15_1_r0_15_eq : ∀ k : Fin 16, kernel15_1Expr 0 15 k = kernel15_1_r0_15 k := by decide +kernel +noncomputable def kernel15_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel15_1_r0_0,kernel15_1_r0_1,kernel15_1_r0_2,kernel15_1_r0_3,kernel15_1_r0_4,kernel15_1_r0_5,kernel15_1_r0_6,kernel15_1_r0_7,kernel15_1_r0_8,kernel15_1_r0_9,kernel15_1_r0_10,kernel15_1_r0_11,kernel15_1_r0_12,kernel15_1_r0_13,kernel15_1_r0_14,kernel15_1_r0_15] +lemma kernel15_1_r0_eq (i k : Fin 16) : kernel15_1Expr 0 i k = kernel15_1_r0 i k := by + fin_cases i + · exact kernel15_1_r0_0_eq k + · exact kernel15_1_r0_1_eq k + · exact kernel15_1_r0_2_eq k + · exact kernel15_1_r0_3_eq k + · exact kernel15_1_r0_4_eq k + · exact kernel15_1_r0_5_eq k + · exact kernel15_1_r0_6_eq k + · exact kernel15_1_r0_7_eq k + · exact kernel15_1_r0_8_eq k + · exact kernel15_1_r0_9_eq k + · exact kernel15_1_r0_10_eq k + · exact kernel15_1_r0_11_eq k + · exact kernel15_1_r0_12_eq k + · exact kernel15_1_r0_13_eq k + · exact kernel15_1_r0_14_eq k + · exact kernel15_1_r0_15_eq k +noncomputable def kernel15_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩] +lemma kernel15_1_r1_0_eq : ∀ k : Fin 16, kernel15_1Expr 1 0 k = kernel15_1_r1_0 k := by decide +kernel +noncomputable def kernel15_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩] +lemma kernel15_1_r1_1_eq : ∀ k : Fin 16, kernel15_1Expr 1 1 k = kernel15_1_r1_1 k := by decide +kernel +noncomputable def kernel15_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-41),21⟩,⟨(-31),31⟩⟩] +lemma kernel15_1_r1_2_eq : ∀ k : Fin 16, kernel15_1Expr 1 2 k = kernel15_1_r1_2 k := by decide +kernel +noncomputable def kernel15_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),21⟩,⟨(-31),31⟩⟩,⟨⟨(-42),21⟩,⟨(-31),31⟩⟩,⟨⟨(-42),21⟩,⟨(-31),31⟩⟩,⟨⟨(-42),21⟩,⟨(-31),31⟩⟩,⟨⟨(-42),21⟩,⟨(-31),31⟩⟩,⟨⟨(-42),21⟩,⟨(-31),31⟩⟩,⟨⟨(-42),21⟩,⟨(-31),31⟩⟩,⟨⟨(-42),21⟩,⟨(-31),32⟩⟩,⟨⟨(-42),21⟩,⟨(-31),32⟩⟩,⟨⟨(-42),21⟩,⟨(-31),32⟩⟩,⟨⟨(-42),21⟩,⟨(-31),32⟩⟩,⟨⟨(-42),21⟩,⟨(-31),32⟩⟩,⟨⟨(-42),21⟩,⟨(-31),32⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel15_1_r1_3_eq : ∀ k : Fin 16, kernel15_1Expr 1 3 k = kernel15_1_r1_3 k := by decide +kernel +noncomputable def kernel15_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel15_1_r1_4_eq : ∀ k : Fin 16, kernel15_1Expr 1 4 k = kernel15_1_r1_4 k := by decide +kernel +noncomputable def kernel15_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel15_1_r1_5_eq : ∀ k : Fin 16, kernel15_1Expr 1 5 k = kernel15_1_r1_5 k := by decide +kernel +noncomputable def kernel15_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel15_1_r1_6_eq : ∀ k : Fin 16, kernel15_1Expr 1 6 k = kernel15_1_r1_6 k := by decide +kernel +noncomputable def kernel15_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel15_1_r1_7_eq : ∀ k : Fin 16, kernel15_1Expr 1 7 k = kernel15_1_r1_7 k := by decide +kernel +noncomputable def kernel15_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel15_1_r1_8_eq : ∀ k : Fin 16, kernel15_1Expr 1 8 k = kernel15_1_r1_8 k := by decide +kernel +noncomputable def kernel15_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel15_1_r1_9_eq : ∀ k : Fin 16, kernel15_1Expr 1 9 k = kernel15_1_r1_9 k := by decide +kernel +noncomputable def kernel15_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r1_10_eq : ∀ k : Fin 16, kernel15_1Expr 1 10 k = kernel15_1_r1_10 k := by decide +kernel +noncomputable def kernel15_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r1_11_eq : ∀ k : Fin 16, kernel15_1Expr 1 11 k = kernel15_1_r1_11 k := by decide +kernel +noncomputable def kernel15_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r1_12_eq : ∀ k : Fin 16, kernel15_1Expr 1 12 k = kernel15_1_r1_12 k := by decide +kernel +noncomputable def kernel15_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r1_13_eq : ∀ k : Fin 16, kernel15_1Expr 1 13 k = kernel15_1_r1_13 k := by decide +kernel +noncomputable def kernel15_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r1_14_eq : ∀ k : Fin 16, kernel15_1Expr 1 14 k = kernel15_1_r1_14 k := by decide +kernel +noncomputable def kernel15_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel15_1_r1_15_eq : ∀ k : Fin 16, kernel15_1Expr 1 15 k = kernel15_1_r1_15 k := by decide +kernel +noncomputable def kernel15_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel15_1_r1_0,kernel15_1_r1_1,kernel15_1_r1_2,kernel15_1_r1_3,kernel15_1_r1_4,kernel15_1_r1_5,kernel15_1_r1_6,kernel15_1_r1_7,kernel15_1_r1_8,kernel15_1_r1_9,kernel15_1_r1_10,kernel15_1_r1_11,kernel15_1_r1_12,kernel15_1_r1_13,kernel15_1_r1_14,kernel15_1_r1_15] +lemma kernel15_1_r1_eq (i k : Fin 16) : kernel15_1Expr 1 i k = kernel15_1_r1 i k := by + fin_cases i + · exact kernel15_1_r1_0_eq k + · exact kernel15_1_r1_1_eq k + · exact kernel15_1_r1_2_eq k + · exact kernel15_1_r1_3_eq k + · exact kernel15_1_r1_4_eq k + · exact kernel15_1_r1_5_eq k + · exact kernel15_1_r1_6_eq k + · exact kernel15_1_r1_7_eq k + · exact kernel15_1_r1_8_eq k + · exact kernel15_1_r1_9_eq k + · exact kernel15_1_r1_10_eq k + · exact kernel15_1_r1_11_eq k + · exact kernel15_1_r1_12_eq k + · exact kernel15_1_r1_13_eq k + · exact kernel15_1_r1_14_eq k + · exact kernel15_1_r1_15_eq k +noncomputable def kernel15_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-2864183165705),(-2864183165681)⟩,⟨(-2588588148401),(-2588588148376)⟩⟩,⟨⟨(-2860064017283),(-2860064017251)⟩,⟨(-2582523921547),(-2582523921515)⟩⟩,⟨⟨(-2851840120159),(-2851840120129)⟩,⟨(-2570435227372),(-2570435227344)⟩⟩,⟨⟨(-2839540237505),(-2839540237473)⟩,⟨(-2552401175217),(-2552401175184)⟩⟩,⟨⟨(-2823207422194),(-2823207422164)⟩,⟨(-2528539410178),(-2528539410150)⟩⟩,⟨⟨(-2802898903767),(-2802898903738)⟩,⟨(-2499004906090),(-2499004906063)⟩⟩,⟨⟨(-2778685933200),(-2778685933159)⟩,⟨(-2463988381563),(-2463988381522)⟩⟩,⟨⟨(-2750653581811),(-2750653581783)⟩,⟨(-2423714360718),(-2423714360688)⟩⟩,⟨⟨(-2718900490113),(-2718900490085)⟩,⟨(-2378438904671),(-2378438904641)⟩⟩,⟨⟨(-2683538562033),(-2683538562006)⟩,⟨(-2328447043986),(-2328447043956)⟩⟩,⟨⟨(-2644692599655),(-2644692599627)⟩,⟨(-2274049946386),(-2274049946356)⟩⟩,⟨⟨(-2602499873809),(-2602499873776)⟩,⟨(-2215581856996),(-2215581856963)⟩⟩,⟨⟨(-2557109626057),(-2557109626017)⟩,⟨(-2153396851154),(-2153396851113)⟩⟩,⟨⟨(-2508682498239),(-2508682498211)⟩,⟨(-2087865441764),(-2087865441734)⟩⟩,⟨⟨(-2457389886504),(-2457389886477)⟩,⟨(-2019371084530),(-2019371084500)⟩⟩,⟨⟨(-2403413217568),(-2403413217540)⟩,⟨(-1948306624993),(-1948306624963)⟩⟩] +lemma kernel15_1_r2_0_eq : ∀ k : Fin 16, kernel15_1Expr 2 0 k = kernel15_1_r2_0 k := by decide +kernel +noncomputable def kernel15_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-2346943146603),(-2346943146570)⟩,⟨(-1875070731500),(-1875070731467)⟩⟩,⟨⟨(-2288178676963),(-2288178676935)⟩,⟨(-1800064357219),(-1800064357189)⟩⟩,⟨⟨(-2227326203845),(-2227326203815)⟩,⟨(-1723687273306),(-1723687273278)⟩⟩,⟨⟨(-2164598485406),(-2164598485381)⟩,⟨(-1646334713166),(-1646334713141)⟩⟩,⟨⟨(-2100213546397),(-2100213546367)⟩,⟨(-1568394165294),(-1568394165266)⟩⟩,⟨⟨(-2034393521240),(-2034393521212)⟩,⟨(-1490242349228),(-1490242349198)⟩⟩,⟨⟨(-1967363444705),(-1967363444677)⟩,⟨(-1412242405592),(-1412242405562)⟩⟩,⟨⟨(-1899350000069),(-1899350000044)⟩,⟨(-1334741327268),(-1334741327243)⟩⟩,⟨⟨(-1830580235893),(-1830580235863)⟩,⟨(-1258067654718),(-1258067654690)⟩⟩,⟨⟨(-1761280263536),(-1761280263503)⟩,⟨(-1182529453946),(-1182529453913)⟩⟩,⟨⟨(-1691673948670),(-1691673948645)⟩,⟨(-1108412590930),(-1108412590905)⟩⟩,⟨⟨(-1621981610675),(-1621981610645)⟩,⟨(-1035979312061),(-1035979312034)⟩⟩,⟨⟨(-1552418744017),(-1552418743976)⟩,⟨(-965467134975),(-965467134934)⟩⟩,⟨⟨(-1483194776124),(-1483194776099)⟩,⟨(-897088050104),(-897088050079)⟩⟩,⟨⟨(-1414511875966),(-1414511875936)⟩,⟨(-831028028792),(-831028028764)⟩⟩,⟨⟨(-1346563826955),(-1346563826927)⟩,⟨(-767446829352),(-767446829322)⟩⟩] +lemma kernel15_1_r2_1_eq : ∀ k : Fin 16, kernel15_1Expr 2 1 k = kernel15_1_r2_1 k := by decide +kernel +noncomputable def kernel15_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-1279534977378),(-1279534977350)⟩,⟨(-706478089155),(-706478089124)⟩⟩,⟨⟨(-1213599280220),(-1213599280190)⟩,⟨(-648229686975),(-648229686947)⟩⟩,⟨⟨(-1148919433363),(-1148919433330)⟩,⟨(-592784356871),(-592784356838)⟩⟩,⟨⟨(-1085646129272),(-1085646129239)⟩,⟨(-540200532322),(-540200532289)⟩⟩,⟨⟨(-1023917422046),(-1023917422013)⟩,⟨(-490513397073),(-490513397039)⟩⟩,⟨⟨(-963858217696),(-963858217668)⟩,⟨(-443736117515),(-443736117484)⟩⟩,⟨⟨(-905579891758),(-905579891733)⟩,⟨(-399861230293),(-399861230268)⟩⟩,⟨⟨(-849180036347),(-849180036319)⟩,⟨(-358862157998),(-358862157968)⟩⟩,⟨⟨(-794742336877),(-794742336847)⟩,⟨(-320694825807),(-320694825779)⟩⟩,⟨⟨(-742336576803),(-742336576775)⟩,⟨(-285299351982),(-285299351952)⟩⟩,⟨⟨(-692018766762),(-692018766729)⟩,⟨(-252601785785),(-252601785752)⟩⟩,⟨⟨(-643831392820),(-643831392779)⟩,⟨(-222515867690),(-222515867649)⟩⟩,⟨⟨(-597803777153),(-597803777124)⟩,⟨(-194944787817),(-194944787787)⟩⟩,⟨⟨(-553952542642),(-553952542609)⟩,⟨(-169782920487),(-169782920453)⟩⟩,⟨⟨(-512282172053),(-512282172012)⟩,⟨(-146917514575),(-146917514533)⟩⟩,⟨⟨(-472785651101),(-472785651076)⟩,⟨(-126230321554),(-126230321529)⟩⟩] +lemma kernel15_1_r2_2_eq : ∀ k : Fin 16, kernel15_1Expr 2 2 k = kernel15_1_r2_2 k := by decide +kernel +noncomputable def kernel15_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-435445184445),(-435445184417)⟩,⟨(-107599145598),(-107599145567)⟩⟩,⟨⟨(-400232972219),(-400232972186)⟩,⟨(-90899301909),(-90899301876)⟩⟩,⟨⟨(-367112035411),(-367112035381)⟩,⟨(-76004972788),(-76004972760)⟩⟩,⟨⟨(-336037077555),(-336037077521)⟩,⟨(-62790452454),(-62790452420)⟩⟩,⟨⟨(-306955370619),(-306955370588)⟩,⟨(-51131274608),(-51131274580)⟩⟩,⟨⟨(-279807653234),(-279807653205)⟩,⟨(-40905218824),(-40905218793)⟩⟩,⟨⟨(-254529030075),(-254529030033)⟩,⟨(-31993193838),(-31993193796)⟩⟩,⟨⟨(-231049861583),(-231049861549)⟩,⟨(-24279998124),(-24279998091)⟩⟩,⟨⟨(-209296634344),(-209296634319)⟩,⟨(-17654959770),(-17654959745)⟩⟩,⟨⟨(-189192803171),(-189192803140)⟩,⟨(-12012459182),(-12012459153)⟩⟩,⟨⟨(-170659597002),(-170659596976)⟩,⟨(-7252339788),(-7252339763)⟩⟩,⟨⟨(-153616781994),(-153616781963)⟩,⟨(-3280212992),(-3280212964)⟩⟩,⟨⟨(-137983375943),(-137983375909)⟩,⟨(-7664449),(-7664415)⟩⟩,⟨⟨(-123678309677),(-123678309632)⟩,⟨2647630235,2647630282⟩⟩,⟨⟨(-110621031943),(-110621031909)⟩,⟨4761872022,4761872056⟩⟩,⟨⟨(-98732055527),(-98732055496)⟩,⟨6405178266,6405178295⟩⟩] +lemma kernel15_1_r2_3_eq : ∀ k : Fin 16, kernel15_1Expr 2 3 k = kernel15_1_r2_3 k := by decide +kernel +noncomputable def kernel15_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-87933443312),(-87933443283)⟩,⟨7641687044,7641687074⟩⟩,⟨⟨(-78149233911),(-78149233877)⟩,⟨8529716959,8529716993⟩⟩,⟨⟨(-69305807598),(-69305807564)⟩,⟨9121973611,9121973645⟩⟩,⟨⟨(-61332193823),(-61332193792)⟩,⟨9465794438,9465794467⟩⟩,⟨⟨(-54160322416),(-54160322385)⟩,⟨9603423832,9603423861⟩⟩,⟨⟨(-47725221107),(-47725221076)⟩,⟨9572310964,9572310993⟩⟩,⟨⟨(-41965162692),(-41965162661)⟩,⟨9405423529,9405423558⟩⟩,⟨⟨(-36821765196),(-36821765162)⟩,⟨9131570890,9131570925⟩⟩,⟨⟨(-32240049124),(-32240049093)⟩,⟨8775731172,8775731201⟩⟩,⟨⟨(-28168455608),(-28168455582)⟩,⟨8359377201,8359377227⟩⟩,⟨⟨(-24558829813),(-24558829778)⟩,⟨7900797079,7900797114⟩⟩,⟨⟨(-21366373648),(-21366373619)⟩,⟨7415405709,7415405741⟩⟩,⟨⟨(-18549572044),(-18549572013)⟩,⟨6916044249,6916044278⟩⟩,⟨⟨(-16070096648),(-16070096613)⟩,⟨6413265206,6413265240⟩⟩,⟨⟨(-13892690990),(-13892690955)⟩,⟨5915601294,5915601329⟩⟩,⟨⟨(-11985040686),(-11985040656)⟩,⟨5429816635,5429816666⟩⟩] +lemma kernel15_1_r2_4_eq : ∀ k : Fin 16, kernel15_1Expr 2 4 k = kernel15_1_r2_4 k := by decide +kernel +noncomputable def kernel15_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-10317632049),(-10317632017)⟩,⟨4961139692,4961139721⟩⟩,⟨⟨(-8863602310),(-8863602275)⟩,⟨4513477323,4513477357⟩⟩,⟨⟨(-7598584319),(-7598584287)⟩,⟨4089609976,4089610005⟩⟩,⟨⟨(-6500548253),(-6500548218)⟩,⟨3691368218,3691368253⟩⟩,⟨⟨(-5549642598),(-5549642563)⟩,⟨3319791171,3319791206⟩⟩,⟨⟨(-4728036339),(-4728036309)⟩,⟨2975267531,2975267563⟩⟩,⟨⟨(-4019764145),(-4019764115)⟩,⟨2657660039,2657660071⟩⟩,⟨⟨(-3410575817),(-3410575782)⟩,⟨2366414411,2366414446⟩⟩,⟨⟨(-2887791191),(-2887791147)⟩,⟨2100653840,2100653884⟩⟩,⟨⟨(-2440161486),(-2440161442)⟩,⟨1859260187,1859260230⟩⟩,⟨⟨(-2057737584),(-2057737555)⟩,⟨1640943027,1640943059⟩⟩,⟨⟨(-1731745984),(-1731745948)⟩,⟨1444297663,1444297698⟩⟩,⟨⟨(-1454472370),(-1454472339)⟩,⟨1267853406,1267853435⟩⟩,⟨⟨(-1219153459),(-1219153428)⟩,⟨1110112968,1110112998⟩⟩,⟨⟨(-1019876525),(-1019876490)⟩,⟨969584251,969584286⟩⟩,⟨⟨(-851487059),(-851487028)⟩,⟨844805371,844805403⟩⟩] +lemma kernel15_1_r2_5_eq : ∀ k : Fin 16, kernel15_1Expr 2 5 k = kernel15_1_r2_5 k := by decide +kernel +noncomputable def kernel15_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-709504072),(-709504028)⟩,⟨734363898,734363941⟩⟩,⟨⟨(-590042710),(-590042675)⟩,⟨636911114,636911149⟩⟩,⟨⟨(-489744232),(-489744200)⟩,⟨551172073,551172103⟩⟩,⟨⟨(-405712463),(-405712427)⟩,⟨475952203,475952238⟩⟩,⟨⟨(-335456795),(-335456751)⟩,⟨410140925,410140970⟩⟩,⟨⟨(-276841008),(-276840972)⟩,⟨352713065,352713100⟩⟩,⟨⟨(-228037613),(-228037577)⟩,⟨302728204,302728240⟩⟩,⟨⟨(-187487264),(-187487228)⟩,⟨259328766,259328802⟩⟩,⟨⟨(-153862789),(-153862758)⟩,⟨221736897,221736929⟩⟩,⟨⟨(-126037455),(-126037423)⟩,⟨189250557,189250588⟩⟩,⟨⟨(-103057114),(-103057078)⟩,⟨161239065,161239101⟩⟩,⟨⟨(-84115735),(-84115690)⟩,⟨137138358,137138403⟩⟩,⟨⟨(-68534032),(-68533997)⟩,⟨116445968,116446004⟩⟩,⟨⟨(-55741017),(-55740981)⟩,⟨98716033,98716069⟩⟩,⟨⟨(-45257786),(-45257750)⟩,⟨83554412,83554448⟩⟩,⟨⟨(-36683626),(-36683594)⟩,⟨70613885,70613916⟩⟩] +lemma kernel15_1_r2_6_eq : ∀ k : Fin 16, kernel15_1Expr 2 6 k = kernel15_1_r2_6 k := by decide +kernel +noncomputable def kernel15_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-29684077),(-29684046)⟩,⟨59589523,59589556⟩⟩,⟨⟨(-23980578),(-23980542)⟩,⟨50214478,50214514⟩⟩,⟨⟨(-19341677),(-19341644)⟩,⟨42255880,42255911⟩⟩,⟨⟨(-15575488),(-15575452)⟩,⟨35511111,35511147⟩⟩,⟨⟨(-12523269),(-12523238)⟩,⟨29804378,29804410⟩⟩,⟨⟨(-10054023),(-10053986)⟩,⟨24983540,24983577⟩⟩,⟨⟨(-8059853),(-8059816)⟩,⟨20917291,20917327⟩⟩,⟨⟨(-6452081),(-6452045)⟩,⟨17492582,17492619⟩⟩,⟨⟨(-5157975),(-5157938)⟩,⟨14612296,14612333⟩⟩,⟨⟨(-4118061),(-4118024)⟩,⟨12193229,12193266⟩⟩,⟨⟨(-3283717),(-3283680)⟩,⟨10164200,10164237⟩⟩,⟨⟨(-2615349),(-2615313)⟩,⟨8464493,8464530⟩⟩,⟨⟨(-2080735),(-2080689)⟩,⟨7042413,7042459⟩⟩,⟨⟨(-1653727),(-1653691)⟩,⟨5854018,5854055⟩⟩,⟨⟨(-1313150),(-1313113)⟩,⟨4862013,4862050⟩⟩,⟨⟨(-1041858),(-1041825)⟩,⟨4034849,4034881⟩⟩] +lemma kernel15_1_r2_7_eq : ∀ k : Fin 16, kernel15_1Expr 2 7 k = kernel15_1_r2_7 k := by decide +kernel +noncomputable def kernel15_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-826036),(-825999)⟩,⟨3345846,3345883⟩⟩,⟨⟨(-654553),(-654498)⟩,⟨2772493,2772549⟩⟩,⟨⟨(-518440),(-518412)⟩,⟨2295841,2295869⟩⟩,⟨⟨(-410517),(-410480)⟩,⟨1899919,1899956⟩⟩,⟨⟨(-325028),(-324990)⟩,⟨1571343,1571380⟩⟩,⟨⟨(-257365),(-257327)⟩,⟨1298861,1298898⟩⟩,⟨⟨(-203841),(-203804)⟩,⟨1073080,1073117⟩⟩,⟨⟨(-161529),(-161492)⟩,⟨886139,886177⟩⟩,⟨⟨(-128092),(-128055)⟩,⟨731443,731481⟩⟩,⟨⟨(-101671),(-101634)⟩,⟨603517,603555⟩⟩,⟨⟨(-80809),(-80777)⟩,⟨497790,497823⟩⟩,⟨⟨(-64320),(-64282)⟩,⟨410457,410495⟩⟩,⟨⟨(-51291),(-51254)⟩,⟨338365,338402⟩⟩,⟨⟨(-40997),(-40959)⟩,⟨278848,278885⟩⟩,⟨⟨(-32832),(-32794)⟩,⟨229770,229808⟩⟩,⟨⟨(-26366),(-26328)⟩,⟨189298,189336⟩⟩] +lemma kernel15_1_r2_8_eq : ∀ k : Fin 16, kernel15_1Expr 2 8 k = kernel15_1_r2_8 k := by decide +kernel +noncomputable def kernel15_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-21248),(-21210)⟩,⟨155931,155969⟩⟩,⟨⟨(-17164),(-17126)⟩,⟨128445,128482⟩⟩,⟨⟨(-13926),(-13889)⟩,⟨105799,105837⟩⟩,⟨⟨(-11337),(-11299)⟩,⟨87141,87179⟩⟩,⟨⟨(-9269),(-9217)⟩,⟨71767,71819⟩⟩,⟨⟨(-7593),(-7555)⟩,⟨59120,59158⟩⟩,⟨⟨(-6255),(-6217)⟩,⟨48699,48737⟩⟩,⟨⟨(-5173),(-5134)⟩,⟨40130,40168⟩⟩,⟨⟨(-4304),(-4265)⟩,⟨33066,33104⟩⟩,⟨⟨(-3586),(-3547)⟩,⟨27250,27289⟩⟩,⟨⟨(-3009),(-2971)⟩,⟨22456,22494⟩⟩,⟨⟨(-2517),(-2479)⟩,⟨18527,18565⟩⟩,⟨⟨(-2122),(-2089)⟩,⟨15279,15314⟩⟩,⟨⟨(-1804),(-1766)⟩,⟨12606,12645⟩⟩,⟨⟨(-1529),(-1491)⟩,⟨10402,10441⟩⟩,⟨⟨(-1304),(-1265)⟩,⟨8577,8616⟩⟩] +lemma kernel15_1_r2_9_eq : ∀ k : Fin 16, kernel15_1Expr 2 9 k = kernel15_1_r2_9 k := by decide +kernel +noncomputable def kernel15_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-1121),(-1082)⟩,⟨7087,7126⟩⟩,⟨⟨(-962),(-923)⟩,⟨5858,5897⟩⟩,⟨⟨(-820),(-781)⟩,⟨4844,4882⟩⟩,⟨⟨(-709),(-670)⟩,⟨4005,4044⟩⟩,⟨⟨(-611),(-576)⟩,⟨3303,3336⟩⟩,⟨⟨(-533),(-494)⟩,⟨2735,2774⟩⟩,⟨⟨(-462),(-423)⟩,⟨2266,2305⟩⟩,⟨⟨(-402),(-367)⟩,⟨1882,1915⟩⟩,⟨⟨(-346),(-307)⟩,⟨1543,1582⟩⟩,⟨⟨(-309),(-260)⟩,⟨1275,1324⟩⟩,⟨⟨(-266),(-227)⟩,⟨1054,1093⟩⟩,⟨⟨(-239),(-199)⟩,⟨875,914⟩⟩,⟨⟨(-201),(-162)⟩,⟨740,779⟩⟩,⟨⟨(-174),(-134)⟩,⟨613,652⟩⟩,⟨⟨(-153),(-114)⟩,⟨500,539⟩⟩,⟨⟨(-150),(-96)⟩,⟨410,463⟩⟩] +lemma kernel15_1_r2_10_eq : ∀ k : Fin 16, kernel15_1Expr 2 10 k = kernel15_1_r2_10 k := by decide +kernel +noncomputable def kernel15_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-133),(-94)⟩,⟨343,383⟩⟩,⟨⟨(-114),(-75)⟩,⟨292,331⟩⟩,⟨⟨(-94),(-55)⟩,⟨231,270⟩⟩,⟨⟨(-95),(-56)⟩,⟨188,227⟩⟩,⟨⟨(-73),(-34)⟩,⟨160,200⟩⟩,⟨⟨(-80),(-41)⟩,⟨131,171⟩⟩,⟨⟨(-59),(-19)⟩,⟨104,143⟩⟩,⟨⟨(-62),(-23)⟩,⟨89,129⟩⟩,⟨⟨(-56),(-17)⟩,⟨75,115⟩⟩,⟨⟨(-60),(-20)⟩,⟨60,100⟩⟩,⟨⟨(-44),(-4)⟩,⟨47,86⟩⟩,⟨⟨(-43),(-3)⟩,⟨27,67⟩⟩,⟨⟨(-43),(-3)⟩,⟨27,67⟩⟩,⟨⟨(-42),(-2)⟩,⟨18,58⟩⟩,⟨⟨(-42),(-2)⟩,⟨18,58⟩⟩,⟨⟨(-27),14⟩,⟨4,44⟩⟩] +lemma kernel15_1_r2_11_eq : ∀ k : Fin 16, kernel15_1Expr 2 11 k = kernel15_1_r2_11 k := by decide +kernel +noncomputable def kernel15_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-27),14⟩,⟨4,44⟩⟩,⟨⟨(-27),14⟩,⟨4,44⟩⟩,⟨⟨(-27),14⟩,⟨4,44⟩⟩,⟨⟨(-30),10⟩,⟨(-11),29⟩⟩,⟨⟨(-31),10⟩,⟨(-11),29⟩⟩,⟨⟨(-31),10⟩,⟨(-11),29⟩⟩,⟨⟨(-31),10⟩,⟨(-11),29⟩⟩,⟨⟨(-31),10⟩,⟨(-11),29⟩⟩,⟨⟨(-31),10⟩,⟨(-11),29⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩] +lemma kernel15_1_r2_12_eq : ∀ k : Fin 16, kernel15_1Expr 2 12 k = kernel15_1_r2_12 k := by decide +kernel +noncomputable def kernel15_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩] +lemma kernel15_1_r2_13_eq : ∀ k : Fin 16, kernel15_1Expr 2 13 k = kernel15_1_r2_13 k := by decide +kernel +noncomputable def kernel15_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-31),10⟩,⟨(-11),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩] +lemma kernel15_1_r2_14_eq : ∀ k : Fin 16, kernel15_1Expr 2 14 k = kernel15_1_r2_14 k := by decide +kernel +noncomputable def kernel15_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩] +lemma kernel15_1_r2_15_eq : ∀ k : Fin 16, kernel15_1Expr 2 15 k = kernel15_1_r2_15 k := by decide +kernel +noncomputable def kernel15_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel15_1_r2_0,kernel15_1_r2_1,kernel15_1_r2_2,kernel15_1_r2_3,kernel15_1_r2_4,kernel15_1_r2_5,kernel15_1_r2_6,kernel15_1_r2_7,kernel15_1_r2_8,kernel15_1_r2_9,kernel15_1_r2_10,kernel15_1_r2_11,kernel15_1_r2_12,kernel15_1_r2_13,kernel15_1_r2_14,kernel15_1_r2_15] +lemma kernel15_1_r2_eq (i k : Fin 16) : kernel15_1Expr 2 i k = kernel15_1_r2 i k := by + fin_cases i + · exact kernel15_1_r2_0_eq k + · exact kernel15_1_r2_1_eq k + · exact kernel15_1_r2_2_eq k + · exact kernel15_1_r2_3_eq k + · exact kernel15_1_r2_4_eq k + · exact kernel15_1_r2_5_eq k + · exact kernel15_1_r2_6_eq k + · exact kernel15_1_r2_7_eq k + · exact kernel15_1_r2_8_eq k + · exact kernel15_1_r2_9_eq k + · exact kernel15_1_r2_10_eq k + · exact kernel15_1_r2_11_eq k + · exact kernel15_1_r2_12_eq k + · exact kernel15_1_r2_13_eq k + · exact kernel15_1_r2_14_eq k + · exact kernel15_1_r2_15_eq k +noncomputable def kernel15_1_r3_0 : Fin 16 → CBox := ![⟨⟨489296619513306884160,489296619513306886830⟩,⟨(-837868763637693970253),(-837868763637693967590)⟩⟩,⟨⟨488215624850621143555,488215624850621146225⟩,⟨(-837237242783982388543),(-837237242783982385879)⟩⟩,⟨⟨486058584684538282321,486058584684538284984⟩,⟨(-835974263612929542346),(-835974263612929539689)⟩⟩,⟨⟨482835368251891990648,482835368251891993295⟩,⟨(-834079967347247894173),(-834079967347247891529)⟩⟩,⟨⟨478560706867556952932,478560706867556955573⟩,⟨(-831554605922443565054),(-831554605922443562416)⟩⟩,⟨⟨473254107335103916906,473254107335103919529⟩,⟨(-828398589346763240417),(-828398589346763237797)⟩⟩,⟨⟨466939737259346367175,466939737259346369786⟩,⟨(-824612547590105955926),(-824612547590105953319)⟩⟩,⟨⟨459646282916061510141,459646282916061512724⟩,⟨(-820197405947607345986),(-820197405947607343412)⟩⟩,⟨⟨451406780497228030516,451406780497228033082⟩,⟨(-815154472589304841966),(-815154472589304839410)⟩⟩,⟨⟨442258421712349996912,442258421712349999434⟩,⟨(-809485536791923973098),(-809485536791923970576)⟩⟩,⟨⟨432242334887352348968,432242334887352351469⟩,⟨(-803192976155597419434),(-803192976155597416940)⟩⟩,⟨⟨421403342861508191298,421403342861508193762⟩,⟨(-796279870940144471263),(-796279870940144468806)⟩⟩,⟨⟨409789699139097427094,409789699139097429517⟩,⟨(-788750123514957291352),(-788750123514957288932)⟩⟩,⟨⟨397452803905036375364,397452803905036377756⟩,⟨(-780608580805735552232),(-780608580805735549847)⟩⟩,⟨⟨384446901661426190823,384446901661426193172⟩,⟨(-771861157542038276399),(-771861157542038274056)⟩⟩,⟨⟨370828762383549196543,370828762383549198844⟩,⟨(-762514958063190185398),(-762514958063190183099)⟩⟩] +lemma kernel15_1_r3_0_eq : ∀ k : Fin 16, kernel15_1Expr 3 0 k = kernel15_1_r3_0 k := by decide +kernel +noncomputable def kernel15_1_r3_1 : Fin 16 → CBox := ![⟨⟨356657348227852685933,356657348227852688192⟩,⟨(-752578394427329355439),(-752578394427329353183)⟩⟩,⟨⟨341993467949325828193,341993467949325830403⟩,⟨(-742061298589667120795),(-742061298589667118592)⟩⟩,⟨⟨326899421299719320781,326899421299719322939⟩,⟨(-730975026471207136579),(-730975026471207134421)⟩⟩,⟨⟨311438635779528351374,311438635779528353482⟩,⟨(-719332551827595542767),(-719332551827595540663)⟩⟩,⟨⟨295675298203768588421,295675298203768590467⟩,⟨(-707148547948309208863),(-707148547948309206819)⟩⟩,⟨⟨279673983612535707660,279673983612535709666⟩,⟨(-694439455367409714932),(-694439455367409712926)⟩⟩,⟨⟨263499284110409673878,263499284110409675822⟩,⟨(-681223533946505762254),(-681223533946505760314)⟩⟩,⟨⟨247215440252293745846,247215440252293747739⟩,⟨(-667520897895843719830),(-667520897895843717943)⟩⟩,⟨⟨230885977605748793470,230885977605748795304⟩,⟨(-653353532527644597911),(-653353532527644596080)⟩⟩,⟨⟨214573351109961257101,214573351109961258876⟩,⟨(-638745291783617567181),(-638745291783617565406)⟩⟩,⟨⟨198338599818058882582,198338599818058884302⟩,⟨(-623721875842375658835),(-623721875842375657115)⟩⟩,⟨⟨182241014551720514209,182241014551720515866⟩,⟨(-608310788388360487214),(-608310788388360485559)⟩⟩,⟨⟨166337820914378179659,166337820914378181263⟩,⟨(-592541273407741448051),(-592541273407741446447)⟩⟩,⟨⟨150683880001582980282,150683880001582981824⟩,⟨(-576444231664335040470),(-576444231664335038932)⟩⟩,⟨⟨135331409014467412510,135331409014467413998⟩,⟨(-560052117295554770611),(-560052117295554769122)⟩⟩,⟨⟨120329723825237196709,120329723825237198141⟩,⟨(-543398815250402380334),(-543398815250402378905)⟩⟩] +lemma kernel15_1_r3_1_eq : ∀ k : Fin 16, kernel15_1Expr 3 1 k = kernel15_1_r3_1 k := by decide +kernel +noncomputable def kernel15_1_r3_2 : Fin 16 → CBox := ![⟨⟨105725005363214342436,105725005363214343813⟩,⟨(-526519500564256025582),(-526519500564256024208)⟩⟩,⟨⟨91560091487480343937,91560091487480345254⟩,⟨(-509450480724538516232),(-509450480724538514914)⟩⟩,⟨⟨77874295789381254284,77874295789381255546⟩,⟨(-492229022623295304151),(-492229022623295302889)⟩⟩,⟨⟨64703254527185512290,64703254527185513496⟩,⟨(-474893165813579706559),(-474893165813579705352)⟩⟩,⟨⟨52078802638522453104,52078802638522454252⟩,⟨(-457481523982963183902),(-457481523982963182759)⟩⟩,⟨⟨40028879506696202379,40028879506696203476⟩,⟨(-440033076726480354152),(-440033076726480353055)⟩⟩,⟨⟨28577464877678901618,28577464877678902665⟩,⟨(-422586953840340849444),(-422586953840340848396)⟩⟩,⟨⟨17744545038896051491,17744545038896052483⟩,⟨(-405182214464737176201),(-405182214464737175209)⟩⟩,⟨⟨7546109082373373935,7546109082373374889⟩,⟨(-387857623477515205434),(-387857623477515204483)⟩⟩,⟨⟨(-2005825212900616858),(-2005825212900615969)⟩,⟨(-370651427579366760203),(-370651427579366759310)⟩⟩,⟨⟨(-10903156627679779321),(-10903156627679778470)⟩,⟨(-353601133515133720701),(-353601133515133719850)⟩⟩,⟨⟨(-19141617901324572476),(-19141617901324571663)⟩,⟨(-336743290844935863482),(-336743290844935862667)⟩⟩,⟨⟨(-26720666568707652940),(-26720666568707652177)⟩,⟨(-320113281613876586430),(-320113281613876585670)⟩⟩,⟨⟨(-33643350768262929287),(-33643350768262928578)⟩,⟨(-303745119171324479168),(-303745119171324478460)⟩⟩,⟨⟨(-39916151782573684928),(-39916151782573684251)⟩,⟨(-287671258262028928679),(-287671258262028928001)⟩⟩,⟨⟨(-45548805279170144797),(-45548805279170144156)⟩,⟨(-271922418353916244616),(-271922418353916243975)⟩⟩] +lemma kernel15_1_r3_2_eq : ∀ k : Fin 16, kernel15_1Expr 3 2 k = kernel15_1_r3_2 k := by decide +kernel +noncomputable def kernel15_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-50554103400691804632),(-50554103400691804035)⟩,⟨(-256527421984093734744),(-256527421984093734147)⟩⟩,⟨⟨(-54947680007868333449),(-54947680007868332883)⟩,⟨(-241513049698527568911),(-241513049698527568344)⟩⟩,⟨⟨(-58747781503908595149),(-58747781503908594620)⟩,⟨(-226903912935560958918),(-226903912935560958389)⟩⟩,⟨⟨(-61975025763342018724),(-61975025763342018237)⟩,⟨(-212722345962680505367),(-212722345962680504876)⟩⟩,⟨⟨(-64652151751098490619),(-64652151751098490163)⟩,⟨(-198988317723701082847),(-198988317723701082387)⟩⟩,⟨⟨(-66803762448115884451),(-66803762448115884021)⟩,⟨(-185719364193931442176),(-185719364193931441746)⟩⟩,⟨⟨(-68456063698016047297),(-68456063698016046897)⟩,⟨(-172930541578062980967),(-172930541578062980563)⟩⟩,⟨⟨(-69636601555890508532),(-69636601555890508165)⟩,⟨(-160634400423626567785),(-160634400423626567417)⟩⟩,⟨⟨(-70374000655986393360),(-70374000655986393010)⟩,⟨(-148840980465920037557),(-148840980465920037203)⟩⟩,⟨⟨(-70697706021558864064),(-70697706021558863747)⟩,⟨(-137557825772182592205),(-137557825772182591887)⟩⟩,⟨⟨(-70637730619282841526),(-70637730619282841233)⟩,⟨(-126790019517102474121),(-126790019517102473828)⟩⟩,⟨⟨(-70224410814723412660),(-70224410814723412388)⟩,⟨(-116540237501810183959),(-116540237501810183690)⟩⟩,⟨⟨(-69488171717138332476),(-69488171717138332221)⟩,⟨(-106808819327294855867),(-106808819327294855612)⟩⟩,⟨⟨(-68459304214317243739),(-68459304214317243502)⟩,⟨(-97593855953248313650),(-97593855953248313414)⟩⟩,⟨⟨(-67167755294483235767),(-67167755294483235537)⟩,⟨(-88891292216813575730),(-88891292216813575499)⟩⟩,⟨⟨(-65642933035904553486),(-65642933035904553288)⟩,⟨(-80695042754250445425),(-80695042754250445226)⟩⟩] +lemma kernel15_1_r3_3_eq : ∀ k : Fin 16, kernel15_1Expr 3 3 k = kernel15_1_r3_3 k := by decide +kernel +noncomputable def kernel15_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-63913527419311653323),(-63913527419311653137)⟩,⟨(-72997119663306132320),(-72997119663306132134)⟩⟩,⟨⟨(-62007347887056910761),(-62007347887056910593)⟩,⟨(-65787770165780175354),(-65787770165780175187)⟩⟩,⟨⟨(-59951178339739767558),(-59951178339739767397)⟩,⟨(-59055622478600976667),(-59055622478600976506)⟩⟩,⟨⟨(-57770650029212478124),(-57770650029212477978)⟩,⟨(-52787838077413949468),(-52787838077413949325)⟩⟩,⟨⟨(-55490132579798521658),(-55490132579798521522)⟩,⟨(-46970268538496155013),(-46970268538496154877)⟩⟩,⟨⟨(-53132643150313005607),(-53132643150313005482)⟩,⟨(-41587615171617188700),(-41587615171617188573)⟩⟩,⟨⟨(-50719773540935931634),(-50719773540935931511)⟩,⟨(-36623589706737330313),(-36623589706737330190)⟩⟩,⟨⟨(-48271634853723839027),(-48271634853723838910)⟩,⟨(-32061074369311026339),(-32061074369311026222)⟩⟩,⟨⟨(-45806819135791113493),(-45806819135791113377)⟩,⟨(-27882279770298809039),(-27882279770298808927)⟩⟩,⟨⟨(-43342377271828835584),(-43342377271828835480)⟩,⟨(-24068899145402225151),(-24068899145402225047)⟩⟩,⟨⟨(-40893812249158636796),(-40893812249158636691)⟩,⟨(-20602257600964945860),(-20602257600964945756)⟩⟩,⟨⟨(-38475086795055706961),(-38475086795055706856)⟩,⟨(-17463455158749011835),(-17463455158749011730)⟩⟩,⟨⟨(-36098644283342587228),(-36098644283342587134)⟩,⟨(-14633502535654440430),(-14633502535654440333)⟩⟩,⟨⟨(-33775441725592947688),(-33775441725592947590)⟩,⟨(-12093448744651172349),(-12093448744651172250)⟩⟩,⟨⟨(-31514993601660437803),(-31514993601660437705)⟩,⟨(-9824499757027002735),(-9824499757027002637)⟩⟩,⟨⟨(-29325425244279552609),(-29325425244279552517)⟩,⟨(-7808127620909692195),(-7808127620909692103)⟩⟩] +lemma kernel15_1_r3_4_eq : ∀ k : Fin 16, kernel15_1Expr 3 4 k = kernel15_1_r3_4 k := by decide +kernel +noncomputable def kernel15_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-27213534472466840856),(-27213534472466840770)⟩,⟨(-6026169584419828811),(-6026169584419828725)⟩⟩,⟨⟨(-25184860167382941559),(-25184860167382941470)⟩,⟨(-4460916921454208225),(-4460916921454208142)⟩⟩,⟨⟨(-23243756500943792530),(-23243756500943792455)⟩,⟨(-3095193301898676158),(-3095193301898676081)⟩⟩,⟨⟨(-21393471560320681063),(-21393471560320680984)⟩,⟨(-1912422684172610646),(-1912422684172610566)⟩⟩,⟨⟨(-19636229158895528373),(-19636229158895528299)⟩,⟨(-896686834819640372),(-896686834819640294)⟩⟩,⟨⟨(-17973312684458359075),(-17973312684458358996)⟩,⟨(-32772696056483301),(-32772696056483221)⟩⟩,⟨⟨(-16405149906575675485),(-16405149906575675425)⟩,⟨693790073272870537,693790073272870597⟩⟩,⟨⟨(-14931397745199225152),(-14931397745199225087)⟩,⟨1296700965785656135,1296700965785656197⟩⟩,⟨⟨(-13551026089792324033),(-13551026089792323964)⟩,⟨1788869405961029594,1788869405961029666⟩⟩,⟨⟨(-12262399850620623900),(-12262399850620623840)⟩,⟨2182403880103453253,2182403880103453313⟩⟩,⟨⟨(-11063358519542262704),(-11063358519542262637)⟩,⟨2488608800245790474,2488608800245790541⟩⟩,⟨⟨(-9951292614886227784),(-9951292614886227725)⟩,⟨2717988446399483791,2717988446399483846⟩⟩,⟨⟨(-8923216482192188876),(-8923216482192188822)⟩,⟨2880257304046439314,2880257304046439368⟩⟩,⟨⟨(-7975837018203377224),(-7975837018203377168)⟩,⟨2984356098084436005,2984356098084436064⟩⟩,⟨⟨(-7105617978215203066),(-7105617978215203005)⟩,⟨3038472819804966220,3038472819804966281⟩⟩,⟨⟨(-6308839615512933769),(-6308839615512933714)⟩,⟨3050068048994173245,3050068048994173299⟩⟩] +lemma kernel15_1_r3_5_eq : ∀ k : Fin 16, kernel15_1Expr 3 5 k = kernel15_1_r3_5 k := by decide +kernel +noncomputable def kernel15_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-5581653485184177405),(-5581653485184177352)⟩,⟨3025903887901802240,3025903887901802290⟩⟩,⟨⟨(-4920132322247394487),(-4920132322247394438)⟩,⟨2972075846548516380,2972075846548516432⟩⟩,⟨⟨(-4320314975155833111),(-4320314975155833063)⟩,⟨2894047048524952200,2894047048524952248⟩⟩,⟨⟨(-3778246439850886963),(-3778246439850886928)⟩,⟨2796684161945932650,2796684161945932684⟩⟩,⟨⟨(-3290013096350230680),(-3290013096350230644)⟩,⟨2684294500436145411,2684294500436145451⟩⟩,⟨⟨(-2851773299220789660),(-2851773299220789614)⟩,⟨2560663782842583186,2560663782842583229⟩⟩,⟨⟨(-2459783515204949276),(-2459783515204949228)⟩,⟨2429094086743271255,2429094086743271303⟩⟩,⟨⟨(-2110420235870028222),(-2110420235870028186)⟩,⟨2292441578761998226,2292441578761998265⟩⟩,⟨⟨(-1800197920679248523),(-1800197920679248486)⟩,⟨2153153653290060691,2153153653290060730⟩⟩,⟨⟨(-1525783246677784322),(-1525783246677784281)⟩,⟨2013305159627973390,2013305159627973431⟩⟩,⟨⟨(-1284005955470972152),(-1284005955470972112)⟩,⟨1874633445053790389,1874633445053790426⟩⟩,⟨⟨(-1071866596828166352),(-1071866596828166315)⟩,⟨1738571987257293619,1738571987257293658⟩⟩,⟨⟨(-886541471607251422),(-886541471607251387)⟩,⟨1606282433406035842,1606282433406035876⟩⟩,⟨⟨(-725385075325694619),(-725385075325694584)⟩,⟨1478684904383018428,1478684904383018463⟩⟩,⟨⟨(-585930338185989303),(-585930338185989266)⟩,⟨1356486461104998140,1356486461104998180⟩⟩,⟨⟨(-465886948282506702),(-465886948282506665)⟩,⟨1240207665034741276,1240207665034741316⟩⟩] +lemma kernel15_1_r3_6_eq : ∀ k : Fin 16, kernel15_1Expr 3 6 k = kernel15_1_r3_6 k := by decide +kernel +noncomputable def kernel15_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-363138032651817006),(-363138032651816985)⟩,⟨1130207196865464215,1130207196865464236⟩⟩,⟨⟨(-275735456340465225),(-275735456340465204)⟩,⟨1026704525785786245,1026704525785786267⟩⟩,⟨⟨(-201893983287655206),(-201893983287655178)⟩,⟨929800646704844248,929800646704844277⟩⟩,⟨⟨(-139984525056556880),(-139984525056556838)⟩,⟨839496924369157819,839496924369157861⟩⟩,⟨⟨(-88526684759330355),(-88526684759330327)⟩,⟨755712101529550105,755712101529550133⟩⟩,⟨⟨(-46180784326846716),(-46180784326846675)⟩,⟨678297543358228704,678297543358228741⟩⟩,⟨⟨(-11739543948328192),(-11739543948328163)⟩,⟨607050802350937080,607050802350937109⟩⟩,⟨⟨15880436624274416,15880436624274459⟩,⟨541727597184197759,541727597184197802⟩⟩,⟨⟨37647263867426691,37647263867426726⟩,⟨482052305661959793,482052305661959829⟩⟩,⟨⟨54422290278875145,54422290278875181⟩,⟨427727076222642166,427727076222642202⟩⟩,⟨⟨66968512125882872,66968512125882908⟩,⟨378439664737593632,378439664737593668⟩⟩,⟨⟨75958745104159534,75958745104159576⟩,⟨333870103768208663,333870103768208706⟩⟩,⟨⟨81983512710488519,81983512710488541⟩,⟨293696310310963294,293696310310963316⟩⟩,⟨⟨85558595753235090,85558595753235126⟩,⟨257598735589504190,257598735589504226⟩⟩,⟨⟨87132203779147892,87132203779147914⟩,⟨225264156881530356,225264156881530377⟩⟩,⟨⟨87091740269924746,87091740269924773⟩,⟨196388706912443745,196388706912443769⟩⟩] +lemma kernel15_1_r3_7_eq : ∀ k : Fin 16, kernel15_1Expr 3 7 k = kernel15_1_r3_7 k := by decide +kernel +noncomputable def kernel15_1_r3_8 : Fin 16 → CBox := ![⟨⟨85770143270069693,85770143270069734⟩,⟨170680231208374101,170680231208374139⟩⟩,⟨⟨83451791681353743,83451791681353765⟩,⟨147860058161325533,147860058161325555⟩⟩,⟨⟨80377974848331294,80377974848331323⟩,⟨127664260583430594,127664260583430623⟩⟩,⟨⟨76751929326876888,76751929326876910⟩,⟨109844481361280364,109844481361280386⟩⟩,⟨⟨72743451946760615,72743451946760637⟩,⟨94168389591810807,94168389591810829⟩⟩,⟨⟨68493102530230793,68493102530230822⟩,⟨80419827396637711,80419827396637740⟩⟩,⟨⟨64116012996291164,64116012996291188⟩,⟨68398701562764632,68398701562764659⟩⟩,⟨⟨59705322151901919,59705322151901948⟩,⟨57920668318328157,57920668318328186⟩⟩,⟨⟨55335257333908769,55335257333908799⟩,⟨48816653981148959,48816653981148988⟩⟩,⟨⟨51063885304775880,51063885304775909⟩,⟨40932248959884330,40932248959884360⟩⟩,⟨⟨46935555503884801,46935555503884826⟩,⟨34127007674408422,34127007674408449⟩⟩,⟨⟨42983058992923976,42983058992923998⟩,⟨28273682414325838,28273682414325861⟩⟩,⟨⟨39229526282491541,39229526282491575⟩,⟨23257414983117803,23257414983117835⟩⟩,⟨⟨35690086755723558,35690086755723581⟩,⟨18974906182819831,18974906182819853⟩⟩,⟨⟨32373311675902072,32373311675902096⟩,⟨15333579775809375,15333579775809402⟩⟩,⟨⟨29282461834863406,29282461834863431⟩,⟨12250754505965653,12250754505965680⟩⟩] +lemma kernel15_1_r3_8_eq : ∀ k : Fin 16, kernel15_1Expr 3 8 k = kernel15_1_r3_8 k := by decide +kernel +noncomputable def kernel15_1_r3_9 : Fin 16 → CBox := ![⟨⟨26416559817753094,26416559817753122⟩,⟨9652835056300804,9652835056300828⟩⟩,⟨⟨23771305671360978,23771305671361000⟩,⟨7474530445796217,7474530445796239⟩⟩,⟨⟨21339853506185548,21339853506185575⟩,⟨5658106303702531,5658106303702555⟩⟩,⟨⟨19113465269243459,19113465269243487⟩,⟨4152675682365297,4152675682365322⟩⟩,⟨⟨17082056622991730,17082056622991752⟩,⟨2913531556129672,2913531556129694⟩⟩,⟨⟨15234648578307898,15234648578307921⟩,⟨1901522880113994,1901522880114016⟩⟩,⟨⟨13559737274652263,13559737274652288⟩,⟨1082475024839385,1082475024839413⟩⟩,⟨⟨12045593092766535,12045593092766558⟩,⟨426654537663518,426654537663541⟩⟩,⟨⟨10680499135508728,10680499135508751⟩,⟨(-91722512593112),(-91722512593089)⟩⟩,⟨⟨9452938028596524,9452938028596547⟩,⟨(-494939896634188),(-494939896634165)⟩⟩,⟨⟨8351734980403992,8351734980404017⟩,⟨(-802189995684575),(-802189995684547)⟩⟩,⟨⟨7366164101557006,7366164101557034⟩,⟨(-1029943991173212),(-1029943991173187)⟩⟩,⟨⟨6486024122047759,6486024122047782⟩,⟨(-1192285691494249),(-1192285691494227)⟩⟩,⟨⟨5701688855539472,5701688855539500⟩,⟨(-1301211344579635),(-1301211344579609)⟩⟩,⟨⟨5004137045814958,5004137045814988⟩,⟨(-1366897849616066),(-1366897849616036)⟩⟩,⟨⟨4384965586321656,4384965586321691⟩,⟨(-1397941792222379),(-1397941792222346)⟩⟩] +lemma kernel15_1_r3_9_eq : ∀ k : Fin 16, kernel15_1Expr 3 9 k = kernel15_1_r3_9 k := by decide +kernel +noncomputable def kernel15_1_r3_10 : Fin 16 → CBox := ![⟨⟨3836389527129316,3836389527129352⟩,⟨(-1401571695450677),(-1401571695450644)⟩⟩,⟨⟨3351231770464004,3351231770464027⟩,⟨(-1383835813401536),(-1383835813401513)⟩⟩,⟨⟨2922904902082609,2922904902082634⟩,⟨(-1349767703096251),(-1349767703096223)⟩⟩,⟨⟨2545387206671971,2545387206671999⟩,⟨(-1303531700401820),(-1303531700401795)⟩⟩,⟨⟨2213194566683495,2213194566683520⟩,⟨(-1248550303068568),(-1248550303068540)⟩⟩,⟨⟨1921349641060727,1921349641060755⟩,⟨(-1187615333161710),(-1187615333161684)⟩⟩,⟨⟨1665349458796268,1665349458796292⟩,⟨(-1122984616341348),(-1122984616341325)⟩⟩,⟨⟨1441132337945240,1441132337945273⟩,⟨(-1056465779801170),(-1056465779801134)⟩⟩,⟨⟨1245044849615135,1245044849615163⟩,⟨(-989488636786499),(-989488636786473)⟩⟩,⟨⟨1073809384778305,1073809384778333⟩,⟨(-923167495473141),(-923167495473115)⟩⟩,⟨⟨924492746010862,924492746010893⟩,⟨(-858354605103262),(-858354605103231)⟩⟩,⟨⟨794476073220867,794476073220893⟩,⟨(-795685833730114),(-795685833730086)⟩⟩,⟨⟨681426319140201,681426319140227⟩,⟨(-735619560455278),(-735619560455250)⟩⟩,⟨⟨583269414142367,583269414142403⟩,⟨(-678469661097966),(-678469661097933)⟩⟩,⟨⟨498165198406117,498165198406145⟩,⟨(-624433370025414),(-624433370025388)⟩⟩,⟨⟨424484150419039,424484150419065⟩,⟨(-573614712419155),(-573614712419126)⟩⟩] +lemma kernel15_1_r3_10_eq : ∀ k : Fin 16, kernel15_1Expr 3 10 k = kernel15_1_r3_10 k := by decide +kernel +noncomputable def kernel15_1_r3_11 : Fin 16 → CBox := ![⟨⟨360785902398262,360785902398288⟩,⟨(-526044120425316),(-526044120425288)⟩⟩,⟨⟨305799503709381,305799503709412⟩,⟨(-481694773198565),(-481694773198534)⟩⟩,⟨⟨258405371316969,258405371316993⟩,⟨(-440496134472698),(-440496134472674)⟩⟩,⟨⟨217618850412638,217618850412661⟩,⟨(-402345101591832),(-402345101591808)⟩⟩,⟨⟨182575297529671,182575297529694⟩,⟨(-367115126491406),(-367115126491383)⟩⟩,⟨⟨152516591710074,152516591710103⟩,⟨(-334663621482627),(-334663621482601)⟩⟩,⟨⟨126778975825641,126778975825670⟩,⟨(-304837920413295),(-304837920413269)⟩⟩,⟨⟨104782129276579,104782129276608⟩,⟨(-277480028401233),(-277480028401207)⟩⟩,⟨⟨86019374418277,86019374418311⟩,⟨(-252430360422602),(-252430360422566)⟩⟩,⟨⟨70048921711333,70048921711357⟩,⟨(-229530640162084),(-229530640162061)⟩⟩,⟨⟨56486062350058,56486062350090⟩,⟨(-208626105292325),(-208626105292294)⟩⟩,⟨⟨44996221669036,44996221669060⟩,⟨(-189567143366937),(-189567143366913)⟩⟩,⟨⟨35288791686908,35288791686937⟩,⟨(-172210463432906),(-172210463432880)⟩⟩,⟨⟨27111666506855,27111666506894⟩,⟨(-156419891966980),(-156419891966941)⟩⟩,⟨⟨20246409780992,20246409781021⟩,⟨(-142066867519255),(-142066867519229)⟩⟩,⟨⟨14503988930241,14503988930265⟩,⟨(-129030696232546),(-129030696232522)⟩⟩] +lemma kernel15_1_r3_11_eq : ∀ k : Fin 16, kernel15_1Expr 3 11 k = kernel15_1_r3_11 k := by decide +kernel +noncomputable def kernel15_1_r3_12 : Fin 16 → CBox := ![⟨⟨9721016188915,9721016188944⟩,⟨(-117198619951467),(-117198619951440)⟩⟩,⟨⟨5756441738803,5756441738830⟩,⟨(-106465739719586),(-106465739719557)⟩⟩,⟨⟨2488649157250,2488649157289⟩,⟨(-96734829886549),(-96734829886509)⟩⟩,⟨⟨(-187091909060),(-187091909034)⟩,⟨(-87916071632141),(-87916071632112)⟩⟩,⟨⟨(-2360856542202),(-2360856542172)⟩,⟨(-79926729305696),(-79926729305669)⟩⟩,⟨⟨(-4110015435894),(-4110015435862)⟩,⟨(-72690788434193),(-72690788434161)⟩⟩,⟨⟨(-5500938702588),(-5500938702559)⟩,⟨(-66138570452579),(-66138570452552)⟩⟩,⟨⟨(-6590481976116),(-6590481976087)⟩,⟨(-60206336044773),(-60206336044747)⟩⟩,⟨⟨(-7427281011401),(-7427281011374)⟩,⟨(-54835886360914),(-54835886360885)⟩⟩,⟨⟨(-8052878097857),(-8052878097827)⟩,⟨(-49974169215356),(-49974169215330)⟩⟩,⟨⟨(-8502700988341),(-8502700988309)⟩,⟨(-45572895597112),(-45572895597080)⟩⟩,⟨⟨(-8806912685244),(-8806912685215)⟩,⟨(-41588170382038),(-41588170382011)⟩⟩,⟨⟨(-8991148300834),(-8991148300810)⟩,⟨(-37980139969033),(-37980139969009)⟩⟩,⟨⟨(-9077153303812),(-9077153303780)⟩,⟨(-34712658626987),(-34712658626955)⟩⟩,⟨⟨(-9083335759904),(-9083335759872)⟩,⟨(-31752974596329),(-31752974596297)⟩⟩,⟨⟨(-9025243654542),(-9025243654512)⟩,⟨(-29071436405550),(-29071436405523)⟩⟩] +lemma kernel15_1_r3_12_eq : ∀ k : Fin 16, kernel15_1Expr 3 12 k = kernel15_1_r3_12 k := by decide +kernel +noncomputable def kernel15_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-8915977033001),(-8915977032972)⟩,⟨(-26641219411859),(-26641219411832)⟩⟩,⟨⟨(-8766543493243),(-8766543493216)⟩,⟨(-24438072231537),(-24438072231507)⟩⟩,⟨⟨(-8586164503287),(-8586164503254)⟩,⟨(-22440082470681),(-22440082470648)⟩⟩,⟨⟨(-8382539075077),(-8382539075037)⟩,⟨(-20627460983471),(-20627460983431)⟩⟩,⟨⟨(-8162070497891),(-8162070497853)⟩,⟨(-18982343758986),(-18982343758951)⟩⟩,⟨⟨(-7930061103891),(-7930061103863)⟩,⟨(-17488610457702),(-17488610457673)⟩⟩,⟨⟨(-7690879396786),(-7690879396754)⟩,⟨(-16131718574528),(-16131718574495)⟩⟩,⟨⟨(-7448103311002),(-7448103310977)⟩,⟨(-14898552189956),(-14898552189932)⟩⟩,⟨⟨(-7204642875124),(-7204642875092)⟩,⟨(-13777284276634),(-13777284276602)⟩⟩,⟨⟨(-6962845121252),(-6962845121227)⟩,⟨(-12757251550844),(-12757251550819)⟩⟩,⟨⟨(-6724583704315),(-6724583704285)⟩,⟨(-11828840892952),(-11828840892925)⟩⟩,⟨⟨(-6491335365842),(-6491335365810)⟩,⟨(-10983386403184),(-10983386403152)⟩⟩,⟨⟨(-6264245089498),(-6264245089460)⟩,⟨(-10213076207652),(-10213076207617)⟩⟩,⟨⟨(-6044181545397),(-6044181545364)⟩,⟨(-9510868181248),(-9510868181216)⟩⟩,⟨⟨(-5831784203024),(-5831784202994)⟩,⟨(-8870413807375),(-8870413807348)⟩⟩,⟨⟨(-5627503303245),(-5627503303205)⟩,⟨(-8285989448366),(-8285989448326)⟩⟩] +lemma kernel15_1_r3_13_eq : ∀ k : Fin 16, kernel15_1Expr 3 13 k = kernel15_1_r3_13 k := by decide +kernel +noncomputable def kernel15_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-5431633716320),(-5431633716295)⟩,⟨(-7752434353492),(-7752434353467)⟩⟩,⟨⟨(-5244343570370),(-5244343570343)⟩,⟨(-7265094783163),(-7265094783133)⟩⟩,⟨⟨(-5065698411731),(-5065698411690)⟩,⟨(-6819773677362),(-6819773677321)⟩⟩,⟨⟨(-4895681552252),(-4895681552220)⟩,⟨(-6412685344194),(-6412685344161)⟩⟩,⟨⟨(-4734211166208),(-4734211166181)⟩,⟨(-6040414688431),(-6040414688401)⟩⟩,⟨⟨(-4581154620197),(-4581154620167)⟩,⟨(-5699880542526),(-5699880542499)⟩⟩,⟨⟨(-4436340450499),(-4436340450466)⟩,⟨(-5388302701340),(-5388302701308)⟩⟩,⟨⟨(-4299568343508),(-4299568343479)⟩,⟨(-5103172298464),(-5103172298436)⟩⟩,⟨⟨(-4170617423491),(-4170617423459)⟩,⟨(-4842225195455),(-4842225195423)⟩⟩,⟨⟨(-4049253108157),(-4049253108130)⟩,⟨(-4603418086624),(-4603418086594)⟩⟩,⟨⟨(-3935232754910),(-3935232754878)⟩,⟨(-4384907050250),(-4384907050218)⟩⟩,⟨⟨(-3828310287836),(-3828310287808)⟩,⟨(-4185028303352),(-4185028303323)⟩⟩,⟨⟨(-3728239968000),(-3728239967967)⟩,⟨(-4002280941262),(-4002280941229)⟩⟩,⟨⟨(-3634779445289),(-3634779445248)⟩,⟨(-3835311464505),(-3835311464464)⟩⟩,⟨⟨(-3547692209868),(-3547692209843)⟩,⟨(-3682899915939),(-3682899915915)⟩⟩,⟨⟨(-3466749543522),(-3466749543498)⟩,⟨(-3543947468925),(-3543947468900)⟩⟩] +lemma kernel15_1_r3_14_eq : ∀ k : Fin 16, kernel15_1Expr 3 14 k = kernel15_1_r3_14 k := by decide +kernel +noncomputable def kernel15_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-3391732056115),(-3391732056087)⟩,⟨(-3417465323520),(-3417465323490)⟩⟩,⟨⟨(-3322430879629),(-3322430879604)⟩,⟨(-3302564782970),(-3302564782945)⟩⟩,⟨⟨(-3258648581140),(-3258648581102)⟩,⟨(-3198448396119),(-3198448396084)⟩⟩,⟨⟨(-3200199846592),(-3200199846562)⟩,⟨(-3104402063445),(-3104402063417)⟩⟩,⟨⟨(-3146911979587),(-3146911979539)⟩,⟨(-3019788016034),(-3019788015986)⟩⟩,⟨⟨(-3098625251760),(-3098625251732)⟩,⟨(-2944038586300),(-2944038586270)⟩⟩,⟨⟨(-3055193136645),(-3055193136613)⟩,⟨(-2876650699093),(-2876650699061)⟩⟩,⟨⟨(-3016482452530),(-3016482452502)⟩,⟨(-2817181019561),(-2817181019531)⟩⟩,⟨⟨(-2982373436940),(-2982373436915)⟩,⟨(-2765241702308),(-2765241702283)⟩⟩,⟨⟨(-2952759770562),(-2952759770537)⟩,⟨(-2720496692994),(-2720496692970)⟩⟩,⟨⟨(-2927548566290),(-2927548566260)⟩,⟨(-2682658540093),(-2682658540065)⟩⟩,⟨⟨(-2906660335539),(-2906660335509)⟩,⟨(-2651485680275),(-2651485680247)⟩⟩,⟨⟨(-2890028942471),(-2890028942438)⟩,⟨(-2626780166603),(-2626780166570)⟩⟩,⟨⟨(-2877601554219),(-2877601554189)⟩,⟨(-2608385813440),(-2608385813412)⟩⟩,⟨⟨(-2869338593702),(-2869338593674)⟩,⟨(-2596186737144),(-2596186737114)⟩⟩,⟨⟨(-2865213699974),(-2865213699944)⟩,⟨(-2590106275807),(-2590106275779)⟩⟩] +lemma kernel15_1_r3_15_eq : ∀ k : Fin 16, kernel15_1Expr 3 15 k = kernel15_1_r3_15 k := by decide +kernel +noncomputable def kernel15_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel15_1_r3_0,kernel15_1_r3_1,kernel15_1_r3_2,kernel15_1_r3_3,kernel15_1_r3_4,kernel15_1_r3_5,kernel15_1_r3_6,kernel15_1_r3_7,kernel15_1_r3_8,kernel15_1_r3_9,kernel15_1_r3_10,kernel15_1_r3_11,kernel15_1_r3_12,kernel15_1_r3_13,kernel15_1_r3_14,kernel15_1_r3_15] +lemma kernel15_1_r3_eq (i k : Fin 16) : kernel15_1Expr 3 i k = kernel15_1_r3 i k := by + fin_cases i + · exact kernel15_1_r3_0_eq k + · exact kernel15_1_r3_1_eq k + · exact kernel15_1_r3_2_eq k + · exact kernel15_1_r3_3_eq k + · exact kernel15_1_r3_4_eq k + · exact kernel15_1_r3_5_eq k + · exact kernel15_1_r3_6_eq k + · exact kernel15_1_r3_7_eq k + · exact kernel15_1_r3_8_eq k + · exact kernel15_1_r3_9_eq k + · exact kernel15_1_r3_10_eq k + · exact kernel15_1_r3_11_eq k + · exact kernel15_1_r3_12_eq k + · exact kernel15_1_r3_13_eq k + · exact kernel15_1_r3_14_eq k + · exact kernel15_1_r3_15_eq k +noncomputable def kernel15_1_r4_0 : Fin 16 → CBox := ![⟨⟨79473259527962212374410137,79473259527962215228077624⟩,⟨107479573573863503754388654,107479573573863506609948052⟩⟩,⟨⟨79481580653336239966654068,79481580653336242818529405⟩,⟨107357612297184086829467351,107357612297184089683231925⟩⟩,⟨⟨79497983754344720406251921,79497983754344723254540763⟩,⟨107113938973985264838129192,107113938973985267688301937⟩⟩,⟨⟨79521992193040886581510656,79521992193040889424424830⟩,⟨106749051873516041930553953,106749051873516044775344036⟩⟩,⟨⟨79552895156564390686406545,79552895156564393522167090⟩,⟨106263697915649912312095787,106263697915649915149721622⟩⟩,⟨⟨79589752602686258866416811,79589752602686261693257029⟩,⟨105658872072483635904603898,105658872072483638733296182⟩⟩,⟨⟨79631401808421862868403655,79631401808421865684572045⟩,⟨104935816541437512347751180,104935816541437515165755834⟩⟩,⟨⟨79676465482954203310908363,79676465482954206114671802⟩,⟨104096019665577352764363953,104096019665577355569945324⟩⟩,⟨⟨79723361396669549056691721,79723361396669551846337885⟩,⟨103141214571555750355645940,103141214571555753147089233⟩⟩,⟨⟨79770313468838093675936619,79770313468838096449777813⟩,⟨102073377490733511250513763,102073377490733514026128838⟩⟩,⟨⟨79815364247412487870959656,79815364247412490627334147⟩,⟨100894725724776139648065873,100894725724776142406188629⟩⟩,⟨⟨79856388705607818084785493,79856388705607820822062344⟩,⟨99607715213403453918073487,99607715213403456657070684⟩⟩,⟨⟨79891109271411135779438510,79891109271411138496017207⟩,⟨98215037659073622220172368,98215037659073624938441253⟩⟩,⟨⟨79917111997992756432056250,79917111997992759126373723⟩,⟨96719617161268624968590816,96719617161268627664566166⟩⟩,⟨⟨79931863775203421004103939,79931863775203423674631378⟩,⟨95124606311769618577870260,95124606311769621250021178⟩⟩,⟨⟨79932730474991516451411198,79932730474991519096663395⟩,⟨93433381701911139195101752,93433381701911141841941054⟩⟩] +lemma kernel15_1_r4_0_eq : ∀ k : Fin 16, kernel15_1Expr 4 0 k = kernel15_1_r4_0 k := by decide +kernel +noncomputable def kernel15_1_r4_1 : Fin 16 → CBox := ![⟨⟨79916995916715412902917744,79916995916715415521446355⟩,⟨91649538793315133434158648,91649538793315136054236090⟩⟩,⟨⟨79881881532011832699194536,79881881532011835289602463⟩,⟨89776886105050787597352840,89776886105050790189269539⟩⟩,⟨⟨79824566603167520434007624,79824566603167522994936623⟩,⟨87819438672553697574396819,87819438672553700136792828⟩⟩,⟨⟨79742208943884538152421493,79742208943884540682570364⟩,⟨85781410736965673559142945,85781410736965676090715482⟩⟩,⟨⟨79631965886985520568743983,79631965886985523066850738⟩,⟨83667207627809716391414667,83667207627809718890900267⟩⟩,⟨⟨79491015440029750141826628,79491015440029752606695370⟩,⟨81481416807066359306156971,81481416807066361772358382⟩⟩,⟨⟨79316577467057986289652168,79316577467057988720126022⟩,⟨79228798048728214437718301,79228798048728216869477405⟩⟩,⟨⟨79105934752805222433040825,79105934752805224828033958⟩,⟨76914272734727601728515551,76914272734727604124745395⟩⟩,⟨⟨78856453804764193490688350,78856453804764195849151596⟩,⟨74542912255694129161756230,74542912255694131521406650⟩⟩,⟨⟨78565605248492398474344288,78565605248492400795310945⟩,⟨72119925513230230037774701,72119925513230232359878133⟩⟩,⟨⟨78230983672570149299812563,78230983672570151582350114⟩,⟨69650645529207397794483806,69650645529207400078106988⟩⟩,⟨⟨77850326781668833542456684,77850326781668835785717894⟩,⟨67140515176888682285061570,67140515176888684529356650⟩⟩,⟨⟨77421533719301930158930609,77421533719301932362098010⟩,⟨64595072058369378787559351,64595072058369380991708388⟩⟩,⟨⟨76942682426022749631297015,76942682426022751793651693⟩,⟨62019932562785242140342380,62019932562785244303626108⟩⟩,⟨⟨76412045904109554821067034,76412045904109556941915117⟩,⟨59420775149846723696219984,59420775149846725817944310⟩⟩,⟨⟨75828107266137775783444051,75828107266137777862191054⟩,⟨56803322913393962237345782,56803322913393964316916129⟩⟩] +lemma kernel15_1_r4_1_eq : ∀ k : Fin 16, kernel15_1Expr 4 1 k = kernel15_1_r4_1 k := by decide +kernel +noncomputable def kernel15_1_r4_2 : Fin 16 → CBox := ![⟨⟨75189573452266814259402934,75189573452266816295471740⟩,⟨54173325489701887012876665,54173325489701889049715969⟩⟩,⟨⟨74495387509540434919295720,74495387509540436912225787⟩,⟨51536540385066707080223160,51536540385066709073871043⟩⟩,⟨⟨73744739335978140173145746,73744739335978142122487284⟩,⟨48898713806642364208314743,48898713806642366158321715⟩⟩,⟨⟨72937074802671291677258701,72937074802671293582831709⟩,⟨46265561089437215225856416,46265561089437217132042974⟩⟩,⟨⟨72072103178430905208668951,72072103178430907070186289⟩,⟨43642746820698924878161006,43642746820698926740240567⟩⟩,⟨⟨71149802793690656587894707,71149802793690658405148953⟩,⟨41035864770485339104400137,41035864770485340922165947⟩⟩,⟨⟨70170424893263414511466911,70170424893263416284244641⟩,⟨38450417743923185193657207,38450417743923186966896622⟩⟩,⟨⟨69134495641085799440529268,69134495641085801168740812⟩,⟨35891797476384922891064906,35891797476384924619689145⟩⟩,⟨⟨68042816254155262776620421,68042816254155264460158711⟩,⟨33365264697466639636986720,33365264697466641320889709⟩⟩,⟨⟨66896461257350414266630167,66896461257350415905535111⟩,⟨30875929493137407324661840,30875929493137408963884584⟩⟩,⟨⟨65696774865601292561125499,65696774865601294155410399⟩,⟨28428732097676521773735409,28428732097676523368292403⟩⟩,⟨⟨64445365514807772039575199,64445365514807773589386579⟩,⟨26028424247957068053749121,26028424247957069603788178⟩⟩,⟨⟨63144098577850840661818672,63144098577850842167267179⟩,⟨23679551232225040550305887,23679551232225042055939021⟩⟩,⟨⟨61795087316857865687493995,61795087316857867149221343⟩,⟨21386434763731758627717657,21386434763731760089588028⟩⟩,⟨⟨60400682137420978524637050,60400682137420979943125339⟩,⟨19153156806389540188635905,19153156806389541607227146⟩⟩,⟨⟨58963458224577970327595631,58963458224577971703181019⟩,⟨16983544475040110262889407,16983544475040111638539255⟩⟩] +lemma kernel15_1_r4_2_eq : ∀ k : Fin 16, kernel15_1Expr 4 2 k = kernel15_1_r4_2 k := by decide +kernel +noncomputable def kernel15_1_r4_3 : Fin 16 → CBox := ![⟨⟨57486201653898948903017936,57486201653898950235977173⟩,⟨14881156126973553707464563,14881156126973555040451413⟩⟩,⟨⟨55971894083833535583235219,55971894083833536874013156⟩,⟨12849268754052319646225473,12849268754052320936995877⟩⟩,⟨⟨54423696147421376113257622,54423696147421377362230165⟩,⟨10890866776237249617747782,10890866776237250866679393⟩⟩,⟨⟨52844929672418735333166993,52844929672418736540853253⟩,⟨9008632327555637665571966,9008632327555638873185667⟩⟩,⟨⟨51239058868720180994191947,51239058868720182161034764⟩,⟨7204937114686442233895972,7204937114686443400636420⟩⟩,⟨⟨49609670630541684440370235,49609670630541685566980869⟩,⟨5481835916472185256888662,5481835916472186383368945⟩⟩,⟨⟨47960454108077126410078800,47960454108077127496983430⟩,⟨3841061779922521236058064,3841061779922522322806212⟩⟩,⟨⟨46295179709155509371786285,46295179709155510419883672⟩,⟨2284022954785700368222342,2284022954785701416138960⟩⟩,⟨⟨44617677695738010839323325,44617677695738011849243998⟩,⟨811801594677294036210892,811801594677295045928372⟩⟩,⟨⟨42931816542846075373955003,42931816542846076346432438⟩,⟨(-574845761773831254516184),(-574845761773830282262514)⟩⟩,⟨⟨41241481228665654712807005,41241481228665655648470529⟩,⟨(-1875485931111239861042838),(-1875485931111238925621822)⟩⟩,⟨⟨39550551624108807483365442,39550551624108808382985468⟩,⟨(-3090005062837609435535050),(-3090005062837608536174452)⟩⟩,⟨⟨37862881148031775296633758,37862881148031776160978259⟩,⟨(-4218602885932232842622657),(-4218602885932231978552484)⟩⟩,⟨⟨36182275850627509510532358,36182275850627510340449722⟩,⟨(-5261785269858514653635237),(-5261785269858513824005309)⟩⟩,⟨⟨34512474082269089263750966,34512474082269090059948607⟩,⟨(-6220355160048957590676624),(-6220355160048956794777824)⟩⟩,⟨⟨32857126898336385428447984,32857126898336386191769880⟩,⟨(-7095401961517068177899125),(-7095401961517067414881424)⟩⟩] +lemma kernel15_1_r4_3_eq : ∀ k : Fin 16, kernel15_1Expr 4 3 k = kernel15_1_r4_3 k := by decide +kernel +noncomputable def kernel15_1_r4_4 : Fin 16 → CBox := ![⟨⟨31219779342388086020225847,31219779342388086751392918⟩,⟨(-7888289457182427709299009),(-7888289457182426978438106)⟩⟩,⟨⟨29603852740538853001020796,29603852740538853700920788⟩,⟨(-8600642359557083495159178),(-8600642359557082795566218)⟩⟩,⟨⟨28012628129177431196232216,28012628129177431865625780⟩,⟨(-9234331605489716079466108),(-9234331605489715410379361)⟩⟩,⟨⟨26449230926341483098554945,26449230926341483738329789⟩,⟨(-9791458513573111201935517),(-9791458513573110562466266)⟩⟩,⟨⟨24916616944287594562341233,24916616944287595173259298⟩,⟨(-10274337932479565511225515),(-10274337932479564900610854)⟩⟩,⟨⟨23417559827210505616608552,23417559827210506199582374⟩,⟨(-10685480515803678154113392),(-10685480515803677571439899)⟩⟩,⟨⟨21954639983833703253324312,21954639983833703809137883⟩,⟨(-11027574264885975048326412),(-11027574264885974492809256)⟩⟩,⟨⟨20530235069880683994179346,20530235069880684523733067⟩,⟨(-11303465485506215233001291),(-11303465485506214703739305)⟩⟩,⟨⟨19146512060413801427875008,19146512060413801931937573⟩,⟨(-11516139307233802583247387),(-11516139307233802079471149)⟩⟩,⟨⟨17805420936869322141282574,17805420936869322620767144⟩,⟨(-11668699915586193569934917),(-11668699915586193090730629)⟩⟩,⟨⟨16508689998496656912324080,16508689998496657368010936⟩,⟨(-11764350646976350689079639),(-11764350646976350233666428)⟩⟩,⟨⟨15257822792997682974659995,15257822792997683407433540⟩,⟨(-11806374094748817040187153),(-11806374094748816607680096)⟩⟩,⟨⟨14054096646624653666326421,14054096646624654078281013⟩,⟨(-11798112371451923506298203),(-11798112371451923094585877)⟩⟩,⟨⟨12898562759991199813352078,12898562759991200205338104⟩,⟨(-11742947667930587378433123),(-11742947667930586986665244)⟩⟩,⟨⟨11792047822529775771236778,11792047822529776143888065⟩,⟨(-11644283243927185414234036),(-11644283243927185041778030)⟩⟩,⟨⟨10735157086028638204060007,10735157086028638558107233⟩,⟨(-11505524977740257513677485),(-11505524977740257159803939)⟩⟩] +lemma kernel15_1_r4_4_eq : ∀ k : Fin 16, kernel15_1Expr 4 4 k = kernel15_1_r4_4 k := by decide +kernel +noncomputable def kernel15_1_r4_5 : Fin 16 → CBox := ![⟨⟨9728278826126963874696197,9728278826126964210746847⟩,⟨(-11330063594220004760444444),(-11330063594220004424547113)⟩⟩,⟨⟨8771590110148208412277531,8771590110148208731061705⟩,⟨(-11121257681096084970307623),(-11121257681096084651657638)⟩⟩,⟨⟨7865063780303475064828787,7865063780303475366954671⟩,⟨(-10882417593468216061277486),(-10882417593468215759267868)⟩⟩,⟨⟨7008476553175668575099518,7008476553175668861260112⟩,⟨(-10616790335383336856319905),(-10616790335383336570258849)⟩⟩,⟨⟨6201418129560957194750423,6201418129560957465524517⟩,⟨(-10327545495920731399771801),(-10327545495920731129081669)⟩⟩,⟨⟨5443301203237748651200010,5443301203237748907268252⟩,⟨(-10017762305258936992847480),(-10017762305258936736848761)⟩⟩,⟨⟨4733372253077839886648528,4733372253077840128579889⟩,⟨(-9690417863957641298225054),(-9690417863957641056349878)⟩⟩,⟨⟨4070723000114251181435554,4070723000114251409871667⟩,⟨(-9348376586305956622016889),(-9348376586305956393624680)⟩⟩,⟨⟨3454302409722348855434361,3454302409722349070908154⟩,⟨(-8994380886214681615766782),(-8994380886214681400325645)⟩⟩,⟨⟨2882929118924965500896476,2882929118924965704033366⟩,⟨(-8631043121908979595665398),(-8631043121908979392550909)⟩⟩,⟨⟨2355304169951987530809975,2355304169951987722145062⟩,⟨(-8260838803747224729308307),(-8260838803747224537986326)⟩⟩,⟨⟨1870023933509001145362445,1870023933509001325520152⟩,⟨(-7886101057981044344737404),(-7886101057981044164584434)⟩⟩,⟨⟨1425593108663218687081543,1425593108663218856540017⟩,⟨(-7509016328300202186175147),(-7509016328300202016713905)⟩⟩,⟨⟨1020437690751198572071364,1020437690751198731382836⟩,⟨(-7131621286681841298045990),(-7131621286681841138725053)⟩⟩,⟨⟨652917804154672796569504,652917804154672946205913⟩,⟨(-6755800915482018521467485),(-6755800915482018371815702)⟩⟩,⟨⟨321340303072456195334299,321340303072456335884456⟩,⟨(-6383287713950137317560072),(-6383287713950137176989353)⟩⟩] +lemma kernel15_1_r4_5_eq : ∀ k : Fin 16, kernel15_1Expr 4 5 k = kernel15_1_r4_5 k := by decide +kernel +noncomputable def kernel15_1_r4_6 : Fin 16 → CBox := ![⟨⟨23971050425653925911433,23971050425654057786530⟩,⟨(-6015661974481310866300913),(-6015661974481310734400751)⟩⟩,⟨⟨(-240953207346788729132070),(-240953207346788605454157)⟩,⟨(-5654353067000701408019167),(-5654353067000701284312337)⟩⟩,⟨⟨(-475213443734545730988162),(-475213443734545615113738)⟩,⟨(-5300641663935506812678007),(-5300641663935506696771406)⟩⟩,⟨⟨(-680597499496094719917134),(-680597499496094611411493)⟩,⟨(-4955662833297788132710832),(-4955662833297788024170306)⟩⟩,⟨⟨(-858889830813548472543951),(-858889830813548371047737)⟩,⟨(-4620409923483618764688601),(-4620409923483618663155319)⟩⟩,⟨⟨(-1011861906319387114593905),(-1011861906319387019696743)⟩,⟨(-4295739160486067029209296),(-4295739160486066934273771)⟩⟩,⟨⟨(-1141263292168901628083616),(-1141263292168901539347047)⟩,⟨(-3982374876303128037687393),(-3982374876303127948912444)⟩⟩,⟨⟨(-1248813455536402384179858),(-1248813455536402301210888)⟩,⟨(-3680915286366487371433732),(-3680915286366487288426622)⟩⟩,⟨⟨(-1336194308305707946247684),(-1336194308305707868756314)⟩,⟨(-3391838733781345920939355),(-3391838733781345843410308)⟩⟩,⟨⟨(-1405043504398597068718116),(-1405043504398596996369889)⟩,⟨(-3115510318999902007450175),(-3115510318999901935064921)⟩⟩,⟨⟨(-1456948496222297465016940),(-1456948496222297397538826)⟩,⟨(-2852188835191230207131144),(-2852188835191230139616828)⟩⟩,⟨⟨(-1493441348192511848703587),(-1493441348192511785796228)⟩,⟨(-2602033931950656240584872),(-2602033931950656177642264)⟩⟩,⟨⟨(-1515994298265519590786511),(-1515994298265519532196208)⟩,⟨(-2365113433038838471602892),(-2365113433038838412978416)⟩⟩,⟨⟨(-1526016051944537845648605),(-1526016051944537791071054)⟩,⟨(-2141410737476685770867559),(-2141410737476685716257005)⟩⟩,⟨⟨(-1524848787354049994848403),(-1524848787354049944060279)⟩,⟨(-1930832237465965963263159),(-1930832237465965912443287)⟩⟩,⟨⟨(-1513765844732791342023253),(-1513765844732791294778734)⟩,⟨(-1733214691174310607606393),(-1733214691174310560332076)⟩⟩] +lemma kernel15_1_r4_6_eq : ∀ k : Fin 16, kernel15_1Expr 4 6 k = kernel15_1_r4_6 k := by decide +kernel +noncomputable def kernel15_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-1493970069102616674933254),(-1493970069102616631029542)⟩,⟨(-1548332493334274360141548),(-1548332493334274316211777)⟩⟩,⟨⟨(-1466592770937534592292651),(-1466592770937534551504571)⟩,⟨(-1375904791777037357835130),(-1375904791777037317024435)⟩⟩,⟨⟨(-1432693266386135641473809),(-1432693266386135603619084)⟩,⟨(-1215602403372182863517651),(-1215602403372182825643475)⟩⟩,⟨⟨(-1393258955983832980186792),(-1393258955983832945067459)⟩,⟨(-1067054488298782625318359),(-1067054488298782590182474)⟩⟩,⟨⟨(-1349205898812886736882448),(-1349205898812886704337584)⟩,⟨(-929854947056855851031720),(-929854947056855818472948)⟩⟩,⟨⟨(-1301379837704767877699367),(-1301379837704767847547922)⟩,⟨(-803568510074043629075827),(-803568510074043598912875)⟩⟩,⟨⟨(-1250557630301146111763506),(-1250557630301146083858419)⟩,⟨(-687736495107464746807750),(-687736495107464718893322)⟩⟩,⟨⟨(-1197449040561135989709396),(-1197449040561135963875912)⟩,⟨(-581882212828620629984713),(-581882212828620604143848)⟩⟩,⟨⟨(-1142698845583196243098809),(-1142698845583196219139646)⟩,⟨(-485516005959740644346598),(-485516005959740620381807)⟩⟩,⟨⟨(-1086889213356307912184269),(-1086889213356307889966493)⟩,⟨(-398139912059620385662891),(-398139912059620363441051)⟩⟩,⟨⟨(-1030542308220025942106689),(-1030542308220025921524381)⟩,⟨(-319251944499122239341258),(-319251944499122218756273)⟩⟩,⟨⟨(-974123082348101599928040),(-974123082348101580865566)⟩,⟨(-248349990291206589365289),(-248349990291206570301358)⟩⟩,⟨⟨(-918042213426003576660743),(-918042213426003559025614)⟩,⟨(-184935327224477450846067),(-184935327224477433210557)⟩⟩,⟨⟨(-862659150819037275826897),(-862659150819037259514059)⟩,⟨(-128515766176094448470588),(-128515766176094432158296)⟩⟩,⟨⟨(-808285234875662271592458),(-808285234875662256517941)⟩,⟨(-78608427539069714117262),(-78608427539069699044093)⟩⟩,⟨⟨(-755186856532082515623297),(-755186856532082501695906)⟩,⟨(-34742163385818419409910),(-34742163385818405484554)⟩⟩] +lemma kernel15_1_r4_7_eq : ∀ k : Fin 16, kernel15_1Expr 4 7 k = kernel15_1_r4_7 k := by decide +kernel +noncomputable def kernel15_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-703588627033140086660368),(-703588627033140073807866)⟩,⟨3540360694844309044874,3540360694844321894767⟩⟩,⟨⟨(-653676530317273016803406),(-653676530317273004935980)⟩,⟨36680908200558097563735,36680908200558109428075⟩⟩,⟨⟨(-605601033388914795481835),(-605601033388914784534764)⟩,⟨65104221277617123213145,65104221277617134156745⟩⟩,⟨⟨(-559480132782505748526457),(-559480132782505738429729)⟩,⟨89216858509947074120009,89216858509947084212950⟩⟩,⟨⟨(-515402317973986057710562),(-515402317973986048408543)⟩,⟨109406301274720471985640,109406301274720481283638⟩⟩,⟨⟨(-473429435287609426748687),(-473429435287609418169230)⟩,⟨126040308381409943484654,126040308381409952059963⟩⟩,⟨⟨(-433599438451260584906840),(-433599438451260577000759)⟩,⟨139466498370371050761541,139466498370371058663519⟩⟩,⟨⟨(-395929014449066635102267),(-395929014449066627817162)⟩,⟨150012138764899015176883,150012138764899022457953⟩⟩,⟨⟨(-360416075686606264751718),(-360416075686606258045899)⟩,⟨157984121722198801254081,157984121722198807955958⟩⟩,⟨⟨(-327042111705759369737310),(-327042111705759363560813)⟩,⟨163669105888282130049735,163669105888282136222404⟩⟩,⟨⟨(-295774395751057307672884),(-295774395751057301989274)⟩,⟨167333804803692560554797,167333804803692566234706⟩⟩,⟨⟨(-266568043388503403794686),(-266568043388503398564540)⟩,⟨169225402905595053739862,169225402905595058966451⟩⟩,⟨⟨(-239367922105589561567454),(-239367922105589556759835)⟩,⟨169572081002141000069541,169572081002141004873747⟩⟩,⟨⟨(-214110412374891221381396),(-214110412374891216961274)⟩,⟨168583634032994074424828,168583634032994078841693⟩⟩,⟨⟨(-190725022043065454525808),(-190725022043065450465732)⟩,⟨166452164952470835322506,166452164952470839379480⟩⟩,⟨⟨(-169135857114544260159639),(-169135857114544256426359)⟩,⟨163352839657259293187852,163352839657259296918268⟩⟩] +lemma kernel15_1_r4_8_eq : ∀ k : Fin 16, kernel15_1Expr 4 8 k = kernel15_1_r4_8 k := by decide +kernel +noncomputable def kernel15_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-149262953039010308279134),(-149262953039010304843059)⟩,⟨159444689009000600551008,159444689009000603984614⟩⟩,⟨⟨(-131023471489943135990562),(-131023471489943132826887)⟩,⟨154871445154680253184422,154871445154680256345977⟩⟩,⟨⟨(-114332768345695658770741),(-114332768345695655860447)⟩,⟨149762400508045776570406,149762400508045779478898⟩⟩,⟨⟨(-99105339163478374746959),(-99105339163478372069305)⟩,⟨144233278908211711399846,144233278908211714075983⟩⟩,⟨⟨(-85255648880008717408459),(-85255648880008714947418)⟩,⟨138387109604103454003718,138387109604103456463495⟩⟩,⟨⟨(-72698852790833450239161),(-72698852790833447976361)⟩,⟨132315095814097456132568,132315095814097458394340⟩⟩,⟨⟨(-61351416064318032211785),(-61351416064318030133040)⟩,⟨126097470669557175826510,126097470669557177904434⟩⟩,⟨⟨(-51131639147127690394905),(-51131639147127688484790)⟩,⟨119804334361049698714915,119804334361049700624389⟩⟩,⟨⟨(-41960096426861474858454),(-41960096426861473104315)⟩,⟨113496467260566980841936,113496467260566982595596⟩⟩,⟨⟨(-33759995445385598653460),(-33759995445385597040801)⟩,⟨107226114687279861278934,107226114687279862891259⟩⟩,⟨⟨(-26457463814122906263942),(-26457463814122904782546)⟩,⟨101037739814823523051791,101037739814823524532971⟩⟩,⟨⟨(-19981770780477425866743),(-19981770780477424505487)⟩,⟨94968741982719812243997,94968741982719813605149⟩⟩,⟨⟨(-14265490142598230418598),(-14265490142598229168985)⟩,⟨89050138372297161683068,89050138372297162932670⟩⟩,⟨⟨(-9244610917129693268509),(-9244610917129692120724)⟩,⟨83307207638399086276203,83307207638399087424059⟩⟩,⟨⟨(-4858601840129911615535),(-4858601840129910562108)⟩,⟨77760094653188869433635,77760094653188870487201⟩⟩,⟨⟨(-1050435432954816060062),(-1050435432954815092838)⟩,⟨72424376019131632225590,72424376019131633193012⟩⟩] +lemma kernel15_1_r4_9_eq : ∀ k : Fin 16, kernel15_1Expr 4 9 k = kernel15_1_r4_9 k := by decide +kernel +noncomputable def kernel15_1_r4_10 : Fin 16 → CBox := ![⟨⟨2233423000121629816127,2233423000121630705451⟩,⟨67311586447072746034021,67311586447072746923589⟩⟩,⟨⟨5043056450900921247395,5043056450900922065953⟩,⟨62429706475061176266999,62429706475061177085838⟩⟩,⟨⟨7425162750606635055285,7425162750606635808159⟩,⟨57783612327426474818248,57783612327426475571441⟩⟩,⟨⟨9423142343873741164259,9423142343873741857089⟩,⟨53375488985156969217936,53375488985156969911105⟩⟩,⟨⟨11077203432964943999792,11077203432964944636776⟩,⟨49205207761609190922638,49205207761609191559983⟩⟩,⟨⟨12424480996085819973210,12424480996085820559302⟩,⟨45270669855902769921396,45270669855902770507862⟩⟩,⟨⟨13499166535826410894443,13499166535826411433505⟩,⟨41568117493977561529678,41568117493977562069111⟩⟩,⟨⟨14332645751244081513560,14332645751244082010028⟩,⟨38092414368160823663991,38092414368160824160825⟩⟩,⟨⟨14953641647926125560534,14953641647926126017349⟩,⟨34837297154099455537836,34837297154099455995001⟩⟩,⟨⟨15388360903031774244127,15388360903031774664873⟩,⟨31795599922833501435922,31795599922833501857010⟩⟩,⟨⟨15660641585760592039849,15660641585760592427123⟩,⟨28959453279251538976807,28959453279251539364411⟩⟩,⟨⟨15792100597275906663406,15792100597275907020123⟩,⟨26320460049625761880129,26320460049625762237165⟩⟩,⟨⟨15802279437528025407977,15802279437528025736596⟩,⟨23869849313620620997220,23869849313620621326146⟩⟩,⟨⟨15708787129678386291825,15708787129678386595345⟩,⟨21598610533129235599471,21598610533129235903280⟩⟩,⟨⟨15527439336189796669232,15527439336189796949425⟩,⟨19497609474309941283597,19497609474309941564067⟩⟩,⟨⟨15272392884606446225346,15272392884606446484222⟩,⟨17557687552826880887990,17557687552826881147127⟩⟩] +lemma kernel15_1_r4_10_eq : ∀ k : Fin 16, kernel15_1Expr 4 10 k = kernel15_1_r4_10 k := by decide +kernel +noncomputable def kernel15_1_r4_11 : Fin 16 → CBox := ![⟨⟨14956275086267863073700,14956275086267863312671⟩,⟨15769746157859682202192,15769746157859682441416⟩⟩,⟨⟨14590307378495215818004,14590307378495216038882⟩,⟨14124817430017327906119,14124817430017328127230⟩⟩,⟨⟨14184422951079593765472,14184422951079593969573⟩,⟨12614122883718524372335,12614122883718524576647⟩⟩,⟨⟨13747378132195086795406,13747378132195086984182⟩,⟨11229121177510789239997,11229121177510789428958⟩⟩,⟨⟨13286857408214845418655,13286857408214845593136⟩,⟨9961546247606646374557,9961546247606646549196⟩⟩,⟨⟨12809572037417992180130,12809572037417992341595⟩,⟨8803436931831507258449,8803436931831507420048⟩⟩,⟨⟨12321352290343180541238,12321352290343180690631⟩,⟨7747159124231453733709,7747159124231453883219⟩⟩,⟨⟨11827233410669127825308,11827233410669127963849⟩,⟨6785421415635509242503,6785421415635509381141⟩⟩,⟨⟨11331535441061917632485,11331535441061917760853⟩,⟨5911285093203881127085,5911285093203881255540⟩⟩,⟨⟨10837937099469633356685,10837937099469633475813⟩,⟨5118169292976097622728,5118169292976097741925⟩⟩,⟨⟨10349543923871758693944,10349543923871758804452⟩,⟨4399852024087798251858,4399852024087798362427⟩⟩,⟨⟨9868950928459593632440,9868950928459593735060⟩,⟨3750467711965063883681,3750467711965063986354⟩⟩,⟨⟨9398300032536025198353,9398300032536025293594⟩,⟨3164501840643225093303,3164501840643225188585⟩⟩,⟨⟨8939332535921402489108,8939332535921402577630⟩,⟨2636783211518436776483,2636783211518436865035⟩⟩,⟨⟨8493436922119418721653,8493436922119418803889⟩,⟨2162474277375291119360,2162474277375291201618⟩⟩,⟨⟨8061692273653569248628,8061692273653569325188⟩,⟨1737059956429037232737,1737059956429037309308⟩⟩] +lemma kernel15_1_r4_11_eq : ∀ k : Fin 16, kernel15_1Expr 4 11 k = kernel15_1_r4_11 k := by decide +kernel +noncomputable def kernel15_1_r4_12 : Fin 16 → CBox := ![⟨⟨7644907583490105364589,7644907583490105435870⟩,⟨1356335281310077165180,1356335281310077236468⟩⟩,⟨⟨7243657242915977004168,7243657242915977070630⟩,⟨1016392192291180889489,1016392192291180955952⟩⟩,⟨⟨6858312980179665345972,6858312980179665407931⟩,⟨713605742469182744962,713605742469182806918⟩⟩,⟨⟨6489072516112036028935,6489072516112036086774⟩,⟨444619944890402482947,444619944890402540783⟩⟩,⟨⟨6135985193252514026862,6135985193252514080823⟩,⟨206333457559877227083,206333457559877281030⟩⟩,⟨⟨5798974824091334832396,5798974824091334882824⟩,⟨(-4114728308505559669),(-4114728308505509254)⟩⟩,⟨⟨5477859992232251264210,5477859992232251311335⟩,⟨(-189359458777111550021),(-189359458777111502912)⟩⟩,⟨⟨5172372027868762706880,5172372027868762751018⟩,⟨(-351823332685607269604),(-351823332685607225483)⟩⟩,⟨⟨4882170866197097670707,4882170866197097712046⟩,⟨(-493730269946620675249),(-493730269946620633930)⟩⟩,⟨⟨4606858984470268164771,4606858984470268203544⟩,⟨(-617118659325864268774),(-617118659325864230024)⟩⟩,⟨⟨4345993600505455975325,4345993600505456011706⟩,⟨(-723854028936000172004),(-723854028936000135649)⟩⟩,⟨⟨4099097302737546095325,4099097302737546129498⟩,⟨(-815641197049361441966),(-815641197049361407816)⟩⟩,⟨⟨3865667269483586563795,3865667269483586595877⟩,⟨(-894035873246553474879),(-894035873246553442823)⟩⟩,⟨⟨3645183223041199625430,3645183223041199655622⟩,⟨(-960455690555913510719),(-960455690555913480553)⟩⟩,⟨⟨3437114252662305037814,3437114252662305066250⟩,⟨(-1016190658282212433703),(-1016190658282212405292)⟩⟩,⟨⟨3240924629377349788195,3240924629377349815022⟩,⟨(-1062413032840125636201),(-1062413032840125609398)⟩⟩] +lemma kernel15_1_r4_12_eq : ∀ k : Fin 16, kernel15_1Expr 4 12 k = kernel15_1_r4_12 k := by decide +kernel +noncomputable def kernel15_1_r4_13 : Fin 16 → CBox := ![⟨⟨3056078725134035864303,3056078725134035889607⟩,⟨(-1100186610255736752601),(-1100186610255736727323)⟩⟩,⟨⟨2882045138784080777240,2882045138784080801152⟩,⟨(-1130475449223014620103),(-1130475449223014596216)⟩⟩,⟨⟨2718300122115984679879,2718300122115984702480⟩,⟨(-1154152037835744392270),(-1154152037835744369693)⟩⟩,⟨⟨2564330390395487616477,2564330390395487637865⟩,⟨(-1172004920481540641095),(-1172004920481540619733)⟩⟩,⟨⟨2419635393734643630499,2419635393734643650753⟩,⟨(-1184745803995238039183),(-1184745803995238018955)⟩⟩,⟨⟨2283729118054849099558,2283729118054849118790⟩,⟨(-1193016164125674653158),(-1193016164125674633952)⟩⟩,⟨⟨2156141477423056634532,2156141477423056652787⟩,⟨(-1197393374764312105232),(-1197393374764312087001)⟩⟩,⟨⟨2036419353103931492973,2036419353103931510336⟩,⟨(-1198396383298619155570),(-1198396383298619138227)⟩⟩,⟨⟨1924127328760847431581,1924127328760847448092⟩,⟨(-1196490955961296991253),(-1196490955961296974762)⟩⟩,⟨⟨1818848165830055724497,1818848165830055740238⟩,⟨(-1192094517213738732958),(-1192094517213738717240)⟩⟩,⟨⟨1720183058158217731026,1720183058158217746028⟩,⟨(-1185580607086569480103),(-1185580607086569465120)⟩⟩,⟨⟨1627751700505959488569,1627751700505959502907⟩,⟨(-1177282980052769096600),(-1177282980052769082284)⟩⟩,⟨⟨1541192201450973102370,1541192201450973116074⟩,⟨(-1167499368474473247655),(-1167499368474473233973)⟩⟩,⟨⟨1460160867545272267623,1460160867545272280742⟩,⟨(-1156494932982054616104),(-1156494932982054603002)⟩⟩,⟨⟨1384331882264713383226,1384331882264713395805⟩,⟨(-1144505421347264474232),(-1144505421347264461673)⟩⟩,⟨⟨1313396900307697254459,1313396900307697266530⟩,⟨(-1131740056530121200573),(-1131740056530121188518)⟩⟩] +lemma kernel15_1_r4_13_eq : ∀ k : Fin 16, kernel15_1Expr 4 13 k = kernel15_1_r4_13 k := by decide +kernel +noncomputable def kernel15_1_r4_14 : Fin 16 → CBox := ![⟨⟨1247064575127843474872,1247064575127843486450⟩,⟨(-1118384173636704944289),(-1118384173636704932730)⟩⟩,⟨⟨1185060035197220938482,1185060035197220949628⟩,⟨(-1104601624543128379918),(-1104601624543128368790)⟩⟩,⟨⟨1127124322368455228832,1127124322368455239566⟩,⟨(-1090536967937427831221),(-1090536967937427820503)⟩⟩,⟨⟨1073013803813024734300,1073013803813024744654⟩,⟨(-1076317461520723079106),(-1076317461520723068770)⟩⟩,⟨⟨1022499567337938569192,1022499567337938579175⟩,⟨(-1062054872103889671457),(-1062054872103889661489)⟩⟩,⟨⟨975366808403750186235,975366808403750195888⟩,⟨(-1047847118346055811487),(-1047847118346055801849)⟩⟩,⟨⟨931414215864845491391,931414215864845500731⟩,⟨(-1033779759914371617160),(-1033779759914371607834)⟩⟩,⟨⟨890453362310836456071,890453362310836465127⟩,⟨(-1019927345906875195172),(-1019927345906875186133)⟩⟩,⟨⟨852308103889681172351,852308103889681181119⟩,⟨(-1006354634476588229139),(-1006354634476588220385)⟩⟩,⟨⟨816813993624094146358,816813993624094154873⟩,⟨(-993117694728634691141),(-993117694728634682639)⟩⟩,⟨⟨783817711479374675956,783817711479374684243⟩,⟨(-980264901135530955448),(-980264901135530947175)⟩⟩,⟨⟨753176513790590061661,753176513790590069727⟩,⟨(-967837829930273160621),(-967837829930273152567)⟩⟩,⟨⟨724757704098821003103,724757704098821010951⟩,⟨(-955872066193113284271),(-955872066193113276434)⟩⟩,⟨⟨698438126969654055607,698438126969654063280⟩,⟨(-944397929645999964591),(-944397929645999956928)⟩⟩,⟨⟨674103685962997961002,674103685962997968493⟩,⟨(-933441126508073381443),(-933441126508073373966)⟩⟩,⟨⟨651648886583210564386,651648886583210571716⟩,⟨(-923023334145432182137),(-923023334145432174818)⟩⟩] +lemma kernel15_1_r4_14_eq : ∀ k : Fin 16, kernel15_1Expr 4 14 k = kernel15_1_r4_14 k := by decide +kernel +noncomputable def kernel15_1_r4_15 : Fin 16 → CBox := ![⟨⟨630976404754885008819,630976404754885015999⟩,⟨(-913162724667382622327),(-913162724667382615155)⟩⟩,⟨⟨611996681135658691747,611996681135658698791⟩,⟨(-903874433078017702002),(-903874433078017694971)⟩⟩,⟨⟨594627541386981473266,594627541386981480166⟩,⟨(-895170975084534290355),(-895170975084534283465)⟩⟩,⟨⟨578793842371461416321,578793842371461423108⟩,⟨(-887062619190303331426),(-887062619190303324646)⟩⟩,⟨⟨564427144126335877915,564427144126335884591⟩,⟨(-879557717259376841830),(-879557717259376835164)⟩⟩,⟨⟨551465407372466534547,551465407372466541126⟩,⟨(-872662997327786262750),(-872662997327786256180)⟩⟩,⟨⟨539852716253186010597,539852716253186017098⟩,⟨(-866383822053555670019),(-866383822053555663528)⟩⟩,⟨⟨529539025953924014000,529539025953924020416⟩,⟨(-860724415839694668491),(-860724415839694662084)⟩⟩,⟨⟨520479934828795905565,520479934828795911898⟩,⟨(-855688063330420435257),(-855688063330420428931)⟩⟩,⟨⟨512636480651578830435,512636480651578836719⟩,⟨(-851277281668367758381),(-851277281668367752103)⟩⟩,⟨⟨505974960613371763586,505974960613371769821⟩,⟨(-847493968607482014873),(-847493968607482008648)⟩⟩,⟨⟨500466774705650628278,500466774705650634477⟩,⟨(-844339528300582172653),(-844339528300582166464)⟩⟩,⟨⟨496088292153540990629,496088292153540996782⟩,⟨(-841814976320189811612),(-841814976320189805463)⟩⟩,⟨⟨492820740598297916914,492820740598297923041⟩,⟨(-839921025224139658127),(-839921025224139652006)⟩⟩,⟨⟨490650117768740689055,490650117768740695164⟩,⟨(-838658151741743849121),(-838658151741743843018)⟩⟩,⟨⟨489567125427422148232,489567125427422154335⟩,⟨(-838026646429933628379),(-838026646429933622283)⟩⟩] +lemma kernel15_1_r4_15_eq : ∀ k : Fin 16, kernel15_1Expr 4 15 k = kernel15_1_r4_15 k := by decide +kernel +noncomputable def kernel15_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel15_1_r4_0,kernel15_1_r4_1,kernel15_1_r4_2,kernel15_1_r4_3,kernel15_1_r4_4,kernel15_1_r4_5,kernel15_1_r4_6,kernel15_1_r4_7,kernel15_1_r4_8,kernel15_1_r4_9,kernel15_1_r4_10,kernel15_1_r4_11,kernel15_1_r4_12,kernel15_1_r4_13,kernel15_1_r4_14,kernel15_1_r4_15] +lemma kernel15_1_r4_eq (i k : Fin 16) : kernel15_1Expr 4 i k = kernel15_1_r4 i k := by + fin_cases i + · exact kernel15_1_r4_0_eq k + · exact kernel15_1_r4_1_eq k + · exact kernel15_1_r4_2_eq k + · exact kernel15_1_r4_3_eq k + · exact kernel15_1_r4_4_eq k + · exact kernel15_1_r4_5_eq k + · exact kernel15_1_r4_6_eq k + · exact kernel15_1_r4_7_eq k + · exact kernel15_1_r4_8_eq k + · exact kernel15_1_r4_9_eq k + · exact kernel15_1_r4_10_eq k + · exact kernel15_1_r4_11_eq k + · exact kernel15_1_r4_12_eq k + · exact kernel15_1_r4_13_eq k + · exact kernel15_1_r4_14_eq k + · exact kernel15_1_r4_15_eq k +noncomputable def kernel15_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-85987313075772222241581920582),(-85987313075772220320860911257)⟩,⟨215310500036417445955635391357,215310500036417447876580772760⟩⟩,⟨⟨(-85840124939296554752130585387),(-85840124939296552831814114365)⟩,⟨215257314399436918083446885647,215257314399436920003991043802⟩⟩,⟨⟨(-85546041291953990334677770146),(-85546041291953988415173627509)⟩,⟨215150792598461329379518890317,215150792598461331299257340106⟩⟩,⟨⟨(-85105647043722672643885326707),(-85105647043722670725601179309)⟩,⟨214990634725730971177708532887,214990634725730973096236893085⟩⟩,⟨⟨(-84519818703415503571702393843),(-84519818703415501655045800985)⟩,⟨214776393779771722889750099464,214776393779771724806664067461⟩⟩,⟨⟨(-83789723342781069926086254738),(-83789723342781068011464543058)⟩,⟨214507479082183294029801030060,214507479082183295944696497423⟩⟩,⟨⟨(-82916817201241908014760221281),(-82916817201241906102580555753)⟩,⟨214183160807709174379597040262,214183160807709176292070012288⟩⟩,⟨⟨(-81902843919468781714179139900),(-81902843919468779804848253334)⟩,⟨213802575605677353675036508820,213802575605677355584683365746⟩⟩,⟨⟨(-80749832387352741578143855923),(-80749832387352739672068368887)⟩,⟨213364733285515466905499125762,213364733285515468811916293591⟩⟩,⟨⟨(-79460094189505064195622777263),(-79460094189505062293208533902)⟩,⟨212868524533722187293884283354,212868524533722189196668889115⟩⟩,⟨⟨(-78036220629226098060680407718),(-78036220629226096162332616328)⟩,⟨212312729624433102531088235684,212312729624433104429837957945⟩⟩,⟨⟨(-76481079309972928283257003152),(-76481079309972926389232339448)⟩,⟨211696028080569646407506402985,211696028080569648301967371443⟩⟩,⟨⟨(-74797810251755675862389846367),(-74797810251755673973081053379)⟩,⟨211017009237520701063255370728,211017009237520702953037535744⟩⟩,⟨⟨(-72989821518633617121582782143),(-72989821518633615237380520008)⟩,⟨210274183656396209217160573780,210274183656396211101875859415⟩⟩,⟨⟨(-71060784332592692505264259752),(-71060784332592690626560710399)⟩,⟨209465995329129761600824248834,209465995329129763480082939773⟩⟩,⟨⟨(-69014627648589736839495677787),(-69014627648589734966679963304)⟩,⟨208590834613113143633725370703,208590834613113145507140687043⟩⟩] +lemma kernel15_1_r5_0_eq : ∀ k : Fin 16, kernel15_1Expr 5 0 k = kernel15_1_r5_0 k := by decide +kernel +noncomputable def kernel15_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-66855532165466824607111140450),(-66855532165466822740575180781)⟩,⟨207647051828641990788001375195,207647051828641992655183606636⟩⟩,⟨⟨(-64587923747788709273365042100),(-64587923747788707413495453910)⟩,⟨206632971448260987939213199469,206632971448260989799777800864⟩⟩,⟨⟨(-62216466234450749150429572415),(-62216466234450747297617178807)⟩,⟨205546906803143570781890648487,205546906803143572635448722098⟩⟩,⟨⟨(-59746053611153130287268522059),(-59746053611153128441897429011)⟩,⟨204387175227949992863383331707,204387175227949994709552546523⟩⟩,⟨⟨(-57181801525544487432796092550),(-57181801525544485595256852524)⟩,⟨203152113562204935540692765535,203152113562204937379084185714⟩⟩,⟨⟨(-54529038126004592659179035152),(-54529038126004590829851442181)⟩,⟨201840093923148280538782921603,201840093923148282369018209205⟩⟩,⟨⟨(-51793294207657446321577394064),(-51793294207657444500850021295)⟩,⟨200449539662267431133914365453,200449539662267432955606234571⟩⟩,⟨⟨(-48980292652274006597938987016),(-48980292652274004786187918570)⟩,⟨198978941415344075676383959430,198978941415344077489157444038⟩⟩,⟨⟨(-46095937152224336382098037518),(-46095937152224334579711703993)⟩,⟨197426873153869891453382633518,197426873153869893256850243328⟩⟩,⟨⟨(-43146300212553779534715084451),(-43146300212553777742062638392)⟩,⟨195792008144131368151924656568,195792008144131369945718004635⟩⟩,⟨⟨(-40137610429563817942101471819),(-40137610429563816159567757680)⟩,⟨194073134719159955707877914133,194073134719159957491612736947⟩⟩,⟨⟨(-37076239048947750259211155278),(-37076239048947748487160421046)⟩,⟨192269171768115305291471305662,192269171768115307064783756987⟩⟩,⟨⟨(-33968685811531950946319324300),(-33968685811531949185136071090)⟩,⟨190379183847540217918805693427,190379183847540219681311484160⟩⟩,⟨⟨(-30821564099968478839406372770),(-30821564099968477089390771502)⟩,⟨188402395819317944402060305799,188402395819317946153459183268⟩⟩,⟨⟨(-27641585405273257151995496091),(-27641585405273255413393143768)⟩,⟨186338206921095354313918658797,186338206921095356053964587140⟩⟩,⟨⟨(-24435543137861020788573094343),(-24435543137861019061729543057)⟩,⟨184186204176426229673389195487,184186204176426231401736282744⟩⟩] +lemma kernel15_1_r5_1_eq : ∀ k : Fin 16, kernel15_1Expr 5 1 k = kernel15_1_r5_1 k := by decide +kernel +noncomputable def kernel15_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-21210295813645124862674938042),(-21210295813645123147967548233)⟩,⟨181946175053951520189404044019,181946175053951521905674396991⟩⟩,⟨⟨(-17972749651795197099475571460),(-17972749651795195397236374511)⟩,⟨179618119287578370537425813170,179618119287578372241286695409⟩⟩,⟨⟨(-14729840626823614327239132578),(-14729840626823612637837550837)⟩,⟨177202259772853842006629668463,177202259772853843697710761015⟩⟩,⟨⟨(-11488516023745491015702286629),(-11488516023745489339463646220)⟩,⟨174699052458555090379723325218,174699052458555092057698237656⟩⟩,⟨⟨(-8255715551066846186478499221),(-8255715551066844523772483234)⟩,⟨172109195156933437469133319291,172109195156933439133631115703⟩⟩,⟨⟨(-5038352072240898957407715628),(-5038352072240897308542414148)⟩,⟨169433635201048621875613163659,169433635201048623526324345667⟩⟩,⟨⟨(-1843292021931094584950323247),(-1843292021931092950284814336)⟩,⟨166673575883199849302316740540,166673575883199850938880638731⟩⟩,⟨⟨1322664421130843244995654924,1322664421130844865161966710⟩,⟨163830481614585170911670041980,163830481614585172533785514309⟩⟩,⟨⟨4452803327764901422235914991,4452803327764903027542568548⟩,⟨160906081752977905842191435611,160906081752977907449496106752⟩⟩,⟨⟨7540517096747533253882030148,7540517096747534844052923508⟩,⟨157902373052370519483593792321,157902373052370521075809519641⟩⟩,⟨⟨10579324531973582380433678279,10579324531973583955133431602⟩,⟨154821620696169286941107249829,154821620696169288517887663778⟩⟩,⟨⟨13562890828503015314406327811,13562890828503016873379187305⟩,⟨151666357883588440412358715138,151666357883588441973434954144⟩⟩,⟨⟨16485047374319609515367792465,16485047374319611058268575176⟩,⟨148439383947346159961928619721,148439383947346161506953302696⟩⟩,⟨⟨19339811271923717623596317297,19339811271923719150184604737⟩,⟨145143760989557336648391584226,145143760989557338177122041844⟩⟩,⟨⟨22121404481818718651618311969,22121404481818720161567591080⟩,⟨141782809031795147442744627673,141782809031795148954851990519⟩⟩,⟨⟨24824272488573044340225945189,24824272488573045833306627932⟩,⟨138360099684596089983517445708,138360099684596091478769729289⟩⟩] +lemma kernel15_1_r5_2_eq : ∀ k : Fin 16, kernel15_1Expr 5 2 k = kernel15_1_r5_2 k := by decide +kernel +noncomputable def kernel15_1_r5_3 : Fin 16 → CBox := ![⟨⟨27443102389483627946474946078,27443102389483629422358026071⟩,⟨134879448351147895014114158475,134879448351147896492179866849⟩⟩,⟨⟨29972840305963221098466415157,29972840305963222556957282143⟩,⟨131344904989459485297931118807,131344904989459486758613139662⟩⟩,⟨⟨32408708018647768431186688188,32408708018647769871982107505⟩,⟨127760743466896376860231932159,127760743466896378303224450297⟩⟩,⟨⟨34746218728888514170966612465,34746218728888515593880995461⟩,⟨124131449550500372993650154806,124131449550500374418765000057⟩⟩,⟨⟨36981191851767023950915735533,36981191851767025355645785556⟩,⟨120461707585923731636151862527,120461707585923733043083093950⟩⟩,⟨⟨39109766749052483281003435337,39109766749052484667401387410⟩,⟨116756385927018430000420278612,116756385927018431389017514236⟩⟩,⟨⟨41128415314604232072002025482,41128415314604233439792816790⟩,⟨113020521187053272486601039662,113020521187053273856586552752⟩⟩,⟨⟨43033953329595197825446014567,43033953329595199174493508500⟩,⟨109259301391108059848323049370,109259301391108061199558078805⟩⟩,⟨⟨44823550510572233749978540904,44823550510572235080004217508⟩,⟨105478048117338441666086279430,105478048117338442998289648672⟩⟩,⟨⟨46494739179747743423904950330,46494739179747744734818841394⟩,⟨101682197722442730501847705144,101682197722442731814926859510⟩⟩,⟨⟨48045421493995728636051650081,48045421493995729927987515599⟩,⟨97877281753720758713428298681,97877281753720760007502165025⟩⟩,⟨⟨49473875176759032977737161753,49473875176759034253446553670⟩,⟨94068906656526111235574003394,94068906656526112513300606929⟩⟩,⟨⟨50778757705410018799599329533,50778757705410020058780398424⟩,⟨90262732891612306273044662469,90262732891612307534123681945⟩⟩,⟨⟨51959108915483993958133195052,51959108915483995200689388081⟩,⟨86464453581801291175131673303,86464453581801292419468295383⟩⟩,⟨⟨53014351992556502541113508500,53014351992556503766773614444⟩,⟨82679772811505343509343118460,82679772811505344736667987062⟩⟩,⟨⟨53944292832289110496755862814,53944292832289111705427393992⟩,⟨78914383705864009222401702910,78914383705864010432624375803⟩⟩] +lemma kernel15_1_r5_3_eq : ∀ k : Fin 16, kernel15_1Expr 5 3 k = kernel15_1_r5_3 k := by decide +kernel +noncomputable def kernel15_1_r5_4 : Fin 16 → CBox := ![⟨⟨54749117759245108645425029287,54749117759245109836823274706⟩,⟨75173946418576148206454768543,75173946418576149399292688144⟩⟩,⟨⟨55429389605393473799783138357,55429389605393474973867077813⟩,⟨71464066158881352940469937136,71464066158881354115884422476⟩⟩,⟨⟨55986042159689434761803462787,55986042159689435918329894665⟩,⟨67790271388551122388800434604,67790271388551123546550721718⟩⟩,⟨⟨56420373010653030809539229230,56420373010653031948465159499⟩,⟨64157992319173113981400572822,64157992319173115121446263700⟩⟩,⟨⟨56734034814370989680301628961,56734034814370990801375706623⟩,⟨60572539838445544189601978215,60572539838445545311694408475⟩⟩,⟨⟨56929025030728844346534182013,56929025030728845449764068549⟩,⟨57039084991646666178381671843,57039084991646667282531334316⟩⟩,⟨⟨57007674180846103377802718088,57007674180846104462978349844⟩,⟨53562639140918978918586468068,53562639140918980004586209433⟩⟩,⟨⟨56972632688545058843656500330,56972632688545059910787805841⟩,⟨50148034920531651469459871404,50148034920531652537322647137⟩⟩,⟨⟨56826856378142979308788372544,56826856378142980357651067031⟩,⟨46799908100889202387147078141,46799908100889203436651698811⟩⟩,⟨⟨56573590709830487105896762087,56573590709830488136561147100⟩,⟨43522680467780564444466140873,43522680467780565475686100648⟩⟩,⟨⟨56216353842302326669677887728,56216353842302327681971339859⟩,⟨40320543816259961367372459572,40320543816259962380138383075⟩⟩,⟨⟨55758918620061903200612828831,55758918620061904194600152520⟩,⟨37197445150677633339496652249,37197445150677634333876659831⟩⟩,⟨⟨55205293589855176984213118894,55205293589855177959712811573⟩,⟨34157073173800375532070738872,34157073173800376507886689104⟩⟩,⟨⟨54559703156936724512756956002,54559703156936725469990806346⟩,⟨31202846138752358588714017162,31202846138752359546191685956⟩⟩,⟨⟨53826566997272511627552888798,53826566997272512566435113648⟩,⟨28337901127745561000773670464,28337901127745561939830973957⟩⟩,⟨⟨53010478846289857235401020267,53010478846289858156045246067⟩,⟨25565084811341835891660269531,25565084811341836812414240748⟩⟩] +lemma kernel15_1_r5_4_eq : ∀ k : Fin 16, kernel15_1Expr 5 4 k = kernel15_1_r5_4 k := by decide +kernel +noncomputable def kernel15_1_r5_5 : Fin 16 → CBox := ![⟨⟨52116184788353697998936053346,52116184788353698901185755249⟩,⟨22886945731385429977870024802,22886945731385430880167567510⟩⟩,⟨⟨51148561173747404102437604972,51148561173747404986535132369⟩,⟨20305728139859771206282655249,20305728139859772090369529524⟩⟩,⟨⟨50112592291543553923561738966,50112592291543554789636918489⟩,⟨17823367414852454935368827424,17823367414852455801378271489⟩⟩,⟨⟨49013347927352735415919218549,49013347927352736264126898061⟩,⟨15441487063656248318560000202,15441487063656249166650252127⟩⟩,⟨⟨47855960934534214104490361479,47855960934534214934710824423⟩,⟨13161397311890925425242741602,13161397311890926255297475481⟩⟩,⟨⟨46645604946048954421139684574,46645604946048955233586718306⟩,⟨10984095266499735532566063875,10984095266499736344802390733⟩⟩,⟨⟨45387472351750819937434279324,45387472351750820732041922512⟩,⟨8910266629652660693698770227,8910266629652661488054042493⟩⟩,⟨⟨44086752662573458414136514062,44086752662573459191110122207⟩,⟨6940288930071098989673757801,6940288930071099766356561391⟩⟩,⟨⟨42748611378815537515119700678,42748611378815538274372781311⟩,⟨5074236228166331581687505683,5074236228166332340614563140⟩⟩,⟨⟨41378169474601802408975098519,41378169474601803151179620247⟩,⟨3311885241743563832741752792,3311885241743564574588130467⟩⟩,⟨⟨39980483604656500065778985791,39980483604656500790985779196⟩,⟨1652722829945359252150792616,1652722829945359976970395410⟩⟩,⟨⟨38560527132831462928169353350,38560527132831463636608296636⟩,⟨95954764667347805475444719,95954764667348513501101118⟩⟩,⟨⟨37123172074452989875400346876,37123172074452990567011079030⟩,⟨(-1359484289057602980662088052),(-1359484289057602289487817473)⟩⟩,⟨⟨35673172036565196494626514681,35673172036565197169696146214⟩,⟨(-2714919669183718944515448062),(-2714919669183718269902685845)⟩⟩,⟨⟨34215146231633571150915386141,34215146231633571809439380070⟩,⟨(-3971924580920930896202050043),(-3971924580920930238145156073)⟩⟩,⟨⟨32753564631316184198030889796,32753564631316184840397228308⟩,⟨(-5132307026086188213637891683),(-5132307026086187571744580611)⟩⟩] +lemma kernel15_1_r5_5_eq : ∀ k : Fin 16, kernel15_1Expr 5 5 k = kernel15_1_r5_5 k := by decide +kernel +noncomputable def kernel15_1_r5_6 : Fin 16 → CBox := ![⟨⟨31292734317599726824436416549,31292734317599727450626796375⟩,⟨(-6198095898889858457431114494),(-6198095898889857831717750947)⟩⟩,⟨⟨29836787079023883843250743537,29836787079023884453594877152⟩,⟨(-7171526353011929209428658735),(-7171526353011928599563783446)⟩⟩,⟨⟨28389668289972198534753725712,28389668289972199129276523583⟩,⟨(-8055024547400150432151833545),(-8055024547400149838108824354)⟩⟩,⟨⟨26955127101182380691552077434,26955127101182381270553544707⟩,⟨(-8851191879871150055594443388),(-8851191879871149477071736106)⟩⟩,⟨⟨25536707959814794817791123271,25536707959814795381278561279⟩,⟨(-9562788818321836692511553118),(-9562788818321836129500328545)⟩⟩,⟨⟨24137743467703521269361536861,24137743467703521817686771437⟩,⟨(-10192718439177271160707920927),(-10192718439177270612855000198)⟩⟩,⟨⟨22761348576885836575073217528,22761348576885837108295777034⟩,⟨(-10744009781636769193562668233),(-10744009781636768660807212703)⟩⟩,⟨⟨21410416112245270102876218955,21410416112245270621325129379⟩,⟨(-11219801124364880547845601307),(-11219801124364880029857422075)⟩⟩,⟨⟨20087613602187904103839509379,20087613602187904608190624403⟩,⟨(-11623323288548566079273317883),(-11623323288548565575351104319)⟩⟩,⟨⟨18795381389773142941510758218,18795381389773143432329096496⟩,⟨(-11957883067754110152699676468),(-11957883067754109662271372013)⟩⟩,⟨⟨17535931988704457201718378858,17535931988704457679046720068⟩,⟨(-12226846880821337027055560933),(-12226846880821336550079985199)⟩⟩,⟨⟨16311250641111511818533794873,16311250641111512282677410705⟩,⟨(-12433624739188563700624819913),(-12433624739188563236798351865)⟩⟩,⟨⟨15123097027174255421710503739,15123097027174255872692200734⟩,⟨(-12581654614614334678890479859),(-12581654614614334228191933583)⟩⟩,⟨⟨13973008070395973586673492648,13973008070395974024844409853⟩,⟨(-12674387287320281166883605723),(-12674387287320280728963502749)⟩⟩,⟨⟨12862301776762056525092276243,12862301776762056950523464923⟩,⟨(-12715271748195474123483491362),(-12715271748195473698272406136)⟩⟩,⟨⟨11792082041152267926133424919,11792082041152268339148712601⟩,⟨(-12707741221950633738541925755),(-12707741221950633325717669506)⟩⟩] +lemma kernel15_1_r5_6_eq : ∀ k : Fin 16, kernel15_1Expr 5 6 k = kernel15_1_r5_6 k := by decide +kernel +noncomputable def kernel15_1_r5_7 : Fin 16 → CBox := ![⟨⟨10763244350226429607856385004,10763244350226430008495186685⟩,⟨(-12655199871066023442558743182),(-12655199871066023042083503529)⟩⟩,⟨⟨9776482307588339158523590730,9776482307588339547194534025⟩,⟨(-12561010233115663168536507619),(-12561010233115662780003258422)⟩⟩,⟨⟨8832294904354120476968560730,8832294904354120853836605709⟩,⟨(-12428481436647992606627963612),(-12428481436647992229873304590)⟩⟩,⟨⟨7930994456305038219202611919,7930994456305038584596117763⟩,⟨(-12260858233333282618388820691),(-12260858233333282253085939411)⟩⟩,⟨⟨7072715127579646901174515498,7072715127579647255158516980⟩,⟨(-12061310876622748232131825917),(-12061310876622747878217196865)⟩⟩,⟨⟨6257421960337557717906862818,6257421960337558060846866185⟩,⟨(-11832925869772367990853697353),(-11832925869772367647963290606)⟩⟩,⟨⟨5484920329982143670274153552,5484920329982144002276711186⟩,⟨(-11578697598831184034654982085),(-11578697598831183702683683245)⟩⟩,⟨⟨4754865746331256606120233853,4754865746331256927518827089⟩,⟨(-11301520859140475230434328406),(-11301520859140474909050048688)⟩⟩,⟨⟨4066773922537228995852226198,4066773922537229306963852413⟩,⟨(-11004184277093071217803503671),(-11004184277093070906690776681)⟩⟩,⟨⟨3420031035539095845858735235,3420031035539096147122867542⟩,⟨(-10689364622412450215058586635),(-10689364622412449913779280941)⟩⟩,⟨⟨2813904104336080387067146226,2813904104336080678583128542⟩,⟨(-10359622000074849862964713590),(-10359622000074849571420729972)⟩⟩,⟨⟨2247551415353588672043653300,2247551415353588954123579038⟩,⟨(-10017395905254324547169755780),(-10017395905254324265050182755)⟩⟩,⟨⟨1720032927580277209832722531,1720032927580277482552345113⟩,⟨(-9665002119354415126827918258),(-9665002119354414854058153293)⟩⟩,⟨⟨1230320593934306898259186910,1230320593934307161960009530⟩,⟨(-9304630420328667906125010163),(-9304630420328667642364626597)⟩⟩,⟨⟨777308539414579284303611077,777308539414579539096212845⟩,⟨(-8938343076107336249040938990),(-8938343076107335994180405315)⟩⟩,⟨⟨359823040953945589234261431,359823040953945835426580968⟩,⟨(-8568074086054841506437083429),(-8568074086054841260169435173)⟩⟩] +lemma kernel15_1_r5_7_eq : ∀ k : Fin 16, kernel15_1Expr 5 7 k = kernel15_1_r5_7 k := by decide +kernel +noncomputable def kernel15_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-23367741538406178965316721),(-23367741538405941277715295)⟩,⟨(-8195629131991645655985485347),(-8195629131991645418216108883)⟩⟩,⟨⟨(-373544328732684576070749800),(-373544328732684346432383012)⟩,⟨(-7822686197429046516052755189),(-7822686197429046286327031271)⟩⟩,⟨⟨(-692026820991277889235705788),(-692026820991277667538645885)⟩,⟨(-7450796811284524527295951903),(-7450796811284524305506796346)⟩⟩,⟨⟨(-980166169116820211186457068),(-980166169116819997139160910)⟩,⟨(-7081387870461969365104656988),(-7081387870461969150962810025)⟩⟩,⟨⟨(-1239335847928955534599261277),(-1239335847928955328116668723)⟩,⟨(-6715763994283926903852300914),(-6715763994283926697274299751)⟩⟩,⟨⟨(-1470923959019718214460585905),(-1470923959019718015231415668)⟩,⟨(-6355110362836080934192795345),(-6355110362836080734867814079)⟩⟩,⟨⟨(-1676325784277590393341078359),(-1676325784277590201206589960)⟩,⟨(-6000495990807723672099647204),(-6000495990807723479869391347)⟩⟩,⟨⟨(-1856936807132969296087842850),(-1856936807132969110754291060)⟩,⟨(-5652877388362697465433632835),(-5652877388362697280004739244)⟩⟩,⟨⟨(-2014146213998203762569740457),(-2014146213998203583960803274)⟩,⟨(-5313102560926928808098531972),(-5313102560926928629395052863)⟩⟩,⟨⟨(-2149330884084918227363685541),(-2149330884084918055181544880)⟩,⟨(-4981915300502433871348224648),(-4981915300502433699072647706)⟩⟩,⟨⟨(-2263849871707446908932275807),(-2263849871707446743037248799)⟩,⟨(-4659959722182739030406188795),(-4659959722182738864419138208)⟩⟩,⟨⟨(-2359039381347238619980842547),(-2359039381347238460115262344)⟩,⟨(-4347785000918679776838529248),(-4347785000918679616882582579)⟩⟩,⟨⟨(-2436208232178418678009172224),(-2436208232178418524088929165)⟩,⟨(-4045850265233102245782496102),(-4045850265233102091774985662)⟩⟩,⟨⟨(-2496633805454677693068713846),(-2496633805454677544811785590)⟩,⟨(-3754529606474070038368900580),(-3754529606474069890033233416)⟩⟩,⟨⟨(-2541558465143772818854887026),(-2541558465143772676159445404)⟩,⟨(-3474117164294575897676180771),(-3474117164294575754910082829)⟩⟩,⟨⟨(-2572186439475893217003976042),(-2572186439475893079632336859)⟩,⟨(-3204832251318503594172842592),(-3204832251318503456738174471)⟩⟩] +lemma kernel15_1_r5_8_eq : ∀ k : Fin 16, kernel15_1Expr 5 8 k = kernel15_1_r5_8 k := by decide +kernel +noncomputable def kernel15_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-2589681148650092607000737014),(-2589681148650092474880321578)⟩,⟨(-2946824482364314702819000931),(-2946824482364314570642753886)⟩⟩,⟨⟨(-2595162961819686606240183103),(-2595162961819686479113417487)⟩,⟨(-2700178876117226992468217035),(-2700178876117226865292378727)⟩⟩,⟨⟨(-2589707364650569177180435731),(-2589707364650569054949174011)⟩,⟨(-2464920899736333660224107970),(-2464920899736333537950118413)⟩⟩,⟨⟨(-2574343517210556139214571516),(-2574343517210556021659207024)⟩,⟨(-2241021429525528096128865848),(-2241021429525527978536706757)⟩⟩,⟨⟨(-2550053180695241933393564902),(-2550053180695241820437492609)⟩,⟨(-2028401603458331613353335915),(-2028401603458331500366011439)⟩⟩,⟨⟨(-2517769990516265998409211269),(-2517769990516265889822528424)⟩,⟨(-1826937544000786031391296830),(-1826937544000785922778518479)⟩⟩,⟨⟨(-2478379052559109103862611904),(-2478379052559108999552698848)⟩,⟨(-1636464932299562943646131446),(-1636464932299562839314913133)⟩⟩,⟨⟨(-2432716838945631717442832853),(-2432716838945631617209134876)⟩,⟨(-1456783417372641698685865874),(-1456783417372641598435297292)⟩⟩,⟨⟨(-2381571359396147753864058756),(-2381571359396147657639169546)⟩,⟨(-1287660846437869422029185600),(-1287660846437869325791521184)⟩⟩,⟨⟨(-2325682584260377853548490540),(-2325682584260377761118729468)⟩,⟨(-1128837304923296365088737464),(-1128837304923296272649970909)⟩⟩,⟨⟨(-2265743095458765961071584073),(-2265743095458765872351158678)⟩,⟨(-980028957007551009156645226),(-980028957007550920430673021)⟩⟩,⟨⟨(-2202398941927398935764564599),(-2202398941927398850572345877)⟩,⟨(-840931679726147668928782875),(-840931679726147583734181187)⟩⟩,⟨⟨(-2136250676672830879507228192),(-2136250676672830797776726910)⟩,⟨(-711224485740215729208884313),(-711224485740215647478880749)⟩⟩,⟨⟨(-2067854553199070380153681612),(-2067854553199070301697223376)⟩,⟨(-590572731789587326983810713),(-590572731789587248530466874)⟩⟩,⟨⟨(-1997723859849545187413042271),(-1997723859849545112152502674)⟩,⟨(-478631111636441121363849860),(-478631111636441046108787114)⟩⟩,⟨⟨(-1926330371494034375353002743),(-1926330371494034302776244839)⟩,⟨(-375046433944702751952916953),(-375046433944702679383728008)⟩⟩] +lemma kernel15_1_r5_9_eq : ∀ k : Fin 16, kernel15_1Expr 5 9 k = kernel15_1_r5_9 k := by decide +kernel +noncomputable def kernel15_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-1854105898966862572916325361),(-1854105898966862502957720507)⟩,⟨(-279460187031917348503311861),(-279460187031917278554139268)⟩⟩,⟨⟨(-1781443917711238969137656399),(-1781443917711238901654037843)⟩,⟨(-191510893773808280442610269),(-191510893773808212970085442)⟩⟩,⟨⟨(-1708701258189427435293136870),(-1708701258189427370243046980)⟩,⟨(-110836261138247041055363115),(-110836261138246976017831446)⟩⟩,⟨⟨(-1636199841764273303105908422),(-1636199841764273240371533242)⟩,⟨(-37075129877312198168851916),(-37075129877312135448322475)⟩⟩,⟨⟨(-1564228446930284740763751614),(-1564228446930284680317857004)⟩,⟨30130769182812628334528738,30130769182812688765463984⟩⟩,⟨⟨(-1493044491958816610308006675),(-1493044491958816552024912008)⟩,⟨91135245039395128798306883,91135245039395187065479589⟩⟩,⟨⟨(-1422875821209872693613626073),(-1422875821209872637454643520)⟩,⟨146286254738918424601843981,146286254738918480744091457⟩⟩,⟨⟨(-1353922483541696223159248229),(-1353922483541696169017602796)⟩,⟨195924681551204176593056601,195924681551204230717368340⟩⟩,⟨⟨(-1286358492408868450658161899),(-1286358492408868398511778433)⟩,⟨240383274308269816432754152,240383274308269868561719856⟩⟩,⟨⟨(-1220333558371430764305921949),(-1220333558371430714037869184)⟩,⟨279985738829741713420649794,279985738829741763671266269⟩⟩,⟨⟨(-1155974785834063206451473560),(-1155974785834063158026369291)⟩,⟨315045972163353807602850447,315045972163353856010568844⟩⟩,⟨⟨(-1093388326889164594270656376),(-1093388326889164547592654351)⟩,⟨345867430268834236845937651,345867430268834283506658148⟩⟩,⟨⟨(-1032660986145419856858632444),(-1032660986145419811904856113)⟩,⟨372742619758005757394799377,372742619758005802331455363⟩⟩,⟨⟨(-973861771379753988546394066),(-973861771379753945215158065)⟩,⟨395952704364869618835805537,395952704364869662150122834⟩⟩,⟨⟨(-917043385752061835714474381),(-917043385752061793973994838)⟩,⟨415767216948556695401085116,415767216948556737124891249⟩⟩,⟨⟨(-862243658166267871364026827),(-862243658166267831128909198)⟩,⟨432443868021226470367016632,432443868021226510585737669⟩⟩] +lemma kernel15_1_r5_10_eq : ∀ k : Fin 16, kernel15_1Expr 5 10 k = kernel15_1_r5_10 k := by decide +kernel +noncomputable def kernel15_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-809486909146440171158789650),(-809486909146440132412297414)⟩,⟨446228442034421626200526767,446228442034421664930934233⟩⟩,⟨⟨(-758785250321950211186367333),(-758785250321950173834424219)⟩,⟨457354772943488629172390330,457354772943488666508581448⟩⟩,⟨⟨(-710139816280818628385098795),(-710139816280818592399433620)⟩,⟨466044790893247226626664272,466044790893247262597073086⟩⟩,⟨⟨(-663541928155820586847212590),(-663541928155820552151268075)⟩,⟨472508632222319936893375086,472508632222319971575383933⟩⟩,⟨⟨(-618974188854595607217662252),(-618974188854595573794133233)⟩,⟨476944805362026234132058190,476944805362026267542901858⟩⟩,⟨⟨(-576411510334347189154764395),(-576411510334347156923683119)⟩,⟨479540405602563148778576094,479540405602563180998147784⟩⟩,⟨⟨(-535822073755569528774863065),(-535822073755569497707347324)⟩,⟨480471372108856453074194788,480471372108856484131309115⟩⟩,⟨⟨(-497168223729789583742696454),(-497168223729789553771981014)⟩,⟨479902780985969205240740659,479902780985969235202094749⟩⟩,⟨⟨(-460407298206033102878412550),(-460407298206033073992650723)⟩,⟨477989168614766576699293214,477989168614766605576672528⟩⟩,⟨⟨(-425492395822307804955996127),(-425492395822307777082711117)⟩,⟨474874879898597675204586840,474874879898597703070405109⟩⟩,⟨⟨(-392373082784710184101340858),(-392373082784710157218459879)⟩,⟨470694436477468173140761113,470694436477468200017034074⟩⟩,⟨⟨(-360996041530788346242242324),(-360996041530788320286407616)⟩,⟨465572920374391596875170400,465572920374391622825199208⟩⟩,⟨⟨(-331305663588589184810937479),(-331305663588589159771073755)⟩,⟨459626368936602402809091992,459626368936602427843900001⟩⟩,⟨⟨(-303244589161473423787036539),(-303244589161473399602122726)⟩,⟨452962177319780902842161528,452962177319780927022718351⟩⟩,⟨⟨(-276754196054380964214443791),(-276754196054380940867561593)⟩,⟨445679505134456431684285275,445679505134456455027461767⟩⟩,⟨⟨(-251775040612818471357941440),(-251775040612818448799159909)⟩,⟨437869684228761094541269373,437869684228761117096950613⟩⟩] +lemma kernel15_1_r5_11_eq : ∀ k : Fin 16, kernel15_1Expr 5 11 k = kernel15_1_r5_11 k := by decide +kernel +noncomputable def kernel15_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-228247253374402470256035375),(-228247253374402448479063853)⟩,⟨429616624919478640459431104,429616624919478662233864937⟩⟩,⟨⟨(-206110892137215931664787287),(-206110892137215910612816700)⟩,⟨420997218302957613375611999,420997218302957634425566478⟩⟩,⟨⟨(-185306255132306224261031560),(-185306255132306203912039730)⟩,⟨412081732578303296369763120,412081732578303316717221899⟩⟩,⟨⟨(-165774156952023098724638333),(-165774156952023079035780036)⟩,⟨402934201596952379658071780,402934201596952399345843860⟩⟩,⟨⟨(-147456169834083825477276035),(-147456169834083806442387235)⟩,⟨393612804115119093037862359,393612804115119112072077187⟩⟩,⟨⟨(-130294832835626917312871622),(-130294832835626898885628248)⟩,⟨384170232468734895949608411,384170232468734914376558283⟩⟩,⟨⟨(-114233831354288902439103433),(-114233831354288884608358729)⟩,⟨374654049614615355106659801,374654049614615372937460813⟩⟩,⟨⟨(-99218149366563856823447839),(-99218149366563839551857983)⟩,⟨365107033687059492148817838,365107033687059509420785906⟩⟩,⟨⟨(-85194196659275220679800963),(-85194196659275203964560874)⟩,⟨355567509406429970392932883,355567509406429987108845582⟩⟩,⟨⟨(-72109913229635414534637201),(-72109913229635398333390604)⟩,⟨346069665846096206332263215,346069665846096222534452874⟩⟩,⟨⟨(-59914852924663921356180738),(-59914852924663905659839554)⟩,⟨336643860217153918391551392,336643860217153934089082158⟩⟩,⟨⟨(-48560248283096886523542784),(-48560248283096871299593366)⟩,⟨327316907467340272648256736,327316907467340287873621290⟩⟩,⟨⟨(-37999058433619049950312548),(-37999058433619035195785718)⟩,⟨318112355612372738648638964,318112355612372753404785078⟩⟩,⟨⟨(-28186001793406236567020062),(-28186001793406222246227773)⟩,⟨309050746825418404640488922,309050746825418418963087012⟩⟩,⟨⟨(-19077575201570982707415984),(-19077575201570968809705423)⟩,⟨300149864404438786181807779,300149864404438800081490874⟩⟩,⟨⟨(-10632061014013027771808935),(-10632061014013014263653450)⟩,⟨291424965818654460568938102,291424965818654474079215356⟩⟩] +lemma kernel15_1_r5_12_eq : ∀ k : Fin 16, kernel15_1Expr 5 12 k = kernel15_1_r5_12 k := by decide +kernel +noncomputable def kernel15_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-2809523580126790031294308),(-2809523580126776913440117)⟩,⟨282889002105236238048797855,282889002105236251168906696⟩⟩,⟨⟨4428203581567088021706619,4428203581567100781934775⟩,⟨274552823946448501227017980,274552823946448513989621568⟩⟩,⟨⟨11117538692000780359249922,11117538692000792767038466⟩,⟨266425374806722706208088589,266425374806722718618359707⟩⟩,⟨⟨17293179584079392313099386,17293179584079404392668322⟩,⟨258513871549378457423636359,258513871549378469505784356⟩⟩,⟨⟨22988137511527608576080536,22988137511527620327485543⟩,⟨250823972984760824630510573,250823972984760836384578830⟩⟩,⟨⟨28233775954906864922599054,28233775954906876373147414⟩,⟨243359936826217120707260230,243359936826217132160547692⟩⟩,⟨⟨33059853569724898110118617,33059853569724909263791924⟩,⟨236124765548348829016697104,236124765548348840173175218⟩⟩,⟨⟨37494570501136108880544513,37494570501136119758606473⟩,⟨229120341654059922858496029,229120341654059933739421246⟩⟩,⟨⟨41564617364742103383806488,41564617364742113984268124⟩,⟨222347552863755328910179124,222347552863755339513505155⟩⟩,⟨⟨45295226263431960138018736,45295226263431970486464421⟩,⟨215806407742254193564547850,215806407742254203915855872⟩⟩,⟨⟨48710223276078827750345971,48710223276078837850649717⟩,⟨209496142277160419046192627,209496142277160429149352566⟩⟩,⟨⟨51832081915297627539323661,51832081915297637410617264⟩,⟨203415317917123225685287289,203415317917123235559429283⟩⟩,⟨⟨54681977108463109112846524,54681977108463118753551130⟩,⟨197561911570126412968237313,197561911570126422611778667⟩⟩,⟨⟨57279839308909233544183787,57279839308909242975937858⟩,⟨191933398051128109305795820,191933398051128118740374441⟩⟩,⟨⟨59644408392821796058744230,59644408392821805283590504⟩,⟨186526825455454320687414659,186526825455454329915070612⟩⟩,⟨⟨61793287041955005075596346,61793287041955014110056113⟩,⟨181338883919711790158540735,181338883919711799195794762⟩⟩] +lemma kernel15_1_r5_13_eq : ∀ k : Fin 16, kernel15_1Expr 5 13 k = kernel15_1_r5_13 k := by decide +kernel +noncomputable def kernel15_1_r5_14 : Fin 16 → CBox := ![⟨⟨63742993353120891827358979,63742993353120900667781158⟩,⟨176365968215973585578599271,176365968215973594421797499⟩⟩,⟨⟨65509012452598778644619425,65509012452598787312040864⟩,⟨171604234607914021912401193,171604234607914030582581039⟩⟩,⟨⟨67105846927377722661922280,67105846927377731157715403⟩,⟨167049652379704070052805556,167049652379704078551337800⟩⟩,⟨⟨68547065915668604727242236,68547065915668613066140209⟩,⟨162698050430068875296193643,162698050430068883637811689⟩⟩,⟨⟨69845352726596327204356531,69845352726596335383756866⟩,⟨158545159305170518261889128,158545159305170526443988797⟩⟩,⟨⟨71012550883597613348578202,71012550883597621386191329⟩,⟨154586649025099406848128691,154586649025099414888421422⟩⟩,⟨⟨72059708507994858205187324,72059708507994866101843639⟩,⟨150818163039899035806496690,150818163039899043705811965⟩⟩,⟨⟨72997120978676106521337514,72997120978676114290285026⟩,⟨147235348632350272497770569,147235348632350280269357174⟩⟩,⟨⟨73834371820965122918159543,73834371820965130555342332⟩,⟨143833884066320392650844921,143833884066320400290645755⟩⟩,⟨⟨74580371792787154185199487,74580371792787161707954476⟩,⟨140609502761436828838748195,140609502761436836364101731⟩⟩,⟨⟨75243396149291971773541360,75243396149291979182278569⟩,⟨137558014757256300140871852,137558014757256307552187719⟩⟩,⟨⟨75831120078345280127303403,75831120078345287434040166⟩,⟨134675325713030924123031895,134675325713030931432328566⟩⟩,⟨⟨76350652308893877238658440,76350652308893884440125532⟩,⟨131957453672673915704957283,131957453672673922908964921⟩⟩,⟨⟨76808566902292216334271481,76808566902292223445514826⟩,⟨129400543808635488075725856,129400543808635495189492063⟩⟩,⟨⟨77210933243383126856031965,77210933243383133877143192⟩,⟨127000881343140032812067705,127000881343140039835684088⟩⟩,⟨⟨77563344253579982974277426,77563344253579989916277859⟩,⟨124754902830623826091816126,124754902830623833036305356⟩⟩] +lemma kernel15_1_r5_14_eq : ∀ k : Fin 16, kernel15_1Expr 5 14 k = kernel15_1_r5_14 k := by decide +kernel +noncomputable def kernel15_1_r5_15 : Fin 16 → CBox := ![⟨⟨77870942852519887150530065,77870942852519894008601912⟩,⟨122659205971254663988247472,122659205971254670848791313⟩⟩,⟨⟨78138446698157685067589031,78138446698157691857169125⟩,⟨120710558112109375084363849,120710558112109381876401122⟩⟩,⟨⟨78370171237551172028235185,78370171237551178749196275⟩,⟨118905903579923632072366667,118905903579923638795770346⟩⟩,⟨⟨78570051102143382248205284,78570051102143388910769392⟩,⟨117242369977296470872309698,117242369977296477537303274⟩⟩,⟨⟨78741659882165747100331190,78741659882165753700829460⟩,⟨115717273562809885232515420,115717273562809891835429959⟩⟩,⟨⟨78888228314946571022099390,78888228314946577573917319⟩,⟨114328123824687863732577620,114328123824687870286800537⟩⟩,⟨⟨79012660921486521650654964,79012660921486528153529299⟩,⟨113072627347341610587479265,113072627347341617092747695⟩⟩,⟨⟨79117551124724292280466068,79117551124724298744007517⟩,⟨111948691060397624399069904,111948691060397630864996102⟩⟩,⟨⟨79205194881523133395936370,79205194881523139815880393⟩,⟨110954424950549344294881788,110954424950549350717192267⟩⟩,⟨⟨79277602858619093221299148,79277602858619099612084241⟩,⟨110088144307775559061783658,110088144307775565454911436⟩⟩,⟨⟨79336511180636191025762018,79336511180636197386910900⟩,⟨109348371569092254351577882,109348371569092260715048659⟩⟩,⟨⟨79383390775839559082334418,79383390775839565422847650⟩,⟨108733837815010111142026621,108733837815010117484844939⟩⟩,⟨⟨79419455342608022012222621,79419455342608028328069712⟩,⟨108243483966217340611106987,108243483966217346929244851⟩⟩,⟨⟨79445667956702279123334265,79445667956702285426926239⟩,⟨107876461720655867749817796,107876461720655874055690528⟩⟩,⟨⟨79462746336320363994753533,79462746336320370285649104⟩,⟨107632134264066230941357978,107632134264066237234527145⟩⟩,⟨⟨79471166778702272671885212,79471166778702278958796541⟩,⟨107510076780200535750550273,107510076780200542039731875⟩⟩] +lemma kernel15_1_r5_15_eq : ∀ k : Fin 16, kernel15_1Expr 5 15 k = kernel15_1_r5_15 k := by decide +kernel +noncomputable def kernel15_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel15_1_r5_0,kernel15_1_r5_1,kernel15_1_r5_2,kernel15_1_r5_3,kernel15_1_r5_4,kernel15_1_r5_5,kernel15_1_r5_6,kernel15_1_r5_7,kernel15_1_r5_8,kernel15_1_r5_9,kernel15_1_r5_10,kernel15_1_r5_11,kernel15_1_r5_12,kernel15_1_r5_13,kernel15_1_r5_14,kernel15_1_r5_15] +lemma kernel15_1_r5_eq (i k : Fin 16) : kernel15_1Expr 5 i k = kernel15_1_r5 i k := by + fin_cases i + · exact kernel15_1_r5_0_eq k + · exact kernel15_1_r5_1_eq k + · exact kernel15_1_r5_2_eq k + · exact kernel15_1_r5_3_eq k + · exact kernel15_1_r5_4_eq k + · exact kernel15_1_r5_5_eq k + · exact kernel15_1_r5_6_eq k + · exact kernel15_1_r5_7_eq k + · exact kernel15_1_r5_8_eq k + · exact kernel15_1_r5_9_eq k + · exact kernel15_1_r5_10_eq k + · exact kernel15_1_r5_11_eq k + · exact kernel15_1_r5_12_eq k + · exact kernel15_1_r5_13_eq k + · exact kernel15_1_r5_14_eq k + · exact kernel15_1_r5_15_eq k +noncomputable def kernel15_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel15_1_r0,kernel15_1_r1,kernel15_1_r2,kernel15_1_r3,kernel15_1_r4,kernel15_1_r5] +lemma kernel15_1_eq (j : Fin 6) (i k : Fin 16) : kernel15_1Expr j i k = kernel15_1 j i k := by + fin_cases j + · exact kernel15_1_r0_eq i k + · exact kernel15_1_r1_eq i k + · exact kernel15_1_r2_eq i k + · exact kernel15_1_r3_eq i k + · exact kernel15_1_r4_eq i k + · exact kernel15_1_r5_eq i k +lemma kernel15_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel15_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(15:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel15_1_eq] + unfold kernel15_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans15_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel16_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans16 j i k) +noncomputable def kernel16_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_0_eq : ∀ k : Fin 16, kernel16_0Expr 0 0 k = kernel16_0_r0_0 k := by decide +kernel +noncomputable def kernel16_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_1_eq : ∀ k : Fin 16, kernel16_0Expr 0 1 k = kernel16_0_r0_1 k := by decide +kernel +noncomputable def kernel16_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_2_eq : ∀ k : Fin 16, kernel16_0Expr 0 2 k = kernel16_0_r0_2 k := by decide +kernel +noncomputable def kernel16_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_3_eq : ∀ k : Fin 16, kernel16_0Expr 0 3 k = kernel16_0_r0_3 k := by decide +kernel +noncomputable def kernel16_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_4_eq : ∀ k : Fin 16, kernel16_0Expr 0 4 k = kernel16_0_r0_4 k := by decide +kernel +noncomputable def kernel16_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_5_eq : ∀ k : Fin 16, kernel16_0Expr 0 5 k = kernel16_0_r0_5 k := by decide +kernel +noncomputable def kernel16_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_6_eq : ∀ k : Fin 16, kernel16_0Expr 0 6 k = kernel16_0_r0_6 k := by decide +kernel +noncomputable def kernel16_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_7_eq : ∀ k : Fin 16, kernel16_0Expr 0 7 k = kernel16_0_r0_7 k := by decide +kernel +noncomputable def kernel16_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_8_eq : ∀ k : Fin 16, kernel16_0Expr 0 8 k = kernel16_0_r0_8 k := by decide +kernel +noncomputable def kernel16_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_9_eq : ∀ k : Fin 16, kernel16_0Expr 0 9 k = kernel16_0_r0_9 k := by decide +kernel +noncomputable def kernel16_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_10_eq : ∀ k : Fin 16, kernel16_0Expr 0 10 k = kernel16_0_r0_10 k := by decide +kernel +noncomputable def kernel16_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r0_11_eq : ∀ k : Fin 16, kernel16_0Expr 0 11 k = kernel16_0_r0_11 k := by decide +kernel +noncomputable def kernel16_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel16_0_r0_12_eq : ∀ k : Fin 16, kernel16_0Expr 0 12 k = kernel16_0_r0_12 k := by decide +kernel +noncomputable def kernel16_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel16_0_r0_13_eq : ∀ k : Fin 16, kernel16_0Expr 0 13 k = kernel16_0_r0_13 k := by decide +kernel +noncomputable def kernel16_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel16_0_r0_14_eq : ∀ k : Fin 16, kernel16_0Expr 0 14 k = kernel16_0_r0_14 k := by decide +kernel +noncomputable def kernel16_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel16_0_r0_15_eq : ∀ k : Fin 16, kernel16_0Expr 0 15 k = kernel16_0_r0_15 k := by decide +kernel +noncomputable def kernel16_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel16_0_r0_0,kernel16_0_r0_1,kernel16_0_r0_2,kernel16_0_r0_3,kernel16_0_r0_4,kernel16_0_r0_5,kernel16_0_r0_6,kernel16_0_r0_7,kernel16_0_r0_8,kernel16_0_r0_9,kernel16_0_r0_10,kernel16_0_r0_11,kernel16_0_r0_12,kernel16_0_r0_13,kernel16_0_r0_14,kernel16_0_r0_15] +lemma kernel16_0_r0_eq (i k : Fin 16) : kernel16_0Expr 0 i k = kernel16_0_r0 i k := by + fin_cases i + · exact kernel16_0_r0_0_eq k + · exact kernel16_0_r0_1_eq k + · exact kernel16_0_r0_2_eq k + · exact kernel16_0_r0_3_eq k + · exact kernel16_0_r0_4_eq k + · exact kernel16_0_r0_5_eq k + · exact kernel16_0_r0_6_eq k + · exact kernel16_0_r0_7_eq k + · exact kernel16_0_r0_8_eq k + · exact kernel16_0_r0_9_eq k + · exact kernel16_0_r0_10_eq k + · exact kernel16_0_r0_11_eq k + · exact kernel16_0_r0_12_eq k + · exact kernel16_0_r0_13_eq k + · exact kernel16_0_r0_14_eq k + · exact kernel16_0_r0_15_eq k +noncomputable def kernel16_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_0_eq : ∀ k : Fin 16, kernel16_0Expr 1 0 k = kernel16_0_r1_0 k := by decide +kernel +noncomputable def kernel16_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_1_eq : ∀ k : Fin 16, kernel16_0Expr 1 1 k = kernel16_0_r1_1 k := by decide +kernel +noncomputable def kernel16_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_2_eq : ∀ k : Fin 16, kernel16_0Expr 1 2 k = kernel16_0_r1_2 k := by decide +kernel +noncomputable def kernel16_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_3_eq : ∀ k : Fin 16, kernel16_0Expr 1 3 k = kernel16_0_r1_3 k := by decide +kernel +noncomputable def kernel16_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_4_eq : ∀ k : Fin 16, kernel16_0Expr 1 4 k = kernel16_0_r1_4 k := by decide +kernel +noncomputable def kernel16_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_5_eq : ∀ k : Fin 16, kernel16_0Expr 1 5 k = kernel16_0_r1_5 k := by decide +kernel +noncomputable def kernel16_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_6_eq : ∀ k : Fin 16, kernel16_0Expr 1 6 k = kernel16_0_r1_6 k := by decide +kernel +noncomputable def kernel16_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_7_eq : ∀ k : Fin 16, kernel16_0Expr 1 7 k = kernel16_0_r1_7 k := by decide +kernel +noncomputable def kernel16_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_8_eq : ∀ k : Fin 16, kernel16_0Expr 1 8 k = kernel16_0_r1_8 k := by decide +kernel +noncomputable def kernel16_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_9_eq : ∀ k : Fin 16, kernel16_0Expr 1 9 k = kernel16_0_r1_9 k := by decide +kernel +noncomputable def kernel16_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_10_eq : ∀ k : Fin 16, kernel16_0Expr 1 10 k = kernel16_0_r1_10 k := by decide +kernel +noncomputable def kernel16_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_11_eq : ∀ k : Fin 16, kernel16_0Expr 1 11 k = kernel16_0_r1_11 k := by decide +kernel +noncomputable def kernel16_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_12_eq : ∀ k : Fin 16, kernel16_0Expr 1 12 k = kernel16_0_r1_12 k := by decide +kernel +noncomputable def kernel16_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_13_eq : ∀ k : Fin 16, kernel16_0Expr 1 13 k = kernel16_0_r1_13 k := by decide +kernel +noncomputable def kernel16_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_14_eq : ∀ k : Fin 16, kernel16_0Expr 1 14 k = kernel16_0_r1_14 k := by decide +kernel +noncomputable def kernel16_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r1_15_eq : ∀ k : Fin 16, kernel16_0Expr 1 15 k = kernel16_0_r1_15 k := by decide +kernel +noncomputable def kernel16_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel16_0_r1_0,kernel16_0_r1_1,kernel16_0_r1_2,kernel16_0_r1_3,kernel16_0_r1_4,kernel16_0_r1_5,kernel16_0_r1_6,kernel16_0_r1_7,kernel16_0_r1_8,kernel16_0_r1_9,kernel16_0_r1_10,kernel16_0_r1_11,kernel16_0_r1_12,kernel16_0_r1_13,kernel16_0_r1_14,kernel16_0_r1_15] +lemma kernel16_0_r1_eq (i k : Fin 16) : kernel16_0Expr 1 i k = kernel16_0_r1 i k := by + fin_cases i + · exact kernel16_0_r1_0_eq k + · exact kernel16_0_r1_1_eq k + · exact kernel16_0_r1_2_eq k + · exact kernel16_0_r1_3_eq k + · exact kernel16_0_r1_4_eq k + · exact kernel16_0_r1_5_eq k + · exact kernel16_0_r1_6_eq k + · exact kernel16_0_r1_7_eq k + · exact kernel16_0_r1_8_eq k + · exact kernel16_0_r1_9_eq k + · exact kernel16_0_r1_10_eq k + · exact kernel16_0_r1_11_eq k + · exact kernel16_0_r1_12_eq k + · exact kernel16_0_r1_13_eq k + · exact kernel16_0_r1_14_eq k + · exact kernel16_0_r1_15_eq k +noncomputable def kernel16_0_r2_0 : Fin 16 → CBox := ![⟨⟨25896206046,25896206050⟩,⟨29177905310,29177905314⟩⟩,⟨⟨25858290601,25858290604⟩,⟨29108055399,29108055403⟩⟩,⟨⟨25782585746,25782585749⟩,⟨28968830436,28968830440⟩⟩,⟨⟨25669343493,25669343498⟩,⟨28761175013,28761175017⟩⟩,⟨⟨25518941684,25518941688⟩,⟨28486493305,28486493308⟩⟩,⟨⟨25331883722,25331883725⟩,⟨28146634009,28146634012⟩⟩,⟨⟨25108798152,25108798156⟩,⟨27743870604,27743870608⟩⟩,⟨⟨24850437983,24850437986⟩,⟨27280877201,27280877204⟩⟩,⟨⟨24557679717,24557679720⟩,⟨26760700341,26760700344⟩⟩,⟨⟨24231521967,24231521970⟩,⟨26186727121,26186727124⟩⟩,⟨⟨23873083598,23873083602⟩,⟨25562650094,25562650098⟩⟩,⟨⟨23483601269,23483601273⟩,⟨24892429443,24892429447⟩⟩,⟨⟨23064426324,23064426327⟩,⟨24180252925,24180252928⟩⟩,⟨⟨22617020914,22617020918⟩,⟨23430494146,23430494150⟩⟩,⟨⟨22142953294,22142953297⟩,⟨22647669718,22647669722⟩⟩,⟨⟨21643892232,21643892235⟩,⟨21836395854,21836395858⟩⟩] +lemma kernel16_0_r2_0_eq : ∀ k : Fin 16, kernel16_0Expr 2 0 k = kernel16_0_r2_0 k := by decide +kernel +noncomputable def kernel16_0_r2_1 : Fin 16 → CBox := ![⟨⟨21121600487,21121600491⟩,⟨21001344969,21001344972⟩⟩,⟨⟨20577927321,20577927326⟩,⟨20147202833,20147202837⟩⟩,⟨⟨20014800060,20014800064⟩,⟨19278626809,19278626813⟩⟩,⟨⟨19434214701,19434214705⟩,⟨18400205659,18400205663⟩⟩,⟨⟨18838225623,18838225628⟩,⟨17516421386,17516421390⟩⟩,⟨⟨18228934462,18228934466⟩,⟨16631613557,16631613561⟩⟩,⟨⟨17608478233,17608478236⟩,⟨15749946441,15749946444⟩⟩,⟨⟨16979016801,16979016804⟩,⟨14875379297,14875379301⟩⟩,⟨⟨16342719865,16342719869⟩,⟨14011640085,14011640089⟩⟩,⟨⟨15701753548,15701753552⟩,⟨13162202790,13162202794⟩⟩,⟨⟨15058266782,15058266785⟩,⟨12330268500,12330268504⟩⟩,⟨⟨14414377653,14414377657⟩,⟨11518750338,11518750342⟩⟩,⟨⟨13772159884,13772159888⟩,⟨10730262243,10730262248⟩⟩,⟨⟨13133629613,13133629617⟩,⟨9967111591,9967111594⟩⟩,⟨⟨12500732667,12500732670⟩,⟨9231295554,9231295558⟩⟩,⟨⟨11875332486,11875332490⟩,⟨8524501049,8524501054⟩⟩] +lemma kernel16_0_r2_1_eq : ∀ k : Fin 16, kernel16_0Expr 2 1 k = kernel16_0_r2_1 k := by decide +kernel +noncomputable def kernel16_0_r2_2 : Fin 16 → CBox := ![⟨⟨11259198865,11259198868⟩,⟨7848108113,7848108117⟩⟩,⟨⟨10653997657,10653997660⟩,⟨7203196434,7203196438⟩⟩,⟨⟨10061281580,10061281585⟩,⟨6590554824,6590554829⟩⟩,⟨⟨9482482227,9482482234⟩,⟨6010693305,6010693311⟩⟩,⟨⟨8918903385,8918903389⟩,⟨5463857497,5463857501⟩⟩,⟨⟨8371715714,8371715719⟩,⟨4950044986,4950044991⟩⟩,⟨⟨7841952868,7841952872⟩,⟨4469023330,4469023334⟩⟩,⟨⟨7330509034,7330509039⟩,⟨4020349344,4020349349⟩⟩,⟨⟨6838137928,6838137932⟩,⟨3603389342,3603389345⟩⟩,⟨⟨6365453194,6365453199⟩,⟨3217339973,3217339977⟩⟩,⟨⟨5912930174,5912930178⟩,⟨2861249374,2861249377⟩⟩,⟨⟨5480908972,5480908975⟩,⟨2534038291,2534038295⟩⟩,⟨⟨5069598735,5069598739⟩,⟨2234520926,2234520930⟩⟩,⟨⟨4679083029,4679083033⟩,⟨1961425227,1961425231⟩⟩,⟨⟨4309326218,4309326222⟩,⟨1713412430,1713412434⟩⟩,⟨⟨3960180694,3960180699⟩,⟨1489095607,1489095612⟩⟩] +lemma kernel16_0_r2_2_eq : ∀ k : Fin 16, kernel16_0Expr 2 2 k = kernel16_0_r2_2 k := by decide +kernel +noncomputable def kernel16_0_r2_3 : Fin 16 → CBox := ![⟨⟨3631394839,3631394843⟩,⟨1287057111,1287057116⟩⟩,⟨⟨3322621569,3322621574⟩,⟨1105864735,1105864740⟩⟩,⟨⟨3033427333,3033427336⟩,⟨944086520,944086523⟩⟩,⟨⟨2763301398,2763301401⟩,⟨800304104,800304108⟩⟩,⟨⟨2511665309,2511665313⟩,⟨673124613,673124617⟩⟩,⟨⟨2277882390,2277882395⟩,⟨561191023,561191027⟩⟩,⟨⟨2061267145,2061267149⟩,⟨463191056,463191060⟩⟩,⟨⟨1861094448,1861094452⟩,⟨377864593,377864597⟩⟩,⟨⟨1676608452,1676608456⟩,⟨304009702,304009706⟩⟩,⟨⟨1507031077,1507031081⟩,⟨240487297,240487301⟩⟩,⟨⟨1351570043,1351570046⟩,⟨186224558,186224562⟩⟩,⟨⟨1209426343,1209426347⟩,⟨140217180,140217183⟩⟩,⟨⟨1079801163,1079801167⟩,⟨101530544,101530548⟩⟩,⟨⟨961902142,961902146⟩,⟨69299948,69299952⟩⟩,⟨⟨854949008,854949011⟩,⟨42729976,42729979⟩⟩,⟨⟨758178541,758178545⟩,⟨21093127,21093131⟩⟩] +lemma kernel16_0_r2_3_eq : ∀ k : Fin 16, kernel16_0Expr 2 3 k = kernel16_0_r2_3 k := by decide +kernel +noncomputable def kernel16_0_r2_4 : Fin 16 → CBox := ![⟨⟨670848891,670848894⟩,⟨3727841,3727845⟩⟩,⟨⟨592243223,592243226⟩,⟨(-9964041),(-9964037)⟩⟩,⟨⟨521672753,521672757⟩,⟨(-20520191),(-20520188)⟩⟩,⟨⟨458479161,458479165⟩,⟨(-28421071),(-28421068)⟩⟩,⟨⟨402036440,402036444⟩,⟨(-34093418),(-34093415)⟩⟩,⟨⟨351752214,351752217⟩,⟨(-37913903),(-37913899)⟩⟩,⟨⟨307068552,307068555⟩,⟨(-40212863),(-40212860)⟩⟩,⟨⟨267462344,267462348⟩,⟨(-41278056),(-41278052)⟩⟩,⟨⟨232445282,232445286⟩,⟨(-41358377),(-41358373)⟩⟩,⟨⟨201563476,201563481⟩,⟨(-40667486),(-40667481)⟩⟩,⟨⟨174396772,174396775⟩,⟨(-39387321),(-39387317)⟩⟩,⟨⟨150557806,150557810⟩,⟨(-37671447),(-37671443)⟩⟩,⟨⟨129690851,129690855⟩,⟨(-35648229),(-35648225)⟩⟩,⟨⟨111470486,111470490⟩,⟨(-33423802),(-33423798)⟩⟩,⟨⟨95600124,95600127⟩,⟨(-31084842),(-31084838)⟩⟩,⟨⟨81810454,81810457⟩,⟨(-28701111),(-28701108)⟩⟩] +lemma kernel16_0_r2_4_eq : ∀ k : Fin 16, kernel16_0Expr 2 4 k = kernel16_0_r2_4 k := by decide +kernel +noncomputable def kernel16_0_r2_5 : Fin 16 → CBox := ![⟨⟨69857813,69857817⟩,⟨(-26327784),(-26327781)⟩⟩,⟨⟨59522526,59522529⟩,⟨(-24007571),(-24007567)⟩⟩,⟨⟨50607222,50607226⟩,⟨(-21772610),(-21772607)⟩⟩,⟨⟨42935183,42935187⟩,⟨(-19646175),(-19646171)⟩⟩,⟨⟨36348707,36348711⟩,⟨(-17644170),(-17644166)⟩⟩,⟨⟨30707538,30707542⟩,⟨(-15776468),(-15776465)⟩⟩,⟨⟨25887321,25887325⟩,⟨(-14048053),(-14048049)⟩⟩,⟨⟨21778175,21778178⟩,⟨(-12460027),(-12460024)⟩⟩,⟨⟨18283294,18283297⟩,⟨(-11010459),(-11010456)⟩⟩,⟨⟨15317673,15317677⟩,⟨(-9695121),(-9695117)⟩⟩,⟨⟨12806889,12806892⟩,⟨(-8508089),(-8508085)⟩⟩,⟨⟨10685981,10685985⟩,⟨(-7442257),(-7442254)⟩⟩,⟨⟨8898421,8898425⟩,⟨(-6489759),(-6489756)⟩⟩,⟨⟨7395158,7395162⟩,⟨(-5642299),(-5642295)⟩⟩,⟨⟨6133756,6133760⟩,⟨(-4891427),(-4891423)⟩⟩,⟨⟨5077606,5077610⟩,⟨(-4228747),(-4228744)⟩⟩] +lemma kernel16_0_r2_5_eq : ∀ k : Fin 16, kernel16_0Expr 2 5 k = kernel16_0_r2_5 k := by decide +kernel +noncomputable def kernel16_0_r2_6 : Fin 16 → CBox := ![⟨⟨4195220,4195223⟩,⟨(-3646082),(-3646078)⟩⟩,⟨⟨3459580,3459583⟩,⟨(-3135581),(-3135578)⟩⟩,⟨⟨2847575,2847578⟩,⟨(-2689825),(-2689821)⟩⟩,⟨⟨2339491,2339495⟩,⟨(-2301859),(-2301855)⟩⟩,⟨⟨1918551,1918555⟩,⟨(-1965237),(-1965234)⟩⟩,⟨⟨1570518,1570521⟩,⟨(-1674034),(-1674031)⟩⟩,⟨⟨1283343,1283347⟩,⟨(-1422841),(-1422837)⟩⟩,⟨⟨1046855,1046858⟩,⟨(-1206760),(-1206756)⟩⟩,⟨⟨852488,852491⟩,⟨(-1021376),(-1021372)⟩⟩,⟨⟨693046,693050⟩,⟨(-862733),(-862729)⟩⟩,⟨⟨562500,562504⟩,⟨(-727311),(-727307)⟩⟩,⟨⟨455814,455818⟩,⟨(-611988),(-611985)⟩⟩,⟨⟨368786,368790⟩,⟨(-514006),(-514002)⟩⟩,⟨⟨297921,297924⟩,⟨(-430943),(-430940)⟩⟩,⟨⟨240318,240322⟩,⟨(-360683),(-360679)⟩⟩,⟨⟨193575,193579⟩,⟨(-301372),(-301369)⟩⟩] +lemma kernel16_0_r2_6_eq : ∀ k : Fin 16, kernel16_0Expr 2 6 k = kernel16_0_r2_6 k := by decide +kernel +noncomputable def kernel16_0_r2_7 : Fin 16 → CBox := ![⟨⟨155708,155712⟩,⟨(-251409),(-251405)⟩⟩,⟨⟨125083,125086⟩,⟨(-209400),(-209396)⟩⟩,⟨⟨100352,100356⟩,⟨(-174145),(-174141)⟩⟩,⟨⟨80415,80419⟩,⟨(-144616),(-144612)⟩⟩,⟨⟨64362,64366⟩,⟨(-119922),(-119919)⟩⟩,⟨⟨51459,51463⟩,⟨(-99311),(-99308)⟩⟩,⟨⟨41101,41106⟩,⟨(-82135),(-82130)⟩⟩,⟨⟨32796,32800⟩,⟨(-67841),(-67837)⟩⟩,⟨⟨26147,26150⟩,⟨(-55969),(-55965)⟩⟩,⟨⟨20828,20833⟩,⟨(-46120),(-46115)⟩⟩,⟨⟨16580,16584⟩,⟨(-37960),(-37956)⟩⟩,⟨⟨13192,13196⟩,⟨(-31211),(-31207)⟩⟩,⟨⟨10491,10494⟩,⟨(-25636),(-25632)⟩⟩,⟨⟨8337,8341⟩,⟨(-21035),(-21031)⟩⟩,⟨⟨6625,6629⟩,⟨(-17246),(-17242)⟩⟩,⟨⟨5263,5267⟩,⟨(-14125),(-14121)⟩⟩] +lemma kernel16_0_r2_7_eq : ∀ k : Fin 16, kernel16_0Expr 2 7 k = kernel16_0_r2_7 k := by decide +kernel +noncomputable def kernel16_0_r2_8 : Fin 16 → CBox := ![⟨⟨4180,4184⟩,⟨(-11559),(-11555)⟩⟩,⟨⟨3321,3325⟩,⟨(-9453),(-9449)⟩⟩,⟨⟨2638,2642⟩,⟨(-7723),(-7719)⟩⟩,⟨⟨2096,2100⟩,⟨(-6306),(-6302)⟩⟩,⟨⟨1667,1671⟩,⟨(-5146),(-5142)⟩⟩,⟨⟨1325,1329⟩,⟨(-4197),(-4193)⟩⟩,⟨⟨1055,1059⟩,⟨(-3420),(-3416)⟩⟩,⟨⟨840,844⟩,⟨(-2786),(-2782)⟩⟩,⟨⟨669,673⟩,⟨(-2269),(-2265)⟩⟩,⟨⟨533,539⟩,⟨(-1847),(-1842)⟩⟩,⟨⟨428,431⟩,⟨(-1502),(-1498)⟩⟩,⟨⟨341,345⟩,⟨(-1221),(-1217)⟩⟩,⟨⟨273,277⟩,⟨(-993),(-989)⟩⟩,⟨⟨220,223⟩,⟨(-808),(-804)⟩⟩,⟨⟨175,179⟩,⟨(-657),(-653)⟩⟩,⟨⟨141,145⟩,⟨(-532),(-528)⟩⟩] +lemma kernel16_0_r2_8_eq : ∀ k : Fin 16, kernel16_0Expr 2 8 k = kernel16_0_r2_8 k := by decide +kernel +noncomputable def kernel16_0_r2_9 : Fin 16 → CBox := ![⟨⟨113,117⟩,⟨(-434),(-430)⟩⟩,⟨⟨92,95⟩,⟨(-352),(-348)⟩⟩,⟨⟨74,78⟩,⟨(-286),(-282)⟩⟩,⟨⟨59,63⟩,⟨(-234),(-230)⟩⟩,⟨⟨49,53⟩,⟨(-189),(-185)⟩⟩,⟨⟨39,43⟩,⟨(-153),(-149)⟩⟩,⟨⟨32,36⟩,⟨(-126),(-122)⟩⟩,⟨⟨26,30⟩,⟨(-103),(-99)⟩⟩,⟨⟨21,24⟩,⟨(-82),(-78)⟩⟩,⟨⟨16,22⟩,⟨(-69),(-64)⟩⟩,⟨⟨13,17⟩,⟨(-55),(-51)⟩⟩,⟨⟨11,15⟩,⟨(-46),(-42)⟩⟩,⟨⟨8,12⟩,⟨(-37),(-33)⟩⟩,⟨⟨6,10⟩,⟨(-30),(-26)⟩⟩,⟨⟨5,9⟩,⟨(-26),(-22)⟩⟩,⟨⟨4,7⟩,⟨(-21),(-17)⟩⟩] +lemma kernel16_0_r2_9_eq : ∀ k : Fin 16, kernel16_0Expr 2 9 k = kernel16_0_r2_9 k := by decide +kernel +noncomputable def kernel16_0_r2_10 : Fin 16 → CBox := ![⟨⟨4,8⟩,⟨(-18),(-14)⟩⟩,⟨⟨2,6⟩,⟨(-14),(-10)⟩⟩,⟨⟨1,5⟩,⟨(-12),(-8)⟩⟩,⟨⟨1,5⟩,⟨(-9),(-5)⟩⟩,⟨⟨1,5⟩,⟨(-9),(-5)⟩⟩,⟨⟨(-1),3⟩,⟨(-8),(-4)⟩⟩,⟨⟨1,5⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-1),3⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-1),3⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-1),3⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩] +lemma kernel16_0_r2_10_eq : ∀ k : Fin 16, kernel16_0Expr 2 10 k = kernel16_0_r2_10 k := by decide +kernel +noncomputable def kernel16_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),2⟩,⟨(-4),0⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel16_0_r2_11_eq : ∀ k : Fin 16, kernel16_0Expr 2 11 k = kernel16_0_r2_11 k := by decide +kernel +noncomputable def kernel16_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel16_0_r2_12_eq : ∀ k : Fin 16, kernel16_0Expr 2 12 k = kernel16_0_r2_12 k := by decide +kernel +noncomputable def kernel16_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩] +lemma kernel16_0_r2_13_eq : ∀ k : Fin 16, kernel16_0Expr 2 13 k = kernel16_0_r2_13 k := by decide +kernel +noncomputable def kernel16_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r2_14_eq : ∀ k : Fin 16, kernel16_0Expr 2 14 k = kernel16_0_r2_14 k := by decide +kernel +noncomputable def kernel16_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel16_0_r2_15_eq : ∀ k : Fin 16, kernel16_0Expr 2 15 k = kernel16_0_r2_15 k := by decide +kernel +noncomputable def kernel16_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel16_0_r2_0,kernel16_0_r2_1,kernel16_0_r2_2,kernel16_0_r2_3,kernel16_0_r2_4,kernel16_0_r2_5,kernel16_0_r2_6,kernel16_0_r2_7,kernel16_0_r2_8,kernel16_0_r2_9,kernel16_0_r2_10,kernel16_0_r2_11,kernel16_0_r2_12,kernel16_0_r2_13,kernel16_0_r2_14,kernel16_0_r2_15] +lemma kernel16_0_r2_eq (i k : Fin 16) : kernel16_0Expr 2 i k = kernel16_0_r2 i k := by + fin_cases i + · exact kernel16_0_r2_0_eq k + · exact kernel16_0_r2_1_eq k + · exact kernel16_0_r2_2_eq k + · exact kernel16_0_r2_3_eq k + · exact kernel16_0_r2_4_eq k + · exact kernel16_0_r2_5_eq k + · exact kernel16_0_r2_6_eq k + · exact kernel16_0_r2_7_eq k + · exact kernel16_0_r2_8_eq k + · exact kernel16_0_r2_9_eq k + · exact kernel16_0_r2_10_eq k + · exact kernel16_0_r2_11_eq k + · exact kernel16_0_r2_12_eq k + · exact kernel16_0_r2_13_eq k + · exact kernel16_0_r2_14_eq k + · exact kernel16_0_r2_15_eq k +noncomputable def kernel16_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-35355296306592068193),(-35355296306592068083)⟩,⟨25935555185727418093,25935555185727418202⟩⟩,⟨⟨(-35295217076296091596),(-35295217076296091486)⟩,⟨25927500057206492451,25927500057206492561⟩⟩,⟨⟨(-35175297710095470370),(-35175297710095470261)⟩,⟨25911297369616623318,25911297369616623425⟩⟩,⟨⟨(-34996015216423413589),(-34996015216423413480)⟩,⟨25886763673438299675,25886763673438299784⟩⟩,⟨⟨(-34758082160553849435),(-34758082160553849327)⟩,⟨25853627304848070913,25853627304848071021⟩⟩,⟨⟨(-34462443137624783338),(-34462443137624783232)⟩,⟨25811532546744225543,25811532546744225649⟩⟩,⟨⟨(-34110270086699169668),(-34110270086699169560)⟩,⟨25760045091623693183,25760045091623693291⟩⟩,⟨⟨(-33702956460642817636),(-33702956460642817531)⟩,⟨25698658734732485563,25698658734732485668⟩⟩,⟨⟨(-33242110270857515589),(-33242110270857515483)⟩,⟨25626803209766000419,25626803209766000524⟩⟩,⟨⟨(-32729546030509075114),(-32729546030509075010)⟩,⟨25543853064384990769,25543853064384990873⟩⟩,⟨⟨(-32167275624871065087),(-32167275624871064985)⟩,⟨25449137459135144302,25449137459135144404⟩⟩,⟨⟨(-31557498142786341832),(-31557498142786341731)⟩,⟨25341950761194235144,25341950761194235245⟩⟩,⟨⟨(-30902588709033282356),(-30902588709033282257)⟩,⟨25221563793883553204,25221563793883553302⟩⟩,⟨⟨(-30205086363556502575),(-30205086363556502479)⟩,⟨25087235594212044767,25087235594212044862⟩⟩,⟨⟨(-29467681040048251404),(-29467681040048251309)⟩,⟨24938225523991924471,24938225523991924566⟩⟩,⟨⟨(-28693199703192889404),(-28693199703192889310)⟩,⟨24773805575368560841,24773805575368560935⟩⟩] +lemma kernel16_0_r3_0_eq : ∀ k : Fin 16, kernel16_0Expr 3 0 k = kernel16_0_r3_0 k := by decide +kernel +noncomputable def kernel16_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-27884591710940479525),(-27884591710940479433)⟩,⟨24593272709014209083,24593272709014209175⟩⟩,⟨⟨(-27044913475366483254),(-27044913475366483164)⟩,⟨24395961062786241808,24395961062786241896⟩⟩,⟨⟨(-26177312502896722218),(-26177312502896722130)⟩,⟨24181253870359022200,24181253870359022288⟩⟩,⟨⟨(-25285010901809938105),(-25285010901809938019)⟩,⟨23948594933188436738,23948594933188436824⟩⟩,⟨⟨(-24371288451842708276),(-24371288451842708192)⟩,⟨23697499495113853632,23697499495113853715⟩⟩,⟨⟨(-23439465337272720215),(-23439465337272720134)⟩,⟨23427564376869018848,23427564376869018928⟩⟩,⟨⟨(-22492884650900580004),(-22492884650900579926)⟩,⟨23138477237657393084,23138477237657393161⟩⟩,⟨⟨(-21534894781739536095),(-21534894781739536019)⟩,⟨22830024842616996877,22830024842616996952⟩⟩,⟨⟨(-20568831803810491629),(-20568831803810491556)⟩,⟨22502100228296766929,22502100228296767003⟩⟩,⟨⟨(-19598001987085579229),(-19598001987085579159)⟩,⟨22154708673007856790,22154708673007856860⟩⟩,⟨⟨(-18625664554195598063),(-18625664554195597994)⟩,⟨21787972394893976496,21787972394893976565⟩⟩,⟨⟨(-17655014807895697799),(-17655014807895697734)⟩,⟨21402133917559832935,21402133917559833001⟩⟩,⟨⟨(-16689167754366922210),(-16689167754366922145)⟩,⟨20997558060864539252,20997558060864539316⟩⟩,⟨⟨(-15731142346134982485),(-15731142346134982424)⟩,⟨20574732532772988417,20574732532772988479⟩⟩,⟨⟨(-14783846465650391565),(-14783846465650391506)⟩,⟨20134267116698864636,20134267116698864695⟩⟩,⟨⟨(-13850062766358760492),(-13850062766358760434)⟩,⟨19676891467299242919,19676891467299242976⟩⟩] +lemma kernel16_0_r3_1_eq : ∀ k : Fin 16, kernel16_0Expr 3 1 k = kernel16_0_r3_1 k := by decide +kernel +noncomputable def kernel16_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-12932435482385803597),(-12932435482385803542)⟩,⟨19203451545922720240,19203451545922720295⟩⟩,⟨⟨(-12033458310785114630),(-12033458310785114577)⟩,⟨18714904744604298465,18714904744604298517⟩⟩,⟨⟨(-11155463461692933559),(-11155463461692933510)⟩,⟨18212313764382231611,18212313764382231660⟩⟩,⟨⟨(-10300611961775989992),(-10300611961775989944)⟩,⟨17696839329538423834,17696839329538423882⟩⟩,⟨⟨(-9470885285146703795),(-9470885285146703749)⟩,⟨17169731833904854619,17169731833904854665⟩⟩,⟨⟨(-8668078373581432548),(-8668078373581432505)⟩,⟨16632322028424528613,16632322028424528657⟩⟩,⟨⟨(-7893794094563311776),(-7893794094563311736)⟩,⟨16086010870521394701,16086010870521394742⟩⟩,⟨⟨(-7149439171554605417),(-7149439171554605377)⟩,⟨15532258665361834142,15532258665361834181⟩⟩,⟨⟨(-6436221606176217847),(-6436221606176217809)⟩,⟨14972573636653284198,14972573636653284235⟩⟩,⟨⟨(-5755149596841209590),(-5755149596841209555)⟩,⟨14408500070128560760,14408500070128560794⟩⟩,⟨⟨(-5107031943073217917),(-5107031943073217882)⟩,⟨13841606176247001963,13841606176247001997⟩⟩,⟨⟨(-4492479909465100093),(-4492479909465100062)⟩,⟨13273471819880568810,13273471819880568842⟩⟩,⟨⟨(-3911910508226009439),(-3911910508226009409)⟩,⟨12705676263855141726,12705676263855141757⟩⟩,⟨⟨(-3365551144752675605),(-3365551144752675576)⟩,⟨12139786070230498643,12139786070230498671⟩⟩,⟨⟨(-2853445556862607695),(-2853445556862607669)⟩,⟨11577343298207316647,11577343298207316673⟩⟩,⟨⟨(-2375460965452073188),(-2375460965452073164)⟩,⟨11019854130659194779,11019854130659194803⟩⟩] +lemma kernel16_0_r3_2_eq : ∀ k : Fin 16, kernel16_0Expr 3 2 k = kernel16_0_r3_2 k := by decide +kernel +noncomputable def kernel16_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-1931296342583691956),(-1931296342583691932)⟩,⟨10468778052645728548,10468778052645728572⟩⟩,⟨⟨(-1520491692541949903),(-1520491692541949881)⟩,⟨9925517695040114184,9925517695040114206⟩⟩,⟨⟨(-1142438232371981596),(-1142438232371981574)⟩,⟨9391409444796651037,9391409444796651059⟩⟩,⟨⟨(-796389350964178382),(-796389350964178362)⟩,⟨8867714910604939255,8867714910604939275⟩⟩,⟨⟨(-481472219963186071),(-481472219963186052)⟩,⟨8355613318959400594,8355613318959400613⟩⟩,⟨⟨(-196699925733554101),(-196699925733554083)⟩,⟨7856194901257043102,7856194901257043120⟩⟩,⟨⟨59016010656315673,59016010656315689⟩,⟨7370455317671655324,7370455317671655342⟩⟩,⟨⟨286852858958550986,286852858958551001⟩,⟨6899291148489002256,6899291148489002271⟩⟩,⟨⟨488063783035571651,488063783035571666⟩,⟨6443496468572124294,6443496468572124309⟩⟩,⟨⟨663964951199537446,663964951199537459⟩,⟨6003760505897785380,6003760505897785393⟩⟩,⟨⟨815922778293243278,815922778293243291⟩,⟨5580666370891635639,5580666370891635652⟩⟩,⟨⟨945341418101771722,945341418101771735⟩,⟨5174690829801768932,5174690829801768944⟩⟩,⟨⟨1053650617205579736,1053650617205579747⟩,⟨4786205082779360327,4786205082779360339⟩⟩,⟨⟨1142294032685298311,1142294032685298322⟩,⟨4415476495849441004,4415476495849441014⟩⟩,⟨⟨1212718106337936975,1212718106337936985⟩,⟨4062671225697746592,4062671225697746602⟩⟩,⟨⟨1266361577448328331,1266361577448328341⟩,⟨3727857667286839633,3727857667286839642⟩⟩] +lemma kernel16_0_r3_3_eq : ∀ k : Fin 16, kernel16_0Expr 3 3 k = kernel16_0_r3_3 k := by decide +kernel +noncomputable def kernel16_0_r3_4 : Fin 16 → CBox := ![⟨⟨1304645704872775630,1304645704872775639⟩,⟨3411010646833697287,3411010646833697295⟩⟩,⟨⟨1328965257433471709,1328965257433471716⟩,⟨3112016276689834042,3112016276689834049⟩⟩,⟨⟨1340680319592984774,1340680319592984782⟩,⟨2830677384192786949,2830677384192786958⟩⟩,⟨⟨1341108947275770458,1341108947275770465⟩,⟨2566719423604873347,2566719423604873353⟩⟩,⟨⟨1331520696719473300,1331520696719473306⟩,⟨2319796778794649390,2319796778794649396⟩⟩,⟨⟨1313131037553813291,1313131037553813299⟩,⟨2089499364295976398,2089499364295976405⟩⟩,⟨⟨1287096650086941607,1287096650086941612⟩,⟨1875359433723199273,1875359433723199278⟩⟩,⟨⟨1254511596180127508,1254511596180127514⟩,⟨1676858507132075312,1676858507132075319⟩⟩,⟨⟨1216404343245076411,1216404343245076417⟩,⟨1493434332680390125,1493434332680390132⟩⟩,⟨⟨1173735611917615074,1173735611917615082⟩,⟨1324487802730689758,1324487802730689765⟩⟩,⟨⟨1127397009939167562,1127397009939167569⟩,⟨1169389750210023566,1169389750210023572⟩⟩,⟨⟨1078210407783626185,1078210407783626190⟩,⟨1027487557449976341,1027487557449976346⟩⟩,⟨⟨1026928005649913723,1026928005649913728⟩,⟨898111516722085618,898111516722085624⟩⟩,⟨⟨974233036625816696,974233036625816703⟩,⟨780580889105383225,780580889105383233⟩⟩,⟨⟨920741047121433115,920741047121433122⟩,⟨674209616022680717,674209616022680724⟩⟩,⟨⟨867001693055687082,867001693055687088⟩,⟨578311645613676416,578311645613676423⟩⟩] +lemma kernel16_0_r3_4_eq : ∀ k : Fin 16, kernel16_0Expr 3 4 k = kernel16_0_r3_4 k := by decide +kernel +noncomputable def kernel16_0_r3_5 : Fin 16 → CBox := ![⟨⟨813500988723193736,813500988723193741⟩,⟨492205843936888362,492205843936888368⟩⟩,⟨⟨760663944721046189,760663944721046194⟩,⟨415220468679543534,415220468679543540⟩⟩,⟨⟨708857531711027433,708857531711027438⟩,⟨346697190487374908,346697190487374913⟩⟩,⟨⟨658393908055237446,658393908055237451⟩,⟨285994654100588997,285994654100589002⟩⟩,⟨⟨609533851405199493,609533851405199498⟩,⟨232491578108298959,232491578108298964⟩⟩,⟨⟨562490337051760120,562490337051760126⟩,⟨185589398236877017,185589398236877022⟩⟩,⟨⟨517432209156105903,517432209156105907⟩,⟨144714464608893057,144714464608893061⟩⟩,⟨⟨474487894778921219,474487894778921223⟩,⟨109319808305005881,109319808305005886⟩⟩,⟨⟨433749114802636103,433749114802636108⟩,⟨78886496802935195,78886496802935200⟩⟩,⟨⟨395274550300066207,395274550300066212⟩,⟨52924601441519359,52924601441519365⟩⟩,⟨⟨359093427544282996,359093427544283001⟩,⟨30973802963455102,30973802963455107⟩⟩,⟨⟨325208989587221299,325208989587221303⟩,⟨12603663439610433,12603663439610437⟩⟩,⟨⟨293601827072871518,293601827072871522⟩,⟨(-2586405506148642),(-2586405506148637)⟩⟩,⟨⟨264233045617171485,264233045617171489⟩,⟨(-14967447237222616),(-14967447237222611)⟩⟩,⟨⟨237047251611742249,237047251611742253⟩,⟨(-24881506019671279),(-24881506019671274)⟩⟩,⟨⟨211975342632410275,211975342632410278⟩,⟨(-32642382979905951),(-32642382979905948)⟩⟩] +lemma kernel16_0_r3_5_eq : ∀ k : Fin 16, kernel16_0Expr 3 5 k = kernel16_0_r3_5 k := by decide +kernel +noncomputable def kernel16_0_r3_6 : Fin 16 → CBox := ![⟨⟨188937092705543092,188937092705543098⟩,⟨(-38536571289605755),(-38536571289605750)⟩⟩,⟨⟨167843526464721330,167843526464721333⟩,⟨(-42824340685712514),(-42824340685712510)⟩⟩,⟨⟨148599079685784910,148599079685784914⟩,⟨(-45740942704125242),(-45740942704125238)⟩⟩,⟨⟨131103546797594245,131103546797594250⟩,⟨(-47497909566441535),(-47497909566441531)⟩⟩,⟨⟨115253818715377534,115253818715377538⟩,⟨(-48284421452602873),(-48284421452602868)⟩⟩,⟨⟨100945416727769280,100945416727769283⟩,⟨(-48268718863209992),(-48268718863209989)⟩⟩,⟨⟨88073830189351900,88073830189351903⟩,⟨(-47599538870931582),(-47599538870931579)⟩⟩,⟨⟨76535667435926765,76535667435926769⟩,⟨(-46407556231693175),(-46407556231693171)⟩⟩,⟨⟨66229630663683679,66229630663683683⟩,⟨(-44806812528187902),(-44806812528187899)⟩⟩,⟨⟨57057326514407083,57057326514407086⟩,⟨(-42896118710262681),(-42896118710262677)⟩⟩,⟨⟨48923924809120850,48923924809120854⟩,⟨(-40760418543352430),(-40760418543352425)⟩⟩,⟨⟨41738678297278894,41738678297278898⟩,⟨(-38472102546853613),(-38472102546853609)⟩⟩,⟨⟨35415316464933624,35415316464933628⟩,⟨(-36092263973710128),(-36092263973710124)⟩⟩,⟨⟨29872326401672141,29872326401672144⟩,⟨(-33671890230074776),(-33671890230074773)⟩⟩,⟨⟨25033133491423081,25033133491423086⟩,⟨(-31252984844047200),(-31252984844047196)⟩⟩,⟨⟨20826194295287056,20826194295287059⟩,⟨(-28869616654033458),(-28869616654033455)⟩⟩] +lemma kernel16_0_r3_6_eq : ∀ k : Fin 16, kernel16_0Expr 3 6 k = kernel16_0_r3_6 k := by decide +kernel +noncomputable def kernel16_0_r3_7 : Fin 16 → CBox := ![⟨⟨17185013463405785,17185013463405789⟩,⟨(-26548894293263264),(-26548894293263260)⟩⟩,⟨⟨14048095874448586,14048095874448591⟩,⟨(-24311865294268216),(-24311865294268212)⟩⟩,⟨⟨11358844480871349,11358844480871353⟩,⟨(-22174340225863253),(-22174340225863248)⟩⟩,⟨⟨9065413559120518,9065413559120522⟩,⟨(-20147643208498623),(-20147643208498620)⟩⟩,⟨⟨7120526247732867,7120526247732870⟩,⟨(-18239290937344033),(-18239290937344030)⟩⟩,⟨⟨5481264421885746,5481264421885751⟩,⟨(-16453602983734212),(-16453602983734208)⟩⟩,⟨⟨4108838117114021,4108838117114024⟩,⟨(-14792246653840563),(-14792246653840560)⟩⟩,⟨⟨2968340892013021,2968340892013026⟩,⟨(-13254720069012996),(-13254720069012992)⟩⟩,⟨⟨2028496721866602,2028496721866605⟩,⟨(-11838777406340996),(-11838777406340992)⟩⟩,⟨⟨1261403252126438,1261403252126442⟩,⟨(-10540800412257175),(-10540800412257171)⟩⟩,⟨⟨642275520271613,642275520271617⟩,⟨(-9356120388251771),(-9356120388251766)⟩⟩,⟨⟨149193582592875,149193582592878⟩,⟨(-8279294857680358),(-8279294857680355)⟩⟩,⟨⟨(-237143137108679),(-237143137108676)⟩,⟨(-7304343067598038),(-7304343067598035)⟩⟩,⟨⟨(-533652524619758),(-533652524619755)⟩,⟨(-6424944370400564),(-6424944370400561)⟩⟩,⟨⟨(-755095734745109),(-755095734745106)⟩,⟨(-5634603377000343),(-5634603377000340)⟩⟩,⟨⟨(-914291142733973),(-914291142733969)⟩,⟨(-4926785585755449),(-4926785585755445)⟩⟩] +lemma kernel16_0_r3_7_eq : ∀ k : Fin 16, kernel16_0Expr 3 7 k = kernel16_0_r3_7 k := by decide +kernel +noncomputable def kernel16_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-1022315395996492),(-1022315395996488)⟩,⟨(-4295026978008714),(-4295026978008711)⟩⟩,⟨⟨(-1088691020559585),(-1088691020559582)⟩,⟨(-3733020839607512),(-3733020839607509)⟩⟩,⟨⟨(-1121560333074959),(-1121560333074956)⟩,⟨(-3234684824990479),(-3234684824990476)⟩⟩,⟨⟨(-1127845658939592),(-1127845658939589)⟩,⟨(-2794211032279746),(-2794211032279743)⟩⟩,⟨⟨(-1113396063747949),(-1113396063747945)⟩,⟨(-2406101609371266),(-2406101609371263)⟩⟩,⟨⟨(-1083120972612974),(-1083120972612970)⟩,⟨(-2065192166506619),(-2065192166506615)⟩⟩,⟨⟨(-1041111183723881),(-1041111183723877)⟩,⟨(-1766665033693437),(-1766665033693434)⟩⟩,⟨⟨(-990747882718478),(-990747882718475)⟩,⟨(-1506054174355306),(-1506054174355302)⟩⟩,⟨⟨(-934800336831108),(-934800336831104)⟩,⟨(-1279243351819394),(-1279243351819390)⟩⟩,⟨⟨(-875512995994076),(-875512995994073)⟩,⟨(-1082458944190507),(-1082458944190504)⟩⟩,⟨⟨(-814682755593571),(-814682755593568)⟩,⟨(-912258616798762),(-912258616798758)⟩⟩,⟨⟨(-753727145658594),(-753727145658590)⟩,⟨(-765516890284845),(-765516890284842)⟩⟩,⟨⟨(-693744206889916),(-693744206889912)⟩,⟨(-639408486664079),(-639408486664075)⟩⟩,⟨⟨(-635564797844327),(-635564797844324)⟩,⟨(-531390195236041),(-531390195236038)⟩⟩,⟨⟨(-579798052230760),(-579798052230757)⟩,⟨(-439181874573370),(-439181874573367)⟩⟩,⟨⟨(-526870672827532),(-526870672827528)⟩,⟨(-360747095422991),(-360747095422987)⟩⟩] +lemma kernel16_0_r3_8_eq : ∀ k : Fin 16, kernel16_0Expr 3 8 k = kernel16_0_r3_8 k := by decide +kernel +noncomputable def kernel16_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-477060710902248),(-477060710902243)⟩,⟨(-294273831425459),(-294273831425455)⟩⟩,⟨⟨(-430526438858081),(-430526438858078)⟩,⟨(-238155519233882),(-238155519233879)⟩⟩,⟨⟨(-387330880547955),(-387330880547952)⟩,⟨(-190972735952641),(-190972735952638)⟩⟩,⟨⟨(-347462519470584),(-347462519470579)⟩,⟨(-151475678838425),(-151475678838420)⟩⟩,⟨⟨(-310852660860464),(-310852660860461)⟩,⟨(-118567578920574),(-118567578920570)⟩⟩,⟨⟨(-277389880290543),(-277389880290540)⟩,⟨(-91289135623300),(-91289135623296)⟩⟩,⟨⟨(-246931949436559),(-246931949436555)⟩,⟨(-68804022656062),(-68804022656058)⟩⟩,⟨⟨(-219315589573323),(-219315589573318)⟩,⟨(-50385485469063),(-50385485469059)⟩⟩,⟨⟨(-194364365524106),(-194364365524103)⟩,⟨(-35404026589339),(-35404026589335)⟩⟩,⟨⟨(-171894997393895),(-171894997393891)⟩,⟨(-23316156359105),(-23316156359101)⟩⟩,⟨⟨(-151722334621211),(-151722334621206)⟩,⟨(-13654172255460),(-13654172255455)⟩⟩,⟨⟨(-133663206740731),(-133663206740727)⟩,⟨(-6016919408027),(-6016919408023)⟩⟩,⟨⟨(-117539337755833),(-117539337755830)⟩,⟨(-61477543870),(-61477543867)⟩⟩,⟨⟨(-103179486123035),(-103179486123032)⟩,⟨4504285163431,4504285163435⟩⟩,⟨⟨(-90420949956509),(-90420949956505)⟩,⟨7928353459042,7928353459045⟩⟩,⟨⟨(-79110557049323),(-79110557049320)⟩,⟨10420464562067,10420464562071⟩⟩] +lemma kernel16_0_r3_9_eq : ∀ k : Fin 16, kernel16_0Expr 3 9 k = kernel16_0_r3_9 k := by decide +kernel +noncomputable def kernel16_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-69105241537322),(-69105241537318)⟩,⟨12157328368358,12157328368361⟩⟩,⟨⟨(-60272293346724),(-60272293346721)⟩,⟨13287229177892,13287229177895⟩⟩,⟨⟨(-52489352805800),(-52489352805797)⟩,⟨13934067445742,13934067445745⟩⟩,⟨⟨(-45644210799644),(-45644210799640)⟩,⟨14200897103850,14200897103854⟩⟩,⟨⟨(-39634464442260),(-39634464442255)⟩,⟨14173010660997,14173010661002⟩⟩,⟨⟨(-34367069273301),(-34367069273295)⟩,⟨13920620712831,13920620712837⟩⟩,⟨⟨(-29757821305827),(-29757821305823)⟩,⟨13501182805949,13501182805952⟩⟩,⟨⟨(-25730795713213),(-25730795713209)⟩,⟨12961400897682,12961400897686⟩⟩,⟨⟨(-22217763413489),(-22217763413486)⟩,⟨12338953012641,12338953012644⟩⟩,⟨⟨(-19157602164344),(-19157602164341)⟩,⟨11663971175738,11663971175741⟩⟩,⟨⟨(-16495714908130),(-16495714908126)⟩,⟨10960306341790,10960306341794⟩⟩,⟨⟨(-14183464900565),(-14183464900562)⟩,⟨10246605872742,10246605872746⟩⟩,⟨⟨(-12177634526643),(-12177634526639)⟩,⟨9537228153857,9537228153860⟩⟩,⟨⟨(-10439912569418),(-10439912569414)⟩,⟨8843016199971,8843016199974⟩⟩,⟨⟨(-8936412978372),(-8936412978369)⟩,⟨8171949585070,8171949585074⟩⟩,⟨⟨(-7637226818764),(-7637226818759)⟩,⟨7529691731192,7529691731197⟩⟩] +lemma kernel16_0_r3_10_eq : ∀ k : Fin 16, kernel16_0Expr 3 10 k = kernel16_0_r3_10 k := by decide +kernel +noncomputable def kernel16_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-6516008014905),(-6516008014902)⟩,⟨6920047509659,6920047509663⟩⟩,⟨⟨(-5549592679190),(-5549592679185)⟩,⟨6345344229830,6345344229835⟩⟩,⟨⟨(-4717651201787),(-4717651201784)⟩,⟨5806747406906,5806747406909⟩⟩,⟨⟨(-4002371826629),(-4002371826625)⟩,⟨5304521197911,5304521197914⟩⟩,⟨⟨(-3388174125926),(-3388174125921)⟩,⟨4838242061069,4838242061074⟩⟩,⟨⟨(-2861450581397),(-2861450581393)⟩,⟨4406973014143,4406973014146⟩⟩,⟨⟨(-2410334362969),(-2410334362964)⟩,⟨4009404829010,4009404829015⟩⟩,⟨⟨(-2024491346162),(-2024491346158)⟩,⟨3643969589072,3643969589077⟩⟩,⟨⟨(-1694934412018),(-1694934412015)⟩,⟨3308931240719,3308931240722⟩⟩,⟨⟨(-1413858115140),(-1413858115137)⟩,⟨3002457077873,3002457077877⟩⟩,⟨⟨(-1174491875925),(-1174491875922)⟩,⟨2722673498431,2722673498434⟩⟩,⟨⟨(-970969943464),(-970969943461)⟩,⟨2467708852716,2467708852719⟩⟩,⟨⟨(-798216479229),(-798216479226)⟩,⟨2235725757593,2235725757596⟩⟩,⟨⟨(-651844223008),(-651844223004)⟩,⟨2024944866566,2024944866569⟩⟩,⟨⟨(-528065317364),(-528065317360)⟩,⟨1833661758488,1833661758492⟩⟩,⟨⟨(-423612981878),(-423612981874)⟩,⟨1660258328094,1660258328097⟩⟩] +lemma kernel16_0_r3_11_eq : ∀ k : Fin 16, kernel16_0Expr 3 11 k = kernel16_0_r3_11 k := by decide +kernel +noncomputable def kernel16_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-335672841245),(-335672841240)⟩,⟨1503209824289,1503209824294⟩⟩,⟨⟨(-261822819955),(-261822819951)⟩,⟨1361088481162,1361088481165⟩⟩,⟨⟨(-199980619817),(-199980619813)⟩,⟨1232564517178,1232564517181⟩⟩,⟨⟨(-148357893854),(-148357893850)⟩,⟨1116405135523,1116405135526⟩⟩,⟨⟨(-105420320888),(-105420320885)⟩,⟨1011472039137,1011472039141⟩⟩,⟨⟨(-69852869079),(-69852869076)⟩,⟨916717874365,916717874369⟩⟩,⟨⟨(-40529613789),(-40529613785)⟩,⟨831181934358,831181934362⟩⟩,⟨⟨(-16487545547),(-16487545543)⟩,⟨753985384778,753985384782⟩⟩,⟨⟨3096132084,3096132088⟩,⟨684326217860,684326217863⟩⟩,⟨⟨18923657196,18923657199⟩,⟨621474094571,621474094575⟩⟩,⟨⟨31593707080,31593707084⟩,⟨564765196769,564765196773⟩⟩,⟨⟨41616082349,41616082353⟩,⟨513597180596,513597180600⟩⟩,⟨⟨49424379551,49424379554⟩,⟨467424297628,467424297631⟩⟩,⟨⟨55386917092,55386917095⟩,⟨425752730464,425752730468⟩⟩,⟨⟨59816146274,59816146277⟩,⟨388136173795,388136173799⟩⟩,⟨⟨62976749993,62976749996⟩,⟨354171679578,354171679582⟩⟩] +lemma kernel16_0_r3_12_eq : ∀ k : Fin 16, kernel16_0Expr 3 12 k = kernel16_0_r3_12 k := by decide +kernel +noncomputable def kernel16_0_r3_13 : Fin 16 → CBox := ![⟨⟨65092605876,65092605879⟩,⟨323495775391,323495775395⟩⟩,⟨⟨66352767829,66352767833⟩,⟨295780857684,295780857688⟩⟩,⟨⟨66916599970,66916599974⟩,⟨270731856111,270731856115⟩⟩,⟨⟨66918179356,66918179360⟩,⟨248083161079,248083161082⟩⟩,⟨⟨66470068484,66470068488⟩,⟨227595803767,227595803770⟩⟩,⟨⟨65666545155,65666545160⟩,⟨209054875909,209054875914⟩⟩,⟨⟨64586365439,64586365443⟩,⟨192267175441,192267175444⟩⟩,⟨⟨63295125326,63295125329⟩,⟨177059063429,177059063432⟩⟩,⟨⟨61847277661,61847277665⟩,⟨163274517552,163274517555⟩⟩,⟨⟨60287853261,60287853265⟩,⟨150773367468,150773367471⟩⟩,⟨⟨58653928306,58653928310⟩,⟨139429697801,139429697805⟩⟩,⟨⟨56975874375,56975874378⟩,⟨129130405039,129130405042⟩⟩,⟨⟨55278422304,55278422307⟩,⟨119773895245,119773895249⟩⟩,⟨⟨53581566812,53581566816⟩,⟨111268910295,111268910298⟩⟩,⟨⟨51901334933,51901334936⟩,⟨103533471067,103533471071⟩⟩,⟨⟨50250438117,50250438120⟩,⟨96493926859,96493926862⟩⟩] +lemma kernel16_0_r3_13_eq : ∀ k : Fin 16, kernel16_0Expr 3 13 k = kernel16_0_r3_13 k := by decide +kernel +noncomputable def kernel16_0_r3_14 : Fin 16 → CBox := ![⟨⟨48638825034,48638825039⟩,⟨90084101069,90084101074⟩⟩,⟨⟨47074149634,47074149638⟩,⟨84244524001,84244524005⟩⟩,⟨⟨45562167005,45562167010⟩,⟨78921744330,78921744335⟩⟩,⟨⟨44107067729,44107067732⟩,⟨74067711572,74067711575⟩⟩,⟨⟨42711759882,42711759886⟩,⟨69639222508,69639222511⟩⟩,⟨⟨41378106553,41378106556⟩,⟨65597425186,65597425190⟩⟩,⟨⟨40107125535,40107125538⟩,⟨61907374691,61907374695⟩⟩,⟨⟨38899156949,38899156953⟩,⟨58537635444,58537635448⟩⟩,⟨⟨37754003657,37754003660⟩,⟨55459925284,55459925287⟩⟩,⟨⟨36671048648,36671048651⟩,⟨52648797039,52648797043⟩⟩,⟨⟨35649352925,35649352928⟩,⟨50081353769,50081353772⟩⟩,⟨⟨34687736957,34687736960⟩,⟨47736994153,47736994157⟩⟩,⟨⟨33784848220,33784848224⟩,⟨45597184985,45597184989⟩⟩,⟨⟨32939217065,32939217068⟩,⟨43645257910,43645257914⟩⟩,⟨⟨32149302751,32149302754⟩,⟨41866227957,41866227960⟩⟩,⟨⟨31413531224,31413531228⟩,⟨40246631594,40246631598⟩⟩] +lemma kernel16_0_r3_14_eq : ∀ k : Fin 16, kernel16_0Expr 3 14 k = kernel16_0_r3_14 k := by decide +kernel +noncomputable def kernel16_0_r3_15 : Fin 16 → CBox := ![⟨⟨30730325998,30730326001⟩,⟨38774382350,38774382354⟩⟩,⟨⟨30098133274,30098133279⟩,⟨37438642155,37438642159⟩⟩,⟨⟨29515442251,29515442254⟩,⟨36229706883,36229706887⟩⟩,⟨⟨28980801454,28980801458⟩,⟨35138904636,35138904639⟩⟩,⟨⟨28492831792,28492831795⟩,⟨34158505522,34158505526⟩⟩,⟨⟨28050236869,28050236873⟩,⟨33281641849,33281641853⟩⟩,⟨⟨27651811114,27651811118⟩,⟨32502237691,32502237695⟩⟩,⟨⟨27296446088,27296446092⟩,⟨31814947039,31814947043⟩⟩,⟨⟨26983135339,26983135343⟩,⟨31215099706,31215099710⟩⟩,⟨⟨26710978088,26710978092⟩,⟨30698654374,30698654379⟩⟩,⟨⟨26479181995,26479181998⟩,⟨30262158198,30262158202⟩⟩,⟨⟨26287065196,26287065200⟩,⟨29902712453,29902712456⟩⟩,⟨⟨26134057769,26134057773⟩,⟨29617943838,29617943841⟩⟩,⟨⟨26019702788,26019702792⟩,⟨29405981076,29405981079⟩⟩,⟨⟨25943657029,25943657033⟩,⟨29265436513,29265436517⟩⟩,⟨⟨25905691444,25905691447⟩,⟨29195392523,29195392527⟩⟩] +lemma kernel16_0_r3_15_eq : ∀ k : Fin 16, kernel16_0Expr 3 15 k = kernel16_0_r3_15 k := by decide +kernel +noncomputable def kernel16_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel16_0_r3_0,kernel16_0_r3_1,kernel16_0_r3_2,kernel16_0_r3_3,kernel16_0_r3_4,kernel16_0_r3_5,kernel16_0_r3_6,kernel16_0_r3_7,kernel16_0_r3_8,kernel16_0_r3_9,kernel16_0_r3_10,kernel16_0_r3_11,kernel16_0_r3_12,kernel16_0_r3_13,kernel16_0_r3_14,kernel16_0_r3_15] +lemma kernel16_0_r3_eq (i k : Fin 16) : kernel16_0Expr 3 i k = kernel16_0_r3 i k := by + fin_cases i + · exact kernel16_0_r3_0_eq k + · exact kernel16_0_r3_1_eq k + · exact kernel16_0_r3_2_eq k + · exact kernel16_0_r3_3_eq k + · exact kernel16_0_r3_4_eq k + · exact kernel16_0_r3_5_eq k + · exact kernel16_0_r3_6_eq k + · exact kernel16_0_r3_7_eq k + · exact kernel16_0_r3_8_eq k + · exact kernel16_0_r3_9_eq k + · exact kernel16_0_r3_10_eq k + · exact kernel16_0_r3_11_eq k + · exact kernel16_0_r3_12_eq k + · exact kernel16_0_r3_13_eq k + · exact kernel16_0_r3_14_eq k + · exact kernel16_0_r3_15_eq k +noncomputable def kernel16_0_r4_0 : Fin 16 → CBox := ![⟨⟨2557523781137077189596235,2557523781137077601706531⟩,⟨(-15736666525015201792796465),(-15736666525015201380619354)⟩⟩,⟨⟨2545816868693902241929334,2545816868693902653750920⟩,⟨(-15726362699268224060668377),(-15726362699268223648779808)⟩⟩,⟨⟨2522450041847866575958503,2522450041847866987202472⟩,⟨(-15705756980325603726649138),(-15705756980325603315337850)⟩⟩,⟨⟨2487517101316422970593804,2487517101316423380972376⟩,⟨(-15674853377207954702689157),(-15674853377207954292242762)⟩⟩,⟨⟨2441158260233684921473896,2441158260233685330700981⟩,⟨(-15633658261506794710916006),(-15633658261506794301620433)⟩⟩,⟨⟨2383559559931364627532488,2383559559931365035324239⟩,⟨(-15582180792217362636187806),(-15582180792217362228326742)⟩⟩,⟨⟨2314952093186443181818105,2314952093186443587893455⟩,⟨(-15520433474163883669511743),(-15520433474163883263366102)⟩⟩,⟨⟨2235611036867652105172831,2235611036867652509254064⟩,⟨(-15448432843239989362325614),(-15448432843239988958172962)⟩⟩,⟨⟨2145854496445631453718675,2145854496445631855531888⟩,⟨(-15366200270111592978961299),(-15366200270111592577075396)⟩⟩,⟨⟨2046042165395577141385675,2046042165395577540661432⟩,⟨(-15273762872532285580838590),(-15273762872532285181488740)⟩⟩,⟨⟨1936573803120558086790635,1936573803120558483264259⟩,⟨(-15171154525016776078836230),(-15171154525016775682286982)⟩⟩,⟨⟨1817887535661709735436737,1817887535661710128849107⟩,⟨(-15058416953319953874028979),(-15058416953319953480539338)⟩⟩,⟨⟨1690457984140284110610695,1690457984140284500708282⟩,⟨(-14935600899990985279301233),(-14935600899990984889124621)⟩⟩,⟨⟨1554794226596893377884801,1554794226596893764420765⟩,⟨(-14802767346225808115603942),(-14802767346225807728987101)⟩⟩,⟨⟨1411437599654720635379296,1411437599654721018113111⟩,⟨(-14659988774338857577791524),(-14659988774338857194974896)⟩⟩,⟨⟨1260959347234084671939540,1260959347234085050638409⟩,⟨(-14507350454426173794081618),(-14507350454426173415297925)⟩⟩] +lemma kernel16_0_r4_0_eq : ∀ k : Fin 16, kernel16_0Expr 4 0 k = kernel16_0_r4_0 k := by decide +kernel +noncomputable def kernel16_0_r4_1 : Fin 16 → CBox := ![⟨⟨1103958124382194495986459,1103958124382194870424415⟩,⟨(-14344951738206365827747344),(-14344951738206365453222489)⟩⟩,⟨⟨941057365149427273896283,941057365149427643856318⟩,⟨(-14172907342611110110553200),(-14172907342611109740504141)⟩⟩,⟨⟨772902524335792318785143,772902524335792684057487⟩,⟨(-13991348605459419987346750),(-13991348605459419621983221)⟩⟩,⟨⟨600158203840799965016289,600158203840800325401057⟩,⟨(-13800424695494813773404295),(-13800424695494813412926156)⟩⟩,⟨⟨423505175267818589913596,423505175267818945218287⟩,⟨(-13600303759195109766012407),(-13600303759195109410612147)⟩⟩,⟨⟨243637311350040116941885,243637311350040466985247⟩,⟨(-13391173987082577860391584),(-13391173987082577510250460)⟩⟩,⟨⟨61258439668156360118628,61258439668156704726833⟩,⟨(-13173244582767500414353577),(-13173244582767500069645430)⟩⟩,⟨⟨(-122920866992394862416848),(-122920866992394523405640)⟩,⟨(-12946746618648925914441618),(-12946746618648925575328318)⟩⟩,⟨⟨(-308186548457164377948273),(-308186548457164044688770)⟩,⟨(-12711933763068735987170195),(-12711933763068735653806491)⟩⟩,⟨⟨(-493824347176050257742908),(-493824347176049930376206)⟩,⟨(-12469082864763364108652788),(-12469082864763363781179830)⟩⟩,⟨⟨(-679123113736581145726933),(-679123113736580824387339)⟩,⟨(-12218494381673937956066635),(-12218494381673937634618800)⟩⟩,⟨⟨(-863378110536666480729178),(-863378110536666165537018)⟩,⟨(-11960492642550666680013842),(-11960492642550666364711534)⟩⟩,⟨⟨(-1045894295727097261466966),(-1045894295727096952536416)⟩,⟨(-11695425931309452105295024),(-11695425931309451796252513)⟩⟩,⟨⟨(-1225989569091888280326215),(-1225989569091887977755666)⟩,⟨(-11423666385754606418815176),(-11423666385754606116130956)⟩⟩,⟨⟨(-1402997961212388255940180),(-1402997961212387959822582)⟩,⟨(-11145609704056068199280323),(-11145609704056067903047457)⟩⟩,⟨⟨(-1576272747071054246943091),(-1576272747071053957355593)⟩,⟨(-10861674654245810232059736),(-10861674654245809942355500)⟩⟩] +lemma kernel16_0_r4_1_eq : ∀ k : Fin 16, kernel16_0Expr 4 1 k = kernel16_0_r4_1 k := by decide +kernel +noncomputable def kernel16_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-1745189465203892182462093),(-1745189465203891899477535)⟩,⟨(-10572302383957870544061201),(-10572302383957870260958570)⟩⟩,⟨⟨(-1909148823616461693681903),(-1909148823616461417355065)⟩,⟨(-10277955529659871810194356),(-10277955529659871533748254)⟩⟩,⟨⟨(-2067579473945112865688936),(-2067579473945112596071304)⟩,⟨(-9979117126690082021718721),(-9979117126690081751980785)⟩⟩,⟨⟨(-2219940635779063866959316),(-2219940635779063604063371)⟩,⟨(-9676289323501077085399168),(-9676289323501076822382036)⟩⟩,⟨⟨(-2365724553664368599289012),(-2365724553664368343140427)⟩,⟨(-9369991905596199629029815),(-9369991905596199372759327)⟩⟩,⟨⟨(-2504458770089954870966946),(-2504458770089954621578787)⟩,⟨(-9060760636705066413905218),(-9060760636705066164394612)⟩⟩,⟨⟨(-2635708198708660623699418),(-2635708198708660381084013)⟩,⟨(-8749145426755922432985670),(-8749145426755922190247450)⟩⟩,⟨⟨(-2759076983170114812056950),(-2759076983170114576208156)⟩,⟨(-8435708338142286868948211),(-8435708338142286632976416)⟩⟩,⟨⟨(-2874210128232524454535608),(-2874210128232524225448233)⟩,⟨(-8121021443626047048073148),(-8121021443626046818862769)⟩⟩,⟨⟨(-2980794891269605205630284),(-2980794891269604983277744)⟩,⟨(-7805664550946547242864923),(-7805664550946547020389561)⟩⟩,⟨⟨(-3078561923887249665743278),(-3078561923887249450101345)⟩,⟨(-7490222810793866363444585),(-7490222810793866147680201)⟩⟩,⟨⟨(-3167286155099895709883113),(-3167286155099895500908318)⟩,⟨(-7175284226234224858382086),(-7175284226234224649285397)⟩⟩,⟨⟨(-3246787409374473060940629),(-3246787409374472858593254)⟩,⟨(-6861437082927712762519273),(-6861437082927712560050748)⟩⟩,⟨⟨(-3316930754813651046416065),(-3316930754813650850577139)⟩,⟨(-6549267320536542822761824),(-6549267320536542626806293)⟩⟩,⟨⟨(-3377626578801286781023424),(-3377626578801286591597144)⟩,⟨(-6239355866571176287065582),(-6239355866571176097529882)⟩⟩,⟨⟨(-3428830390551121561422666),(-3428830390551121378337440)⟩,⟨(-5932275954549676416276949),(-5932275954549676233089350)⟩⟩] +lemma kernel16_0_r4_2_eq : ∀ k : Fin 16, kernel16_0Expr 4 2 k = kernel16_0_r4_2 k := by decide +kernel +noncomputable def kernel16_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-3470542352163023885989840),(-3470542352163023709181264)⟩,⟨(-5628590448742826010107453),(-5628590448742825833203403)⟩⟩,⟨⟨(-3502806541976332699963101),(-3502806541976332529343792)⟩,⟨(-5328849197936972549886018),(-5328849197936972379177971)⟩⟩,⟨⟨(-3525709956193100704403110),(-3525709956193100539894284)⟩,⟨(-5033586440564220778226639),(-5033586440564220613635641)⟩⟩,⟨⟨(-3539381256900679931427201),(-3539381256900679772930722)⟩,⟨(-4743318283224478990032709),(-4743318283224478831460440)⟩⟩,⟨⟨(-3543989276728306363591411),(-3543989276728306211018814)⟩,⟨(-4458540274058066665196366),(-4458540274058066512554172)⟩⟩,⟨⟨(-3539741292401438739868473),(-3539741292401438593108956)⟩,⟨(-4179725091626294666185064),(-4179725091626294519361941)⟩⟩,⟨⟨(-3526881081386406262129843),(-3526881081386406121083552)⟩,⟨(-3907320368928897329326764),(-3907320368928897188222653)⟩⟩,⟨⟨(-3505686777623113735895781),(-3505686777623113600414553)⟩,⟨(-3641746670942690101286709),(-3641746670942689965753233)⟩⟩,⟨⟨(-3476468544003072039519550),(-3476468544003071909490158)⟩,⟨(-3383395642619484880734102),(-3383395642619484750657814)⟩⟩,⟨⟨(-3439566080743385160263022),(-3439566080743385035559065)⟩,⟨(-3132628342649962397053598),(-3132628342649962272307875)⟩⟩,⟨⟨(-3395345990115966655610540),(-3395345990115966536119194)⟩,⟨(-2889773776503213359627664),(-2889773776503213240099451)⟩⟩,⟨⟨(-3344199019098830753978486),(-3344199019098830639569111)⟩,⟨(-2655127640310590170700294),(-2655127640310590056258720)⟩⟩,⟨⟨(-3286537202408947145552758),(-3286537202408947036095458)⟩,⟨(-2428951285100872626379923),(-2428951285100872516894848)⟩⟩,⟨⟨(-3222790929042725519865796),(-3222790929042725415220960)⟩,⟨(-2211470908736671620193409),(-2211470908736671515524986)⟩⟩,⟨⟨(-3153405955882479253018141),(-3153405955882479153064492)⟩,⟨(-2002876980675858795314093),(-2002876980675858695340809)⟩⟩,⟨⟨(-3078840392120036534155352),(-3078840392120036438755116)⟩,⟨(-1803323902413879661900592),(-1803323902413879566484438)⟩⟩] +lemma kernel16_0_r4_3_eq : ∀ k : Fin 16, kernel16_0Expr 4 3 k = kernel16_0_r4_3 k := by decide +kernel +noncomputable def kernel16_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-2999561678200002362809473),(-2999561678200002271840820)⟩,⟨(-1612929904180827756614533),(-1612929904180827665633447)⟩⟩,⟨⟨(-2916043582696202776188600),(-2916043582696202689509504)⟩,⟨(-1431777176198950506133406),(-1431777176198950419445129)⟩⟩,⟨⟨(-2828763240009927660013231),(-2828763240009927577498213)⟩,⟨(-1259912230579316390941093),(-1259912230579316308419919)⟩⟩,⟨⟨(-2738198251025222015544350),(-2738198251025221937053031)⟩,⟨(-1097346487777458142151244),(-1097346487777458063656568)⟩⟩,⟨⟨(-2644823867885163989594733),(-2644823867885163915003062)⟩,⟨(-944057079462554868741930),(-944057079462554794149481)⟩⟩,⟨⟨(-2549110282877170623199064),(-2549110282877170552365461)⟩,⟨(-799987857707268108088169),(-799987857707268037256151)⟩⟩,⟨⟨(-2451520040050892372101960),(-2451520040050892304901484)⟩,⟨(-665050598598000643934390),(-665050598598000576737655)⟩⟩,⟨⟨(-2352505586657590029494533),(-2352505586657589965789135)⟩,⟨(-539126386718241537724400),(-539126386718241474024692)⟩⟩,⟨⟨(-2252506979815528870187577),(-2252506979815528809856126)⟩,⟨(-422067165488497517108179),(-422067165488497456784170)⟩⟩,⟨⟨(-2151949761994147999898443),(-2151949761994147942803549)⟩,⟨(-313697437070116322111607),(-313697437070116265025718)⟩⟩,⟨⟨(-2051243016994267586315434),(-2051243016994267532336702)⟩,⟨(-213816094469242558540707),(-213816094469242504572360)⟩⟩,⟨⟨(-1950777616107136931857417),(-1950777616107136880863224)⟩,⟨(-122198367620363530630993),(-122198367620363479648389)⟩⟩,⟨⟨(-1850924662087125358205720),(-1850924662087125309920221)⟩,⟨(-38597864592454383332840),(-38597864592454335059950)⟩⟩,⟨⟨(-1752034136497015770078793),(-1752034136497015724378475)⟩,⟨37251311352466925882553,37251311352466971569400⟩⟩,⟨⟨(-1654433753906763250597919),(-1654433753906763207385920)⟩,⟨105632388308724685918470,105632388308724729116281⟩⟩,⟨⟨(-1558428024371315549187097),(-1558428024371315508356294)⟩,⟨166843715315053847941862,166843715315053888757902⟩⟩] +lemma kernel16_0_r4_4_eq : ∀ k : Fin 16, kernel16_0Expr 4 4 k = kernel16_0_r4_4 k := by decide +kernel +noncomputable def kernel16_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-1464297523604878810597641),(-1464297523604878772056157)⟩,⟨221196534168939602528315,221196534168939641054590⟩⟩,⟨⟨(-1372298368330854662931057),(-1372298368330854626573932)⟩,⟨269012752207114919292958,269012752207114955634549⟩⟩,⟨⟨(-1282661892440041411211239),(-1282661892440041376948508)⟩,⟨310622734151441676013809,310622734151441710260793⟩⟩,⟨⟨(-1195594517854224767407149),(-1195594517854224735140237)⟩,⟨346363130299704607712758,346363130299704639963813⟩⟩,⟨⟨(-1111277812385547511311942),(-1111277812385547480956220)⟩,⟨376574757358104897304356,376574757358104927644208⟩⟩,⟨⟨(-1029868725419320242780692),(-1029868725419320214241112)⟩,⟨401600547084202440717881,401600547084202469241664⟩⟩,⟨⟨(-951499990942039815453917),(-951499990942039788648968)⟩,⟨421783576654910589868409,421783576654910616657712⟩⟩,⟨⟨(-876280686297565122136495),(-876280686297565096977619)⟩,⟨437465193314180803648132,437465193314180828791583⟩⟩,⟨⟨(-804296934090258286586416),(-804296934090258262996909)⟩,⟨448983244410264603143402,448983244410264626718931⟩⟩,⟨⟨(-735612733869351689575201),(-735612733869351667470351)⟩,⟨456670422424346382195391,456670422424346404287788⟩⟩,⟨⟨(-670270909626106624531402),(-670270909626106603837568)⟩,⟨460852733042401172703653,460852733042401193386462⟩⟩,⟨⟨(-608294158714149527708963),(-608294158714149508343854)⟩,⟨461848092751569908608454,461848092751569927963868⟩⟩,⟨⟨(-549686187560875244912132),(-549686187560875226810215)⟩,⟨459965060871793536602822,459965060871793554696279⟩⟩,⟨⟨(-494432919468811294581154),(-494432919468811277669888)⟩,⟨455501709382653512878005,455501709382653529781956⟩⟩,⟨⟨(-442503759902985638625704),(-442503759902985622842045)⟩,⟨448744632392923568090670,448744632392923583868071⟩⟩,⟨⟨(-393852904914307706782140),(-393852904914307692051688)⟩,⟨439968095643449272212545,439968095643449286937712⟩⟩] +lemma kernel16_0_r4_5_eq : ∀ k : Fin 16, kernel16_0Expr 4 5 k = kernel16_0_r4_5 k := by decide +kernel +noncomputable def kernel16_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-348420678748695296446046),(-348420678748695282713988)⟩,⟨429433325048246743059777,429433325048246756787442⟩⟩,⟨⟨(-306134887224607961411659),(-306134887224607948617047)⟩,⟨417387931977996699505824,417387931977996712296854⟩⟩,⟨⟨(-266912174114006725138849),(-266912174114006713230304)⟩,⟨404065471786359772323437,404065471786359784229137⟩⟩,⟨⟨(-230659368518825737345730),(-230659368518825726268435)⟩,⟨389685130982724484864497,389685130982724495939614⟩⟩,⟨⟨(-197274812081413950332871),(-197274812081413940040493)⟩,⟨374451537473054088683530,374451537473054098974330⟩⟩,⟨⟨(-166649655787282241956411),(-166649655787282232398226)⟩,⟨358554687429302343044829,358554687429302352601973⟩⟩,⟨⟨(-138669117095936081364363),(-138669117095936072487727)⟩,⟨342169981611267254844221,342169981611267263720289⟩⟩,⟨⟨(-113213689154766770536612),(-113213689154766762294115)⟩,⟨325458363354610980749593,325458363354610988991941⟩⟩,⟨⟨(-90160294896453384552626),(-90160294896453376907789)⟩,⟨308566549955062301321142,308566549955062308966197⟩⟩,⟨⟨(-69383379877206538225568),(-69383379877206531138127)⟩,⟨291627348819719428431384,291627348819719435519361⟩⟩,⟨⟨(-50755938767350137564332),(-50755938767350131000672)⟩,⟨274760049518420715717872,274760049518420722282342⟩⟩,⟨⟨(-34150471444018427553407),(-34150471444018421477917)⟩,⟨258070882746391546018068,258070882746391552094599⟩⟩,⟨⟨(-19439865646062064053651),(-19439865646062058435708)⟩,⟨241653537197528771598520,241653537197528777217698⟩⟩,⟨⟨(-6498204122734194160444),(-6498204122734188965125)⟩,⟨225589725438333906333621,225589725438333911530335⟩⟩,⟨⟨4798504869213114676077,4798504869213119475430⟩,⟨209949790057291378027262,209949790057291382828138⟩⟩,⟨⟨14571673998972125437770,14571673998972129869619⟩,⟨194793341634296357601957,194793341634296362035427⟩⟩] +lemma kernel16_0_r4_6_eq : ∀ k : Fin 16, kernel16_0Expr 4 6 k = kernel16_0_r4_6 k := by decide +kernel +noncomputable def kernel16_0_r4_7 : Fin 16 → CBox := ![⟨⟨22939559701663489062013,22939559701663493150570⟩,⟨180169920419899779593896,180169920419899783684146⟩⟩,⟨⟨30016760166816473332226,30016760166816477102885⟩,⟨166119674024622739464312,166119674024622743236712⟩⟩,⟨⟨35913786556208637673061,35913786556208641146814⟩,⟨152674043884183492877883,152674043884183496353406⟩⟩,⟨⟨40736704946497635991588,40736704946497639190483⟩,⟨139856453776954678861730,139856453776954682062407⟩⟩,⟨⟨44586845983733141826248,44586845983733144768581⟩,⟨127682994215255760208031,127682994215255763152141⟩⟩,⟨⟨47560578805795912989239,47560578805795915694777⟩,⟨116163097102414472435306,116163097102414475142602⟩⟩,⟨⟨49749145434176554504579,49749145434176556989693⟩,⟨105300195633558332641471,105300195633558335128313⟩⟩,⟨⟨51238551556369947890148,51238551556369950173407⟩,⟨95092365011020817099441,95092365011020819384359⟩⟩,⟨⟨52109509411715092721752,52109509411715094823535⟩,⟨85532940136899263282923,85532940136899265386157⟩⟩,⟨⟨52437428353166757475876,52437428353166759410265⟩,⟨76611107028225629256423,76611107028225631192074⟩⟩,⟨⟨52292448580999733423929,52292448580999735202403⟩,⟨68312465267716772494494,68312465267716774274056⟩⟩,⟨⟨51739513527039164900850,51739513527039166535505⟩,⟨60619559349273726422651,60619559349273728058235⟩⟩,⟨⟨50838476404489438597702,50838476404489440098427⟩,⟨53512377297243134615354,53512377297243136116867⟩⟩,⟨⟨49644236523313251668208,49644236523313253045773⟩,⟨46968815427715471004522,46968815427715472382746⟩⟩,⟨⟨48206901098724033917153,48206901098724035180346⟩,⟨40965108575414973288770,40965108575414974552505⟩⟩,⟨⟨46571968444955281595467,46571968444955282753506⟩,⟨35476225528437965984410,35476225528437967142887⟩⟩] +lemma kernel16_0_r4_7_eq : ∀ k : Fin 16, kernel16_0Expr 4 7 k = kernel16_0_r4_7 k := by decide +kernel +noncomputable def kernel16_0_r4_8 : Fin 16 → CBox := ![⟨⟨44780528642337277017905,44780528642337278078265⟩,⟨30476229793389406273091,30476229793389407333796⟩⟩,⟨⟨42869477987231826189407,42869477987231827160851⟩,⟨25938606154245130858055,25938606154245131829761⟩⟩,⟨⟨40871743776122223457295,40871743776122224346368⟩,⟨21836553789093197525232,21836553789093198414496⟩⟩,⟨⟨38816516231955067190985,38816516231955068004535⟩,⟨18143246969957514514018,18143246969957515327696⟩⟩,⟨⟨36729484647818327304395,36729484647818328047980⟩,⟨14832064592904488853790,14832064592904489597447⟩⟩,⟨⟨34633075095705817150534,34633075095705817830902⟩,⟨11876789969784138597729,11876789969784139278122⟩⟩,⟨⟨32546687322340009043603,32546687322340009665557⟩,⟨9251782460879848498551,9251782460879849120489⟩⟩,⟨⟨30486928726093629229067,30486928726093629797570⟩,⟨6932122641399692692800,6932122641399693261252⟩⟩,⟨⟨28467843575683543088323,28467843575683543607399⟩,⟨4893732776379062885694,4893732776379063404692⟩⟩,⟨⟨26501135889658877690537,26501135889658878164770⟩,⟨3113474430634609035866,3113474430634609509996⟩⟩,⟨⟨24596384643350520887119,24596384643350521319961⟩,⟨1569225065520454623579,1569225065520455056298⟩⟩,⟨⟨22761250204893668631183,22761250204893669026240⟩,⟨239935475090974617952,239935475090975012871⟩⟩,⟨⟨21001671122587153641666,21001671122587154001836⟩,⟨(-894330106386444585976),(-894330106386444225956)⟩⟩,⟨⟨19322050591005890790116,19322050591005891118533⟩,⟨(-1852369433062667586829),(-1852369433062667258570)⟩⟩,⟨⟨17725432112088747217060,17725432112088747516237⟩,⟨(-2651831475300310633656),(-2651831475300310334644)⟩⟩,⟨⟨16213664039367848215605,16213664039367848488458⟩,⟨(-3309217778653256249015),(-3309217778653255976331)⟩⟩] +lemma kernel16_0_r4_8_eq : ∀ k : Fin 16, kernel16_0Expr 4 8 k = kernel16_0_r4_8 k := by decide +kernel +noncomputable def kernel16_0_r4_9 : Fin 16 → CBox := ![⟨⟨14787552848371988116639,14787552848371988365777⟩,⟨(-3839894366052550842661),(-3839894366052550593692)⟩⟩,⟨⟨13447005114080319137038,13447005114080319364603⟩,⟨(-4258112683856720269426),(-4258112683856720042031)⟩⟩,⟨⟨12191158297412441747139,12191158297412441954813⟩,⟨(-4577038187513519022694),(-4577038187513518815188)⟩⟩,⟨⟨11018500547609719603454,11018500547609719793005⟩,⟨(-4808785262105612796524),(-4808785262105612607138)⟩⟩,⟨⟨9926979816652644881603,9926979816652645054429⟩,⟨(-4964457275184797234536),(-4964457275184797061872)⟩⟩,⟨⟨8914102656371837049567,8914102656371837207209⟩,⟨(-5054190662398736713102),(-5054190662398736555613)⟩⟩,⟨⟨7977023129556298498380,7977023129556298642059⟩,⟨(-5087202049033754324753),(-5087202049033754181208)⟩⟩,⟨⟨7112622314133555580871,7112622314133555711855⟩,⟨(-5071837511480252253811),(-5071837511480252122944)⟩⟩,⟨⟨6317578915439362498548,6317578915439362617887⟩,⟨(-5015623180702888930508),(-5015623180702888811268)⟩⟩,⟨⟨5588431526788825031331,5588431526788825140181⟩,⟨(-4925316484173038649058),(-4925316484173038540293)⟩⟩,⟨⟨4921633094096307059325,4921633094096307158524⟩,⟨(-4806957412672641432089),(-4806957412672641332962)⟩⟩,⟨⟨4313598147251269469336,4313598147251269559771⟩,⟨(-4665919283340622348105),(-4665919283340622257732)⟩⟩,⟨⟨3760743360401170247273,3760743360401170329634⟩,⟨(-4506958549885691194011),(-4506958549885691111699)⟩⟩,⟨⟨3259521996244293656033,3259521996244293731086⟩,⟨(-4334263284745324677364),(-4334263284745324602352)⟩⟩,⟨⟨2806452776871202024795,2806452776871202093133⟩,⟨(-4151500025962099710442),(-4151500025962099642136)⟩⟩,⟨⟨2398143706533883514166,2398143706533883576415⟩,⟨(-3961858743612844427210),(-3961858743612844364986)⟩⟩] +lemma kernel16_0_r4_9_eq : ∀ k : Fin 16, kernel16_0Expr 4 9 k = kernel16_0_r4_9 k := by decide +kernel +noncomputable def kernel16_0_r4_10 : Fin 16 → CBox := ![⟨⟨2031311350824716387418,2031311350824716444202⟩,⟨(-3768095736792831384983),(-3768095736792831328218)⟩⟩,⟨⟨1702796052904294517267,1702796052904294569117⟩,⟨(-3572574322534726820019),(-3572574322534726768182)⟩⟩,⟨⟨1409573541349474973983,1409573541349475021295⟩,⟨(-3377303222804549832783),(-3377303222804549785480)⟩⟩,⟨⟨1148763356551305253436,1148763356551305296629⟩,⟨(-3183972595092844393817),(-3183972595092844350628)⟩⟩,⟨⟨917634493956556412388,917634493956556451785⟩,⟨(-2993987686379822591644),(-2993987686379822552248)⟩⟩,⟨⟨713608633326714651255,713608633326714687218⟩,⟨(-2808500119702130354990),(-2808500119702130319026)⟩⟩,⟨⟨534261294027509663332,534261294027509696146⟩,⟨(-2628436847513026194008),(-2628436847513026161188)⟩⟩,⟨⟨377321227539231905461,377321227539231935442⟩,⟨(-2454526826848863052804),(-2454526826848863022817)⟩⟩,⟨⟨240668330211535219645,240668330211535247011⟩,⟨(-2287325488341954547385),(-2287325488341954520009)⟩⟩,⟨⟨122330332038058673715,122330332038058698721⟩,⟨(-2127237084703325203223),(-2127237084703325178208)⟩⟩,⟨⟨20478491105998133965,20478491105998156798⟩,⟨(-1974535014784158495376),(-1974535014784158472532)⟩⟩,⟨⟨(-66577501453644749390),(-66577501453644728526)⟩,⟨(-1829380227048595781445),(-1829380227048595760569)⟩⟩,⟨⟨(-140395224607984807913),(-140395224607984788844)⟩,⟨(-1691837811576764194711),(-1691837811576764175629)⟩⟩,⟨⟨(-202405679174844022444),(-202405679174844004970)⟩,⟨(-1561891892873665638744),(-1561891892873665621258)⟩⟩,⟨⟨(-253919749088460128485),(-253919749088460112483)⟩,⟨(-1439458937077032475009),(-1439458937077032458993)⟩⟩,⟨⟨(-296134851903157968994),(-296134851903157954325)⟩,⟨(-1324399586906091013217),(-1324399586906090998535)⟩⟩] +lemma kernel16_0_r4_10_eq : ∀ k : Fin 16, kernel16_0Expr 4 10 k = kernel16_0_r4_10 k := by decide +kernel +noncomputable def kernel16_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-330141675525505049398),(-330141675525505035966)⟩,⟨(-1216529136123441334159),(-1216529136123441320713)⟩⟩,⟨⟨(-356930913900019315741),(-356930913900019303423)⟩,⟨(-1115626752622930521805),(-1115626752622930509473)⟩⟩,⟨⟨(-377399928619589895354),(-377399928619589884053)⟩,⟨(-1021443555715234636792),(-1021443555715234625478)⟩⟩,⟨⟨(-392359276245817703371),(-392359276245817692995)⟩,⟨(-933709648946701676849),(-933709648946701666459)⟩⟩,⟨⟨(-402539052573579719690),(-402539052573579710168)⟩,⟨(-852140205022291903581),(-852140205022291894046)⟩⟩,⟨⟨(-408595015233332445439),(-408595015233332436693)⟩,⟨(-776440694257050746640),(-776440694257050737881)⟩⟩,⟨⟨(-411114454974617831867),(-411114454974617823830)⟩,⟨(-706311342580735547464),(-706311342580735539414)⟩⟩,⟨⟨(-410621793798992059096),(-410621793798992051693)⟩,⟨(-641450899577793273595),(-641450899577793266181)⟩⟩,⟨⟨(-407583894895874545290),(-407583894895874538476)⟩,⟨(-581559791454406016509),(-581559791454406009687)⟩⟩,⟨⟨(-402415075166418922367),(-402415075166418916087)⟩,⟨(-526342728265370318931),(-526342728265370312643)⟩⟩,⟨⟨(-395481816083057966907),(-395481816083057961119)⟩,⟨(-475510829272079882262),(-475510829272079876468)⟩⟩,⟨⟨(-387107172808248842559),(-387107172808248837219)⟩,⟨(-428783324992409657506),(-428783324992409652160)⟩⟩,⟨⟨(-377574884964442720837),(-377574884964442715915)⟩,⟨(-385888889386353500987),(-385888889386353496059)⟩⟩,⟨⟨(-367133195283996502784),(-367133195283996498239)⟩,⟨(-346566650730521436096),(-346566650730521431546)⟩⟩,⟨⟨(-355998384644001757595),(-355998384644001753398)⟩,⟨(-310566925094090889046),(-310566925094090884846)⟩⟩,⟨⟨(-344358033773660431969),(-344358033773660428088)⟩,⟨(-277651711955046071599),(-277651711955046067714)⟩⟩] +lemma kernel16_0_r4_11_eq : ∀ k : Fin 16, kernel16_0Expr 4 11 k = kernel16_0_r4_11 k := by decide +kernel +noncomputable def kernel16_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-332374023272985948106),(-332374023272985944514)⟩,⟨(-247594987398577619132),(-247594987398577615537)⟩⟩,⟨⟨(-320185284558522165032),(-320185284558522161705)⟩,⟨(-220182826523895384095),(-220182826523895380765)⟩⟩,⟨⟨(-307910315006894333146),(-307910315006894330064)⟩,⟨(-195213383151360501430),(-195213383151360498346)⟩⟩,⟨⟨(-295649470948027521054),(-295649470948027518194)⟩,⟨(-172496751664887303688),(-172496751664887300825)⟩⟩,⟨⟨(-283487052309866993018),(-283487052309866990366)⟩,⟨(-151854732838032406956),(-151854732838032404303)⟩⟩,⟨⟨(-271493192674060816581),(-271493192674060814117)⟩,⟨(-133120522766664343788),(-133120522766664341324)⟩⟩,⟨⟨(-259725568301759360425),(-259725568301759358137)⟩,⟨(-116138341555303361479),(-116138341555303359190)⟩⟩,⟨⟨(-248230939360931216086),(-248230939360931213956)⟩,⟨(-100763016165468158439),(-100763016165468156308)⟩⟩,⟨⟨(-237046536158177244823),(-237046536158177242839)⟩,⟨(-86859529819043738290),(-86859529819043736305)⟩⟩,⟨⟨(-226201302672310062884),(-226201302672310061034)⟩,⟨(-74302548543586705136),(-74302548543586703285)⟩⟩,⟨⟨(-215717009124178668294),(-215717009124178666569)⟩,⟨(-62975933835130309274),(-62975933835130307549)⟩⟩,⟨⟨(-205609244714713582910),(-205609244714713581299)⟩,⟨(-52772248982942797639),(-52772248982942796027)⟩⟩,⟨⟨(-195888301035706408742),(-195888301035706407237)⟩,⟨(-43592265335523971281),(-43592265335523969776)⟩⟩,⟨⟨(-186559956017842206568),(-186559956017842205160)⟩,⟨(-35344473673954189352),(-35344473673954187944)⟩⟩,⟨⟨(-177626167638308797423),(-177626167638308796104)⟩,⟨(-27944604884091292277),(-27944604884091290958)⟩⟩,⟨⟨(-169085685974395918434),(-169085685974395917196)⟩,⟨(-21315163270194924182),(-21315163270194922945)⟩⟩] +lemma kernel16_0_r4_12_eq : ∀ k : Fin 16, kernel16_0Expr 4 12 k = kernel16_0_r4_12 k := by decide +kernel +noncomputable def kernel16_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-160934591566717430632),(-160934591566717429470)⟩,⟨(-15384975117165585259),(-15384975117165584097)⟩⟩,⟨⟨(-153166767451459838057),(-153166767451459836964)⟩,⟨(-10088754475258174546),(-10088754475258173454)⟩⟩,⟨⟨(-145774311639556175327),(-145774311639556174300)⟩,⟨(-5366687599156566334),(-5366687599156565307)⟩⟩,⟨⟨(-138747896265010689121),(-138747896265010688154)⟩,⟨(-1164037012728281009),(-1164037012728280042)⟩⟩,⟨⟨(-132077079096945804825),(-132077079096945803914)⟩,⟨2569234217571709283,2569234217571710193⟩⟩,⟨⟨(-125750572611722041680),(-125750572611722040821)⟩,⟨5878817742251945604,5878817742251946463⟩⟩,⟨⟨(-119756475353456764446),(-119756475353456763633)⟩,⟨8806394731403824459,8806394731403825271⟩⟩,⟨⟨(-114082469873662742379),(-114082469873662741609)⟩,⟨11389950449964817620,11389950449964818389⟩⟩,⟨⟨(-108715991133325363465),(-108715991133325362736)⟩,⟨13664069011965446964,13664069011965447691⟩⟩,⟨⟨(-103644368872966246966),(-103644368872966246274)⟩,⟨15660208859888718008,15660208859888718699⟩⟩,⟨⟨(-98854947107249425899),(-98854947107249425243)⟩,⟨17406959623216758724,17406959623216759380⟩⟩,⟨⟨(-94335183579407852000),(-94335183579407851375)⟩,⟨18930281090926604063,18930281090926604686⟩⟩,⟨⟨(-90072731715977001270),(-90072731715977000675)⟩,⟨20253725090201241554,20253725090201242147⟩⟩,⟨⟨(-86055507352681036501),(-86055507352681035935)⟩,⟨21398641101551294194,21398641101551294758⟩⟩,⟨⟨(-82271742256415232016),(-82271742256415231474)⟩,⟨22384366462076908316,22384366462076908856⟩⟩,⟨⟨(-78710026244656986906),(-78710026244656986389)⟩,⟨23228402016528230254,23228402016528230770⟩⟩] +lemma kernel16_0_r4_13_eq : ∀ k : Fin 16, kernel16_0Expr 4 13 k = kernel16_0_r4_13 k := by decide +kernel +noncomputable def kernel16_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-75359339500855761615),(-75359339500855761120)⟩,⟨23946574072582266379,23946574072582266874⟩⟩,⟨⟨(-72209076500949102602),(-72209076500949102129)⟩,⟨24553183504460676889,24553183504460677362⟩⟩,⟨⟨(-69249062800705165901),(-69249062800705165446)⟩,⟨25061142829497111338,25061142829497111792⟩⟩,⟨⟨(-66469565784721449654),(-66469565784721449216)⟩,⟨25482102057097470959,25482102057097471396⟩⟩,⟨⟨(-63861300344287047604),(-63861300344287047184)⟩,⟨25826564080066902216,25826564080066902635⟩⟩,⟨⟨(-61415430331674248366),(-61415430331674247962)⟩,⟨26103990345645656482,26103990345645656886⟩⟩,⟨⟨(-59123566531563062466),(-59123566531563062074)⟩,⟨26322897508765482933,26322897508765483324⟩⟩,⟨⟨(-56977761795086691621),(-56977761795086691243)⟩,⟨26490945733814847996,26490945733814848372⟩⟩,⟨⟨(-54970503897355314892),(-54970503897355314528)⟩,⟨26615019274253059538,26615019274253059902⟩⟩,⟨⟨(-53094706604279304017),(-53094706604279303663)⟩,⟨26701299922288217915,26701299922288218268⟩⟩,⟨⟨(-51343699368151032005),(-51343699368151031661)⟩,⟨26755333883975424897,26755333883975425240⟩⟩,⟨⟨(-49711216012905657014),(-49711216012905656680)⟩,⟨26782092598853359756,26782092598853360088⟩⟩,⟨⟨(-48191382718481177969),(-48191382718481177646)⟩,⟨26786027987895220354,26786027987895220677⟩⟩,⟨⟨(-46778705568516137928),(-46778705568516137612)⟩,⟨26771122579313906505,26771122579313906820⟩⟩,⟨⟨(-45468057886099900726),(-45468057886099900418)⟩,⟨26740934928784602487,26740934928784602794⟩⟩,⟨⟨(-44254667547823238174),(-44254667547823237873)⟩,⟨26698640719036321407,26698640719036321707⟩⟩] +lemma kernel16_0_r4_14_eq : ∀ k : Fin 16, kernel16_0Expr 4 14 k = kernel16_0_r4_14 k := by decide +kernel +noncomputable def kernel16_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-43134104436417818205),(-43134104436417817911)⟩,⟨26647069893583148969,26647069893583149262⟩⟩,⟨⟨(-42102268166324274548),(-42102268166324274259)⟩,⟨26588740150648043050,26588740150648043339⟩⟩,⟨⟨(-41155376194138894454),(-41155376194138894172)⟩,⟨26525887096081546577,26525887096081546858⟩⟩,⟨⟨(-40289952406650905564),(-40289952406650905287)⟩,⟨26460491328276293012,26460491328276293288⟩⟩,⟨⟨(-39502816262728029518),(-39502816262728029246)⟩,⟨26394302703688796810,26394302703688797082⟩⟩,⟨⟨(-38791072551306027970),(-38791072551306027702)⟩,⟨26328862008550829288,26328862008550829555⟩⟩,⟨⟨(-38152101815890274402),(-38152101815890274138)⟩,⟨26265520240619868145,26265520240619868408⟩⟩,⟨⟨(-37583551486015983132),(-37583551486015982871)⟩,⟨26205455684308497758,26205455684308498019⟩⟩,⟨⟨(-37083327747797879649),(-37083327747797879390)⟩,⟨26149688943165812568,26149688943165812825⟩⟩,⟨⟨(-36649588178813506081),(-36649588178813505825)⟩,⟨26099096075373937515,26099096075373937769⟩⟩,⟨⟨(-36280735166912523930),(-36280735166912523677)⟩,⟨26054419960579766741,26054419960579766994⟩⟩,⟨⟨(-35975410127952113320),(-35975410127952113069)⟩,⟨26016280009913054734,26016280009913054984⟩⟩,⟨⟨(-35732488533767637361),(-35732488533767637112)⟩,⟨25985180315352172622,25985180315352172870⟩⟩,⟨⟨(-35551075758754633247),(-35551075758754632998)⟩,⟨25961516319591936727,25961516319591936974⟩⟩,⟨⟨(-35430503751132019260),(-35430503751132019013)⟩,⟨25945580073146883796,25945580073146884042⟩⟩,⟨⟨(-35370328533156895387),(-35370328533156895140)⟩,⟨25937564131490719532,25937564131490719778⟩⟩] +lemma kernel16_0_r4_15_eq : ∀ k : Fin 16, kernel16_0Expr 4 15 k = kernel16_0_r4_15 k := by decide +kernel +noncomputable def kernel16_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel16_0_r4_0,kernel16_0_r4_1,kernel16_0_r4_2,kernel16_0_r4_3,kernel16_0_r4_4,kernel16_0_r4_5,kernel16_0_r4_6,kernel16_0_r4_7,kernel16_0_r4_8,kernel16_0_r4_9,kernel16_0_r4_10,kernel16_0_r4_11,kernel16_0_r4_12,kernel16_0_r4_13,kernel16_0_r4_14,kernel16_0_r4_15] +lemma kernel16_0_r4_eq (i k : Fin 16) : kernel16_0Expr 4 i k = kernel16_0_r4 i k := by + fin_cases i + · exact kernel16_0_r4_0_eq k + · exact kernel16_0_r4_1_eq k + · exact kernel16_0_r4_2_eq k + · exact kernel16_0_r4_3_eq k + · exact kernel16_0_r4_4_eq k + · exact kernel16_0_r4_5_eq k + · exact kernel16_0_r4_6_eq k + · exact kernel16_0_r4_7_eq k + · exact kernel16_0_r4_8_eq k + · exact kernel16_0_r4_9_eq k + · exact kernel16_0_r4_10_eq k + · exact kernel16_0_r4_11_eq k + · exact kernel16_0_r4_12_eq k + · exact kernel16_0_r4_13_eq k + · exact kernel16_0_r4_14_eq k + · exact kernel16_0_r4_15_eq k +noncomputable def kernel16_0_r5_0 : Fin 16 → CBox := ![⟨⟨53103734884958343390297899131,53103734884958343955024645057⟩,⟨(-1993657603904062930839891550),(-1993657603904062366739170002)⟩⟩,⟨⟨53076698754533012587215977168,53076698754533013151802994405⟩,⟨(-2020780354675111486307535773),(-2020780354675110922346914338)⟩⟩,⟨⟨53022624737609565812011293560,53022624737609566376317923166⟩,⟨(-2074940107583744905398714569),(-2074940107583744341719221381)⟩⟩,⟨⟨52941509562041577980535282663,52941509562041578544420955132⟩,⟨(-2155965593642737847645280170),(-2155965593642737284387849680)⟩⟩,⟨⟨52833348917758023721083196845,52833348917758024284407454137⟩,⟨(-2263600480106904201103404495),(-2263600480106903638408853342)⟩⟩,⟨⟨52698138169373313890346205866,52698138169373314452968764846⟩,⟨(-2397504055448035675675925557),(-2397504055448035113684887053)⟩⟩,⟨⟨52535873297748992394506430416,52535873297748992956287188597⟩,⟨(-2557252142779277110883557448),(-2557252142779276549736473789)⟩⟩,⟨⟨52346552063206125293221886828,52346552063206125854021028523⟩,⟨(-2742338241777742161486306205),(-2742338241777741601323320320)⟩⟩,⟨⟨52130175381334183458656476468,52130175381334184018334405337⟩,⟨(-2952174899094926853443592974),(-2952174899094926294404614015)⟩⟩,⟨⟨51886748900636969190364383768,51886748900636969748781944591⟩,⟨(-3186095307138985359539370488),(-3186095307138984801763850178)⟩⟩,⟨⟨51616284769608420607404847160,51616284769608421164423310315⟩,⟨(-3443355130953312330625561800),(-3443355130953311774252508099)⟩⟩,⟨⟨51318803579250459920178561169,51318803579250460475702919465⟩,⟨(-3723134562694977361990965016),(-3723134562694976807115644759)⟩⟩,⟨⟨50994336465540886973609024783,50994336465540887527504714371⟩,⟨(-4024540602928061386135471605),(-4024540602928060832892685536)⟩⟩,⟨⟨50642927354941025054133727293,50642927354941025606267104779⟩,⟨(-4346609567585465578191739416),(-4346609567585465026715344689)⟩⟩,⟨⟨50264635334709649536583105075,50264635334709650086820415833⟩,⟨(-4688309819013936335605735364),(-4688309819013935786029675597)⟩⟩,⟨⟨49859537128570760041006906249,49859537128570760589215653424⟩,⟨(-5048544718997613502568371728),(-5048544718997612955025306764)⟩⟩] +lemma kernel16_0_r5_0_eq : ∀ k : Fin 16, kernel16_0Expr 5 0 k = kernel16_0_r5_0 k := by decide +kernel +noncomputable def kernel16_0_r5_1 : Fin 16 → CBox := ![⟨⟨49427729657176876343157050970,49427729657176876889204304697⟩,⟨(-5426155801053275267808840894),(-5426155801053274722431836074)⟩⟩,⟨⟨48969332661825371365609420704,48969332661825371909364216162⟩,⟨(-5819926158604767301244876746),(-5819926158604766758165003960)⟩⟩,⟨⟨48484491369031206049731731839,48484491369031206591062311121⟩,⟨(-6228584044875291871391798306),(-6228584044875291330740892717)⟩⟩,⟨⟨47973379172843219740688516248,47973379172843220279465549043⟩,⟨(-6650806679486036983067086457),(-6650806679486036444974525268)⟩⟩,⟨⟨47436200311220316116192784172,47436200311220316652285545406⟩,⟨(-7085224255821125516971849075),(-7085224255821124981568372588)⟩⟩,⟨⟨46873192512365391791238802012,46873192512365392324520222189⟩,⟨(-7530424142216484301752230681),(-7530424142216483769164891915)⟩⟩,⟨⟨46284629586654985627822913666,46284629586654986158163900687⟩,⟨(-7984955268959734918876915738),(-7984955268959734389234757327)⟩⟩,⟨⟨45670823939706977840252005217,45670823939706978367527672118⟩,⟨(-8447332691956668868144685189),(-8447332691956668341572512043)⟩⟩,⟨⟨45032128982202039589864246267,45032128982202040113946699044⟩,⟨(-8916042322735643763780892221),(-8916042322735643240406482475)⟩⟩,⟨⟨44368941412320839682363454451,44368941412320840203131022992⟩,⟨(-9389545813233902388267140789),(-9389545813233901868212015989)⟩⟩,⟨⟨43681703347081191824634049386,43681703347081192341961137735⟩,⟨(-9866285582550104943477617698),(-9866285582550104426867191182)⟩⟩,⟨⟨42970904279459244079642297497,42970904279459244593409953870⟩,⟨(-10344689971567078367445624834),(-10344689971567077854398633329)⟩⟩,⟨⟨42237082838957189994035991052,42237082838957190504120072107⟩,⟨(-10823178510060695955620099051),(-10823178510060695446260437083)⟩⟩,⟨⟨41480828334236303454321147093,41480828334236303960622568141⟩,⟨(-11300167279628530601260705115),(-11300167279628530095687165847)⟩⟩,⟨⟨40702782057566543872441667016,40702782057566544374877683094⟩,⟨(-11774074354509825305984548732),(-11774074354509824804279536410)⟩⟩,⟨⟨39903638332149347702444432045,39903638332149348200904237661⟩,⟨(-12243325301141326747176617538),(-12243325301141326249450595211)⟩⟩] +lemma kernel16_0_r5_1_eq : ∀ k : Fin 16, kernel16_0Expr 5 1 k = kernel16_0_r5_1 k := by decide +kernel +noncomputable def kernel16_0_r5_2 : Fin 16 → CBox := ![⟨⟨39084145284843888568573519583,39084145284843889062937887747⟩,⟨(-12706358716116990122759289826),(-12706358716116989629131110614)⟩⟩,⟨⟨38245105328462947623154020748,38245105328462948113317593092⟩,⟨(-13161631781109105607890014452),(-13161631781109105118464635775)⟩⟩,⟨⟨37387375339594976700573705369,37387375339594977186421152805⟩,⟨(-13607625812279723141028378532),(-13607625812279722655920699058)⟩⟩,⟨⟨36511866519844823200757165564,36511866519844823682186680207⟩,⟨(-14042851780779969077160030271),(-14042851780779968596471402856)⟩⟩,⟨⟨35619543930456255426224428613,35619543930456255903124709386⟩,⟨(-14465855780116273518107786551),(-14465855780116273041945458350)⟩⟩,⟨⟨34711425692472708703145693390,34711425692472709175437718333⟩,⟨(-14875224415471496881288342942),(-14875224415471496409706914315)⟩⟩,⟨⟨33788581846894919284649081712,33788581846894919752223755939⟩,⟨(-15269590089519616775592748603),(-15269590089519616308701113262)⟩⟩,⟨⟨32852132871690256391280540815,32852132871690256854046710470⟩,⟨(-15647636158878296662241269189),(-15647636158878296200130424875)⟩⟩,⟨⟨31903247854982185948431148952,31903247854982186406281085918⟩,⟨(-16008101935116525515799529635),(-16008101935116525058577088922)⟩⟩,⟨⟨30943142326281730363444471631,30943142326281730816295416349⟩,⟨(-16349787504185559203036355838),(-16349787504185558750785009657)⟩⟩,⟨⟨29973075750197212282650697113,29973075750197212730401202436⟩,⟨(-16671558338280143597602892644),(-16671558338280143150424060729)⟩⟩,⟨⟨28994348689654161923326307595,28994348689654162365897879265⟩,⟨(-16972349674471389232321623488),(-16972349674471388790293819677)⟩⟩,⟨⟨28008299648253343989469674396,28008299648253344426762729129⟩,⟨(-17251170634988872966446210524),(-17251170634988872529669079140)⟩⟩,⟨⟨27016301603970048945052080524,27016301603970049376997699114⟩,⟨(-17507108064771841471733704556),(-17507108064771841040276273630)⟩⟩,⟨⟨26019758248930219163825914952,26019758248930219590331759362⟩,⟨(-17739330062860042017742648518),(-17739330062860041591697406106)⟩⟩,⟨⟨25020099952466466109302958474,25020099952466466530305054337⟩,⟨(-17947089185353843567788750838),(-17947089185353843147219868102)⟩⟩] +lemma kernel16_0_r5_2_eq : ∀ k : Fin 16, kernel16_0Expr 5 2 k = kernel16_0_r5_2 k := by decide +kernel +noncomputable def kernel16_0_r5_3 : Fin 16 → CBox := ![⟨⟨24018779467037315848259445335,24018779467037316263666759249⟩,⟨(-18129725299038869128045267755),(-18129725299038868713044015283)⟩⟩,⟨⟨23017267398863970608521500172,23017267398863971018281828609⟩,⟨(-18286668066338014742988239007),(-18286668066338014333607104047)⟩⟩,⟨⟨22017047467278739507422790744,22017047467278739911454375669⟩,⟨(-18417439044016870645336018285),(-18417439044016870241657081722)⟩⟩,⟨⟨21019611578766929376097218623,21019611578766929774352296516⟩,⟨(-18521653380018285766898559744),(-18521653380018285368969952081)⟩⟩,⟨⟨20026454743499108194680270417,20026454743499108587079123186⟩,⟨(-18599021094926964838120869371),(-18599021094926964446022713186)⟩⟩,⟨⟨19039069863774066507356042506,19039069863774066893863404719⟩,⟨(-18649347936852186249443367390),(-18649347936852185863211375069)⟩⟩,⟨⟨18058942425206648250592459619,18058942425206648631138543120⟩,⟨(-18672535800950483464158411273),(-18672535800950483083862853179)⟩⟩,⟨⟨17087545122682609508850169841,17087545122682609883404833916⟩,⟨(-18668582707372937392834480562),(-18668582707372937018506018623)⟩⟩,⟨⟨16126332454050286464500007036,16126332454050286832994565641⟩,⟨(-18637582334094207693182207147),(-18637582334094207324890081234)⟩⟩,⟨⟨15176735315213600901362576303,15176735315213601263781566686⟩,⟨(-18579723103841514614576855706),(-18579723103841514252337118528)⟩⟩,⟨⟨14240155630722475790738251753,14240155630722476147126884137⟩,⟨(-18495286827168893992122481052),(-18495286827168893635890573702)⟩⟩,⟨⟨13317961054117101247787958140,13317961054117101598900415823⟩,⟨(-18384646906591327800526645654),(-18384646906591327449549273710)⟩⟩,⟨⟨12411479772166209175312552698,12411479772166209521074891433⟩,⟨(-18248266109579902331482338184),(-18248266109579901985834113704)⟩⟩,⟨⟨11521995446743730305737541354,11521995446743730646133161380⟩,⟨(-18086693921097287886035552538),(-18086693921097287545733770156)⟩⟩,⟨⟨10650742327412779343245011076,10650742327412779678210367482⟩,⟨(-17900563489196389613275950974),(-17900563489196389278384872468)⟩⟩,⟨⟨9798900566833474741143688359,9798900566833475070665038440⟩,⟨(-17690588179987601235759318626),(-17690588179987600906293425525)⟩⟩] +lemma kernel16_0_r5_3_eq : ∀ k : Fin 16, kernel16_0Expr 5 3 k = kernel16_0_r5_3 k := by decide +kernel +noncomputable def kernel16_0_r5_4 : Fin 16 → CBox := ![⟨⟨8967591769887083167105349973,8967591769887083491117452206⟩,⟨(-17457557760975405606408306953),(-17457557760975405282433597728)⟩⟩,⟨⟨8157874805921614974712550825,8157874805921615293217393007⟩,⟨(-17202334234347209603527644865),(-17202334234347209285042905630)⟩⟩,⟨⟨7370741911784272452657531041,7370741911784272765603062781⟩,⟨(-16925847344241082165069461897),(-16925847344241081852127530865)⟩⟩,⟨⟨6607115111327735183970538975,6607115111327735491359805937⟩,⟨(-16629089784300299692156681685),(-16629089784300299384755312519)⟩⟩,⟨⟨5867842974876396290981425847,5867842974876396592762048086⟩,⟨(-16313112133918416892062662815),(-16313112133918416590255044638)⟩⟩,⟨⟨5153697739734007552547604609,5153697739734007848737836153⟩,⟨(-15979017553467692133526553798),(-15979017553467691837295247591)⟩⟩,⟨⟨4465372810226669797182009929,4465372810226670087742349601⟩,⟨(-15627956270466688875138254219),(-15627956270466688584523581724)⟩⟩,⟨⟨3803480653027680921443589880,3803480653027681206394301051⟩,⟨(-15261119890062450200752366606),(-15261119890062449915734885532)⟩⟩,⟨⟨3168551100628198111436141047,3168551100628198390735634562⟩,⟨(-14879735564363848851808307675),(-14879735564363848572430429886)⟩⟩,⟨⟨2561030072826299004338479292,2561030072826299278024460926⟩,⟨(-14485060056053144016298845243),(-14485060056053143742523682109)⟩⟩,⟨⟨1981278723034413800644665346,1981278723034414068690877759⟩,⟨(-14078373732312740062675527548),(-14078373732312739794530151125)⟩⟩,⟨⟨1429573013079776818321211753,1429573013079777080765042311⟩,⟨(-13660974525426809127493931923),(-13660974525426808864941759350)⟩⟩,⟨⟨906103717023676798259972634,906103717023677055074310803⟩,⟨(-13234171896448935853195068805),(-13234171896448935596264009061)⟩⟩,⟨⟨410976851382339680540988002,410976851382339931805631465⟩,⟨(-12799280838066420491537139585),(-12799280838066420240148217660)⟩⟩,⟨⟨(-55785473975308452680272055),(-55785473975308206966094336)⟩,⟨(-12357615952241540258976477015),(-12357615952241540013131253725)⟩⟩,⟨⟨(-494243793020913647974165570),(-494243793020913407758467151)⟩,⟨(-11910485637375163047399207680),(-11910485637375162807046445017)⟩⟩] +lemma kernel16_0_r5_4_eq : ∀ k : Fin 16, kernel16_0Expr 5 4 k = kernel16_0_r5_4 k := by decide +kernel +noncomputable def kernel16_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-904539620569302703450880889),(-904539620569302468751781091)⟩,⟨(-11459186418626866581726254881),(-11459186418626866346884808345)⟩⟩,⟨⟨(-1286893403639021222735618639),(-1286893403639020993466877573)⟩,⟨(-11004997453649273554471029574),(-11004997453649273325055369696)⟩⟩,⟨⟨(-1641602104403630235727416023),(-1641602104403630011832101593)⟩,⟨(-10549175244366574464270649498),(-10549175244366574240224539051)⟩⟩,⟨⟨(-1969036434480462885024245410),(-1969036434480462666438676921)⟩,⟨(-10092948583564687826145108379),(-10092948583564687607405534806)⟩⟩,⟨⟨(-2269637762624676527564681619),(-2269637762624676314295711617)⟩,⟨(-9637513762982124829242252893),(-9637513762982124615816719638)⟩⟩,⟨⟨(-2543914720004642835999996527),(-2543914720004642627968244424)⟩,⟨(-9184030067317485747042123567),(-9184030067317485538851868576)⟩⟩,⟨⟨(-2792439529112222760966739036),(-2792439529112222558164404334)⟩,⟨(-8733615576124645335268516607),(-8733615576124645132306338885)⟩⟩,⟨⟨(-3015844083993103194723115352),(-3015844083993102997072703211)⟩,⟨(-8287343292974753124745289087),(-8287343292974752926934259912)⟩⟩,⟨⟨(-3214815810855720220754612006),(-3214815810855720028252823941)⟩,⟨(-7846237618551191507362304030),(-7846237618551191314699671060)⟩⟩,⟨⟨(-3390093339222838060025933634),(-3390093339222837872459953433)⟩,⟨(-7411271181536632476909552046),(-7411271181536632289193047385)⟩⟩,⟨⟨(-3542462014621040866884548618),(-3542462014621040684213844447)⟩,⟨(-6983362038278039798741407411),(-6983362038278039615932542734)⟩⟩,⟨⟨(-3672749284356688098365045883),(-3672749284356687920507979570)⟩,⟨(-6563371249303963332649154281),(-6563371249303963154665850807)⟩⟩,⟨⟨(-3781819988201763969953983640),(-3781819988201763796901821432)⟩,⟨(-6152100837846874521480929783),(-6152100837846874348314009615)⟩⟩,⟨⟨(-3870571585811982778572117320),(-3870571585811982610228846314)⟩,⟨(-5750292132619393540108741030),(-5750292132619393371661731297)⟩⟩,⟨⟨(-3939929352427871471331632970),(-3939929352427871307674431499)⟩,⟨(-5358624494234218927861134197),(-5358624494234218764110752682)⟩⟩,⟨⟨(-3990841573875517239995251974),(-3990841573875517080903445097)⟩,⟨(-4977714421869598999776062286),(-4977714421869598840601169622)⟩⟩] +lemma kernel16_0_r5_5_eq : ∀ k : Fin 16, kernel16_0Expr 5 5 k = kernel16_0_r5_5 k := by decide +kernel +noncomputable def kernel16_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-4024274771098076162212903937),(-4024274771098076007666729337)⟩,⟨(-4608115034090243589697191494),(-4608115034090243435077557213)⟩⟩,⟨⟨(-4041208983425303084575769666),(-4041208983425302934469403391)⟩,⟨(-4250315915161105396693950265),(-4250315915161105246523274266)⟩⟩,⟨⟨(-4042633138541869180104308334),(-4042633138541869034407217357)⟩,⟨(-3904743315760130349219072107),(-3904743315760130203466349895)⟩⟩,⟨⟨(-4029540535663707078535680206),(-4029540535663706937149848138)⟩,⟨(-3571760694725558353602631603),(-3571760694725558212169373962)⟩⟩,⟨⟨(-4002924466794473082533718523),(-4002924466794472945432877231)⟩,⟨(-3251669586381134024547726650),(-3251669586381133887407199106)⟩⟩,⟨⟨(-3963773999132361050517491260),(-3963773999132360917591515226)⟩,⟨(-2944710776083798560511517324),(-2944710776083798427553129843)⟩⟩,⟨⟨(-3913069939753085477253564671),(-3913069939753085348463616838)⟩,⟨(-2651065764945743376849891228),(-2651065764945743248034350765)⟩⟩,⟨⟨(-3851781001630941074988742205),(-3851781001630940950230978392)⟩,⟨(-2370858503206215979577999214),(-2370858503206215854801011556)⟩⟩,⟨⟨(-3780860187900136634599114464),(-3780860187900136513681616212)⟩,⟨(-2104157370475665865247902629),(-2104157370475665744317039352)⟩⟩,⟨⟨(-3701241409027109003044224889),(-3701241409027108885807130054)⟩,⟨(-1850977380050556954725091252),(-1850977380050556837480041381)⟩⟩,⟨⟨(-3613836345285290480802321945),(-3613836345285290367213314492)⟩,⟨(-1611282583703691959334318161),(-1611282583703691845742352876)⟩⟩,⟨⟨(-3519531564620606761678566682),(-3519531564620606651642964778)⟩,⟨(-1384988652791868600055365642),(-1384988652791868490021401795)⟩⟩,⟨⟨(-3419185903692057039873019619),(-3419185903692056933363485313)⟩,⟨(-1171965611187314314216764068),(-1171965611187314207713074353)⟩⟩,⟨⟨(-3313628117589502927863252638),(-3313628117589502824775023323)⟩,⟨(-972040695426457319620771420),(-972040695426457216542217684)⟩⟩,⟨⟨(-3203654801491650933929173326),(-3203654801491650834223909027)⟩,⟨(-785001317571798126295799648),(-785001317571798026603679085)⟩⟩,⟨⟨(-3090028585351269071857123593),(-3090028585351268975437452204)⟩,⟨(-610598106590502529606170139),(-610598106590502433202763189)⟩⟩] +lemma kernel16_0_r5_6_eq : ∀ k : Fin 16, kernel16_0Expr 5 6 k = kernel16_0_r5_6 k := by decide +kernel +noncomputable def kernel16_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-2973476600600582247942126717),(-2973476600600582154777542875)⟩,⟨(-448548004555534423338963031),(-448548004555534330193429719)⟩⟩,⟨⟨(-2854689215874560251174268641),(-2854689215874560161148662447)⟩,⟨(-298537394658714666350396629),(-298537394658714576346309875)⟩⟩,⟨⟨(-2734319036868688125626350682),(-2734319036868688038680824900)⟩,⟨(-160225238875622577180775152),(-160225238875622490258933609)⟩⟩,⟨⟨(-2612980163694145515886213327),(-2612980163694145431924578880)⟩,⟨(-33246204124134602202274571),(-33246204124134518266202411)⟩⟩,⟨⟨(-2491247697478502969952433469),(-2491247697478502888939549491)⟩,⟨82786243104962668844977180,82786243104962749830694835⟩⟩,⟨⟨(-2369657486493429435130094822),(-2369657486493429356962348334)⟩,⟨188276792412750166456051649,188276792412750244595282903⟩⟩,⟨⟨(-2248706100779809232111170825),(-2248706100779809156744639713)⟩,⟨283645312866051681700047016,283645312866051757036956760⟩⟩,⟨⟨(-2128851023090358736013165906),(-2128851023090358663352780411)⟩,⟨369323960058738984477184063,369323960058739057107066521⟩⟩,⟨⟨(-2010511042983571587442434750),(-2010511042983571517397780169)⟩,⟨445754381339869169011985084,445754381339869239025473233⟩⟩,⟨⟨(-1894066840081910831404799769),(-1894066840081910763858679920)⟩,⟨513385032143433796088629409,513385032143433863603114034⟩⟩,⟨⟨(-1779861741851037096997688117),(-1779861741851037031909962736)⟩,⟨572668614781638022511166492,572668614781638087566969809⟩⟩,⟨⟨(-1668202640763171152321647554),(-1668202640763171089605045936)⟩,⟨624059649479385205731175468,624059649479385268415732486⟩⟩,⟨⟨(-1559361055372441405870519140),(-1559361055372441345490905845)⟩,⟨668012185848104857425884982,668012185848104917773485611⟩⟩,⟨⟨(-1453574319647749686383380036),(-1453574319647749628246261554)⟩,⟨704977661437390889339552064,704977661437390947447347078⟩⟩,⟨⟨(-1351046884872421358897967241),(-1351046884872421302962282989)⟩,⟨735402912477216042223102261,735402912477216098132344695⟩⟩,⟨⟨(-1251951718521599085845916355),(-1251951718521599032027947432)⟩,⟨759728340444689724718763355,759728340444689778513021001⟩⟩] +lemma kernel16_0_r5_7_eq : ∀ k : Fin 16, kernel16_0Expr 5 7 k = kernel16_0_r5_7 k := by decide +kernel +noncomputable def kernel16_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-1156431784758861508011869923),(-1156431784758861456274941609)⟩,⟨778386236669101602710801925,778386236669101654426602861⟩⟩,⟨⟨(-1064601591542895666286335078),(-1064601591542895616516002539)⟩,⟨791799265837683910253435089,791799265837683960005075449⟩⟩,⟨⟨(-976548789792523423939876509),(-976548789792523376097885406)⟩,⟨800379107991096889211332988,800379107991096937036923550⟩⟩,⟨⟨(-892335810612749164011576137),(-892335810612749118020865049)⟩,⟨804525257409657145673509523,804525257409657191649968704⟩⟩,⟨⟨(-812001527224172240401275231),(-812001527224172196229559989)⟩,⟨804623975694943614310431069,804623975694943658469905263⟩⟩,⟨⟨(-735562928951311585453581277),(-735562928951311543020323697)⟩,⟨801047395351391933209174418,801047395351391975632065417⟩⟩,⟨⟨(-663016795400300292156342202),(-663016795400300251414213847)⟩,⟨794152769272224582229590753,794152769272224622963096125⟩⟩,⟨⟨(-594341359781309833327448279),(-594341359781309794201031172)⟩,⟨784281860735645468282530961,784281860735645507401940779⟩⟩,⟨⟨(-529497951194482907255255801),(-529497951194482869715623958)⟩,⟨771760467821485219666092155,771760467821485257200209986⟩⟩,⟨⟨(-468432606588980649628635651),(-468432606588980613600720731)⟩,⟨756898075565070443626808213,756898075565070479650583521⟩⟩,⟨⟨(-411077644012347521489489937),(-411077644012347486931995183)⟩,⟨739987628672566704154735302,739987628672566738709351572⟩⟩,⟨⟨(-357353189681698133456715643),(-357353189681698100304254131)⟩,⟨721305417227971914203452827,721305417227971947354188073⟩⟩,⟨⟨(-307168652319817699990182992),(-307168652319817668213760586)⟩,⟨701111067522976576548993701,701111067522976608324734882⟩⟩,⟨⟨(-260424139099442286083363611),(-260424139099442255613036088)⟩,⟨679647629932929028431957630,679647629932929058902535255⟩⟩,⟨⟨(-217011808419816983116272972),(-217011808419816953920445964)⟩,⟨657141755640331805885380674,657141755640331835082297119⟩⟩,⟨⟨(-176817155593998378519638835),(-176817155593998350539344014)⟩,⟨633803953966258136105565624,633803953966258164087702394⟩⟩] +lemma kernel16_0_r5_8_eq : ∀ k : Fin 16, kernel16_0Expr 5 8 k = kernel16_0_r5_8 k := by decide +kernel +noncomputable def kernel16_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-139720228346983896791982794),(-139720228346983870002396898)⟩,⟨609828922103957310934844793,609828922103957337726942795⟩⟩,⟨⟨(-105596769808171264967057601),(-105596769808171239306233849)⟩,⟨585395939151496105554992415,585395939151496131218921580⟩⟩,⟨⟨(-74319287422277328232656518),(-74319287422277303671409028)⟩,⟨560669316505085373155693879,560669316505085397720567384⟩⟩,⟨⟨(-45758046896910351215908176),(-45758046896910327701042912)⟩,⟨535798896895132870963801123,535798896895132894482745626⟩⟩,⟨⟨(-19781990949538542157001915),(-19781990949538519664425140)⟩,⟨510920594616345846660318000,510920594616345869157363574⟩⟩,⟨⟨3740416790544965063363016,3740416790544986587904684⟩,⟨486156969814700717945599397,486156969814700739474941270⟩⟩,⟨⟨24940421829926879738443594,24940421829926900321460440⟩,⟨461617830041221942409973237,461617830041221962998066855⟩⟩,⟨⟨43948281427240823954186770,43948281427240843643119260⟩,⟨437400852658857137979286292,437400852658857157673522368⟩⟩,⟨⟨60892637964665051429815994,60892637964665070245493616⟩,⟨413592222088122050793338566,413592222088122069614499637⟩⟩,⟨⟨75899960883142253086978011,75899960883142271078502813⟩,⟨390267276293724661468164229,390267276293724679465310692⟩⟩,⟨⟨89094054663647104220335035,89094054663647121411419632⟩,⟨367491157342501962177677406,367491157342501979374482616⟩⟩,⟨⟨100595630061662056590905675,100595630061662073023401426⟩,⟨345319461297524103995194336,345319461297524120433474979⟩⟩,⟨⟨110521935575833110944302555,110521935575833126637528201⟩,⟨323798883149345081603219197,323798883149345097302261348⟩⟩,⟨⟨118986445952287450933455506,118986445952287465929698404⟩,⟨302967852918732394503272411,302967852918732409505335435⟩⟩,⟨⟨126098604390732813067926153,126098604390732827388094635⟩,⟨282857159491848529154692452,282857159491848543480658308⟩⟩,⟨⟨131963615024417581575170693,131963615024417595322879741⟩,⟨263490559165282530409833663,263490559165282544162852716⟩⟩] +lemma kernel16_0_r5_9_eq : ∀ k : Fin 16, kernel16_0Expr 5 9 k = kernel16_0_r5_9 k := by decide +kernel +noncomputable def kernel16_0_r5_10 : Fin 16 → CBox := ![⟨⟨136682282190324029024549693,136682282190324042217142602⟩,⟨244885366281478161951292521,244885366281478175148683868⟩⟩,⟨⟨140350892985480639013282226,140350892985480651682391145⟩,⟨227053023722348427676078454,227053023722348440349504811⟩⟩,⟨⟨143061139616820639291013128,143061139616820651448862160⟩,⟨209999651398000618403385363,209999651398000630565099407⟩⟩,⟨⟨144900078092357625786391315,144900078092357637459289090⟩,⟨193726571216726363559176077,193726571216726375235515012⟩⟩,⟨⟨145950119867379079882387518,145950119867379091079534265⟩,⟨178230807350331991728748596,178230807350332002928939426⟩⟩,⟨⟨146289053147704182371995279,146289053147704193120661282⟩,⟨163505560914458053550431613,163505560914458064301771367⟩⟩,⟨⟨145990090659721869423099464,145990090659721879734238609⟩,⟨149540658466068296730981229,149540658466068307044448799⟩⟩,⟨⟨145121940820934046147249501,145121940820934056044141737⟩,⟨136322973979399172710508489,136322973979399182609408344⟩⟩,⟨⟨143748899382224150563975391,143748899382224160054179536⟩,⟨123836824197260878370289739,123836824197260887862203625⟩⟩,⟨⟨141930958761351059295039983,141930958761351068403248252⟩,⟨112064337466839265430004318,112064337466839274539646909⟩⟩,⟨⟨139723932443698099551047652,139723932443698108286928467⟩,⟨100985796358464303137297954,100985796358464311874358641⟩⟩,⟨⟨137179591988731423353185594,137179591988731431737160465⟩,⟨90579954532786088541029598,90579954532786096925950087⟩⟩,⟨⟨134345814346773701588640358,134345814346773709627824953⟩,⟨80824328467207398487347649,80824328467207406527262513⟩⟩,⟨⟨131266737358603370334774846,131266737358603378050241557⟩,⟨71695464777181349977156060,71695464777181357693155805⟩⟩,⟨⟨127982921478266837672358234,127982921478266845072521356⟩,⟨63169183973131413625742939,63169183973131421026258808⟩⟩,⟨⟨124531515925755786481035151,124531515925755793583676242⟩,⟨55220801580419890216246693,55220801580419897319076283⟩⟩] +lemma kernel16_0_r5_10_eq : ∀ k : Fin 16, kernel16_0Expr 5 10 k = kernel16_0_r5_10 k := by decide +kernel +noncomputable def kernel16_0_r5_11 : Fin 16 → CBox := ![⟨⟨120946427639459910771165176,120946427639459917581774910⟩,⟨47825327619181141198139296,47825327619181148008788331⟩⟩,⟨⟨117258491557349139609219448,117258491557349146146764485⟩,⟨40957645494196770425542666,40957645494196776962991918⟩⟩,⟨⟨113495640909639850991278677,113495640909639857263077076⟩,⟨34592671383599367180884980,34592671383599373452466123⟩⟩,⟨⟨109683076353398721707541371,109683076353398727729487927⟩,⟨28705495240337487153966318,28705495240337493175588618⟩⟩,⟨⟨105843432920438785755831156,105843432920438791533013329⟩,⟨23271504533299726721499437,23271504533299732498261705⟩⟩,⟨⟨101996943883418642441920258,101996943883418647990153285⟩,⟨18266491857042680376784232,18266491857042685924512095⟩⟩,⟨⟨98161600770860582253244299,98161600770860587579390588⟩,⟨13666747531426876089426670,13666747531426881414992335⟩⟩,⟨⟨94353308879577402618269345,94353308879577407735578776⟩,⟨9449138296324670172756005,9449138296324675289418275⟩⟩,⟨⟨90586037742577417146464206,90586037742577422058685737⟩,⟨5591173183061759748341661,5591173183061764659857980⟩⟩,⟨⟨86871966111843095555544462,86871966111843100276652584⟩,⟨2071057614468708388570020,2071057614468713108922411⟩⟩,⟨⟨83221621108483539480574125,83221621108483544015870038⟩,⟨(-1132263249633350453870359),(-1132263249633345919373510)⟩⟩,⟨⟨79644011277757900346675861,79644011277757904708334084⟩,⟨(-4039070944059120682570972),(-4039070944059116321748768)⟩⟩,⟨⟨76146753363538760252138195,76146753363538764443436575⟩,⟨(-6668848972353701795244965),(-6668848972353697604813434)⟩⟩,⟨⟨72736192686173302916473540,72736192686173306948978571⟩,⟨(-9040266034152701544687548),(-9040266034152697513074937)⟩⟩,⟨⟨69417517069696676680892816,69417517069696680558707439⟩,⟨(-11171166363942176372601953),(-11171166363942172495700236)⟩⟩,⟨⟨66194864319286817143579832,66194864319286820876220128⟩,⟨(-13078566387919949625104295),(-13078566387919945893393022)⟩⟩] +lemma kernel16_0_r5_11_eq : ∀ k : Fin 16, kernel16_0Expr 5 11 k = kernel16_0_r5_11 k := by decide +kernel +noncomputable def kernel16_0_r5_12 : Fin 16 → CBox := ![⟨⟨63071423298084658138304603,63071423298084661727979651⟩,⟨(-14778656954862057323200218),(-14778656954862053734466011)⟩⟩,⟨⟨60049528694422657215913772,60049528694422660673101635⟩,⟨(-16286810446207260793353076),(-16286810446207257337114409)⟩⟩,⟨⟨57130749606508261597228215,57130749606508264926590793⟩,⟨(-17617592119525725045909330),(-17617592119525721717500844)⟩⟩,⟨⟨54315972102107053563515373,54315972102107056773056340⟩,⟨(-18784775087733894997903636),(-18784775087733891789318821)⟩⟩,⟨⟨51605475936176143884444219,51605475936176146976115923⟩,⟨(-19801358383513485272456569),(-19801358383513482181740212)⟩⟩,⟨⟨48999005630123774516439907,48999005630123777498669779⟩,⟨(-20679587604100173701483124),(-20679587604100170720205636)⟩⟩,⟨⟨46495836132822069908111453,46495836132822072783557576⟩,⟨(-21430977675689665864401897),(-21430977675689662989902957)⟩⟩,⟨⟨44094833296072915380517847,44094833296072918156054720⟩,⟨(-22066337318974669822994576),(-22066337318974667048351539)⟩⟩,⟨⟨41794509406305859021400313,41794509406305861698260703⟩,⟨(-22595794837628126882599252),(-22595794837628124206570309)⟩⟩,⟨⟨39593074020240344821583439,39593074020240347407285781⟩,⟨(-23028824889776667526170084),(-23028824889776664941240391)⟩⟩,⟨⟨37488480355423882161061729,37488480355423884657749845⟩,⟨(-23374275938589386859619491),(-23374275938589384363648355)⟩⟩,⟨⟨35478467487295569305879261,35478467487295571719384650⟩,⟨(-23640398111997327751301519),(-23640398111997325338460664)⟩⟩,⟨⟨33560598603033476013083484,33560598603033478344505197⟩,⟨(-23834871233242493897839999),(-23834871233242491567033201)⟩⟩,⟨⟨31732295559216922560315821,31732295559216924815891040⟩,⟨(-23964832813439567073524120),(-23964832813439564818517185)⟩⟩,⟨⟨29990869985541875346530382,29990869985541877528498419⟩,⟨(-24036905824647052127594757),(-24036905824647049946151029)⟩⟩,⟨⟨28333551170719677849192684,28333551170719679963346183⟩,⟨(-24057226097133010640885853),(-24057226097133008527215409)⟩⟩] +lemma kernel16_0_r5_12_eq : ∀ k : Fin 16, kernel16_0Expr 5 12 k = kernel16_0_r5_12 k := by decide +kernel +noncomputable def kernel16_0_r5_13 : Fin 16 → CBox := ![⟨⟨26757510959495459757938519,26757510959495461804664419⟩,⟨(-24031469207644101381200820),(-24031469207644099334919053)⟩⟩,⟨⟨25259885881651673302656638,25259885881651675287532563⟩,⟨(-23964876746617455532095908),(-23964876746617453547627646)⟩⟩,⟨⟨23837796725103286901696056,23837796725103288825980230⟩,⟨(-23862281871494597645223913),(-23862281871494595721313081)⟩⟩,⟨⟨22488365755914087487408143,22488365755914089355286016⟩,⟨(-23728134070694104514811295),(-23728134070694102647274603)⟩⟩,⟨⟨21208731778419899737870099,21208731778419901549759285⟩,⟨(-23566523078469240791111621),(-23566523078469238979533367)⟩⟩,⟨⟨19996063218768595278261488,19996063218768597038761250⟩,⟨(-23381201894916286622889389),(-23381201894916284862672270)⟩⟩,⟨⟨18847569405196501436488331,18847569405196503146577549⟩,⟨(-23175608877908600617729065),(-23175608877908598907895935)⟩⟩,⟨⟨17760510208358938313913327,17760510208358939977200607⟩,⟨(-22952888884811277828917693),(-22952888884811276165861671)⟩⟩,⟨⟨16732204195107654585764612,16732204195107656202268887⟩,⟨(-22715913451581759830127737),(-22715913451581758213831424)⟩⟩,⟨⟨15760035439335351618392135,15760035439335353192331289⟩,⟨(-22467300005381694539986715),(-22467300005381692966233783)⟩⟩,⟨⟨14841459123950732744759189,14841459123950734277019890⟩,⟨(-22209430114211230656479771),(-22209430114211229124384936)⟩⟩,⟨⟨13974006058759094209095937,13974006058759095702862690⟩,⟨(-21944466783422328499693447),(-21944466783422327006073561)⟩⟩,⟨⟨13155286230045974093307352,13155286230045975548610231⟩,⟨(-21674370814362648207292188),(-21674370814362646752118399)⟩⟩,⟨⟨12382991489028455763640390,12382991489028457184001349⟩,⟨(-21400916244932290245234064),(-21400916244932288824985630)⟩⟩,⟨⟨11654897478076061718091766,11654897478076063104059366⟩,⟨(-21125704895584021050573894),(-21125704895584019664703349)⟩⟩,⟨⟨10968864885729363419090402,10968864885729364773375695⟩,⟨(-20850180047341056211854091),(-20850180047341054857651440)⟩⟩] +lemma kernel16_0_r5_13_eq : ∀ k : Fin 16, kernel16_0Expr 5 13 k = kernel16_0_r5_13 k := by decide +kernel +noncomputable def kernel16_0_r5_14 : Fin 16 → CBox := ![⟨⟨10322840114071818868679003,10322840114071820190953587⟩,⟨(-20575639280817816101670358),(-20575639280817814779464967)⟩⟩,⟨⟨9714855434945818353863271,9714855434945819647481600⟩,⟨(-20303246507076447158260351),(-20303246507076445864698703)⟩⟩,⟨⟨9143028704849625677618335,9143028704849626942980918⟩,⟨(-20034043222498749742719037),(-20034043222498748477401484)⟩⟩,⟨⟨8605562702105943906953976,8605562702105945146441073⟩,⟨(-19768959020758248749870042),(-19768959020758247510417137)⟩⟩,⟨⟨8100744144049864905729464,8100744144049866119131904⟩,⟨(-19508821395494694760380768),(-19508821395494693547002441)⟩⟩,⟨⟨7626942436535750827027151,7626942436535752017141088⟩,⟨(-19254364867473055370486120),(-19254364867473054180386937)⟩⟩,⟨⟨7182608202998537223811840,7182608202998538390919682⟩,⟨(-19006239469896519431888480),(-19006239469896518264786700)⟩⟩,⟨⟨6766271635612513566114993,6766271635612514712326412⟩,⟨(-18765018625179545875236636),(-18765018625179544729023216)⟩⟩,⟨⟨6376540706755784769918542,6376540706755785894780626⟩,⟨(-18531206445909974106814757),(-18531206445909972981943203)⟩⟩,⟨⟨6012099274996148056496968,6012099274996149162701644⟩,⟨(-18305244491972387073303201),(-18305244491972385967082135)⟩⟩,⟨⟨5671705116147995513290621,5671705116147996601028949⟩,⟨(-18087518014898487843142133),(-18087518014898486755381015)⟩⟩,⟨⟨5354187906593473088635735,5354187906593474159796691⟩,⟨(-17878361719481135259319919),(-17878361719481134188130254)⟩⟩,⟨⟨5058447182997565968038962,5058447182997567022262964⟩,⟨(-17678065071560733305517203),(-17678065071560732251259042)⟩⟩,⟨⟨4783450299758991683868976,4783450299758992723472740⟩,⟨(-17486877179686879050551030),(-17486877179686878010908072)⟩⟩,⟨⟨4528230403009770874794988,4528230403009771899900379⟩,⟨(-17305011277092901407458529),(-17305011277092900382309324)⟩⟩,⟨⟨4291884437689310731664180,4291884437689311743984056⟩,⟨(-17132648829112090086347147),(-17132648829112089073979201)⟩⟩] +lemma kernel16_0_r5_14_eq : ∀ k : Fin 16, kernel16_0Expr 5 14 k = kernel16_0_r5_14 k := by decide +kernel +noncomputable def kernel16_0_r5_15 : Fin 16 → CBox := ![⟨⟨4073571202157289532222587,4073571202157290531154672⟩,⟨(-16969943289825709170337972),(-16969943289825708171353944)⟩⟩,⟨⟨3872509462957489451215476,3872509462957490439104243⟩,⟨(-16817023530375958038996732),(-16817023530375957051052460)⟩⟩,⟨⟨3687976140686384941494189,3687976140686385918412684⟩,⟨(-16673996960011667804867780),(-16673996960011666827890550)⟩⟩,⟨⟨3519304576440683380036772,3519304576440684347558816⟩,⟨(-16540952359568799238772987),(-16540952359568798271189262)⟩⟩,⟨⟨3365882887002631167199176,3365882887002632124877396⟩,⟨(-16417962445728306452725411),(-16417962445728305494982871)⟩⟩,⟨⟨3227152415756831632340498,3227152415756832582199302⟩,⟨(-16305086183045842935175752),(-16305086183045841985250242)⟩⟩,⟨⟨3102606285304262456753547,3102606285304263398834116⟩,⟨(-16202370859415073124202972),(-16202370859415072182053576)⟩⟩,⟨⟨2991788056835421137879061,2991788056835422073650575⟩,⟨(-16109853939311872905610862),(-16109853939311871969768633)⟩⟩,⟨⟨2894290500532947387004080,2894290500532948315927409⟩,⟨(-16027564707872336411240845),(-16027564707872335482245196)⟩⟩,⟨⟨2809754480583119831482292,2809754480583120755722172⟩,⟨(-15955525717584268823129368),(-15955525717584267898815782)⟩⟩,⟨⟨2737867957774291416753156,2737867957774292336310849⟩,⟨(-15893754048119988285251515),(-15893754048119987365618954)⟩⟩,⟨⟨2678365112138112033877628,2678365112138112950123080⟩,⟨(-15842262388607372033514518),(-15842262388607371117193228)⟩⟩,⟨⟨2631025587636256881780438,2631025587636257794199217⟩,⟨(-15801059950425172946387558),(-15801059950425172033892198)⟩⟩,⟨⟨2595673860501730491702265,2595673860501731402154201⟩,⟨(-15770153217416218561135038),(-15770153217416217650605947)⟩⟩,⟨⟨2572178732500425691458673,2572178732500426599946190⟩,⟨(-15749546539236281108095973),(-15749546539236280199530936)⟩⟩,⟨⟨2560452950076591541760091,2560452950076592449606925⟩,⟨(-15739242572394921096523704),(-15739242572394920188599159)⟩⟩] +lemma kernel16_0_r5_15_eq : ∀ k : Fin 16, kernel16_0Expr 5 15 k = kernel16_0_r5_15 k := by decide +kernel +noncomputable def kernel16_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel16_0_r5_0,kernel16_0_r5_1,kernel16_0_r5_2,kernel16_0_r5_3,kernel16_0_r5_4,kernel16_0_r5_5,kernel16_0_r5_6,kernel16_0_r5_7,kernel16_0_r5_8,kernel16_0_r5_9,kernel16_0_r5_10,kernel16_0_r5_11,kernel16_0_r5_12,kernel16_0_r5_13,kernel16_0_r5_14,kernel16_0_r5_15] +lemma kernel16_0_r5_eq (i k : Fin 16) : kernel16_0Expr 5 i k = kernel16_0_r5 i k := by + fin_cases i + · exact kernel16_0_r5_0_eq k + · exact kernel16_0_r5_1_eq k + · exact kernel16_0_r5_2_eq k + · exact kernel16_0_r5_3_eq k + · exact kernel16_0_r5_4_eq k + · exact kernel16_0_r5_5_eq k + · exact kernel16_0_r5_6_eq k + · exact kernel16_0_r5_7_eq k + · exact kernel16_0_r5_8_eq k + · exact kernel16_0_r5_9_eq k + · exact kernel16_0_r5_10_eq k + · exact kernel16_0_r5_11_eq k + · exact kernel16_0_r5_12_eq k + · exact kernel16_0_r5_13_eq k + · exact kernel16_0_r5_14_eq k + · exact kernel16_0_r5_15_eq k +noncomputable def kernel16_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel16_0_r0,kernel16_0_r1,kernel16_0_r2,kernel16_0_r3,kernel16_0_r4,kernel16_0_r5] +lemma kernel16_0_eq (j : Fin 6) (i k : Fin 16) : kernel16_0Expr j i k = kernel16_0 j i k := by + fin_cases j + · exact kernel16_0_r0_eq i k + · exact kernel16_0_r1_eq i k + · exact kernel16_0_r2_eq i k + · exact kernel16_0_r3_eq i k + · exact kernel16_0_r4_eq i k + · exact kernel16_0_r5_eq i k +lemma kernel16_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel16_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(16:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel16_0_eq] + unfold kernel16_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans16_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel16_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans16 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel16_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r0_0_eq : ∀ k : Fin 16, kernel16_1Expr 0 0 k = kernel16_1_r0_0 k := by decide +kernel +noncomputable def kernel16_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r0_1_eq : ∀ k : Fin 16, kernel16_1Expr 0 1 k = kernel16_1_r0_1 k := by decide +kernel +noncomputable def kernel16_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r0_2_eq : ∀ k : Fin 16, kernel16_1Expr 0 2 k = kernel16_1_r0_2 k := by decide +kernel +noncomputable def kernel16_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r0_3_eq : ∀ k : Fin 16, kernel16_1Expr 0 3 k = kernel16_1_r0_3 k := by decide +kernel +noncomputable def kernel16_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r0_4_eq : ∀ k : Fin 16, kernel16_1Expr 0 4 k = kernel16_1_r0_4 k := by decide +kernel +noncomputable def kernel16_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel16_1_r0_5_eq : ∀ k : Fin 16, kernel16_1Expr 0 5 k = kernel16_1_r0_5 k := by decide +kernel +noncomputable def kernel16_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel16_1_r0_6_eq : ∀ k : Fin 16, kernel16_1Expr 0 6 k = kernel16_1_r0_6 k := by decide +kernel +noncomputable def kernel16_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel16_1_r0_7_eq : ∀ k : Fin 16, kernel16_1Expr 0 7 k = kernel16_1_r0_7 k := by decide +kernel +noncomputable def kernel16_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel16_1_r0_8_eq : ∀ k : Fin 16, kernel16_1Expr 0 8 k = kernel16_1_r0_8 k := by decide +kernel +noncomputable def kernel16_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel16_1_r0_9_eq : ∀ k : Fin 16, kernel16_1Expr 0 9 k = kernel16_1_r0_9 k := by decide +kernel +noncomputable def kernel16_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel16_1_r0_10_eq : ∀ k : Fin 16, kernel16_1Expr 0 10 k = kernel16_1_r0_10 k := by decide +kernel +noncomputable def kernel16_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel16_1_r0_11_eq : ∀ k : Fin 16, kernel16_1Expr 0 11 k = kernel16_1_r0_11 k := by decide +kernel +noncomputable def kernel16_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel16_1_r0_12_eq : ∀ k : Fin 16, kernel16_1Expr 0 12 k = kernel16_1_r0_12 k := by decide +kernel +noncomputable def kernel16_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel16_1_r0_13_eq : ∀ k : Fin 16, kernel16_1Expr 0 13 k = kernel16_1_r0_13 k := by decide +kernel +noncomputable def kernel16_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel16_1_r0_14_eq : ∀ k : Fin 16, kernel16_1Expr 0 14 k = kernel16_1_r0_14 k := by decide +kernel +noncomputable def kernel16_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel16_1_r0_15_eq : ∀ k : Fin 16, kernel16_1Expr 0 15 k = kernel16_1_r0_15 k := by decide +kernel +noncomputable def kernel16_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel16_1_r0_0,kernel16_1_r0_1,kernel16_1_r0_2,kernel16_1_r0_3,kernel16_1_r0_4,kernel16_1_r0_5,kernel16_1_r0_6,kernel16_1_r0_7,kernel16_1_r0_8,kernel16_1_r0_9,kernel16_1_r0_10,kernel16_1_r0_11,kernel16_1_r0_12,kernel16_1_r0_13,kernel16_1_r0_14,kernel16_1_r0_15] +lemma kernel16_1_r0_eq (i k : Fin 16) : kernel16_1Expr 0 i k = kernel16_1_r0 i k := by + fin_cases i + · exact kernel16_1_r0_0_eq k + · exact kernel16_1_r0_1_eq k + · exact kernel16_1_r0_2_eq k + · exact kernel16_1_r0_3_eq k + · exact kernel16_1_r0_4_eq k + · exact kernel16_1_r0_5_eq k + · exact kernel16_1_r0_6_eq k + · exact kernel16_1_r0_7_eq k + · exact kernel16_1_r0_8_eq k + · exact kernel16_1_r0_9_eq k + · exact kernel16_1_r0_10_eq k + · exact kernel16_1_r0_11_eq k + · exact kernel16_1_r0_12_eq k + · exact kernel16_1_r0_13_eq k + · exact kernel16_1_r0_14_eq k + · exact kernel16_1_r0_15_eq k +noncomputable def kernel16_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel16_1_r1_0_eq : ∀ k : Fin 16, kernel16_1Expr 1 0 k = kernel16_1_r1_0 k := by decide +kernel +noncomputable def kernel16_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel16_1_r1_1_eq : ∀ k : Fin 16, kernel16_1Expr 1 1 k = kernel16_1_r1_1 k := by decide +kernel +noncomputable def kernel16_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel16_1_r1_2_eq : ∀ k : Fin 16, kernel16_1Expr 1 2 k = kernel16_1_r1_2 k := by decide +kernel +noncomputable def kernel16_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel16_1_r1_3_eq : ∀ k : Fin 16, kernel16_1Expr 1 3 k = kernel16_1_r1_3 k := by decide +kernel +noncomputable def kernel16_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel16_1_r1_4_eq : ∀ k : Fin 16, kernel16_1Expr 1 4 k = kernel16_1_r1_4 k := by decide +kernel +noncomputable def kernel16_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel16_1_r1_5_eq : ∀ k : Fin 16, kernel16_1Expr 1 5 k = kernel16_1_r1_5 k := by decide +kernel +noncomputable def kernel16_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel16_1_r1_6_eq : ∀ k : Fin 16, kernel16_1Expr 1 6 k = kernel16_1_r1_6 k := by decide +kernel +noncomputable def kernel16_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel16_1_r1_7_eq : ∀ k : Fin 16, kernel16_1Expr 1 7 k = kernel16_1_r1_7 k := by decide +kernel +noncomputable def kernel16_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel16_1_r1_8_eq : ∀ k : Fin 16, kernel16_1Expr 1 8 k = kernel16_1_r1_8 k := by decide +kernel +noncomputable def kernel16_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel16_1_r1_9_eq : ∀ k : Fin 16, kernel16_1Expr 1 9 k = kernel16_1_r1_9 k := by decide +kernel +noncomputable def kernel16_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r1_10_eq : ∀ k : Fin 16, kernel16_1Expr 1 10 k = kernel16_1_r1_10 k := by decide +kernel +noncomputable def kernel16_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r1_11_eq : ∀ k : Fin 16, kernel16_1Expr 1 11 k = kernel16_1_r1_11 k := by decide +kernel +noncomputable def kernel16_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r1_12_eq : ∀ k : Fin 16, kernel16_1Expr 1 12 k = kernel16_1_r1_12 k := by decide +kernel +noncomputable def kernel16_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r1_13_eq : ∀ k : Fin 16, kernel16_1Expr 1 13 k = kernel16_1_r1_13 k := by decide +kernel +noncomputable def kernel16_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r1_14_eq : ∀ k : Fin 16, kernel16_1Expr 1 14 k = kernel16_1_r1_14 k := by decide +kernel +noncomputable def kernel16_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel16_1_r1_15_eq : ∀ k : Fin 16, kernel16_1Expr 1 15 k = kernel16_1_r1_15 k := by decide +kernel +noncomputable def kernel16_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel16_1_r1_0,kernel16_1_r1_1,kernel16_1_r1_2,kernel16_1_r1_3,kernel16_1_r1_4,kernel16_1_r1_5,kernel16_1_r1_6,kernel16_1_r1_7,kernel16_1_r1_8,kernel16_1_r1_9,kernel16_1_r1_10,kernel16_1_r1_11,kernel16_1_r1_12,kernel16_1_r1_13,kernel16_1_r1_14,kernel16_1_r1_15] +lemma kernel16_1_r1_eq (i k : Fin 16) : kernel16_1Expr 1 i k = kernel16_1_r1 i k := by + fin_cases i + · exact kernel16_1_r1_0_eq k + · exact kernel16_1_r1_1_eq k + · exact kernel16_1_r1_2_eq k + · exact kernel16_1_r1_3_eq k + · exact kernel16_1_r1_4_eq k + · exact kernel16_1_r1_5_eq k + · exact kernel16_1_r1_6_eq k + · exact kernel16_1_r1_7_eq k + · exact kernel16_1_r1_8_eq k + · exact kernel16_1_r1_9_eq k + · exact kernel16_1_r1_10_eq k + · exact kernel16_1_r1_11_eq k + · exact kernel16_1_r1_12_eq k + · exact kernel16_1_r1_13_eq k + · exact kernel16_1_r1_14_eq k + · exact kernel16_1_r1_15_eq k +noncomputable def kernel16_1_r2_0 : Fin 16 → CBox := ![⟨⟨75762689232,75762689264⟩,⟨(-214858746025),(-214858745993)⟩⟩,⟨⟨75510761483,75510761513⟩,⟨(-214471756473),(-214471756445)⟩⟩,⟨⟨75008991493,75008991523⟩,⟨(-213699705983),(-213699705956)⟩⟩,⟨⟨74261524233,74261524269⟩,⟨(-212546437919),(-212546437881)⟩⟩,⟨⟨73274512663,73274512690⟩,⟨(-211017682775),(-211017682745)⟩⟩,⟨⟨72056041409,72056041434⟩,⟨(-209121017043),(-209121017018)⟩⟩,⟨⟨70616026993,70616027026⟩,⟨(-206865808781),(-206865808748)⟩⟩,⟨⟨68966096173,68966096198⟩,⟨(-204263150176),(-204263150151)⟩⟩,⟨⟨67119444292,67119444317⟩,⟨(-201325777964),(-201325777939)⟩⟩,⟨⟨65090675997,65090676022⟩,⟨(-198067981779),(-198067981754)⟩⟩,⟨⟨62895630657,62895630690⟩,⟨(-194505501556),(-194505501523)⟩⟩,⟨⟨60551195454,60551195487⟩,⟨(-190655414449),(-190655414416)⟩⟩,⟨⟨58075108738,58075108763⟩,⟨(-186536012455),(-186536012430)⟩⟩,⟨⟨55485756880,55485756913⟩,⟨(-182166671478),(-182166671446)⟩⟩,⟨⟨52801967609,52801967639⟩,⟨(-177567712949),(-177567712922)⟩⟩,⟨⟨50042802736,50042802766⟩,⟨(-172760259371),(-172760259344)⟩⟩] +lemma kernel16_1_r2_0_eq : ∀ k : Fin 16, kernel16_1Expr 2 0 k = kernel16_1_r2_0 k := by decide +kernel +noncomputable def kernel16_1_r2_1 : Fin 16 → CBox := ![⟨⟨47227353440,47227353468⟩,⟨(-167766084735),(-167766084705)⟩⟩,⟨⟨44374540885,44374540921⟩,⟨(-162607461308),(-162607461270)⟩⟩,⟨⟨41502924927,41502924959⟩,⟨(-157307004134),(-157307004102)⟩⟩,⟨⟨38630523349,38630523382⟩,⟨(-151887514652),(-151887514619)⟩⟩,⟨⟨35774643963,35774643999⟩,⟨(-146371824756),(-146371824718)⟩⟩,⟨⟨32951731611,32951731644⟩,⟨(-140782642994),(-140782642961)⟩⟩,⟨⟨30177231603,30177231628⟩,⟨(-135142404178),(-135142404153)⟩⟩,⟨⟨27465471087,27465471117⟩,⟨(-129473123763),(-129473123736)⟩⟩,⟨⟨24829559274,24829559307⟩,⟨(-123796258626),(-123796258593)⟩⟩,⟨⟨22281307294,22281307327⟩,⟨(-118132575315),(-118132575282)⟩⟩,⟨⟨19831167868,19831167899⟩,⟨(-112502027080),(-112502027052)⟩⟩,⟨⟨17488194941,17488194974⟩,⟨(-106923640858),(-106923640825)⟩⟩,⟨⟨15260022765,15260022803⟩,⟨(-101415415086),(-101415415050)⟩⟩,⟨⟨13152863930,13152863958⟩,⟨(-95994229313),(-95994229283)⟩⟩,⟨⟨11171525374,11171525404⟩,⟨(-90675766304),(-90675766276)⟩⟩,⟨⟨9319441118,9319441156⟩,⟨(-85474447062),(-85474447026)⟩⟩] +lemma kernel16_1_r2_1_eq : ∀ k : Fin 16, kernel16_1Expr 2 1 k = kernel16_1_r2_1 k := by decide +kernel +noncomputable def kernel16_1_r2_2 : Fin 16 → CBox := ![⟨⟨7598720540,7598720570⟩,⟨(-80403379286),(-80403379258)⟩⟩,⟨⟨6010210288,6010210318⟩,⟨(-75474319412),(-75474319384)⟩⟩,⟨⟨4553568483,4553568524⟩,⟨(-70697648201),(-70697648160)⟩⟩,⟨⟨3227349169,3227349221⟩,⟨(-66082359755),(-66082359701)⟩⟩,⟨⟨2029095139,2029095172⟩,⟨(-61636063635),(-61636063601)⟩⟩,⟨⟨955437287,955437329⟩,⟨(-57364999640),(-57364999599)⟩⟩,⟨⟨2198682,2198715⟩,⟨(-53274064342),(-53274064309)⟩⟩,⟨⟨(-835498734),(-835498693)⟩,⟨(-49366849011),(-49366848970)⟩⟩,⟨⟨(-1563126295),(-1563126267)⟩,⟨(-45645687580),(-45645687550)⟩⟩,⟨⟨(-2186641598),(-2186641562)⟩,⟨(-42111714016),(-42111713978)⟩⟩,⟨⟨(-2712383472),(-2712383444)⟩,⟨(-38764927621),(-38764927591)⟩⟩,⟨⟨(-3146970723),(-3146970692)⟩,⟨(-35604265497),(-35604265469)⟩⟩,⟨⟨(-3497205572),(-3497205538)⟩,⟨(-32627680634),(-32627680600)⟩⟩,⟨⟨(-3769982977),(-3769982943)⟩,⟨(-29832224509),(-29832224476)⟩⟩,⟨⟨(-3972206647),(-3972206613)⟩,⟨(-27214133149),(-27214133116)⟩⟩,⟨⟨(-4110712522),(-4110712481)⟩,⟨(-24768915097),(-24768915055)⟩⟩] +lemma kernel16_1_r2_2_eq : ∀ k : Fin 16, kernel16_1Expr 2 2 k = kernel16_1_r2_2 k := by decide +kernel +noncomputable def kernel16_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-4192200026),(-4192199988)⟩,⟨(-22491440401),(-22491440365)⟩⟩,⟨⟨(-4223171670),(-4223171629)⟩,⟨(-20376029446),(-20376029405)⟩⟩,⟨⟨(-4209880897),(-4209880871)⟩,⟨(-18416540493),(-18416540468)⟩⟩,⟨⟨(-4158288440),(-4158288410)⟩,⟨(-16606455128),(-16606455099)⟩⟩,⟨⟨(-4074026701),(-4074026667)⟩,⟨(-14938960548),(-14938960514)⟩⟩,⟨⟨(-3962372304),(-3962372267)⟩,⟨(-13407028211),(-13407028172)⟩⟩,⟨⟨(-3828226051),(-3828226017)⟩,⟨(-12003487980),(-12003487946)⟩⟩,⟨⟨(-3676100072),(-3676100038)⟩,⟨(-10721097254),(-10721097220)⟩⟩,⟨⟨(-3510111443),(-3510111409)⟩,⟨(-9552604828),(-9552604795)⟩⟩,⟨⟨(-3333981843),(-3333981809)⟩,⟨(-8490808930),(-8490808897)⟩⟩,⟨⟨(-3151042451),(-3151042420)⟩,⟨(-7528609469),(-7528609440)⟩⟩,⟨⟨(-2964243452),(-2964243423)⟩,⟨(-6659054201),(-6659054171)⟩⟩,⟨⟨(-2776167624),(-2776167590)⟩,⟨(-5875378971),(-5875378938)⟩⟩,⟨⟨(-2589047093),(-2589047059)⟩,⟨(-5171041967),(-5171041933)⟩⟩,⟨⟨(-2404782823),(-2404782797)⟩,⟨(-4539752278),(-4539752253)⟩⟩,⟨⟨(-2224966153),(-2224966119)⟩,⟨(-3975492896),(-3975492862)⟩⟩] +lemma kernel16_1_r2_3_eq : ∀ k : Fin 16, kernel16_1Expr 2 3 k = kernel16_1_r2_3 k := by decide +kernel +noncomputable def kernel16_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-2050901655),(-2050901624)⟩,⟨(-3472538507),(-3472538478)⟩⟩,⟨⟨(-1883631142),(-1883631111)⟩,⟨(-3025468336),(-3025468307)⟩⟩,⟨⟨(-1723957862),(-1723957833)⟩,⟨(-2629174538),(-2629174507)⟩⟩,⟨⟨(-1572470876),(-1572470847)⟩,⟨(-2278866338),(-2278866307)⟩⟩,⟨⟨(-1429568943),(-1429568914)⟩,⟨(-1970070581),(-1970070550)⟩⟩,⟨⟨(-1295483782),(-1295483751)⟩,⟨(-1698628917),(-1698628888)⟩⟩,⟨⟨(-1170302308),(-1170302282)⟩,⟨(-1460692105),(-1460692079)⟩⟩,⟨⟨(-1053987704),(-1053987670)⟩,⟨(-1252711887),(-1252711853)⟩⟩,⟨⟨(-946399169),(-946399134)⟩,⟨(-1071430796),(-1071430762)⟩⟩,⟨⟨(-847310156),(-847310114)⟩,⟨(-913870342),(-913870300)⟩⟩,⟨⟨(-756425099),(-756425067)⟩,⟨(-777317752),(-777317723)⟩⟩,⟨⟨(-673394564),(-673394530)⟩,⟨(-659311933),(-659311899)⟩⟩,⟨⟨(-597828769),(-597828734)⟩,⟨(-557628545),(-557628511)⟩⟩,⟨⟨(-529309593),(-529309559)⟩,⟨(-470264894),(-470264859)⟩⟩,⟨⟨(-467401050),(-467401018)⟩,⟨(-395424472),(-395424442)⟩⟩,⟨⟨(-411658331),(-411658305)⟩,⟨(-331501710),(-331501684)⟩⟩] +lemma kernel16_1_r2_4_eq : ∀ k : Fin 16, kernel16_1Expr 2 4 k = kernel16_1_r2_4 k := by decide +kernel +noncomputable def kernel16_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-361635456),(-361635426)⟩,⟨(-277066917),(-277066885)⟩⟩,⟨⟨(-316891722),(-316891691)⟩,⟨(-230851583),(-230851554)⟩⟩,⟨⟨(-276996907),(-276996878)⟩,⟨(-191734268),(-191734237)⟩⟩,⟨⟨(-241535485),(-241535451)⟩,⟨(-158727063),(-158727028)⟩⟩,⟨⟨(-210109817),(-210109782)⟩,⟨(-130962783),(-130962748)⟩⟩,⟨⟨(-182342652),(-182342623)⟩,⟨(-107682917),(-107682886)⟩⟩,⟨⟨(-157878656),(-157878621)⟩,⟨(-88226280),(-88226245)⟩⟩,⟨⟨(-136385561),(-136385534)⟩,⟨(-72018592),(-72018566)⟩⟩,⟨⟨(-117554554),(-117554527)⟩,⟨(-58562779),(-58562752)⟩⟩,⟨⟨(-101100404),(-101100369)⟩,⟨(-47430098),(-47430063)⟩⟩,⟨⟨(-86761028),(-86760996)⟩,⟨(-38252019),(-38251989)⟩⟩,⟨⟨(-74296924),(-74296894)⟩,⟨(-30712914),(-30712882)⟩⟩,⟨⟨(-63490291),(-63490261)⟩,⟨(-24543366),(-24543334)⟩⟩,⟨⟨(-54143961),(-54143926)⟩,⟨(-19514242),(-19514207)⟩⟩,⟨⟨(-46080257),(-46080222)⟩,⟨(-15431335),(-15431300)⟩⟩,⟨⟨(-39139732),(-39139702)⟩,⟨(-12130646),(-12130615)⟩⟩] +lemma kernel16_1_r2_5_eq : ∀ k : Fin 16, kernel16_1Expr 2 5 k = kernel16_1_r2_5 k := by decide +kernel +noncomputable def kernel16_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-33179907),(-33179875)⟩,⟨(-9474197),(-9474167)⟩⟩,⟨⟨(-28073883),(-28073857)⟩,⟨(-7346294),(-7346267)⟩⟩,⟨⟨(-23709175),(-23709143)⟩,⟨(-5650280),(-5650250)⟩⟩,⟨⟨(-19986341),(-19986306)⟩,⟨(-4305752),(-4305716)⟩⟩,⟨⟨(-16817804),(-16817774)⟩,⟨(-3246022),(-3245990)⟩⟩,⟨⟨(-14126709),(-14126682)⟩,⟨(-2416031),(-2416004)⟩⟩,⟨⟨(-11845822),(-11845787)⟩,⟨(-1770515),(-1770479)⟩⟩,⟨⟨(-9916515),(-9916483)⟩,⟨(-1272344),(-1272314)⟩⟩,⟨⟨(-8287814),(-8287782)⟩,⟨(-891277),(-891246)⟩⟩,⟨⟨(-6915513),(-6915478)⟩,⟨(-602736),(-602700)⟩⟩,⟨⟨(-5761422),(-5761386)⟩,⟨(-386830),(-386794)⟩⟩,⟨⟨(-4792638),(-4792607)⟩,⟨(-227580),(-227548)⟩⟩,⟨⟨(-3980853),(-3980817)⟩,⟨(-112200),(-112164)⟩⟩,⟨⟨(-3301807),(-3301780)⟩,⟨(-30474),(-30447)⟩⟩,⟨⟨(-2734787),(-2734751)⟩,⟨25657,25694⟩⟩,⟨⟨(-2262061),(-2262030)⟩,⟨62562,62595⟩⟩] +lemma kernel16_1_r2_6_eq : ∀ k : Fin 16, kernel16_1Expr 2 6 k = kernel16_1_r2_6 k := by decide +kernel +noncomputable def kernel16_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-1868604),(-1868568)⟩,⟨85205,85241⟩⟩,⟨⟨(-1541624),(-1541591)⟩,⟨97437,97468⟩⟩,⟨⟨(-1270298),(-1270262)⟩,⟨102222,102258⟩⟩,⟨⟨(-1045509),(-1045473)⟩,⟨101833,101869⟩⟩,⟨⟨(-859501),(-859470)⟩,⟨97986,98019⟩⟩,⟨⟨(-705832),(-705801)⟩,⟨91940,91973⟩⟩,⟨⟨(-579042),(-578997)⟩,⟨84624,84669⟩⟩,⟨⟨(-474531),(-474495)⟩,⟨76737,76773⟩⟩,⟨⟨(-388530),(-388497)⟩,⟨68741,68773⟩⟩,⟨⟨(-317828),(-317783)⟩,⟨60941,60986⟩⟩,⟨⟨(-259757),(-259720)⟩,⟨53568,53605⟩⟩,⟨⟨(-212138),(-212101)⟩,⟨46725,46762⟩⟩,⟨⟨(-173115),(-173082)⟩,⟨40498,40529⟩⟩,⟨⟨(-141162),(-141125)⟩,⟨34899,34936⟩⟩,⟨⟨(-115047),(-115010)⟩,⟨29922,29959⟩⟩,⟨⟨(-93694),(-93657)⟩,⟨25531,25568⟩⟩] +lemma kernel16_1_r2_7_eq : ∀ k : Fin 16, kernel16_1Expr 2 7 k = kernel16_1_r2_7 k := by decide +kernel +noncomputable def kernel16_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-76259),(-76222)⟩,⟨21696,21733⟩⟩,⟨⟨(-62047),(-62010)⟩,⟨18366,18403⟩⟩,⟨⟨(-50448),(-50411)⟩,⟨15490,15527⟩⟩,⟨⟨(-41004),(-40967)⟩,⟨13025,13063⟩⟩,⟨⟨(-33323),(-33285)⟩,⟨10916,10953⟩⟩,⟨⟨(-27067),(-27030)⟩,⟨9131,9168⟩⟩,⟨⟨(-21979),(-21942)⟩,⟨7607,7644⟩⟩,⟨⟨(-17845),(-17807)⟩,⟨6328,6365⟩⟩,⟨⟨(-14487),(-14450)⟩,⟨5255,5293⟩⟩,⟨⟨(-11766),(-11716)⟩,⟨4341,4393⟩⟩,⟨⟨(-9546),(-9512)⟩,⟨3588,3620⟩⟩,⟨⟨(-7744),(-7706)⟩,⟨2958,2995⟩⟩,⟨⟨(-6288),(-6250)⟩,⟨2434,2472⟩⟩,⟨⟨(-5110),(-5076)⟩,⟨2001,2033⟩⟩,⟨⟨(-4148),(-4111)⟩,⟨1644,1682⟩⟩,⟨⟨(-3361),(-3324)⟩,⟨1335,1373⟩⟩] +lemma kernel16_1_r2_8_eq : ∀ k : Fin 16, kernel16_1Expr 2 8 k = kernel16_1_r2_8 k := by decide +kernel +noncomputable def kernel16_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-2739),(-2701)⟩,⟨1099,1136⟩⟩,⟨⟨(-2223),(-2189)⟩,⟨892,925⟩⟩,⟨⟨(-1811),(-1773)⟩,⟨721,759⟩⟩,⟨⟨(-1479),(-1441)⟩,⟨594,632⟩⟩,⟨⟨(-1204),(-1166)⟩,⟨468,506⟩⟩,⟨⟨(-976),(-937)⟩,⟨377,415⟩⟩,⟨⟨(-806),(-768)⟩,⟨306,344⟩⟩,⟨⟨(-662),(-624)⟩,⟨246,284⟩⟩,⟨⟨(-528),(-494)⟩,⟨193,226⟩⟩,⟨⟨(-452),(-400)⟩,⟨147,200⟩⟩,⟨⟨(-358),(-320)⟩,⟨120,159⟩⟩,⟨⟨(-303),(-265)⟩,⟨94,133⟩⟩,⟨⟨(-244),(-205)⟩,⟨73,112⟩⟩,⟨⟨(-199),(-160)⟩,⟨55,94⟩⟩,⟨⟨(-174),(-135)⟩,⟨44,83⟩⟩,⟨⟨(-140),(-105)⟩,⟨34,67⟩⟩] +lemma kernel16_1_r2_9_eq : ∀ k : Fin 16, kernel16_1Expr 2 9 k = kernel16_1_r2_9 k := by decide +kernel +noncomputable def kernel16_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-128),(-90)⟩,⟨16,55⟩⟩,⟨⟨(-99),(-60)⟩,⟨10,49⟩⟩,⟨⟨(-84),(-46)⟩,⟨7,46⟩⟩,⟨⟨(-69),(-30)⟩,⟨(-6),33⟩⟩,⟨⟨(-69),(-30)⟩,⟨(-5),33⟩⟩,⟨⟨(-55),(-16)⟩,⟨1,40⟩⟩,⟨⟨(-58),(-19)⟩,⟨(-14),25⟩⟩,⟨⟨(-39),0⟩,⟨(-12),27⟩⟩,⟨⟨(-40),0⟩,⟨(-12),27⟩⟩,⟨⟨(-40),0⟩,⟨(-12),27⟩⟩,⟨⟨(-25),9⟩,⟨(-11),24⟩⟩,⟨⟨(-25),9⟩,⟨(-11),24⟩⟩,⟨⟨(-25),9⟩,⟨(-11),24⟩⟩,⟨⟨(-25),9⟩,⟨(-11),24⟩⟩,⟨⟨(-25),9⟩,⟨(-11),24⟩⟩,⟨⟨(-25),9⟩,⟨(-11),24⟩⟩] +lemma kernel16_1_r2_10_eq : ∀ k : Fin 16, kernel16_1Expr 2 10 k = kernel16_1_r2_10 k := by decide +kernel +noncomputable def kernel16_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-25),9⟩,⟨(-11),24⟩⟩,⟨⟨(-25),9⟩,⟨(-11),24⟩⟩,⟨⟨(-30),9⟩,⟨(-11),29⟩⟩,⟨⟨(-30),9⟩,⟨(-11),29⟩⟩,⟨⟨(-30),9⟩,⟨(-11),29⟩⟩,⟨⟨(-30),9⟩,⟨(-11),29⟩⟩,⟨⟨(-30),9⟩,⟨(-11),29⟩⟩,⟨⟨(-30),9⟩,⟨(-11),29⟩⟩,⟨⟨(-30),9⟩,⟨(-11),29⟩⟩,⟨⟨(-39),20⟩,⟨(-30),29⟩⟩,⟨⟨(-30),10⟩,⟨(-11),29⟩⟩,⟨⟨(-39),20⟩,⟨(-30),29⟩⟩,⟨⟨(-39),20⟩,⟨(-30),29⟩⟩,⟨⟨(-39),20⟩,⟨(-30),29⟩⟩,⟨⟨(-40),20⟩,⟨(-30),29⟩⟩,⟨⟨(-40),20⟩,⟨(-30),29⟩⟩] +lemma kernel16_1_r2_11_eq : ∀ k : Fin 16, kernel16_1Expr 2 11 k = kernel16_1_r2_11 k := by decide +kernel +noncomputable def kernel16_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),20⟩,⟨(-30),29⟩⟩,⟨⟨(-40),20⟩,⟨(-30),29⟩⟩,⟨⟨(-40),20⟩,⟨(-30),29⟩⟩,⟨⟨(-40),20⟩,⟨(-30),29⟩⟩,⟨⟨(-40),20⟩,⟨(-31),29⟩⟩,⟨⟨(-40),20⟩,⟨(-31),29⟩⟩,⟨⟨(-40),20⟩,⟨(-31),29⟩⟩,⟨⟨(-40),20⟩,⟨(-31),29⟩⟩,⟨⟨(-40),20⟩,⟨(-31),29⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩] +lemma kernel16_1_r2_12_eq : ∀ k : Fin 16, kernel16_1Expr 2 12 k = kernel16_1_r2_12 k := by decide +kernel +noncomputable def kernel16_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-40),20⟩,⟨(-31),30⟩⟩] +lemma kernel16_1_r2_13_eq : ∀ k : Fin 16, kernel16_1Expr 2 13 k = kernel16_1_r2_13 k := by decide +kernel +noncomputable def kernel16_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),20⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),21⟩,⟨(-31),30⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel16_1_r2_14_eq : ∀ k : Fin 16, kernel16_1Expr 2 14 k = kernel16_1_r2_14 k := by decide +kernel +noncomputable def kernel16_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel16_1_r2_15_eq : ∀ k : Fin 16, kernel16_1Expr 2 15 k = kernel16_1_r2_15 k := by decide +kernel +noncomputable def kernel16_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel16_1_r2_0,kernel16_1_r2_1,kernel16_1_r2_2,kernel16_1_r2_3,kernel16_1_r2_4,kernel16_1_r2_5,kernel16_1_r2_6,kernel16_1_r2_7,kernel16_1_r2_8,kernel16_1_r2_9,kernel16_1_r2_10,kernel16_1_r2_11,kernel16_1_r2_12,kernel16_1_r2_13,kernel16_1_r2_14,kernel16_1_r2_15] +lemma kernel16_1_r2_eq (i k : Fin 16) : kernel16_1Expr 2 i k = kernel16_1_r2 i k := by + fin_cases i + · exact kernel16_1_r2_0_eq k + · exact kernel16_1_r2_1_eq k + · exact kernel16_1_r2_2_eq k + · exact kernel16_1_r2_3_eq k + · exact kernel16_1_r2_4_eq k + · exact kernel16_1_r2_5_eq k + · exact kernel16_1_r2_6_eq k + · exact kernel16_1_r2_7_eq k + · exact kernel16_1_r2_8_eq k + · exact kernel16_1_r2_9_eq k + · exact kernel16_1_r2_10_eq k + · exact kernel16_1_r2_11_eq k + · exact kernel16_1_r2_12_eq k + · exact kernel16_1_r2_13_eq k + · exact kernel16_1_r2_14_eq k + · exact kernel16_1_r2_15_eq k +noncomputable def kernel16_1_r3_0 : Fin 16 → CBox := ![⟨⟨173398333111417847639,173398333111417848311⟩,⟨124039408063803990303,124039408063803990978⟩⟩,⟨⟨173273846019362843310,173273846019362843986⟩,⟨123773503695535844469,123773503695535845146⟩⟩,⟨⟨173024777244457298895,173024777244457299557⟩,⟨123242928496267034397,123242928496267035065⟩⟩,⟨⟨172650942559727875523,172650942559727876193⟩,⟨122450142206099748297,122450142206099748967⟩⟩,⟨⟨172152077930227351781,172152077930227352445⟩,⟨121398816138776654290,121398816138776654955⟩⟩,⟨⟨171527854053960892545,171527854053960893197⟩,⟨120093811337152534156,120093811337152534808⟩⟩,⟨⟨170777895377220625984,170777895377220626648⟩,⟨118541149632673161525,118541149632673162190⟩⟩,⟨⟨169901803272096577228,169901803272096577874⟩,⟨116747977768326239299,116747977768326239945⟩⟩,⟨⟨168899182994648025881,168899182994648026528⟩,⟨114722524784880954280,114722524784880954931⟩⟩,⟨⟨167769673978606984542,167769673978606985182⟩,⟨112474052910790248020,112474052910790248660⟩⟩,⟨⟨166512982962503721332,166512982962503721960⟩,⟨110012802236821456122,110012802236821456750⟩⟩,⟨⟨165128919398619484482,165128919398619485104⟩,⟨107349929497179292110,107349929497179292732⟩⟩,⟨⟨163617432550944797147,163617432550944797752⟩,⟨104497441319403197020,104497441319403197628⟩⟩,⟨⟨161978649656996746104,161978649656996746691⟩,⟨101468122345409663340,101468122345409663930⟩⟩,⟨⟨160212914505442065682,160212914505442066268⟩,⟨98275458665397782715,98275458665397783301⟩⟩,⟨⟨158320825768364870631,158320825768364871211⟩,⟨94933557044571202168,94933557044571202747⟩⟩] +lemma kernel16_1_r3_0_eq : ∀ k : Fin 16, kernel16_1Expr 3 0 k = kernel16_1_r3_0 k := by decide +kernel +noncomputable def kernel16_1_r3_1 : Fin 16 → CBox := ![⟨⟨156303274423945823231,156303274423945823799⟩,⟨91457060459324141285,91457060459324141853⟩⟩,⟨⟨154161479612372239870,154161479612372240416⟩,⟨87861060494215798050,87861060494215798602⟩⟩,⟨⟨151897022284913632960,151897022284913633503⟩,⟨84161007183197967354,84161007183197967897⟩⟩,⟨⟨149511876033059514864,149511876033059515395⟩,⟨80372616907615959798,80372616907615960329⟩⟩,⟨⟨147008434521059868533,147008434521059869047⟩,⟨76511778988905266557,76511778988905267074⟩⟩,⟨⟨144389534990619837293,144389534990619837789⟩,⟨72594461635083012214,72594461635083012713⟩⟩,⟨⟨141658477360223563353,141658477360223563831⟩,⟨68636617916520516170,68636617916520516651⟩⟩,⟨⟨138819038502809002705,138819038502809003171⟩,⟨64654092457542169767,64654092457542170236⟩⟩,⟨⟨135875481353374490338,135875481353374490794⟩,⟨60662529535627215563,60662529535627216016⟩⟩,⟨⟨132832558571547434149,132832558571547434583⟩,⟨56677283278951095922,56677283278951096355⟩⟩,⟨⟨129695510562069420686,129695510562069421114⟩,⟨52713330645318186997,52713330645318187424⟩⟩,⟨⟨126470057737355772238,126470057737355772646⟩,⟨48785187850918352953,48785187850918353357⟩⟩,⟨⟨123162386989517237857,123162386989517238255⟩,⟨44906830895592804410,44906830895592804812⟩⟩,⟨⟨119779132423193552412,119779132423193552795⟩,⟨41091620802334519267,41091620802334519647⟩⟩,⟨⟨116327350483931174563,116327350483931174929⟩,⟨37352234152605305601,37352234152605305967⟩⟩,⟨⟨112814489698332192846,112814489698332193202⟩,⟨33700599455878106267,33700599455878106626⟩⟩] +lemma kernel16_1_r3_1_eq : ∀ k : Fin 16, kernel16_1Expr 3 1 k = kernel16_1_r3_1 k := by decide +kernel +noncomputable def kernel16_1_r3_2 : Fin 16 → CBox := ![⟨⟨109248355320525430902,109248355320525431244⟩,⟨30147839841888001876,30147839841888002218⟩⟩,⟨⟨105637069253429313624,105637069253429313949⟩,⟨26704222507804037223,26704222507804037552⟩⟩,⟨⟨101989025681623759633,101989025681623759938⟩,⟨23379115290446679812,23379115290446680117⟩⟩,⟨⟨98312842914350259608,98312842914350259907⟩,⟨20180950666422281601,20180950666422281900⟩⟩,⟨⟨94617311991250155308,94617311991250155595⟩,⟨17117197411387853394,17117197411387853681⟩⟩,⟨⟨90911342649093113035,90911342649093113309⟩,⟨14194340074459053474,14194340074459053744⟩⟩,⟨⟨87203907284245908575,87203907284245908829⟩,⟨11417866345981103678,11417866345981103929⟩⟩,⟨⟨83503983572446712237,83503983572446712483⟩,⟨8792262317517351384,8792262317517351632⟩⟩,⟨⟨79820496424208746607,79820496424208746840⟩,⟨6321015553047857444,6321015553047857681⟩⟩,⟨⟨76162259960678972326,76162259960678972541⟩,⟨4006625811119071902,4006625811119072120⟩⟩,⟨⟨72537920190998306849,72537920190998307064⟩,⟨1850623180166826563,1850623180166826781⟩⟩,⟨⟨68955899058302472952,68955899058302473151⟩,⟨(-146406685438453202),(-146406685438453006)⟩⟩,⟨⟨65424340497793047607,65424340497793047800⟩,⟨(-1984790611820430641),(-1984790611820430450)⟩⟩,⟨⟨61951059117289548709,61951059117289548887⟩,⟨(-3665729683481151809),(-3665729683481151628)⟩⟩,⟨⟨58543492068995122572,58543492068995122736⟩,⟨(-5191255261490151446),(-5191255261490151282)⟩⟩,⟨⟨55208654631663851230,55208654631663851381⟩,⟨(-6564179803909966401),(-6564179803909966250)⟩⟩] +lemma kernel16_1_r3_2_eq : ∀ k : Fin 16, kernel16_1Expr 3 2 k = kernel16_1_r3_2 k := by decide +kernel +noncomputable def kernel16_1_r3_3 : Fin 16 → CBox := ![⟨⟨51953099965867743201,51953099965867743353⟩,⟨(-7788043095929337005),(-7788043095929336853)⟩⟩,⟨⟨48782883442656018619,48782883442656018759⟩,⟨(-8867054534539410333),(-8867054534539410194)⟩⟩,⟨⟨45703531878696657994,45703531878696658133⟩,⟨(-9806032141281144976),(-9806032141281144837)⟩⟩,⟨⟨42720017940174747238,42720017940174747364⟩,⟨(-10610338996265631326),(-10610338996265631199)⟩⟩,⟨⟨39836739904520913335,39836739904520913456⟩,⟨(-11285817797128910422),(-11285817797128910301)⟩⟩,⟨⟨37057506894701593876,37057506894701593990⟩,⟨(-11838724247792117872),(-11838724247792117758)⟩⟩,⟨⟨34385529626560790410,34385529626560790521⟩,⟨(-12275659973976672297),(-12275659973976672191)⟩⟩,⟨⟨31823416636770628183,31823416636770628279⟩,⟨(-12603505645646858894),(-12603505645646858798)⟩⟩,⟨⟨29373175888483553716,29373175888483553812⟩,⟨(-12829354961339717903),(-12829354961339717807)⟩⟩,⟨⟨27036221584866899101,27036221584866899184⟩,⟨(-12960450116253095661),(-12960450116253095578)⟩⟩,⟨⟨24813385958332523202,24813385958332523285⟩,⟨(-13004119335680115820),(-13004119335680115737)⟩⟩,⟨⟨22704935746332168496,22704935746332168574⟩,⟨(-12967717008694663319),(-12967717008694663237)⟩⟩,⟨⟨20710593013830799892,20710593013830799967⟩,⟨(-12858566904792339744),(-12858566904792339671)⟩⟩,⟨⟨18829559938617865957,18829559938617866023⟩,⟨(-12683908899432469228),(-12683908899432469159)⟩⟩,⟨⟨17060547138948957933,17060547138948957998⟩,⟨(-12450849574119771964),(-12450849574119771899)⟩⟩,⟨⟨15401805093958182610,15401805093958182670⟩,⟨(-12166316993851986683),(-12166316993851986620)⟩⟩] +lemma kernel16_1_r3_3_eq : ∀ k : Fin 16, kernel16_1Expr 3 3 k = kernel16_1_r3_3 k := by decide +kernel +noncomputable def kernel16_1_r3_4 : Fin 16 → CBox := ![⟨⟨13851158186025261937,13851158186025261991⟩,⟨(-11837019900495684186),(-11837019900495684129)⟩⟩,⟨⟨12406040880853314501,12406040880853314547⟩,⟨(-11469411495980627036),(-11469411495980626991)⟩⟩,⟨⟨11063535555302549569,11063535555302549626⟩,⟨(-11069657925137351155),(-11069657925137351101)⟩⟩,⟨⟨9820411484785269703,9820411484785269744⟩,⟨(-10643611505508691081),(-10643611505508691037)⟩⟩,⟨⟨8673164510887063153,8673164510887063192⟩,⟨(-10196788691443631725),(-10196788691443631685)⟩⟩,⟨⟨7618056925353885135,7618056925353885183⟩,⟨(-9734352703050320178),(-9734352703050320127)⟩⟩,⟨⟨6651157128093088326,6651157128093088359⟩,⟨(-9261100697869982393),(-9261100697869982359)⟩⟩,⟨⟨5768378643714903479,5768378643714903523⟩,⟨(-8781455315056746077),(-8781455315056746036)⟩⟩,⟨⟨4965518112661421801,4965518112661421845⟩,⟨(-8299460378920460063),(-8299460378920460022)⟩⟩,⟨⟨4238291908358105812,4238291908358105860⟩,⟨(-7818780511304735972),(-7818780511304735922)⟩⟩,⟨⟨3582371070274794039,3582371070274794081⟩,⟨(-7342704370706419020),(-7342704370706418975)⟩⟩,⟨⟨2993414283484498944,2993414283484498978⟩,⟨(-6874151210453444110),(-6874151210453444077)⟩⟩,⟨⟨2467098677450347687,2467098677450347725⟩,⟨(-6415680428688655130),(-6415680428688655095)⟩⟩,⟨⟨1999148259566929429,1999148259566929480⟩,⟨(-5969503769291355709),(-5969503769291355661)⟩⟩,⟨⟨1585359841681642430,1585359841681642476⟩,⟨(-5537499825037897582),(-5537499825037897536)⟩⟩,⟨⟨1221626359723258793,1221626359723258838⟩,⟨(-5121230491996663630),(-5121230491996663588)⟩⟩] +lemma kernel16_1_r3_4_eq : ∀ k : Fin 16, kernel16_1Expr 3 4 k = kernel16_1_r3_4 k := by decide +kernel +noncomputable def kernel16_1_r3_5 : Fin 16 → CBox := ![⟨⟨903957527028123853,903957527028123891⟩,⟨(-4721959027028701903),(-4721959027028701867)⟩⟩,⟨⟨628497800407911277,628497800407911315⟩,⟨(-4340669367910448148),(-4340669367910448113)⟩⟩,⟨⟨391541673951795395,391541673951795429⟩,⟨(-3978086387539688203),(-3978086387539688169)⟩⟩,⟨⟨189546348586607990,189546348586608023⟩,⟨(-3634696769416386640),(-3634696769416386607)⟩⟩,⟨⟨19141855201232400,19141855201232433⟩,⟨(-3310770210561706712),(-3310770210561706678)⟩⟩,⟨⟨(-122861264569111599),(-122861264569111564)⟩,⟨(-3006380679689196871),(-3006380679689196832)⟩⟩,⟨⟨(-239466593168943223),(-239466593168943195)⟩,⟨(-2721427482204224180),(-2721427482204224153)⟩⟩,⟨⟨(-333488641932224124),(-333488641932224092)⟩,⟨(-2455655908920296728),(-2455655908920296698)⟩⟩,⟨⟨(-407551665095264029),(-407551665095263995)⟩,⟨(-2208677271700148363),(-2208677271700148329)⟩⟩,⟨⟨(-464090310758453620),(-464090310758453581)⟩,⟨(-1979988156038304383),(-1979988156038304347)⟩⟩,⟨⟨(-505351928621967007),(-505351928621966973)⟩,⟨(-1768988747418168171),(-1768988747418168137)⟩⟩,⟨⟨(-533400349772368971),(-533400349772368943)⟩,⟨(-1575000114660010204),(-1575000114660010176)⟩⟩,⟨⟨(-550120952393413112),(-550120952393413080)⟩,⟨(-1397280359033113769),(-1397280359033113740)⟩⟩,⟨⟨(-557226828749698617),(-557226828749698585)⟩,⟨(-1235039562293024188),(-1235039562293024159)⟩⟩,⟨⟨(-556265872851720546),(-556265872851720514)⟩,⟨(-1087453489733780233),(-1087453489733780203)⟩⟩,⟨⟨(-548628614540303208),(-548628614540303188)⟩,⟨(-953676025579708166),(-953676025579708145)⟩⟩] +lemma kernel16_1_r3_5_eq : ∀ k : Fin 16, kernel16_1Expr 3 5 k = kernel16_1_r3_5 k := by decide +kernel +noncomputable def kernel16_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-535556634000520744),(-535556634000520708)⟩,⟨(-832850337400162940),(-832850337400162901)⟩⟩,⟨⟨(-518151400598850162),(-518151400598850136)⟩,⟨(-724118783584173572),(-724118783584173549)⟩⟩,⟨⟨(-497383391104303835),(-497383391104303808)⟩,⟨(-626631593180805665),(-626631593180805637)⟩⟩,⟨⟨(-474101354485863517),(-474101354485863488)⟩,⟨(-539554360562202069),(-539554360562202037)⟩⟩,⟨⟨(-449041603270851560),(-449041603270851527)⟩,⟨(-462074408409164412),(-462074408409164382)⟩⟩,⟨⟨(-422837224617713479),(-422837224617713458)⟩,⟨(-393406081501113038),(-393406081501113017)⟩⟩,⟨⟨(-396027117541219700),(-396027117541219679)⟩,⟨(-332795040793549103),(-332795040793549082)⟩⟩,⟨⟨(-369064775893712553),(-369064775893712525)⟩,⟨(-279521632394722329),(-279521632394722301)⟩⟩,⟨⟨(-342326749546291329),(-342326749546291306)⟩,⟨(-232903409439585799),(-232903409439585773)⟩⟩,⟨⟨(-316120728551587833),(-316120728551587807)⟩,⟨(-192296886651155901),(-192296886651155877)⟩⟩,⟨⟨(-290693206757498717),(-290693206757498684)⟩,⟨(-157098607737336209),(-157098607737336179)⟩⟩,⟨⟨(-266236692260615945),(-266236692260615917)⟩,⟨(-126745604863045824),(-126745604863045796)⟩⟩,⟨⟨(-242896442149107950),(-242896442149107922)⟩,⟨(-100715327434420559),(-100715327434420531)⟩⟩,⟨⟨(-220776708124195994),(-220776708124195973)⟩,⟨(-78525114504710606),(-78525114504710585)⟩⟩,⟨⟨(-199946487768737027),(-199946487768736997)⟩,⟨(-59731281427114772),(-59731281427114739)⟩⟩,⟨⟨(-180444783434964099),(-180444783434964078)⟩,⟨(-43927887098136127),(-43927887098136106)⟩⟩] +lemma kernel16_1_r3_6_eq : ∀ k : Fin 16, kernel16_1Expr 3 6 k = kernel16_1_r3_6 k := by decide +kernel +noncomputable def kernel16_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-162285376955475439),(-162285376955475411)⟩,⟨(-30745243406809514),(-30745243406809486)⟩⟩,⟨⟨(-145461133663936984),(-145461133663936953)⟩,⟨(-19848223469847964),(-19848223469847931)⟩⟩,⟨⟨(-129947853581333533),(-129947853581333500)⟩,⟨(-10934420017304411),(-10934420017304381)⟩⟩,⟨⟨(-115707691128785872),(-115707691128785848)⟩,⟨(-3732200011120931),(-3732200011120904)⟩⟩,⟨⟨(-102692167427325076),(-102692167427325054)⟩,⟨2001303670751232,2001303670751253⟩⟩,⟨⟨(-90844801204048301),(-90844801204048271)⟩,⟨6482227784035605,6482227784035639⟩⟩,⟨⟨(-80103385613039298),(-80103385613039277)⟩,⟨9902010744341038,9902010744341059⟩⟩,⟨⟨(-70401938971286067),(-70401938971286036)⟩,⟨12429395069714618,12429395069714652⟩⟩,⟨⟨(-61672357578369140),(-61672357578369114)⟩,⟨14212378585470063,14212378585470087⟩⟩,⟨⟨(-53845798506937923),(-53845798506937895)⟩,⟨15380096819559017,15380096819559045⟩⟩,⟨⟨(-46853819589776842),(-46853819589776808)⟩,⟨16044622753379301,16044622753379332⟩⟩,⟨⟨(-40629302856127820),(-40629302856127798)⟩,⟨16302673471648707,16302673471648729⟩⟩,⟨⟨(-35107186448214375),(-35107186448214354)⟩,⟨16237216272192239,16237216272192261⟩⟩,⟨⟨(-30225028637073062),(-30225028637073040)⟩,⟨15918969455925175,15918969455925197⟩⟩,⟨⟨(-25923426007970134),(-25923426007970112)⟩,⟨15407795328863408,15407795328863430⟩⟩,⟨⟨(-22146306247386734),(-22146306247386705)⟩,⟨14753984926579076,14753984926579105⟩⟩] +lemma kernel16_1_r3_7_eq : ∀ k : Fin 16, kernel16_1Expr 3 7 k = kernel16_1_r3_7 k := by decide +kernel +noncomputable def kernel16_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-18841114277598019),(-18841114277597995)⟩,⟨13999435636003602,13999435636003629⟩⟩,⟨⟨(-15958908787370782),(-15958908787370760)⟩,⟨13178724261661645,13178724261661667⟩⟩,⟨⟨(-13454384528853706),(-13454384528853684)⟩,⟨12320079187119357,12320079187119379⟩⟩,⟨⟨(-11285834116656198),(-11285834116656176)⟩,⟨11446256142683469,11446256142683491⟩⟩,⟨⟨(-9415061495785047),(-9415061495785023)⟩,⟨10575322732728943,10575322732728970⟩⟩,⟨⟨(-7807257756357808),(-7807257756357779)⟩,⟨9721357325894130,9721357325894160⟩⟩,⟨⟨(-6430848576534983),(-6430848576534959)⟩,⟨8895068193582773,8895068193582800⟩⟩,⟨⟨(-5257321278922149),(-5257321278922122)⟩,⟨8104338920556998,8104338920557023⟩⟩,⟨⟨(-4261038294574602),(-4261038294574573)⟩,⟨7354706128360945,7354706128360974⟩⟩,⟨⟨(-3419042744696890),(-3419042744696868)⟩,⟨6649775468780864,6649775468780886⟩⟩,⟨⟨(-2710860872829762),(-2710860872829735)⟩,⟨5991581679693881,5991581679693906⟩⟩,⟨⟨(-2118305187487325),(-2118305187487300)⟩,⟨5380898266832789,5380898266832817⟩⟩,⟨⟨(-1625281403027986),(-1625281403027957)⟩,⟨4817502097686154,4817502097686184⟩⟩,⟨⟨(-1217601589994599),(-1217601589994577)⟩,⟨4300397881603337,4300397881603359⟩⟩,⟨⟨(-882805359342472),(-882805359342450)⟩,⟨3828007175023987,3828007175024010⟩⟩,⟨⟨(-609990401378315),(-609990401378286)⟩,⟨3398326202726937,3398326202726966⟩⟩] +lemma kernel16_1_r3_8_eq : ∀ k : Fin 16, kernel16_1Expr 3 8 k = kernel16_1_r3_8 k := by decide +kernel +noncomputable def kernel16_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-389653272991790),(-389653272991759)⟩,⟨3009056433604664,3009056433604698⟩⟩,⟨⟨(-213540968843799),(-213540968843777)⟩,⟨2657711499737327,2657711499737350⟩⟩,⟨⟨(-74513516569866),(-74513516569843)⟩,⟨2341703706123147,2341703706123170⟩⟩,⟨⟨33582404096932,33582404096969⟩,⟨2058413049756839,2058413049756876⟩⟩,⟨⟨116029009676172,116029009676200⟩,⟨1805241354187351,1805241354187376⟩⟩,⟨⟨177342468844036,177342468844064⟩,⟨1579653831636226,1579653831636251⟩⟩,⟨⟨221367917889116,221367917889146⟩,⟨1379210110809092,1379210110809122⟩⟩,⟨⟨251364968256042,251364968256074⟩,⟨1201586515583155,1201586515583189⟩⟩,⟨⟨270084292791762,270084292791790⟩,⟨1044591148128389,1044591148128414⟩⟩,⟨⟨279835909371790,279835909371820⟩,⟨906173119572675,906173119572705⟩⟩,⟨⟨282549794597305,282549794597343⟩,⟨784427081532039,784427081532076⟩⟩,⟨⟨279829459728499,279829459728529⟩,⟨677594041887338,677594041887368⟩⟩,⟨⟨272999109022562,272999109022585⟩,⟨584059297074415,584059297074438⟩⟩,⟨⟨263144979834343,263144979834371⟩,⟨502348179691477,502348179691502⟩⟩,⟨⟨251151436486745,251151436486770⟩,⟨431120203144073,431120203144100⟩⟩,⟨⟨237732357951188,237732357951215⟩,⟨369162083023547,369162083023572⟩⟩] +lemma kernel16_1_r3_9_eq : ∀ k : Fin 16, kernel16_1Expr 3 9 k = kernel16_1_r3_9 k := by decide +kernel +noncomputable def kernel16_1_r3_10 : Fin 16 → CBox := ![⟨⟨223458324402314,223458324402339⟩,⟨315380026614810,315380026614838⟩⟩,⟨⟨208780071048707,208780071048730⟩,⟨268791606034960,268791606034983⟩⟩,⟨⟨194048640365503,194048640365526⟩,⟨228517465738960,228517465738983⟩⟩,⟨⟨179532626817377,179532626817407⟩,⟨193773060271372,193773060271403⟩⟩,⟨⟨165432872023966,165432872024003⟩,⟨163860572044381,163860572044419⟩⟩,⟨⟨151894933583199,151894933583245⟩,⟨138161120512047,138161120512092⟩⟩,⟨⟨139019617792157,139019617792183⟩,⟨116127342400402,116127342400430⟩⟩,⟨⟨126871835536123,126871835536153⟩,⟨97276396743018,97276396743049⟩⟩,⟨⟨115488011804728,115488011804752⟩,⟨81183427545644,81183427545668⟩⟩,⟨⟨104882252711926,104882252711949⟩,⟨67475500229337,67475500229360⟩⟩,⟨⟨95051449557961,95051449557992⟩,⟨55826014928651,55826014928682⟩⟩,⟨⟨85979477337561,85979477337590⟩,⟨45949589672239,45949589672264⟩⟩,⟨⟨77640625098354,77640625098380⟩,⟨37597398944161,37597398944189⟩⟩,⟨⟨70002377587384,70002377587410⟩,⟨30552947673872,30552947673901⟩⟩,⟨⟨63027651572586,63027651572614⟩,⟨24628256951728,24628256951754⟩⟩,⟨⟨56676575962066,56676575962105⟩,⟨19660435388015,19660435388053⟩⟩] +lemma kernel16_1_r3_10_eq : ∀ k : Fin 16, kernel16_1Expr 3 10 k = kernel16_1_r3_10 k := by decide +kernel +noncomputable def kernel16_1_r3_11 : Fin 16 → CBox := ![⟨⟨50907892229749,50907892229778⟩,⟨15508608748662,15508608748688⟩⟩,⟨⟨45680040553905,45680040553943⟩,⟨12051180075004,12051180075043⟩⟩,⟨⟨40951987349364,40951987349387⟩,⟨9183392730867,9183392730890⟩⟩,⟨⟨36683841389868,36683841389894⟩,⟨6815169552859,6815169552888⟩⟩,⟨⟨32837298351082,32837298351121⟩,⟨4869202375872,4869202375911⟩⟩,⟨⟨29375947232984,29375947233010⟩,⟨3279267552504,3279267552533⟩⟩,⟨⟨26265466635491,26265466635529⟩,⟨1988744595357,1988744595396⟩⟩,⟨⟨23473734156686,23473734156723⟩,⟨949316673632,949316673665⟩⟩,⟨⟨20970868166295,20970868166318⟩,⟨119833333425,119833333449⟩⟩,⟨⟨18729217791661,18729217791690⟩,⟨(-534682556368),(-534682556342)⟩⟩,⟨⟨16723314061926,16723314061950⟩,⟨(-1043900037236),(-1043900037213)⟩⟩,⟨⟨14929792718027,14929792718051⟩,⟨(-1432932346632),(-1432932346608)⟩⟩,⟨⟨13327297151569,13327297151593⟩,⟨(-1722989676174),(-1722989676150)⟩⟩,⟨⟨11896368226812,11896368226838⟩,⟨(-1931944458862),(-1931944458833)⟩⟩,⟨⟨10619326320986,10619326321018⟩,⟨(-2074819972930),(-2074819972898)⟩⟩,⟨⟨9480149744429,9480149744455⟩,⟨(-2164211879299),(-2164211879270)⟩⟩] +lemma kernel16_1_r3_11_eq : ∀ k : Fin 16, kernel16_1Expr 3 11 k = kernel16_1_r3_11 k := by decide +kernel +noncomputable def kernel16_1_r3_12 : Fin 16 → CBox := ![⟨⟨8464352738038,8464352738078⟩,⟨(-2210651236240),(-2210651236200)⟩⟩,⟨⟨7558865457370,7558865457396⟩,⟨(-2222916557366),(-2222916557337)⟩⟩,⟨⟨6751917713720,6751917713747⟩,⟨(-2208301593319),(-2208301593290)⟩⟩,⟨⟨6032927728126,6032927728152⟩,⟨(-2172844718573),(-2172844718544)⟩⟩,⟨⟨5392396743066,5392396743095⟩,⟨(-2121525088445),(-2121525088418)⟩⟩,⟨⟨4821810012396,4821810012425⟩,⟨(-2058430090005),(-2058430089978)⟩⟩,⟨⟨4313544436590,4313544436622⟩,⟨(-1986898040222),(-1986898040190)⟩⟩,⟨⟨3860782915199,3860782915231⟩,⟨(-1909639578142),(-1909639578111)⟩⟩,⟨⟨3457435341141,3457435341167⟩,⟨(-1828840749529),(-1828840749500)⟩⟩,⟨⟨3098066052672,3098066052701⟩,⟨(-1746250387576),(-1746250387549)⟩⟩,⟨⟨2777827481202,2777827481234⟩,⟨(-1663254045265),(-1663254045233)⟩⟩,⟨⟨2492399680069,2492399680101⟩,⟨(-1580936430455),(-1580936430423)⟩⟩,⟨⟨2237935386233,2237935386257⟩,⟨(-1500134027724),(-1500134027699)⟩⟩,⟨⟨2011010248534,2011010248564⟩,⟨(-1421479358064),(-1421479358038)⟩⟩,⟨⟨1808577850136,1808577850166⟩,⟨(-1345438124891),(-1345438124864)⟩⟩,⟨⟨1627929155098,1627929155127⟩,⟨(-1272340318294),(-1272340318267)⟩⟩] +lemma kernel16_1_r3_12_eq : ∀ k : Fin 16, kernel16_1Expr 3 12 k = kernel16_1_r3_12 k := by decide +kernel +noncomputable def kernel16_1_r3_13 : Fin 16 → CBox := ![⟨⟨1466656018353,1466656018383⟩,⟨(-1202406196690),(-1202406196663)⟩⟩,⟨⟨1322618412266,1322618412298⟩,⟨(-1135767932588),(-1135767932556)⟩⟩,⟨⟨1193915040032,1193915040064⟩,⟨(-1072487594751),(-1072487594719)⟩⟩,⟨⟨1078857025380,1078857025407⟩,⟨(-1012572040560),(-1012572040531)⟩⟩,⟨⟨975944388573,975944388600⟩,⟨(-955985207100),(-955985207071)⟩⟩,⟨⟨883845039201,883845039241⟩,⟨(-902658216933),(-902658216893)⟩⟩,⟨⟨801376037432,801376037459⟩,⟨(-852497651324),(-852497651294)⟩⟩,⟨⟨727486895133,727486895158⟩,⟨(-805392290614),(-805392290589)⟩⟩,⟨⟨661244708444,661244708471⟩,⟨(-761218574831),(-761218574801)⟩⟩,⟨⟨601820931300,601820931327⟩,⟨(-719844999039),(-719844999009)⟩⟩,⟨⟨548479617365,548479617397⟩,⟨(-681135623926),(-681135623894)⟩⟩,⟨⟨500566974010,500566974035⟩,⟨(-644952854138),(-644952854114)⟩⟩,⟨⟨457502087134,457502087164⟩,⟨(-611159612116),(-611159612089)⟩⟩,⟨⟨418768689754,418768689781⟩,⟨(-579621015130),(-579621015100)⟩⟩,⟨⟨383907860043,383907860073⟩,⟨(-550205645358),(-550205645331)⟩⟩,⟨⟨352511546328,352511546352⟩,⟨(-522786488330),(-522786488306)⟩⟩] +lemma kernel16_1_r3_13_eq : ∀ k : Fin 16, kernel16_1Expr 3 13 k = kernel16_1_r3_13 k := by decide +kernel +noncomputable def kernel16_1_r3_14 : Fin 16 → CBox := ![⟨⟨324216827175,324216827215⟩,⟨(-497241602547),(-497241602507)⟩⟩,⟨⟨298700824734,298700824766⟩,⟨(-473454572325),(-473454572293)⟩⟩,⟨⟨275676197645,275676197686⟩,⟨(-451314787559),(-451314787519)⟩⟩,⟨⟨254887148624,254887148648⟩,⟨(-430717585865),(-430717585840)⟩⟩,⟨⟨236105888204,236105888231⟩,⟨(-411564287186),(-411564287156)⟩⟩,⟨⟨219129503103,219129503133⟩,⟨(-393762144820),(-393762144792)⟩⟩,⟨⟨203777183015,203777183045⟩,⟨(-377224233160),(-377224233132)⟩⟩,⟨⟨189887765117,189887765150⟩,⟨(-361869288265),(-361869288233)⟩⟩,⟨⟨177317560011,177317560036⟩,⟨(-347621514549),(-347621514525)⟩⟩,⟨⟨165938426833,165938426863⟩,⟨(-334410368383),(-334410368356)⟩⟩,⟨⟨155636069400,155636069424⟩,⟨(-322170326984),(-322170326959)⟩⟩,⟨⟨146308527668,146308527697⟩,⟨(-310840649749),(-310840649721)⟩⟩,⟨⟨137864842799,137864842832⟩,⟨(-300365137168),(-300365137135)⟩⟩,⟨⟨130223875589,130223875618⟩,⟨(-290691891707),(-290691891679)⟩⟩,⟨⟨123313261130,123313261155⟩,⟨(-281773083982),(-281773083957)⟩⟩,⟨⟨117068484244,117068484277⟩,⟨(-273564726483),(-273564726450)⟩⟩] +lemma kernel16_1_r3_14_eq : ∀ k : Fin 16, kernel16_1Expr 3 14 k = kernel16_1_r3_14 k := by decide +kernel +noncomputable def kernel16_1_r3_15 : Fin 16 → CBox := ![⟨⟨111432062181,111432062211⟩,⟨(-266026456971),(-266026456944)⟩⟩,⟨⟨106352822306,106352822342⟩,⟨(-259121332795),(-259121332757)⟩⟩,⟨⟨101785264731,101785264761⟩,⟨(-252815636899),(-252815636871)⟩⟩,⟨⟨97689000116,97689000144⟩,⟨(-247078696495),(-247078696465)⟩⟩,⟨⟨94028254749,94028254779⟩,⟨(-241882714390),(-241882714362)⟩⟩,⟨⟨90771435782,90771435814⟩,⟨(-237202613378),(-237202613346)⟩⟩,⟨⟨87890750087,87890750120⟩,⟨(-233015893601),(-233015893569)⟩⟩,⟨⟨85361871619,85361871652⟩,⟨(-229302502949),(-229302502916)⟩⟩,⟨⟨83163652209,83163652242⟩,⟨(-226044720122),(-226044720089)⟩⟩,⟨⟨81277871874,81277871912⟩,⟨(-223227050339),(-223227050303)⟩⟩,⟨⟨79689025041,79689025071⟩,⟨(-220836133426),(-220836133399)⟩⟩,⟨⟨78384139540,78384139568⟩,⟨(-218860664031),(-218860664001)⟩⟩,⟨⟨77352626053,77352626081⟩,⟨(-217291323611),(-217291323581)⟩⟩,⟨⟨76586155653,76586155681⟩,⟨(-216120724323),(-216120724293)⟩⟩,⟨⟨76078563864,76078563896⟩,⟨(-215343364189),(-215343364156)⟩⟩,⟨⟨75825779884,75825779914⟩,⟨(-214955593715),(-214955593688)⟩⟩] +lemma kernel16_1_r3_15_eq : ∀ k : Fin 16, kernel16_1Expr 3 15 k = kernel16_1_r3_15 k := by decide +kernel +noncomputable def kernel16_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel16_1_r3_0,kernel16_1_r3_1,kernel16_1_r3_2,kernel16_1_r3_3,kernel16_1_r3_4,kernel16_1_r3_5,kernel16_1_r3_6,kernel16_1_r3_7,kernel16_1_r3_8,kernel16_1_r3_9,kernel16_1_r3_10,kernel16_1_r3_11,kernel16_1_r3_12,kernel16_1_r3_13,kernel16_1_r3_14,kernel16_1_r3_15] +lemma kernel16_1_r3_eq (i k : Fin 16) : kernel16_1Expr 3 i k = kernel16_1_r3 i k := by + fin_cases i + · exact kernel16_1_r3_0_eq k + · exact kernel16_1_r3_1_eq k + · exact kernel16_1_r3_2_eq k + · exact kernel16_1_r3_3_eq k + · exact kernel16_1_r3_4_eq k + · exact kernel16_1_r3_5_eq k + · exact kernel16_1_r3_6_eq k + · exact kernel16_1_r3_7_eq k + · exact kernel16_1_r3_8_eq k + · exact kernel16_1_r3_9_eq k + · exact kernel16_1_r3_10_eq k + · exact kernel16_1_r3_11_eq k + · exact kernel16_1_r3_12_eq k + · exact kernel16_1_r3_13_eq k + · exact kernel16_1_r3_14_eq k + · exact kernel16_1_r3_15_eq k +noncomputable def kernel16_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-66090309338852887212147368),(-66090309338852885237815662)⟩,⟨635253851647816166741879,635253851647818140705849⟩⟩,⟨⟨(-66040697181520087566027107),(-66040697181520085593042045)⟩,⟨676479950817266645363365,676479950817268617980099⟩⟩,⟨⟨(-65941508040202042332470449),(-65941508040202040362179773)⟩,⟨758741214211688262231078,758741214211690232152243⟩⟩,⟨⟨(-65792812748001564136995616),(-65792812748001562170741973)⟩,⟨881656645296414715403624,881656645296416681285982⟩⟩,⟨⟨(-65594718763719529329814437),(-65594718763719527368932866)⟩,⟨1044656929948735614139917,1044656929948737574647866⟩⟩,⟨⟨(-65347371603655953583792762),(-65347371603655951629608165)⟩,⟨1246987045673016686639837,1246987045673018640447914⟩⟩,⟨⟨(-65050956718924563021878479),(-65050956718924561075703221)⟩,⟨1487709727822247382854992,1487709727822249328650299⟩⟩,⟨⟨(-64705701791471378866250879),(-64705701791471376929382177)⟩,⟨1765709781784741353256017,1765709781784743289740816⟩⟩,⟨⟨(-64311879415791894286084711),(-64311879415791892359802577)⟩,⟨2079699227179289714778762,2079699227179291640672546⟩⟩,⟨⟨(-63869810127477873653232392),(-63869810127477871738796646)⟩,⟨2428223257091094096605007,2428223257091096010647504⟩⟩,⟨⟨(-63379865734254877136842180),(-63379865734254875235491153)⟩,⟨2809666992262855063190188,2809666992262856964142633⟩⟩,⟨⟨(-62842472900153655272522197),(-62842472900153653385469062)⟩,⟨3222263006922993613349754,3222263006922995499998582⟩⟩,⟨⟨(-62258116928947540815658100),(-62258116928947538944090804)⟩,⟨3664099599583111040811983,3664099599583112911968892⟩⟩,⟨⟨(-61627345689034989897958049),(-61627345689034988043034161)⟩,⟨4133129778671253950516310,4133129778671255805023411⟩⟩,⟨⟨(-60950773618598226887792690),(-60950773618598225050641318)⟩,⟨4627180929293299018286226,4627180929293300855014142⟩⟩,⟨⟨(-60229085747167407094811916),(-60229085747167405276526995)⟩,⟨5143965123744113675279419,5143965123744115493133986⟩⟩] +lemma kernel16_1_r4_0_eq : ∀ k : Fin 16, kernel16_1Expr 4 0 k = kernel16_1_r4_0 k := by decide +kernel +noncomputable def kernel16_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-59463041667701370086042979),(-59463041667701368287687674)⟩,⟨5681090034640855969150794,5681090034640857767068657⟩⟩,⟨⟨(-58653479391991648625556399),(-58653479391991646848152972)⟩,⟨6236070405746087484049195,6236070405746089261007955⟩⟩,⟨⟨(-57801319021630403115993431),(-57801319021630401360531574)⟩,⟨6806340031716884378789678,6806340031716886133799562⟩⟩,⟨⟨(-56907566166973169913294626),(-56907566166973168180718788)⟩,⟨7389264194191580622010033,7389264194191582354126552⟩⟩,⟨⟨(-55973315047484479060053668),(-55973315047484477351275127)⟩,⟨7982152497846712661085637,7982152497846714369397524⟩⟩,⟨⟨(-54999751208581836532905656),(-54999751208581834848783996)⟩,⟨8582272046366077505134822,8582272046366079188782566⟩⟩,⟨⟨(-53988153792586896126744658),(-53988153792586894468106148)⟩,⟨9186860894708318739260309,9186860894708320397417748⟩⟩,⟨⟨(-52939897304639544906904134),(-52939897304639543274519245)⟩,⟨9793141710689059194709553,9793141710689060826609077⟩⟩,⟨⟨(-51856452818410666931894157),(-51856452818410665326501777)⟩,⟨10398335575760704320024944,10398335575760705924929255⟩⟩,⟨⟨(-50739388571133912947331420),(-50739388571133911369607668)⟩,⟨10999675852031690087247042,10999675852031691664480302⟩⟩,⟨⟨(-49590369902829074218185390),(-49590369902829072668776188)⟩,⟨11594422040071946807462746,11594422040071948356379362⟩⟩,⟨⟨(-48411158500564717891341463),(-48411158500564716370827821)⟩,⟨12179873549957317221690988,12179873549957318741710291⟩⟩,⟨⟨(-47203610915152757342057515),(-47203610915152755850993283)⟩,⟨12753383306366059084051877,12753383306366060574620406⟩⟩,⟨⟨(-45969676324722154452662192),(-45969676324722152991527515)⟩,⟨13312371107406655979670836,13312371107406657440308854⟩⟩,⟨⟨(-44711393527115319386391291),(-44711393527115317955642466)⟩,⟨13854336656276030403988977,13854336656276031834240617⟩⟩,⟨⟨(-43430887150914627573021704),(-43430887150914626173041118)⟩,⟨14376872184864757143089391,14376872184864758542572734⟩⟩] +lemma kernel16_1_r4_1_eq : ∀ k : Fin 16, kernel16_1Expr 4 1 k = kernel16_1_r4_1 k := by decide +kernel +noncomputable def kernel16_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-42130363083057383527066576),(-42130363083057382158218122)⟩,⟨14877674589079660202904991,14877674589079661571256628⟩⟩,⟨⟨(-40812103119349763624090690),(-40812103119349762286653224)⟩,⟨15354556996976733020936884,15354556996976734357878460⟩⟩,⟨⟨(-39478458852653511382986770),(-39478458852653510077225413)⟩,⟨15805459692814096338302557,15805459692814097643569468⟩⟩,⟨⟨(-38131844821999637746460789),(-38131844821999636472453924)⟩,⟨16228460322863299010955556,16228460322863300284469944⟩⟩,⟨⟨(-36774730954284780724856279),(-36774730954284779482748105)⟩,⟨16621783312266715706150397,16621783312266716947768611⟩⟩,⟨⟨(-35409634338430491490109541),(-35409634338430490279985087)⟩,⟨16983808426398993190860750,16983808426398994400498314⟩⟩,⟨⟨(-34039110379835612162192885),(-34039110379835610984135461)⟩,⟨17313078415071720658648526,17313078415071721836222686⟩⟩,⟨⟨(-32665743390530193226959125),(-32665743390530192080964196)⟩,⟨17608305683493090060109532,17608305683493091205625391⟩⟩,⟨⟨(-31292136677551464194018323),(-31292136677551463080087632)⟩,⟨17868377940128506721705132,17868377940128507835161505⟩⟩,⟨⟨(-29920902198617210963651119),(-29920902198617209881684027)⟩,⟨18092362778464036982407116,18092362778464038063905199⟩⟩,⟨⟨(-28554649860083403713766962),(-28554649860083402663675731)⟩,⟨18279511157102421934080401,18279511157102422983708493⟩⟩,⟨⟨(-27195976537361091647443700),(-27195976537361090629048280)⟩,⟨18429259750561720416850717,18429259750561721434789407⟩⟩,⟨⟨(-25847454902359849587637526),(-25847454902359848600777348)⟩,⟨18541232151530947277535253,18541232151530948263945646⟩⟩,⟨⟨(-24511622146057383809250137),(-24511622146057382853394145)⟩,⟨18615238914088401964041997,18615238914088402919467855⟩⟩,⟨⟨(-23190968686912856424717569),(-23190968686912855499443298)⟩,⟨18651276436422218249436622,18651276436422219174309192⟩⟩,⟨⟨(-21887926957501229253336345),(-21887926957501228358328624)⟩,⟨18649524690817908567071269,18649524690817909461705131⟩⟩] +lemma kernel16_1_r4_2_eq : ∀ k : Fin 16, kernel16_1Expr 4 2 k = kernel16_1_r4_2 k := by decide +kernel +noncomputable def kernel16_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-20604860362415041959270394),(-20604860362415041094249869)⟩,⟨18610343817997784647359344,18610343817997785512033220⟩⟩,⟨⟨(-19344052500138221506277979),(-19344052500138220670853525)⟩,⟨18534269612211390752927496,18534269612211391588031823⟩⟩,⟨⟨(-18107696740236108163042203),(-18107696740236107356865217)⟩,⟨18422007932680961282275306,18422007932680962088157968⟩⟩,⟨⟨(-16897886244832206367216377),(-16897886244832205589843809)⟩,⟨18274428085996536050089569,18274428085996536827192844⟩⟩,⟨⟨(-15716604519973708056747221),(-15716604519973707307783654)⟩,⟨18092555232727029664665883,18092555232727030413384397⟩⟩,⟨⟨(-14565716578156188747186683),(-14565716578156188026127208)⟩,⟨17877561879763278561402011,17877561879763279282239834⟩⟩,⟨⟨(-13446960788027516555835314),(-13446960788027515862228747)⟩,⟨17630758527637196778485624,17630758527637197471893084⟩⟩,⟨⟨(-12361941481178849328200372),(-12361941481178848661357816)⟩,⟨17353583549172819333029465,17353583549172819999694574⟩⟩,⟨⟨(-11312122379025322446971615),(-11312122379025321806375485)⟩,⟨17047592382231707661379700,17047592382231708301819134⟩⟩,⟨⟨(-10298820895160297625585093),(-10298820895160297010652551)⟩,⟨16714446124936221324938070,16714446124936221939733751⟩⟩,⟨⟨(-9323203360324424972840976),(-9323203360324424383055597)⟩,⟨16355899626517919808630361,16355899626517920398297764⟩⟩,⟨⟨(-8386281208362571719774187),(-8386281208362571154531137)⟩,⟨15973789170783557653574393,15973789170783558218717407⟩⟩,⟨⟨(-7488908152353578044281548),(-7488908152353577502978890)⟩,⟨15570019852067854359761338,15570019852067854900980907⟩⟩,⟨⟨(-6631778370601400438946302),(-6631778370601399920933258)⟩,⟨15146552745412789255789131,15146552745412789773735072⟩⟩,⟨⟨(-5815425712487392246926975),(-5815425712487391751642599)⟩,⟨14705391973552869595461441,14705391973552870090693738⟩⟩,⟨⟨(-5040223924420780700443835),(-5040223924420780227244582)⟩,⟨14248571773083362629408220,14248571773083363102569464⟩⟩] +lemma kernel16_1_r4_3_eq : ∀ k : Fin 16, kernel16_1Expr 4 3 k = kernel16_1_r4_3 k := by decide +kernel +noncomputable def kernel16_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-4306387886407267675980720),(-4306387886407267224301111)⟩,⟨13778143660946294322902868,13778143660946294774557595⟩⟩,⟨⟨(-3613975840202697361208764),(-3613975840202696930382024)⟩,⟨13296163800103283863107384,13296163800103284293921428⟩⟩,⟨⟨(-2962892580745891747882758),(-2962892580745891337323162)⟩,⟨12804680660004773332596020,12804680660004773743154188⟩⟩,⟨⟨(-2352893573683739375245571),(-2352893573683738984292083)⟩,⟨12305723063254878297885830,12305723063254878688848249⟩⟩,⟨⟨(-1783589953418164897824318),(-1783589953418164525895937)⟩,⟨11801288704765443093039208,11801288704765443464985993⟩⟩,⟨⟨(-1254454348316934041112137),(-1254454348316933687539176)⟩,⟨11293333223759183839004576,11293333223759184192604549⟩⟩,⟨⟨(-764827472627658318034814),(-764827472627657982229224)⟩,⟨10783759902298002505709624,10783759902298002841550005⟩⟩,⟨⟨(-313925418295949171993402),(-313925418295948853300216)⟩,⟨10274410056666126031463915,10274410056666126350198848⟩⟩,⟨⟨99152425617784637322831,99152425617784939475418⟩,⟨9767054180024289238769664,9767054180024289540970168⟩⟩,⟨⟨475414902847337838032446,475414902847338124299126⟩,⟨9263383886373030899895830,9263383886373031186215848⟩⟩,⟨⟨815970149768728691436447,815970149768728962388288⟩,⟨8765004697127680189023946,8765004697127680460033822⟩⟩,⟨⟨1122016268529861097198733,1122016268529861353464701⟩,⟨8273429702625564261541461,8273429702625564517869470⟩⟩,⟨⟨1394831698558925927753144,1394831698558926170689729⟩,⟨7790074121769866598390313,7790074121769866841392227⟩⟩,⟨⟨1635765372326339437819237,1635765372326339668020987⟩,⟨7316250773876903960087785,7316250773876904190356586⟩⟩,⟨⟨1846226741047603784207760,1846226741047604002136279⟩,⟨6853166467745157812742569,6853166467745158030738483⟩⟩,⟨⟨2027675754886696754714631,2027675754886696960883370⟩,⟨6401919304112633948417574,6401919304112634154653674⟩⟩] +lemma kernel16_1_r4_4_eq : ∀ k : Fin 16, kernel16_1Expr 4 4 k = kernel16_1_r4_4 k := by decide +kernel +noncomputable def kernel16_1_r4_5 : Fin 16 → CBox := ![⟨⟨2181612880188661865251132,2181612880188662060097919⟩,⟨5963496879116554088586846,5963496879116554283500622⟩⟩,⟨⟨2309569233384816051436794,2309569233384816235466956⟩,⟨5538775368212150710400404,5538775368212150894496877⟩⟩,⟨⟨2413096907533888660954740,2413096907533888834599120⟩,⟨5128519462333882122149142,5128519462333882295858875⟩⟩,⟨⟨2493759563056387690345855,2493759563056387854080298⟩,⟨4733383120972273442130462,4733383120972273605929055⟩⟩,⟨⟨2553123349164665123964137,2553123349164665278195113⟩,⟨4353911100362509824269795,4353911100362509978563488⟩⟩,⟨⟨2592748216871402459330544,2592748216871402604518808⟩,⟨3990541209195864408726567,3990541209195864553975923⟩⟩,⟨⟨2614179678363732094959909,2614179678363732231498739⟩,⟨3643607239219741247158889,3643607239219741383757017⟩⟩,⟨⟨2618941061051885870379574,2618941061051885998699485⟩,⟨3313342513822556285434123,3313342513822556413811397⟩⟩,⟨⟨2608526297835269009719096,2608526297835269130196402⟩,⟨2999883994229970711012575,2999883994229970831541303⟩⟩,⟨⟨2584393288171020936788178,2584393288171021049836600⟩,⟨2703276880281342839117824,2703276880281342952211559⟩⟩,⟨⟨2547957857475440311989420,2547957857475440417966694⟩,⟨2423479640910207894373970,2423479640910208000390856⟩⟩,⟨⟨2500588335329848585264270,2500588335329848684573775⟩,⟨2160369408409378779383588,2160369408409378878727416⟩⟩,⟨⟨2443600765988653396574907,2443600765988653489535430⟩,⟨1913747670298430511681586,1913747670298430604671539⟩⟩,⟨⟨2378254757882798770315812,2378254757882798857283371⟩,⟨1683346193097466141932023,1683346193097466228924498⟩⟩,⟨⟨2305749972254729330966831,2305749972254729412249864⟩,⟨1468833113505656686877170,1468833113505656768180970⟩⟩,⟨⟨2227223244822787721856079,2227223244822787797822771⟩,⟨1269819134337510503118422,1269819134337510579102083⟩⟩] +lemma kernel16_1_r4_5_eq : ∀ k : Fin 16, kernel16_1Expr 4 5 k = kernel16_1_r4_5 k := by decide +kernel +noncomputable def kernel16_1_r4_6 : Fin 16 → CBox := ![⟨⟨2143746328517196889761695,2143746328517196960680491⟩,⟨1085863765028579051969657,1085863765028579122901959⟩⟩,⟨⟨2056324239911649844509408,2056324239911649910681512⟩,⟨916481549523948760395415,916481549523948826577895⟩⟩,⟨⟨1965894187040374623809575,1965894187040374685487828⟩,⟨761148227841405914256463,761148227841405975942268⟩⟩,⟨⟨1873325051877536440349994,1873325051877536497806076⟩,⟨619306781487239100239554,619306781487239157700650⟩⟩,⟨⟨1779417396891868731262886,1779417396891868784725495⟩,⟨490373317124791496846313,490373317124791550311673⟩⟩,⟨⟨1684903961793125183160311,1684903961793125232881916⟩,⟨373742747381724716924915,373742747381724766647263⟩⟩,⟨⟨1590450613867893560342446,1590450613867893606586527⟩,⟨268794232359412181176549,268794232359412227419624⟩⟩,⟨⟨1496657713161368928480925,1496657713161368971484786⟩,⟨174896350206229548060949,174896350206229591062274⟩⟩,⟨⟨1404061852191460705487086,1404061852191460745431908⟩,⟨91411969967445041403399,91411969967445081344365⟩⟩,⟨⟨1313137928867055789544021,1313137928867055826631546⟩,⟨17702804762959985473527,17702804762960022556071⟩⟩,⟨⟨1224301510801353455037923,1224301510801353489435915⟩,⟨(-46866371890511752031094),(-46866371890511717639030)⟩⟩,⟨⟨1137911449235690227068493,1137911449235690258955896⟩,⟨(-102923859160076252069045),(-102923859160076220188349)⟩⟩,⟨⟨1054272701285563129942379,1054272701285563159472705⟩,⟨(-151087519470913610776817),(-151087519470913581253829)⟩⟩,⟨⟨973639320150499702326402,973639320150499729676455⟩,⟨(-191961630432908149384406),(-191961630432908122042189)⟩⟩,⟨⟨896217574251250415782422,896217574251250441086262⟩,⟨(-226134098009214795894605),(-226134098009214770598831)⟩⟩,⟨⟨822169157927003149798373,822169157927003173200167⟩,⟨(-254174027142078362783870),(-254174027142078339390109)⟩⟩] +lemma kernel16_1_r4_6_eq : ∀ k : Fin 16, kernel16_1Expr 4 6 k = kernel16_1_r4_6 k := by decide +kernel +noncomputable def kernel16_1_r4_7 : Fin 16 → CBox := ![⟨⟨751614458295606528008418,751614458295606549630445⟩,⟨(-276629642697568503838894),(-276629642697568482224807)⟩⟩,⟨⟨684635845103819240396720,684635845103819260368055⟩,⟨(-294026550577060850326069),(-294026550577060830362525)⟩⟩,⟨⟨621280952824884385504072,621280952824884403931037⟩,⟨(-306866326182264407953056),(-306866326182264389533695)⟩⟩,⟨⟨561565926850358327739544,561565926850358344734545⟩,⟨(-315625415119345392799605),(-315625415119345375811986)⟩⟩,⟨⟨505478608326483240956782,505478608326483256612769⟩,⟨(-320754329087541198226485),(-320754329087541182577626)⟩⟩,⟨⟨452981634958767505262861,452981634958767519681042⟩,⟨(-322677118314650931516680),(-322677118314650917105347)⟩⟩,⟨⟨404015437910562027305626,404015437910562040569560⟩,⟨(-321791100667198146739182),(-321791100667198133481799)⟩⟩,⟨⟨358501117713932548928010,358501117713932561133251⟩,⟨(-318466826663880645317761),(-318466826663880633118667)⟩⟩,⟨⟨316343184858944890222970,316343184858944901474746⟩,⟨(-313048259040419836118601),(-313048259040419824872124)⟩⟩,⟨⟨277432153399081889427660,277432153399081899798628⟩,⟨(-305853145232209837187837),(-305853145232209826821402)⟩⟩,⟨⟨241646978478141660897278,241646978478141670446435⟩,⟨(-297173561135776058511804),(-297173561135776048966481)⟩⟩,⟨⟨208857331123753947167556,208857331123753955957482⟩,⟨(-287276604756509617315517),(-287276604756509608528788)⟩⟩,⟨⟨178925705944647113173809,178925705944647121255504⟩,⟨(-276405218822525536636129),(-276405218822525528557069)⟩⟩,⟨⟨151709359496950603725990,151709359496950611155408⟩,⟨(-264779122115966021497099),(-264779122115966014069807)⟩⟩,⟨⟨127062079036875681779838,127062079036875688602490⟩,⟨(-252595830116395516935399),(-252595830116395510114415)⟩⟩,⟨⟨104835783144480059357404,104835783144480065621337⟩,⟨(-240031746538932273315390),(-240031746538932267052721)⟩⟩] +lemma kernel16_1_r4_7_eq : ∀ k : Fin 16, kernel16_1Expr 4 7 k = kernel16_1_r4_7 k := by decide +kernel +noncomputable def kernel16_1_r4_8 : Fin 16 → CBox := ![⟨⟨84881957280737767760259,84881957280737773504293⟩,⟨(-227243308455735751891711),(-227243308455735746148582)⟩⟩,⟨⟨67052928725859671320834,67052928725859676590951⟩,⟨(-214368168887583560342688),(-214368168887583555073160)⟩⟩,⟨⟨51202986541730506953784,51202986541730511784136⟩,⟨(-201526402017873693928540),(-201526402017873689098508)⟩⟩,⟨⟨37189353209067049911999,37189353209067054338529⟩,⟨(-188821717491284574912373),(-188821717491284570485929)⟩⟩,⟨⟨24873015416399008552275,24873015416399012604058⟩,⟨(-176342671592004905740577),(-176342671592004901688674)⟩⟩,⟨⟨14119422131163326631983,14119422131163330344731⟩,⟨(-164163864432248585019647),(-164163864432248581306610)⟩⟩,⟨⟨4799058572684780196766,4799058572684783595714⟩,⟨(-152347113603012874626612),(-152347113603012871227230)⟩⟩,⟨⟨(-3212094956462720692165),(-3212094956462717580788)⟩,⟨(-140942596030087632252206),(-140942596030087629140274)⟩⟩,⟨⟨(-10032210228279783419649),(-10032210228279780574632)⟩,⟨(-129989951025630431622460),(-129989951025630428776798)⟩⟩,⟨⟨(-15773355016042898498792),(-15773355016042895895777)⟩,⟨(-119519338717714605078484),(-119519338717714602474744)⟩⟩,⟨⟨(-20541324616599050862125),(-20541324616599048482852)⟩,⟨(-109552449167697944086027),(-109552449167697941705968)⟩⟩,⟨⟨(-24435551943516005609329),(-24435551943516003434604)⟩,⟨(-100103458540575499183611),(-100103458540575497008058)⟩⟩,⟨⟨(-27549087403082193203127),(-27549087403082191217539)⟩,⟨(-91179929671062230763182),(-91179929671062228776766)⟩⟩,⟨⟨(-29968640076964760250109),(-29968640076964758436905)⟩,⟨(-82783655264137459482889),(-82783655264137457668875)⟩⟩,⟨⟨(-31774672109547735326422),(-31774672109547733672231)⟩,⟨(-74911442780920055521814),(-74911442780920053866830)⟩⟩,⟨⟨(-33041538622468620716452),(-33041538622468619205599)⟩,⟨(-67555840788239305596779),(-67555840788239304085156)⟩⟩] +lemma kernel16_1_r4_8_eq : ∀ k : Fin 16, kernel16_1Expr 4 8 k = kernel16_1_r4_8 k := by decide +kernel +noncomputable def kernel16_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-33837665942228414286625),(-33837665942228412905061)⟩,⟨(-60705807193634532233036),(-60705807193634530850733)⟩⟩,⟨⟨(-34225761418335735040660),(-34225761418335733776885)⟩,⟨(-54347320348414210680370),(-54347320348414209415884)⟩⟩,⟨⟨(-34263048619493405090111),(-34263048619493403935116)⟩,⟨(-48463934482472819477542),(-48463934482472818321868)⟩⟩,⟨⟨(-34001522214992581044052),(-34001522214992579988312)⟩,⟨(-43037281339265098524267),(-43037281339265097467883)⟩⟩,⟨⟨(-33488217369834431904428),(-33488217369834430940446)⟩,⟨(-38047520211806725991680),(-38047520211806725027085)⟩⟩,⟨⟨(-32765488998192114553076),(-32765488998192113672493)⟩,⟨(-33473738845464701971047),(-33473738845464701089900)⟩⟩,⟨⟨(-31871296724637927078666),(-31871296724637926274857)⟩,⟨(-29294307875662445268261),(-29294307875662444463966)⟩⟩,⟨⟨(-30839491890991669299170),(-30839491890991668565269)⟩,⟨(-25487191613754652602536),(-25487191613754651868219)⟩⟩,⟨⟨(-29700103414477790932177),(-29700103414477790262497)⟩,⟨(-22030218087669089679564),(-22030218087669089009540)⟩⟩,⟨⟨(-28479619746727212164107),(-28479619746727211552361)⟩,⟨(-18901311290950044971312),(-18901311290950044359278)⟩⟩,⟨⟨(-27201264600421117468272),(-27201264600421116909920)⟩,⟨(-16078688600003484085997),(-16078688600003483527410)⟩⟩,⟨⟨(-25885264499163837465500),(-25885264499163836955715)⟩,⟨(-13541026289940207683897),(-13541026289940207173917)⟩⟩,⟨⟨(-24549106565259085813817),(-24549106565259085348834)⟩,⟨(-11267596019549049754793),(-11267596019549049289664)⟩⟩,⟨⟨(-23207785288803193968793),(-23207785288803193544436)⟩,⟨(-9238375070467547968666),(-9238375070467547544196)⟩⟩,⟨⟨(-21874037319772840610267),(-21874037319772840223295)⟩,⟨(-7434133019122208405627),(-7434133019122208018575)⟩⟩,⟨⟨(-20558563592894662888716),(-20558563592894662535697)⟩,⟨(-5836497396731932818643),(-5836497396731932465571)⟩⟩] +lemma kernel16_1_r4_9_eq : ∀ k : Fin 16, kernel16_1Expr 4 9 k = kernel16_1_r4_9 k := by decide +kernel +noncomputable def kernel16_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-19270238333744549595883),(-19270238333744549273379)⟩,⟨(-4428000756509799879350),(-4428000756509799556816)⟩⟩,⟨⟨(-18016304704759063895032),(-18016304704759063600111)⟩,⟨(-3192111421706531270221),(-3192111421706530975292)⟩⟩,⟨⟨(-16802557032933028749974),(-16802557032933028480471)⟩,⟨(-2113250036497669041465),(-2113250036497668771969)⟩⟩,⟨⟨(-15633509718411375134013),(-15633509718411374887607)⟩,⟨(-1176793886749098909080),(-1176793886749098662699)⟩⟩,⟨⟨(-14512553056596663629811),(-14512553056596663404734)⟩,⟨(-369070801872198580873),(-369070801872198355831)⟩⟩,⟨⟨(-13442096317527428035755),(-13442096317527427830003)⟩,⟨322655705570220952769,322655705570221158480⟩⟩,⟨⟨(-12423698516940445003851),(-12423698516940444815832)⟩,⟨910208557318325733022,910208557318325920983⟩⟩,⟨⟨(-11458187385441804618872),(-11458187385441804446847)⟩,⟨1404525125636442199774,1404525125636442371741⟩⟩,⟨⟨(-10545767097400801666108),(-10545767097400801508853)⟩,⟨1815689931110144882899,1815689931110145040084⟩⟩,⟨⟨(-9686115361337653498149),(-9686115361337653354262)⟩,⟨2152970939183536720464,2152970939183536864285⟩⟩,⟨⟨(-8878470500435773537903),(-8878470500435773406330)⟩,⟨2424858499490115611306,2424858499490115742807⟩⟩,⟨⟨(-8121709167032923745933),(-8121709167032923625535)⟩,⟨2639106090947272820387,2639106090947272940712⟩⟩,⟨⟨(-7414415340106187154236),(-7414415340106187044040)⟩,⟨2802772146210132832009,2802772146210132942133⟩⟩,⟨⟨(-6754941251337913027576),(-6754941251337912926463)⟩,⟨2922262331260791554369,2922262331260791655418⟩⟩,⟨⟨(-6141460874702234375801),(-6141460874702234283071)⟩,⟨3003371749631164232804,3003371749631164325467⟩⟩,⟨⟨(-5572016597902690632048),(-5572016597902690546930)⟩,⟨3051326626128612471111,3051326626128612556168⟩⟩] +lemma kernel16_1_r4_10_eq : ∀ k : Fin 16, kernel16_1Expr 4 10 k = kernel16_1_r4_10 k := by decide +kernel +noncomputable def kernel16_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-5044559672566814923909),(-5044559672566814845858)⟩,⟨3070825102159947393718,3070825102159947471706⟩⟩,⟨⟨(-4556985014897032910604),(-4556985014897032838930)⟩,⟨3066076844118956416541,3066076844118956488156⟩⟩,⟨⟨(-4107160900412507397042),(-4107160900412507331201)⟩,⟨3040841228166845400394,3040841228166845466181⟩⟩,⟨⟨(-3692954066310657053996),(-3692954066310656993458)⟩,⟨2998463919494004904009,2998463919494004964491⟩⟩,⟨⟨(-3312250703545036551573),(-3312250703545036495948)⟩,⟨2941911712240141698482,2941911712240141754057⟩⟩,⟨⟨(-2962973788576791782175),(-2962973788576791731014)⟩,⟨2873805538125568546936,2873805538125568598047⟩⟩,⟨⟨(-2643097172438602986102),(-2643097172438602939027)⟩,⟨2796451587978966161406,2796451587978966208434⟩⟩,⟨⟨(-2350656812698112854231),(-2350656812698112810821)⟩,⟨2711870521209014682777,2711870521209014726147⟩⟩,⟨⟨(-2083759502491084190957),(-2083759502491084150962)⟩,⟨2621824764327295835454,2621824764327295875419⟩⟩,⟨⟨(-1840589420312335794802),(-1840589420312335757895)⟩,⟨2527843921345453791898,2527843921345453828777⟩⟩,⟨⟨(-1619412794941876016452),(-1619412794941875982403)⟩,⟨2431248336682690376767,2431248336682690410796⟩⟩,⟨⟨(-1418580951926057843109),(-1418580951926057811657)⟩,⟨2333170865552476170516,2333170865552476201948⟩⟩,⟨⟨(-1236531981561527110164),(-1236531981561527081139)⟩,⟨2234576918049425383878,2234576918049425412885⟩⟩,⟨⟨(-1071791243433040617034),(-1071791243433040590204)⟩,⟨2136282851703364954100,2136282851703364980915⟩⟩,⟨⟨(-922970899287895257060),(-922970899287895232264)⟩,⟨2038972793456340494676,2038972793456340519464⟩⟩,⟨⟨(-788768644411390839036),(-788768644411390816076)⟩,⟨1943213976171406215141,1943213976171406238090⟩⟩] +lemma kernel16_1_r4_11_eq : ∀ k : Fin 16, kernel16_1Expr 4 11 k = kernel16_1_r4_11 k := by decide +kernel +noncomputable def kernel16_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-667965787694793652353),(-667965787694793631082)⟩,⟨1849470677194295596737,1849470677194295618000⟩⟩,⟨⟨(-559424812233291119481),(-559424812233291099757)⟩,⟨1758116847428504821403,1758116847428504841119⟩⟩,⟨⟨(-462086531512451118159),(-462086531512451099871)⟩,⟨1669447519092938839141,1669447519092938857424⟩⟩,⟨⟨(-374966940979842324581),(-374966940979842307588)⟩,⟨1583689079025989132929,1583689079025989149916⟩⟩,⟨⟨(-297153850985219781321),(-297153850985219765556)⟩,⟨1501008492273764563818,1501008492273764579583⟩⟩,⟨⟨(-227803374631745381896),(-227803374631745367237)⟩,⟨1421521557923685696668,1421521557923685711330⟩⟩,⟨⟨(-166136332930513923585),(-166136332930513909955)⟩,⟨1345300275867226441403,1345300275867226455032⟩⟩,⟨⟨(-111434629706436911073),(-111434629706436898371)⟩,⟨1272379399527177909810,1272379399527177922512⟩⟩,⟨⟨(-63037639879164483077),(-63037639879164471234)⟩,⟨1202762245677408625778,1202762245677408637621⟩⟩,⟨⟨(-20338646952182235333),(-20338646952182224279)⟩,⟨1136425828412320937373,1136425828412320948427⟩⟩,⟨⟨17218641298174408758,17218641298174419071⟩,⟨1073325380169844712208,1073325380169844722524⟩⟩,⟨⟨50143475916646616886,50143475916646626531⟩,⟨1013398318543320668711,1013398318543320678356⟩⟩,⟨⟨78901330815850734310,78901330815850743324⟩,⟨956567713489557367455,956567713489557376472⟩⟩,⟨⟨103917034421018260927,103917034421018269367⟩,⟨902745305497698195103,902745305497698203547⟩⟩,⟨⟨125577759392450791660,125577759392450799574⟩,⟨851834121362027045507,851834121362027053425⟩⟩,⟨⟨144235864166865907287,144235864166865914717⟩,⟨803730730429091703453,803730730429091710890⟩⟩] +lemma kernel16_1_r4_12_eq : ∀ k : Fin 16, kernel16_1Expr 4 12 k = kernel16_1_r4_12 k := by decide +kernel +noncomputable def kernel16_1_r4_13 : Fin 16 → CBox := ![⟨⟨160211582809511101853,160211582809511108837⟩,⟨758327180586134953833,758327180586134960821⟩⟩,⟨⟨173795561966930394519,173795561966930401089⟩,⟨715512649838375982015,715512649838375988592⟩⟩,⟨⟨185251245609016803342,185251245609016809525⟩,⟨675174846096638463120,675174846096638469306⟩⟩,⟨⟨194817109797420028133,194817109797420033959⟩,⟨637201184769326867366,637201184769326873195⟩⟩,⟨⟨202708750960098874841,202708750960098880330⟩,⟨601479770925374530453,601479770925374535948⟩⟩,⟨⟨209120832129235808234,209120832129235813418⟩,⟨567900210166150940669,567900210166150945856⟩⟩,⟨⟨214228892348324633646,214228892348324638552⟩,⟨536354269910673184018,536354269910673188930⟩⟩,⟨⟨218191025006721987968,218191025006721992618⟩,⟨506736410554192184760,506736410554192189415⟩⟩,⟨⟨221149431245542405140,221149431245542409541⟩,⟨478944203898246475306,478944203898246479715⟩⟩,⟨⟨223231854823449076473,223231854823449080658⟩,⟨452878654362447229275,452878654362447233465⟩⟩,⟨⟨224552904957621385646,224552904957621389621⟩,⟨428444436765671391141,428444436765671395117⟩⟩,⟨⟨225215273684184805364,225215273684184809144⟩,⟨405550062897596257424,405550062897596261212⟩⟩,⟨⟨225310854231373327349,225310854231373330950⟩,⟨384107987680941939340,384107987680941942949⟩⟩,⟨⟨224921766783080572412,224921766783080575839⟩,⟨364034664440647543421,364034664440647546856⟩⟩,⟨⟨224121297843601668972,224121297843601672255⟩,⟨345250557638809690886,345250557638809694178⟩⟩,⟨⟨222974759207778098716,222974759207778101854⟩,⟨327680120394063138355,327680120394063141498⟩⟩] +lemma kernel16_1_r4_13_eq : ∀ k : Fin 16, kernel16_1Expr 4 13 k = kernel16_1_r4_13 k := by decide +kernel +noncomputable def kernel16_1_r4_14 : Fin 16 → CBox := ![⟨⟨221540272304277168656,221540272304277171667⟩,⟨311251743171970347711,311251743171970350723⟩⟩,⟨⟨219869483421734555945,219869483421734558824⟩,⟨295897679200052334407,295897679200052337287⟩⟩,⟨⟨218008215055021357953,218008215055021360719⟩,⟨281553951418887435397,281553951418887438168⟩⟩,⟨⟨215997058327870497059,215997058327870499723⟩,⟨268160245121223098829,268160245121223101497⟩⟩,⟨⟨213871911163401876944,213871911163401879500⟩,⟨255659789846751903888,255659789846751906448⟩⟩,⟨⟨211664466589726743815,211664466589726746280⟩,⟨243999233584040464566,243999233584040467032⟩⟩,⟨⟨209402655287025207508,209402655287025209896⟩,⟨233128511876495313823,233128511876495316215⟩⟩,⟨⟨207111046207847525011,207111046207847527310⟩,⟨223000714030108242557,223000714030108244863⟩⟩,⟨⟨204811208835888260546,204811208835888262770⟩,⟨213571948271417492589,213571948271417494814⟩⟩,⟨⟨202522040391632591552,202522040391632593712⟩,⟨204801207399475774759,204801207399475776922⟩⟩,⟨⟨200260061047170270392,200260061047170272491⟩,⟨196650236210890255725,196650236210890257828⟩⟩,⟨⟨198039679977859099083,198039679977859101117⟩,⟨189083401747865121098,189083401747865123139⟩⟩,⟨⟨195873434855846809671,195873434855846811648⟩,⟨182067567221695708104,182067567221695710081⟩⟩,⟨⟨193772207179934864891,193772207179934866822⟩,⟨175571970294762271971,175571970294762273905⟩⟩,⟨⟨191745415637896355743,191745415637896357625⟩,⟨169568106259520840806,169568106259520842691⟩⟩,⟨⟨189801189510986232874,189801189510986234714⟩,⟨164029616530375544212,164029616530375546055⟩⟩] +lemma kernel16_1_r4_14_eq : ∀ k : Fin 16, kernel16_1Expr 4 14 k = kernel16_1_r4_14 k := by decide +kernel +noncomputable def kernel16_1_r4_15 : Fin 16 → CBox := ![⟨⟨187946523955717921336,187946523955717923133⟩,⟨158932182761022129637,158932182761022131438⟩⟩,⟨⟨186187418834634672311,186187418834634674083⟩,⟨154253426813527265519,154253426813527267292⟩⟩,⟨⟨184529002615305143891,184529002615305145615⟩,⟨149972816733951598968,149972816733951600696⟩⟩,⟨⟨182975642714588147153,182975642714588148848⟩,⟨146071578830861521757,146071578830861523455⟩⟩,⟨⟨181531043532764125116,181531043532764126785⟩,⟨142532615905936038881,142532615905936040551⟩⟩,⟨⟨180198333298812461914,180198333298812463554⟩,⟨139340431648578185549,139340431648578187192⟩⟩,⟨⟨178980140733295631679,178980140733295633295⟩,⟨136481061177670353555,136481061177670355175⟩⟩,⟨⟨177878662428353511476,177878662428353513079⟩,⟨133942007692205926998,133942007692205928600⟩⟩,⟨⟨176895721744569354194,176895721744569355775⟩,⟨131712185177457111375,131712185177457112963⟩⟩,⟨⟨176032819931299109093,176032819931299110656⟩,⟨129781867103692283698,129781867103692285268⟩⟩,⟨⟨175291180089818749047,175291180089818750601⟩,⟨128142641049433470333,128142641049433471887⟩⟩,⟨⟨174671784516708074538,174671784516708076075⟩,⟨126787369180137051690,126787369180137053231⟩⟩,⟨⟨174175405887631173772,174175405887631175297⟩,⟨125710154515361408645,125710154515361410173⟩⟩,⟨⟨173802632668480231432,173802632668480232952⟩,⟨124906312922397260437,124906312922397261964⟩⟩,⟨⟨173553889071117593762,173553889071117595275⟩,⟨124372350781483158850,124372350781483160366⟩⟩,⟨⟨173429449804087360318,173429449804087361831⟩,⟨124105948276663452760,124105948276663454277⟩⟩] +lemma kernel16_1_r4_15_eq : ∀ k : Fin 16, kernel16_1Expr 4 15 k = kernel16_1_r4_15 k := by decide +kernel +noncomputable def kernel16_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel16_1_r4_0,kernel16_1_r4_1,kernel16_1_r4_2,kernel16_1_r4_3,kernel16_1_r4_4,kernel16_1_r4_5,kernel16_1_r4_6,kernel16_1_r4_7,kernel16_1_r4_8,kernel16_1_r4_9,kernel16_1_r4_10,kernel16_1_r4_11,kernel16_1_r4_12,kernel16_1_r4_13,kernel16_1_r4_14,kernel16_1_r4_15] +lemma kernel16_1_r4_eq (i k : Fin 16) : kernel16_1Expr 4 i k = kernel16_1_r4 i k := by + fin_cases i + · exact kernel16_1_r4_0_eq k + · exact kernel16_1_r4_1_eq k + · exact kernel16_1_r4_2_eq k + · exact kernel16_1_r4_3_eq k + · exact kernel16_1_r4_4_eq k + · exact kernel16_1_r4_5_eq k + · exact kernel16_1_r4_6_eq k + · exact kernel16_1_r4_7_eq k + · exact kernel16_1_r4_8_eq k + · exact kernel16_1_r4_9_eq k + · exact kernel16_1_r4_10_eq k + · exact kernel16_1_r4_11_eq k + · exact kernel16_1_r4_12_eq k + · exact kernel16_1_r4_13_eq k + · exact kernel16_1_r4_14_eq k + · exact kernel16_1_r4_15_eq k +noncomputable def kernel16_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-17170831568158424500914488868),(-17170831568158422357832281496)⟩,⟨(-191384823686758781547607883856),(-191384823686758779401825709028)⟩⟩,⟨⟨(-17265421003384845762243360139),(-17265421003384843619656830946)⟩,⟨(-191283780957307886172605617878),(-191283780957307884027318408051)⟩⟩,⟨⟨(-17454290060722545724964266693),(-17454290060722543583372677834)⟩,⟨(-191081694669053236686491561275),(-191081694669053234542197872979)⟩⟩,⟨⟨(-17736819939614984215762898044),(-17736819939614982075665272572)⟩,⟨(-190778564028606129541379468942),(-190778564028606127398577632692)⟩⟩,⟨⟨(-18112084503637523758579221230),(-18112084503637521620474309791)⟩,⟨(-190374390002501969423107771036),(-190374390002501967282295864490)⟩⟩,⟨⟨(-18578852758385676937013448775),(-18578852758385674801399538909)⟩,⟨(-189869177886488641294282467518),(-189869177886488639155958131150)⟩⟩,⟨⟨(-19135592156211275524251095736),(-19135592156211273391626040290)⟩,⟨(-189262940700255611580247096957),(-189262940700255609444907568758)⟩⟩,⟨⟨(-19780472728350268332343786265),(-19780472728350266203204650160)⟩,⟨(-188555703381243850057053618427),(-188555703381243847925195386747)⟩⟩,⟨⟨(-20511372044856249541794239119),(-20511372044856247416637605705)⟩,⟨(-187747507744839106856314095769),(-187747507744839104728433211709)⟩⟩,⟨⟨(-21325881002452194616502300098),(-21325881002452192495823478112)⟩,⟨(-186838418172081922511687808640),(-186838418172081920388279098599)⟩⟩,⟨⟨(-22221310439909783773496343516),(-22221310439909781657789475554)⟩,⟨(-185828527980060740927140245036),(-185828527980060738808697424946)⟩⟩,⟨⟨(-23194698579834305972502056480),(-23194698579834303862095513466)⟩,⟨(-184717966424423353962895119101),(-184717966424423351849746189713)⟩⟩,⟨⟨(-24242819294749662968876576572),(-24242819294749660864249642651)⟩,⟨(-183506906277980262690975729349),(-183506906277980260583599674604)⟩⟩,⟨⟨(-25362191194122017711758429324),(-25362191194122015613387471039)⟩,⟨(-182195571924214856069229140186),(-182195571924214853968102096433)⟩⟩,⟨⟨(-26549087527415451786652228605),(-26549087527415449695014666869)⟩,⟨(-180784247899692769853354042291),(-180784247899692767758953275745)⟩⟩,⟨⟨(-27799546896425923073610541511),(-27799546896425920989179690310)⟩,⟨(-179273287814909177232950442920),(-179273287814909175145749191011)⟩⟩] +lemma kernel16_1_r5_0_eq : ∀ k : Fin 16, kernel16_1Expr 5 0 k = kernel16_1_r5_0 k := by decide +kernel +noncomputable def kernel16_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-29109384767982435092020774913),(-29109384767982433015272322984)⟩,⟨(-177663123579060292183710131521),(-177663123579060290104184090017)⟩⟩,⟨⟨(-30474205775632734733051265801),(-30474205775632732664454194746)⟩,⟨(-175954274850605498582503332084),(-175954274850605496511121574079)⟩⟩,⟨⟨(-31889416796145823745715423524),(-31889416796145821685742555718)⟩,⟨(-174147358632329748168171220498),(-174147358632329746105406750028)⟩⟩,⟨⟨(-33350240783570706585613650745),(-33350240783570704534729428692)⟩,⟨(-172243098926951487609498955173),(-172243098926951485555816485822)⟩⟩,⟨⟨(-34851731340200626403917548019),(-34851731340200624362592642730)⟩,⟨(-170242336367177197408384032975),(-170242336367177195364254602160)⟩⟩,⟨⟨(-36388788000120044938427310645),(-36388788000120042907119418758)⟩,⟨(-168146037732505712929984993410),(-168146037732505710895866756054)⟩⟩,⟨⟨(-37956172197078232146099714388),(-37956172197078230125275248670)⟩,⟨(-165955305264057844881193374784),(-165955305264057842857553300624)⟩⟩,⟨⟨(-39548523884263861693336102781),(-39548523884263859683446485433)⟩,⟨(-163671385688271028509488219271),(-163671385688271026496778380691)⟩⟩,⟨⟨(-41160378769179534353763056155),(-41160378769179532355272277521)⟩,⟨(-161295678860473688362271681275),(-161295678860473686360956819336)⟩⟩,⟨⟨(-42786186122268331322188606514),(-42786186122268329335538035420)⟩,⟨(-158829745940155520909507435435),(-158829745940155518920029760875)⟩⟩,⟨⟨(-44420327113265338766703574179),(-44420327113265336792350749260)⟩,⟨(-156275317011190368121632236044),(-156275317011190366144450229755)⟩⟩,⟨⟨(-46057133624478642465830261182),(-46057133624478640504208558097)⟩,⟨(-153634298062356420115075185053),(-153634298062356418150623253835)⟩⟩,⟨⟨(-47690907485393329208891911131),(-47690907485393327260455811093)⟩,⟨(-150908777246238689537575850058),(-150908777246238687586309604769)⟩⟩,⟨⟨(-49315940068188609259557916147),(-49315940068188607324667297980)⟩,⟨(-148101030337991175912851582966),(-148101030337991173975132153696)⟩⟩,⟨⟨(-50926532179015189027708400775),(-50926532179015187106661760154)⟩,⟨(-145213525319476303203478441223),(-145213525319476301279605725461)⟩⟩,⟨⟨(-52517014175252700237920947200),(-52517014175252698331125539713)⟩,⟨(-142248926018977502570898045785),(-142248926018977500661280681159)⟩⟩] +lemma kernel16_1_r5_1_eq : ∀ k : Fin 16, kernel16_1Expr 5 1 k = kernel16_1_r5_1 k := by decide +kernel +noncomputable def kernel16_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-54081766234512326296485776721),(-54081766234512324404382511524)⟩,⟨(-139210094741982437426926700150),(-139210094741982435532007067047)⟩⟩,⟨⟨(-55615238696925922168983320497),(-55615238696925920291961406064)⟩,⟨(-136100093834439124134883369923),(-136100093834439122255052212587)⟩⟩,⟨⟨(-57111972398328594581332327086),(-57111972398328592719820660322)⟩,⟨(-132922186126369316318312293136),(-132922186126369314454000126183)⟩⟩,⟨⟨(-58566618908355446509712293801),(-58566618908355444664089411347)⟩,⟨(-129679834210751556483416563449),(-129679834210751554635003596997)⟩⟩,⟨⟨(-59973960584292705800663542283),(-59973960584292703971332967641)⟩,⟨(-126376698520123115455599063118),(-126376698520123113623502797897)⟩⟩,⟨⟨(-61328930348804908070218756396),(-61328930348804906257387610026)⟩,⟨(-123016634171352819597090953082),(-123016634171352817781602199857)⟩⟩,⟨⟨(-62626631097457060288181617782),(-62626631097457058492262135784)⟩,⟨(-119603686557457103323446207721),(-119603686557457101524977939473)⟩⟩,⟨⟨(-63862354640314630392637639222),(-63862354640314628613974917761)⟩,⟨(-116142085674115692240575862819),(-116142085674115690459473728095)⟩⟩,⟨⟨(-65031600080881907265741152832),(-65031600080881905504745917164)⟩,⟨(-112636239177632105627912105337),(-112636239177632103864587222928)⟩⟩,⟨⟨(-66130091535273423182795333353),(-66130091535273421439784062659)⟩,⟨(-109090724180413776067453240973),(-109090724180413774322222291130)⟩⟩,⟨⟨(-67153795094841263048401582271),(-67153795094841261323764621690)⟩,⟨(-105510277799548640698113063738),(-105510277799548638971366431532)⟩⟩,⟨⟨(-68098934936534953909247583820),(-68098934936534952203288695981)⟩,⟨(-101899786483657158910622444765),(-101899786483657157202663741408)⟩⟩,⟨⟨(-68962008487075598068873113964),(-68962008487075596381979326352)⟩,⟨(-98264274152824960965486064329),(-98264274152824959276702003711)⟩⟩,⟨⟨(-69739800549600406524134085022),(-69739800549600404856575962874)⟩,⟨(-94608889195992952191447102955),(-94608889195992950522107742208)⟩⟩,⟨⟨(-70429396304788799725393127832),(-70429396304788798077533601503)⟩,⟨(-90938890379617696723467813980),(-90938890379617695073935414221)⟩⟩,⟨⟨(-71028193102619916980072662816),(-71028193102619915352166917376)⟩,⟨(-87259631730632811865315223734),(-87259631730632810235844111856)⟩⟩] +lemma kernel16_1_r5_2_eq : ∀ k : Fin 16, kernel16_1Expr 5 2 k = kernel16_1_r5_2 k := by decide +kernel +noncomputable def kernel16_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-71533910965828678982443600690),(-71533910965828677374853423066)⟩,⟨(-83576546465658754463907044879),(-83576546465658752854857991319)⟩⟩,⟨⟨(-71944601731810014478591951312),(-71944601731810012891530678543)⟩,⟨(-79895130046940748930947627615),(-79895130046940747342532765487)⟩⟩,⟨⟨(-72258656766146443102711384191),(-72258656766146441536508729596)⟩,⟨(-76220922453560676847872752891),(-76220922453560675280420437948)⟩⟩,⟨⟨(-72474813188072217335302288894),(-72474813188072215790157998757)⟩,⟨(-72559489763988411099676830040),(-72559489763988409553385274904)⟩⟩,⟨⟨(-72592158555998399769084344446),(-72592158555998398245324038888)⟩,⟨(-68916405152934043958642264834),(-68916405152934042433835407833)⟩⟩,⟨⟨(-72610133969659898265886960003),(-72610133969659896763665411562)⟩,⟨(-65297229411661177708440528436),(-65297229411661176205271292333)⟩⟩,⟨⟨(-72528535554451762057328484066),(-72528535554451760576936440990)⟩,⟨(-61707491106354016791110447116),(-61707491106354015309867590439)⟩⟩,⟨⟨(-72347514303034349807875255971),(-72347514303034348349450964309)⟩,⟨(-58152666493734060629866519336),(-58152666493734059170686145856)⟩⟩,⟨⟨(-72067574259234433935292465209),(-72067574259234432499126022953)⟩,⟨(-54638159316838782355672007912),(-54638159316838780918841942379)⟩⟩,⟨⟨(-71689569039574344868461797941),(-71689569039574343454637547691)⟩,⟨(-51169280606655035831218479696),(-51169280606655034416820653036)⟩⟩,⟨⟨(-71214696698340348857107149601),(-71214696698340347465474003711)⟩,⟨(-47751228617102268301629269810),(-47751228617102266909509953855)⟩⟩,⟨⟨(-70644492952865878233201031724),(-70644492952865876860837787858)⟩,⟨(-44389069021651777911645581796),(-44389069021651776538880109087)⟩⟩,⟨⟨(-69980822796561983651378341436),(-69980822796561982298596298251)⟩,⟨(-41087715499624333505474684141),(-41087715499624332152371626613)⟩⟩,⟨⟨(-69225870538080112807687324658),(-69225870538080111474575038446)⟩,⟨(-37851910838915301147505368314),(-37851910838915299814150457965)⟩⟩,⟨⟨(-68382128315742399052370877908),(-68382128315742397739202230526)⟩,⟨(-34686208679549971884592081171),(-34686208679549970571256282034)⟩⟩,⟨⟨(-67452383146922214319702982790),(-67452383146922213026558171522)⟩,⟨(-31594956019078459648539624760),(-31594956019078458355300139880)⟩⟩] +lemma kernel16_1_r5_3_eq : ∀ k : Fin 16, kernel16_1Expr 5 3 k = kernel16_1_r5_3 k := by decide +kernel +noncomputable def kernel16_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-66439702582302870324492479132),(-66439702582302869051655234127)⟩,⟨(-28582276596396328888067678681),(-28582276596396327615205163111)⟩⟩,⟨⟨(-65347419044786183264915805880),(-65347419044786182012407271845)⟩,⟨(-25652055265151639005604602796),(-25652055265151637753137075330)⟩⟩,⟨⟨(-64179112942168541170322696986),(-64179112942168539938377753318)⟩,⟨(-22807923461509512056643776749),(-22807923461509510824802924947)⟩⟩,⟨⟨(-62938594651456936062680082365),(-62938594651456934851318137189)⟩,⟨(-20053245863740104398453114802),(-20053245863740103187255125191)⟩⟩,⟨⟨(-61629885480772516048815304998),(-61629885480772514858275374196)⟩,⟨(-17391108332933402284012345046),(-17391108332933401093692959762)⟩⟩,⟨⟨(-60257197722101623420609701486),(-60257197722101622250853515588)⟩,⟨(-14824307215192430919897425046),(-14824307215192429750415100037)⟩⟩,⟨⟨(-58824913914627800223112898483),(-58824913914627799074331247839)⟩,⟨(-12355340075991965553965066325),(-12355340075991964405507280261)⟩⟩,⟨⟨(-57337565443944380668323637750),(-57337565443944379540472271307)⟩,⟨(-9986397927097452142034250843),(-9986397927097451014553460152)⟩⟩,⟨⟨(-55799810607046210399352519571),(-55799810607046209292632906702)⟩,⟨(-7719358995610607676620730691),(-7719358995610606570315087386)⟩⟩,⟨⟨(-54216412276580351540383720330),(-54216412276580350454684328851)⟩,⟨(-5555784073442370360489594696),(-5555784073442369275244301178)⟩⟩,⟨⟨(-52592215300359123806164433232),(-52592215300359122741628102865)⟩,⟨(-3496913473914015437541876973),(-3496913473914014373496496773)⟩⟩,⟨⟨(-50932123773575009783150262003),(-50932123773575008739668113930)⟩,⟨(-1543665610360928864070470168),(-1543665610360927821112915088)⟩⟩,⟨⟨(-49241078321487520598541191223),(-49241078321487519576261372043)⟩,⟨303362800328802004344301677,303362800328803026069092936⟩⟩,⟨⟨(-47524033529570280073111282856),(-47524033529570279071757462667)⟩,⟨2043894918255081668362410502,2043894918255082669134015202⟩⟩,⟨⟨(-45785935656217208493943504645),(-45785935656217207513560163254)⟩,⟨3677970365977652651068605554,3677970365977653630847112235⟩⟩,⟨⟨(-44031700760126317165911638364),(-44031700760126316206332331677)⟩,⟨5205940251388783693681157730,5205940251388784652645727613⟩⟩] +lemma kernel16_1_r5_4_eq : ∀ k : Fin 16, kernel16_1Expr 5 4 k = kernel16_1_r5_4 k := by decide +kernel +noncomputable def kernel16_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-42266193370436349222821896616),(-42266193370436348284161735683)⟩,⟨6628460671745166948816793396,6628460671745167886854623061⟩⟩,⟨⟨(-40494205822624662125535991341),(-40494205822624661207493489783)⟩,⟨7946484753471269977462141474,7946484753471270894876884839⟩⟩,⟨⟨(-38720438377134502830540946160),(-38720438377134501932931634186)⟩,⟨9161253292664586417973558539,9161253292664587314951816136⟩⟩,⟨⟨(-36949480230746578832261817348),(-36949480230746577954874029625)⟩,⟨10274284070920819573697892584,10274284070920820450453330376⟩⟩,⟨⟨(-35185791522913506692477182419),(-35185791522913505835382346039)⟩,⟨11287359930066149710826248641,11287359930066150567289395297⟩⟩,⟨⟨(-33433686430714944645336781683),(-33433686430714943808260359047)⟩,⟨12202515697554588785098907419,12202515697554589621546106011⟩⟩,⟨⟨(-31697317436852347386347509280),(-31697317436852346569302675882)⟩,⟨13022024061590213104756802584,13022024061590213921176631822⟩⟩,⟨⟨(-29980660845278367661790661352),(-29980660845278366864510196371)⟩,⟨13748380501405762670465285136,13748380501405763467126577240⟩⟩,⟨⟨(-28287503608745571496550581387),(-28287503608745570719066217745)⟩,⟨14384287383520126972418902904,14384287383520127749291480657⟩⟩,⟨⟨(-26621431521865280257465428532),(-26621431521865279499000387630)⟩,⟨14932637339167990973351720336,14932637339167991731248149272⟩⟩,⟨⟨(-24985818822296043612872468887),(-24985818822296042873312736303)⟩,⟨15396496041417130046203665743,15396496041417130785244627874⟩⟩,⟨⟨(-23383819231540326749821326776),(-23383819231540326028877149751)⟩,⟨15779084502745833559927890030,15779084502745834280401279589⟩⟩,⟨⟨(-21818358455625807820213491899),(-21818358455625807117890209132)⟩,⟨16083761015039670578668126230,16083761015039671280566743681⟩⟩,⟨⟨(-20292128154791775714593246579),(-20292128154791775030542195974)⟩,⟨16314002854089828943651734815,16314002854089829627322312866⟩⟩,⟨⟨(-18807581380296971091586368372),(-18807581380296970425755638562)⟩,⟨16473387869752447575466309214,16473387869752448240958836945⟩⟩,⟨⟨(-17366929465714998840206589904),(-17366929465714998192146110156)⟩,⟨16565576080988578182465741528,16565576080988578830228347970⟩⟩] +lemma kernel16_1_r5_5_eq : ∀ k : Fin 16, kernel16_1Expr 5 5 k = kernel16_1_r5_5 k := by decide +kernel +noncomputable def kernel16_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-15972140349684854494015080448),(-15972140349684853863684843861)⟩,⟨16594291392086969506533512952,16594291392086970136604257571⟩⟩,⟨⟨(-14624938297129272149744474380),(-14624938297129271536753389776)⟩,⟨16563303542525888339750155838,16563303542525888952518153144⟩⟩,⟨⟨(-13326804976528055803279495044),(-13326804976528055207543104552)⟩,⟨16476410398213846816719528121,16476410398213847412267281507⟩⟩,⟨⟨(-12078981842015351299013796163),(-12078981842015350720171490353)⟩,⟨16337420686328740273570448740,16337420686328740852256613001⟩⟩,⟨⟨(-10882473760928727755136682994),(-10882473760928727193120856056)⟩,⟨16150137269724071619441659063,16150137269724072181331911278⟩⟩,⟨⟨(-9738053820034800478262284873),(-9738053820034799932661297396)⟩,⟨15918341049969375663133164949,15918341049969376208637232215⟩⟩,⟨⟨(-8646269237042304448617847500),(-8646269237042303919311714248)⟩,⟨15645775580624460167784544309,15645775580624460697020531325⟩⟩,⟨⟨(-7607448298230513338706207925),(-7607448298230512825307322298)⟩,⟨15336132464402376574298716433,15336132464402377087652383482⟩⟩,⟨⟨(-6621708238100066242734173191),(-6621708238100065744490624751)⟩,⟨14993037599545606799396736625,14993037599545607297617942576⟩⟩,⟨⟨(-5688963972915749100599840745),(-5688963972915748616889395869)⟩,⟨14620038332116867352158639368,14620038332116867835867796386⟩⟩,⟨⟨(-4808937596867505364820804100),(-4808937596867504895546008211)⟩,⟨14220591562083663422302572226,14220591562083663891595435627⟩⟩,⟨⟨(-3981168547327795508573167632),(-3981168547327795053378458216)⟩,⟨13798052842147017308228651413,13798052842147017763459145057⟩⟩,⟨⟨(-3205024344321501911867056702),(-3205024344321501470674668987)⟩,⟨13355666499320559309003423824,13355666499320559750247711637⟩⟩,⟨⟨(-2479711808830650466093244047),(-2479711808830650038504192535)⟩,⟨12896556800394441079166037304,12896556800394441506821579209⟩⟩,⟨⟨(-1804288664903234533899530195),(-1804288664903234119789352816)⟩,⟨12423720173703498760623114961,12423720173703499174812886581⟩⟩,⟨⟨(-1177675431688123353078825697),(-1177675431688122952077246255)⟩,⟨11940018491140203963240041788,11940018491140204364332912249⟩⟩] +lemma kernel16_1_r5_6_eq : ∀ k : Fin 16, kernel16_1Expr 5 6 k = kernel16_1_r5_6 k := by decide +kernel +noncomputable def kernel16_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-598667513433673407029600138),(-598667513433673019043560036)⟩,⟨11448173406184106163045412074,11448173406184106551133069823⟩⟩,⟨⟨(-65947398116800495920097757),(-65947398116800120499319701)⟩,⟨10950761735928369073174381041,10950761735928369448705827650⟩⟩,⟨⟨421903121343368964214445259,421903121343369327282936864⟩,⟨10450211867731494931981188862,10450211867731495295168160708⟩⟩,⟨⟨866390785447793776179827487,866390785447794127265674140⟩,⟨9948801164261979279993334699,9948801164261979631204323430⟩⟩,⟨⟨1269098843797181557073173449,1269098843797181896294539490⟩,⟨9448654334381357303228048470,9448654334381357642577677309⟩⟩,⟨⟨1631675240944897705995633416,1631675240944898033756136879⟩,⟨8951742731564910225460625167,8951742731564910553350809400⟩⟩,⟨⟨1955821079996450975010873587,1955821079996451291463816096⟩,⟨8459884536419196427204574509,8459884536419196743787908678⟩⟩,⟨⟨2243279425919954017290805673,2243279425919954322805118531⟩,⟨7974745775343524988882413303,7974745775343525294527202404⟩⟩,⟨⟨2495824504667525237546087698,2495824504667525532472540996⟩,⟨7497842123512531133990405202,7497842123512531429046798796⟩⟩,⟨⟨2715251348157949248180518673,2715251348157949532984188714⟩,⟨7030541437135437311268603221,7030541437135437596201157174⟩⟩,⟨⟨2903365929004897500622881119,2903365929004897775445214720⟩,⟨6574066957373238718616206623,6574066957373238993565876161⟩⟩,⟨⟨3061975822659277903775178853,3061975822659278168957478013⟩,⟨6129501126359719652531528148,6129501126359719917839194589⟩⟩,⟨⟨3192881428432579997807977360,3192881428432580253467823414⟩,⟨5697789954461057669915201753,5697789954461057925698047666⟩⟩,⟨⟨3297867774740628257206556248,3297867774740628503727641574⟩,⟨5279747877200886834286691027,5279747877200887080919458100⟩⟩,⟨⟨3378696927910090285473248951,3378696927910090523004407296⟩,⟨4876063040146636654270575159,4876063040146636891901568581⟩⟩,⟨⟨3437101018075006621028272312,3437101018075006849899119622⟩,⟨4487302950467414027384697966,4487302950467414256344184276⟩⟩] +lemma kernel16_1_r5_7_eq : ∀ k : Fin 16, kernel16_1Expr 5 7 k = kernel16_1_r5_7 k := by decide +kernel +noncomputable def kernel16_1_r5_8 : Fin 16 → CBox := ![⟨⟨3474775890104191414381667917,3474775890104191634722805225⟩,⟨4113920434798085561737517972,4113920434798085782156724776⟩⟩,⟨⟨3493375382184062815797880596,3493375382184063028072256175⟩,⟨3756259844439414325203359192,3756259844439414537545871018⟩⟩,⟨⟨3494506229671345610061313283,3494506229671345814408354992⟩,⟨3414563450748092574464190111,3414563450748092778870045886⟩⟩,⟨⟨3479723587156655617019186438,3479723587156655813744972115⟩,⟨3088977975779074367958133705,3088977975779074564734018920⟩⟩,⟨⟨3450527157368157964514667911,3450527157368158153734756086⟩,⟨2779561205790005297301449917,2779561205790005486563507513⟩⟩,⟨⟨3408357911613683205392005680,3408357911613683387429526014⟩,⟨2486288638057151333081150197,2486288638057151515153085969⟩⟩,⟨⟨3354595382923851768537790157,3354595382923851943574590756⟩,⟨2209060114537173745399823109,2209060114537173920464038211⟩⟩,⟨⟨3290555509926611683323116345,3290555509926611851662736407⟩,⟨1947706399192847415589709150,1947706399192847583950280149⟩⟩,⟨⟨3217489006758833618536428177,3217489006758833780283410798⟩,⟨1701995659237723247395755470,1701995659237723409157741781⟩⟩,⟨⟨3136580232002198596779144286,3136580232002198752237648371⟩,⟨1471639814100520360314979018,1471639814100520515783035720⟩⟩,⟨⟨3048946527713127523974867442,3048946527713127673304460854⟩,⟨1256300719522256589390914654,1256300719522256738725085373⟩⟩,⟨⟨2955637998090479071431943631,2955637998090479214897187238⟩,⟨1055596157837562484006038564,1055596157837562627471336727⟩⟩,⟨⟨2857637696177092483113816776,2857637696177092620822728954⟩,⟨869105609118605312778949745,869105609118605450483840517⟩⟩,⟨⟨2755862186205669082631156387,2755862186205669214869951755⟩,⟨696375781440738511816234592,696375781440738644047391012⟩⟩,⟨⟨2651162448756881602439372676,2651162448756881729328944817⟩,⟨536925882031603256093016380,536925882031603382971717304⟩⟩,⟨⟨2544325095776538176324199406,2544325095776538298105157810⟩,⟨390252614461371454574918074,390252614461371576342130697⟩⟩] +lemma kernel16_1_r5_8_eq : ∀ k : Fin 16, kernel16_1Expr 5 8 k = kernel16_1_r5_8 k := by decide +kernel +noncomputable def kernel16_1_r5_9 : Fin 16 → CBox := ![⟨⟨2436073862675761366571322842,2436073862675761483336550452⟩,⟨255834890295884544561123875,255834890295884661310076156⟩⟩,⟨⟨2327071345188643273472599865,2327071345188643385477465103⟩,⟨133138246744738086805126095,133138246744738198791499733⟩⟩,⟨⟨2217920949359810633075782119,2217920949359810740433618873⟩,⟨21618964774399171739270999,21618964774399279076702310⟩⟩,⟨⟨2109169023953215286904254053,2109169023953215389834020322⟩,⟨(-79272115092924418638803416),(-79272115092924315731082759)⟩⟩,⟨⟨2001307145686398685791289153,2001307145686398784385395011⟩,⟨(-170086079522602681763420906),(-170086079522602583192736003)⟩⟩,⟨⟨1894774528974663228216311473,1894774528974663322700021314⟩,⟨(-251372729537719947275809063),(-251372729537719852816537526)⟩⟩,⟨⟨1789960533290593257356467710,1789960533290593347834236334⟩,⟨(-323677663871134225521053789),(-323677663871134135067928929)⟩⟩,⟨⟨1687207242780444061790633624,1687207242780444148459388148⟩,⟨(-387539652341758295074968662),(-387539652341758208430932929)⟩⟩,⟨⟨1586812094405218131903116403,1586812094405218214843397253⟩,⟨(-443488291401599468867674834),(-443488291401599385952059576)⟩⟩,⟨⟨1489030532567076084821738440,1489030532567076164239262547⟩,⟨(-492041932519306145100770113),(-492041932519306065707755791)⟩⟩,⟨⟨1394078669918716444160740379,1394078669918716520149944002⟩,⟨(-533705872795920121138167245),(-533705872795920045173216404)⟩⟩,⟨⟨1302135935813618154757728666,1302135935813618227493774679⟩,⟨(-568970796143068019148567182),(-568970796143067946436435312)⟩⟩,⟨⟨1213347695619289869370231804,1213347695619289938929222934⟩,⟨(-598311452485108459305415344),(-598311452485108389769919564)⟩⟩,⟨⟨1127827825866319662532966630,1127827825866319729093301673⟩,⟨(-622185561765515654710772482),(-622185561765515588173453797)⟩⟩,⟨⟨1045661231927226250904560052,1045661231927226314550438917⟩,⟨(-641032929033564669015561051),(-641032929033564605392160128)⟩⟩,⟨⟨966906296596815115763572346,966906296596815176945787405⟩,⟨(-655274756548771558717820715),(-655274756548771497555992878)⟩⟩] +lemma kernel16_1_r5_9_eq : ∀ k : Fin 16, kernel16_1Expr 5 9 k = kernel16_1_r5_9 k := by decide +kernel +noncomputable def kernel16_1_r5_10 : Fin 16 → CBox := ![⟨⟨891597249567659186152555144,891597249567659244941203490⟩,⟨(-665313138655384908202424783),(-665313138655384849432019209)⟩⟩,⟨⟨819746449349934338500479448,819746449349934395029943149⟩,⟨(-671530725134859094705938094),(-671530725134859038192707590)⟩⟩,⟨⟨751346570665344820989215223,751346570665344875307762854⟩,⟨(-674290538827683250190450675),(-674290538827683195886251397)⟩⟩,⟨⟨686372691743131787508443539,686372691743131839727572668⟩,⟨(-673935933514082184508554257),(-673935933514082132302013491)⟩⟩,⟨⟨624784277256611164766047367,624784277256611214921118064⟩,⟨(-670790678342874087964658645),(-670790678342874037820532715)⟩⟩,⟨⟨566527053857269955969944259,566527053857270004177527204⟩,⟨(-665159155486282993039086977),(-665159155486282944840921238)⟩⟩,⟨⟨511534776387490652193647477,511534776387490698497547792⟩,⟨(-657326658163205166918042634),(-657326658163205120622140252)⟩⟩,⟨⟨459730883881084132679051409,459730883881084177178698727⟩,⟨(-647559776702202904191859809),(-647559776702202859698896758)⟩⟩,⟨⟨411030045392775291535865605,411030045392775334260344400⟩,⟨(-636106860896772219568329258),(-636106860896772176849320173)⟩⟩,⟨⟨365339596534438561816477852,365339596534438602872244951⟩,⟨(-623198547528250588962199178),(-623198547528250547910783165)⟩⟩,⟨⟨322560868338992314882179855,322560868338992354308336174⟩,⟨(-609048342585832369853349644),(-609048342585832330430515982)⟩⟩,⟨⟨282590410725016727277961106,282590410725016765162379033⟩,⟨(-593853248389014730105358598),(-593853248389014692223320677)⟩⟩,⟨⟨245321113399642528469783045,245321113399642564840506351⟩,⟨(-577794426506648881730900851),(-577794426506648845361696186)⟩⟩,⟨⟨210643227517936685819270701,210643227517936720767700689⟩,⟨(-561037888060655226316519967),(-561037888060655191368823437)⟩⟩,⟨⟨178445291818230847893469054,178445291818230881453975549⟩,⟨(-543735203694212083641884743),(-543735203694212050081398977)⟩⟩,⟨⟨148614967279318379412625325,148614967279318411662270800⟩,⟨(-526024226167478850117897854),(-526024226167478817867627499)⟩⟩] +lemma kernel16_1_r5_10_eq : ∀ k : Fin 16, kernel16_1Expr 5 10 k = kernel16_1_r5_10 k := by decide +kernel +noncomputable def kernel16_1_r5_11 : Fin 16 → CBox := ![⟨⟨121039784602182728739841744,121039784602182759700129652⟩,⟨(-508029819213083137364441377),(-508029819213083106402947513)⟩⟩,⟨⟨95607809011098657910390773,95607809011098687664269351⟩,⟨(-489864586933868142529306106),(-489864586933868112773698705)⟩⟩,⟨⟨72208227001860301177074008,72208227001860329754743229⟩,⟨(-471629598652675799166135470),(-471629598652675770586272104)⟩⟩,⟨⟨50731859743860932611263325,50731859743860960082196581⟩,⟨(-453415104724846852353006355),(-453415104724846824879471629)⟩⟩,⟨⟨31071607873070929581788295,31071607873070955966364472⟩,⟨(-435301239395923708538408161),(-435301239395923682150871808)⟩⟩,⟨⟨13122832399834589137464505,13122832399834614505217567⟩,⟨(-417358707327633887371559234),(-417358707327633862000529451)⟩⟩,⟨⟨(-3216323596105116339804978),(-3216323596105091960055277)⟩,⟨(-399649450923068105878133403),(-399649450923068081494832004)⟩⟩,⟨⟨(-18044667895962788307380425),(-18044667895962764857413266)⟩,⟨(-382227296056024912830989371),(-382227296056024889377231617)⟩⟩,⟨⟨(-31457742224119332437413776),(-31457742224119309902373573)⟩,⟨(-365138574249222106274482573),(-365138574249222083735449193)⟩⟩,⟨⟨(-43547651146945067889672894),(-43547651146945046207659322)⟩,⟨(-348422719751344639663655514),(-348422719751344617977475792)⟩⟩,⟨⟨(-54402932611567694255073584),(-54402932611567673403780633)⟩,⟨(-332112840333953335807493644),(-332112840333953314951934583)⟩⟩,⟨⟨(-64108466122895079402695274),(-64108466122895059328047091)⟩,⟨(-316236260966688198418346771),(-316236260966688178339425082)⟩⟩,⟨⟨(-72745414745018553835210675),(-72745414745018534524025975)⟩,⟨(-300815039833814039939960668),(-300815039833814020624511064)⟩⟩,⟨⟨(-80391197310497507152772132),(-80391197310497488553565974)⟩,⟨(-285866456428060308931282692),(-285866456428060290327831083)⟩⟩,⟨⟨(-87119487424982376052275723),(-87119487424982358147840581)⟩,⟨(-271403471700182074546800632),(-271403471700182056638151838)⟩⟩,⟨⟨(-93000236062488051278589106),(-93000236062488034026615919)⟩,⟨(-257435160456152126838332381),(-257435160456152109582185996)⟩⟩] +lemma kernel16_1_r5_11_eq : ∀ k : Fin 16, kernel16_1Expr 5 11 k = kernel16_1_r5_11 k := by decide +kernel +noncomputable def kernel16_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-98099714755990128046399813),(-98099714755990111438237810)⟩,⟨(-243967116379942756667570173),(-243967116379942740055285692)⟩⟩,⟨⟨(-102480576596769359852235310),(-102480576596769343840880757)⟩,⟨(-231001830220115665498688962),(-231001830220115649483268345)⟩⟩,⟨⟨(-106201932462231067360911336),(-106201932462231051926164524)⟩,⟨(-218539041814613686437084084),(-218539041814613670998334981)⟩⟩,⟨⟨(-109319440094187588548785667),(-109319440094187573654854422)⟩,⟨(-206576066741974491705685888),(-206576066741974476807820550)⟩⟩,⟨⟨(-111885403846465460057292995),(-111885403846465445696373507)⟩,⟨(-195108098480408469309392299),(-195108098480408454944612726)⟩⟩,⟨⟨(-113948883111062293580298399),(-113948883111062279714431678)⟩,⟨(-184128487030532496165863755),(-184128487030532482296213370)⟩⟩,⟨⟨(-115555807615017245743298188),(-115555807615017232361252718)⟩,⟨(-173628995014730468474307698),(-173628995014730455088558804)⟩⟩,⟨⟨(-116749097954951296426101566),(-116749097954951283496762600)⟩,⟨(-163600032307777217969710107),(-163600032307777205036907116)⟩⟩,⟨⟨(-117568789902331715329267785),(-117568789902331702847884951)⟩,⟨(-154030870281114369616101690),(-154030870281114357131521548)⟩⟩,⟨⟨(-118052161169529478687535807),(-118052161169529466620035352)⟩,⟨(-144909836758536645380972870),(-144909836758536633310525624)⟩⟩,⟨⟨(-118233859474420747467680281),(-118233859474420735804988526)⟩,⟨(-136224492785491313408234774),(-136224492785491301742832921)⟩⟩,⟨⟨(-118146030879510966296057564),(-118146030879510955011814196)⟩,⟨(-127961792309086525897661919),(-127961792309086514610930788)⟩⟩,⟨⟨(-117818447510319837392710127),(-117818447510319826482618207)⟩,⟨(-120108225852534965919420697),(-120108225852534955007050905)⟩⟩,⟨⟨(-117278633877139943644509578),(-117278633877139933080175286)⟩,⟨(-112649949247327910181667874),(-112649949247327899615252371)⟩⟩,⟨⟨(-116551991134435393282446176),(-116551991134435383054131207)⟩,⟨(-105572898460052295857973319),(-105572898460052285627762161)⟩⟩,⟨⟨(-115661918713312633903845390),(-115661918713312623985098657)⟩,⟨(-98862891519450905421864460),(-98862891519450895501394677)⟩⟩] +lemma kernel16_1_r5_12_eq : ∀ k : Fin 16, kernel16_1Expr 5 12 k = kernel16_1_r5_12 k := by decide +kernel +noncomputable def kernel16_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-114629932854963586177573153),(-114629932854963576567249485)⟩,⟨(-92505718514016176609780669),(-92505718514016166997896839)⟩⟩,⟨⟨(-113475781657087568582698323),(-113475781657087559255240065)⟩,⟨(-86487220591947812762524534),(-86487220591947803433658335)⟩⟩,⟨⟨(-112217556321415308593135709),(-112217556321415299543227756)⟩,⟨(-80793358854456049801475926),(-80793358854456040750302844)⟩⟩,⟨⟨(-110871798358984969130880293),(-110871798358984960339403152)⟩,⟨(-75410273990838556171191792),(-75410273990838547378583004)⟩⟩,⟨⟨(-109453602571174949594302303),(-109453602571174941059829919)⟩,⟨(-70324337460105435832926368),(-70324337460105427297447423)⟩⟩,⟨⟨(-107976715679111598376226715),(-107976715679111590077604344)⟩,⟨(-65522194979707301921633087),(-65522194979707293622120878)⟩⟩,⟨⟨(-106453630522377951107034946),(-106453630522377943040129777)⟩,⟨(-60990803037601643119218253),(-60990803037601635051532399)⟩⟩,⟨⟨(-104895675790388515098675859),(-104895675790388507246920109)⟩,⟨(-56717459099875188377523269),(-56717459099875180525088665)⟩⟩,⟨⟨(-103313101286796898846018035),(-103313101286796891209757355)⟩,⟨(-52689826142768543205589644),(-52689826142768535568745182)⟩⟩,⟨⟨(-101715158759291358398144703),(-101715158759291350957864459)⟩,⟨(-48895952095513939005789530),(-48895952095513931565014096)⟩⟩,⟨⟨(-100110178354520120919140118),(-100110178354520113671035569)⟩,⟨(-45324284739138101467795210),(-45324284739138094219278038)⟩⟩,⟨⟨(-98505640781071403518217726),(-98505640781071396447589961)⟩,⟨(-41963682566495801207389520),(-41963682566495794136426047)⟩⟩,⟨⟨(-96908245282793734606419092),(-96908245282793727713473761)⟩,⟨(-38803422070440965499560299),(-38803422070440958606350786)⟩⟩,⟨⟨(-95323973540643854941578370),(-95323973540643848209962681)⟩,⟨(-35833201890330438233717592),(-35833201890330431501904326)⟩⟩,⟨⟨(-93758149634036273985186782),(-93758149634036267412611147)⟩,⟨(-33043144212077465389424557),(-33043144212077458816713189)⟩⟩,⟨⟨(-92215496202664639352712661),(-92215496202664632926614110)⟩,⟨(-30423793783786171763865898),(-30423793783786165337689157)⟩⟩] +lemma kernel16_1_r5_13_eq : ∀ k : Fin 16, kernel16_1Expr 5 13 k = kernel16_1_r5_13 k := by decide +kernel +noncomputable def kernel16_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-90700186957274147259214486),(-90700186957274140981431925)⟩,⟨(-27966114877638153195258243),(-27966114877638146917450729)⟩⟩,⟨⟨(-89215895693169377263008328),(-89215895693169371117881073)⟩,⟨(-25661486499179656138785490),(-25661486499179649993682868)⟩⟩,⟨⟨(-87765841963605754222705291),(-87765841963605748208580468)⟩,⟨(-23501696117465856331300682),(-23501696117465850317246339)⟩⟩,⟨⟨(-86352833571877692839321670),(-86352833571877686945122609)⟩,⟨(-21478932163634864594645745),(-21478932163634858700559793)⟩⟩,⟨⟨(-84979306041105000938594879),(-84979306041104995165541851)⟩,⟨(-19585775521372391738395907),(-19585775521372385965495227)⟩⟩,⟨⟨(-83647359219634836630659134),(-83647359219634830965662528)⟩,⟨(-17815190210341649710153903),(-17815190210341644045346175)⟩⟩,⟨⟨(-82358791177804589910366235),(-82358791177804584352283300)⟩,⟨(-16160513442936327827282690),(-16160513442936322269422257)⟩⟩,⟨⟨(-81115129548719105704521633),(-81115129548719100243496800)⟩,⟨(-14615445215604624368195387),(-14615445215604618907424279)⟩⟩,⟨⟨(-79917660461834638734735979),(-79917660461834633373109978)⟩,⟨(-13174037578421238015579086),(-13174037578421232654235315)⟩⟩,⟨⟨(-78767455213647062432566341),(-78767455213647057157681984)⟩,⟨(-11830683710479935312143241),(-11830683710479930037567699)⟩⟩,⟨⟨(-77665394814773605070967222),(-77665394814773599882077091)⟩,⟨(-10580106913967188034048630),(-10580106913967182845491627)⟩⟩,⟨⟨(-76612192547302414924520779),(-76612192547302409812769597)⟩,⟨(-9417349626381278643020374),(-9417349626381273531624878)⟩⟩,⟨⟨(-75608414660556379257799441),(-75608414660556374225052095)⟩,⟨(-8337762538204489400575659),(-8337762538204484368204403)⟩⟩,⟨⟨(-74654499327458765629535462),(-74654499327458760664874341)⟩,⟨(-7336993892342040175315655),(-7336993892342035211049661)⟩⟩,⟨⟨(-73750773977569377112328709),(-73750773977569372215306230)⟩,⟨(-6410979031734740518540646),(-6410979031734735621930519)⟩⟩,⟨⟨(-72897471116641904890995299),(-72897471116641900053557483)⟩,⟨(-5555930252658746746870548),(-5555930252658741909861052)⟩⟩] +lemma kernel16_1_r5_14_eq : ∀ k : Fin 16, kernel16_1Expr 5 14 k = kernel16_1_r5_14 k := by decide +kernel +noncomputable def kernel16_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-72094742736287698940293761),(-72094742736287694165442038)⟩,⟨(-4768327013273133096421274),(-4768327013273128322012012)⟩⟩,⟨⟨(-71342673411061546125854158),(-71342673411061541402500610)⟩,⟨(-4044906539894210238169736),(-4044906539894205515271915)⟩⟩,⟨⟨(-70641292174046914143578328),(-70641292174046909471486003)⟩,⟨(-3382654867197168718743234),(-3382654867197164047118446)⟩⟩,⟨⟨(-69990583255840275228969845),(-69990583255840270600720087)⟩,⟨(-2778798343005890614646493),(-2778798343005885986875170)⟩⟩,⟨⟨(-69390495765739151208288113),(-69390495765739146626125059)⟩,⟨(-2230795623468661178253195),(-2230795623468656596578006)⟩⟩,⟨⟨(-68840952387943448675525153),(-68840952387943444129863552)⟩,⟨(-1736330180171883450780036),(-1736330180171878905615072)⟩⟩,⟨⟨(-68341857159696540100664921),(-68341857159696535591404084)⟩,⟨(-1293303337059472540770215),(-1293303337059468032013611)⟩⟩,⟨⟨(-67893102392529038538641558),(-67893102392529034058842972)⟩,⟨(-899827851848923840523480),(-899827851848919361236032)⟩⟩,⟨⟨(-67494574792128044196197291),(-67494574792128039748532873)⟩,⟨(-554222053915391351446963),(-554222053915386904299199)⟩⟩,⟨⟨(-67146160826838101449500485),(-67146160826838097023694597)⟩,⟨(-255004548304387536961073),(-255004548304383111676895)⟩⟩,⟨⟨(-66847751389404468073049047),(-66847751389404463669181378)⟩,⟨(-889493586318433444159),(-889493586314030102256)⟩⟩,⟨⟨(-66599245791289213567903256),(-66599245791289209179497360)⟩,⟨209217540361287377892313,209217540361291765768918⟩⟩,⟨⟨(-66400555123718511849434219),(-66400555123718507479036552)⟩,⟨376223129906460487794238,376223129906464857660220⟩⟩,⟨⟨(-66251605014545719725563628),(-66251605014545715364347775)⟩,⟨500848966921775020761581,500848966921779381443664⟩⟩,⟨⟨(-66152337805028243552263936),(-66152337805028239200298669)⟩,⟨583634237027639515836465,583634237027643867266808⟩⟩,⟨⟨(-66102714165704242097102715),(-66102714165704237748127020)⟩,⟨624937404838343503664305,624937404838347852104381⟩⟩] +lemma kernel16_1_r5_15_eq : ∀ k : Fin 16, kernel16_1Expr 5 15 k = kernel16_1_r5_15 k := by decide +kernel +noncomputable def kernel16_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel16_1_r5_0,kernel16_1_r5_1,kernel16_1_r5_2,kernel16_1_r5_3,kernel16_1_r5_4,kernel16_1_r5_5,kernel16_1_r5_6,kernel16_1_r5_7,kernel16_1_r5_8,kernel16_1_r5_9,kernel16_1_r5_10,kernel16_1_r5_11,kernel16_1_r5_12,kernel16_1_r5_13,kernel16_1_r5_14,kernel16_1_r5_15] +lemma kernel16_1_r5_eq (i k : Fin 16) : kernel16_1Expr 5 i k = kernel16_1_r5 i k := by + fin_cases i + · exact kernel16_1_r5_0_eq k + · exact kernel16_1_r5_1_eq k + · exact kernel16_1_r5_2_eq k + · exact kernel16_1_r5_3_eq k + · exact kernel16_1_r5_4_eq k + · exact kernel16_1_r5_5_eq k + · exact kernel16_1_r5_6_eq k + · exact kernel16_1_r5_7_eq k + · exact kernel16_1_r5_8_eq k + · exact kernel16_1_r5_9_eq k + · exact kernel16_1_r5_10_eq k + · exact kernel16_1_r5_11_eq k + · exact kernel16_1_r5_12_eq k + · exact kernel16_1_r5_13_eq k + · exact kernel16_1_r5_14_eq k + · exact kernel16_1_r5_15_eq k +noncomputable def kernel16_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel16_1_r0,kernel16_1_r1,kernel16_1_r2,kernel16_1_r3,kernel16_1_r4,kernel16_1_r5] +lemma kernel16_1_eq (j : Fin 6) (i k : Fin 16) : kernel16_1Expr j i k = kernel16_1 j i k := by + fin_cases j + · exact kernel16_1_r0_eq i k + · exact kernel16_1_r1_eq i k + · exact kernel16_1_r2_eq i k + · exact kernel16_1_r3_eq i k + · exact kernel16_1_r4_eq i k + · exact kernel16_1_r5_eq i k +lemma kernel16_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel16_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(16:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel16_1_eq] + unfold kernel16_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans16_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel19_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans19 j i k) +noncomputable def kernel19_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_0_eq : ∀ k : Fin 16, kernel19_0Expr 0 0 k = kernel19_0_r0_0 k := by decide +kernel +noncomputable def kernel19_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_1_eq : ∀ k : Fin 16, kernel19_0Expr 0 1 k = kernel19_0_r0_1 k := by decide +kernel +noncomputable def kernel19_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_2_eq : ∀ k : Fin 16, kernel19_0Expr 0 2 k = kernel19_0_r0_2 k := by decide +kernel +noncomputable def kernel19_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_3_eq : ∀ k : Fin 16, kernel19_0Expr 0 3 k = kernel19_0_r0_3 k := by decide +kernel +noncomputable def kernel19_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_4_eq : ∀ k : Fin 16, kernel19_0Expr 0 4 k = kernel19_0_r0_4 k := by decide +kernel +noncomputable def kernel19_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_5_eq : ∀ k : Fin 16, kernel19_0Expr 0 5 k = kernel19_0_r0_5 k := by decide +kernel +noncomputable def kernel19_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_6_eq : ∀ k : Fin 16, kernel19_0Expr 0 6 k = kernel19_0_r0_6 k := by decide +kernel +noncomputable def kernel19_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_7_eq : ∀ k : Fin 16, kernel19_0Expr 0 7 k = kernel19_0_r0_7 k := by decide +kernel +noncomputable def kernel19_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_8_eq : ∀ k : Fin 16, kernel19_0Expr 0 8 k = kernel19_0_r0_8 k := by decide +kernel +noncomputable def kernel19_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_9_eq : ∀ k : Fin 16, kernel19_0Expr 0 9 k = kernel19_0_r0_9 k := by decide +kernel +noncomputable def kernel19_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_10_eq : ∀ k : Fin 16, kernel19_0Expr 0 10 k = kernel19_0_r0_10 k := by decide +kernel +noncomputable def kernel19_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r0_11_eq : ∀ k : Fin 16, kernel19_0Expr 0 11 k = kernel19_0_r0_11 k := by decide +kernel +noncomputable def kernel19_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel19_0_r0_12_eq : ∀ k : Fin 16, kernel19_0Expr 0 12 k = kernel19_0_r0_12 k := by decide +kernel +noncomputable def kernel19_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel19_0_r0_13_eq : ∀ k : Fin 16, kernel19_0Expr 0 13 k = kernel19_0_r0_13 k := by decide +kernel +noncomputable def kernel19_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel19_0_r0_14_eq : ∀ k : Fin 16, kernel19_0Expr 0 14 k = kernel19_0_r0_14 k := by decide +kernel +noncomputable def kernel19_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel19_0_r0_15_eq : ∀ k : Fin 16, kernel19_0Expr 0 15 k = kernel19_0_r0_15 k := by decide +kernel +noncomputable def kernel19_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel19_0_r0_0,kernel19_0_r0_1,kernel19_0_r0_2,kernel19_0_r0_3,kernel19_0_r0_4,kernel19_0_r0_5,kernel19_0_r0_6,kernel19_0_r0_7,kernel19_0_r0_8,kernel19_0_r0_9,kernel19_0_r0_10,kernel19_0_r0_11,kernel19_0_r0_12,kernel19_0_r0_13,kernel19_0_r0_14,kernel19_0_r0_15] +lemma kernel19_0_r0_eq (i k : Fin 16) : kernel19_0Expr 0 i k = kernel19_0_r0 i k := by + fin_cases i + · exact kernel19_0_r0_0_eq k + · exact kernel19_0_r0_1_eq k + · exact kernel19_0_r0_2_eq k + · exact kernel19_0_r0_3_eq k + · exact kernel19_0_r0_4_eq k + · exact kernel19_0_r0_5_eq k + · exact kernel19_0_r0_6_eq k + · exact kernel19_0_r0_7_eq k + · exact kernel19_0_r0_8_eq k + · exact kernel19_0_r0_9_eq k + · exact kernel19_0_r0_10_eq k + · exact kernel19_0_r0_11_eq k + · exact kernel19_0_r0_12_eq k + · exact kernel19_0_r0_13_eq k + · exact kernel19_0_r0_14_eq k + · exact kernel19_0_r0_15_eq k +noncomputable def kernel19_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_0_eq : ∀ k : Fin 16, kernel19_0Expr 1 0 k = kernel19_0_r1_0 k := by decide +kernel +noncomputable def kernel19_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_1_eq : ∀ k : Fin 16, kernel19_0Expr 1 1 k = kernel19_0_r1_1 k := by decide +kernel +noncomputable def kernel19_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_2_eq : ∀ k : Fin 16, kernel19_0Expr 1 2 k = kernel19_0_r1_2 k := by decide +kernel +noncomputable def kernel19_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_3_eq : ∀ k : Fin 16, kernel19_0Expr 1 3 k = kernel19_0_r1_3 k := by decide +kernel +noncomputable def kernel19_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_4_eq : ∀ k : Fin 16, kernel19_0Expr 1 4 k = kernel19_0_r1_4 k := by decide +kernel +noncomputable def kernel19_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_5_eq : ∀ k : Fin 16, kernel19_0Expr 1 5 k = kernel19_0_r1_5 k := by decide +kernel +noncomputable def kernel19_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_6_eq : ∀ k : Fin 16, kernel19_0Expr 1 6 k = kernel19_0_r1_6 k := by decide +kernel +noncomputable def kernel19_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_7_eq : ∀ k : Fin 16, kernel19_0Expr 1 7 k = kernel19_0_r1_7 k := by decide +kernel +noncomputable def kernel19_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_8_eq : ∀ k : Fin 16, kernel19_0Expr 1 8 k = kernel19_0_r1_8 k := by decide +kernel +noncomputable def kernel19_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_9_eq : ∀ k : Fin 16, kernel19_0Expr 1 9 k = kernel19_0_r1_9 k := by decide +kernel +noncomputable def kernel19_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_10_eq : ∀ k : Fin 16, kernel19_0Expr 1 10 k = kernel19_0_r1_10 k := by decide +kernel +noncomputable def kernel19_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_11_eq : ∀ k : Fin 16, kernel19_0Expr 1 11 k = kernel19_0_r1_11 k := by decide +kernel +noncomputable def kernel19_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_12_eq : ∀ k : Fin 16, kernel19_0Expr 1 12 k = kernel19_0_r1_12 k := by decide +kernel +noncomputable def kernel19_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_13_eq : ∀ k : Fin 16, kernel19_0Expr 1 13 k = kernel19_0_r1_13 k := by decide +kernel +noncomputable def kernel19_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_14_eq : ∀ k : Fin 16, kernel19_0Expr 1 14 k = kernel19_0_r1_14 k := by decide +kernel +noncomputable def kernel19_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r1_15_eq : ∀ k : Fin 16, kernel19_0Expr 1 15 k = kernel19_0_r1_15 k := by decide +kernel +noncomputable def kernel19_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel19_0_r1_0,kernel19_0_r1_1,kernel19_0_r1_2,kernel19_0_r1_3,kernel19_0_r1_4,kernel19_0_r1_5,kernel19_0_r1_6,kernel19_0_r1_7,kernel19_0_r1_8,kernel19_0_r1_9,kernel19_0_r1_10,kernel19_0_r1_11,kernel19_0_r1_12,kernel19_0_r1_13,kernel19_0_r1_14,kernel19_0_r1_15] +lemma kernel19_0_r1_eq (i k : Fin 16) : kernel19_0Expr 1 i k = kernel19_0_r1 i k := by + fin_cases i + · exact kernel19_0_r1_0_eq k + · exact kernel19_0_r1_1_eq k + · exact kernel19_0_r1_2_eq k + · exact kernel19_0_r1_3_eq k + · exact kernel19_0_r1_4_eq k + · exact kernel19_0_r1_5_eq k + · exact kernel19_0_r1_6_eq k + · exact kernel19_0_r1_7_eq k + · exact kernel19_0_r1_8_eq k + · exact kernel19_0_r1_9_eq k + · exact kernel19_0_r1_10_eq k + · exact kernel19_0_r1_11_eq k + · exact kernel19_0_r1_12_eq k + · exact kernel19_0_r1_13_eq k + · exact kernel19_0_r1_14_eq k + · exact kernel19_0_r1_15_eq k +noncomputable def kernel19_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-2694663),(-2694659)⟩,⟨(-7551080),(-7551077)⟩⟩,⟨⟨(-2692428),(-2692424)⟩,⟨(-7531799),(-7531796)⟩⟩,⟨⟨(-2687940),(-2687935)⟩,⟨(-7493378),(-7493373)⟩⟩,⟨⟨(-2681165),(-2681161)⟩,⟨(-7436096),(-7436093)⟩⟩,⟨⟨(-2672056),(-2672052)⟩,⟨(-7360374),(-7360371)⟩⟩,⟨⟨(-2660551),(-2660547)⟩,⟨(-7266760),(-7266756)⟩⟩,⟨⟨(-2646577),(-2646572)⟩,⟨(-7155926),(-7155921)⟩⟩,⟨⟨(-2630053),(-2630050)⟩,⟨(-7028664),(-7028660)⟩⟩,⟨⟨(-2610891),(-2610888)⟩,⟨(-6885876),(-6885872)⟩⟩,⟨⟨(-2589005),(-2589002)⟩,⟨(-6728559),(-6728555)⟩⟩,⟨⟨(-2564309),(-2564306)⟩,⟨(-6557800),(-6557796)⟩⟩,⟨⟨(-2536723),(-2536720)⟩,⟨(-6374760),(-6374756)⟩⟩,⟨⟨(-2506174),(-2506170)⟩,⟨(-6180663),(-6180660)⟩⟩,⟨⟨(-2472607),(-2472603)⟩,⟨(-5976782),(-5976779)⟩⟩,⟨⟨(-2435977),(-2435973)⟩,⟨(-5764428),(-5764424)⟩⟩,⟨⟨(-2396265),(-2396261)⟩,⟨(-5544931),(-5544926)⟩⟩] +lemma kernel19_0_r2_0_eq : ∀ k : Fin 16, kernel19_0Expr 2 0 k = kernel19_0_r2_0 k := by decide +kernel +noncomputable def kernel19_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-2353468),(-2353465)⟩,⟨(-5319636),(-5319632)⟩⟩,⟨⟨(-2307613),(-2307609)⟩,⟨(-5089878),(-5089874)⟩⟩,⟨⟨(-2258751),(-2258748)⟩,⟨(-4856980),(-4856977)⟩⟩,⟨⟨(-2206958),(-2206955)⟩,⟨(-4622236),(-4622233)⟩⟩,⟨⟨(-2152340),(-2152337)⟩,⟨(-4386899),(-4386896)⟩⟩,⟨⟨(-2095035),(-2095031)⟩,⟨(-4152172),(-4152169)⟩⟩,⟨⟨(-2035200),(-2035195)⟩,⟨(-3919198),(-3919194)⟩⟩,⟨⟨(-1973021),(-1973018)⟩,⟨(-3689053),(-3689049)⟩⟩,⟨⟨(-1908718),(-1908714)⟩,⟨(-3462737),(-3462733)⟩⟩,⟨⟨(-1842518),(-1842515)⟩,⟨(-3241168),(-3241164)⟩⟩,⟨⟨(-1774678),(-1774673)⟩,⟨(-3025181),(-3025176)⟩⟩,⟨⟨(-1705469),(-1705466)⟩,⟨(-2815517),(-2815513)⟩⟩,⟨⟨(-1635176),(-1635172)⟩,⟨(-2612831),(-2612826)⟩⟩,⟨⟨(-1564093),(-1564088)⟩,⟨(-2417681),(-2417676)⟩⟩,⟨⟨(-1492518),(-1492513)⟩,⟨(-2230534),(-2230530)⟩⟩,⟨⟨(-1420756),(-1420751)⟩,⟨(-2051768),(-2051763)⟩⟩] +lemma kernel19_0_r2_1_eq : ∀ k : Fin 16, kernel19_0Expr 2 1 k = kernel19_0_r2_1 k := by decide +kernel +noncomputable def kernel19_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-1349106),(-1349103)⟩,⟨(-1881668),(-1881664)⟩⟩,⟨⟨(-1277868),(-1277865)⟩,⟨(-1720436),(-1720432)⟩⟩,⟨⟨(-1207326),(-1207323)⟩,⟨(-1568195),(-1568192)⟩⟩,⟨⟨(-1137759),(-1137755)⟩,⟨(-1424984),(-1424981)⟩⟩,⟨⟨(-1069426),(-1069423)⟩,⟨(-1290778),(-1290775)⟩⟩,⟨⟨(-1002573),(-1002570)⟩,⟨(-1165483),(-1165479)⟩⟩,⟨⟨(-937424),(-937419)⟩,⟨(-1048944),(-1048940)⟩⟩,⟨⟨(-874181),(-874176)⟩,⟨(-940956),(-940951)⟩⟩,⟨⟨(-813025),(-813022)⟩,⟨(-841265),(-841261)⟩⟩,⟨⟨(-754114),(-754110)⟩,⟨(-749581),(-749578)⟩⟩,⟨⟨(-697578),(-697575)⟩,⟨(-665579),(-665575)⟩⟩,⟨⟨(-643526),(-643522)⟩,⟨(-588905),(-588901)⟩⟩,⟨⟨(-592038),(-592034)⟩,⟨(-519185),(-519181)⟩⟩,⟨⟨(-543174),(-543170)⟩,⟨(-456031),(-456028)⟩⟩,⟨⟨(-496973),(-496969)⟩,⟨(-399047),(-399044)⟩⟩,⟨⟨(-453442),(-453438)⟩,⟨(-347829),(-347825)⟩⟩] +lemma kernel19_0_r2_2_eq : ∀ k : Fin 16, kernel19_0Expr 2 2 k = kernel19_0_r2_2 k := by decide +kernel +noncomputable def kernel19_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-412577),(-412574)⟩,⟨(-301976),(-301972)⟩⟩,⟨⟨(-374352),(-374349)⟩,⟨(-261088),(-261084)⟩⟩,⟨⟨(-338724),(-338720)⟩,⟨(-224777),(-224773)⟩⟩,⟨⟨(-305628),(-305624)⟩,⟨(-192661),(-192658)⟩⟩,⟨⟨(-274998),(-274994)⟩,⟨(-164376),(-164372)⟩⟩,⟨⟨(-246743),(-246740)⟩,⟨(-139570),(-139566)⟩⟩,⟨⟨(-220773),(-220769)⟩,⟨(-117910),(-117906)⟩⟩,⟨⟨(-196983),(-196979)⟩,⟨(-99081),(-99078)⟩⟩,⟨⟨(-175263),(-175258)⟩,⟨(-82790),(-82785)⟩⟩,⟨⟨(-155500),(-155497)⟩,⟨(-68760),(-68756)⟩⟩,⟨⟨(-137580),(-137576)⟩,⟨(-56738),(-56735)⟩⟩,⟨⟨(-121384),(-121380)⟩,⟨(-46487),(-46484)⟩⟩,⟨⟨(-106795),(-106792)⟩,⟨(-37795),(-37792)⟩⟩,⟨⟨(-93695),(-93692)⟩,⟨(-30465),(-30462)⟩⟩,⟨⟨(-81974),(-81970)⟩,⟨(-24320),(-24316)⟩⟩,⟨⟨(-71518),(-71513)⟩,⟨(-19199),(-19194)⟩⟩] +lemma kernel19_0_r2_3_eq : ∀ k : Fin 16, kernel19_0Expr 2 3 k = kernel19_0_r2_3 k := by decide +kernel +noncomputable def kernel19_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-62222),(-62219)⟩,⟨(-14961),(-14957)⟩⟩,⟨⟨(-53985),(-53981)⟩,⟨(-11481),(-11478)⟩⟩,⟨⟨(-46706),(-46703)⟩,⟨(-8644),(-8640)⟩⟩,⟨⟨(-40299),(-40295)⟩,⟨(-6352),(-6348)⟩⟩,⟨⟨(-34675),(-34670)⟩,⟨(-4517),(-4512)⟩⟩,⟨⟨(-29752),(-29749)⟩,⟨(-3065),(-3061)⟩⟩,⟨⟨(-25459),(-25455)⟩,⟨(-1930),(-1926)⟩⟩,⟨⟨(-21724),(-21720)⟩,⟨(-1058),(-1054)⟩⟩,⟨⟨(-18488),(-18484)⟩,⟨(-398),(-394)⟩⟩,⟨⟨(-15691),(-15687)⟩,⟨88,92⟩⟩,⟨⟨(-13281),(-13276)⟩,⟨434,439⟩⟩,⟨⟨(-11211),(-11208)⟩,⟨673,676⟩⟩,⟨⟨(-9438),(-9434)⟩,⟨824,828⟩⟩,⟨⟨(-7924),(-7921)⟩,⟨909,913⟩⟩,⟨⟨(-6635),(-6631)⟩,⟨944,948⟩⟩,⟨⟨(-5541),(-5538)⟩,⟨944,947⟩⟩] +lemma kernel19_0_r2_4_eq : ∀ k : Fin 16, kernel19_0Expr 2 4 k = kernel19_0_r2_4 k := by decide +kernel +noncomputable def kernel19_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-4616),(-4612)⟩,⟨914,918⟩⟩,⟨⟨(-3834),(-3830)⟩,⟨868,872⟩⟩,⟨⟨(-3178),(-3174)⟩,⟨809,813⟩⟩,⟨⟨(-2627),(-2623)⟩,⟨746,749⟩⟩,⟨⟨(-2166),(-2162)⟩,⟨677,681⟩⟩,⟨⟨(-1780),(-1777)⟩,⟨610,613⟩⟩,⟨⟨(-1461),(-1457)⟩,⟨543,547⟩⟩,⟨⟨(-1195),(-1191)⟩,⟨481,484⟩⟩,⟨⟨(-975),(-972)⟩,⟨421,425⟩⟩,⟨⟨(-794),(-791)⟩,⟨369,373⟩⟩,⟨⟨(-644),(-641)⟩,⟨319,323⟩⟩,⟨⟨(-523),(-519)⟩,⟨276,280⟩⟩,⟨⟨(-423),(-419)⟩,⟨237,241⟩⟩,⟨⟨(-341),(-337)⟩,⟨200,204⟩⟩,⟨⟨(-276),(-272)⟩,⟨171,175⟩⟩,⟨⟨(-220),(-216)⟩,⟨145,148⟩⟩] +lemma kernel19_0_r2_5_eq : ∀ k : Fin 16, kernel19_0Expr 2 5 k = kernel19_0_r2_5 k := by decide +kernel +noncomputable def kernel19_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-176),(-173)⟩,⟨122,125⟩⟩,⟨⟨(-143),(-139)⟩,⟨102,106⟩⟩,⟨⟨(-113),(-109)⟩,⟨86,90⟩⟩,⟨⟨(-90),(-87)⟩,⟨71,75⟩⟩,⟨⟨(-73),(-68)⟩,⟨57,62⟩⟩,⟨⟨(-58),(-53)⟩,⟨47,52⟩⟩,⟨⟨(-46),(-43)⟩,⟨40,43⟩⟩,⟨⟨(-37),(-33)⟩,⟨33,37⟩⟩,⟨⟨(-29),(-26)⟩,⟨27,31⟩⟩,⟨⟨(-24),(-20)⟩,⟨22,26⟩⟩,⟨⟨(-18),(-14)⟩,⟨17,20⟩⟩,⟨⟨(-15),(-11)⟩,⟨14,18⟩⟩,⟨⟨(-12),(-8)⟩,⟨11,15⟩⟩,⟨⟨(-9),(-5)⟩,⟨9,13⟩⟩,⟨⟨(-9),(-4)⟩,⟨6,11⟩⟩,⟨⟨(-8),(-4)⟩,⟨5,9⟩⟩] +lemma kernel19_0_r2_6_eq : ∀ k : Fin 16, kernel19_0Expr 2 6 k = kernel19_0_r2_6 k := by decide +kernel +noncomputable def kernel19_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-6),(-2)⟩,⟨3,7⟩⟩,⟨⟨(-5),(-1)⟩,⟨2,6⟩⟩,⟨⟨(-5),(-1)⟩,⟨2,6⟩⟩,⟨⟨(-3),0⟩,⟨1,5⟩⟩,⟨⟨(-3),0⟩,⟨1,5⟩⟩,⟨⟨(-3),2⟩,⟨0,5⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩] +lemma kernel19_0_r2_7_eq : ∀ k : Fin 16, kernel19_0Expr 2 7 k = kernel19_0_r2_7 k := by decide +kernel +noncomputable def kernel19_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-2),2⟩,⟨0,3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel19_0_r2_8_eq : ∀ k : Fin 16, kernel19_0Expr 2 8 k = kernel19_0_r2_8 k := by decide +kernel +noncomputable def kernel19_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel19_0_r2_9_eq : ∀ k : Fin 16, kernel19_0Expr 2 9 k = kernel19_0_r2_9 k := by decide +kernel +noncomputable def kernel19_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel19_0_r2_10_eq : ∀ k : Fin 16, kernel19_0Expr 2 10 k = kernel19_0_r2_10 k := by decide +kernel +noncomputable def kernel19_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r2_11_eq : ∀ k : Fin 16, kernel19_0Expr 2 11 k = kernel19_0_r2_11 k := by decide +kernel +noncomputable def kernel19_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r2_12_eq : ∀ k : Fin 16, kernel19_0Expr 2 12 k = kernel19_0_r2_12 k := by decide +kernel +noncomputable def kernel19_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r2_13_eq : ∀ k : Fin 16, kernel19_0Expr 2 13 k = kernel19_0_r2_13 k := by decide +kernel +noncomputable def kernel19_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r2_14_eq : ∀ k : Fin 16, kernel19_0Expr 2 14 k = kernel19_0_r2_14 k := by decide +kernel +noncomputable def kernel19_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel19_0_r2_15_eq : ∀ k : Fin 16, kernel19_0Expr 2 15 k = kernel19_0_r2_15 k := by decide +kernel +noncomputable def kernel19_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel19_0_r2_0,kernel19_0_r2_1,kernel19_0_r2_2,kernel19_0_r2_3,kernel19_0_r2_4,kernel19_0_r2_5,kernel19_0_r2_6,kernel19_0_r2_7,kernel19_0_r2_8,kernel19_0_r2_9,kernel19_0_r2_10,kernel19_0_r2_11,kernel19_0_r2_12,kernel19_0_r2_13,kernel19_0_r2_14,kernel19_0_r2_15] +lemma kernel19_0_r2_eq (i k : Fin 16) : kernel19_0Expr 2 i k = kernel19_0_r2 i k := by + fin_cases i + · exact kernel19_0_r2_0_eq k + · exact kernel19_0_r2_1_eq k + · exact kernel19_0_r2_2_eq k + · exact kernel19_0_r2_3_eq k + · exact kernel19_0_r2_4_eq k + · exact kernel19_0_r2_5_eq k + · exact kernel19_0_r2_6_eq k + · exact kernel19_0_r2_7_eq k + · exact kernel19_0_r2_8_eq k + · exact kernel19_0_r2_9_eq k + · exact kernel19_0_r2_10_eq k + · exact kernel19_0_r2_11_eq k + · exact kernel19_0_r2_12_eq k + · exact kernel19_0_r2_13_eq k + · exact kernel19_0_r2_14_eq k + · exact kernel19_0_r2_15_eq k +noncomputable def kernel19_0_r3_0 : Fin 16 → CBox := ![⟨⟨161999228357173732,161999228357173738⟩,⟨436041835374095438,436041835374095444⟩⟩,⟨⟨162107580356244960,162107580356244965⟩,⟨435285303100701272,435285303100701277⟩⟩,⟨⟨162321990813710132,162321990813710137⟩,⟨433775304217227606,433775304217227611⟩⟩,⟨⟨162637902212695805,162637902212695810⟩,⟨431517956640982453,431517956640982458⟩⟩,⟨⟨163048551799298276,163048551799298281⟩,⟨428522403693399210,428522403693399215⟩⟩,⟨⟨163545058721947630,163545058721947635⟩,⟨424800773750583829,424800773750583834⟩⟩,⟨⟨164116538421951376,164116538421951383⟩,⟨420368126314144347,420368126314144355⟩⟩,⟨⟨164750242766769401,164750242766769406⟩,⟨415242384410889213,415242384410889218⟩⟩,⟨⟨165431724078026363,165431724078026368⟩,⟨409444253231300538,409444253231300543⟩⟩,⟨⟨166145020891170743,166145020891170748⟩,⟨402997124932996611,402997124932996616⟩⟩,⟨⟨166872862997334615,166872862997334620⟩,⟨395926969568603338,395926969568603343⟩⟩,⟨⟨167596893064301571,167596893064301576⟩,⟨388262212148920742,388262212148920747⟩⟩,⟨⟨168297901916138447,168297901916138452⟩,⟨380033595922762465,380033595922762470⟩⟩,⟨⟨168956074373142468,168956074373142474⟩,⟨371274032044493806,371274032044493811⟩⟩,⟨⟨169551242417967545,169551242417967550⟩,⟨362018435908572452,362018435908572457⟩⟩,⟨⟨170063142362257017,170063142362257022⟩,⟨352303550556125271,352303550556125276⟩⟩] +lemma kernel19_0_r3_0_eq : ∀ k : Fin 16, kernel19_0Expr 3 0 k = kernel19_0_r3_0 k := by decide +kernel +noncomputable def kernel19_0_r3_1 : Fin 16 → CBox := ![⟨⟨170471672642383166,170471672642383171⟩,⟨342167757699954562,342167757699954567⟩⟩,⟨⟨170757148873917185,170757148873917190⟩,⟨331650877068933003,331650877068933008⟩⟩,⟨⟨170900552842517971,170900552842517976⟩,⟨320793954937540519,320793954937540525⟩⟩,⟨⟨170883772203649767,170883772203649772⟩,⟨309639042877855193,309639042877855198⟩⟩,⟨⟨170689827803840903,170689827803840907⟩,⟨298228967945768816,298228967945768820⟩⟩,⟨⟨170303085720304769,170303085720304773⟩,⟨286607095686382944,286607095686382948⟩⟩,⟨⟨169709451341192669,169709451341192674⟩,⟨274817087511079182,274817087511079187⟩⟩,⟨⟨168896543072394590,168896543072394595⟩,⟨262902654156185514,262902654156185518⟩⟩,⟨⟨167853843554861603,167853843554861607⟩,⟨250907307076046349,250907307076046353⟩⟩,⟨⟨166572826604505292,166572826604505295⟩,⟨238874109747365124,238874109747365127⟩⟩,⟨⟨165047058439904796,165047058439904801⟩,⟨226845430962910319,226845430962910324⟩⟩,⟨⟨163272272135916914,163272272135916919⟩,⟨214862702267426469,214862702267426474⟩⟩,⟨⟨161246414628045461,161246414628045466⟩,⟨202966181733726349,202966181733726354⟩⟩,⟨⟨158969665986992368,158969665986992373⟩,⟨191194726289897463,191194726289897467⟩⟩,⟨⟨156444431078901984,156444431078901988⟩,⟨179585574787437226,179585574787437230⟩⟩,⟨⟨153675304118057753,153675304118057757⟩,⟨168174143943768984,168174143943768987⟩⟩] +lemma kernel19_0_r3_1_eq : ∀ k : Fin 16, kernel19_0Expr 3 1 k = kernel19_0_r3_1 k := by decide +kernel +noncomputable def kernel19_0_r3_2 : Fin 16 → CBox := ![⟨⟨150669006998868697,150669006998868701⟩,⟨156993839200593470,156993839200593473⟩⟩,⟨⟨147434302656719998,147434302656720001⟩,⟨146075882412310644,146075882412310647⟩⟩,⟨⟨143981885046761732,143981885046761737⟩,⟨135449158117529162,135449158117529167⟩⟩,⟨⟨140324247640471130,140324247640471133⟩,⟨125140079953486614,125140079953486617⟩⟩,⟨⟨136475532616851580,136475532616851584⟩,⟨115172478550816481,115172478550816485⟩⟩,⟨⟨132451363164041358,132451363164041362⟩,⟨105567511998007640,105567511998007645⟩⟩,⟨⟨128268661504214274,128268661504214278⟩,⟨96343599695231030,96343599695231034⟩⟩,⟨⟨123945455407062313,123945455407062317⟩,⟨87516380130618565,87516380130618569⟩⟩,⟨⟨119500676062798729,119500676062798732⟩,⟨79098692813667828,79098692813667831⟩⟩,⟨⟨114953950243338846,114953950243338850⟩,⟨71100584295624994,71100584295624998⟩⟩,⟨⟨110325389689846506,110325389689846512⟩,⟨63529337901068802,63529337901068807⟩⟩,⟨⟨105635380626834323,105635380626834326⟩,⟨56389526494137273,56389526494137276⟩⟩,⟨⟨100904376219032347,100904376219032351⟩,⟨49683087312485861,49683087312485864⟩⟩,⟨⟨96152694659710576,96152694659710580⟩,⟨43409417627509976,43409417627509979⟩⟩,⟨⟨91400325411277867,91400325411277870⟩,⟨37565489735639162,37565489735639166⟩⟩,⟨⟨86666745914733232,86666745914733237⟩,⟨32145983557193674,32145983557193679⟩⟩] +lemma kernel19_0_r3_2_eq : ∀ k : Fin 16, kernel19_0Expr 3 2 k = kernel19_0_r3_2 k := by decide +kernel +noncomputable def kernel19_0_r3_3 : Fin 16 → CBox := ![⟨⟨81970750848499837,81970750848499841⟩,⟨27143434920406007,27143434920406011⟩⟩,⟨⟨77330295754440067,77330295754440070⟩,⟨22548397442120712,22548397442120715⟩⟩,⟨⟨72762356564953930,72762356564953933⟩,⟨18349615786043501,18349615786043504⟩⟩,⟨⟨68282806265807271,68282806265807276⟩,⟨14534207986088004,14534207986088008⟩⟩,⟨⟨63906309620676092,63906309620676095⟩,⟨11087854467429764,11087854467429767⟩⟩,⟨⟨59646236571300897,59646236571300901⟩,⟨7994991381566204,7994991381566209⟩⟩,⟨⟨55514594617478828,55514594617478831⟩,⟨5239005893431306,5239005893431310⟩⟩,⟨⟨51521980179499336,51521980179499339⟩,⟨2802431117076695,2802431117076698⟩⟩,⟨⟨47677548657312354,47677548657312357⟩,⟨667138489526770,667138489526773⟩⟩,⟨⟨43989002630504007,43989002630504011⟩,⟨(-1185474502600987),(-1185474502600983)⟩⟩,⟨⟨40462597395287492,40462597395287495⟩,⟨(-2774303175576873),(-2774303175576870)⟩⟩,⟨⟨37103162812809449,37103162812809452⟩,⟨(-4118362833723604),(-4118362833723601)⟩⟩,⟨⟨33914140250051568,33914140250051572⟩,⟨(-5236625842024784),(-5236625842024780)⟩⟩,⟨⟨30897633232674077,30897633232674080⟩,⟨(-6147869926052511),(-6147869926052508)⟩⟩,⟨⟨28054470299757743,28054470299757748⟩,⟨(-6870538812779495),(-6870538812779491)⟩⟩,⟨⟨25384278454264399,25384278454264402⟩,⟨(-7422616092789544),(-7422616092789541)⟩⟩] +lemma kernel19_0_r3_3_eq : ∀ k : Fin 16, kernel19_0Expr 3 3 k = kernel19_0_r3_3 k := by decide +kernel +noncomputable def kernel19_0_r3_4 : Fin 16 → CBox := ![⟨⟨22885565540135698,22885565540135701⟩,⟨(-7821512949226812),(-7821512949226809)⟩⟩,⟨⟨20555809846577427,20555809846577430⟩,⟨(-8083970165979958),(-8083970165979955)⟩⟩,⟨⟨18391555240882656,18391555240882660⟩,⟨(-8225974601269712),(-8225974601269707)⟩⟩,⟨⟨16388510161206314,16388510161206317⟩,⟨(-8262690096835738),(-8262690096835735)⟩⟩,⟨⟨14541648857590354,14541648857590357⟩,⟨(-8208402590719841),(-8208402590719838)⟩⟩,⟨⟨12845313350410967,12845313350410971⟩,⟨(-8076479016157970),(-8076479016157966)⟩⟩,⟨⟨11293314677109432,11293314677109437⟩,⟨(-7879339402744705),(-7879339402744700)⟩⟩,⟨⟨9879032117175594,9879032117175597⟩,⟨(-7628441450695354),(-7628441450695351)⟩⟩,⟨⟨8595509218337874,8595509218337878⟩,⟨(-7334276726019962),(-7334276726019957)⟩⟩,⟨⟨7435545590188279,7435545590188285⟩,⟨(-7006377524503981),(-7006377524503976)⟩⟩,⟨⟨6391783581486013,6391783581486017⟩,⟨(-6653333375789597),(-6653333375789594)⟩⟩,⟨⟨5456789110708624,5456789110708627⟩,⟨(-6282816105291606),(-6282816105291603)⟩⟩,⟨⟨4623126072814970,4623126072814973⟩,⟨(-5901612340419663),(-5901612340419660)⟩⟩,⟨⟨3883423895661129,3883423895661132⟩,⟨(-5515662337457797),(-5515662337457794)⟩⟩,⟨⟨3230437964383028,3230437964383031⟩,⟨(-5130104014958796),(-5130104014958793)⟩⟩,⟨⟨2657102768983722,2657102768983725⟩,⟨(-4749321106837242),(-4749321106837239)⟩⟩] +lemma kernel19_0_r3_4_eq : ∀ k : Fin 16, kernel19_0Expr 3 4 k = kernel19_0_r3_4 k := by decide +kernel +noncomputable def kernel19_0_r3_5 : Fin 16 → CBox := ![⟨⟨2156577757363985,2156577757363988⟩,⟨(-4376994391453656),(-4376994391453653)⟩⟩,⟨⟨1722285991521982,1722285991521985⟩,⟨(-4016155009672841),(-4016155009672838)⟩⟩,⟨⟨1347945807420823,1347945807420827⟩,⟨(-3669238952853877),(-3669238952853874)⟩⟩,⟨⟨1027595768264813,1027595768264816⟩,⟨(-3338141878652836),(-3338141878652832)⟩⟩,⟨⟨755613276188117,755613276188121⟩,⟨(-3024273496079745),(-3024273496079741)⟩⟩,⟨⟨526727268540498,526727268540501⟩,⟨(-2728610849210528),(-2728610849210525)⟩⟩,⟨⟨336025472266025,336025472266028⟩,⟨(-2451749919194183),(-2451749919194180)⟩⟩,⟨⟨178956723804651,178956723804654⟩,⟨(-2193955054755587),(-2193955054755584)⟩⟩,⟨⟨51328883235814,51328883235818⟩,⟨(-1955205830504445),(-1955205830504442)⟩⟩,⟨⟨(-50697119040348),(-50697119040344)⟩,⟨(-1735241018462460),(-1735241018462456)⟩⟩,⟨⟨(-130616565837252),(-130616565837249)⟩,⟨(-1533599439982853),(-1533599439982850)⟩⟩,⟨⟨(-191593040156535),(-191593040156530)⟩,⟨(-1349657541563070),(-1349657541563064)⟩⟩,⟨⟨(-236472807448515),(-236472807448511)⟩,⟨(-1182663608083134),(-1182663608083131)⟩⟩,⟨⟨(-267801010463461),(-267801010463458)⟩,⟨(-1031768590110317),(-1031768590110314)⟩⟩,⟨⟨(-287839224988796),(-287839224988793)⟩,⟨(-896053577686715),(-896053577686712)⟩⟩,⟨⟨(-298583960011286),(-298583960011283)⟩,⟨(-774554001257355),(-774554001257352)⟩⟩] +lemma kernel19_0_r3_5_eq : ∀ k : Fin 16, kernel19_0Expr 3 5 k = kernel19_0_r3_5 k := by decide +kernel +noncomputable def kernel19_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-301785724122743),(-301785724122740)⟩,⟨(-666280681085137),(-666280681085133)⟩⟩,⟨⟨(-298968320165719),(-298968320165715)⟩,⟨(-570237879783637),(-570237879783633)⟩⟩,⟨⟨(-291448071153548),(-291448071153543)⟩,⟨(-485438538769040),(-485438538769036)⟩⟩,⟨⟨(-280352721469466),(-280352721469463)⟩,⟨(-410916898895414),(-410916898895411)⟩⟩,⟨⟨(-266639797444935),(-266639797444932)⟩,⟨(-345738718793675),(-345738718793671)⟩⟩,⟨⟨(-251114249953974),(-251114249953970)⟩,⟨(-289009312053759),(-289009312053756)⟩⟩,⟨⟨(-234445238079093),(-234445238079090)⟩,⟨(-239879626989014),(-239879626989011)⟩⟩,⟨⟨(-217181946767369),(-217181946767365)⟩,⟨(-197550590944575),(-197550590944570)⟩⟩,⟨⟨(-199768362380408),(-199768362380403)⟩,⟨(-161275935608420),(-161275935608414)⟩⟩,⟨⟨(-182556957935427),(-182556957935424)⟩,⟨(-130363711196279),(-130363711196276)⟩⟩,⟨⟨(-165821264520191),(-165821264520186)⟩,⟨(-104176686327852),(-104176686327848)⟩⟩,⟨⟨(-149767326813772),(-149767326813769)⟩,⟨(-82131817475574),(-82131817475570)⟩⟩,⟨⟨(-134544058904727),(-134544058904724)⟩,⟨(-63698957588358),(-63698957588355)⟩⟩,⟨⟨(-120252531778545),(-120252531778542)⟩,⟨(-48398958360596),(-48398958360592)⟩⟩,⟨⟨(-106954236109542),(-106954236109539)⟩,⟨(-35801305066434),(-35801305066431)⟩⟩,⟨⟨(-94678373540173),(-94678373540168)⟩,⟨(-25521407288487),(-25521407288483)⟩⟩] +lemma kernel19_0_r3_6_eq : ∀ k : Fin 16, kernel19_0Expr 3 6 k = kernel19_0_r3_6 k := by decide +kernel +noncomputable def kernel19_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-83428236694587),(-83428236694584)⟩,⟨(-17217653559307),(-17217653559304)⟩⟩,⟨⟨(-73186743003035),(-73186743003032)⟩,⟨(-10588323167216),(-10588323167213)⟩⟩,⟨⟨(-63921190269923),(-63921190269920)⟩,⟨(-5368434365523),(-5368434365520)⟩⟩,⟨⟨(-55587303063277),(-55587303063274)⟩,⟨(-1326595125604),(-1326595125601)⟩⟩,⟨⟨(-48132638695312),(-48132638695309)⟩,⟨1738089496927,1738089496930⟩⟩,⟨⟨(-41499420050568),(-41499420050564)⟩,⟨3999010285748,3999010285751⟩⟩,⟨⟨(-35626860033552),(-35626860033549)⟩,⟨5604913817083,5604913817086⟩⟩,⟨⟨(-30453039167913),(-30453039167910)⟩,⟨6682604881094,6682604881097⟩⟩,⟨⟨(-25916394080138),(-25916394080135)⟩,⟨7339474390998,7339474391001⟩⟩,⟨⟨(-21956870417310),(-21956870417307)⟩,⟨7665842306690,7665842306693⟩⟩,⟨⟨(-18516789333821),(-18516789333817)⟩,⟨7737110592041,7737110592046⟩⟩,⟨⟨(-15541472166953),(-15541472166949)⟩,⟨7615725774315,7615725774319⟩⟩,⟨⟨(-12979663416443),(-12979663416439)⟩,⟨7352954359941,7352954359944⟩⟩,⟨⟨(-10783787738098),(-10783787738094)⟩,⟨6990477268030,6990477268033⟩⟩,⟨⟨(-8910072428021),(-8910072428018)⟩,⟨6561811657752,6561811657755⟩⟩,⟨⟨(-7318562866242),(-7318562866239)⟩,⟨6093570134291,6093570134294⟩⟩] +lemma kernel19_0_r3_7_eq : ∀ k : Fin 16, kernel19_0Expr 3 7 k = kernel19_0_r3_7 k := by decide +kernel +noncomputable def kernel19_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-5973054645817),(-5973054645813)⟩,⟨5606568403855,5606568403859⟩⟩,⟨⟨(-4840962661837),(-4840962661834)⟩,⟨5116793090499,5116793090502⟩⟩,⟨⟨(-3893144288513),(-3893144288510)⟩,⟨4636241700530,4636241700534⟩⟩,⟨⟨(-3103690936804),(-3103690936800)⟩,⟨4173646692060,4173646692065⟩⟩,⟨⟨(-2449699756532),(-2449699756528)⟩,⟨3735095339180,3735095339184⟩⟩,⟨⟨(-1911035016615),(-1911035016612)⟩,⟨3324556627394,3324556627397⟩⟩,⟨⟨(-1470086750508),(-1470086750505)⟩,⟨2944325826870,2944325826873⟩⟩,⟨⟨(-1111532573681),(-1111532573678)⟩,⟨2595396704509,2595396704512⟩⟩,⟨⟨(-822107145765),(-822107145761)⟩,⟨2277770589607,2277770589612⟩⟩,⟨⟨(-590382540402),(-590382540398)⟩,⟨1990710730426,1990710730429⟩⟩,⟨⟨(-406561778648),(-406561778645)⟩,⟨1732949593879,1732949593882⟩⟩,⟨⟨(-262286954946),(-262286954942)⟩,⟨1502855987014,1502855987018⟩⟩,⟨⟨(-150462716660),(-150462716657)⟩,⟨1298568131455,1298568131458⟩⟩,⟨⟨(-65095328442),(-65095328439)⟩,⟨1118098111491,1118098111495⟩⟩,⟨⟨(-1147141947),(-1147141942)⟩,⟨959412450775,959412450781⟩⟩,⟨⟨45594018110,45594018114⟩,⟨820492956341,820492956344⟩⟩] +lemma kernel19_0_r3_8_eq : ∀ k : Fin 16, kernel19_0Expr 3 8 k = kernel19_0_r3_8 k := by decide +kernel +noncomputable def kernel19_0_r3_9 : Fin 16 → CBox := ![⟨⟨78631265018,78631265022⟩,⟨699381404843,699381404847⟩⟩,⟨⟨100861725868,100861725872⟩,⟨594211135204,594211135208⟩⟩,⟨⟨114667246172,114667246175⟩,⟨503228153678,503228153682⟩⟩,⟨⟨121993737817,121993737822⟩,⟨424803950081,424803950086⟩⟩,⟨⟨124420198904,124420198907⟩,⟨357441864935,357441864938⟩⟩,⟨⟨123218420050,123218420053⟩,⟨299778533519,299778533522⟩⟩,⟨⟨119404357061,119404357065⟩,⟨250581660885,250581660889⟩⟩,⟨⟨113782100136,113782100142⟩,⟨208745147899,208745147904⟩⟩,⟨⟨106981310107,106981310111⟩,⟨173282388998,173282389002⟩⟩,⟨⟨99488926406,99488926409⟩,⟨143318393465,143318393468⟩⟩,⟨⟨91675882708,91675882711⟩,⟨118081240552,118081240555⟩⟩,⟨⟨83819496912,83819496917⟩,⟨96893260959,96893260963⟩⟩,⟨⟨76122134232,76122134237⟩,⟨79162240288,79162240292⟩⟩,⟨⟨68726676892,68726676895⟩,⟨64372860895,64372860899⟩⟩,⟨⟨61729272391,61729272394⟩,⟨52078534812,52078534815⟩⟩,⟨⟨55189774966,55189774970⟩,⟨41893729478,41893729481⟩⟩] +lemma kernel19_0_r3_9_eq : ∀ k : Fin 16, kernel19_0Expr 3 9 k = kernel19_0_r3_9 k := by decide +kernel +noncomputable def kernel19_0_r3_10 : Fin 16 → CBox := ![⟨⟨49140242134,49140242137⟩,⟨33486848083,33486848086⟩⟩,⟨⟨43591800337,43591800340⟩,⟨26573695347,26573695350⟩⟩,⟨⟨38540150447,38540150451⟩,⟨20911536149,20911536152⟩⟩,⟨⟨33969945312,33969945317⟩,⟨16293737060,16293737064⟩⟩,⟨⟨29858237316,29858237319⟩,⟨12544968450,12544968454⟩⟩,⟨⟨26177163836,26177163840⟩,⟨9516936340,9516936344⟩⟩,⟨⟨22896012177,22896012183⟩,⟨7084607899,7084607905⟩⟩,⟨⟨19982782701,19982782704⟩,⟨5142891443,5142891446⟩⟩,⟨⟨17405349188,17405349191⟩,⟨3603730775,3603730779⟩⟩,⟨⟨15132298591,15132298596⟩,⟨2393573950,2393573955⟩⟩,⟨⟨13133517857,13133517860⟩,⟨1451177748,1451177751⟩⟩,⟨⟨11380583335,11380583338⟩,⟨725711137,725711140⟩⟩,⟨⟨9846997995,9846998001⟩,⟨175123354,175123359⟩⟩,⟨⟨8508312955,8508312961⟩,⟨(-235255130),(-235255124)⟩⟩,⟨⟨7342162711,7342162715⟩,⟨(-533907788),(-533907785)⟩⟩,⟨⟨6328237428,6328237433⟩,⟨(-744149561),(-744149557)⟩⟩] +lemma kernel19_0_r3_10_eq : ∀ k : Fin 16, kernel19_0Expr 3 10 k = kernel19_0_r3_10 k := by decide +kernel +noncomputable def kernel19_0_r3_11 : Fin 16 → CBox := ![⟨⟨5448210778,5448210781⟩,⟨(-884990274),(-884990271)⟩⟩,⟨⟨4685637697,4685637701⟩,⟨(-971864986),(-971864983)⟩⟩,⟨⟨4025833270,4025833273⟩,⟨(-1017249810),(-1017249806)⟩⟩,⟨⟨3455741159,3455741163⟩,⟨(-1031179574),(-1031179570)⟩⟩,⟨⟨2963798010,2963798013⟩,⟨(-1021681673),(-1021681670)⟩⟩,⟨⟨2539798417,2539798420⟩,⟨(-995138560),(-995138557)⟩⟩,⟨⟨2174763839,2174763845⟩,⟨(-956589707),(-956589701)⟩⟩,⟨⟨1860817675,1860817680⟩,⟨(-909982394),(-909982390)⟩⟩,⟨⟨1591068001,1591068005⟩,⟨(-858379352),(-858379348)⟩⟩,⟨⟨1359498800,1359498804⟩,⟨(-804130139),(-804130135)⟩⟩,⟨⟨1160870051,1160870055⟩,⟨(-749012147),(-749012143)⟩⟩,⟨⟨990626739,990626743⟩,⟨(-694346225),(-694346222)⟩⟩,⟨⟨844816550,844816554⟩,⟨(-641091160),(-641091157)⟩⟩,⟨⟨720015895,720015901⟩,⟨(-589920610),(-589920604)⟩⟩,⟨⟨613263784,613263788⟩,⟨(-541285489),(-541285485)⟩⟩,⟨⟨522002960,522002964⟩,⟨(-495464378),(-495464374)⟩⟩] +lemma kernel19_0_r3_11_eq : ∀ k : Fin 16, kernel19_0Expr 3 11 k = kernel19_0_r3_11 k := by decide +kernel +noncomputable def kernel19_0_r3_12 : Fin 16 → CBox := ![⟨⟨444027764,444027768⟩,⟨(-452604025),(-452604021)⟩⟩,⟨⟨377438086,377438089⟩,⟨(-412751780),(-412751777)⟩⟩,⟨⟨320598875,320598879⟩,⟨(-375881378),(-375881375)⟩⟩,⟨⟨272104601,272104605⟩,⟨(-341913348),(-341913345)⟩⟩,⟨⟨230748182,230748185⟩,⟨(-310731017),(-310731014)⟩⟩,⟨⟨195493863,195493867⟩,⟨(-282192995),(-282192991)⟩⟩,⟨⟨165453606,165453610⟩,⟨(-256142781),(-256142776)⟩⟩,⟨⟨139866585,139866590⟩,⟨(-232416107),(-232416102)⟩⟩,⟨⟨118081398,118081401⟩,⟨(-210846428),(-210846425)⟩⟩,⟨⟨99540664,99540668⟩,⟨(-191268992),(-191268989)⟩⟩,⟨⟨83767727,83767730⟩,⟨(-173523745),(-173523742)⟩⟩,⟨⟨70355171,70355175⟩,⟨(-157457362),(-157457358)⟩⟩,⟨⟨58954917,58954921⟩,⟨(-142924568),(-142924564)⟩⟩,⟨⟨49269713,49269716⟩,⟨(-129788942),(-129788938)⟩⟩,⟨⟨41045800,41045804⟩,⟨(-117923304),(-117923300)⟩⟩,⟨⟨34066635,34066638⟩,⟨(-107209809),(-107209806)⟩⟩] +lemma kernel19_0_r3_12_eq : ∀ k : Fin 16, kernel19_0Expr 3 12 k = kernel19_0_r3_12 k := by decide +kernel +noncomputable def kernel19_0_r3_13 : Fin 16 → CBox := ![⟨⟨28147472,28147475⟩,⟨(-97539818),(-97539815)⟩⟩,⟨⟨23130753,23130757⟩,⟨(-88813605),(-88813601)⟩⟩,⟨⟨18882134,18882138⟩,⟨(-80939966),(-80939963)⟩⟩,⟨⟨15287085,15287089⟩,⟨(-73835753),(-73835750)⟩⟩,⟨⟨12247997,12248001⟩,⟨(-67425358),(-67425354)⟩⟩,⟨⟨9681689,9681693⟩,⟨(-61640201),(-61640197)⟩⟩,⟨⟨7517293,7517297⟩,⟨(-56418195),(-56418192)⟩⟩,⟨⟨5694436,5694439⟩,⟨(-51703221),(-51703218)⟩⟩,⟨⟨4161692,4161696⟩,⟨(-47444645),(-47444642)⟩⟩,⟨⟨2875271,2875275⟩,⟨(-43596824),(-43596821)⟩⟩,⟨⟨1797878,1797882⟩,⟨(-40118670),(-40118666)⟩⟩,⟨⟨897760,897763⟩,⟨(-36973218),(-36973214)⟩⟩,⟨⟨147884,147888⟩,⟨(-34127246),(-34127242)⟩⟩,⟨⟨(-474757),(-474753)⟩,⟨(-31550914),(-31550911)⟩⟩,⟨⟨(-989753),(-989749)⟩,⟨(-29217432),(-29217428)⟩⟩,⟨⟨(-1413763),(-1413760)⟩,⟨(-27102758),(-27102754)⟩⟩] +lemma kernel19_0_r3_13_eq : ∀ k : Fin 16, kernel19_0Expr 3 13 k = kernel19_0_r3_13 k := by decide +kernel +noncomputable def kernel19_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-1760973),(-1760969)⟩,⟨(-25185320),(-25185316)⟩⟩,⟨⟨(-2043443),(-2043439)⟩,⟨(-23445776),(-23445772)⟩⟩,⟨⟨(-2271431),(-2271427)⟩,⟨(-21866777),(-21866774)⟩⟩,⟨⟨(-2453663),(-2453659)⟩,⟨(-20432770),(-20432765)⟩⟩,⟨⟨(-2597554),(-2597550)⟩,⟨(-19129809),(-19129806)⟩⟩,⟨⟨(-2709404),(-2709400)⟩,⟨(-17945393),(-17945389)⟩⟩,⟨⟨(-2794570),(-2794566)⟩,⟨(-16868314),(-16868310)⟩⟩,⟨⟨(-2857597),(-2857593)⟩,⟨(-15888522),(-15888518)⟩⟩,⟨⟨(-2902346),(-2902341)⟩,⟨(-14997009),(-14997004)⟩⟩,⟨⟨(-2932087),(-2932084)⟩,⟨(-14185698),(-14185694)⟩⟩,⟨⟨(-2949601),(-2949598)⟩,⟨(-13447350),(-13447346)⟩⟩,⟨⟨(-2957239),(-2957236)⟩,⟨(-12775472),(-12775469)⟩⟩,⟨⟨(-2956992),(-2956988)⟩,⟨(-12164252),(-12164249)⟩⟩,⟨⟨(-2950547),(-2950543)⟩,⟨(-11608472),(-11608468)⟩⟩,⟨⟨(-2939327),(-2939324)⟩,⟨(-11103469),(-11103465)⟩⟩,⟨⟨(-2924541),(-2924537)⟩,⟨(-10645062),(-10645058)⟩⟩] +lemma kernel19_0_r3_14_eq : ∀ k : Fin 16, kernel19_0Expr 3 14 k = kernel19_0_r3_14 k := by decide +kernel +noncomputable def kernel19_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-2907198),(-2907195)⟩,⟨(-10229510),(-10229506)⟩⟩,⟨⟨(-2888157),(-2888154)⟩,⟨(-9853476),(-9853473)⟩⟩,⟨⟨(-2868136),(-2868132)⟩,⟨(-9513978),(-9513975)⟩⟩,⟨⟨(-2847741),(-2847736)⟩,⟨(-9208363),(-9208358)⟩⟩,⟨⟨(-2827475),(-2827471)⟩,⟨(-8934269),(-8934265)⟩⟩,⟨⟨(-2807765),(-2807762)⟩,⟨(-8689607),(-8689604)⟩⟩,⟨⟨(-2788966),(-2788962)⟩,⟨(-8472535),(-8472531)⟩⟩,⟨⟨(-2771367),(-2771362)⟩,⟨(-8281436),(-8281431)⟩⟩,⟨⟨(-2755213),(-2755209)⟩,⟨(-8114895),(-8114891)⟩⟩,⟨⟨(-2740701),(-2740697)⟩,⟨(-7971699),(-7971696)⟩⟩,⟨⟨(-2727997),(-2727993)⟩,⟨(-7850809),(-7850805)⟩⟩,⟨⟨(-2717229),(-2717226)⟩,⟨(-7751355),(-7751352)⟩⟩,⟨⟨(-2708500),(-2708496)⟩,⟨(-7672626),(-7672622)⟩⟩,⟨⟨(-2701887),(-2701883)⟩,⟨(-7614062),(-7614058)⟩⟩,⟨⟨(-2697449),(-2697445)⟩,⟨(-7575248),(-7575244)⟩⟩,⟨⟨(-2695221),(-2695217)⟩,⟨(-7555907),(-7555903)⟩⟩] +lemma kernel19_0_r3_15_eq : ∀ k : Fin 16, kernel19_0Expr 3 15 k = kernel19_0_r3_15 k := by decide +kernel +noncomputable def kernel19_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel19_0_r3_0,kernel19_0_r3_1,kernel19_0_r3_2,kernel19_0_r3_3,kernel19_0_r3_4,kernel19_0_r3_5,kernel19_0_r3_6,kernel19_0_r3_7,kernel19_0_r3_8,kernel19_0_r3_9,kernel19_0_r3_10,kernel19_0_r3_11,kernel19_0_r3_12,kernel19_0_r3_13,kernel19_0_r3_14,kernel19_0_r3_15] +lemma kernel19_0_r3_eq (i k : Fin 16) : kernel19_0Expr 3 i k = kernel19_0_r3 i k := by + fin_cases i + · exact kernel19_0_r3_0_eq k + · exact kernel19_0_r3_1_eq k + · exact kernel19_0_r3_2_eq k + · exact kernel19_0_r3_3_eq k + · exact kernel19_0_r3_4_eq k + · exact kernel19_0_r3_5_eq k + · exact kernel19_0_r3_6_eq k + · exact kernel19_0_r3_7_eq k + · exact kernel19_0_r3_8_eq k + · exact kernel19_0_r3_9_eq k + · exact kernel19_0_r3_10_eq k + · exact kernel19_0_r3_11_eq k + · exact kernel19_0_r3_12_eq k + · exact kernel19_0_r3_13_eq k + · exact kernel19_0_r3_14_eq k + · exact kernel19_0_r3_15_eq k +noncomputable def kernel19_0_r4_0 : Fin 16 → CBox := ![⟨⟨875539070692218901336054,875539070692219037374286⟩,⟨(-1716896260299863140986895),(-1716896260299863004954330)⟩⟩,⟨⟨873487118227198854202406,873487118227198990123322⟩,⟨(-1715996323431502063984574),(-1715996323431501928069288)⟩⟩,⟨⟨869390927935918430522724,869390927935918566209046⟩,⟨(-1714194344709481941442554),(-1714194344709481805761786)⟩⟩,⟨⟨863265900489437380866745,863265900489437516201767⟩,⟨(-1711486153476345954303334),(-1711486153476345818973756)⟩⟩,⟨⟨855135065359794556949200,855135065359794691817084⟩,⟨(-1707865591606595718645071),(-1707865591606595583782484)⟩⟩,⟨⟨845028994930178477573075,845028994930178611859121⟩,⟨(-1703324629761102839166035),(-1703324629761102704885101)⟩⟩,⟨⟨832985689903942951051440,832985689903943084642373⟩,⟨(-1697853520439871268344024),(-1697853520439871134757985)⟩⟩,⟨⟨819050435970023628691692,819050435970023761475935⟩,⟨(-1691440986180810445277011),(-1691440986180810312497410)⟩⟩,⟨⟨803275631694473945671523,803275631694474077539443⟩,⟨(-1684074440866205230854655),(-1684074440866205098991095)⟩⟩,⟨⟨785720587634461583781819,785720587634461714626029⟩,⟨(-1675740241730521130831546),(-1675740241730520999991381)⟩⟩,⟨⟨766451296714333668279249,766451296714333797994792⟩,⟨(-1666423969316492501421498),(-1666423969316492371709655)⟩⟩,⟨⟨745540175965087075811287,745540175965087204295972⟩,⟨(-1656110732304444074040946),(-1656110732304443945559590)⟩⟩,⟨⟨723065779810172375146106,723065779810172502300596⟩,⟨(-1644785493845712738935021),(-1644785493845712611783463)⟩⟩,⟨⟨699112485182965657856728,699112485182965783584969⟩,⟨(-1632433415767946142415325),(-1632433415767946016689595)⟩⟩,⟨⟨673770148884926126663685,673770148884926250872846⟩,⟨(-1619040216790866888741562),(-1619040216790866764534467)⟩⟩,⟨⟨647133737738373824525701,647133737738373947126692⟩,⟨(-1604592540698515627411439),(-1604592540698515504812050)⟩⟩] +lemma kernel19_0_r4_0_eq : ∀ k : Fin 16, kernel19_0Expr 4 0 k = kernel19_0_r4_0 k := by decide +kernel +noncomputable def kernel19_0_r4_1 : Fin 16 → CBox := ![⟨⟨619302932253401842770757,619302932253401963677995⟩,⟨(-1589078330260499858440200),(-1589078330260499737534084)⟩⟩,⟨⟨590381704713580695709833,590381704713580814841969⟩,⟨(-1572487202582587121599768),(-1572487202582587002468258)⟩⟩,⟨⟨560477872788192077437824,560477872788192194717230⟩,⟨(-1554810821497996817945402),(-1554810821497996700666114)⟩⟩,⟨⟨529702629997603661596816,529702629997603776950470⟩,⟨(-1536043262586529045750532),(-1536043262586528930396476)⟩⟩,⟨⟨498170054590433556682567,498170054590433670041273⟩,⟨(-1516181366430408753728487),(-1516181366430408640368853)⟩⟩,⟨⟨465996598633261523411119,465996598633261634710769⟩,⟨(-1495225075784192859819728),(-1495225075784192748518619)⟩⟩,⟨⟨433300559362316619409955,433300559362316728590308⟩,⟨(-1473177752451612574371238),(-1473177752451612465188892)⟩⟩,⟨⟨400201535097934648119633,400201535097934755125780⟩,⟨(-1450046469824649598241451),(-1450046469824649491232776)⟩⟩,⟨⟨366819868272454839413776,366819868272454944194597⟩,⟨(-1425842277248812949865452),(-1425842277248812845081572)⟩⟩,⟨⟨333276078366196097229704,333276078366196199739898⟩,⟨(-1400580432632303264828475),(-1400580432632303162314694)⟩⟩,⟨⟨299690287779636779642831,299690287779636879840759⟩,⟨(-1374280600013787645369287),(-1374280600013787545167252)⟩⟩,⟨⟨266181643888251254268412,266181643888251352118321⟩,⟨(-1346967009141568562756807),(-1346967009141568464902280)⟩⟩,⟨⟨232867740724963558165750,232867740724963653635302⟩,⟨(-1318668574493164788685485),(-1318668574493164693210816)⟩⟩,⟨⟨199864043909282052525939,199864043909282145589908⟩,⟨(-1289418971575328974270651),(-1289418971575328881201084)⟩⟩,⟨⟨167283322587473036669122,167283322587473127306122⟩,⟨(-1259256668786367348762012),(-1259256668786367258118954)⟩⟩,⟨⟨135235092260474160957994,135235092260474249151410⟩,⟨(-1228224913590853366989275),(-1228224913590853278789361)⟩⟩] +lemma kernel19_0_r4_1_eq : ∀ k : Fin 16, kernel19_0Expr 4 1 k = kernel19_0_r4_1 k := by decide +kernel +noncomputable def kernel19_0_r4_2 : Fin 16 → CBox := ![⟨⟨103825072451849916611383,103825072451850002347285⟩,⟨(-1196371672246514827914704),(-1196371672246514742171881)⟩⟩,⟨⟨73154663203596586773845,73154663203596670045112⟩,⟨(-1163749522828868718738331),(-1163749522828868635459743)⟩⟩,⟨⟨43320444380172059747945,43320444380172140549725⟩,⟨(-1130415501815350595694283),(-1130415501815350514884806)⟩⟩,⟨⟨14413701708502241571310,14413701708502319911620⟩,⟨(-1096430905011196278089004),(-1096430905011196199740643)⟩⟩,⟨⟨(-13480016617704327504167),(-13480016617704251620146)⟩,⟨(-1061861044117906971178727),(-1061861044117906895286330)⟩⟩,⟨⟨(-40281309088119932633635),(-40281309088119859195891)⟩,⟨(-1026774960755333571430442),(-1026774960755333497984023)⟩⟩,⟨⟨(-65917292294196536857237),(-65917292294196465854504)⟩,⟨(-991245100243754195818059),(-991245100243754124806381)⟩⟩,⟨⟨(-90321931371761228632130),(-90321931371761160046756)⟩,⟨(-955346947926320716948132),(-955346947926320648353572)⟩⟩,⟨⟨(-113436326511793943680639),(-113436326511793877494346)⟩,⟨(-919158631258570576922116),(-919158631258570510726425)⟩⟩,⟨⟨(-135208952915012104977643),(-135208952915012041165128)⟩,⟨(-882760491304220554909544),(-882760491304220491087449)⟩⟩,⟨⟨(-155595851938153297680223),(-155595851938153236216118)⟩,⟨(-846234627649387321854039),(-846234627649387260380204)⟩⟩,⟨⟨(-174560771589001287839707),(-174560771589001228692470)⟩,⟨(-809664421075349390280927),(-809664421075349331123838)⟩⟩,⟨⟨(-192075254968793075166482),(-192075254968793018305040)⟩,⟨(-773134038608132138128917),(-773134038608132081257534)⟩⟩,⟨⟨(-208118675729573646613216),(-208118675729573591983767)⟩,⟨(-736727925787329697833604),(-736727925787329643194152)⟩⟩,⟨⟨(-222678220104648563297908),(-222678220104648510852999)⟩,⟨(-700530291163137130644450),(-700530291163137078189508)⟩⟩,⟨⟨(-235748815576344242332267),(-235748815576344192030955)⟩,⟨(-664624588136783813679930),(-664624588136783763368583)⟩⟩] +lemma kernel19_0_r4_2_eq : ∀ k : Fin 16, kernel19_0Expr 4 2 k = kernel19_0_r4_2 k := by decide +kernel +noncomputable def kernel19_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-247333006760243316405590),(-247333006760243268208615)⟩,⟨(-629092999303494442583671),(-629092999303494394376687)⟩⟩,⟨⟨(-257440779602044780434994),(-257440779602044734296589)⟩,⟨(-594015928437696213553229),(-594015928437696167404871)⟩⟩,⟨⟨(-266089335495151944258010),(-266089335495151900134613)⟩,⟨(-559471505177291496240773),(-559471505177291452107503)⟩⟩,⟨⟨(-273302817426900367865145),(-273302817426900325707007)⟩,⟨(-525535107318208806856422),(-525535107318208764688983)⟩⟩,⟨⟨(-279111990741949569831889),(-279111990741949529592427)⟩,⟨(-492278905423850328146879),(-492278905423850287898880)⟩⟩,⟨⟨(-283553881565908887218455),(-283553881565908848845679)⟩,⟨(-459771434189111768503112),(-459771434189111730122537)⟩⟩,⟨⟨(-286671376354190605245754),(-286671376354190568690706)⟩,⟨(-428077194678890149816807),(-428077194678890113254668)⟩⟩,⟨⟨(-288512786414251019915457),(-288512786414250985116944)⟩,⟨(-397256291190789548735417),(-397256291190789513930494)⟩⟩,⟨⟨(-289131381588200935124626),(-289131381588200902030863)⟩,⟨(-367364106076234654024338),(-367364106076234620924816)⟩⟩,⟨⟨(-288584897572293065931105),(-288584897572293034487291)⟩,⟨(-338451015399257372388567),(-338451015399257340939615)⟩⟩,⟨⟨(-286935021585812515544622),(-286935021585812485699803)⟩,⟨(-310562147824289262378821),(-310562147824289232529452)⟩⟩,⟨⟨(-284246861281010529603881),(-284246861281010501303071)⟩,⟨(-283737188610330457192688),(-283737188610330428887888)⟩⟩,⟨⟨(-280588401905413078748945),(-280588401905413051937904)⟩,⟨(-258010230056218404966059),(-258010230056218378151554)⟩⟩,⟨⟨(-276029956786513755950046),(-276029956786513730572740)⟩,⟨(-233409669197994765218109),(-233409669197994739837833)⟩⟩,⟨⟨(-270643616205892013611063),(-270643616205891989616535)⟩,⟨(-209958153012308061068609),(-209958153012308037071577)⟩⟩,⟨⟨(-264502699665519846250174),(-264502699665519823582814)⟩,⟨(-187672570837137741449062),(-187672570837137718779630)⟩⟩] +lemma kernel19_0_r4_3_eq : ∀ k : Fin 16, kernel19_0Expr 4 3 k = kernel19_0_r4_3 k := by decide +kernel +noncomputable def kernel19_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-257681216424733108815149),(-257681216424733087424868)⟩,⟨(-166564093190497317603337),(-166564093190497296211387)⟩⟩,⟨⟨(-250253339004286825204317),(-250253339004286805037364)⟩,⟨(-146638255656526382209349),(-146638255656526362041098)⟩⟩,⟨⟨(-242292894117221860221434),(-242292894117221841228681)⟩,⟨(-127895086023486269862918),(-127895086023486250869209)⟩⟩,⟨⟨(-233872875198913648195922),(-233872875198913630325554)⟩,⟨(-110329272406104170358080),(-110329272406104152487070)⟩⟩,⟨⟨(-225064980375382570286126),(-225064980375382553490857)⟩,⟨(-93930369671330763457573),(-93930369671330746661946)⟩⟩,⟨⟨(-215939179335120146850739),(-215939179335120131080126)⟩,⟨(-78683041117050236665554),(-78683041117050220894841)⟩⟩,⟨⟨(-206563312161293158534079),(-206563312161293143742243)⟩,⟨(-64567332031989997378969),(-64567332031989982587265)⟩⟩,⟨⟨(-197002722744652238661331),(-197002722744652224800338)⟩,⟨(-51558971495554695745443),(-51558971495554681884789)⟩⟩,⟨⟨(-187319928939551194728737),(-187319928939551181755210)⟩,⟨(-39629698561194833717387),(-39629698561194820744382)⟩⟩,⟨⟨(-177574331153148180740507),(-177574331153148168608416)⟩,⟨(-28747608807929043427824),(-28747608807929031296415)⟩⟩,⟨⟨(-167821960578163901231216),(-167821960578163889899047)⟩,⟨(-18877517142549340953958),(-18877517142549329622610)⟩⟩,⟨⟨(-158115267799527116567418),(-158115267799527105992160)⟩,⟨(-9981332689698404227159),(-9981332689698393652839)⟩⟩,⟨⟨(-148502952031690205991658),(-148502952031690196101103)⟩,⟨(-2018441617359264347271),(-2018441617359254457750)⟩⟩,⟨⟨(-139029830782910778697688),(-139029830782910769453102)⟩,⟨5053906190582112448114,5053906190582121691586⟩⟩,⟨⟨(-129736749301540162519930),(-129736749301540153888840)⟩,⟨11280210587882947015254,11280210587882955645168⟩⟩,⟨⟨(-120660528743015180684505),(-120660528743015172633108)⟩,⟨16706338556052148252881,16706338556052156303055⟩⟩] +lemma kernel19_0_r4_4_eq : ∀ k : Fin 16, kernel19_0Expr 4 4 k = kernel19_0_r4_4 k := by decide +kernel +noncomputable def kernel19_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-111833951609916253317613),(-111833951609916245815859)⟩,⟨21379149135298196070107,21379149135298203570605⟩⟩,⟨⟨(-103285782665580564926128),(-103285782665580557942131)⟩,⟨25346129255648728916911,25346129255648735899631⟩⟩,⟨⟨(-95040823208081036772891),(-95040823208081030278391)⟩,⟨28655043548999713452751,28655043548999719945966⟩⟩,⟨⟨(-87119996318883699420875),(-87119996318883693386675)⟩,⟨31353600916135917069451,31353600916135923102367⟩⟩,⟨⟨(-79540460471381029658603),(-79540460471381024058826)⟩,⟨33489140293633448637888,33489140293633454236391⟩⟩,⟨⟨(-72315748700179408546171),(-72315748700179403353686)⟩,⟨35108337719863422071305,35108337719863427262535⟩⟩,⟨⟨(-65455930393122323154291),(-65455930393122318345038)⟩,⟨36256936442934394740656,36256936442934399548770⟩⟩,⟨⟨(-58967792674419984789824),(-58967792674419980339186)⟩,⟨36979501452122025014340,36979501452122029463982⟩⟩,⟨⟨(-52855038298063799530003),(-52855038298063795415797)⟩,⟨37319199453729929042815,37319199453729933156158⟩⟩,⟨⟨(-47118496964382040308157),(-47118496964382036507768)⟩,⟨37317604957716988719829,37317604957716992519479⟩⟩,⟨⟨(-41756347006970154253989),(-41756347006970150747385)⟩,⟨37014532797760183190680,37014532797760186696657⟩⟩,⟨⟨(-36764344469580901030825),(-36764344469580897797105)⟩,⟨36447897079209351936773,36447897079209355169968⟩⟩,⟨⟨(-32136056699684572915064),(-32136056699684569936712)⟩,⟨35653596240646613529968,35653596240646616507887⟩⟩,⟨⟨(-27863097723711959749070),(-27863097723711957007944)⟩,⟨34665423628961505923244,34665423628961508664021⟩⟩,⟨⟨(-23935362834568013104449),(-23935362834568010584484)⟩,⟨33515002727890125212664,33515002727890127732356⟩⟩,⟨⟨(-20341260010726952400692),(-20341260010726950084534)⟩,⟨32231745948142688442529,32231745948142690758481⟩⟩] +lemma kernel19_0_r4_5_eq : ∀ k : Fin 16, kernel19_0Expr 4 5 k = kernel19_0_r4_5 k := by decide +kernel +noncomputable def kernel19_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-17067935993830850302963),(-17067935993830848176850)⟩,⟨30842835685254723153564,30842835685254725279532⟩⟩,⟨⟨(-14101495073906015723380),(-14101495073906013773029)⟩,⟨29373226180238643971331,29373226180238645921589⟩⟩,⟨⟨(-11427208863809858785826),(-11427208863809856998621)⟩,⟨27845664578497916066882,27845664578497917854039⟩⟩,⟨⟨(-9029715583158772003632),(-9029715583158770367135)⟩,⟨26280729474252492629498,26280729474252494265987⟩⟩,⟨⟨(-6893207612775490051316),(-6893207612775488554739)⟩,⟨24696885150349508858132,24696885150349510354734⟩⟩,⟨⟨(-5001606319881213817520),(-5001606319881212449801)⟩,⟨23110549675760253307614,23110549675760254675387⟩⟩,⟨⟨(-3338723388382865006231),(-3338723388382863756427)⟩,⟨21536175003832489768459,21536175003832491018341⟩⟩,⟨⟨(-1888408114542123896871),(-1888408114542122755151)⟩,⟨19986337221648083915737,19986337221648085057555⟩⟩,⟨⟨(-634680343300365022404),(-634680343300363980772)⟩,⟨18471835132493656681130,18471835132493657722875⟩⟩,⟨⟨438151077797011603991,438151077797012553758⟩,⟨17001795407104597563279,17001795407104598513172⟩⟩,⟨⟨1345384263746305413286,1345384263746306278329⟩,⟨15583782612424216158958,15583782612424217024136⟩⟩,⟨⟨2101834443420208933186,2101834443420209720583⟩,⟨14223912516441338611308,14223912516441339398846⟩⟩,⟨⟨2721757912643986451252,2721757912643987167147⟩,⟨12926967171478826782811,12926967171478827498851⟩⟩,⟨⟨3218789271735884648685,3218789271735885299539⟩,⟨11696510393341932159897,11696510393341932810897⟩⟩,⟨⟨3605891316517140669092,3605891316517141260101⟩,⟨10535002377282265717227,10535002377282266308381⟩⟩,⟨⟨3895316857215489665722,3895316857215490202107⟩,⟨9443912321163634003121,9443912321163634539651⟩⟩] +lemma kernel19_0_r4_6_eq : ∀ k : Fin 16, kernel19_0Expr 4 6 k = kernel19_0_r4_6 k := by decide +kernel +noncomputable def kernel19_0_r4_7 : Fin 16 → CBox := ![⟨⟨4098581663941368235412,4098581663941368721689⟩,⟨8423828059034003856386,8423828059034004342805⟩⟩,⟨⟨4226447679919738961398,4226447679919739402066⟩,⟨7474561842182839699888,7474561842182840140685⟩⟩,⟨⟨4288915603571586941504,4288915603571587340374⟩,⟨6595251537558294811595,6595251537558295210576⟩⟩,⟨⟨4295225916802232808005,4295225916802233168847⟩,⟨5784456643213351166754,5784456643213351527690⟩⟩,⟨⟨4253867428238044839741,4253867428238045165753⟩,⟨5040248645554595078580,5040248645554595404670⟩⟩,⟨⟨4172592405292232493888,4172592405292232788308⟩,⟨4360295362133526771593,4360295362133527066077⟩⟩,⟨⟨4058437386369647685430,4058437386369647950997⟩,⟨3741939025344605150211,3741939025344605415829⟩⟩,⟨⟨3917748792714119595178,3917748792714119834756⟩,⟨3182267965716433762522,3182267965716434002142⟩⟩,⟨⟨3756212496807003128814,3756212496807003345348⟩,⟨2678181847779481328942,2678181847779481545507⟩⟩,⟨⟨3578886549293947354354,3578886549293947550003⟩,⟨2226450496269021790338,2226450496269021986010⟩⟩,⟨⟨3390236317632612789054,3390236317632612965627⟩,⟨1823766425391776742388,1823766425391776918977⟩⟩,⟨⟨3194171345558675235757,3194171345558675395049⟩,⟨1466791248961099557732,1466791248961099717034⟩⟩,⟨⟨2994083301680650737152,2994083301680650880672⟩,⟨1152196204477317702647,1152196204477317846172⟩⟩,⟨⟨2792884446750935575218,2792884446750935704493⟩,⟨876697069942116046621,876697069942116175896⟩⟩,⟨⟨2593046111244822865364,2593046111244822981679⟩,⟨637083788728321434604,637083788728321550915⟩⟩,⟨⟨2396636736753496355425,2396636736753496460065⟩,⟨430245145671586018104,430245145671586122737⟩⟩] +lemma kernel19_0_r4_7_eq : ∀ k : Fin 16, kernel19_0Expr 4 7 k = kernel19_0_r4_7 k := by decide +kernel +noncomputable def kernel19_0_r4_8 : Fin 16 → CBox := ![⟨⟨2205359095428270805820,2205359095428270899835⟩,⟨253188857291657267245,253188857291657361250⟩⟩,⟨⟨2020586360496655363829,2020586360496655448332⟩,⟨103057451341329058681,103057451341329143174⟩⟩,⟨⟨1843396757029148186520,1843396757029148262392⟩,⟨(-22859683576450929493),(-22859683576450853633)⟩⟩,⟨⟨1674606575117522490198,1674606575117522558300⟩,⟨(-127117698054978628973),(-127117698054978560884)⟩⟩,⟨⟨1514801377000028518772,1514801377000028579823⟩,⟨(-212110757065009936174),(-212110757065009875136)⟩⟩,⟨⟨1364365275119913750646,1364365275119913805445⟩,⟨(-280069226004267193294),(-280069226004267138510)⟩⟩,⟨⟨1223508199420567630148,1223508199420567679285⟩,⟨(-333059217403918067448),(-333059217403918018325)⟩⟩,⟨⟨1092291109249903848031,1092291109249903892082⟩,⟨(-372984165226690186349),(-372984165226690142312)⟩⟩,⟨⟨970649138041588430774,970649138041588470221⟩,⟨(-401588113262537222189),(-401588113262537182756)⟩⟩,⟨⟨858412687510957612091,858412687510957647432⟩,⟨(-420460425503253889608),(-420460425503253854281)⟩⟩,⟨⟨755326512564024562441,755326512564024594072⟩,⟨(-431041648986364899744),(-431041648986364868126)⟩⟩,⟨⟨661066858638777646931,661066858638777675240⟩,⟨(-434630282924503347042),(-434630282924503318743)⟩⟩,⟨⟨575256729993414813297,575256729993414838602⟩,⟨(-432390231519587509326),(-432390231519587484030)⟩⟩,⟨⟨497479380775176085164,497479380775176107787⟩,⟨(-425358741299326246824),(-425358741299326224210)⟩⟩,⟨⟨427290130820228713898,427290130820228734101⟩,⟨(-414454646762213452262),(-414454646762213432064)⟩⟩,⟨⟨364226615340551754014,364226615340551772076⟩,⟨(-400486770287412462029),(-400486770287412443971)⟩⟩] +lemma kernel19_0_r4_8_eq : ∀ k : Fin 16, kernel19_0Expr 4 8 k = kernel19_0_r4_8 k := by decide +kernel +noncomputable def kernel19_0_r4_9 : Fin 16 → CBox := ![⟨⟨307817582247900897876,307817582247900914041⟩,⟨(-384162343422538124047),(-384162343422538107885)⟩⟩,⟨⟨257590353149848066278,257590353149848080749⟩,⟨(-366095336620514481004),(-366095336620514466536)⟩⟩,⟨⟨213077064327004499317,213077064327004512260⟩,⟨(-346814603118366163495),(-346814603118366150555)⟩⟩,⟨⟨173819802553553583900,173819802553553595476⟩,⟨(-326771759840578839210),(-326771759840578827636)⟩⟩,⟨⟨139374747732013019315,139374747732013029657⟩,⟨(-306348743910389610906),(-306348743910389600564)⟩⟩,⟨⟨109315430238497418184,109315430238497427429⟩,⟨(-285864997540645107697),(-285864997540645098452)⟩⟩,⟨⟨83235205858892118041,83235205858892126301⟩,⟨(-265584246757517948251),(-265584246757517939991)⟩⟩,⟨⟨60749045461227604650,60749045461227612029⟩,⟨(-245720850616000386889),(-245720850616000379509)⟩⟩,⟨⟨41494730295769231780,41494730295769238371⟩,⟨(-226445707346789795684),(-226445707346789789093)⟩⟩,⟨⟨25133537220696807139,25133537220696813030⟩,⟨(-207891712297483154745),(-207891712297483148853)⟩⟩,⟨⟨11350491374743233400,11350491374743238662⟩,⟨(-190158769677131328176),(-190158769677131322913)⟩⟩,⟨⟨(-145743005534612407),(-145743005534607705)⟩,⟨(-173318366071640778808),(-173318366071640774105)⟩⟩,⟨⟨(-9623269681900620934),(-9623269681900616735)⟩,⟨(-157417718563880341149),(-157417718563880336949)⟩⟩,⟨⟨(-17327608074039298341),(-17327608074039294589)⟩,⟨(-142483514165710981165),(-142483514165710977412)⟩⟩,⟨⟨(-23482530483257450048),(-23482530483257446698)⟩,⟨(-128525260249623677380),(-128525260249623674028)⟩⟩,⟨⟨(-28291043929138493320),(-28291043929138490329)⟩,⟨(-115538267854407919758),(-115538267854407916766)⟩⟩] +lemma kernel19_0_r4_9_eq : ∀ k : Fin 16, kernel19_0Expr 4 9 k = kernel19_0_r4_9 k := by decide +kernel +noncomputable def kernel19_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-31936477347858993481),(-31936477347858990804)⟩,⟨(-103506291228820038577),(-103506291228820035899)⟩⟩,⟨⟨(-34583640219918577936),(-34583640219918575539)⟩,⟨(-92403847862143487745),(-92403847862143485347)⟩⟩,⟨⟨(-36380023612645016494),(-36380023612645014348)⟩,⟨(-82198243618377349046),(-82198243618377346898)⟩⟩,⟨⟨(-37457019128678892239),(-37457019128678890317)⟩,⟨(-72851327523300684762),(-72851327523300682840)⟩⟩,⟨⟨(-37931135344133635277),(-37931135344133633558)⟩,⟨(-64321000326252413162),(-64321000326252411441)⟩⟩,⟨⟨(-37905195004995905445),(-37905195004995903906)⟩,⟨(-56562500239901034901),(-56562500239901033361)⟩⟩,⟨⟨(-37469499539277089572),(-37469499539277088193)⟩,⟨(-49529488313532322847),(-49529488313532321467)⟩⟩,⟨⟨(-36702950351884658094),(-36702950351884656858)⟩,⟨(-43174954773669907880),(-43174954773669906643)⟩⟩,⟨⟨(-35674118919209852470),(-35674118919209851363)⟩,⟨(-37451966418766994518),(-37451966418766993410)⟩⟩,⟨⟨(-34442259913711057101),(-34442259913711056108)⟩,⟨(-32314273824516255712),(-32314273824516254719)⟩⟩,⟨⟨(-33058263489750471821),(-33058263489750470931)⟩,⟨(-27716795739250403809),(-27716795739250402919)⟩⟩,⟨⟨(-31565544476055642199),(-31565544476055641402)⟩,⟨(-23615996655556999172),(-23615996655556998374)⟩⟩,⟨⟨(-30000867573226048094),(-30000867573226047378)⟩,⟨(-19970172160030879882),(-19970172160030879166)⟩⟩,⟨⟨(-28395108772311486876),(-28395108772311486232)⟩,⟨(-16739655308733898797),(-16739655308733898153)⟩⟩,⟨⟨(-26773954117665180631),(-26773954117665180052)⟩,⟨(-13886955967867326629),(-13886955967867326050)⟩⟩,⟨⟨(-25158537658075443663),(-25158537658075443140)⟩,⟨(-11376843810044410835),(-11376843810044410312)⟩⟩] +lemma kernel19_0_r4_10_eq : ∀ k : Fin 16, kernel19_0Expr 4 10 k = kernel19_0_r4_10 k := by decide +kernel +noncomputable def kernel19_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-23566020987439640079),(-23566020987439639610)⟩,⟨(-9176384475708404903),(-9176384475708404434)⟩⟩,⟨⟨(-22010117191384381235),(-22010117191384380813)⟩,⟨(-7254937303115580674),(-7254937303115580252)⟩⟩,⟨⟨(-20501562309135472474),(-20501562309135472094)⟩,⟨(-5584122002860331990),(-5584122002860331610)⟩⟩,⟨⟨(-19048537608861176538),(-19048537608861176196)⟩,⟨(-4137760706040201296),(-4137760706040200953)⟩⟩,⟨⟨(-17657046076266127906),(-17657046076266127597)⟩,⟨(-2891800948990029769),(-2891800948990029460)⟩⟩,⟨⟨(-16331246545373447613),(-16331246545373447333)⟩,⟨(-1824224370794029791),(-1824224370794029512)⟩⟩,⟨⟨(-15073748870569366043),(-15073748870569365791)⟩,⟨(-914945190129015711),(-914945190129015459)⟩⟩,⟨⟨(-13885873461927066086),(-13885873461927065858)⟩,⟨(-145701892152906119),(-145701892152905892)⟩⟩,⟨⟨(-12767878391942301200),(-12767878391942300993)⟩,⟨500055009759515386,500055009759515593⟩⟩,⟨⟨(-11719157140101706003),(-11719157140101705815)⟩,⟨1037276772953745529,1037276772953745717⟩⟩,⟨⟨(-10738409879897122611),(-10738409879897122442)⟩,⟨1479429859977694788,1479429859977694958⟩⟩,⟨⟨(-9823791037565627017),(-9823791037565626862)⟩,⟨1838607466626632952,1838607466626633107⟩⟩,⟨⟨(-8973035668491214745),(-8973035668491214604)⟩,⟨2125637933302459920,2125637933302460060⟩⟩,⟨⟨(-8183567010419119217),(-8183567010419119089)⟩,⟨2350189114492146597,2350189114492146724⟩⟩,⟨⟨(-7452587386133150917),(-7452587386133150799)⟩,⟨2520868024139312506,2520868024139312623⟩⟩,⟨⟨(-6777154445012322261),(-6777154445012322155)⟩,⟨2645315279972332376,2645315279972332482⟩⟩] +lemma kernel19_0_r4_11_eq : ∀ k : Fin 16, kernel19_0Expr 4 11 k = kernel19_0_r4_11 k := by decide +kernel +noncomputable def kernel19_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-6154244555247830569),(-6154244555247830471)⟩,⟨2730294041633677836,2730294041633677934⟩⟩,⟨⟨(-5580804988235736956),(-5580804988235736868)⟩,⟨2781773279638440211,2781773279638440299⟩⟩,⟨⟨(-5053796375053783640),(-5053796375053783558)⟩,⟨2805005328405733727,2805005328405733809⟩⟩,⟨⟨(-4570226762864655670),(-4570226762864655596)⟩,⟨2804597770197097573,2804597770197097647⟩⟩,⟨⟨(-4127178457103604796),(-4127178457103604727)⟩,⟨2784579770813125282,2784579770813125351⟩⟩,⟨⟨(-3721828703665256671),(-3721828703665256608)⟩,⟨2748463045109402270,2748463045109402333⟩⟩,⟨⟨(-3351465144033407216),(-3351465144033407159)⟩,⟨2699297673284224897,2699297673284224954⟩⟩,⟨⟨(-3013496865246939692),(-3013496865246939639)⟩,⟨2639723019687228506,2639723019687228559⟩⟩,⟨⟨(-2705461765470564689),(-2705461765470564640)⟩,⟨2572014026573288030,2572014026573288079⟩⟩,⟨⟨(-2425030864339013632),(-2425030864339013586)⟩,⟨2498123167519159862,2498123167519159908⟩⟩,⟨⟨(-2170010104687359678),(-2170010104687359636)⟩,⟨2419718350653939636,2419718350653939679⟩⟩,⟨⟨(-1938340118234488493),(-1938340118234488454)⟩,⟨2338217061752329535,2338217061752329575⟩⟩,⟨⟨(-1728094361684640659),(-1728094361684640623)⟩,⟨2254817032744774722,2254817032744774758⟩⟩,⟨⟨(-1537475970970620885),(-1537475970970620851)⟩,⟨2170523713290090569,2170523713290090603⟩⟩,⟨⟨(-1364813629396585623),(-1364813629396585592)⟩,⟨2086174812566997600,2086174812566997631⟩⟩,⟨⟨(-1208556699671627944),(-1208556699671627915)⟩,⟨2002462166073185146,2002462166073185175⟩⟩] +lemma kernel19_0_r4_12_eq : ∀ k : Fin 16, kernel19_0Expr 4 12 k = kernel19_0_r4_12 k := by decide +kernel +noncomputable def kernel19_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-1067269829697888190),(-1067269829697888163)⟩,⟨1919951168560839758,1919951168560839785⟩⟩,⟨⟨(-939627206952002550),(-939627206952002525)⟩,⟨1839097999771261482,1839097999771261507⟩⟩,⟨⟨(-824406605867418157),(-824406605867418132)⟩,⟨1760264854755000209,1760264854755000234⟩⟩,⟨⟨(-720483346309250819),(-720483346309250796)⟩,⟨1683733375597923073,1683733375597923096⟩⟩,⟨⟨(-626824258587309017),(-626824258587308996)⟩,⟨1609716466571817214,1609716466571817235⟩⟩,⟨⟨(-542481731064435899),(-542481731064435879)⟩,⟨1538368660288204752,1538368660288204772⟩⟩,⟨⟨(-466587899907668036),(-466587899907668017)⟩,⟨1469795188505871008,1469795188505871027⟩⟩,⟨⟨(-398349026552995851),(-398349026552995834)⟩,⟨1404059897935879764,1404059897935879782⟩⟩,⟨⟨(-337040096696685099),(-337040096696685082)⟩,⟨1341192138778796982,1341192138778796999⟩⟩,⟨⟨(-281999664803555825),(-281999664803555810)⟩,⟨1281192741866087536,1281192741866087551⟩⟩,⟨⟨(-232624959980460336),(-232624959980460321)⟩,⟨1224039189187299603,1224039189187299619⟩⟩,⟨⟨(-188367262373556776),(-188367262373556761)⟩,⟨1169690072274706744,1169690072274706760⟩⟩,⟨⟨(-148727553807990597),(-148727553807990584)⟩,⟨1118088923381191659,1118088923381191672⟩⟩,⟨⟨(-113252442018528645),(-113252442018528631)⟩,⟨1069167495607841745,1069167495607841759⟩⟩,⟨⟨(-81530354360968009),(-81530354360967996)⟩,⟨1022848560089063355,1022848560089063369⟩⟩,⟨⟨(-53187994207474021),(-53187994207474009)⟩,⟨979048280992918025,979048280992918037⟩⟩] +lemma kernel19_0_r4_13_eq : ∀ k : Fin 16, kernel19_0Expr 4 13 k = kernel19_0_r4_13 k := by decide +kernel +noncomputable def kernel19_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-27887051192559824),(-27887051192559811)⟩,⟨937678222406458332,937678222406458344⟩⟩,⟨⟨(-5321154984104563),(-5321154984104552)⟩,⟨898647035110964065,898647035110964076⟩⟩,⟨⟨14786938786381852,14786938786381863⟩,⟨861861865769527752,861861865769527763⟩⟩,⟨⟨32687942467524983,32687942467524994⟩,⟨827229526108298583,827229526108298594⟩⟩,⟨⟨48608422602194534,48608422602194544⟩,⟨794657455232052882,794657455232052892⟩⟩,⟨⟨62752990925225172,62752990925225183⟩,⟨764054504234718151,764054504234718162⟩⟩,⟨⟨75306312578581459,75306312578581468⟩,⟨735331568707510757,735331568707510767⟩⟩,⟨⟨86434943744020732,86434943744020741⟩,⟨708402091574637636,708402091574637647⟩⟩,⟨⟨96289010540587307,96289010540587317⟩,⟨683182455864183091,683182455864183100⟩⟩,⟨⟨105003740592216875,105003740592216884⟩,⟨659592284517061892,659592284517061901⟩⟩,⟨⟨112700858163935932,112700858163935941⟩,⟨637554662119142672,637554662119142681⟩⟩,⟨⟨119489853213876967,119489853213876975⟩,⟨616996291482390752,616996291482390760⟩⟩,⟨⟨125469134129150747,125469134129150757⟩,⟨597847596273874386,597847596273874396⟩⟩,⟨⟨130727073319900637,130727073319900646⟩,⟨580042779372564444,580042779372564453⟩⟩,⟨⟨135342954248283377,135342954248283386⟩,⟨563519845300913555,563519845300913564⟩⟩,⟨⟨139387827876056655,139387827876056663⟩,⟨548220593911047654,548220593911047662⟩⟩] +lemma kernel19_0_r4_14_eq : ∀ k : Fin 16, kernel19_0Expr 4 14 k = kernel19_0_r4_14 k := by decide +kernel +noncomputable def kernel19_0_r4_15 : Fin 16 → CBox := ![⟨⟨142925285932352556,142925285932352565⟩,⟨534090591485695967,534090591485695976⟩⟩,⟨⟨146012157836901010,146012157836901018⟩,⟨521079124525100347,521079124525100355⟩⟩,⟨⟨148699137566907219,148699137566907227⟩,⟨509139140718057153,509139140718057161⟩⟩,⟨⟨151031346230325430,151031346230325438⟩,⟨498227180924411353,498227180924411362⟩⟩,⟨⟨153048835605824573,153048835605824580⟩,⟨488303305415560965,488303305415560973⟩⟩,⟨⟨154787037430964671,154787037430964678⟩,⟨479331017117903259,479331017117903266⟩⟩,⟨⟨156277162765033926,156277162765033934⟩,⟨471277184171857575,471277184171857584⟩⟩,⟨⟨157546555321172325,157546555321172332⟩,⟨464111963747352888,464111963747352895⟩⟩,⟨⟨158619002252966889,158619002252966896⟩,⟨457808728737613073,457808728737613080⟩⟩,⟨⟨159515005492467237,159515005492467245⟩,⟨452343998679675702,452343998679675710⟩⟩,⟨⟨160252016368110703,160252016368110711⟩,⟨447697376016040704,447697376016040711⟩⟩,⟨⟨160844635880743898,160844635880743905⟩,⟨443851488611510258,443851488611510265⟩⟩,⟨⟨161304782682014677,161304782682014686⟩,⟨440791939267563758,440791939267563765⟩⟩,⟨⟨161641830480006286,161641830480006293⟩,⟨438507262828914789,438507262828914796⟩⟩,⟨⟨161862716290132628,161862716290132635⟩,⟨436988891349042652,436988891349042659⟩⟩,⟨⟨161972020652988698,161972020652988705⟩,⟨436231127669652141,436231127669652148⟩⟩] +lemma kernel19_0_r4_15_eq : ∀ k : Fin 16, kernel19_0Expr 4 15 k = kernel19_0_r4_15 k := by decide +kernel +noncomputable def kernel19_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel19_0_r4_0,kernel19_0_r4_1,kernel19_0_r4_2,kernel19_0_r4_3,kernel19_0_r4_4,kernel19_0_r4_5,kernel19_0_r4_6,kernel19_0_r4_7,kernel19_0_r4_8,kernel19_0_r4_9,kernel19_0_r4_10,kernel19_0_r4_11,kernel19_0_r4_12,kernel19_0_r4_13,kernel19_0_r4_14,kernel19_0_r4_15] +lemma kernel19_0_r4_eq (i k : Fin 16) : kernel19_0Expr 4 i k = kernel19_0_r4 i k := by + fin_cases i + · exact kernel19_0_r4_0_eq k + · exact kernel19_0_r4_1_eq k + · exact kernel19_0_r4_2_eq k + · exact kernel19_0_r4_3_eq k + · exact kernel19_0_r4_4_eq k + · exact kernel19_0_r4_5_eq k + · exact kernel19_0_r4_6_eq k + · exact kernel19_0_r4_7_eq k + · exact kernel19_0_r4_8_eq k + · exact kernel19_0_r4_9_eq k + · exact kernel19_0_r4_10_eq k + · exact kernel19_0_r4_11_eq k + · exact kernel19_0_r4_12_eq k + · exact kernel19_0_r4_13_eq k + · exact kernel19_0_r4_14_eq k + · exact kernel19_0_r4_15_eq k +noncomputable def kernel19_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-3770639512377223573088647755),(-3770639512377222789785915197)⟩,⟨30017842617320012925541501970,30017842617320013709076828744⟩⟩,⟨⟨(-3749606210558000686930468983),(-3749606210557999903870152644)⟩,⟨30002707496263112058236551375,30002707496263112841529814821⟩⟩,⟨⟨(-3707607073803335365046852215),(-3707607073803334582472588744)⟩,⟨29972424893428618556044009002,29972424893428619338851923520⟩⟩,⟨⟨(-3644776860661369856846019322),(-3644776860661369075001175796)⟩,⟨29926970344849406378280992427,29926970344849407160360538403⟩⟩,⟨⟨(-3561317270531471734741176218),(-3561317270531470953868746841)⟩,⟨29866307796259967405351117587,29866307796259968186459642916⟩⟩,⟨⟨(-3457496416523167028289342472),(-3457496416523166248631787856)⟩,⟨29790390367527392507551855827,29790390367527393287447234884⟩⟩,⟨⟨(-3333648120921601275465376239),(-3333648120921600497264542971)⟩,⟨29699161362604162479830718492,29699161362604163258271430828⟩⟩,⟨⟨(-3190171031905067313519913827),(-3190171031905066537016814789)⟩,⟨29592555517101675228159449656,29592555517101676004904798001⟩⟩,⟨⟨(-3027527559926898233942004441),(-3027527559926897459376840346)⟩,⟨29470500473684011342002403491,29470500473684012116812490560⟩⟩,⟨⟨(-2846242632008997776197659579),(-2846242632008997003809439475)⟩,⟨29332918473632879700972830415,29332918473632880473608936817⟩⟩,⟨⟨(-2646902262109097059370985398),(-2646902262109096289397478340)⟩,⟨29179728251147434106583804743,29179728251147434876808435752⟩⟩,⟨⟨(-2430151935729043009026218285),(-2430151935729042241644253997)⟩,⟨29010847115227271659588955685,29010847115227272427225539066⟩⟩,⟨⟨(-2196694807036369950485120764),(-2196694807036369185925300085)⟩,⟨28826193202354079997768442698,28826193202354080762586616930⟩⟩,⟨⟨(-1947289706984039036218969998),(-1947289706984038274709777224)⟩,⟨28625687881647844961536934973,28625687881647845723308435567⟩⟩,⟨⟨(-1682748961240002490365006330),(-1682748961240001732134167377)⟩,⟨28409258292738065866990029815,28409258292738066625487329838⟩⟩,⟨⟨(-1403936017183988464814370187),(-1403936017183987710086892913)⟩,⟨28176839995269860215025050330,28176839995269860970023318993⟩⟩] +lemma kernel19_0_r5_0_eq : ∀ k : Fin 16, kernel19_0Expr 5 0 k = kernel19_0_r5_0 k := by decide +kernel +noncomputable def kernel19_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-1111762879796706300168725804),(-1111762879796705549169166344)⟩,⟨27928379707769925149633009061,27928379707769925900907844226⟩⟩,⟨⟨(-807187356957823923013111959),(-807187356957823175962200542)⟩,⟨27663838112538680106366272891,27663838112538680853697074400⟩⟩,⟨⟨(-491210115482966756453008921),(-491210115482966013571384194)⟩,⟨27383192702322944945177960166,27383192702322945688344194503⟩⟩,⟨⟨(-164871550164094226129467452),(-164871550164093487633177903)⟩,⟨27086440643768289766411574214,27086440643768290505197272499⟩⟩,⟨⟨170751530872573884556889997,170751530872574618451196350⟩,⟨26773601632061369698621812455,26773601632061370432810379889⟩⟩,⟨⟨514549400017852326897324997,514549400017853055979398658⟩,⟨26444720710759211532322199134,26444720710759212261703412807⟩⟩,⟨⟨865383077507002220424968837,865383077507002944483233291⟩,⟨26099871030572933359471278420,26099871030572934083833561036⟩⟩,⟨⟨1222088165139795201315439026,1222088165139795920145582600⟩,⟨25739156520835297388566286135,25739156520835298107705297947⟩⟩,⟨⟨1583478837881100751472924827,1583478837881101464868098242⟩,⟨25362714447541374971436574968,25362714447541375685145410739⟩⟩,⟨⟨1948351983336836262437608786,1948351983336836970201089418⟩,⟨24970717832214855916419053309,24970717832214856624500907101⟩⟩,⟨⟨2315491477558299939110114933,2315491477558300641041520929⟩,⟨24563377706423282410337754841,24563377706423283112592133598⟩⟩,⟨⟨2683672584054378653352964669,2683672584054379349262703526⟩,⟨24140945177546408950317554876,24140945177546409646554727898⟩⟩,⟨⟨3051666461304301987097501821,3051666461304302676790739129⟩,⟨23703713282394073034271408274,23703713282394073724296375558⟩⟩,⟨⟨3418244762483063199841205028,3418244762483063883158795409⟩,⟨23252018606472771973474143312,23252018606472772657127568400⟩⟩,⟨⟨3782184309557847565952611997,3782184309557848242759099760⟩,⟨22786242648111095099592095533,22786242648111095776738305899⟩⟩,⟨⟨4142271822408003066160678213,4142271822408003736284728886⟩,⟨22306812908268815307880822146,22306812908268815978348240788⟩⟩] +lemma kernel19_0_r5_1_eq : ∀ k : Fin 16, kernel19_0Expr 5 1 k = kernel19_0_r5_1 k := by decide +kernel +noncomputable def kernel19_0_r5_2 : Fin 16 → CBox := ![⟨⟨4497308682184916409814253092,4497308682184917073075182724⟩,⟨21814203688666306728928316916,21814203688666307392535992412⟩⟩,⟨⟨4846115706783464134475728400,4846115706783464790713560213⟩,⟨21308936582871413391324644893,21308936582871414047912310625⟩⟩,⟨⟨5187537915065244971970378785,5187537915065245621013836662⟩,⟨20791580647159167360279010132,20791580647159168009675077177⟩⟩,⟨⟨5520449255376930408464882200,5520449255376931050162940956⟩,⟨20262752240302877955416075147,20262752240302878597469185481⟩⟩,⟨⟨5843757272965474645496965215,5843757272965475279690045329⟩,⟨19723114523947943076344313248,19723114523947943710894530357⟩⟩,⟨⟨6156407690125294251273881195,6156407690125294877858880120⟩,⟨19173376617844989225047875154,19173376617844989851991702612⟩⟩,⟨⟨6457388872339262898808578421,6457388872339263517631297903⟩,⟨18614292406957283908917942474,18614292406957284528100794761⟩⟩,⟨⟨6745736153312281647017606943,6745736153312282257949911160⟩,⟨18046659000287479691412886177,18046659000287480302706226557⟩⟩,⟨⟨7020535991658218872474823028,7020535991658219475368913855⟩,⟨17471314844167521672680182236,17471314844167522275935796995⟩⟩,⟨⟨7280929932100955344665390913,7280929932100955939435877809⟩,⟨16889137495698213360447369633,16889137495698213955563262586⟩⟩,⟨⟨7526118344398502888327199454,7526118344398503474840849939⟩,⟨16301041064985285775725032458,16301041064985286362566593302⟩⟩,⟨⟨7755363913803435212921384294,7755363913803435791075057069⟩,⟨15707973337769448519680250286,15707973337769449098144392365⟩⟩,⟨⟨7967994857738078692355231606,7967994857738079262020454492⟩,⟨15110912592960486907678354441,15110912592960487477636690394⟩⟩,⟨⟨8163407844490943323191007176,8163407844490943884281689559⟩,⟨14510864132431040266390678709,14510864132431040827757236482⟩⟩,⟨⟨8341070591130457819336411370,8341070591130458371738248756⟩,⟨13908856543174974526678367248,13908856543174975079338990723⟩⟩,⟨⟨8500524119478680361232956720,8500524119478680904870823686⟩,⟨13305937714558997316638142745,13305937714558997860517887714⟩⟩] +lemma kernel19_0_r5_2_eq : ∀ k : Fin 16, kernel19_0Expr 5 2 k = kernel19_0_r5_2 k := by decide +kernel +noncomputable def kernel19_0_r5_3 : Fin 16 → CBox := ![⟨⟨8641384650883447803964583254,8641384650883448338730652353⟩,⟨12703170635865491867928410285,12703170635865492402919659500⟩⟩,⟨⟨8763345122661236004217881153,8763345122661236530056801921⟩,⟨12101629001611358061550215707,12101629001611358587597861080⟩⟩,⟨⟨8866176311440376485128892659,8866176311440377001949565501⟩,⟨11502392654204965610427426550,11502392654204966127440638559⟩⟩,⟨⟨8949727551197545696148145879,8949727551197546203905410737⟩,⟨10906542895345671890759918374,10906542895345672398693837152⟩⟩,⟨⟨9013927036528871007318141335,9013927036528871505928291681⟩,⟨10315157699154137128997366470,10315157699154137627768611714⟩⟩,⟨⟨9058781704606942551116517837,9058781704606943040554800153⟩,⟨9729306861325518808544355666,9729306861325519298128528374⟩⟩,⟨⟨9084376692320170870199982512,9084376692320171350400022312⟩,⟨9150047119602757282597782263,9150047119602757762928886319⟩⟩,⟨⟨9090874368242576470953372993,9090874368242576941901224593⟩,⟨8578417281557681009544218648,8578417281557681480608712047⟩⟩,⟨⟨9078512942309443826095576946,9078512942309444287730914634⟩,⟨8015433396030849317113498018,8015433396030849778851480057⟩⟩,⟨⟨9047604659344793913467462009,9047604659344794365799024892⟩,⟨7462084004607634119107636948,7462084004607634571528294243⟩⟩,⟨⟨8998533585866459866701818379,8998533585866460309817821130⟩,⟨6919325509192387053630381692,6919325509192387496822413397⟩⟩,⟨⟨8931753002848901853364938040,8931753002848902288247513696⟩,⟨6388077691082826117957720414,6388077691082826552903881833⟩⟩,⟨⟨8847782420317503790422187628,8847782420317504217004321995⟩,⟨5869219415945118192700720142,5869219415945118619334489851⟩⟩,⟨⟨8747204232745673138466153847,8747204232745673556753879586⟩,⟨5363584557752638788737216873,5363584557752639207065135137⟩⟩,⟨⟨8630660037192789013888672562,8630660037192789423832149143⟩,⟨4871958173088170784231339141,4871958173088171194204084707⟩⟩,⟨⟨8498846638923019107883543326,8498846638923019509496080748⟩,⟨4395072955234429410459481025,4395072955234429812090893856⟩⟩] +lemma kernel19_0_r5_3_eq : ∀ k : Fin 16, kernel19_0Expr 5 3 k = kernel19_0_r5_3 k := by decide +kernel +noncomputable def kernel19_0_r5_4 : Fin 16 → CBox := ![⟨⟨8352511771849764325623369582,8352511771849764718857332211⟩,⟨3933605995209191399355710896,3933605995209191792598693552⟩⟩,⟨⟨8192449563527371700426795485,8192449563527372085318325606⟩,⟨3488175874360568330863421320,3488175874360568715754660827⟩⟩,⟨⟨8019495776532472752108736475,8019495776532473128630281581⟩,⟨3059340110350169407578796197,3059340110350169784091289410⟩⟩,⟨⟨7834522859916276855129946959,7834522859916277223322279253⟩,⟨2647592975345308431374129883,2647592975345308799549200678⟩⟩,⟨⟨7638434845943911284370654984,7638434845943911644209764891⟩,⟨2253363702047147787941140639,2253363702047148147755332281⟩⟩,⟨⟨7432162128548442365415870520,7432162128548442716963948895⟩,⟨1877015089833351657818970061,1877015089833352009335024227⟩⟩,⟨⟨7216656160800281177747132392,7216656160800281520999189417⟩,⟨1518842519827127060595682810,1518842519827127403809158191⟩⟩,⟨⟨6992884109216018550506732843,6992884109216018885530182065⟩,⟨1179073384156770783966748802,1179073384156771118945601537⟩⟩,⟨⟨6761823502897283283777705489,6761823502897283610568584156⟩,⟨857866931079457742779373722,857866931079458069520178205⟩⟩,⟨⟨6524456915297228704842479340,6524456915297229023491327554⟩,⟨555314524049082071708341174,555314524049082390302164513⟩⟩,⟨⟨6281766715861364056523323231,6281766715861364367061764553⟩,⟨271440309249693840252957906,271440309249694150731965428⟩⟩,⟨⟨6034729927886681955410795229,6034729927886682257938078636⟩,⟨6202282632252652927816025,6202282632252955391772257⟩⟩,⟨⟨5784313227698734612973684781,5784313227698734907507515655⟩,⟨(-240506255879092584605040299),(-240506255879092290137938781)⟩⟩,⟨⟨5531468118675013571622871145,5531468118675013858304676034⟩,⟨(-468854876567766715779661066),(-468854876567766429167513898)⟩⟩,⟨⟨5277126311763221871400848437,5277126311763222150280506449⟩,⟨(-679073841088693810056967551),(-679073841088693531249434825)⟩⟩,⟨⟨5022195341977069552219647303,5022195341977069823407997128⟩,⟨(-871451592035727969727397642),(-871451592035727698613198641)⟩⟩] +lemma kernel19_0_r5_4_eq : ∀ k : Fin 16, kernel19_0Expr 5 4 k = kernel19_0_r5_4 k := by decide +kernel +noncomputable def kernel19_0_r5_5 : Fin 16 → CBox := ![⟨⟨4767554447925783287650571606,4767554447925783551180007461⟩,⟨(-1046331934912551811488522393),(-1046331934912551548034835994)⟩⟩,⟨⟨4514050738775381690069354160,4514050738775381946090368797⟩,⟨(-1204110938815954081312533782),(-1204110938815953825368462421)⟩⟩,⟨⟨4262495670181378124556194917,4262495670181378373186163883⟩,⟨(-1345233584156158470054120458),(-1345233584156158221501900361)⟩⟩,⟨⟨4013661847707601022096337867,4013661847707601263460463333⟩,⟨(-1470190187442762137565472515),(-1470190187442761896279536303)⟩⟩,⟨⟨3768280173089677920469455673,3768280173089678154615625090⟩,⟨(-1579512634542227058221175781),(-1579512634542226824153010234)⟩⟩,⟨⟨3527037345451064634573428453,3527037345451064861649384172⟩,⟨(-1673770454853343699350191868),(-1673770454853343472345173756)⟩⟩,⟨⟨3290573726271690059193952755,3290573726271690279264289151⟩,⟨(-1753566769544568270327825217),(-1753566769544568050321635411)⟩⟩,⟨⟨3059481573581906176636019314,3059481573581906389841453520⟩,⟨(-1819534147349888003877342893),(-1819534147349887790729549974)⟩⟩,⟨⟨2834303647544738026765150855,2834303647544738233166381360⟩,⟨(-1872330401430479173173807060),(-1872330401430478966824001723)⟩⟩,⟨⟨2615532186333845716150633728,2615532186333845916029565031⟩,⟨(-1912634360484696557844984284),(-1912634360484696358011555109)⟩⟩,⟨⟨2403608248048244779846349181,2403608248048244973302021544⟩,⟨(-1941141646639738062855705573),(-1941141646639737869439909839)⟩⟩,⟨⟨2198921411361001791317639197,2198921411361001978493237177⟩,⟨(-1958560491699371904188627757),(-1958560491699371717047583222)⟩⟩,⟨⟨2001809824708933438032302141,2001809824708933618994004109⟩,⟨(-1965607622071669658215096870),(-1965607622071669477282926187)⟩⟩,⟨⟨1812560591122290015885096943,1812560591122290190790448759⟩,⟨(-1963004241180271487233645811),(-1963004241180271312353105209)⟩⟩,⟨⟨1631410473293053648513383098,1631410473293053817443232664⟩,⟨(-1951472136396708893717522527),(-1951472136396708724808062726)⟩⟩,⟨⟨1458546901210147188969053620,1458546901210147352104834928⟩,⟨(-1931729935546584304341913168),(-1931729935546584141222396670)⟩⟩] +lemma kernel19_0_r5_5_eq : ∀ k : Fin 16, kernel19_0Expr 5 5 k = kernel19_0_r5_5 k := by decide +kernel +noncomputable def kernel19_0_r5_6 : Fin 16 → CBox := ![⟨⟨1294109262668381505903963950,1294109262668381663322657823⟩,⟨(-1904489535867851500817963606),(-1904489535867851343411700799)⟩⟩,⟨⟨1138190455200570614997749966,1138190455200570766866106050⟩,⟨(-1870452725965535047859295268),(-1870452725965534895999837925)⟩⟩,⟨⟨990838676500358093727650439,990838676500358240138658970⟩,⟨(-1830308018845564458400552569),(-1830308018845564311995226261)⟩⟩,⟨⟨852059429204549668117005446,852059429204549809224584089⟩,⟨(-1784727711553216895478753177),(-1784727711553216754373908508)⟩⟩,⟨⟨721817714991948985426898052,721817714991949121312406822⟩,⟨(-1734365184321371231632344761),(-1734365184321371095746882056)⟩⟩,⟨⟨600040392330910826787519748,600040392330910957614932664⟩,⟨(-1679852449482501545394317628),(-1679852449482501414564514608)⟩⟩,⟨⟨486618671866493151396430789,486618671866493277258275557⟩,⟨(-1621797957747479088779631795),(-1621797957747478962913203538)⟩⟩,⟨⟨381410723373182742763772873,381410723373182863815398847⟩,⟨(-1560784666834066498260955678),(-1560784666834066377202785591)⟩⟩,⟨⟨284244368400425695610592564,284244368400425812090102824⟩,⟨(-1497368374867208892873253975),(-1497368374867208776385461946)⟩⟩,⟨⟨194919833192372282440007891,194919833192372394551610253⟩,⟨(-1432076318498712461267245583),(-1432076318498712349145835679)⟩⟩,⟨⟨113212537154424597773738984,113212537154424705597702021⟩,⟨(-1365406033330331360104454714),(-1365406033330331252269360375)⟩⟩,⟨⟨38875893049081933462993380,38875893049082037138093120⟩,⟨(-1297824471993896281347800709),(-1297824471993896177660436090)⟩⟩,⟨⟨(-28355903788059191367570008),(-28355903788059091767222896)⟩,⟨(-1229767373164496246404872805),(-1229767373164496146791307382)⟩⟩,⟨⟨(-88765118636378689685507644),(-88765118636378594014140603)⟩,⟨(-1161638872874633701555482143),(-1161638872874633605870110988)⟩⟩,⟨⟨(-142647772968295071399854055),(-142647772968294979574530173)⟩,⟨(-1093811347772544152011296388),(-1093811347772544060171340547)⟩⟩,⟨⟨(-190311010835541666893299422),(-190311010835541578771869888)⟩,⟨(-1026625478437342042523787611),(-1026625478437341954387248547)⟩⟩] +lemma kernel19_0_r5_6_eq : ∀ k : Fin 16, kernel19_0Expr 5 6 k = kernel19_0_r5_6 k := by decide +kernel +noncomputable def kernel19_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-232070552809330773347962912),(-232070552809330688857423196)⟩,⟨(-960390519535151181845552191),(-960390519535151097339560566)⟩⟩,⟨⟨(-268248252467299884559621906),(-268248252467299803550299363)⟩,⟨(-895384762478750815845672773),(-895384762478750734820678575)⟩⟩,⟨⟨(-299169768611528254283825788),(-299169768611528176659431223)⟩,⟨(-831856175340468559460249033),(-831856175340468481820076772)⟩⟩,⟨⟨(-325162364561316191945608310),(-325162364561316117577798778)⟩,⟨(-770023204063249780144360754),(-770023204063249705760769545)⟩⟩,⟨⟨(-346552844014796833723075722),(-346552844014796762536594565)⟩,⟨(-710075718514576647232868129),(-710075718514576576032113426)⟩⟩,⟨⟨(-363665631136612451144967517),(-363665631136612383007813386)⟩,⟨(-652176086626310694177994992),(-652176086626310626028196387)⟩⟩,⟨⟨(-376821000725249370355642832),(-376821000725249305189891812)⟩,⟨(-596460359752483601876225467),(-596460359752483536699363341)⟩⟩,⟨⟨(-386333462561994262698604376),(-386333462561994200383236179)⟩,⟨(-543039552446476039552312409),(-543039552446475977227270226)⟩⟩,⟨⟨(-392510302360875179785053464),(-392510302360875120205037708)⟩,⟨(-492001000097095426586864995),(-492001000097095366998518381)⟩⟩,⟨⟨(-395650280140490389520151203),(-395650280140490332539568794)⟩,⟨(-443409778256528533684070526),(-443409778256528476696406759)⟩⟩,⟨⟨(-396042485337397262564794654),(-396042485337397208114583959)⟩,⟨(-397310168027564288306604735),(-397310168027564233850471464)⟩⟩,⟨⟨(-393965346587744569702338109),(-393965346587744517675101474)⟩,⟨(-353727152537516123403113748),(-353727152537516071371024290)⟩⟩,⟨⟨(-389685792827993686695335724),(-389685792827993637029201007)⟩,⟨(-312667930295956102666449613),(-312667930295956052996446046)⟩⟩,⟨⟨(-383458561213702211537148315),(-383458561213702164119311431)⟩,⟨(-274123432096380513706739982),(-274123432096380466285935001)⟩⟩,⟨⟨(-375525646332198982565303520),(-375525646332198937330447097)⟩,⟨(-238069829061830948289316235),(-238069829061830903052312591)⟩⟩,⟨⟨(-366115884293341086696102577),(-366115884293341043545855513)⟩,⟨(-204470020435005326252210399),(-204470020435005283100560190)⟩⟩] +lemma kernel19_0_r5_7_eq : ∀ k : Fin 16, kernel19_0Expr 5 7 k = kernel19_0_r5_7 k := by decide +kernel +noncomputable def kernel19_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-355444664523303244135125312),(-355444664523303203009995836)⟩,⟨(-173275090758578050056804121),(-173275090758578008930940857)⟩⟩,⟨⟨(-343713761458632638513556100),(-343713761458632599292102261)⟩,⟨(-144425727165935872708181536),(-144425727165935833486584178)⟩⟩,⟨⟨(-331111277839103451935060022),(-331111277839103414559671489)⟩,⟨(-117853588591693130904860893),(-117853588591693093529854430)⟩⟩,⟨⟨(-317811690924245452031187203),(-317811690924245416414999791)⟩,⟨(-93482619801436637253128460),(-93482619801436601637787750)⟩⟩,⟨⟨(-303975992704510703921336974),(-303975992704510670013491195)⟩,⟨(-71230304218448663137331885),(-71230304218448629230740010)⟩⟩,⟨⟨(-289751915037456656574258550),(-289751915037456624287865591)⟩,⟨(-51008850580073714006651525),(-51008850580073681721866137)⟩⟩,⟨⟨(-275274230604679623781127635),(-275274230604679593056066278)⟩,⟨(-32726309477542883419072055),(-32726309477542852695921786)⟩⟩,⟨⟨(-260665120648369000048066522),(-260665120648368970804213954)⟩,⟨(-16287616811317807888990609),(-16287616811317778647306341)⟩⟩,⟨⟨(-246034600598507712910564768),(-246034600598507685103829853)⟩,⟨(-1595562121521461977211018),(-1595562121521434172858434)⟩⟩,⟨⟨(-231480994933728796976675986),(-231480994933728770529731737)⟩,⟨11448319376762976288639867,11448319376763002733027049⟩⟩,⟨⟨(-217091452921199456697023033),(-217091452921199431558711491)⟩,⟨22942931415887721994694946,22942931415887747130311105⟩⟩,⟨⟨(-202942497244083816541314001),(-202942497244083792643992455)⟩,⟨32986877577211417402182626,32986877577211441296703313⟩⟩,⟨⟨(-189100597939612850756196623),(-189100597939612828059609426)⟩,⟨41677797421635851428295811,41677797421635874122006940⟩⟩,⟨⟨(-175622764527213337842449328),(-175622764527213316278014722)⟩,⟨49111776198277378512205589,49111776198277400073715680⟩⟩,⟨⟨(-162557149695452796065408769),(-162557149695452775592815556)⟩,⟨55382825951506981254541237,55382825951507001724186015⟩⟩,⟨⟨(-149943658430069886519043007),(-149943658430069867078527909)⟩,⟨60582435388984019080201710,60582435388984038517766118⟩⟩] +lemma kernel19_0_r5_8_eq : ∀ k : Fin 16, kernel19_0Expr 5 8 k = kernel19_0_r5_8 k := by decide +kernel +noncomputable def kernel19_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-137814556994882988575856372),(-137814556994882970133673527)⟩,⟨64799185485782183161953411,64799185485782201601324929⟩⟩,⟨⟨(-126195076715256776677368871),(-126195076715256759174977519)⟩,⟨68118427480232618832196000,68118427480232636332099970⟩⟩,⟨⟨(-115104008053018005963442885),(-115104008053017989365882957)⟩,⟨70622019662974866159775743,70622019662974882755150925⟩⟩,⟨⟨(-104554280995857311541193816),(-104554280995857295798074980)⟩,⟨72388119168615674273472222,72388119168615690014687745⟩⟩,⟨⟨(-94553528307621646879862174),(-94553528307621631961198489)⟩,⟨73491024845573330570643089,73491024845573345487664652⟩⟩,⟨⟨(-85104628693473321656969630),(-85104628693473307513499689)⟩,⟨74001067199974855950629644,74001067199974870092698669⟩⟩,⟨⟨(-76206227421344083485205780),(-76206227421344070086836273)⟩,⟨73984541379434393518311121,73984541379434406915501966⟩⟩,⟨⟨(-67853232404812332481231815),(-67853232404812319784955378)⟩,⟨73503679177538397117920330,73503679177538409813221950⟩⟩,⟨⟨(-60037284189514960542343141),(-60037284189514948523119520)⟩,⟨72616656095152407243225023,72616656095152419261660285⟩⟩,⟨⟨(-52747198693153346083513766),(-52747198693153334698884139)⟩,⟨71377629585469255839652224,71377629585469267223663180⟩⟩,⟨⟨(-45969381926357330708441658),(-45969381926357319932844878)⟩,⟨69836804731302168231023885,69836804731302179006155920⟩⟩,⟨⟨(-39688216266994478427043422),(-39688216266994468224173221)⟩,⟨68040523750852341288500776,68040523750852351491045171⟩⟩,⟨⟨(-33886418173344702826356122),(-33886418173344693174601718)⟩,⟨66031375897568694032847041,66031375897568703684400519⟩⟩,⟨⟨(-28545367501772291430432615),(-28545367501772282294621736)⟩,⟨63848324506488987906416935,63848324506488997042138521⟩⟩,⟨⟨(-23645408842418265173778891),(-23645408842418256532469477)⟩,⟨61526848139567839540227382,61526848139567848181546764⟩⟩,⟨⟨(-19166125502684713758574105),(-19166125502684705540905190)⟩,⟨59099092992190188977776356,59099092992190197195541298⟩⟩] +lemma kernel19_0_r5_9_eq : ∀ k : Fin 16, kernel19_0Expr 5 9 k = kernel19_0_r5_9 k := by decide +kernel +noncomputable def kernel19_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-15086586953895949716949033),(-15086586953895941905416857)⟩,⟨56594033938863811359885402,56594033938863819171588925⟩⟩,⟨⟨(-11385570712783132984239065),(-11385570712783125553378731)⟩,⟨54037641814816025354064651,54037641814816032785161954⟩⟩,⟨⟨(-8041759757861890626184773),(-8041759757861883562411204)⟩,⟨51453054749041115508974669,51453054749041122573041819⟩⟩,⟨⟨(-5033916683050239334113945),(-5033916683050232616009803)⟩,⟨48860751580731597550524633,48860751580731604268970744⟩⟩,⟨⟨(-2341035868837691828212663),(-2341035868837685444618317)⟩,⟨46278725602774160918737062,46278725602774167302714135⟩⟩,⟨⟨57524993107583621865323,57524993107589692097104⟩,⟨43722657081209698285979667,43722657081209704356628080⟩⟩,⟨⟨2181932650833838935314018,2181932650833844703694206⟩,⟨41206083196659527694456593,41206083196659533463280980⟩⟩,⟨⟨4051783930665711450870662,4051783930665716935501849⟩,⟨38740564241409627898272643,38740564241409633383369950⟩⟩,⟨⟨5686027875208460265061287,5686027875208465474981800⟩,⟨36335845083097438161346305,36335845083097443371749634⟩⟩,⟨⟨7102903006619982878607215,7102903006619987831994517⟩,⟨34000011071991929533116242,34000011071991934486998519⟩⟩,⟨⟨8319888367535606072335664,8319888367535610778828637⟩,⟨31739637723161812660085205,31739637723161817367081123⟩⟩,⟨⟨9353667029275709183242964,9353667029275713658014357⟩,⟨29559933647066362236172996,29559933647066366711451691⟩⟩,⟨⟨10220100803153180546141765,10220100803153184796960478⟩,⟨27464876332146893239607175,27464876332146897490934215⟩⟩,⟨⟨10934214944189355332864396,10934214944189359374650631⟩,⟨25457340500881940274316357,25457340500881944316609171⟩⟩,⟨⟨11510191695820110841178597,11510191695820114681959194⟩,⟨23539218866680480944865087,23539218866680484786123859⟩⟩,⟨⟨11961371587825158958312958,11961371587825162610749734⟩,⟨21711535213236021942677189,21711535213236025595542194⟩⟩] +lemma kernel19_0_r5_10_eq : ∀ k : Fin 16, kernel19_0Expr 5 10 k = kernel19_0_r5_10 k := by decide +kernel +noncomputable def kernel19_0_r5_11 : Fin 16 → CBox := ![⟨⟨12300261466464326035319976,12300261466464329505579750⟩,⟨19974549800966698160486748,19974549800966701631128114⟩⟩,⟨⟨12538548304501364812474164,12538548304501368113346786⟩,⟨18327857177425837847890826,18327857177425841149101729⟩⟩,⟨⟨12687117908410199722040376,12687117908410202860088003⟩,⟨16770476530655222172223853,16770476530655225310569510⟩⟩,⟨⟨12756077709684679922716227,12756077709684682908609273⟩,⟨15300934776992689930233073,15300934776992692916386899⟩⟩,⟨⟨12754782896023867957540209,12754782896023870796377865⟩,⟨13917342618496393248264810,13917342618496396087328778⟩⟩,⟨⟨12691865205567232238618532,12691865205567234940616019⟩,⟨12617463840592128598423667,12617463840592131300615722⟩⟩,⟨⟨12575263772741992141149450,12575263772741994711949222⟩,⟨11398778148480378315745643,11398778148480380886710758⟩⟩,⟨⟨12412257477193130809865069,12412257477193133258039276⟩,⟨10258537861948284636485224,10258537861948287084797970⟩⟩,⟨⟨12209498307323383789930296,12209498307323386119337154⟩,⟨9193818803201409288715904,9193818803201411618236737⟩⟩,⟨⟨11973045306889517738628673,11973045306889519957851054⟩,⟨8201565721826002177994461,8201565721826004397308405⟩⟩,⟨⟨11708398726673738403594671,11708398726673740516963685⟩,⟨7278632605655823094752449,7278632605655825208192597⟩⟩,⟨⟨11420534053336079127696556,11420534053336081142620445⟩,⟨6421818226760299501069425,6421818226760301516045896⟩⟩,⟨⟨11113935634077899106088395,11113935634077901025721996⟩,⟨5627897268571597615720092,5627897268571599535389458⟩⟩,⟨⟨10792629658685110606292951,10792629658685112437486534⟩,⟨4893647373869305974636793,4893647373869307805850955⟩⟩,⟨⟨10460216299896230597767256,10460216299896232343844817⟩,⟨4215872444446718721230615,4215872444446720467315077⟩⟩,⟨⟨10119900848918449128321878,10119900848918450794949693⟩,⟨3591422512256343190804504,3591422512256344857426939⟩⟩] +lemma kernel19_0_r5_11_eq : ∀ k : Fin 16, kernel19_0Expr 5 11 k = kernel19_0_r5_11 k := by decide +kernel +noncomputable def kernel19_0_r5_12 : Fin 16 → CBox := ![⟨⟨9774523715391581429411282,9774523715391583018884462⟩,⟨3017210489098299669550100,3017210489098301259006922⟩⟩,⟨⟨9426589190299231608825466,9426589190299233127024922⟩,⟨2490226087857833680543130,2490226087857835198716456⟩⟩,⟨⟨9078292896394627203332896,9078292896394628653511337⟩,⟨2007547193262094930252347,2007547193262096380396194⟩⟩,⟨⟨8731547873807876279800921,8731547873807877666526838⟩,⟨1566348944418469964229269,1566348944418471350913111⟩⟩,⟨⟨8388009268806391473612716,8388009268806392798753569⟩,⟨1163910775287399070686094,1163910775287400395778312⟩⟩,⟨⟨8049097611373452279588885,8049097611373453547724413⟩,⟨797621642967403812045098,797621642967405080126254⟩⟩,⟨⟨7716020682538305255810685,7716020682538306468979777⟩,⟨464983657432028313995194,464983657432029527104945⟩⟩,⟨⟨7389793985423140911896049,7389793985423142073899968⟩,⟨163614310330179069074462,163614310330180231014752⟩⟩,⟨⟨7071259844954744835847824,7071259844954745948020860⟩,⟨(-108752515212539961209881),(-108752515212538849104112)⟩⟩,⟨⟨6761105170305082888676620,6761105170305083954904363⟩,⟨(-354266587054679530891898),(-354266587054678464734507)⟩⟩,⟨⟨6459877921553669938892676,6459877921553670960772927⟩,⟨(-574962266657451474955299),(-574962266657450453147956)⟩⟩,⟨⟨6168002327976572795526273,6168002327976573776119477⟩,⟨(-772760213745829451662540),(-772760213745828471144346)⟩⟩,⟨⟨5885792909925599947997442,5885792909925600888386676⟩,⟨(-949469728188341867446102),(-949469728188340927133540)⟩⟩,⟨⟨5613467359621061480138104,5613467359621062383439996⟩,⟨(-1106791616825632673709099),(-1106791616825631770485183)⟩⟩,⟨⟨5351158338487401534286896,5351158338487402401959270⟩,⟨(-1246321484770375198853396),(-1246321484770374331259952)⟩⟩,⟨⟨5098924250048121357779906,5098924250048122192651443⟩,⟨(-1369553361720508367068726),(-1369553361720507532276784)⟩⟩] +lemma kernel19_0_r5_12_eq : ∀ k : Fin 16, kernel19_0Expr 5 12 k = kernel19_0_r5_12 k := by decide +kernel +noncomputable def kernel19_0_r5_13 : Fin 16 → CBox := ![⟨⟨4856759047989795125107270,4856759047989795927826391⟩,⟨(-1477883584073184582885809),(-1477883584073183780246661)⟩⟩,⟨⟨4624601138919649697942006,4624601138919650471164391⟩,⟨(-1572614863106577121347425),(-1572614863106576348205177)⟩⟩,⟨⟨4402341438682216836689645,4402341438682217581343310⟩,⟨(-1654960478226699796924445),(-1654960478226699052350859)⟩⟩,⟨⟨4189830639963361276715035,4189830639963361994832941⟩,⟨(-1726048542278759695709958),(-1726048542278758977671904)⟩⟩,⟨⟨3986885747380568585096138,3986885747380569277229417⟩,⟨(-1786926293224361947395915),(-1786926293224361255342084)⟩⟩,⟨⟨3793295934413816024529399,3793295934413816692804959⟩,⟨(-1838564373118008078515690),(-1838564373118007410317660)⟩⟩,⟨⟨3608827774440229146900293,3608827774440229792037514⟩,⟨(-1881861061312502460413236),(-1881861061312501815348547)⟩⟩,⟨⟨3433229895858638181879874,3433229895858638805565666⟩,⟨(-1917646434218790644618496),(-1917646434218790021000543)⟩⟩,⟨⟨3266237108880222354252707,3266237108880222956802212⟩,⟨(-1946686428778287014323838),(-1946686428778286411837738)⟩⟩,⟨⟨3107574049064879385940846,3107574049064879969217235⟩,⟨(-1969686791112347480346850),(-1969686791112346897129713)⟩⟩,⟨⟨2956958380139622186264922,2956958380139622750868166⟩,⟨(-1987296895631646646498057),(-1987296895631646081950156)⟩⟩,⟨⟨2814103596079195325067787,2814103596079195872427102⟩,⟨(-2000113423254808306206318),(-2000113423254807758898680)⟩⟩,⟨⟨2678721459888930537901545,2678721459888931068269689⟩,⟨(-2008683890336853666781678),(-2008683890336853136461761)⟩⟩,⟨⟨2550524114029545766879452,2550524114029546281768361⟩,⟨(-2013510022478868389605292),(-2013510022478867874761384)⟩⟩,⟨⟨2429225894982762119425771,2429225894982762619247985⟩,⟨(-2015050969614356799929825),(-2015050969614356300149580)⟩⟩,⟨⟨2314544882091062561960113,2314544882091063047895122⟩,⟨(-2013726360677091481373212),(-2013726360677090995477341)⟩⟩] +lemma kernel19_0_r5_13_eq : ∀ k : Fin 16, kernel19_0Expr 5 13 k = kernel19_0_r5_13 k := by decide +kernel +noncomputable def kernel19_0_r5_14 : Fin 16 → CBox := ![⟨⟨2206204208527047508334549,2206204208527047980466760⟩,⟨(-2009919197780221957368465),(-2009919197780221485272736)⟩⟩,⟨⟨2103933160067074374035604,2103933160067074833746219⟩,⟨(-2003978591205534273865127),(-2003978591205533814188518)⟩⟩,⟨⟨2007468085267015178913216,2007468085267015626512285⟩,⟨(-1996222337641775126746377),(-1996222337641774679178996)⟩⟩,⟨⟨1916553138669587683020606,1916553138669588119508627⟩,⟨(-1986939345046737554169535),(-1986939345046737117711039)⟩⟩,⟨⟨1830940876815434928957991,1830940876815435354411378⟩,⟨(-1976391908262373549643399),(-1976391908262373124217511)⟩⟩,⟨⟨1750392725084923136154590,1750392725084923551695823⟩,⟨(-1964817840106762632614102),(-1964817840106762217098483)⟩⟩,⟨⟨1674679331764092532203232,1674679331764092938063936⟩,⟨(-1952432463120770440578211),(-1952432463120770034741361)⟩⟩,⟨⟨1603580824204774545291681,1603580824204774942331414⟩,⟨(-1939430467478422578316899),(-1939430467478422181299382)⟩⟩,⟨⟨1536886980533086643890517,1536886980533087032071977⟩,⟨(-1925987640794513287929913),(-1925987640794512899769137)⟩⟩,⟨⟨1474397329049082919647332,1474397329049083300012967⟩,⟨(-1912262475695336946916637),(-1912262475695336566570270)⟩⟩,⟨⟨1415921186249432209993305,1415921186249432582715030⟩,⟨(-1898397661071784499947907),(-1898397661071784127244129)⟩⟩,⟨⟨1361277643290323788439373,1361277643290324154265276⟩,⟨(-1884521462920129121031912),(-1884521462920128755222734)⟩⟩,⟨⟨1310295509684743741524097,1310295509684744100427208⟩,⟨(-1870749000605100344091253),(-1870749000605099985203730)⟩⟩,⟨⟨1262813222091981178428316,1262813222091981531288574⟩,⟨(-1857183424261592187254518),(-1857183424261591834408800)⟩⟩,⟨⟨1218678725202737817259110,1218678725202738164203723⟩,⟨(-1843916998893750970484057),(-1843916998893750623553014)⟩⟩,⟨⟨1177749330945494881597809,1177749330945495223288308⟩,⟨(-1831032100540417256787605),(-1831032100540416915109782)⟩⟩] +lemma kernel19_0_r5_14_eq : ∀ k : Fin 16, kernel19_0Expr 5 14 k = kernel19_0_r5_14 k := by decide +kernel +noncomputable def kernel19_0_r5_15 : Fin 16 → CBox := ![⟨⟨1139891561533809770181411,1139891561533810106492739⟩,⟨(-1818602129660205184090629),(-1818602129660204847791154)⟩⟩,⟨⟨1104980981234998735386377,1104980981234999067182749⟩,⟨(-1806692346653301370695573),(-1806692346653301038910301)⟩⟩,⟨⟨1072902021163333470464612,1072902021163333797841256⟩,⟨(-1795360634185000091553342),(-1795360634184999764187107)⟩⟩,⟨⟨1043547800880688421124316,1043547800880688744676447⟩,⟨(-1784658190712015797519805),(-1784658190712015473977458)⟩⟩,⟨⟨1016819950119921489011335,1016819950119921808654446⟩,⟨(-1774630159340059627855905),(-1774630159340059308222007)⟩⟩,⟨⟨992628433526719881296282,992628433526720197768845⟩,⟨(-1765316195862805960485822),(-1765316195862805644021962)⟩⟩,⟨⟨970891380939938749628906,970891380939939063004566⟩,⟨(-1756750979550481422362995),(-1756750979550481108995577)⟩⟩,⟨⟨951534925394528863843785,951534925394529174669265⟩,⟨(-1748964669972711106974386),(-1748964669972710796156741)⟩⟩,⟨⟨934493050731100103437805,934493050731100411590108⟩,⟨(-1741983312856390384487140),(-1741983312856390076342314)⟩⟩,⟨⟨919707450428289362779389,919707450428289669031276⟩,⟨(-1735829197696304297995116),(-1735829197696303991750398)⟩⟩,⟨⟨907127399034857930830960,907127399034858235235673⟩,⟨(-1730521169554774760506302),(-1730521169554774456108494)⟩⟩,⟨⟨896709637364462793658891,896709637364463096721723⟩,⟨(-1726074897207298696779082),(-1726074897207298393722941)⟩⟩,⟨⟨888418272424110705319677,888418272424111006921186⟩,⟨(-1722503099514239291028825),(-1722503099514238989433833)⟩⟩,⟨⟨882224692874335872288013,882224692874336173093114⟩,⟨(-1719815731624243461021379),(-1719815731624243160222666)⟩⟩,⟨⟨878107500662190288090313,878107500662190588149036⟩,⟨(-1718020132343112079162210),(-1718020132343111779109789)⟩⟩,⟨⟨876052459324358614588683,876052459324358914387192⟩,⟨(-1717121133732138605502329),(-1717121133732138305710080)⟩⟩] +lemma kernel19_0_r5_15_eq : ∀ k : Fin 16, kernel19_0Expr 5 15 k = kernel19_0_r5_15 k := by decide +kernel +noncomputable def kernel19_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel19_0_r5_0,kernel19_0_r5_1,kernel19_0_r5_2,kernel19_0_r5_3,kernel19_0_r5_4,kernel19_0_r5_5,kernel19_0_r5_6,kernel19_0_r5_7,kernel19_0_r5_8,kernel19_0_r5_9,kernel19_0_r5_10,kernel19_0_r5_11,kernel19_0_r5_12,kernel19_0_r5_13,kernel19_0_r5_14,kernel19_0_r5_15] +lemma kernel19_0_r5_eq (i k : Fin 16) : kernel19_0Expr 5 i k = kernel19_0_r5 i k := by + fin_cases i + · exact kernel19_0_r5_0_eq k + · exact kernel19_0_r5_1_eq k + · exact kernel19_0_r5_2_eq k + · exact kernel19_0_r5_3_eq k + · exact kernel19_0_r5_4_eq k + · exact kernel19_0_r5_5_eq k + · exact kernel19_0_r5_6_eq k + · exact kernel19_0_r5_7_eq k + · exact kernel19_0_r5_8_eq k + · exact kernel19_0_r5_9_eq k + · exact kernel19_0_r5_10_eq k + · exact kernel19_0_r5_11_eq k + · exact kernel19_0_r5_12_eq k + · exact kernel19_0_r5_13_eq k + · exact kernel19_0_r5_14_eq k + · exact kernel19_0_r5_15_eq k +noncomputable def kernel19_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel19_0_r0,kernel19_0_r1,kernel19_0_r2,kernel19_0_r3,kernel19_0_r4,kernel19_0_r5] +lemma kernel19_0_eq (j : Fin 6) (i k : Fin 16) : kernel19_0Expr j i k = kernel19_0 j i k := by + fin_cases j + · exact kernel19_0_r0_eq i k + · exact kernel19_0_r1_eq i k + · exact kernel19_0_r2_eq i k + · exact kernel19_0_r3_eq i k + · exact kernel19_0_r4_eq i k + · exact kernel19_0_r5_eq i k +lemma kernel19_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel19_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(19:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel19_0_eq] + unfold kernel19_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans19_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel19_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans19 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel19_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r0_0_eq : ∀ k : Fin 16, kernel19_1Expr 0 0 k = kernel19_1_r0_0 k := by decide +kernel +noncomputable def kernel19_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r0_1_eq : ∀ k : Fin 16, kernel19_1Expr 0 1 k = kernel19_1_r0_1 k := by decide +kernel +noncomputable def kernel19_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r0_2_eq : ∀ k : Fin 16, kernel19_1Expr 0 2 k = kernel19_1_r0_2 k := by decide +kernel +noncomputable def kernel19_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r0_3_eq : ∀ k : Fin 16, kernel19_1Expr 0 3 k = kernel19_1_r0_3 k := by decide +kernel +noncomputable def kernel19_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r0_4_eq : ∀ k : Fin 16, kernel19_1Expr 0 4 k = kernel19_1_r0_4 k := by decide +kernel +noncomputable def kernel19_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel19_1_r0_5_eq : ∀ k : Fin 16, kernel19_1Expr 0 5 k = kernel19_1_r0_5 k := by decide +kernel +noncomputable def kernel19_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel19_1_r0_6_eq : ∀ k : Fin 16, kernel19_1Expr 0 6 k = kernel19_1_r0_6 k := by decide +kernel +noncomputable def kernel19_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel19_1_r0_7_eq : ∀ k : Fin 16, kernel19_1Expr 0 7 k = kernel19_1_r0_7 k := by decide +kernel +noncomputable def kernel19_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel19_1_r0_8_eq : ∀ k : Fin 16, kernel19_1Expr 0 8 k = kernel19_1_r0_8 k := by decide +kernel +noncomputable def kernel19_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel19_1_r0_9_eq : ∀ k : Fin 16, kernel19_1Expr 0 9 k = kernel19_1_r0_9 k := by decide +kernel +noncomputable def kernel19_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel19_1_r0_10_eq : ∀ k : Fin 16, kernel19_1Expr 0 10 k = kernel19_1_r0_10 k := by decide +kernel +noncomputable def kernel19_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel19_1_r0_11_eq : ∀ k : Fin 16, kernel19_1Expr 0 11 k = kernel19_1_r0_11 k := by decide +kernel +noncomputable def kernel19_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel19_1_r0_12_eq : ∀ k : Fin 16, kernel19_1Expr 0 12 k = kernel19_1_r0_12 k := by decide +kernel +noncomputable def kernel19_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel19_1_r0_13_eq : ∀ k : Fin 16, kernel19_1Expr 0 13 k = kernel19_1_r0_13 k := by decide +kernel +noncomputable def kernel19_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel19_1_r0_14_eq : ∀ k : Fin 16, kernel19_1Expr 0 14 k = kernel19_1_r0_14 k := by decide +kernel +noncomputable def kernel19_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel19_1_r0_15_eq : ∀ k : Fin 16, kernel19_1Expr 0 15 k = kernel19_1_r0_15 k := by decide +kernel +noncomputable def kernel19_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel19_1_r0_0,kernel19_1_r0_1,kernel19_1_r0_2,kernel19_1_r0_3,kernel19_1_r0_4,kernel19_1_r0_5,kernel19_1_r0_6,kernel19_1_r0_7,kernel19_1_r0_8,kernel19_1_r0_9,kernel19_1_r0_10,kernel19_1_r0_11,kernel19_1_r0_12,kernel19_1_r0_13,kernel19_1_r0_14,kernel19_1_r0_15] +lemma kernel19_1_r0_eq (i k : Fin 16) : kernel19_1Expr 0 i k = kernel19_1_r0 i k := by + fin_cases i + · exact kernel19_1_r0_0_eq k + · exact kernel19_1_r0_1_eq k + · exact kernel19_1_r0_2_eq k + · exact kernel19_1_r0_3_eq k + · exact kernel19_1_r0_4_eq k + · exact kernel19_1_r0_5_eq k + · exact kernel19_1_r0_6_eq k + · exact kernel19_1_r0_7_eq k + · exact kernel19_1_r0_8_eq k + · exact kernel19_1_r0_9_eq k + · exact kernel19_1_r0_10_eq k + · exact kernel19_1_r0_11_eq k + · exact kernel19_1_r0_12_eq k + · exact kernel19_1_r0_13_eq k + · exact kernel19_1_r0_14_eq k + · exact kernel19_1_r0_15_eq k +noncomputable def kernel19_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel19_1_r1_0_eq : ∀ k : Fin 16, kernel19_1Expr 1 0 k = kernel19_1_r1_0 k := by decide +kernel +noncomputable def kernel19_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel19_1_r1_1_eq : ∀ k : Fin 16, kernel19_1Expr 1 1 k = kernel19_1_r1_1 k := by decide +kernel +noncomputable def kernel19_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel19_1_r1_2_eq : ∀ k : Fin 16, kernel19_1Expr 1 2 k = kernel19_1_r1_2 k := by decide +kernel +noncomputable def kernel19_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel19_1_r1_3_eq : ∀ k : Fin 16, kernel19_1Expr 1 3 k = kernel19_1_r1_3 k := by decide +kernel +noncomputable def kernel19_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel19_1_r1_4_eq : ∀ k : Fin 16, kernel19_1Expr 1 4 k = kernel19_1_r1_4 k := by decide +kernel +noncomputable def kernel19_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel19_1_r1_5_eq : ∀ k : Fin 16, kernel19_1Expr 1 5 k = kernel19_1_r1_5 k := by decide +kernel +noncomputable def kernel19_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel19_1_r1_6_eq : ∀ k : Fin 16, kernel19_1Expr 1 6 k = kernel19_1_r1_6 k := by decide +kernel +noncomputable def kernel19_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel19_1_r1_7_eq : ∀ k : Fin 16, kernel19_1Expr 1 7 k = kernel19_1_r1_7 k := by decide +kernel +noncomputable def kernel19_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel19_1_r1_8_eq : ∀ k : Fin 16, kernel19_1Expr 1 8 k = kernel19_1_r1_8 k := by decide +kernel +noncomputable def kernel19_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel19_1_r1_9_eq : ∀ k : Fin 16, kernel19_1Expr 1 9 k = kernel19_1_r1_9 k := by decide +kernel +noncomputable def kernel19_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r1_10_eq : ∀ k : Fin 16, kernel19_1Expr 1 10 k = kernel19_1_r1_10 k := by decide +kernel +noncomputable def kernel19_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r1_11_eq : ∀ k : Fin 16, kernel19_1Expr 1 11 k = kernel19_1_r1_11 k := by decide +kernel +noncomputable def kernel19_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r1_12_eq : ∀ k : Fin 16, kernel19_1Expr 1 12 k = kernel19_1_r1_12 k := by decide +kernel +noncomputable def kernel19_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r1_13_eq : ∀ k : Fin 16, kernel19_1Expr 1 13 k = kernel19_1_r1_13 k := by decide +kernel +noncomputable def kernel19_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r1_14_eq : ∀ k : Fin 16, kernel19_1Expr 1 14 k = kernel19_1_r1_14 k := by decide +kernel +noncomputable def kernel19_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel19_1_r1_15_eq : ∀ k : Fin 16, kernel19_1Expr 1 15 k = kernel19_1_r1_15 k := by decide +kernel +noncomputable def kernel19_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel19_1_r1_0,kernel19_1_r1_1,kernel19_1_r1_2,kernel19_1_r1_3,kernel19_1_r1_4,kernel19_1_r1_5,kernel19_1_r1_6,kernel19_1_r1_7,kernel19_1_r1_8,kernel19_1_r1_9,kernel19_1_r1_10,kernel19_1_r1_11,kernel19_1_r1_12,kernel19_1_r1_13,kernel19_1_r1_14,kernel19_1_r1_15] +lemma kernel19_1_r1_eq (i k : Fin 16) : kernel19_1Expr 1 i k = kernel19_1_r1 i k := by + fin_cases i + · exact kernel19_1_r1_0_eq k + · exact kernel19_1_r1_1_eq k + · exact kernel19_1_r1_2_eq k + · exact kernel19_1_r1_3_eq k + · exact kernel19_1_r1_4_eq k + · exact kernel19_1_r1_5_eq k + · exact kernel19_1_r1_6_eq k + · exact kernel19_1_r1_7_eq k + · exact kernel19_1_r1_8_eq k + · exact kernel19_1_r1_9_eq k + · exact kernel19_1_r1_10_eq k + · exact kernel19_1_r1_11_eq k + · exact kernel19_1_r1_12_eq k + · exact kernel19_1_r1_13_eq k + · exact kernel19_1_r1_14_eq k + · exact kernel19_1_r1_15_eq k +noncomputable def kernel19_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-30947170),(-30947142)⟩,⟨35134655,35134685⟩⟩,⟨⟨(-30854877),(-30854850)⟩,⟨35069691,35069721⟩⟩,⟨⟨(-30671065),(-30671024)⟩,⟨34940044,34940084⟩⟩,⟨⟨(-30397242),(-30397214)⟩,⟨34746332,34746362⟩⟩,⟨⟨(-30035696),(-30035668)⟩,⟨34489432,34489462⟩⟩,⟨⟨(-29589393),(-29589360)⟩,⟨34170528,34170561⟩⟩,⟨⟨(-29061970),(-29061929)⟩,⟨33791078,33791118⟩⟩,⟨⟨(-28457683),(-28457653)⟩,⟨33352854,33352882⟩⟩,⟨⟨(-27781397),(-27781368)⟩,⟨32857837,32857865⟩⟩,⟨⟨(-27038437),(-27038407)⟩,⟨32308322,32308350⟩⟩,⟨⟨(-26234593),(-26234563)⟩,⟨31706842,31706869⟩⟩,⟨⟨(-25376019),(-25375989)⟩,⟨31056163,31056190⟩⟩,⟨⟨(-24469176),(-24469149)⟩,⟨30359261,30359291⟩⟩,⟨⟨(-23520718),(-23520690)⟩,⟨29619348,29619378⟩⟩,⟨⟨(-22537475),(-22537442)⟩,⟨28839786,28839819⟩⟩,⟨⟨(-21526302),(-21526264)⟩,⟨28024133,28024168⟩⟩] +lemma kernel19_1_r2_0_eq : ∀ k : Fin 16, kernel19_1Expr 2 0 k = kernel19_1_r2_0 k := by decide +kernel +noncomputable def kernel19_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-20494085),(-20494055)⟩,⟨27176083,27176111⟩⟩,⟨⟨(-19447590),(-19447557)⟩,⟨26299428,26299461⟩⟩,⟨⟨(-18393434),(-18393409)⟩,⟨25398103,25398128⟩⟩,⟨⟨(-17338041),(-17338016)⟩,⟨24476052,24476077⟩⟩,⟨⟨(-16287532),(-16287507)⟩,⟨23537293,23537318⟩⟩,⟨⟨(-15247689),(-15247662)⟩,⟨22585865,22585895⟩⟩,⟨⟨(-14223932),(-14223897)⟩,⟨21625750,21625788⟩⟩,⟨⟨(-13221252),(-13221222)⟩,⟨20660922,20660950⟩⟩,⟨⟨(-12244181),(-12244148)⟩,⟨19695270,19695303⟩⟩,⟨⟨(-11296785),(-11296755)⟩,⟨18732555,18732583⟩⟩,⟨⟨(-10382647),(-10382606)⟩,⟨17776417,17776458⟩⟩,⟨⟨(-9504796),(-9504766)⟩,⟨16830385,16830412⟩⟩,⟨⟨(-8665823),(-8665785)⟩,⟨15897734,15897769⟩⟩,⟨⟨(-7867765),(-7867724)⟩,⟨14981592,14981633⟩⟩,⟨⟨(-7112189),(-7112153)⟩,⟨14084843,14084881⟩⟩,⟨⟨(-6400188),(-6400147)⟩,⟨13210140,13210181⟩⟩] +lemma kernel19_1_r2_1_eq : ∀ k : Fin 16, kernel19_1Expr 2 1 k = kernel19_1_r2_1 k := by decide +kernel +noncomputable def kernel19_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-5732388),(-5732358)⟩,⟨12359888,12359916⟩⟩,⟨⟨(-5109000),(-5108970)⟩,⟨11536215,11536243⟩⟩,⟨⟨(-4529856),(-4529830)⟩,⟨10740995,10741020⟩⟩,⟨⟨(-3994378),(-3994350)⟩,⟨9975816,9975847⟩⟩,⟨⟨(-3501702),(-3501677)⟩,⟨9242014,9242039⟩⟩,⟨⟨(-3050663),(-3050633)⟩,⟨8540626,8540654⟩⟩,⟨⟨(-2639835),(-2639799)⟩,⟨7872427,7872465⟩⟩,⟨⟨(-2267581),(-2267540)⟩,⟨7237947,7237989⟩⟩,⟨⟨(-1932082),(-1932052)⟩,⟨6637467,6637495⟩⟩,⟨⟨(-1631411),(-1631383)⟩,⟨6071001,6071031⟩⟩,⟨⟨(-1363509),(-1363478)⟩,⟨5538373,5538401⟩⟩,⟨⟨(-1126251),(-1126218)⟩,⟨5039181,5039214⟩⟩,⟨⟨(-917472),(-917439)⟩,⟨4572835,4572869⟩⟩,⟨⟨(-735000),(-734972)⟩,⟨4138589,4138620⟩⟩,⟨⟨(-576678),(-576650)⟩,⟨3735555,3735585⟩⟩,⟨⟨(-440398),(-440365)⟩,⟨3362659,3362693⟩⟩] +lemma kernel19_1_r2_2_eq : ∀ k : Fin 16, kernel19_1Expr 2 2 k = kernel19_1_r2_2 k := by decide +kernel +noncomputable def kernel19_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-324095),(-324064)⟩,⟨3018788,3018816⟩⟩,⟨⟨(-225779),(-225749)⟩,⟨2702687,2702715⟩⟩,⟨⟨(-143566),(-143533)⟩,⟨2413058,2413091⟩⟩,⟨⟨(-75660),(-75632)⟩,⟨2148515,2148546⟩⟩,⟨⟨(-20367),(-20333)⟩,⟨1907688,1907722⟩⟩,⟨⟨23877,23908⟩,⟨1689135,1689163⟩⟩,⟨⟨58530,58564⟩,⟨1491436,1491469⟩⟩,⟨⟨84931,84959⟩,⟨1313180,1313211⟩⟩,⟨⟨104274,104316⟩,⟨1152950,1152992⟩⟩,⟨⟨117682,117712⟩,⟨1009415,1009444⟩⟩,⟨⟨126118,126146⟩,⟨881227,881258⟩⟩,⟨⟨130478,130507⟩,⟨767114,767145⟩⟩,⟨⟨131523,131549⟩,⟨665868,665893⟩⟩,⟨⟨129925,129951⟩,⟨576303,576329⟩⟩,⟨⟨126282,126316⟩,⟨497341,497374⟩⟩,⟨⟨121099,121142⟩,⟨427934,427976⟩⟩] +lemma kernel19_1_r2_3_eq : ∀ k : Fin 16, kernel19_1Expr 2 3 k = kernel19_1_r2_3 k := by decide +kernel +noncomputable def kernel19_1_r2_4 : Fin 16 → CBox := ![⟨⟨114811,114842⟩,⟨367154,367183⟩⟩,⟨⟨107751,107780⟩,⟨314080,314111⟩⟩,⟨⟨100235,100266⟩,⟨267874,267902⟩⟩,⟨⟨92507,92541⟩,⟨227793,227827⟩⟩,⟨⟨84767,84809⟩,⟨193125,193167⟩⟩,⟨⟨77165,77196⟩,⟨163252,163281⟩⟩,⟨⟨69815,69849⟩,⟨137572,137606⟩⟩,⟨⟨62797,62831⟩,⟨115578,115612⟩⟩,⟨⟨56196,56230⟩,⟨96806,96840⟩⟩,⟨⟨50030,50064⟩,⟨80834,80869⟩⟩,⟨⟨44317,44360⟩,⟨67284,67327⟩⟩,⟨⟨39101,39127⟩,⟨55845,55871⟩⟩,⟨⟨34330,34365⟩,⟨46188,46223⟩⟩,⟨⟨30022,30053⟩,⟨38089,38118⟩⟩,⟨⟨26142,26177⟩,⟨31299,31334⟩⟩,⟨⟨22692,22718⟩,⟨25641,25667⟩⟩] +lemma kernel19_1_r2_4_eq : ∀ k : Fin 16, kernel19_1Expr 2 4 k = kernel19_1_r2_4 k := by decide +kernel +noncomputable def kernel19_1_r2_5 : Fin 16 → CBox := ![⟨⟨19604,19639⟩,⟨20936,20970⟩⟩,⟨⟨16883,16917⟩,⟨17029,17064⟩⟩,⟨⟨14487,14522⟩,⟨13817,13851⟩⟩,⟨⟨12400,12430⟩,⟨11164,11196⟩⟩,⟨⟨10565,10600⟩,⟨8991,9026⟩⟩,⟨⟨8980,9006⟩,⟨7213,7239⟩⟩,⟨⟨7600,7635⟩,⟨5765,5800⟩⟩,⟨⟨6418,6448⟩,⟨4588,4620⟩⟩,⟨⟨5396,5427⟩,⟨3643,3672⟩⟩,⟨⟨4537,4568⟩,⟨2872,2902⟩⟩,⟨⟨3787,3819⟩,⟨2256,2286⟩⟩,⟨⟨3164,3199⟩,⟨1763,1798⟩⟩,⟨⟨2633,2668⟩,⟨1371,1406⟩⟩,⟨⟨2170,2205⟩,⟨1067,1102⟩⟩,⟨⟨1804,1839⟩,⟨825,860⟩⟩,⟨⟨1483,1513⟩,⟨623,655⟩⟩] +lemma kernel19_1_r2_5_eq : ∀ k : Fin 16, kernel19_1Expr 2 5 k = kernel19_1_r2_5 k := by decide +kernel +noncomputable def kernel19_1_r2_6 : Fin 16 → CBox := ![⟨⟨1220,1247⟩,⟨476,503⟩⟩,⟨⟨1003,1038⟩,⟨363,398⟩⟩,⟨⟨819,854⟩,⟨260,295⟩⟩,⟨⟨667,699⟩,⟨196,226⟩⟩,⟨⟨530,574⟩,⟨141,185⟩⟩,⟨⟨427,471⟩,⟨97,141⟩⟩,⟨⟨356,383⟩,⟨75,102⟩⟩,⟨⟨286,322⟩,⟨43,79⟩⟩,⟨⟨231,263⟩,⟨27,58⟩⟩,⟨⟨184,220⟩,⟨13,49⟩⟩,⟨⟨137,168⟩,⟨2,35⟩⟩,⟨⟨111,147⟩,⟨(-6),30⟩⟩,⟨⟨85,121⟩,⟨(-12),24⟩⟩,⟨⟨64,100⟩,⟨(-20),16⟩⟩,⟨⟨45,90⟩,⟨(-19),26⟩⟩,⟨⟨40,76⟩,⟨(-12),24⟩⟩] +lemma kernel19_1_r2_6_eq : ∀ k : Fin 16, kernel19_1Expr 2 6 k = kernel19_1_r2_6 k := by decide +kernel +noncomputable def kernel19_1_r2_7 : Fin 16 → CBox := ![⟨⟨22,58⟩,⟨(-15),21⟩⟩,⟨⟨14,50⟩,⟨(-17),19⟩⟩,⟨⟨14,50⟩,⟨(-17),19⟩⟩,⟨⟨5,37⟩,⟨(-19),13⟩⟩,⟨⟨5,37⟩,⟨(-19),13⟩⟩,⟨⟨(-8),38⟩,⟨(-29),16⟩⟩,⟨⟨(-8),23⟩,⟨(-22),11⟩⟩,⟨⟨(-8),23⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩] +lemma kernel19_1_r2_7_eq : ∀ k : Fin 16, kernel19_1Expr 2 7 k = kernel19_1_r2_7 k := by decide +kernel +noncomputable def kernel19_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-8),24⟩,⟨(-22),11⟩⟩,⟨⟨(-19),28⟩,⟨(-22),24⟩⟩,⟨⟨(-19),28⟩,⟨(-22),24⟩⟩,⟨⟨(-19),28⟩,⟨(-22),24⟩⟩,⟨⟨(-19),28⟩,⟨(-23),24⟩⟩,⟨⟨(-19),28⟩,⟨(-23),24⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel19_1_r2_8_eq : ∀ k : Fin 16, kernel19_1Expr 2 8 k = kernel19_1_r2_8 k := by decide +kernel +noncomputable def kernel19_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel19_1_r2_9_eq : ∀ k : Fin 16, kernel19_1Expr 2 9 k = kernel19_1_r2_9 k := by decide +kernel +noncomputable def kernel19_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel19_1_r2_10_eq : ∀ k : Fin 16, kernel19_1Expr 2 10 k = kernel19_1_r2_10 k := by decide +kernel +noncomputable def kernel19_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel19_1_r2_11_eq : ∀ k : Fin 16, kernel19_1Expr 2 11 k = kernel19_1_r2_11 k := by decide +kernel +noncomputable def kernel19_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel19_1_r2_12_eq : ∀ k : Fin 16, kernel19_1Expr 2 12 k = kernel19_1_r2_12 k := by decide +kernel +noncomputable def kernel19_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel19_1_r2_13_eq : ∀ k : Fin 16, kernel19_1Expr 2 13 k = kernel19_1_r2_13 k := by decide +kernel +noncomputable def kernel19_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel19_1_r2_14_eq : ∀ k : Fin 16, kernel19_1Expr 2 14 k = kernel19_1_r2_14 k := by decide +kernel +noncomputable def kernel19_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel19_1_r2_15_eq : ∀ k : Fin 16, kernel19_1Expr 2 15 k = kernel19_1_r2_15 k := by decide +kernel +noncomputable def kernel19_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel19_1_r2_0,kernel19_1_r2_1,kernel19_1_r2_2,kernel19_1_r2_3,kernel19_1_r2_4,kernel19_1_r2_5,kernel19_1_r2_6,kernel19_1_r2_7,kernel19_1_r2_8,kernel19_1_r2_9,kernel19_1_r2_10,kernel19_1_r2_11,kernel19_1_r2_12,kernel19_1_r2_13,kernel19_1_r2_14,kernel19_1_r2_15] +lemma kernel19_1_r2_eq (i k : Fin 16) : kernel19_1Expr 2 i k = kernel19_1_r2 i k := by + fin_cases i + · exact kernel19_1_r2_0_eq k + · exact kernel19_1_r2_1_eq k + · exact kernel19_1_r2_2_eq k + · exact kernel19_1_r2_3_eq k + · exact kernel19_1_r2_4_eq k + · exact kernel19_1_r2_5_eq k + · exact kernel19_1_r2_6_eq k + · exact kernel19_1_r2_7_eq k + · exact kernel19_1_r2_8_eq k + · exact kernel19_1_r2_9_eq k + · exact kernel19_1_r2_10_eq k + · exact kernel19_1_r2_11_eq k + · exact kernel19_1_r2_12_eq k + · exact kernel19_1_r2_13_eq k + · exact kernel19_1_r2_14_eq k + · exact kernel19_1_r2_15_eq k +noncomputable def kernel19_1_r3_0 : Fin 16 → CBox := ![⟨⟨1769022668794824351,1769022668794824389⟩,⟨(-1409198506768214178),(-1409198506768214140)⟩⟩,⟨⟨1765368675676531322,1765368675676531353⟩,⟨(-1408592706292093983),(-1408592706292093951)⟩⟩,⟨⟨1758078091239348939,1758078091239348970⟩,⟨(-1407374831066161285),(-1407374831066161254)⟩⟩,⟨⟨1747185616915020560,1747185616915020592⟩,⟨(-1405532450956486970),(-1405532450956486938)⟩⟩,⟨⟨1732743049799421194,1732743049799421226⟩,⟨(-1403047214952958338),(-1403047214952958307)⟩⟩,⟨⟨1714818977624394527,1714818977624394558⟩,⟨(-1399895199066123257),(-1399895199066123225)⟩⟩,⟨⟨1693498373804363853,1693498373804363901⟩,⟨(-1396047361719509846),(-1396047361719509800)⟩⟩,⟨⟨1668882094112335305,1668882094112335336⟩,⟨(-1391470099542812580),(-1391470099542812548)⟩⟩,⟨⟨1641086276992997984,1641086276992998015⟩,⟨(-1386125894901908785),(-1386125894901908754)⟩⟩,⟨⟨1610241650012174857,1610241650012174889⟩,⟨(-1379974045064270414),(-1379974045064270382)⟩⟩,⟨⟨1576492745475266682,1576492745475266713⟩,⟨(-1372971461615290578),(-1372971461615290547)⟩⟩,⟨⟨1539997028823812501,1539997028823812533⟩,⟨(-1365073527632500290),(-1365073527632500259)⟩⟩,⟨⟨1500923944037802727,1500923944037802759⟩,⟨(-1356234999208268501),(-1356234999208268469)⟩⟩,⟨⟨1459453880928457533,1459453880928457566⟩,⟨(-1346410937202232839),(-1346410937202232802)⟩⟩,⟨⟨1415777069895913913,1415777069895913944⟩,⟨(-1335557654614228306),(-1335557654614228275)⟩⟩,⟨⟨1370092410440353290,1370092410440353322⟩,⟨(-1323633664705418114),(-1323633664705418082)⟩⟩] +lemma kernel19_1_r3_0_eq : ∀ k : Fin 16, kernel19_1Expr 3 0 k = kernel19_1_r3_0 k := by decide +kernel +noncomputable def kernel19_1_r3_1 : Fin 16 → CBox := ![⟨⟨1322606240442997088,1322606240442997120⟩,⟨(-1310600614964769452),(-1310600614964769420)⟩⟩,⟨⟨1273531053962501499,1273531053962501531⟩,⟨(-1296424192221428812),(-1296424192221428780)⟩⟩,⟨⟨1223084176008234229,1223084176008234265⟩,⟨(-1281074984638699014),(-1281074984638698981)⟩⟩,⟨⟨1171486403438935975,1171486403438936007⟩,⟨(-1264529286986218969),(-1264529286986218937)⟩⟩,⟨⟨1118960621776570519,1118960621776570545⟩,⟨(-1246769836463881894),(-1246769836463881868)⟩⟩,⟨⟨1065730408303402247,1065730408303402273⟩,⟨(-1227786467430638626),(-1227786467430638600)⟩⟩,⟨⟨1012018632308091863,1012018632308091895⟩,⟨(-1207576674656760417),(-1207576674656760385)⟩⟩,⟨⟨958046063746890327,958046063746890355⟩,⟨(-1186146076149241016),(-1186146076149240986)⟩⟩,⟨⟨904030001872811413,904030001872811439⟩,⟨(-1163508768173661114),(-1163508768173661089)⟩⟩,⟨⟨850182935544410123,850182935544410142⟩,⟨(-1139687566786229445),(-1139687566786229426)⟩⟩,⟨⟨796711246943867429,796711246943867460⟩,⟨(-1114714131968823984),(-1114714131968823953)⟩⟩,⟨⟨743813970301256760,743813970301256792⟩,⟨(-1088628972297877825),(-1088628972297877793)⟩⟩,⟨⟨691681616930705667,691681616930705699⟩,⟨(-1061481329943825728),(-1061481329943825696)⟩⟩,⟨⟨640495077430352272,640495077430352299⟩,⟨(-1033328947659783366),(-1033328947659783336)⟩⟩,⟨⟨590424611280587668,590424611280587694⟩,⟨(-1004237721244294610),(-1004237721244294585)⟩⟩,⟨⟨541628933296681313,541628933296681334⟩,⟨(-974281242721964450),(-974281242721964426)⟩⟩] +lemma kernel19_1_r3_1_eq : ∀ k : Fin 16, kernel19_1Expr 3 1 k = kernel19_1_r3_1 k := by decide +kernel +noncomputable def kernel19_1_r3_2 : Fin 16 → CBox := ![⟨⟨494254405458738511,494254405458738532⟩,⟨(-943540241147310715),(-943540241147310691)⟩⟩,⟨⟨448434341563882000,448434341563882020⟩,⟨(-912101929472636127),(-912101929472636107)⟩⟩,⟨⟨404288430935921571,404288430935921603⟩,⟨(-880059267303845497),(-880059267303845465)⟩⟩,⟨⟨361922286103200096,361922286103200116⟩,⟨(-847510150575441536),(-847510150575441516)⟩⟩,⟨⟨321427117935383475,321427117935383501⟩,⟨(-814556540187275416),(-814556540187275390)⟩⟩,⟨⟨282879540236889215,282879540236889246⟩,⟨(-781303542444598566),(-781303542444598539)⟩⟩,⟨⟨246341504252738077,246341504252738103⟩,⟨(-747858454717253836),(-747858454717253811)⟩⟩,⟨⟨211860361977774806,211860361977774832⟩,⟨(-714329790075509839),(-714329790075509813)⟩⟩,⟨⟨179469055599353431,179469055599353451⟩,⟨(-680826294765669724),(-680826294765669704)⟩⟩,⟨⟨149186428874031352,149186428874031378⟩,⟨(-647455972259363348),(-647455972259363322)⟩⟩,⟨⟨121017654767632294,121017654767632328⟩,⟨(-614325127252115695),(-614325127252115658)⟩⟩,⟨⟨94954772301409329,94954772301409349⟩,⟨(-581537442409559975),(-581537442409559955)⟩⟩,⟨⟨70977324269657681,70977324269657703⟩,⟨(-549193099877903101),(-549193099877903077)⟩⟩,⟨⟨49053086348599953,49053086348599975⟩,⟨(-517387958607176655),(-517387958607176631)⟩⟩,⟨⟨29138877122683633,29138877122683658⟩,⟨(-486212797403064241),(-486212797403064220)⟩⟩,⟨⟨11181437729498136,11181437729498169⟩,⟨(-455752632350247823),(-455752632350247790)⟩⟩] +lemma kernel19_1_r3_2_eq : ∀ k : Fin 16, kernel19_1Expr 3 2 k = kernel19_1_r3_2 k := by decide +kernel +noncomputable def kernel19_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-4881630818238354),(-4881630818238328)⟩,⟨(-426086115864172892),(-426086115864172866)⟩⟩,⟨⟨(-19120885026100122),(-19120885026100102)⟩,⟨(-397285023157530031),(-397285023157530011)⟩⟩,⟨⟨(-31614023672690710),(-31614023672690690)⟩,⟨(-369413830382292825),(-369413830382292805)⟩⟩,⟨⟨(-42444852625943201),(-42444852625943173)⟩,⟨(-342529387157940767),(-342529387157940737)⟩⟩,⟨⟨(-51702242278969720),(-51702242278969700)⟩,⟨(-316680684651352201),(-316680684651352181)⟩⟩,⟨⟨(-59479089831036553),(-59479089831036522)⟩,⟨(-291908718862666743),(-291908718862666715)⟩⟩,⟨⟨(-65871298126903529),(-65871298126903504)⟩,⟨(-268246447321523962),(-268246447321523941)⟩⟩,⟨⟨(-70976782089181476),(-70976782089181456)⟩,⟨(-245718836034698841),(-245718836034698821)⟩⟩,⟨⟨(-74894512950292212),(-74894512950292192)⟩,⟨(-224342992271855762),(-224342992271855742)⟩⟩,⟨⟨(-77723609532455239),(-77723609532455213)⟩,⟨(-204128377650459663),(-204128377650459637)⟩⟩,⟨⟨(-79562484757385501),(-79562484757385481)⟩,⟨(-185077094999941627),(-185077094999941607)⟩⟩,⟨⟨(-80508054415150864),(-80508054415150844)⟩,⟨(-167184241661498580),(-167184241661498560)⟩⟩,⟨⟨(-80655014007983283),(-80655014007983256)⟩,⟨(-150438321222096445),(-150438321222096419)⟩⟩,⟨⟨(-80095188234252256),(-80095188234252236)⟩,⟨(-134821705194181135),(-134821705194181115)⟩⟩,⟨⟨(-78916956414615383),(-78916956414615355)⟩,⟨(-120311135837316209),(-120311135837316178)⟩⟩,⟨⟨(-77204755910163532),(-77204755910163512)⟩,⟨(-106878261171833706),(-106878261171833686)⟩⟩] +lemma kernel19_1_r3_3_eq : ∀ k : Fin 16, kernel19_1Expr 3 3 k = kernel19_1_r3_3 k := by decide +kernel +noncomputable def kernel19_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-75038664363549682),(-75038664363549661)⟩,⟨(-94490193251541233),(-94490193251541213)⟩⟩,⟨⟨(-72494060429306334),(-72494060429306314)⟩,⟨(-83110080933371811),(-83110080933371791)⟩⟩,⟨⟨(-69641361567396295),(-69641361567396264)⟩,⟨(-72697688694624042),(-72697688694624014)⟩⟩,⟨⟨(-66545836470653786),(-66545836470653766)⟩,⟨(-63209973488795734),(-63209973488795714)⟩⟩,⟨⟨(-63267488795625089),(-63267488795625068)⟩,⟨(-54601652182749276),(-54601652182749256)⟩⟩,⟨⟨(-59861008078016843),(-59861008078016817)⟩,⟨(-46825752763434027),(-46825752763434001)⟩⟩,⟨⟨(-56375783046166118),(-56375783046166085)⟩,⟨(-39834143223083086),(-39834143223083053)⟩⟩,⟨⟨(-52855972003351799),(-52855972003351779)⟩,⟨(-33578032808717837),(-33578032808717817)⟩⟩,⟨⟨(-49340624534167470),(-49340624534167438)⟩,⟨(-28008441135993008),(-28008441135992980)⟩⟩,⟨⟨(-45863848500598653),(-45863848500598618)⟩,⟨(-23076631500433149),(-23076631500433111)⟩⟩,⟨⟨(-42455016126349103),(-42455016126349081)⟩,⟨(-18734505553367634),(-18734505553367609)⟩⟩,⟨⟨(-39139002917476831),(-39139002917476811)⟩,⟨(-14934957329014206),(-14934957329014185)⟩⟩,⟨⟨(-35936453225638567),(-35936453225638546)⟩,⟨(-11632185398374462),(-11632185398374442)⟩⟩,⟨⟨(-32864066417604830),(-32864066417604809)⟩,⟨(-8781962671839253),(-8781962671839233)⟩⟩,⟨⟨(-29934897860244347),(-29934897860244326)⟩,⟨(-6341864064553469),(-6341864064553449)⟩⟩,⟨⟨(-27158669251932216),(-27158669251932196)⟩,⟨(-4271452867613147),(-4271452867613127)⟩⟩] +lemma kernel19_1_r3_4_eq : ∀ k : Fin 16, kernel19_1Expr 3 4 k = kernel19_1_r3_4 k := by decide +kernel +noncomputable def kernel19_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-24542083216714506),(-24542083216714485)⟩,⟨(-2532427227125720),(-2532427227125700)⟩⟩,⟨⟨(-22089137513664587),(-22089137513664566)⟩,⟨(-1088728617221842),(-1088728617221821)⟩⟩,⟨⟨(-19801434687824921),(-19801434687824899)⟩,⟨93385400528700,93385400528725⟩⟩,⟨⟨(-17678483488397547),(-17678483488397522)⟩,⟨1045301511035129,1045301511035152⟩⟩,⟨⟨(-15717988892475834),(-15717988892475806)⟩,⟨1796041202497892,1796041202497920⟩⟩,⟨⟨(-13916128087467852),(-13916128087467832)⟩,⟨2372278500604795,2372278500604815⟩⟩,⟨⟨(-12267810272322896),(-12267810272322875)⟩,⟨2798381730720749,2798381730720770⟩⟩,⟨⟨(-10766918627764526),(-10766918627764505)⟩,⟨3096476120905551,3096476120905571⟩⟩,⟨⟨(-9406533271235776),(-9406533271235753)⟩,⟨3286524080903396,3286524080903421⟩⟩,⟨⟨(-8179134446765643),(-8179134446765615)⟩,⟨3386420067924241,3386420067924269⟩⟩,⟨⟨(-7076785598394699),(-7076785598394679)⟩,⟨3412097071895294,3412097071895315⟩⟩,⟨⟨(-6091296334389789),(-6091296334389750)⟩,⟨3377641913469392,3377641913469428⟩⟩,⟨⟨(-5214365605737161),(-5214365605737138)⟩,⟨3295416739961408,3295416739961434⟩⟩,⟨⟨(-4437705695026245),(-4437705695026224)⟩,⟨3176184320209680,3176184320209701⟩⟩,⟨⟨(-3753147840603897),(-3753147840603876)⟩,⟨3029234972095595,3029234972095616⟩⟩,⟨⟨(-3152730506553143),(-3152730506553122)⟩,⟨2862513199503446,2862513199503467⟩⟩] +lemma kernel19_1_r3_5_eq : ∀ k : Fin 16, kernel19_1Expr 3 5 k = kernel19_1_r3_5 k := by decide +kernel +noncomputable def kernel19_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-2628771453230197),(-2628771453230171)⟩,⟨2682742362814757,2682742362814779⟩⟩,⟨⟨(-2173924868091789),(-2173924868091762)⟩,⟨2495545953181247,2495545953181274⟩⟩,⟨⟨(-1781224885239911),(-1781224885239882)⟩,⟨2305564281068239,2305564281068271⟩⟩,⟨⟨(-1444116857814508),(-1444116857814487)⟩,⟨2116565619878558,2116565619878579⟩⟩,⟨⟨(-1156477753686957),(-1156477753686931)⟩,⟨1931551062553595,1931551062553618⟩⟩,⟨⟨(-912627025633789),(-912627025633766)⟩,⟨1752852550313040,1752852550313066⟩⟩,⟨⟨(-707329266150894),(-707329266150872)⟩,⟨1582223716232299,1582223716232320⟩⟩,⟨⟨(-535789898112652),(-535789898112619)⟩,⟨1420923350903211,1420923350903240⟩⟩,⟨⟨(-393645079276543),(-393645079276504)⟩,⟨1269791442303053,1269791442303090⟩⟩,⟨⟨(-276946914672094),(-276946914672073)⟩,⟨1129317867058824,1129317867058845⟩⟩,⟨⟨(-182144979431988),(-182144979431958)⟩,⟨999703915844512,999703915844545⟩⟩,⟨⟨(-106065058565454),(-106065058565428)⟩,⟨880916922383971,880916922383994⟩⟩,⟨⟨(-45885912158826),(-45885912158805)⟩,⟨772738334459059,772738334459080⟩⟩,⟨⟨885223209498,885223209524⟩,⟨674805617700217,674805617700240⟩⟩,⟨⟨36437781499460,36437781499482⟩,⟨586648420200226,586648420200247⟩⟩,⟨⟨62683138954036,62683138954066⟩,⟨507719449698086,507719449698119⟩⟩] +lemma kernel19_1_r3_6_eq : ∀ k : Fin 16, kernel19_1Expr 3 6 k = kernel19_1_r3_6 k := by decide +kernel +noncomputable def kernel19_1_r3_7 : Fin 16 → CBox := ![⟨⟨81279573337589,81279573337610⟩,⟨437420526849453,437420526849475⟩⟩,⟨⟨93656553907631,93656553907652⟩,⟨375124279566631,375124279566653⟩⟩,⟨⟨101038079105269,101038079105290⟩,⟨320191936185235,320191936185256⟩⟩,⟨⟨104464845568061,104464845568083⟩,⟨271987660840113,271987660840134⟩⟩,⟨⟨104815091377654,104815091377675⟩,⟨229889854370878,229889854370900⟩⟩,⟨⟨102824008461180,102824008461203⟩,⟨193299819671350,193299819671376⟩⟩,⟨⟨99101663941323,99101663941344⟩,⟨161648162871787,161648162871808⟩⟩,⟨⟨94149408277402,94149408277424⟩,⟨134399272184055,134399272184077⟩⟩,⟨⟨88374779662021,88374779662043⟩,⟨111054185598964,111054185598986⟩⟩,⟨⟨82104939813814,82104939813836⟩,⟨91152127711171,91152127711193⟩⟩,⟨⟨75598696565280,75598696565314⟩,⟨74270965440144,74270965440174⟩⟩,⟨⟨69057184042745,69057184042773⟩,⟨60026802862391,60026802862420⟩⟩,⟨⟨62633282340989,62633282341013⟩,⟨48072907204131,48072907204158⟩⟩,⟨⟨56439865970152,56439865970176⟩,⟨38098131585343,38098131585370⟩⟩,⟨⟨50556974539711,50556974539733⟩,⟨29824975583315,29824975583337⟩⟩,⟨⟨45038000660252,45038000660274⟩,⟨23007402236848,23007402236870⟩⟩] +lemma kernel19_1_r3_7_eq : ∀ k : Fin 16, kernel19_1Expr 3 7 k = kernel19_1_r3_7 k := by decide +kernel +noncomputable def kernel19_1_r3_8 : Fin 16 → CBox := ![⟨⟨39914989367081,39914989367110⟩,⟨17428509810001,17428509810030⟩⟩,⟨⟨35203140939325,35203140939347⟩,⟨12898138484753,12898138484775⟩⟩,⟨⟨30904605199054,30904605199081⟩,⟨9250476111975,9250476111999⟩⟩,⟨⟨27011650577232,27011650577266⟩,⟨6341713140238,6341713140269⟩⟩,⟨⟨23509285729489,23509285729518⟩,⟨4047784748310,4047784748339⟩⟩,⟨⟨20377405538370,20377405538392⟩,⟨2262227899589,2262227899611⟩⟩,⟨⟨17592527165440,17592527165462⟩,⟨894172366860,894172366882⟩⟩,⟨⟨15129175598854,15129175598877⟩,⟨(-133522410029),(-133522410007)⟩⟩,⟨⟨12960972022569,12960972022604⟩,⟨(-885978629553),(-885978629521)⟩⟩,⟨⟨11061472426067,11061472426092⟩,⟨(-1417858278759),(-1417858278732)⟩⟩,⟨⟨9404798261186,9404798261208⟩,⟨(-1774770473382),(-1774770473360)⟩⟩,⟨⟨7966095696784,7966095696814⟩,⟨(-1994533113981),(-1994533113952)⟩⟩,⟨⟨6721855160029,6721855160051⟩,⟨(-2108296016300),(-2108296016278)⟩⟩,⟨⟨5650118407358,5650118407385⟩,⟨(-2141534077049),(-2141534077024)⟩⟩,⟨⟨4730596346064,4730596346105⟩,⟨(-2114919919885),(-2114919919846)⟩⟩,⟨⟨3944717223132,3944717223156⟩,⟨(-2045085928600),(-2045085928573)⟩⟩] +lemma kernel19_1_r3_8_eq : ∀ k : Fin 16, kernel19_1Expr 3 8 k = kernel19_1_r3_8 k := by decide +kernel +noncomputable def kernel19_1_r3_9 : Fin 16 → CBox := ![⟨⟨3275621600387,3275621600417⟩,⟨(-1945285700274),(-1945285700244)⟩⟩,⟨⟨2708117722694,2708117722724⟩,⟨(-1825964815792),(-1825964815762)⟩⟩,⟨⟨2228608434914,2228608434941⟩,⟨(-1695250492883),(-1695250492858)⟩⟩,⟨⟨1824998686583,1824998686620⟩,⟨(-1559369210797),(-1559369210760)⟩⟩,⟨⟨1486590850691,1486590850713⟩,⟨(-1423000822184),(-1423000822161)⟩⟩,⟨⟨1203973545334,1203973545357⟩,⟨(-1289577033235),(-1289577033212)⟩⟩,⟨⟨968908355257,968908355287⟩,⟨(-1161531467085),(-1161531467055)⟩⟩,⟨⟨774217774320,774217774360⟩,⟨(-1040507852566),(-1040507852524)⟩⟩,⟨⟨613676805287,613676805317⟩,⟨(-927532217597),(-927532217567)⟩⟩,⟨⟨481909931859,481909931882⟩,⟨(-823154328170),(-823154328147)⟩⟩,⟨⟨374294599208,374294599231⟩,⟨(-727563009060),(-727563009037)⟩⟩,⟨⟨286871879675,286871879708⟩,⟨(-640679418371),(-640679418335)⟩⟩,⟨⟨216264643372,216264643404⟩,⟨(-562231827770),(-562231827735)⟩⟩,⟨⟨159603280169,159603280196⟩,⟨(-491814986073),(-491814986048)⟩⟩,⟨⟨114458817042,114458817065⟩,⟨(-428936715926),(-428936715903)⟩⟩,⟨⟨78783128700,78783128725⟩,⟨(-373054010518),(-373054010490)⟩⟩] +lemma kernel19_1_r3_9_eq : ∀ k : Fin 16, kernel19_1Expr 3 9 k = kernel19_1_r3_9 k := by decide +kernel +noncomputable def kernel19_1_r3_10 : Fin 16 → CBox := ![⟨⟨50855840030,50855840053⟩,⟨(-323600557520),(-323600557497)⟩⟩,⟨⟨29237455490,29237455513⟩,⟨(-280007318746),(-280007318723)⟩⟩,⟨⟨12728216583,12728216608⟩,⟨(-241717532448),(-241717532420)⟩⟩,⟨⟨332175984,332176017⟩,⟨(-208197278765),(-208197278729)⟩⟩,⟨⟨(-8774018661),(-8774018632)⟩,⟨(-178942553348),(-178942553322)⟩⟩,⟨⟨(-15268122318),(-15268122288)⟩,⟨(-153483626998),(-153483626968)⟩⟩,⟨⟨(-19705537339),(-19705537294)⟩,⟨(-131387326742),(-131387326697)⟩⟩,⟨⟨(-22539241740),(-22539241717)⟩,⟨(-112257753557),(-112257753534)⟩⟩,⟨⟨(-24136803419),(-24136803391)⟩,⟨(-95735851136),(-95735851110)⟩⟩,⟨⟨(-24794847888),(-24794847850)⟩,⟨(-81498155312),(-81498155274)⟩⟩,⟨⟨(-24751312481),(-24751312458)⟩,⟨(-69254984478),(-69254984454)⟩⟩,⟨⟨(-24195785431),(-24195785408)⟩,⟨(-58748273564),(-58748273541)⟩⟩,⟨⟨(-23278195653),(-23278195612)⟩,⟨(-49749207097),(-49749207054)⟩⟩,⟨⟨(-22116088363),(-22116088318)⟩,⟨(-42055768874),(-42055768828)⟩⟩,⟨⟨(-20800693574),(-20800693548)⟩,⟨(-35490295261),(-35490295233)⟩⟩,⟨⟨(-19401967881),(-19401967848)⟩,⟨(-29897094412),(-29897094376)⟩⟩] +lemma kernel19_1_r3_10_eq : ∀ k : Fin 16, kernel19_1Expr 3 10 k = kernel19_1_r3_10 k := by decide +kernel +noncomputable def kernel19_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-17972766739),(-17972766716)⟩,⟨(-25140174671),(-25140174648)⟩⟩,⟨⟨(-16552283430),(-16552283404)⟩,⟨(-21101110423),(-21101110394)⟩⟩,⟨⟨(-15168871506),(-15168871477)⟩,⟨(-17677061831),(-17677061805)⟩⟩,⟨⟨(-13842351155),(-13842351124)⟩,⟨(-14778956517),(-14778956486)⟩⟩,⟨⟨(-12585885290),(-12585885266)⟩,⟨(-12329834438),(-12329834415)⟩⟩,⟨⟨(-11407497976),(-11407497953)⟩,⟨(-10263352676),(-10263352653)⟩⟩,⟨⟨(-10311296956),(-10311296909)⟩,⟨(-8522443595),(-8522443549)⟩⟩,⟨⟨(-9298452202),(-9298452168)⟩,⟨(-7058117360),(-7058117324)⟩⟩,⟨⟨(-8367974313),(-8367974282)⟩,⟨(-5828399216),(-5828399185)⟩⟩,⟨⟨(-7517329064),(-7517329032)⟩,⟨(-4797390200),(-4797390169)⟩⟩,⟨⟨(-6742918786),(-6742918755)⟩,⟨(-3934440692),(-3934440660)⟩⟩,⟨⟨(-6040455839),(-6040455812)⟩,⟨(-3213425975),(-3213425946)⟩⟩,⟨⟨(-5405249022),(-5405248996)⟩,⟨(-2612113296),(-2612113268)⟩⟩,⟨⟨(-4832420330),(-4832420283)⟩,⟨(-2111610672),(-2111610626)⟩⟩,⟨⟨(-4317066078),(-4317066047)⟩,⟨(-1695888284),(-1695888253)⟩⟩,⟨⟨(-3854374203),(-3854374171)⟩,⟨(-1351364064),(-1351364033)⟩⟩] +lemma kernel19_1_r3_11_eq : ∀ k : Fin 16, kernel19_1Expr 3 11 k = kernel19_1_r3_11 k := by decide +kernel +noncomputable def kernel19_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-3439706798),(-3439706766)⟩,⟨(-1066545630),(-1066545598)⟩⟩,⟨⟨(-3068655952),(-3068655928)⟩,⟨(-831721699),(-831721675)⟩⟩,⟨⟨(-2737078749),(-2737078722)⟩,⟨(-638696879),(-638696850)⟩⟩,⟨⟨(-2441116508),(-2441116482)⟩,⟨(-480563814),(-480563785)⟩⟩,⟨⟨(-2177202152),(-2177202128)⟩,⟨(-351508256),(-351508231)⟩⟩,⟨⟨(-1942058931),(-1942058899)⟩,⟨(-246642246),(-246642214)⟩⟩,⟨⟨(-1732692754),(-1732692717)⟩,⟨(-161861738),(-161861704)⟩⟩,⟨⟨(-1546380388),(-1546380349)⟩,⟨(-93725342),(-93725302)⟩⟩,⟨⟨(-1380654590),(-1380654566)⟩,⟨(-39351063),(-39351039)⟩⟩,⟨⟨(-1233287733),(-1233287707)⟩,⟨3671380,3671409⟩⟩,⟨⟨(-1102274417),(-1102274393)⟩,⟨37355044,37355068⟩⟩,⟨⟨(-985814043),(-985814012)⟩,⟨63378736,63378768⟩⟩,⟨⟨(-882293458),(-882293426)⟩,⟨83140505,83140537⟩⟩,⟨⟨(-790270366),(-790270336)⟩,⟨97802671,97802698⟩⟩,⟨⟨(-708457408),(-708457376)⟩,⟨108329972,108330004⟩⟩,⟨⟨(-635707270),(-635707246)⟩,⟨115521683,115521707⟩⟩] +lemma kernel19_1_r3_12_eq : ∀ k : Fin 16, kernel19_1Expr 3 12 k = kernel19_1_r3_12 k := by decide +kernel +noncomputable def kernel19_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-570998779),(-570998755)⟩,⟨120038714,120038738⟩⟩,⟨⟨(-513424060),(-513424028)⟩,⟨122426343,122426375⟩⟩,⟨⟨(-462176761),(-462176734)⟩,⟨123133427,123133456⟩⟩,⟨⟨(-416541299),(-416541272)⟩,⟨122528462,122528492⟩⟩,⟨⟨(-375883059),(-375883026)⟩,⟨120913046,120913078⟩⟩,⟨⟨(-339639608),(-339639575)⟩,⟨118533258,118533291⟩⟩,⟨⟨(-307312708),(-307312681)⟩,⟨115589073,115589102⟩⟩,⟨⟨(-278461108),(-278461084)⟩,⟨112242283,112242308⟩⟩,⟨⟨(-252694228),(-252694201)⟩,⟨108623161,108623190⟩⟩,⟨⟨(-229666332),(-229666305)⟩,⟨104835913,104835943⟩⟩,⟨⟨(-209071471),(-209071438)⟩,⟨100963348,100963380⟩⟩,⟨⟨(-190638863),(-190638833)⟩,⟨97070668,97070695⟩⟩,⟨⟨(-174128905),(-174128872)⟩,⟨93208648,93208681⟩⟩,⟨⟨(-159329549),(-159329521)⟩,⟨89416322,89416351⟩⟩,⟨⟨(-146053093),(-146053060)⟩,⟨85723165,85723197⟩⟩,⟨⟨(-134133395),(-134133366)⟩,⟨82150864,82150891⟩⟩] +lemma kernel19_1_r3_13_eq : ∀ k : Fin 16, kernel19_1Expr 3 13 k = kernel19_1_r3_13 k := by decide +kernel +noncomputable def kernel19_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-123423304),(-123423271)⟩,⟨78714880,78714912⟩⟩,⟨⟨(-113792523),(-113792490)⟩,⟨75425669,75425701⟩⟩,⟨⟨(-105125603),(-105125576)⟩,⟨72289674,72289704⟩⟩,⟨⟨(-97320234),(-97320196)⟩,⟨69310206,69310241⟩⟩,⟨⟨(-90285711),(-90285683)⟩,⟨66488118,66488148⟩⟩,⟨⟨(-83941610),(-83941577)⟩,⟨63822327,63822359⟩⟩,⟨⟨(-78216565),(-78216533)⟩,⟨61310358,61310390⟩⟩,⟨⟨(-73047247),(-73047214)⟩,⟨58948625,58948658⟩⟩,⟨⟨(-68377435),(-68377394)⟩,⟨56732790,56732831⟩⟩,⟨⟨(-64157200),(-64157171)⟩,⟨54657991,54658019⟩⟩,⟨⟨(-60342202),(-60342172)⟩,⟨52719021,52719049⟩⟩,⟨⟨(-56893020),(-56892995)⟩,⟨50910502,50910527⟩⟩,⟨⟨(-53774669),(-53774641)⟩,⟨49226997,49227027⟩⟩,⟨⟨(-50955991),(-50955958)⟩,⟨47663114,47663147⟩⟩,⟨⟨(-48409366),(-48409336)⟩,⟨46213586,46213613⟩⟩,⟨⟨(-46110210),(-46110178)⟩,⟨44873311,44873343⟩⟩] +lemma kernel19_1_r3_14_eq : ∀ k : Fin 16, kernel19_1Expr 3 14 k = kernel19_1_r3_14 k := by decide +kernel +noncomputable def kernel19_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-44036701),(-44036671)⟩,⟨43637379,43637407⟩⟩,⟨⟨(-42169494),(-42169469)⟩,⟨42501162,42501187⟩⟩,⟨⟨(-40491427),(-40491399)⟩,⟨41460266,41460296⟩⟩,⟨⟨(-38987313),(-38987273)⟩,⟨40510618,40510658⟩⟩,⟨⟨(-37643725),(-37643693)⟩,⟨39648417,39648450⟩⟩,⟨⟨(-36448844),(-36448819)⟩,⟨38870170,38870195⟩⟩,⟨⟨(-35392305),(-35392272)⟩,⟨38172682,38172714⟩⟩,⟨⟨(-34465060),(-34465019)⟩,⟨37553058,37553098⟩⟩,⟨⟨(-33659211),(-33659178)⟩,⟨37008724,37008757⟩⟩,⟨⟨(-32968033),(-32968006)⟩,⟨36537373,36537403⟩⟩,⟨⟨(-32385766),(-32385733)⟩,⟨36137028,36137061⟩⟩,⟨⟨(-31907613),(-31907588)⟩,⟨35805995,35806020⟩⟩,⟨⟨(-31529670),(-31529637)⟩,⟨35542838,35542871⟩⟩,⟨⟨(-31248858),(-31248825)⟩,⟨35346452,35346485⟩⟩,⟨⟨(-31062898),(-31062865)⟩,⟨35216000,35216033⟩⟩,⟨⟨(-30970280),(-30970247)⟩,⟨35150908,35150941⟩⟩] +lemma kernel19_1_r3_15_eq : ∀ k : Fin 16, kernel19_1Expr 3 15 k = kernel19_1_r3_15 k := by decide +kernel +noncomputable def kernel19_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel19_1_r3_0,kernel19_1_r3_1,kernel19_1_r3_2,kernel19_1_r3_3,kernel19_1_r3_4,kernel19_1_r3_5,kernel19_1_r3_6,kernel19_1_r3_7,kernel19_1_r3_8,kernel19_1_r3_9,kernel19_1_r3_10,kernel19_1_r3_11,kernel19_1_r3_12,kernel19_1_r3_13,kernel19_1_r3_14,kernel19_1_r3_15] +lemma kernel19_1_r3_eq (i k : Fin 16) : kernel19_1Expr 3 i k = kernel19_1_r3 i k := by + fin_cases i + · exact kernel19_1_r3_0_eq k + · exact kernel19_1_r3_1_eq k + · exact kernel19_1_r3_2_eq k + · exact kernel19_1_r3_3_eq k + · exact kernel19_1_r3_4_eq k + · exact kernel19_1_r3_5_eq k + · exact kernel19_1_r3_6_eq k + · exact kernel19_1_r3_7_eq k + · exact kernel19_1_r3_8_eq k + · exact kernel19_1_r3_9_eq k + · exact kernel19_1_r3_10_eq k + · exact kernel19_1_r3_11_eq k + · exact kernel19_1_r3_12_eq k + · exact kernel19_1_r3_13_eq k + · exact kernel19_1_r3_14_eq k + · exact kernel19_1_r3_15_eq k +noncomputable def kernel19_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-7630689580609415720768778),(-7630689580609415069197306)⟩,⟨(-2367611522424749207283520),(-2367611522424748555701942)⟩⟩,⟨⟨(-7625675818531664467764327),(-7625675818531663816742861)⟩,⟨(-2359813755665274832087003),(-2359813755665274181055570)⟩⟩,⟨⟨(-7615644320441101636648299),(-7615644320441100986726717)⟩,⟨(-2344251007919707646904270),(-2344251007919706996973003)⟩⟩,⟨⟨(-7600587283399689059934392),(-7600587283399688411659976)⟩,⟨(-2320988712244448280636467),(-2320988712244447632352777)⟩⟩,⟨⟨(-7580493363596207333235275),(-7580493363596206687151321)⟩,⟨(-2290124672134003901553315),(-2290124672134003255460635)⟩⟩,⟨⟨(-7555348104221322360273345),(-7555348104221321716917938)⟩,⟨(-2251788646604409135494986),(-2251788646604408492131542)⟩⟩,⟨⟨(-7525134497949908217272723),(-7525134497949907577177446)⟩,⟨(-2206141797657182276186883),(-2206141797657181636084381)⟩⟩,⟨⟨(-7489833677255604281241401),(-7489833677255603644930056)⟩,⟨(-2153376000778038491733997),(-2153376000778037855416365)⟩⟩,⟨⟨(-7449425724209948331536400),(-7449425724209947699523910)⟩,⟨(-2093713019368965905115066),(-2093713019368965273097337)⟩⟩,⟨⟨(-7403890589925641656001042),(-7403890589925641028792019)⟩,⟨(-2027403544307647214774391),(-2027403544307646587561300)⟩⟩,⟨⟨(-7353209112405616556933418),(-7353209112405615935021363)⟩,⟨(-1954726100181946557222658),(-1954726100181945935307815)⟩⟩,⟨⟨(-7297364120271107992929434),(-7297364120271107376795172)⟩,⟨(-1875985820165180642452225),(-1875985820165180026316551)⟩⟩,⟨⟨(-7236341608676751804702730),(-7236341608676751194814017)⟩,⟨(-1791513091984411258770318),(-1791513091984410648881663)⟩⟩,⟨⟨(-7170131972691949381495231),(-7170131972691948778304742)⟩,⟨(-1701662077991492229467449),(-1701662077991491626278576)⟩⟩,⟨⟨(-7098731282547566166191822),(-7098731282547565570137469)⟩,⟨(-1606809112975619537550092),(-1606809112975618941498998)⟩⟩,⟨⟨(-7022142584426652263992969),(-7022142584426651675495469)⟩,⟨(-1507350984055206882476837),(-1507350984055206293984307)⟩⟩] +lemma kernel19_1_r4_0_eq : ∀ k : Fin 16, kernel19_1Expr 4 0 k = kernel19_1_r4_0 k := by decide +kernel +noncomputable def kernel19_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-6940377209927297940383600),(-6940377209927297359847614)⟩,⟨(-1403703097752525662457447),(-1403703097752525081928197)⟩⟩,⟨⟨(-6853456076953655344008105),(-6853456076953654771818762)⟩,⟨(-1296297540181129287209088),(-1296297540181128715028304)⟩⟩,⟨⟨(-6761410964604791519730320),(-6761410964604790956255717)⟩,⟨(-1185581037156011799861784),(-1185581037156011236397601)⟩⟩,⟨⟨(-6664285744635989926612308),(-6664285744635989372199254)⟩,⟨(-1072012821960147422663033),(-1072012821960146868262301)⟩⟩,⟨⟨(-6562137552267228651685081),(-6562137552267228106662882)⟩,⟨(-956062419457079324970669),(-956062419457078779962709)⟩⟩,⟨⟨(-6455037879510773269397874),(-6455037879510772734072250)⟩,⟨(-838207356214420490459897),(-838207356214419955150445)⟩⟩,⟨⟨(-6343073574784043847660615),(-6343073574784043322319580)⟩,⟨(-718930807282820809153175),(-718930807282820283830248)⟩⟩,⟨⟨(-6226347733362923639297112),(-6226347733362923124203919)⟩,⟨(-598719191243164982508684),(-598719191243164467435531)⟩⟩,⟨⟨(-6104980464210015755418711),(-6104980464210015250819283)⟩,⟨(-478059726074473185748936),(-478059726074472681171459)⟩⟩,⟨⟨(-5979109519875268507645007),(-5979109519875268013758126)⟩,⟨(-357437959288399941625633),(-357437959288399447762594)⟩⟩,⟨⟨(-5848890777503784076477546),(-5848890777503783593505249)⟩,⟨(-237335286605139541438614),(-237335286605139058492014)⟩⟩,⟨⟨(-5714498560486050926556093),(-5714498560486050454672916)⟩,⟨(-118226474191609280912121),(-118226474191608809056455)⟩⟩,⟨⟨(-5576125791935521806048939),(-5576125791935521345413815)⟩,⟨(-577200127892117349310),(-577200127891656743457)⟩⟩,⟨⟨(-5433983972961352049367722),(-5433983972961351600106126)⟩,⟨115158368705428883354201,115158368705429332584840⟩⟩,⟨⟨(-5288302980602004390138086),(-5288302980602003952357770)⟩,⟨228539947734769751028398,228539947734770188776156⟩⟩,⟨⟨(-5139330682278074931934514),(-5139330682278074505720962)⟩,⟨339143436970202384425051,339143436970202810604527⟩⟩] +lemma kernel19_1_r4_1_eq : ∀ k : Fin 16, kernel19_1Expr 4 1 k = kernel19_1_r4_1 k := by decide +kernel +noncomputable def kernel19_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-4987332365688010857697122),(-4987332365688010443123584)⟩,⟨446563137547998672455695,446563137547999086993713⟩⟩,⟨⟨(-4832589985184658437044529),(-4832589985184658034152082)⟩,⟨550413865733575417617694,550413865733575820473269⟩⟩,⟨⟨(-4675401227808719892089535),(-4675401227808719500908968)⟩,⟨650332947861782901648854,650332947861783292791296⟩⟩,⟨⟨(-4516078404291063910246540),(-4516078404291063530746974)⟩,⟨745982080165245760713986,745982080165246140174266⟩⟩,⟨⟨(-4354947172442548438621276),(-4354947172442548070786089)⟩,⟨837049038110444252068203,837049038110444619863360⟩⟩,⟨⟨(-4192345102400327376067746),(-4192345102400327019857450)⟩,⟨923249220726288477063922,923249220726288833233852⟩⟩,⟨⟨(-4028620095166294295644772),(-4028620095166293951014404)⟩,⟨1004327016468811246341568,1004327016468811590931327⟩⟩,⟨⟨(-3864128667729560238740061),(-3864128667729559905614147)⟩,⟨1080056978412774959366204,1080056978412775292451355⟩⟩,⟨⟨(-3699234119784705804525306),(-3699234119784705482825765)⟩,⟨1150244797987676976973763,1150244797987677298632479⟩⟩,⟨⟨(-3534304598616293240513669),(-3534304598616292930128671)⟩,⟨1214728068069835831323132,1214728068069836141667331⟩⟩,⟨⟨(-3369711080094760854096494),(-3369711080094760554914234)⟩,⟨1273376827988797170237673,1273376827988797469379260⟩⟩,⟨⟨(-3205825284898432331895984),(-3205825284898432043774882)⟩,⟨1326093884887081009509988,1326093884887081297590624⟩⟩,⟨⟨(-3043017550022521255511434),(-3043017550022520978312447)⟩,⟨1372814907866404336444749,1372814907866404613603573⟩⟩,⟨⟨(-2881654676343100068307095),(-2881654676343099801780505)⟩,⟨1413508293437573401768311,1413508293437573668255119⟩⟩,⟨⟨(-2722097773459598578314118),(-2722097773459598322241158)⟩,⟨1448174802939714370793113,1448174802939714626826762⟩⟩,⟨⟨(-2564700123234504001034887),(-2564700123234503755228563)⟩,⟨1476846974780098225575173,1476846974780098471342733⟩⟩] +lemma kernel19_1_r4_2_eq : ∀ k : Fin 16, kernel19_1Expr 4 2 k = kernel19_1_r4_2 k := by decide +kernel +noncomputable def kernel19_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-2409805083378220183519176),(-2409805083378219947800763)⟩,⟨1499588316539876184075175,1499588316539876419755448⟩⟩,⟨⟨(-2257744052089005455347347),(-2257744052089005229506319)⟩,⟨1516492284164062750396291,1516492284164062976199883⟩⟩,⟨⟨(-2108834514154976493364303),(-2108834514154976277200845)⟩,⟨1527681057576193233740880,1527681057576193449867669⟩⟩,⟨⟨(-1963378188063737092937277),(-1963378188063736886223116)⟩,⟨1533304124099483689390717,1533304124099483896070611⟩⟩,⟨⟨(-1821659292555595084315448),(-1821659292555594886836443)⟩,⟨1533536682997932408552677,1533536682997932606000441⟩⟩,⟨⟨(-1683942949712721509860441),(-1683942949712721321374846)⟩,⟨1528577886244698658726610,1528577886244698847183879⟩⟩,⟨⟨(-1550473740116782677170868),(-1550473740116782497451580)⟩,⟨1518648932255036690423190,1518648932255036870116944⟩⟩,⟨⟨(-1421474423852733561248634),(-1421474423852733390008134)⟩,⟨1503991030762981797447796,1503991030762981968665438⟩⟩,⟨⟨(-1297144839210877542506123),(-1297144839210877379502787)⟩,⟨1484863258253433583562577,1484863258253433746545607⟩⟩,⟨⟨(-1177660988869955069759206),(-1177660988869954914736220)⟩,⟨1461540324365843864647982,1461540324365844019653090⟩⟩,⟨⟨(-1063174321160178760657686),(-1063174321160178613376811)⟩,⟨1434310270447364685165627,1434310270447364832430915⟩⟩,⟨⟨(-953811211737836308233239),(-953811211737836168435982)⟩,⟨1403472121940700968264353,1403472121940701108048197⟩⟩,⟨⟨(-849672648684665809194797),(-849672648684665676625882)⟩,⟨1369333516537609291232819,1369333516537609423790358⟩⟩,⟨⟨(-750834121708735464014607),(-750834121708735338409422)⟩,⟨1332208330009623232806410,1332208330009623358402125⟩⟩,⟨⟨(-657345713802268036043959),(-657345713802267917162544)⟩,⟨1292414321343946326202657,1292414321343946445076389⟩⟩,⟨⟨(-569232391438581448601387),(-569232391438581336180219)⟩,⟨1250270818269460426477399,1250270818269460538892536⟩⟩] +lemma kernel19_1_r4_3_eq : ∀ k : Fin 16, kernel19_1Expr 4 3 k = kernel19_1_r4_3 k := by decide +kernel +noncomputable def kernel19_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-486494487196954066927936),(-486494487196953960730357)⟩,⟨1206096463464439357163391,1206096463464439463356472⟩⟩,⟨⟨(-409108366621147301984226),(-409108366621147201754868)⟩,⟨1160207040706729908181869,1160207040706730008408134⟩⟩,⟨⟨(-337027269172890514193933),(-337027269172890419699854)⟩,⟨1112913398975431173637236,1112913398975431268129507⟩⟩,⟨⟨(-270182311361718412780987),(-270182311361718323775336)⟩,⟨1064519491060402453445380,1064519491060402542450396⟩⟩,⟨⟨(-208483638540089008535773),(-208483638540088924793671)⟩,⟨1015320541605191377148051,1015320541605191460890572⟩⟩,⟨⟨(-151821710467345415895228),(-151821710467345337175506)⟩,⟨965601357725702613072541,965601357725702691793630⟩⟩,⟨⟨(-100068704583862397659073),(-100068704583862323742748)⟩,⟨915634793438729541754455,915634793438729615672991⟩⟩,⟨⟨(-53080020009850547913101),(-53080020009850478570344)⟩,⟨865680377130544416931358,865680377130544486277069⟩⟩,⟨⟨(-10695864599999225551302),(-10695864599999160574489)⟩,⟨815983109226341260473163,815983109226341325453579⟩⟩,⟨⟨27257093050423379365582,27257093050423440197939⟩,⟨766772435117211535256258,766772435117211596092776⟩⟩,⟨⟨60964024940143820137132,60964024940143877024472⟩,⟨718261396293221822195952,718261396293221879087926⟩⟩,⟨⟨90620216573101666739804,90620216573101719889664⟩,⟨670645960549183255675344,670645960549183308830228⟩⟩,⟨⟨116429329389954106631103,116429329389954156398557⟩,⟨624104530102871281151368,624104530102871330924153⟩⟩,⟨⟨138601670146356959144864,138601670146357005717648⟩,⟨578797624521185878700013,578797624521185925278241⟩⟩,⟨⟨157352483937203338583059,157352483937203382117783⟩,⟨534867733513398548460444,534867733513398592000627⟩⟩,⟨⟨172900286646168007789324,172900286646168048449719⟩,⟨492439332945121941209196,492439332945121981875026⟩⟩] +lemma kernel19_1_r4_4_eq : ∀ k : Fin 16, kernel19_1Expr 4 4 k = kernel19_1_r4_4 k := by decide +kernel +noncomputable def kernel19_1_r4_5 : Fin 16 → CBox := ![⟨⟨185465251507750789021894,185465251507750826953224⟩,⟨451619055872074170828056,451619055872074208764760⟩⟩,⟨⟨195267663226871134657036,195267663226871170014313⟩,⟨412496009006130704178933,412496009006130739541496⟩⟩,⟨⟨202526451732937792275754,202526451732937825196119⟩,⟨375142223821314067675573,375142223821314100601102⟩⟩,⟨⟨207457816176381066642887,207457816176381097268672⟩,⟨339613230494590186319523,339613230494590216950332⟩⟩,⟨⟨210273948231754497883442,210273948231754526340584⟩,⟨305948742062448732098737,305948742062448760560743⟩⟩,⟨⟨211181862178746681399101,211181862178746707820344⟩,⟨274173435562578259294623,274173435562578285720552⟩⟩,⟨⟨210382337616569011686358,210382337616569036189630⟩,⟨244297816520416988499976,244297816520417013007441⟩⟩,⟨⟨208068979053241705106268,208068979053241727812456⟩,⟨216319152929591550382621,216319152929591573092428⟩⟩,⟨⟨204427395023170917490171,204427395023170938507997⟩,⟨190222464856781951983366,190222464856781973004282⟩⟩,⟨⟨199634497846436664757771,199634497846436684198565⟩,⟨165981555966062035369329,165981555966062054812721⟩⟩,⟨⟨193857923671862083446948,193857923671862101409199⟩,⟨143560073593403606199818,143560073593403624164225⟩⟩,⟨⟨187255571061518511709461,187255571061518528296488⟩,⟨122912584494726917392099,122912584494726933980881⟩⟩,⟨⟨179975255092761312696712,179975255092761327994833⟩,⟨103985654024704328284256,103985654024704343583772⟩⟩,⟨⟨172154472788556650855313,172154472788556664954397⟩,⟨86718917261079366339214,86718917261079380439369⟩⟩,⟨⟨163920274648452841229403,163920274648452854208965⟩,⟨71046131452071303400151,71046131452071316380491⟩⟩,⟨⟨155389236149058290883647,155389236149058302830151⟩,⟨56896200113330090975231,56896200113330102922257⟩⟩] +lemma kernel19_1_r4_5_eq : ∀ k : Fin 16, kernel19_1Expr 4 5 k = kernel19_1_r4_5 k := by decide +kernel +noncomputable def kernel19_1_r4_6 : Fin 16 → CBox := ![⟨⟨146667522319587468966655,146667522319587479948362⟩,⟨44194160116422257335539,44194160116422268317538⟩⟩,⟨⟨137851037877551347643620,137851037877551357731740⟩,⟨32862124173570796225915,32862124173570806314132⟩⟩,⟨⟨129025654932081487620802,129025654932081496878200⟩,⟨22820172214367683425257,22820172214367692682585⟩⟩,⟨⟨120267509925380643568422,120267509925380652057301⟩,⟨13987186251194599006756,13987186251194607495419⟩⟩,⟨⟨111643361281883958255099,111643361281883966029330⟩,⟨6281624423922327077086,6281624423922334850984⟩⟩,⟨⟨103210999163417624403555,103210999163417631518668⟩,⟨(-377769014814168179663),(-377769014814161064986)⟩⟩,⟨⟨95019698778757689116194,95019698778757695627319⟩,⟨(-6071319979291786258826),(-6071319979291779748219)⟩⟩,⟨⟨87110708857866988277980,87110708857866994234680⟩,⟨(-10877848318020902993523),(-10877848318020897037407)⟩⟩,⟨⟨79517767163893893928723,79517767163893899371175⟩,⟨(-14874159369943610841553),(-14874159369943605399732)⟩⟩,⟨⟨72267635268031418130602,72267635268031423100357⟩,⟨(-18134602759825600714265),(-18134602759825595745168)⟩⟩,⟨⟨65380645241227432466605,65380645241227436999709⟩,⟨(-20730697110095842343013),(-20730697110095837810563)⟩⟩,⟨⟨58871251409837324632152,58871251409837328764472⟩,⟨(-22730818656606223956194),(-22730818656606219824518)⟩⟩,⟨⟨52748580866873010640942,52748580866873014403594⟩,⟨(-24199951152883249146025),(-24199951152883245384003)⟩⟩,⟨⟨47016977013944935336352,47016977013944938762248⟩,⟨(-25199493933275310166532),(-25199493933275306741244)⟩⟩,⟨⟨41676531019118583455616,41676531019118586571149⟩,⟨(-25787124580166367121970),(-25787124580166364007019)⟩⟩,⟨⟨36723596701094480109339,36723596701094482941160⟩,⟨(-26016712302820407070537),(-26016712302820404239279)⟩⟩] +lemma kernel19_1_r4_6_eq : ∀ k : Fin 16, kernel19_1Expr 4 6 k = kernel19_1_r4_6 k := by decide +kernel +noncomputable def kernel19_1_r4_7 : Fin 16 → CBox := ![⟨⟨32151284979496276544592,32151284979496279115723⟩,⟨(-25938277882768096426982),(-25938277882768093856384)⟩⟩,⟨⟨27949934654624026907114,27949934654624029240560⟩,⟨(-25597995869077699161770),(-25597995869077696828799)⟩⟩,⟨⟨24107556888799409178478,24107556888799411293717⟩,⟨(-25038234611475648932334),(-25038234611475646817495)⟩⟩,⟨⟨20610251347467108368727,20610251347467110285133⟩,⟨(-24297629694367518893621),(-24297629694367516977548)⟩⟩,⟨⟨17442592514713258415223,17442592514713260149212⟩,⟨(-23411186373969633086401),(-23411186373969631352681)⟩⟩,⟨⟨14587985219152896621727,14587985219152898190006⟩,⟨(-22410406717129264505020),(-22410406717129262936954)⟩⟩,⟨⟨12028988887700521969550,12028988887700523386236⟩,⟨(-21323437286815707890605),(-21323437286815706474082)⟩⟩,⟨⟨9747610483164144798049,9747610483164146078002⟩,⟨(-20175233408390795793103),(-20175233408390794513278)⟩⟩,⟨⟨7725566474557738853116,7725566474557740011669⟩,⟨(-18987736275307664253397),(-18987736275307663094930)⟩⟩,⟨⟨5944514535182120668435,5944514535182121716803⟩,⟨(-17780059405674687414121),(-17780059405674686365809)⟩⟩,⟨⟨4386255962483696651975,4386255962483697599535⟩,⟨(-16568681235252235829304),(-16568681235252234881773)⟩⟩,⟨⟨3032910065911193595233,3032910065911194451330⟩,⟨(-15367640921380526700448),(-15367640921380525844357)⟩⟩,⟨⟨1867061975646434063863,1867061975646434836346⟩,⟨(-14188734729971012338526),(-14188734729971011566031)⟩⟩,⟨⟨871885488026148842185,871885488026149539030⟩,⟨(-13041710678447750714851),(-13041710678447750017975)⟩⟩,⟨⟨31242685079417103862,31242685079417731781⟩,⟨(-11934459406376588723194),(-11934459406376588095231)⟩⟩,⟨⟨(-670237851300347395926),(-670237851300346830192)⟩,⟨(-10873199538039771482168),(-10873199538039770916380)⟩⟩] +lemma kernel19_1_r4_7_eq : ∀ k : Fin 16, kernel19_1Expr 4 7 k = kernel19_1_r4_7 k := by decide +kernel +noncomputable def kernel19_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-1247102362291630265865),(-1247102362291629756820)⟩,⟨(-9862656083582791283858),(-9862656083582790774750)⟩⟩,⟨⟨(-1713030888152087776522),(-1713030888152087318290)⟩,⟨(-8906230694372310623142),(-8906230694372310164847)⟩⟩,⟨⟨(-2080812025890854159817),(-2080812025890853747776)⟩,⟨(-8006162841254298046828),(-8006162841254297634719)⟩⟩,⟨⟨(-2362331634628831441599),(-2362331634628831071199)⟩,⟨(-7163681219466273326782),(-7163681219466272956314)⟩⟩,⟨⟨(-2568573713292264392419),(-2568573713292264059867)⟩,⟨(-6379144899562992161145),(-6379144899562991828528)⟩⟩,⟨⟨(-2709631751571434596734),(-2709631751571434297796)⟩,⟨(-5652173938899082377350),(-5652173938899082078344)⟩⟩,⟨⟨(-2794728945629621290414),(-2794728945629621021955)⟩,⟨(-4981769342480971199898),(-4981769342480970931378)⟩⟩,⟨⟨(-2832245771649205944823),(-2832245771649205703790)⟩,⟨(-4366422415279457036400),(-4366422415279456795310)⟩⟩,⟨⟨(-2829753519950379381433),(-2829753519950379165268)⟩,⟨(-3804213680677881490586),(-3804213680677881274366)⟩⟩,⟨⟨(-2794052507357278127802),(-2794052507357277933848)⟩,⟨(-3292901652230365795934),(-3292901652230365601927)⟩⟩,⟨⟨(-2731213803226071798540),(-2731213803226071624685)⟩,⟨(-2830001839196397387200),(-2830001839196397213297)⟩⟩,⟨⟨(-2646623422876863312983),(-2646623422876863157143)⟩,⟨(-2412856441493096197118),(-2412856441493096041242)⟩⟩,⟨⟨(-2545028059156318891507),(-2545028059156318751992)⟩,⟨(-2038695248021771595946),(-2038695248021771456399)⟩⟩,⟨⟨(-2430581536852141331916),(-2430581536852141207003)⟩,⟨(-1704688295158590359170),(-1704688295158590234226)⟩⟩,⟨⟨(-2306891284309717741305),(-2306891284309717629572)⟩,⟨(-1407990871006821254992),(-1407990871006821143242)⟩⟩,⟨⟨(-2177064220754316889925),(-2177064220754316789879)⟩,⟨(-1145781467287682162700),(-1145781467287682062642)⟩⟩] +lemma kernel19_1_r4_8_eq : ∀ k : Fin 16, kernel19_1Expr 4 8 k = kernel19_1_r4_8 k := by decide +kernel +noncomputable def kernel19_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-2043751555635532228229),(-2043751555635532138553)⟩,⟨(-915293286003198518070),(-915293286003198428386)⟩⟩,⟨⟨(-1909192087150171628576),(-1909192087150171548178)⟩,⟨(-713839903720928917982),(-713839903720928837576)⟩⟩,⟨⟨(-1775253670540547522587),(-1775253670540547450572)⟩,⟨(-538835683943879421404),(-538835683943879349381)⟩⟩,⟨⟨(-1643472602569665199285),(-1643472602569665134777)⟩,⟨(-387811508909846492774),(-387811508909846428261)⟩⟩,⟨⟨(-1515090736670781713961),(-1515090736670781656235)⟩,⟨(-258426377600691135345),(-258426377600691077622)⟩⟩,⟨⟨(-1391090203726441192372),(-1391090203726441140692)⟩,⟨(-148475387926941740362),(-148475387926941688685)⟩⟩,⟨⟨(-1272225666442081104600),(-1272225666442081058358)⟩,⟨(-55894589076928620534),(-55894589076928574295)⟩⟩,⟨⟨(-1159054081131504578535),(-1159054081131504537159)⟩,⟨21236844135464070940,21236844135464112309⟩⟩,⟨⟨(-1051961979794787057707),(-1051961979794787020699)⟩,⟨84696698552498179657,84696698552498216661⟩⟩,⟨⟨(-951190318072663471181),(-951190318072663438051)⟩,⟨136121691219018854522,136121691219018887646⟩⟩,⟨⟨(-856856961477407258655),(-856856961477407229019)⟩,⟨177010974726600938489,177010974726600968119⟩⟩,⟨⟨(-768976903728718852319),(-768976903728718825798)⟩,⟨208730870125024155982,208730870125024182497⟩⟩,⟨⟨(-687480327578440680381),(-687480327578440656662)⟩,⟨232520552292178496460,232520552292178520174⟩⟩,⟨⟨(-612228630706707542963),(-612228630706707521738)⟩,⟨249498445296292492982,249498445296292514202⟩⟩,⟨⟨(-543028547623611260386),(-543028547623611241402)⟩,⟨260669116168029954959,260669116168029973934⟩⟩,⟨⟨(-479644503508043626261),(-479644503508043609291)⟩,⟨266930484419140927850,266930484419140944816⟩⟩] +lemma kernel19_1_r4_9_eq : ∀ k : Fin 16, kernel19_1Expr 4 9 k = kernel19_1_r4_9 k := by decide +kernel +noncomputable def kernel19_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-421809338030161515177),(-421809338030161499966)⟩,⟨269081191460452002544,269081191460452017750⟩⟩,⟨⟨(-369233536879516055500),(-369233536879516041860)⟩,⟨267827998705117030524,267827998705117044159⟩⟩,⟨⟨(-321613106369747647410),(-321613106369747635176)⟩,⟨263793105563831367571,263793105563831379797⟩⟩,⟨⟨(-278636222491640563119),(-278636222491640552155)⟩,⟨257521298760521995055,257521298760522006019⟩⟩,⟨⟨(-239988780482940340206),(-239988780482940330377)⟩,⟨249486862468682077343,249486862468682087165⟩⟩,⟨⟨(-205358964683785751718),(-205358964683785742909)⟩,⟨240100194767461691880,240100194767461700685⟩⟩,⟨⟨(-174440951423760432295),(-174440951423760424391)⟩,⟨229714089942672089790,229714089942672097691⟩⟩,⟨⟨(-146937850178992483545),(-146937850178992476450)⟩,⟨218629658327565823841,218629658327565830933⟩⟩,⟨⟨(-122563980451161213919),(-122563980451161207555)⟩,⟨207101865819910800982,207101865819910807342⟩⟩,⟨⟨(-101046573929488769915),(-101046573929488764203)⟩,⟨195344684061128021593,195344684061128027305⟩⟩,⟨⟨(-82126983647782635747),(-82126983647782630620)⟩,⟨183535849659340436708,183535849659340441835⟩⟩,⟨⟨(-65561474160888357497),(-65561474160888352895)⟩,⟨171821236920714813713,171821236920714818311⟩⟩,⟨⟨(-51121659334060903158),(-51121659334060899022)⟩,⟨160318853459867815378,160318853459867819514⟩⟩,⟨⟨(-38594647238832454518),(-38594647238832450794)⟩,⟨149122471923392332461,149122471923392336185⟩⟩,⟨⟨(-27782944935000419203),(-27782944935000415850)⟩,⟨138304914007762582080,138304914007762585433⟩⟩,⟨⟨(-18504169628837368880),(-18504169628837365847)⟩,⟨127921005103754627871,127921005103754630904⟩⟩] +lemma kernel19_1_r4_10_eq : ∀ k : Fin 16, kernel19_1Expr 4 10 k = kernel19_1_r4_10 k := by decide +kernel +noncomputable def kernel19_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-10590606856688056013),(-10590606856688053290)⟩,⟨118010219365688236327,118010219365688239051⟩⟩,⟨⟨(-3888650962781866997),(-3888650962781864544)⟩,⟨108599035888169638243,108599035888169640697⟩⟩,⟨⟨1741841777768089850,1741841777768092062⟩,⟨99703027069516850863,99703027069516853076⟩⟩,⟨⟨6428261501605470603,6428261501605472601⟩,⟨91328700234555877206,91328700234555879201⟩⟩,⟨⟨10285992695036984037,10285992695036985840⟩,⟨83475113255944382148,83475113255944383952⟩⟩,⟨⟨13419183450859818946,13419183450859820578⟩,⟨76135284319925969394,76135284319925971029⟩⟩,⟨⟨15921520959112234163,15921520959112235638⟩,⟨69297415188513831236,69297415188513832711⟩⟩,⟨⟨17877000960232133120,17877000960232134451⟩,⟨62945946366853100622,62945946366853101956⟩⟩,⟨⟨19360681351305398439,19360681351305399653⟩,⟨57062461535997731759,57062461535997732974⟩⟩,⟨⟨20439412274514677020,20439412274514678124⟩,⟨51626457494993899123,51626457494993900227⟩⟩,⟨⟨21172536859336849836,21172536859336850834⟩,⟨46615994703369679577,46615994703369680572⟩⟩,⟨⟨21612558363964381547,21612558363964382459⟩,⟨42008242351818126857,42008242351818127770⟩⟩,⟨⟨21805770793585429168,21805770793585429995⟩,⟨37779930736089054167,37779930736089054997⟩⟩,⟨⟨21792851189214416398,21792851189214417149⟩,⟨33907722583635335034,33907722583635335789⟩⟩,⟨⟨21609412705050444788,21609412705050445481⟩,⟨30368513897392535940,30368513897392536636⟩⟩,⟨⟨21286518347676094124,21286518347676094752⟩,⟨27139673845950246502,27139673845950247130⟩⟩] +lemma kernel19_1_r4_11_eq : ∀ k : Fin 16, kernel19_1Expr 4 11 k = kernel19_1_r4_11 k := by decide +kernel +noncomputable def kernel19_1_r4_12 : Fin 16 → CBox := ![⟨⟨20851155857989469398,20851155857989469979⟩,⟨24199232251255153071,24199232251255153652⟩⟩,⟨⟨20326674696098060525,20326674696098061047⟩,⟨21526022308465103513,21526022308465104036⟩⟩,⟨⟨19733186458303059319,19733186458303059807⟩,⟨19099785320273346193,19099785320273346680⟩⟩,⟨⟨19087930329894609792,19087930329894610232⟩,⟨16901243440941740055,16901243440941740495⟩⟩,⟨⟨18405605372255688645,18405605372255689056⟩,⟨14912145703104567833,14912145703104568244⟩⟩,⟨⟨17698671570664098539,17698671570664098915⟩,⟨13115291941770247067,13115291941770247442⟩⟩,⟨⟨16977621641638085479,16977621641638085819⟩,⟨11494538632688589557,11494538632688589897⟩⟩,⟨⟨16251225625757280248,16251225625757280564⟩,⟨10034790123593810338,10034790123593810655⟩⟩,⟨⟨15526750282391521683,15526750282391521977⟩,⟨8721978253574559813,8721978253574560107⟩⟩,⟨⟨14810155264294323406,14810155264294323682⟩,⟨7543032924472766698,7543032924472766974⟩⟩,⟨⟨14106267989104133537,14106267989104133793⟩,⟨6485845805119623785,6485845805119624039⟩⟩,⟨⟨13418939047018331137,13418939047018331376⟩,⟨5539229010660994872,5539229010660995108⟩⟩,⟨⟨12751179893970443833,12751179893970444050⟩,⟨4692870301501766946,4692870301501767163⟩⟩,⟨⟨12105284481489791051,12105284481489791256⟩,⟨3937286085882484814,3937286085882485018⟩⟩,⟨⟨11482936371315490066,11482936371315490253⟩,⟨3263773283290870968,3263773283290871155⟩⟩,⟨⟨10885302777439790016,10885302777439790192⟩,⟨2664360909465825577,2664360909465825753⟩⟩] +lemma kernel19_1_r4_12_eq : ∀ k : Fin 16, kernel19_1Expr 4 12 k = kernel19_1_r4_12 k := by decide +kernel +noncomputable def kernel19_1_r4_13 : Fin 16 → CBox := ![⟨⟨10313116872718205718,10313116872718205881⟩,⟨2131762074519109874,2131762074519110037⟩⟩,⟨⟨9766749593208718392,9766749593208718544⟩,⟨1659326940730070524,1659326940730070675⟩⟩,⟨⟨9246272072309878288,9246272072309878440⟩,⟨1240997063123603715,1240997063123603866⟩⟩,⟨⟨8751509739553672594,8751509739553672734⟩,⟨871261431498726937,871261431498727076⟩⟩,⟨⟨8282089026295691193,8282089026295691321⟩,⟨545114444826365453,545114444826365580⟩⟩,⟨⟨7837477533026496145,7837477533026496267⟩,⟨258015975781060993,258015975781061115⟩⟩,⟨⟨7417018430909988745,7417018430909988861⟩,⟨5853622714292180,5853622714292296⟩⟩,⟨⟨7019959793589309294,7019959793589309402⟩,⟨(-215092803089625591),(-215092803089625485)⟩⟩,⟨⟨6645479484317367965,6645479484317368069⟩,⟨(-408184547036942028),(-408184547036941924)⟩⟩,⟨⟨6292706157998961623,6292706157998961715⟩,⟨(-576454961786387059),(-576454961786386967)⟩⟩,⟨⟨5960736877630617245,5960736877630617341⟩,⟨(-722638387803461395),(-722638387803461302)⟩⟩,⟨⟨5648651789692072806,5648651789692072902⟩,⟨(-849196932112911566),(-849196932112911473)⟩⟩,⟨⟨5355526253037775339,5355526253037775419⟩,⟨(-958345227694059420),(-958345227694059340)⟩⟩,⟨⟨5080440770487906050,5080440770487906136⟩,⟨(-1052073266100827475),(-1052073266100827389)⟩⟩,⟨⟨4822489031338706670,4822489031338706755⟩,⟨(-1132167402628587102),(-1132167402628587021)⟩⟩,⟨⟨4580784336104923648,4580784336104923722⟩,⟨(-1200229637302572458),(-1200229637302572384)⟩⟩] +lemma kernel19_1_r4_13_eq : ∀ k : Fin 16, kernel19_1Expr 4 13 k = kernel19_1_r4_13 k := by decide +kernel +noncomputable def kernel19_1_r4_14 : Fin 16 → CBox := ![⟨⟨4354464641674746521,4354464641674746597⟩,⟨(-1257695276651490993),(-1257695276651490914)⟩⟩,⟨⟨4142696435404970478,4142696435404970546⟩,⟨(-1305849081103369968),(-1305849081103369900)⟩⟩,⟨⟨3944677620224269991,3944677620224270059⟩,⟨(-1345840001279987666),(-1345840001279987598)⟩⟩,⟨⟨3759639569269303570,3759639569269303638⟩,⟨(-1378694603794039923),(-1378694603794039855)⟩⟩,⟨⟨3586848487688873024,3586848487688873086⟩,⟨(-1405329283640630143),(-1405329283640630081)⟩⟩,⟨⟨3425606200767177725,3425606200767177793⟩,⟨(-1426561356148071491),(-1426561356148071423)⟩⟩,⟨⟨3275250471205564112,3275250471205564173⟩,⟨(-1443119116899825221),(-1443119116899825163)⟩⟩,⟨⟨3135154934046344005,3135154934046344071⟩,⟨(-1455650953213609169),(-1455650953213609110)⟩⟩,⟨⟨3004728725121634117,3004728725121634174⟩,⟨(-1464733585790436074),(-1464733585790436014)⟩⟩,⟨⟨2883415867880044209,2883415867880044265⟩,⟨(-1470879514126114599),(-1470879514126114543)⟩⟩,⟨⟨2770694473815159194,2770694473815159250⟩,⟨(-1474543734290172260),(-1474543734290172204)⟩⟩,⟨⟨2666075803337705010,2666075803337705059⟩,⟨(-1476129792784152983),(-1476129792784152933)⟩⟩,⟨⟨2569103226657751849,2569103226657751912⟩,⟨(-1475995235439838515),(-1475995235439838453)⟩⟩,⟨⟨2479351117947274594,2479351117947274650⟩,⟨(-1474456505742748457),(-1474456505742748401)⟩⟩,⟨⟨2396423710622275182,2396423710622275238⟩,⟨(-1471793342591577497),(-1471793342591577441)⟩⟩,⟨⟨2319953936914441950,2319953936914442000⟩,⟨(-1468252723345816719),(-1468252723345816669)⟩⟩] +lemma kernel19_1_r4_14_eq : ∀ k : Fin 16, kernel19_1Expr 4 14 k = kernel19_1_r4_14 k := by decide +kernel +noncomputable def kernel19_1_r4_15 : Fin 16 → CBox := ![⟨⟨2249602270902606634,2249602270902606690⟩,⟨(-1464052394080522254),(-1464052394080522198)⟩⟩,⟨⟨2185055590761491040,2185055590761491090⟩,⟨(-1459384025262254105),(-1459384025262254055)⟩⟩,⟨⟨2126026073085790608,2126026073085790658⟩,⟨(-1454416027582326116),(-1454416027582326066)⟩⟩,⟨⟨2072250129696046886,2072250129696046940⟩,⟨(-1449296059427830917),(-1449296059427830865)⟩⟩,⟨⟨2023487395270911114,2023487395270911162⟩,⟨(-1444153254429805916),(-1444153254429805870)⟩⟩,⟨⟨1979519772426843622,1979519772426843666⟩,⟨(-1439100194691630128),(-1439100194691630084)⟩⟩,⟨⟨1940150539435541929,1940150539435541984⟩,⟨(-1434234652657944355),(-1434234652657944304)⟩⟩,⟨⟨1905203524591293438,1905203524591293482⟩,⟨(-1429641122122566550),(-1429641122122566506)⟩⟩,⟨⟨1874522350279600802,1874522350279600846⟩,⟨(-1425392156579726395),(-1425392156579726351)⟩⟩,⟨⟨1847969749023626367,1847969749023626418⟩,⟨(-1421549530982633187),(-1421549530982633137)⟩⟩,⟨⟨1825426953168741057,1825426953168741102⟩,⟨(-1418165240972773766),(-1418165240972773717)⟩⟩,⟨⟨1806793159383473493,1806793159383473537⟩,⟨(-1415282351768114482),(-1415282351768114438)⟩⟩,⟨⟨1791985068785974392,1791985068785974439⟩,⟨(-1412935707134224251),(-1412935707134224198)⟩⟩,⟨⟨1780936503229688941,1780936503229688985⟩,⟨(-1411152507194966126),(-1411152507194966082)⟩⟩,⟨⟨1773598098083262348,1773598098083262392⟩,⟨(-1409952762254645471),(-1409952762254645427)⟩⟩,⟨⟨1769937071702494007,1769937071702494051⟩,⟨(-1409349628287304648),(-1409349628287304604)⟩⟩] +lemma kernel19_1_r4_15_eq : ∀ k : Fin 16, kernel19_1Expr 4 15 k = kernel19_1_r4_15 k := by decide +kernel +noncomputable def kernel19_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel19_1_r4_0,kernel19_1_r4_1,kernel19_1_r4_2,kernel19_1_r4_3,kernel19_1_r4_4,kernel19_1_r4_5,kernel19_1_r4_6,kernel19_1_r4_7,kernel19_1_r4_8,kernel19_1_r4_9,kernel19_1_r4_10,kernel19_1_r4_11,kernel19_1_r4_12,kernel19_1_r4_13,kernel19_1_r4_14,kernel19_1_r4_15] +lemma kernel19_1_r4_eq (i k : Fin 16) : kernel19_1Expr 4 i k = kernel19_1_r4 i k := by + fin_cases i + · exact kernel19_1_r4_0_eq k + · exact kernel19_1_r4_1_eq k + · exact kernel19_1_r4_2_eq k + · exact kernel19_1_r4_3_eq k + · exact kernel19_1_r4_4_eq k + · exact kernel19_1_r4_5_eq k + · exact kernel19_1_r4_6_eq k + · exact kernel19_1_r4_7_eq k + · exact kernel19_1_r4_8_eq k + · exact kernel19_1_r4_9_eq k + · exact kernel19_1_r4_10_eq k + · exact kernel19_1_r4_11_eq k + · exact kernel19_1_r4_12_eq k + · exact kernel19_1_r4_13_eq k + · exact kernel19_1_r4_14_eq k + · exact kernel19_1_r4_15_eq k +noncomputable def kernel19_1_r5_0 : Fin 16 → CBox := ![⟨⟨109103374807059331351894245806,109103374807059334328697658607⟩,⟨7979224669503625862282380657,7979224669503628838003558526⟩⟩,⟨⟨109045873597693668971343157493,109045873597693671947276971352⟩,⟨7905300176208012228226518738,7905300176208015203076809123⟩⟩,⟨⟨108930832178338354960849267454,108930832178338357935039142246⟩,⟨7757695881541888769890989735,7757695881541891742994771444⟩⟩,⟨⟨108758173471539668261716402563,108758173471539671233288813477⟩,⟨7536900527956091611236488894,7536900527956094581718970014⟩⟩,⟨⟨108527784163386229876479629036,108527784163386232844562154907⟩,⟨7243645624247794921688125986,7243645624247797888675639137⟩⟩,⟨⟨108239517446061429715444736133,108239517446061432679166566461⟩,⟨6878903515892338959860742885,6878903515892341922481259041⟩⟩,⟨⟨107893196641068687321275348169,107893196641068690279767485696⟩,⟨6443884805953844505131710611,6443884805953847462515048440⟩⟩,⟨⟨107488619674618738714104312664,107488619674618741666500306053⟩,⟨5940035121573454109452781154,5940035121573457060731346212⟩⟩,⟨⟨107025564369807779670716342004,107025564369807782616152102709⟩,⟨5369031220168811382356760660,5369031220168814326665368725⟩⟩,⟨⟨106503794513534465834917732350,106503794513534468772532877083⟩,⟨4732776428862551947356848538,4732776428862554883834074201⟩⟩,⟨⟨105923066649639580708059188019,105923066649639583636997123808⟩,⟨4033395410333769500545152480,4033395410333772428333420320⟩⟩,⟨⟨105283137543542269069198306143,105283137543542271988833171691⟩,⟨3273228248293415889623866660,3273228248293418808096398326⟩⟩,⟨⟨104583772257729241490118739356,104583772257729244399619156782⟩,⟨2454823846156751478497318260,2454823846156754386821889596⟩⟩,⟨⟨103824752771866881023402073845,103824752771866883921943526249⟩,⟨1580932633252687064991870263,1580932633252689962343193767⟩⟩,⟨⟨103005887076089662808904208634,103005887076089665695663782369⟩,⟨654498574095120589873262323,654498574095123475427734840⟩⟩,⟨⟨102127018661210849937432811321,102127018661210852811596564707⟩,⟨(-321349522136734893124932776),(-321349522136732020181857574)⟩⟩] +lemma kernel19_1_r5_0_eq : ∀ k : Fin 16, kernel19_1Expr 5 0 k = kernel19_1_r5_0 k := by decide +kernel +noncomputable def kernel19_1_r5_1 : Fin 16 → CBox := ![⟨⟨101188036325242142683628948655,101188036325242145544383199081⟩,⟨(-1343307392691677079004488223),(-1343307392691674219487007700)⟩⟩,⟨⟨100188884211736625577624801980,100188884211736628424168888337⟩,⟨(-2407905411172068685826222201),(-2407905411172065840535419844)⟩⟩,⟨⟨99129571992122156199688305487,99129571992122159031220285818⟩,⟨(-3511519371574015009390436427),(-3511519371574012179128579363)⟩⟩,⟨⟨98010185101407466574473493468,98010185101407469390207202501⟩,⟨(-4650381958304916792967889818),(-4650381958304913978521370158)⟩⟩,⟨⟨96830894934456498258263792622,96830894934456501057409215568⟩,⟨(-5820594890193853112937196518),(-5820594890193850315092389200)⟩⟩,⟨⟨95591968908471800836007437110,95591968908471803617797095684⟩,⟨(-7018141722258308966620339073),(-7018141722258306186140917058)⟩⟩,⟨⟨94293780296436766507543771011,94293780296436769271202971581⟩,⟨(-8238901284364352502595644044),(-8238901284364349740256042402)⟩⟩,⟨⟨92936817736067737084100430829,92936817736067739828880185096⟩,⟨(-9478661730953693164435525598),(-9478661730953690420984393653)⟩⟩,⟨⟨91521694319345846657097793406,91521694319345849382237350813⟩,⟨(-10733135170754135852052965500),(-10733135170754133128250630434)⟩⟩,⟨⟨90049156168956083219361761768,90049156168956085924136893552⟩,⟨(-11997972839890316445272067841),(-11997972839890313741842256185)⟩⟩,⟨⟨88520090409974108173337481230,88520090409974110857007783587⟩,⟨(-13268780776125897021164735310),(-13268780776125894338847265080)⟩⟩,⟨⟨86935532447921350178821734864,86935532447921352840685773553⟩,⟨(-14541135946158866732454993286),(-14541135946158864071950636452)⟩⟩,⟨⟨85296672467861566419266742637,85296672467861569058600733023⟩,⟨(-15810602772025521570672389667),(-15810602772025518932704187475)⟩⟩,⟨⟨83604861073536983826786751806,83604861073536986443001086244⟩,⟨(-17072749996817730541797234055),(-17072749996817727926953981221)⟩⟩,⟨⟨81861613990632120871836588467,81861613990632123464430088192⟩,⟨(-18323167824157492074318531892),(-18323167824157489483100519459)⟩⟩,⟨⟨80068615764094122702823462568,80068615764094125271155344202⟩,⟨(-19557485260280571188189382668),(-19557485260280568621236436911)⟩⟩] +lemma kernel19_1_r5_1_eq : ∀ k : Fin 16, kernel19_1Expr 5 1 k = kernel19_1_r5_1 k := by decide +kernel +noncomputable def kernel19_1_r5_2 : Fin 16 → CBox := ![⟨⟨78227722386008075750351974654,78227722386008078293743175594⟩,⟨(-20771387582237080509394814818),(-20771387582237077967384969737)⟩⟩,⟨⟨76340962797794648387078160381,76340962797794650904926470046⟩,⟨(-21960633850702018254734893514),(-21960633850702015738269274864)⟩⟩,⟨⟨74410539218427860897624391348,74410539218427863389281754026⟩,⟨(-23121074381283666106183611126),(-23121074381283663615909125542)⟩⟩,⟨⟨72438826258917023841688303692,72438826258917026306581799294⟩,⟨(-24248668084101842983000301740),(-24248668084101840519488672310)⟩⟩,⟨⟨70428368792404972585096712802,70428368792404975022618010007⟩,⟨(-25339499577858471071790298105),(-25339499577858468635648591212)⟩⟩,⟨⟨68381878558842722212364627931,68381878558842724622119760975⟩,⟨(-26389795981713483726757162493),(-26389795981713481318377974690)⟩⟩,⟨⟨66302229493238837723354232876,66302229493238840104750527550⟩,⟨(-27395943286078996266517295357),(-27395943286078993886491969273)⟩⟩,⟨⟨64192451776872992363740993788,64192451776872994716283396319⟩,⟨(-28354502202017425479329062572),(-28354502202017423128151295473)⟩⟩,⟨⟨62055724621523253678014350114,62055724621523256001129543469⟩,⟨(-29262223388331705923304163872),(-29262223388331703601545881041)⟩⟩,⟨⟨59895367807595132056450526177,59895367807595134349744084247⟩,⟨(-30116061955716968454682441655),(-30116061955716966162681259291)⟩⟩,⟨⟨57714832007961283543270583169,57714832007961285806216725136⟩,⟨(-30913191148543337036143183278),(-30913191148543334774420231598)⟩⟩,⟨⟨55517687940223162044985622696,55517687940223164277177248227⟩,⟨(-31651015106989549584943060021),(-31651015106989547353905715741)⟩⟩,⟨⟨53307614400885274713193991445,53307614400885276914123845627⟩,⟨(-32327180615367174341402264814),(-32327180615367172141558177448)⟩⟩,⟨⟨51088385245481721289524485224,51088385245481723458846528672⟩,⟨(-32939587746574419310735207851),(-32939587746574417142430948752)⟩⟩,⟨⟨48863855388904586641295215465,48863855388904588778552040660⟩,⟨(-33486399317694394706344612976),(-33486399317694392570038238232)⟩⟩,⟨⟨46637945909945436571813468181,46637945909945438676696782981⟩,⟨(-33966049077790580767537772953),(-33966049077790578663538355870)⟩⟩] +lemma kernel19_1_r5_2_eq : ∀ k : Fin 16, kernel19_1Expr 5 2 k = kernel19_1_r5_2 k := by decide +kernel +noncomputable def kernel19_1_r5_3 : Fin 16 → CBox := ![⟨⟨44414628353266634087901552966,44414628353266636159974190229⟩,⟨(-34377248555925227856050854733),(-34377248555925225784796456931)⟩⟩,⟨⟨42197908330562877493717015302,42197908330562879532742700748⟩,⟨(-34718992505295087905643622301),(-34718992505295085867371542110)⟩⟩,⟨⟨39991808530453535138847799620,39991808530453537144449498370⟩,⟨(-34990562888091503489491389179),(-34990562888091501484579793734)⟩⟩,⟨⟨37800351253566541512656369765,37800351253566543484632984816⟩,⟨(-35191531355184619482625067676),(-35191531355184617511276306292)⟩⟩,⟨⟨35627540595245008861473281713,35627540595245010799471922722⟩,⟨(-35321760184928827460233157951),(-35321760184928825522801475277)⟩⟩,⟨⟨33477344403246502707222854869,33477344403246504611117500528⟩,⟨(-35381401656201959717580786360),(-35381401656201957814193669849)⟩⟩,⟨⟨31353676141639663020401646088,31353676141639664889902436620⟩,⟨(-35370895842127434817412538416),(-35370895842127432948361407586)⟩⟩,⟨⟨29260376794771614991745508558,29260376794771616826764565940⟩,⟨(-35290966822680473410532210666),(-35290966822680471575906602073)⟩⟩,⟨⟨27201196946632170803924487677,27201196946632172604191353935⟩,⟨(-35142617326432482197410708940),(-35142617326432480397482823349)⟩⟩,⟨⟨25179779171139615116269374995,25179779171139616881780891678⟩,⟨(-34927121823920745612973312922),(-34927121823920743847748137641)⟩⟩,⟨⟨23199640867793851540511269702,23199640867793853271573228380⟩,⟨(-34646018107417269756039845305),(-34646018107417268025213554352)⟩⟩,⟨⟨21264157674776028395304824990,21264157674776030095717416415⟩,⟨(-34301097404080742404361588231),(-34301097404080740704136434364)⟩⟩,⟨⟨19376547587924327312677019900,19376547587924328982143787725⟩,⟨(-33894393081476657368463553621),(-33894393081476655699138002493)⟩⟩,⟨⟨17539855909103264645073967624,17539855909103266283582410155⟩,⟨(-33428168016109776289275872711),(-33428168016109774650864487996)⟩⟩,⟨⟨15756941141343606079623954346,15756941141343607686941151645⟩,⟨(-32904900706798641740445809667),(-32904900706798640133183621439)⟩⟩,⟨⟨14030461940811799740013199934,14030461940811801316152067556⟩,⟨(-32327270225305287811728725025),(-32327270225305286235604963438)⟩⟩] +lemma kernel19_1_r5_3_eq : ∀ k : Fin 16, kernel19_1Expr 5 3 k = kernel19_1_r5_3 k := by decide +kernel +noncomputable def kernel19_1_r5_4 : Fin 16 → CBox := ![⟨⟨12362865227236312256204925252,12362865227236313800937693683⟩,⟨(-31698140106490989220525731279),(-31698140106490987675770347372)⟩⟩,⟨⟨10756375544952116099961995925,10756375544952117613388337853⟩,⟨(-31020541289283877046997490016),(-31020541289283875533513008693)⟩⟩,⟨⟨9212985756315849743481420393,9212985756315851225449300719⟩,⟨(-30297654227807917484594458097),(-30297654227807916002535134397)⟩⟩,⟨⟨7734449137997207641750122561,7734449137997209092374956929⟩,⟨(-29532790299036458903979450850),(-29532790299036457453232088583)⟩⟩,⟨⟨6322272938682409524749765407,6322272938682410943890539107⟩,⟨(-28729372639210124103045176850),(-28729372639210122683753019944)⟩⟩,⟨⟨4977713444158414295777847800,4977713444158415683632173305⟩,⟨(-27890916545923891577508239895),(-27890916545923890189475884172)⟩⟩,⟨⟨3701772582715383671158465597,3701772582715385027657800202⟩,⟨(-27021009586181394142881754137),(-27021009586181392786179947506)⟩⟩,⟨⟨2495196090449817719007775040,2495196090449819044368580150⟩,⟨(-26123291552790364695779359362),(-26123291552790363370193809870)⟩⟩,⟨⟨1358473242516582229237943142,1358473242516583523393444602⟩,⟨(-25201434412202131589904158410),(-25201434412202130295503795716)⟩⟩,⟨⟨291838142812385192859482023,291838142812386456116183385⟩,⟨(-24259122386266770959028267975),(-24259122386266769695508687330)⟩⟩,⟨⟨(-704727448875307992993312567),(-704727448875306760562874070)⟩,⟨(-23300032308387241731110843775),(-23300032308387240498401661327)⟩⟩,⟨⟨(-1631489786403943090804466772),(-1631489786403941888860011014)⟩,⟨(-22327814391230530886964925276),(-22327814391230529684727902807)⟩⟩,⟨⟨(-2488957350421234709874623820),(-2488957350421233538393566990)⟩,⟨(-21346073538527998197173196129),(-21346073538527997025393767507)⟩⟩,⟨⟨(-3277873664272145545484538828),(-3277873664272144403959685044)⟩,⟨(-20358351327623283567899681575),(-20358351327623282426072260899)⟩⟩,⟨⟨(-3999208783365607719147259410),(-3999208783365606607435988002)⟩,⟨(-19368108782372279491244231589),(-19368108782372278379227611220)⟩⟩,⟨⟨(-4654149539441016816162374845),(-4654149539441015733879320223)⟩,⟨(-18378710047848220637258484755),(-18378710047848219554668627253)⟩⟩] +lemma kernel19_1_r5_4_eq : ∀ k : Fin 16, kernel19_1Expr 5 4 k = kernel19_1_r5_4 k := by decide +kernel +noncomputable def kernel19_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-5244088630998941141142842046),(-5244088630998940088215860314)⟩,⟨(-17393407069151707937676312784),(-17393407069151706884442354223)⟩⟩,⟨⟨(-5770612659966123019685736404),(-5770612659966121995570940277)⟩,⟨(-16415325366578298434860191577),(-16415325366578297410439428402)⟩⟩,⟨⟨(-6235489222363708906755771182),(-6235489222363707911041024939)⟩,⟨(-15447450988573499162163740188),(-15447450988573498166145167821)⟩⟩,⟨⟨(-6640653167266157422385114134),(-6640653167266156454626405936)⟩,⟨(-14492618712433787005842447755),(-14492618712433786037783092627)⟩⟩,⟨⟨(-6988192143618209850146614833),(-6988192143618208910208705420)⟩,⟨(-13553501550726857689976186292),(-13553501550726856749742743709)⟩⟩,⟨⟨(-7280331558476465652744098165),(-7280331558476464740067359316)⟩,⟨(-12632601609044042613179661945),(-12632601609044041700235851800)⟩⟩,⟨⟨(-7519419072934753571809432669),(-7519419072934752686194409047)⟩,⟨(-11732242328105246443797790686),(-11732242328105245557942997481)⟩⟩,⟨⟨(-7707908763369548852738289826),(-7707908763369547993678819217)⟩,⟨(-10854562130555539481730364189),(-10854562130555538622457222614)⟩⟩,⟨⟨(-7848345075710668212370166891),(-7848345075710667379681877480)⟩,⟨(-10001509480165534974106919027),(-10001509480165534141229846370)⟩⟩,⟨⟨(-7943346699227154264208031586),(-7943346699227153456812892323)⟩,⟨(-9174839348714928958376706407),(-9174839348714928150816442593)⟩⟩,⟨⟨(-7995590483858124626117873134),(-7995590483858123843674251912)⟩,⟨(-8376111073735395824024132386),(-8376111073735395041437805430)⟩⟩,⟨⟨(-8007795521467804637389173960),(-8007795521467803879376015633)⟩,⟨(-7606687578644203738611134816),(-7606687578644202980476433049)⟩⟩,⟨⟨(-7982707506631285238375426069),(-7982707506631284504582625241)⟩,⟨(-6867735915734011776432846447),(-6867735915734011042538416261)⟩⟩,⟨⟨(-7923083486743743110825907806),(-7923083486743742400672141895)⟩,⟨(-6160229082108156990138990572),(-6160229082108156279902260235)⟩⟩,⟨⟨(-7831677104483237371413406291),(-7831677104483236684627532128)⟩,⟨(-5484949049064048638279029570),(-5484949049064047951427622621)⟩⟩,⟨⟨(-7711224428047851406216226984),(-7711224428047850742117092955)⟩,⟨(-4842490936717500977171742465),(-4842490936717500313023287005)⟩⟩] +lemma kernel19_1_r5_5_eq : ∀ k : Fin 16, kernel19_1Expr 5 5 k = kernel19_1_r5_5 k := by decide +kernel +noncomputable def kernel19_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-7564430456242114121247415693),(-7564430456242113479577522215)⟩,⟨(-4233268257902175033380304648),(-4233268257902174391676102201)⟩⟩,⟨⟨(-7393956376521947612828801381),(-7393956376521946992963756483)⟩,⟨(-3657519148631031965286716708),(-3657519148631031345401150558)⟩⟩,⟨⟨(-7202407644643088538016172518),(-7202407644643087939631123133)⟩,⟨(-3115313496716646066811647414),(-3115313496716645468418593665)⟩⟩,⟨⟨(-6992322944719039934132621268),(-6992322944719039356652348224)⟩,⟨(-2606560875545493644099188468),(-2606560875545493066622330454)⟩⟩,⟨⟨(-6766164078406111663783905656),(-6766164078406111106928637660)⟩,⟨(-2131019186504294959528771954),(-2131019186504294402687270604)⟩⟩,⟨⟨(-6526306821719159527079382219),(-6526306821719158990229598336)⟩,⟨(-1688303911165970548418553246),(-1688303911165970011591862970)⟩⟩,⟨⟨(-6275032777763847592537754769),(-6275032777763847075365360286)⟩,⟨(-1277897873046489790697173357),(-1277897873046489273556207681)⟩⟩,⟨⟨(-6014522243567070447697080782),(-6014522243567069949614501596)⟩,⟨(-899161408516051758297790428),(-899161408516051260254031688)⟩⟩,⟨⟨(-5746848099308324324825943147),(-5746848099308323844902614662)⟩,⟨(-551342847250177090557923416),(-551342847250176610679898231)⟩⟩,⟨⟨(-5473970718705981023236358676),(-5473970718705980560678020369)⟩,⟨(-233589204388238216727990070),(-233589204388237754220584290)⟩⟩,⟨⟨(-5197733890189978238811561622),(-5197733890189977793332962814)⟩,⟨55043010732018864584150770,55043010732019310007006900⟩⟩,⟨⟨(-4919861729883437248261718858),(-4919861729883436819334628815)⟩,⟨315576960845347156039997700,315576960845347584907297774⟩⟩,⟨⟨(-4641956559396993059090676243),(-4641956559396992646452641372)⟩,⟨549104709295553690265295291,549104709295554102841025955⟩⟩,⟨⟨(-4365497714077135789971846467),(-4365497714077135393062228712)⟩,⟨756776593090418446784928676,756776593090418843631315278⟩⟩,⟨⟨(-4091841240698224528592715407),(-4091841240698224147109923830)⟩,⟨939790817123130514029766835,939790817123130895448861281⟩⟩,⟨⟨(-3822220437690021904012990701),(-3822220437690021537408054692)⟩,⟨1099383340100103662757250421,1099383340100104029298450018⟩⟩] +lemma kernel19_1_r5_6_eq : ∀ k : Fin 16, kernel19_1Expr 5 6 k = kernel19_1_r5_6 k := by decide +kernel +noncomputable def kernel19_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-3557747185879863810720869273),(-3557747185879863458730664555)⟩,⟨1236818116198227707578022732,1236818116198228059504832481⟩⟩,⟨⟨(-3299414013420557138731111682),(-3299414013420556800771742139)⟩,⟨1353377749645182511768968466,1353377749645182849665614618⟩⟩,⟨⟨(-3048096835080076066090934444),(-3048096835080075741799158326)⟩,⟨1450354612369529697980784308,1450354612369530022210813811⟩⟩,⟨⟨(-2804558303384485421758058003),(-2804558303384485110635125411)⟩,⟨1529042467695980369945221845,1529042467695980681007646349⟩⟩,⟨⟨(-2569451707218321189572682161),(-2569451707218320891345593616)⟩,⟨1590728635855309899113355892,1590728635855310197286267279⟩⟩,⟨⟨(-2343325352374369410179223649),(-2343325352374369124330614871)⟩,⟨1636686729923257974484261342,1636686729923258260285351992⟩⟩,⟨⟨(-2126627358176107152671301827),(-2126627358176106878908042558)⟩,⟨1668169983778447712047971171,1668169983778447985769962536⟩⟩,⟨⟨(-1919710804631865994704615184),(-1919710804631865732551144362)⟩,⟨1686405186849699224133452085,1686405186849699486251494613⟩⟩,⟨⟨(-1722839165574072223806657979),(-1722839165574071972810723774)⟩,⟨1692587233874999122441998824,1692587233874999373407945372⟩⟩,⟨⟨(-1536191964837940346317734114),(-1536191964837940105937115429)⟩,⟨1687874291677241906175503837,1687874291677242146531178912⟩⟩,⟨⟨(-1359870594685267839089390352),(-1359870594685267609062042566)⟩,⟨1673383579127224692228651007,1673383579127224922235716193⟩⟩,⟨⟨(-1193904238320398885869865094),(-1193904238320398665770516117)⟩,⟨1650187751055654757626583052,1650187751055654977709935909⟩⟩,⟨⟨(-1038255841414353117630616591),(-1038255841414352907225085325)⟩,⟨1619311871928263362869463197,1619311871928263573262924228⟩⟩,⟨⟨(-892828080985427414909130274),(-892828080985427213746218313)⟩,⟨1581730960638414192720863169,1581730960638414393875282821⟩⟩,⟨⟨(-757469283715676771297536653),(-757469283715676579125886274)⟩,⟨1538368083818663916350271718,1538368083818664108516673600⟩⟩,⟨⟨(-631979249748447049403572911),(-631979249748446865830164248)⟩,⟨1490092971637561989506330515,1490092971637562173077415382⟩⟩] +lemma kernel19_1_r5_7_eq : ∀ k : Fin 16, kernel19_1Expr 5 7 k = kernel19_1_r5_7 k := by decide +kernel +noncomputable def kernel19_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-516114942149815690031017571),(-516114942149815514826804157)⟩,⟨1437721127134095172932150943,1437721127134095348136654921⟩⟩,⟨⟨(-409596006465811152465475599),(-409596006465810985136123731)⟩,⟨1382013397746120909795253368,1382013397746121077127190576⟩⟩,⟨⟨(-312110089109924726633614995),(-312110089109924566955439532)⟩,⟨1323675975800966748602688711,1323675975800966908285475210⟩⟩,⟨⟨(-223317927617496606020341844),(-223317927617496453643548313)⟩,⟨1263360793340319345656772343,1263360793340319498039951661⟩⟩,⟨⟨(-142858190054869512718675079),(-142858190054869367446237395)⟩,⟨1201666275726601153446509817,1201666275726601298726869866⟩⟩,⟨⟨(-70352045026015304981413536),(-70352045026015166460875109)⟩,⟨1139138417998731680362566838,1139138417998731818892345685⟩⟩,⟨⟨(-5407447736668876407016867),(-5407447736668744399420342)⟩,⟨1076272147882175295283932229,1076272147882175427301880584⟩⟩,⟨⟨52376868580156118506341888,52376868580156244327046223⟩,⟨1013512939679068517862189712,1013512939679068643694169433⟩⟩,⟨⟨103407702933945121087135245,103407702933945240893147448⟩,⟨951258643934178841116774863,951258643934178960934808563⟩⟩,⟨⟨148094002189131546085578091,148094002189131660193701688⟩,⟨889861498754946714125098249,889861498754946828245467147⟩⟩,⟨⟨186843782509118101777626993,186843782509118210392520222⟩,⟨829630289921324178324172898,829630289921324286951382700⟩⟩,⟨⟨220061354228818937053692388,220061354228819040452180958⟩,⟨770832628415541365450156580,770832628415541468860945727⟩⟩,⟨⟨248144845138163870781323951,248144845138163969122762230⟩,⟨713697315695448674118371471,713697315695448772472013249⟩⟩,⟨⟨271484014828338877896415637,271484014828338971463783790⟩,⟨658416768890517383350421945,658416768890517476929829639⟩⟩,⟨⟨290458350707874154000674659,290458350707874242955334224⟩,⟨605149480080902101236312121,605149480080902190202785592⟩⟩,⟨⟨305435434535305584064021293,305435434535305668652700624⟩,⟨554022485892702854092251053,554022485892702938692467697⟩⟩] +lemma kernel19_1_r5_8_eq : ∀ k : Fin 16, kernel19_1Expr 5 8 k = kernel19_1_r5_8 k := by decide +kernel +noncomputable def kernel19_1_r5_9 : Fin 16 → CBox := ![⟨⟨316769566833779234201575406,316769566833779314559176712⟩,⟨505133825774153791228165883,505133825774153871596565143⟩⟩,⟨⟨324800635342263987760400768,324800635342264064130812338⟩,⟨458554969477554275500724117,458554969477554351880585700⟩⟩,⟨⟨329853212706882573110281210,329853212706882645634612174⟩,⟨414333196432425611379948216,414333196432425683912474107⟩⟩,⟨⟨332235867910849539672813986,332235867910849608560339967⟩,⟨372493911831307323790333257,372493911831307392684891423⟩⟩,⟨⟨332240675467293402876586909,332240675467293468248093744⟩,⟨333042886338205477334942599,333042886338205542712406483⟩⟩,⟨⟨330142906139008967413478602,330142906139009029474894054⟩,⟨295968408351158627871709911,295968408351158689938093585⟩⟩,⟨⟨326200882884981324313087848,326200882884981383187016321⟩,⟨261243339687675695817404731,261243339687675754695394146⟩⟩,⟨⟨320655985846632843698349761,320655985846632899564783621⟩,⟨228827067400667828301275170,228827067400667884170941543⟩⟩,⟨⟨313732790458037581265234647,313732790458037634225789667⟩,⟨198667346161377411534376884,198667346161377464497410466⟩⟩,⟨⟨305639323174586830020983007,305639323174586880254605761⟩,⟨170702027255720561301649287,170702027255720611537067891⟩⟩,⟨⟨296567419844714863186232992,296567419844714910797991851⟩,⟨144860671724872483516836441,144860671724872531129775554⟩⟩,⟨⟨286693172380672963986200503,286693172380673009129187215⟩,⟨121066046535595464975454130,121066046535595510119068735⟩⟩,⟨⟨276177450098986842276616798,276177450098986885039486440⟩,⟨99235503888605626286781581,99235503888605669049786416⟩⟩,⟨⟨265166482881993813917891764,265166482881993854449875512⟩,⟨79282244863984736503354470,79282244863984777035036094⟩⟩,⟨⟨253792494142563214152749573,253792494142563252542732316⟩,⟨61116469562772891641139006,61116469562772930030434475⟩⟩,⟨⟨242174372439694703854457147,242174372439694740411557911⟩,⟨44646416736443781805901516,44646416736443818361983450⟩⟩] +lemma kernel19_1_r5_9_eq : ∀ k : Fin 16, kernel19_1Expr 5 9 k = kernel19_1_r5_9 k := by decide +kernel +noncomputable def kernel19_1_r5_10 : Fin 16 → CBox := ![⟨⟨230418371479300722342748173,230418371479300757139703433⟩,⟨29779296605288227605804314,29779296605288262401454406⟩⟩,⟨⟨218618829129508554807168476,218618829129508587952556833⟩,⟨16422121158235453213353301,16422121158235486357190075⟩⟩,⟨⟨206858896971959002961433198,206858896971959034511245208⟩,⟨4482436706648680032014698,4482436706648711580066449⟩⟩,⟨⟨195211272789837175476033764,195211272789837205521546707⟩,⟨(-6131036159822790122003130),(-6131036159822760078425469)⟩⟩,⟨⟨183738929251052304308760055,183738929251052332895713697⟩,⟨(-15507849788601317016950552),(-15507849788601288432075322)⟩⟩,⟨⟨172495832873666965327107422,172495832873666992546240154⟩,⟨(-23735358234324510863301497),(-23735358234324483646360673)⟩⟩,⟨⟨161527648154170278743787743,161527648154170304642981618⟩,⟨(-30898321858476513569501511),(-30898321858476487672513501)⟩⟩,⟨⟨150872422492475082617028735,150872422492475107273997066⟩,⟨(-37078581996931853688753982),(-37078581996931829033991430)⟩⟩,⟨⟨140561248256679496255989409,140561248256679519707979002⟩,⟨(-42354799961987487660030411),(-42354799961987464210232993)⟩⟩,⟨⟨130618898992778635389676615,130618898992778657715298097⟩,⟨(-46802254730024686743699559),(-46802254730024664420246241)⟩⟩,⟨⟨121064437397695151802339664,121064437397695173042003944⟩,⟨(-50492693799160900279849533),(-50492693799160879042319362)⟩⟩,⟨⟨111911793237125572409192998,111911793237125592628497289⟩,⟨(-53494231875686572009306901),(-53494231875686551792094908)⟩⟩,⟨⟨103170309902446408006260808,103170309902446427237584952⟩,⟨(-55871292256686787888958707),(-55871292256686768659677606)⟩⟩,⟨⟨94845258763638309476087389,94845258763638327784351611⟩,⟨(-57684586012415228541144308),(-57684586012415210234868669)⟩⟩,⟨⟨86938320888803065520584175,86938320888803082939620426⟩,⟨(-58991124329586216749504501),(-58991124329586199332315291)⟩⟩,⟨⟨79448036066801492939212667,79448036066801509524067523⟩,⟨(-59844259650147813560423049),(-59844259650147796977204137)⟩⟩] +lemma kernel19_1_r5_10_eq : ∀ k : Fin 16, kernel19_1Expr 5 10 k = kernel19_1_r5_10 k := by decide +kernel +noncomputable def kernel19_1_r5_11 : Fin 16 → CBox := ![⟨⟨72370219389681334106071265,72370219389681349882590713⟩,⟨(-60293751524177173275887108),(-60293751524177157500807121)⟩⟩,⟨⟨65698345928082053607708097,65698345928082068631998634⟩,⟨(-60385853385699626839604306),(-60385853385699611816571498)⟩⟩,⟨⟨59423904268151117088888260,59423904268151131388902504⟩,⟨(-60163416752390968606985752),(-60163416752390954308060974)⟩⟩,⟨⟨53536719875333522710953487,53536719875333536333507386⟩,⟨(-59666009640697749179343771),(-59666009640697735557724262)⟩⟩,⟨⟨48025249411487113435755321,48025249411487126402405244⟩,⟨(-58930046273809355557280242),(-58930046273809342591421816)⟩⟩,⟨⟨42876847259993394232900305,42876847259993406588692078⟩,⟨(-57988925438509327336939694),(-57988925438509314981808391)⟩⟩,⟨⟨38078005611769460750384675,38078005611769472519606168⟩,⟨(-56873175116031450733250302),(-56873175116031438964569226)⟩⟩,⟨⟨33614569536219637194254972,33614569536219648414723214⟩,⟨(-55610601269868129740841516),(-55610601269868118520804095)⟩⟩,⟨⟨29471928508022987050175634,29471928508022997738225919⟩,⟨(-54226438918622364105079742),(-54226438918622353417360419)⟩⟩,⟨⟨25635185885980195021699439,25635185885980205215441236⟩,⟨(-52743503853404491637380480),(-52743503853404481443878983)⟩⟩,⟨⟨22089307846577560615583485,22089307846577570333719005⟩,⟨(-51182343576207826129568074),(-51182343576207816411590755)⟩⟩,⟨⟨18819253264975443286408001,18819253264975452561882293⟩,⟨(-49561386237690519404571327),(-49561386237690510129181106)⟩⟩,⟨⟨15810086012157360080642289,15810086012157368926922510⟩,⟨(-47897086539628816362370493),(-47897086539628807516107698)⟩⟩,⟨⟨13047071101191892450766877,13047071101191900898426310⟩,⟨(-46204067738989500399460253),(-46204067738989491951758439)⟩⟩,⟨⟨10515756070006762700944434,10515756070006770764383731⟩,⟨(-44495259047282314128885457),(-44495259047282306065350425)⟩⟩,⟨⟨8202038934629213696409839,8202038934629221400916824⟩,⟨(-42782027860938807838925792),(-42782027860938800134275543)⟩⟩] +lemma kernel19_1_r5_11_eq : ∀ k : Fin 16, kernel19_1Expr 5 11 k = kernel19_1_r5_11 k := by decide +kernel +noncomputable def kernel19_1_r5_12 : Fin 16 → CBox := ![⟨⟨6092223987216545146173291,6092223987216552501527450⟩,⟨(-41074306386394635993206269),(-41074306386394628637666914)⟩⟩,⟨⟨4173066648925245665084988,4173066648925252697719244⟩,⟨(-39380712337905058294607225),(-39380712337905051261750758)⟩⟩,⟨⟨2431808520122772125766875,2431808520122778850020644⟩,⟨(-37708663487557850757445239),(-37708663487557844032937624)⟩⟩,⟨⟨856203700850577626535704,856203700850584062909497⟩,⟨(-36064485936185189086587817),(-36064485936185182649932565)⟩⟩,⟨⟨(-565462616132878647161779),(-565462616132872490644735)⟩,⟨(-34453516051680687798607608),(-34453516051680681641785437)⟩⟩,⟨⟨(-1844362348041201207764836),(-1844362348041195310433496)⟩,⟨(-32880196088390810571407456),(-32880196088390804673750602)⟩⟩,⟨⟨(-2991118658705692566185909),(-2991118658705686919126925)⟩,⟨(-31348163558574918889037706),(-31348163558574913241636069)⟩⟩,⟨⟨(-4015805235921453606370842),(-4015805235921448192424155)⟩,⟨(-29860334475219007887263897),(-29860334475219002472960122)⟩⟩,⟨⟨(-4927949982814413230160308),(-4927949982814408043607899)⟩,⟨(-28418980625537993021126028),(-28418980625537987834209128)⟩⟩,⟨⟨(-5736542460738387976905331),(-5736542460738383000093629)⟩,⟨(-27025801067084383016708414),(-27025801067084378039532312)⟩⟩,⟨⟨(-6450044482661720850382916),(-6450044482661716076298503)⟩,⟨(-25681988064245076490405604),(-25681988064245071715958154)⟩⟩,⟨⟨(-7076403314450062896787265),(-7076403314450058311549863)⟩,⟨(-24388287702768571633292812),(-24388287702768567047694618)⟩⟩,⟨⟨(-7623066996705731020393391),(-7623066996705726619332744)⟩,⟨(-23145055434501365876951505),(-23145055434501361475533344)⟩⟩,⟨⟨(-8097001351761549313067667),(-8097001351761545081967853)⟩,⟨(-21952306814364405742559785),(-21952306814364401511106317)⟩⟩,⟨⟨(-8504708288982760485806235),(-8504708288982756418184547)⟩,⟨(-20809763697366013809341506),(-20809763697366009741370760)⟩⟩,⟨⟨(-8852245066688866311495998),(-8852245066688862394414146)⟩,⟨(-19716896165681658538258066),(-19716896165681654620832193)⟩⟩] +lemma kernel19_1_r5_12_eq : ∀ k : Fin 16, kernel19_1Expr 5 12 k = kernel19_1_r5_12 k := by decide +kernel +noncomputable def kernel19_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-9145244210794791963916225),(-9145244210794788194635776)⟩,⟨(-18672960455044691443591200),(-18672960455044687673972355)⟩⟩,⟨⟨(-9388933828749616431223009),(-9388933828749612797558934)⟩,⟨(-17677033146353995566121937),(-17677033146353991932125299)⟩⟩,⟨⟨(-9588158092612384992326752),(-9588158092612381490184814)⟩,⟨(-16728041882940192368611869),(-16728041882940188866143579)⟩⟩,⟨⟨(-9747397697262696491346520),(-9747397697262693111416115)⟩,⟨(-15824792866726298514355827),(-15824792866726295134105420)⟩⟩,⟨⟨(-9870790128931552270233559),(-9870790128931549010157461)⟩,⟨(-14965995377916615399740806),(-14965995377916612139351332)⟩⟩,⟨⟨(-9962149605601767099152478),(-9962149605601763949128880)⟩,⟨(-14150283553156628244513508),(-14150283553156625094187891)⟩⟩,⟨⟨(-10024986574523153453838747),(-10024986574523150410672843)⟩,⟨(-13376235646598698682855073),(-13376235646598695639408638)⟩⟩,⟨⟨(-10062526673277959887453949),(-10062526673277956943385252)⟩,⟨(-12642390987221974352157705),(-12642390987221971407828591)⟩⟩,⟨⟨(-10077729079682099387625334),(-10077729079682096541352558)⟩,⟨(-11947264834297875289924128),(-11947264834297872443409907)⟩⟩,⟨⟨(-10073304192483571703078358),(-10073304192483568945975008)⟩,⟨(-11289361321243838054610439),(-11289361321243835297283353)⟩⟩,⟨⟨(-10051730599485631578509593),(-10051730599485628907902885)⟩,⟨(-10667184666420588671863981),(-10667184666420586001050174)⟩⟩,⟨⟨(-10015271302539805697345833),(-10015271302539803106628387)⟩,⟨(-10079248817831094415817664),(-10079248817831091824908674)⟩⟩,⟨⟨(-9965989179979144412269669),(-9965989179979141900389719)⟩,⟨(-9524085687279938457792274),(-9524085687279935945735389)⟩⟩,⟨⟨(-9905761676645501185285014),(-9905761676645498745217385)⟩,⟨(-9000252118438191621782310),(-9000252118438189181551366)⟩⟩,⟨⟨(-9836294719849735538776244),(-9836294719849733168692872)⟩,⟨(-8506335722501618871791068),(-8506335722501616501557149)⟩⟩,⟨⟨(-9759135866526645912498428),(-9759135866526643606925520)⟩,⟨(-8040959704784595752822023),(-8040959704784593447110464)⟩⟩] +lemma kernel19_1_r5_13_eq : ∀ k : Fin 16, kernel19_1Expr 5 13 k = kernel19_1_r5_13 k := by decide +kernel +noncomputable def kernel19_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-9675686692635367759217962),(-9675686692635365517868031)⟩,⟨(-7602786795700247534345518),(-7602786795700245292868070)⟩⟩,⟨⟨(-9587214440630967828421152),(-9587214440630965644843100)⟩,⟨(-7190522390169085202038194),(-7190522390169083018342980)⟩⟩,⟨⟨(-9494862944705800051532544),(-9494862944705797924352684)⟩,⟨(-6802916990593598604137075),(-6802916990593596476849722)⟩⟩,⟨⟨(-9399662856573372526519298),(-9399662856573370451075814)⟩,⟨(-6438768040145905125668079),(-6438768040145903050126103)⟩⟩,⟨⟨(-9302541196938374682058534),(-9302541196938372658076162)⟩,⟨(-6096921225243212418187609),(-6096921225243210394115151)⟩⟩,⟨⟨(-9204330259551553556134076),(-9204330259551551578355584)⟩,⟨(-5776271318728842262457095),(-5776271318728840284596323)⟩⟩,⟨⟨(-9105775895967060473379855),(-9105775895967058540780339)⟩,⟨(-5475762628426991239485425),(-5475762628426989306810896)⟩⟩,⟨⟨(-9007545209875116834989136),(-9007545209875114943548492)⟩,⟨(-5194389109385145762253261),(-5194389109385143870744355)⟩⟩,⟨⟨(-8910233690239782223440485),(-8910233690239780373405676)⟩,⟨(-4931194192243604024376740),(-4931194192243602174279955)⟩⟩,⟨⟨(-8814371812489058980962150),(-8814371812489057167430096)⟩,⟨(-4685270374758717454530840),(-4685270374758715640942621)⟩⟩,⟨⟨(-8720431136735144298939431),(-8720431136735142521151501)⟩,⟨(-4455758618535081978384294),(-4455758618535080200545597)⟩⟩,⟨⟨(-8628829931493166169125436),(-8628829931493164423570980)⟩,⟨(-4241847588470381832420877),(-4241847588470380086820644)⟩⟩,⟨⟨(-8539938350658660955667525),(-8539938350658659242529947)⟩,⟨(-4042772768262358992129027),(-4042772768262357278950290)⟩⟩,⟨⟨(-8454083190633850176766285),(-8454083190633848491897017)⟩,⟨(-3857815481547349864746917),(-3857815481547348179840750)⟩⟩,⟨⟨(-8371552253492367341216413),(-8371552253492365684056665)⟩,⟨(-3686301844810698725063816),(-3686301844810697067871095)⟩⟩,⟨⟨(-8292598340969206951655692),(-8292598340969205319091692)⟩,⟨(-3527601675107912273988445),(-3527601675107910641395091)⟩⟩] +lemma kernel19_1_r5_14_eq : ∀ k : Fin 16, kernel19_1Expr 5 14 k = kernel19_1_r5_14 k := by decide +kernel +noncomputable def kernel19_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-8217442902881240165097579),(-8217442902881238557770869)⟩,⟨(-3381127372838767901392716),(-3381127372838766294039958)⟩⟩,⟨⟨(-8146279362344129423627399),(-8146279362344127837449352)⟩,⟨(-3246332797302340868498596),(-3246332797302339282297538)⟩⟩,⟨⟨(-8079276138871214477205880),(-8079276138871212911760676)⟩,⟨(-3122712150507331930216127),(-3122712150507330364750682)⟩⟩,⟨⟨(-8016579389133456634467719),(-8016579389133455086946723)⟩,⟨(-3009798882698172884288857),(-3009798882698171336750132)⟩⟩,⟨⟨(-7958315483838813960823653),(-7958315483838812431667121)⟩,⟨(-2907164631263010939265090),(-2907164631263009410093100)⟩⟩,⟨⟨(-7904593237864220777585334),(-7904593237864219263294921)⟩,⟨(-2814418203095552530431032),(-2814418203095551016127206)⟩⟩,⟨⟨(-7855505909451398162805972),(-7855505909451396663062217)⟩,⟨(-2731204609070516968925905),(-2731204609070515469170568)⟩⟩,⟨⟨(-7811132982964991299083671),(-7811132982964989811301747)⟩,⟨(-2657204158044653678778261),(-2657204158044652190986381)⟩⟩,⟨⟨(-7771541748412412264485373),(-7771541748412410789284739)⟩,⟨(-2592131616695353293021284),(-2592131616695351817812100)⟩⟩,⟨⟨(-7736788689642288921076078),(-7736788689642287454786969)⟩,⟨(-2535735440541141056438496),(-2535735440541139590142064)⟩⟩,⟨⟨(-7706920691874410051955115),(-7706920691874408594351273)⟩,⟨(-2487797080637917379461122),(-2487797080637915921850996)⟩⟩,⟨⟨(-7681976077969304821483075),(-7681976077969303370172915)⟩,⟨(-2448130369697620044820668),(-2448130369697618593505078)⟩⟩,⟨⟨(-7661985481619999216342086),(-7661985481619997771925018)⟩,⟨(-2416580990718659324938455),(-2416580990718657880516627)⟩⟩,⟨⟨(-7646972564441191841030637),(-7646972564441190400349177)⟩,⟨(-2393026030637308793190253),(-2393026030637307352504546)⟩⟩,⟨⟨(-7636954582740584687328706),(-7636954582740583250169758)⟩,⟨(-2377373620994090114476834),(-2377373620994088677313968)⟩⟩,⟨⟨(-7631942808581360729673740),(-7631942808581359293735022)⟩,⟨(-2369562667147445170586340),(-2369562667147443734643872)⟩⟩] +lemma kernel19_1_r5_15_eq : ∀ k : Fin 16, kernel19_1Expr 5 15 k = kernel19_1_r5_15 k := by decide +kernel +noncomputable def kernel19_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel19_1_r5_0,kernel19_1_r5_1,kernel19_1_r5_2,kernel19_1_r5_3,kernel19_1_r5_4,kernel19_1_r5_5,kernel19_1_r5_6,kernel19_1_r5_7,kernel19_1_r5_8,kernel19_1_r5_9,kernel19_1_r5_10,kernel19_1_r5_11,kernel19_1_r5_12,kernel19_1_r5_13,kernel19_1_r5_14,kernel19_1_r5_15] +lemma kernel19_1_r5_eq (i k : Fin 16) : kernel19_1Expr 5 i k = kernel19_1_r5 i k := by + fin_cases i + · exact kernel19_1_r5_0_eq k + · exact kernel19_1_r5_1_eq k + · exact kernel19_1_r5_2_eq k + · exact kernel19_1_r5_3_eq k + · exact kernel19_1_r5_4_eq k + · exact kernel19_1_r5_5_eq k + · exact kernel19_1_r5_6_eq k + · exact kernel19_1_r5_7_eq k + · exact kernel19_1_r5_8_eq k + · exact kernel19_1_r5_9_eq k + · exact kernel19_1_r5_10_eq k + · exact kernel19_1_r5_11_eq k + · exact kernel19_1_r5_12_eq k + · exact kernel19_1_r5_13_eq k + · exact kernel19_1_r5_14_eq k + · exact kernel19_1_r5_15_eq k +noncomputable def kernel19_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel19_1_r0,kernel19_1_r1,kernel19_1_r2,kernel19_1_r3,kernel19_1_r4,kernel19_1_r5] +lemma kernel19_1_eq (j : Fin 6) (i k : Fin 16) : kernel19_1Expr j i k = kernel19_1 j i k := by + fin_cases j + · exact kernel19_1_r0_eq i k + · exact kernel19_1_r1_eq i k + · exact kernel19_1_r2_eq i k + · exact kernel19_1_r3_eq i k + · exact kernel19_1_r4_eq i k + · exact kernel19_1_r5_eq i k +lemma kernel19_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel19_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(19:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel19_1_eq] + unfold kernel19_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans19_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +end SharpPlanar.CachedData + +end OAI diff --git a/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues30.lean b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues30.lean new file mode 100644 index 0000000000000000000000000000000000000000..4ba0cef927f1e60cb33e76949e21d1329dea9b26 --- /dev/null +++ b/lean/OAI/Analysis/PlanarPacking/Certificate/KernelValues30.lean @@ -0,0 +1,3287 @@ +import OAI.Analysis.PlanarPacking.Grid +import OAI.Analysis.PlanarPacking.Certificate.TransformedPowers30 + +namespace OAI + +/-! +# Finite interval certificates for the planar Fourier construction + +These rational enclosures certify the numerical bounds in the sharp planar +Fourier construction of OpenAI. All interval endpoints are exact integers. +-/ + +namespace SharpPlanar.CachedData +open IntegerIntervals IntegerBasis IntegerGrid IntegerAlpha IntegerCompact +noncomputable def kernel21_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans21 j i k) +noncomputable def kernel21_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_0_eq : ∀ k : Fin 16, kernel21_0Expr 0 0 k = kernel21_0_r0_0 k := by decide +kernel +noncomputable def kernel21_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_1_eq : ∀ k : Fin 16, kernel21_0Expr 0 1 k = kernel21_0_r0_1 k := by decide +kernel +noncomputable def kernel21_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_2_eq : ∀ k : Fin 16, kernel21_0Expr 0 2 k = kernel21_0_r0_2 k := by decide +kernel +noncomputable def kernel21_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_3_eq : ∀ k : Fin 16, kernel21_0Expr 0 3 k = kernel21_0_r0_3 k := by decide +kernel +noncomputable def kernel21_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_4_eq : ∀ k : Fin 16, kernel21_0Expr 0 4 k = kernel21_0_r0_4 k := by decide +kernel +noncomputable def kernel21_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_5_eq : ∀ k : Fin 16, kernel21_0Expr 0 5 k = kernel21_0_r0_5 k := by decide +kernel +noncomputable def kernel21_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_6_eq : ∀ k : Fin 16, kernel21_0Expr 0 6 k = kernel21_0_r0_6 k := by decide +kernel +noncomputable def kernel21_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_7_eq : ∀ k : Fin 16, kernel21_0Expr 0 7 k = kernel21_0_r0_7 k := by decide +kernel +noncomputable def kernel21_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_8_eq : ∀ k : Fin 16, kernel21_0Expr 0 8 k = kernel21_0_r0_8 k := by decide +kernel +noncomputable def kernel21_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_9_eq : ∀ k : Fin 16, kernel21_0Expr 0 9 k = kernel21_0_r0_9 k := by decide +kernel +noncomputable def kernel21_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_10_eq : ∀ k : Fin 16, kernel21_0Expr 0 10 k = kernel21_0_r0_10 k := by decide +kernel +noncomputable def kernel21_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r0_11_eq : ∀ k : Fin 16, kernel21_0Expr 0 11 k = kernel21_0_r0_11 k := by decide +kernel +noncomputable def kernel21_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r0_12_eq : ∀ k : Fin 16, kernel21_0Expr 0 12 k = kernel21_0_r0_12 k := by decide +kernel +noncomputable def kernel21_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r0_13_eq : ∀ k : Fin 16, kernel21_0Expr 0 13 k = kernel21_0_r0_13 k := by decide +kernel +noncomputable def kernel21_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r0_14_eq : ∀ k : Fin 16, kernel21_0Expr 0 14 k = kernel21_0_r0_14 k := by decide +kernel +noncomputable def kernel21_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r0_15_eq : ∀ k : Fin 16, kernel21_0Expr 0 15 k = kernel21_0_r0_15 k := by decide +kernel +noncomputable def kernel21_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel21_0_r0_0,kernel21_0_r0_1,kernel21_0_r0_2,kernel21_0_r0_3,kernel21_0_r0_4,kernel21_0_r0_5,kernel21_0_r0_6,kernel21_0_r0_7,kernel21_0_r0_8,kernel21_0_r0_9,kernel21_0_r0_10,kernel21_0_r0_11,kernel21_0_r0_12,kernel21_0_r0_13,kernel21_0_r0_14,kernel21_0_r0_15] +lemma kernel21_0_r0_eq (i k : Fin 16) : kernel21_0Expr 0 i k = kernel21_0_r0 i k := by + fin_cases i + · exact kernel21_0_r0_0_eq k + · exact kernel21_0_r0_1_eq k + · exact kernel21_0_r0_2_eq k + · exact kernel21_0_r0_3_eq k + · exact kernel21_0_r0_4_eq k + · exact kernel21_0_r0_5_eq k + · exact kernel21_0_r0_6_eq k + · exact kernel21_0_r0_7_eq k + · exact kernel21_0_r0_8_eq k + · exact kernel21_0_r0_9_eq k + · exact kernel21_0_r0_10_eq k + · exact kernel21_0_r0_11_eq k + · exact kernel21_0_r0_12_eq k + · exact kernel21_0_r0_13_eq k + · exact kernel21_0_r0_14_eq k + · exact kernel21_0_r0_15_eq k +noncomputable def kernel21_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_0_eq : ∀ k : Fin 16, kernel21_0Expr 1 0 k = kernel21_0_r1_0 k := by decide +kernel +noncomputable def kernel21_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_1_eq : ∀ k : Fin 16, kernel21_0Expr 1 1 k = kernel21_0_r1_1 k := by decide +kernel +noncomputable def kernel21_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_2_eq : ∀ k : Fin 16, kernel21_0Expr 1 2 k = kernel21_0_r1_2 k := by decide +kernel +noncomputable def kernel21_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_3_eq : ∀ k : Fin 16, kernel21_0Expr 1 3 k = kernel21_0_r1_3 k := by decide +kernel +noncomputable def kernel21_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_4_eq : ∀ k : Fin 16, kernel21_0Expr 1 4 k = kernel21_0_r1_4 k := by decide +kernel +noncomputable def kernel21_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_5_eq : ∀ k : Fin 16, kernel21_0Expr 1 5 k = kernel21_0_r1_5 k := by decide +kernel +noncomputable def kernel21_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_6_eq : ∀ k : Fin 16, kernel21_0Expr 1 6 k = kernel21_0_r1_6 k := by decide +kernel +noncomputable def kernel21_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_7_eq : ∀ k : Fin 16, kernel21_0Expr 1 7 k = kernel21_0_r1_7 k := by decide +kernel +noncomputable def kernel21_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_8_eq : ∀ k : Fin 16, kernel21_0Expr 1 8 k = kernel21_0_r1_8 k := by decide +kernel +noncomputable def kernel21_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_9_eq : ∀ k : Fin 16, kernel21_0Expr 1 9 k = kernel21_0_r1_9 k := by decide +kernel +noncomputable def kernel21_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_10_eq : ∀ k : Fin 16, kernel21_0Expr 1 10 k = kernel21_0_r1_10 k := by decide +kernel +noncomputable def kernel21_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_11_eq : ∀ k : Fin 16, kernel21_0Expr 1 11 k = kernel21_0_r1_11 k := by decide +kernel +noncomputable def kernel21_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_12_eq : ∀ k : Fin 16, kernel21_0Expr 1 12 k = kernel21_0_r1_12 k := by decide +kernel +noncomputable def kernel21_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_13_eq : ∀ k : Fin 16, kernel21_0Expr 1 13 k = kernel21_0_r1_13 k := by decide +kernel +noncomputable def kernel21_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_14_eq : ∀ k : Fin 16, kernel21_0Expr 1 14 k = kernel21_0_r1_14 k := by decide +kernel +noncomputable def kernel21_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r1_15_eq : ∀ k : Fin 16, kernel21_0Expr 1 15 k = kernel21_0_r1_15 k := by decide +kernel +noncomputable def kernel21_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel21_0_r1_0,kernel21_0_r1_1,kernel21_0_r1_2,kernel21_0_r1_3,kernel21_0_r1_4,kernel21_0_r1_5,kernel21_0_r1_6,kernel21_0_r1_7,kernel21_0_r1_8,kernel21_0_r1_9,kernel21_0_r1_10,kernel21_0_r1_11,kernel21_0_r1_12,kernel21_0_r1_13,kernel21_0_r1_14,kernel21_0_r1_15] +lemma kernel21_0_r1_eq (i k : Fin 16) : kernel21_0Expr 1 i k = kernel21_0_r1 i k := by + fin_cases i + · exact kernel21_0_r1_0_eq k + · exact kernel21_0_r1_1_eq k + · exact kernel21_0_r1_2_eq k + · exact kernel21_0_r1_3_eq k + · exact kernel21_0_r1_4_eq k + · exact kernel21_0_r1_5_eq k + · exact kernel21_0_r1_6_eq k + · exact kernel21_0_r1_7_eq k + · exact kernel21_0_r1_8_eq k + · exact kernel21_0_r1_9_eq k + · exact kernel21_0_r1_10_eq k + · exact kernel21_0_r1_11_eq k + · exact kernel21_0_r1_12_eq k + · exact kernel21_0_r1_13_eq k + · exact kernel21_0_r1_14_eq k + · exact kernel21_0_r1_15_eq k +noncomputable def kernel21_0_r2_0 : Fin 16 → CBox := ![⟨⟨25303,25308⟩,⟨11795,11800⟩⟩,⟨⟨25246,25250⟩,⟨11750,11753⟩⟩,⟨⟨25128,25131⟩,⟨11658,11661⟩⟩,⟨⟨24952,24957⟩,⟨11521,11526⟩⟩,⟨⟨24721,24724⟩,⟨11343,11347⟩⟩,⟨⟨24434,24437⟩,⟨11122,11125⟩⟩,⟨⟨24093,24097⟩,⟨10862,10866⟩⟩,⟨⟨23701,23704⟩,⟨10566,10569⟩⟩,⟨⟨23261,23265⟩,⟨10236,10239⟩⟩,⟨⟨22775,22780⟩,⟨9875,9880⟩⟩,⟨⟨22244,22248⟩,⟨9487,9491⟩⟩,⟨⟨21676,21679⟩,⟨9076,9079⟩⟩,⟨⟨21071,21074⟩,⟨8645,8648⟩⟩,⟨⟨20433,20436⟩,⟨8199,8202⟩⟩,⟨⟨19764,19769⟩,⟨7740,7745⟩⟩,⟨⟨19073,19076⟩,⟨7274,7277⟩⟩] +lemma kernel21_0_r2_0_eq : ∀ k : Fin 16, kernel21_0Expr 2 0 k = kernel21_0_r2_0 k := by decide +kernel +noncomputable def kernel21_0_r2_1 : Fin 16 → CBox := ![⟨⟨18359,18363⟩,⟨6802,6806⟩⟩,⟨⟨17627,17632⟩,⟨6330,6335⟩⟩,⟨⟨16883,16887⟩,⟨5860,5864⟩⟩,⟨⟨16129,16133⟩,⟨5397,5401⟩⟩,⟨⟨15370,15373⟩,⟨4942,4946⟩⟩,⟨⟨14609,14612⟩,⟨4500,4504⟩⟩,⟨⟨13849,13852⟩,⟨4071,4075⟩⟩,⟨⟨13095,13098⟩,⟨3660,3664⟩⟩,⟨⟨12350,12354⟩,⟨3266,3270⟩⟩,⟨⟨11615,11620⟩,⟨2892,2897⟩⟩,⟨⟨10894,10898⟩,⟨2540,2543⟩⟩,⟨⟨10193,10196⟩,⟨2211,2214⟩⟩,⟨⟨9509,9514⟩,⟨1901,1906⟩⟩,⟨⟨8848,8852⟩,⟨1618,1622⟩⟩,⟨⟨8210,8213⟩,⟨1356,1359⟩⟩,⟨⟨7597,7600⟩,⟨1119,1123⟩⟩] +lemma kernel21_0_r2_1_eq : ∀ k : Fin 16, kernel21_0Expr 2 1 k = kernel21_0_r2_1 k := by decide +kernel +noncomputable def kernel21_0_r2_2 : Fin 16 → CBox := ![⟨⟨7009,7013⟩,⟨903,907⟩⟩,⟨⟨6449,6453⟩,⟨708,713⟩⟩,⟨⟨5916,5920⟩,⟨536,540⟩⟩,⟨⟨5413,5417⟩,⟨384,388⟩⟩,⟨⟨4937,4940⟩,⟨251,255⟩⟩,⟨⟨4491,4495⟩,⟨137,141⟩⟩,⟨⟨4072,4075⟩,⟨39,43⟩⟩,⟨⟨3682,3685⟩,⟨(-43),(-39)⟩⟩,⟨⟨3319,3323⟩,⟨(-113),(-109)⟩⟩,⟨⟨2984,2987⟩,⟨(-166),(-163)⟩⟩,⟨⟨2673,2676⟩,⟨(-210),(-206)⟩⟩,⟨⟨2388,2391⟩,⟨(-244),(-240)⟩⟩,⟨⟨2126,2131⟩,⟨(-268),(-263)⟩⟩,⟨⟨1887,1890⟩,⟨(-283),(-279)⟩⟩,⟨⟨1670,1674⟩,⟨(-293),(-289)⟩⟩,⟨⟨1473,1478⟩,⟨(-296),(-291)⟩⟩] +lemma kernel21_0_r2_2_eq : ∀ k : Fin 16, kernel21_0Expr 2 2 k = kernel21_0_r2_2 k := by decide +kernel +noncomputable def kernel21_0_r2_3 : Fin 16 → CBox := ![⟨⟨1295,1299⟩,⟨(-294),(-290)⟩⟩,⟨⟨1136,1140⟩,⟨(-289),(-285)⟩⟩,⟨⟨993,997⟩,⟨(-279),(-275)⟩⟩,⟨⟨865,868⟩,⟨(-268),(-265)⟩⟩,⟨⟨750,754⟩,⟨(-255),(-251)⟩⟩,⟨⟨650,653⟩,⟨(-239),(-235)⟩⟩,⟨⟨560,563⟩,⟨(-224),(-221)⟩⟩,⟨⟨481,485⟩,⟨(-207),(-204)⟩⟩,⟨⟨410,416⟩,⟨(-193),(-187)⟩⟩,⟨⟨351,355⟩,⟨(-177),(-173)⟩⟩,⟨⟨299,302⟩,⟨(-160),(-156)⟩⟩,⟨⟨253,256⟩,⟨(-146),(-142)⟩⟩,⟨⟨214,217⟩,⟨(-133),(-129)⟩⟩,⟨⟨180,183⟩,⟨(-119),(-115)⟩⟩,⟨⟨150,153⟩,⟨(-106),(-102)⟩⟩,⟨⟨125,129⟩,⟨(-95),(-91)⟩⟩] +lemma kernel21_0_r2_3_eq : ∀ k : Fin 16, kernel21_0Expr 2 3 k = kernel21_0_r2_3 k := by decide +kernel +noncomputable def kernel21_0_r2_4 : Fin 16 → CBox := ![⟨⟨103,108⟩,⟨(-84),(-79)⟩⟩,⟨⟨85,88⟩,⟨(-74),(-70)⟩⟩,⟨⟨71,74⟩,⟨(-64),(-61)⟩⟩,⟨⟨58,62⟩,⟨(-56),(-53)⟩⟩,⟨⟨47,51⟩,⟨(-49),(-46)⟩⟩,⟨⟨37,41⟩,⟨(-44),(-40)⟩⟩,⟨⟨30,34⟩,⟨(-38),(-34)⟩⟩,⟨⟨25,28⟩,⟨(-33),(-29)⟩⟩,⟨⟨19,23⟩,⟨(-28),(-24)⟩⟩,⟨⟨15,18⟩,⟨(-24),(-21)⟩⟩,⟨⟨12,15⟩,⟨(-22),(-18)⟩⟩,⟨⟨9,14⟩,⟨(-18),(-13)⟩⟩,⟨⟨7,11⟩,⟨(-16),(-12)⟩⟩,⟨⟨4,8⟩,⟨(-13),(-10)⟩⟩,⟨⟨3,7⟩,⟨(-12),(-9)⟩⟩,⟨⟨3,6⟩,⟨(-10),(-6)⟩⟩] +lemma kernel21_0_r2_4_eq : ∀ k : Fin 16, kernel21_0Expr 2 4 k = kernel21_0_r2_4 k := by decide +kernel +noncomputable def kernel21_0_r2_5 : Fin 16 → CBox := ![⟨⟨1,5⟩,⟨(-8),(-5)⟩⟩,⟨⟨0,4⟩,⟨(-7),(-3)⟩⟩,⟨⟨0,4⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-2),2⟩,⟨(-6),(-2)⟩⟩,⟨⟨0,3⟩,⟨(-4),(-1)⟩⟩,⟨⟨0,3⟩,⟨(-4),(-1)⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩] +lemma kernel21_0_r2_5_eq : ∀ k : Fin 16, kernel21_0Expr 2 5 k = kernel21_0_r2_5 k := by decide +kernel +noncomputable def kernel21_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩] +lemma kernel21_0_r2_6_eq : ∀ k : Fin 16, kernel21_0Expr 2 6 k = kernel21_0_r2_6 k := by decide +kernel +noncomputable def kernel21_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r2_7_eq : ∀ k : Fin 16, kernel21_0Expr 2 7 k = kernel21_0_r2_7 k := by decide +kernel +noncomputable def kernel21_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r2_8_eq : ∀ k : Fin 16, kernel21_0Expr 2 8 k = kernel21_0_r2_8 k := by decide +kernel +noncomputable def kernel21_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r2_9_eq : ∀ k : Fin 16, kernel21_0Expr 2 9 k = kernel21_0_r2_9 k := by decide +kernel +noncomputable def kernel21_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel21_0_r2_10_eq : ∀ k : Fin 16, kernel21_0Expr 2 10 k = kernel21_0_r2_10 k := by decide +kernel +noncomputable def kernel21_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r2_11_eq : ∀ k : Fin 16, kernel21_0Expr 2 11 k = kernel21_0_r2_11 k := by decide +kernel +noncomputable def kernel21_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r2_12_eq : ∀ k : Fin 16, kernel21_0Expr 2 12 k = kernel21_0_r2_12 k := by decide +kernel +noncomputable def kernel21_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r2_13_eq : ∀ k : Fin 16, kernel21_0Expr 2 13 k = kernel21_0_r2_13 k := by decide +kernel +noncomputable def kernel21_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r2_14_eq : ∀ k : Fin 16, kernel21_0Expr 2 14 k = kernel21_0_r2_14 k := by decide +kernel +noncomputable def kernel21_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel21_0_r2_15_eq : ∀ k : Fin 16, kernel21_0Expr 2 15 k = kernel21_0_r2_15 k := by decide +kernel +noncomputable def kernel21_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel21_0_r2_0,kernel21_0_r2_1,kernel21_0_r2_2,kernel21_0_r2_3,kernel21_0_r2_4,kernel21_0_r2_5,kernel21_0_r2_6,kernel21_0_r2_7,kernel21_0_r2_8,kernel21_0_r2_9,kernel21_0_r2_10,kernel21_0_r2_11,kernel21_0_r2_12,kernel21_0_r2_13,kernel21_0_r2_14,kernel21_0_r2_15] +lemma kernel21_0_r2_eq (i k : Fin 16) : kernel21_0Expr 2 i k = kernel21_0_r2 i k := by + fin_cases i + · exact kernel21_0_r2_0_eq k + · exact kernel21_0_r2_1_eq k + · exact kernel21_0_r2_2_eq k + · exact kernel21_0_r2_3_eq k + · exact kernel21_0_r2_4_eq k + · exact kernel21_0_r2_5_eq k + · exact kernel21_0_r2_6_eq k + · exact kernel21_0_r2_7_eq k + · exact kernel21_0_r2_8_eq k + · exact kernel21_0_r2_9_eq k + · exact kernel21_0_r2_10_eq k + · exact kernel21_0_r2_11_eq k + · exact kernel21_0_r2_12_eq k + · exact kernel21_0_r2_13_eq k + · exact kernel21_0_r2_14_eq k + · exact kernel21_0_r2_15_eq k +noncomputable def kernel21_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-3820085210085947),(-3820085210085943)⟩,⟨(-22130901038230117),(-22130901038230113)⟩⟩,⟨⟨(-3833158840148647),(-3833158840148644)⟩,⟨(-22092253880327093),(-22092253880327089)⟩⟩,⟨⟨(-3859140347368056),(-3859140347368052)⟩,⟨(-22015112633859589),(-22015112633859586)⟩⟩,⟨⟨(-3897700271867997),(-3897700271867993)⟩,⟨(-21899782927280850),(-21899782927280846)⟩⟩,⟨⟨(-3948349511652186),(-3948349511652181)⟩,⟨(-21746721920537635),(-21746721920537630)⟩⟩,⟨⟨(-4010445352673160),(-4010445352673156)⟩,⟨(-21556536746039479),(-21556536746039475)⟩⟩,⟨⟨(-4083199384443406),(-4083199384443403)⟩,⟨(-21329982398027056),(-21329982398027053)⟩⟩,⟨⟨(-4165687196561905),(-4165687196561902)⟩,⟨(-21067959044934165),(-21067959044934162)⟩⟩,⟨⟨(-4256859727939999),(-4256859727939994)⟩,⟨(-20771508735365625),(-20771508735365621)⟩⟩,⟨⟨(-4355556118598912),(-4355556118598909)⟩,⟨(-20441811465822809),(-20441811465822806)⟩⟩,⟨⟨(-4460517893978483),(-4460517893978480)⟩,⟨(-20080180577495278),(-20080180577495275)⟩⟩,⟨⟨(-4570404294024001),(-4570404294023997)⟩,⟨(-19688057450446139),(-19688057450446135)⟩⟩,⟨⟨(-4683808544163400),(-4683808544163397)⟩,⟨(-19267005466439826),(-19267005466439823)⟩⟩,⟨⟨(-4799274852880775),(-4799274852880772)⟩,⟨(-18818703216525051),(-18818703216525048)⟩⟩,⟨⟨(-4915315911132944),(-4915315911132941)⟩,⟨(-18344936936262809),(-18344936936262806)⟩⟩,⟨⟨(-5030430662507026),(-5030430662507021)⟩,⟨(-17847592160089323),(-17847592160089319)⟩⟩] +lemma kernel21_0_r3_0_eq : ∀ k : Fin 16, kernel21_0Expr 3 0 k = kernel21_0_r3_0 k := by decide +kernel +noncomputable def kernel21_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-5143122109902094),(-5143122109902091)⟩,⟨(-17328644596576913),(-17328644596576908)⟩⟩,⟨⟨(-5251914924717560),(-5251914924717556)⟩,⟨(-16790150238096477),(-16790150238096474)⟩⟩,⟨⟨(-5355372628078677),(-5355372628078673)⟩,⟨(-16234234731336877),(-16234234731336873)⟩⟩,⟨⟨(-5452114120510013),(-5452114120510010)⟩,⟨(-15663082048997232),(-15663082048997229)⟩⟩,⟨⟨(-5540829346613661),(-5540829346613658)⟩,⟨(-15078922517399242),(-15078922517399239)⟩⟩,⟨⟨(-5620293894600413),(-5620293894600410)⟩,⟨(-14484020269400566),(-14484020269400563)⟩⟩,⟨⟨(-5689382346785773),(-5689382346785769)⟩,⟨(-13880660206441061),(-13880660206441057)⟩⟩,⟨⟨(-5747080216172525),(-5747080216172521)⟩,⟨(-13271134567426647),(-13271134567426642)⟩⟩,⟨⟨(-5792494325720863),(-5792494325720858)⟩,⟨(-12657729215058777),(-12657729215058772)⟩⟩,⟨⟨(-5824861510531011),(-5824861510531006)⟩,⟨(-12042709761772103),(-12042709761772098)⟩⟩,⟨⟨(-5843555548563739),(-5843555548563735)⟩,⟨(-11428307667294349),(-11428307667294345)⟩⟩,⟨⟨(-5848092252294441),(-5848092252294436)⟩,⟨(-10816706447670115),(-10816706447670111)⟩⟩,⟨⟨(-5838132681398695),(-5838132681398690)⟩,⟨(-10210028141117542),(-10210028141117539)⟩⟩,⟨⟨(-5813484464739355),(-5813484464739350)⟩,⟨(-9610320179088673),(-9610320179088669)⟩⟩,⟨⟨(-5774101248089877),(-5774101248089874)⟩,⟨(-9019542811215000),(-9019542811214997)⟩⟩,⟨⟨(-5720080311702590),(-5720080311702586)⟩,⟨(-8439557230337729),(-8439557230337725)⟩⟩] +lemma kernel21_0_r3_1_eq : ∀ k : Fin 16, kernel21_0Expr 3 1 k = kernel21_0_r3_1 k := by decide +kernel +noncomputable def kernel21_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-5651658428534283),(-5651658428534279)⟩,⟨(-7872114538514177),(-7872114538514173)⟩⟩,⟨⟨(-5569206059209430),(-5569206059209427)⟩,⟨(-7318845686794317),(-7318845686794314)⟩⟩,⟨⟨(-5473220003191980),(-5473220003191976)⟩,⟨(-6781252510780989),(-6781252510780984)⟩⟩,⟨⟨(-5364314646742493),(-5364314646742490)⟩,⟨(-6260699970698358),(-6260699970698355)⟩⟩,⟨⟨(-5243211966694380),(-5243211966694377)⟩,⟨(-5758409689133944),(-5758409689133939)⟩⟩,⟨⟨(-5110730464578369),(-5110730464578366)⟩,⟨(-5275454862086504),(-5275454862086501)⟩⟩,⟨⟨(-4967773217905288),(-4967773217905284)⟩,⟨(-4812756599792632),(-4812756599792628)⟩⟩,⟨⟨(-4815315244295492),(-4815315244295489)⟩,⟨(-4371081733408111),(-4371081733408108)⟩⟩,⟨⟨(-4654390379500861),(-4654390379500856)⟩,⟨(-3951042102407383),(-3951042102407379)⟩⟩,⟨⟨(-4486077872156794),(-4486077872156790)⟩,⟨(-3553095315977667),(-3553095315977664)⟩⟩,⟨⟨(-4311488896355406),(-4311488896355403)⟩,⟨(-3177546960175317),(-3177546960175314)⟩⟩,⟨⟨(-4131753177948417),(-4131753177948412)⟩,⟨(-2824554201629984),(-2824554201629980)⟩⟩,⟨⟨(-3948005922040792),(-3948005922040789)⟩,⟨(-2494130718562718),(-2494130718562715)⟩⟩,⟨⟨(-3761375217661480),(-3761375217661477)⟩,⟨(-2186152871237564),(-2186152871237561)⟩⟩,⟨⟨(-3572970081392798),(-3572970081392795)⟩,⟨(-1900367007067434),(-1900367007067430)⟩⟩,⟨⟨(-3383869285154668),(-3383869285154665)⟩,⟨(-1636397780774279),(-1636397780774276)⟩⟩] +lemma kernel21_0_r3_2_eq : ∀ k : Fin 16, kernel21_0Expr 3 2 k = kernel21_0_r3_2 k := by decide +kernel +noncomputable def kernel21_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-3195111094766258),(-3195111094766253)⟩,⟨(-1393757357538234),(-1393757357538230)⟩⟩,⟨⟨(-3007684025771543),(-3007684025771538)⟩,⟨(-1171855357178899),(-1171855357178894)⟩⟩,⟨⟨(-2822518701764840),(-2822518701764836)⟩,⟨(-970009390249034),(-970009390249031)⟩⟩,⟨⟨(-2640480878547039),(-2640480878547036)⟩,⟨(-787456032574922),(-787456032574919)⟩⟩,⟨⟨(-2462365675342487),(-2462365675342484)⟩,⟨(-623362083269497),(-623362083269494)⟩⟩,⟨⟨(-2288893032458871),(-2288893032458868)⟩,⟨(-476835952528999),(-476835952528995)⟩⟩,⟨⟨(-2120704393605002),(-2120704393604998)⟩,⟨(-346939029492571),(-346939029492567)⟩⟩,⟨⟨(-1958360590990110),(-1958360590990106)⟩,⟨(-232696886929769),(-232696886929764)⟩⟩,⟨⟨(-1802340892669423),(-1802340892669420)⟩,⟨(-133110188303086),(-133110188303082)⟩⟩,⟨⟨(-1653043154683618),(-1653043154683615)⟩,⟨(-47165173566006),(-47165173566002)⟩⟩,⟨⟨(-1510785005621096),(-1510785005621093)⟩,⟨26156387400807,26156387400811⟩⟩,⟨⟨(-1375805978511543),(-1375805978511539)⟩,⟨87867870871918,87867870871923⟩⟩,⟨⟨(-1248270494577707),(-1248270494577703)⟩,⟨138969187044529,138969187044532⟩⟩,⟨⟨(-1128271595410137),(-1128271595410134)⟩,⟨180438945974256,180438945974259⟩⟩,⟨⟨(-1015835314608454),(-1015835314608451)⟩,⟨213227452143529,213227452143532⟩⟩,⟨⟨(-910925576817186),(-910925576817182)⟩,⟨238250562117783,238250562117787⟩⟩] +lemma kernel21_0_r3_3_eq : ∀ k : Fin 16, kernel21_0Expr 3 3 k = kernel21_0_r3_3 k := by decide +kernel +noncomputable def kernel21_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-813449511286628),(-813449511286622)⟩,⟨256384424073977,256384424073982⟩⟩,⟨⟨(-723263068473725),(-723263068473722)⟩,⟨268461102955721,268461102955724⟩⟩,⟨⟨(-640176831588025),(-640176831588021)⟩,⟨275265080889962,275265080889967⟩⟩,⟨⟨(-563961920171329),(-563961920171325)⟩,⟨277530609524544,277530609524548⟩⟩,⟨⟨(-494355889538770),(-494355889538767)⟩,⟨275939879306204,275939879306209⟩⟩,⟨⟨(-431068537945404),(-431068537945400)⟩,⟨271121960563467,271121960563470⟩⟩,⟨⟨(-373787542407282),(-373787542407279)⟩,⟨263652462692642,263652462692645⟩⟩,⟨⟨(-322183853926212),(-322183853926209)⟩,⟨254053850828200,254053850828203⟩⟩,⟨⟨(-275916793173520),(-275916793173516)⟩,⟨242796354128709,242796354128712⟩⟩,⟨⟨(-234638798220851),(-234638798220848)⟩,⟨230299396204053,230299396204056⟩⟩,⟨⟨(-197999786421529),(-197999786421526)⟩,⟨216933476190103,216933476190106⟩⟩,⟨⟨(-165651102821852),(-165651102821849)⟩,⟨203022428452279,203022428452282⟩⟩,⟨⟨(-137249037319909),(-137249037319905)⟩,⟨188845989751676,188845989751679⟩⟩,⟨⟨(-112457902020087),(-112457902020083)⟩,⟨174642604796033,174642604796037⟩⟩,⟨⟨(-90952668714312),(-90952668714307)⟩,⟨160612404266472,160612404266477⟩⟩,⟨⟨(-72421174046616),(-72421174046613)⟩,⟨146920293491435,146920293491438⟩⟩] +lemma kernel21_0_r3_4_eq : ∀ k : Fin 16, kernel21_0Expr 3 4 k = kernel21_0_r3_4 k := by decide +kernel +noncomputable def kernel21_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-56565906607269),(-56565906607265)⟩,⟨133699094758363,133699094758367⟩⟩,⟨⟨(-43105395907544),(-43105395907540)⟩,⟨121052691636712,121052691636717⟩⟩,⟨⟨(-31775227885798),(-31775227885795)⟩,⟨109059129462560,109059129462563⟩⟩,⟨⟨(-22328715295208),(-22328715295205)⟩,⟨97773632142608,97773632142611⟩⟩,⟨⟨(-14537254052104),(-14537254052101)⟩,⟨87231501522283,87231501522286⟩⟩,⟨⟨(-8190398430071),(-8190398430067)⟩,⟨77450871591653,77450871591658⟩⟩,⟨⟨(-3095688934204),(-3095688934201)⟩,⟨68435295652733,68435295652737⟩⟩,⟨⟨921733139083,921733139087⟩,⟨60176150138704,60176150138707⟩⟩,⟨⟨4019690970556,4019690970559⟩,⟨52654843974563,52654843974566⟩⟩,⟨⟨6339684943527,6339684943531⟩,⟨45844827132542,45844827132545⟩⟩,⟨⟨8007722067678,8007722067682⟩,⟨39713396316057,39713396316062⟩⟩,⟨⟨9135233356241,9135233356245⟩,⟨34223299471246,34223299471250⟩⟩,⟨⟨9820052730219,9820052730222⟩,⟨29334144060212,29334144060215⟩⟩,⟨⟨10147433556793,10147433556797⟩,⟨25003616733986,25003616733990⟩⟩,⟨⟨10191081593305,10191081593309⟩,⟨21188524227867,21188524227871⟩⟩,⟨⟨10014185826915,10014185826920⟩,⟨17845666989932,17845666989938⟩⟩] +lemma kernel21_0_r3_5_eq : ∀ k : Fin 16, kernel21_0Expr 3 5 k = kernel21_0_r3_5 k := by decide +kernel +noncomputable def kernel21_0_r3_6 : Fin 16 → CBox := ![⟨⟨9670431405924,9670431405927⟩,⟨14932558276605,14932558276608⟩⟩,⟨⟨9204981493788,9204981493792⟩,⟨12408002245654,12408002245657⟩⟩,⟨⟨8655417392986,8655417392991⟩,⟨10232544990100,10232544990104⟩⟩,⟨⟨8052628644314,8052628644318⟩,⟨8368812532637,8368812532641⟩⟩,⟨⟨7421646978945,7421646978949⟩,⟨6781749587213,6781749587217⟩⟩,⟨⟨6782419964997,6782419965000⟩,⟨5438772440279,5438772440282⟩⟩,⟨⟨6150521935120,6150521935125⟩,⟨4309848655343,4309848655347⟩⟩,⟨⟨5537801301584,5537801301587⟩,⟨3367515505430,3367515505433⟩⟩,⟨⟨4952964661480,4952964661483⟩,⟨2586848129775,2586848129778⟩⟩,⟨⟨4402099173520,4402099173524⟩,⟨1945387431260,1945387431263⟩⟩,⟨⟨3889135559960,3889135559965⟩,⟨1423036712860,1423036712864⟩⟩,⟨⟨3416254766741,3416254766745⟩,⟨1001935023692,1001935023696⟩⟩,⟨⟨2984241818271,2984241818274⟩,⟨666314172633,666314172636⟩⟩,⟨⟨2592790748657,2592790748662⟩,⟨402345389948,402345389952⟩⟩,⟨⟨2240764697563,2240764697566⟩,⟨197980690740,197980690743⟩⟩,⟨⟨1926415345424,1926415345429⟩,⟨42793130365,42793130369⟩⟩] +lemma kernel21_0_r3_6_eq : ∀ k : Fin 16, kernel21_0Expr 3 6 k = kernel21_0_r3_6 k := by decide +kernel +noncomputable def kernel21_0_r3_7 : Fin 16 → CBox := ![⟨⟨1647565848472,1647565848476⟩,⟨(-72180650480),(-72180650477)⟩⟩,⟨⟨1401761336825,1401761336829⟩,⟨(-154592909399),(-154592909394)⟩⟩,⟨⟨1186390876027,1186390876030⟩,⟨(-210930270303),(-210930270300)⟩⟩,⟨⟨998784579199,998784579202⟩,⟨(-246650690084),(-246650690081)⟩⟩,⟨⟨836289307637,836289307641⟩,⟨(-266310919880),(-266310919876)⟩⟩,⟨⟨696326124478,696326124481⟩,⟨(-273683865373),(-273683865370)⟩⟩,⟨⟨576432379738,576432379741⟩,⟨(-271865590275),(-271865590272)⟩⟩,⟨⟨474291014626,474291014629⟩,⟨(-263371983688),(-263371983685)⟩⟩,⟨⟨387749385816,387749385821⟩,⟨(-250225331426),(-250225331422)⟩⟩,⟨⟨314829632542,314829632545⟩,⟨(-234031199801),(-234031199798)⟩⟩,⟨⟨253732345134,253732345139⟩,⟨(-216046164310),(-216046164306)⟩⟩,⟨⟨202835046641,202835046644⟩,⟨(-197237000999),(-197237000996)⟩⟩,⟨⟨160686771339,160686771343⟩,⟨(-178332011405),(-178332011402)⟩⟩,⟨⟨125999816892,125999816895⟩,⟨(-159865177851),(-159865177848)⟩⟩,⟨⟨97639560884,97639560888⟩,⟨(-142213850113),(-142213850110)⟩⟩,⟨⟨74613067520,74613067523⟩,⟨(-125630651295),(-125630651291)⟩⟩] +lemma kernel21_0_r3_7_eq : ∀ k : Fin 16, kernel21_0Expr 3 7 k = kernel21_0_r3_7 k := by decide +kernel +noncomputable def kernel21_0_r3_8 : Fin 16 → CBox := ![⟨⟨56057065778,56057065782⟩,⟨(-110270264379),(-110270264376)⟩⟩,⟨⟨41225755196,41225755200⟩,⟨(-96211724884),(-96211724880)⟩⟩,⟨⟨29478788470,29478788473⟩,⟨(-83476802313),(-83476802310)⟩⟩,⟨⟨20269689829,20269689832⟩,⟨(-72045006287),(-72045006283)⟩⟩,⟨⟨13134892933,13134892937⟩,⟨(-61865704341),(-61865704337)⟩⟩,⟨⟨7683520393,7683520396⟩,⟨(-52867789220),(-52867789217)⟩⟩,⟨⟨3587977277,3587977280⟩,⟨(-44967285233),(-44967285230)⟩⟩,⟨⟨575391544,575391547⟩,⟨(-38073236976),(-38073236973)⟩⟩,⟨⟨(-1580096075),(-1580096071)⟩,⟨(-32092180128),(-32092180123)⟩⟩,⟨⟨(-3064213235),(-3064213232)⟩,⟨(-26931453606),(-26931453602)⟩⟩,⟨⟨(-4028645207),(-4028645203)⟩,⟨(-22501575330),(-22501575325)⟩⟩,⟨⟨(-4596380654),(-4596380651)⟩,⟨(-18717870440),(-18717870436)⟩⟩,⟨⟨(-4866369673),(-4866369669)⟩,⟨(-15501510913),(-15501510910)⟩⟩,⟨⟨(-4917553548),(-4917553544)⟩,⟨(-12780099134),(-12780099130)⟩⟩,⟨⟨(-4812327082),(-4812327079)⟩,⟨(-10487904851),(-10487904848)⟩⟩,⟨⟨(-4599493430),(-4599493425)⟩,⟨(-8565844971),(-8565844967)⟩⟩] +lemma kernel21_0_r3_8_eq : ∀ k : Fin 16, kernel21_0Expr 3 8 k = kernel21_0_r3_8 k := by decide +kernel +noncomputable def kernel21_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-4316769309),(-4316769305)⟩,⟨(-6961278409),(-6961278405)⟩⟩,⟨⟨(-3992895191),(-3992895188)⟩,⟨(-5627673674),(-5627673671)⟩⟩,⟨⟨(-3649401184),(-3649401180)⟩,⟨(-4524194553),(-4524194548)⟩⟩,⟨⟨(-3302075115),(-3302075112)⟩,⟨(-3615239001),(-3615238998)⟩⟩,⟨⟨(-2962174872),(-2962174867)⟩,⟨(-2869957947),(-2869957942)⟩⟩,⟨⟨(-2637422632),(-2637422629)⟩,⟨(-2261773758),(-2261773755)⟩⟩,⟨⟨(-2332814426),(-2332814423)⟩,⟨(-1767912611),(-1767912608)⟩⟩,⟨⟨(-2051274299),(-2051274295)⟩,⟨(-1368960538),(-1368960534)⟩⟩,⟨⟨(-1794178667),(-1794178664)⟩,⟨(-1048449447),(-1048449444)⟩⟩,⟨⟨(-1561772942),(-1561772937)⟩,⟨(-792476752),(-792476747)⟩⟩,⟨⟨(-1353499338),(-1353499334)⟩,⟨(-589360168),(-589360164)⟩⟩,⟨⟨(-1168252035),(-1168252032)⟩,⟨(-429327759),(-429327756)⟩⟩,⟨⟨(-1004573307),(-1004573301)⟩,⟨(-304242220),(-304242214)⟩⟩,⟨⟨(-860802051),(-860802048)⟩,⟨(-207357654),(-207357651)⟩⟩,⟨⟨(-735184317),(-735184313)⟩,⟨(-133106632),(-133106628)⟩⟩,⟨⟨(-625953677),(-625953673)⟩,⟨(-76915012),(-76915009)⟩⟩] +lemma kernel21_0_r3_9_eq : ∀ k : Fin 16, kernel21_0Expr 3 9 k = kernel21_0_r3_9 k := by decide +kernel +noncomputable def kernel21_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-531387972),(-531387968)⟩,⟨(-35041968),(-35041965)⟩⟩,⟨⟨(-449847739),(-449847736)⟩,⟨(-4442558),(-4442554)⟩⟩,⟨⟨(-379800591),(-379800586)⟩,⟨17349643,17349648⟩⟩,⟨⟨(-319835016),(-319835012)⟩,⟨32322278,32322281⟩⟩,⟨⟨(-268666357),(-268666352)⟩,⟨42068506,42068511⟩⟩,⟨⟨(-225137113),(-225137108)⟩,⟨47857940,47857944⟩⟩,⟨⟨(-188213286),(-188213281)⟩,⟨50696028,50696033⟩⟩,⟨⟨(-156978063),(-156978060)⟩,⟨51373556,51373560⟩⟩,⟨⟨(-130623855),(-130623851)⟩,⟨50507717,50507720⟩⟩,⟨⟨(-108443401),(-108443397)⟩,⟨48576032,48576036⟩⟩,⟨⟨(-89820539),(-89820536)⟩,⟨45944258,45944262⟩⟩,⟨⟨(-74220995),(-74220990)⟩,⟨42889209,42889214⟩⟩,⟨⟨(-61183487),(-61183484)⟩,⟨39617379,39617382⟩⟩,⟨⟨(-50311323),(-50311320)⟩,⟨36280022,36280026⟩⟩,⟨⟨(-41264592),(-41264589)⟩,⟨32985348,32985351⟩⟩,⟨⟨(-33753017),(-33753013)⟩,⟨29808293,29808298⟩⟩] +lemma kernel21_0_r3_10_eq : ∀ k : Fin 16, kernel21_0Expr 3 10 k = kernel21_0_r3_10 k := by decide +kernel +noncomputable def kernel21_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-27529477),(-27529474)⟩,⟨26798346,26798350⟩⟩,⟨⟨(-22384221),(-22384217)⟩,⟨23985746,23985749⟩⟩,⟨⟨(-18139694),(-18139689)⟩,⟨21386384,21386388⟩⟩,⟨⟨(-14645996),(-14645993)⟩,⟨19005652,19005656⟩⟩,⟨⟨(-11776881),(-11776878)⟩,⟨16841420,16841424⟩⟩,⟨⟨(-9426278),(-9426275)⟩,⟨14886352,14886355⟩⟩,⟨⟨(-7505263),(-7505259)⟩,⟨13129659,13129662⟩⟩,⟨⟨(-5939450),(-5939446)⟩,⟨11558436,11558439⟩⟩,⟨⟨(-4666743),(-4666740)⟩,⟨10158649,10158652⟩⟩,⟨⟨(-3635412),(-3635407)⟩,⟨8915860,8915864⟩⟩,⟨⟨(-2802441),(-2802438)⟩,⟨7815743,7815747⟩⟩,⟨⟨(-2132138),(-2132134)⟩,⟨6844444,6844447⟩⟩,⟨⟨(-1594935),(-1594932)⟩,⟨5988818,5988821⟩⟩,⟨⟨(-1166387),(-1166383)⟩,⟨5236572,5236575⟩⟩,⟨⟨(-826327),(-826322)⟩,⟨4576349,4576354⟩⟩,⟨⟨(-558136),(-558132)⟩,⟨3997753,3997757⟩⟩] +lemma kernel21_0_r3_11_eq : ∀ k : Fin 16, kernel21_0Expr 3 11 k = kernel21_0_r3_11 k := by decide +kernel +noncomputable def kernel21_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-348160),(-348155)⟩,⟨3491338,3491342⟩⟩,⟨⟨(-185189),(-185186)⟩,⟨3048586,3048590⟩⟩,⟨⟨(-60052),(-60047)⟩,⟨2661851,2661856⟩⟩,⟨⟨34757,34760⟩,⟨2324308,2324312⟩⟩,⟨⟨105346,105352⟩,⟨2029885,2029891⟩⟩,⟨⟨156696,156700⟩,⟨1773205,1773208⟩⟩,⟨⟨192840,192843⟩,⟨1549510,1549514⟩⟩,⟨⟨217046,217050⟩,⟨1354617,1354621⟩⟩,⟨⟨231954,231957⟩,⟨1184845,1184849⟩⟩,⟨⟨239684,239687⟩,⟨1036966,1036969⟩⟩,⟨⟨241938,241943⟩,⟨908153,908157⟩⟩,⟨⟨240077,240080⟩,⟨795936,795939⟩⟩,⟨⟨235180,235184⟩,⟨698158,698161⟩⟩,⟨⟨228105,228108⟩,⟨612939,612942⟩⟩,⟨⟨219521,219526⟩,⟨538638,538643⟩⟩,⟨⟨209956,209960⟩,⟨473834,473837⟩⟩] +lemma kernel21_0_r3_12_eq : ∀ k : Fin 16, kernel21_0Expr 3 12 k = kernel21_0_r3_12 k := by decide +kernel +noncomputable def kernel21_0_r3_13 : Fin 16 → CBox := ![⟨⟨199815,199818⟩,⟨417284,417287⟩⟩,⟨⟨189410,189414⟩,⟨367910,367913⟩⟩,⟨⟨178978,178981⟩,⟨324774,324778⟩⟩,⟨⟨168695,168698⟩,⟨287068,287072⟩⟩,⟨⟨158686,158691⟩,⟨254082,254087⟩⟩,⟨⟨149045,149048⟩,⟨225207,225211⟩⟩,⟨⟨139831,139834⟩,⟨199907,199911⟩⟩,⟨⟨131081,131085⟩,⟨177723,177727⟩⟩,⟨⟨122816,122819⟩,⟨158253,158257⟩⟩,⟨⟨115045,115049⟩,⟨141151,141155⟩⟩,⟨⟨107763,107766⟩,⟨126114,126118⟩⟩,⟨⟨100961,100964⟩,⟨112880,112884⟩⟩,⟨⟨94622,94625⟩,⟨101221,101224⟩⟩,⟨⟨88727,88732⟩,⟨90939,90944⟩⟩,⟨⟨83258,83261⟩,⟨81863,81866⟩⟩,⟨⟨78188,78191⟩,⟨73843,73846⟩⟩] +lemma kernel21_0_r3_13_eq : ∀ k : Fin 16, kernel21_0Expr 3 13 k = kernel21_0_r3_13 k := by decide +kernel +noncomputable def kernel21_0_r3_14 : Fin 16 → CBox := ![⟨⟨73496,73499⟩,⟨66746,66750⟩⟩,⟨⟨69158,69162⟩,⟨60462,60466⟩⟩,⟨⟨65152,65156⟩,⟨54892,54896⟩⟩,⟨⟨61454,61458⟩,⟨49949,49952⟩⟩,⟨⟨58046,58049⟩,⟨45557,45561⟩⟩,⟨⟨54902,54907⟩,⟨41652,41657⟩⟩,⟨⟨52009,52013⟩,⟨38176,38180⟩⟩,⟨⟨49344,49349⟩,⟨35080,35085⟩⟩,⟨⟨46896,46899⟩,⟨32319,32323⟩⟩,⟨⟨44642,44646⟩,⟨29856,29859⟩⟩,⟨⟨42572,42577⟩,⟨27656,27661⟩⟩,⟨⟨40673,40677⟩,⟨25692,25696⟩⟩,⟨⟨38930,38934⟩,⟨23937,23941⟩⟩,⟨⟨37334,37337⟩,⟨22366,22370⟩⟩,⟨⟨35874,35877⟩,⟨20963,20967⟩⟩,⟨⟨34539,34544⟩,⟨19709,19714⟩⟩] +lemma kernel21_0_r3_14_eq : ∀ k : Fin 16, kernel21_0Expr 3 14 k = kernel21_0_r3_14 k := by decide +kernel +noncomputable def kernel21_0_r3_15 : Fin 16 → CBox := ![⟨⟨33322,33327⟩,⟨18589,18594⟩⟩,⟨⟨32215,32220⟩,⟨17591,17595⟩⟩,⟨⟨31211,31215⟩,⟨16701,16704⟩⟩,⟨⟨30302,30307⟩,⟨15910,15914⟩⟩,⟨⟨29485,29489⟩,⟨15208,15212⟩⟩,⟨⟨28752,28756⟩,⟨14589,14593⟩⟩,⟨⟨28098,28102⟩,⟨14045,14049⟩⟩,⟨⟨27522,27527⟩,⟨13570,13575⟩⟩,⟨⟨27019,27023⟩,⟨13160,13163⟩⟩,⟨⟨26585,26589⟩,⟨12810,12813⟩⟩,⟨⟨26218,26222⟩,⟨12516,12520⟩⟩,⟨⟨25914,25919⟩,⟨12275,12280⟩⟩,⟨⟨25674,25678⟩,⟨12086,12090⟩⟩,⟨⟨25497,25500⟩,⟨11945,11949⟩⟩,⟨⟨25378,25382⟩,⟨11853,11857⟩⟩,⟨⟨25319,25322⟩,⟨11807,11810⟩⟩] +lemma kernel21_0_r3_15_eq : ∀ k : Fin 16, kernel21_0Expr 3 15 k = kernel21_0_r3_15 k := by decide +kernel +noncomputable def kernel21_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel21_0_r3_0,kernel21_0_r3_1,kernel21_0_r3_2,kernel21_0_r3_3,kernel21_0_r3_4,kernel21_0_r3_5,kernel21_0_r3_6,kernel21_0_r3_7,kernel21_0_r3_8,kernel21_0_r3_9,kernel21_0_r3_10,kernel21_0_r3_11,kernel21_0_r3_12,kernel21_0_r3_13,kernel21_0_r3_14,kernel21_0_r3_15] +lemma kernel21_0_r3_eq (i k : Fin 16) : kernel21_0Expr 3 i k = kernel21_0_r3 i k := by + fin_cases i + · exact kernel21_0_r3_0_eq k + · exact kernel21_0_r3_1_eq k + · exact kernel21_0_r3_2_eq k + · exact kernel21_0_r3_3_eq k + · exact kernel21_0_r3_4_eq k + · exact kernel21_0_r3_5_eq k + · exact kernel21_0_r3_6_eq k + · exact kernel21_0_r3_7_eq k + · exact kernel21_0_r3_8_eq k + · exact kernel21_0_r3_9_eq k + · exact kernel21_0_r3_10_eq k + · exact kernel21_0_r3_11_eq k + · exact kernel21_0_r3_12_eq k + · exact kernel21_0_r3_13_eq k + · exact kernel21_0_r3_14_eq k + · exact kernel21_0_r3_15_eq k +noncomputable def kernel21_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-465528789371381079488937),(-465528789371381014583053)⟩,⟨(-72721084419493861804894),(-72721084419493796901050)⟩⟩,⟨⟨(-465124421372518213812471),(-465124421372518148969551)⟩,⟨(-72270123600341617450434),(-72270123600341552609560)⟩⟩,⟨⟨(-464315808845429596514426),(-464315808845429531797380)⟩,⟨(-71370583693727019123812),(-71370583693726954408825)⟩⟩,⟨⟨(-463103208050036202000836),(-463103208050036137472224)⟩,⟨(-70027215200309584125627),(-70027215200309519599093)⟩⟩,⟨⟨(-461487026526097896665921),(-461487026526097832387776)⟩,⟨(-68247111505718734768297),(-68247111505718670492256)⟩⟩,⟨⟨(-459467850463959474040793),(-459467850463959410074450)⟩,⟨(-66039670158890416212392),(-66039670158890352248184)⟩⟩,⟨⟨(-457046480522296503893910),(-457046480522296440299846)⟩,⟨(-63416541439973284708391),(-63416541439973221116499)⟩⟩,⟨⟨(-454223975523417259855525),(-454223975523417196693177)⟩,⟨(-60391564390754492590103),(-60391564390754429429969)⟩⟩,⟨⟨(-451001703327318801555251),(-451001703327318738882883)⟩,⟨(-56980690528952546703226),(-56980690528952484033119)⟩⟩,⟨⟨(-447381398064846133864936),(-447381398064846071739447)⟩,⟨(-53201895519285783139280),(-53201895519285721016105)⟩⟩,⟨⟨(-443365222799504470616297),(-443365222799504409093118)⟩,⟨(-49075079129313721480648),(-49075079129313659959840)⟩⟩,⟨⟨(-438955836588178345685541),(-438955836588178284818435)⟩,⟨(-44621953856892029585773),(-44621953856891968721100)⟩⟩,⟨⟨(-434156464824565463174063),(-434156464824565403015068)⟩,⟨(-39865922678755167269370),(-39865922678755107112871)⟩⟩,⟨⟨(-428970971676765227159918),(-428970971676765167759111)⟩,⟨(-34831946436155481253640),(-34831946436155421855396)⟩⟩,⟨⟨(-423403933373263082791369),(-423403933373263024196877)⟩,⟨(-29546401443383507977832),(-29546401443383449385972)⟩⟩,⟨⟨(-417460711050461415510870),(-417460711050461357768608)⟩,⟨(-24036927977935830191143),(-24036927977935772451584)⟩⟩] +lemma kernel21_0_r4_0_eq : ∀ k : Fin 16, kernel21_0Expr 4 0 k = kernel21_0_r4_0 k := by decide +kernel +noncomputable def kernel21_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-411147521850697726483938),(-411147521850697669637699)⟩,⟨(-18332270386472903684122),(-18332270386472846840659)⟩⟩,⟨⟨(-404471506952950942047212),(-404471506952950886138315)⟩,⟨(-12462109617737648826206),(-12462109617737592920157)⟩⟩,⟨⟨(-397440795229560864257292),(-397440795229560809324806)⟩,⟨(-6456889071341761286187),(-6456889071341706356623)⟩⟩,⟨⟨(-390064561251459208693420),(-390064561251459154773749)⟩,⟨(-347634728676701913656),(-347634728676647996980)⟩⟩,⟨⟨(-382353076411599161597716),(-382353076411599108724954)⟩,⟨5834229392056109156134,5834229392056162025830⟩⟩,⟨⟨(-374317752001211202855371),(-374317752001211151060712)⟩,⟨12057069341913932230681,12057069341913984022204⟩⟩,⟨⟨(-365971173155708336624584),(-365971173155708285936889)⟩,⟨18289231725185469359385,18289231725185520043876⟩⟩,⟨⟨(-357327122685777297055102),(-357327122685777247500224)⟩,⟨24499235315518684996471,24499235315518734548079⟩⟩,⟨⟨(-348400593923447766705279),(-348400593923447718306786)⟩,⟨30655962503271122897563,30655962503271171292724⟩⟩,⟨⟨(-339207791841516576652364),(-339207791841516529430608)⟩,⟨36728849226846117329618,36728849226846164547985⟩⟩,⟨⟨(-329766121846175657490220),(-329766121846175611463339)⟩,⟨42688072004824402899805,42688072004824448923243⟩⟩,⟨⟨(-320094165795389138451461),(-320094165795389093634381)⟩,⟨48504730661494696667371,48504730661494741480960⟩⟩,⟨⟨(-310211644957619638608559),(-310211644957619595014138)⟩,⟨54151025327218770840331,54151025327218814431217⟩⟩,⟨⟨(-300139369794863747095617),(-300139369794863704732976)⟩,⟨59600426298083979586079,59600426298084021945148⟩⟩,⟨⟨(-289899176628406352901148),(-289899176628406311777192)⟩,⟨64827835357471554523771,64827835357471595644123⟩⟩,⟨⟨(-279513851422891425691519),(-279513851422891385810531)⟩,⟨69809737196268728971094,69809737196268768848452⟩⟩] +lemma kernel21_0_r4_1_eq : ∀ k : Fin 16, kernel21_0Expr 4 1 k = kernel21_0_r4_1 k := by decide +kernel +noncomputable def kernel21_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-269007041101776631105192),(-269007041101776592469807)⟩,⟨74524339619009778701856,74524339619009817333592⟩⟩,⟨⟨(-258403152982463628534082),(-258403152982463591143447)⟩,⟨78951701290520732099932,78951701290520769486906⟩⟩,⟨⟨(-247727243089814440551777),(-247727243089814404403628)⟩,⟨83073845861663139151294,83073845861663175295778⟩⟩,⟨⟨(-237004894269822562019094),(-237004894269822527105048)⟩,⟨86874861413230780859498,86874861413230815769881⟩⟩,⟨⟨(-226262085178398925257849),(-226262085178398891570472)⟩,⟨90340984273356144426357,90340984273356178110081⟩⟩,⟨⟨(-215525051361141214321556),(-215525051361141181850953)⟩,⟨93460666395034367424654,93460666395034399891621⟩⟩,⟨⟨(-204820139766297211982413),(-204820139766297180717845)⟩,⟨96224625625375026356292,96224625625375057617247⟩⟩,⟨⟨(-194173658142801060965795),(-194173658142801030893331)⟩,⟨98625878355460823997818,98625878355460854066827⟩⟩,⟨⟨(-183611720866363686605457),(-183611720866363657710699)⟩,⟨100659754207467965706032,100659754207467994597579⟩⟩,⟨⟨(-173160092807497513285511),(-173160092807497485550876)⟩,⟨102323892591976561347386,102323892591976589079050⟩⟩,⟨⟨(-162844032904702434706219),(-162844032904702408113925)⟩,⟨103618221150940174298221,103618221150940200887777⟩⟩,⟨⟨(-152688139132805922775327),(-152688139132805897304773)⟩,⟨104544916288174399470155,104544916288174424938198⟩⟩,⟨⟨(-142716196559951688305697),(-142716196559951663936377)⟩,⟨105108346176900856251936,105108346176900880618967⟩⟩,⟨⟨(-132951030166650138648582),(-132951030166650115350196)⟩,⟨105314996820178106330996,105314996820178129627306⟩⟩,⟨⟨(-123414364056700331255048),(-123414364056700309000048)⟩,⟨105173381922242322540235,105173381922242344793364⟩⟩,⟨⟨(-114126688623112632590300),(-114126688623112611353911)⟩,⟨104693937504140439526686,104693937504140460761401⟩⟩] +lemma kernel21_0_r4_2_eq : ∀ k : Fin 16, kernel21_0Expr 4 2 k = kernel21_0_r4_2 k := by decide +kernel +noncomputable def kernel21_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-105107137143233609576672),(-105107137143233589334830)⟩,⟨103888902362885851428569,103888902362885871668927⟩⟩,⟨⟨(-96373373167305566466241),(-96373373167305547192171)⟩,⟨102772185627118761175049,102772185627118780447815⟩⟩,⟨⟨(-87941489935248508719782),(-87941489935248490387681)⟩,⟨101359222801476940197656,101359222801476958528624⟩⟩,⟨⟨(-79825922909434971444584),(-79825922909434954026136)⟩,⟨99666821814343706987018,99666821814343724404495⟩⟩,⟨⟨(-72039376348847427927996),(-72039376348847411396310)⟩,⟨97713000687349150429589,97713000687349166960457⟩⟩,⟨⟨(-64592764674742802428871),(-64592764674742786754974)⟩,⟨95516818528255670443488,95516818528255686116710⟩⟩,⟨⟨(-57495169192504543816186),(-57495169192504528972501)⟩,⟨93098201610280980957449,93098201610280995800593⟩⟩,⟨⟨(-50753810541624053426113),(-50753810541624039380286)⟩,⟨90477766339476024438320,90477766339476038483732⟩⟩,⟨⟨(-44374037048730827546280),(-44374037048730814269987)⟩,⟨87676640926834509893103,87676640926834523169098⟩⟩,⟨⟨(-38359328960366642101583),(-38359328960366629565505)⟩,⟨84716287573111172426846,84716287573111184962732⟩⟩,⟨⟨(-32711318335869902594184),(-32711318335869890770766)⟩,⟨81618326942014830644401,81618326942014842467726⟩⟩,⟨⟨(-27429824189354866934882),(-27429824189354855795211)⟩,⟨78404366642068206329814,78404366642068217469480⟩⟩,⟨⟨(-22512902286289222487343),(-22512902286289212003071)⟩,⟨75095835359929597729230,75095835359929608213578⟩⟩,⟨⟨(-17956908827389117851496),(-17956908827389107993853)⟩,⟨71713824189667116672147,71713824189667126529937⟩⟩,⟨⟨(-13756577093052095204907),(-13756577093052085947392)⟩,⟨68278936585029498841984,68278936585029508099710⟩⟩,⟨⟨(-9905105977668841566552),(-9905105977668832881156)⟩,⟨64811148227151243335735,64811148227151252021399⟩⟩] +lemma kernel21_0_r4_3_eq : ∀ k : Fin 16, kernel21_0Expr 4 3 k = kernel21_0_r4_3 k := by decide +kernel +noncomputable def kernel21_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-6394259216929900850849),(-6394259216929892711992)⟩,⟨61329677950625383080525,61329677950625391219700⟩⟩,⟨⟨(-3214474004375369107249),(-3214474004375361488064)⟩,⟨57852870708969717559738,57852870708969725179282⟩⟩,⟨⟨(-354977607263535785181),(-354977607263528661014)⟩,⟨54398093388881408840119,54398093388881415964679⟩⟩,⟨⟨2196089472685672541339,2196089472685679195754⟩,⟨50981644104131341059663,50981644104131347714500⟩⟩,⟨⟨4451545290425157164827,4451545290425163372749⟩,⟨47618675417380431135831,47618675417380437344197⟩⟩,⟨⟨6425034717283842803305,6425034717283848588835⟩,⟨44323131754511571843644,44323131754511577629635⟩⟩,⟨⟨8130895683734733898168,8130895683734739283400⟩,⟨41107701094132917927346,41107701094132923313051⟩⟩,⟨⟨9584024896018334280691,9584024896018339288147⟩,⟨37983780837499442785787,37983780837499447793723⟩⟩,⟨⟨10799744473181215755674,10799744473181220405896⟩,⟨34961457593855772027049,34961457593855776677756⟩⟩,⟨⟨11793670887656019519830,11793670887656023833999⟩,⟨32049500455569089288114,32049500455569093602765⟩⟩,⟨⟨12581587511497599942455,12581587511497603939811⟩,⟨29255367188607573081612,29255367188607577079447⟩⟩,⟨⟨13179321973687815516516,13179321973687819216520⟩,⟨26585222628867871663175,26585222628867875363649⟩⟩,⟨⟨13602629423634542930071,13602629423634546362058⟩,⟨24043968455204072661527,24043968455204076093931⟩⟩,⟨⟨13867082674395475340645,13867082674395478521766⟩,⟨21635283407075841149881,21635283407075844331364⟩⟩,⟨⟨13987970068651528965907,13987970068651531910867⟩,⟨19361672929490490500092,19361672929490493445365⟩⟩,⟨⟨13980201773505251443804,13980201773505254167503⟩,⟨17224527160990669094671,17224527160990671818637⟩⟩] +lemma kernel21_0_r4_4_eq : ∀ k : Fin 16, kernel21_0Expr 4 4 k = kernel21_0_r4_4 k := by decide +kernel +noncomputable def kernel21_0_r4_5 : Fin 16 → CBox := ![⟨⟨13858225069272290806554,13858225069272293322366⟩,⟨15224186132116182846049,15224186132116185362087⟩⟩,⟨⟨13635949055023733032544,13635949055023735354214⟩,⟨13360011011984701564105,13360011011984703885962⟩⟩,⟨⟨13326679052101016772339,13326679052101018912157⟩,⟨11630460229004867881234,11630460229004870021205⟩⟩,⟨⟨12943060848418679346867,12943060848418681317197⟩,⟨10033169297564244571789,10033169297564246542240⟩⟩,⟨⟨12497034793187997602049,12497034793187999413940⟩,⟨8565033204852189639401,8565033204852191451385⟩⟩,⟨⟨11999799625636212775679,11999799625636214440365⟩,⟨7222290249565168858903,7222290249565170523656⟩⟩,⟨⟨11461785804037465183814,11461785804037466711375⟩,⟨6000606275668116255566,6000606275668117783172⟩⟩,⟨⟨10892637994342889396268,10892637994342890796719⟩,⟨4895158308045464015799,4895158308045465416276⟩⟩,⟨⟨10301206282066716843707,10301206282066718126070⟩,⟨3900716671031320147034,3900716671031321429406⟩⟩,⟨⟨9695545587749479114225,9695545587749480287466⟩,⟨3011724753629923336061,3011724753629924509297⟩⟩,⟨⟨9082922695900744601092,9082922695900745673194⟩,⟨2222375674844120004489,2222375674844121076574⟩⟩,⟨⟨8469830250172964221305,8469830250172965200339⟩,⟨1526685197029723587805,1526685197029724566811⟩⟩,⟨⟨7862007023722875335743,7862007023722876228581⟩,⟨918560332723316793662,918560332723317686463⟩⟩,⟨⟨7264463743116637193091,7264463743116638006638⟩,⟨391863189149412680618,391863189149413494123⟩⟩,⟨⟨6681513726338345136442,6681513726338345876839⟩,⟨(-59530307106057256445),(-59530307106056516095)⟩⟩,⟨⟨6116807589869957396220,6116807589869958069873⟩,⟨(-441677066548200940294),(-441677066548200266693)⟩⟩] +lemma kernel21_0_r4_5_eq : ∀ k : Fin 16, kernel21_0Expr 4 5 k = kernel21_0_r4_5 k := by decide +kernel +noncomputable def kernel21_0_r4_6 : Fin 16 → CBox := ![⟨⟨5573371285643015442452,5573371285643016054535⟩,⟨(-760519042919834220766),(-760519042919833608737)⟩⟩,⟨⟨5053646744983734216514,5053646744983734772228⟩,⟨(-1021841069654436477938),(-1021841069654435922281)⟩⟩,⟨⟨4559534432423286334280,4559534432423286838228⟩,⟨(-1231234325150790293925),(-1231234325150789790035)⟩⟩,⟨⟨4092437146270123288040,4092437146270123744661⟩,⟨(-1394065350050724769906),(-1394065350050724313342)⟩⟩,⟨⟨3653304443922352341134,3653304443922352754302⟩,⟨(-1515450471840455096496),(-1515450471840454683385)⟩⟩,⟨⟨3242677116781963817423,3242677116781964190992⟩,⟨(-1600235432225829014635),(-1600235432225828641121)⟩⟩,⟨⟨2860731191058565779430,2860731191058566117126⟩,⟨(-1652979961181798197563),(-1652979961181797859916)⟩⟩,⟨⟨2507320985476772385690,2507320985476772690842⟩,⟨(-1677946998496027321968),(-1677946998496027016857)⟩⟩,⟨⟨2182020813729672170310,2182020813729672445669⟩,⟨(-1679096228996610331729),(-1679096228996610056404)⟩⟩,⟨⟨1884164977315408752289,1884164977315409000600⟩,⟨(-1660081571301045564788),(-1660081571301045316506)⟩⟩,⟨⟨1612885752100403686137,1612885752100403909785⟩,⟨(-1624252241536920393885),(-1624252241536920170260)⟩⟩,⟨⟨1367149128612125673852,1367149128612125875145⟩,⟨(-1574657002633682228999),(-1574657002633682027724)⟩⟩,⟨⟨1145788120824025053481,1145788120824025234430⟩,⟨(-1514051205938726773081),(-1514051205938726592146)⟩⟩,⟨⟨947533510316981880513,947533510316982043150⟩,⟨(-1444906234458706060431),(-1444906234458705897805)⟩⟩,⟨⟨771041941565764453250,771041941565764599239⟩,⟨(-1369420965296733711577),(-1369420965296733565594)⟩⟩,⟨⟨614921329206175382503,614921329206175513468⟩,⟨(-1289534882135064457125),(-1289534882135064326164)⟩⟩] +lemma kernel21_0_r4_6_eq : ∀ k : Fin 16, kernel21_0Expr 4 6 k = kernel21_0_r4_6 k := by decide +kernel +noncomputable def kernel21_0_r4_7 : Fin 16 → CBox := ![⟨⟨477753579108273371169,477753579108273488518⟩,⟨(-1206942486165058179254),(-1206942486165058061907)⟩⟩,⟨⟨358114661647855504530,358114661647855609627⟩,⟨(-1123108674950405205025),(-1123108674950405099928)⟩⟩,⟨⟨254592107575866455077,254592107575866549085⟩,⟨(-1039284782594340274183),(-1039284782594340180173)⟩⟩,⟨⟨165800024278374753497,165800024278374837536⟩,⟨(-956525000559499978613),(-956525000559499894571)⟩⟩,⟨⟨90391753034942235639,90391753034942310660⟩,⟨(-875702925888677365121),(-875702925888677290096)⟩⟩,⟨⟨27070306238860288381,27070306238860355319⟩,⟨(-797528011770332422164),(-797528011770332355222)⟩⟩,⟨⟨(-25403262372497284049),(-25403262372497224401)⟩,⟨(-722561723812384595894),(-722561723812384536240)⟩⟩,⟨⟨(-68203391367461757993),(-68203391367461704837)⟩,⟨(-651233233519171986583),(-651233233519171933420)⟩⟩,⟨⟨(-102435279707099034603),(-102435279707098987143)⟩,⟨(-583854507860606661475),(-583854507860606614008)⟩⟩,⟨⟨(-129131716890810306086),(-129131716890810263726)⟩,⟨(-520634680096103060520),(-520634680096103018153)⟩⟩,⟨⟨(-149251302887357601586),(-149251302887357563824)⟩,⟨(-461693611851312228820),(-461693611851312191052)⟩⟩,⟨⟨(-163677888353977632480),(-163677888353977598835)⟩,⟨(-407074579590313094697),(-407074579590313061046)⟩⟩,⟨⟨(-173221070715760669442),(-173221070715760639504)⟩,⟨(-356756039889247619270),(-356756039889247589326)⟩⟩,⟨⟨(-178617588666922438569),(-178617588666922411940)⟩,⟨(-310662447167745136844),(-310662447167745110209)⟩⟩,⟨⟨(-180533466201359703514),(-180533466201359679852)⟩,⟨(-268674114694486062598),(-268674114694486038931)⟩⟩,⟨⟨(-179566767034679385233),(-179566767034679364214)⟩,⟨(-230636124724740771128),(-230636124724740750106)⟩⟩] +lemma kernel21_0_r4_7_eq : ∀ k : Fin 16, kernel21_0Expr 4 7 k = kernel21_0_r4_7 k := by decide +kernel +noncomputable def kernel21_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-176250830917889368243),(-176250830917889349597)⟩,⟨(-196366306566155521784),(-196366306566155503134)⟩⟩,⟨⟨(-171057874563711869952),(-171057874563711853403)⟩,⟨(-165662312257695953705),(-165662312257695937154)⟩⟩,⟨⟨(-164402851437922412821),(-164402851437922398151)⟩,⟨(-138307828470579844200),(-138307828470579829529)⟩⟩,⟨⟨(-156647476268347454037),(-156647476268347441040)⟩,⟨(-114077970310242007555),(-114077970310241994556)⟩⟩,⟨⟨(-148104331582496564324),(-148104331582496552821)⟩,⟨(-92743908046099486323),(-92743908046099474818)⟩⟩,⟨⟨(-139040984721950739651),(-139040984721950729460)⟩,⟨(-74076781567156406577),(-74076781567156396385)⟩⟩,⟨⟨(-129684054449070705116),(-129684054449070696097)⟩,⟨(-57850959712128248897),(-57850959712128239877)⟩⟩,⟨⟨(-120223176340453717446),(-120223176340453709465)⟩,⟨(-43846702713833648097),(-43846702713833640116)⟩⟩,⟨⟨(-110814825560941026548),(-110814825560941019494)⟩,⟨(-31852285991344671153),(-31852285991344664099)⟩⟩,⟨⟨(-101585964266846147452),(-101585964266846141216)⟩,⟨(-21665642579725584576),(-21665642579725578340)⟩⟩,⟨⟨(-92637488755971143888),(-92637488755971138379)⟩,⟨(-13095579760755533646),(-13095579760755528137)⟩⟩,⟨⟨(-84047458544448688717),(-84047458544448683851)⟩,⟨(-5962623095734030848),(-5962623095734025983)⟩⟩,⟨⟨(-75874095804403961921),(-75874095804403957628)⟩,⟨(-99538200597680154),(-99538200597675862)⟩⟩,⟨⟨(-68158549055486317446),(-68158549055486313659)⟩,⟨4648422629616837067,4648422629616840854⟩⟩,⟨⟨(-60927419694168729313),(-60927419694168725975)⟩,⟨8423505331189824034,8423505331189827372⟩⟩,⟨⟨(-54195053904601705133),(-54195053904601702188)⟩,⟨11355630548861134188,11355630548861137133⟩⟩] +lemma kernel21_0_r4_8_eq : ∀ k : Fin 16, kernel21_0Expr 4 8 k = kernel21_0_r4_8 k := by decide +kernel +noncomputable def kernel21_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-47965605769164114259),(-47965605769164111657)⟩,⟨13562725426542135021,13562725426542137623⟩⟩,⟨⟨(-42234880037083514715),(-42234880037083512415)⟩,⟨15151178164446583198,15151178164446585497⟩⟩,⟨⟨(-36991965070999366013),(-36991965070999363983)⟩,⟨16216386428350501002,16216386428350503031⟩⟩,⟨⟨(-32220668031728862081),(-32220668031728860289)⟩,⟨16843374203876094342,16843374203876096134⟩⟩,⟨⟨(-27900765439059297722),(-27900765439059296142)⟩,⟨17107455028532476415,17107455028532477996⟩⟩,⟨⟨(-24009082918791341713),(-24009082918791340318)⟩,⟨17074922675040941963,17074922675040943358⟩⟩,⟨⟨(-20520418269432318857),(-20520418269432317627)⟩,⟨16803753278542440951,16803753278542442181⟩⟩,⟨⟨(-17408322009232940169),(-17408322009232939084)⟩,⟨16344305582953538962,16344305582953540047⟩⟩,⟨⟨(-14645749345755745372),(-14645749345755744416)⟩,⟨15740008420314513615,15740008420314514572⟩⟩,⟨⟨(-12205597092186965422),(-12205597092186964578)⟩,⟨15028026729749031367,15028026729749032211⟩⟩,⟨⟨(-10061138479407395253),(-10061138479407394508)⟩,⟨14239899372927304579,14239899372927305325⟩⟩,⟨⟨(-8186368118419016438),(-8186368118419015780)⟩,⟨13402143718081767815,13402143718081768473⟩⟩,⟨⟨(-6556268587770339394),(-6556268587770338816)⟩,⟨12536823455290705925,12536823455290706503⟩⟩,⟨⟨(-5147009284564224185),(-5147009284564223674)⟩,⟨11662077385003386160,11662077385003386671⟩⟩,⟨⟨(-3936087310774603347),(-3936087310774602897)⟩,⟨10792608004472081127,10792608004472081577⟩⟩,⟨⟨(-2902419290331825173),(-2902419290331824777)⟩,⟨9940129618867956306,9940129618867956703⟩⟩] +lemma kernel21_0_r4_9_eq : ∀ k : Fin 16, kernel21_0Expr 4 9 k = kernel21_0_r4_9 k := by decide +kernel +noncomputable def kernel21_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-2026392144484861418),(-2026392144484861067)⟩,⟨9113776441986746750,9113776441986747101⟩⟩,⟨⟨(-1289880007663043478),(-1289880007663043166)⟩,⟨8320471742354134232,8320471742354134544⟩⟩,⟨⟨(-676233654729821392),(-676233654729821117)⟩,⟨7565259550763210818,7565259550763211092⟩⟩,⟨⟨(-170248041698566804),(-170248041698566561)⟩,⟨6851600790844553486,6851600790844553729⟩⟩,⟨⟨241887158193895490,241887158193895706⟩,⟨6181635940458370134,6181635940458370351⟩⟩,⟨⟨572649808639039355,572649808639039544⟩,⟨5556416492854997398,5556416492854997588⟩⟩,⟨⟨833256752739065249,833256752739065418⟩,⟨4976107575970703355,4976107575970703524⟩⟩,⟨⟨1033741398729137403,1033741398729137553⟩,⟨4440164118078070190,4440164118078070341⟩⟩,⟨⟨1183034905402336185,1183034905402336318⟩,⟨3947482929296025540,3947482929296025673⟩⟩,⟨⟨1289048871459786613,1289048871459786732⟩,⟨3496533011014657539,3496533011014657658⟩⟩,⟨⟨1358757829197378412,1358757829197378518⟩,⟨3085466317785693089,3085466317785693194⟩⟩,⟨⟨1398280190356260341,1398280190356260434⟩,⟨2712211086245658081,2712211086245658175⟩⟩,⟨⟨1412956593808856399,1412956593808856481⟩,⟨2374549719702036935,2374549719702037018⟩⟩,⟨⟨1407424864486842211,1407424864486842285⟩,⟨2070183080672315828,2070183080672315901⟩⟩,⟨⟨1385691014180493911,1385691014180493977⟩,⟨1796782901571047163,1796782901571047230⟩⟩,⟨⟨1351195901183667028,1351195901183667087⟩,⟨1552033879723048844,1552033879723048903⟩⟩] +lemma kernel21_0_r4_10_eq : ∀ k : Fin 16, kernel21_0Expr 4 10 k = kernel21_0_r4_10 k := by decide +kernel +noncomputable def kernel21_0_r4_11 : Fin 16 → CBox := ![⟨⟨1306877320812309702,1306877320812309756⟩,⟨1333666880040091772,1333666880040091826⟩⟩,⟨⟨1255227426062430446,1255227426062430494⟩,⟨1139484529482172451,1139484529482172499⟩⟩,⟨⟨1198345480410737207,1198345480410737249⟩,⟨967380353711365228,967380353711365270⟩⟩,⟨⟨1137986026116158841,1137986026116158879⟩,⟨815352479522218312,815352479522218350⟩⟩,⟨⟨1075602614250799443,1075602614250799477⟩,⟨681512807662884671,681512807662884706⟩⟩,⟨⟨1012387289736932092,1012387289736932124⟩,⟨564092450156585143,564092450156585174⟩⟩,⟨⟨949306058313107484,949306058313107513⟩,⟨461444124510778193,461444124510778221⟩⟩,⟨⟨887130584776536940,887130584776536964⟩,⟨372042104339444545,372042104339444570⟩⟩,⟨⟨826466384993716065,826466384993716088⟩,⟨294480241809092216,294480241809092239⟩⟩,⟨⟨767777779753199844,767777779753199865⟩,⟨227468501689763039,227468501689763060⟩⟩,⟨⟨711409878055598901,711409878055598920⟩,⟨169828379274915784,169828379274915803⟩⟩,⟨⟨657607852198377011,657607852198377029⟩,⟨120487514574537624,120487514574537643⟩⟩,⟨⟨606533758134770828,606533758134770844⟩,⟨78473762476169100,78473762476169115⟩⟩,⟨⟨558281143017078920,558281143017078936⟩,⟨42908932468714397,42908932468714412⟩⟩,⟨⟨512887668373179814,512887668373179827⟩,⟨13002371479959113,13002371479959125⟩⟩,⟨⟨470345962674690752,470345962674690765⟩,⟨(-11955471162919420),(-11955471162919407)⟩⟩] +lemma kernel21_0_r4_11_eq : ∀ k : Fin 16, kernel21_0Expr 4 11 k = kernel21_0_r4_11 k := by decide +kernel +noncomputable def kernel21_0_r4_12 : Fin 16 → CBox := ![⟨⟨430612901679300712,430612901679300723⟩,⟨(-32599387221702817),(-32599387221702806)⟩⟩,⟨⟨393617499307327452,393617499307327463⟩,⟨(-49495577198321834),(-49495577198321823)⟩⟩,⟨⟨359267576291326983,359267576291326994⟩,⟨(-63147579060848088),(-63147579060848077)⟩⟩,⟨⟨327455358687311185,327455358687311196⟩,⟨(-74001912674019068),(-74001912674019057)⟩⟩,⟨⟨298062143759963226,298062143759963235⟩,⟨(-82453409231849776),(-82453409231849767)⟩⟩,⟨⟨270962156899319683,270962156899319692⟩,⟨(-88850207002969604),(-88850207002969595)⟩⟩,⟨⟨246025710193219216,246025710193219225⟩,⟨(-93498404417496694),(-93498404417496687)⟩⟩,⟨⟨223121761130572952,223121761130572959⟩,⟨(-96666369272462406),(-96666369272462398)⟩⟩,⟨⟨202119958676299604,202119958676299610⟩,⟨(-98588708902212292),(-98588708902212285)⟩⟩,⟨⟨182892253645937959,182892253645937968⟩,⟨(-99469910809875443),(-99469910809875436)⟩⟩,⟨⟨165314140903509292,165314140903509299⟩,⟨(-99487666714729216),(-99487666714729209)⟩⟩,⟨⟨149265592382430333,149265592382430340⟩,⟨(-98795895438827915),(-98795895438827908)⟩⟩,⟨⟨134631732247601683,134631732247601689⟩,⟨(-97527481709519107),(-97527481709519102)⟩⟩,⟨⟨121303298631027472,121303298631027478⟩,⟨(-95796748943808436),(-95796748943808431)⟩⟩,⟨⟨109176930232311490,109176930232311496⟩,⟨(-93701684536051221),(-93701684536051215)⟩⟩,⟨⟨98155310625173207,98155310625173212⟩,⟨(-91325936203176592),(-91325936203176587)⟩⟩] +lemma kernel21_0_r4_12_eq : ∀ k : Fin 16, kernel21_0Expr 4 12 k = kernel21_0_r4_12 k := by decide +kernel +noncomputable def kernel21_0_r4_13 : Fin 16 → CBox := ![⟨⟨88147198296707215,88147198296707220⟩,⟨(-88740597645649494),(-88740597645649489)⟩⟩,⟨⟨79067366212718462,79067366212718467⟩,⟨(-86005801236719436),(-86005801236719431)⟩⟩,⟨⟨70836470996658935,70836470996658940⟩,⟨(-83172134723112301),(-83172134723112296)⟩⟩,⟨⟨63380868580104045,63380868580104050⟩,⟨(-80281898061651266),(-80281898061651261)⟩⟩,⟨⟨56632390380599886,56632390380599891⟩,⟨(-77370215572883432),(-77370215572883427)⟩⟩,⟨⟨50528091642340978,50528091642340983⟩,⟨(-74466017600649327),(-74466017600649322)⟩⟩,⟨⟨45009981493970198,45009981493970203⟩,⟨(-71592904854390664),(-71592904854390659)⟩⟩,⟨⟨40024742496610766,40024742496610770⟩,⟨(-68769907601401510),(-68769907601401506)⟩⟩,⟨⟨35523445938151617,35523445938151620⟩,⟨(-66012150886549204),(-66012150886549200)⟩⟩,⟨⟨31461267844181403,31461267844181408⟩,⟨(-63331436000246709),(-63331436000246704)⟩⟩,⟨⟨27797209592320336,27797209592320341⟩,⟨(-60736747501081777),(-60736747501081772)⟩⟩,⟨⟨24493826108546700,24493826108546705⟩,⟨(-58234694233991019),(-58234694233991014)⟩⟩,⟨⟨21516963867787328,21516963867787333⟩,⟨(-55829891972312189),(-55829891972312184)⟩⟩,⟨⟨18835510295493762,18835510295493766⟩,⟨(-53525294554645511),(-53525294554645507)⟩⟩,⟨⟨16421155653535972,16421155653535977⟩,⟨(-51322479685882532),(-51322479685882527)⟩⟩,⟨⟨14248168076109091,14248168076109095⟩,⟨(-49221894925522848),(-49221894925522844)⟩⟩] +lemma kernel21_0_r4_13_eq : ∀ k : Fin 16, kernel21_0Expr 4 13 k = kernel21_0_r4_13 k := by decide +kernel +noncomputable def kernel21_0_r4_14 : Fin 16 → CBox := ![⟨⟨12293182085080379,12293182085080384⟩,⟨(-47223068794107680),(-47223068794107675)⟩⟩,⟨⟨10535000646741721,10535000646741724⟩,⟨(-45324791388209119),(-45324791388209115)⟩⟩,⟨⟨8954410622355531,8954410622355534⟩,⟨(-43525268403414065),(-43525268403414062)⟩⟩,⟨⟨7534011303731999,7534011303732003⟩,⟨(-41822252020311038),(-41822252020311034)⟩⟩,⟨⟨6258055604199393,6258055604199396⟩,⟨(-40213151707620856),(-40213151707620852)⟩⟩,⟨⟨5112303387726267,5112303387726272⟩,⟨(-38695127636217879),(-38695127636217873)⟩⟩,⟨⟨4083886358640575,4083886358640579⟩,⟨(-37265169074768905),(-37265169074768900)⟩⟩,⟨⟨3161183896272969,3161183896272973⟩,⟨(-35920159849025920),(-35920159849025916)⟩⟩,⟨⟨2333709198615954,2333709198615958⟩,⟨(-34656932689496546),(-34656932689496542)⟩⟩,⟨⟨1592005093100162,1592005093100166⟩,⟨(-33472314063460830),(-33472314063460826)⟩⟩,⟨⟨927548877794373,927548877794377⟩,⟨(-32363160884433174),(-32363160884433170)⟩⟩,⟨⟨332665570193741,332665570193745⟩,⟨(-31326390312676251),(-31326390312676247)⟩⟩,⟨⟨(-199551038836374),(-199551038836369)⟩,⟨(-30359003701923206),(-30359003701923201)⟩⟩,⟨⟨(-675310103180197),(-675310103180194)⟩,⟨(-29458105607892432),(-29458105607892429)⟩⟩,⟨⟨(-1100188760267009),(-1100188760267006)⟩,⟨(-28620918651494784),(-28620918651494781)⟩⟩,⟨⟨(-1479191008299561),(-1479191008299557)⟩,⟨(-27844794922012513),(-27844794922012509)⟩⟩] +lemma kernel21_0_r4_14_eq : ∀ k : Fin 16, kernel21_0Expr 4 14 k = kernel21_0_r4_14 k := by decide +kernel +noncomputable def kernel21_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-1816800907488550),(-1816800907488547)⟩,⟨(-27127224511309679),(-27127224511309675)⟩⟩,⟨⟨(-2117030558077743),(-2117030558077739)⟩,⟨(-26465841687804569),(-26465841687804565)⟩⟩,⟨⟨(-2383463275115740),(-2383463275115735)⟩,⟨(-25858429147128630),(-25858429147128625)⟩⟩,⟨⟨(-2619292347490856),(-2619292347490853)⟩,⟨(-25302920713879637),(-25302920713879634)⟩⟩,⟨⟨(-2827355737012384),(-2827355737012381)⟩,⟨(-24797402814539002),(-24797402814538998)⟩⟩,⟨⟨(-3010167042519612),(-3010167042519608)⟩,⟨(-24340114994466908),(-24340114994466903)⟩⟩,⟨⟨(-3169943024277954),(-3169943024277951)⟩,⟨(-23929449711020915),(-23929449711020912)⟩⟩,⟨⟨(-3308627955366175),(-3308627955366170)⟩,⟨(-23563951599463464),(-23563951599463460)⟩⟩,⟨⟨(-3427915039405860),(-3427915039405856)⟩,⟨(-23242316377715972),(-23242316377715969)⟩⟩,⟨⟨(-3529265107829583),(-3529265107829580)⟩,⟨(-22963389529541968),(-22963389529541965)⟩⟩,⟨⟨(-3613922784889961),(-3613922784889958)⟩,⟨(-22726164882826171),(-22726164882826168)⟩⟩,⟨⟨(-3682930284714984),(-3682930284714980)⟩,⟨(-22529783179747409),(-22529783179747406)⟩⟩,⟨⟨(-3737138981831599),(-3737138981831595)⟩,⟨(-22373530718359219),(-22373530718359215)⟩⟩,⟨⟨(-3777218874609792),(-3777218874609789)⟩,⟨(-22256838129976526),(-22256838129976523)⟩⟩,⟨⟨(-3803666039911139),(-3803666039911135)⟩,⟨(-22179279343441784),(-22179279343441780)⟩⟩,⟨⟨(-3816808156737373),(-3816808156737370)⟩,⟨(-22140570775463374),(-22140570775463371)⟩⟩] +lemma kernel21_0_r4_15_eq : ∀ k : Fin 16, kernel21_0Expr 4 15 k = kernel21_0_r4_15 k := by decide +kernel +noncomputable def kernel21_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel21_0_r4_0,kernel21_0_r4_1,kernel21_0_r4_2,kernel21_0_r4_3,kernel21_0_r4_4,kernel21_0_r4_5,kernel21_0_r4_6,kernel21_0_r4_7,kernel21_0_r4_8,kernel21_0_r4_9,kernel21_0_r4_10,kernel21_0_r4_11,kernel21_0_r4_12,kernel21_0_r4_13,kernel21_0_r4_14,kernel21_0_r4_15] +lemma kernel21_0_r4_eq (i k : Fin 16) : kernel21_0Expr 4 i k = kernel21_0_r4 i k := by + fin_cases i + · exact kernel21_0_r4_0_eq k + · exact kernel21_0_r4_1_eq k + · exact kernel21_0_r4_2_eq k + · exact kernel21_0_r4_3_eq k + · exact kernel21_0_r4_4_eq k + · exact kernel21_0_r4_5_eq k + · exact kernel21_0_r4_6_eq k + · exact kernel21_0_r4_7_eq k + · exact kernel21_0_r4_8_eq k + · exact kernel21_0_r4_9_eq k + · exact kernel21_0_r4_10_eq k + · exact kernel21_0_r4_11_eq k + · exact kernel21_0_r4_12_eq k + · exact kernel21_0_r4_13_eq k + · exact kernel21_0_r4_14_eq k + · exact kernel21_0_r4_15_eq k +noncomputable def kernel21_0_r5_0 : Fin 16 → CBox := ![⟨⟨15107803184316977970576957550,15107803184316978943881861916⟩,⟨14269785276079697801387422849,14269785276079698774883643216⟩⟩,⟨⟨15107939674178277227936334300,15107939674178278200900249101⟩,⟨14250103837407955002736200578,14250103837407955975890935245⟩⟩,⟨⟨15108170961633134736275460984,15108170961633135708555950441⟩,⟨14210780473944423744817566198,14210780473944424717287884683⟩⟩,⟨⟨15108413948781255202396003838,15108413948781256173651109358⟩,⟨14151894223381036466856074265,14151894223381037438299526196⟩⟩,⟨⟨15108544703955511744704030421,15108544703955512714592469965⟩,⟨14073563665584557984190563960,14073563665584558954265379896⟩⟩,⟨⟨15108399316008421651123452406,15108399316008422619304891036⟩,⟨13975946946407286413253717103,13975946946407287381619080518⟩⟩,⟨⟨15107775026803661067125150250,15107775026803662033260370630⟩,⟨13859241802519471301308238552,13859241802519472267624457777⟩⟩,⟨⟨15106431636290181070764746094,15106431636290182034515991620⟩,⟨13723685581451741031251801417,13723685581451741995180654182⟩⟩,⟨⟨15104093173129457302678939277,15104093173129458263709957201⟩,⟨13569555249726261742406798051,13569555249726262703611576007⟩⟩,⟨⟨15100449822440176418861313248,15100449822440177376837895236⟩,⟨13397167380739590026695880180,13397167380739590984841930829⟩⟩,⟨⟨15095160100821098082113639566,15095160100821099036703784957⟩,⟨13206878112955232900437204034,13206878112955233855192095614⟩⟩,⟨⟨15087853267414664873289252090,15087853267414665824244638283⟩,⟨12999083067985833961128625296,12999083067985834912243676493⟩⟩,⟨⟨15078131958384867160342220419,15078131958384868107341676455⟩,⟨12774217217308591504653989095,12774217217308592451807631550⟩⟩,⟨⟨15065575030807654630354422438,15065575030807655573080194757⟩,⟨12532754685676639224503043334,12532754685676640167377142515⟩⟩,⟨⟨15049740600616670656879271012,15049740600616671595015403727⟩,⟨12275208478775916668085776347,12275208478775917606364013002⟩⟩,⟨⟨15030169257918250347084113868,15030169257918251280318937650⟩,⟨12002130122342188010469075417,12002130122342188943839435626⟩⟩] +lemma kernel21_0_r5_0_eq : ∀ k : Fin 16, kernel21_0Expr 5 0 k = kernel21_0_r5_0 k := by decide +kernel +noncomputable def kernel21_0_r5_1 : Fin 16 → CBox := ![⟨⟨15006387441695582696530317120,15006387441695583624553706114⟩,⟨11714109199805284278907144248,11714109199805285207059177401⟩⟩,⟨⟨14977910954671917145439426725,14977910954671918067947031941⟩,⟨11411772775574448551977660221,11411772775574449474606713506⟩⟩,⟨⟨14944248597906979370116921209,14944248597906980286805614231⟩,⟨11095784691324984855934312547,11095784691324985772736975584⟩⟩,⟨⟨14904905903570613810337577904,14904905903570614720911065521⟩,⟨10766844723095289945205699481,10766844723095290855885419934⟩⟩,⟨⟨14859388943285225660896360624,14859388943285226565058837512⟩,⟨10425687587655633086262194423,10425687587655633990522931479⟩⟩,⟨⟨14807208188466722697649117333,14807208188466723595113951271⟩,⟨10073081787464316029637222031,10073081787464316927192132472⟩⟩,⟨⟨14747882398235800755859207867,14747882398235801646339474117⟩,⟨9709828284579322186799619791,9709828284579323077361593002⟩⟩,⟨⟨14680942509731406286135342669,14680942509731407169354454683⟩,⟨9336758995138085892554106974,9336758995138086775846396358⟩⟩,⟨⟨14605935505050053383380256105,14605935505050054259059961191⟩,⟨8954735097445995604463198271,8954735097445996480207417373⟩⟩,⟨⟨14522428228572328034664790821,14522428228572328902540779819⟩,⟨8564645148314684798552833898,8564645148314685666484566628⟩⟩,⟨⟨14430011128135039052976464686,14430011128135039912781494394⟩,⟨8167403004050662582786341860,8167403004050663442638265191⟩⟩,⟨⟨14328301893377177113319469758,14328301893377177964801127609⟩,⟨7763945544397654279223761522,7763945544397655130743410501⟩⟩,⟨⟨14216948964642399816908950080,14216948964642400659810062011⟩,⟨7355230199764167231208096573,7355230199764168074138272297⟩⟩,⟨⟨14095634886071353229548248722,14095634886071354063656903018⟩,⟨6942232284201137526413593304,6942232284201138360542386930⟩⟩,⟨⟨13964079476973578794476615158,13964079476973579619611360022⟩,⟨6525942138810928837840446760,6525942138810929662986437017⟩⟩,⟨⟨13822042796239208260213184631,13822042796239209076150542941⟩,⟨6107362092544517830970752225,6107362092544518646910519809⟩⟩] +lemma kernel21_0_r5_1_eq : ∀ k : Fin 16, kernel21_0Expr 5 1 k = kernel21_0_r5_1 k := by decide +kernel +noncomputable def kernel21_0_r5_2 : Fin 16 → CBox := ![⟨⟨13669327875441387742029189933,13669327875441388548536109698⟩,⟨5687503249652891970209862742,5687503249652892776710440680⟩⟩,⟨⟨13505783197395520375363014947,13505783197395521172233489227⟩,⟨5267382115374639944013781456,5267382115374640740869274583⟩⟩,⟨⟨13331304898282731714600670324,13331304898282732501616843500⟩,⟨4848017073736498989304393799,4848017073736499776297084650⟩⟩,⟨⟨13145838673011631910874908432,13145838673011632687845412871⟩,⟨4430424733588541623355036578,4430424733588542400293721313⟩⟩,⟨⟨12949381365280926130199805163,12949381365280926896924836222⟩,⟨4015616161161611013574429169,4015616161161611780259491693⟩⟩,⟨⟨12741982225809291665880734779,12741982225809292422230612243⟩,⟨3604593019492348337563402577,3604593019492349093865373060⟩⟩,⟨⟨12523743824408813797369839370,12523743824408814543155125781⟩,⟨3198343636981794020750339673,3198343636981794766480017260⟩⟩,⟨⟨12294822603981753148937855174,12294822603981753884002555281⟩,⟨2797839029108870570956286958,2797839029108871305957935044⟩⟩,⟨⟨12055429067102083835816385335,12055429067102084559982871469⟩,⟨2404028898882933514830752488,2404028898882934238927023502⟩⟩,⟨⟨11805827588584694685984190325,11805827588584695399140818700⟩,⟨2017837642964357498427356641,2017837642964358211506953925⟩⟩,⟨⟨11546335850325102253227427939,11546335850325102955217656298⟩,⟨1640160391485036786474162446,1640160391485037488380864717⟩⟩,⟨⟨11277323897686963601193601127,11277323897686964291899966222⟩,⟨1271859110440222951549006395,1271859110440223642165683921⟩⟩,⟨⟨10999212819797038747352001076,10999212819797039426628853748⟩,⟨913758796080440536548435832,913758796080441215729789148⟩⟩,⟨⟨10712473059248686287855194308,10712473059248686955609547468⟩,⟨566643790991451251332731804,566643790991451918986136939⟩⟩,⟨⟨10417622359884637417038318345,10417622359884638073145645795⟩,⟨231254251498832456564971672,231254251498833112566278706⟩⟩,⟨⟨10115223364495191131358399630,10115223364495191775742817407⟩,⟨(-91717204337247496916298530),(-91717204337246852642587133)⟩⟩] +lemma kernel21_0_r5_2_eq : ∀ k : Fin 16, kernel21_0Expr 5 2 k = kernel21_0_r5_2 k := by decide +kernel +noncomputable def kernel21_0_r5_3 : Fin 16 → CBox := ![⟨⟨9805880877395352844621398537,9805880877395353477170292676⟩,⟨(-401628639567132936873435329),(-401628639567132304439537107)⟩⟩,⟨⟨9490238809899208348036462249,9490238809899208968701384525⟩,⟨(-697891704488126595592243794),(-697891704488125975046204211)⟩⟩,⟨⟨9168976829657012073974033397,9168976829657012682666284827⟩,⟨(-979974279867723269754254441),(-979974279867722661184363078)⟩⟩,⟨⟨8842806737625200195166631583,8842806737625200791853656654⟩,⟨(-1247402832708250650122455306),(-1247402832708250053560855428)⟩⟩,⟨⟨8512468599067542216561737225,8512468599067542801167596951⟩,⟨(-1499764461970199582809990397),(-1499764461970198998332205484)⟩⟩,⟨⟨8178726657403755821849300882,8178726657403756394369168772⟩,⟨(-1736708613921722882758862008),(-1736708613921722310369304219)⟩⟩,⟨⟨7842365061898585936664151101,7842365061898586497046303647⟩,⟨(-1957948449299408789461197965),(-1957948449299408229211176610)⟩⟩,⟨⟨7504183442090172067635461864,7504183442090172615891260010⟩,⟨(-2163261847226414726095473667),(-2163261847226414177973218207)⟩⟩,⟨⟨7164992363464692192004506130,7164992363464692728093047833⟩,⟨(-2352492033810568444216048975),(-2352492033810567908262055203)⟩⟩,⟨⟨6825608700171045785312283098,6825608700171046309274700935⟩,⟨(-2525547826505868179205991577),(-2525547826505867655378729258)⟩⟩,⟨⟨6486850961514494796088505881,6486850961514495308059812711⟩,⟨(-2682403488631641307370010719),(-2682403488631640795532893457)⟩⟩,⟨⟨6149534609555379316681938089,6149534609555379817832133272⟩,⟨(-2823098191867515628882062554),(-2823098191867515127856034080)⟩⟩,⟨⟨5814467405356146422150164958,5814467405356146912430799448⟩,⟨(-2947735088040221663780578894),(-2947735088040221173614321724)⟩⟩,⟨⟨5482444821259356374346079547,5482444821259356853794404675⟩,⟨(-3056479995049341988838694534),(-3056479995049341509495210765)⟩⟩,⟨⟨5154245556038149713587539557,5154245556038150182178199590⟩,⟨(-3149559705301638213514389391),(-3149559705301637745019303275)⟩⟩,⟨⟨4830627188840811474530541734,4830627188840811932311992434⟩,⟨(-3227259928495209075247413575),(-3227259928495208617552555031)⟩⟩] +lemma kernel21_0_r5_3_eq : ∀ k : Fin 16, kernel21_0Expr 5 3 k = kernel21_0_r5_3 k := by decide +kernel +noncomputable def kernel21_0_r5_4 : Fin 16 → CBox := ![⟨⟨4512322006559411441721573534,4512322006559411888674183480⟩,⟨(-3289922883973270804334355812),(-3289922883973270357459654760)⟩⟩,⟨⟨4200033037600794254278804529,4200033037600794690479714836⟩,⟨(-3337944561111341938882778577),(-3337944561111341502751407219)⟩⟩,⟨⟨3894430323043018318585914388,3894430323043018744041238905⟩,⟨(-3371771669270945604530405677),(-3371771669270945179136573750)⟩⟩,⟨⟨3596147453842922644366728512,3596147453842923059161175802⟩,⟨(-3391898301709451407696141070),(-3391898301709450992955475009)⟩⟩,⟨⟨3305778400146460698218609230,3305778400146461102365002997⟩,⟨(-3398862340443738735359484567),(-3398862340443738331259503352)⟩⟩,⟨⟨3023874655872483662646604594,3023874655872484056255866932⟩,⟨(-3393241631392428060863957154),(-3393241631392427667294089826)⟩⟩,⟨⟨2750942718626172664545353827,2750942718626173047654042902⟩,⟨(-3375649961138539516899971264),(-3375649961138539133824015673)⟩⟩,⟨⟨2487441921686932193925612288,2487441921686932566652199315⟩,⟨(-3346732868336682327650503250),(-3346732868336681954950349157)⟩⟩,⟨⟨2233782631346604502235471803,2233782631346604864629155289⟩,⟨(-3307163324115771483027027652),(-3307163324115771120653903921)⟩⟩,⟨⟨1990324819288842476840440038,1990324819288842829048611895⟩,⟨(-3257637316784082184783480072),(-3257637316784081832590371451)⟩⟩,⟨⟨1757377016042436029612469700,1757377016042436371715288466⟩,⟨(-3198869376717465044204971913),(-3198869376717464702112077027)⟩⟩,⟨⟨1535195647854298207619051371,1535195647854298539771815339⟩,⟨(-3131588077498204604794341310),(-3131588077498204272646718468)⟩⟩,⟨⟨1323984755655931599578682889,1323984755655931921847527328⟩,⟨(-3056531549171015372801326619),(-3056531549171015050533194878)⟩⟩,⟨⟨1123896091184383596813672067,1123896091184383909400622645⟩,⟨(-2974443038898992642456773168),(-2974443038898992329866456821)⟩⟩,⟨⟨935029581807802191768976715,935029581807802494776117090⟩,⟨(-2886066553346096717069527706),(-2886066553346096414055287553)⟩⟩,⟨⟨757434152237901820599542640,757434152237902114195551222⟩,⟨(-2792142615799070725721517319),(-2792142615799070432115012292)⟩⟩] +lemma kernel21_0_r5_4_eq : ∀ k : Fin 16, kernel21_0Expr 5 4 k = kernel21_0_r5_4 k := by decide +kernel +noncomputable def kernel21_0_r5_5 : Fin 16 → CBox := ![⟨⟨591108888125853971970607234,591108888125854256239333698⟩,⟨(-2693404169390438073447347335),(-2693404169390437789165057590)⟩⟩,⟨⟨436004523570409713169351938,436004523570409988322302493⟩,⟨(-2590572655819671078597077480),(-2590572655819670803427816975)⟩⟩,⟨⟨292025231850170970227689643,292025231850171236440123161⟩,⟨(-2484354296720053130956773973),(-2484354296720052864725594667)⟩⟩,⟨⟨159030696254775842035798679,159030696254776099491021681⟩,⟨(-2375436602316003770704908580),(-2375436602316003513228803206)⟩⟩,⟨⟨36838435757070849718370746,36838435757071098517206825⟩,⟨(-2264485129294556392724874943),(-2264485129294556143903308984)⟩⟩,⟨⟨(-74773641539690573184788972),(-74773641539690332830615263)⟩,⟨(-2152140506912590206229262549),(-2152140506912589965850799941)⟩⟩,⟨⟨(-176064485713521706991291201),(-176064485713521474963962250)⟩,⟨(-2039015747317502416955017751),(-2039015747317502184902102469)⟩⟩,⟨⟨(-267326982745473652486855638),(-267326982745473428588462787)⟩,⟨(-1925693852913684217449977051),(-1925693852913683993524947568)⟩⟩,⟨⟨(-348884893063929559935700823),(-348884893063929344052925198)⟩,⟨(-1812725730401461829095340727),(-1812725730401461613185112821)⟩⟩,⟨⟨(-421089681728395947864066960),(-421089681728395739653092010)⟩,⟨(-1700628417890079840053476615),(-1700628417890079631814452533)⟩⟩,⟨⟨(-484317271122036474137862081),(-484317271122036273447303610)⟩,⟨(-1589883628282185192814592077),(-1589883628282184992095593700)⟩⟩,⟨⟨(-538964746731292870516560022),(-538964746731292677149848441)⟩,⟨(-1480936608983211032802343555),(-1480936608983210839406991653)⟩⟩,⟨⟨(-585447045970453976029373355),(-585447045970453789869785603)⟩,⟨(-1374195314942335068083556860),(-1374195314942334881895586086)⟩⟩,⟨⟨(-624193659076724595770894448),(-624193659076724416604195779)⟩,⟨(-1270029889117227194838674262),(-1270029889117227015646619756)⟩⟩,⟨⟨(-655645369878760021148640295),(-655645369878759848845181318)⟩,⟨(-1168772441704717608124102963),(-1168772441704717435798164615)⟩⟩,⟨⟨(-680251062753677510298028065),(-680251062753677344626355408)⟩,⟨(-1070717116922688047446422985),(-1070717116922687881754993037)⟩⟩] +lemma kernel21_0_r5_5_eq : ∀ k : Fin 16, kernel21_0Expr 5 5 k = kernel21_0_r5_5 k := by decide +kernel +noncomputable def kernel21_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-698464620362023332765662530),(-698464620362023173601673148)⟩,⟨(-976120433790211045870092815),(-976120433790210886688913639)⟩⟩,⟨⟨(-710741934817224125988299738),(-710741934817223973117873675)⟩,⟨(-885201885254668287848312382),(-885201885254668134963108052)⟩⟩,⟨⟨(-717538052837678918335813883),(-717538052837678771620396475)⟩,⟨(-798144778173633293234686849),(-798144778173633146506748740)⟩⟩,⟨⟨(-719304473179130313230472671),(-719304473179130172471341958)⟩,⟨(-715097295088868211022613682),(-715097295088868070253065033)⟩⟩,⟨⟨(-716486612286294438573894553),(-716486612286294303645915528)⟩,⟨(-636173757438763875039066151),(-636173757438763740102619853)⟩⟩,⟨⟨(-709521451670112582813083141),(-709521451670112453510008502)⟩,⟨(-561456068848609370968326156),(-561456068848609241658584839)⟩⟩,⟨⟨(-698835378044242700445968563),(-698835378044242576633586971)⟩,⟨(-490995316415721432297936660),(-490995316415721308480542772)⟩⟩,⟨⟨(-684842224774505682874104398),(-684842224774505564357464492)⟩,⟨(-424813507465205284076194450),(-424813507465205165556054037)⟩⟩,⟨⟨(-667941520739575894326050209),(-667941520739575780828703142)⟩,⟨(-362905419084684701829635505),(-362905419084684588330145451)⟩⟩,⟨⟨(-648516950300129893064787125),(-648516950300129784348018507)⟩,⟨(-305240537841946753347803284),(-305240537841946644630112466)⟩⟩,⟨⟨(-626935025754665117189705316),(-626935025754665013137784643)⟩,⟨(-251765067434121641223011676),(-251765067434121537171264040)⟩⟩,⟨⟨(-603543971448515986208450013),(-603543971448515886650186176)⟩,⟨(-202403982593955219778616652),(-202403982593955120221501087)⟩⟩,⟨⟨(-578672816620719219223631995),(-578672816620719124051220367)⟩,⟨(-157063108368687570342395884),(-157063108368687475171993418)⟩⟩,⟨⟨(-552630692140835577046384392),(-552630692140835486084574847)⟩,⟨(-115631204868759009940255593),(-115631204868758918981207958)⟩⟩,⟨⟨(-525706324521021163936556418),(-525706324521021077071293480)⟩,⟨(-77982038734165860059546435),(-77982038734165773197695903)⟩⟩,⟨⟨(-498167719000740590879429807),(-498167719000740507941804852)⟩,⟨(-43976423861766406981115754),(-43976423861766324047458047)⟩⟩] +lemma kernel21_0_r5_6_eq : ∀ k : Fin 16, kernel21_0Expr 5 6 k = kernel21_0_r5_6 k := by decide +kernel +noncomputable def kernel21_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-470262022102458180923257050),(-470262022102458101810851779)⟩,⟨(-13464215352454086244890865),(-13464215352454007136917787)⟩⟩,⟨⟨(-442215552853134800382251670),(-442215552853134724922010991)⟩,⟨13713757852168019516769618,13713757852168094972196249⟩⟩,⟨⟨(-414233990861947201785951375),(-414233990861947129856208684)⟩,⟨37723834593091371148846481,37723834593091443073470620⟩⟩,⟨⟨(-386502708639857569655466655),(-386502708639857501106158968)⟩,⟨58737748700053600542232117,58737748700053669086187488⟩⟩,⟨⟨(-359187234939160119592787768),(-359187234939160054324126319)⟩,⟨76930951454673457673030566,76930951454673522936172849⟩⟩,⟨⟨(-332433835475937990684286057),(-332433835475937928545648227)⟩,⟨92481037336297501559179069,92481037336297563692189570⟩⟩,⟨⟨(-306370197168089559516489895),(-306370197168089500408065326)⟩,⟨105566279449216962283623500,105566279449217021386365953⟩⟩,⟨⟨(-281106201966701952138297470),(-281106201966701895922375380)⟩,⟨116364279443520976363873337,116364279443521032574105873⟩⟩,⟨⟨(-256734776467682409123011939),(-256734776467682355668560413)⟩,⟨125050735213613143911368431,125050735213613197360652084⟩⟩,⟨⟨(-233332803750775276057953394),(-233332803750775225217125168)⟩,⟨131798328203793016584495555,131798328203793067420812271⟩⟩,⟨⟨(-210962084290219267815906415),(-210962084290219219502187164)⟩,⟨136775730782634456218497703,136775730782634504528317709⟩⟩,⟨⟨(-189670333300224856607757780),(-189670333300224810701714163)⟩,⟨140146732878339657146373451,140146732878339703049086101⟩⟩,⟨⟨(-169492202503429080454251749),(-169492202503429036877889644)⟩,⟨142069485904770728047999957,142069485904770771621556620⟩⟩,⟨⟨(-150450315025425889771474025),(-150450315025425848403192034)⟩,⟨142695860959237452619633856,142695860959237493985593798⟩⟩,⟨⟨(-132556302907219377364607878),(-132556302907219338125596749)⟩,⟨142170917342999906099785524,142170917342999945336917433⟩⟩,⟨⟨(-115811837574041317720870585),(-115811837574041280504711658)⟩,⟨140632476646437055087757144,140632476646437092302440304⟩⟩] +lemma kernel21_0_r5_7_eq : ∀ k : Fin 16, kernel21_0Expr 5 7 k = kernel21_0_r5_7 k := by decide +kernel +noncomputable def kernel21_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-100209644487876154621281582),(-100209644487876119356306350)⟩,⟨138210796953621070894641476,138210796953621106158506786⟩⟩,⟨⟨(-85734494127344728820170885),(-85734494127344695382732510)⟩,⟨135028341154519709946922834,135028341154519743383581043⟩⟩,⟨⟨(-72364162368229928902370731),(-72364162368229897224686880)⟩,⟨131199632904496805265973066,131199632904496836943172232⟩⟩,⟨⟨(-60070354267772877075016441),(-60070354267772847065352029)⟩,⟨126831193436012105127714360,126831193436012135137156393⟩⟩,⟨⟨(-48819586173914440938783513),(-48819586173914412536265253)⟩,⟨122021552200987158953275081,122021552200987187355798963⟩⟩,⟨⟨(-38574021976084318852678697),(-38574021976084291967952961)⟩,⟨116861324197678138682795143,116861324197678165567726332⟩⟩,⟨⟨(-29292260177389976666980809),(-29292260177389951234131127)⟩,⟨111433346805671235612450310,111433346805671261045678945⟩⟩,⟨⟨(-20930069290872575178150445),(-20930069290872551115676959)⟩,⟨105812869008693045234433073,105812869008693069297434582⟩⟩,⟨⟨(-13441069837934416203592626),(-13441069837934393460648521)⟩,⟨100067786018705575969913118,100067786018705598713511618⟩⟩,⟨⟨(-6777361949466246504095571),(-6777361949466225003461015)⟩,⟨94258912517307989485254236,94258912517308010986648787⟩⟩,⟨⟨(-890098235252379560479508),(-890098235252359247232218)⟩,⟨88440287992714908442860593,88440287992714928756954320⟩⟩,⟨⟨4269997808227751461878408,4269997808227770655144226⟩,⟨82659507963445415348131262,82659507963445434542312615⟩⟩,⟨⟨8752167039426221169814857,8752167039426239287632967⟩,⟨76958075234401939338615093,76958075234401957457401955⟩⟩,⟨⟨12605202271927704176412602,12605202271927721285187434⟩,⟨71371765718577101531277636,71371765718577118641060307⟩⟩,⟨⟨15877086526976015673640941,15877086526976031816460928⟩,⟨65931003769910356971414870,65931003769910373115268952⟩⟩,⟨⟨18614679878977842187716825,18614679878977857422306945⟩,⟨60661242402006359055263896,60661242402006374290903102⟩⟩] +lemma kernel21_0_r5_8_eq : ∀ k : Fin 16, kernel21_0Expr 5 8 k = kernel21_0_r5_8 k := by decide +kernel +noncomputable def kernel21_0_r5_9 : Fin 16 → CBox := ![⟨⟨20863452542057660257103065,20863452542057674620164072⟩,⟨55583344206250337095547094,55583344206250351459661984⟩⟩,⟨⟨22667261611226413208178096,22667261611226426755148321⟩,⟨50713959224643318392003946,50713959224643331940020677⟩⟩,⟨⟨24068168692253343054256632,24068168692253355821533145⟩,⟨46065896471408836366606601,46065896471408849134799218⟩⟩,⟨⟨25106295526400930015136920,25106295526400942050150846⟩,⟨41648486227743070118864779,41648486227743082154673933⟩⟩,⟨⟨25819714635939476248460004,25819714635939487582389358⟩,⟨37467930651328233621096019,37467930651328244955708847⟩⟩,⟨⟨26244371979678175877781723,26244371979678186555902823⟩,⟨33527640642426140350297022,33527640642426151028998852⟩⟩,⟨⟨26414038610339173852354052,26414038610339183904830219⟩,⟨29828557288210621761618073,29828557288210631814580774⟩⟩,⟨⟨26360288363079162066059534,26360288363079171532227798⟩,⟨26369456563831045416915294,26369456563831054883484189⟩⟩,⟨⟨26112498672439500636537117,26112498672439509541783771⟩,⟨23147236300492887358917056,23147236300492896264486261⟩⟩,⟨⟨25697871709150804825754398,25697871709150813207909564⟩,⟨20157184736146923040716566,20157184736146931423123717⟩⟩,⟨⟨25141473144322009291225143,25141473144322017175130117⟩,⟨17393230242287959369465226,17393230242287967253558666⟩⟩,⟨⟨24466285982569687695902789,24466285982569695113825211⟩,⟨14848172070461522273452183,14848172070461529691506219⟩⟩,⟨⟨23693277053768096080234158,23693277053768103053290142⟩,⟨12513892184389069653414655,12513892184389076626551625⟩⟩,⟨⟨22841473911750007505281533,22841473911750014063995422⟩,⟨10381548438565796903218629,10381548438565803461968710⟩⟩,⟨⟨21928050054163571503789371,21928050054163577668377458⟩,⟨8441749532514316126985457,8441749532514322291570357⟩⟩,⟨⟨20968416547784713286184180,20968416547784719111696572⟩,⟨6684712312632584591316947,6684712312632590416792441⟩⟩] +lemma kernel21_0_r5_9_eq : ∀ k : Fin 16, kernel21_0Expr 5 9 k = kernel21_0_r5_9 k := by decide +kernel +noncomputable def kernel21_0_r5_10 : Fin 16 → CBox := ![⟨⟨19976318315195539303065342,19976318315195544805856719⟩,⟨5100402112030914115577180,5100402112030919618302571⟩⟩,⟨⟨18963933509473060583230693,18963933509473065784953232⟩,⟨3678656914373207771619254,3678656914373212973250873⟩⟩,⟨⟨17941974571303098559716717,17941974571303103473393337⟩,⟨2409296202125748269400672,2409296202125753182965253⟩⟩,⟨⟨16919789725956807840971644,16919789725956812484834052⟩,⟨1282215404476168778728293,1282215404476173422461002⟩⟩,⟨⟨15905463834348270681412883,15905463834348275066339704⟩,⟨287466897279586174042508,287466897279590558825140⟩⟩,⟨⟨14905917661714721783446587,14905917661714725926963408⟩,⟨(-584671471491921097537739),(-584671471491916954176779)⟩⟩,⟨⟨13927004768370217126971557,13927004768370221039768896⟩,⟨(-1343639350391290145621714),(-1343639350391286232989332)⟩⟩,⟨⟨12973605358764522098555141,12973605358764525795594617⟩,⟨(-1998547372332461967347225),(-1998547372332458270479535)⟩⟩,⟨⟨12049716547238210727990063,12049716547238214217906858⟩,⟨(-2558140202968317469376224),(-2558140202968313979635982)⟩⟩,⟨⟨11158538611108503371013832,11158538611108506668389155⟩,⟨(-3030768216315435280856285),(-3030768216315431983660512)⟩⟩,⟨⟨10302556903931866441948576,10302556903931869555464253⟩,⟨(-3424366897261176436279404),(-3424366897261173322944669)⟩⟩,⟨⟨9483619194008125163123495,9483619194008128104957259⟩,⟨(-3746443109654903703319405),(-3746443109654900761666615)⟩⟩,⟨⟨8703008275590137863002854,8703008275590140640286908⟩,⟨(-4004067412557355644759011),(-4004067412557352867654116)⟩⟩,⟨⟨7961509773129512277617344,7961509773129514902024791⟩,⟨(-4203871654684303401823977),(-4203871654684300777575252)⟩⟩,⟨⟨7259475122602351325697458,7259475122602353804249185⟩,⟨(-4352051127033214539415509),(-4352051127033212061003546)⟩⟩,⟨⟨6596879768974272697928416,6596879768974275040499615⟩,⟨(-4454370605142480588050844),(-4454370605142478245601908)⟩⟩] +lemma kernel21_0_r5_10_eq : ∀ k : Fin 16, kernel21_0Expr 5 10 k = kernel21_0_r5_10 k := by decide +kernel +noncomputable def kernel21_0_r5_11 : Fin 16 → CBox := ![⟨⟨5973376665693093358037738,5973376665693095570180182⟩,⟨(-4516173664535280276714213),(-4516173664535278064677878)⟩⟩,⟨⟨5388345201294425589205970,5388345201294427680576354⟩,⟨(-4542394704890350505787996),(-4542394704890348414508895)⟩⟩,⟨⟨4840935710351262674268765,4840935710351264650435291⟩,⟨(-4537573169713834279611081),(-4537573169713832303522240)⟩⟩,⟨⟨4330109751689505130194928,4330109751689506999204251⟩,⟨(-4505869498216334730287663),(-4505869498216332861343610)⟩⟩,⟨⟨3854676356627086224266735,3854676356627087990561008⟩,⟨(-4451082394279531154156331),(-4451082394279529387916008)⟩⟩,⟨⟨3413324464568891140099238,3413324464568892811211027⟩,⟨(-4376667043468120680986882),(-4376667043468119009918771)⟩⟩,⟨⟨3004651773183177503243953,3004651773183179083764891⟩,⟨(-4285753952727530866975414),(-4285753952727529286488851)⟩⟩,⟨⟨2627190236157365411289101,2627190236157366907524359⟩,⟨(-4181168128501338164389887),(-4181168128501336668180613)⟩⟩,⟨⟨2279428443715739472970713,2279428443715740888253599⟩,⟨(-4065448347365817559968179),(-4065448347365816144703728)⟩⟩,⟨⟨1959831120182744098956678,1959831120182745439418908⟩,⟨(-3940866308831710246718185),(-3940866308831708906267631)⟩⟩,⟨⟨1666855969364177310884389,1666855969364178579999681⟩,⟨(-3809445492674813820494878),(-3809445492674812551385229)⟩⟩,⟨⟨1398968092830759032044962,1398968092830760235065909⟩,⟨(-3672979573040425404393230),(-3672979573040424201372567)⟩⟩,⟨⟨1154652198724209734135441,1154652198724210873700686⟩,⟨(-3533050268671664894967286),(-3533050268671663755397587)⟩⟩,⟨⟨932422809828543061152768,932422809828544142039790⟩,⟨(-3391044533018238384875428),(-3391044533018237303979783)⟩⟩,⟨⟨730832669685888078082272,730832669685889102937904⟩,⟨(-3248171009794716993136946),(-3248171009794715968269131)⟩⟩,⟨⟨548479534778448555233531,548479534778449528004197⟩,⟨(-3105475698899522694925039),(-3105475698899521722139092)⟩⟩] +lemma kernel21_0_r5_11_eq : ∀ k : Fin 16, kernel21_0Expr 5 11 k = kernel21_0_r5_11 k := by decide +kernel +noncomputable def kernel21_0_r5_12 : Fin 16 → CBox := ![⟨⟨384011529503537501762708,384011529503538424372104⟩,⟨(-2963856794615534950005624),(-2963856794615534027378277)⟩⟩,⟨⟨236131229061653440730821,236131229061654317140658⟩,⟨(-2824078672838687126182965),(-2824078672838686249752888)⟩⟩,⟨⟨103598623652093421034358,103598623652094253631674⟩,⟨(-2686785016876607483084788),(-2686785016876606650465295)⟩⟩,⟨⟨(-14766894308387902041016),(-14766894308387110156991)⟩,⟨(-2552511082282887335756926),(-2552511082282886543849099)⟩⟩,⟨⟨(-120085389722527184421109),(-120085389722526431736243)⟩,⟨(-2421695110401867432946121),(-2421695110401866680236114)⟩⟩,⟨⟨(-213415972079179305527204),(-213415972079178589019959)⟩,⟨(-2294688907949843716509247),(-2294688907949842999975776)⟩⟩,⟨⟨(-295757002228586461629811),(-295757002228585779755752)⟩,⟨(-2171767616203273851208209),(-2171767616203273169307067)⟩⟩,⟨⟨(-368046820787763409392626),(-368046820787762759647235)⟩,⟨(-2053138698349372575620624),(-2053138698349371925847495)⟩⟩,⟨⟨(-431164910123461664264272),(-431164910123461045555636)⟩,⟨(-1938950177419141393119304),(-1938950177419140774382461)⟩⟩,⟨⟨(-485933411131130417262327),(-485933411131129827104448)⟩,⟨(-1829298160099463896542349),(-1829298160099463306355948)⟩⟩,⟨⟨(-533118924719324301181244),(-533118924719323738387330)⟩,⟨(-1724233683733196320726971),(-1724233683733195757904363)⟩⟩,⟨⟨(-573434536006974586152273),(-573434536006974048753215)⟩,⟨(-1623768925079274025550146),(-1623768925079273488122344)⟩⟩,⟨⟨(-607542006742694549228170),(-607542006742694036364070)⟩,⟨(-1527882810024906053064679),(-1527882810024905540171898)⟩⟩,⟨⟨(-636054088366072488518861),(-636054088366071998240223)⟩,⟨(-1436526063516160144196311),(-1436526063516159653889141)⟩⟩,⟨⟨(-659536914462876119844622),(-659536914462875651126489)⟩,⟨(-1349625738590025507954860),(-1349625738590025039209207)⟩⟩,⟨⟨(-678512437137000074167634),(-678512437136999625263463)⟩,⟨(-1267089262630137776444678),(-1267089262630137327515216)⟩⟩] +lemma kernel21_0_r5_12_eq : ∀ k : Fin 16, kernel21_0Expr 5 12 k = kernel21_0_r5_12 k := by decide +kernel +noncomputable def kernel21_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-693460877053986959416976),(-693460877053986529775683)⟩,⟨(-1188808037901216508932312),(-1188808037901216079267821)⟩⟩,⟨⟨(-704823161629544925167969),(-704823161629544513178203)⟩,⟨(-1114660632107445983053300),(-1114660632107445571042284)⟩⟩,⟨⟨(-713003330069599080637137),(-713003330069598685627580)⟩,⟨(-1044515593223602645647397),(-1044515593223602250618414)⟩⟩,⟨⟨(-718370887745601343442539),(-718370887745600964168925)⟩,⟨(-978233921213788011578776),(-978233921213787632287432)⟩⟩,⟨⟨(-721263095740567338942181),(-721263095740566974957570)⟩,⟨(-915671227523770034565823),(-915671227523769670565067)⟩⟩,⟨⟨(-721987184358442789582685),(-721987184358442439620621)⟩,⟨(-856679611445804530717784),(-856679611445804180741047)⟩⟩,⟨⟨(-720822481982618668707619),(-720822481982618332251456)⟩,⟨(-801109280640580021057931),(-801109280640579684588462)⟩⟩,⟨⟨(-718022452928866481578745),(-718022452928866157621447)⟩,⟨(-748809941285833206709321),(-748809941285832882739987)⟩⟩,⟨⟨(-713816639892939975855328),(-713816639892939664113454)⟩,⟨(-699631981526988446102058),(-699631981526988134349331)⟩⟩,⟨⟨(-708412508271756490522378),(-708412508271756189919644)⟩,⟨(-653427470149666722260945),(-653427470149666421648453)⟩⟩,⟨⟨(-701997191066287560118567),(-701997191066287270241375)⟩,⟨(-610050990691332477315068),(-610050990691332187429133)⟩⟩,⟨⟨(-694739134279460796752984),(-694739134279460516769780)⟩,⟨(-569360329570827685978953),(-569360329570827405987947)⟩⟩,⟨⟨(-686789643727365086055552),(-686789643727364815745159)⟩,⟨(-531217035248483908155888),(-531217035248483637838565)⟩⟩,⟨⟨(-678284335009121158699075),(-678284335009120897204683)⟩,⟨(-495486863941945080141459),(-495486863941944818640943)⟩⟩,⟨⟨(-669344489050571155955127),(-669344489050570902986890)⟩,⟨(-462040126017787458293871),(-462040126017787205320256)⟩⟩,⟨⟨(-660078316168480532817660),(-660078316168480287703244)⟩,⟨(-430751945858773300833435),(-430751945858773055714330)⟩⟩] +lemma kernel21_0_r5_13_eq : ∀ k : Fin 16, kernel21_0Expr 5 13 k = kernel21_0_r5_13 k := by decide +kernel +noncomputable def kernel21_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-650582132012673290133111),(-650582132012673052758918)⟩,⟨(-401502446771954069233695),(-401502446771953831855451)⟩⟩,⟨⟨(-640941449049336074211614),(-640941449049335843816540)⟩,⟨(-374176871353473177810123),(-374176871353472947411585)⟩⟩,⟨⟨(-631231987464045989785611),(-631231987464045766152276)⟩,⟨(-348665646660445963689373),(-348665646660445740053117)⟩⟩,⟨⟨(-621520609500908115160002),(-621520609500907897730316)⟩,⟨(-324864402556560029262494),(-324864402556559811830386)⟩⟩,⟨⟨(-611866181326205429040484),(-611866181326205217721557)⟩,⟨(-302673950693262814626258),(-302673950693262603305369)⟩⟩,⟨⟨(-602320366521589133983613),(-602320366521588928166382)⟩,⟨(-282000230759329736765055),(-282000230759329530946286)⟩⟩,⟨⟨(-592928355282328386215907),(-592928355282328185737596)⟩,⟨(-262754229874631982205797),(-262754229874631781726338)⟩⟩,⟨⟨(-583729533328672755278738),(-583729533328672559669570)⟩,⟨(-244851880315206168721511),(-244851880315205973111553)⟩⟩,⟨⟨(-574758094440141516516806),(-574758094440141325752466)⟩,⟨(-228213940132281081584857),(-228213940132280890820056)⟩⟩,⟨⟨(-566043600399813687287677),(-566043600399813500815664)⟩,⟨(-212765860663684414634660),(-212765860663684228162489)⟩⟩,⟨⟨(-557611491993894305934160),(-557611491993894123632703)⟩,⟨(-198437644427976579061332),(-198437644427976396759993)⟩⟩,⟨⟨(-549483554555666356707866),(-549483554555666178175730)⟩,⟨(-185163696435730414251545),(-185163696435730235719781)⟩⟩,⟨⟨(-541678341376415700616534),(-541678341376415525833458)⟩,⟨(-172882671544677914666661),(-172882671544677739884188)⟩⟩,⟨⟨(-534211558132440634176234),(-534211558132440462682117)⟩,⟨(-161537320122185531408789),(-161537320122185359915488)⟩⟩,⟨⟨(-527096411299685584304172),(-527096411299685416007598)⟩,⟨(-151074333956055644296197),(-151074333956055476000632)⟩⟩,⟨⟨(-520343923348242446467692),(-520343923348242281019763)⟩,⟨(-141444194069508968888385),(-141444194069508803441641)⟩⟩] +lemma kernel21_0_r5_14_eq : ∀ k : Fin 16, kernel21_0Expr 5 14 k = kernel21_0_r5_14 k := by decide +kernel +noncomputable def kernel21_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-513963217329886071890824),(-513963217329885909325444)⟩,⟨(-132601021845086893591598),(-132601021845086731027563)⟩⟩,⟨⟨(-507961773294516504749912),(-507961773294516344624025)⟩,⟨(-124502434642017860259729),(-124502434642017700135332)⟩⟩,⟨⟨(-502345658797101198037523),(-502345658797101040281376)⟩,⟨(-117109406899402763737445),(-117109406899402605982919)⟩⟩,⟨⟨(-497119735586386368814638),(-497119735586386213118737)⟩,⟨(-110386137550666685074865),(-110386137550666529380704)⟩⟩,⟨⟨(-492287844400965690937493),(-492287844400965537320830)⟩,⟨(-104299924430561500629900),(-104299924430561347015082)⟩⟩,⟨⟨(-487852969637725494550466),(-487852969637725342637395)⟩,⟨(-98821046232231778111017),(-98821046232231626199886)⟩⟩,⟨⟨(-483817385502508575025965),(-483817385502508424761401)⟩,⟨(-93922652466295589465733),(-93922652466295439203193)⟩⟩,⟨⟨(-480182785103171816464552),(-480182785103171667567358)⟩,⟨(-89580661784529433897395),(-89580661784529285002300)⟩⟩,⟨⟨(-476950393801036182709949),(-476950393801036035220483)⟩,⟨(-85773668955725676294897),(-85773668955725528807591)⟩⟩,⟨⟨(-474121067997904180161626),(-474121067997904033692089)⟩,⟨(-82482860718900721768931),(-82482860718900575301609)⟩⟩,⟨⟨(-471695380402113751017511),(-471695380402113605525433)⟩,⟨(-79691940687695724857269),(-79691940687695579367451)⟩⟩,⟨⟨(-469673692688190047765386),(-469673692688189902992669)⟩,⟨(-77387063438074618837261),(-77387063438074474066841)⟩⟩,⟨⟨(-468056216340160090747423),(-468056216340159946734897)⟩,⟨(-75556777877942615673754),(-75556777877942471663554)⟩⟩,⟨⟨(-466843062348065606288025),(-466843062348065462702230)⟩,⟨(-74191979970836194077083),(-74191979970836050493637)⟩⟩,⟨⟨(-466034280310155738111890),(-466034280310155594913273)⟩,⟨(-73285874865212819719355),(-73285874865212676523101)⟩⟩,⟨⟨(-465629887379136030897962),(-465629887379135887838961)⟩,⟨(-72833948465008542391801),(-72833948465008399335170)⟩⟩] +lemma kernel21_0_r5_15_eq : ∀ k : Fin 16, kernel21_0Expr 5 15 k = kernel21_0_r5_15 k := by decide +kernel +noncomputable def kernel21_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel21_0_r5_0,kernel21_0_r5_1,kernel21_0_r5_2,kernel21_0_r5_3,kernel21_0_r5_4,kernel21_0_r5_5,kernel21_0_r5_6,kernel21_0_r5_7,kernel21_0_r5_8,kernel21_0_r5_9,kernel21_0_r5_10,kernel21_0_r5_11,kernel21_0_r5_12,kernel21_0_r5_13,kernel21_0_r5_14,kernel21_0_r5_15] +lemma kernel21_0_r5_eq (i k : Fin 16) : kernel21_0Expr 5 i k = kernel21_0_r5 i k := by + fin_cases i + · exact kernel21_0_r5_0_eq k + · exact kernel21_0_r5_1_eq k + · exact kernel21_0_r5_2_eq k + · exact kernel21_0_r5_3_eq k + · exact kernel21_0_r5_4_eq k + · exact kernel21_0_r5_5_eq k + · exact kernel21_0_r5_6_eq k + · exact kernel21_0_r5_7_eq k + · exact kernel21_0_r5_8_eq k + · exact kernel21_0_r5_9_eq k + · exact kernel21_0_r5_10_eq k + · exact kernel21_0_r5_11_eq k + · exact kernel21_0_r5_12_eq k + · exact kernel21_0_r5_13_eq k + · exact kernel21_0_r5_14_eq k + · exact kernel21_0_r5_15_eq k +noncomputable def kernel21_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel21_0_r0,kernel21_0_r1,kernel21_0_r2,kernel21_0_r3,kernel21_0_r4,kernel21_0_r5] +lemma kernel21_0_eq (j : Fin 6) (i k : Fin 16) : kernel21_0Expr j i k = kernel21_0 j i k := by + fin_cases j + · exact kernel21_0_r0_eq i k + · exact kernel21_0_r1_eq i k + · exact kernel21_0_r2_eq i k + · exact kernel21_0_r3_eq i k + · exact kernel21_0_r4_eq i k + · exact kernel21_0_r5_eq i k +lemma kernel21_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel21_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(21:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel21_0_eq] + unfold kernel21_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans21_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel21_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans21 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel21_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r0_0_eq : ∀ k : Fin 16, kernel21_1Expr 0 0 k = kernel21_1_r0_0 k := by decide +kernel +noncomputable def kernel21_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r0_1_eq : ∀ k : Fin 16, kernel21_1Expr 0 1 k = kernel21_1_r0_1 k := by decide +kernel +noncomputable def kernel21_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r0_2_eq : ∀ k : Fin 16, kernel21_1Expr 0 2 k = kernel21_1_r0_2 k := by decide +kernel +noncomputable def kernel21_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r0_3_eq : ∀ k : Fin 16, kernel21_1Expr 0 3 k = kernel21_1_r0_3 k := by decide +kernel +noncomputable def kernel21_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r0_4_eq : ∀ k : Fin 16, kernel21_1Expr 0 4 k = kernel21_1_r0_4 k := by decide +kernel +noncomputable def kernel21_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel21_1_r0_5_eq : ∀ k : Fin 16, kernel21_1Expr 0 5 k = kernel21_1_r0_5 k := by decide +kernel +noncomputable def kernel21_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel21_1_r0_6_eq : ∀ k : Fin 16, kernel21_1Expr 0 6 k = kernel21_1_r0_6 k := by decide +kernel +noncomputable def kernel21_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel21_1_r0_7_eq : ∀ k : Fin 16, kernel21_1Expr 0 7 k = kernel21_1_r0_7 k := by decide +kernel +noncomputable def kernel21_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel21_1_r0_8_eq : ∀ k : Fin 16, kernel21_1Expr 0 8 k = kernel21_1_r0_8 k := by decide +kernel +noncomputable def kernel21_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel21_1_r0_9_eq : ∀ k : Fin 16, kernel21_1Expr 0 9 k = kernel21_1_r0_9 k := by decide +kernel +noncomputable def kernel21_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel21_1_r0_10_eq : ∀ k : Fin 16, kernel21_1Expr 0 10 k = kernel21_1_r0_10 k := by decide +kernel +noncomputable def kernel21_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel21_1_r0_11_eq : ∀ k : Fin 16, kernel21_1Expr 0 11 k = kernel21_1_r0_11 k := by decide +kernel +noncomputable def kernel21_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel21_1_r0_12_eq : ∀ k : Fin 16, kernel21_1Expr 0 12 k = kernel21_1_r0_12 k := by decide +kernel +noncomputable def kernel21_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel21_1_r0_13_eq : ∀ k : Fin 16, kernel21_1Expr 0 13 k = kernel21_1_r0_13 k := by decide +kernel +noncomputable def kernel21_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel21_1_r0_14_eq : ∀ k : Fin 16, kernel21_1Expr 0 14 k = kernel21_1_r0_14 k := by decide +kernel +noncomputable def kernel21_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel21_1_r0_15_eq : ∀ k : Fin 16, kernel21_1Expr 0 15 k = kernel21_1_r0_15 k := by decide +kernel +noncomputable def kernel21_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel21_1_r0_0,kernel21_1_r0_1,kernel21_1_r0_2,kernel21_1_r0_3,kernel21_1_r0_4,kernel21_1_r0_5,kernel21_1_r0_6,kernel21_1_r0_7,kernel21_1_r0_8,kernel21_1_r0_9,kernel21_1_r0_10,kernel21_1_r0_11,kernel21_1_r0_12,kernel21_1_r0_13,kernel21_1_r0_14,kernel21_1_r0_15] +lemma kernel21_1_r0_eq (i k : Fin 16) : kernel21_1Expr 0 i k = kernel21_1_r0 i k := by + fin_cases i + · exact kernel21_1_r0_0_eq k + · exact kernel21_1_r0_1_eq k + · exact kernel21_1_r0_2_eq k + · exact kernel21_1_r0_3_eq k + · exact kernel21_1_r0_4_eq k + · exact kernel21_1_r0_5_eq k + · exact kernel21_1_r0_6_eq k + · exact kernel21_1_r0_7_eq k + · exact kernel21_1_r0_8_eq k + · exact kernel21_1_r0_9_eq k + · exact kernel21_1_r0_10_eq k + · exact kernel21_1_r0_11_eq k + · exact kernel21_1_r0_12_eq k + · exact kernel21_1_r0_13_eq k + · exact kernel21_1_r0_14_eq k + · exact kernel21_1_r0_15_eq k +noncomputable def kernel21_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel21_1_r1_0_eq : ∀ k : Fin 16, kernel21_1Expr 1 0 k = kernel21_1_r1_0 k := by decide +kernel +noncomputable def kernel21_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel21_1_r1_1_eq : ∀ k : Fin 16, kernel21_1Expr 1 1 k = kernel21_1_r1_1 k := by decide +kernel +noncomputable def kernel21_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel21_1_r1_2_eq : ∀ k : Fin 16, kernel21_1Expr 1 2 k = kernel21_1_r1_2 k := by decide +kernel +noncomputable def kernel21_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel21_1_r1_3_eq : ∀ k : Fin 16, kernel21_1Expr 1 3 k = kernel21_1_r1_3 k := by decide +kernel +noncomputable def kernel21_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel21_1_r1_4_eq : ∀ k : Fin 16, kernel21_1Expr 1 4 k = kernel21_1_r1_4 k := by decide +kernel +noncomputable def kernel21_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel21_1_r1_5_eq : ∀ k : Fin 16, kernel21_1Expr 1 5 k = kernel21_1_r1_5 k := by decide +kernel +noncomputable def kernel21_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel21_1_r1_6_eq : ∀ k : Fin 16, kernel21_1Expr 1 6 k = kernel21_1_r1_6 k := by decide +kernel +noncomputable def kernel21_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel21_1_r1_7_eq : ∀ k : Fin 16, kernel21_1Expr 1 7 k = kernel21_1_r1_7 k := by decide +kernel +noncomputable def kernel21_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel21_1_r1_8_eq : ∀ k : Fin 16, kernel21_1Expr 1 8 k = kernel21_1_r1_8 k := by decide +kernel +noncomputable def kernel21_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel21_1_r1_9_eq : ∀ k : Fin 16, kernel21_1Expr 1 9 k = kernel21_1_r1_9 k := by decide +kernel +noncomputable def kernel21_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r1_10_eq : ∀ k : Fin 16, kernel21_1Expr 1 10 k = kernel21_1_r1_10 k := by decide +kernel +noncomputable def kernel21_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r1_11_eq : ∀ k : Fin 16, kernel21_1Expr 1 11 k = kernel21_1_r1_11 k := by decide +kernel +noncomputable def kernel21_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r1_12_eq : ∀ k : Fin 16, kernel21_1Expr 1 12 k = kernel21_1_r1_12 k := by decide +kernel +noncomputable def kernel21_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r1_13_eq : ∀ k : Fin 16, kernel21_1Expr 1 13 k = kernel21_1_r1_13 k := by decide +kernel +noncomputable def kernel21_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r1_14_eq : ∀ k : Fin 16, kernel21_1Expr 1 14 k = kernel21_1_r1_14 k := by decide +kernel +noncomputable def kernel21_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel21_1_r1_15_eq : ∀ k : Fin 16, kernel21_1Expr 1 15 k = kernel21_1_r1_15 k := by decide +kernel +noncomputable def kernel21_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel21_1_r1_0,kernel21_1_r1_1,kernel21_1_r1_2,kernel21_1_r1_3,kernel21_1_r1_4,kernel21_1_r1_5,kernel21_1_r1_6,kernel21_1_r1_7,kernel21_1_r1_8,kernel21_1_r1_9,kernel21_1_r1_10,kernel21_1_r1_11,kernel21_1_r1_12,kernel21_1_r1_13,kernel21_1_r1_14,kernel21_1_r1_15] +lemma kernel21_1_r1_eq (i k : Fin 16) : kernel21_1Expr 1 i k = kernel21_1_r1 i k := by + fin_cases i + · exact kernel21_1_r1_0_eq k + · exact kernel21_1_r1_1_eq k + · exact kernel21_1_r1_2_eq k + · exact kernel21_1_r1_3_eq k + · exact kernel21_1_r1_4_eq k + · exact kernel21_1_r1_5_eq k + · exact kernel21_1_r1_6_eq k + · exact kernel21_1_r1_7_eq k + · exact kernel21_1_r1_8_eq k + · exact kernel21_1_r1_9_eq k + · exact kernel21_1_r1_10_eq k + · exact kernel21_1_r1_11_eq k + · exact kernel21_1_r1_12_eq k + · exact kernel21_1_r1_13_eq k + · exact kernel21_1_r1_14_eq k + · exact kernel21_1_r1_15_eq k +noncomputable def kernel21_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-11370),(-11329)⟩,⟨(-162675),(-162634)⟩⟩,⟨⟨(-11439),(-11411)⟩,⟨(-162248),(-162218)⟩⟩,⟨⟨(-11577),(-11553)⟩,⟨(-161384),(-161359)⟩⟩,⟨⟨(-11793),(-11752)⟩,⟨(-160119),(-160079)⟩⟩,⟨⟨(-12054),(-12024)⟩,⟨(-158431),(-158403)⟩⟩,⟨⟨(-12384),(-12359)⟩,⟨(-156347),(-156322)⟩⟩,⟨⟨(-12766),(-12733)⟩,⟨(-153888),(-153856)⟩⟩,⟨⟨(-13183),(-13159)⟩,⟨(-151053),(-151028)⟩⟩,⟨⟨(-13647),(-13619)⟩,⟨(-147891),(-147861)⟩⟩,⟨⟨(-14139),(-14099)⟩,⟨(-144412),(-144371)⟩⟩,⟨⟨(-14638),(-14606)⟩,⟨(-140609),(-140576)⟩⟩,⟨⟨(-15151),(-15127)⟩,⟨(-136552),(-136527)⟩⟩,⟨⟨(-15665),(-15641)⟩,⟨(-132257),(-132232)⟩⟩,⟨⟨(-16163),(-16138)⟩,⟨(-127750),(-127726)⟩⟩,⟨⟨(-16645),(-16605)⟩,⟨(-123064),(-123023)⟩⟩,⟨⟨(-17090),(-17065)⟩,⟨(-118213),(-118188)⟩⟩] +lemma kernel21_1_r2_0_eq : ∀ k : Fin 16, kernel21_1Expr 2 0 k = kernel21_1_r2_0 k := by decide +kernel +noncomputable def kernel21_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-17508),(-17475)⟩,⟨(-113250),(-113217)⟩⟩,⟨⟨(-17874),(-17833)⟩,⟨(-108194),(-108153)⟩⟩,⟨⟨(-18189),(-18156)⟩,⟨(-103065),(-103032)⟩⟩,⟨⟨(-18442),(-18409)⟩,⟨(-97911),(-97878)⟩⟩,⟨⟨(-18635),(-18605)⟩,⟨(-92747),(-92719)⟩⟩,⟨⟨(-18758),(-18728)⟩,⟨(-87613),(-87585)⟩⟩,⟨⟨(-18815),(-18785)⟩,⟨(-82518),(-82491)⟩⟩,⟨⟨(-18795),(-18765)⟩,⟨(-77504),(-77476)⟩⟩,⟨⟨(-18714),(-18681)⟩,⟨(-72587),(-72554)⟩⟩,⟨⟨(-18557),(-18516)⟩,⟨(-67779),(-67738)⟩⟩,⟨⟨(-18320),(-18292)⟩,⟨(-63084),(-63054)⟩⟩,⟨⟨(-18019),(-17994)⟩,⟨(-58560),(-58535)⟩⟩,⟨⟨(-17675),(-17634)⟩,⟨(-54197),(-54156)⟩⟩,⟨⟨(-17247),(-17214)⟩,⟨(-50003),(-49970)⟩⟩,⟨⟨(-16775),(-16750)⟩,⟨(-45984),(-45959)⟩⟩,⟨⟨(-16247),(-16217)⟩,⟨(-42174),(-42146)⟩⟩] +lemma kernel21_1_r2_1_eq : ∀ k : Fin 16, kernel21_1Expr 2 1 k = kernel21_1_r2_1 k := by decide +kernel +noncomputable def kernel21_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-15683),(-15650)⟩,⟨(-38552),(-38519)⟩⟩,⟨⟨(-15086),(-15048)⟩,⟨(-35130),(-35094)⟩⟩,⟨⟨(-14446),(-14413)⟩,⟨(-31905),(-31872)⟩⟩,⟨⟨(-13787),(-13754)⟩,⟨(-28893),(-28860)⟩⟩,⟨⟨(-13104),(-13073)⟩,⟨(-26067),(-26039)⟩⟩,⟨⟨(-12412),(-12379)⟩,⟨(-23459),(-23425)⟩⟩,⟨⟨(-11708),(-11678)⟩,⟨(-21023),(-20995)⟩⟩,⟨⟨(-11007),(-10977)⟩,⟨(-18787),(-18759)⟩⟩,⟨⟨(-10323),(-10290)⟩,⟨(-16728),(-16695)⟩⟩,⟨⟨(-9625),(-9600)⟩,⟨(-14849),(-14823)⟩⟩,⟨⟨(-8952),(-8921)⟩,⟨(-13128),(-13100)⟩⟩,⟨⟨(-8300),(-8270)⟩,⟨(-11567),(-11539)⟩⟩,⟨⟨(-7669),(-7628)⟩,⟨(-10165),(-10124)⟩⟩,⟨⟨(-7045),(-7015)⟩,⟨(-8881),(-8853)⟩⟩,⟨⟨(-6467),(-6434)⟩,⟨(-7743),(-7709)⟩⟩,⟨⟨(-5911),(-5869)⟩,⟨(-6730),(-6688)⟩⟩] +lemma kernel21_1_r2_2_eq : ∀ k : Fin 16, kernel21_1Expr 2 2 k = kernel21_1_r2_2 k := by decide +kernel +noncomputable def kernel21_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-5377),(-5343)⟩,⟨(-5813),(-5780)⟩⟩,⟨⟨(-4885),(-4852)⟩,⟨(-5010),(-4977)⟩⟩,⟨⟨(-4414),(-4380)⟩,⟨(-4305),(-4271)⟩⟩,⟨⟨(-3978),(-3952)⟩,⟨(-3671),(-3645)⟩⟩,⟨⟨(-3575),(-3541)⟩,⟨(-3126),(-3092)⟩⟩,⟨⟨(-3194),(-3163)⟩,⟨(-2653),(-2625)⟩⟩,⟨⟨(-2850),(-2824)⟩,⟨(-2232),(-2206)⟩⟩,⟨⟨(-2531),(-2502)⟩,⟨(-1881),(-1850)⟩⟩,⟨⟨(-2253),(-2203)⟩,⟨(-1576),(-1526)⟩⟩,⟨⟨(-1989),(-1955)⟩,⟨(-1304),(-1270)⟩⟩,⟨⟨(-1743),(-1712)⟩,⟨(-1082),(-1053)⟩⟩,⟨⟨(-1533),(-1502)⟩,⟨(-887),(-858)⟩⟩,⟨⟨(-1349),(-1318)⟩,⟨(-725),(-696)⟩⟩,⟨⟨(-1174),(-1144)⟩,⟨(-592),(-563)⟩⟩,⟨⟨(-1017),(-986)⟩,⟨(-476),(-448)⟩⟩,⟨⟨(-888),(-854)⟩,⟨(-386),(-352)⟩⟩] +lemma kernel21_1_r2_3_eq : ∀ k : Fin 16, kernel21_1Expr 2 3 k = kernel21_1_r2_3 k := by decide +kernel +noncomputable def kernel21_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-767),(-725)⟩,⟨(-314),(-272)⟩⟩,⟨⟨(-655),(-624)⟩,⟨(-238),(-209)⟩⟩,⟨⟨(-560),(-535)⟩,⟨(-193),(-167)⟩⟩,⟨⟨(-482),(-454)⟩,⟨(-156),(-125)⟩⟩,⟨⟨(-413),(-384)⟩,⟨(-120),(-89)⟩⟩,⟨⟨(-356),(-322)⟩,⟨(-87),(-53)⟩⟩,⟨⟨(-303),(-269)⟩,⟨(-70),(-35)⟩⟩,⟨⟨(-259),(-228)⟩,⟨(-54),(-25)⟩⟩,⟨⟨(-218),(-183)⟩,⟨(-44),(-9)⟩⟩,⟨⟨(-182),(-156)⟩,⟨(-27),(-1)⟩⟩,⟨⟨(-162),(-131)⟩,⟨(-21),8⟩⟩,⟨⟨(-138),(-95)⟩,⟨(-32),11⟩⟩,⟨⟨(-118),(-84)⟩,⟨(-19),15⟩⟩,⟨⟨(-93),(-64)⟩,⟨(-10),21⟩⟩,⟨⟨(-85),(-56)⟩,⟨(-8),23⟩⟩,⟨⟨(-72),(-40)⟩,⟨(-12),17⟩⟩] +lemma kernel21_1_r2_4_eq : ∀ k : Fin 16, kernel21_1Expr 2 4 k = kernel21_1_r2_4 k := by decide +kernel +noncomputable def kernel21_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-58),(-29)⟩,⟨(-10),21⟩⟩,⟨⟨(-50),(-15)⟩,⟨(-12),23⟩⟩,⟨⟨(-50),(-15)⟩,⟨(-12),23⟩⟩,⟨⟨(-38),(-3)⟩,⟨(-4),30⟩⟩,⟨⟨(-31),(-5)⟩,⟨(-13),14⟩⟩,⟨⟨(-31),(-5)⟩,⟨(-13),14⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩] +lemma kernel21_1_r2_5_eq : ∀ k : Fin 16, kernel21_1Expr 2 5 k = kernel21_1_r2_5 k := by decide +kernel +noncomputable def kernel21_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),7⟩,⟨(-11),21⟩⟩,⟨⟨(-23),21⟩,⟨(-18),26⟩⟩,⟨⟨(-23),21⟩,⟨(-18),27⟩⟩,⟨⟨(-23),21⟩,⟨(-18),27⟩⟩,⟨⟨(-23),21⟩,⟨(-18),27⟩⟩,⟨⟨(-23),21⟩,⟨(-18),27⟩⟩,⟨⟨(-23),21⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩] +lemma kernel21_1_r2_6_eq : ∀ k : Fin 16, kernel21_1Expr 2 6 k = kernel21_1_r2_6 k := by decide +kernel +noncomputable def kernel21_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-23),22⟩,⟨(-18),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel21_1_r2_7_eq : ∀ k : Fin 16, kernel21_1Expr 2 7 k = kernel21_1_r2_7 k := by decide +kernel +noncomputable def kernel21_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel21_1_r2_8_eq : ∀ k : Fin 16, kernel21_1Expr 2 8 k = kernel21_1_r2_8 k := by decide +kernel +noncomputable def kernel21_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel21_1_r2_9_eq : ∀ k : Fin 16, kernel21_1Expr 2 9 k = kernel21_1_r2_9 k := by decide +kernel +noncomputable def kernel21_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel21_1_r2_10_eq : ∀ k : Fin 16, kernel21_1Expr 2 10 k = kernel21_1_r2_10 k := by decide +kernel +noncomputable def kernel21_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel21_1_r2_11_eq : ∀ k : Fin 16, kernel21_1Expr 2 11 k = kernel21_1_r2_11 k := by decide +kernel +noncomputable def kernel21_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel21_1_r2_12_eq : ∀ k : Fin 16, kernel21_1Expr 2 12 k = kernel21_1_r2_12 k := by decide +kernel +noncomputable def kernel21_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel21_1_r2_13_eq : ∀ k : Fin 16, kernel21_1Expr 2 13 k = kernel21_1_r2_13 k := by decide +kernel +noncomputable def kernel21_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel21_1_r2_14_eq : ∀ k : Fin 16, kernel21_1Expr 2 14 k = kernel21_1_r2_14 k := by decide +kernel +noncomputable def kernel21_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel21_1_r2_15_eq : ∀ k : Fin 16, kernel21_1Expr 2 15 k = kernel21_1_r2_15 k := by decide +kernel +noncomputable def kernel21_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel21_1_r2_0,kernel21_1_r2_1,kernel21_1_r2_2,kernel21_1_r2_3,kernel21_1_r2_4,kernel21_1_r2_5,kernel21_1_r2_6,kernel21_1_r2_7,kernel21_1_r2_8,kernel21_1_r2_9,kernel21_1_r2_10,kernel21_1_r2_11,kernel21_1_r2_12,kernel21_1_r2_13,kernel21_1_r2_14,kernel21_1_r2_15] +lemma kernel21_1_r2_eq (i k : Fin 16) : kernel21_1Expr 2 i k = kernel21_1_r2 i k := by + fin_cases i + · exact kernel21_1_r2_0_eq k + · exact kernel21_1_r2_1_eq k + · exact kernel21_1_r2_2_eq k + · exact kernel21_1_r2_3_eq k + · exact kernel21_1_r2_4_eq k + · exact kernel21_1_r2_5_eq k + · exact kernel21_1_r2_6_eq k + · exact kernel21_1_r2_7_eq k + · exact kernel21_1_r2_8_eq k + · exact kernel21_1_r2_9_eq k + · exact kernel21_1_r2_10_eq k + · exact kernel21_1_r2_11_eq k + · exact kernel21_1_r2_12_eq k + · exact kernel21_1_r2_13_eq k + · exact kernel21_1_r2_14_eq k + · exact kernel21_1_r2_15_eq k +noncomputable def kernel21_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-96455809492851085),(-96455809492851059)⟩,⟨51185188004546161,51185188004546186⟩⟩,⟨⟨(-96258058503187719),(-96258058503187695)⟩,⟨51188875696491262,51188875696491283⟩⟩,⟨⟨(-95863499294256738),(-95863499294256717)⟩,⟨51195702595306492,51195702595306516⟩⟩,⟨⟨(-95274012237388770),(-95274012237388745)⟩,⟨51204580485065019,51204580485065044⟩⟩,⟨⟨(-94492404968665220),(-94492404968665188)⟩,⟨51213898793001195,51213898793001227⟩⟩,⟨⟨(-93522396892587937),(-93522396892587911)⟩,⟨51221550316484395,51221550316484421⟩⟩,⟨⟨(-92368598538179551),(-92368598538179531)⟩,⟨51224964907777418,51224964907777437⟩⟩,⟨⟨(-91036485789229008),(-91036485789228989)⟩,⟨51221150599063989,51221150599064008⟩⟩,⟨⟨(-89532369023528640),(-89532369023528613)⟩,⟨51206741535779692,51206741535779722⟩⟩,⟨⟨(-87863357213775188),(-87863357213775169)⟩,⟨51178051981497486,51178051981497505⟩⟩,⟨⟨(-86037317065843554),(-86037317065843535)⟩,⟨51131135564150625,51131135564150645⟩⟩,⟨⟨(-84062827298695072),(-84062827298695047)⟩,⟨51061848852718044,51061848852718070⟩⟩,⟨⟨(-81949128204330477),(-81949128204330457)⟩,⟨50965918286964874,50965918286964894⟩⟩,⟨⟨(-79706066665783140),(-79706066665783121)⟩,⟨50839009431542012,50839009431542032⟩⟩,⟨⟨(-77344036855770238),(-77344036855770218)⟩,⟨50676797490595150,50676797490595170⟩⟩,⟨⟨(-74873916887642284),(-74873916887642257)⟩,⟨50475038000669228,50475038000669258⟩⟩] +lemma kernel21_1_r3_0_eq : ∀ k : Fin 16, kernel21_1Expr 3 0 k = kernel21_1_r3_0 k := by decide +kernel +noncomputable def kernel21_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-72307001742832900),(-72307001742832871)⟩,⟨50229636618512788,50229636618512810⟩⟩,⟨⟨(-69654932854044625),(-69654932854044604)⟩,⟨49936716936510629,49936716936510653⟩⟩,⟨⟨(-66929624779667679),(-66929624779667653)⟩,⟨49592685291744708,49592685291744734⟩⟩,⟨⟨(-64143189461025241),(-64143189461025222)⟩,⟨49194291584654795,49194291584654814⟩⟩,⟨⟨(-61307858608472284),(-61307858608472264)⟩,⟨48738685189209663,48738685189209682⟩⟩,⟨⟨(-58435904813580181),(-58435904813580162)⟩,⟨48223465117387342,48223465117387362⟩⟩,⟨⟨(-55539562031033385),(-55539562031033359)⟩,⟨47646723695307894,47646723695307920⟩⟩,⟨⟨(-52630946113890925),(-52630946113890895)⟩,⟨47007083115014497,47007083115014524⟩⟩,⟨⟨(-49721976118046217),(-49721976118046185)⟩,⟨46303724342871173,46303724342871205⟩⟩,⟨⟨(-46824297114697696),(-46824297114697664)⟩,⟨45536407990842643,45536407990842675⟩⟩,⟨⟨(-43949205262233887),(-43949205262233861)⟩,⟨44705486888371436,44705486888371462⟩⟩,⟨⟨(-41107575890162269),(-41107575890162242)⟩,⟨43811910227858869,43811910227858900⟩⟩,⟨⟨(-38309795336839743),(-38309795336839720)⟩,⟨42857219293484571,42857219293484599⟩⟩,⟨⟨(-35565697259337053),(-35565697259337026)⟩,⟨41843534918808493,41843534918808523⟩⟩,⟨⟨(-32884504097629795),(-32884504097629775)⟩,⟨40773536950835563,40773536950835582⟩⟩,⟨⟨(-30274774326606237),(-30274774326606211)⟩,⟨39650436124581704,39650436124581730⟩⟩] +lemma kernel21_1_r3_1_eq : ∀ k : Fin 16, kernel21_1Expr 3 1 k = kernel21_1_r3_1 k := by decide +kernel +noncomputable def kernel21_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-27744356068583434),(-27744356068583408)⟩,⟨38477938870359547,38477938870359573⟩⟩,⟨⟨(-25300347566908772),(-25300347566908753)⟩,⟨37260205683852185,37260205683852205⟩⟩,⟨⟨(-22949064938871232),(-22949064938871202)⟩,⟨36001803784615424,36001803784615452⟩⟩,⟨⟨(-20696017534912963),(-20696017534912943)⟩,⟨34707654870237101,34707654870237120⟩⟩,⟨⟨(-18545891132619277),(-18545891132619248)⟩,⟨33382978839566694,33382978839566716⟩⟩,⟨⟨(-16502539089986932),(-16502539089986912)⟩,⟨32033234408105892,32033234408105911⟩⟩,⟨⟨(-14568981475004591),(-14568981475004565)⟩,⟨30664057571061863,30664057571061889⟩⟩,⟨⟨(-12747412079717588),(-12747412079717569)⟩,⟨29281198884312840,29281198884312860⟩⟩,⟨⟨(-11039213118849266),(-11039213118849239)⟩,⟨27890460530593098,27890460530593129⟩⟩,⟨⟨(-9444977307872942),(-9444977307872920)⟩,⟨26497634117918654,26497634117918678⟩⟩,⟨⟨(-7964536915287729),(-7964536915287710)⟩,⟨25108440120352177,25108440120352196⟩⟩,⟨⟨(-6596999290754952),(-6596999290754924)⟩,⟨23728469818700306,23728469818700336⟩⟩,⟨⟨(-5340788286554303),(-5340788286554284)⟩,⟨22363130532016661,22363130532016681⟩⟩,⟨⟨(-4193690916168460),(-4193690916168440)⟩,⟨21017594851503191,21017594851503211⟩⟩,⟨⟨(-3152908532105217),(-3152908532105193)⟩,⟨19696754498453619,19696754498453640⟩⟩,⟨⟨(-2215111756441049),(-2215111756441029)⟩,⟨18405179329349960,18405179329349980⟩⟩] +lemma kernel21_1_r3_2_eq : ∀ k : Fin 16, kernel21_1Expr 3 2 k = kernel21_1_r3_2 k := by decide +kernel +noncomputable def kernel21_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-1376498362834307),(-1376498362834279)⟩,⟨17147081906332742,17147081906332773⟩⟩,⟨⟨(-632853288401482),(-632853288401450)⟩,⟨15926287942326032,15926287942326064⟩⟩,⟨⟨20390051966725,20390051966746⟩,⟨14746212819445972,14746212819445996⟩⟩,⟨⟨588087967727506,588087967727526⟩,⟨13609844269264013,13609844269264033⟩⟩,⟨⟨1075325007715169,1075325007715189⟩,⟨12519731196253848,12519731196253868⟩⟩,⟨⟨1487353549075631,1487353549075656⟩,⟨11477978523411120,11477978523411141⟩⟩,⟨⟨1829535173651848,1829535173651874⟩,⟨10486247843498826,10486247843498852⟩⟩,⟨⟨2107284487252418,2107284487252449⟩,⟨9545763572317892,9545763572317920⟩⟩,⟨⟨2326015969986785,2326015969986810⟩,⟨8657324223252168,8657324223252189⟩⟩,⟨⟨2491094371148002,2491094371148026⟩,⟨7821318356227649,7821318356227671⟩⟩,⟨⟨2607789081761810,2607789081761835⟩,⟨7037744699994692,7037744699994713⟩⟩,⟨⟨2681232833751691,2681232833751722⟩,⟨6306235904816461,6306235904816489⟩⟩,⟨⟨2716384988561079,2716384988561100⟩,⟨5626085353447459,5626085353447484⟩⟩,⟨⟨2717999591854605,2717999591854625⟩,⟨4996276441630241,4996276441630262⟩⟩,⟨⟨2690598286340850,2690598286340870⟩,⟨4415513734863215,4415513734863235⟩⟩,⟨⟨2638448093445690,2638448093445717⟩,⟨3882255415270689,3882255415270715⟩⟩] +lemma kernel21_1_r3_3_eq : ∀ k : Fin 16, kernel21_1Expr 3 3 k = kernel21_1_r3_3 k := by decide +kernel +noncomputable def kernel21_1_r3_4 : Fin 16 → CBox := ![⟨⟨2565543997990615,2565543997990650⟩,⟨3394746450183175,3394746450183212⟩⟩,⟨⟨2475596199476007,2475596199476028⟩,⟨2951051941456692,2951051941456712⟩⟩,⟨⟨2372021830111919,2372021830111950⟩,⟨2549090150413407,2549090150413435⟩⟩,⟨⟨2257940884225764,2257940884225791⟩,⟨2186664736240639,2186664736240666⟩⟩,⟨⟨2136176056723305,2136176056723335⟩,⟨1861495794332133,1861495794332157⟩⟩,⟨⟨2009256150266024,2009256150266046⟩,⟨1571249333950494,1571249333950519⟩⟩,⟨⟨1879422681902080,1879422681902100⟩,⟨1313564890288532,1313564890288552⟩⟩,⟨⟨1748639299979950,1748639299979970⟩,⟨1086081023107736,1086081023107756⟩⟩,⟨⟨1618603611008975,1618603611008997⟩,⟨886458511302875,886458511302900⟩⟩,⟨⟨1490761013254830,1490761013254850⟩,⟨712401108753905,712401108753926⟩⟩,⟨⟨1366320138658055,1366320138658076⟩,⟨561673780575079,561673780575099⟩⟩,⟨⟨1246269516398607,1246269516398627⟩,⟨432118389398118,432118389398138⟩⟩,⟨⟨1131395089257978,1131395089258000⟩,⟨321666847826758,321666847826783⟩⟩,⟨⟨1022298236939119,1022298236939146⟩,⟨228351795038072,228351795038099⟩⟩,⟨⟨919413987740847,919413987740880⟩,⟨150314892210195,150314892210228⟩⟩,⟨⟨823029130479042,823029130479063⟩,⟨85812862721843,85812862721863⟩⟩] +lemma kernel21_1_r3_4_eq : ∀ k : Fin 16, kernel21_1Expr 3 4 k = kernel21_1_r3_4 k := by decide +kernel +noncomputable def kernel21_1_r3_5 : Fin 16 → CBox := ![⟨⟨733299971348582,733299971348609⟩,⟨33221428748098,33221428748125⟩⟩,⟨⟨650269514608209,650269514608241⟩,⟨(-8962684029286),(-8962684029258)⟩⟩,⟨⟨573883880684047,573883880684067⟩,⟨(-42121487238959),(-42121487238939)⟩⟩,⟨⟨504007809738084,504007809738104⟩,⟨(-67517020368499),(-67517020368479)⟩⟩,⟨⟨440439132232833,440439132232854⟩,⟨(-86293990665187),(-86293990665166)⟩⟩,⟨⟨382922119937225,382922119937257⟩,⟨(-99483561852219),(-99483561852190)⟩⟩,⟨⟨331159660657340,331159660657365⟩,⟨(-108008094903524),(-108008094903502)⟩⟩,⟨⟨284824227338342,284824227338364⟩,⟨(-112686651308727),(-112686651308702)⟩⟩,⟨⟨243567636775432,243567636775453⟩,⟨(-114241079305556),(-114241079305535)⟩⟩,⟨⟨207029614792824,207029614792846⟩,⟨(-113302515902732),(-113302515902707)⟩⟩,⟨⟨174845203299134,174845203299166⟩,⟨(-110418151615532),(-110418151615503)⟩⟩,⟨⟨146651060085164,146651060085191⟩,⟨(-106058120164561),(-106058120164534)⟩⟩,⟨⟨122090714654464,122090714654485⟩,⟨(-100622391456356),(-100622391456336)⟩⟩,⟨⟨100818852890416,100818852890443⟩,⟨(-94447562525320),(-94447562525292)⟩⟩,⟨⟨82504710142622,82504710142649⟩,⟨(-87813457373010),(-87813457372982)⟩⟩,⟨⟨66834656579243,66834656579282⟩,⟨(-80949462449678),(-80949462449642)⟩⟩] +lemma kernel21_1_r3_5_eq : ∀ k : Fin 16, kernel21_1Expr 3 5 k = kernel21_1_r3_5 k := by decide +kernel +noncomputable def kernel21_1_r3_6 : Fin 16 → CBox := ![⟨⟨53514060651080,53514060651101⟩,⟨(-74040539595858),(-74040539595837)⟩⟩,⟨⟨42268516518756,42268516518779⟩,⟨(-67232872368854),(-67232872368828)⟩⟩,⟨⟨32844519588448,32844519588478⟩,⟨(-60639114642118),(-60639114642085)⟩⟩,⟨⟨25009671167753,25009671167781⟩,⟨(-54343222062324),(-54343222062297)⟩⟩,⟨⟨18552488970038,18552488970066⟩,⟨(-48404857301926),(-48404857301898)⟩⟩,⟨⟨13281895028794,13281895028816⟩,⟨(-42863369023026),(-42863369023005)⟩⟩,⟨⟨9026446780371,9026446780401⟩,⟨(-37741352076792),(-37741352076760)⟩⟩,⟨⟨5633370862174,5633370862195⟩,⟨(-33047802739617),(-33047802739596)⟩⟩,⟨⟨2967452754360,2967452754381⟩,⟨(-28780887798665),(-28780887798644)⟩⟩,⟨⟨909828944143,909828944166⟩,⟨(-24930350130065),(-24930350130039)⟩⟩,⟨⟨(-643278039248),(-643278039218)⟩,⟨(-21479576166203),(-21479576166170)⟩⟩,⟨⟨(-1781847460520),(-1781847460492)⟩,⟨(-18407352434530),(-18407352434502)⟩⟩,⟨⟨(-2583342578014),(-2583342577993)⟩,⟨(-15689339288204),(-15689339288182)⟩⟩,⟨⟨(-3113964040234),(-3113964040204)⟩,⟨(-13299290157336),(-13299290157303)⟩⟩,⟨⟨(-3429856191078),(-3429856191057)⟩,⟨(-11210044246960),(-11210044246939)⟩⟩,⟨⟨(-3578252381809),(-3578252381778)⟩,⟨(-9394319707176),(-9394319707143)⟩⟩] +lemma kernel21_1_r3_6_eq : ∀ k : Fin 16, kernel21_1Expr 3 6 k = kernel21_1_r3_6 k := by decide +kernel +noncomputable def kernel21_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-3598549267936),(-3598549267913)⟩,⟨(-7825333007629),(-7825333007603)⟩⟩,⟨⟨(-3523303445808),(-3523303445775)⟩,⟨(-6477268662307),(-6477268662277)⟩⟩,⟨⟨(-3379146668555),(-3379146668534)⟩,⟨(-5325621656813),(-5325621656792)⟩⟩,⟨⟨(-3187618300171),(-3187618300149)⟩,⟨(-4347433009251),(-4347433009230)⟩⟩,⟨⟨(-2965915647796),(-2965915647767)⟩,⟨(-3521436912133),(-3521436912105)⟩⟩,⟨⟨(-2727564394624),(-2727564394603)⟩,⟨(-2828135914484),(-2828135914462)⟩⟩,⟨⟨(-2483012576656),(-2483012576634)⟩,⟨(-2249818655474),(-2249818655452)⟩⟩,⟨⟨(-2240152447617),(-2240152447595)⟩,⟨(-1770532790906),(-1770532790885)⟩⟩,⟨⟨(-2004775199222),(-2004775199191)⟩,⟨(-1376023989008),(-1376023988974)⟩⟩,⟨⟨(-1780963888391),(-1780963888369)⟩,⟨(-1053650232549),(-1053650232527)⟩⟩,⟨⟨(-1571430108333),(-1571430108302)⟩,⟨(-792279162905),(-792279162872)⟩⟩,⟨⟨(-1377799961113),(-1377799961091)⟩,⟨(-582174845411),(-582174845389)⟩⟩,⟨⟨(-1200854781002),(-1200854780979)⟩,⟨(-414879126822),(-414879126795)⟩⟩,⟨⟨(-1040731846689),(-1040731846668)⟩,⟨(-283091691268),(-283091691247)⟩⟩,⟨⟨(-897090036195),(-897090036171)⟩,⟨(-180551997832),(-180551997806)⟩⟩,⟨⟨(-769245040699),(-769245040672)⟩,⟨(-101925490059),(-101925490035)⟩⟩] +lemma kernel21_1_r3_7_eq : ∀ k : Fin 16, kernel21_1Expr 3 7 k = kernel21_1_r3_7 k := by decide +kernel +noncomputable def kernel21_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-656278383920),(-656278383896)⟩,⟨(-42695799266),(-42695799239)⟩⟩,⟨⟨(-557124107037),(-557124107008)⟩,⟨935894415,935894444⟩⟩,⟨⟨(-470636588948),(-470636588926)⟩,⟨32143635430,32143635452⟩⟩,⟨⟨(-395642588582),(-395642588555)⟩,⟨53561259670,53561259694⟩⟩,⟨⟨(-330980227084),(-330980227055)⟩,⟨67358702594,67358702623⟩⟩,⟨⟨(-275527279992),(-275527279970)⟩,⟨75310217060,75310217082⟩⟩,⟨⟨(-228220825922),(-228220825900)⟩,⟨78854832778,78854832800⟩⟩,⟨⟨(-188070001770),(-188070001748)⟩,⟨79149504709,79149504732⟩⟩,⟨⟨(-154163346383),(-154163346349)⟩,⟨77115472554,77115472586⟩⟩,⟨⟨(-125671974628),(-125671974601)⟩,⟨73478397444,73478397469⟩⟩,⟨⟨(-101849611760),(-101849611725)⟩,⟨68802858786,68802858818⟩⟩,⟨⟨(-82030332386),(-82030332359)⟩,⟨63521792804,63521792828⟩⟩,⟨⟨(-65624687715),(-65624687690)⟩,⟨57961436705,57961436732⟩⟩,⟨⟨(-52114767197),(-52114767168)⟩,⟨52362314967,52362314997⟩⟩,⟨⟨(-41048623752),(-41048623730)⟩,⟨46896769307,46896769329⟩⟩,⟨⟨(-32034394301),(-32034394270)⟩,⟨41683493956,41683493990⟩⟩] +lemma kernel21_1_r3_8_eq : ∀ k : Fin 16, kernel21_1Expr 3 8 k = kernel21_1_r3_8 k := by decide +kernel +noncomputable def kernel21_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-24734365509),(-24734365480)⟩,⟨36799496655,36799496684⟩⟩,⟨⟨(-18859168599),(-18859168576)⟩,⟨32289862833,32289862855⟩⟩,⟨⟨(-14162232805),(-14162232771)⟩,⟨28175659396,28175659428⟩⟩,⟨⟨(-10434583958),(-10434583935)⟩,⟨24460274500,24460274522⟩⟩,⟨⟨(-7500041123),(-7500041086)⟩,⟨21134452067,21134452104⟩⟩,⟨⟨(-5210837646),(-5210837623)⟩,⟨18180245656,18180245679⟩⟩,⟨⟨(-3443673600),(-3443673578)⟩,⟨15574084179,15574084202⟩⟩,⟨⟨(-2096191880),(-2096191850)⟩,⟨13289114120,13289114150⟩⟩,⟨⟨(-1083860038),(-1083860015)⟩,⟨11296957033,11296957056⟩⟩,⟨⟨(-337233197),(-337233160)⟩,⟨9568999167,9568999204⟩⟩,⟨⟨200431078,200431108⟩,⟨8077310489,8077310519⟩⟩,⟨⟨575236947,575236970⟩,⟨6795273269,6795273292⟩⟩,⟨⟨824425413,824425458⟩,⟨5697986380,5697986425⟩⟩,⟨⟨977891526,977891549⟩,⟨4762498705,4762498728⟩⟩,⟨⟨1059473586,1059473616⟩,⟨3967914654,3967914684⟩⟩,⟨⟨1088042747,1088042772⟩,⟨3295406694,3295406722⟩⟩] +lemma kernel21_1_r3_9_eq : ∀ k : Fin 16, kernel21_1Expr 3 9 k = kernel21_1_r3_9 k := by decide +kernel +noncomputable def kernel21_1_r3_10 : Fin 16 → CBox := ![⟨⟨1078418529,1078418555⟩,⟨2728161488,2728161516⟩⟩,⟨⟨1042134370,1042134398⟩,⟨2251281361,2251281387⟩⟩,⟨⟨988074073,988074111⟩,⟨1851657102,1851657140⟩⟩,⟨⟨922998411,922998436⟩,⟨1517824703,1517824731⟩⟩,⟨⟨851978299,851978337⟩,⟨1239815047,1239815085⟩⟩,⟨⟨778749493,778749526⟩,⟨1009003480,1009003515⟩⟩,⟨⟨706001163,706001201⟩,⟨817963649,817963687⟩⟩,⟨⟨635609534,635609562⟩,⟨660329071,660329096⟩⟩,⟨⟨568825839,568825865⟩,⟨530664182,530664211⟩⟩,⟨⟨506426586,506426617⟩,⟨424346097,424346128⟩⟩,⟨⟨448832959,448832987⟩,⟨337457386,337457411⟩⟩,⟨⟨396204819,396204857⟩,⟨266689891,266689929⟩⟩,⟨⟨348514388,348514412⟩,⟨209259272,209259295⟩⟩,⟨⟨305603163,305603192⟩,⟨162829424,162829450⟩⟩,⟨⟨267225754,267225778⟩,⟨125446441,125446465⟩⟩,⟨⟨233082930,233082966⟩,⟨95480923,95480957⟩⟩] +lemma kernel21_1_r3_10_eq : ∀ k : Fin 16, kernel21_1Expr 3 10 k = kernel21_1_r3_10 k := by decide +kernel +noncomputable def kernel21_1_r3_11 : Fin 16 → CBox := ![⟨⟨202846412,202846440⟩,⟨71578069,71578095⟩⟩,⟨⟨176176967,176176993⟩,⟨52614643,52614672⟩⟩,⟨⟨152737402,152737436⟩,⟨37662053,37662089⟩⟩,⟨⟨132201621,132201650⟩,⟨25954826,25954852⟩⟩,⟨⟨114260490,114260518⟩,⟨16863698,16863724⟩⟩,⟨⟨98625600,98625624⟩,⟨9872938,9872961⟩⟩,⟨⟨85031144,85031170⟩,⟨4561062,4561091⟩⟩,⟨⟨73234681,73234707⟩,⟨584688,584717⟩⟩,⟨⟨63016919,63016943⟩,⟨(-2335086),(-2335062)⟩⟩,⟨⟨54180929,54180963⟩,⟨(-4424045),(-4424008)⟩⟩,⟨⟨46550951,46550980⟩,⟨(-5864290),(-5864264)⟩⟩,⟨⟨39970920,39970946⟩,⟨(-6802216),(-6802187)⟩⟩,⟨⟨34302931,34302955⟩,⟨(-7354982),(-7354958)⟩⟩,⟨⟨29425564,29425591⟩,⟨(-7615983),(-7615954)⟩⟩,⟨⟨25232370,25232409⟩,⟨(-7659254),(-7659215)⟩⟩,⟨⟨21630256,21630288⟩,⟨(-7543215),(-7543183)⟩⟩] +lemma kernel21_1_r3_11_eq : ∀ k : Fin 16, kernel21_1Expr 3 11 k = kernel21_1_r3_11 k := by decide +kernel +noncomputable def kernel21_1_r3_12 : Fin 16 → CBox := ![⟨⟨18538046,18538080⟩,⟨(-7313656),(-7313619)⟩⟩,⟨⟨15885169,15885198⟩,⟨(-7006210),(-7006183)⟩⟩,⟨⟨13610366,13610406⟩,⟨(-6648385),(-6648346)⟩⟩,⟨⟨11660605,11660634⟩,⟨(-6261186),(-6261159)⟩⟩,⟨⟨9990019,9990066⟩,⟨(-5860488),(-5860440)⟩⟩,⟨⟨8559059,8559086⟩,⟨(-5458036),(-5458006)⟩⟩,⟨⟨7333585,7333614⟩,⟨(-5062420),(-5062393)⟩⟩,⟨⟨6284257,6284289⟩,⟨(-4679711),(-4679679)⟩⟩,⟨⟨5385836,5385866⟩,⟨(-4314027),(-4314000)⟩⟩,⟨⟨4616643,4616668⟩,⟨(-3968001),(-3967977)⟩⟩,⟨⟨3958069,3958103⟩,⟨(-3643145),(-3643108)⟩⟩,⟨⟨3394177,3394201⟩,⟨(-3340072),(-3340048)⟩⟩,⟨⟨2911285,2911312⟩,⟨(-3058833),(-3058803)⟩⟩,⟨⟨2497698,2497722⟩,⟨(-2798976),(-2798951)⟩⟩,⟨⟨2143380,2143420⟩,⟨(-2559748),(-2559708)⟩⟩,⟨⟨1839792,1839819⟩,⟨(-2340156),(-2340127)⟩⟩] +lemma kernel21_1_r3_12_eq : ∀ k : Fin 16, kernel21_1Expr 3 12 k = kernel21_1_r3_12 k := by decide +kernel +noncomputable def kernel21_1_r3_13 : Fin 16 → CBox := ![⟨⟨1579585,1579609⟩,⟨(-2139109),(-2139084)⟩⟩,⟨⟨1356483,1356510⟩,⟨(-1955431),(-1955401)⟩⟩,⟨⟨1165126,1165156⟩,⟨(-1787898),(-1787871)⟩⟩,⟨⟨1000951,1000981⟩,⟨(-1635335),(-1635308)⟩⟩,⟨⟨860027,860067⟩,⟨(-1496554),(-1496514)⟩⟩,⟨⟨739033,739063⟩,⟨(-1370419),(-1370392)⟩⟩,⟨⟨635077,635107⟩,⟨(-1255881),(-1255854)⟩⟩,⟨⟨545732,545765⟩,⟨(-1151927),(-1151895)⟩⟩,⟨⟨468909,468939⟩,⟨(-1057603),(-1057576)⟩⟩,⟨⟨402814,402846⟩,⟨(-972073),(-972040)⟩⟩,⟨⟨345929,345959⟩,⟨(-894499),(-894471)⟩⟩,⟨⟨296938,296968⟩,⟨(-824164),(-824137)⟩⟩,⟨⟨254728,254753⟩,⟨(-760378),(-760353)⟩⟩,⟨⟨218336,218376⟩,⟨(-702542),(-702502)⟩⟩,⟨⟨186954,186979⟩,⟨(-650067),(-650043)⟩⟩,⟨⟨159876,159900⟩,⟨(-602466),(-602442)⟩⟩] +lemma kernel21_1_r3_13_eq : ∀ k : Fin 16, kernel21_1Expr 3 13 k = kernel21_1_r3_13 k := by decide +kernel +noncomputable def kernel21_1_r3_14 : Fin 16 → CBox := ![⟨⟨136483,136513⟩,⟨(-559268),(-559241)⟩⟩,⟨⟨116277,116309⟩,⟨(-520058),(-520026)⟩⟩,⟨⟨98817,98850⟩,⟨(-484456),(-484423)⟩⟩,⟨⟨83722,83749⟩,⟨(-452109),(-452079)⟩⟩,⟨⟨70654,70683⟩,⟨(-422727),(-422700)⟩⟩,⟨⟨59345,59386⟩,⟨(-396022),(-395982)⟩⟩,⟨⟨49552,49585⟩,⟨(-371737),(-371705)⟩⟩,⟨⟨41072,41113⟩,⟨(-349660),(-349620)⟩⟩,⟨⟨33719,33749⟩,⟨(-329578),(-329551)⟩⟩,⟨⟨27350,27377⟩,⟨(-311311),(-311281)⟩⟩,⟨⟨21820,21861⟩,⟨(-294706),(-294666)⟩⟩,⟨⟨17033,17066⟩,⟨(-279599),(-279566)⟩⟩,⟨⟨12884,12916⟩,⟨(-265865),(-265833)⟩⟩,⟨⟨9273,9303⟩,⟨(-253380),(-253352)⟩⟩,⟨⟨6145,6175⟩,⟨(-242053),(-242025)⟩⟩,⟨⟨3429,3469⟩,⟨(-231785),(-231744)⟩⟩] +lemma kernel21_1_r3_14_eq : ∀ k : Fin 16, kernel21_1Expr 3 14 k = kernel21_1_r3_14 k := by decide +kernel +noncomputable def kernel21_1_r3_15 : Fin 16 → CBox := ![⟨⟨1078,1118⟩,⟨(-222474),(-222434)⟩⟩,⟨⟨(-953),(-918)⟩,⟨(-214057),(-214019)⟩⟩,⟨⟨(-2714),(-2686)⟩,⟨(-206458),(-206428)⟩⟩,⟨⟨(-4236),(-4200)⟩,⟨(-199632),(-199594)⟩⟩,⟨⟨(-5552),(-5520)⟩,⟨(-193508),(-193475)⟩⟩,⟨⟨(-6680),(-6647)⟩,⟨(-188047),(-188014)⟩⟩,⟨⟨(-7643),(-7610)⟩,⟨(-183197),(-183164)⟩⟩,⟨⟨(-8472),(-8431)⟩,⟨(-178944),(-178903)⟩⟩,⟨⟨(-9166),(-9138)⟩,⟨(-175225),(-175195)⟩⟩,⟨⟨(-9747),(-9720)⟩,⟨(-172036),(-172006)⟩⟩,⟨⟨(-10229),(-10196)⟩,⟨(-169346),(-169314)⟩⟩,⟨⟨(-10617),(-10577)⟩,⟨(-167131),(-167091)⟩⟩,⟨⟨(-10913),(-10880)⟩,⟨(-165372),(-165339)⟩⟩,⟨⟨(-11138),(-11108)⟩,⟨(-164070),(-164043)⟩⟩,⟨⟨(-11280),(-11247)⟩,⟨(-163212),(-163179)⟩⟩,⟨⟨(-11348),(-11323)⟩,⟨(-162774),(-162749)⟩⟩] +lemma kernel21_1_r3_15_eq : ∀ k : Fin 16, kernel21_1Expr 3 15 k = kernel21_1_r3_15 k := by decide +kernel +noncomputable def kernel21_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel21_1_r3_0,kernel21_1_r3_1,kernel21_1_r3_2,kernel21_1_r3_3,kernel21_1_r3_4,kernel21_1_r3_5,kernel21_1_r3_6,kernel21_1_r3_7,kernel21_1_r3_8,kernel21_1_r3_9,kernel21_1_r3_10,kernel21_1_r3_11,kernel21_1_r3_12,kernel21_1_r3_13,kernel21_1_r3_14,kernel21_1_r3_15] +lemma kernel21_1_r3_eq (i k : Fin 16) : kernel21_1Expr 3 i k = kernel21_1_r3 i k := by + fin_cases i + · exact kernel21_1_r3_0_eq k + · exact kernel21_1_r3_1_eq k + · exact kernel21_1_r3_2_eq k + · exact kernel21_1_r3_3_eq k + · exact kernel21_1_r3_4_eq k + · exact kernel21_1_r3_5_eq k + · exact kernel21_1_r3_6_eq k + · exact kernel21_1_r3_7_eq k + · exact kernel21_1_r3_8_eq k + · exact kernel21_1_r3_9_eq k + · exact kernel21_1_r3_10_eq k + · exact kernel21_1_r3_11_eq k + · exact kernel21_1_r3_12_eq k + · exact kernel21_1_r3_13_eq k + · exact kernel21_1_r3_14_eq k + · exact kernel21_1_r3_15_eq k +noncomputable def kernel21_1_r4_0 : Fin 16 → CBox := ![⟨⟨30789556680024420817292,30789556680024731684942⟩,⟨1953043420752047102077462,1953043420752047412956237⟩⟩,⟨⟨32366612529163011524146,32366612529163322095800⟩,⟨1951095206936787677800915,1951095206936787988383714⟩⟩,⟨⟨35511067741702211303812,35511067741702521283695⟩,⟨1947200735978753550080646,1947200735978753860071720⟩⟩,⟨⟨40203667567999817541656,40203667568000126635607⟩,⟨1941363951991053877740838,1941363951991054186846046⟩⟩,⟨⟨46415675192701569207409,46415675192701877123689⟩,⟨1933590847485589241117954,1933590847485589549045583⟩⟩,⟨⟨54109045416175931341703,54109045416176237791795⟩,⟨1923889553372560267258932,1923889553372560573720481⟩⟩,⟨⟨63236655074204982679910,63236655074205287379242⟩,⟨1912270456297067752453815,1912270456297068057164732⟩⟩,⟨⟨73742589192975921619992,73742589192976224288785⟩,⟨1898746341075327693613151,1898746341075327996293675⟩⟩,⟨⟨85562481610772983606116,85562481610773283969991⟩,⟨1883332555489255400418079,1883332555489255700793848⟩⟩,⟨⟨98623908523248309055251,98623908523248606846116⟩,⟨1866047194230698989698933,1866047194230699287501876⟩⟩,⟨⟨112846833125006150730059,112846833125006445686593⟩,⟨1846911298361910294367957,1846911298361910589336765⟩⟩,⟨⟨128144099226242845522425,128144099226243137390996⟩,⟨1825949066282993751984072,1825949066282994043865130⟩⟩,⟨⟨144421971419696412050165,144421971419696700585104⟩,⟨1803188071875640420012360,1803188071875640708560002⟩⟩,⟨⟨161580719061142633450590,161580719061142918415276⟩,⟨1778659485230439917698769,1778659485230440202676386⟩⟩,⟨⟨179515241007739824864600,179515241007740106031408⟩,⟨1752398291166839633571003,1752398291166839914750974⟩⟩,⟨⟨198115727734935094716026,198115727734935371867559⟩,⟨1724443500624059700724253,1724443500624059977889189⟩⟩] +lemma kernel21_1_r4_0_eq : ∀ k : Fin 16, kernel21_1Expr 4 0 k = kernel21_1_r4_0 k := by decide +kernel +noncomputable def kernel21_1_r4_1 : Fin 16 → CBox := ![⟨⟨217268357127308542426220,217268357127308815354869⟩,⟨1694838349940881915348241,1694838349940882188290537⟩⟩,⟨⟨236856019915176527668637,236856019915176796178270⟩,⟨1663630483054295459803852,1663630483054295728327369⟩⟩,⟨⟨256759070411107403063686,256759070411107666968538⟩,⟨1630872111732709102567648,1630872111732709366486628⟩⟩,⟨⟨276856097893349144555506,276856097893349403682196⟩,⟨1596620149119111119585308,1596620149119111378726364⟩⟩,⟨⟨297024713691599065751654,297024713691599319937621⟩,⟨1560936312092493977620037,1560936312092494231820470⟩⟩,⟨⟨317142348759986674378924,317142348759986923474955⟩,⟨1523887188260388327305669,1523887188260388576416252⟩⟩,⟨⟨337087056278267616340593,337087056278267860208243⟩,⟨1485544263768788172760419,1485544263768788416642697⟩⟩,⟨⟨356738313610849925725639,356738313610850164240491⟩,⟨1445983908554400344558235,1445983908554400583087779⟩⟩,⟨⟨375977817780212389662182,375977817780212622710378⟩,⟨1405287316163316321988640,1405287316163316555051578⟩⟩,⟨⟨394690268482222840005229,394690268482223067487964⟩,⟨1363540395814203199480735,1363540395814203426978240⟩⟩,⟨⟨412764132591252658659304,412764132591252880487995⟩,⟨1320833614986324891390624,1320833614986325113234103⟩⟩,⟨⟨430092384077840667902798,430092384077840884003934⟩,⟨1277261791455635781287356,1277261791455635997403276⟩⟩,⟨⟨446573213295470806131883,446573213295471016441504⟩,⟨1232923834377532977631996,1232923834377533187956383⟩⟩,⟨⟨462110699689603017202598,462110699689603221674386⟩,⟨1187922434713593376158112,1187922434713593580644623⟩⟩,⟨⟨476615442144441764627434,476615442144441963225380⟩,⟨1142363706012137529871293,1142363706012137728483903⟩⟩,⟨⟨490005141413128450333549,490005141413128643033946⟩,⟨1096356777268655194716704,1096356777268655387431686⟩⟩] +lemma kernel21_1_r4_1_eq : ∀ k : Fin 16, kernel21_1Expr 4 1 k = kernel21_1_r4_1 k := by decide +kernel +noncomputable def kernel21_1_r4_2 : Fin 16 → CBox := ![⟨⟨502205129376168569639049,502205129376168756425809⟩,⟨1050013340301560141688105,1050013340301560328489348⟩⟩,⟨⟨513148840240911407791153,513148840240911588664721⟩,⟨1003447154770791493568489,1003447154770791674456415⟩⟩,⟨⟨522778219230577912350642,522778219230578087317987⟩,⟨956773514630800471630908,956773514630800646612463⟩⟩,⟨⟨531044064812254995489603,531044064812255164587028⟩,⟨910108680434959843943106,910108680434960013054575⟩⟩,⟨⟨537906301075782197215221,537906301075782360474200⟩,⟨863569282485240384413273,863569282485240547686104⟩⟩,⟨⟨543334177494662314145061,543334177494662471608755⟩,⟨817271700339452411581972,817271700339452569059307⟩⟩,⟨⟨547306393969949707751165,547306393969949859466614⟩,⟨771331424639473272499205,771331424639473424228068⟩⟩,⟨⟨549811149771292177619701,549811149771292323649779⟩,⟨725862407599552667863108,725862407599552813905921⟩⟩,⟨⟨550846115737659662213410,550846115737659802622899⟩,⟨680976408786906915504473,680976408786907055925732⟩⟩,⟨⟨550418329874584361168212,550418329874584496036864⟩,⟨636782343031452405092270,636782343031452539971746⟩⟩,⟨⟨548544017274960861088605,548544017274960990497023⟩,⟨593385637413065923849052,593385637413066053267376⟩⟩,⟨⟨545248336085968590032187,545248336085968714074613⟩,⟨550887604289994795096601,550887604289994919148043⟩⟩,⟨⟨540565052034375712035046,540565052034375830805212⟩,⟨509384837249285198467740,509384837249285317246053⟩⟩,⟨⟨534536144794986688357982,534536144794986801997332⟩,⟨468968636679243190599138,468968636679243304245803⟩⟩,⟨⟨527211350230864472179729,527211350230864580816361⟩,⟨429724471386495647073808,429724471386495755716956⟩⟩,⟨⟨518647643237901928270634,518647643237902032019161⟩,⟨391731482309305510399395,391731482309305614153672⟩⟩] +lemma kernel21_1_r4_2_eq : ∀ k : Fin 16, kernel21_1Expr 4 2 k = kernel21_1_r4_2 k := by decide +kernel +noncomputable def kernel21_1_r4_3 : Fin 16 → CBox := ![⟨⟨508908666579412132673928,508908666579412231645537⟩,⟨355062033919142764371781,355062033919142863348404⟩⟩,⟨⟨498064111688313441457071,498064111688313535776253⟩,⟨319781318360385910192166,319781318360386004515667⟩⟩,⟨⟨486189057935655068415346,486189057935655158201932⟩,⟨285947016761147815743973,285947016761147905534218⟩⟩,⟨⟨473363277306105809869669,473363277306105895255907⟩,⟨253609021465638376480278,253609021465638461869554⟩⟩,⟨⟨459670511776229163333097,459670511776229244444386⟩,⟨222809222200435022515683,222809222200435103629426⟩⟩,⟨⟨445197730953844020587771,445197730953844097559870⟩,⟨193581358404784329081349,193581358404784406055358⟩⟩,⟨⟨430034377701945029935655,430034377701945102897646⟩,⟨165950939140673591967493,165950939140673664930886⟩⟩,⟨⟨414271609535535162757555,414271609535535231862203⟩,⟨139935231164559993836540,139935231164560062942115⟩⟩,⟨⟨398001543542968054546337,398001543542968119926811⟩,⟨115543314902365726746040,115543314902365792127004⟩⟩,⟨⟨381316512445375036327453,381316512445375098122036⟩,⟨92776207235807009481109,92776207235807071275787⟩⟩,⟨⟨364308339170538919435025,364308339170538977773553⟩,⟨71627049194372439375873,71627049194372497714130⟩⟩,⟨⟨347067636984936261842583,347067636984936316861818⟩,⟨52081355865987636919115,52081355865987691937756⟩⟩,⟨⟨329683141804987962389808,329683141804988014223997⟩,⟨34117325102682569521180,34117325102682621354482⟩⟩,⟨⟨312241082802747347280766,312241082802747396066503⟩,⟨17706200916669204525183,17706200916669253309778⟩⟩,⟨⟨294824596840626136058906,294824596840626181921849⟩,⟨2812686847353050338459,2812686847353096200033⟩⟩,⟨⟨277513191623861905923059,277513191623861948996612⟩,⟨(-10604595960075327452788),(-10604595960075284380802)⟩⟩] +lemma kernel21_1_r4_3_eq : ∀ k : Fin 16, kernel21_1Expr 4 3 k = kernel21_1_r4_3 k := by decide +kernel +noncomputable def kernel21_1_r4_4 : Fin 16 → CBox := ![⟨⟨260382261758870669224103,260382261758870709629917⟩,⟨(-22592611681106380975683),(-22592611681106340571605)⟩⟩,⟨⟨243502661161857578226330,243502661161857616092725⟩,⟨(-33203379828704650058576),(-33203379828704612194054)⟩⟩,⟨⟨226940334487154048856402,226940334487154084301006⟩,⟨(-42493418721251352954126),(-42493418721251317511505)⟩⟩,⟨⟨210756009451174900661119,210756009451174933804921⟩,⟨(-50523168942204743055562),(-50523168942204709913778)⟩⟩,⟨⟨195004951128253470250126,195004951128253501204395⟩,⟨(-57356403414985296444125),(-57356403414985265491879)⟩⟩,⟨⟨179736778501426157876338,179736778501426186756841⟩,⟨(-63059630703448749040949),(-63059630703448720162463)⟩⟩,⟨⟨164995342776672461694161,164995342776672488606947⟩,⟨(-67701498041488792615774),(-67701498041488765704986)⟩⟩,⟨⟨150818666224776944070959,150818666224776969124507⟩,⟨(-71352200398823488416203),(-71352200398823463364620)⟩⟩,⟨⟨137238939611689384355183,137238939611689407648374⟩,⟨(-74082901609371244361365),(-74082901609371221070103)⟩⟩,⟨⟨124282575625867346421603,124282575625867368056779⟩,⟨(-75965173230675853907573),(-75965173230675832274268)⟩⟩,⟨⟨111970315118295811621914,111970315118295831692008⟩,⟨(-77070456375648901958187),(-77070456375648881889909)⟩⟩,⟨⟨100317382445109395819396,100317382445109414418700⟩,⟨(-77469551270518973315382),(-77469551270518954717823)⟩⟩,⟨⟨89333685750014399349838,89333685750014416622463⟩,⟨(-77232138755167456815564),(-77232138755167439544469)⟩⟩,⟨⟨79024057648564561814909,79024057648564577844231⟩,⟨(-76426337364430868406032),(-76426337364430852378022)⟩⟩,⟨⟨69388531481808348441641,69388531481808363298994⟩,⟨(-75118299022260941169990),(-75118299022260926313754)⟩⟩,⟨⟨60422648094386354225671,60422648094386367983587⟩,⟨(-73371845755794466213083),(-73371845755794452456103)⟩⟩] +lemma kernel21_1_r4_4_eq : ∀ k : Fin 16, kernel21_1Expr 4 4 k = kernel21_1_r4_4 k := by decide +kernel +noncomputable def kernel21_1_r4_5 : Fin 16 → CBox := ![⟨⟨52117787961793306147481,52117787961793318871018⟩,⟨(-71248149204249887135778),(-71248149204249874413015)⟩⟩,⟨⟨44461523441750947185803,44461523441750958942097⟩,⟨(-68805454068697287489603),(-68805454068697275733931)⟩⟩,⟨⟨37437985952612133887320,37437985952612144736367⟩,⟨(-66098846033210898031018),(-66098846033210887182461)⟩⟩,⟨⟨31028242983314429914958,31028242983314439917320⟩,⟨(-63180064095104939066400),(-63180064095104929064405)⟩⟩,⟨⟨25210680009373226514115,25210680009373235723885⟩,⟨(-60097356680440578946262),(-60097356680440569736752)⟩⟩,⟨⟨19961382621520209103531,19961382621520217575922⟩,⟨(-56895380398375763532938),(-56895380398375755060708)⟩⟩,⟨⟨15254514460810405111192,15254514460810412895741⟩,⟨(-53615139810740495860138),(-53615139810740488075668)⟩⟩,⟨⟨11062686888662382887491,11062686888662390033573⟩,⟨(-50293966166836219693886),(-50293966166836212547811)⟩⟩,⟨⟨7357316694231523326403,7357316694231529878496⟩,⟨(-46965532682055354979582),(-46965532682055348427434)⟩⟩,⟨⟨4108968546347833776696,4108968546347839779156⟩,⟨(-43659903625447198863007),(-43659903625447192860442)⟩⟩,⟨⟨1287679324492818231210,1287679324492823723516⟩,⟨(-40403614227551682733529),(-40403614227551677241073)⟩⟩,⟨⟨(-1136738095453441693549),(-1136738095453436671322)⟩,⟨(-37219778226227920356282),(-37219778226227915333867)⟩⟩,⟨⟨(-3194413577842129902271),(-3194413577842125316052)⟩,⟨(-34128219734233939879243),(-34128219734233935292806)⟩⟩,⟨⟨(-4915162518173776523298),(-4915162518173772338709)⟩,⟨(-31145626036327816472387),(-31145626036327812287564)⟩⟩,⟨⟨(-6328253784088277132129),(-6328253784088273318609)⟩,⟨(-28285717903061819987249),(-28285717903061816173482)⟩⟩,⟨⟨(-7462203481773035828142),(-7462203481773032353637)⟩,⟨(-25559434039787864711969),(-25559434039787861237212)⟩⟩] +lemma kernel21_1_r4_5_eq : ∀ k : Fin 16, kernel21_1Expr 4 5 k = kernel21_1_r4_5 k := by decide +kernel +noncomputable def kernel21_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-8344594824238480972748),(-8344594824238477811440)⟩,⟨(-22975126368520076662494),(-22975126368520073500940)⟩⟩,⟨⟨(-9001924005603690296514),(-9001924005603687422363)⟩,⟨(-20538762962453626859685),(-20538762962453623985288)⟩⟩,⟨⟨(-9459471644020796748793),(-9459471644020794138738)⟩,⟨(-18254135612908386409064),(-18254135612908383798769)⟩⟩,⟨⟨(-9741199048474009407317),(-9741199048474007039057)⟩,⟨(-16123069200723919591379),(-16123069200723917222891)⟩⟩,⟨⟨(-9869668293868539564092),(-9869668293868537418181)⟩,⟨(-14145630262968021426951),(-14145630262968019280820)⟩⟩,⟨⟨(-9865984856164976810168),(-9865984856164974867174)⟩,⟨(-12320332385469341215713),(-12320332385469339272512)⟩⟩,⟨⟨(-9749761365574722168893),(-9749761365574720409960)⟩,⟨(-10644336306447146589496),(-10644336306447144830384)⟩⟩,⟨⟨(-9539100880990359591295),(-9539100880990357999570)⟩,⟨(-9113642880866537683320),(-9113642880866536091447)⟩⟩,⟨⟨(-9250597972141523030321),(-9250597972141521591914)⟩,⟨(-7723277323849080910044),(-7723277323849079471516)⟩⟩,⟨⟨(-8899355816057240990677),(-8899355816057239691673)⟩,⟨(-6467463419629963361241),(-6467463419629962062138)⟩⟩,⟨⟨(-8499017469332163651326),(-8499017469332162479626)⟩,⟨(-5339786645715428607104),(-5339786645715427435327)⟩⟩,⟨⟨(-8061809465013143857094),(-8061809465013142800959)⟩,⟨(-4333345416083853855634),(-4333345416083852799443)⟩⟩,⟨⟨(-7598595899836062408272),(-7598595899836061457476)⟩,⟨(-3440889889038209572067),(-3440889889038208621230)⟩⟩,⟨⟨(-7118941220948742449501),(-7118941220948741593661)⟩,⟨(-2654948011751203012868),(-2654948011751202156998)⟩⟩,⟨⟨(-6631179987848824589386),(-6631179987848823820002)⟩,⟨(-1967938682297963245308),(-1967938682297962475912)⟩⟩,⟨⟨(-6142491971622796044435),(-6142491971622795353202)⟩,⟨(-1372272099248525655747),(-1372272099248524964510)⟩⟩] +lemma kernel21_1_r4_6_eq : ∀ k : Fin 16, kernel21_1Expr 4 6 k = kernel21_1_r4_6 k := by decide +kernel +noncomputable def kernel21_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-5658981056234907575851),(-5658981056234906955556)⟩,⟨(-860437537435122389242),(-860437537435121768951)⟩⟩,⟨⟨(-5185756522161333853310),(-5185756522161333296944)⟩,⟨(-425078935570637387155),(-425078935570636830800)⟩⟩,⟨⟨(-4727015417778736541382),(-4727015417778736042967)⟩,⟨(-59058806704722031568),(-59058806704721533172)⟩⟩,⟨⟨(-4286124855442231388678),(-4286124855442230942446)⟩,⟨244488913771965456540,244488913771965902750⟩⟩,⟨⟨(-3865703204180454242454),(-3865703204180453843503)⟩,⟨492116385174811763562,492116385174812162487⟩⟩,⟨⟨(-3467699286698378119172),(-3467699286698377762668)⟩,⟨690028983678533693027,690028983678534049505⟩⟩,⟨⟨(-3093468822492877543660),(-3093468822492877225493)⟩,⟨844061226062359567497,844061226062359885633⟩⟩,⟨⟨(-2743847489230461664182),(-2743847489230461380210)⟩,⟨959660665540256031750,959660665540256315691⟩⟩,⟨⟨(-2419220099298463442020),(-2419220099298463188090)⟩,⟨1041878920180792401553,1041878920180792655452⟩⟩,⟨⟨(-2119585506119296392806),(-2119585506119296165817)⟩,⟨1095368998741106983430,1095368998741107210389⟩⟩,⟨⟨(-1844616964218547747723),(-1844616964218547545067)⟩,⟨1124388105598199352004,1124388105598199554635⟩⟩,⟨⟨(-1593717767264710589968),(-1593717767264710409130)⟩,⟨1132805134059751173355,1132805134059751354169⟩⟩,⟨⟨(-1366072078734877378035),(-1366072078734877216874)⟩,⟨1124112093888498725376,1124112093888498886514⟩⟩,⟨⟨(-1160690950150391852260),(-1160690950150391708692)⟩,⟨1101438762638234918301,1101438762638235061848⟩⟩,⟨⟨(-976453591849104537998),(-976453591849104410233)⟩,⟨1067569899712221415550,1067569899712221543296⟩⟩,⟨⟨(-812144021106137761545),(-812144021106137647885)⟩,⟨1024964415354489020373,1024964415354489134022⟩⟩] +lemma kernel21_1_r4_7_eq : ∀ k : Fin 16, kernel21_1Expr 4 7 k = kernel21_1_r4_7 k := by decide +kernel +noncomputable def kernel21_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-666483262354571896453),(-666483262354571795465)⟩,⟨975775942631080543248,975775942631080644222⟩⟩,⟨⟨(-538157314716374337341),(-538157314716374247582)⟩,⟨921874317547633812316,921874317547633902069⟩⟩,⟨⟨(-425841133582550071349),(-425841133582549991663)⟩,⟨864867529623322080518,864867529623322160201⟩⟩,⟨⟨(-328218896227880088308),(-328218896227880017598)⟩,⟨806123761491328686355,806123761491328757060⟩⟩,⟨⟨(-244000837129166966700),(-244000837129166904022)⟩,⟨746793190566851440184,746793190566851502857⟩⟩,⟨⟨(-171936947543147861935),(-171936947543147806324)⟩,⟨687829277808641092372,687829277808641147981⟩⟩,⟨⟨(-110827836782575230805),(-110827836782575181514)⟩,⟨630009317536756468602,630009317536756517891⟩⟩,⟨⟨(-59533050302928116612),(-59533050302928072931)⟩,⟨573954067731038817983,573954067731038861664⟩⟩,⟨⟨(-16977132962231673005),(-16977132962231634340)⟩,⟨520146321921316755327,520146321921316793994⟩⟩,⟨⟨17846284599699577322,17846284599699611556⟩,⟨468948321505796367817,468948321505796402052⟩⟩,⟨⟨45872111879446264040,45872111879446294329⟩,⟨420617941015053449802,420617941015053480091⟩⟩,⟨⟨67962887781435874390,67962887781435901179⟩,⟨375323608481544253881,375323608481544280675⟩⟩,⟨⟨84909101597088155687,84909101597088179357⟩,⟨333157948760973263916,333157948760973287591⟩⟩,⟨⟨97430532447742914950,97430532447742935866⟩,⟨294150159528068600112,294150159528068621029⟩⟩,⟨⟨106178412958075654954,106178412958075673418⟩,⟨258277147932244220370,258277147932244238835⟩⟩,⟨⟨111738242115469655865,111738242115469672180⟩,⟨225473470784531400045,225473470784531416360⟩⟩] +lemma kernel21_1_r4_8_eq : ∀ k : Fin 16, kernel21_1Expr 4 8 k = kernel21_1_r4_8 k := by decide +kernel +noncomputable def kernel21_1_r4_9 : Fin 16 → CBox := ![⟨⟨114633091269582757602,114633091269582772038⟩,⟨195640132920777601351,195640132920777615788⟩⟩,⟨⟨115327265727702334137,115327265727702346913⟩,⟨168652307330807849807,168652307330807862587⟩⟩,⟨⟨114230202155711620098,114230202155711631390⟩,⟨144366047052264642375,144366047052264653671⟩⟩,⟨⟨111700498805758432158,111700498805758442145⟩,⟨122624062996678489232,122624062996678499220⟩⟩,⟨⟨108049991313621949011,108049991313621957835⟩,⟨103260644095228864146,103260644095228872966⟩⟩,⟨⟨103547801339503686768,103547801339503694567⟩,⟨86105796704290866556,86105796704290874354⟩⟩,⟨⟨98424298603236947453,98424298603236954339⟩,⟨70988679363987250003,70988679363987256889⟩⟩,⟨⟨92874928860815099149,92874928860815105233⟩,⟨57740407007151415409,57740407007151421492⟩⟩,⟨⟨87063871085105046020,87063871085105051393⟩,⟨46196295802365547352,46196295802365552722⟩⟩,⟨⟨81127496575493010306,81127496575493015053⟩,⟨36197616192971404577,36197616192971409324⟩⟩,⟨⟨75177610974669853533,75177610974669857733⟩,⟨27592917552132681479,27592917552132685676⟩⟩,⟨⟨69304467276985947586,69304467276985951297⟩,⟨20238983378007989149,20238983378007992860⟩⟩,⟨⟨63579543944581217954,63579543944581221219⟩,⟨14001471246932079950,14001471246932083215⟩⟩,⟨⟨58058087285717733425,58058087285717736316⟩,⟨8755286949229096939,8755286949229099830⟩⟩,⟨⟨52781421380325066850,52781421380325069400⟩,⟨4384737454991500292,4384737454991502841⟩⟩,⟨⟨47779032148990533239,47779032148990535490⟩,⟨783502680365480610,783502680365482858⟩⟩] +lemma kernel21_1_r4_9_eq : ∀ k : Fin 16, kernel21_1Expr 4 9 k = kernel21_1_r4_9 k := by decide +kernel +noncomputable def kernel21_1_r4_10 : Fin 16 → CBox := ![⟨⟨43070434741882176684,43070434741882178678⟩,⟨(-2145538483953724327),(-2145538483953722332)⟩⟩,⟨⟨38666835360041430343,38666835360041432119⟩,⟨(-4490596709155907664),(-4490596709155905888)⟩⟩,⟨⟨34572599996564365018,34572599996564366581⟩,⟨(-6331348187358860888),(-6331348187358859322)⟩⟩,⟨⟨30786543478478608386,30786543478478609773⟩,⟨(-7739374616911556944),(-7739374616911555557)⟩⟩,⟨⟨27303052675481630638,27303052675481631877⟩,⟨(-8778647263137672164),(-8778647263137670928)⟩⟩,⟨⟨24113057887216830945,24113057887216832031⟩,⟨(-9506038281721734017),(-9506038281721732934)⟩⟩,⟨⟨21204866288385533126,21204866288385534095⟩,⟨(-9971845322718296767),(-9971845322718295798)⟩⟩,⟨⟨18564870956419668734,18564870956419669600⟩,⟨(-10220317962915288724),(-10220317962915287862)⟩⟩,⟨⟨16178148479123955458,16178148479123956223⟩,⟨(-10290176753928988891),(-10290176753928988126)⟩⟩,⟨⟨14028957483005011227,14028957483005011912⟩,⟨(-10215117637461859610),(-10215117637461858925)⟩⟩,⟨⟨12101149674481453014,12101149674481453621⟩,⟨(-10024296184731402682),(-10024296184731402072)⟩⟩,⟨⟨10378504177873033245,10378504177873033787⟩,⟨(-9742787583043095538),(-9742787583043094999)⟩⟩,⟨⟨8844995112969268064,8844995112969268543⟩,⟨(-9392019538717882001),(-9392019538717881525)⟩⟩,⟨⟨7485001503392563037,7485001503392563462⟩,⟨(-8990176312388248159),(-8990176312388247731)⟩⟩,⟨⟨6283467763003826964,6283467763003827352⟩,⟨(-8552572970248315927),(-8552572970248315543)⟩⟩,⟨⟨5226022185603010838,5226022185603011181⟩,⟨(-8091999642891654228),(-8091999642891653885)⟩⟩] +lemma kernel21_1_r4_10_eq : ∀ k : Fin 16, kernel21_1Expr 4 10 k = kernel21_1_r4_10 k := by decide +kernel +noncomputable def kernel21_1_r4_11 : Fin 16 → CBox := ![⟨⟨4299060074199849197,4299060074199849511⟩,⟨(-7619036150801036525),(-7619036150801036210)⟩⟩,⟨⟨3489797398343193424,3489797398343193704⟩,⟨(-7142337800237347209),(-7142337800237346930)⟩⟩,⟨⟨2786300167105612862,2786300167105613107⟩,⟨(-6668893491882607552),(-6668893491882607307)⟩⟩,⟨⟨2177494054941524838,2177494054941525060⟩,⟨(-6204257532495489619),(-6204257532495489396)⟩⟩,⟨⟨1653158219652431593,1653158219652431797⟩,⟨(-5752756711051838101),(-5752756711051837901)⟩⟩,⟨⟨1203906706560801903,1203906706560802087⟩,⟨(-5317674308013548731),(-5317674308013548545)⟩⟩,⟨⟨821160340034746862,821160340034747028⟩,⟨(-4901412760792616717),(-4901412760792616548)⟩⟩,⟨⟨497111561149414819,497111561149414965⟩,⟨(-4505636720144060276),(-4505636720144060133)⟩⟩,⟨⟨224684276276248447,224684276276248583⟩,⟨(-4131398209881419926),(-4131398209881419790)⟩⟩,⟨⟨(-2509566969279232),(-2509566969279108)⟩,⟨(-3779245553548025901),(-3779245553548025777)⟩⟩,⟨⟨(-190215265771434053),(-190215265771433940)⟩,⟨(-3449317663006263660),(-3449317663006263548)⟩⟩,⟨⟨(-343581365949441195),(-343581365949441083)⟩,⟨(-3141425200851487385),(-3141425200851487276)⟩⟩,⟨⟨(-467205469839146229),(-467205469839146139)⟩,⟨(-2855120035752771395),(-2855120035752771301)⟩⟩,⟨⟨(-565179132271009483),(-565179132271009392)⟩,⟨(-2589754311108491523),(-2589754311108491430)⟩⟩,⟨⟨(-641131297094203965),(-641131297094203892)⟩,⟨(-2344530345914221586),(-2344530345914221510)⟩⟩,⟨⟨(-698269868844396951),(-698269868844396873)⟩,⟨(-2118542484988071425),(-2118542484988071347)⟩⟩] +lemma kernel21_1_r4_11_eq : ∀ k : Fin 16, kernel21_1Expr 4 11 k = kernel21_1_r4_11 k := by decide +kernel +noncomputable def kernel21_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-739421133030791368),(-739421133030791302)⟩,⟨(-1910811915661362280),(-1910811915661362214)⟩⟩,⟨⟨(-767066836921008027),(-767066836921007960)⟩,⟨(-1720315371235469031),(-1720315371235468965)⟩⟩,⟨⟨(-783378823220913010),(-783378823220912944)⟩,⟨(-1546008549050978945),(-1546008549050978878)⟩⟩,⟨⟨(-790251174057963419),(-790251174057963353)⟩,⟨(-1386844983704986184),(-1386844983704986117)⟩⟩,⟨⟨(-789329874343137592),(-789329874343137538)⟩,⟨(-1241791034304057091),(-1241791034304057036)⟩⟩,⟨⟨(-782040043857652770),(-782040043857652716)⟩,⟨(-1109837568947197921),(-1109837568947197866)⟩⟩,⟨⟨(-769610818030430873),(-769610818030430828)⟩,⟨(-990008860006906036),(-990008860006905984)⟩⟩,⟨⟨(-753097979888722849),(-753097979888722802)⟩,⟨(-881369140185563092),(-881369140185563048)⟩⟩,⟨⟨(-733404461441382736),(-733404461441382695)⟩,⟨(-783027211626564360),(-783027211626564322)⟩⟩,⟨⟨(-711298842984902754),(-711298842984902709)⟩,⟨(-694139448328855176),(-694139448328855124)⟩⟩,⟨⟨(-687431984542183755),(-687431984542183713)⟩,⟨(-613911485464002302),(-613911485464002259)⟩⟩,⟨⟨(-662351925745707703),(-662351925745707660)⟩,⟨(-541598847599746146),(-541598847599746103)⟩⟩,⟨⟨(-636517189723732142),(-636517189723732110)⟩,⟨(-476506730941291536),(-476506730941291501)⟩⟩,⟨⟨(-610308623588183973),(-610308623588183941)⟩,⟨(-417989122147265079),(-417989122147265044)⟩⟩,⟨⟨(-584039903501288829),(-584039903501288792)⟩,⟨(-365447407695028443),(-365447407695028406)⟩⟩,⟨⟨(-557966826469372684),(-557966826469372653)⟩,⟨(-318328602799381414),(-318328602799381383)⟩⟩] +lemma kernel21_1_r4_12_eq : ∀ k : Fin 16, kernel21_1Expr 4 12 k = kernel21_1_r4_12 k := by decide +kernel +noncomputable def kernel21_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-532295504352315877),(-532295504352315846)⟩,⟨(-276123307180829067),(-276123307180829036)⟩⟩,⟨⟨(-507189568392703380),(-507189568392703349)⟩,⟨(-238363476201818728),(-238363476201818697)⟩⟩,⟨⟨(-482776485107425129),(-482776485107425098)⟩,⟨(-204620079728068377),(-204620079728068346)⟩⟩,⟨⟨(-459153076843259018),(-459153076843258987)⟩,⟨(-174500707234732628),(-174500707234732597)⟩⟩,⟨⟨(-436390332830683270),(-436390332830683239)⟩,⟨(-147647165893176222),(-147647165893176191)⟩⟩,⟨⟨(-414537589294406879),(-414537589294406848)⟩,⟨(-123733108395450582),(-123733108395450551)⟩⟩,⟨⟨(-393626150182173917),(-393626150182173886)⟩,⟨(-102461718874302822),(-102461718874302791)⟩⟩,⟨⟨(-373672413417510435),(-373672413417510410)⟩,⟨(-83563478252376677),(-83563478252376652)⟩⟩,⟨⟨(-354680561308925371),(-354680561308925347)⟩,⟨(-66794024521540736),(-66794024521540715)⟩⟩,⟨⟨(-336644867882694464),(-336644867882694433)⟩,⟨(-51932118647869321),(-51932118647869289)⟩⟩,⟨⟨(-319551670460503863),(-319551670460503831)⟩,⟨(-38777722873819482),(-38777722873819451)⟩⟩,⟨⟨(-303381047778202955),(-303381047778202924)⟩,⟨(-27150195017599913),(-27150195017599882)⟩⟩,⟨⟨(-288108242330941881),(-288108242330941850)⟩,⟨(-16886599837124277),(-16886599837124246)⟩⟩,⟨⟨(-273704860420203964),(-273704860420203939)⟩,⟨(-7840136532922114),(-7840136532922088)⟩⟩,⟨⟨(-260139879552423073),(-260139879552423042)⟩,⟨121320075631706,121320075631738⟩⟩,⟨⟨(-247380489376673306),(-247380489376673281)⟩,⟨7116568328496794,7116568328496819⟩⟩] +lemma kernel21_1_r4_13_eq : ∀ k : Fin 16, kernel21_1Expr 4 13 k = kernel21_1_r4_13 k := by decide +kernel +noncomputable def kernel21_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-235392789228044047),(-235392789228044016)⟩,⟨13252322934253946,13252322934253977⟩⟩,⟨⟨(-224142362540393053),(-224142362540393029)⟩,⟨18624357678721943,18624357678721964⟩⟩,⟨⟨(-213594745883448240),(-213594745883448221)⟩,⟨23318553082798973,23318553082798992⟩⟩,⟨⟨(-203715808141099294),(-203715808141099268)⟩,⟨27411854671727319,27411854671727344⟩⟩,⟨⟨(-194472053357146635),(-194472053357146611)⟩,⟨30973147595172560,30973147595172580⟩⟩,⟨⟨(-185830859009585144),(-185830859009585108)⟩,⟨34064053308423105,34064053308423138⟩⟩,⟨⟨(-177760659913603144),(-177760659913603114)⟩,⟨36739653913774617,36739653913774643⟩⟩,⟨⟨(-170231086577007828),(-170231086577007803)⟩,⟨39049149587822748,39049149587822773⟩⟩,⟨⟨(-163213065621186537),(-163213065621186511)⟩,⟨41036454301507326,41036454301507351⟩⟩,⟨⟨(-156678888818769385),(-156678888818769359)⟩,⟨42740734788896730,42740734788896755⟩⟩,⟨⟨(-150602256370011167),(-150602256370011142)⟩,⟨44196897448890909,44196897448890935⟩⟩,⟨⟨(-144958299229027005),(-144958299229026980)⟩,⟨45436027580110025,45436027580110050⟩⟩,⟨⟨(-139723584585147630),(-139723584585147599)⟩,⟨46485785060254041,46485785060254072⟩⟩,⟨⟨(-134876107991783189),(-134876107991783170)⟩,⟨47370760292667136,47370760292667155⟩⟩,⟨⟨(-130395275104433548),(-130395275104433529)⟩,⟨48112793958941485,48112793958941504⟩⟩,⟨⟨(-126261875531076168),(-126261875531076142)⟩,⟨48731263840308527,48731263840308552⟩⟩] +lemma kernel21_1_r4_14_eq : ∀ k : Fin 16, kernel21_1Expr 4 14 k = kernel21_1_r4_14 k := by decide +kernel +noncomputable def kernel21_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-122458050903324917),(-122458050903324893)⟩,⟨49243341704578573,49243341704578594⟩⟩,⟨⟨(-118967258937636388),(-118967258937636362)⟩,⟨49664223001069876,49664223001069901⟩⟩,⟨⟨(-115774234965448224),(-115774234965448192)⟩,⟨50007331864302575,50007331864302606⟩⟩,⟨⟨(-112864952163244320),(-112864952163244301)⟩,⟨50284503698735865,50284503698735884⟩⟩,⟨⟨(-110226581502635923),(-110226581502635899)⟩,⟨50506147401638910,50506147401638931⟩⟩,⟨⟨(-107847452261738744),(-107847452261738714)⟩,⟨50681389079150194,50681389079150221⟩⟩,⟨⟨(-105717013788099482),(-105717013788099462)⟩,⟨50818198921306096,50818198921306115⟩⟩,⟨⟨(-103825799076369678),(-103825799076369651)⟩,⟨50923502724741609,50923502724741639⟩⟩,⟨⟨(-102165390617485416),(-102165390617485395)⟩,⟨51003279386180399,51003279386180423⟩⟩,⟨⟨(-100728388887329719),(-100728388887329699)⟩,⟨51062645534935884,51062645534935903⟩⟩,⟨⟨(-99508383769123847),(-99508383769123828)⟩,⟨51105928327565804,51105928327565823⟩⟩,⟨⟨(-98499929142815258),(-98499929142815237)⟩,⟨51136727291634189,51136727291634213⟩⟩,⟨⟨(-97698520824468603),(-97698520824468577)⟩,⟨51157965977279801,51157965977279827⟩⟩,⟨⟨(-97100577997316730),(-97100577997316710)⟩,⟨51171934053989645,51171934053989665⟩⟩,⟨⟨(-96703428242077853),(-96703428242077827)⟩,⟨51180320374640053,51180320374640079⟩⟩,⟨⟨(-96505296245940672),(-96505296245940653)⟩,⟨51184237418500557,51184237418500576⟩⟩] +lemma kernel21_1_r4_15_eq : ∀ k : Fin 16, kernel21_1Expr 4 15 k = kernel21_1_r4_15 k := by decide +kernel +noncomputable def kernel21_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel21_1_r4_0,kernel21_1_r4_1,kernel21_1_r4_2,kernel21_1_r4_3,kernel21_1_r4_4,kernel21_1_r4_5,kernel21_1_r4_6,kernel21_1_r4_7,kernel21_1_r4_8,kernel21_1_r4_9,kernel21_1_r4_10,kernel21_1_r4_11,kernel21_1_r4_12,kernel21_1_r4_13,kernel21_1_r4_14,kernel21_1_r4_15] +lemma kernel21_1_r4_eq (i k : Fin 16) : kernel21_1Expr 4 i k = kernel21_1_r4 i k := by + fin_cases i + · exact kernel21_1_r4_0_eq k + · exact kernel21_1_r4_1_eq k + · exact kernel21_1_r4_2_eq k + · exact kernel21_1_r4_3_eq k + · exact kernel21_1_r4_4_eq k + · exact kernel21_1_r4_5_eq k + · exact kernel21_1_r4_6_eq k + · exact kernel21_1_r4_7_eq k + · exact kernel21_1_r4_8_eq k + · exact kernel21_1_r4_9_eq k + · exact kernel21_1_r4_10_eq k + · exact kernel21_1_r4_11_eq k + · exact kernel21_1_r4_12_eq k + · exact kernel21_1_r4_13_eq k + · exact kernel21_1_r4_14_eq k + · exact kernel21_1_r4_15_eq k +noncomputable def kernel21_1_r5_0 : Fin 16 → CBox := ![⟨⟨48691722835115470466869326002,48691722835115474165131101108⟩,⟨(-57234273847612000380559604485),(-57234273847611996682943620858)⟩⟩,⟨⟨48620622390040683126067953631,48620622390040686823094717857⟩,⟨(-57232012129036812101539044602),(-57232012129036808405156157290)⟩⟩,⟨⟨48478568097714204528565762751,48478568097714208223116879768⟩,⟨(-57227341814779020652168017980),(-57227341814779016958256954469)⟩⟩,⟨⟨48265853175846743116943187212,48265853175846746807779571057⟩,⟨(-57219970186114221294517752232),(-57219970186114217604315701267)⟩⟩,⟨⟨47982917500751605757198894060,47982917500751609443083635738⟩,⟨(-57209460748604832799368830199),(-57209460748604829114110820961)⟩⟩,⟨⟨47630347651952075781234963259,47630347651952079460934228456⟩,⟨(-57195236318260727501882491244),(-57195236318260723822800501348)⟩⟩,⟨⟨47208876946718539369028759936,47208876946718543041312307621⟩,⟨(-57176583112716179636119228712),(-57176583112716175964441671333)⟩⟩,⟨⟨46719385443575936720661423977,46719385443575940384303782136⟩,⟨(-57152655827093617888850385842),(-57152655827093614225800939582)⟩⟩,⟨⟨46162899889099745282073063955,46162899889099748935853566640⟩,⟨(-57122483669131632757434534145),(-57122483669131629104232111537)⟩⟩,⟨⟨45540593577935106965284536152,45540593577935110607989252857⟩,⟨(-57084977323061003594927600066),(-57084977323060999952784423637)⟩⟩,⟨⟨44853786091990425310024212114,44853786091990428940446446237⟩,⟨(-57038936806624332266466324384),(-57038936806624328636587434494)⟩⟩,⟨⟨44103942881231924792719933468,44103942881231928409970145184⟩,⟨(-56983060180561579155537387423),(-56983060180561575538810923179)⟩⟩,⟨⟨43292674645493471317888581975,43292674645493474920798717334⟩,⟨(-56915953064838359083604233800),(-56915953064838355481196724410)⟩⟩,⟨⟨42421736474266077178081800796,42421736474266080765495313027⟩,⟨(-56836138910893114382450428063),(-56836138910893110795516960842)⟩⟩,⟨⟨41493026699588572407860586901,41493026699588575978626162242⟩,⟨(-56742069974244171878544933414),(-56742069974244168308235432655)⟩⟩,⟨⟨40508585415963938542936343503,40508585415963942095917261786⟩,⟨(-56632138926953347965866105301),(-56632138926953344413315976238)⟩⟩] +lemma kernel21_1_r5_0_eq : ∀ k : Fin 16, kernel21_1Expr 5 0 k = kernel21_1_r5_0 k := by decide +kernel +noncomputable def kernel21_1_r5_1 : Fin 16 → CBox := ![⟨⟨39470592620707676860854510508,39470592620707680394918097974⟩,⟨(-56504691044718558870537665847),(-56504691044718555336878346106)⟩⟩,⟨⟨38381365928321617610898636840,38381365928321621124932278984⟩,⟨(-56358036898797342736985764207),(-56358036898797339223328715155)⟩⟩,⟨⟨37243357813397989801439100588,37243357813397993294332792250⟩,⟨(-56190465478583802212511256336),(-56190465478583798719965416766)⟩⟩,⟨⟨36059152338206077799480326820,36059152338206081270147961486⟩,⟨(-56000257666514419087103998430),(-56000257666514415616754498919)⟩⟩,⟨⟨34831461323501216666822130598,34831461323501220114177222508⟩,⟨(-55785699983107971020676888950),(-55785699983107967573609333103)⟩⟩,⟨⟨33563119924218827317527552051,33563119924218830740516250679⟩,⟨(-55545098516398708303036292849),(-55545098516398704880303745807)⟩⟩,⟨⟨32257081575561779616466316669,32257081575561783014031234477⟩,⟨(-55276792946849573878336244857),(-55276792946849570480995408378)⟩⟩,⟨⟨30916412279536022302794592866,30916412279536025673915269509⟩,⟨(-54979170576084677594962641206),(-54979170576084674224033391729)⟩⟩,⟨⟨29544284207206751825692549856,29544284207206755169339574126⟩,⟨(-54650680265509366526003500074),(-54650680265509363182514769085)⟩⟩,⟨⟨28143968597796189222447974561,28143968597796192537642495088⟩,⟨(-54289846189143926843596819705),(-54289846189143923528527084362)⟩⟩,⟨⟨26718827942176305623201700963,26718827942176308908950919759⟩,⟨(-53895281303834126579874999503),(-53895281303834123294216790954)⟩⟩,⟨⟨25272307445268993146944261292,25272307445268996402309230926⟩,⟨(-53465700439467485387857074771),(-53465700439467482132549181264)⟩⟩,⟨⟨23807925769287310073116046093,23807925769287313297136739769⟩,⟨(-52999932911964475175128268392),(-52999932911964471951130666644)⟩⟩,⟨⟨22329265067561706307736427962,22329265067561709499623031575⟩,⟨(-52496934562671056016863632324),(-52496934562671052824966194559)⟩⟩,⟨⟨20839960326814320818236426005,20839960326814323977312913895⟩,⟨(-51955799129390364255499192212),(-51955799129390361096378111673)⟩⟩,⟨⟨19343688044085533026130588204,19343688044085536151557242129⟩,⟨(-51375768856688407588431332534),(-51375768856688404462926601371)⟩⟩] +lemma kernel21_1_r5_1_eq : ∀ k : Fin 16, kernel21_1Expr 5 1 k = kernel21_1_r5_1 k := by decide +kernel +noncomputable def kernel21_1_r5_2 : Fin 16 → CBox := ![⟨⟨17844154272986933912970848249,17844154272986937003868211006⟩,⟨(-50756244256315811564338363776),(-50756244256315808473329820900)⟩⟩,⟨⟨16345082082455621093143803900,16345082082455624148732939842⟩,⟨(-50096792932621722208536760535),(-50096792932621719152803826644)⟩⟩,⟨⟨14850198479613944565042364143,14850198479613947584495782123⟩,⟨(-49397157392704962137633020393),(-49397157392704959118003776282)⟩⟩,⟨⟨13363220856591237933818647542,13363220856591240916407292621⟩,⟨(-48657261766750106482376251415),(-48657261766750103499580440305)⟩⟩,⟨⟨11887843029132542170750709873,11887843029132545115709969969⟩,⟨(-47877217370520864323386934015),(-47877217370520861378189954801)⟩⟩,⟨⟨10427720942396213860333179106,10427720942396216767164677707⟩,⟨(-47057327049307999133101023858),(-47057327049307996226002123618)⟩⟩,⟨⟨8986458126420793200381808887,8986458126420796068354520010⟩,⟨(-46198088250720995855496190227),(-46198088250720992987227368295)⟩⟩,⟨⟨7567590990217037748700154620,7567590990217040577208418098⟩,⟨(-45300194782527573973249197587),(-45300194782527571144417170608)⟩⟩,⟨⟨6174574049212783857866933385,6174574049212786646218642148⟩,⟨(-44364537221227482910249274150),(-44364537221227480121547291404)⟩⟩,⟨⟨4810765185750670473883296071,4810765185750673221637406079⟩,⟨(-43392201947130186087530670396),(-43392201947130183339401152569)⟩⟩,⟨⟨3479411046422837022054637618,3479411046422839728593905172⟩,⟨(-42384468792312601896959847735),(-42384468792312599190021336846)⟩⟩,⟨⟨2183632683141727664782698025,2183632683141730329637345093⟩,⟨(-41342807298875257958706118386),(-41342807298875255293429737133)⟩⟩,⟨⟨926411546920893955962009501,926411546920896578550379299⟩,⟨(-40268871596295636150773845126),(-40268871596295633527742660530)⟩⟩,⟨⟨(-289424055686132541894591343),(-289424055686129961953982046)⟩,⟨(-39164493918290008704496050427),(-39164493918290006124093001983)⟩⟩,⟨⟨(-1461211933715434169175228260),(-1461211933715431632388742138)⟩,⟨(-38031676791325895286784418475),(-38031676791325892749517379114)⟩⟩,⟨⟨(-2586468302075694791678876802),(-2586468302075692298365568863)⟩,⟨(-36872583938656199875330155751),(-36872583938656197381521844406)⟩⟩] +lemma kernel21_1_r5_2_eq : ∀ k : Fin 16, kernel21_1Expr 5 2 k = kernel21_1_r5_2 k := by decide +kernel +noncomputable def kernel21_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-3662899285132514489685126574),(-3662899285132512040305939115)⟩,⟨(-35689529955347907595484156346),(-35689529955347905145602167910)⟩⟩,⟨⟨(-4688411531515500591592659500),(-4688411531515498186368802772)⟩,⟨(-34484968821124288847145237995),(-34484968821124286441412102797)⟩⟩,⟨⟨(-5661121843043983300102996285),(-5661121843043980939414459714)⟩,⟨(-33261481328799468934547113060),(-33261481328799466573344155584)⟩⟩,⟨⟨(-6579365726816968564726069407),(-6579365726816966248737926819)⟩,⟨(-32021761516527604645878029406),(-32021761516527602329371649682)⟩⟩,⟨⟨(-7441704786796519814319458386),(-7441704786796517543367868918)⟩,⟨(-30768602201887284908835511700),(-30768602201887282637363198524)⟩⟩,⟨⟨(-8246932879573666796531766112),(-8246932879573664570679319244)⟩,⟨(-29504879724850458683885966381),(-29504879724850456457511615751)⟩⟩,⟨⟨(-8994080968369095942549396184),(-8994080968369093762043469680)⟩,⟨(-28233538014825225712333552872),(-28233538014825223531305841355)⟩⟩,⟨⟨(-9682420619599209247466561781),(-9682420619599207112311542909)⟩,⟨(-26957572104101860396285274161),(-26957572104101858260609855080)⟩⟩,⟨⟨(-10311466097429426413397577132),(-10311466097429424323803712853)⟩,⟨(-25680011216069600141758011213),(-25680011216069598051646379399)⟩⟩,⟨⟨(-10880975023525571171991610259),(-10880975023525569127851672286)⟩,⟨(-24403901561417371300379156483),(-24403901561417369255725285250)⟩⟩,⟨⟨(-11390947581573822812453513230),(-11390947581573820813291043252)⟩,⟨(-23132288979106973658542404154),(-23132288979106971658875058293)⟩⟩,⟨⟨(-11841624258932844433555619605),(-11841624258932842474821338701)⟩,⟨(-21868201561148881512108626469),(-21868201561148879552909367828)⟩⟩,⟨⟨(-12233482130862707364398977862),(-12233482130862705446334710452)⟩,⟨(-20614632401070989166768500283),(-20614632401070987248278168442)⟩⟩,⟨⟨(-12567229705992001428227817932),(-12567229705991999550742256783)⟩,⟨(-19374522605418323761446143499),(-19374522605418321883572365239)⟩⟩,⟨⟨(-12843800364880512083887473202),(-12843800364880510247136316329)⟩,⟨(-18150744705643559909364771080),(-18150744705643558072262122099)⟩⟩,⟨⟨(-13064344436551285262756259934),(-13064344436551283466607798937)⟩,⟨(-16946086604348878553041329917),(-16946086604348876756576910987)⟩⟩] +lemma kernel21_1_r5_3_eq : ∀ k : Fin 16, kernel21_1Expr 5 3 k = kernel21_1_r5_3 k := by decide +kernel +noncomputable def kernel21_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-13230219970544060934386071213),(-13230219970544059178977430637)⟩,⟨(-15763236185042595571042615807),(-15763236185042593815352312866)⟩⟩,⟨⟨(-13342982274225576483922621759),(-13342982274225574769012563492)⟩,⟨(-14604766708420843319135517124),(-14604766708420841603976794929)⟩⟩,⟨⟨(-13404372296629455550003354768),(-13404372296629453875631183458)⟩,⟨(-13473123110735462389206666530),(-13473123110735460714617494606)⟩⟩,⟨⟨(-13416303950844631012198774988),(-13416303950844629378095928474)⟩,⟨(-12370609311141859117296574774),(-12370609311141857483007012182)⟩⟩,⟨⟨(-13380850476791034151952133796),(-13380850476791032558134380586)⟩,⟨(-11299376625129407029222992954),(-11299376625129405435247400944)⟩⟩,⟨⟨(-13300229954990458680148727382),(-13300229954990457126246183053)⟩,⟨(-10261413370332151002923681767),(-10261413370332149448890737888)⟩⟩,⟨⟨(-13176790089548181477376537982),(-13176790089548179963313632958)⟩,⟨(-9258535739323447793409015367),(-9258535739323446279241694164)⟩⟩,⟨⟨(-13012992384911212800551749906),(-13012992384911211325930112756)⟩,⟨(-8292380001551604467994782805),(-8292380001551602993293240957)⟩⟩,⟨⟨(-12811395845982629843151720747),(-12811395845982628407847804603)⟩,⟨(-7364396083522033795953557971),(-7364396083522032360592548735)⟩⟩,⟨⟨(-12574640334786821049535618497),(-12574640334786819653037384002)⟩,⟨(-6475842562830929404846905336),(-6475842562830928008312867446)⟩⟩,⟨⟨(-12305429719054964329839755621),(-12305429719054962971901706873)⟩,⟨(-5627783097868234301043655017),(-5627783097868232943089637792)⟩⟩,⟨⟨(-12006514948810535240576851769),(-12006514948810533920655453542)⟩,⟨(-4821084301099883452030433830),(-4821084301099882132111455538)⟩⟩,⟨⟨(-11680677196277852809258524849),(-11680677196277851527164471225)⟩,⟨(-4056415049978528441823061845),(-4056415049978527159748378708)⟩⟩,⟨⟨(-11330711192229346029539626711),(-11330711192229344784543031768)⟩,⟨(-3334247215884729493927539267),(-3334247215884728248965852159)⟩⟩,⟨⟨(-10959408888265780963291239300),(-10959408888265779755059473997)⟩,⟨(-2654857778229923552100967009),(-2654857778229922343918254041)⟩⟩,⟨⟨(-10569543569543642944320872434),(-10569543569543641772255512018)⟩,⟨(-2018332278115383824754721450),(-2018332278115382652751200422)⟩⟩] +lemma kernel21_1_r5_4_eq : ∀ k : Fin 16, kernel21_1Expr 5 4 k = kernel21_1_r5_4 k := by decide +kernel +noncomputable def kernel21_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-10163854536198926127096413237),(-10163854536198924990937136943)⟩,⟨(-1424569553886626742557058031),(-1424569553886625606471078022)⟩⟩,⟨⟨(-9745032464257431857990464135),(-9745032464257430756966363823)⟩,⟨(-873287689688572670720023957),(-873287689688571569779394417)⟩⟩,⟨⟨(-9315705548274505992536511740),(-9315705548274504926020243544)⟩,⟨(-364031097839019717657918067),(-364031097839018651234046630)⟩⟩,⟨⟨(-8878426518431909035637298676),(-8878426518431908002968021166)⟩,⟨103821353391838289061003354,103821353391839321630152376⟩⟩,⟨⟨(-8435660614467986463931607138),(-8435660614467985464778309077)⟩,⟨531047263084335266356167298,531047263084336265402762422⟩⟩,⟨⟨(-7989774587770954205777265340),(-7989774587770953239362603897)⟩,⟨918570775387191509904136280,918570775387192476208601669⟩⟩,⟨⟨(-7543026791372820160440045564),(-7543026791372819226362853503)⟩,⟨1267451920534077368022342111,1267451920534078301987594170⟩⟩,⟨⟨(-7097558405597162402742879085),(-7097558405597161500278712767)⟩,⟨1578875332259412920679221891,1578875332259413823030438921⟩⟩,⟨⟨(-6655385834894242365034932602),(-6655385834894241493798837515)⟩,⟨1854138457573485103229679307,1854138457573485974352510051⟩⟩,⟨⟨(-6218394299098506648491304887),(-6218394299098505807166427183)⟩,⟨2094639376355719669407513680,2094639376355720510619441674⟩⟩,⟨⟨(-5788332630120981608723155165),(-5788332630120980796766889445)⟩,⟨2301864348378139796395249466,2301864348378140608239469147⟩⟩,⟨⟨(-5366809273092425270471400537),(-5366809273092424487156771547)⟩,⟨2477375204212121449253709447,2477375204212122232457725090⟩⟩,⟨⟨(-4955289479345682097340446169),(-4955289479345681342263258941)⟩,⟨2622796694051278049951497699,2622796694051278804920951881⟩⟩,⟨⟨(-4555093667502030046395498906),(-4555093667502029318763392588)⟩,⟨2739803904868578358446308872,2739803904868579085982924495⟩⟩,⟨⟨(-4167396918430337403411147780),(-4167396918430336702762330287)⟩,⟨2830109851598255659717695726,2830109851598256360282626856⟩⟩,⟨⟨(-3793229560091228193433952418),(-3793229560091227518891004903)⟩,⟨2895453342287435694478163826,2895453342287436368948177084⟩⟩] +lemma kernel21_1_r5_5_eq : ∀ k : Fin 16, kernel21_1Expr 5 5 k = kernel21_1_r5_5 k := by decide +kernel +noncomputable def kernel21_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-3433478789359221772896707696),(-3433478789359221124016993121)⟩,⟨2937587210504715413251127283,2937587210504716062068210162⟩⟩,⟨⟨(-3088891269917241826486796306),(-3088891269917241202459079418)⟩,⟨2958267000838518867098840004,2958267000838519491073573365⟩⟩,⟨⟨(-2760076638307666441215242709),(-2760076638307665841534479693)⟩,⟨2959240185189571976973184225,2959240185189572576609967986⟩⟩,⟨⟨(-2447511844253754940845843010),(-2447511844253754364759260687)⟩,⟨2942235978887063604451683816,2942235978887064180502646597⟩⟩,⟨⟨(-2151546246469975997012250798),(-2151546246469975444066119195)⟩,⟨2908955816567801081607955178,2908955816567801634526194992⟩⟩,⟨⟨(-1872407381378235212144661443),(-1872407381378234681551063949)⟩,⟨2861064538383620849644200229,2861064538383621380217012557⟩⟩,⟨⟨(-1610207319441944476151926807),(-1610207319441943967416202280)⟩,⟨2800182327575000695193336850,2800182327575001203914778289⟩⟩,⟨⟨(-1364949522208466080682991537),(-1364949522208465593058989592)⟩,⟨2727877430895611493080985706,2727877430895611980696619629⟩⟩,⟨⟨(-1136536112585175949211578778),(-1136536112585175481614710419)⟩,⟨2645659683915818352191349474,2645659683915818819785140875⟩⟩,⟨⟨(-924775471324020920103190650),(-924775471324020471600532094)⟩,⟨2554974853988579138858737274,2554974853988579587363052720⟩⟩,⟨⟨(-729390074100335625569682362),(-729390074100335195732905132)⟩,⟨2457199804736277761167824783,2457199804736278191010476659⟩⟩,⟨⟨(-550024485879097837575785510),(-550024485879097425745696160)⟩,⟨2353638477409746526044058600,2353638477409746937883750273⟩⟩,⟨⟨(-386253432391430650973600799),(-386253432391430256751152513)⟩,⟨2245518676468452911649159173,2245518676468453305884469194⟩⟩,⟨⟨(-237589872413734554583789950),(-237589872413734177288798981)⟩,⟨2133989639309466773833878667,2133989639309467151144552017⟩⟩,⟨⟨(-103492999062783526831186011),(-103492999062783166035089961)⟩,⟨2020120363296212517621322752,2020120363296212878435505371⟩⟩,⟨⟨16623896600724937771532395,16623896600725282726996918⟩,⟨1904898657157497570396057279,1904898657157497915371626564⟩⟩] +lemma kernel21_1_r5_6_eq : ∀ k : Fin 16, kernel21_1Expr 5 6 k = kernel21_1_r5_6 k := by decide +kernel +noncomputable def kernel21_1_r5_7 : Fin 16 → CBox := ![⟨⟨123385760826400180840854075,123385760826400510339531864⟩,⟨1789230878481608219136152921,1789230878481608548656588929⟩⟩,⟨⟨217448366546351037366023839,217448366546351352088250696⟩,⟨1673942314445520898364145868,1673942314445521213109054954⟩⟩,⟨⟨299491205951706746523516785,299491205951707046937544694⟩,⟨1559778159109342546244565101,1559778159109342846681585311⟩⟩,⟨⟨370210729013436934365803025,370210729013437221059999509⟩,⟨1447405037572997925194697291,1447405037572998211911996653⟩⟩,⟨⟨430313964260439245193047083,430313964260439518547543441⟩,⟨1337413025026782495245257342,1337413025026782768622778351⟩⟩,⟨⟨480512551707763218231115545,480512551707763478840720055⟩,⟨1230318107210184189565006581,1230318107210184450197399835⟩⟩,⟨⟨521517211496587300541309980,521517211496587548789801762⟩,⟨1126565027995397248614620952,1126565027995397496885523579⟩⟩,⟨⟨554032665640605613218058338,554032665640605849650149972⟩,⟨1026530469695859293529753418,1026530469695859529983757874⟩⟩,⟨⟨578753024338982369126215604,578753024338982594262560686⟩,⟨930526512221313391103475129,930526512221313616259464051⟩⟩,⟨⟨596357642674294724841845560,596357642674294939274666599⟩,⟨838804318308598562648084901,838804318308598777097860451⟩⟩,⟨⟨607507448216915875560066187,607507448216916079624296194⟩,⟨751557993695969970285455216,751557993695970174364139526⟩⟩,⟨⟨612841735148549138907788334,612841735148549333078994900⟩,⟨668928573218911884231570189,668928573218912078414919052⟩⟩,⟨⟨612975416031934216711642545,612975416031934401291854865⟩,⟨591008086325292129384865851,591008086325292313975090457⟩⟩,⟨⟨608496718317361134976996149,608496718317361310454495149⟩,⟨517843658374116661400972943,517843658374116836886532997⟩⟩,⟨⟨599965309107434235076069742,599965309107434401759426397⟩,⟨449441607231610397816270994,449441607231610564505909044⟩⟩,⟨⟨587910828609389167113600040,587910828609389325430153263⟩,⟨385771498048158397066076467,385771498048158555387297234⟩⟩] +lemma kernel21_1_r5_7_eq : ∀ k : Fin 16, kernel21_1Expr 5 7 k = kernel21_1_r5_7 k := by decide +kernel +noncomputable def kernel21_1_r5_8 : Fin 16 → CBox := ![⟨⟨572831810091463006088600803,572831810091463156319478008⟩,⟨326770122628752220907094663,326770122628752371141183813⟩⟩,⟨⟨555194962021601586956250691,555194962021601729605541698⟩,⟨272345373439472129988816807,272345373439472272640015014⟩⟩,⟨⟨535434786392001102959438376,535434786392001238294734558⟩,⟨222379985967902922678934427,222379985967903058014976394⟩⟩,⟨⟨513953506004742834010083809,513953506004742962402617881⟩,⟨176735126824781724838530659,176735126824781853230786340⟩⟩,⟨⟨491121272690217721211498493,491121272690217842901876664⟩,⟨135253808590504610841005027,135253808590504732530220697⟩⟩,⟨⟨467276628025041770020065094,467276628025041885372164978⟩,⟨97764115930995095255388416,97764115930995210605558072⟩⟩,⟨⟨442727188080153943180265355,442727188080154052458848950⟩,⟨64082230895474974827045305,64082230895475084103040227⟩⟩,⟨⟨417750524030476317814123532,417750524030476421352171598⟩,⟨34015248531645516229244803,34015248531645619764145993⟩⟩,⟨⟨392595211060646728747161136,392595211060646826747032015⟩,⟨7363776984667196660951876,7363776984667294657211487⟩⟩,⟨⟨367482018871397558949462069,367482018871397651728217907⟩,⟨(-16075680936720376414593192),(-16075680936720283639828688)⟩⟩,⟨⟨342605218192057644734698115,342605218192057732514442095⟩,⟨(-36508565157353248311966113),(-36508565157353160536515035)⟩⟩,⟨⟨318133979000340656684571610,318133979000340739742444955⟩,⟨(-54140312782878089597550100),(-54140312782878006544064224)⟩⟩,⟨⟨294213837605595232796476793,294213837605595311311701992⟩,⟨(-69174625590225357845251440),(-69174625590225279334435728)⟩⟩,⟨⟨270968211331671532042123195,270968211331671606289631494⟩,⟨(-81811944713841581384442090),(-81811944713841507141328307)⟩⟩,⟨⟨248499941207681565329506786,248499941207681635484117825⟩,⟨(-92248125091704688920047043),(-92248125091704618769781934)⟩⟩,⟨⟨226892844808272803500232027,226892844808272869801246656⟩,⟨(-100673300894393206530376961),(-100673300894393140233631888)⟩⟩] +lemma kernel21_1_r5_8_eq : ∀ k : Fin 16, kernel21_1Expr 5 8 k = kernel21_1_r5_8 k := by decide +kernel +noncomputable def kernel21_1_r5_9 : Fin 16 → CBox := ![⟨⟨206213263150871043951816006,206213263150871106547971151⟩,⟨(-107270932059964203846967390),(-107270932059964141254980356)⟩⟩,⟨⟨186511587329384286501550994,186511587329384345624014850⟩,⟨(-112217021186926285858861700),(-112217021186926226740433076)⟩⟩,⟨⟨167823752318396143817142429,167823752318396199614454667⟩,⟨(-115679489384730433507702855),(-115679489384730377713882084)⟩⟩,⟨⟨150172687097918983504464446,150172687097919036174634158⟩,⟨(-117817699231673857670430195),(-117817699231673805003250004)⟩⟩,⟨⟨133569711908078107396441294,133569711908078157067121536⟩,⟨(-118782112728236932314260306),(-118782112728236882646107362)⟩⟩,⟨⟨118015875030160463176804044,118015875030160510038090031⟩,⟨(-118714072042947368528942883),(-118714072042947321669761128)⟩⟩,⟨⟨103503222992483436884753393,103503222992483481061158701⟩,⟨(-117745690910535507715726179),(-117745690910535463541038989)⟩⟩,⟨⟨90015999506326506542244552,90015999506326548199207928⟩,⟨(-115999844740747509360342739),(-115999844740747467704747061)⟩⟩,⟨⟨77531769741007664977260864,77531769741007704219470003⟩,⟨(-113590247813057589842126580),(-113590247813057550600968325)⟩⟩,⟨⟨66022467742692026059380967,66022467742692063046902769⟩,⟨(-110621606350281046083726256),(-110621606350281009096970582)⟩⟩,⟨⟨55455365885458053713746267,55455365885458088549950635⟩,⟨(-107189836765868018617832901),(-107189836765867983782139970)⟩⟩,⟨⟨45793966214242324159277445,45793966214242356980852652⟩,⟨(-103382338949306561191239373),(-103382338949306528369949127)⟩⟩,⟨⟨36998814398016227462214023,36998814398016258357033946⟩,⟨(-99278315076325673109485754),(-99278315076325642214750745)⟩⟩,⟨⟨29028237759941359745710976,29028237759941388843781558⟩,⟨(-94949125091232457278462556),(-94949125091232428180301295)⟩⟩,⟨⟨21839009492660591126700861,21839009492660618512794489⟩,⟨(-90458670694636773414703141),(-90458670694636746028366067)⟩⟩,⟨⟨15386941705787541877889567,15386941705787567792110390⟩,⟨(-85863800369102796891563049),(-85863800369102770976969102)⟩⟩] +lemma kernel21_1_r5_9_eq : ∀ k : Fin 16, kernel21_1Expr 5 9 k = kernel21_1_r5_9 k := by decide +kernel +noncomputable def kernel21_1_r5_10 : Fin 16 → CBox := ![⟨⟨9627410394456052937470370,9627410394456077448551106⟩,⟨(-81214728677249631269294024),(-81214728677249606757729920)⟩⟩,⟨⟨4515815768605104537234806,4515815768605127737838730⟩,⟨(-76555463762087101462041595),(-76555463762087078260861180)⟩⟩,⟨⟨7981649166582102986225,7981649166604047632650⟩,⟨(-71924237659750136063068401),(-71924237659750114117768302)⟩⟩,⟨⟨(-3939502173472270200705516),(-3939502173472249433961532)⟩,⟨(-67353934693338058029056494),(-67353934693338037261595802)⟩⟩,⟨⟨(-7368990604192077094039583),(-7368990604192057459735823)⟩,⟨(-62872513847501799493924290),(-62872513847501779858853976)⟩⟩,⟨⟨(-10321542860051348460585006),(-10321542860051329883227916)⟩,⟨(-58503421622097958789085018),(-58503421622097940210943540)⟩⟩,⟨⟨(-12836726967351073854421660),(-12836726967351056288902781)⟩,⟨(-54265992426036483528915310),(-54265992426036465962611113)⟩⟩,⟨⟨(-14952465114083616202977059),(-14952465114083599584802741)⟩,⟨(-50175834096750186340403791),(-50175834096750169721448752)⟩⟩,⟨⟨(-16704915921664069116522714),(-16704915921664053409402510)⟩,⟨(-46245196614755118058319349),(-46245196614755102350428166)⟩⟩,⟨⟨(-18128389823344715618006624),(-18128389823344700758692276)⟩,⟨(-42483322525592799068573396),(-42483322525592784208501745)⟩⟩,⟨⟨(-19255293888852737843512735),(-19255293888852723795113366)⟩,⟨(-38896777982796134979097854),(-38896777982796120929958521)⟩⟩,⟨⟨(-20116102609791507404077322),(-20116102609791494113747396)⟩,⟨(-35489763685764347378428055),(-35489763685764334087378266)⟩⟩,⟨⟨(-20739351352882965744990300),(-20739351352882953182486800)⟩,⟨(-32264405306460374809979883),(-32264405306460362246781262)⟩⟩,⟨⟨(-21151649393352056145196222),(-21151649393352044259509989)⟩,⟨(-29221023279992104517686105),(-29221023279992092631391199)⟩⟩,⟨⟨(-21377709654295740388143489),(-21377709654295729149233364)⟩,⟨(-26358382078104181091767721),(-26358382078104169852328811)⟩⟩,⟨⟨(-21440392495853575872318400),(-21440392495853565237054704)⟩,⟨(-23673919293374655734106416),(-23673919293374645098387362)⟩⟩] +lemma kernel21_1_r5_10_eq : ∀ k : Fin 16, kernel21_1Expr 5 10 k = kernel21_1_r5_10 k := by decide +kernel +noncomputable def kernel21_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-21360761116994098914958968),(-21360761116994088859689155)⟩,⟨(-21163955037682129799207850),(-21163955037682119743550167)⟩⟩,⟨⟨(-21158146349802062941825347),(-21158146349802053424111628)⟩,⟨(-18823882303639460695651334),(-18823882303639451177611393)⟩⟩,⟨⟨(-20850218838787357978223643),(-20850218838787348974088151)⟩,⟨(-16648339054630854345064308),(-16648339054630845340658865)⟩⟩,⟨⟨(-20453066803844960814321734),(-20453066803844952288378529)⟩,⟨(-14631362900337053219938127),(-14631362900337044693776092)⟩⟩,⟨⟨(-19981277783372877511300239),(-19981277783372869444485306)⟩,⟨(-12766529282686398362073335),(-12766529282686390295085922)⟩⟩,⟨⟨(-19448022942356549901495016),(-19448022942356542260531680)⟩,⟨(-11047074144489276792076396),(-11047074144489269150982412)⟩⟩,⟨⟨(-18865142707935273377630369),(-18865142707935266142574956)⟩,⟨(-9466002081993001207456226),(-9466002081992993972307804)⟩⟩,⟨⟨(-18243232661355035567286505),(-18243232661355028710259972)⟩,⟨(-8016180995532307703102744),(-8016180995532300846016940)⟩⟩,⟨⟨(-17591728769821257862387745),(-17591728769821251369038119)⟩,⟨(-6690424251531220291044274),(-6690424251531213797665483)⟩⟩,⟨⟨(-16918991184363024644982296),(-16918991184363018488042906)⟩,⟨(-5481561356388151746226107),(-5481561356388145589284319)⟩⟩,⟨⟨(-16232385960375938477377278),(-16232385960375932641700507)⟩,⟨(-4382498120158984027053744),(-4382498120158978191398236)⟩⟩,⟨⟨(-15538364176162372807119729),(-15538364176162367269307731)⟩,⟨(-3386267257204496670257537),(-3386267257204491132487638)⟩⟩,⟨⟨(-14842538031816749429781482),(-14842538031816744178394612)⟩,⟨(-2486070333697931168597358),(-2486070333697925917270769)⟩⟩,⟨⟨(-14149753606607434462327080),(-14149753606607429476011340)⟩,⟨(-1675311929551063003002778),(-1675311929551058016763152)⟩⟩,⟨⟨(-13464160038076858709076769),(-13464160038076853976239546)⟩,⟨(-947626836216452069451443),(-947626836216447336703663)⟩⟩,⟨⟨(-12789274960979976513146381),(-12789274960979972016140588)⟩,⟨(-296901063115297543759789),(-296901063115293046854865)⟩⟩] +lemma kernel21_1_r5_11_eq : ∀ k : Fin 16, kernel21_1Expr 5 11 k = kernel21_1_r5_11 k := by decide +kernel +noncomputable def kernel21_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-12128046109522808874819943),(-12128046109522804605294603)⟩,⟨282712624861790542718669,282712624861794812133539⟩⟩,⟨⟨(-11482909042797228467898635),(-11482909042797224408027433)⟩,⟨796783967351046085006712,796783967351050144759375⟩⟩,⟨⟨(-10855841001505004876896929),(-10855841001505001016092605)⟩,⟨1250598645559243436072287,1250598645559247296751478⟩⟩,⟨⟨(-10248410944700159431149986),(-10248410944700155755479571)⟩,⟨1649155326214943133007629,1649155326214946808548134⟩⟩,⟨⟨(-9661825849026638019445061),(-9661825849026634522290395)⟩,⟨1997165791400906534473574,1997165791400910031498275⟩⟩,⟨⟨(-9096973380447799997986798),(-9096973380447796665693840)⟩,⟨2299057680732270657836152,2299057680732273989999628⟩⟩,⟨⟨(-8554461070394178246791638),(-8554461070394175072535969)⟩,⟨2558979417876601762407922,2558979417876604936535121⟩⟩,⟨⟨(-8034652145208689038413234),(-8034652145208686010870987)⟩,⟨2780806936727138836330150,2780806936727141863745341⟩⟩,⟨⟨(-7537698170325035700125371),(-7537698170325032814522661)⟩,⟨2968151863453356178495698,2968151863453359063973184⟩⟩,⟨⟨(-7063568679321959725278698),(-7063568679321956970314814)⟩,⟨3124370849039448954840679,3124370849039451709681427⟩⟩,⟨⟨(-6612077963362914251044326),(-6612077963362911621452230)⟩,⟨3252575782711274116432567,3252575782711276745903895⟩⟩,⟨⟨(-6182909199029185009023435),(-6182909199029182495858163)⟩,⟨3355644649821448135888843,3355644649821450648935902⟩⟩,⟨⟨(-5775636092617322359141922),(-5775636092617319958621315)⟩,⟨3436232828325289148580836,3436232828325291548985985⟩⟩,⟨⟨(-5389742216993353410268827),(-5389742216993351113491808)⟩,⟨3496784645983855098139420,3496784645983857394803825⟩⟩,⟨⟨(-5024638213433251650759195),(-5024638213433249453135030)⟩,⟨3539545045947420714438368,3539545045947422911955521⟩⟩,⟨⟨(-4679677025851644197439086),(-4679677025851642090976720)⟩,⟨3566571231497097249925530,3566571231497099356290437⟩⟩] +lemma kernel21_1_r5_12_eq : ∀ k : Fin 16, kernel21_1Expr 5 12 k = kernel21_1_r5_12 k := by decide +kernel +noncomputable def kernel21_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-4354167328713833869937861),(-4354167328713831852230828)⟩,⟨3579744181563663286879056,3579744181563665304497576⟩⟩,⟨⟨(-4047385302991842050790626),(-4047385302991840114439609)⟩,⟨3580779947322530160024678,3580779947322532096295477⟩⟩,⟨⟨(-3758584906984134001702710),(-3758584906984132143708555)⟩,⟨3571240656811659547734840,3571240656811661405656518⟩⟩,⟨⟨(-3487006780862775996405327),(-3487006780862774211061396)⟩,⟨3552545169269603655984850,3552545169269605441263479⟩⟩,⟨⟨(-3231885915606028375833624),(-3231885915606026661172825)⟩,⟨3525979333880228523545374,3525979333880230238147555⟩⟩,⟨⟨(-2992458208659310678916838),(-2992458208659309029101138)⟩,⟨3492705818975562970693692,3492705818975564620456961⟩⟩,⟨⟨(-2767966020361294715554640),(-2767966020361293128267386)⟩,⟨3453773487623036262991601,3453773487623037850232151⟩⟩,⟨⟨(-2557662836972675584048912),(-2557662836972674054650537)⟩,⟨3410126304039035612734133,3410126304039037142091106⟩⟩,⟨⟨(-2360817138132999697572160),(-2360817138132998224828958)⟩,⟨3362611762553392255871717,3362611762553393728578437⟩⟩,⟨⟨(-2176715558809829216150109),(-2176715558809827795075176)⟩,⟨3311988837019577993530614,3311988837019579414573604⟩⟩,⟨⟨(-2004665428344394398763789),(-2004665428344393027492506)⟩,⟨3258935453737191974797554,3258935453737193346041084⟩⟩,⟨⟨(-1843996762076261781150666),(-1843996762076260455834033)⟩,⟨3204055495234043913661663,3204055495234045238954416⟩⟩,⟨⟨(-1694063774273228775294257),(-1694063774273227494964686)⟩,⟨3147885345744989341622265,3147885345744990621931526⟩⟩,⟨⟨(-1554245974719223498832418),(-1554245974719222259505910)⟩,⟨3090899992016599271982006,3090899992016600511291495⟩⟩,⟨⟨(-1423948905332173102604434),(-1423948905332171902976366)⟩,⟨3033518695246464947941430,3033518695246466147555510⟩⟩,⟨⟨(-1302604567598732953211932),(-1302604567598731790158601)⟩,⟨2976110251612026235734052,2976110251612027398776186⟩⟩] +lemma kernel21_1_r5_13_eq : ∀ k : Fin 16, kernel21_1Expr 5 13 k = kernel21_1_r5_13 k := by decide +kernel +noncomputable def kernel21_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-1189671586421087677729480),(-1189671586421086550772637)⟩,⟨2918997860027902282302740,2918997860027903409250953⟩⟩,⟨⟨(-1084635151165904537846094),(-1084635151165903443429203)⟩,⟨2862463616557738170801159,2862463616557739265211778⟩⟩,⟨⟨(-987006770276501634615359),(-987006770276500571758624)⟩,⟨2806752655355122321955658,2806752655355123384808289⟩⟩,⟨⟨(-896323871743128710504079),(-896323871743127676604509)⟩,⟨2752076956170697927160749,2752076956170698961058203⟩⟩,⟨⟨(-812149278007543832539241),(-812149278007542827201593)⟩,⟨2698618838386038754566942,2698618838386039759904290⟩⟩,⟨⟨(-734070580489845320252801),(-734070580489844340623027)⟩,⟨2646534161260747203265226,2646534161260748182896373⟩⟩,⟨⟨(-661699435849770180918452),(-661699435849769226262310)⟩,⟨2595955249644222062438151,2595955249644223017097195⟩⟩,⟨⟨(-594670803312754878836983),(-594670803312753946955429)⟩,⟨2546993563839782382953179,2546993563839783314839034⟩⟩,⟨⟨(-532642139884056716332713),(-532642139884055807145732)⟩,⟨2499742131644335603897168,2499742131644336513089722⟩⟩,⟨⟨(-475292568023264484089641),(-475292568023263594997616)⟩,⟨2454277759845789850516600,2454277759845790739615372⟩⟩,⟨⟨(-422322028337960988504692),(-422322028337960118958310)⟩,⟨2410663041663767090680810,2410663041663767960234998⟩⟩,⟨⟨(-373450428060972524125820),(-373450428060971672240659)⟩,⟨2368948175784633519979749,2368948175784634371873690⟩⟩,⟨⟨(-328416794482996092222980),(-328416794482995257930116)⟩,⟨2329172611784423940535449,2329172611784424774837967⟩⟩,⟨⟨(-286978441104603712508104),(-286978441104602893637453)⟩,⟨2291366535865431038081668,2291366535865431856962782⟩⟩,⟨⟨(-248910153032661214372469),(-248910153032660410511961)⟩,⟨2255552209964401845511070,2255552209964402649382764⟩⟩,⟨⟨(-214003397060906632334028),(-214003397060905841840208)⟩,⟨2221745176430839193614686,2221745176430839984120354⟩⟩] +lemma kernel21_1_r5_14_eq : ∀ k : Fin 16, kernel21_1Expr 5 14 k = kernel21_1_r5_14 k := by decide +kernel +noncomputable def kernel21_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-182065560928547073364879),(-182065560928546296421640)⟩,⟨2189955339629548621258365,2189955339629549398214042⟩⟩,⟨⟨(-152919225430899399212410),(-152919225430898633722959)⟩,⟨2160187934997511446179275,2160187934997512211681704⟩⟩,⟨⟨(-126401472349873922358919),(-126401472349873168009244)⟩,⟨2132444395285312495293937,2132444395285313249657071⟩⟩,⟨⟨(-102363230567929455326463),(-102363230567928710655090)⟩,⟨2106723122940488352718139,2106723122940489097403411⟩⟩,⟨⟨(-80668662216327536999390),(-80668662216326802114770)⟩,⟨2083020176846098181593802,2083020176846098916492697⟩⟩,⟨⟨(-61194590277232097373453),(-61194590277231370495321)⟩,⟨2061329880913528331756894,2061329880913529058649649⟩⟩,⟨⟨(-43829968700379326040082),(-43829968700378606920819)⟩,⟨2041645361344285811282947,2041645361344286530417134⟩⟩,⟨⟨(-28475395800369535641495),(-28475395800368822950953)⟩,⟨2023959018720971093267389,2023959018720971805973128⟩⟩,⟨⟨(-15042671462494492352616),(-15042671462493786298711)⟩,⟨2008262940461894517101149,2008262940461895223170463⟩⟩,⟨⟨(-3454398496442382461230),(-3454398496441681201717)⟩,⟨1994549258575631719161598,1994549258575632420436718⟩⟩,⟨⟨6356371668157071678629,6356371668157768333409⟩,⟨1982810457079565141358362,1982810457079565838028906⟩⟩,⟨⟨14446448858410134928456,14446448858410828201044⟩,⟨1973039632898199156290532,1973039632898199849579018⟩⟩,⟨⟨20862769597147629021409,20862769597148318703257⟩,⟨1965230713530592920997966,1965230713530593610695808⟩⟩,⟨⟨25642618143265673812001,25642618143266361487308⟩,⟨1959378634269258588104805,1959378634269259275796188⟩⟩,⟨⟨28813803198893776441823,28813803198894462287482⟩,⟨1955479477262796471917269,1955479477262797157779049⟩⟩,⟨⟨30394790357016676451568,30394790357017361640865⟩,⟨1953530574238731794288902,1953530574238732479494344⟩⟩] +lemma kernel21_1_r5_15_eq : ∀ k : Fin 16, kernel21_1Expr 5 15 k = kernel21_1_r5_15 k := by decide +kernel +noncomputable def kernel21_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel21_1_r5_0,kernel21_1_r5_1,kernel21_1_r5_2,kernel21_1_r5_3,kernel21_1_r5_4,kernel21_1_r5_5,kernel21_1_r5_6,kernel21_1_r5_7,kernel21_1_r5_8,kernel21_1_r5_9,kernel21_1_r5_10,kernel21_1_r5_11,kernel21_1_r5_12,kernel21_1_r5_13,kernel21_1_r5_14,kernel21_1_r5_15] +lemma kernel21_1_r5_eq (i k : Fin 16) : kernel21_1Expr 5 i k = kernel21_1_r5 i k := by + fin_cases i + · exact kernel21_1_r5_0_eq k + · exact kernel21_1_r5_1_eq k + · exact kernel21_1_r5_2_eq k + · exact kernel21_1_r5_3_eq k + · exact kernel21_1_r5_4_eq k + · exact kernel21_1_r5_5_eq k + · exact kernel21_1_r5_6_eq k + · exact kernel21_1_r5_7_eq k + · exact kernel21_1_r5_8_eq k + · exact kernel21_1_r5_9_eq k + · exact kernel21_1_r5_10_eq k + · exact kernel21_1_r5_11_eq k + · exact kernel21_1_r5_12_eq k + · exact kernel21_1_r5_13_eq k + · exact kernel21_1_r5_14_eq k + · exact kernel21_1_r5_15_eq k +noncomputable def kernel21_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel21_1_r0,kernel21_1_r1,kernel21_1_r2,kernel21_1_r3,kernel21_1_r4,kernel21_1_r5] +lemma kernel21_1_eq (j : Fin 6) (i k : Fin 16) : kernel21_1Expr j i k = kernel21_1 j i k := by + fin_cases j + · exact kernel21_1_r0_eq i k + · exact kernel21_1_r1_eq i k + · exact kernel21_1_r2_eq i k + · exact kernel21_1_r3_eq i k + · exact kernel21_1_r4_eq i k + · exact kernel21_1_r5_eq i k +lemma kernel21_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel21_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(21:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel21_1_eq] + unfold kernel21_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans21_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel24_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans24 j i k) +noncomputable def kernel24_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_0_eq : ∀ k : Fin 16, kernel24_0Expr 0 0 k = kernel24_0_r0_0 k := by decide +kernel +noncomputable def kernel24_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_1_eq : ∀ k : Fin 16, kernel24_0Expr 0 1 k = kernel24_0_r0_1 k := by decide +kernel +noncomputable def kernel24_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_2_eq : ∀ k : Fin 16, kernel24_0Expr 0 2 k = kernel24_0_r0_2 k := by decide +kernel +noncomputable def kernel24_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_3_eq : ∀ k : Fin 16, kernel24_0Expr 0 3 k = kernel24_0_r0_3 k := by decide +kernel +noncomputable def kernel24_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_4_eq : ∀ k : Fin 16, kernel24_0Expr 0 4 k = kernel24_0_r0_4 k := by decide +kernel +noncomputable def kernel24_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_5_eq : ∀ k : Fin 16, kernel24_0Expr 0 5 k = kernel24_0_r0_5 k := by decide +kernel +noncomputable def kernel24_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_6_eq : ∀ k : Fin 16, kernel24_0Expr 0 6 k = kernel24_0_r0_6 k := by decide +kernel +noncomputable def kernel24_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_7_eq : ∀ k : Fin 16, kernel24_0Expr 0 7 k = kernel24_0_r0_7 k := by decide +kernel +noncomputable def kernel24_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_8_eq : ∀ k : Fin 16, kernel24_0Expr 0 8 k = kernel24_0_r0_8 k := by decide +kernel +noncomputable def kernel24_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_9_eq : ∀ k : Fin 16, kernel24_0Expr 0 9 k = kernel24_0_r0_9 k := by decide +kernel +noncomputable def kernel24_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_10_eq : ∀ k : Fin 16, kernel24_0Expr 0 10 k = kernel24_0_r0_10 k := by decide +kernel +noncomputable def kernel24_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r0_11_eq : ∀ k : Fin 16, kernel24_0Expr 0 11 k = kernel24_0_r0_11 k := by decide +kernel +noncomputable def kernel24_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r0_12_eq : ∀ k : Fin 16, kernel24_0Expr 0 12 k = kernel24_0_r0_12 k := by decide +kernel +noncomputable def kernel24_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r0_13_eq : ∀ k : Fin 16, kernel24_0Expr 0 13 k = kernel24_0_r0_13 k := by decide +kernel +noncomputable def kernel24_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r0_14_eq : ∀ k : Fin 16, kernel24_0Expr 0 14 k = kernel24_0_r0_14 k := by decide +kernel +noncomputable def kernel24_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r0_15_eq : ∀ k : Fin 16, kernel24_0Expr 0 15 k = kernel24_0_r0_15 k := by decide +kernel +noncomputable def kernel24_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel24_0_r0_0,kernel24_0_r0_1,kernel24_0_r0_2,kernel24_0_r0_3,kernel24_0_r0_4,kernel24_0_r0_5,kernel24_0_r0_6,kernel24_0_r0_7,kernel24_0_r0_8,kernel24_0_r0_9,kernel24_0_r0_10,kernel24_0_r0_11,kernel24_0_r0_12,kernel24_0_r0_13,kernel24_0_r0_14,kernel24_0_r0_15] +lemma kernel24_0_r0_eq (i k : Fin 16) : kernel24_0Expr 0 i k = kernel24_0_r0 i k := by + fin_cases i + · exact kernel24_0_r0_0_eq k + · exact kernel24_0_r0_1_eq k + · exact kernel24_0_r0_2_eq k + · exact kernel24_0_r0_3_eq k + · exact kernel24_0_r0_4_eq k + · exact kernel24_0_r0_5_eq k + · exact kernel24_0_r0_6_eq k + · exact kernel24_0_r0_7_eq k + · exact kernel24_0_r0_8_eq k + · exact kernel24_0_r0_9_eq k + · exact kernel24_0_r0_10_eq k + · exact kernel24_0_r0_11_eq k + · exact kernel24_0_r0_12_eq k + · exact kernel24_0_r0_13_eq k + · exact kernel24_0_r0_14_eq k + · exact kernel24_0_r0_15_eq k +noncomputable def kernel24_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_0_eq : ∀ k : Fin 16, kernel24_0Expr 1 0 k = kernel24_0_r1_0 k := by decide +kernel +noncomputable def kernel24_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_1_eq : ∀ k : Fin 16, kernel24_0Expr 1 1 k = kernel24_0_r1_1 k := by decide +kernel +noncomputable def kernel24_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_2_eq : ∀ k : Fin 16, kernel24_0Expr 1 2 k = kernel24_0_r1_2 k := by decide +kernel +noncomputable def kernel24_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_3_eq : ∀ k : Fin 16, kernel24_0Expr 1 3 k = kernel24_0_r1_3 k := by decide +kernel +noncomputable def kernel24_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_4_eq : ∀ k : Fin 16, kernel24_0Expr 1 4 k = kernel24_0_r1_4 k := by decide +kernel +noncomputable def kernel24_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_5_eq : ∀ k : Fin 16, kernel24_0Expr 1 5 k = kernel24_0_r1_5 k := by decide +kernel +noncomputable def kernel24_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_6_eq : ∀ k : Fin 16, kernel24_0Expr 1 6 k = kernel24_0_r1_6 k := by decide +kernel +noncomputable def kernel24_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_7_eq : ∀ k : Fin 16, kernel24_0Expr 1 7 k = kernel24_0_r1_7 k := by decide +kernel +noncomputable def kernel24_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_8_eq : ∀ k : Fin 16, kernel24_0Expr 1 8 k = kernel24_0_r1_8 k := by decide +kernel +noncomputable def kernel24_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_9_eq : ∀ k : Fin 16, kernel24_0Expr 1 9 k = kernel24_0_r1_9 k := by decide +kernel +noncomputable def kernel24_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_10_eq : ∀ k : Fin 16, kernel24_0Expr 1 10 k = kernel24_0_r1_10 k := by decide +kernel +noncomputable def kernel24_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_11_eq : ∀ k : Fin 16, kernel24_0Expr 1 11 k = kernel24_0_r1_11 k := by decide +kernel +noncomputable def kernel24_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_12_eq : ∀ k : Fin 16, kernel24_0Expr 1 12 k = kernel24_0_r1_12 k := by decide +kernel +noncomputable def kernel24_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_13_eq : ∀ k : Fin 16, kernel24_0Expr 1 13 k = kernel24_0_r1_13 k := by decide +kernel +noncomputable def kernel24_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_14_eq : ∀ k : Fin 16, kernel24_0Expr 1 14 k = kernel24_0_r1_14 k := by decide +kernel +noncomputable def kernel24_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r1_15_eq : ∀ k : Fin 16, kernel24_0Expr 1 15 k = kernel24_0_r1_15 k := by decide +kernel +noncomputable def kernel24_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel24_0_r1_0,kernel24_0_r1_1,kernel24_0_r1_2,kernel24_0_r1_3,kernel24_0_r1_4,kernel24_0_r1_5,kernel24_0_r1_6,kernel24_0_r1_7,kernel24_0_r1_8,kernel24_0_r1_9,kernel24_0_r1_10,kernel24_0_r1_11,kernel24_0_r1_12,kernel24_0_r1_13,kernel24_0_r1_14,kernel24_0_r1_15] +lemma kernel24_0_r1_eq (i k : Fin 16) : kernel24_0Expr 1 i k = kernel24_0_r1 i k := by + fin_cases i + · exact kernel24_0_r1_0_eq k + · exact kernel24_0_r1_1_eq k + · exact kernel24_0_r1_2_eq k + · exact kernel24_0_r1_3_eq k + · exact kernel24_0_r1_4_eq k + · exact kernel24_0_r1_5_eq k + · exact kernel24_0_r1_6_eq k + · exact kernel24_0_r1_7_eq k + · exact kernel24_0_r1_8_eq k + · exact kernel24_0_r1_9_eq k + · exact kernel24_0_r1_10_eq k + · exact kernel24_0_r1_11_eq k + · exact kernel24_0_r1_12_eq k + · exact kernel24_0_r1_13_eq k + · exact kernel24_0_r1_14_eq k + · exact kernel24_0_r1_15_eq k +noncomputable def kernel24_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-2)⟩,⟨(-6),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩] +lemma kernel24_0_r2_0_eq : ∀ k : Fin 16, kernel24_0Expr 2 0 k = kernel24_0_r2_0 k := by decide +kernel +noncomputable def kernel24_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-5),(-2)⟩,⟨(-5),(-1)⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),(-1)⟩,⟨(-3),0⟩⟩,⟨⟨(-4),0⟩,⟨(-3),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩] +lemma kernel24_0_r2_1_eq : ∀ k : Fin 16, kernel24_0Expr 2 1 k = kernel24_0_r2_1 k := by decide +kernel +noncomputable def kernel24_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩] +lemma kernel24_0_r2_2_eq : ∀ k : Fin 16, kernel24_0Expr 2 2 k = kernel24_0_r2_2 k := by decide +kernel +noncomputable def kernel24_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩] +lemma kernel24_0_r2_3_eq : ∀ k : Fin 16, kernel24_0Expr 2 3 k = kernel24_0_r2_3 k := by decide +kernel +noncomputable def kernel24_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r2_4_eq : ∀ k : Fin 16, kernel24_0Expr 2 4 k = kernel24_0_r2_4 k := by decide +kernel +noncomputable def kernel24_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r2_5_eq : ∀ k : Fin 16, kernel24_0Expr 2 5 k = kernel24_0_r2_5 k := by decide +kernel +noncomputable def kernel24_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r2_6_eq : ∀ k : Fin 16, kernel24_0Expr 2 6 k = kernel24_0_r2_6 k := by decide +kernel +noncomputable def kernel24_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r2_7_eq : ∀ k : Fin 16, kernel24_0Expr 2 7 k = kernel24_0_r2_7 k := by decide +kernel +noncomputable def kernel24_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r2_8_eq : ∀ k : Fin 16, kernel24_0Expr 2 8 k = kernel24_0_r2_8 k := by decide +kernel +noncomputable def kernel24_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r2_9_eq : ∀ k : Fin 16, kernel24_0Expr 2 9 k = kernel24_0_r2_9 k := by decide +kernel +noncomputable def kernel24_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel24_0_r2_10_eq : ∀ k : Fin 16, kernel24_0Expr 2 10 k = kernel24_0_r2_10 k := by decide +kernel +noncomputable def kernel24_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r2_11_eq : ∀ k : Fin 16, kernel24_0Expr 2 11 k = kernel24_0_r2_11 k := by decide +kernel +noncomputable def kernel24_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r2_12_eq : ∀ k : Fin 16, kernel24_0Expr 2 12 k = kernel24_0_r2_12 k := by decide +kernel +noncomputable def kernel24_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r2_13_eq : ∀ k : Fin 16, kernel24_0Expr 2 13 k = kernel24_0_r2_13 k := by decide +kernel +noncomputable def kernel24_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r2_14_eq : ∀ k : Fin 16, kernel24_0Expr 2 14 k = kernel24_0_r2_14 k := by decide +kernel +noncomputable def kernel24_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel24_0_r2_15_eq : ∀ k : Fin 16, kernel24_0Expr 2 15 k = kernel24_0_r2_15 k := by decide +kernel +noncomputable def kernel24_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel24_0_r2_0,kernel24_0_r2_1,kernel24_0_r2_2,kernel24_0_r2_3,kernel24_0_r2_4,kernel24_0_r2_5,kernel24_0_r2_6,kernel24_0_r2_7,kernel24_0_r2_8,kernel24_0_r2_9,kernel24_0_r2_10,kernel24_0_r2_11,kernel24_0_r2_12,kernel24_0_r2_13,kernel24_0_r2_14,kernel24_0_r2_15] +lemma kernel24_0_r2_eq (i k : Fin 16) : kernel24_0Expr 2 i k = kernel24_0_r2 i k := by + fin_cases i + · exact kernel24_0_r2_0_eq k + · exact kernel24_0_r2_1_eq k + · exact kernel24_0_r2_2_eq k + · exact kernel24_0_r2_3_eq k + · exact kernel24_0_r2_4_eq k + · exact kernel24_0_r2_5_eq k + · exact kernel24_0_r2_6_eq k + · exact kernel24_0_r2_7_eq k + · exact kernel24_0_r2_8_eq k + · exact kernel24_0_r2_9_eq k + · exact kernel24_0_r2_10_eq k + · exact kernel24_0_r2_11_eq k + · exact kernel24_0_r2_12_eq k + · exact kernel24_0_r2_13_eq k + · exact kernel24_0_r2_14_eq k + · exact kernel24_0_r2_15_eq k +noncomputable def kernel24_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-236904307576393),(-236904307576388)⟩,⟨(-25267469908998),(-25267469908993)⟩⟩,⟨⟨(-236496540065906),(-236496540065903)⟩,⟨(-24987083248663),(-24987083248660)⟩⟩,⟨⟨(-235682421525805),(-235682421525800)⟩,⟨(-24429093027609),(-24429093027605)⟩⟩,⟨⟨(-234464785872493),(-234464785872490)⟩,⟨(-23599032215392),(-23599032215389)⟩⟩,⟨⟨(-232847886113737),(-232847886113734)⟩,⟨(-22505117624512),(-22505117624509)⟩⟩,⟨⟨(-230837396206946),(-230837396206941)⟩,⟨(-21158151945774),(-21158151945769)⟩⟩,⟨⟨(-228440412392852),(-228440412392849)⟩,⟨(-19571395122973),(-19571395122970)⟩⟩,⟨⟨(-225665453073443),(-225665453073440)⟩,⟨(-17760406746176),(-17760406746173)⟩⟩,⟨⟨(-222522456130321),(-222522456130317)⟩,⟨(-15742861525076),(-15742861525072)⟩⟩,⟨⟨(-219022772444747),(-219022772444744)⟩,⟨(-13538340261354),(-13538340261351)⟩⟩,⟨⟨(-215179154288213),(-215179154288209)⟩,⟨(-11168099066615),(-11168099066611)⟩⟩,⟨⟨(-211005737206586),(-211005737206582)⟩,⟨(-8654819865760),(-8654819865756)⟩⟩,⟨⟨(-206518014024249),(-206518014024246)⟩,⟨(-6022345480189),(-6022345480186)⟩⟩,⟨⟨(-201732799648042),(-201732799648039)⟩,⟨(-3295402796611),(-3295402796608)⟩⟩,⟨⟨(-196668185454179),(-196668185454174)⟩,⟨(-499317691918),(-499317691914)⟩⟩,⟨⟨(-191343482192625),(-191343482192621)⟩,⟨2340274501029,2340274501033⟩⟩] +lemma kernel24_0_r3_0_eq : ∀ k : Fin 16, kernel24_0Expr 3 0 k = kernel24_0_r3_0 k := by decide +kernel +noncomputable def kernel24_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-185779150539450),(-185779150539445)⟩,⟨5197719140479,5197719140484⟩⟩,⟨⟨(-179996718663850),(-179996718663846)⟩,⟨8047629183274,8047629183278⟩⟩,⟨⟨(-174018686446974),(-174018686446971)⟩,⟨10865165050619,10865165050622⟩⟩,⟨⟨(-167868416287415),(-167868416287411)⟩,⟨13626303757522,13626303757526⟩⟩,⟨⟨(-161570010745433),(-161570010745428)⟩,⟨16308093775448,16308093775451⟩⟩,⟨⟨(-155148177606108),(-155148177606104)⟩,⟨18888892317209,18888892317213⟩⟩,⟨⟨(-148628083271657),(-148628083271653)⟩,⟨21348582005561,21348582005565⟩⟩,⟨⟨(-142035195715925),(-142035195715922)⟩,⟨23668764208631,23668764208634⟩⟩,⟨⟨(-135395118540474),(-135395118540469)⟩,⟨25832926691824,25832926691829⟩⟩,⟨⟨(-128733417952818),(-128733417952814)⟩,⟨27826583641535,27826583641539⟩⟩,⟨⟨(-122075444735129),(-122075444735126)⟩,⟨29637386554085,29637386554088⟩⟩,⟨⟨(-115446153478602),(-115446153478596)⟩,⟨31255204946786,31255204946791⟩⟩,⟨⟨(-108869921518352),(-108869921518349)⟩,⟨32672176328206,32672176328209⟩⟩,⟨⟨(-102370370111095),(-102370370111092)⟩,⟨33882725353281,33882725353284⟩⟩,⟨⟨(-95970190449109),(-95970190449106)⟩,⟨34883552576580,34883552576583⟩⟩,⟨⟨(-89690977097039),(-89690977097036)⟩,⟨35673593694444,35673593694447⟩⟩] +lemma kernel24_0_r3_1_eq : ∀ k : Fin 16, kernel24_0Expr 3 1 k = kernel24_0_r3_1 k := by decide +kernel +noncomputable def kernel24_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-83553071372169),(-83553071372166)⟩,⟨36253950624799,36253950624802⟩⟩,⟨⟨(-77575417064957),(-77575417064954)⟩,⟨36627796203110,36627796203113⟩⟩,⟨⟨(-71775430717417),(-71775430717413)⟩,⟨36800254665811,36800254665814⟩⟩,⟨⟨(-66168888446391),(-66168888446386)⟩,⟨36778260440823,36778260440829⟩⟩,⟨⟨(-60769831022422),(-60769831022419)⟩,⟨36570398061793,36570398061796⟩⟩,⟨⟨(-55590488599461),(-55590488599456)⟩,⟨36186726262653,36186726262658⟩⟩,⟨⟨(-50641226143806),(-50641226143803)⟩,⟨35638589487848,35638589487851⟩⟩,⟨⟨(-45930510241091),(-45930510241088)⟩,⟨34938420167901,34938420167904⟩⟩,⟨⟨(-41464897576749),(-41464897576745)⟩,⟨34099535158725,34099535158729⟩⟩,⟨⟨(-37249044997919),(-37249044997915)⟩,⟨33135929726084,33135929726087⟩⟩,⟨⟨(-33285740682295),(-33285740682290)⟩,⟨32062072375620,32062072375624⟩⟩,⟨⟨(-29575955571367),(-29575955571363)⟩,⟨30892703687001,30892703687006⟩⟩,⟨⟨(-26118913880492),(-26118913880488)⟩,⟨29642642112440,29642642112444⟩⟩,⟨⟨(-22912181183964),(-22912181183961)⟩,⟨28326599450956,28326599450959⟩⟩,⟨⟨(-19951768296928),(-19951768296924)⟩,⟨26959008417142,26959008417146⟩⟩,⟨⟨(-17232248943117),(-17232248943114)⟩,⟨25553864394559,25553864394562⟩⟩] +lemma kernel24_0_r3_2_eq : ∀ k : Fin 16, kernel24_0Expr 3 2 k = kernel24_0_r3_2 k := by decide +kernel +noncomputable def kernel24_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-14746889012603),(-14746889012599)⟩,⟨24124583107755,24124583107759⟩⟩,⟨⟨(-12487785080009),(-12487785080005)⟩,⟨22683875572088,22683875572092⟩⟩,⟨⟨(-10446009772685),(-10446009772681)⟩,⟨21243641296004,21243641296009⟩⟩,⟨⟨(-8611761550230),(-8611761550226)⟩,⟨19814880325318,19814880325322⟩⟩,⟨⟨(-6974516480398),(-6974516480393)⟩,⟨18407624341821,18407624341826⟩⟩,⟨⟨(-5523179669142),(-5523179669138)⟩,⟨17030886667395,17030886667398⟩⟩,⟨⟨(-4246234120762),(-4246234120759)⟩,⟨15692630687126,15692630687129⟩⟩,⟨⟨(-3131884962849),(-3131884962845)⟩,⟨14399755897061,14399755897064⟩⟩,⟨⟨(-2168197164505),(-2168197164500)⟩,⟨13158100509620,13158100509625⟩⟩,⟨⟨(-1343225098741),(-1343225098738)⟩,⟨11972459316562,11972459316565⟩⟩,⟨⟨(-645132544249),(-645132544246)⟩,⟨10846615318649,10846615318652⟩⟩,⟨⟨(-62301981044),(-62301981040)⟩,⟨9783383484709,9783383484712⟩⟩,⟨⟨416567698271,416567698274⟩,⟨8784664900935,8784664900938⟩⟩,⟨⟨802375671546,802375671549⟩,⟨7851509513536,7851509513539⟩⟩,⟨⟨1105546211210,1105546211214⟩,⟨6984185652402,6984185652406⟩⟩,⟨⟨1335968344260,1335968344263⟩,⟨6182254547603,6182254547606⟩⟩] +lemma kernel24_0_r3_3_eq : ∀ k : Fin 16, kernel24_0Expr 3 3 k = kernel24_0_r3_3 k := by decide +kernel +noncomputable def kernel24_0_r3_4 : Fin 16 → CBox := ![⟨⟨1502948007314,1502948007319⟩,⟨5444648110640,5444648110643⟩⟩,⟨⟨1615172340993,1615172340996⟩,⟨4769748344411,4769748344414⟩⟩,⟨⟨1680685577317,1680685577321⟩,⟨4155466864816,4155466864820⟩⟩,⟨⟨1706875810215,1706875810219⟩,⟨3599323157950,3599323157954⟩⟩,⟨⟨1700471804172,1700471804176⟩,⟨3098520354593,3098520354597⟩⟩,⟨⟨1667548890701,1667548890704⟩,⟨2650017472957,2650017472960⟩⟩,⟨⟨1613542926270,1613542926273⟩,⟨2250597256259,2250597256262⟩⟩,⟨⟨1543271238094,1543271238098⟩,⟨1896928908979,1896928908983⟩⟩,⟨⟨1460959464104,1460959464108⟩,⟨1585625210021,1585625210026⟩⟩,⟨⟨1370273198470,1370273198473⟩,⟨1313293648640,1313293648643⟩⟩,⟨⟨1274353381682,1274353381686⟩,⟨1076581386499,1076581386502⟩⟩,⟨⟨1175854421499,1175854421502⟩,⟨872213993874,872213993877⟩⟩,⟨⟨1076984094823,1076984094827⟩,⟨697028037502,697028037506⟩⟩,⟨⟨979544357663,979544357667⟩,⟨547997710702,547997710705⟩⟩,⟨⟨884972277322,884972277326⟩,⟨422255791858,422255791862⟩⟩,⟨⟨794380394722,794380394726⟩,⟨317109295198,317109295201⟩⟩] +lemma kernel24_0_r3_4_eq : ∀ k : Fin 16, kernel24_0Expr 3 4 k = kernel24_0_r3_4 k := by decide +kernel +noncomputable def kernel24_0_r3_5 : Fin 16 → CBox := ![⟨⟨708595922266,708595922269⟩,⟨230050237881,230050237884⟩⟩,⟨⟨628198281105,628198281109⟩,⟨158761990616,158761990620⟩⟩,⟨⟨553554578540,553554578545⟩,⟨101121706188,101121706192⟩⟩,⟨⟨484852719510,484852719513⟩,⟨55199332815,55199332818⟩⟩,⟨⟨422131933737,422131933740⟩,⟨19253718747,19253718750⟩⟩,⟨⟨365310580926,365310580929⟩,⟨(-8273697383),(-8273697379)⟩⟩,⟨⟨314211169078,314211169083⟩,⟨(-28767137433),(-28767137429)⟩⟩,⟨⟨268582585083,268582585086⟩,⟨(-43446231912),(-43446231909)⟩⟩,⟨⟨228119591678,228119591681⟩,⟨(-53376856654),(-53376856651)⟩⟩,⟨⟨192479690697,192479690700⟩,⟨(-59482688464),(-59482688461)⟩⟩,⟨⟨161297489305,161297489308⟩,⟨(-62557152130),(-62557152127)⟩⟩,⟨⟨134196734138,134196734142⟩,⟨(-63275474278),(-63275474273)⟩⟩,⟨⟨110800198483,110800198486⟩,⟨(-62206602501),(-62206602498)⟩⟩,⟨⟨90737620490,90737620494⟩,⟨(-59824790110),(-59824790106)⟩⟩,⟨⟨73651896808,73651896812⟩,⟨(-56520686530),(-56520686526)⟩⟩,⟨⟨59203736743,59203736746⟩,⟨(-52611810570),(-52611810566)⟩⟩] +lemma kernel24_0_r3_5_eq : ∀ k : Fin 16, kernel24_0Expr 3 5 k = kernel24_0_r3_5 k := by decide +kernel +noncomputable def kernel24_0_r3_6 : Fin 16 → CBox := ![⟨⟨47074978006,47074978010⟩,⟨(-48352317481),(-48352317477)⟩⟩,⟨⟨36970757184,36970757188⟩,⟨(-43942001059),(-43942001056)⟩⟩,⟨⟨28620717054,28620717058⟩,⟨(-39534498503),(-39534498500)⟩⟩,⟨⟨21779419627,21779419630⟩,⟨(-35244688406),(-35244688402)⟩⟩,⟨⟨16226119000,16226119003⟩,⟨(-31155291217),(-31155291213)⟩⟩,⟨⟨11764032380,11764032384⟩,⟨(-27322696840),(-27322696836)⟩⟩,⟨⟨8219231619,8219231623⟩,⟨(-23782056058),(-23782056054)⟩⟩,⟨⟨5439261644,5439261648⟩,⟨(-20551681393),(-20551681389)⟩⟩,⟨⟨3291576809,3291576812⟩,⟨(-17636809201),(-17636809198)⟩⟩,⟨⟨1661871545,1661871549⟩,⟨(-15032778614),(-15032778609)⟩⟩,⟨⟨452368164,452368169⟩,⟨(-12727684650),(-12727684646)⟩⟩,⟨⟨(-419887725),(-419887721)⟩,⟨(-10704562888),(-10704562884)⟩⟩,⟨⟨(-1024684811),(-1024684808)⟩,⟨(-8943161677),(-8943161674)⟩⟩,⟨⟨(-1420227078),(-1420227073)⟩,⟨(-7421355490),(-7421355486)⟩⟩,⟨⟨(-1654617055),(-1654617051)⟩,⟨(-6116249724),(-6116249720)⟩⟩,⟨⟨(-1767227391),(-1767227387)⟩,⟨(-5005023502),(-5005023498)⟩⟩] +lemma kernel24_0_r3_6_eq : ∀ k : Fin 16, kernel24_0Expr 3 6 k = kernel24_0_r3_6 k := by decide +kernel +noncomputable def kernel24_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-1789952766),(-1789952762)⟩,⟨(-4065552844),(-4065552840)⟩⟩,⟨⟨(-1748339094),(-1748339091)⟩,⟨(-3276852281),(-3276852278)⟩⟩,⟨⟨(-1662590788),(-1662590785)⟩,⟨(-2619368671),(-2619368668)⟩⟩,⟨⟨(-1548459912),(-1548459909)⟩,⟨(-2075156724),(-2075156721)⟩⟩,⟨⟨(-1418023174),(-1418023170)⟩,⟨(-1627961734),(-1627961730)⟩⟩,⟨⟨(-1280354309),(-1280354306)⟩,⟨(-1263231237),(-1263231234)⟩⟩,⟨⟨(-1142100337),(-1142100334)⟩,⟨(-968073849),(-968073845)⟩⟩,⟨⟨(-1007970699),(-1007970693)⟩,⟨(-731180386),(-731180381)⟩⟩,⟨⟨(-881148417),(-881148414)⟩,⟨(-542719624),(-542719621)⟩⟩,⟨⟨(-763632295),(-763632291)⟩,⟨(-394218539),(-394218534)⟩⟩,⟨⟨(-656518743),(-656518739)⟩,⟨(-278434790),(-278434787)⟩⟩,⟨⟨(-560231405),(-560231400)⟩,⟨(-189227397),(-189227391)⟩⟩,⟨⟨(-474706030),(-474706027)⟩,⟨(-121429996),(-121429993)⟩⟩,⟨⟨(-399537440),(-399537437)⟩,⟨(-70729883),(-70729880)⟩⟩,⟨⟨(-334094671),(-334094668)⟩,⟨(-33554896),(-33554892)⟩⟩,⟨⟨(-277609729),(-277609726)⟩,⟨(-6969526),(-6969523)⟩⟩] +lemma kernel24_0_r3_7_eq : ∀ k : Fin 16, kernel24_0Expr 3 7 k = kernel24_0_r3_7 k := by decide +kernel +noncomputable def kernel24_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-229244674),(-229244671)⟩,⟨11419136,11419140⟩⟩,⟨⟨(-188141124),(-188141121)⟩,⟨23545433,23545436⟩⟩,⟨⟨(-153455685),(-153455682)⟩,⟨30959320,30959324⟩⟩,⟨⟨(-124384244),(-124384241)⟩,⟨34891178,34891181⟩⟩,⟨⟨(-100177612),(-100177608)⟩,⟨36307859,36307863⟩⟩,⟨⟨(-80150548),(-80150543)⟩,⟨35960693,35960698⟩⟩,⟨⟨(-63685840),(-63685837)⟩,⟨34426254,34426258⟩⟩,⟨⟨(-50234787),(-50234783)⟩,⟨32140662,32140665⟩⟩,⟨⟨(-39315128),(-39315123)⟩,⟨29428206,29428210⟩⟩,⟨⟨(-30507305),(-30507301)⟩,⟨26525024,26525028⟩⟩,⟨⟨(-23449659),(-23449656)⟩,⟨23598522,23598525⟩⟩,⟨⟨(-17833079),(-17833076)⟩,⟨20763171,20763174⟩⟩,⟨⟨(-13395445),(-13395442)⟩,⟨18093228,18093231⟩⟩,⟨⟨(-9916136),(-9916133)⟩,⟨15632896,15632899⟩⟩,⟨⟨(-7210782),(-7210779)⟩,⟨13404355,13404358⟩⟩,⟨⟨(-5126357),(-5126352)⟩,⟨11414034,11414038⟩⟩] +lemma kernel24_0_r3_8_eq : ∀ k : Fin 16, kernel24_0Expr 3 8 k = kernel24_0_r3_8 k := by decide +kernel +noncomputable def kernel24_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-3536692),(-3536689)⟩,⟨9657465,9657468⟩⟩,⟨⟨(-2338453),(-2338450)⟩,⟨8122971,8122974⟩⟩,⟨⟨(-1447551),(-1447546)⟩,⟨6794449,6794453⟩⟩,⟨⟨(-796007),(-796002)⟩,⟨5653403,5653407⟩⟩,⟨⟨(-329233),(-329228)⟩,⟨4680421,4680426⟩⟩,⟨⟨(-3689),(-3685)⟩,⟨3856200,3856205⟩⟩,⟨⟨215103,215107⟩,⟨3162233,3162238⟩⟩,⟨⟨354245,354249⟩,⟨2581246,2581250⟩⟩,⟨⟨434870,434873⟩,⟨2097440,2097444⟩⟩,⟨⟨473315,473320⟩,⟨1696600,1696605⟩⟩,⟨⟨482090,482093⟩,⟨1366116,1366119⟩⟩,⟨⟨470669,470673⟩,⟨1094914,1094917⟩⟩,⟨⟨446142,446146⟩,⟨873377,873381⟩⟩,⟨⟨413738,413741⟩,⟨693226,693229⟩⟩,⟨⟨377239,377244⟩,⟨547380,547384⟩⟩,⟨⟨339333,339336⟩,⟨429833,429837⟩⟩] +lemma kernel24_0_r3_9_eq : ∀ k : Fin 16, kernel24_0Expr 3 9 k = kernel24_0_r3_9 k := by decide +kernel +noncomputable def kernel24_0_r3_10 : Fin 16 → CBox := ![⟨⟨301857,301860⟩,⟨335519,335523⟩⟩,⟨⟨266030,266034⟩,⟨260193,260198⟩⟩,⟨⟨232599,232603⟩,⟨200318,200321⟩⟩,⟨⟨201979,201983⟩,⟨152956,152960⟩⟩,⟨⟨174341,174345⟩,⟨115688,115691⟩⟩,⟨⟨149688,149692⟩,⟨86523,86528⟩⟩,⟨⟨127918,127921⟩,⟨63838,63841⟩⟩,⟨⟨108849,108852⟩,⟨46308,46312⟩⟩,⟨⟨92270,92274⟩,⟨32863,32866⟩⟩,⟨⟨77943,77946⟩,⟨22634,22637⟩⟩,⟨⟨65632,65635⟩,⟨14930,14933⟩⟩,⟨⟨55104,55107⟩,⟨9193,9197⟩⟩,⟨⟨46139,46144⟩,⟨4980,4985⟩⟩,⟨⟨38537,38541⟩,⟨1941,1945⟩⟩,⟨⟨32112,32116⟩,⟨(-201),(-196)⟩⟩,⟨⟨26701,26704⟩,⟨(-1664),(-1660)⟩⟩] +lemma kernel24_0_r3_10_eq : ∀ k : Fin 16, kernel24_0Expr 3 10 k = kernel24_0_r3_10 k := by decide +kernel +noncomputable def kernel24_0_r3_11 : Fin 16 → CBox := ![⟨⟨22154,22158⟩,⟨(-2617),(-2614)⟩⟩,⟨⟨18348,18351⟩,⟨(-3193),(-3190)⟩⟩,⟨⟨15165,15170⟩,⟨(-3495),(-3491)⟩⟩,⟨⟨12513,12517⟩,⟨(-3598),(-3594)⟩⟩,⟨⟨10307,10312⟩,⟨(-3564),(-3559)⟩⟩,⟨⟨8477,8481⟩,⟨(-3436),(-3433)⟩⟩,⟨⟨6959,6962⟩,⟨(-3248),(-3245)⟩⟩,⟨⟨5704,5707⟩,⟨(-3025),(-3022)⟩⟩,⟨⟨4667,4672⟩,⟨(-2785),(-2780)⟩⟩,⟨⟨3814,3818⟩,⟨(-2540),(-2536)⟩⟩,⟨⟨3111,3114⟩,⟨(-2299),(-2296)⟩⟩,⟨⟨2533,2537⟩,⟨(-2068),(-2065)⟩⟩,⟨⟨2058,2061⟩,⟨(-1851),(-1847)⟩⟩,⟨⟨1669,1673⟩,⟨(-1650),(-1647)⟩⟩,⟨⟨1351,1354⟩,⟨(-1465),(-1462)⟩⟩,⟨⟨1091,1094⟩,⟨(-1298),(-1294)⟩⟩] +lemma kernel24_0_r3_11_eq : ∀ k : Fin 16, kernel24_0Expr 3 11 k = kernel24_0_r3_11 k := by decide +kernel +noncomputable def kernel24_0_r3_12 : Fin 16 → CBox := ![⟨⟨879,883⟩,⟨(-1147),(-1143)⟩⟩,⟨⟨706,709⟩,⟨(-1011),(-1008)⟩⟩,⟨⟨566,569⟩,⟨(-890),(-887)⟩⟩,⟨⟨450,453⟩,⟨(-782),(-779)⟩⟩,⟨⟨358,361⟩,⟨(-686),(-683)⟩⟩,⟨⟨283,286⟩,⟨(-603),(-599)⟩⟩,⟨⟨223,226⟩,⟨(-529),(-525)⟩⟩,⟨⟨173,176⟩,⟨(-464),(-461)⟩⟩,⟨⟨133,137⟩,⟨(-405),(-402)⟩⟩,⟨⟨100,105⟩,⟨(-357),(-352)⟩⟩,⟨⟨76,79⟩,⟨(-313),(-309)⟩⟩,⟨⟨55,60⟩,⟨(-274),(-269)⟩⟩,⟨⟨40,43⟩,⟨(-241),(-238)⟩⟩,⟨⟨27,31⟩,⟨(-211),(-208)⟩⟩,⟨⟨16,21⟩,⟨(-186),(-182)⟩⟩,⟨⟨8,12⟩,⟨(-163),(-160)⟩⟩] +lemma kernel24_0_r3_12_eq : ∀ k : Fin 16, kernel24_0Expr 3 12 k = kernel24_0_r3_12 k := by decide +kernel +noncomputable def kernel24_0_r3_13 : Fin 16 → CBox := ![⟨⟨3,7⟩,⟨(-144),(-140)⟩⟩,⟨⟨(-1),2⟩,⟨(-127),(-123)⟩⟩,⟨⟨(-6),(-2)⟩,⟨(-112),(-109)⟩⟩,⟨⟨(-7),(-4)⟩,⟨(-100),(-96)⟩⟩,⟨⟨(-10),(-5)⟩,⟨(-89),(-84)⟩⟩,⟨⟨(-11),(-8)⟩,⟨(-79),(-75)⟩⟩,⟨⟨(-13),(-9)⟩,⟨(-69),(-66)⟩⟩,⟨⟨(-14),(-10)⟩,⟨(-62),(-58)⟩⟩,⟨⟨(-13),(-10)⟩,⟨(-55),(-52)⟩⟩,⟨⟨(-14),(-9)⟩,⟨(-50),(-45)⟩⟩,⟨⟨(-13),(-10)⟩,⟨(-44),(-40)⟩⟩,⟨⟨(-12),(-9)⟩,⟨(-40),(-36)⟩⟩,⟨⟨(-13),(-10)⟩,⟨(-35),(-31)⟩⟩,⟨⟨(-13),(-10)⟩,⟨(-32),(-29)⟩⟩,⟨⟨(-13),(-8)⟩,⟨(-30),(-25)⟩⟩,⟨⟨(-12),(-8)⟩,⟨(-27),(-24)⟩⟩] +lemma kernel24_0_r3_13_eq : ∀ k : Fin 16, kernel24_0Expr 3 13 k = kernel24_0_r3_13 k := by decide +kernel +noncomputable def kernel24_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-12),(-8)⟩,⟨(-25),(-21)⟩⟩,⟨⟨(-12),(-7)⟩,⟨(-23),(-19)⟩⟩,⟨⟨(-11),(-8)⟩,⟨(-21),(-17)⟩⟩,⟨⟨(-10),(-6)⟩,⟨(-19),(-16)⟩⟩,⟨⟨(-10),(-7)⟩,⟨(-17),(-13)⟩⟩,⟨⟨(-9),(-6)⟩,⟨(-15),(-12)⟩⟩,⟨⟨(-9),(-6)⟩,⟨(-15),(-12)⟩⟩,⟨⟨(-9),(-5)⟩,⟨(-14),(-9)⟩⟩,⟨⟨(-9),(-6)⟩,⟨(-13),(-9)⟩⟩,⟨⟨(-8),(-5)⟩,⟨(-11),(-8)⟩⟩,⟨⟨(-8),(-5)⟩,⟨(-11),(-8)⟩⟩,⟨⟨(-7),(-4)⟩,⟨(-10),(-7)⟩⟩,⟨⟨(-7),(-4)⟩,⟨(-10),(-7)⟩⟩,⟨⟨(-7),(-4)⟩,⟨(-10),(-7)⟩⟩,⟨⟨(-7),(-3)⟩,⟨(-10),(-5)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-9),(-5)⟩⟩] +lemma kernel24_0_r3_14_eq : ∀ k : Fin 16, kernel24_0Expr 3 14 k = kernel24_0_r3_14 k := by decide +kernel +noncomputable def kernel24_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-8),(-3)⟩,⟨(-9),(-4)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-9),(-4)⟩⟩,⟨⟨(-8),(-4)⟩,⟨(-8),(-4)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-8),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-6),(-3)⟩⟩] +lemma kernel24_0_r3_15_eq : ∀ k : Fin 16, kernel24_0Expr 3 15 k = kernel24_0_r3_15 k := by decide +kernel +noncomputable def kernel24_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel24_0_r3_0,kernel24_0_r3_1,kernel24_0_r3_2,kernel24_0_r3_3,kernel24_0_r3_4,kernel24_0_r3_5,kernel24_0_r3_6,kernel24_0_r3_7,kernel24_0_r3_8,kernel24_0_r3_9,kernel24_0_r3_10,kernel24_0_r3_11,kernel24_0_r3_12,kernel24_0_r3_13,kernel24_0_r3_14,kernel24_0_r3_15] +lemma kernel24_0_r3_eq (i k : Fin 16) : kernel24_0Expr 3 i k = kernel24_0_r3 i k := by + fin_cases i + · exact kernel24_0_r3_0_eq k + · exact kernel24_0_r3_1_eq k + · exact kernel24_0_r3_2_eq k + · exact kernel24_0_r3_3_eq k + · exact kernel24_0_r3_4_eq k + · exact kernel24_0_r3_5_eq k + · exact kernel24_0_r3_6_eq k + · exact kernel24_0_r3_7_eq k + · exact kernel24_0_r3_8_eq k + · exact kernel24_0_r3_9_eq k + · exact kernel24_0_r3_10_eq k + · exact kernel24_0_r3_11_eq k + · exact kernel24_0_r3_12_eq k + · exact kernel24_0_r3_13_eq k + · exact kernel24_0_r3_14_eq k + · exact kernel24_0_r3_15_eq k +noncomputable def kernel24_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-50898410541543450217014),(-50898410541543428837642)⟩,⟨(-25562548808538625380695),(-25562548808538604001164)⟩⟩,⟨⟨(-50864138092481215769609),(-50864138092481194414446)⟩,⟨(-25486165093034274966832),(-25486165093034253611511)⟩⟩,⟨⟨(-50795497715262793550305),(-50795497715262772243517)⟩,⟨(-25333761245301638734487),(-25333761245301617427544)⟩⟩,⟨⟨(-50692300748916797465591),(-50692300748916776231191)⟩,⟨(-25106062724191903703361),(-25106062724191882468811)⟩⟩,⟨⟨(-50554269914015853115054),(-50554269914015831976811)⟩,⟨(-24804153447715819796000),(-24804153447715798657611)⟩⟩,⟨⟨(-50381046080615112852108),(-50381046080615091833478)⟩,⟨(-24429470666170146190719),(-24429470666170125171950)⟩⟩,⟨⟨(-50172197149012881437100),(-50172197149012860561151)⟩,⟨(-23983798122893401165249),(-23983798122893380289170)⟩⟩,⟨⟨(-49927228922631111898406),(-49927228922631091187739)⟩,⟨(-23469257501390668765614),(-23469257501390648054825)⟩⟩,⟨⟨(-49645597824631872801645),(-49645597824631852278329)⟩,⟨(-22888298159280723965658),(-22888298159280703442231)⟩⟩,⟨⟨(-49326725283848813241354),(-49326725283848792926851)⟩,⟨(-22243685152503728264982),(-22243685152503707950379)⟩⟩,⟨⟨(-48970013591530076138778),(-48970013591530056053886)⟩,⟨(-21538485557659663524113),(-21538485557659643439134)⟩⟩,⟨⟨(-48574863008559394410045),(-48574863008559374574821)⟩,⟨(-20776053106361519515504),(-20776053106361499680206)⟩⟩,⟨⟨(-48140689883529224661582),(-48140689883529205095312)⟩,⟨(-19960011153172958677626),(-19960011153172939111297)⟩⟩,⟨⟨(-47666945525550167911828),(-47666945525550148632933)⟩,⟨(-19094234008098879662355),(-19094234008098860383416)⟩⟩,⟨⟨(-47153135562240034209105),(-47153135562240015235136)⟩,⟨(-18182826675698614161141),(-18182826675698595187142)⟩⟩,⟨⟨(-46598839503164427727556),(-46598839503164409075101)⟩,⟨(-17230103055631927294310),(-17230103055631908641842)⟩⟩] +lemma kernel24_0_r4_0_eq : ∀ k : Fin 16, kernel24_0Expr 4 0 k = kernel24_0_r4_0 k := by decide +kernel +noncomputable def kernel24_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-46003730222290667724565),(-46003730222290649409266)⟩,⟨(-16240562673710488357826),(-16240562673710470042532)⟩⟩,⟨⟨(-45367593069927435239468),(-45367593069927417275908)⟩,⟨(-15218866028142151338499),(-15218866028142133374961)⟩⟩,⟨⟨(-44690344325276027611766),(-44690344325276010013533)⟩,⟨(-14169808652401498444642),(-14169808652401480846448)⟩⟩,⟨⟨(-43972048705196779575607),(-43972048705196762355157)⟩,⟨(-13098294013769265920241),(-13098294013769248699849)⟩⟩,⟨⟨(-43212935653132430531307),(-43212935653132413700081)⟩,⟨(-12009305384743841920577),(-12009305384743825089426)⟩⟩,⟨⟨(-42413414144316867470732),(-42413414144316851038965)⟩,⟨(-10907876842890639589118),(-10907876842890623157443)⟩⟩,⟨⟨(-41574085759369060085861),(-41574085759369044062768)⟩,⟨(-9799063572879346680908),(-9799063572879330657924)⟩⟩,⟨⟨(-40695755798010367842698),(-40695755798010352236265)⟩,⟨(-8687911662060869492112),(-8687911662060853885805)⟩⟩,⟨⟨(-39779442227775165932448),(-39779442227775150749665)⟩,⟨(-7579427597536177421846),(-7579427597536162239205)⟩⟩,⟨⟨(-38826382288979665117010),(-38826382288979650363582)⟩,⟨(-6478547687843206966197),(-6478547687843192212929)⟩⟩,⟨⟨(-37838036606585119425371),(-37838036606585105105981)⟩,⟨(-5390107645714158550307),(-5390107645714144231091)⟩⟩,⟨⟨(-36816090691597275566383),(-36816090691597261684525)⟩,⟨(-4318812579426184224012),(-4318812579426170342345)⟩⟩,⟨⟨(-35762453748889019369514),(-35762453748889005927795)⟩,⟨(-3269207648699539877749),(-3269207648699526436235)⟩⟩,⟨⟨(-34679254744373632739919),(-34679254744373619739553)⟩,⟨(-2245649646538252979567),(-2245649646538239979418)⟩⟩,⟨⟨(-33568835721803537630791),(-33568835721803525072087)⟩,⟨(-1252279770551850225394),(-1252279770551837666920)⟩⟩,⟨⟨(-32433742397597411083953),(-32433742397597398966207)⟩,⟨(-292997845887389568430),(-292997845887377450926)⟩⟩] +lemma kernel24_0_r4_1_eq : ∀ k : Fin 16, kernel24_0Expr 4 1 k = kernel24_0_r4_1 k := by decide +kernel +noncomputable def kernel24_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-31276712100449887522627),(-31276712100449875844428)⟩,⟨628561743256169933868,628561743256181611815⟩⟩,⟨⟨(-30100659160473193345079),(-30100659160473182103776)⟩,⟨1509052165592224356742,1509052165592235597783⟩⟩,⟨⟨(-28908657889666578614163),(-28908657889666567806504)⟩,⟨2345434063214012657588,2345434063214023464976⟩⟩,⟨⟨(-27703923331012285116609),(-27703923331012274737360)⟩,⟨3134993062461758965641,3134993062461769344612⟩⟩,⟨⟨(-26489789986869224042156),(-26489789986869214086231)⟩,⟨3875354677763411827140,3875354677763421782780⟩⟩,⟨⟨(-25269688768010246721648),(-25269688768010237183111)⟩,⟨4564496435322740065905,4564496435322749604153⟩⟩,⟨⟨(-24047122432089528583493),(-24047122432089519456048)⟩,⟨5200757071187249528522,5200757071187258655673⟩⟩,⟨⟨(-22825639804039038465585),(-22825639804039029741873)⟩,⟨5782842688905375326650,5782842688905384050066⟩⟩,⟨⟨(-21608809090436367079158),(-21608809090436358751619)⟩,⟨6309829795264595374022,6309829795264603701262⟩⟩,⟨⟨(-20400190614882745667924),(-20400190614882737728050)⟩,⟨6781165168010485242608,6781165168010493182184⟩⟩,⟨⟨(-19203309311574938880607),(-19203309311574931319786)⟩,⟨7196662546444635203447,7196662546444642763969⟩⟩,⟨⟨(-18021627319323550342885),(-18021627319323543151679)⟩,⟨7556496173802372122058,7556496173802379312966⟩⟩,⟨⟨(-16858517018126058247625),(-16858517018126051416611)⟩,⟨7861191258698506255877,7861191258698513086596⟩⟩,⟨⟨(-15717234845000594255854),(-15717234845000587772870)⟩,⟨8111611461055980954575,8111611461055987437281⟩⟩,⟨⟨(-14600896215176126031803),(-14600896215176119885514)⟩,⟨8308943545142790844838,8308943545142796990875⟩⟩,⟨⟨(-13512451859062328193392),(-13512451859062322373292)⟩,⟨8454679377984531486057,8454679377984537305930⟩⟩] +lemma kernel24_0_r4_2_eq : ∀ k : Fin 16, kernel24_0Expr 4 2 k = kernel24_0_r4_2 k := by decide +kernel +noncomputable def kernel24_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-12454665864928888625836),(-12454665864928883121659)⟩,⟨8550595484858509173305,8550595484858514677277⟩⟩,⟨⟨(-11430095692241688181534),(-11430095692241682982335)⟩,⟨8598730404206946972994,8598730404206952172011⟩⟩,⟨⟨(-10441074391550707201228),(-10441074391550702296398)⟩,⟨8601360111572931982491,8601360111572936887161⟩⟩,⟨⟨(-9489695234198781972247),(-9489695234198777350585)⟩,⟨8560971805562558678874,8560971805562563300395⟩⟩,⟨⟨(-8577798919487846898505),(-8577798919487842549290)⟩,⟨8480236367938771454031,8480236367938775803124⟩⟩,⟨⟨(-7706963488924612906795),(-7706963488924608818864)⟩,⟨8361979824404700687494,8361979824404704775323⟩⟩,⟨⟨(-6878497037440921761953),(-6878497037440917924620)⟩,⟨8209154142172674406458,8209154142172678243704⟩⟩,⟨⟨(-6093433270747328744186),(-6093433270747325145620)⟩,⟨8024807704869670667070,8024807704869674265565⟩⟩,⟨⟨(-5352529916951140022663),(-5352529916951136652246)⟩,⟨7812055804629325436831,7812055804629328807191⟩⟩,⟨⟨(-4656269959973707026220),(-4656269959973703873240)⟩,⟨7574051485393697704430,7574051485393700857365⟩⟩,⟨⟨(-4004865622844796047571),(-4004865622844793101905)⟩,⟨7313957060623749491217,7313957060623752436851⟩⟩,⟨⟨(-3398264991314896771639),(-3398264991314894022973)⟩,⟨7034916613022008225210,7034916613022010973855⟩⟩,⟨⟨(-2836161133047744397253),(-2836161133047741835569)⟩,⟨6740029763822266940759,6740029763822269502434⟩⟩,⟨⟨(-2318003535517889287852),(-2318003535517886903192)⟩,⟨6432326975102314603755,6432326975102316988413⟩⟩,⟨⟨(-1843011657157129432785),(-1843011657157127215905)⟩,⟨6114746620904906739580,6114746620904908956467⟩⟩,⟨⟨(-1410190361706481206355),(-1410190361706479147811)⟩,⟨5790114032252245986694,5790114032252248045251⟩⟩] +lemma kernel24_0_r4_3_eq : ∀ k : Fin 16, kernel24_0Expr 4 3 k = kernel24_0_r4_3 k := by decide +kernel +noncomputable def kernel24_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-1018346985488340011635),(-1018346985488338102724)⟩,⟨5461122688004842415802,5461122688004844324731⟩⟩,⟨⟨(-666109771675299543944),(-666109771675297775830)⟩,⟨5130317688579787719145,5130317688579789487283⟩⟩,⟨⟨(-351947394759933788420),(-351947394759932152938)⟩,⟨4800081613463175480235,4800081613463177115745⟩⟩,⟨⟨(-74189292387631204156),(-74189292387629693151)⟩,⟨4472622826892787887000,4472622826892789398036⟩⟩,⟨⟨168953479531350705206,168953479531352099245⟩,⟨4149966259710836036032,4149966259710837430105⟩⟩,⟨⟨379367149092352083618,379367149092353368237⟩,⟨3833946659833142983467,3833946659833144268121⟩⟩,⟨⟨559014160838691530744,559014160838692712879⟩,⟨3526204269657814459079,3526204269657815641251⟩⟩,⟨⟨709912399142796120330,709912399142797206855⟩,⟨3228182856604225480279,3228182856604226566843⟩⟩,⟨⟨834114947493530035553,834114947493531032761⟩,⟨2941129993335988960589,2941129993335989957837⟩⟩,⟨⟨933690609517185557148,933690609517186471322⟩,⟨2666099457516806459107,2666099457516807373321⟩⟩,⟨⟨1010705395566396734013,1010705395566397570874⟩,⟨2403955597538920154576,2403955597538920991476⟩⟩,⟨⟨1067205154390787789221,1067205154390788554397⟩,⟨2155379490833776745345,2155379490833777510560⟩⟩,⟨⟨1105199503306957795162,1105199503306958496164⟩,⟨1920876705323825386983,1920876705323826088017⟩⟩,⟨⟨1126647182977183164714,1126647182977183806364⟩,⟨1700786462419003357927,1700786462419003999606⟩⟩,⟨⟨1133442934948967473317,1133442934948968059825⟩,⟨1495291991733660820668,1495291991733661407200⟩⟩,⟨⟨1127405972050970832325,1127405972050971367827⟩,⟨1304431863350827733956,1304431863350828269479⟩⟩] +lemma kernel24_0_r4_4_eq : ∀ k : Fin 16, kernel24_0Expr 4 4 k = kernel24_0_r4_4 k := by decide +kernel +noncomputable def kernel24_0_r4_5 : Fin 16 → CBox := ![⟨⟨1110270084109628915231,1110270084109629403453⟩,⟨1128112082866013584831,1128112082866014073068⟩⟩,⟨⟨1083675394734118238605,1083675394734118683244⟩,⟨966118737407442553641,966118737407442998293⟩⟩,⟨⟨1049161759559691882502,1049161759559692286877⟩,⟨818130987096894070306,818130987096894474691⟩⟩,⟨⟨1008163772732828154199,1008163772732828521547⟩,⟨683734205675008645024,683734205675009012380⟩⟩,⟨⟨962007326899693638651,962007326899693971873⟩,⟨562433085913395958527,562433085913396291754⟩⟩,⟨⟨911907652792999265196,911907652792999567150⟩,⟨453664539586336665792,453664539586336967749⟩⟩,⟨⟨858968747907086715933,858968747907086989178⟩,⟨356810237767908835822,356810237767909109068⟩⟩,⟨⟨804184089846713472707,804184089846713719704⟩,⟨271208654634578784155,271208654634579031152⟩⟩,⟨⟨748438518806137271137,748438518806137494106⟩,⟨196166496365482199218,196166496365482422186⟩⟩,⟨⟨692511165293763232902,692511165293763433977⟩,⟨130969415727494552261,130969415727494753334⟩⟩,⟨⟨637079293617091099591,637079293617091280676⟩,⟨74891932111245078145,74891932111245259227⟩⟩,⟨⟨582722928682578881665,582722928682579044614⟩,⟨27206495773647015058,27206495773647178004⟩⟩,⟨⟨529930133197278803798,529930133197278950209⟩,⟨(-12808346500068909603),(-12808346500068763196)⟩⟩,⟨⟨479102804194837461668,479102804194837593092⟩,⟨(-45860709481811227048),(-45860709481811095629)⟩⟩,⟨⟨430562861725348115213,430562861725348233023⟩,⟨(-72639059982139395853),(-72639059982139278047)⟩⟩,⟨⟨384558708298434311092,384558708298434416655⟩,⟨(-93806833179669506243),(-93806833179669400684)⟩⟩] +lemma kernel24_0_r4_5_eq : ∀ k : Fin 16, kernel24_0Expr 4 5 k = kernel24_0_r4_5 k := by decide +kernel +noncomputable def kernel24_0_r4_6 : Fin 16 → CBox := ![⟨⟨341271844985550821650,341271844985550916097⟩,⟨(-109997954549642862381),(-109997954549642767939)⟩⟩,⟨⟨300823538693984730530,300823538693984814953⟩,⟨(-121813235066983858355),(-121813235066983773936)⟩⟩,⟨⟨263281444741287265766,263281444741287341131⟩,⟨(-129817596991203698127),(-129817596991203622767)⟩⟩,⟨⟨228666099208138811516,228666099208138878729⟩,⟨(-134538078920634362580),(-134538078920634295371)⟩⟩,⟨⟨196957206362709414742,196957206362709474592⟩,⟨(-136462561931436836757),(-136462561931436776910)⟩⟩,⟨⟨168099657478000063027,168099657478000116276⟩,⟨(-136039153455558308061),(-136039153455558254815)⟩⟩,⟨⟨142009228372303985632,142009228372304032991⟩,⟨(-133676162031661496589),(-133676162031661449231)⟩⟩,⟨⟨118577913781567922724,118577913781567964823⟩,⟨(-129742594086410877784),(-129742594086410835685)⟩⟩,⟨⟨97678867036393364751,97678867036393402119⟩,⟨(-124569103349735254728),(-124569103349735217362)⟩⟩,⟨⟨79170923308399753762,79170923308399786902⟩,⟨(-118449324238150347810),(-118449324238150314671)⟩⟩,⟨⟨62902693781679656958,62902693781679686310⟩,⟨(-111641522403272176283),(-111641522403272146932)⟩⟩,⟨⟨48716226394542621464,48716226394542647440⟩,⟨(-104370498478468545335),(-104370498478468519359)⟩⟩,⟨⟨36450236211928448396,36450236211928471350⟩,⟨(-96829684701757925946),(-96829684701757902991)⟩⟩,⟨⟨25942914983613575592,25942914983613595873⟩,⟨(-89183378384718180217),(-89183378384718159936)⟩⟩,⟨⟨17034334996276174383,17034334996276192278⟩,⟨(-81569060976756064461),(-81569060976756046566)⟩⟩,⟨⟨9568466939843910381,9568466939843926157⟩,⟨(-74099756590576924009),(-74099756590576908232)⟩⟩] +lemma kernel24_0_r4_6_eq : ∀ k : Fin 16, kernel24_0Expr 4 6 k = kernel24_0_r4_6 k := by decide +kernel +noncomputable def kernel24_0_r4_7 : Fin 16 → CBox := ![⟨⟨3394835201567313520,3394835201567327411⟩,⟨(-66866389167249256183),(-66866389167249242292)⟩⟩,⟨⟨(-1630163186562690620),(-1630163186562678396)⟩,⟨(-59940102839375828448),(-59940102839375816225)⟩⟩,⟨⟨(-5642247737253415280),(-5642247737253404539)⟩,⟨(-53374515383958726204),(-53374515383958715462)⟩⟩,⟨⟨(-8768522403946486891),(-8768522403946477457)⟩,⟨(-47207879842919428032),(-47207879842919418597)⟩⟩,⟨⟨(-11126992223636104780),(-11126992223636096508)⟩,⟨(-41465134344728249612),(-41465134344728241339)⟩⟩,⟨⟨(-12826298829384362836),(-12826298829384355587)⟩,⟨(-36159824816596361880),(-36159824816596354631)⟩⟩,⟨⟨(-13965645568617880029),(-13965645568617873685)⟩,⟨(-31295889579816018096),(-31295889579816011752)⟩⟩,⟨⟨(-14634884024150519900),(-14634884024150514349)⟩,⟨(-26869298732300102863),(-26869298732300097311)⟩⟩,⟨⟨(-14914735161841777291),(-14914735161841772425)⟩,⟨(-22869544716984842303),(-22869544716984837437)⟩⟩,⟨⟨(-14877120043213556491),(-14877120043213552226)⟩,⟨(-19280983539767037335),(-19280983539767033070)⟩⟩,⟨⟨(-14585576968950875306),(-14585576968950871574)⟩,⟨(-16084028734385365641),(-16084028734385361908)⟩⟩,⟨⟨(-14095743991304643691),(-14095743991304640429)⟩,⟨(-13256202382097616686),(-13256202382097613423)⟩⟩,⟨⟨(-13455887887720967494),(-13455887887720964643)⟩,⟨(-10773049297260523777),(-10773049297260520928)⟩⟩,⟨⟨(-12707462869272993059),(-12707462869272990571)⟩,⟨(-8608921908722755923),(-8608921908722753435)⟩⟩,⟨⟨(-11885684457732263078),(-11885684457732260908)⟩,⟨(-6737644429190946065),(-6737644429190943895)⟩⟩,⟨⟨(-11020106063875915605),(-11020106063875913714)⟩,⟨(-5133065642083948141),(-5133065642083946249)⟩⟩] +lemma kernel24_0_r4_7_eq : ∀ k : Fin 16, kernel24_0Expr 4 7 k = kernel24_0_r4_7 k := by decide +kernel +noncomputable def kernel24_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-10135187803687341422),(-10135187803687339775)⟩,⟨(-3769510081982572269),(-3769510081982570623)⟩⟩,⟨⟨(-9250848972307626061),(-9250848972307624626)⟩,⟨(-2622137576040192182),(-2622137576040190747)⟩⟩,⟨⟨(-8382997338382328839),(-8382997338382327592)⟩,⟨(-1667221085337497461),(-1667221085337496213)⟩⟩,⟨⟨(-7544030010356942169),(-7544030010356941084)⟩,⟨(-882352572211666017),(-882352572211664932)⟩⟩,⟨⟨(-6743302053319180604),(-6743302053319179662)⟩,⟨(-246586255771692531),(-246586255771691589)⟩⟩,⟨⟨(-5987560297008496542),(-5987560297008495724)⟩,⟨259471865124076987,259471865124077805⟩⟩,⟨⟨(-5281340873604363343),(-5281340873604362632)⟩,⟨653619914865362398,653619914865363108⟩⟩,⟨⟨(-4627329962328131880),(-4627329962328131262)⟩,⟨952053799379294473,952053799379295091⟩⟩,⟨⟨(-4026688004022931277),(-4026688004022930743)⟩,⟨1169391624392564858,1169391624392565394⟩⟩,⟨⟨(-3479338292169721654),(-3479338292169721190)⟩,⟨1318722572533873228,1318722572533873692⟩⟩,⟨⟨(-2984221358313318686),(-2984221358313318284)⟩,⟨1411674633513579873,1411674633513580276⟩⟩,⟨⟨(-2539516961739653131),(-2539516961739652781)⟩,⟨1458496263473896116,1458496263473896466⟩⟩,⟨⟨(-2142835778196533073),(-2142835778196532770)⟩,⟨1468147706054489909,1468147706054490211⟩⟩,⟨⟨(-1791383073412067337),(-1791383073412067075)⟩,⟨1448398329488166299,1448398329488166562⟩⟩,⟨⟨(-1482096756917283911),(-1482096756917283684)⟩,⟨1405926914243131915,1405926914243132141⟩⟩,⟨⟨(-1211762252573210953),(-1211762252573210755)⟩,⟨1346422359619249652,1346422359619249849⟩⟩] +lemma kernel24_0_r4_8_eq : ∀ k : Fin 16, kernel24_0Expr 4 8 k = kernel24_0_r4_8 k := by decide +kernel +noncomputable def kernel24_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-977106605938296594),(-977106605938296422)⟩,⟨1274682762425700012,1274682762425700184⟩⟩,⟨⟨(-774874186073311906),(-774874186073311757)⟩,⟨1194711255176467509,1194711255176467657⟩⟩,⟨⟨(-601886240518716503),(-601886240518716374)⟩,⟨1109807375259075229,1109807375259075358⟩⟩,⟨⟨(-455086435940358877),(-455086435940358765)⟩,⟨1022653071495353280,1022653071495353392⟩⟩,⟨⟨(-331574371232529615),(-331574371232529518)⟩,⟨935392742536433629,935392742536433726⟩⟩,⟨⟨(-228628891564445996),(-228628891564445910)⟩,⟨849706945401937496,849706945401937582⟩⟩,⟨⟨(-143722866817849567),(-143722866817849493)⟩,⟨766879615447398292,766879615447398366⟩⟩,⟨⟨(-74530930986769471),(-74530930986769407)⟩,⟨687858804695824426,687858804695824490⟩⟩,⟨⟨(-18931514393021091),(-18931514393021036)⟩,⟨613311077535248815,613311077535248870⟩⟩,⟨⟨24995658815028142,24995658815028192⟩,⟨543669805043481561,543669805043481611⟩⟩,⟨⟨58975587038435886,58975587038435928⟩,⟨479177675376700642,479177675376700685⟩⟩,⟨⟨84546642730357435,84546642730357472⟩,⟨419923791336663671,419923791336663708⟩⟩,⟨⟨103071111640777115,103071111640777146⟩,⟨365875760802525320,365875760802525351⟩⟩,⟨⟨115746992340976169,115746992340976198⟩,⟨316907204327873372,316907204327873402⟩⟩,⟨⟨123620536744511646,123620536744511672⟩,⟨272821109743230456,272821109743230482⟩⟩,⟨⟨127599108809069882,127599108809069904⟩,⟨233369458665486269,233369458665486291⟩⟩] +lemma kernel24_0_r4_9_eq : ∀ k : Fin 16, kernel24_0Expr 4 9 k = kernel24_0_r4_9 k := by decide +kernel +noncomputable def kernel24_0_r4_10 : Fin 16 → CBox := ![⟨⟨128464023656866334,128464023656866354⟩,⟨198269536704482990,198269536704483010⟩⟩,⟨⟨126883103491633318,126883103491633336⟩,⟨167217319891609500,167217319891609518⟩⟩,⟨⟨123422750568926280,123422750568926297⟩,⟨139898306176293038,139898306176293055⟩⟩,⟨⟨118559391847682213,118559391847682228⟩,⟨115996134221391248,115996134221391263⟩⟩,⟨⟨112690195631863561,112690195631863573⟩,⟨95199303411185312,95199303411185325⟩⟩,⟨⟨106142998348513695,106142998348513708⟩,⟨77206279976366629,77206279976366642⟩⟩,⟨⟨99185410452167189,99185410452167200⟩,⟨61729245248847865,61729245248847877⟩⟩,⟨⟨92033095126028558,92033095126028569⟩,⟨48496713917395253,48496713917395264⟩⟩,⟨⟨84857232763183437,84857232763183445⟩,⟨37255223239800252,37255223239800261⟩⟩,⟨⟨77791198904676406,77791198904676414⟩,⟨27770268822050489,27770268822050498⟩⟩,⟨⟨70936494078549921,70936494078549930⟩,⟨19826639030372402,19826639030372411⟩⟩,⟨⟨64367971457509975,64367971457509982⟩,⟨13228278494944987,13228278494944995⟩⟩,⟨⟨58138413002706910,58138413002706917⟩,⟨7797791554852552,7797791554852558⟩⟩,⟨⟨52282507294256147,52282507294256153⟩,⟨3375678881734167,3375678881734172⟩⟩,⟨⟨46820283011229682,46820283011229688⟩,⟨(-180615143535288),(-180615143535282)⟩⟩,⟨⟨41760051401909973,41760051401909979⟩,⟨(-2997780524654257),(-2997780524654251)⟩⟩] +lemma kernel24_0_r4_10_eq : ∀ k : Fin 16, kernel24_0Expr 4 10 k = kernel24_0_r4_10 k := by decide +kernel +noncomputable def kernel24_0_r4_11 : Fin 16 → CBox := ![⟨⟨37100909411068473,37100909411068478⟩,⟨(-5187793479510142),(-5187793479510137)⟩⟩,⟨⟨32834852686084364,32834852686084369⟩,⟨(-6849100682848668),(-6849100682848663)⟩⟩,⟨⟨28948544702845989,28948544702845995⟩,⟨(-8067803517495112),(-8067803517495106)⟩⟩,⟨⟨25424784929137389,25424784929137394⟩,⟨(-8918817494694313),(-8918817494694308)⟩⟩,⟨⟨22243715434468556,22243715434468561⟩,⟨(-9466988356349127),(-9466988356349122)⟩⟩,⟨⟨19383801785824903,19383801785824908⟩,⟨(-9768151647999233),(-9768151647999228)⟩⟩,⟨⟨16822620535619232,16822620535619236⟩,⟨(-9870126881821448),(-9870126881821445)⟩⟩,⟨⟨14537482184593328,14537482184593333⟩,⟨(-9813640916295123),(-9813640916295118)⟩⟩,⟨⟨12505915241966955,12505915241966960⟩,⟨(-9633177976851938),(-9633177976851933)⟩⟩,⟨⟨10706033944637307,10706033944637312⟩,⟨(-9357755933390236),(-9357755933390231)⟩⟩,⟨⟨9116809360002280,9116809360002285⟩,⟨(-9011630129481177),(-9011630129481172)⟩⟩,⟨⟨7718260995412142,7718260995412147⟩,⟨(-8614927307927478),(-8614927307927475)⟩⟩,⟨⟨6491583675126252,6491583675126257⟩,⟨(-8184213071863766),(-8184213071863761)⟩⟩,⟨⟨5419222320097857,5419222320097862⟩,⟨(-7732996924415829),(-7732996924415824)⟩⟩,⟨⟨4484905369088668,4484905369088673⟩,⟨(-7272179299073751),(-7272179299073746)⟩⟩,⟨⟨3673645900103485,3673645900103488⟩,⟨(-6810445175478307),(-6810445175478304)⟩⟩] +lemma kernel24_0_r4_11_eq : ∀ k : Fin 16, kernel24_0Expr 4 11 k = kernel24_0_r4_11 k := by decide +kernel +noncomputable def kernel24_0_r4_12 : Fin 16 → CBox := ![⟨⟨2971718035081909,2971718035081913⟩,⟨(-6354608912179268),(-6354608912179264)⟩⟩,⟨⟨2366614922842132,2366614922842136⟩,⟨(-5909914853549051),(-5909914853549046)⟩⟩,⟨⟨1846993479343125,1846993479343127⟩,⟨(-5480298111139971),(-5480298111139968)⟩⟩,⟨⟨1402610104150433,1402610104150438⟩,⟨(-5068609704027602),(-5068609704027597)⟩⟩,⟨⟨1024250771566070,1024250771566073⟩,⟨(-4676809987363201),(-4676809987363196)⟩⟩,⟨⟨703658198826188,703658198826192⟩,⟨(-4306134018953095),(-4306134018953090)⟩⟩,⟨⟨433458207526399,433458207526403⟩,⟨(-3957232222443939),(-3957232222443935)⟩⟩,⟨⟨207086904434272,207086904434276⟩,⟨(-3630289412133998),(-3630289412133994)⟩⟩,⟨⟨18719901597965,18719901597970⟩,⟨(-3325124955772391),(-3325124955772386)⟩⟩,⟨⟨(-136795538220305),(-136795538220302)⟩,⟨(-3041276573270406),(-3041276573270403)⟩⟩,⟨⟨(-264004816530171),(-264004816530166)⟩,⟨(-2778070004793211),(-2778070004793207)⟩⟩,⟨⟨(-366906379102752),(-366906379102747)⟩,⟨(-2534676533726954),(-2534676533726949)⟩⟩,⟨⟨(-449007939590010),(-449007939590005)⟩,⟨(-2310160120019095),(-2310160120019090)⟩⟩,⟨⟨(-513378461798979),(-513378461798976)⟩,⟨(-2103515688070837),(-2103515688070834)⟩⟩,⟨⟨(-562695920652993),(-562695920652990)⟩,⟨(-1913699920812824),(-1913699920812821)⟩⟩,⟨⟨(-599290940906411),(-599290940906407)⟩,⟨(-1739655737452414),(-1739655737452409)⟩⟩] +lemma kernel24_0_r4_12_eq : ∀ k : Fin 16, kernel24_0Expr 4 12 k = kernel24_0_r4_12 k := by decide +kernel +noncomputable def kernel24_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-625186470409127),(-625186470409124)⟩,⟨(-1580331475942634),(-1580331475942631)⟩⟩,⟨⟨(-642133685134992),(-642133685134987)⟩,⟨(-1434695661555574),(-1434695661555569)⟩⟩,⟨⟨(-651644349686213),(-651644349686208)⟩,⟨(-1301748118960803),(-1301748118960798)⟩⟩,⟨⟨(-655019872426108),(-655019872426105)⟩,⟨(-1180528075739576),(-1180528075739572)⟩⟩,⟨⟨(-653377301172441),(-653377301172437)⟩,⟨(-1070119809097243),(-1070119809097239)⟩⟩,⟨⟨(-647672505497030),(-647672505497025)⟩,⟨(-969656303460374),(-969656303460369)⟩⟩,⟨⟨(-638720786769214),(-638720786769209)⟩,⟨(-878321313481125),(-878321313481120)⟩⟩,⟨⟨(-627215148496613),(-627215148496609)⟩,⟨(-795350163589422),(-795350163589417)⟩⟩,⟨⟨(-613742448347416),(-613742448347413)⟩,⟨(-720029560566991),(-720029560566988)⟩⟩,⟨⟨(-598797640358873),(-598797640358870)⟩,⟨(-651696648672574),(-651696648672571)⟩⟩,⟨⟨(-582796301940370),(-582796301940366)⟩,⟨(-589737496708414),(-589737496708410)⟩⟩,⟨⟨(-566085625908494),(-566085625908491)⟩,⟨(-533585172247196),(-533585172247193)⟩⟩,⟨⟨(-548954043362348),(-548954043362345)⟩,⟨(-482717529277242),(-482717529277239)⟩⟩,⟨⟨(-531639629033549),(-531639629033546)⟩,⟨(-436654811089017),(-436654811089012)⟩⟩,⟨⟨(-514337427056045),(-514337427056041)⟩,⟨(-394957149707643),(-394957149707639)⟩⟩,⟨⟨(-497205822057379),(-497205822057375)⟩,⟨(-357222026031383),(-357222026031378)⟩⟩] +lemma kernel24_0_r4_13_eq : ∀ k : Fin 16, kernel24_0Expr 4 13 k = kernel24_0_r4_13 k := by decide +kernel +noncomputable def kernel24_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-480372068182319),(-480372068182315)⟩,⟨(-323081740585574),(-323081740585570)⟩⟩,⟨⟨(-463937077185781),(-463937077185777)⟩,⟨(-292200933023618),(-292200933023614)⟩⟩,⟨⟨(-447979556105257),(-447979556105253)⟩,⟨(-264274178832208),(-264274178832204)⟩⟩,⟨⟨(-432559575248448),(-432559575248445)⟩,⟨(-239023683805772),(-239023683805769)⟩⟩,⟨⟨(-417721638295038),(-417721638295035)⟩,⟨(-216197090466168),(-216197090466165)⟩⟩,⟨⟨(-403497318184291),(-403497318184288)⟩,⟨(-195565405477310),(-195565405477307)⟩⟩,⟨⟨(-389907515104092),(-389907515104089)⟩,⟨(-176921053033607),(-176921053033604)⟩⟩,⟨⟨(-376964386267565),(-376964386267562)⟩,⟨(-160076056008336),(-160076056008333)⟩⟩,⟨⟨(-364672991211813),(-364672991211808)⟩,⟨(-144860344182237),(-144860344182232)⟩⟩,⟨⟨(-353032691029342),(-353032691029339)⟩,⟨(-131120187004966),(-131120187004963)⟩⟩,⟨⟨(-342038335195467),(-342038335195463)⟩,⟨(-118716746963950),(-118716746963946)⟩⟩,⟨⟨(-331681265434788),(-331681265434785)⟩,⟨(-107524748654767),(-107524748654764)⟩⟩,⟨⟨(-321950162328510),(-321950162328507)⟩,⟨(-97431257987790),(-97431257987787)⟩⟩,⟨⟨(-312831757055993),(-312831757055990)⟩,⟨(-88334565562967),(-88334565562964)⟩⟩,⟨⟨(-304311427745532),(-304311427745529)⟩,⟨(-80143168045061),(-80143168045058)⟩⟩,⟨⟨(-296373697340643),(-296373697340639)⟩,⟨(-72774841331222),(-72774841331218)⟩⟩] +lemma kernel24_0_r4_14_eq : ∀ k : Fin 16, kernel24_0Expr 4 14 k = kernel24_0_r4_14 k := by decide +kernel +noncomputable def kernel24_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-289002647631685),(-289002647631681)⟩,⟨(-66155799385057),(-66155799385053)⟩⟩,⟨⟨(-282182262124602),(-282182262124598)⟩,⟨(-60219932786872),(-60219932786869)⟩⟩,⟨⟨(-275896708687198),(-275896708687194)⟩,⟨(-54908121294260),(-54908121294256)⟩⟩,⟨⟨(-270130571400596),(-270130571400592)⟩,⟨(-50167615001464),(-50167615001459)⟩⟩,⟨⟨(-264869039723342),(-264869039723337)⟩,⟨(-45951479014508),(-45951479014503)⟩⟩,⟨⟨(-260098061924857),(-260098061924853)⟩,⟨(-42218096909716),(-42218096909712)⟩⟩,⟨⟨(-255804468742688),(-255804468742684)⟩,⟨(-38930728606664),(-38930728606660)⟩⟩,⟨⟨(-251976072345359),(-251976072345355)⟩,⟨(-36057118655537),(-36057118655532)⟩⟩,⟨⟨(-248601744922909),(-248601744922906)⟩,⟨(-33569151308008),(-33569151308005)⟩⟩,⟨⟨(-245671480565097),(-245671480565093)⟩,⟨(-31442549106382),(-31442549106379)⟩⟩,⟨⟨(-243176443509449),(-243176443509445)⟩,⟨(-29656612085132),(-29656612085128)⟩⟩,⟨⟨(-241109005335500),(-241109005335495)⟩,⟨(-28193995030795),(-28193995030790)⟩⟩,⟨⟨(-239462773236967),(-239462773236964)⟩,⟨(-27040520589422),(-27040520589419)⟩⟩,⟨⟨(-238232611110213),(-238232611110210)⟩,⟨(-26185026345655),(-26185026345651)⟩⟩,⟨⟨(-237414654846355),(-237414654846352)⟩,⟨(-25619244324060),(-25619244324057)⟩⟩,⟨⟨(-237006322897526),(-237006322897523)⟩,⟨(-25337711682794),(-25337711682791)⟩⟩] +lemma kernel24_0_r4_15_eq : ∀ k : Fin 16, kernel24_0Expr 4 15 k = kernel24_0_r4_15 k := by decide +kernel +noncomputable def kernel24_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel24_0_r4_0,kernel24_0_r4_1,kernel24_0_r4_2,kernel24_0_r4_3,kernel24_0_r4_4,kernel24_0_r4_5,kernel24_0_r4_6,kernel24_0_r4_7,kernel24_0_r4_8,kernel24_0_r4_9,kernel24_0_r4_10,kernel24_0_r4_11,kernel24_0_r4_12,kernel24_0_r4_13,kernel24_0_r4_14,kernel24_0_r4_15] +lemma kernel24_0_r4_eq (i k : Fin 16) : kernel24_0Expr 4 i k = kernel24_0_r4 i k := by + fin_cases i + · exact kernel24_0_r4_0_eq k + · exact kernel24_0_r4_1_eq k + · exact kernel24_0_r4_2_eq k + · exact kernel24_0_r4_3_eq k + · exact kernel24_0_r4_4_eq k + · exact kernel24_0_r4_5_eq k + · exact kernel24_0_r4_6_eq k + · exact kernel24_0_r4_7_eq k + · exact kernel24_0_r4_8_eq k + · exact kernel24_0_r4_9_eq k + · exact kernel24_0_r4_10_eq k + · exact kernel24_0_r4_11_eq k + · exact kernel24_0_r4_12_eq k + · exact kernel24_0_r4_13_eq k + · exact kernel24_0_r4_14_eq k + · exact kernel24_0_r4_15_eq k +noncomputable def kernel24_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-9408298398555501714898596975),(-9408298398555500367662103399)⟩,⟨7173516462981802642393666494,7173516462981803989472909557⟩⟩,⟨⟨(-9395666311574470002867150614),(-9395666311574468656186326699)⟩,⟨7175658021339889741458601509,7175658021339891087982516315⟩⟩,⟨⟨(-9370426099135918385195781040),(-9370426099135917039628119812)⟩,⟨7179905901694940634887847737,7179905901694941980299281690⟩⟩,⟨⟨(-9332625731701183663306731285),(-9332625731701182319408707132)⟩,⟨7186189868296899092035048422,7186189868296900435777865571⟩⟩,⟨⟨(-9282337281865065109036609857),(-9282337281865063767363224003)⟩,⟨7194405158863890325012340740,7194405158863891666531875310⟩⟩,⟨⟨(-9219657060087343293990376001),(-9219657060087341955094604322)⟩,⟨7204413191145743575321768740,7204413191145744914065376328⟩⟩,⟨⟨(-9144705788143194665290937140),(-9144705788143193329723317547)⟩,⟨7216042499916420525540287773,7216042499916421860957756979⟩⟩,⟨⟨(-9057628803964943926957134280),(-9057628803964942595265116773)⟩,⟨7229089900007822142842443487,7229089900007823474386644891⟩⟩,⟨⟨(-8958596290117575278620875370),(-8958596290117573951348588584)⟩,⟨7243321869873750739753688687,7243321869873752066880807337⟩⟩,⟨⟨(-8847803516819894446764226982),(-8847803516819893124451559321)⟩,⟨7258476149033676251286724992,7258476149033677573457178314⟩⟩,⟨⟨(-8725471089210331699572930018),(-8725471089210330382755135355)⟩,⟨7274263541590691628421108800,7274263541590692945099939982⟩⟩,⟨⟨(-8591845187478265069064798421),(-8591845187478263758160092306)⟩,⟨7290369916847158786361887869,7290369916847160097131171446⟩⟩,⟨⟨(-8447197787554445038723194302),(-8447197787554443734248396925)⟩,⟨7306458396856921840182910521,7306458396856923144526103212⟩⟩,⟨⟨(-8291826849292327395378963588),(-8291826849292326097844140312)⟩,⟨7322171719557949593641768818,7322171719557950891049070653⟩⟩,⟨⟨(-8126056458489097114574331253),(-8126056458489095824484867815)⟩,⟨7337134764928769634452455138,7337134764928770924418733421⟩⟩,⟨⟨(-7950236908702466777554857865),(-7950236908702465495407881930)⟩,⟨7350957230412578626705392987,7350957230412579908733759887⟩⟩] +lemma kernel24_0_r5_0_eq : ∀ k : Fin 16, kernel24_0Expr 5 0 k = kernel24_0_r5_0 k := by decide +kernel +noncomputable def kernel24_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-7764744708626710155803196551),(-7764744708626708882091200500)⟩,⟨7363236440662577531450903398,7363236440662578805049092398⟩⟩,⟨⟨(-7569982500806612150337872200),(-7569982500806610885542752087)⟩,⟨7373560275490594614056070615,7373560275490595878742396757⟩⟩,⟨⟨(-7366378877696705610984772182),(-7366378877696704355583941191)⟩,⟨7381510198759655820928878684,7381510198759657076226124436⟩⟩,⟨⟨(-7154388081518661108631560709),(-7154388081518659863090114352)⟩,⟨7386664369862496432684611308,7386664369862497678127860633⟩⟩,⟨⟨(-6934489575032913659810433406),(-6934489575032912424589710063)⟩,⟨7388600818386016713781295909,7388600818386017948909373159⟩⟩,⟨⟨(-6707187471219928840758786704),(-6707187471219927616304361821)⟩,⟨7386900661591408358570052914,7386900661591409582937527972⟩⟩,⟨⟨(-6473009810957673088683931145),(-6473009810957671875438430323)⟩,⟨7381151343457048682926030252,7381151343457049896090405003⟩⟩,⟨⟨(-6232507679077895039779312330),(-6232507679077893838163169391)⟩,⟨7370949873252849133236611224,7370949873252850334777525812⟩⟩,⟨⟨(-5986254150675029124765594581),(-5986254150675027935197901784)⟩,⟨7355906040957491854701186611,7355906040957493044199604017⟩⟩,⟨⟨(-5734843061215414312300204570),(-5734843061215413135181950555)⟩,⟨7335645586310890830866082313,7335645586310892007921084681⟩⟩,⟨⟨(-5478887595835847011412608983),(-5478887595835845847144990662)⟩,⟨7309813297930003505557742953,7309813297930004669768185102⟩⟩,⟨⟨(-5219018695211334234280372377),(-5219018695211333083240608098)⟩,⟨7278076018722914617665357690,7278076018722915768654053658⟩⟩,⟨⟨(-4955883277491764209961466192),(-4955883277491763072529243386)⟩,⟨7240125533829069053206600630,7240125533829070190593876011⟩⟩,⟨⟨(-4690142278033095433053207430),(-4690142278033094309543142183)⟩,⟨7195681317506469740485997471,7195681317506470863957229694⟩⟩,⟨⟨(-4422468510955338582289564295),(-4422468510955337472971451217)⟩,⟨7144493115791717386041968258,7144493115791718495327336876⟩⟩,⟨⟨(-4153544358919780707019138226),(-4153544358919779612215299252)⟩,⟨7086343342386050015566795096,7086343342386051110343933006⟩⟩] +lemma kernel24_0_r5_1_eq : ∀ k : Fin 16, kernel24_0Expr 5 1 k = kernel24_0_r5_1 k := by decide +kernel +noncomputable def kernel24_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-3884059299902514848552544188),(-3884059299902513768593905800)⟩,⟨7021049266077766844828059521,7021049266077767924765976039⟩⟩,⟨⟨(-3614707282119866929081848095),(-3614707282119865864258769415)⟩,⟨6948464969103632007457091038,6948464969103633072265344036⟩⟩,⟨⟨(-3346183960602124307516112455),(-3346183960602123258130453943)⟩,⟨6868483057181120658196833590,6868483057181121707573461235⟩⟩,⟨⟨(-3079183811182720619939869772),(-3079183811182719586253727219)⟩,⟨6781036103508553223799789219,6781036103508554257482576428⟩⟩,⟨⟨(-2814397139838083384363636348),(-2814397139838082366645935479)⟩,⟨6686097810826712932047605262,6686097810826713949767489632⟩⟩,⟨⟨(-2552507007346232678558021091),(-2552507007346231676980289040)⟩,⟨6583683877655348474408280326,6583683877655349475993581286⟩⟩,⟨⟨(-2294186091098100301107540782),(-2294186091098099315916226446)⟩,⟨6473852557049268998560926948,6473852557049269983765026239⟩⟩,⟨⟨(-2040093507563721778140201878),(-2040093507563720809533034386)⟩,⟨6356704898646103980637267064,6356704898646104949262251075⟩⟩,⟨⟨(-1790871620356874388048840356),(-1790871620356873436247599277)⟩,⟨6232384667382143146417496238,6232384667382144098241386527⟩⟩,⟨⟨(-1547142860029462082433178054),(-1547142860029461147568422225)⟩,⟨6101077935011368629230362763,6101077935011369564122390049⟩⟩,⟨⟨(-1309506582636674847039493329),(-1309506582636673929296424791)⟩,⟨5963012343449853951752364568,5963012343449854869527102310⟩⟩,⟨⟨(-1078535994724461794785448249),(-1078535994724460894292231331)⟩,⟨5818456041954021117060555002,5818456041954022017589600017⟩⟩,⟨⟨(-854775172684476698507236643),(-854775172684475815413335024)⟩,⟨5667716303194898023668225597,5667716303194898906801841186⟩⟩,⟨⟨(-638736204384645007056061111),(-638736204384644141451071999)⟩,⟨5511137826377153874838776819,5511137826377154740487112700⟩⟩,⟨⟨(-430896480606423110503230733),(-430896480606422262513478595)⟩,⟨5349100738634972405754681054,5349100738634973253791151828⟩⟩,⟨⟨(-231696163097831367468381369),(-231696163097830537153030871)⟩,⟨5182018308978923626896222128,5182018308978924457261396217⟩⟩] +lemma kernel24_0_r5_2_eq : ∀ k : Fin 16, kernel24_0Expr 5 2 k = kernel24_0_r5_2 k := by decide +kernel +noncomputable def kernel24_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-41535854984432000648307392),(-41535854984431188109791438)⟩,⟨5010334392030143658950958366,5010334392030144471542130569⟩⟩,⟨⟨139225502126423913298457629,139225502126424708044305704⟩,⟨4834520621621203990253899206,4834520621621204785054960725⟩⟩,⟨⟨310272481749475968360301832,310272481749476745249910495⟩,⟨4655073377028186234968111499,4655073377028187011915212533⟩⟩,⟨⟨471334756286406208316340908,471334756286406967361761352⟩,⟨4472510547087721686662150534,4472510547087722445767063493⟩⟩,⟨⟨622188392750554481986374902,622188392750555223148120107⟩,⟨4287368119709706503794003392,4287368119709707245016962243⟩⟩,⟨⟨762656844866078741804036990,762656844866079465136553067⟩,⟨4100196626286862975735548007,4100196626286863699130722199⟩⟩,⟨⟨892611628811974366911489839,892611628811975072413287872⟩,⟨3911557472194913945609813886,3911557472194914651175440137⟩⟩,⟨⟨1011972672943642201209365808,1011972672943642888961873366⟩,⟨3722019185943929387747629287,3722019185943930075564865666⟩⟩,⟨⟨1120708335055952541717575466,1120708335055953211739766804⟩,⟨3532153620558437195523280829,3532153620558437865610836738⟩⟩,⟨⟨1218835084111284826981494297,1218835084111285479398126608⟩,⟨3342532141411701727494806565,3342532141411702379977181893⟩⟩,⟨⟨1306416846800463580943875969,1306416846800464216000343417⟩,⟨3153721835003630308774416801,3153721835003630943896098136⟩⟩,⟨⟨1383564022788482116192612932,1383564022788482735425488708⟩,⟨2966281773042827168114407222,2966281773042827787406937420⟩⟩,⟨⟨1450432175973716534910685452,1450432175973717138328795880⟩,⟨2780759365667699852194888385,2780759365667700455667255200⟩⟩,⟨⟨1507220412511720372553507989,1507220412511720960274144438⟩,⟨2597686836721306375750213055,2597686836721306963519881290⟩⟩,⟨⟨1554169459675582847272393893,1554169459675583419338483857⟩,⟨2417577852687713231160771033,2417577852687713803270850915⟩⟩,⟨⟨1591559462798126458788837181,1591559462798127015336085026⟩,⟨2240924335217723247405603304,2240924335217723803991991767⟩⟩] +lemma kernel24_0_r5_3_eq : ∀ k : Fin 16, kernel24_0Expr 5 3 k = kernel24_0_r5_3 k := by decide +kernel +noncomputable def kernel24_0_r5_4 : Fin 16 → CBox := ![⟨⟨1619707520522548277953499521,1619707520522548819037021410⟩,⟨2068193485138316088453382776,2068193485138316629571395950⟩⟩,⟨⟨1638964981335603806208110204,1638964981335604332002594290⟩,⟨1899825043477856706346847729,1899825043477857232171381562⟩⟩,⟨⟨1649714526832438156093117600,1649714526832438666689326161⟩,⟨1736228812378011443832259509,1736228812378011954454289414⟩⟩,⟨⟨1652367069329919419135658123,1652367069329919914720707969⟩,⟨1577782455837985244915995011,1577782455837985740522856264⟩⟩,⟨⟨1647358493275553777819302475,1647358493275554258495911009⟩,⟨1424829597085922410702884723,1424829597085922891397516477⟩⟩,⟨⟨1635146271366523414589677431,1635146271366523880578973724⟩,⟨1277678226038403379143178154,1277678226038403845146934281⟩⟩,⟨⟨1616205987378328301171268263,1616205987378328752609970228⟩,⟨1136599426837087639253680479,1136599426837088090703523334⟩⟩,⟨⟨1591027798391003507355833209,1591027798391003944479314839⟩,⟨1001826431888987584142475575,1001826431888988021274029655⟩⟩,⟨⟨1560112869385073130670442805,1560112869385073553629535167⟩,⟨873554005232240405424990911,873554005232240828389308372⟩⟩,⟨⟨1523969813057650737460258527,1523969813057651146521339085⟩,⟨751938154451735845834554283,751938154451736254898233036⟩⟩,⟨⟨1483111167185998648211600584,1483111167185999043563020009⟩,⟨637096166827424281886703797,637096166827424677238312519⟩⟩,⟨⟨1438049940952149741109082250,1438049940952150123026395934⟩,⟨529106961960326529459718936,529106961960326911375027374⟩⟩,⟨⟨1389296260354545628522703358,1389296260354545997178850469⟩,⟨428011749833035428005646389,428011749833035796657803623⟩⟩,⟨⟨1337354141193343143935622746,1337354141193343499659082539⟩,⟨333814980166004972570973504,333814980166005328288663188⟩⟩,⟨⟨1282718416152576802717726434,1282718416152577145722232574⟩,⟨246485566067943202996932757,246485566067943545994087038⟩⟩,⟨⟨1225871840246915913475301223,1225871840246916244049703174⟩,⟨165958362383904874613091427,165958362383905205178751187⟩⟩] +lemma kernel24_0_r5_4_eq : ∀ k : Fin 16, kernel24_0Expr 5 4 k = kernel24_0_r5_4 k := by decide +kernel +noncomputable def kernel24_0_r5_5 : Fin 16 → CBox := ![⟨⟨1167282396389590555680360485,1167282396389590874017313454⟩,⟨92135876849364385054106602,92135876849364703381111357⟩⟩,⟨⟨1107400820110874091216944188,1107400820110874397652782075⟩,⟨24890190188708069457085207,24890190188708375881946467⟩⟩,⟨⟨1046658359555694331760176291,1046658359555694626591952874⟩,⟨(-35934940327165435846086491),(-35934940327165141026141099)⟩⟩,⟨⟨985464783858827368224066361,985464783858827651751419617⟩,⟨(-90521820612214642273020504),(-90521820612214358758195474)⟩⟩,⟨⟨924206649882174991958528116,924206649882175264388965828⟩,⟨(-139076430426446624411244707),(-139076430426446351993883382)⟩⟩,⟨⟨863245834146645781700960534,863245834146646043362396737⟩,⟨(-181825933127488497907043034),(-181825933127488236259092681)⟩⟩,⟨⟨802918333646503561020238112,802918333646503812136445899⟩,⟨(-219016112822527102442208150),(-219016112822526851339765833)⟩⟩,⟨⟨743533336140841070784202286,743533336140841311664326973⟩,⟨(-250908767018247087587058615),(-250908767018246846720859437)⟩⟩,⟨⟨685372557517248423744875806,685372557517248654605171623⟩,⟨(-277779082306158341952350197),(-277779082306158111106029408)⟩⟩,⟨⟨628689840956303468926292894,628689840956303690227977861⟩,⟨(-299913019731535836945210441),(-299913019731535615656163131)⟩⟩,⟨⟨573711009928489951543998730,573711009928490163538814551⟩,⟨(-317604735299637877366719096),(-317604735299637665382971366)⟩⟩,⟨⟨520633964560034553506343848,520633964560034756491486272⟩,⟨(-331154059600514094024084817),(-331154059600513891048533445)⟩⟩,⟨⟨469629008639189641133032224,469629008639189835319595386⟩,⟨(-340864058814609165295269588),(-340864058814608971116913295)⟩⟩,⟨⟨420839392523319919845015891,420839392523320105543432753⟩,⟨(-347038697429368872438577382),(-347038697429368686747076067)⟩⟩,⟨⟨374382055468564558798364669,374382055468564736229395451⟩,⟨(-349980620888148578819559762),(-349980620888148401394246338)⟩⟩,⟨⟨330348549451610142765473992,330348549451610312252367643⟩,⟨(-349989074144329296890929683),(-349989074144329127408647666)⟩⟩] +lemma kernel24_0_r5_5_eq : ∀ k : Fin 16, kernel24_0Expr 5 5 k = kernel24_0_r5_5 k := by decide +kernel +noncomputable def kernel24_0_r5_6 : Fin 16 → CBox := ![⟨⟨288806125395916251391701653,288806125395916413144851149⟩,⟨(-347357969743811253361885981),(-347357969743811091612333057)⟩⟩,⟨⟨249798961856240962402246849,249798961856241116721254259⟩,⟨(-342374116646165012888218043),(-342374116646164858571881066)⟩⟩,⟨⟨213349515654273753878469796,213349515654273900983595925⟩,⟨(-335315618556232024023606909),(-335315618556231876920311349)⟩⟩,⟨⟨179459973688676379094457425,179459973688676519265389505⟩,⟨(-326450448110177188676777887),(-326450448110177048506929939)⟩⟩,⟨⟨148113785154563043385368889,148113785154563176824155534⟩,⟨(-316035200877363741535044167),(-316035200877363608096676161)⟩⟩,⟨⟨119277253686125699957077966,119277253686125826943175130⟩,⟨(-304314030834043224521695078),(-304314030834043097535426536)⟩⟩,⟨⟨92901169463871091892446238,92901169463871212631396716⟩,⟨(-291517766766015217034900097),(-291517766766015096295260060)⟩⟩,⟨⟨68922462083846226015410311,68922462083846340769351535⟩,⟨(-277863206991205203943966933),(-277863206991205089188885912)⟩⟩,⟨⟨47265855946791827434267314,47265855946791936540072523⟩,⟨(-263552587882134991038091285),(-263552587882134881930760046)⟩⟩,⟨⟨27845511064867360678564420,27845511064867464431860853⟩,⟨(-248773219931408533523772127),(-248773219931408429768623259)⟩⟩,⟨⟨10566633475465234305379201,10566633475465332880731916⟩,⟨(-233697283555650556221006049),(-233697283555650457643530356)⟩⟩,⟨⟨(-4672959132200027600326238),(-4672959132199933978229925)⟩,⟨(-218481775485957915571755960),(-218481775485957821947317666)⟩⟩,⟨⟨(-17981329459817511753034395),(-17981329459817422921922030)⟩,⟨(-203268595453117514564113167),(-203268595453117425730487417)⟩⟩,⟨⟨(-29470981613910325879825194),(-29470981613910241616074977)⟩,⟨(-188184761947090467523249709),(-188184761947090383256858651)⟩⟩,⟨⟨(-39257500772120658824919533),(-39257500772120578964871666)⟩,⟨(-173342745112422019117003995),(-173342745112421939254227710)⟩⟩,⟨⟨(-47458279548065418330967868),(-47458279548065342663758354)⟩,⟨(-158840904330777361741095006),(-158840904330777286071104650)⟩⟩] +lemma kernel24_0_r5_6_eq : ∀ k : Fin 16, kernel24_0Expr 5 6 k = kernel24_0_r5_6 k := by decide +kernel +noncomputable def kernel24_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-54191337476707104037378188),(-54191337476707032415676681)⟩,⟨(-144764017732072719935428004),(-144764017732072648310924896)⟩⟩,⟨⟨(-59574238451599899237526193),(-59574238451599831452308725)⟩,⟨(-131183890757216449528167332),(-131183890757216381740268411)⟩⟩,⟨⟨(-63723109409376277265793388),(-63723109409376213157130968)⟩,⟨(-118160030956396550755338542),(-118160030956396486644364720)⟩⟩,⟨⟨(-66751762093990196612402464),(-66751762093990135998141575)⟩,⟨(-105740376433178599303336966),(-105740376433178538687107701)⟩⟩,⟨⟨(-68770918359569949595781430),(-68770918359569892340915124)⟩,⟨(-93962065720762657198305508),(-93962065720762599941787288)⟩⟩,⟨⟨(-69887538199676298308357766),(-69887538199676244235637478)⟩,⟨(-82852237385658905867378784),(-82852237385658851793296734)⟩⟩,⟨⟨(-70204248533059272270924771),(-70204248533059221250058709)⟩,⟨(-72428848277962047410540781),(-72428848277961996388577602)⟩⟩,⟨⟨(-69818869739746595017054918),(-69818869739746546887337016)⟩,⟨(-62701500068012246265430251),(-62701500068012198134855054)⟩⟩,⟨⟨(-68824036031959881268493770),(-68824036031959835877308793)⟩,⟨(-53672264508064108554562649),(-53672264508064063162736459)⟩⟩,⟨⟨(-67306904964922424188313696),(-67306904964922381371951624)⟩,⟨(-45336498716383500641657215),(-45336498716383457824847167)⟩⟩,⟨⟨(-65348950743719316654948354),(-65348950743719276304173005)⟩,⟨(-37683642682203122475168521),(-37683642682203082124116758)⟩⟩,⟨⟨(-63025835462444390929747723),(-63025835462444352909698053)⟩,⟨(-30697992116224954738657312),(-30697992116224916718481335)⟩⟩,⟨⟨(-60407352017396299775738068),(-60407352017396263988005751)⟩,⟨(-24359440706917329103687904),(-24359440706917293315958693)⟩⟩,⟨⟨(-57557432161803204361292584),(-57557432161803170673921248)⟩,⟨(-18644186772994456301762463),(-18644186772994422614505992)⟩⟩,⟨⟨(-54534213008698069626054262),(-54534213008698037944200554)⟩,⟨(-13525400213844776808599340),(-13525400213844745126955847)⟩⟩,⟨⟨(-51390155233122864579557628),(-51390155233122834787950122)⟩,⟨(-8973846540447396177985741),(-8973846540447366386668671)⟩⟩] +lemma kernel24_0_r5_7_eq : ∀ k : Fin 16, kernel24_0Expr 5 7 k = kernel24_0_r5_7 k := by decide +kernel +noncomputable def kernel24_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-48172206265804458478177292),(-48172206265804430491378155)⟩,⟨(-4958465609215576146849374),(-4958465609215548160406963)⟩⟩,⟨⟨(-44922001898068859062213703),(-44922001898068832755429117)⟩,⟨(-1446903471582742323422149),(-1446903471582716017047930)⟩⟩,⟨⟨(-41676099921794055776683565),(-41676099921794031071291629)⟩,⟨1594003514026924400483393,1594003514026949105422843⟩⟩,⟨⟨(-38466239698124751322067313),(-38466239698124728122385845)⟩,⟨4197792489354058909434234,4197792489354082108631416⟩⟩,⟨⟨(-35319621873907358035194656),(-35319621873907336271142109)⟩,⟨6397985398116090718743231,6397985398116112482288986⟩⟩,⟨⟨(-32259202834911104335314645),(-32259202834911083916492694)⟩,⟨8227746820316674110462016,8227746820316694528762827⟩⟩,⟨⟨(-29303998889752001520255424),(-29303998889751982375594504)⟩,⟨9719586908558051095633492,9719586908558070239766257⟩⟩,⟨⟨(-26469395608362686971767897),(-26469395608362669020141675)⟩,⟨10905107596696968345506592,10905107596696986296603906⟩⟩,⟨⟨(-23767458184771736829735073),(-23767458184771720014467833)⟩,⟨11814789919891933816915240,11814789919891950631704816⟩⟩,⟨⟨(-21207239147478888556375771),(-21207239147478872802595499)⟩,⟨12477820019392458830403960,12477820019392474583777404⟩⟩,⟨⟨(-18795080194212789922197513),(-18795080194212775172870559)⟩,⟨12921951202208384816608356,12921951202208399565593402⟩⟩,⟨⟨(-16534905374532593414225264),(-16534905374532579604511527)⟩,⟨13173399281267724813202642,13173399281267738622633595⟩⟩,⟨⟨(-14428503277636509077910553),(-14428503277636496160696071)⟩,⟨13256768331474619511810544,13256768331474632428795827⟩⟩,⟨⟨(-12475796298790301821699173),(-12475796298790289735382805)⟩,⟨13195003956454271829814541,13195003956454283915949951⟩⟩,⟨⟨(-10675095451770847475555272),(-10675095451770836176240952)⟩,⟨13009371164678206282855917,13009371164678217582032474⟩⟩,⟨⟨(-9023339563260216437737743),(-9023339563260205872303394)⟩,⟨12719453996901437422592717,12719453996901447987927704⟩⟩] +lemma kernel24_0_r5_8_eq : ∀ k : Fin 16, kernel24_0Expr 5 8 k = kernel24_0_r5_8 k := by decide +kernel +noncomputable def kernel24_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-7516318025656774051548987),(-7516318025656764182519679)⟩,⟨12343174124166062586273067,12343174124166072455236929⟩⟩,⟨⟨(-6148876595483445770200693),(-6148876595483436548135390)⟩,⟨11896825741838029212927102,11896825741838038434956672⟩⟩,⟨⟨(-4915106004364849511023916),(-4915106004364840900431714)⟩,⟨11395124215188484110240227,11395124215188492720822512⟩⟩,⟨⟨(-3808513397949693798685533),(-3808513397949685757431547)⟩,⟨10851266081063816621216467,10851266081063824662482346⟩⟩,⟨⟨(-2822176835279711965098414),(-2822176835279704462865483)⟩,⟨10276998173638528885034840,10276998173638536387298179⟩⟩,⟨⟨(-1948883267559182051083707),(-1948883267559175048981211)⟩,⟨9682693815863827460636693,9682693815863834462785156⟩⟩,⟨⟨(-1181250572096045671937611),(-1181250572096039141809321)⟩,⟨9077434198122309463621985,9077434198122315993809106⟩⟩,⟨⟨(-511834345760035428613023),(-511834345760029337029892)⟩,⟨8469093248268841458957142,8469093248268847550609542⟩⟩,⟨⟨66779735684309720747661,66779735684315397529617⟩,⟨7864424479571265475556096,7864424479571271152415570⟩⟩,⟨⟨561897108659660580914613,561897108659665873966007⟩,⟨7269148482356491440613354,7269148482356496733748577⟩⟩,⟨⟨980648124810460293754169,980648124810465225271632⟩,⟨6688039899112013655123255,6688039899112018586729123⟩⟩,⟨⟨1329933493212914438956295,1329933493212919035228525⟩,⟨6125012889472979683340026,6125012889472984279703730⟩⟩,⟨⟨1616380372894620964515277,1616380372894625244351446⟩,⟨5583204249395807920118084,5583204249395812200047457⟩⟩,⟨⟨1846308126719686545913214,1846308126719690533410416⟩,⟨5065053496686518209960563,5065053496686522197551565⟩⟩,⟨⟨2025702761447493949862153,2025702761447497662319442⟩,⟨4572379372045697925969331,4572379372045701638520023⟩⟩,⟨⟨2160199104246556394698339,2160199104246559869847976⟩,⟨4106452330339031145646936,4106452330339034620878316⟩⟩] +lemma kernel24_0_r5_9_eq : ∀ k : Fin 16, kernel24_0Expr 5 9 k = kernel24_0_r5_9 k := by decide +kernel +noncomputable def kernel24_0_r5_10 : Fin 16 → CBox := ![⟨⟨2255069801127195636799474,2255069801127198888457859⟩,⟨3668062710595363239552756,3668062710595366491280987⟩⟩,⟨⟨2315220265756205215808251,2315220265756208260561677⟩,⟨3257584375201087323243540,3257584375201090368055969⟩⟩,⟨⟨2345188756178165831211839,2345188756178168680235232⟩,⟨2875033699031513539212353,2875033699031516388284898⟩⟩,⟨⟨2349150810485350373094622,2349150810485353040295020⟩,⟨2520123868140775504103363,2520123868140778171344013⟩⟩,⟨⟨2330927329000957012672371,2330927329000959507432093⟩,⟨2192314515568536695997205,2192314515568539190789169⟩⟩,⟨⟨2293995648777906402963541,2293995648777908738193943⟩,⟨1890856779375601756971689,1890856779375604092227171⟩⟩,⟨⟨2241503015036007824174259,2241503015036010008650354⟩,⟨1614833915840929540088114,1614833915840931724582913⟩⟩,⟨⟨2176281912588319663321089,2176281912588321707972968⟩,⟨1363197639552725130511552,1363197639552727175176494⟩⟩,⟨⟨2100866777517689280631205,2100866777517691192652085⟩,⟨1134800392661384751282866,1134800392661386663311846⟩⟩,⟨⟨2017511664674033458596993,2017511664674035248238911⟩,⟨928423768609602829536468,928423768609604619182151⟩⟩,⟨⟨1928208499422508266532877,1928208499422509940619249⟩,⟨742803331997826732885886,742803331997828406972263⟩⟩,⟨⟨1834705592055820158087218,1834705592055821725145212⟩,⟨576650086655180143073672,576650086655181710128456⟩⟩,⟨⟨1738526140075803271983839,1738526140075804737671725⟩,⟨428668849219322044239064,428668849219323509921050⟩⟩,⟨⟨1640986486935468407750794,1640986486935469779971239⟩,⟨297573786304528043155032,297573786304529415367309⟩⟩,⟨⟨1543213945686958387986790,1543213945686959672015417⟩,⟨182101370337546642734494,182101370337547926753068⟩⟩,⟨⟨1446164032254131536543502,1446164032254132738994208⟩,⟨81021003002519702824634,81021003002520905263746⟩⟩] +lemma kernel24_0_r5_10_eq : ∀ k : Fin 16, kernel24_0Expr 5 10 k = kernel24_0_r5_10 k := by decide +kernel +noncomputable def kernel24_0_r5_11 : Fin 16 → CBox := ![⟨⟨1350636985757535606539185,1350636985757536731661981⟩,⟨(-6856453452554379544150),(-6856453452553254434181)⟩⟩,⟨⟨1257293482536153664612756,1257293482536154718625278⟩,⟨(-82672007498284401126920),(-82672007498283347128190)⟩⟩,⟨⟨1166669476351455284038859,1166669476351456270961012⟩,⟨(-147513514879154169046214),(-147513514879153182138572)⟩⟩,⟨⟨1079190119877805784581340,1079190119877806709562625⟩,⟨(-202412096458379883658174),(-202412096458378958691911)⟩⟩,⟨⟨995182742159458969979326,995182742159459836273103⟩,⟨(-248339807422315334195274),(-248339807422314467916842)⟩⟩,⟨⟨914888873448344651453161,914888873448345463737127⟩,⟨(-286208382358486242989133),(-286208382358485430720677)⟩⟩,⟨⟨838475322941985207955365,838475322941985969373805⟩,⟨(-316868895274578900351401),(-316868895274578138948497)⟩⟩,⟨⟨766044326637770656426686,766044326637771370866026⟩,⟨(-341112188050808028619691),(-341112188050807314195796)⟩⟩,⟨⟨697642792031415544300802,697642792031416214145716⟩,⟨(-359669934919079618124009),(-359669934919078948293109)⟩⟩,⟨⟨633270673934703631144540,633270673934704260034917⟩,⟨(-373216224181094660316214),(-373216224181094031438118)⟩⟩,⟨⟨572888521486169280821451,572888521486169871072076⟩,⟨(-382369551390068386968061),(-382369551390067796728123)⟩⟩,⟨⟨516424240685524574301025,516424240685525128995047⟩,⟨(-387695130533710298591638),(-387695130533709743906846)⟩⟩,⟨⟨463779119695390962384883,463779119695391483328759⟩,⟨(-389707441303175208680104),(-389707441303174687744129)⟩⟩,⟨⟨414833165907213298230213,414833165907213788156869⟩,⟨(-388872941271054132630135),(-388872941271053642710170)⟩⟩,⟨⟨369449804533996853266634,369449804533997313884729⟩,⟨(-385612881708572283962256),(-385612881708571823349754)⟩⟩,⟨⟨327479988428803730793647,327479988428804164350321⟩,⟨(-380306174842591715742377),(-380306174842591282190301)⟩⟩] +lemma kernel24_0_r5_11_eq : ∀ k : Fin 16, kernel24_0Expr 5 11 k = kernel24_0_r5_11 k := by decide +kernel +noncomputable def kernel24_0_r5_12 : Fin 16 → CBox := ![⟨⟨288765768078768501340985,288765768078768909135062⟩,⟨(-373292268595639566179121),(-373292268595639158388746)⟩⟩,⟨⟨253143369419644964526800,253143369419645348719828⟩,⟨(-364873992287495839308509),(-364873992287495455118377)⟩⟩,⟨⟨220445825371642451668819,220445825371642813685747⟩,⟨(-355320343434624605288064),(-355320343434624243273308)⟩⟩,⟨⟨190505204916245073428388,190505204916245414967652⟩,⟨(-344869191700786904074252),(-344869191700786562536517)⟩⟩,⟨⟨163154481205777353511895,163154481205777675553463⟩,⟨(-333729881270637552114850),(-333729881270637230074235)⟩⟩,⟨⟨138229077700627036308289,138229077700627340448998⟩,⟨(-322085717483683009066869),(-322085717483682704926603)⟩⟩,⟨⟨115568128730025526366486,115568128730025813543612⟩,⟨(-310096327526549115898180),(-310096327526548828721047)⟩⟩,⟨⟨95015488227585296539090,95015488227585568069244⟩,⟨(-297899888385948625158919),(-297899888385948353628362)⟩⟩,⟨⟨76420517749475846969076,76420517749476103552528⟩,⟨(-285615218161910392759795),(-285615218161910136175594)⟩⟩,⟨⟨59638682279775770107085,59638682279776013002855⟩,⟨(-273343729278768388596199),(-273343729278768145699382)⟩⟩,⟨⟨44531979795169703473498,44531979795169933380449⟩,⟨(-261171244156662035852437),(-261171244156661805944186)⟩⟩,⟨⟨30969228124044068956066,30969228124044286873451⟩,⟨(-249169675563435279934672),(-249169675563435062015769)⟩⟩,⟨⟨18826230311556597885090,18826230311556804343123⟩,⟨(-237398575198040354079317),(-237398575198040147619581)⟩⟩,⟨⟨7985837505675195326332,7985837505675391278531⟩,⟨(-225906555101422322134768),(-225906555101422126180708)⟩⟩,⟨⟨(-1662073681629133763267),(-1662073681628947750996)⟩,⟨(-214732587286149549608522),(-214732587286149363594259)⟩⟩,⟨⟨(-10220694303751303152341),(-10220694303751126242226)⟩,⟨(-203907187555640452563199),(-203907187555640275650983)⟩⟩] +lemma kernel24_0_r5_12_eq : ∀ k : Fin 16, kernel24_0Expr 5 12 k = kernel24_0_r5_12 k := by decide +kernel +noncomputable def kernel24_0_r5_13 : Fin 16 → CBox := ![⟨⟨(-17786433442068217550781),(-17786433442068049391772)⟩,⟨(-193453489878683659392729),(-193453489878683491231532)⟩⟩,⟨⟨(-24449114179074778136686),(-24449114179074617973579)⟩,⟨(-183388217923144730058247),(-183388217923144569892882)⟩⟩,⟨⟨(-30292205054151247711412),(-30292205054151095168055)⟩,⟨(-173722560459585338038107),(-173722560459585185492440)⟩⟩,⟨⟨(-35393078233443179177466),(-35393078233443033666221)⟩,⟨(-164462957343589833740611),(-164462957343589688227019)⟩⟩,⟨⟨(-39823286854784882475200),(-39823286854784743724683)⟩,⟨(-155611802694948280139084),(-155611802694948141386193)⟩⟩,⟨⟨(-43648855114614760273214),(-43648855114614627707707)⟩,⟨(-147168071730138397578869),(-147168071730138265010972)⟩⟩,⟨⟨(-46930575653559265452298),(-46930575653559138790057)⟩,⟨(-139127877487207729137070),(-139127877487207602472433)⟩⟩,⟨⟨(-49724309678361253398028),(-49724309678361132179907)⟩,⟨(-131484963422554198861538),(-131484963422554077641024)⟩⟩,⟨⟨(-52081286037872665891084),(-52081286037872549936269)⟩,⟨(-124231137568732180793497),(-124231137568732064836298)⟩⟩,⟨⟨(-54048396157744543924952),(-54048396157744432763539)⟩,⟨(-117356653631061989895266),(-117356653631061878731484)⟩⟩,⟨⟨(-55668482339967569224630),(-55668482339967462639215)⟩,⟨(-110850544076748141146814),(-110850544076748034559151)⟩⟩,⟨⟨(-56980617457089404905699),(-56980617457089302530710)⟩,⟨(-104700909940298416512030),(-104700909940298314134957)⟩⟩,⟨⟨(-58020374524031194382472),(-58020374524031096081311)⟩,⟨(-98895171738946481760200),(-98895171738946383457110)⟩⟩,⟨⟨(-58820085019877165500169),(-58820085019877070909351)⟩,⟨(-93420285566107341606968),(-93420285566107247014365)⟩⟩,⟨⟨(-59409085164368802328325),(-59409085164368711294950)⟩,⟨(-88262928113290831117441),(-88262928113290740082414)⟩⟩,⟨⟨(-59813949635237694228014),(-59813949635237606465378)⟩,⟨(-83409654064202918247240),(-83409654064202830483077)⟩⟩] +lemma kernel24_0_r5_13_eq : ∀ k : Fin 16, kernel24_0Expr 5 13 k = kernel24_0_r5_13 k := by decide +kernel +noncomputable def kernel24_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-60058712448670260202348),(-60058712448670175627892)⟩,⟨(-78847029011116189937612),(-78847029011116105361744)⟩⟩,⟨⟨(-60165074921390324111254),(-60165074921390242414780)⟩,⟨(-74561740764529675699515),(-74561740764529594001737)⟩⟩,⟨⟨(-60152600793917325508794),(-60152600793917246577143)⟩,⟨(-70540691663698442733366),(-70540691663698363800510)⟩⟩,⟨⟨(-60038898724931185624556),(-60038898724931109227083)⟩,⟨(-66771074248406196820601),(-66771074248406120422015)⟩⟩,⟨⟨(-59839792470363008831056),(-59839792470362934903192)⟩,⟨(-63240432421640269698463),(-63240432421640195769572)⟩⟩,⟨⟨(-59569479141456548958297),(-59569479141456477257651)⟩,⟨(-59936710018582929667215),(-59936710018582857965622)⟩⟩,⟨⟨(-59240675996861288491880),(-59240675996861218934563)⟩,⟨(-56848288499301427649098),(-56848288499301358090908)⟩⟩,⟨⟨(-58864756267729287147829),(-58864756267729219545472)⟩,⟨(-53964015300266375605701),(-53964015300266308002538)⟩⟩,⟨⟨(-58451874544376241547700),(-58451874544376175868078)⟩,⟨(-51273224212779956761393),(-51273224212779891081029)⟩⟩,⟨⟨(-58011082270614685017455),(-58011082270614621048070)⟩,⟨(-48765749003875179351127),(-48765749003875115381057)⟩⟩,⟨⟨(-57550433899380948618108),(-57550433899380886296539)⟩,⟨(-46431931356505339079595),(-46431931356505276757396)⟩⟩,⟨⟨(-57077084262512939618578),(-57077084262512878788329)⟩,⟨(-44262624080082227121245),(-44262624080082166290415)⟩⟩,⟨⟨(-56597377700019955067511),(-56597377700019895703511)⟩,⟨(-42249190428819300039336),(-42249190428819240674800)⟩⟩,⟨⟨(-56116929481239042298311),(-56116929481238984227251)⟩,⟨(-40383500263059825250369),(-40383500263059767178815)⟩⟩,⟨⟨(-55640700033029402050467),(-55640700033029345225516)⟩,⟨(-38657923696992443144328),(-38657923696992386318921)⟩⟩,⟨⟨(-55173062469585223383628),(-55173062469585167672060)⟩,⟨(-37065322794065810062576),(-37065322794065754350586)⟩⟩] +lemma kernel24_0_r5_14_eq : ∀ k : Fin 16, kernel24_0Expr 5 14 k = kernel24_0_r5_14 k := by decide +kernel +noncomputable def kernel24_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-54717863895368117048869),(-54717863895368062447983)⟩,⟨(-35599041798222203334228),(-35599041798222148732953)⟩⟩,⟨⟨(-54278480927761481770761),(-54278480927761428118440)⟩,⟨(-34252896324019719521068),(-34252896324019665868388)⟩⟩,⟨⟨(-53857869859903070425214),(-53857869859903017685637)⟩,⟨(-33021161871081288543119),(-33021161871081235803209)⟩⟩,⟨⟨(-53458611857229013177204),(-53458611857228961235127)⟩,⟨(-31898561977411202945670),(-31898561977411151003283)⟩⟩,⟨⟨(-53082953553943497250342),(-53082953553943446100898)⟩,⟨(-30880256281310629656994),(-30880256281310578507263)⟩⟩,⟨⟨(-52732843388216199372245),(-52732843388216148879710)⟩,⟨(-29961828722297038846956),(-29961828722296988354154)⟩⟩,⟨⟨(-52409963987639791388242),(-52409963987639741524222)⟩,⟨(-29139276077022772062350),(-29139276077022722198080)⟩⟩,⟨⟨(-52115760889529371179283),(-52115760889529321840848)⟩,⟨(-28408996996167990060680),(-28408996996167940722011)⟩⟩,⟨⟨(-51851467854141251357537),(-51851467854141202548793)⟩,⟨(-27767781682163148528846),(-27767781682163099719881)⟩⟩,⟨⟨(-51618129002913952817124),(-51618129002913904400826)⟩,⟨(-27212802324921430342211),(-27212802324921381925704)⟩⟩,⟨⟨(-51416617988436706172857),(-51416617988436658126411)⟩,⟨(-26741604393110702895163),(-26741604393110654848516)⟩⟩,⟨⟨(-51247654378046556016606),(-51247654378046508246470)⟩,⟨(-26352098861476532287874),(-26352098861476484517546)⟩⟩,⟨⟨(-51111817408734600096050),(-51111817408734552607586)⟩,⟨(-26042555439979240055207),(-26042555439979192566557)⟩⟩,⟨⟨(-51009557247373678925171),(-51009557247373631600472)⟩,⟨(-25811596857690443958106),(-25811596857690396633227)⟩⟩,⟨⟨(-50941203867114845487934),(-50941203867114798306173)⟩,⟨(-25658194243191323546061),(-25658194243191276364122)⟩⟩,⟨⟨(-50906973628074648935751),(-50906973628074601807644)⟩,⟨(-25581663633328139302280),(-25581663633328092173996)⟩⟩] +lemma kernel24_0_r5_15_eq : ∀ k : Fin 16, kernel24_0Expr 5 15 k = kernel24_0_r5_15 k := by decide +kernel +noncomputable def kernel24_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel24_0_r5_0,kernel24_0_r5_1,kernel24_0_r5_2,kernel24_0_r5_3,kernel24_0_r5_4,kernel24_0_r5_5,kernel24_0_r5_6,kernel24_0_r5_7,kernel24_0_r5_8,kernel24_0_r5_9,kernel24_0_r5_10,kernel24_0_r5_11,kernel24_0_r5_12,kernel24_0_r5_13,kernel24_0_r5_14,kernel24_0_r5_15] +lemma kernel24_0_r5_eq (i k : Fin 16) : kernel24_0Expr 5 i k = kernel24_0_r5 i k := by + fin_cases i + · exact kernel24_0_r5_0_eq k + · exact kernel24_0_r5_1_eq k + · exact kernel24_0_r5_2_eq k + · exact kernel24_0_r5_3_eq k + · exact kernel24_0_r5_4_eq k + · exact kernel24_0_r5_5_eq k + · exact kernel24_0_r5_6_eq k + · exact kernel24_0_r5_7_eq k + · exact kernel24_0_r5_8_eq k + · exact kernel24_0_r5_9_eq k + · exact kernel24_0_r5_10_eq k + · exact kernel24_0_r5_11_eq k + · exact kernel24_0_r5_12_eq k + · exact kernel24_0_r5_13_eq k + · exact kernel24_0_r5_14_eq k + · exact kernel24_0_r5_15_eq k +noncomputable def kernel24_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel24_0_r0,kernel24_0_r1,kernel24_0_r2,kernel24_0_r3,kernel24_0_r4,kernel24_0_r5] +lemma kernel24_0_eq (j : Fin 6) (i k : Fin 16) : kernel24_0Expr j i k = kernel24_0 j i k := by + fin_cases j + · exact kernel24_0_r0_eq i k + · exact kernel24_0_r1_eq i k + · exact kernel24_0_r2_eq i k + · exact kernel24_0_r3_eq i k + · exact kernel24_0_r4_eq i k + · exact kernel24_0_r5_eq i k +lemma kernel24_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel24_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(24:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel24_0_eq] + unfold kernel24_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans24_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel24_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans24 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel24_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r0_0_eq : ∀ k : Fin 16, kernel24_1Expr 0 0 k = kernel24_1_r0_0 k := by decide +kernel +noncomputable def kernel24_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r0_1_eq : ∀ k : Fin 16, kernel24_1Expr 0 1 k = kernel24_1_r0_1 k := by decide +kernel +noncomputable def kernel24_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r0_2_eq : ∀ k : Fin 16, kernel24_1Expr 0 2 k = kernel24_1_r0_2 k := by decide +kernel +noncomputable def kernel24_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r0_3_eq : ∀ k : Fin 16, kernel24_1Expr 0 3 k = kernel24_1_r0_3 k := by decide +kernel +noncomputable def kernel24_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r0_4_eq : ∀ k : Fin 16, kernel24_1Expr 0 4 k = kernel24_1_r0_4 k := by decide +kernel +noncomputable def kernel24_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel24_1_r0_5_eq : ∀ k : Fin 16, kernel24_1Expr 0 5 k = kernel24_1_r0_5 k := by decide +kernel +noncomputable def kernel24_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel24_1_r0_6_eq : ∀ k : Fin 16, kernel24_1Expr 0 6 k = kernel24_1_r0_6 k := by decide +kernel +noncomputable def kernel24_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel24_1_r0_7_eq : ∀ k : Fin 16, kernel24_1Expr 0 7 k = kernel24_1_r0_7 k := by decide +kernel +noncomputable def kernel24_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel24_1_r0_8_eq : ∀ k : Fin 16, kernel24_1Expr 0 8 k = kernel24_1_r0_8 k := by decide +kernel +noncomputable def kernel24_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel24_1_r0_9_eq : ∀ k : Fin 16, kernel24_1Expr 0 9 k = kernel24_1_r0_9 k := by decide +kernel +noncomputable def kernel24_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel24_1_r0_10_eq : ∀ k : Fin 16, kernel24_1Expr 0 10 k = kernel24_1_r0_10 k := by decide +kernel +noncomputable def kernel24_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel24_1_r0_11_eq : ∀ k : Fin 16, kernel24_1Expr 0 11 k = kernel24_1_r0_11 k := by decide +kernel +noncomputable def kernel24_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel24_1_r0_12_eq : ∀ k : Fin 16, kernel24_1Expr 0 12 k = kernel24_1_r0_12 k := by decide +kernel +noncomputable def kernel24_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel24_1_r0_13_eq : ∀ k : Fin 16, kernel24_1Expr 0 13 k = kernel24_1_r0_13 k := by decide +kernel +noncomputable def kernel24_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel24_1_r0_14_eq : ∀ k : Fin 16, kernel24_1Expr 0 14 k = kernel24_1_r0_14 k := by decide +kernel +noncomputable def kernel24_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel24_1_r0_15_eq : ∀ k : Fin 16, kernel24_1Expr 0 15 k = kernel24_1_r0_15 k := by decide +kernel +noncomputable def kernel24_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel24_1_r0_0,kernel24_1_r0_1,kernel24_1_r0_2,kernel24_1_r0_3,kernel24_1_r0_4,kernel24_1_r0_5,kernel24_1_r0_6,kernel24_1_r0_7,kernel24_1_r0_8,kernel24_1_r0_9,kernel24_1_r0_10,kernel24_1_r0_11,kernel24_1_r0_12,kernel24_1_r0_13,kernel24_1_r0_14,kernel24_1_r0_15] +lemma kernel24_1_r0_eq (i k : Fin 16) : kernel24_1Expr 0 i k = kernel24_1_r0 i k := by + fin_cases i + · exact kernel24_1_r0_0_eq k + · exact kernel24_1_r0_1_eq k + · exact kernel24_1_r0_2_eq k + · exact kernel24_1_r0_3_eq k + · exact kernel24_1_r0_4_eq k + · exact kernel24_1_r0_5_eq k + · exact kernel24_1_r0_6_eq k + · exact kernel24_1_r0_7_eq k + · exact kernel24_1_r0_8_eq k + · exact kernel24_1_r0_9_eq k + · exact kernel24_1_r0_10_eq k + · exact kernel24_1_r0_11_eq k + · exact kernel24_1_r0_12_eq k + · exact kernel24_1_r0_13_eq k + · exact kernel24_1_r0_14_eq k + · exact kernel24_1_r0_15_eq k +noncomputable def kernel24_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel24_1_r1_0_eq : ∀ k : Fin 16, kernel24_1Expr 1 0 k = kernel24_1_r1_0 k := by decide +kernel +noncomputable def kernel24_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel24_1_r1_1_eq : ∀ k : Fin 16, kernel24_1Expr 1 1 k = kernel24_1_r1_1 k := by decide +kernel +noncomputable def kernel24_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel24_1_r1_2_eq : ∀ k : Fin 16, kernel24_1Expr 1 2 k = kernel24_1_r1_2 k := by decide +kernel +noncomputable def kernel24_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel24_1_r1_3_eq : ∀ k : Fin 16, kernel24_1Expr 1 3 k = kernel24_1_r1_3 k := by decide +kernel +noncomputable def kernel24_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel24_1_r1_4_eq : ∀ k : Fin 16, kernel24_1Expr 1 4 k = kernel24_1_r1_4 k := by decide +kernel +noncomputable def kernel24_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel24_1_r1_5_eq : ∀ k : Fin 16, kernel24_1Expr 1 5 k = kernel24_1_r1_5 k := by decide +kernel +noncomputable def kernel24_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel24_1_r1_6_eq : ∀ k : Fin 16, kernel24_1Expr 1 6 k = kernel24_1_r1_6 k := by decide +kernel +noncomputable def kernel24_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel24_1_r1_7_eq : ∀ k : Fin 16, kernel24_1Expr 1 7 k = kernel24_1_r1_7 k := by decide +kernel +noncomputable def kernel24_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel24_1_r1_8_eq : ∀ k : Fin 16, kernel24_1Expr 1 8 k = kernel24_1_r1_8 k := by decide +kernel +noncomputable def kernel24_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel24_1_r1_9_eq : ∀ k : Fin 16, kernel24_1Expr 1 9 k = kernel24_1_r1_9 k := by decide +kernel +noncomputable def kernel24_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r1_10_eq : ∀ k : Fin 16, kernel24_1Expr 1 10 k = kernel24_1_r1_10 k := by decide +kernel +noncomputable def kernel24_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r1_11_eq : ∀ k : Fin 16, kernel24_1Expr 1 11 k = kernel24_1_r1_11 k := by decide +kernel +noncomputable def kernel24_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r1_12_eq : ∀ k : Fin 16, kernel24_1Expr 1 12 k = kernel24_1_r1_12 k := by decide +kernel +noncomputable def kernel24_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r1_13_eq : ∀ k : Fin 16, kernel24_1Expr 1 13 k = kernel24_1_r1_13 k := by decide +kernel +noncomputable def kernel24_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r1_14_eq : ∀ k : Fin 16, kernel24_1Expr 1 14 k = kernel24_1_r1_14 k := by decide +kernel +noncomputable def kernel24_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel24_1_r1_15_eq : ∀ k : Fin 16, kernel24_1Expr 1 15 k = kernel24_1_r1_15 k := by decide +kernel +noncomputable def kernel24_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel24_1_r1_0,kernel24_1_r1_1,kernel24_1_r1_2,kernel24_1_r1_3,kernel24_1_r1_4,kernel24_1_r1_5,kernel24_1_r1_6,kernel24_1_r1_7,kernel24_1_r1_8,kernel24_1_r1_9,kernel24_1_r1_10,kernel24_1_r1_11,kernel24_1_r1_12,kernel24_1_r1_13,kernel24_1_r1_14,kernel24_1_r1_15] +lemma kernel24_1_r1_eq (i k : Fin 16) : kernel24_1Expr 1 i k = kernel24_1_r1 i k := by + fin_cases i + · exact kernel24_1_r1_0_eq k + · exact kernel24_1_r1_1_eq k + · exact kernel24_1_r1_2_eq k + · exact kernel24_1_r1_3_eq k + · exact kernel24_1_r1_4_eq k + · exact kernel24_1_r1_5_eq k + · exact kernel24_1_r1_6_eq k + · exact kernel24_1_r1_7_eq k + · exact kernel24_1_r1_8_eq k + · exact kernel24_1_r1_9_eq k + · exact kernel24_1_r1_10_eq k + · exact kernel24_1_r1_11_eq k + · exact kernel24_1_r1_12_eq k + · exact kernel24_1_r1_13_eq k + · exact kernel24_1_r1_14_eq k + · exact kernel24_1_r1_15_eq k +noncomputable def kernel24_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-25),12⟩,⟨13,48⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-20),10⟩,⟨13,40⟩⟩] +lemma kernel24_1_r2_0_eq : ∀ k : Fin 16, kernel24_1Expr 2 0 k = kernel24_1_r2_0 k := by decide +kernel +noncomputable def kernel24_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-20),10⟩,⟨13,40⟩⟩,⟨⟨(-13),12⟩,⟨5,29⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-13),12⟩,⟨5,30⟩⟩,⟨⟨(-16),22⟩,⟨(-6),30⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩] +lemma kernel24_1_r2_1_eq : ∀ k : Fin 16, kernel24_1Expr 2 1 k = kernel24_1_r2_1 k := by decide +kernel +noncomputable def kernel24_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),19⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩] +lemma kernel24_1_r2_2_eq : ∀ k : Fin 16, kernel24_1Expr 2 2 k = kernel24_1_r2_2 k := by decide +kernel +noncomputable def kernel24_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-11),20⟩,⟨(-6),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩] +lemma kernel24_1_r2_3_eq : ∀ k : Fin 16, kernel24_1Expr 2 3 k = kernel24_1_r2_3 k := by decide +kernel +noncomputable def kernel24_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-17),25⟩,⟨(-20),22⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel24_1_r2_4_eq : ∀ k : Fin 16, kernel24_1Expr 2 4 k = kernel24_1_r2_4 k := by decide +kernel +noncomputable def kernel24_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel24_1_r2_5_eq : ∀ k : Fin 16, kernel24_1Expr 2 5 k = kernel24_1_r2_5 k := by decide +kernel +noncomputable def kernel24_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel24_1_r2_6_eq : ∀ k : Fin 16, kernel24_1Expr 2 6 k = kernel24_1_r2_6 k := by decide +kernel +noncomputable def kernel24_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel24_1_r2_7_eq : ∀ k : Fin 16, kernel24_1Expr 2 7 k = kernel24_1_r2_7 k := by decide +kernel +noncomputable def kernel24_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel24_1_r2_8_eq : ∀ k : Fin 16, kernel24_1Expr 2 8 k = kernel24_1_r2_8 k := by decide +kernel +noncomputable def kernel24_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel24_1_r2_9_eq : ∀ k : Fin 16, kernel24_1Expr 2 9 k = kernel24_1_r2_9 k := by decide +kernel +noncomputable def kernel24_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel24_1_r2_10_eq : ∀ k : Fin 16, kernel24_1Expr 2 10 k = kernel24_1_r2_10 k := by decide +kernel +noncomputable def kernel24_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel24_1_r2_11_eq : ∀ k : Fin 16, kernel24_1Expr 2 11 k = kernel24_1_r2_11 k := by decide +kernel +noncomputable def kernel24_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel24_1_r2_12_eq : ∀ k : Fin 16, kernel24_1Expr 2 12 k = kernel24_1_r2_12 k := by decide +kernel +noncomputable def kernel24_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel24_1_r2_13_eq : ∀ k : Fin 16, kernel24_1Expr 2 13 k = kernel24_1_r2_13 k := by decide +kernel +noncomputable def kernel24_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel24_1_r2_14_eq : ∀ k : Fin 16, kernel24_1Expr 2 14 k = kernel24_1_r2_14 k := by decide +kernel +noncomputable def kernel24_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel24_1_r2_15_eq : ∀ k : Fin 16, kernel24_1Expr 2 15 k = kernel24_1_r2_15 k := by decide +kernel +noncomputable def kernel24_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel24_1_r2_0,kernel24_1_r2_1,kernel24_1_r2_2,kernel24_1_r2_3,kernel24_1_r2_4,kernel24_1_r2_5,kernel24_1_r2_6,kernel24_1_r2_7,kernel24_1_r2_8,kernel24_1_r2_9,kernel24_1_r2_10,kernel24_1_r2_11,kernel24_1_r2_12,kernel24_1_r2_13,kernel24_1_r2_14,kernel24_1_r2_15] +lemma kernel24_1_r2_eq (i k : Fin 16) : kernel24_1Expr 2 i k = kernel24_1_r2 i k := by + fin_cases i + · exact kernel24_1_r2_0_eq k + · exact kernel24_1_r2_1_eq k + · exact kernel24_1_r2_2_eq k + · exact kernel24_1_r2_3_eq k + · exact kernel24_1_r2_4_eq k + · exact kernel24_1_r2_5_eq k + · exact kernel24_1_r2_6_eq k + · exact kernel24_1_r2_7_eq k + · exact kernel24_1_r2_8_eq k + · exact kernel24_1_r2_9_eq k + · exact kernel24_1_r2_10_eq k + · exact kernel24_1_r2_11_eq k + · exact kernel24_1_r2_12_eq k + · exact kernel24_1_r2_13_eq k + · exact kernel24_1_r2_14_eq k + · exact kernel24_1_r2_15_eq k +noncomputable def kernel24_1_r3_0 : Fin 16 → CBox := ![⟨⟨242261177234286,242261177234317⟩,⟨1132786019608471,1132786019608503⟩⟩,⟨⟨242955770579770,242955770579789⟩,⟨1130488843870372,1130488843870392⟩⟩,⟨⟨244334126360675,244334126360702⟩,⟨1125905023900553,1125905023900584⟩⟩,⟨⟨246374737646147,246374737646167⟩,⟨1119055580878426,1119055580878446⟩⟩,⟨⟨249045728922142,249045728922161⟩,⟨1109971941402140,1109971941402159⟩⟩,⟨⟨252305311429812,252305311429843⟩,⟨1098695809670868,1098695809670900⟩⟩,⟨⟨256102379518754,256102379518773⟩,⟨1085278994469697,1085278994469717⟩⟩,⟨⟨260377238992128,260377238992148⟩,⟨1069783188925059,1069783188925078⟩⟩,⟨⟨265062456417852,265062456417877⟩,⟨1052279700719524,1052279700719549⟩⟩,⟨⟨270083816541116,270083816541136⟩,⟨1032849130316689,1032849130316709⟩⟩,⟨⟨275361373288728,275361373288754⟩,⟨1011580994767235,1011580994767261⟩⟩,⟨⟨280810578431252,280810578431278⟩,⟨988573294857592,988573294857618⟩⟩,⟨⟨286343470788689,286343470788708⟩,⟨963932023728904,963932023728924⟩⟩,⟨⟨291869907951336,291869907951356⟩,⟨937770615635512,937770615635531⟩⟩,⟨⟨297298821855888,297298821855916⟩,⟨910209334222586,910209334222616⟩⟩,⟨⟨302539479222130,302539479222155⟩,⟨881374600568528,881374600568554⟩⟩] +lemma kernel24_1_r3_0_eq : ∀ k : Fin 16, kernel24_1Expr 3 0 k = kernel24_1_r3_0 k := by decide +kernel +noncomputable def kernel24_1_r3_1 : Fin 16 → CBox := ![⟨⟨307502727826385,307502727826417⟩,⟨851398262240295,851398262240327⟩⟩,⟨⟨312102209868495,312102209868521⟩,⟨820416805725418,820416805725443⟩⟩,⟨⟨316255524278342,316255524278361⟩,⟨788570515802367,788570515802386⟩⟩,⟨⟨319885320700254,319885320700280⟩,⟨756002586660061,756002586660086⟩⟩,⟨⟨322920309076093,322920309076115⟩,⟨722858190839663,722858190839692⟩⟩,⟨⟨325296170203575,325296170203600⟩,⟨689283513310828,689283513310853⟩⟩,⟨⟨326956354352772,326956354352797⟩,⟨655424759170774,655424759170800⟩⟩,⟨⟨327852756951269,327852756951289⟩,⟨621427144529904,621427144529923⟩⟩,⟨⟨327946262465121,327946262465152⟩,⟨587433881085547,587433881085579⟩⟩,⟨⟨327207149870341,327207149870366⟩,⟨553585165652127,553585165652153⟩⟩,⟨⟨325615355485874,325615355485894⟩,⟨520017186481405,520017186481424⟩⟩,⟨⟨323160591381461,323160591381494⟩,⟨486861158546633,486861158546670⟩⟩,⟨⟨319842320033014,319842320033033⟩,⟨454242400059033,454242400059053⟩⟩,⟨⟨315669588328752,315669588328771⟩,⟨422279462322516,422279462322536⟩⟩,⟨⟨310660726382779,310660726382798⟩,⟨391083324608161,391083324608181⟩⟩,⟨⟨304842918841594,304842918841614⟩,⟨360756665043151,360756665043171⟩⟩] +lemma kernel24_1_r3_1_eq : ∀ k : Fin 16, kernel24_1Expr 3 1 k = kernel24_1_r3_1 k := by decide +kernel +noncomputable def kernel24_1_r3_2 : Fin 16 → CBox := ![⟨⟨298251658430314,298251658430334⟩,⟨331393217572194,331393217572214⟩⟩,⟨⟨290930093336867,290930093336886⟩,⟨303077223876641,303077223876661⟩⟩,⟨⟨282928281638229,282928281638250⟩,⟨275882987752443,275882987752467⟩⟩,⟨⟨274302367301132,274302367301169⟩,⟨249874537881643,249874537881677⟩⟩,⟨⟨265113693316262,265113693316282⟩,⟨225105403218259,225105403218279⟩⟩,⟨⟨255427868230999,255427868231031⟩,⟨201618503387255,201618503387288⟩⟩,⟨⟨245313802721660,245313802721680⟩,⟨179446154607970,179446154607989⟩⟩,⟨⟨234842732887638,234842732887658⟩,⟨158610189743608,158610189743627⟩⟩,⟨⟨224087246663573,224087246663599⟩,⟨139122189194030,139122189194056⟩⟩,⟨⟨213120329142824,213120329142845⟩,⟨120983817531645,120983817531669⟩⟩,⟨⟨202014441706840,202014441706868⟩,⟨104187259074633,104187259074664⟩⟩,⟨⟨190840648687290,190840648687321⟩,⟨88715744036155,88715744036183⟩⟩,⟨⟨179667803883166,179667803883192⟩,⟨74544155518043,74544155518069⟩⟩,⟨⟨168561807651889,168561807651909⟩,⟨61639706462760,61639706462779⟩⟩,⟨⟨157584943533114,157584943533140⟩,⟨49962674761474,49962674761500⟩⟩,⟨⟨146795301490828,146795301490848⟩,⟨39467184056756,39467184056776⟩⟩] +lemma kernel24_1_r3_2_eq : ∀ k : Fin 16, kernel24_1Expr 3 2 k = kernel24_1_r3_2 k := by decide +kernel +noncomputable def kernel24_1_r3_3 : Fin 16 → CBox := ![⟨⟨136246292919722,136246292919748⟩,⟨30102017384582,30102017384608⟩⟩,⟨⟨125986260601949,125986260601976⟩,⟨21811450676355,21811450676381⟩⟩,⟨⟨116058184864751,116058184864782⟩,⟨14536093281590,14536093281618⟩⟩,⟨⟨106499485322337,106499485322363⟩,⟨8213723066250,8213723066276⟩⟩,⟨⟨97341915825134,97341915825166⟩,⟨2780104271801,2780104271833⟩⟩,⟨⟨88611548622152,88611548622174⟩,⟨(-1830222836221),(-1830222836197)⟩⟩,⟨⟨80328842297859,80328842297879⟩,⟨(-5683190472402),(-5683190472382)⟩⟩,⟨⟨72508786797903,72508786797925⟩,⟨(-8844498747425),(-8844498747401)⟩⟩,⟨⟨65161117826402,65161117826435⟩,⟨(-11378965452316),(-11378965452284)⟩⟩,⟨⟨58290592093545,58290592093565⟩,⟨(-13349936280744),(-13349936280725)⟩⟩,⟨⟨51897314320568,51897314320588⟩,⟨(-14818760125539),(-14818760125519)⟩⟩,⟨⟨45977106569866,45977106569888⟩,⟨(-15844332639880),(-15844332639855)⟩⟩,⟨⟨40521910352814,40521910352834⟩,⟨(-16482709831384),(-16482709831364)⟩⟩,⟨⟨35520212065821,35520212065841⟩,⟨(-16786792089287),(-16786792089267)⟩⟩,⟨⟨30957482598522,30957482598548⟩,⟨(-16806077760063),(-16806077760036)⟩⟩,⟨⟨26816622426090,26816622426110⟩,⟨(-16586484209989),(-16586484209968)⟩⟩] +lemma kernel24_1_r3_3_eq : ∀ k : Fin 16, kernel24_1Expr 3 3 k = kernel24_1_r3_3 k := by decide +kernel +noncomputable def kernel24_1_r3_4 : Fin 16 → CBox := ![⟨⟨23078404115778,23078404115801⟩,⟨(-16170233264396),(-16170233264366)⟩⟩,⟨⟨19721904921021,19721904921041⟩,⟨(-15595797007701),(-15595797007681)⟩⟩,⟨⟨16724922975225,16724922975252⟩,⟨(-14897899178003),(-14897899177977)⟩⟩,⟨⟨14064371505403,14064371505430⟩,⟨(-14107566798724),(-14107566798698)⟩⟩,⟨⟨11716646434434,11716646434460⟩,⟨(-13252226260984),(-13252226260957)⟩⟩,⟨⟨9657963703921,9657963703942⟩,⟨(-12355837799322),(-12355837799302)⟩⟩,⟨⟨7864663602409,7864663602429⟩,⟨(-11439062183844),(-11439062183824)⟩⟩,⟨⟨6313480304636,6313480304663⟩,⟨(-10519453473211),(-10519453473184)⟩⟩,⟨⟨4981775696329,4981775696360⟩,⟨(-9611671821849),(-9611671821820)⟩⟩,⟨⟨3847737360244,3847737360264⟩,⟨(-8727710595813),(-8727710595793)⟩⟩,⟨⟨2890541319764,2890541319786⟩,⟨(-7877132407968),(-7877132407943)⟩⟩,⟨⟨2090480767082,2090480767102⟩,⟨(-7067309116690),(-7067309116670)⟩⟩,⟨⟨1429062537144,1429062537171⟩,⟨(-6303661324690),(-6303661324663)⟩⟩,⟨⟨889073524793,889073524815⟩,⟨(-5589893447891),(-5589893447866)⟩⟩,⟨⟨454619578941,454619578967⟩,⟨(-4928220981865),(-4928220981838)⟩⟩,⟨⟨111139649218,111139649240⟩,⟨(-4319587157928),(-4319587157903)⟩⟩] +lemma kernel24_1_r3_4_eq : ∀ k : Fin 16, kernel24_1Expr 3 4 k = kernel24_1_r3_4 k := by decide +kernel +noncomputable def kernel24_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-154601889549),(-154601889528)⟩,⟨(-3763866739533),(-3763866739512)⟩⟩,⟨⟨(-354541742979),(-354541742952)⟩,⟨(-3260055248343),(-3260055248316)⟩⟩,⟨⟨(-499360049845),(-499360049816)⟩,⟨(-2806442417896),(-2806442417864)⟩⟩,⟨⟨(-598535673738),(-598535673717)⟩,⟨(-2400769142856),(-2400769142836)⟩⟩,⟨⟨(-660411655867),(-660411655846)⟩,⟨(-2040367615875),(-2040367615855)⟩⟩,⟨⟨(-692268227196),(-692268227171)⟩,⟨(-1722284718785),(-1722284718762)⟩⟩,⟨⟨(-700400989189),(-700400989160)⟩,⟨(-1443389056553),(-1443389056521)⟩⟩,⟨⟨(-690202107928),(-690202107907)⟩,⟨(-1200462290740),(-1200462290719)⟩⟩,⟨⟨(-666242618572),(-666242618551)⟩,⟨(-990275644866),(-990275644845)⟩⟩,⟨⟨(-632354195524),(-632354195503)⟩,⟨(-809652618620),(-809652618599)⟩⟩,⟨⟨(-591709002634),(-591709002613)⟩,⟨(-655519065462),(-655519065442)⟩⟩,⟨⟨(-546896489368),(-546896489336)⟩,⟨(-524941861171),(-524941861142)⟩⟩,⟨⟨(-499996238460),(-499996238439)⟩,⟨(-415157425789),(-415157425768)⟩⟩,⟨⟨(-452646194177),(-452646194150)⟩,⟨(-323591361768),(-323591361740)⟩⟩,⟨⟨(-406105803429),(-406105803401)⟩,⟨(-247870442631),(-247870442603)⟩⟩,⟨⟨(-361313784765),(-361313784739)⟩,⟨(-185828134860),(-185828134838)⟩⟩] +lemma kernel24_1_r3_5_eq : ∀ k : Fin 16, kernel24_1Expr 3 5 k = kernel24_1_r3_5 k := by decide +kernel +noncomputable def kernel24_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-318940398630),(-318940398603)⟩,⟨(-135504764926),(-135504764899)⟩⟩,⟨⟨(-279434228601),(-279434228578)⟩,⟨(-95143359244),(-95143359218)⟩⟩,⟨⟨(-243063596009),(-243063595986)⟩,⟨(-63182091277),(-63182091251)⟩⟩,⟨⟨(-209952821049),(-209952821023)⟩,⟨(-38244170742),(-38244170719)⟩⟩,⟨⟨(-180113613814),(-180113613788)⟩,⟨(-19125909101),(-19125909078)⟩⟩,⟨⟨(-153471929639),(-153471929612)⟩,⟨(-4783595170),(-4783595142)⟩⟩,⟨⟨(-129890657611),(-129890657584)⟩,⟨5680281860,5680281888⟩⟩,⟨⟨(-109188530236),(-109188530208)⟩,⟨13031016371,13031016398⟩⟩,⟨⟨(-91155649001),(-91155648980)⟩,⟨17915516306,17915516327⟩⟩,⟨⟨(-75566016681),(-75566016648)⟩,⟨20875695602,20875695631⟩⟩,⟨⟨(-62187454629),(-62187454599)⟩,⟨22361214498,22361214531⟩⟩,⟨⟨(-50789264557),(-50789264529)⟩,⟨22741413543,22741413571⟩⟩,⟨⟨(-41147969959),(-41147969938)⟩,⟨22316339477,22316339498⟩⟩,⟨⟨(-33051445568),(-33051445538)⟩,⟨21326805035,21326805068⟩⟩,⟨⟨(-26301713763),(-26301713735)⟩,⟨19963461056,19963461084⟩⟩,⟨⟨(-20716657192),(-20716657163)⟩,⟨18374888373,18374888401⟩⟩] +lemma kernel24_1_r3_6_eq : ∀ k : Fin 16, kernel24_1Expr 3 6 k = kernel24_1_r3_6 k := by decide +kernel +noncomputable def kernel24_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-16130866799),(-16130866771)⟩,⟨16674740008,16674740036⟩⟩,⟨⟨(-12395815786),(-12395815764)⟩,⟨14947980909,14947980931⟩⟩,⟨⟨(-9379522667),(-9379522646)⟩,⟨13256284643,13256284664⟩⟩,⟨⟨(-6965840901),(-6965840879)⟩,⟨11642654524,11642654545⟩⟩,⟨⟨(-5053489550),(-5053489521)⟩,⟨10135340460,10135340489⟩⟩,⟨⟨(-3554918261),(-3554918239)⟩,⟨8751124726,8751124747⟩⟩,⟨⟨(-2395081447),(-2395081420)⟩,⟨7498048506,7498048530⟩⟩,⟨⟨(-1510180139),(-1510180102)⟩,⟨6377648866,6377648906⟩⟩,⟨⟨(-846416402),(-846416380)⟩,⟨5386771578,5386771599⟩⟩,⟨⟨(-358793092),(-358793058)⟩,⟨4519020432,4519020463⟩⟩,⟨⟨(-9982053),(-9982029)⟩,⟨3765898837,3765898863⟩⟩,⟨⟨230724018,230724058⟩,⟨3117693171,3117693208⟩⟩,⟨⟨388367589,388367611⟩,⟨2564142537,2564142559⟩⟩,⟨⟨483186283,483186305⟩,⟨2094933447,2094933469⟩⟩,⟨⟨531377486,531377513⟩,⟨1700053324,1700053348⟩⟩,⟨⟨545770217,545770239⟩,⟨1370031437,1370031458⟩⟩] +lemma kernel24_1_r3_7_eq : ∀ k : Fin 16, kernel24_1Expr 3 7 k = kernel24_1_r3_7 k := by decide +kernel +noncomputable def kernel24_1_r3_8 : Fin 16 → CBox := ![⟨⟨536409633,536409659⟩,⟨1096091689,1096091713⟩⟩,⟨⟨511060496,511060518⟩,⟨870237619,870237641⟩⟩,⟨⟨475636649,475636676⟩,⟨685286440,685286465⟩⟩,⟨⟨434564134,434564156⟩,⟨534865759,534865781⟩⟩,⟨⟨391085368,391085397⟩,⟨413383997,413384027⟩⟩,⟨⟨347511622,347511658⟩,⟨315983334,315983370⟩⟩,⟨⟨305430745,305430772⟩,⟨238481794,238481818⟩⟩,⟨⟨265876397,265876421⟩,⟨177309719,177309746⟩⟩,⟨⟨229464629,229464660⟩,⟨129444518,129444552⟩⟩,⟨⟨196502968,196502998⟩,⟨92346417,92346447⟩⟩,⟨⟨167076527,167076549⟩,⟨63897058,63897081⟩⟩,⟨⟨141115261,141115283⟩,⟨42342351,42342373⟩⟩,⟨⟨118445680,118445702⟩,⟨26240188,26240211⟩⟩,⟨⟨98830051,98830073⟩,⟨14413372,14413394⟩⟩,⟨⟨81995590,81995612⟩,⟨5907866,5907888⟩⟩,⟨⟨67655627,67655659⟩,⟨(-43860),(-43826)⟩⟩] +lemma kernel24_1_r3_8_eq : ∀ k : Fin 16, kernel24_1Expr 3 8 k = kernel24_1_r3_8 k := by decide +kernel +noncomputable def kernel24_1_r3_9 : Fin 16 → CBox := ![⟨⟨55524622,55524645⟩,⟨(-4054594),(-4054571)⟩⟩,⟨⟨45328261,45328284⟩,⟨(-6609736),(-6609714)⟩⟩,⟨⟨36810016,36810048⟩,⟨(-8090528),(-8090493)⟩⟩,⟨⟨29734853,29734885⟩,⟨(-8793652),(-8793617)⟩⟩,⟨⟨23890993,23891030⟩,⟨(-8947742),(-8947705)⟩⟩,⟨⟨19090226,19090261⟩,⟨(-8726997),(-8726965)⟩⟩,⟨⟨15167241,15167275⟩,⟨(-8262458),(-8262426)⟩⟩,⟨⟨11978330,11978360⟩,⟨(-7651220),(-7651190)⟩⟩,⟨⟨9399687,9399715⟩,⟨(-6963924),(-6963899)⟩⟩,⟨⟨7325499,7325536⟩,⟨(-6250816),(-6250779)⟩⟩,⟨⟨5666075,5666098⟩,⟨(-5546509),(-5546486)⟩⟩,⟨⟨4345796,4345821⟩,⟨(-4873920),(-4873892)⟩⟩,⟨⟨3301408,3301438⟩,⟨(-4247182),(-4247152)⟩⟩,⟨⟨2480299,2480322⟩,⟨(-3674081),(-3674058)⟩⟩,⟨⟨1838926,1838959⟩,⟨(-3157830),(-3157795)⟩⟩,⟨⟨1341490,1341518⟩,⟨(-2698464),(-2698439)⟩⟩] +lemma kernel24_1_r3_9_eq : ∀ k : Fin 16, kernel24_1Expr 3 9 k = kernel24_1_r3_9 k := by decide +kernel +noncomputable def kernel24_1_r3_10 : Fin 16 → CBox := ![⟨⟨958689,958717⟩,⟨(-2293903),(-2293877)⟩⟩,⟨⟨666675,666711⟩,⟨(-1940747),(-1940714)⟩⟩,⟨⟨446165,446191⟩,⟨(-1634784),(-1634756)⟩⟩,⟨⟨281583,281613⟩,⟨(-1371503),(-1371473)⟩⟩,⟨⟨160481,160507⟩,⟨(-1146292),(-1146264)⟩⟩,⟨⟨72922,72957⟩,⟨(-954673),(-954640)⟩⟩,⟨⟨11038,11061⟩,⟨(-792432),(-792409)⟩⟩,⟨⟨(-31377),(-31349)⟩,⟨(-655668),(-655642)⟩⟩,⟨⟨(-59186),(-59160)⟩,⟨(-540867),(-540839)⟩⟩,⟨⟨(-76180),(-76156)⟩,⟨(-444839),(-444816)⟩⟩,⟨⟨(-85278),(-85254)⟩,⟨(-364825),(-364802)⟩⟩,⟨⟨(-88731),(-88703)⟩,⟨(-298368),(-298342)⟩⟩,⟨⟨(-88252),(-88214)⟩,⟨(-243346),(-243307)⟩⟩,⟨⟨(-85116),(-85085)⟩,⟨(-197914),(-197883)⟩⟩,⟨⟨(-80286),(-80250)⟩,⟨(-160523),(-160489)⟩⟩,⟨⟨(-74469),(-74441)⟩,⟨(-129826),(-129800)⟩⟩] +lemma kernel24_1_r3_10_eq : ∀ k : Fin 16, kernel24_1Expr 3 10 k = kernel24_1_r3_10 k := by decide +kernel +noncomputable def kernel24_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-68167),(-68141)⟩,⟨(-104693),(-104665)⟩⟩,⟨⟨(-61748),(-61724)⟩,⟨(-84177),(-84153)⟩⟩,⟨⟨(-55461),(-55427)⟩,⟨(-67466),(-67429)⟩⟩,⟨⟨(-49450),(-49419)⟩,⟨(-53885),(-53854)⟩⟩,⟨⟨(-43837),(-43799)⟩,⟨(-42889),(-42851)⟩⟩,⟨⟨(-38661),(-38635)⟩,⟨(-33995),(-33966)⟩⟩,⟨⟨(-33944),(-33920)⟩,⟨(-26821),(-26797)⟩⟩,⟨⟨(-29697),(-29673)⟩,⟨(-21061),(-21037)⟩⟩,⟨⟨(-25904),(-25865)⟩,⟨(-16455),(-16416)⟩⟩,⟨⟨(-22531),(-22500)⟩,⟨(-12765),(-12734)⟩⟩,⟨⟨(-19549),(-19525)⟩,⟨(-9821),(-9797)⟩⟩,⟨⟨(-16931),(-16905)⟩,⟨(-7495),(-7466)⟩⟩,⟨⟨(-14634),(-14606)⟩,⟨(-5645),(-5619)⟩⟩,⟨⟨(-12638),(-12611)⟩,⟨(-4195),(-4166)⟩⟩,⟨⟨(-10894),(-10870)⟩,⟨(-3055),(-3031)⟩⟩,⟨⟨(-9389),(-9360)⟩,⟨(-2170),(-2144)⟩⟩] +lemma kernel24_1_r3_11_eq : ∀ k : Fin 16, kernel24_1Expr 3 11 k = kernel24_1_r3_11 k := by decide +kernel +noncomputable def kernel24_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-8088),(-8056)⟩,⟨(-1490),(-1459)⟩⟩,⟨⟨(-6956),(-6932)⟩,⟨(-957),(-933)⟩⟩,⟨⟨(-5985),(-5961)⟩,⟨(-560),(-536)⟩⟩,⟨⟨(-5140),(-5116)⟩,⟨(-251),(-227)⟩⟩,⟨⟨(-4418),(-4394)⟩,⟨(-34),(-10)⟩⟩,⟨⟨(-3804),(-3775)⟩,⟨128,155⟩⟩,⟨⟨(-3274),(-3245)⟩,⟨240,267⟩⟩,⟨⟨(-2815),(-2791)⟩,⟨327,351⟩⟩,⟨⟨(-2415),(-2388)⟩,⟨371,400⟩⟩,⟨⟨(-2088),(-2048)⟩,⟨402,442⟩⟩,⟨⟨(-1797),(-1768)⟩,⟨422,448⟩⟩,⟨⟨(-1549),(-1510)⟩,⟨413,453⟩⟩,⟨⟨(-1337),(-1313)⟩,⟨418,442⟩⟩,⟨⟨(-1154),(-1127)⟩,⟨399,429⟩⟩,⟨⟨(-1001),(-966)⟩,⟨382,419⟩⟩,⟨⟨(-860),(-833)⟩,⟨369,398⟩⟩] +lemma kernel24_1_r3_12_eq : ∀ k : Fin 16, kernel24_1Expr 3 12 k = kernel24_1_r3_12 k := by decide +kernel +noncomputable def kernel24_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-750),(-718)⟩,⟨341,373⟩⟩,⟨⟨(-651),(-621)⟩,⟨322,349⟩⟩,⟨⟨(-564),(-537)⟩,⟨305,334⟩⟩,⟨⟨(-498),(-468)⟩,⟨280,307⟩⟩,⟨⟨(-439),(-399)⟩,⟨253,293⟩⟩,⟨⟨(-380),(-351)⟩,⟨244,271⟩⟩,⟨⟨(-327),(-300)⟩,⟨225,255⟩⟩,⟨⟨(-288),(-256)⟩,⟨209,241⟩⟩,⟨⟨(-253),(-228)⟩,⟨193,217⟩⟩,⟨⟨(-230),(-190)⟩,⟨169,209⟩⟩,⟨⟨(-197),(-167)⟩,⟨160,187⟩⟩,⟨⟨(-179),(-150)⟩,⟨144,172⟩⟩,⟨⟨(-151),(-122)⟩,⟨136,163⟩⟩,⟨⟨(-136),(-111)⟩,⟨130,155⟩⟩,⟨⟨(-131),(-91)⟩,⟨109,150⟩⟩,⟨⟨(-116),(-89)⟩,⟨107,136⟩⟩] +lemma kernel24_1_r3_13_eq : ∀ k : Fin 16, kernel24_1Expr 3 13 k = kernel24_1_r3_13 k := by decide +kernel +noncomputable def kernel24_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-106),(-73)⟩,⟨98,131⟩⟩,⟨⟨(-98),(-63)⟩,⟨88,125⟩⟩,⟨⟨(-85),(-56)⟩,⟨87,115⟩⟩,⟨⟨(-81),(-53)⟩,⟨75,104⟩⟩,⟨⟨(-68),(-38)⟩,⟨71,99⟩⟩,⟨⟨(-60),(-36)⟩,⟨64,88⟩⟩,⟨⟨(-60),(-36)⟩,⟨64,88⟩⟩,⟨⟨(-58),(-20)⟩,⟨50,85⟩⟩,⟨⟨(-50),(-20)⟩,⟨55,83⟩⟩,⟨⟨(-43),(-18)⟩,⟨47,72⟩⟩,⟨⟨(-43),(-18)⟩,⟨47,72⟩⟩,⟨⟨(-40),(-16)⟩,⟨40,64⟩⟩,⟨⟨(-40),(-16)⟩,⟨40,64⟩⟩,⟨⟨(-40),(-16)⟩,⟨40,64⟩⟩,⟨⟨(-43),(-5)⟩,⟨29,64⟩⟩,⟨⟨(-38),(-8)⟩,⟨29,56⟩⟩] +lemma kernel24_1_r3_14_eq : ∀ k : Fin 16, kernel24_1Expr 3 14 k = kernel24_1_r3_14 k := by decide +kernel +noncomputable def kernel24_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-38),3⟩,⟨26,67⟩⟩,⟨⟨(-38),3⟩,⟨26,67⟩⟩,⟨⟨(-30),3⟩,⟨31,64⟩⟩,⟨⟨(-33),8⟩,⟨23,64⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩,⟨⟨(-23),2⟩,⟨23,48⟩⟩] +lemma kernel24_1_r3_15_eq : ∀ k : Fin 16, kernel24_1Expr 3 15 k = kernel24_1_r3_15 k := by decide +kernel +noncomputable def kernel24_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel24_1_r3_0,kernel24_1_r3_1,kernel24_1_r3_2,kernel24_1_r3_3,kernel24_1_r3_4,kernel24_1_r3_5,kernel24_1_r3_6,kernel24_1_r3_7,kernel24_1_r3_8,kernel24_1_r3_9,kernel24_1_r3_10,kernel24_1_r3_11,kernel24_1_r3_12,kernel24_1_r3_13,kernel24_1_r3_14,kernel24_1_r3_15] +lemma kernel24_1_r3_eq (i k : Fin 16) : kernel24_1Expr 3 i k = kernel24_1_r3 i k := by + fin_cases i + · exact kernel24_1_r3_0_eq k + · exact kernel24_1_r3_1_eq k + · exact kernel24_1_r3_2_eq k + · exact kernel24_1_r3_3_eq k + · exact kernel24_1_r3_4_eq k + · exact kernel24_1_r3_5_eq k + · exact kernel24_1_r3_6_eq k + · exact kernel24_1_r3_7_eq k + · exact kernel24_1_r3_8_eq k + · exact kernel24_1_r3_9_eq k + · exact kernel24_1_r3_10_eq k + · exact kernel24_1_r3_11_eq k + · exact kernel24_1_r3_12_eq k + · exact kernel24_1_r3_13_eq k + · exact kernel24_1_r3_14_eq k + · exact kernel24_1_r3_15_eq k +noncomputable def kernel24_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-68582390013560802217631),(-68582390013560699817640)⟩,⟨225939305056129746817543,225939305056129849217269⟩⟩,⟨⟨(-68293017158172963943017),(-68293017158172861657136)⟩,⟨225748674620972844796916,225748674620972947082536⟩⟩,⟨⟨(-67715816333187416581838),(-67715816333187314523988)⟩,⟨225367249597854415137099,225367249597854517194700⟩⟩,⟨⟨(-66853868997489155818319),(-66853868997489054101712)⟩,⟨224794710074980760488623,224794710074980862204998⟩⟩,⟨⟨(-65711776570320515885970),(-65711776570320414622677)⟩,⟨224030597041936623251565,224030597041936724514642⟩⟩,⟨⟨(-64295635544799205292980),(-64295635544799104593639)⟩,⟨223074337063590440054343,223074337063590540753495⟩⟩,⟨⟨(-62613004369588005900873),(-62613004369587905874318)⟩,⟨221925274591788695778845,221925274591788795805243⟩⟩,⟨⟨(-60672862159065717732872),(-60672862159065618485764)⟩,⟨220582711420855933850052,220582711420856033097033⟩⟩,⟨⟨(-58485559314471204954276),(-58485559314471106590825)⟩,⟨219045952680635007854247,219045952680635106217612⟩⟩,⟨⟨(-56062760164982326443028),(-56062760164982229064619)⟩,⟨217314358655884846461869,217314358655884943840233⟩⟩,⟨⟨(-53417377769109165211269),(-53417377769109068916216)⟩,⟨215387401624658867097847,215387401624658963392903⟩⟩,⟨⟨(-50563501053526391207464),(-50563501053526296090635)⟩,⟨213264726822108557308593,213264726822108652425472⟩⟩,⟨⟨(-47516314508765238094087),(-47516314508765144246783)⟩,⟨210946216561205993795518,210946216561206087642927⟩⟩,⟨⟨(-44292010709062446266081),(-44292010709062353775575)⟩,⟨208432056479273787093791,208432056479273879584457⟩⟩,⟨⟨(-40907695976951686458770),(-40907695976951595408295)⟩,⟨205722802829958397928134,205722802829958488978821⟩⟩,⟨⟨(-37381289571506665873932),(-37381289571506576342260)⟩,⟨202819449705263692857112,202819449705263782389059⟩⟩] +lemma kernel24_1_r4_0_eq : ∀ k : Fin 16, kernel24_1Expr 4 0 k = kernel24_1_r4_0 k := by decide +kernel +noncomputable def kernel24_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-33731416841922683309083),(-33731416841922595370581)⟩,⟨199723495052213557099540,199723495052213645038381⟩⟩,⟨⟨(-29977296854572246582884),(-29977296854572160306982)⟩,⟨196437004344213107162517,196437004344213193438821⟩⟩,⟨⟨(-26138625070816938273719),(-26138625070816853725224)⟩,⟨192962670778629159064571,192962670778629243613529⟩⟩,⟨⟨(-22235451723552483508359),(-22235451723552400746807)⟩,⟨189303870899722088083055,189303870899722170845139⟩⟩,⟨⟨(-18288056611401269201325),(-18288056611401188281514)⟩,⟨185464714589837217568057,185464714589837298488462⟩⟩,⟨⟨(-14316821099209014267807),(-14316821099208935238905)⟩,⟨181450088431490393335170,181450088431490472364727⟩⟩,⟨⟨(-10342098180509464529819),(-10342098180509387436246)⟩,⟨177265691518217347463530,177265691518217424557819⟩⟩,⟨⟨(-6384081520281785474253),(-6384081520281710354670)⟩,⟨172918062882122690287718,172918062882122765408077⟩⟩,⟨⟨(-2462674452993522953000),(-2462674452993449841426)⟩,⟨168414599810046221196647,168414599810046294309054⟩⟩,⟨⟨1402640040045756891485,1402640040045827967058⟩,⟨163763566437008011703674,163763566437008082780142⟩⟩,⟨⟨5192927310199541605112,5192927310199610621494⟩,⟨158974092133712537877246,158974092133712606894572⟩⟩,⟨⟨8889925885026511410601,8889925885026578350163⟩,⟨154056159342775652832501,154056159342775719773067⟩⟩,⟨⟨12476168066055702892798,12476168066055767742079⟩,⟨149020580664167095863740,149020580664167160714071⟩⟩,⟨⟨15935095167548225262273,15935095167548288014399⟩,⟨143878965142126988286616,143878965142127051039833⟩⟩,⟨⟨19251166293877667169779,19251166293877727822112⟩,⟨138643673861344327190335,138643673861344387843802⟩⟩,⟨⟨22409959579267524555825,22409959579267583110516⟩,⟨133327765117170986056730,133327765117171044612595⟩⟩] +lemma kernel24_1_r4_1_eq : ∀ k : Fin 16, kernel24_1Expr 4 1 k = kernel24_1_r4_1 k := by decide +kernel +noncomputable def kernel24_1_r4_2 : Fin 16 → CBox := ![⟨⟨25398264855469423562583,25398264855469480025114⟩,⟨127944929580677733128300,127944929580677789592023⟩⟩,⟨⟨28204166770791966946361,28204166770792021328095⟩,⟨122509416031968705030515,122509416031968759413453⟩⟩,⟨⟨30817117457628037204366,30817117457628089519483⟩,⟨117035948381866849264567,117035948381866901580896⟩⟩,⟨⟨33227997934886403658132,33227997934886453930335⟩,⟨111539634840398840677735,111539634840398890951151⟩⟩,⟨⟨35429167535790071804968,35429167535790120057171⟩,⟨106035870218048834996980,106035870218048883250399⟩⟩,⟨⟨37414500769309341477699,37414500769309387736891⟩,⟨100540232460239843081078,100540232460239889341478⟩⟩,⟨⟨39179411153683210053159,39179411153683254348013⟩,⟨95068374614829331380155,95068374614829375676214⟩⟩,⟨⟨40720861701377519087957,40720861701377561452281⟩,⟨89635913514673949652548,89635913514673992018063⟩⟩,⟨⟨42037361884483434992846,42037361884483475461381⟩,⟨84258316520884975868104,84258316520885016337820⟩⟩,⟨⟨43128951065781253164130,43128951065781291776225⟩,⟨78950787715914875678585,78950787715914914291839⟩⟩,⟨⟨43997168541081272871520,43997168541081309666998⟩,⟨73728154958070998435777,73728154958071035232401⟩⟩,⟨⟨44645010500443224022977,44645010500443259045702⟩,⟨68604759209789851579987,68604759209789886603836⟩⟩,⟨⟨45076874376794837823010,45076874376794871116780⟩,⟨63594347530752351977149,63594347530752385272016⟩⟩,⟨⟨45298491207588282696061,45298491207588314318103⟩,⟨58709971083802288131813,58709971083802319754879⟩⟩,⟨⟨45316846785720569063564,45316846785720599067100⟩,⟨53963889437176419886556,53963889437176449891014⟩⟩,⟨⟨45140092517330376960467,45140092517330405394677⟩,⟨49367482361696586335429,49367482361696614770462⟩⟩] +lemma kernel24_1_r4_2_eq : ∀ k : Fin 16, kernel24_1Expr 4 2 k = kernel24_1_r4_2 k := by decide +kernel +noncomputable def kernel24_1_r4_3 : Fin 16 → CBox := ![⟨⟨44777447033717258267090,44777447033717285180017⟩,⟨44931170217633981281247,44931170217634008194911⟩⟩,⟨⟨44239089720134040073241,44239089720134065516317⟩,⟨40664343904625961231111,40664343904625986674833⟩⟩,⟨⟨43536047423434489929526,43536047423434513952588⟩,⟨36575305211340445999650,36575305211340470023273⟩⟩,⟨⟨42680075681651995767919,42680075681652018423763⟩,⟨32671218251880467842797,32671218251880490499126⟩⟩,⟨⟨41683535880003033302748,41683535880003054641900⟩,⟨28958072515799455059905,28958072515799476399470⟩⟩,⟨⟨40559269778376886718293,40559269778376906793532⟩,⟨25440657890862127180204,25440657890862147255779⟩⟩,⟨⟨39320472874308944579958,39320472874308963441778⟩,⟨22122551845293263837693,22122551845293282699790⟩⟩,⟨⟨37980568062371302575411,37980568062371320280048⟩,⟨19006118782254002084305,19006118782254019789158⟩⟩,⟨⟨36553081025908849049373,36553081025908865647185⟩,⟨16092521406746018618408,16092521406746035216383⟩⟩,⟨⟨35051518750585285645683,35051518750585301187586⟩,⟨13381743777102852639802,13381743777102868181822⟩⟩,⟨⟨33489252482182891706543,33489252482182906240660⟩,⟨10872625552616912516039,10872625552616927050225⟩⟩,⟨⟨31879406364822165393789,31879406364822178969273⟩,⟨8562906798437734501469,8562906798437748076979⟩⟩,⟨⟨30234752891902968099509,30234752891902980764164⟩,⟨6449282571205921453084,6449282571205934117723⟩⟩,⟨⟨28567616182620822730303,28567616182620834531721⟩,⟨4527466386225547201080,4527466386225559002456⟩⟩,⟨⟨26889783964172056809243,26889783964172067791616⟩,⟨2792261561270315653794,2792261561270326636092⟩⟩,⟨⟨25212428996257394486107,25212428996257404694702⟩,⟨1237639344948250811493,1237639344948261019991⟩⟩] +lemma kernel24_1_r4_3_eq : ∀ k : Fin 16, kernel24_1Expr 4 3 k = kernel24_1_r4_3 k := by decide +kernel +noncomputable def kernel24_1_r4_4 : Fin 16 → CBox := ![⟨⟨23546040522932496883838,23546040522932506360361⟩,⟨(-143177329892832819286),(-143177329892823342878)⟩⟩,⟨⟨21900366180061210982935,21900366180061219769866⟩,⟨(-1357625674172726388890),(-1357625674172717602095)⟩⟩,⟨⟨20284364627483338871287,20284364627483347007863⟩,⟨(-2413711684526266163745),(-2413711684526258027318)⟩⟩,⟨⟨18706169016385226711433,18706169016385234236950⟩,⟨(-3319916836996712840175),(-3319916836996705314817)⟩⟩,⟨⟨17173061247058518201853,17173061247058525152505⟩,⟨(-4085104055246042742338),(-4085104055246035791849)⟩⟩,⟨⟨15691456822918578603700,15691456822918585015948⟩,⟨(-4718424141579950588904),(-4718424141579944176816)⟩⟩,⟨⟨14266899965810559484194,14266899965810565391564⟩,⟨(-5229223806415141306798),(-5229223806415135399589)⟩⟩,⟨⟨12904068527501472953771,12904068527501478389569⟩,⟨(-5626956362519625401107),(-5626956362519619965471)⟩⟩,⟨⟨11606788114803705728355,11606788114803710723074⟩,⟨(-5921096066289202001823),(-5921096066289197007265)⟩⟩,⟨⟨10378054742645435613414,10378054742645440197584⟩,⟨(-6121056991577237730376),(-6121056991577233146361)⟩⟩,⟨⟨9220065241899374203183,9220065241899378404608⟩,⟨(-6236117214444736485169),(-6236117214444732283892)⟩⟩,⟨⟨8134254577844911748277,8134254577844915594386⟩,⟨(-6275348972043851227000),(-6275348972043847381036)⟩⟩,⟨⟨7121339181342111991808,7121339181342115519558⟩,⟨(-6247555338158661377073),(-6247555338158657849440)⟩⟩,⟨⟨6181365358342117584316,6181365358342120817287⟩,⟨(-6161213834180853489150),(-6161213834180850256283)⟩⟩,⟨⟨5313761824091076006285,5313761824091078965019⟩,⟨(-6024427269928134359475),(-6024427269928131400826)⟩⟩,⟨⟨4517395405806134558307,4517395405806137263056⟩,⟨(-5844881986055062693673),(-5844881986055059988996)⟩⟩] +lemma kernel24_1_r4_4_eq : ∀ k : Fin 16, kernel24_1Expr 4 4 k = kernel24_1_r4_4 k := by decide +kernel +noncomputable def kernel24_1_r4_5 : Fin 16 → CBox := ![⟨⟨3790628970899296398738,3790628970899298867729⟩,⟨(-5629813551048771802072),(-5629813551048769333132)⟩⟩,⟨⟨3131380665901718763644,3131380665901721015045⟩,⟨(-5385979852946516151869),(-5385979852946513900510)⟩⟩,⟨⟨2537183592755827117942,2537183592755829168048⟩,⟨(-5119641420734326388596),(-5119641420734324338521)⟩⟩,⟨⟨2005245102550773441893,2005245102550775306646⟩,⟨(-4836548714409148064511),(-4836548714409146199781)⟩⟩,⟨⟨1532504950375704086584,1532504950375705780265⟩,⟨(-4541936037158918459490),(-4541936037158916765820)⟩⟩,⟨⟨1115691626941304350503,1115691626941305887235⟩,⟨(-4240521648996352678186),(-4240521648996351141458)⟩⟩,⟨⟨751376261095402081349,751376261095403473777⟩,⟨(-3936513599139410378314),(-3936513599139408985882)⟩⟩,⟨⟨436023570437396418778,436023570437397679096⟩,⟨(-3633620744839490469725),(-3633620744839489209400)⟩⟩,⟨⟨166039423049380357472,166039423049381496685⟩,⟨(-3335068387309741084303),(-3335068387309739945080)⟩⟩,⟨⟨(-62185339893631175444),(-62185339893630146732)⟩,⟨(-3043617930725773824582),(-3043617930725772795856)⟩⟩,⟨⟨(-252235084895124330838),(-252235084895123403160)⟩,⟨(-2761589957538932897245),(-2761589957538931969550)⟩⟩,⟨⟨(-407633750905629639414),(-407633750905628803521)⟩,⟨(-2490890111917550578240),(-2490890111917549742330)⟩⟩,⟨⟨(-531813498792252111920),(-531813498792251359851)⟩,⟨(-2233037192183578859744),(-2233037192183578107654)⟩⟩,⟨⟨(-628087671254994885229),(-628087671254994209227)⟩,⟨(-1989192871652153432229),(-1989192871652152756205)⟩⟩,⟨⟨(-699628019954111169429),(-699628019954110562618)⟩,⟨(-1760192494197974494655),(-1760192494197973887825)⟩⟩,⟨⟨(-749446094424983902455),(-749446094424983357975)⟩,⟨(-1546576424964051802372),(-1546576424964051257875)⟩⟩] +lemma kernel24_1_r4_5_eq : ∀ k : Fin 16, kernel24_1Expr 4 5 k = kernel24_1_r4_5 k := by decide +kernel +noncomputable def kernel24_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-780378632571969879167),(-780378632571969391351)⟩,⟨(-1348621476640201260918),(-1348621476640200773082)⟩⟩,⟨⟨(-795076745553089867207),(-795076745553089430553)⟩,⟨(-1166371976394411136767),(-1166371976394410700098)⟩⟩,⟨⟨(-795998650897698787753),(-795998650897698397408)⟩,⟨(-999670086573548320879),(-999670086573547930516)⟩⟩,⟨⟨(-785405676756937979133),(-785405676756937630517)⟩,⟨(-848185042472999767032),(-848185042472999418401)⟩⟩,⟨⟨(-765361237118318961389),(-765361237118318650520)⟩,⟨(-711441021643418019938),(-711441021643417709059)⟩⟩,⟨⟨(-737732462315071298290),(-737732462315071021315)⟩,⟨(-588843410277360340684),(-588843410277360063698)⟩⟩,⟨⟨(-704194160789924503911),(-704194160789924257213)⟩,⟨(-479703282222207334331),(-479703282222207087630)⟩⟩,⟨⟨(-666234786284214958549),(-666234786284214738932)⟩,⟨(-383259954236872178206),(-383259954236871958589)⟩⟩,⟨⟨(-625164088782447198256),(-625164088782447003046)⟩,⟨(-298701526511815568207),(-298701526511815372991)⟩⟩,⟨⟨(-582122136951977084897),(-582122136951976911520)⟩,⟨(-225183359598084374811),(-225183359598084201431)⟩⟩,⟨⟨(-538089413738515928652),(-538089413738515774869)⟩,⟨(-161844477266182617555),(-161844477266182463769)⟩⟩,⟨⟨(-493897704452107380224),(-493897704452107243926)⟩,⟨(-107821919093560713683),(-107821919093560577386)⟩⟩,⟨⟨(-450241517346474714245),(-450241517346474593623)⟩,⟨(-62263096538554160695),(-62263096538554040077)⟩⟩,⟨⟨(-407689799616208124493),(-407689799616208017765)⟩,⟨(-24336231793323759368),(-24336231793323652640)⟩⟩,⟨⟨(-366697736203293816412),(-366697736203293722100)⟩,⟨6761020180126193113,6761020180126287423⟩⟩,⟨⟨(-327618444155186767838),(-327618444155186684567)⟩,⟨31794649242366957126,31794649242367040393⟩⟩] +lemma kernel24_1_r4_6_eq : ∀ k : Fin 16, kernel24_1Expr 4 6 k = kernel24_1_r4_6 k := by decide +kernel +noncomputable def kernel24_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-290714400905687510798),(-290714400905687437371)⟩,⟨51488937473326810286,51488937473326883712⟩⟩,⟨⟨(-256168470216306757588),(-256168470216306692882)⟩,⟨66522537815504747770,66522537815504812479⟩⟩,⟨⟨(-224094414148236119371),(-224094414148236062421)⟩,⟨77525840271378463960,77525840271378520905⟩⟩,⟨⟨(-194546802934719534948),(-194546802934719484853)⟩,⟨85079480084247279276,85079480084247329368⟩⟩,⟨⟨(-167530256665110247439),(-167530256665110203447)⟩,⟨89713843336703638879,89713843336703682867⟩⟩,⟨⟨(-143007973021912664377),(-143007973021912625772)⟩,⟨91909428900707564135,91909428900707602739⟩⟩,⟨⟨(-120909513746598097267),(-120909513746598063430)⟩,⟨92097931274034707477,92097931274034741313⟩⟩,⟨⟨(-101137838929827919372),(-101137838929827889716)⟩,⟨90663916150641121729,90663916150641151382⟩⟩,⟨⟨(-83575592567290702605),(-83575592567290676573)⟩,⟨87946969221554599301,87946969221554625333⟩⟩,⟨⟨(-68090655087258963424),(-68090655087258940573)⟩,⟨84244208333099993084,84244208333100015936⟩⟩,⟨⟨(-54540988780190398393),(-54540988780190378362)⟩,⟨79813059411668329995,79813059411668350022⟩⟩,⟨⟨(-42778810323503006504),(-42778810323502988969)⟩,⟨74874207200461760786,74874207200461778318⟩⟩,⟨⟨(-32654131007390491594),(-32654131007390476258)⟩,⟨69614642578797179446,69614642578797194789⟩⟩,⟨⟨(-24017709966597662541),(-24017709966597649130)⟩,⟨64190738818931684465,64190738818931697877⟩⟩,⟨⟨(-16723468863138617609),(-16723468863138605894)⟩,⟨58731299385041359681,58731299385041371397⟩⟩,⟨⟨(-10630418212749983277),(-10630418212749973048)⟩,⟨53340529635327030325,53340529635327040552⟩⟩] +lemma kernel24_1_r4_7_eq : ∀ k : Fin 16, kernel24_1Expr 4 7 k = kernel24_1_r4_7 k := by decide +kernel +noncomputable def kernel24_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-5604146076511126266),(-5604146076511117351)⟩,⟨48100893926674010362,48100893926674019280⟩⟩,⟨⟨(-1517919322915333458),(-1517919322915325675)⟩,⟨43075828049377392762,43075828049377400545⟩⟩,⟨⟨1746553723932225965,1746553723932232743⟩,⟨38312284574254007892,38312284574254014667⟩⟩,⟨⟨4298652532748167499,4298652532748173402⟩,⟨33843095539762546507,33843095539762552410⟩⟩,⟨⟨6238621445140482529,6238621445140487661⟩,⟨29689142929824477641,29689142929824482774⟩⟩,⟨⟨7657553585220939581,7657553585220944045⟩,⟨25861332601386022927,25861332601386027391⟩⟩,⟨⟨8637543940524557632,8637543940524561514⟩,⟨22362371738808313730,22362371738808317615⟩⟩,⟨⟨9251977465565252223,9251977465565255606⟩,⟨19188353578024032788,19188353578024036172⟩⟩,⟨⟨9565921634309244129,9565921634309247065⟩,⟨16330156105759177051,16330156105759179981⟩⟩,⟨⟨9636596422809106450,9636596422809108998⟩,⟨13774663754423664987,13774663754423667536⟩⟩,⟨⟨9513898167399566157,9513898167399568372⟩,⟨11505822843080825129,11505822843080827341⟩⟩,⟨⟨9240957060277294987,9240957060277296915⟩,⟨9505542723570749859,9505542723570751788⟩⟩,⟨⟨8854711168980039325,8854711168980040993⟩,⟨7754455343531690179,7754455343531691849⟩⟩,⟨⟨8386482767083823934,8386482767083825387⟩,⟨6232546298970815527,6232546298970816976⟩⟩,⟨⟨7862545418785002483,7862545418785003735⟩,⟨4919670480110450754,4919670480110452009⟩⟩,⟨⟨7304672657658978177,7304672657658979270⟩,⟨3795965174006795392,3795965174006796489⟩⟩] +lemma kernel24_1_r4_8_eq : ∀ k : Fin 16, kernel24_1Expr 4 8 k = kernel24_1_r4_8 k := by decide +kernel +noncomputable def kernel24_1_r4_9 : Fin 16 → CBox := ![⟨⟨6730661235503478606,6730661235503479561⟩,⟨2842173030210628183,2842173030210629138⟩⟩,⟨⟨6154823793181881046,6154823793181881871⟩,⟨2039886671025463891,2039886671025464718⟩⟩,⟨⟨5588447429626599245,5588447429626599964⟩,⟨1371725980089112884,1371725980089113602⟩⟩,⟨⟨5040216029770707816,5040216029770708441⟩,⟨821458271136753843,821458271136754468⟩⟩,⟨⟨4516595372489185432,4516595372489185975⟩,⟨374070656691753207,374070656691753749⟩⟩,⟨⟨4022180993247545691,4022180993247546173⟩,⟨15803032731561131,15803032731561612⟩⟩,⟨⟨3560009542087946050,3560009542087946465⟩,⟨(-265850806138227608),(-265850806138227193)⟩⟩,⟨⟨3131834975534271852,3131834975534272212⟩,⟨(-482167286579731367),(-482167286579731007)⟩⟩,⟨⟨2738371370753827220,2738371370753827530⟩,⟨(-643236620721332495),(-643236620721332185)⟩⟩,⟨⟨2379504471245870735,2379504471245871018⟩,⟨(-758020819778085189),(-758020819778084907)⟩⟩,⟨⟨2054474284002139754,2054474284002139996⟩,⟨(-834421902320697075),(-834421902320696837)⟩⟩,⟨⟨1762031165965092002,1762031165965092212⟩,⟨(-879356721597399447),(-879356721597399237)⟩⟩,⟨⟨1500567878845748338,1500567878845748514⟩,⟨(-898835451837980790),(-898835451837980614)⟩⟩,⟨⟨1268230070654988944,1268230070654989113⟩,⟨(-898041324637027210),(-898041324637027044)⟩⟩,⟨⟨1063007572828515727,1063007572828515876⟩,⟨(-881409694255219372),(-881409694255219224)⟩⟩,⟨⟨882808795224919320,882808795224919446⟩,⟨(-852704937211064792),(-852704937211064666)⟩⟩] +lemma kernel24_1_r4_9_eq : ∀ k : Fin 16, kernel24_1Expr 4 9 k = kernel24_1_r4_9 k := by decide +kernel +noncomputable def kernel24_1_r4_10 : Fin 16 → CBox := ![⟨⟨725520367671865459,725520367671865574⟩,⟨(-815094060051627200),(-815094060051627086)⟩⟩,⟨⟨589054024795140319,589054024795140422⟩,⟨(-771216203578184636),(-771216203578184533)⟩⟩,⟨⟨471382567886328334,471382567886328432⟩,⟨(-723247496409397250),(-723247496409397152)⟩⟩,⟨⟨370566569576988909,370566569576988996⟩,⟨(-672960930196670023),(-672960930196669937)⟩⟩,⟨⟨284773318967594378,284773318967594452⟩,⟨(-621781107761385711),(-621781107761385640)⟩⟩,⟨⟨212289340453946277,212289340453946353⟩,⟨(-570833858555543506),(-570833858555543431)⟩⟩,⟨⟨151527661739119730,151527661739119799⟩,⟨(-520990827661093454),(-520990827661093389)⟩⟩,⟨⟨101030857563493901,101030857563493965⟩,⟨(-472909229315456674),(-472909229315456610)⟩⟩,⟨⟨59470757004299421,59470757004299473⟩,⟨(-427067017672663866),(-427067017672663818)⟩⟩,⟨⟨25645574699750313,25645574699750365⟩,⟨(-383793769849982493),(-383793769849982445)⟩⟩,⟨⟨(-1524889513400322),(-1524889513400270)⟩,⟨(-343297602594109259),(-343297602594109206)⟩⟩,⟨⟨(-23005442225489542),(-23005442225489496)⟩,⟨(-305688457103282480),(-305688457103282437)⟩⟩,⟨⟨(-39652631707686983),(-39652631707686946)⟩,⟨(-270998089288588992),(-270998089288588952)⟩⟩,⟨⟨(-52222460817445344),(-52222460817445313)⟩,⟨(-239197097339710732),(-239197097339710698)⟩⟩,⟨⟨(-61378382818768410),(-61378382818768375)⟩,⟨(-210209306849374597),(-210209306849374561)⟩⟩,⟨⟨(-67699346922735912),(-67699346922735876)⟩,⟨(-183923817622514566),(-183923817622514530)⟩⟩] +lemma kernel24_1_r4_10_eq : ∀ k : Fin 16, kernel24_1Expr 4 10 k = kernel24_1_r4_10 k := by decide +kernel +noncomputable def kernel24_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-71687712989318824),(-71687712989318794)⟩,⟨(-160204997054865886),(-160204997054865856)⟩⟩,⟨⟨(-73776899384186798),(-73776899384186768)⟩,⟨(-138900683770532712),(-138900683770532682)⟩⟩,⟨⟨(-74338665283036856),(-74338665283036820)⟩,⟨(-119848842999844181),(-119848842999844146)⟩⟩,⟨⟨(-73689959573473283),(-73689959573473252)⟩,⟨(-102882892706460692),(-102882892706460662)⟩⟩,⟨⟨(-72099293700140450),(-72099293700140420)⟩,⟨(-87835897318576011),(-87835897318575981)⟩⟩,⟨⟨(-69792616067319362),(-69792616067319332)⟩,⟨(-74543804522867469),(-74543804522867439)⟩⟩,⟨⟨(-66958681636449902),(-66958681636449882)⟩,⟨(-62847880260670325),(-62847880260670302)⟩⟩,⟨⟨(-63753922758452439),(-63753922758452409)⟩,⟨(-52596478042302396),(-52596478042302366)⟩⟩,⟨⟨(-60306836627097292),(-60306836627097262)⟩,⟨(-43646261103705484),(-43646261103705453)⟩⟩,⟨⟨(-56721911535109320),(-56721911535109289)⟩,⟨(-35862979839281322),(-35862979839281292)⟩⟩,⟨⟨(-53083118806080468),(-53083118806080437)⟩,⟨(-29121892373119393),(-29121892373119363)⟩⟩,⟨⟨(-49457000253909134),(-49457000253909113)⟩,⟨(-23307903054348570),(-23307903054348542)⟩⟩,⟨⟨(-45895382626590866),(-45895382626590836)⟩,⟨(-18315482027390163),(-18315482027390133)⟩⟩,⟨⟨(-42437751013826600),(-42437751013826570)⟩,⟨(-14048418758999257),(-14048418758999227)⟩⟩,⟨⟨(-39113312885324732),(-39113312885324702)⟩,⟨(-10419453411053848),(-10419453411053817)⟩⟩,⟨⟨(-35942783486627971),(-35942783486627953)⟩,⟨(-7349822132094487),(-7349822132094468)⟩⟩] +lemma kernel24_1_r4_11_eq : ∀ k : Fin 16, kernel24_1Expr 4 11 k = kernel24_1_r4_11 k := by decide +kernel +noncomputable def kernel24_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-32939921924470379),(-32939921924470354)⟩,⟨(-4768745598353982),(-4768745598353957)⟩⟩,⟨⟨(-30112845565840920),(-30112845565840890)⟩,⟨(-2612884362487226),(-2612884362487200)⟩⟩,⟨⟨(-27465148468963459),(-27465148468963441)⟩,⟨(-825779663518799),(-825779663518785)⟩⟩,⟨⟨(-24996847551958422),(-24996847551958391)⟩,⟨642705783140370,642705783140400⟩⟩,⟨⟨(-22705178157882058),(-22705178157882030)⟩,⟨1836935953696246,1836935953696267⟩⟩,⟨⟨(-20585258648268762),(-20585258648268733)⟩,⟨2796030445155991,2796030445156017⟩⟩,⟨⟨(-18630641692369079),(-18630641692369054)⟩,⟨3554368320937823,3554368320937848⟩⟩,⟨⟨(-16833768045570099),(-16833768045570074)⟩,⟨4142062938915697,4142062938915722⟩⟩,⟨⟨(-15186336848162699),(-15186336848162668)⟩,⟨4585405361838676,4585405361838707⟩⟩,⟨⟨(-13679604837250445),(-13679604837250426)⟩,⟨4907275164645603,4907275164645622⟩⟩,⟨⟨(-12304625356728932),(-12304625356728906)⟩,⟨5127518399243894,5127518399243923⟩⟩,⟨⟨(-11052436674771954),(-11052436674771923)⟩,⟨5263293199397659,5263293199397690⟩⟩,⟨⟨(-9914207873452843),(-9914207873452812)⟩,⟨5329384045248741,5329384045248772⟩⟩,⟨⟨(-8881349456681995),(-8881349456681976)⟩,⟨5338486092163834,5338486092163853⟩⟩,⟨⟨(-7945594824367152),(-7945594824367133)⟩,⟨5301461230769407,5301461230769426⟩⟩,⟨⟨(-7099057875159190),(-7099057875159160)⟩,⟨5227567708634819,5227567708634845⟩⟩] +lemma kernel24_1_r4_12_eq : ∀ k : Fin 16, kernel24_1Expr 4 12 k = kernel24_1_r4_12 k := by decide +kernel +noncomputable def kernel24_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-6334271219136950),(-6334271219136931)⟩,⟨5124665229726594,5124665229726613⟩⟩,⟨⟨(-5644208796743106),(-5644208796743075)⟩,⟨4999397472778081,4999397472778112⟩⟩,⟨⟨(-5022296102572283),(-5022296102572252)⟩,⟨4857353948476066,4857353948476097⟩⟩,⟨⟨(-4462410693751670),(-4462410693751646)⟩,⟨4703213059712129,4703213059712149⟩⟩,⟨⟨(-3958875214477232),(-3958875214477207)⟩,⟨4540868148760680,4540868148760705⟩⟩,⟨⟨(-3506444783046091),(-3506444783046060)⟩,⟨4373538217952610,4373538217952642⟩⟩,⟨⟨(-3100290258230524),(-3100290258230493)⟩,⟨4203864902466172,4203864902466203⟩⟩,⟨⟨(-2735978621397718),(-2735978621397688)⟩,⟨4033997160185842,4033997160185868⟩⟩,⟨⟨(-2409451473282727),(-2409451473282707)⟩,⟨3865665028012039,3865665028012058⟩⟩,⟨⟨(-2117002444230900),(-2117002444230881)⟩,⟨3700243679452017,3700243679452036⟩⟩,⟨⟨(-1855254149052311),(-1855254149052286)⟩,⟨3538808906946979,3538808906947004⟩⟩,⟨⟨(-1621135177917264),(-1621135177917245)⟩,⟨3382185045743333,3382185045743352⟩⟩,⟨⟨(-1411857499009053),(-1411857499009033)⟩,⟨3230986255255872,3230986255255892⟩⟩,⟨⟨(-1224894553441374),(-1224894553441345)⟩,⟨3085651979465565,3085651979465587⟩⟩,⟨⟨(-1057960245174573),(-1057960245174547)⟩,⟨2946477320303694,2946477320303719⟩⟩,⟨⟨(-908988965644665),(-908988965644635)⟩,⟨2813638977320279,2813638977320305⟩⟩] +lemma kernel24_1_r4_13_eq : ∀ k : Fin 16, kernel24_1Expr 4 13 k = kernel24_1_r4_13 k := by decide +kernel +noncomputable def kernel24_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-776116742222475),(-776116742222450)⟩,⟨2687217333159299,2687217333159324⟩⟩,⟨⟨(-657663559431753),(-657663559431728)⟩,⟨2567215197275333,2567215197275358⟩⟩,⟨⟨(-552116870339250),(-552116870339225)⟩,⟨2453573659639143,2453573659639168⟩⟩,⟨⟨(-458116291200652),(-458116291200632)⟩,⟨2346185451543073,2346185451543092⟩⟩,⟨⟨(-374439454035306),(-374439454035287)⟩,⟨2244906161638978,2244906161638998⟩⟩,⟨⟨(-299988978233513),(-299988978233494)⟩,⟨2149563611609941,2149563611609960⟩⟩,⟨⟨(-233780512663303),(-233780512663283)⟩,⟨2059965656971834,2059965656971854⟩⟩,⟨⟨(-174931793272974),(-174931793272955)⟩,⟨1975906644007470,1975906644007489⟩⟩,⟨⟨(-122652657241881),(-122652657241850)⟩,⟨1897172723350351,1897172723350383⟩⟩,⟨⟨(-76235952780716),(-76235952780697)⟩,⟨1823546193872550,1823546193872570⟩⟩,⟨⟨(-35049283283436),(-35049283283410)⟩,⟨1754809026926792,1754809026926818⟩⟩,⟨⟨1472474679095,1472474679115⟩,⟨1690745700308762,1690745700308781⟩⟩,⟨⟨33833938353954,33833938353973⟩,⟨1631145453224771,1631145453224790⟩⟩,⟨⟨62485327291611,62485327291630⟩,⟨1575804057785938,1575804057785957⟩⟩,⟨⟨87827967040540,87827967040560⟩,⟨1524525188836529,1524525188836548⟩⟩,⟨⟨110219238686486,110219238686511⟩,⟨1477121462024068,1477121462024093⟩⟩] +lemma kernel24_1_r4_14_eq : ∀ k : Fin 16, kernel24_1Expr 4 14 k = kernel24_1_r4_14 k := by decide +kernel +noncomputable def kernel24_1_r4_15 : Fin 16 → CBox := ![⟨⟨129977021611336,129977021611362⟩,⟨1433415199713427,1433415199713452⟩⟩,⟨⟨147383673503804,147383673503825⟩,⟨1393238975444413,1393238975444437⟩⟩,⟨⟨162689588302086,162689588302112⟩,⟨1356435979956224,1356435979956250⟩⟩,⟨⟨176116369441791,176116369441821⟩,⟨1322860245198542,1322860245198569⟩⟩,⟨⟨187859652559974,187859652560006⟩,⟨1292376757079088,1292376757079120⟩⟩,⟨⟨198091608696026,198091608696052⟩,⟨1264861482838879,1264861482838905⟩⟩,⟨⟨206963156049201,206963156049226⟩,⟨1240201334790621,1240201334790646⟩⟩,⟨⟨214605905511152,214605905511182⟩,⟨1218294088606833,1218294088606860⟩⟩,⟨⟨221133862493119,221133862493138⟩,⟨1199048271317657,1199048271317677⟩⟩,⟨⟨226644905009876,226644905009897⟩,⟨1182383031599469,1182383031599493⟩⟩,⟨⟨231222055561778,231222055561803⟩,⟨1168228002738654,1168228002738679⟩⟩,⟨⟨234934562062571,234934562062603⟩,⟨1156523166781351,1156523166781383⟩⟩,⟨⟨237838800885804,237838800885823⟩,⟨1147218726779604,1147218726779624⟩⟩,⟨⟨239979013032060,239979013032084⟩,⟨1140274992669624,1140274992669645⟩⟩,⟨⟨241387882442174,241387882442193⟩,⟨1135662285129774,1135662285129794⟩⟩,⟨⟨242086963581163,242086963581182⟩,⟨1133360860725654,1133360860725673⟩⟩] +lemma kernel24_1_r4_15_eq : ∀ k : Fin 16, kernel24_1Expr 4 15 k = kernel24_1_r4_15 k := by decide +kernel +noncomputable def kernel24_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel24_1_r4_0,kernel24_1_r4_1,kernel24_1_r4_2,kernel24_1_r4_3,kernel24_1_r4_4,kernel24_1_r4_5,kernel24_1_r4_6,kernel24_1_r4_7,kernel24_1_r4_8,kernel24_1_r4_9,kernel24_1_r4_10,kernel24_1_r4_11,kernel24_1_r4_12,kernel24_1_r4_13,kernel24_1_r4_14,kernel24_1_r4_15] +lemma kernel24_1_r4_eq (i k : Fin 16) : kernel24_1Expr 4 i k = kernel24_1_r4 i k := by + fin_cases i + · exact kernel24_1_r4_0_eq k + · exact kernel24_1_r4_1_eq k + · exact kernel24_1_r4_2_eq k + · exact kernel24_1_r4_3_eq k + · exact kernel24_1_r4_4_eq k + · exact kernel24_1_r4_5_eq k + · exact kernel24_1_r4_6_eq k + · exact kernel24_1_r4_7_eq k + · exact kernel24_1_r4_8_eq k + · exact kernel24_1_r4_9_eq k + · exact kernel24_1_r4_10_eq k + · exact kernel24_1_r4_11_eq k + · exact kernel24_1_r4_12_eq k + · exact kernel24_1_r4_13_eq k + · exact kernel24_1_r4_14_eq k + · exact kernel24_1_r4_15_eq k +noncomputable def kernel24_1_r5_0 : Fin 16 → CBox := ![⟨⟨27670448663494842392804254587,27670448663494847510216460215⟩,⟨32626625818269127323067542711,32626625818269132441042408207⟩⟩,⟨⟨27676338995777301754810839145,27676338995777306870199697220⟩,⟨32580692897007383050904025899,32580692897007388166854215733⟩⟩,⟨⟨27687994928751962186394355035,27687994928751967297729366090⟩,⟨32488917292913423033481179437,32488917292913428145374869932⟩⟩,⟨⟨27705167858020758583815192240,27705167858020763689069276063⟩,⟨32351479638587865891251816940,32351479638587870997060611668⟩⟩,⟨⟨27727487019974416018263582395,27727487019974421115414580583⟩,⟨32168651266418500941322062351,32168651266418506039022498687⟩⟩,⟨⟨27754462052251958676940962007,27754462052251963763973513155⟩,⟨31940794652410879896306124522,31940794652410884983881552787⟩⟩,⟨⟨27785486389100559836438003043,27785486389100564911344889738⟩,⟨31668363980928040200442322472,31668363980928045275884256883⟩⟩,⟨⟨27819841475621277554096924810,27819841475621282614881325145⟩,⟨31351905807608595993671757406,31351905807608601054982131468⟩⟩,⟨⟨27856701780784089225211830446,27856701780784094269887989881⟩,⟨30992059792597735373518240661,30992059792597740418710082896⟩⟩,⟨⟨27895140584936735792953929733,27895140584936740819550441723⟩,⟨30589559471450082848298174465,30589559471450087875398892858⟩⟩,⟨⟨27934136513313543804871075019,27934136513313548811432172567⟩,⟨30145233026712497307550271974,30145233026712502314602949191⟩⟩,⟨⟨27972580782774397753894510318,27972580782774402738907347609⟩,⟨29660004019330798614519750607,29660004019330803600010420016⟩⟩,⟨⟨28009285124677143187228426508,28009285124677148148802942103⟩,⟨29134892035705210127293301612,29134892035705215089330832193⟩⟩,⟨⟨28042990342421052264507753030,28042990342421057200777036312⟩,⟨28571013203498355669673586282,28571013203498360606390043893⟩⟩,⟨⟨28072375457812400288173328731,28072375457812405197285540726⟩,⟨27969580527225049714557343982,27969580527225054624099915481⟩⟩,⟨⟨28096067396019369340032761056,28096067396019374220164570990⟩,⟨27331903993267048044374141393,27331903993267052924918574587⟩⟩] +lemma kernel24_1_r5_0_eq : ∀ k : Fin 16, kernel24_1Expr 5 0 k = kernel24_1_r5_0 k := by decide +kernel +noncomputable def kernel24_1_r5_1 : Fin 16 → CBox := ![⟨⟨28112651154532011918088447627,28112651154532016767431072433⟩,⟨26659390393294036366727793293,26659390393294041216464439456⟩⟩,⟨⟨28120680397259300594196427714,28120680397259305410978159187⟩,⟨25953542815162954630176018563,25953542815162959447332362728⟩⟩,⟨⟨28118688410720391997795748645,28118688410720396780258517326⟩,⟨25215959751232111934022697150,25215959751232116716839924659⟩⟩,⟨⟨28105199355267419204483068608,28105199355267423950912134940⟩,⟨24448333775677023110978452316,24448333775677027857741142821⟩⟩,⟨⟨28078739740463407465230102121,28078739740463412173921297824⟩,⟨23652449744835332472412852808,23652449744835337181416223892⟩⟩,⟨⟨28037850050186391388936435364,28037850050186396058241788225⟩,⟨22830182477833238171061793424,22830182477833242840657327890⟩⟩,⟨⟨27981096439797926553684458033,27981096439797931181963219835⟩,⟨21983493878740593370053918974,21983493878740597998600394548⟩⟩,⟨⟨27907082424861789193853295121,27907082424861793779545096514⟩,⟨21114429466241599033289724931,21114429466241603619226491411⟩⟩,⟨⟨27814460478489012427691863900,27814460478489016969237201796⟩,⟨20225114282257950724367567240,20225114282257955266134915019⟩⟩,⟨⟨27701943452481088554887420877,27701943452481093050791657447⟩,⟨19317748157076586712015745871,19317748157076591208118787551⟩⟩,⟨⟨27568315736105855645990340235,27568315736105860094753565331⟩,⟨18394600315259878189557100255,18394600315259882638495751790⟩⟩,⟨⟨27412444065629813348479824142,27412444065629817748689169015⟩,⟨17458003313887401879317566952,17458003313887406279678862128⟩⟩,⟨⟨27233287897702451452094688993,27233287897702455802323192422⟩,⟨16510346312420993203113158304,16510346312420997553470115234⟩⟩,⟨⟨27029909260393914575032854541,27029909260393918874097751833⟩,⟨15554067681615185163762322349,15554067681615189462932232450⟩⟩,⟨⟨26801481997172145598141080176,26801481997172149845026631782⟩,⟨14591646967321565588435322165,14591646967321569835402578655⟩⟩,⟨⟨26547300321407317375397037103,26547300321407321568881888071⟩,⟨13625596233658591437168812713,13625596233658595630712269208⟩⟩] +lemma kernel24_1_r5_1_eq : ∀ k : Fin 16, kernel24_1Expr 5 1 k = kernel24_1_r5_1 k := by decide +kernel +noncomputable def kernel24_1_r5_2 : Fin 16 → CBox := ![⟨⟨26266786602138990090279039228,26266786602138994229104025603⟩,⟨12658450818731896632653994457,12658450818731900771514770900⟩⟩,⟨⟨25959498305854315399651644288,25959498305854319482708159418⟩,⟨11692759544782515962287263414,11692759544782520045357110319⟩⟩,⟨⟨25625134023912170180707438264,25625134023912174206837894514⟩,⟨10731074433195883462060091297,10731074433195887488181850792⟩⟩,⟨⟨25263538521004972010616886324,25263538521004975978811318829⟩,⟨9775939983104299269841592225,9775939983104303238005798706⟩⟩,⟨⟨24874706746661184897870940828,24874706746661188807088288278⟩,⟨8829882080239884656477836462,8829882080239888565643996556⟩⟩,⟨⟨24458786759228123440361075464,24458786759228127289929626786⟩,⟨7895396610124353802248016953,7895396610124357651745051810⟩⟩,⟨⟨24016081519994073346022303264,24016081519994077134977828367⟩,⟨6974937856498869079805267709,6974937856498872868669642386⟩⟩,⟨⟨23547049524054803025988831391,23547049524054806753549603080⟩,⟨6070906771988427499608620686,6070906771988431227059360700⟩⟩,⟨⟨23052304244132552106854906163,23052304244132555772141887291⟩,⟨5185639213253079282193382073,5185639213253082947352259880⟩⟩,⟨⟨22532612373732678448506229857,22532612373732682050986955306⟩,⟨4321394237202904555347283182,4321394237202908157682686870⟩⟩,⟨⟨21988890866678890246574462443,21988890866678893785501472688⟩,⟨3480342558154664178025011191,3480342558154667716790389195⟩⟩,⟨⟨21422202781095255347569689521,21422202781095258822410845356⟩,⟨2664555268006243213522710649,2664555268006246688186883571⟩⟩,⟨⟨20833751947184273818289533049,20833751947184277228426022350⟩,⟨1875992922534183324568636822,1875992922534186734513874942⟩⟩,⟨⟨20224876489558344813635545512,20224876489558348158675451744⟩,⟨1116495096727956372896498076,1116495096727959717731899472⟩⟩,⟨⟨19597041246282505321713880110,19597041246282508601119190799⟩,⟨387770510626163401588228070,387770510626166680776826244⟩⟩,⟨⟨18951829138039171600533031232,18951829138039174814021238849⟩,⟨(-308612175604507595595628534),(-308612175604504382335275553)⟩⟩] +lemma kernel24_1_r5_2_eq : ∀ k : Fin 16, kernel24_1Expr 5 2 k = kernel24_1_r5_2 k := by decide +kernel +noncomputable def kernel24_1_r5_3 : Fin 16 → CBox := ![⟨⟨18290931551786849973767699695,18290931551786853120884890594⟩,⟨(-971232802608167197856035444),(-971232802608164050976753866)⟩⟩,⟨⟨17616137813808923081037113054,17616137813808926161661078254⟩,⟨(-1598827299318273748817216687),(-1598827299318270668436886065)⟩⟩,⟨⟨16929323836990924128559146489,16929323836990927142378861180⟩,⟨(-2190294333982504116856740137),(-2190294333982501103284521360)⟩⟩,⟨⟨16232440036383572021055435940,16232440036383574968049508063⟩,⟨(-2744700953393987432849089225),(-2744700953393984486105483110)⟩⟩,⟨⟨15527498615468186346008719097,15527498615468189225952360366⟩,⟨(-3261287143737165778176311589),(-3261287143737162898485220322)⟩⟩,⟨⟨14816560332912826212391825051,14816560332912829025421898763⟩,⟨(-3739469256207875434533967381),(-3739469256207872621757661432)⟩⟩,⟨⟨14101720865873819125793194999,14101720865873821871826181677⟩,⟨(-4178842251212864856368494766),(-4178842251212862110589640712)⟩⟩,⟨⟨13385096890953071117974889420,13385096890953073797247052870⟩,⟨(-4579180726369257026688607837),(-4579180726369254347670115988)⟩⟩,⟨⟨12668812007676183802099738562,12668812007676186414601515871⟩,⟨(-4940438705570580091223933041),(-4940438705570577478974561261)⟩⟩,⟨⟨11954982631736072450401395347,11954982631736074996533083092⟩,⟨(-5262748178911754399622843095),(-5262748178911751853741525458)⟩⟩,⟨⟨11245703986195900966999362958,11245703986195903447628231281⟩,⟨(-5546416396109486498523776251),(-5546416396109484018140250216)⟩⟩,⟨⟨10543036318327834363849706499,10543036318327836784875059894⟩,⟨(-5791921929047756827946725685),(-5791921929047754407144581224)⟩⟩,⟨⟨9848991467765234964638239478,9848991467765237326014169615⟩,⟨(-5999909532046197068945891306),(-5999909532046194707771716895)⟩⟩,⟨⟨9165519908171871048113459738,9165519908171873350216259902⟩,⟨(-6171183841215411651850989460),(-6171183841215409349929219853)⟩⟩,⟨⟨8494498379710698118368664960,8494498379710700361281697818⟩,⟨(-6306701966651418317955771566),(-6306701966651416075203806706)⟩⟩,⟨⟨7837718223276869858119592776,7837718223276872042288118940⟩,⟨(-6407565043058425906823358672),(-6407565043058423722796738969)⟩⟩] +lemma kernel24_1_r5_3_eq : ∀ k : Fin 16, kernel24_1Expr 5 3 k = kernel24_1_r5_3 k := by decide +kernel +noncomputable def kernel24_1_r5_4 : Fin 16 → CBox := ![⟨⟨7196874519816290241316080224,7196874519816292366867718493⟩,⟨(-6475008815508451652926133191),(-6475008815508449527498068130)⟩⟩,⟨⟨6573556129174249726906352948,6573556129174251794436914528⟩,⟨(-6510393347290229427735025288),(-6510393347290227360310561909)⟩⟩,⟨⟨5969236712919865662304921229,5969236712919867672079373007⟩,⟨(-6515191946022735921739462756),(-6515191946022733912054511662)⟩⟩,⟨⟨5385266814600295224948220411,5385266814600297177609710957⟩,⟨(-6490979412279120114517724754),(-6490979412279118161930034225)⟩⟩,⟨⟨4822867059038948599200052650,4822867059038950495058621911⟩,⟨(-6439419721770244196319741095),(-6439419721770242300520179491)⟩⟩,⟨⟨4283122519762697887113631986,4283122519762699726945623557⟩,⟨(-6362253257577591672431253099),(-6362253257577589832644394792)⟩⟩,⟨⟨3766978290593874561221107101,3766978290593876345469639695⟩,⟨(-6261283712927640859454665936),(-6261283712927639075238376777)⟩⟩,⟨⟨3275236284051458024964967010,3275236284051459754462853592⟩,⟨(-6138364787510490326690155343),(-6138364787510488597212625183)⟩⟩,⟨⟨2808553265655387410567515764,2808553265655389085813271690⟩,⟨(-5995386801333967661446779219),(-5995386801333965986210393465)⟩⟩,⟨⟨2367440119703753890688463783,2367440119703755512638410551⟩,⟨(-5834263349563488389525803408),(-5834263349563486767575134585)⟩⟩,⟨⟨1952262328779282093244899401,1952262328779283662546867554⟩,⟨(-5656918119743949563476221269),(-5656918119743947994164322483)⟩⟩,⟨⟨1563241636319562907255086006,1563241636319564424903732184⟩,⟨(-5465271989272590509288726748),(-5465271989272588991621806801)⟩⟩,⟨⟨1200458849228536396672694277,1200458849228537863255973440⟩,⟨(-5261230516053203803046608030),(-5261230516053202336437559689)⟩⟩,⟨⟨863857725878414719140114383,863857725878416135865696166⟩,⟨(-5046671928995879703083837363),(-5046671928995878286325812309)⟩⟩,⟨⟨553249884102620808036587606,553249884102622175657050955⟩,⟨(-4823435717535994018134031891),(-4823435717535992650475249268)⟩⟩,⟨⟨268320654047326788591777385,268320654047328108160512809⟩,⟨(-4593311910752701995242724078),(-4593311910752700675630559153)⟩⟩] +lemma kernel24_1_r5_4_eq : ∀ k : Fin 16, kernel24_1Expr 5 4 k = kernel24_1_r5_4 k := by decide +kernel +noncomputable def kernel24_1_r5_5 : Fin 16 → CBox := ![⟨⟨8635792150435905254848938,8635792150437177442892823⟩,⟨(-4358031127107768694681986265),(-4358031127107767422446140998)⟩⟩,⟨⟨(-226351034848155098199510466),(-226351034848153872145404487)⟩,⟨(-4119255465450319830748246497),(-4119255465450318604642672826)⟩⟩,⟨⟨(-437290093013590884206935180),(-437290093013589703193368889)⟩,⟨(-3878570296902653065264520833),(-3878570296902651884197433936)⟩⟩,⟨⟨(-624926853271628888550448110),(-624926853271627751471686009)⟩,⟨(-3637477005724769876893337949),(-3637477005724768739760114372)⟩⟩,⟨⟨(-790092797522086102919822730),(-790092797522085009038162585)⟩,⟨(-3397386715423469938824691409),(-3397386715423468844888073559)⟩⟩,⟨⟨(-933695865780808988365236576),(-933695865780807936457525432)⟩,⟨(-3159615024399873969203376627),(-3159615024399872917240615842)⟩⟩,⟨⟨(-1056710651775479550317791818),(-1056710651775478539576835563)⟩,⟨(-2925377763489736545665433920),(-2925377763489735534869710683)⟩⟩,⟨⟨(-1160168453500496545407718128),(-1160168453500495574680474769)⟩,⟨(-2695787776012002027648245064),(-2695787776012001056866853487)⟩⟩,⟨⟨(-1245147282993998019661121721),(-1245147282993997088166232760)⟩,⟨(-2471852709563551158342014395),(-2471852709563550226793902130)⟩⟩,⟨⟨(-1312761936107805793233789674),(-1312761936107804899193574810)⟩,⟨(-2254473797932854237905795311),(-2254473797932853343817957683)⟩⟩,⟨⟨(-1364154218388277645831563861),(-1364154218388276788314349220)⟩,⟨(-2044445601290852651991261282),(-2044445601290851794432746473)⟩⟩,⟨⟨(-1400483417477949031888164706),(-1400483417477948209776793248)⟩,⟨(-1842456663378008259338676227),(-1842456663378007437191936498)⟩⟩,⟨⟨(-1422917105802963457416117147),(-1422917105802962669939239898)⟩,⟨(-1649091035850118518000362031),(-1649091035850117730493658418)⟩⟩,⟨⟨(-1432622349859030534765382282),(-1432622349859029780746152266)⟩,⟨(-1464830612362676661781314253),(-1464830612362675907737410352)⟩⟩,⟨⟨(-1430757394286689387465590371),(-1430757394286688666088008790)⟩,⟨(-1290058208436169995959714069),(-1290058208436169274562222905)⟩⟩,⟨⟨(-1418463880278268214173899058),(-1418463880278267524202307870)⟩,⟨(-1125061317705450811279828643),(-1125061317705450121292708101)⟩⟩] +lemma kernel24_1_r5_5_eq : ∀ k : Fin 16, kernel24_1Expr 5 5 k = kernel24_1_r5_5 k := by decide +kernel +noncomputable def kernel24_1_r5_6 : Fin 16 → CBox := ![⟨⟨(-1396859648830296498973650689),(-1396859648830295839628308833)⟩,⟨(-970036470848411586733440253),(-970036470848410927376573640)⟩⟩,⟨⟨(-1367032170092663099438842452),(-1367032170092662469573481158)⟩,⟨(-825094120326537710310567143),(-825094120326537080437318797)⟩⟩,⟨⟨(-1330032630713607419273946816),(-1330032630713606818062658307)⟩,⟨(-690263972047539709048877324),(-690263972047539107832984064)⟩⟩,⟨⟨(-1286870701777003007026840050),(-1286870701777002433397852833)⟩,⟨(-565500684155216846641426978),(-565500684155216273010740856)⟩⟩,⟨⟨(-1238510000807651235747489314),(-1238510000807650688943408975)⟩,⟨(-450689853324149950270192058),(-450689853324149403466987317)⟩⟩,⟨⟨(-1185864252504720146172898399),(-1185864252504719625116161423)⟩,⟨(-345654210131507401134138335),(-345654210131506880080543020)⟩⟩,⟨⟨(-1129794144465514206862327881),(-1129794144465513710775189905)⟩,⟨(-250159947226151556442887627),(-250159947226151060360863728)⟩⟩,⟨⟨(-1071104866281641286351787344),(-1071104866281640814220941193)⟩,⟨(-163923107035420684052493858),(-163923107035420211928458206)⟩⟩,⟨⟨(-1010544313114097402340075100),(-1010544313114096952840608229)⟩,⟨(-86615959551592803526321149),(-86615959551592354035100790)⟩⟩,⟨⟨(-948801928255248438739327296),(-948801928255248010711448615)⟩,⟨(-17873305224462152443492096),(-17873305224461724425054733)⟩⟩,⟨⟨(-886508153321725931834737187),(-886508153321725524614348210)⟩,⟨42701356950636784823637559,42701356950637192033616112⟩⟩,⟨⟨(-824234449635362315136830841),(-824234449635361927850044018)⟩,⟨95529850526466443835852244,95529850526466831111598029⟩⟩,⟨⟨(-762493850066952136790066953),(-762493850066951768818189276)⟩,⟨141053580361323677756596621,141053580361324045717239913⟩⟩,⟨⟨(-701741997152674986926816885),(-701741997152674637394419815)⟩,⟨179728071374665826413501819,179728071374666175934596335⟩⟩,⟨⟨(-642378620644266064297891436),(-642378620644265732575206175)⟩,⟨212017823340913007648294693,212017823340913339359721441⟩⟩,⟨⟨(-584749405807122633772753448),(-584749405807122319031249463)⟩,⟨238391511422258211982077476,238391511422258526712462045⟩⟩] +lemma kernel24_1_r5_6_eq : ∀ k : Fin 16, kernel24_1Expr 5 6 k = kernel24_1_r5_6 k := by decide +kernel +noncomputable def kernel24_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-529148202709043464457140230),(-529148202709043166129645923)⟩,⟨259317555853509887577198547,259317555853510185893796719⟩⟩,⟨⟨(-475819526408906378752407957),(-475819526408906096012648943)⟩,⟨275260078044503267224523586,275260078044503549954067285⟩⟩,⟨⟨(-424961298312496024997372343),(-424961298312495757221243512)⟩,⟨286675254439157389973075123,286675254439157657740501218⟩⟩,⟨⟨(-376727779957072273045009973),(-376727779957072019511912715)⟩,⟨294008073836385714585879530,294008073836385968111670662⟩⟩,⟨⟨(-331232652055789320140711081),(-331232652055789080324611621)⟩,⟨297689498598546532176622640,297689498598546771986699350⟩⟩,⟨⟨(-288552193711453348880693670),(-288552193711453122076272228)⟩,⟨298134025299478484954708402,298134025299478711754278704⟩⟩,⟨⟨(-248728519226643702045918014),(-248728519226643487742201829)⟩,⟨295737635937524480296279016,295737635937524694596207836⟩⟩,⟨⟨(-211772832822300750348054040),(-211772832822300547904063050)⟩,⟨290876126890031559340549092,290876126890031761781711991⟩⟩,⟨⟨(-177668664757389761440304612),(-177668664757389570246494382)⟩,⟨283903799335186927646574216,283903799335187118838415915⟩⟩,⟨⟨(-146375055746904888122250033),(-146375055746904707519749748)⟩,⟨275152491925514874960562611,275152491925515055561858546⟩⟩,⟨⟨(-117829660135047313300379851),(-117829660135047142857666435)⟩,⟨264930934066526856825825580,264930934066527027268008467⟩⟩,⟨⟨(-91951741928786797246477169),(-91951741928786636421835169)⟩,⟨253524396227008048946434777,253524396227008209771131855⟩⟩,⟨⟨(-68645041472142063545013360),(-68645041472141911948863511)⟩,⟨241194612269679891682547550,241194612269680043279253358⟩⟩,⟨⟨(-47800494186171261631788707),(-47800494186171118730610941)⟩,⟨228179947821158577671134410,228179947821158720573296249⟩⟩,⟨⟨(-29298786362079657036521287),(-29298786362079522452193298)⟩,⟨214695788171065371218784166,214695788171065505804456608⟩⟩,⟨⟨(-13012736429170612564534626),(-13012736429170485830427916)⟩,⟨200935119069827906833395866,200935119069828033569145539⟩⟩] +lemma kernel24_1_r5_7_eq : ∀ k : Fin 16, kernel24_1Expr 5 7 k = kernel24_1_r5_7 k := by decide +kernel +noncomputable def kernel24_1_r5_8 : Fin 16 → CBox := ![⟨⟨1190506614051390064261882,1190506614051509289670068⟩,⟨187069274047292841899958420,187069274047292961127250914⟩⟩,⟨⟨13447452851734390861547675,13447452851734503089139472⟩,⟨173248822461044998453347578,173248822461045110683013860⟩⟩,⟨⟨23896451593885357028668736,23896451593885462574317119⟩,⟨159604573363691158245760972,159604573363691263793577785⟩⟩,⟨⟨32676061830066293176695669,32676061830066392430601535⟩,⟨146248671410716809534346222,146248671410716908790441281⟩⟩,⟨⟨39923610486429196010581151,39923610486429289254890505⟩,⟨133275762373105363865204195,133275762373105457111698059⟩⟩,⟨⟨45773933924393422560526270,45773933924393510165778038⟩,⟨120764207330575924865103806,120764207330576012472514199⟩⟩,⟨⟨50358296339889999284495494,50358296339890081539784860⟩,⟨108777326262192426949404368,108777326262192509206807634⟩⟩,⟨⟨53803477216428659221624752,53803477216428736460575985⟩,⟨97364653483248298335867431,97364653483248375576872729⟩⟩,⟨⟨56231018747463701579735575,56231018747463774032248557⟩,⟨86563189165135066476579843,86563189165135138930915186⟩⟩,⟨⟨57756623164006910507431892,57756623164006978482808332⟩,⟨76398632985531099793628451,76398632985531167770534447⟩⟩,⟨⟨58489689169274337705761960,58489689169274401437473556⟩,⟨66886587759944533212211179,66886587759944596945185194⟩⟩,⟨⟨58532976177797608249984887,58532976177797668006310807⟩,⟨58033722675947137560854933,58033722675947197318201186⟩⟩,⟨⟨57982384764207358139055687,57982384764207414112637333⟩,⟨49838887465292275949586934,49838887465292331923970635⟩⟩,⟨⟨56926841627568916019928553,56926841627568968467126800⟩,⟨42294170486928738200644835,42294170486928790648449720⟩⟩,⟨⟨55448277450432832619668397,55448277450432881721028298⟩,⟨35385895239544878963694184,35385895239544928065486821⟩⟩,⟨⟨53621686256802770987581333,53621686256802816964596682⟩,⟨29095551262888228879573593,29095551262888274856868088⟩⟩] +lemma kernel24_1_r5_8_eq : ∀ k : Fin 16, kernel24_1Expr 5 8 k = kernel24_1_r5_8 k := by decide +kernel +noncomputable def kernel24_1_r5_9 : Fin 16 → CBox := ![⟨⟨51515255229039676465279032,51515255229039719472228404⟩,⟨23400656713085347732362450,23400656713085390739456367⟩⟩,⟨⟨49190554409596459978558621,49190554409596500222626077⟩,⟨18275551101920834761707198,18275551101920875005802235⟩⟩,⟨⟨46702776269299250175876961,46702776269299287804191794⟩,⟨13692117769685443311532031,13692117769685480939773847⟩⟩,⟨⟨44101015750442854069675536,44101015750442889259093212⟩,⟨9620436614454181700165022,9620436614454216889425448⟩⟩,⟨⟨41428582072167331925730783,41428582072167364802096169⟩,⟨6029368428434826167474221,6029368428434859043611887⟩⟩,⟨⟨38723334300670648501827743,38723334300670679229168585⟩,⟨2887072897223777623842489,2887072897223808350897346⟩⟩,⟨⟨36018033422493658755273295,36018033422493687451163296⟩,⟨161462904977940796014037,161462904977969491570971⟩⟩,⟨⟨33340704401650643863542933,33340704401650670669279479⟩,⟨(-2179401736400423218299722),(-2179401736400396412933409)⟩⟩,⟨⟨30715002438644366123920443,30715002438644391138741391⟩,⟨(-4166977645918233356713411),(-4166977645918208342288585)⟩⟩,⟨⟨28160578370897887088567184,28160578370897910444482789⟩,⟨(-5831954558939428194819536),(-5831954558939404839303618)⟩⟩,⟨⟨25693438850962014899109443,25693438850962036689489017⟩,⟨(-7204021394156966197808720),(-7204021394156944407827824)⟩⟩,⟨⟨23326297603682829093601150,23326297603682849430331477⟩,⟨(-8311677652431633953613138),(-8311677652431613617276745)⟩⟩,⟨⟨21068914690492294815940710,21068914690492313778255156⟩,⟨(-9182086064288138081439560),(-9182086064288119119511009)⟩⟩,⟨⟨18928421293668060043255185,18928421293668077734196726⟩,⟨(-9840962431167464225902711),(-9840962431167446535336471)⟩⟩,⟨⟨16909628072639275896351820,16909628072639292389206750⟩,⟨(-10312498686909043414746519),(-10312498686909026922254101)⟩⟩,⟨⟨15015315636211693249158325,15015315636211708708387747⟩,⟨(-10619315331895812326327606),(-10619315331895796867410669)⟩⟩] +lemma kernel24_1_r5_9_eq : ∀ k : Fin 16, kernel24_1Expr 5 9 k = kernel24_1_r5_9 k := by decide +kernel +noncomputable def kernel24_1_r5_10 : Fin 16 → CBox := ![⟨⟨13246506118016536285056841,13246506118016550769318851⟩,⟨(-10782439554781185513828571),(-10782439554781171029829289)⟩⟩,⟨⟨11602715237546926329881902,11602715237546939910449614⟩,⟨(-10821305548179066004545768),(-10821305548179052424195674)⟩⟩,⟨⟨10082184576622693415482671,10082184576622706139764682⟩,⟨(-10753773738158811832971676),(-10753773738158799108866514)⟩⟩,⟨⟨8682094102480500252664799,8682094102480512180494601⟩,⟨(-10596165876486165145828393),(-10596165876486153218138814)⟩⟩,⟨⟨7398755225933555637371296,7398755225933566808575477⟩,⟨(-10363313183571546542871007),(-10363313183571535371774287)⟩⟩,⟨⟨6227784898633046192551788,6227784898633056662953725⟩,⟨(-10068614973965462104617492),(-10068614973965451634293908)⟩⟩,⟨⟨5164261430171899078821696,5164261430171908885909387⟩,⟨(-9724105440563559493428856),(-9724105440563549686393792)⟩⟩,⟨⟨4202862846614478151589356,4202862846614487342699842⟩,⟨(-9340526514671783462966208),(-9340526514671774271885761)⟩⟩,⟨⟨3337988720173440349972352,3337988720173448955821193⟩,⟨(-8927404953564453746206476),(-8927404953564445140367985)⟩⟩,⟨⟨2563866478416166207537753,2563866478416174272758060⟩,⟨(-8493132032549498323015499),(-8493132032549490257788503)⟩⟩,⟨⟨1874643253798361145063542,1874643253798368699001534⟩,⟨(-8045044432775897982705793),(-8045044432775890428746512)⟩⟩,⟨⟨1264464363666254133510290,1264464363666261213334300⟩,⟨(-7589505117511043087895140),(-7589505117511036008037502)⟩⟩,⟨⟨727539520212573574812038,727539520212580204865483⟩,⟨(-7131983177258067107313547),(-7131983177258060477216314)⟩⟩,⟨⟨258197862144645273254906,258197862144651488149394⟩,⟨(-6677131797150746643629718),(-6677131797150740428683028)⟩⟩,⟨⟨(-149067122216602995029404),(-149067122216597172455028)⟩,⟨(-6228863658181076985478067),(-6228863658181071162844679)⟩⟩,⟨⟨(-499561744475984231812693),(-499561744475978772548309)⟩,⟨(-5790423226909024265059150),(-5790423226909018805730351)⟩⟩] +lemma kernel24_1_r5_10_eq : ∀ k : Fin 16, kernel24_1Expr 5 10 k = kernel24_1_r5_10 k := by decide +kernel +noncomputable def kernel24_1_r5_11 : Fin 16 → CBox := ![⟨⟨(-798364345591783934884744),(-798364345591778820548726)⟩,⟨(-5364455516558439319500748),(-5364455516558434205096449)⟩⟩,⟨⟨(-1050304662876884244424648),(-1050304662876879447600825)⟩,⟨(-4953071016213870347104957),(-4953071016213865550212599)⟩⟩,⟨⟨(-1259949448029169728537289),(-1259949448029165231718891)⟩,⟨(-4557906584768605291177534),(-4557906584768600794290965)⟩⟩,⟨⟨(-1431593509054511870273603),(-1431593509054507650729162)⟩,⟨(-4180182193038329732781652),(-4180182193038325513169877)⟩⟩,⟨⟨(-1569255410503646754250375),(-1569255410503642797819275)⟩,⟨(-3820753471852051986693474),(-3820753471852048030196315)⟩⟩,⟨⟨(-1676677128871967166408880),(-1676677128871963452359781)⟩,⟨(-3480160086837966502930410),(-3480160086837962788816851)⟩⟩,⟨⟨(-1757327022221756325355500),(-1757327022221752839896617)⟩,⟨(-3158670012956292496509459),(-3158670012956289010987999)⟩⟩,⟨⟨(-1814405534174041696715624),(-1814405534174038422599014)⟩,⟨(-2856319824534291317050501),(-2856319824534288042873409)⟩⟩,⟨⟨(-1850853111643550340956091),(-1850853111643547267753024)⟩,⟨(-2572951150572184453239064),(-2572951150572181379982001)⟩⟩,⟨⟨(-1869359872469014496163735),(-1869359872469011607642143)⟩,⟨(-2308243471338705253541417),(-2308243471338702364973174)⟩⟩,⟨⟨(-1872376612973212728845910),(-1872376612973210014807854)⟩,⟨(-2061743451658782228453722),(-2061743451658779514375738)⟩⟩,⟨⟨(-1862126796145433539322868),(-1862126796145430985993542)⟩,⟨(-1832891019671080446550252),(-1832891019671077893187114)⟩⟩,⟨⟨(-1840619208353304564662016),(-1840619208353302164098909)⟩,⟨(-1621042408009841630066345),(-1621042408009839229474979)⟩⟩,⟨⟨(-1809661016133584321733018),(-1809661016133582061688419)⟩,⟨(-1425490378100125200623960),(-1425490378100122940556128)⟩⟩,⟨⟨(-1770870994634058134455412),(-1770870994634056007367172)⟩,⟨(-1245481848247182971628174),(-1245481848247180844521239)⟩⟩,⟨⟨(-1725692735698941912061002),(-1725692735698939907848751)⟩,⟨(-1080233143088726271961374),(-1080233143088724267734512)⟩⟩] +lemma kernel24_1_r5_11_eq : ∀ k : Fin 16, kernel24_1Expr 5 11 k = kernel24_1_r5_11 k := by decide +kernel +noncomputable def kernel24_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-1675407676480596178775099),(-1675407676480594291710603)⟩,⟨(-928943076342410340959944),(-928943076342408453884493)⟩⟩,⟨⟨(-1621147818937202705095231),(-1621147818937200925431671)⟩,⟨(-790804071139368177827768),(-790804071139366398156521)⟩⟩,⟨⟨(-1563908036789933889582960),(-1563908036789932210955077)⟩,⟨(-665011513049269590375813),(-665011513049267911743154)⟩⟩,⟨⟨(-1504557889640325891601338),(-1504557889640324306351308)⟩,⟨(-550771520578481029800183),(-550771520578479444547946)⟩⟩,⟨⟨(-1443852884183503693624681),(-1443852884183502197406152)⟩,⟨(-447307306812839076311190),(-447307306812837580092731)⟩⟩,⟨⟨(-1382445140001717512451407),(-1382445140001716098032907)⟩,⟨(-353864294283146193015888),(-353864294283144778599457)⟩⟩,⟨⟨(-1320893432497553353889991),(-1320893432497552017085977)⟩,⟨(-269714133311685657473047),(-269714133311684320672846)⟩⟩,⟨⟨(-1259672598340819410081187),(-1259672598340818144923495)⟩,⟨(-194157762266726716135778),(-194157762266725450983416)⟩⟩,⟨⟨(-1199182299568693680335193),(-1199182299568692483710265)⟩,⟨(-126527636485914270518000),(-126527636485913073899706)⟩⟩,⟨⟨(-1139755151400906278770111),(-1139755151400905144944667)⟩,⟨(-66189241271133730840317),(-66189241271132597022618)⟩⟩,⟨⟨(-1081664226108182082529215),(-1081664226108181008368746)⟩,⟨(-12541993418992542131100),(-12541993418991467979301)⟩⟩,⟨⟨(-1025129951090687501328930),(-1025129951090686482283203)⟩,⟨34980374682245681791867,34980374682246700828144⟩⟩,⟨⟨(-970326423860411200507161),(-970326423860410234206756)⟩,⟨76909864224645953445771,76909864224646919736085⟩⟩,⟨⟨(-917387170041770952893167),(-917387170041770034977272)⟩,⟨113744617514128531618666,113744617514129449523937⟩⟩,⟨⟨(-866410372960177755580293),(-866410372960176883492007)⟩,⟨145949617581698932990761,145949617581699805068067⟩⟩,⟨⟨(-817463605017902042909563),(-817463605017901212807793)⟩,⟨173957621567970763386515,173957621567971593477311⟩⟩] +lemma kernel24_1_r5_12_eq : ∀ k : Fin 16, kernel24_1Expr 5 12 k = kernel24_1_r5_12 k := by decide +kernel +noncomputable def kernel24_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-770588091986738697537717),(-770588091986737907855709)⟩,⟨198170276913363791260161,198170276913364580931255⟩⟩,⟨⟨(-725802541691566806564626),(-725802541691566053830571)⟩,⟨218959376091638219709199,218959376091638972432429⟩⟩,⟨⟨(-683106568419847619840798),(-683106568419846902355759)⟩,⟨236668211716975659056500,236668211716976376530843⟩⟩,⟨⟨(-642483743859865815333515),(-642483743859865130397490)⟩,⟨251612999359347023894802,251612999359347708820287⟩⟩,⟨⟨(-603904304524789747060315),(-603904304524789093455321)⟩,⟨264084340348535752690640,264084340348536406285266⟩⟩,⟨⟨(-567327544530056027217471),(-567327544530055402286696)⟩,⟨274348701266134078029556,274348701266134702950151⟩⟩,⟨⟨(-532703921318540029534394),(-532703921318539432000634)⟩,⟨282649890751318400922331,282649890751318998446117⟩⟩,⟨⟨(-499976900523319286086769),(-499976900523318713831299)⟩,⟨289210517715517505911510,289210517715518078157223⟩⟩,⟨⟨(-469084564665703981878113),(-469084564665703434091384)⟩,⟨294233418108785772651069,294233418108786320428265⟩⟩,⟨⟨(-439961008843760328377783),(-439961008843759802880818)⟩,⟨297903040042016255671559,297903040042016781159217⟩⟩,⟨⟨(-412537545004713029843084),(-412537545004712525646267)⟩,⟨300386779378470077176073,300386779378470581364159⟩⟩,⟨⟨(-386743734838766775244618),(-386743734838766290653766)⟩,⟨301836259898624038025374,301836259898624522608200⟩⟩,⟨⟨(-362508269802534511197566),(-362508269802534045598588)⟩,⟨302388553845689883793370,302388553845690349384986⟩⟩,⟨⟨(-339759715293631748244875),(-339759715293631299946327)⟩,⟨302167340105244592645637,302167340105245040937437⟩⟩,⟨⟨(-318427134566614446214656),(-318427134566614014519772)⟩,⟨301283998489265807030308,301283998489266238719010⟩⟩,⟨⟨(-298440606613637277456504),(-298440606613636861031608)⟩,⟨299838639608569012285943,299838639608569428705187⟩⟩] +lemma kernel24_1_r5_13_eq : ∀ k : Fin 16, kernel24_1Expr 5 13 k = kernel24_1_r5_13 k := by decide +kernel +noncomputable def kernel24_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-279731650937603761337016),(-279731650937603359814542)⟩,⟨297921070652284296950519,297921070652284698467829⟩⟩,⟨⟨(-262233570925487878580552),(-262233570925487490510297)⟩,⟨295611698070700432814013,295611698070700820879559⟩⟩,⟨⟨(-245881726387327598912270),(-245881726387327223777433)⟩,⟨292982368698710277463541,292982368698710652594087⟩⟩,⟨⟨(-230613744762940549799897),(-230613744762940186523582)⟩,⟨290097151279502578755618,290097151279502942028028⟩⟩,⟨⟨(-216369679513219199394028),(-216369679513218847687187)⟩,⟨287013060668552369203469,287013060668552720906765⟩⟩,⟨⟨(-203092123304426317160751),(-203092123304425975886962)⟩,⟨283780727231154189357924,283780727231154530628500⟩⟩,⟨⟨(-190726282759924165754772),(-190726282759923834530225)⟩,⟨280445014105910362599352,280445014105910693820994⟩⟩,⟨⟨(-179220020791312862851048),(-179220020791312540793156)⟩,⟨277045585103432840530507,277045585103433162585773⟩⟩,⟨⟨(-168523871826655581575241),(-168523871826655268543979)⟩,⟨273617426054367607685251,273617426054367920714151⟩⟩,⟨⟨(-158591034623651557946415),(-158591034623651252941574)⟩,⟨270191322422766239781037,270191322422766544783751⟩⟩,⟨⟨(-149377346786408748520271),(-149377346786408451255868)⟩,⟨266794295967716026828891,266794295967716324091391⟩⟩,⟨⟨(-140841244591894652400676),(-140841244591894362141095)⟩,⟨263450003174855434418039,263450003174855724675919⟩⟩,⟨⟨(-132943711272214181886359),(-132943711272213898522139)⟩,⟨260179098095856063476403,260179098095856346839106⟩⟩,⟨⟨(-125648216487627985716511),(-125648216487627708429900)⟩,⟨256999562133205408850221,256999562133205686135487⟩⟩,⟨⟨(-118920649358825403315411),(-118920649358825131891626)⟩,⟨253927003193976076154641,253927003193976347577235⟩⟩,⟨⟨(-112729247101674939516653),(-112729247101674673330004)⟩,⟨250974926513339752811824,250974926513340018997421⟩⟩] +lemma kernel24_1_r5_14_eq : ∀ k : Fin 16, kernel24_1Expr 5 14 k = kernel24_1_r5_14 k := by decide +kernel +noncomputable def kernel24_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-107044521019920808356955),(-107044521019920547402348)⟩,⟨248154979319402541692551,248154979319402802646238⟩⟩,⟨⟨(-101839181357682776636536),(-101839181357682520146496)⟩,⟨245477171377998996061156,245477171377999252550396⟩⟩,⟨⟨(-97088062290943810850887),(-97088062290943558661003)⟩,⟨242950073321419427219283,242950073321419679408472⟩⟩,⟨⟨(-92768048142467869421507),(-92768048142467620987154)⟩,⟨240580994530288811203281,240580994530289059637032⟩⟩,⟨⟨(-88858001734968791436302),(-88858001734968546740325)⟩,⟨238376142204244915218396,238376142204245159913863⟩⟩,⟨⟨(-85338695650237281399253),(-85338695650237039798146)⟩,⟨236340763125653360094672,236340763125653601695349⟩⟩,⟨⟨(-82192747034904403503923),(-82192747034904164867288)⟩,⟨234479269492062134618509,234479269492062373254781⟩⟩,⟨⟨(-79404556484338576537959),(-79404556484338340378416)⟩,⟨232795350067927443510710,232795350067927679669954⟩⟩,⟨⟨(-76960251442774875698990),(-76960251442774642041185)⟩,⟨231292067784635724174545,231292067784635957832101⟩⟩,⟨⟨(-74847634478260057523059),(-74847634478259825714767)⟩,⟨229971944800140301459819,229971944800140533267911⟩⟩,⟨⟨(-73056136723615020424597),(-73056136723614790362222)⟩,⟨228837035915626174389653,228837035915626404451860⟩⟩,⟨⟨(-71576776717757950130184),(-71576776717757721370271)⟩,⟨227888991136399191187712,227888991136399419947491⟩⟩,⟨⟨(-70402124833910922837127),(-70402124833910695409681)⟩,⟨227129108057457730088332,227129108057457957515668⟩⟩,⟨⟨(-69526273441056632705123),(-69526273441056406049716)⟩,⟨226558374650658893578243,226558374650659120233563⟩⟩,⟨⟨(-68944812911244168081999),(-68944812911243942103023)⟩,⟨226177502929686238797388,226177502929686464776286⟩⟩,⟨⟨(-68654813556771121617050),(-68654813556770895890981)⟩,⟨225986953870759893558359,225986953870760119284354⟩⟩] +lemma kernel24_1_r5_15_eq : ∀ k : Fin 16, kernel24_1Expr 5 15 k = kernel24_1_r5_15 k := by decide +kernel +noncomputable def kernel24_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel24_1_r5_0,kernel24_1_r5_1,kernel24_1_r5_2,kernel24_1_r5_3,kernel24_1_r5_4,kernel24_1_r5_5,kernel24_1_r5_6,kernel24_1_r5_7,kernel24_1_r5_8,kernel24_1_r5_9,kernel24_1_r5_10,kernel24_1_r5_11,kernel24_1_r5_12,kernel24_1_r5_13,kernel24_1_r5_14,kernel24_1_r5_15] +lemma kernel24_1_r5_eq (i k : Fin 16) : kernel24_1Expr 5 i k = kernel24_1_r5 i k := by + fin_cases i + · exact kernel24_1_r5_0_eq k + · exact kernel24_1_r5_1_eq k + · exact kernel24_1_r5_2_eq k + · exact kernel24_1_r5_3_eq k + · exact kernel24_1_r5_4_eq k + · exact kernel24_1_r5_5_eq k + · exact kernel24_1_r5_6_eq k + · exact kernel24_1_r5_7_eq k + · exact kernel24_1_r5_8_eq k + · exact kernel24_1_r5_9_eq k + · exact kernel24_1_r5_10_eq k + · exact kernel24_1_r5_11_eq k + · exact kernel24_1_r5_12_eq k + · exact kernel24_1_r5_13_eq k + · exact kernel24_1_r5_14_eq k + · exact kernel24_1_r5_15_eq k +noncomputable def kernel24_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel24_1_r0,kernel24_1_r1,kernel24_1_r2,kernel24_1_r3,kernel24_1_r4,kernel24_1_r5] +lemma kernel24_1_eq (j : Fin 6) (i k : Fin 16) : kernel24_1Expr j i k = kernel24_1 j i k := by + fin_cases j + · exact kernel24_1_r0_eq i k + · exact kernel24_1_r1_eq i k + · exact kernel24_1_r2_eq i k + · exact kernel24_1_r3_eq i k + · exact kernel24_1_r4_eq i k + · exact kernel24_1_r5_eq i k +lemma kernel24_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel24_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(24:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel24_1_eq] + unfold kernel24_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans24_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel25_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans25 j i k) +noncomputable def kernel25_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_0_eq : ∀ k : Fin 16, kernel25_0Expr 0 0 k = kernel25_0_r0_0 k := by decide +kernel +noncomputable def kernel25_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_1_eq : ∀ k : Fin 16, kernel25_0Expr 0 1 k = kernel25_0_r0_1 k := by decide +kernel +noncomputable def kernel25_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_2_eq : ∀ k : Fin 16, kernel25_0Expr 0 2 k = kernel25_0_r0_2 k := by decide +kernel +noncomputable def kernel25_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_3_eq : ∀ k : Fin 16, kernel25_0Expr 0 3 k = kernel25_0_r0_3 k := by decide +kernel +noncomputable def kernel25_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_4_eq : ∀ k : Fin 16, kernel25_0Expr 0 4 k = kernel25_0_r0_4 k := by decide +kernel +noncomputable def kernel25_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_5_eq : ∀ k : Fin 16, kernel25_0Expr 0 5 k = kernel25_0_r0_5 k := by decide +kernel +noncomputable def kernel25_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_6_eq : ∀ k : Fin 16, kernel25_0Expr 0 6 k = kernel25_0_r0_6 k := by decide +kernel +noncomputable def kernel25_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_7_eq : ∀ k : Fin 16, kernel25_0Expr 0 7 k = kernel25_0_r0_7 k := by decide +kernel +noncomputable def kernel25_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_8_eq : ∀ k : Fin 16, kernel25_0Expr 0 8 k = kernel25_0_r0_8 k := by decide +kernel +noncomputable def kernel25_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_9_eq : ∀ k : Fin 16, kernel25_0Expr 0 9 k = kernel25_0_r0_9 k := by decide +kernel +noncomputable def kernel25_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_10_eq : ∀ k : Fin 16, kernel25_0Expr 0 10 k = kernel25_0_r0_10 k := by decide +kernel +noncomputable def kernel25_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r0_11_eq : ∀ k : Fin 16, kernel25_0Expr 0 11 k = kernel25_0_r0_11 k := by decide +kernel +noncomputable def kernel25_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r0_12_eq : ∀ k : Fin 16, kernel25_0Expr 0 12 k = kernel25_0_r0_12 k := by decide +kernel +noncomputable def kernel25_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r0_13_eq : ∀ k : Fin 16, kernel25_0Expr 0 13 k = kernel25_0_r0_13 k := by decide +kernel +noncomputable def kernel25_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r0_14_eq : ∀ k : Fin 16, kernel25_0Expr 0 14 k = kernel25_0_r0_14 k := by decide +kernel +noncomputable def kernel25_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r0_15_eq : ∀ k : Fin 16, kernel25_0Expr 0 15 k = kernel25_0_r0_15 k := by decide +kernel +noncomputable def kernel25_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel25_0_r0_0,kernel25_0_r0_1,kernel25_0_r0_2,kernel25_0_r0_3,kernel25_0_r0_4,kernel25_0_r0_5,kernel25_0_r0_6,kernel25_0_r0_7,kernel25_0_r0_8,kernel25_0_r0_9,kernel25_0_r0_10,kernel25_0_r0_11,kernel25_0_r0_12,kernel25_0_r0_13,kernel25_0_r0_14,kernel25_0_r0_15] +lemma kernel25_0_r0_eq (i k : Fin 16) : kernel25_0Expr 0 i k = kernel25_0_r0 i k := by + fin_cases i + · exact kernel25_0_r0_0_eq k + · exact kernel25_0_r0_1_eq k + · exact kernel25_0_r0_2_eq k + · exact kernel25_0_r0_3_eq k + · exact kernel25_0_r0_4_eq k + · exact kernel25_0_r0_5_eq k + · exact kernel25_0_r0_6_eq k + · exact kernel25_0_r0_7_eq k + · exact kernel25_0_r0_8_eq k + · exact kernel25_0_r0_9_eq k + · exact kernel25_0_r0_10_eq k + · exact kernel25_0_r0_11_eq k + · exact kernel25_0_r0_12_eq k + · exact kernel25_0_r0_13_eq k + · exact kernel25_0_r0_14_eq k + · exact kernel25_0_r0_15_eq k +noncomputable def kernel25_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_0_eq : ∀ k : Fin 16, kernel25_0Expr 1 0 k = kernel25_0_r1_0 k := by decide +kernel +noncomputable def kernel25_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_1_eq : ∀ k : Fin 16, kernel25_0Expr 1 1 k = kernel25_0_r1_1 k := by decide +kernel +noncomputable def kernel25_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_2_eq : ∀ k : Fin 16, kernel25_0Expr 1 2 k = kernel25_0_r1_2 k := by decide +kernel +noncomputable def kernel25_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_3_eq : ∀ k : Fin 16, kernel25_0Expr 1 3 k = kernel25_0_r1_3 k := by decide +kernel +noncomputable def kernel25_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_4_eq : ∀ k : Fin 16, kernel25_0Expr 1 4 k = kernel25_0_r1_4 k := by decide +kernel +noncomputable def kernel25_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_5_eq : ∀ k : Fin 16, kernel25_0Expr 1 5 k = kernel25_0_r1_5 k := by decide +kernel +noncomputable def kernel25_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_6_eq : ∀ k : Fin 16, kernel25_0Expr 1 6 k = kernel25_0_r1_6 k := by decide +kernel +noncomputable def kernel25_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_7_eq : ∀ k : Fin 16, kernel25_0Expr 1 7 k = kernel25_0_r1_7 k := by decide +kernel +noncomputable def kernel25_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_8_eq : ∀ k : Fin 16, kernel25_0Expr 1 8 k = kernel25_0_r1_8 k := by decide +kernel +noncomputable def kernel25_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_9_eq : ∀ k : Fin 16, kernel25_0Expr 1 9 k = kernel25_0_r1_9 k := by decide +kernel +noncomputable def kernel25_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_10_eq : ∀ k : Fin 16, kernel25_0Expr 1 10 k = kernel25_0_r1_10 k := by decide +kernel +noncomputable def kernel25_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_11_eq : ∀ k : Fin 16, kernel25_0Expr 1 11 k = kernel25_0_r1_11 k := by decide +kernel +noncomputable def kernel25_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_12_eq : ∀ k : Fin 16, kernel25_0Expr 1 12 k = kernel25_0_r1_12 k := by decide +kernel +noncomputable def kernel25_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_13_eq : ∀ k : Fin 16, kernel25_0Expr 1 13 k = kernel25_0_r1_13 k := by decide +kernel +noncomputable def kernel25_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_14_eq : ∀ k : Fin 16, kernel25_0Expr 1 14 k = kernel25_0_r1_14 k := by decide +kernel +noncomputable def kernel25_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r1_15_eq : ∀ k : Fin 16, kernel25_0Expr 1 15 k = kernel25_0_r1_15 k := by decide +kernel +noncomputable def kernel25_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel25_0_r1_0,kernel25_0_r1_1,kernel25_0_r1_2,kernel25_0_r1_3,kernel25_0_r1_4,kernel25_0_r1_5,kernel25_0_r1_6,kernel25_0_r1_7,kernel25_0_r1_8,kernel25_0_r1_9,kernel25_0_r1_10,kernel25_0_r1_11,kernel25_0_r1_12,kernel25_0_r1_13,kernel25_0_r1_14,kernel25_0_r1_15] +lemma kernel25_0_r1_eq (i k : Fin 16) : kernel25_0Expr 1 i k = kernel25_0_r1 i k := by + fin_cases i + · exact kernel25_0_r1_0_eq k + · exact kernel25_0_r1_1_eq k + · exact kernel25_0_r1_2_eq k + · exact kernel25_0_r1_3_eq k + · exact kernel25_0_r1_4_eq k + · exact kernel25_0_r1_5_eq k + · exact kernel25_0_r1_6_eq k + · exact kernel25_0_r1_7_eq k + · exact kernel25_0_r1_8_eq k + · exact kernel25_0_r1_9_eq k + · exact kernel25_0_r1_10_eq k + · exact kernel25_0_r1_11_eq k + · exact kernel25_0_r1_12_eq k + · exact kernel25_0_r1_13_eq k + · exact kernel25_0_r1_14_eq k + · exact kernel25_0_r1_15_eq k +noncomputable def kernel25_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩] +lemma kernel25_0_r2_0_eq : ∀ k : Fin 16, kernel25_0Expr 2 0 k = kernel25_0_r2_0 k := by decide +kernel +noncomputable def kernel25_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩] +lemma kernel25_0_r2_1_eq : ∀ k : Fin 16, kernel25_0Expr 2 1 k = kernel25_0_r2_1 k := by decide +kernel +noncomputable def kernel25_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩] +lemma kernel25_0_r2_2_eq : ∀ k : Fin 16, kernel25_0Expr 2 2 k = kernel25_0_r2_2 k := by decide +kernel +noncomputable def kernel25_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_3_eq : ∀ k : Fin 16, kernel25_0Expr 2 3 k = kernel25_0_r2_3 k := by decide +kernel +noncomputable def kernel25_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_4_eq : ∀ k : Fin 16, kernel25_0Expr 2 4 k = kernel25_0_r2_4 k := by decide +kernel +noncomputable def kernel25_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_5_eq : ∀ k : Fin 16, kernel25_0Expr 2 5 k = kernel25_0_r2_5 k := by decide +kernel +noncomputable def kernel25_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_6_eq : ∀ k : Fin 16, kernel25_0Expr 2 6 k = kernel25_0_r2_6 k := by decide +kernel +noncomputable def kernel25_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_7_eq : ∀ k : Fin 16, kernel25_0Expr 2 7 k = kernel25_0_r2_7 k := by decide +kernel +noncomputable def kernel25_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_8_eq : ∀ k : Fin 16, kernel25_0Expr 2 8 k = kernel25_0_r2_8 k := by decide +kernel +noncomputable def kernel25_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_9_eq : ∀ k : Fin 16, kernel25_0Expr 2 9 k = kernel25_0_r2_9 k := by decide +kernel +noncomputable def kernel25_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel25_0_r2_10_eq : ∀ k : Fin 16, kernel25_0Expr 2 10 k = kernel25_0_r2_10 k := by decide +kernel +noncomputable def kernel25_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r2_11_eq : ∀ k : Fin 16, kernel25_0Expr 2 11 k = kernel25_0_r2_11 k := by decide +kernel +noncomputable def kernel25_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r2_12_eq : ∀ k : Fin 16, kernel25_0Expr 2 12 k = kernel25_0_r2_12 k := by decide +kernel +noncomputable def kernel25_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r2_13_eq : ∀ k : Fin 16, kernel25_0Expr 2 13 k = kernel25_0_r2_13 k := by decide +kernel +noncomputable def kernel25_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r2_14_eq : ∀ k : Fin 16, kernel25_0Expr 2 14 k = kernel25_0_r2_14 k := by decide +kernel +noncomputable def kernel25_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel25_0_r2_15_eq : ∀ k : Fin 16, kernel25_0Expr 2 15 k = kernel25_0_r2_15 k := by decide +kernel +noncomputable def kernel25_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel25_0_r2_0,kernel25_0_r2_1,kernel25_0_r2_2,kernel25_0_r2_3,kernel25_0_r2_4,kernel25_0_r2_5,kernel25_0_r2_6,kernel25_0_r2_7,kernel25_0_r2_8,kernel25_0_r2_9,kernel25_0_r2_10,kernel25_0_r2_11,kernel25_0_r2_12,kernel25_0_r2_13,kernel25_0_r2_14,kernel25_0_r2_15] +lemma kernel25_0_r2_eq (i k : Fin 16) : kernel25_0Expr 2 i k = kernel25_0_r2 i k := by + fin_cases i + · exact kernel25_0_r2_0_eq k + · exact kernel25_0_r2_1_eq k + · exact kernel25_0_r2_2_eq k + · exact kernel25_0_r2_3_eq k + · exact kernel25_0_r2_4_eq k + · exact kernel25_0_r2_5_eq k + · exact kernel25_0_r2_6_eq k + · exact kernel25_0_r2_7_eq k + · exact kernel25_0_r2_8_eq k + · exact kernel25_0_r2_9_eq k + · exact kernel25_0_r2_10_eq k + · exact kernel25_0_r2_11_eq k + · exact kernel25_0_r2_12_eq k + · exact kernel25_0_r2_13_eq k + · exact kernel25_0_r2_14_eq k + · exact kernel25_0_r2_15_eq k +noncomputable def kernel25_0_r3_0 : Fin 16 → CBox := ![⟨⟨10330996295898,10330996295903⟩,⟨(-51320175019991),(-51320175019986)⟩⟩,⟨⟨10258499608403,10258499608408⟩,⟨(-51233131818635),(-51233131818631)⟩⟩,⟨⟨10114197706300,10114197706305⟩,⟨(-51059320842701),(-51059320842696)⟩⟩,⟨⟨9899465348982,9899465348985⟩,⟨(-50799293932550),(-50799293932547)⟩⟩,⟨⟨9616344314759,9616344314762⟩,⟨(-50453881240517),(-50453881240514)⟩⟩,⟨⟨9267519261258,9267519261261⟩,⟨(-50024193892749),(-50024193892746)⟩⟩,⟨⟨8856286024779,8856286024782⟩,⟨(-49511627198237),(-49511627198233)⟩⟩,⟨⟨8386512767868,8386512767872⟩,⟨(-48917864127429),(-48917864127425)⟩⟩,⟨⟨7862594478145,7862594478148⟩,⟨(-48244878730401),(-48244878730398)⟩⟩,⟨⟨7289401409380,7289401409383⟩,⟨(-47494939122663),(-47494939122660)⟩⟩,⟨⟨6672222136925,6672222136928⟩,⟨(-46670609636898),(-46670609636895)⟩⟩,⟨⟨6016701972620,6016701972624⟩,⟨(-45774751722235),(-45774751722230)⟩⟩,⟨⟨5328777548128,5328777548132⟩,⟨(-44810523169833),(-44810523169828)⟩⟩,⟨⟨4614608429254,4614608429257⟩,⟨(-43781375254968),(-43781375254965)⟩⟩,⟨⟨3880506666080,3880506666083⟩,⟨(-42691047411303),(-42691047411300)⟩⟩,⟨⟨3132865213858,3132865213861⟩,⟨(-41543559092149),(-41543559092146)⟩⟩] +lemma kernel25_0_r3_0_eq : ∀ k : Fin 16, kernel25_0Expr 3 0 k = kernel25_0_r3_0 k := by decide +kernel +noncomputable def kernel25_0_r3_1 : Fin 16 → CBox := ![⟨⟨2378086176690,2378086176694⟩,⟨(-40343198525434),(-40343198525430)⟩⟩,⟨⟨1622509829482,1622509829486⟩,⟨(-39094508132417),(-39094508132414)⟩⟩,⟨⟨872345363009,872345363012⟩,⟨(-37802266453395),(-37802266453392)⟩⟩,⟨⟨133604271905,133604271908⟩,⟨(-36471466504780),(-36471466504777)⟩⟩,⟨⟨(-587962733981),(-587962733977)⟩,⟨(-35107290578822),(-35107290578818)⟩⟩,⟨⟨(-1286924467903),(-1286924467900)⟩,⟨(-33715081587503),(-33715081587500)⟩⟩,⟨⟨(-1958222894337),(-1958222894332)⟩,⟨(-32300311143317),(-32300311143312)⟩⟩,⟨⟨(-2597220966819),(-2597220966816)⟩,⟨(-30868544659130),(-30868544659127)⟩⟩,⟨⟨(-3199744086937),(-3199744086933)⟩,⟨(-29425403834648),(-29425403834643)⟩⟩,⟨⟨(-3762114697560),(-3762114697555)⟩,⟨(-27976526975654),(-27976526975649)⟩⟩,⟨⟨(-4281179633733),(-4281179633729)⟩,⟨(-26527527661962),(-26527527661959)⟩⟩,⟨⟨(-4754329971601),(-4754329971596)⟩,⟨(-25083952338791),(-25083952338786)⟩⟩,⟨⟨(-5179513237239),(-5179513237234)⟩,⟨(-23651237452285),(-23651237452279)⟩⟩,⟨⟨(-5555237961084),(-5555237961081)⟩,⟨(-22234666781904),(-22234666781901)⟩⟩,⟨⟨(-5880570687332),(-5880570687328)⟩,⟨(-20839329639056),(-20839329639053)⟩⟩,⟨⟨(-6155125668778),(-6155125668775)⟩,⟨(-19470080602379),(-19470080602376)⟩⟩] +lemma kernel25_0_r3_1_eq : ∀ k : Fin 16, kernel25_0Expr 3 1 k = kernel25_0_r3_1 k := by decide +kernel +noncomputable def kernel25_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-6379047593759),(-6379047593754)⟩,⟨(-18131501445185),(-18131501445182)⟩⟩,⟨⟨(-6552987800558),(-6552987800555)⟩,⟨(-16827865879930),(-16827865879926)⟩⟩,⟨⟨(-6678074533857),(-6678074533854)⟩,⟨(-15563107699174),(-15563107699171)⟩⟩,⟨⟨(-6755877885304),(-6755877885301)⟩,⟨(-14340792833197),(-14340792833194)⟩⟩,⟨⟨(-6788370134442),(-6788370134438)⟩,⟨(-13164095772964),(-13164095772959)⟩⟩,⟨⟨(-6777882265432),(-6777882265428)⟩,⟨(-12035780725249),(-12035780725245)⟩⟩,⟨⟨(-6727057478250),(-6727057478247)⟩,⟨(-10958187776596),(-10958187776593)⟩⟩,⟨⟨(-6638802539524),(-6638802539521)⟩,⟨(-9933224246707),(-9933224246704)⟩⟩,⟨⟨(-6516237827572),(-6516237827568)⟩,⟨(-8962361312446),(-8962361312442)⟩⟩,⟨⟨(-6362646918636),(-6362646918632)⟩,⟨(-8046635883270),(-8046635883266)⟩⟩,⟨⟨(-6181426537249),(-6181426537245)⟩,⟨(-7186657610256),(-7186657610252)⟩⟩,⟨⟨(-5976037654020),(-5976037654014)⟩,⟨(-6382620816367),(-6382620816362)⟩⟩,⟨⟨(-5749958460173),(-5749958460170)⟩,⟨(-5634321047477),(-5634321047474)⟩⟩,⟨⟨(-5506639881550),(-5506639881547)⟩,⟨(-4941175864089),(-4941175864086)⟩⟩,⟨⟨(-5249464217256),(-5249464217252)⟩,⟨(-4302249424271),(-4302249424267)⟩⟩,⟨⟨(-4981707402029),(-4981707402026)⟩,⟨(-3716280350797),(-3716280350794)⟩⟩] +lemma kernel25_0_r3_2_eq : ∀ k : Fin 16, kernel25_0Expr 3 2 k = kernel25_0_r3_2 k := by decide +kernel +noncomputable def kernel25_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-4706505298738),(-4706505298735)⟩,⟨(-3181712330629),(-3181712330626)⟩⟩,⟨⟨(-4426824330793),(-4426824330790)⟩,⟨(-2696726863643),(-2696726863640)⟩⟩,⟨⟨(-4145436665880),(-4145436665877)⟩,⟨(-2259277560083),(-2259277560080)⟩⟩,⟨⟨(-3864900064797),(-3864900064791)⟩,⟨(-1867125382581),(-1867125382576)⟩⟩,⟨⟨(-3587542414375),(-3587542414370)⟩,⟨(-1517874238210),(-1517874238205)⟩⟩,⟨⟨(-3315450873752),(-3315450873749)⟩,⟨(-1209006348221),(-1209006348218)⟩⟩,⟨⟨(-3050465480258),(-3050465480255)⟩,⟨(-937916856639),(-937916856635)⟩⟩,⟨⟨(-2794176986677),(-2794176986674)⟩,⟨(-701947182467),(-701947182464)⟩⟩,⟨⟨(-2547928636799),(-2547928636796)⟩,⟨(-498416672238),(-498416672235)⟩⟩,⟨⟨(-2312821531911),(-2312821531908)⟩,⟨(-324652168348),(-324652168345)⟩⟩,⟨⟨(-2089723197998),(-2089723197995)⟩,⟨(-178015172154),(-178015172151)⟩⟩,⟨⟨(-1879278931968),(-1879278931965)⟩,⟨(-55926347439),(-55926347436)⟩⟩,⟨⟨(-1681925485374),(-1681925485371)⟩,⟨44112822451,44112822456⟩⟩,⟨⟨(-1497906635379),(-1497906635373)⟩,⟨124501343232,124501343237⟩⟩,⟨⟨(-1327290194552),(-1327290194547)⟩,⟨187523038515,187523038520⟩⟩,⟨⟨(-1169986022699),(-1169986022696)⟩,⟨235333891943,235333891946⟩⟩] +lemma kernel25_0_r3_3_eq : ∀ k : Fin 16, kernel25_0Expr 3 3 k = kernel25_0_r3_3 k := by decide +kernel +noncomputable def kernel25_0_r3_4 : Fin 16 → CBox := ![⟨⟨(-1025764624050),(-1025764624047)⟩,⟨269952339181,269952339185⟩⟩,⟨⟨(-894275940849),(-894275940846)⟩,⟨293252395795,293252395798⟩⟩,⟨⟨(-775067988167),(-775067988164)⟩,⟨306959463128,306959463131⟩⟩,⟨⟨(-667605013280),(-667605013277)⟩,⟨312648617693,312648617696⟩⟩,⟨⟨(-571284904922),(-571284904917)⟩,⟨311745160425,311745160429⟩⟩,⟨⟨(-485455621650),(-485455621645)⟩,⟨305527180709,305527180713⟩⟩,⟨⟨(-409430453274),(-409430453270)⟩,⟨295129875905,295129875909⟩⟩,⟨⟨(-342501973516),(-342501973513)⟩,⟨281551360229,281551360233⟩⟩,⟨⟨(-283954584819),(-283954584814)⟩,⟨265659696366,265659696370⟩⟩,⟨⟨(-233075596481),(-233075596478)⟩,⟨248200888762,248200888765⟩⟩,⟨⟨(-189164814481),(-189164814478)⟩,⟨229807588281,229807588284⟩⟩,⟨⟨(-151542654574),(-151542654570)⟩,⟨211008273049,211008273053⟩⟩,⟨⟨(-119556819529),(-119556819525)⟩,⟨192236688915,192236688918⟩⟩,⟨⟨(-92587605949),(-92587605944)⟩,⟨173841354325,173841354329⟩⟩,⟨⟨(-70051926341),(-70051926338)⟩,⟨156094957561,156094957564⟩⟩,⟨⟨(-51406147672),(-51406147669)⟩,⟨139203498440,139203498443⟩⟩] +lemma kernel25_0_r3_4_eq : ∀ k : Fin 16, kernel25_0Expr 3 4 k = kernel25_0_r3_4 k := by decide +kernel +noncomputable def kernel25_0_r3_5 : Fin 16 → CBox := ![⟨⟨(-36147858908),(-36147858905)⟩,⟨123315051147,123315051151⟩⟩,⟨⟨(-23816687225),(-23816687221)⟩,⟨108528048943,108528048947⟩⟩,⟨⟨(-13994285920),(-13994285917)⟩,⟨94899014772,94899014775⟩⟩,⟨⟨(-6303617141),(-6303617137)⟩,⟨82449683618,82449683622⟩⟩,⟨⟨(-407649656),(-407649653)⟩,⟨71173482545,71173482548⟩⟩,⟨⟨3992413353,3992413357⟩,⟨61041352405,61041352410⟩⟩,⟨⟨7159268803,7159268806⟩,⟨52006911050,52006911054⟩⟩,⟨⟨9321911513,9321911516⟩,⟨44010971382,44010971385⟩⟩,⟨⟨10678206104,10678206108⟩,⟨36985438846,36985438851⟩⟩,⟨⟨11397554197,11397554200⟩,⟨30856621835,30856621838⟩⟩,⟨⟨11623588745,11623588748⟩,⟨25547995287,25547995290⟩⟩,⟨⟨11476838011,11476838015⟩,⟨20982462554,20982462557⟩⟩,⟨⟨11057311916,11057311919⟩,⟨17084163476,17084163479⟩⟩,⟨⟨10446973257,10446973261⟩,⟨13779878037,13779878042⟩⟩,⟨⟨9712065324,9712065328⟩,⟨11000074860,11000074865⟩⟩,⟨⟨8905275585,8905275588⟩,⟨8679652595,8679652598⟩⟩] +lemma kernel25_0_r3_5_eq : ∀ k : Fin 16, kernel25_0Expr 3 5 k = kernel25_0_r3_5 k := by decide +kernel +noncomputable def kernel25_0_r3_6 : Fin 16 → CBox := ![⟨⟨8067722394,8067722399⟩,⟨6758420167,6758420171⟩⟩,⟨⟨7230758013,7230758017⟩,⟨5181358934,5181358938⟩⟩,⟨⟨6417586518,6417586521⟩,⟨3898706463,3898706466⟩⟩,⟨⟨5644699668,5644699671⟩,⟨2865897884,2865897888⟩⟩,⟨⟨4923137262,4923137265⟩,⟨2043396941,2043396944⟩⟩,⟨⟨4259581283,4259581286⟩,⟨1396444838,1396444842⟩⟩,⟨⟨3657295060,3657295063⟩,⟨894751186,894751190⟩⟩,⟨⟨3116919992,3116919995⟩,⟨512147569,512147572⟩⟩,⟨⟨2637143130,2637143134⟩,⟨226220826,226220830⟩⟩,⟨⟨2215249175,2215249179⟩,⟨17939896,17939899⟩⟩,⟨⟨1847570275,1847570279⟩,⟨(-128712818),(-128712813)⟩⟩,⟨⟨1529846630,1529846635⟩,⟨(-227097142),(-227097138)⟩⟩,⟨⟨1257510155,1257510159⟩,⟨(-288251766),(-288251761)⟩⟩,⟨⟨1025902655,1025902658⟩,⟨(-321207545),(-321207541)⟩⟩,⟨⟨830438957,830438961⟩,⟨(-333274847),(-333274844)⟩⟩,⟨⟨666724469,666724473⟩,⟨(-330303625),(-330303622)⟩⟩] +lemma kernel25_0_r3_6_eq : ∀ k : Fin 16, kernel25_0Expr 3 6 k = kernel25_0_r3_6 k := by decide +kernel +noncomputable def kernel25_0_r3_7 : Fin 16 → CBox := ![⟨⟨530635511,530635514⟩,⟨(-316915948),(-316915945)⟩⟩,⟨⟨418369812,418369815⟩,⟨(-296711542),(-296711539)⟩⟩,⟨⟨326473518,326473522⟩,⟨(-272447507),(-272447503)⟩⟩,⟨⟨251850155,251850158⟩,⟨(-246193812),(-246193808)⟩⟩,⟨⟨191756074,191756078⟩,⟨(-219466448),(-219466443)⟩⟩,⟨⟨143786213,143786216⟩,⟨(-193340294),(-193340291)⟩⟩,⟨⟨105853207,105853211⟩,⟨(-168543804),(-168543799)⟩⟩,⟨⟨76162356,76162361⟩,⟨(-145537593),(-145537589)⟩⟩,⟨⟨53184356,53184359⟩,⟨(-124578995),(-124578992)⟩⟩,⟨⟨35627298,35627301⟩,⟨(-105774438),(-105774435)⟩⟩,⟨⟨22409036,22409039⟩,⟨(-89121452),(-89121449)⟩⟩,⟨⟨12630708,12630712⟩,⟨(-74541899),(-74541896)⟩⟩,⟨⟨5551940,5551944⟩,⟨(-61907864),(-61907859)⟩⟩,⟨⟨568079,568084⟩,⟨(-51061484),(-51061479)⟩⟩,⟨⟨(-2810389),(-2810385)⟩,⟨(-41829829),(-41829825)⟩⟩,⟨⟨(-4976180),(-4976177)⟩,⟨(-34035780),(-34035776)⟩⟩] +lemma kernel25_0_r3_7_eq : ∀ k : Fin 16, kernel25_0Expr 3 7 k = kernel25_0_r3_7 k := by decide +kernel +noncomputable def kernel25_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-6241350),(-6241347)⟩,⟨(-27505735),(-27505731)⟩⟩,⟨⟨(-6851323),(-6851319)⟩,⟨(-22074815),(-22074812)⟩⟩,⟨⟨(-6996982),(-6996977)⟩,⟨(-17590152),(-17590148)⟩⟩,⟨⟨(-6824948),(-6824945)⟩,⟨(-13912711),(-13912708)⟩⟩,⟨⟨(-6446272),(-6446267)⟩,⟨(-10918050),(-10918045)⟩⟩,⟨⟨(-5943677),(-5943674)⟩,⟨(-8496289),(-8496286)⟩⟩,⟨⟨(-5377579),(-5377576)⟩,⟨(-6551573),(-6551569)⟩⟩,⟨⟨(-4791006),(-4791003)⟩,⟨(-5001153),(-5001150)⟩⟩,⟨⟨(-4213610),(-4213606)⟩,⟨(-3774299),(-3774294)⟩⟩,⟨⟨(-3664892),(-3664889)⟩,⟨(-2811083),(-2811079)⟩⟩,⟨⟨(-3156775),(-3156772)⟩,⟨(-2061161),(-2061157)⟩⟩,⟨⟨(-2695629),(-2695626)⟩,⟨(-1482571),(-1482567)⟩⟩,⟨⟨(-2283860),(-2283856)⟩,⟨(-1040610),(-1040606)⟩⟩,⟨⟨(-1921119),(-1921115)⟩,⟨(-706779),(-706776)⟩⟩,⟨⟨(-1605239),(-1605236)⟩,⟨(-457858),(-457855)⟩⟩,⟨⟨(-1332922),(-1332919)⟩,⟨(-275054),(-275051)⟩⟩] +lemma kernel25_0_r3_8_eq : ∀ k : Fin 16, kernel25_0Expr 3 8 k = kernel25_0_r3_8 k := by decide +kernel +noncomputable def kernel25_0_r3_9 : Fin 16 → CBox := ![⟨⟨(-1100249),(-1100244)⟩,⟨(-143272),(-143266)⟩⟩,⟨⟨(-903040),(-903037)⟩,⟨(-50471),(-50468)⟩⟩,⟨⟨(-737116),(-737112)⟩,⟨12870,12873⟩⟩,⟨⟨(-598458),(-598455)⟩,⟨54230,54233⟩⟩,⟨⟨(-483321),(-483315)⟩,⟨79430,79436⟩⟩,⟨⟨(-388283),(-388280)⟩,⟨92969,92972⟩⟩,⟨⟨(-310287),(-310284)⟩,⟨98272,98275⟩⟩,⟨⟨(-246628),(-246624)⟩,⟨97936,97940⟩⟩,⟨⟨(-194948),(-194945)⟩,⟨93895,93898⟩⟩,⟨⟨(-153215),(-153211)⟩,⟨87574,87577⟩⟩,⟨⟨(-119687),(-119684)⟩,⟨80000,80003⟩⟩,⟨⟨(-92894),(-92890)⟩,⟨71899,71904⟩⟩,⟨⟨(-71593),(-71590)⟩,⟨63773,63776⟩⟩,⟨⟨(-54752),(-54748)⟩,⟨55950,55953⟩⟩,⟨⟨(-41512),(-41509)⟩,⟨48633,48636⟩⟩,⟨⟨(-31162),(-31158)⟩,⟨41936,41940⟩⟩] +lemma kernel25_0_r3_9_eq : ∀ k : Fin 16, kernel25_0Expr 3 9 k = kernel25_0_r3_9 k := by decide +kernel +noncomputable def kernel25_0_r3_10 : Fin 16 → CBox := ![⟨⟨(-23121),(-23118)⟩,⟨35910,35913⟩⟩,⟨⟨(-16918),(-16914)⟩,⟨30561,30565⟩⟩,⟨⟨(-12167),(-12162)⟩,⟨25864,25869⟩⟩,⟨⟨(-8556),(-8551)⟩,⟨21782,21787⟩⟩,⟨⟨(-5838),(-5835)⟩,⟨18261,18265⟩⟩,⟨⟨(-3814),(-3810)⟩,⟨15246,15249⟩⟩,⟨⟨(-2327),(-2324)⟩,⟨12680,12683⟩⟩,⟨⟨(-1250),(-1245)⟩,⟨10507,10512⟩⟩,⟨⟨(-485),(-481)⟩,⟨8679,8683⟩⟩,⟨⟨44,48⟩,⟨7146,7150⟩⟩,⟨⟨396,401⟩,⟨5866,5871⟩⟩,⟨⟨619,622⟩,⟨4802,4806⟩⟩,⟨⟨747,750⟩,⟨3920,3924⟩⟩,⟨⟨807,811⟩,⟨3192,3195⟩⟩,⟨⟨820,824⟩,⟨2591,2595⟩⟩,⟨⟨802,806⟩,⟨2099,2103⟩⟩] +lemma kernel25_0_r3_10_eq : ∀ k : Fin 16, kernel25_0Expr 3 10 k = kernel25_0_r3_10 k := by decide +kernel +noncomputable def kernel25_0_r3_11 : Fin 16 → CBox := ![⟨⟨763,766⟩,⟨1695,1699⟩⟩,⟨⟨710,714⟩,⟨1366,1370⟩⟩,⟨⟨651,654⟩,⟨1098,1101⟩⟩,⟨⟨590,594⟩,⟨879,884⟩⟩,⟨⟨530,533⟩,⟨703,706⟩⟩,⟨⟨473,477⟩,⟨560,563⟩⟩,⟨⟨417,421⟩,⟨444,448⟩⟩,⟨⟨368,371⟩,⟨352,355⟩⟩,⟨⟨323,326⟩,⟨277,281⟩⟩,⟨⟨281,284⟩,⟨218,221⟩⟩,⟨⟨244,248⟩,⟨169,173⟩⟩,⟨⟨212,215⟩,⟨131,134⟩⟩,⟨⟨182,187⟩,⟨101,106⟩⟩,⟨⟨158,162⟩,⟨77,81⟩⟩,⟨⟨136,139⟩,⟨59,63⟩⟩,⟨⟨117,121⟩,⟨43,46⟩⟩] +lemma kernel25_0_r3_11_eq : ∀ k : Fin 16, kernel25_0Expr 3 11 k = kernel25_0_r3_11 k := by decide +kernel +noncomputable def kernel25_0_r3_12 : Fin 16 → CBox := ![⟨⟨100,103⟩,⟨32,35⟩⟩,⟨⟨86,90⟩,⟨23,26⟩⟩,⟨⟨74,78⟩,⟨15,19⟩⟩,⟨⟨63,67⟩,⟨9,13⟩⟩,⟨⟨54,57⟩,⟨6,9⟩⟩,⟨⟨45,49⟩,⟨3,7⟩⟩,⟨⟨39,43⟩,⟨1,5⟩⟩,⟨⟨33,37⟩,⟨(-1),3⟩⟩,⟨⟨27,32⟩,⟨(-3),2⟩⟩,⟨⟨25,28⟩,⟨(-3),0⟩⟩,⟨⟨20,23⟩,⟨(-4),(-1)⟩⟩,⟨⟨17,21⟩,⟨(-4),(-1)⟩⟩,⟨⟨15,18⟩,⟨(-5),(-1)⟩⟩,⟨⟨13,16⟩,⟨(-5),(-2)⟩⟩,⟨⟨10,14⟩,⟨(-5),(-2)⟩⟩,⟨⟨9,12⟩,⟨(-4),(-1)⟩⟩] +lemma kernel25_0_r3_12_eq : ∀ k : Fin 16, kernel25_0Expr 3 12 k = kernel25_0_r3_12 k := by decide +kernel +noncomputable def kernel25_0_r3_13 : Fin 16 → CBox := ![⟨⟨8,11⟩,⟨(-6),(-2)⟩⟩,⟨⟨6,10⟩,⟨(-5),(-1)⟩⟩,⟨⟨5,10⟩,⟨(-5),0⟩⟩,⟨⟨4,7⟩,⟨(-5),(-1)⟩⟩,⟨⟨4,7⟩,⟨(-5),(-1)⟩⟩,⟨⟨2,6⟩,⟨(-4),0⟩⟩,⟨⟨2,6⟩,⟨(-4),0⟩⟩,⟨⟨2,6⟩,⟨(-4),0⟩⟩,⟨⟨1,6⟩,⟨(-4),1⟩⟩,⟨⟨1,4⟩,⟨(-3),1⟩⟩,⟨⟨0,4⟩,⟨(-4),1⟩⟩,⟨⟨0,4⟩,⟨(-4),1⟩⟩,⟨⟨0,3⟩,⟨(-4),(-1)⟩⟩,⟨⟨0,3⟩,⟨(-4),(-1)⟩⟩,⟨⟨(-2),4⟩,⟨(-4),2⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩] +lemma kernel25_0_r3_13_eq : ∀ k : Fin 16, kernel25_0Expr 3 13 k = kernel25_0_r3_13 k := by decide +kernel +noncomputable def kernel25_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩] +lemma kernel25_0_r3_14_eq : ∀ k : Fin 16, kernel25_0Expr 3 14 k = kernel25_0_r3_14 k := by decide +kernel +noncomputable def kernel25_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩] +lemma kernel25_0_r3_15_eq : ∀ k : Fin 16, kernel25_0Expr 3 15 k = kernel25_0_r3_15 k := by decide +kernel +noncomputable def kernel25_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel25_0_r3_0,kernel25_0_r3_1,kernel25_0_r3_2,kernel25_0_r3_3,kernel25_0_r3_4,kernel25_0_r3_5,kernel25_0_r3_6,kernel25_0_r3_7,kernel25_0_r3_8,kernel25_0_r3_9,kernel25_0_r3_10,kernel25_0_r3_11,kernel25_0_r3_12,kernel25_0_r3_13,kernel25_0_r3_14,kernel25_0_r3_15] +lemma kernel25_0_r3_eq (i k : Fin 16) : kernel25_0Expr 3 i k = kernel25_0_r3 i k := by + fin_cases i + · exact kernel25_0_r3_0_eq k + · exact kernel25_0_r3_1_eq k + · exact kernel25_0_r3_2_eq k + · exact kernel25_0_r3_3_eq k + · exact kernel25_0_r3_4_eq k + · exact kernel25_0_r3_5_eq k + · exact kernel25_0_r3_6_eq k + · exact kernel25_0_r3_7_eq k + · exact kernel25_0_r3_8_eq k + · exact kernel25_0_r3_9_eq k + · exact kernel25_0_r3_10_eq k + · exact kernel25_0_r3_11_eq k + · exact kernel25_0_r3_12_eq k + · exact kernel25_0_r3_13_eq k + · exact kernel25_0_r3_14_eq k + · exact kernel25_0_r3_15_eq k +noncomputable def kernel25_0_r4_0 : Fin 16 → CBox := ![⟨⟨25002143465050387602580,25002143465050402366574⟩,⟨(-12961798437210941025298),(-12961798437210926261746)⟩⟩,⟨⟨24959920311603932575086,24959920311603947321563⟩,⟨(-12970576298502117141155),(-12970576298502102395118)⟩⟩,⟨⟨24875601919630535114808,24875601919630549826289⟩,⟨(-12987976222370262220404),(-12987976222370247509364)⟩⟩,⟨⟨24749444098552024234577,24749444098552038893695⟩,⟨(-13013688208076461440268),(-13013688208076446781586)⟩⟩,⟨⟨24581830500438581547627,24581830500438596137205⟩,⟨(-13047251232009773106282),(-13047251232009758517137)⟩⟩,⟨⟨24373272514935940331654,24373272514935954834747⟩,⟨(-13088057980913882951285),(-13088057980913868448620)⟩⟩,⟨⟨24124409078938926985785,24124409078938941385748⟩,⟨(-13135361096764491455217),(-13135361096764477055676)⟩⟩,⟨⟨23836006359477442619690,23836006359477456900232⟩,⟨(-13188280877038352428964),(-13188280877038338148838)⟩⟩,⟨⟨23508957259766487011703,23508957259766501156932⟩,⟨(-13245814360552192193248),(-13245814360552178048429)⟩⟩,⟨⟨23144280691055723350202,23144280691055737344688⟩,⟨(-13306845715842238967181),(-13306845715842224973094)⟩⟩,⟨⟨22743120546989156182240,22743120546989170011059⟩,⟨(-13370157836292993834705),(-13370157836292980006277)⟩⟩,⟨⟨22306744312819857624098,22306744312819871272878⟩,⟨(-13434445034006247327219),(-13434445034006233678820)⟩⟩,⟨⟨21836541239158413169573,21836541239158426624535⟩,⟨(-13498326712836323796191),(-13498326712836310341599)⟩⟩,⟨⟨21334020009075938251677,21334020009075951499688⟩,⟨(-13560361890222011347645),(-13560361890221998099992)⟩⟩,⟨⟨20800805828408622306404,20800805828408635334989⟩,⟨(-13619064427544408291514),(-13619064427544395263276)⟩⟩,⟨⟨20238636872060582936516,20238636872060595733924⟩,⟨(-13672918819864295948935),(-13672918819864283151860)⟩⟩] +lemma kernel25_0_r4_0_eq : ∀ k : Fin 16, kernel25_0Expr 4 0 k = kernel25_0_r4_0 k := by decide +kernel +noncomputable def kernel25_0_r4_1 : Fin 16 → CBox := ![⟨⟨19649360023977892039145,19649360023977904594338⟩,⟨(-13720396388178506119069),(-13720396388178493564196)⟩⟩,⟨⟨19034925855233244497342,19034925855233256800073⟩,⟨(-13759971710920071543111),(-13759971710920059240686)⟩⟩,⟨⟨18397382793243526010552,18397382793243538051325⟩,⟨(-13790139126448891529980),(-13790139126448879489499)⟩⟩,⟨⟨17738870445428813284580,17738870445428825054739⟩,⟨(-13809429134871219196237),(-13809429134871207426357)⟩⟩,⟨⟨17061612052461077662943,17061612052461089154595⟩,⟨(-13816424525812668177212),(-13816424525812656685823)⟩⟩,⟨⟨16367906059458401136722,16367906059458412342866⟩,⟨(-13809776058864112746969),(-13809776058864101541073)⟩⟩,⟨⟨15660116807836999453151,15660116807837010367551⟩,⟨(-13788217525420537859260),(-13788217525420526945093)⟩⟩,⟨⟨14940664365789904745238,14940664365789915362562⟩,⟨(-13750580024617524119859),(-13750580024617513502754)⟩⟩,⟨⟨14212013531242763407576,14212013531242773723236⟩,⟨(-13695805292092862559356),(-13695805292092852243898)⟩⟩,⟨⟨13476662057347221477108,13476662057347231487454⟩,⟨(-13622957928388639528016),(-13622957928388629517857)⟩⟩,⟨⟨12737128166797722325213,12737128166797732027351⟩,⟨(-13531236383958183179369),(-13531236383958173477403)⟩⟩,⟨⟨11995937437174414234068,11995937437174423625970⟩,⟨(-13419982569915203946528),(-13419982569915194554782)⟩⟩,⟨⟨11255609154794865664737,11255609154794874745034⟩,⟨(-13288689977786308946817),(-13288689977786299866661)⟩⟩,⟨⟨10518642248873953887459,10518642248873962655779⟩,⟨(-13137010207492721659622),(-13137010207492712891429)⟩⟩,⟨⟨9787500930826836482116,9787500930826844938749⟩,⟨(-12964757820444641496594),(-12964757820444633040073)⟩⟩,⟨⟨9064600175002035318052,9064600175002043464017⟩,⟨(-12771913453796899286359),(-12771913453796891140494)⟩⟩] +lemma kernel25_0_r4_1_eq : ∀ k : Fin 16, kernel25_0Expr 4 1 k = kernel25_0_r4_1 k := by decide +kernel +noncomputable def kernel25_0_r4_2 : Fin 16 → CBox := ![⟨⟨8352291186720315435399,8352291186720323272234⟩,⟨(-12558625152365806521510),(-12558625152365798684760)⟩⟩,⟨⟨7652847010968987745851,7652847010968995275971⟩,⟨(-12325207896188693068951),(-12325207896188685538902)⟩⟩,⟨⟨6968448440244242235498,6968448440244249461756⟩,⟨(-12072141323933022893106),(-12072141323933015666906)⟩⟩,⟨⟨6301170382670476598754,6301170382670483525359⟩,⟨(-11800065675017850463473),(-11800065675017843536913)⟩⟩,⟨⟨5652968851525226533382,5652968851525233164473⟩,⟨(-11509775996061675193722),(-11509775996061668562664)⟩⟩,⟨⟨5025668734580785278912,5025668734580791619217⟩,⟨(-11202214679766511476945),(-11202214679766505136664)⟩⟩,⟨⟨4420952496211260025314,4420952496211266079821⟩,⟨(-10878462426227899220641),(-10878462426227893166147)⟩⟩,⟨⟨3840349957033810031774,3840349957033815806189⟩,⟨(-10539727737562051450862),(-10539727737562045676449)⟩⟩,⟨⟨3285229285037981532160,3285229285037987032338⟩,⟨(-10187335076307022075881),(-10187335076307016575696)⟩⟩,⟨⟨2756789318845522290068,2756789318845527522495⟩,⟨(-9822711835940279855357),(-9822711835940274622914)⟩⟩,⟨⟨2256053328126567525563,2256053328126572496795⟩,⟨(-9447374287736689627545),(-9447374287736684656291)⟩⟩,⟨⟨1783864298519048006547,1783864298519052723682⟩,⟨(-9062912681773183643012),(-9062912681773178925848)⟩⟩,⟨⟨1340881808945450168014,1340881808945454638135⟩,⟨(-8670975690909348459855),(-8670975690909343989697)⟩⟩,⟨⟨927580548324597599597,927580548324601831579⟩,⟨(-8273254394818781201578),(-8273254394818776969554)⟩⟩,⟨⟨544250496700460567289,544250496700464569439⟩,⟨(-7871466006444247043269),(-7871466006444243041072)⟩⟩,⟨⟨190998773146846577962,190998773146850358019⟩,⟨(-7467337545482946366259),(-7467337545482942586150)⟩⟩] +lemma kernel25_0_r4_2_eq : ∀ k : Fin 16, kernel25_0Expr 4 2 k = kernel25_0_r4_2 k := by decide +kernel +noncomputable def kernel25_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-132246870133143075773),(-132246870133139510245)⟩,⟨(-7062589662615533999970),(-7062589662615530434386)⟩⟩,⟨⟨(-425732950889949485925),(-425732950889946126943)⟩,⟨(-6658920814171767980436),(-6658920814171764621396)⟩⟩,⟨⟨(-689873622699846754501),(-689873622699843594326)⟩,⟨(-6257991979834654266822),(-6257991979834651106586)⟩⟩,⟨⟨(-925242590484656881246),(-925242590484653911788)⟩,⟨(-5861412105941271347748),(-5861412105941268378226)⟩⟩,⟨⟨(-1132563682412534022720),(-1132563682412531236226)⟩,⟨(-5470724444117675821785),(-5470724444117673035226)⟩⟩,⟨⟨(-1312700203044714809243),(-1312700203044712197712)⟩,⟨(-5087393939617829602565),(-5087393939617826990968)⟩⟩,⟨⟨(-1466643208645584365117),(-1466643208645581920891)⟩,⟨(-4712795806103117386991),(-4712795806103114942699)⟩⟩,⟨⟨(-1595498859255187197267),(-1595498859255184911996)⟩,⟨(-4348205404025074981793),(-4348205404025072696455)⟩⟩,⟨⟨(-1700475013191636181140),(-1700475013191634047287)⟩,⟨(-3994789518622426102947),(-3994789518622423969028)⟩⟩,⟨⟨(-1782867237917473599951),(-1782867237917471609962)⟩,⟨(-3653599111207229901646),(-3653599111207227911591)⟩⟩,⟨⟨(-1844044416539262165603),(-1844044416539260312325)⟩,⟨(-3325563594307852778886),(-3325563594307850925549)⟩⟩,⟨⟨(-1885434131545158874391),(-1885434131545157150605)⟩,⟨(-3011486657784589635315),(-3011486657784587911478)⟩⟩,⟨⟨(-1908508006715018779684),(-1908508006715017178404)⟩,⟨(-2712043649665621175893),(-2712043649665619574568)⟩⟩,⟨⟨(-1914767184517820773028),(-1914767184517819287350)⟩,⟨(-2427780492588206975244),(-2427780492588205489528)⟩⟩,⟨⟨(-1905728109858196398040),(-1905728109858195021551)⟩,⟨(-2159114094777935976527),(-2159114094777934600004)⟩⟩,⟨⟨(-1882908781920662519008),(-1882908781920661245211)⟩,⟨(-1906334193837758335937),(-1906334193837757062113)⟩⟩] +lemma kernel25_0_r4_3_eq : ∀ k : Fin 16, kernel25_0Expr 4 3 k = kernel25_0_r4_3 k := by decide +kernel +noncomputable def kernel25_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-1847815624311954761434),(-1847815624311953584340)⟩,⟨(-1669606552595438244083),(-1669606552595437066967)⟩⟩,⟨⟨(-1801931109989870597742),(-1801931109989869511322)⟩,⟨(-1448977409179542157725),(-1448977409179541071287)⟩⟩,⟨⟨(-1746702261901571653201),(-1746702261901570651885)⟩,⟨(-1244379068620008379962),(-1244379068620007378633)⟩⟩,⟨⟨(-1683530133176875315015),(-1683530133176874393280)⟩,⟨(-1055636510808063989213),(-1055636510808063067468)⟩⟩,⟨⟨(-1613760352496890076181),(-1613760352496889228943)⟩,⟨(-882474879754970181766),(-882474879754969334520)⟩⟩,⟨⟨(-1538674801263419221894),(-1538674801263418444086)⟩,⟨(-724527711855741793256),(-724527711855741015444)⟩⟩,⟨⟨(-1459484469812636040728),(-1459484469812635327697)⟩,⟨(-581345756330642524647),(-581345756330641811614)⟩⟩,⟨⟨(-1377323520526212064118),(-1377323520526211411286)⟩,⟨(-452406239164824977612),(-452406239164824324781)⟩⟩,⟨⟨(-1293244566660191371597),(-1293244566660190774777)⟩,⟨(-337122422620956737247),(-337122422620956140429)⟩⟩,⟨⟨(-1208215157381507597302),(-1208215157381507052347)⟩,⟨(-234853315635614547821),(-234853315635614002870)⟩⟩,⟨⟨(-1123115442191175729679),(-1123115442191175232819)⟩,⟨(-144913395955449863050),(-144913395955449366196)⟩⟩,⟨⟨(-1038736971904581536240),(-1038736971904581083791)⟩,⟨(-66582212510382318749),(-66582212510381866307)⟩⟩,⟨⟨(-955782578896136065375),(-955782578896135652583)⟩,⟨886253989424108683,886253989424521468⟩⟩,⟨⟨(-874867266597521033040),(-874867266597520656777)⟩,⟨58254583183484669460,58254583183485045716⟩⟩,⟨⟨(-796520027419191482530),(-796520027419191140057)⟩,⟨106293358527893768885,106293358527894111350⟩⟩,⟨⟨(-721186499449337959491),(-721186499449337648142)⟩,⟨145773147397755610808,145773147397755922148⟩⟩] +lemma kernel25_0_r4_4_eq : ∀ k : Fin 16, kernel25_0Expr 4 4 k = kernel25_0_r4_4 k := by decide +kernel +noncomputable def kernel25_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-649232365530811981947),(-649232365530811699318)⟩,⟨177457089152790352774,177457089152790635395⟩⟩,⟨⟨(-580947393635353550107),(-580947393635353293839)⟩,⟨202094148171938550108,202094148171938806368⟩⟩,⟨⟨(-516550014811876916738),(-516550014811876684711)⟩,⟨220413074488453649223,220413074488453881242⟩⟩,⟨⟨(-456192334306114802580),(-456192334306114592745)⟩,⟨233117100512048814822,233117100512049024647⟩⟩,⟨⟨(-399965472619734417568),(-399965472619734228091)⟩,⟨240879388668940211583,240879388668940401052⟩⟩,⟨⟨(-347905136152697296350),(-347905136152697125441)⟩,⟨244339231856988035329,244339231856988206232⟩⟩,⟨⟨(-299997321480541372193),(-299997321480541218252)⟩,⟨244098996603742494539,244098996603742648475⟩⟩,⟨⟨(-256184063064415798051),(-256184063064415659552)⟩,⟨240721787898694521582,240721787898694660077⟩⟩,⟨⟨(-216369141066654675222),(-216369141066654550790)⟩,⟨234729804980755071232,234729804980755195662⟩⟩,⟨⟨(-180423673729534634923),(-180423673729534523246)⟩,⟨226603348995238645374,226603348995238757049⟩⟩,⟨⟨(-148191527247095603651),(-148191527247095503564)⟩,⟨216780436452875813529,216780436452875913614⟩⟩,⟨⟨(-119494484998887455790),(-119494484998887366168)⟩,⟨205656966853397353115,205656966853397442737⟩⟩,⟨⟨(-94137127206602656228),(-94137127206602576099)⟩,⟨193587388672034787042,193587388672034867169⟩⟩,⟨⟨(-71911381317664585772),(-71911381317664514206)⟩,⟨180885805112774440516,180885805112774512082⟩⟩,⟨⟨(-52600712527298606812),(-52600712527298542983)⟩,⟨167827459544406533074,167827459544406596904⟩⟩,⟨⟨(-35983932654395761530),(-35983932654395704626)⟩,⟨154650540268137368427,154650540268137425331⟩⟩] +lemma kernel25_0_r4_5_eq : ∀ k : Fin 16, kernel25_0Expr 4 5 k = kernel25_0_r4_5 k := by decide +kernel +noncomputable def kernel25_0_r4_6 : Fin 16 → CBox := ![⟨⟨(-21838613939675310545),(-21838613939675259896)⟩,⟨141558245113361980731,141558245113362031380⟩⟩,⟨⟨(-9944102113180373022),(-9944102113180327983)⟩,⟨128721048200634088269,128721048200634133308⟩⟩,⟨⟨(-84130181732525238),(-84130181732485242)⟩,⟨116279113916554088199,116279113916554128195⟩⟩,⟨⟨7950959260548512890,7950959260548548372⟩,⟨104344806576106857696,104344806576106893179⟩⟩,⟨⟨14362369846638696659,14362369846638728086⟩,⟨93005248262985127568,93005248262985158995⟩⟩,⟨⟨19341367308234676762,19341367308234704573⟩,⟨82324881797532711946,82324881797532739758⟩⟩,⟨⟨23068133462908969275,23068133462908993876⟩,⟨72348000549165278170,72348000549165302772⟩⟩,⟨⟨25710933331684756389,25710933331684778140⟩,⟨63101211756507275919,63101211756507297671⟩⟩,⟨⟨27425568160873185467,27425568160873204666⟩,⟨54595805024469078758,54595805024469097959⟩⟩,⟨⟨28355085640311882500,28355085640311899433⟩,⟨46830002624866231446,46830002624866248380⟩⟩,⟨⟨28629717832567691112,28629717832567706027⟩,⟨39791073040516126896,39791073040516141812⟩⟩,⟨⟨28367017189445704557,28367017189445717682⟩,⟨33457293780325690476,33457293780325703602⟩⟩,⟨⟨27672161461554585359,27672161461554596893⟩,⟨27799753787211816319,27799753787211827853⟩⟩,⟨⟨26638399227546681336,26638399227546691468⟩,⟨22783989708558500315,22783989708558510448⟩⟩,⟨⟨25347609103721247616,25347609103721256505⟩,⟨18371453861054320867,18371453861054329756⟩⟩,⟨⟨23870947363743274637,23870947363743282429⟩,⟨14520814872222226271,14520814872222234063⟩⟩] +lemma kernel25_0_r4_6_eq : ∀ k : Fin 16, kernel25_0Expr 4 6 k = kernel25_0_r4_6 k := by decide +kernel +noncomputable def kernel25_0_r4_7 : Fin 16 → CBox := ![⟨⟨22269560626032177994,22269560626032184815⟩,⟨11189094706180870709,11189094706180877531⟩⟩,⟨⟨20595342380232960328,20595342380232966294⟩,⟨8332648078825445303,8332648078825451268⟩⟩,⟨⟨18891714356331333517,18891714356331338729⟩,⟨5907992145272457713,5907992145272462926⟩⟩,⟨⟨17194416028610381408,17194416028610385960⟩,⟨3872495816174657159,3872495816174661711⟩⟩,⟨⟨15532287836690838996,15532287836690842963⟩,⟨2184939152522955695,2184939152522959662⟩⟩,⟨⟨13928035949484410945,13928035949484414401⟩,⟨805954029533030809,805954029533034265⟩⟩,⟨⟨12398968554603168077,12398968554603171083⟩,⟨(-301642317965928194),(-301642317965925187)⟩⟩,⟨⟨10957695692648196536,10957695692648199152⟩,⟨(-1172609117903496093),(-1172609117903493477)⟩⟩,⟨⟨9612786547153455659,9612786547153457936⟩,⟨(-1839127608344927844),(-1839127608344925566)⟩⟩,⟨⟨8369379827999819751,8369379827999821736⟩,⟨(-2330718983782159161),(-2330718983782157176)⟩⟩,⟨⟨7229744436467196776,7229744436467198503⟩,⟨(-2674223902555898971),(-2674223902555897245)⟩⟩,⟨⟨6193788967205044211,6193788967205045711⟩,⟨(-2893833341936475671),(-2893833341936474171)⟩⟩,⟨⟨5259519784869370670,5259519784869371973⟩,⟨(-3011161314151603755),(-3011161314151602451)⟩⟩,⟨⟨4423448414033176125,4423448414033177255⟩,⟨(-3045350754920284650),(-3045350754920283520)⟩⟩,⟨⟨3680949806976387864,3680949806976388843⟩,⟨(-3013204737891206770),(-3013204737891205789)⟩⟩,⟨⟨3026573714843579751,3026573714843580601⟩,⟨(-2929336029092899105),(-2929336029092898255)⟩⟩] +lemma kernel25_0_r4_7_eq : ∀ k : Fin 16, kernel25_0Expr 4 7 k = kernel25_0_r4_7 k := by decide +kernel +noncomputable def kernel25_0_r4_8 : Fin 16 → CBox := ![⟨⟨2454311895466591851,2454311895466592587⟩,⟨(-2806328853751323984),(-2806328853751323248)⟩⟩,⟨⟨1957824259577954619,1957824259577955256⟩,⟨(-2654907585672096092),(-2654907585672095456)⟩⟩,⟨⟨1530627300937065783,1530627300937066334⟩,⟨(-2484107872179112174),(-2484107872179111624)⟩⟩,⟨⟨1166248290323218795,1166248290323219271⟩,⟨(-2301446463861836174),(-2301446463861835699)⟩⟩,⟨⟨858348753744919489,858348753744919901⟩,⟨(-2113086719561178630),(-2113086719561178219)⟩⟩,⟨⟨600820716567063957,600820716567064312⟩,⟨(-1923997397249817779),(-1923997397249817425)⟩⟩,⟨⟨387859091906512017,387859091906512324⟩,⟨(-1738102917258164925),(-1738102917258164618)⟩⟩,⟨⟨214013437028054121,214013437028054386⟩,⟨(-1558423794266882237),(-1558423794266881971)⟩⟩,⟨⟨74222107932649984,74222107932650213⟩,⟨(-1387206379007273843),(-1387206379007273614)⟩⟩,⟨⟨(-36168379001153259),(-36168379001153061)⟩,⟨(-1226041431521821635),(-1226041431521821437)⟩⟩,⟨⟨(-121396208739740240),(-121396208739740069)⟩,⟨(-1075971368146337528),(-1075971368146337358)⟩⟩,⟨⟨(-185287031791225699),(-185287031791225551)⟩,⟨(-937586287981450652),(-937586287981450503)⟩⟩,⟨⟨(-231264560860848671),(-231264560860848543)⟩,⟨(-811109096061091080),(-811109096061090953)⟩⟩,⟨⟨(-262367177020062873),(-262367177020062763)⟩,⟨(-696470204647344451),(-696470204647344340)⟩⟩,⟨⟨(-281268960906285476),(-281268960906285382)⟩,⟨(-593372416246263579),(-593372416246263485)⟩⟩,⟨⟨(-290303790604510791),(-290303790604510709)⟩,⟨(-501346677254877585),(-501346677254877502)⟩⟩] +lemma kernel25_0_r4_8_eq : ∀ k : Fin 16, kernel25_0Expr 4 8 k = kernel25_0_r4_8 k := by decide +kernel +noncomputable def kernel25_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-291491358932868533),(-291491358932868462)⟩,⟨(-419799444728423702),(-419799444728423631)⟩⟩,⟨⟨(-286564156997189309),(-286564156997189248)⟩,⟨(-348052435505500235),(-348052435505500174)⟩⟩,⟨⟨(-276994646986712038),(-276994646986711984)⟩,⟨(-285375531462533408),(-285375531462533354)⟩⟩,⟨⟨(-264022004788790666),(-264022004788790620)⟩,⟨(-231013601249173242),(-231013601249173196)⟩⟩,⟨⟨(-248677952172000196),(-248677952172000156)⟩,⟨(-184207971349969414),(-184207971349969373)⟩⟩,⟨⟨(-231811319520573444),(-231811319520573409)⟩,⟨(-144213241174841374),(-144213241174841339)⟩⟩,⟨⟨(-214111084228324043),(-214111084228324012)⟩,⟨(-110310091127283899),(-110310091127283868)⟩⟩,⟨⟨(-196127717954240924),(-196127717954240897)⟩,⟨(-81814681842479962),(-81814681842479934)⟩⟩,⟨⟨(-178292749253191642),(-178292749253191618)⟩,⟨(-58085189232727594),(-58085189232727570)⟩⟩,⟨⟨(-160936507977528038),(-160936507977528017)⟩,⟨(-38525965451385355),(-38525965451385334)⟩⟩,⟨⟨(-144304065702505951),(-144304065702505933)⟩,⟨(-22589761866071966),(-22589761866071947)⟩⟩,⟨⟨(-128569423667806258),(-128569423667806242)⟩,⟨(-9778397777768800),(-9778397777768784)⟩⟩,⟨⟨(-113848027723598902),(-113848027723598888)⟩,⟨357791186277377,357791186277391⟩⟩,⟨⟨(-100207709835615538),(-100207709835615524)⟩,⟨8221437708723917,8221437708723930⟩⟩,⟨⟨(-87678169070273627),(-87678169070273614)⟩,⟨14170316181874010,14170316181874022⟩⟩,⟨⟨(-76259112781881437),(-76259112781881426)⟩,⟨18519999794924921,18519999794924932⟩⟩] +lemma kernel25_0_r4_9_eq : ∀ k : Fin 16, kernel25_0Expr 4 9 k = kernel25_0_r4_9 k := by decide +kernel +noncomputable def kernel25_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-65927181987578989),(-65927181987578981)⟩,⟨21546831483692116,21546831483692125⟩⟩,⟨⟨(-56641784560446384),(-56641784560446376)⟩,⟨23491070252353714,23491070252353722⟩⟩,⟨⟨(-48349956705681917),(-48349956705681908)⟩,⟨24560101909114601,24560101909114609⟩⟩,⟨⟨(-40990367910283333),(-40990367910283325)⟩,⟨24931627171511771,24931627171511778⟩⟩,⟨⟨(-34496577772545407),(-34496577772545400)⟩,⟨24756760625668701,24756760625668708⟩⟩,⟨⟨(-28799645327905333),(-28799645327905326)⟩,⟨24162991433158619,24162991433158626⟩⟩,⟨⟨(-23830183108806995),(-23830183108806988)⟩,⟨23256971253847668,23256971253847675⟩⟩,⟨⟨(-19519939546036107),(-19519939546036100)⟩,⟨22127106884815453,22127106884815460⟩⟩,⟨⟨(-15802984705062952),(-15802984705062945)⟩,⟨20845944893735858,20845944893735863⟩⟩,⟨⟨(-12616565959681471),(-12616565959681467)⟩,⟨19472343330296550,19472343330296554⟩⟩,⟨⟨(-9901692190187548),(-9901692190187542)⟩,⟨18053431697254876,18053431697254882⟩⟩,⟨⟨(-7603497563206162),(-7603497563206158)⟩,⟨16626365001376820,16626365001376825⟩⟩,⟨⟨(-5671428976357849),(-5671428976357844)⟩,⟨15219881111138310,15219881111138314⟩⟩,⟨⟨(-4059294873885403),(-4059294873885400)⟩,⟨13855673028335881,13855673028335885⟩⟩,⟨⟨(-2725207375149131),(-2725207375149127)⟩,⟨12549589218234055,12549589218234059⟩⟩,⟨⟨(-1631444503235726),(-1631444503235722)⟩,⟨11312675999392493,11312675999392496⟩⟩] +lemma kernel25_0_r4_10_eq : ∀ k : Fin 16, kernel25_0Expr 4 10 k = kernel25_0_r4_10 k := by decide +kernel +noncomputable def kernel25_0_r4_11 : Fin 16 → CBox := ![⟨⟨(-744254737800768),(-744254737800765)⟩,⟨10152076310773758,10152076310773762⟩⟩,⟨⟨(-33622115897150),(-33622115897146)⟩,⟨9071799071338822,9071799071338827⟩⟩,⟨⟨526993369311905,526993369311909⟩,⟨8073372929068658,8073372929068661⟩⟩,⟨⟨960928310373017,960928310373021⟩,⟨7156397548573075,7156397548573080⟩⟩,⟨⟨1288592152591586,1288592152591591⟩,⟨6319004780612466,6319004780612471⟩⟩,⟨⟨1527740119511811,1527740119511816⟩,⟨5558241151192841,5558241151192846⟩⟩,⟨⟨1693737524448606,1693737524448609⟩,⟨4870382149060021,4870382149060025⟩⟩,⟨⟨1799811678109619,1799811678109624⟩,⟨4251187815076817,4251187815076822⟩⟩,⟨⟨1857288812529544,1857288812529547⟩,⟨3696108173246378,3696108173246381⟩⟩,⟨⟨1875814416455577,1875814416455582⟩,⟨3200446111982430,3200446111982433⟩⟩,⟨⟨1863556150846794,1863556150846799⟩,⟨2759484440579641,2759484440579646⟩⟩,⟨⟨1827389115932212,1827389115932215⟩,⟨2368583019758478,2368583019758481⟩⟩,⟨⟨1773063700727170,1773063700727174⟩,⟨2023251102746204,2023251102746208⟩⟩,⟨⟨1705356586293198,1705356586293203⟩,⟨1719199327570635,1719199327570640⟩⟩,⟨⟨1628205716590311,1628205716590315⟩,⟨1452375172613493,1452375172613497⟩⟩,⟨⟨1544830213941445,1544830213941449⟩,⟨1218985124684367,1218985124684371⟩⟩] +lemma kernel25_0_r4_11_eq : ∀ k : Fin 16, kernel25_0Expr 4 11 k = kernel25_0_r4_11 k := by decide +kernel +noncomputable def kernel25_0_r4_12 : Fin 16 → CBox := ![⟨⟨1457836315737539,1457836315737544⟩,⟨1015506309277771,1015506309277776⟩⟩,⟨⟨1369310458528226,1369310458528230⟩,⟨838689892672160,838689892672165⟩⟩,⟨⟨1280900646416561,1280900646416564⟩,⟨685558180922008,685558180922011⟩⟩,⟨⟨1193887222173880,1193887222173885⟩,⟨553397007040659,553397007040664⟩⟩,⟨⟨1109244119526152,1109244119526157⟩,⟨439744710094331,439744710094336⟩⟩,⟨⟨1027691620011883,1027691620011887⟩,⟨342378763868427,342378763868431⟩⟩,⟨⟨949741572811034,949741572811039⟩,⟨259300903705695,259300903705699⟩⟩,⟨⟨875735965075481,875735965075485⟩,⟨188721423750734,188721423750738⟩⟩,⟨⟨805879656743060,805879656743063⟩,⟨129043169142297,129043169142300⟩⟩,⟨⟨740268020031513,740268020031517⟩,⟨78845624958497,78845624958500⟩⟩,⟨⟨678910151609832,678910151609835⟩,⟨36869402552047,36869402552050⟩⟩,⟨⟨621748256150717,621748256150720⟩,⟨2001341254736,2001341254740⟩⟩,⟨⟨568673734487562,568673734487566⟩,⟨(-26739623451434),(-26739623451430)⟩⟩,⟨⟨519540448513454,519540448513458⟩,⟨(-50215727727847),(-50215727727843)⟩⟩,⟨⟨474175578591888,474175578591891⟩,⟨(-69182727875223),(-69182727875220)⟩⟩,⟨⟨432388437723515,432388437723518⟩,⟨(-84301307211884),(-84301307211881)⟩⟩] +lemma kernel25_0_r4_12_eq : ∀ k : Fin 16, kernel25_0Expr 4 12 k = kernel25_0_r4_12 k := by decide +kernel +noncomputable def kernel25_0_r4_13 : Fin 16 → CBox := ![⟨⟨393977560004136,393977560004139⟩,⟨(-96147544202988),(-96147544202985)⟩⟩,⟨⟨358736338879233,358736338879236⟩,⟨(-105222463529426),(-105222463529423)⟩⟩,⟨⟨326457453134104,326457453134107⟩,⟨(-111960705419649),(-111960705419646)⟩⟩,⟨⟨296936285187824,296936285187829⟩,⟨(-116738358020964),(-116738358020959)⟩⟩,⟨⟨269973506783613,269973506783616⟩,⟨(-119880003704743),(-119880003704740)⟩⟩,⟨⟨245376981271140,245376981271143⟩,⟨(-121665033690780),(-121665033690777)⟩⟩,⟨⟨222963109037348,222963109037353⟩,⟨(-122333286827928),(-122333286827922)⟩⟩,⟨⟨202557722946015,202557722946018⟩,⟨(-122090068266422),(-122090068266419)⟩⟩,⟨⟨183996623588558,183996623588563⟩,⟨(-121110602498760),(-121110602498756)⟩⟩,⟨⟨167125829441776,167125829441779⟩,⟨(-119543973152356),(-119543973152353)⟩⟩,⟨⟨151801604403219,151801604403223⟩,⟨(-117516599247073),(-117516599247070)⟩⟩,⟨⟨137890314383867,137890314383870⟩,⟨(-115135294589208),(-115135294589205)⟩⟩,⟨⟨125268155453415,125268155453418⟩,⟨(-112489953721604),(-112489953721601)⟩⟩,⟨⟨113820788250460,113820788250465⟩,⟨(-109655904511772),(-109655904511767)⟩⟩,⟨⟨103442906803123,103442906803127⟩,⟨(-106695964130340),(-106695964130336)⟩⟩,⟨⟨94037764389916,94037764389919⟩,⟨(-103662231920866),(-103662231920863)⟩⟩] +lemma kernel25_0_r4_13_eq : ∀ k : Fin 16, kernel25_0Expr 4 13 k = kernel25_0_r4_13 k := by decide +kernel +noncomputable def kernel25_0_r4_14 : Fin 16 → CBox := ![⟨⟨85516674459534,85516674459539⟩,⟨(-100597649538952),(-100597649538948)⟩⟩,⟨⟨77798500792041,77798500792044⟩,⟨(-97537355778127),(-97537355778122)⟩⟩,⟨⟨70809147909147,70809147909151⟩,⟨(-94509860723916),(-94509860723912)⟩⟩,⟨⟨64481060128737,64481060128741⟩,⟨(-91538061297933),(-91538061297930)⟩⟩,⟨⟨58752735521914,58752735521918⟩,⟨(-88640117875454),(-88640117875450)⟩⟩,⟨⟨53568259295167,53568259295171⟩,⟨(-85830209481591),(-85830209481587)⟩⟩,⟨⟨48876859721157,48876859721160⟩,⟨(-83119183087947),(-83119183087943)⟩⟩,⟨⟨44632488623905,44632488623909⟩,⟨(-80515110735103),(-80515110735099)⟩⟩,⟨⟨40793427540512,40793427540517⟩,⟨(-78023766586697),(-78023766586692)⟩⟩,⟨⟨37321919991619,37321919991622⟩,⟨(-75649034566597),(-75649034566594)⟩⟩,⟨⟨34183829762590,34183829762593⟩,⟨(-73393255929946),(-73393255929943)⟩⟩,⟨⟨31348324697906,31348324697909⟩,⟨(-71257524959264),(-71257524959261)⟩⟩,⟨⟨28787585218226,28787585218229⟩,⟨(-69241939946426),(-69241939946423)⟩⟩,⟨⟨26476536562689,26476536562692⟩,⟨(-67345815708243),(-67345815708240)⟩⟩,⟨⟨24392603621329,24392603621332⟩,⟨(-65567863076402),(-65567863076399)⟩⟩,⟨⟨22515487139757,22515487139761⟩,⟨(-63906340091088),(-63906340091084)⟩⟩] +lemma kernel25_0_r4_14_eq : ∀ k : Fin 16, kernel25_0Expr 4 14 k = kernel25_0_r4_14 k := by decide +kernel +noncomputable def kernel25_0_r4_15 : Fin 16 → CBox := ![⟨⟨20826960039040,20826960039044⟩,⟨(-62359179001704),(-62359179001701)⟩⟩,⟨⟨19310682588213,19310682588217⟩,⟨(-60924092628631),(-60924092628626)⟩⟩,⟨⟨17952035187471,17952035187474⟩,⟨(-59598663158406),(-59598663158403)⟩⟩,⟨⟨16737967560232,16737967560236⟩,⟨(-58380416023379),(-58380416023375)⟩⟩,⟨⟨15656863207047,15656863207051⟩,⟨(-57266881148738),(-57266881148734)⟩⟩,⟨⟨14698418039463,14698418039466⟩,⟨(-56255643528512),(-56255643528509)⟩⟩,⟨⟨13853532184329,13853532184333⟩,⟨(-55344384811890),(-55344384811887)⟩⟩,⟨⟨13114214026152,13114214026155⟩,⟨(-54530917336876),(-54530917336873)⟩⟩,⟨⟨12473495634876,12473495634879⟩,⟨(-53813211835252),(-53813211835249)⟩⟩,⟨⟨11925358807672,11925358807677⟩,⟨(-53189419846824),(-53189419846819)⟩⟩,⟨⟨11464671034725,11464671034728⟩,⟨(-52657891718355),(-52657891718352)⟩⟩,⟨⟨11087130779908,11087130779911⟩,⟨(-52217190919948),(-52217190919945)⟩⟩,⟨⟨10789221547343,10789221547346⟩,⟨(-51866105285987),(-51866105285984)⟩⟩,⟨⟨10568174283565,10568174283569⟩,⟨(-51603655676394),(-51603655676390)⟩⟩,⟨⟨10421937742619,10421937742623⟩,⟨(-51429102454265),(-51429102454261)⟩⟩,⟨⟨10349156517633,10349156517636⟩,⟨(-51341950085819),(-51341950085816)⟩⟩] +lemma kernel25_0_r4_15_eq : ∀ k : Fin 16, kernel25_0Expr 4 15 k = kernel25_0_r4_15 k := by decide +kernel +noncomputable def kernel25_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel25_0_r4_0,kernel25_0_r4_1,kernel25_0_r4_2,kernel25_0_r4_3,kernel25_0_r4_4,kernel25_0_r4_5,kernel25_0_r4_6,kernel25_0_r4_7,kernel25_0_r4_8,kernel25_0_r4_9,kernel25_0_r4_10,kernel25_0_r4_11,kernel25_0_r4_12,kernel25_0_r4_13,kernel25_0_r4_14,kernel25_0_r4_15] +lemma kernel25_0_r4_eq (i k : Fin 16) : kernel25_0Expr 4 i k = kernel25_0_r4 i k := by + fin_cases i + · exact kernel25_0_r4_0_eq k + · exact kernel25_0_r4_1_eq k + · exact kernel25_0_r4_2_eq k + · exact kernel25_0_r4_3_eq k + · exact kernel25_0_r4_4_eq k + · exact kernel25_0_r4_5_eq k + · exact kernel25_0_r4_6_eq k + · exact kernel25_0_r4_7_eq k + · exact kernel25_0_r4_8_eq k + · exact kernel25_0_r4_9_eq k + · exact kernel25_0_r4_10_eq k + · exact kernel25_0_r4_11_eq k + · exact kernel25_0_r4_12_eq k + · exact kernel25_0_r4_13_eq k + · exact kernel25_0_r4_14_eq k + · exact kernel25_0_r4_15_eq k +noncomputable def kernel25_0_r5_0 : Fin 16 → CBox := ![⟨⟨4264459887589814585565063983,4264459887589816086675011967⟩,⟨(-8829759522912750485972789307),(-8829759522912748984872900846)⟩⟩,⟨⟨4253897428398276241107125347,4253897428398277741567116623⟩,⟨(-8826469956148504083623432843),(-8826469956148502583173274749)⟩⟩,⟨⟨4232806046118958263241417340,4232806046118959762399537021⟩,⟨(-8819872333590396017288506868),(-8819872333590394518139768723)⟩⟩,⟨⟨4201252752315355514998334133,4201252752315357012203949633⟩,⟨(-8809929894731983809006535241),(-8809929894731982311809626397)⟩⟩,⟨⟨4159337911785045414752023918,4159337911785046909356364761⟩,⟨(-8796588041037434020056145708),(-8796588041037432525459616500)⟩⟩,⟨⟨4107195056897470709190654054,4107195056897472200547500046⟩,⟨(-8779774981973084043753387488),(-8779774981973082552403242072)⟩⟩,⟨⟨4044990635763214966751373794,4044990635763216454217587129⟩,⟨(-8759402588671876813915725357),(-8759402588671875326454890610)⟩⟩,⟨⟨3972923690685647940892906855,3972923690685649423829227840⟩,⟨(-8735367448656507815740636872),(-8735367448656506332808167632)⟩⟩,⟨⟨3891225462607228209011132415,3891225462607229686782510432⟩,⟨(-8707552113448605126554598915),(-8707552113448603648785347988)⟩⟩,⟨⟨3800158916620499817949268096,3800158916620501289925954821⟩,⟨(-8675826529324211194358014767),(-8675826529324209722381540619)⟩⟩,⟨⟨3700018183084409066480552241,3700018183084410532038609262⟩,⟨(-8640049639947930923485041757),(-8640049639947929457925101795)⟩⟩,⟨⟨3591127908485016838131179841,3591127908485018296777604516⟩,⟨(-8600071148137712152814523413),(-8600071148137710694163947994)⟩⟩,⟨⟨3473842509919307117574542543,3473842509919308568707350910⟩,⟨(-8555733422588413910228391669),(-8555733422588412459089003937)⟩⟩,⟨⟨3348545326972995440065309465,3348545326972996883090870491⟩,⟨(-8506873534024921542568027737),(-8506873534024920099533309217)⟩⟩,⟨⟨3215647664817314183602741958,3215647664817315617933531312⟩,⟨(-8453325403975147225281117491),(-8453325403975145790938455051)⟩⟩,⟨⟨3075587722572698591088653460,3075587722572700016147293941⟩,⟨(-8394922048161063760100237313),(-8394922048161062335026883402)⟩⟩] +lemma kernel25_0_r5_0_eq : ∀ k : Fin 16, kernel25_0Expr 5 0 k = kernel25_0_r5_0 k := by decide +kernel +noncomputable def kernel25_0_r5_1 : Fin 16 → CBox := ![⟨⟨2928829401383674973650972213,2928829401383676388866264849⟩,⟨(-8331497895413831875919775167),(-8331497895413830460686817352)⟩⟩,⟨⟨2775860987221034565633827280,2775860987221035970447433636⟩,⟨(-8262891162039480364978573718),(-8262891162039478960144252919)⟩⟩,⟨⟨2617193704173843777040839701,2617193704173845170900543673⟩,⟨(-8188946260707238833027740825),(-8188946260707237439144190033)⟩⟩,⟨⟨2453360134911500353181570937,2453360134911501735550033702⟩,⟨(-8109516222216457751623811624),(-8109516222216456369228301377)⟩⟩,⟨⟨2284912506078576988943468119,2284912506078578359288773781⟩,⟨(-8024465107933029952282751402),(-8024465107933028581907144518)⟩⟩,⟨⟨2112420837623441146539288863,2112420837623442504348316590⟩,⟨(-7933670390285070128527906873),(-7933670390285068770685286570)⟩⟩,⟨⟨1936470956443625793203269662,1936470956443627137967522968⟩,⟨(-7837025278482549086838514529),(-7837025278482547742037355406)⟩⟩,⟨⟨1757662376241916807304549230,1757662376241918138541517731⟩,⟨(-7734440966588097349197033252),(-7734440966588096017919851951)⟩⟩,⟨⟨1576606047109730191403330412,1576606047109731508633427678⟩,⟨(-7625848781226727956682750223),(-7625848781226726639409155257)⟩⟩,⟨⟨1393921980068677328148797609,1393921980068678630913985235⟩,⟨(-7511202206589886362563338194),(-7511202206589885059751393652)⟩⟩,⟨⟨1210236753585039418551879714,1210236753585040706395412311⟩,⟨(-7390478764971490666858998982),(-7390478764971489378965491658)⟩⟩,⟨⟨1026180910900884314143632657,1026180910900885586636857771⟩,⟨(-7263681731876029255173917713),(-7263681731876027982627556896)⟩⟩,⟨⟨842386258873638598570622740,842386258873639855283752871⟩,⟨(-7130841665764681292511102804),(-7130841665764680035741748122)⟩⟩,⟨⟨659483080855458075706415626,659483080855459316283167391⟩,⟨(-6992017733755696122948289887),(-6992017733755694882312311615)⟩⟩,⟨⟨478097277945965779460198884,478097277945967003595316656⟩,⟨(-6847298816068081335573371587),(-6847298816068080111376126771)⟩⟩,⟨⟨298847454687348749363062848,298847454687349956694902191⟩,⟨(-6696804373688264364715668731),(-6696804373688263157318917034)⟩⟩] +lemma kernel25_0_r5_1_eq : ∀ k : Fin 16, kernel25_0Expr 5 1 k = kernel25_0_r5_1 k := by decide +kernel +noncomputable def kernel25_0_r5_2 : Fin 16 → CBox := ![⟨⟨122341966909604971510012486,122341966909606161669126881⟩,⟨(-6540685065639988020820615293),(-6540685065639986830593931914)⟩⟩,⟨⟨(-50824049053773806942709478),(-50824049053772634279336462)⟩,⟨(-6379123104337255062180511257),(-6379123104337253889447053779)⟩⟩,⟨⟨(-220071645202284810529529784),(-220071645202283655695869442)⟩,⟨(-6212332339784359843714533584),(-6212332339784358688808426527)⟩⟩,⟨⟨(-384841007005911616449200675),(-384841007005910479733715749)⟩,⟨(-6040558065838362637463804800),(-6040558065838361500673675031)⟩⟩,⟨⟨(-544594352128481473061073000),(-544594352128480354758011548)⟩,⟨(-5864076544346966162325145819),(-5864076544346965043945415955)⟩⟩,⟨⟨(-698818759291776552089641088),(-698818759291775452384528713)⟩,⟨(-5683194245694713131016009557),(-5683194245694712031232388772)⟩⟩,⟨⟨(-847028903361132443740043717),(-847028903361131362899033697)⟩,⟨(-5498246807105862045813936594),(-5498246807105860964892770234)⟩⟩,⟨⟨(-988769672533597475648846517),(-988769672533596413882884634)⟩,⟨(-5309597712933638896275624837),(-5309597712933637834428057695)⟩⟩,⟨⟨(-1123618643599818153169980089),(-1123618643599817110714657089)⟩,⟨(-5117636704080836427521264963),(-5117636704080835384983093263)⟩⟩,⟨⟨(-1251188391642056961876761541),(-1251188391642055938866041344)⟩,⟨(-4922777926611953668434838904),(-4922777926611952645340236102)⟩⟩,⟨⟨(-1371128611230339797484058172),(-1371128611230338794110080461)⟩,⟨(-4725457832496664187186548216),(-4725457832496663183727868303)⟩⟩,⟨⟨(-1483128027189388731381853639),(-1483128027189387747772695938)⟩,⟨(-4526132848231700876094778131),(-4526132848231699892400316271)⟩⟩,⟨⟨(-1586916074328734792719266346),(-1586916074328733829024654768)⟩,⟨(-4325276829786011808109260755),(-4325276829786010844328970248)⟩⟩,⟨⟨(-1682264327150386497799484778),(-1682264327150385554101454389)⟩,⟨(-4123378324865047883244322313),(-4123378324865046939460876006)⟩⟩,⟨⟨(-1768987662460895267408228355),(-1768987662460894343818644063)⟩,⟨(-3920937665857671474418174786),(-3920937665857670550749224275)⟩⟩,⟨⟨(-1846945140000948673831691319),(-1846945140000947770397538346)⟩,⟨(-3718463918978041410757864903),(-3718463918978040507250298325)⟩⟩] +lemma kernel25_0_r5_2_eq : ∀ k : Fin 16, kernel25_0Expr 5 2 k = kernel25_0_r5_2 k := by decide +kernel +noncomputable def kernel25_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-1916040588644279606330976548),(-1916040588644278723144829256)⟩,⟨(-3516471717011409995715980073),(-3516471717011409112462261358)⟩⟩,⟨⟨(-1976222888382645044858603909),(-1976222888382644181917392352)⟩,⟨(-3315478004686023958259028937),(-3315478004686023095255963612)⟩⟩,⟨⟨(-2027485941174526716149420064),(-2027485941174525873500531888)⟩,⟨(-3115998726995305665345872426),(-3115998726995304822640711215)⟩⟩,⟨⟨(-2069868326757718913401259330),(-2069868326757718091008641421)⟩,⟨(-2918545491760921506593779913),(-2918545491760920684150319991)⟩⟩,⟨⟨(-2103452642672292373838729566),(-2103452642672291571720866058)⟩,⟨(-2723622238338135285233770874),(-2723622238338134483070335487)⟩⟩,⟨⟨(-2128364530969804707964843913),(-2128364530969803926037236931)⟩,⟨(-2531721944604580342916202311),(-2531721944604579560948121295)⟩⟩,⟨⟨(-2144771397353973338934551923),(-2144771397353972577172008942)⟩,⟨(-2343323404231925772666710427),(-2343323404231925010868609317)⟩⟩,⟨⟨(-2152880831762569298068136806),(-2152880831762568556354738127)⟩,⟨(-2158888105711922756263284807),(-2158888105711922014519052413)⟩⟩,⟨⟨(-2152938742614308532880821652),(-2152938742614307811166936066)⟩,⟨(-1978857243694700238348589020),(-1978857243694699516608394726)⟩⟩,⟨⟨(-2145227220062092754885617220),(-2145227220062092053006586585)⟩,⟨(-1803648891904419208986554922),(-1803648891904418507085533522)⟩⟩,⟨⟨(-2130062146569747130267083535),(-2130062146569746447928208586)⟩,⟨(-1633655365237795098194473752),(-1633655365237794415837707087)⟩⟩,⟨⟨(-2107790575919449904958428196),(-2107790575919449240481528774)⟩,⟨(-1469240796642611502079924235),(-1469240796642610837588970932)⟩⟩,⟨⟨(-2078787904319532559057253411),(-2078787904319531912403611343)⟩,⟨(-1310738952039801417806738250),(-1310738952039800771142660958)⟩⟩,⟨⟨(-2043454859578339871248125257),(-2043454859578339242261811919)⟩,⟨(-1158451303922876960491093487),(-1158451303922876331497741208)⟩⟩,⟨⟨(-2002214336304095878233527852),(-2002214336304095266837431878)⟩,⟨(-1012645381376253741283910785),(-1012645381376253129883947912)⟩⟩,⟨⟨(-1955508106752233987218756431),(-1955508106752233393235777890)⟩,⟨(-873553411137555901101188814),(-873553411137555307117290242)⟩⟩] +lemma kernel25_0_r5_3_eq : ∀ k : Fin 16, kernel25_0Expr 5 3 k = kernel25_0_r5_3 k := by decide +kernel +noncomputable def kernel25_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-1903793438244313418772092976),(-1903793438244312842110470773)⟩,⟨(-741371261030339360608456359),(-741371261030338783948635971)⟩⟩,⟨⟨(-1847539649005754331299878244),(-1847539649005753771739702944)⟩,⟨(-616257693658029934905129405),(-616257693658029375349254013)⟩⟩,⟨⟨(-1787224634798291220410328858),(-1787224634798290677820543028)⟩,⟨(-498333934724859417734351565),(-498333934724858875151142113)⟩⟩,⟨⟨(-1723331398848508498589411741),(-1723331398848507972736013720)⟩,⟨(-387683556784450011499339124),(-387683556784449485654575667)⟩⟩,⟨⟨(-1656344617293652885340797329),(-1656344617293652376078977316)⟩,⟨(-284352675661501335614361426),(-284352675661500826363019805)⟩⟩,⟨⟨(-1586747271684094921239909862),(-1586747271684094428298985186)⟩,⟨(-188350453296777422552854794),(-188350453296776929624043290)⟩⟩,⟨⟨(-1515017379008688718953235545),(-1515017379008688242151662810)⟩,⟨(-99649897379361138018998704),(-99649897379360661230965693)⟩⟩,⟨⟨(-1441624848261417424303529393),(-1441624848261416963355328779)⟩,⟨(-18188944900261557751745730),(-18188944900261096818308881)⟩⟩,⟨⟨(-1367028490767603687998649901),(-1367028490767603242706987869)⟩,⟨56128186267341479654840995,56128186267341924930703444⟩⟩,⟨⟨(-1291673209363635939819529716),(-1291673209363635509865844212)⟩,⟨123429396442284585303701938,123429396442285015240732061⟩⟩,⟨⟨(-1215987389108670926822081575),(-1215987389108670511970044032)⟩,⟨183872875051724971502166401,183872875051725386336864848⟩⟩,⟨⟨(-1140380509537613112500190802),(-1140380509537612712422096807)⟩,⟨237645066771552181165361075,237645066771552581225594906⟩⟩,⟨⟨(-1065240995583085314857315648),(-1065240995583084929333253243)⟩,⟨284958458127578956287548167,284958458127579341793383149⟩⟩,⟨⟨(-990934321244333647161132280),(-990934321244333275808777274)⟩,⟨326049211287628014321852228,326049211287628385655756010⟩⟩,⟨⟨(-917801376909485807685977433),(-917801376909485450243431173)⟩,⟨361174672891263343419043216,361174672891263700843048542⟩⟩,⟨⟨(-846157107992084721618663681),(-846157107992084377745165659)⟩,⟨390610786494401543655764045,390610786494401887512145320⟩⟩] +lemma kernel25_0_r5_4_eq : ∀ k : Fin 16, kernel25_0Expr 5 4 k = kernel25_0_r5_4 k := by decide +kernel +noncomputable def kernel25_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-776289429271613518467849785),(-776289429271613187923881184)⟩,⟨414649437547385677188709280,414649437547386007717575165⟩⟩,⟨⟨(-708458416078697690274885603),(-708458416078697372672701183)⟩,⟨433595759780619525965479137,433595759780619843554468606⟩⟩,⟨⟨(-642895770285475587811440551),(-642895770285475282805005797)⟩,⟨447765431451001565948631074,447765431451001870943671544⟩⟩,⟨⟨(-579804555994892631914858289),(-579804555994892339156350264)⟩,⟨457481989120500058182632200,457481989120500350931435973⟩⟩,⟨⟨(-519359196911226177342858170),(-519359196911225896580353846)⟩,⟨463074185516103605380639305,463074185516103886135018439⟩⟩,⟨⟨(-461705724656328739804266927),(-461705724656328470662434738)⟩,⟨464873416583908660221693580,464873416583908929356868235⟩⟩,⟨⟨(-406962264806131988310959458),(-406962264806131730522582027)⟩,⟨463211241129552264049805061,463211241129552521832882238⟩⟩,⟨⟨(-355219745189512040430644870),(-355219745189511793641652196)⟩,⟨458417014466646146910468006,458417014466646393695408453⟩⟩,⟨⟨(-306542809041276308688704125),(-306542809041276072641186046)⟩,⟨450815655311488419946691032,450815655311488655991297775⟩⟩,⟨⟨(-260970913952052595898934503),(-260970913952052370084677974)⟩,⟨440725562805632470558730933,440725562805632696371099735⟩⟩,⟨⟨(-218519596223967634749590570),(-218519596223967418876773005)⟩,⟨428456698058953518165404849,428456698058953734037255198⟩⟩,⟨⟨(-179181879230305611743752356),(-179181879230305405475557656)⟩,⟨414308842026522628890923283,414308842026522835158974640⟩⟩,⟨⟨(-142929803692365927635235680),(-142929803692365730723442369)⟩,⟨398570038904724884920762476,398570038904725081833143459⟩⟩,⟨⟨(-109716057424581205876858222),(-109716057424581017973490614)⟩,⟨381515231596735004890286114,381515231596735192794883836⟩⟩,⟨⟨(-79475682051502466591083694),(-79475682051502287440160130)⟩,⟨363405093194309741882273626,363405093194309921034985272⟩⟩,⟨⟨(-52127834454541738039834970),(-52127834454541567283017860)⟩,⟨344485055889357066898854654,344485055889357237657938039⟩⟩] +lemma kernel25_0_r5_5_eq : ∀ k : Fin 16, kernel25_0Expr 5 5 k = kernel25_0_r5_5 k := by decide +kernel +noncomputable def kernel25_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-27577581244981466875559262),(-27577581244981304269579991)⟩,⟨324984536299652116966067151,324984536299652279574715740⟩⟩,⟨⟨(-5717705361373072552027112),(-5717705361372917765036817)⟩,⟨305116353899893540900237922,305116353899893695690230524⟩⟩,⟨⟨13569495070674484840477780,13569495070674632059382878⟩,⟨285076337119850605422668820,285076337119850752644843938⟩⟩,⟨⟨30410434227687805982234625,30410434227687945942256393⟩,⟨265043109729431803764877600,265043109729431943728375338⟩⟩,⟨⟨44938509606175902374755455,44938509606176035306273968⟩,⟨245178048395622481352743687,245178048395622614287888732⟩⟩,⟨⟨57292432167224792328488345,57292432167224918537844103⟩,⟨225625400783474186420946335,225625400783474312634029356⟩⟩,⟨⟨67614629506544134875904715,67614629506544254594597858⟩,⟨206512552293275834737888392,206512552293275954460364253⟩⟩,⟨⟨76049734163778554144011567,76049734163778667658464023⟩,⟨187950428484836488393658255,187950428484836601911908553⟩⟩,⟨⟨82743167346451391780967781,82743167346451499450477799⟩,⟨170034019439269910116668632,170034019439270017789590028⟩⟩,⟨⟨87839826482932403200377847,87839826482932505341071894⟩,⟨152843011746470576139737207,152843011746470678283357569⟩⟩,⟨⟨91482883164891613092704912,91482883164891709899789563⟩,⟨136442513476432049688906899,136442513476432146498467934⟩⟩,⟨⟨93812696220493838669891049,93812696220493930386718198⟩,⟨120883857384984012073487897,120883857384984103792376603⟩⟩,⟨⟨94965842900477738128576462,94965842900477824936156654⟩,⟨106205467706583606722164924,106205467706583693531426263⟩⟩,⟨⟨95074269482999407609287270,95074269482999489747516686⟩,⟨92433776182954679036903595,92433776182954761176467494⟩⟩,⟨⟨94264561029573391649174769,94264561029573469298255997⟩,⟨79584173448840469852022323,79584173448840547502124060⟩⟩,⟨⟨92657328570422752981238234,92657328570422826366182030⟩,⟨67661982525360645375825913,67661982525360718761507948⟩⟩] +lemma kernel25_0_r5_6_eq : ∀ k : Fin 16, kernel25_0Expr 5 6 k = kernel25_0_r5_6 k := by decide +kernel +noncomputable def kernel25_0_r5_7 : Fin 16 → CBox := ![⟨⟨90366710676695529900421004,90366710676695599183433867⟩,⟨56663441936583909978552756,56663441936583979262051909⟩⟩,⟨⟨87499985199753140090639482,87499985199753205492558915⟩,⟨46576686844260259149901811,46576686844260324552085637⟩⟩,⟨⟨84157285931347368501625472,84157285931347430194671627⟩,⟨37382717567153505481326529,37382717567153567174444763⟩⟩,⟨⟨80431418067153247727022134,80431418067153305903720708⟩,⟨29056345893094271018083346,29056345893094329194686961⟩⟩,⟨⟨76407765641056042053897152,76407765641056096860426375⟩,⟨21567110682225346902227461,21567110682225401708518340⟩⟩,⟨⟨72164283537302160765277580,72164283537302212387267951⟩,⟨14880155378257766453426216,14880155378257818075056816⟩⟩,⟨⟨67771566278113205162086629,67771566278113253739244893⟩,⟨8957061171372952054680007,8957061171373000631377392⟩⟩,⟨⟨63292985519392428223155277,63292985519392473923196858⟩,⟨3756630673595263446243168,3756630673595309145741369⟩⟩,⟨⟨58784888058546050117983575,58784888058546093099838138⟩,⟨(-764381941430393051336839),(-764381941430350070091133)⟩⟩,⟨⟨54296846156389521909720801,54296846156389562341723708⟩,⟨(-4650597331920529273745068),(-4650597331920488842401159)⟩⟩,⟨⟨49871952088488861920153189,49871952088488899918167268⟩,⟨(-7947395915358607394768005),(-7947395915358569397449204)⟩⟩,⟨⟨45547149057981851648599874,45547149057981887351791066⟩,⟨(-10700362397565708376604424),(-10700362397565672674132411)⟩⟩,⟨⟨41353590909131003419678959,41353590909131036932103161⟩,⟨(-12954790110974550820343841),(-12954790110974517308651646)⟩⟩,⟨⟨37317023465391560711590695,37317023465391592167932603⟩,⟨(-14755244588782701656618045),(-14755244588782670201011530)⟩⟩,⟨⟨33458180764339099495392484,33458180764339128994847046⟩,⟨(-16145185104799990520913817),(-16145185104799961022135184)⟩⟩,⟨⟨29793189961249464787003938,29793189961249492447031217⟩,⟨(-17166642298737224307956537),(-17166642298737196648502836)⟩⟩] +lemma kernel25_0_r5_7_eq : ∀ k : Fin 16, kernel25_0Expr 5 7 k = kernel25_0_r5_7 k := by decide +kernel +noncomputable def kernel25_0_r5_8 : Fin 16 → CBox := ![⟨⟨26333979210697632035094965,26333979210697657944637237⟩,⟨(-17859949484452084649864461),(-17859949484452058740801923)⟩⟩,⟨⟨23088683399064046684243611,23088683399064070967944044⟩,⟨(-18263524803715528580997363),(-18263524803715504297691215)⟩⟩,⟨⟨20062043178883925752695177,20062043178883948491747710⟩,⟨(-18413701038392645131814423),(-18413701038392622393078794)⟩⟩,⟨⟨17255793338017377508305193,17255793338017398798972538⟩,⟨(-18344599626290671863394318),(-18344599626290650572974290)⟩⟩,⟨⟨14669037113127618644532325,14669037113127638558919617⟩,⟨(-18088045235984987696187803),(-18088045235984967781985646)⟩⟩,⟨⟨12298603619480349907511858,12298603619480368535728906⟩,⟨(-17673517138478184820021563),(-17673517138478166191934518)⟩⟩,⟨⟨10139386110293528604140865,10139386110293546018014456⟩,⟨(-17128133562668230906230347),(-17128133562668213492438243)⟩⟩,⟨⟨8184659292591540329104858,8184659292591556609033342⟩,⟨(-16476665230876253556127648),(-16476665230876237276238340)⟩⟩,⟨⟨6426374407707710588923681,6426374407707725792617442⟩,⟨(-15741574333350393588544309),(-15741574333350378384853635)⟩⟩,⟨⟨4855431229300988516951732,4855431229301002718047787⟩,⟨(-14943075309780758276048581),(-14943075309780744074925004)⟩⟩,⟨⟨3461926537135804581631597,3461926537135817837113216⟩,⟨(-14099213954465329043757332),(-14099213954465315788222383)⟩⟩,⟨⟨2235378989046455168732760,2235378989046467542128887⟩,⟨(-13225961542996755532081704),(-13225961542996743158610818)⟩⟩,⟨⟨1164930635518284883715066,1164930635518296422204346⟩,⟨(-12337320885556046991494602),(-12337320885556035452913119)⟩⟩,⟨⟨239525601051191530164271,239525601051202293453505⟩,⟨(-11445441438782495680121967),(-11445441438782484916726660)⟩⟩,⟨⟨(-551933305449338806006566),(-551933305449328774423762)⟩,⟨(-10560740848822508749379027),(-10560740848822498717679493)⟩⟩,⟨⟨(-1220449091316121233283695),(-1220449091316111882099132)⟩,⟨(-9692030547091262798297049),(-9692030547091253446987940)⟩⟩] +lemma kernel25_0_r5_8_eq : ∀ k : Fin 16, kernel25_0Expr 5 8 k = kernel25_0_r5_8 k := by decide +kernel +noncomputable def kernel25_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-1776815072747867530792452),(-1776815072747858822932980)⟩,⟨(-8846643272569940954343080),(-8846643272569932246353772)⟩⟩,⟨⟨(-2231518117581966560483489),(-2231518117581958448652082)⟩,⟨(-8030560645710166565660100),(-8030560645710158453695745)⟩⟩,⟨⟨(-2594659307313016690675752),(-2594659307313009140209534)⟩,⟨(-7248539165387378633283985),(-7248539165387371082683620)⟩⟩,⟨⟨(-2875890629266779244148345),(-2875890629266772214864648)⟩,⟨(-6504233238559368993604930),(-6504233238559361964187514)⟩⟩,⟨⟨(-3084366279490780582394966),(-3084366279490774044722582)⟩,⟨(-5800314079621108922864354),(-5800314079621102385077106)⟩⟩,⟨⟨(-3228707151296118738470370),(-3228707151296112655671257)⟩,⟨(-5138583530712608402768816),(-5138583530712602319872835)⟩⟩,⟨⟨(-3316977100336384327661320),(-3316977100336378672612623)⟩,⟨(-4520082053750098868098578),(-4520082053750093212969367)⟩⟩,⟨⟨(-3356669611533775597869911),(-3356669611533770339127213)⟩,⟨(-3945190328502510551463638),(-3945190328502505292655198)⟩⟩,⟨⟨(-3354703543045651760534986),(-3354703543045646875262365)⟩,⟨(-3413724057849090352726251),(-3413724057849085467401162)⟩⟩,⟨⟨(-3317426684928599380860786),(-3317426684928594840132142)⟩,⟨(-2925021731045264612386624),(-2925021731045260071617358)⟩⟩,⟨⟨(-3250625942494296213801579),(-3250625942494291996534338)⟩,⟨(-2478025228353851245128697),(-2478025228353847027831344)⟩⟩,⟨⟨(-3159543034053157219232703),(-3159543034053153301038714)⟩,⟨(-2071353266029088191352847),(-2071353266029084273138005)⟩⟩,⟨⟨(-3048894677517121014441131),(-3048894677517117377504069)⟩,⟨(-1703367779887813988163335),(-1703367779887810351213520)⟩⟩,⟨⟨(-2922896328121844050646343),(-2922896328121840672825850)⟩,⟨(-1372233429291578595538948),(-1372233429291575217712728)⟩⟩,⟨⟨(-2785288618507793911358309),(-2785288618507790776452171)⟩,⟨(-1075970472188809641249921),(-1075970472188806506344096)⟩⟩,⟨⟨(-2639365740983589983036902),(-2639365740983587057781428)⟩,⟨(-812501316947945502515378),(-812501316947942577265256)⟩⟩] +lemma kernel25_0_r5_9_eq : ∀ k : Fin 16, kernel25_0Expr 5 9 k = kernel25_0_r5_9 k := by decide +kernel +noncomputable def kernel25_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-2488005098631057622985417),(-2488005098631054894494820)⟩,⟨(-579691099161441709610582),(-579691099161438981129562)⟩⟩,⟨⟨(-2333697635872487406392201),(-2333697635872484859578440)⟩,⟨(-375382662584253958100271),(-375382662584251411299591)⟩⟩,⟨⟨(-2178578339292585282692998),(-2178578339292582907115855)⟩,⟨(-197426344083180902266824),(-197426344083178526705612)⟩⟩,⟨⟨(-2024456475175859298805345),(-2024456475175857081846248)⟩,⟨(-43704974110542597492052),(-43704974110540380551158)⟩⟩,⟨⟨(-1872845200853162384218581),(-1872845200853160317121771)⟩,⟨87845492049095343980176,87845492049097411057031⟩⟩,⟨⟨(-1724990252183045462829388),(-1724990252183043534002095)⟩,⟨199219300043168319688870,199219300043170248494907⟩⟩,⟨⟨(-1581897469106445427272155),(-1581897469106443628632450)⟩,⟨292327775732042120863662,292327775732043919481214⟩⟩,⟨⟨(-1444358975118452860755571),(-1444358975118451182525106)⟩,⟨368989367890544095143184,368989367890545773350941⟩⟩,⟨⟨(-1312977874721243873959605),(-1312977874721242309506390)⟩,⟨430922481371351257884794,430922481371352822315051⟩⟩,⟨⟨(-1188191375574317605833475),(-1188191375574316146090076)⟩,⟨479740747791393538805802,479740747791394998526244⟩⟩,⟨⟨(-1070292279335703462255637),(-1070292279335702101024356)⟩,⟨516950402932413050899364,516950402932414412108854⟩⟩,⟨⟨(-959448817346077256855609),(-959448817346075986613069)⟩,⟨543949463599554393522203,543949463599555663745980⟩⟩,⟨⟨(-855722834649202388019420),(-855722834649201203630727)⟩,⟨562028421054408207810456,562028421054409392183153⟩⟩,⟨⟨(-759086348703369726410035),(-759086348703368620978675)⟩,⟨572372192810427300640050,572372192810428406057923⟩⟩,⟨⟨(-669436527878627467217887),(-669436527878626436019967)⟩,⟨576063099106730778614984,576063099106731809801690⟩⟩,⟨⟨(-586609149824948209171434),(-586609149824947246454412)⟩,⟨574084654392630902575771,574084654392631865283624⟩⟩] +lemma kernel25_0_r5_10_eq : ∀ k : Fin 16, kernel25_0Expr 5 10 k = kernel25_0_r5_10 k := by decide +kernel +noncomputable def kernel25_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-510390611411959467220255),(-510390611411958569170749)⟩,⟨567325987360102675585609,567325987360103573627783⟩⟩,⟨⟨(-440528570552430013875663),(-440528570552429175149120)⟩,⟨556586725218180212955171,556586725218181051676019⟩⟩,⟨⟨(-376741306190271967050066),(-376741306190271184094023)⟩,⟨542582198832151289775674,542582198832152072727476⟩⟩,⟨⟨(-318725886405333408984442),(-318725886405332677385223)⟩,⟨525948844922454639174090,525948844922455370770353⟩⟩,⟨⟨(-266165236288890059099385),(-266165236288889375978516)⟩,⟨507249699649044110678356,507249699649044793797400⟩⟩,⟨⟨(-218734197281093753849851),(-218734197281093115235137)⟩,⟨486979894551043141563583,486979894551043780177459⟩⟩,⟨⟨(-176104668316814325013913),(-176104668316813728170991)⟩,⟨465572080956128187594716,465572080956128784437657⟩⟩,⟨⟨(-137949916656825868477503),(-137949916656825310116707)⟩,⟨443401722634208156599996,443401722634208714961548⟩⟩,⟨⟨(-103948142919580464563785),(-103948142919579942593299)⟩,⟨420792208683171808687782,420792208683172330659643⟩⟩,⟨⟨(-73785380782369723663381),(-73785380782369235036601)⟩,⟨398019749456352352648982,398019749456352841277657⟩⟩,⟨⟨(-47157807272602903142948),(-47157807272602445867716)⟩,⟨375318027841407465316415,375318027841407922593978⟩⟩,⟨⟨(-23773534679898204746708),(-23773534679897776255191)⟩,⟨352882586458258904473562,352882586458259332967769⟩⟩,⟨⟨(-3353950025152400165956),(-3353950025151998896471)⟩,⟨330874938446300809666718,330874938446301210939182⟩⟩,⟨⟨14365337159582034089767,14365337159582410396514⟩,⟨309426395549194444610451,309426395549194820920407⟩⟩,⟨⟨29633883159211526514542,29633883159211879313479⟩,⟨288641612271968722118630,288641612271969074920954⟩⟩,⟨⟨42686084013429586365840,42686084013429917510251⟩,⟨268601849072424980348029,268601849072425311495956⟩⟩] +lemma kernel25_0_r5_11_eq : ∀ k : Fin 16, kernel25_0Expr 5 11 k = kernel25_0_r5_11 k := by decide +kernel +noncomputable def kernel25_0_r5_12 : Fin 16 → CBox := ![⟨⟨53741089495008236157702,53741089495008546762390⟩,⟨249367960947792842222118,249367960947793152830412⟩⟩,⟨⟨63002916284357345132713,63002916284357636957868⟩,⟨230983120475899855251646,230983120475900147080460⟩⟩,⟨⟨70660723979611723422993,70660723979611997655660⟩,⟨213475286451400639611173,213475286451400913847522⟩⟩,⟨⟨76889221796592159783560,76889221796592417807065⟩,⟨196859430800618362431485,196859430800618620458670⟩⟩,⟨⟨81849177742285184931568,81849177742285427576075⟩,⟨181139537536681135995150,181139537536681378643310⟩⟩,⟨⟨85688005679521687349029,85688005679521915901451⟩,⟨166310388197609475741687,166310388197609704297455⟩⟩,⟨⟨88540409036477965337756,88540409036478180579444⟩,⟨152359148555719152027385,152359148555719367272045⟩⟩,⟨⟨90529062955111778734126,90529062955111981723091⟩,⟨139266771453192858297058,139266771453193061288651⟩⟩,⟨⟨91765319424721094158061,91765319424721285483920⟩,⟨127009230456244059461082,127009230456244250789252⟩⟩,⟨⟨92349922420972146361788,92349922420972327024625⟩,⟨115558598673688470040179,115558598673688650705037⟩⟩,⟨⟨92373722280108473870753,92373722280108644446903⟩,⟨104883986594392008582300,104883986594392179160204⟩⟩,⟨⟨91918380497646693913057,91918380497646855196290⟩,⟨94952352196422661922419,94952352196422823207164⟩⟩,⟨⟨91057057866989985435354,91057057866990137866733⟩,⟨85729195898587859162370,85729195898588011595040⟩⟩,⟨⟨89855080383100729523059,89855080383100873851664⟩,⟨77179152187888483167747,77179152187888627497442⟩⟩,⟨⟨88370578647036142912192,88370578647036279596377⟩,⟨69266488985847797656813,69266488985847934341905⟩⟩,⟨⟨86655097636083044860703,86655097636083174554367⟩,⟨61955525030716686061142,61955525030716815755548⟩⟩] +lemma kernel25_0_r5_12_eq : ∀ k : Fin 16, kernel25_0Expr 5 12 k = kernel25_0_r5_12 k := by decide +kernel +noncomputable def kernel25_0_r5_13 : Fin 16 → CBox := ![⟨⟨84754174668409214890802,84754174668409337886804⟩,⟨55210974766077111012970,55210974766077234009564⟩⟩,⟨⟨82707884206991348344373,82707884206991465228014⟩,⟨48998229451402299569718,48998229451402416453816⟩⟩,⟨⟨80551348830755649017700,80551348830755760093863⟩,⟨43283582456238020271331,43283582456238131347830⟩⟩,⟨⟨78315216266182978131305,78315216266183083856054⟩,⟨38034405974228884961068,38034405974228990686043⟩⟩,⟨⟨76026102833941341540666,76026102833941442137373⟩,⟨33219285701737030852150,33219285701737131448984⟩⟩,⟨⟨73707004035266833137286,73707004035266929047648⟩,⟨28808119372194258836086,28808119372194354746488⟩⟩,⟨⟨71377673293646825786300,71377673293646917236586⟩,⟨24772184424141944378862,24772184424142035829110⟩⟩,⟨⟨69054970089667430330194,69054970089667517672710⟩,⟨21084179509560006723296,21084179509560094065704⟩⟩,⟨⟨66753178890465172392107,66753178890465255776509⟩,⟨17718244020044856204979,17718244020044939589211⟩⟩,⟨⟨64484300388890406614507,64484300388890486396677⟩,⟨14649959321384172795366,14649959321384252577312⟩⟩,⟨⟨62258316639136791450931,62258316639136867803570⟩,⟨11856334941205557242897,11856334941205633595263⟩⟩,⟨⟨60083431712228035691077,60083431712228108891458⟩,⟨9315782548287275761257,9315782548287348961322⟩⟩,⟨⟨57966289502569192898734,57966289502569263058794⟩,⟨7008080194098011815830,7008080194098081975540⟩⟩,⟨⟨55912170301192378023161,55912170301192445415578⟩,⟨4914328955207986751082,4914328955208054143115⟩⟩,⟨⟨53925167717083008735098,53925167717083073481040⟩,⟨3016903817242621087038,3016903817242685832570⟩⟩,⟨⟨52008347479150693866637,52008347479150756181380⟩,⟨1299400374785794173447,1299400374785856487755⟩⟩] +lemma kernel25_0_r5_13_eq : ∀ k : Fin 16, kernel25_0Expr 5 13 k = kernel25_0_r5_13 k := by decide +kernel +noncomputable def kernel25_0_r5_14 : Fin 16 → CBox := ![⟨⟨50163889591518130626450,50163889591518190579213⟩,⟨(-253421315208923955833),(-253421315208864003525)⟩⟩,⟨⟨48393215246830573511590,48393215246830631332108⟩,⟨(-1655694598664339826638),(-1655694598664282006595)⟩⟩,⟨⟨46697099828761051664902,46697099828761107442341⟩,⟨(-2920504865298810167894),(-2920504865298754390944)⟩⟩,⟨⟨45075773257912825937109,45075773257912879842891⟩,⟨(-4059948184396302622689),(-4059948184396248717409)⟩⟩,⟨⟨43529008856646421906758,43529008856646473994311⟩,⟨(-5085189296173759779420),(-5085189296173707692380)⟩⟩,⟨⟨42056201829410289327622,42056201829410339775046⟩,⟨(-6006518442457511114223),(-6006518442457460667321)⟩⟩,⟨⟨40656438377079873487519,40656438377079922360601⟩,⟨(-6833406626616438238136),(-6833406626616389365583)⟩⟩,⟨⟨39328556387517132009667,39328556387517179447057⟩,⟨(-7574558983957405300989),(-7574558983957357864134)⟩⟩,⟨⟨38071198570752091328808,38071198570752137359009⟩,⟨(-8237966021693352211804),(-8237966021693306182143)⟩⟩,⟨⟨36882858836384442272481,36882858836384487049904⟩,⟨(-8830952553645258329598),(-8830952553645213552717)⟩⟩,⟨⟨35761922643381861773862,35761922643381905347276⟩,⟨(-9360224210410121105472),(-9360224210410077532603)⟩⟩,⟨⟨34706701988663075127891,34706701988663117611445⟩,⟨(-9831911452071238442005),(-9831911452071195958999)⟩⟩,⟨⟨33715465640844095866419,33715465640844137282057⟩,⟨(-10251611048781158214077),(-10251611048781116798988)⟩⟩,⟨⟨32786465169356614517791,32786465169356654990564⟩,⟨(-10624425025737787847689),(-10624425025737747375466)⟩⟩,⟨⟨31917957266809810205076,31917957266809849771470⟩,⟨(-10954997094122217214862),(-10954997094122177649016)⟩⟩,⟨⟨31108222813897046112337,31108222813897084868372⟩,⟨(-11247546609297225988245),(-11247546609297187232759)⟩⟩] +lemma kernel25_0_r5_14_eq : ∀ k : Fin 16, kernel25_0Expr 5 14 k = kernel25_0_r5_14 k := by decide +kernel +noncomputable def kernel25_0_r5_15 : Fin 16 → CBox := ![⟨⟨30355583091239428271117,30355583091239466222068⟩,⟨(-11505900112712147159729),(-11505900112712109209327)⟩⟩,⟨⟨29658413501167874203803,29658413501167911465539⟩,⟨(-11733520525173196107923),(-11733520525173158846735)⟩⟩,⟨⟨29015155124407834739035,29015155124407871339409⟩,⟨(-11933534066992428688026),(-11933534066992392088200)⟩⟩,⟨⟨28424324401761724055787,28424324401761760077578⟩,⟨(-12108754985527219105723),(-12108754985527183084477)⟩⟩,⟨⟨27884521198986773656954,27884521198986809106194⟩,⟨(-12261708173206232741365),(-12261708173206197292669)⟩⟩,⟨⟨27394435483936232720648,27394435483936267693918⟩,⟨(-12394649759690805607197),(-12394649759690770634471)⟩⟩,⟨⟨26952852818461664513800,26952852818461699033139⟩,⟨(-12509585760674533149822),(-12509585760674498631026)⟩⟩,⟨⟨26558658843354840760223,26558658843354874899147⟩,⟨(-12608288863264903663852),(-12608288863264869525468)⟩⟩,⟨⟨26210842912532236604115,26210842912532270361955⟩,⟨(-12692313424164325268395),(-12692313424164291511091)⟩⟩,⟨⟨25908501012529367215858,25908501012529400689616⟩,⟨(-12763008752183124115980),(-12763008752183090642750)⟩⟩,⟨⟨25650838084976509150698,25650838084976542357986⟩,⟨(-12821530741151511944233),(-12821530741151478737465)⟩⟩,⟨⟨25437169852877077300317,25437169852877110307713⟩,⟨(-12868851913200901107404),(-12868851913200868100523)⟩⟩,⟨⟨25266924236015851159374,25266924236015883965047⟩,⟨(-12905769925783038606207),(-12905769925783005801045)⟩⟩,⟨⟨25139642426502567877711,25139642426502600564947⟩,⟨(-12932914588793419135398),(-12932914588793386448669)⟩⟩,⟨⟨25054979682128581771022,25054979682128614356004⟩,⟨(-12950753430851071252471),(-12950753430851038667994)⟩⟩,⟨⟨25012705882706612181349,25012705882706644727513⟩,⟨(-12959595846233355402947),(-12959595846233322857285)⟩⟩] +lemma kernel25_0_r5_15_eq : ∀ k : Fin 16, kernel25_0Expr 5 15 k = kernel25_0_r5_15 k := by decide +kernel +noncomputable def kernel25_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel25_0_r5_0,kernel25_0_r5_1,kernel25_0_r5_2,kernel25_0_r5_3,kernel25_0_r5_4,kernel25_0_r5_5,kernel25_0_r5_6,kernel25_0_r5_7,kernel25_0_r5_8,kernel25_0_r5_9,kernel25_0_r5_10,kernel25_0_r5_11,kernel25_0_r5_12,kernel25_0_r5_13,kernel25_0_r5_14,kernel25_0_r5_15] +lemma kernel25_0_r5_eq (i k : Fin 16) : kernel25_0Expr 5 i k = kernel25_0_r5 i k := by + fin_cases i + · exact kernel25_0_r5_0_eq k + · exact kernel25_0_r5_1_eq k + · exact kernel25_0_r5_2_eq k + · exact kernel25_0_r5_3_eq k + · exact kernel25_0_r5_4_eq k + · exact kernel25_0_r5_5_eq k + · exact kernel25_0_r5_6_eq k + · exact kernel25_0_r5_7_eq k + · exact kernel25_0_r5_8_eq k + · exact kernel25_0_r5_9_eq k + · exact kernel25_0_r5_10_eq k + · exact kernel25_0_r5_11_eq k + · exact kernel25_0_r5_12_eq k + · exact kernel25_0_r5_13_eq k + · exact kernel25_0_r5_14_eq k + · exact kernel25_0_r5_15_eq k +noncomputable def kernel25_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel25_0_r0,kernel25_0_r1,kernel25_0_r2,kernel25_0_r3,kernel25_0_r4,kernel25_0_r5] +lemma kernel25_0_eq (j : Fin 6) (i k : Fin 16) : kernel25_0Expr j i k = kernel25_0 j i k := by + fin_cases j + · exact kernel25_0_r0_eq i k + · exact kernel25_0_r1_eq i k + · exact kernel25_0_r2_eq i k + · exact kernel25_0_r3_eq i k + · exact kernel25_0_r4_eq i k + · exact kernel25_0_r5_eq i k +lemma kernel25_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel25_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(25:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel25_0_eq] + unfold kernel25_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans25_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel25_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans25 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel25_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r0_0_eq : ∀ k : Fin 16, kernel25_1Expr 0 0 k = kernel25_1_r0_0 k := by decide +kernel +noncomputable def kernel25_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r0_1_eq : ∀ k : Fin 16, kernel25_1Expr 0 1 k = kernel25_1_r0_1 k := by decide +kernel +noncomputable def kernel25_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r0_2_eq : ∀ k : Fin 16, kernel25_1Expr 0 2 k = kernel25_1_r0_2 k := by decide +kernel +noncomputable def kernel25_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r0_3_eq : ∀ k : Fin 16, kernel25_1Expr 0 3 k = kernel25_1_r0_3 k := by decide +kernel +noncomputable def kernel25_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r0_4_eq : ∀ k : Fin 16, kernel25_1Expr 0 4 k = kernel25_1_r0_4 k := by decide +kernel +noncomputable def kernel25_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel25_1_r0_5_eq : ∀ k : Fin 16, kernel25_1Expr 0 5 k = kernel25_1_r0_5 k := by decide +kernel +noncomputable def kernel25_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel25_1_r0_6_eq : ∀ k : Fin 16, kernel25_1Expr 0 6 k = kernel25_1_r0_6 k := by decide +kernel +noncomputable def kernel25_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel25_1_r0_7_eq : ∀ k : Fin 16, kernel25_1Expr 0 7 k = kernel25_1_r0_7 k := by decide +kernel +noncomputable def kernel25_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel25_1_r0_8_eq : ∀ k : Fin 16, kernel25_1Expr 0 8 k = kernel25_1_r0_8 k := by decide +kernel +noncomputable def kernel25_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel25_1_r0_9_eq : ∀ k : Fin 16, kernel25_1Expr 0 9 k = kernel25_1_r0_9 k := by decide +kernel +noncomputable def kernel25_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel25_1_r0_10_eq : ∀ k : Fin 16, kernel25_1Expr 0 10 k = kernel25_1_r0_10 k := by decide +kernel +noncomputable def kernel25_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel25_1_r0_11_eq : ∀ k : Fin 16, kernel25_1Expr 0 11 k = kernel25_1_r0_11 k := by decide +kernel +noncomputable def kernel25_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel25_1_r0_12_eq : ∀ k : Fin 16, kernel25_1Expr 0 12 k = kernel25_1_r0_12 k := by decide +kernel +noncomputable def kernel25_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel25_1_r0_13_eq : ∀ k : Fin 16, kernel25_1Expr 0 13 k = kernel25_1_r0_13 k := by decide +kernel +noncomputable def kernel25_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel25_1_r0_14_eq : ∀ k : Fin 16, kernel25_1Expr 0 14 k = kernel25_1_r0_14 k := by decide +kernel +noncomputable def kernel25_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel25_1_r0_15_eq : ∀ k : Fin 16, kernel25_1Expr 0 15 k = kernel25_1_r0_15 k := by decide +kernel +noncomputable def kernel25_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel25_1_r0_0,kernel25_1_r0_1,kernel25_1_r0_2,kernel25_1_r0_3,kernel25_1_r0_4,kernel25_1_r0_5,kernel25_1_r0_6,kernel25_1_r0_7,kernel25_1_r0_8,kernel25_1_r0_9,kernel25_1_r0_10,kernel25_1_r0_11,kernel25_1_r0_12,kernel25_1_r0_13,kernel25_1_r0_14,kernel25_1_r0_15] +lemma kernel25_1_r0_eq (i k : Fin 16) : kernel25_1Expr 0 i k = kernel25_1_r0 i k := by + fin_cases i + · exact kernel25_1_r0_0_eq k + · exact kernel25_1_r0_1_eq k + · exact kernel25_1_r0_2_eq k + · exact kernel25_1_r0_3_eq k + · exact kernel25_1_r0_4_eq k + · exact kernel25_1_r0_5_eq k + · exact kernel25_1_r0_6_eq k + · exact kernel25_1_r0_7_eq k + · exact kernel25_1_r0_8_eq k + · exact kernel25_1_r0_9_eq k + · exact kernel25_1_r0_10_eq k + · exact kernel25_1_r0_11_eq k + · exact kernel25_1_r0_12_eq k + · exact kernel25_1_r0_13_eq k + · exact kernel25_1_r0_14_eq k + · exact kernel25_1_r0_15_eq k +noncomputable def kernel25_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel25_1_r1_0_eq : ∀ k : Fin 16, kernel25_1Expr 1 0 k = kernel25_1_r1_0 k := by decide +kernel +noncomputable def kernel25_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel25_1_r1_1_eq : ∀ k : Fin 16, kernel25_1Expr 1 1 k = kernel25_1_r1_1 k := by decide +kernel +noncomputable def kernel25_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel25_1_r1_2_eq : ∀ k : Fin 16, kernel25_1Expr 1 2 k = kernel25_1_r1_2 k := by decide +kernel +noncomputable def kernel25_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel25_1_r1_3_eq : ∀ k : Fin 16, kernel25_1Expr 1 3 k = kernel25_1_r1_3 k := by decide +kernel +noncomputable def kernel25_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel25_1_r1_4_eq : ∀ k : Fin 16, kernel25_1Expr 1 4 k = kernel25_1_r1_4 k := by decide +kernel +noncomputable def kernel25_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel25_1_r1_5_eq : ∀ k : Fin 16, kernel25_1Expr 1 5 k = kernel25_1_r1_5 k := by decide +kernel +noncomputable def kernel25_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel25_1_r1_6_eq : ∀ k : Fin 16, kernel25_1Expr 1 6 k = kernel25_1_r1_6 k := by decide +kernel +noncomputable def kernel25_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel25_1_r1_7_eq : ∀ k : Fin 16, kernel25_1Expr 1 7 k = kernel25_1_r1_7 k := by decide +kernel +noncomputable def kernel25_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel25_1_r1_8_eq : ∀ k : Fin 16, kernel25_1Expr 1 8 k = kernel25_1_r1_8 k := by decide +kernel +noncomputable def kernel25_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel25_1_r1_9_eq : ∀ k : Fin 16, kernel25_1Expr 1 9 k = kernel25_1_r1_9 k := by decide +kernel +noncomputable def kernel25_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r1_10_eq : ∀ k : Fin 16, kernel25_1Expr 1 10 k = kernel25_1_r1_10 k := by decide +kernel +noncomputable def kernel25_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r1_11_eq : ∀ k : Fin 16, kernel25_1Expr 1 11 k = kernel25_1_r1_11 k := by decide +kernel +noncomputable def kernel25_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r1_12_eq : ∀ k : Fin 16, kernel25_1Expr 1 12 k = kernel25_1_r1_12 k := by decide +kernel +noncomputable def kernel25_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r1_13_eq : ∀ k : Fin 16, kernel25_1Expr 1 13 k = kernel25_1_r1_13 k := by decide +kernel +noncomputable def kernel25_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r1_14_eq : ∀ k : Fin 16, kernel25_1Expr 1 14 k = kernel25_1_r1_14 k := by decide +kernel +noncomputable def kernel25_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel25_1_r1_15_eq : ∀ k : Fin 16, kernel25_1Expr 1 15 k = kernel25_1_r1_15 k := by decide +kernel +noncomputable def kernel25_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel25_1_r1_0,kernel25_1_r1_1,kernel25_1_r1_2,kernel25_1_r1_3,kernel25_1_r1_4,kernel25_1_r1_5,kernel25_1_r1_6,kernel25_1_r1_7,kernel25_1_r1_8,kernel25_1_r1_9,kernel25_1_r1_10,kernel25_1_r1_11,kernel25_1_r1_12,kernel25_1_r1_13,kernel25_1_r1_14,kernel25_1_r1_15] +lemma kernel25_1_r1_eq (i k : Fin 16) : kernel25_1Expr 1 i k = kernel25_1_r1 i k := by + fin_cases i + · exact kernel25_1_r1_0_eq k + · exact kernel25_1_r1_1_eq k + · exact kernel25_1_r1_2_eq k + · exact kernel25_1_r1_3_eq k + · exact kernel25_1_r1_4_eq k + · exact kernel25_1_r1_5_eq k + · exact kernel25_1_r1_6_eq k + · exact kernel25_1_r1_7_eq k + · exact kernel25_1_r1_8_eq k + · exact kernel25_1_r1_9_eq k + · exact kernel25_1_r1_10_eq k + · exact kernel25_1_r1_11_eq k + · exact kernel25_1_r1_12_eq k + · exact kernel25_1_r1_13_eq k + · exact kernel25_1_r1_14_eq k + · exact kernel25_1_r1_15_eq k +noncomputable def kernel25_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩] +lemma kernel25_1_r2_0_eq : ∀ k : Fin 16, kernel25_1Expr 2 0 k = kernel25_1_r2_0 k := by decide +kernel +noncomputable def kernel25_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),6⟩,⟨(-11),19⟩⟩,⟨⟨(-22),19⟩,⟨(-16),24⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩] +lemma kernel25_1_r2_1_eq : ∀ k : Fin 16, kernel25_1Expr 2 1 k = kernel25_1_r2_1 k := by decide +kernel +noncomputable def kernel25_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),19⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩] +lemma kernel25_1_r2_2_eq : ∀ k : Fin 16, kernel25_1Expr 2 2 k = kernel25_1_r2_2 k := by decide +kernel +noncomputable def kernel25_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-22),20⟩,⟨(-17),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel25_1_r2_3_eq : ∀ k : Fin 16, kernel25_1Expr 2 3 k = kernel25_1_r2_3 k := by decide +kernel +noncomputable def kernel25_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel25_1_r2_4_eq : ∀ k : Fin 16, kernel25_1Expr 2 4 k = kernel25_1_r2_4 k := by decide +kernel +noncomputable def kernel25_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel25_1_r2_5_eq : ∀ k : Fin 16, kernel25_1Expr 2 5 k = kernel25_1_r2_5 k := by decide +kernel +noncomputable def kernel25_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel25_1_r2_6_eq : ∀ k : Fin 16, kernel25_1Expr 2 6 k = kernel25_1_r2_6 k := by decide +kernel +noncomputable def kernel25_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel25_1_r2_7_eq : ∀ k : Fin 16, kernel25_1Expr 2 7 k = kernel25_1_r2_7 k := by decide +kernel +noncomputable def kernel25_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel25_1_r2_8_eq : ∀ k : Fin 16, kernel25_1Expr 2 8 k = kernel25_1_r2_8 k := by decide +kernel +noncomputable def kernel25_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel25_1_r2_9_eq : ∀ k : Fin 16, kernel25_1Expr 2 9 k = kernel25_1_r2_9 k := by decide +kernel +noncomputable def kernel25_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel25_1_r2_10_eq : ∀ k : Fin 16, kernel25_1Expr 2 10 k = kernel25_1_r2_10 k := by decide +kernel +noncomputable def kernel25_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel25_1_r2_11_eq : ∀ k : Fin 16, kernel25_1Expr 2 11 k = kernel25_1_r2_11 k := by decide +kernel +noncomputable def kernel25_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel25_1_r2_12_eq : ∀ k : Fin 16, kernel25_1Expr 2 12 k = kernel25_1_r2_12 k := by decide +kernel +noncomputable def kernel25_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel25_1_r2_13_eq : ∀ k : Fin 16, kernel25_1Expr 2 13 k = kernel25_1_r2_13 k := by decide +kernel +noncomputable def kernel25_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel25_1_r2_14_eq : ∀ k : Fin 16, kernel25_1Expr 2 14 k = kernel25_1_r2_14 k := by decide +kernel +noncomputable def kernel25_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel25_1_r2_15_eq : ∀ k : Fin 16, kernel25_1Expr 2 15 k = kernel25_1_r2_15 k := by decide +kernel +noncomputable def kernel25_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel25_1_r2_0,kernel25_1_r2_1,kernel25_1_r2_2,kernel25_1_r2_3,kernel25_1_r2_4,kernel25_1_r2_5,kernel25_1_r2_6,kernel25_1_r2_7,kernel25_1_r2_8,kernel25_1_r2_9,kernel25_1_r2_10,kernel25_1_r2_11,kernel25_1_r2_12,kernel25_1_r2_13,kernel25_1_r2_14,kernel25_1_r2_15] +lemma kernel25_1_r2_eq (i k : Fin 16) : kernel25_1Expr 2 i k = kernel25_1_r2 i k := by + fin_cases i + · exact kernel25_1_r2_0_eq k + · exact kernel25_1_r2_1_eq k + · exact kernel25_1_r2_2_eq k + · exact kernel25_1_r2_3_eq k + · exact kernel25_1_r2_4_eq k + · exact kernel25_1_r2_5_eq k + · exact kernel25_1_r2_6_eq k + · exact kernel25_1_r2_7_eq k + · exact kernel25_1_r2_8_eq k + · exact kernel25_1_r2_9_eq k + · exact kernel25_1_r2_10_eq k + · exact kernel25_1_r2_11_eq k + · exact kernel25_1_r2_12_eq k + · exact kernel25_1_r2_13_eq k + · exact kernel25_1_r2_14_eq k + · exact kernel25_1_r2_15_eq k +noncomputable def kernel25_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-252754157736909),(-252754157736877)⟩,⟨30039706712727,30039706712758⟩⟩,⟨⟨(-252245043595106),(-252245043595079)⟩,⟨30246250365592,30246250365622⟩⟩,⟨⟨(-251229080687673),(-251229080687641)⟩,⟨30656538052353,30656538052385⟩⟩,⟨⟨(-249710792894031),(-249710792894011)⟩,⟨31265009743382,31265009743401⟩⟩,⟨⟨(-247696948646190),(-247696948646170)⟩,⟨32063422826674,32063422826694⟩⟩,⟨⟨(-245196539499797),(-245196539499778)⟩,⟨33040967388229,33040967388249⟩⟩,⟨⟨(-242220750649958),(-242220750649934)⟩,⟨34184417213033,34184417213054⟩⟩,⟨⟨(-238782922664959),(-238782922664933)⟩,⟨35478314237494,35478314237520⟩⟩,⟨⟨(-234898503596653),(-234898503596633)⟩,⟨36905183678523,36905183678542⟩⟩,⟨⟨(-230584990552769),(-230584990552749)⟩,⟨38445776599847,38445776599866⟩⟩,⟨⟨(-225861859789787),(-225861859789767)⟩,⟨40079336259528,40079336259547⟩⟩,⟨⟨(-220750484408386),(-220750484408355)⟩,⟨41783884220243,41783884220270⟩⟩,⟨⟨(-215274038808621),(-215274038808591)⟩,⟨43536521903115,43536521903142⟩⟩,⟨⟨(-209457389189621),(-209457389189601)⟩,⟨45313743030797,45313743030817⟩⟩,⟨⟨(-203326969556128),(-203326969556109)⟩,⟨47091752242220,47091752242240⟩⟩,⟨⟨(-196910642918821),(-196910642918802)⟩,⟨48846785072390,48846785072409⟩⟩] +lemma kernel25_1_r3_0_eq : ∀ k : Fin 16, kernel25_1Expr 3 0 k = kernel25_1_r3_0 k := by decide +kernel +noncomputable def kernel25_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-190237547641689),(-190237547641664)⟩,⟨50555424479170,50555424479195⟩⟩,⟨⟨(-183337929190680),(-183337929190659)⟩,⟨52194909166499,52194909166523⟩⟩,⟨⟨(-176242957865799),(-176242957865779)⟩,⟨53743429099425,53743429099444⟩⟩,⟨⟨(-168984533444061),(-168984533444042)⟩,⟨55180403830383,55180403830402⟩⟩,⟨⟨(-161595078013405),(-161595078013380)⟩,⟨56486739554574,56486739554599⟩⟩,⟨⟨(-154107318626856),(-154107318626836)⟩,⟨57645061181347,57645061181366⟩⟩,⟨⟨(-146554061741241),(-146554061741209)⟩,⟨58639916142480,58639916142512⟩⟩,⟨⟨(-138967961714470),(-138967961714450)⟩,⟨59457947149994,59457947150013⟩⟩,⟨⟨(-131381285909955),(-131381285909925)⟩,⟨60088031656363,60088031656390⟩⟩,⟨⟨(-123825679185754),(-123825679185722)⟩,⟨60521386350864,60521386350895⟩⟩,⟨⟨(-116331930722243),(-116331930722222)⟩,⟨60751635633662,60751635633686⟩⟩,⟨⟨(-108929746257182),(-108929746257150)⟩,⟨60774843635675,60774843635707⟩⟩,⟨⟨(-101647528846356),(-101647528846319)⟩,⟨60589509982350,60589509982384⟩⟩,⟨⟨(-94512171248264),(-94512171248244)⟩,⟨60196530122090,60196530122110⟩⟩,⟨⟨(-87548862939519),(-87548862939498)⟩,⟨59599121642414,59599121642438⟩⟩,⟨⟨(-80780914605907),(-80780914605888)⟩,⟨58802718566395,58802718566414⟩⟩] +lemma kernel25_1_r3_1_eq : ∀ k : Fin 16, kernel25_1Expr 3 1 k = kernel25_1_r3_1 k := by decide +kernel +noncomputable def kernel25_1_r3_2 : Fin 16 → CBox := ![⟨⟨(-74229602724132),(-74229602724109)⟩,⟨57814836146743,57814836146772⟩⟩,⟨⟨(-67914036554953),(-67914036554929)⟩,⟨56644909145030,56644909145051⟩⟩,⟨⟨(-61851049517877),(-61851049517857)⟩,⟨55304106987996,55304106988015⟩⟩,⟨⟨(-56055116516788),(-56055116516769)⟩,⟨53805129525257,53805129525277⟩⟩,⟨⟨(-50538298346310),(-50538298346279)⟩,⟨52161987364863,52161987364891⟩⟩,⟨⟨(-45310213839670),(-45310213839644)⟩,⟨50389770931882,50389770931908⟩⟩,⟨⟨(-40378039932876),(-40378039932857)⟩,⟨48504412477020,48504412477040⟩⟩,⟨⟨(-35746539328309),(-35746539328289)⟩,⟨46522445257611,46522445257631⟩⟩,⟨⟨(-31418114956812),(-31418114956786)⟩,⟨44460764023047,44460764023073⟩⟩,⟨⟨(-27392889971671),(-27392889971645)⟩,⟨42336390765171,42336390765197⟩⟩,⟨⟨(-23668811572797),(-23668811572771)⟩,⟨40166249446871,40166249446897⟩⟩,⟨⟨(-20241776565070),(-20241776565036)⟩,⟨37966953106608,37966953106644⟩⟩,⟨⟨(-17105776210296),(-17105776210276)⟩,⟨35754606361728,35754606361748⟩⟩,⟨⟨(-14253057645582),(-14253057645563)⟩,⟨33544625909800,33544625909820⟩⟩,⟨⟨(-11674298917275),(-11674298917248)⟩,⟨31351581166317,31351581166343⟩⟩,⟨⟨(-9358794524495),(-9358794524475)⟩,⟨29189056690004,29189056690024⟩⟩] +lemma kernel25_1_r3_2_eq : ∀ k : Fin 16, kernel25_1Expr 3 2 k = kernel25_1_r3_2 k := by decide +kernel +noncomputable def kernel25_1_r3_3 : Fin 16 → CBox := ![⟨⟨(-7294648280225),(-7294648280206)⟩,⟨27069537547146,27069537547166⟩⟩,⟨⟨(-5468970282201),(-5468970282181)⟩,⟨25004318265387,25004318265407⟩⟩,⟨⟨(-3868074838545),(-3868074838525)⟩,⟨23003435536628,23003435536648⟩⟩,⟨⟨(-2477676310327),(-2477676310292)⟩,⟨21075624360417,21075624360454⟩⟩,⟨⟨(-1283080010055),(-1283080010023)⟩,⟨19228296882204,19228296882236⟩⟩,⟨⟨(-269365525122),(-269365525102)⟩,⟨17467542784638,17467542784658⟩⟩,⟨⟨578439890001,578439890026⟩,⟨15798149742195,15798149742216⟩⟩,⟨⟨1275199897437,1275199897457⟩,⟨14223642154709,14223642154729⟩⟩,⟨⟨1835521341594,1835521341614⟩,⟨12746336138629,12746336138649⟩⟩,⟨⟨2273621546931,2273621546951⟩,⟨11367408578058,11367408578078⟩⟩,⟨⟨2603211633982,2603211634002⟩,⟨10086977921248,10086977921268⟩⟩,⟨⟨2837396476988,2837396477008⟩,⟨8904194351188,8904194351208⟩⟩,⟨⟨2988591574376,2988591574405⟩,⟨7817336958618,7817336958642⟩⟩,⟨⟨3068456768586,3068456768621⟩,⟨6823915598326,6823915598363⟩⟩,⟨⟨3087846442577,3087846442610⟩,⟨5920775209478,5920775209511⟩⟩,⟨⟨3056775541916,3056775541936⟩,⟨5104200522344,5104200522364⟩⟩] +lemma kernel25_1_r3_3_eq : ∀ k : Fin 16, kernel25_1Expr 3 3 k = kernel25_1_r3_3 k := by decide +kernel +noncomputable def kernel25_1_r3_4 : Fin 16 → CBox := ![⟨⟨2984400528145,2984400528170⟩,⟨4370019250075,4370019250097⟩⟩,⟨⟨2879014165019,2879014165039⟩,⟨3713702067969,3713702067989⟩⟩,⟨⟨2748052875516,2748052875537⟩,⟨3130457906646,3130457906666⟩⟩,⟨⟨2598115285674,2598115285694⟩,⟨2615323322507,2615323322527⟩⟩,⟨⟨2434990489930,2434990489959⟩,⟨2163244951459,2163244951491⟩⟩,⟨⟨2263694531477,2263694531505⟩,⟨1769154293612,1769154293643⟩⟩,⟨⟨2088513585826,2088513585852⟩,⟨1428034311623,1428034311650⟩⟩,⟨⟨1913052365392,1913052365417⟩,⟨1134977548240,1134977548262⟩⟩,⟨⟨1740286321069,1740286321098⟩,⟨885235674780,885235674811⟩⟩,⟨⟨1572616300884,1572616300904⟩,⟨674260568523,674260568543⟩⟩,⟨⟨1411924430443,1411924430464⟩,⟨497737180473,497737180493⟩⟩,⟨⟨1259630100506,1259630100532⟩,⟨351608594039,351608594065⟩⟩,⟨⟨1116745078505,1116745078527⟩,⟨232093789006,232093789032⟩⟩,⟨⟨983926899394,983926899422⟩,⟨135698713440,135698713472⟩⟩,⟨⟨861529832115,861529832136⟩,⟨59221330372,59221330392⟩⟩,⟨⟨749652857050,749652857071⟩,⟨(-248653986),(-248653965)⟩⟩] +lemma kernel25_1_r3_4_eq : ∀ k : Fin 16, kernel25_1Expr 3 4 k = kernel25_1_r3_4 k := by decide +kernel +noncomputable def kernel25_1_r3_5 : Fin 16 → CBox := ![⟨⟨648184225059,648184225084⟩,⟨(-45334654407),(-45334654385)⟩⟩,⟨⟨556842295428,556842295455⟩,⟨(-78381938042),(-78381938015)⟩⟩,⟨⟨475212467722,475212467743⟩,⟨(-101469515129),(-101469515108)⟩⟩,⟨⟨402780128262,402780128289⟩,⟨(-116424513065),(-116424513038)⟩⟩,⟨⟨338959625127,338959625148⟩,⟨(-124838400959),(-124838400939)⟩⟩,⟨⟨283119365290,283119365322⟩,⟨(-128084484341),(-128084484312)⟩⟩,⟨⟨234603193770,234603193796⟩,⟨(-127336147831),(-127336147808)⟩⟩,⟨⟨192748267297,192748267318⟩,⟨(-123585386378),(-123585386357)⟩⟩,⟨⟨156899675346,156899675378⟩,⟨(-117661229313),(-117661229284)⟩⟩,⟨⟨126422088940,126422088960⟩,⟨(-110247725739),(-110247725718)⟩⟩,⟨⟨100708734996,100708735017⟩,⟨(-101901221522),(-101901221501)⟩⟩,⟨⟨79188001451,79188001473⟩,⟨(-93066716926),(-93066716900)⟩⟩,⟨⟨61327976986,61327977007⟩,⟨(-84093148469),(-84093148448)⟩⟩,⟨⟨46639221588,46639221621⟩,⟨(-75247488029),(-75247488000)⟩⟩,⟨⟨34676050118,34676050150⟩,⟨(-66727595962),(-66727595933)⟩⟩,⟨⟨25036592814,25036592835⟩,⟨(-58673803297),(-58673803276)⟩⟩] +lemma kernel25_1_r3_5_eq : ∀ k : Fin 16, kernel25_1Expr 3 5 k = kernel25_1_r3_5 k := by decide +kernel +noncomputable def kernel25_1_r3_6 : Fin 16 → CBox := ![⟨⟨17361875648,17361875678⟩,⟨(-51179229987),(-51179229955)⟩⟩,⟨⟨11334139580,11334139607⟩,⟨(-44298872834),(-44298872806)⟩⟩,⟨⟨6674593389,6674593410⟩,⟨(-38057517763),(-38057517742)⟩⟩,⟨⟨3140769803,3140769829⟩,⟨(-32456546715),(-32456546692)⟩⟩,⟨⟨523630480,523630501⟩,⟨(-27479721010),(-27479720989)⟩⟩,⟨⟨(-1355458392),(-1355458366)⟩,⟨(-23098030189),(-23098030166)⟩⟩,⟨⟨(-2647779559),(-2647779533)⟩,⟨(-19273698849),(-19273698826)⟩⟩,⟨⟨(-3480267468),(-3480267447)⟩,⟨(-15963444789),(-15963444768)⟩⟩,⟨⟨(-3958398399),(-3958398371)⟩,⟨(-13121080005),(-13121079977)⟩⟩,⟨⟨(-4168922304),(-4168922280)⟩,⟨(-10699542319),(-10699542293)⟩⟩,⟨⟨(-4182404568),(-4182404536)⟩,⟨(-8652440285),(-8652440255)⟩⟩,⟨⟨(-4055557622),(-4055557592)⟩,⟨(-6935187841),(-6935187809)⟩⟩,⟨⟨(-3833352457),(-3833352424)⟩,⟨(-5505798271),(-5505798241)⟩⟩,⟨⟨(-3550907863),(-3550907837)⟩,⟨(-4325399956),(-4325399933)⟩⟩,⟨⟨(-3235161590),(-3235161566)⟩,⟨(-3358528986),(-3358528960)⟩⟩,⟨⟨(-2906332524),(-2906332500)⟩,⟨(-2573246772),(-2573246746)⟩⟩] +lemma kernel25_1_r3_6_eq : ∀ k : Fin 16, kernel25_1Expr 3 6 k = kernel25_1_r3_6 k := by decide +kernel +noncomputable def kernel25_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-2579186316),(-2579186294)⟩,⟨(-1941123816),(-1941123794)⟩⟩,⟨⟨(-2264119312),(-2264119290)⟩,⟨(-1437124595),(-1437124574)⟩⟩,⟨⟨(-1968076992),(-1968076964)⟩,⟨(-1039422521),(-1039422493)⟩⟩,⟨⟨(-1695323816),(-1695323789)⟩,⟨(-729168834),(-729168811)⟩⟩,⟨⟨(-1448081203),(-1448081170)⟩,⟨(-490234421),(-490234391)⟩⟩,⟨⟨(-1227050080),(-1227050059)⟩,⟨(-308939540),(-308939519)⟩⟩,⟨⟨(-1031833475),(-1031833441)⟩,⟨(-173783032),(-173783001)⟩⟩,⟨⟨(-861273457),(-861273427)⟩,⟨(-75179297),(-75179264)⟩⟩,⟨⟨(-713715880),(-713715858)⟩,⟨(-5209214),(-5209192)⟩⟩,⟨⟨(-587214483),(-587214461)⟩,⟨42611073,42611095⟩⟩,⟨⟨(-479685069),(-479685048)⟩,⟨73541264,73541286⟩⟩,⟨⟨(-389018976),(-389018952)⟩,⟨91806646,91806673⟩⟩,⟨⟨(-313163706),(-313163672)⟩,⟨100766562,100766593⟩⟩,⟨⟨(-250177645),(-250177609)⟩,⟨103062036,103062072⟩⟩,⟨⟨(-198264511),(-198264482)⟩,⟨100743828,100743857⟩⟩,⟨⟨(-155792347),(-155792321)⟩,⟨95382214,95382238⟩⟩] +lemma kernel25_1_r3_7_eq : ∀ k : Fin 16, kernel25_1Expr 3 7 k = kernel25_1_r3_7 k := by decide +kernel +noncomputable def kernel25_1_r3_8 : Fin 16 → CBox := ![⟨⟨(-121300982),(-121300955)⟩,⟨88160284,88160309⟩⟩,⟨⟨(-93501133),(-93501109)⟩,⟨79952301,79952328⟩⟩,⟨⟨(-71267682),(-71267650)⟩,⟨71389042,71389076⟩⟩,⟨⟨(-53629112),(-53629090)⟩,⟨62911594,62911616⟩⟩,⟨⟨(-39754717),(-39754681)⟩,⟨54815279,54815315⟩⟩,⟨⟨(-28940548),(-28940526)⟩,⟨47285250,47285272⟩⟩,⟨⟨(-20595291),(-20595264)⟩,⟨40424790,40424814⟩⟩,⟨⟨(-14226218),(-14226196)⟩,⟨34277834,34277856⟩⟩,⟨⟨(-9426115),(-9426080)⟩,⟨28846464,28846496⟩⟩,⟨⟨(-5861006),(-5860979)⟩,⟨24104458,24104482⟩⟩,⟨⟨(-3259174),(-3259146)⟩,⟨20007466,20007491⟩⟩,⟨⟨(-1401245),(-1401217)⟩,⟨16500693,16500718⟩⟩,⟨⟨(-111551),(-111522)⟩,⟨13524462,13524491⟩⟩,⟨⟨749465,749490⟩,⟨11018106,11018134⟩⟩,⟨⟨1291665,1291687⟩,⟨8922719,8922742⟩⟩,⟨⟨1600779,1600801⟩,⟨7182850,7182872⟩⟩] +lemma kernel25_1_r3_8_eq : ∀ k : Fin 16, kernel25_1Expr 3 8 k = kernel25_1_r3_8 k := by decide +kernel +noncomputable def kernel25_1_r3_9 : Fin 16 → CBox := ![⟨⟨1743033,1743075⟩,⟨5747558,5747597⟩⟩,⟨⟨1769062,1769085⟩,⟨4570960,4570982⟩⟩,⟨⟨1717035,1717060⟩,⟨3612279,3612306⟩⟩,⟨⟨1615392,1615415⟩,⟨2835849,2835871⟩⟩,⟨⟨1484925,1484969⟩,⟨2210744,2210788⟩⟩,⟨⟨1340598,1340621⟩,⟨1710504,1710527⟩⟩,⟨⟨1192786,1192809⟩,⟨1312597,1312620⟩⟩,⟨⟨1048531,1048561⟩,⟨998057,998087⟩⟩,⟨⟨912326,912349⟩,⟨751047,751070⟩⟩,⟨⟨786820,786845⟩,⟨558378,558406⟩⟩,⟨⟨673323,673346⟩,⟨409199,409222⟩⟩,⟨⟨572217,572252⟩,⟨294604,294636⟩⟩,⟨⟨483276,483299⟩,⟨207354,207377⟩⟩,⟨⟨405849,405874⟩,⟨141568,141596⟩⟩,⟨⟨339057,339080⟩,⟨92552,92575⟩⟩,⟨⟨281879,281909⟩,⟨56495,56525⟩⟩] +lemma kernel25_1_r3_9_eq : ∀ k : Fin 16, kernel25_1Expr 3 9 k = kernel25_1_r3_9 k := by decide +kernel +noncomputable def kernel25_1_r3_10 : Fin 16 → CBox := ![⟨⟨233286,233309⟩,⟨30420,30443⟩⟩,⟨⟨192245,192275⟩,⟨11940,11970⟩⟩,⟨⟨157771,157809⟩,⟨(-798),(-760)⟩⟩,⟨⟨128980,129018⟩,⟨(-9257),(-9220)⟩⟩,⟨⟨105048,105076⟩,⟨(-14543),(-14517)⟩⟩,⟨⟨85236,85261⟩,⟨(-17549),(-17521)⟩⟩,⟨⟨68915,68938⟩,⟨(-18909),(-18886)⟩⟩,⟨⟨55503,55541⟩,⟨(-19154),(-19116)⟩⟩,⟨⟨44550,44581⟩,⟨(-18624),(-18594)⟩⟩,⟨⟨35623,35654⟩,⟨(-17613),(-17582)⟩⟩,⟨⟨28374,28413⟩,⟨(-16318),(-16279)⟩⟩,⟨⟨22518,22547⟩,⟨(-14866),(-14841)⟩⟩,⟨⟨17793,17822⟩,⟨(-13383),(-13357)⟩⟩,⟨⟨13999,14025⟩,⟨(-11927),(-11898)⟩⟩,⟨⟨10955,10986⟩,⟨(-10537),(-10506)⟩⟩,⟨⟨8531,8562⟩,⟨(-9250),(-9219)⟩⟩] +lemma kernel25_1_r3_10_eq : ∀ k : Fin 16, kernel25_1Expr 3 10 k = kernel25_1_r3_10 k := by decide +kernel +noncomputable def kernel25_1_r3_11 : Fin 16 → CBox := ![⟨⟨6602,6631⟩,⟨(-8064),(-8038)⟩⟩,⟨⟨5078,5109⟩,⟨(-6998),(-6967)⟩⟩,⟨⟨3880,3903⟩,⟨(-6036),(-6013)⟩⟩,⟨⟨2927,2963⟩,⟨(-5201),(-5167)⟩⟩,⟨⟨2193,2217⟩,⟨(-4454),(-4431)⟩⟩,⟨⟨1613,1639⟩,⟨(-3819),(-3790)⟩⟩,⟨⟨1169,1200⟩,⟨(-3251),(-3220)⟩⟩,⟨⟨830,854⟩,⟨(-2768),(-2744)⟩⟩,⟨⟨565,594⟩,⟨(-2357),(-2330)⟩⟩,⟨⟨373,397⟩,⟨(-1995),(-1971)⟩⟩,⟨⟨217,248⟩,⟨(-1693),(-1661)⟩⟩,⟨⟨109,132⟩,⟨(-1428),(-1404)⟩⟩,⟨⟨28,67⟩,⟨(-1216),(-1177)⟩⟩,⟨⟨(-30),2⟩,⟨(-1027),(-995)⟩⟩,⟨⟨(-62),(-33)⟩,⟨(-865),(-838)⟩⟩,⟨⟨(-97),(-70)⟩,⟨(-731),(-702)⟩⟩] +lemma kernel25_1_r3_11_eq : ∀ k : Fin 16, kernel25_1Expr 3 11 k = kernel25_1_r3_11 k := by decide +kernel +noncomputable def kernel25_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-107),(-83)⟩,⟨(-612),(-588)⟩⟩,⟨⟨(-119),(-92)⟩,⟨(-523),(-494)⟩⟩,⟨⟨(-128),(-97)⟩,⟨(-444),(-413)⟩⟩,⟨⟨(-130),(-99)⟩,⟨(-373),(-342)⟩⟩,⟨⟨(-120),(-96)⟩,⟨(-312),(-288)⟩⟩,⟨⟨(-114),(-82)⟩,⟨(-267),(-235)⟩⟩,⟨⟨(-109),(-77)⟩,⟨(-231),(-200)⟩⟩,⟨⟨(-103),(-72)⟩,⟨(-196),(-164)⟩⟩,⟨⟨(-100),(-61)⟩,⟨(-168),(-128)⟩⟩,⟨⟨(-90),(-66)⟩,⟨(-142),(-118)⟩⟩,⟨⟨(-82),(-58)⟩,⟨(-114),(-90)⟩⟩,⟨⟨(-77),(-50)⟩,⟨(-104),(-75)⟩⟩,⟨⟨(-74),(-45)⟩,⟨(-89),(-62)⟩⟩,⟨⟨(-69),(-44)⟩,⟨(-76),(-52)⟩⟩,⟨⟨(-63),(-36)⟩,⟨(-66),(-37)⟩⟩,⟨⟨(-53),(-29)⟩,⟨(-59),(-34)⟩⟩] +lemma kernel25_1_r3_12_eq : ∀ k : Fin 16, kernel25_1Expr 3 12 k = kernel25_1_r3_12 k := by decide +kernel +noncomputable def kernel25_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-61),(-31)⟩,⟨(-51),(-24)⟩⟩,⟨⟨(-53),(-21)⟩,⟨(-49),(-16)⟩⟩,⟨⟨(-53),(-13)⟩,⟨(-51),(-11)⟩⟩,⟨⟨(-45),(-15)⟩,⟨(-33),(-6)⟩⟩,⟨⟨(-45),(-15)⟩,⟨(-33),(-6)⟩⟩,⟨⟨(-37),(-5)⟩,⟨(-31),1⟩⟩,⟨⟨(-37),(-5)⟩,⟨(-31),1⟩⟩,⟨⟨(-37),(-5)⟩,⟨(-31),1⟩⟩,⟨⟨(-37),3⟩,⟨(-34),6⟩⟩,⟨⟨(-27),3⟩,⟨(-24),4⟩⟩,⟨⟨(-32),6⟩,⟨(-24),11⟩⟩,⟨⟨(-32),6⟩,⟨(-24),11⟩⟩,⟨⟨(-29),(-5)⟩,⟨(-13),12⟩⟩,⟨⟨(-29),(-5)⟩,⟨(-13),12⟩⟩,⟨⟨(-32),16⟩,⟨(-26),22⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩] +lemma kernel25_1_r3_13_eq : ∀ k : Fin 16, kernel25_1Expr 3 13 k = kernel25_1_r3_13 k := by decide +kernel +noncomputable def kernel25_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩] +lemma kernel25_1_r3_14_eq : ∀ k : Fin 16, kernel25_1Expr 3 14 k = kernel25_1_r3_14 k := by decide +kernel +noncomputable def kernel25_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩,⟨⟨(-21),6⟩,⟨(-11),19⟩⟩] +lemma kernel25_1_r3_15_eq : ∀ k : Fin 16, kernel25_1Expr 3 15 k = kernel25_1_r3_15 k := by decide +kernel +noncomputable def kernel25_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel25_1_r3_0,kernel25_1_r3_1,kernel25_1_r3_2,kernel25_1_r3_3,kernel25_1_r3_4,kernel25_1_r3_5,kernel25_1_r3_6,kernel25_1_r3_7,kernel25_1_r3_8,kernel25_1_r3_9,kernel25_1_r3_10,kernel25_1_r3_11,kernel25_1_r3_12,kernel25_1_r3_13,kernel25_1_r3_14,kernel25_1_r3_15] +lemma kernel25_1_r3_eq (i k : Fin 16) : kernel25_1Expr 3 i k = kernel25_1_r3 i k := by + fin_cases i + · exact kernel25_1_r3_0_eq k + · exact kernel25_1_r3_1_eq k + · exact kernel25_1_r3_2_eq k + · exact kernel25_1_r3_3_eq k + · exact kernel25_1_r3_4_eq k + · exact kernel25_1_r3_5_eq k + · exact kernel25_1_r3_6_eq k + · exact kernel25_1_r3_7_eq k + · exact kernel25_1_r3_8_eq k + · exact kernel25_1_r3_9_eq k + · exact kernel25_1_r3_10_eq k + · exact kernel25_1_r3_11_eq k + · exact kernel25_1_r3_12_eq k + · exact kernel25_1_r3_13_eq k + · exact kernel25_1_r3_14_eq k + · exact kernel25_1_r3_15_eq k +noncomputable def kernel25_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-70562131758178844627892),(-70562131758178773915671)⟩,⟨(-93012140214832148668723),(-93012140214832077954878)⟩⟩,⟨⟨(-70569950994102135036908),(-70569950994102064407303)⟩,⟨(-92833801458825117564777),(-92833801458825046933555)⟩⟩,⟨⟨(-70585032820513541929973),(-70585032820513471465448)⟩,⟨(-92477743923236301300966),(-92477743923236230834822)⟩⟩,⟨⟨(-70606270458495286354308),(-70606270458495216136772)⟩,⟨(-91945206541749240280476),(-91945206541749170061339)⟩⟩,⟨⟨(-70632019955385456147702),(-70632019955385386258212)⟩,⟨(-91238045129741429455085),(-91238045129741359564008)⟩⟩,⟨⟨(-70660119464359442932338),(-70660119464359373450863)⟩,⟨(-90358729178879768601486),(-90358729178879699118442)⟩⟩,⟨⟨(-70687914652922012448906),(-70687914652921943454025)⟩,⟨(-89310337414237775682016),(-89310337414237706685589)⟩⟩,⟨⟨(-70712289987583459107448),(-70712289987583390676100)⟩,⟨(-88096551975080022195151),(-88096551975079953762281)⟩⟩,⟨⟨(-70729705581819381549910),(-70729705581819313757183)⟩,⟨(-86721651053127119456145),(-86721651053127051661921)⟩⟩,⟨⟨(-70736239236305925834393),(-70736239236305858753209)⟩,⟨(-85190499799499224684815),(-85190499799499157602176)⟩⟩,⟨⟨(-70727633244850216230193),(-70727633244850149931157)⟩,⟨(-83508539294380005382420),(-83508539294379939081961)⟩⟩,⟨⟨(-70699345486892915905789),(-70699345486892850456922)⟩,⟨(-81681773362383726083349),(-81681773362383660633099)⟩⟩,⟨⟨(-70646604278463885710310),(-70646604278463821176880)⟩,⟨(-79716753012164048253817),(-79716753012163983719046)⟩⟩,⟨⟨(-70564466408561136837560),(-70564466408561073281830)⟩,⟨(-77620558281361583444936),(-77620558281361519887911)⟩⟩,⟨⟨(-70447877747652285859270),(-70447877747652223340452)⟩,⟨(-75400777277794214960813),(-75400777277794152440745)⟩⟩,⟨⟨(-70291735779930484547399),(-70291735779930423121318)⟩,⟨(-73065482224946375239223),(-73065482224946313811945)⟩⟩] +lemma kernel25_1_r4_0_eq : ∀ k : Fin 16, kernel25_1Expr 4 0 k = kernel25_1_r4_0 k := by decide +kernel +noncomputable def kernel25_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-70090953381657872739111),(-70090953381657812458289)⟩,⟨(-70623202344252561302948),(-70623202344252501020981)⟩⟩,⟨⟨(-69840523144953504652327),(-69840523144953445565591)⟩,⟨(-68082893438180161363473),(-68082893438180102275646)⟩⟩,⟨⟨(-69535581530261607560248),(-69535581530261549712930)⟩,⟨(-65453904076322738676307),(-65453904076322680827952)⟩⟩,⟨⟨(-69171472121966131724862),(-69171472121966075158374)⟩,⟨(-62745938331087363998984),(-62745938331087307431511)⟩⟩,⟨⟨(-68743807260644338936188),(-68743807260644283688372)⟩,⟨(-59969015059418709210119),(-59969015059418653961378)⟩⟩,⟨⟨(-68248527332655133833531),(-68248527332655079938068)⟩,⟨(-57133423781527715013452),(-57133423781527661117123)⟩⟩,⟨⟨(-67681957013434911352965),(-67681957013434858839962)⟩,⟨(-54249677265833886361849),(-54249677265833833848039)⟩⟩,⟨⟨(-67040857785226057319655),(-67040857785226006214986)⟩,⟨(-51328460990223536786971),(-51328460990223485681549)⟩⟩,⟨⟨(-66322476083080892700905),(-66322476083080843026952)⟩,⟨(-48380579712110953379499),(-48380579712110903704858)⟩⟩,⟨⟨(-65524586464832498158413),(-65524586464832449933167)⟩,⟨(-45416901442428732194086),(-45416901442428683968209)⟩⟩,⟨⟨(-64645529251133631871249),(-64645529251133585109149)⟩,⟨(-42448299180277387919694),(-42448299180277341157022)⟩⟩,⟨⟨(-63684242140321486234813),(-63684242140321440946220)⟩,⟨(-39485590824214287003940),(-39485590824214241714836)⟩⟩,⟨⟨(-62640285369304268612609),(-62640285369304224804806)⟩,⟨(-36539477731737558283323),(-36539477731737514475066)⟩⟩,⟨⟨(-61513860065266834843809),(-61513860065266792519355)⟩,⟨(-33620482449127141191160),(-33620482449127098866306)⟩⟩,⟨⟨(-60305819512985036817239),(-60305819512984995975573)⟩,⟨(-30738886178201657693053),(-30738886178201616851044)⟩⟩,⟨⟨(-59017673148001453961741),(-59017673148001414598870)⟩,⟨(-27904666583577523331753),(-27904666583577483968586)⟩⟩] +lemma kernel25_1_r4_1_eq : ∀ k : Fin 16, kernel25_1Expr 4 1 k = kernel25_1_r4_1 k := by decide +kernel +noncomputable def kernel25_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-57651583175787592628740),(-57651583175787554738210)⟩,⟨(-25127436572626422849554),(-25127436572626384958785)⟩⟩,⟨⟨(-56210353810109948757657),(-56210353810109912328855)⟩,⟨(-22416384699605550577124),(-22416384699605514148135)⟩⟩,⟨⟨(-54697413218827825080602),(-54697413218827790100851)⟩,⟨(-19780217854628466606397),(-19780217854628431626507)⟩⟩,⟨⟨(-53116788360885423699790),(-53116788360885390149892)⟩,⟨(-17227106896681258614743),(-17227106896681225064754)⟩⟩,⟨⟨(-51473072992856408010560),(-51473072992856375871699)⟩,⟨(-14764635877397031927195),(-14764635877396999788288)⟩⟩,⟨⟨(-49771389215550028763624),(-49771389215549998014173)⟩,⟨(-12399755478624011567241),(-12399755478623980817779)⟩⟩,⟨⟨(-48017343019374296168024),(-48017343019374266785102)⟩,⟨(-10138741252025556835994),(-10138741252025527453101)⟩⟩,⟨⟨(-46216974369870547145344),(-46216974369870519102613)⟩,⟨(-7987157203330652316185),(-7987157203330624273523)⟩⟩,⟨⟨(-44376702450630639099419),(-44376702450630612369840)⟩,⟨(-5949825207937262052198),(-5949825207937235322720)⟩⟩,⟨⟨(-42503266748309146210599),(-42503266748309120764064)⟩,⟨(-4030800679109299975512),(-4030800679109274529111)⟩⟩,⟨⟨(-40603664722387006113245),(-40603664722386981919316)⟩,⟨(-2233354835966006313135),(-2233354835965982119362)⟩⟩,⟨⟨(-38685086849611532016819),(-38685086849611509042398)⟩,⟨(-559963837003667468991),(-559963837003644494751)⟩⟩,⟨⟨(-36754849868683050369546),(-36754849868683028581591)⟩,⟨987695042645280974418,987695042645302762164⟩⟩,⟨⟨(-34820329074029353230931),(-34820329074029332587660)⟩,⟨2408740104129052332644,2408740104129072975690⟩⟩,⟨⟨(-32888890517872028574617),(-32888890517872009036962)⟩,⟨3703074796969681605915,3703074796969701143326⟩⟩,⟨⟨(-30967823976944523899630),(-30967823976944505431261)⟩,⟨4871370275686003884706,4871370275686022352815⟩⟩] +lemma kernel25_1_r4_2_eq : ∀ k : Fin 16, kernel25_1Expr 4 2 k = kernel25_1_r4_2 k := by decide +kernel +noncomputable def kernel25_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-29064277524117981840595),(-29064277524117964406002)⟩,⟨5915041142163174536054,5915041142163191970379⟩⟩,⟨⟨(-27185194516027785184973),(-27185194516027768746558)⟩,⟨6836214668589544303993,6836214668589560742140⟩⟩,⟨⟨(-25337253766025024169885),(-25337253766025008691188)⟩,⟨7637693885382000359815,7637693885382015838242⟩⟩,⟨⟨(-23526813618104204571370),(-23526813618104190014164)⟩,⟨8322915002437083061049,8322915002437097617983⟩⟩,⟨⟨(-21759860572819118373623),(-21759860572819104701283)⟩,⟨8895899708699413565870,8895899708699427237941⟩⟩,⟨⟨(-20041963041749343595825),(-20041963041749330770444)⟩,⟨9361202962992005152790,9361202962992017977904⟩⟩,⟨⟨(-18378230724172592220174),(-18378230724172580205470)⟩,⟨9723856947037565287234,9723856947037577301677⟩⟩,⟨⟨(-16773280009753212929072),(-16773280009753201685287)⟩,⟨9989311898549862234126,9989311898549873477653⟩⟩,⟨⟨(-15231205715930262393208),(-15231205715930251884522)⟩,⟨10163374577349472659809,10163374577349483168246⟩⟩,⟨⟨(-13755559370035073693177),(-13755559370035063883603)⟩,⟨10252145140063758718870,10252145140063768528199⟩⟩,⟨⟨(-12349334145804778889231),(-12349334145804769744723)⟩,⟨10261953208770252526018,10261953208770261670310⟩⟩,⟨⟨(-11014956463722484695894),(-11014956463722476181982)⟩,⟨10199293915864753931898,10199293915864762445625⟩⟩,⟨⟨(-9754284166324844044768),(-9754284166324836128045)⟩,⟨10070764691675337481645,10070764691675345398207⟩⟩,⟨⟨(-8568611085031883321074),(-8568611085031875968477)⟩,⟨9883003533355956556208,9883003533355963908671⟩⟩,⟨⟨(-7458677725831953926246),(-7458677725831947107049)⟩,⟨9642629454080673580608,9642629454080680399687⟩⟩,⟨⟨(-6424687718821909852839),(-6424687718821903535853)⟩,⟨9356185761452880758364,9356185761452887075259⟩⟩] +lemma kernel25_1_r4_3_eq : ∀ k : Fin 16, kernel25_1Expr 4 3 k = kernel25_1_r4_3 k := by decide +kernel +noncomputable def kernel25_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-5466329602517438711600),(-5466329602517432868057)⟩,⟨9030086754479233220922,9030086754479239064393⟩⟩,⟨⟨(-4582803449174228603907),(-4582803449174223204774)⟩,⟨8670568360747456236771,8670568360747461635848⟩⟩,⟨⟨(-3772851783042702367903),(-3772851783042697386362)⟩,⟨8283643161045945971461,8283643161045950952965⟩⟩,⟨⟨(-3034794200227545538019),(-3034794200227540947402)⟩,⟨7875060169133630738748,7875060169133635329339⟩⟩,⟨⟨(-2366565067101984265733),(-2366565067101980041494)⟩,⟨7450269651342594946321,7450269651342599170543⟩⟩,⟨⟨(-1765753654248323236633),(-1765753654248319354253)⟩,⟨7014393185835395965664,7014393185835399848041⟩⟩,⟨⟨(-1229646054623517934903),(-1229646054623514371847)⟩,⟨6572199076296982339641,6572199076296985902701⟩⟩,⟨⟨(-755268237802394232188),(-755268237802390966244)⟩,⟨6128083151224226808043,6128083151224230074003⟩⟩,⟨⟨(-339429606223904971245),(-339429606223901982079)⟩,⟨5686054899308610069372,5686054899308613058557⟩⟩,⟨⟨21233556359741958436,21233556359744691004⟩,⟨5249728815098879015716,5249728815098881748310⟩⟩,⟨⟨330215320458478995874,330215320458481490198⟩,⟨4822320758446168855498,4822320758446171349855⟩⟩,⟨⟨591098564862524739274,591098564862527013337⟩,⟨4406649067271747572530,4406649067271749846629⟩⟩,⟨⟨807515134665911761634,807515134665913838860⟩,⟨4005140106867670564022,4005140106867672641283⟩⟩,⟨⟨983108134241345441742,983108134241347337438⟩,⟨3619837890952761652524,3619837890952763548254⟩⟩,⟨⟨1121496727081455005099,1121496727081456732655⟩,⟨3252417370560956989659,3252417370560958717251⟩⟩,⟨⟨1226243752350809353264,1226243752350810925748⟩,⟨2904200956825121174505,2904200956825122747027⟩⟩] +lemma kernel25_1_r4_4_eq : ∀ k : Fin 16, kernel25_1Expr 4 4 k = kernel25_1_r4_4 k := by decide +kernel +noncomputable def kernel25_1_r4_5 : Fin 16 → CBox := ![⟨⟨1300826404251241897591,1300826404251243326798⟩,⟨2576177822917399953066,2576177822917401382306⟩⟩,⟨⟨1348610156221350171333,1348610156221351468859⟩,⟨2269025518697094594667,2269025518697095892225⟩⟩,⟨⟨1372826048834234789792,1372826048834235966064⟩,⟨1983133428691580794968,1983133428691581971270⟩⟩,⟨⟨1376551399197726542932,1376551399197727608044⟩,⟨1718627609417242740709,1718627609417243805857⟩⟩,⟨⟨1362693931755656465936,1362693931755657428951⟩,⟨1475396555108246251873,1475396555108247214917⟩⟩,⟨⟨1333979276561102340269,1333979276561103210043⟩,⟨1253117460907235131850,1253117460907236001644⟩⟩,⟨⟨1292941732119975640391,1292941732119976424835⟩,⟨1051282578628465522181,1051282578628466306643⟩⟩,⟨⟨1241918146406588296548,1241918146406589003232⟩,⟨869225291400419226805,869225291400419933503⟩⟩,⟨⟨1183044732091918274371,1183044732091918910126⟩,⟨706145568853388317461,706145568853388953223⟩⟩,⟨⟨1118256600699085160926,1118256600699085732271⟩,⟨561134503037954231971,561134503037954803322⟩⟩,⟨⟨1049289775450856043895,1049289775450856556630⟩,⟨433197665946162162535,433197665946162675276⟩⟩,⟨⟨977685423993266733831,977685423993267193582⟩,⟨321277071388818512456,321277071388818972206⟩⟩,⟨⟨904796039821802030375,904796039821802441977⟩,⟨224271566137971385092,224271566137971796700⟩⟩,⟨⟨831793294831725394539,831793294831725762665⟩,⟨141055516817856277254,141055516817856645379⟩⟩,⟨⟨759677284583397437833,759677284583397766616⟩,⟨70495699246625571600,70495699246625900379⟩⟩,⟨⟨689286892147370516295,689286892147370809809⟩,⟨11466335114930016936,11466335114930310448⟩⟩] +lemma kernel25_1_r4_5_eq : ∀ k : Fin 16, kernel25_1Expr 4 5 k = kernel25_1_r4_5 k := by decide +kernel +noncomputable def kernel25_1_r4_6 : Fin 16 → CBox := ![⟨⟨621311005231216278489,621311005231216540102⟩,⟨(-37137743541877604555),(-37137743541877342943)⟩⟩,⟨⟨556300334095910380391,556300334095910613353⟩,⟨(-76389789133603165654),(-76389789133602932694)⟩⟩,⟨⟨494679593915436718373,494679593915436925540⟩,⟨(-107321650578831861749),(-107321650578831654583)⟩⟩,⟨⟨436759834074295947135,436759834074296131185⟩,⟨(-130916035305211347669),(-130916035305211163624)⟩⟩,⟨⟨382750717789954046427,382750717789954209671⟩,⟨(-148100432342328355883),(-148100432342328192641)⟩⟩,⟨⟨332772577763476661940,332772577763476806610⟩,⟨(-159742590045705376613),(-159742590045705231947)⟩⟩,⟨⟨286868096704198484175,286868096704198612331⟩,⟨(-166647428219647352876),(-166647428219647224724)⟩⟩,⟨⟨245013484987373550422,245013484987373663895⟩,⟨(-169555254358606491213),(-169555254358606377744)⟩⟩,⟨⟨207129050882371917801,207129050882372018110⟩,⟨(-169141147207600757711),(-169141147207600657409)⟩⟩,⟨⟨173089081286202686373,173089081286202774968⟩,⟨(-166015367600028769310),(-166015367600028680719)⟩⟩,⟨⟨142730972328941193104,142730972328941271254⟩,⟨(-160724656267904273958),(-160724656267904195811)⟩⟩,⟨⟨115863569265643133670,115863569265643202542⟩,⟨(-153754280703031632327),(-153754280703031563459)⟩⟩,⟨⟨92274693481504221198,92274693481504281806⟩,⟨(-145530697823640356254),(-145530697823640295645)⟩⟩,⟨⟨71737851026552590150,71737851026552643474⟩,⟨(-136424705803976265332),(-136424705803976212011)⟩⟩,⟨⟨54018131738718326714,54018131738718373562⟩,⟨(-126754966587760821148),(-126754966587760774301)⟩⟩,⟨⟨38877320643804117074,38877320643804158200⟩,⟨(-116791789971764533486),(-116791789971764492360)⟩⟩] +lemma kernel25_1_r4_6_eq : ∀ k : Fin 16, kernel25_1Expr 4 6 k = kernel25_1_r4_6 k := by decide +kernel +noncomputable def kernel25_1_r4_7 : Fin 16 → CBox := ![⟨⟨26078253925031855793,26078253925031891853⟩,⟨(-106761080370347374067),(-106761080370347338011)⟩⟩,⟨⟨15388460368084808309,15388460368084839887⟩,⟨(-96848358135430043423),(-96848358135430011841)⟩⟩,⟨⟨6583135885265327418,6583135885265355055⟩,⟨(-87202778316241501935),(-87202778316241474301)⟩⟩,⟨⟨(-552496386192184677),(-552496386192160507)⟩,⟨(-77941080737954462983),(-77941080737954438813)⟩⟩,⟨⟨(-6221384695217083911),(-6221384695217062816)⟩,⟨(-69151416030449680491),(-69151416030449659396)⟩⟩,⟨⟨(-10613348573120044950),(-10613348573120026545)⟩,⟨(-60897002555590118043),(-60897002555590099637)⟩⟩,⟨⟨(-13904222226100780665),(-13904222226100764628)⟩,⟨(-53219578906562499538),(-53219578906562483504)⟩⟩,⟨⟨(-16255384435978092177),(-16255384435978078203)⟩,⟨(-46142625663696690957),(-46142625663696676983)⟩⟩,⟨⟨(-17813619766817921491),(-17813619766817909305)⟩,⟨(-39674338298373926914),(-39674338298373914731)⟩⟩,⟨⟨(-18711258467973701067),(-18711258467973690431)⟩,⟨(-33810340461628790883),(-33810340461628780247)⟩⟩,⟨⟨(-19066545692615494967),(-19066545692615485704)⟩,⟨(-28536133346282860801),(-28536133346282851534)⟩⟩,⟨⟨(-18984194353592698910),(-18984194353592690849)⟩,⟨(-23829282365221624299),(-23829282365221616237)⟩⟩,⟨⟨(-18556079966401538979),(-18556079966401531961)⟩,⟨(-19661347059524505641),(-19661347059524498626)⟩⟩,⟨⟨(-17862040047449962760),(-17862040047449956668)⟩,⟨(-15999563972372442818),(-15999563972372436726)⟩⟩,⟨⟨(-16970744925707120933),(-16970744925707115638)⟩,⟨(-12808295246326995877),(-12808295246326990589)⟩⟩,⟨⟨(-15940611084469050034),(-15940611084469045437)⟩,⟨(-10050257982234443160),(-10050257982234438563)⟩⟩] +lemma kernel25_1_r4_7_eq : ∀ k : Fin 16, kernel25_1Expr 4 7 k = kernel25_1_r4_7 k := by decide +kernel +noncomputable def kernel25_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-14820732291064580393),(-14820732291064576406)⟩,⟨(-7687551005229922589),(-7687551005229918602)⟩⟩,⟨⟨(-13651807725650395251),(-13651807725650391800)⟩,⟨(-5682496689804787184),(-5682496689804783729)⟩⟩,⟨⟨(-12467050030955818876),(-12467050030955815887)⟩,⟨(-3998315976886658311),(-3998315976886655318)⟩⟩,⟨⟨(-11293059632440490549),(-11293059632440487963)⟩,⟨(-2599654746850340904),(-2599654746850338314)⟩⟩,⟨⟨(-10150654795428028944),(-10150654795428026703)⟩,⟨(-1452979367135934479),(-1452979367135932235)⟩⟩,⟨⟨(-9055649676680439804),(-9055649676680437870)⟩,⟨(-526858582246337329),(-526858582246335393)⟩⟩,⟨⟨(-8019575087087443180),(-8019575087087441501)⟩,⟨207851976623811374,207851976623813053⟩⟩,⟨⟨(-7050338812839637007),(-7050338812839635552)⟩,⟨777907454589439233,777907454589440685⟩⟩,⟨⟨(-6152824154968662317),(-6152824154968661060)⟩,⟨1207639594902788457,1207639594902789714⟩⟩,⟨⟨(-5329426857503922580),(-5329426857503921492)⟩,⟨1518977975995526273,1518977975995527361⟩⟩,⟨⟨(-4580531823076173085),(-4580531823076172149)⟩,⟨1731515224944681037,1731515224944681977⟩⟩,⟨⟨(-3904931985030424163),(-3904931985030423342)⟩,⟨1862606072861040432,1862606072861041249⟩⟩,⟨⟨(-3300192442381991154),(-3300192442381990452)⟩,⟨1927491392525210787,1927491392525211493⟩⟩,⟨⟨(-2762963494616270692),(-2762963494616270079)⟩,⟨1939439580900817983,1939439580900818593⟩⟩,⟨⟨(-2289246563881712479),(-2289246563881711958)⟩,⟨1909898801290279601,1909898801290280122⟩⟩,⟨⟨(-1874617188480549459),(-1874617188480548999)⟩,⟨1848654669111044865,1848654669111045322⟩⟩] +lemma kernel25_1_r4_8_eq : ∀ k : Fin 16, kernel25_1Expr 4 8 k = kernel25_1_r4_8 k := by decide +kernel +noncomputable def kernel25_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-1514409338529815916),(-1514409338529815521)⟩,⟨1763988943133102443,1763988943133102838⟩⟩,⟨⟨(-1203865265510725042),(-1203865265510724702)⟩,⟨1662835665857108183,1662835665857108523⟩⟩,⟨⟨(-938254973564695804),(-938254973564695502)⟩,⟨1550931981029011375,1550931981029011676⟩⟩,⟨⟨(-712969211199268648),(-712969211199268391)⟩,⟨1432961544206326038,1432961544206326295⟩⟩,⟨⟨(-523589644752832073),(-523589644752831845)⟩,⟨1312689037037682454,1312689037037682679⟩⟩,⟨⟨(-365939604566852567),(-365939604566852370)⟩,⟨1193084802333561222,1193084802333561419⟩⟩,⟨⟨(-236118504214835979),(-236118504214835804)⟩,⟨1076439041118469247,1076439041118469422⟩⟩,⟨⟨(-130522733165833902),(-130522733165833745)⟩,⟨964465361489905258,964465361489905412⟩⟩,⟨⟨(-45855522811149579),(-45855522811149444)⟩,⟨858393749563068930,858393749563069065⟩⟩,⟨⟨20872008028716262,20872008028716381⟩,⟨759053252537891930,759053252537892049⟩⟩,⟨⟨72346703665359828,72346703665359935⟩,⟨666944830432124620,666944830432124723⟩⟩,⟨⟨110964459156433470,110964459156433561⟩,⟨582304953503346489,582304953503346580⟩⟩,⟨⟨138845132320575686,138845132320575766⟩,⟨505160603692848663,505160603692848743⟩⟩,⟨⟨157850093011269952,157850093011270027⟩,⟨435376386958636601,435376386958636680⟩⟩,⟨⟨169601426268408985,169601426268409055⟩,⟨372694484982142564,372694484982142638⟩⟩,⟨⟨175501987809809623,175501987809809686⟩,⟨316768174717878825,316768174717878888⟩⟩] +lemma kernel25_1_r4_9_eq : ∀ k : Fin 16, kernel25_1Expr 4 9 k = kernel25_1_r4_9 k := by decide +kernel +noncomputable def kernel25_1_r4_10 : Fin 16 → CBox := ![⟨⟨176755670660769351,176755670660769402⟩,⟨267189627300722879,267189627300722927⟩⟩,⟨⟨174387381403176349,174387381403176395⟩,⟨223512668037870268,223512668037870314⟩⟩,⟨⟨169262344740339158,169262344740339206⟩,⟨185271140128936413,185271140128936464⟩⟩,⟨⟨162104457230518365,162104457230518407⟩,⟨151993469376781916,151993469376781962⟩⟩,⟨⟨153513496693529445,153513496693529486⟩,⟨123213977971679612,123213977971679653⟩⟩,⟨⟨143981064563415550,143981064563415591⟩,⟨98481444494326511,98481444494326552⟩⟩,⟨⟨133905195981295350,133905195981295391⟩,⟨77365356221199534,77365356221199575⟩⟩,⟨⟨123603618298404144,123603618298404185⟩,⟨59460249899298881,59460249899298922⟩⟩,⟨⟨113325674424919250,113325674424919282⟩,⟨44388489342198734,44388489342198772⟩⟩,⟨⟨103262954557687470,103262954557687494⟩,⟨31801783172010397,31801783172010421⟩⟩,⟨⟨93558699582227162,93558699582227197⟩,⟨21381704252154919,21381704252154955⟩⟩,⟨⟨84316053084453251,84316053084453279⟩,⟨12839434096129891,12839434096129917⟩⟩,⟨⟨75605247514293713,75605247514293738⟩,⟨5914920918268903,5914920918268932⟩⟩,⟨⟨67469814581145061,67469814581145084⟩,⟨375609014141825,375609014141845⟩⟩,⟨⟨59931911273256776,59931911273256800⟩,⟨(-3985130271477470),(-3985130271477445)⟩⟩,⟨⟨52996851707706986,52996851707707005⟩,⟨(-7349759773083238),(-7349759773083215)⟩⟩] +lemma kernel25_1_r4_10_eq : ∀ k : Fin 16, kernel25_1Expr 4 10 k = kernel25_1_r4_10 k := by decide +kernel +noncomputable def kernel25_1_r4_11 : Fin 16 → CBox := ![⟨⟨46656931955129427,46656931955129450⟩,⟨(-9878444576748363),(-9878444576748343)⟩⟩,⟨⟨40894630565542141,40894630565542169⟩,⟨(-11710959509298020),(-11710959509297994)⟩⟩,⟨⟨35685262181036642,35685262181036662⟩,⟨(-12968583863767652),(-12968583863767629)⟩⟩,⟨⟨30999155710696210,30999155710696239⟩,⟨(-13755944012987052),(-13755944012987026)⟩⟩,⟨⟨26803422345967492,26803422345967522⟩,⟨(-14162775244947388),(-14162775244947358)⟩⟩,⟨⟨23063372433145028,23063372433145059⟩,⟨(-14265582939791436),(-14265582939791405)⟩⟩,⟨⟨19743634063975274,19743634063975298⟩,⟨(-14129190340669583),(-14129190340669563)⟩⟩,⟨⟨16809020322004761,16809020322004791⟩,⟨(-13808165874825945),(-13808165874825915)⟩⟩,⟨⟨14225186520891730,14225186520891748⟩,⟨(-13348127464262551),(-13348127464262533)⟩⟩,⟨⟨11959113551060241,11959113551060262⟩,⟨(-12786924714953154),(-12786924714953126)⟩⟩,⟨⟨9979448648057767,9979448648057797⟩,⟨(-12155702458010969),(-12155702458010939)⟩⟩,⟨⟨8256730525735758,8256730525735777⟩,⟨(-11479850984389906),(-11479850984389888)⟩⟩,⟨⟨6763521880893237,6763521880893261⟩,⟨(-10779849597100255),(-10779849597100231)⟩⟩,⟨⟨5474468762990988,5474468762991018⟩,⟨(-10072010914702539),(-10072010914702508)⟩⟩,⟨⟨4366303194415664,4366303194415689⟩,⟨(-9369133794134561),(-9369133794134537)⟩⟩,⟨⟨3417802699319390,3417802699319415⟩,⟨(-8681072882253207),(-8681072882253182)⟩⟩] +lemma kernel25_1_r4_11_eq : ∀ k : Fin 16, kernel25_1Expr 4 11 k = kernel25_1_r4_11 k := by decide +kernel +noncomputable def kernel25_1_r4_12 : Fin 16 → CBox := ![⟨⟨2609718024414099,2609718024414130⟩,⟨(-8015232723227591),(-8015232723227560)⟩⟩,⟨⟨1924678283408792,1924678283408821⟩,⟨(-7376994100823024),(-7376994100822998)⟩⟩,⟨⟨1347080997483292,1347080997483311⟩,⟨(-6770079928122536),(-6770079928122517)⟩⟩,⟨⟨862973007011751,862973007011782⟩,⟨(-6196867550877831),(-6196867550877800)⟩⟩,⟨⟨459926965402036,459926965402066⟩,⟨(-5658653835312705),(-5658653835312674)⟩⟩,⟨⟨126917066636257,126917066636282⟩,⟨(-5155878891122238),(-5155878891122213)⟩⟩,⟨⟨(-145803222024826),(-145803222024800)⟩,⟨(-4688313754400599),(-4688313754400569)⟩⟩,⟨⟨(-366819375524458),(-366819375524434)⟩,⟨(-4255216837463390),(-4255216837463365)⟩⟩,⟨⟨(-543668519223776),(-543668519223757)⟩,⟨(-3855463453377480),(-3855463453377461)⟩⟩,⟨⟨(-682945651483947),(-682945651483927)⟩,⟨(-3487652249742180),(-3487652249742156)⟩⟩,⟨⟨(-790402782642416),(-790402782642397)⟩,⟨(-3150191943655391),(-3150191943655372)⟩⟩,⟨⟨(-871040691462751),(-871040691462728)⟩,⟨(-2841371340641070),(-2841371340641050)⟩⟩,⟨⟨(-929193231319301),(-929193231319276)⟩,⟨(-2559415245862363),(-2559415245862338)⟩⟩,⟨⟨(-968604293390048),(-968604293390023)⟩,⟨(-2302528536271938),(-2302528536271913)⟩⟩,⟨⟨(-992497663067311),(-992497663067292)⟩,⟨(-2068930356654662),(-2068930356654643)⟩⟩,⟨⟨(-1003640097297563),(-1003640097297544)⟩,⟨(-1856880129366167),(-1856880129366148)⟩⟩] +lemma kernel25_1_r4_12_eq : ∀ k : Fin 16, kernel25_1Expr 4 12 k = kernel25_1_r4_12 k := by decide +kernel +noncomputable def kernel25_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-1004398011972667),(-1004398011972648)⟩,⟨(-1664696825102028),(-1664696825102009)⟩⟩,⟨⟨(-996788206009940),(-996788206009921)⟩,⟨(-1490772728113193),(-1490772728113174)⟩⟩,⟨⟨(-982523067563125),(-982523067563106)⟩,⟨(-1333582741634021),(-1333582741634002)⟩⟩,⟨⟨(-963050712208834),(-963050712208803)⟩,⟨(-1191690115579062),(-1191690115579031)⟩⟩,⟨⟨(-939590496500778),(-939590496500759)⟩,⟨(-1063749336484331),(-1063749336484311)⟩⟩,⟨⟨(-913164335875109),(-913164335875090)⟩,⟨(-948506796982862),(-948506796982843)⟩⟩,⟨⟨(-884624235866351),(-884624235866315)⟩,⟨(-844799756686833),(-844799756686801)⟩⟩,⟨⟨(-854676421829897),(-854676421829878)⟩,⟨(-751554016211693),(-751554016211674)⟩⟩,⟨⟨(-823902426344087),(-823902426344061)⟩,⟨(-667780649378838),(-667780649378808)⟩⟩,⟨⟨(-792777466335620),(-792777466335601)⟩,⟨(-592572073689233),(-592572073689214)⟩⟩,⟨⟨(-761686414620701),(-761686414620680)⟩,⟨(-525097684443982),(-525097684443959)⟩⟩,⟨⟨(-730937643640390),(-730937643640371)⟩,⟨(-464599232023435),(-464599232023416)⟩⟩,⟨⟨(-700774993174174),(-700774993174155)⟩,⟨(-410386083600200),(-410386083600181)⟩⟩,⟨⟨(-671388089076684),(-671388089076653)⟩,⟨(-361830478862227),(-361830478862196)⟩⟩,⟨⟨(-642921216819672),(-642921216819647)⟩,⟨(-318362863203945),(-318362863203919)⟩⟩,⟨⟨(-615480931965489),(-615480931965470)⟩,⟨(-279467360463200),(-279467360463181)⟩⟩] +lemma kernel25_1_r4_13_eq : ∀ k : Fin 16, kernel25_1Expr 4 13 k = kernel25_1_r4_13 k := by decide +kernel +noncomputable def kernel25_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-589142569709490),(-589142569709463)⟩,⟨(-244677429907976),(-244677429907946)⟩⟩,⟨⟨(-563955797314628),(-563955797314600)⟩,⟨(-213571738173648),(-213571738173625)⟩⟩,⟨⟨(-539949336589497),(-539949336589472)⟩,⟨(-185770265669752),(-185770265669727)⟩⟩,⟨⟨(-517134968470232),(-517134968470211)⟩,⟨(-160930658143717),(-160930658143694)⟩⟩,⟨⟨(-495510918177245),(-495510918177219)⟩,⟨(-138744827205092),(-138744827205066)⟩⟩,⟨⟨(-475064707235716),(-475064707235690)⟩,⟨(-118935798333382),(-118935798333357)⟩⟩,⟨⟨(-455775547775197),(-455775547775173)⟩,⟨(-101254800925756),(-101254800925735)⟩⟩,⟨⟨(-437616344853806),(-437616344853780)⟩,⟨(-85478592041806),(-85478592041781)⟩⟩,⟨⟨(-420555363984796),(-420555363984764)⟩,⟨(-71407003465392),(-71407003465360)⟩⟩,⟨⟨(-404557613475972),(-404557613475953)⟩,⟨(-58860700356180),(-58860700356161)⟩⟩,⟨⟨(-389585984529805),(-389585984529786)⟩,⟨(-47679138962788),(-47679138962768)⟩⟩,⟨⟨(-375602186202169),(-375602186202150)⟩,⟨(-37718710496682),(-37718710496662)⟩⟩,⟨⟨(-362567507196060),(-362567507196041)⟩,⟨(-28851058224639),(-28851058224620)⟩⟩,⟨⟨(-350443431993261),(-350443431993241)⟩,⟨(-20961555046555),(-20961555046535)⟩⟩,⟨⟨(-339192134929837),(-339192134929818)⟩,⟨(-13947929221833),(-13947929221814)⟩⟩,⟨⟨(-328776872434124),(-328776872434098)⟩,⟨(-7719026437736),(-7719026437710)⟩⟩] +lemma kernel25_1_r4_14_eq : ∀ k : Fin 16, kernel25_1Expr 4 14 k = kernel25_1_r4_14 k := by decide +kernel +noncomputable def kernel25_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-319162290708146),(-319162290708125)⟩,⟨(-2193697036528),(-2193697036504)⟩⟩,⟨⟨(-310314663591270),(-310314663591240)⟩,⟨2700202098679,2700202098706⟩⟩,⟨⟨(-302202073149319),(-302202073149300)⟩,⟨7026700782147,7026700782166⟩⟩,⟨⟨(-294794543640064),(-294794543640039)⟩,⟨10842512938684,10842512938709⟩⟩,⟨⟨(-288064137877769),(-288064137877743)⟩,⟨14197746511576,14197746511602⟩⟩,⟨⟨(-281985023621303),(-281985023621283)⟩,⟨17136533464934,17136533464953⟩⟩,⟨⟨(-276533516410906),(-276533516410885)⟩,⟨19697586779855,19697586779879⟩⟩,⟨⟨(-271688104251679),(-271688104251660)⟩,⟨21914690667039,21914690667059⟩⟩,⟨⟨(-267429458662942),(-267429458662922)⟩,⟨23817129569664,23817129569683⟩⟩,⟨⟨(-263740435860505),(-263740435860473)⟩,⟨25430060910169,25430060910201⟩⟩,⟨⟨(-260606071195720),(-260606071195700)⟩,⟨26774835943100,26774835943120⟩⟩,⟨⟨(-258013569423384),(-258013569423365)⟩,⟨27869272512917,27869272512936⟩⟩,⟨⟨(-255952292896441),(-255952292896422)⟩,⟨28727882978762,28727882978782⟩⟩,⟨⟨(-254413749375857),(-254413749375832)⟩,⟨29362060054849,29362060054874⟩⟩,⟨⟨(-253391580786835),(-253391580786810)⟩,⟨29780222823570,29780222823595⟩⟩,⟨⟨(-252881553937957),(-252881553937938)⟩,⟨29987924704641,29987924704660⟩⟩] +lemma kernel25_1_r4_15_eq : ∀ k : Fin 16, kernel25_1Expr 4 15 k = kernel25_1_r4_15 k := by decide +kernel +noncomputable def kernel25_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel25_1_r4_0,kernel25_1_r4_1,kernel25_1_r4_2,kernel25_1_r4_3,kernel25_1_r4_4,kernel25_1_r4_5,kernel25_1_r4_6,kernel25_1_r4_7,kernel25_1_r4_8,kernel25_1_r4_9,kernel25_1_r4_10,kernel25_1_r4_11,kernel25_1_r4_12,kernel25_1_r4_13,kernel25_1_r4_14,kernel25_1_r4_15] +lemma kernel25_1_r4_eq (i k : Fin 16) : kernel25_1Expr 4 i k = kernel25_1_r4 i k := by + fin_cases i + · exact kernel25_1_r4_0_eq k + · exact kernel25_1_r4_1_eq k + · exact kernel25_1_r4_2_eq k + · exact kernel25_1_r4_3_eq k + · exact kernel25_1_r4_4_eq k + · exact kernel25_1_r4_5_eq k + · exact kernel25_1_r4_6_eq k + · exact kernel25_1_r4_7_eq k + · exact kernel25_1_r4_8_eq k + · exact kernel25_1_r4_9_eq k + · exact kernel25_1_r4_10_eq k + · exact kernel25_1_r4_11_eq k + · exact kernel25_1_r4_12_eq k + · exact kernel25_1_r4_13_eq k + · exact kernel25_1_r4_14_eq k + · exact kernel25_1_r4_15_eq k +noncomputable def kernel25_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-32685296368000142849802051965),(-32685296368000137147306754964)⟩,⟨(-13741065131691219793238704882),(-13741065131691214090758717980)⟩⟩,⟨⟨(-32671856847954880993567176622),(-32671856847954875293444024961)⟩,⟨(-13703405216944597538334929923),(-13703405216944591838227945183)⟩⟩,⟨⟨(-32644914674009676943423775657),(-32644914674009671248052615909)⟩,⟨(-13628208502133953056313048147),(-13628208502133947360959764822)⟩⟩,⟨⟨(-32604344359771989424266780608),(-32604344359771983736023112606)⟩,⟨(-13515720982396093093541465063),(-13515720982396087405318227500)⟩⟩,⟨⟨(-32549959622928036668724052124),(-32549959622928030989977087181)⟩,⟨(-13366311061534135882964212813),(-13366311061534130204241064647)⟩⟩,⟨⟨(-32481515705145877331858655927),(-32481515705145871664968961351)⟩,⟨(-13180468836081142388407390521),(-13180468836081136721545715204)⟩⟩,⟨⟨(-32398712437297192941792218160),(-32398712437297187289109952103)⟩,⟨(-12958805125514013525514803430),(-12958805125514007872865555123)⟩⟩,⟨⟨(-32301198026139712600765282784),(-32301198026139706964627423934)⟩,⟨(-12702050236020177044555165130),(-12702050236020171408456094593)⟩⟩,⟨⟨(-32188573532799720463431425973),(-32188573532799714846160765571)⟩,⟨(-12411052442607212136997061888),(-12411052442607206519771704693)⟩⟩,⟨⟨(-32060398007704949164964860390),(-32060398007704943568866092337)⟩,⟨(-12086776172081172419066470915),(-12086776172081166823020233964)⟩⟩,⟨⟨(-31916194241070179456455966525),(-31916194241070173883813997548)⟩,⟨(-11730299867562631507942738398),(-11730299867562625935361206560)⟩⟩,⟨⟨(-31755455082661328924323250389),(-31755455082661323376927573580)⟩,⟨(-11342813513814728635019590020),(-11342813513814723087692899716)⟩⟩,⟨⟨(-31577650279391691742689217348),(-31577650279391686222746362133)⟩,⟨(-10925615801772944893578833936),(-10925615801772939373714113268)⟩⟩,⟨⟨(-31382233774372017175845689308),(-31382233774372011685533364293)⟩,⟨(-10480110910333313432930666136),(-10480110910333307942706177952)⟩⟩,⟨⟨(-31168651406382746529699843961),(-31168651406382741071175693765)⟩,⟨(-10007804883707976666104491672),(-10007804883707971207678387462)⟩⟩,⟨⟨(-30936348944403009275105716840),(-30936348944403003850492153034)⟩,⟨(-9510301583519914116609780793),(-9510301583519908692104929129)⟩⟩] +lemma kernel25_1_r5_0_eq : ∀ k : Fin 16, kernel25_1Expr 5 0 k = kernel25_1_r5_0 k := by decide +kernel +noncomputable def kernel25_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-30684780387860269123493097291),(-30684780387860263734892600086)⟩,⟨(-8989298196298904061489276336),(-8989298196298898673008561981)⟩⟩,⟨⟨(-30413416459702099433563230631),(-30413416459702094083033097848)⟩,⟨(-8446580279165641644833773289),(-8446580279165636294434844226)⟩⟩,⟨⟨(-30121753216284165338492131679),(-30121753216284160028070314025)⟩,⟨(-7884016329247958864503037134),(-7884016329247953554224137683)⟩⟩,⟨⟨(-29809320695463605077582422679),(-29809320695463599809254345999)⟩,⟨(-7303551865749764630323012069),(-7303551865749759362149803744)⟩⟩,⟨⟨(-29475691522232205469320666805),(-29475691522232200245055412719)⟩,⟨(-6707203017566880765148303713),(-6707203017566875541050044137)⟩⟩,⟨⟨(-29120489389765855050065171508),(-29120489389765849871764658958)⟩,⟨(-6097049613881302979968535745),(-6097049613881297801847259624)⟩⟩,⟨⟨(-28743397332950838907600275817),(-28743397332950833777153421276)⟩,⟨(-5475227780223212174861058808),(-5475227780223207044605736738)⟩⟩,⟨⟨(-28344165711316030837137688170),(-28344165711316025756339091963)⟩,⟨(-4843922048014889265032559144),(-4843922048014884184437741916)⟩⟩,⟨⟨(-27922619818891625773176866130),(-27922619818891620743814852640)⟩,⟨(-4205356991539428699307428525),(-4205356991539423670161328952)⟩⟩,⟨⟨(-27478667039863606536249476015),(-27478667039863601560035075536)⟩,⟨(-3561788412537488063251209798),(-3561788412537483087264727285)⟩⟩,⟨⟨(-27012303471026611232319365559),(-27012303471026606310963794868)⟩,⟨(-2915494099146412154441062042),(-2915494099146407233325220923)⟩⟩,⟨⟨(-26523619934977226124758967051),(-26523619934977221259871334772)⟩,⟨(-2268764192569390307003595041),(-2268764192569385442367252037)⟩⟩,⟨⟨(-26012807311747901361771681094),(-26012807311747896554970745570)⟩,⟨(-1623891201602597454113167143),(-1623891201602592647574768862)⟩⟩,⟨⟨(-25480161121162583309826868336),(-25480161121162578562455591831)⟩,⟨(-983159711854719953119726915),(-983159711854715206021867467)⟩⟩,⟨⟨(-24926085293592777794841103319),(-24926085293592773108052300507)⟩,⟨(-348835843060791261367624346),(-348835843060786574862693479)⟩⟩,⟨⟨(-24351095072990419400428817983),(-24351095072990414775596323527)⟩,⟨276843485787070028929917528,276843485787074653468562514⟩⟩] +lemma kernel25_1_r5_1_eq : ∀ k : Fin 16, kernel25_1Expr 5 1 k = kernel25_1_r5_1 k := by decide +kernel +noncomputable def kernel25_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-23755819003043621712639502035),(-23755819003043617151172532876)⟩,⟨891681417804842010160348900,891681417804846571324020993⟩⟩,⟨⟨(-23140999955003335647966685759),(-23140999955003331151101998324)⟩,⟨1493532074890887977712801685,1493532074890892474266462322⟩⟩,⟨⟨(-22507495164111296694763460824),(-22507495164111292263785217804)⟩,⟨2080311453594628152470070097,2080311453594632583132848391⟩⟩,⟨⟨(-21856275250558408732744764038),(-21856275250558404368768276629)⟩,⟨2650008219811576415161514490,2650008219811580778818676298⟩⟩,⟨⟨(-21188422210441917190928145142),(-21188422210441912895096415559)⟩,⟨3200694318455230017890669647,3200694318455234313399818252⟩⟩,⟨⟨(-20505126372181792337175587330),(-20505126372181788110219351586)⟩,⟨3730535311636267739037605309,3730535311636271965668630945⟩⟩,⟨⟨(-19807682324203128134894508737),(-19807682324203123977859498721)⟩,⟨4237800357201291597276912942,4237800357201295753984731633⟩⟩,⟨⟨(-19097483830283421903064691355),(-19097483830283417816789746749)⟩,⟨4720871738816263881355698566,4720871738816267967302132269⟩⟩,⟨⟨(-18376017759683718454519829088),(-18376017759683714439943922573)⟩,⟨5178253859180531647634714492,5178253859180535661881466874⟩⟩,⟨⟨(-17644857069905544666059627203),(-17644857069905540723735605930)⟩,⟨5608581609468471156710720937,5608581609468475098705624732⟩⟩,⟨⟨(-16905652890510053556174238760),(-16905652890510049686884023448)⟩,⟨6010628030744492906539207130,6010628030744496775501030533⟩⟩,⟨⟨(-16160125766766314437047955792),(-16160125766766310641331523100)⟩,⟨6383311186894094386032447488,6383311186894098181421904342⟩⟩,⟨⟨(-15410056131824412267685359361),(-15410056131824408546171080293)⟩,⟨6725700173552156044967865049,6725700173552159766157300446⟩⟩,⟨⟨(-14657274085497965907377016640),(-14657274085497962260438165516)⟩,⟨7037020193565141988652226009,7037020193565145635270478197⟩⟩,⟨⟨(-13903648566453909271396269992),(-13903648566453905699544684659)⟩,⟨7316656636653470132929982235,7316656636653473704484952253⟩⟩,⟨⟨(-13151076012513333056820675373),(-13151076012513329560300387083)⟩,⟨7564158109083044402388060117,7564158109083047898635297793⟩⟩] +lemma kernel25_1_r5_2_eq : ∀ k : Fin 16, kernel25_1Expr 5 2 k = kernel25_1_r5_2 k := by decide +kernel +noncomputable def kernel25_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-12401468610740993969585401595),(-12401468610740990548821110169)⟩,⟨7779238368231939945553184947,7779238368231943366067519611⟩⟩,⟨⟨(-11656742244926932762126587896),(-11656742244926929417176796306)⟩,⟨7961777126853490956909415666,7961777126853494301631817114⟩⟩,⟨⟨(-10918804252836973391165828451),(-10918804252836970122288418023)⟩,⟨8111819702478404379944526546,8111819702478407648616538226⟩⟩,⟨⟨(-10189541109138636886054870665),(-10189541109138633693187896774)⟩,⟨8229575498639083253448149163,8229575498639086446131089917⟩⟩,⟨⟨(-9470806152119593623690770263),(-9470806152119590506987495269)⟩,⟨8315415316299048713189463378,8315415316299051829729401920⟩⟩,⟨⟨(-8764407473148858190656991308),(-8764407473148855149874026868)⟩,⟨8369867505878010253379426304,8369867505878013294019037413⟩⟩,⟨⟨(-8072096087246974709485464546),(-8072096087246971744613014588)⟩,⟨8393612982418649153059765212,8393612982418652117808094359⟩⟩,⟨⟨(-7395554501110988812678974967),(-7395554501110985923357161730)⟩,⟨8387479138578009280567586693,8387479138578012169783724287⟩⟩,⟨⟨(-6736385791484594699451493980),(-6736385791484591885581255779)⟩,⟨8352432702074217469681194627,8352432702074220283463384746⟩⟩,⟨⟨(-6096103301896590056495804577),(-6096103301896587317532226832)⟩,⟨8289571595806805012466787336,8289571595806807751359098262⟩⟩,⟨⟨(-5476121059556533039718551402),(-5476121059556530374610553673)⟩,⟨8200115869926841771009427601,8200115869926844436062050807⟩⟩,⟨⟨(-4877745006661684755463570897),(-4877745006661682157751776138)⟩,⟨8085397785496989167993412653,8085397785496991765664690408⟩⟩,⟨⟨(-4302165131621275671076607500),(-4302165131621273140701983111)⟩,⟨7946851138894817341440701519,7946851138894819871788774350⟩⟩,⟨⟨(-3750448575850095040551532178),(-3750448575850092576998640644)⟩,⟨7785999924629381713821311046,7785999924629384177360714420⟩⟩,⟨⟨(-3223533780949087764531925666),(-3223533780949085367595648543)⟩,⟨7604446441628573419320862511,7604446441628575816255806132⟩⟩,⟨⟨(-2722225729418450881927829079),(-2722225729418448551012825176)⟩,⟨7403858954196513131061553437,7403858954196515461986468992⟩⟩] +lemma kernel25_1_r5_3_eq : ∀ k : Fin 16, kernel25_1Expr 5 3 k = kernel25_1_r5_3 k := by decide +kernel +noncomputable def kernel25_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-2247192319695576213696580130),(-2247192319695573948543679929)⟩,⟨7185959023637789497825551576,7185959023637791762998700059⟩⟩,⟨⟨(-1798961903445071564387539178),(-1798961903445069364235579480)⟩,⟨6952508629920326224366281528,6952508629920328424547926392⟩⟩,⟨⟨(-1377921999829319492043367077),(-1377921999829317356481211091)⟩,⟨6705297204644514944759643571,6705297204644517080360030461⟩⟩,⟨⟨(-984319188140278170331356051),(-984319188140276098543568003)⟩,⟨6446128696969358258159833435,6446128696969360329993523862⟩⟩,⟨⟨(-618260166864423266642873579),(-618260166864421258165767651)⟩,⟨6176808793006876246805603531,6176808793006878255335424476⟩⟩,⟨⟨(-279713954170837999928240671),(-279713954170836053802162336)⟩,⟨5899132406548206752185699602,5899132406548208698370472186⟩⟩,⟨⟨31484807857770973890434065,31484807857772858273504906⟩,⟨5614871554866957391061368576,5614871554866959275508284895⟩⟩,⟨⟨315631495011608328370476514,315631495011610152031385201⟩,⟨5325763727819182247687704727,5325763727819184071416809529⟩⟩,⟨⟨573146149839871791241650386,573146149839873554850717810⟩,⟨5033500851609032989253631165,5033500851609034752933102224⟩⟩,⟨⟨804567209124910902428768375,804567209124912607137731814⟩,⟨4739718940519834023640839536,4739718940519835728421415092⟩⟩,⟨⟨1010544390783520409086945003,1010544390783522055722288606⟩,⟨4445988520746342578526203393,4445988520746344225233847314⟩⟩,⟨⟨1191830829205595858459551503,1191830829205597448211553989⟩,⟨4153805900346461759469891869,4153805900346463349294400498⟩⟩,⟨⟨1349274554928607247247928156,1349274554928608780880048563⟩,⟨3864585348415202123262767256,3864585348415203656967148188⟩⟩,⟨⟨1483809420069530765808877822,1483809420069532244732077717⟩,⟨3579652235037270320617709080,3579652235037271799612512489⟩⟩,⟨⟨1596445575034692539608780628,1596445575034693964756818404⟩,⟨3300237171572806357585336947,3300237171572807782803941866⟩⟩,⟨⟨1688259604666719711960776449,1688259604666721084588805709⟩,⟨3027471178554277405549517234,3027471178554278778241974148⟩⟩] +lemma kernel25_1_r5_4_eq : ∀ k : Fin 16, kernel25_1Expr 5 4 k = kernel25_1_r5_4 k := by decide +kernel +noncomputable def kernel25_1_r5_5 : Fin 16 → CBox := ![⟨⟨1760384433154770203216616348,1760384433154771524174426151⟩,⟨2762381896104157720495389168,2762381896104159041509548730⟩⟩,⟨⟨1813999106741654933096225726,1813999106741656203825463658⟩,⟨2505890839504299768010352793,2505890839504301038788310286⟩⟩,⟨⟨1850318561544984164595126892,1850318561544985386373897324⟩,⟨2258811690535853741070534704,2258811690535854962890843808⟩⟩,⟨⟨1870583480727052334082991035,1870583480727053508199640821⟩,⟨2021849603632651387827873084,2021849603632652561979342026⟩⟩,⟨⟨1876050340878774006587812690,1876050340878775133948826206⟩,⟨1795601494910067526087175580,1795601494910068653476749656⟩⟩,⟨⟨1867981741924702587657197685,1867981741924703669667137779⟩,⟨1580557271891287649654610051,1580557271891288731687313301⟩⟩,⟨⟨1847637108224112159447172800,1847637108224113197079263653⟩,⟨1377101952383916588441429890,1377101952383917626090942103⟩⟩,⟨⟨1816263840966970813015863022,1816263840966971807595718013⟩,⟨1185518612574727414096815696,1185518612574728408689199641⟩⟩,⟨⟨1775088993584932394864251364,1775088993584933347333218230⟩,⟨1005992097102712785013791112,1005992097102713737490834398⟩⟩,⟨⟨1725311532866802964898561784,1725311532866803877211608713⟩,⟨838613417713774114683610912,838613417713775027000752931⟩⟩,⟨⟨1668095238941946050494608577,1668095238941946923737706563⟩,⟨683384762146574534192341276,683384762146575407435973124⟩⟩,⟨⟨1604562287433486588101422426,1604562287433487423545926275⟩,⟨540225031179054649657828793,540225031179055485099699231⟩⟩,⟨⟨1535787547045746118488584091,1535787547045746917050479732⟩,⟨408975819288284120899732461,408975819288284919456205863⟩⟩,⟨⟨1462793615794062013183291551,1462793615794062776186271151⟩,⟨289407753131284516961069823,289407753131285279956197309⟩⟩,⟨⟨1386546609161412210266306057,1386546609161412938664314062⟩,⟨181227102009878805833483649,181227102009879534221551985⟩⟩,⟨⟨1307952703818364003020264312,1307952703818364698186873226⟩,⟨84082575588529116626741739,84082575588529811781644731⟩⟩] +lemma kernel25_1_r5_5_eq : ∀ k : Fin 16, kernel25_1Expr 5 5 k = kernel25_1_r5_5 k := by decide +kernel +noncomputable def kernel25_1_r5_6 : Fin 16 → CBox := ![⟨⟨1227855431303647704785853919,1227855431303648367630210812⟩,⟨(-2427773676489157691977409),(-2427773676488494860789651)⟩⟩,⟨⟨1147033707352545708360182297,1147033707352546340155881738⟩,⟨(-78749622747517759115584232),(-78749622747517127334237093)⟩⟩,⟨⟨1066200574485584519601049075,1066200574485585121295306522⟩,⟨(-145365500109643770828617822),(-145365500109643169149264101)⟩⟩,⟨⟨986002628121560079001211352,986002628121560651782941498⟩,⟨(-202788028125563384148520188),(-202788028125562811381908344)⟩⟩,⟨⟨907020089931116526142975703,907020089931117070882265464⟩,⟨(-251553350415211631775938174),(-251553350415211087051821161)⟩⟩,⟨⟨829767486457295060387132737,829767486457295578268730950⟩,⟨(-292214802885338564129319669),(-292214802885338046262809326)⟩⟩,⟨⟨754694886237753486007299796,754694886237753977912743571⟩,⟨(-325336880443000839157564540),(-325336880443000347266999128)⟩⟩,⟨⟨682189644792650281377572922,682189644792650748417486404⟩,⟨(-351489544517784335622323217),(-351489544517783868596971591)⟩⟩,⟨⟨612578603898710634521923540,612578603898711078109879948⟩,⟨(-371242909413502083797991410),(-371242909413501640222935301)⟩⟩,⟨⟨546130689544035954115263631,546130689544036375493249350⟩,⟨(-385162338330561028071010707),(-385162338330560606703956417)⟩⟩,⟨⟨483059851825192041605128359,483059851825192441520842557⟩,⟨(-393803972759009649523500868),(-393803972759009249616898574)⟩⟩,⟨⟨423528289769835171543968412,423528289769835550947017116⟩,⟨(-397710711945940708231002575),(-397710711945940328835394902)⟩⟩,⟨⟨367649904594336575514898618,367649904594336935100266160⟩,⟨(-397408652386991738153512812),(-397408652386991378574060451)⟩⟩,⟨⟨315493926175829580154542011,315493926175829920864069482⟩,⟨(-393403990867540316625944027),(-393403990867539975920947580)⟩⟩,⟨⟨267088659462439406693684805,267088659462439729224920132⟩,⟨(-386180388561038093518183162),(-386180388561037770990231451)⟩⟩,⟨⟨222425300087930613832681461,222425300087930919072223846⟩,⟨(-376196788144094888837943072),(-376196788144094583600568852)⟩⟩] +lemma kernel25_1_r5_6_eq : ∀ k : Fin 16, kernel25_1Expr 5 6 k = kernel25_1_r5_6 k := by decide +kernel +noncomputable def kernel25_1_r5_7 : Fin 16 → CBox := ![⟨⟨181461771516403744147085678,181461771516404032723434966⟩,⟨(-363885670862438911552753685),(-363885670862438622977583082)⟩⟩,⟨⟨144126539534627480740679734,144126539534627753529331569⟩,⟨(-349651736018321195536497366),(-349651736018320922748158053)⟩⟩,⟨⟨110322363748377979663334651,110322363748378237340227632⟩,⟨(-333870981475548953161404863),(-333870981475548695484078748)⟩⟩,⟨⟨79929949839370198438375409,79929949839370441767060408⟩,⟨(-316890160508394671535109121),(-316890160508394428205349296)⟩⟩,⟨⟨52811470617494353157789933,52811470617494582710777292⟩,⟨(-299026587659003927944545262),(-299026587659003698389938708)⟩⟩,⟨⟨28813928278907580666538782,28813928278907797184115537⟩,⟨(-280568264207845235516259870),(-280568264207845018996609103)⟩⟩,⟨⟨7772334678422155616853306,7772334678422359649444611⟩,⟨(-261774292386725526788544812),(-261774292386725322753507655)⟩⟩,⟨⟨(-10487309225463873518424568),(-10487309225463681300341057)⟩,⟨(-242875546548788774299456204),(-242875546548788582078630277)⟩⟩,⟨⟨(-26145249356191442053285653),(-26145249356191261013442810)⟩,⟨(-224075569122061940645917155),(-224075569122061759603127155)⟩⟩,⟨⟨(-39385440468324658861626761),(-39385440468324488321360812)⟩,⟨(-205551659273547670611847445),(-205551659273547500068584473)⟩⟩,⟨⟨(-50393240739565230959113330),(-50393240739565070458700647)⟩,⟨(-187456122755561632434072681),(-187456122755561471930651966)⟩⟩,⟨⟨(-59353342088900448556639833),(-59353342088900297535867762)⟩,⟨(-169917652347132360030425480),(-169917652347132209006667781)⟩⟩,⟨⟨(-66447935998805630937977534),(-66447935998805488983002139)⟩,⟨(-153042809590383114053983184),(-153042809590382972096073971)⟩⟩,⟨⟨(-71855111629635017457084915),(-71855111629634884022393542)⟩,⟨(-136917580103029398517585997),(-136917580103029265080036252)⟩⟩,⟨⟨(-75747480357476485263737667),(-75747480357476359952056146)⟩,⟨(-121608976571250041126436810),(-121608976571249915812179192)⟩⟩,⟨⟨(-78291018552837364127572653),(-78291018552837246462309861)⟩,⟨(-107166665540695661998112668),(-107166665540695544330694670)⟩⟩] +lemma kernel25_1_r5_7_eq : ∀ k : Fin 16, kernel25_1Expr 5 7 k = kernel25_1_r5_7 k := by decide +kernel +noncomputable def kernel25_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-79644118449765297040366392),(-79644118449765186664579645)⟩,⟨(-93624596277333947469562084),(-93624596277333837092004325)⟩⟩,⟨⟨(-79956835330333590999348599),(-79956835330333487402255504)⟩,⟨(-81002612216609229239238346),(-81002612216609125640722357)⟩⟩,⟨⟨(-79370317959179551574576349),(-79370317959179454428823957)⟩,⟨(-69308027814458770243878432),(-69308027814458673097016795)⟩⟩,⟨⟨(-78016408233425668573929114),(-78016408233425577486279067)⟩,⟨(-58537155916097662295533659),(-58537155916097571207054874)⟩⟩,⟨⟨(-76017395347125146182361105),(-76017395347125060861374858)⟩,⟨(-48676773031166525562353070),(-48676773031166440240787215)⟩⟩,⟨⟨(-73485909385230033823820052),(-73485909385229953899540538)⟩,⟨(-39705512114124752357992234),(-39705512114124672433352547)⟩⟩,⟨⟨(-70524939136186611373591561),(-70524939136186536553010232)⟩,⟨(-31595174568423887988465636),(-31595174568423813167715757)⟩⟩,⟨⟨(-67227959018874636649376662),(-67227959018874566601324263)⟩,⟨(-24311955198300862637270348),(-24311955198300792589215116)⟩⟩,⟨⟨(-63679150331719009525270872),(-63679150331718944014895530)⟩,⟨(-17817575703782046635096062),(-17817575703781981124857968)⟩⟩,⟨⟨(-59953702521788225901235816),(-59953702521788164623928621)⟩,⟨(-12070324037863767865282606),(-12070324037863706588230196)⟩⟩,⟨⟨(-56118180811892443394344223),(-56118180811892386116127182)⟩,⟨(-7025998509199531680713292),(-7025998509199474402848626)⟩⟩,⟨⟨(-52230947286931735026776756),(-52230947286931681484318205)⟩,⟨(-2638756912275213916530857),(-2638756912275160374504271)⟩⟩,⟨⟨(-48342623400792589464117299),(-48342623400792539463783496)⟩,⟨1138127803093460969494851,1138127803093510969333533⟩⟩,⟨⟨(-44496582797048132345306603),(-44496582797048085638242255)⟩,⟨4351602749867031317571121,4351602749867078024091701⟩⟩,⟨⟨(-40729464317330354651838573),(-40729464317330311058550714)⟩,⟨7048257740714335275162396,7048257740714378867888882⟩⟩,⟨⟨(-37071696079147570573279970),(-37071696079147529879478227)⟩,⟨9273831139249064611430998,9273831139249105304669108⟩⟩] +lemma kernel25_1_r5_8_eq : ∀ k : Fin 16, kernel25_1Expr 5 8 k = kernel25_1_r5_8 k := by decide +kernel +noncomputable def kernel25_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-33548022520824438207925696),(-33548022520824400260415483)⟩,⟨11072794137587462477593565,11072794137587500424544572⟩⟩,⟨⟨(-30178027318038527406057678),(-30178027318038492006348608)⟩,⟨12488008231677986395012021,12488008231678021794171709⟩⟩,⟨⟨(-26976646059254061517761261),(-26976646059254028521705979)⟩,⟨13560450357472630263072096,13560450357472663258592484⟩⟩,⟨⟨(-23954663513596909010914774),(-23954663513596878249572910)⟩,⟨14328999963138431376627292,14328999963138462137452441⟩⟩,⟨⟨(-21119191223970302665482734),(-21119191223970274015742385)⟩,⟨14830282212846435519439490,14830282212846464168742501⟩⟩,⟨⟨(-18474122002200869796186877),(-18474122002200843102866073)⟩,⟨15098561533607475695610680,15098561533607502388568893⟩⟩,⟨⟨(-16020558685465949537182020),(-16020558685465924686672149)⟩,⟨15165679815493003196708574,15165679815493028046923438⟩⟩,⟨⟨(-13757215229796124180083081),(-13757215229796101039258383)⟩,⟨15061033744930730974867591,15061033744930754115457985⟩⟩,⟨⟨(-11680788864395222331461864),(-11680788864395200804550619)⟩,⟨14811585978554400541270866,14811585978554422068002035⟩⟩,⟨⟨(-9786302608737103107269467),(-9786302608737083071204771)⟩,⟨14441905139851514308983870,14441905139851534344916578⟩⟩,⟨⟨(-8067417963104808300246068),(-8067417963104789666085636)⟩,⟨13974229931848584856288228,13974229931848603490359036⟩⟩,⟨⟨(-6516718023825266131350509),(-6516718023825248795136763)⟩,⟨13428552996380660872372807,13428552996380678208533969⟩⟩,⟨⟨(-5125961649300961520727836),(-5125961649300945407171218)⟩,⟨12822720505089209160126001,12822720505089225273662145⟩⟩,⟨⟨(-3886309615236116049262055),(-3886309615236101063559834)⟩,⟨12172543831102737589578833,12172543831102752575288168⟩⟩,⟨⟨(-2788523951023138338928446),(-2788523951023124412251546)⟩,⟨11491920016265610946219457,11491920016265624872926903⟩⟩,⟨⟨(-1823141848396378343990175),(-1823141848396365331313915)⟩,⟨10792958110643340299583420,10792958110643353312309560⟩⟩] +lemma kernel25_1_r5_9_eq : ∀ k : Fin 16, kernel25_1Expr 5 9 k = kernel25_1_r5_9 k := by decide +kernel +noncomputable def kernel25_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-980625682804924204562834),(-980625682804912051031011)⟩,⟨10086108813640617225293421,10086108813640629378891044⟩⟩,⟨⟨(-251490792330955038875584),(-251490792330943679571954)⟩,⟨9380295185120465125383068,9380295185120476484765441⟩⟩,⟨⟨373587276710203702841958,373587276710214312351597⟩,⟨8683042516963809431238840,8683042516963820040837447⟩⟩,⟨⟨903684319227380275793015,903684319227390189877048⟩,⟨8000605757909208187555915,8000605757909218101736779⟩⟩,⟨⟨1347556078898730507951874,1347556078898739763915787⟩,⟨7338093165342029816591382,7338093165342039072654751⟩⟩,⟨⟨1713582203958324710734759,1713582203958333358762897⟩,⟨6699585115697693975400427,6699585115697702623527984⟩⟩,⟨⟨2009723889989264265299521,2009723889989272340023063⟩,⟨6088247239624145135118894,6088247239624153209940801⟩⟩,⟨⟨2243493614531582968959118,2243493614531590512783267⟩,⟨5506437258841840547129640,5506437258841848091050309⟩⟩,⟨⟨2421935448048826088028392,2421935448048833129373784⟩,⟨4955805089006723282019024,4955805089006730323458383⟩⟩,⟨⟨2551614515824927235424996,2551614515824933813809633⟩,⟨4437385937447463015903970,4437385937447469594379508⟩⟩,⟨⟨2638614282631857518898472,2638614282631863661057729⟩,⟨3951686267332794735462198,3951686267332800877705626⟩⟩,⟨⟨2688540433819154074116893,2688540433819159812891217⟩,⟨3498762621780842454500913,3498762621780848193346637⟩⟩,⟨⟨2706530230475956072862790,2706530230475961430414420⟩,⟨3078293403977611977842543,3078293403977617335453959⟩⟩,⟨⟨2697266320486929153968975,2697266320486934160532235⟩,⟨2689643793976958377318543,2689643793976963383931117⟩⟩,⟨⟨2664994089946937230175890,2664994089946941906255261⟩,⟨2331924051036450424992792,2331924051036455101112043⟩⟩,⟨⟨2613541739116332102848722,2613541739116336473704091⟩,⟨2004041503666028437626584,2004041503666032808513395⟩⟩] +lemma kernel25_1_r5_10_eq : ∀ k : Fin 16, kernel25_1Expr 5 10 k = kernel25_1_r5_10 k := by decide +kernel +noncomputable def kernel25_1_r5_11 : Fin 16 → CBox := ![⟨⟨2546342362766848696995875,2546342362766852779173837⟩,⟨1704746569594141459643705,1704746569594145541845580⟩⟩,⟨⟨2466457405517296098506906,2466457405517299915591304⟩,⟨1432673176126688865597375,1432673176126692682699021⟩⟩,⟨⟨2376600947945562594685421,2376600947945566162187513⟩,⟨1186373969373962131905867,1186373969373965699419333⟩⟩,⟨⟨2279164358447366186154553,2279164358447369523577519⟩,⟨964350709966295223338985,964350709966298560768174⟩⟩,⟨⟨2176240918727216083725550,2176240918727219203637415⟩,⟨765080254502406714614409,765080254502409834528011⟩⟩,⟨⟨2069650097339249704096460,2069650097339252624117377⟩,⟨587036517313005089641625,587036517313008009660399⟩⟩,⟨⟨1960961205859126904982696,1960961205859129637134269⟩,⟨428708797312419877511564,428708797312422609657670⟩⟩,⟨⟨1851516226183315302838555,1851516226183317861734980⟩,⟨288616840784258022015451,288616840784260580903586⟩⟩,⟨⟨1742451645325092549060418,1742451645325094943875851⟩,⟨165322993829038966984410,165322993829041361789221⟩⟩,⟨⟨1634719176181043332695185,1634719176181045577025957⟩,⟨57441778713626895506306,57441778713629139824531⟩⟩,⟨⟨1529105279402181815296166,1529105279402183917940847⟩,⟨(-36352792776126470070949),(-36352792776124367440387)⟩⟩,⟨⟨1426249433080646013604261,1426249433080647986045531⟩,⟨(-117321878043814625907250),(-117321878043812653481356)⟩⟩,⟨⟨1326661123840042043486035,1326661123840043892612384⟩,⟨(-186658166177514949918643),(-186658166177513100808635)⟩⟩,⟨⟨1230735555491079563688496,1230735555491081299633551⟩,⟨(-245483698666835490907684),(-245483698666833754979152)⟩⟩,⟨⟨1138768090083203090720998,1138768090083204719940397⟩,⟨(-294848925166884780854405),(-294848925166883151651458)⟩⟩,⟨⟨1050967451341791178009258,1050967451341792708824561⟩,⟨(-335732792905001561969946),(-335732792905000031170914)⟩⟩] +lemma kernel25_1_r5_11_eq : ∀ k : Fin 16, kernel25_1Expr 5 11 k = kernel25_1_r5_11 k := by decide +kernel +noncomputable def kernel25_1_r5_12 : Fin 16 → CBox := ![⟨⟨967467732512464779085379,967467732512466216430626⟩,⟨(-369043689243682027579205),(-369043689243680590249960)⟩⟩,⟨⟨888339259906498912276996,888339259906500264094667⟩,⟨(-395621076799024634144297),(-395621076799023282342286)⟩⟩,⟨⟨813598370302016447705043,813598370302017719307622⟩,⟨(-416237679239161089811061),(-416237679239159818223740)⟩⟩,⟨⟨743216165130007378843468,743216165130008576473678⟩,⟨(-431602093365290913208585),(-431602093365289715593193)⟩⟩,⟨⟨677126307363655113713170,677126307363656241065248⟩,⟨(-442361719259332791025105),(-442361719259331663687355)⟩⟩,⟨⟨615231928510327446395637,615231928510328509300601⟩,⟨(-449105915147822319403693),(-449105915147821256511655)⟩⟩,⟨⟨557411713328919820292653,557411713328920822248529⟩,⟨(-452369297187919183182833),(-452369297187918181238288)⟩⟩,⟨⟨503525229086908958440475,503525229086909904247233⟩,⟨(-452635116655255785431227),(-452635116655254839634340)⟩⟩,⟨⟨453417564532897845290727,453417564532898737579753⟩,⟨(-450338658048205676233185),(-450338658048204783952691)⟩⟩,⟨⟨406923341469538177110020,406923341469539020438271⟩,⟨(-445870611474837935595594),(-445870611474837092274657)⟩⟩,⟨⟨363870159024200221279240,363870159024201018238393⟩,⟨(-439580381422415434268077),(-439580381422414637315121)⟩⟩,⟨⟨324081527565515246166428,324081527565516000373906⟩,⟨(-431779301696183048353594),(-431779301696182294151305)⟩⟩,⟨⟨287379345818580310102769,287379345818581023536631⟩,⟨(-422743733029654317253692),(-422743733029653603824105)⟩⟩,⟨⟨253585971188185589328427,253585971188186265416510⟩,⟨(-412718025689753856401275),(-412718025689753180316637)⟩⟩,⟨⟨222525929689889669815385,222525929689890310632949⟩,⟨(-401917334404260004849276),(-401917334404259364034409)⟩⟩,⟨⟨194027308280727737283386,194027308280728345830009⟩,⟨(-390530277202037971154197),(-390530277202037362609600)⟩⟩] +lemma kernel25_1_r5_12_eq : ∀ k : Fin 16, kernel25_1Expr 5 12 k = kernel25_1_r5_12 k := by decide +kernel +noncomputable def kernel25_1_r5_13 : Fin 16 → CBox := ![⟨⟨167922868829574692882979,167922868829575270471666⟩,⟨(-378721433352261267537318),(-378721433352260689950051)⟩⟩,⟨⟨144050919515172879874810,144050919515173429197544⟩,⟨(-366633678587742113287363),(-366633678587741563965506)⟩⟩,⟨⟨122255976121157871929149,122255976121158394366704⟩,⟨(-354390358266420179546835),(-354390358266419657109675)⟩⟩,⟨⟨102389242537100916548362,102389242537101414197569⟩,⟨(-342097301126596189271565),(-342097301126595691622318)⟩⟩,⟨⟨84308936790323730866562,84308936790324204734101⟩,⟨(-329844677883791666023715),(-329844677883791192155748)⟩⟩,⟨⟨67880486136505298223707,67880486136505750348818⟩,⟨(-317708710153732513324511),(-317708710153732061198633)⟩⟩,⟨⟨52976612134163297288626,52976612134163728699782⟩,⟨(-305753236115847841756493),(-305753236115847410344270)⟩⟩,⟨⟨39477324220931644978449,39477324220932057302300⟩,⟨(-294031139999259729064655),(-294031139999259316739471)⟩⟩,⟨⟨27269838096658154006959,27269838096658547917167⟩,⟨(-282585652918519397058791),(-282585652918519003147017)⟩⟩,⟨⟨16248433195420320552785,16248433195420697700152⟩,⟨(-271451532845105113244494),(-271451532845104736095361)⟩⟩,⟨⟨6314261689149236887332,6314261689149598060273⟩,⟨(-260656131604726765467922),(-260656131604726404293037)⟩⟩,⟨⟨(-2624880198419590083128),(-2624880198419243598898)⟩,⟨(-250220356767829386657669),(-250220356767829040171338)⟩⟩,⟨⟨(-10654809286536286534266),(-10654809286535954232925)⟩,⟨(-240159536175927564766596),(-240159536175927232463035)⟩⟩,⟨⟨(-17855233001674626377690),(-17855233001674306990030)⟩,⟨(-230484192640913139728978),(-230484192640912820338979)⟩⟩,⟨⟨(-24300040667917297817078),(-24300040667916990789378)⟩,⟨(-221200736086719916918100),(-221200736086719609887975)⟩⟩,⟨⟨(-30057602841229867341067),(-30057602841229571671525)⟩,⟨(-212312080088516715250073),(-212312080088516419578025)⟩⟩] +lemma kernel25_1_r5_13_eq : ∀ k : Fin 16, kernel25_1Expr 5 13 k = kernel25_1_r5_13 k := by decide +kernel +noncomputable def kernel25_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-35191073942135263862017),(-35191073942134979239911)⟩,⟨(-203818189417369444303864),(-203818189417369159679200)⟩⟩,⟨⟨(-39758694264286866563837),(-39758694264286591914894)⟩,⟨(-195716564829373057080580),(-195716564829372782429073)⟩⟩,⟨⟨(-43814088155803542274209),(-43814088155803277190014)⟩,⟨(-188002670957026475299473),(-188002670957026210212727)⟩⟩,⟨⟨(-47406555795711909044394),(-47406555795711652724307)⟩,⟨(-180670312774865149635489),(-180670312774864893312863)⟩⟩,⟨⟨(-50581356528678546012977),(-50581356528678298216029)⟩,⟨(-173711965727376572839572),(-173711965727376325040099)⟩⟩,⟨⟨(-53379982186098265434953),(-53379982186098025326000)⟩,⟨(-167119064230036170238706),(-167119064230035930127245)⟩⟩,⟨⟨(-55840419218645565058280),(-55840419218645332335408)⟩,⟨(-160882252887852251965107),(-160882252887852019239751)⟩⟩,⟨⟨(-57997398802113817600371),(-57997398802113591613771)⟩,⟨(-154991604423098627064779),(-154991604423098401075715)⟩⟩,⟨⟨(-59882634361685268667910),(-59882634361685049291524)⟩,⟨(-149436807967143506184918),(-149436807967143286806091)⟩⟩,⟨⟨(-61525046196034159160080),(-61525046196033945667026)⟩,⟨(-144207331051982052359106),(-144207331051981838863641)⟩⟩,⟨⟨(-62950973077636854156412),(-62950973077636646322525)⟩,⟨(-139292558336213697468228),(-139292558336213489631953)⟩⟩,⟨⟨(-64184370864573474033791),(-64184370864573271322384)⟩,⟨(-134681909818275658229877),(-134681909818275455516102)⟩⟩,⟨⟨(-65246998286664338803527),(-65246998286664141117160)⟩,⟨(-130364941026872621229567),(-130364941026872423540858)⟩⟩,⟨⟨(-66158590169213632085884),(-66158590169213438834437)⟩,⟨(-126331427434545000947524),(-126331427434544807693758)⟩⟩,⟨⟨(-66937018434699115434264),(-66937018434698926449802)⟩,⟨(-122571435114767600789012),(-122571435114767411802264)⟩⟩,⟨⟨(-67598441279795638777525),(-67598441279795453607310)⟩,⟨(-119075379455251828461666),(-119075379455251643289183)⟩⟩] +lemma kernel25_1_r5_14_eq : ∀ k : Fin 16, kernel25_1Expr 5 14 k = kernel25_1_r5_14 k := by decide +kernel +noncomputable def kernel25_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-68157440965107889746684),(-68157440965107708371044)⟩,⟨(-115834073549480439772998),(-115834073549480258395110)⟩⟩,⟨⟨(-68627150680514468091312),(-68627150680514289961660)⟩,⟨(-112838767714073161871351),(-112838767714072983739475)⟩⟩,⟨⟨(-69019370962366578977548),(-69019370962366403965568)⟩,⟨(-110081181420431987980984),(-110081181420431812966796)⟩⟩,⟨⟨(-69344676141921985608533),(-69344676141921813322928)⟩,⟨(-107553528784268896622639),(-107553528784268724334852)⟩⟩,⟨⟨(-69612511299044647567974),(-69612511299044477984201)⟩,⟨(-105248538625074898328617),(-105248538625074728742681)⟩⟩,⟨⟨(-69831280182841019573822),(-69831280182840852233916)⟩,⟨(-103159469988339657028595),(-103159469988339489686539)⟩⟩,⟨⟨(-70008424542800956663201),(-70008424542800791465535)⟩,⟨(-101280123915373957822951),(-101280123915373792623150)⟩⟩,⟨⟨(-70150495291241281483287),(-70150495291241118079669)⟩,⟨(-99604852147938079225763),(-99604852147937915820029)⟩⟩,⟨⟨(-70263215891322820211078),(-70263215891322658608193)⟩,⟨(-98128563366576508319354),(-98128563366576346714377)⟩⟩,⟨⟨(-70351538335389576525641),(-70351538335389416262444)⟩,⟨(-96846727481670990235120),(-96846727481670829969866)⟩⟩,⟨⟨(-70419692046495460205094),(-70419692046495301200455)⟩,⟨(-95755378423848784617628),(-95755378423848625610965)⟩⟩,⟨⟨(-70471226002261641522977),(-70471226002261483461199)⟩,⟨(-94851115814653293741156),(-94851115814653135677376)⟩⟩,⟨⟨(-70509044345071760332766),(-70509044345071603225626)⟩,⟨(-94131105838464726268838),(-94131105838464569159714)⟩⟩,⟨⟨(-70535435706406230457134),(-70535435706406073908703)⟩,⟨(-93593081581745505180657),(-93593081581745348630260)⟩⟩,⟨⟨(-70552096436114664366588),(-70552096436114508302242)⟩,⟨(-93235343055004304527395),(-93235343055004148461091)⟩⟩,⟨⟨(-70560147889843436376201),(-70560147889843280494947)⟩,⟨(-93056757065675873223342),(-93056757065675717340142)⟩⟩] +lemma kernel25_1_r5_15_eq : ∀ k : Fin 16, kernel25_1Expr 5 15 k = kernel25_1_r5_15 k := by decide +kernel +noncomputable def kernel25_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel25_1_r5_0,kernel25_1_r5_1,kernel25_1_r5_2,kernel25_1_r5_3,kernel25_1_r5_4,kernel25_1_r5_5,kernel25_1_r5_6,kernel25_1_r5_7,kernel25_1_r5_8,kernel25_1_r5_9,kernel25_1_r5_10,kernel25_1_r5_11,kernel25_1_r5_12,kernel25_1_r5_13,kernel25_1_r5_14,kernel25_1_r5_15] +lemma kernel25_1_r5_eq (i k : Fin 16) : kernel25_1Expr 5 i k = kernel25_1_r5 i k := by + fin_cases i + · exact kernel25_1_r5_0_eq k + · exact kernel25_1_r5_1_eq k + · exact kernel25_1_r5_2_eq k + · exact kernel25_1_r5_3_eq k + · exact kernel25_1_r5_4_eq k + · exact kernel25_1_r5_5_eq k + · exact kernel25_1_r5_6_eq k + · exact kernel25_1_r5_7_eq k + · exact kernel25_1_r5_8_eq k + · exact kernel25_1_r5_9_eq k + · exact kernel25_1_r5_10_eq k + · exact kernel25_1_r5_11_eq k + · exact kernel25_1_r5_12_eq k + · exact kernel25_1_r5_13_eq k + · exact kernel25_1_r5_14_eq k + · exact kernel25_1_r5_15_eq k +noncomputable def kernel25_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel25_1_r0,kernel25_1_r1,kernel25_1_r2,kernel25_1_r3,kernel25_1_r4,kernel25_1_r5] +lemma kernel25_1_eq (j : Fin 6) (i k : Fin 16) : kernel25_1Expr j i k = kernel25_1 j i k := by + fin_cases j + · exact kernel25_1_r0_eq i k + · exact kernel25_1_r1_eq i k + · exact kernel25_1_r2_eq i k + · exact kernel25_1_r3_eq i k + · exact kernel25_1_r4_eq i k + · exact kernel25_1_r5_eq i k +lemma kernel25_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel25_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(25:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel25_1_eq] + unfold kernel25_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans25_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel27_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans27 j i k) +noncomputable def kernel27_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_0_eq : ∀ k : Fin 16, kernel27_0Expr 0 0 k = kernel27_0_r0_0 k := by decide +kernel +noncomputable def kernel27_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_1_eq : ∀ k : Fin 16, kernel27_0Expr 0 1 k = kernel27_0_r0_1 k := by decide +kernel +noncomputable def kernel27_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_2_eq : ∀ k : Fin 16, kernel27_0Expr 0 2 k = kernel27_0_r0_2 k := by decide +kernel +noncomputable def kernel27_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_3_eq : ∀ k : Fin 16, kernel27_0Expr 0 3 k = kernel27_0_r0_3 k := by decide +kernel +noncomputable def kernel27_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_4_eq : ∀ k : Fin 16, kernel27_0Expr 0 4 k = kernel27_0_r0_4 k := by decide +kernel +noncomputable def kernel27_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_5_eq : ∀ k : Fin 16, kernel27_0Expr 0 5 k = kernel27_0_r0_5 k := by decide +kernel +noncomputable def kernel27_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_6_eq : ∀ k : Fin 16, kernel27_0Expr 0 6 k = kernel27_0_r0_6 k := by decide +kernel +noncomputable def kernel27_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_7_eq : ∀ k : Fin 16, kernel27_0Expr 0 7 k = kernel27_0_r0_7 k := by decide +kernel +noncomputable def kernel27_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_8_eq : ∀ k : Fin 16, kernel27_0Expr 0 8 k = kernel27_0_r0_8 k := by decide +kernel +noncomputable def kernel27_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_9_eq : ∀ k : Fin 16, kernel27_0Expr 0 9 k = kernel27_0_r0_9 k := by decide +kernel +noncomputable def kernel27_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_10_eq : ∀ k : Fin 16, kernel27_0Expr 0 10 k = kernel27_0_r0_10 k := by decide +kernel +noncomputable def kernel27_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r0_11_eq : ∀ k : Fin 16, kernel27_0Expr 0 11 k = kernel27_0_r0_11 k := by decide +kernel +noncomputable def kernel27_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r0_12_eq : ∀ k : Fin 16, kernel27_0Expr 0 12 k = kernel27_0_r0_12 k := by decide +kernel +noncomputable def kernel27_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r0_13_eq : ∀ k : Fin 16, kernel27_0Expr 0 13 k = kernel27_0_r0_13 k := by decide +kernel +noncomputable def kernel27_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r0_14_eq : ∀ k : Fin 16, kernel27_0Expr 0 14 k = kernel27_0_r0_14 k := by decide +kernel +noncomputable def kernel27_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r0_15_eq : ∀ k : Fin 16, kernel27_0Expr 0 15 k = kernel27_0_r0_15 k := by decide +kernel +noncomputable def kernel27_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel27_0_r0_0,kernel27_0_r0_1,kernel27_0_r0_2,kernel27_0_r0_3,kernel27_0_r0_4,kernel27_0_r0_5,kernel27_0_r0_6,kernel27_0_r0_7,kernel27_0_r0_8,kernel27_0_r0_9,kernel27_0_r0_10,kernel27_0_r0_11,kernel27_0_r0_12,kernel27_0_r0_13,kernel27_0_r0_14,kernel27_0_r0_15] +lemma kernel27_0_r0_eq (i k : Fin 16) : kernel27_0Expr 0 i k = kernel27_0_r0 i k := by + fin_cases i + · exact kernel27_0_r0_0_eq k + · exact kernel27_0_r0_1_eq k + · exact kernel27_0_r0_2_eq k + · exact kernel27_0_r0_3_eq k + · exact kernel27_0_r0_4_eq k + · exact kernel27_0_r0_5_eq k + · exact kernel27_0_r0_6_eq k + · exact kernel27_0_r0_7_eq k + · exact kernel27_0_r0_8_eq k + · exact kernel27_0_r0_9_eq k + · exact kernel27_0_r0_10_eq k + · exact kernel27_0_r0_11_eq k + · exact kernel27_0_r0_12_eq k + · exact kernel27_0_r0_13_eq k + · exact kernel27_0_r0_14_eq k + · exact kernel27_0_r0_15_eq k +noncomputable def kernel27_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_0_eq : ∀ k : Fin 16, kernel27_0Expr 1 0 k = kernel27_0_r1_0 k := by decide +kernel +noncomputable def kernel27_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_1_eq : ∀ k : Fin 16, kernel27_0Expr 1 1 k = kernel27_0_r1_1 k := by decide +kernel +noncomputable def kernel27_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_2_eq : ∀ k : Fin 16, kernel27_0Expr 1 2 k = kernel27_0_r1_2 k := by decide +kernel +noncomputable def kernel27_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_3_eq : ∀ k : Fin 16, kernel27_0Expr 1 3 k = kernel27_0_r1_3 k := by decide +kernel +noncomputable def kernel27_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_4_eq : ∀ k : Fin 16, kernel27_0Expr 1 4 k = kernel27_0_r1_4 k := by decide +kernel +noncomputable def kernel27_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_5_eq : ∀ k : Fin 16, kernel27_0Expr 1 5 k = kernel27_0_r1_5 k := by decide +kernel +noncomputable def kernel27_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_6_eq : ∀ k : Fin 16, kernel27_0Expr 1 6 k = kernel27_0_r1_6 k := by decide +kernel +noncomputable def kernel27_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_7_eq : ∀ k : Fin 16, kernel27_0Expr 1 7 k = kernel27_0_r1_7 k := by decide +kernel +noncomputable def kernel27_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_8_eq : ∀ k : Fin 16, kernel27_0Expr 1 8 k = kernel27_0_r1_8 k := by decide +kernel +noncomputable def kernel27_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_9_eq : ∀ k : Fin 16, kernel27_0Expr 1 9 k = kernel27_0_r1_9 k := by decide +kernel +noncomputable def kernel27_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_10_eq : ∀ k : Fin 16, kernel27_0Expr 1 10 k = kernel27_0_r1_10 k := by decide +kernel +noncomputable def kernel27_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_11_eq : ∀ k : Fin 16, kernel27_0Expr 1 11 k = kernel27_0_r1_11 k := by decide +kernel +noncomputable def kernel27_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_12_eq : ∀ k : Fin 16, kernel27_0Expr 1 12 k = kernel27_0_r1_12 k := by decide +kernel +noncomputable def kernel27_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_13_eq : ∀ k : Fin 16, kernel27_0Expr 1 13 k = kernel27_0_r1_13 k := by decide +kernel +noncomputable def kernel27_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_14_eq : ∀ k : Fin 16, kernel27_0Expr 1 14 k = kernel27_0_r1_14 k := by decide +kernel +noncomputable def kernel27_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r1_15_eq : ∀ k : Fin 16, kernel27_0Expr 1 15 k = kernel27_0_r1_15 k := by decide +kernel +noncomputable def kernel27_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel27_0_r1_0,kernel27_0_r1_1,kernel27_0_r1_2,kernel27_0_r1_3,kernel27_0_r1_4,kernel27_0_r1_5,kernel27_0_r1_6,kernel27_0_r1_7,kernel27_0_r1_8,kernel27_0_r1_9,kernel27_0_r1_10,kernel27_0_r1_11,kernel27_0_r1_12,kernel27_0_r1_13,kernel27_0_r1_14,kernel27_0_r1_15] +lemma kernel27_0_r1_eq (i k : Fin 16) : kernel27_0Expr 1 i k = kernel27_0_r1 i k := by + fin_cases i + · exact kernel27_0_r1_0_eq k + · exact kernel27_0_r1_1_eq k + · exact kernel27_0_r1_2_eq k + · exact kernel27_0_r1_3_eq k + · exact kernel27_0_r1_4_eq k + · exact kernel27_0_r1_5_eq k + · exact kernel27_0_r1_6_eq k + · exact kernel27_0_r1_7_eq k + · exact kernel27_0_r1_8_eq k + · exact kernel27_0_r1_9_eq k + · exact kernel27_0_r1_10_eq k + · exact kernel27_0_r1_11_eq k + · exact kernel27_0_r1_12_eq k + · exact kernel27_0_r1_13_eq k + · exact kernel27_0_r1_14_eq k + · exact kernel27_0_r1_15_eq k +noncomputable def kernel27_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_0_eq : ∀ k : Fin 16, kernel27_0Expr 2 0 k = kernel27_0_r2_0 k := by decide +kernel +noncomputable def kernel27_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_1_eq : ∀ k : Fin 16, kernel27_0Expr 2 1 k = kernel27_0_r2_1 k := by decide +kernel +noncomputable def kernel27_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_2_eq : ∀ k : Fin 16, kernel27_0Expr 2 2 k = kernel27_0_r2_2 k := by decide +kernel +noncomputable def kernel27_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_3_eq : ∀ k : Fin 16, kernel27_0Expr 2 3 k = kernel27_0_r2_3 k := by decide +kernel +noncomputable def kernel27_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_4_eq : ∀ k : Fin 16, kernel27_0Expr 2 4 k = kernel27_0_r2_4 k := by decide +kernel +noncomputable def kernel27_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_5_eq : ∀ k : Fin 16, kernel27_0Expr 2 5 k = kernel27_0_r2_5 k := by decide +kernel +noncomputable def kernel27_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_6_eq : ∀ k : Fin 16, kernel27_0Expr 2 6 k = kernel27_0_r2_6 k := by decide +kernel +noncomputable def kernel27_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_7_eq : ∀ k : Fin 16, kernel27_0Expr 2 7 k = kernel27_0_r2_7 k := by decide +kernel +noncomputable def kernel27_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_8_eq : ∀ k : Fin 16, kernel27_0Expr 2 8 k = kernel27_0_r2_8 k := by decide +kernel +noncomputable def kernel27_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_9_eq : ∀ k : Fin 16, kernel27_0Expr 2 9 k = kernel27_0_r2_9 k := by decide +kernel +noncomputable def kernel27_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r2_10_eq : ∀ k : Fin 16, kernel27_0Expr 2 10 k = kernel27_0_r2_10 k := by decide +kernel +noncomputable def kernel27_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r2_11_eq : ∀ k : Fin 16, kernel27_0Expr 2 11 k = kernel27_0_r2_11 k := by decide +kernel +noncomputable def kernel27_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r2_12_eq : ∀ k : Fin 16, kernel27_0Expr 2 12 k = kernel27_0_r2_12 k := by decide +kernel +noncomputable def kernel27_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r2_13_eq : ∀ k : Fin 16, kernel27_0Expr 2 13 k = kernel27_0_r2_13 k := by decide +kernel +noncomputable def kernel27_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r2_14_eq : ∀ k : Fin 16, kernel27_0Expr 2 14 k = kernel27_0_r2_14 k := by decide +kernel +noncomputable def kernel27_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel27_0_r2_15_eq : ∀ k : Fin 16, kernel27_0Expr 2 15 k = kernel27_0_r2_15 k := by decide +kernel +noncomputable def kernel27_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel27_0_r2_0,kernel27_0_r2_1,kernel27_0_r2_2,kernel27_0_r2_3,kernel27_0_r2_4,kernel27_0_r2_5,kernel27_0_r2_6,kernel27_0_r2_7,kernel27_0_r2_8,kernel27_0_r2_9,kernel27_0_r2_10,kernel27_0_r2_11,kernel27_0_r2_12,kernel27_0_r2_13,kernel27_0_r2_14,kernel27_0_r2_15] +lemma kernel27_0_r2_eq (i k : Fin 16) : kernel27_0Expr 2 i k = kernel27_0_r2 i k := by + fin_cases i + · exact kernel27_0_r2_0_eq k + · exact kernel27_0_r2_1_eq k + · exact kernel27_0_r2_2_eq k + · exact kernel27_0_r2_3_eq k + · exact kernel27_0_r2_4_eq k + · exact kernel27_0_r2_5_eq k + · exact kernel27_0_r2_6_eq k + · exact kernel27_0_r2_7_eq k + · exact kernel27_0_r2_8_eq k + · exact kernel27_0_r2_9_eq k + · exact kernel27_0_r2_10_eq k + · exact kernel27_0_r2_11_eq k + · exact kernel27_0_r2_12_eq k + · exact kernel27_0_r2_13_eq k + · exact kernel27_0_r2_14_eq k + · exact kernel27_0_r2_15_eq k +noncomputable def kernel27_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-945552475253),(-945552475249)⟩,⟨2343922409527,2343922409531⟩⟩,⟨⟨(-941003741908),(-941003741904)⟩,⟨2340152462577,2340152462581⟩⟩,⟨⟨(-931947368053),(-931947368050)⟩,⟨2332620704445,2332620704448⟩⟩,⟨⟨(-918465061765),(-918465061762)⟩,⟨2321343555804,2321343555808⟩⟩,⟨⟨(-900678197050),(-900678197045)⟩,⟨2306346014452,2306346014457⟩⟩,⟨⟨(-878746404500),(-878746404496)⟩,⟨2287662078593,2287662078596⟩⟩,⟨⟨(-852865719367),(-852865719364)⟩,⟨2265335283693,2265335283696⟩⟩,⟨⟨(-823266310015),(-823266310011)⟩,⟨2239419330340,2239419330344⟩⟩,⟨⟨(-790209815150),(-790209815146)⟩,⟨2209978776185,2209978776190⟩⟩,⟨⟨(-753986323273),(-753986323269)⟩,⟨2177089761495,2177089761498⟩⟩,⟨⟨(-714911032615),(-714911032610)⟩,⟨2140840735167,2140840735171⟩⟩,⟨⟨(-673320634165),(-673320634161)⟩,⟨2101333146433,2101333146437⟩⟩,⟨⟨(-629569464344),(-629569464341)⟩,⟨2058682066825,2058682066828⟩⟩,⟨⟨(-584025477233),(-584025477228)⟩,⟨2013016707475,2013016707480⟩⟩,⟨⟨(-537066089054),(-537066089051)⟩,⟨1964480798381,1964480798384⟩⟩,⟨⟨(-489073949730),(-489073949725)⟩,⟨1913232798776,1913232798782⟩⟩] +lemma kernel27_0_r3_0_eq : ∀ k : Fin 16, kernel27_0Expr 3 0 k = kernel27_0_r3_0 k := by decide +kernel +noncomputable def kernel27_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-440432697631),(-440432697628)⟩,⟨1859445911433,1859445911436⟩⟩,⟨⟨(-391522754308),(-391522754305)⟩,⟨1803307878023,1803307878027⟩⟩,⟨⟨(-342717215606),(-342717215602)⟩,⟨1745020538037,1745020538042⟩⟩,⟨⟨(-294377894515),(-294377894512)⟩,⟨1684799139450,1684799139453⟩⟩,⟨⟨(-246851568997),(-246851568994)⟩,⟨1622871395730,1622871395733⟩⟩,⟨⟨(-200466485098),(-200466485095)⟩,⟨1559476290362,1559476290365⟩⟩,⟨⟨(-155529161866),(-155529161863)⟩,⟨1494862636705,1494862636708⟩⟩,⟨⟨(-112321539884),(-112321539881)⟩,⟨1429287407704,1429287407707⟩⟩,⟨⟨(-71098509806),(-71098509803)⟩,⟨1363013856227,1363013856230⟩⟩,⟨⟨(-32085851159),(-32085851156)⟩,⟨1296309452774,1296309452777⟩⟩,⟨⟨4521395124,4521395128⟩,⟨1229443672512,1229443672517⟩⟩,⟨⟨38560104131,38560104135⟩,⟨1162685668117,1162685668122⟩⟩,⟨⟨69899785628,69899785632⟩,⟨1096301868475,1096301868478⟩⟩,⟨⟨98442842987,98442842991⟩,⟨1030553545888,1030553545892⟩⟩,⟨⟨124124379141,124124379144⟩,⟨965694395968,965694395972⟩⟩,⟨⟨146911563995,146911563999⟩,⟨901968174699,901968174702⟩⟩] +lemma kernel27_0_r3_1_eq : ∀ k : Fin 16, kernel27_0Expr 3 1 k = kernel27_0_r3_1 k := by decide +kernel +noncomputable def kernel27_0_r3_2 : Fin 16 → CBox := ![⟨⟨166802585027,166802585030⟩,⟨839606436498,839606436501⟩⟩,⟨⟨183825209645,183825209648⟩,⟨778826415179,778826415183⟩⟩,⟨⟨198034994147,198034994150⟩,⟨719829086844,719829086847⟩⟩,⟨⟨209513179506,209513179510⟩,⟨662797449822,662797449827⟩⟩,⟨⟨218364318882,218364318887⟩,⟨607895052095,607895052098⟩⟩,⟨⟨224713685260,224713685265⟩,⟨555264791143,555264791148⟩⟩,⟨⟨228704510184,228704510188⟩,⟨505028005214,505028005218⟩⟩,⟨⟨230495105992,230495105996⟩,⟨457283868549,457283868553⟩⟩,⟨⟨230255924221,230255924224⟩,⟨412109096619,412109096622⟩⟩,⟨⟨228166602042,228166602047⟩,⟨369557960669,369557960673⟩⟩,⟨⟨224413046750,224413046756⟩,⟨329662604564,329662604569⟩⟩,⟨⟨219184605366,219184605370⟩,⟨292433650652,292433650656⟩⟩,⟨⟨212671362704,212671362709⟩,⟨257861075810,257861075813⟩⟩,⟨⟨205061606664,205061606667⟩,⟨225915333759,225915333762⟩⟩,⟨⟨196539494259,196539494262⟩,⟨196548695462,196548695465⟩⟩,⟨⟨187282946228,187282946231⟩,⟨169696775919,169696775922⟩⟩] +lemma kernel27_0_r3_2_eq : ∀ k : Fin 16, kernel27_0Expr 3 2 k = kernel27_0_r3_2 k := by decide +kernel +noncomputable def kernel27_0_r3_3 : Fin 16 → CBox := ![⟨⟨177461792005,177461792008⟩,⟨145280213134,145280213137⟩⟩,⟨⟨167236180587,167236180592⟩,⟨123206463355,123206463360⟩⟩,⟨⟨156755266636,156755266639⟩,⟨103371675934,103371675937⟩⟩,⟨⟨146156175007,146156175010⟩,⟨85662611360,85662611363⟩⟩,⟨⟨135563241164,135563241168⟩,⟨69958567067,69958567071⟩⟩,⟨⟨125087519487,125087519490⟩,⟨56133277373,56133277376⟩⟩,⟨⟨114826546664,114826546667⟩,⟨44056756498,44056756501⟩⟩,⟨⟨104864343119,104864343123⟩,⟨33597056655,33597056660⟩⟩,⟨⟨95271631887,95271631890⟩,⟨24621916835,24621916838⟩⟩,⟨⟨86106251525,86106251528⟩,⟨17000281761,17000281764⟩⟩,⟨⟨77413737632,77413737635⟩,⟨10603674728,10603674731⟩⟩,⟨⟨69228046215,69228046219⟩,⟨5307412151,5307412154⟩⟩,⟨⟨61572391588,61572391593⟩,⟨991651994,991651998⟩⟩,⟨⟨54460171634,54460171637⟩,⟨(-2457727805),(-2457727802)⟩⟩,⟨⟨47895953966,47895953970⟩,⟨(-5148420878),(-5148420873)⟩⟩,⟨⟨41876497890,41876497893⟩,⟨(-7181150414),(-7181150411)⟩⟩] +lemma kernel27_0_r3_3_eq : ∀ k : Fin 16, kernel27_0Expr 3 3 k = kernel27_0_r3_3 k := by decide +kernel +noncomputable def kernel27_0_r3_4 : Fin 16 → CBox := ![⟨⟨36391788772,36391788775⟩,⟨(-8649286962),(-8649286959)⟩⟩,⟨⟨31426063676,31426063679⟩,⟨(-9638616690),(-9638616687)⟩⟩,⟨⟨26958809507,26958809510⟩,⟨(-10227248553),(-10227248550)⟩⟩,⟨⟨22965717587,22965717592⟩,⟨(-10485647083),(-10485647079)⟩⟩,⟨⟨19419581353,19419581356⟩,⟨(-10476776287),(-10476776284)⟩⟩,⟨⟨16291126621,16291126624⟩,⟨(-10256339344),(-10256339341)⟩⟩,⟨⟨13549766630,13549766633⟩,⟨(-9873098502),(-9873098499)⟩⟩,⟨⟨11164276616,11164276621⟩,⟨(-9369259660),(-9369259656)⟩⟩,⟨⟨9103385191,9103385195⟩,⟨(-8780906562),(-8780906558)⟩⟩,⟨⟨7336281879,7336281882⟩,⟨(-8138470296),(-8138470293)⟩⟩,⟨⟨5833042231,5833042234⟩,⟨(-7467220848),(-7467220845)⟩⟩,⟨⟨4564973508,4564973511⟩,⟨(-6787768604),(-6787768601)⟩⟩,⟨⟨3504885353,3504885357⟩,⟨(-6116565135),(-6116565131)⟩⟩,⟨⟨2627290930,2627290936⟩,⟨(-5466393985),(-5466393980)⟩⟩,⟨⟨1908544801,1908544804⟩,⟨(-4846843709),(-4846843706)⟩⟩,⟨⟨1326924361,1326924364⟩,⟨(-4264756842),(-4264756839)⟩⟩] +lemma kernel27_0_r3_4_eq : ∀ k : Fin 16, kernel27_0Expr 3 4 k = kernel27_0_r3_4 k := by decide +kernel +noncomputable def kernel27_0_r3_5 : Fin 16 → CBox := ![⟨⟨862661941,862661945⟩,⟨(-3724649933),(-3724649928)⟩⟩,⟨⟨497934705,497934708⟩,⟨(-3229101132),(-3229101129)⟩⟩,⟨⟨216819395,216819399⟩,⟨(-2779103038),(-2779103033)⟩⟩,⟨⟨5218653,5218656⟩,⟨(-2374379617),(-2374379614)⟩⟩,⟨⟨(-149234742),(-149234739)⟩,⟨(-2013667053),(-2013667050)⟩⟩,⟨⟨(-257289924),(-257289921)⟩,⟨(-1694959100),(-1694959096)⟩⟩,⟨⟨(-328201043),(-328201040)⟩,⟨(-1415718328),(-1415718325)⟩⟩,⟨⟨(-369856809),(-369856806)⟩,⟨(-1173055092),(-1173055089)⟩⟩,⟨⟨(-388912516),(-388912513)⟩,⟨(-963876515),(-963876512)⟩⟩,⟨⟨(-390921210),(-390921207)⟩,⟨(-785008053),(-785008049)⟩⟩,⟨⟨(-380461291),(-380461287)⟩,⟨(-633290361),(-633290358)⟩⟩,⟨⟨(-361258396),(-361258393)⟩,⟨(-505654272),(-505654269)⟩⟩,⟨⟨(-336299974),(-336299970)⟩,⟨(-399176676),(-399176672)⟩⟩,⟨⟨(-307941400),(-307941397)⟩,⟨(-311119998),(-311119995)⟩⟩,⟨⟨(-278002957),(-278002954)⟩,⟨(-238957876),(-238957873)⟩⟩,⟨⟨(-247857297),(-247857294)⟩,⟨(-180389385),(-180389382)⟩⟩] +lemma kernel27_0_r3_5_eq : ∀ k : Fin 16, kernel27_0Expr 3 5 k = kernel27_0_r3_5 k := by decide +kernel +noncomputable def kernel27_0_r3_6 : Fin 16 → CBox := ![⟨⟨(-218507383),(-218507380)⟩,⟨(-133344038),(-133344035)⟩⟩,⟨⟨(-190655075),(-190655072)⟩,⟨(-95979502),(-95979498)⟩⟩,⟨⟨(-164760788),(-164760785)⟩,⟨(-66673762),(-66673759)⟩⟩,⟨⟨(-141094740),(-141094736)⟩,⟨(-44013246),(-44013243)⟩⟩,⟨⟨(-119780427),(-119780423)⟩,⟨(-26778166),(-26778162)⟩⟩,⟨⟨(-100831050),(-100831047)⟩,⟨(-13926160),(-13926157)⟩⟩,⟨⟨(-84179584),(-84179581)⟩,⟨(-4575093),(-4575090)⟩⟩,⟨⟨(-69703262),(-69703259)⟩,⟨2014311,2014315⟩⟩,⟨⟨(-57243159),(-57243156)⟩,⟨6455431,6455434⟩⟩,⟨⟨(-46619572),(-46619569)⟩,⟨9251956,9251959⟩⟩,⟨⟨(-37643836),(-37643833)⟩,⟨10813033,10813037⟩⟩,⟨⟨(-30127139),(-30127135)⟩,⟨11467194,11467198⟩⟩,⟨⟨(-23886887),(-23886884)⟩,⟨11474945,11474948⟩⟩,⟨⟨(-18751062),(-18751059)⟩,⟨11040004,11040007⟩⟩,⟨⟨(-14560992),(-14560987)⟩,⟨10319197,10319201⟩⟩,⟨⟨(-11172870),(-11172864)⟩,⟨9431064,9431069⟩⟩] +lemma kernel27_0_r3_6_eq : ∀ k : Fin 16, kernel27_0Expr 3 6 k = kernel27_0_r3_6 k := by decide +kernel +noncomputable def kernel27_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-8458342),(-8458339)⟩,⟨8463251,8463254⟩⟩,⟨⟨(-6304385),(-6304382)⟩,⟨7478793,7478796⟩⟩,⟨⟨(-4612683),(-4612680)⟩,⟨6521392,6521395⟩⟩,⟨⟨(-3298687),(-3298682)⟩,⟨5619800,5619804⟩⟩,⟨⟨(-2290446),(-2290442)⟩,⟨4791408,4791411⟩⟩,⟨⟨(-1527364),(-1527360)⟩,⟨4045161,4045165⟩⟩,⟨⟨(-958895),(-958892)⟩,⟨3383891,3383894⟩⟩,⟨⟨(-543295),(-543291)⟩,⟨2806141,2806145⟩⟩,⟨⟨(-246411),(-246408)⟩,⟨2307611,2307614⟩⟩,⟨⟨(-40575),(-40572)⟩,⟨1882224,1882228⟩⟩,⟨⟨96406,96409⟩,⟨1522956,1522960⟩⟩,⟨⟨182148,182151⟩,⟨1222416,1222419⟩⟩,⟨⟨230487,230491⟩,⟨973262,973265⟩⟩,⟨⟨252158,252161⟩,⟨768492,768495⟩⟩,⟨⟨255387,255391⟩,⟨601608,601611⟩⟩,⟨⟨246387,246391⟩,⟨466722,466725⟩⟩] +lemma kernel27_0_r3_7_eq : ∀ k : Fin 16, kernel27_0Expr 3 7 k = kernel27_0_r3_7 k := by decide +kernel +noncomputable def kernel27_0_r3_8 : Fin 16 → CBox := ![⟨⟨229773,229776⟩,⟨358592,358596⟩⟩,⟨⟨208904,208908⟩,⟨272630,272633⟩⟩,⟨⟨186171,186175⟩,⟨204869,204874⟩⟩,⟨⟨163220,163223⟩,⟨151925,151929⟩⟩,⟨⟨141137,141141⟩,⟨110939,110943⟩⟩,⟨⟨120592,120596⟩,⟨79524,79528⟩⟩,⟨⟨101957,101960⟩,⟨55704,55707⟩⟩,⟨⟨85384,85389⟩,⟨37855,37860⟩⟩,⟨⟨70887,70890⟩,⟨24667,24671⟩⟩,⟨⟨58377,58381⟩,⟨15074,15077⟩⟩,⟨⟨47710,47713⟩,⟨8229,8232⟩⟩,⟨⟨38711,38714⟩,⟨3463,3466⟩⟩,⟨⟨31191,31194⟩,⟨248,251⟩⟩,⟨⟨24959,24963⟩,⟨(-1826),(-1822)⟩⟩,⟨⟨19840,19843⟩,⟨(-3072),(-3068)⟩⟩,⟨⟨15662,15666⟩,⟨(-3732),(-3727)⟩⟩] +lemma kernel27_0_r3_8_eq : ∀ k : Fin 16, kernel27_0Expr 3 8 k = kernel27_0_r3_8 k := by decide +kernel +noncomputable def kernel27_0_r3_9 : Fin 16 → CBox := ![⟨⟨12282,12286⟩,⟨(-3986),(-3982)⟩⟩,⟨⟨9563,9567⟩,⟨(-3969),(-3965)⟩⟩,⟨⟨7392,7396⟩,⟨(-3779),(-3774)⟩⟩,⟨⟨5671,5674⟩,⟨(-3486),(-3482)⟩⟩,⟨⟨4314,4317⟩,⟨(-3143),(-3139)⟩⟩,⟨⟨3252,3256⟩,⟨(-2781),(-2778)⟩⟩,⟨⟨2428,2431⟩,⟨(-2426),(-2423)⟩⟩,⟨⟨1791,1795⟩,⟨(-2091),(-2086)⟩⟩,⟨⟨1305,1308⟩,⟨(-1781),(-1778)⟩⟩,⟨⟨936,939⟩,⟨(-1505),(-1502)⟩⟩,⟨⟨656,661⟩,⟨(-1262),(-1258)⟩⟩,⟨⟨450,453⟩,⟨(-1051),(-1047)⟩⟩,⟨⟨297,300⟩,⟨(-868),(-864)⟩⟩,⟨⟨186,189⟩,⟨(-714),(-710)⟩⟩,⟨⟨107,111⟩,⟨(-583),(-579)⟩⟩,⟨⟨52,55⟩,⟨(-475),(-471)⟩⟩] +lemma kernel27_0_r3_9_eq : ∀ k : Fin 16, kernel27_0Expr 3 9 k = kernel27_0_r3_9 k := by decide +kernel +noncomputable def kernel27_0_r3_10 : Fin 16 → CBox := ![⟨⟨13,16⟩,⟨(-384),(-381)⟩⟩,⟨⟨(-13),(-8)⟩,⟨(-310),(-305)⟩⟩,⟨⟨(-27),(-24)⟩,⟨(-249),(-246)⟩⟩,⟨⟨(-37),(-33)⟩,⟨(-198),(-195)⟩⟩,⟨⟨(-41),(-37)⟩,⟨(-158),(-154)⟩⟩,⟨⟨(-42),(-39)⟩,⟨(-125),(-122)⟩⟩,⟨⟨(-40),(-37)⟩,⟨(-99),(-96)⟩⟩,⟨⟨(-39),(-34)⟩,⟨(-78),(-74)⟩⟩,⟨⟨(-36),(-32)⟩,⟨(-61),(-57)⟩⟩,⟨⟨(-33),(-29)⟩,⟨(-48),(-45)⟩⟩,⟨⟨(-29),(-26)⟩,⟨(-38),(-34)⟩⟩,⟨⟨(-26),(-22)⟩,⟨(-30),(-26)⟩⟩,⟨⟨(-23),(-19)⟩,⟨(-23),(-19)⟩⟩,⟨⟨(-19),(-16)⟩,⟨(-18),(-14)⟩⟩,⟨⟨(-17),(-13)⟩,⟨(-14),(-9)⟩⟩,⟨⟨(-15),(-10)⟩,⟨(-11),(-6)⟩⟩] +lemma kernel27_0_r3_10_eq : ∀ k : Fin 16, kernel27_0Expr 3 10 k = kernel27_0_r3_10 k := by decide +kernel +noncomputable def kernel27_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-12),(-8)⟩,⟨(-8),(-5)⟩⟩,⟨⟨(-11),(-7)⟩,⟨(-7),(-3)⟩⟩,⟨⟨(-10),(-6)⟩,⟨(-5),(-2)⟩⟩,⟨⟨(-9),(-5)⟩,⟨(-4),(-1)⟩⟩,⟨⟨(-8),(-3)⟩,⟨(-4),1⟩⟩,⟨⟨(-6),(-3)⟩,⟨(-4),0⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-2),1⟩⟩,⟨⟨(-5),(-2)⟩,⟨(-2),1⟩⟩,⟨⟨(-5),(-1)⟩,⟨(-2),3⟩⟩,⟨⟨(-4),0⟩,⟨(-2),3⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩] +lemma kernel27_0_r3_11_eq : ∀ k : Fin 16, kernel27_0Expr 3 11 k = kernel27_0_r3_11 k := by decide +kernel +noncomputable def kernel27_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),0⟩,⟨(-2),2⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),2⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r3_12_eq : ∀ k : Fin 16, kernel27_0Expr 3 12 k = kernel27_0_r3_12 k := by decide +kernel +noncomputable def kernel27_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-2),3⟩,⟨(-2),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r3_13_eq : ∀ k : Fin 16, kernel27_0Expr 3 13 k = kernel27_0_r3_13 k := by decide +kernel +noncomputable def kernel27_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r3_14_eq : ∀ k : Fin 16, kernel27_0Expr 3 14 k = kernel27_0_r3_14 k := by decide +kernel +noncomputable def kernel27_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel27_0_r3_15_eq : ∀ k : Fin 16, kernel27_0Expr 3 15 k = kernel27_0_r3_15 k := by decide +kernel +noncomputable def kernel27_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel27_0_r3_0,kernel27_0_r3_1,kernel27_0_r3_2,kernel27_0_r3_3,kernel27_0_r3_4,kernel27_0_r3_5,kernel27_0_r3_6,kernel27_0_r3_7,kernel27_0_r3_8,kernel27_0_r3_9,kernel27_0_r3_10,kernel27_0_r3_11,kernel27_0_r3_12,kernel27_0_r3_13,kernel27_0_r3_14,kernel27_0_r3_15] +lemma kernel27_0_r3_eq (i k : Fin 16) : kernel27_0Expr 3 i k = kernel27_0_r3 i k := by + fin_cases i + · exact kernel27_0_r3_0_eq k + · exact kernel27_0_r3_1_eq k + · exact kernel27_0_r3_2_eq k + · exact kernel27_0_r3_3_eq k + · exact kernel27_0_r3_4_eq k + · exact kernel27_0_r3_5_eq k + · exact kernel27_0_r3_6_eq k + · exact kernel27_0_r3_7_eq k + · exact kernel27_0_r3_8_eq k + · exact kernel27_0_r3_9_eq k + · exact kernel27_0_r3_10_eq k + · exact kernel27_0_r3_11_eq k + · exact kernel27_0_r3_12_eq k + · exact kernel27_0_r3_13_eq k + · exact kernel27_0_r3_14_eq k + · exact kernel27_0_r3_15_eq k +noncomputable def kernel27_0_r4_0 : Fin 16 → CBox := ![⟨⟨(-4914556692000333723038),(-4914556692000326682919)⟩,⟨(-4822031132464135001833),(-4822031132464127961648)⟩⟩,⟨⟨(-4913280562691399929797),(-4913280562691392898792)⟩,⟨(-4810713316940196149274),(-4810713316940189118203)⟩⟩,⟨⟨(-4910697515213254761497),(-4910697515213247748697)⟩,⟨(-4788126168767738944277),(-4788126168767731931412)⟩⟩,⟨⟨(-4906746435497192338867),(-4906746435497185353295)⟩,⟨(-4754366494610866373468),(-4754366494610859387830)⟩⟩,⟨⟨(-4901336805967537260962),(-4901336805967530311538)⟩,⟨(-4709579104759785808269),(-4709579104759778858780)⟩⟩,⟨⟨(-4894350074138183615883),(-4894350074138176711392)⟩,⟨(-4653956327993859730798),(-4653956327993852826244)⟩⟩,⟨⟨(-4885641451497495186969),(-4885641451497488336028)⟩,⟨(-4587737355819838762856),(-4587737355819831911853)⟩⟩,⟨⟨(-4875042120773274813476),(-4875042120773268024497)⟩,⟨(-4511207408914634895440),(-4511207408914628106402)⟩⟩,⟨⟨(-4862361824569548808383),(-4862361824569542089554)⟩,⟨(-4424696717382349184472),(-4424696717382342465584)⟩⟩,⟨⟨(-4847391803520055560959),(-4847391803520048920206)⟩,⟨(-4328579305577986462084),(-4328579305577979821274)⟩⟩,⟨⟨(-4829908047561483978348),(-4829908047561477423311)⟩,⟨(-4223271571808631744175),(-4223271571808625189084)⟩⟩,⟨⟨(-4809674819744783877683),(-4809674819744777415690)⟩,⟨(-4109230653240168056483),(-4109230653240161594438)⟩⟩,⟨⟨(-4786448408227214658727),(-4786448408227208296771)⟩,⟨(-3986952566846103786556),(-3986952566846097424551)⟩⟩,⟨⟨(-4759981058772492096751),(-4759981058772485841464)⟩,⟨(-3856970118254860984156),(-3856970118254854728821)⟩⟩,⟨⟨(-4730025037281392264147),(-4730025037281386121786)⟩,⟨(-3719850571890196819422),(-3719850571890190677017)⟩⟩,⟨⟨(-4696336769628302994176),(-4696336769628296970602)⟩,⟨(-3576193077850153934832),(-3576193077850147911217)⟩⟩] +lemma kernel27_0_r4_0_eq : ∀ k : Fin 16, kernel27_0Expr 4 0 k = kernel27_0_r4_0 k := by decide +kernel +noncomputable def kernel27_0_r4_1 : Fin 16 → CBox := ![⟨⟨(-4658681004435235896287),(-4658681004435229996960)⟩,⟨(-3426625853513312238880),(-3426625853513306339515)⟩⟩,⟨⟨(-4616834943414365468753),(-4616834943414359698692)⟩,⟨(-3271803120863828970345),(-3271803120863823200248)⟩⟩,⟨⟨(-4570592283588627530760),(-4570592283588621894566)⟩,⟨(-3112401803942268171741),(-3112401803942262535515)⟩⟩,⟨⟨(-4519767116086214543527),(-4519767116086209045344)⟩,⟨(-2949117994598422543575),(-2949117994598417045363)⟩⟩,⟨⟨(-4464197627320210538740),(-4464197627320205182285)⟩,⟨(-2782663198774480482470),(-2782663198774475125989)⟩⟩,⟨⟨(-4403749550221515066436),(-4403749550221509854943)⟩,⟨(-2613760379800865265654),(-2613760379800860054138)⟩⟩,⟨⟨(-4338319315794033240044),(-4338319315794028176327)⟩,⟨(-2443139819552888228672),(-2443139819552883164936)⟩⟩,⟨⟨(-4267836858597283764226),(-4267836858597278850615)⟩,⟨(-2271534822696954806521),(-2271534822696949892893)⟩⟩,⟨⟨(-4192268033812679737521),(-4192268033812674975935)⟩,⟨(-2099677293548325650826),(-2099677293548320889226)⟩⟩,⟨⟨(-4111616608282855304602),(-4111616608282850696465)⟩,⟨(-1928293219163407039722),(-1928293219163402431576)⟩⟩,⟨⟨(-4025925793282734825479),(-4025925793282730371811)⟩,⟨(-1758098096092796820402),(-1758098096092792366727)⟩⟩,⟨⟨(-3935279292727740401631),(-3935279292727736102994)⟩,⟨(-1589792341623422251541),(-1589792341623417952900)⟩⟩,⟨⟨(-3839801846976948086836),(-3839801846976943943440)⟩,⟨(-1424056733240189364180),(-1424056733240185220782)⟩⟩,⟨⟨(-3739659259263165011812),(-3739659259263161023356)⟩,⟨(-1261547922347795547259),(-1261547922347791558804)⟩⟩,⟨⟨(-3635057898982403209806),(-3635057898982399375645)⟩,⟨(-1102894069929429285072),(-1102894069929425450916)⟩⟩,⟨⟨(-3526243683496447218980),(-3526243683496443538098)⟩,⟨(-948690652710522031064),(-948690652710518350189)⟩⟩] +lemma kernel27_0_r4_1_eq : ∀ k : Fin 16, kernel27_0Expr 4 1 k = kernel27_0_r4_1 k := by decide +kernel +noncomputable def kernel27_0_r4_2 : Fin 16 → CBox := ![⟨⟨(-3413500547629871035448),(-3413500547629867506546)⟩,⟨(-799496488486017473033),(-799496488486013944140)⟩⟩,⟨⟨(-3297148417555902755949),(-3297148417555899377307)⟩,⟨(-655830028518098984758),(-655830028518095606126)⟩⟩,⟨⟨(-3177540713138312846961),(-3177540713138309616621)⟩,⟨(-518165963294653121489),(-518165963294649891163)⟩⟩,⟨⟨(-3055061409901194313197),(-3055061409901191228572)⟩,⟨(-386932185452173566441),(-386932185452170481831)⟩⟩,⟨⟨(-2930121698507742732869),(-2930121698507739791381)⟩,⟨(-262507150324848042686),(-262507150324845101215)⟩⟩,⟨⟨(-2803156285818775923914),(-2803156285818773122709)⟩,⟨(-145217670418333181916),(-145217670418330380730)⟩⟩,⟨⟨(-2674619387153639793674),(-2674619387153637129770)⟩,⟨(-35337175175727820350),(-35337175175725156466)⟩⟩,⟨⟨(-2544980464181067277981),(-2544980464181064748072)⟩,⟨66915538223251537425,66915538223254067313⟩⟩,⟨⟨(-2414719766827815385022),(-2414719766827812985730)⟩,⟨161377043521111773968,161377043521114173238⟩⟩,⟨⟨(-2284323740624973263899),(-2284323740624970991569)⟩,⟨247939500722904073914,247939500722906346221⟩⟩,⟨⟨(-2154280362948647144036),(-2154280362948644994988)⟩,⟨326550342454271069552,326550342454273218576⟩⟩,⟨⟨(-2025074472604677822760),(-2025074472604675793083)⟩,⟨397211433036029258913,397211433036031288566⟩⟩,⟨⟨(-1897183157127584567157),(-1897183157127582652961)⟩,⟨459977709447272653304,459977709447274567476⟩⟩,⟨⟨(-1771071261004719849346),(-1771071261004718045989)⟩,⟨514955320788355108339,514955320788356911672⟩⟩,⟨⟨(-1647187075812193671916),(-1647187075812191975022)⟩,⟨562299290114358541146,562299290114360238015⟩⟩,⟨⟨(-1525958269996005405440),(-1525958269996003810902)⟩,⟨602210729444044394701,602210729444045989214⟩⟩] +lemma kernel27_0_r4_2_eq : ∀ k : Fin 16, kernel27_0Expr 4 2 k = kernel27_0_r4_2 k := by decide +kernel +noncomputable def kernel27_0_r4_3 : Fin 16 → CBox := ![⟨⟨(-1407788111808085507681),(-1407788111808084011488)⟩,⟨634933645219156308392,634933645219157804560⟩⟩,⟨⟨(-1293052033791253283387),(-1293052033791251881378)⟩,⟨660751377363137594202,660751377363138996189⟩⟩,⟨⟨(-1182094581297139434841),(-1182094581297138122983)⟩,⟨679982720247454347539,679982720247455659377⟩⟩,⟨⟨(-1075226780931608395293),(-1075226780931607169443)⟩,⟨692977778213136162197,692977778213137388030⟩⟩,⟨⟨(-972723957682350299283),(-972723957682349155469)⟩,⟨700113611727622037293,700113611727623181091⟩⟩,⟨⟨(-874824021933892574238),(-874824021933891508423)⟩,⟨701789732714899988153,701789732714901053954⟩⟩,⟨⟨(-781726239765458677636),(-781726239765457685961)⟩,⟨698423509033950598026,698423509033951589688⟩⟩,⟨⟨(-693590492010907122454),(-693590492010906200820)⟩,⟨690445538472831038074,690445538472831959699⟩⟩,⟨⟨(-610537019692704503570),(-610537019692703648246)⟩,⟨678295051972614930767,678295051972615786083⟩⟩,⟨⟨(-532646645776398482380),(-532646645776397689666)⟩,⟨662415404119115837020,662415404119116629726⟩⟩,⟨⟨(-459961455875220227902),(-459961455875219494307)⟩,⟨643249706285542902957,643249706285543636546⟩⟩,⟨⟨(-392485913703658340394),(-392485913703657662439)⟩,⟨621236654241805177700,621236654241805855652⟩⟩,⟨⟨(-330188380858858765299),(-330188380858858139637)⟩,⟨596806597651315106198,596806597651315731859⟩⟩,⟨⟨(-273003005008787697797),(-273003005008787121157)⟩,⟨570377893756154652561,570377893756155229200⟩⟩,⟨⟨(-220831935877631955754),(-220831935877631425097)⟩,⟨542353581823047680849,542353581823048211506⟩⟩,⟨⟨(-173547824613495763858),(-173547824613495276157)⟩,⟨513118408713722776350,513118408713723264051⟩⟩] +lemma kernel27_0_r4_3_eq : ∀ k : Fin 16, kernel27_0Expr 4 3 k = kernel27_0_r4_3 k := by decide +kernel +noncomputable def kernel27_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-130996559251522123599),(-130996559251521676062)⟩,⟨483036229389919815459,483036229389920262998⟩⟩,⟨⟨(-93000187075623114682),(-93000187075622704542)⟩,⟨452447799405944420894,452447799405944831036⟩⟩,⟨⟨(-59359973740426364113),(-59359973740425988815)⟩,⟨421668969621698202675,421668969621698577975⟩⟩,⟨⟨(-29859549026495923016),(-29859549026495580060)⟩,⟨390989286625338812877,390989286625339155834⟩⟩,⟨⟨(-4268090030280332137),(-4268090030280019231)⟩,⟨360670995820067917072,360670995820068229980⟩⟩,⟨⟨17656505619750577714,17656505619750862825⟩,⟨330948437927899129390,330948437927899414503⟩⟩,⟨⟨36164501350295244768,36164501350295504147⟩,⟨302027823906707575356,302027823906707834739⟩⟩,⟨⟨51511299582704898135,51511299582705133783⟩,⟨274087368063305445595,274087368063305681246⟩⟩,⟨⟨63954553691343154654,63954553691343368402⟩,⟨247277754556509241309,247277754556509455059⟩⟩,⟨⟨73751447272103626336,73751447272103819961⟩,⟨221722908584415933851,221722908584416127479⟩⟩,⟨⟨81156169259268740934,81156169259268916053⟩,⟨197521040385209202441,197521040385209377563⟩⟩,⟨⟨86417608416143326692,86417608416143484861⟩,⟨174745927777805739681,174745927777805897853⟩⟩,⟨⟨89777285570616288992,89777285570616432107⟩,⟨153448401335933261846,153448401335933404965⟩⟩,⟨⟨91467536786134229617,91467536786134358981⟩,⟨133657995417255098588,133657995417255227953⟩⟩,⟨⟨91709955560946793234,91709955560946909987⟩,⟨115384728131535694395,115384728131535811150⟩⟩,⟨⟨90714097235191262457,90714097235191367691⟩,⟨98620973886888745757,98620973886888850992⟩⟩] +lemma kernel27_0_r4_4_eq : ∀ k : Fin 16, kernel27_0Expr 4 4 k = kernel27_0_r4_4 k := by decide +kernel +noncomputable def kernel27_0_r4_5 : Fin 16 → CBox := ![⟨⟨88676444147465664254,88676444147465758953⟩,⟨83343393345747008969,83343393345747103669⟩⟩,⟨⟨85779625799088455935,85779625799088541049⟩,⟨69514887385935417293,69514887385935502408⟩⟩,⟨⟨82191884421118989976,82191884421119066357⟩,⟨57086543921761257007,57086543921761333388⟩⟩,⟨⟨78066772948197213603,78066772948197282059⟩,⟨45999549113498059250,45999549113498127706⟩⟩,⟨⟨73543069521645776575,73543069521645837829⟩,⟨36187037495153682465,36187037495153743719⟩⟩,⟨⟨68744890294882132599,68744890294882187344⟩,⟨27575858792516062009,27575858792516116754⟩⟩,⟨⟨63781980505772032500,63781980505772081352⟩,⟨20088242599445390455,20088242599445439307⟩⟩,⟨⟨58750162508593544286,58750162508593587827⟩,⟨13643345546408476662,13643345546408520203⟩⟩,⟨⟨53731918706050160535,53731918706050199284⟩,⟨8158669052328767741,8158669052328806490⟩⟩,⟨⟨48797087061702304225,48797087061702338670⟩,⟨3551339126425595495,3551339126425629939⟩⟩,⟨⟨44003647068410332678,44003647068410363251⟩,⟨(-260757083865478700),(-260757083865448128)⟩⟩,⟨⟨39398574654423364886,39398574654423391995⟩,⟨(-3357980275410863803),(-3357980275410836694)⟩⟩,⟨⟨35018745475293719473,35018745475293743472⟩,⟨(-5818092999784142308),(-5818092999784118309)⟩⟩,⟨⟨30891867312485068555,30891867312485089777⟩,⟨(-7715555704598423840),(-7715555704598402618)⟩⟩,⟨⟨27037423821717662018,27037423821717680755⟩,⟨(-9120959625392052716),(-9120959625392033980)⟩⟩,⟨⟨23467613588473525523,23467613588473542059⟩,⟨(-10100589491805589283),(-10100589491805572748)⟩⟩] +lemma kernel27_0_r4_5_eq : ∀ k : Fin 16, kernel27_0Expr 4 5 k = kernel27_0_r4_5 k := by decide +kernel +noncomputable def kernel27_0_r4_6 : Fin 16 → CBox := ![⟨⟨20188270298297920409,20188270298297934975⟩,⟨(-10716107490625884314),(-10716107490625869749)⟩⟩,⟨⟨17199751761496782385,17199751761496795205⟩,⟨(-11024348740395631817),(-11024348740395618997)⟩⟩,⟨⟨14497787494929329262,14497787494929340528⟩,⟨(-11077217668478150522),(-11077217668478139256)⟩⟩,⟨⟨12074276511659651197,12074276511659661088⟩,⟨(-10921674125741142274),(-10921674125741132384)⟩⟩,⟨⟨9918028861286686200,9918028861286694867⟩,⟨(-10599797804720523485),(-10599797804720514818)⟩⟩,⟨⟨8015446264573128244,8015446264573135833⟩,⟨(-10148919518061788513),(-10148919518061780924)⟩⟩,⟨⟨6351138866339998599,6351138866340005240⟩,⟨(-9601808115661371900),(-9601808115661365259)⟩⟩,⟨⟨4908476667441482610,4908476667441488418⟩,⟨(-8986902239461320269),(-8986902239461314461)⟩⟩,⟨⟨3670075573024011616,3670075573024016687⟩,⟨(-8328576701348240440),(-8328576701348235370)⟩⟩,⟨⟨2618219199089038939,2618219199089043363⟩,⟨(-7647433988968786201),(-7647433988968781778)⟩⟩,⟨⟨1735218606972058718,1735218606972062571⟩,⟨(-6960612224118220441),(-6960612224118216588)⟩⟩,⟨⟨1003712985049291601,1003712985049294953⟩,⟨(-6282101787793424306),(-6282101787793420954)⟩⟩,⟨⟨406914972517632465,406914972517635378⟩,⟨(-5623063756257894675),(-5623063756257891761)⟩⟩,⟨⟨(-71195171038943523),(-71195171038940993)⟩,⟨(-4992144237397443710),(-4992144237397441180)⟩⟩,⟨⟨(-445721993779700309),(-445721993779698115)⟩,⟨(-4395779633092991933),(-4395779633092989739)⟩⟩,⟨⟨(-730749111142118206),(-730749111142116304)⟩,⟨(-3838488761365415456),(-3838488761365413555)⟩⟩] +lemma kernel27_0_r4_6_eq : ∀ k : Fin 16, kernel27_0Expr 4 6 k = kernel27_0_r4_6 k := by decide +kernel +noncomputable def kernel27_0_r4_7 : Fin 16 → CBox := ![⟨⟨(-939270448931130635),(-939270448931128988)⟩,⟨(-3323148635057854297),(-3323148635057852650)⟩⟩,⟨⟨(-1083153652808036855),(-1083153652808035431)⟩,⟨(-2851251498554710052),(-2851251498554708628)⟩⟩,⟨⟨(-1173130973437096515),(-1173130973437095284)⟩,⟨(-2423141460483597285),(-2423141460483596054)⟩⟩,⟨⟨(-1218813142082538656),(-1218813142082537593)⟩,⟨(-2038229721571867561),(-2038229721571866499)⟩⟩,⟨⟨(-1228722019903428067),(-1228722019903427150)⟩,⟨(-1695187978735280430),(-1695187978735279514)⟩⟩,⟨⟨(-1210338120136137319),(-1210338120136136531)⟩,⟨(-1392120087515301894),(-1392120087515301106)⟩⟩,⟨⟨(-1170159451424423230),(-1170159451424422553)⟩,⟨(-1126712485835136002),(-1126712485835135325)⟩⟩,⟨⟨(-1113768499697909778),(-1113768499697909195)⟩,⟨(-896364225284442684),(-896364225284442101)⟩⟩,⟨⟨(-1045904543615241424),(-1045904543615240922)⟩,⟨(-698297725884444120),(-698297725884443618)⟩⟩,⟨⟨(-970538874637906060),(-970538874637905628)⟩,⟨(-529651571848705007),(-529651571848704575)⟩⟩,⟨⟨(-890950858835141064),(-890950858835140692)⟩,⟨(-387556805439889709),(-387556805439889337)⟩⟩,⟨⟨(-809803126664684087),(-809803126664683768)⟩,⟨(-269198260407075194),(-269198260407074875)⟩⟩,⟨⟨(-729214503869462197),(-729214503869461923)⟩,⟨(-171862512755367156),(-171862512755366883)⟩⟩,⟨⟨(-650829597339639462),(-650829597339639226)⟩,⟨(-92974021899754776),(-92974021899754540)⟩⟩,⟨⟨(-575884221677357458),(-575884221677357256)⟩,⟨(-30120996601095935),(-30120996601095734)⟩⟩,⟨⟨(-505266093795115588),(-505266093795115414)⟩,⟨18927545818383909,18927545818384083⟩⟩] +lemma kernel27_0_r4_7_eq : ∀ k : Fin 16, kernel27_0Expr 4 7 k = kernel27_0_r4_7 k := by decide +kernel +noncomputable def kernel27_0_r4_8 : Fin 16 → CBox := ![⟨⟨(-439570433717182107),(-439570433717181959)⟩,⟨56212145358731726,56212145358731874⟩⟩,⟨⟨(-379150290232438278),(-379150290232438151)⟩,⟨83579410818857028,83579410818857155⟩⟩,⟨⟨(-324161561264253726),(-324161561264253616)⟩,⟨102683509578347097,102683509578347206⟩⟩,⟨⟨(-274602802428542629),(-274602802428542536)⟩,⟨114991586220858965,114991586220859058⟩⟩,⟨⟨(-230350015307604580),(-230350015307604500)⟩,⟨121792180118159220,121792180118159300⟩⟩,⟨⟨(-191186681821420910),(-191186681821420841)⟩,⟨124205830230456864,124205830230456933⟩⟩,⟨⟨(-156829365246342128),(-156829365246342068)⟩,⟨123197169480690568,123197169480690629⟩⟩,⟨⟨(-126949234500816288),(-126949234500816236)⟩,⟨119587919116561878,119587919116561930⟩⟩,⟨⟨(-101189888863220724),(-101189888863220680)⟩,⟨114070294000914056,114070294000914100⟩⟩,⟨⟨(-79181867800950605),(-79181867800950567)⟩,⟨107220421757187407,107220421757187445⟩⟩,⟨⟨(-60554227430908284),(-60554227430908250)⟩,⟨99511461543358117,99511461543358150⟩⟩,⟨⟨(-44943553483174357),(-44943553483174329)⟩,⟨91326181688117718,91326181688117746⟩⟩,⟨⟨(-32000762483975307),(-32000762483975282)⟩,⟨82968819542380261,82968819542380285⟩⟩,⟨⟨(-21396019975258705),(-21396019975258683)⟩,⟨74676101957901160,74676101957901182⟩⟩,⟨⟨(-12822078485811168),(-12822078485811149)⟩,⟨66627351265152909,66627351265152928⟩⟩,⟨⟨(-5996309979052347),(-5996309979052331)⟩,⟨58953640080510455,58953640080510471⟩⟩] +lemma kernel27_0_r4_8_eq : ∀ k : Fin 16, kernel27_0Expr 4 8 k = kernel27_0_r4_8 k := by decide +kernel +noncomputable def kernel27_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-661678725664861),(-661678725664846)⟩,⟨51745989414825903,51745989414825918⟩⟩,⟨⟨3413128118146467,3413128118146480⟩,⟨45062629121712168,45062629121712180⟩⟩,⟨⟨6434222794468302,6434222794468313⟩,⟨38935358476525152,38935358476525163⟩⟩,⟨⟨8583529146834161,8583529146834171⟩,⟨33375058374693381,33375058374693392⟩⟩,⟨⟨10020146540158891,10020146540158901⟩,⟨28376416015120841,28376416015120851⟩⟩,⟨⟨10881950024735547,10881950024735555⟩,⟨23921928685589508,23921928685589517⟩⟩,⟨⟨11287331839958599,11287331839958606⟩,⟨19985256036186353,19985256036186361⟩⟩,⟨⟨11337007700078611,11337007700078617⟩,⟨16533990599241971,16533990599241977⟩⟩,⟨⟨11115827442138969,11115827442138976⟩,⟨13531914813152191,13531914813152197⟩⟩,⟨⟨10694543615360911,10694543615360918⟩,⟨10940809892028312,10940809892028318⟩⟩,⟨⟨10131503564453400,10131503564453406⟩,⟨8721877949674277,8721877949674284⟩⟩,⟨⟨9474240649664383,9474240649664390⟩,⟨6836834170739347,6836834170739353⟩⟩,⟨⟨8760948616377672,8760948616377678⟩,⟨5248720803160450,5248720803160455⟩⟩,⟨⟨8021829949733248,8021829949733253⟩,⟨3922489551242228,3922489551242233⟩⟩,⟨⟨7280314501365252,7280314501365257⟩,⟨2825393758081376,2825393758081381⟩⟩,⟨⟨6554148929612557,6554148929612562⟩,⟨1927226718208506,1927226718208511⟩⟩] +lemma kernel27_0_r4_9_eq : ∀ k : Fin 16, kernel27_0Expr 4 9 k = kernel27_0_r4_9 k := by decide +kernel +noncomputable def kernel27_0_r4_10 : Fin 16 → CBox := ![⟨⟨5856360718202721,5856360718202725⟩,⟨1200437658955536,1200437658955540⟩⟩,⟨⟨5196102888020951,5196102888020956⟩,⟨620152444095191,620152444095196⟩⟩,⟨⟨4579387136401167,4579387136401171⟩,⟨164121931969918,164121931969922⟩⟩,⟨⟨4009714159036299,4009714159036304⟩,⟨(-187382812210509),(-187382812210504)⟩⟩,⟨⟨3488610447498805,3488610447498808⟩,⟨(-451712585677554),(-451712585677550)⟩⟩,⟨⟨3016081012644486,3016081012644491⟩,⟨(-644006478005060),(-644006478005056)⟩⟩,⟨⟨2590987349163653,2590987349163658⟩,⟨(-777372306278120),(-777372306278115)⟩⟩,⟨⟨2211359604461471,2211359604461474⟩,⟨(-863072910183464),(-863072910183461)⟩⟩,⟨⟨1874651408964317,1874651408964320⟩,⟨(-910712042509682),(-910712042509679)⟩⟩,⟨⟨1577945216876970,1577945216876974⟩,⟨(-928415171631780),(-928415171631776)⟩⟩,⟨⟨1318115338483963,1318115338483966⟩,⟨(-923001824569921),(-923001824569917)⟩⟩,⟨⟨1091955150720492,1091955150720497⟩,⟨(-900147172904786),(-900147172904782)⟩⟩,⟨⟨896274277811458,896274277811463⟩,⟨(-864531429101017),(-864531429101012)⟩⟩,⟨⟨727970857729702,727970857729707⟩,⟨(-819976306018057),(-819976306018052)⟩⟩,⟨⟨584083367083271,584083367083276⟩,⟨(-769568323982250),(-769568323982245)⟩⟩,⟨⟨461825876360918,461825876360921⟩,⟨(-715769151904708),(-715769151904705)⟩⟩] +lemma kernel27_0_r4_10_eq : ∀ k : Fin 16, kernel27_0Expr 4 10 k = kernel27_0_r4_10 k := by decide +kernel +noncomputable def kernel27_0_r4_11 : Fin 16 → CBox := ![⟨⟨358610055168709,358610055168713⟩,⟨(-660513463302428),(-660513463302425)⟩⟩,⟨⟨272056746211764,272056746211767⟩,⟨(-605294994023473),(-605294994023470)⟩⟩,⟨⟨199999478100337,199999478100341⟩,⟨(-551241622908572),(-551241622908568)⟩⟩,⟨⟨140481889676830,140481889676834⟩,⟨(-499180374177681),(-499180374177677)⟩⟩,⟨⟨91750690321103,91750690321108⟩,⟨(-449693273516978),(-449693273516974)⟩⟩,⟨⟨52245478591002,52245478591005⟩,⟨(-403164989212237),(-403164989212234)⟩⟩,⟨⟨20586482042530,20586482042535⟩,⟨(-359823164019886),(-359823164019882)⟩⟩,⟨⟨(-4438939701175),(-4438939701171)⟩,⟨(-319772300012936),(-319772300012932)⟩⟩,⟨⟨(-23890372559569),(-23890372559565)⟩,⟨(-283022003238663),(-283022003238659)⟩⟩,⟨⟨(-38688505349940),(-38688505349936)⟩,⟨(-249510332343856),(-249510332343852)⟩⟩,⟨⟨(-49628994014869),(-49628994014865)⟩,⟨(-219122929012653),(-219122929012649)⟩⟩,⟨⟨(-57395764389173),(-57395764389170)⟩,⟨(-191708540915945),(-191708540915942)⟩⟩,⟨⟨(-62573569489794),(-62573569489791)⟩,⟨(-167091481971866),(-167091481971863)⟩⟩,⟨⟨(-65659684406027),(-65659684406022)⟩,⟨(-145081511559334),(-145081511559330)⟩⟩,⟨⟨(-67074674437821),(-67074674437818)⟩,⟨(-125481554931865),(-125481554931862)⟩⟩,⟨⟨(-67172212572739),(-67172212572736)⟩,⟨(-108093632089021),(-108093632089018)⟩⟩] +lemma kernel27_0_r4_11_eq : ∀ k : Fin 16, kernel27_0Expr 4 11 k = kernel27_0_r4_11 k := by decide +kernel +noncomputable def kernel27_0_r4_12 : Fin 16 → CBox := ![⟨⟨(-66247952811165),(-66247952811160)⟩,⟨(-92723312123389),(-92723312123384)⟩⟩,⟨⟨(-64547488072238),(-64547488072234)⟩,⟨(-79182964690230),(-79182964690227)⟩⟩,⟨⟨(-62273437011345),(-62273437011340)⟩,⟨(-67294039692924),(-67294039692919)⟩⟩,⟨⟨(-59591714392387),(-59591714392383)⟩,⟨(-56888570365640),(-56888570365636)⟩⟩,⟨⟨(-56637045813502),(-56637045813498)⟩,⟨(-47810063406340),(-47810063406336)⟩⟩,⟨⟨(-53517790525933),(-53517790525930)⟩,⟨(-39913912354746),(-39913912354743)⟩⟩,⟨⟨(-50320136592197),(-50320136592193)⟩,⟨(-33067446678091),(-33067446678087)⟩⟩,⟨⟨(-47111731339088),(-47111731339085)⟩,⟨(-27149708666306),(-27149708666303)⟩⟩,⟨⟨(-43944807489483),(-43944807489480)⟩,⟨(-22051032893929),(-22051032893926)⟩⟩,⟨⟨(-40858861916581),(-40858861916577)⟩,⟨(-17672488335444),(-17672488335440)⟩⟩,⟨⟨(-37882939980083),(-37882939980080)⟩,⟨(-13925230899693),(-13925230899690)⟩⟩,⟨⟨(-35037574127949),(-35037574127945)⟩,⟨(-10729803875355),(-10729803875351)⟩⟩,⟨⟨(-32336421071415),(-32336421071412)⟩,⟨(-8015415276568),(-8015415276565)⟩⟩,⟨⟨(-29787637507566),(-29787637507562)⟩,⟨(-5719214095143),(-5719214095140)⟩⟩,⟨⟨(-27395030175396),(-27395030175391)⟩,⟨(-3785581778865),(-3785581778861)⟩⟩,⟨⟨(-25159012058894),(-25159012058889)⟩,⟨(-2165450665579),(-2165450665574)⟩⟩] +lemma kernel27_0_r4_12_eq : ∀ k : Fin 16, kernel27_0Expr 4 12 k = kernel27_0_r4_12 k := by decide +kernel +noncomputable def kernel27_0_r4_13 : Fin 16 → CBox := ![⟨⟨(-23077392839776),(-23077392839772)⟩,⟨(-815657434978),(-815657434973)⟩⟩,⟨⟨(-21146028279176),(-21146028279171)⟩,⟨301663257820,301663257823⟩⟩,⟨⟨(-19359350083251),(-19359350083247)⟩,⟨1219642062617,1219642062622⟩⟩,⟨⟨(-17710794982181),(-17710794982178)⟩,⟨1967193958930,1967193958933⟩⟩,⟨⟨(-16193149217643),(-16193149217640)⟩,⟨2569493161906,2569493161909⟩⟩,⟨⟨(-14798822376876),(-14798822376873)⟩,⟨3048405005503,3048405005506⟩⟩,⟨⟨(-13520062514738),(-13520062514735)⟩,⟨3422876580015,3422876580018⟩⟩,⟨⟨(-12349122749149),(-12349122749145)⟩,⟨3709288361328,3709288361331⟩⟩,⟨⟨(-11278387979610),(-11278387979606)⟩,⟨3921769356086,3921769356090⟩⟩,⟨⟨(-10300469042335),(-10300469042331)⟩,⟨4072478439754,4072478439758⟩⟩,⟨⟨(-9408270458645),(-9408270458641)⟩,⟨4171854615148,4171854615152⟩⟩,⟨⟨(-8595036936278),(-8595036936275)⟩,⟨4228838893569,4228838893572⟩⟩,⟨⟨(-7854382927851),(-7854382927846)⟩,⟨4251070419986,4251070419991⟩⟩,⟨⟨(-7180308819907),(-7180308819902)⟩,⟨4245059344452,4245059344456⟩⟩,⟨⟨(-6567206704400),(-6567206704395)⟩,⟨4216338797182,4216338797186⟩⟩,⟨⟨(-6009858157741),(-6009858157738)⟩,⟨4169598164827,4169598164830⟩⟩] +lemma kernel27_0_r4_13_eq : ∀ k : Fin 16, kernel27_0Expr 4 13 k = kernel27_0_r4_13 k := by decide +kernel +noncomputable def kernel27_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-5503426008335),(-5503426008332)⟩,⟨4108799698047,4108799698050⟩⟩,⟨⟨(-5043441700231),(-5043441700228)⟩,⟨4037280311655,4037280311658⟩⟩,⟨⟨(-4625789548333),(-4625789548330)⟩,⟨3957840272516,3957840272519⟩⟩,⟨⟨(-4246688920550),(-4246688920546)⟩,⟨3872820310373,3872820310377⟩⟩,⟨⟨(-3902675166667),(-3902675166662)⟩,⟨3784168534669,3784168534674⟩⟩,⟨⟨(-3590579935886),(-3590579935883)⟩,⟨3693498397941,3693498397944⟩⟩,⟨⟨(-3307511378916),(-3307511378913)⟩,⟨3602138813865,3602138813868⟩⟩,⟨⟨(-3050834611372),(-3050834611369)⟩,⟨3511177416264,3511177416267⟩⟩,⟨⟨(-2818152718506),(-2818152718502)⟩,⟨3421497833849,3421497833853⟩⟩,⟨⟨(-2607288503431),(-2607288503427)⟩,⟨3333811754402,3333811754405⟩⟩,⟨⟨(-2416267118691),(-2416267118687)⟩,⟨3248686460614,3248686460618⟩⟩,⟨⟨(-2243299671698),(-2243299671695)⟩,⟨3166568437710,3166568437713⟩⟩,⟨⟨(-2086767855893),(-2086767855890)⟩,⟨3087803579366,3087803579369⟩⟩,⟨⟨(-1945209629564),(-1945209629560)⟩,⟨3012654452908,3012654452912⟩⟩,⟨⟨(-1817305941490),(-1817305941487)⟩,⟨2941315026482,2941315026485⟩⟩,⟨⟨(-1701868485650),(-1701868485646)⟩,⟨2873923209252,2873923209257⟩⟩] +lemma kernel27_0_r4_14_eq : ∀ k : Fin 16, kernel27_0Expr 4 14 k = kernel27_0_r4_14 k := by decide +kernel +noncomputable def kernel27_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-1597828454917),(-1597828454912)⟩,⟨2810571510074,2810571510079⟩⟩,⟨⟨(-1504226255238),(-1504226255233)⟩,⟨2751316079919,2751316079924⟩⟩,⟨⟨(-1420202136238),(-1420202136232)⟩,⟨2696184367916,2696184367921⟩⟩,⟨⟨(-1344987691080),(-1344987691076)⟩,⟨2645181589919,2645181589923⟩⟩,⟨⟨(-1277898177177),(-1277898177173)⟩,⟨2598296181242,2598296181246⟩⟩,⟨⟨(-1218325609458),(-1218325609454)⟩,⟨2555504381464,2555504381468⟩⟩,⟨⟨(-1165732579234),(-1165732579231)⟩,⟨2516774078320,2516774078323⟩⟩,⟨⟨(-1119646753775),(-1119646753772)⟩,⟨2482068019546,2482068019549⟩⟩,⟨⟨(-1079656014425),(-1079656014422)⟩,⟨2451346485608,2451346485612⟩⟩,⟨⟨(-1045404194293),(-1045404194288)⟩,⟨2424569502276,2424569502280⟩⟩,⟨⟨(-1016587380015),(-1016587380012)⟩,⟨2401698659824,2401698659828⟩⟩,⟨⟨(-992950745800),(-992950745797)⟩,⟨2382698594870,2382698594873⟩⟩,⟨⟨(-974285891802),(-974285891799)⟩,⟨2367538181330,2367538181333⟩⟩,⟨⟨(-960428662824),(-960428662821)⟩,⟨2356191468548,2356191468551⟩⟩,⟨⟨(-951257427323),(-951257427319)⟩,⟨2348638397033,2348638397037⟩⟩,⟨⟨(-946691800669),(-946691800665)⟩,⟨2344865315346,2344865315349⟩⟩] +lemma kernel27_0_r4_15_eq : ∀ k : Fin 16, kernel27_0Expr 4 15 k = kernel27_0_r4_15 k := by decide +kernel +noncomputable def kernel27_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel27_0_r4_0,kernel27_0_r4_1,kernel27_0_r4_2,kernel27_0_r4_3,kernel27_0_r4_4,kernel27_0_r4_5,kernel27_0_r4_6,kernel27_0_r4_7,kernel27_0_r4_8,kernel27_0_r4_9,kernel27_0_r4_10,kernel27_0_r4_11,kernel27_0_r4_12,kernel27_0_r4_13,kernel27_0_r4_14,kernel27_0_r4_15] +lemma kernel27_0_r4_eq (i k : Fin 16) : kernel27_0Expr 4 i k = kernel27_0_r4 i k := by + fin_cases i + · exact kernel27_0_r4_0_eq k + · exact kernel27_0_r4_1_eq k + · exact kernel27_0_r4_2_eq k + · exact kernel27_0_r4_3_eq k + · exact kernel27_0_r4_4_eq k + · exact kernel27_0_r4_5_eq k + · exact kernel27_0_r4_6_eq k + · exact kernel27_0_r4_7_eq k + · exact kernel27_0_r4_8_eq k + · exact kernel27_0_r4_9_eq k + · exact kernel27_0_r4_10_eq k + · exact kernel27_0_r4_11_eq k + · exact kernel27_0_r4_12_eq k + · exact kernel27_0_r4_13_eq k + · exact kernel27_0_r4_14_eq k + · exact kernel27_0_r4_15_eq k +noncomputable def kernel27_0_r5_0 : Fin 16 → CBox := ![⟨⟨(-3163679937696320872062229872),(-3163679937696319008644992362)⟩,⟨(-5946339941829223230571595925),(-5946339941829221367039705128)⟩⟩,⟨⟨(-3166334280078559708639783255),(-3166334280078557846105651515)⟩,⟨(-5938571792634636007467722692),(-5938571792634634144819162671)⟩⟩,⟨⟨(-3171615181012724424141773621),(-3171615181012722563376088844)⟩,⟨(-5923048424803509036630695769),(-5923048424803507175751032101)⟩⟩,⟨⟨(-3179467254936695785050519732),(-3179467254936693926936639692)⟩,⟨(-5899795768048739879782674741),(-5899795768048738021555488315)⟩⟩,⟨⟨(-3189807878029322969159792142),(-3189807878029321114578176538)⟩,⟨(-5868852886822788500808314392),(-5868852886822786646114286109)⟩⟩,⟨⟨(-3202527731601645763880415941),(-3202527731601643913707578576)⟩,⟨(-5830272179692151626315848835),(-5830272179692149776031711152)⟩⟩,⟨⟨(-3217491523204756626628494109),(-3217491523204754781736150514)⟩,⟨(-5784119637753341589009555937),(-5784119637753339744007239862)⟩⟩,⟨⟨(-3234538882485596946521505398),(-3234538882485595107775395596)⟩,⟨(-5730475155850389031151052680),(-5730475155850387192296509902)⟩⟩,⟨⟨(-3253485428028489481433551816),(-3253485428028487649692842240)⟩,⟨(-5669432888939393135254776076),(-5669432888939391303407380257)⟩⟩,⟨⟨(-3274124000595510660651643165),(-3274124000595508836767386442)⟩,⟨(-5601101644626671941147833976),(-5601101644626670117158839909)⟩⟩,⟨⟨(-3296226057319592174987087941),(-3296226057319590359801412934)⟩,⟨(-5525605301701224804306192227),(-5525605301701222989017925261)⟩⟩,⟨⟨(-3319543220508707002016983022),(-3319543220508705196208034206)⟩,⟨(-5443083243406268879857201193),(-5443083243406267073947995864)⟩⟩,⟨⟨(-3343808973787517872759510895),(-3343808973787516077138405000)⟩,⟨(-5353690793264302728789774554),(-5353690793264300933070930887)⟩⟩,⟨⟨(-3368740497336146096873404655),(-3368740497336144312238702949)⟩,⟨(-5257599640500055485043427746),(-5257599640500053700313682811)⟩⟩,⟨⟨(-3394040632987882770295897198),(-3394040632987880997436222640)⟩,⟨(-5154998241509017836899322022),(-5154998241509016063947466516)⟩⟩,⟨⟨(-3419399968924331168029141785),(-3419399968924329407718024866)⟩,⟨(-5046092183407704108916745337),(-5046092183407702348516468846)⟩⟩] +lemma kernel27_0_r5_0_eq : ∀ k : Fin 16, kernel27_0Expr 5 0 k = kernel27_0_r5_0 k := by decide +kernel +noncomputable def kernel27_0_r5_1 : Fin 16 → CBox := ![⟨⟨(-3444499032665269436844152817),(-3444499032665267689844784845)⟩,⟨(-4931104495485325767768705160),(-4931104495485324020683348917)⟩⟩,⟨⟨(-3469010580001075811393561564),(-3469010580001074078450394902)⟩,⟨(-4810275894363223681415683124),(-4810275894363221948389839684)⟩⟩,⟨⟨(-3492601966469401691650332417),(-3492601966469399973497258919)⟩,⟨(-4683864948864180353375587127),(-4683864948864178635143278332)⟩⟩,⟨⟨(-3514937586948248664751928643),(-3514937586948246962101346710)⟩,⟨(-4552148151002322198744025890),(-4552148151002320496017769406)⟩⟩,⟨⟨(-3535681367939677511035494112),(-3535681367939675824589835184)⟩,⟨(-4415419880127005776799828134),(-4415419880127004090282163541)⟩⟩,⟨⟨(-3554499296168449568217698237),(-3554499296168447898652839427)⟩,⟨(-4273992248089562899888368552),(-4273992248089561230255269492)⟩⟩,⟨⟨(-3571061966235543910851106978),(-3571061966235542258833700385)⟩,⟨(-4128194814346052286865351246),(-4128194814346050634783554419)⟩⟩,⟨⟨(-3585047129266153658559420705),(-3585047129266152024720543746)⟩,⟨(-3978374161155412601662540630),(-3978374161155410967763197243)⟩⟩,⟨⟨(-3596142223794430071088166285),(-3596142223794428456051560350)⟩,⟨(-3824893320470930219318310677),(-3824893320470928604225223296)⟩⟩,⟨⟨(-3604046869552079670789226564),(-3604046869552078075148339468)⟩,⟨(-3668131045741097680626835374),(-3668131045741096084933498564)⟩⟩,⟨⟨(-3608475304393877504374623405),(-3608475304393875928717365136)⟩,⟨(-3508480923618196147443583435),(-3508480923618194571737940900)⟩⟩,⟨⟨(-3609158744318559861290589434),(-3609158744318558306166439961)⟩,⟨(-3346350322500862286599003951),(-3346350322500860731430556094)⟩⟩,⟨⟨(-3605847646445667761410370778),(-3605847646445666227366077073)⟩,⟨(-3182159176889291314194543643),(-3182159176889289780110044591)⟩⟩,⟨⟨(-3598313854903506342619643622),(-3598313854903504830106218242)⟩,⟨(-3016338608684743593044411445),(-3016338608684742080494853310)⟩⟩,⟨⟨(-3586352609884327055676745457),(-3586352609884325565076392108)⟩,⟨(-2849329388792387914271381272),(-2849329388792386423638914119)⟩⟩,⟨⟨(-3569784400641659533629118015),(-3569784400641658065393237871)⟩,⟨(-2681580244659775971174371816),(-2681580244659774502910364724)⟩⟩] +lemma kernel27_0_r5_1_eq : ∀ k : Fin 16, kernel27_0Expr 5 1 k = kernel27_0_r5_1 k := by decide +kernel +noncomputable def kernel27_0_r5_2 : Fin 16 → CBox := ![⟨⟨(-3548456643950222263982785425),(-3548456643950220818567973247)⟩,⟨(-2513546021672073555091584423),(-2513546021672072109652587174)⟩⟩,⟨⟨(-3522245170526740910994388854),(-3522245170526739488796489100)⟩,⟨(-2345685708597738614206853081),(-2345685708597737191988652380)⟩⟩,⟨⟨(-3491055503122604397918487495),(-3491055503122602999342297375)⟩,⟨(-2178460339501699986326134015),(-2178460339501698587733456914)⟩⟩,⟨⟨(-3454823911445212423269024108),(-3454823911445211048659828437)⟩,⟨(-2012330786683677821569541509),(-2012330786683676446947590536)⟩⟩,⟨⟨(-3413518230738837582616236605),(-3413518230738836232321973503)⟩,⟨(-1847755461223378724829607940),(-1847755461223377374526227261)⟩⟩,⟨⟨(-3367138432748519680633649931),(-3367138432748518354866735555)⟩,⟨(-1685187939588564661581899630),(-1685187939588563335809400217)⟩⟩,⟨⟨(-3315716939888489071128482368),(-3315716939888487770194438465)⟩,⟨(-1525074536454047944269277341),(-1525074536454046643333065080)⟩⟩,⟨⟨(-3259318675722325179619502602),(-3259318675722323903753042260)⟩,⟨(-1367851845358634205530631670),(-1367851845358632929665293712)⟩⟩,⟨⟨(-3198040847313913565489247139),(-3198040847313912314950431437)⟩,⟨(-1213944270064142747594699808),(-1213944270064141497060161855)⟩⟩,⟨⟨(-3132012457600833280450654752),(-3132012457600832055373411971)⟩,⟨(-1063761570449763524319790239),(-1063761570449762299249836459)⟩⟩,⟨⟨(-3061393548646053929326669148),(-3061393548646052729910598286)⟩,⟨(-917696447453261620870594463),(-917696447453260421464671805)⟩⟩,⟨⟨(-2986374179407466151883742901),(-2986374179407464978247713856)⟩,⟨(-776122191938748867811481454),(-776122191938747694188300798)⟩⟩,⟨⟨(-2907173144492703859398603719),(-2907173144492702711683353097)⟩,⟨(-639390422413957518800230358),(-639390422413956371100363679)⟩⟩,⟨⟨(-2824036443201515449295195423),(-2824036443201514327557150619)⟩,⟨(-507828936227858378290861548),(-507828936227857256570564160)⟩⟩,⟨⟨(-2737235510960432879314007505),(-2737235510960431783644607701)⟩,⟨(-381739698246742345261538602),(-381739698246741249612058245)⟩⟩,⟨⟨(-2647065227984390218931189029),(-2647065227984389149337270232)⟩,⟨(-261396990033475228165547506),(-261396990033474158593542360)⟩⟩] +lemma kernel27_0_r5_2_eq : ∀ k : Fin 16, kernel27_0Expr 5 2 k = kernel27_0_r5_2 k := by decide +kernel +noncomputable def kernel27_0_r5_3 : Fin 16 → CBox := ![⟨⟨(-2553841722616550680231889241),(-2553841722616549636770660252)⟩,⟨(-147045741245943368200321275),(-147045741245942324762819572)⟩⟩,⟨⟨(-2457899989260505098411021461),(-2457899989260504081023086067)⟩,⟨(-38900063337684977927328536),(-38900063337683960564752114)⟩⟩,⟨⟨(-2359591343088842387069130773),(-2359591343088841395751313015)⟩,⟨62857996297156802697957490,62857996297157793988967401⟩⟩,⟨⟨(-2259280735751300900606716935),(-2259280735751299935254366243)⟩,⟨158079463819199055643164962,158079463819200020967441204⟩⟩,⟨⟨(-2157343958079274018680203799),(-2157343958079273079249665717)⟩,⟨246649198649715544971952974,246649198649716484373331284⟩⟩,⟨⟨(-2054164757259620167609666443),(-2054164757259619253933647815)⟩,⟨328486392669660835827364258,328486392669661749473316554⟩⟩,⟨⟨(-1950131897101727702659545241),(-1950131897101726814637432478)⟩,⟨403544801097195708642547161,403544801097196596633863022⟩⟩,⟨⟨(-1845636190824399516181431697),(-1845636190824398653604175120)⟩,⟨471812700281952638885406351,471812700281953501431307175⟩⟩,⟨⟨(-1741067536225275234926488964),(-1741067536225274397659808066)⟩,⟨533312570813667416660260674,533312570813668253895194284⟩⟩,⟨⟨(-1636811983152724479001038893),(-1636811983152723666774870314)⟩,⟨588100507562599550869047858,588100507562600363063238909⟩⟩,⟨⟨(-1533248862871913082954677616),(-1533248862871912295347018324)⟩,⟨636265361501490929516295226,636265361501491717092261685⟩⟩,⟨⟨(-1430748008202777481979936582),(-1430748008202776716974275283)⟩,⟨677927621354859283034654275,677927621354860048011657706⟩⟩,⟨⟨(-1329667092214010766984244127),(-1329667092214010024460526798)⟩,⟨713238046232321959611725206,713238046232322702109713993⟩⟩,⟨⟨(-1230349111796306217356298769),(-1230349111796305497057854526)⟩,⟨742376063380361772490499619,742376063380362492766031989⟩⟩,⟨⟨(-1133120040628710238208330581),(-1133120040628709539967242126)⟩,⟨765547947985172300085008458,765547947985172998305883595⟩⟩,⟨⟨(-1038286673918700368067678376),(-1038286673918699691600191396)⟩,⟨782984804534247606885094391,782984804534248283334943087⟩⟩] +lemma kernel27_0_r5_3_eq : ∀ k : Fin 16, kernel27_0Expr 5 3 k = kernel27_0_r5_3 k := by decide +kernel +noncomputable def kernel27_0_r5_4 : Fin 16 → CBox := ![⟨⟨(-946134684869849766016877468),(-946134684869849111135199374)⟩,⟨794940371555939996769831881,794940371555940651636319212⟩⟩,⟨⟨(-856926910146128940320667995),(-856926910146128306690156628)⟩,⟨801688673568242970075711568,801688673568243603693348324⟩⟩,⟨⟨(-770901878699022112387362327),(-770901878699021499773282930)⟩,⟨803521545749426928425434004,803521545749427541028821121⟩⟩,⟨⟨(-688272595246520509910121204),(-688272595246519917960613604)⟩,⟨800746058168253412735482457,800746058168254004676344175⟩⟩,⟨⟨(-609225586488556036643928279),(-609225586488555465107104426)⟩,⟨793681867360744551078184228,793681867360745122608271723⟩⟩,⟨⟨(-533920214860591992221148510),(-533920214860591440700963688)⟩,⟨782658523600731889404792241,782658523600732440919996617⟩⟩,⟨⟨(-462488261316196794084623563),(-462488261316196262286337902)⟩,⟨768012762376172759163899046,768012762376173290958817777⟩⟩,⟨⟨(-395033775341123955427936567),(-395033775341123442941402927)⟩,⟨750085808352819805573501382,750085808352820318058148440⟩⟩,⟨⟨(-331633187185716895611768389),(-331633187185716402126378605)⟩,⟨729220719488356613316236157,729220719488357106801087918⟩⟩,⟨⟨(-272335674207800124170866378),(-272335674207799649241401574)⟩,⟨705759797967288143215816833,705759797967288618145962891⟩⟩,⟨⟨(-217163770290592317090328864),(-217163770290591860363381854)⟩,⟨680042093279746685830069645,680042093279747142558791004⟩⟩,⟨⟨(-166114204582246081434989142),(-166114204582245642457343756)⟩,⟨652401021091896277139677706,652401021091896716120068096⟩⟩,⟨⟨(-119158953333948235577834366),(-119158953333947814015715581)⟩,⟨623162119583108477183216306,623162119583108898748932425⟩⟩,⟨⟨(-76246486425876709002935690),(-76246486425876304346034530)⟩,⟨592640962691570582131200959,592640962691570986792438268⟩⟩,⟨⟨(-37303188293101814502411112),(-37303188293101426373577821)⟩,⟨561141247255474522268756264,561141247255474910402555950⟩⟩,⟨⟨(-2234931419290482366315405),(-2234931419290110303171204)⟩,⟨528953068404574180729442963,528953068404574552798077764⟩⟩] +lemma kernel27_0_r5_4_eq : ∀ k : Fin 16, kernel27_0Expr 5 4 k = kernel27_0_r5_4 k := by decide +kernel +noncomputable def kernel27_0_r5_5 : Fin 16 → CBox := ![⟨⟨29071220628816341094006205,29071220628816697441925054⟩,⟨496351394792122746986125241,496351394792123103339960490⟩⟩,⟨⟨56745204488765433059224123,56745204488765774200073430⟩,⟨463594752406811563840094389,463594752406811904987195270⟩⟩,⟨⟨80932066946984011265884775,80932066946984337660290507⟩,⟨430924122815574956811926602,430924122815575283212834389⟩⟩,⟨⟨101790017988877682945516817,101790017988877995053531127⟩,⟨398562058807777364027519701,398562058807777676142208253⟩⟩,⟨⟨119488451164803920461480863,119488451164804218638681679⟩,⟨366712017584773912269650323,366712017584774210453625322⟩⟩,⟨⟨134205954908592391358042563,134205954908592676089027859⟩,⟨335557908909343515569895562,335557908909343800307689389⟩⟩,⟨⟨146128337556220846189510705,146128337556221117842908138⟩,⟨305263853037263485793849394,305263853037263757453374094⟩⟩,⟨⟨155446687633155746403119846,155446687633156005435867504⟩,⟨275974140834878898026000914,275974140834879157064040457⟩⟩,⟨⟨162355489539318963499352888,162355489539319210264422053⟩,⟨247813386274195034956399207,247813386274195281725979019⟩⟩,⟨⟨167050813093790070820477448,167050813093790305929474440⟩,⟨220886859518295633557687831,220886859518295868670468646⟩⟩,⟨⟨169728593543137967769627914,169728593543138191604552544⟩,⟨195280987087127485423383197,195280987087127709261419535⟩⟩,⟨⟨170583016625635951227569172,170583016625636164214312708⟩,⟨171064004143857542157320056,171064004143857755146557764⟩⟩,⟨⟨169805021157679877824302103,169805021157680080294411110⟩,⟨148286742776534545462306738,148286742776534747934346014⟩⟩,⟨⟨167580929408009601121088803,167580929408009793506074252⟩,⟨126983539274564151182868176,126983539274564343569272585⟩⟩,⟨⟨164091213288934071524044959,164091213288934254158068950⟩,⟨107173242814992294273368255,107173242814992476908350904⟩⟩,⟨⟨159509402159632888882543731,159509402159633062202077805⟩,⟨88860307675030973456670461,88860307675031146776757564⟩⟩] +lemma kernel27_0_r5_5_eq : ∀ k : Fin 16, kernel27_0Expr 5 5 k = kernel27_0_r5_5 k := by decide +kernel +noncomputable def kernel27_0_r5_6 : Fin 16 → CBox := ![⟨⟨154001135840860294028120752,154001135840860458348675660⟩,⟨72035951065008130333514197,72035951065008294654263937⟩⟩,⟨⟨147723364316653213494933579,147723364316653369218579534⟩,⟨56679358915856067020202695,56679358915856222743729539⟩⟩,⟨⟨140823693577575184360502518,140823693577575331804571613⟩,⟨42758922439261577825810565,42758922439261725269488525⟩⟩,⟨⟨133439875168782417720500064,133439875168782557257805873⟩,⟨30233488985143128787367703,30233488985143268324049731⟩⟩,⟨⟨125699435268127058192376789,125699435268127190114004921⟩,⟨19053611625820566938838105,19053611625820698859646721⟩⟩,⟨⟨117719437553889303422354787,117719437553889428091937175⟩,⟨9162782972523710611797801,9162782972523835280399168⟩⟩,⟨⟨109606372743594914247373227,109606372743595031951360453⟩,⟨498639949614378642890714,498639949614496345767057⟩⟩,⟨⟨101456166505478323402292369,101456166505478434478254351⟩,⟨(-7005872413973057796710366),(-7005872413972946721960221)⟩⟩,⟨⟨93354296468993309466304655,93354296468993414319282944⟩,⟨(-13421388697362962008310298),(-13421388697362857156617874)⟩⟩,⟨⟨85376008292729006115490819,85376008292729105104202046⟩,⟨(-18821071350466517569454369),(-18821071350466418582079295)⟩⟩,⟨⟨77586620185620876475477420,77586620185620969838046681⟩,⟨(-23279627049647227229668009),(-23279627049647133868464056)⟩⟩,⟨⟨70041904915283307055007958,70041904915283395073431046⟩,⟨(-26872397184828391012782857),(-26872397184828302995735623)⟩⟩,⟨⟨62788538167170759096395407,62788538167170841990146439⟩,⟨(-29674527036009958953372735),(-29674527036009876060891714)⟩⟩,⟨⟨55864602128735965674681106,55864602128736043716950443⟩,⟨(-31760216763183697263528255),(-31760216763183619222333309)⟩⟩,⟨⟨49300133349962097965620204,49300133349962171369990243⟩,⟨(-33202055966483220404802933),(-33202055966483147001327435)⟩⟩,⟨⟨43117704259746357421204669,43117704259746426441121027⟩,⟨(-34070442290626946925762441),(-34070442290626877906576429)⟩⟩] +lemma kernel27_0_r5_6_eq : ∀ k : Fin 16, kernel27_0Expr 5 6 k = kernel27_0_r5_6 k := by decide +kernel +noncomputable def kernel27_0_r5_7 : Fin 16 → CBox := ![⟨⟨37333028179193966909497948,37333028179194031736676937⟩,⟨(-34433083363983585588030400),(-34433083363983520761432818)⟩⟩,⟨⟨31955578249440964743032746,31955578249441025621679700⟩,⟨(-34354580289637034878125008),(-34354580289636973999925382)⟩⟩,⟨⟨26989211364020330698288333,26989211364020387824616394⟩,⟨(-33896089952416905830008341),(-33896089952416848704007767)⟩⟩,⟨⟨22432788944672701264009764,22432788944672754850641185⟩,⟨(-33115062577855367994391610),(-33115062577855314407981509)⟩⟩,⟨⟨18280787205733462598263535,18280787205733512812735048⟩,⟨(-32065050279505520420181266),(-32065050279505470205837853)⟩⟩,⟨⟨14523890397222558739530602,14523890397222605783550304⟩,⟨(-30795581760464151891165459),(-30795581760464104847193896)⟩⟩,⟨⟨11149561382834693026901192,11149561382834737057825229⟩,⟨(-29352097891324170466874025),(-29352097891324126435929719)⟩⟩,⟨⟨8142584779660117852234773,8142584779660159050691930⟩,⟨(-27775942566014499324364769),(-27775942566014458125829321)⟩⟩,⟨⟨5485578746545757550858610,5485578746545796087249948⟩,⟨(-26104403033048710981561937),(-26104403033048672445043869)⟩⟩,⟨⟨3159472343999671818491605,3159472343999707869370578⟩,⟨(-24370793804974072259802198),(-24370793804974036208756808)⟩⟩,⟨⟨1143946188625350884988230,1143946188625384577986824⟩,⟨(-22604578254360120673237682),(-22604578254360086980040955)⟩⟩,⟨⟨(-582165120787620589814191),(-582165120787589108147694)⟩,⟨(-20831522100555304823670176),(-20831522100555273341780994)⟩⟩,⟨⟨(-2040509628403670961374461),(-2040509628403641577268748)⟩,⟨(-19073873167026267213092141),(-19073873167026237828745624)⟩⟩,⟨⟨(-3252893881163050871018597),(-3252893881163023445480288)⟩,⟨(-17350562033304320481637647),(-17350562033304293055846085)⟩⟩,⟨⟨(-4240997632480916140475835),(-4240997632480890567171641)⟩,⟨(-15677418507162683503844077),(-15677418507162657930279237)⟩⟩,⟨⟨(-5026126492892028684517300),(-5026126492892004842818867)⟩,⟨(-14067399190482016423729126),(-14067399190481992581767005)⟩⟩] +lemma kernel27_0_r5_7_eq : ∀ k : Fin 16, kernel27_0Expr 5 7 k = kernel27_0_r5_7 k := by decide +kernel +noncomputable def kernel27_0_r5_8 : Fin 16 → CBox := ![⟨⟨(-5629001194085038298134446),(-5629001194085016093606397)⟩,⟨(-12530821795474575666479332),(-12530821795474553461693773)⟩⟩,⟨⟨(-6069581765585080805395167),(-6069581765585060114431018)⟩,⟨(-11075602276159442921475847),(-11075602276159422230295176)⟩⟩,⟨⟨(-6366924624247148431509936),(-6366924624247129169206141)⟩,⟨(-9707491263488729476638812),(-9707491263488710214155836)⟩⟩,⟨⟨(-6539070343242880860748366),(-6539070343242862930700751)⟩,⟨(-8430306722366863244540493),(-8430306722366845314347459)⟩⟩,⟨⟨(-6602959695936753249240125),(-6602959695936736576688436)⟩,⟨(-7246160176902483109332421),(-7246160176902466436665643)⟩⟩,⟨⟨(-6574375456753687577869520),(-6574375456753672074132351)⟩,⟨(-6155674269444504285684238),(-6155674269444488781859004)⟩⟩,⟨⟨(-6467907381033173462109779),(-6467907381033159054966790)⟩,⟨(-5158189823118870314967322),(-5158189823118855907760173)⟩⟩,⟨⟨(-6296937773699993757673266),(-6296937773699980368920302)⟩,⟨(-4251960961531587649075921),(-4251960961531574260279754)⟩⟩,⟨⟨(-6073645086831033812429897),(-6073645086831021383604869)⟩,⟨(-3434337198851673309196410),(-3434337198851660880346388)⟩⟩,⟨⟨(-5809023053196377519953890),(-5809023053196365980513786)⟩,⟨(-2701931745403275103122772),(-2701931745403263563673326)⟩⟩,⟨⟨(-5512912960929654538344092),(-5512912960929643832247034)⟩,⟨(-2050775575854658463402548),(-2050775575854647757309207)⟩⟩,⟨⟨(-5194046798075676223747396),(-5194046798075666290599556)⟩,⟨(-1476457077613244835935692),(-1476457077613234902802499)⟩⟩,⟨⟨(-4860099139520210072041897),(-4860099139520200865446289)⟩,⟨(-974247335413030623807013),(-974247335413021417235064)⟩⟩,⟨⟨(-4517745807666781713878744),(-4517745807666773178210776)⟩,⟨(-539211314297665970957697),(-539211314297657435320675)⟩⟩,⟨⟨(-4172727507486508671669670),(-4172727507486500764973676)⟩,⟨(-166305377848928415770533),(-166305377848920509111220)⟩⟩,⟨⟨(-3829916811935555777873126),(-3829916811935548452724744)⟩,⟨149538277307013109824200,149538277307020434931537⟩⟩] +lemma kernel27_0_r5_8_eq : ∀ k : Fin 16, kernel27_0Expr 5 8 k = kernel27_0_r5_8 k := by decide +kernel +noncomputable def kernel27_0_r5_9 : Fin 16 → CBox := ![⟨⟨(-3493387051360685857774673),(-3493387051360679078596786)⟩,⟨413339574429273425492178,413339574429280204625872⟩⟩,⟨⟨(-3166481837010534414928463),(-3166481837010528138791291)⟩,⟨630010112539898426192579,630010112539904702283464⟩⟩,⟨⟨(-2851884121224640869229278),(-2851884121224635063621107)⟩,⟨804303477476754551874286,804303477476760357434993⟩⟩,⟨⟨(-2551683862838399158190043),(-2551683862838393786901279)⟩,⟨940775419664944917646764,940775419664950288887665⟩⟩,⟨⟨(-2267443523829627987247661),(-2267443523829623022716979)⟩,⟨1043752989641127252263405,1043752989641132216747578⟩⟩,⟨⟨(-2000260770684823401651417),(-2000260770684818811355997)⟩,⟨1117311719560189547046491,1117311719560194137302821⟩⟩,⟨⟨(-1750827890229460791205971),(-1750827890229456550382591)⟩,⟨1165259951352768291403280,1165259951352772532194291⟩⟩,⟨⟨(-1519487553968730435302822),(-1519487553968726516372830)⟩,⟨1191129437484490144216912,1191129437484494063120578⟩⟩,⟨⟨(-1306284676880649459442556),(-1306284676880645841666104)⟩,⟨1198171376092840830701067,1198171376092844448456598⟩⟩,⟨⟨(-1111014215947698965625215),(-1111014215947695624121560)⟩,⟨1189357086476828096494068,1189357086476831437981596⟩⟩,⟨⟨(-933264840618611473403521),(-933264840618608389451272)⟩,⟨1167382581477072939848484,1167382581477076023788833⟩⟩,⟨⟨(-772458482189164940626622),(-772458482189162093414649)⟩,⟨1134676348373915483424337,1134676348373918330628104⟩⟩,⟨⟨(-627885832289523452897005),(-627885832289520826715377)⟩,⟨1093409707899687063407541,1093409707899689689584169⟩⟩,⟨⟨(-498737912917837327807276),(-498737912917834904106645)⟩,⟨1045509180352216688238496,1045509180352219111936881⟩⟩,⟨⟨(-384133882525343824875671),(-384133882525341589660789)⟩,⟨992670347346969065963366,992670347346971301178342⟩⟩,⟨⟨(-283145275373110078505207),(-283145275373108005922305)⟩,⟨936372756381731474891325,936372756381733547476251⟩⟩] +lemma kernel27_0_r5_9_eq : ∀ k : Fin 16, kernel27_0Expr 5 9 k = kernel27_0_r5_9 k := by decide +kernel +noncomputable def kernel27_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-194816895628452084903592),(-194816895628450163917738)⟩,⟨877895472219788228175132,877895472219790149164605⟩⟩,⟨⟨(-118184604355954470959645),(-118184604355952689183569)⟩,⟨818332933406828156011024,818332933406829937792016⟩⟩,⟨⟨(-52290247590483868972570),(-52290247590482217465197)⟩,⟨758610823465428216067485,758610823465429867580809⟩⟩,⟨⟨3806022053643827353498,3806022053645358886365⟩,⟨699501714047247629770544,699501714047249161310163⟩⟩,⟨⟨51015778426398177821890,51015778426399596843890⟩,⟨641640281287026483417965,641640281287027902447312⟩⟩,⟨⟨90214462470242613821100,90214462470243929604355⟩,⟨585537936630327938039881,585537936630329253830903⟩⟩,⟨⟨122235391449685256706744,122235391449686475981327⟩,⟨531596749435762552108746,531596749435763771391361⟩⟩,⟨⟨147865408531250288177403,147865408531251418700752⟩,⟨480122570705014250776677,480122570705015381308190⟩⟩,⟨⟨167841957210971679896467,167841957210972727184109⟩,⟨431337295464448190912862,431337295464449238208689⟩⟩,⟨⟨182851379286065572527568,182851379286066543621154⟩,⟨385390225762138490207975,385390225762139461309438⟩⟩,⟨⟨193528250221320613092148,193528250221321513014530⟩,⟨342368517150510366690310,342368517150511266619391⟩⟩,⟨⟨200455581437611331604999,200455581437612166162475⟩,⟨302306709127635108388712,302306709127635942951821⟩⟩,⟨⟨204165734881863491048052,204165734881864264383111⟩,⟨265195354562937264787329,265195354562938038127057⟩⟩,⟨⟨205141910916891434509267,205141910916892151836147⟩,⟨230988774903220076416591,230988774903220793747277⟩⟩,⟨⟨203820085843831114269340,203820085843831779309531⟩,⟨199611977216392304701761,199611977216392969744989⟩⟩,⟨⟨200591290038796606258735,200591290038797223328641⟩,⟨170966776156750737748033,170966776156751354820292⟩⟩] +lemma kernel27_0_r5_10_eq : ∀ k : Fin 16, kernel27_0Expr 5 10 k = kernel27_0_r5_10 k := by decide +kernel +noncomputable def kernel27_0_r5_11 : Fin 16 → CBox := ![⟨⟨195804131594725666784238,195804131594726238889312⟩,⟨144937168995110809018037,144937168995111381124861⟩⟩,⟨⟨189767483396392432623957,189767483396392963687306⟩,⟨121394015207388653360513,121394015207389184425084⟩⟩,⟨⟨182753263644865230194256,182753263644865722942408⟩,⟨100199074000867656691394,100199074000868149440307⟩⟩,⟨⟨174999250942336197728833,174999250942336655379885⟩,⟨81208453806812497017343,81208453806812954668757⟩⟩,⟨⟨166711885131042227355501,166711885131042652116829⟩,⟨64275527392122361163168,64275527392122785924516⟩⟩,⟨⟨158069014155023042116296,158069014155023436833244⟩,⟨49253365033424148545033,49253365033424543261710⟩⟩,⟨⟨149222555302994151931987,149222555302994518641063⟩,⟨35996736327311891894456,35996736327312258603022⟩⟩,⟨⟨140301046331353659909812,140301046331354000950434⟩,⟨24363728834129348466520,24363728834129689506431⟩⟩,⟨⟨131412068206056701481597,131412068206057018425166⟩,⟨14217029004868647600054,14217029004868964542749⟩⟩,⟨⟨122644526596619130486944,122644526596619425454302⟩,⟨5424907838582259464796,5424907838582554431148⟩⟩,⟨⟨114070783866164100236987,114070783866164374679646⟩,⟨(-2138049438602415467414),(-2138049438602141025864)⟩⟩,⟨⟨105748637192749700753690,105748637192749956441859⟩,⟨(-8590433607776537705320),(-8590433607776282018340)⟩⟩,⟨⟨97723141695113903225512,97723141695114141302205⟩,⟨(-14043688765512991094426),(-14043688765512753018979)⟩⟩,⟨⟨90028280086140331703603,90028280086140553703949⟩,⟨(-18601947035477069993707),(-18601947035476847994646)⟩⟩,⟨⟨82688482504016145918728,82688482504016352879971⟩,⟨(-22361994079448576185099),(-22361994079448369225164)⟩⟩,⟨⟨75720001835999787814103,75720001835999980988330⟩,⟨(-25413341733916594408501),(-25413341733916401235592)⟩⟩] +lemma kernel27_0_r5_11_eq : ∀ k : Fin 16, kernel27_0Expr 5 11 k = kernel27_0_r5_11 k := by decide +kernel +noncomputable def kernel27_0_r5_12 : Fin 16 → CBox := ![⟨⟨69132151111518515761320,69132151111518695951160⟩,⟨(-27838386866483157633429),(-27838386866482977444903)⟩⟩,⟨⟨62928410454811676904504,62928410454811845271429⟩,⟨(-29712638134804790163793),(-29712638134804621798159)⟩⟩,⟨⟨57107411703269256091128,57107411703269413448524⟩,⟨(-31104994728852627210149),(-31104994728852469853887)⟩⟩,⟨⟨51663809162434096828182,51663809162434244087802⟩,⟨(-32078063379639717937896),(-32078063379639570679264)⟩⟩,⟨⟨46589045124419174554642,46589045124419312299210⟩,⟨(-32688501923631824954253),(-32688501923631687210541)⟩⟩,⟨⟨41872018760980224779341,41872018760980353840001⟩,⟨(-32987379524943952867386),(-32987379524943823807463)⟩⟩,⟨⟨37499666849199026125945,37499666849199147036211⟩,⟨(-33020545283188837745097),(-33020545283188716835458)⟩⟩,⟨⟨33457464526151716669102,33457464526151830108283⟩,⟨(-32828998401789996705106),(-32828998401789883266453)⟩⟩,⟨⟨29729853924722787303372,29729853924722893679446⟩,⟨(-32449254369644461243482),(-32449254369644354867848)⟩⟩,⟨⟨26300608137987222952739,26300608137987322894078⟩,⟨(-31913702729284451321539),(-31913702729284351380560)⟩⟩,⟨⟨23153137513155337832037,23153137513155431723851⟩,⟨(-31250952978892863961168),(-31250952978892770069639)⟩⟩,⟨⟨20270744803809543212652,20270744803809631553062⟩,⟨(-30486165995745629721716),(-30486165995745541381528)⟩⟩,⟨⟨17636835224223154443182,17636835224223237530288⟩,⟨(-29641369086980447029431),(-29641369086980363942490)⟩⟩,⟨⟨15235086962701799109345,15235086962701877403555⟩,⟨(-28735753381909596304001),(-28735753381909518009905)⟩⟩,⟨⟨13049587230770079857331,13049587230770153655059⟩,⟨(-27785952789891147472190),(-27785952789891073674530)⟩⟩,⟨⟨11064938458425323164153,11064938458425392862281⟩,⟨(-26806304169999067953841),(-26806304169998998255741)⟩⟩] +lemma kernel27_0_r5_12_eq : ∀ k : Fin 16, kernel27_0Expr 5 12 k = kernel27_0_r5_12 k := by decide +kernel +noncomputable def kernel27_0_r5_13 : Fin 16 → CBox := ![⟨⟨9266338797773487514931,9266338797773553311266⟩,⟨(-25809088703704537706590),(-25809088703704471910248)⟩⟩,⟨⟨7639640671947590674435,7639640671947652919387⟩,⟨(-24804754739112780894080),(-24804754739112718649090)⟩⟩,⟨⟨6171390705915279735914,6171390705915338626097⟩,⟨(-23802122593866480161460),(-23802122593866421271211)⟩⟩,⟨⟨4848854002259190168692,4848854002259245977562⟩,⟨(-22808571971747101000319),(-22808571971747045191361)⟩⟩,⟨⟨3660025379102293702603,3660025379102346577411⟩,⟨(-21830212772644704806822),(-21830212772644651931906)⟩⟩,⟨⟨2593629869233088358552,2593629869233138558430⟩,⟨(-20872040163554353051616),(-20872040163554302851611)⟩⟩,⟨⟨1639114488819094732305,1639114488819142400478⟩,⟨(-19938074835514131021939),(-19938074835514083353627)⟩⟩,⟨⟨786633020127971804705,786633020128017147697⟩,⟨(-19031489403175376122089),(-19031489403175330778945)⟩⟩,⟨⟨27025314338515332526,27025314338558449232⟩,⟨(-18154721914609054921898),(-18154721914609011805029)⟩⟩,⟨⟨(-648207593473309417956),(-648207593473268323928)⟩,⟨(-17309577433037997245722),(-17309577433037956151522)⟩⟩,⟨⟨(-1246931456193387741768),(-1246931456193348563491)⟩,⟨(-16497318632940202962215),(-16497318632940163783759)⟩⟩,⟨⟨(-1776408942151847190953),(-1776408942151809769565)⟩,⟨(-15718746323401615370373),(-15718746323401577948800)⟩⟩,⟨⟨(-2243331137011495077709),(-2243331137011459340626)⟩,⟨(-14974270774273324993684),(-14974270774273289256411)⟩⟩,⟨⟨(-2653849770697712111433),(-2653849770697677905566)⟩,⟨(-14263974677777453519871),(-14263974677777419313811)⟩⟩,⟨⟨(-3013609635286665529274),(-3013609635286632780059)⟩,⟨(-13587668531524589028816),(-13587668531524556279406)⟩⟩,⟨⟨(-3327780760013308095860),(-3327780760013276682333)⟩,⟨(-12944939179958732586820),(-12944939179958701173097)⟩⟩] +lemma kernel27_0_r5_13_eq : ∀ k : Fin 16, kernel27_0Expr 5 13 k = kernel27_0_r5_13 k := by decide +kernel +noncomputable def kernel27_0_r5_14 : Fin 16 → CBox := ![⟨⟨(-3601089996238882714889),(-3601089996238852590944)⟩,⟨(-12335192201265279106969),(-12335192201265248982826)⟩⟩,⟨⟨(-3837851739723196648844),(-3837851739723167688674)⟩,⟨(-11757688776757889955395),(-11757688776757860995027)⟩⟩,⟨⟨(-4041997581187807213926),(-4041997581187779363342)⟩,⟨(-11211577630490136397847),(-11211577630490108547065)⟩⟩,⟨⟨(-4217104730149701010338),(-4217104730149674174927)⟩,⟨(-10695922578930355242813),(-10695922578930328407203)⟩⟩,⟨⟨(-4366423102475045921412),(-4366423102475020066384)⟩,⟨(-10209726184456370012155),(-10209726184456344156931)⟩⟩,⟨⟨(-4492901000079787760346),(-4492901000079762789710)⟩,⟨(-9751949962507461502033),(-9751949962507436531202)⟩⟩,⟨⟨(-4599209342627148810578),(-4599209342627124684774)⟩,⟨(-9321531550705624843056),(-9321531550705600717062)⟩⟩,⟨⟨(-4687764436791619209589),(-4687764436791595853688)⟩,⟨(-8917399209270955933594),(-8917399209270932577513)⟩⟩,⟨⟨(-4760749289440193895832),(-4760749289440171289765)⟩,⟨(-8538483985679955229624),(-8538483985679932623388)⟩⟩,⟨⟨(-4820133487609696359902),(-4820133487609674422238)⟩,⟨(-8183729842766193566589),(-8183729842766171628764)⟩⟩,⟨⟨(-4867691681044384685990),(-4867691681044363387676)⟩,⟨(-7852102018310175490109),(-7852102018310154191644)⟩⟩,⟨⟨(-4905020712841437413497),(-4905020712841416693946)⟩,⟨(-7542593855543982527684),(-7542593855543961807990)⟩⟩,⟨⟨(-4933555450910061842615),(-4933555450910041686651)⟩,⟨(-7254232317814169056467),(-7254232317814148900367)⟩⟩,⟨⟨(-4954583377900927291431),(-4954583377900907634034)⟩,⟨(-6986082376791579470013),(-6986082376791559812488)⟩⟩,⟨⟨(-4969258000371155450678),(-4969258000371136270272)⟩,⟨(-6737250441963762763438),(-6737250441963743582911)⟩⟩,⟨⟨(-4978611139532765387400),(-4978611139532746633845)⟩,⟨(-6506886979560255615703),(-6506886979560236862032)⟩⟩] +lemma kernel27_0_r5_14_eq : ∀ k : Fin 16, kernel27_0Expr 5 14 k = kernel27_0_r5_14 k := by decide +kernel +noncomputable def kernel27_0_r5_15 : Fin 16 → CBox := ![⟨⟨(-4983564166262497062444),(-4983564166262478729813)⟩,⟨(-6294188451404213157166),(-6294188451404194824424)⟩⟩,⟨⟨(-4984938242362787682706),(-4984938242362769711867)⟩,⟨(-6098398688315165442639),(-6098398688315147471694)⟩⟩,⟨⟨(-4983463628557294871510),(-4983463628557277246098)⟩,⟨(-5918809798467492224621),(-5918809798467474599107)⟩⟩,⟨⟨(-4979788117549118172941),(-4979788117549100850336)⟩,⟨(-5754762698400844950877),(-5754762698400827628174)⟩⟩,⟨⟨(-4974484647808153734799),(-4974484647808136709497)⟩,⟨(-5605647343049808774877),(-5605647343049791749480)⟩⟩,⟨⟨(-4968058150704531326417),(-4968058150704514549577)⟩,⟨(-5470902721083520223383),(-5470902721083503446452)⟩⟩,⟨⟨(-4960951680265818946672),(-4960951680265802405414)⟩,⟨(-5350016672900654289557),(-5350016672900637748211)⟩⟩,⟨⟨(-4953551871286610315896),(-4953551871286593972796)⟩,⟨(-5242525580696463502081),(-5242525580696447158897)⟩⟩,⟨⟨(-4946193767824588565917),(-4946193767824572419195)⟩,⟨(-5148013972998206063182),(-5148013972998189916377)⟩⟩,⟨⟨(-4939165060328084824738),(-4939165060328068825988)⟩,⟨(-5066114079851644529682),(-5066114079851628530851)⟩⟩,⟨⟨(-4932709765795877573888),(-4932709765795861712782)⟩,⟨(-4996505369338921456083),(-4996505369338905594897)⟩⟩,⟨⟨(-4927031381500031063976),(-4927031381500015306864)⟩,⟨(-4938914091227595111731),(-4938914091227579354541)⟩⟩,⟨⟨(-4922295538928144677831),(-4922295538928129023790)⟩,⟨(-4893112849208078222263),(-4893112849208062568145)⟩⟩,⟨⟨(-4918632180736699243798),(-4918632180736683651334)⟩,⟨(-4858920219293380560727),(-4858920219293364968187)⟩⟩,⟨⟨(-4916137279660665831833),(-4916137279660650291509)⟩,⟨(-4836200428456657907276),(-4836200428456642366878)⟩⟩,⟨⟨(-4914874114499888766608),(-4914874114499873246477)⟩,⟨(-4824863104398314143312),(-4824863104398298623105)⟩⟩] +lemma kernel27_0_r5_15_eq : ∀ k : Fin 16, kernel27_0Expr 5 15 k = kernel27_0_r5_15 k := by decide +kernel +noncomputable def kernel27_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel27_0_r5_0,kernel27_0_r5_1,kernel27_0_r5_2,kernel27_0_r5_3,kernel27_0_r5_4,kernel27_0_r5_5,kernel27_0_r5_6,kernel27_0_r5_7,kernel27_0_r5_8,kernel27_0_r5_9,kernel27_0_r5_10,kernel27_0_r5_11,kernel27_0_r5_12,kernel27_0_r5_13,kernel27_0_r5_14,kernel27_0_r5_15] +lemma kernel27_0_r5_eq (i k : Fin 16) : kernel27_0Expr 5 i k = kernel27_0_r5 i k := by + fin_cases i + · exact kernel27_0_r5_0_eq k + · exact kernel27_0_r5_1_eq k + · exact kernel27_0_r5_2_eq k + · exact kernel27_0_r5_3_eq k + · exact kernel27_0_r5_4_eq k + · exact kernel27_0_r5_5_eq k + · exact kernel27_0_r5_6_eq k + · exact kernel27_0_r5_7_eq k + · exact kernel27_0_r5_8_eq k + · exact kernel27_0_r5_9_eq k + · exact kernel27_0_r5_10_eq k + · exact kernel27_0_r5_11_eq k + · exact kernel27_0_r5_12_eq k + · exact kernel27_0_r5_13_eq k + · exact kernel27_0_r5_14_eq k + · exact kernel27_0_r5_15_eq k +noncomputable def kernel27_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel27_0_r0,kernel27_0_r1,kernel27_0_r2,kernel27_0_r3,kernel27_0_r4,kernel27_0_r5] +lemma kernel27_0_eq (j : Fin 6) (i k : Fin 16) : kernel27_0Expr j i k = kernel27_0 j i k := by + fin_cases j + · exact kernel27_0_r0_eq i k + · exact kernel27_0_r1_eq i k + · exact kernel27_0_r2_eq i k + · exact kernel27_0_r3_eq i k + · exact kernel27_0_r4_eq i k + · exact kernel27_0_r5_eq i k +lemma kernel27_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel27_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(27:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel27_0_eq] + unfold kernel27_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans27_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel27_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans27 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel27_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r0_0_eq : ∀ k : Fin 16, kernel27_1Expr 0 0 k = kernel27_1_r0_0 k := by decide +kernel +noncomputable def kernel27_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r0_1_eq : ∀ k : Fin 16, kernel27_1Expr 0 1 k = kernel27_1_r0_1 k := by decide +kernel +noncomputable def kernel27_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r0_2_eq : ∀ k : Fin 16, kernel27_1Expr 0 2 k = kernel27_1_r0_2 k := by decide +kernel +noncomputable def kernel27_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r0_3_eq : ∀ k : Fin 16, kernel27_1Expr 0 3 k = kernel27_1_r0_3 k := by decide +kernel +noncomputable def kernel27_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r0_4_eq : ∀ k : Fin 16, kernel27_1Expr 0 4 k = kernel27_1_r0_4 k := by decide +kernel +noncomputable def kernel27_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel27_1_r0_5_eq : ∀ k : Fin 16, kernel27_1Expr 0 5 k = kernel27_1_r0_5 k := by decide +kernel +noncomputable def kernel27_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel27_1_r0_6_eq : ∀ k : Fin 16, kernel27_1Expr 0 6 k = kernel27_1_r0_6 k := by decide +kernel +noncomputable def kernel27_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel27_1_r0_7_eq : ∀ k : Fin 16, kernel27_1Expr 0 7 k = kernel27_1_r0_7 k := by decide +kernel +noncomputable def kernel27_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel27_1_r0_8_eq : ∀ k : Fin 16, kernel27_1Expr 0 8 k = kernel27_1_r0_8 k := by decide +kernel +noncomputable def kernel27_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel27_1_r0_9_eq : ∀ k : Fin 16, kernel27_1Expr 0 9 k = kernel27_1_r0_9 k := by decide +kernel +noncomputable def kernel27_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel27_1_r0_10_eq : ∀ k : Fin 16, kernel27_1Expr 0 10 k = kernel27_1_r0_10 k := by decide +kernel +noncomputable def kernel27_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel27_1_r0_11_eq : ∀ k : Fin 16, kernel27_1Expr 0 11 k = kernel27_1_r0_11 k := by decide +kernel +noncomputable def kernel27_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel27_1_r0_12_eq : ∀ k : Fin 16, kernel27_1Expr 0 12 k = kernel27_1_r0_12 k := by decide +kernel +noncomputable def kernel27_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel27_1_r0_13_eq : ∀ k : Fin 16, kernel27_1Expr 0 13 k = kernel27_1_r0_13 k := by decide +kernel +noncomputable def kernel27_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel27_1_r0_14_eq : ∀ k : Fin 16, kernel27_1Expr 0 14 k = kernel27_1_r0_14 k := by decide +kernel +noncomputable def kernel27_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel27_1_r0_15_eq : ∀ k : Fin 16, kernel27_1Expr 0 15 k = kernel27_1_r0_15 k := by decide +kernel +noncomputable def kernel27_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel27_1_r0_0,kernel27_1_r0_1,kernel27_1_r0_2,kernel27_1_r0_3,kernel27_1_r0_4,kernel27_1_r0_5,kernel27_1_r0_6,kernel27_1_r0_7,kernel27_1_r0_8,kernel27_1_r0_9,kernel27_1_r0_10,kernel27_1_r0_11,kernel27_1_r0_12,kernel27_1_r0_13,kernel27_1_r0_14,kernel27_1_r0_15] +lemma kernel27_1_r0_eq (i k : Fin 16) : kernel27_1Expr 0 i k = kernel27_1_r0 i k := by + fin_cases i + · exact kernel27_1_r0_0_eq k + · exact kernel27_1_r0_1_eq k + · exact kernel27_1_r0_2_eq k + · exact kernel27_1_r0_3_eq k + · exact kernel27_1_r0_4_eq k + · exact kernel27_1_r0_5_eq k + · exact kernel27_1_r0_6_eq k + · exact kernel27_1_r0_7_eq k + · exact kernel27_1_r0_8_eq k + · exact kernel27_1_r0_9_eq k + · exact kernel27_1_r0_10_eq k + · exact kernel27_1_r0_11_eq k + · exact kernel27_1_r0_12_eq k + · exact kernel27_1_r0_13_eq k + · exact kernel27_1_r0_14_eq k + · exact kernel27_1_r0_15_eq k +noncomputable def kernel27_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel27_1_r1_0_eq : ∀ k : Fin 16, kernel27_1Expr 1 0 k = kernel27_1_r1_0 k := by decide +kernel +noncomputable def kernel27_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel27_1_r1_1_eq : ∀ k : Fin 16, kernel27_1Expr 1 1 k = kernel27_1_r1_1 k := by decide +kernel +noncomputable def kernel27_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel27_1_r1_2_eq : ∀ k : Fin 16, kernel27_1Expr 1 2 k = kernel27_1_r1_2 k := by decide +kernel +noncomputable def kernel27_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel27_1_r1_3_eq : ∀ k : Fin 16, kernel27_1Expr 1 3 k = kernel27_1_r1_3 k := by decide +kernel +noncomputable def kernel27_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel27_1_r1_4_eq : ∀ k : Fin 16, kernel27_1Expr 1 4 k = kernel27_1_r1_4 k := by decide +kernel +noncomputable def kernel27_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel27_1_r1_5_eq : ∀ k : Fin 16, kernel27_1Expr 1 5 k = kernel27_1_r1_5 k := by decide +kernel +noncomputable def kernel27_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel27_1_r1_6_eq : ∀ k : Fin 16, kernel27_1Expr 1 6 k = kernel27_1_r1_6 k := by decide +kernel +noncomputable def kernel27_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel27_1_r1_7_eq : ∀ k : Fin 16, kernel27_1Expr 1 7 k = kernel27_1_r1_7 k := by decide +kernel +noncomputable def kernel27_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel27_1_r1_8_eq : ∀ k : Fin 16, kernel27_1Expr 1 8 k = kernel27_1_r1_8 k := by decide +kernel +noncomputable def kernel27_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel27_1_r1_9_eq : ∀ k : Fin 16, kernel27_1Expr 1 9 k = kernel27_1_r1_9 k := by decide +kernel +noncomputable def kernel27_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r1_10_eq : ∀ k : Fin 16, kernel27_1Expr 1 10 k = kernel27_1_r1_10 k := by decide +kernel +noncomputable def kernel27_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r1_11_eq : ∀ k : Fin 16, kernel27_1Expr 1 11 k = kernel27_1_r1_11 k := by decide +kernel +noncomputable def kernel27_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r1_12_eq : ∀ k : Fin 16, kernel27_1Expr 1 12 k = kernel27_1_r1_12 k := by decide +kernel +noncomputable def kernel27_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r1_13_eq : ∀ k : Fin 16, kernel27_1Expr 1 13 k = kernel27_1_r1_13 k := by decide +kernel +noncomputable def kernel27_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r1_14_eq : ∀ k : Fin 16, kernel27_1Expr 1 14 k = kernel27_1_r1_14 k := by decide +kernel +noncomputable def kernel27_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel27_1_r1_15_eq : ∀ k : Fin 16, kernel27_1Expr 1 15 k = kernel27_1_r1_15 k := by decide +kernel +noncomputable def kernel27_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel27_1_r1_0,kernel27_1_r1_1,kernel27_1_r1_2,kernel27_1_r1_3,kernel27_1_r1_4,kernel27_1_r1_5,kernel27_1_r1_6,kernel27_1_r1_7,kernel27_1_r1_8,kernel27_1_r1_9,kernel27_1_r1_10,kernel27_1_r1_11,kernel27_1_r1_12,kernel27_1_r1_13,kernel27_1_r1_14,kernel27_1_r1_15] +lemma kernel27_1_r1_eq (i k : Fin 16) : kernel27_1Expr 1 i k = kernel27_1_r1 i k := by + fin_cases i + · exact kernel27_1_r1_0_eq k + · exact kernel27_1_r1_1_eq k + · exact kernel27_1_r1_2_eq k + · exact kernel27_1_r1_3_eq k + · exact kernel27_1_r1_4_eq k + · exact kernel27_1_r1_5_eq k + · exact kernel27_1_r1_6_eq k + · exact kernel27_1_r1_7_eq k + · exact kernel27_1_r1_8_eq k + · exact kernel27_1_r1_9_eq k + · exact kernel27_1_r1_10_eq k + · exact kernel27_1_r1_11_eq k + · exact kernel27_1_r1_12_eq k + · exact kernel27_1_r1_13_eq k + · exact kernel27_1_r1_14_eq k + · exact kernel27_1_r1_15_eq k +noncomputable def kernel27_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel27_1_r2_0_eq : ∀ k : Fin 16, kernel27_1Expr 2 0 k = kernel27_1_r2_0 k := by decide +kernel +noncomputable def kernel27_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel27_1_r2_1_eq : ∀ k : Fin 16, kernel27_1Expr 2 1 k = kernel27_1_r2_1 k := by decide +kernel +noncomputable def kernel27_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel27_1_r2_2_eq : ∀ k : Fin 16, kernel27_1Expr 2 2 k = kernel27_1_r2_2 k := by decide +kernel +noncomputable def kernel27_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel27_1_r2_3_eq : ∀ k : Fin 16, kernel27_1Expr 2 3 k = kernel27_1_r2_3 k := by decide +kernel +noncomputable def kernel27_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel27_1_r2_4_eq : ∀ k : Fin 16, kernel27_1Expr 2 4 k = kernel27_1_r2_4 k := by decide +kernel +noncomputable def kernel27_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel27_1_r2_5_eq : ∀ k : Fin 16, kernel27_1Expr 2 5 k = kernel27_1_r2_5 k := by decide +kernel +noncomputable def kernel27_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel27_1_r2_6_eq : ∀ k : Fin 16, kernel27_1Expr 2 6 k = kernel27_1_r2_6 k := by decide +kernel +noncomputable def kernel27_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel27_1_r2_7_eq : ∀ k : Fin 16, kernel27_1Expr 2 7 k = kernel27_1_r2_7 k := by decide +kernel +noncomputable def kernel27_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel27_1_r2_8_eq : ∀ k : Fin 16, kernel27_1Expr 2 8 k = kernel27_1_r2_8 k := by decide +kernel +noncomputable def kernel27_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel27_1_r2_9_eq : ∀ k : Fin 16, kernel27_1Expr 2 9 k = kernel27_1_r2_9 k := by decide +kernel +noncomputable def kernel27_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel27_1_r2_10_eq : ∀ k : Fin 16, kernel27_1Expr 2 10 k = kernel27_1_r2_10 k := by decide +kernel +noncomputable def kernel27_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel27_1_r2_11_eq : ∀ k : Fin 16, kernel27_1Expr 2 11 k = kernel27_1_r2_11 k := by decide +kernel +noncomputable def kernel27_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel27_1_r2_12_eq : ∀ k : Fin 16, kernel27_1Expr 2 12 k = kernel27_1_r2_12 k := by decide +kernel +noncomputable def kernel27_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel27_1_r2_13_eq : ∀ k : Fin 16, kernel27_1Expr 2 13 k = kernel27_1_r2_13 k := by decide +kernel +noncomputable def kernel27_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel27_1_r2_14_eq : ∀ k : Fin 16, kernel27_1Expr 2 14 k = kernel27_1_r2_14 k := by decide +kernel +noncomputable def kernel27_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel27_1_r2_15_eq : ∀ k : Fin 16, kernel27_1Expr 2 15 k = kernel27_1_r2_15 k := by decide +kernel +noncomputable def kernel27_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel27_1_r2_0,kernel27_1_r2_1,kernel27_1_r2_2,kernel27_1_r2_3,kernel27_1_r2_4,kernel27_1_r2_5,kernel27_1_r2_6,kernel27_1_r2_7,kernel27_1_r2_8,kernel27_1_r2_9,kernel27_1_r2_10,kernel27_1_r2_11,kernel27_1_r2_12,kernel27_1_r2_13,kernel27_1_r2_14,kernel27_1_r2_15] +lemma kernel27_1_r2_eq (i k : Fin 16) : kernel27_1Expr 2 i k = kernel27_1_r2 i k := by + fin_cases i + · exact kernel27_1_r2_0_eq k + · exact kernel27_1_r2_1_eq k + · exact kernel27_1_r2_2_eq k + · exact kernel27_1_r2_3_eq k + · exact kernel27_1_r2_4_eq k + · exact kernel27_1_r2_5_eq k + · exact kernel27_1_r2_6_eq k + · exact kernel27_1_r2_7_eq k + · exact kernel27_1_r2_8_eq k + · exact kernel27_1_r2_9_eq k + · exact kernel27_1_r2_10_eq k + · exact kernel27_1_r2_11_eq k + · exact kernel27_1_r2_12_eq k + · exact kernel27_1_r2_13_eq k + · exact kernel27_1_r2_14_eq k + · exact kernel27_1_r2_15_eq k +noncomputable def kernel27_1_r3_0 : Fin 16 → CBox := ![⟨⟨12261766318864,12261766318890⟩,⟨816546617387,816546617412⟩⟩,⟨⟨12237624172527,12237624172552⟩,⟨801103277976,801103278002⟩⟩,⟨⟨12189436709814,12189436709834⟩,⟨770394742349,770394742369⟩⟩,⟨⟨12117397608623,12117397608647⟩,⟨724774880340,724774880361⟩⟩,⟨⟨12021797410804,12021797410835⟩,⟨664768490838,664768490870⟩⟩,⟨⟨11903023496686,11903023496707⟩,⟨591064193590,591064193614⟩⟩,⟨⟨11761559961147,11761559961166⟩,⟨504505114909,504505114929⟩⟩,⟨⟨11597987318459,11597987318485⟩,⟨406077504626,406077504651⟩⟩,⟨⟨11412981950370,11412981950400⟩,⟨296897452306,296897452333⟩⟩,⟨⟨11207315202470,11207315202491⟩,⟨178195899257,178195899281⟩⟩,⟨⟨10981852028180,10981852028207⟩,⟨51302168926,51302168956⟩⟩,⟨⟨10737549078192,10737549078217⟩,⟨(-82373739319),(-82373739293)⟩⟩,⟨⟨10475452135579,10475452135599⟩,⟨(-221359828893),(-221359828873)⟩⟩,⟨⟨10196692803936,10196692803968⟩,⟨(-364141477739),(-364141477707)⟩⟩,⟨⟨9902484366933,9902484366952⟩,⟨(-509181212897),(-509181212878)⟩⟩,⟨⟨9594116752321,9594116752358⟩,⟨(-654938591352),(-654938591318)⟩⟩] +lemma kernel27_1_r3_0_eq : ∀ k : Fin 16, kernel27_1Expr 3 0 k = kernel27_1_r3_0 k := by decide +kernel +noncomputable def kernel27_1_r3_1 : Fin 16 → CBox := ![⟨⟨9272950552582,9272950552601⟩,⟨(-799889888669),(-799889888650)⟩⟩,⟨⟨8940410075079,8940410075103⟩,⟨(-942547300742),(-942547300721)⟩⟩,⟨⟨8597975419503,8597975419533⟩,⟨(-1081477371549),(-1081477371522)⟩⟩,⟨⟨8247173605124,8247173605143⟩,⟨(-1215318373523),(-1215318373503)⟩⟩,⟨⟨7889568797593,7889568797613⟩,⟨(-1342796384872),(-1342796384853)⟩⟩,⟨⟨7526751711624,7526751711644⟩,⟨(-1462739830747),(-1462739830727)⟩⟩,⟨⟨7160328291638,7160328291658⟩,⟨(-1574092282072),(-1574092282053)⟩⟩,⟨⟨6791907797353,6791907797372⟩,⟨(-1675923336555),(-1675923336535)⟩⟩,⟨⟨6423090442956,6423090442975⟩,⟨(-1767437440266),(-1767437440247)⟩⟩,⟨⟨6055454758018,6055454758038⟩,⟨(-1847980544890),(-1847980544870)⟩⟩,⟨⟨5690544853254,5690544853284⟩,⟨(-1917044534532),(-1917044534505)⟩⟩,⟨⟨5329857785531,5329857785561⟩,⟨(-1974269395571),(-1974269395544)⟩⟩,⟨⟨4974831222758,4974831222779⟩,⟨(-2019443143524),(-2019443143499)⟩⟩,⟨⟨4626831610704,4626831610730⟩,⟨(-2052499560568),(-2052499560543)⟩⟩,⟨⟨4287143040255,4287143040280⟩,⟨(-2073513835881),(-2073513835859)⟩⟩,⟨⟨3956957004415,3956957004436⟩,⟨(-2082696237309),(-2082696237285)⟩⟩] +lemma kernel27_1_r3_1_eq : ∀ k : Fin 16, kernel27_1Expr 3 1 k = kernel27_1_r3_1 k := by decide +kernel +noncomputable def kernel27_1_r3_2 : Fin 16 → CBox := ![⟨⟨3637363221143,3637363221162⟩,⟨(-2080383976181),(-2080383976162)⟩⟩,⟨⟨3329341679523,3329341679547⟩,⟨(-2067031456860),(-2067031456839)⟩⟩,⟨⟨3033756044560,3033756044580⟩,⟨(-2043199127897),(-2043199127877)⟩⟩,⟨⟨2751348529933,2751348529964⟩,⟨(-2009541172033),(-2009541172006)⟩⟩,⟨⟨2482736319515,2482736319538⟩,⟨(-1966792287610),(-1966792287581)⟩⟩,⟨⟨2228409587588,2228409587620⟩,⟨(-1915753823281),(-1915753823249)⟩⟩,⟨⟨1988731136108,1988731136134⟩,⟨(-1857279531631),(-1857279531605)⟩⟩,⟨⟨1763937634792,1763937634818⟩,⟨(-1792261205598),(-1792261205572)⟩⟩,⟨⟨1554142418775,1554142418795⟩,⟨(-1721614453688),(-1721614453668)⟩⟩,⟨⟨1359339767706,1359339767733⟩,⟨(-1646264857290),(-1646264857259)⟩⟩,⟨⟨1179410562903,1179410562937⟩,⟨(-1567134735697),(-1567134735660)⟩⟩,⟨⟨1014129193453,1014129193479⟩,⟨(-1485130722340),(-1485130722314)⟩⟩,⟨⟨863171561048,863171561070⟩,⟨(-1401132330217),(-1401132330188)⟩⟩,⟨⟨726124015645,726124015665⟩,⟨(-1315981655851),(-1315981655831)⟩⟩,⟨⟨602493040921,602493040941⟩,⟨(-1230474340858),(-1230474340838)⟩⟩,⟨⟨491715499927,491715499946⟩,⟨(-1145351877868),(-1145351877849)⟩⟩] +lemma kernel27_1_r3_2_eq : ∀ k : Fin 16, kernel27_1Expr 3 2 k = kernel27_1_r3_2 k := by decide +kernel +noncomputable def kernel27_1_r3_3 : Fin 16 → CBox := ![⟨⟨393169247563,393169247583⟩,⟨(-1061295315958),(-1061295315938)⟩⟩,⟨⟨306183917339,306183917371⟩,⟨(-978920388448),(-978920388416)⟩⟩,⟨⟨230051694877,230051694897⟩,⟨(-898774055589),(-898774055569)⟩⟩,⟨⟨164037900157,164037900177⟩,⟨(-821332426069),(-821332426049)⟩⟩,⟨⟨107391213599,107391213625⟩,⟨(-746999994866),(-746999994840)⟩⟩,⟨⟨59353396928,59353396948⟩,⟨(-676110112269),(-676110112249)⟩⟩,⟨⟨19168378931,19168378951⟩,⟨(-608926579160),(-608926579140)⟩⟩,⟨⟨(-13909403254),(-13909403223)⟩,⟨(-545646247694),(-545646247666)⟩⟩,⟨⟨(-40607494524),(-40607494504)⟩,⟨(-486402495029),(-486402495009)⟩⟩,⟨⟨(-61628808611),(-61628808591)⟩,⟨(-431269429597),(-431269429577)⟩⟩,⟨⟨(-77645952924),(-77645952904)⟩,⟨(-380266685482),(-380266685462)⟩⟩,⟨⟨(-89296511615),(-89296511594)⟩,⟨(-333364660374),(-333364660350)⟩⟩,⟨⟨(-97179285362),(-97179285334)⟩,⟨(-290490055622),(-290490055591)⟩⟩,⟨⟨(-101851467765),(-101851467745)⟩,⟨(-251531583385),(-251531583365)⟩⟩,⟨⟨(-103826720440),(-103826720409)⟩,⟨(-216345714821),(-216345714793)⟩⟩,⟨⟨(-103574094006),(-103574093985)⟩,⟨(-184762354362),(-184762354342)⟩⟩] +lemma kernel27_1_r3_3_eq : ∀ k : Fin 16, kernel27_1Expr 3 3 k = kernel27_1_r3_3 k := by decide +kernel +noncomputable def kernel27_1_r3_4 : Fin 16 → CBox := ![⟨⟨(-101517729884),(-101517729864)⟩,⟨(-156590338373),(-156590338353)⟩⟩,⟨⟨(-98037267700),(-98037267680)⟩,⟨(-131622670308),(-131622670288)⟩⟩,⟨⟨(-93468876096),(-93468876076)⟩,⟨(-109641419743),(-109641419723)⟩⟩,⟨⟨(-88106820167),(-88106820139)⟩,⟨(-90422227528),(-90422227497)⟩⟩,⟨⟨(-82205476733),(-82205476713)⟩,⟨(-73738374454),(-73738374434)⟩⟩,⟨⟨(-75981708891),(-75981708871)⟩,⟨(-59364385434),(-59364385414)⟩⟩,⟨⟨(-69617513638),(-69617513617)⟩,⟨(-47079154273),(-47079154253)⟩⟩,⟨⟨(-63262860614),(-63262860586)⟩,⟨(-36668586999),(-36668586967)⟩⟩,⟨⟨(-57038645595),(-57038645568)⟩,⟨(-27927772452),(-27927772425)⟩⟩,⟨⟨(-51039689129),(-51039689108)⟩,⟨(-20662698364),(-20662698343)⟩⟩,⟨⟨(-45337718696),(-45337718675)⟩,⟨(-14691538977),(-14691538956)⟩⟩,⟨⟨(-39984280621),(-39984280601)⟩,⟨(-9845546636),(-9845546616)⟩⟩,⟨⟨(-35013536949),(-35013536923)⟩,⟨(-5969584376),(-5969584349)⟩⟩,⟨⟨(-30444910685),(-30444910650)⟩,⟨(-2922339541),(-2922339503)⟩⟩,⟨⟨(-26285551343),(-26285551323)⟩,⟨(-576260201),(-576260181)⟩⟩,⟨⟨(-22532600526),(-22532600505)⟩,⟨1182743244,1182743265⟩⟩] +lemma kernel27_1_r3_4_eq : ∀ k : Fin 16, kernel27_1Expr 3 4 k = kernel27_1_r3_4 k := by decide +kernel +noncomputable def kernel27_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-19175244501),(-19175244469)⟩,⟨2455790124,2455790152⟩⟩,⟨⟨(-16196547579),(-16196547558)⟩,⟨3331675172,3331675193⟩⟩,⟨⟨(-13575065685),(-13575065653)⟩,⟨3887630516,3887630545⟩⟩,⟨⟨(-11286244392),(-11286244371)⟩,⟨4190169904,4190169924⟩⟩,⟨⟨(-9303610323),(-9303610302)⟩,⟨4295983958,4295983978⟩⟩,⟨⟨(-7599767263),(-7599767238)⟩,⟨4252859715,4252859738⟩⟩,⟨⟨(-6147211654),(-6147211634)⟩,⟨4100600963,4100600984⟩⟩,⟨⟨(-4918983198),(-4918983178)⟩,⟨3871929966,3871929986⟩⟩,⟨⟨(-3889167655),(-3889167634)⟩,⟨3593354920,3593354941⟩⟩,⟨⟨(-3033269270),(-3033269245)⟩,⟨3285990849,3285990872⟩⟩,⟨⟨(-2328470105),(-2328470083)⟩,⟨2966325004,2966325030⟩⟩,⟨⟨(-1753793113),(-1753793092)⟩,⟨2646920656,2646920677⟩⟩,⟨⟨(-1290184899),(-1290184871)⟩,⟨2337055798,2337055826⟩⟩,⟨⟨(-920532915),(-920532894)⟩,⟨2043295483,2043295504⟩⟩,⟨⟨(-629630771),(-629630750)⟩,⟨1769998293,1769998314⟩⟩,⟨⟨(-404103526),(-404103505)⟩,⟨1519758997,1519759018⟩⟩] +lemma kernel27_1_r3_5_eq : ∀ k : Fin 16, kernel27_1Expr 3 5 k = kernel27_1_r3_5 k := by decide +kernel +noncomputable def kernel27_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-232303799),(-232303778)⟩,⟨1293790609,1293790630⟩⟩,⟨⟨(-104187786),(-104187761)⟩,⟨1092249797,1092249819⟩⟩,⟨⟨(-11178904),(-11178883)⟩,⟨914510378,914510399⟩⟩,⟨⟨53974435,53974458⟩,⟨759389766,759389791⟩⟩,⟨⟨97341863,97341891⟩,⟨625333496,625333523⟩⟩,⟨⟨123950785,123950806⟩,⟨510562962,510562983⟩⟩,⟨⟨137919760,137919781⟩,⟨413191119,413191140⟩⟩,⟨⟨142583533,142583559⟩,⟨331311022,331311045⟩⟩,⟨⟨140607990,140608011⟩,⟨263061333,263061355⟩⟩,⟨⟨134094505,134094527⟩,⟨206672782,206672803⟩⟩,⟨⟨124673230,124673256⟩,⟨160499208,160499231⟩⟩,⟨⟨113585453,113585481⟩,⟨123036119,123036147⟩⟩,⟨⟨101755385,101755407⟩,⟨92929681,92929702⟩⟩,⟨⟨89851988,89852009⟩,⟨68978204,68978225⟩⟩,⟨⟨78341643,78341673⟩,⟨50128331,50128364⟩⟩,⟨⟨67532433,67532470⟩,⟨35467318,35467358⟩⟩] +lemma kernel27_1_r3_6_eq : ∀ k : Fin 16, kernel27_1Expr 3 6 k = kernel27_1_r3_6 k := by decide +kernel +noncomputable def kernel27_1_r3_7 : Fin 16 → CBox := ![⟨⟨57610933,57610955⟩,⟨24212858,24212879⟩⟩,⟨⟨48672398,48672420⟩,⟨15701330,15701352⟩⟩,⟨⟨40745258,40745280⟩,⟨9375535,9375557⟩⟩,⟨⟨33810659,33810690⟩,⟨4772236,4772269⟩⟩,⟨⟨27817801,27817825⟩,⟨1510140,1510166⟩⟩,⟨⟨22695818,22695847⟩,⟨(-721475),(-721447)⟩⟩,⟨⟨18362778,18362800⟩,⟨(-2173207),(-2173185)⟩⟩,⟨⟨14732263,14732291⟩,⟨(-3044982),(-3044954)⟩⟩,⟨⟨11718211,11718233⟩,⟨(-3494492),(-3494470)⟩⟩,⟨⟨9238059,9238085⟩,⟨(-3644616),(-3644592)⟩⟩,⟨⟨7214938,7214965⟩,⟨(-3589783),(-3589759)⟩⟩,⟨⟨5578843,5578864⟩,⟨(-3401461),(-3401439)⟩⟩,⟨⟨4267170,4267194⟩,⟨(-3132804),(-3132777)⟩⟩,⟨⟨3224894,3224916⟩,⟨(-2822475),(-2822453)⟩⟩,⟨⟨2404229,2404252⟩,⟨(-2497900),(-2497874)⟩⟩,⟨⟨1764248,1764272⟩,⟨(-2177821),(-2177794)⟩⟩] +lemma kernel27_1_r3_7_eq : ∀ k : Fin 16, kernel27_1Expr 3 7 k = kernel27_1_r3_7 k := by decide +kernel +noncomputable def kernel27_1_r3_8 : Fin 16 → CBox := ![⟨⟨1270258,1270285⟩,⟨(-1874436),(-1874412)⟩⟩,⟨⟨893186,893210⟩,⟨(-1595084),(-1595057)⟩⟩,⟨⟨608890,608924⟩,⟨(-1343562),(-1343531)⟩⟩,⟨⟨397532,397559⟩,⟨(-1121157),(-1121133)⟩⟩,⟨⟨242934,242963⟩,⟨(-927478),(-927449)⟩⟩,⟨⟨132064,132093⟩,⟨(-760986),(-760957)⟩⟩,⟨⟨54484,54506⟩,⟨(-619511),(-619489)⟩⟩,⟨⟨1914,1950⟩,⟨(-500531),(-500495)⟩⟩,⟨⟨(-32087),(-32060)⟩,⟨(-401401),(-401377)⟩⟩,⟨⟨(-52587),(-52563)⟩,⟨(-319544),(-319517)⟩⟩,⟨⟨(-63440),(-63418)⟩,⟨(-252492),(-252470)⟩⟩,⟨⟨(-67582),(-67560)⟩,⟨(-198017),(-197995)⟩⟩,⟨⟨(-67216),(-67193)⟩,⟨(-154093),(-154071)⟩⟩,⟨⟨(-63964),(-63935)⟩,⟨(-118934),(-118905)⟩⟩,⟨⟨(-58998),(-58971)⟩,⟨(-91007),(-90983)⟩⟩,⟨⟨(-53158),(-53124)⟩,⟨(-68982),(-68950)⟩⟩] +lemma kernel27_1_r3_8_eq : ∀ k : Fin 16, kernel27_1Expr 3 8 k = kernel27_1_r3_8 k := by decide +kernel +noncomputable def kernel27_1_r3_9 : Fin 16 → CBox := ![⟨⟨(-47025),(-46995)⟩,⟨(-51752),(-51723)⟩⟩,⟨⟨(-40977),(-40947)⟩,⟨(-38370),(-38340)⟩⟩,⟨⟨(-35258),(-35224)⟩,⟨(-28069),(-28037)⟩⟩,⟨⟨(-30005),(-29977)⟩,⟨(-20206),(-20181)⟩⟩,⟨⟨(-25299),(-25271)⟩,⟨(-14257),(-14232)⟩⟩,⟨⟨(-21146),(-21121)⟩,⟨(-9812),(-9785)⟩⟩,⟨⟨(-17545),(-17523)⟩,⟨(-6522),(-6499)⟩⟩,⟨⟨(-14460),(-14425)⟩,⟨(-4128),(-4096)⟩⟩,⟨⟨(-11827),(-11804)⟩,⟨(-2408),(-2385)⟩⟩,⟨⟨(-9625),(-9602)⟩,⟨(-1202),(-1179)⟩⟩,⟨⟨(-7789),(-7757)⟩,⟨(-376),(-341)⟩⟩,⟨⟨(-6268),(-6241)⟩,⟨176,201⟩⟩,⟨⟨(-5010),(-4982)⟩,⟨518,543⟩⟩,⟨⟨(-3990),(-3963)⟩,⟨717,742⟩⟩,⟨⟨(-3160),(-3130)⟩,⟨803,833⟩⟩,⟨⟨(-2493),(-2465)⟩,⟨833,858⟩⟩] +lemma kernel27_1_r3_9_eq : ∀ k : Fin 16, kernel27_1Expr 3 9 k = kernel27_1_r3_9 k := by decide +kernel +noncomputable def kernel27_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-1950),(-1927)⟩,⟨818,841⟩⟩,⟨⟨(-1526),(-1488)⟩,⟨761,799⟩⟩,⟨⟨(-1184),(-1161)⟩,⟨703,726⟩⟩,⟨⟨(-909),(-884)⟩,⟨629,657⟩⟩,⟨⟨(-700),(-670)⟩,⟨552,583⟩⟩,⟨⟨(-531),(-508)⟩,⟨487,510⟩⟩,⟨⟨(-406),(-383)⟩,⟨415,438⟩⟩,⟨⟨(-308),(-275)⟩,⟨348,384⟩⟩,⟨⟨(-228),(-197)⟩,⟨298,328⟩⟩,⟨⟨(-170),(-144)⟩,⟨254,282⟩⟩,⟨⟨(-127),(-99)⟩,⟨212,238⟩⟩,⟨⟨(-97),(-66)⟩,⟨173,204⟩⟩,⟨⟨(-69),(-38)⟩,⟨141,172⟩⟩,⟨⟨(-51),(-23)⟩,⟨114,140⟩⟩,⟨⟨(-39),(-3)⟩,⟨87,120⟩⟩,⟨⟨(-31),8⟩,⟨65,103⟩⟩] +lemma kernel27_1_r3_10_eq : ∀ k : Fin 16, kernel27_1Expr 3 10 k = kernel27_1_r3_10 k := by decide +kernel +noncomputable def kernel27_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-21),5⟩,⟨52,81⟩⟩,⟨⟨(-18),13⟩,⟨42,73⟩⟩,⟨⟨(-11),15⟩,⟨35,63⟩⟩,⟨⟨(-8),18⟩,⟨27,56⟩⟩,⟨⟨(-13),26⟩,⟨12,51⟩⟩,⟨⟨(-13),16⟩,⟨15,41⟩⟩,⟨⟨(-6),18⟩,⟨7,31⟩⟩,⟨⟨(-5),18⟩,⟨7,31⟩⟩,⟨⟨(-8),28⟩,⟨(-3),31⟩⟩,⟨⟨(-11),26⟩,⟨(-8),26⟩⟩,⟨⟨(-11),18⟩,⟨(-6),21⟩⟩,⟨⟨(-11),18⟩,⟨(-6),21⟩⟩,⟨⟨(-11),18⟩,⟨(-6),21⟩⟩,⟨⟨(-11),18⟩,⟨(-6),21⟩⟩,⟨⟨(-11),18⟩,⟨(-6),21⟩⟩,⟨⟨(-11),18⟩,⟨(-6),21⟩⟩] +lemma kernel27_1_r3_11_eq : ∀ k : Fin 16, kernel27_1Expr 3 11 k = kernel27_1_r3_11 k := by decide +kernel +noncomputable def kernel27_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-11),18⟩,⟨(-6),21⟩⟩,⟨⟨(-11),18⟩,⟨(-6),21⟩⟩,⟨⟨(-16),23⟩,⟨(-18),21⟩⟩,⟨⟨(-16),24⟩,⟨(-18),21⟩⟩,⟨⟨(-16),24⟩,⟨(-18),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-16),24⟩,⟨(-19),21⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel27_1_r3_12_eq : ∀ k : Fin 16, kernel27_1Expr 3 12 k = kernel27_1_r3_12 k := by decide +kernel +noncomputable def kernel27_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-19),21⟩,⟨(-24),16⟩⟩,⟨⟨(-19),21⟩,⟨(-24),16⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-19),21⟩,⟨(-24),16⟩⟩,⟨⟨(-19),21⟩,⟨(-24),16⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel27_1_r3_13_eq : ∀ k : Fin 16, kernel27_1Expr 3 13 k = kernel27_1_r3_13 k := by decide +kernel +noncomputable def kernel27_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel27_1_r3_14_eq : ∀ k : Fin 16, kernel27_1Expr 3 14 k = kernel27_1_r3_14 k := by decide +kernel +noncomputable def kernel27_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel27_1_r3_15_eq : ∀ k : Fin 16, kernel27_1Expr 3 15 k = kernel27_1_r3_15 k := by decide +kernel +noncomputable def kernel27_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel27_1_r3_0,kernel27_1_r3_1,kernel27_1_r3_2,kernel27_1_r3_3,kernel27_1_r3_4,kernel27_1_r3_5,kernel27_1_r3_6,kernel27_1_r3_7,kernel27_1_r3_8,kernel27_1_r3_9,kernel27_1_r3_10,kernel27_1_r3_11,kernel27_1_r3_12,kernel27_1_r3_13,kernel27_1_r3_14,kernel27_1_r3_15] +lemma kernel27_1_r3_eq (i k : Fin 16) : kernel27_1Expr 3 i k = kernel27_1_r3 i k := by + fin_cases i + · exact kernel27_1_r3_0_eq k + · exact kernel27_1_r3_1_eq k + · exact kernel27_1_r3_2_eq k + · exact kernel27_1_r3_3_eq k + · exact kernel27_1_r3_4_eq k + · exact kernel27_1_r3_5_eq k + · exact kernel27_1_r3_6_eq k + · exact kernel27_1_r3_7_eq k + · exact kernel27_1_r3_8_eq k + · exact kernel27_1_r3_9_eq k + · exact kernel27_1_r3_10_eq k + · exact kernel27_1_r3_11_eq k + · exact kernel27_1_r3_12_eq k + · exact kernel27_1_r3_13_eq k + · exact kernel27_1_r3_14_eq k + · exact kernel27_1_r3_15_eq k +noncomputable def kernel27_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-16238071356120884828464),(-16238071356120851108682)⟩,⟨23473652374419728395259,23473652374419762114819⟩⟩,⟨⟨(-16192682740068812705537),(-16192682740068779028800)⟩,⟨23460887736160021258758,23460887736160054935273⟩⟩,⟨⟨(-16102123013662007905783),(-16102123013661974315034)⟩,⟨23435263239858478278402,23435263239858511868933⟩⟩,⟨⟨(-15966826262554370802594),(-15966826262554337340448)⟩,⟨23396590245740161221580,23396590245740194683505⟩⟩,⟨⟨(-15787441295881027515854),(-15787441295880994224462)⟩,⟨23344590269613285406913,23344590269613318698087⟩⟩,⟨⟨(-15564828849360227949688),(-15564828849360194870571)⟩,⟨23278900286472356203727,23278900286472389282634⟩⟩,⟨⟨(-15300057834180941676990),(-15300057834180908850877)⟩,⟨23199079691103888703065,23199079691103921528971⟩⟩,⟨⟨(-14994400614649127222450),(-14994400614649094689130)⟩,⟨23104618822142191923315,23104618822142224456440⟩⟩,⟨⟨(-14649327295452529337038),(-14649327295452497135235)⟩,⟨22994948934476789440601,22994948934476821642209⟩⟩,⟨⟨(-14266498998638689826958),(-14266498998638657994198)⟩,⟨22869453484592577415938,22869453484592609248511⟩⟩,⟨⟨(-13847760111174074303745),(-13847760111174042876216)⟩,⟨22727480574569688835188,22727480574569720262540⟩⟩,⟨⟨(-13395129486413578878109),(-13395129486413547890540)⟩,⟨22568356383319052180819,22568356383319083168220⟩⟩,⟨⟨(-12910790587063544422944),(-12910790587063513908509)⟩,⟨22391399398412461451699,22391399398412491965978⟩⟩,⟨⟨(-12397080563322910031673),(-12397080563322880021848)⟩,⟨22195935248804528300227,22195935248804558309900⟩⟩,⟨⟨(-11856478267839396553765),(-11856478267839367078300)⟩,⟨21981311928048240392674,21981311928048269868001⟩⟩,⟨⟨(-11291591218870011812769),(-11291591218869982899549)⟩,⟨21746915189470656453530,21746915189470685366624⟩⟩] +lemma kernel27_1_r4_0_eq : ∀ k : Fin 16, kernel27_1Expr 4 0 k = kernel27_1_r4_0 k := by decide +kernel +noncomputable def kernel27_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-10705141534482835966393),(-10705141534482807641434)⟩,⟨21492183889375762207326,21492183889375790532170⟩⟩,⟨⟨(-10099950873621534552467),(-10099950873621506839719)⟩,⟨21216625051829177391354,21216625051829205103995⟩⟩,⟨⟨(-9478924434165297024271),(-9478924434165269945745)⟩,⟨20919828429077426940863,20919828429077454019296⟩⟩,⟨⟨(-8845034073496450493185),(-8845034073496424068738)⟩,⟨20601480335253117812488,20601480335253144236853⟩⟩,⟨⟨(-8201300633233462692739),(-8201300633233436940237)⟩,⟨20261376537769340017792,20261376537769365770224⟩⟩,⟨⟨(-7550775566357779390859),(-7550775566357754325901)⟩,⟨19899434000722840437477,19899434000722865502377⟩⟩,⟨⟨(-6896521981586841621086),(-6896521981586817257307)⟩,⟨19515701287671143596555,19515701287671167960290⟩⟩,⟨⟨(-6241595236126975584056),(-6241595236126951932807)⟩,⟨19110367447239865717575,19110367447239889368788⟩⟩,⟨⟨(-5589023223468016477937),(-5589023223467993548653)⟩,⟨18683769224017385182937,18683769224017408112197⟩⟩,⟨⟨(-4941786517240429675766),(-4941786517240407475553)⟩,⟨18236396458915915747406,18236396458915937947614⟩⟩,⟨⟨(-4302798544933757375228),(-4302798544933735909272)⟩,⟨17768895567378189359421,17768895567378210825379⟩⟩,⟨⟨(-3674885976075683164003),(-3674885976075662435345)⟩,⟨17282071010191577314524,17282071010191598043194⟩⟩,⟨⟨(-3060769517922285578899),(-3060769517922265588919)⟩,⟨16776884699889621494248,16776884699889641484248⟩⟩,⟨⟨(-2463045317475929290263),(-2463045317475910037922)⟩,⟨16254453315379934134964,16254453315379953387336⟩⟩,⟨⟨(-1884167171436623759873),(-1884167171436605242509)⟩,⟨15716043528099637794514,15716043528099656311923⟩⟩,⟨⟨(-1326429745268629190207),(-1326429745268611403387)⟩,⟨15163065174190591797966,15163065174190609584839⟩⟩] +lemma kernel27_1_r4_1_eq : ∀ k : Fin 16, kernel27_1Expr 4 1 k = kernel27_1_r4_1 k := by decide +kernel +noncomputable def kernel27_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-791952998751899228427),(-791952998751882166388)⟩,⟨14597062438402997810218,14597062438403014872317⟩⟩,⟨⟨(-282668008081974238080),(-282668008081957893048)⟩,⟨14019703146153527530260,14019703146153543875356⟩⟩,⟨⟨199695636249025022037,199695636249040658950⟩,⟨13432766289848138528703,13432766289848154165693⟩⟩,⟨⟨653620690866654174019,653620690866669114751⟩,⟨12838127943695528912586,12838127943695543853397⟩⟩,⟨⟨1077811232960056550125,1077811232960070806539⟩,⟨12237745747261351369227,12237745747261365625728⟩⟩,⟨⟨1471199619300104873164,1471199619300118458455⟩,⟨11633642161445491483681,11633642161445505069066⟩⟩,⟨⟨1832951328033876279354,1832951328033889207334⟩,⟨11027886720939276071950,11027886720939289000027⟩⟩,⟨⟨2162467606624035883204,2162467606624048169250⟩,⟨10422577524116971319558,10422577524116983605703⟩⟩,⟨⟨2459385877541270906240,2459385877541282566079⟩,⟨9819822214373976346839,9819822214373988006777⟩⟩,⟨⟨2723577883147426573399,2723577883147437624103⟩,⟨9221718715847337796367,9221718715847348847172⟩⟩,⟨⟨2955145582091907239344,2955145582091917698117⟩,⟨8630335991022930245194,8630335991022940704068⟩⟩,⟨⟨3154414840911773856416,3154414840911783741597⟩,⟨8047695087811052946368,8047695087811062831648⟩⟩,⟨⟨3321926995779212923361,3321926995779222253197⟩,⟨7475750739209692842036,7475750739209702171969⟩⟩,⟨⟨3458428389869723573812,3458428389869732370233⟩,⟨6916373769715260507059,6916373769715269303576⟩⟩,⟨⟨3564858021024543007117,3564858021024551290776⟩,⟨6371334549319888092427,6371334549319896376183⟩⟩,⟨⟨3642333461663245422237,3642333461663253212507⟩,⟨5842287718479613136764,5842287718479620927129⟩⟩] +lemma kernel27_1_r4_2_eq : ∀ k : Fin 16, kernel27_1Expr 4 2 k = kernel27_1_r4_2 k := by decide +kernel +noncomputable def kernel27_1_r4_3 : Fin 16 → CBox := ![⟨⟨3692135237710998819580,3692135237711006135383⟩,⟨5330758386164262511137,5330758386164269827033⟩⟩,⟨⟨3715689875129620000672,3715689875129626861701⟩,⟨4838129978405187320137,4838129978405194181248⟩⟩,⟨⟨3714551841031346017662,3714551841031352442997⟩,⟨4365633887113064792400,4365633887113071217808⟩⟩,⟨⟨3690384620928814035658,3690384620928820044953⟩,⟨3914341038880918704804,3914341038880924714162⟩⟩,⟨⟨3644941184134362893561,3644941184134368505654⟩,⟨3485155471605883720143,3485155471605889332294⟩⟩,⟨⟨3580044095455184741430,3580044095455189975521⟩,⟨3078809973684709403483,3078809973684714637624⟩⟩,⟨⟨3497565533020967825755,3497565533020972700197⟩,⟨2695863806914825303206,2695863806914830177692⟩⟩,⟨⟨3399407469307767407597,3399407469307771941974⟩,⟨2336702500726575967944,2336702500726580502351⟩⟩,⟨⟨3287482265264260122211,3287482265264264334310⟩,⟨2001539672638345121536,2001539672638349333660⟩⟩,⟨⟨3163693916078752558229,3163693916078756465728⟩,⟨1690420798498339038930,1690420798498342946454⟩⟩,⟨⟨3029920171813472953394,3029920171813476572991⟩,⟨1403228826751703100285,1403228826751706719901⟩⟩,⟨⟨2887995737227700598337,2887995737227703946705⟩,⟨1139691504195611295481,1139691504195614643856⟩⟩,⟨⟨2739696733039764605523,2739696733039767698709⟩,⟨899390256940866069166,899390256940869162352⟩⟩,⟨⟨2586726576131029954840,2586726576131032808551⟩,⟨681770449994994895474,681770449994997749184⟩⟩,⟨⟨2430703409315694525729,2430703409315697154571⟩,⟨486152832344319565731,486152832344322194569⟩⟩,⟨⟨2273149182869427318915,2273149182869429737464⟩,⟨311745961876758842709,311745961876761261254⟩⟩] +lemma kernel27_1_r4_3_eq : ∀ k : Fin 16, kernel27_1Expr 4 3 k = kernel27_1_r4_3 k := by decide +kernel +noncomputable def kernel27_1_r4_4 : Fin 16 → CBox := ![⟨⟨2115480460631510392494,2115480460631512614208⟩,⟨157659396095069462879,157659396095071684582⟩⟩,⟨⟨1959000993780940476042,1959000993780942514274⟩,⟨22917430368198955037,22917430368200993258⟩⟩,⟨⟨1804896075941253112398,1804896075941254979489⟩,⟨(-93526834591767926599),(-93526834591766059519)⟩⟩,⟨⟨1654228664673910349082,1654228664673912057130⟩,⟨(-192777310397224002315),(-192777310397222294275)⟩⟩,⟨⟨1507937227222296660450,1507937227222298220561⟩,⟨(-275980830447032980036),(-275980830447031419936)⟩⟩,⟨⟨1366835243065625779658,1366835243065627202774⟩,⟨(-344313346636336418726),(-344313346636334995620)⟩⟩,⟨⟨1231612272872981356597,1231612272872982652743⟩,⟨(-398966594464647568934),(-398966594464646272805)⟩⟩,⟨⟨1102836483182593998842,1102836483182595177741⟩,⟨(-441135390708813905042),(-441135390708812726156)⟩⟩,⟨⟨980958498865412905987,980958498865413976554⟩,⟨(-472005708631929904876),(-472005708631928834318)⟩⟩,⟨⟨866316441380389180007,866316441380390150922⟩,⟨(-492743654791882490989),(-492743654791881520087)⟩⟩,⟨⟨759142000124906253992,759142000124907133144⟩,⟨(-504485449410377838152),(-504485449410376959013)⟩⟩,⟨⟨659567376878691656100,659567376878692451101⟩,⟨(-508328489484671945823),(-508328489484671150833)⟩⟩,⟨⟨567632939404779001468,567632939404779721671⟩,⟨(-505323550879506379777),(-505323550879505659588)⟩⟩,⟨⟨483295419602702196827,483295419602702848607⟩,⟨(-496468163013391450209),(-496468163013390798433)⟩⟩,⟨⟨406436494033947793400,406436494033948382365⟩,⟨(-482701167905453578330),(-482701167905452989373)⟩⟩,⟨⟨336871589923258113600,336871589923258645108⟩,⟨(-464898454687549288574),(-464898454687548757070)⟩⟩] +lemma kernel27_1_r4_4_eq : ∀ k : Fin 16, kernel27_1Expr 4 4 k = kernel27_1_r4_4 k := by decide +kernel +noncomputable def kernel27_1_r4_5 : Fin 16 → CBox := ![⟨⟨274358767594929893939,274358767594930372831⟩,⟨(-443869841571076513090),(-443869841571076034200)⟩⟩,⟨⟨218607540401925387671,218607540401925818633⟩,⟨(-420357059991334788867),(-420357059991334357909)⟩⟩,⟨⟨169287505187133083174,169287505187133470402⟩,⟨(-395032780475145985727),(-395032780475145598499)⟩⟩,⟨⟨126036669799795034053,126036669799795381546⟩,⟨(-368500606866408164608),(-368500606866407817115)⟩⟩,⟨⟨88469378785768977633,88469378785769288967⟩,⟨(-341295955011419514141),(-341295955011419202807)⟩⟩,⟨⟨56183753688748043890,56183753688748322501⟩,⟨(-313887723900058334874),(-313887723900058056263)⟩⟩,⟨⟨28768580062504083059,28768580062504332002⟩,⟨(-286680661568902034623),(-286680661568901785679)⟩⟩,⟨⟨5809588943082925874,5809588943083148045⟩,⟨(-260018324731034494929),(-260018324731034272758)⟩⟩,⟨⟨(-13104904166418069916),(-13104904166417871935)⟩,⟨(-234186529987527010765),(-234186529987526812783)⟩⟩,⟨⟨(-28379025084466684212),(-28379025084466507992)⟩,⟨(-209417195436972650587),(-209417195436972474362)⟩⟩,⟨⟨(-40405040038185487033),(-40405040038185330413)⟩,⟨(-185892474335716964711),(-185892474335716808087)⟩⟩,⟨⟨(-49559723929244966508),(-49559723929244827442)⟩,⟨(-163749086948265749176),(-163749086948265610110)⟩⟩,⟨⟨(-56201382301304587558),(-56201382301304464279)⟩,⟨(-143082762620517320615),(-143082762620517197335)⟩⟩,⟨⟨(-60667501587000664118),(-60667501587000554955)⟩,⟨(-123952711151734792530),(-123952711151734683366)⟩⟩,⟨⟨(-63272993761550841036),(-63272993761550744527)⟩,⟨(-106386050473987436704),(-106386050473987340192)⟩⟩,⟨⟨(-64308994611039077073),(-64308994611038991783)⟩,⟨(-90382126212397083569),(-90382126212396998276)⟩⟩] +lemma kernel27_1_r4_5_eq : ∀ k : Fin 16, kernel27_1Expr 4 5 k = kernel27_1_r4_5 k := by decide +kernel +noncomputable def kernel27_1_r4_6 : Fin 16 → CBox := ![⟨⟨(-64042169434478108854),(-64042169434478033622)⟩,⟨(-75916667647412829465),(-75916667647412754229)⟩⟩,⟨⟨(-62714476101691266145),(-62714476101691199834)⟩,⟨(-62945733697836122770),(-62945733697836056459)⟩⟩,⟨⟨(-60543332913969421423),(-60543332913969363068)⟩,⟨(-51409411576278714680),(-51409411576278656325)⟩⟩,⟨⟨(-57722137564494792876),(-57722137564494741575)⟩,⟨(-41235239546214460676),(-41235239546214409372)⟩⟩,⟨⟨(-54421083552131168624),(-54421083552131123604)⟩,⟨(-32341333566723432453),(-32341333566723387433)⟩⟩,⟨⟨(-50788221530411660479),(-50788221530411621002)⟩,⟨(-24639205409931232027),(-24639205409931192550)⟩⟩,⟨⟨(-46950715127300845813),(-46950715127300811218)⟩,⟨(-18036266967825199395),(-18036266967825164800)⟩⟩,⟨⟨(-43016243598312907081),(-43016243598312876782)⟩,⟨(-12438021848543220586),(-12438021848543190287)⟩⟩,⟨⟨(-39074507122093437874),(-39074507122093411385)⟩,⟨(-7749950943563712947),(-7749950943563686455)⟩⟩,⟨⟨(-35198794462604602439),(-35198794462604579297)⟩,⟨(-3879103398278349154),(-3879103398278326009)⟩⟩,⟨⟨(-31447576960964523836),(-31447576960964503648)⟩,⟨(-735408334462240393),(-735408334462220205)⟩⟩,⟨⟨(-27866097247617553427),(-27866097247617535838)⟩,⟨1767274229697536777,1767274229697554366⟩⟩,⟨⟨(-24487925558602466968),(-24487925558602451656)⟩,⟨3710342503975831247,3710342503975846556⟩⟩,⟨⟨(-21336460988731423370),(-21336460988731410055)⟩,⟨5169859760194395154,5169859760194408469⟩⟩,⟨⟨(-18426359324941325580),(-18426359324941314017)⟩,⟨6216155639563624951,6216155639563636514⟩⟩,⟨⟨(-15764873195975988253),(-15764873195975978217)⟩,⟨6913598400405838440,6913598400405848479⟩⟩] +lemma kernel27_1_r4_6_eq : ∀ k : Fin 16, kernel27_1Expr 4 6 k = kernel27_1_r4_6 k := by decide +kernel +noncomputable def kernel27_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-13353094086658881412),(-13353094086658872705)⟩,⟨7320514807003768164,7320514807003776871⟩⟩,⟨⟨(-11187089248439673367),(-11187089248439665828)⟩,⟨7489235045667405718,7489235045667413257⟩⟩,⟨⟨(-9258929659374529934),(-9258929659374523407)⟩,⟨7466241112358942578,7466241112358949105⟩⟩,⟨⟨(-7557607926505045761),(-7557607926505040120)⟩,⟨7292398470176238805,7292398470176244449⟩⟩,⟨⟨(-6069847374234435768),(-6069847374234430895)⟩,⟨7003252350975897141,7003252350975902017⟩⟩,⟨⟨(-4780805526996084271),(-4780805526996080074)⟩,⟨6629371804702657980,6629371804702662178⟩⟩,⟨⟨(-3674676785638417317),(-3674676785638413705)⟩,⟨6196726419988857936,6196726419988861547⟩⟩,⟨⟨(-2735200334378229764),(-2735200334378226649)⟩,⟨5727082494630121164,5727082494630124279⟩⟩,⟨⟨(-1946080224642992066),(-1946080224642989380)⟩,⟨5238407276384692618,5238407276384695304⟩⟩,⟨⟨(-1291325193686638299),(-1291325193686635984)⟩,⟨4745271682563017118,4745271682563019434⟩⟩,⟨⟨(-755516122436007333),(-755516122436005336)⟩,⟨4259243608031448004,4259243608031450001⟩⟩,⟨⟨(-324009153053915751),(-324009153053914035)⟩,⟨3789265519832500309,3789265519832502024⟩⟩,⟨⟨16917592997121852,16917592997123323⟩,⟨3342011493798348196,3342011493798349670⟩⟩,⟨⟨279965996861229973,279965996861231246⟩,⟨2922220161804122471,2922220161804123744⟩⟩,⟨⟨476761294727972313,476761294727973401⟩,⟨2533001200835821404,2533001200835822495⟩⟩,⟨⟨617829939695714101,617829939695715043⟩,⟨2176114004937025986,2176114004937026927⟩⟩] +lemma kernel27_1_r4_7_eq : ∀ k : Fin 16, kernel27_1Expr 4 7 k = kernel27_1_r4_7 k := by decide +kernel +noncomputable def kernel27_1_r4_8 : Fin 16 → CBox := ![⟨⟨712605650525675671,712605650525676473⟩,⟨1852218040639821771,1852218040639822574⟩⟩,⟨⟨769457908516452146,769457908516452835⟩,⟨1561095101404423059,1561095101404423749⟩⟩,⟨⟨795737770759414173,795737770759414767⟩,⟨1301844255320552512,1301844255320553110⟩⟩,⟨⟨797836479612074651,797836479612075158⟩,⟨1073050733310861813,1073050733310862319⟩⟩,⟨⟨781252948794088188,781252948794088625⟩,⟨872930344158026391,872930344158026828⟩⟩,⟨⟨750666783557317229,750666783557317606⟩,⟨699451240509639457,699451240509639835⟩⟩,⟨⟨710014036248431047,710014036248431380⟩,⟨550435009585790103,550435009585790433⟩⟩,⟨⟨662563402222605043,662563402222605328⟩,⟨423639136524920255,423639136524920541⟩⟩,⟨⟨610991019769323792,610991019769324034⟩,⟨316822899630718477,316822899630718719⟩⟩,⟨⟨557452448806976676,557452448806976886⟩,⟨227798717011132578,227798717011132788⟩⟩,⟨⟨503650765662771262,503650765662771446⟩,⟨154470884124835200,154470884124835387⟩⟩,⟨⟨450900025791557561,450900025791557716⟩,⟨94863531439720157,94863531439720313⟩⟩,⟨⟨400183614471387467,400183614471387601⟩,⟨47139499525121376,47139499525121513⟩⟩,⟨⟨352207229905626591,352207229905626714⟩,⟨9611683068289687,9611683068289809⟩⟩,⟨⟨307446426970209007,307446426970209113⟩,⟨(-19251757981947215),(-19251757981947109)⟩⟩,⟨⟨266188796712409793,266188796712409883⟩,⟨(-40827077286615328),(-40827077286615238)⟩⟩] +lemma kernel27_1_r4_8_eq : ∀ k : Fin 16, kernel27_1Expr 4 8 k = kernel27_1_r4_8 k := by decide +kernel +noncomputable def kernel27_1_r4_9 : Fin 16 → CBox := ![⟨⟨228570970523208766,228570970523208851⟩,⟨(-56338421178397574),(-56338421178397490)⟩⟩,⟨⟨194610722646983312,194610722646983381⟩,⟨(-66864165387328142),(-66864165387328070)⟩⟩,⟨⟨164234504297922944,164234504297923006⟩,⟨(-73345305898141801),(-73345305898141739)⟩⟩,⟨⟨137300780917870086,137300780917870147⟩,⟨(-76595229280950982),(-76595229280950924)⟩⟩,⟨⟨113619564610993861,113619564610993918⟩,⟨(-77310305424352748),(-77310305424352692)⟩⟩,⟨⟨92968539827272185,92968539827272236⟩,⟨(-76080851283891896),(-76080851283891849)⟩⟩,⟨⟨75106174928576708,75106174928576753⟩,⟨(-73402107874105790),(-73402107874105749)⟩⟩,⟨⟨59782198017348400,59782198017348435⟩,⟨(-69684954476149646),(-69684954476149611)⟩⟩,⟨⟨46745794661937610,46745794661937646⟩,⟨(-65266154381907769),(-65266154381907730)⟩⟩,⟨⟨35751859908368256,35751859908368292⟩,⟨(-60417986132552360),(-60417986132552321)⟩⟩,⟨⟨26565608903874332,26565608903874371⟩,⟨(-55357163960172236),(-55357163960172200)⟩⟩,⟨⟨18965820956701976,18965820956702012⟩,⟨(-50252991918754803),(-50252991918754763)⟩⟩,⟨⟨12746962033464186,12746962033464217⟩,⟨(-45234728951435948),(-45234728951435914)⟩⟩,⟨⟨7720401422016014,7720401422016043⟩,⟨(-40398167846307930),(-40398167846307901)⟩⟩,⟨⟨3714910223644915,3714910223644944⟩,⟨(-35811450621897520),(-35811450621897491)⟩⟩,⟨⟨576602958508799,576602958508828⟩,⟨(-31520157249535219),(-31520157249535189)⟩⟩] +lemma kernel27_1_r4_9_eq : ∀ k : Fin 16, kernel27_1Expr 4 9 k = kernel27_1_r4_9 k := by decide +kernel +noncomputable def kernel27_1_r4_10 : Fin 16 → CBox := ![⟨⟨(-1831540808248728),(-1831540808248704)⟩,⟨(-27551714596619205),(-27551714596619181)⟩⟩,⟨⟨(-3630460096106201),(-3630460096106172)⟩,⟨(-23919178824910739),(-23919178824910710)⟩⟩,⟨⟨(-4926006578146765),(-4926006578146741)⟩,⟨(-20624447887632554),(-20624447887632531)⟩⟩,⟨⟨(-5810071903298582),(-5810071903298552)⟩,⟨(-17660961845734581),(-17660961845734552)⟩⟩,⟨⟨(-6361786502521929),(-6361786502521906)⟩,⟨(-15015947996698247),(-15015947996698227)⟩⟩,⟨⟨(-6648741423777914),(-6648741423777889)⟩,⟨(-12672265733031274),(-12672265733031245)⟩⟩,⟨⟨(-6728196095678201),(-6728196095678172)⟩,⟨(-10609903005909410),(-10609903005909380)⟩⟩,⟨⟨(-6648244480105165),(-6648244480105147)⟩,⟨(-8807172580975868),(-8807172580975849)⟩⟩,⟨⟨(-6448920015258103),(-6448920015258084)⟩,⟨(-7241652198040900),(-7241652198040882)⟩⟩,⟨⟨(-6163226251230158),(-6163226251230134)⟩,⟨(-5890908492002924),(-5890908492002900)⟩⟩,⟨⟨(-5818085316285230),(-5818085316285208)⟩,⟨(-4733040260704954),(-4733040260704935)⟩⟩,⟨⟨(-5435200492158488),(-5435200492158462)⟩,⟨(-3747072499280348),(-3747072499280319)⟩⟩,⟨⟨(-5031832379179935),(-5031832379179905)⟩,⟨(-2913228649152586),(-2913228649152556)⟩⟩,⟨⟨(-4621490542523541),(-4621490542523511)⟩,⟨(-2213104794818535),(-2213104794818506)⟩⟩,⟨⟨(-4214544281398705),(-4214544281398675)⟩,⟨(-1629766121752467),(-1629766121752437)⟩⟩,⟨⟨(-3818757371311245),(-3818757371311227)⟩,⟨(-1147782844914779),(-1147782844914760)⟩⟩] +lemma kernel27_1_r4_10_eq : ∀ k : Fin 16, kernel27_1Expr 4 10 k = kernel27_1_r4_10 k := by decide +kernel +noncomputable def kernel27_1_r4_11 : Fin 16 → CBox := ![⟨⟨(-3439752399284275),(-3439752399284255)⟩,⟨(-753220035871763),(-753220035871740)⟩⟩,⟨⟨(-3081410733160757),(-3081410733160739)⟩,⟨(-433593312999434),(-433593312999416)⟩⟩,⟨⟨(-2746214315965244),(-2746214315965220)⟩,⟨(-177800201232712),(-177800201232688)⟩⟩,⟨⟨(-2435535420055152),(-2435535420055128)⟩,⟨23964902694931,23964902694955⟩⟩,⟨⟨(-2149880287928321),(-2149880287928296)⟩,⟨180305828258707,180305828258735⟩⟩,⟨⟨(-1889092271915863),(-1889092271915844)⟩,⟨298724823717497,298724823717515⟩⟩,⟨⟨(-1652519699927216),(-1652519699927190)⟩,⟨385724019625810,385724019625839⟩⟩,⟨⟨(-1439153267895544),(-1439153267895520)⟩,⟨446905291625178,446905291625203⟩⟩,⟨⟨(-1247737314237092),(-1247737314237068)⟩,⟨487066433405971,487066433405995⟩⟩,⟨⟨(-1076858884772059),(-1076858884772035)⟩,⟨510292186213117,510292186213142⟩⟩,⟨⟨(-925018060973451),(-925018060973426)⟩,⟨520039180419830,520039180419855⟩⟩,⟨⟨(-790682609247837),(-790682609247819)⟩,⟨519214246439574,519214246439592⟩⟩,⟨⟨(-672329620360256),(-672329620360237)⟩,⟨510245863618905,510245863618924⟩⟩,⟨⟨(-568476449864357),(-568476449864331)⟩,⟨495148751884341,495148751884371⟩⟩,⟨⟨(-477702944397229),(-477702944397210)⟩,⟨475581785092342,475581785092361⟩⟩,⟨⟨(-398666645428343),(-398666645428324)⟩,⟨452899528792172,452899528792190⟩⟩] +lemma kernel27_1_r4_11_eq : ∀ k : Fin 16, kernel27_1Expr 4 11 k = kernel27_1_r4_11 k := by decide +kernel +noncomputable def kernel27_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-330112400935098),(-330112400935067)⟩,⟨428197788372190,428197788372220⟩⟩,⟨⟨(-270877585174723),(-270877585174703)⟩,⟨402353604752461,402353604752484⟩⟩,⟨⟨(-219893925374479),(-219893925374448)⟩,⟨376060161008238,376060161008268⟩⟩,⟨⟨(-176186759586522),(-176186759586497)⟩,⟨349857070470289,349857070470314⟩⟩,⟨⟨(-138872399793769),(-138872399793745)⟩,⟨324156509818760,324156509818785⟩⟩,⟨⟨(-107154146192033),(-107154146192014)⟩,⟨299265643434112,299265643434131⟩⟩,⟨⟨(-80317390026423),(-80317390026398)⟩,⟨275405760981113,275405760981138⟩⟩,⟨⟨(-57724151127960),(-57724151127941)⟩,⟨252728521411543,252728521411562⟩⟩,⟨⟨(-38807320216838),(-38807320216819)⟩,⟨231329665253394,231329665253413⟩⟩,⟨⟨(-23064813105724),(-23064813105699)⟩,⟨211260524724620,211260524724645⟩⟩,⟨⟨(-10053792320812),(-10053792320793)⟩,⟨192537629000800,192537629000819⟩⟩,⟨⟨614930291710,614930291735⟩,⟨175150670704599,175150670704624⟩⟩,⟨⟨9282230162303,9282230162322⟩,⟨159069069945416,159069069945435⟩⟩,⟨⟨16245692848445,16245692848466⟩,⟨144247344398137,144247344398160⟩⟩,⟨⟨21764291296669,21764291296695⟩,⟨130629468194719,130629468194749⟩⟩,⟨⟨26062702012220,26062702012251⟩,⟨118152378915130,118152378915161⟩⟩] +lemma kernel27_1_r4_12_eq : ∀ k : Fin 16, kernel27_1Expr 4 12 k = kernel27_1_r4_12 k := by decide +kernel +noncomputable def kernel27_1_r4_13 : Fin 16 → CBox := ![⟨⟨29335257052980,29335257053010⟩,⟨106748770721627,106748770721653⟩⟩,⟨⟨31749537992162,31749537992184⟩,⟨96349292631899,96349292631927⟩⟩,⟨⟨33449624646236,33449624646266⟩,⟨86884253977619,86884253977645⟩⟩,⟨⟨34559015957960,34559015957979⟩,⟨78284924118166,78284924118185⟩⟩,⟨⟨35183243392033,35183243392052⟩,⟨70484500331130,70484500331149⟩⟩,⟨⟨35412198902746,35412198902765⟩,⟨63418806325798,63418806325817⟩⟩,⟨⟨35322200262321,35322200262340⟩,⟨57026773867470,57026773867489⟩⟩,⟨⟨34977816538398,34977816538418⟩,⟨51250751403663,51250751403687⟩⟩,⟨⟨34433475972348,34433475972374⟩,⟨46036676200126,46036676200151⟩⟩,⟨⟨33734877594139,33734877594164⟩,⟨41334140184647,41334140184672⟩⟩,⟨⟨32920226736894,32920226736919⟩,⟨37096374330323,37096374330349⟩⟩,⟨⟨32021313282866,32021313282885⟩,⟨33280171867521,33280171867540⟩⟩,⟨⟨31064450056339,31064450056370⟩,⟨29845766787237,29845766787268⟩⟩,⟨⟨30071287334979,30071287335006⟩,⟨26756680890693,26756680890723⟩⟩,⟨⟨29059518021156,29059518021183⟩,⟨23979549963785,23979549963814⟩⟩,⟨⟨28043486629831,28043486629851⟩,⟨21483937433963,21483937433982⟩⟩] +lemma kernel27_1_r4_13_eq : ∀ k : Fin 16, kernel27_1Expr 4 13 k = kernel27_1_r4_13 k := by decide +kernel +noncomputable def kernel27_1_r4_14 : Fin 16 → CBox := ![⟨⟨27034713929719,27034713929739⟩,⟨19242142033298,19242142033317⟩⟩,⟨⟨26042347834452,26042347834471⟩,⟨17229004486375,17229004486394⟩⟩,⟨⟨25073549987396,25073549987415⟩,⟨15421717013416,15421717013435⟩⟩,⟨⟨24133826422632,24133826422657⟩,⟨13799638443770,13799638443796⟩⟩,⟨⟨23227309714231,23227309714263⟩,⟨12344116934147,12344116934178⟩⟩,⟨⟨22356999146483,22356999146502⟩,⟨11038321647239,11038321647258⟩⟩,⟨⟨21524964643383,21524964643403⟩,⟨9867084241622,9867084241641⟩⟩,⟨⟨20732519484365,20732519484384⟩,⟨8816750630030,8816750630050⟩⟩,⟨⟨19980366196567,19980366196593⟩,⟨7875043159021,7875043159046⟩⟩,⟨⟨19268719449431,19268719449452⟩,⟨7030933133829,7030933133853⟩⟩,⟨⟨18597409276160,18597409276185⟩,⟨6274523441777,6274523441802⟩⟩,⟨⟨17965967505244,17965967505263⟩,⟨5596940905908,5596940905928⟩⟩,⟨⟨17373699896142,17373699896162⟩,⟨4990237916677,4990237916696⟩⟩,⟨⟨16819746132728,16819746132754⟩,⟨4447302836436,4447302836462⟩⟩,⟨⟨16303129529823,16303129529842⟩,⟨3961778641633,3961778641652⟩⟩,⟨⟨15822798048116,15822798048146⟩,⟨3527989256587,3527989256614⟩⟩] +lemma kernel27_1_r4_14_eq : ∀ k : Fin 16, kernel27_1Expr 4 14 k = kernel27_1_r4_14 k := by decide +kernel +noncomputable def kernel27_1_r4_15 : Fin 16 → CBox := ![⟨⟨15377657986480,15377657986512⟩,⟨3140873035493,3140873035525⟩⟩,⟨⟨14966601524257,14966601524288⟩,⟨2795922862294,2795922862325⟩⟩,⟨⟨14588529115617,14588529115650⟩,⟨2489132359256,2489132359293⟩⟩,⟨⟨14242367591094,14242367591120⟩,⟨2216947721055,2216947721081⟩⟩,⟨⟨13927084693908,13927084693933⟩,⟨1976224721227,1976224721253⟩⟩,⟨⟨13641700669377,13641700669403⟩,⟨1764190470048,1764190470074⟩⟩,⟨⟨13385297430955,13385297430974⟩,⟨1578409536153,1578409536172⟩⟩,⟨⟨13157025745444,13157025745464⟩,⟨1416754078242,1416754078261⟩⟩,⟨⟨12956110809984,12956110810008⟩,⟨1277377666807,1277377666827⟩⟩,⟨⟨12781856533087,12781856533114⟩,⟨1158692509147,1158692509177⟩⟩,⟨⟨12633648780488,12633648780512⟩,⟨1059349823421,1059349823442⟩⟩,⟨⟨12510957801655,12510957801674⟩,⟨978223138760,978223138779⟩⟩,⟨⟨12413340014087,12413340014107⟩,⟨914394329501,914394329520⟩⟩,⟨⟨12340439288772,12340439288791⟩,⟨867142220638,867142220658⟩⟩,⟨⟨12291987850404,12291987850430⟩,⟨835933630688,835933630713⟩⟩,⟨⟨12267806879468,12267806879489⟩,⟨820416745740,820416745764⟩⟩] +lemma kernel27_1_r4_15_eq : ∀ k : Fin 16, kernel27_1Expr 4 15 k = kernel27_1_r4_15 k := by decide +kernel +noncomputable def kernel27_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel27_1_r4_0,kernel27_1_r4_1,kernel27_1_r4_2,kernel27_1_r4_3,kernel27_1_r4_4,kernel27_1_r4_5,kernel27_1_r4_6,kernel27_1_r4_7,kernel27_1_r4_8,kernel27_1_r4_9,kernel27_1_r4_10,kernel27_1_r4_11,kernel27_1_r4_12,kernel27_1_r4_13,kernel27_1_r4_14,kernel27_1_r4_15] +lemma kernel27_1_r4_eq (i k : Fin 16) : kernel27_1Expr 4 i k = kernel27_1_r4 i k := by + fin_cases i + · exact kernel27_1_r4_0_eq k + · exact kernel27_1_r4_1_eq k + · exact kernel27_1_r4_2_eq k + · exact kernel27_1_r4_3_eq k + · exact kernel27_1_r4_4_eq k + · exact kernel27_1_r4_5_eq k + · exact kernel27_1_r4_6_eq k + · exact kernel27_1_r4_7_eq k + · exact kernel27_1_r4_8_eq k + · exact kernel27_1_r4_9_eq k + · exact kernel27_1_r4_10_eq k + · exact kernel27_1_r4_11_eq k + · exact kernel27_1_r4_12_eq k + · exact kernel27_1_r4_13_eq k + · exact kernel27_1_r4_14_eq k + · exact kernel27_1_r4_15_eq k +noncomputable def kernel27_1_r5_0 : Fin 16 → CBox := ![⟨⟨(-20878345603994386618840989597),(-20878345603994379539593538943)⟩,⟨12540731035921948793008036936,12540731035921955871832678773⟩⟩,⟨⟨(-20849892077436619692209482217),(-20849892077436612616198339866)⟩,⟨12549146769659618706161945928,12549146769659625781751161429⟩⟩,⟨⟨(-20793034895094315321540188668),(-20793034895094308252010502729)⟩,⟨12565879379060924342303290632,12565879379060931411412811157⟩⟩,⟨⟨(-20707874031888910628625255677),(-20707874031888903568815334640)⟩,⟨12590731810920319800205367130,12590731810920326859597758508⟩⟩,⟨⟨(-20594560027862905834035113271),(-20594560027862898787173296673)⟩,⟨12623410140100560805914655523,12623410140100567852362444774⟩⟩,⟨⟨(-20453294665267356403436515909),(-20453294665267349372737536088)⟩,⟨12663525547593025201458294542,12663525547593032231747605557⟩⟩,⟨⟨(-20284331844716075997814135678),(-20284331844716068986476218118)⟩,⟨12710596945278581033732053400,12710596945278588044665504044⟩⟩,⟨⟨(-20087978638004944791191651428),(-20087978638004937802392375627)⟩,⟨12764054236390955464333494050,12764054236390962452734332732⟩⟩,⟨⟨(-19864596490120165147261609762),(-19864596490120158184155965065)⟩,⟨12823242197751248313593599800,12823242197751255276307647115⟩⟩,⟨⟨(-19614602538230065658588249599),(-19614602538230058724303103267)⟩,⟨12887424966797274267272813891,12887424966797281201173992022⟩⟩,⟨⟨(-19338471011134842803229576649),(-19338471011134835900860909006)⟩,⟨12955791113263094673230943689,12955791113263101575224038784⟩⟩,⟨⟨(-19036734668798140619963890438),(-19036734668798133751987400604)⟩,⟨13027459272066158461909693658,13027459272066165329519747178⟩⟩,⟨⟨(-18709986238260687173576676473),(-18709986238260680342977171388)⟩,⟨13101484310531751841110634062,13101484310531758671353552247⟩⟩,⟨⟨(-18358879799492194008552767625),(-18358879799492187218271188749)⟩,⟨13176863999533408777766803732,13176863999533415567702328053⟩⟩,⟨⟨(-17984132072621382072892745357),(-17984132072621375325836398074)⟩,⟨13252546154467002767022849304,13252546154467009513744324806⟩⟩,⟨⟨(-17586523556537805514626963917),(-17586523556537798813650168977)⟩,⟨13327436208226098451863482901,13327436208226105152517204430⟩⟩] +lemma kernel27_1_r5_0_eq : ∀ k : Fin 16, kernel27_1Expr 5 0 k = kernel27_1_r5_0 k := by decide +kernel +noncomputable def kernel27_1_r5_1 : Fin 16 → CBox := ![⟨⟨(-17166899468119391491213654557),(-17166899468119384839136089119)⟩,⟨13400405174534773375948846646,13400405174534780027715715746⟩⟩,⟨⟨(-16726170431335718720869533686),(-16726170431335712120444492494)⟩,⟨13470297956156738014989489137,13470297956156744615116750618⟩⟩,⟨⟨(-16265312866230900691505158221),(-16265312866230894145450918439)⟩,⟨13535941948678376580829775109,13535941948678383126599650395⟩⟩,⟨⟨(-15785369029315215731140251023),(-15785369029315209242098640419)⟩,⟨13596155886807048482807588224,13596155886807054971578705102⟩⟩,⟨⟨(-15287446659196232429935626792),(-15287446659196226000516135969)⟩,⟨13649758876489341099218456360,13649758876489347528381735209⟩⟩,⟨⟨(-14772718184353656727504697483),(-14772718184353650360221439431)⟩,⟨13695579552696862825850106552,13695579552696869192891798874⟩⟩,⟨⟨(-14242419453793176513688621504),(-14242419453793170211026559970)⟩,⟨13732465299513808310565637150,13732465299513814613001096017⟩⟩,⟨⟨(-13697847955878664252885023153),(-13697847955878658017199616475)⟩,⟨13759291466258323331325792239,13759291466258329566799832086⟩⟩,⟨⟨(-13140360495904158866937853655),(-13140360495904152700562896603)⟩,⟨13774970510848054023024325019,13774970510848060189203373576⟩⟩,⟨⟨(-12571370308881346073093461708),(-12571370308881339978253580734)⟩,⟨13778460999549263491894764198,13778460999549269586554360913⟩⟩,⟨⟨(-11992343590528361955004515316),(-11992343590528355933909803146)⟩,⟨13768776390697856248603392632,13768776390697862269533558834⟩⟩,⟨⟨(-11404795436484688938885306516),(-11404795436484682993605758603)⟩,⟨13744993529016614638046964649,13744993529016620583177766225⟩⟩,⟨⟨(-10810285187267516957809475439),(-10810285187267511090411463763)⟩,⟨13706260776839137751052338459,13706260776839143618317412069⟩⟩,⟨⟨(-10210411184340331783763440426),(-10210411184340325995953970374)⟩,⟨13651805708945184747858814663,13651805708945190535551061948⟩⟩,⟨⟨(-9606804950788812879646207732),(-9606804950788807172875452379)⟩,⟨13580942298865176801555695452,13580942298865182508224729586⟩⟩,⟨⟨(-9001124818388453677966767686),(-9001124818388448053956501120)⟩,⟨13493077526465802928471269291,13493077526465808552395169362⟩⟩] +lemma kernel27_1_r5_1_eq : ∀ k : Fin 16, kernel27_1Expr 5 1 k = kernel27_1_r5_1 k := by decide +kernel +noncomputable def kernel27_1_r5_2 : Fin 16 → CBox := ![⟨⟨(-8395049031191785489633346925),(-8395049031191779950132227265)⟩,⟨13387717339416330970580964526,13387717339416336510010874594⟩⟩,⟨⟨(-7790268364044179932656878521),(-7790268364044174479187789233)⟩,⟨13264471904777357954341526809,13264471904777363407754315488⟩⟩,⟨⟨(-7188478302535269862066121649),(-7188478302535264496193236198)⟩,⟨13123060091458845996573173463,13123060091458851362404370396⟩⟩,⟨⟨(-6591370838684939913451008759),(-6591370838684934636517179871)⟩,⟨12963313129657357307986786326,12963313129657362584893194572⟩⟩,⟨⟨(-6000625944024820457463181291),(-6000625944024815270828325650)⟩,⟨12785177399584072177339793826,12785177399584077363961106532⟩⟩,⟨⟨(-5417902788545798504283171315),(-5417902788545793408793346083)⟩,⟨12588716308801203935222277828,12588716308801209030712004252⟩⟩,⟨⟨(-4844830780120107265675355608),(-4844830780120102262540834996)⟩,⟨12374111225245386627919457813,12374111225245391631066848230⟩⟩,⟨⟨(-4283000504359398075393204194),(-4283000504359393165558675166)⟩,⟨12141661441467885833866391318,12141661441467890743726244640⟩⟩,⟨⟨(-3733954649331745326127787353),(-3733954649331740510642013562)⟩,⟨11891783154683561457641678935,11891783154683566273164680366⟩⟩,⟨⟨(-3199179003034397457260333352),(-3199179003034392736692785374)⟩,⟨11625007456799609012538680692,11625007456799613733154775695⟩⟩,⟨⟨(-2680093613920625363429970595),(-2680093613920620738609162427)⟩,⟨11341977338584098630780936693,11341977338584103255660996251⟩⟩,⟨⟨(-2178044206037286821711904392),(-2178044206037282293161233088)⟩,⟨11043443722414006808923797496,11043443722414011337543783775⟩⟩,⟨⟨(-1694293940389254042841928263),(-1694293940389249611175005611)⟩,⟨10730260548483053574105710937,10730260548483058005851349119⟩⟩,⟨⟨(-1230015612969239362560143237),(-1230015612969235028070777640)⟩,⟨10403378949812794332885509089,10403378949812798667462301768⟩⟩,⟨⟨(-786284377456806437592143639),(-786284377456802200714778277)⟩,⟨10063840561751077027520379647,10063840561751081264493126226⟩⟩,⟨⟨(-364071076897938421381460813),(-364071076897934282228801598)⟩,⟨9712770021710937547480278765,9712770021710941686735563164⟩⟩] +lemma kernel27_1_r5_2_eq : ∀ k : Fin 16, kernel27_1Expr 5 2 k = kernel27_1_r5_2 k := by decide +kernel +noncomputable def kernel27_1_r5_3 : Fin 16 → CBox := ![⟨⟨35763736253887345941609555,35763736253891387056901786⟩,⟨9351366724549348750681658744,9351366724549352791906099312⟩⟩,⟨⟨412475018482360827892890572,412475018482364771104795991⟩,⟨8980895908059020782081369529,8980895908059024725408223169⟩⟩,⟨⟨765437625951133003922968170,765437625951136849144746320⟩,⟨8602679151401484832634666854,8602679151401488677975002513⟩⟩,⟨⟨1094149819978265828535690102,1094149819978269576069062872⟩,⟨8218084376806352849295529095,8218084376806356596949583931⟩⟩,⟨⟨1398235838852602515846608457,1398235838852606165751600286⟩,⟨7828515451369655073810511004,7828515451369658723837736131⟩⟩,⟨⟨1677447497716141750630557060,1677447497716145303443706309⟩,⟨7435401491185292459468967540,7435401491185296012405343855⟩⟩,⟨⟨1931664789052297488924831324,1931664789052300944920165598⟩,⟨7040185974234291867543694441,7040185974234295323662705397⟩⟩,⟨⟨2160895467688011319242235341,2160895467688014679112576322⟩,⟨6644315771350074215177537750,6644315771350077575171481734⟩⟩,⟨⟨2365273615976101124674919070,2365273615976104388819163616⟩,⟨6249230206106748881772039969,6249230206106752146039308945⟩⟩,⟨⟨2545057196801393239090090930,2545057196801396408433876408⟩,⟨5856350254594762781923984316,5856350254594765951389737052⟩⟩,⟨⟨2700624614071780490132549885,2700624614071783566194665441⟩,⟨5467067994729511682155550808,5467067994729514758336889295⟩⟩,⟨⟨2832470312231437686797376167,2832470312231440677338397827⟩,⟨5082736411982426107778631841,5082736411982429098426792977⟩⟩,⟨⟨2941199457885703538979176992,2941199457885706444346252818⟩,⟨4704659664252989810106076058,4704659664252992715568652549⟩⟩,⟨⟨3027521757676265398293402325,3027521757676268219366152386⟩,⟨4334083903060379806605036319,4334083903060382627762120368⟩⟩,⟨⟨3092244476918235732564268131,3092244476918238469873362808⟩,⟨3972188741394601516128988123,3972188741394604253511742327⟩⟩,⟨⟨3136264733044057623324479705,3136264733044060277853254952⟩,⟨3620079450521330555635631259,3620079450521333210227904404⟩⟩] +lemma kernel27_1_r5_3_eq : ∀ k : Fin 16, kernel27_1Expr 5 3 k = kernel27_1_r5_3 k := by decide +kernel +noncomputable def kernel27_1_r5_4 : Fin 16 → CBox := ![⟨⟨3160561146442234786789840628,3160561146442237359144213637⟩,⟨3278779958895531039810372325,3278779958895533612218608811⟩⟩,⟨⟨3166184938696644972827674231,3166184938696647464189487061⟩,⟨2949226716239010109365570255,2949226716239012600772153513⟩⟩,⟨⟨3154250574408003629299884509,3154250574408006040458106818⟩,⟨2632263474926202375442058720,2632263474926204786636508122⟩⟩,⟨⟨3125926047616903490594092518,3125926047616905822798446981⟩,⟨2328637029264945053062364591,2328637029264947385294959425⟩⟩,⟨⟨3082422917274364276844129890,3082422917274366530950871144⟩,⟨2038993941230618862392293496,2038993941230621116519847559⟩⟩,⟨⟨3024986198171658946734905716,3024986198171661124169098887⟩,⟨1763878268896912733717431460,1763878268896914911165624817⟩⟩,⟨⟨2954884214222087960544924225,2954884214222090062332927142⟩,⟨1503730301393636176504354530,1503730301393638278300120197⟩⟩,⟨⟨2873398519984665750359662562,2873398519984667777984974625⟩,⟨1258886291901821548988337845,1258886291901823576615716223⟩⟩,⟨⟨2781813993860212218601324862,2781813993860214173155300300⟩,⟨1029579168156973283597782204,1029579168156975238148661997⟩⟩,⟨⟨2681409202525928727261181233,2681409202525930610369878823⟩,⟨815940188355105001315228954,815940188355106884416191080⟩⟩,⟨⟨2573447130980903973391724228,2573447130980905786319618907⟩,⟨618001499416330433401557838,618001499416332246317586480⟩⟩,⟨⟨2459166366150192826741066418,2459166366150194571151052420⟩,⟨435699544417975677888479639,435699544417977422282961113⟩⟩,⟨⟨2339772814457498683725486797,2339772814457500360808560175⟩,⟨268879256808788566880952470,268879256808790243945358226⟩⟩,⟨⟨2216432025262293435491315592,2216432025262295047143372454⟩,⟨117298970885124767707349282,117298970885126379338029090⟩⟩,⟨⟨2090262182717730869840488434,2090262182717732417430829670⟩,⟨(-19364028944005367878502895),(-19364028944003820311814252)⟩⟩,⟨⟨1962327818604244336960720881,1962327818604245822201543713⟩,⟨(-141507403268521078736213880),(-141507403268519593520899399)⟩⟩] +lemma kernel27_1_r5_4_eq : ∀ k : Fin 16, kernel27_1Expr 5 4 k = kernel27_1_r5_4 k := by decide +kernel +noncomputable def kernel27_1_r5_5 : Fin 16 → CBox := ![⟨⟨1833634288202254912639915375,1833634288202256336800253076⟩,⟨(-249597184700223246915487741),(-249597184700221822781381191)⟩⟩,⟨⟨1705123040463188406792886559,1705123040463189771775225838⟩,⟨(-344160827350677670754956787),(-344160827350676305799243964)⟩⟩,⟨⟨1577667702799989668039019720,1577667702799990975560386248⟩,⟨(-425779970943236808024637411),(-425779970943235500530042601)⟩⟩,⟨⟨1452070989923771350544791564,1452070989923772602324342768⟩,⟨(-495083012012403020602115219),(-495083012012401768849255131)⟩⟩,⟨⟨1329062435474254417133288453,1329062435474255614475241112⟩,⟨(-552737573591189511439926930),(-552737573591188314124379513)⟩⟩,⟨⟨1209296934892020734507846534,1209296934892021879238316282⟩,⟨(-599442962465509582334633792),(-599442962465508437630102436)⟩⟩,⟨⟨1093354078212765928896263302,1093354078212767022377328122⟩,⟨(-635922699562084415671194406),(-635922699562083322213193025)⟩⟩,⟨⟨981738242366204154524848522,981738242366205198480196445⟩,⟨(-662917204429710060263047345),(-662917204429709016327403557)⟩⟩,⟨⟨874879404257257166613707807,874879404257258162353341852⟩,⟨(-681176709186011272097523044),(-681176709186010276374461908)⟩⟩,⟨⟨773134628498718285693466050,773134628498719235575934822⟩,⟨(-691454470859636190802013159),(-691454470859635240933214794)⟩⟩,⟨⟨676790177237164488867297327,676790177237165394330018194⟩,⟨(-694500343898477089883322787),(-694500343898476184431598269)⟩⟩,⟨⟨586064184131340279143308023,586064184131341141805795909⟩,⟨(-691054766882833200164793982),(-691054766882832337510855313)⟩⟩,⟨⟨501109830247275649237578663,501109830247276470341854775⟩,⟨(-681843209327886229902735459),(-681843209327885408804783657)⟩⟩,⟨⟨422018956448574138040089155,422018956448574919237857334⟩,⟨(-667571116033301304015682168),(-667571116033300522822230404)⟩⟩,⟨⟨348826044784392586478536994,348826044784393329031131246⟩,⟨(-648919377888487310592431460),(-648919377888486568042355673)⟩⟩,⟨⟨281512500392471685519575062,281512500392472391108869228⟩,⟨(-626540349514906726777433250),(-626540349514906021189080020)⟩⟩] +lemma kernel27_1_r5_5_eq : ∀ k : Fin 16, kernel27_1Expr 5 5 k = kernel27_1_r5_5 k := by decide +kernel +noncomputable def kernel27_1_r5_6 : Fin 16 → CBox := ![⟨⟨220011165502296301448839363,220011165502296971269347198⟩,⟨(-601054425759579008028190251),(-601054425759578338207239786)⟩⟩,⟨⟨164210998189066019412346046,164210998189066655015798132⟩,⟨(-573047180974849531238916758),(-573047180974848895633819054)⟩⟩,⟨⟨113961850522385333545076030,113961850522385936142276245⟩,⟨(-543067067345298793702341872),(-543067067345298191102463958)⟩⟩,⟨⟨69079283591053749349574054,69079283591054320382505862⟩,⟨(-511623661356724878746238042),(-511623661356724307709756087)⟩⟩,⟨⟨29349360472836556997902397,29349360472837097578764035⟩,⟨(-479186440933129820957951985),(-479186440933129280372817331)⟩⟩,⟨⟨(-5466637546985416767243396),(-5466637546984905224706383)⟩,⟨(-446184069868570936897077344),(-446184069868570425349682071)⟩⟩,⟨⟨(-35627621430682173566959786),(-35627621430681689960973146)⟩,⟨(-413004161008299939535015197),(-413004161008299455923712313)⟩⟩,⟨⟨(-61408276238417410739035170),(-61408276238416953753328310)⟩,⟨(-379993485227988130506464774),(-379993485227987673515293960)⟩⟩,⟨⟨(-83094853580837028738059892),(-83094853580836596773758640)⟩,⟨(-347458589644839159427040392),(-347458589644838727457219638)⟩⟩,⟨⟨(-100981208163898621993132340),(-100981208163898213636398984)⟩,⟨(-315666785677961060928915507),(-315666785677960652566673697)⟩⟩,⟨⟨(-115365106104910791218630851),(-115365106104910405548386771)⟩,⟨(-284847465550379971241308580),(-284847465550379585565625206)⟩⟩,⟨⟨(-126544826896514065668734256),(-126544826896513701578988206)⟩,⟨(-255193704570423891319391611),(-255193704570423527224324649)⟩⟩,⟨⟨(-134816075197635243389325527),(-134816075197634900028447267)⟩,⟨(-226864106012125816525940235),(-226864106012125473160243966)⟩⟩,⟨⟨(-140469213124492697399913918),(-140469213124492373690318576)⟩,⟨(-199984845587890611121551767),(-199984845587890287407934742)⟩⟩,⟨⟨(-143786818478026910867221017),(-143786818478026605975098859)⟩,⟨(-174651873317555481681446978),(-174651873317555176786032168)⟩⟩,⟨⟨(-145041569443605075799874210),(-145041569443604788722364529)⟩,⟨(-150933231984036234147402278),(-150933231984035947067262477)⟩⟩] +lemma kernel27_1_r5_6_eq : ∀ k : Fin 16, kernel27_1Expr 5 6 k = kernel27_1_r5_6 k := by decide +kernel +noncomputable def kernel27_1_r5_7 : Fin 16 → CBox := ![⟨⟨(-144494451790265252144820214),(-144494451790264982132192923)⟩,⟨(-128871453258947532002579905),(-128871453258947261987920574)⟩⟩,⟨⟨(-142393280524426528016480307),(-142393280524426274097117782)⟩,⟨(-108485994909744550072959182),(-108485994909744296152100196)⟩⟩,⟨⟨(-138971524349709351643237854),(-138971524349709113042058862)⟩,⟨(-89775685188518981996499340),(-89775685188518743394299807)⟩⟩,⟨⟨(-134447418171832986896859176),(-134447418171832762767029547)⟩,⟨(-72721143476373175666132521),(-72721143476372951535701294)⟩⟩,⟨⟨(-129023346276223225671639543),(-129023346276223015351716477)⟩,⟨(-57287149441955087025277401),(-57287149441954876705117863)⟩⟩,⟨⟨(-122885476696556865003854347),(-122885476696556667686383447)⟩,⟨(-43424936296237204817225049),(-43424936296237007499828788)⟩⟩,⟨⟨(-116203625676244387938788605),(-116203625676244202999273908)⟩,⟨(-31074387119510582936053443),(-31074387119510397996876948)⟩⟩,⟨⟨(-109131329984695793266278625),(-109131329984695619979762424)⟩,⟨(-20166116637039765593001465),(-20166116637039592307044355)⟩⟩,⟨⟨(-101806104161711263334819822),(-101806104161711101016410298)⟩,⟨(-10623424168626334490214217),(-10623424168626172172545297)⟩⟩,⟨⟨(-94349859495904933390652306),(-94349859495904781326645949)⟩,⟨(-2364106722431255729414964),(-2364106722431103666295121)⟩⟩,⟨⟨(-86869461661125637331527100),(-86869461661125495011867316)⟩,⟨4697875700490974289256866,4697875700491116607916678⟩⟩,⟨⟨(-79457404398981297936197540),(-79457404398981164768665039)⟩,⟨10650887615661085643474144,10650887615661218809939621⟩⟩,⟨⟨(-72192577403734145224585521),(-72192577403734020753297781)⟩,⟨15584260712920543286580673,15584260712920667756786940⟩⟩,⟨⟨(-65141107594380529431859759),(-65141107594380413092016065)⟩,⟨19587091548696644060016050,19587091548696760398779256⟩⟩,⟨⟨(-58357254203503367683059395),(-58357254203503259046194693)⟩,⟨22747191970523820916572277,22747191970523929552371010⟩⟩,⟨⟨(-51884339529749768484713928),(-51884339529749667059720190)⟩,⟨25150188053119522191604836,25150188053119623615558208⟩⟩] +lemma kernel27_1_r5_7_eq : ∀ k : Fin 16, kernel27_1Expr 5 7 k = kernel27_1_r5_7 k := by decide +kernel +noncomputable def kernel27_1_r5_8 : Fin 16 → CBox := ![⟨⟨(-45755698748070206574222491),(-45755698748070111979493539)⟩,⟨26878761681357924594921364,26878761681358019188663508⟩⟩,⟨⟨(-39995633808688023150796188),(-39995633808687934878735828)⟩,⟨28012027544834254504402752,28012027544834342775645358⟩⟩,⟨⟨(-34620358144293612368269197),(-34620358144293530074299408)⟩,⟨28625037205197701847858938,28625037205197784141164226⟩⟩,⟨⟨(-29638920610430661147566049),(-29638920610430584436416871)⟩,⟨28788401050543304891834597,28788401050543381602457099⟩⟩,⟨⟨(-25054098775200047770106337),(-25054098775199976337531676)⟩,⟨28568018346722831954540289,28568018346722903386711396⟩⟩,⟨⟨(-20863253323729313940086895),(-20863253323729247420790723)⟩,⟨28024905216316648072069280,28024905216316714591070932⟩⟩,⟨⟨(-17059136926709011313700439),(-17059136926708949411530395)⟩,⟨27215110202760484294719987,27215110202760546196691310⟩⟩,⟨⟨(-13630652420982243032070738),(-13630652420982185423838787)⟩,⟨26189707088656724335676246,26189707088656781943792841⟩⟩,⟨⟨(-10563556547878120987514998),(-10563556547878067433693697)⟩,⟨24994854811505969946930413,24994854811506023500708158⟩⟩,⟨⟨(-7841106779651915129433596),(-7841106779651865337318859)⟩,⟨23671914634400118353794498,23671914634400168145926809⟩⟩,⟨⟨(-5444649927548261030986114),(-5444649927548214769258940)⟩,⟨22257615161107882469920323,22257615161107928731715569⟩⟩,⟨⟨(-3354152261467768917564575),(-3354152261467725935062941)⟩,⟨20784256312451021492580389,20784256312451064475191776⟩⟩,⟨⟨(-1548671778841630894455416),(-1548671778841590999574199)⟩,⟨19279943982804100599643071,19279943982804140494667759⟩⟩,⟨⟨(-6774039649200139563757),(-6774039649163099813586)⟩,⟨17768847752059349577314441,17768847752059386617234732⟩⟩,⟨⟨1293106361552999946967530,1293106361553034305690873⟩,⟨16271474721060822021333853,16271474721060856380247591⟩⟩,⟨⟨2372356082291596732783725,2372356082291628609153172⟩,⟨14804953250572214700779563,14804953250572246577349250⟩⟩] +lemma kernel27_1_r5_8_eq : ∀ k : Fin 16, kernel27_1Expr 5 8 k = kernel27_1_r5_8 k := by decide +kernel +noncomputable def kernel27_1_r5_9 : Fin 16 → CBox := ![⟨⟨3251922053760877138585989,3251922053760906680512574⟩,⟨13383321100338694811379991,13383321100338724353507943⟩⟩,⟨⟨3952095900228709772147694,3952095900228737160273222⟩,⟨12017813172642441613444059,12017813172642469001769364⟩⟩,⟨⟨4492340203145456754093072,4492340203145482124319638⟩,⟨10717144752734988578022768,10717144752735013948445204⟩⟩,⟨⟨4891152928675386966537223,4891152928675410471546144⟩,⟨9487786797329704562060966,9487786797329728067260010⟩⟩,⟨⟨5165966287212717475760246,5165966287212739231004094⟩,⟨8334230444440618669858240,8334230444440640425281229⟩⟩,⟨⟨5333076311314668288346281,5333076311314688431574666⟩,⟨7259238497466622372867078,7259238497466642516243655⟩⟩,⟨⟨5407599514497779784858003,5407599514497798420294451⟩,⟨6264082169355050078473285,6264082169355068714030041⟩⟩,⟨⟨5403453117899031971583939,5403453117899049216297992⟩,⟨5348761856216642027829233,5348761856216659272638669⟩⟩,⟨⟨5333355495736280313095597,5333355495736296254530044⟩,⟨4512211142505006088700734,4512211142505022030208411⟩⟩,⟨⟨5208843685212943781422640,5208843685212958525675328⟩,⟨3752483621579553396525075,3752483621579568140831474⟩⟩,⟨⟨5040305024058038810249786,5040305024058052436661437⟩,⟨3066922446903862620649871,3066922446903876247098151⟩⟩,⟨⟨4837020212058373831923000,4837020212058386429426377⟩,⟨2452312811894837065343563,2452312811894849662868759⟩⟩,⟨⟨4607215335275796583579261,4607215335275808218889188⟩,⟨1905017792820942539521939,1905017792820954174840955⟩⟩,⟨⟨4358120637485156657954011,4358120637485167410672799⟩,⟨1421098181977560862594282,1421098181977571615311334⟩⟩,⟨⟨4096034067838635504606572,4096034067838645434445710⟩,⟨996417090872022409352267,996417090872032339180591⟩⟩,⟨⟨3826387872745703725769271,3826387872745712945449625⟩,⟨626730218832935054192421,626730218832944273854564⟩⟩] +lemma kernel27_1_r5_9_eq : ∀ k : Fin 16, kernel27_1Expr 5 9 k = kernel27_1_r5_9 k := by decide +kernel +noncomputable def kernel27_1_r5_10 : Fin 16 → CBox := ![⟨⟨3553816730075160901084228,3553816730075169457787205⟩,⟨307762764982601571034501,307762764982610127713274⟩⟩,⟨⟨3282226142346605281928032,3282226142346613229070067⟩,⟨35274014604731232322522,35274014604739179435587⟩⟩,⟨⟨3014860010531688326274305,3014860010531695702107140⟩,⟨(-194889341693507484050805),(-194889341693500108250614)⟩⟩,⟨⟨2754366499959614376833885,2754366499959621225825135⟩,⟨(-386750092376259545278176),(-386750092376252696322159)⟩⟩,⟨⟨2502861483664730051236483,2502861483664736405367145⟩,⟨(-544166542692622597826268),(-544166542692616243731051)⟩⟩,⟨⟨2261989005831077003802156,2261989005831082903298725⟩,⟨(-670806684285382739024656),(-670806684285376839563315)⟩⟩,⟨⟨2032978348677099799373650,2032978348677105273218440⟩,⟨(-770129516464552027936384),(-770129516464546554126226)⟩⟩,⟨⟨1816697410412858333552405,1816697410412863415469066⟩,⟨(-845372589721178961152397),(-845372589721173879269469)⟩⟩,⟨⟨1613702210294905540957538,1613702210294910254719259⟩,⟨(-899544899979282376235964),(-899544899979277662506834)⟩⟩,⟨⟨1424282430021526551823940,1424282430021530928181427⟩,⟨(-935424324904465507025343),(-935424324904461130698319)⟩⟩,⟨⟨1248502979641940070433044,1248502979641944131151609⟩,⟨(-955558859364962483445535),(-955558859364958422752464)⟩⟩,⟨⟨1086241641807649437811289,1086241641807653208290651⟩,⟨(-962270974202397226927738),(-962270974202393456469399)⟩⟩,⟨⟨937222901663522314455647,937222901663525812672734⟩,⟨(-957664489401444825033123),(-957664489401441326833040)⟩⟩,⟨⟨801048112096585062718701,801048112096588311579331⟩,⟨(-943633418379022005437449),(-943633418379018756590247)⟩⟩,⟨⟨677222176582615324226103,677222176582618339959075⟩,⟨(-921872303499037174717069),(-921872303499034158994360)⟩⟩,⟨⟨565176955633843179334783,565176955633845980936437⟩,⟨(-893887623318235418199807),(-893887623318232616605622)⟩⟩] +lemma kernel27_1_r5_10_eq : ∀ k : Fin 16, kernel27_1Expr 5 10 k = kernel27_1_r5_10 k := by decide +kernel +noncomputable def kernel27_1_r5_11 : Fin 16 → CBox := ![⟨⟨464291618962607419297234,464291618962610019880575⟩,⟨(-861009908927450748815759),(-861009908927448148237442)⟩⟩,⟨⟨373910174993896686563379,373910174993899103471343⟩,⟨(-824406259679789914352235),(-824406259679787497447173)⟩⟩,⟨⟨293356413280919983579398,293356413280922228770748⟩,⟨(-785092997345186099497531),(-785092997345183854307249)⟩⟩,⟨⟨221946494627975274156190,221946494627977361880175⟩,⟨(-743948242174470999406150),(-743948242174468911681662)⟩⟩,⟨⟨158999419152878750513039,158999419152880690458195⟩,⟨(-701724234474227336012266),(-701724234474225396065279)⟩⟩,⟨⟨103845594895925649635375,103845594895927454446045⟩,⟨(-659059261150243558847187),(-659059261150241754033570)⟩⟩,⟨⟨55833719591513956380489,55833719591515635046829⟩,⟨(-616489078405219789919005),(-616489078405218111248818)⟩⟩,⟨⟨14336176469720742986541,14336176469722305922020⟩,⟨(-574457749561960643782805),(-574457749561959080842737)⟩⟩,⟨⟨(-21246868021910615580909),(-21246868021909161447039)⟩,⟨(-533327841053294121484628),(-533327841053292667345586)⟩⟩,⟨⟨(-51484490435597963725792),(-51484490435596608913505)⟩,⟨(-493389940229316784619773),(-493389940229315429801858)⟩⟩,⟨⟨(-76913000474502318508809),(-76913000474501056580501)⟩,⟨(-454871476054210922269730),(-454871476054209660335539)⟩⟩,⟨⟨(-98034749272855464591371),(-98034749272854287617730)⟩,⟨(-417944838280955291460273),(-417944838280954114480750)⟩⟩,⟨⟨(-115317624001267923537413),(-115317624001266826450563)⟩,⟨(-382734802586792027572668),(-382734802586790930479996)⟩⟩,⟨⟨(-129195110585714169109381),(-129195110585713145013276)⟩,⟨(-349325278705247708384874),(-349325278705246684283042)⟩⟩,⟨⟨(-140066819348966410391346),(-140066819348965454664344)⟩,⟨(-317765406072880791675105),(-317765406072879835942507)⟩⟩,⟨⟨(-148299380709999287514932),(-148299380709998394525032)⟩,⟨(-288075027179215217615560),(-288075027179214324620220)⟩⟩] +lemma kernel27_1_r5_11_eq : ∀ k : Fin 16, kernel27_1Expr 5 11 k = kernel27_1_r5_11 k := by decide +kernel +noncomputable def kernel27_1_r5_12 : Fin 16 → CBox := ![⟨⟨(-154227629624566599092474),(-154227629624565765267526)⟩,⟨(-260249572909705282338300),(-260249572909704448508097)⟩⟩,⟨⟨(-158156008164008614726618),(-158156008164007834818881)⟩,⟨(-234264396930076811736465),(-234264396930076031823704)⟩⟩,⟨⟨(-160360125480600840680040),(-160360125480600111037208)⟩,⟨(-210078597783695828925611),(-210078597783695099278427)⟩⟩,⟨⟨(-161088423389142959456189),(-161088423389142275956969)⟩,⟨(-187638368050544672327436),(-187638368050543988824482)⟩⟩,⟨⟨(-160563903916247829041707),(-160563903916247189079379)⟩,⟨(-166879909816827546076002),(-166879909816826906110499)⟩⟩,⟨⟨(-158985882455055614831842),(-158985882455055014634985)⟩,⟨(-147731954979501687677227),(-147731954979501087477695)⟩⟩,⟨⟨(-156531736648704673804414),(-156531736648704110974484)⟩,⟨(-130117927693553289649218),(-130117927693552726817072)⟩⟩,⟨⟨(-153358626853603028307077),(-153358626853602499757837)⟩,⟨(-113957784678032240486751),(-113957784678031711935707)⟩⟩,⟨⟨(-149605169051659442518232),(-149605169051658946418710)⟩,⟨(-99169567230236342586600),(-99169567230235846485638)⟩⟩,⟨⟨(-145393045440949711197212),(-145393045440949244681197)⟩,⟨(-85670696741784007723707),(-85670696741783541206579)⟩⟩,⟨⟨(-140828541690412498687399),(-140828541690412060015643)⟩,⟨(-73379043337963018430933),(-73379043337962579758369)⟩⟩,⟨⟨(-136004003050097857165247),(-136004003050097444064658)⟩,⟨(-62213795032841468667989),(-62213795032841055566848)⟩⟩,⟨⟨(-130999204217522264221654),(-130999204217521875348139)⟩,⟨(-52096152556419996510140),(-52096152556419607636302)⟩⟩,⟨⟨(-125882630124511019626094),(-125882630124510652870695)⟩,⟨(-42949872806170991888630),(-42949872806170625133112)⟩⟩,⟨⟨(-120712666676958267375873),(-120712666676957921392091)⟩,⟨(-34701681734749206315664),(-34701681734748860331944)⟩⟩,⟨⟨(-115538701998876824743016),(-115538701998876497708626)⟩,⟨(-27281575432203933380705),(-27281575432203606346533)⟩⟩] +lemma kernel27_1_r5_12_eq : ∀ k : Fin 16, kernel27_1Expr 5 12 k = kernel27_1_r5_12 k := by decide +kernel +noncomputable def kernel27_1_r5_13 : Fin 16 → CBox := ![⟨⟨(-110402139945525533643994),(-110402139945525224666251)⟩,⟨(-20623026212084376253511),(-20623026212084067276121)⟩⟩,⟨⟨(-105337328598581255285787),(-105337328598580962751768)⟩,⟨(-14663108678442975119020),(-14663108678442682585472)⟩⟩,⟨⟨(-100372407176170772307520),(-100372407176170495323057)⟩,⟨(-9342559042435128180403),(-9342559042434851196516)⟩⟩,⟨⟨(-95530075315607518387842),(-95530075315607255694278)⟩,⟨(-4605779376787550983678),(-4605779376787288290772)⟩⟩,⟨⟨(-90828289047072197035055),(-90828289047071947964659)⟩,⟨(-400797044623617577709),(-400797044623368508043)⟩⟩,⟨⟨(-86280887999204341156569),(-86280887999204104512060)⟩,⟨3320811785673681525461,3320811785673918169172⟩⟩,⟨⟨(-81898158486545147954551),(-81898158486544923082233)⟩,⟨6604026829275697252041,6604026829275922123520⟩⟩,⟨⟨(-77687337145028235288214),(-77687337145028021233574)⟩,⟨9490509950099335111955,9490509950099549165713⟩⟩,⟨⟨(-73653059723620619950895),(-73653059723620416265345)⟩,⟨12018747345704475927054,12018747345704679611687⟩⟩,⟨⟨(-69797759523678921512542),(-69797759523678727251064)⟩,⟨14224202860269466245771,14224202860269660506329⟩⟩,⟨⟨(-66122019816270838588726),(-66122019816270653261287)⟩,⟨16139478400690209711415,16139478400690395037939⟩⟩,⟨⟨(-62624884373257011254565),(-62624884373256834123901)⟩,⟨17794478106588702836960,17794478106588879966714⟩⟩,⟨⟨(-59304130030152388108590),(-59304130030152218844268)⟩,⟨19216573517297062137612,19216573517297231401032⟩⟩,⟨⟨(-56156504965889550866541),(-56156504965889388755596)⟩,⟨20430767495069281305877,20430767495069443415933⟩⟩,⟨⟨(-53177936143359957401515),(-53177936143359802101696)⟩,⟨21459855111012436121956,21459855111012591420899⟩⟩,⟨⟨(-50363709110530675543213),(-50363709110530526491167)⟩,⟨22324580085366390273870,22324580085366539325055⟩⟩] +lemma kernel27_1_r5_13_eq : ∀ k : Fin 16, kernel27_1Expr 5 13 k = kernel27_1_r5_13 k := by decide +kernel +noncomputable def kernel27_1_r5_14 : Fin 16 → CBox := ![⟨⟨(-47708623119451889634778),(-47708623119451746621250)⟩,⟨23043785703277977357105,23043785703278120369784⟩⟩,⟨⟨(-45207124283071624524826),(-45207124283071486961338)⟩,⟨23634559407190490911710,23634559407190628474366⟩⟩,⟨⟨(-42853419260140675727346),(-42853419260140543364549)⟩,⟨24112370503053012189305,24112370503053144551284⟩⟩,⟨⟨(-40641571738620927104792),(-40641571738620799501416)⟩,⟨24491200614959136603722,24491200614959264206292⟩⟩,⟨⟨(-38565583779327164473375),(-38565583779327041470905)⟩,⟨24783666686324898676031,24783666686325021677718⟩⟩,⟨⟨(-36619463884980263899746),(-36619463884980145047881)⟩,⟨25001136459654329383337,25001136459654448234434⟩⟩,⟨⟨(-34797283475977766038398),(-34797283475977651154723)⟩,⟨25153836475245039113979,25153836475245153996914⟩⟩,⟨⟨(-33093223283225020668036),(-33093223283224909401194)⟩,⟨25250952715385115419977,25250952715385226686123⟩⟩,⟨⟨(-31501611010287841411939),(-31501611010287733671365)⟩,⟨25300724087841105567251,25300724087841213307175⟩⟩,⟨⟨(-30016951471695207872991),(-30016951471695103275243)⟩,⟨25310528993538935202044,25310528993539039799178⟩⟩,⟨⟨(-28633950281051579677635),(-28633950281051478088489)⟩,⟨25286965260774315075170,25286965260774416663743⟩⟩,⟨⟨(-27347532041210263622821),(-27347532041210164757262)⟩,⟨25235923754236449748232,25235923754236548613253⟩⟩,⟨⟨(-26152853878526201040180),(-26152853878526104829494)⟩,⟨25162655983495412632567,25162655983495508842744⟩⟩,⟨⟨(-25045315063506913910307),(-25045315063506820047580)⟩,⟨25071836044047994641061,25071836044048088503313⟩⟩,⟨⟨(-24020563370339102889260),(-24020563370339011274644)⟩,⟨24967617225973876253741,24967617225973967867911⟩⟩,⟨⟨(-23074498747095174789691),(-23074498747095085186645)⟩,⟨24853683621957296193141,24853683621957385795763⟩⟩] +lemma kernel27_1_r5_14_eq : ∀ k : Fin 16, kernel27_1Expr 5 14 k = kernel27_1_r5_14 k := by decide +kernel +noncomputable def kernel27_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-22203274796227498205592),(-22203274796227410588568)⟩,⟨24733297058933229704847,24733297058933317321469⟩⟩,⟨⟨(-21403298500557500309527),(-21403298500557414398504)⟩,⟨24609339666816203933616,24609339666816289844257⟩⟩,⟨⟨(-20671228572699720936802),(-20671228572699636655942)⟩,⟨24484352384418070399223,24484352384418154679718⟩⟩,⟨⟨(-20003972755090686760802),(-20003972755090603908554)⟩,⟨24360569687388036505874,24360569687388119357775⟩⟩,⟨⟨(-19398684352911489977644),(-19398684352911408529795)⟩,⟨24239950806335084702352,24239950806335166149866⟩⟩,⟨⟨(-18852758242626102421005),(-18852758242626022145903)⟩,⟨24124207685645835490030,24124207685645915764813⟩⟩,⟨⟨(-18363826564063338256581),(-18363826564063259094464)⟩,⟨24014829915233949883152,24014829915234029044963⟩⟩,⟨⟨(-17929754273441852230823),(-17929754273441774004368)⟩,⟨23913106848823217675857,23913106848823295902022⟩⟩,⟨⟨(-17548634708001265410346),(-17548634708001188112712)⟩,⟨23820147103587326635092,23820147103587403932442⟩⟩,⟨⟨(-17218785289517819916805),(-17218785289517743317881)⟩,⟨23736895617204405207735,23736895617204481806383⟩⟩,⟨⟨(-16938743473540313662443),(-16938743473540237714314)⟩,⟨23664148419748726011186,23664148419748801959044⟩⟩,⟨⟨(-16707263033300953231954),(-16707263033300877774981)⟩,⟨23602565259412711383389,23602565259412786840098⟩⟩,⟨⟨(-16523310751582346461910),(-16523310751582271493109)⟩,⟨23552680202875240604835,23552680202875315573376⟩⟩,⟨⟨(-16386063580026404866359),(-16386063580026330188415)⟩,⟨23514910313226494589982,23514910313226569267671⟩⟩,⟨⟨(-16294906313145006292840),(-16294906313144931861933)⟩,⟨23489562490722781345263,23489562490722855775921⟩⟩,⟨⟨(-16249429813345893404569),(-16249429813345819069026)⟩,⟨23476838544256929980001,23476838544257004315289⟩⟩] +lemma kernel27_1_r5_15_eq : ∀ k : Fin 16, kernel27_1Expr 5 15 k = kernel27_1_r5_15 k := by decide +kernel +noncomputable def kernel27_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel27_1_r5_0,kernel27_1_r5_1,kernel27_1_r5_2,kernel27_1_r5_3,kernel27_1_r5_4,kernel27_1_r5_5,kernel27_1_r5_6,kernel27_1_r5_7,kernel27_1_r5_8,kernel27_1_r5_9,kernel27_1_r5_10,kernel27_1_r5_11,kernel27_1_r5_12,kernel27_1_r5_13,kernel27_1_r5_14,kernel27_1_r5_15] +lemma kernel27_1_r5_eq (i k : Fin 16) : kernel27_1Expr 5 i k = kernel27_1_r5 i k := by + fin_cases i + · exact kernel27_1_r5_0_eq k + · exact kernel27_1_r5_1_eq k + · exact kernel27_1_r5_2_eq k + · exact kernel27_1_r5_3_eq k + · exact kernel27_1_r5_4_eq k + · exact kernel27_1_r5_5_eq k + · exact kernel27_1_r5_6_eq k + · exact kernel27_1_r5_7_eq k + · exact kernel27_1_r5_8_eq k + · exact kernel27_1_r5_9_eq k + · exact kernel27_1_r5_10_eq k + · exact kernel27_1_r5_11_eq k + · exact kernel27_1_r5_12_eq k + · exact kernel27_1_r5_13_eq k + · exact kernel27_1_r5_14_eq k + · exact kernel27_1_r5_15_eq k +noncomputable def kernel27_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel27_1_r0,kernel27_1_r1,kernel27_1_r2,kernel27_1_r3,kernel27_1_r4,kernel27_1_r5] +lemma kernel27_1_eq (j : Fin 6) (i k : Fin 16) : kernel27_1Expr j i k = kernel27_1 j i k := by + fin_cases j + · exact kernel27_1_r0_eq i k + · exact kernel27_1_r1_eq i k + · exact kernel27_1_r2_eq i k + · exact kernel27_1_r3_eq i k + · exact kernel27_1_r4_eq i k + · exact kernel27_1_r5_eq i k +lemma kernel27_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel27_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(27:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel27_1_eq] + unfold kernel27_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans27_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +noncomputable def kernel28_0Expr (j : Fin 6) (i k : Fin 16) : CBox := (gridRows j i k).lam.mul (trans28 j i k) +noncomputable def kernel28_0_r0_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_0_eq : ∀ k : Fin 16, kernel28_0Expr 0 0 k = kernel28_0_r0_0 k := by decide +kernel +noncomputable def kernel28_0_r0_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_1_eq : ∀ k : Fin 16, kernel28_0Expr 0 1 k = kernel28_0_r0_1 k := by decide +kernel +noncomputable def kernel28_0_r0_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_2_eq : ∀ k : Fin 16, kernel28_0Expr 0 2 k = kernel28_0_r0_2 k := by decide +kernel +noncomputable def kernel28_0_r0_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_3_eq : ∀ k : Fin 16, kernel28_0Expr 0 3 k = kernel28_0_r0_3 k := by decide +kernel +noncomputable def kernel28_0_r0_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_4_eq : ∀ k : Fin 16, kernel28_0Expr 0 4 k = kernel28_0_r0_4 k := by decide +kernel +noncomputable def kernel28_0_r0_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_5_eq : ∀ k : Fin 16, kernel28_0Expr 0 5 k = kernel28_0_r0_5 k := by decide +kernel +noncomputable def kernel28_0_r0_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_6_eq : ∀ k : Fin 16, kernel28_0Expr 0 6 k = kernel28_0_r0_6 k := by decide +kernel +noncomputable def kernel28_0_r0_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_7_eq : ∀ k : Fin 16, kernel28_0Expr 0 7 k = kernel28_0_r0_7 k := by decide +kernel +noncomputable def kernel28_0_r0_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_8_eq : ∀ k : Fin 16, kernel28_0Expr 0 8 k = kernel28_0_r0_8 k := by decide +kernel +noncomputable def kernel28_0_r0_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_9_eq : ∀ k : Fin 16, kernel28_0Expr 0 9 k = kernel28_0_r0_9 k := by decide +kernel +noncomputable def kernel28_0_r0_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_10_eq : ∀ k : Fin 16, kernel28_0Expr 0 10 k = kernel28_0_r0_10 k := by decide +kernel +noncomputable def kernel28_0_r0_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r0_11_eq : ∀ k : Fin 16, kernel28_0Expr 0 11 k = kernel28_0_r0_11 k := by decide +kernel +noncomputable def kernel28_0_r0_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r0_12_eq : ∀ k : Fin 16, kernel28_0Expr 0 12 k = kernel28_0_r0_12 k := by decide +kernel +noncomputable def kernel28_0_r0_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r0_13_eq : ∀ k : Fin 16, kernel28_0Expr 0 13 k = kernel28_0_r0_13 k := by decide +kernel +noncomputable def kernel28_0_r0_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r0_14_eq : ∀ k : Fin 16, kernel28_0Expr 0 14 k = kernel28_0_r0_14 k := by decide +kernel +noncomputable def kernel28_0_r0_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r0_15_eq : ∀ k : Fin 16, kernel28_0Expr 0 15 k = kernel28_0_r0_15 k := by decide +kernel +noncomputable def kernel28_0_r0 : Fin 16 → Fin 16 → CBox := ![kernel28_0_r0_0,kernel28_0_r0_1,kernel28_0_r0_2,kernel28_0_r0_3,kernel28_0_r0_4,kernel28_0_r0_5,kernel28_0_r0_6,kernel28_0_r0_7,kernel28_0_r0_8,kernel28_0_r0_9,kernel28_0_r0_10,kernel28_0_r0_11,kernel28_0_r0_12,kernel28_0_r0_13,kernel28_0_r0_14,kernel28_0_r0_15] +lemma kernel28_0_r0_eq (i k : Fin 16) : kernel28_0Expr 0 i k = kernel28_0_r0 i k := by + fin_cases i + · exact kernel28_0_r0_0_eq k + · exact kernel28_0_r0_1_eq k + · exact kernel28_0_r0_2_eq k + · exact kernel28_0_r0_3_eq k + · exact kernel28_0_r0_4_eq k + · exact kernel28_0_r0_5_eq k + · exact kernel28_0_r0_6_eq k + · exact kernel28_0_r0_7_eq k + · exact kernel28_0_r0_8_eq k + · exact kernel28_0_r0_9_eq k + · exact kernel28_0_r0_10_eq k + · exact kernel28_0_r0_11_eq k + · exact kernel28_0_r0_12_eq k + · exact kernel28_0_r0_13_eq k + · exact kernel28_0_r0_14_eq k + · exact kernel28_0_r0_15_eq k +noncomputable def kernel28_0_r1_0 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_0_eq : ∀ k : Fin 16, kernel28_0Expr 1 0 k = kernel28_0_r1_0 k := by decide +kernel +noncomputable def kernel28_0_r1_1 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_1_eq : ∀ k : Fin 16, kernel28_0Expr 1 1 k = kernel28_0_r1_1 k := by decide +kernel +noncomputable def kernel28_0_r1_2 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_2_eq : ∀ k : Fin 16, kernel28_0Expr 1 2 k = kernel28_0_r1_2 k := by decide +kernel +noncomputable def kernel28_0_r1_3 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_3_eq : ∀ k : Fin 16, kernel28_0Expr 1 3 k = kernel28_0_r1_3 k := by decide +kernel +noncomputable def kernel28_0_r1_4 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_4_eq : ∀ k : Fin 16, kernel28_0Expr 1 4 k = kernel28_0_r1_4 k := by decide +kernel +noncomputable def kernel28_0_r1_5 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_5_eq : ∀ k : Fin 16, kernel28_0Expr 1 5 k = kernel28_0_r1_5 k := by decide +kernel +noncomputable def kernel28_0_r1_6 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_6_eq : ∀ k : Fin 16, kernel28_0Expr 1 6 k = kernel28_0_r1_6 k := by decide +kernel +noncomputable def kernel28_0_r1_7 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_7_eq : ∀ k : Fin 16, kernel28_0Expr 1 7 k = kernel28_0_r1_7 k := by decide +kernel +noncomputable def kernel28_0_r1_8 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_8_eq : ∀ k : Fin 16, kernel28_0Expr 1 8 k = kernel28_0_r1_8 k := by decide +kernel +noncomputable def kernel28_0_r1_9 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_9_eq : ∀ k : Fin 16, kernel28_0Expr 1 9 k = kernel28_0_r1_9 k := by decide +kernel +noncomputable def kernel28_0_r1_10 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_10_eq : ∀ k : Fin 16, kernel28_0Expr 1 10 k = kernel28_0_r1_10 k := by decide +kernel +noncomputable def kernel28_0_r1_11 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_11_eq : ∀ k : Fin 16, kernel28_0Expr 1 11 k = kernel28_0_r1_11 k := by decide +kernel +noncomputable def kernel28_0_r1_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_12_eq : ∀ k : Fin 16, kernel28_0Expr 1 12 k = kernel28_0_r1_12 k := by decide +kernel +noncomputable def kernel28_0_r1_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_13_eq : ∀ k : Fin 16, kernel28_0Expr 1 13 k = kernel28_0_r1_13 k := by decide +kernel +noncomputable def kernel28_0_r1_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_14_eq : ∀ k : Fin 16, kernel28_0Expr 1 14 k = kernel28_0_r1_14 k := by decide +kernel +noncomputable def kernel28_0_r1_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r1_15_eq : ∀ k : Fin 16, kernel28_0Expr 1 15 k = kernel28_0_r1_15 k := by decide +kernel +noncomputable def kernel28_0_r1 : Fin 16 → Fin 16 → CBox := ![kernel28_0_r1_0,kernel28_0_r1_1,kernel28_0_r1_2,kernel28_0_r1_3,kernel28_0_r1_4,kernel28_0_r1_5,kernel28_0_r1_6,kernel28_0_r1_7,kernel28_0_r1_8,kernel28_0_r1_9,kernel28_0_r1_10,kernel28_0_r1_11,kernel28_0_r1_12,kernel28_0_r1_13,kernel28_0_r1_14,kernel28_0_r1_15] +lemma kernel28_0_r1_eq (i k : Fin 16) : kernel28_0Expr 1 i k = kernel28_0_r1 i k := by + fin_cases i + · exact kernel28_0_r1_0_eq k + · exact kernel28_0_r1_1_eq k + · exact kernel28_0_r1_2_eq k + · exact kernel28_0_r1_3_eq k + · exact kernel28_0_r1_4_eq k + · exact kernel28_0_r1_5_eq k + · exact kernel28_0_r1_6_eq k + · exact kernel28_0_r1_7_eq k + · exact kernel28_0_r1_8_eq k + · exact kernel28_0_r1_9_eq k + · exact kernel28_0_r1_10_eq k + · exact kernel28_0_r1_11_eq k + · exact kernel28_0_r1_12_eq k + · exact kernel28_0_r1_13_eq k + · exact kernel28_0_r1_14_eq k + · exact kernel28_0_r1_15_eq k +noncomputable def kernel28_0_r2_0 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_0_eq : ∀ k : Fin 16, kernel28_0Expr 2 0 k = kernel28_0_r2_0 k := by decide +kernel +noncomputable def kernel28_0_r2_1 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_1_eq : ∀ k : Fin 16, kernel28_0Expr 2 1 k = kernel28_0_r2_1 k := by decide +kernel +noncomputable def kernel28_0_r2_2 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_2_eq : ∀ k : Fin 16, kernel28_0Expr 2 2 k = kernel28_0_r2_2 k := by decide +kernel +noncomputable def kernel28_0_r2_3 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_3_eq : ∀ k : Fin 16, kernel28_0Expr 2 3 k = kernel28_0_r2_3 k := by decide +kernel +noncomputable def kernel28_0_r2_4 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_4_eq : ∀ k : Fin 16, kernel28_0Expr 2 4 k = kernel28_0_r2_4 k := by decide +kernel +noncomputable def kernel28_0_r2_5 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_5_eq : ∀ k : Fin 16, kernel28_0Expr 2 5 k = kernel28_0_r2_5 k := by decide +kernel +noncomputable def kernel28_0_r2_6 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_6_eq : ∀ k : Fin 16, kernel28_0Expr 2 6 k = kernel28_0_r2_6 k := by decide +kernel +noncomputable def kernel28_0_r2_7 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_7_eq : ∀ k : Fin 16, kernel28_0Expr 2 7 k = kernel28_0_r2_7 k := by decide +kernel +noncomputable def kernel28_0_r2_8 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_8_eq : ∀ k : Fin 16, kernel28_0Expr 2 8 k = kernel28_0_r2_8 k := by decide +kernel +noncomputable def kernel28_0_r2_9 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_9_eq : ∀ k : Fin 16, kernel28_0Expr 2 9 k = kernel28_0_r2_9 k := by decide +kernel +noncomputable def kernel28_0_r2_10 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r2_10_eq : ∀ k : Fin 16, kernel28_0Expr 2 10 k = kernel28_0_r2_10 k := by decide +kernel +noncomputable def kernel28_0_r2_11 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r2_11_eq : ∀ k : Fin 16, kernel28_0Expr 2 11 k = kernel28_0_r2_11 k := by decide +kernel +noncomputable def kernel28_0_r2_12 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r2_12_eq : ∀ k : Fin 16, kernel28_0Expr 2 12 k = kernel28_0_r2_12 k := by decide +kernel +noncomputable def kernel28_0_r2_13 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r2_13_eq : ∀ k : Fin 16, kernel28_0Expr 2 13 k = kernel28_0_r2_13 k := by decide +kernel +noncomputable def kernel28_0_r2_14 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r2_14_eq : ∀ k : Fin 16, kernel28_0Expr 2 14 k = kernel28_0_r2_14 k := by decide +kernel +noncomputable def kernel28_0_r2_15 : Fin 16 → CBox := ![⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩,⟨⟨(-4),4⟩,⟨(-4),4⟩⟩] +lemma kernel28_0_r2_15_eq : ∀ k : Fin 16, kernel28_0Expr 2 15 k = kernel28_0_r2_15 k := by decide +kernel +noncomputable def kernel28_0_r2 : Fin 16 → Fin 16 → CBox := ![kernel28_0_r2_0,kernel28_0_r2_1,kernel28_0_r2_2,kernel28_0_r2_3,kernel28_0_r2_4,kernel28_0_r2_5,kernel28_0_r2_6,kernel28_0_r2_7,kernel28_0_r2_8,kernel28_0_r2_9,kernel28_0_r2_10,kernel28_0_r2_11,kernel28_0_r2_12,kernel28_0_r2_13,kernel28_0_r2_14,kernel28_0_r2_15] +lemma kernel28_0_r2_eq (i k : Fin 16) : kernel28_0Expr 2 i k = kernel28_0_r2 i k := by + fin_cases i + · exact kernel28_0_r2_0_eq k + · exact kernel28_0_r2_1_eq k + · exact kernel28_0_r2_2_eq k + · exact kernel28_0_r2_3_eq k + · exact kernel28_0_r2_4_eq k + · exact kernel28_0_r2_5_eq k + · exact kernel28_0_r2_6_eq k + · exact kernel28_0_r2_7_eq k + · exact kernel28_0_r2_8_eq k + · exact kernel28_0_r2_9_eq k + · exact kernel28_0_r2_10_eq k + · exact kernel28_0_r2_11_eq k + · exact kernel28_0_r2_12_eq k + · exact kernel28_0_r2_13_eq k + · exact kernel28_0_r2_14_eq k + · exact kernel28_0_r2_15_eq k +noncomputable def kernel28_0_r3_0 : Fin 16 → CBox := ![⟨⟨(-493659014814),(-493659014811)⟩,⟨(-254395787759),(-254395787756)⟩⟩,⟨⟨(-492898943350),(-492898943347)⟩,⟨(-253284529765),(-253284529762)⟩⟩,⟨⟨(-491379823837),(-491379823834)⟩,⟨(-251071856956),(-251071856953)⟩⟩,⟨⟨(-489103750146),(-489103750142)⟩,⟨(-247777342602),(-247777342598)⟩⟩,⟨⟨(-486073978999),(-486073978994)⟩,⟨(-243430065219),(-243430065214)⟩⟩,⟨⟨(-482295064447),(-482295064444)⟩,⟨(-238068274660),(-238068274657)⟩⟩,⟨⟨(-477773029597),(-477773029594)⟩,⟨(-231738953132),(-231738953128)⟩⟩,⟨⟨(-472515569380),(-472515569377)⟩,⟨(-224497276410),(-224497276407)⟩⟩,⟨⟨(-466532276946),(-466532276942)⟩,⟨(-216405981809),(-216405981805)⟩⟩,⟨⟨(-459834885258),(-459834885253)⟩,⟨(-207534650627),(-207534650622)⟩⟩,⟨⟨(-452437514743),(-452437514739)⟩,⟨(-197958913949),(-197958913945)⟩⟩,⟨⟨(-444356917315),(-444356917311)⟩,⟨(-187759591729),(-187759591725)⟩⟩,⟨⟨(-435612706943),(-435612706940)⟩,⟨(-177021776050),(-177021776047)⟩⟩,⟨⟨(-426227566983),(-426227566980)⟩,⟨(-165833870278),(-165833870275)⟩⟩,⟨⟨(-416227424900),(-416227424897)⟩,⟨(-154286596571),(-154286596567)⟩⟩,⟨⟨(-405641585630),(-405641585624)⟩,⟨(-142471984725),(-142471984720)⟩⟩] +lemma kernel28_0_r3_0_eq : ∀ k : Fin 16, kernel28_0Expr 3 0 k = kernel28_0_r3_0 k := by decide +kernel +noncomputable def kernel28_0_r3_1 : Fin 16 → CBox := ![⟨⟨(-394502815799),(-394502815796)⟩,⟨(-130482355757),(-130482355754)⟩⟩,⟨⟨(-382847372151),(-382847372148)⟩,⟨(-118409313809),(-118409313806)⟩⟩,⟨⟨(-370714968894),(-370714968891)⟩,⟨(-106342759959),(-106342759956)⟩⟩,⟨⟨(-358148680270),(-358148680266)⟩,⟨(-94369941292),(-94369941288)⟩⟩,⟨⟨(-345194776262),(-345194776259)⟩,⟨(-82574548213),(-82574548210)⟩⟩,⟨⟨(-331902491166),(-331902491161)⟩,⟨(-71035872230),(-71035872225)⟩⟩,⟨⟨(-318323726458),(-318323726454)⟩,⟨(-59828035618),(-59828035615)⟩⟩,⟨⟨(-304512691275),(-304512691271)⟩,⟨(-49019303283),(-49019303280)⟩⟩,⟨⟨(-290525485373),(-290525485369)⟩,⟨(-38671485786),(-38671485782)⟩⟩,⟨⟨(-276419631152),(-276419631149)⟩,⟨(-28839441081),(-28839441078)⟩⟩,⟨⟨(-262253562653),(-262253562649)⟩,⟨(-19570680828),(-19570680824)⟩⟩,⟨⟨(-248086080684),(-248086080679)⟩,⟨(-10905085399),(-10905085395)⟩⟩,⟨⟨(-233975784228),(-233975784224)⟩,⟨(-2874729833),(-2874729829)⟩⟩,⟨⟨(-219980488950),(-219980488946)⟩,⟨4496178916,4496178919⟩⟩,⟨⟨(-206156644098),(-206156644095)⟩,⟨11191255039,11191255044⟩⟩,⟨⟨(-192558759182),(-192558759178)⟩,⟨17201780708,17201780712⟩⟩] +lemma kernel28_0_r3_1_eq : ∀ k : Fin 16, kernel28_0Expr 3 1 k = kernel28_0_r3_1 k := by decide +kernel +noncomputable def kernel28_0_r3_2 : Fin 16 → CBox := ![⟨⟨(-179238851675),(-179238851672)⟩,⟨22526451994,22526451997⟩⟩,⟨⟨(-166245926518),(-166245926515)⟩,⟨27171030905,27171030908⟩⟩,⟨⟨(-153625497463),(-153625497459)⟩,⟨31147912085,31147912089⟩⟩,⟨⟨(-141419159315),(-141419159312)⟩,⟨34475614110,34475614113⟩⟩,⟨⟨(-129664218928),(-129664218925)⟩,⟨37178206441,37178206444⟩⟩,⟨⟨(-118393391387),(-118393391383)⟩,⟨39284683979,39284683982⟩⟩,⟨⟨(-107634566331),(-107634566328)⟩,⟨40828301770,40828301773⟩⟩,⟨⟨(-97410647661),(-97410647656)⟩,⟨41845882758,41845882763⟩⟩,⟨⟨(-87739468264),(-87739468260)⟩,⟨42377111520,42377111524⟩⟩,⟨⟨(-78633779650),(-78633779645)⟩,⟨42463826673,42463826677⟩⟩,⟨⟨(-70101314788),(-70101314784)⟩,⟨42149324166,42149324170⟩⟩,⟨⟨(-62144920868),(-62144920863)⟩,⟨41477682892,41477682898⟩⟩,⟨⟨(-54762757276),(-54762757271)⟩,⟨40493123081,40493123085⟩⟩,⟨⟨(-47948552867),(-47948552863)⟩,⟨39239406747,39239406752⟩⟩,⟨⟨(-41691915494),(-41691915491)⟩,⟨37759288193,37759288196⟩⟩,⟨⟨(-35978685964),(-35978685960)⟩,⟨36094021022,36094021026⟩⟩] +lemma kernel28_0_r3_2_eq : ∀ k : Fin 16, kernel28_0Expr 3 2 k = kernel28_0_r3_2 k := by decide +kernel +noncomputable def kernel28_0_r3_3 : Fin 16 → CBox := ![⟨⟨(-30791327933),(-30791327929)⟩,⟨34282926700,34282926705⟩⟩,⟨⟨(-26109344924),(-26109344921)⟩,⟨32363028061,32363028064⟩⟩,⟨⟨(-21909715476),(-21909715471)⟩,⟨30368749642,30368749646⟩⟩,⟨⟨(-18167337512),(-18167337507)⟩,⟨28331685259,28331685265⟩⟩,⟨⟨(-14855473403),(-14855473399)⟩,⟨26280431731,26280431735⟩⟩,⟨⟨(-11946187580),(-11946187576)⟩,⟨24240486445,24240486449⟩⟩,⟨⟨(-9410769326),(-9410769323)⟩,⟨22234205277,22234205280⟩⟩,⟨⟨(-7220134133),(-7220134129)⟩,⟨20280816327,20280816331⟩⟩,⟨⟨(-5345197948),(-5345197945)⟩,⟨18396484215,18396484218⟩⟩,⟨⟨(-3757219612),(-3757219608)⟩,⟨16594418960,16594418965⟩⟩,⟨⟨(-2428107876),(-2428107873)⟩,⟨14885023119,14885023122⟩⟩,⟨⟨(-1330690365),(-1330690361)⟩,⟨13276070534,13276070539⟩⟩,⟨⟨(-438942963),(-438942960)⟩,⟨11772910051,11772910054⟩⟩,⟨⟨271820959,271820963⟩,⟨10378687616,10378687620⟩⟩,⟨⟨824801154,824801158⟩,⟨9094580453,9094580457⟩⟩,⟨⟨1241599735,1241599739⟩,⟨7920037374,7920037378⟩⟩] +lemma kernel28_0_r3_3_eq : ∀ k : Fin 16, kernel28_0Expr 3 3 k = kernel28_0_r3_3 k := by decide +kernel +noncomputable def kernel28_0_r3_4 : Fin 16 → CBox := ![⟨⟨1542147163,1542147167⟩,⟨6853019796,6853019799⟩⟩,⟨⟨1744662484,1744662488⟩,⟨5890238599,5890238603⟩⟩,⟨⟨1865644812,1865644815⟩,⟨5027382609,5027382612⟩⟩,⟨⟨1919892716,1919892719⟩,⟨4259335128,4259335131⟩⟩,⟨⟨1920547896,1920547899⟩,⟨3580375682,3580375685⟩⟩,⟨⟨1879159455,1879159458⟩,⟨2984364783,2984364786⟩⟩,⟨⟨1805764996,1805764999⟩,⟨2464910182,2464910185⟩⟩,⟨⟨1708984898,1708984901⟩,⟨2015513704,2015513707⟩⟩,⟨⟨1596126253,1596126257⟩,⟨1629698325,1629698328⟩⟩,⟨⟨1473293204,1473293207⟩,⟨1301115640,1301115643⟩⟩,⟨⟨1345500655,1345500660⟩,⟨1023634312,1023634318⟩⟩,⟨⟨1216788728,1216788731⟩,⟨791410462,791410465⟩⟩,⟨⟨1090335593,1090335596⟩,⟨598941201,598941205⟩⟩,⟨⟨968566748,968566752⟩,⟨441102825,441102829⟩⟩,⟨⟨853259109,853259113⟩,⟨313175183,313175186⟩⟩,⟨⟨745638694,745638697⟩,⟨210853984,210853987⟩⟩] +lemma kernel28_0_r3_4_eq : ∀ k : Fin 16, kernel28_0Expr 3 4 k = kernel28_0_r3_4 k := by decide +kernel +noncomputable def kernel28_0_r3_5 : Fin 16 → CBox := ![⟨⟨646470946,646470950⟩,⟨130252690,130252694⟩⟩,⟨⟨556143119,556143123⟩,⟨67895734,67895739⟩⟩,⟨⟨474738366,474738369⟩,⟨20704652,20704655⟩⟩,⟨⟨402101454,402101457⟩,⟨(-14021322),(-14021319)⟩⟩,⟨⟨337896218,337896221⟩,⟨(-38628788),(-38628784)⟩⟩,⟨⟨281655053,281655056⟩,⟨(-55136575),(-55136572)⟩⟩,⟨⟨232820852,232820855⟩,⟨(-65263884),(-65263881)⟩⟩,⟨⟨190781946,190781949⟩,⟨(-70459211),(-70459208)⟩⟩,⟨⟨154900607,154900610⟩,⟨(-71929222),(-71929219)⟩⟩,⟨⟨124535797,124535800⟩,⟨(-70666967),(-70666964)⟩⟩,⟨⟨99060796,99060799⟩,⟨(-67478848),(-67478845)⟩⟩,⟨⟨77876380,77876383⟩,⟨(-63010014),(-63010011)⟩⟩,⟨⟨60420180,60420185⟩,⟨(-57767863),(-57767858)⟩⟩,⟨⟨46172838,46172843⟩,⟨(-52143497),(-52143493)⟩⟩,⟨⟨34661516,34661520⟩,⟨(-46431054),(-46431050)⟩⟩,⟨⟨25461266,25461271⟩,⟨(-40844872),(-40844868)⟩⟩] +lemma kernel28_0_r3_5_eq : ∀ k : Fin 16, kernel28_0Expr 3 5 k = kernel28_0_r3_5 k := by decide +kernel +noncomputable def kernel28_0_r3_6 : Fin 16 → CBox := ![⟨⟨18194743,18194746⟩,⟨(-35534576),(-35534573)⟩⟩,⟨⟨12530624,12530628⟩,⟨(-30598134),(-30598131)⟩⟩,⟨⟨8181135,8181138⟩,⟨(-26093040),(-26093037)⟩⟩,⟨⟨4898920,4898924⟩,⟨(-22045753),(-22045750)⟩⟩,⟨⟨2473555,2473558⟩,⟨(-18459572),(-18459569)⟩⟩,⟨⟨727850,727853⟩,⟨(-15321087),(-15321084)⟩⟩,⟨⟨(-485854),(-485851)⟩,⟨(-12605416),(-12605413)⟩⟩,⟨⟨(-1289315),(-1289310)⟩,⟨(-10280338),(-10280334)⟩⟩,⟨⟨(-1781831),(-1781828)⟩,⟨(-8309539),(-8309536)⟩⟩,⟨⟨(-2043462),(-2043459)⟩,⟨(-6655056),(-6655053)⟩⟩,⟨⟨(-2137954),(-2137950)⟩,⟨(-5279101),(-5279097)⟩⟩,⟨⟨(-2115386),(-2115382)⟩,⟨(-4145333),(-4145329)⟩⟩,⟨⟨(-2014512),(-2014508)⟩,⟨(-3219732),(-3219729)⟩⟩,⟨⟨(-1864809),(-1864806)⟩,⟨(-2471124),(-2471121)⟩⟩,⟨⟨(-1688248),(-1688244)⟩,⟨(-1871456),(-1871452)⟩⟩,⟨⟨(-1500802),(-1500799)⟩,⟨(-1395872),(-1395869)⟩⟩] +lemma kernel28_0_r3_6_eq : ∀ k : Fin 16, kernel28_0Expr 3 6 k = kernel28_0_r3_6 k := by decide +kernel +noncomputable def kernel28_0_r3_7 : Fin 16 → CBox := ![⟨⟨(-1313718),(-1313715)⟩,⟨(-1022654),(-1022650)⟩⟩,⟨⟨(-1134578),(-1134575)⟩,⟨(-733066),(-733062)⟩⟩,⟨⟨(-968164),(-968161)⟩,⟨(-511133),(-511129)⟩⟩,⟨⟨(-817171),(-817168)⟩,⟨(-343382),(-343378)⟩⟩,⟨⟨(-682766),(-682762)⟩,⟨(-218575),(-218572)⟩⟩,⟨⟨(-565045),(-565041)⟩,⟨(-127435),(-127430)⟩⟩,⟨⟨(-463371),(-463367)⟩,⟨(-62375),(-62371)⟩⟩,⟨⟨(-376643),(-376639)⟩,⟨(-17264),(-17261)⟩⟩,⟨⟨(-303496),(-303493)⟩,⟨12806,12809⟩⟩,⟨⟨(-242448),(-242445)⟩,⟨31723,31727⟩⟩,⟨⟨(-191995),(-191992)⟩,⟨42528,42531⟩⟩,⟨⟨(-150689),(-150686)⟩,⟨47571,47574⟩⟩,⟨⟨(-117179),(-117175)⟩,⟨48648,48651⟩⟩,⟨⟨(-90235),(-90232)⟩,⟨47106,47109⟩⟩,⟨⟨(-68763),(-68760)⟩,⟨43941,43944⟩⟩,⟨⟨(-51806),(-51802)⟩,⟨39874,39877⟩⟩] +lemma kernel28_0_r3_7_eq : ∀ k : Fin 16, kernel28_0Expr 3 7 k = kernel28_0_r3_7 k := by decide +kernel +noncomputable def kernel28_0_r3_8 : Fin 16 → CBox := ![⟨⟨(-38535),(-38532)⟩,⟨35411,35414⟩⟩,⟨⟨(-28250),(-28247)⟩,⟨30902,30906⟩⟩,⟨⟨(-20358),(-20355)⟩,⟨26573,26576⟩⟩,⟨⟨(-14369),(-14366)⟩,⟨22561,22565⟩⟩,⟨⟨(-9875),(-9872)⟩,⟨18941,18944⟩⟩,⟨⟨(-6552),(-6548)⟩,⟨15740,15745⟩⟩,⟨⟨(-4129),(-4126)⟩,⟨12960,12963⟩⟩,⟨⟨(-2396),(-2392)⟩,⟨10577,10582⟩⟩,⟨⟨(-1184),(-1179)⟩,⟨8563,8567⟩⟩,⟨⟨(-359),(-356)⟩,⟨6877,6881⟩⟩,⟨⟨180,183⟩,⟨5482,5486⟩⟩,⟨⟨511,514⟩,⟨4338,4341⟩⟩,⟨⟨695,699⟩,⟨3404,3409⟩⟩,⟨⟨777,782⟩,⟨2652,2657⟩⟩,⟨⟨792,796⟩,⟨2052,2056⟩⟩,⟨⟨764,767⟩,⟨1574,1577⟩⟩] +lemma kernel28_0_r3_8_eq : ∀ k : Fin 16, kernel28_0Expr 3 8 k = kernel28_0_r3_8 k := by decide +kernel +noncomputable def kernel28_0_r3_9 : Fin 16 → CBox := ![⟨⟨709,713⟩,⟨1197,1201⟩⟩,⟨⟨640,643⟩,⟨901,905⟩⟩,⟨⟨566,569⟩,⟨673,677⟩⟩,⟨⟨492,495⟩,⟨495,499⟩⟩,⟨⟨422,425⟩,⟨361,365⟩⟩,⟨⟨357,360⟩,⟨258,261⟩⟩,⟨⟨299,303⟩,⟨182,185⟩⟩,⟨⟨248,252⟩,⟨124,129⟩⟩,⟨⟨205,208⟩,⟨83,86⟩⟩,⟨⟨167,170⟩,⟨53,56⟩⟩,⟨⟨137,140⟩,⟨31,34⟩⟩,⟨⟨109,112⟩,⟨15,19⟩⟩,⟨⟨88,91⟩,⟨6,9⟩⟩,⟨⟨70,73⟩,⟨(-2),1⟩⟩,⟨⟨55,58⟩,⟨(-6),(-3)⟩⟩,⟨⟨43,46⟩,⟨(-8),(-5)⟩⟩] +lemma kernel28_0_r3_9_eq : ∀ k : Fin 16, kernel28_0Expr 3 9 k = kernel28_0_r3_9 k := by decide +kernel +noncomputable def kernel28_0_r3_10 : Fin 16 → CBox := ![⟨⟨34,37⟩,⟨(-9),(-6)⟩⟩,⟨⟨26,30⟩,⟨(-11),(-7)⟩⟩,⟨⟨20,24⟩,⟨(-10),(-7)⟩⟩,⟨⟨14,18⟩,⟨(-10),(-7)⟩⟩,⟨⟨11,14⟩,⟨(-10),(-6)⟩⟩,⟨⟨8,11⟩,⟨(-8),(-4)⟩⟩,⟨⟨5,9⟩,⟨(-8),(-5)⟩⟩,⟨⟨4,7⟩,⟨(-7),(-4)⟩⟩,⟨⟨3,6⟩,⟨(-6),(-3)⟩⟩,⟨⟨1,5⟩,⟨(-5),(-2)⟩⟩,⟨⟨1,5⟩,⟨(-5),(-2)⟩⟩,⟨⟨0,3⟩,⟨(-4),(-1)⟩⟩,⟨⟨0,3⟩,⟨(-4),(-1)⟩⟩,⟨⟨(-2),3⟩,⟨(-4),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩] +lemma kernel28_0_r3_10_eq : ∀ k : Fin 16, kernel28_0Expr 3 10 k = kernel28_0_r3_10 k := by decide +kernel +noncomputable def kernel28_0_r3_11 : Fin 16 → CBox := ![⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-2),2⟩,⟨(-3),0⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩] +lemma kernel28_0_r3_11_eq : ∀ k : Fin 16, kernel28_0Expr 3 11 k = kernel28_0_r3_11 k := by decide +kernel +noncomputable def kernel28_0_r3_12 : Fin 16 → CBox := ![⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),2⟩,⟨(-3),2⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r3_12_eq : ∀ k : Fin 16, kernel28_0Expr 3 12 k = kernel28_0_r3_12 k := by decide +kernel +noncomputable def kernel28_0_r3_13 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r3_13_eq : ∀ k : Fin 16, kernel28_0Expr 3 13 k = kernel28_0_r3_13 k := by decide +kernel +noncomputable def kernel28_0_r3_14 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r3_14_eq : ∀ k : Fin 16, kernel28_0Expr 3 14 k = kernel28_0_r3_14 k := by decide +kernel +noncomputable def kernel28_0_r3_15 : Fin 16 → CBox := ![⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩,⟨⟨(-3),3⟩,⟨(-3),3⟩⟩] +lemma kernel28_0_r3_15_eq : ∀ k : Fin 16, kernel28_0Expr 3 15 k = kernel28_0_r3_15 k := by decide +kernel +noncomputable def kernel28_0_r3 : Fin 16 → Fin 16 → CBox := ![kernel28_0_r3_0,kernel28_0_r3_1,kernel28_0_r3_2,kernel28_0_r3_3,kernel28_0_r3_4,kernel28_0_r3_5,kernel28_0_r3_6,kernel28_0_r3_7,kernel28_0_r3_8,kernel28_0_r3_9,kernel28_0_r3_10,kernel28_0_r3_11,kernel28_0_r3_12,kernel28_0_r3_13,kernel28_0_r3_14,kernel28_0_r3_15] +lemma kernel28_0_r3_eq (i k : Fin 16) : kernel28_0Expr 3 i k = kernel28_0_r3 i k := by + fin_cases i + · exact kernel28_0_r3_0_eq k + · exact kernel28_0_r3_1_eq k + · exact kernel28_0_r3_2_eq k + · exact kernel28_0_r3_3_eq k + · exact kernel28_0_r3_4_eq k + · exact kernel28_0_r3_5_eq k + · exact kernel28_0_r3_6_eq k + · exact kernel28_0_r3_7_eq k + · exact kernel28_0_r3_8_eq k + · exact kernel28_0_r3_9_eq k + · exact kernel28_0_r3_10_eq k + · exact kernel28_0_r3_11_eq k + · exact kernel28_0_r3_12_eq k + · exact kernel28_0_r3_13_eq k + · exact kernel28_0_r3_14_eq k + · exact kernel28_0_r3_15_eq k +noncomputable def kernel28_0_r4_0 : Fin 16 → CBox := ![⟨⟨3356518001426402206426,3356518001426407067893⟩,⟨(-568613715308961988245),(-568613715308957126815)⟩⟩,⟨⟨3351433506516547833384,3351433506516552688294⟩,⟨(-571488048693419417483),(-571488048693414562610)⟩⟩,⟨⟨3341275793303463697086,3341275793303468538901⟩,⟨(-577208346578649747905),(-577208346578644906127)⟩⟩,⟨⟨3326067493746987001001,3326067493746991823234⟩,⟨(-585718129370816408775),(-585718129370811586580)⟩⟩,⟨⟨3305842749861964495578,3305842749861969291819⟩,⟨(-596933321190561783326),(-596933321190556987123)⟩⟩,⟨⟨3280647438847860154041,3280647438847864917979⟩,⟨(-610743016700185105282),(-610743016700180341382)⟩⟩,⟨⟨3250539460492640705978,3250539460492645431433⟩,⟨(-627010494552084642622),(-627010494552079917205)⟩⟩,⟨⟨3215589076234015694999,3215589076234020375941⟩,⟨(-645574469736388497389),(-645574469736383816486)⟩⟩,⟨⟨3175879287010835866881,3175879287010840497448⟩,⟨(-666250575157549435970),(-666250575157544805442)⟩⟩,⟨⟨3131506235047380313897,3131506235047384888424⟩,⟨(-688833060817631337470),(-688833060817626762982)⟩⟩,⟨⟨3082579613026395624007,3082579613026400137042⟩,⟨(-713096697034770713209),(-713096697034766200213)⟩⟩,⟨⟨3029223062761267251675,3029223062761271698000⟩,⟨(-738798866189178306773),(-738798866189173860487)⟩⟩,⟨⟨2971574544506239234383,2971574544506243609030⟩,⟨(-765681825580229904649),(-765681825580225530042)⟩⟩,⟨⟨2909786657472580595454,2909786657472584893723⟩,⟨(-793475122114797811385),(-793475122114793513155)⟩⟩,⟨⟨2844026891967643268561,2844026891967647486031⟩,⟨(-821898137750972514676),(-821898137750968297245)⟩⟩,⟨⟨2774477793855149488511,2774477793855153621057⟩,⟨(-850662742918315122122),(-850662742918310989615)⟩⟩] +lemma kernel28_0_r4_0_eq : ∀ k : Fin 16, kernel28_0Expr 4 0 k = kernel28_0_r4_0 k := by decide +kernel +noncomputable def kernel28_0_r4_1 : Fin 16 → CBox := ![⟨⟨2701337022753296917118,2701337022753300960915⟩,⟨(-879476033554574795298),(-879476033554570751540)⟩⟩,⟨⟨2624817286538785140552,2624817286538789092099⟩,⟨(-908043125970856428171),(-908043125970852476665)⟩⟩,⟨⟨2545146136297741651057,2545146136297745507160⟩,⟨(-936069982515915501300),(-936069982515911645236)⟩⟩,⟨⟨2462565607838462812800,2462565607838466570604⟩,⟨(-963266239990050332768),(-963266239990046575003)⟩⟩,⟨⟨2377331698227270392618,2377331698227274049586⟩,⟨(-989348011994530613970),(-989348011994526957042)⟩⟩,⟨⟨2289713668490913132954,2289713668490916686901⟩,⟨(-1014040635927277596649),(-1014040635927274042742)⟩⟩,⟨⟨2199993166602421264388,2199993166602424713441⟩,⟨(-1037081335181171762373),(-1037081335181168313359)⟩⟩,⟨⟨2108463168080636708659,2108463168080640051295⟩,⟨(-1058221767296284456477),(-1058221767296281113878)⟩⟩,⟨⟨2015426734928907670366,2015426734928910905366⟩,⟨(-1077230429385549004310),(-1077230429385545769345)⟩⟩,⟨⟨1921195597152314287537,1921195597152317414039⟩,⟨(-1093894893113508294791),(-1093894893113505168322)⟩⟩,⟨⟨1826088564657571828726,1826088564657574846162⟩,⟨(-1108023842871952140968),(-1108023842871949123562)⟩⟩,⟨⟨1730429780884591852786,1730429780884594760921⟩,⟨(-1119448892569287349058),(-1119448892569284440953)⟩⟩,⟨⟨1634546832970950478080,1634546832970953276929⟩,⟨(-1128026158629058329763),(-1128026158629055530940)⟩⟩,⟨⟨1538768736537300079575,1538768736537302769522⟩,⟨(-1133637569365171323517),(-1133637569365168633595)⟩⟩,⟨⟨1443423816231407086603,1443423816231409668275⟩,⟨(-1136191893846048676003),(-1136191893846046094353)⟩⟩,⟨⟨1348837505912202170982,1348837505912204645275⟩,⟨(-1135625476646964610887),(-1135625476646962136613)⟩⟩] +lemma kernel28_0_r4_1_eq : ∀ k : Fin 16, kernel28_0Expr 4 1 k = kernel28_0_r4_1 k := by decide +kernel +noncomputable def kernel28_0_r4_2 : Fin 16 → CBox := ![⟨⟨1255330094728654330443,1255330094728656698451⟩,⟨(-1131902668479963278886),(-1131902668479960910896)⟩⟩,⟨⟨1163214447293134897037,1163214447293137160153⟩,⟨(-1125015946536149498878),(-1125015946536147235779)⟩⟩,⟨⟨1072793727614475405838,1072793727614477565618⟩,⟨(-1114985722419879332617),(-1114985722419877172851)⟩⟩,⟨⟨984359157400330704931,984359157400332763364⟩,⟨(-1101859839735464496191),(-1101859839735462437771)⟩⟩,⟨⟨898187839730080000667,898187839730081959742⟩,⟨(-1085712767635490569669),(-1085712767635488610605)⟩⟩,⟨⟨814540678917862241670,814540678917864103561⟩,⟨(-1066644500882200762288),(-1066644500882198900406)⟩⟩,⟨⟨733660426621950314912,733660426621952081883⟩,⟨(-1044779181133063153369),(-1044779181133061386406)⟩⟩,⟨⟨655769882915516836447,655769882915518510980⟩,⟨(-1020263458160769031463),(-1020263458160767356935)⟩⟩,⟨⟨581070279131648941880,581070279131650526502⟩,⟨(-993264613479182721428),(-993264613479181136811)⟩⟩,⟨⟨509739866861580575036,509739866861582072458⟩,⟨(-963968472295280466441),(-963968472295278969022)⟩⟩,⟨⟨441932734561104608805,441932734561106021749⟩,⟨(-932577132772300644400),(-932577132772299231458)⟩⟩,⟨⟨377777869859075837468,377777869859077168805⟩,⟨(-899306544206777799205),(-899306544206776467869)⟩⟩,⟨⟨317378481927344335263,317378481927345587846⟩,⟨(-864383967835371416263),(-864383967835370163682)⟩⟩,⟨⟨260811594236007679566,260811594236008856727⟩,⟨(-828045355549466801679),(-828045355549465624516)⟩⟩,⟨⟨208127913761695131360,208127913761696236252⟩,⟨(-790532682770359150343),(-790532682770358045450)⟩⟩,⟨⟨159351978325537599754,159351978325538635341⟩,⟨(-752091272101398258258),(-752091272101397222669)⟩⟩] +lemma kernel28_0_r4_2_eq : ∀ k : Fin 16, kernel28_0Expr 4 2 k = kernel28_0_r4_2 k := by decide +kernel +noncomputable def kernel28_0_r4_3 : Fin 16 → CBox := ![⟨⟨114482579301050451287,114482579301051420462⟩,⟨(-712967144114591950972),(-712967144114590981794)⟩⟩,⟨⟨73493452541416225144,73493452541417130887⟩,⟨(-673404430750021452027),(-673404430750020546281)⟩⟩,⟨⟨36334226120985532103,36334226120986377297⟩,⟨(-633642885322702941525),(-633642885322702096327)⟩⟩,⟨⟨2931609454715593898,2931609454716381485⟩,⟨(-593915521072229740959),(-593915521072228953367)⟩⟩,⟨⟨(-26809195365810501597),(-26809195365809768797)⟩,⟨(-554446407597373145534),(-554446407597372412730)⟩⟩,⟨⟨(-53002882524830909968),(-53002882524830229112)⟩,⟨(-515448651444340454438),(-515448651444339773577)⟩⟩,⟨⟨(-75782257124258387985),(-75782257124257756355)⟩,⟨(-477122583627679218898),(-477122583627678587263)⟩⟩,⟨⟨(-95296303308146791522),(-95296303308146206260)⟩,⟨(-439654173029984863066),(-439654173029984277799)⟩⟩,⟨⟨(-111708135507720201622),(-111708135507719660128)⟩,⟨(-403213680530940504627),(-403213680530939963127)⟩⟩,⟨⟨(-125192863711187426684),(-125192863711186926387)⟩,⟨(-367954564443340205336),(-367954564443339705034)⟩⟩,⟨⟨(-135935404333047291258),(-135935404333046829734)⟩,⟨(-334012643472249715174),(-334012643472249253644)⟩⟩,⟨⟨(-144128268328881238170),(-144128268328880813021)⟩,⟨(-301505519052836712508),(-301505519052836287353)⟩⟩,⟨⟨(-149969357684164190441),(-149969357684163799368)⟩,⟨(-270532254650784766432),(-270532254650784375354)⟩⟩,⟨⟨(-153659800323211815978),(-153659800323211456744)⟩,⟨(-241173305511178496885),(-241173305511178137647)⟩⟩,⟨⟨(-155401851873384825470),(-155401851873384495997)⟩,⟨(-213490688496296956761),(-213490688496296627284)⟩⟩,⟨⟨(-155396890627850159054),(-155396890627849857290)⟩,⟨(-187528378131381335302),(-187528378131381033535)⟩⟩] +lemma kernel28_0_r4_3_eq : ∀ k : Fin 16, kernel28_0Expr 4 3 k = kernel28_0_r4_3 k := by decide +kernel +noncomputable def kernel28_0_r4_4 : Fin 16 → CBox := ![⟨⟨(-153843529535266796348),(-153843529535266520401)⟩,⟨(-163312911842524964620),(-163312911842524688671)⟩⟩,⟨⟨(-150935866172687387163),(-150935866172687135169)⟩,⟨(-140854184674242769354),(-140854184674242517358)⟩⟩,⟨⟨(-146861888501080083565),(-146861888501079853806)⟩,⟨(-120146411556336268811),(-120146411556336039051)⟩⟩,⟨⟨(-141802050837859195263),(-141802050837858986071)⟩,⟨(-101169233478438336324),(-101169233478438127131)⟩⟩,⟨⟨(-135928030986608228059),(-135928030986608037903)⟩,⟨(-83888942741540255762),(-83888942741540065604)⟩⟩,⟨⟨(-129401675919889092197),(-129401675919888919582)⟩,⟨(-68259801791699184020),(-68259801791699011405)⟩⟩,⟨⟨(-122374139893891616470),(-122374139893891460032)⟩,⟨(-54225429992563846336),(-54225429992563689898)⟩⟩,⟨⟨(-114985215457136753147),(-114985215457136611572)⟩,⟨(-41720233039330827642),(-41720233039330686066)⟩⟩,⟨⟨(-107362854567424108039),(-107362854567423980123)⟩,⟨(-30670850525650706455),(-30670850525650578539)⟩⟩,⟨⟨(-99622874012575315021),(-99622874012575199608)⟩,⟨(-20997598405889942628),(-20997598405889827215)⟩⟩,⟨⟨(-91868836593815940609),(-91868836593815836646)⟩,⟨(-12615884699174479036),(-12615884699174375073)⟩⟩,⟨⟨(-84192097119109218400),(-84192097119109124882)⟩,⟨(-5437578703671618198),(-5437578703671524680)⟩⟩,⟨⟨(-76672000200683463069),(-76672000200683378800)⟩,⟨627683830068443761,627683830068528029⟩⟩,⟨⟨(-69376215179328999910),(-69376215179328924057)⟩,⟨5671274741649245620,5671274741649321472⟩⟩,⟨⟨(-62361192220345917765),(-62361192220345849595)⟩,⟨9784439385540061174,9784439385540129343⟩⟩,⟨⟨(-55672722744731783851),(-55672722744731722671)⟩,⟨13057264526011303488,13057264526011364666⟩⟩] +lemma kernel28_0_r4_4_eq : ∀ k : Fin 16, kernel28_0Expr 4 4 k = kernel28_0_r4_4 k := by decide +kernel +noncomputable def kernel28_0_r4_5 : Fin 16 → CBox := ![⟨⟨(-49346586867125120536),(-49346586867125065720)⟩,⟨15577755702997354327,15577755702997409142⟩⟩,⟨⟨(-43409270393132906252),(-43409270393132857200)⟩,⟨17431029029949066953,17431029029949116005⟩⟩,⟨⟨(-37878734159058401251),(-37878734159058357427)⟩,⟨18698619944629172341,18698619944629216163⟩⟩,⟨⟨(-32765219046059669686),(-32765219046059630585)⟩,⟨19457909139058682260,19457909139058721359⟩⟩,⟨⟨(-28072070832278974903),(-28072070832278940074)⟩,⟨19781663784476056833,19781663784476091661⟩⟩,⟨⟨(-23796570120210621451),(-23796570120210590467)⟩,⟨19737690272911423365,19737690272911454349⟩⟩,⟨⟨(-19930753849455041994),(-19930753849455014473)⟩,⟨19388593042843342884,19388593042843370405⟩⟩,⟨⟨(-16462216332534085695),(-16462216332534061281)⟩,⟨18791632658720242544,18791632658720266958⟩⟩,⟨⟨(-13374879288958595023),(-13374879288958573397)⟩,⟨17998675181667115303,17998675181667136928⟩⟩,⟨⟨(-10649721956631047938),(-10649721956631028808)⟩,⟨17056224003052097315,17056224003052116446⟩⟩,⟨⟨(-8265463988438168815),(-8265463988438151918)⟩,⟨16005524708711584951,16005524708711601848⟩⟩,⟨⟨(-6199195457090914798),(-6199195457090899888)⟩,⟨14882733188537253441,14882733188537268351⟩⟩,⟨⟨(-4426949858259567579),(-4426949858259554445)⟩,⟨13719137087688034781,13719137087688047915⟩⟩,⟨⟨(-2924217490582353289),(-2924217490582341733)⟩,⟨12541420791530480460,12541420791530492017⟩⟩,⟨⟨(-1666397975753704913),(-1666397975753694760)⟩,⟨11371964422842118317,11371964422842128470⟩⟩,⟨⟨(-629191942216560640),(-629191942216551726)⟩,⟨10229167780774596952,10229167780774605866⟩⟩] +lemma kernel28_0_r4_5_eq : ∀ k : Fin 16, kernel28_0Expr 4 5 k = kernel28_0_r4_5 k := by decide +kernel +noncomputable def kernel28_0_r4_6 : Fin 16 → CBox := ![⟨⟨211066983312474342,211066983312482154⟩,⟨9127790739064127846,9127790739064135658⟩⟩,⟨⟨877137761457784168,877137761457791008⟩,⟨8079302317932470169,8079302317932477009⟩⟩,⟨⟨1390652172526215029,1390652172526221009⟩,⟨7092231422230386400,7092231422230392380⟩⟩,⟨⟨1771946106255388360,1771946106255393582⟩,⟨6172513070800935180,6172513070800940403⟩⟩,⟨⟨2039937814284679610,2039937814284684162⟩,⟨5323824803544057898,5323824803544062450⟩⟩,⟨⟨2212048672416106823,2212048672416110789⟩,⟨4547908820117289020,4547908820117292986⟩⟩,⟨⟨2304161779239667002,2304161779239670452⟩,⟨3844876256983896062,3844876256983899512⟩⟩,⟨⟨2330613623252451357,2330613623252454360⟩,⟨3213490829774366002,3213490829774369005⟩⟩,⟨⟨2304214068734236497,2304214068734239104⟩,⟨2651429840761500387,2651429840761502993⟩⟩,⟨⟨2236290026697837114,2236290026697839375⟩,⟨2155521264771472742,2155521264771475004⟩⟩,⟨⟨2136748375908238548,2136748375908240508⟩,⟨1721956272141777907,1721956272141779867⟩⟩,⟨⟨2014153964809276612,2014153964809278307⟩,⟨1346477118322416657,1346477118322418352⟩⟩,⟨⟨1875818843051390598,1875818843051392064⟩,⟨1024540822991910635,1024540822991912101⟩⟩,⟨⟨1727899226690126214,1727899226690127480⟩,⟨751459476136016876,751459476136018143⟩⟩,⟨⟨1575497080515388928,1575497080515390020⟩,⟨522518345558277166,522518345558278258⟩⟩,⟨⟨1422763592092323091,1422763592092324032⟩,⟨333073222722390104,333073222722391045⟩⟩] +lemma kernel28_0_r4_6_eq : ∀ k : Fin 16, kernel28_0Expr 4 6 k = kernel28_0_r4_6 k := by decide +kernel +noncomputable def kernel28_0_r4_7 : Fin 16 → CBox := ![⟨⟨1273002204060486296,1273002204060487107⟩,⟨178628636126483645,178628636126484456⟩⟩,⟨⟨1128769254670829797,1128769254670830493⟩,⟨54898689206536968,54898689206537665⟩⟩,⟨⟨991970643619908659,991970643619909256⟩,⟨(-42147650461053014),(-42147650461052416)⟩⟩,⟨⟨863953284702526655,863953284702527170⟩,⟨(-116254965109622180),(-116254965109621665)⟩⟩,⟨⟨745590423888207227,745590423888207668⟩,⟨(-170861683246285288),(-170861683246284847)⟩⟩,⟨⟨637360187792731607,637360187792731985⟩,⟨(-209090499246788902),(-209090499246788524)⟩⟩,⟨⟨539416981124613417,539416981124613741⟩,⟨(-233747247134631368),(-233747247134631045)⟩⟩,⟨⟨451655571662060470,451655571662060747⟩,⟨(-247326672398551865),(-247326672398551588)⟩⟩,⟨⟨373767887793244338,373767887793244575⟩,⟨(-252023674536555661),(-252023674536555425)⟩⟩,⟨⟨305292707616253781,305292707616253984⟩,⟨(-249748732139390157),(-249748732139389954)⟩⟩,⟨⟨245658541718740923,245658541718741099⟩,⟨(-242146366655598788),(-242146366655598613)⟩⟩,⟨⟨194220106247151497,194220106247151647⟩,⟨(-230615646122444191),(-230615646122444041)⟩⟩,⟨⟨150288851322128810,150288851322128937⟩,⟨(-216331872416539674),(-216331872416539547)⟩⟩,⟨⟨113158055099290794,113158055099290903⟩,⟨(-200268731983500883),(-200268731983500774)⟩⟩,⟨⟨82123018779431640,82123018779431733⟩,⟨(-183220318219127638),(-183220318219127545)⟩⟩,⟨⟨56496905627698737,56496905627698818⟩,⟨(-165822551984800810),(-165822551984800729)⟩⟩] +lemma kernel28_0_r4_7_eq : ∀ k : Fin 16, kernel28_0Expr 4 7 k = kernel28_0_r4_7 k := by decide +kernel +noncomputable def kernel28_0_r4_8 : Fin 16 → CBox := ![⟨⟨35622760489640734,35622760489640803⟩,⟨(-148573633996802143),(-148573633996802074)⟩⟩,⟨⟨18882228177861717,18882228177861775⟩,⟨(-131853258379434563),(-131853258379434503)⟩⟩,⟨⟨5701462038492596,5701462038492647⟩,⟨(-115940400289621804),(-115940400289621754)⟩⟩,⟨⟨(-4445319648137454),(-4445319648137411)⟩,⟨(-101029562339380585),(-101029562339380543)⟩⟩,⟨⟨(-12034209920981552),(-12034209920981516)⟩,⟨(-87245424986167356),(-87245424986167320)⟩⟩,⟨⟨(-17491543333358406),(-17491543333358374)⟩,⟨(-74655895779463237),(-74655895779463205)⟩⟩,⟨⟨(-21195043274439475),(-21195043274439447)⟩,⟨(-63283592160783329),(-63283592160783302)⟩⟩,⟨⟨(-23475891306637297),(-23475891306637273)⟩,⟨(-53115823340993266),(-53115823340993241)⟩⟩,⟨⟨(-24621463883508843),(-24621463883508822)⟩,⟨(-44113159614933397),(-44113159614933377)⟩⟩,⟨⟨(-24878520256866248),(-24878520256866230)⟩,⟨(-36216693333910416),(-36216693333910398)⟩⟩,⟨⟨(-24456661206617219),(-24456661206617203)⟩,⟨(-29354105646403158),(-29354105646403142)⟩⟩,⟨⟨(-23531911032971373),(-23531911032971359)⟩,⟨(-23444658003926483),(-23444658003926469)⟩⟩,⟨⟨(-22250304801760688),(-22250304801760676)⟩,⟨(-18403228222154797),(-18403228222154785)⟩⟩,⟨⟨(-20731389031045453),(-20731389031045442)⟩,⟨(-14143508424207173),(-14143508424207161)⟩⟩,⟨⟨(-19071566865057660),(-19071566865057649)⟩,⟨(-10580477228171015),(-10580477228171005)⟩⟩,⟨⟨(-17347238403547008),(-17347238403547000)⟩,⟨(-7632251741646507),(-7632251741646498)⟩⟩] +lemma kernel28_0_r4_8_eq : ∀ k : Fin 16, kernel28_0Expr 4 8 k = kernel28_0_r4_8 k := by decide +kernel +noncomputable def kernel28_0_r4_9 : Fin 16 → CBox := ![⟨⟨(-15617703412574527),(-15617703412574518)⟩,⟨(-5221416870430250),(-5221416870430241)⟩⟩,⟨⟨(-13927807357609401),(-13927807357609395)⟩,⟨(-3275920627031674),(-3275920627031667)⟩⟩,⟨⟨(-12310322824606424),(-12310322824606417)⟩,⟨(-1729614944586951),(-1729614944586944)⟩⟩,⟨⟨(-10788067200822040),(-10788067200822033)⟩,⟨(-522512292111539),(-522512292111533)⟩⟩,⟨⟨(-9375764251957018),(-9375764251957012)⟩,⟨399180593807528,399180593807534⟩⟩,⟨⟨(-8081662230005621),(-8081662230005615)⟩,⟨1083199102836168,1083199102836173⟩⟩,⟨⟨(-6908924640491768),(-6908924640491762)⟩,⟨1571482505766539,1571482505766544⟩⟩,⟨⟨(-5856812035995286),(-5856812035995281)⟩,⟨1900523643682769,1900523643682775⟩⟩,⟨⟨(-4921674412518233),(-4921674412518228)⟩,⟨2101775753731109,2101775753731114⟩⟩,⟨⟨(-4097774171572303),(-4097774171572298)⟩,⟨2202091533793545,2202091533793550⟩⟩,⟨⟨(-3377959355779501),(-3377959355779496)⟩,⟨2224174724511214,2224174724511218⟩⟩,⟨⟨(-2754206127658863),(-2754206127658858)⟩,⟨2187028964353420,2187028964353425⟩⟩,⟨⟨(-2218048375628953),(-2218048375628949)⟩,⟨2106392491170944,2106392491170949⟩⟩,⟨⟨(-1760911011913702),(-1760911011913697)⟩,⟨1995150471236701,1995150471236706⟩⟩,⟨⟨(-1374362067744411),(-1374362067744406)⟩,⟨1863719389633958,1863719389633963⟩⟩,⟨⟨(-1050297167538907),(-1050297167538903)⟩,⟨1720400092504862,1720400092504865⟩⟩] +lemma kernel28_0_r4_9_eq : ∀ k : Fin 16, kernel28_0Expr 4 9 k = kernel28_0_r4_9 k := by decide +kernel +noncomputable def kernel28_0_r4_10 : Fin 16 → CBox := ![⟨⟨(-781068434939454),(-781068434939449)⟩,⟨1571697791168102,1571697791168107⟩⟩,⟨⟨(-559568394875084),(-559568394875079)⟩,⟨1422608678127481,1422608678127485⟩⟩,⟨⟨(-379278020205067),(-379278020205063)⟩,⟨1276873820395688,1276873820395692⟩⟩,⟨⟨(-234286751792384),(-234286751792379)⟩,⟨1137201737424698,1137201737424703⟩⟩,⟨⟨(-119291111396430),(-119291111396425)⟩,⟨1005461585902565,1005461585902570⟩⟩,⟨⟨(-29577435084624),(-29577435084620)⟩,⟨882849203600798,882849203600802⟩⟩,⟨⟨39006716915792,39006716915796⟩,⟨770028446299471,770028446299475⟩⟩,⟨⟨90088771847794,90088771847799⟩,⟨667250317722336,667250317722341⟩⟩,⟨⟨126812016376217,126812016376219⟩,⟨574452369913901,574452369913904⟩⟩,⟨⟨151878802823072,151878802823076⟩,⟨491340763810019,491340763810023⟩⟩,⟨⟨167594301472965,167594301472968⟩,⟨417457246176472,417457246176475⟩⟩,⟨⟨175909460517541,175909460517544⟩,⟨352233135357785,352233135357788⟩⟩,⟨⟨178462206484240,178462206484245⟩,⟨295032227003778,295032227003783⟩⟩,⟨⟨176616220212062,176616220212066⟩,⟨245184342015158,245184342015162⟩⟩,⟨⟨171496865684458,171496865684462⟩,⟨202011049934032,202011049934036⟩⟩,⟨⟨164024039846781,164024039846785⟩,⟨164844917498835,164844917498839⟩⟩] +lemma kernel28_0_r4_10_eq : ∀ k : Fin 16, kernel28_0Expr 4 10 k = kernel28_0_r4_10 k := by decide +kernel +noncomputable def kernel28_0_r4_11 : Fin 16 → CBox := ![⟨⟨154941858790367,154941858790372⟩,⟨133043458055795,133043458055800⟩⟩,⟨⟨144845206502802,144845206502807⟩,⟨105998795612597,105998795612602⟩⟩,⟨⟨134203253119181,134203253119186⟩,⟨83143909113300,83143909113305⟩⟩,⟨⟨123380105851196,123380105851199⟩,⟨63956188753109,63956188753112⟩⟩,⟨⟨112652792370348,112652792370352⟩,⟨47958916947102,47958916947105⟩⟩,⟨⟨102226797534924,102226797534927⟩,⟨34721181557315,34721181557318⟩⟩,⟨⟨92249383494419,92249383494422⟩,⟨23856637471882,23856637471885⟩⟩,⟨⟨82820923318738,82820923318741⟩,⟨15021453699100,15021453699103⟩⟩,⟨⟨74004471805522,74004471805527⟩,⟨7911715734270,7911715734275⟩⟩,⟨⟨65833785988517,65833785988520⟩,⟨2260495958250,2260495958253⟩⟩,⟨⟨58319993681637,58319993681642⟩,⟨(-2165242898766),(-2165242898761)⟩⟩,⟨⟨51457092391355,51457092391358⟩,⟨(-5567785753294),(-5567785753291)⟩⟩,⟨⟨45226444074889,45226444074892⟩,⟨(-8121751594824),(-8121751594821)⟩⟩,⟨⟨39600414238794,39600414238797⟩,⟨(-9977061625931),(-9977061625927)⟩⟩,⟨⟨34545287292710,34545287292713⟩,⟨(-11261743480438),(-11261743480435)⟩⟩,⟨⟨30023574270234,30023574270237⟩,⟨(-12084542542195),(-12084542542192)⟩⟩] +lemma kernel28_0_r4_11_eq : ∀ k : Fin 16, kernel28_0Expr 4 11 k = kernel28_0_r4_11 k := by decide +kernel +noncomputable def kernel28_0_r4_12 : Fin 16 → CBox := ![⟨⟨25995814250762,25995814250764⟩,⟨(-12537324345152),(-12537324345149)⟩⟩,⟨⟨22421957211976,22421957211979⟩,⟨(-12697261928176),(-12697261928173)⟩⟩,⟨⟨19262403685029,19262403685033⟩,⟨(-12628809397374),(-12628809397370)⟩⟩,⟨⟨16478765489029,16478765489033⟩,⟨(-12385468290112),(-12385468290108)⟩⟩,⟨⟨14034401961554,14034401961558⟩,⟨(-12011357043184),(-12011357043180)⟩⟩,⟨⟨11894777421537,11894777421540⟩,⟨(-11542596284509),(-11542596284506)⟩⟩,⟨⟨10027678024564,10027678024568⟩,⟨(-11008524078870),(-11008524078866)⟩⟩,⟨⟨8403319610863,8403319610866⟩,⟨(-10432755899651),(-10432755899648)⟩⟩,⟨⟨6994372509985,6994372509989⟩,⟨(-9834104163856),(-9834104163852)⟩⟩,⟨⟨5775924458822,5775924458826⟩,⟨(-9227371813512),(-9227371813508)⟩⟩,⟨⟨4725398718548,4725398718551⟩,⟨(-8624033778334),(-8624033778332)⟩⟩,⟨⟨3822441052955,3822441052959⟩,⟨(-8032819311522),(-8032819311518)⟩⟩,⟨⟨3048786372740,3048786372743⟩,⟨(-7460207229849),(-7460207229846)⟩⟩,⟨⟨2388113481509,2388113481512⟩,⟨(-6910845070165),(-6910845070162)⟩⟩,⟨⟨1825894410552,1825894410555⟩,⟨(-6387902141139),(-6387902141135)⟩⟩,⟨⟨1349243238853,1349243238858⟩,⟨(-5893365434195),(-5893365434190)⟩⟩] +lemma kernel28_0_r4_12_eq : ∀ k : Fin 16, kernel28_0Expr 4 12 k = kernel28_0_r4_12 k := by decide +kernel +noncomputable def kernel28_0_r4_13 : Fin 16 → CBox := ![⟨⟨946768007405,946768007409⟩,⟨(-5428286383776),(-5428286383771)⟩⟩,⟨⟨608428304433,608428304437⟩,⟨(-4992985549654),(-4992985549650)⟩⟩,⟨⟨325400278493,325400278497⟩,⟨(-4587221442440),(-4587221442437)⟩⟩,⟨⟨89950193140,89950193143⟩,⟨(-4210328932591),(-4210328932588)⟩⟩,⟨⟨(-104682861011),(-104682861007)⟩,⟨(-3861331974671),(-3861331974667)⟩⟩,⟨⟨(-264394860404),(-264394860400)⟩,⟨(-3539034741423),(-3539034741420)⟩⟩,⟨⟨(-394315395489),(-394315395486)⟩,⟨(-3242094693776),(-3242094693773)⟩⟩,⟨⟨(-498897123057),(-498897123053)⟩,⟨(-2969080609299),(-2969080609295)⟩⟩,⟨⟨(-581996520825),(-581996520821)⟩,⟨(-2718518148439),(-2718518148435)⟩⟩,⟨⟨(-646946437108),(-646946437105)⟩,⟨(-2488925150000),(-2488925149997)⟩⟩,⟨⟨(-696620986570),(-696620986565)⟩,⟨(-2278838509817),(-2278838509814)⟩⟩,⟨⟨(-733493372446),(-733493372443)⟩,⟨(-2086834204283),(-2086834204280)⟩⟩,⟨⟨(-759687223150),(-759687223145)⟩,⟨(-1911541768547),(-1911541768542)⟩⟩,⟨⟨(-777022022723),(-777022022718)⟩,⟨(-1751654323113),(-1751654323108)⟩⟩,⟨⟨(-787053194708),(-787053194705)⟩,⟨(-1605935058033),(-1605935058030)⟩⟩,⟨⟨(-791107371194),(-791107371189)⟩,⟨(-1473220926917),(-1473220926912)⟩⟩] +lemma kernel28_0_r4_13_eq : ∀ k : Fin 16, kernel28_0Expr 4 13 k = kernel28_0_r4_13 k := by decide +kernel +noncomputable def kernel28_0_r4_14 : Fin 16 → CBox := ![⟨⟨(-790313346022),(-790313346018)⟩,⟨(-1352424170011),(-1352424170007)⟩⟩,⟨⟨(-785629175512),(-785629175507)⟩,⟨(-1242532173519),(-1242532173515)⟩⟩,⟨⟨(-777865853131),(-777865853127)⟩,⟨(-1142606078014),(-1142606078010)⟩⟩,⟨⟨(-767707947754),(-767707947750)⟩,⟨(-1051778470062),(-1051778470058)⟩⟩,⟨⟨(-755731559135),(-755731559131)⟩,⟨(-969250425442),(-969250425437)⟩⟩,⟨⟨(-742419909814),(-742419909811)⟩,⟨(-894288117879),(-894288117876)⟩⟩,⟨⟨(-728176860165),(-728176860162)⟩,⟨(-826219162231),(-826219162228)⟩⟩,⟨⟨(-713338602917),(-713338602914)⟩,⟨(-764428824053),(-764428824050)⟩⟩,⟨⟨(-698183765518),(-698183765515)⟩,⟨(-708356197279),(-708356197276)⟩⟩,⟨⟨(-682942122958),(-682942122955)⟩,⟨(-657490427116),(-657490427113)⟩⟩,⟨⟨(-667802100343),(-667802100339)⟩,⟨(-611367035428),(-611367035424)⟩⟩,⟨⟨(-652917223299),(-652917223294)⟩,⟨(-569564389886),(-569564389881)⟩⟩,⟨⟨(-638411655319),(-638411655316)⟩,⟨(-531700345509),(-531700345506)⟩⟩,⟨⟨(-624384944061),(-624384944058)⟩,⟨(-497429077173),(-497429077170)⟩⟩,⟨⟨(-610916083396),(-610916083393)⟩,⟨(-466438113826),(-466438113823)⟩⟩,⟨⟨(-598066984531),(-598066984528)⟩,⟨(-438445579195),(-438445579192)⟩⟩] +lemma kernel28_0_r4_14_eq : ∀ k : Fin 16, kernel28_0Expr 4 14 k = kernel28_0_r4_14 k := by decide +kernel +noncomputable def kernel28_0_r4_15 : Fin 16 → CBox := ![⟨⟨(-585885437458),(-585885437454)⟩,⟨(-413197639113),(-413197639109)⟩⟩,⟨⟨(-574407633481),(-574407633477)⟩,⟨(-390466152330),(-390466152327)⟩⟩,⟨⟨(-563660310169),(-563660310164)⟩,⟨(-370046519171),(-370046519166)⟩⟩,⟨⟨(-553662571898),(-553662571894)⟩,⟨(-351755720779),(-351755720775)⟩⟩,⟨⟨(-544427431946),(-544427431942)⟩,⟨(-335430540667),(-335430540662)⟩⟩,⟨⟨(-535963115748),(-535963115745)⟩,⟨(-320925959654),(-320925959651)⟩⟩,⟨⟨(-528274159400),(-528274159396)⟩,⟨(-308113715159),(-308113715155)⟩⟩,⟨⟨(-521362332652),(-521362332649)⟩,⟨(-296881015827),(-296881015824)⟩⟩,⟨⟨(-515227411371),(-515227411367)⟩,⟨(-287129402867),(-287129402864)⟩⟩,⟨⟨(-509867820723),(-509867820719)⟩,⟨(-278773749891),(-278773749886)⟩⟩,⟨⟨(-505281167069),(-505281167064)⟩,⟨(-271741393696),(-271741393692)⟩⟩,⟨⟨(-501464673674),(-501464673670)⟩,⟨(-265971389130),(-265971389126)⟩⟩,⟨⟨(-498415532770),(-498415532765)⟩,⟨(-261413881922),(-261413881917)⟩⟩,⟨⟨(-496131184253),(-496131184249)⟩,⟨(-258029594212),(-258029594209)⟩⟩,⟨⟨(-494609529242),(-494609529239)⟩,⟨(-255789418344),(-255789418341)⟩⟩,⟨⟨(-493849084852),(-493849084849)⟩,⟨(-254674115330),(-254674115326)⟩⟩] +lemma kernel28_0_r4_15_eq : ∀ k : Fin 16, kernel28_0Expr 4 15 k = kernel28_0_r4_15 k := by decide +kernel +noncomputable def kernel28_0_r4 : Fin 16 → Fin 16 → CBox := ![kernel28_0_r4_0,kernel28_0_r4_1,kernel28_0_r4_2,kernel28_0_r4_3,kernel28_0_r4_4,kernel28_0_r4_5,kernel28_0_r4_6,kernel28_0_r4_7,kernel28_0_r4_8,kernel28_0_r4_9,kernel28_0_r4_10,kernel28_0_r4_11,kernel28_0_r4_12,kernel28_0_r4_13,kernel28_0_r4_14,kernel28_0_r4_15] +lemma kernel28_0_r4_eq (i k : Fin 16) : kernel28_0Expr 4 i k = kernel28_0_r4 i k := by + fin_cases i + · exact kernel28_0_r4_0_eq k + · exact kernel28_0_r4_1_eq k + · exact kernel28_0_r4_2_eq k + · exact kernel28_0_r4_3_eq k + · exact kernel28_0_r4_4_eq k + · exact kernel28_0_r4_5_eq k + · exact kernel28_0_r4_6_eq k + · exact kernel28_0_r4_7_eq k + · exact kernel28_0_r4_8_eq k + · exact kernel28_0_r4_9_eq k + · exact kernel28_0_r4_10_eq k + · exact kernel28_0_r4_11_eq k + · exact kernel28_0_r4_12_eq k + · exact kernel28_0_r4_13_eq k + · exact kernel28_0_r4_14_eq k + · exact kernel28_0_r4_15_eq k +noncomputable def kernel28_0_r5_0 : Fin 16 → CBox := ![⟨⟨4567906916323653674604916940,4567906916323655750796715769⟩,⟨3209012861755465191739243893,3209012861755467267961241674⟩⟩,⟨⟨4566918641748539577064959488,4566918641748541652230176535⟩,⟨3202025941493723806859718858,3202025941493725882054972007⟩⟩,⟨⟨4564925235595256915566435446,4564925235595258988676115927⟩,⟨3188073575304709263448137887,3188073575304711336587529487⟩⟩,⟨⟨4561893162312162048247828198,4561893162312164118275462380⟩,⟨3167198692312459108413229017,3167198692312461178470088637⟩⟩,⟨⟨4557772563396996647372499292,4557772563396998713295158536⟩,⟨3139465636282907482119179860,3139465636282909548070420311⟩⟩,⟨⟨4552497787518741649573517400,4552497787518743710373137665⟩,⟨3104960102778265113281955513,3104960102778267174109357058⟩⟩,⟨⟨4545988091239807625629962347,4545988091239809680294408784⟩,⟨3063789050521883751203635766,3063789050521885805894911406⟩⟩,⟨⟨4538148505118728591620454926,4538148505118730639144946815⟩,⟨3016080582946375680265560214,3016080582946377727815781309⟩⟩,⟨⟨4528870858688286109287933293,4528870858688288148675822221⟩,⟨2961983795041917768993029285,2961983795041919808405404393⟩⟩,⟨⟨4518034956533951224875781759,4518034956533953255140376777⟩,⟨2901668579863746383026489044,2901668579863748413314189739⟩⟩,⟨⟨4505509896447708477977621450,4505509896447710498143198471⟩,⟨2835325388414714531168025892,2835325388414716551355196778⟩⟩,⟨⟨4491155519408710419746094025,4491155519408712429020517200⟩,⟨2763164936105842949675265556,2763164936105844958969646297⟩⟩,⟨⟨4474823979951852142289273470,4474823979951854139733625702⟩,⟨2685417848628768871989059051,2685417848628770869451615378⟩⟩,⟨⟨4456361424336406904845720709,4456361424336408889536380085⟩,⟨2602334239860687123502966078,2602334239860689108209966807⟩⟩,⟨⟨4435609762828592817633524453,4435609762828594788659348695⟩,⟨2514183214374478989005329230,2514183214374480960045531236⟩⟩,⟨⟨4412408521374695262773870697,4412408521374697219242020834⟩,⟨2421252287251617725547913464,2421252287251619682028385831⟩⟩] +lemma kernel28_0_r5_0_eq : ∀ k : Fin 16, kernel28_0Expr 5 0 k = kernel28_0_r5_0 k := by decide +kernel +noncomputable def kernel28_0_r5_1 : Fin 16 → CBox := ![⟨⟨4386596756976507847729724798,4386596756976509788760469789⟩,⟨2323846714198025461116604288,2323846714198027402157533380⟩⟩,⟨⟨4358015020200627900130096871,4358015020200629824866233089⟩,⟨2222288725445598131439518771,2222288725445600056183628114⟩⟩,⟨⟨4326507347470540196128948112,4326507347470542103726793551⟩,⟨2116916657584112029237686073,2116916657584113936841230929⟩⟩,⟨⟨4291923265118975057964900471,4291923265118976947606513041⟩,⟨2008083978306312140635759130,2008083978306314030280745102⟩⟩,⟨⟨4254119786631570731656404727,4254119786631572602536857919⟩,⟨1896158200056862122832945749,1896158200056863993714404708⟩⟩,⟨⟨4212963384105278775400751810,4212963384105280626746608416⟩,⟨1781519679744250245546861156,1781519679744252096891325176⟩⟩,⟨⟨4168331914689836650983817811,4168331914689838482033967655⟩,⟨1664560302991484716088386632,1664560302991486547134725887⟩⟩,⟨⟨4120116482691019261406414374,4120116482691021071441340323⟩,⟨1545682052851366939694317087,1545682052851368749723005417⟩⟩,⟨⟨4068223218102367547792355144,4068223218102369336102882082⟩,⟨1425295464477395385772035163,1425295464477397174073899660⟩⟩,⟨⟨4012574952608491417977739550,4012574952608493183890516174⟩,⟨1303817968901369184029564514,1303817968901370949931267806⟩⟩,⟨⟨3953112774577029708369730832,3953112774577031451219862882⟩,⟨1181672130800522411126199115,1181672130800524153962872012⟩⟩,⟨⟨3889797445235101501395853262,3889797445235103220563337492⟩,⟨1059283786915320468051264311,1059283786915322187202939605⟩⟩,⟨⟨3822610659114447696871000220,3822610659114449391741270952⟩,⟨937080093576783733882588413,937080093576785428734747280⟩⟩,⟨⟨3751556132949635780128899658,3751556132949637450195592281⟩,⟨815487493590717905944777024,815487493590719575991117071⟩⟩,⟨⟨3676660508524945049655970030,3676660508524946694491024399⟩,⟨694929614475722268639317907,694929614475723913451858204⟩⟩,⟨⟨3597974056483944393414265937,3597974056483946012515605348⟩,⟨575825111731804582598777294,575825111731806201675518097⟩⟩] +lemma kernel28_0_r5_1_eq : ∀ k : Fin 16, kernel28_0Expr 5 1 k = kernel28_0_r5_1 k := by decide +kernel +noncomputable def kernel28_0_r5_2 : Fin 16 → CBox := ![⟨⟨3515571169834024025957068652,3515571169834025618819398350⟩,⟨458585472396111898977419246,458585472396113491813152130⟩⟩,⟨⟨3429550637785435680661728798,3429550637785437246849241000⟩,⟨343612795591227670671209801,343612795591229236830222059⟩⟩,⟨⟨3340035692646332997776031850,3340035692646334536845577389⟩,⟨231297568060038173918911436,231297568060039712958157309⟩⟩,⟨⟨3247173824733893129614053975,3247173824733894641190520147⟩,⟨122016453781049594749739722,122016453781051106294217492⟩⟩,⟨⟨3151136362635328818811502192,3151136362635330302519366198⟩,⟨16130117642872720703290652,16130117642874204377595603⟩⟩,⟨⟨3052117818636583546681815126,3052117818636585002296913193⟩,⟨(-86018896197517064346342214),(-86018896197515608766249595)⟩⟩,⟨⟨2950335001702716642048316103,2950335001702718069246610210⟩,⟨(-184108210262094421654076392),(-184108210262092994492104177)⟩⟩,⟨⟨2846025903011576592954354046,2846025903011577991491975617⟩,⟨(-277837562885230928598390120),(-277837562885229530098272280)⟩⟩,⟨⟨2739448361678034235735795173,2739448361678035605343515850⟩,⟨(-366930639595726341693839259),(-366930639595724972124665408)⟩⟩,⟨⟨2630878520924529572965353299,2630878520924530913514479440⟩,⟨(-451136766291519911282362374),(-451136766291518570772684434)⟩⟩,⟨⟨2520609087518255416025680551,2520609087518256727317909123⟩,⟨(-530232444536910821177794893),(-530232444536909509925771703)⟩⟩,⟨⟨2408947409768379214777679662,2408947409768380496705294790⟩,⟨(-604022710401288836637766590),(-604022710401287554750968614)⟩⟩,⟨⟨2296213391720495809005628015,2296213391720497061439241763⟩,⟨(-672342299645156388196461247),(-672342299645155135804130448)⟩⟩,⟨⟨2182737263362674778359451675,2182737263362676001263876188⟩,⟨(-735056603732508001933706090),(-735056603732506779070884213)⟩⟩,⟨⟨2068857228631848698867998065,2068857228631849892171953577⟩,⟨(-792062403092050883822330314),(-792062403092049690560147270)⟩⟩,⟨⟨1954917014746595204960055855,1954917014746596368687693645⟩,⟨(-843288366241772089050054605),(-843288366241770925362418505)⟩⟩] +lemma kernel28_0_r5_2_eq : ∀ k : Fin 16, kernel28_0Expr 5 2 k = kernel28_0_r5_2 k := by decide +kernel +noncomputable def kernel28_0_r5_3 : Fin 16 → CBox := ![⟨⟨1841263347860898214795187614,1841263347860899348917569958⟩,⟨(-888695305805511565198443019),(-888695305805510431112702228)⟩⟩,⟨⟨1728243381204811906362965311,1728243381204813010978703170⟩,⟨(-928276185055395917088029266),(-928276185055394812505653665)⟩⟩,⟨⟨1616202102727603808476624360,1616202102727604883625026515⟩,⟨(-962055871374942754198822004),(-962055871374941679080591696)⟩⟩,⟨⟨1505479749766955416098678582,1505479749766956461930862046⟩,⟨(-990090635915412812518840296),(-990090635915411766713735269)⟩⟩,⟨⟨1396409258419238373714898172,1396409258419239390317475274⟩,⟨(-1012467401670573387709509727),(-1012467401670572371131021742)⟩⟩,⟨⟨1289313775071346897351788682,1289313775071347884946735928⟩,⟨(-1029302745178103167777944897),(-1029302745178102180204208576)⟩⟩,⟨⟨1184504256970481380763616198,1184504256970482339502165763⟩,⟨(-1040741660023501109551001537),(-1040741660023500150830901756)⟩⟩,⟨⟨1082277187757153338298744562,1082277187757154268450546057⟩,⟨(-1046956093227896047180411483),(-1046956093227895117044421355)⟩⟩,⟨⟨982912432577227398716343481,982912432577228300471561087⟩,⟨(-1048143268398037930647036257),(-1048143268398037028905118940)⟩⟩,⟨⟨886671255735936470962072165,886671255735937344658248652⟩,⟨(-1044523812159431910220881869),(-1044523812159431036535626185)⟩⟩,⟨⟨793794521881467654669447665,793794521881468500808293385⟩,⟨(-1036339702838381561832009762),(-1036339702838380715701843333)⟩⟩,⟨⟨704501099434684347213761701,704501099434685168009082427⟩,⟨(-1023852062564715927839940192),(-1023852062564715107051217890)⟩⟩,⟨⟨618986482446999638320711779,618986482447000433945960154⟩,⟨(-1007338815896844041949997893),(-1007338815896843246329404156)⟩⟩,⟨⟨537421644307422233750188299,537421644307423004526146888⟩,⟨(-987092239691517480191566204),(-987092239691516709418456645)⟩⟩,⟨⟨459952133773710081178326151,459952133773710827331454307⟩,⟨(-963416430224337965684546978),(-963416430224337219532600647)⟩⟩,⟨⟨386697420716292304279574471,386697420716293026160828271⟩,⟨(-936624714491320399870257533),(-936624714491319677988656301)⟩⟩] +lemma kernel28_0_r5_3_eq : ∀ k : Fin 16, kernel28_0Expr 5 3 k = kernel28_0_r5_3 k := by decide +kernel +noncomputable def kernel28_0_r5_4 : Fin 16 → CBox := ![⟨⟨317750495784803110019822154,317750495784803807878229284⟩,⟨(-907037033170546068456083541),(-907037033170545370595936498)⟩⟩,⟨⟨253177724985220536593391272,253177724985221210834977114⟩,⟨(-874977322886456879021228950),(-874977322886456204776645551)⟩⟩,⟨⟨193018956941158961143821225,193018956941159612068473570⟩,⟨(-840770925194733234653354482),(-840770925194732583724579282)⟩⟩,⟨⟨137287877456239692443866987,137287877456240320476185801⟩,⟨(-804742049096889707370768956),(-804742049096889079333331067)⟩⟩,⟨⟨85972602945074442275757862,85972602945075047734281032⟩,⟨(-767211312911431720721246748),(-767211312911431115256733705)⟩⟩,⟨⟨39036501405706107363158383,39036501405706690719180879⟩,⟨(-728493389989963346117039431),(-728493389989962762754281423)⟩⟩,⟨⟨(-3580773089046146802801036),(-3580773089045585185437989)⟩,⟨(-688894781095612292979313543),(-688894781095611731354586988)⟩⟩,⟨⟨(-41962048859132993170267158),(-41962048859132452806050820)⟩,⟨(-648711734286939332185582887),(-648711734286938791813485161)⟩⟩,⟨⟨(-76211226700248560335482176),(-76211226700248040844340268)⟩,⟨(-608228330907736530548770984),(-608228330907736011049334658)⟩⟩,⟨⟨(-106451712109863242666207896),(-106451712109862743526790962)⟩,⟨(-567714753810916314376501530),(-567714753810915815228475798)⟩⟩,⟨⟨(-132824711722031652393868985),(-132824711722031173182114673)⟩,⟨(-527425751285894021926562673),(-527425751285893542705977879)⟩⟩,⟨⟨(-155487417202627107009913244),(-155487417202626647197741075)⟩,⟨(-487599307359158847908345714),(-487599307359158388087207428)⟩⟩,⟨⟨(-174611100677844730306940348),(-174611100677844289492290078)⟩,⟨(-448455526244718983366259992),(-448455526244718542542587738)⟩⟩,⟨⟨(-190379146219378354177292230),(-190379146219377931773138611)⟩,⟨(-410195735783360390615193120),(-410195735783359968202755575)⟩⟩,⟨⟨(-202985041990467735654499563),(-202985041990467331214909720)⟩,⟨(-373001811775723451733460144),(-373001811775723047286656855)⟩⟩,⟨⟨(-212630357375506840179505645),(-212630357375506453171449814)⟩,⟨(-337035722231649501798253842),(-337035722231649114783992712)⟩⟩] +lemma kernel28_0_r5_4_eq : ∀ k : Fin 16, kernel28_0Expr 5 4 k = kernel28_0_r5_4 k := by decide +kernel +noncomputable def kernel28_0_r5_5 : Fin 16 → CBox := ![⟨⟨(-219522728785933815176241913),(-219522728785933445184317226)⟩,⟨(-302439287772748231644201398),(-302439287772747861647015680)⟩⟩,⟨⟨(-223873876876485409866057539),(-223873876876485056312285316)⟩,⟨(-269334151779580268748512197),(-269334151779579915190358011)⟩⟩,⟨⟨(-225897676643836979232578948),(-225897676643836641589971349)⟩,⟨(-237821951408558567660845601),(-237821951408558230014669893)⟩⟩,⟨⟨(-225808300344230445660686293),(-225808300344230123404459734)⟩,⟨(-207984678351694080042867175),(-207984678351693757783821338)⟩⟩,⟨⟨(-223818451392089353682309030),(-223818451392089046397025943)⟩,⟨(-179885216204820921536685690),(-179885216204820614249268000)⟩⟩,⟨⟨(-220137705425321630633007304),(-220137705425321337771650798)⟩,⟨(-153568039571761941906222904),(-153568039571761649043353396)⟩⟩,⟨⟨(-214970972584980083496197291),(-214970972584979804632942010)⟩,⟨(-129060058582170053104727710),(-129060058582169774240513247)⟩⟩,⟨⟨(-208517092798751110339425258),(-208517092798750844959119396)⟩,⟨(-106371591352727366091401624),(-106371591352727100710629846)⟩⟩,⟨⟨(-200967573521652100970198036),(-200967573521651848665852589)⟩,⟨(-85497446082238583297259210),(-85497446082238330992884755)⟩⟩,⟨⟨(-192505477015458127487839066),(-192505477015457887589911204)⟩,⟨(-66418093942219611679466968),(-66418093942219371781893184)⟩⟩,⟨⟨(-183304461881869482310720585),(-183304461881869254386486218)⟩,⟨(-49100913701409865282027085),(-49100913701409637358478599)⟩⟩,⟨⟨(-173527981242602883546068743),(-173527981242602667119850152)⟩,⟨(-33501489095334255042958080),(-33501489095334038617708733)⟩⟩,⟨⟨(-163328637719255323466943648),(-163328637719255118160715029)⟩,⟨(-19564940305682338363238522),(-19564940305682133058216989)⟩⟩,⟨⟨(-152847693240609388596650828),(-152847693240609193932672280)⟩,⟨(-7227271529406532101963484),(-7227271529406337439387499)⟩⟩,⟨⟨(-142214729724979454309871214),(-142214729724979269910829814)⟩,⟨3583282529319298547648216,3583282529319482945130878⟩⟩,⟨⟨(-131547454876053196102306235),(-131547454876053021489369334)⟩,⟨12944927346469478824461145,12944927346469653435720158⟩⟩] +lemma kernel28_0_r5_5_eq : ∀ k : Fin 16, kernel28_0Expr 5 5 k = kernel28_0_r5_5 k := by decide +kernel +noncomputable def kernel28_0_r5_6 : Fin 16 → CBox := ![⟨⟨(-120951645713802039862988640),(-120951645713801874681204020)⟩,⟨20941011300217715047434619,20941011300217880227455181⟩⟩,⟨⟨(-110521221054066423521459849),(-110521221054066267330586452)⟩,⟨27658773885158151477507388,27658773885158307666560094⟩⟩,⟨⟨(-100338432963222737164781713),(-100338432963222589611542333)⟩,⟨33188151359566655154744574,33188151359566802706133215⟩⟩,⟨⟨(-90474166254979949110949843),(-90474166254979809788307543)⟩,⟨37620650163901542667025782,37620650163901681987810783⟩⟩,⟨⟨(-80988334367237147824246341),(-80988334367237016408471824)⟩,⟨41048296792450161790283606,41048296792450293204451891⟩⟩,⟨⟨(-71930359456003704832236427),(-71930359456003580929225709)⟩,⟨43562671121627858750040962,43562671121627982651699420⟩⟩,⟨⟨(-63339724264430197103339198),(-63339724264430080397623361)⟩,⟨45254028527933687565693736,45254028527933804270290851⟩⟩,⟨⟨(-55246583258028895776805943),(-55246583258028785903943326)⟩,⟨46210514493932121435080921,46210514493932231307038039⟩⟩,⟨⟨(-47672420648843781907177171),(-47672420648843678438143339)⟩,⟨46517473827346548704029634,46517473827346652172351410⟩⟩,⟨⟨(-40630743245472562352015043),(-40630743245472464905904679)⟩,⟨46256855129051423908092454,46256855129051521353664819⟩⟩,⟨⟨(-34127796543922712398582629),(-34127796543922620715146916)⟩,⟨45506709759936863037684222,45506709759936954720737305⟩⟩,⟨⟨(-28163293095979775476353147),(-28163293095979689253770052)⟩,⟨44340783290469817534197933,44340783290469903756535851⟩⟩,⟨⟨(-22731142935506285011128253),(-22731142935506204010330195)⟩,⟨42828196283038891465871015,42828196283038972466543356⟩⟩,⟨⟨(-17820176686583586841358570),(-17820176686583510772267504)⟩,⟨41033210265145392298919910,41033210265145468367987921⟩⟩,⟨⟨(-13414852898162582784637197),(-13414852898162511416977686)⟩,⟨39015073907100426455222541,39015073907100497822946905⟩⟩,⟨⟨(-9495942125686625034589859),(-9495942125686558100766729)⟩,⟨36827943723755242853875804,36827943723755309787837987⟩⟩] +lemma kernel28_0_r5_6_eq : ∀ k : Fin 16, kernel28_0Expr 5 6 k = kernel28_0_r5_6 k := by decide +kernel +noncomputable def kernel28_0_r5_7 : Fin 16 → CBox := ![⟨⟨(-6041181289491367617794023),(-6041181289491304911584384)⟩,⟨34520873075511556510590338,34520873075511619217000561⟩⟩,⟨⟨(-3025892862280839782034552),(-3025892862280781047801085)⟩,⟨32137862846194216967860961,32137862846194275702344964⟩⟩,⟨⟨(-423564454677630139130989),(-423564454677575169062879)⟩,⟨29717966918559142176591729,29717966918559197146949785⟩⟩,⟨⟨1793614638482016157460464,1793614638482067585616646⟩,⟨27295445444295193929195509,27295445444295245357671561⟩⟩,⟨⟨3654262413086369623583289,3654262413086417687473024⟩,⟨24899958904551156135535611,24899958904551204199766634⟩⟩,⟨⟨5187360230077869766285101,5187360230077914675045934⟩,⟨22556796067983516493810731,22556796067983561402926656⟩⟩,⟨⟨6421856726072519827888861,6421856726072561747023535⟩,⟨20287129163661897485944026,20287129163661939405440983⟩⟩,⟨⟨7386319527280407716601071,7386319527280446832623411⟩,⟨18108289882709629433290514,18108289882709668549676668⟩⟩,⟨⟨8108634041839686606067883,8108634041839723094594744⟩,⟨16034060191702950362296586,16034060191702986851143126⟩⟩,⟨⟨8615747996247369664382072,8615747996247403705560648⟩,⟨14074972368915359008817986,14074972368915393050261865⟩⟩,⟨⟨8933459857069233978475065,8933459857069265705077213⟩,⟨12238613147986607114076694,12238613147986638840894800⟩⟩,⟨⟨9086248840115274266925375,9086248840115303828573886⟩,⟨10529927359495699975222209,10529927359495729537042260⟩⟩,⟨⟨9097143854645960464233305,9097143854645987978786121⟩,⟨8951516986892475969457086,8951516986892503484141749⟩⟩,⟨⟨8987628457284307497441265,8987628457284333105481725⟩,⟨7503932087842004024113822,7503932087842029632250972⟩⟩,⟨⟨8777578695202192303752635,8777578695202216114419003⟩,⟨6185950564840606906079501,6185950564840630716811676⟩⟩,⟨⟨8485230595793663803561115,8485230595793685938477509⟩,⟨4994844290695356911988944,4994844290695379046944293⟩⟩] +lemma kernel28_0_r5_7_eq : ∀ k : Fin 16, kernel28_0Expr 5 7 k = kernel28_0_r5_7 k := by decide +kernel +noncomputable def kernel28_0_r5_8 : Fin 16 → CBox := ![⟨⟨8127174004545106849583237,8127174004545127405217806⟩,⟨3926629597061454170912880,3926629597061474726563359⟩⟩,⟨⟨7718369477615460532708192,7718369477615479631753187⟩,⟨2976300610901387932113665,2976300610901407031155312⟩⟩,⟨⟨7272184993762593825050957,7272184993762611553621796⟩,⟨2138044368926101447669228,2138044368926119176220590⟩⟩,⟨⟨6800449354463477095793070,6800449354463493549914034⟩,⟨1405437049500693286236020,1405437049500709740324224⟩⟩,⟨⟨6313519284080545563922472,6313519284080560819069895⟩,⟨771621032035045151648960,771621032035060406752923⟩⟩,⟨⟨5820357416525838426476956,5820357416525852570252719⟩,⟨229462823542616739499697,229462823542630883223605⟩⟩,⟨⟨5328618554106518136097101,5328618554106531240437996⟩,⟨(-228307820120118513906288),(-228307820120105409623587)⟩⟩,⟨⟨4844741801494740946006573,4844741801494753087712600⟩,⟨(-608977004853469930789115),(-608977004853457789145812)⟩⟩,⟨⟨4374046406899046719265157,4374046406899057956670509⟩,⟨(-919743262375265512565258),(-919743262375254275225573)⟩⟩,⟨⟨3920829377898919835032144,3920829377898930236902130⟩,⟨(-1167630624039510844444759),(-1167630624039500442642025)⟩⟩,⟨⟨3488463175996292067396355,3488463175996301688903428⟩,⟨(-1359417132876779568753143),(-1359417132876769947313723)⟩⟩,⟨⟨3079492027310800981019880,3079492027310809880794237⟩,⟨(-1501577629427752950232407),(-1501577629427744050520277)⟩⟩,⟨⟨2695725613204603200908827,2695725613204611424594437⟩,⟨(-1600239586083196563085959),(-1600239586083188339451963)⟩⟩,⟨⟨2338329120803625132614642,2338329120803632733697214⟩,⟨(-1661150732664484373854523),(-1661150732664476772814001)⟩⟩,⟨⟨2007908836837710640326383,2007908836837717659708382⟩,⟨(-1689657209573427477043782),(-1689657209573420457695271)⟩⟩,⟨⟨1704592656993825452271778,1704592656993831935357811⟩,⟨(-1690691000643272421430787),(-1690691000643265938370638)⟩⟩] +lemma kernel28_0_r5_8_eq : ∀ k : Fin 16, kernel28_0Expr 5 8 k = kernel28_0_r5_8 k := by decide +kernel +noncomputable def kernel28_0_r5_9 : Fin 16 → CBox := ![⟨⟨1428105055658279303080205,1428105055658285284437744⟩,⟨(-1668765432487904883528226),(-1668765432487898902189870)⟩⟩,⟨⟨1177836216617581732456970,1177836216617587252832567⟩,⟨(-1627977577414356937941338),(-1627977577414351417579070)⟩⟩,⟨⟨952905163552443797704904,952905163552448888360536⟩,⟨(-1572016459719816614195125),(-1572016459719811523547756)⟩⟩,⟨⟨752216849958857870832804,752216849958862565997964⟩,⟨(-1504176037513980492968163),(-1504176037513975797806925)⟩⟩,⟨⟨574513271775778646639526,574513271775782972713198⟩,⟨(-1427372011391995130437709),(-1427372011391990804364292)⟩⟩,⟨⟨418418753094980970498454,418418753094984957969780⟩,⟨(-1344161594884638320608964),(-1344161594884634333134886)⟩⟩,⟨⟨282479626717596896509154,282479626717600568872782⟩,⟨(-1256765467450065454871186),(-1256765467450061782502330)⟩⟩,⟨⟨165198588032005310706043,165198588032008693683794⟩,⟨(-1167091216939350584655559),(-1167091216939347201670583)⟩⟩,⟨⟨65064043884621349765412,65064043884624462967792⟩,⟨(-1076757663335145793071122),(-1076757663335142679859948)⟩⟩,⟨⟨(-19425190943604182411778),(-19425190943601315992807)⟩,⟨(-987119537767037282140536),(-987119537767034415711576)⟩⟩,⟨⟨(-89739477046942777867216),(-89739477046940140711020)⟩,⟨(-899292069244355114169657),(-899292069244352477002606)⟩⟩,⟨⟨(-147301830507749137148762),(-147301830507746710107612)⟩,⟨(-814175105355449055187944),(-814175105355446628135358)⟩⟩,⟨⟨(-193474914762478813705793),(-193474914762476582137673)⟩,⟨(-732476461723730462206108),(-732476461723728230626215)⟩⟩,⟨⟨(-229551164140429439354360),(-229551164140427386341728)⟩,⟨(-654734257850017999647391),(-654734257850015946622857)⟩⟩,⟨⟨(-256745669789055256645271),(-256745669789053369268252)⟩,⟨(-581338053853551836976595),(-581338053853549949587721)⟩⟩,⟨⟨(-276191474183870384583658),(-276191474183868640053678)⟩,⟨(-512548653453928258050333),(-512548653453926513510215)⟩⟩] +lemma kernel28_0_r5_9_eq : ∀ k : Fin 16, kernel28_0Expr 5 9 k = kernel28_0_r5_9 k := by decide +kernel +noncomputable def kernel28_0_r5_10 : Fin 16 → CBox := ![⟨⟨(-288936939548655292205453),(-288936939548653680380233)⟩,⟨(-448516483351578069297832),(-448516483351576457464200)⟩⟩,⟨⟨(-295944877333108486725212),(-295944877333106996422513)⟩,⟨(-389298498116327678308541),(-389298498116326187998979)⟩⟩,⟨⟨(-298093149561524136359689),(-298093149561522759371914)⟩,⟨(-334873593024431781440100),(-334873593024430404446842)⟩⟩,⟨⟨(-296176477631425045333364),(-296176477631423772401938)⟩,⟨(-285156535308036268330316),(-285156535308034995394630)⟩⟩,⟨⟨(-290909219360812708035711),(-290909219360811532331297)⟩,⟨(-240010447364186238378641),(-240010447364185062671044)⟩⟩,⟨⟨(-282928900210699849745634),(-282928900210698763006704)⟩,⟨(-199257894016680458999365),(-199257894016679372258191)⟩⟩,⟨⟨(-272800309193307483232170),(-272800309193306479365442)⟩,⟨(-162690640358707034941286),(-162690640358706031073129)⟩⟩,⟨⟨(-261019993650576741900179),(-261019993650575814024326)⟩,⟨(-130078157462004611105188),(-130078157462003683228604)⟩⟩,⟨⟨(-248021009567610822531194),(-248021009567609965661956)⟩,⟨(-101174960752578153097583),(-101174960752577296228210)⟩⟩,⟨⟨(-234177805159081896017817),(-234177805159081103971233)⟩,⟨(-75726870546739793709450),(-75726870546739001663229)⟩⟩,⟨⟨(-219811134985869799641365),(-219811134985869067931101)⟩,⟨(-53476286519970569125965),(-53476286519969837416468)⟩⟩,⟨⟨(-205192919733120472111666),(-205192919733119795657789)⟩,⟨(-34166568127366650585233),(-34166568127365974132455)⟩⟩,⟨⟨(-190550982966970947603992),(-190550982966970322717426)⟩,⟨(-17545611563791952617586),(-17545611563791327732386)⟩⟩,⟨⟨(-176073610683760051927424),(-176073610683759474089327)⟩,⟨(-3368711070116922320719),(-3368711070116344484196)⟩⟩,⟨⟨(-161913892304718881514034),(-161913892304718347445630)⟩,⟨8599211446430825939005,8599211446431360005678⟩⟩,⟨⟨(-148193813010028973284713),(-148193813010028479260816)⟩,⟨18581929142176854501251,18581929142177348523302⟩⟩] +lemma kernel28_0_r5_10_eq : ∀ k : Fin 16, kernel28_0Expr 5 10 k = kernel28_0_r5_10 k := by decide +kernel +noncomputable def kernel28_0_r5_11 : Fin 16 → CBox := ![⟨⟨(-135008077028797585828251),(-135008077028797129203990)⟩,⟨26790711177119359522020,26790711177119816144362⟩⟩,⟨⟨(-122427649801446651802078),(-122427649801446229226463)⟩,⟨33423533283901850552688,33423533283902273126341⟩⟩,⟨⟨(-110503013914414198209523),(-110503013914413807311317)⟩,⟨38664635135440887801216,38664635135441278697444⟩⟩,⟨⟨(-99267139486570894621345),(-99267139486570532662086)⟩,⟨42684367481557533451868,42684367481557895409158⟩⟩,⟨⟨(-88738174377932069173223),(-88738174377931734236144)⟩,⟨45639277757319452677579,45639277757319787612875⟩⟩,⟨⟨(-78921863309636125476386),(-78921863309635815160645)⟩,⟨47672388435616699606473,47672388435617009920696⟩⟩,⟨⟨(-69813707842862502240452),(-69813707842862214800955)⟩,⟨48913627730275535546775,48913627730275822984992⟩⟩,⟨⟨(-61400881272132745818050),(-61400881272132479288755)⟩,⟨49480377298746868264457,49480377298747134792687⟩⟩,⟨⟨(-53663913948244099201263),(-53663913948243852232245)⟩,⟨49478106306211121623629,49478106306211368591775⟩⟩,⟨⟨(-46578165454059478576919),(-46578165454059249403548)⟩,⟨49001065570823343664163,49001065570823572836834⟩⟩,⟨⟨(-40115100501125401359486),(-40115100501125188751398)⟩,⟨48133019499536256361142,48133019499536468968683⟩⟩,⟨⟨(-34243385477291060878222),(-34243385477290863369899)⟩,⟨46947997142010436167903,46947997142010633675814⟩⟩,⟨⟨(-28929822327769289363470),(-28929822327769105985472)⟩,⟨45511046941032948246358,45511046941033131624063⟩⟩,⟨⟨(-24140135959017552953412),(-24140135959017382443791)⟩,⟨43878982652422592169231,43878982652422762678662⟩⟩,⟨⟨(-19839630673244553081449),(-19839630673244394570674)⟩,⟨42101110461270954695915,42101110461271113206591⟩⟩,⟨⟨(-15993730320652771788756),(-15993730320652624250907)⟩,⟨40219929553811834915823,40219929553811982453651⟩⟩] +lemma kernel28_0_r5_11_eq : ∀ k : Fin 16, kernel28_0Expr 5 11 k = kernel28_0_r5_11 k := by decide +kernel +noncomputable def kernel28_0_r5_12 : Fin 16 → CBox := ![⟨⟨(-12568415939107831691995),(-12568415939107694452417)⟩,⟨38271800336970666188385,38271800336970803428008⟩⟩,⟨⟨(-9530573672700113891945),(-9530573672699986009372)⟩,⟨36287576154009677190249,36287576154009805072924⟩⟩,⟨⟨(-6848264751619194475389),(-6848264751619075280130)⟩,⟨34293195748703319523794,34293195748703438719201⟩⟩,⟨⟨(-4490928300519870883941),(-4490928300519759638037)⟩,⟨32310234906316498910107,32310234906316610156198⟩⟩,⟨⟨(-2429526740948402939660),(-2429526740948299159343)⟩,⟨30356416671076888624745,30356416671076992405281⟩⟩,⟨⟨(-636642581012489995308),(-636642581012393014344)⟩,⟨28446080329785683562772,28446080329785780543981⟩⟩,⟨⟨913465545786342972316,913465545786433591503⟩,⟨26590609981539062063013,26590609981539152682466⟩⟩,⟨⟨2244840612079355639302,2244840612079440439532⟩,⟨24798824004743552859606,24798824004743637660118⟩⟩,⟨⟨3379832543666784255207,3379832543666863572482⟩,⟨23077327103732729496286,23077327103732808813854⟩⟩,⟨⟨4339125793330927158249,4339125793331001489610⟩,⟨21430826885798432251377,21430826885798506583041⟩⟩,⟨⟨5141784457487451939690,5141784457487521597739⟩,⟨19862417101210063757634,19862417101210133415989⟩⟩,⟨⟨5805310894936167520357,5805310894936232898638⟩,⟨18373829788095839618128,18373829788095904996717⟩⟩,⟨⟨6345714389533804024194,6345714389533865365410⟩,⟨16965658613638005256728,16965658613638066598252⟩⟩,⟨⟨6777586922443231167753,6777586922443288832121⟩,⟨15637555704144626121812,15637555704144683786488⟩⟩,⟨⟨7114183587342738564816,7114183587342792789246⟩,⟨14388404219057684495961,14388404219057738720682⟩⟩,⟨⟨7367505596747822884207,7367505596747873977342⟩,⟨13216468856389105079738,13216468856389156173134⟩⟩] +lemma kernel28_0_r5_12_eq : ∀ k : Fin 16, kernel28_0Expr 5 12 k = kernel28_0_r5_12 k := by decide +kernel +noncomputable def kernel28_0_r5_13 : Fin 16 → CBox := ![⟨⟨7548384192894077038783,7548384192894125161257⟩,⟨12119526386787824100535,12119526386787872223242⟩⟩,⟨⟨7666564096144711453463,7666564096144756875947⟩,⟨11094978206679635014906,11094978206679680437595⟩⟩,⟨⟨7730785401399315883776,7730785401399358762921⟩,⟨10139946782944177595626,10139946782944220474951⟩⟩,⟨⟨7748863072265812083245,7748863072265852630283⟩,⟨9251357736771041809193,9251357736771082356390⟩⟩,⟨⟨7727763387510887308952,7727763387510925642053⟩,⟨8426009186255482947428,8426009186255521280667⟩⟩,⟨⟨7673676868086936994643,7673676868086973311971⟩,⟨7660629838850279342914,7660629838850315660361⟩⟩,⟨⟨7592087359231611198586,7592087359231645613200⟩,⟨6951927198280541572312,6951927198280575987029⟩⟩,⟨⟨7487837063931182938717,7487837063931215608414⟩,⟨6296627127732319188276,6296627127732351858060⟩⟩,⟨⟨7365187424390363528872,7365187424390394532940⟩,⟨5691505893381498870259,5691505893381529874401⟩⟩,⟨⟨7227875829785775540139,7227875829785805032388⟩,⟨5133415700601215750998,5133415700601245243309⟩⟩,⟨⟨7079168193989703620884,7079168193989731684833⟩,⟨4619304630126092224611,4619304630126120288610⟩⟩,⟨⟨6921907498393846640456,6921907498393873396138⟩,⟨4146231783454447016077,4146231783454473771799⟩⟩,⟨⟨6758558434472379099134,6758558434472404604206⟩,⟨3711378356019401941808,3711378356019427446910⟩⟩,⟨⟨6591248310116181168889,6591248310116205537923⟩,⟨3312055273172221446702,3312055273172245815759⟩⟩,⟨⟨6421804404657836472012,6421804404657859763006⟩,⟨2945707947679327589654,2945707947679350880663⟩⟩,⟨⟨6251787971311363881413,6251787971311386184895⟩,⟨2609918648019477620090,2609918648019499923579⟩⟩] +lemma kernel28_0_r5_13_eq : ∀ k : Fin 16, kernel28_0Expr 5 13 k = kernel28_0_r5_13 k := by decide +kernel +noncomputable def kernel28_0_r5_14 : Fin 16 → CBox := ![⟨⟨6082525093716676322356,6082525093716697675226⟩,⟨2302406903985061960837,2302406903985083313709⟩⟩,⟨⟨5915134606489785861466,5915134606489806356745⟩,⟨2021028319592983626636,2021028319593004121911⟩⟩,⟨⟨5750553289072166870358,5750553289072186549917⟩,⟨1763772112712004093876,1763772112712023773426⟩⟩,⟨⟨5589558538550205958288,5589558538550224892097⟩,⟨1528757655709815753996,1528757655709834687793⟩⟩,⟨⟨5432788721163294240222,5432788721163312455839⟩,⟨1314230251400627042993,1314230251400645258592⟩⟩,⟨⟨5280761394516159174831,5280761394516176742667⟩,⟨1118556343219624137673,1118556343219641705489⟩⟩,⟨⟨5133889583543400251536,5133889583543417201989⟩,⟨940218327459345606841,940218327459362557271⟩⟩,⟨⟨4992496283445767010621,4992496283445783398706⟩,⟨777809108183580138915,777809108183596526975⟩⟩,⟨⟨4856827352460808755742,4856827352460824597739⟩,⟨630026511713577345817,630026511713593187786⟩⟩,⟨⟨4727062946715370075372,4727062946715385430380⟩,⟨495667657006610342533,495667657006625697510⟩⟩,⟨⟨4603327638750769684138,4603327638750784574362⟩,⟨373623360488314517754,373623360488329407946⟩⟩,⟨⟨4485699350784367403338,4485699350784381872866⟩,⟨262872638651415107234,262872638651429576730⟩⟩,⟨⟨4374217223505668598819,4374217223505682659865⟩,⟨162477358712050927859,162477358712064988870⟩⟩,⟨⟨4268888531300354952274,4268888531300368651692⟩,⟨71577076562243225436,71577076562256924817⟩⟩,⟨⟨4169694745323366369285,4169694745323379723494⟩,⟨(-10615908062364048774),(-10615908062350694603)⟩⟩,⟨⟨4076596836851220463749,4076596836851233508945⟩,⟨(-84821257079821579555),(-84821257079808534397)⟩⟩] +lemma kernel28_0_r5_14_eq : ∀ k : Fin 16, kernel28_0Expr 5 14 k = kernel28_0_r5_14 k := by decide +kernel +noncomputable def kernel28_0_r5_15 : Fin 16 → CBox := ![⟨⟨3989539904864144568004,3989539904864157309514⟩,⟨(-151695044576198194788),(-151695044576185453317)⟩⟩,⟨⟨3908457203854953140708,3908457203854965620751⟩,⟨(-211833942004904338292),(-211833942004891858288)⟩⟩,⟨⟨3833273640436197932461,3833273640436210163445⟩,⟨(-265779132053213267479),(-265779132053201036535)⟩⟩,⟨⟨3763908800412361676401,3763908800412373688877⟩,⟨(-314019948607144711779),(-314019948607132699345)⟩⟩,⟨⟨3700279561584454456322,3700279561584466255024⟩,⟨(-356997242950474845256),(-356997242950463046596)⟩⟩,⟨⟨3642302341639058741427,3642302341639070361067⟩,⟨(-395106478400390985106),(-395106478400379365509)⟩⟩,⟨⟨3589895025016947322018,3589895025016958772328⟩,⟨(-428700557104731990177),(-428700557104720539909)⟩⟩,⟨⟨3542978607628901081232,3542978607628912388885⟩,⟨(-458092383785643303341),(-458092383785631995730)⟩⟩,⟨⟨3501478593657036604030,3501478593657047770991⟩,⟨(-483557171883129639315),(-483557171883118472397)⟩⟩,⟨⟨3465326174416066087183,3465326174416077147626⟩,⟨(-505334497891374741371),(-505334497891363680971)⟩⟩,⟨⟨3434459215316808279027,3434459215316819240759⟩,⟨(-523630109744526086363),(-523630109744515124674)⟩⟩,⟨⟨3408823073339863291960,3408823073339874178876⟩,⟨(-538617494943384733329),(-538617494943373846457)⟩⟩,⟨⟨3388371264056473484835,3388371264056484298197⟩,⟨(-550439213760267580125),(-550439213760256766805)⟩⟩,⟨⟨3373065994092165722627,3373065994092176491706⟩,⟨(-559208002350975057408),(-559208002350964288374)⟩⟩,⟨⟨3362878571983041489056,3362878571983052220962⟩,⟨(-565007649970449418600),(-565007649970438686738)⟩⟩,⟨⟨3357789707591142136224,3357789707591152853606⟩,⟨(-567893653758657375287),(-567893653758646657949)⟩⟩] +lemma kernel28_0_r5_15_eq : ∀ k : Fin 16, kernel28_0Expr 5 15 k = kernel28_0_r5_15 k := by decide +kernel +noncomputable def kernel28_0_r5 : Fin 16 → Fin 16 → CBox := ![kernel28_0_r5_0,kernel28_0_r5_1,kernel28_0_r5_2,kernel28_0_r5_3,kernel28_0_r5_4,kernel28_0_r5_5,kernel28_0_r5_6,kernel28_0_r5_7,kernel28_0_r5_8,kernel28_0_r5_9,kernel28_0_r5_10,kernel28_0_r5_11,kernel28_0_r5_12,kernel28_0_r5_13,kernel28_0_r5_14,kernel28_0_r5_15] +lemma kernel28_0_r5_eq (i k : Fin 16) : kernel28_0Expr 5 i k = kernel28_0_r5 i k := by + fin_cases i + · exact kernel28_0_r5_0_eq k + · exact kernel28_0_r5_1_eq k + · exact kernel28_0_r5_2_eq k + · exact kernel28_0_r5_3_eq k + · exact kernel28_0_r5_4_eq k + · exact kernel28_0_r5_5_eq k + · exact kernel28_0_r5_6_eq k + · exact kernel28_0_r5_7_eq k + · exact kernel28_0_r5_8_eq k + · exact kernel28_0_r5_9_eq k + · exact kernel28_0_r5_10_eq k + · exact kernel28_0_r5_11_eq k + · exact kernel28_0_r5_12_eq k + · exact kernel28_0_r5_13_eq k + · exact kernel28_0_r5_14_eq k + · exact kernel28_0_r5_15_eq k +noncomputable def kernel28_0 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel28_0_r0,kernel28_0_r1,kernel28_0_r2,kernel28_0_r3,kernel28_0_r4,kernel28_0_r5] +lemma kernel28_0_eq (j : Fin 6) (i k : Fin 16) : kernel28_0Expr j i k = kernel28_0 j i k := by + fin_cases j + · exact kernel28_0_r0_eq i k + · exact kernel28_0_r1_eq i k + · exact kernel28_0_r2_eq i k + · exact kernel28_0_r3_eq i k + · exact kernel28_0_r4_eq i k + · exact kernel28_0_r5_eq i k +lemma kernel28_0_contains (j : Fin 6) (i k : Fin 16) : + (kernel28_0 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(28:ℕ))* + (if false then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel28_0_eq] + unfold kernel28_0Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans28_contains j i k) + simpa only [Bool.false_eq_true,ite_false,mul_one] using hh +noncomputable def kernel28_1Expr (j : Fin 6) (i k : Fin 16) : CBox := ((gridRows j i k).lam.mul (trans28 j i k)).mul (piI.mul (gridRows j i k).z) +noncomputable def kernel28_1_r0_0 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r0_0_eq : ∀ k : Fin 16, kernel28_1Expr 0 0 k = kernel28_1_r0_0 k := by decide +kernel +noncomputable def kernel28_1_r0_1 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r0_1_eq : ∀ k : Fin 16, kernel28_1Expr 0 1 k = kernel28_1_r0_1 k := by decide +kernel +noncomputable def kernel28_1_r0_2 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r0_2_eq : ∀ k : Fin 16, kernel28_1Expr 0 2 k = kernel28_1_r0_2 k := by decide +kernel +noncomputable def kernel28_1_r0_3 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r0_3_eq : ∀ k : Fin 16, kernel28_1Expr 0 3 k = kernel28_1_r0_3 k := by decide +kernel +noncomputable def kernel28_1_r0_4 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r0_4_eq : ∀ k : Fin 16, kernel28_1Expr 0 4 k = kernel28_1_r0_4 k := by decide +kernel +noncomputable def kernel28_1_r0_5 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel28_1_r0_5_eq : ∀ k : Fin 16, kernel28_1Expr 0 5 k = kernel28_1_r0_5 k := by decide +kernel +noncomputable def kernel28_1_r0_6 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel28_1_r0_6_eq : ∀ k : Fin 16, kernel28_1Expr 0 6 k = kernel28_1_r0_6 k := by decide +kernel +noncomputable def kernel28_1_r0_7 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel28_1_r0_7_eq : ∀ k : Fin 16, kernel28_1Expr 0 7 k = kernel28_1_r0_7 k := by decide +kernel +noncomputable def kernel28_1_r0_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel28_1_r0_8_eq : ∀ k : Fin 16, kernel28_1Expr 0 8 k = kernel28_1_r0_8 k := by decide +kernel +noncomputable def kernel28_1_r0_9 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel28_1_r0_9_eq : ∀ k : Fin 16, kernel28_1Expr 0 9 k = kernel28_1_r0_9 k := by decide +kernel +noncomputable def kernel28_1_r0_10 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel28_1_r0_10_eq : ∀ k : Fin 16, kernel28_1Expr 0 10 k = kernel28_1_r0_10 k := by decide +kernel +noncomputable def kernel28_1_r0_11 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel28_1_r0_11_eq : ∀ k : Fin 16, kernel28_1Expr 0 11 k = kernel28_1_r0_11 k := by decide +kernel +noncomputable def kernel28_1_r0_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel28_1_r0_12_eq : ∀ k : Fin 16, kernel28_1Expr 0 12 k = kernel28_1_r0_12 k := by decide +kernel +noncomputable def kernel28_1_r0_13 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel28_1_r0_13_eq : ∀ k : Fin 16, kernel28_1Expr 0 13 k = kernel28_1_r0_13 k := by decide +kernel +noncomputable def kernel28_1_r0_14 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel28_1_r0_14_eq : ∀ k : Fin 16, kernel28_1Expr 0 14 k = kernel28_1_r0_14 k := by decide +kernel +noncomputable def kernel28_1_r0_15 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel28_1_r0_15_eq : ∀ k : Fin 16, kernel28_1Expr 0 15 k = kernel28_1_r0_15 k := by decide +kernel +noncomputable def kernel28_1_r0 : Fin 16 → Fin 16 → CBox := ![kernel28_1_r0_0,kernel28_1_r0_1,kernel28_1_r0_2,kernel28_1_r0_3,kernel28_1_r0_4,kernel28_1_r0_5,kernel28_1_r0_6,kernel28_1_r0_7,kernel28_1_r0_8,kernel28_1_r0_9,kernel28_1_r0_10,kernel28_1_r0_11,kernel28_1_r0_12,kernel28_1_r0_13,kernel28_1_r0_14,kernel28_1_r0_15] +lemma kernel28_1_r0_eq (i k : Fin 16) : kernel28_1Expr 0 i k = kernel28_1_r0 i k := by + fin_cases i + · exact kernel28_1_r0_0_eq k + · exact kernel28_1_r0_1_eq k + · exact kernel28_1_r0_2_eq k + · exact kernel28_1_r0_3_eq k + · exact kernel28_1_r0_4_eq k + · exact kernel28_1_r0_5_eq k + · exact kernel28_1_r0_6_eq k + · exact kernel28_1_r0_7_eq k + · exact kernel28_1_r0_8_eq k + · exact kernel28_1_r0_9_eq k + · exact kernel28_1_r0_10_eq k + · exact kernel28_1_r0_11_eq k + · exact kernel28_1_r0_12_eq k + · exact kernel28_1_r0_13_eq k + · exact kernel28_1_r0_14_eq k + · exact kernel28_1_r0_15_eq k +noncomputable def kernel28_1_r1_0 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel28_1_r1_0_eq : ∀ k : Fin 16, kernel28_1Expr 1 0 k = kernel28_1_r1_0 k := by decide +kernel +noncomputable def kernel28_1_r1_1 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel28_1_r1_1_eq : ∀ k : Fin 16, kernel28_1Expr 1 1 k = kernel28_1_r1_1 k := by decide +kernel +noncomputable def kernel28_1_r1_2 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel28_1_r1_2_eq : ∀ k : Fin 16, kernel28_1Expr 1 2 k = kernel28_1_r1_2 k := by decide +kernel +noncomputable def kernel28_1_r1_3 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩] +lemma kernel28_1_r1_3_eq : ∀ k : Fin 16, kernel28_1Expr 1 3 k = kernel28_1_r1_3 k := by decide +kernel +noncomputable def kernel28_1_r1_4 : Fin 16 → CBox := ![⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-42),42⟩,⟨(-42),42⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel28_1_r1_4_eq : ∀ k : Fin 16, kernel28_1Expr 1 4 k = kernel28_1_r1_4 k := by decide +kernel +noncomputable def kernel28_1_r1_5 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩] +lemma kernel28_1_r1_5_eq : ∀ k : Fin 16, kernel28_1Expr 1 5 k = kernel28_1_r1_5 k := by decide +kernel +noncomputable def kernel28_1_r1_6 : Fin 16 → CBox := ![⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-43),43⟩,⟨(-43),43⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel28_1_r1_6_eq : ∀ k : Fin 16, kernel28_1Expr 1 6 k = kernel28_1_r1_6 k := by decide +kernel +noncomputable def kernel28_1_r1_7 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩] +lemma kernel28_1_r1_7_eq : ∀ k : Fin 16, kernel28_1Expr 1 7 k = kernel28_1_r1_7 k := by decide +kernel +noncomputable def kernel28_1_r1_8 : Fin 16 → CBox := ![⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-44),44⟩,⟨(-44),44⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel28_1_r1_8_eq : ∀ k : Fin 16, kernel28_1Expr 1 8 k = kernel28_1_r1_8 k := by decide +kernel +noncomputable def kernel28_1_r1_9 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩] +lemma kernel28_1_r1_9_eq : ∀ k : Fin 16, kernel28_1Expr 1 9 k = kernel28_1_r1_9 k := by decide +kernel +noncomputable def kernel28_1_r1_10 : Fin 16 → CBox := ![⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-45),45⟩,⟨(-45),45⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r1_10_eq : ∀ k : Fin 16, kernel28_1Expr 1 10 k = kernel28_1_r1_10 k := by decide +kernel +noncomputable def kernel28_1_r1_11 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r1_11_eq : ∀ k : Fin 16, kernel28_1Expr 1 11 k = kernel28_1_r1_11 k := by decide +kernel +noncomputable def kernel28_1_r1_12 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r1_12_eq : ∀ k : Fin 16, kernel28_1Expr 1 12 k = kernel28_1_r1_12 k := by decide +kernel +noncomputable def kernel28_1_r1_13 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r1_13_eq : ∀ k : Fin 16, kernel28_1Expr 1 13 k = kernel28_1_r1_13 k := by decide +kernel +noncomputable def kernel28_1_r1_14 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r1_14_eq : ∀ k : Fin 16, kernel28_1Expr 1 14 k = kernel28_1_r1_14 k := by decide +kernel +noncomputable def kernel28_1_r1_15 : Fin 16 → CBox := ![⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩,⟨⟨(-46),46⟩,⟨(-46),46⟩⟩] +lemma kernel28_1_r1_15_eq : ∀ k : Fin 16, kernel28_1Expr 1 15 k = kernel28_1_r1_15 k := by decide +kernel +noncomputable def kernel28_1_r1 : Fin 16 → Fin 16 → CBox := ![kernel28_1_r1_0,kernel28_1_r1_1,kernel28_1_r1_2,kernel28_1_r1_3,kernel28_1_r1_4,kernel28_1_r1_5,kernel28_1_r1_6,kernel28_1_r1_7,kernel28_1_r1_8,kernel28_1_r1_9,kernel28_1_r1_10,kernel28_1_r1_11,kernel28_1_r1_12,kernel28_1_r1_13,kernel28_1_r1_14,kernel28_1_r1_15] +lemma kernel28_1_r1_eq (i k : Fin 16) : kernel28_1Expr 1 i k = kernel28_1_r1 i k := by + fin_cases i + · exact kernel28_1_r1_0_eq k + · exact kernel28_1_r1_1_eq k + · exact kernel28_1_r1_2_eq k + · exact kernel28_1_r1_3_eq k + · exact kernel28_1_r1_4_eq k + · exact kernel28_1_r1_5_eq k + · exact kernel28_1_r1_6_eq k + · exact kernel28_1_r1_7_eq k + · exact kernel28_1_r1_8_eq k + · exact kernel28_1_r1_9_eq k + · exact kernel28_1_r1_10_eq k + · exact kernel28_1_r1_11_eq k + · exact kernel28_1_r1_12_eq k + · exact kernel28_1_r1_13_eq k + · exact kernel28_1_r1_14_eq k + · exact kernel28_1_r1_15_eq k +noncomputable def kernel28_1_r2_0 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel28_1_r2_0_eq : ∀ k : Fin 16, kernel28_1Expr 2 0 k = kernel28_1_r2_0 k := by decide +kernel +noncomputable def kernel28_1_r2_1 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel28_1_r2_1_eq : ∀ k : Fin 16, kernel28_1Expr 2 1 k = kernel28_1_r2_1 k := by decide +kernel +noncomputable def kernel28_1_r2_2 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel28_1_r2_2_eq : ∀ k : Fin 16, kernel28_1Expr 2 2 k = kernel28_1_r2_2 k := by decide +kernel +noncomputable def kernel28_1_r2_3 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩] +lemma kernel28_1_r2_3_eq : ∀ k : Fin 16, kernel28_1Expr 2 3 k = kernel28_1_r2_3 k := by decide +kernel +noncomputable def kernel28_1_r2_4 : Fin 16 → CBox := ![⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-25),25⟩,⟨(-25),25⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel28_1_r2_4_eq : ∀ k : Fin 16, kernel28_1Expr 2 4 k = kernel28_1_r2_4 k := by decide +kernel +noncomputable def kernel28_1_r2_5 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩] +lemma kernel28_1_r2_5_eq : ∀ k : Fin 16, kernel28_1Expr 2 5 k = kernel28_1_r2_5 k := by decide +kernel +noncomputable def kernel28_1_r2_6 : Fin 16 → CBox := ![⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-26),26⟩,⟨(-26),26⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel28_1_r2_6_eq : ∀ k : Fin 16, kernel28_1Expr 2 6 k = kernel28_1_r2_6 k := by decide +kernel +noncomputable def kernel28_1_r2_7 : Fin 16 → CBox := ![⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩,⟨⟨(-27),27⟩,⟨(-27),27⟩⟩] +lemma kernel28_1_r2_7_eq : ∀ k : Fin 16, kernel28_1Expr 2 7 k = kernel28_1_r2_7 k := by decide +kernel +noncomputable def kernel28_1_r2_8 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩] +lemma kernel28_1_r2_8_eq : ∀ k : Fin 16, kernel28_1Expr 2 8 k = kernel28_1_r2_8 k := by decide +kernel +noncomputable def kernel28_1_r2_9 : Fin 16 → CBox := ![⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-28),28⟩,⟨(-28),28⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel28_1_r2_9_eq : ∀ k : Fin 16, kernel28_1Expr 2 9 k = kernel28_1_r2_9 k := by decide +kernel +noncomputable def kernel28_1_r2_10 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩] +lemma kernel28_1_r2_10_eq : ∀ k : Fin 16, kernel28_1Expr 2 10 k = kernel28_1_r2_10 k := by decide +kernel +noncomputable def kernel28_1_r2_11 : Fin 16 → CBox := ![⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-29),29⟩,⟨(-29),29⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-39),39⟩,⟨(-39),39⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel28_1_r2_11_eq : ∀ k : Fin 16, kernel28_1Expr 2 11 k = kernel28_1_r2_11 k := by decide +kernel +noncomputable def kernel28_1_r2_12 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel28_1_r2_12_eq : ∀ k : Fin 16, kernel28_1Expr 2 12 k = kernel28_1_r2_12 k := by decide +kernel +noncomputable def kernel28_1_r2_13 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-40),40⟩,⟨(-40),40⟩⟩] +lemma kernel28_1_r2_13_eq : ∀ k : Fin 16, kernel28_1Expr 2 13 k = kernel28_1_r2_13 k := by decide +kernel +noncomputable def kernel28_1_r2_14 : Fin 16 → CBox := ![⟨⟨(-40),40⟩,⟨(-40),40⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel28_1_r2_14_eq : ∀ k : Fin 16, kernel28_1Expr 2 14 k = kernel28_1_r2_14 k := by decide +kernel +noncomputable def kernel28_1_r2_15 : Fin 16 → CBox := ![⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩,⟨⟨(-41),41⟩,⟨(-41),41⟩⟩] +lemma kernel28_1_r2_15_eq : ∀ k : Fin 16, kernel28_1Expr 2 15 k = kernel28_1_r2_15 k := by decide +kernel +noncomputable def kernel28_1_r2 : Fin 16 → Fin 16 → CBox := ![kernel28_1_r2_0,kernel28_1_r2_1,kernel28_1_r2_2,kernel28_1_r2_3,kernel28_1_r2_4,kernel28_1_r2_5,kernel28_1_r2_6,kernel28_1_r2_7,kernel28_1_r2_8,kernel28_1_r2_9,kernel28_1_r2_10,kernel28_1_r2_11,kernel28_1_r2_12,kernel28_1_r2_13,kernel28_1_r2_14,kernel28_1_r2_15] +lemma kernel28_1_r2_eq (i k : Fin 16) : kernel28_1Expr 2 i k = kernel28_1_r2 i k := by + fin_cases i + · exact kernel28_1_r2_0_eq k + · exact kernel28_1_r2_1_eq k + · exact kernel28_1_r2_2_eq k + · exact kernel28_1_r2_3_eq k + · exact kernel28_1_r2_4_eq k + · exact kernel28_1_r2_5_eq k + · exact kernel28_1_r2_6_eq k + · exact kernel28_1_r2_7_eq k + · exact kernel28_1_r2_8_eq k + · exact kernel28_1_r2_9_eq k + · exact kernel28_1_r2_10_eq k + · exact kernel28_1_r2_11_eq k + · exact kernel28_1_r2_12_eq k + · exact kernel28_1_r2_13_eq k + · exact kernel28_1_r2_14_eq k + · exact kernel28_1_r2_15_eq k +noncomputable def kernel28_1_r3_0 : Fin 16 → CBox := ![⟨⟨(-427232981831),(-427232981812)⟩,⟨2666204580367,2666204580387⟩⟩,⟨⟨(-423223304598),(-423223304579)⟩,⟨2661048700681,2661048700700⟩⟩,⟨⟨(-415247952662),(-415247952642)⟩,⟨2650755885571,2650755885590⟩⟩,⟨⟨(-403394342221),(-403394342195)⟩,⟨2635364081561,2635364081586⟩⟩,⟨⟨(-387792133890),(-387792133858)⟩,⟨2614930347492,2614930347524⟩⟩,⟨⟨(-368611500004),(-368611499985)⟩,⟨2589531005185,2589531005205⟩⟩,⟨⟨(-346060853578),(-346060853554)⟩,⟨2559261813807,2559261813828⟩⟩,⟨⟨(-320384071788),(-320384071769)⟩,⟨2524238146728,2524238146747⟩⟩,⟨⟨(-291857254583),(-291857254557)⟩,⟨2484595145297,2484595145322⟩⟩,⟨⟨(-260785065654),(-260785065622)⟩,⟨2440487821492,2440487821524⟩⟩,⟨⟨(-227496709530),(-227496709505)⟩,⟨2392091079269,2392091079294⟩⟩,⟨⟨(-192341604045),(-192341604019)⟩,⟨2339599623537,2339599623562⟩⟩,⟨⟨(-155684812194),(-155684812175)⟩,⟨2283227726520,2283227726540⟩⟩,⟨⟨(-117902301234),(-117902301214)⟩,⟨2223208822242,2223208822261⟩⟩,⟨⟨(-79376099679),(-79376099655)⟩,⟨2159794903268,2159794903289⟩⟩,⟨⟨(-40489424604),(-40489424571)⟩,⟨2093255697067,2093255697103⟩⟩] +lemma kernel28_1_r3_0_eq : ∀ k : Fin 16, kernel28_1Expr 3 0 k = kernel28_1_r3_0 k := by decide +kernel +noncomputable def kernel28_1_r3_1 : Fin 16 → CBox := ![⟨⟨(-1621852160),(-1621852141)⟩,⟨2023877604787,2023877604807⟩⟩,⟨⟨36855396247,36855396266⟩,⟨1951962390295,1951962390314⟩⟩,⟨⟨74583981749,74583981768⟩,⟨1877825614484,1877825614504⟩⟩,⟨⟨111222722343,111222722369⟩,⟨1801794815917,1801794815943⟩⟩,⟨⟨146451550450,146451550470⟩,⟨1724207446771,1724207446790⟩⟩,⟨⟨179975096210,179975096241⟩,⟨1645408579832,1645408579864⟩⟩,⟨⟨211525845267,211525845288⟩,⟨1565748409680,1565748409705⟩⟩,⟨⟨240866827287,240866827308⟩,⟨1485579577733,1485579577757⟩⟩,⟨⟨267793800070,267793800095⟩,⟨1405254357084,1405254357110⟩⟩,⟨⟨292136902901,292136902921⟩,⟨1325121738353,1325121738373⟩⟩,⟨⟨313761762547,313761762573⟩,⟨1245524462024,1245524462050⟩⟩,⟨⟨332570045190,332570045218⟩,⟨1166796046185,1166796046216⟩⟩,⟨⟨348499457603,348499457629⟩,⟨1089257860347,1089257860373⟩⟩,⟨⟨361523210796,361523210818⟩,⟨1013216296798,1013216296823⟩⟩,⟨⟨371648969154,371648969183⟩,⟨938960090381,938960090403⟩⟩,⟨⟨378917316885,378917316911⟩,⟨866757835264,866757835290⟩⟩] +lemma kernel28_1_r3_1_eq : ∀ k : Fin 16, kernel28_1Expr 3 1 k = kernel28_1_r3_1 k := by decide +kernel +noncomputable def kernel28_1_r3_2 : Fin 16 → CBox := ![⟨⟨383399782177,383399782197⟩,⟨796855744290,796855744309⟩⟩,⟨⟨385196466830,385196466849⟩,⟨729475691625,729475691644⟩⟩,⟨⟨384433335327,384433335352⟩,⟨664813574168,664813574194⟩⟩,⟨⟨381259222435,381259222455⟩,⟨603038020298,603038020318⟩⟩,⟨⟨375842622118,375842622138⟩,⟨544289467427,544289467446⟩⟩,⟨⟨368368322804,368368322825⟩,⟨488679622072,488679622096⟩⟩,⟨⟨359033954820,359033954839⟩,⟨436291307987,436291308007⟩⟩,⟨⟨348046515129,348046515161⟩,⟨387178699532,387178699564⟩⟩,⟨⟨335618932550,335618932576⟩,⟨341367929945,341367929971⟩⟩,⟨⟨321966732937,321966732964⟩,⟨298858055778,298858055809⟩⟩,⟨⟨307304859572,307304859598⟩,⟨259622352599,259622352625⟩⟩,⟨⟨291844697971,291844698008⟩,⟨223609909884,223609909918⟩⟩,⟨⟨275791347921,275791347949⟩,⟨190747488393,190747488423⟩⟩,⟨⟨259341178137,259341178168⟩,⟨160941598522,160941598550⟩⟩,⟨⟨242679691481,242679691501⟩,⟨134080755225,134080755245⟩⟩,⟨⟨225979720183,225979720209⟩,⟨110037862997,110037863023⟩⟩] +lemma kernel28_1_r3_2_eq : ∀ k : Fin 16, kernel28_1Expr 3 2 k = kernel28_1_r3_2 k := by decide +kernel +noncomputable def kernel28_1_r3_3 : Fin 16 → CBox := ![⟨⟨209399962967,209399962997⟩,⟨88672683670,88672683698⟩⟩,⟨⟨193083867654,193083867674⟩,⟨69834340116,69834340136⟩⟩,⟨⟨177158855515,177158855543⟩,⟨53363810569,53363810600⟩⟩,⟨⟨161735876704,161735876742⟩,⟨39096370691,39096370725⟩⟩,⟨⟨146909279480,146909279506⟩,⟨26863944065,26863944091⟩⟩,⟨⟨132756970769,132756970795⟩,⟨16497325880,16497325906⟩⟩,⟨⟨119340841047,119340841067⟩,⟨7828249601,7828249621⟩⟩,⟨⟨106707422536,106707422562⟩,⟨691271402,691271428⟩⟩,⟨⟨94888747735,94888747755⟩,⟨(-5074546971),(-5074546951)⟩⟩,⟨⟨83903373089,83903373120⟩,⟨(-9624171093),(-9624171065)⟩⟩,⟨⟨73757532655,73757532675⟩,⟨(-13105350393),(-13105350373)⟩⟩,⟨⟨64446386249,64446386280⟩,⟨(-15657601791),(-15657601763)⟩⟩,⟨⟨55955328392,55955328412⟩,⟨(-17411417781),(-17411417761)⟩⟩,⟨⟨48261325717,48261325744⟩,⟨(-18487692792),(-18487692766)⟩⟩,⟨⟨41334253394,41334253421⟩,⟨(-18997356772),(-18997356746)⟩⟩,⟨⟨35138203862,35138203888⟩,⟨(-19041202098),(-19041202071)⟩⟩] +lemma kernel28_1_r3_3_eq : ∀ k : Fin 16, kernel28_1Expr 3 3 k = kernel28_1_r3_3 k := by decide +kernel +noncomputable def kernel28_1_r3_4 : Fin 16 → CBox := ![⟨⟨29632744772,29632744794⟩,⟨(-18709886745),(-18709886720)⟩⟩,⟨⟨24774106501,24774106527⟩,⟨(-18084094891),(-18084094864)⟩⟩,⟨⟨20516283476,20516283496⟩,⟨(-17234834420),(-17234834400)⟩⟩,⟨⟨16812037069,16812037089⟩,⟨(-16223850249),(-16223850229)⟩⟩,⟨⟨13613791836,13613791856⟩,⟨(-15104131917),(-15104131896)⟩⟩,⟨⟨10874419912,10874419932⟩,⟨(-13920494699),(-13920494679)⟩⟩,⟨⟨8547911840,8547911860⟩,⟨(-12710213860),(-12710213840)⟩⟩,⟨⟨6589934811,6589934831⟩,⟨(-11503693259),(-11503693239)⟩⟩,⟨⟨4958281871,4958281893⟩,⟨(-10325150952),(-10325150927)⟩⟩,⟨⟨3613217633,3613217653⟩,⟨(-9193306318),(-9193306297)⟩⟩,⟨⟨2517727763,2517727801⟩,⟨(-8122055144),(-8122055109)⟩⟩,⟨⟨1637680820,1637680840⟩,⟨(-7121121224),(-7121121204)⟩⟩,⟨⟨941911622,941911647⟩,⟨(-6196675276),(-6196675254)⟩⟩,⟨⟨402236459,402236486⟩,⟨(-5351913594),(-5351913567)⟩⟩,⟨⟨(-6590253),(-6590231)⟩,⟨(-4587591307),(-4587591282)⟩⟩,⟨⟨(-306967519),(-306967499)⟩,⟨(-3902506751),(-3902506730)⟩⟩] +lemma kernel28_1_r3_4_eq : ∀ k : Fin 16, kernel28_1Expr 3 4 k = kernel28_1_r3_4 k := by decide +kernel +noncomputable def kernel28_1_r3_5 : Fin 16 → CBox := ![⟨⟨(-518578141),(-518578114)⟩,⟨(-3293934845),(-3293934818)⟩⟩,⟨⟨(-658548681),(-658548649)⟩,⟨(-2758009274),(-2758009245)⟩⟩,⟨⟨(-741630848),(-741630828)⟩,⟨(-2290054220),(-2290054200)⟩⟩,⟨⟨(-780396679),(-780396659)⟩,⟨(-1884867505),(-1884867484)⟩⟩,⟨⟨(-785440894),(-785440868)⟩,⟨(-1536957757),(-1536957735)⟩⟩,⟨⟨(-765584798),(-765584777)⟩,⟨(-1240739093),(-1240739073)⟩⟩,⟨⟨(-728076946),(-728076925)⟩,⟨(-990686861),(-990686840)⟩⟩,⟨⟨(-678786745),(-678786724)⟩,⟨(-781458587),(-781458566)⟩⟩,⟨⟨(-622387850),(-622387829)⟩,⟨(-607984152),(-607984132)⟩⟩,⟨⟨(-562529441),(-562529420)⟩,⟨(-465529365),(-465529344)⟩⟩,⟨⟨(-501993512),(-501993491)⟩,⟨(-349736913),(-349736892)⟩⟩,⟨⟨(-442837634),(-442837614)⟩,⟨(-256648422),(-256648402)⟩⟩,⟨⟨(-386522612),(-386522578)⟩,⟨(-182711169),(-182711135)⟩⟩,⟨⟨(-334025222),(-334025193)⟩,⟨(-124772582),(-124772550)⟩⟩,⟨⟨(-285936585),(-285936558)⟩,⟨(-80065534),(-80065507)⟩⟩,⟨⟨(-242546670),(-242546641)⟩,⟨(-46186698),(-46186666)⟩⟩] +lemma kernel28_1_r3_5_eq : ∀ k : Fin 16, kernel28_1Expr 3 5 k = kernel28_1_r3_5 k := by decide +kernel +noncomputable def kernel28_1_r3_6 : Fin 16 → CBox := ![⟨⟨(-203916155),(-203916134)⟩,⟨(-21070256),(-21070235)⟩⟩,⟨⟨(-169936477),(-169936455)⟩,⟨(-2958802),(-2958776)⟩⟩,⟨⟨(-140379369),(-140379348)⟩,⟨9627244,9627265⟩⟩,⟨⟨(-114936989),(-114936966)⟩,⟨17920324,17920350⟩⟩,⟨⟨(-93253897),(-93253876)⟩,⟨22935785,22935806⟩⟩,⟨⟨(-74951857),(-74951836)⟩,⟨25500448,25500469⟩⟩,⟨⟨(-59648755),(-59648734)⟩,⟨26279334,26279355⟩⟩,⟨⟨(-46972330),(-46972301)⟩,⟨25800115,25800148⟩⟩,⟨⟨(-36569923),(-36569902)⟩,⟨24475287,24475308⟩⟩,⟨⟨(-28114761),(-28114739)⟩,⟨22621766,22621788⟩⟩,⟨⟨(-21309689),(-21309661)⟩,⟨20478234,20478262⟩⟩,⟨⟨(-15888741),(-15888713)⟩,⟨18220067,18220095⟩⟩,⟨⟨(-11617302),(-11617279)⟩,⟨15972139,15972165⟩⟩,⟨⟨(-8291061),(-8291039)⟩,⟨13819642,13819664⟩⟩,⟨⟨(-5734252),(-5734224)⟩,⟨11817112,11817140⟩⟩,⟨⟨(-3797351),(-3797330)⟩,⟨9995901,9995922⟩⟩] +lemma kernel28_1_r3_6_eq : ∀ k : Fin 16, kernel28_1Expr 3 6 k = kernel28_1_r3_6 k := by decide +kernel +noncomputable def kernel28_1_r3_7 : Fin 16 → CBox := ![⟨⟨(-2354567),(-2354540)⟩,⟨8370142,8370165⟩⟩,⟨⟨(-1301186),(-1301159)⟩,⟨6941692,6941715⟩⟩,⟨⟨(-550970),(-550943)⟩,⟨5703876,5703899⟩⟩,⟨⟨(-33623),(-33596)⟩,⟨4644498,4644521⟩⟩,⟨⟨307506,307530⟩,⟨3748063,3748090⟩⟩,⟨⟨517585,517618⟩,⟨2997514,2997544⟩⟩,⟨⟨632214,632243⟩,⟨2375373,2375402⟩⟩,⟨⟨679063,679087⟩,⟨1864613,1864639⟩⟩,⟨⟨679367,679388⟩,⟨1449217,1449238⟩⟩,⟨⟨649175,649202⟩,⟨1114505,1114529⟩⟩,⟨⟨600382,600404⟩,⟨847311,847332⟩⟩,⟨⟨541622,541644⟩,⟨636029,636051⟩⟩,⟨⟨479015,479039⟩,⟨470586,470613⟩⟩,⟨⟨416730,416752⟩,⟨342374,342396⟩⟩,⟨⟨357474,357496⟩,⟨244090,244112⟩⟩,⟨⟨302882,302906⟩,⟨169646,169673⟩⟩] +lemma kernel28_1_r3_7_eq : ∀ k : Fin 16, kernel28_1Expr 3 7 k = kernel28_1_r3_7 k := by decide +kernel +noncomputable def kernel28_1_r3_8 : Fin 16 → CBox := ![⟨⟨253792,253814⟩,⟨114011,114033⟩⟩,⟨⟨210521,210548⟩,⟨73051,73075⟩⟩,⟨⟨172994,173016⟩,⟨43430,43452⟩⟩,⟨⟨140900,140927⟩,⟨22469,22493⟩⟩,⟨⟨113788,113810⟩,⟨8027,8049⟩⟩,⟨⟨91134,91168⟩,⟨(-1552),(-1521)⟩⟩,⟨⟨72407,72429⟩,⟨(-7571),(-7548)⟩⟩,⟨⟨57053,57087⟩,⟨(-11046),(-11015)⟩⟩,⟨⟨44593,44625⟩,⟨(-12726),(-12692)⟩⟩,⟨⟨34560,34587⟩,⟨(-13179),(-13154)⟩⟩,⟨⟨26552,26579⟩,⟨(-12846),(-12821)⟩⟩,⟨⟨20215,20238⟩,⟨(-12017),(-11995)⟩⟩,⟨⟨15221,15255⟩,⟨(-10920),(-10888)⟩⟩,⟨⟨11339,11376⟩,⟨(-9703),(-9666)⟩⟩,⟨⟨8353,8382⟩,⟨(-8468),(-8438)⟩⟩,⟨⟨6059,6082⟩,⟨(-7281),(-7259)⟩⟩] +lemma kernel28_1_r3_8_eq : ∀ k : Fin 16, kernel28_1Expr 3 8 k = kernel28_1_r3_8 k := by decide +kernel +noncomputable def kernel28_1_r3_9 : Fin 16 → CBox := ![⟨⟨4318,4347⟩,⟨(-6193),(-6163)⟩⟩,⟨⟨3011,3038⟩,⟨(-5198),(-5173)⟩⟩,⟨⟨2048,2075⟩,⟨(-4330),(-4305)⟩⟩,⟨⟨1332,1359⟩,⟨(-3571),(-3546)⟩⟩,⟨⟨824,852⟩,⟨(-2927),(-2902)⟩⟩,⟨⟨460,482⟩,⟨(-2374),(-2351)⟩⟩,⟨⟨211,236⟩,⟨(-1922),(-1894)⟩⟩,⟨⟨38,73⟩,⟨(-1544),(-1511)⟩⟩,⟨⟨(-66),(-43)⟩,⟨(-1229),(-1206)⟩⟩,⟨⟨(-129),(-106)⟩,⟨(-972),(-950)⟩⟩,⟨⟨(-170),(-147)⟩,⟨(-774),(-751)⟩⟩,⟨⟨(-186),(-158)⟩,⟨(-601),(-575)⟩⟩,⟨⟨(-182),(-159)⟩,⟨(-474),(-451)⟩⟩,⟨⟨(-181),(-158)⟩,⟨(-366),(-343)⟩⟩,⟨⟨(-166),(-143)⟩,⟨(-282),(-259)⟩⟩,⟨⟨(-148),(-125)⟩,⟨(-218),(-195)⟩⟩] +lemma kernel28_1_r3_9_eq : ∀ k : Fin 16, kernel28_1Expr 3 9 k = kernel28_1_r3_9 k := by decide +kernel +noncomputable def kernel28_1_r3_10 : Fin 16 → CBox := ![⟨⟨(-133),(-110)⟩,⟨(-171),(-148)⟩⟩,⟨⟨(-126),(-96)⟩,⟨(-133),(-103)⟩⟩,⟨⟨(-107),(-82)⟩,⟨(-103),(-75)⟩⟩,⟨⟨(-93),(-68)⟩,⟨(-74),(-45)⟩⟩,⟨⟨(-84),(-56)⟩,⟨(-56),(-30)⟩⟩,⟨⟨(-67),(-39)⟩,⟨(-46),(-20)⟩⟩,⟨⟨(-62),(-36)⟩,⟨(-33),(-5)⟩⟩,⟨⟨(-52),(-29)⟩,⟨(-26),(-3)⟩⟩,⟨⟨(-45),(-22)⟩,⟨(-23),0⟩⟩,⟨⟨(-38),(-12)⟩,⟨(-21),8⟩⟩,⟨⟨(-38),(-12)⟩,⟨(-21),8⟩⟩,⟨⟨(-28),(-5)⟩,⟨(-13),10⟩⟩,⟨⟨(-28),(-5)⟩,⟨(-13),10⟩⟩,⟨⟨(-28),5⟩,⟨(-16),20⟩⟩,⟨⟨(-20),5⟩,⟨(-11),18⟩⟩,⟨⟨(-20),5⟩,⟨(-11),18⟩⟩] +lemma kernel28_1_r3_10_eq : ∀ k : Fin 16, kernel28_1Expr 3 10 k = kernel28_1_r3_10 k := by decide +kernel +noncomputable def kernel28_1_r3_11 : Fin 16 → CBox := ![⟨⟨(-21),5⟩,⟨(-11),18⟩⟩,⟨⟨(-21),5⟩,⟨(-11),18⟩⟩,⟨⟨(-21),5⟩,⟨(-11),18⟩⟩,⟨⟨(-21),6⟩,⟨(-11),18⟩⟩,⟨⟨(-21),6⟩,⟨(-11),18⟩⟩,⟨⟨(-21),6⟩,⟨(-11),18⟩⟩,⟨⟨(-21),6⟩,⟨(-11),18⟩⟩,⟨⟨(-21),6⟩,⟨(-11),18⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩] +lemma kernel28_1_r3_11_eq : ∀ k : Fin 16, kernel28_1Expr 3 11 k = kernel28_1_r3_11 k := by decide +kernel +noncomputable def kernel28_1_r3_12 : Fin 16 → CBox := ![⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-21),18⟩,⟨(-16),23⟩⟩,⟨⟨(-23),23⟩,⟨(-23),23⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel28_1_r3_12_eq : ∀ k : Fin 16, kernel28_1Expr 3 12 k = kernel28_1_r3_12 k := by decide +kernel +noncomputable def kernel28_1_r3_13 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel28_1_r3_13_eq : ∀ k : Fin 16, kernel28_1Expr 3 13 k = kernel28_1_r3_13 k := by decide +kernel +noncomputable def kernel28_1_r3_14 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel28_1_r3_14_eq : ∀ k : Fin 16, kernel28_1Expr 3 14 k = kernel28_1_r3_14 k := by decide +kernel +noncomputable def kernel28_1_r3_15 : Fin 16 → CBox := ![⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩,⟨⟨(-24),24⟩,⟨(-24),24⟩⟩] +lemma kernel28_1_r3_15_eq : ∀ k : Fin 16, kernel28_1Expr 3 15 k = kernel28_1_r3_15 k := by decide +kernel +noncomputable def kernel28_1_r3 : Fin 16 → Fin 16 → CBox := ![kernel28_1_r3_0,kernel28_1_r3_1,kernel28_1_r3_2,kernel28_1_r3_3,kernel28_1_r3_4,kernel28_1_r3_5,kernel28_1_r3_6,kernel28_1_r3_7,kernel28_1_r3_8,kernel28_1_r3_9,kernel28_1_r3_10,kernel28_1_r3_11,kernel28_1_r3_12,kernel28_1_r3_13,kernel28_1_r3_14,kernel28_1_r3_15] +lemma kernel28_1_r3_eq (i k : Fin 16) : kernel28_1Expr 3 i k = kernel28_1_r3 i k := by + fin_cases i + · exact kernel28_1_r3_0_eq k + · exact kernel28_1_r3_1_eq k + · exact kernel28_1_r3_2_eq k + · exact kernel28_1_r3_3_eq k + · exact kernel28_1_r3_4_eq k + · exact kernel28_1_r3_5_eq k + · exact kernel28_1_r3_6_eq k + · exact kernel28_1_r3_7_eq k + · exact kernel28_1_r3_8_eq k + · exact kernel28_1_r3_9_eq k + · exact kernel28_1_r3_10_eq k + · exact kernel28_1_r3_11_eq k + · exact kernel28_1_r3_12_eq k + · exact kernel28_1_r3_13_eq k + · exact kernel28_1_r3_14_eq k + · exact kernel28_1_r3_15_eq k +noncomputable def kernel28_1_r4_0 : Fin 16 → CBox := ![⟨⟨(-4686990769410652007319),(-4686990769410628722914)⟩,⟨(-13311904924414078495788),(-13311904924414055211228)⟩⟩,⟨⟨(-4695335088993066310968),(-4695335088993043057548)⟩,⟨(-13289210343392547359927),(-13289210343392524106353)⟩⟩,⟨⟨(-4711914962025229766074),(-4711914962025206574539)⟩,⟨(-13243885219562373866211),(-13243885219562350674520)⟩⟩,⟨⟨(-4736513958221979324882),(-4736513958221956225895)⟩,⟨(-13176057796552570836417),(-13176057796552547737271)⟩⟩,⟨⟨(-4768810177675723862446),(-4768810177675700886305)⟩,⟨(-13085920847494637716961),(-13085920847494614740662)⟩⟩,⟨⟨(-4808379519090216440619),(-4808379519090193617165)⟩,⟨(-12973732135579985658472),(-12973732135579962834861)⟩⟩,⟨⟨(-4854699993487217399762),(-4854699993487194758226)⟩,⟨(-12839814981036918847807),(-12839814981036896206114)⟩⟩,⟨⟨(-4907157045824166612867),(-4907157045824144181783)⟩,⟨(-12684558895505562045111),(-12684558895505539613867)⟩⟩,⟨⟨(-4965049837713239806050),(-4965049837713217613164)⟩,⟨(-12508420236693946557088),(-12508420236693924364043)⟩⟩,⟨⟨(-5027598435307132711640),(-5027598435307110783781)⟩,⟨(-12311922829168977058865),(-12311922829168955130848)⟩⟩,⟨⟨(-5093951837465214729961),(-5093951837465193092966)⟩,⟨(-12095658491344678932924),(-12095658491344657295771)⟩⟩,⟨⟨(-5163196770598317625816),(-5163196770598296304430)⟩,⟨(-11860287404327889605904),(-11860287404327868284361)⟩⟩,⟨⟨(-5234367168187353642125),(-5234367168187332659930)⟩,⟨(-11606538255394715945919),(-11606538255394694963565)⟩⟩,⟨⟨(-5306454244969157912705),(-5306454244969137292020)⟩,⟨(-11335208087598554770846),(-11335208087598534150006)⟩⟩,⟨⟨(-5378417068283753226453),(-5378417068283732988306)⟩,⟨(-11047161787421355614417),(-11047161787421335376116)⟩⟩,⟨⟨(-5449193522193072010294),(-5449193522193052174324)⟩,⟨(-10743331144511298211433),(-10743331144511278375311)⟩⟩] +lemma kernel28_1_r4_0_eq : ∀ k : Fin 16, kernel28_1Expr 4 0 k = kernel28_1_r4_0 k := by decide +kernel +noncomputable def kernel28_1_r4_1 : Fin 16 → CBox := ![⟨⟨(-5517711553833673594708),(-5517711553833654179155)⟩,⟨(-10424713421405871667039),(-10424713421405852251334)⟩⟩,⟨⟨(-5582900586183495387391),(-5582900586183476408983)⟩,⟨(-10092369376688593841861),(-10092369376688574863296)⟩⟩,⟨⟨(-5643702977137144133125),(-5643702977137125607133)⟩,⟨(-9747420692204284862014),(-9747420692204266335873)⟩⟩,⟨⟨(-5699085401627730231415),(-5699085401627712171543)⟩,⟨(-9391046763660848274578),(-9391046763660830214557)⟩⟩,⟨⟨(-5748050031633985434688),(-5748050031633967853146)⟩,⟨(-9024480824039557757642),(-9024480824039540175950)⟩⟩,⟨⟨(-5789645388389507957285),(-5789645388389490864623)⟩,⟨(-8649005380552683225690),(-8649005380552666132879)⟩⟩,⟨⟨(-5822976742074085408832),(-5822976742074068814137)⟩,⟨(-8265946958228019874934),(-8265946958228003280095)⟩⟩,⟨⟨(-5847215936805862611256),(-5847215936805846521969)⟩,⟨(-7876670156337825665344),(-7876670156337809575920)⟩⟩,⟨⟨(-5861610522937095425012),(-5861610522937079847149)⟩,⟨(-7482571037573984867089),(-7482571037573969289098)⟩⟩,⟨⟨(-5865492084529473690035),(-5865492084529458627928)⟩,⟨(-7085069883831212204579),(-7085069883831197142351)⟩⟩,⟨⟨(-5858283657462607691640),(-5858283657462593148234)⟩,⟨(-6685603366410226910041),(-6685603366410212366526)⟩⟩,⟨⟨(-5839506142894221411971),(-5839506142894207388653)⟩,⟨(-6285616192098145864509),(-6285616192098131841084)⟩⟩,⟨⟨(-5808783631691276891841),(-5808783631691263388794)⟩,⟨(-5886552299625627927351),(-5886552299625614424210)⟩⟩,⟨⟨(-5765847567899853813643),(-5765847567899840829324)⟩,⟨(-5489845693144360441330),(-5489845693144347456922)⟩⟩,⟨⟨(-5710539693193379797850),(-5710539693193367329548)⟩,⟨(-5096911010328800167153),(-5096911010328787698772)⟩⟩,⟨⟨(-5642813729372333698969),(-5642813729372321742702)⟩,⟨(-4709133932213527676406),(-4709133932213515720073)⟩⟩] +lemma kernel28_1_r4_1_eq : ∀ k : Fin 16, kernel28_1Expr 4 1 k = kernel28_1_r4_1 k := by decide +kernel +noncomputable def kernel28_1_r4_2 : Fin 16 → CBox := ![⟨⟨(-5562735772187049721042),(-5562735772187038271902)⟩,⟨(-4327861549686010403585),(-4327861549685998954382)⟩⟩,⟨⟨(-5470483386788974219702),(-5470483386788963271343)⟩,⟨(-3954392807447231763977),(-3954392807447220815560)⟩⟩,⟨⟨(-5366343412725362722724),(-5366343412725352268017)⟩,⟨(-3589969150048083164496),(-3589969150048072709742)⟩⟩,⟨⟨(-5250708504293553360809),(-5250708504293543390558)⟩,⟨(-3235765496166832593365),(-3235765496166822623071)⟩⟩,⟨⟨(-5124072449959520545381),(-5124072449959511050385)⟩,⟨(-2892881666516783036810),(-2892881666516773541779)⟩⟩,⟨⟨(-4987024332103837832619),(-4987024332103828802790)⟩,⟨(-2562334387616645573569),(-2562334387616636543712)⟩⟩,⟨⟨(-4840241605262349657279),(-4840241605262341082099)⟩,⟨(-2245049988123770319356),(-2245049988123761744153)⟩⟩,⟨⟨(-4684482186955542429496),(-4684482186955534297381)⟩,⟨(-1941857896579510893451),(-1941857896579502761323)⟩⟩,⟨⟨(-4520575669835237404790),(-4520575669835229703953)⟩,⟨(-1653485039356730707591),(-1653485039356723006743)⟩⟩,⟨⟨(-4349413776921739284044),(-4349413776921732001783)⟩,⟨(-1380551225493387524573),(-1380551225493380242306)⟩⟩,⟨⟨(-4171940192885175745775),(-4171940192885168869335)⟩,⟨(-1123565591153740560899),(-1123565591153733684458)⟩⟩,⟨⟨(-3989139913399340864488),(-3989139913399334380380)⟩,⟨(-882924160935436463456),(-882924160935429979351)⟩⟩,⟨⟨(-3802028261361298342380),(-3802028261361292237199)⟩,⟨(-658908566431699655307),(-658908566431693550126)⟩⟩,⟨⟨(-3611639723066223658378),(-3611639723066217916341)⟩,⟨(-451685944691589854196),(-451685944691584112172)⟩⟩,⟨⟨(-3419016759144928235942),(-3419016759144922842160)⟩,⟨(-261310020852279769154),(-261310020852274375382)⟩⟩,⟨⟨(-3225198744155055753473),(-3225198744155050693934)⟩,⟨(-87723360617789443761),(-87723360617784384235)⟩⟩] +lemma kernel28_1_r4_2_eq : ∀ k : Fin 16, kernel28_1Expr 4 2 k = kernel28_1_r4_2 k := by decide +kernel +noncomputable def kernel28_1_r4_3 : Fin 16 → CBox := ![⟨⟨(-3031211185165799454487),(-3031211185165794715516)⟩,⟨69239240190254391964,69239240190259130918⟩⟩,⟨⟨(-2838055363546840203284),(-2838055363546835770765)⟩,⟨209846279701641229333,209846279701645661835⟩⟩,⟨⟨(-2646698535578238530340),(-2646698535578234390602)⟩,⟨334464055392895984464,334464055392900124180⟩⟩,⟨⟨(-2458064816606961984412),(-2458064816606958123479)⟩,⟨443550234275158423176,443550234275162284085⟩⟩,⟨⟨(-2273026860506397041714),(-2273026860506393446191)⟩,⟨537646585521097979884,537646585521101575387⟩⟩,⟨⟨(-2092398431412569552846),(-2092398431412566209185)⟩,⟨617370985489290547117,617370985489293890756⟩⟩,⟨⟨(-1916927948419854995892),(-1916927948419851891147)⟩,⟨683408815302561417518,683408815302564522241⟩⟩,⟨⟨(-1747293066457336664185),(-1747293066457333784692)⟩,⟨736503879024614679770,736503879024617559242⟩⟩,⟨⟨(-1584096338296706574991),(-1584096338296703908324)⟩,⟨777448975914467161078,777448975914469827721⟩⟩,⟨⟨(-1427861983941192445940),(-1427861983941189979802)⟩,⟨807076263135800425404,807076263135802891522⟩⟩,⟨⟨(-1279033774895994640602),(-1279033774895992363378)⟩,⟨826247545632503109252,826247545632505386454⟩⟩,⟨⟨(-1137974022404218569178),(-1137974022404216469368)⟩,⟨835844627685871178793,835844627685873278580⟩⟩,⟨⟨(-1004963641015496977796),(-1004963641015495044364)⟩,⟨836759856034482492221,836759856034484425635⟩⟩,⟨⟨(-880203242182732589365),(-880203242182730811549)⟩,⟨829886977510788609236,829886977510790387038⟩⟩,⟨⟨(-763815197270757607842),(-763815197270755975638)⟩,⟨816112425125393072138,816112425125394704327⟩⟩,⟨⟨(-655846595686677037952),(-655846595686675541469)⟩,⟨796307135651694036643,796307135651695533116⟩⟩] +lemma kernel28_1_r4_3_eq : ∀ k : Fin 16, kernel28_1Expr 4 3 k = kernel28_1_r4_3 k := by decide +kernel +noncomputable def kernel28_1_r4_4 : Fin 16 → CBox := ![⟨⟨(-556273012038803055796),(-556273012038801685907)⟩,⟨771318989308427132994,771318989308428502876⟩⟩,⟨⟨(-465002986484080897044),(-465002986484079644732)⟩,⟨741965948413610126082,741965948413611378386⟩⟩,⟨⟨(-381883114865018171873),(-381883114865017028834)⟩,⟨709029957219454778539,709029957219455921575⟩⟩,⟨⟨(-306703639944192302312),(-306703639944191260458)⟩,⟨673251649875038596788,673251649875039638639⟩⟩,⟨⟨(-239204432040364962359),(-239204432040364014262)⟩,⟨635325897945982150706,635325897945983098797⟩⟩,⟨⟨(-179081246624198990761),(-179081246624198129169)⟩,⟨595898213486193285308,595898213486194146901⟩⟩,⟨⟨(-125992147861394599056),(-125992147861393817329)⟩,⟨555562008629628244740,555562008629629026468⟩⟩,⟨⟨(-79563990567193908764),(-79563990567193200497)⟩,⟨514856698351431635338,514856698351432343602⟩⟩,⟨⟨(-39398858386803784202),(-39398858386803143535)⟩,⟨474266619709993661043,474266619709994301711⟩⟩,⟨⟨(-5080363033309079255),(-5080363033308500536)⟩,⟨434220728761556916765,434220728761557495485⟩⟩,⟨⟨23820282139282033773,23820282139282555690⟩,⟨395093025634411935615,395093025634412457534⟩⟩,⟨⟨47738491334374095873,47738491334374565912⟩,⟨357203649114720763995,357203649114721234035⟩⟩,⟨⟨67110904876835684590,67110904876836108645⟩,⟨320820574639769080852,320820574639769504912⟩⟩,⟨⟨82370412608412204032,82370412608412586199⟩,⟨286161843880396342907,286161843880396725077⟩⟩,⟨⟨93941646113566433516,93941646113566777392⟩,⟨253398250140873231167,253398250140873575048⟩⟩,⟨⟨102236972240562366493,102236972240562675485⟩,⟨222656401586869088528,222656401586869397527⟩⟩] +lemma kernel28_1_r4_4_eq : ∀ k : Fin 16, kernel28_1Expr 4 4 k = kernel28_1_r4_4 k := by decide +kernel +noncomputable def kernel28_1_r4_5 : Fin 16 → CBox := ![⟨⟨107653009035939949585,107653009035940226782⟩,⟨194022083765629917255,194022083765630194457⟩⟩,⟨⟨110567674285940402012,110567674285940650377⟩,⟨167543843906331365711,167543843906331614076⟩⟩,⟨⟨111337766564805454257,111337766564805676423⟩,⟨143236721950893180692,143236721950893402865⟩⟩,⟨⟨110297069206585999118,110297069206586197593⟩,⟨121086057008748875471,121086057008749073952⟩⟩,⟨⟨107754959091309127524,107754959091309304545⟩,⟨101051302775703388475,101051302775703565499⟩⟩,⟨⟨103995494681307289524,103995494681307447209⟩,⟨83069791215808238996,83069791215808396682⟩⟩,⟨⟨99276951437951223449,99276951437951363693⟩,⟨67060390277079108900,67060390277079249144⟩⟩,⟨⟨93831767637639028226,93831767637639152801⟩,⟨52927008395874754550,52927008395874879124⟩⟩,⟨⟨87866859700708736600,87866859700708847090⟩,⟨40561905843390639231,40561905843390749725⟩⟩,⟨⟨81564263429566234212,81564263429566332088⟩,⟨29848780392056540032,29848780392056637904⟩⟩,⟨⟨75082055976873663024,75082055976873749588⟩,⟨20665602153596160237,20665602153596246800⟩⟩,⟨⟨68555512861262452649,68555512861262529136⟩,⟨12887179604548034642,12887179604548111129⟩⟩,⟨⟨62098454826788301013,62098454826788368481⟩,⟨6387445628972662756,6387445628972730224⟩⟩,⟨⟨55804740697401901043,55804740697401960490⟩,⟨1041458753128115040,1041458753128174484⟩⟩,⟨⟨49749864491611470184,49749864491611522482⟩,⟨(-3272879472969291756),(-3272879472969239458)⟩⟩,⟨⟨43992617810410426888,43992617810410472868⟩,⟨(-6673384849837403175),(-6673384849837357195)⟩⟩] +lemma kernel28_1_r4_5_eq : ∀ k : Fin 16, kernel28_1Expr 4 5 k = kernel28_1_r4_5 k := by decide +kernel +noncomputable def kernel28_1_r4_6 : Fin 16 → CBox := ![⟨⟨38576781765256390514,38576781765256430865⟩,⟨(-9272418106763665775),(-9272418106763625424)⟩⟩,⟨⟨33532816344690651219,33532816344690686599⟩,⟨(-11175965392951491156),(-11175965392951455776)⟩⟩,⟨⟨28879519004216856258,28879519004216887234⟩,⟨(-12482954374140961676),(-12482954374140930701)⟩⟩,⟨⟨24625628287272921856,24625628287272948947⟩,⟨(-13284786322038675229),(-13284786322038648141)⟩⟩,⟨⟨20771352337775922396,20771352337775946041⟩,⟨(-13665062961826942133),(-13665062961826918488)⟩⟩,⟨⟨17309806150263733287,17309806150263753918⟩,⟨(-13699485862154484693),(-13699485862154464062)⟩⟩,⟨⟨14228345238193584738,14228345238193602711⟩,⟨(-13455905759076721905),(-13455905759076703933)⟩⟩,⟨⟨11509787014087126777,11509787014087142443⟩,⟨(-12994499338563519093),(-12994499338563503426)⟩⟩,⟨⟨9133514510426599646,9133514510426613262⟩,⟨(-12368051593651451783),(-12368051593651438164)⟩⟩,⟨⟨7076460084823065227,7076460084823077061⟩,⟨(-11622322850926588656),(-11622322850926576826)⟩⟩,⟨⟨5313969417665112023,5313969417665122293⟩,⟨(-10796480854586162299),(-10796480854586152029)⟩⟩,⟨⟨3820548408428710200,3820548408428719095⟩,⟨(-9923579833714359331),(-9923579833714350436)⟩⟩,⟨⟨2570497502758565517,2570497502758573222⟩,⟨(-9031070191378807472),(-9031070191378799768)⟩⟩,⟨⟨1538439541156785556,1538439541156792224⟩,⟨(-8141324278872997610),(-8141324278872990946)⟩⟩,⟨⟨699748425205421240,699748425205426996⟩,⟨(-7272165596656769368),(-7272165596656763612)⟩⟩,⟨⟨30886769493116556,30886769493121523⟩,⟨(-6437390643518641584),(-6437390643518636617)⟩⟩] +lemma kernel28_1_r4_6_eq : ∀ k : Fin 16, kernel28_1Expr 4 6 k = kernel28_1_r4_6 k := by decide +kernel +noncomputable def kernel28_1_r4_7 : Fin 16 → CBox := ![⟨⟨(-490338726714541247),(-490338726714536959)⟩,⟨(-5647274472483953160),(-5647274472483948872)⟩⟩,⟨⟨(-884595163869820355),(-884595163869816665)⟩,⟨(-4909052768638977041),(-4909052768638973354)⟩⟩,⟨⟨(-1170905510563389256),(-1170905510563386086)⟩,⟨(-4227374910313867328),(-4227374910313864161)⟩⟩,⟨⟨(-1366585943528190044),(-1366585943528187308)⟩,⟨(-3604723988115217869),(-3604723988115215133)⟩⟩,⟨⟨(-1487229878700662909),(-1487229878700660563)⟩,⟨(-3041801120056764574),(-3041801120056762228)⟩⟩,⟨⟨(-1546730582674295659),(-1546730582674293645)⟩,⟨(-2537872605692958802),(-2537872605692956788)⟩⟩,⟨⟨(-1557334828912253693),(-1557334828912251968)⟩,⟨(-2091079503513900926),(-2091079503513899198)⟩⟩,⟨⟨(-1529720712794832444),(-1529720712794830964)⟩,⟨(-1698710094602587634),(-1698710094602586154)⟩⟩,⟨⟨(-1473093436260133950),(-1473093436260132686)⟩,⟨(-1357436416510162738),(-1357436416510161470)⟩⟩,⟨⟨(-1395293591888843929),(-1395293591888842840)⟩,⟨(-1063516622657730364),(-1063516622657729275)⟩⟩,⟨⟨(-1302913196563813600),(-1302913196563812659)⟩,⟨(-812965355118153611),(-812965355118152667)⟩⟩,⟨⟨(-1201415428490972709),(-1201415428490971902)⟩,⟨(-601694625053502278),(-601694625053501471)⟩⟩,⟨⟨(-1095254693955358671),(-1095254693955357987)⟩,⟨(-425627889299003689),(-425627889299003004)⟩⟩,⟨⟨(-987994280487858717),(-987994280487858128)⟩,⟨(-280790108144876641),(-280790108144876053)⟩⟩,⟨⟨(-882419432930965070),(-882419432930964567)⟩,⟨(-163376582945518946),(-163376582945518443)⟩⟩,⟨⟨(-780644212754223637),(-780644212754223198)⟩,⟨(-69803317137178529),(-69803317137178090)⟩⟩] +lemma kernel28_1_r4_7_eq : ∀ k : Fin 16, kernel28_1Expr 4 7 k = kernel28_1_r4_7 k := by decide +kernel +noncomputable def kernel28_1_r4_8 : Fin 16 → CBox := ![⟨⟨(-684210965854195165),(-684210965854194790)⟩,⟨3258465743940263,3258465743940638⟩⟩,⟨⟨(-594181629053835872),(-594181629053835548)⟩,⟨58861165640328626,58861165640328944⟩⟩,⟨⟨(-511220451429751983),(-511220451429751709)⟩,⟨99770712537626502,99770712537626779⟩⟩,⟨⟨(-435667995709518573),(-435667995709518343)⟩,⟨128465440474574028,128465440474574262⟩⟩,⟨⟨(-367606520671761675),(-367606520671761478)⟩,⟨147142047825360095,147142047825360292⟩⟩,⟨⟨(-306917031938628472),(-306917031938628296)⟩,⟨157726980719647315,157726980719647491⟩⟩,⟨⟨(-253328430507779170),(-253328430507779020)⟩,⟨161891791877686166,161891791877686319⟩⟩,⟨⟨(-206459290871242005),(-206459290871241868)⟩,⟨161071234890004520,161071234890004653⟩⟩,⟨⟨(-165852868758792294),(-165852868758792182)⟩,⟨156483050201730885,156483050201731000⟩⟩,⟨⟨(-131005977508341667),(-131005977508341567)⟩,⟨149148580971343192,149148580971343291⟩⟩,⟨⟨(-101392386691705573),(-101392386691705484)⟩,⟨139913522703108737,139913522703108826⟩⟩,⟨⟨(-76481391496587857),(-76481391496587779)⟩,⟨129468259054296187,129468259054296265⟩⟩,⟨⟨(-55752180695051734),(-55752180695051667)⟩,⟨118367367128675011,118367367128675078⟩⟩,⟨⟨(-38704598602130952),(-38704598602130886)⟩,⟨107047989082309097,107047989082309160⟩⟩,⟨⟨(-24866855583469100),(-24866855583469043)⟩,⟨95846863623441262,95846863623441323⟩⟩,⟨⟨(-13800695289982800),(-13800695289982750)⟩,⟨85015891956647671,85015891956647718⟩⟩] +lemma kernel28_1_r4_8_eq : ∀ k : Fin 16, kernel28_1Expr 4 8 k = kernel28_1_r4_8 k := by decide +kernel +noncomputable def kernel28_1_r4_9 : Fin 16 → CBox := ![⟨⟨(-5104477315347409),(-5104477315347359)⟩,⟨74736179111250104,74736179111250155⟩⟩,⟨⟨1585416603036040,1585416603036079⟩,⟨65130544767229613,65130544767229649⟩⟩,⟨⟨6594494775397421,6594494775397461⟩,⟨56274539091922557,56274539091922597⟩⟩,⟨⟨10211076366104318,10211076366104353⟩,⟨48206030192674116,48206030192674155⟩⟩,⟨⟨12687956626198765,12687956626198800⟩,⟨40933452013343937,40933452013343972⟩⟩,⟨⟨14244594602363450,14244594602363481⟩,⟨34442816231995100,34442816231995133⟩⟩,⟨⟨15069639852875033,15069639852875063⟩,⟨28703600238894584,28703600238894618⟩⟩,⟨⟨15323649209966759,15323649209966793⟩,⟨23673626764975993,23673626764976024⟩⟩,⟨⟨15141875115125971,15141875115126000⟩,⟨19303050248114586,19303050248114616⟩⟩,⟨⟨14637033595872951,14637033595872980⟩,⟨15537561500018394,15537561500018423⟩⟩,⟨⟨13901982722585629,13901982722585654⟩,⟨12320916477493513,12320916477493541⟩⟩,⟨⟨13012261624487335,13012261624487365⟩,⟨9596887654653282,9596887654653311⟩⟩,⟨⟨12028456143901237,12028456143901265⟩,⟨7310728209631088,7310728209631113⟩⟩,⟨⟨10998370283217894,10998370283217923⟩,⟨5410230447704904,5410230447704933⟩⟩,⟨⟨9958993076874389,9958993076874418⟩,⟨3846450954662224,3846450954662253⟩⟩,⟨⟨8938258726865926,8938258726865945⟩,⟨2574166197814140,2574166197814162⟩⟩] +lemma kernel28_1_r4_9_eq : ∀ k : Fin 16, kernel28_1Expr 4 9 k = kernel28_1_r4_9 k := by decide +kernel +noncomputable def kernel28_1_r4_10 : Fin 16 → CBox := ![⟨⟨7956604089881967,7956604089881996⟩,⟨1552113882256991,1552113882257021⟩⟩,⟨⟨7028332194165082,7028332194165107⟩,⟨743067479330689,743067479330717⟩⟩,⟨⟨6162793669021607,6162793669021631⟩,⟨113784073086443,113784073086467⟩⟩,⟨⟨5365400038322178,5365400038322208⟩,⟨(-365140923452759),(-365140923452730)⟩⟩,⟨⟨4638483982994830,4638483982994860⟩,⟨(-719484523994146),(-719484523994117)⟩⟩,⟨⟨3982022110816613,3982022110816637⟩,⟨(-971649934675128),(-971649934675104)⟩⟩,⟨⟨3394235652529538,3394235652529562⟩,⟨(-1140945390067127),(-1140945390067103)⟩⟩,⟨⟨2872083973995475,2872083973995505⟩,⟨(-1243874005675333),(-1243874005675304)⟩⟩,⟨⟨2411664973930453,2411664973930470⟩,⟨(-1294423889912635),(-1294423889912621)⟩⟩,⟨⟨2008535423644331,2008535423644355⟩,⟨(-1304350519292012),(-1304350519291988)⟩⟩,⟨⟨1657963178120671,1657963178120689⟩,⟨(-1283445661108161),(-1283445661108143)⟩⟩,⟨⟨1355122009031989,1355122009032007⟩,⟨(-1239788984241003),(-1239788984240984)⟩⟩,⟨⟨1095238627869482,1095238627869512⟩,⟨(-1179979985461433),(-1179979985461403)⟩⟩,⟨⟨873700317044889,873700317044913⟩,⟨(-1109349027477880),(-1109349027477856)⟩⟩,⟨⟨686130494179598,686130494179622⟩,⟨(-1032147183936560),(-1032147183936536)⟩⟩,⟨⟨528438517044714,528438517044738⟩,⟨(-951715259430936),(-951715259430912)⟩⟩] +lemma kernel28_1_r4_10_eq : ∀ k : Fin 16, kernel28_1Expr 4 10 k = kernel28_1_r4_10 k := by decide +kernel +noncomputable def kernel28_1_r4_11 : Fin 16 → CBox := ![⟨⟨396849104224909,396849104224939⟩,⟨(-870632838517795),(-870632838517765)⟩⟩,⟨⟨287915904696103,287915904696133⟩,⟨(-790848551436558),(-790848551436528)⟩⟩,⟨⟨198522999183941,198522999183971⟩,⟨(-713792955882006),(-713792955881976)⟩⟩,⟨⟨125877455403065,125877455403084⟩,⟨(-640475549745656),(-640475549745638)⟩⟩,⟨⟨67495483870836,67495483870855⟩,⟨(-571567471241360),(-571567471241337)⟩⟩,⟨⟨21184245268240,21184245268258⟩,⟨(-507471428702943),(-507471428702925)⟩⟩,⟨⟨(-14979062302173),(-14979062302154)⟩,⟨(-448380347811823),(-448380347811804)⟩⟩,⟨⟨(-42669564385928),(-42669564385910)⟩,⟨(-394326141471940),(-394326141471921)⟩⟩,⟨⟨(-63337545493202),(-63337545493172)⟩,⟨(-345219906925143),(-345219906925112)⟩⟩,⟨⟨(-78231030428331),(-78231030428313)⟩,⟨(-300884743803631),(-300884743803613)⟩⟩,⟨⟨(-88417584108116),(-88417584108085)⟩,⟨(-261082271669072),(-261082271669042)⟩⟩,⟨⟨(-94804964185104),(-94804964185086)⟩,⟨(-225533810714894),(-225533810714875)⟩⟩,⟨⟨(-98160389513361),(-98160389513342)⟩,⟨(-193937078003374),(-193937078003356)⟩⟩,⟨⟨(-99128288284684),(-99128288284661)⟩,⟨(-165979146162331),(-165979146162311)⟩⟩,⟨⟨(-98246467149174),(-98246467149156)⟩,⟨(-141346313371923),(-141346313371904)⟩⟩,⟨⟨(-95960700879363),(-95960700879345)⟩,⟨(-119731443592293),(-119731443592275)⟩⟩] +lemma kernel28_1_r4_11_eq : ∀ k : Fin 16, kernel28_1Expr 4 11 k = kernel28_1_r4_11 k := by decide +kernel +noncomputable def kernel28_1_r4_12 : Fin 16 → CBox := ![⟨⟨(-92637784678360),(-92637784678343)⟩,⟨(-100839254699443),(-100839254699428)⟩⟩,⟨⟨(-88577121110185),(-88577121110166)⟩,⟨(-84389959528015),(-84389959527997)⟩⟩,⟨⟨(-84020933430067),(-84020933430043)⟩,⟨(-70121600519974),(-70121600519949)⟩⟩,⟨⟨(-79163208994051),(-79163208994026)⟩,⟨(-57791362320148),(-57791362320123)⟩⟩,⟨⟨(-74157482244510),(-74157482244485)⟩,⟨(-47176097695019),(-47176097694995)⟩⟩,⟨⟨(-69123567998281),(-69123567998262)⟩,⟨(-38072259962807),(-38072259962788)⟩⟩,⟨⟨(-64153353627525),(-64153353627500)⟩,⟨(-30295399063475),(-30295399063451)⟩⟩,⟨⟨(-59315754202135),(-59315754202117)⟩,⟨(-23679347814584),(-23679347814565)⟩⟩,⟨⟨(-54660928539357),(-54660928539332)⟩,⟨(-18075199161634),(-18075199161610)⟩⟩,⟨⟨(-50223846992899),(-50223846992874)⟩,⟨(-13350153737710),(-13350153737686)⟩⟩,⟨⟨(-46027294182622),(-46027294182607)⟩,⟨(-9386299240088),(-9386299240070)⟩⟩,⟨⟨(-42084382073096),(-42084382073071)⟩,⟨(-6079368497221),(-6079368497196)⟩⟩,⟨⟨(-38400641116617),(-38400641116598)⟩,⟨(-3337511177698),(-3337511177679)⟩⟩,⟨⟨(-34975749771019),(-34975749771000)⟩,⟨(-1080104469842),(-1080104469823)⟩⟩,⟨⟨(-31804955709674),(-31804955709651)⟩,⟨763379628419,763379628440⟩⟩,⟨⟨(-28880235541427),(-28880235541396)⟩,⟨2254438842694,2254438842725⟩⟩] +lemma kernel28_1_r4_12_eq : ∀ k : Fin 16, kernel28_1Expr 4 12 k = kernel28_1_r4_12 k := by decide +kernel +noncomputable def kernel28_1_r4_13 : Fin 16 → CBox := ![⟨⟨(-26191233893595),(-26191233893565)⟩,⟨3446530146815,3446530146841⟩⟩,⟨⟨(-23726017298183),(-23726017298158)⟩,⟨4385981081435,4385981081460⟩⟩,⟨⟨(-21471673455463),(-21471673455442)⟩,⟨5112822406263,5112822406286⟩⟩,⟨⟨(-19414782111589),(-19414782111570)⟩,⟨5661543637201,5661543637220⟩⟩,⟨⟨(-17541779949781),(-17541779949756)⟩,⟨6061774450763,6061774450788⟩⟩,⟨⟨(-15839238522702),(-15839238522682)⟩,⟨6338895909908,6338895909932⟩⟩,⟨⟨(-14294071310137),(-14294071310118)⟩,⟨6514586076597,6514586076616⟩⟩,⟨⟨(-12893683430271),(-12893683430246)⟩,⟨6607304910982,6607304911007⟩⟩,⟨⟨(-11626075327262),(-11626075327237)⟩,⟨6632723480386,6632723480411⟩⟩,⟨⟨(-10479909863102),(-10479909863083)⟩,⟨6604102468716,6604102468735⟩⟩,⟨⟨(-9444550623165),(-9444550623143)⟩,⟨6532624831398,6532624831426⟩⟩,⟨⟨(-8510077868188),(-8510077868169)⟩,⟨6427687217241,6427687217260⟩⟩,⟨⟨(-7667287400805),(-7667287400774)⟩,⟨6297154502917,6297154502948⟩⟩,⟨⟨(-6907676633261),(-6907676633230)⟩,⟨6147581480885,6147581480917⟩⟩,⟨⟨(-6223421320630),(-6223421320611)⟩,⟨5984405420739,5984405420758⟩⟩,⟨⟨(-5607345737362),(-5607345737331)⟩,⟨5812112901847,5812112901879⟩⟩] +lemma kernel28_1_r4_13_eq : ∀ k : Fin 16, kernel28_1Expr 4 13 k = kernel28_1_r4_13 k := by decide +kernel +noncomputable def kernel28_1_r4_14 : Fin 16 → CBox := ![⟨⟨(-5052888505112),(-5052888505087)⟩,⟨5634383998573,5634383998599⟩⟩,⟨⟨(-4554065809460),(-4554065809433)⟩,⟨5454216594976,5454216595006⟩⟩,⟨⟨(-4105433355712),(-4105433355687)⟩,⟨5274033318642,5274033318668⟩⟩,⟨⟨(-3702048098580),(-3702048098554)⟩,⟨5095773314127,5095773314153⟩⟩,⟨⟨(-3339430523486),(-3339430523456)⟩,⟨4920970828542,4920970828568⟩⟩,⟨⟨(-3013528050445),(-3013528050426)⟩,⟨4750822354067,4750822354086⟩⟩,⟨⟨(-2720679965716),(-2720679965697)⟩,⟨4586243865649,4586243865668⟩⟩,⟨⟨(-2457584154821),(-2457584154801)⟩,⟨4427919505184,4427919505204⟩⟩,⟨⟨(-2221265807307),(-2221265807288)⟩,⟨4276342895957,4276342895976⟩⟩,⟨⟨(-2009048183158),(-2009048183139)⟩,⟨4131852121165,4131852121185⟩⟩,⟨⟨(-1818525469452),(-1818525469427)⟩,⟨3994659267307,3994659267332⟩⟩,⟨⟨(-1647537709538),(-1647537709506)⟩,⟨3864875314915,3864875314947⟩⟩,⟨⟨(-1494147753202),(-1494147753183)⟩,⟨3742531055319,3742531055339⟩⟩,⟨⟨(-1356620152190),(-1356620152171)⟩,⟨3627594620234,3627594620253⟩⟩,⟨⟨(-1233401909018),(-1233401908999)⟩,⟨3519986130923,3519986130942⟩⟩,⟨⟨(-1123104977247),(-1123104977228)⟩,⟨3419589903316,3419589903336⟩⟩] +lemma kernel28_1_r4_14_eq : ∀ k : Fin 16, kernel28_1Expr 4 14 k = kernel28_1_r4_14 k := by decide +kernel +noncomputable def kernel28_1_r4_15 : Fin 16 → CBox := ![⟨⟨(-1024490405602),(-1024490405576)⟩,⟨3326264584172,3326264584197⟩⟩,⟨⟨(-936454017038),(-936454017017)⟩,⟨3239851540424,3239851540448⟩⟩,⟨⟨(-858013514738),(-858013514707)⟩,⟨3160181777166,3160181777198⟩⟩,⟨⟨(-788296910213),(-788296910187)⟩,⟨3087081620047,3087081620072⟩⟩,⟨⟨(-726532173626),(-726532173596)⟩,⟨3020377362900,3020377362927⟩⟩,⟨⟨(-672038011764),(-672038011745)⟩,⟨2959899051755,2959899051774⟩⟩,⟨⟨(-624215686071),(-624215686046)⟩,⟨2905483550180,2905483550206⟩⟩,⟨⟨(-582541789477),(-582541789458)⟩,⟨2856977009135,2856977009155⟩⟩,⟨⟨(-546561908479),(-546561908458)⟩,⟨2814236844746,2814236844770⟩⟩,⟨⟨(-515885103640),(-515885103610)⟩,⟨2777133311417,2777133311444⟩⟩,⟨⟨(-490179149227),(-490179149200)⟩,⟨2745550742893,2745550742923⟩⟩,⟨⟨(-469166479700),(-469166479674)⟩,⟨2719388521933,2719388521958⟩⟩,⟨⟨(-452620797733),(-452620797701)⟩,⟨2698561828130,2698561828162⟩⟩,⟨⟨(-440364305379),(-440364305358)⟩,⟨2683002204412,2683002204436⟩⟩,⟨⟨(-432265526688),(-432265526668)⟩,⟨2672657973950,2672657973969⟩⟩,⟨⟨(-428237696454),(-428237696430)⟩,⟨2667494532255,2667494532275⟩⟩] +lemma kernel28_1_r4_15_eq : ∀ k : Fin 16, kernel28_1Expr 4 15 k = kernel28_1_r4_15 k := by decide +kernel +noncomputable def kernel28_1_r4 : Fin 16 → Fin 16 → CBox := ![kernel28_1_r4_0,kernel28_1_r4_1,kernel28_1_r4_2,kernel28_1_r4_3,kernel28_1_r4_4,kernel28_1_r4_5,kernel28_1_r4_6,kernel28_1_r4_7,kernel28_1_r4_8,kernel28_1_r4_9,kernel28_1_r4_10,kernel28_1_r4_11,kernel28_1_r4_12,kernel28_1_r4_13,kernel28_1_r4_14,kernel28_1_r4_15] +lemma kernel28_1_r4_eq (i k : Fin 16) : kernel28_1Expr 4 i k = kernel28_1_r4 i k := by + fin_cases i + · exact kernel28_1_r4_0_eq k + · exact kernel28_1_r4_1_eq k + · exact kernel28_1_r4_2_eq k + · exact kernel28_1_r4_3_eq k + · exact kernel28_1_r4_4_eq k + · exact kernel28_1_r4_5_eq k + · exact kernel28_1_r4_6_eq k + · exact kernel28_1_r4_7_eq k + · exact kernel28_1_r4_8_eq k + · exact kernel28_1_r4_9_eq k + · exact kernel28_1_r4_10_eq k + · exact kernel28_1_r4_11_eq k + · exact kernel28_1_r4_12_eq k + · exact kernel28_1_r4_13_eq k + · exact kernel28_1_r4_14_eq k + · exact kernel28_1_r4_15_eq k +noncomputable def kernel28_1_r5_0 : Fin 16 → CBox := ![⟨⟨10730093117577432240166278742,10730093117577440127367716113⟩,⟨(-17097429199280346133579744315),(-17097429199280338246466878226)⟩⟩,⟨⟨10705011058567530951152324479,10705011058567538834586265274⟩,⟨(-17092798465362505545901650885),(-17092798465362497662555657752)⟩⟩,⟨⟨10654926460498358114024960221,10654926460498365989914489581⟩,⟨(-17083478631992671054157006710),(-17083478631992663178354180637)⟩⟩,⟨⟨10579998277973854679869166846,10579998277973862544445851500⟩,⟨(-17069353610879590739813698494),(-17069353610879582875321857698)⟩⟩,⟨⟨10480464725901168152468307828,10480464725901176001976111077⟩,⟨(-17050250871744255930923197378),(-17050250871744248081497772036)⟩⟩,⟨⟨10356643008651069850764465227,10356643008651077681464225854⟩,⟨(-17025943351520557358416228100),(-17025943351520549527795784235)⟩⟩,⟨⟨10208928941758568683621077306,10208928941758576491794161631⟩,⟨(-16996151977667911846965864712),(-16996151977667904038868454889)⟩⟩,⟨⟨10037796451878912514343408046,10037796451878920296296737380⟩,⟨(-16960548786546649507799496067),(-16960548786546641725917634647)⟩⟩,⟨⟨9843796937687717297164157891,9843796937687725049232785422⟩,⟨(-16918760613118306057711787239),(-16918760613118298305709876112)⟩⟩,⟨⟨9627558471740873150295547425,9627558471740880868849222916⟩,⟨(-16870373323600888832633844415),(-16870373323600881114141610909)⟩⟩,⟨⟨9389784821051050951200271100,9389784821051058632646915290⟩,⟨(-16814936558152165260706033972),(-16814936558152157579315058895)⟩⟩,⟨⟨9131254262348708401404621459,9131254262348716042846457116⟩,⟨(-16751968946194093890921564447),(-16751968946194086249529153577)⟩⟩,⟨⟨8852818166726012096159098055,8852818166726019694136174109⟩,⟨(-16680963752654559993653982734),(-16680963752654552395719644687)⟩⟩,⟨⟨8555399327654706614549479585,8555399327654714165655515488⟩,⟨(-16601394909218484855435959978),(-16601394909218477304365564107)⟩⟩,⟨⟨8239990006258689400358094823,8239990006258696901229456427⟩,⟨(-16512723380683093293806728583),(-16512723380683085792963531176)⟩⟩,⟨⟨7907649668235568501646469125,7907649668235575948984026816⟩,⟨(-16414403812739527236245728480),(-16414403812739519788928516455)⟩⟩] +lemma kernel28_1_r5_0_eq : ∀ k : Fin 16, kernel28_1Expr 5 0 k = kernel28_1_r5_0 k := by decide +kernel +noncomputable def kernel28_1_r5_1 : Fin 16 → CBox := ![⟨⟨7559502387976489011372344707,7559502387976496401921414882⟩,⟨(-16305891403996637539494653235),(-16305891403996630148957804455)⟩⟩,⟨⟨7196733897238172642039330139,7196733897238179972625263287⟩,⟨(-16186648941867482224925435640),(-16186648941867474894343332309)⟩⟩,⟨⟨6820588258173567534451728971,6820588258173574801945365408⟩,⟨(-16056153939102307304245413120),(-16056153939102300036746987541)⟩⟩,⟨⟨6432364143615509641185893039,6432364143615516842549863614⟩,⟨(-15913905805323061471827097488),(-15913905805323054270449532445)⟩⟩,⟨⟨6033410711208469242417060277,6033410711208476374657087311⟩,⟨(-15759432985944394392125837594),(-15759432985944387259863266526)⟩⟩,⟨⟨5625123062263148991740154104,5625123062263156051975260759⟩,⟨(-15592299999405347241754704746),(-15592299999405340181488003020)⟩⟩,⟨⟨5208937281023025039015772332,5208937281023032024405050326⟩,⟨(-15412114302734350361990800989),(-15412114302734343376560818968)⟩⟩,⟨⟨4786325055325931894612070811,4786325055325938802466150336⟩,⟨(-15218532915175349818477697026),(-15218532915175342910573788418)⟩⟩,⟨⟨4358787885352326608094324142,4358787885352333435756028460⟩,⟨(-15011268729959160322106206943),(-15011268729959153494385576524)⟩⟩,⟨⟨3927850893200088918884861836,3927850893200095663826334593⟩,⟨(-14790096445351072955148361285),(-14790096445351066210138938843)⟩⟩,⟨⟨3495056252329813190743455024,3495056252329819850461556867⟩,⟨(-14554858047876926437448954432),(-14554858047876919777653996437)⟩⟩,⟨⟨3061956262392649176077474923,3061956262392655748232875695⟩,⟨(-14305467783151585320001937559),(-14305467783151578747760933831)⟩⟩,⟨⟨2630106101485995923250224604,2630106101486002405516580350⟩,⟨(-14041916553023824496439833183),(-14041916553023818014079329671)⟩⟩,⟨⟨2201056294376180803461815672,2201056294376187193918824856⟩,⟨(-13764275681818056812944887675),(-13764275681818050422385445005)⟩⟩,⟨⟨1776344941572832728878613990,1776344941572839025898165630⟩,⟨(-13472699999293457236499605766),(-13472699999293450939369657130)⟩⟩,⟨⟨1357489760225493343660100220,1357489760225499545323193083⟩,⟨(-13167430193540460406188086888),(-13167430193540454204406951958)⟩⟩] +lemma kernel28_1_r5_1_eq : ∀ k : Fin 16, kernel28_1Expr 5 1 k = kernel28_1_r5_1 k := by decide +kernel +noncomputable def kernel28_1_r5_2 : Fin 16 → CBox := ![⟨⟨945979993526696133954708196,945979993526702238322070873⟩,⟨(-12848794393366565485011761752),(-12848794393366559380519066923)⟩⟩,⟨⟨543268250535825981024403717,543268250535831986415074961⟩,⟨(-12517208946748178199252689101),(-12517208946748172193729783659)⟩⟩,⟨⟨150762342976003602869031330,150762342976009507566017767⟩,⟨(-12173178369589951522258292184),(-12173178369589945617422589944)⟩⟩,⟨⟨(-230182810501602222867317999),(-230182810501596420327896149)⟩,⟨(-11817294447271613351893054937),(-11817294447271607549208884435)⟩⟩,⟨⟨(-598273138941905546137192120),(-598273138941899847228545048)⟩,⟨(-11450234480195462211558888163),(-11450234480195456512499935854)⟩⟩,⟨⟨(-952283156684724717945583414),(-952283156684719123564987776)⟩,⟨(-11072758673683988669624717748),(-11072758673683983075090704994)⟩⟩,⟨⟨(-1291063406711737060011006313),(-1291063406711731571448539031)⟩,⟨(-10685706682013239828397088954),(-10685706682013234339678894563)⟩⟩,⟨⟨(-1613547532222918570654140195),(-1613547532222913188899492994)⟩,⟨(-10289993325989896234094826526),(-10289993325989890852182589276)⟩⟩,⟨⟨(-1918758899701799355107627606),(-1918758899701794081255381012)⟩,⟨(-9886603513165813620482100594),(-9886603513165808346470857224)⟩⟩,⟨⟨(-2205816698610199627940566127),(-2205816698610194462551282828)⟩,⟨(-9476586399402858676019146876),(-9476586399402853510469919734)⟩⟩,⟨⟨(-2473941445853719262145013367),(-2473941445853714206054141605)⟩,⟨(-9061048839917673358871227592),(-9061048839917668302619928130)⟩⟩,⟨⟨(-2722459827276663579863442960),(-2722459827276658633563959215)⟩,⟨(-8641148187011716484069005241),(-8641148187011711537609070932)⟩⟩,⟨⟨(-2950808813657721411588678708),(-2950808813657716575663618185)⟩,⟨(-8218084500286842091563192783),(-8218084500286837255478117011)⟩⟩,⟨⟨(-3158538994944511553348300203),(-3158538994944506828023270296)⟩,⟨(-7793092243122684925623089154),(-7793092243122680200138931762)⟩⟩,⟨⟨(-3345317083725538193993642954),(-3345317083725533579639595685)⟩,⟨(-7367431546415359298579746895),(-7367431546415354684067920769)⟩⟩,⟨⟨(-3510927547112495158053981823),(-3510927547112490654672122499)⟩,⟨(-6942379126920435737465063404),(-6942379126920431233933361875)⟩⟩] +lemma kernel28_1_r5_2_eq : ∀ k : Fin 16, kernel28_1Expr 5 2 k = kernel28_1_r5_2 k := by decide +kernel +noncomputable def kernel28_1_r5_3 : Fin 16 → CBox := ![⟨⟨(-3655273335196250182037272702),(-3655273335196245789840931976)⟩,⟨(-6519218952889346356491217521),(-6519218952889341964158352597)⟩⟩,⟨⟨(-3778375683931079092545707149),(-3778375683931074811265629706)⟩,⟨(-6099232753931864693544640003),(-6099232753931860412141012883)⟩⟩,⟨⟨(-3880372980563059297597454827),(-3880372980563055127198943846)⟩,⟨(-5683690475087192532794676757),(-5683690475087188362285216131)⟩⟩,⟨⟨(-3961518690405557451387461449),(-3961518690405553391406786983)⟩,⟨(-5273840776868288369171676406),(-5273840776868284309092245930)⟩⟩,⟨⟨(-4022178354721652171901588218),(-4022178354721648222129548431)⟩,⟨(-4870901683502934672346996191),(-4870901683502930722487960463)⟩⟩,⟨⟨(-4062825680535511126163007624),(-4062825680535507285868476690)⟩,⟨(-4476051480695604049795186426),(-4476051480695600209424958689)⟩⟩,⟨⟨(-4084037754191632873310119524),(-4084037754191629142040349442)⟩,⟨(-4090419961963097241747762141),(-4090419961963093510413110993)⟩⟩,⟨⟨(-4086489421239017888004644024),(-4086489421239014264849271801)⟩,⟨(-3715080118963459628605443563),(-3715080118963456005395501007)⟩⟩,⟨⟨(-4070946885563621781314381075),(-4070946885563618265675288739)⟩,⟨(-3351040366274204598714112300),(-3351040366274201083030238051)⟩⟩,⟨⟨(-4038260590457354237944587775),(-4038260590457350828651618498)⟩,⟨(-2999237384837855778482573557),(-2999237384837852369154072822)⟩⟩,⟨⟨(-3989357453332828998150743153),(-3989357453332825693393962105)⟩,⟨(-2660529660858378781229023433),(-2660529660858375476445400819)⟩⟩,⟨⟨(-3925232533917619618566117941),(-3925232533917616409842057557)⟩,⟨(-2335691788401007564624767615),(-2335691788401004355881917359)⟩⟩,⟨⟨(-3846940222850784226128896454),(-3846940222850781112898364158)⟩,⟨(-2025409594440342070971675855),(-2025409594440338957729847843)⟩⟩,⟨⟨(-3755585043534915416108922361),(-3755585043534912397258140571)⟩,⟨(-1730276134755841344430485748),(-1730276134755838325575342301)⟩⟩,⟨⟨(-3652312164764765680720024032),(-3652312164764762755505707998)⟩,⟨(-1450788598044467054258687107),(-1450788598044464129046383280)⟩⟩,⟨⟨(-3538297724975475221999793564),(-3538297724975472389191755929)⟩,⟨(-1187346144075131898732365168),(-1187346144075129065932157124)⟩⟩] +lemma kernel28_1_r5_3_eq : ∀ k : Fin 16, kernel28_1Expr 5 3 k = kernel28_1_r5_3 k := by decide +kernel +noncomputable def kernel28_1_r5_4 : Fin 16 → CBox := ![⟨⟨(-3414739070869398756351586528),(-3414739070869396015120121858)⟩,⟨(-940248689827018446691222602),(-940248689827015705472853690)⟩⟩,⟨⟨(-3282845013654644868691370060),(-3282845013654642217590615313)⟩,⟨(-709696645519070315898329459),(-709696645519067664815395401)⟩⟩,⟨⟨(-3143826205150118642581708562),(-3143826205150116080582723621)⟩,⟨(-495791590439920236659977143),(-495791590439917674683006949)⟩⟩,⟨⟨(-2998885733596161224570530038),(-2998885733596158750153308035)⟩,⟨(-298537866715094714149500867),(-298537866715092239757971955)⟩⟩,⟨⟨(-2849210035197379960081690476),(-2849210035197377572143175271)⟩,⟨(-117845057786753352779904351),(-117845057786750964870259670)⟩⟩,⟨⟨(-2695960212280347574749388742),(-2695960212280345271583227418)⟩,⟨46468692391537469700889204,46468692391539772835497651⟩⟩,⟨⟨(-2540263842562501250861230472),(-2540263842562499031183483252)⟩,⟨194672573459168849307610472,194672573459171068951677530⟩⟩,⟨⟨(-2383207356510640232447212901),(-2383207356510638094491387739)⟩,⟨327118279173458977086299814,327118279173461115007615551⟩⟩,⟨⟨(-2225829051248415493573598571),(-2225829051248413435988159919)⟩,⟨444234525538265262424280501,444234525538267319974698785⟩⟩,⟨⟨(-2069112800099679028532573164),(-2069112800099677049404235286)⟩,⟨546520994618324101193854107,546520994618326080286954229⟩⟩,⟨⟨(-1913982506790119425727623948),(-1913982506790117523525697268)⟩,⟨634541787762877859779339682,634541787762879761946083690⟩⟩,⟨⟨(-1761297342745635092207680944),(-1761297342745633264985657099)⟩,⟨708918476274462004680283182,708918476274463831867426874⟩⟩,⟨⟨(-1611847795002045835672704187),(-1611847795002044081981394976)⟩,⟨770322840494963925295800892,770322840494965678952758161⟩⟩,⟨⟨(-1466352541160325145421500960),(-1466352541160323463075225726)⟩,⟨819469389819660016442710287,819469389819661698757832305⟩⟩,⟨⟨(-1325456156767827218272360005),(-1325456156767825605641162355)⟩,⟨857107756294784673191863944,857107756294786285796197070⟩⟩,⟨⟨(-1189727649658592411189589291),(-1189727649658590866290978630)⟩,⟨884015053234212758116392692,884015053234214302992164837⟩⟩] +lemma kernel28_1_r5_4_eq : ∀ k : Fin 16, kernel28_1Expr 5 4 k = kernel28_1_r5_4 k := by decide +kernel +noncomputable def kernel28_1_r5_5 : Fin 16 → CBox := ![⟨⟨(-1059659805317163528811618875),(-1059659805317162050128431428)⟩,⟨900988287759040176133621436,900988287759041654797729123⟩⟩,⟨⟨(-935669317402356126782475577),(-935669317402354712143766082)⟩,⟨908836912395809437557097747,908836912395810852180214774⟩⟩,⟨⟨(-818097668328492427414240215),(-818097668328491074847594902)⟩,⟨908375595961079170116128714,908375595961080522670398503⟩⟩,⟨⟨(-707212716383912126846199070),(-707212716383910834382856891)⟩,⟨900417288026497509732138601,900417288026498802186053637⟩⟩,⟨⟨(-603210938383807289973426645),(-603210938383806056078378833)⟩,⟨885766644429605856287840969,885766644429607090176145856⟩⟩,⟨⟨(-506220270399973412837748222),(-506220270399972235443103918)⟩,⟨865213873713952674579944869,865213873713953851970271792⟩⟩,⟨⟨(-416303483755656503340684962),(-416303483755655380860388813)⟩,⟨839529056199803346164522212,839529056199804468642653416⟩⟩,⟨⟨(-333462029268561818611621253),(-333462029268560749095309822)⟩,⟨809456978761918964396347852,809456978761920033912400680⟩⟩,⟨⟨(-257640279695740042362404760),(-257640279695739024290371269)⟩,⟨775712519484364998607792411,775712519484366016681243718⟩⟩,⟨⟨(-188730098484357367412629822),(-188730098484356398200098236)⟩,⟨738976607334283591267263009,738976607334284560482670336⟩⟩,⟨⟨(-126575662244263330478921250),(-126575662244262408490654143)⟩,⟨699892773003354000728327420,699892773003354922720720279⟩⟩,⟨⟨(-70978464793021687152089687),(-70978464793020810573879061)⟩,⟨659064298256732668903407083,659064298256733545486798159⟩⟩,⟨⟨(-21702432123713512489576414),(-21702432123712679897445232)⟩,⟨617051962644423133597152148,617051962644423966195335025⟩⟩,⟨⟨21520919864834938800725697,21520919864835729240055035⟩,⟨574372378396994911327828027,574372378396995701773910783⟩⟩,⟨⟨58987349646893423656564293,58987349646894173374241336⟩,⟨531496896859878418489386019,531496896859879168214264656⟩⟩,⟨⟨91014836943564789095976632,91014836943565499941137013⟩,⟨488851063015755250065387768,488851063015755960917894790⟩⟩] +lemma kernel28_1_r5_5_eq : ∀ k : Fin 16, kernel28_1Expr 5 5 k = kernel28_1_r5_5 k := by decide +kernel +noncomputable def kernel28_1_r5_6 : Fin 16 → CBox := ![⟨⟨117938667907307858347977357,117938667907308531670901529⟩,⟨446814588583331414753075346,446814588583332088083395348⟩⟩,⟨⟨140106708898555041428331295,140106708898555678931907525⟩,⟨405721808925530541279797393,405721808925531178790735500⟩⟩,⟨⟨157874913260421862714427204,157874913260422465752086624⟩,⟨365862584594998812629007320,365862584594999415673921247⟩⟩,⟨⟨171603099306906502700512123,171603099306907072850358335⟩,⟨327483604815550690556049354,327483604815551260712980163⟩⟩,⟨⟨181651031358409500974052379,181651031358410039479342171⟩,⟨290790047552676539257510608,290790047552677077768850202⟩⟩,⟨⟨188374829206567393394756012,188374829206567901790939640⟩,⟨255947549055266109607878625,255947549055266618009084628⟩⟩,⟨⟨192123724983092534138025124,192123724983093013643005403⟩,⟨223084434829133020689048654,223084434829133500198110465⟩⟩,⟨⟨193237180151429602099833191,193237180151430054137420296⟩,⟨192294163891133895575299150,192294163891134347616112632⟩⟩,⟨⟨192042369332815920757248115,192042369332816347022634001⟩,⟨163637938798254029043258470,163637938798254455311098656⟩⟩,⟨⟨188852032005950521572210445,188852032005950923568561878⟩,⟨137147435285663719039345808,137147435285664121037460451⟩⟩,⟨⟨183962687855987801105115282,183962687855988179842941664⟩,⟨112827607309221219078903800,112827607309221597817880062⟩⟩,⟨⟨177653206755162085811191756,177653206755162442476784945⟩,⟨90659525792179284022922495,90659525792179640689126418⟩⟩,⟨⟨170183720081942957624795222,170183720081943293149077662⟩,⟨70603212339197596984549467,70603212339197932508977124⟩⟩,⟨⟨161794856362806452938142630,161794856362806768467198200⟩,⟨52600432516781061002741821,52600432516781376531545553⟩⟩,⟨⟨152707281071971793682044176,152707281071972090118062815⟩,⟨36577416920900499734922390,36577416920900796170352811⟩⟩,⟨⟨143121517858696730923970322,143121517858697009327899638⟩,⟨22447482073953011511918722,22447482073953289914979437⟩⟩] +lemma kernel28_1_r5_6_eq : ∀ k : Fin 16, kernel28_1Expr 5 6 k = kernel28_1_r5_6 k := by decide +kernel +noncomputable def kernel28_1_r5_7 : Fin 16 → CBox := ![⟨⟨133218026486019088084622523,133218026486019349266010232⟩,⟨10113527131426910832220717,10113527131427172012511171⟩⟩,⟨⟨123157511345394109124454996,123157511345394354102164621⟩,⟨(-529613644901686937978603),(-529613644901441961548041)⟩⟩,⟨⟨113081433535010958771062852,113081433535011188368313424⟩,⟨(-9592978748552290991947780),(-9592978748552061396115423)⟩⟩,⟨⟨103112699123743567458083562,103112699123743782561835795⟩,⟨(-17191459884849945580259729),(-17191459884849730477974500)⟩⟩,⟨⟨93356496328693615044457405,93356496328693816358443138⟩,⟨(-23441963600549704922858825),(-23441963600549503610352418)⟩⟩,⟨⟨83901254867448826337215766,83901254867449014700122448⟩,⟨(-28461759192353187654321140),(-28461759192352999292885237)⟩⟩,⟨⟨74819701657602977126455537,74819701657603153197155201⟩,⟨(-32367014779052755002090299),(-32367014779052578932835206)⟩⟩,⟨⟨66169988274021483455428631,66169988274021647983888720⟩,⟨(-35271520485538974719581452),(-35271520485538810192525345)⟩⟩,⟨⟨57996867085546797251373684,57996867085546950944628803⟩,⟨(-37285595059556153733678339),(-37285595059556000041635085)⟩⟩,⟨⟨50332894723837326837304132,50332894723837470424586593⟩,⟨(-38515169940197687377514130),(-38515169940197543791221045)⟩⟩,⟨⟨43199643435242961867637244,43199643435243095881186346⟩,⟨(-39061042829141504451228627),(-39061042829141370438468009)⟩⟩,⟨⟨36608902881384409603561897,36608902881384534649132032⟩,⟨(-39018291182686603098548121),(-39018291182686478053586618)⟩⟩,⟨⟨30563857037570949516933543,30563857037571066068283246⟩,⟨(-38475834739306145482820940),(-38475834739306028931920083)⟩⟩,⟨⟨25060222946044620139288388,25060222946044728768583452⟩,⟨(-37516135212382160763161133),(-37516135212382052134174286)⟩⟩,⟨⟨20087340173073458422703232,20087340173073559570964189⟩,⟨(-36215020594719171992804383),(-36215020594719070844729001)⟩⟩,⟨⟨15629201859466311150154989,15629201859466405313399371⟩,⟨(-34641621119881000268413332),(-34641621119880906105248738)⟩⟩] +lemma kernel28_1_r5_7_eq : ∀ k : Fin 16, kernel28_1Expr 5 7 k = kernel28_1_r5_7 k := by decide +kernel +noncomputable def kernel28_1_r5_8 : Fin 16 → CBox := ![⟨⟨11665420212299329444906027,11665420212299417014106648⟩,⟨(-32858403781598545491463854),(-32858403781598457922253079)⟩⟩,⟨⟨8172121135640570158849769,8172121135640651638535397⟩,⟨(-30921292400259330772607292),(-30921292400259249292837017)⟩⟩,⟨⟨5122764418916101452348738,5122764418916177192949581⟩,⟨(-28879860516992566906589042),(-28879860516992491165842040)⟩⟩,⟨⟨2488887477228807714386999,2488887477228878110239122⟩,⟨(-26777584862430949765007495),(-26777584862430879368959406)⟩⟩,⟨⟨240772057035383206736611,240772057035448565843194⟩,⟨(-24652147760032972137359786),(-24652147760032906778018051)⟩⟩,⟨⟨(-1651965423897980682493344),(-1651965423897919998768380)⟩,⟨(-22535777554531797955360500),(-22535777554531737271370565)⟩⟩,⟨⟨(-3219858144386899067248504),(-3219858144386842763273839)⟩,⟨(-20455616977303450889921148),(-20455616977303394585667243)⟩⟩,⟨⟨(-4493145074664435549483841),(-4493145074664383307420383)⟩,⟨(-18434110246363488320249429),(-18434110246363436077904594)⟩⟩,⟨⟨(-5501395656343879752033489),(-5501395656343831332235860)⟩,⟨(-16489400625306235807191945),(-16489400625306187387115050)⟩⟩,⟨⟨(-6273198920365342776626422),(-6273198920365297893392071)⟩,⟨(-14635731110932883343803880),(-14635731110932838460295808)⟩⟩,⟨⟨(-6835912537275164035306411),(-6835912537275122460424822)⟩,⟨(-12883841864056450682431664),(-12883841864056409107284817)⟩⟩,⟨⟨(-7215466971946621972582626),(-7215466971946583461864345)⟩,⟨(-11241358924973253091709115),(-11241358924973214580752848)⟩⟩,⟨⟨(-7436219716991734551369111),(-7436219716991698915834957)⟩,⟨(-9713169649823802463762763),(-9713169649823766828034589)⟩⟩,⟨⟨(-7520854492839252781984840),(-7520854492839219797821339)⟩,⟨(-8301781154512877701857077),(-8301781154512844717538945)⟩⟩,⟨⟨(-7490320314442366416171641),(-7490320314442335913270087)⟩,⟨(-7007658849443345541983934),(-7007658849443315038962802)⟩⟩,⟨⟨(-7363805421338334256918596),(-7363805421338306044831315)⟩,⟨(-5829542883793932901016868),(-5829542883793904688840939)⟩⟩] +lemma kernel28_1_r5_8_eq : ∀ k : Fin 16, kernel28_1Expr 5 8 k = kernel28_1_r5_8 k := by decide +kernel +noncomputable def kernel28_1_r5_9 : Fin 16 → CBox := ![⟨⟨(-7158741235956000295370616),(-7158741235955974230044360)⟩,⟨(-4764740987365469462685089),(-4764740987365443397297247)⟩⟩,⟨⟨(-6890831741703933650748109),(-6890831741703909560531038)⟩,⟨(-3809396798053680039497104),(-3809396798053655949241906)⟩⟩,⟨⟨(-6574103945143822000531071),(-6574103945143799754470855)⟩,⟨(-2958733292488738745559581),(-2958733292488716499481359)⟩⟩,⟨⟨(-6220975393933777512902895),(-6220975393933756966486223)⟩,⟨(-2207271396593400486785116),(-2207271396593379940367505)⟩⟩,⟨⟨(-5842335053622648331875595),(-5842335053622629374274306)⟩,⟨(-1549024243381588541193257),(-1549024243381569583605271)⟩⟩,⟨⟨(-5447634192227133796093750),(-5447634192227116298044560)⟩,⟨(-977667870001545010766538),(-977667870001527512742190)⟩⟩,⟨⟨(-5044984273353534529308698),(-5044984273353518391722896)⟩,⟨(-486689408482631218969621),(-486689408482615081417982)⟩⟩,⟨⟨(-4641259209072177485820715),(-4641259209072162599375569)⟩,⟨(-69514029232367728224116),(-69514029232352841820478)⟩⟩,⟨⟨(-4242199666559242366732029),(-4242199666559228648560168)⟩,⟨280387952084661471742234,280387952084675189867013⟩⟩,⟨⟨(-3852517452510641596584680),(-3852517452510628948535543)⟩,⟨569412289878983944442267,569412289878996592440925⟩⟩,⟨⟨(-3475998312357611956317850),(-3475998312357600303992577)⟩,⟨803748770444799649624946,803748770444811301899418⟩⟩,⟨⟨(-3115601774189131853343054),(-3115601774189121114820623)⟩,⟨989324320238886498878405,989324320238897237350437⟩⟩,⟨⟨(-2773556937713346734516066),(-2773556937713336847485852)⟩,⟨1131759668106653036024677,1131759668106662923005498⟩⟩,⟨⟨(-2451453355069643830885985),(-2451453355069634722671602)⟩,⟨1236338003055552837246350,1236338003055561945412824⟩⟩,⟨⟨(-2150326372044003503048623),(-2150326372043995118422702)⟩,⟨1307984125094567440539286,1307984125094575825119173⟩⟩,⟨⟨(-1870736495066952170598098),(-1870736495066944410201393)⟩,⟨1351252659855947829883559,1351252659855955590241595⟩⟩] +lemma kernel28_1_r5_9_eq : ∀ k : Fin 16, kernel28_1Expr 5 9 k = kernel28_1_r5_9 k := by decide +kernel +noncomputable def kernel28_1_r5_10 : Fin 16 → CBox := ![⟨⟨(-1612842521632288266754805),(-1612842521632281087139554)⟩,⟨1370323994049428034037427,1370323994049435213621219⟩⟩,⟨⟨(-1376468320244355956238105),(-1376468320244349309130896)⟩,⟨1369006684529655033407089,1369006684529661680489269⟩⟩,⟨⟨(-1161163271807156984151029),(-1161163271807150834359453)⟩,⟨1350745195562076191580012,1350745195562082341352251⟩⟩,⟨⟨(-966256488901948796358672),(-966256488901943103839602)⟩,⟨1318631923849106065907269,1318631923849111758412010⟩⟩,⟨⟨(-790905014246929220953614),(-790905014246923956373035)⟩,⟨1275422576538952771645036,1275422576538958036215662⟩⟩,⟨⟨(-634136266507288153157843),(-634136266507283280635067)⟩,⟨1223554071694533149843778,1223554071694538022360385⟩⟩,⟨⟨(-494885052311232225824658),(-494885052311227719063610)⟩,⟨1165164231836888943554419,1165164231836893450312550⟩⟩,⟨⟨(-372025499633622329961934),(-372025499633618159013010)⟩,⟨1102112637834172250924268,1102112637834176421873033⟩⟩,⟨⟨(-264398291418997773228822),(-264398291418993916556877)⟩,⟨1036002101541533910091455,1036002101541537766765562⟩⟩,⟨⟨(-170833591160424300177980),(-170833591160420730750547)⟩,⟨968200300454992194711907,968200300454995764143416⟩⟩,⟨⟨(-90170055778042397681874),(-90170055778039096016016)⟩,⟨899861195724106592611671,899861195724109894283131⟩⟩,⟨⟨(-21270327096774152876558),(-21270327096771096726563)⟩,⟨831945925895892898507973,831945925895895954664797⟩⟩,⟨⟨36966617065944924418804,36966617065947751097501⟩,⟨765242932646536844238842,765242932646539670925320⟩⟩,⟨⟨85595886423880465855806,85595886423883082932249⟩,⟨700387131566387859205008,700387131566390476289947⟩⟩,⟨⟨125619529586576265223945,125619529586578687023991⟩,⟨637877990994166903992950,637877990994169325801682⟩⟩,⟨⟨157981488243079038765121,157981488243081281699498⟩,⟨578096425246515796106594,578096425246518039049623⟩⟩] +lemma kernel28_1_r5_10_eq : ∀ k : Fin 16, kernel28_1Expr 5 10 k = kernel28_1_r5_10 k := by decide +kernel +noncomputable def kernel28_1_r5_11 : Fin 16 → CBox := ![⟨⟨183564352729630125702667,183564352729632201336541⟩,⟨521320445734230532204859,521320445734232607847248⟩⟩,⟨⟨203187642193886446053164,203187642193888369212275⟩,⟨467739544827333185166547,467739544827335108333972⟩⟩,⟨⟨217607357620911670405188,217607357620913451509089⟩,⟨417467813394339020553638,417467813394340801665595⟩⟩,⟨⟨227516580899591926481174,227516580899593577666271⟩,⟨370555814183257242239516,370555814183258893432360⟩⟩,⟨⟨233546917441023648024205,233546917441025177721793⟩,⟨327001250125555906397864,327001250125557436102318⟩⟩,⟨⟨236270603264741204790153,236270603264742623678051⟩,⟨286758479716558443851849,286758479716559862745492⟩⟩,⟨⟨236203119679534488698923,236203119679535804493499⟩,⟨249746941328866839791161,249746941328868155590481⟩⟩,⟨⟨233806179511379059784007,233806179511380281244252⟩,⟨215858555099930756555915,215858555099931978020004⟩⟩,⟨⟨229490968143437415324567,229490968143438548415814⟩,⟨184964175324146692181522,184964175324147825275813⟩⟩,⟨⟨223621540358095466854024,223621540358096519469609⟩,⟨156919168466343435198293,156919168466344487816212⟩⟩,⟨⟨216518290079869371820101,216518290079870349425939⟩,⟨131568192356455437744418,131568192356456415351965⟩⟩,⟨⟨208461424619363373706164,208461424619364282871398⟩,⟨108749251149522977567443,108749251149523886733837⟩⟩,⟨⟨199694387950853172561602,199694387950854017593366⟩,⟨88297098531292577308086,88297098531293422340531⟩⟩,⟨⟨190427188981460772320742,190427188981461558891834⟩,⟨70046058674141569632171,70046058674142356203533⟩⟩,⟨⟨180839600767777135891074,180839600767777867882498⟩,⟨53832330824700090766688,53832330824700822758024⟩⟩,⟨⟨171084205298159565981406,171084205298160248011456⟩,⟨39495839326363631929397,39495839326364313959055⟩⟩] +lemma kernel28_1_r5_11_eq : ∀ k : Fin 16, kernel28_1Expr 5 11 k = kernel28_1_r5_11 k := by decide +kernel +noncomputable def kernel28_1_r5_12 : Fin 16 → CBox := ![⟨⟨161289265885893123005944,161289265885893758083798⟩,⟨26881686511003745597642,26881686511004380674850⟩⟩,⟨⟨151561415514531471496746,151561415514532063877713⟩,⟨15841261372158513794632,15841261372159106174738⟩⟩,⟨⟨141988154748015349188492,141988154748015901883284⟩,⟨6233052370239342755227,6233052370239895448988⟩⟩,⟨⟨132640157169555284052792,132640157169555800399653⟩,⟨(-2076791789435002345554),(-2076791789434485999865)⟩⟩,⟨⟨123573383846715562713868,123573383846716044881460⟩,⟨(-9214113950176144942657),(-9214113950175662776350)⟩⟩,⟨⟨114831011133120301398788,114831011133120752412090⟩,⟨(-15296577618507031755097),(-15296577618506580743168)⟩⟩,⟨⟨106445178301613475431202,106445178301613897260859⟩,⟨(-20433642133188989081592),(-20433642133188567253337)⟩⟩,⟨⟨98438563145107672124840,98438563145108067238698⟩,⟨(-24726656356389524668893),(-24726656356389129556432)⟩⟩,⟨⟨90825794858525923384412,90825794858526293293854⟩,⟨(-28269046821388650861866),(-28269046821388280953804)⟩⟩,⟨⟨83614714299941181707141,83614714299941528680538⟩,⟨(-31146579461156439630232),(-31146579461156092658199)⟩⟩,⟨⟨76807492185977471818419,76807492185977797269583⟩,⟨(-33437676953286169144212),(-33437676953285843694374)⟩⟩,⟨⟨70401615963579884612584,70401615963580190338589⟩,⟨(-35213776352858378315244),(-35213776352858072590531)⟩⟩,⟨⟨64390756068559521854413,64390756068559808951966⟩,⟨(-36539714054046833603642),(-36539714054046546507343)⟩⟩,⟨⟨58765522075735343867814,58765522075735613987777⟩,⟨(-37474127235256514489662),(-37474127235256244370918)⟩⟩,⟨⟨53514118904982416519718,53514118904982670739774⟩,⟨(-38069862815363085737232),(-38069862815362831518307)⟩⟩,⟨⟨48622912805548951839242,48622912805549191577098⟩,⟨(-38374386595926503137564),(-38374386595926263400710)⟩⟩] +lemma kernel28_1_r5_12_eq : ∀ k : Fin 16, kernel28_1Expr 5 12 k = kernel28_1_r5_12 k := by decide +kernel +noncomputable def kernel28_1_r5_13 : Fin 16 → CBox := ![⟨⟨44076916326122943523477,44076916326123169506017⟩,⟨(-38430186702807654706433),(-38430186702807428724775)⟩⟩,⟨⟨39860200914294123931024,39860200914294337404656⟩,⟨(-38275166687618358488191),(-38275166687618145015323)⟩⟩,⟨⟨35956245196199861401493,35956245196200063079904⟩,⟨(-37943024722098244757087),(-37943024722098043079334)⟩⟩,⟨⟨32348226381601255683254,32348226381601446539263⟩,⟨(-37463616233732424784494),(-37463616233732233929054)⟩⟩,⟨⟨29019261634583936497899,29019261634584117068671⟩,⟨(-36863298105009631316345),(-36863298105009450746055)⟩⟩,⟨⟨25952605655938955268040,25952605655939126469528⟩,⟨(-36165253207195995383387),(-36165253207195824182302)⟩⟩,⟨⟨23131810148098543293705,23131810148098705642849⟩,⟨(-35389794576966394671466),(-35389794576966232322657)⟩⟩,⟨⟨20540850283294949159601,20540850283295103386063⟩,⟨(-34554648984282543819541),(-34554648984282389593351)⟩⟩,⟨⟨18164222774677106935033,18164222774677253399531⟩,⟨(-33675219995061680448162),(-33675219995061533983881)⟩⟩,⟨⟨15987019661323517661210,15987019661323657077854⟩,⟨(-32764830913889590792302),(-32764830913889451375827)⟩⟩,⟨⟨13994981463109797124722,13994981463109929876896⟩,⟨(-31834948210673944555233),(-31834948210673811803179)⟩⟩,⟨⟨12174532940940930474874,12174532940941057119882⟩,⟨(-30895386200043740437751),(-30895386200043613792822)⟩⟩,⟨⟨10512804311884655519032,10512804311884776320104⟩,⟨(-29954493861815113363244),(-29954493861814992562211)⟩⟩,⟨⟨8997640416581292642473,8997640416581408133363⟩,⟨(-29019324772356110558900),(-29019324772355995068022)⟩⟩,⟨⟨7617600016831426704344,7617600016831537151746⟩,⟨(-28095791166704483014010),(-28095791166704372566587)⟩⟩,⟨⟨6361947113008443723085,6361947113008549548769⟩,⟨(-27188803175518211031362),(-27188803175518105205627)⟩⟩] +lemma kernel28_1_r5_13_eq : ∀ k : Fin 16, kernel28_1Expr 5 13 k = kernel28_1_r5_13 k := by decide +kernel +noncomputable def kernel28_1_r5_14 : Fin 16 → CBox := ![⟨⟨5220635912199364364516,5220635912199465736624⟩,⟨(-26302394284315417863724),(-26302394284315316491545)⟩⟩,⟨⟨4184290846878976724204,4184290846879074077942⟩,⟨(-25439834049255564881923),(-25439834049255467528091)⟩⟩,⟨⟨3244182838515003227783,3244182838515096756182⟩,⟨(-24603729077581049065450),(-24603729077580955536939)⟩⟩,⟨⟨2392202818799157327567,2392202818799247357767⟩,⟨(-23796113244882152452655),(-23796113244882062422331)⟩⟩,⟨⟨1620833361224845867652,1620833361224932525681⟩,⟨(-23018528078185167902550),(-23018528078185081244375)⟩⟩,⟨⟨923119135556545493895,923119135556629110131⟩,⟨(-22272094185678929110890),(-22272094185678845494501)⟩⟩,⟨⟨292636775499095468195,292636775499176183085⟩,⟨(-21557574562496368536445),(-21557574562496287821391)⟩⟩,⟨⟨(-276535356192519185122),(-276535356192441113508)⟩,⟨(-20875430548833289207543),(-20875430548833211135758)⟩⟩,⟨⟨(-789847112488199037733),(-789847112488123535466)⟩,⟨(-20225871163009419484335),(-20225871163009343981886)⟩⟩,⟨⟨(-1252305902688810577178),(-1252305902688737365941)⟩,⟨(-19608896478805229892537),(-19608896478805156681107)⟩⟩,⟨⟨(-1668505181927686377488),(-1668505181927615354475)⟩,⟨(-19024335664281013377503),(-19024335664280942354295)⟩⟩,⟨⟨(-2042651899573724908802),(-2042651899573655866564)⟩,⟨(-18471880248864295749760),(-18471880248864226707326)⟩⟩,⟨⟨(-2378592764519858434005),(-2378592764519791316914)⟩,⟨(-17951113137190694009995),(-17951113137190626892699)⟩⟩,⟨⟨(-2679839225455048545372),(-2679839225454983132227)⟩,⟨(-17461533842290634317091),(-17461533842290568903734)⟩⟩,⟨⟨(-2949591097463661094471),(-2949591097463597309126)⟩,⟨(-17002580367415995886352),(-17002580367415932100792)⟩⟩,⟨⟨(-3190758793566657648215),(-3190758793566595319870)⟩,⟨(-16573648125198972712426),(-16573648125198910383870)⟩⟩] +lemma kernel28_1_r5_14_eq : ∀ k : Fin 16, kernel28_1Expr 5 14 k = kernel28_1_r5_14 k := by decide +kernel +noncomputable def kernel28_1_r5_15 : Fin 16 → CBox := ![⟨⟨(-3405984141913389680756),(-3405984141913328785925)⟩,⟨(-16174106244964583820118),(-16174106244964522925076)⟩⟩,⟨⟨(-3597659786961683697082),(-3597659786961624035811)⟩,⟨(-15803311583858551970797),(-15803311583858492309318)⟩⟩,⟨⟨(-3767947186776802986313),(-3767947186776744500980)⟩,⟨(-15460620724941437848137),(-15460620724941379362595)⟩⟩,⟨⟨(-3918793229091668502504),(-3918793229091611048606)⟩,⟨(-15145400215442990245952),(-15145400215442932791840)⟩⟩,⟨⟨(-4051945496488393579168),(-4051945496488337135540)⟩,⟨(-14857035270848088437089),(-14857035270848031993250)⟩⟩,⟨⟨(-4168966216410245688413),(-4168966216410190090398)⟩,⟨(-14594937145260001615673),(-14594937145259946017446)⟩⟩,⟨⟨(-4271244935063742985085),(-4271244935063688187416)⟩,⟨(-14358549345408151007608),(-14358549345408096209732)⟩⟩,⟨⟨(-4360009955943353736027),(-4360009955943299612297)⟩,⟨(-14147352844578325556024),(-14147352844578271432088)⟩⟩,⟨⟨(-4436338583982721739439),(-4436338583982668281424)⟩,⟨(-13960870433481013594495),(-13960870433480960136272)⟩⟩,⟨⟨(-4501166215444031895192),(-4501166215443978940413)⟩,⟨(-13798670327473967859865),(-13798670327473914904879)⟩⟩,⟨⟨(-4555294311804296652010),(-4555294311804244164156)⟩,⟨(-13660369133454245169733),(-13660369133454192681673)⟩⟩,⟨⟨(-4599397293257313011968),(-4599397293257260877655)⟩,⟨(-13545634264970273498423),(-13545634264970221363902)⟩⟩,⟨⟨(-4634028384170217195456),(-4634028384170165409626)⟩,⟨(-13454185880516037166792),(-13454185880515985380761)⟩⟩,⟨⟨(-4659624439039173362555),(-4659624439039121786018)⟩,⟨(-13385798407400386606433),(-13385798407400335029686)⟩⟩,⟨⟨(-4676509773286205432388),(-4676509773286154032026)⟩,⟨(-13340301701881238156210),(-13340301701881186755640)⟩⟩,⟨⟨(-4684899018719352290631),(-4684899018719300958904)⟩,⟨(-13317581885266805849454),(-13317581885266754517521)⟩⟩] +lemma kernel28_1_r5_15_eq : ∀ k : Fin 16, kernel28_1Expr 5 15 k = kernel28_1_r5_15 k := by decide +kernel +noncomputable def kernel28_1_r5 : Fin 16 → Fin 16 → CBox := ![kernel28_1_r5_0,kernel28_1_r5_1,kernel28_1_r5_2,kernel28_1_r5_3,kernel28_1_r5_4,kernel28_1_r5_5,kernel28_1_r5_6,kernel28_1_r5_7,kernel28_1_r5_8,kernel28_1_r5_9,kernel28_1_r5_10,kernel28_1_r5_11,kernel28_1_r5_12,kernel28_1_r5_13,kernel28_1_r5_14,kernel28_1_r5_15] +lemma kernel28_1_r5_eq (i k : Fin 16) : kernel28_1Expr 5 i k = kernel28_1_r5 i k := by + fin_cases i + · exact kernel28_1_r5_0_eq k + · exact kernel28_1_r5_1_eq k + · exact kernel28_1_r5_2_eq k + · exact kernel28_1_r5_3_eq k + · exact kernel28_1_r5_4_eq k + · exact kernel28_1_r5_5_eq k + · exact kernel28_1_r5_6_eq k + · exact kernel28_1_r5_7_eq k + · exact kernel28_1_r5_8_eq k + · exact kernel28_1_r5_9_eq k + · exact kernel28_1_r5_10_eq k + · exact kernel28_1_r5_11_eq k + · exact kernel28_1_r5_12_eq k + · exact kernel28_1_r5_13_eq k + · exact kernel28_1_r5_14_eq k + · exact kernel28_1_r5_15_eq k +noncomputable def kernel28_1 : Fin 6 → Fin 16 → Fin 16 → CBox := ![kernel28_1_r0,kernel28_1_r1,kernel28_1_r2,kernel28_1_r3,kernel28_1_r4,kernel28_1_r5] +lemma kernel28_1_eq (j : Fin 6) (i k : Fin 16) : kernel28_1Expr j i k = kernel28_1 j i k := by + fin_cases j + · exact kernel28_1_r0_eq i k + · exact kernel28_1_r1_eq i k + · exact kernel28_1_r2_eq i k + · exact kernel28_1_r3_eq i k + · exact kernel28_1_r4_eq i k + · exact kernel28_1_r5_eq i k +lemma kernel28_1_contains (j : Fin 6) (i k : Fin 16) : + (kernel28_1 j i k).Contains (lambda (quadraturePoint j.val (16*i.val+k.val))* + Complex.exp (Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val))*(28:ℕ))* + (if true then Complex.I*Real.pi*z (quadraturePoint j.val (16*i.val+k.val)) else 1)) := by + rw [← kernel28_1_eq] + unfold kernel28_1Expr + have hl := (gridRows_contains j i k).2.1 + rw [pointLambda_eq] at hl + have hh := CBox.contains_mul hl (trans28_contains j i k) + have hz := (gridRows_contains j i k).2.2.1 + rw [pointZ_eq] at hz + simpa only [ite_true] using CBox.contains_mul hh (CBox.contains_mul piI_contains hz) +end SharpPlanar.CachedData + +end OAI